Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(-0.651946i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.43 |
Dual form | 74.7.d.a.31.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | − | 4.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | − | 4.65195i | − | 0.172294i | −0.996282 | − | 0.0861471i | \(-0.972544\pi\) | ||
0.996282 | − | 0.0861471i | \(-0.0274555\pi\) | |||||||
\(4\) | − | 32.0000i | − | 0.500000i | ||||||
\(5\) | −62.1985 | − | 62.1985i | −0.497588 | − | 0.497588i | 0.413098 | − | 0.910686i | \(-0.364447\pi\) |
−0.910686 | + | 0.413098i | \(0.864447\pi\) | |||||||
\(6\) | −18.6078 | − | 18.6078i | −0.0861471 | − | 0.0861471i | ||||
\(7\) | 564.672 | 1.64628 | 0.823138 | − | 0.567842i | \(-0.192221\pi\) | ||||
0.823138 | + | 0.567842i | \(0.192221\pi\) | |||||||
\(8\) | −128.000 | − | 128.000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 707.359 | 0.970315 | ||||||||
\(10\) | −497.588 | −0.497588 | ||||||||
\(11\) | 447.353i | 0.336103i | 0.985778 | + | 0.168051i | \(0.0537474\pi\) | ||||
−0.985778 | + | 0.168051i | \(0.946253\pi\) | |||||||
\(12\) | −148.862 | −0.0861471 | ||||||||
\(13\) | −2851.44 | − | 2851.44i | −1.29788 | − | 1.29788i | −0.929791 | − | 0.368088i | \(-0.880012\pi\) |
−0.368088 | − | 0.929791i | \(-0.619988\pi\) | |||||||
\(14\) | 2258.69 | − | 2258.69i | 0.823138 | − | 0.823138i | ||||
\(15\) | −289.344 | + | 289.344i | −0.0857316 | + | 0.0857316i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | −4948.00 | − | 4948.00i | −1.00712 | − | 1.00712i | −0.999974 | − | 0.00715051i | \(-0.997724\pi\) |
−0.00715051 | − | 0.999974i | \(-0.502276\pi\) | |||||||
\(18\) | 2829.44 | − | 2829.44i | 0.485157 | − | 0.485157i | ||||
\(19\) | −749.331 | − | 749.331i | −0.109248 | − | 0.109248i | 0.650370 | − | 0.759618i | \(-0.274614\pi\) |
−0.759618 | + | 0.650370i | \(0.774614\pi\) | |||||||
\(20\) | −1990.35 | + | 1990.35i | −0.248794 | + | 0.248794i | ||||
\(21\) | − | 2626.83i | − | 0.283644i | ||||||
\(22\) | 1789.41 | + | 1789.41i | 0.168051 | + | 0.168051i | ||||
\(23\) | 4599.01 | + | 4599.01i | 0.377991 | + | 0.377991i | 0.870377 | − | 0.492386i | \(-0.163875\pi\) |
−0.492386 | + | 0.870377i | \(0.663875\pi\) | |||||||
\(24\) | −595.449 | + | 595.449i | −0.0430736 | + | 0.0430736i | ||||
\(25\) | − | 7887.69i | − | 0.504812i | ||||||
\(26\) | −22811.5 | −1.29788 | ||||||||
\(27\) | − | 6681.87i | − | 0.339474i | ||||||
\(28\) | − | 18069.5i | − | 0.823138i | ||||||
\(29\) | 14323.9 | − | 14323.9i | 0.587308 | − | 0.587308i | −0.349593 | − | 0.936902i | \(-0.613680\pi\) |
0.936902 | + | 0.349593i | \(0.113680\pi\) | |||||||
\(30\) | 2314.75i | 0.0857316i | ||||||||
\(31\) | −869.772 | + | 869.772i | −0.0291958 | + | 0.0291958i | −0.721554 | − | 0.692358i | \(-0.756572\pi\) |
0.692358 | + | 0.721554i | \(0.256572\pi\) | |||||||
\(32\) | −4096.00 | + | 4096.00i | −0.125000 | + | 0.125000i | ||||
\(33\) | 2081.06 | 0.0579086 | ||||||||
\(34\) | −39584.0 | −1.00712 | ||||||||
\(35\) | −35121.8 | − | 35121.8i | −0.819167 | − | 0.819167i | ||||
\(36\) | − | 22635.5i | − | 0.485157i | ||||||
\(37\) | −23486.3 | + | 44878.9i | −0.463671 | + | 0.886008i | ||||
\(38\) | −5994.65 | −0.109248 | ||||||||
\(39\) | −13264.7 | + | 13264.7i | −0.223617 | + | 0.223617i | ||||
\(40\) | 15922.8i | 0.248794i | ||||||||
\(41\) | − | 81678.3i | − | 1.18510i | −0.805533 | − | 0.592550i | \(-0.798121\pi\) | ||
0.805533 | − | 0.592550i | \(-0.201879\pi\) | |||||||
\(42\) | −10507.3 | − | 10507.3i | −0.141822 | − | 0.141822i | ||||
\(43\) | 101901. | + | 101901.i | 1.28166 | + | 1.28166i | 0.939721 | + | 0.341941i | \(0.111084\pi\) |
0.341941 | + | 0.939721i | \(0.388916\pi\) | |||||||
\(44\) | 14315.3 | 0.168051 | ||||||||
\(45\) | −43996.7 | − | 43996.7i | −0.482817 | − | 0.482817i | ||||
\(46\) | 36792.1 | 0.377991 | ||||||||
\(47\) | −52628.1 | −0.506902 | −0.253451 | − | 0.967348i | \(-0.581566\pi\) | ||||
−0.253451 | + | 0.967348i | \(0.581566\pi\) | |||||||
\(48\) | 4763.59i | 0.0430736i | ||||||||
\(49\) | 201206. | 1.71022 | ||||||||
\(50\) | −31550.8 | − | 31550.8i | −0.252406 | − | 0.252406i | ||||
\(51\) | −23017.8 | + | 23017.8i | −0.173522 | + | 0.173522i | ||||
\(52\) | −91246.1 | + | 91246.1i | −0.648940 | + | 0.648940i | ||||
\(53\) | −25583.6 | −0.171844 | −0.0859219 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859219 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(54\) | −26727.5 | − | 26727.5i | −0.169737 | − | 0.169737i | ||||
\(55\) | 27824.7 | − | 27824.7i | 0.167241 | − | 0.167241i | ||||
\(56\) | −72278.1 | − | 72278.1i | −0.411569 | − | 0.411569i | ||||
\(57\) | −3485.85 | + | 3485.85i | −0.0188228 | + | 0.0188228i | ||||
\(58\) | − | 114591.i | − | 0.587308i | ||||||
\(59\) | −27162.1 | − | 27162.1i | −0.132254 | − | 0.132254i | 0.637881 | − | 0.770135i | \(-0.279811\pi\) |
−0.770135 | + | 0.637881i | \(0.779811\pi\) | |||||||
\(60\) | 9259.01 | + | 9259.01i | 0.0428658 | + | 0.0428658i | ||||
\(61\) | 158791. | − | 158791.i | 0.699580 | − | 0.699580i | −0.264740 | − | 0.964320i | \(-0.585286\pi\) |
0.964320 | + | 0.264740i | \(0.0852861\pi\) | |||||||
\(62\) | 6958.18i | 0.0291958i | ||||||||
\(63\) | 399426. | 1.59741 | ||||||||
\(64\) | 32768.0i | 0.125000i | ||||||||
\(65\) | 354711.i | 1.29162i | ||||||||
\(66\) | 8324.24 | − | 8324.24i | 0.0289543 | − | 0.0289543i | ||||
\(67\) | 419546.i | 1.39494i | 0.716614 | + | 0.697470i | \(0.245691\pi\) | ||||
−0.716614 | + | 0.697470i | \(0.754309\pi\) | |||||||
\(68\) | −158336. | + | 158336.i | −0.503562 | + | 0.503562i | ||||
\(69\) | 21394.4 | − | 21394.4i | 0.0651256 | − | 0.0651256i | ||||
\(70\) | −280974. | −0.819167 | ||||||||
\(71\) | 470162. | 1.31363 | 0.656814 | − | 0.754052i | \(-0.271904\pi\) | ||||
0.656814 | + | 0.754052i | \(0.271904\pi\) | |||||||
\(72\) | −90542.0 | − | 90542.0i | −0.242579 | − | 0.242579i | ||||
\(73\) | − | 20202.9i | − | 0.0519331i | −0.999663 | − | 0.0259666i | \(-0.991734\pi\) | ||
0.999663 | − | 0.0259666i | \(-0.00826634\pi\) | |||||||
\(74\) | 85570.5 | + | 273461.i | 0.211168 | + | 0.674839i | ||||
\(75\) | −36693.1 | −0.0869763 | ||||||||
\(76\) | −23978.6 | + | 23978.6i | −0.0546240 | + | 0.0546240i | ||||
\(77\) | 252608.i | 0.553318i | ||||||||
\(78\) | 106118.i | 0.223617i | ||||||||
\(79\) | 159040. | + | 159040.i | 0.322571 | + | 0.322571i | 0.849753 | − | 0.527182i | \(-0.176751\pi\) |
−0.527182 | + | 0.849753i | \(0.676751\pi\) | |||||||
\(80\) | 63691.3 | + | 63691.3i | 0.124397 | + | 0.124397i | ||||
\(81\) | 484581. | 0.911825 | ||||||||
\(82\) | −326713. | − | 326713.i | −0.592550 | − | 0.592550i | ||||
\(83\) | 115661. | 0.202279 | 0.101140 | − | 0.994872i | \(-0.467751\pi\) | ||||
0.101140 | + | 0.994872i | \(0.467751\pi\) | |||||||
\(84\) | −84058.4 | −0.141822 | ||||||||
\(85\) | 615517.i | 1.00227i | ||||||||
\(86\) | 815209. | 1.28166 | ||||||||
\(87\) | −66633.8 | − | 66633.8i | −0.101190 | − | 0.101190i | ||||
\(88\) | 57261.1 | − | 57261.1i | 0.0840257 | − | 0.0840257i | ||||
\(89\) | −768017. | + | 768017.i | −1.08943 | + | 1.08943i | −0.0938470 | + | 0.995587i | \(0.529916\pi\) |
−0.995587 | + | 0.0938470i | \(0.970084\pi\) | |||||||
\(90\) | −351974. | −0.482817 | ||||||||
\(91\) | −1.61013e6 | − | 1.61013e6i | −2.13667 | − | 2.13667i | ||||
\(92\) | 147168. | − | 147168.i | 0.188995 | − | 0.188995i | ||||
\(93\) | 4046.13 | + | 4046.13i | 0.00503027 | + | 0.00503027i | ||||
\(94\) | −210512. | + | 210512.i | −0.253451 | + | 0.253451i | ||||
\(95\) | 93214.6i | 0.108721i | ||||||||
\(96\) | 19054.4 | + | 19054.4i | 0.0215368 | + | 0.0215368i | ||||
\(97\) | 580932. | + | 580932.i | 0.636517 | + | 0.636517i | 0.949695 | − | 0.313177i | \(-0.101393\pi\) |
−0.313177 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(98\) | 804824. | − | 804824.i | 0.855111 | − | 0.855111i | ||||
\(99\) | 316439.i | 0.326125i | ||||||||
\(100\) | −252406. | −0.252406 | ||||||||
\(101\) | 114954.i | 0.111573i | 0.998443 | + | 0.0557865i | \(0.0177666\pi\) | ||||
−0.998443 | + | 0.0557865i | \(0.982233\pi\) | |||||||
\(102\) | 184143.i | 0.173522i | ||||||||
\(103\) | 1.47116e6 | − | 1.47116e6i | 1.34632 | − | 1.34632i | 0.456703 | − | 0.889619i | \(-0.349030\pi\) |
0.889619 | − | 0.456703i | \(-0.150970\pi\) | |||||||
\(104\) | 729969.i | 0.648940i | ||||||||
\(105\) | −163385. | + | 163385.i | −0.141138 | + | 0.141138i | ||||
\(106\) | −102334. | + | 102334.i | −0.0859219 | + | 0.0859219i | ||||
\(107\) | −636333. | −0.519437 | −0.259719 | − | 0.965684i | \(-0.583630\pi\) | ||||
−0.259719 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(108\) | −213820. | −0.169737 | ||||||||
\(109\) | −707487. | − | 707487.i | −0.546310 | − | 0.546310i | 0.379062 | − | 0.925371i | \(-0.376247\pi\) |
−0.925371 | + | 0.379062i | \(0.876247\pi\) | |||||||
\(110\) | − | 222597.i | − | 0.167241i | ||||||
\(111\) | 208774. | + | 109257.i | 0.152654 | + | 0.0798878i | ||||
\(112\) | −578225. | −0.411569 | ||||||||
\(113\) | 960416. | − | 960416.i | 0.665617 | − | 0.665617i | −0.291082 | − | 0.956698i | \(-0.594015\pi\) |
0.956698 | + | 0.291082i | \(0.0940151\pi\) | |||||||
\(114\) | 27886.8i | 0.0188228i | ||||||||
\(115\) | − | 572103.i | − | 0.376167i | ||||||
\(116\) | −458363. | − | 458363.i | −0.293654 | − | 0.293654i | ||||
\(117\) | −2.01699e6 | − | 2.01699e6i | −1.25935 | − | 1.25935i | ||||
\(118\) | −217297. | −0.132254 | ||||||||
\(119\) | −2.79400e6 | − | 2.79400e6i | −1.65800 | − | 1.65800i | ||||
\(120\) | 74072.1 | 0.0428658 | ||||||||
\(121\) | 1.57144e6 | 0.887035 | ||||||||
\(122\) | − | 1.27033e6i | − | 0.699580i | ||||||
\(123\) | −379963. | −0.204186 | ||||||||
\(124\) | 27832.7 | + | 27832.7i | 0.0145979 | + | 0.0145979i | ||||
\(125\) | −1.46245e6 | + | 1.46245e6i | −0.748777 | + | 0.748777i | ||||
\(126\) | 1.59771e6 | − | 1.59771e6i | 0.798703 | − | 0.798703i | ||||
\(127\) | 1.63807e6 | 0.799688 | 0.399844 | − | 0.916583i | \(-0.369064\pi\) | ||||
0.399844 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(128\) | 131072. | + | 131072.i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 474039. | − | 474039.i | 0.220823 | − | 0.220823i | ||||
\(130\) | 1.41884e6 | + | 1.41884e6i | 0.645809 | + | 0.645809i | ||||
\(131\) | −2.46727e6 | + | 2.46727e6i | −1.09750 | + | 1.09750i | −0.102793 | + | 0.994703i | \(0.532778\pi\) |
−0.994703 | + | 0.102793i | \(0.967222\pi\) | |||||||
\(132\) | − | 66593.9i | − | 0.0289543i | ||||||
\(133\) | −423127. | − | 423127.i | −0.179852 | − | 0.179852i | ||||
\(134\) | 1.67818e6 | + | 1.67818e6i | 0.697470 | + | 0.697470i | ||||
\(135\) | −415602. | + | 415602.i | −0.168918 | + | 0.168918i | ||||
\(136\) | 1.26669e6i | 0.503562i | ||||||||
\(137\) | 1.85122e6 | 0.719941 | 0.359970 | − | 0.932964i | \(-0.382787\pi\) | ||||
0.359970 | + | 0.932964i | \(0.382787\pi\) | |||||||
\(138\) | − | 171155.i | − | 0.0651256i | ||||||
\(139\) | 147469.i | 0.0549106i | 0.999623 | + | 0.0274553i | \(0.00874040\pi\) | ||||
−0.999623 | + | 0.0274553i | \(0.991260\pi\) | |||||||
\(140\) | −1.12390e6 | + | 1.12390e6i | −0.409583 | + | 0.409583i | ||||
\(141\) | 244823.i | 0.0873363i | ||||||||
\(142\) | 1.88065e6 | − | 1.88065e6i | 0.656814 | − | 0.656814i | ||||
\(143\) | 1.27560e6 | − | 1.27560e6i | 0.436221 | − | 0.436221i | ||||
\(144\) | −724336. | −0.242579 | ||||||||
\(145\) | −1.78185e6 | −0.584475 | ||||||||
\(146\) | −80811.5 | − | 80811.5i | −0.0259666 | − | 0.0259666i | ||||
\(147\) | − | 935999.i | − | 0.294662i | ||||||
\(148\) | 1.43613e6 | + | 751562.i | 0.443004 | + | 0.231835i | ||||
\(149\) | −4.05100e6 | −1.22462 | −0.612312 | − | 0.790616i | \(-0.709761\pi\) | ||||
−0.612312 | + | 0.790616i | \(0.709761\pi\) | |||||||
\(150\) | −146772. | + | 146772.i | −0.0434881 | + | 0.0434881i | ||||
\(151\) | 4.50298e6i | 1.30788i | 0.756545 | + | 0.653941i | \(0.226886\pi\) | ||||
−0.756545 | + | 0.653941i | \(0.773114\pi\) | |||||||
\(152\) | 191829.i | 0.0546240i | ||||||||
\(153\) | −3.50002e6 | − | 3.50002e6i | −0.977228 | − | 0.977228i | ||||
\(154\) | 1.01043e6 | + | 1.01043e6i | 0.276659 | + | 0.276659i | ||||
\(155\) | 108197. | 0.0290550 | ||||||||
\(156\) | 424472. | + | 424472.i | 0.111809 | + | 0.111809i | ||||
\(157\) | 1.70734e6 | 0.441185 | 0.220592 | − | 0.975366i | \(-0.429201\pi\) | ||||
0.220592 | + | 0.975366i | \(0.429201\pi\) | |||||||
\(158\) | 1.27232e6 | 0.322571 | ||||||||
\(159\) | 119013.i | 0.0296077i | ||||||||
\(160\) | 509530. | 0.124397 | ||||||||
\(161\) | 2.59694e6 | + | 2.59694e6i | 0.622277 | + | 0.622277i | ||||
\(162\) | 1.93833e6 | − | 1.93833e6i | 0.455913 | − | 0.455913i | ||||
\(163\) | −1.88528e6 | + | 1.88528e6i | −0.435324 | + | 0.435324i | −0.890435 | − | 0.455111i | \(-0.849600\pi\) |
0.455111 | + | 0.890435i | \(0.349600\pi\) | |||||||
\(164\) | −2.61371e6 | −0.592550 | ||||||||
\(165\) | −129439. | − | 129439.i | −0.0288146 | − | 0.0288146i | ||||
\(166\) | 462642. | − | 462642.i | 0.101140 | − | 0.101140i | ||||
\(167\) | 5.71148e6 | + | 5.71148e6i | 1.22631 | + | 1.22631i | 0.965351 | + | 0.260956i | \(0.0840377\pi\) |
0.260956 | + | 0.965351i | \(0.415962\pi\) | |||||||
\(168\) | −336234. | + | 336234.i | −0.0709110 | + | 0.0709110i | ||||
\(169\) | 1.14346e7i | 2.36898i | ||||||||
\(170\) | 2.46207e6 | + | 2.46207e6i | 0.501133 | + | 0.501133i | ||||
\(171\) | −530047. | − | 530047.i | −0.106005 | − | 0.106005i | ||||
\(172\) | 3.26084e6 | − | 3.26084e6i | 0.640831 | − | 0.640831i | ||||
\(173\) | 8.07343e6i | 1.55926i | 0.626237 | + | 0.779632i | \(0.284594\pi\) | ||||
−0.626237 | + | 0.779632i | \(0.715406\pi\) | |||||||
\(174\) | −533070. | −0.101190 | ||||||||
\(175\) | − | 4.45396e6i | − | 0.831060i | ||||||
\(176\) | − | 458089.i | − | 0.0840257i | ||||||
\(177\) | −126357. | + | 126357.i | −0.0227866 | + | 0.0227866i | ||||
\(178\) | 6.14414e6i | 1.08943i | ||||||||
\(179\) | 7.03144e6 | − | 7.03144e6i | 1.22599 | − | 1.22599i | 0.260516 | − | 0.965470i | \(-0.416107\pi\) |
0.965470 | − | 0.260516i | \(-0.0838927\pi\) | |||||||
\(180\) | −1.40789e6 | + | 1.40789e6i | −0.241409 | + | 0.241409i | ||||
\(181\) | 2.49584e6 | 0.420902 | 0.210451 | − | 0.977604i | \(-0.432507\pi\) | ||||
0.210451 | + | 0.977604i | \(0.432507\pi\) | |||||||
\(182\) | −1.28810e7 | −2.13667 | ||||||||
\(183\) | −738689. | − | 738689.i | −0.120534 | − | 0.120534i | ||||
\(184\) | − | 1.17735e6i | − | 0.188995i | ||||||
\(185\) | 4.25222e6 | − | 1.33059e6i | 0.671584 | − | 0.210150i | ||||
\(186\) | 32369.1 | 0.00503027 | ||||||||
\(187\) | 2.21350e6 | − | 2.21350e6i | 0.338497 | − | 0.338497i | ||||
\(188\) | 1.68410e6i | 0.253451i | ||||||||
\(189\) | − | 3.77307e6i | − | 0.558868i | ||||||
\(190\) | 372858. | + | 372858.i | 0.0543605 | + | 0.0543605i | ||||
\(191\) | −8.88871e6 | − | 8.88871e6i | −1.27567 | − | 1.27567i | −0.943067 | − | 0.332604i | \(-0.892073\pi\) |
−0.332604 | − | 0.943067i | \(-0.607927\pi\) | |||||||
\(192\) | 152435. | 0.0215368 | ||||||||
\(193\) | 1.80279e6 | + | 1.80279e6i | 0.250769 | + | 0.250769i | 0.821286 | − | 0.570517i | \(-0.193257\pi\) |
−0.570517 | + | 0.821286i | \(0.693257\pi\) | |||||||
\(194\) | 4.64746e6 | 0.636517 | ||||||||
\(195\) | 1.65009e6 | 0.222538 | ||||||||
\(196\) | − | 6.43859e6i | − | 0.855111i | ||||||
\(197\) | −1.27623e7 | −1.66929 | −0.834643 | − | 0.550791i | \(-0.814326\pi\) | ||||
−0.834643 | + | 0.550791i | \(0.814326\pi\) | |||||||
\(198\) | 1.26576e6 | + | 1.26576e6i | 0.163063 | + | 0.163063i | ||||
\(199\) | 1.61419e6 | − | 1.61419e6i | 0.204831 | − | 0.204831i | −0.597235 | − | 0.802066i | \(-0.703734\pi\) |
0.802066 | + | 0.597235i | \(0.203734\pi\) | |||||||
\(200\) | −1.00962e6 | + | 1.00962e6i | −0.126203 | + | 0.126203i | ||||
\(201\) | 1.95171e6 | 0.240340 | ||||||||
\(202\) | 459815. | + | 459815.i | 0.0557865 | + | 0.0557865i | ||||
\(203\) | 8.08829e6 | − | 8.08829e6i | 0.966871 | − | 0.966871i | ||||
\(204\) | 736571. | + | 736571.i | 0.0867609 | + | 0.0867609i | ||||
\(205\) | −5.08027e6 | + | 5.08027e6i | −0.589692 | + | 0.589692i | ||||
\(206\) | − | 1.17693e7i | − | 1.34632i | ||||||
\(207\) | 3.25315e6 | + | 3.25315e6i | 0.366770 | + | 0.366770i | ||||
\(208\) | 2.91987e6 | + | 2.91987e6i | 0.324470 | + | 0.324470i | ||||
\(209\) | 335215. | − | 335215.i | 0.0367185 | − | 0.0367185i | ||||
\(210\) | 1.30708e6i | 0.141138i | ||||||||
\(211\) | 5.58652e6 | 0.594695 | 0.297347 | − | 0.954769i | \(-0.403898\pi\) | ||||
0.297347 | + | 0.954769i | \(0.403898\pi\) | |||||||
\(212\) | 818674.i | 0.0859219i | ||||||||
\(213\) | − | 2.18717e6i | − | 0.226331i | ||||||
\(214\) | −2.54533e6 | + | 2.54533e6i | −0.259719 | + | 0.259719i | ||||
\(215\) | − | 1.26762e7i | − | 1.27548i | ||||||
\(216\) | −855279. | + | 855279.i | −0.0848685 | + | 0.0848685i | ||||
\(217\) | −491136. | + | 491136.i | −0.0480643 | + | 0.0480643i | ||||
\(218\) | −5.65989e6 | −0.546310 | ||||||||
\(219\) | −93982.7 | −0.00894778 | ||||||||
\(220\) | −890389. | − | 890389.i | −0.0836203 | − | 0.0836203i | ||||
\(221\) | 2.82179e7i | 2.61425i | ||||||||
\(222\) | 1.27213e6 | − | 398069.i | 0.116271 | − | 0.0363831i | ||||
\(223\) | 2.11007e6 | 0.190276 | 0.0951378 | − | 0.995464i | \(-0.469671\pi\) | ||||
0.0951378 | + | 0.995464i | \(0.469671\pi\) | |||||||
\(224\) | −2.31290e6 | + | 2.31290e6i | −0.205784 | + | 0.205784i | ||||
\(225\) | − | 5.57943e6i | − | 0.489827i | ||||||
\(226\) | − | 7.68333e6i | − | 0.665617i | ||||||
\(227\) | −9.94008e6 | − | 9.94008e6i | −0.849791 | − | 0.849791i | 0.140316 | − | 0.990107i | \(-0.455188\pi\) |
−0.990107 | + | 0.140316i | \(0.955188\pi\) | |||||||
\(228\) | 111547. | + | 111547.i | 0.00941140 | + | 0.00941140i | ||||
\(229\) | 1.89642e7 | 1.57917 | 0.789583 | − | 0.613644i | \(-0.210297\pi\) | ||||
0.789583 | + | 0.613644i | \(0.210297\pi\) | |||||||
\(230\) | −2.28841e6 | − | 2.28841e6i | −0.188084 | − | 0.188084i | ||||
\(231\) | 1.17512e6 | 0.0953334 | ||||||||
\(232\) | −3.66691e6 | −0.293654 | ||||||||
\(233\) | 1.40728e7i | 1.11254i | 0.831003 | + | 0.556268i | \(0.187767\pi\) | ||||
−0.831003 | + | 0.556268i | \(0.812233\pi\) | |||||||
\(234\) | −1.61359e7 | −1.25935 | ||||||||
\(235\) | 3.27339e6 | + | 3.27339e6i | 0.252228 | + | 0.252228i | ||||
\(236\) | −869188. | + | 869188.i | −0.0661269 | + | 0.0661269i | ||||
\(237\) | 739846. | − | 739846.i | 0.0555771 | − | 0.0555771i | ||||
\(238\) | −2.23520e7 | −1.65800 | ||||||||
\(239\) | −6.59523e6 | − | 6.59523e6i | −0.483099 | − | 0.483099i | 0.423021 | − | 0.906120i | \(-0.360970\pi\) |
−0.906120 | + | 0.423021i | \(0.860970\pi\) | |||||||
\(240\) | 296288. | − | 296288.i | 0.0214329 | − | 0.0214329i | ||||
\(241\) | −1.24712e7 | − | 1.24712e7i | −0.890955 | − | 0.890955i | 0.103658 | − | 0.994613i | \(-0.466945\pi\) |
−0.994613 | + | 0.103658i | \(0.966945\pi\) | |||||||
\(242\) | 6.28575e6 | − | 6.28575e6i | 0.443518 | − | 0.443518i | ||||
\(243\) | − | 7.12533e6i | − | 0.496576i | ||||||
\(244\) | −5.08132e6 | − | 5.08132e6i | −0.349790 | − | 0.349790i | ||||
\(245\) | −1.25147e7 | − | 1.25147e7i | −0.850986 | − | 0.850986i | ||||
\(246\) | −1.51985e6 | + | 1.51985e6i | −0.102093 | + | 0.102093i | ||||
\(247\) | 4.27335e6i | 0.283581i | ||||||||
\(248\) | 222662. | 0.0145979 | ||||||||
\(249\) | − | 538046.i | − | 0.0348515i | ||||||
\(250\) | 1.16996e7i | 0.748777i | ||||||||
\(251\) | −3.07516e6 | + | 3.07516e6i | −0.194467 | + | 0.194467i | −0.797623 | − | 0.603156i | \(-0.793910\pi\) |
0.603156 | + | 0.797623i | \(0.293910\pi\) | |||||||
\(252\) | − | 1.27816e7i | − | 0.798703i | ||||||
\(253\) | −2.05738e6 | + | 2.05738e6i | −0.127044 | + | 0.127044i | ||||
\(254\) | 6.55227e6 | − | 6.55227e6i | 0.399844 | − | 0.399844i | ||||
\(255\) | 2.86335e6 | 0.172685 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 4.61967e6 | + | 4.61967e6i | 0.272152 | + | 0.272152i | 0.829966 | − | 0.557814i | \(-0.188360\pi\) |
−0.557814 | + | 0.829966i | \(0.688360\pi\) | |||||||
\(258\) | − | 3.79231e6i | − | 0.220823i | ||||||
\(259\) | −1.32621e7 | + | 2.53419e7i | −0.763330 | + | 1.45861i | ||||
\(260\) | 1.13507e7 | 0.645809 | ||||||||
\(261\) | 1.01321e7 | − | 1.01321e7i | 0.569874 | − | 0.569874i | ||||
\(262\) | 1.97382e7i | 1.09750i | ||||||||
\(263\) | − | 1.06190e7i | − | 0.583736i | −0.956459 | − | 0.291868i | \(-0.905723\pi\) | ||
0.956459 | − | 0.291868i | \(-0.0942768\pi\) | |||||||
\(264\) | −266376. | − | 266376.i | −0.0144771 | − | 0.0144771i | ||||
\(265\) | 1.59126e6 | + | 1.59126e6i | 0.0855074 | + | 0.0855074i | ||||
\(266\) | −3.38501e6 | −0.179852 | ||||||||
\(267\) | 3.57277e6 | + | 3.57277e6i | 0.187703 | + | 0.187703i | ||||
\(268\) | 1.34255e7 | 0.697470 | ||||||||
\(269\) | 1.77872e7 | 0.913798 | 0.456899 | − | 0.889519i | \(-0.348960\pi\) | ||||
0.456899 | + | 0.889519i | \(0.348960\pi\) | |||||||
\(270\) | 3.32482e6i | 0.168918i | ||||||||
\(271\) | 3.14639e7 | 1.58090 | 0.790451 | − | 0.612526i | \(-0.209846\pi\) | ||||
0.790451 | + | 0.612526i | \(0.209846\pi\) | |||||||
\(272\) | 5.06676e6 | + | 5.06676e6i | 0.251781 | + | 0.251781i | ||||
\(273\) | −7.49024e6 | + | 7.49024e6i | −0.368135 | + | 0.368135i | ||||
\(274\) | 7.40489e6 | − | 7.40489e6i | 0.359970 | − | 0.359970i | ||||
\(275\) | 3.52858e6 | 0.169669 | ||||||||
\(276\) | −684619. | − | 684619.i | −0.0325628 | − | 0.0325628i | ||||
\(277\) | −1.77649e6 | + | 1.77649e6i | −0.0835841 | + | 0.0835841i | −0.747663 | − | 0.664079i | \(-0.768824\pi\) |
0.664079 | + | 0.747663i | \(0.268824\pi\) | |||||||
\(278\) | 589876. | + | 589876.i | 0.0274553 | + | 0.0274553i | ||||
\(279\) | −615242. | + | 615242.i | −0.0283291 | + | 0.0283291i | ||||
\(280\) | 8.99118e6i | 0.409583i | ||||||||
\(281\) | −2.20419e7 | − | 2.20419e7i | −0.993411 | − | 0.993411i | 0.00656705 | − | 0.999978i | \(-0.497910\pi\) |
−0.999978 | + | 0.00656705i | \(0.997910\pi\) | |||||||
\(282\) | 979291. | + | 979291.i | 0.0436681 | + | 0.0436681i | ||||
\(283\) | −1.19827e7 | + | 1.19827e7i | −0.528682 | + | 0.528682i | −0.920179 | − | 0.391497i | \(-0.871957\pi\) |
0.391497 | + | 0.920179i | \(0.371957\pi\) | |||||||
\(284\) | − | 1.50452e7i | − | 0.656814i | ||||||
\(285\) | 433629. | 0.0187320 | ||||||||
\(286\) | − | 1.02048e7i | − | 0.436221i | ||||||
\(287\) | − | 4.61215e7i | − | 1.95100i | ||||||
\(288\) | −2.89734e6 | + | 2.89734e6i | −0.121289 | + | 0.121289i | ||||
\(289\) | 2.48279e7i | 1.02860i | ||||||||
\(290\) | −7.12738e6 | + | 7.12738e6i | −0.292238 | + | 0.292238i | ||||
\(291\) | 2.70247e6 | − | 2.70247e6i | 0.109668 | − | 0.109668i | ||||
\(292\) | −646492. | −0.0259666 | ||||||||
\(293\) | 1.05846e7 | 0.420797 | 0.210399 | − | 0.977616i | \(-0.432524\pi\) | ||||
0.210399 | + | 0.977616i | \(0.432524\pi\) | |||||||
\(294\) | −3.74400e6 | − | 3.74400e6i | −0.147331 | − | 0.147331i | ||||
\(295\) | 3.37889e6i | 0.131616i | ||||||||
\(296\) | 8.75075e6 | − | 2.73825e6i | 0.337420 | − | 0.105584i | ||||
\(297\) | 2.98915e6 | 0.114098 | ||||||||
\(298\) | −1.62040e7 | + | 1.62040e7i | −0.612312 | + | 0.612312i | ||||
\(299\) | − | 2.62276e7i | − | 0.981172i | ||||||
\(300\) | 1.17418e6i | 0.0434881i | ||||||||
\(301\) | 5.75408e7 | + | 5.75408e7i | 2.10997 | + | 2.10997i | ||||
\(302\) | 1.80119e7 | + | 1.80119e7i | 0.653941 | + | 0.653941i | ||||
\(303\) | 534758. | 0.0192234 | ||||||||
\(304\) | 767315. | + | 767315.i | 0.0273120 | + | 0.0273120i | ||||
\(305\) | −1.97532e7 | −0.696205 | ||||||||
\(306\) | −2.80001e7 | −0.977228 | ||||||||
\(307\) | 1.92323e7i | 0.664684i | 0.943159 | + | 0.332342i | \(0.107839\pi\) | ||||
−0.943159 | + | 0.332342i | \(0.892161\pi\) | |||||||
\(308\) | 8.08345e6 | 0.276659 | ||||||||
\(309\) | −6.84377e6 | − | 6.84377e6i | −0.231964 | − | 0.231964i | ||||
\(310\) | 432788. | − | 432788.i | 0.0145275 | − | 0.0145275i | ||||
\(311\) | −1.52351e7 | + | 1.52351e7i | −0.506483 | + | 0.506483i | −0.913445 | − | 0.406962i | \(-0.866588\pi\) |
0.406962 | + | 0.913445i | \(0.366588\pi\) | |||||||
\(312\) | 3.39577e6 | 0.111809 | ||||||||
\(313\) | 1.55419e7 | + | 1.55419e7i | 0.506840 | + | 0.506840i | 0.913555 | − | 0.406715i | \(-0.133326\pi\) |
−0.406715 | + | 0.913555i | \(0.633326\pi\) | |||||||
\(314\) | 6.82935e6 | − | 6.82935e6i | 0.220592 | − | 0.220592i | ||||
\(315\) | −2.48437e7 | − | 2.48437e7i | −0.794850 | − | 0.794850i | ||||
\(316\) | 5.08928e6 | − | 5.08928e6i | 0.161285 | − | 0.161285i | ||||
\(317\) | − | 4.24209e6i | − | 0.133169i | −0.997781 | − | 0.0665843i | \(-0.978790\pi\) | ||
0.997781 | − | 0.0665843i | \(-0.0212101\pi\) | |||||||
\(318\) | 476054. | + | 476054.i | 0.0148038 | + | 0.0148038i | ||||
\(319\) | 6.40782e6 | + | 6.40782e6i | 0.197396 | + | 0.197396i | ||||
\(320\) | 2.03812e6 | − | 2.03812e6i | 0.0621985 | − | 0.0621985i | ||||
\(321\) | 2.96019e6i | 0.0894961i | ||||||||
\(322\) | 2.07755e7 | 0.622277 | ||||||||
\(323\) | 7.41539e6i | 0.220053i | ||||||||
\(324\) | − | 1.55066e7i | − | 0.455913i | ||||||
\(325\) | −2.24913e7 | + | 2.24913e7i | −0.655185 | + | 0.655185i | ||||
\(326\) | 1.50822e7i | 0.435324i | ||||||||
\(327\) | −3.29119e6 | + | 3.29119e6i | −0.0941260 | + | 0.0941260i | ||||
\(328\) | −1.04548e7 | + | 1.04548e7i | −0.296275 | + | 0.296275i | ||||
\(329\) | −2.97176e7 | −0.834500 | ||||||||
\(330\) | −1.03551e6 | −0.0288146 | ||||||||
\(331\) | −2.14024e7 | − | 2.14024e7i | −0.590171 | − | 0.590171i | 0.347507 | − | 0.937678i | \(-0.387028\pi\) |
−0.937678 | + | 0.347507i | \(0.887028\pi\) | |||||||
\(332\) | − | 3.70114e6i | − | 0.101140i | ||||||
\(333\) | −1.66133e7 | + | 3.17455e7i | −0.449907 | + | 0.859706i | ||||
\(334\) | 4.56918e7 | 1.22631 | ||||||||
\(335\) | 2.60951e7 | − | 2.60951e7i | 0.694105 | − | 0.694105i | ||||
\(336\) | 2.68987e6i | 0.0709110i | ||||||||
\(337\) | 5.02488e7i | 1.31291i | 0.754364 | + | 0.656456i | \(0.227945\pi\) | ||||
−0.754364 | + | 0.656456i | \(0.772055\pi\) | |||||||
\(338\) | 4.57385e7 | + | 4.57385e7i | 1.18449 | + | 1.18449i | ||||
\(339\) | −4.46780e6 | − | 4.46780e6i | −0.114682 | − | 0.114682i | ||||
\(340\) | 1.96965e7 | 0.501133 | ||||||||
\(341\) | −389095. | − | 389095.i | −0.00981279 | − | 0.00981279i | ||||
\(342\) | −4.24037e6 | −0.106005 | ||||||||
\(343\) | 4.71823e7 | 1.16922 | ||||||||
\(344\) | − | 2.60867e7i | − | 0.640831i | ||||||
\(345\) | −2.66139e6 | −0.0648115 | ||||||||
\(346\) | 3.22937e7 | + | 3.22937e7i | 0.779632 | + | 0.779632i | ||||
\(347\) | 2.40332e7 | − | 2.40332e7i | 0.575206 | − | 0.575206i | −0.358373 | − | 0.933579i | \(-0.616668\pi\) |
0.933579 | + | 0.358373i | \(0.116668\pi\) | |||||||
\(348\) | −2.13228e6 | + | 2.13228e6i | −0.0505949 | + | 0.0505949i | ||||
\(349\) | −2.15497e7 | −0.506950 | −0.253475 | − | 0.967342i | \(-0.581574\pi\) | ||||
−0.253475 | + | 0.967342i | \(0.581574\pi\) | |||||||
\(350\) | −1.78158e7 | − | 1.78158e7i | −0.415530 | − | 0.415530i | ||||
\(351\) | −1.90529e7 | + | 1.90529e7i | −0.440596 | + | 0.440596i | ||||
\(352\) | −1.83236e6 | − | 1.83236e6i | −0.0420128 | − | 0.0420128i | ||||
\(353\) | −5.13793e6 | + | 5.13793e6i | −0.116806 | + | 0.116806i | −0.763094 | − | 0.646288i | \(-0.776321\pi\) |
0.646288 | + | 0.763094i | \(0.276321\pi\) | |||||||
\(354\) | 1.01085e6i | 0.0227866i | ||||||||
\(355\) | −2.92434e7 | − | 2.92434e7i | −0.653646 | − | 0.653646i | ||||
\(356\) | 2.45765e7 | + | 2.45765e7i | 0.544717 | + | 0.544717i | ||||
\(357\) | −1.29975e7 | + | 1.29975e7i | −0.285665 | + | 0.285665i | ||||
\(358\) | − | 5.62515e7i | − | 1.22599i | ||||||
\(359\) | −4.76138e7 | −1.02908 | −0.514540 | − | 0.857466i | \(-0.672037\pi\) | ||||
−0.514540 | + | 0.857466i | \(0.672037\pi\) | |||||||
\(360\) | 1.12632e7i | 0.241409i | ||||||||
\(361\) | − | 4.59229e7i | − | 0.976130i | ||||||
\(362\) | 9.98335e6 | − | 9.98335e6i | 0.210451 | − | 0.210451i | ||||
\(363\) | − | 7.31024e6i | − | 0.152831i | ||||||
\(364\) | −5.15242e7 | + | 5.15242e7i | −1.06833 | + | 1.06833i | ||||
\(365\) | −1.25659e6 | + | 1.25659e6i | −0.0258413 | + | 0.0258413i | ||||
\(366\) | −5.90951e6 | −0.120534 | ||||||||
\(367\) | 3.34092e7 | 0.675877 | 0.337939 | − | 0.941168i | \(-0.390270\pi\) | ||||
0.337939 | + | 0.941168i | \(0.390270\pi\) | |||||||
\(368\) | −4.70939e6 | − | 4.70939e6i | −0.0944977 | − | 0.0944977i | ||||
\(369\) | − | 5.77759e7i | − | 1.14992i | ||||||
\(370\) | 1.16865e7 | − | 2.23312e7i | 0.230717 | − | 0.440867i | ||||
\(371\) | −1.44463e7 | −0.282902 | ||||||||
\(372\) | 129476. | − | 129476.i | 0.00251514 | − | 0.00251514i | ||||
\(373\) | − | 6.45549e7i | − | 1.24395i | −0.783037 | − | 0.621975i | \(-0.786331\pi\) | ||
0.783037 | − | 0.621975i | \(-0.213669\pi\) | |||||||
\(374\) | − | 1.77080e7i | − | 0.338497i | ||||||
\(375\) | 6.80326e6 | + | 6.80326e6i | 0.129010 | + | 0.129010i | ||||
\(376\) | 6.73639e6 | + | 6.73639e6i | 0.126725 | + | 0.126725i | ||||
\(377\) | −8.16872e7 | −1.52451 | ||||||||
\(378\) | −1.50923e7 | − | 1.50923e7i | −0.279434 | − | 0.279434i | ||||
\(379\) | −5.21159e7 | −0.957310 | −0.478655 | − | 0.878003i | \(-0.658875\pi\) | ||||
−0.478655 | + | 0.878003i | \(0.658875\pi\) | |||||||
\(380\) | 2.98287e6 | 0.0543605 | ||||||||
\(381\) | − | 7.62020e6i | − | 0.137782i | ||||||
\(382\) | −7.11097e7 | −1.27567 | ||||||||
\(383\) | 1.81165e7 | + | 1.81165e7i | 0.322462 | + | 0.322462i | 0.849711 | − | 0.527249i | \(-0.176777\pi\) |
−0.527249 | + | 0.849711i | \(0.676777\pi\) | |||||||
\(384\) | 609740. | − | 609740.i | 0.0107684 | − | 0.0107684i | ||||
\(385\) | 1.57118e7 | − | 1.57118e7i | 0.275324 | − | 0.275324i | ||||
\(386\) | 1.44224e7 | 0.250769 | ||||||||
\(387\) | 7.20807e7 | + | 7.20807e7i | 1.24362 | + | 1.24362i | ||||
\(388\) | 1.85898e7 | − | 1.85898e7i | 0.318259 | − | 0.318259i | ||||
\(389\) | −6.35528e6 | − | 6.35528e6i | −0.107966 | − | 0.107966i | 0.651060 | − | 0.759026i | \(-0.274324\pi\) |
−0.759026 | + | 0.651060i | \(0.774324\pi\) | |||||||
\(390\) | 6.60038e6 | − | 6.60038e6i | 0.111269 | − | 0.111269i | ||||
\(391\) | − | 4.55119e7i | − | 0.761368i | ||||||
\(392\) | −2.57544e7 | − | 2.57544e7i | −0.427556 | − | 0.427556i | ||||
\(393\) | 1.14776e7 | + | 1.14776e7i | 0.189092 | + | 0.189092i | ||||
\(394\) | −5.10493e7 | + | 5.10493e7i | −0.834643 | + | 0.834643i | ||||
\(395\) | − | 1.97841e7i | − | 0.321015i | ||||||
\(396\) | 1.01261e7 | 0.163063 | ||||||||
\(397\) | 3.62833e7i | 0.579876i | 0.957046 | + | 0.289938i | \(0.0936346\pi\) | ||||
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(398\) | − | 1.29135e7i | − | 0.204831i | ||||||
\(399\) | −1.96836e6 | + | 1.96836e6i | −0.0309875 | + | 0.0309875i | ||||
\(400\) | 8.07700e6i | 0.126203i | ||||||||
\(401\) | 3.88483e7 | − | 3.88483e7i | 0.602476 | − | 0.602476i | −0.338493 | − | 0.940969i | \(-0.609917\pi\) |
0.940969 | + | 0.338493i | \(0.109917\pi\) | |||||||
\(402\) | 7.80682e6 | − | 7.80682e6i | 0.120170 | − | 0.120170i | ||||
\(403\) | 4.96021e6 | 0.0757852 | ||||||||
\(404\) | 3.67852e6 | 0.0557865 | ||||||||
\(405\) | −3.01402e7 | − | 3.01402e7i | −0.453713 | − | 0.453713i | ||||
\(406\) | − | 6.47063e7i | − | 0.966871i | ||||||
\(407\) | −2.00767e7 | − | 1.05067e7i | −0.297789 | − | 0.155841i | ||||
\(408\) | 5.89257e6 | 0.0867609 | ||||||||
\(409\) | −1.58858e7 | + | 1.58858e7i | −0.232188 | + | 0.232188i | −0.813605 | − | 0.581417i | \(-0.802498\pi\) |
0.581417 | + | 0.813605i | \(0.302498\pi\) | |||||||
\(410\) | 4.06422e7i | 0.589692i | ||||||||
\(411\) | − | 8.61178e6i | − | 0.124042i | ||||||
\(412\) | −4.70772e7 | − | 4.70772e7i | −0.673161 | − | 0.673161i | ||||
\(413\) | −1.53377e7 | − | 1.53377e7i | −0.217726 | − | 0.217726i | ||||
\(414\) | 2.60252e7 | 0.366770 | ||||||||
\(415\) | −7.19391e6 | − | 7.19391e6i | −0.100652 | − | 0.100652i | ||||
\(416\) | 2.33590e7 | 0.324470 | ||||||||
\(417\) | 686018. | 0.00946079 | ||||||||
\(418\) | − | 2.68172e6i | − | 0.0367185i | ||||||
\(419\) | −2.15441e7 | −0.292878 | −0.146439 | − | 0.989220i | \(-0.546781\pi\) | ||||
−0.146439 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(420\) | 5.22831e6 | + | 5.22831e6i | 0.0705689 | + | 0.0705689i | ||||
\(421\) | 1.03580e8 | − | 1.03580e8i | 1.38812 | − | 1.38812i | 0.558865 | − | 0.829258i | \(-0.311237\pi\) |
0.829258 | − | 0.558865i | \(-0.188763\pi\) | |||||||
\(422\) | 2.23461e7 | − | 2.23461e7i | 0.297347 | − | 0.297347i | ||||
\(423\) | −3.72270e7 | −0.491854 | ||||||||
\(424\) | 3.27470e6 | + | 3.27470e6i | 0.0429609 | + | 0.0429609i | ||||
\(425\) | −3.90283e7 | + | 3.90283e7i | −0.508409 | + | 0.508409i | ||||
\(426\) | −8.74867e6 | − | 8.74867e6i | −0.113165 | − | 0.113165i | ||||
\(427\) | 8.96651e7 | − | 8.96651e7i | 1.15170 | − | 1.15170i | ||||
\(428\) | 2.03627e7i | 0.259719i | ||||||||
\(429\) | −5.93402e6 | − | 5.93402e6i | −0.0751583 | − | 0.0751583i | ||||
\(430\) | −5.07048e7 | − | 5.07048e7i | −0.637740 | − | 0.637740i | ||||
\(431\) | −4.17269e7 | + | 4.17269e7i | −0.521176 | + | 0.521176i | −0.917926 | − | 0.396751i | \(-0.870138\pi\) |
0.396751 | + | 0.917926i | \(0.370138\pi\) | |||||||
\(432\) | 6.84223e6i | 0.0848685i | ||||||||
\(433\) | −6.68121e6 | −0.0822984 | −0.0411492 | − | 0.999153i | \(-0.513102\pi\) | ||||
−0.0411492 | + | 0.999153i | \(0.513102\pi\) | |||||||
\(434\) | 3.92909e6i | 0.0480643i | ||||||||
\(435\) | 8.28905e6i | 0.100702i | ||||||||
\(436\) | −2.26396e7 | + | 2.26396e7i | −0.273155 | + | 0.273155i | ||||
\(437\) | − | 6.89237e6i | − | 0.0825894i | ||||||
\(438\) | −375931. | + | 375931.i | −0.00447389 | + | 0.00447389i | ||||
\(439\) | −9.36036e7 | + | 9.36036e7i | −1.10637 | + | 1.10637i | −0.112742 | + | 0.993624i | \(0.535963\pi\) |
−0.993624 | + | 0.112742i | \(0.964037\pi\) | |||||||
\(440\) | −7.12311e6 | −0.0836203 | ||||||||
\(441\) | 1.42325e8 | 1.65945 | ||||||||
\(442\) | 1.12872e8 | + | 1.12872e8i | 1.30713 | + | 1.30713i | ||||
\(443\) | − | 816162.i | − | 0.00938783i | −0.999989 | − | 0.00469392i | \(-0.998506\pi\) | ||
0.999989 | − | 0.00469392i | \(-0.00149413\pi\) | |||||||
\(444\) | 3.49623e6 | − | 6.68078e6i | 0.0399439 | − | 0.0763270i | ||||
\(445\) | 9.55390e7 | 1.08418 | ||||||||
\(446\) | 8.44030e6 | − | 8.44030e6i | 0.0951378 | − | 0.0951378i | ||||
\(447\) | 1.88450e7i | 0.210996i | ||||||||
\(448\) | 1.85032e7i | 0.205784i | ||||||||
\(449\) | −6.58475e7 | − | 6.58475e7i | −0.727446 | − | 0.727446i | 0.242665 | − | 0.970110i | \(-0.421979\pi\) |
−0.970110 | + | 0.242665i | \(0.921979\pi\) | |||||||
\(450\) | −2.23177e7 | − | 2.23177e7i | −0.244913 | − | 0.244913i | ||||
\(451\) | 3.65390e7 | 0.398316 | ||||||||
\(452\) | −3.07333e7 | − | 3.07333e7i | −0.332808 | − | 0.332808i | ||||
\(453\) | 2.09476e7 | 0.225341 | ||||||||
\(454\) | −7.95206e7 | −0.849791 | ||||||||
\(455\) | 2.00295e8i | 2.12636i | ||||||||
\(456\) | 892377. | 0.00941140 | ||||||||
\(457\) | −8.37919e6 | − | 8.37919e6i | −0.0877917 | − | 0.0877917i | 0.661847 | − | 0.749639i | \(-0.269773\pi\) |
−0.749639 | + | 0.661847i | \(0.769773\pi\) | |||||||
\(458\) | 7.58568e7 | − | 7.58568e7i | 0.789583 | − | 0.789583i | ||||
\(459\) | −3.30619e7 | + | 3.30619e7i | −0.341893 | + | 0.341893i | ||||
\(460\) | −1.83073e7 | −0.188084 | ||||||||
\(461\) | −2.79962e7 | − | 2.79962e7i | −0.285756 | − | 0.285756i | 0.549643 | − | 0.835400i | \(-0.314764\pi\) |
−0.835400 | + | 0.549643i | \(0.814764\pi\) | |||||||
\(462\) | 4.70047e6 | − | 4.70047e6i | 0.0476667 | − | 0.0476667i | ||||
\(463\) | 6.92275e7 | + | 6.92275e7i | 0.697486 | + | 0.697486i | 0.963868 | − | 0.266382i | \(-0.0858282\pi\) |
−0.266382 | + | 0.963868i | \(0.585828\pi\) | |||||||
\(464\) | −1.46676e7 | + | 1.46676e7i | −0.146827 | + | 0.146827i | ||||
\(465\) | − | 503327.i | − | 0.00500600i | ||||||
\(466\) | 5.62913e7 | + | 5.62913e7i | 0.556268 | + | 0.556268i | ||||
\(467\) | 5.23779e7 | + | 5.23779e7i | 0.514277 | + | 0.514277i | 0.915834 | − | 0.401557i | \(-0.131531\pi\) |
−0.401557 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(468\) | −6.45438e7 | + | 6.45438e7i | −0.629676 | + | 0.629676i | ||||
\(469\) | 2.36906e8i | 2.29645i | ||||||||
\(470\) | 2.61871e7 | 0.252228 | ||||||||
\(471\) | − | 7.94244e6i | − | 0.0760136i | ||||||
\(472\) | 6.95351e6i | 0.0661269i | ||||||||
\(473\) | −4.55857e7 | + | 4.55857e7i | −0.430770 | + | 0.430770i | ||||
\(474\) | − | 5.91876e6i | − | 0.0555771i | ||||||
\(475\) | −5.91049e6 | + | 5.91049e6i | −0.0551497 | + | 0.0551497i | ||||
\(476\) | −8.94081e7 | + | 8.94081e7i | −0.829002 | + | 0.829002i | ||||
\(477\) | −1.80968e7 | −0.166742 | ||||||||
\(478\) | −5.27619e7 | −0.483099 | ||||||||
\(479\) | −1.18221e7 | − | 1.18221e7i | −0.107570 | − | 0.107570i | 0.651274 | − | 0.758843i | \(-0.274235\pi\) |
−0.758843 | + | 0.651274i | \(0.774235\pi\) | |||||||
\(480\) | − | 2.37031e6i | − | 0.0214329i | ||||||
\(481\) | 1.94939e8 | − | 6.09998e7i | 1.75172 | − | 0.548142i | ||||
\(482\) | −9.97693e7 | −0.890955 | ||||||||
\(483\) | 1.20808e7 | − | 1.20808e7i | 0.107215 | − | 0.107215i | ||||
\(484\) | − | 5.02860e7i | − | 0.443518i | ||||||
\(485\) | − | 7.22662e7i | − | 0.633447i | ||||||
\(486\) | −2.85013e7 | − | 2.85013e7i | −0.248288 | − | 0.248288i | ||||
\(487\) | 4.59488e7 | + | 4.59488e7i | 0.397821 | + | 0.397821i | 0.877464 | − | 0.479643i | \(-0.159234\pi\) |
−0.479643 | + | 0.877464i | \(0.659234\pi\) | |||||||
\(488\) | −4.06506e7 | −0.349790 | ||||||||
\(489\) | 8.77022e6 | + | 8.77022e6i | 0.0750039 | + | 0.0750039i | ||||
\(490\) | −1.00118e8 | −0.850986 | ||||||||
\(491\) | 1.34051e8 | 1.13247 | 0.566233 | − | 0.824245i | \(-0.308400\pi\) | ||||
0.566233 | + | 0.824245i | \(0.308400\pi\) | |||||||
\(492\) | 1.21588e7i | 0.102093i | ||||||||
\(493\) | −1.41749e8 | −1.18299 | ||||||||
\(494\) | 1.70934e7 | + | 1.70934e7i | 0.141791 | + | 0.141791i | ||||
\(495\) | 1.96820e7 | − | 1.96820e7i | 0.162276 | − | 0.162276i | ||||
\(496\) | 890647. | − | 890647.i | 0.00729895 | − | 0.00729895i | ||||
\(497\) | 2.65488e8 | 2.16259 | ||||||||
\(498\) | −2.15219e6 | − | 2.15219e6i | −0.0174258 | − | 0.0174258i | ||||
\(499\) | −2.73371e7 | + | 2.73371e7i | −0.220014 | + | 0.220014i | −0.808504 | − | 0.588490i | \(-0.799723\pi\) |
0.588490 | + | 0.808504i | \(0.299723\pi\) | |||||||
\(500\) | 4.67985e7 | + | 4.67985e7i | 0.374388 | + | 0.374388i | ||||
\(501\) | 2.65695e7 | − | 2.65695e7i | 0.211286 | − | 0.211286i | ||||
\(502\) | 2.46013e7i | 0.194467i | ||||||||
\(503\) | 1.42209e8 | + | 1.42209e8i | 1.11744 | + | 1.11744i | 0.992116 | + | 0.125322i | \(0.0399964\pi\) |
0.125322 | + | 0.992116i | \(0.460004\pi\) | |||||||
\(504\) | −5.11266e7 | − | 5.11266e7i | −0.399351 | − | 0.399351i | ||||
\(505\) | 7.14995e6 | − | 7.14995e6i | 0.0555174 | − | 0.0555174i | ||||
\(506\) | 1.64590e7i | 0.127044i | ||||||||
\(507\) | 5.31932e7 | 0.408162 | ||||||||
\(508\) | − | 5.24181e7i | − | 0.399844i | ||||||
\(509\) | − | 9.38003e7i | − | 0.711297i | −0.934620 | − | 0.355649i | \(-0.884260\pi\) | ||
0.934620 | − | 0.355649i | \(-0.115740\pi\) | |||||||
\(510\) | 1.14534e7 | − | 1.14534e7i | 0.0863424 | − | 0.0863424i | ||||
\(511\) | − | 1.14080e7i | − | 0.0854962i | ||||||
\(512\) | 4.19430e6 | − | 4.19430e6i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.00693e6 | + | 5.00693e6i | −0.0370868 | + | 0.0370868i | ||||
\(514\) | 3.69574e7 | 0.272152 | ||||||||
\(515\) | −1.83008e8 | −1.33983 | ||||||||
\(516\) | −1.51692e7 | − | 1.51692e7i | −0.110412 | − | 0.110412i | ||||
\(517\) | − | 2.35433e7i | − | 0.170371i | ||||||
\(518\) | 4.83193e7 | + | 1.54416e8i | 0.347641 | + | 1.11097i | ||||
\(519\) | 3.75572e7 | 0.268652 | ||||||||
\(520\) | 4.54030e7 | − | 4.54030e7i | 0.322905 | − | 0.322905i | ||||
\(521\) | 1.35717e7i | 0.0959670i | 0.998848 | + | 0.0479835i | \(0.0152795\pi\) | ||||
−0.998848 | + | 0.0479835i | \(0.984721\pi\) | |||||||
\(522\) | − | 8.10569e7i | − | 0.569874i | ||||||
\(523\) | −9.71683e7 | − | 9.71683e7i | −0.679234 | − | 0.679234i | 0.280593 | − | 0.959827i | \(-0.409469\pi\) |
−0.959827 | + | 0.280593i | \(0.909469\pi\) | |||||||
\(524\) | 7.89526e7 | + | 7.89526e7i | 0.548748 | + | 0.548748i | ||||
\(525\) | −2.07196e7 | −0.143187 | ||||||||
\(526\) | −4.24760e7 | − | 4.24760e7i | −0.291868 | − | 0.291868i | ||||
\(527\) | 8.60727e6 | 0.0588076 | ||||||||
\(528\) | −2.13101e6 | −0.0144771 | ||||||||
\(529\) | − | 1.05734e8i | − | 0.714246i | ||||||
\(530\) | 1.27301e7 | 0.0855074 | ||||||||
\(531\) | −1.92134e7 | − | 1.92134e7i | −0.128328 | − | 0.128328i | ||||
\(532\) | −1.35401e7 | + | 1.35401e7i | −0.0899261 | + | 0.0899261i | ||||
\(533\) | −2.32901e8 | + | 2.32901e8i | −1.53812 | + | 1.53812i | ||||
\(534\) | 2.85822e7 | 0.187703 | ||||||||
\(535\) | 3.95790e7 | + | 3.95790e7i | 0.258466 | + | 0.258466i | ||||
\(536\) | 5.37019e7 | − | 5.37019e7i | 0.348735 | − | 0.348735i | ||||
\(537\) | −3.27099e7 | − | 3.27099e7i | −0.211230 | − | 0.211230i | ||||
\(538\) | 7.11487e7 | − | 7.11487e7i | 0.456899 | − | 0.456899i | ||||
\(539\) | 9.00100e7i | 0.574810i | ||||||||
\(540\) | 1.32993e7 | + | 1.32993e7i | 0.0844591 | + | 0.0844591i | ||||
\(541\) | −1.30347e8 | − | 1.30347e8i | −0.823207 | − | 0.823207i | 0.163360 | − | 0.986567i | \(-0.447767\pi\) |
−0.986567 | + | 0.163360i | \(0.947767\pi\) | |||||||
\(542\) | 1.25856e8 | − | 1.25856e8i | 0.790451 | − | 0.790451i | ||||
\(543\) | − | 1.16105e7i | − | 0.0725189i | ||||||
\(544\) | 4.05341e7 | 0.251781 | ||||||||
\(545\) | 8.80092e7i | 0.543674i | ||||||||
\(546\) | 5.99219e7i | 0.368135i | ||||||||
\(547\) | −1.51034e8 | + | 1.51034e8i | −0.922813 | + | 0.922813i | −0.997227 | − | 0.0744148i | \(-0.976291\pi\) |
0.0744148 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(548\) | − | 5.92391e7i | − | 0.359970i | ||||||
\(549\) | 1.12323e8 | − | 1.12323e8i | 0.678813 | − | 0.678813i | ||||
\(550\) | 1.41143e7 | − | 1.41143e7i | 0.0848344 | − | 0.0848344i | ||||
\(551\) | −2.14666e7 | −0.128324 | ||||||||
\(552\) | −5.47696e6 | −0.0325628 | ||||||||
\(553\) | 8.98055e7 | + | 8.98055e7i | 0.531041 | + | 0.531041i | ||||
\(554\) | 1.42119e7i | 0.0835841i | ||||||||
\(555\) | −6.18983e6 | − | 1.97811e7i | −0.0362076 | − | 0.115710i | ||||
\(556\) | 4.71901e6 | 0.0274553 | ||||||||
\(557\) | 9.43010e7 | − | 9.43010e7i | 0.545696 | − | 0.545696i | −0.379497 | − | 0.925193i | \(-0.623903\pi\) |
0.925193 | + | 0.379497i | \(0.123903\pi\) | |||||||
\(558\) | 4.92193e6i | 0.0283291i | ||||||||
\(559\) | − | 5.81130e8i | − | 3.32689i | ||||||
\(560\) | 3.59647e7 | + | 3.59647e7i | 0.204792 | + | 0.204792i | ||||
\(561\) | −1.02971e7 | − | 1.02971e7i | −0.0583212 | − | 0.0583212i | ||||
\(562\) | −1.76335e8 | −0.993411 | ||||||||
\(563\) | −2.14467e8 | − | 2.14467e8i | −1.20181 | − | 1.20181i | −0.973615 | − | 0.228196i | \(-0.926717\pi\) |
−0.228196 | − | 0.973615i | \(-0.573283\pi\) | |||||||
\(564\) | 7.83433e6 | 0.0436681 | ||||||||
\(565\) | −1.19473e8 | −0.662406 | ||||||||
\(566\) | 9.58614e7i | 0.528682i | ||||||||
\(567\) | 2.73630e8 | 1.50112 | ||||||||
\(568\) | −6.01807e7 | − | 6.01807e7i | −0.328407 | − | 0.328407i | ||||
\(569\) | 1.07458e8 | − | 1.07458e8i | 0.583312 | − | 0.583312i | −0.352500 | − | 0.935812i | \(-0.614668\pi\) |
0.935812 | + | 0.352500i | \(0.114668\pi\) | |||||||
\(570\) | 1.73452e6 | − | 1.73452e6i | 0.00936600 | − | 0.00936600i | ||||
\(571\) | −3.58986e8 | −1.92828 | −0.964138 | − | 0.265403i | \(-0.914495\pi\) | ||||
−0.964138 | + | 0.265403i | \(0.914495\pi\) | |||||||
\(572\) | −4.08192e7 | − | 4.08192e7i | −0.218110 | − | 0.218110i | ||||
\(573\) | −4.13498e7 | + | 4.13498e7i | −0.219791 | + | 0.219791i | ||||
\(574\) | −1.84486e8 | − | 1.84486e8i | −0.975501 | − | 0.975501i | ||||
\(575\) | 3.62756e7 | − | 3.62756e7i | 0.190814 | − | 0.190814i | ||||
\(576\) | 2.31788e7i | 0.121289i | ||||||||
\(577\) | −2.06129e8 | − | 2.06129e8i | −1.07303 | − | 1.07303i | −0.997114 | − | 0.0759143i | \(-0.975812\pi\) |
−0.0759143 | − | 0.997114i | \(-0.524188\pi\) | |||||||
\(578\) | 9.93117e7 | + | 9.93117e7i | 0.514301 | + | 0.514301i | ||||
\(579\) | 8.38650e6 | − | 8.38650e6i | 0.0432061 | − | 0.0432061i | ||||
\(580\) | 5.70190e7i | 0.292238i | ||||||||
\(581\) | 6.53103e7 | 0.333007 | ||||||||
\(582\) | − | 2.16197e7i | − | 0.109668i | ||||||
\(583\) | − | 1.14449e7i | − | 0.0577571i | ||||||
\(584\) | −2.58597e6 | + | 2.58597e6i | −0.0129833 | + | 0.0129833i | ||||
\(585\) | 2.50908e8i | 1.25328i | ||||||||
\(586\) | 4.23385e7 | − | 4.23385e7i | 0.210399 | − | 0.210399i | ||||
\(587\) | −1.18964e6 | + | 1.18964e6i | −0.00588167 | + | 0.00588167i | −0.710041 | − | 0.704160i | \(-0.751324\pi\) |
0.704160 | + | 0.710041i | \(0.251324\pi\) | |||||||
\(588\) | −2.99520e7 | −0.147331 | ||||||||
\(589\) | 1.30350e6 | 0.00637916 | ||||||||
\(590\) | 1.35156e7 | + | 1.35156e7i | 0.0658079 | + | 0.0658079i | ||||
\(591\) | 5.93696e7i | 0.287609i | ||||||||
\(592\) | 2.40500e7 | − | 4.59560e7i | 0.115918 | − | 0.221502i | ||||
\(593\) | −2.58098e8 | −1.23772 | −0.618858 | − | 0.785503i | \(-0.712404\pi\) | ||||
−0.618858 | + | 0.785503i | \(0.712404\pi\) | |||||||
\(594\) | 1.19566e7 | − | 1.19566e7i | 0.0570490 | − | 0.0570490i | ||||
\(595\) | 3.47566e8i | 1.65001i | ||||||||
\(596\) | 1.29632e8i | 0.612312i | ||||||||
\(597\) | −7.50914e6 | − | 7.50914e6i | −0.0352913 | − | 0.0352913i | ||||
\(598\) | −1.04910e8 | − | 1.04910e8i | −0.490586 | − | 0.490586i | ||||
\(599\) | −2.47513e8 | −1.15164 | −0.575821 | − | 0.817576i | \(-0.695317\pi\) | ||||
−0.575821 | + | 0.817576i | \(0.695317\pi\) | |||||||
\(600\) | 4.69672e6 | + | 4.69672e6i | 0.0217441 | + | 0.0217441i | ||||
\(601\) | 3.27613e8 | 1.50917 | 0.754585 | − | 0.656202i | \(-0.227838\pi\) | ||||
0.754585 | + | 0.656202i | \(0.227838\pi\) | |||||||
\(602\) | 4.60326e8 | 2.10997 | ||||||||
\(603\) | 2.96770e8i | 1.35353i | ||||||||
\(604\) | 1.44095e8 | 0.653941 | ||||||||
\(605\) | −9.77410e7 | − | 9.77410e7i | −0.441378 | − | 0.441378i | ||||
\(606\) | 2.13903e6 | − | 2.13903e6i | 0.00961169 | − | 0.00961169i | ||||
\(607\) | 2.11040e8 | − | 2.11040e8i | 0.943623 | − | 0.943623i | −0.0548704 | − | 0.998493i | \(-0.517475\pi\) |
0.998493 | + | 0.0548704i | \(0.0174746\pi\) | |||||||
\(608\) | 6.13852e6 | 0.0273120 | ||||||||
\(609\) | −3.76263e7 | − | 3.76263e7i | −0.166586 | − | 0.166586i | ||||
\(610\) | −7.90127e7 | + | 7.90127e7i | −0.348103 | + | 0.348103i | ||||
\(611\) | 1.50066e8 | + | 1.50066e8i | 0.657897 | + | 0.657897i | ||||
\(612\) | −1.12001e8 | + | 1.12001e8i | −0.488614 | + | 0.488614i | ||||
\(613\) | 6.47850e7i | 0.281250i | 0.990063 | + | 0.140625i | \(0.0449113\pi\) | ||||
−0.990063 | + | 0.140625i | \(0.955089\pi\) | |||||||
\(614\) | 7.69291e7 | + | 7.69291e7i | 0.332342 | + | 0.332342i | ||||
\(615\) | 2.36331e7 | + | 2.36331e7i | 0.101601 | + | 0.101601i | ||||
\(616\) | 3.23338e7 | − | 3.23338e7i | 0.138329 | − | 0.138329i | ||||
\(617\) | − | 3.68167e8i | − | 1.56743i | −0.621118 | − | 0.783717i | \(-0.713321\pi\) | ||
0.621118 | − | 0.783717i | \(-0.286679\pi\) | |||||||
\(618\) | −5.47501e7 | −0.231964 | ||||||||
\(619\) | − | 2.12013e8i | − | 0.893905i | −0.894558 | − | 0.446953i | \(-0.852509\pi\) | ||
0.894558 | − | 0.446953i | \(-0.147491\pi\) | |||||||
\(620\) | − | 3.46231e6i | − | 0.0145275i | ||||||
\(621\) | 3.07300e7 | − | 3.07300e7i | 0.128318 | − | 0.128318i | ||||
\(622\) | 1.21881e8i | 0.506483i | ||||||||
\(623\) | −4.33678e8 | + | 4.33678e8i | −1.79351 | + | 1.79351i | ||||
\(624\) | 1.35831e7 | − | 1.35831e7i | 0.0559043 | − | 0.0559043i | ||||
\(625\) | 5.86798e7 | 0.240352 | ||||||||
\(626\) | 1.24335e8 | 0.506840 | ||||||||
\(627\) | −1.55940e6 | − | 1.55940e6i | −0.00632639 | − | 0.00632639i | ||||
\(628\) | − | 5.46348e7i | − | 0.220592i | ||||||
\(629\) | 3.38272e8 | − | 1.05851e8i | 1.35929 | − | 0.425346i | ||||
\(630\) | −1.98750e8 | −0.794850 | ||||||||
\(631\) | −6.06974e7 | + | 6.06974e7i | −0.241592 | + | 0.241592i | −0.817508 | − | 0.575917i | \(-0.804645\pi\) |
0.575917 | + | 0.817508i | \(0.304645\pi\) | |||||||
\(632\) | − | 4.07143e7i | − | 0.161285i | ||||||
\(633\) | − | 2.59882e7i | − | 0.102463i | ||||||
\(634\) | −1.69684e7 | − | 1.69684e7i | −0.0665843 | − | 0.0665843i | ||||
\(635\) | −1.01885e8 | − | 1.01885e8i | −0.397915 | − | 0.397915i | ||||
\(636\) | 3.80843e6 | 0.0148038 | ||||||||
\(637\) | −5.73727e8 | − | 5.73727e8i | −2.21966 | − | 2.21966i | ||||
\(638\) | 5.12625e7 | 0.197396 | ||||||||
\(639\) | 3.32574e8 | 1.27463 | ||||||||
\(640\) | − | 1.63050e7i | − | 0.0621985i | ||||||
\(641\) | −3.13151e8 | −1.18899 | −0.594496 | − | 0.804098i | \(-0.702649\pi\) | ||||
−0.594496 | + | 0.804098i | \(0.702649\pi\) | |||||||
\(642\) | 1.18407e7 | + | 1.18407e7i | 0.0447480 | + | 0.0447480i | ||||
\(643\) | −2.91728e8 | + | 2.91728e8i | −1.09735 | + | 1.09735i | −0.102630 | + | 0.994720i | \(0.532726\pi\) |
−0.994720 | + | 0.102630i | \(0.967274\pi\) | |||||||
\(644\) | 8.31019e7 | − | 8.31019e7i | 0.311138 | − | 0.311138i | ||||
\(645\) | −5.89690e7 | −0.219758 | ||||||||
\(646\) | 2.96616e7 | + | 2.96616e7i | 0.110026 | + | 0.110026i | ||||
\(647\) | −2.72642e8 | + | 2.72642e8i | −1.00665 | + | 1.00665i | −0.00667447 | + | 0.999978i | \(0.502125\pi\) |
−0.999978 | + | 0.00667447i | \(0.997875\pi\) | |||||||
\(648\) | −6.20264e7 | − | 6.20264e7i | −0.227956 | − | 0.227956i | ||||
\(649\) | 1.21511e7 | − | 1.21511e7i | 0.0444508 | − | 0.0444508i | ||||
\(650\) | 1.79930e8i | 0.655185i | ||||||||
\(651\) | 2.28474e6 | + | 2.28474e6i | 0.00828121 | + | 0.00828121i | ||||
\(652\) | 6.03289e7 | + | 6.03289e7i | 0.217662 | + | 0.217662i | ||||
\(653\) | 2.69430e8 | − | 2.69430e8i | 0.967622 | − | 0.967622i | −0.0318702 | − | 0.999492i | \(-0.510146\pi\) |
0.999492 | + | 0.0318702i | \(0.0101463\pi\) | |||||||
\(654\) | 2.63295e7i | 0.0941260i | ||||||||
\(655\) | 3.06921e8 | 1.09220 | ||||||||
\(656\) | 8.36386e7i | 0.296275i | ||||||||
\(657\) | − | 1.42907e7i | − | 0.0503915i | ||||||
\(658\) | −1.18870e8 | + | 1.18870e8i | −0.417250 | + | 0.417250i | ||||
\(659\) | 3.81340e8i | 1.33247i | 0.745743 | + | 0.666233i | \(0.232095\pi\) | ||||
−0.745743 | + | 0.666233i | \(0.767905\pi\) | |||||||
\(660\) | −4.14204e6 | + | 4.14204e6i | −0.0144073 | + | 0.0144073i | ||||
\(661\) | 3.32314e8 | − | 3.32314e8i | 1.15065 | − | 1.15065i | 0.164231 | − | 0.986422i | \(-0.447486\pi\) |
0.986422 | − | 0.164231i | \(-0.0525144\pi\) | |||||||
\(662\) | −1.71219e8 | −0.590171 | ||||||||
\(663\) | 1.31268e8 | 0.450421 | ||||||||
\(664\) | −1.48045e7 | − | 1.48045e7i | −0.0505698 | − | 0.0505698i | ||||
\(665\) | 5.26357e7i | 0.178985i | ||||||||
\(666\) | 6.05291e7 | + | 1.93435e8i | 0.204900 | + | 0.654806i | ||||
\(667\) | 1.31751e8 | 0.443994 | ||||||||
\(668\) | 1.82767e8 | − | 1.82767e8i | 0.613153 | − | 0.613153i | ||||
\(669\) | − | 9.81595e6i | − | 0.0327834i | ||||||
\(670\) | − | 2.08761e8i | − | 0.694105i | ||||||
\(671\) | 7.10357e7 | + | 7.10357e7i | 0.235131 | + | 0.235131i | ||||
\(672\) | 1.07595e7 | + | 1.07595e7i | 0.0354555 | + | 0.0354555i | ||||
\(673\) | −1.69976e8 | −0.557626 | −0.278813 | − | 0.960345i | \(-0.589941\pi\) | ||||
−0.278813 | + | 0.960345i | \(0.589941\pi\) | |||||||
\(674\) | 2.00995e8 | + | 2.00995e8i | 0.656456 | + | 0.656456i | ||||
\(675\) | −5.27045e7 | −0.171371 | ||||||||
\(676\) | 3.65908e8 | 1.18449 | ||||||||
\(677\) | 4.09547e8i | 1.31989i | 0.751315 | + | 0.659944i | \(0.229420\pi\) | ||||
−0.751315 | + | 0.659944i | \(0.770580\pi\) | |||||||
\(678\) | −3.57424e7 | −0.114682 | ||||||||
\(679\) | 3.28036e8 | + | 3.28036e8i | 1.04788 | + | 1.04788i | ||||
\(680\) | 7.87862e7 | − | 7.87862e7i | 0.250567 | − | 0.250567i | ||||
\(681\) | −4.62407e7 | + | 4.62407e7i | −0.146414 | + | 0.146414i | ||||
\(682\) | −3.11276e6 | −0.00981279 | ||||||||
\(683\) | −1.83633e8 | − | 1.83633e8i | −0.576353 | − | 0.576353i | 0.357544 | − | 0.933896i | \(-0.383614\pi\) |
−0.933896 | + | 0.357544i | \(0.883614\pi\) | |||||||
\(684\) | −1.69615e7 | + | 1.69615e7i | −0.0530024 | + | 0.0530024i | ||||
\(685\) | −1.15143e8 | − | 1.15143e8i | −0.358234 | − | 0.358234i | ||||
\(686\) | 1.88729e8 | − | 1.88729e8i | 0.584611 | − | 0.584611i | ||||
\(687\) | − | 8.82204e7i | − | 0.272081i | ||||||
\(688\) | −1.04347e8 | − | 1.04347e8i | −0.320416 | − | 0.320416i | ||||
\(689\) | 7.29500e7 | + | 7.29500e7i | 0.223032 | + | 0.223032i | ||||
\(690\) | −1.06456e7 | + | 1.06456e7i | −0.0324057 | + | 0.0324057i | ||||
\(691\) | − | 1.02763e8i | − | 0.311462i | −0.987800 | − | 0.155731i | \(-0.950227\pi\) | ||
0.987800 | − | 0.155731i | \(-0.0497733\pi\) | |||||||
\(692\) | 2.58350e8 | 0.779632 | ||||||||
\(693\) | 1.78684e8i | 0.536892i | ||||||||
\(694\) | − | 1.92266e8i | − | 0.575206i | ||||||
\(695\) | 9.17236e6 | − | 9.17236e6i | 0.0273229 | − | 0.0273229i | ||||
\(696\) | 1.70583e7i | 0.0505949i | ||||||||
\(697\) | −4.04145e8 | + | 4.04145e8i | −1.19354 | + | 1.19354i | ||||
\(698\) | −8.61989e7 | + | 8.61989e7i | −0.253475 | + | 0.253475i | ||||
\(699\) | 6.54661e7 | 0.191684 | ||||||||
\(700\) | −1.42527e8 | −0.415530 | ||||||||
\(701\) | 1.73047e8 | + | 1.73047e8i | 0.502354 | + | 0.502354i | 0.912169 | − | 0.409815i | \(-0.134407\pi\) |
−0.409815 | + | 0.912169i | \(0.634407\pi\) | |||||||
\(702\) | 1.52424e8i | 0.440596i | ||||||||
\(703\) | 5.12282e7 | − | 1.60302e7i | 0.147450 | − | 0.0461394i | ||||
\(704\) | −1.46589e7 | −0.0420128 | ||||||||
\(705\) | 1.52276e7 | − | 1.52276e7i | 0.0434575 | − | 0.0434575i | ||||
\(706\) | 4.11034e7i | 0.116806i | ||||||||
\(707\) | 6.49112e7i | 0.183680i | ||||||||
\(708\) | 4.04342e6 | + | 4.04342e6i | 0.0113933 | + | 0.0113933i | ||||
\(709\) | 4.64822e8 | + | 4.64822e8i | 1.30421 | + | 1.30421i | 0.925526 | + | 0.378684i | \(0.123623\pi\) |
0.378684 | + | 0.925526i | \(0.376377\pi\) | |||||||
\(710\) | −2.33947e8 | −0.653646 | ||||||||
\(711\) | 1.12498e8 | + | 1.12498e8i | 0.312995 | + | 0.312995i | ||||
\(712\) | 1.96612e8 | 0.544717 | ||||||||
\(713\) | −8.00019e6 | −0.0220715 | ||||||||
\(714\) | 1.03980e8i | 0.285665i | ||||||||
\(715\) | −1.58681e8 | −0.434116 | ||||||||
\(716\) | −2.25006e8 | − | 2.25006e8i | −0.612993 | − | 0.612993i | ||||
\(717\) | −3.06807e7 | + | 3.06807e7i | −0.0832352 | + | 0.0832352i | ||||
\(718\) | −1.90455e8 | + | 1.90455e8i | −0.514540 | + | 0.514540i | ||||
\(719\) | 9.21702e7 | 0.247973 | 0.123986 | − | 0.992284i | \(-0.460432\pi\) | ||||
0.123986 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(720\) | 4.50526e7 | + | 4.50526e7i | 0.120704 | + | 0.120704i | ||||
\(721\) | 8.30725e8 | − | 8.30725e8i | 2.21642 | − | 2.21642i | ||||
\(722\) | −1.83692e8 | − | 1.83692e8i | −0.488065 | − | 0.488065i | ||||
\(723\) | −5.80151e7 | + | 5.80151e7i | −0.153506 | + | 0.153506i | ||||
\(724\) | − | 7.98668e7i | − | 0.210451i | ||||||
\(725\) | −1.12982e8 | − | 1.12982e8i | −0.296480 | − | 0.296480i | ||||
\(726\) | −2.92410e7 | − | 2.92410e7i | −0.0764155 | − | 0.0764155i | ||||
\(727\) | −3.63916e7 | + | 3.63916e7i | −0.0947104 | + | 0.0947104i | −0.752875 | − | 0.658164i | \(-0.771333\pi\) |
0.658164 | + | 0.752875i | \(0.271333\pi\) | |||||||
\(728\) | 4.12193e8i | 1.06833i | ||||||||
\(729\) | 3.20113e8 | 0.826268 | ||||||||
\(730\) | 1.00527e7i | 0.0258413i | ||||||||
\(731\) | − | 1.00841e9i | − | 2.58159i | ||||||
\(732\) | −2.36380e7 | + | 2.36380e7i | −0.0602668 | + | 0.0602668i | ||||
\(733\) | 4.82858e8i | 1.22605i | 0.790064 | + | 0.613024i | \(0.210047\pi\) | ||||
−0.790064 | + | 0.613024i | \(0.789953\pi\) | |||||||
\(734\) | 1.33637e8 | − | 1.33637e8i | 0.337939 | − | 0.337939i | ||||
\(735\) | −5.82178e7 | + | 5.82178e7i | −0.146620 | + | 0.146620i | ||||
\(736\) | −3.76751e7 | −0.0944977 | ||||||||
\(737\) | −1.87685e8 | −0.468843 | ||||||||
\(738\) | −2.31104e8 | − | 2.31104e8i | −0.574960 | − | 0.574960i | ||||
\(739\) | 5.23013e7i | 0.129592i | 0.997899 | + | 0.0647961i | \(0.0206397\pi\) | ||||
−0.997899 | + | 0.0647961i | \(0.979360\pi\) | |||||||
\(740\) | −4.25788e7 | − | 1.36071e8i | −0.105075 | − | 0.335792i | ||||
\(741\) | 1.98794e7 | 0.0488594 | ||||||||
\(742\) | −5.77854e7 | + | 5.77854e7i | −0.141451 | + | 0.141451i | ||||
\(743\) | 8.32627e7i | 0.202994i | 0.994836 | + | 0.101497i | \(0.0323633\pi\) | ||||
−0.994836 | + | 0.101497i | \(0.967637\pi\) | |||||||
\(744\) | − | 1.03581e6i | − | 0.00251514i | ||||||
\(745\) | 2.51966e8 | + | 2.51966e8i | 0.609359 | + | 0.609359i | ||||
\(746\) | −2.58220e8 | − | 2.58220e8i | −0.621975 | − | 0.621975i | ||||
\(747\) | 8.18135e7 | 0.196274 | ||||||||
\(748\) | −7.08321e7 | − | 7.08321e7i | −0.169249 | − | 0.169249i | ||||
\(749\) | −3.59320e8 | −0.855137 | ||||||||
\(750\) | 5.44261e7 | 0.129010 | ||||||||
\(751\) | − | 4.38765e8i | − | 1.03589i | −0.855415 | − | 0.517944i | \(-0.826698\pi\) | ||
0.855415 | − | 0.517944i | \(-0.173302\pi\) | |||||||
\(752\) | 5.38911e7 | 0.126725 | ||||||||
\(753\) | 1.43055e7 | + | 1.43055e7i | 0.0335056 | + | 0.0335056i | ||||
\(754\) | −3.26749e8 | + | 3.26749e8i | −0.762255 | + | 0.762255i | ||||
\(755\) | 2.80078e8 | − | 2.80078e8i | 0.650787 | − | 0.650787i | ||||
\(756\) | −1.20738e8 | −0.279434 | ||||||||
\(757\) | 1.46317e8 | + | 1.46317e8i | 0.337293 | + | 0.337293i | 0.855348 | − | 0.518055i | \(-0.173344\pi\) |
−0.518055 | + | 0.855348i | \(0.673344\pi\) | |||||||
\(758\) | −2.08464e8 | + | 2.08464e8i | −0.478655 | + | 0.478655i | ||||
\(759\) | 9.57082e6 | + | 9.57082e6i | 0.0218889 | + | 0.0218889i | ||||
\(760\) | 1.19315e7 | − | 1.19315e7i | 0.0271802 | − | 0.0271802i | ||||
\(761\) | 5.43738e8i | 1.23377i | 0.787052 | + | 0.616887i | \(0.211606\pi\) | ||||
−0.787052 | + | 0.616887i | \(0.788394\pi\) | |||||||
\(762\) | −3.04808e7 | − | 3.04808e7i | −0.0688908 | − | 0.0688908i | ||||
\(763\) | −3.99498e8 | − | 3.99498e8i | −0.899376 | − | 0.899376i | ||||
\(764\) | −2.84439e8 | + | 2.84439e8i | −0.637835 | + | 0.637835i | ||||
\(765\) | 4.35392e8i | 0.972514i | ||||||||
\(766\) | 1.44932e8 | 0.322462 | ||||||||
\(767\) | 1.54902e8i | 0.343299i | ||||||||
\(768\) | − | 4.87792e6i | − | 0.0107684i | ||||||
\(769\) | −6.06989e8 | + | 6.06989e8i | −1.33476 | + | 1.33476i | −0.433699 | + | 0.901058i | \(0.642792\pi\) |
−0.901058 | + | 0.433699i | \(0.857208\pi\) | |||||||
\(770\) | − | 1.25695e8i | − | 0.275324i | ||||||
\(771\) | 2.14905e7 | − | 2.14905e7i | 0.0468903 | − | 0.0468903i | ||||
\(772\) | 5.76894e7 | − | 5.76894e7i | 0.125385 | − | 0.125385i | ||||
\(773\) | 6.07034e8 | 1.31424 | 0.657120 | − | 0.753786i | \(-0.271775\pi\) | ||||
0.657120 | + | 0.753786i | \(0.271775\pi\) | |||||||
\(774\) | 5.76646e8 | 1.24362 | ||||||||
\(775\) | 6.86049e6 | + | 6.86049e6i | 0.0147384 | + | 0.0147384i | ||||
\(776\) | − | 1.48719e8i | − | 0.318259i | ||||||
\(777\) | 1.17889e8 | + | 6.16945e7i | 0.251311 | + | 0.131517i | ||||
\(778\) | −5.08422e7 | −0.107966 | ||||||||
\(779\) | −6.12041e7 | + | 6.12041e7i | −0.129470 | + | 0.129470i | ||||
\(780\) | − | 5.28030e7i | − | 0.111269i | ||||||
\(781\) | 2.10328e8i | 0.441514i | ||||||||
\(782\) | −1.82047e8 | − | 1.82047e8i | −0.380684 | − | 0.380684i | ||||
\(783\) | −9.57101e7 | − | 9.57101e7i | −0.199376 | − | 0.199376i | ||||
\(784\) | −2.06035e8 | −0.427556 | ||||||||
\(785\) | −1.06194e8 | − | 1.06194e8i | −0.219528 | − | 0.219528i | ||||
\(786\) | 9.18208e7 | 0.189092 | ||||||||
\(787\) | 9.02274e7 | 0.185103 | 0.0925517 | − | 0.995708i | \(-0.470498\pi\) | ||||
0.0925517 | + | 0.995708i | \(0.470498\pi\) | |||||||
\(788\) | 4.08394e8i | 0.834643i | ||||||||
\(789\) | −4.93990e7 | −0.100574 | ||||||||
\(790\) | −7.91364e7 | − | 7.91364e7i | −0.160507 | − | 0.160507i | ||||
\(791\) | 5.42321e8 | − | 5.42321e8i | 1.09579 | − | 1.09579i | ||||
\(792\) | 4.05042e7 | − | 4.05042e7i | 0.0815313 | − | 0.0815313i | ||||
\(793\) | −9.05568e8 | −1.81594 | ||||||||
\(794\) | 1.45133e8 | + | 1.45133e8i | 0.289938 | + | 0.289938i | ||||
\(795\) | 7.40246e6 | − | 7.40246e6i | 0.0147324 | − | 0.0147324i | ||||
\(796\) | −5.16542e7 | − | 5.16542e7i | −0.102416 | − | 0.102416i | ||||
\(797\) | 6.32067e8 | − | 6.32067e8i | 1.24850 | − | 1.24850i | 0.292115 | − | 0.956383i | \(-0.405641\pi\) |
0.956383 | − | 0.292115i | \(-0.0943591\pi\) | |||||||
\(798\) | 1.57469e7i | 0.0309875i | ||||||||
\(799\) | 2.60404e8 | + | 2.60404e8i | 0.510513 | + | 0.510513i | ||||
\(800\) | 3.23080e7 | + | 3.23080e7i | 0.0631015 | + | 0.0631015i | ||||
\(801\) | −5.43264e8 | + | 5.43264e8i | −1.05709 | + | 1.05709i | ||||
\(802\) | − | 3.10787e8i | − | 0.602476i | ||||||
\(803\) | 9.03781e6 | 0.0174549 | ||||||||
\(804\) | − | 6.24546e7i | − | 0.120170i | ||||||
\(805\) | − | 3.23051e8i | − | 0.619275i | ||||||
\(806\) | 1.98408e7 | − | 1.98408e7i | 0.0378926 | − | 0.0378926i | ||||
\(807\) | − | 8.27450e7i | − | 0.157442i | ||||||
\(808\) | 1.47141e7 | − | 1.47141e7i | 0.0278932 | − | 0.0278932i | ||||
\(809\) | 1.03089e8 | − | 1.03089e8i | 0.194701 | − | 0.194701i | −0.603023 | − | 0.797724i | \(-0.706037\pi\) |
0.797724 | + | 0.603023i | \(0.206037\pi\) | |||||||
\(810\) | −2.41122e8 | −0.453713 | ||||||||
\(811\) | −2.99249e8 | −0.561009 | −0.280504 | − | 0.959853i | \(-0.590502\pi\) | ||||
−0.280504 | + | 0.959853i | \(0.590502\pi\) | |||||||
\(812\) | −2.58825e8 | − | 2.58825e8i | −0.483435 | − | 0.483435i | ||||
\(813\) | − | 1.46368e8i | − | 0.272380i | ||||||
\(814\) | −1.22334e8 | + | 3.82802e7i | −0.226815 | + | 0.0709742i | ||||
\(815\) | 2.34523e8 | 0.433224 | ||||||||
\(816\) | 2.35703e7 | − | 2.35703e7i | 0.0433805 | − | 0.0433805i | ||||
\(817\) | − | 1.52715e8i | − | 0.280038i | ||||||
\(818\) | 1.27087e8i | 0.232188i | ||||||||
\(819\) | −1.13894e9 | − | 1.13894e9i | −2.07324 | − | 2.07324i | ||||
\(820\) | 1.62569e8 | + | 1.62569e8i | 0.294846 | + | 0.294846i | ||||
\(821\) | −7.74937e6 | −0.0140035 | −0.00700175 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700175 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(822\) | −3.44471e7 | − | 3.44471e7i | −0.0620208 | − | 0.0620208i | ||||
\(823\) | 4.19229e8 | 0.752058 | 0.376029 | − | 0.926608i | \(-0.377289\pi\) | ||||
0.376029 | + | 0.926608i | \(0.377289\pi\) | |||||||
\(824\) | −3.76618e8 | −0.673161 | ||||||||
\(825\) | − | 1.64148e7i | − | 0.0292330i | ||||||
\(826\) | −1.22702e8 | −0.217726 | ||||||||
\(827\) | 6.29822e8 | + | 6.29822e8i | 1.11353 | + | 1.11353i | 0.992670 | + | 0.120858i | \(0.0385646\pi\) |
0.120858 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(828\) | 1.04101e8 | − | 1.04101e8i | 0.183385 | − | 0.183385i | ||||
\(829\) | −2.06988e8 | + | 2.06988e8i | −0.363314 | + | 0.363314i | −0.865031 | − | 0.501718i | \(-0.832702\pi\) |
0.501718 | + | 0.865031i | \(0.332702\pi\) | |||||||
\(830\) | −5.75513e7 | −0.100652 | ||||||||
\(831\) | 8.26414e6 | + | 8.26414e6i | 0.0144011 | + | 0.0144011i | ||||
\(832\) | 9.34360e7 | − | 9.34360e7i | 0.162235 | − | 0.162235i | ||||
\(833\) | −9.95568e8 | − | 9.95568e8i | −1.72241 | − | 1.72241i | ||||
\(834\) | 2.74407e6 | − | 2.74407e6i | 0.00473040 | − | 0.00473040i | ||||
\(835\) | − | 7.10491e8i | − | 1.22039i | ||||||
\(836\) | −1.07269e7 | − | 1.07269e7i | −0.0183593 | − | 0.0183593i | ||||
\(837\) | 5.81170e6 | + | 5.81170e6i | 0.00991121 | + | 0.00991121i | ||||
\(838\) | −8.61764e7 | + | 8.61764e7i | −0.146439 | + | 0.146439i | ||||
\(839\) | 2.85697e8i | 0.483749i | 0.970308 | + | 0.241875i | \(0.0777623\pi\) | ||||
−0.970308 | + | 0.241875i | \(0.922238\pi\) | |||||||
\(840\) | 4.18265e7 | 0.0705689 | ||||||||
\(841\) | 1.84478e8i | 0.310138i | ||||||||
\(842\) | − | 8.28637e8i | − | 1.38812i | ||||||
\(843\) | −1.02537e8 | + | 1.02537e8i | −0.171159 | + | 0.171159i | ||||
\(844\) | − | 1.78769e8i | − | 0.297347i | ||||||
\(845\) | 7.11216e8 | − | 7.11216e8i | 1.17878 | − | 1.17878i | ||||
\(846\) | −1.48908e8 | + | 1.48908e8i | −0.245927 | + | 0.245927i | ||||
\(847\) | 8.87347e8 | 1.46030 | ||||||||
\(848\) | 2.61976e7 | 0.0429609 | ||||||||
\(849\) | 5.57427e7 | + | 5.57427e7i | 0.0910889 | + | 0.0910889i | ||||
\(850\) | 3.12227e8i | 0.508409i | ||||||||
\(851\) | −3.14413e8 | + | 9.83849e7i | −0.510166 | + | 0.159639i | ||||
\(852\) | −6.99894e7 | −0.113165 | ||||||||
\(853\) | −6.46168e8 | + | 6.46168e8i | −1.04111 | + | 1.04111i | −0.0419961 | + | 0.999118i | \(0.513372\pi\) |
−0.999118 | + | 0.0419961i | \(0.986628\pi\) | |||||||
\(854\) | − | 7.17321e8i | − | 1.15170i | ||||||
\(855\) | 6.59362e7i | 0.105493i | ||||||||
\(856\) | 8.14506e7 | + | 8.14506e7i | 0.129859 | + | 0.129859i | ||||
\(857\) | 1.96760e8 | + | 1.96760e8i | 0.312604 | + | 0.312604i | 0.845918 | − | 0.533313i | \(-0.179053\pi\) |
−0.533313 | + | 0.845918i | \(0.679053\pi\) | |||||||
\(858\) | −4.74721e7 | −0.0751583 | ||||||||
\(859\) | −6.42288e7 | − | 6.42288e7i | −0.101333 | − | 0.101333i | 0.654623 | − | 0.755956i | \(-0.272827\pi\) |
−0.755956 | + | 0.654623i | \(0.772827\pi\) | |||||||
\(860\) | −4.05638e8 | −0.637740 | ||||||||
\(861\) | −2.14555e8 | −0.336147 | ||||||||
\(862\) | 3.33815e8i | 0.521176i | ||||||||
\(863\) | 1.14737e8 | 0.178514 | 0.0892568 | − | 0.996009i | \(-0.471551\pi\) | ||||
0.0892568 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(864\) | 2.73689e7 | + | 2.73689e7i | 0.0424342 | + | 0.0424342i | ||||
\(865\) | 5.02155e8 | − | 5.02155e8i | 0.775872 | − | 0.775872i | ||||
\(866\) | −2.67248e7 | + | 2.67248e7i | −0.0411492 | + | 0.0411492i | ||||
\(867\) | 1.15498e8 | 0.177222 | ||||||||
\(868\) | 1.57164e7 | + | 1.57164e7i | 0.0240322 | + | 0.0240322i | ||||
\(869\) | −7.11470e7 | + | 7.11470e7i | −0.108417 | + | 0.108417i | ||||
\(870\) | 3.31562e7 | + | 3.31562e7i | 0.0503509 | + | 0.0503509i | ||||
\(871\) | 1.19631e9 | − | 1.19631e9i | 1.81046 | − | 1.81046i | ||||
\(872\) | 1.81117e8i | 0.273155i | ||||||||
\(873\) | 4.10928e8 | + | 4.10928e8i | 0.617622 | + | 0.617622i | ||||
\(874\) | −2.75695e7 | − | 2.75695e7i | −0.0412947 | − | 0.0412947i | ||||
\(875\) | −8.25808e8 | + | 8.25808e8i | −1.23269 | + | 1.23269i | ||||
\(876\) | 3.00745e6i | 0.00447389i | ||||||||
\(877\) | 5.99142e7 | 0.0888241 | 0.0444121 | − | 0.999013i | \(-0.485859\pi\) | ||||
0.0444121 | + | 0.999013i | \(0.485859\pi\) | |||||||
\(878\) | 7.48829e8i | 1.10637i | ||||||||
\(879\) | − | 4.92391e7i | − | 0.0725010i | ||||||
\(880\) | −2.84925e7 | + | 2.84925e7i | −0.0418102 | + | 0.0418102i | ||||
\(881\) | − | 3.00403e8i | − | 0.439316i | −0.975577 | − | 0.219658i | \(-0.929506\pi\) | ||
0.975577 | − | 0.219658i | \(-0.0704941\pi\) | |||||||
\(882\) | 5.69300e8 | − | 5.69300e8i | 0.829727 | − | 0.829727i | ||||
\(883\) | −7.28935e8 | + | 7.28935e8i | −1.05878 | + | 1.05878i | −0.0606219 | + | 0.998161i | \(0.519308\pi\) |
−0.998161 | + | 0.0606219i | \(0.980692\pi\) | |||||||
\(884\) | 9.02972e8 | 1.30713 | ||||||||
\(885\) | 1.57184e7 | 0.0226766 | ||||||||
\(886\) | −3.26465e6 | − | 3.26465e6i | −0.00469392 | − | 0.00469392i | ||||
\(887\) | − | 2.27806e8i | − | 0.326434i | −0.986590 | − | 0.163217i | \(-0.947813\pi\) | ||
0.986590 | − | 0.163217i | \(-0.0521870\pi\) | |||||||
\(888\) | −1.27382e7 | − | 4.07080e7i | −0.0181915 | − | 0.0581355i | ||||
\(889\) | 9.24971e8 | 1.31651 | ||||||||
\(890\) | 3.82156e8 | − | 3.82156e8i | 0.542089 | − | 0.542089i | ||||
\(891\) | 2.16779e8i | 0.306467i | ||||||||
\(892\) | − | 6.75224e7i | − | 0.0951378i | ||||||
\(893\) | 3.94359e7 | + | 3.94359e7i | 0.0553780 | + | 0.0553780i | ||||
\(894\) | 7.53801e7 | + | 7.53801e7i | 0.105498 | + | 0.105498i | ||||
\(895\) | −8.74690e8 | −1.22007 | ||||||||
\(896\) | 7.40127e7 | + | 7.40127e7i | 0.102892 | + | 0.102892i | ||||
\(897\) | −1.22009e8 | −0.169050 | ||||||||
\(898\) | −5.26780e8 | −0.727446 | ||||||||
\(899\) | 2.49170e7i | 0.0342939i | ||||||||
\(900\) | −1.78542e8 | −0.244913 | ||||||||
\(901\) | 1.26588e8 | + | 1.26588e8i | 0.173068 | + | 0.173068i | ||||
\(902\) | 1.46156e8 | − | 1.46156e8i | 0.199158 | − | 0.199158i | ||||
\(903\) | 2.67677e8 | − | 2.67677e8i | 0.363536 | − | 0.363536i | ||||
\(904\) | −2.45867e8 | −0.332808 | ||||||||
\(905\) | −1.55237e8 | − | 1.55237e8i | −0.209436 | − | 0.209436i | ||||
\(906\) | 8.37904e7 | − | 8.37904e7i | 0.112670 | − | 0.112670i | ||||
\(907\) | −2.01517e8 | − | 2.01517e8i | −0.270079 | − | 0.270079i | 0.559053 | − | 0.829132i | \(-0.311165\pi\) |
−0.829132 | + | 0.559053i | \(0.811165\pi\) | |||||||
\(908\) | −3.18083e8 | + | 3.18083e8i | −0.424896 | + | 0.424896i | ||||
\(909\) | 8.13136e7i | 0.108261i | ||||||||
\(910\) | 8.01181e8 | + | 8.01181e8i | 1.06318 | + | 1.06318i | ||||
\(911\) | 9.91925e8 | + | 9.91925e8i | 1.31197 | + | 1.31197i | 0.919962 | + | 0.392007i | \(0.128219\pi\) |
0.392007 | + | 0.919962i | \(0.371781\pi\) | |||||||
\(912\) | 3.56951e6 | − | 3.56951e6i | 0.00470570 | − | 0.00470570i | ||||
\(913\) | 5.17410e7i | 0.0679865i | ||||||||
\(914\) | −6.70336e7 | −0.0877917 | ||||||||
\(915\) | 9.18907e7i | 0.119952i | ||||||||
\(916\) | − | 6.06854e8i | − | 0.789583i | ||||||
\(917\) | −1.39320e9 | + | 1.39320e9i | −1.80678 | + | 1.80678i | ||||
\(918\) | 2.64495e8i | 0.341893i | ||||||||
\(919\) | −5.79876e8 | + | 5.79876e8i | −0.747117 | + | 0.747117i | −0.973937 | − | 0.226819i | \(-0.927167\pi\) |
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(920\) | −7.32292e7 | + | 7.32292e7i | −0.0940418 | + | 0.0940418i | ||||
\(921\) | 8.94674e7 | 0.114521 | ||||||||
\(922\) | −2.23969e8 | −0.285756 | ||||||||
\(923\) | −1.34064e9 | − | 1.34064e9i | −1.70493 | − | 1.70493i | ||||
\(924\) | − | 3.76038e7i | − | 0.0476667i | ||||||
\(925\) | 3.53991e8 | + | 1.85253e8i | 0.447267 | + | 0.234067i | ||||
\(926\) | 5.53820e8 | 0.697486 | ||||||||
\(927\) | 1.04064e9 | − | 1.04064e9i | 1.30636 | − | 1.30636i | ||||
\(928\) | 1.17341e8i | 0.146827i | ||||||||
\(929\) | 8.81650e8i | 1.09964i | 0.835285 | + | 0.549818i | \(0.185303\pi\) | ||||
−0.835285 | + | 0.549818i | \(0.814697\pi\) | |||||||
\(930\) | −2.01331e6 | − | 2.01331e6i | −0.00250300 | − | 0.00250300i | ||||
\(931\) | −1.50770e8 | − | 1.50770e8i | −0.186838 | − | 0.186838i | ||||
\(932\) | 4.50331e8 | 0.556268 | ||||||||
\(933\) | 7.08730e7 | + | 7.08730e7i | 0.0872641 | + | 0.0872641i | ||||
\(934\) | 4.19023e8 | 0.514277 | ||||||||
\(935\) | −2.75353e8 | −0.336865 | ||||||||
\(936\) | 5.16350e8i | 0.629676i | ||||||||
\(937\) | −1.24092e9 | −1.50843 | −0.754215 | − | 0.656627i | \(-0.771983\pi\) | ||||
−0.754215 | + | 0.656627i | \(0.771983\pi\) | |||||||
\(938\) | 9.47625e8 | + | 9.47625e8i | 1.14823 | + | 1.14823i | ||||
\(939\) | 7.23000e7 | − | 7.23000e7i | 0.0873256 | − | 0.0873256i | ||||
\(940\) | 1.04748e8 | − | 1.04748e8i | 0.126114 | − | 0.126114i | ||||
\(941\) | 3.40137e8 | 0.408211 | 0.204106 | − | 0.978949i | \(-0.434571\pi\) | ||||
0.204106 | + | 0.978949i | \(0.434571\pi\) | |||||||
\(942\) | −3.17698e7 | − | 3.17698e7i | −0.0380068 | − | 0.0380068i | ||||
\(943\) | 3.75640e8 | − | 3.75640e8i | 0.447957 | − | 0.447957i | ||||
\(944\) | 2.78140e7 | + | 2.78140e7i | 0.0330634 | + | 0.0330634i | ||||
\(945\) | −2.34679e8 | + | 2.34679e8i | −0.278086 | + | 0.278086i | ||||
\(946\) | 3.64686e8i | 0.430770i | ||||||||
\(947\) | 5.10039e8 | + | 5.10039e8i | 0.600556 | + | 0.600556i | 0.940460 | − | 0.339904i | \(-0.110394\pi\) |
−0.339904 | + | 0.940460i | \(0.610394\pi\) | |||||||
\(948\) | −2.36751e7 | − | 2.36751e7i | −0.0277886 | − | 0.0277886i | ||||
\(949\) | −5.76073e7 | + | 5.76073e7i | −0.0674029 | + | 0.0674029i | ||||
\(950\) | 4.72840e7i | 0.0551497i | ||||||||
\(951\) | −1.97340e7 | −0.0229442 | ||||||||
\(952\) | 7.15265e8i | 0.829002i | ||||||||
\(953\) | − | 2.42837e7i | − | 0.0280566i | −0.999902 | − | 0.0140283i | \(-0.995535\pi\) | ||
0.999902 | − | 0.0140283i | \(-0.00446550\pi\) | |||||||
\(954\) | −7.23871e7 | + | 7.23871e7i | −0.0833712 | + | 0.0833712i | ||||
\(955\) | 1.10573e9i | 1.26952i | ||||||||
\(956\) | −2.11047e8 | + | 2.11047e8i | −0.241550 | + | 0.241550i | ||||
\(957\) | 2.98088e7 | − | 2.98088e7i | 0.0340102 | − | 0.0340102i | ||||
\(958\) | −9.45771e7 | −0.107570 | ||||||||
\(959\) | 1.04533e9 | 1.18522 | ||||||||
\(960\) | −9.48123e6 | − | 9.48123e6i | −0.0107164 | − | 0.0107164i | ||||
\(961\) | 8.85991e8i | 0.998295i | ||||||||
\(962\) | 5.35759e8 | − | 1.02376e9i | 0.601789 | − | 1.14993i | ||||
\(963\) | −4.50116e8 | −0.504018 | ||||||||
\(964\) | −3.99077e8 | + | 3.99077e8i | −0.445477 | + | 0.445477i | ||||
\(965\) | − | 2.24262e8i | − | 0.249560i | ||||||
\(966\) | − | 9.66464e7i | − | 0.107215i | ||||||
\(967\) | 9.08688e8 | + | 9.08688e8i | 1.00493 | + | 1.00493i | 0.999988 | + | 0.00494063i | \(0.00157266\pi\) |
0.00494063 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(968\) | −2.01144e8 | − | 2.01144e8i | −0.221759 | − | 0.221759i | ||||
\(969\) | 3.44960e7 | 0.0379138 | ||||||||
\(970\) | −2.89065e8 | − | 2.89065e8i | −0.316724 | − | 0.316724i | ||||
\(971\) | −1.44810e9 | −1.58176 | −0.790879 | − | 0.611973i | \(-0.790376\pi\) | ||||
−0.790879 | + | 0.611973i | \(0.790376\pi\) | |||||||
\(972\) | −2.28010e8 | −0.248288 | ||||||||
\(973\) | 8.32717e7i | 0.0903980i | ||||||||
\(974\) | 3.67591e8 | 0.397821 | ||||||||
\(975\) | 1.04628e8 | + | 1.04628e8i | 0.112885 | + | 0.112885i | ||||
\(976\) | −1.62602e8 | + | 1.62602e8i | −0.174895 | + | 0.174895i | ||||
\(977\) | 1.63465e8 | − | 1.63465e8i | 0.175283 | − | 0.175283i | −0.614013 | − | 0.789296i | \(-0.710446\pi\) |
0.789296 | + | 0.614013i | \(0.210446\pi\) | |||||||
\(978\) | 7.01617e7 | 0.0750039 | ||||||||
\(979\) | −3.43574e8 | − | 3.43574e8i | −0.366162 | − | 0.366162i | ||||
\(980\) | −4.00471e8 | + | 4.00471e8i | −0.425493 | + | 0.425493i | ||||
\(981\) | −5.00447e8 | − | 5.00447e8i | −0.530092 | − | 0.530092i | ||||
\(982\) | 5.36203e8 | − | 5.36203e8i | 0.566233 | − | 0.566233i | ||||
\(983\) | − | 7.18044e8i | − | 0.755946i | −0.925817 | − | 0.377973i | \(-0.876621\pi\) | ||
0.925817 | − | 0.377973i | \(-0.123379\pi\) | |||||||
\(984\) | 4.86353e7 | + | 4.86353e7i | 0.0510465 | + | 0.0510465i | ||||
\(985\) | 7.93797e8 | + | 7.93797e8i | 0.830617 | + | 0.830617i | ||||
\(986\) | −5.66996e8 | + | 5.66996e8i | −0.591493 | + | 0.591493i | ||||
\(987\) | 1.38245e8i | 0.143780i | ||||||||
\(988\) | 1.36747e8 | 0.141791 | ||||||||
\(989\) | 9.37289e8i | 0.968913i | ||||||||
\(990\) | − | 1.57456e8i | − | 0.162276i | ||||||
\(991\) | −5.45227e7 | + | 5.45227e7i | −0.0560217 | + | 0.0560217i | −0.734563 | − | 0.678541i | \(-0.762613\pi\) |
0.678541 | + | 0.734563i | \(0.262613\pi\) | |||||||
\(992\) | − | 7.12517e6i | − | 0.00729895i | ||||||
\(993\) | −9.95626e7 | + | 9.95626e7i | −0.101683 | + | 0.101683i | ||||
\(994\) | 1.06195e9 | − | 1.06195e9i | 1.08130 | − | 1.08130i | ||||
\(995\) | −2.00801e8 | −0.203843 | ||||||||
\(996\) | −1.72175e7 | −0.0174258 | ||||||||
\(997\) | −2.73710e8 | − | 2.73710e8i | −0.276188 | − | 0.276188i | 0.555397 | − | 0.831585i | \(-0.312566\pi\) |
−0.831585 | + | 0.555397i | \(0.812566\pi\) | |||||||
\(998\) | 2.18697e8i | 0.220014i | ||||||||
\(999\) | 2.99875e8 | + | 1.56932e8i | 0.300776 | + | 0.157404i |
(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 | 74.7.d.a.43.5 | yes | 18 | |
37.31 | odd | 4 | inner | 74.7.d.a.31.5 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.a.31.5 | ✓ | 18 | 37.31 | odd | 4 | inner | |
74.7.d.a.43.5 | yes | 18 | 1.1 | even | 1 | trivial |