Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [218,2,Mod(45,218)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(218, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("218.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 218 = 2 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 218.c (of order \(3\), 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: | \(1.74073876406\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 14x^{8} + 6x^{7} + 95x^{6} + 2x^{5} + 231x^{4} + 53x^{3} + 389x^{2} - 76x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 63.4 | ||
Root | \(1.90833 - 3.30532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 218.63 |
Dual form | 218.2.c.c.45.4 |
$q$-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 \(\left(\mathbb{Z}/218\mathbb{Z}\right)^\times\).
\(n\) | \(115\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.09691 | + | 1.89990i | 0.633300 | + | 1.09691i | 0.986873 | + | 0.161501i | \(0.0516336\pi\) |
−0.353572 | + | 0.935407i | \(0.615033\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.908328 | + | 1.57327i | 0.406217 | + | 0.703588i | 0.994462 | − | 0.105095i | \(-0.0335145\pi\) |
−0.588246 | + | 0.808682i | \(0.700181\pi\) | |||||||
\(6\) | 1.09691 | + | 1.89990i | 0.447811 | + | 0.775631i | ||||
\(7\) | −2.27819 | − | 3.94595i | −0.861077 | − | 1.49143i | −0.870891 | − | 0.491476i | \(-0.836457\pi\) |
0.00981431 | − | 0.999952i | \(-0.496876\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.906417 | + | 1.56996i | −0.302139 | + | 0.523320i | ||||
\(10\) | 0.908328 | + | 1.57327i | 0.287239 | + | 0.497512i | ||||
\(11\) | −0.369866 | + | 0.640628i | −0.111519 | + | 0.193156i | −0.916383 | − | 0.400303i | \(-0.868905\pi\) |
0.804864 | + | 0.593459i | \(0.202238\pi\) | |||||||
\(12\) | 1.09691 | + | 1.89990i | 0.316650 | + | 0.548454i | ||||
\(13\) | 0.0935834 | + | 0.162091i | 0.0259554 | + | 0.0449560i | 0.878711 | − | 0.477354i | \(-0.158404\pi\) |
−0.852756 | + | 0.522310i | \(0.825071\pi\) | |||||||
\(14\) | −2.27819 | − | 3.94595i | −0.608873 | − | 1.05460i | ||||
\(15\) | −1.99271 | + | 3.45147i | −0.514514 | + | 0.891165i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.07692 | −0.988799 | −0.494400 | − | 0.869235i | \(-0.664612\pi\) | ||||
−0.494400 | + | 0.869235i | \(0.664612\pi\) | |||||||
\(18\) | −0.906417 | + | 1.56996i | −0.213644 | + | 0.370043i | ||||
\(19\) | −3.64790 | −0.836886 | −0.418443 | − | 0.908243i | \(-0.637424\pi\) | ||||
−0.418443 | + | 0.908243i | \(0.637424\pi\) | |||||||
\(20\) | 0.908328 | + | 1.57327i | 0.203108 | + | 0.351794i | ||||
\(21\) | 4.99794 | − | 8.65669i | 1.09064 | − | 1.88904i | ||||
\(22\) | −0.369866 | + | 0.640628i | −0.0788558 | + | 0.136582i | ||||
\(23\) | −0.810006 | −0.168898 | −0.0844489 | − | 0.996428i | \(-0.526913\pi\) | ||||
−0.0844489 | + | 0.996428i | \(0.526913\pi\) | |||||||
\(24\) | 1.09691 | + | 1.89990i | 0.223906 | + | 0.387816i | ||||
\(25\) | 0.849881 | − | 1.47204i | 0.169976 | − | 0.294407i | ||||
\(26\) | 0.0935834 | + | 0.162091i | 0.0183532 | + | 0.0317887i | ||||
\(27\) | 2.60443 | 0.501222 | ||||||||
\(28\) | −2.27819 | − | 3.94595i | −0.430538 | − | 0.745714i | ||||
\(29\) | 4.03117 | + | 6.98219i | 0.748569 | + | 1.29656i | 0.948509 | + | 0.316751i | \(0.102592\pi\) |
−0.199940 | + | 0.979808i | \(0.564075\pi\) | |||||||
\(30\) | −1.99271 | + | 3.45147i | −0.363817 | + | 0.630149i | ||||
\(31\) | 4.96281 | − | 8.59583i | 0.891346 | − | 1.54386i | 0.0530836 | − | 0.998590i | \(-0.483095\pi\) |
0.838263 | − | 0.545267i | \(-0.183572\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.62284 | −0.282500 | ||||||||
\(34\) | −4.07692 | −0.699187 | ||||||||
\(35\) | 4.13870 | − | 7.16843i | 0.699567 | − | 1.21169i | ||||
\(36\) | −0.906417 | + | 1.56996i | −0.151069 | + | 0.261660i | ||||
\(37\) | 0.869866 | − | 1.50665i | 0.143005 | − | 0.247692i | −0.785622 | − | 0.618707i | \(-0.787657\pi\) |
0.928627 | + | 0.371015i | \(0.120990\pi\) | |||||||
\(38\) | −3.64790 | −0.591768 | ||||||||
\(39\) | −0.205305 | + | 0.355598i | −0.0328751 | + | 0.0569413i | ||||
\(40\) | 0.908328 | + | 1.57327i | 0.143619 | + | 0.248756i | ||||
\(41\) | −8.73179 | −1.36368 | −0.681839 | − | 0.731503i | \(-0.738819\pi\) | ||||
−0.681839 | + | 0.731503i | \(0.738819\pi\) | |||||||
\(42\) | 4.99794 | − | 8.65669i | 0.771199 | − | 1.33576i | ||||
\(43\) | −4.45791 | −0.679824 | −0.339912 | − | 0.940457i | \(-0.610397\pi\) | ||||
−0.339912 | + | 0.940457i | \(0.610397\pi\) | |||||||
\(44\) | −0.369866 | + | 0.640628i | −0.0557595 | + | 0.0965782i | ||||
\(45\) | −3.29329 | −0.490935 | ||||||||
\(46\) | −0.810006 | −0.119429 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 1.09691 | + | 1.89990i | 0.158325 | + | 0.274227i | ||||
\(49\) | −6.88034 | + | 11.9171i | −0.982906 | + | 1.70244i | ||||
\(50\) | 0.849881 | − | 1.47204i | 0.120191 | − | 0.208177i | ||||
\(51\) | −4.47201 | − | 7.74575i | −0.626207 | − | 1.08462i | ||||
\(52\) | 0.0935834 | + | 0.162091i | 0.0129777 | + | 0.0224780i | ||||
\(53\) | 5.34520 | + | 9.25816i | 0.734220 | + | 1.27171i | 0.955065 | + | 0.296398i | \(0.0957853\pi\) |
−0.220845 | + | 0.975309i | \(0.570881\pi\) | |||||||
\(54\) | 2.60443 | 0.354418 | ||||||||
\(55\) | −1.34384 | −0.181203 | ||||||||
\(56\) | −2.27819 | − | 3.94595i | −0.304437 | − | 0.527300i | ||||
\(57\) | −4.00141 | − | 6.93065i | −0.530000 | − | 0.917987i | ||||
\(58\) | 4.03117 | + | 6.98219i | 0.529318 | + | 0.916806i | ||||
\(59\) | 7.10009 | − | 12.2977i | 0.924353 | − | 1.60103i | 0.131753 | − | 0.991283i | \(-0.457939\pi\) |
0.792599 | − | 0.609743i | \(-0.208727\pi\) | |||||||
\(60\) | −1.99271 | + | 3.45147i | −0.257257 | + | 0.445582i | ||||
\(61\) | −0.823951 | − | 1.42712i | −0.105496 | − | 0.182725i | 0.808445 | − | 0.588572i | \(-0.200310\pi\) |
−0.913941 | + | 0.405848i | \(0.866976\pi\) | |||||||
\(62\) | 4.96281 | − | 8.59583i | 0.630277 | − | 1.09167i | ||||
\(63\) | 8.25997 | 1.04066 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.170009 | + | 0.294464i | −0.0210870 | + | 0.0365237i | ||||
\(66\) | −1.62284 | −0.199758 | ||||||||
\(67\) | −6.69049 | + | 11.5883i | −0.817374 | + | 1.41573i | 0.0902372 | + | 0.995920i | \(0.471237\pi\) |
−0.907611 | + | 0.419812i | \(0.862096\pi\) | |||||||
\(68\) | −4.07692 | −0.494400 | ||||||||
\(69\) | −0.888502 | − | 1.53893i | −0.106963 | − | 0.185265i | ||||
\(70\) | 4.13870 | − | 7.16843i | 0.494669 | − | 0.856791i | ||||
\(71\) | 0.883106 | 0.104805 | 0.0524027 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524027 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(72\) | −0.906417 | + | 1.56996i | −0.106822 | + | 0.185022i | ||||
\(73\) | −3.68064 | + | 6.37506i | −0.430786 | + | 0.746144i | −0.996941 | − | 0.0781549i | \(-0.975097\pi\) |
0.566155 | + | 0.824299i | \(0.308430\pi\) | |||||||
\(74\) | 0.869866 | − | 1.50665i | 0.101120 | − | 0.175145i | ||||
\(75\) | 3.72897 | 0.430584 | ||||||||
\(76\) | −3.64790 | −0.418443 | ||||||||
\(77\) | 3.37051 | 0.384105 | ||||||||
\(78\) | −0.205305 | + | 0.355598i | −0.0232462 | + | 0.0402636i | ||||
\(79\) | −6.92767 | + | 11.9991i | −0.779424 | + | 1.35000i | 0.152851 | + | 0.988249i | \(0.451155\pi\) |
−0.932274 | + | 0.361752i | \(0.882179\pi\) | |||||||
\(80\) | 0.908328 | + | 1.57327i | 0.101554 | + | 0.175897i | ||||
\(81\) | 5.57607 | + | 9.65803i | 0.619563 | + | 1.07311i | ||||
\(82\) | −8.73179 | −0.964265 | ||||||||
\(83\) | −2.02926 | − | 3.51477i | −0.222740 | − | 0.385797i | 0.732899 | − | 0.680337i | \(-0.238167\pi\) |
−0.955639 | + | 0.294541i | \(0.904833\pi\) | |||||||
\(84\) | 4.99794 | − | 8.65669i | 0.545320 | − | 0.944522i | ||||
\(85\) | −3.70318 | − | 6.41410i | −0.401667 | − | 0.695707i | ||||
\(86\) | −4.45791 | −0.480708 | ||||||||
\(87\) | −8.84364 | + | 15.3176i | −0.948138 | + | 1.64222i | ||||
\(88\) | −0.369866 | + | 0.640628i | −0.0394279 | + | 0.0682911i | ||||
\(89\) | −1.65727 | − | 2.87047i | −0.175670 | − | 0.304269i | 0.764723 | − | 0.644359i | \(-0.222876\pi\) |
−0.940393 | + | 0.340090i | \(0.889542\pi\) | |||||||
\(90\) | −3.29329 | −0.347144 | ||||||||
\(91\) | 0.426402 | − | 0.738550i | 0.0446991 | − | 0.0774211i | ||||
\(92\) | −0.810006 | −0.0844489 | ||||||||
\(93\) | 21.7750 | 2.25796 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.31349 | − | 5.73913i | −0.339957 | − | 0.588823i | ||||
\(96\) | 1.09691 | + | 1.89990i | 0.111953 | + | 0.193908i | ||||
\(97\) | −1.10547 | − | 1.91473i | −0.112243 | − | 0.194411i | 0.804431 | − | 0.594046i | \(-0.202470\pi\) |
−0.916674 | + | 0.399635i | \(0.869137\pi\) | |||||||
\(98\) | −6.88034 | + | 11.9171i | −0.695019 | + | 1.20381i | ||||
\(99\) | −0.670506 | − | 1.16135i | −0.0673884 | − | 0.116720i | ||||
\(100\) | 0.849881 | − | 1.47204i | 0.0849881 | − | 0.147204i | ||||
\(101\) | 12.0690 | 1.20091 | 0.600454 | − | 0.799659i | \(-0.294986\pi\) | ||||
0.600454 | + | 0.799659i | \(0.294986\pi\) | |||||||
\(102\) | −4.47201 | − | 7.74575i | −0.442795 | − | 0.766944i | ||||
\(103\) | −4.46472 | − | 7.73312i | −0.439922 | − | 0.761967i | 0.557761 | − | 0.830001i | \(-0.311660\pi\) |
−0.997683 | + | 0.0680348i | \(0.978327\pi\) | |||||||
\(104\) | 0.0935834 | + | 0.162091i | 0.00917661 | + | 0.0158943i | ||||
\(105\) | 18.1591 | 1.77214 | ||||||||
\(106\) | 5.34520 | + | 9.25816i | 0.519172 | + | 0.899232i | ||||
\(107\) | 3.02920 | 0.292844 | 0.146422 | − | 0.989222i | \(-0.453224\pi\) | ||||
0.146422 | + | 0.989222i | \(0.453224\pi\) | |||||||
\(108\) | 2.60443 | 0.250611 | ||||||||
\(109\) | 7.93466 | + | 6.78537i | 0.760002 | + | 0.649920i | ||||
\(110\) | −1.34384 | −0.128130 | ||||||||
\(111\) | 3.81666 | 0.362261 | ||||||||
\(112\) | −2.27819 | − | 3.94595i | −0.215269 | − | 0.372857i | ||||
\(113\) | −7.84869 | −0.738342 | −0.369171 | − | 0.929361i | \(-0.620358\pi\) | ||||
−0.369171 | + | 0.929361i | \(0.620358\pi\) | |||||||
\(114\) | −4.00141 | − | 6.93065i | −0.374767 | − | 0.649115i | ||||
\(115\) | −0.735751 | − | 1.27436i | −0.0686091 | − | 0.118834i | ||||
\(116\) | 4.03117 | + | 6.98219i | 0.374284 | + | 0.648280i | ||||
\(117\) | −0.339302 | −0.0313685 | ||||||||
\(118\) | 7.10009 | − | 12.2977i | 0.653616 | − | 1.13210i | ||||
\(119\) | 9.28802 | + | 16.0873i | 0.851432 | + | 1.47472i | ||||
\(120\) | −1.99271 | + | 3.45147i | −0.181908 | + | 0.315074i | ||||
\(121\) | 5.22640 | + | 9.05239i | 0.475127 | + | 0.822944i | ||||
\(122\) | −0.823951 | − | 1.42712i | −0.0745970 | − | 0.129206i | ||||
\(123\) | −9.57798 | − | 16.5895i | −0.863617 | − | 1.49583i | ||||
\(124\) | 4.96281 | − | 8.59583i | 0.445673 | − | 0.771928i | ||||
\(125\) | 12.1712 | 1.08862 | ||||||||
\(126\) | 8.25997 | 0.735857 | ||||||||
\(127\) | 4.76899 | − | 8.26013i | 0.423179 | − | 0.732968i | −0.573069 | − | 0.819507i | \(-0.694247\pi\) |
0.996248 | + | 0.0865390i | \(0.0275807\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.88992 | − | 8.46958i | −0.430533 | − | 0.745705i | ||||
\(130\) | −0.170009 | + | 0.294464i | −0.0149108 | + | 0.0258262i | ||||
\(131\) | −0.0784964 | + | 0.135960i | −0.00685827 | + | 0.0118789i | −0.869434 | − | 0.494049i | \(-0.835516\pi\) |
0.862576 | + | 0.505928i | \(0.168850\pi\) | |||||||
\(132\) | −1.62284 | −0.141250 | ||||||||
\(133\) | 8.31063 | + | 14.3944i | 0.720623 | + | 1.24816i | ||||
\(134\) | −6.69049 | + | 11.5883i | −0.577970 | + | 1.00107i | ||||
\(135\) | 2.36567 | + | 4.09747i | 0.203605 | + | 0.352654i | ||||
\(136\) | −4.07692 | −0.349593 | ||||||||
\(137\) | 4.43617 | + | 7.68367i | 0.379008 | + | 0.656460i | 0.990918 | − | 0.134467i | \(-0.0429321\pi\) |
−0.611911 | + | 0.790927i | \(0.709599\pi\) | |||||||
\(138\) | −0.888502 | − | 1.53893i | −0.0756343 | − | 0.131002i | ||||
\(139\) | −5.56892 | + | 9.64565i | −0.472350 | + | 0.818134i | −0.999499 | − | 0.0316389i | \(-0.989927\pi\) |
0.527150 | + | 0.849772i | \(0.323261\pi\) | |||||||
\(140\) | 4.13870 | − | 7.16843i | 0.349784 | − | 0.605843i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.883106 | 0.0741086 | ||||||||
\(143\) | −0.138453 | −0.0115781 | ||||||||
\(144\) | −0.906417 | + | 1.56996i | −0.0755347 | + | 0.130830i | ||||
\(145\) | −7.32324 | + | 12.6842i | −0.608162 | + | 1.05337i | ||||
\(146\) | −3.68064 | + | 6.37506i | −0.304612 | + | 0.527604i | ||||
\(147\) | −30.1884 | −2.48990 | ||||||||
\(148\) | 0.869866 | − | 1.50665i | 0.0715026 | − | 0.123846i | ||||
\(149\) | −2.92902 | − | 5.07321i | −0.239955 | − | 0.415614i | 0.720746 | − | 0.693199i | \(-0.243799\pi\) |
−0.960701 | + | 0.277585i | \(0.910466\pi\) | |||||||
\(150\) | 3.72897 | 0.304469 | ||||||||
\(151\) | −4.46472 | + | 7.73312i | −0.363333 | + | 0.629312i | −0.988507 | − | 0.151174i | \(-0.951695\pi\) |
0.625174 | + | 0.780486i | \(0.285028\pi\) | |||||||
\(152\) | −3.64790 | −0.295884 | ||||||||
\(153\) | 3.69539 | − | 6.40060i | 0.298755 | − | 0.517458i | ||||
\(154\) | 3.37051 | 0.271604 | ||||||||
\(155\) | 18.0314 | 1.44832 | ||||||||
\(156\) | −0.205305 | + | 0.355598i | −0.0164375 | + | 0.0284707i | ||||
\(157\) | −10.7296 | − | 18.5842i | −0.856313 | − | 1.48318i | −0.875421 | − | 0.483361i | \(-0.839416\pi\) |
0.0191079 | − | 0.999817i | \(-0.493917\pi\) | |||||||
\(158\) | −6.92767 | + | 11.9991i | −0.551136 | + | 0.954595i | ||||
\(159\) | −11.7264 | + | 20.3107i | −0.929964 | + | 1.61074i | ||||
\(160\) | 0.908328 | + | 1.57327i | 0.0718096 | + | 0.124378i | ||||
\(161\) | 1.84535 | + | 3.19624i | 0.145434 | + | 0.251899i | ||||
\(162\) | 5.57607 | + | 9.65803i | 0.438097 | + | 0.758807i | ||||
\(163\) | −9.03968 | −0.708042 | −0.354021 | − | 0.935237i | \(-0.615186\pi\) | ||||
−0.354021 | + | 0.935237i | \(0.615186\pi\) | |||||||
\(164\) | −8.73179 | −0.681839 | ||||||||
\(165\) | −1.47407 | − | 2.55316i | −0.114756 | − | 0.198764i | ||||
\(166\) | −2.02926 | − | 3.51477i | −0.157501 | − | 0.272799i | ||||
\(167\) | −10.3311 | − | 17.8940i | −0.799444 | − | 1.38468i | −0.919978 | − | 0.391969i | \(-0.871794\pi\) |
0.120534 | − | 0.992709i | \(-0.461539\pi\) | |||||||
\(168\) | 4.99794 | − | 8.65669i | 0.385600 | − | 0.667878i | ||||
\(169\) | 6.48248 | − | 11.2280i | 0.498653 | − | 0.863692i | ||||
\(170\) | −3.70318 | − | 6.41410i | −0.284021 | − | 0.491939i | ||||
\(171\) | 3.30652 | − | 5.72706i | 0.252856 | − | 0.437959i | ||||
\(172\) | −4.45791 | −0.339912 | ||||||||
\(173\) | 2.92973 | 0.222743 | 0.111372 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(174\) | −8.84364 | + | 15.3176i | −0.670435 | + | 1.16123i | ||||
\(175\) | −7.74477 | −0.585450 | ||||||||
\(176\) | −0.369866 | + | 0.640628i | −0.0278797 | + | 0.0482891i | ||||
\(177\) | 31.1526 | 2.34157 | ||||||||
\(178\) | −1.65727 | − | 2.87047i | −0.124217 | − | 0.215151i | ||||
\(179\) | −8.12411 | + | 14.0714i | −0.607224 | + | 1.05174i | 0.384472 | + | 0.923137i | \(0.374384\pi\) |
−0.991696 | + | 0.128606i | \(0.958950\pi\) | |||||||
\(180\) | −3.29329 | −0.245468 | ||||||||
\(181\) | −2.51062 | + | 4.34852i | −0.186613 | + | 0.323223i | −0.944119 | − | 0.329605i | \(-0.893084\pi\) |
0.757506 | + | 0.652828i | \(0.226418\pi\) | |||||||
\(182\) | 0.426402 | − | 0.738550i | 0.0316070 | − | 0.0547450i | ||||
\(183\) | 1.80760 | − | 3.13085i | 0.133621 | − | 0.231439i | ||||
\(184\) | −0.810006 | −0.0597144 | ||||||||
\(185\) | 3.16050 | 0.232364 | ||||||||
\(186\) | 21.7750 | 1.59662 | ||||||||
\(187\) | 1.50792 | − | 2.61179i | 0.110270 | − | 0.190993i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.93339 | − | 10.2769i | −0.431591 | − | 0.747537i | ||||
\(190\) | −3.31349 | − | 5.73913i | −0.240386 | − | 0.416361i | ||||
\(191\) | 18.4219 | 1.33296 | 0.666480 | − | 0.745523i | \(-0.267800\pi\) | ||||
0.666480 | + | 0.745523i | \(0.267800\pi\) | |||||||
\(192\) | 1.09691 | + | 1.89990i | 0.0791626 | + | 0.137114i | ||||
\(193\) | 9.25021 | − | 16.0218i | 0.665844 | − | 1.15328i | −0.313211 | − | 0.949683i | \(-0.601405\pi\) |
0.979056 | − | 0.203593i | \(-0.0652619\pi\) | |||||||
\(194\) | −1.10547 | − | 1.91473i | −0.0793681 | − | 0.137470i | ||||
\(195\) | −0.745936 | −0.0534176 | ||||||||
\(196\) | −6.88034 | + | 11.9171i | −0.491453 | + | 0.851221i | ||||
\(197\) | −10.1147 | + | 17.5192i | −0.720642 | + | 1.24819i | 0.240101 | + | 0.970748i | \(0.422819\pi\) |
−0.960743 | + | 0.277440i | \(0.910514\pi\) | |||||||
\(198\) | −0.670506 | − | 1.16135i | −0.0476508 | − | 0.0825336i | ||||
\(199\) | 23.1486 | 1.64096 | 0.820482 | − | 0.571673i | \(-0.193705\pi\) | ||||
0.820482 | + | 0.571673i | \(0.193705\pi\) | |||||||
\(200\) | 0.849881 | − | 1.47204i | 0.0600956 | − | 0.104089i | ||||
\(201\) | −29.3554 | −2.07057 | ||||||||
\(202\) | 12.0690 | 0.849171 | ||||||||
\(203\) | 18.3676 | − | 31.8136i | 1.28915 | − | 2.23287i | ||||
\(204\) | −4.47201 | − | 7.74575i | −0.313103 | − | 0.542311i | ||||
\(205\) | −7.93133 | − | 13.7375i | −0.553948 | − | 0.959467i | ||||
\(206\) | −4.46472 | − | 7.73312i | −0.311072 | − | 0.538792i | ||||
\(207\) | 0.734202 | − | 1.27168i | 0.0510306 | − | 0.0883876i | ||||
\(208\) | 0.0935834 | + | 0.162091i | 0.00648884 | + | 0.0112390i | ||||
\(209\) | 1.34924 | − | 2.33695i | 0.0933286 | − | 0.161650i | ||||
\(210\) | 18.1591 | 1.25310 | ||||||||
\(211\) | −9.85638 | − | 17.0718i | −0.678541 | − | 1.17527i | −0.975420 | − | 0.220353i | \(-0.929279\pi\) |
0.296879 | − | 0.954915i | \(-0.404054\pi\) | |||||||
\(212\) | 5.34520 | + | 9.25816i | 0.367110 | + | 0.635853i | ||||
\(213\) | 0.968686 | + | 1.67781i | 0.0663733 | + | 0.114962i | ||||
\(214\) | 3.02920 | 0.207072 | ||||||||
\(215\) | −4.04924 | − | 7.01349i | −0.276156 | − | 0.478316i | ||||
\(216\) | 2.60443 | 0.177209 | ||||||||
\(217\) | −45.2249 | −3.07007 | ||||||||
\(218\) | 7.93466 | + | 6.78537i | 0.537403 | + | 0.459563i | ||||
\(219\) | −16.1493 | −1.09127 | ||||||||
\(220\) | −1.34384 | −0.0906017 | ||||||||
\(221\) | −0.381532 | − | 0.660833i | −0.0256646 | − | 0.0444525i | ||||
\(222\) | 3.81666 | 0.256157 | ||||||||
\(223\) | −6.26671 | − | 10.8543i | −0.419650 | − | 0.726855i | 0.576254 | − | 0.817270i | \(-0.304514\pi\) |
−0.995904 | + | 0.0904158i | \(0.971180\pi\) | |||||||
\(224\) | −2.27819 | − | 3.94595i | −0.152218 | − | 0.263650i | ||||
\(225\) | 1.54069 | + | 2.66856i | 0.102713 | + | 0.177904i | ||||
\(226\) | −7.84869 | −0.522087 | ||||||||
\(227\) | −10.3730 | + | 17.9666i | −0.688483 | + | 1.19249i | 0.283845 | + | 0.958870i | \(0.408390\pi\) |
−0.972329 | + | 0.233618i | \(0.924944\pi\) | |||||||
\(228\) | −4.00141 | − | 6.93065i | −0.265000 | − | 0.458994i | ||||
\(229\) | −11.8310 | + | 20.4918i | −0.781811 | + | 1.35414i | 0.149074 | + | 0.988826i | \(0.452371\pi\) |
−0.930886 | + | 0.365311i | \(0.880963\pi\) | |||||||
\(230\) | −0.735751 | − | 1.27436i | −0.0485140 | − | 0.0840286i | ||||
\(231\) | 3.69714 | + | 6.40364i | 0.243254 | + | 0.421328i | ||||
\(232\) | 4.03117 | + | 6.98219i | 0.264659 | + | 0.458403i | ||||
\(233\) | 9.34973 | − | 16.1942i | 0.612521 | − | 1.06092i | −0.378293 | − | 0.925686i | \(-0.623489\pi\) |
0.990814 | − | 0.135232i | \(-0.0431780\pi\) | |||||||
\(234\) | −0.339302 | −0.0221809 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.10009 | − | 12.2977i | 0.462176 | − | 0.800513i | ||||
\(237\) | −30.3961 | −1.97444 | ||||||||
\(238\) | 9.28802 | + | 16.0873i | 0.602053 | + | 1.04279i | ||||
\(239\) | 10.4734 | − | 18.1405i | 0.677470 | − | 1.17341i | −0.298271 | − | 0.954481i | \(-0.596410\pi\) |
0.975740 | − | 0.218930i | \(-0.0702568\pi\) | |||||||
\(240\) | −1.99271 | + | 3.45147i | −0.128629 | + | 0.222791i | ||||
\(241\) | 22.1150 | 1.42455 | 0.712276 | − | 0.701900i | \(-0.247664\pi\) | ||||
0.712276 | + | 0.701900i | \(0.247664\pi\) | |||||||
\(242\) | 5.22640 | + | 9.05239i | 0.335966 | + | 0.581909i | ||||
\(243\) | −8.32623 | + | 14.4215i | −0.534128 | + | 0.925137i | ||||
\(244\) | −0.823951 | − | 1.42712i | −0.0527480 | − | 0.0913623i | ||||
\(245\) | −24.9984 | −1.59709 | ||||||||
\(246\) | −9.57798 | − | 16.5895i | −0.610670 | − | 1.05771i | ||||
\(247\) | −0.341383 | − | 0.591293i | −0.0217217 | − | 0.0376230i | ||||
\(248\) | 4.96281 | − | 8.59583i | 0.315138 | − | 0.545836i | ||||
\(249\) | 4.45182 | − | 7.71077i | 0.282122 | − | 0.488650i | ||||
\(250\) | 12.1712 | 0.769772 | ||||||||
\(251\) | 9.23077 | 0.582641 | 0.291320 | − | 0.956626i | \(-0.405905\pi\) | ||||
0.291320 | + | 0.956626i | \(0.405905\pi\) | |||||||
\(252\) | 8.25997 | 0.520329 | ||||||||
\(253\) | 0.299594 | − | 0.518912i | 0.0188353 | − | 0.0326237i | ||||
\(254\) | 4.76899 | − | 8.26013i | 0.299233 | − | 0.518287i | ||||
\(255\) | 8.12411 | − | 14.0714i | 0.508751 | − | 0.881183i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.95863 | − | 15.5168i | 0.558824 | − | 0.967911i | −0.438771 | − | 0.898599i | \(-0.644586\pi\) |
0.997595 | − | 0.0693123i | \(-0.0220805\pi\) | |||||||
\(258\) | −4.88992 | − | 8.46958i | −0.304433 | − | 0.527293i | ||||
\(259\) | −7.92690 | −0.492554 | ||||||||
\(260\) | −0.170009 | + | 0.294464i | −0.0105435 | + | 0.0182619i | ||||
\(261\) | −14.6157 | −0.904687 | ||||||||
\(262\) | −0.0784964 | + | 0.135960i | −0.00484953 | + | 0.00839963i | ||||
\(263\) | −12.0847 | −0.745174 | −0.372587 | − | 0.927997i | \(-0.621529\pi\) | ||||
−0.372587 | + | 0.927997i | \(0.621529\pi\) | |||||||
\(264\) | −1.62284 | −0.0998788 | ||||||||
\(265\) | −9.71039 | + | 16.8189i | −0.596505 | + | 1.03318i | ||||
\(266\) | 8.31063 | + | 14.3944i | 0.509557 | + | 0.882579i | ||||
\(267\) | 3.63574 | − | 6.29729i | 0.222504 | − | 0.385388i | ||||
\(268\) | −6.69049 | + | 11.5883i | −0.408687 | + | 0.707866i | ||||
\(269\) | −1.35123 | − | 2.34040i | −0.0823860 | − | 0.142697i | 0.821888 | − | 0.569649i | \(-0.192921\pi\) |
−0.904274 | + | 0.426952i | \(0.859587\pi\) | |||||||
\(270\) | 2.36567 | + | 4.09747i | 0.143970 | + | 0.249364i | ||||
\(271\) | 11.1822 | + | 19.3682i | 0.679273 | + | 1.17654i | 0.975200 | + | 0.221325i | \(0.0710381\pi\) |
−0.295927 | + | 0.955211i | \(0.595629\pi\) | |||||||
\(272\) | −4.07692 | −0.247200 | ||||||||
\(273\) | 1.87090 | 0.113232 | ||||||||
\(274\) | 4.43617 | + | 7.68367i | 0.267999 | + | 0.464188i | ||||
\(275\) | 0.628685 | + | 1.08891i | 0.0379111 | + | 0.0656640i | ||||
\(276\) | −0.888502 | − | 1.53893i | −0.0534815 | − | 0.0926327i | ||||
\(277\) | 1.86971 | − | 3.23843i | 0.112340 | − | 0.194578i | −0.804373 | − | 0.594124i | \(-0.797499\pi\) |
0.916713 | + | 0.399546i | \(0.130832\pi\) | |||||||
\(278\) | −5.56892 | + | 9.64565i | −0.334002 | + | 0.578508i | ||||
\(279\) | 8.99674 | + | 15.5828i | 0.538621 | + | 0.932918i | ||||
\(280\) | 4.13870 | − | 7.16843i | 0.247334 | − | 0.428396i | ||||
\(281\) | −18.0874 | −1.07900 | −0.539502 | − | 0.841984i | \(-0.681387\pi\) | ||||
−0.539502 | + | 0.841984i | \(0.681387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.08906 | − | 3.61835i | 0.124181 | − | 0.215089i | −0.797231 | − | 0.603674i | \(-0.793703\pi\) |
0.921413 | + | 0.388585i | \(0.127036\pi\) | |||||||
\(284\) | 0.883106 | 0.0524027 | ||||||||
\(285\) | 7.26919 | − | 12.5906i | 0.430590 | − | 0.745803i | ||||
\(286\) | −0.138453 | −0.00818692 | ||||||||
\(287\) | 19.8927 | + | 34.4552i | 1.17423 | + | 2.03383i | ||||
\(288\) | −0.906417 | + | 1.56996i | −0.0534111 | + | 0.0925108i | ||||
\(289\) | −0.378700 | −0.0222765 | ||||||||
\(290\) | −7.32324 | + | 12.6842i | −0.430036 | + | 0.744844i | ||||
\(291\) | 2.42520 | − | 4.20057i | 0.142168 | − | 0.246242i | ||||
\(292\) | −3.68064 | + | 6.37506i | −0.215393 | + | 0.373072i | ||||
\(293\) | −7.24950 | −0.423520 | −0.211760 | − | 0.977322i | \(-0.567920\pi\) | ||||
−0.211760 | + | 0.977322i | \(0.567920\pi\) | |||||||
\(294\) | −30.1884 | −1.76062 | ||||||||
\(295\) | 25.7968 | 1.50195 | ||||||||
\(296\) | 0.869866 | − | 1.50665i | 0.0505600 | − | 0.0875724i | ||||
\(297\) | −0.963290 | + | 1.66847i | −0.0558958 | + | 0.0968143i | ||||
\(298\) | −2.92902 | − | 5.07321i | −0.169674 | − | 0.293883i | ||||
\(299\) | −0.0758031 | − | 0.131295i | −0.00438380 | − | 0.00759297i | ||||
\(300\) | 3.72897 | 0.215292 | ||||||||
\(301\) | 10.1560 | + | 17.5907i | 0.585381 | + | 1.01391i | ||||
\(302\) | −4.46472 | + | 7.73312i | −0.256916 | + | 0.444991i | ||||
\(303\) | 13.2386 | + | 22.9299i | 0.760536 | + | 1.31729i | ||||
\(304\) | −3.64790 | −0.209221 | ||||||||
\(305\) | 1.49683 | − | 2.59259i | 0.0857085 | − | 0.148451i | ||||
\(306\) | 3.69539 | − | 6.40060i | 0.211251 | − | 0.365898i | ||||
\(307\) | −12.2735 | − | 21.2584i | −0.700487 | − | 1.21328i | −0.968296 | − | 0.249806i | \(-0.919633\pi\) |
0.267809 | − | 0.963472i | \(-0.413700\pi\) | |||||||
\(308\) | 3.37051 | 0.192053 | ||||||||
\(309\) | 9.79477 | − | 16.9650i | 0.557205 | − | 0.965108i | ||||
\(310\) | 18.0314 | 1.02412 | ||||||||
\(311\) | 18.0129 | 1.02142 | 0.510708 | − | 0.859754i | \(-0.329383\pi\) | ||||
0.510708 | + | 0.859754i | \(0.329383\pi\) | |||||||
\(312\) | −0.205305 | + | 0.355598i | −0.0116231 | + | 0.0201318i | ||||
\(313\) | 0.664077 | + | 1.15021i | 0.0375358 | + | 0.0650140i | 0.884183 | − | 0.467141i | \(-0.154716\pi\) |
−0.846647 | + | 0.532155i | \(0.821382\pi\) | |||||||
\(314\) | −10.7296 | − | 18.5842i | −0.605505 | − | 1.04877i | ||||
\(315\) | 7.50276 | + | 12.9952i | 0.422733 | + | 0.732195i | ||||
\(316\) | −6.92767 | + | 11.9991i | −0.389712 | + | 0.675001i | ||||
\(317\) | −2.88508 | − | 4.99710i | −0.162042 | − | 0.280665i | 0.773559 | − | 0.633725i | \(-0.218475\pi\) |
−0.935601 | + | 0.353059i | \(0.885141\pi\) | |||||||
\(318\) | −11.7264 | + | 20.3107i | −0.657584 | + | 1.13897i | ||||
\(319\) | −5.96397 | −0.333918 | ||||||||
\(320\) | 0.908328 | + | 1.57327i | 0.0507771 | + | 0.0879485i | ||||
\(321\) | 3.32276 | + | 5.75519i | 0.185458 | + | 0.321223i | ||||
\(322\) | 1.84535 | + | 3.19624i | 0.102837 | + | 0.178119i | ||||
\(323\) | 14.8722 | 0.827512 | ||||||||
\(324\) | 5.57607 | + | 9.65803i | 0.309782 | + | 0.536557i | ||||
\(325\) | 0.318139 | 0.0176472 | ||||||||
\(326\) | −9.03968 | −0.500661 | ||||||||
\(327\) | −4.18794 | + | 22.5180i | −0.231593 | + | 1.24525i | ||||
\(328\) | −8.73179 | −0.482133 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.47407 | − | 2.55316i | −0.0811449 | − | 0.140547i | ||||
\(331\) | 33.1868 | 1.82411 | 0.912057 | − | 0.410064i | \(-0.134494\pi\) | ||||
0.912057 | + | 0.410064i | \(0.134494\pi\) | |||||||
\(332\) | −2.02926 | − | 3.51477i | −0.111370 | − | 0.192898i | ||||
\(333\) | 1.57692 | + | 2.73131i | 0.0864148 | + | 0.149675i | ||||
\(334\) | −10.3311 | − | 17.8940i | −0.565293 | − | 0.979115i | ||||
\(335\) | −24.3086 | −1.32812 | ||||||||
\(336\) | 4.99794 | − | 8.65669i | 0.272660 | − | 0.472261i | ||||
\(337\) | −0.547183 | − | 0.947748i | −0.0298069 | − | 0.0516271i | 0.850737 | − | 0.525591i | \(-0.176156\pi\) |
−0.880544 | + | 0.473964i | \(0.842823\pi\) | |||||||
\(338\) | 6.48248 | − | 11.2280i | 0.352601 | − | 0.610722i | ||||
\(339\) | −8.60929 | − | 14.9117i | −0.467593 | − | 0.809894i | ||||
\(340\) | −3.70318 | − | 6.41410i | −0.200833 | − | 0.347853i | ||||
\(341\) | 3.67115 | + | 6.35862i | 0.198804 | + | 0.344339i | ||||
\(342\) | 3.30652 | − | 5.72706i | 0.178796 | − | 0.309684i | ||||
\(343\) | 30.8043 | 1.66327 | ||||||||
\(344\) | −4.45791 | −0.240354 | ||||||||
\(345\) | 1.61410 | − | 2.79571i | 0.0869003 | − | 0.150516i | ||||
\(346\) | 2.92973 | 0.157503 | ||||||||
\(347\) | 16.0397 | + | 27.7816i | 0.861058 | + | 1.49140i | 0.870909 | + | 0.491444i | \(0.163531\pi\) |
−0.00985130 | + | 0.999951i | \(0.503136\pi\) | |||||||
\(348\) | −8.84364 | + | 15.3176i | −0.474069 | + | 0.821112i | ||||
\(349\) | 13.4131 | − | 23.2321i | 0.717986 | − | 1.24359i | −0.243811 | − | 0.969823i | \(-0.578398\pi\) |
0.961797 | − | 0.273765i | \(-0.0882690\pi\) | |||||||
\(350\) | −7.74477 | −0.413976 | ||||||||
\(351\) | 0.243731 | + | 0.422155i | 0.0130094 | + | 0.0225329i | ||||
\(352\) | −0.369866 | + | 0.640628i | −0.0197139 | + | 0.0341456i | ||||
\(353\) | 7.92894 | + | 13.7333i | 0.422015 | + | 0.730951i | 0.996136 | − | 0.0878191i | \(-0.0279897\pi\) |
−0.574122 | + | 0.818770i | \(0.694656\pi\) | |||||||
\(354\) | 31.1526 | 1.65574 | ||||||||
\(355\) | 0.802150 | + | 1.38936i | 0.0425737 | + | 0.0737398i | ||||
\(356\) | −1.65727 | − | 2.87047i | −0.0878350 | − | 0.152135i | ||||
\(357\) | −20.3762 | + | 35.2927i | −1.07842 | + | 1.86789i | ||||
\(358\) | −8.12411 | + | 14.0714i | −0.429372 | + | 0.743695i | ||||
\(359\) | 11.8615 | 0.626028 | 0.313014 | − | 0.949748i | \(-0.398661\pi\) | ||||
0.313014 | + | 0.949748i | \(0.398661\pi\) | |||||||
\(360\) | −3.29329 | −0.173572 | ||||||||
\(361\) | −5.69282 | −0.299622 | ||||||||
\(362\) | −2.51062 | + | 4.34852i | −0.131955 | + | 0.228553i | ||||
\(363\) | −11.4658 | + | 19.8593i | −0.601796 | + | 1.04234i | ||||
\(364\) | 0.426402 | − | 0.738550i | 0.0223496 | − | 0.0387106i | ||||
\(365\) | −13.3729 | −0.699970 | ||||||||
\(366\) | 1.80760 | − | 3.13085i | 0.0944846 | − | 0.163652i | ||||
\(367\) | −10.4807 | − | 18.1531i | −0.547087 | − | 0.947582i | −0.998472 | − | 0.0552529i | \(-0.982403\pi\) |
0.451386 | − | 0.892329i | \(-0.350930\pi\) | |||||||
\(368\) | −0.810006 | −0.0422245 | ||||||||
\(369\) | 7.91464 | − | 13.7086i | 0.412020 | − | 0.713639i | ||||
\(370\) | 3.16050 | 0.164306 | ||||||||
\(371\) | 24.3548 | − | 42.1838i | 1.26444 | − | 2.19007i | ||||
\(372\) | 21.7750 | 1.12898 | ||||||||
\(373\) | 23.6208 | 1.22304 | 0.611520 | − | 0.791229i | \(-0.290558\pi\) | ||||
0.611520 | + | 0.791229i | \(0.290558\pi\) | |||||||
\(374\) | 1.50792 | − | 2.61179i | 0.0779725 | − | 0.135052i | ||||
\(375\) | 13.3507 | + | 23.1240i | 0.689425 | + | 1.19412i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.754500 | + | 1.30683i | −0.0388587 | + | 0.0673053i | ||||
\(378\) | −5.93339 | − | 10.2769i | −0.305181 | − | 0.528588i | ||||
\(379\) | −4.12753 | − | 7.14909i | −0.212017 | − | 0.367224i | 0.740329 | − | 0.672245i | \(-0.234670\pi\) |
−0.952346 | + | 0.305021i | \(0.901336\pi\) | |||||||
\(380\) | −3.31349 | − | 5.73913i | −0.169978 | − | 0.294411i | ||||
\(381\) | 20.9246 | 1.07200 | ||||||||
\(382\) | 18.4219 | 0.942545 | ||||||||
\(383\) | 5.50001 | + | 9.52630i | 0.281038 | + | 0.486771i | 0.971641 | − | 0.236463i | \(-0.0759881\pi\) |
−0.690603 | + | 0.723234i | \(0.742655\pi\) | |||||||
\(384\) | 1.09691 | + | 1.89990i | 0.0559764 | + | 0.0969539i | ||||
\(385\) | 3.06153 | + | 5.30272i | 0.156030 | + | 0.270252i | ||||
\(386\) | 9.25021 | − | 16.0218i | 0.470823 | − | 0.815489i | ||||
\(387\) | 4.04072 | − | 6.99873i | 0.205401 | − | 0.355766i | ||||
\(388\) | −1.10547 | − | 1.91473i | −0.0561217 | − | 0.0972057i | ||||
\(389\) | 8.79667 | − | 15.2363i | 0.446009 | − | 0.772510i | −0.552113 | − | 0.833769i | \(-0.686178\pi\) |
0.998122 | + | 0.0612592i | \(0.0195116\pi\) | |||||||
\(390\) | −0.745936 | −0.0377720 | ||||||||
\(391\) | 3.30233 | 0.167006 | ||||||||
\(392\) | −6.88034 | + | 11.9171i | −0.347510 | + | 0.601904i | ||||
\(393\) | −0.344414 | −0.0173734 | ||||||||
\(394\) | −10.1147 | + | 17.5192i | −0.509571 | + | 0.882602i | ||||
\(395\) | −25.1704 | −1.26646 | ||||||||
\(396\) | −0.670506 | − | 1.16135i | −0.0336942 | − | 0.0583601i | ||||
\(397\) | 5.74007 | − | 9.94209i | 0.288086 | − | 0.498979i | −0.685267 | − | 0.728292i | \(-0.740314\pi\) |
0.973353 | + | 0.229313i | \(0.0736478\pi\) | |||||||
\(398\) | 23.1486 | 1.16034 | ||||||||
\(399\) | −18.2320 | + | 31.5787i | −0.912741 | + | 1.58091i | ||||
\(400\) | 0.849881 | − | 1.47204i | 0.0424940 | − | 0.0736018i | ||||
\(401\) | −2.03569 | + | 3.52593i | −0.101658 | + | 0.176076i | −0.912368 | − | 0.409372i | \(-0.865748\pi\) |
0.810710 | + | 0.585448i | \(0.199081\pi\) | |||||||
\(402\) | −29.3554 | −1.46412 | ||||||||
\(403\) | 1.85774 | 0.0925408 | ||||||||
\(404\) | 12.0690 | 0.600454 | ||||||||
\(405\) | −10.1298 | + | 17.5453i | −0.503354 | + | 0.871834i | ||||
\(406\) | 18.3676 | − | 31.8136i | 0.911567 | − | 1.57888i | ||||
\(407\) | 0.643469 | + | 1.11452i | 0.0318956 | + | 0.0552447i | ||||
\(408\) | −4.47201 | − | 7.74575i | −0.221398 | − | 0.383472i | ||||
\(409\) | 3.60651 | 0.178331 | 0.0891653 | − | 0.996017i | \(-0.471580\pi\) | ||||
0.0891653 | + | 0.996017i | \(0.471580\pi\) | |||||||
\(410\) | −7.93133 | − | 13.7375i | −0.391701 | − | 0.678445i | ||||
\(411\) | −9.73214 | + | 16.8566i | −0.480051 | + | 0.831473i | ||||
\(412\) | −4.46472 | − | 7.73312i | −0.219961 | − | 0.380983i | ||||
\(413\) | −64.7015 | −3.18375 | ||||||||
\(414\) | 0.734202 | − | 1.27168i | 0.0360841 | − | 0.0624995i | ||||
\(415\) | 3.68646 | − | 6.38513i | 0.180961 | − | 0.313434i | ||||
\(416\) | 0.0935834 | + | 0.162091i | 0.00458830 | + | 0.00794717i | ||||
\(417\) | −24.4344 | −1.19656 | ||||||||
\(418\) | 1.34924 | − | 2.33695i | 0.0659933 | − | 0.114304i | ||||
\(419\) | −25.7552 | −1.25822 | −0.629111 | − | 0.777316i | \(-0.716581\pi\) | ||||
−0.629111 | + | 0.777316i | \(0.716581\pi\) | |||||||
\(420\) | 18.1591 | 0.886072 | ||||||||
\(421\) | −0.209884 | + | 0.363530i | −0.0102291 | + | 0.0177174i | −0.871095 | − | 0.491115i | \(-0.836589\pi\) |
0.860866 | + | 0.508833i | \(0.169923\pi\) | |||||||
\(422\) | −9.85638 | − | 17.0718i | −0.479801 | − | 0.831040i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.34520 | + | 9.25816i | 0.259586 | + | 0.449616i | ||||
\(425\) | −3.46490 | + | 6.00138i | −0.168072 | + | 0.291110i | ||||
\(426\) | 0.968686 | + | 1.67781i | 0.0469330 | + | 0.0812903i | ||||
\(427\) | −3.75424 | + | 6.50253i | −0.181680 | + | 0.314680i | ||||
\(428\) | 3.02920 | 0.146422 | ||||||||
\(429\) | −0.151871 | − | 0.263048i | −0.00733239 | − | 0.0127001i | ||||
\(430\) | −4.04924 | − | 7.01349i | −0.195272 | − | 0.338221i | ||||
\(431\) | −8.80723 | − | 15.2546i | −0.424229 | − | 0.734786i | 0.572119 | − | 0.820171i | \(-0.306122\pi\) |
−0.996348 | + | 0.0853842i | \(0.972788\pi\) | |||||||
\(432\) | 2.60443 | 0.125306 | ||||||||
\(433\) | 2.38588 | + | 4.13247i | 0.114658 | + | 0.198594i | 0.917643 | − | 0.397406i | \(-0.130089\pi\) |
−0.802985 | + | 0.595999i | \(0.796756\pi\) | |||||||
\(434\) | −45.2249 | −2.17087 | ||||||||
\(435\) | −32.1317 | −1.54060 | ||||||||
\(436\) | 7.93466 | + | 6.78537i | 0.380001 | + | 0.324960i | ||||
\(437\) | 2.95482 | 0.141348 | ||||||||
\(438\) | −16.1493 | −0.771644 | ||||||||
\(439\) | −6.74066 | − | 11.6752i | −0.321714 | − | 0.557225i | 0.659128 | − | 0.752031i | \(-0.270926\pi\) |
−0.980842 | + | 0.194806i | \(0.937592\pi\) | |||||||
\(440\) | −1.34384 | −0.0640651 | ||||||||
\(441\) | −12.4729 | − | 21.6037i | −0.593948 | − | 1.02875i | ||||
\(442\) | −0.381532 | − | 0.660833i | −0.0181476 | − | 0.0314326i | ||||
\(443\) | −5.77644 | − | 10.0051i | −0.274447 | − | 0.475356i | 0.695548 | − | 0.718479i | \(-0.255161\pi\) |
−0.969995 | + | 0.243123i | \(0.921828\pi\) | |||||||
\(444\) | 3.81666 | 0.181130 | ||||||||
\(445\) | 3.01068 | − | 5.21466i | 0.142720 | − | 0.247198i | ||||
\(446\) | −6.26671 | − | 10.8543i | −0.296737 | − | 0.513964i | ||||
\(447\) | 6.42574 | − | 11.1297i | 0.303927 | − | 0.526417i | ||||
\(448\) | −2.27819 | − | 3.94595i | −0.107635 | − | 0.186429i | ||||
\(449\) | −7.00968 | − | 12.1411i | −0.330807 | − | 0.572975i | 0.651863 | − | 0.758337i | \(-0.273988\pi\) |
−0.982670 | + | 0.185362i | \(0.940654\pi\) | |||||||
\(450\) | 1.54069 | + | 2.66856i | 0.0726289 | + | 0.125797i | ||||
\(451\) | 3.22960 | − | 5.59383i | 0.152076 | − | 0.263403i | ||||
\(452\) | −7.84869 | −0.369171 | ||||||||
\(453\) | −19.5895 | −0.920397 | ||||||||
\(454\) | −10.3730 | + | 17.9666i | −0.486831 | + | 0.843216i | ||||
\(455\) | 1.54925 | 0.0726301 | ||||||||
\(456\) | −4.00141 | − | 6.93065i | −0.187383 | − | 0.324558i | ||||
\(457\) | 17.1130 | − | 29.6405i | 0.800510 | − | 1.38652i | −0.118770 | − | 0.992922i | \(-0.537895\pi\) |
0.919281 | − | 0.393603i | \(-0.128771\pi\) | |||||||
\(458\) | −11.8310 | + | 20.4918i | −0.552824 | + | 0.957519i | ||||
\(459\) | −10.6180 | −0.495608 | ||||||||
\(460\) | −0.735751 | − | 1.27436i | −0.0343046 | − | 0.0594172i | ||||
\(461\) | −1.73166 | + | 2.99932i | −0.0806513 | + | 0.139692i | −0.903530 | − | 0.428525i | \(-0.859033\pi\) |
0.822879 | + | 0.568217i | \(0.192367\pi\) | |||||||
\(462\) | 3.69714 | + | 6.40364i | 0.172007 | + | 0.297924i | ||||
\(463\) | −22.8231 | −1.06068 | −0.530341 | − | 0.847785i | \(-0.677936\pi\) | ||||
−0.530341 | + | 0.847785i | \(0.677936\pi\) | |||||||
\(464\) | 4.03117 | + | 6.98219i | 0.187142 | + | 0.324140i | ||||
\(465\) | 19.7788 | + | 34.2579i | 0.917221 | + | 1.58867i | ||||
\(466\) | 9.34973 | − | 16.1942i | 0.433118 | − | 0.750182i | ||||
\(467\) | −20.1124 | + | 34.8357i | −0.930691 | + | 1.61200i | −0.148548 | + | 0.988905i | \(0.547460\pi\) |
−0.782143 | + | 0.623099i | \(0.785873\pi\) | |||||||
\(468\) | −0.339302 | −0.0156842 | ||||||||
\(469\) | 60.9690 | 2.81529 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.5387 | − | 40.7703i | 1.08461 | − | 1.87859i | ||||
\(472\) | 7.10009 | − | 12.2977i | 0.326808 | − | 0.566048i | ||||
\(473\) | 1.64883 | − | 2.85586i | 0.0758133 | − | 0.131312i | ||||
\(474\) | −30.3961 | −1.39614 | ||||||||
\(475\) | −3.10028 | + | 5.36984i | −0.142251 | + | 0.246385i | ||||
\(476\) | 9.28802 | + | 16.0873i | 0.425716 | + | 0.737361i | ||||
\(477\) | −19.3799 | −0.887346 | ||||||||
\(478\) | 10.4734 | − | 18.1405i | 0.479043 | − | 0.829727i | ||||
\(479\) | 37.3552 | 1.70680 | 0.853400 | − | 0.521256i | \(-0.174536\pi\) | ||||
0.853400 | + | 0.521256i | \(0.174536\pi\) | |||||||
\(480\) | −1.99271 | + | 3.45147i | −0.0909541 | + | 0.157537i | ||||
\(481\) | 0.325620 | 0.0148470 | ||||||||
\(482\) | 22.1150 | 1.00731 | ||||||||
\(483\) | −4.04836 | + | 7.01197i | −0.184207 | + | 0.319056i | ||||
\(484\) | 5.22640 | + | 9.05239i | 0.237564 | + | 0.411472i | ||||
\(485\) | 2.00826 | − | 3.47841i | 0.0911903 | − | 0.157946i | ||||
\(486\) | −8.32623 | + | 14.4215i | −0.377686 | + | 0.654171i | ||||
\(487\) | 4.42640 | + | 7.66675i | 0.200579 | + | 0.347414i | 0.948715 | − | 0.316132i | \(-0.102384\pi\) |
−0.748136 | + | 0.663546i | \(0.769051\pi\) | |||||||
\(488\) | −0.823951 | − | 1.42712i | −0.0372985 | − | 0.0646029i | ||||
\(489\) | −9.91570 | − | 17.1745i | −0.448403 | − | 0.776657i | ||||
\(490\) | −24.9984 | −1.12931 | ||||||||
\(491\) | −4.42687 | −0.199782 | −0.0998909 | − | 0.994998i | \(-0.531849\pi\) | ||||
−0.0998909 | + | 0.994998i | \(0.531849\pi\) | |||||||
\(492\) | −9.57798 | − | 16.5895i | −0.431809 | − | 0.747915i | ||||
\(493\) | −16.4348 | − | 28.4658i | −0.740184 | − | 1.28204i | ||||
\(494\) | −0.341383 | − | 0.591293i | −0.0153595 | − | 0.0266035i | ||||
\(495\) | 1.21808 | − | 2.10977i | 0.0547486 | − | 0.0948273i | ||||
\(496\) | 4.96281 | − | 8.59583i | 0.222837 | − | 0.385964i | ||||
\(497\) | −2.01189 | − | 3.48469i | −0.0902455 | − | 0.156310i | ||||
\(498\) | 4.45182 | − | 7.71077i | 0.199491 | − | 0.345528i | ||||
\(499\) | −10.5737 | −0.473344 | −0.236672 | − | 0.971590i | \(-0.576057\pi\) | ||||
−0.236672 | + | 0.971590i | \(0.576057\pi\) | |||||||
\(500\) | 12.1712 | 0.544311 | ||||||||
\(501\) | 22.6645 | − | 39.2561i | 1.01258 | − | 1.75383i | ||||
\(502\) | 9.23077 | 0.411989 | ||||||||
\(503\) | −16.2187 | + | 28.0917i | −0.723158 | + | 1.25255i | 0.236570 | + | 0.971615i | \(0.423977\pi\) |
−0.959728 | + | 0.280932i | \(0.909356\pi\) | |||||||
\(504\) | 8.25997 | 0.367928 | ||||||||
\(505\) | 10.9626 | + | 18.9878i | 0.487829 | + | 0.844945i | ||||
\(506\) | 0.299594 | − | 0.518912i | 0.0133186 | − | 0.0230684i | ||||
\(507\) | 28.4428 | 1.26319 | ||||||||
\(508\) | 4.76899 | − | 8.26013i | 0.211590 | − | 0.366484i | ||||
\(509\) | 0.961938 | − | 1.66612i | 0.0426371 | − | 0.0738497i | −0.843919 | − | 0.536470i | \(-0.819757\pi\) |
0.886556 | + | 0.462620i | \(0.153091\pi\) | |||||||
\(510\) | 8.12411 | − | 14.0714i | 0.359741 | − | 0.623090i | ||||
\(511\) | 33.5409 | 1.48376 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.50069 | −0.419466 | ||||||||
\(514\) | 8.95863 | − | 15.5168i | 0.395148 | − | 0.684416i | ||||
\(515\) | 8.11085 | − | 14.0484i | 0.357407 | − | 0.619047i | ||||
\(516\) | −4.88992 | − | 8.46958i | −0.215267 | − | 0.372853i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.92690 | −0.348288 | ||||||||
\(519\) | 3.21364 | + | 5.56619i | 0.141063 | + | 0.244329i | ||||
\(520\) | −0.170009 | + | 0.294464i | −0.00745538 | + | 0.0129131i | ||||
\(521\) | 15.7442 | + | 27.2697i | 0.689765 | + | 1.19471i | 0.971914 | + | 0.235337i | \(0.0756195\pi\) |
−0.282149 | + | 0.959371i | \(0.591047\pi\) | |||||||
\(522\) | −14.6157 | −0.639710 | ||||||||
\(523\) | −5.97494 | + | 10.3489i | −0.261266 | + | 0.452526i | −0.966579 | − | 0.256371i | \(-0.917473\pi\) |
0.705313 | + | 0.708896i | \(0.250807\pi\) | |||||||
\(524\) | −0.0784964 | + | 0.135960i | −0.00342913 | + | 0.00593943i | ||||
\(525\) | −8.49531 | − | 14.7143i | −0.370766 | − | 0.642185i | ||||
\(526\) | −12.0847 | −0.526918 | ||||||||
\(527\) | −20.2330 | + | 35.0445i | −0.881362 | + | 1.52656i | ||||
\(528\) | −1.62284 | −0.0706250 | ||||||||
\(529\) | −22.3439 | −0.971474 | ||||||||
\(530\) | −9.71039 | + | 16.8189i | −0.421793 | + | 0.730566i | ||||
\(531\) | 12.8713 | + | 22.2937i | 0.558566 | + | 0.967464i | ||||
\(532\) | 8.31063 | + | 14.3944i | 0.360311 | + | 0.624078i | ||||
\(533\) | −0.817151 | − | 1.41535i | −0.0353947 | − | 0.0613055i | ||||
\(534\) | 3.63574 | − | 6.29729i | 0.157334 | − | 0.272510i | ||||
\(535\) | 2.75151 | + | 4.76576i | 0.118958 | + | 0.206042i | ||||
\(536\) | −6.69049 | + | 11.5883i | −0.288985 | + | 0.500537i | ||||
\(537\) | −35.6456 | −1.53822 | ||||||||
\(538\) | −1.35123 | − | 2.34040i | −0.0582557 | − | 0.100902i | ||||
\(539\) | −5.08961 | − | 8.81547i | −0.219225 | − | 0.379709i | ||||
\(540\) | 2.36567 | + | 4.09747i | 0.101802 | + | 0.176327i | ||||
\(541\) | 14.8696 | 0.639294 | 0.319647 | − | 0.947537i | \(-0.396436\pi\) | ||||
0.319647 | + | 0.947537i | \(0.396436\pi\) | |||||||
\(542\) | 11.1822 | + | 19.3682i | 0.480319 | + | 0.831936i | ||||
\(543\) | −11.0157 | −0.472728 | ||||||||
\(544\) | −4.07692 | −0.174797 | ||||||||
\(545\) | −3.46795 | + | 18.6467i | −0.148550 | + | 0.798737i | ||||
\(546\) | 1.87090 | 0.0800670 | ||||||||
\(547\) | −0.574928 | −0.0245822 | −0.0122911 | − | 0.999924i | \(-0.503912\pi\) | ||||
−0.0122911 | + | 0.999924i | \(0.503912\pi\) | |||||||
\(548\) | 4.43617 | + | 7.68367i | 0.189504 | + | 0.328230i | ||||
\(549\) | 2.98737 | 0.127498 | ||||||||
\(550\) | 0.628685 | + | 1.08891i | 0.0268072 | + | 0.0464315i | ||||
\(551\) | −14.7053 | − | 25.4703i | −0.626467 | − | 1.08507i | ||||
\(552\) | −0.888502 | − | 1.53893i | −0.0378172 | − | 0.0655012i | ||||
\(553\) | 63.1303 | 2.68457 | ||||||||
\(554\) | 1.86971 | − | 3.23843i | 0.0794362 | − | 0.137588i | ||||
\(555\) | 3.46678 | + | 6.00463i | 0.147156 | + | 0.254882i | ||||
\(556\) | −5.56892 | + | 9.64565i | −0.236175 | + | 0.409067i | ||||
\(557\) | −9.49000 | − | 16.4372i | −0.402104 | − | 0.696465i | 0.591875 | − | 0.806029i | \(-0.298388\pi\) |
−0.993980 | + | 0.109564i | \(0.965054\pi\) | |||||||
\(558\) | 8.99674 | + | 15.5828i | 0.380862 | + | 0.659673i | ||||
\(559\) | −0.417186 | − | 0.722587i | −0.0176451 | − | 0.0305622i | ||||
\(560\) | 4.13870 | − | 7.16843i | 0.174892 | − | 0.302921i | ||||
\(561\) | 6.61619 | 0.279336 | ||||||||
\(562\) | −18.0874 | −0.762971 | ||||||||
\(563\) | 15.9532 | − | 27.6318i | 0.672349 | − | 1.16454i | −0.304887 | − | 0.952388i | \(-0.598619\pi\) |
0.977236 | − | 0.212154i | \(-0.0680479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.12918 | − | 12.3481i | −0.299927 | − | 0.519489i | ||||
\(566\) | 2.08906 | − | 3.61835i | 0.0878095 | − | 0.152091i | ||||
\(567\) | 25.4067 | − | 44.0058i | 1.06698 | − | 1.84807i | ||||
\(568\) | 0.883106 | 0.0370543 | ||||||||
\(569\) | −23.0525 | − | 39.9281i | −0.966412 | − | 1.67387i | −0.705774 | − | 0.708437i | \(-0.749401\pi\) |
−0.260638 | − | 0.965437i | \(-0.583933\pi\) | |||||||
\(570\) | 7.26919 | − | 12.5906i | 0.304473 | − | 0.527363i | ||||
\(571\) | 4.13891 | + | 7.16880i | 0.173208 | + | 0.300005i | 0.939540 | − | 0.342440i | \(-0.111253\pi\) |
−0.766332 | + | 0.642445i | \(0.777920\pi\) | |||||||
\(572\) | −0.138453 | −0.00578903 | ||||||||
\(573\) | 20.2071 | + | 34.9998i | 0.844164 | + | 1.46214i | ||||
\(574\) | 19.8927 | + | 34.4552i | 0.830306 | + | 1.43813i | ||||
\(575\) | −0.688408 | + | 1.19236i | −0.0287086 | + | 0.0497248i | ||||
\(576\) | −0.906417 | + | 1.56996i | −0.0377674 | + | 0.0654150i | ||||
\(577\) | 12.2923 | 0.511736 | 0.255868 | − | 0.966712i | \(-0.417639\pi\) | ||||
0.255868 | + | 0.966712i | \(0.417639\pi\) | |||||||
\(578\) | −0.378700 | −0.0157518 | ||||||||
\(579\) | 40.5865 | 1.68672 | ||||||||
\(580\) | −7.32324 | + | 12.6842i | −0.304081 | + | 0.526684i | ||||
\(581\) | −9.24608 | + | 16.0147i | −0.383592 | + | 0.664401i | ||||
\(582\) | 2.42520 | − | 4.20057i | 0.100528 | − | 0.174119i | ||||
\(583\) | −7.90805 | −0.327518 | ||||||||
\(584\) | −3.68064 | + | 6.37506i | −0.152306 | + | 0.263802i | ||||
\(585\) | −0.308198 | − | 0.533814i | −0.0127424 | − | 0.0220705i | ||||
\(586\) | −7.24950 | −0.299474 | ||||||||
\(587\) | −4.14152 | + | 7.17333i | −0.170939 | + | 0.296075i | −0.938748 | − | 0.344603i | \(-0.888013\pi\) |
0.767809 | + | 0.640678i | \(0.221347\pi\) | |||||||
\(588\) | −30.1884 | −1.24495 | ||||||||
\(589\) | −18.1038 | + | 31.3567i | −0.745955 | + | 1.29203i | ||||
\(590\) | 25.7968 | 1.06204 | ||||||||
\(591\) | −44.3796 | −1.82553 | ||||||||
\(592\) | 0.869866 | − | 1.50665i | 0.0357513 | − | 0.0619231i | ||||
\(593\) | −16.8492 | − | 29.1836i | −0.691912 | − | 1.19843i | −0.971211 | − | 0.238222i | \(-0.923435\pi\) |
0.279299 | − | 0.960204i | \(-0.409898\pi\) | |||||||
\(594\) | −0.963290 | + | 1.66847i | −0.0395243 | + | 0.0684580i | ||||
\(595\) | −16.8731 | + | 29.2251i | −0.691731 | + | 1.19811i | ||||
\(596\) | −2.92902 | − | 5.07321i | −0.119977 | − | 0.207807i | ||||
\(597\) | 25.3919 | + | 43.9801i | 1.03922 | + | 1.79999i | ||||
\(598\) | −0.0758031 | − | 0.131295i | −0.00309982 | − | 0.00536904i | ||||
\(599\) | 11.5125 | 0.470388 | 0.235194 | − | 0.971948i | \(-0.424427\pi\) | ||||
0.235194 | + | 0.971948i | \(0.424427\pi\) | |||||||
\(600\) | 3.72897 | 0.152234 | ||||||||
\(601\) | −3.09676 | − | 5.36375i | −0.126320 | − | 0.218792i | 0.795928 | − | 0.605391i | \(-0.206983\pi\) |
−0.922248 | + | 0.386599i | \(0.873650\pi\) | |||||||
\(602\) | 10.1560 | + | 17.5907i | 0.413927 | + | 0.716942i | ||||
\(603\) | −12.1287 | − | 21.0076i | −0.493921 | − | 0.855496i | ||||
\(604\) | −4.46472 | + | 7.73312i | −0.181667 | + | 0.314656i | ||||
\(605\) | −9.49457 | + | 16.4451i | −0.386009 | + | 0.668587i | ||||
\(606\) | 13.2386 | + | 22.9299i | 0.537780 | + | 0.931463i | ||||
\(607\) | −22.2075 | + | 38.4645i | −0.901373 | + | 1.56122i | −0.0756605 | + | 0.997134i | \(0.524107\pi\) |
−0.825713 | + | 0.564091i | \(0.809227\pi\) | |||||||
\(608\) | −3.64790 | −0.147942 | ||||||||
\(609\) | 80.5901 | 3.26568 | ||||||||
\(610\) | 1.49683 | − | 2.59259i | 0.0606051 | − | 0.104971i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.69539 | − | 6.40060i | 0.149377 | − | 0.258729i | ||||
\(613\) | −8.54777 | −0.345241 | −0.172621 | − | 0.984988i | \(-0.555223\pi\) | ||||
−0.172621 | + | 0.984988i | \(0.555223\pi\) | |||||||
\(614\) | −12.2735 | − | 21.2584i | −0.495319 | − | 0.857917i | ||||
\(615\) | 17.3999 | − | 30.1375i | 0.701631 | − | 1.21526i | ||||
\(616\) | 3.37051 | 0.135802 | ||||||||
\(617\) | 6.64868 | − | 11.5159i | 0.267666 | − | 0.463611i | −0.700593 | − | 0.713561i | \(-0.747081\pi\) |
0.968259 | + | 0.249950i | \(0.0804143\pi\) | |||||||
\(618\) | 9.79477 | − | 16.9650i | 0.394003 | − | 0.682434i | ||||
\(619\) | 0.953972 | − | 1.65233i | 0.0383434 | − | 0.0664127i | −0.846217 | − | 0.532839i | \(-0.821125\pi\) |
0.884560 | + | 0.466426i | \(0.154459\pi\) | |||||||
\(620\) | 18.0314 | 0.724159 | ||||||||
\(621\) | −2.10960 | −0.0846553 | ||||||||
\(622\) | 18.0129 | 0.722251 | ||||||||
\(623\) | −7.55115 | + | 13.0790i | −0.302531 | + | 0.523998i | ||||
\(624\) | −0.205305 | + | 0.355598i | −0.00821877 | + | 0.0142353i | ||||
\(625\) | 6.80600 | + | 11.7883i | 0.272240 | + | 0.471534i | ||||
\(626\) | 0.664077 | + | 1.15021i | 0.0265419 | + | 0.0459718i | ||||
\(627\) | 5.91996 | 0.236420 | ||||||||
\(628\) | −10.7296 | − | 18.5842i | −0.428157 | − | 0.741589i | ||||
\(629\) | −3.54638 | + | 6.14251i | −0.141403 | + | 0.244918i | ||||
\(630\) | 7.50276 | + | 12.9952i | 0.298917 | + | 0.517740i | ||||
\(631\) | −22.3869 | −0.891208 | −0.445604 | − | 0.895230i | \(-0.647011\pi\) | ||||
−0.445604 | + | 0.895230i | \(0.647011\pi\) | |||||||
\(632\) | −6.92767 | + | 11.9991i | −0.275568 | + | 0.477298i | ||||
\(633\) | 21.6231 | − | 37.4523i | 0.859441 | − | 1.48860i | ||||
\(634\) | −2.88508 | − | 4.99710i | −0.114581 | − | 0.198460i | ||||
\(635\) | 17.3272 | 0.687610 | ||||||||
\(636\) | −11.7264 | + | 20.3107i | −0.464982 | + | 0.805372i | ||||
\(637\) | −2.57554 | −0.102047 | ||||||||
\(638\) | −5.96397 | −0.236116 | ||||||||
\(639\) | −0.800462 | + | 1.38644i | −0.0316658 | + | 0.0548467i | ||||
\(640\) | 0.908328 | + | 1.57327i | 0.0359048 | + | 0.0621890i | ||||
\(641\) | 13.5438 | + | 23.4585i | 0.534946 | + | 0.926554i | 0.999166 | + | 0.0408342i | \(0.0130015\pi\) |
−0.464220 | + | 0.885720i | \(0.653665\pi\) | |||||||
\(642\) | 3.32276 | + | 5.75519i | 0.131139 | + | 0.227139i | ||||
\(643\) | −1.83870 | + | 3.18473i | −0.0725113 | + | 0.125593i | −0.900001 | − | 0.435887i | \(-0.856435\pi\) |
0.827490 | + | 0.561480i | \(0.189768\pi\) | |||||||
\(644\) | 1.84535 | + | 3.19624i | 0.0727170 | + | 0.125950i | ||||
\(645\) | 8.88329 | − | 15.3863i | 0.349779 | − | 0.605836i | ||||
\(646\) | 14.8722 | 0.585139 | ||||||||
\(647\) | 16.9055 | + | 29.2811i | 0.664622 | + | 1.15116i | 0.979388 | + | 0.201990i | \(0.0647409\pi\) |
−0.314765 | + | 0.949170i | \(0.601926\pi\) | |||||||
\(648\) | 5.57607 | + | 9.65803i | 0.219049 | + | 0.379403i | ||||
\(649\) | 5.25217 | + | 9.09702i | 0.206166 | + | 0.357089i | ||||
\(650\) | 0.318139 | 0.0124784 | ||||||||
\(651\) | −49.6076 | − | 85.9229i | −1.94428 | − | 3.36758i | ||||
\(652\) | −9.03968 | −0.354021 | ||||||||
\(653\) | −8.20619 | −0.321133 | −0.160567 | − | 0.987025i | \(-0.551332\pi\) | ||||
−0.160567 | + | 0.987025i | \(0.551332\pi\) | |||||||
\(654\) | −4.18794 | + | 22.5180i | −0.163761 | + | 0.880523i | ||||
\(655\) | −0.285202 | −0.0111438 | ||||||||
\(656\) | −8.73179 | −0.340919 | ||||||||
\(657\) | −6.67239 | − | 11.5569i | −0.260315 | − | 0.450878i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.23419 | − | 2.13768i | −0.0480772 | − | 0.0832722i | 0.840985 | − | 0.541058i | \(-0.181976\pi\) |
−0.889063 | + | 0.457786i | \(0.848643\pi\) | |||||||
\(660\) | −1.47407 | − | 2.55316i | −0.0573781 | − | 0.0993818i | ||||
\(661\) | −12.5082 | − | 21.6648i | −0.486513 | − | 0.842665i | 0.513367 | − | 0.858169i | \(-0.328398\pi\) |
−0.999880 | + | 0.0155043i | \(0.995065\pi\) | |||||||
\(662\) | 33.1868 | 1.28984 | ||||||||
\(663\) | 0.837012 | − | 1.44975i | 0.0325068 | − | 0.0563035i | ||||
\(664\) | −2.02926 | − | 3.51477i | −0.0787504 | − | 0.136400i | ||||
\(665\) | −15.0976 | + | 26.1497i | −0.585458 | + | 1.01404i | ||||
\(666\) | 1.57692 | + | 2.73131i | 0.0611045 | + | 0.105836i | ||||
\(667\) | −3.26527 | − | 5.65561i | −0.126432 | − | 0.218986i | ||||
\(668\) | −10.3311 | − | 17.8940i | −0.399722 | − | 0.692339i | ||||
\(669\) | 13.7480 | − | 23.8122i | 0.531529 | − | 0.920635i | ||||
\(670\) | −24.3086 | −0.939125 | ||||||||
\(671\) | 1.21901 | 0.0470592 | ||||||||
\(672\) | 4.99794 | − | 8.65669i | 0.192800 | − | 0.333939i | ||||
\(673\) | −48.0836 | −1.85348 | −0.926742 | − | 0.375697i | \(-0.877403\pi\) | ||||
−0.926742 | + | 0.375697i | \(0.877403\pi\) | |||||||
\(674\) | −0.547183 | − | 0.947748i | −0.0210767 | − | 0.0365059i | ||||
\(675\) | 2.21345 | − | 3.83381i | 0.0851958 | − | 0.147563i | ||||
\(676\) | 6.48248 | − | 11.2280i | 0.249326 | − | 0.431846i | ||||
\(677\) | −17.4257 | −0.669723 | −0.334862 | − | 0.942267i | \(-0.608690\pi\) | ||||
−0.334862 | + | 0.942267i | \(0.608690\pi\) | |||||||
\(678\) | −8.60929 | − | 14.9117i | −0.330638 | − | 0.572682i | ||||
\(679\) | −5.03695 | + | 8.72426i | −0.193300 | + | 0.334806i | ||||
\(680\) | −3.70318 | − | 6.41410i | −0.142011 | − | 0.245970i | ||||
\(681\) | −45.5131 | −1.74407 | ||||||||
\(682\) | 3.67115 | + | 6.35862i | 0.140576 | + | 0.243484i | ||||
\(683\) | 9.88955 | + | 17.1292i | 0.378413 | + | 0.655430i | 0.990832 | − | 0.135103i | \(-0.0431366\pi\) |
−0.612419 | + | 0.790534i | \(0.709803\pi\) | |||||||
\(684\) | 3.30652 | − | 5.72706i | 0.126428 | − | 0.218980i | ||||
\(685\) | −8.05899 | + | 13.9586i | −0.307918 | + | 0.533330i | ||||
\(686\) | 30.8043 | 1.17611 | ||||||||
\(687\) | −51.9099 | −1.98049 | ||||||||
\(688\) | −4.45791 | −0.169956 | ||||||||
\(689\) | −1.00044 | + | 1.73282i | −0.0381139 | + | 0.0660152i | ||||
\(690\) | 1.61410 | − | 2.79571i | 0.0614478 | − | 0.106431i | ||||
\(691\) | −14.6887 | + | 25.4416i | −0.558785 | + | 0.967844i | 0.438813 | + | 0.898578i | \(0.355399\pi\) |
−0.997598 | + | 0.0692659i | \(0.977934\pi\) | |||||||
\(692\) | 2.92973 | 0.111372 | ||||||||
\(693\) | −3.05509 | + | 5.29157i | −0.116053 | + | 0.201010i | ||||
\(694\) | 16.0397 | + | 27.7816i | 0.608860 | + | 1.05458i | ||||
\(695\) | −20.2336 | −0.767505 | ||||||||
\(696\) | −8.84364 | + | 15.3176i | −0.335217 | + | 0.580614i | ||||
\(697\) | 35.5988 | 1.34840 | ||||||||
\(698\) | 13.4131 | − | 23.2321i | 0.507693 | − | 0.879349i | ||||
\(699\) | 41.0232 | 1.55164 | ||||||||
\(700\) | −7.74477 | −0.292725 | ||||||||
\(701\) | −19.0461 | + | 32.9888i | −0.719362 | + | 1.24597i | 0.241892 | + | 0.970303i | \(0.422232\pi\) |
−0.961253 | + | 0.275667i | \(0.911101\pi\) | |||||||
\(702\) | 0.243731 | + | 0.422155i | 0.00919904 | + | 0.0159332i | ||||
\(703\) | −3.17319 | + | 5.49612i | −0.119679 | + | 0.207290i | ||||
\(704\) | −0.369866 | + | 0.640628i | −0.0139399 | + | 0.0241446i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.92894 | + | 13.7333i | 0.298409 | + | 0.516860i | ||||
\(707\) | −27.4955 | − | 47.6236i | −1.03407 | − | 1.79107i | ||||
\(708\) | 31.1526 | 1.17079 | ||||||||
\(709\) | 12.0913 | 0.454100 | 0.227050 | − | 0.973883i | \(-0.427092\pi\) | ||||
0.227050 | + | 0.973883i | \(0.427092\pi\) | |||||||
\(710\) | 0.802150 | + | 1.38936i | 0.0301041 | + | 0.0521419i | ||||
\(711\) | −12.5587 | − | 21.7523i | −0.470988 | − | 0.815776i | ||||
\(712\) | −1.65727 | − | 2.87047i | −0.0621087 | − | 0.107575i | ||||
\(713\) | −4.01990 | + | 6.96267i | −0.150546 | + | 0.260754i | ||||
\(714\) | −20.3762 | + | 35.2927i | −0.762561 | + | 1.32079i | ||||
\(715\) | −0.125761 | − | 0.217825i | −0.00470320 | − | 0.00814618i | ||||
\(716\) | −8.12411 | + | 14.0714i | −0.303612 | + | 0.525872i | ||||
\(717\) | 45.9536 | 1.71617 | ||||||||
\(718\) | 11.8615 | 0.442669 | ||||||||
\(719\) | −14.4294 | + | 24.9924i | −0.538125 | + | 0.932059i | 0.460880 | + | 0.887462i | \(0.347534\pi\) |
−0.999005 | + | 0.0445970i | \(0.985800\pi\) | |||||||
\(720\) | −3.29329 | −0.122734 | ||||||||
\(721\) | −20.3430 | + | 35.2351i | −0.757612 | + | 1.31222i | ||||
\(722\) | −5.69282 | −0.211865 | ||||||||
\(723\) | 24.2581 | + | 42.0163i | 0.902169 | + | 1.56260i | ||||
\(724\) | −2.51062 | + | 4.34852i | −0.0933065 | + | 0.161612i | ||||
\(725\) | 13.7040 | 0.508955 | ||||||||
\(726\) | −11.4658 | + | 19.8593i | −0.425534 | + | 0.737047i | ||||
\(727\) | 0.387073 | − | 0.670430i | 0.0143557 | − | 0.0248649i | −0.858758 | − | 0.512381i | \(-0.828764\pi\) |
0.873114 | + | 0.487516i | \(0.162097\pi\) | |||||||
\(728\) | 0.426402 | − | 0.738550i | 0.0158035 | − | 0.0273725i | ||||
\(729\) | −3.07605 | −0.113928 | ||||||||
\(730\) | −13.3729 | −0.494954 | ||||||||
\(731\) | 18.1745 | 0.672210 | ||||||||
\(732\) | 1.80760 | − | 3.13085i | 0.0668107 | − | 0.115720i | ||||
\(733\) | 15.7484 | − | 27.2770i | 0.581679 | − | 1.00750i | −0.413601 | − | 0.910458i | \(-0.635729\pi\) |
0.995280 | − | 0.0970400i | \(-0.0309375\pi\) | |||||||
\(734\) | −10.4807 | − | 18.1531i | −0.386849 | − | 0.670042i | ||||
\(735\) | −27.4210 | − | 47.4945i | −1.01144 | − | 1.75186i | ||||
\(736\) | −0.810006 | −0.0298572 | ||||||||
\(737\) | −4.94918 | − | 8.57223i | −0.182305 | − | 0.315762i | ||||
\(738\) | 7.91464 | − | 13.7086i | 0.291342 | − | 0.504619i | ||||
\(739\) | −4.74219 | − | 8.21372i | −0.174444 | − | 0.302147i | 0.765524 | − | 0.643407i | \(-0.222480\pi\) |
−0.939969 | + | 0.341260i | \(0.889146\pi\) | |||||||
\(740\) | 3.16050 | 0.116182 | ||||||||
\(741\) | 0.748932 | − | 1.29719i | 0.0275127 | − | 0.0476534i | ||||
\(742\) | 24.3548 | − | 42.1838i | 0.894094 | − | 1.54862i | ||||
\(743\) | 9.17668 | + | 15.8945i | 0.336660 | + | 0.583112i | 0.983802 | − | 0.179257i | \(-0.0573694\pi\) |
−0.647142 | + | 0.762369i | \(0.724036\pi\) | |||||||
\(744\) | 21.7750 | 0.798309 | ||||||||
\(745\) | 5.32102 | − | 9.21628i | 0.194947 | − | 0.337659i | ||||
\(746\) | 23.6208 | 0.864820 | ||||||||
\(747\) | 7.35740 | 0.269193 | ||||||||
\(748\) | 1.50792 | − | 2.61179i | 0.0551349 | − | 0.0954965i | ||||
\(749\) | −6.90112 | − | 11.9531i | −0.252161 | − | 0.436756i | ||||
\(750\) | 13.3507 | + | 23.1240i | 0.487497 | + | 0.844369i | ||||
\(751\) | 19.7074 | + | 34.1341i | 0.719132 | + | 1.24557i | 0.961344 | + | 0.275349i | \(0.0887935\pi\) |
−0.242213 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1253 | + | 17.5375i | 0.368987 | + | 0.639104i | ||||
\(754\) | −0.754500 | + | 1.30683i | −0.0274773 | + | 0.0475921i | ||||
\(755\) | −16.2217 | −0.590368 | ||||||||
\(756\) | −5.93339 | − | 10.2769i | −0.215795 | − | 0.373768i | ||||
\(757\) | −7.20275 | − | 12.4755i | −0.261788 | − | 0.453431i | 0.704929 | − | 0.709278i | \(-0.250979\pi\) |
−0.966717 | + | 0.255847i | \(0.917646\pi\) | |||||||
\(758\) | −4.12753 | − | 7.14909i | −0.149919 | − | 0.259667i | ||||
\(759\) | 1.31451 | 0.0477136 | ||||||||
\(760\) | −3.31349 | − | 5.73913i | −0.120193 | − | 0.208180i | ||||
\(761\) | 10.8956 | 0.394966 | 0.197483 | − | 0.980306i | \(-0.436723\pi\) | ||||
0.197483 | + | 0.980306i | \(0.436723\pi\) | |||||||
\(762\) | 20.9246 | 0.758017 | ||||||||
\(763\) | 8.69802 | − | 46.7681i | 0.314889 | − | 1.69312i | ||||
\(764\) | 18.4219 | 0.666480 | ||||||||
\(765\) | 13.4265 | 0.485436 | ||||||||
\(766\) | 5.50001 | + | 9.52630i | 0.198724 | + | 0.344199i | ||||
\(767\) | 2.65780 | 0.0959676 | ||||||||
\(768\) | 1.09691 | + | 1.89990i | 0.0395813 | + | 0.0685568i | ||||
\(769\) | 11.9943 | + | 20.7748i | 0.432526 | + | 0.749157i | 0.997090 | − | 0.0762324i | \(-0.0242891\pi\) |
−0.564564 | + | 0.825389i | \(0.690956\pi\) | |||||||
\(770\) | 3.06153 | + | 5.30272i | 0.110330 | + | 0.191097i | ||||
\(771\) | 39.3072 | 1.41561 | ||||||||
\(772\) | 9.25021 | − | 16.0218i | 0.332922 | − | 0.576638i | ||||
\(773\) | −4.95699 | − | 8.58576i | −0.178290 | − | 0.308808i | 0.763005 | − | 0.646393i | \(-0.223723\pi\) |
−0.941295 | + | 0.337585i | \(0.890390\pi\) | |||||||
\(774\) | 4.04072 | − | 6.99873i | 0.145241 | − | 0.251564i | ||||
\(775\) | −8.43559 | − | 14.6109i | −0.303015 | − | 0.524838i | ||||
\(776\) | −1.10547 | − | 1.91473i | −0.0396841 | − | 0.0687348i | ||||
\(777\) | −8.69508 | − | 15.0603i | −0.311934 | − | 0.540286i | ||||
\(778\) | 8.79667 | − | 15.2363i | 0.315376 | − | 0.546247i | ||||
\(779\) | 31.8527 | 1.14124 | ||||||||
\(780\) | −0.745936 | −0.0267088 | ||||||||
\(781\) | −0.326631 | + | 0.565742i | −0.0116878 | + | 0.0202438i | ||||
\(782\) | 3.30233 | 0.118091 | ||||||||
\(783\) | 10.4989 | + | 18.1846i | 0.375199 | + | 0.649864i | ||||
\(784\) | −6.88034 | + | 11.9171i | −0.245726 | + | 0.425611i | ||||
\(785\) | 19.4919 | − | 33.7610i | 0.695697 | − | 1.20498i | ||||
\(786\) | −0.344414 | −0.0122848 | ||||||||
\(787\) | 0.722207 | + | 1.25090i | 0.0257439 | + | 0.0445897i | 0.878610 | − | 0.477539i | \(-0.158471\pi\) |
−0.852866 | + | 0.522129i | \(0.825138\pi\) | |||||||
\(788\) | −10.1147 | + | 17.5192i | −0.360321 | + | 0.624094i | ||||
\(789\) | −13.2558 | − | 22.9597i | −0.471919 | − | 0.817388i | ||||
\(790\) | −25.1704 | −0.895522 | ||||||||
\(791\) | 17.8808 | + | 30.9705i | 0.635769 | + | 1.10118i | ||||
\(792\) | −0.670506 | − | 1.16135i | −0.0238254 | − | 0.0412668i | ||||
\(793\) | 0.154216 | − | 0.267110i | 0.00547638 | − | 0.00948536i | ||||
\(794\) | 5.74007 | − | 9.94209i | 0.203707 | − | 0.352832i | ||||
\(795\) | −42.6057 | −1.51107 | ||||||||
\(796\) | 23.1486 | 0.820482 | ||||||||
\(797\) | −11.4030 | −0.403916 | −0.201958 | − | 0.979394i | \(-0.564730\pi\) | ||||
−0.201958 | + | 0.979394i | \(0.564730\pi\) | |||||||
\(798\) | −18.2320 | + | 31.5787i | −0.645406 | + | 1.11788i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.849881 | − | 1.47204i | 0.0300478 | − | 0.0520444i | ||||
\(801\) | 6.00870 | 0.212307 | ||||||||
\(802\) | −2.03569 | + | 3.52593i | −0.0718829 | + | 0.124505i | ||||
\(803\) | −2.72269 | − | 4.71584i | −0.0960817 | − | 0.166418i | ||||
\(804\) | −29.3554 | −1.03529 | ||||||||
\(805\) | −3.35237 | + | 5.80647i | −0.118155 | + | 0.204651i | ||||
\(806\) | 1.85774 | 0.0654363 | ||||||||
\(807\) | 2.96435 | − | 5.13441i | 0.104350 | − | 0.180740i | ||||
\(808\) | 12.0690 | 0.424585 | ||||||||
\(809\) | 5.14272 | 0.180809 | 0.0904043 | − | 0.995905i | \(-0.471184\pi\) | ||||
0.0904043 | + | 0.995905i | \(0.471184\pi\) | |||||||
\(810\) | −10.1298 | + | 17.5453i | −0.355925 | + | 0.616480i | ||||
\(811\) | 15.0837 | + | 26.1258i | 0.529661 | + | 0.917401i | 0.999401 | + | 0.0345958i | \(0.0110144\pi\) |
−0.469740 | + | 0.882805i | \(0.655652\pi\) | |||||||
\(812\) | 18.3676 | − | 31.8136i | 0.644575 | − | 1.11644i | ||||
\(813\) | −24.5318 | + | 42.4903i | −0.860368 | + | 1.49020i | ||||
\(814\) | 0.643469 | + | 1.11452i | 0.0225536 | + | 0.0390639i | ||||
\(815\) | −8.21099 | − | 14.2219i | −0.287618 | − | 0.498170i | ||||
\(816\) | −4.47201 | − | 7.74575i | −0.156552 | − | 0.271156i | ||||
\(817\) | 16.2620 | 0.568935 | ||||||||
\(818\) | 3.60651 | 0.126099 | ||||||||
\(819\) | 0.772996 | + | 1.33887i | 0.0270107 | + | 0.0467839i | ||||
\(820\) | −7.93133 | − | 13.7375i | −0.276974 | − | 0.479733i | ||||
\(821\) | 24.1111 | + | 41.7617i | 0.841484 | + | 1.45749i | 0.888640 | + | 0.458606i | \(0.151651\pi\) |
−0.0471555 | + | 0.998888i | \(0.515016\pi\) | |||||||
\(822\) | −9.73214 | + | 16.8566i | −0.339448 | + | 0.587940i | ||||
\(823\) | 14.6019 | − | 25.2913i | 0.508991 | − | 0.881598i | −0.490955 | − | 0.871185i | \(-0.663352\pi\) |
0.999946 | − | 0.0104128i | \(-0.00331456\pi\) | |||||||
\(824\) | −4.46472 | − | 7.73312i | −0.155536 | − | 0.269396i | ||||
\(825\) | −1.37922 | + | 2.38888i | −0.0480183 | + | 0.0831701i | ||||
\(826\) | −64.7015 | −2.25125 | ||||||||
\(827\) | 1.63983 | 0.0570226 | 0.0285113 | − | 0.999593i | \(-0.490923\pi\) | ||||
0.0285113 | + | 0.999593i | \(0.490923\pi\) | |||||||
\(828\) | 0.734202 | − | 1.27168i | 0.0255153 | − | 0.0441938i | ||||
\(829\) | −41.3360 | −1.43566 | −0.717829 | − | 0.696219i | \(-0.754864\pi\) | ||||
−0.717829 | + | 0.696219i | \(0.754864\pi\) | |||||||
\(830\) | 3.68646 | − | 6.38513i | 0.127959 | − | 0.221631i | ||||
\(831\) | 8.20359 | 0.284579 | ||||||||
\(832\) | 0.0935834 | + | 0.162091i | 0.00324442 | + | 0.00561950i | ||||
\(833\) | 28.0506 | − | 48.5851i | 0.971896 | − | 1.68337i | ||||
\(834\) | −24.4344 | −0.846093 | ||||||||
\(835\) | 18.7680 | − | 32.5072i | 0.649495 | − | 1.12496i | ||||
\(836\) | 1.34924 | − | 2.33695i | 0.0466643 | − | 0.0808250i | ||||
\(837\) | 12.9253 | − | 22.3872i | 0.446762 | − | 0.773815i | ||||
\(838\) | −25.7552 | −0.889697 | ||||||||
\(839\) | −38.2977 | −1.32218 | −0.661091 | − | 0.750305i | \(-0.729906\pi\) | ||||
−0.661091 | + | 0.750305i | \(0.729906\pi\) | |||||||
\(840\) | 18.1591 | 0.626548 | ||||||||
\(841\) | −18.0006 | + | 31.1780i | −0.620711 | + | 1.07510i | ||||
\(842\) | −0.209884 | + | 0.363530i | −0.00723308 | + | 0.0125281i | ||||
\(843\) | −19.8402 | − | 34.3643i | −0.683333 | − | 1.18357i | ||||
\(844\) | −9.85638 | − | 17.0718i | −0.339271 | − | 0.587634i | ||||
\(845\) | 23.5529 | 0.810244 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.8135 | − | 41.2462i | 0.818242 | − | 1.41724i | ||||
\(848\) | 5.34520 | + | 9.25816i | 0.183555 | + | 0.317927i | ||||
\(849\) | 9.16601 | 0.314577 | ||||||||
\(850\) | −3.46490 | + | 6.00138i | −0.118845 | + | 0.205846i | ||||
\(851\) | −0.704597 | + | 1.22040i | −0.0241533 | + | 0.0418347i | ||||
\(852\) | 0.968686 | + | 1.67781i | 0.0331866 | + | 0.0574810i | ||||
\(853\) | −22.6562 | −0.775733 | −0.387867 | − | 0.921716i | \(-0.626788\pi\) | ||||
−0.387867 | + | 0.921716i | \(0.626788\pi\) | |||||||
\(854\) | −3.75424 | + | 6.50253i | −0.128467 | + | 0.222512i | ||||
\(855\) | 12.0136 | 0.410857 | ||||||||
\(856\) | 3.02920 | 0.103536 | ||||||||
\(857\) | −27.4589 | + | 47.5603i | −0.937979 | + | 1.62463i | −0.168747 | + | 0.985659i | \(0.553972\pi\) |
−0.769233 | + | 0.638969i | \(0.779361\pi\) | |||||||
\(858\) | −0.151871 | − | 0.263048i | −0.00518478 | − | 0.00898031i | ||||
\(859\) | −19.2703 | − | 33.3771i | −0.657493 | − | 1.13881i | −0.981263 | − | 0.192675i | \(-0.938284\pi\) |
0.323770 | − | 0.946136i | \(-0.395050\pi\) | |||||||
\(860\) | −4.04924 | − | 7.01349i | −0.138078 | − | 0.239158i | ||||
\(861\) | −43.6410 | + | 75.5884i | −1.48728 | + | 2.57605i | ||||
\(862\) | −8.80723 | − | 15.2546i | −0.299975 | − | 0.519572i | ||||
\(863\) | 1.45489 | − | 2.51994i | 0.0495250 | − | 0.0857798i | −0.840200 | − | 0.542276i | \(-0.817563\pi\) |
0.889725 | + | 0.456497i | \(0.150896\pi\) | |||||||
\(864\) | 2.60443 | 0.0886044 | ||||||||
\(865\) | 2.66115 | + | 4.60925i | 0.0904819 | + | 0.156719i | ||||
\(866\) | 2.38588 | + | 4.13247i | 0.0810756 | + | 0.140427i | ||||
\(867\) | −0.415399 | − | 0.719493i | −0.0141077 | − | 0.0244352i | ||||
\(868\) | −45.2249 | −1.53503 | ||||||||
\(869\) | −5.12463 | − | 8.87611i | −0.173841 | − | 0.301101i | ||||
\(870\) | −32.1317 | −1.08937 | ||||||||
\(871\) | −2.50448 | −0.0848609 | ||||||||
\(872\) | 7.93466 | + | 6.78537i | 0.268701 | + | 0.229782i | ||||
\(873\) | 4.00807 | 0.135652 | ||||||||
\(874\) | 2.95482 | 0.0999483 | ||||||||
\(875\) | −27.7283 | − | 48.0268i | −0.937387 | − | 1.62360i | ||||
\(876\) | −16.1493 | −0.545635 | ||||||||
\(877\) | −1.99276 | − | 3.45156i | −0.0672906 | − | 0.116551i | 0.830417 | − | 0.557142i | \(-0.188102\pi\) |
−0.897708 | + | 0.440591i | \(0.854769\pi\) | |||||||
\(878\) | −6.74066 | − | 11.6752i | −0.227486 | − | 0.394018i | ||||
\(879\) | −7.95204 | − | 13.7733i | −0.268216 | − | 0.464563i | ||||
\(880\) | −1.34384 | −0.0453008 | ||||||||
\(881\) | −22.2964 | + | 38.6185i | −0.751186 | + | 1.30109i | 0.196063 | + | 0.980591i | \(0.437184\pi\) |
−0.947248 | + | 0.320500i | \(0.896149\pi\) | |||||||
\(882\) | −12.4729 | − | 21.6037i | −0.419985 | − | 0.727435i | ||||
\(883\) | −23.6273 | + | 40.9236i | −0.795120 | + | 1.37719i | 0.127642 | + | 0.991820i | \(0.459259\pi\) |
−0.922763 | + | 0.385369i | \(0.874074\pi\) | |||||||
\(884\) | −0.381532 | − | 0.660833i | −0.0128323 | − | 0.0222262i | ||||
\(885\) | 28.2968 | + | 49.0114i | 0.951185 | + | 1.64750i | ||||
\(886\) | −5.77644 | − | 10.0051i | −0.194063 | − | 0.336128i | ||||
\(887\) | 14.3803 | − | 24.9075i | 0.482845 | − | 0.836311i | −0.516961 | − | 0.856009i | \(-0.672937\pi\) |
0.999806 | + | 0.0196974i | \(0.00627028\pi\) | |||||||
\(888\) | 3.81666 | 0.128079 | ||||||||
\(889\) | −43.4587 | −1.45756 | ||||||||
\(890\) | 3.01068 | − | 5.21466i | 0.100918 | − | 0.174796i | ||||
\(891\) | −8.24960 | −0.276372 | ||||||||
\(892\) | −6.26671 | − | 10.8543i | −0.209825 | − | 0.363427i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.42574 | − | 11.1297i | 0.214909 | − | 0.372233i | ||||
\(895\) | −29.5174 | −0.986658 | ||||||||
\(896\) | −2.27819 | − | 3.94595i | −0.0761091 | − | 0.131825i | ||||
\(897\) | 0.166298 | − | 0.288037i | 0.00555253 | − | 0.00961726i | ||||
\(898\) | −7.00968 | − | 12.1411i | −0.233916 | − | 0.405155i | ||||
\(899\) | 80.0236 | 2.66894 | ||||||||
\(900\) | 1.54069 | + | 2.66856i | 0.0513564 | + | 0.0889519i | ||||
\(901\) | −21.7920 | − | 37.7448i | −0.725996 | − | 1.25746i | ||||
\(902\) | 3.22960 | − | 5.59383i | 0.107534 | − | 0.186254i | ||||
\(903\) | −22.2804 | + | 38.5907i | −0.741444 | + | 1.28422i | ||||
\(904\) | −7.84869 | −0.261043 | ||||||||
\(905\) | −9.12186 | −0.303221 | ||||||||
\(906\) | −19.5895 | −0.650819 | ||||||||
\(907\) | −25.1864 | + | 43.6240i | −0.836299 | + | 1.44851i | 0.0566692 | + | 0.998393i | \(0.481952\pi\) |
−0.892968 | + | 0.450120i | \(0.851381\pi\) | |||||||
\(908\) | −10.3730 | + | 17.9666i | −0.344242 | + | 0.596244i | ||||
\(909\) | −10.9395 | + | 18.9478i | −0.362841 | + | 0.628459i | ||||
\(910\) | 1.54925 | 0.0513572 | ||||||||
\(911\) | 14.1757 | − | 24.5531i | 0.469663 | − | 0.813479i | −0.529736 | − | 0.848163i | \(-0.677709\pi\) |
0.999398 | + | 0.0346833i | \(0.0110422\pi\) | |||||||
\(912\) | −4.00141 | − | 6.93065i | −0.132500 | − | 0.229497i | ||||
\(913\) | 3.00221 | 0.0993588 | ||||||||
\(914\) | 17.1130 | − | 29.6405i | 0.566046 | − | 0.980421i | ||||
\(915\) | 6.56756 | 0.217117 | ||||||||
\(916\) | −11.8310 | + | 20.4918i | −0.390906 | + | 0.677068i | ||||
\(917\) | 0.715321 | 0.0236220 | ||||||||
\(918\) | −10.6180 | −0.350448 | ||||||||
\(919\) | −1.57255 | + | 2.72374i | −0.0518737 | + | 0.0898479i | −0.890796 | − | 0.454403i | \(-0.849853\pi\) |
0.838923 | + | 0.544251i | \(0.183186\pi\) | |||||||
\(920\) | −0.735751 | − | 1.27436i | −0.0242570 | − | 0.0420143i | ||||
\(921\) | 26.9258 | − | 46.6369i | 0.887237 | − | 1.53674i | ||||
\(922\) | −1.73166 | + | 2.99932i | −0.0570291 | + | 0.0987772i | ||||
\(923\) | 0.0826440 | + | 0.143144i | 0.00272026 | + | 0.00471163i | ||||
\(924\) | 3.69714 | + | 6.40364i | 0.121627 | + | 0.210664i | ||||
\(925\) | −1.47857 | − | 2.56095i | −0.0486149 | − | 0.0842035i | ||||
\(926\) | −22.8231 | −0.750015 | ||||||||
\(927\) | 16.1876 | 0.531670 | ||||||||
\(928\) | 4.03117 | + | 6.98219i | 0.132330 | + | 0.229201i | ||||
\(929\) | 0.652432 | + | 1.13005i | 0.0214056 | + | 0.0370756i | 0.876530 | − | 0.481348i | \(-0.159853\pi\) |
−0.855124 | + | 0.518423i | \(0.826519\pi\) | |||||||
\(930\) | 19.7788 | + | 34.2579i | 0.648573 | + | 1.12336i | ||||
\(931\) | 25.0988 | − | 43.4724i | 0.822580 | − | 1.42475i | ||||
\(932\) | 9.34973 | − | 16.1942i | 0.306261 | − | 0.530459i | ||||
\(933\) | 19.7585 | + | 34.2227i | 0.646864 | + | 1.12040i | ||||
\(934\) | −20.1124 | + | 34.8357i | −0.658098 | + | 1.13986i | ||||
\(935\) | 5.47873 | 0.179174 | ||||||||
\(936\) | −0.339302 | −0.0110904 | ||||||||
\(937\) | 21.8111 | − | 37.7780i | 0.712538 | − | 1.23415i | −0.251363 | − | 0.967893i | \(-0.580879\pi\) |
0.963901 | − | 0.266260i | \(-0.0857879\pi\) | |||||||
\(938\) | 60.9690 | 1.99071 | ||||||||
\(939\) | −1.45686 | + | 2.52336i | −0.0475429 | + | 0.0823468i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.74084 | − | 6.47933i | −0.121948 | − | 0.211220i | 0.798588 | − | 0.601878i | \(-0.205581\pi\) |
−0.920536 | + | 0.390658i | \(0.872247\pi\) | |||||||
\(942\) | 23.5387 | − | 40.7703i | 0.766933 | − | 1.32837i | ||||
\(943\) | 7.07280 | 0.230322 | ||||||||
\(944\) | 7.10009 | − | 12.2977i | 0.231088 | − | 0.400256i | ||||
\(945\) | 10.7789 | − | 18.6697i | 0.350639 | − | 0.607324i | ||||
\(946\) | 1.64883 | − | 2.85586i | 0.0536081 | − | 0.0928519i | ||||
\(947\) | −25.3649 | −0.824250 | −0.412125 | − | 0.911127i | \(-0.635213\pi\) | ||||
−0.412125 | + | 0.911127i | \(0.635213\pi\) | |||||||
\(948\) | −30.3961 | −0.987219 | ||||||||
\(949\) | −1.37779 | −0.0447249 | ||||||||
\(950\) | −3.10028 | + | 5.36984i | −0.100586 | + | 0.174221i | ||||
\(951\) | 6.32933 | − | 10.9627i | 0.205243 | − | 0.355491i | ||||
\(952\) | 9.28802 | + | 16.0873i | 0.301027 | + | 0.521393i | ||||
\(953\) | −0.415160 | − | 0.719078i | −0.0134484 | − | 0.0232932i | 0.859223 | − | 0.511601i | \(-0.170948\pi\) |
−0.872671 | + | 0.488308i | \(0.837614\pi\) | |||||||
\(954\) | −19.3799 | −0.627448 | ||||||||
\(955\) | 16.7331 | + | 28.9826i | 0.541471 | + | 0.937855i | ||||
\(956\) | 10.4734 | − | 18.1405i | 0.338735 | − | 0.586706i | ||||
\(957\) | −6.54193 | − | 11.3310i | −0.211471 | − | 0.366278i | ||||
\(958\) | 37.3552 | 1.20689 | ||||||||
\(959\) | 20.2129 | − | 35.0098i | 0.652709 | − | 1.13053i | ||||
\(960\) | −1.99271 | + | 3.45147i | −0.0643143 | + | 0.111396i | ||||
\(961\) | −33.7589 | − | 58.4721i | −1.08900 | − | 1.88620i | ||||
\(962\) | 0.325620 | 0.0104984 | ||||||||
\(963\) | −2.74572 | + | 4.75573i | −0.0884796 | + | 0.153251i | ||||
\(964\) | 22.1150 | 0.712276 | ||||||||
\(965\) | 33.6089 | 1.08191 | ||||||||
\(966\) | −4.04836 | + | 7.01197i | −0.130254 | + | 0.225606i | ||||
\(967\) | 17.4574 | + | 30.2371i | 0.561392 | + | 0.972359i | 0.997375 | + | 0.0724044i | \(0.0230672\pi\) |
−0.435984 | + | 0.899955i | \(0.643599\pi\) | |||||||
\(968\) | 5.22640 | + | 9.05239i | 0.167983 | + | 0.290955i | ||||
\(969\) | 16.3135 | + | 28.2557i | 0.524064 | + | 0.907705i | ||||
\(970\) | 2.00826 | − | 3.47841i | 0.0644813 | − | 0.111685i | ||||
\(971\) | 13.6652 | + | 23.6688i | 0.438537 | + | 0.759568i | 0.997577 | − | 0.0695728i | \(-0.0221636\pi\) |
−0.559040 | + | 0.829141i | \(0.688830\pi\) | |||||||
\(972\) | −8.32623 | + | 14.4215i | −0.267064 | + | 0.462568i | ||||
\(973\) | 50.7483 | 1.62692 | ||||||||
\(974\) | 4.42640 | + | 7.66675i | 0.141831 | + | 0.245659i | ||||
\(975\) | 0.348969 | + | 0.604432i | 0.0111760 | + | 0.0193573i | ||||
\(976\) | −0.823951 | − | 1.42712i | −0.0263740 | − | 0.0456811i | ||||
\(977\) | 27.3018 | 0.873461 | 0.436731 | − | 0.899592i | \(-0.356136\pi\) | ||||
0.436731 | + | 0.899592i | \(0.356136\pi\) | |||||||
\(978\) | −9.91570 | − | 17.1745i | −0.317069 | − | 0.549180i | ||||
\(979\) | 2.45187 | 0.0783621 | ||||||||
\(980\) | −24.9984 | −0.798545 | ||||||||
\(981\) | −17.8449 | + | 6.30672i | −0.569742 | + | 0.201358i | ||||
\(982\) | −4.42687 | −0.141267 | ||||||||
\(983\) | −44.4347 | −1.41725 | −0.708623 | − | 0.705587i | \(-0.750683\pi\) | ||||
−0.708623 | + | 0.705587i | \(0.750683\pi\) | |||||||
\(984\) | −9.57798 | − | 16.5895i | −0.305335 | − | 0.528855i | ||||
\(985\) | −36.7498 | −1.17095 | ||||||||
\(986\) | −16.4348 | − | 28.4658i | −0.523389 | − | 0.906537i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.341383 | − | 0.591293i | −0.0108608 | − | 0.0188115i | ||||
\(989\) | 3.61093 | 0.114821 | ||||||||
\(990\) | 1.21808 | − | 2.10977i | 0.0387131 | − | 0.0670530i | ||||
\(991\) | −11.0807 | − | 19.1923i | −0.351989 | − | 0.609663i | 0.634609 | − | 0.772833i | \(-0.281161\pi\) |
−0.986598 | + | 0.163171i | \(0.947828\pi\) | |||||||
\(992\) | 4.96281 | − | 8.59583i | 0.157569 | − | 0.272918i | ||||
\(993\) | 36.4029 | + | 63.0517i | 1.15521 | + | 2.00089i | ||||
\(994\) | −2.01189 | − | 3.48469i | −0.0638132 | − | 0.110528i | ||||
\(995\) | 21.0265 | + | 36.4191i | 0.666586 | + | 1.15456i | ||||
\(996\) | 4.45182 | − | 7.71077i | 0.141061 | − | 0.244325i | ||||
\(997\) | 12.2002 | 0.386386 | 0.193193 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193193 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(998\) | −10.5737 | −0.334705 | ||||||||
\(999\) | 2.26550 | − | 3.92397i | 0.0716774 | − | 0.124149i |
(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 | 218.2.c.c.63.4 | yes | 10 | |
3.2 | odd | 2 | 1962.2.f.k.1153.1 | 10 | |||
109.45 | even | 3 | inner | 218.2.c.c.45.4 | ✓ | 10 | |
327.263 | odd | 6 | 1962.2.f.k.1135.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
218.2.c.c.45.4 | ✓ | 10 | 109.45 | even | 3 | inner | |
218.2.c.c.63.4 | yes | 10 | 1.1 | even | 1 | trivial | |
1962.2.f.k.1135.1 | 10 | 327.263 | odd | 6 | |||
1962.2.f.k.1153.1 | 10 | 3.2 | odd | 2 |