Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.12 | ||
Root | \(1.66557 - 0.475255i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.b.881.6 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.68006 | + | 0.421203i | 0.969981 | + | 0.243182i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.421203 | + | 1.68006i | −0.171955 | + | 0.685880i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.64518 | + | 1.41529i | 0.881725 | + | 0.471763i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 0.193822i | − | 0.0584397i | −0.999573 | − | 0.0292198i | \(-0.990698\pi\) | ||
0.999573 | − | 0.0292198i | \(-0.00930228\pi\) | |||||||
\(12\) | −1.68006 | − | 0.421203i | −0.484990 | − | 0.121591i | ||||
\(13\) | − | 1.54892i | − | 0.429594i | −0.976659 | − | 0.214797i | \(-0.931091\pi\) | ||
0.976659 | − | 0.214797i | \(-0.0689090\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68006 | − | 0.421203i | −0.433789 | − | 0.108754i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.529533 | −0.128431 | −0.0642153 | − | 0.997936i | \(-0.520454\pi\) | ||||
−0.0642153 | + | 0.997936i | \(0.520454\pi\) | |||||||
\(18\) | −1.41529 | + | 2.64518i | −0.333587 | + | 0.623474i | ||||
\(19\) | 6.38933i | 1.46581i | 0.680329 | + | 0.732906i | \(0.261837\pi\) | ||||
−0.680329 | + | 0.732906i | \(0.738163\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.193822 | 0.0413231 | ||||||||
\(23\) | 4.24976i | 0.886135i | 0.896488 | + | 0.443068i | \(0.146110\pi\) | ||||
−0.896488 | + | 0.443068i | \(0.853890\pi\) | |||||||
\(24\) | 0.421203 | − | 1.68006i | 0.0859777 | − | 0.342940i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.54892 | 0.303769 | ||||||||
\(27\) | 3.84792 | + | 3.49192i | 0.740532 | + | 0.672021i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.87349i | 0.904984i | 0.891768 | + | 0.452492i | \(0.149465\pi\) | ||||
−0.891768 | + | 0.452492i | \(0.850535\pi\) | |||||||
\(30\) | 0.421203 | − | 1.68006i | 0.0769008 | − | 0.306735i | ||||
\(31\) | 9.26715i | 1.66443i | 0.554454 | + | 0.832214i | \(0.312927\pi\) | ||||
−0.554454 | + | 0.832214i | \(0.687073\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.0816386 | − | 0.325633i | 0.0142115 | − | 0.0566853i | ||||
\(34\) | − | 0.529533i | − | 0.0908141i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.64518 | − | 1.41529i | −0.440863 | − | 0.235882i | ||||
\(37\) | 1.76327 | 0.289880 | 0.144940 | − | 0.989440i | \(-0.453701\pi\) | ||||
0.144940 | + | 0.989440i | \(0.453701\pi\) | |||||||
\(38\) | −6.38933 | −1.03649 | ||||||||
\(39\) | 0.652411 | − | 2.60228i | 0.104469 | − | 0.416698i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 9.91573 | 1.54858 | 0.774289 | − | 0.632833i | \(-0.218108\pi\) | ||||
0.774289 | + | 0.632833i | \(0.218108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4865 | 1.75168 | 0.875838 | − | 0.482606i | \(-0.160310\pi\) | ||||
0.875838 | + | 0.482606i | \(0.160310\pi\) | |||||||
\(44\) | 0.193822i | 0.0292198i | ||||||||
\(45\) | −2.64518 | − | 1.41529i | −0.394320 | − | 0.210979i | ||||
\(46\) | −4.24976 | −0.626592 | ||||||||
\(47\) | −9.80373 | −1.43002 | −0.715010 | − | 0.699114i | \(-0.753578\pi\) | ||||
−0.715010 | + | 0.699114i | \(0.753578\pi\) | |||||||
\(48\) | 1.68006 | + | 0.421203i | 0.242495 | + | 0.0607954i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −0.889645 | − | 0.223041i | −0.124575 | − | 0.0312320i | ||||
\(52\) | 1.54892i | 0.214797i | ||||||||
\(53\) | 0.0649809i | 0.00892582i | 0.999990 | + | 0.00446291i | \(0.00142059\pi\) | ||||
−0.999990 | + | 0.00446291i | \(0.998579\pi\) | |||||||
\(54\) | −3.49192 | + | 3.84792i | −0.475190 | + | 0.523635i | ||||
\(55\) | 0.193822i | 0.0261350i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.69121 | + | 10.7344i | −0.356459 | + | 1.42181i | ||||
\(58\) | −4.87349 | −0.639920 | ||||||||
\(59\) | −12.0274 | −1.56584 | −0.782918 | − | 0.622125i | \(-0.786270\pi\) | ||||
−0.782918 | + | 0.622125i | \(0.786270\pi\) | |||||||
\(60\) | 1.68006 | + | 0.421203i | 0.216894 | + | 0.0543771i | ||||
\(61\) | − | 4.28602i | − | 0.548769i | −0.961620 | − | 0.274384i | \(-0.911526\pi\) | ||
0.961620 | − | 0.274384i | \(-0.0884741\pi\) | |||||||
\(62\) | −9.26715 | −1.17693 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.54892i | 0.192120i | ||||||||
\(66\) | 0.325633 | + | 0.0816386i | 0.0400826 | + | 0.0100490i | ||||
\(67\) | 4.83058 | 0.590149 | 0.295075 | − | 0.955474i | \(-0.404656\pi\) | ||||
0.295075 | + | 0.955474i | \(0.404656\pi\) | |||||||
\(68\) | 0.529533 | 0.0642153 | ||||||||
\(69\) | −1.79001 | + | 7.13983i | −0.215492 | + | 0.859534i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.29103i | − | 0.746608i | −0.927709 | − | 0.373304i | \(-0.878225\pi\) | ||
0.927709 | − | 0.373304i | \(-0.121775\pi\) | |||||||
\(72\) | 1.41529 | − | 2.64518i | 0.166793 | − | 0.311737i | ||||
\(73\) | − | 8.09171i | − | 0.947063i | −0.880777 | − | 0.473532i | \(-0.842979\pi\) | ||
0.880777 | − | 0.473532i | \(-0.157021\pi\) | |||||||
\(74\) | 1.76327i | 0.204976i | ||||||||
\(75\) | 1.68006 | + | 0.421203i | 0.193996 | + | 0.0486363i | ||||
\(76\) | − | 6.38933i | − | 0.732906i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.60228 | + | 0.652411i | 0.294650 | + | 0.0738710i | ||||
\(79\) | 6.77766 | 0.762546 | 0.381273 | − | 0.924462i | \(-0.375486\pi\) | ||||
0.381273 | + | 0.924462i | \(0.375486\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 4.99391 | + | 7.48738i | 0.554879 | + | 0.831931i | ||||
\(82\) | 9.91573i | 1.09501i | ||||||||
\(83\) | −2.11036 | −0.231642 | −0.115821 | − | 0.993270i | \(-0.536950\pi\) | ||||
−0.115821 | + | 0.993270i | \(0.536950\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.529533 | 0.0574359 | ||||||||
\(86\) | 11.4865i | 1.23862i | ||||||||
\(87\) | −2.05273 | + | 8.18773i | −0.220076 | + | 0.877817i | ||||
\(88\) | −0.193822 | −0.0206615 | ||||||||
\(89\) | −16.3755 | −1.73580 | −0.867898 | − | 0.496742i | \(-0.834529\pi\) | ||||
−0.867898 | + | 0.496742i | \(0.834529\pi\) | |||||||
\(90\) | 1.41529 | − | 2.64518i | 0.149185 | − | 0.278826i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 4.24976i | − | 0.443068i | ||||||
\(93\) | −3.90335 | + | 15.5693i | −0.404759 | + | 1.61446i | ||||
\(94\) | − | 9.80373i | − | 1.01118i | ||||||
\(95\) | − | 6.38933i | − | 0.655531i | ||||||
\(96\) | −0.421203 | + | 1.68006i | −0.0429889 | + | 0.171470i | ||||
\(97\) | 8.24463i | 0.837115i | 0.908190 | + | 0.418557i | \(0.137464\pi\) | ||||
−0.908190 | + | 0.418557i | \(0.862536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.274315 | − | 0.512694i | 0.0275697 | − | 0.0515277i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −4.45663 | −0.443451 | −0.221725 | − | 0.975109i | \(-0.571169\pi\) | ||||
−0.221725 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(102\) | 0.223041 | − | 0.889645i | 0.0220843 | − | 0.0880879i | ||||
\(103\) | − | 8.42187i | − | 0.829832i | −0.909860 | − | 0.414916i | \(-0.863811\pi\) | ||
0.909860 | − | 0.414916i | \(-0.136189\pi\) | |||||||
\(104\) | −1.54892 | −0.151884 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0649809 | −0.00631151 | ||||||||
\(107\) | 17.8136i | 1.72211i | 0.508514 | + | 0.861054i | \(0.330195\pi\) | ||||
−0.508514 | + | 0.861054i | \(0.669805\pi\) | |||||||
\(108\) | −3.84792 | − | 3.49192i | −0.370266 | − | 0.336010i | ||||
\(109\) | 0.147803 | 0.0141570 | 0.00707850 | − | 0.999975i | \(-0.497747\pi\) | ||||
0.00707850 | + | 0.999975i | \(0.497747\pi\) | |||||||
\(110\) | −0.193822 | −0.0184802 | ||||||||
\(111\) | 2.96239 | + | 0.742694i | 0.281178 | + | 0.0704934i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.44771i | − | 0.324334i | −0.986763 | − | 0.162167i | \(-0.948152\pi\) | ||
0.986763 | − | 0.162167i | \(-0.0518483\pi\) | |||||||
\(114\) | −10.7344 | − | 2.69121i | −1.00537 | − | 0.252055i | ||||
\(115\) | − | 4.24976i | − | 0.396292i | ||||||
\(116\) | − | 4.87349i | − | 0.452492i | ||||||
\(117\) | 2.19217 | − | 4.09717i | 0.202667 | − | 0.378784i | ||||
\(118\) | − | 12.0274i | − | 1.10721i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.421203 | + | 1.68006i | −0.0384504 | + | 0.153367i | ||||
\(121\) | 10.9624 | 0.996585 | ||||||||
\(122\) | 4.28602 | 0.388038 | ||||||||
\(123\) | 16.6590 | + | 4.17654i | 1.50209 | + | 0.376586i | ||||
\(124\) | − | 9.26715i | − | 0.832214i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.49965 | 0.488015 | 0.244007 | − | 0.969773i | \(-0.421538\pi\) | ||||
0.244007 | + | 0.969773i | \(0.421538\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 19.2980 | + | 4.83815i | 1.69909 | + | 0.425975i | ||||
\(130\) | −1.54892 | −0.135850 | ||||||||
\(131\) | 5.99687 | 0.523949 | 0.261974 | − | 0.965075i | \(-0.415626\pi\) | ||||
0.261974 | + | 0.965075i | \(0.415626\pi\) | |||||||
\(132\) | −0.0816386 | + | 0.325633i | −0.00710573 | + | 0.0283427i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.83058i | 0.417298i | ||||||||
\(135\) | −3.84792 | − | 3.49192i | −0.331176 | − | 0.300537i | ||||
\(136\) | 0.529533i | 0.0454071i | ||||||||
\(137\) | 0.862112i | 0.0736552i | 0.999322 | + | 0.0368276i | \(0.0117252\pi\) | ||||
−0.999322 | + | 0.0368276i | \(0.988275\pi\) | |||||||
\(138\) | −7.13983 | − | 1.79001i | −0.607783 | − | 0.152376i | ||||
\(139\) | − | 16.1843i | − | 1.37274i | −0.727254 | − | 0.686368i | \(-0.759204\pi\) | ||
0.727254 | − | 0.686368i | \(-0.240796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4708 | − | 4.12936i | −1.38709 | − | 0.347755i | ||||
\(142\) | 6.29103 | 0.527932 | ||||||||
\(143\) | −0.300216 | −0.0251053 | ||||||||
\(144\) | 2.64518 | + | 1.41529i | 0.220431 | + | 0.117941i | ||||
\(145\) | − | 4.87349i | − | 0.404721i | ||||||
\(146\) | 8.09171 | 0.669675 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.76327 | −0.144940 | ||||||||
\(149\) | − | 12.7600i | − | 1.04534i | −0.852535 | − | 0.522671i | \(-0.824936\pi\) | ||
0.852535 | − | 0.522671i | \(-0.175064\pi\) | |||||||
\(150\) | −0.421203 | + | 1.68006i | −0.0343911 | + | 0.137176i | ||||
\(151\) | −17.5002 | −1.42415 | −0.712075 | − | 0.702103i | \(-0.752244\pi\) | ||||
−0.712075 | + | 0.702103i | \(0.752244\pi\) | |||||||
\(152\) | 6.38933 | 0.518243 | ||||||||
\(153\) | −1.40071 | − | 0.749442i | −0.113240 | − | 0.0605888i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9.26715i | − | 0.744355i | ||||||
\(156\) | −0.652411 | + | 2.60228i | −0.0522347 | + | 0.208349i | ||||
\(157\) | − | 2.84609i | − | 0.227143i | −0.993530 | − | 0.113571i | \(-0.963771\pi\) | ||
0.993530 | − | 0.113571i | \(-0.0362291\pi\) | |||||||
\(158\) | 6.77766i | 0.539201i | ||||||||
\(159\) | −0.0273702 | + | 0.109172i | −0.00217060 | + | 0.00865787i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.48738 | + | 4.99391i | −0.588264 | + | 0.392359i | ||||
\(163\) | 12.3586 | 0.968002 | 0.484001 | − | 0.875067i | \(-0.339183\pi\) | ||||
0.484001 | + | 0.875067i | \(0.339183\pi\) | |||||||
\(164\) | −9.91573 | −0.774289 | ||||||||
\(165\) | −0.0816386 | + | 0.325633i | −0.00635556 | + | 0.0253505i | ||||
\(166\) | − | 2.11036i | − | 0.163795i | ||||||
\(167\) | −4.99920 | −0.386850 | −0.193425 | − | 0.981115i | \(-0.561960\pi\) | ||||
−0.193425 | + | 0.981115i | \(0.561960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6008 | 0.815449 | ||||||||
\(170\) | 0.529533i | 0.0406133i | ||||||||
\(171\) | −9.04275 | + | 16.9009i | −0.691517 | + | 1.29244i | ||||
\(172\) | −11.4865 | −0.875838 | ||||||||
\(173\) | 7.60806 | 0.578430 | 0.289215 | − | 0.957264i | \(-0.406606\pi\) | ||||
0.289215 | + | 0.957264i | \(0.406606\pi\) | |||||||
\(174\) | −8.18773 | − | 2.05273i | −0.620710 | − | 0.155617i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.193822i | − | 0.0146099i | ||||||
\(177\) | −20.2067 | − | 5.06598i | −1.51883 | − | 0.380783i | ||||
\(178\) | − | 16.3755i | − | 1.22739i | ||||||
\(179\) | − | 16.2259i | − | 1.21278i | −0.795167 | − | 0.606390i | \(-0.792617\pi\) | ||
0.795167 | − | 0.606390i | \(-0.207383\pi\) | |||||||
\(180\) | 2.64518 | + | 1.41529i | 0.197160 | + | 0.105489i | ||||
\(181\) | − | 4.03153i | − | 0.299661i | −0.988712 | − | 0.149831i | \(-0.952127\pi\) | ||
0.988712 | − | 0.149831i | \(-0.0478729\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.80529 | − | 7.20076i | 0.133451 | − | 0.532295i | ||||
\(184\) | 4.24976 | 0.313296 | ||||||||
\(185\) | −1.76327 | −0.129638 | ||||||||
\(186\) | −15.5693 | − | 3.90335i | −1.14160 | − | 0.286208i | ||||
\(187\) | 0.102635i | 0.00750544i | ||||||||
\(188\) | 9.80373 | 0.715010 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.38933 | 0.463531 | ||||||||
\(191\) | − | 25.2353i | − | 1.82596i | −0.408005 | − | 0.912980i | \(-0.633775\pi\) | ||
0.408005 | − | 0.912980i | \(-0.366225\pi\) | |||||||
\(192\) | −1.68006 | − | 0.421203i | −0.121248 | − | 0.0303977i | ||||
\(193\) | 25.2366 | 1.81657 | 0.908286 | − | 0.418349i | \(-0.137391\pi\) | ||||
0.908286 | + | 0.418349i | \(0.137391\pi\) | |||||||
\(194\) | −8.24463 | −0.591930 | ||||||||
\(195\) | −0.652411 | + | 2.60228i | −0.0467201 | + | 0.186353i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7364i | 1.04993i | 0.851125 | + | 0.524964i | \(0.175921\pi\) | ||||
−0.851125 | + | 0.524964i | \(0.824079\pi\) | |||||||
\(198\) | 0.512694 | + | 0.274315i | 0.0364356 | + | 0.0194947i | ||||
\(199\) | 25.8642i | 1.83347i | 0.399499 | + | 0.916734i | \(0.369184\pi\) | ||||
−0.399499 | + | 0.916734i | \(0.630816\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 8.11564 | + | 2.03465i | 0.572433 | + | 0.143513i | ||||
\(202\) | − | 4.45663i | − | 0.313567i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.889645 | + | 0.223041i | 0.0622876 | + | 0.0156160i | ||||
\(205\) | −9.91573 | −0.692545 | ||||||||
\(206\) | 8.42187 | 0.586780 | ||||||||
\(207\) | −6.01464 | + | 11.2414i | −0.418046 | + | 0.781328i | ||||
\(208\) | − | 1.54892i | − | 0.107398i | ||||||
\(209\) | 1.23840 | 0.0856616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8721 | −1.57458 | −0.787289 | − | 0.616585i | \(-0.788516\pi\) | ||||
−0.787289 | + | 0.616585i | \(0.788516\pi\) | |||||||
\(212\) | − | 0.0649809i | − | 0.00446291i | ||||||
\(213\) | 2.64980 | − | 10.5693i | 0.181562 | − | 0.724196i | ||||
\(214\) | −17.8136 | −1.21771 | ||||||||
\(215\) | −11.4865 | −0.783373 | ||||||||
\(216\) | 3.49192 | − | 3.84792i | 0.237595 | − | 0.261818i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.147803i | 0.0100105i | ||||||||
\(219\) | 3.40825 | − | 13.5945i | 0.230308 | − | 0.918633i | ||||
\(220\) | − | 0.193822i | − | 0.0130675i | ||||||
\(221\) | 0.820205i | 0.0551730i | ||||||||
\(222\) | −0.742694 | + | 2.96239i | −0.0498464 | + | 0.198823i | ||||
\(223\) | − | 0.00626282i | − | 0.000419390i | −1.00000 | 0.000209695i | \(-0.999933\pi\) | |||
1.00000 | 0.000209695i | \(-6.67479e-5\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.64518 | + | 1.41529i | 0.176345 | + | 0.0943526i | ||||
\(226\) | 3.44771 | 0.229338 | ||||||||
\(227\) | 18.8275 | 1.24962 | 0.624811 | − | 0.780776i | \(-0.285176\pi\) | ||||
0.624811 | + | 0.780776i | \(0.285176\pi\) | |||||||
\(228\) | 2.69121 | − | 10.7344i | 0.178229 | − | 0.710905i | ||||
\(229\) | − | 7.79658i | − | 0.515212i | −0.966250 | − | 0.257606i | \(-0.917066\pi\) | ||
0.966250 | − | 0.257606i | \(-0.0829337\pi\) | |||||||
\(230\) | 4.24976 | 0.280221 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.87349 | 0.319960 | ||||||||
\(233\) | − | 12.9944i | − | 0.851289i | −0.904890 | − | 0.425645i | \(-0.860047\pi\) | ||
0.904890 | − | 0.425645i | \(-0.139953\pi\) | |||||||
\(234\) | 4.09717 | + | 2.19217i | 0.267841 | + | 0.143307i | ||||
\(235\) | 9.80373 | 0.639525 | ||||||||
\(236\) | 12.0274 | 0.782918 | ||||||||
\(237\) | 11.3868 | + | 2.85477i | 0.739655 | + | 0.185437i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.1710i | 1.11070i | 0.831618 | + | 0.555349i | \(0.187415\pi\) | ||||
−0.831618 | + | 0.555349i | \(0.812585\pi\) | |||||||
\(240\) | −1.68006 | − | 0.421203i | −0.108447 | − | 0.0271885i | ||||
\(241\) | 8.20640i | 0.528620i | 0.964438 | + | 0.264310i | \(0.0851443\pi\) | ||||
−0.964438 | + | 0.264310i | \(0.914856\pi\) | |||||||
\(242\) | 10.9624i | 0.704692i | ||||||||
\(243\) | 5.23634 | + | 14.6827i | 0.335911 | + | 0.941894i | ||||
\(244\) | 4.28602i | 0.274384i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.17654 | + | 16.6590i | −0.266286 | + | 1.06214i | ||||
\(247\) | 9.89658 | 0.629704 | ||||||||
\(248\) | 9.26715 | 0.588464 | ||||||||
\(249\) | −3.54552 | − | 0.888888i | −0.224688 | − | 0.0563310i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −22.9102 | −1.44608 | −0.723038 | − | 0.690808i | \(-0.757255\pi\) | ||||
−0.723038 | + | 0.690808i | \(0.757255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.823698 | 0.0517855 | ||||||||
\(254\) | 5.49965i | 0.345079i | ||||||||
\(255\) | 0.889645 | + | 0.223041i | 0.0557117 | + | 0.0139674i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.08648 | 0.442042 | 0.221021 | − | 0.975269i | \(-0.429061\pi\) | ||||
0.221021 | + | 0.975269i | \(0.429061\pi\) | |||||||
\(258\) | −4.83815 | + | 19.2980i | −0.301210 | + | 1.20144i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.54892i | − | 0.0960601i | ||||||
\(261\) | −6.89740 | + | 12.8912i | −0.426938 | + | 0.797947i | ||||
\(262\) | 5.99687i | 0.370488i | ||||||||
\(263\) | − | 17.8683i | − | 1.10181i | −0.834569 | − | 0.550904i | \(-0.814283\pi\) | ||
0.834569 | − | 0.550904i | \(-0.185717\pi\) | |||||||
\(264\) | −0.325633 | − | 0.0816386i | −0.0200413 | − | 0.00502451i | ||||
\(265\) | − | 0.0649809i | − | 0.00399175i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.5117 | − | 6.89740i | −1.68369 | − | 0.422114i | ||||
\(268\) | −4.83058 | −0.295075 | ||||||||
\(269\) | 6.92546 | 0.422253 | 0.211126 | − | 0.977459i | \(-0.432287\pi\) | ||||
0.211126 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(270\) | 3.49192 | − | 3.84792i | 0.212512 | − | 0.234177i | ||||
\(271\) | 16.9186i | 1.02773i | 0.857870 | + | 0.513867i | \(0.171788\pi\) | ||||
−0.857870 | + | 0.513867i | \(0.828212\pi\) | |||||||
\(272\) | −0.529533 | −0.0321076 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.862112 | −0.0520821 | ||||||||
\(275\) | − | 0.193822i | − | 0.0116879i | ||||||
\(276\) | 1.79001 | − | 7.13983i | 0.107746 | − | 0.429767i | ||||
\(277\) | −21.3009 | −1.27985 | −0.639924 | − | 0.768438i | \(-0.721034\pi\) | ||||
−0.639924 | + | 0.768438i | \(0.721034\pi\) | |||||||
\(278\) | 16.1843 | 0.970671 | ||||||||
\(279\) | −13.1157 | + | 24.5132i | −0.785216 | + | 1.46757i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.5927i | − | 1.16880i | −0.811464 | − | 0.584402i | \(-0.801329\pi\) | ||
0.811464 | − | 0.584402i | \(-0.198671\pi\) | |||||||
\(282\) | 4.12936 | − | 16.4708i | 0.245900 | − | 0.980823i | ||||
\(283\) | − | 15.0978i | − | 0.897474i | −0.893664 | − | 0.448737i | \(-0.851874\pi\) | ||
0.893664 | − | 0.448737i | \(-0.148126\pi\) | |||||||
\(284\) | 6.29103i | 0.373304i | ||||||||
\(285\) | 2.69121 | − | 10.7344i | 0.159413 | − | 0.635853i | ||||
\(286\) | − | 0.300216i | − | 0.0177521i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.41529 | + | 2.64518i | −0.0833967 | + | 0.155868i | ||||
\(289\) | −16.7196 | −0.983506 | ||||||||
\(290\) | 4.87349 | 0.286181 | ||||||||
\(291\) | −3.47266 | + | 13.8514i | −0.203571 | + | 0.811985i | ||||
\(292\) | 8.09171i | 0.473532i | ||||||||
\(293\) | −8.00534 | −0.467677 | −0.233839 | − | 0.972275i | \(-0.575129\pi\) | ||||
−0.233839 | + | 0.972275i | \(0.575129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0274 | 0.700263 | ||||||||
\(296\) | − | 1.76327i | − | 0.102488i | ||||||
\(297\) | 0.676813 | − | 0.745813i | 0.0392727 | − | 0.0432765i | ||||
\(298\) | 12.7600 | 0.739168 | ||||||||
\(299\) | 6.58255 | 0.380678 | ||||||||
\(300\) | −1.68006 | − | 0.421203i | −0.0969981 | − | 0.0243182i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 17.5002i | − | 1.00703i | ||||||
\(303\) | −7.48738 | − | 1.87714i | −0.430139 | − | 0.107839i | ||||
\(304\) | 6.38933i | 0.366453i | ||||||||
\(305\) | 4.28602i | 0.245417i | ||||||||
\(306\) | 0.749442 | − | 1.40071i | 0.0428428 | − | 0.0800731i | ||||
\(307\) | − | 4.33663i | − | 0.247505i | −0.992313 | − | 0.123752i | \(-0.960507\pi\) | ||
0.992313 | − | 0.123752i | \(-0.0394928\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.54732 | − | 14.1492i | 0.201800 | − | 0.804921i | ||||
\(310\) | 9.26715 | 0.526339 | ||||||||
\(311\) | 22.8384 | 1.29505 | 0.647523 | − | 0.762046i | \(-0.275805\pi\) | ||||
0.647523 | + | 0.762046i | \(0.275805\pi\) | |||||||
\(312\) | −2.60228 | − | 0.652411i | −0.147325 | − | 0.0369355i | ||||
\(313\) | − | 25.3042i | − | 1.43028i | −0.698982 | − | 0.715140i | \(-0.746363\pi\) | ||
0.698982 | − | 0.715140i | \(-0.253637\pi\) | |||||||
\(314\) | 2.84609 | 0.160614 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.77766 | −0.381273 | ||||||||
\(317\) | − | 15.0898i | − | 0.847526i | −0.905773 | − | 0.423763i | \(-0.860709\pi\) | ||
0.905773 | − | 0.423763i | \(-0.139291\pi\) | |||||||
\(318\) | −0.109172 | − | 0.0273702i | −0.00612204 | − | 0.00153484i | ||||
\(319\) | 0.944591 | 0.0528870 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −7.50315 | + | 29.9279i | −0.418785 | + | 1.67041i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.38336i | − | 0.188255i | ||||||
\(324\) | −4.99391 | − | 7.48738i | −0.277439 | − | 0.415966i | ||||
\(325\) | − | 1.54892i | − | 0.0859188i | ||||||
\(326\) | 12.3586i | 0.684481i | ||||||||
\(327\) | 0.248318 | + | 0.0622552i | 0.0137320 | + | 0.00344272i | ||||
\(328\) | − | 9.91573i | − | 0.547505i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.325633 | − | 0.0816386i | −0.0179255 | − | 0.00449406i | ||||
\(331\) | 15.0617 | 0.827867 | 0.413933 | − | 0.910307i | \(-0.364155\pi\) | ||||
0.413933 | + | 0.910307i | \(0.364155\pi\) | |||||||
\(332\) | 2.11036 | 0.115821 | ||||||||
\(333\) | 4.66415 | + | 2.49554i | 0.255594 | + | 0.136754i | ||||
\(334\) | − | 4.99920i | − | 0.273544i | ||||||
\(335\) | −4.83058 | −0.263923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9611 | 0.814983 | 0.407491 | − | 0.913209i | \(-0.366404\pi\) | ||||
0.407491 | + | 0.913209i | \(0.366404\pi\) | |||||||
\(338\) | 10.6008i | 0.576610i | ||||||||
\(339\) | 1.45219 | − | 5.79235i | 0.0788720 | − | 0.314597i | ||||
\(340\) | −0.529533 | −0.0287179 | ||||||||
\(341\) | 1.79618 | 0.0972687 | ||||||||
\(342\) | −16.9009 | − | 9.04275i | −0.913896 | − | 0.488976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 11.4865i | − | 0.619311i | ||||||
\(345\) | 1.79001 | − | 7.13983i | 0.0963709 | − | 0.384395i | ||||
\(346\) | 7.60806i | 0.409012i | ||||||||
\(347\) | − | 4.04662i | − | 0.217234i | −0.994084 | − | 0.108617i | \(-0.965358\pi\) | ||
0.994084 | − | 0.108617i | \(-0.0346422\pi\) | |||||||
\(348\) | 2.05273 | − | 8.18773i | 0.110038 | − | 0.438909i | ||||
\(349\) | − | 12.3695i | − | 0.662124i | −0.943609 | − | 0.331062i | \(-0.892593\pi\) | ||
0.943609 | − | 0.331062i | \(-0.107407\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.40872 | − | 5.96013i | 0.288696 | − | 0.318128i | ||||
\(352\) | 0.193822 | 0.0103308 | ||||||||
\(353\) | 3.66715 | 0.195183 | 0.0975914 | − | 0.995227i | \(-0.468886\pi\) | ||||
0.0975914 | + | 0.995227i | \(0.468886\pi\) | |||||||
\(354\) | 5.06598 | − | 20.2067i | 0.269254 | − | 1.07398i | ||||
\(355\) | 6.29103i | 0.333893i | ||||||||
\(356\) | 16.3755 | 0.867898 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.2259 | 0.857565 | ||||||||
\(359\) | 7.32269i | 0.386477i | 0.981152 | + | 0.193238i | \(0.0618990\pi\) | ||||
−0.981152 | + | 0.193238i | \(0.938101\pi\) | |||||||
\(360\) | −1.41529 | + | 2.64518i | −0.0745923 | + | 0.139413i | ||||
\(361\) | −21.8235 | −1.14861 | ||||||||
\(362\) | 4.03153 | 0.211893 | ||||||||
\(363\) | 18.4175 | + | 4.61741i | 0.966668 | + | 0.242351i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.09171i | 0.423540i | ||||||||
\(366\) | 7.20076 | + | 1.80529i | 0.376390 | + | 0.0943638i | ||||
\(367\) | − | 4.76624i | − | 0.248796i | −0.992232 | − | 0.124398i | \(-0.960300\pi\) | ||
0.992232 | − | 0.124398i | \(-0.0396999\pi\) | |||||||
\(368\) | 4.24976i | 0.221534i | ||||||||
\(369\) | 26.2289 | + | 14.0336i | 1.36542 | + | 0.730562i | ||||
\(370\) | − | 1.76327i | − | 0.0916679i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.90335 | − | 15.5693i | 0.202379 | − | 0.807232i | ||||
\(373\) | −17.2963 | −0.895567 | −0.447783 | − | 0.894142i | \(-0.647786\pi\) | ||||
−0.447783 | + | 0.894142i | \(0.647786\pi\) | |||||||
\(374\) | −0.102635 | −0.00530715 | ||||||||
\(375\) | −1.68006 | − | 0.421203i | −0.0867577 | − | 0.0217508i | ||||
\(376\) | 9.80373i | 0.505589i | ||||||||
\(377\) | 7.54866 | 0.388776 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.76645 | −0.450302 | −0.225151 | − | 0.974324i | \(-0.572288\pi\) | ||||
−0.225151 | + | 0.974324i | \(0.572288\pi\) | |||||||
\(380\) | 6.38933i | 0.327766i | ||||||||
\(381\) | 9.23972 | + | 2.31647i | 0.473365 | + | 0.118676i | ||||
\(382\) | 25.2353 | 1.29115 | ||||||||
\(383\) | 28.4753 | 1.45502 | 0.727511 | − | 0.686096i | \(-0.240677\pi\) | ||||
0.727511 | + | 0.686096i | \(0.240677\pi\) | |||||||
\(384\) | 0.421203 | − | 1.68006i | 0.0214944 | − | 0.0857350i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.2366i | 1.28451i | ||||||||
\(387\) | 30.3838 | + | 16.2567i | 1.54450 | + | 0.826376i | ||||
\(388\) | − | 8.24463i | − | 0.418557i | ||||||
\(389\) | 21.0696i | 1.06827i | 0.845399 | + | 0.534136i | \(0.179363\pi\) | ||||
−0.845399 | + | 0.534136i | \(0.820637\pi\) | |||||||
\(390\) | −2.60228 | − | 0.652411i | −0.131771 | − | 0.0330361i | ||||
\(391\) | − | 2.25039i | − | 0.113807i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.0751 | + | 2.52590i | 0.508220 | + | 0.127415i | ||||
\(394\) | −14.7364 | −0.742411 | ||||||||
\(395\) | −6.77766 | −0.341021 | ||||||||
\(396\) | −0.274315 | + | 0.512694i | −0.0137848 | + | 0.0257639i | ||||
\(397\) | − | 6.59809i | − | 0.331149i | −0.986197 | − | 0.165574i | \(-0.947052\pi\) | ||
0.986197 | − | 0.165574i | \(-0.0529478\pi\) | |||||||
\(398\) | −25.8642 | −1.29646 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 16.1310i | − | 0.805546i | −0.915300 | − | 0.402773i | \(-0.868046\pi\) | ||
0.915300 | − | 0.402773i | \(-0.131954\pi\) | |||||||
\(402\) | −2.03465 | + | 8.11564i | −0.101479 | + | 0.404771i | ||||
\(403\) | 14.3541 | 0.715029 | ||||||||
\(404\) | 4.45663 | 0.221725 | ||||||||
\(405\) | −4.99391 | − | 7.48738i | −0.248149 | − | 0.372051i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.341761i | − | 0.0169405i | ||||||
\(408\) | −0.223041 | + | 0.889645i | −0.0110422 | + | 0.0440440i | ||||
\(409\) | − | 26.4033i | − | 1.30556i | −0.757548 | − | 0.652779i | \(-0.773603\pi\) | ||
0.757548 | − | 0.652779i | \(-0.226397\pi\) | |||||||
\(410\) | − | 9.91573i | − | 0.489703i | ||||||
\(411\) | −0.363124 | + | 1.44840i | −0.0179116 | + | 0.0714441i | ||||
\(412\) | 8.42187i | 0.414916i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.2414 | − | 6.01464i | −0.552482 | − | 0.295603i | ||||
\(415\) | 2.11036 | 0.103593 | ||||||||
\(416\) | 1.54892 | 0.0759422 | ||||||||
\(417\) | 6.81689 | − | 27.1906i | 0.333824 | − | 1.33153i | ||||
\(418\) | 1.23840i | 0.0605719i | ||||||||
\(419\) | 19.8312 | 0.968819 | 0.484409 | − | 0.874841i | \(-0.339035\pi\) | ||||
0.484409 | + | 0.874841i | \(0.339035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.28009 | 0.306073 | 0.153036 | − | 0.988221i | \(-0.451095\pi\) | ||||
0.153036 | + | 0.988221i | \(0.451095\pi\) | |||||||
\(422\) | − | 22.8721i | − | 1.11339i | ||||||
\(423\) | −25.9326 | − | 13.8751i | −1.26089 | − | 0.674631i | ||||
\(424\) | 0.0649809 | 0.00315575 | ||||||||
\(425\) | −0.529533 | −0.0256861 | ||||||||
\(426\) | 10.5693 | + | 2.64980i | 0.512084 | + | 0.128383i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 17.8136i | − | 0.861054i | ||||||
\(429\) | −0.504380 | − | 0.126452i | −0.0243517 | − | 0.00610516i | ||||
\(430\) | − | 11.4865i | − | 0.553928i | ||||||
\(431\) | − | 4.55329i | − | 0.219324i | −0.993969 | − | 0.109662i | \(-0.965023\pi\) | ||
0.993969 | − | 0.109662i | \(-0.0349769\pi\) | |||||||
\(432\) | 3.84792 | + | 3.49192i | 0.185133 | + | 0.168005i | ||||
\(433\) | 2.62801i | 0.126294i | 0.998004 | + | 0.0631471i | \(0.0201137\pi\) | ||||
−0.998004 | + | 0.0631471i | \(0.979886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05273 | − | 8.18773i | 0.0984208 | − | 0.392572i | ||||
\(436\) | −0.147803 | −0.00707850 | ||||||||
\(437\) | −27.1531 | −1.29891 | ||||||||
\(438\) | 13.5945 | + | 3.40825i | 0.649572 | + | 0.162853i | ||||
\(439\) | 5.83672i | 0.278572i | 0.990252 | + | 0.139286i | \(0.0444807\pi\) | ||||
−0.990252 | + | 0.139286i | \(0.955519\pi\) | |||||||
\(440\) | 0.193822 | 0.00924012 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.820205 | −0.0390132 | ||||||||
\(443\) | − | 26.3461i | − | 1.25174i | −0.779927 | − | 0.625870i | \(-0.784744\pi\) | ||
0.779927 | − | 0.625870i | \(-0.215256\pi\) | |||||||
\(444\) | −2.96239 | − | 0.742694i | −0.140589 | − | 0.0352467i | ||||
\(445\) | 16.3755 | 0.776272 | ||||||||
\(446\) | 0.00626282 | 0.000296553 | ||||||||
\(447\) | 5.37456 | − | 21.4375i | 0.254208 | − | 1.01396i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.76638i | 0.272132i | 0.990700 | + | 0.136066i | \(0.0434460\pi\) | ||||
−0.990700 | + | 0.136066i | \(0.956554\pi\) | |||||||
\(450\) | −1.41529 | + | 2.64518i | −0.0667174 | + | 0.124695i | ||||
\(451\) | − | 1.92189i | − | 0.0904983i | ||||||
\(452\) | 3.44771i | 0.162167i | ||||||||
\(453\) | −29.4014 | − | 7.37116i | −1.38140 | − | 0.346327i | ||||
\(454\) | 18.8275i | 0.883617i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.7344 | + | 2.69121i | 0.502686 | + | 0.126027i | ||||
\(457\) | −0.721513 | −0.0337509 | −0.0168755 | − | 0.999858i | \(-0.505372\pi\) | ||||
−0.0168755 | + | 0.999858i | \(0.505372\pi\) | |||||||
\(458\) | 7.79658 | 0.364310 | ||||||||
\(459\) | −2.03760 | − | 1.84909i | −0.0951070 | − | 0.0863080i | ||||
\(460\) | 4.24976i | 0.198146i | ||||||||
\(461\) | −34.3692 | −1.60073 | −0.800365 | − | 0.599512i | \(-0.795361\pi\) | ||||
−0.800365 | + | 0.599512i | \(0.795361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.3815 | 1.92316 | 0.961581 | − | 0.274522i | \(-0.0885197\pi\) | ||||
0.961581 | + | 0.274522i | \(0.0885197\pi\) | |||||||
\(464\) | 4.87349i | 0.226246i | ||||||||
\(465\) | 3.90335 | − | 15.5693i | 0.181014 | − | 0.722010i | ||||
\(466\) | 12.9944 | 0.601952 | ||||||||
\(467\) | 17.9669 | 0.831407 | 0.415704 | − | 0.909500i | \(-0.363535\pi\) | ||||
0.415704 | + | 0.909500i | \(0.363535\pi\) | |||||||
\(468\) | −2.19217 | + | 4.09717i | −0.101333 | + | 0.189392i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.80373i | 0.452212i | ||||||||
\(471\) | 1.19878 | − | 4.78159i | 0.0552370 | − | 0.220324i | ||||
\(472\) | 12.0274i | 0.553607i | ||||||||
\(473\) | − | 2.22634i | − | 0.102367i | ||||||
\(474\) | −2.85477 | + | 11.3868i | −0.131124 | + | 0.523015i | ||||
\(475\) | 6.38933i | 0.293163i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0919668 | + | 0.171886i | −0.00421087 | + | 0.00787012i | ||||
\(478\) | −17.1710 | −0.785382 | ||||||||
\(479\) | −9.01118 | −0.411731 | −0.205866 | − | 0.978580i | \(-0.566001\pi\) | ||||
−0.205866 | + | 0.978580i | \(0.566001\pi\) | |||||||
\(480\) | 0.421203 | − | 1.68006i | 0.0192252 | − | 0.0766837i | ||||
\(481\) | − | 2.73117i | − | 0.124530i | ||||||
\(482\) | −8.20640 | −0.373791 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9624 | −0.498292 | ||||||||
\(485\) | − | 8.24463i | − | 0.374369i | ||||||
\(486\) | −14.6827 | + | 5.23634i | −0.666019 | + | 0.237525i | ||||
\(487\) | −22.7295 | −1.02997 | −0.514987 | − | 0.857198i | \(-0.672203\pi\) | ||||
−0.514987 | + | 0.857198i | \(0.672203\pi\) | |||||||
\(488\) | −4.28602 | −0.194019 | ||||||||
\(489\) | 20.7632 | + | 5.20549i | 0.938944 | + | 0.235401i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1654i | 1.45160i | 0.687904 | + | 0.725801i | \(0.258531\pi\) | ||||
−0.687904 | + | 0.725801i | \(0.741469\pi\) | |||||||
\(492\) | −16.6590 | − | 4.17654i | −0.751045 | − | 0.188293i | ||||
\(493\) | − | 2.58067i | − | 0.116228i | ||||||
\(494\) | 9.89658i | 0.445268i | ||||||||
\(495\) | −0.274315 | + | 0.512694i | −0.0123295 | + | 0.0230439i | ||||
\(496\) | 9.26715i | 0.416107i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.888888 | − | 3.54552i | 0.0398320 | − | 0.158878i | ||||
\(499\) | 21.2508 | 0.951316 | 0.475658 | − | 0.879630i | \(-0.342210\pi\) | ||||
0.475658 | + | 0.879630i | \(0.342210\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.39893 | − | 2.10568i | −0.375237 | − | 0.0940748i | ||||
\(502\) | − | 22.9102i | − | 1.02253i | ||||||
\(503\) | 20.9913 | 0.935957 | 0.467978 | − | 0.883740i | \(-0.344982\pi\) | ||||
0.467978 | + | 0.883740i | \(0.344982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.45663 | 0.198317 | ||||||||
\(506\) | 0.823698i | 0.0366178i | ||||||||
\(507\) | 17.8100 | + | 4.46511i | 0.790970 | + | 0.198302i | ||||
\(508\) | −5.49965 | −0.244007 | ||||||||
\(509\) | −13.9681 | −0.619124 | −0.309562 | − | 0.950879i | \(-0.600182\pi\) | ||||
−0.309562 | + | 0.950879i | \(0.600182\pi\) | |||||||
\(510\) | −0.223041 | + | 0.889645i | −0.00987641 | + | 0.0393941i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −22.3110 | + | 24.5856i | −0.985057 | + | 1.08548i | ||||
\(514\) | 7.08648i | 0.312571i | ||||||||
\(515\) | 8.42187i | 0.371112i | ||||||||
\(516\) | −19.2980 | − | 4.83815i | −0.849546 | − | 0.212988i | ||||
\(517\) | 1.90018i | 0.0835699i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.7820 | + | 3.20454i | 0.561066 | + | 0.140664i | ||||
\(520\) | 1.54892 | 0.0679248 | ||||||||
\(521\) | 14.4242 | 0.631934 | 0.315967 | − | 0.948770i | \(-0.397671\pi\) | ||||
0.315967 | + | 0.948770i | \(0.397671\pi\) | |||||||
\(522\) | −12.8912 | − | 6.89740i | −0.564234 | − | 0.301891i | ||||
\(523\) | 29.1682i | 1.27543i | 0.770270 | + | 0.637717i | \(0.220121\pi\) | ||||
−0.770270 | + | 0.637717i | \(0.779879\pi\) | |||||||
\(524\) | −5.99687 | −0.261974 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8683 | 0.779096 | ||||||||
\(527\) | − | 4.90726i | − | 0.213764i | ||||||
\(528\) | 0.0816386 | − | 0.325633i | 0.00355286 | − | 0.0141713i | ||||
\(529\) | 4.93957 | 0.214764 | ||||||||
\(530\) | 0.0649809 | 0.00282259 | ||||||||
\(531\) | −31.8146 | − | 17.0223i | −1.38064 | − | 0.738704i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15.3587i | − | 0.665259i | ||||||
\(534\) | 6.89740 | − | 27.5117i | 0.298480 | − | 1.19055i | ||||
\(535\) | − | 17.8136i | − | 0.770150i | ||||||
\(536\) | − | 4.83058i | − | 0.208649i | ||||||
\(537\) | 6.83440 | − | 27.2604i | 0.294926 | − | 1.17637i | ||||
\(538\) | 6.92546i | 0.298578i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.84792 | + | 3.49192i | 0.165588 | + | 0.150268i | ||||
\(541\) | −24.9036 | −1.07069 | −0.535345 | − | 0.844633i | \(-0.679819\pi\) | ||||
−0.535345 | + | 0.844633i | \(0.679819\pi\) | |||||||
\(542\) | −16.9186 | −0.726718 | ||||||||
\(543\) | 1.69809 | − | 6.77320i | 0.0728722 | − | 0.290666i | ||||
\(544\) | − | 0.529533i | − | 0.0227035i | ||||||
\(545\) | −0.147803 | −0.00633120 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.655376 | −0.0280219 | −0.0140109 | − | 0.999902i | \(-0.504460\pi\) | ||||
−0.0140109 | + | 0.999902i | \(0.504460\pi\) | |||||||
\(548\) | − | 0.862112i | − | 0.0368276i | ||||||
\(549\) | 6.06596 | − | 11.3373i | 0.258889 | − | 0.483863i | ||||
\(550\) | 0.193822 | 0.00826462 | ||||||||
\(551\) | −31.1383 | −1.32654 | ||||||||
\(552\) | 7.13983 | + | 1.79001i | 0.303891 | + | 0.0761879i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 21.3009i | − | 0.904990i | ||||||
\(555\) | −2.96239 | − | 0.742694i | −0.125746 | − | 0.0315256i | ||||
\(556\) | 16.1843i | 0.686368i | ||||||||
\(557\) | − | 17.7842i | − | 0.753542i | −0.926306 | − | 0.376771i | \(-0.877034\pi\) | ||
0.926306 | − | 0.376771i | \(-0.122966\pi\) | |||||||
\(558\) | −24.5132 | − | 13.1157i | −1.03773 | − | 0.555232i | ||||
\(559\) | − | 17.7917i | − | 0.752509i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0432303 | + | 0.172433i | −0.00182519 | + | 0.00728013i | ||||
\(562\) | 19.5927 | 0.826469 | ||||||||
\(563\) | 20.2723 | 0.854376 | 0.427188 | − | 0.904163i | \(-0.359504\pi\) | ||||
0.427188 | + | 0.904163i | \(0.359504\pi\) | |||||||
\(564\) | 16.4708 | + | 4.12936i | 0.693546 | + | 0.173877i | ||||
\(565\) | 3.44771i | 0.145046i | ||||||||
\(566\) | 15.0978 | 0.634610 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.29103 | −0.263966 | ||||||||
\(569\) | 44.9448i | 1.88418i | 0.335356 | + | 0.942092i | \(0.391143\pi\) | ||||
−0.335356 | + | 0.942092i | \(0.608857\pi\) | |||||||
\(570\) | 10.7344 | + | 2.69121i | 0.449616 | + | 0.112722i | ||||
\(571\) | −11.1890 | −0.468246 | −0.234123 | − | 0.972207i | \(-0.575222\pi\) | ||||
−0.234123 | + | 0.972207i | \(0.575222\pi\) | |||||||
\(572\) | 0.300216 | 0.0125527 | ||||||||
\(573\) | 10.6292 | − | 42.3967i | 0.444040 | − | 1.77115i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24976i | 0.177227i | ||||||||
\(576\) | −2.64518 | − | 1.41529i | −0.110216 | − | 0.0589704i | ||||
\(577\) | − | 9.73375i | − | 0.405221i | −0.979259 | − | 0.202611i | \(-0.935057\pi\) | ||
0.979259 | − | 0.202611i | \(-0.0649426\pi\) | |||||||
\(578\) | − | 16.7196i | − | 0.695443i | ||||||
\(579\) | 42.3989 | + | 10.6297i | 1.76204 | + | 0.441757i | ||||
\(580\) | 4.87349i | 0.202361i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.8514 | − | 3.47266i | −0.574160 | − | 0.143946i | ||||
\(583\) | 0.0125948 | 0.000521622 | ||||||||
\(584\) | −8.09171 | −0.334837 | ||||||||
\(585\) | −2.19217 | + | 4.09717i | −0.0906353 | + | 0.169397i | ||||
\(586\) | − | 8.00534i | − | 0.330698i | ||||||
\(587\) | 32.0185 | 1.32155 | 0.660773 | − | 0.750585i | \(-0.270228\pi\) | ||||
0.660773 | + | 0.750585i | \(0.270228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.2109 | −2.43974 | ||||||||
\(590\) | 12.0274i | 0.495161i | ||||||||
\(591\) | −6.20703 | + | 24.7580i | −0.255323 | + | 1.01841i | ||||
\(592\) | 1.76327 | 0.0724699 | ||||||||
\(593\) | −32.4012 | −1.33056 | −0.665280 | − | 0.746594i | \(-0.731688\pi\) | ||||
−0.665280 | + | 0.746594i | \(0.731688\pi\) | |||||||
\(594\) | 0.745813 | + | 0.676813i | 0.0306011 | + | 0.0277700i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.7600i | 0.522671i | ||||||||
\(597\) | −10.8941 | + | 43.4534i | −0.445866 | + | 1.77843i | ||||
\(598\) | 6.58255i | 0.269180i | ||||||||
\(599\) | − | 10.5437i | − | 0.430802i | −0.976526 | − | 0.215401i | \(-0.930894\pi\) | ||
0.976526 | − | 0.215401i | \(-0.0691059\pi\) | |||||||
\(600\) | 0.421203 | − | 1.68006i | 0.0171955 | − | 0.0685880i | ||||
\(601\) | 24.6793i | 1.00669i | 0.864086 | + | 0.503344i | \(0.167897\pi\) | ||||
−0.864086 | + | 0.503344i | \(0.832103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.7777 | + | 6.83667i | 0.520349 | + | 0.278411i | ||||
\(604\) | 17.5002 | 0.712075 | ||||||||
\(605\) | −10.9624 | −0.445686 | ||||||||
\(606\) | 1.87714 | − | 7.48738i | 0.0762538 | − | 0.304154i | ||||
\(607\) | 12.9854i | 0.527059i | 0.964651 | + | 0.263530i | \(0.0848867\pi\) | ||||
−0.964651 | + | 0.263530i | \(0.915113\pi\) | |||||||
\(608\) | −6.38933 | −0.259122 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.28602 | −0.173536 | ||||||||
\(611\) | 15.1852i | 0.614328i | ||||||||
\(612\) | 1.40071 | + | 0.749442i | 0.0566202 | + | 0.0302944i | ||||
\(613\) | −26.7286 | −1.07956 | −0.539780 | − | 0.841806i | \(-0.681493\pi\) | ||||
−0.539780 | + | 0.841806i | \(0.681493\pi\) | |||||||
\(614\) | 4.33663 | 0.175012 | ||||||||
\(615\) | −16.6590 | − | 4.17654i | −0.671755 | − | 0.168414i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2804i | 0.534650i | 0.963606 | + | 0.267325i | \(0.0861397\pi\) | ||||
−0.963606 | + | 0.267325i | \(0.913860\pi\) | |||||||
\(618\) | 14.1492 | + | 3.54732i | 0.569165 | + | 0.142694i | ||||
\(619\) | 9.88711i | 0.397396i | 0.980061 | + | 0.198698i | \(0.0636714\pi\) | ||||
−0.980061 | + | 0.198698i | \(0.936329\pi\) | |||||||
\(620\) | 9.26715i | 0.372178i | ||||||||
\(621\) | −14.8398 | + | 16.3527i | −0.595501 | + | 0.656212i | ||||
\(622\) | 22.8384i | 0.915736i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.652411 | − | 2.60228i | 0.0261174 | − | 0.104174i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.3042 | 1.01136 | ||||||||
\(627\) | 2.08057 | + | 0.521616i | 0.0830901 | + | 0.0208313i | ||||
\(628\) | 2.84609i | 0.113571i | ||||||||
\(629\) | −0.933708 | −0.0372294 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4695 | −1.05373 | −0.526867 | − | 0.849948i | \(-0.676633\pi\) | ||||
−0.526867 | + | 0.849948i | \(0.676633\pi\) | |||||||
\(632\) | − | 6.77766i | − | 0.269601i | ||||||
\(633\) | −38.4263 | − | 9.63378i | −1.52731 | − | 0.382908i | ||||
\(634\) | 15.0898 | 0.599292 | ||||||||
\(635\) | −5.49965 | −0.218247 | ||||||||
\(636\) | 0.0273702 | − | 0.109172i | 0.00108530 | − | 0.00432894i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.944591i | 0.0373967i | ||||||||
\(639\) | 8.90363 | − | 16.6409i | 0.352222 | − | 0.658303i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 23.5134i | 0.928723i | 0.885646 | + | 0.464362i | \(0.153716\pi\) | ||||
−0.885646 | + | 0.464362i | \(0.846284\pi\) | |||||||
\(642\) | −29.9279 | − | 7.50315i | −1.18116 | − | 0.296126i | ||||
\(643\) | − | 20.1307i | − | 0.793876i | −0.917846 | − | 0.396938i | \(-0.870073\pi\) | ||
0.917846 | − | 0.396938i | \(-0.129927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.2980 | − | 4.83815i | −0.759857 | − | 0.190502i | ||||
\(646\) | 3.38336 | 0.133116 | ||||||||
\(647\) | 10.3218 | 0.405790 | 0.202895 | − | 0.979200i | \(-0.434965\pi\) | ||||
0.202895 | + | 0.979200i | \(0.434965\pi\) | |||||||
\(648\) | 7.48738 | − | 4.99391i | 0.294132 | − | 0.196179i | ||||
\(649\) | 2.33118i | 0.0915069i | ||||||||
\(650\) | 1.54892 | 0.0607538 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.3586 | −0.484001 | ||||||||
\(653\) | − | 3.33429i | − | 0.130481i | −0.997870 | − | 0.0652404i | \(-0.979219\pi\) | ||
0.997870 | − | 0.0652404i | \(-0.0207814\pi\) | |||||||
\(654\) | −0.0622552 | + | 0.248318i | −0.00243437 | + | 0.00971000i | ||||
\(655\) | −5.99687 | −0.234317 | ||||||||
\(656\) | 9.91573 | 0.387144 | ||||||||
\(657\) | 11.4521 | − | 21.4040i | 0.446790 | − | 0.835050i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.1387i | − | 0.511809i | −0.966702 | − | 0.255905i | \(-0.917627\pi\) | ||
0.966702 | − | 0.255905i | \(-0.0823733\pi\) | |||||||
\(660\) | 0.0816386 | − | 0.325633i | 0.00317778 | − | 0.0126752i | ||||
\(661\) | − | 0.281918i | − | 0.0109653i | −0.999985 | − | 0.00548266i | \(-0.998255\pi\) | ||
0.999985 | − | 0.00548266i | \(-0.00174519\pi\) | |||||||
\(662\) | 15.0617i | 0.585390i | ||||||||
\(663\) | −0.345473 | + | 1.37799i | −0.0134171 | + | 0.0535167i | ||||
\(664\) | 2.11036i | 0.0818977i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.49554 | + | 4.66415i | −0.0967000 | + | 0.180732i | ||||
\(667\) | −20.7111 | −0.801939 | ||||||||
\(668\) | 4.99920 | 0.193425 | ||||||||
\(669\) | 0.00263792 | − | 0.0105219i | 0.000101988 | − | 0.000406800i | ||||
\(670\) | − | 4.83058i | − | 0.186622i | ||||||
\(671\) | −0.830727 | −0.0320699 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0090 | −1.38805 | −0.694023 | − | 0.719953i | \(-0.744163\pi\) | ||||
−0.694023 | + | 0.719953i | \(0.744163\pi\) | |||||||
\(674\) | 14.9611i | 0.576280i | ||||||||
\(675\) | 3.84792 | + | 3.49192i | 0.148106 | + | 0.134404i | ||||
\(676\) | −10.6008 | −0.407725 | ||||||||
\(677\) | −4.01490 | −0.154305 | −0.0771526 | − | 0.997019i | \(-0.524583\pi\) | ||||
−0.0771526 | + | 0.997019i | \(0.524583\pi\) | |||||||
\(678\) | 5.79235 | + | 1.45219i | 0.222454 | + | 0.0557709i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 0.529533i | − | 0.0203067i | ||||||
\(681\) | 31.6312 | + | 7.93019i | 1.21211 | + | 0.303885i | ||||
\(682\) | 1.79618i | 0.0687793i | ||||||||
\(683\) | 36.4916i | 1.39631i | 0.715945 | + | 0.698156i | \(0.245996\pi\) | ||||
−0.715945 | + | 0.698156i | \(0.754004\pi\) | |||||||
\(684\) | 9.04275 | − | 16.9009i | 0.345758 | − | 0.646222i | ||||
\(685\) | − | 0.862112i | − | 0.0329396i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.28394 | − | 13.0987i | 0.125290 | − | 0.499746i | ||||
\(688\) | 11.4865 | 0.437919 | ||||||||
\(689\) | 0.100650 | 0.00383448 | ||||||||
\(690\) | 7.13983 | + | 1.79001i | 0.271809 | + | 0.0681445i | ||||
\(691\) | 8.74478i | 0.332667i | 0.986070 | + | 0.166334i | \(0.0531928\pi\) | ||||
−0.986070 | + | 0.166334i | \(0.946807\pi\) | |||||||
\(692\) | −7.60806 | −0.289215 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.04662 | 0.153608 | ||||||||
\(695\) | 16.1843i | 0.613906i | ||||||||
\(696\) | 8.18773 | + | 2.05273i | 0.310355 | + | 0.0778085i | ||||
\(697\) | −5.25070 | −0.198885 | ||||||||
\(698\) | 12.3695 | 0.468193 | ||||||||
\(699\) | 5.47327 | − | 21.8313i | 0.207018 | − | 0.825734i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.5875i | − | 0.815349i | −0.913127 | − | 0.407674i | \(-0.866340\pi\) | ||
0.913127 | − | 0.407674i | \(-0.133660\pi\) | |||||||
\(702\) | 5.96013 | + | 5.40872i | 0.224951 | + | 0.204139i | ||||
\(703\) | 11.2661i | 0.424909i | ||||||||
\(704\) | 0.193822i | 0.00730496i | ||||||||
\(705\) | 16.4708 | + | 4.12936i | 0.620327 | + | 0.155521i | ||||
\(706\) | 3.66715i | 0.138015i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20.2067 | + | 5.06598i | 0.759415 | + | 0.190391i | ||||
\(709\) | −5.01486 | −0.188337 | −0.0941685 | − | 0.995556i | \(-0.530019\pi\) | ||||
−0.0941685 | + | 0.995556i | \(0.530019\pi\) | |||||||
\(710\) | −6.29103 | −0.236098 | ||||||||
\(711\) | 17.9281 | + | 9.59235i | 0.672356 | + | 0.359741i | ||||
\(712\) | 16.3755i | 0.613697i | ||||||||
\(713\) | −39.3831 | −1.47491 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.300216 | 0.0112274 | ||||||||
\(716\) | 16.2259i | 0.606390i | ||||||||
\(717\) | −7.23246 | + | 28.8482i | −0.270101 | + | 1.07736i | ||||
\(718\) | −7.32269 | −0.273280 | ||||||||
\(719\) | −34.3017 | −1.27924 | −0.639619 | − | 0.768692i | \(-0.720908\pi\) | ||||
−0.639619 | + | 0.768692i | \(0.720908\pi\) | |||||||
\(720\) | −2.64518 | − | 1.41529i | −0.0985799 | − | 0.0527447i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 21.8235i | − | 0.812188i | ||||||
\(723\) | −3.45656 | + | 13.7872i | −0.128551 | + | 0.512752i | ||||
\(724\) | 4.03153i | 0.149831i | ||||||||
\(725\) | 4.87349i | 0.180997i | ||||||||
\(726\) | −4.61741 | + | 18.4175i | −0.171368 | + | 0.683538i | ||||
\(727\) | − | 17.4763i | − | 0.648159i | −0.946030 | − | 0.324080i | \(-0.894945\pi\) | ||
0.946030 | − | 0.324080i | \(-0.105055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.61296 | + | 26.8733i | 0.0967764 | + | 0.995306i | ||||
\(730\) | −8.09171 | −0.299488 | ||||||||
\(731\) | −6.08248 | −0.224969 | ||||||||
\(732\) | −1.80529 | + | 7.20076i | −0.0667253 | + | 0.266148i | ||||
\(733\) | − | 51.9985i | − | 1.92061i | −0.278955 | − | 0.960304i | \(-0.589988\pi\) | ||
0.278955 | − | 0.960304i | \(-0.410012\pi\) | |||||||
\(734\) | 4.76624 | 0.175925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.24976 | −0.156648 | ||||||||
\(737\) | − | 0.936275i | − | 0.0344881i | ||||||
\(738\) | −14.0336 | + | 26.2289i | −0.516585 | + | 0.965497i | ||||
\(739\) | −24.2066 | −0.890453 | −0.445226 | − | 0.895418i | \(-0.646877\pi\) | ||||
−0.445226 | + | 0.895418i | \(0.646877\pi\) | |||||||
\(740\) | 1.76327 | 0.0648190 | ||||||||
\(741\) | 16.6268 | + | 4.16847i | 0.610801 | + | 0.153133i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.1794i | 1.76753i | 0.467932 | + | 0.883765i | \(0.344999\pi\) | ||||
−0.467932 | + | 0.883765i | \(0.655001\pi\) | |||||||
\(744\) | 15.5693 | + | 3.90335i | 0.570799 | + | 0.143104i | ||||
\(745\) | 12.7600i | 0.467491i | ||||||||
\(746\) | − | 17.2963i | − | 0.633261i | ||||||
\(747\) | −5.58226 | − | 2.98676i | −0.204244 | − | 0.109280i | ||||
\(748\) | − | 0.102635i | − | 0.00375272i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.421203 | − | 1.68006i | 0.0153802 | − | 0.0613470i | ||||
\(751\) | 5.16293 | 0.188398 | 0.0941991 | − | 0.995553i | \(-0.469971\pi\) | ||||
0.0941991 | + | 0.995553i | \(0.469971\pi\) | |||||||
\(752\) | −9.80373 | −0.357505 | ||||||||
\(753\) | −38.4903 | − | 9.64983i | −1.40267 | − | 0.351659i | ||||
\(754\) | 7.54866i | 0.274906i | ||||||||
\(755\) | 17.5002 | 0.636899 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0842 | −0.584591 | −0.292295 | − | 0.956328i | \(-0.594419\pi\) | ||||
−0.292295 | + | 0.956328i | \(0.594419\pi\) | |||||||
\(758\) | − | 8.76645i | − | 0.318412i | ||||||
\(759\) | 1.38386 | + | 0.346944i | 0.0502309 | + | 0.0125933i | ||||
\(760\) | −6.38933 | −0.231765 | ||||||||
\(761\) | −10.1579 | −0.368224 | −0.184112 | − | 0.982905i | \(-0.558941\pi\) | ||||
−0.184112 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(762\) | −2.31647 | + | 9.23972i | −0.0839168 | + | 0.334720i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25.2353i | 0.912980i | ||||||||
\(765\) | 1.40071 | + | 0.749442i | 0.0506427 | + | 0.0270961i | ||||
\(766\) | 28.4753i | 1.02886i | ||||||||
\(767\) | 18.6295i | 0.672674i | ||||||||
\(768\) | 1.68006 | + | 0.421203i | 0.0606238 | + | 0.0151989i | ||||
\(769\) | 6.68859i | 0.241197i | 0.992701 | + | 0.120598i | \(0.0384813\pi\) | ||||
−0.992701 | + | 0.120598i | \(0.961519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9057 | + | 2.98485i | 0.428773 | + | 0.107497i | ||||
\(772\) | −25.2366 | −0.908286 | ||||||||
\(773\) | −26.5704 | −0.955672 | −0.477836 | − | 0.878449i | \(-0.658579\pi\) | ||||
−0.477836 | + | 0.878449i | \(0.658579\pi\) | |||||||
\(774\) | −16.2567 | + | 30.3838i | −0.584336 | + | 1.09212i | ||||
\(775\) | 9.26715i | 0.332886i | ||||||||
\(776\) | 8.24463 | 0.295965 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.0696 | −0.755382 | ||||||||
\(779\) | 63.3549i | 2.26992i | ||||||||
\(780\) | 0.652411 | − | 2.60228i | 0.0233601 | − | 0.0931765i | ||||
\(781\) | −1.21934 | −0.0436315 | ||||||||
\(782\) | 2.25039 | 0.0804736 | ||||||||
\(783\) | −17.0178 | + | 18.7528i | −0.608168 | + | 0.670170i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.84609i | 0.101581i | ||||||||
\(786\) | −2.52590 | + | 10.0751i | −0.0900959 | + | 0.359366i | ||||
\(787\) | 29.5917i | 1.05483i | 0.849607 | + | 0.527416i | \(0.176839\pi\) | ||||
−0.849607 | + | 0.527416i | \(0.823161\pi\) | |||||||
\(788\) | − | 14.7364i | − | 0.524964i | ||||||
\(789\) | 7.52619 | − | 30.0198i | 0.267940 | − | 1.06873i | ||||
\(790\) | − | 6.77766i | − | 0.241138i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.512694 | − | 0.274315i | −0.0182178 | − | 0.00974735i | ||||
\(793\) | −6.63872 | −0.235748 | ||||||||
\(794\) | 6.59809 | 0.234158 | ||||||||
\(795\) | 0.0273702 | − | 0.109172i | 0.000970720 | − | 0.00387192i | ||||
\(796\) | − | 25.8642i | − | 0.916734i | ||||||
\(797\) | 34.6019 | 1.22566 | 0.612830 | − | 0.790215i | \(-0.290031\pi\) | ||||
0.612830 | + | 0.790215i | \(0.290031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.19139 | 0.183658 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | −43.3160 | − | 23.1760i | −1.53050 | − | 0.818885i | ||||
\(802\) | 16.1310 | 0.569607 | ||||||||
\(803\) | −1.56836 | −0.0553461 | ||||||||
\(804\) | −8.11564 | − | 2.03465i | −0.286217 | − | 0.0717567i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.3541i | 0.505602i | ||||||||
\(807\) | 11.6352 | + | 2.91703i | 0.409577 | + | 0.102684i | ||||
\(808\) | 4.45663i | 0.156784i | ||||||||
\(809\) | 16.8707i | 0.593143i | 0.955011 | + | 0.296571i | \(0.0958433\pi\) | ||||
−0.955011 | + | 0.296571i | \(0.904157\pi\) | |||||||
\(810\) | 7.48738 | − | 4.99391i | 0.263080 | − | 0.175468i | ||||
\(811\) | 11.1600i | 0.391880i | 0.980616 | + | 0.195940i | \(0.0627758\pi\) | ||||
−0.980616 | + | 0.195940i | \(0.937224\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.12619 | + | 28.4243i | −0.249926 | + | 0.996883i | ||||
\(814\) | 0.341761 | 0.0119787 | ||||||||
\(815\) | −12.3586 | −0.432904 | ||||||||
\(816\) | −0.889645 | − | 0.223041i | −0.0311438 | − | 0.00780799i | ||||
\(817\) | 73.3911i | 2.56763i | ||||||||
\(818\) | 26.4033 | 0.923169 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.91573 | 0.346272 | ||||||||
\(821\) | − | 39.3637i | − | 1.37380i | −0.726751 | − | 0.686901i | \(-0.758971\pi\) | ||
0.726751 | − | 0.686901i | \(-0.241029\pi\) | |||||||
\(822\) | −1.44840 | − | 0.363124i | −0.0505186 | − | 0.0126654i | ||||
\(823\) | 40.7171 | 1.41931 | 0.709654 | − | 0.704551i | \(-0.248851\pi\) | ||||
0.709654 | + | 0.704551i | \(0.248851\pi\) | |||||||
\(824\) | −8.42187 | −0.293390 | ||||||||
\(825\) | 0.0816386 | − | 0.325633i | 0.00284229 | − | 0.0113371i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7892i | 0.862006i | 0.902350 | + | 0.431003i | \(0.141840\pi\) | ||||
−0.902350 | + | 0.431003i | \(0.858160\pi\) | |||||||
\(828\) | 6.01464 | − | 11.2414i | 0.209023 | − | 0.390664i | ||||
\(829\) | − | 1.03670i | − | 0.0360062i | −0.999838 | − | 0.0180031i | \(-0.994269\pi\) | ||
0.999838 | − | 0.0180031i | \(-0.00573088\pi\) | |||||||
\(830\) | 2.11036i | 0.0732515i | ||||||||
\(831\) | −35.7867 | − | 8.97202i | −1.24143 | − | 0.311236i | ||||
\(832\) | 1.54892i | 0.0536992i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 27.1906 | + | 6.81689i | 0.941533 | + | 0.236050i | ||||
\(835\) | 4.99920 | 0.173004 | ||||||||
\(836\) | −1.23840 | −0.0428308 | ||||||||
\(837\) | −32.3602 | + | 35.6592i | −1.11853 | + | 1.23256i | ||||
\(838\) | 19.8312i | 0.685058i | ||||||||
\(839\) | 19.4880 | 0.672801 | 0.336401 | − | 0.941719i | \(-0.390790\pi\) | ||||
0.336401 | + | 0.941719i | \(0.390790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.24911 | 0.181004 | ||||||||
\(842\) | 6.28009i | 0.216426i | ||||||||
\(843\) | 8.25252 | − | 32.9169i | 0.284232 | − | 1.13372i | ||||
\(844\) | 22.8721 | 0.787289 | ||||||||
\(845\) | −10.6008 | −0.364680 | ||||||||
\(846\) | 13.8751 | − | 25.9326i | 0.477036 | − | 0.891581i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.0649809i | 0.00223145i | ||||||||
\(849\) | 6.35926 | − | 25.3652i | 0.218249 | − | 0.870532i | ||||
\(850\) | − | 0.529533i | − | 0.0181628i | ||||||
\(851\) | 7.49346i | 0.256873i | ||||||||
\(852\) | −2.64980 | + | 10.5693i | −0.0907808 | + | 0.362098i | ||||
\(853\) | 3.93413i | 0.134702i | 0.997729 | + | 0.0673510i | \(0.0214547\pi\) | ||||
−0.997729 | + | 0.0673510i | \(0.978545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.04275 | − | 16.9009i | 0.309256 | − | 0.577999i | ||||
\(856\) | 17.8136 | 0.608857 | ||||||||
\(857\) | −8.99608 | −0.307300 | −0.153650 | − | 0.988125i | \(-0.549103\pi\) | ||||
−0.153650 | + | 0.988125i | \(0.549103\pi\) | |||||||
\(858\) | 0.126452 | − | 0.504380i | 0.00431700 | − | 0.0172192i | ||||
\(859\) | − | 40.6455i | − | 1.38681i | −0.720549 | − | 0.693404i | \(-0.756110\pi\) | ||
0.720549 | − | 0.693404i | \(-0.243890\pi\) | |||||||
\(860\) | 11.4865 | 0.391687 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.55329 | 0.155086 | ||||||||
\(863\) | − | 33.2476i | − | 1.13176i | −0.824487 | − | 0.565880i | \(-0.808536\pi\) | ||
0.824487 | − | 0.565880i | \(-0.191464\pi\) | |||||||
\(864\) | −3.49192 | + | 3.84792i | −0.118798 | + | 0.130909i | ||||
\(865\) | −7.60806 | −0.258682 | ||||||||
\(866\) | −2.62801 | −0.0893035 | ||||||||
\(867\) | −28.0899 | − | 7.04235i | −0.953981 | − | 0.239171i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.31366i | − | 0.0445629i | ||||||
\(870\) | 8.18773 | + | 2.05273i | 0.277590 | + | 0.0695940i | ||||
\(871\) | − | 7.48220i | − | 0.253525i | ||||||
\(872\) | − | 0.147803i | − | 0.00500525i | ||||||
\(873\) | −11.6685 | + | 21.8085i | −0.394920 | + | 0.738105i | ||||
\(874\) | − | 27.1531i | − | 0.918467i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.40825 | + | 13.5945i | −0.115154 | + | 0.459317i | ||||
\(877\) | 28.2628 | 0.954367 | 0.477184 | − | 0.878804i | \(-0.341658\pi\) | ||||
0.477184 | + | 0.878804i | \(0.341658\pi\) | |||||||
\(878\) | −5.83672 | −0.196980 | ||||||||
\(879\) | −13.4494 | − | 3.37188i | −0.453638 | − | 0.113731i | ||||
\(880\) | 0.193822i | 0.00653375i | ||||||||
\(881\) | −34.2140 | −1.15270 | −0.576350 | − | 0.817203i | \(-0.695523\pi\) | ||||
−0.576350 | + | 0.817203i | \(0.695523\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.09672 | 0.137866 | 0.0689328 | − | 0.997621i | \(-0.478041\pi\) | ||||
0.0689328 | + | 0.997621i | \(0.478041\pi\) | |||||||
\(884\) | − | 0.820205i | − | 0.0275865i | ||||||
\(885\) | 20.2067 | + | 5.06598i | 0.679242 | + | 0.170291i | ||||
\(886\) | 26.3461 | 0.885114 | ||||||||
\(887\) | −1.85399 | −0.0622510 | −0.0311255 | − | 0.999515i | \(-0.509909\pi\) | ||||
−0.0311255 | + | 0.999515i | \(0.509909\pi\) | |||||||
\(888\) | 0.742694 | − | 2.96239i | 0.0249232 | − | 0.0994113i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.3755i | 0.548907i | ||||||||
\(891\) | 1.45122 | − | 0.967932i | 0.0486178 | − | 0.0324269i | ||||
\(892\) | 0.00626282i | 0.000209695i | ||||||||
\(893\) | − | 62.6393i | − | 2.09614i | ||||||
\(894\) | 21.4375 | + | 5.37456i | 0.716979 | + | 0.179752i | ||||
\(895\) | 16.2259i | 0.542372i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0590 | + | 2.77259i | 0.369251 | + | 0.0925740i | ||||
\(898\) | −5.76638 | −0.192427 | ||||||||
\(899\) | −45.1633 | −1.50628 | ||||||||
\(900\) | −2.64518 | − | 1.41529i | −0.0881725 | − | 0.0471763i | ||||
\(901\) | − | 0.0344095i | − | 0.00114635i | ||||||
\(902\) | 1.92189 | 0.0639920 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.44771 | −0.114669 | ||||||||
\(905\) | 4.03153i | 0.134013i | ||||||||
\(906\) | 7.37116 | − | 29.4014i | 0.244890 | − | 0.976796i | ||||
\(907\) | 33.7423 | 1.12039 | 0.560197 | − | 0.828360i | \(-0.310726\pi\) | ||||
0.560197 | + | 0.828360i | \(0.310726\pi\) | |||||||
\(908\) | −18.8275 | −0.624811 | ||||||||
\(909\) | −11.7886 | − | 6.30742i | −0.391002 | − | 0.209204i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.90180i | − | 0.228667i | −0.993442 | − | 0.114333i | \(-0.963527\pi\) | ||
0.993442 | − | 0.114333i | \(-0.0364732\pi\) | |||||||
\(912\) | −2.69121 | + | 10.7344i | −0.0891147 | + | 0.355453i | ||||
\(913\) | 0.409034i | 0.0135371i | ||||||||
\(914\) | − | 0.721513i | − | 0.0238655i | ||||||
\(915\) | −1.80529 | + | 7.20076i | −0.0596809 | + | 0.238050i | ||||
\(916\) | 7.79658i | 0.257606i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.84909 | − | 2.03760i | 0.0610290 | − | 0.0672508i | ||||
\(919\) | −35.0255 | −1.15539 | −0.577693 | − | 0.816254i | \(-0.696047\pi\) | ||||
−0.577693 | + | 0.816254i | \(0.696047\pi\) | |||||||
\(920\) | −4.24976 | −0.140110 | ||||||||
\(921\) | 1.82660 | − | 7.28578i | 0.0601886 | − | 0.240075i | ||||
\(922\) | − | 34.3692i | − | 1.13189i | ||||||
\(923\) | −9.74433 | −0.320738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.76327 | 0.0579759 | ||||||||
\(926\) | 41.3815i | 1.35988i | ||||||||
\(927\) | 11.9194 | − | 22.2773i | 0.391484 | − | 0.731684i | ||||
\(928\) | −4.87349 | −0.159980 | ||||||||
\(929\) | −21.0894 | −0.691919 | −0.345960 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345960 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(930\) | 15.5693 | + | 3.90335i | 0.510538 | + | 0.127996i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.9944i | 0.425645i | ||||||||
\(933\) | 38.3698 | + | 9.61960i | 1.25617 | + | 0.314932i | ||||
\(934\) | 17.9669i | 0.587894i | ||||||||
\(935\) | − | 0.102635i | − | 0.00335653i | ||||||
\(936\) | −4.09717 | − | 2.19217i | −0.133920 | − | 0.0716535i | ||||
\(937\) | 44.5007i | 1.45378i | 0.686756 | + | 0.726888i | \(0.259034\pi\) | ||||
−0.686756 | + | 0.726888i | \(0.740966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6582 | − | 42.5125i | 0.347818 | − | 1.38734i | ||||
\(940\) | −9.80373 | −0.319762 | ||||||||
\(941\) | −43.6395 | −1.42261 | −0.711303 | − | 0.702885i | \(-0.751895\pi\) | ||||
−0.711303 | + | 0.702885i | \(0.751895\pi\) | |||||||
\(942\) | 4.78159 | + | 1.19878i | 0.155793 | + | 0.0390584i | ||||
\(943\) | 42.1394i | 1.37225i | ||||||||
\(944\) | −12.0274 | −0.391459 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.22634 | 0.0723846 | ||||||||
\(947\) | − | 12.8918i | − | 0.418927i | −0.977816 | − | 0.209463i | \(-0.932828\pi\) | ||
0.977816 | − | 0.209463i | \(-0.0671717\pi\) | |||||||
\(948\) | −11.3868 | − | 2.85477i | −0.369827 | − | 0.0927186i | ||||
\(949\) | −12.5334 | −0.406853 | ||||||||
\(950\) | −6.38933 | −0.207297 | ||||||||
\(951\) | 6.35586 | − | 25.3517i | 0.206103 | − | 0.822084i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.2228i | − | 1.52970i | −0.644211 | − | 0.764848i | \(-0.722814\pi\) | ||
0.644211 | − | 0.764848i | \(-0.277186\pi\) | |||||||
\(954\) | −0.171886 | − | 0.0919668i | −0.00556501 | − | 0.00297754i | ||||
\(955\) | 25.2353i | 0.816594i | ||||||||
\(956\) | − | 17.1710i | − | 0.555349i | ||||||
\(957\) | 1.58697 | + | 0.397865i | 0.0512993 | + | 0.0128611i | ||||
\(958\) | − | 9.01118i | − | 0.291138i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.68006 | + | 0.421203i | 0.0542236 | + | 0.0135943i | ||||
\(961\) | −54.8800 | −1.77032 | ||||||||
\(962\) | 2.73117 | 0.0880564 | ||||||||
\(963\) | −25.2114 | + | 47.1202i | −0.812427 | + | 1.51843i | ||||
\(964\) | − | 8.20640i | − | 0.264310i | ||||||
\(965\) | −25.2366 | −0.812396 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.93428 | −0.255149 | −0.127575 | − | 0.991829i | \(-0.540719\pi\) | ||||
−0.127575 | + | 0.991829i | \(0.540719\pi\) | |||||||
\(968\) | − | 10.9624i | − | 0.352346i | ||||||
\(969\) | 1.42508 | − | 5.68423i | 0.0457802 | − | 0.182604i | ||||
\(970\) | 8.24463 | 0.264719 | ||||||||
\(971\) | 33.5265 | 1.07592 | 0.537958 | − | 0.842972i | \(-0.319196\pi\) | ||||
0.537958 | + | 0.842972i | \(0.319196\pi\) | |||||||
\(972\) | −5.23634 | − | 14.6827i | −0.167956 | − | 0.470947i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 22.7295i | − | 0.728302i | ||||||
\(975\) | 0.652411 | − | 2.60228i | 0.0208939 | − | 0.0833396i | ||||
\(976\) | − | 4.28602i | − | 0.137192i | ||||||
\(977\) | − | 13.2522i | − | 0.423974i | −0.977272 | − | 0.211987i | \(-0.932007\pi\) | ||
0.977272 | − | 0.211987i | \(-0.0679935\pi\) | |||||||
\(978\) | −5.20549 | + | 20.7632i | −0.166453 | + | 0.663933i | ||||
\(979\) | 3.17393i | 0.101439i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.390966 | + | 0.209185i | 0.0124826 | + | 0.00667875i | ||||
\(982\) | −32.1654 | −1.02644 | ||||||||
\(983\) | 43.9478 | 1.40172 | 0.700858 | − | 0.713300i | \(-0.252800\pi\) | ||||
0.700858 | + | 0.713300i | \(0.252800\pi\) | |||||||
\(984\) | 4.17654 | − | 16.6590i | 0.133143 | − | 0.531069i | ||||
\(985\) | − | 14.7364i | − | 0.469542i | ||||||
\(986\) | 2.58067 | 0.0821853 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.89658 | −0.314852 | ||||||||
\(989\) | 48.8148i | 1.55222i | ||||||||
\(990\) | −0.512694 | − | 0.274315i | −0.0162945 | − | 0.00871830i | ||||
\(991\) | 10.8651 | 0.345142 | 0.172571 | − | 0.984997i | \(-0.444793\pi\) | ||||
0.172571 | + | 0.984997i | \(0.444793\pi\) | |||||||
\(992\) | −9.26715 | −0.294232 | ||||||||
\(993\) | 25.3045 | + | 6.34404i | 0.803015 | + | 0.201322i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 25.8642i | − | 0.819952i | ||||||
\(996\) | 3.54552 | + | 0.888888i | 0.112344 | + | 0.0281655i | ||||
\(997\) | − | 40.2056i | − | 1.27332i | −0.771143 | − | 0.636662i | \(-0.780315\pi\) | ||
0.771143 | − | 0.636662i | \(-0.219685\pi\) | |||||||
\(998\) | 21.2508i | 0.672682i | ||||||||
\(999\) | 6.78491 | + | 6.15720i | 0.214665 | + | 0.194805i |
(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 | 1470.2.b.b.881.12 | 12 | ||
3.2 | odd | 2 | 1470.2.b.a.881.1 | 12 | |||
7.4 | even | 3 | 210.2.r.a.131.2 | yes | 12 | ||
7.5 | odd | 6 | 210.2.r.b.101.6 | yes | 12 | ||
7.6 | odd | 2 | 1470.2.b.a.881.7 | 12 | |||
21.5 | even | 6 | 210.2.r.a.101.2 | ✓ | 12 | ||
21.11 | odd | 6 | 210.2.r.b.131.6 | yes | 12 | ||
21.20 | even | 2 | inner | 1470.2.b.b.881.6 | 12 | ||
35.4 | even | 6 | 1050.2.s.g.551.5 | 12 | |||
35.12 | even | 12 | 1050.2.u.h.899.2 | 12 | |||
35.18 | odd | 12 | 1050.2.u.f.299.5 | 12 | |||
35.19 | odd | 6 | 1050.2.s.f.101.1 | 12 | |||
35.32 | odd | 12 | 1050.2.u.g.299.2 | 12 | |||
35.33 | even | 12 | 1050.2.u.e.899.5 | 12 | |||
105.32 | even | 12 | 1050.2.u.e.299.5 | 12 | |||
105.47 | odd | 12 | 1050.2.u.f.899.5 | 12 | |||
105.53 | even | 12 | 1050.2.u.h.299.2 | 12 | |||
105.68 | odd | 12 | 1050.2.u.g.899.2 | 12 | |||
105.74 | odd | 6 | 1050.2.s.f.551.1 | 12 | |||
105.89 | even | 6 | 1050.2.s.g.101.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.r.a.101.2 | ✓ | 12 | 21.5 | even | 6 | ||
210.2.r.a.131.2 | yes | 12 | 7.4 | even | 3 | ||
210.2.r.b.101.6 | yes | 12 | 7.5 | odd | 6 | ||
210.2.r.b.131.6 | yes | 12 | 21.11 | odd | 6 | ||
1050.2.s.f.101.1 | 12 | 35.19 | odd | 6 | |||
1050.2.s.f.551.1 | 12 | 105.74 | odd | 6 | |||
1050.2.s.g.101.5 | 12 | 105.89 | even | 6 | |||
1050.2.s.g.551.5 | 12 | 35.4 | even | 6 | |||
1050.2.u.e.299.5 | 12 | 105.32 | even | 12 | |||
1050.2.u.e.899.5 | 12 | 35.33 | even | 12 | |||
1050.2.u.f.299.5 | 12 | 35.18 | odd | 12 | |||
1050.2.u.f.899.5 | 12 | 105.47 | odd | 12 | |||
1050.2.u.g.299.2 | 12 | 35.32 | odd | 12 | |||
1050.2.u.g.899.2 | 12 | 105.68 | odd | 12 | |||
1050.2.u.h.299.2 | 12 | 105.53 | even | 12 | |||
1050.2.u.h.899.2 | 12 | 35.12 | even | 12 | |||
1470.2.b.a.881.1 | 12 | 3.2 | odd | 2 | |||
1470.2.b.a.881.7 | 12 | 7.6 | odd | 2 | |||
1470.2.b.b.881.6 | 12 | 21.20 | even | 2 | inner | ||
1470.2.b.b.881.12 | 12 | 1.1 | even | 1 | trivial |