Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,7,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.7195728007\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.10 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.7.c.a.58.51 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 11.8923i | − | 1.48654i | −0.668991 | − | 0.743270i | \(-0.733274\pi\) | ||
0.668991 | − | 0.743270i | \(-0.266726\pi\) | |||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −77.4273 | −1.20980 | ||||||||
\(5\) | 54.6144 | 0.436915 | 0.218458 | − | 0.975846i | \(-0.429897\pi\) | ||||
0.218458 | + | 0.975846i | \(0.429897\pi\) | |||||||
\(6\) | − | 185.383i | − | 0.858254i | ||||||
\(7\) | −559.219 | −1.63038 | −0.815188 | − | 0.579197i | \(-0.803366\pi\) | ||||
−0.815188 | + | 0.579197i | \(0.803366\pi\) | |||||||
\(8\) | 159.682i | 0.311879i | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 649.492i | − | 0.649492i | ||||||
\(11\) | 2296.89i | 1.72569i | 0.505472 | + | 0.862843i | \(0.331318\pi\) | ||||
−0.505472 | + | 0.862843i | \(0.668682\pi\) | |||||||
\(12\) | −1206.97 | −0.698480 | ||||||||
\(13\) | − | 2227.74i | − | 1.01399i | −0.861949 | − | 0.506995i | \(-0.830756\pi\) | ||
0.861949 | − | 0.506995i | \(-0.169244\pi\) | |||||||
\(14\) | 6650.41i | 2.42362i | ||||||||
\(15\) | 851.354 | 0.252253 | ||||||||
\(16\) | −3056.36 | −0.746181 | ||||||||
\(17\) | −3185.15 | −0.648311 | −0.324156 | − | 0.946004i | \(-0.605080\pi\) | ||||
−0.324156 | + | 0.946004i | \(0.605080\pi\) | |||||||
\(18\) | − | 2889.83i | − | 0.495513i | ||||||
\(19\) | 7584.09 | 1.10571 | 0.552857 | − | 0.833276i | \(-0.313538\pi\) | ||||
0.552857 | + | 0.833276i | \(0.313538\pi\) | |||||||
\(20\) | −4228.65 | −0.528581 | ||||||||
\(21\) | −8717.36 | −0.941298 | ||||||||
\(22\) | 27315.3 | 2.56530 | ||||||||
\(23\) | 11089.9i | 0.911473i | 0.890115 | + | 0.455737i | \(0.150624\pi\) | ||||
−0.890115 | + | 0.455737i | \(0.849376\pi\) | |||||||
\(24\) | 2489.20i | 0.180064i | ||||||||
\(25\) | −12642.3 | −0.809105 | ||||||||
\(26\) | −26493.0 | −1.50734 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 43298.8 | 1.97243 | ||||||||
\(29\) | 32846.9 | 1.34679 | 0.673396 | − | 0.739282i | \(-0.264835\pi\) | ||||
0.673396 | + | 0.739282i | \(0.264835\pi\) | |||||||
\(30\) | − | 10124.6i | − | 0.374984i | ||||||
\(31\) | 9813.00i | 0.329395i | 0.986344 | + | 0.164697i | \(0.0526648\pi\) | ||||
−0.986344 | + | 0.164697i | \(0.947335\pi\) | |||||||
\(32\) | 46566.8i | 1.42111i | ||||||||
\(33\) | 35804.9i | 0.996325i | ||||||||
\(34\) | 37878.9i | 0.963741i | ||||||||
\(35\) | −30541.4 | −0.712335 | ||||||||
\(36\) | −18814.8 | −0.403267 | ||||||||
\(37\) | 48671.8i | 0.960888i | 0.877026 | + | 0.480444i | \(0.159524\pi\) | ||||
−0.877026 | + | 0.480444i | \(0.840476\pi\) | |||||||
\(38\) | − | 90192.5i | − | 1.64369i | ||||||
\(39\) | − | 34727.0i | − | 0.585428i | ||||||
\(40\) | 8720.94i | 0.136265i | ||||||||
\(41\) | 44741.9 | 0.649177 | 0.324588 | − | 0.945855i | \(-0.394774\pi\) | ||||
0.324588 | + | 0.945855i | \(0.394774\pi\) | |||||||
\(42\) | 103670.i | 1.39928i | ||||||||
\(43\) | 140560.i | 1.76790i | 0.467586 | + | 0.883948i | \(0.345124\pi\) | ||||
−0.467586 | + | 0.883948i | \(0.654876\pi\) | |||||||
\(44\) | − | 177842.i | − | 2.08774i | ||||||
\(45\) | 13271.3 | 0.145638 | ||||||||
\(46\) | 131885. | 1.35494 | ||||||||
\(47\) | 138791.i | 1.33680i | 0.743801 | + | 0.668401i | \(0.233021\pi\) | ||||
−0.743801 | + | 0.668401i | \(0.766979\pi\) | |||||||
\(48\) | −47643.9 | −0.430808 | ||||||||
\(49\) | 195077. | 1.65812 | ||||||||
\(50\) | 150346.i | 1.20277i | ||||||||
\(51\) | −49651.6 | −0.374303 | ||||||||
\(52\) | 172488.i | 1.22673i | ||||||||
\(53\) | −127534. | −0.856639 | −0.428319 | − | 0.903627i | \(-0.640894\pi\) | ||||
−0.428319 | + | 0.903627i | \(0.640894\pi\) | |||||||
\(54\) | − | 45048.1i | − | 0.286085i | ||||||
\(55\) | 125443.i | 0.753978i | ||||||||
\(56\) | − | 89297.2i | − | 0.508480i | ||||||
\(57\) | 118224. | 0.638384 | ||||||||
\(58\) | − | 390626.i | − | 2.00206i | ||||||
\(59\) | 204540. | − | 18540.2i | 0.995917 | − | 0.0902731i | ||||
\(60\) | −65918.1 | −0.305176 | ||||||||
\(61\) | − | 29116.6i | − | 0.128278i | −0.997941 | − | 0.0641388i | \(-0.979570\pi\) | ||
0.997941 | − | 0.0641388i | \(-0.0204300\pi\) | |||||||
\(62\) | 116699. | 0.489659 | ||||||||
\(63\) | −135890. | −0.543458 | ||||||||
\(64\) | 358181. | 1.36635 | ||||||||
\(65\) | − | 121667.i | − | 0.443028i | ||||||
\(66\) | 425804. | 1.48108 | ||||||||
\(67\) | − | 401180.i | − | 1.33387i | −0.745115 | − | 0.666936i | \(-0.767605\pi\) | ||
0.745115 | − | 0.666936i | \(-0.232395\pi\) | |||||||
\(68\) | 246618. | 0.784328 | ||||||||
\(69\) | 172874.i | 0.526239i | ||||||||
\(70\) | 363208.i | 1.05892i | ||||||||
\(71\) | −697835. | −1.94974 | −0.974872 | − | 0.222765i | \(-0.928492\pi\) | ||||
−0.974872 | + | 0.222765i | \(0.928492\pi\) | |||||||
\(72\) | 38802.8i | 0.103960i | ||||||||
\(73\) | − | 209791.i | − | 0.539285i | −0.962961 | − | 0.269642i | \(-0.913095\pi\) | ||
0.962961 | − | 0.269642i | \(-0.0869055\pi\) | |||||||
\(74\) | 578821. | 1.42840 | ||||||||
\(75\) | −197073. | −0.467137 | ||||||||
\(76\) | −587216. | −1.33770 | ||||||||
\(77\) | − | 1.28446e6i | − | 2.81352i | ||||||
\(78\) | −412985. | −0.870262 | ||||||||
\(79\) | −457805. | −0.928536 | −0.464268 | − | 0.885695i | \(-0.653683\pi\) | ||||
−0.464268 | + | 0.885695i | \(0.653683\pi\) | |||||||
\(80\) | −166921. | −0.326018 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | − | 532085.i | − | 0.965028i | ||||||
\(83\) | 267609.i | 0.468022i | 0.972234 | + | 0.234011i | \(0.0751852\pi\) | ||||
−0.972234 | + | 0.234011i | \(0.924815\pi\) | |||||||
\(84\) | 674962. | 1.13878 | ||||||||
\(85\) | −173955. | −0.283257 | ||||||||
\(86\) | 1.67159e6 | 2.62805 | ||||||||
\(87\) | 512033. | 0.777571 | ||||||||
\(88\) | −366772. | −0.538206 | ||||||||
\(89\) | 220394.i | 0.312629i | 0.987707 | + | 0.156315i | \(0.0499614\pi\) | ||||
−0.987707 | + | 0.156315i | \(0.950039\pi\) | |||||||
\(90\) | − | 157827.i | − | 0.216497i | ||||||
\(91\) | 1.24579e6i | 1.65318i | ||||||||
\(92\) | − | 858661.i | − | 1.10270i | ||||||
\(93\) | 152970.i | 0.190176i | ||||||||
\(94\) | 1.65055e6 | 1.98721 | ||||||||
\(95\) | 414201. | 0.483103 | ||||||||
\(96\) | 725905.i | 0.820477i | ||||||||
\(97\) | − | 955116.i | − | 1.04650i | −0.852178 | − | 0.523252i | \(-0.824719\pi\) | ||
0.852178 | − | 0.523252i | \(-0.175281\pi\) | |||||||
\(98\) | − | 2.31991e6i | − | 2.46487i | ||||||
\(99\) | 558144.i | 0.575229i | ||||||||
\(100\) | 978857. | 0.978857 | ||||||||
\(101\) | − | 805727.i | − | 0.782031i | −0.920384 | − | 0.391015i | \(-0.872124\pi\) | ||
0.920384 | − | 0.391015i | \(-0.127876\pi\) | |||||||
\(102\) | 590473.i | 0.556416i | ||||||||
\(103\) | 1.08040e6i | 0.988716i | 0.869258 | + | 0.494358i | \(0.164597\pi\) | ||||
−0.869258 | + | 0.494358i | \(0.835403\pi\) | |||||||
\(104\) | 355730. | 0.316243 | ||||||||
\(105\) | −476093. | −0.411267 | ||||||||
\(106\) | 1.51667e6i | 1.27343i | ||||||||
\(107\) | 1.90839e6 | 1.55782 | 0.778908 | − | 0.627138i | \(-0.215774\pi\) | ||||
0.778908 | + | 0.627138i | \(0.215774\pi\) | |||||||
\(108\) | −293294. | −0.232827 | ||||||||
\(109\) | 1.43192e6i | 1.10570i | 0.833280 | + | 0.552851i | \(0.186460\pi\) | ||||
−0.833280 | + | 0.552851i | \(0.813540\pi\) | |||||||
\(110\) | 1.49181e6 | 1.12082 | ||||||||
\(111\) | 758719.i | 0.554769i | ||||||||
\(112\) | 1.70917e6 | 1.21655 | ||||||||
\(113\) | 1.08804e6i | 0.754063i | 0.926200 | + | 0.377032i | \(0.123055\pi\) | ||||
−0.926200 | + | 0.377032i | \(0.876945\pi\) | |||||||
\(114\) | − | 1.40596e6i | − | 0.948984i | ||||||
\(115\) | 605668.i | 0.398237i | ||||||||
\(116\) | −2.54325e6 | −1.62935 | ||||||||
\(117\) | − | 541340.i | − | 0.337997i | ||||||
\(118\) | −220486. | − | 2.43246e6i | −0.134195 | − | 1.48047i | ||||
\(119\) | 1.78120e6 | 1.05699 | ||||||||
\(120\) | 135946.i | 0.0786725i | ||||||||
\(121\) | −3.50413e6 | −1.97799 | ||||||||
\(122\) | −346264. | −0.190690 | ||||||||
\(123\) | 697458. | 0.374802 | ||||||||
\(124\) | − | 759795.i | − | 0.398503i | ||||||
\(125\) | −1.54380e6 | −0.790425 | ||||||||
\(126\) | 1.61605e6i | 0.807873i | ||||||||
\(127\) | −2.36792e6 | −1.15600 | −0.577998 | − | 0.816038i | \(-0.696166\pi\) | ||||
−0.577998 | + | 0.816038i | \(0.696166\pi\) | |||||||
\(128\) | − | 1.27933e6i | − | 0.610030i | ||||||
\(129\) | 2.19111e6i | 1.02070i | ||||||||
\(130\) | −1.44690e6 | −0.658579 | ||||||||
\(131\) | 275445.i | 0.122524i | 0.998122 | + | 0.0612619i | \(0.0195125\pi\) | ||||
−0.998122 | + | 0.0612619i | \(0.980488\pi\) | |||||||
\(132\) | − | 2.77228e6i | − | 1.20536i | ||||||
\(133\) | −4.24117e6 | −1.80273 | ||||||||
\(134\) | −4.77096e6 | −1.98286 | ||||||||
\(135\) | 206879. | 0.0840843 | ||||||||
\(136\) | − | 508612.i | − | 0.202195i | ||||||
\(137\) | −3.89100e6 | −1.51321 | −0.756606 | − | 0.653871i | \(-0.773144\pi\) | ||||
−0.756606 | + | 0.653871i | \(0.773144\pi\) | |||||||
\(138\) | 2.05588e6 | 0.782276 | ||||||||
\(139\) | −2.75589e6 | −1.02617 | −0.513083 | − | 0.858339i | \(-0.671497\pi\) | ||||
−0.513083 | + | 0.858339i | \(0.671497\pi\) | |||||||
\(140\) | 2.36474e6 | 0.861785 | ||||||||
\(141\) | 2.16354e6i | 0.771803i | ||||||||
\(142\) | 8.29888e6i | 2.89837i | ||||||||
\(143\) | 5.11686e6 | 1.74983 | ||||||||
\(144\) | −742695. | −0.248727 | ||||||||
\(145\) | 1.79391e6 | 0.588434 | ||||||||
\(146\) | −2.49490e6 | −0.801668 | ||||||||
\(147\) | 3.04094e6 | 0.957318 | ||||||||
\(148\) | − | 3.76853e6i | − | 1.16248i | ||||||
\(149\) | 136843.i | 0.0413679i | 0.999786 | + | 0.0206839i | \(0.00658437\pi\) | ||||
−0.999786 | + | 0.0206839i | \(0.993416\pi\) | |||||||
\(150\) | 2.34366e6i | 0.694418i | ||||||||
\(151\) | 1.92740e6i | 0.559809i | 0.960028 | + | 0.279905i | \(0.0903028\pi\) | ||||
−0.960028 | + | 0.279905i | \(0.909697\pi\) | |||||||
\(152\) | 1.21104e6i | 0.344849i | ||||||||
\(153\) | −773992. | −0.216104 | ||||||||
\(154\) | −1.52752e7 | −4.18240 | ||||||||
\(155\) | 535931.i | 0.143918i | ||||||||
\(156\) | 2.68882e6i | 0.708252i | ||||||||
\(157\) | 4.07228e6i | 1.05230i | 0.850392 | + | 0.526149i | \(0.176365\pi\) | ||||
−0.850392 | + | 0.526149i | \(0.823635\pi\) | |||||||
\(158\) | 5.44436e6i | 1.38031i | ||||||||
\(159\) | −1.98805e6 | −0.494580 | ||||||||
\(160\) | 2.54322e6i | 0.620903i | ||||||||
\(161\) | − | 6.20168e6i | − | 1.48604i | ||||||
\(162\) | − | 702230.i | − | 0.165171i | ||||||
\(163\) | −2.90630e6 | −0.671085 | −0.335542 | − | 0.942025i | \(-0.608920\pi\) | ||||
−0.335542 | + | 0.942025i | \(0.608920\pi\) | |||||||
\(164\) | −3.46425e6 | −0.785376 | ||||||||
\(165\) | 1.95546e6i | 0.435310i | ||||||||
\(166\) | 3.18249e6 | 0.695734 | ||||||||
\(167\) | 4.58396e6 | 0.984219 | 0.492110 | − | 0.870533i | \(-0.336226\pi\) | ||||
0.492110 | + | 0.870533i | \(0.336226\pi\) | |||||||
\(168\) | − | 1.39201e6i | − | 0.293571i | ||||||
\(169\) | −136004. | −0.0281769 | ||||||||
\(170\) | 2.06873e6i | 0.421073i | ||||||||
\(171\) | 1.84293e6 | 0.368571 | ||||||||
\(172\) | − | 1.08832e7i | − | 2.13880i | ||||||
\(173\) | − | 6.14754e6i | − | 1.18731i | −0.804721 | − | 0.593653i | \(-0.797685\pi\) | ||
0.804721 | − | 0.593653i | \(-0.202315\pi\) | |||||||
\(174\) | − | 6.08926e6i | − | 1.15589i | ||||||
\(175\) | 7.06979e6 | 1.31914 | ||||||||
\(176\) | − | 7.02011e6i | − | 1.28767i | ||||||
\(177\) | 3.18847e6 | − | 289013.i | 0.574993 | − | 0.0521192i | ||||
\(178\) | 2.62100e6 | 0.464736 | ||||||||
\(179\) | 4.13101e6i | 0.720273i | 0.932900 | + | 0.360137i | \(0.117270\pi\) | ||||
−0.932900 | + | 0.360137i | \(0.882730\pi\) | |||||||
\(180\) | −1.02756e6 | −0.176194 | ||||||||
\(181\) | 4.09393e6 | 0.690406 | 0.345203 | − | 0.938528i | \(-0.387810\pi\) | ||||
0.345203 | + | 0.938528i | \(0.387810\pi\) | |||||||
\(182\) | 1.48154e7 | 2.45753 | ||||||||
\(183\) | − | 453882.i | − | 0.0740611i | ||||||
\(184\) | −1.77086e6 | −0.284270 | ||||||||
\(185\) | 2.65818e6i | 0.419826i | ||||||||
\(186\) | 1.81916e6 | 0.282705 | ||||||||
\(187\) | − | 7.31594e6i | − | 1.11878i | ||||||
\(188\) | − | 1.07462e7i | − | 1.61727i | ||||||
\(189\) | −2.11832e6 | −0.313766 | ||||||||
\(190\) | − | 4.92581e6i | − | 0.718152i | ||||||
\(191\) | 1.09834e7i | 1.57630i | 0.615485 | + | 0.788149i | \(0.288960\pi\) | ||||
−0.615485 | + | 0.788149i | \(0.711040\pi\) | |||||||
\(192\) | 5.58349e6 | 0.788864 | ||||||||
\(193\) | −9.97789e6 | −1.38793 | −0.693964 | − | 0.720010i | \(-0.744137\pi\) | ||||
−0.693964 | + | 0.720010i | \(0.744137\pi\) | |||||||
\(194\) | −1.13586e7 | −1.55567 | ||||||||
\(195\) | − | 1.89659e6i | − | 0.255782i | ||||||
\(196\) | −1.51043e7 | −2.00600 | ||||||||
\(197\) | −8.47028e6 | −1.10790 | −0.553948 | − | 0.832551i | \(-0.686879\pi\) | ||||
−0.553948 | + | 0.832551i | \(0.686879\pi\) | |||||||
\(198\) | 6.63763e6 | 0.855101 | ||||||||
\(199\) | 5.05790e6 | 0.641816 | 0.320908 | − | 0.947110i | \(-0.396012\pi\) | ||||
0.320908 | + | 0.947110i | \(0.396012\pi\) | |||||||
\(200\) | − | 2.01874e6i | − | 0.252343i | ||||||
\(201\) | − | 6.25377e6i | − | 0.770112i | ||||||
\(202\) | −9.58196e6 | −1.16252 | ||||||||
\(203\) | −1.83686e7 | −2.19578 | ||||||||
\(204\) | 3.84439e6 | 0.452832 | ||||||||
\(205\) | 2.44355e6 | 0.283635 | ||||||||
\(206\) | 1.28484e7 | 1.46977 | ||||||||
\(207\) | 2.69485e6i | 0.303824i | ||||||||
\(208\) | 6.80876e6i | 0.756621i | ||||||||
\(209\) | 1.74198e7i | 1.90812i | ||||||||
\(210\) | 5.66185e6i | 0.611365i | ||||||||
\(211\) | 4.47808e6i | 0.476700i | 0.971179 | + | 0.238350i | \(0.0766065\pi\) | ||||
−0.971179 | + | 0.238350i | \(0.923394\pi\) | |||||||
\(212\) | 9.87460e6 | 1.03636 | ||||||||
\(213\) | −1.08782e7 | −1.12569 | ||||||||
\(214\) | − | 2.26952e7i | − | 2.31576i | ||||||
\(215\) | 7.67660e6i | 0.772420i | ||||||||
\(216\) | 604875.i | 0.0600212i | ||||||||
\(217\) | − | 5.48762e6i | − | 0.537037i | ||||||
\(218\) | 1.70288e7 | 1.64367 | ||||||||
\(219\) | − | 3.27032e6i | − | 0.311356i | ||||||
\(220\) | − | 9.71273e6i | − | 0.912164i | ||||||
\(221\) | 7.09568e6i | 0.657381i | ||||||||
\(222\) | 9.02293e6 | 0.824686 | ||||||||
\(223\) | −6.43240e6 | −0.580041 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(224\) | − | 2.60410e7i | − | 2.31694i | ||||||
\(225\) | −3.07207e6 | −0.269702 | ||||||||
\(226\) | 1.29393e7 | 1.12095 | ||||||||
\(227\) | − | 1.97765e7i | − | 1.69072i | −0.534197 | − | 0.845360i | \(-0.679386\pi\) | ||
0.534197 | − | 0.845360i | \(-0.320614\pi\) | |||||||
\(228\) | −9.15379e6 | −0.772319 | ||||||||
\(229\) | 1.78077e7i | 1.48286i | 0.671028 | + | 0.741432i | \(0.265853\pi\) | ||||
−0.671028 | + | 0.741432i | \(0.734147\pi\) | |||||||
\(230\) | 7.20280e6 | 0.591995 | ||||||||
\(231\) | − | 2.00228e7i | − | 1.62438i | ||||||
\(232\) | 5.24506e6i | 0.420036i | ||||||||
\(233\) | 1.83620e6i | 0.145162i | 0.997363 | + | 0.0725808i | \(0.0231235\pi\) | ||||
−0.997363 | + | 0.0725808i | \(0.976876\pi\) | |||||||
\(234\) | −6.43779e6 | −0.502446 | ||||||||
\(235\) | 7.57998e6i | 0.584069i | ||||||||
\(236\) | −1.58370e7 | + | 1.43552e6i | −1.20486 | + | 0.109213i | ||||
\(237\) | −7.13647e6 | −0.536091 | ||||||||
\(238\) | − | 2.11826e7i | − | 1.57126i | ||||||
\(239\) | −1.30376e7 | −0.955002 | −0.477501 | − | 0.878631i | \(-0.658457\pi\) | ||||
−0.477501 | + | 0.878631i | \(0.658457\pi\) | |||||||
\(240\) | −2.60204e6 | −0.188226 | ||||||||
\(241\) | 2.10381e7 | 1.50299 | 0.751495 | − | 0.659739i | \(-0.229333\pi\) | ||||
0.751495 | + | 0.659739i | \(0.229333\pi\) | |||||||
\(242\) | 4.16723e7i | 2.94037i | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 2.25442e6i | 0.155190i | ||||||||
\(245\) | 1.06540e7 | 0.724459 | ||||||||
\(246\) | − | 8.29439e6i | − | 0.557159i | ||||||
\(247\) | − | 1.68954e7i | − | 1.12118i | ||||||
\(248\) | −1.56696e6 | −0.102731 | ||||||||
\(249\) | 4.17161e6i | 0.270213i | ||||||||
\(250\) | 1.83594e7i | 1.17500i | ||||||||
\(251\) | −1.54860e7 | −0.979308 | −0.489654 | − | 0.871917i | \(-0.662877\pi\) | ||||
−0.489654 | + | 0.871917i | \(0.662877\pi\) | |||||||
\(252\) | 1.05216e7 | 0.657477 | ||||||||
\(253\) | −2.54723e7 | −1.57292 | ||||||||
\(254\) | 2.81601e7i | 1.71843i | ||||||||
\(255\) | −2.71169e6 | −0.163538 | ||||||||
\(256\) | 7.70942e6 | 0.459517 | ||||||||
\(257\) | 1.79898e7 | 1.05981 | 0.529904 | − | 0.848058i | \(-0.322228\pi\) | ||||
0.529904 | + | 0.848058i | \(0.322228\pi\) | |||||||
\(258\) | 2.60574e7 | 1.51730 | ||||||||
\(259\) | − | 2.72182e7i | − | 1.56661i | ||||||
\(260\) | 9.42031e6i | 0.535976i | ||||||||
\(261\) | 7.98180e6 | 0.448931 | ||||||||
\(262\) | 3.27568e6 | 0.182137 | ||||||||
\(263\) | 1.18555e7 | 0.651707 | 0.325853 | − | 0.945420i | \(-0.394348\pi\) | ||||
0.325853 | + | 0.945420i | \(0.394348\pi\) | |||||||
\(264\) | −5.71741e6 | −0.310733 | ||||||||
\(265\) | −6.96518e6 | −0.374278 | ||||||||
\(266\) | 5.04373e7i | 2.67983i | ||||||||
\(267\) | 3.43560e6i | 0.180497i | ||||||||
\(268\) | 3.10623e7i | 1.61372i | ||||||||
\(269\) | − | 1.76151e7i | − | 0.904957i | −0.891775 | − | 0.452478i | \(-0.850540\pi\) | ||
0.891775 | − | 0.452478i | \(-0.149460\pi\) | |||||||
\(270\) | − | 2.46027e6i | − | 0.124995i | ||||||
\(271\) | 2.56878e6 | 0.129068 | 0.0645341 | − | 0.997916i | \(-0.479444\pi\) | ||||
0.0645341 | + | 0.997916i | \(0.479444\pi\) | |||||||
\(272\) | 9.73497e6 | 0.483757 | ||||||||
\(273\) | 1.94200e7i | 0.954467i | ||||||||
\(274\) | 4.62730e7i | 2.24945i | ||||||||
\(275\) | − | 2.90379e7i | − | 1.39626i | ||||||
\(276\) | − | 1.33852e7i | − | 0.636646i | ||||||
\(277\) | −3.26458e7 | −1.53599 | −0.767994 | − | 0.640457i | \(-0.778745\pi\) | ||||
−0.767994 | + | 0.640457i | \(0.778745\pi\) | |||||||
\(278\) | 3.27739e7i | 1.52544i | ||||||||
\(279\) | 2.38456e6i | 0.109798i | ||||||||
\(280\) | − | 4.87691e6i | − | 0.222163i | ||||||
\(281\) | 2.87372e7 | 1.29516 | 0.647582 | − | 0.761996i | \(-0.275780\pi\) | ||||
0.647582 | + | 0.761996i | \(0.275780\pi\) | |||||||
\(282\) | 2.57295e7 | 1.14732 | ||||||||
\(283\) | 2.46553e7i | 1.08781i | 0.839148 | + | 0.543903i | \(0.183054\pi\) | ||||
−0.839148 | + | 0.543903i | \(0.816946\pi\) | |||||||
\(284\) | 5.40315e7 | 2.35880 | ||||||||
\(285\) | 6.45675e6 | 0.278920 | ||||||||
\(286\) | − | 6.08514e7i | − | 2.60119i | ||||||
\(287\) | −2.50205e7 | −1.05840 | ||||||||
\(288\) | 1.13157e7i | 0.473702i | ||||||||
\(289\) | −1.39924e7 | −0.579693 | ||||||||
\(290\) | − | 2.13338e7i | − | 0.874730i | ||||||
\(291\) | − | 1.48888e7i | − | 0.604200i | ||||||
\(292\) | 1.62435e7i | 0.652428i | ||||||||
\(293\) | 6.34529e6 | 0.252260 | 0.126130 | − | 0.992014i | \(-0.459744\pi\) | ||||
0.126130 | + | 0.992014i | \(0.459744\pi\) | |||||||
\(294\) | − | 3.61639e7i | − | 1.42309i | ||||||
\(295\) | 1.11709e7 | − | 1.01256e6i | 0.435131 | − | 0.0394417i | ||||
\(296\) | −7.77202e6 | −0.299681 | ||||||||
\(297\) | 8.70060e6i | 0.332108i | ||||||||
\(298\) | 1.62738e6 | 0.0614950 | ||||||||
\(299\) | 2.47054e7 | 0.924225 | ||||||||
\(300\) | 1.52589e7 | 0.565143 | ||||||||
\(301\) | − | 7.86038e7i | − | 2.88233i | ||||||
\(302\) | 2.29212e7 | 0.832179 | ||||||||
\(303\) | − | 1.25600e7i | − | 0.451506i | ||||||
\(304\) | −2.31797e7 | −0.825063 | ||||||||
\(305\) | − | 1.59018e6i | − | 0.0560464i | ||||||
\(306\) | 9.20456e6i | 0.321247i | ||||||||
\(307\) | 2.12802e7 | 0.735464 | 0.367732 | − | 0.929932i | \(-0.380134\pi\) | ||||
0.367732 | + | 0.929932i | \(0.380134\pi\) | |||||||
\(308\) | 9.94525e7i | 3.40380i | ||||||||
\(309\) | 1.68417e7i | 0.570835i | ||||||||
\(310\) | 6.37347e6 | 0.213939 | ||||||||
\(311\) | 2.24785e6 | 0.0747284 | 0.0373642 | − | 0.999302i | \(-0.488104\pi\) | ||||
0.0373642 | + | 0.999302i | \(0.488104\pi\) | |||||||
\(312\) | 5.54528e6 | 0.182583 | ||||||||
\(313\) | − | 1.36818e7i | − | 0.446179i | −0.974798 | − | 0.223090i | \(-0.928386\pi\) | ||
0.974798 | − | 0.223090i | \(-0.0716143\pi\) | |||||||
\(314\) | 4.84289e7 | 1.56428 | ||||||||
\(315\) | −7.42156e6 | −0.237445 | ||||||||
\(316\) | 3.54466e7 | 1.12335 | ||||||||
\(317\) | −2.87039e7 | −0.901079 | −0.450539 | − | 0.892757i | \(-0.648768\pi\) | ||||
−0.450539 | + | 0.892757i | \(0.648768\pi\) | |||||||
\(318\) | 2.36426e7i | 0.735214i | ||||||||
\(319\) | 7.54457e7i | 2.32414i | ||||||||
\(320\) | 1.95618e7 | 0.596980 | ||||||||
\(321\) | 2.97489e7 | 0.899406 | ||||||||
\(322\) | −7.37524e7 | −2.20906 | ||||||||
\(323\) | −2.41565e7 | −0.716847 | ||||||||
\(324\) | −4.57201e6 | −0.134422 | ||||||||
\(325\) | 2.81637e7i | 0.820425i | ||||||||
\(326\) | 3.45626e7i | 0.997595i | ||||||||
\(327\) | 2.23214e7i | 0.638378i | ||||||||
\(328\) | 7.14449e6i | 0.202465i | ||||||||
\(329\) | − | 7.76145e7i | − | 2.17949i | ||||||
\(330\) | 2.32550e7 | 0.647105 | ||||||||
\(331\) | 3.54730e7 | 0.978169 | 0.489085 | − | 0.872236i | \(-0.337331\pi\) | ||||
0.489085 | + | 0.872236i | \(0.337331\pi\) | |||||||
\(332\) | − | 2.07202e7i | − | 0.566214i | ||||||
\(333\) | 1.18273e7i | 0.320296i | ||||||||
\(334\) | − | 5.45140e7i | − | 1.46308i | ||||||
\(335\) | − | 2.19102e7i | − | 0.582789i | ||||||
\(336\) | 2.66434e7 | 0.702378 | ||||||||
\(337\) | 5.56747e7i | 1.45468i | 0.686276 | + | 0.727342i | \(0.259244\pi\) | ||||
−0.686276 | + | 0.727342i | \(0.740756\pi\) | |||||||
\(338\) | 1.61741e6i | 0.0418860i | ||||||||
\(339\) | 1.69608e7i | 0.435359i | ||||||||
\(340\) | 1.34689e7 | 0.342685 | ||||||||
\(341\) | −2.25394e7 | −0.568432 | ||||||||
\(342\) | − | 2.19168e7i | − | 0.547896i | ||||||
\(343\) | −4.32989e7 | −1.07299 | ||||||||
\(344\) | −2.24449e7 | −0.551370 | ||||||||
\(345\) | 9.44143e6i | 0.229922i | ||||||||
\(346\) | −7.31085e7 | −1.76498 | ||||||||
\(347\) | 2.90745e7i | 0.695862i | 0.937520 | + | 0.347931i | \(0.113116\pi\) | ||||
−0.937520 | + | 0.347931i | \(0.886884\pi\) | |||||||
\(348\) | −3.96453e7 | −0.940707 | ||||||||
\(349\) | 2.35075e7i | 0.553007i | 0.961013 | + | 0.276503i | \(0.0891757\pi\) | ||||
−0.961013 | + | 0.276503i | \(0.910824\pi\) | |||||||
\(350\) | − | 8.40763e7i | − | 1.96096i | ||||||
\(351\) | − | 8.43866e6i | − | 0.195143i | ||||||
\(352\) | −1.06959e8 | −2.45239 | ||||||||
\(353\) | − | 6.92167e7i | − | 1.57357i | −0.617226 | − | 0.786786i | \(-0.711743\pi\) | ||
0.617226 | − | 0.786786i | \(-0.288257\pi\) | |||||||
\(354\) | −3.43704e6 | − | 3.79183e7i | −0.0774773 | − | 0.854750i | ||||
\(355\) | −3.81118e7 | −0.851873 | ||||||||
\(356\) | − | 1.70645e7i | − | 0.378219i | ||||||
\(357\) | 2.77661e7 | 0.610254 | ||||||||
\(358\) | 4.91273e7 | 1.07071 | ||||||||
\(359\) | −9.18314e7 | −1.98476 | −0.992379 | − | 0.123220i | \(-0.960678\pi\) | ||||
−0.992379 | + | 0.123220i | \(0.960678\pi\) | |||||||
\(360\) | 2.11919e6i | 0.0454216i | ||||||||
\(361\) | 1.04726e7 | 0.222604 | ||||||||
\(362\) | − | 4.86863e7i | − | 1.02632i | ||||||
\(363\) | −5.46240e7 | −1.14199 | ||||||||
\(364\) | − | 9.64584e7i | − | 2.00003i | ||||||
\(365\) | − | 1.14576e7i | − | 0.235622i | ||||||
\(366\) | −5.39772e6 | −0.110095 | ||||||||
\(367\) | − | 7.23105e7i | − | 1.46286i | −0.681916 | − | 0.731430i | \(-0.738853\pi\) | ||
0.681916 | − | 0.731430i | \(-0.261147\pi\) | |||||||
\(368\) | − | 3.38947e7i | − | 0.680124i | ||||||
\(369\) | 1.08723e7 | 0.216392 | ||||||||
\(370\) | 3.16120e7 | 0.624089 | ||||||||
\(371\) | 7.13193e7 | 1.39664 | ||||||||
\(372\) | − | 1.18440e7i | − | 0.230076i | ||||||
\(373\) | 7.66390e7 | 1.47681 | 0.738403 | − | 0.674360i | \(-0.235580\pi\) | ||||
0.738403 | + | 0.674360i | \(0.235580\pi\) | |||||||
\(374\) | −8.70035e7 | −1.66311 | ||||||||
\(375\) | −2.40655e7 | −0.456352 | ||||||||
\(376\) | −2.21624e7 | −0.416921 | ||||||||
\(377\) | − | 7.31743e7i | − | 1.36563i | ||||||
\(378\) | 2.51917e7i | 0.466426i | ||||||||
\(379\) | −1.34455e7 | −0.246978 | −0.123489 | − | 0.992346i | \(-0.539408\pi\) | ||||
−0.123489 | + | 0.992346i | \(0.539408\pi\) | |||||||
\(380\) | −3.20705e7 | −0.584459 | ||||||||
\(381\) | −3.69122e7 | −0.667414 | ||||||||
\(382\) | 1.30619e8 | 2.34323 | ||||||||
\(383\) | −5.06181e6 | −0.0900969 | −0.0450484 | − | 0.998985i | \(-0.514344\pi\) | ||||
−0.0450484 | + | 0.998985i | \(0.514344\pi\) | |||||||
\(384\) | − | 1.99427e7i | − | 0.352201i | ||||||
\(385\) | − | 7.01501e7i | − | 1.22927i | ||||||
\(386\) | 1.18660e8i | 2.06321i | ||||||||
\(387\) | 3.41561e7i | 0.589299i | ||||||||
\(388\) | 7.39521e7i | 1.26606i | ||||||||
\(389\) | 1.04201e7 | 0.177020 | 0.0885098 | − | 0.996075i | \(-0.471790\pi\) | ||||
0.0885098 | + | 0.996075i | \(0.471790\pi\) | |||||||
\(390\) | −2.25549e7 | −0.380231 | ||||||||
\(391\) | − | 3.53230e7i | − | 0.590918i | ||||||
\(392\) | 3.11502e7i | 0.517134i | ||||||||
\(393\) | 4.29376e6i | 0.0707392i | ||||||||
\(394\) | 1.00731e8i | 1.64693i | ||||||||
\(395\) | −2.50027e7 | −0.405692 | ||||||||
\(396\) | − | 4.32156e7i | − | 0.695913i | ||||||
\(397\) | 3.94584e7i | 0.630620i | 0.948989 | + | 0.315310i | \(0.102108\pi\) | ||||
−0.948989 | + | 0.315310i | \(0.897892\pi\) | |||||||
\(398\) | − | 6.01501e7i | − | 0.954086i | ||||||
\(399\) | −6.61132e7 | −1.04081 | ||||||||
\(400\) | 3.86393e7 | 0.603739 | ||||||||
\(401\) | − | 7.49107e7i | − | 1.16174i | −0.813995 | − | 0.580872i | \(-0.802712\pi\) | ||
0.813995 | − | 0.580872i | \(-0.197288\pi\) | |||||||
\(402\) | −7.43719e7 | −1.14480 | ||||||||
\(403\) | 2.18608e7 | 0.334003 | ||||||||
\(404\) | 6.23853e7i | 0.946102i | ||||||||
\(405\) | 3.22492e6 | 0.0485461 | ||||||||
\(406\) | 2.18445e8i | 3.26411i | ||||||||
\(407\) | −1.11794e8 | −1.65819 | ||||||||
\(408\) | − | 7.92848e6i | − | 0.116737i | ||||||
\(409\) | − | 1.05414e8i | − | 1.54073i | −0.637600 | − | 0.770367i | \(-0.720073\pi\) | ||
0.637600 | − | 0.770367i | \(-0.279927\pi\) | |||||||
\(410\) | − | 2.90595e7i | − | 0.421635i | ||||||
\(411\) | −6.06547e7 | −0.873653 | ||||||||
\(412\) | − | 8.36522e7i | − | 1.19615i | ||||||
\(413\) | −1.14383e8 | + | 1.03680e7i | −1.62372 | + | 0.147179i | ||||
\(414\) | 3.20480e7 | 0.451647 | ||||||||
\(415\) | 1.46153e7i | 0.204486i | ||||||||
\(416\) | 1.03739e8 | 1.44099 | ||||||||
\(417\) | −4.29601e7 | −0.592457 | ||||||||
\(418\) | 2.07162e8 | 2.83649 | ||||||||
\(419\) | − | 1.08862e8i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(420\) | 3.68626e7 | 0.497552 | ||||||||
\(421\) | 5.53501e7i | 0.741775i | 0.928678 | + | 0.370887i | \(0.120946\pi\) | ||||
−0.928678 | + | 0.370887i | \(0.879054\pi\) | |||||||
\(422\) | 5.32548e7 | 0.708633 | ||||||||
\(423\) | 3.37262e7i | 0.445601i | ||||||||
\(424\) | − | 2.03649e7i | − | 0.267168i | ||||||
\(425\) | 4.02676e7 | 0.524552 | ||||||||
\(426\) | 1.29367e8i | 1.67338i | ||||||||
\(427\) | 1.62825e7i | 0.209141i | ||||||||
\(428\) | −1.47762e8 | −1.88465 | ||||||||
\(429\) | 7.97640e7 | 1.01026 | ||||||||
\(430\) | 9.12926e7 | 1.14823 | ||||||||
\(431\) | 6.15442e7i | 0.768697i | 0.923188 | + | 0.384348i | \(0.125574\pi\) | ||||
−0.923188 | + | 0.384348i | \(0.874426\pi\) | |||||||
\(432\) | −1.15775e7 | −0.143603 | ||||||||
\(433\) | −7.93377e7 | −0.977273 | −0.488636 | − | 0.872488i | \(-0.662505\pi\) | ||||
−0.488636 | + | 0.872488i | \(0.662505\pi\) | |||||||
\(434\) | −6.52605e7 | −0.798328 | ||||||||
\(435\) | 2.79643e7 | 0.339732 | ||||||||
\(436\) | − | 1.10870e8i | − | 1.33768i | ||||||
\(437\) | 8.41068e7i | 1.00783i | ||||||||
\(438\) | −3.88917e7 | −0.462843 | ||||||||
\(439\) | 6.40118e7 | 0.756600 | 0.378300 | − | 0.925683i | \(-0.376509\pi\) | ||||
0.378300 | + | 0.925683i | \(0.376509\pi\) | |||||||
\(440\) | −2.00310e7 | −0.235150 | ||||||||
\(441\) | 4.74036e7 | 0.552708 | ||||||||
\(442\) | 8.43842e7 | 0.977224 | ||||||||
\(443\) | − | 8.42361e7i | − | 0.968918i | −0.874814 | − | 0.484459i | \(-0.839016\pi\) | ||
0.874814 | − | 0.484459i | \(-0.160984\pi\) | |||||||
\(444\) | − | 5.87456e7i | − | 0.671160i | ||||||
\(445\) | 1.20367e7i | 0.136592i | ||||||||
\(446\) | 7.64962e7i | 0.862255i | ||||||||
\(447\) | 2.13317e6i | 0.0238838i | ||||||||
\(448\) | −2.00302e8 | −2.22767 | ||||||||
\(449\) | 1.28794e8 | 1.42285 | 0.711423 | − | 0.702764i | \(-0.248051\pi\) | ||||
0.711423 | + | 0.702764i | \(0.248051\pi\) | |||||||
\(450\) | 3.65341e7i | 0.400923i | ||||||||
\(451\) | 1.02767e8i | 1.12028i | ||||||||
\(452\) | − | 8.42437e7i | − | 0.912267i | ||||||
\(453\) | 3.00451e7i | 0.323206i | ||||||||
\(454\) | −2.35188e8 | −2.51332 | ||||||||
\(455\) | 6.80382e7i | 0.722301i | ||||||||
\(456\) | 1.88783e7i | 0.199099i | ||||||||
\(457\) | 3.91733e7i | 0.410432i | 0.978717 | + | 0.205216i | \(0.0657897\pi\) | ||||
−0.978717 | + | 0.205216i | \(0.934210\pi\) | |||||||
\(458\) | 2.11775e8 | 2.20434 | ||||||||
\(459\) | −1.20653e7 | −0.124768 | ||||||||
\(460\) | − | 4.68953e7i | − | 0.481787i | ||||||
\(461\) | 6.45172e7 | 0.658526 | 0.329263 | − | 0.944238i | \(-0.393200\pi\) | ||||
0.329263 | + | 0.944238i | \(0.393200\pi\) | |||||||
\(462\) | −2.38117e8 | −2.41471 | ||||||||
\(463\) | 5.08703e7i | 0.512533i | 0.966606 | + | 0.256266i | \(0.0824924\pi\) | ||||
−0.966606 | + | 0.256266i | \(0.917508\pi\) | |||||||
\(464\) | −1.00392e8 | −1.00495 | ||||||||
\(465\) | 8.35434e6i | 0.0830909i | ||||||||
\(466\) | 2.18367e7 | 0.215789 | ||||||||
\(467\) | − | 1.13345e8i | − | 1.11289i | −0.830885 | − | 0.556444i | \(-0.812166\pi\) | ||
0.830885 | − | 0.556444i | \(-0.187834\pi\) | |||||||
\(468\) | 4.19145e7i | 0.408909i | ||||||||
\(469\) | 2.24347e8i | 2.17471i | ||||||||
\(470\) | 9.01435e7 | 0.868243 | ||||||||
\(471\) | 6.34806e7i | 0.607545i | ||||||||
\(472\) | 2.96054e6 | + | 3.26615e7i | 0.0281543 | + | 0.310606i | ||||
\(473\) | −3.22851e8 | −3.05083 | ||||||||
\(474\) | 8.48692e7i | 0.796921i | ||||||||
\(475\) | −9.58802e7 | −0.894639 | ||||||||
\(476\) | −1.37913e8 | −1.27875 | ||||||||
\(477\) | −3.09907e7 | −0.285546 | ||||||||
\(478\) | 1.55047e8i | 1.41965i | ||||||||
\(479\) | −6.43260e7 | −0.585302 | −0.292651 | − | 0.956219i | \(-0.594537\pi\) | ||||
−0.292651 | + | 0.956219i | \(0.594537\pi\) | |||||||
\(480\) | 3.96449e7i | 0.358479i | ||||||||
\(481\) | 1.08428e8 | 0.974331 | ||||||||
\(482\) | − | 2.50192e8i | − | 2.23425i | ||||||
\(483\) | − | 9.66746e7i | − | 0.857968i | ||||||
\(484\) | 2.71316e8 | 2.39298 | ||||||||
\(485\) | − | 5.21631e7i | − | 0.457234i | ||||||
\(486\) | − | 1.09467e7i | − | 0.0953616i | ||||||
\(487\) | 1.51710e8 | 1.31349 | 0.656745 | − | 0.754112i | \(-0.271933\pi\) | ||||
0.656745 | + | 0.754112i | \(0.271933\pi\) | |||||||
\(488\) | 4.64940e6 | 0.0400071 | ||||||||
\(489\) | −4.53047e7 | −0.387451 | ||||||||
\(490\) | − | 1.26701e8i | − | 1.07694i | ||||||
\(491\) | 4.86573e7 | 0.411059 | 0.205529 | − | 0.978651i | \(-0.434108\pi\) | ||||
0.205529 | + | 0.978651i | \(0.434108\pi\) | |||||||
\(492\) | −5.40023e7 | −0.453437 | ||||||||
\(493\) | −1.04622e8 | −0.873140 | ||||||||
\(494\) | −2.00925e8 | −1.66668 | ||||||||
\(495\) | 3.04827e7i | 0.251326i | ||||||||
\(496\) | − | 2.99920e7i | − | 0.245788i | ||||||
\(497\) | 3.90242e8 | 3.17881 | ||||||||
\(498\) | 4.96101e7 | 0.401682 | ||||||||
\(499\) | −7.52996e7 | −0.606025 | −0.303013 | − | 0.952987i | \(-0.597992\pi\) | ||||
−0.303013 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(500\) | 1.19532e8 | 0.956258 | ||||||||
\(501\) | 7.14569e7 | 0.568239 | ||||||||
\(502\) | 1.84165e8i | 1.45578i | ||||||||
\(503\) | − | 7.64741e6i | − | 0.0600911i | −0.999549 | − | 0.0300456i | \(-0.990435\pi\) | ||
0.999549 | − | 0.0300456i | \(-0.00956524\pi\) | |||||||
\(504\) | − | 2.16992e7i | − | 0.169493i | ||||||
\(505\) | − | 4.40043e7i | − | 0.341681i | ||||||
\(506\) | 3.02924e8i | 2.33820i | ||||||||
\(507\) | −2.12010e6 | −0.0162679 | ||||||||
\(508\) | 1.83342e8 | 1.39853 | ||||||||
\(509\) | 1.63756e8i | 1.24178i | 0.783897 | + | 0.620891i | \(0.213229\pi\) | ||||
−0.783897 | + | 0.620891i | \(0.786771\pi\) | |||||||
\(510\) | 3.22483e7i | 0.243107i | ||||||||
\(511\) | 1.17319e8i | 0.879236i | ||||||||
\(512\) | − | 1.73560e8i | − | 1.29312i | ||||||
\(513\) | 2.87285e7 | 0.212795 | ||||||||
\(514\) | − | 2.13940e8i | − | 1.57545i | ||||||
\(515\) | 5.90052e7i | 0.431985i | ||||||||
\(516\) | − | 1.69652e8i | − | 1.23484i | ||||||
\(517\) | −3.18787e8 | −2.30690 | ||||||||
\(518\) | −3.23688e8 | −2.32882 | ||||||||
\(519\) | − | 9.58306e7i | − | 0.685492i | ||||||
\(520\) | 1.94280e7 | 0.138171 | ||||||||
\(521\) | 4.58496e7 | 0.324207 | 0.162104 | − | 0.986774i | \(-0.448172\pi\) | ||||
0.162104 | + | 0.986774i | \(0.448172\pi\) | |||||||
\(522\) | − | 9.49221e7i | − | 0.667353i | ||||||
\(523\) | 1.15456e8 | 0.807074 | 0.403537 | − | 0.914963i | \(-0.367781\pi\) | ||||
0.403537 | + | 0.914963i | \(0.367781\pi\) | |||||||
\(524\) | − | 2.13269e7i | − | 0.148230i | ||||||
\(525\) | 1.10207e8 | 0.761609 | ||||||||
\(526\) | − | 1.40989e8i | − | 0.968789i | ||||||
\(527\) | − | 3.12559e7i | − | 0.213550i | ||||||
\(528\) | − | 1.09433e8i | − | 0.743439i | ||||||
\(529\) | 2.50501e7 | 0.169216 | ||||||||
\(530\) | 8.28321e7i | 0.556380i | ||||||||
\(531\) | 4.97033e7 | − | 4.50527e6i | 0.331972 | − | 0.0300910i | ||||
\(532\) | 3.28382e8 | 2.18095 | ||||||||
\(533\) | − | 9.96732e7i | − | 0.658259i | ||||||
\(534\) | 4.08573e7 | 0.268315 | ||||||||
\(535\) | 1.04226e8 | 0.680634 | ||||||||
\(536\) | 6.40612e7 | 0.416007 | ||||||||
\(537\) | 6.43961e7i | 0.415850i | ||||||||
\(538\) | −2.09484e8 | −1.34525 | ||||||||
\(539\) | 4.48069e8i | 2.86140i | ||||||||
\(540\) | −1.60181e7 | −0.101725 | ||||||||
\(541\) | − | 8.19781e7i | − | 0.517733i | −0.965913 | − | 0.258867i | \(-0.916651\pi\) | ||
0.965913 | − | 0.258867i | \(-0.0833490\pi\) | |||||||
\(542\) | − | 3.05488e7i | − | 0.191865i | ||||||
\(543\) | 6.38180e7 | 0.398606 | ||||||||
\(544\) | − | 1.48323e8i | − | 0.921320i | ||||||
\(545\) | 7.82033e7i | 0.483098i | ||||||||
\(546\) | 2.30949e8 | 1.41885 | ||||||||
\(547\) | −1.00028e8 | −0.611166 | −0.305583 | − | 0.952166i | \(-0.598851\pi\) | ||||
−0.305583 | + | 0.952166i | \(0.598851\pi\) | |||||||
\(548\) | 3.01270e8 | 1.83069 | ||||||||
\(549\) | − | 7.07533e6i | − | 0.0427592i | ||||||
\(550\) | −3.45328e8 | −2.07560 | ||||||||
\(551\) | 2.49114e8 | 1.48917 | ||||||||
\(552\) | −2.76050e7 | −0.164123 | ||||||||
\(553\) | 2.56013e8 | 1.51386 | ||||||||
\(554\) | 3.88234e8i | 2.28331i | ||||||||
\(555\) | 4.14370e7i | 0.242387i | ||||||||
\(556\) | 2.13381e8 | 1.24146 | ||||||||
\(557\) | −1.27519e8 | −0.737922 | −0.368961 | − | 0.929445i | \(-0.620286\pi\) | ||||
−0.368961 | + | 0.929445i | \(0.620286\pi\) | |||||||
\(558\) | 2.83580e7 | 0.163220 | ||||||||
\(559\) | 3.13131e8 | 1.79263 | ||||||||
\(560\) | 9.33454e7 | 0.531531 | ||||||||
\(561\) | − | 1.14044e8i | − | 0.645929i | ||||||
\(562\) | − | 3.41752e8i | − | 1.92531i | ||||||
\(563\) | − | 2.14829e8i | − | 1.20384i | −0.798558 | − | 0.601918i | \(-0.794403\pi\) | ||
0.798558 | − | 0.601918i | \(-0.205597\pi\) | |||||||
\(564\) | − | 1.67517e8i | − | 0.933729i | ||||||
\(565\) | 5.94224e7i | 0.329462i | ||||||||
\(566\) | 2.93209e8 | 1.61707 | ||||||||
\(567\) | −3.30213e7 | −0.181153 | ||||||||
\(568\) | − | 1.11432e8i | − | 0.608085i | ||||||
\(569\) | 1.07673e8i | 0.584478i | 0.956345 | + | 0.292239i | \(0.0944003\pi\) | ||||
−0.956345 | + | 0.292239i | \(0.905600\pi\) | |||||||
\(570\) | − | 7.67857e7i | − | 0.414626i | ||||||
\(571\) | − | 1.35569e8i | − | 0.728200i | −0.931360 | − | 0.364100i | \(-0.881377\pi\) | ||
0.931360 | − | 0.364100i | \(-0.118623\pi\) | |||||||
\(572\) | −3.96185e8 | −2.11695 | ||||||||
\(573\) | 1.71215e8i | 0.910076i | ||||||||
\(574\) | 2.97552e8i | 1.57336i | ||||||||
\(575\) | − | 1.40201e8i | − | 0.737478i | ||||||
\(576\) | 8.70380e7 | 0.455451 | ||||||||
\(577\) | −615313. | −0.00320308 | −0.00160154 | − | 0.999999i | \(-0.500510\pi\) | ||||
−0.00160154 | + | 0.999999i | \(0.500510\pi\) | |||||||
\(578\) | 1.66402e8i | 0.861736i | ||||||||
\(579\) | −1.55540e8 | −0.801320 | ||||||||
\(580\) | −1.38898e8 | −0.711888 | ||||||||
\(581\) | − | 1.49652e8i | − | 0.763052i | ||||||
\(582\) | −1.77062e8 | −0.898167 | ||||||||
\(583\) | − | 2.92931e8i | − | 1.47829i | ||||||
\(584\) | 3.34999e7 | 0.168192 | ||||||||
\(585\) | − | 2.95650e7i | − | 0.147676i | ||||||
\(586\) | − | 7.54602e7i | − | 0.374995i | ||||||
\(587\) | − | 1.76327e8i | − | 0.871777i | −0.900001 | − | 0.435888i | \(-0.856434\pi\) | ||
0.900001 | − | 0.435888i | \(-0.143566\pi\) | |||||||
\(588\) | −2.35452e8 | −1.15816 | ||||||||
\(589\) | 7.44227e7i | 0.364217i | ||||||||
\(590\) | −1.20417e7 | − | 1.32847e8i | −0.0586316 | − | 0.646840i | ||||
\(591\) | −1.32039e8 | −0.639644 | ||||||||
\(592\) | − | 1.48759e8i | − | 0.716996i | ||||||
\(593\) | 2.44819e8 | 1.17403 | 0.587017 | − | 0.809574i | \(-0.300302\pi\) | ||||
0.587017 | + | 0.809574i | \(0.300302\pi\) | |||||||
\(594\) | 1.03470e8 | 0.493693 | ||||||||
\(595\) | 9.72790e7 | 0.461815 | ||||||||
\(596\) | − | 1.05954e7i | − | 0.0500470i | ||||||
\(597\) | 7.88448e7 | 0.370553 | ||||||||
\(598\) | − | 2.93804e8i | − | 1.37390i | ||||||
\(599\) | 1.26127e8 | 0.586851 | 0.293425 | − | 0.955982i | \(-0.405205\pi\) | ||||
0.293425 | + | 0.955982i | \(0.405205\pi\) | |||||||
\(600\) | − | 3.14691e7i | − | 0.145690i | ||||||
\(601\) | 3.93713e8i | 1.81366i | 0.421494 | + | 0.906831i | \(0.361506\pi\) | ||||
−0.421494 | + | 0.906831i | \(0.638494\pi\) | |||||||
\(602\) | −9.34782e8 | −4.28470 | ||||||||
\(603\) | − | 9.74866e7i | − | 0.444624i | ||||||
\(604\) | − | 1.49233e8i | − | 0.677258i | ||||||
\(605\) | −1.91376e8 | −0.864215 | ||||||||
\(606\) | −1.49368e8 | −0.671181 | ||||||||
\(607\) | 3.80721e8 | 1.70232 | 0.851158 | − | 0.524909i | \(-0.175901\pi\) | ||||
0.851158 | + | 0.524909i | \(0.175901\pi\) | |||||||
\(608\) | 3.53167e8i | 1.57134i | ||||||||
\(609\) | −2.86338e8 | −1.26773 | ||||||||
\(610\) | −1.89110e7 | −0.0833152 | ||||||||
\(611\) | 3.09190e8 | 1.35551 | ||||||||
\(612\) | 5.99281e7 | 0.261443 | ||||||||
\(613\) | 2.52903e8i | 1.09793i | 0.835847 | + | 0.548963i | \(0.184977\pi\) | ||||
−0.835847 | + | 0.548963i | \(0.815023\pi\) | |||||||
\(614\) | − | 2.53071e8i | − | 1.09330i | ||||||
\(615\) | 3.80912e7 | 0.163757 | ||||||||
\(616\) | 2.05106e8 | 0.877477 | ||||||||
\(617\) | −2.57534e8 | −1.09642 | −0.548212 | − | 0.836339i | \(-0.684691\pi\) | ||||
−0.548212 | + | 0.836339i | \(0.684691\pi\) | |||||||
\(618\) | 2.00287e8 | 0.848570 | ||||||||
\(619\) | 4.37180e8 | 1.84327 | 0.921635 | − | 0.388059i | \(-0.126854\pi\) | ||||
0.921635 | + | 0.388059i | \(0.126854\pi\) | |||||||
\(620\) | − | 4.14957e7i | − | 0.174112i | ||||||
\(621\) | 4.20085e7i | 0.175413i | ||||||||
\(622\) | − | 2.67321e7i | − | 0.111087i | ||||||
\(623\) | − | 1.23248e8i | − | 0.509703i | ||||||
\(624\) | 1.06138e8i | 0.436835i | ||||||||
\(625\) | 1.13222e8 | 0.463756 | ||||||||
\(626\) | −1.62708e8 | −0.663263 | ||||||||
\(627\) | 2.71548e8i | 1.10165i | ||||||||
\(628\) | − | 3.15306e8i | − | 1.27307i | ||||||
\(629\) | − | 1.55027e8i | − | 0.622954i | ||||||
\(630\) | 8.82595e7i | 0.352972i | ||||||||
\(631\) | −3.94167e7 | −0.156889 | −0.0784444 | − | 0.996918i | \(-0.524995\pi\) | ||||
−0.0784444 | + | 0.996918i | \(0.524995\pi\) | |||||||
\(632\) | − | 7.31032e7i | − | 0.289591i | ||||||
\(633\) | 6.98064e7i | 0.275223i | ||||||||
\(634\) | 3.41356e8i | 1.33949i | ||||||||
\(635\) | −1.29323e8 | −0.505072 | ||||||||
\(636\) | 1.53930e8 | 0.598344 | ||||||||
\(637\) | − | 4.34579e8i | − | 1.68132i | ||||||
\(638\) | 8.97224e8 | 3.45493 | ||||||||
\(639\) | −1.69574e8 | −0.649915 | ||||||||
\(640\) | − | 6.98696e7i | − | 0.266532i | ||||||
\(641\) | −4.90871e7 | −0.186377 | −0.0931887 | − | 0.995648i | \(-0.529706\pi\) | ||||
−0.0931887 | + | 0.995648i | \(0.529706\pi\) | |||||||
\(642\) | − | 3.53783e8i | − | 1.33700i | ||||||
\(643\) | −6.12735e7 | −0.230484 | −0.115242 | − | 0.993337i | \(-0.536764\pi\) | ||||
−0.115242 | + | 0.993337i | \(0.536764\pi\) | |||||||
\(644\) | 4.80179e8i | 1.79782i | ||||||||
\(645\) | 1.19666e8i | 0.445957i | ||||||||
\(646\) | 2.87277e8i | 1.06562i | ||||||||
\(647\) | −9.21937e7 | −0.340399 | −0.170199 | − | 0.985410i | \(-0.554441\pi\) | ||||
−0.170199 | + | 0.985410i | \(0.554441\pi\) | |||||||
\(648\) | 9.42907e6i | 0.0346532i | ||||||||
\(649\) | 4.25848e7 | + | 4.69807e8i | 0.155783 | + | 1.71864i | ||||
\(650\) | 3.34931e8 | 1.21959 | ||||||||
\(651\) | − | 8.55435e7i | − | 0.310059i | ||||||
\(652\) | 2.25027e8 | 0.811880 | ||||||||
\(653\) | −8.97788e6 | −0.0322429 | −0.0161215 | − | 0.999870i | \(-0.505132\pi\) | ||||
−0.0161215 | + | 0.999870i | \(0.505132\pi\) | |||||||
\(654\) | 2.65453e8 | 0.948974 | ||||||||
\(655\) | 1.50432e7i | 0.0535325i | ||||||||
\(656\) | −1.36747e8 | −0.484403 | ||||||||
\(657\) | − | 5.09792e7i | − | 0.179762i | ||||||
\(658\) | −9.23016e8 | −3.23990 | ||||||||
\(659\) | 1.22907e8i | 0.429457i | 0.976674 | + | 0.214728i | \(0.0688866\pi\) | ||||
−0.976674 | + | 0.214728i | \(0.931113\pi\) | |||||||
\(660\) | − | 1.51406e8i | − | 0.526638i | ||||||
\(661\) | −8.72373e7 | −0.302063 | −0.151032 | − | 0.988529i | \(-0.548260\pi\) | ||||
−0.151032 | + | 0.988529i | \(0.548260\pi\) | |||||||
\(662\) | − | 4.21856e8i | − | 1.45409i | ||||||
\(663\) | 1.10611e8i | 0.379539i | ||||||||
\(664\) | −4.27324e7 | −0.145966 | ||||||||
\(665\) | −2.31629e8 | −0.787639 | ||||||||
\(666\) | 1.40654e8 | 0.476133 | ||||||||
\(667\) | 3.64269e8i | 1.22756i | ||||||||
\(668\) | −3.54924e8 | −1.19071 | ||||||||
\(669\) | −1.00271e8 | −0.334887 | ||||||||
\(670\) | −2.60563e8 | −0.866340 | ||||||||
\(671\) | 6.68775e7 | 0.221367 | ||||||||
\(672\) | − | 4.05940e8i | − | 1.33768i | ||||||
\(673\) | − | 5.16451e8i | − | 1.69428i | −0.531373 | − | 0.847138i | \(-0.678324\pi\) | ||
0.531373 | − | 0.847138i | \(-0.321676\pi\) | |||||||
\(674\) | 6.62102e8 | 2.16245 | ||||||||
\(675\) | −4.78889e7 | −0.155712 | ||||||||
\(676\) | 1.05305e7 | 0.0340884 | ||||||||
\(677\) | −3.66895e8 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(678\) | 2.01703e8 | 0.647178 | ||||||||
\(679\) | 5.34119e8i | 1.70619i | ||||||||
\(680\) | − | 2.77775e7i | − | 0.0883420i | ||||||
\(681\) | − | 3.08285e8i | − | 0.976138i | ||||||
\(682\) | 2.68045e8i | 0.844997i | ||||||||
\(683\) | 3.14474e8i | 0.987013i | 0.869742 | + | 0.493507i | \(0.164285\pi\) | ||||
−0.869742 | + | 0.493507i | \(0.835715\pi\) | |||||||
\(684\) | −1.42694e8 | −0.445898 | ||||||||
\(685\) | −2.12505e8 | −0.661145 | ||||||||
\(686\) | 5.14925e8i | 1.59504i | ||||||||
\(687\) | 2.77594e8i | 0.856131i | ||||||||
\(688\) | − | 4.29602e8i | − | 1.31917i | ||||||
\(689\) | 2.84112e8i | 0.868623i | ||||||||
\(690\) | 1.12281e8 | 0.341788 | ||||||||
\(691\) | − | 5.37088e8i | − | 1.62784i | −0.580978 | − | 0.813920i | \(-0.697330\pi\) | ||
0.580978 | − | 0.813920i | \(-0.302670\pi\) | |||||||
\(692\) | 4.75987e8i | 1.43641i | ||||||||
\(693\) | − | 3.12124e8i | − | 0.937838i | ||||||
\(694\) | 3.45763e8 | 1.03443 | ||||||||
\(695\) | −1.50511e8 | −0.448347 | ||||||||
\(696\) | 8.17625e7i | 0.242508i | ||||||||
\(697\) | −1.42510e8 | −0.420869 | ||||||||
\(698\) | 2.79559e8 | 0.822067 | ||||||||
\(699\) | 2.86235e7i | 0.0838091i | ||||||||
\(700\) | −5.47395e8 | −1.59590 | ||||||||
\(701\) | 2.47147e8i | 0.717466i | 0.933440 | + | 0.358733i | \(0.116791\pi\) | ||||
−0.933440 | + | 0.358733i | \(0.883209\pi\) | |||||||
\(702\) | −1.00355e8 | −0.290087 | ||||||||
\(703\) | 3.69132e8i | 1.06247i | ||||||||
\(704\) | 8.22702e8i | 2.35790i | ||||||||
\(705\) | 1.18160e8i | 0.337213i | ||||||||
\(706\) | −8.23147e8 | −2.33918 | ||||||||
\(707\) | 4.50578e8i | 1.27500i | ||||||||
\(708\) | −2.46875e8 | + | 2.23775e7i | −0.695628 | + | 0.0630539i | ||||
\(709\) | 2.98391e8 | 0.837236 | 0.418618 | − | 0.908163i | \(-0.362515\pi\) | ||||
0.418618 | + | 0.908163i | \(0.362515\pi\) | |||||||
\(710\) | 4.53238e8i | 1.26634i | ||||||||
\(711\) | −1.11247e8 | −0.309512 | ||||||||
\(712\) | −3.51930e7 | −0.0975025 | ||||||||
\(713\) | −1.08825e8 | −0.300235 | ||||||||
\(714\) | − | 3.30204e8i | − | 0.907167i | ||||||
\(715\) | 2.79454e8 | 0.764527 | ||||||||
\(716\) | − | 3.19853e8i | − | 0.871388i | ||||||
\(717\) | −2.03236e8 | −0.551371 | ||||||||
\(718\) | 1.09209e9i | 2.95042i | ||||||||
\(719\) | − | 7.32429e7i | − | 0.197051i | −0.995135 | − | 0.0985255i | \(-0.968587\pi\) | ||
0.995135 | − | 0.0985255i | \(-0.0314126\pi\) | |||||||
\(720\) | −4.05618e7 | −0.108673 | ||||||||
\(721\) | − | 6.04178e8i | − | 1.61198i | ||||||
\(722\) | − | 1.24544e8i | − | 0.330910i | ||||||
\(723\) | 3.27952e8 | 0.867752 | ||||||||
\(724\) | −3.16982e8 | −0.835255 | ||||||||
\(725\) | −4.15259e8 | −1.08970 | ||||||||
\(726\) | 6.49607e8i | 1.69762i | ||||||||
\(727\) | 4.61548e8 | 1.20119 | 0.600597 | − | 0.799552i | \(-0.294930\pi\) | ||||
0.600597 | + | 0.799552i | \(0.294930\pi\) | |||||||
\(728\) | −1.98931e8 | −0.515594 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −1.36257e8 | −0.350261 | ||||||||
\(731\) | − | 4.47705e8i | − | 1.14615i | ||||||
\(732\) | 3.51429e7i | 0.0895993i | ||||||||
\(733\) | 2.07069e7 | 0.0525778 | 0.0262889 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262889 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(734\) | −8.59939e8 | −2.17460 | ||||||||
\(735\) | 1.66079e8 | 0.418267 | ||||||||
\(736\) | −5.16422e8 | −1.29530 | ||||||||
\(737\) | 9.21465e8 | 2.30185 | ||||||||
\(738\) | − | 1.29297e8i | − | 0.321676i | ||||||
\(739\) | 1.68742e8i | 0.418110i | 0.977904 | + | 0.209055i | \(0.0670388\pi\) | ||||
−0.977904 | + | 0.209055i | \(0.932961\pi\) | |||||||
\(740\) | − | 2.05816e8i | − | 0.507907i | ||||||
\(741\) | − | 2.63373e8i | − | 0.647316i | ||||||
\(742\) | − | 8.48152e8i | − | 2.07616i | ||||||
\(743\) | 4.95574e8 | 1.20821 | 0.604105 | − | 0.796905i | \(-0.293531\pi\) | ||||
0.604105 | + | 0.796905i | \(0.293531\pi\) | |||||||
\(744\) | −2.44265e7 | −0.0593120 | ||||||||
\(745\) | 7.47359e6i | 0.0180743i | ||||||||
\(746\) | − | 9.11415e8i | − | 2.19533i | ||||||
\(747\) | 6.50290e7i | 0.156007i | ||||||||
\(748\) | 5.66454e8i | 1.35350i | ||||||||
\(749\) | −1.06721e9 | −2.53983 | ||||||||
\(750\) | 2.86194e8i | 0.678386i | ||||||||
\(751\) | 8.42475e7i | 0.198901i | 0.995042 | + | 0.0994506i | \(0.0317085\pi\) | ||||
−0.995042 | + | 0.0994506i | \(0.968291\pi\) | |||||||
\(752\) | − | 4.24195e8i | − | 0.997497i | ||||||
\(753\) | −2.41404e8 | −0.565404 | ||||||||
\(754\) | −8.70212e8 | −2.03007 | ||||||||
\(755\) | 1.05264e8i | 0.244589i | ||||||||
\(756\) | 1.64016e8 | 0.379595 | ||||||||
\(757\) | 3.60531e8 | 0.831104 | 0.415552 | − | 0.909569i | \(-0.363588\pi\) | ||||
0.415552 | + | 0.909569i | \(0.363588\pi\) | |||||||
\(758\) | 1.59898e8i | 0.367142i | ||||||||
\(759\) | −3.97073e8 | −0.908124 | ||||||||
\(760\) | 6.61405e7i | 0.150670i | ||||||||
\(761\) | 7.12021e8 | 1.61562 | 0.807810 | − | 0.589443i | \(-0.200653\pi\) | ||||
0.807810 | + | 0.589443i | \(0.200653\pi\) | |||||||
\(762\) | 4.38972e8i | 0.992138i | ||||||||
\(763\) | − | 8.00755e8i | − | 1.80271i | ||||||
\(764\) | − | 8.50418e8i | − | 1.90701i | ||||||
\(765\) | −4.22711e7 | −0.0944190 | ||||||||
\(766\) | 6.01967e7i | 0.133933i | ||||||||
\(767\) | −4.13027e7 | − | 4.55662e8i | −0.0915361 | − | 1.00985i | ||||
\(768\) | 1.20178e8 | 0.265303 | ||||||||
\(769\) | 5.27498e8i | 1.15996i | 0.814632 | + | 0.579978i | \(0.196939\pi\) | ||||
−0.814632 | + | 0.579978i | \(0.803061\pi\) | |||||||
\(770\) | −8.34248e8 | −1.82736 | ||||||||
\(771\) | 2.80433e8 | 0.611880 | ||||||||
\(772\) | 7.72562e8 | 1.67912 | ||||||||
\(773\) | 6.12907e8i | 1.32696i | 0.748196 | + | 0.663478i | \(0.230920\pi\) | ||||
−0.748196 | + | 0.663478i | \(0.769080\pi\) | |||||||
\(774\) | 4.06195e8 | 0.876016 | ||||||||
\(775\) | − | 1.24059e8i | − | 0.266515i | ||||||
\(776\) | 1.52515e8 | 0.326383 | ||||||||
\(777\) | − | 4.24290e8i | − | 0.904481i | ||||||
\(778\) | − | 1.23919e8i | − | 0.263147i | ||||||
\(779\) | 3.39327e8 | 0.717804 | ||||||||
\(780\) | 1.46848e8i | 0.309446i | ||||||||
\(781\) | − | 1.60285e9i | − | 3.36465i | ||||||
\(782\) | −4.20073e8 | −0.878424 | ||||||||
\(783\) | 1.24424e8 | 0.259190 | ||||||||
\(784\) | −5.96224e8 | −1.23726 | ||||||||
\(785\) | 2.22405e8i | 0.459765i | ||||||||
\(786\) | 5.10627e7 | 0.105157 | ||||||||
\(787\) | −1.41629e8 | −0.290555 | −0.145278 | − | 0.989391i | \(-0.546408\pi\) | ||||
−0.145278 | + | 0.989391i | \(0.546408\pi\) | |||||||
\(788\) | 6.55831e8 | 1.34033 | ||||||||
\(789\) | 1.84809e8 | 0.376263 | ||||||||
\(790\) | 2.97340e8i | 0.603077i | ||||||||
\(791\) | − | 6.08450e8i | − | 1.22941i | ||||||
\(792\) | −8.91256e7 | −0.179402 | ||||||||
\(793\) | −6.48641e7 | −0.130072 | ||||||||
\(794\) | 4.69252e8 | 0.937442 | ||||||||
\(795\) | −1.08576e8 | −0.216090 | ||||||||
\(796\) | −3.91619e8 | −0.776471 | ||||||||
\(797\) | − | 9.01642e8i | − | 1.78098i | −0.455003 | − | 0.890490i | \(-0.650362\pi\) | ||
0.455003 | − | 0.890490i | \(-0.349638\pi\) | |||||||
\(798\) | 7.86240e8i | 1.54720i | ||||||||
\(799\) | − | 4.42070e8i | − | 0.866664i | ||||||
\(800\) | − | 5.88711e8i | − | 1.14983i | ||||||
\(801\) | 5.35557e7i | 0.104210i | ||||||||
\(802\) | −8.90862e8 | −1.72698 | ||||||||
\(803\) | 4.81866e8 | 0.930636 | ||||||||
\(804\) | 4.84213e8i | 0.931683i | ||||||||
\(805\) | − | 3.38701e8i | − | 0.649275i | ||||||
\(806\) | − | 2.59976e8i | − | 0.496509i | ||||||
\(807\) | − | 2.74592e8i | − | 0.522477i | ||||||
\(808\) | 1.28660e8 | 0.243899 | ||||||||
\(809\) | − | 1.64708e8i | − | 0.311079i | −0.987830 | − | 0.155539i | \(-0.950288\pi\) | ||
0.987830 | − | 0.155539i | \(-0.0497115\pi\) | |||||||
\(810\) | − | 3.83518e7i | − | 0.0721658i | ||||||
\(811\) | 4.65977e8i | 0.873578i | 0.899564 | + | 0.436789i | \(0.143884\pi\) | ||||
−0.899564 | + | 0.436789i | \(0.856116\pi\) | |||||||
\(812\) | 1.42223e9 | 2.65645 | ||||||||
\(813\) | 4.00434e7 | 0.0745176 | ||||||||
\(814\) | 1.32949e9i | 2.46497i | ||||||||
\(815\) | −1.58726e8 | −0.293207 | ||||||||
\(816\) | 1.51753e8 | 0.279298 | ||||||||
\(817\) | 1.06602e9i | 1.95479i | ||||||||
\(818\) | −1.25362e9 | −2.29036 | ||||||||
\(819\) | 3.02728e8i | 0.551062i | ||||||||
\(820\) | −1.89198e8 | −0.343142 | ||||||||
\(821\) | 3.62423e8i | 0.654916i | 0.944866 | + | 0.327458i | \(0.106192\pi\) | ||||
−0.944866 | + | 0.327458i | \(0.893808\pi\) | |||||||
\(822\) | 7.21325e8i | 1.29872i | ||||||||
\(823\) | 1.32234e8i | 0.237216i | 0.992941 | + | 0.118608i | \(0.0378432\pi\) | ||||
−0.992941 | + | 0.118608i | \(0.962157\pi\) | |||||||
\(824\) | −1.72520e8 | −0.308360 | ||||||||
\(825\) | − | 4.52656e8i | − | 0.806132i | ||||||
\(826\) | 1.23300e8 | + | 1.36028e9i | 0.218788 | + | 2.41372i | ||||
\(827\) | −4.16054e8 | −0.735585 | −0.367793 | − | 0.929908i | \(-0.619886\pi\) | ||||
−0.367793 | + | 0.929908i | \(0.619886\pi\) | |||||||
\(828\) | − | 2.08655e8i | − | 0.367567i | ||||||
\(829\) | −8.36251e8 | −1.46782 | −0.733911 | − | 0.679246i | \(-0.762307\pi\) | ||||
−0.733911 | + | 0.679246i | \(0.762307\pi\) | |||||||
\(830\) | 1.73810e8 | 0.303977 | ||||||||
\(831\) | −5.08898e8 | −0.886804 | ||||||||
\(832\) | − | 7.97933e8i | − | 1.38547i | ||||||
\(833\) | −6.21348e8 | −1.07498 | ||||||||
\(834\) | 5.10895e8i | 0.880712i | ||||||||
\(835\) | 2.50350e8 | 0.430020 | ||||||||
\(836\) | − | 1.34877e9i | − | 2.30844i | ||||||
\(837\) | 3.71716e7i | 0.0633921i | ||||||||
\(838\) | −1.29462e9 | −2.19994 | ||||||||
\(839\) | − | 3.18245e8i | − | 0.538859i | −0.963020 | − | 0.269430i | \(-0.913165\pi\) | ||
0.963020 | − | 0.269430i | \(-0.0868351\pi\) | |||||||
\(840\) | − | 7.60236e7i | − | 0.128266i | ||||||
\(841\) | 4.84096e8 | 0.813848 | ||||||||
\(842\) | 6.58241e8 | 1.10268 | ||||||||
\(843\) | 4.47968e8 | 0.747763 | ||||||||
\(844\) | − | 3.46726e8i | − | 0.576712i | ||||||
\(845\) | −7.42779e6 | −0.0123109 | ||||||||
\(846\) | 4.01083e8 | 0.662404 | ||||||||
\(847\) | 1.95958e9 | 3.22487 | ||||||||
\(848\) | 3.89789e8 | 0.639207 | ||||||||
\(849\) | 3.84339e8i | 0.628046i | ||||||||
\(850\) | − | 4.78875e8i | − | 0.779768i | ||||||
\(851\) | −5.39766e8 | −0.875824 | ||||||||
\(852\) | 8.42268e8 | 1.36186 | ||||||||
\(853\) | −1.03180e9 | −1.66245 | −0.831225 | − | 0.555936i | \(-0.812360\pi\) | ||||
−0.831225 | + | 0.555936i | \(0.812360\pi\) | |||||||
\(854\) | 1.93637e8 | 0.310896 | ||||||||
\(855\) | 1.00651e8 | 0.161034 | ||||||||
\(856\) | 3.04736e8i | 0.485851i | ||||||||
\(857\) | − | 6.65285e8i | − | 1.05698i | −0.848941 | − | 0.528488i | \(-0.822759\pi\) | ||
0.848941 | − | 0.528488i | \(-0.177241\pi\) | |||||||
\(858\) | − | 9.48579e8i | − | 1.50180i | ||||||
\(859\) | − | 2.42282e8i | − | 0.382245i | −0.981566 | − | 0.191122i | \(-0.938787\pi\) | ||
0.981566 | − | 0.191122i | \(-0.0612128\pi\) | |||||||
\(860\) | − | 5.94379e8i | − | 0.934476i | ||||||
\(861\) | −3.90031e8 | −0.611069 | ||||||||
\(862\) | 7.31903e8 | 1.14270 | ||||||||
\(863\) | 2.46630e8i | 0.383718i | 0.981422 | + | 0.191859i | \(0.0614517\pi\) | ||||
−0.981422 | + | 0.191859i | \(0.938548\pi\) | |||||||
\(864\) | 1.76395e8i | 0.273492i | ||||||||
\(865\) | − | 3.35744e8i | − | 0.518752i | ||||||
\(866\) | 9.43509e8i | 1.45276i | ||||||||
\(867\) | −2.18119e8 | −0.334686 | ||||||||
\(868\) | 4.24891e8i | 0.649709i | ||||||||
\(869\) | − | 1.05153e9i | − | 1.60236i | ||||||
\(870\) | − | 3.32561e8i | − | 0.505026i | ||||||
\(871\) | −8.93723e8 | −1.35253 | ||||||||
\(872\) | −2.28652e8 | −0.344846 | ||||||||
\(873\) | − | 2.32093e8i | − | 0.348835i | ||||||
\(874\) | 1.00023e9 | 1.49818 | ||||||||
\(875\) | 8.63321e8 | 1.28869 | ||||||||
\(876\) | 2.53212e8i | 0.376679i | ||||||||
\(877\) | −8.91733e8 | −1.32201 | −0.661007 | − | 0.750380i | \(-0.729871\pi\) | ||||
−0.661007 | + | 0.750380i | \(0.729871\pi\) | |||||||
\(878\) | − | 7.61248e8i | − | 1.12472i | ||||||
\(879\) | 9.89132e7 | 0.145642 | ||||||||
\(880\) | − | 3.83399e8i | − | 0.562604i | ||||||
\(881\) | 5.51826e8i | 0.807002i | 0.914979 | + | 0.403501i | \(0.132207\pi\) | ||||
−0.914979 | + | 0.403501i | \(0.867793\pi\) | |||||||
\(882\) | − | 5.63739e8i | − | 0.821622i | ||||||
\(883\) | −9.51639e8 | −1.38226 | −0.691131 | − | 0.722730i | \(-0.742887\pi\) | ||||
−0.691131 | + | 0.722730i | \(0.742887\pi\) | |||||||
\(884\) | − | 5.49400e8i | − | 0.795301i | ||||||
\(885\) | 1.74136e8 | − | 1.57843e7i | 0.251223 | − | 0.0227717i | ||||
\(886\) | −1.00176e9 | −1.44034 | ||||||||
\(887\) | − | 5.04297e8i | − | 0.722630i | −0.932444 | − | 0.361315i | \(-0.882328\pi\) | ||
0.932444 | − | 0.361315i | \(-0.117672\pi\) | |||||||
\(888\) | −1.21154e8 | −0.173021 | ||||||||
\(889\) | 1.32419e9 | 1.88471 | ||||||||
\(890\) | 1.43144e8 | 0.203050 | ||||||||
\(891\) | 1.35629e8i | 0.191743i | ||||||||
\(892\) | 4.98044e8 | 0.701735 | ||||||||
\(893\) | 1.05260e9i | 1.47812i | ||||||||
\(894\) | 2.53683e7 | 0.0355042 | ||||||||
\(895\) | 2.25613e8i | 0.314698i | ||||||||
\(896\) | 7.15423e8i | 0.994579i | ||||||||
\(897\) | 3.85119e8 | 0.533602 | ||||||||
\(898\) | − | 1.53167e9i | − | 2.11512i | ||||||
\(899\) | 3.22327e8i | 0.443626i | ||||||||
\(900\) | 2.37862e8 | 0.326286 | ||||||||
\(901\) | 4.06215e8 | 0.555368 | ||||||||
\(902\) | 1.22214e9 | 1.66533 | ||||||||
\(903\) | − | 1.22531e9i | − | 1.66412i | ||||||
\(904\) | −1.73740e8 | −0.235177 | ||||||||
\(905\) | 2.23587e8 | 0.301649 | ||||||||
\(906\) | 3.57306e8 | 0.480459 | ||||||||
\(907\) | 9.91964e6 | 0.0132946 | 0.00664728 | − | 0.999978i | \(-0.497884\pi\) | ||||
0.00664728 | + | 0.999978i | \(0.497884\pi\) | |||||||
\(908\) | 1.53124e9i | 2.04544i | ||||||||
\(909\) | − | 1.95792e8i | − | 0.260677i | ||||||
\(910\) | 8.09132e8 | 1.07373 | ||||||||
\(911\) | −3.53401e7 | −0.0467425 | −0.0233713 | − | 0.999727i | \(-0.507440\pi\) | ||||
−0.0233713 | + | 0.999727i | \(0.507440\pi\) | |||||||
\(912\) | −3.61336e8 | −0.476350 | ||||||||
\(913\) | −6.14668e8 | −0.807659 | ||||||||
\(914\) | 4.65861e8 | 0.610123 | ||||||||
\(915\) | − | 2.47885e7i | − | 0.0323584i | ||||||
\(916\) | − | 1.37880e9i | − | 1.79397i | ||||||
\(917\) | − | 1.54034e8i | − | 0.199760i | ||||||
\(918\) | 1.43485e8i | 0.185472i | ||||||||
\(919\) | 7.65464e8i | 0.986230i | 0.869964 | + | 0.493115i | \(0.164142\pi\) | ||||
−0.869964 | + | 0.493115i | \(0.835858\pi\) | |||||||
\(920\) | −9.67144e7 | −0.124202 | ||||||||
\(921\) | 3.31726e8 | 0.424620 | ||||||||
\(922\) | − | 7.67260e8i | − | 0.978926i | ||||||
\(923\) | 1.55459e9i | 1.97702i | ||||||||
\(924\) | 1.55031e9i | 1.96518i | ||||||||
\(925\) | − | 6.15322e8i | − | 0.777459i | ||||||
\(926\) | 6.04966e8 | 0.761900 | ||||||||
\(927\) | 2.62536e8i | 0.329572i | ||||||||
\(928\) | 1.52958e9i | 1.91394i | ||||||||
\(929\) | 6.28566e8i | 0.783978i | 0.919970 | + | 0.391989i | \(0.128213\pi\) | ||||
−0.919970 | + | 0.391989i | \(0.871787\pi\) | |||||||
\(930\) | 9.93525e7 | 0.123518 | ||||||||
\(931\) | 1.47948e9 | 1.83341 | ||||||||
\(932\) | − | 1.42172e8i | − | 0.175617i | ||||||
\(933\) | 3.50405e7 | 0.0431445 | ||||||||
\(934\) | −1.34793e9 | −1.65435 | ||||||||
\(935\) | − | 3.99556e8i | − | 0.488813i | ||||||
\(936\) | 8.64424e7 | 0.105414 | ||||||||
\(937\) | 3.75888e8i | 0.456919i | 0.973553 | + | 0.228460i | \(0.0733689\pi\) | ||||
−0.973553 | + | 0.228460i | \(0.926631\pi\) | |||||||
\(938\) | 2.66801e9 | 3.23280 | ||||||||
\(939\) | − | 2.13278e8i | − | 0.257602i | ||||||
\(940\) | − | 5.86898e8i | − | 0.706608i | ||||||
\(941\) | 5.27329e8i | 0.632868i | 0.948615 | + | 0.316434i | \(0.102486\pi\) | ||||
−0.948615 | + | 0.316434i | \(0.897514\pi\) | |||||||
\(942\) | 7.54932e8 | 0.903140 | ||||||||
\(943\) | 4.96183e8i | 0.591708i | ||||||||
\(944\) | −6.25149e8 | + | 5.66655e7i | −0.743134 | + | 0.0673601i | ||||
\(945\) | −1.15691e8 | −0.137089 | ||||||||
\(946\) | 3.83945e9i | 4.53519i | ||||||||
\(947\) | −3.45296e8 | −0.406575 | −0.203288 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203288 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(948\) | 5.52558e8 | 0.648564 | ||||||||
\(949\) | −4.67359e8 | −0.546829 | ||||||||
\(950\) | 1.14024e9i | 1.32992i | ||||||||
\(951\) | −4.47449e8 | −0.520238 | ||||||||
\(952\) | 2.84425e8i | 0.329653i | ||||||||
\(953\) | 1.54856e8 | 0.178916 | 0.0894579 | − | 0.995991i | \(-0.471487\pi\) | ||||
0.0894579 | + | 0.995991i | \(0.471487\pi\) | |||||||
\(954\) | 3.68551e8i | 0.424476i | ||||||||
\(955\) | 5.99854e8i | 0.688708i | ||||||||
\(956\) | 1.00947e9 | 1.15536 | ||||||||
\(957\) | 1.17608e9i | 1.34184i | ||||||||
\(958\) | 7.64985e8i | 0.870075i | ||||||||
\(959\) | 2.17592e9 | 2.46710 | ||||||||
\(960\) | 3.04939e8 | 0.344667 | ||||||||
\(961\) | 7.91209e8 | 0.891499 | ||||||||
\(962\) | − | 1.28946e9i | − | 1.44838i | ||||||
\(963\) | 4.63739e8 | 0.519272 | ||||||||
\(964\) | −1.62893e9 | −1.81832 | ||||||||
\(965\) | −5.44936e8 | −0.606407 | ||||||||
\(966\) | −1.14969e9 | −1.27540 | ||||||||
\(967\) | − | 1.66150e9i | − | 1.83748i | −0.394867 | − | 0.918738i | \(-0.629209\pi\) | ||
0.394867 | − | 0.918738i | \(-0.370791\pi\) | |||||||
\(968\) | − | 5.59548e8i | − | 0.616895i | ||||||
\(969\) | −3.76563e8 | −0.413872 | ||||||||
\(970\) | −6.20340e8 | −0.679696 | ||||||||
\(971\) | −1.02179e8 | −0.111610 | −0.0558050 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558050 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(972\) | −7.12705e7 | −0.0776088 | ||||||||
\(973\) | 1.54115e9 | 1.67304 | ||||||||
\(974\) | − | 1.80418e9i | − | 1.95256i | ||||||
\(975\) | 4.39028e8i | 0.473673i | ||||||||
\(976\) | 8.89906e7i | 0.0957183i | ||||||||
\(977\) | − | 1.06880e9i | − | 1.14607i | −0.819530 | − | 0.573036i | \(-0.805766\pi\) | ||
0.819530 | − | 0.573036i | \(-0.194234\pi\) | |||||||
\(978\) | 5.38778e8i | 0.575962i | ||||||||
\(979\) | −5.06220e8 | −0.539500 | ||||||||
\(980\) | −8.24910e8 | −0.876452 | ||||||||
\(981\) | 3.47956e8i | 0.368568i | ||||||||
\(982\) | − | 5.78649e8i | − | 0.611055i | ||||||
\(983\) | − | 9.29494e7i | − | 0.0978556i | −0.998802 | − | 0.0489278i | \(-0.984420\pi\) | ||
0.998802 | − | 0.0489278i | \(-0.0155804\pi\) | |||||||
\(984\) | 1.11372e8i | 0.116893i | ||||||||
\(985\) | −4.62599e8 | −0.484056 | ||||||||
\(986\) | 1.24420e9i | 1.29796i | ||||||||
\(987\) | − | 1.20989e9i | − | 1.25833i | ||||||
\(988\) | 1.30816e9i | 1.35641i | ||||||||
\(989\) | −1.55880e9 | −1.61139 | ||||||||
\(990\) | 3.62510e8 | 0.373606 | ||||||||
\(991\) | 1.04353e9i | 1.07222i | 0.844149 | + | 0.536109i | \(0.180106\pi\) | ||||
−0.844149 | + | 0.536109i | \(0.819894\pi\) | |||||||
\(992\) | −4.56961e8 | −0.468106 | ||||||||
\(993\) | 5.52969e8 | 0.564746 | ||||||||
\(994\) | − | 4.64089e9i | − | 4.72544i | ||||||
\(995\) | 2.76234e8 | 0.280419 | ||||||||
\(996\) | − | 3.22997e8i | − | 0.326904i | ||||||
\(997\) | −8.57607e8 | −0.865372 | −0.432686 | − | 0.901545i | \(-0.642434\pi\) | ||||
−0.432686 | + | 0.901545i | \(0.642434\pi\) | |||||||
\(998\) | 8.95487e8i | 0.900881i | ||||||||
\(999\) | 1.84369e8i | 0.184923i |
(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 | 177.7.c.a.58.10 | ✓ | 60 | |
59.58 | odd | 2 | inner | 177.7.c.a.58.51 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.7.c.a.58.10 | ✓ | 60 | 1.1 | even | 1 | trivial | |
177.7.c.a.58.51 | yes | 60 | 59.58 | odd | 2 | inner |