Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.9 | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.f.191.9 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1.65121 | + | 0.522966i | 0.953329 | + | 0.301934i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | −1.53738 | + | 0.797792i | −0.627632 | + | 0.325697i | ||||
\(7\) | 3.44243 | 1.30111 | 0.650557 | − | 0.759457i | \(-0.274535\pi\) | ||||
0.650557 | + | 0.759457i | \(0.274535\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.45301 | + | 1.72706i | 0.817671 | + | 0.575685i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.04782 | 0.918952 | 0.459476 | − | 0.888190i | \(-0.348037\pi\) | ||||
0.459476 | + | 0.888190i | \(0.348037\pi\) | |||||||
\(12\) | 0.522966 | − | 1.65121i | 0.150967 | − | 0.476664i | ||||
\(13\) | 0.571765 | − | 0.571765i | 0.158579 | − | 0.158579i | −0.623358 | − | 0.781937i | \(-0.714232\pi\) |
0.781937 | + | 0.623358i | \(0.214232\pi\) | |||||||
\(14\) | −2.43416 | + | 2.43416i | −0.650557 | + | 0.650557i | ||||
\(15\) | 0.797792 | + | 1.53738i | 0.205989 | + | 0.396949i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.58006 | − | 1.58006i | −0.383220 | − | 0.383220i | 0.489041 | − | 0.872261i | \(-0.337347\pi\) |
−0.872261 | + | 0.489041i | \(0.837347\pi\) | |||||||
\(18\) | −2.95576 | + | 0.513330i | −0.696678 | + | 0.120993i | ||||
\(19\) | 2.90693 | − | 2.90693i | 0.666896 | − | 0.666896i | −0.290100 | − | 0.956996i | \(-0.593689\pi\) |
0.956996 | + | 0.290100i | \(0.0936885\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | 5.68418 | + | 1.80027i | 1.24039 | + | 0.392851i | ||||
\(22\) | −2.15513 | + | 2.15513i | −0.459476 | + | 0.459476i | ||||
\(23\) | −2.05150 | − | 2.05150i | −0.427768 | − | 0.427768i | 0.460100 | − | 0.887867i | \(-0.347814\pi\) |
−0.887867 | + | 0.460100i | \(0.847814\pi\) | |||||||
\(24\) | 0.797792 | + | 1.53738i | 0.162849 | + | 0.313816i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0.808598i | 0.158579i | ||||||||
\(27\) | 3.14726 | + | 4.13458i | 0.605691 | + | 0.795700i | ||||
\(28\) | − | 3.44243i | − | 0.650557i | ||||||
\(29\) | −1.83352 | + | 1.83352i | −0.340476 | + | 0.340476i | −0.856546 | − | 0.516070i | \(-0.827394\pi\) |
0.516070 | + | 0.856546i | \(0.327394\pi\) | |||||||
\(30\) | −1.65121 | − | 0.522966i | −0.301469 | − | 0.0954800i | ||||
\(31\) | −6.33851 | − | 6.33851i | −1.13843 | − | 1.13843i | −0.988732 | − | 0.149699i | \(-0.952169\pi\) |
−0.149699 | − | 0.988732i | \(-0.547831\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 5.03260 | + | 1.59390i | 0.876064 | + | 0.277463i | ||||
\(34\) | 2.23454 | 0.383220 | ||||||||
\(35\) | 2.43416 | + | 2.43416i | 0.411449 | + | 0.411449i | ||||
\(36\) | 1.72706 | − | 2.45301i | 0.287843 | − | 0.408836i | ||||
\(37\) | −1.89635 | − | 5.77961i | −0.311757 | − | 0.950162i | ||||
\(38\) | 4.11103i | 0.666896i | ||||||||
\(39\) | 1.24312 | − | 0.645093i | 0.199059 | − | 0.103298i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −8.00829 | −1.25069 | −0.625343 | − | 0.780350i | \(-0.715041\pi\) | ||||
−0.625343 | + | 0.780350i | \(0.715041\pi\) | |||||||
\(42\) | −5.29231 | + | 2.74634i | −0.816621 | + | 0.423769i | ||||
\(43\) | 3.17436 | − | 3.17436i | 0.484086 | − | 0.484086i | −0.422348 | − | 0.906434i | \(-0.638794\pi\) |
0.906434 | + | 0.422348i | \(0.138794\pi\) | |||||||
\(44\) | − | 3.04782i | − | 0.459476i | ||||||
\(45\) | 0.513330 | + | 2.95576i | 0.0765227 | + | 0.440618i | ||||
\(46\) | 2.90126 | 0.427768 | ||||||||
\(47\) | 7.90227i | 1.15266i | 0.817216 | + | 0.576332i | \(0.195517\pi\) | ||||
−0.817216 | + | 0.576332i | \(0.804483\pi\) | |||||||
\(48\) | −1.65121 | − | 0.522966i | −0.238332 | − | 0.0754836i | ||||
\(49\) | 4.85029 | 0.692899 | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.100000 | − | 0.100000i | ||||
\(51\) | −1.78270 | − | 3.43533i | −0.249627 | − | 0.481042i | ||||
\(52\) | −0.571765 | − | 0.571765i | −0.0792896 | − | 0.0792896i | ||||
\(53\) | 12.4574i | 1.71115i | 0.517680 | + | 0.855574i | \(0.326796\pi\) | ||||
−0.517680 | + | 0.855574i | \(0.673204\pi\) | |||||||
\(54\) | −5.14904 | − | 0.698141i | −0.700695 | − | 0.0950049i | ||||
\(55\) | 2.15513 | + | 2.15513i | 0.290598 | + | 0.290598i | ||||
\(56\) | 2.43416 | + | 2.43416i | 0.325279 | + | 0.325279i | ||||
\(57\) | 6.32020 | − | 3.27974i | 0.837131 | − | 0.434413i | ||||
\(58\) | − | 2.59299i | − | 0.340476i | ||||||
\(59\) | 2.00686 | + | 2.00686i | 0.261271 | + | 0.261271i | 0.825570 | − | 0.564300i | \(-0.190854\pi\) |
−0.564300 | + | 0.825570i | \(0.690854\pi\) | |||||||
\(60\) | 1.53738 | − | 0.797792i | 0.198475 | − | 0.102995i | ||||
\(61\) | 2.00335 | + | 2.00335i | 0.256502 | + | 0.256502i | 0.823630 | − | 0.567128i | \(-0.191945\pi\) |
−0.567128 | + | 0.823630i | \(0.691945\pi\) | |||||||
\(62\) | 8.96401 | 1.13843 | ||||||||
\(63\) | 8.44432 | + | 5.94526i | 1.06388 | + | 0.749032i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.808598 | 0.100294 | ||||||||
\(66\) | −4.68565 | + | 2.43153i | −0.576763 | + | 0.299300i | ||||
\(67\) | − | 9.46914i | − | 1.15684i | −0.815739 | − | 0.578420i | \(-0.803670\pi\) | ||
0.815739 | − | 0.578420i | \(-0.196330\pi\) | |||||||
\(68\) | −1.58006 | + | 1.58006i | −0.191610 | + | 0.191610i | ||||
\(69\) | −2.31460 | − | 4.46033i | −0.278645 | − | 0.536961i | ||||
\(70\) | −3.44243 | −0.411449 | ||||||||
\(71\) | − | 11.8558i | − | 1.40702i | −0.710685 | − | 0.703511i | \(-0.751615\pi\) | ||
0.710685 | − | 0.703511i | \(-0.248385\pi\) | |||||||
\(72\) | 0.513330 | + | 2.95576i | 0.0604965 | + | 0.348339i | ||||
\(73\) | 4.40734i | 0.515841i | 0.966166 | + | 0.257920i | \(0.0830372\pi\) | ||||
−0.966166 | + | 0.257920i | \(0.916963\pi\) | |||||||
\(74\) | 5.42772 | + | 2.74588i | 0.630960 | + | 0.319202i | ||||
\(75\) | −0.522966 | + | 1.65121i | −0.0603869 | + | 0.190666i | ||||
\(76\) | −2.90693 | − | 2.90693i | −0.333448 | − | 0.333448i | ||||
\(77\) | 10.4919 | 1.19566 | ||||||||
\(78\) | −0.422869 | + | 1.33517i | −0.0478805 | + | 0.151178i | ||||
\(79\) | −8.20854 | + | 8.20854i | −0.923533 | + | 0.923533i | −0.997277 | − | 0.0737442i | \(-0.976505\pi\) |
0.0737442 | + | 0.997277i | \(0.476505\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | 3.03456 | + | 8.47298i | 0.337173 | + | 0.941443i | ||||
\(82\) | 5.66272 | − | 5.66272i | 0.625343 | − | 0.625343i | ||||
\(83\) | 10.8401i | 1.18986i | 0.803779 | + | 0.594928i | \(0.202819\pi\) | ||||
−0.803779 | + | 0.594928i | \(0.797181\pi\) | |||||||
\(84\) | 1.80027 | − | 5.68418i | 0.196426 | − | 0.620195i | ||||
\(85\) | − | 2.23454i | − | 0.242370i | ||||||
\(86\) | 4.48922i | 0.484086i | ||||||||
\(87\) | −3.98641 | + | 2.06867i | −0.427388 | + | 0.221784i | ||||
\(88\) | 2.15513 | + | 2.15513i | 0.229738 | + | 0.229738i | ||||
\(89\) | −9.90966 | + | 9.90966i | −1.05042 | + | 1.05042i | −0.0517620 | + | 0.998659i | \(0.516484\pi\) |
−0.998659 | + | 0.0517620i | \(0.983516\pi\) | |||||||
\(90\) | −2.45301 | − | 1.72706i | −0.258570 | − | 0.182048i | ||||
\(91\) | 1.96826 | − | 1.96826i | 0.206330 | − | 0.206330i | ||||
\(92\) | −2.05150 | + | 2.05150i | −0.213884 | + | 0.213884i | ||||
\(93\) | −7.15142 | − | 13.7811i | −0.741568 | − | 1.42903i | ||||
\(94\) | −5.58775 | − | 5.58775i | −0.576332 | − | 0.576332i | ||||
\(95\) | 4.11103 | 0.421782 | ||||||||
\(96\) | 1.53738 | − | 0.797792i | 0.156908 | − | 0.0814243i | ||||
\(97\) | 2.40351 | − | 2.40351i | 0.244040 | − | 0.244040i | −0.574479 | − | 0.818519i | \(-0.694795\pi\) |
0.818519 | + | 0.574479i | \(0.194795\pi\) | |||||||
\(98\) | −3.42968 | + | 3.42968i | −0.346450 | + | 0.346450i | ||||
\(99\) | 7.47635 | + | 5.26376i | 0.751401 | + | 0.529027i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.17467 | −0.216387 | −0.108194 | − | 0.994130i | \(-0.534507\pi\) | ||||
−0.108194 | + | 0.994130i | \(0.534507\pi\) | |||||||
\(102\) | 3.68970 | + | 1.16859i | 0.365335 | + | 0.115707i | ||||
\(103\) | −0.494936 | − | 0.494936i | −0.0487675 | − | 0.0487675i | 0.682302 | − | 0.731070i | \(-0.260979\pi\) |
−0.731070 | + | 0.682302i | \(0.760979\pi\) | |||||||
\(104\) | 0.808598 | 0.0792896 | ||||||||
\(105\) | 2.74634 | + | 5.29231i | 0.268015 | + | 0.516476i | ||||
\(106\) | −8.80868 | − | 8.80868i | −0.855574 | − | 0.855574i | ||||
\(107\) | − | 0.470042i | − | 0.0454406i | −0.999742 | − | 0.0227203i | \(-0.992767\pi\) | ||
0.999742 | − | 0.0227203i | \(-0.00723272\pi\) | |||||||
\(108\) | 4.13458 | − | 3.14726i | 0.397850 | − | 0.302845i | ||||
\(109\) | −3.18770 | + | 3.18770i | −0.305327 | + | 0.305327i | −0.843094 | − | 0.537767i | \(-0.819268\pi\) |
0.537767 | + | 0.843094i | \(0.319268\pi\) | |||||||
\(110\) | −3.04782 | −0.290598 | ||||||||
\(111\) | −0.108737 | − | 10.5351i | −0.0103208 | − | 0.999947i | ||||
\(112\) | −3.44243 | −0.325279 | ||||||||
\(113\) | −2.24895 | + | 2.24895i | −0.211563 | + | 0.211563i | −0.804931 | − | 0.593368i | \(-0.797798\pi\) |
0.593368 | + | 0.804931i | \(0.297798\pi\) | |||||||
\(114\) | −2.14992 | + | 6.78818i | −0.201359 | + | 0.635772i | ||||
\(115\) | − | 2.90126i | − | 0.270544i | ||||||
\(116\) | 1.83352 | + | 1.83352i | 0.170238 | + | 0.170238i | ||||
\(117\) | 2.39002 | − | 0.415078i | 0.220957 | − | 0.0383740i | ||||
\(118\) | −2.83813 | −0.261271 | ||||||||
\(119\) | −5.43923 | − | 5.43923i | −0.498613 | − | 0.498613i | ||||
\(120\) | −0.522966 | + | 1.65121i | −0.0477400 | + | 0.150735i | ||||
\(121\) | −1.71079 | −0.155526 | ||||||||
\(122\) | −2.83316 | −0.256502 | ||||||||
\(123\) | −13.2234 | − | 4.18806i | −1.19231 | − | 0.377625i | ||||
\(124\) | −6.33851 | + | 6.33851i | −0.569215 | + | 0.569215i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | −10.1750 | + | 1.76710i | −0.906458 | + | 0.157426i | ||||
\(127\) | −3.84862 | −0.341510 | −0.170755 | − | 0.985314i | \(-0.554621\pi\) | ||||
−0.170755 | + | 0.985314i | \(0.554621\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 6.90163 | − | 3.58147i | 0.607655 | − | 0.315331i | ||||
\(130\) | −0.571765 | + | 0.571765i | −0.0501471 | + | 0.0501471i | ||||
\(131\) | 9.42329 | − | 9.42329i | 0.823317 | − | 0.823317i | −0.163265 | − | 0.986582i | \(-0.552203\pi\) |
0.986582 | + | 0.163265i | \(0.0522027\pi\) | |||||||
\(132\) | 1.59390 | − | 5.03260i | 0.138732 | − | 0.438032i | ||||
\(133\) | 10.0069 | − | 10.0069i | 0.867709 | − | 0.867709i | ||||
\(134\) | 6.69569 | + | 6.69569i | 0.578420 | + | 0.578420i | ||||
\(135\) | −0.698141 | + | 5.14904i | −0.0600864 | + | 0.443159i | ||||
\(136\) | − | 2.23454i | − | 0.191610i | ||||||
\(137\) | − | 14.5392i | − | 1.24217i | −0.783745 | − | 0.621083i | \(-0.786693\pi\) | ||
0.783745 | − | 0.621083i | \(-0.213307\pi\) | |||||||
\(138\) | 4.79060 | + | 1.51726i | 0.407803 | + | 0.129158i | ||||
\(139\) | 16.7132i | 1.41760i | 0.705410 | + | 0.708799i | \(0.250763\pi\) | ||||
−0.705410 | + | 0.708799i | \(0.749237\pi\) | |||||||
\(140\) | 2.43416 | − | 2.43416i | 0.205724 | − | 0.205724i | ||||
\(141\) | −4.13261 | + | 13.0483i | −0.348029 | + | 1.09887i | ||||
\(142\) | 8.38330 | + | 8.38330i | 0.703511 | + | 0.703511i | ||||
\(143\) | 1.74264 | − | 1.74264i | 0.145727 | − | 0.145727i | ||||
\(144\) | −2.45301 | − | 1.72706i | −0.204418 | − | 0.143921i | ||||
\(145\) | −2.59299 | −0.215336 | ||||||||
\(146\) | −3.11646 | − | 3.11646i | −0.257920 | − | 0.257920i | ||||
\(147\) | 8.00887 | + | 2.53654i | 0.660561 | + | 0.209210i | ||||
\(148\) | −5.77961 | + | 1.89635i | −0.475081 | + | 0.155879i | ||||
\(149\) | 11.2348i | 0.920388i | 0.887818 | + | 0.460194i | \(0.152220\pi\) | ||||
−0.887818 | + | 0.460194i | \(0.847780\pi\) | |||||||
\(150\) | −0.797792 | − | 1.53738i | −0.0651394 | − | 0.125526i | ||||
\(151\) | 18.1204i | 1.47462i | 0.675557 | + | 0.737308i | \(0.263903\pi\) | ||||
−0.675557 | + | 0.737308i | \(0.736097\pi\) | |||||||
\(152\) | 4.11103 | 0.333448 | ||||||||
\(153\) | −1.14706 | − | 6.60475i | −0.0927339 | − | 0.533962i | ||||
\(154\) | −7.41889 | + | 7.41889i | −0.597831 | + | 0.597831i | ||||
\(155\) | − | 8.96401i | − | 0.720007i | ||||||
\(156\) | −0.645093 | − | 1.24312i | −0.0516488 | − | 0.0995293i | ||||
\(157\) | 15.7039 | 1.25331 | 0.626653 | − | 0.779298i | \(-0.284424\pi\) | ||||
0.626653 | + | 0.779298i | \(0.284424\pi\) | |||||||
\(158\) | − | 11.6086i | − | 0.923533i | ||||||
\(159\) | −6.51476 | + | 20.5697i | −0.516654 | + | 1.63129i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −7.06214 | − | 7.06214i | −0.556575 | − | 0.556575i | ||||
\(162\) | −8.13706 | − | 3.84555i | −0.639308 | − | 0.302135i | ||||
\(163\) | 4.76257 | + | 4.76257i | 0.373033 | + | 0.373033i | 0.868581 | − | 0.495548i | \(-0.165033\pi\) |
−0.495548 | + | 0.868581i | \(0.665033\pi\) | |||||||
\(164\) | 8.00829i | 0.625343i | ||||||||
\(165\) | 2.43153 | + | 4.68565i | 0.189294 | + | 0.364777i | ||||
\(166\) | −7.66511 | − | 7.66511i | −0.594928 | − | 0.594928i | ||||
\(167\) | −7.41766 | − | 7.41766i | −0.573996 | − | 0.573996i | 0.359247 | − | 0.933243i | \(-0.383034\pi\) |
−0.933243 | + | 0.359247i | \(0.883034\pi\) | |||||||
\(168\) | 2.74634 | + | 5.29231i | 0.211885 | + | 0.408310i | ||||
\(169\) | 12.3462i | 0.949705i | ||||||||
\(170\) | 1.58006 | + | 1.58006i | 0.121185 | + | 0.121185i | ||||
\(171\) | 12.1512 | − | 2.11031i | 0.929225 | − | 0.161380i | ||||
\(172\) | −3.17436 | − | 3.17436i | −0.242043 | − | 0.242043i | ||||
\(173\) | −22.1763 | −1.68603 | −0.843016 | − | 0.537889i | \(-0.819222\pi\) | ||||
−0.843016 | + | 0.537889i | \(0.819222\pi\) | |||||||
\(174\) | 1.35605 | − | 4.28158i | 0.102802 | − | 0.324586i | ||||
\(175\) | 3.44243i | 0.260223i | ||||||||
\(176\) | −3.04782 | −0.229738 | ||||||||
\(177\) | 2.26423 | + | 4.36327i | 0.170190 | + | 0.327963i | ||||
\(178\) | − | 14.0144i | − | 1.05042i | ||||||
\(179\) | −6.95933 | + | 6.95933i | −0.520165 | + | 0.520165i | −0.917621 | − | 0.397456i | \(-0.869893\pi\) |
0.397456 | + | 0.917621i | \(0.369893\pi\) | |||||||
\(180\) | 2.95576 | − | 0.513330i | 0.220309 | − | 0.0382614i | ||||
\(181\) | −0.826713 | −0.0614491 | −0.0307246 | − | 0.999528i | \(-0.509781\pi\) | ||||
−0.0307246 | + | 0.999528i | \(0.509781\pi\) | |||||||
\(182\) | 2.78354i | 0.206330i | ||||||||
\(183\) | 2.26027 | + | 4.35563i | 0.167084 | + | 0.321978i | ||||
\(184\) | − | 2.90126i | − | 0.213884i | ||||||
\(185\) | 2.74588 | − | 5.42772i | 0.201881 | − | 0.399054i | ||||
\(186\) | 14.8015 | + | 4.68787i | 1.08530 | + | 0.343731i | ||||
\(187\) | −4.81573 | − | 4.81573i | −0.352161 | − | 0.352161i | ||||
\(188\) | 7.90227 | 0.576332 | ||||||||
\(189\) | 10.8342 | + | 14.2330i | 0.788073 | + | 1.03530i | ||||
\(190\) | −2.90693 | + | 2.90693i | −0.210891 | + | 0.210891i | ||||
\(191\) | −1.75243 | − | 1.75243i | −0.126801 | − | 0.126801i | 0.640858 | − | 0.767659i | \(-0.278579\pi\) |
−0.767659 | + | 0.640858i | \(0.778579\pi\) | |||||||
\(192\) | −0.522966 | + | 1.65121i | −0.0377418 | + | 0.119166i | ||||
\(193\) | 5.62234 | − | 5.62234i | 0.404705 | − | 0.404705i | −0.475183 | − | 0.879887i | \(-0.657618\pi\) |
0.879887 | + | 0.475183i | \(0.157618\pi\) | |||||||
\(194\) | 3.39908i | 0.244040i | ||||||||
\(195\) | 1.33517 | + | 0.422869i | 0.0956134 | + | 0.0302823i | ||||
\(196\) | − | 4.85029i | − | 0.346450i | ||||||
\(197\) | − | 17.8517i | − | 1.27188i | −0.771738 | − | 0.635941i | \(-0.780612\pi\) | ||
0.771738 | − | 0.635941i | \(-0.219388\pi\) | |||||||
\(198\) | −9.00861 | + | 1.56454i | −0.640214 | + | 0.111187i | ||||
\(199\) | 1.86996 | + | 1.86996i | 0.132558 | + | 0.132558i | 0.770273 | − | 0.637715i | \(-0.220120\pi\) |
−0.637715 | + | 0.770273i | \(0.720120\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.0500000 | + | 0.0500000i | ||||
\(201\) | 4.95203 | − | 15.6356i | 0.349290 | − | 1.10285i | ||||
\(202\) | 1.53772 | − | 1.53772i | 0.108194 | − | 0.108194i | ||||
\(203\) | −6.31176 | + | 6.31176i | −0.442999 | + | 0.442999i | ||||
\(204\) | −3.43533 | + | 1.78270i | −0.240521 | + | 0.124814i | ||||
\(205\) | −5.66272 | − | 5.66272i | −0.395501 | − | 0.395501i | ||||
\(206\) | 0.699945 | 0.0487675 | ||||||||
\(207\) | −1.48930 | − | 8.57542i | −0.103514 | − | 0.596033i | ||||
\(208\) | −0.571765 | + | 0.571765i | −0.0396448 | + | 0.0396448i | ||||
\(209\) | 8.85981 | − | 8.85981i | 0.612846 | − | 0.612846i | ||||
\(210\) | −5.68418 | − | 1.80027i | −0.392246 | − | 0.124230i | ||||
\(211\) | −19.4431 | −1.33852 | −0.669258 | − | 0.743030i | \(-0.733388\pi\) | ||||
−0.669258 | + | 0.743030i | \(0.733388\pi\) | |||||||
\(212\) | 12.4574 | 0.855574 | ||||||||
\(213\) | 6.20016 | − | 19.5764i | 0.424828 | − | 1.34135i | ||||
\(214\) | 0.332370 | + | 0.332370i | 0.0227203 | + | 0.0227203i | ||||
\(215\) | 4.48922 | 0.306163 | ||||||||
\(216\) | −0.698141 | + | 5.14904i | −0.0475024 | + | 0.350348i | ||||
\(217\) | −21.8199 | − | 21.8199i | −1.48123 | − | 1.48123i | ||||
\(218\) | − | 4.50809i | − | 0.305327i | ||||||
\(219\) | −2.30489 | + | 7.27747i | −0.155750 | + | 0.491766i | ||||
\(220\) | 2.15513 | − | 2.15513i | 0.145299 | − | 0.145299i | ||||
\(221\) | −1.80684 | −0.121541 | ||||||||
\(222\) | 7.52632 | + | 7.37255i | 0.505134 | + | 0.494813i | ||||
\(223\) | 24.8953 | 1.66711 | 0.833555 | − | 0.552436i | \(-0.186302\pi\) | ||||
0.833555 | + | 0.552436i | \(0.186302\pi\) | |||||||
\(224\) | 2.43416 | − | 2.43416i | 0.162639 | − | 0.162639i | ||||
\(225\) | −1.72706 | + | 2.45301i | −0.115137 | + | 0.163534i | ||||
\(226\) | − | 3.18049i | − | 0.211563i | ||||||
\(227\) | −6.99137 | − | 6.99137i | −0.464033 | − | 0.464033i | 0.435942 | − | 0.899975i | \(-0.356415\pi\) |
−0.899975 | + | 0.435942i | \(0.856415\pi\) | |||||||
\(228\) | −3.27974 | − | 6.32020i | −0.217206 | − | 0.418565i | ||||
\(229\) | −19.5563 | −1.29232 | −0.646158 | − | 0.763204i | \(-0.723625\pi\) | ||||
−0.646158 | + | 0.763204i | \(0.723625\pi\) | |||||||
\(230\) | 2.05150 | + | 2.05150i | 0.135272 | + | 0.135272i | ||||
\(231\) | 17.3244 | + | 5.48690i | 1.13986 | + | 0.361011i | ||||
\(232\) | −2.59299 | −0.170238 | ||||||||
\(233\) | 17.7356 | 1.16190 | 0.580949 | − | 0.813940i | \(-0.302682\pi\) | ||||
0.580949 | + | 0.813940i | \(0.302682\pi\) | |||||||
\(234\) | −1.39649 | + | 1.98350i | −0.0912917 | + | 0.129666i | ||||
\(235\) | −5.58775 | + | 5.58775i | −0.364504 | + | 0.364504i | ||||
\(236\) | 2.00686 | − | 2.00686i | 0.130635 | − | 0.130635i | ||||
\(237\) | −17.8468 | + | 9.26127i | −1.15928 | + | 0.601584i | ||||
\(238\) | 7.69223 | 0.498613 | ||||||||
\(239\) | −4.92552 | − | 4.92552i | −0.318606 | − | 0.318606i | 0.529626 | − | 0.848231i | \(-0.322332\pi\) |
−0.848231 | + | 0.529626i | \(0.822332\pi\) | |||||||
\(240\) | −0.797792 | − | 1.53738i | −0.0514973 | − | 0.0992373i | ||||
\(241\) | 18.5971 | − | 18.5971i | 1.19794 | − | 1.19794i | 0.223163 | − | 0.974781i | \(-0.428362\pi\) |
0.974781 | − | 0.223163i | \(-0.0716383\pi\) | |||||||
\(242\) | 1.20971 | − | 1.20971i | 0.0777632 | − | 0.0777632i | ||||
\(243\) | 0.579624 | + | 15.5777i | 0.0371829 | + | 0.999308i | ||||
\(244\) | 2.00335 | − | 2.00335i | 0.128251 | − | 0.128251i | ||||
\(245\) | 3.42968 | + | 3.42968i | 0.219114 | + | 0.219114i | ||||
\(246\) | 12.3118 | − | 6.38895i | 0.784969 | − | 0.407345i | ||||
\(247\) | − | 3.32417i | − | 0.211512i | ||||||
\(248\) | − | 8.96401i | − | 0.569215i | ||||||
\(249\) | −5.66900 | + | 17.8993i | −0.359258 | + | 1.13432i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 15.0856 | − | 15.0856i | 0.952195 | − | 0.952195i | −0.0467134 | − | 0.998908i | \(-0.514875\pi\) |
0.998908 | + | 0.0467134i | \(0.0148747\pi\) | |||||||
\(252\) | 5.94526 | − | 8.44432i | 0.374516 | − | 0.531942i | ||||
\(253\) | −6.25261 | − | 6.25261i | −0.393098 | − | 0.393098i | ||||
\(254\) | 2.72139 | − | 2.72139i | 0.170755 | − | 0.170755i | ||||
\(255\) | 1.16859 | − | 3.68970i | 0.0731797 | − | 0.231058i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.20693 | + | 2.20693i | 0.137665 | + | 0.137665i | 0.772581 | − | 0.634916i | \(-0.218965\pi\) |
−0.634916 | + | 0.772581i | \(0.718965\pi\) | |||||||
\(258\) | −2.34771 | + | 7.41267i | −0.146162 | + | 0.461493i | ||||
\(259\) | −6.52803 | − | 19.8959i | −0.405632 | − | 1.23627i | ||||
\(260\) | − | 0.808598i | − | 0.0501471i | ||||||
\(261\) | −7.66425 | + | 1.33106i | −0.474405 | + | 0.0823906i | ||||
\(262\) | 13.3265i | 0.823317i | ||||||||
\(263\) | 4.11676 | 0.253850 | 0.126925 | − | 0.991912i | \(-0.459489\pi\) | ||||
0.126925 | + | 0.991912i | \(0.459489\pi\) | |||||||
\(264\) | 2.43153 | + | 4.68565i | 0.149650 | + | 0.288382i | ||||
\(265\) | −8.80868 | + | 8.80868i | −0.541113 | + | 0.541113i | ||||
\(266\) | 14.1519i | 0.867709i | ||||||||
\(267\) | −21.5454 | + | 11.1806i | −1.31856 | + | 0.684239i | ||||
\(268\) | −9.46914 | −0.578420 | ||||||||
\(269\) | − | 5.19624i | − | 0.316820i | −0.987373 | − | 0.158410i | \(-0.949363\pi\) | ||
0.987373 | − | 0.158410i | \(-0.0506368\pi\) | |||||||
\(270\) | −3.14726 | − | 4.13458i | −0.191536 | − | 0.251623i | ||||
\(271\) | −4.74810 | −0.288426 | −0.144213 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144213 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(272\) | 1.58006 | + | 1.58006i | 0.0958050 | + | 0.0958050i | ||||
\(273\) | 4.27935 | − | 2.22069i | 0.258998 | − | 0.134402i | ||||
\(274\) | 10.2807 | + | 10.2807i | 0.621083 | + | 0.621083i | ||||
\(275\) | 3.04782i | 0.183790i | ||||||||
\(276\) | −4.46033 | + | 2.31460i | −0.268480 | + | 0.139323i | ||||
\(277\) | −2.25502 | − | 2.25502i | −0.135491 | − | 0.135491i | 0.636109 | − | 0.771599i | \(-0.280543\pi\) |
−0.771599 | + | 0.636109i | \(0.780543\pi\) | |||||||
\(278\) | −11.8180 | − | 11.8180i | −0.708799 | − | 0.708799i | ||||
\(279\) | −4.60150 | − | 26.4954i | −0.275484 | − | 1.58624i | ||||
\(280\) | 3.44243i | 0.205724i | ||||||||
\(281\) | −11.4729 | − | 11.4729i | −0.684416 | − | 0.684416i | 0.276576 | − | 0.960992i | \(-0.410800\pi\) |
−0.960992 | + | 0.276576i | \(0.910800\pi\) | |||||||
\(282\) | −6.30437 | − | 12.1488i | −0.375420 | − | 0.723448i | ||||
\(283\) | −20.8649 | − | 20.8649i | −1.24029 | − | 1.24029i | −0.959881 | − | 0.280407i | \(-0.909531\pi\) |
−0.280407 | − | 0.959881i | \(-0.590469\pi\) | |||||||
\(284\) | −11.8558 | −0.703511 | ||||||||
\(285\) | 6.78818 | + | 2.14992i | 0.402097 | + | 0.127351i | ||||
\(286\) | 2.46446i | 0.145727i | ||||||||
\(287\) | −27.5680 | −1.62728 | ||||||||
\(288\) | 2.95576 | − | 0.513330i | 0.174170 | − | 0.0302483i | ||||
\(289\) | − | 12.0068i | − | 0.706285i | ||||||
\(290\) | 1.83352 | − | 1.83352i | 0.107668 | − | 0.107668i | ||||
\(291\) | 5.22567 | − | 2.71176i | 0.306334 | − | 0.158966i | ||||
\(292\) | 4.40734 | 0.257920 | ||||||||
\(293\) | − | 8.29342i | − | 0.484507i | −0.970213 | − | 0.242253i | \(-0.922113\pi\) | ||
0.970213 | − | 0.242253i | \(-0.0778865\pi\) | |||||||
\(294\) | −7.45673 | + | 3.86953i | −0.434885 | + | 0.225675i | ||||
\(295\) | 2.83813i | 0.165242i | ||||||||
\(296\) | 2.74588 | − | 5.42772i | 0.159601 | − | 0.315480i | ||||
\(297\) | 9.59228 | + | 12.6015i | 0.556601 | + | 0.731211i | ||||
\(298\) | −7.94418 | − | 7.94418i | −0.460194 | − | 0.460194i | ||||
\(299\) | −2.34596 | −0.135670 | ||||||||
\(300\) | 1.65121 | + | 0.522966i | 0.0953329 | + | 0.0301934i | ||||
\(301\) | 10.9275 | − | 10.9275i | 0.629851 | − | 0.629851i | ||||
\(302\) | −12.8130 | − | 12.8130i | −0.737308 | − | 0.737308i | ||||
\(303\) | −3.59084 | − | 1.13727i | −0.206288 | − | 0.0653347i | ||||
\(304\) | −2.90693 | + | 2.90693i | −0.166724 | + | 0.166724i | ||||
\(305\) | 2.83316i | 0.162226i | ||||||||
\(306\) | 5.48135 | + | 3.85917i | 0.313348 | + | 0.220614i | ||||
\(307\) | 7.03890i | 0.401731i | 0.979619 | + | 0.200866i | \(0.0643755\pi\) | ||||
−0.979619 | + | 0.200866i | \(0.935625\pi\) | |||||||
\(308\) | − | 10.4919i | − | 0.597831i | ||||||
\(309\) | −0.558411 | − | 1.07608i | −0.0317669 | − | 0.0612160i | ||||
\(310\) | 6.33851 | + | 6.33851i | 0.360003 | + | 0.360003i | ||||
\(311\) | 5.36146 | − | 5.36146i | 0.304020 | − | 0.304020i | −0.538564 | − | 0.842585i | \(-0.681033\pi\) |
0.842585 | + | 0.538564i | \(0.181033\pi\) | |||||||
\(312\) | 1.33517 | + | 0.422869i | 0.0755891 | + | 0.0239402i | ||||
\(313\) | 16.4404 | − | 16.4404i | 0.929266 | − | 0.929266i | −0.0683922 | − | 0.997659i | \(-0.521787\pi\) |
0.997659 | + | 0.0683922i | \(0.0217869\pi\) | |||||||
\(314\) | −11.1043 | + | 11.1043i | −0.626653 | + | 0.626653i | ||||
\(315\) | 1.76710 | + | 10.1750i | 0.0995648 | + | 0.573295i | ||||
\(316\) | 8.20854 | + | 8.20854i | 0.461766 | + | 0.461766i | ||||
\(317\) | 19.4530 | 1.09259 | 0.546296 | − | 0.837592i | \(-0.316037\pi\) | ||||
0.546296 | + | 0.837592i | \(0.316037\pi\) | |||||||
\(318\) | −9.93838 | − | 19.1516i | −0.557316 | − | 1.07397i | ||||
\(319\) | −5.58825 | + | 5.58825i | −0.312882 | + | 0.312882i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 0.245816 | − | 0.776139i | 0.0137201 | − | 0.0433199i | ||||
\(322\) | 9.98738 | 0.556575 | ||||||||
\(323\) | −9.18624 | −0.511136 | ||||||||
\(324\) | 8.47298 | − | 3.03456i | 0.470721 | − | 0.168586i | ||||
\(325\) | 0.571765 | + | 0.571765i | 0.0317158 | + | 0.0317158i | ||||
\(326\) | −6.73529 | −0.373033 | ||||||||
\(327\) | −6.93064 | + | 3.59652i | −0.383265 | + | 0.198888i | ||||
\(328\) | −5.66272 | − | 5.66272i | −0.312671 | − | 0.312671i | ||||
\(329\) | 27.2030i | 1.49975i | ||||||||
\(330\) | −5.03260 | − | 1.59390i | −0.277036 | − | 0.0877416i | ||||
\(331\) | −16.9551 | + | 16.9551i | −0.931938 | + | 0.931938i | −0.997827 | − | 0.0658890i | \(-0.979012\pi\) |
0.0658890 | + | 0.997827i | \(0.479012\pi\) | |||||||
\(332\) | 10.8401 | 0.594928 | ||||||||
\(333\) | 5.32994 | − | 17.4526i | 0.292079 | − | 0.956394i | ||||
\(334\) | 10.4902 | 0.573996 | ||||||||
\(335\) | 6.69569 | − | 6.69569i | 0.365825 | − | 0.365825i | ||||
\(336\) | −5.68418 | − | 1.80027i | −0.310097 | − | 0.0982128i | ||||
\(337\) | − | 7.08308i | − | 0.385840i | −0.981214 | − | 0.192920i | \(-0.938204\pi\) | ||
0.981214 | − | 0.192920i | \(-0.0617958\pi\) | |||||||
\(338\) | −8.73006 | − | 8.73006i | −0.474853 | − | 0.474853i | ||||
\(339\) | −4.88961 | + | 2.53737i | −0.265567 | + | 0.137811i | ||||
\(340\) | −2.23454 | −0.121185 | ||||||||
\(341\) | −19.3187 | − | 19.3187i | −1.04616 | − | 1.04616i | ||||
\(342\) | −7.09997 | + | 10.0844i | −0.383922 | + | 0.545302i | ||||
\(343\) | −7.40020 | −0.399573 | ||||||||
\(344\) | 4.48922 | 0.242043 | ||||||||
\(345\) | 1.51726 | − | 4.79060i | 0.0816865 | − | 0.257917i | ||||
\(346\) | 15.6810 | − | 15.6810i | 0.843016 | − | 0.843016i | ||||
\(347\) | 8.15272 | − | 8.15272i | 0.437661 | − | 0.437661i | −0.453563 | − | 0.891224i | \(-0.649847\pi\) |
0.891224 | + | 0.453563i | \(0.149847\pi\) | |||||||
\(348\) | 2.06867 | + | 3.98641i | 0.110892 | + | 0.213694i | ||||
\(349\) | −9.72270 | −0.520444 | −0.260222 | − | 0.965549i | \(-0.583796\pi\) | ||||
−0.260222 | + | 0.965549i | \(0.583796\pi\) | |||||||
\(350\) | −2.43416 | − | 2.43416i | −0.130111 | − | 0.130111i | ||||
\(351\) | 4.16350 | + | 0.564515i | 0.222231 | + | 0.0301316i | ||||
\(352\) | 2.15513 | − | 2.15513i | 0.114869 | − | 0.114869i | ||||
\(353\) | −0.400840 | + | 0.400840i | −0.0213345 | + | 0.0213345i | −0.717694 | − | 0.696359i | \(-0.754802\pi\) |
0.696359 | + | 0.717694i | \(0.254802\pi\) | |||||||
\(354\) | −4.68635 | − | 1.48424i | −0.249077 | − | 0.0788866i | ||||
\(355\) | 8.38330 | − | 8.38330i | 0.444939 | − | 0.444939i | ||||
\(356\) | 9.90966 | + | 9.90966i | 0.525211 | + | 0.525211i | ||||
\(357\) | −6.13680 | − | 11.8259i | −0.324794 | − | 0.625891i | ||||
\(358\) | − | 9.84198i | − | 0.520165i | ||||||
\(359\) | − | 35.3458i | − | 1.86548i | −0.360548 | − | 0.932741i | \(-0.617410\pi\) | ||
0.360548 | − | 0.932741i | \(-0.382590\pi\) | |||||||
\(360\) | −1.72706 | + | 2.45301i | −0.0910238 | + | 0.129285i | ||||
\(361\) | 2.09946i | 0.110498i | ||||||||
\(362\) | 0.584575 | − | 0.584575i | 0.0307246 | − | 0.0307246i | ||||
\(363\) | −2.82488 | − | 0.894685i | −0.148268 | − | 0.0469588i | ||||
\(364\) | −1.96826 | − | 1.96826i | −0.103165 | − | 0.103165i | ||||
\(365\) | −3.11646 | + | 3.11646i | −0.163123 | + | 0.163123i | ||||
\(366\) | −4.67815 | − | 1.48164i | −0.244531 | − | 0.0774468i | ||||
\(367\) | 4.27483 | 0.223144 | 0.111572 | − | 0.993756i | \(-0.464411\pi\) | ||||
0.111572 | + | 0.993756i | \(0.464411\pi\) | |||||||
\(368\) | 2.05150 | + | 2.05150i | 0.106942 | + | 0.106942i | ||||
\(369\) | −19.6445 | − | 13.8308i | −1.02265 | − | 0.720001i | ||||
\(370\) | 1.89635 | + | 5.77961i | 0.0985863 | + | 0.300468i | ||||
\(371\) | 42.8835i | 2.22640i | ||||||||
\(372\) | −13.7811 | + | 7.15142i | −0.714515 | + | 0.370784i | ||||
\(373\) | − | 32.8415i | − | 1.70047i | −0.526405 | − | 0.850234i | \(-0.676460\pi\) | ||
0.526405 | − | 0.850234i | \(-0.323540\pi\) | |||||||
\(374\) | 6.81047 | 0.352161 | ||||||||
\(375\) | −1.53738 | + | 0.797792i | −0.0793898 | + | 0.0411978i | ||||
\(376\) | −5.58775 | + | 5.58775i | −0.288166 | + | 0.288166i | ||||
\(377\) | 2.09669i | 0.107985i | ||||||||
\(378\) | −17.7252 | − | 2.40330i | −0.911685 | − | 0.123612i | ||||
\(379\) | 7.66460 | 0.393704 | 0.196852 | − | 0.980433i | \(-0.436928\pi\) | ||||
0.196852 | + | 0.980433i | \(0.436928\pi\) | |||||||
\(380\) | − | 4.11103i | − | 0.210891i | ||||||
\(381\) | −6.35490 | − | 2.01270i | −0.325571 | − | 0.103114i | ||||
\(382\) | 2.47831 | 0.126801 | ||||||||
\(383\) | 3.54407 | + | 3.54407i | 0.181094 | + | 0.181094i | 0.791832 | − | 0.610739i | \(-0.209127\pi\) |
−0.610739 | + | 0.791832i | \(0.709127\pi\) | |||||||
\(384\) | −0.797792 | − | 1.53738i | −0.0407122 | − | 0.0784539i | ||||
\(385\) | 7.41889 | + | 7.41889i | 0.378102 | + | 0.378102i | ||||
\(386\) | 7.95118i | 0.404705i | ||||||||
\(387\) | 13.2691 | − | 2.30445i | 0.674504 | − | 0.117142i | ||||
\(388\) | −2.40351 | − | 2.40351i | −0.122020 | − | 0.122020i | ||||
\(389\) | −18.3139 | − | 18.3139i | −0.928551 | − | 0.928551i | 0.0690616 | − | 0.997612i | \(-0.478000\pi\) |
−0.997612 | + | 0.0690616i | \(0.978000\pi\) | |||||||
\(390\) | −1.24312 | + | 0.645093i | −0.0629479 | + | 0.0326656i | ||||
\(391\) | 6.48298i | 0.327858i | ||||||||
\(392\) | 3.42968 | + | 3.42968i | 0.173225 | + | 0.173225i | ||||
\(393\) | 20.4879 | − | 10.6318i | 1.03348 | − | 0.536304i | ||||
\(394\) | 12.6231 | + | 12.6231i | 0.635941 | + | 0.635941i | ||||
\(395\) | −11.6086 | −0.584094 | ||||||||
\(396\) | 5.26376 | − | 7.47635i | 0.264514 | − | 0.375701i | ||||
\(397\) | 0.886715i | 0.0445029i | 0.999752 | + | 0.0222515i | \(0.00708345\pi\) | ||||
−0.999752 | + | 0.0222515i | \(0.992917\pi\) | |||||||
\(398\) | −2.64453 | −0.132558 | ||||||||
\(399\) | 21.7568 | − | 11.2903i | 1.08920 | − | 0.565221i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −21.7682 | + | 21.7682i | −1.08705 | + | 1.08705i | −0.0912209 | + | 0.995831i | \(0.529077\pi\) |
−0.995831 | + | 0.0912209i | \(0.970923\pi\) | |||||||
\(402\) | 7.55440 | + | 14.5576i | 0.376779 | + | 0.726069i | ||||
\(403\) | −7.24829 | −0.361063 | ||||||||
\(404\) | 2.17467i | 0.108194i | ||||||||
\(405\) | −3.84555 | + | 8.13706i | −0.191087 | + | 0.404334i | ||||
\(406\) | − | 8.92618i | − | 0.442999i | ||||||
\(407\) | −5.77972 | − | 17.6152i | −0.286490 | − | 0.873153i | ||||
\(408\) | 1.16859 | − | 3.68970i | 0.0578536 | − | 0.182667i | ||||
\(409\) | 9.72183 | + | 9.72183i | 0.480713 | + | 0.480713i | 0.905359 | − | 0.424646i | \(-0.139601\pi\) |
−0.424646 | + | 0.905359i | \(0.639601\pi\) | |||||||
\(410\) | 8.00829 | 0.395501 | ||||||||
\(411\) | 7.60348 | − | 24.0073i | 0.375052 | − | 1.18419i | ||||
\(412\) | −0.494936 | + | 0.494936i | −0.0243837 | + | 0.0243837i | ||||
\(413\) | 6.90846 | + | 6.90846i | 0.339943 | + | 0.339943i | ||||
\(414\) | 7.11684 | + | 5.01064i | 0.349773 | + | 0.246260i | ||||
\(415\) | −7.66511 | + | 7.66511i | −0.376266 | + | 0.376266i | ||||
\(416\) | − | 0.808598i | − | 0.0396448i | ||||||
\(417\) | −8.74045 | + | 27.5971i | −0.428021 | + | 1.35144i | ||||
\(418\) | 12.5297i | 0.612846i | ||||||||
\(419\) | 36.1112i | 1.76415i | 0.471109 | + | 0.882075i | \(0.343854\pi\) | ||||
−0.471109 | + | 0.882075i | \(0.656146\pi\) | |||||||
\(420\) | 5.29231 | − | 2.74634i | 0.258238 | − | 0.134008i | ||||
\(421\) | 16.4019 | + | 16.4019i | 0.799382 | + | 0.799382i | 0.982998 | − | 0.183616i | \(-0.0587803\pi\) |
−0.183616 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(422\) | 13.7483 | − | 13.7483i | 0.669258 | − | 0.669258i | ||||
\(423\) | −13.6477 | + | 19.3844i | −0.663572 | + | 0.942501i | ||||
\(424\) | −8.80868 | + | 8.80868i | −0.427787 | + | 0.427787i | ||||
\(425\) | 1.58006 | − | 1.58006i | 0.0766440 | − | 0.0766440i | ||||
\(426\) | 9.45844 | + | 18.2268i | 0.458263 | + | 0.883091i | ||||
\(427\) | 6.89637 | + | 6.89637i | 0.333739 | + | 0.333739i | ||||
\(428\) | −0.470042 | −0.0227203 | ||||||||
\(429\) | 3.78881 | − | 1.96613i | 0.182925 | − | 0.0949256i | ||||
\(430\) | −3.17436 | + | 3.17436i | −0.153081 | + | 0.153081i | ||||
\(431\) | −18.1679 | + | 18.1679i | −0.875118 | + | 0.875118i | −0.993025 | − | 0.117906i | \(-0.962382\pi\) |
0.117906 | + | 0.993025i | \(0.462382\pi\) | |||||||
\(432\) | −3.14726 | − | 4.13458i | −0.151423 | − | 0.198925i | ||||
\(433\) | 31.3276 | 1.50551 | 0.752755 | − | 0.658301i | \(-0.228725\pi\) | ||||
0.752755 | + | 0.658301i | \(0.228725\pi\) | |||||||
\(434\) | 30.8579 | 1.48123 | ||||||||
\(435\) | −4.28158 | − | 1.35605i | −0.205286 | − | 0.0650174i | ||||
\(436\) | 3.18770 | + | 3.18770i | 0.152663 | + | 0.152663i | ||||
\(437\) | −11.9272 | −0.570553 | ||||||||
\(438\) | −3.51614 | − | 6.77575i | −0.168008 | − | 0.323758i | ||||
\(439\) | 21.7605 | + | 21.7605i | 1.03857 | + | 1.03857i | 0.999226 | + | 0.0393487i | \(0.0125283\pi\) |
0.0393487 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(440\) | 3.04782i | 0.145299i | ||||||||
\(441\) | 11.8978 | + | 8.37673i | 0.566564 | + | 0.398892i | ||||
\(442\) | 1.27763 | − | 1.27763i | 0.0607707 | − | 0.0607707i | ||||
\(443\) | 7.20883 | 0.342502 | 0.171251 | − | 0.985227i | \(-0.445219\pi\) | ||||
0.171251 | + | 0.985227i | \(0.445219\pi\) | |||||||
\(444\) | −10.5351 | + | 0.108737i | −0.499973 | + | 0.00516042i | ||||
\(445\) | −14.0144 | −0.664345 | ||||||||
\(446\) | −17.6036 | + | 17.6036i | −0.833555 | + | 0.833555i | ||||
\(447\) | −5.87540 | + | 18.5510i | −0.277897 | + | 0.877432i | ||||
\(448\) | 3.44243i | 0.162639i | ||||||||
\(449\) | 2.23081 | + | 2.23081i | 0.105278 | + | 0.105278i | 0.757784 | − | 0.652506i | \(-0.226282\pi\) |
−0.652506 | + | 0.757784i | \(0.726282\pi\) | |||||||
\(450\) | −0.513330 | − | 2.95576i | −0.0241986 | − | 0.139336i | ||||
\(451\) | −24.4078 | −1.14932 | ||||||||
\(452\) | 2.24895 | + | 2.24895i | 0.105782 | + | 0.105782i | ||||
\(453\) | −9.47633 | + | 29.9206i | −0.445237 | + | 1.40579i | ||||
\(454\) | 9.88729 | 0.464033 | ||||||||
\(455\) | 2.78354 | 0.130494 | ||||||||
\(456\) | 6.78818 | + | 2.14992i | 0.317886 | + | 0.100679i | ||||
\(457\) | 1.56539 | − | 1.56539i | 0.0732256 | − | 0.0732256i | −0.669545 | − | 0.742771i | \(-0.733511\pi\) |
0.742771 | + | 0.669545i | \(0.233511\pi\) | |||||||
\(458\) | 13.8284 | − | 13.8284i | 0.646158 | − | 0.646158i | ||||
\(459\) | 1.56002 | − | 11.5057i | 0.0728155 | − | 0.537041i | ||||
\(460\) | −2.90126 | −0.135272 | ||||||||
\(461\) | −5.71858 | − | 5.71858i | −0.266341 | − | 0.266341i | 0.561283 | − | 0.827624i | \(-0.310308\pi\) |
−0.827624 | + | 0.561283i | \(0.810308\pi\) | |||||||
\(462\) | −16.1300 | + | 8.37035i | −0.750435 | + | 0.389424i | ||||
\(463\) | −24.0600 | + | 24.0600i | −1.11816 | + | 1.11816i | −0.126154 | + | 0.992011i | \(0.540263\pi\) |
−0.992011 | + | 0.126154i | \(0.959737\pi\) | |||||||
\(464\) | 1.83352 | − | 1.83352i | 0.0851191 | − | 0.0851191i | ||||
\(465\) | 4.68787 | − | 14.8015i | 0.217395 | − | 0.686403i | ||||
\(466\) | −12.5410 | + | 12.5410i | −0.580949 | + | 0.580949i | ||||
\(467\) | −2.39895 | − | 2.39895i | −0.111010 | − | 0.111010i | 0.649420 | − | 0.760430i | \(-0.275012\pi\) |
−0.760430 | + | 0.649420i | \(0.775012\pi\) | |||||||
\(468\) | −0.415078 | − | 2.39002i | −0.0191870 | − | 0.110479i | ||||
\(469\) | − | 32.5968i | − | 1.50518i | ||||||
\(470\) | − | 7.90227i | − | 0.364504i | ||||||
\(471\) | 25.9305 | + | 8.21259i | 1.19481 | + | 0.378416i | ||||
\(472\) | 2.83813i | 0.130635i | ||||||||
\(473\) | 9.67488 | − | 9.67488i | 0.444852 | − | 0.444852i | ||||
\(474\) | 6.07091 | − | 19.1683i | 0.278846 | − | 0.880431i | ||||
\(475\) | 2.90693 | + | 2.90693i | 0.133379 | + | 0.133379i | ||||
\(476\) | −5.43923 | + | 5.43923i | −0.249307 | + | 0.249307i | ||||
\(477\) | −21.5145 | + | 30.5581i | −0.985083 | + | 1.39916i | ||||
\(478\) | 6.96574 | 0.318606 | ||||||||
\(479\) | 11.9467 | + | 11.9467i | 0.545859 | + | 0.545859i | 0.925240 | − | 0.379381i | \(-0.123863\pi\) |
−0.379381 | + | 0.925240i | \(0.623863\pi\) | |||||||
\(480\) | 1.65121 | + | 0.522966i | 0.0753673 | + | 0.0238700i | ||||
\(481\) | −4.38885 | − | 2.22032i | −0.200114 | − | 0.101238i | ||||
\(482\) | 26.3003i | 1.19794i | ||||||||
\(483\) | −7.96785 | − | 15.3544i | −0.362550 | − | 0.698648i | ||||
\(484\) | 1.71079i | 0.0777632i | ||||||||
\(485\) | 3.39908 | 0.154344 | ||||||||
\(486\) | −11.4249 | − | 10.6052i | −0.518246 | − | 0.481063i | ||||
\(487\) | −13.5166 | + | 13.5166i | −0.612496 | + | 0.612496i | −0.943596 | − | 0.331100i | \(-0.892580\pi\) |
0.331100 | + | 0.943596i | \(0.392580\pi\) | |||||||
\(488\) | 2.83316i | 0.128251i | ||||||||
\(489\) | 5.37336 | + | 10.3547i | 0.242992 | + | 0.468255i | ||||
\(490\) | −4.85029 | −0.219114 | ||||||||
\(491\) | − | 22.2070i | − | 1.00219i | −0.865392 | − | 0.501095i | \(-0.832931\pi\) | ||
0.865392 | − | 0.501095i | \(-0.167069\pi\) | |||||||
\(492\) | −4.18806 | + | 13.2234i | −0.188812 | + | 0.596157i | ||||
\(493\) | 5.79414 | 0.260955 | ||||||||
\(494\) | 2.35054 | + | 2.35054i | 0.105756 | + | 0.105756i | ||||
\(495\) | 1.56454 | + | 9.00861i | 0.0703208 | + | 0.404907i | ||||
\(496\) | 6.33851 | + | 6.33851i | 0.284608 | + | 0.284608i | ||||
\(497\) | − | 40.8126i | − | 1.83070i | ||||||
\(498\) | −8.64815 | − | 16.6653i | −0.387533 | − | 0.746791i | ||||
\(499\) | 14.5069 | + | 14.5069i | 0.649417 | + | 0.649417i | 0.952852 | − | 0.303435i | \(-0.0981336\pi\) |
−0.303435 | + | 0.952852i | \(0.598134\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | −8.36896 | − | 16.1273i | −0.373898 | − | 0.720516i | ||||
\(502\) | 21.3343i | 0.952195i | ||||||||
\(503\) | 29.5224 | + | 29.5224i | 1.31634 | + | 1.31634i | 0.916652 | + | 0.399686i | \(0.130881\pi\) |
0.399686 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(504\) | 1.76710 | + | 10.1750i | 0.0787129 | + | 0.453229i | ||||
\(505\) | −1.53772 | − | 1.53772i | −0.0684277 | − | 0.0684277i | ||||
\(506\) | 8.84252 | 0.393098 | ||||||||
\(507\) | −6.45662 | + | 20.3862i | −0.286749 | + | 0.905381i | ||||
\(508\) | 3.84862i | 0.170755i | ||||||||
\(509\) | −10.8887 | −0.482631 | −0.241316 | − | 0.970447i | \(-0.577579\pi\) | ||||
−0.241316 | + | 0.970447i | \(0.577579\pi\) | |||||||
\(510\) | 1.78270 | + | 3.43533i | 0.0789391 | + | 0.152119i | ||||
\(511\) | 15.1720i | 0.671168i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 21.1678 | + | 2.87007i | 0.934583 | + | 0.126717i | ||||
\(514\) | −3.12108 | −0.137665 | ||||||||
\(515\) | − | 0.699945i | − | 0.0308433i | ||||||
\(516\) | −3.58147 | − | 6.90163i | −0.157665 | − | 0.303827i | ||||
\(517\) | 24.0847i | 1.05924i | ||||||||
\(518\) | 18.6845 | + | 9.45249i | 0.820951 | + | 0.415319i | ||||
\(519\) | −36.6178 | − | 11.5974i | −1.60734 | − | 0.509071i | ||||
\(520\) | 0.571765 | + | 0.571765i | 0.0250736 | + | 0.0250736i | ||||
\(521\) | 3.34544 | 0.146566 | 0.0732831 | − | 0.997311i | \(-0.476652\pi\) | ||||
0.0732831 | + | 0.997311i | \(0.476652\pi\) | |||||||
\(522\) | 4.47824 | − | 6.36064i | 0.196007 | − | 0.278398i | ||||
\(523\) | 13.0218 | − | 13.0218i | 0.569405 | − | 0.569405i | −0.362557 | − | 0.931962i | \(-0.618096\pi\) |
0.931962 | + | 0.362557i | \(0.118096\pi\) | |||||||
\(524\) | −9.42329 | − | 9.42329i | −0.411658 | − | 0.411658i | ||||
\(525\) | −1.80027 | + | 5.68418i | −0.0785702 | + | 0.248078i | ||||
\(526\) | −2.91099 | + | 2.91099i | −0.126925 | + | 0.126925i | ||||
\(527\) | 20.0304i | 0.872539i | ||||||||
\(528\) | −5.03260 | − | 1.59390i | −0.219016 | − | 0.0693658i | ||||
\(529\) | − | 14.5827i | − | 0.634030i | ||||||
\(530\) | − | 12.4574i | − | 0.541113i | ||||||
\(531\) | 1.45690 | + | 8.38881i | 0.0632239 | + | 0.364043i | ||||
\(532\) | −10.0069 | − | 10.0069i | −0.433854 | − | 0.433854i | ||||
\(533\) | −4.57887 | + | 4.57887i | −0.198333 | + | 0.198333i | ||||
\(534\) | 7.32903 | − | 23.1407i | 0.317158 | − | 1.00140i | ||||
\(535\) | 0.332370 | − | 0.332370i | 0.0143696 | − | 0.0143696i | ||||
\(536\) | 6.69569 | − | 6.69569i | 0.289210 | − | 0.289210i | ||||
\(537\) | −15.1308 | + | 7.85185i | −0.652944 | + | 0.338833i | ||||
\(538\) | 3.67429 | + | 3.67429i | 0.158410 | + | 0.158410i | ||||
\(539\) | 14.7828 | 0.636741 | ||||||||
\(540\) | 5.14904 | + | 0.698141i | 0.221579 | + | 0.0300432i | ||||
\(541\) | 2.84989 | − | 2.84989i | 0.122526 | − | 0.122526i | −0.643185 | − | 0.765711i | \(-0.722387\pi\) |
0.765711 | + | 0.643185i | \(0.222387\pi\) | |||||||
\(542\) | 3.35741 | − | 3.35741i | 0.144213 | − | 0.144213i | ||||
\(543\) | −1.36508 | − | 0.432343i | −0.0585812 | − | 0.0185536i | ||||
\(544\) | −2.23454 | −0.0958050 | ||||||||
\(545\) | −4.50809 | −0.193105 | ||||||||
\(546\) | −1.45570 | + | 4.59622i | −0.0622980 | + | 0.196700i | ||||
\(547\) | 31.6848 | + | 31.6848i | 1.35474 | + | 1.35474i | 0.880269 | + | 0.474475i | \(0.157362\pi\) |
0.474475 | + | 0.880269i | \(0.342638\pi\) | |||||||
\(548\) | −14.5392 | −0.621083 | ||||||||
\(549\) | 1.45435 | + | 8.37412i | 0.0620700 | + | 0.357399i | ||||
\(550\) | −2.15513 | − | 2.15513i | −0.0918952 | − | 0.0918952i | ||||
\(551\) | 10.6599i | 0.454125i | ||||||||
\(552\) | 1.51726 | − | 4.79060i | 0.0645789 | − | 0.203902i | ||||
\(553\) | −28.2573 | + | 28.2573i | −1.20162 | + | 1.20162i | ||||
\(554\) | 3.18907 | 0.135491 | ||||||||
\(555\) | 7.37255 | − | 7.52632i | 0.312947 | − | 0.319475i | ||||
\(556\) | 16.7132 | 0.708799 | ||||||||
\(557\) | 30.2213 | − | 30.2213i | 1.28052 | − | 1.28052i | 0.340143 | − | 0.940374i | \(-0.389525\pi\) |
0.940374 | − | 0.340143i | \(-0.110475\pi\) | |||||||
\(558\) | 21.9889 | + | 15.4814i | 0.930862 | + | 0.655378i | ||||
\(559\) | − | 3.62998i | − | 0.153532i | ||||||
\(560\) | −2.43416 | − | 2.43416i | −0.102862 | − | 0.102862i | ||||
\(561\) | −5.43334 | − | 10.4703i | −0.229396 | − | 0.442055i | ||||
\(562\) | 16.2251 | 0.684416 | ||||||||
\(563\) | 10.7209 | + | 10.7209i | 0.451833 | + | 0.451833i | 0.895963 | − | 0.444129i | \(-0.146487\pi\) |
−0.444129 | + | 0.895963i | \(0.646487\pi\) | |||||||
\(564\) | 13.0483 | + | 4.13261i | 0.549434 | + | 0.174014i | ||||
\(565\) | −3.18049 | −0.133804 | ||||||||
\(566\) | 29.5074 | 1.24029 | ||||||||
\(567\) | 10.4462 | + | 29.1676i | 0.438701 | + | 1.22492i | ||||
\(568\) | 8.38330 | − | 8.38330i | 0.351755 | − | 0.351755i | ||||
\(569\) | 30.3297 | − | 30.3297i | 1.27149 | − | 1.27149i | 0.326179 | − | 0.945308i | \(-0.394239\pi\) |
0.945308 | − | 0.326179i | \(-0.105761\pi\) | |||||||
\(570\) | −6.32020 | + | 3.27974i | −0.264724 | + | 0.137373i | ||||
\(571\) | 26.1370 | 1.09380 | 0.546900 | − | 0.837198i | \(-0.315808\pi\) | ||||
0.546900 | + | 0.837198i | \(0.315808\pi\) | |||||||
\(572\) | −1.74264 | − | 1.74264i | −0.0728634 | − | 0.0728634i | ||||
\(573\) | −1.97718 | − | 3.81010i | −0.0825978 | − | 0.159169i | ||||
\(574\) | 19.4935 | − | 19.4935i | 0.813642 | − | 0.813642i | ||||
\(575\) | 2.05150 | − | 2.05150i | 0.0855535 | − | 0.0855535i | ||||
\(576\) | −1.72706 | + | 2.45301i | −0.0719607 | + | 0.102209i | ||||
\(577\) | 18.6883 | − | 18.6883i | 0.778004 | − | 0.778004i | −0.201487 | − | 0.979491i | \(-0.564578\pi\) |
0.979491 | + | 0.201487i | \(0.0645775\pi\) | |||||||
\(578\) | 8.49012 | + | 8.49012i | 0.353142 | + | 0.353142i | ||||
\(579\) | 12.2240 | − | 6.34339i | 0.508011 | − | 0.263622i | ||||
\(580\) | 2.59299i | 0.107668i | ||||||||
\(581\) | 37.3163i | 1.54814i | ||||||||
\(582\) | −1.77760 | + | 5.61261i | −0.0736840 | + | 0.232650i | ||||
\(583\) | 37.9678i | 1.57246i | ||||||||
\(584\) | −3.11646 | + | 3.11646i | −0.128960 | + | 0.128960i | ||||
\(585\) | 1.98350 | + | 1.39649i | 0.0820078 | + | 0.0577379i | ||||
\(586\) | 5.86433 | + | 5.86433i | 0.242253 | + | 0.242253i | ||||
\(587\) | −6.84341 | + | 6.84341i | −0.282458 | + | 0.282458i | −0.834088 | − | 0.551631i | \(-0.814006\pi\) |
0.551631 | + | 0.834088i | \(0.314006\pi\) | |||||||
\(588\) | 2.53654 | − | 8.00887i | 0.104605 | − | 0.330280i | ||||
\(589\) | −36.8513 | −1.51843 | ||||||||
\(590\) | −2.00686 | − | 2.00686i | −0.0826210 | − | 0.0826210i | ||||
\(591\) | 9.33583 | − | 29.4770i | 0.384025 | − | 1.21252i | ||||
\(592\) | 1.89635 | + | 5.77961i | 0.0779393 | + | 0.237540i | ||||
\(593\) | − | 25.8530i | − | 1.06166i | −0.847480 | − | 0.530828i | \(-0.821881\pi\) | ||
0.847480 | − | 0.530828i | \(-0.178119\pi\) | |||||||
\(594\) | −15.6933 | − | 2.12781i | −0.643906 | − | 0.0873050i | ||||
\(595\) | − | 7.69223i | − | 0.315351i | ||||||
\(596\) | 11.2348 | 0.460194 | ||||||||
\(597\) | 2.10978 | + | 4.06564i | 0.0863477 | + | 0.166395i | ||||
\(598\) | 1.65884 | − | 1.65884i | 0.0678351 | − | 0.0678351i | ||||
\(599\) | 28.9337i | 1.18220i | 0.806598 | + | 0.591100i | \(0.201306\pi\) | ||||
−0.806598 | + | 0.591100i | \(0.798694\pi\) | |||||||
\(600\) | −1.53738 | + | 0.797792i | −0.0627632 | + | 0.0325697i | ||||
\(601\) | −6.17236 | −0.251776 | −0.125888 | − | 0.992044i | \(-0.540178\pi\) | ||||
−0.125888 | + | 0.992044i | \(0.540178\pi\) | |||||||
\(602\) | 15.4538i | 0.629851i | ||||||||
\(603\) | 16.3537 | − | 23.2279i | 0.665976 | − | 0.945915i | ||||
\(604\) | 18.1204 | 0.737308 | ||||||||
\(605\) | −1.20971 | − | 1.20971i | −0.0491818 | − | 0.0491818i | ||||
\(606\) | 3.34328 | − | 1.73493i | 0.135811 | − | 0.0704767i | ||||
\(607\) | −9.27354 | − | 9.27354i | −0.376401 | − | 0.376401i | 0.493401 | − | 0.869802i | \(-0.335754\pi\) |
−0.869802 | + | 0.493401i | \(0.835754\pi\) | |||||||
\(608\) | − | 4.11103i | − | 0.166724i | ||||||
\(609\) | −13.7229 | + | 7.12124i | −0.556080 | + | 0.288567i | ||||
\(610\) | −2.00335 | − | 2.00335i | −0.0811131 | − | 0.0811131i | ||||
\(611\) | 4.51824 | + | 4.51824i | 0.182789 | + | 0.182789i | ||||
\(612\) | −6.60475 | + | 1.14706i | −0.266981 | + | 0.0463670i | ||||
\(613\) | 3.85367i | 0.155648i | 0.996967 | + | 0.0778241i | \(0.0247973\pi\) | ||||
−0.996967 | + | 0.0778241i | \(0.975203\pi\) | |||||||
\(614\) | −4.97725 | − | 4.97725i | −0.200866 | − | 0.200866i | ||||
\(615\) | −6.38895 | − | 12.3118i | −0.257627 | − | 0.496458i | ||||
\(616\) | 7.41889 | + | 7.41889i | 0.298916 | + | 0.298916i | ||||
\(617\) | 25.4539 | 1.02474 | 0.512369 | − | 0.858766i | \(-0.328768\pi\) | ||||
0.512369 | + | 0.858766i | \(0.328768\pi\) | |||||||
\(618\) | 1.15576 | + | 0.366047i | 0.0464914 | + | 0.0147246i | ||||
\(619\) | 13.3502i | 0.536588i | 0.963337 | + | 0.268294i | \(0.0864599\pi\) | ||||
−0.963337 | + | 0.268294i | \(0.913540\pi\) | |||||||
\(620\) | −8.96401 | −0.360003 | ||||||||
\(621\) | 2.02549 | − | 14.9387i | 0.0812800 | − | 0.599470i | ||||
\(622\) | 7.58225i | 0.304020i | ||||||||
\(623\) | −34.1133 | + | 34.1133i | −1.36672 | + | 1.36672i | ||||
\(624\) | −1.24312 | + | 0.645093i | −0.0497647 | + | 0.0258244i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 23.2502i | 0.929266i | ||||||||
\(627\) | 19.2628 | − | 9.99607i | 0.769283 | − | 0.399205i | ||||
\(628\) | − | 15.7039i | − | 0.626653i | ||||||
\(629\) | −6.13577 | + | 12.1284i | −0.244649 | + | 0.483593i | ||||
\(630\) | −8.44432 | − | 5.94526i | −0.336430 | − | 0.236865i | ||||
\(631\) | −34.7483 | − | 34.7483i | −1.38331 | − | 1.38331i | −0.838676 | − | 0.544631i | \(-0.816670\pi\) |
−0.544631 | − | 0.838676i | \(-0.683330\pi\) | |||||||
\(632\) | −11.6086 | −0.461766 | ||||||||
\(633\) | −32.1047 | − | 10.1681i | −1.27605 | − | 0.404144i | ||||
\(634\) | −13.7554 | + | 13.7554i | −0.546296 | + | 0.546296i | ||||
\(635\) | −2.72139 | − | 2.72139i | −0.107995 | − | 0.107995i | ||||
\(636\) | 20.5697 | + | 6.51476i | 0.815644 | + | 0.258327i | ||||
\(637\) | 2.77323 | − | 2.77323i | 0.109879 | − | 0.109879i | ||||
\(638\) | − | 7.90297i | − | 0.312882i | ||||||
\(639\) | 20.4756 | − | 29.0824i | 0.810001 | − | 1.15048i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 5.61943i | − | 0.221954i | −0.993823 | − | 0.110977i | \(-0.964602\pi\) | ||
0.993823 | − | 0.110977i | \(-0.0353980\pi\) | |||||||
\(642\) | 0.374995 | + | 0.722631i | 0.0147999 | + | 0.0285200i | ||||
\(643\) | 20.4006 | + | 20.4006i | 0.804522 | + | 0.804522i | 0.983799 | − | 0.179277i | \(-0.0573757\pi\) |
−0.179277 | + | 0.983799i | \(0.557376\pi\) | |||||||
\(644\) | −7.06214 | + | 7.06214i | −0.278287 | + | 0.278287i | ||||
\(645\) | 7.41267 | + | 2.34771i | 0.291874 | + | 0.0924410i | ||||
\(646\) | 6.49565 | − | 6.49565i | 0.255568 | − | 0.255568i | ||||
\(647\) | −26.1415 | + | 26.1415i | −1.02773 | + | 1.02773i | −0.0281258 | + | 0.999604i | \(0.508954\pi\) |
−0.999604 | + | 0.0281258i | \(0.991046\pi\) | |||||||
\(648\) | −3.84555 | + | 8.13706i | −0.151067 | + | 0.319654i | ||||
\(649\) | 6.11654 | + | 6.11654i | 0.240095 | + | 0.240095i | ||||
\(650\) | −0.808598 | −0.0317158 | ||||||||
\(651\) | −24.6182 | − | 47.4403i | −0.964864 | − | 1.85933i | ||||
\(652\) | 4.76257 | − | 4.76257i | 0.186517 | − | 0.186517i | ||||
\(653\) | −21.1720 | + | 21.1720i | −0.828525 | + | 0.828525i | −0.987313 | − | 0.158788i | \(-0.949242\pi\) |
0.158788 | + | 0.987313i | \(0.449242\pi\) | |||||||
\(654\) | 2.35758 | − | 7.44383i | 0.0921886 | − | 0.291077i | ||||
\(655\) | 13.3265 | 0.520711 | ||||||||
\(656\) | 8.00829 | 0.312671 | ||||||||
\(657\) | −7.61173 | + | 10.8113i | −0.296962 | + | 0.421788i | ||||
\(658\) | −19.2354 | − | 19.2354i | −0.749874 | − | 0.749874i | ||||
\(659\) | 28.6785 | 1.11716 | 0.558578 | − | 0.829452i | \(-0.311347\pi\) | ||||
0.558578 | + | 0.829452i | \(0.311347\pi\) | |||||||
\(660\) | 4.68565 | − | 2.43153i | 0.182389 | − | 0.0946471i | ||||
\(661\) | −9.63627 | − | 9.63627i | −0.374807 | − | 0.374807i | 0.494417 | − | 0.869225i | \(-0.335382\pi\) |
−0.869225 | + | 0.494417i | \(0.835382\pi\) | |||||||
\(662\) | − | 23.9782i | − | 0.931938i | ||||||
\(663\) | −2.98348 | − | 0.944917i | −0.115869 | − | 0.0366975i | ||||
\(664\) | −7.66511 | + | 7.66511i | −0.297464 | + | 0.297464i | ||||
\(665\) | 14.1519 | 0.548787 | ||||||||
\(666\) | 8.57198 | + | 16.1097i | 0.332158 | + | 0.624237i | ||||
\(667\) | 7.52295 | 0.291290 | ||||||||
\(668\) | −7.41766 | + | 7.41766i | −0.286998 | + | 0.286998i | ||||
\(669\) | 41.1074 | + | 13.0194i | 1.58930 | + | 0.503358i | ||||
\(670\) | 9.46914i | 0.365825i | ||||||||
\(671\) | 6.10584 | + | 6.10584i | 0.235713 | + | 0.235713i | ||||
\(672\) | 5.29231 | − | 2.74634i | 0.204155 | − | 0.105942i | ||||
\(673\) | −32.2049 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(674\) | 5.00850 | + | 5.00850i | 0.192920 | + | 0.192920i | ||||
\(675\) | −4.13458 | + | 3.14726i | −0.159140 | + | 0.121138i | ||||
\(676\) | 12.3462 | 0.474853 | ||||||||
\(677\) | −4.54053 | −0.174507 | −0.0872533 | − | 0.996186i | \(-0.527809\pi\) | ||||
−0.0872533 | + | 0.996186i | \(0.527809\pi\) | |||||||
\(678\) | 1.66329 | − | 5.25167i | 0.0638782 | − | 0.201689i | ||||
\(679\) | 8.27392 | − | 8.27392i | 0.317524 | − | 0.317524i | ||||
\(680\) | 1.58006 | − | 1.58006i | 0.0605924 | − | 0.0605924i | ||||
\(681\) | −7.88800 | − | 15.2005i | −0.302269 | − | 0.582484i | ||||
\(682\) | 27.3207 | 1.04616 | ||||||||
\(683\) | −17.4943 | − | 17.4943i | −0.669399 | − | 0.669399i | 0.288178 | − | 0.957577i | \(-0.406951\pi\) |
−0.957577 | + | 0.288178i | \(0.906951\pi\) | |||||||
\(684\) | −2.11031 | − | 12.1512i | −0.0806899 | − | 0.464612i | ||||
\(685\) | 10.2807 | − | 10.2807i | 0.392807 | − | 0.392807i | ||||
\(686\) | 5.23273 | − | 5.23273i | 0.199787 | − | 0.199787i | ||||
\(687\) | −32.2916 | − | 10.2273i | −1.23200 | − | 0.390194i | ||||
\(688\) | −3.17436 | + | 3.17436i | −0.121021 | + | 0.121021i | ||||
\(689\) | 7.12268 | + | 7.12268i | 0.271353 | + | 0.271353i | ||||
\(690\) | 2.31460 | + | 4.46033i | 0.0881154 | + | 0.169802i | ||||
\(691\) | 5.34751i | 0.203429i | 0.994814 | + | 0.101714i | \(0.0324328\pi\) | ||||
−0.994814 | + | 0.101714i | \(0.967567\pi\) | |||||||
\(692\) | 22.1763i | 0.843016i | ||||||||
\(693\) | 25.7368 | + | 18.1201i | 0.977659 | + | 0.688325i | ||||
\(694\) | 11.5297i | 0.437661i | ||||||||
\(695\) | −11.8180 | + | 11.8180i | −0.448284 | + | 0.448284i | ||||
\(696\) | −4.28158 | − | 1.35605i | −0.162293 | − | 0.0514008i | ||||
\(697\) | 12.6536 | + | 12.6536i | 0.479288 | + | 0.479288i | ||||
\(698\) | 6.87499 | − | 6.87499i | 0.260222 | − | 0.260222i | ||||
\(699\) | 29.2853 | + | 9.27511i | 1.10767 | + | 0.350817i | ||||
\(700\) | 3.44243 | 0.130111 | ||||||||
\(701\) | −14.9583 | − | 14.9583i | −0.564967 | − | 0.564967i | 0.365747 | − | 0.930714i | \(-0.380814\pi\) |
−0.930714 | + | 0.365747i | \(0.880814\pi\) | |||||||
\(702\) | −3.34322 | + | 2.54487i | −0.126182 | + | 0.0960499i | ||||
\(703\) | −22.3135 | − | 11.2884i | −0.841569 | − | 0.425750i | ||||
\(704\) | 3.04782i | 0.114869i | ||||||||
\(705\) | −12.1488 | + | 6.30437i | −0.457549 | + | 0.237436i | ||||
\(706\) | − | 0.566873i | − | 0.0213345i | ||||||
\(707\) | −7.48612 | −0.281545 | ||||||||
\(708\) | 4.36327 | − | 2.26423i | 0.163982 | − | 0.0850951i | ||||
\(709\) | −30.3690 | + | 30.3690i | −1.14053 | + | 1.14053i | −0.152178 | + | 0.988353i | \(0.548629\pi\) |
−0.988353 | + | 0.152178i | \(0.951371\pi\) | |||||||
\(710\) | 11.8558i | 0.444939i | ||||||||
\(711\) | −34.3123 | + | 5.95906i | −1.28681 | + | 0.223482i | ||||
\(712\) | −14.0144 | −0.525211 | ||||||||
\(713\) | 26.0069i | 0.973968i | ||||||||
\(714\) | 12.7015 | + | 4.02277i | 0.475342 | + | 0.150548i | ||||
\(715\) | 2.46446 | 0.0921657 | ||||||||
\(716\) | 6.95933 | + | 6.95933i | 0.260082 | + | 0.260082i | ||||
\(717\) | −5.55721 | − | 10.7090i | −0.207538 | − | 0.399934i | ||||
\(718\) | 24.9933 | + | 24.9933i | 0.932741 | + | 0.932741i | ||||
\(719\) | 12.6121i | 0.470351i | 0.971953 | + | 0.235175i | \(0.0755665\pi\) | ||||
−0.971953 | + | 0.235175i | \(0.924434\pi\) | |||||||
\(720\) | −0.513330 | − | 2.95576i | −0.0191307 | − | 0.110155i | ||||
\(721\) | −1.70378 | − | 1.70378i | −0.0634521 | − | 0.0634521i | ||||
\(722\) | −1.48455 | − | 1.48455i | −0.0552491 | − | 0.0552491i | ||||
\(723\) | 40.4334 | − | 20.9821i | 1.50374 | − | 0.780334i | ||||
\(724\) | 0.826713i | 0.0307246i | ||||||||
\(725\) | −1.83352 | − | 1.83352i | −0.0680953 | − | 0.0680953i | ||||
\(726\) | 2.63013 | − | 1.36486i | 0.0976133 | − | 0.0506545i | ||||
\(727\) | −0.256819 | − | 0.256819i | −0.00952488 | − | 0.00952488i | 0.702328 | − | 0.711853i | \(-0.252144\pi\) |
−0.711853 | + | 0.702328i | \(0.752144\pi\) | |||||||
\(728\) | 2.78354 | 0.103165 | ||||||||
\(729\) | −7.18951 | + | 26.0252i | −0.266278 | + | 0.963896i | ||||
\(730\) | − | 4.40734i | − | 0.163123i | ||||||
\(731\) | −10.0313 | −0.371022 | ||||||||
\(732\) | 4.35563 | − | 2.26027i | 0.160989 | − | 0.0835420i | ||||
\(733\) | 12.0159i | 0.443816i | 0.975068 | + | 0.221908i | \(0.0712285\pi\) | ||||
−0.975068 | + | 0.221908i | \(0.928771\pi\) | |||||||
\(734\) | −3.02276 | + | 3.02276i | −0.111572 | + | 0.111572i | ||||
\(735\) | 3.86953 | + | 7.45673i | 0.142730 | + | 0.275046i | ||||
\(736\) | −2.90126 | −0.106942 | ||||||||
\(737\) | − | 28.8602i | − | 1.06308i | ||||||
\(738\) | 23.6706 | − | 4.11090i | 0.871325 | − | 0.151324i | ||||
\(739\) | − | 44.3596i | − | 1.63179i | −0.578198 | − | 0.815896i | \(-0.696244\pi\) | ||
0.578198 | − | 0.815896i | \(-0.303756\pi\) | |||||||
\(740\) | −5.42772 | − | 2.74588i | −0.199527 | − | 0.100941i | ||||
\(741\) | 1.73843 | − | 5.48891i | 0.0638627 | − | 0.201640i | ||||
\(742\) | −30.3232 | − | 30.3232i | −1.11320 | − | 1.11320i | ||||
\(743\) | 40.0701 | 1.47003 | 0.735014 | − | 0.678052i | \(-0.237176\pi\) | ||||
0.735014 | + | 0.678052i | \(0.237176\pi\) | |||||||
\(744\) | 4.68787 | − | 14.8015i | 0.171866 | − | 0.542649i | ||||
\(745\) | −7.94418 | + | 7.94418i | −0.291052 | + | 0.291052i | ||||
\(746\) | 23.2224 | + | 23.2224i | 0.850234 | + | 0.850234i | ||||
\(747\) | −18.7215 | + | 26.5909i | −0.684983 | + | 0.972911i | ||||
\(748\) | −4.81573 | + | 4.81573i | −0.176080 | + | 0.176080i | ||||
\(749\) | − | 1.61808i | − | 0.0591235i | ||||||
\(750\) | 0.522966 | − | 1.65121i | 0.0190960 | − | 0.0602938i | ||||
\(751\) | 44.0250i | 1.60650i | 0.595645 | + | 0.803248i | \(0.296897\pi\) | ||||
−0.595645 | + | 0.803248i | \(0.703103\pi\) | |||||||
\(752\) | − | 7.90227i | − | 0.288166i | ||||||
\(753\) | 32.7988 | − | 17.0203i | 1.19526 | − | 0.620255i | ||||
\(754\) | −1.48258 | − | 1.48258i | −0.0539925 | − | 0.0539925i | ||||
\(755\) | −12.8130 | + | 12.8130i | −0.466314 | + | 0.466314i | ||||
\(756\) | 14.2330 | − | 10.8342i | 0.517649 | − | 0.394036i | ||||
\(757\) | 4.69837 | − | 4.69837i | 0.170765 | − | 0.170765i | −0.616550 | − | 0.787315i | \(-0.711470\pi\) |
0.787315 | + | 0.616550i | \(0.211470\pi\) | |||||||
\(758\) | −5.41969 | + | 5.41969i | −0.196852 | + | 0.196852i | ||||
\(759\) | −7.05449 | − | 13.5943i | −0.256062 | − | 0.493442i | ||||
\(760\) | 2.90693 | + | 2.90693i | 0.105446 | + | 0.105446i | ||||
\(761\) | 10.9188 | 0.395805 | 0.197902 | − | 0.980222i | \(-0.436587\pi\) | ||||
0.197902 | + | 0.980222i | \(0.436587\pi\) | |||||||
\(762\) | 5.91678 | − | 3.07040i | 0.214342 | − | 0.111229i | ||||
\(763\) | −10.9734 | + | 10.9734i | −0.397265 | + | 0.397265i | ||||
\(764\) | −1.75243 | + | 1.75243i | −0.0634007 | + | 0.0634007i | ||||
\(765\) | 3.85917 | − | 5.48135i | 0.139529 | − | 0.198179i | ||||
\(766\) | −5.01207 | −0.181094 | ||||||||
\(767\) | 2.29490 | 0.0828642 | ||||||||
\(768\) | 1.65121 | + | 0.522966i | 0.0595830 | + | 0.0188709i | ||||
\(769\) | 32.6754 | + | 32.6754i | 1.17830 | + | 1.17830i | 0.980176 | + | 0.198128i | \(0.0634863\pi\) |
0.198128 | + | 0.980176i | \(0.436514\pi\) | |||||||
\(770\) | −10.4919 | −0.378102 | ||||||||
\(771\) | 2.48997 | + | 4.79827i | 0.0896741 | + | 0.172806i | ||||
\(772\) | −5.62234 | − | 5.62234i | −0.202352 | − | 0.202352i | ||||
\(773\) | − | 46.7775i | − | 1.68247i | −0.540669 | − | 0.841235i | \(-0.681829\pi\) | ||
0.540669 | − | 0.841235i | \(-0.318171\pi\) | |||||||
\(774\) | −7.75314 | + | 11.0121i | −0.278681 | + | 0.395823i | ||||
\(775\) | 6.33851 | − | 6.33851i | 0.227686 | − | 0.227686i | ||||
\(776\) | 3.39908 | 0.122020 | ||||||||
\(777\) | −0.374319 | − | 36.2663i | −0.0134286 | − | 1.30105i | ||||
\(778\) | 25.8997 | 0.928551 | ||||||||
\(779\) | −23.2796 | + | 23.2796i | −0.834078 | + | 0.834078i | ||||
\(780\) | 0.422869 | − | 1.33517i | 0.0151411 | − | 0.0478067i | ||||
\(781\) | − | 36.1343i | − | 1.29299i | ||||||
\(782\) | −4.58416 | − | 4.58416i | −0.163929 | − | 0.163929i | ||||
\(783\) | −13.3514 | − | 1.81027i | −0.477141 | − | 0.0646939i | ||||
\(784\) | −4.85029 | −0.173225 | ||||||||
\(785\) | 11.1043 | + | 11.1043i | 0.396330 | + | 0.396330i | ||||
\(786\) | −6.96932 | + | 22.0050i | −0.248588 | + | 0.784892i | ||||
\(787\) | 20.1224 | 0.717286 | 0.358643 | − | 0.933475i | \(-0.383240\pi\) | ||||
0.358643 | + | 0.933475i | \(0.383240\pi\) | |||||||
\(788\) | −17.8517 | −0.635941 | ||||||||
\(789\) | 6.79765 | + | 2.15292i | 0.242003 | + | 0.0766461i | ||||
\(790\) | 8.20854 | − | 8.20854i | 0.292047 | − | 0.292047i | ||||
\(791\) | −7.74183 | + | 7.74183i | −0.275268 | + | 0.275268i | ||||
\(792\) | 1.56454 | + | 9.00861i | 0.0555934 | + | 0.320107i | ||||
\(793\) | 2.29089 | 0.0813518 | ||||||||
\(794\) | −0.627002 | − | 0.627002i | −0.0222515 | − | 0.0222515i | ||||
\(795\) | −19.1516 | + | 9.93838i | −0.679239 | + | 0.352478i | ||||
\(796\) | 1.86996 | − | 1.86996i | 0.0662791 | − | 0.0662791i | ||||
\(797\) | −0.721582 | + | 0.721582i | −0.0255597 | + | 0.0255597i | −0.719771 | − | 0.694211i | \(-0.755753\pi\) |
0.694211 | + | 0.719771i | \(0.255753\pi\) | |||||||
\(798\) | −7.40096 | + | 23.3678i | −0.261991 | + | 0.827212i | ||||
\(799\) | 12.4860 | − | 12.4860i | 0.441724 | − | 0.441724i | ||||
\(800\) | 0.707107 | + | 0.707107i | 0.0250000 | + | 0.0250000i | ||||
\(801\) | −41.4231 | + | 7.19400i | −1.46361 | + | 0.254187i | ||||
\(802\) | − | 30.7849i | − | 1.08705i | ||||||
\(803\) | 13.4328i | 0.474033i | ||||||||
\(804\) | −15.6356 | − | 4.95203i | −0.551424 | − | 0.174645i | ||||
\(805\) | − | 9.98738i | − | 0.352009i | ||||||
\(806\) | 5.12531 | − | 5.12531i | 0.180531 | − | 0.180531i | ||||
\(807\) | 2.71745 | − | 8.58010i | 0.0956588 | − | 0.302034i | ||||
\(808\) | −1.53772 | − | 1.53772i | −0.0540968 | − | 0.0540968i | ||||
\(809\) | −25.3308 | + | 25.3308i | −0.890584 | + | 0.890584i | −0.994578 | − | 0.103994i | \(-0.966838\pi\) |
0.103994 | + | 0.994578i | \(0.466838\pi\) | |||||||
\(810\) | −3.03456 | − | 8.47298i | −0.106623 | − | 0.297710i | ||||
\(811\) | −45.6593 | −1.60331 | −0.801657 | − | 0.597784i | \(-0.796048\pi\) | ||||
−0.801657 | + | 0.597784i | \(0.796048\pi\) | |||||||
\(812\) | 6.31176 | + | 6.31176i | 0.221499 | + | 0.221499i | ||||
\(813\) | −7.84013 | − | 2.48309i | −0.274965 | − | 0.0870858i | ||||
\(814\) | 16.5427 | + | 8.36895i | 0.579822 | + | 0.293332i | ||||
\(815\) | 6.73529i | 0.235927i | ||||||||
\(816\) | 1.78270 | + | 3.43533i | 0.0624068 | + | 0.120260i | ||||
\(817\) | − | 18.4553i | − | 0.645670i | ||||||
\(818\) | −13.7487 | −0.480713 | ||||||||
\(819\) | 8.22746 | − | 1.42887i | 0.287491 | − | 0.0499289i | ||||
\(820\) | −5.66272 | + | 5.66272i | −0.197751 | + | 0.197751i | ||||
\(821\) | − | 41.4366i | − | 1.44615i | −0.690770 | − | 0.723074i | \(-0.742728\pi\) | ||
0.690770 | − | 0.723074i | \(-0.257272\pi\) | |||||||
\(822\) | 11.5992 | + | 22.3522i | 0.404570 | + | 0.779622i | ||||
\(823\) | 48.2079 | 1.68042 | 0.840210 | − | 0.542261i | \(-0.182431\pi\) | ||||
0.840210 | + | 0.542261i | \(0.182431\pi\) | |||||||
\(824\) | − | 0.699945i | − | 0.0243837i | ||||||
\(825\) | −1.59390 | + | 5.03260i | −0.0554926 | + | 0.175213i | ||||
\(826\) | −9.77004 | −0.339943 | ||||||||
\(827\) | −3.90758 | − | 3.90758i | −0.135880 | − | 0.135880i | 0.635895 | − | 0.771775i | \(-0.280631\pi\) |
−0.771775 | + | 0.635895i | \(0.780631\pi\) | |||||||
\(828\) | −8.57542 | + | 1.48930i | −0.298016 | + | 0.0517569i | ||||
\(829\) | −23.7888 | − | 23.7888i | −0.826221 | − | 0.826221i | 0.160771 | − | 0.986992i | \(-0.448602\pi\) |
−0.986992 | + | 0.160771i | \(0.948602\pi\) | |||||||
\(830\) | − | 10.8401i | − | 0.376266i | ||||||
\(831\) | −2.54422 | − | 4.90281i | −0.0882579 | − | 0.170077i | ||||
\(832\) | 0.571765 | + | 0.571765i | 0.0198224 | + | 0.0198224i | ||||
\(833\) | −7.66374 | − | 7.66374i | −0.265533 | − | 0.265533i | ||||
\(834\) | −13.3337 | − | 25.6945i | −0.461708 | − | 0.889729i | ||||
\(835\) | − | 10.4902i | − | 0.363027i | ||||||
\(836\) | −8.85981 | − | 8.85981i | −0.306423 | − | 0.306423i | ||||
\(837\) | 6.25814 | − | 46.1561i | 0.216313 | − | 1.59539i | ||||
\(838\) | −25.5345 | − | 25.5345i | −0.882075 | − | 0.882075i | ||||
\(839\) | −34.3994 | −1.18760 | −0.593799 | − | 0.804613i | \(-0.702373\pi\) | ||||
−0.593799 | + | 0.804613i | \(0.702373\pi\) | |||||||
\(840\) | −1.80027 | + | 5.68418i | −0.0621152 | + | 0.196123i | ||||
\(841\) | 22.2764i | 0.768152i | ||||||||
\(842\) | −23.1959 | −0.799382 | ||||||||
\(843\) | −12.9443 | − | 24.9441i | −0.445825 | − | 0.859122i | ||||
\(844\) | 19.4431i | 0.669258i | ||||||||
\(845\) | −8.73006 | + | 8.73006i | −0.300323 | + | 0.300323i | ||||
\(846\) | −4.05647 | − | 23.3572i | −0.139464 | − | 0.803036i | ||||
\(847\) | −5.88927 | −0.202358 | ||||||||
\(848\) | − | 12.4574i | − | 0.427787i | ||||||
\(849\) | −23.5408 | − | 45.3640i | −0.807917 | − | 1.55689i | ||||
\(850\) | 2.23454i | 0.0766440i | ||||||||
\(851\) | −7.96652 | + | 15.7472i | −0.273089 | + | 0.539808i | ||||
\(852\) | −19.5764 | − | 6.20016i | −0.670677 | − | 0.212414i | ||||
\(853\) | 1.23013 | + | 1.23013i | 0.0421189 | + | 0.0421189i | 0.727853 | − | 0.685734i | \(-0.240519\pi\) |
−0.685734 | + | 0.727853i | \(0.740519\pi\) | |||||||
\(854\) | −9.75294 | −0.333739 | ||||||||
\(855\) | 10.0844 | + | 7.09997i | 0.344879 | + | 0.242814i | ||||
\(856\) | 0.332370 | − | 0.332370i | 0.0113602 | − | 0.0113602i | ||||
\(857\) | 3.69140 | + | 3.69140i | 0.126096 | + | 0.126096i | 0.767338 | − | 0.641242i | \(-0.221581\pi\) |
−0.641242 | + | 0.767338i | \(0.721581\pi\) | |||||||
\(858\) | −1.28883 | + | 4.06936i | −0.0439999 | + | 0.138925i | ||||
\(859\) | 22.5969 | − | 22.5969i | 0.770995 | − | 0.770995i | −0.207285 | − | 0.978281i | \(-0.566463\pi\) |
0.978281 | + | 0.207285i | \(0.0664629\pi\) | |||||||
\(860\) | − | 4.48922i | − | 0.153081i | ||||||
\(861\) | −45.5206 | − | 14.4171i | −1.55134 | − | 0.491333i | ||||
\(862\) | − | 25.6933i | − | 0.875118i | ||||||
\(863\) | 10.7938i | 0.367427i | 0.982980 | + | 0.183713i | \(0.0588118\pi\) | ||||
−0.982980 | + | 0.183713i | \(0.941188\pi\) | |||||||
\(864\) | 5.14904 | + | 0.698141i | 0.175174 | + | 0.0237512i | ||||
\(865\) | −15.6810 | − | 15.6810i | −0.533170 | − | 0.533170i | ||||
\(866\) | −22.1520 | + | 22.1520i | −0.752755 | + | 0.752755i | ||||
\(867\) | 6.27917 | − | 19.8259i | 0.213252 | − | 0.673322i | ||||
\(868\) | −21.8199 | + | 21.8199i | −0.740614 | + | 0.740614i | ||||
\(869\) | −25.0182 | + | 25.0182i | −0.848683 | + | 0.848683i | ||||
\(870\) | 3.98641 | − | 2.06867i | 0.135152 | − | 0.0701344i | ||||
\(871\) | −5.41413 | − | 5.41413i | −0.183451 | − | 0.183451i | ||||
\(872\) | −4.50809 | −0.152663 | ||||||||
\(873\) | 10.0469 | − | 1.74485i | 0.340035 | − | 0.0590543i | ||||
\(874\) | 8.43378 | − | 8.43378i | 0.285277 | − | 0.285277i | ||||
\(875\) | −2.43416 | + | 2.43416i | −0.0822897 | + | 0.0822897i | ||||
\(876\) | 7.27747 | + | 2.30489i | 0.245883 | + | 0.0778750i | ||||
\(877\) | 20.3881 | 0.688456 | 0.344228 | − | 0.938886i | \(-0.388141\pi\) | ||||
0.344228 | + | 0.938886i | \(0.388141\pi\) | |||||||
\(878\) | −30.7741 | −1.03857 | ||||||||
\(879\) | 4.33717 | − | 13.6942i | 0.146289 | − | 0.461894i | ||||
\(880\) | −2.15513 | − | 2.15513i | −0.0726496 | − | 0.0726496i | ||||
\(881\) | 36.8813 | 1.24256 | 0.621281 | − | 0.783588i | \(-0.286613\pi\) | ||||
0.621281 | + | 0.783588i | \(0.286613\pi\) | |||||||
\(882\) | −14.3363 | + | 2.48980i | −0.482728 | + | 0.0838360i | ||||
\(883\) | 10.5222 | + | 10.5222i | 0.354100 | + | 0.354100i | 0.861633 | − | 0.507533i | \(-0.169442\pi\) |
−0.507533 | + | 0.861633i | \(0.669442\pi\) | |||||||
\(884\) | 1.80684i | 0.0607707i | ||||||||
\(885\) | −1.48424 | + | 4.68635i | −0.0498922 | + | 0.157530i | ||||
\(886\) | −5.09741 | + | 5.09741i | −0.171251 | + | 0.171251i | ||||
\(887\) | −4.34349 | −0.145840 | −0.0729201 | − | 0.997338i | \(-0.523232\pi\) | ||||
−0.0729201 | + | 0.997338i | \(0.523232\pi\) | |||||||
\(888\) | 7.37255 | − | 7.52632i | 0.247406 | − | 0.252567i | ||||
\(889\) | −13.2486 | −0.444344 | ||||||||
\(890\) | 9.90966 | − | 9.90966i | 0.332172 | − | 0.332172i | ||||
\(891\) | 9.24878 | + | 25.8241i | 0.309846 | + | 0.865141i | ||||
\(892\) | − | 24.8953i | − | 0.833555i | ||||||
\(893\) | 22.9714 | + | 22.9714i | 0.768708 | + | 0.768708i | ||||
\(894\) | −8.96301 | − | 17.2721i | −0.299768 | − | 0.577665i | ||||
\(895\) | −9.84198 | −0.328981 | ||||||||
\(896\) | −2.43416 | − | 2.43416i | −0.0813197 | − | 0.0813197i | ||||
\(897\) | −3.87367 | − | 1.22685i | −0.129338 | − | 0.0409635i | ||||
\(898\) | −3.15484 | −0.105278 | ||||||||
\(899\) | 23.2436 | 0.775218 | ||||||||
\(900\) | 2.45301 | + | 1.72706i | 0.0817671 | + | 0.0575685i | ||||
\(901\) | 19.6833 | − | 19.6833i | 0.655746 | − | 0.655746i | ||||
\(902\) | 17.2589 | − | 17.2589i | 0.574660 | − | 0.574660i | ||||
\(903\) | 23.7584 | − | 12.3289i | 0.790628 | − | 0.410281i | ||||
\(904\) | −3.18049 | −0.105782 | ||||||||
\(905\) | −0.584575 | − | 0.584575i | −0.0194319 | − | 0.0194319i | ||||
\(906\) | −14.4563 | − | 27.8579i | −0.480278 | − | 0.925515i | ||||
\(907\) | −9.06099 | + | 9.06099i | −0.300865 | + | 0.300865i | −0.841352 | − | 0.540487i | \(-0.818240\pi\) |
0.540487 | + | 0.841352i | \(0.318240\pi\) | |||||||
\(908\) | −6.99137 | + | 6.99137i | −0.232017 | + | 0.232017i | ||||
\(909\) | −5.33448 | − | 3.75577i | −0.176934 | − | 0.124571i | ||||
\(910\) | −1.96826 | + | 1.96826i | −0.0652472 | + | 0.0652472i | ||||
\(911\) | −24.1539 | − | 24.1539i | −0.800254 | − | 0.800254i | 0.182881 | − | 0.983135i | \(-0.441458\pi\) |
−0.983135 | + | 0.182881i | \(0.941458\pi\) | |||||||
\(912\) | −6.32020 | + | 3.27974i | −0.209283 | + | 0.108603i | ||||
\(913\) | 33.0387i | 1.09342i | ||||||||
\(914\) | 2.21379i | 0.0732256i | ||||||||
\(915\) | −1.48164 | + | 4.67815i | −0.0489816 | + | 0.154655i | ||||
\(916\) | 19.5563i | 0.646158i | ||||||||
\(917\) | 32.4390 | − | 32.4390i | 1.07123 | − | 1.07123i | ||||
\(918\) | 7.03267 | + | 9.23887i | 0.232113 | + | 0.304928i | ||||
\(919\) | −40.5578 | − | 40.5578i | −1.33788 | − | 1.33788i | −0.898111 | − | 0.439768i | \(-0.855061\pi\) |
−0.439768 | − | 0.898111i | \(-0.644939\pi\) | |||||||
\(920\) | 2.05150 | − | 2.05150i | 0.0676360 | − | 0.0676360i | ||||
\(921\) | −3.68110 | + | 11.6227i | −0.121296 | + | 0.382982i | ||||
\(922\) | 8.08730 | 0.266341 | ||||||||
\(923\) | −6.77872 | − | 6.77872i | −0.223124 | − | 0.223124i | ||||
\(924\) | 5.48690 | − | 17.3244i | 0.180506 | − | 0.569930i | ||||
\(925\) | 5.77961 | − | 1.89635i | 0.190032 | − | 0.0623515i | ||||
\(926\) | − | 34.0260i | − | 1.11816i | ||||||
\(927\) | −0.359303 | − | 2.06887i | −0.0118011 | − | 0.0679505i | ||||
\(928\) | 2.59299i | 0.0851191i | ||||||||
\(929\) | 31.9349 | 1.04775 | 0.523874 | − | 0.851796i | \(-0.324486\pi\) | ||||
0.523874 | + | 0.851796i | \(0.324486\pi\) | |||||||
\(930\) | 7.15142 | + | 13.7811i | 0.234504 | + | 0.451899i | ||||
\(931\) | 14.0995 | − | 14.0995i | 0.462092 | − | 0.462092i | ||||
\(932\) | − | 17.7356i | − | 0.580949i | ||||||
\(933\) | 11.6568 | − | 6.04906i | 0.381626 | − | 0.198037i | ||||
\(934\) | 3.39263 | 0.111010 | ||||||||
\(935\) | − | 6.81047i | − | 0.222726i | ||||||
\(936\) | 1.98350 | + | 1.39649i | 0.0648328 | + | 0.0456459i | ||||
\(937\) | 23.4147 | 0.764926 | 0.382463 | − | 0.923971i | \(-0.375076\pi\) | ||||
0.382463 | + | 0.923971i | \(0.375076\pi\) | |||||||
\(938\) | 23.0494 | + | 23.0494i | 0.752590 | + | 0.752590i | ||||
\(939\) | 35.7444 | − | 18.5489i | 1.16647 | − | 0.605319i | ||||
\(940\) | 5.58775 | + | 5.58775i | 0.182252 | + | 0.182252i | ||||
\(941\) | − | 51.9908i | − | 1.69485i | −0.530915 | − | 0.847425i | \(-0.678152\pi\) | ||
0.530915 | − | 0.847425i | \(-0.321848\pi\) | |||||||
\(942\) | −24.1428 | + | 12.5284i | −0.786615 | + | 0.408199i | ||||
\(943\) | 16.4290 | + | 16.4290i | 0.535003 | + | 0.535003i | ||||
\(944\) | −2.00686 | − | 2.00686i | −0.0653177 | − | 0.0653177i | ||||
\(945\) | −2.40330 | + | 17.7252i | −0.0781793 | + | 0.576600i | ||||
\(946\) | 13.6824i | 0.444852i | ||||||||
\(947\) | −32.1776 | − | 32.1776i | −1.04563 | − | 1.04563i | −0.998908 | − | 0.0467229i | \(-0.985122\pi\) |
−0.0467229 | − | 0.998908i | \(-0.514878\pi\) | |||||||
\(948\) | 9.26127 | + | 17.8468i | 0.300792 | + | 0.579638i | ||||
\(949\) | 2.51997 | + | 2.51997i | 0.0818016 | + | 0.0818016i | ||||
\(950\) | −4.11103 | −0.133379 | ||||||||
\(951\) | 32.1211 | + | 10.1733i | 1.04160 | + | 0.329891i | ||||
\(952\) | − | 7.69223i | − | 0.249307i | ||||||
\(953\) | −56.7619 | −1.83870 | −0.919349 | − | 0.393443i | \(-0.871284\pi\) | ||||
−0.919349 | + | 0.393443i | \(0.871284\pi\) | |||||||
\(954\) | −6.39473 | − | 36.8209i | −0.207037 | − | 1.19212i | ||||
\(955\) | − | 2.47831i | − | 0.0801963i | ||||||
\(956\) | −4.92552 | + | 4.92552i | −0.159303 | + | 0.159303i | ||||
\(957\) | −12.1498 | + | 6.30493i | −0.392749 | + | 0.203809i | ||||
\(958\) | −16.8952 | −0.545859 | ||||||||
\(959\) | − | 50.0500i | − | 1.61620i | ||||||
\(960\) | −1.53738 | + | 0.797792i | −0.0496186 | + | 0.0257486i | ||||
\(961\) | 49.3535i | 1.59205i | ||||||||
\(962\) | 4.67338 | − | 1.53338i | 0.150676 | − | 0.0494382i | ||||
\(963\) | 0.811788 | − | 1.15302i | 0.0261595 | − | 0.0371555i | ||||
\(964\) | −18.5971 | − | 18.5971i | −0.598972 | − | 0.598972i | ||||
\(965\) | 7.95118 | 0.255958 | ||||||||
\(966\) | 16.4913 | + | 5.22305i | 0.530599 | + | 0.168049i | ||||
\(967\) | −36.7593 | + | 36.7593i | −1.18210 | + | 1.18210i | −0.202900 | + | 0.979199i | \(0.565037\pi\) |
−0.979199 | + | 0.202900i | \(0.934963\pi\) | |||||||
\(968\) | −1.20971 | − | 1.20971i | −0.0388816 | − | 0.0388816i | ||||
\(969\) | −15.1684 | − | 4.80409i | −0.487281 | − | 0.154330i | ||||
\(970\) | −2.40351 | + | 2.40351i | −0.0771722 | + | 0.0771722i | ||||
\(971\) | 1.14129i | 0.0366258i | 0.999832 | + | 0.0183129i | \(0.00582950\pi\) | ||||
−0.999832 | + | 0.0183129i | \(0.994171\pi\) | |||||||
\(972\) | 15.5777 | − | 0.579624i | 0.499654 | − | 0.0185914i | ||||
\(973\) | 57.5341i | 1.84446i | ||||||||
\(974\) | − | 19.1154i | − | 0.612496i | ||||||
\(975\) | 0.645093 | + | 1.24312i | 0.0206595 | + | 0.0398117i | ||||
\(976\) | −2.00335 | − | 2.00335i | −0.0641255 | − | 0.0641255i | ||||
\(977\) | 25.0361 | − | 25.0361i | 0.800977 | − | 0.800977i | −0.182271 | − | 0.983248i | \(-0.558345\pi\) |
0.983248 | + | 0.182271i | \(0.0583449\pi\) | |||||||
\(978\) | −11.1214 | − | 3.52233i | −0.355623 | − | 0.112632i | ||||
\(979\) | −30.2029 | + | 30.2029i | −0.965287 | + | 0.965287i | ||||
\(980\) | 3.42968 | − | 3.42968i | 0.109557 | − | 0.109557i | ||||
\(981\) | −13.3248 | + | 2.31414i | −0.425429 | + | 0.0738848i | ||||
\(982\) | 15.7028 | + | 15.7028i | 0.501095 | + | 0.501095i | ||||
\(983\) | −21.8595 | −0.697210 | −0.348605 | − | 0.937270i | \(-0.613344\pi\) | ||||
−0.348605 | + | 0.937270i | \(0.613344\pi\) | |||||||
\(984\) | −6.38895 | − | 12.3118i | −0.203672 | − | 0.392485i | ||||
\(985\) | 12.6231 | − | 12.6231i | 0.402204 | − | 0.402204i | ||||
\(986\) | −4.09707 | + | 4.09707i | −0.130477 | + | 0.130477i | ||||
\(987\) | −14.2262 | + | 44.9179i | −0.452825 | + | 1.42975i | ||||
\(988\) | −3.32417 | −0.105756 | ||||||||
\(989\) | −13.0244 | −0.414152 | ||||||||
\(990\) | −7.47635 | − | 5.26376i | −0.237614 | − | 0.167293i | ||||
\(991\) | 10.1383 | + | 10.1383i | 0.322053 | + | 0.322053i | 0.849554 | − | 0.527501i | \(-0.176871\pi\) |
−0.527501 | + | 0.849554i | \(0.676871\pi\) | |||||||
\(992\) | −8.96401 | −0.284608 | ||||||||
\(993\) | −36.8635 | + | 19.1296i | −1.16983 | + | 0.607059i | ||||
\(994\) | 28.8589 | + | 28.8589i | 0.915348 | + | 0.915348i | ||||
\(995\) | 2.64453i | 0.0838372i | ||||||||
\(996\) | 17.8993 | + | 5.66900i | 0.567162 | + | 0.179629i | ||||
\(997\) | −12.2091 | + | 12.2091i | −0.386667 | + | 0.386667i | −0.873497 | − | 0.486830i | \(-0.838153\pi\) |
0.486830 | + | 0.873497i | \(0.338153\pi\) | |||||||
\(998\) | −20.5158 | −0.649417 | ||||||||
\(999\) | 17.9280 | − | 26.0305i | 0.567216 | − | 0.823569i |
(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 | 1110.2.u.f.401.9 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.f.401.15 | yes | 40 | |
37.6 | odd | 4 | inner | 1110.2.u.f.191.15 | yes | 40 | |
111.80 | even | 4 | inner | 1110.2.u.f.191.9 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.f.191.9 | ✓ | 40 | 111.80 | even | 4 | inner | |
1110.2.u.f.191.15 | yes | 40 | 37.6 | odd | 4 | inner | |
1110.2.u.f.401.9 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.f.401.15 | yes | 40 | 3.2 | odd | 2 | inner |