Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,7,Mod(6,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.6");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.d (of order \(4\), 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: | \(8.51200109393\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.12 | ||
Character | \(\chi\) | \(=\) | 37.31 |
Dual form | 37.7.d.a.6.12 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77875 | + | 2.77875i | 0.347343 | + | 0.347343i | 0.859119 | − | 0.511776i | \(-0.171012\pi\) |
−0.511776 | + | 0.859119i | \(0.671012\pi\) | |||||||
\(3\) | 27.0135i | 1.00050i | 0.865881 | + | 0.500250i | \(0.166759\pi\) | ||||
−0.865881 | + | 0.500250i | \(0.833241\pi\) | |||||||
\(4\) | − | 48.5571i | − | 0.758705i | ||||||
\(5\) | 96.7657 | − | 96.7657i | 0.774126 | − | 0.774126i | −0.204699 | − | 0.978825i | \(-0.565622\pi\) |
0.978825 | + | 0.204699i | \(0.0656215\pi\) | |||||||
\(6\) | −75.0636 | + | 75.0636i | −0.347517 | + | 0.347517i | ||||
\(7\) | 312.208 | 0.910228 | 0.455114 | − | 0.890433i | \(-0.349599\pi\) | ||||
0.455114 | + | 0.890433i | \(0.349599\pi\) | |||||||
\(8\) | 312.768 | − | 312.768i | 0.610874 | − | 0.610874i | ||||
\(9\) | −0.728696 | −0.000999583 | ||||||||
\(10\) | 537.775 | 0.537775 | ||||||||
\(11\) | 1621.10i | 1.21796i | 0.793186 | + | 0.608980i | \(0.208421\pi\) | ||||
−0.793186 | + | 0.608980i | \(0.791579\pi\) | |||||||
\(12\) | 1311.70 | 0.759084 | ||||||||
\(13\) | −1599.67 | + | 1599.67i | −0.728116 | + | 0.728116i | −0.970244 | − | 0.242128i | \(-0.922155\pi\) |
0.242128 | + | 0.970244i | \(0.422155\pi\) | |||||||
\(14\) | 867.547 | + | 867.547i | 0.316161 | + | 0.316161i | ||||
\(15\) | 2613.98 | + | 2613.98i | 0.774513 | + | 0.774513i | ||||
\(16\) | −1369.45 | −0.334339 | ||||||||
\(17\) | 1956.65 | − | 1956.65i | 0.398259 | − | 0.398259i | −0.479359 | − | 0.877619i | \(-0.659131\pi\) |
0.877619 | + | 0.479359i | \(0.159131\pi\) | |||||||
\(18\) | −2.02486 | − | 2.02486i | −0.000347198 | − | 0.000347198i | ||||
\(19\) | 9305.33 | − | 9305.33i | 1.35666 | − | 1.35666i | 0.478659 | − | 0.878001i | \(-0.341123\pi\) |
0.878001 | − | 0.478659i | \(-0.158877\pi\) | |||||||
\(20\) | −4698.67 | − | 4698.67i | −0.587334 | − | 0.587334i | ||||
\(21\) | 8433.83i | 0.910682i | ||||||||
\(22\) | −4504.64 | + | 4504.64i | −0.423050 | + | 0.423050i | ||||
\(23\) | 3528.74 | − | 3528.74i | 0.290026 | − | 0.290026i | −0.547065 | − | 0.837090i | \(-0.684255\pi\) |
0.837090 | + | 0.547065i | \(0.184255\pi\) | |||||||
\(24\) | 8448.95 | + | 8448.95i | 0.611180 | + | 0.611180i | ||||
\(25\) | − | 3102.22i | − | 0.198542i | ||||||
\(26\) | −8890.16 | −0.505813 | ||||||||
\(27\) | 19673.2i | 0.999500i | ||||||||
\(28\) | − | 15159.9i | − | 0.690595i | ||||||
\(29\) | 6587.87 | + | 6587.87i | 0.270116 | + | 0.270116i | 0.829147 | − | 0.559031i | \(-0.188827\pi\) |
−0.559031 | + | 0.829147i | \(0.688827\pi\) | |||||||
\(30\) | 14527.2i | 0.538044i | ||||||||
\(31\) | −31435.5 | − | 31435.5i | −1.05520 | − | 1.05520i | −0.998385 | − | 0.0568156i | \(-0.981905\pi\) |
−0.0568156 | − | 0.998385i | \(-0.518095\pi\) | |||||||
\(32\) | −23822.5 | − | 23822.5i | −0.727005 | − | 0.727005i | ||||
\(33\) | −43791.7 | −1.21857 | ||||||||
\(34\) | 10874.1 | 0.276665 | ||||||||
\(35\) | 30211.0 | − | 30211.0i | 0.704631 | − | 0.704631i | ||||
\(36\) | 35.3834i | 0.000758389i | ||||||||
\(37\) | −20359.1 | + | 46381.4i | −0.401934 | + | 0.915669i | ||||
\(38\) | 51714.3 | 0.942453 | ||||||||
\(39\) | −43212.7 | − | 43212.7i | −0.728480 | − | 0.728480i | ||||
\(40\) | − | 60530.4i | − | 0.945787i | ||||||
\(41\) | − | 1010.89i | − | 0.0146674i | −0.999973 | − | 0.00733371i | \(-0.997666\pi\) | ||
0.999973 | − | 0.00733371i | \(-0.00233441\pi\) | |||||||
\(42\) | −23435.5 | + | 23435.5i | −0.316319 | + | 0.316319i | ||||
\(43\) | −62136.0 | + | 62136.0i | −0.781517 | + | 0.781517i | −0.980087 | − | 0.198570i | \(-0.936370\pi\) |
0.198570 | + | 0.980087i | \(0.436370\pi\) | |||||||
\(44\) | 78716.2 | 0.924073 | ||||||||
\(45\) | −70.5128 | + | 70.5128i | −0.000773803 | + | 0.000773803i | ||||
\(46\) | 19611.0 | 0.201477 | ||||||||
\(47\) | −95688.6 | −0.921651 | −0.460826 | − | 0.887491i | \(-0.652447\pi\) | ||||
−0.460826 | + | 0.887491i | \(0.652447\pi\) | |||||||
\(48\) | − | 36993.7i | − | 0.334506i | ||||||
\(49\) | −20175.1 | −0.171486 | ||||||||
\(50\) | 8620.28 | − | 8620.28i | 0.0689623 | − | 0.0689623i | ||||
\(51\) | 52855.9 | + | 52855.9i | 0.398458 | + | 0.398458i | ||||
\(52\) | 77675.5 | + | 77675.5i | 0.552426 | + | 0.552426i | ||||
\(53\) | −116072. | −0.779648 | −0.389824 | − | 0.920889i | \(-0.627464\pi\) | ||||
−0.389824 | + | 0.920889i | \(0.627464\pi\) | |||||||
\(54\) | −54666.7 | + | 54666.7i | −0.347169 | + | 0.347169i | ||||
\(55\) | 156867. | + | 156867.i | 0.942854 | + | 0.942854i | ||||
\(56\) | 97648.6 | − | 97648.6i | 0.556035 | − | 0.556035i | ||||
\(57\) | 251369. | + | 251369.i | 1.35734 | + | 1.35734i | ||||
\(58\) | 36612.0i | 0.187646i | ||||||||
\(59\) | 167627. | − | 167627.i | 0.816185 | − | 0.816185i | −0.169368 | − | 0.985553i | \(-0.554173\pi\) |
0.985553 | + | 0.169368i | \(0.0541726\pi\) | |||||||
\(60\) | 126927. | − | 126927.i | 0.587627 | − | 0.587627i | ||||
\(61\) | −2678.47 | − | 2678.47i | −0.0118004 | − | 0.0118004i | 0.701182 | − | 0.712982i | \(-0.252656\pi\) |
−0.712982 | + | 0.701182i | \(0.752656\pi\) | |||||||
\(62\) | − | 174702.i | − | 0.733033i | ||||||
\(63\) | −227.505 | −0.000909848 | ||||||||
\(64\) | − | 44748.3i | − | 0.170701i | ||||||
\(65\) | 309587.i | 1.12731i | ||||||||
\(66\) | −121686. | − | 121686.i | −0.423262 | − | 0.423262i | ||||
\(67\) | − | 409672.i | − | 1.36211i | −0.732232 | − | 0.681055i | \(-0.761521\pi\) | ||
0.732232 | − | 0.681055i | \(-0.238479\pi\) | |||||||
\(68\) | −95009.2 | − | 95009.2i | −0.302161 | − | 0.302161i | ||||
\(69\) | 95323.7 | + | 95323.7i | 0.290171 | + | 0.290171i | ||||
\(70\) | 167898. | 0.489497 | ||||||||
\(71\) | −296668. | −0.828887 | −0.414443 | − | 0.910075i | \(-0.636024\pi\) | ||||
−0.414443 | + | 0.910075i | \(0.636024\pi\) | |||||||
\(72\) | −227.913 | + | 227.913i | −0.000610620 | + | 0.000610620i | ||||
\(73\) | 540265.i | 1.38880i | 0.719591 | + | 0.694398i | \(0.244329\pi\) | ||||
−0.719591 | + | 0.694398i | \(0.755671\pi\) | |||||||
\(74\) | −185455. | + | 72309.1i | −0.457660 | + | 0.178442i | ||||
\(75\) | 83801.8 | 0.198641 | ||||||||
\(76\) | −451840. | − | 451840.i | −1.02931 | − | 1.02931i | ||||
\(77\) | 506122.i | 1.10862i | ||||||||
\(78\) | − | 240154.i | − | 0.506065i | ||||||
\(79\) | −121002. | + | 121002.i | −0.245420 | + | 0.245420i | −0.819088 | − | 0.573668i | \(-0.805520\pi\) |
0.573668 | + | 0.819088i | \(0.305520\pi\) | |||||||
\(80\) | −132516. | + | 132516.i | −0.258821 | + | 0.258821i | ||||
\(81\) | −531972. | −1.00100 | ||||||||
\(82\) | 2809.02 | − | 2809.02i | 0.00509463 | − | 0.00509463i | ||||
\(83\) | −9274.43 | −0.0162201 | −0.00811004 | − | 0.999967i | \(-0.502582\pi\) | ||||
−0.00811004 | + | 0.999967i | \(0.502582\pi\) | |||||||
\(84\) | 409523. | 0.690940 | ||||||||
\(85\) | − | 378673.i | − | 0.616606i | ||||||
\(86\) | −345321. | −0.542909 | ||||||||
\(87\) | −177961. | + | 177961.i | −0.270251 | + | 0.270251i | ||||
\(88\) | 507029. | + | 507029.i | 0.744021 | + | 0.744021i | ||||
\(89\) | −737069. | − | 737069.i | −1.04553 | − | 1.04553i | −0.998913 | − | 0.0466209i | \(-0.985155\pi\) |
−0.0466209 | − | 0.998913i | \(-0.514845\pi\) | |||||||
\(90\) | −391.875 | −0.000537551 | ||||||||
\(91\) | −499430. | + | 499430.i | −0.662752 | + | 0.662752i | ||||
\(92\) | −171346. | − | 171346.i | −0.220044 | − | 0.220044i | ||||
\(93\) | 849182. | − | 849182.i | 1.05573 | − | 1.05573i | ||||
\(94\) | −265894. | − | 265894.i | −0.320129 | − | 0.320129i | ||||
\(95\) | − | 1.80087e6i | − | 2.10045i | ||||||
\(96\) | 643529. | − | 643529.i | 0.727368 | − | 0.727368i | ||||
\(97\) | −86996.9 | + | 86996.9i | −0.0953209 | + | 0.0953209i | −0.753159 | − | 0.657838i | \(-0.771471\pi\) |
0.657838 | + | 0.753159i | \(0.271471\pi\) | |||||||
\(98\) | −56061.6 | − | 56061.6i | −0.0595644 | − | 0.0595644i | ||||
\(99\) | − | 1181.29i | − | 0.00121745i | ||||||
\(100\) | −150635. | −0.150635 | ||||||||
\(101\) | 1.34686e6i | 1.30725i | 0.756820 | + | 0.653623i | \(0.226752\pi\) | ||||
−0.756820 | + | 0.653623i | \(0.773248\pi\) | |||||||
\(102\) | 293746.i | 0.276804i | ||||||||
\(103\) | 1.27890e6 | + | 1.27890e6i | 1.17037 | + | 1.17037i | 0.982120 | + | 0.188254i | \(0.0602828\pi\) |
0.188254 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(104\) | 1.00065e6i | 0.889575i | ||||||||
\(105\) | 816106. | + | 816106.i | 0.704983 | + | 0.704983i | ||||
\(106\) | −322534. | − | 322534.i | −0.270806 | − | 0.270806i | ||||
\(107\) | −218651. | −0.178485 | −0.0892424 | − | 0.996010i | \(-0.528445\pi\) | ||||
−0.0892424 | + | 0.996010i | \(0.528445\pi\) | |||||||
\(108\) | 955272. | 0.758326 | ||||||||
\(109\) | 478923. | − | 478923.i | 0.369817 | − | 0.369817i | −0.497594 | − | 0.867410i | \(-0.665783\pi\) |
0.867410 | + | 0.497594i | \(0.165783\pi\) | |||||||
\(110\) | 871789.i | 0.654988i | ||||||||
\(111\) | −1.25292e6 | − | 549972.i | −0.916126 | − | 0.402135i | ||||
\(112\) | −427554. | −0.304325 | ||||||||
\(113\) | −580115. | − | 580115.i | −0.402049 | − | 0.402049i | 0.476906 | − | 0.878954i | \(-0.341758\pi\) |
−0.878954 | + | 0.476906i | \(0.841758\pi\) | |||||||
\(114\) | 1.39698e6i | 0.942924i | ||||||||
\(115\) | − | 682923.i | − | 0.449033i | ||||||
\(116\) | 319888. | − | 319888.i | 0.204939 | − | 0.204939i | ||||
\(117\) | 1165.67 | − | 1165.67i | 0.000727813 | − | 0.000727813i | ||||
\(118\) | 931587. | 0.566993 | ||||||||
\(119\) | 610881. | − | 610881.i | 0.362507 | − | 0.362507i | ||||
\(120\) | 1.63514e6 | 0.946260 | ||||||||
\(121\) | −856419. | −0.483426 | ||||||||
\(122\) | − | 14885.6i | − | 0.00819760i | ||||||
\(123\) | 27307.8 | 0.0146748 | ||||||||
\(124\) | −1.52642e6 | + | 1.52642e6i | −0.800586 | + | 0.800586i | ||||
\(125\) | 1.21178e6 | + | 1.21178e6i | 0.620429 | + | 0.620429i | ||||
\(126\) | −632.178 | − | 632.178i | −0.000316030 | − | 0.000316030i | ||||
\(127\) | 3.60881e6 | 1.76178 | 0.880892 | − | 0.473317i | \(-0.156943\pi\) | ||||
0.880892 | + | 0.473317i | \(0.156943\pi\) | |||||||
\(128\) | −1.40030e6 | + | 1.40030e6i | −0.667713 | + | 0.667713i | ||||
\(129\) | −1.67851e6 | − | 1.67851e6i | −0.781907 | − | 0.781907i | ||||
\(130\) | −860263. | + | 860263.i | −0.391563 | + | 0.391563i | ||||
\(131\) | −2.14260e6 | − | 2.14260e6i | −0.953074 | − | 0.953074i | 0.0458735 | − | 0.998947i | \(-0.485393\pi\) |
−0.998947 | + | 0.0458735i | \(0.985393\pi\) | |||||||
\(132\) | 2.12640e6i | 0.924535i | ||||||||
\(133\) | 2.90520e6 | − | 2.90520e6i | 1.23487 | − | 1.23487i | ||||
\(134\) | 1.13838e6 | − | 1.13838e6i | 0.473120 | − | 0.473120i | ||||
\(135\) | 1.90369e6 | + | 1.90369e6i | 0.773739 | + | 0.773739i | ||||
\(136\) | − | 1.22395e6i | − | 0.486573i | ||||||
\(137\) | −2.05943e6 | −0.800914 | −0.400457 | − | 0.916316i | \(-0.631149\pi\) | ||||
−0.400457 | + | 0.916316i | \(0.631149\pi\) | |||||||
\(138\) | 529761.i | 0.201578i | ||||||||
\(139\) | 4.44757e6i | 1.65607i | 0.560676 | + | 0.828035i | \(0.310541\pi\) | ||||
−0.560676 | + | 0.828035i | \(0.689459\pi\) | |||||||
\(140\) | −1.46696e6 | − | 1.46696e6i | −0.534607 | − | 0.534607i | ||||
\(141\) | − | 2.58488e6i | − | 0.922112i | ||||||
\(142\) | −824364. | − | 824364.i | −0.287908 | − | 0.287908i | ||||
\(143\) | −2.59324e6 | − | 2.59324e6i | −0.886817 | − | 0.886817i | ||||
\(144\) | 997.916 | 0.000334200 | ||||||||
\(145\) | 1.27496e6 | 0.418208 | ||||||||
\(146\) | −1.50126e6 | + | 1.50126e6i | −0.482389 | + | 0.482389i | ||||
\(147\) | − | 545001.i | − | 0.171572i | ||||||
\(148\) | 2.25215e6 | + | 988582.i | 0.694723 | + | 0.304949i | ||||
\(149\) | 2.19421e6 | 0.663313 | 0.331656 | − | 0.943400i | \(-0.392393\pi\) | ||||
0.331656 | + | 0.943400i | \(0.392393\pi\) | |||||||
\(150\) | 232864. | + | 232864.i | 0.0689967 | + | 0.0689967i | ||||
\(151\) | − | 248.395i | − | 7.21460e-5i | −1.00000 | 3.60730e-5i | \(-0.999989\pi\) | |||
1.00000 | 3.60730e-5i | \(-1.14824e-5\pi\) | ||||||||
\(152\) | − | 5.82081e6i | − | 1.65750i | ||||||
\(153\) | −1425.80 | + | 1425.80i | −0.000398093 | + | 0.000398093i | ||||
\(154\) | −1.40638e6 | + | 1.40638e6i | −0.385072 | + | 0.385072i | ||||
\(155\) | −6.08375e6 | −1.63372 | ||||||||
\(156\) | −2.09829e6 | + | 2.09829e6i | −0.552702 | + | 0.552702i | ||||
\(157\) | 3.43503e6 | 0.887629 | 0.443814 | − | 0.896119i | \(-0.353625\pi\) | ||||
0.443814 | + | 0.896119i | \(0.353625\pi\) | |||||||
\(158\) | −672466. | −0.170490 | ||||||||
\(159\) | − | 3.13550e6i | − | 0.780038i | ||||||
\(160\) | −4.61040e6 | −1.12559 | ||||||||
\(161\) | 1.10170e6 | − | 1.10170e6i | 0.263990 | − | 0.263990i | ||||
\(162\) | −1.47821e6 | − | 1.47821e6i | −0.347690 | − | 0.347690i | ||||
\(163\) | 1.25799e6 | + | 1.25799e6i | 0.290478 | + | 0.290478i | 0.837269 | − | 0.546791i | \(-0.184151\pi\) |
−0.546791 | + | 0.837269i | \(0.684151\pi\) | |||||||
\(164\) | −49086.1 | −0.0111283 | ||||||||
\(165\) | −4.23754e6 | + | 4.23754e6i | −0.943326 | + | 0.943326i | ||||
\(166\) | −25771.3 | − | 25771.3i | −0.00563393 | − | 0.00563393i | ||||
\(167\) | −2.97309e6 | + | 2.97309e6i | −0.638349 | + | 0.638349i | −0.950148 | − | 0.311799i | \(-0.899068\pi\) |
0.311799 | + | 0.950148i | \(0.399068\pi\) | |||||||
\(168\) | 2.63783e6 | + | 2.63783e6i | 0.556313 | + | 0.556313i | ||||
\(169\) | − | 291089.i | − | 0.0603067i | ||||||
\(170\) | 1.05224e6 | − | 1.05224e6i | 0.214174 | − | 0.214174i | ||||
\(171\) | −6780.76 | + | 6780.76i | −0.00135609 | + | 0.00135609i | ||||
\(172\) | 3.01715e6 | + | 3.01715e6i | 0.592941 | + | 0.592941i | ||||
\(173\) | − | 1.03507e6i | − | 0.199908i | −0.994992 | − | 0.0999538i | \(-0.968130\pi\) | ||
0.994992 | − | 0.0999538i | \(-0.0318695\pi\) | |||||||
\(174\) | −989019. | −0.187740 | ||||||||
\(175\) | − | 968538.i | − | 0.180718i | ||||||
\(176\) | − | 2.22003e6i | − | 0.407212i | ||||||
\(177\) | 4.52820e6 | + | 4.52820e6i | 0.816593 | + | 0.816593i | ||||
\(178\) | − | 4.09625e6i | − | 0.726318i | ||||||
\(179\) | −7.36165e6 | − | 7.36165e6i | −1.28356 | − | 1.28356i | −0.938628 | − | 0.344932i | \(-0.887902\pi\) |
−0.344932 | − | 0.938628i | \(-0.612098\pi\) | |||||||
\(180\) | 3423.90 | + | 3423.90i | 0.000587089 | + | 0.000587089i | ||||
\(181\) | 7.60699e6 | 1.28285 | 0.641426 | − | 0.767185i | \(-0.278343\pi\) | ||||
0.641426 | + | 0.767185i | \(0.278343\pi\) | |||||||
\(182\) | −2.77558e6 | −0.460404 | ||||||||
\(183\) | 72354.9 | − | 72354.9i | 0.0118063 | − | 0.0118063i | ||||
\(184\) | − | 2.20735e6i | − | 0.354339i | ||||||
\(185\) | 2.51806e6 | + | 6.45820e6i | 0.397696 | + | 1.01999i | ||||
\(186\) | 4.71932e6 | 0.733400 | ||||||||
\(187\) | 3.17193e6 | + | 3.17193e6i | 0.485064 | + | 0.485064i | ||||
\(188\) | 4.64637e6i | 0.699262i | ||||||||
\(189\) | 6.14212e6i | 0.909772i | ||||||||
\(190\) | 5.00417e6 | − | 5.00417e6i | 0.729578 | − | 0.729578i | ||||
\(191\) | 7.05801e6 | − | 7.05801e6i | 1.01294 | − | 1.01294i | 0.0130219 | − | 0.999915i | \(-0.495855\pi\) |
0.999915 | − | 0.0130219i | \(-0.00414510\pi\) | |||||||
\(192\) | 1.20881e6 | 0.170786 | ||||||||
\(193\) | 1.35373e6 | − | 1.35373e6i | 0.188305 | − | 0.188305i | −0.606658 | − | 0.794963i | \(-0.707490\pi\) |
0.794963 | + | 0.606658i | \(0.207490\pi\) | |||||||
\(194\) | −483484. | −0.0662182 | ||||||||
\(195\) | −8.36302e6 | −1.12787 | ||||||||
\(196\) | 979647.i | 0.130107i | ||||||||
\(197\) | −2.09646e6 | −0.274213 | −0.137106 | − | 0.990556i | \(-0.543780\pi\) | ||||
−0.137106 | + | 0.990556i | \(0.543780\pi\) | |||||||
\(198\) | 3282.51 | − | 3282.51i | 0.000422874 | − | 0.000422874i | ||||
\(199\) | −4.92359e6 | − | 4.92359e6i | −0.624774 | − | 0.624774i | 0.321974 | − | 0.946748i | \(-0.395653\pi\) |
−0.946748 | + | 0.321974i | \(0.895653\pi\) | |||||||
\(200\) | −970274. | − | 970274.i | −0.121284 | − | 0.121284i | ||||
\(201\) | 1.10667e7 | 1.36279 | ||||||||
\(202\) | −3.74258e6 | + | 3.74258e6i | −0.454063 | + | 0.454063i | ||||
\(203\) | 2.05679e6 | + | 2.05679e6i | 0.245867 | + | 0.245867i | ||||
\(204\) | 2.56653e6 | − | 2.56653e6i | 0.302312 | − | 0.302312i | ||||
\(205\) | −97819.9 | − | 97819.9i | −0.0113544 | − | 0.0113544i | ||||
\(206\) | 7.10747e6i | 0.813043i | ||||||||
\(207\) | −2571.38 | + | 2571.38i | −0.000289905 | + | 0.000289905i | ||||
\(208\) | 2.19068e6 | − | 2.19068e6i | 0.243438 | − | 0.243438i | ||||
\(209\) | 1.50849e7 | + | 1.50849e7i | 1.65236 | + | 1.65236i | ||||
\(210\) | 4.53550e6i | 0.489742i | ||||||||
\(211\) | −2.68590e6 | −0.285918 | −0.142959 | − | 0.989729i | \(-0.545662\pi\) | ||||
−0.142959 | + | 0.989729i | \(0.545662\pi\) | |||||||
\(212\) | 5.63611e6i | 0.591523i | ||||||||
\(213\) | − | 8.01403e6i | − | 0.829301i | ||||||
\(214\) | −607577. | − | 607577.i | −0.0619955 | − | 0.0619955i | ||||
\(215\) | 1.20253e7i | 1.20998i | ||||||||
\(216\) | 6.15313e6 | + | 6.15313e6i | 0.610569 | + | 0.610569i | ||||
\(217\) | −9.81441e6 | − | 9.81441e6i | −0.960472 | − | 0.960472i | ||||
\(218\) | 2.66161e6 | 0.256907 | ||||||||
\(219\) | −1.45945e7 | −1.38949 | ||||||||
\(220\) | 7.61703e6 | − | 7.61703e6i | 0.715349 | − | 0.715349i | ||||
\(221\) | 6.25999e6i | 0.579958i | ||||||||
\(222\) | −1.95332e6 | − | 5.00979e6i | −0.178532 | − | 0.457889i | ||||
\(223\) | −1.25337e7 | −1.13022 | −0.565110 | − | 0.825015i | \(-0.691166\pi\) | ||||
−0.565110 | + | 0.825015i | \(0.691166\pi\) | |||||||
\(224\) | −7.43757e6 | − | 7.43757e6i | −0.661740 | − | 0.661740i | ||||
\(225\) | 2260.58i | 0.000198459i | ||||||||
\(226\) | − | 3.22398e6i | − | 0.279298i | ||||||
\(227\) | 172677. | − | 172677.i | 0.0147624 | − | 0.0147624i | −0.699687 | − | 0.714449i | \(-0.746677\pi\) |
0.714449 | + | 0.699687i | \(0.246677\pi\) | |||||||
\(228\) | 1.22058e7 | − | 1.22058e7i | 1.02982 | − | 1.02982i | ||||
\(229\) | −5.67922e6 | −0.472914 | −0.236457 | − | 0.971642i | \(-0.575986\pi\) | ||||
−0.236457 | + | 0.971642i | \(0.575986\pi\) | |||||||
\(230\) | 1.89767e6 | − | 1.89767e6i | 0.155969 | − | 0.155969i | ||||
\(231\) | −1.36721e7 | −1.10917 | ||||||||
\(232\) | 4.12094e6 | 0.330014 | ||||||||
\(233\) | − | 1.95636e7i | − | 1.54661i | −0.634034 | − | 0.773305i | \(-0.718602\pi\) | ||
0.634034 | − | 0.773305i | \(-0.281398\pi\) | |||||||
\(234\) | 6478.23 | 0.000505602 | ||||||||
\(235\) | −9.25938e6 | + | 9.25938e6i | −0.713474 | + | 0.713474i | ||||
\(236\) | −8.13950e6 | − | 8.13950e6i | −0.619244 | − | 0.619244i | ||||
\(237\) | −3.26868e6 | − | 3.26868e6i | −0.245543 | − | 0.245543i | ||||
\(238\) | 3.39497e6 | 0.251828 | ||||||||
\(239\) | 1.06868e7 | − | 1.06868e7i | 0.782807 | − | 0.782807i | −0.197497 | − | 0.980304i | \(-0.563281\pi\) |
0.980304 | + | 0.197497i | \(0.0632813\pi\) | |||||||
\(240\) | −3.57973e6 | − | 3.57973e6i | −0.258950 | − | 0.258950i | ||||
\(241\) | −294213. | + | 294213.i | −0.0210189 | + | 0.0210189i | −0.717538 | − | 0.696519i | \(-0.754731\pi\) |
0.696519 | + | 0.717538i | \(0.254731\pi\) | |||||||
\(242\) | −2.37977e6 | − | 2.37977e6i | −0.167915 | − | 0.167915i | ||||
\(243\) | − | 28685.8i | − | 0.00199917i | ||||||
\(244\) | −130059. | + | 130059.i | −0.00895305 | + | 0.00895305i | ||||
\(245\) | −1.95226e6 | + | 1.95226e6i | −0.132752 | + | 0.132752i | ||||
\(246\) | 75881.4 | + | 75881.4i | 0.00509718 | + | 0.00509718i | ||||
\(247\) | 2.97709e7i | 1.97561i | ||||||||
\(248\) | −1.96640e7 | −1.28919 | ||||||||
\(249\) | − | 250535.i | − | 0.0162282i | ||||||
\(250\) | 6.73444e6i | 0.431004i | ||||||||
\(251\) | −5.10056e6 | − | 5.10056e6i | −0.322550 | − | 0.322550i | 0.527195 | − | 0.849744i | \(-0.323244\pi\) |
−0.849744 | + | 0.527195i | \(0.823244\pi\) | |||||||
\(252\) | 11047.0i | 0.000690307i | ||||||||
\(253\) | 5.72047e6 | + | 5.72047e6i | 0.353240 | + | 0.353240i | ||||
\(254\) | 1.00280e7 | + | 1.00280e7i | 0.611944 | + | 0.611944i | ||||
\(255\) | 1.02293e7 | 0.616914 | ||||||||
\(256\) | −1.06460e7 | −0.634552 | ||||||||
\(257\) | −1.27735e7 | + | 1.27735e7i | −0.752506 | + | 0.752506i | −0.974946 | − | 0.222440i | \(-0.928598\pi\) |
0.222440 | + | 0.974946i | \(0.428598\pi\) | |||||||
\(258\) | − | 9.32831e6i | − | 0.543180i | ||||||
\(259\) | −6.35629e6 | + | 1.44806e7i | −0.365851 | + | 0.833467i | ||||
\(260\) | 1.50327e7 | 0.855294 | ||||||||
\(261\) | −4800.56 | − | 4800.56i | −0.000270004 | − | 0.000270004i | ||||
\(262\) | − | 1.19075e7i | − | 0.662087i | ||||||
\(263\) | − | 2.37210e7i | − | 1.30397i | −0.758233 | − | 0.651984i | \(-0.773937\pi\) | ||
0.758233 | − | 0.651984i | \(-0.226063\pi\) | |||||||
\(264\) | −1.36966e7 | + | 1.36966e7i | −0.744392 | + | 0.744392i | ||||
\(265\) | −1.12318e7 | + | 1.12318e7i | −0.603546 | + | 0.603546i | ||||
\(266\) | 1.61456e7 | 0.857847 | ||||||||
\(267\) | 1.99108e7 | − | 1.99108e7i | 1.04606 | − | 1.04606i | ||||
\(268\) | −1.98925e7 | −1.03344 | ||||||||
\(269\) | 1.91018e7 | 0.981335 | 0.490667 | − | 0.871347i | \(-0.336753\pi\) | ||||
0.490667 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(270\) | 1.05797e7i | 0.537506i | ||||||||
\(271\) | 7.63706e6 | 0.383723 | 0.191862 | − | 0.981422i | \(-0.438547\pi\) | ||||
0.191862 | + | 0.981422i | \(0.438547\pi\) | |||||||
\(272\) | −2.67954e6 | + | 2.67954e6i | −0.133154 | + | 0.133154i | ||||
\(273\) | −1.34914e7 | − | 1.34914e7i | −0.663083 | − | 0.663083i | ||||
\(274\) | −5.72264e6 | − | 5.72264e6i | −0.278192 | − | 0.278192i | ||||
\(275\) | 5.02902e6 | 0.241816 | ||||||||
\(276\) | 4.62865e6 | − | 4.62865e6i | 0.220154 | − | 0.220154i | ||||
\(277\) | 2.25266e7 | + | 2.25266e7i | 1.05988 | + | 1.05988i | 0.998089 | + | 0.0617906i | \(0.0196811\pi\) |
0.0617906 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(278\) | −1.23587e7 | + | 1.23587e7i | −0.575225 | + | 0.575225i | ||||
\(279\) | 22906.9 | + | 22906.9i | 0.00105476 | + | 0.00105476i | ||||
\(280\) | − | 1.88981e7i | − | 0.860882i | ||||||
\(281\) | 9.53578e6 | − | 9.53578e6i | 0.429771 | − | 0.429771i | −0.458779 | − | 0.888550i | \(-0.651713\pi\) |
0.888550 | + | 0.458779i | \(0.151713\pi\) | |||||||
\(282\) | 7.18273e6 | − | 7.18273e6i | 0.320289 | − | 0.320289i | ||||
\(283\) | −5.54800e6 | − | 5.54800e6i | −0.244781 | − | 0.244781i | 0.574044 | − | 0.818825i | \(-0.305374\pi\) |
−0.818825 | + | 0.574044i | \(0.805374\pi\) | |||||||
\(284\) | 1.44053e7i | 0.628881i | ||||||||
\(285\) | 4.86479e7 | 2.10150 | ||||||||
\(286\) | − | 1.44119e7i | − | 0.616059i | ||||||
\(287\) | − | 315609.i | − | 0.0133507i | ||||||
\(288\) | 17359.4 | + | 17359.4i | 0.000726702 | + | 0.000726702i | ||||
\(289\) | 1.64806e7i | 0.682779i | ||||||||
\(290\) | 3.54279e6 | + | 3.54279e6i | 0.145262 | + | 0.145262i | ||||
\(291\) | −2.35009e6 | − | 2.35009e6i | −0.0953686 | − | 0.0953686i | ||||
\(292\) | 2.62337e7 | 1.05369 | ||||||||
\(293\) | 4.26848e7 | 1.69695 | 0.848477 | − | 0.529232i | \(-0.177520\pi\) | ||||
0.848477 | + | 0.529232i | \(0.177520\pi\) | |||||||
\(294\) | 1.51442e6 | − | 1.51442e6i | 0.0595942 | − | 0.0595942i | ||||
\(295\) | − | 3.24411e7i | − | 1.26366i | ||||||
\(296\) | 8.13891e6 | + | 2.08743e7i | 0.313828 | + | 0.804890i | ||||
\(297\) | −3.18922e7 | −1.21735 | ||||||||
\(298\) | 6.09714e6 | + | 6.09714e6i | 0.230397 | + | 0.230397i | ||||
\(299\) | 1.12897e7i | 0.422345i | ||||||||
\(300\) | − | 4.06918e6i | − | 0.150710i | ||||||
\(301\) | −1.93994e7 | + | 1.93994e7i | −0.711358 | + | 0.711358i | ||||
\(302\) | 690.227 | − | 690.227i | 2.50594e−5 | − | 2.50594e-5i | ||||
\(303\) | −3.63833e7 | −1.30790 | ||||||||
\(304\) | −1.27432e7 | + | 1.27432e7i | −0.453585 | + | 0.453585i | ||||
\(305\) | −518369. | −0.0182700 | ||||||||
\(306\) | −7923.88 | −0.000276550 | ||||||||
\(307\) | − | 3.12106e7i | − | 1.07867i | −0.842092 | − | 0.539334i | \(-0.818676\pi\) | ||
0.842092 | − | 0.539334i | \(-0.181324\pi\) | |||||||
\(308\) | 2.45758e7 | 0.841116 | ||||||||
\(309\) | −3.45475e7 | + | 3.45475e7i | −1.17096 | + | 1.17096i | ||||
\(310\) | −1.69052e7 | − | 1.69052e7i | −0.567460 | − | 0.567460i | ||||
\(311\) | 3.74637e7 | + | 3.74637e7i | 1.24546 | + | 1.24546i | 0.957704 | + | 0.287756i | \(0.0929091\pi\) |
0.287756 | + | 0.957704i | \(0.407091\pi\) | |||||||
\(312\) | −2.70311e7 | −0.890020 | ||||||||
\(313\) | −8.97758e6 | + | 8.97758e6i | −0.292770 | + | 0.292770i | −0.838173 | − | 0.545404i | \(-0.816376\pi\) |
0.545404 | + | 0.838173i | \(0.316376\pi\) | |||||||
\(314\) | 9.54507e6 | + | 9.54507e6i | 0.308312 | + | 0.308312i | ||||
\(315\) | −22014.7 | + | 22014.7i | −0.000704337 | + | 0.000704337i | ||||
\(316\) | 5.87550e6 | + | 5.87550e6i | 0.186202 | + | 0.186202i | ||||
\(317\) | 1.60622e6i | 0.0504227i | 0.999682 | + | 0.0252114i | \(0.00802587\pi\) | ||||
−0.999682 | + | 0.0252114i | \(0.991974\pi\) | |||||||
\(318\) | 8.71276e6 | − | 8.71276e6i | 0.270941 | − | 0.270941i | ||||
\(319\) | −1.06796e7 | + | 1.06796e7i | −0.328991 | + | 0.328991i | ||||
\(320\) | −4.33010e6 | − | 4.33010e6i | −0.132144 | − | 0.132144i | ||||
\(321\) | − | 5.90654e6i | − | 0.178574i | ||||||
\(322\) | 6.12270e6 | 0.183390 | ||||||||
\(323\) | − | 3.64145e7i | − | 1.08060i | ||||||
\(324\) | 2.58310e7i | 0.759463i | ||||||||
\(325\) | 4.96253e6 | + | 4.96253e6i | 0.144562 | + | 0.144562i | ||||
\(326\) | 6.99126e6i | 0.201791i | ||||||||
\(327\) | 1.29374e7 | + | 1.29374e7i | 0.370001 | + | 0.370001i | ||||
\(328\) | −316175. | − | 316175.i | −0.00895996 | − | 0.00895996i | ||||
\(329\) | −2.98748e7 | −0.838912 | ||||||||
\(330\) | −2.35501e7 | −0.655315 | ||||||||
\(331\) | 2.20997e7 | − | 2.20997e7i | 0.609401 | − | 0.609401i | −0.333388 | − | 0.942790i | \(-0.608192\pi\) |
0.942790 | + | 0.333388i | \(0.108192\pi\) | |||||||
\(332\) | 450340.i | 0.0123063i | ||||||||
\(333\) | 14835.6 | − | 33797.9i | 0.000401766 | − | 0.000915287i | ||||
\(334\) | −1.65229e7 | −0.443452 | ||||||||
\(335\) | −3.96422e7 | − | 3.96422e7i | −1.05444 | − | 1.05444i | ||||
\(336\) | − | 1.15497e7i | − | 0.304477i | ||||||
\(337\) | − | 4.33371e7i | − | 1.13232i | −0.824295 | − | 0.566161i | \(-0.808428\pi\) | ||
0.824295 | − | 0.566161i | \(-0.191572\pi\) | |||||||
\(338\) | 808863. | − | 808863.i | 0.0209471 | − | 0.0209471i | ||||
\(339\) | 1.56709e7 | − | 1.56709e7i | 0.402250 | − | 0.402250i | ||||
\(340\) | −1.83873e7 | −0.467822 | ||||||||
\(341\) | 5.09602e7 | − | 5.09602e7i | 1.28519 | − | 1.28519i | ||||
\(342\) | −37684.0 | −0.000942061 | ||||||||
\(343\) | −4.30298e7 | −1.06632 | ||||||||
\(344\) | 3.88683e7i | 0.954817i | ||||||||
\(345\) | 1.84481e7 | 0.449258 | ||||||||
\(346\) | 2.87618e6 | − | 2.87618e6i | 0.0694366 | − | 0.0694366i | ||||
\(347\) | 1.17530e7 | + | 1.17530e7i | 0.281295 | + | 0.281295i | 0.833625 | − | 0.552330i | \(-0.186261\pi\) |
−0.552330 | + | 0.833625i | \(0.686261\pi\) | |||||||
\(348\) | 8.64129e6 | + | 8.64129e6i | 0.205041 | + | 0.205041i | ||||
\(349\) | −3.23257e7 | −0.760452 | −0.380226 | − | 0.924894i | \(-0.624154\pi\) | ||||
−0.380226 | + | 0.924894i | \(0.624154\pi\) | |||||||
\(350\) | 2.69132e6 | − | 2.69132e6i | 0.0627713 | − | 0.0627713i | ||||
\(351\) | −3.14706e7 | − | 3.14706e7i | −0.727752 | − | 0.727752i | ||||
\(352\) | 3.86188e7 | − | 3.86188e7i | 0.885463 | − | 0.885463i | ||||
\(353\) | 2.28251e7 | + | 2.28251e7i | 0.518906 | + | 0.518906i | 0.917240 | − | 0.398335i | \(-0.130412\pi\) |
−0.398335 | + | 0.917240i | \(0.630412\pi\) | |||||||
\(354\) | 2.51654e7i | 0.567276i | ||||||||
\(355\) | −2.87073e7 | + | 2.87073e7i | −0.641663 | + | 0.641663i | ||||
\(356\) | −3.57900e7 | + | 3.57900e7i | −0.793252 | + | 0.793252i | ||||
\(357\) | 1.65020e7 | + | 1.65020e7i | 0.362688 | + | 0.362688i | ||||
\(358\) | − | 4.09123e7i | − | 0.891672i | ||||||
\(359\) | −4.71855e7 | −1.01982 | −0.509912 | − | 0.860227i | \(-0.670322\pi\) | ||||
−0.509912 | + | 0.860227i | \(0.670322\pi\) | |||||||
\(360\) | 44108.3i | 0.000945393i | ||||||||
\(361\) | − | 1.26132e8i | − | 2.68105i | ||||||
\(362\) | 2.11379e7 | + | 2.11379e7i | 0.445590 | + | 0.445590i | ||||
\(363\) | − | 2.31349e7i | − | 0.483668i | ||||||
\(364\) | 2.42509e7 | + | 2.42509e7i | 0.502833 | + | 0.502833i | ||||
\(365\) | 5.22792e7 | + | 5.22792e7i | 1.07510 | + | 1.07510i | ||||
\(366\) | 402112. | 0.00820170 | ||||||||
\(367\) | 5.37578e7 | 1.08753 | 0.543767 | − | 0.839236i | \(-0.316997\pi\) | ||||
0.543767 | + | 0.839236i | \(0.316997\pi\) | |||||||
\(368\) | −4.83245e6 | + | 4.83245e6i | −0.0969670 | + | 0.0969670i | ||||
\(369\) | 736.635i | 1.46613e-5i | ||||||||
\(370\) | −1.09486e7 | + | 2.49427e7i | −0.216150 | + | 0.492424i | ||||
\(371\) | −3.62385e7 | −0.709657 | ||||||||
\(372\) | −4.12338e7 | − | 4.12338e7i | −0.800986 | − | 0.800986i | ||||
\(373\) | − | 3.02093e7i | − | 0.582122i | −0.956704 | − | 0.291061i | \(-0.905992\pi\) | ||
0.956704 | − | 0.291061i | \(-0.0940083\pi\) | |||||||
\(374\) | 1.76280e7i | 0.336967i | ||||||||
\(375\) | −3.27343e7 | + | 3.27343e7i | −0.620739 | + | 0.620739i | ||||
\(376\) | −2.99283e7 | + | 2.99283e7i | −0.563013 | + | 0.563013i | ||||
\(377\) | −2.10769e7 | −0.393352 | ||||||||
\(378\) | −1.70674e7 | + | 1.70674e7i | −0.316003 | + | 0.316003i | ||||
\(379\) | −5.36124e6 | −0.0984798 | −0.0492399 | − | 0.998787i | \(-0.515680\pi\) | ||||
−0.0492399 | + | 0.998787i | \(0.515680\pi\) | |||||||
\(380\) | −8.74453e7 | −1.59362 | ||||||||
\(381\) | 9.74865e7i | 1.76266i | ||||||||
\(382\) | 3.92249e7 | 0.703674 | ||||||||
\(383\) | 6.46446e7 | − | 6.46446e7i | 1.15063 | − | 1.15063i | 0.164205 | − | 0.986426i | \(-0.447494\pi\) |
0.986426 | − | 0.164205i | \(-0.0525059\pi\) | |||||||
\(384\) | −3.78269e7 | − | 3.78269e7i | −0.668047 | − | 0.668047i | ||||
\(385\) | 4.89753e7 | + | 4.89753e7i | 0.858212 | + | 0.858212i | ||||
\(386\) | 7.52337e6 | 0.130813 | ||||||||
\(387\) | 45278.3 | − | 45278.3i | 0.000781191 | − | 0.000781191i | ||||
\(388\) | 4.22432e6 | + | 4.22432e6i | 0.0723205 | + | 0.0723205i | ||||
\(389\) | −1.08514e7 | + | 1.08514e7i | −0.184348 | + | 0.184348i | −0.793247 | − | 0.608900i | \(-0.791611\pi\) |
0.608900 | + | 0.793247i | \(0.291611\pi\) | |||||||
\(390\) | −2.32387e7 | − | 2.32387e7i | −0.391758 | − | 0.391758i | ||||
\(391\) | − | 1.38090e7i | − | 0.231011i | ||||||
\(392\) | −6.31013e6 | + | 6.31013e6i | −0.104756 | + | 0.104756i | ||||
\(393\) | 5.78790e7 | − | 5.78790e7i | 0.953550 | − | 0.953550i | ||||
\(394\) | −5.82553e6 | − | 5.82553e6i | −0.0952460 | − | 0.0952460i | ||||
\(395\) | 2.34176e7i | 0.379972i | ||||||||
\(396\) | −57360.2 | −0.000923688 | ||||||||
\(397\) | 9.83200e7i | 1.57134i | 0.618646 | + | 0.785670i | \(0.287682\pi\) | ||||
−0.618646 | + | 0.785670i | \(0.712318\pi\) | |||||||
\(398\) | − | 2.73628e7i | − | 0.434022i | ||||||
\(399\) | 7.84796e7 | + | 7.84796e7i | 1.23549 | + | 1.23549i | ||||
\(400\) | 4.24835e6i | 0.0663804i | ||||||||
\(401\) | 3.55520e6 | + | 3.55520e6i | 0.0551354 | + | 0.0551354i | 0.734137 | − | 0.679001i | \(-0.237587\pi\) |
−0.679001 | + | 0.734137i | \(0.737587\pi\) | |||||||
\(402\) | 3.07515e7 | + | 3.07515e7i | 0.473356 | + | 0.473356i | ||||
\(403\) | 1.00573e8 | 1.53662 | ||||||||
\(404\) | 6.53996e7 | 0.991815 | ||||||||
\(405\) | −5.14766e7 | + | 5.14766e7i | −0.774899 | + | 0.774899i | ||||
\(406\) | 1.14306e7i | 0.170801i | ||||||||
\(407\) | −7.51891e7 | − | 3.30043e7i | −1.11525 | − | 0.489539i | ||||
\(408\) | 3.30632e7 | 0.486816 | ||||||||
\(409\) | 1.14150e7 | + | 1.14150e7i | 0.166842 | + | 0.166842i | 0.785590 | − | 0.618748i | \(-0.212360\pi\) |
−0.618748 | + | 0.785590i | \(0.712360\pi\) | |||||||
\(410\) | − | 543633.i | − | 0.00788777i | ||||||
\(411\) | − | 5.56324e7i | − | 0.801314i | ||||||
\(412\) | 6.20997e7 | − | 6.20997e7i | 0.887969 | − | 0.887969i | ||||
\(413\) | 5.23346e7 | − | 5.23346e7i | 0.742914 | − | 0.742914i | ||||
\(414\) | −14290.4 | −0.000201393 | ||||||||
\(415\) | −897447. | + | 897447.i | −0.0125564 | + | 0.0125564i | ||||
\(416\) | 7.62163e7 | 1.05869 | ||||||||
\(417\) | −1.20145e8 | −1.65690 | ||||||||
\(418\) | 8.38343e7i | 1.14787i | ||||||||
\(419\) | 1.46466e7 | 0.199110 | 0.0995551 | − | 0.995032i | \(-0.468258\pi\) | ||||
0.0995551 | + | 0.995032i | \(0.468258\pi\) | |||||||
\(420\) | 3.96278e7 | − | 3.96278e7i | 0.534874 | − | 0.534874i | ||||
\(421\) | −3.82769e7 | − | 3.82769e7i | −0.512968 | − | 0.512968i | 0.402467 | − | 0.915435i | \(-0.368153\pi\) |
−0.915435 | + | 0.402467i | \(0.868153\pi\) | |||||||
\(422\) | −7.46343e6 | − | 7.46343e6i | −0.0993118 | − | 0.0993118i | ||||
\(423\) | 69727.9 | 0.000921267 | ||||||||
\(424\) | −3.63035e7 | + | 3.63035e7i | −0.476267 | + | 0.476267i | ||||
\(425\) | −6.06995e6 | − | 6.06995e6i | −0.0790712 | − | 0.0790712i | ||||
\(426\) | 2.22690e7 | − | 2.22690e7i | 0.288052 | − | 0.288052i | ||||
\(427\) | −836241. | − | 836241.i | −0.0107411 | − | 0.0107411i | ||||
\(428\) | 1.06171e7i | 0.135417i | ||||||||
\(429\) | 7.00523e7 | − | 7.00523e7i | 0.887260 | − | 0.887260i | ||||
\(430\) | −3.34152e7 | + | 3.34152e7i | −0.420280 | + | 0.420280i | ||||
\(431\) | −4.68551e7 | − | 4.68551e7i | −0.585228 | − | 0.585228i | 0.351108 | − | 0.936335i | \(-0.385805\pi\) |
−0.936335 | + | 0.351108i | \(0.885805\pi\) | |||||||
\(432\) | − | 2.69415e7i | − | 0.334172i | ||||||
\(433\) | 6.30773e7 | 0.776979 | 0.388489 | − | 0.921453i | \(-0.372997\pi\) | ||||
0.388489 | + | 0.921453i | \(0.372997\pi\) | |||||||
\(434\) | − | 5.45435e7i | − | 0.667227i | ||||||
\(435\) | 3.44411e7i | 0.418417i | ||||||||
\(436\) | −2.32551e7 | − | 2.32551e7i | −0.280582 | − | 0.280582i | ||||
\(437\) | − | 6.56723e7i | − | 0.786933i | ||||||
\(438\) | −4.05543e7 | − | 4.05543e7i | −0.482630 | − | 0.482630i | ||||
\(439\) | 8.56013e7 | + | 8.56013e7i | 1.01178 | + | 1.01178i | 0.999930 | + | 0.0118524i | \(0.00377282\pi\) |
0.0118524 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(440\) | 9.81261e7 | 1.15193 | ||||||||
\(441\) | 14701.5 | 0.000171414 | ||||||||
\(442\) | −1.73949e7 | + | 1.73949e7i | −0.201445 | + | 0.201445i | ||||
\(443\) | 1.87227e7i | 0.215356i | 0.994186 | + | 0.107678i | \(0.0343416\pi\) | ||||
−0.994186 | + | 0.107678i | \(0.965658\pi\) | |||||||
\(444\) | −2.67051e7 | + | 6.08383e7i | −0.305102 | + | 0.695070i | ||||
\(445\) | −1.42646e8 | −1.61875 | ||||||||
\(446\) | −3.48278e7 | − | 3.48278e7i | −0.392574 | − | 0.392574i | ||||
\(447\) | 5.92732e7i | 0.663644i | ||||||||
\(448\) | − | 1.39708e7i | − | 0.155377i | ||||||
\(449\) | −1.21322e8 | + | 1.21322e8i | −1.34029 | + | 1.34029i | −0.444528 | + | 0.895765i | \(0.646628\pi\) |
−0.895765 | + | 0.444528i | \(0.853372\pi\) | |||||||
\(450\) | −6281.57 | + | 6281.57i | −6.89335e−5 | + | 6.89335e-5i | ||||
\(451\) | 1.63876e6 | 0.0178643 | ||||||||
\(452\) | −2.81687e7 | + | 2.81687e7i | −0.305037 | + | 0.305037i | ||||
\(453\) | 6710.02 | 7.21821e−5 | ||||||||
\(454\) | 959650. | 0.0102552 | ||||||||
\(455\) | 9.66555e7i | 1.02611i | ||||||||
\(456\) | 1.57240e8 | 1.65833 | ||||||||
\(457\) | −8.60733e7 | + | 8.60733e7i | −0.901820 | + | 0.901820i | −0.995594 | − | 0.0937737i | \(-0.970107\pi\) |
0.0937737 | + | 0.995594i | \(0.470107\pi\) | |||||||
\(458\) | −1.57811e7 | − | 1.57811e7i | −0.164264 | − | 0.164264i | ||||
\(459\) | 3.84934e7 | + | 3.84934e7i | 0.398060 | + | 0.398060i | ||||
\(460\) | −3.31608e7 | −0.340684 | ||||||||
\(461\) | 1.26205e7 | − | 1.26205e7i | 0.128817 | − | 0.128817i | −0.639759 | − | 0.768576i | \(-0.720966\pi\) |
0.768576 | + | 0.639759i | \(0.220966\pi\) | |||||||
\(462\) | −3.79913e7 | − | 3.79913e7i | −0.385264 | − | 0.385264i | ||||
\(463\) | −1.27678e8 | + | 1.27678e8i | −1.28639 | + | 1.28639i | −0.349434 | + | 0.936961i | \(0.613626\pi\) |
−0.936961 | + | 0.349434i | \(0.886374\pi\) | |||||||
\(464\) | −9.02178e6 | − | 9.02178e6i | −0.0903105 | − | 0.0903105i | ||||
\(465\) | − | 1.64343e8i | − | 1.63453i | ||||||
\(466\) | 5.43623e7 | − | 5.43623e7i | 0.537205 | − | 0.537205i | ||||
\(467\) | 8.98782e7 | − | 8.98782e7i | 0.882477 | − | 0.882477i | −0.111308 | − | 0.993786i | \(-0.535504\pi\) |
0.993786 | + | 0.111308i | \(0.0355042\pi\) | |||||||
\(468\) | −56601.8 | − | 56601.8i | −0.000552196 | − | 0.000552196i | ||||
\(469\) | − | 1.27903e8i | − | 1.23983i | ||||||
\(470\) | −5.14589e7 | −0.495641 | ||||||||
\(471\) | 9.27921e7i | 0.888072i | ||||||||
\(472\) | − | 1.04857e8i | − | 0.997173i | ||||||
\(473\) | −1.00729e8 | − | 1.00729e8i | −0.951856 | − | 0.951856i | ||||
\(474\) | − | 1.81657e7i | − | 0.170575i | ||||||
\(475\) | −2.88672e7 | − | 2.88672e7i | −0.269354 | − | 0.269354i | ||||
\(476\) | −2.96626e7 | − | 2.96626e7i | −0.275036 | − | 0.275036i | ||||
\(477\) | 84581.0 | 0.000779324 | ||||||||
\(478\) | 5.93919e7 | 0.543805 | ||||||||
\(479\) | −1.32583e8 | + | 1.32583e8i | −1.20637 | + | 1.20637i | −0.234178 | + | 0.972194i | \(0.575240\pi\) |
−0.972194 | + | 0.234178i | \(0.924760\pi\) | |||||||
\(480\) | − | 1.24543e8i | − | 1.12615i | ||||||
\(481\) | −4.16270e7 | − | 1.06763e8i | −0.374059 | − | 0.959368i | ||||
\(482\) | −1.63509e6 | −0.0146016 | ||||||||
\(483\) | 2.97608e7 | + | 2.97608e7i | 0.264121 | + | 0.264121i | ||||
\(484\) | 4.15853e7i | 0.366778i | ||||||||
\(485\) | 1.68366e7i | 0.147581i | ||||||||
\(486\) | 79710.7 | − | 79710.7i | 0.000694397 | − | 0.000694397i | ||||
\(487\) | 4.17057e6 | − | 4.17057e6i | 0.0361085 | − | 0.0361085i | −0.688822 | − | 0.724930i | \(-0.741872\pi\) |
0.724930 | + | 0.688822i | \(0.241872\pi\) | |||||||
\(488\) | −1.67548e6 | −0.0144172 | ||||||||
\(489\) | −3.39827e7 | + | 3.39827e7i | −0.290624 | + | 0.290624i | ||||
\(490\) | −1.08497e7 | −0.0922208 | ||||||||
\(491\) | −2.01953e8 | −1.70611 | −0.853053 | − | 0.521824i | \(-0.825252\pi\) | ||||
−0.853053 | + | 0.521824i | \(0.825252\pi\) | |||||||
\(492\) | − | 1.32599e6i | − | 0.0111338i | ||||||
\(493\) | 2.57803e7 | 0.215153 | ||||||||
\(494\) | −8.27259e7 | + | 8.27259e7i | −0.686216 | + | 0.686216i | ||||
\(495\) | −114309. | − | 114309.i | −0.000942462 | − | 0.000942462i | ||||
\(496\) | 4.30494e7 | + | 4.30494e7i | 0.352795 | + | 0.352795i | ||||
\(497\) | −9.26220e7 | −0.754476 | ||||||||
\(498\) | 696172. | − | 696172.i | 0.00563675 | − | 0.00563675i | ||||
\(499\) | 1.42856e8 | + | 1.42856e8i | 1.14974 | + | 1.14974i | 0.986604 | + | 0.163132i | \(0.0521595\pi\) |
0.163132 | + | 0.986604i | \(0.447840\pi\) | |||||||
\(500\) | 5.88404e7 | − | 5.88404e7i | 0.470723 | − | 0.470723i | ||||
\(501\) | −8.03134e7 | − | 8.03134e7i | −0.638668 | − | 0.638668i | ||||
\(502\) | − | 2.83463e7i | − | 0.224071i | ||||||
\(503\) | 1.63993e8 | − | 1.63993e8i | 1.28861 | − | 1.28861i | 0.352972 | − | 0.935634i | \(-0.385171\pi\) |
0.935634 | − | 0.352972i | \(-0.114829\pi\) | |||||||
\(504\) | −71156.2 | + | 71156.2i | −0.000555803 | + | 0.000555803i | ||||
\(505\) | 1.30330e8 | + | 1.30330e8i | 1.01197 | + | 1.01197i | ||||
\(506\) | 3.17914e7i | 0.245391i | ||||||||
\(507\) | 7.86333e6 | 0.0603369 | ||||||||
\(508\) | − | 1.75233e8i | − | 1.33668i | ||||||
\(509\) | − | 2.04090e8i | − | 1.54764i | −0.633407 | − | 0.773819i | \(-0.718344\pi\) | ||
0.633407 | − | 0.773819i | \(-0.281656\pi\) | |||||||
\(510\) | 2.84246e7 | + | 2.84246e7i | 0.214281 | + | 0.214281i | ||||
\(511\) | 1.68675e8i | 1.26412i | ||||||||
\(512\) | 6.00363e7 | + | 6.00363e7i | 0.447306 | + | 0.447306i | ||||
\(513\) | 1.83065e8 | + | 1.83065e8i | 1.35598 | + | 1.35598i | ||||
\(514\) | −7.09885e7 | −0.522756 | ||||||||
\(515\) | 2.47507e8 | 1.81203 | ||||||||
\(516\) | −8.15037e7 | + | 8.15037e7i | −0.593237 | + | 0.593237i | ||||
\(517\) | − | 1.55121e8i | − | 1.12253i | ||||||
\(518\) | −5.79005e7 | + | 2.25755e7i | −0.416575 | + | 0.162423i | ||||
\(519\) | 2.79607e7 | 0.200008 | ||||||||
\(520\) | 9.68288e7 | + | 9.68288e7i | 0.688643 | + | 0.688643i | ||||
\(521\) | 2.11052e8i | 1.49237i | 0.665737 | + | 0.746186i | \(0.268117\pi\) | ||||
−0.665737 | + | 0.746186i | \(0.731883\pi\) | |||||||
\(522\) | − | 26679.0i | − | 0.000187568i | ||||||
\(523\) | 4.67969e7 | − | 4.67969e7i | 0.327123 | − | 0.327123i | −0.524368 | − | 0.851492i | \(-0.675698\pi\) |
0.851492 | + | 0.524368i | \(0.175698\pi\) | |||||||
\(524\) | −1.04038e8 | + | 1.04038e8i | −0.723102 | + | 0.723102i | ||||
\(525\) | 2.61636e7 | 0.180809 | ||||||||
\(526\) | 6.59148e7 | − | 6.59148e7i | 0.452924 | − | 0.452924i | ||||
\(527\) | −1.23016e8 | −0.840487 | ||||||||
\(528\) | 5.99707e7 | 0.407415 | ||||||||
\(529\) | 1.23132e8i | 0.831770i | ||||||||
\(530\) | −6.24204e7 | −0.419275 | ||||||||
\(531\) | −122149. | + | 122149.i | −0.000815845 | + | 0.000815845i | ||||
\(532\) | −1.41068e8 | − | 1.41068e8i | −0.936902 | − | 0.936902i | ||||
\(533\) | 1.61710e6 | + | 1.61710e6i | 0.0106796 | + | 0.0106796i | ||||
\(534\) | 1.10654e8 | 0.726681 | ||||||||
\(535\) | −2.11580e7 | + | 2.11580e7i | −0.138170 | + | 0.138170i | ||||
\(536\) | −1.28132e8 | − | 1.28132e8i | −0.832078 | − | 0.832078i | ||||
\(537\) | 1.98864e8 | − | 1.98864e8i | 1.28420 | − | 1.28420i | ||||
\(538\) | 5.30790e7 | + | 5.30790e7i | 0.340860 | + | 0.340860i | ||||
\(539\) | − | 3.27060e7i | − | 0.208863i | ||||||
\(540\) | 9.24376e7 | − | 9.24376e7i | 0.587040 | − | 0.587040i | ||||
\(541\) | −2.79693e7 | + | 2.79693e7i | −0.176640 | + | 0.176640i | −0.789889 | − | 0.613249i | \(-0.789862\pi\) |
0.613249 | + | 0.789889i | \(0.289862\pi\) | |||||||
\(542\) | 2.12215e7 | + | 2.12215e7i | 0.133284 | + | 0.133284i | ||||
\(543\) | 2.05491e8i | 1.28349i | ||||||||
\(544\) | −9.32245e7 | −0.579073 | ||||||||
\(545\) | − | 9.26867e7i | − | 0.572569i | ||||||
\(546\) | − | 7.49781e7i | − | 0.460635i | ||||||
\(547\) | 1.02550e8 | + | 1.02550e8i | 0.626574 | + | 0.626574i | 0.947204 | − | 0.320630i | \(-0.103895\pi\) |
−0.320630 | + | 0.947204i | \(0.603895\pi\) | |||||||
\(548\) | 1.00000e8i | 0.607657i | ||||||||
\(549\) | 1951.79 | + | 1951.79i | 1.17955e−5 | + | 1.17955e-5i | ||||
\(550\) | 1.39744e7 | + | 1.39744e7i | 0.0839933 | + | 0.0839933i | ||||
\(551\) | 1.22605e8 | 0.732912 | ||||||||
\(552\) | 5.96284e7 | 0.354516 | ||||||||
\(553\) | −3.77777e7 | + | 3.77777e7i | −0.223388 | + | 0.223388i | ||||
\(554\) | 1.25191e8i | 0.736284i | ||||||||
\(555\) | −1.74458e8 | + | 6.80216e7i | −1.02050 | + | 0.397894i | ||||
\(556\) | 2.15962e8 | 1.25647 | ||||||||
\(557\) | 3.47578e7 | + | 3.47578e7i | 0.201135 | + | 0.201135i | 0.800486 | − | 0.599351i | \(-0.204575\pi\) |
−0.599351 | + | 0.800486i | \(0.704575\pi\) | |||||||
\(558\) | 127305.i | 0.000732728i | ||||||||
\(559\) | − | 1.98795e8i | − | 1.13807i | ||||||
\(560\) | −4.13726e7 | + | 4.13726e7i | −0.235586 | + | 0.235586i | ||||
\(561\) | −8.56849e7 | + | 8.56849e7i | −0.485306 | + | 0.485306i | ||||
\(562\) | 5.29950e7 | 0.298556 | ||||||||
\(563\) | 2.47754e8 | − | 2.47754e8i | 1.38834 | − | 1.38834i | 0.559519 | − | 0.828818i | \(-0.310986\pi\) |
0.828818 | − | 0.559519i | \(-0.189014\pi\) | |||||||
\(564\) | −1.25515e8 | −0.699611 | ||||||||
\(565\) | −1.12271e8 | −0.622473 | ||||||||
\(566\) | − | 3.08330e7i | − | 0.170046i | ||||||
\(567\) | −1.66086e8 | −0.911136 | ||||||||
\(568\) | −9.27881e7 | + | 9.27881e7i | −0.506346 | + | 0.506346i | ||||
\(569\) | −1.63682e8 | − | 1.63682e8i | −0.888515 | − | 0.888515i | 0.105866 | − | 0.994380i | \(-0.466239\pi\) |
−0.994380 | + | 0.105866i | \(0.966239\pi\) | |||||||
\(570\) | 1.35180e8 | + | 1.35180e8i | 0.729942 | + | 0.729942i | ||||
\(571\) | 1.83910e8 | 0.987866 | 0.493933 | − | 0.869500i | \(-0.335559\pi\) | ||||
0.493933 | + | 0.869500i | \(0.335559\pi\) | |||||||
\(572\) | −1.25920e8 | + | 1.25920e8i | −0.672832 | + | 0.672832i | ||||
\(573\) | 1.90662e8 | + | 1.90662e8i | 1.01344 | + | 1.01344i | ||||
\(574\) | 876998. | − | 876998.i | 0.00463727 | − | 0.00463727i | ||||
\(575\) | −1.09469e7 | − | 1.09469e7i | −0.0575824 | − | 0.0575824i | ||||
\(576\) | 32607.9i | 0.000170630i | ||||||||
\(577\) | −4.57640e7 | + | 4.57640e7i | −0.238230 | + | 0.238230i | −0.816117 | − | 0.577887i | \(-0.803878\pi\) |
0.577887 | + | 0.816117i | \(0.303878\pi\) | |||||||
\(578\) | −4.57955e7 | + | 4.57955e7i | −0.237159 | + | 0.237159i | ||||
\(579\) | 3.65691e7 | + | 3.65691e7i | 0.188399 | + | 0.188399i | ||||
\(580\) | − | 6.19084e7i | − | 0.317297i | ||||||
\(581\) | −2.89555e6 | −0.0147640 | ||||||||
\(582\) | − | 1.30606e7i | − | 0.0662513i | ||||||
\(583\) | − | 1.88164e8i | − | 0.949580i | ||||||
\(584\) | 1.68978e8 | + | 1.68978e8i | 0.848380 | + | 0.848380i | ||||
\(585\) | − | 225595.i | − | 0.00112684i | ||||||
\(586\) | 1.18610e8 | + | 1.18610e8i | 0.589426 | + | 0.589426i | ||||
\(587\) | −2.16299e8 | − | 2.16299e8i | −1.06940 | − | 1.06940i | −0.997405 | − | 0.0719930i | \(-0.977064\pi\) |
−0.0719930 | − | 0.997405i | \(-0.522936\pi\) | |||||||
\(588\) | −2.64637e7 | −0.130172 | ||||||||
\(589\) | −5.85035e8 | −2.86310 | ||||||||
\(590\) | 9.01457e7 | − | 9.01457e7i | 0.438924 | − | 0.438924i | ||||
\(591\) | − | 5.66327e7i | − | 0.274350i | ||||||
\(592\) | 2.78809e7 | − | 6.35171e7i | 0.134382 | − | 0.306144i | ||||
\(593\) | −1.18610e8 | −0.568797 | −0.284398 | − | 0.958706i | \(-0.591794\pi\) | ||||
−0.284398 | + | 0.958706i | \(0.591794\pi\) | |||||||
\(594\) | −8.86204e7 | − | 8.86204e7i | −0.422838 | − | 0.422838i | ||||
\(595\) | − | 1.18225e8i | − | 0.561252i | ||||||
\(596\) | − | 1.06544e8i | − | 0.503259i | ||||||
\(597\) | 1.33003e8 | − | 1.33003e8i | 0.625086 | − | 0.625086i | ||||
\(598\) | −3.13711e7 | + | 3.13711e7i | −0.146699 | + | 0.146699i | ||||
\(599\) | 3.57437e8 | 1.66310 | 0.831551 | − | 0.555448i | \(-0.187453\pi\) | ||||
0.831551 | + | 0.555448i | \(0.187453\pi\) | |||||||
\(600\) | 2.62105e7 | − | 2.62105e7i | 0.121345 | − | 0.121345i | ||||
\(601\) | −2.16744e8 | −0.998443 | −0.499221 | − | 0.866474i | \(-0.666381\pi\) | ||||
−0.499221 | + | 0.866474i | \(0.666381\pi\) | |||||||
\(602\) | −1.07812e8 | −0.494171 | ||||||||
\(603\) | 298527.i | 0.00136154i | ||||||||
\(604\) | −12061.4 | −5.47376e−5 | ||||||||
\(605\) | −8.28721e7 | + | 8.28721e7i | −0.374233 | + | 0.374233i | ||||
\(606\) | −1.01100e8 | − | 1.01100e8i | −0.454290 | − | 0.454290i | ||||
\(607\) | 1.61996e8 | + | 1.61996e8i | 0.724332 | + | 0.724332i | 0.969485 | − | 0.245152i | \(-0.0788380\pi\) |
−0.245152 | + | 0.969485i | \(0.578838\pi\) | |||||||
\(608\) | −4.43352e8 | −1.97260 | ||||||||
\(609\) | −5.55610e7 | + | 5.55610e7i | −0.245990 | + | 0.245990i | ||||
\(610\) | −1.44042e6 | − | 1.44042e6i | −0.00634598 | − | 0.00634598i | ||||
\(611\) | 1.53070e8 | − | 1.53070e8i | 0.671069 | − | 0.671069i | ||||
\(612\) | 69232.9 | + | 69232.9i | 0.000302036 | + | 0.000302036i | ||||
\(613\) | − | 1.88349e8i | − | 0.817678i | −0.912607 | − | 0.408839i | \(-0.865934\pi\) | ||
0.912607 | − | 0.408839i | \(-0.134066\pi\) | |||||||
\(614\) | 8.67264e7 | − | 8.67264e7i | 0.374668 | − | 0.374668i | ||||
\(615\) | 2.64246e6 | − | 2.64246e6i | 0.0113601 | − | 0.0113601i | ||||
\(616\) | 1.58299e8 | + | 1.58299e8i | 0.677228 | + | 0.677228i | ||||
\(617\) | − | 1.89641e7i | − | 0.0807376i | −0.999185 | − | 0.0403688i | \(-0.987147\pi\) | ||
0.999185 | − | 0.0403688i | \(-0.0128533\pi\) | |||||||
\(618\) | −1.91998e8 | −0.813449 | ||||||||
\(619\) | − | 3.44440e8i | − | 1.45225i | −0.687561 | − | 0.726126i | \(-0.741319\pi\) | ||
0.687561 | − | 0.726126i | \(-0.258681\pi\) | |||||||
\(620\) | 2.95410e8i | 1.23951i | ||||||||
\(621\) | 6.94215e7 | + | 6.94215e7i | 0.289881 | + | 0.289881i | ||||
\(622\) | 2.08204e8i | 0.865204i | ||||||||
\(623\) | −2.30119e8 | − | 2.30119e8i | −0.951673 | − | 0.951673i | ||||
\(624\) | 5.91778e7 | + | 5.91778e7i | 0.243560 | + | 0.243560i | ||||
\(625\) | 2.82989e8 | 1.15912 | ||||||||
\(626\) | −4.98928e7 | −0.203383 | ||||||||
\(627\) | −4.07496e8 | + | 4.07496e8i | −1.65318 | + | 1.65318i | ||||
\(628\) | − | 1.66795e8i | − | 0.673449i | ||||||
\(629\) | 5.09163e7 | + | 1.30588e8i | 0.204600 | + | 0.524747i | ||||
\(630\) | −122346. | −0.000489293 | ||||||||
\(631\) | −1.92646e7 | − | 1.92646e7i | −0.0766781 | − | 0.0766781i | 0.667728 | − | 0.744406i | \(-0.267267\pi\) |
−0.744406 | + | 0.667728i | \(0.767267\pi\) | |||||||
\(632\) | 7.56909e7i | 0.299842i | ||||||||
\(633\) | − | 7.25555e7i | − | 0.286061i | ||||||
\(634\) | −4.46327e6 | + | 4.46327e6i | −0.0175140 | + | 0.0175140i | ||||
\(635\) | 3.49209e8 | − | 3.49209e8i | 1.36384 | − | 1.36384i | ||||
\(636\) | −1.52251e8 | −0.591819 | ||||||||
\(637\) | 3.22736e7 | − | 3.22736e7i | 0.124862 | − | 0.124862i | ||||
\(638\) | −5.93519e7 | −0.228546 | ||||||||
\(639\) | 216181. | 0.000828542 | ||||||||
\(640\) | 2.71001e8i | 1.03379i | ||||||||
\(641\) | −8.30007e7 | −0.315143 | −0.157571 | − | 0.987508i | \(-0.550366\pi\) | ||||
−0.157571 | + | 0.987508i | \(0.550366\pi\) | |||||||
\(642\) | 1.64128e7 | − | 1.64128e7i | 0.0620264 | − | 0.0620264i | ||||
\(643\) | −3.28002e6 | − | 3.28002e6i | −0.0123380 | − | 0.0123380i | 0.700911 | − | 0.713249i | \(-0.252777\pi\) |
−0.713249 | + | 0.700911i | \(0.752777\pi\) | |||||||
\(644\) | −5.34955e7 | − | 5.34955e7i | −0.200290 | − | 0.200290i | ||||
\(645\) | −3.24845e8 | −1.21059 | ||||||||
\(646\) | 1.01187e8 | − | 1.01187e8i | 0.375341 | − | 0.375341i | ||||
\(647\) | 3.02480e8 | + | 3.02480e8i | 1.11682 | + | 1.11682i | 0.992205 | + | 0.124618i | \(0.0397706\pi\) |
0.124618 | + | 0.992205i | \(0.460229\pi\) | |||||||
\(648\) | −1.66384e8 | + | 1.66384e8i | −0.611484 | + | 0.611484i | ||||
\(649\) | 2.71741e8 | + | 2.71741e8i | 0.994080 | + | 0.994080i | ||||
\(650\) | 2.75792e7i | 0.100425i | ||||||||
\(651\) | 2.65121e8 | − | 2.65121e8i | 0.960952 | − | 0.960952i | ||||
\(652\) | 6.10843e7 | − | 6.10843e7i | 0.220388 | − | 0.220388i | ||||
\(653\) | 3.73455e7 | + | 3.73455e7i | 0.134122 | + | 0.134122i | 0.770980 | − | 0.636859i | \(-0.219767\pi\) |
−0.636859 | + | 0.770980i | \(0.719767\pi\) | |||||||
\(654\) | 7.18994e7i | 0.257035i | ||||||||
\(655\) | −4.14660e8 | −1.47560 | ||||||||
\(656\) | 1.38437e6i | 0.00490390i | ||||||||
\(657\) | − | 393689.i | − | 0.00138822i | ||||||
\(658\) | −8.30143e7 | − | 8.30143e7i | −0.291391 | − | 0.291391i | ||||
\(659\) | − | 1.51351e8i | − | 0.528846i | −0.964407 | − | 0.264423i | \(-0.914819\pi\) | ||
0.964407 | − | 0.264423i | \(-0.0851815\pi\) | |||||||
\(660\) | 2.05763e8 | + | 2.05763e8i | 0.715706 | + | 0.715706i | ||||
\(661\) | 1.18555e8 | + | 1.18555e8i | 0.410502 | + | 0.410502i | 0.881913 | − | 0.471412i | \(-0.156255\pi\) |
−0.471412 | + | 0.881913i | \(0.656255\pi\) | |||||||
\(662\) | 1.22819e8 | 0.423343 | ||||||||
\(663\) | −1.69104e8 | −0.580248 | ||||||||
\(664\) | −2.90074e6 | + | 2.90074e6i | −0.00990843 | + | 0.00990843i | ||||
\(665\) | − | 5.62248e8i | − | 1.91189i | ||||||
\(666\) | 135140. | − | 52691.4i | 0.000457470 | − | 0.000178368i | ||||
\(667\) | 4.64938e7 | 0.156681 | ||||||||
\(668\) | 1.44365e8 | + | 1.44365e8i | 0.484319 | + | 0.484319i | ||||
\(669\) | − | 3.38578e8i | − | 1.13078i | ||||||
\(670\) | − | 2.20311e8i | − | 0.732508i | ||||||
\(671\) | 4.34209e6 | − | 4.34209e6i | 0.0143725 | − | 0.0143725i | ||||
\(672\) | 2.00915e8 | − | 2.00915e8i | 0.662070 | − | 0.662070i | ||||
\(673\) | 3.22503e7 | 0.105801 | 0.0529003 | − | 0.998600i | \(-0.483153\pi\) | ||||
0.0529003 | + | 0.998600i | \(0.483153\pi\) | |||||||
\(674\) | 1.20423e8 | − | 1.20423e8i | 0.393304 | − | 0.393304i | ||||
\(675\) | 6.10304e7 | 0.198443 | ||||||||
\(676\) | −1.41345e7 | −0.0457551 | ||||||||
\(677\) | 4.12810e8i | 1.33041i | 0.746662 | + | 0.665204i | \(0.231655\pi\) | ||||
−0.746662 | + | 0.665204i | \(0.768345\pi\) | |||||||
\(678\) | 8.70911e7 | 0.279437 | ||||||||
\(679\) | −2.71611e7 | + | 2.71611e7i | −0.0867637 | + | 0.0867637i | ||||
\(680\) | −1.18437e8 | − | 1.18437e8i | −0.376669 | − | 0.376669i | ||||
\(681\) | 4.66460e6 | + | 4.66460e6i | 0.0147698 | + | 0.0147698i | ||||
\(682\) | 2.83211e8 | 0.892805 | ||||||||
\(683\) | −2.99971e8 | + | 2.99971e8i | −0.941493 | + | 0.941493i | −0.998381 | − | 0.0568873i | \(-0.981882\pi\) |
0.0568873 | + | 0.998381i | \(0.481882\pi\) | |||||||
\(684\) | 329254. | + | 329254.i | 0.00102888 | + | 0.00102888i | ||||
\(685\) | −1.99282e8 | + | 1.99282e8i | −0.620008 | + | 0.620008i | ||||
\(686\) | −1.19569e8 | − | 1.19569e8i | −0.370379 | − | 0.370379i | ||||
\(687\) | − | 1.53416e8i | − | 0.473151i | ||||||
\(688\) | 8.50924e7 | − | 8.50924e7i | 0.261292 | − | 0.261292i | ||||
\(689\) | 1.85677e8 | − | 1.85677e8i | 0.567675 | − | 0.567675i | ||||
\(690\) | 5.12627e7 | + | 5.12627e7i | 0.156047 | + | 0.156047i | ||||
\(691\) | 1.60183e8i | 0.485491i | 0.970090 | + | 0.242746i | \(0.0780481\pi\) | ||||
−0.970090 | + | 0.242746i | \(0.921952\pi\) | |||||||
\(692\) | −5.02598e7 | −0.151671 | ||||||||
\(693\) | − | 368809.i | − | 0.00110816i | ||||||
\(694\) | 6.53174e7i | 0.195412i | ||||||||
\(695\) | 4.30373e8 | + | 4.30373e8i | 1.28201 | + | 1.28201i | ||||
\(696\) | 1.11321e8i | 0.330179i | ||||||||
\(697\) | −1.97796e6 | − | 1.97796e6i | −0.00584144 | − | 0.00584144i | ||||
\(698\) | −8.98249e7 | − | 8.98249e7i | −0.264138 | − | 0.264138i | ||||
\(699\) | 5.28481e8 | 1.54738 | ||||||||
\(700\) | −4.70294e7 | −0.137112 | ||||||||
\(701\) | −4.77668e7 | + | 4.77668e7i | −0.138667 | + | 0.138667i | −0.773033 | − | 0.634366i | \(-0.781261\pi\) |
0.634366 | + | 0.773033i | \(0.281261\pi\) | |||||||
\(702\) | − | 1.74897e8i | − | 0.505559i | ||||||
\(703\) | 2.42145e8 | + | 6.21043e8i | 0.696964 | + | 1.78754i | ||||
\(704\) | 7.25416e7 | 0.207907 | ||||||||
\(705\) | −2.50128e8 | − | 2.50128e8i | −0.713831 | − | 0.713831i | ||||
\(706\) | 1.26850e8i | 0.360477i | ||||||||
\(707\) | 4.20500e8i | 1.18989i | ||||||||
\(708\) | 2.19876e8 | − | 2.19876e8i | 0.619553 | − | 0.619553i | ||||
\(709\) | −6.77257e7 | + | 6.77257e7i | −0.190027 | + | 0.190027i | −0.795708 | − | 0.605681i | \(-0.792901\pi\) |
0.605681 | + | 0.795708i | \(0.292901\pi\) | |||||||
\(710\) | −1.59540e8 | −0.445754 | ||||||||
\(711\) | 88173.5 | − | 88173.5i | 0.000245318 | − | 0.000245318i | ||||
\(712\) | −4.61063e8 | −1.27738 | ||||||||
\(713\) | −2.21856e8 | −0.612071 | ||||||||
\(714\) | 9.17099e7i | 0.251954i | ||||||||
\(715\) | −5.01873e8 | −1.37302 | ||||||||
\(716\) | −3.57461e8 | + | 3.57461e8i | −0.973844 | + | 0.973844i | ||||
\(717\) | 2.88688e8 | + | 2.88688e8i | 0.783198 | + | 0.783198i | ||||
\(718\) | −1.31117e8 | − | 1.31117e8i | −0.354229 | − | 0.354229i | ||||
\(719\) | 2.47474e8 | 0.665798 | 0.332899 | − | 0.942963i | \(-0.391973\pi\) | ||||
0.332899 | + | 0.942963i | \(0.391973\pi\) | |||||||
\(720\) | 96564.1 | − | 96564.1i | 0.000258713 | − | 0.000258713i | ||||
\(721\) | 3.99283e8 | + | 3.99283e8i | 1.06531 | + | 1.06531i | ||||
\(722\) | 3.50490e8 | − | 3.50490e8i | 0.931245 | − | 0.931245i | ||||
\(723\) | −7.94772e6 | − | 7.94772e6i | −0.0210294 | − | 0.0210294i | ||||
\(724\) | − | 3.69373e8i | − | 0.973307i | ||||||
\(725\) | 2.04370e7 | − | 2.04370e7i | 0.0536295 | − | 0.0536295i | ||||
\(726\) | 6.42859e7 | − | 6.42859e7i | 0.167999 | − | 0.167999i | ||||
\(727\) | 8.46540e7 | + | 8.46540e7i | 0.220315 | + | 0.220315i | 0.808631 | − | 0.588316i | \(-0.200209\pi\) |
−0.588316 | + | 0.808631i | \(0.700209\pi\) | |||||||
\(728\) | 3.12411e8i | 0.809716i | ||||||||
\(729\) | −3.87032e8 | −0.998998 | ||||||||
\(730\) | 2.90541e8i | 0.746859i | ||||||||
\(731\) | 2.43157e8i | 0.622493i | ||||||||
\(732\) | −3.51335e6 | − | 3.51335e6i | −0.00895753 | − | 0.00895753i | ||||
\(733\) | − | 2.88451e8i | − | 0.732419i | −0.930532 | − | 0.366209i | \(-0.880655\pi\) | ||
0.930532 | − | 0.366209i | \(-0.119345\pi\) | |||||||
\(734\) | 1.49379e8 | + | 1.49379e8i | 0.377748 | + | 0.377748i | ||||
\(735\) | −5.27374e7 | − | 5.27374e7i | −0.132818 | − | 0.132818i | ||||
\(736\) | −1.68127e8 | −0.421700 | ||||||||
\(737\) | 6.64122e8 | 1.65900 | ||||||||
\(738\) | −2046.92 | + | 2046.92i | −5.09251e−6 | + | 5.09251e-6i | ||||
\(739\) | − | 6.58561e8i | − | 1.63178i | −0.578204 | − | 0.815892i | \(-0.696246\pi\) | ||
0.578204 | − | 0.815892i | \(-0.303754\pi\) | |||||||
\(740\) | 3.13592e8 | − | 1.22270e8i | 0.773872 | − | 0.301734i | ||||
\(741\) | −8.04217e8 | −1.97660 | ||||||||
\(742\) | −1.00698e8 | − | 1.00698e8i | −0.246495 | − | 0.246495i | ||||
\(743\) | − | 5.42185e7i | − | 0.132185i | −0.997814 | − | 0.0660923i | \(-0.978947\pi\) | ||
0.997814 | − | 0.0660923i | \(-0.0210532\pi\) | |||||||
\(744\) | − | 5.31193e8i | − | 1.28983i | ||||||
\(745\) | 2.12324e8 | − | 2.12324e8i | 0.513488 | − | 0.513488i | ||||
\(746\) | 8.39439e7 | − | 8.39439e7i | 0.202196 | − | 0.202196i | ||||
\(747\) | 6758.24 | 1.62133e−5 | ||||||||
\(748\) | 1.54020e8 | − | 1.54020e8i | 0.368021 | − | 0.368021i | ||||
\(749\) | −6.82647e7 | −0.162462 | ||||||||
\(750\) | −1.81921e8 | −0.431219 | ||||||||
\(751\) | − | 5.30131e8i | − | 1.25159i | −0.779986 | − | 0.625797i | \(-0.784774\pi\) | ||
0.779986 | − | 0.625797i | \(-0.215226\pi\) | |||||||
\(752\) | 1.31041e8 | 0.308144 | ||||||||
\(753\) | 1.37784e8 | − | 1.37784e8i | 0.322711 | − | 0.322711i | ||||
\(754\) | −5.85672e7 | − | 5.85672e7i | −0.136628 | − | 0.136628i | ||||
\(755\) | −24036.2 | − | 24036.2i | −5.58501e−5 | − | 5.58501e-5i | ||||
\(756\) | 2.98244e8 | 0.690249 | ||||||||
\(757\) | 6.99440e7 | − | 6.99440e7i | 0.161236 | − | 0.161236i | −0.621878 | − | 0.783114i | \(-0.713630\pi\) |
0.783114 | + | 0.621878i | \(0.213630\pi\) | |||||||
\(758\) | −1.48975e7 | − | 1.48975e7i | −0.0342063 | − | 0.0342063i | ||||
\(759\) | −1.54530e8 | + | 1.54530e8i | −0.353416 | + | 0.353416i | ||||
\(760\) | −5.63255e8 | − | 5.63255e8i | −1.28311 | − | 1.28311i | ||||
\(761\) | 7.24366e8i | 1.64363i | 0.569755 | + | 0.821815i | \(0.307038\pi\) | ||||
−0.569755 | + | 0.821815i | \(0.692962\pi\) | |||||||
\(762\) | −2.70890e8 | + | 2.70890e8i | −0.612250 | + | 0.612250i | ||||
\(763\) | 1.49524e8 | − | 1.49524e8i | 0.336617 | − | 0.336617i | ||||
\(764\) | −3.42717e8 | − | 3.42717e8i | −0.768521 | − | 0.768521i | ||||
\(765\) | 275938.i | 0.000616349i | ||||||||
\(766\) | 3.59262e8 | 0.799328 | ||||||||
\(767\) | 5.36297e8i | 1.18856i | ||||||||
\(768\) | − | 2.87586e8i | − | 0.634869i | ||||||
\(769\) | −4.23501e7 | − | 4.23501e7i | −0.0931270 | − | 0.0931270i | 0.659009 | − | 0.752135i | \(-0.270976\pi\) |
−0.752135 | + | 0.659009i | \(0.770976\pi\) | |||||||
\(770\) | 2.72180e8i | 0.596188i | ||||||||
\(771\) | −3.45056e8 | − | 3.45056e8i | −0.752882 | − | 0.752882i | ||||
\(772\) | −6.57335e7 | − | 6.57335e7i | −0.142868 | − | 0.142868i | ||||
\(773\) | −1.79798e8 | −0.389267 | −0.194633 | − | 0.980876i | \(-0.562352\pi\) | ||||
−0.194633 | + | 0.980876i | \(0.562352\pi\) | |||||||
\(774\) | 251634. | 0.000542683 | ||||||||
\(775\) | −9.75198e7 | + | 9.75198e7i | −0.209502 | + | 0.209502i | ||||
\(776\) | 5.44196e7i | 0.116458i | ||||||||
\(777\) | −3.91173e8 | − | 1.71706e8i | −0.833883 | − | 0.366034i | ||||
\(778\) | −6.03067e7 | −0.128064 | ||||||||
\(779\) | −9.40670e6 | − | 9.40670e6i | −0.0198987 | − | 0.0198987i | ||||
\(780\) | 4.06084e8i | 0.855722i | ||||||||
\(781\) | − | 4.80929e8i | − | 1.00955i | ||||||
\(782\) | 3.83718e7 | − | 3.83718e7i | 0.0802401 | − | 0.0802401i | ||||
\(783\) | −1.29604e8 | + | 1.29604e8i | −0.269981 | + | 0.269981i | ||||
\(784\) | 2.76289e7 | 0.0573345 | ||||||||
\(785\) | 3.32393e8 | − | 3.32393e8i | 0.687137 | − | 0.687137i | ||||
\(786\) | 3.21662e8 | 0.662418 | ||||||||
\(787\) | −6.54412e8 | −1.34254 | −0.671270 | − | 0.741213i | \(-0.734251\pi\) | ||||
−0.671270 | + | 0.741213i | \(0.734251\pi\) | |||||||
\(788\) | 1.01798e8i | 0.208047i | ||||||||
\(789\) | 6.40788e8 | 1.30462 | ||||||||
\(790\) | −6.50717e7 | + | 6.50717e7i | −0.131981 | + | 0.131981i | ||||
\(791\) | −1.81117e8 | − | 1.81117e8i | −0.365956 | − | 0.365956i | ||||
\(792\) | −369470. | − | 369470.i | −0.000743711 | − | 0.000743711i | ||||
\(793\) | 8.56936e6 | 0.0171842 | ||||||||
\(794\) | −2.73206e8 | + | 2.73206e8i | −0.545794 | + | 0.545794i | ||||
\(795\) | −3.03409e8 | − | 3.03409e8i | −0.603848 | − | 0.603848i | ||||
\(796\) | −2.39076e8 | + | 2.39076e8i | −0.474019 | + | 0.474019i | ||||
\(797\) | −9.93044e7 | − | 9.93044e7i | −0.196152 | − | 0.196152i | 0.602196 | − | 0.798348i | \(-0.294293\pi\) |
−0.798348 | + | 0.602196i | \(0.794293\pi\) | |||||||
\(798\) | 4.36150e8i | 0.858276i | ||||||||
\(799\) | −1.87229e8 | + | 1.87229e8i | −0.367056 | + | 0.367056i | ||||
\(800\) | −7.39026e7 | + | 7.39026e7i | −0.144341 | + | 0.144341i | ||||
\(801\) | 537099. | + | 537099.i | 0.00104510 | + | 0.00104510i | ||||
\(802\) | 1.97580e7i | 0.0383018i | ||||||||
\(803\) | −8.75827e8 | −1.69150 | ||||||||
\(804\) | − | 5.37366e8i | − | 1.03396i | ||||||
\(805\) | − | 2.13214e8i | − | 0.408722i | ||||||
\(806\) | 2.79466e8 | + | 2.79466e8i | 0.533734 | + | 0.533734i | ||||
\(807\) | 5.16006e8i | 0.981825i | ||||||||
\(808\) | 4.21254e8 | + | 4.21254e8i | 0.798564 | + | 0.798564i | ||||
\(809\) | 5.21521e8 | + | 5.21521e8i | 0.984977 | + | 0.984977i | 0.999889 | − | 0.0149123i | \(-0.00474690\pi\) |
−0.0149123 | + | 0.999889i | \(0.504747\pi\) | |||||||
\(810\) | −2.86081e8 | −0.538312 | ||||||||
\(811\) | −2.86457e8 | −0.537029 | −0.268514 | − | 0.963276i | \(-0.586533\pi\) | ||||
−0.268514 | + | 0.963276i | \(0.586533\pi\) | |||||||
\(812\) | 9.98716e7 | − | 9.98716e7i | 0.186541 | − | 0.186541i | ||||
\(813\) | 2.06304e8i | 0.383915i | ||||||||
\(814\) | −1.17221e8 | − | 3.00642e8i | −0.217336 | − | 0.557412i | ||||
\(815\) | 2.43460e8 | 0.449734 | ||||||||
\(816\) | −7.23837e7 | − | 7.23837e7i | −0.133220 | − | 0.133220i | ||||
\(817\) | 1.15639e9i | 2.12050i | ||||||||
\(818\) | 6.34387e7i | 0.115903i | ||||||||
\(819\) | 363933. | − | 363933.i | 0.000662475 | − | 0.000662475i | ||||
\(820\) | −4.74986e6 | + | 4.74986e6i | −0.00861467 | + | 0.00861467i | ||||
\(821\) | −4.76469e8 | −0.861005 | −0.430502 | − | 0.902589i | \(-0.641664\pi\) | ||||
−0.430502 | + | 0.902589i | \(0.641664\pi\) | |||||||
\(822\) | 1.54588e8 | − | 1.54588e8i | 0.278331 | − | 0.278331i | ||||
\(823\) | −3.78454e8 | −0.678912 | −0.339456 | − | 0.940622i | \(-0.610243\pi\) | ||||
−0.339456 | + | 0.940622i | \(0.610243\pi\) | |||||||
\(824\) | 7.99997e8 | 1.42990 | ||||||||
\(825\) | 1.35851e8i | 0.241937i | ||||||||
\(826\) | 2.90849e8 | 0.516092 | ||||||||
\(827\) | 3.37054e8 | − | 3.37054e8i | 0.595914 | − | 0.595914i | −0.343309 | − | 0.939223i | \(-0.611548\pi\) |
0.939223 | + | 0.343309i | \(0.111548\pi\) | |||||||
\(828\) | 124859. | + | 124859.i | 0.000219953 | + | 0.000219953i | ||||
\(829\) | −1.77566e8 | − | 1.77566e8i | −0.311670 | − | 0.311670i | 0.533886 | − | 0.845556i | \(-0.320731\pi\) |
−0.845556 | + | 0.533886i | \(0.820731\pi\) | |||||||
\(830\) | −4.98755e6 | −0.00872275 | ||||||||
\(831\) | −6.08522e8 | + | 6.08522e8i | −1.06041 | + | 1.06041i | ||||
\(832\) | 7.15825e7 | + | 7.15825e7i | 0.124290 | + | 0.124290i | ||||
\(833\) | −3.94756e7 | + | 3.94756e7i | −0.0682958 | + | 0.0682958i | ||||
\(834\) | −3.33851e8 | − | 3.33851e8i | −0.575512 | − | 0.575512i | ||||
\(835\) | 5.75386e8i | 0.988325i | ||||||||
\(836\) | 7.32480e8 | − | 7.32480e8i | 1.25365 | − | 1.25365i | ||||
\(837\) | 6.18435e8 | − | 6.18435e8i | 1.05467 | − | 1.05467i | ||||
\(838\) | 4.06991e7 | + | 4.06991e7i | 0.0691596 | + | 0.0691596i | ||||
\(839\) | − | 1.14796e9i | − | 1.94376i | −0.235487 | − | 0.971878i | \(-0.575668\pi\) | ||
0.235487 | − | 0.971878i | \(-0.424332\pi\) | |||||||
\(840\) | 5.10503e8 | 0.861312 | ||||||||
\(841\) | − | 5.08023e8i | − | 0.854074i | ||||||
\(842\) | − | 2.12723e8i | − | 0.356352i | ||||||
\(843\) | 2.57595e8 | + | 2.57595e8i | 0.429986 | + | 0.429986i | ||||
\(844\) | 1.30420e8i | 0.216928i | ||||||||
\(845\) | −2.81675e7 | − | 2.81675e7i | −0.0466850 | − | 0.0466850i | ||||
\(846\) | 193756. | + | 193756.i | 0.000319996 | + | 0.000319996i | ||||
\(847\) | −2.67381e8 | −0.440028 | ||||||||
\(848\) | 1.58955e8 | 0.260667 | ||||||||
\(849\) | 1.49871e8 | − | 1.49871e8i | 0.244903 | − | 0.244903i | ||||
\(850\) | − | 3.37337e7i | − | 0.0549297i | ||||||
\(851\) | 9.18258e7 | + | 2.35510e8i | 0.148996 | + | 0.382139i | ||||
\(852\) | −3.89138e8 | −0.629195 | ||||||||
\(853\) | 2.42046e8 | + | 2.42046e8i | 0.389987 | + | 0.389987i | 0.874683 | − | 0.484695i | \(-0.161070\pi\) |
−0.484695 | + | 0.874683i | \(0.661070\pi\) | |||||||
\(854\) | − | 4.64740e6i | − | 0.00746168i | ||||||
\(855\) | 1.31229e6i | 0.00209958i | ||||||||
\(856\) | −6.83871e7 | + | 6.83871e7i | −0.109032 | + | 0.109032i | ||||
\(857\) | −7.49539e6 | + | 7.49539e6i | −0.0119084 | + | 0.0119084i | −0.713036 | − | 0.701128i | \(-0.752680\pi\) |
0.701128 | + | 0.713036i | \(0.252680\pi\) | |||||||
\(858\) | 3.89315e8 | 0.616367 | ||||||||
\(859\) | 4.55655e8 | − | 4.55655e8i | 0.718880 | − | 0.718880i | −0.249496 | − | 0.968376i | \(-0.580265\pi\) |
0.968376 | + | 0.249496i | \(0.0802648\pi\) | |||||||
\(860\) | 5.83913e8 | 0.918022 | ||||||||
\(861\) | 8.52571e6 | 0.0133574 | ||||||||
\(862\) | − | 2.60397e8i | − | 0.406550i | ||||||
\(863\) | 4.85694e8 | 0.755667 | 0.377833 | − | 0.925874i | \(-0.376669\pi\) | ||||
0.377833 | + | 0.925874i | \(0.376669\pi\) | |||||||
\(864\) | 4.68664e8 | − | 4.68664e8i | 0.726641 | − | 0.726641i | ||||
\(865\) | −1.00159e8 | − | 1.00159e8i | −0.154754 | − | 0.154754i | ||||
\(866\) | 1.75276e8 | + | 1.75276e8i | 0.269878 | + | 0.269878i | ||||
\(867\) | −4.45199e8 | −0.683120 | ||||||||
\(868\) | −4.76560e8 | + | 4.76560e8i | −0.728716 | + | 0.728716i | ||||
\(869\) | −1.96156e8 | − | 1.96156e8i | −0.298912 | − | 0.298912i | ||||
\(870\) | −9.57031e7 | + | 9.57031e7i | −0.145334 | + | 0.145334i | ||||
\(871\) | 6.55341e8 | + | 6.55341e8i | 0.991775 | + | 0.991775i | ||||
\(872\) | − | 2.99583e8i | − | 0.451823i | ||||||
\(873\) | 63394.3 | − | 63394.3i | 9.52812e−5 | − | 9.52812e-5i | ||||
\(874\) | 1.82487e8 | − | 1.82487e8i | 0.273336 | − | 0.273336i | ||||
\(875\) | 3.78326e8 | + | 3.78326e8i | 0.564732 | + | 0.564732i | ||||
\(876\) | 7.08665e8i | 1.05421i | ||||||||
\(877\) | 1.20239e9 | 1.78256 | 0.891282 | − | 0.453449i | \(-0.149807\pi\) | ||||
0.891282 | + | 0.453449i | \(0.149807\pi\) | |||||||
\(878\) | 4.75729e8i | 0.702871i | ||||||||
\(879\) | 1.15306e9i | 1.69780i | ||||||||
\(880\) | −2.14823e8 | − | 2.14823e8i | −0.315233 | − | 0.315233i | ||||
\(881\) | − | 5.38730e8i | − | 0.787850i | −0.919143 | − | 0.393925i | \(-0.871117\pi\) | ||
0.919143 | − | 0.393925i | \(-0.128883\pi\) | |||||||
\(882\) | 40851.9 | + | 40851.9i | 5.95396e−5 | + | 5.95396e-5i | ||||
\(883\) | 4.14609e8 | + | 4.14609e8i | 0.602222 | + | 0.602222i | 0.940902 | − | 0.338680i | \(-0.109980\pi\) |
−0.338680 | + | 0.940902i | \(0.609980\pi\) | |||||||
\(884\) | 3.03967e8 | 0.440017 | ||||||||
\(885\) | 8.76349e8 | 1.26429 | ||||||||
\(886\) | −5.20256e7 | + | 5.20256e7i | −0.0748025 | + | 0.0748025i | ||||
\(887\) | 1.79308e8i | 0.256938i | 0.991714 | + | 0.128469i | \(0.0410063\pi\) | ||||
−0.991714 | + | 0.128469i | \(0.958994\pi\) | |||||||
\(888\) | −5.63887e8 | + | 2.19860e8i | −0.805292 | + | 0.313984i | ||||
\(889\) | 1.12670e9 | 1.60362 | ||||||||
\(890\) | −3.96377e8 | − | 3.96377e8i | −0.562262 | − | 0.562262i | ||||
\(891\) | − | 8.62382e8i | − | 1.21918i | ||||||
\(892\) | 6.08598e8i | 0.857504i | ||||||||
\(893\) | −8.90414e8 | + | 8.90414e8i | −1.25037 | + | 1.25037i | ||||
\(894\) | −1.64705e8 | + | 1.64705e8i | −0.230512 | + | 0.230512i | ||||
\(895\) | −1.42471e9 | −1.98727 | ||||||||
\(896\) | −4.37184e8 | + | 4.37184e8i | −0.607771 | + | 0.607771i | ||||
\(897\) | −3.04973e8 | −0.422556 | ||||||||
\(898\) | −6.74245e8 | −0.931083 | ||||||||
\(899\) | − | 4.14186e8i | − | 0.570054i | ||||||
\(900\) | 109767. | 0.000150572 | ||||||||
\(901\) | −2.27111e8 | + | 2.27111e8i | −0.310502 | + | 0.310502i | ||||
\(902\) | 4.55371e6 | + | 4.55371e6i | 0.00620506 | + | 0.00620506i | ||||
\(903\) | −5.24045e8 | − | 5.24045e8i | −0.711713 | − | 0.711713i | ||||
\(904\) | −3.62882e8 | −0.491203 | ||||||||
\(905\) | 7.36096e8 | − | 7.36096e8i | 0.993090 | − | 0.993090i | ||||
\(906\) | 18645.4 | + | 18645.4i | 2.50720e−5 | + | 2.50720e-5i | ||||
\(907\) | 6.91792e8 | − | 6.91792e8i | 0.927157 | − | 0.927157i | −0.0703640 | − | 0.997521i | \(-0.522416\pi\) |
0.997521 | + | 0.0703640i | \(0.0224161\pi\) | |||||||
\(908\) | −8.38469e6 | − | 8.38469e6i | −0.0112003 | − | 0.0112003i | ||||
\(909\) | − | 981450.i | − | 0.00130670i | ||||||
\(910\) | −2.68581e8 | + | 2.68581e8i | −0.356411 | + | 0.356411i | ||||
\(911\) | −4.02074e8 | + | 4.02074e8i | −0.531803 | + | 0.531803i | −0.921109 | − | 0.389305i | \(-0.872715\pi\) |
0.389305 | + | 0.921109i | \(0.372715\pi\) | |||||||
\(912\) | −3.44239e8 | − | 3.44239e8i | −0.453811 | − | 0.453811i | ||||
\(913\) | − | 1.50348e7i | − | 0.0197554i | ||||||
\(914\) | −4.78352e8 | −0.626482 | ||||||||
\(915\) | − | 1.40030e7i | − | 0.0182792i | ||||||
\(916\) | 2.75767e8i | 0.358803i | ||||||||
\(917\) | −6.68936e8 | − | 6.68936e8i | −0.867514 | − | 0.867514i | ||||
\(918\) | 2.13927e8i | 0.276527i | ||||||||
\(919\) | −4.89071e8 | − | 4.89071e8i | −0.630123 | − | 0.630123i | 0.317976 | − | 0.948099i | \(-0.396997\pi\) |
−0.948099 | + | 0.317976i | \(0.896997\pi\) | |||||||
\(920\) | −2.13596e8 | − | 2.13596e8i | −0.274303 | − | 0.274303i | ||||
\(921\) | 8.43108e8 | 1.07921 | ||||||||
\(922\) | 7.01384e7 | 0.0894877 | ||||||||
\(923\) | 4.74571e8 | − | 4.74571e8i | 0.603526 | − | 0.603526i | ||||
\(924\) | 6.63879e8i | 0.841537i | ||||||||
\(925\) | 1.43885e8 | + | 6.31586e7i | 0.181799 | + | 0.0798008i | ||||
\(926\) | −7.09571e8 | −0.893641 | ||||||||
\(927\) | −931929. | − | 931929.i | −0.00116989 | − | 0.00116989i | ||||
\(928\) | − | 3.13879e8i | − | 0.392752i | ||||||
\(929\) | 1.11849e9i | 1.39503i | 0.716569 | + | 0.697516i | \(0.245711\pi\) | ||||
−0.716569 | + | 0.697516i | \(0.754289\pi\) | |||||||
\(930\) | 4.56669e8 | − | 4.56669e8i | 0.567744 | − | 0.567744i | ||||
\(931\) | −1.87736e8 | + | 1.87736e8i | −0.232648 | + | 0.232648i | ||||
\(932\) | −9.49952e8 | −1.17342 | ||||||||
\(933\) | −1.01203e9 | + | 1.01203e9i | −1.24608 | + | 1.24608i | ||||
\(934\) | 4.99497e8 | 0.613045 | ||||||||
\(935\) | 6.13869e8 | 0.751001 | ||||||||
\(936\) | − | 729171.i | − | 0.000889205i | ||||||
\(937\) | −4.06978e8 | −0.494712 | −0.247356 | − | 0.968925i | \(-0.579562\pi\) | ||||
−0.247356 | + | 0.968925i | \(0.579562\pi\) | |||||||
\(938\) | 3.55410e8 | − | 3.55410e8i | 0.430647 | − | 0.430647i | ||||
\(939\) | −2.42516e8 | − | 2.42516e8i | −0.292916 | − | 0.292916i | ||||
\(940\) | 4.49609e8 | + | 4.49609e8i | 0.541317 | + | 0.541317i | ||||
\(941\) | 7.61871e8 | 0.914350 | 0.457175 | − | 0.889377i | \(-0.348861\pi\) | ||||
0.457175 | + | 0.889377i | \(0.348861\pi\) | |||||||
\(942\) | −2.57846e8 | + | 2.57846e8i | −0.308466 | + | 0.308466i | ||||
\(943\) | −3.56719e6 | − | 3.56719e6i | −0.00425393 | − | 0.00425393i | ||||
\(944\) | −2.29558e8 | + | 2.29558e8i | −0.272883 | + | 0.272883i | ||||
\(945\) | 5.94346e8 | + | 5.94346e8i | 0.704278 | + | 0.704278i | ||||
\(946\) | − | 5.59801e8i | − | 0.661241i | ||||||
\(947\) | 7.04599e8 | − | 7.04599e8i | 0.829645 | − | 0.829645i | −0.157823 | − | 0.987467i | \(-0.550447\pi\) |
0.987467 | + | 0.157823i | \(0.0504475\pi\) | |||||||
\(948\) | −1.58718e8 | + | 1.58718e8i | −0.186295 | + | 0.186295i | ||||
\(949\) | −8.64247e8 | − | 8.64247e8i | −1.01121 | − | 1.01121i | ||||
\(950\) | − | 1.60429e8i | − | 0.187117i | ||||||
\(951\) | −4.33895e7 | −0.0504479 | ||||||||
\(952\) | − | 3.82128e8i | − | 0.442892i | ||||||
\(953\) | − | 9.45156e8i | − | 1.09201i | −0.837783 | − | 0.546003i | \(-0.816149\pi\) | ||
0.837783 | − | 0.546003i | \(-0.183851\pi\) | |||||||
\(954\) | 235029. | + | 235029.i | 0.000270693 | + | 0.000270693i | ||||
\(955\) | − | 1.36595e9i | − | 1.56828i | ||||||
\(956\) | −5.18921e8 | − | 5.18921e8i | −0.593920 | − | 0.593920i | ||||
\(957\) | −2.88494e8 | − | 2.88494e8i | −0.329155 | − | 0.329155i | ||||
\(958\) | −7.36828e8 | −0.838050 | ||||||||
\(959\) | −6.42971e8 | −0.729014 | ||||||||
\(960\) | 1.16971e8 | − | 1.16971e8i | 0.132210 | − | 0.132210i | ||||
\(961\) | 1.08887e9i | 1.22690i | ||||||||
\(962\) | 1.80996e8 | − | 4.12338e8i | 0.203303 | − | 0.463157i | ||||
\(963\) | 159331. | 0.000178410 | ||||||||
\(964\) | 1.42861e7 | + | 1.42861e7i | 0.0159472 | + | 0.0159472i | ||||
\(965\) | − | 2.61990e8i | − | 0.291543i | ||||||
\(966\) | 1.65396e8i | 0.183482i | ||||||||
\(967\) | −2.91627e8 | + | 2.91627e8i | −0.322514 | + | 0.322514i | −0.849731 | − | 0.527217i | \(-0.823236\pi\) |
0.527217 | + | 0.849731i | \(0.323236\pi\) | |||||||
\(968\) | −2.67860e8 | + | 2.67860e8i | −0.295313 | + | 0.295313i | ||||
\(969\) | 9.83683e8 | 1.08114 | ||||||||
\(970\) | −4.67847e7 | + | 4.67847e7i | −0.0512612 | + | 0.0512612i | ||||
\(971\) | −8.23647e8 | −0.899671 | −0.449835 | − | 0.893112i | \(-0.648517\pi\) | ||||
−0.449835 | + | 0.893112i | \(0.648517\pi\) | |||||||
\(972\) | −1.39290e6 | −0.00151678 | ||||||||
\(973\) | 1.38857e9i | 1.50740i | ||||||||
\(974\) | 2.31779e7 | 0.0250841 | ||||||||
\(975\) | −1.34055e8 | + | 1.34055e8i | −0.144634 | + | 0.144634i | ||||
\(976\) | 3.66805e6 | + | 3.66805e6i | 0.00394535 | + | 0.00394535i | ||||
\(977\) | 4.81437e8 | + | 4.81437e8i | 0.516245 | + | 0.516245i | 0.916433 | − | 0.400188i | \(-0.131055\pi\) |
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(978\) | −1.88858e8 | −0.201892 | ||||||||
\(979\) | 1.19487e9 | − | 1.19487e9i | 1.27342 | − | 1.27342i | ||||
\(980\) | 9.47963e7 | + | 9.47963e7i | 0.100719 | + | 0.100719i | ||||
\(981\) | −348990. | + | 348990.i | −0.000369662 | + | 0.000369662i | ||||
\(982\) | −5.61176e8 | − | 5.61176e8i | −0.592605 | − | 0.592605i | ||||
\(983\) | − | 4.08253e8i | − | 0.429802i | −0.976636 | − | 0.214901i | \(-0.931057\pi\) | ||
0.976636 | − | 0.214901i | \(-0.0689429\pi\) | |||||||
\(984\) | 8.54099e6 | − | 8.54099e6i | 0.00896443 | − | 0.00896443i | ||||
\(985\) | −2.02865e8 | + | 2.02865e8i | −0.212275 | + | 0.212275i | ||||
\(986\) | 7.16368e7 | + | 7.16368e7i | 0.0747318 | + | 0.0747318i | ||||
\(987\) | − | 8.07021e8i | − | 0.839332i | ||||||
\(988\) | 1.44559e9 | 1.49891 | ||||||||
\(989\) | 4.38525e8i | 0.453320i | ||||||||
\(990\) | − | 635270.i | − | 0.000654715i | ||||||
\(991\) | −1.03761e9 | − | 1.03761e9i | −1.06614 | − | 1.06614i | −0.997652 | − | 0.0684853i | \(-0.978183\pi\) |
−0.0684853 | − | 0.997652i | \(-0.521817\pi\) | |||||||
\(992\) | 1.49774e9i | 1.53427i | ||||||||
\(993\) | 5.96991e8 | + | 5.96991e8i | 0.609706 | + | 0.609706i | ||||
\(994\) | −2.57373e8 | − | 2.57373e8i | −0.262062 | − | 0.262062i | ||||
\(995\) | −9.52870e8 | −0.967307 | ||||||||
\(996\) | −1.21652e7 | −0.0123124 | ||||||||
\(997\) | −3.43762e8 | + | 3.43762e8i | −0.346875 | + | 0.346875i | −0.858944 | − | 0.512069i | \(-0.828879\pi\) |
0.512069 | + | 0.858944i | \(0.328879\pi\) | |||||||
\(998\) | 7.93923e8i | 0.798706i | ||||||||
\(999\) | −9.12468e8 | − | 4.00529e8i | −0.915211 | − | 0.401733i |
(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 | 37.7.d.a.31.12 | yes | 36 | |
37.6 | odd | 4 | inner | 37.7.d.a.6.12 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.7.d.a.6.12 | ✓ | 36 | 37.6 | odd | 4 | inner | |
37.7.d.a.31.12 | yes | 36 | 1.1 | even | 1 | trivial |