Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(10,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Character | \(\chi\) | \(=\) | 37.26 |
Dual form | 37.6.c.a.10.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.15115 | − | 8.92206i | −0.910604 | − | 1.57721i | −0.813213 | − | 0.581966i | \(-0.802284\pi\) |
−0.0973912 | − | 0.995246i | \(-0.531050\pi\) | |||||||
\(3\) | 13.8137 | − | 23.9261i | 0.886150 | − | 1.53486i | 0.0417606 | − | 0.999128i | \(-0.486703\pi\) |
0.844390 | − | 0.535730i | \(-0.179963\pi\) | |||||||
\(4\) | −37.0688 | + | 64.2050i | −1.15840 | + | 2.00641i | ||||
\(5\) | −33.8746 | + | 58.6725i | −0.605967 | + | 1.04956i | 0.385931 | + | 0.922527i | \(0.373880\pi\) |
−0.991898 | + | 0.127037i | \(0.959453\pi\) | |||||||
\(6\) | −284.626 | −3.22773 | ||||||||
\(7\) | −29.2828 | + | 50.7192i | −0.225874 | + | 0.391226i | −0.956581 | − | 0.291465i | \(-0.905857\pi\) |
0.730707 | + | 0.682691i | \(0.239191\pi\) | |||||||
\(8\) | 434.114 | 2.39817 | ||||||||
\(9\) | −260.137 | − | 450.571i | −1.07052 | − | 1.85420i | ||||
\(10\) | 697.972 | 2.20718 | ||||||||
\(11\) | −622.545 | −1.55128 | −0.775638 | − | 0.631178i | \(-0.782572\pi\) | ||||
−0.775638 | + | 0.631178i | \(0.782572\pi\) | |||||||
\(12\) | 1024.12 | + | 1773.82i | 2.05303 | + | 3.55596i | ||||
\(13\) | 5.07443 | − | 8.78917i | 0.00832778 | − | 0.0144241i | −0.861831 | − | 0.507195i | \(-0.830682\pi\) |
0.870159 | + | 0.492771i | \(0.164016\pi\) | |||||||
\(14\) | 603.360 | 0.822729 | ||||||||
\(15\) | 935.867 | + | 1620.97i | 1.07395 | + | 1.86014i | ||||
\(16\) | −1049.99 | − | 1818.63i | −1.02538 | − | 1.77601i | ||||
\(17\) | −763.151 | − | 1321.82i | −0.640455 | − | 1.10930i | −0.985331 | − | 0.170652i | \(-0.945413\pi\) |
0.344877 | − | 0.938648i | \(-0.387921\pi\) | |||||||
\(18\) | −2680.02 | + | 4641.92i | −1.94965 | + | 3.37689i | ||||
\(19\) | 909.917 | − | 1576.02i | 0.578253 | − | 1.00156i | −0.417427 | − | 0.908710i | \(-0.637068\pi\) |
0.995680 | − | 0.0928525i | \(-0.0295985\pi\) | |||||||
\(20\) | −2511.38 | − | 4349.83i | −1.40390 | − | 2.43163i | ||||
\(21\) | 809.008 | + | 1401.24i | 0.400317 | + | 0.693370i | ||||
\(22\) | 3206.83 | + | 5554.39i | 1.41260 | + | 2.44669i | ||||
\(23\) | −2069.18 | −0.815603 | −0.407801 | − | 0.913071i | \(-0.633704\pi\) | ||||
−0.407801 | + | 0.913071i | \(0.633704\pi\) | |||||||
\(24\) | 5996.73 | − | 10386.6i | 2.12513 | − | 3.68084i | ||||
\(25\) | −732.472 | − | 1268.68i | −0.234391 | − | 0.405977i | ||||
\(26\) | −104.557 | −0.0303332 | ||||||||
\(27\) | −7660.39 | −2.02228 | ||||||||
\(28\) | −2170.95 | − | 3760.20i | −0.523306 | − | 0.906392i | ||||
\(29\) | −297.317 | −0.0656484 | −0.0328242 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328242 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(30\) | 9641.59 | − | 16699.7i | 1.95590 | − | 3.38771i | ||||
\(31\) | −2740.49 | −0.512182 | −0.256091 | − | 0.966653i | \(-0.582435\pi\) | ||||
−0.256091 | + | 0.966653i | \(0.582435\pi\) | |||||||
\(32\) | −3871.48 | + | 6705.60i | −0.668347 | + | 1.15761i | ||||
\(33\) | −8599.66 | + | 14895.1i | −1.37466 | + | 2.38099i | ||||
\(34\) | −7862.22 | + | 13617.8i | −1.16640 | + | 2.02027i | ||||
\(35\) | −1983.88 | − | 3436.18i | −0.273745 | − | 0.474140i | ||||
\(36\) | 38571.9 | 4.96038 | ||||||||
\(37\) | 7295.76 | + | 4014.46i | 0.876125 | + | 0.482084i | ||||
\(38\) | −18748.5 | −2.10624 | ||||||||
\(39\) | −140.194 | − | 242.822i | −0.0147593 | − | 0.0255639i | ||||
\(40\) | −14705.4 | + | 25470.6i | −1.45321 | + | 2.51703i | ||||
\(41\) | 7986.65 | − | 13833.3i | 0.742002 | − | 1.28519i | −0.209580 | − | 0.977791i | \(-0.567210\pi\) |
0.951582 | − | 0.307394i | \(-0.0994570\pi\) | |||||||
\(42\) | 8334.65 | − | 14436.0i | 0.729061 | − | 1.26277i | ||||
\(43\) | −15024.7 | −1.23918 | −0.619589 | − | 0.784926i | \(-0.712701\pi\) | ||||
−0.619589 | + | 0.784926i | \(0.712701\pi\) | |||||||
\(44\) | 23077.0 | − | 39970.5i | 1.79700 | − | 3.11249i | ||||
\(45\) | 35248.2 | 2.59481 | ||||||||
\(46\) | 10658.7 | + | 18461.4i | 0.742691 | + | 1.28638i | ||||
\(47\) | 757.172 | 0.0499977 | 0.0249988 | − | 0.999687i | \(-0.492042\pi\) | ||||
0.0249988 | + | 0.999687i | \(0.492042\pi\) | |||||||
\(48\) | −58017.0 | −3.63456 | ||||||||
\(49\) | 6688.54 | + | 11584.9i | 0.397962 | + | 0.689290i | ||||
\(50\) | −7546.15 | + | 13070.3i | −0.426875 | + | 0.739369i | ||||
\(51\) | −42167.8 | −2.27016 | ||||||||
\(52\) | 376.206 | + | 651.608i | 0.0192938 | + | 0.0334178i | ||||
\(53\) | 8184.07 | + | 14175.2i | 0.400203 | + | 0.693171i | 0.993750 | − | 0.111628i | \(-0.0356064\pi\) |
−0.593548 | + | 0.804799i | \(0.702273\pi\) | |||||||
\(54\) | 39459.9 | + | 68346.5i | 1.84150 | + | 3.18957i | ||||
\(55\) | 21088.4 | − | 36526.3i | 0.940022 | − | 1.62817i | ||||
\(56\) | −12712.1 | + | 22017.9i | −0.541684 | + | 0.938225i | ||||
\(57\) | −25138.7 | − | 43541.4i | −1.02484 | − | 1.77507i | ||||
\(58\) | 1531.52 | + | 2652.68i | 0.0597797 | + | 0.103542i | ||||
\(59\) | −16896.4 | − | 29265.4i | −0.631923 | − | 1.09452i | −0.987158 | − | 0.159745i | \(-0.948933\pi\) |
0.355236 | − | 0.934777i | \(-0.384401\pi\) | |||||||
\(60\) | −138766. | −4.97628 | ||||||||
\(61\) | −1207.78 | + | 2091.94i | −0.0415588 | + | 0.0719820i | −0.886057 | − | 0.463577i | \(-0.846566\pi\) |
0.844498 | + | 0.535559i | \(0.179899\pi\) | |||||||
\(62\) | 14116.7 | + | 24450.8i | 0.466395 | + | 0.807820i | ||||
\(63\) | 30470.2 | 0.967216 | ||||||||
\(64\) | 12571.1 | 0.383639 | ||||||||
\(65\) | 343.788 | + | 595.459i | 0.0100927 | + | 0.0174811i | ||||
\(66\) | 177193. | 5.00710 | ||||||||
\(67\) | 16220.9 | − | 28095.4i | 0.441456 | − | 0.764624i | −0.556342 | − | 0.830953i | \(-0.687795\pi\) |
0.997798 | + | 0.0663294i | \(0.0211288\pi\) | |||||||
\(68\) | 113156. | 2.96761 | ||||||||
\(69\) | −28583.1 | + | 49507.3i | −0.722747 | + | 1.25183i | ||||
\(70\) | −20438.6 | + | 35400.6i | −0.498546 | + | 0.863507i | ||||
\(71\) | 6628.21 | − | 11480.4i | 0.156045 | − | 0.270278i | −0.777394 | − | 0.629014i | \(-0.783459\pi\) |
0.933439 | + | 0.358736i | \(0.116792\pi\) | |||||||
\(72\) | −112929. | − | 195599.i | −2.56729 | − | 4.44669i | ||||
\(73\) | 13382.6 | 0.293922 | 0.146961 | − | 0.989142i | \(-0.453051\pi\) | ||||
0.146961 | + | 0.989142i | \(0.453051\pi\) | |||||||
\(74\) | −1764.29 | − | 85772.3i | −0.0374533 | − | 1.82082i | ||||
\(75\) | −40472.6 | −0.830822 | ||||||||
\(76\) | 67459.0 | + | 116842.i | 1.33970 | + | 2.32042i | ||||
\(77\) | 18229.8 | − | 31575.0i | 0.350394 | − | 0.606900i | ||||
\(78\) | −1444.32 | + | 2501.63i | −0.0268798 | + | 0.0465572i | ||||
\(79\) | −15736.9 | + | 27257.1i | −0.283695 | + | 0.491374i | −0.972292 | − | 0.233770i | \(-0.924894\pi\) |
0.688597 | + | 0.725144i | \(0.258227\pi\) | |||||||
\(80\) | 142272. | 2.48538 | ||||||||
\(81\) | −42605.1 | + | 73794.2i | −0.721521 | + | 1.24971i | ||||
\(82\) | −164562. | −2.70268 | ||||||||
\(83\) | −26635.2 | − | 46133.5i | −0.424386 | − | 0.735058i | 0.571977 | − | 0.820270i | \(-0.306177\pi\) |
−0.996363 | + | 0.0852117i | \(0.972843\pi\) | |||||||
\(84\) | −119956. | −1.85491 | ||||||||
\(85\) | 103406. | 1.55238 | ||||||||
\(86\) | 77394.4 | + | 134051.i | 1.12840 | + | 1.95445i | ||||
\(87\) | −4107.05 | + | 7113.62i | −0.0581744 | + | 0.100761i | ||||
\(88\) | −270256. | −3.72022 | ||||||||
\(89\) | −14441.9 | − | 25014.2i | −0.193264 | − | 0.334743i | 0.753066 | − | 0.657945i | \(-0.228574\pi\) |
−0.946330 | + | 0.323202i | \(0.895241\pi\) | |||||||
\(90\) | −181569. | − | 314486.i | −2.36284 | − | 4.09256i | ||||
\(91\) | 297.187 | + | 514.743i | 0.00376206 | + | 0.00651608i | ||||
\(92\) | 76702.0 | − | 132852.i | 0.944794 | − | 1.63643i | ||||
\(93\) | −37856.4 | + | 65569.1i | −0.453870 | + | 0.786126i | ||||
\(94\) | −3900.31 | − | 6755.53i | −0.0455281 | − | 0.0788569i | ||||
\(95\) | 61646.0 | + | 106774.i | 0.700803 | + | 1.21383i | ||||
\(96\) | 106959. | + | 185259.i | 1.18451 | + | 2.05163i | ||||
\(97\) | 32958.4 | 0.355661 | 0.177831 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177831 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(98\) | 68907.4 | − | 119351.i | 0.724771 | − | 1.25534i | ||||
\(99\) | 161947. | + | 280501.i | 1.66068 | + | 2.87638i | ||||
\(100\) | 108607. | 1.08607 | ||||||||
\(101\) | −106657. | −1.04036 | −0.520182 | − | 0.854056i | \(-0.674136\pi\) | ||||
−0.520182 | + | 0.854056i | \(0.674136\pi\) | |||||||
\(102\) | 217213. | + | 376224.i | 2.06721 | + | 3.58052i | ||||
\(103\) | −19481.0 | −0.180933 | −0.0904664 | − | 0.995900i | \(-0.528836\pi\) | ||||
−0.0904664 | + | 0.995900i | \(0.528836\pi\) | |||||||
\(104\) | 2202.88 | − | 3815.51i | 0.0199714 | − | 0.0345915i | ||||
\(105\) | −109619. | −0.970316 | ||||||||
\(106\) | 84314.9 | − | 146038.i | 0.728852 | − | 1.26241i | ||||
\(107\) | −84036.8 | + | 145556.i | −0.709594 | + | 1.22905i | 0.255414 | + | 0.966832i | \(0.417788\pi\) |
−0.965008 | + | 0.262221i | \(0.915545\pi\) | |||||||
\(108\) | 283961. | − | 491836.i | 2.34261 | − | 4.05752i | ||||
\(109\) | −92438.8 | − | 160109.i | −0.745226 | − | 1.29077i | −0.950089 | − | 0.311979i | \(-0.899008\pi\) |
0.204862 | − | 0.978791i | \(-0.434325\pi\) | |||||||
\(110\) | −434519. | −3.42395 | ||||||||
\(111\) | 196832. | − | 119104.i | 1.51631 | − | 0.917527i | ||||
\(112\) | 122986. | 0.926428 | ||||||||
\(113\) | −13837.5 | − | 23967.3i | −0.101944 | − | 0.176572i | 0.810541 | − | 0.585681i | \(-0.199173\pi\) |
−0.912486 | + | 0.409109i | \(0.865840\pi\) | |||||||
\(114\) | −258986. | + | 448577.i | −1.86644 | + | 3.23277i | ||||
\(115\) | 70092.6 | − | 121404.i | 0.494228 | − | 0.856028i | ||||
\(116\) | 11021.2 | − | 19089.2i | 0.0760471 | − | 0.131717i | ||||
\(117\) | −5280.20 | −0.0356604 | ||||||||
\(118\) | −174072. | + | 301501.i | −1.15086 | + | 1.99335i | ||||
\(119\) | 89388.7 | 0.578649 | ||||||||
\(120\) | 406273. | + | 703686.i | 2.57552 | + | 4.46093i | ||||
\(121\) | 226512. | 1.40646 | ||||||||
\(122\) | 24885.8 | 0.151375 | ||||||||
\(123\) | −220651. | − | 382178.i | −1.31505 | − | 2.27773i | ||||
\(124\) | 101587. | − | 175953.i | 0.593311 | − | 1.02765i | ||||
\(125\) | −112467. | −0.643801 | ||||||||
\(126\) | −156957. | − | 271857.i | −0.880751 | − | 1.52551i | ||||
\(127\) | 34319.4 | + | 59443.0i | 0.188813 | + | 0.327033i | 0.944855 | − | 0.327490i | \(-0.106203\pi\) |
−0.756042 | + | 0.654523i | \(0.772869\pi\) | |||||||
\(128\) | 59131.7 | + | 102419.i | 0.319004 | + | 0.552531i | ||||
\(129\) | −207546. | + | 359481.i | −1.09810 | + | 1.90196i | ||||
\(130\) | 3541.81 | − | 6134.60i | 0.0183809 | − | 0.0318367i | ||||
\(131\) | 50589.2 | + | 87623.0i | 0.257561 | + | 0.446108i | 0.965588 | − | 0.260077i | \(-0.0837480\pi\) |
−0.708027 | + | 0.706185i | \(0.750415\pi\) | |||||||
\(132\) | −637558. | − | 1.10428e6i | −3.18482 | − | 5.51627i | ||||
\(133\) | 53289.7 | + | 92300.5i | 0.261225 | + | 0.452455i | ||||
\(134\) | −334225. | −1.60797 | ||||||||
\(135\) | 259492. | − | 449454.i | 1.22543 | − | 2.12252i | ||||
\(136\) | −331295. | − | 573820.i | −1.53592 | − | 2.66029i | ||||
\(137\) | −121328. | −0.552282 | −0.276141 | − | 0.961117i | \(-0.589056\pi\) | ||||
−0.276141 | + | 0.961117i | \(0.589056\pi\) | |||||||
\(138\) | 588943. | 2.63254 | ||||||||
\(139\) | 16704.8 | + | 28933.5i | 0.0733336 | + | 0.127018i | 0.900360 | − | 0.435145i | \(-0.143303\pi\) |
−0.827027 | + | 0.562163i | \(0.809970\pi\) | |||||||
\(140\) | 294160. | 1.26842 | ||||||||
\(141\) | 10459.4 | − | 18116.1i | 0.0443054 | − | 0.0767393i | ||||
\(142\) | −136572. | −0.568382 | ||||||||
\(143\) | −3159.06 | + | 5471.66i | −0.0129187 | + | 0.0223758i | ||||
\(144\) | −546283. | + | 946190.i | −2.19539 | + | 3.80252i | ||||
\(145\) | 10071.5 | − | 17444.3i | 0.0397808 | − | 0.0689023i | ||||
\(146\) | −68935.6 | − | 119400.i | −0.267646 | − | 0.463577i | ||||
\(147\) | 369574. | 1.41061 | ||||||||
\(148\) | −528193. | + | 319613.i | −1.98216 | + | 1.19942i | ||||
\(149\) | 502499. | 1.85425 | 0.927127 | − | 0.374747i | \(-0.122271\pi\) | ||||
0.927127 | + | 0.374747i | \(0.122271\pi\) | |||||||
\(150\) | 208481. | + | 361099.i | 0.756550 | + | 1.31038i | ||||
\(151\) | 142884. | − | 247482.i | 0.509965 | − | 0.883285i | −0.489969 | − | 0.871740i | \(-0.662992\pi\) |
0.999933 | − | 0.0115449i | \(-0.00367493\pi\) | |||||||
\(152\) | 395008. | − | 684174.i | 1.38675 | − | 2.40191i | ||||
\(153\) | −397049. | + | 687708.i | −1.37124 | + | 2.37507i | ||||
\(154\) | −375619. | −1.27628 | ||||||||
\(155\) | 92832.9 | − | 160791.i | 0.310365 | − | 0.537568i | ||||
\(156\) | 20787.2 | 0.0683888 | ||||||||
\(157\) | −20802.2 | − | 36030.5i | −0.0673535 | − | 0.116660i | 0.830382 | − | 0.557194i | \(-0.188122\pi\) |
−0.897736 | + | 0.440535i | \(0.854789\pi\) | |||||||
\(158\) | 324253. | 1.03334 | ||||||||
\(159\) | 452210. | 1.41856 | ||||||||
\(160\) | −262289. | − | 454299.i | −0.809992 | − | 1.40295i | ||||
\(161\) | 60591.3 | − | 104947.i | 0.184224 | − | 0.319085i | ||||
\(162\) | 877861. | 2.62808 | ||||||||
\(163\) | 186781. | + | 323515.i | 0.550635 | + | 0.953729i | 0.998229 | + | 0.0594914i | \(0.0189479\pi\) |
−0.447593 | + | 0.894237i | \(0.647719\pi\) | |||||||
\(164\) | 592111. | + | 1.02557e6i | 1.71907 | + | 2.97752i | ||||
\(165\) | −582620. | − | 1.00913e6i | −1.66600 | − | 2.88560i | ||||
\(166\) | −274404. | + | 475282.i | −0.772895 | + | 1.33869i | ||||
\(167\) | 78686.0 | − | 136288.i | 0.218326 | − | 0.378152i | −0.735970 | − | 0.677014i | \(-0.763274\pi\) |
0.954296 | + | 0.298862i | \(0.0966069\pi\) | |||||||
\(168\) | 351202. | + | 608299.i | 0.960027 | + | 1.66282i | ||||
\(169\) | 185595. | + | 321460.i | 0.499861 | + | 0.865785i | ||||
\(170\) | −532659. | − | 922592.i | −1.41360 | − | 2.44843i | ||||
\(171\) | −946813. | −2.47613 | ||||||||
\(172\) | 556946. | − | 964659.i | 1.43546 | − | 2.48630i | ||||
\(173\) | −58627.6 | − | 101546.i | −0.148932 | − | 0.257957i | 0.781901 | − | 0.623402i | \(-0.214250\pi\) |
−0.930833 | + | 0.365445i | \(0.880917\pi\) | |||||||
\(174\) | 84624.2 | 0.211895 | ||||||||
\(175\) | 85795.2 | 0.211772 | ||||||||
\(176\) | 653666. | + | 1.13218e6i | 1.59065 | + | 2.75508i | ||||
\(177\) | −933608. | −2.23991 | ||||||||
\(178\) | −148785. | + | 257704.i | −0.351973 | + | 0.609636i | ||||
\(179\) | 71604.8 | 0.167036 | 0.0835179 | − | 0.996506i | \(-0.473384\pi\) | ||||
0.0835179 | + | 0.996506i | \(0.473384\pi\) | |||||||
\(180\) | −1.30661e6 | + | 2.26311e6i | −3.00582 | + | 5.20624i | ||||
\(181\) | 266097. | − | 460893.i | 0.603730 | − | 1.04569i | −0.388520 | − | 0.921440i | \(-0.627014\pi\) |
0.992251 | − | 0.124252i | \(-0.0396530\pi\) | |||||||
\(182\) | 3061.71 | − | 5303.04i | 0.00685150 | − | 0.0118671i | ||||
\(183\) | 33367.9 | + | 57794.8i | 0.0736547 | + | 0.127574i | ||||
\(184\) | −898261. | −1.95595 | ||||||||
\(185\) | −482679. | + | 292072.i | −1.03688 | + | 0.627423i | ||||
\(186\) | 780016. | 1.65318 | ||||||||
\(187\) | 475096. | + | 822891.i | 0.993522 | + | 1.72083i | ||||
\(188\) | −28067.4 | + | 48614.2i | −0.0579173 | + | 0.100316i | ||||
\(189\) | 224317. | − | 388529.i | 0.456782 | − | 0.791169i | ||||
\(190\) | 635097. | − | 1.10002e6i | 1.27631 | − | 2.21063i | ||||
\(191\) | −935329. | −1.85516 | −0.927579 | − | 0.373627i | \(-0.878114\pi\) | ||||
−0.927579 | + | 0.373627i | \(0.878114\pi\) | |||||||
\(192\) | 173653. | − | 300777.i | 0.339962 | − | 0.588831i | ||||
\(193\) | −484455. | −0.936181 | −0.468091 | − | 0.883680i | \(-0.655058\pi\) | ||||
−0.468091 | + | 0.883680i | \(0.655058\pi\) | |||||||
\(194\) | −169774. | − | 294057.i | −0.323867 | − | 0.560953i | ||||
\(195\) | 18996.0 | 0.0357746 | ||||||||
\(196\) | −991744. | −1.84399 | ||||||||
\(197\) | 334566. | + | 579485.i | 0.614209 | + | 1.06384i | 0.990523 | + | 0.137348i | \(0.0438580\pi\) |
−0.376314 | + | 0.926492i | \(0.622809\pi\) | |||||||
\(198\) | 1.66843e6 | − | 2.88981e6i | 3.02444 | − | 5.23849i | ||||
\(199\) | −506514. | −0.906690 | −0.453345 | − | 0.891335i | \(-0.649769\pi\) | ||||
−0.453345 | + | 0.891335i | \(0.649769\pi\) | |||||||
\(200\) | −317976. | − | 550751.i | −0.562108 | − | 0.973600i | ||||
\(201\) | −448141. | − | 776203.i | −0.782392 | − | 1.35514i | ||||
\(202\) | 549405. | + | 951598.i | 0.947359 | + | 1.64087i | ||||
\(203\) | 8706.26 | − | 15079.7i | 0.0148283 | − | 0.0256834i | ||||
\(204\) | 1.56311e6 | − | 2.70739e6i | 2.62975 | − | 4.55486i | ||||
\(205\) | 541089. | + | 937193.i | 0.899257 | + | 1.55756i | ||||
\(206\) | 100349. | + | 173810.i | 0.164758 | + | 0.285370i | ||||
\(207\) | 538271. | + | 932313.i | 0.873123 | + | 1.51229i | ||||
\(208\) | −21312.4 | −0.0341565 | ||||||||
\(209\) | −566464. | + | 981145.i | −0.897030 | + | 1.55370i | ||||
\(210\) | 564665. | + | 978028.i | 0.883573 | + | 1.53039i | ||||
\(211\) | 822328. | 1.27157 | 0.635783 | − | 0.771868i | \(-0.280677\pi\) | ||||
0.635783 | + | 0.771868i | \(0.280677\pi\) | |||||||
\(212\) | −1.21349e6 | −1.85438 | ||||||||
\(213\) | −183121. | − | 317174.i | −0.276559 | − | 0.479014i | ||||
\(214\) | 1.73155e6 | 2.58464 | ||||||||
\(215\) | 508954. | − | 881534.i | 0.750901 | − | 1.30060i | ||||
\(216\) | −3.32549e6 | −4.84977 | ||||||||
\(217\) | 80249.2 | − | 138996.i | 0.115689 | − | 0.200379i | ||||
\(218\) | −952334. | + | 1.64949e6i | −1.35721 | + | 2.35076i | ||||
\(219\) | 184863. | − | 320192.i | 0.260459 | − | 0.451128i | ||||
\(220\) | 1.56345e6 | + | 2.70797e6i | 2.17784 | + | 3.77213i | ||||
\(221\) | −15490.2 | −0.0213343 | ||||||||
\(222\) | −2.07656e6 | − | 1.14262e6i | −2.82789 | − | 1.55604i | ||||
\(223\) | −1.39322e6 | −1.87610 | −0.938050 | − | 0.346499i | \(-0.887370\pi\) | ||||
−0.938050 | + | 0.346499i | \(0.887370\pi\) | |||||||
\(224\) | −226735. | − | 392717.i | −0.301925 | − | 0.522949i | ||||
\(225\) | −381087. | + | 660061.i | −0.501842 | + | 0.869217i | ||||
\(226\) | −142558. | + | 246918.i | −0.185661 | + | 0.321575i | ||||
\(227\) | 601186. | − | 1.04128e6i | 0.774362 | − | 1.34123i | −0.160791 | − | 0.986989i | \(-0.551404\pi\) |
0.935152 | − | 0.354246i | \(-0.115262\pi\) | |||||||
\(228\) | 3.72744e6 | 4.74868 | ||||||||
\(229\) | −388054. | + | 672128.i | −0.488993 | + | 0.846961i | −0.999920 | − | 0.0126632i | \(-0.995969\pi\) |
0.510927 | + | 0.859624i | \(0.329302\pi\) | |||||||
\(230\) | −1.44423e6 | −1.80018 | ||||||||
\(231\) | −503644. | − | 872337.i | −0.621003 | − | 1.07561i | ||||
\(232\) | −129069. | −0.157436 | ||||||||
\(233\) | 865545. | 1.04448 | 0.522239 | − | 0.852799i | \(-0.325097\pi\) | ||||
0.522239 | + | 0.852799i | \(0.325097\pi\) | |||||||
\(234\) | 27199.1 | + | 47110.3i | 0.0324725 | + | 0.0562440i | ||||
\(235\) | −25648.9 | + | 44425.1i | −0.0302969 | + | 0.0524758i | ||||
\(236\) | 2.50531e6 | 2.92808 | ||||||||
\(237\) | 434771. | + | 753045.i | 0.502793 | + | 0.870863i | ||||
\(238\) | −460455. | − | 797532.i | −0.526920 | − | 0.912653i | ||||
\(239\) | −540209. | − | 935670.i | −0.611741 | − | 1.05957i | −0.990947 | − | 0.134254i | \(-0.957136\pi\) |
0.379206 | − | 0.925312i | \(-0.376197\pi\) | |||||||
\(240\) | 1.96530e6 | − | 3.40400e6i | 2.20242 | − | 3.81471i | ||||
\(241\) | 512514. | − | 887700.i | 0.568411 | − | 0.984517i | −0.428312 | − | 0.903631i | \(-0.640892\pi\) |
0.996723 | − | 0.0808865i | \(-0.0257751\pi\) | |||||||
\(242\) | −1.16680e6 | − | 2.02095e6i | −1.28073 | − | 2.21828i | ||||
\(243\) | 246331. | + | 426658.i | 0.267611 | + | 0.463516i | ||||
\(244\) | −89541.9 | − | 155091.i | −0.0962835 | − | 0.166768i | ||||
\(245\) | −906285. | −0.964605 | ||||||||
\(246\) | −2.27321e6 | + | 3.93732e6i | −2.39498 | + | 4.14823i | ||||
\(247\) | −9234.62 | − | 15994.8i | −0.00963112 | − | 0.0166816i | ||||
\(248\) | −1.18969e6 | −1.22830 | ||||||||
\(249\) | −1.47173e6 | −1.50428 | ||||||||
\(250\) | 579337. | + | 1.00344e6i | 0.586248 | + | 1.01541i | ||||
\(251\) | −42030.1 | −0.0421091 | −0.0210545 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210545 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(252\) | −1.12949e6 | + | 1.95634e6i | −1.12042 | + | 1.94063i | ||||
\(253\) | 1.28816e6 | 1.26523 | ||||||||
\(254\) | 353570. | − | 612400.i | 0.343867 | − | 0.595595i | ||||
\(255\) | 1.42842e6 | − | 2.47409e6i | 1.37564 | − | 2.38268i | ||||
\(256\) | 810331. | − | 1.40353e6i | 0.772792 | − | 1.33851i | ||||
\(257\) | −169959. | − | 294378.i | −0.160514 | − | 0.278018i | 0.774539 | − | 0.632526i | \(-0.217982\pi\) |
−0.935053 | + | 0.354508i | \(0.884648\pi\) | |||||||
\(258\) | 4.27642e6 | 3.99973 | ||||||||
\(259\) | −417250. | + | 252481.i | −0.386498 | + | 0.233872i | ||||
\(260\) | −50975.3 | −0.0467656 | ||||||||
\(261\) | 77343.2 | + | 133962.i | 0.0702783 | + | 0.121726i | ||||
\(262\) | 521185. | − | 902719.i | 0.469071 | − | 0.812455i | ||||
\(263\) | 11725.8 | − | 20309.6i | 0.0104533 | − | 0.0181056i | −0.860751 | − | 0.509025i | \(-0.830006\pi\) |
0.871205 | + | 0.490920i | \(0.163339\pi\) | |||||||
\(264\) | −3.73324e6 | + | 6.46616e6i | −3.29667 | + | 5.71000i | ||||
\(265\) | −1.10893e6 | −0.970037 | ||||||||
\(266\) | 549007. | − | 950909.i | 0.475745 | − | 0.824014i | ||||
\(267\) | −797987. | −0.685043 | ||||||||
\(268\) | 1.20258e6 | + | 2.08292e6i | 1.02276 | + | 1.77148i | ||||
\(269\) | −273681. | −0.230603 | −0.115301 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115301 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(270\) | −5.34674e6 | −4.46354 | ||||||||
\(271\) | 216147. | + | 374377.i | 0.178783 | + | 0.309661i | 0.941464 | − | 0.337114i | \(-0.109451\pi\) |
−0.762681 | + | 0.646775i | \(0.776117\pi\) | |||||||
\(272\) | −1.60260e6 | + | 2.77579e6i | −1.31342 | + | 2.27491i | ||||
\(273\) | 16421.0 | 0.0133350 | ||||||||
\(274\) | 624981. | + | 1.08250e6i | 0.502910 | + | 0.871066i | ||||
\(275\) | 455997. | + | 789810.i | 0.363605 | + | 0.629783i | ||||
\(276\) | −2.11908e6 | − | 3.67035e6i | −1.67446 | − | 2.90025i | ||||
\(277\) | 1.12776e6 | − | 1.95335e6i | 0.883119 | − | 1.52961i | 0.0352640 | − | 0.999378i | \(-0.488773\pi\) |
0.847855 | − | 0.530229i | \(-0.177894\pi\) | |||||||
\(278\) | 172098. | − | 298082.i | 0.133556 | − | 0.231325i | ||||
\(279\) | 712904. | + | 1.23479e6i | 0.548303 | + | 0.949689i | ||||
\(280\) | −861231. | − | 1.49170e6i | −0.656485 | − | 1.13707i | ||||
\(281\) | 922687. | + | 1.59814e6i | 0.697089 | + | 1.20739i | 0.969471 | + | 0.245205i | \(0.0788553\pi\) |
−0.272382 | + | 0.962189i | \(0.587811\pi\) | |||||||
\(282\) | −215511. | −0.161379 | ||||||||
\(283\) | 358728. | − | 621336.i | 0.266256 | − | 0.461169i | −0.701636 | − | 0.712536i | \(-0.747547\pi\) |
0.967892 | + | 0.251367i | \(0.0808800\pi\) | |||||||
\(284\) | 491400. | + | 851129.i | 0.361526 | + | 0.626181i | ||||
\(285\) | 3.40624e6 | 2.48407 | ||||||||
\(286\) | 65091.3 | 0.0470552 | ||||||||
\(287\) | 467743. | + | 810154.i | 0.335199 | + | 0.580581i | ||||
\(288\) | 4.02847e6 | 2.86193 | ||||||||
\(289\) | −454872. | + | 787861.i | −0.320364 | + | 0.554888i | ||||
\(290\) | −207519. | −0.144898 | ||||||||
\(291\) | 455278. | − | 788564.i | 0.315169 | − | 0.545889i | ||||
\(292\) | −496075. | + | 859227.i | −0.340479 | + | 0.589727i | ||||
\(293\) | −1.40056e6 | + | 2.42583e6i | −0.953084 | + | 1.65079i | −0.214392 | + | 0.976748i | \(0.568777\pi\) |
−0.738693 | + | 0.674043i | \(0.764556\pi\) | |||||||
\(294\) | −1.90373e6 | − | 3.29736e6i | −1.28451 | − | 2.22484i | ||||
\(295\) | 2.28943e6 | 1.53170 | ||||||||
\(296\) | 3.16719e6 | + | 1.74274e6i | 2.10109 | + | 1.15612i | ||||
\(297\) | 4.76894e6 | 3.13712 | ||||||||
\(298\) | −2.58845e6 | − | 4.48332e6i | −1.68849 | − | 2.92455i | ||||
\(299\) | −10499.9 | + | 18186.4i | −0.00679216 | + | 0.0117644i | ||||
\(300\) | 1.50027e6 | − | 2.59855e6i | 0.962424 | − | 1.66697i | ||||
\(301\) | 439964. | − | 762040.i | 0.279899 | − | 0.484799i | ||||
\(302\) | −2.94406e6 | −1.85750 | ||||||||
\(303\) | −1.47333e6 | + | 2.55188e6i | −0.921918 | + | 1.59681i | ||||
\(304\) | −3.82161e6 | −2.37171 | ||||||||
\(305\) | −81826.0 | − | 141727.i | −0.0503665 | − | 0.0872374i | ||||
\(306\) | 8.18103e6 | 4.99464 | ||||||||
\(307\) | 309132. | 0.187197 | 0.0935983 | − | 0.995610i | \(-0.470163\pi\) | ||||
0.0935983 | + | 0.995610i | \(0.470163\pi\) | |||||||
\(308\) | 1.35152e6 | + | 2.34090e6i | 0.811792 | + | 1.40606i | ||||
\(309\) | −269105. | + | 466103.i | −0.160334 | + | 0.277706i | ||||
\(310\) | −1.91279e6 | −1.13048 | ||||||||
\(311\) | −806132. | − | 1.39626e6i | −0.472612 | − | 0.818589i | 0.526896 | − | 0.849930i | \(-0.323356\pi\) |
−0.999509 | + | 0.0313409i | \(0.990022\pi\) | |||||||
\(312\) | −60860.0 | − | 105413.i | −0.0353953 | − | 0.0613065i | ||||
\(313\) | −1.53468e6 | − | 2.65814e6i | −0.885434 | − | 1.53362i | −0.845216 | − | 0.534426i | \(-0.820528\pi\) |
−0.0402183 | − | 0.999191i | \(-0.512805\pi\) | |||||||
\(314\) | −214311. | + | 371197.i | −0.122665 | + | 0.212462i | ||||
\(315\) | −1.03216e6 | + | 1.78776e6i | −0.586101 | + | 1.01516i | ||||
\(316\) | −1.16670e6 | − | 2.02078e6i | −0.657265 | − | 1.13842i | ||||
\(317\) | −472314. | − | 818071.i | −0.263987 | − | 0.457239i | 0.703311 | − | 0.710882i | \(-0.251704\pi\) |
−0.967298 | + | 0.253644i | \(0.918371\pi\) | |||||||
\(318\) | −2.32940e6 | − | 4.03464e6i | −1.29174 | − | 2.23737i | ||||
\(319\) | 185093. | 0.101839 | ||||||||
\(320\) | −425840. | + | 737577.i | −0.232473 | + | 0.402654i | ||||
\(321\) | 2.32172e6 | + | 4.02134e6i | 1.25761 | + | 2.17825i | ||||
\(322\) | −1.24846e6 | −0.671020 | ||||||||
\(323\) | −2.77762e6 | −1.48138 | ||||||||
\(324\) | −3.15864e6 | − | 5.47092e6i | −1.67162 | − | 2.89533i | ||||
\(325\) | −14867.5 | −0.00780782 | ||||||||
\(326\) | 1.92428e6 | − | 3.33295e6i | 1.00282 | − | 1.73694i | ||||
\(327\) | −5.10770e6 | −2.64153 | ||||||||
\(328\) | 3.46712e6 | − | 6.00523e6i | 1.77944 | − | 3.08209i | ||||
\(329\) | −22172.1 | + | 38403.2i | −0.0112932 | + | 0.0195604i | ||||
\(330\) | −6.00233e6 | + | 1.03963e7i | −3.03413 | + | 5.25528i | ||||
\(331\) | 65267.1 | + | 113046.i | 0.0327434 | + | 0.0567133i | 0.881933 | − | 0.471375i | \(-0.156242\pi\) |
−0.849189 | + | 0.528089i | \(0.822909\pi\) | |||||||
\(332\) | 3.94934e6 | 1.96643 | ||||||||
\(333\) | −89098.0 | − | 4.33157e6i | −0.0440309 | − | 2.14060i | ||||
\(334\) | −1.62129e6 | −0.795236 | ||||||||
\(335\) | 1.09895e6 | + | 1.90344e6i | 0.535015 | + | 0.926673i | ||||
\(336\) | 1.69890e6 | − | 2.94258e6i | 0.820954 | − | 1.42193i | ||||
\(337\) | −1.29235e6 | + | 2.23841e6i | −0.619876 | + | 1.07366i | 0.369632 | + | 0.929178i | \(0.379484\pi\) |
−0.989508 | + | 0.144479i | \(0.953849\pi\) | |||||||
\(338\) | 1.91206e6 | − | 3.31178e6i | 0.910351 | − | 1.57678i | ||||
\(339\) | −764590. | −0.361351 | ||||||||
\(340\) | −3.83312e6 | + | 6.63916e6i | −1.79827 | + | 3.11470i | ||||
\(341\) | 1.70608e6 | 0.794536 | ||||||||
\(342\) | 4.87718e6 | + | 8.44753e6i | 2.25478 | + | 3.90539i | ||||
\(343\) | −1.76775e6 | −0.811306 | ||||||||
\(344\) | −6.52242e6 | −2.97175 | ||||||||
\(345\) | −1.93648e6 | − | 3.35408e6i | −0.875921 | − | 1.51714i | ||||
\(346\) | −604000. | + | 1.04616e6i | −0.271236 | + | 0.469794i | ||||
\(347\) | 228919. | 0.102061 | 0.0510303 | − | 0.998697i | \(-0.483750\pi\) | ||||
0.0510303 | + | 0.998697i | \(0.483750\pi\) | |||||||
\(348\) | −304487. | − | 527386.i | −0.134778 | − | 0.233443i | ||||
\(349\) | −1.13772e6 | − | 1.97059e6i | −0.500003 | − | 0.866031i | −1.00000 | 4.02675e-6i | \(-0.999999\pi\) | |
0.499997 | − | 0.866027i | \(-0.333335\pi\) | |||||||
\(350\) | −441944. | − | 765470.i | −0.192840 | − | 0.334009i | ||||
\(351\) | −38872.1 | + | 67328.5i | −0.0168411 | + | 0.0291697i | ||||
\(352\) | 2.41017e6 | − | 4.17454e6i | 1.03679 | − | 1.79578i | ||||
\(353\) | 1.18083e6 | + | 2.04527e6i | 0.504373 | + | 0.873600i | 0.999987 | + | 0.00505739i | \(0.00160982\pi\) |
−0.495614 | + | 0.868543i | \(0.665057\pi\) | |||||||
\(354\) | 4.80916e6 | + | 8.32971e6i | 2.03967 | + | 3.53282i | ||||
\(355\) | 449056. | + | 777787.i | 0.189116 | + | 0.327559i | ||||
\(356\) | 2.14138e6 | 0.895506 | ||||||||
\(357\) | 1.23479e6 | − | 2.13872e6i | 0.512770 | − | 0.888144i | ||||
\(358\) | −368848. | − | 638863.i | −0.152104 | − | 0.263451i | ||||
\(359\) | 2.67447e6 | 1.09522 | 0.547611 | − | 0.836733i | \(-0.315537\pi\) | ||||
0.547611 | + | 0.836733i | \(0.315537\pi\) | |||||||
\(360\) | 1.53017e7 | 6.22278 | ||||||||
\(361\) | −417847. | − | 723732.i | −0.168752 | − | 0.292287i | ||||
\(362\) | −5.48282e6 | −2.19904 | ||||||||
\(363\) | 3.12897e6 | − | 5.41953e6i | 1.24633 | − | 2.15871i | ||||
\(364\) | −44065.4 | −0.0174319 | ||||||||
\(365\) | −453328. | + | 785187.i | −0.178107 | + | 0.308490i | ||||
\(366\) | 343766. | − | 595420.i | 0.134141 | − | 0.232338i | ||||
\(367\) | 2.04245e6 | − | 3.53763e6i | 0.791566 | − | 1.37103i | −0.133431 | − | 0.991058i | \(-0.542600\pi\) |
0.924997 | − | 0.379974i | \(-0.124067\pi\) | |||||||
\(368\) | 2.17262e6 | + | 3.76308e6i | 0.836303 | + | 1.44852i | ||||
\(369\) | −8.31051e6 | −3.17733 | ||||||||
\(370\) | 5.09224e6 | + | 2.80198e6i | 1.93377 | + | 1.06405i | ||||
\(371\) | −958609. | −0.361582 | ||||||||
\(372\) | −2.80658e6 | − | 4.86114e6i | −1.05153 | − | 1.82130i | ||||
\(373\) | −1.80412e6 | + | 3.12483e6i | −0.671419 | + | 1.16293i | 0.306083 | + | 0.952005i | \(0.400982\pi\) |
−0.977502 | + | 0.210927i | \(0.932352\pi\) | |||||||
\(374\) | 4.89459e6 | − | 8.47768e6i | 1.80941 | − | 3.13399i | ||||
\(375\) | −1.55359e6 | + | 2.69090e6i | −0.570504 | + | 0.988142i | ||||
\(376\) | 328699. | 0.119903 | ||||||||
\(377\) | −1508.71 | + | 2613.17i | −0.000546705 | + | 0.000946922i | ||||
\(378\) | −4.62198e6 | −1.66379 | ||||||||
\(379\) | −1.65768e6 | − | 2.87119e6i | −0.592793 | − | 1.02675i | −0.993854 | − | 0.110697i | \(-0.964692\pi\) |
0.401061 | − | 0.916051i | \(-0.368641\pi\) | |||||||
\(380\) | −9.14058e6 | −3.24724 | ||||||||
\(381\) | 1.89632e6 | 0.669265 | ||||||||
\(382\) | 4.81802e6 | + | 8.34506e6i | 1.68931 | + | 2.92598i | ||||
\(383\) | −783022. | + | 1.35623e6i | −0.272758 | + | 0.472430i | −0.969567 | − | 0.244826i | \(-0.921269\pi\) |
0.696809 | + | 0.717257i | \(0.254602\pi\) | |||||||
\(384\) | 3.26732e6 | 1.13074 | ||||||||
\(385\) | 1.23506e6 | + | 2.13918e6i | 0.424654 | + | 0.735522i | ||||
\(386\) | 2.49550e6 | + | 4.32233e6i | 0.852490 | + | 1.47656i | ||||
\(387\) | 3.90848e6 | + | 6.76968e6i | 1.32657 | + | 2.29769i | ||||
\(388\) | −1.22173e6 | + | 2.11609e6i | −0.411998 | + | 0.713601i | ||||
\(389\) | −1.07043e6 | + | 1.85404e6i | −0.358661 | + | 0.621219i | −0.987737 | − | 0.156124i | \(-0.950100\pi\) |
0.629076 | + | 0.777343i | \(0.283433\pi\) | |||||||
\(390\) | −97851.2 | − | 169483.i | −0.0325765 | − | 0.0564242i | ||||
\(391\) | 1.57910e6 | + | 2.73508e6i | 0.522357 | + | 0.904748i | ||||
\(392\) | 2.90359e6 | + | 5.02917e6i | 0.954378 | + | 1.65303i | ||||
\(393\) | 2.79530e6 | 0.912949 | ||||||||
\(394\) | 3.44680e6 | − | 5.97003e6i | 1.11860 | − | 1.93747i | ||||
\(395\) | −1.06616e6 | − | 1.84665e6i | −0.343820 | − | 0.595513i | ||||
\(396\) | −2.40128e7 | −7.69492 | ||||||||
\(397\) | 271798. | 0.0865505 | 0.0432752 | − | 0.999063i | \(-0.486221\pi\) | ||||
0.0432752 | + | 0.999063i | \(0.486221\pi\) | |||||||
\(398\) | 2.60913e6 | + | 4.51915e6i | 0.825635 | + | 1.43004i | ||||
\(399\) | 2.94452e6 | 0.925938 | ||||||||
\(400\) | −1.53817e6 | + | 2.66420e6i | −0.480679 | + | 0.832561i | ||||
\(401\) | 320744. | 0.0996088 | 0.0498044 | − | 0.998759i | \(-0.484140\pi\) | ||||
0.0498044 | + | 0.998759i | \(0.484140\pi\) | |||||||
\(402\) | −4.61689e6 | + | 7.99669e6i | −1.42490 | + | 2.46800i | ||||
\(403\) | −13906.4 | + | 24086.7i | −0.00426534 | + | 0.00738778i | ||||
\(404\) | 3.95364e6 | − | 6.84790e6i | 1.20516 | − | 2.08739i | ||||
\(405\) | −2.88646e6 | − | 4.99949e6i | −0.874435 | − | 1.51457i | ||||
\(406\) | −179389. | −0.0540108 | ||||||||
\(407\) | −4.54194e6 | − | 2.49918e6i | −1.35911 | − | 0.747846i | ||||
\(408\) | −1.83057e7 | −5.44421 | ||||||||
\(409\) | −2.92323e6 | − | 5.06319e6i | −0.864082 | − | 1.49663i | −0.867956 | − | 0.496641i | \(-0.834566\pi\) |
0.00387378 | − | 0.999992i | \(-0.498767\pi\) | |||||||
\(410\) | 5.57446e6 | − | 9.65525e6i | 1.63773 | − | 2.83664i | ||||
\(411\) | −1.67599e6 | + | 2.90291e6i | −0.489405 | + | 0.847674i | ||||
\(412\) | 722136. | − | 1.25078e6i | 0.209593 | − | 0.363025i | ||||
\(413\) | 1.97909e6 | 0.570941 | ||||||||
\(414\) | 5.54544e6 | − | 9.60498e6i | 1.59014 | − | 2.75420i | ||||
\(415\) | 3.60902e6 | 1.02865 | ||||||||
\(416\) | 39291.1 | + | 68054.2i | 0.0111317 | + | 0.0192807i | ||||
\(417\) | 923019. | 0.259938 | ||||||||
\(418\) | 1.16718e7 | 3.26736 | ||||||||
\(419\) | 918043. | + | 1.59010e6i | 0.255463 | + | 0.442475i | 0.965021 | − | 0.262172i | \(-0.0844388\pi\) |
−0.709558 | + | 0.704647i | \(0.751105\pi\) | |||||||
\(420\) | 4.06345e6 | − | 7.03810e6i | 1.12401 | − | 1.94685i | ||||
\(421\) | 1.48350e6 | 0.407927 | 0.203963 | − | 0.978979i | \(-0.434618\pi\) | ||||
0.203963 | + | 0.978979i | \(0.434618\pi\) | |||||||
\(422\) | −4.23594e6 | − | 7.33686e6i | −1.15789 | − | 2.00553i | ||||
\(423\) | −196969. | − | 341160.i | −0.0535237 | − | 0.0927058i | ||||
\(424\) | 3.55282e6 | + | 6.15367e6i | 0.959752 | + | 1.66234i | ||||
\(425\) | −1.11797e6 | + | 1.93639e6i | −0.300234 | + | 0.520020i | ||||
\(426\) | −1.88656e6 | + | 3.26763e6i | −0.503672 | + | 0.872385i | ||||
\(427\) | −70734.3 | − | 122515.i | −0.0187741 | − | 0.0325178i | ||||
\(428\) | −6.23028e6 | − | 1.07912e7i | −1.64399 | − | 2.84747i | ||||
\(429\) | 87276.8 | + | 151168.i | 0.0228958 | + | 0.0396567i | ||||
\(430\) | −1.04868e7 | −2.73509 | ||||||||
\(431\) | −2.69018e6 | + | 4.65953e6i | −0.697571 | + | 1.20823i | 0.271735 | + | 0.962372i | \(0.412402\pi\) |
−0.969306 | + | 0.245856i | \(0.920931\pi\) | |||||||
\(432\) | 8.04333e6 | + | 1.39315e7i | 2.07361 | + | 3.59159i | ||||
\(433\) | −6.39127e6 | −1.63820 | −0.819100 | − | 0.573650i | \(-0.805527\pi\) | ||||
−0.819100 | + | 0.573650i | \(0.805527\pi\) | |||||||
\(434\) | −1.65350e6 | −0.421387 | ||||||||
\(435\) | −278249. | − | 481941.i | −0.0705034 | − | 0.122116i | ||||
\(436\) | 1.37064e7 | 3.45308 | ||||||||
\(437\) | −1.88278e6 | + | 3.26107e6i | −0.471624 | + | 0.816878i | ||||
\(438\) | −3.80903e6 | −0.948700 | ||||||||
\(439\) | 1.12104e6 | − | 1.94169e6i | 0.277625 | − | 0.480861i | −0.693169 | − | 0.720775i | \(-0.743786\pi\) |
0.970794 | + | 0.239914i | \(0.0771194\pi\) | |||||||
\(440\) | 9.15480e6 | − | 1.58566e7i | 2.25433 | − | 3.90461i | ||||
\(441\) | 3.47988e6 | − | 6.02733e6i | 0.852055 | − | 1.47580i | ||||
\(442\) | 79792.6 | + | 138205.i | 0.0194271 | + | 0.0336487i | ||||
\(443\) | −5.81591e6 | −1.40802 | −0.704009 | − | 0.710191i | \(-0.748609\pi\) | ||||
−0.704009 | + | 0.710191i | \(0.748609\pi\) | |||||||
\(444\) | 350763. | + | 1.70526e7i | 0.0844416 | + | 4.10520i | ||||
\(445\) | 1.95686e6 | 0.468445 | ||||||||
\(446\) | 7.17667e6 | + | 1.24304e7i | 1.70838 | + | 2.95901i | ||||
\(447\) | 6.94137e6 | − | 1.20228e7i | 1.64315 | − | 2.84601i | ||||
\(448\) | −368116. | + | 637596.i | −0.0866543 | + | 0.150090i | ||||
\(449\) | 2.41736e6 | − | 4.18699e6i | 0.565881 | − | 0.980134i | −0.431086 | − | 0.902311i | \(-0.641870\pi\) |
0.996967 | − | 0.0778238i | \(-0.0247971\pi\) | |||||||
\(450\) | 7.85214e6 | 1.82792 | ||||||||
\(451\) | −4.97205e6 | + | 8.61185e6i | −1.15105 | + | 1.99368i | ||||
\(452\) | 2.05176e6 | 0.472368 | ||||||||
\(453\) | −3.94751e6 | − | 6.83729e6i | −0.903811 | − | 1.56545i | ||||
\(454\) | −1.23872e7 | −2.82055 | ||||||||
\(455\) | −40268.3 | −0.00911874 | ||||||||
\(456\) | −1.09131e7 | − | 1.89020e7i | −2.45773 | − | 4.25691i | ||||
\(457\) | −692319. | + | 1.19913e6i | −0.155066 | + | 0.268582i | −0.933083 | − | 0.359661i | \(-0.882892\pi\) |
0.778017 | + | 0.628243i | \(0.216226\pi\) | |||||||
\(458\) | 7.99569e6 | 1.78112 | ||||||||
\(459\) | 5.84604e6 | + | 1.01256e7i | 1.29518 | + | 2.24332i | ||||
\(460\) | 5.19649e6 | + | 9.00059e6i | 1.14503 | + | 1.98325i | ||||
\(461\) | 1.69242e6 | + | 2.93136e6i | 0.370900 | + | 0.642417i | 0.989704 | − | 0.143128i | \(-0.0457161\pi\) |
−0.618805 | + | 0.785545i | \(0.712383\pi\) | |||||||
\(462\) | −5.18869e6 | + | 8.98708e6i | −1.13098 | + | 1.95891i | ||||
\(463\) | −368477. | + | 638220.i | −0.0798836 | + | 0.138362i | −0.903200 | − | 0.429221i | \(-0.858788\pi\) |
0.823316 | + | 0.567583i | \(0.192122\pi\) | |||||||
\(464\) | 312179. | + | 540710.i | 0.0673146 | + | 0.116592i | ||||
\(465\) | −2.56474e6 | − | 4.44225e6i | −0.550060 | − | 0.952732i | ||||
\(466\) | −4.45855e6 | − | 7.72244e6i | −0.951107 | − | 1.64737i | ||||
\(467\) | 6.97139e6 | 1.47920 | 0.739600 | − | 0.673047i | \(-0.235015\pi\) | ||||
0.739600 | + | 0.673047i | \(0.235015\pi\) | |||||||
\(468\) | 195731. | − | 339015.i | 0.0413089 | − | 0.0715492i | ||||
\(469\) | 949984. | + | 1.64542e6i | 0.199427 | + | 0.345418i | ||||
\(470\) | 528485. | 0.110354 | ||||||||
\(471\) | −1.14942e6 | −0.238741 | ||||||||
\(472\) | −7.33497e6 | − | 1.27045e7i | −1.51546 | − | 2.62485i | ||||
\(473\) | 9.35354e6 | 1.92231 | ||||||||
\(474\) | 4.47914e6 | − | 7.75810e6i | 0.915691 | − | 1.58602i | ||||
\(475\) | −2.66595e6 | −0.542149 | ||||||||
\(476\) | −3.31353e6 | + | 5.73921e6i | −0.670307 | + | 1.16101i | ||||
\(477\) | 4.25797e6 | − | 7.37502e6i | 0.856853 | − | 1.48411i | ||||
\(478\) | −5.56540e6 | + | 9.63956e6i | −1.11411 | + | 1.92969i | ||||
\(479\) | 978758. | + | 1.69526e6i | 0.194911 | + | 0.337596i | 0.946871 | − | 0.321613i | \(-0.104225\pi\) |
−0.751960 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(480\) | −1.44928e7 | −2.87110 | ||||||||
\(481\) | 72305.6 | − | 43752.6i | 0.0142498 | − | 0.00862265i | ||||
\(482\) | −1.05601e7 | −2.07039 | ||||||||
\(483\) | −1.67398e6 | − | 2.89942e6i | −0.326500 | − | 0.565514i | ||||
\(484\) | −8.39651e6 | + | 1.45432e7i | −1.62924 | + | 2.82193i | ||||
\(485\) | −1.11645e6 | + | 1.93375e6i | −0.215519 | + | 0.373290i | ||||
\(486\) | 2.53778e6 | − | 4.39556e6i | 0.487375 | − | 0.844158i | ||||
\(487\) | −8.85483e6 | −1.69183 | −0.845917 | − | 0.533314i | \(-0.820946\pi\) | ||||
−0.845917 | + | 0.533314i | \(0.820946\pi\) | |||||||
\(488\) | −524315. | + | 908140.i | −0.0996649 | + | 0.172625i | ||||
\(489\) | 1.03206e7 | 1.95178 | ||||||||
\(490\) | 4.66842e6 | + | 8.08593e6i | 0.878374 | + | 1.52139i | ||||
\(491\) | 5.47395e6 | 1.02470 | 0.512350 | − | 0.858776i | \(-0.328775\pi\) | ||||
0.512350 | + | 0.858776i | \(0.328775\pi\) | |||||||
\(492\) | 3.27170e7 | 6.09342 | ||||||||
\(493\) | 226898. | + | 392998.i | 0.0420448 | + | 0.0728238i | ||||
\(494\) | −95137.9 | + | 164784.i | −0.0175403 | + | 0.0303806i | ||||
\(495\) | −2.19436e7 | −4.02526 | ||||||||
\(496\) | 2.87748e6 | + | 4.98395e6i | 0.525181 | + | 0.909640i | ||||
\(497\) | 388185. | + | 672356.i | 0.0704933 | + | 0.122098i | ||||
\(498\) | 7.58108e6 | + | 1.31308e7i | 1.36980 | + | 2.37257i | ||||
\(499\) | 587413. | − | 1.01743e6i | 0.105607 | − | 0.182917i | −0.808379 | − | 0.588662i | \(-0.799655\pi\) |
0.913986 | + | 0.405746i | \(0.132988\pi\) | |||||||
\(500\) | 4.16903e6 | − | 7.22097e6i | 0.745779 | − | 1.29173i | ||||
\(501\) | −2.17389e6 | − | 3.76529e6i | −0.386940 | − | 0.670200i | ||||
\(502\) | 216503. | + | 374995.i | 0.0383447 | + | 0.0664150i | ||||
\(503\) | 1.29629e6 | + | 2.24524e6i | 0.228445 | + | 0.395679i | 0.957348 | − | 0.288939i | \(-0.0933024\pi\) |
−0.728902 | + | 0.684618i | \(0.759969\pi\) | |||||||
\(504\) | 1.32275e7 | 2.31954 | ||||||||
\(505\) | 3.61295e6 | − | 6.25781e6i | 0.630425 | − | 1.09193i | ||||
\(506\) | −6.63550e6 | − | 1.14930e7i | −1.15212 | − | 1.99553i | ||||
\(507\) | 1.02550e7 | 1.77181 | ||||||||
\(508\) | −5.08872e6 | −0.874882 | ||||||||
\(509\) | 3.22509e6 | + | 5.58603e6i | 0.551757 | + | 0.955671i | 0.998148 | + | 0.0608332i | \(0.0193758\pi\) |
−0.446391 | + | 0.894838i | \(0.647291\pi\) | |||||||
\(510\) | −2.94320e7 | −5.01065 | ||||||||
\(511\) | −391878. | + | 678753.i | −0.0663894 | + | 0.114990i | ||||
\(512\) | −1.29121e7 | −2.17682 | ||||||||
\(513\) | −6.97032e6 | + | 1.20729e7i | −1.16939 | + | 2.02544i | ||||
\(514\) | −1.75097e6 | + | 3.03277e6i | −0.292329 | + | 0.506329i | ||||
\(515\) | 659909. | − | 1.14300e6i | 0.109639 | − | 0.189901i | ||||
\(516\) | −1.53870e7 | − | 2.66511e7i | −2.54407 | − | 4.40646i | ||||
\(517\) | −471374. | −0.0775602 | ||||||||
\(518\) | 4.40197e6 | + | 2.42217e6i | 0.720813 | + | 0.396625i | ||||
\(519\) | −3.23946e6 | −0.527903 | ||||||||
\(520\) | 149243. | + | 258497.i | 0.0242040 | + | 0.0419225i | ||||
\(521\) | −2.48180e6 | + | 4.29860e6i | −0.400564 | + | 0.693797i | −0.993794 | − | 0.111236i | \(-0.964519\pi\) |
0.593230 | + | 0.805033i | \(0.297852\pi\) | |||||||
\(522\) | 796814. | − | 1.38012e6i | 0.127991 | − | 0.221687i | ||||
\(523\) | 2.48257e6 | − | 4.29994e6i | 0.396869 | − | 0.687398i | −0.596469 | − | 0.802636i | \(-0.703430\pi\) |
0.993338 | + | 0.115239i | \(0.0367633\pi\) | |||||||
\(524\) | −7.50112e6 | −1.19343 | ||||||||
\(525\) | 1.18515e6 | − | 2.05274e6i | 0.187661 | − | 0.325039i | ||||
\(526\) | −241605. | −0.0380752 | ||||||||
\(527\) | 2.09141e6 | + | 3.62243e6i | 0.328029 | + | 0.568163i | ||||
\(528\) | 3.61182e7 | 5.63821 | ||||||||
\(529\) | −2.15484e6 | −0.334792 | ||||||||
\(530\) | 5.71226e6 | + | 9.89392e6i | 0.883320 | + | 1.52996i | ||||
\(531\) | −8.79077e6 | + | 1.52261e7i | −1.35298 | + | 2.34343i | ||||
\(532\) | −7.90154e6 | −1.21041 | ||||||||
\(533\) | −81055.5 | − | 140392.i | −0.0123585 | − | 0.0214055i | ||||
\(534\) | 4.11055e6 | + | 7.11969e6i | 0.623803 | + | 1.08046i | ||||
\(535\) | −5.69342e6 | − | 9.86129e6i | −0.859980 | − | 1.48953i | ||||
\(536\) | 7.04172e6 | − | 1.21966e7i | 1.05868 | − | 1.83370i | ||||
\(537\) | 989129. | − | 1.71322e6i | 0.148019 | − | 0.256376i | ||||
\(538\) | 1.40977e6 | + | 2.44180e6i | 0.209988 | + | 0.363709i | ||||
\(539\) | −4.16392e6 | − | 7.21212e6i | −0.617348 | − | 1.06928i | ||||
\(540\) | 1.92381e7 | + | 3.33214e7i | 2.83909 | + | 4.91744i | ||||
\(541\) | −2.86146e6 | −0.420334 | −0.210167 | − | 0.977665i | \(-0.567401\pi\) | ||||
−0.210167 | + | 0.977665i | \(0.567401\pi\) | |||||||
\(542\) | 2.22681e6 | − | 3.85695e6i | 0.325600 | − | 0.563956i | ||||
\(543\) | −7.35157e6 | − | 1.27333e7i | −1.06999 | − | 1.85328i | ||||
\(544\) | 1.18181e7 | 1.71218 | ||||||||
\(545\) | 1.25253e7 | 1.80633 | ||||||||
\(546\) | −84587.2 | − | 146509.i | −0.0121429 | − | 0.0210321i | ||||
\(547\) | 5.10835e6 | 0.729982 | 0.364991 | − | 0.931011i | \(-0.381072\pi\) | ||||
0.364991 | + | 0.931011i | \(0.381072\pi\) | |||||||
\(548\) | 4.49749e6 | − | 7.78989e6i | 0.639763 | − | 1.10810i | ||||
\(549\) | 1.25676e6 | 0.177959 | ||||||||
\(550\) | 4.69782e6 | − | 8.13686e6i | 0.662201 | − | 1.14697i | ||||
\(551\) | −270533. | + | 468578.i | −0.0379614 | + | 0.0657510i | ||||
\(552\) | −1.24083e7 | + | 2.14918e7i | −1.73327 | + | 3.00211i | ||||
\(553\) | −921641. | − | 1.59633e6i | −0.128159 | − | 0.221978i | ||||
\(554\) | −2.32372e7 | −3.21669 | ||||||||
\(555\) | 320538. | + | 1.55832e7i | 0.0441720 | + | 2.14746i | ||||
\(556\) | −2.47690e6 | −0.339799 | ||||||||
\(557\) | 1.95324e6 | + | 3.38310e6i | 0.266758 | + | 0.462038i | 0.968023 | − | 0.250863i | \(-0.0807144\pi\) |
−0.701265 | + | 0.712901i | \(0.747381\pi\) | |||||||
\(558\) | 7.34456e6 | − | 1.27212e7i | 0.998574 | − | 1.72958i | ||||
\(559\) | −76241.7 | + | 132054.i | −0.0103196 | + | 0.0178741i | ||||
\(560\) | −4.16611e6 | + | 7.21591e6i | −0.561384 | + | 0.972346i | ||||
\(561\) | 2.62514e7 | 3.52164 | ||||||||
\(562\) | 9.50580e6 | − | 1.64645e7i | 1.26954 | − | 2.19892i | ||||
\(563\) | −9.99075e6 | −1.32839 | −0.664197 | − | 0.747557i | \(-0.731227\pi\) | ||||
−0.664197 | + | 0.747557i | \(0.731227\pi\) | |||||||
\(564\) | 775431. | + | 1.34309e6i | 0.102647 | + | 0.177790i | ||||
\(565\) | 1.87496e6 | 0.247099 | ||||||||
\(566\) | −7.39146e6 | −0.969816 | ||||||||
\(567\) | −2.49519e6 | − | 4.32179e6i | −0.325946 | − | 0.564555i | ||||
\(568\) | 2.87740e6 | − | 4.98381e6i | 0.374222 | − | 0.648172i | ||||
\(569\) | −3.17236e6 | −0.410773 | −0.205386 | − | 0.978681i | \(-0.565845\pi\) | ||||
−0.205386 | + | 0.978681i | \(0.565845\pi\) | |||||||
\(570\) | −1.75461e7 | − | 3.03907e7i | −2.26200 | − | 3.91790i | ||||
\(571\) | −1.42508e6 | − | 2.46831e6i | −0.182915 | − | 0.316817i | 0.759957 | − | 0.649973i | \(-0.225220\pi\) |
−0.942872 | + | 0.333156i | \(0.891886\pi\) | |||||||
\(572\) | −234205. | − | 405655.i | −0.0299300 | − | 0.0518403i | ||||
\(573\) | −1.29204e7 | + | 2.23787e7i | −1.64395 | + | 2.84740i | ||||
\(574\) | 4.81883e6 | − | 8.34646e6i | 0.610466 | − | 1.05736i | ||||
\(575\) | 1.51562e6 | + | 2.62512e6i | 0.191170 | + | 0.331116i | ||||
\(576\) | −3.27021e6 | − | 5.66417e6i | −0.410695 | − | 0.711345i | ||||
\(577\) | 2.25629e6 | + | 3.90800e6i | 0.282134 | + | 0.488670i | 0.971910 | − | 0.235353i | \(-0.0756245\pi\) |
−0.689776 | + | 0.724022i | \(0.742291\pi\) | |||||||
\(578\) | 9.37246e6 | 1.16690 | ||||||||
\(579\) | −6.69212e6 | + | 1.15911e7i | −0.829597 | + | 1.43690i | ||||
\(580\) | 746675. | + | 1.29328e6i | 0.0921640 | + | 0.159633i | ||||
\(581\) | 3.11981e6 | 0.383432 | ||||||||
\(582\) | −9.38082e6 | −1.14798 | ||||||||
\(583\) | −5.09496e6 | − | 8.82472e6i | −0.620825 | − | 1.07530i | ||||
\(584\) | 5.80956e6 | 0.704873 | ||||||||
\(585\) | 178864. | − | 309802.i | 0.0216090 | − | 0.0374279i | ||||
\(586\) | 2.88579e7 | 3.47153 | ||||||||
\(587\) | 7.75988e6 | − | 1.34405e7i | 0.929522 | − | 1.60998i | 0.145399 | − | 0.989373i | \(-0.453554\pi\) |
0.784123 | − | 0.620605i | \(-0.213113\pi\) | |||||||
\(588\) | −1.36997e7 | + | 2.37285e7i | −1.63406 | + | 2.83027i | ||||
\(589\) | −2.49362e6 | + | 4.31907e6i | −0.296170 | + | 0.512982i | ||||
\(590\) | −1.17932e7 | − | 2.04264e7i | −1.39477 | − | 2.41581i | ||||
\(591\) | 1.84864e7 | 2.17712 | ||||||||
\(592\) | −359625. | − | 1.74834e7i | −0.0421741 | − | 2.05033i | ||||
\(593\) | 9.61371e6 | 1.12268 | 0.561338 | − | 0.827587i | \(-0.310287\pi\) | ||||
0.561338 | + | 0.827587i | \(0.310287\pi\) | |||||||
\(594\) | −2.45656e7 | − | 4.25488e7i | −2.85667 | − | 4.94790i | ||||
\(595\) | −3.02800e6 | + | 5.24466e6i | −0.350642 | + | 0.607330i | ||||
\(596\) | −1.86270e7 | + | 3.22629e7i | −2.14797 | + | 3.72039i | ||||
\(597\) | −6.99684e6 | + | 1.21189e7i | −0.803463 | + | 1.39164i | ||||
\(598\) | 216347. | 0.0247399 | ||||||||
\(599\) | 4.37141e6 | − | 7.57151e6i | 0.497800 | − | 0.862214i | −0.502197 | − | 0.864753i | \(-0.667475\pi\) |
0.999997 | + | 0.00253877i | \(0.000808116\pi\) | |||||||
\(600\) | −1.75697e7 | −1.99245 | ||||||||
\(601\) | 1.65794e6 | + | 2.87164e6i | 0.187233 | + | 0.324298i | 0.944327 | − | 0.329009i | \(-0.106715\pi\) |
−0.757094 | + | 0.653306i | \(0.773381\pi\) | |||||||
\(602\) | −9.06529e6 | −1.01951 | ||||||||
\(603\) | −1.68786e7 | −1.89036 | ||||||||
\(604\) | 1.05930e7 | + | 1.83477e7i | 1.18149 | + | 2.04639i | ||||
\(605\) | −7.67298e6 | + | 1.32900e7i | −0.852267 | + | 1.47617i | ||||
\(606\) | 3.03573e7 | 3.35801 | ||||||||
\(607\) | −7.99468e6 | − | 1.38472e7i | −0.880703 | − | 1.52542i | −0.850561 | − | 0.525876i | \(-0.823738\pi\) |
−0.0301414 | − | 0.999546i | \(-0.509596\pi\) | |||||||
\(608\) | 7.04545e6 | + | 1.22031e7i | 0.772947 | + | 1.33878i | ||||
\(609\) | −240531. | − | 416613.i | −0.0262802 | − | 0.0455186i | ||||
\(610\) | −842997. | + | 1.46011e6i | −0.0917279 | + | 0.158877i | ||||
\(611\) | 3842.22 | − | 6654.91i | 0.000416369 | − | 0.000721173i | ||||
\(612\) | −2.94362e7 | − | 5.09850e7i | −3.17690 | − | 5.50255i | ||||
\(613\) | 1.17552e6 | + | 2.03606e6i | 0.126351 | + | 0.218846i | 0.922260 | − | 0.386570i | \(-0.126340\pi\) |
−0.795909 | + | 0.605416i | \(0.793007\pi\) | |||||||
\(614\) | −1.59239e6 | − | 2.75809e6i | −0.170462 | − | 0.295249i | ||||
\(615\) | 2.98978e7 | 3.18751 | ||||||||
\(616\) | 7.91384e6 | − | 1.37072e7i | 0.840302 | − | 1.45545i | ||||
\(617\) | −5.22671e6 | − | 9.05293e6i | −0.552733 | − | 0.957362i | −0.998076 | − | 0.0620018i | \(-0.980252\pi\) |
0.445343 | − | 0.895360i | \(-0.353082\pi\) | |||||||
\(618\) | 5.54480e6 | 0.584002 | ||||||||
\(619\) | 1.64855e6 | 0.172932 | 0.0864658 | − | 0.996255i | \(-0.472443\pi\) | ||||
0.0864658 | + | 0.996255i | \(0.472443\pi\) | |||||||
\(620\) | 6.88241e6 | + | 1.19207e7i | 0.719054 | + | 1.24544i | ||||
\(621\) | 1.58507e7 | 1.64938 | ||||||||
\(622\) | −8.30502e6 | + | 1.43847e7i | −0.860726 | + | 1.49082i | ||||
\(623\) | 1.69160e6 | 0.174613 | ||||||||
\(624\) | −294403. | + | 509921.i | −0.0302678 | + | 0.0524254i | ||||
\(625\) | 6.09876e6 | − | 1.05634e7i | 0.624513 | − | 1.08169i | ||||
\(626\) | −1.58107e7 | + | 2.73850e7i | −1.61256 | + | 2.79303i | ||||
\(627\) | 1.56500e7 | + | 2.71065e7i | 1.58981 | + | 2.75362i | ||||
\(628\) | 3.08445e6 | 0.312089 | ||||||||
\(629\) | −261382. | − | 1.27073e7i | −0.0263420 | − | 1.28064i | ||||
\(630\) | 2.12673e7 | 2.13482 | ||||||||
\(631\) | −1.90948e6 | − | 3.30732e6i | −0.190916 | − | 0.330676i | 0.754638 | − | 0.656141i | \(-0.227812\pi\) |
−0.945554 | + | 0.325465i | \(0.894479\pi\) | |||||||
\(632\) | −6.83162e6 | + | 1.18327e7i | −0.680348 | + | 1.17840i | ||||
\(633\) | 1.13594e7 | − | 1.96751e7i | 1.12680 | − | 1.95167i | ||||
\(634\) | −4.86592e6 | + | 8.42802e6i | −0.480775 | + | 0.832727i | ||||
\(635\) | −4.65022e6 | −0.457657 | ||||||||
\(636\) | −1.67629e7 | + | 2.90341e7i | −1.64326 | + | 2.84621i | ||||
\(637\) | 135762. | 0.0132565 | ||||||||
\(638\) | −953443. | − | 1.65141e6i | −0.0927349 | − | 0.160622i | ||||
\(639\) | −6.89699e6 | −0.668201 | ||||||||
\(640\) | −8.01225e6 | −0.773222 | ||||||||
\(641\) | −8.57348e6 | − | 1.48497e7i | −0.824161 | − | 1.42749i | −0.902559 | − | 0.430567i | \(-0.858314\pi\) |
0.0783975 | − | 0.996922i | \(-0.475020\pi\) | |||||||
\(642\) | 2.39191e7 | − | 4.14291e7i | 2.29038 | − | 3.96705i | ||||
\(643\) | −629612. | −0.0600545 | −0.0300273 | − | 0.999549i | \(-0.509559\pi\) | ||||
−0.0300273 | + | 0.999549i | \(0.509559\pi\) | |||||||
\(644\) | 4.49209e6 | + | 7.78053e6i | 0.426810 | + | 0.739256i | ||||
\(645\) | −1.40611e7 | − | 2.43545e7i | −1.33082 | − | 2.30505i | ||||
\(646\) | 1.43079e7 | + | 2.47821e7i | 1.34895 | + | 2.33645i | ||||
\(647\) | 9.33797e6 | − | 1.61738e7i | 0.876984 | − | 1.51898i | 0.0223495 | − | 0.999750i | \(-0.492885\pi\) |
0.854634 | − | 0.519230i | \(-0.173781\pi\) | |||||||
\(648\) | −1.84955e7 | + | 3.20351e7i | −1.73033 | + | 2.99701i | ||||
\(649\) | 1.05188e7 | + | 1.82190e7i | 0.980287 | + | 1.69791i | ||||
\(650\) | 76584.8 | + | 132649.i | 0.00710983 | + | 0.0123146i | ||||
\(651\) | −2.21708e6 | − | 3.84009e6i | −0.205035 | − | 0.355131i | ||||
\(652\) | −2.76950e7 | −2.55142 | ||||||||
\(653\) | −6.19483e6 | + | 1.07298e7i | −0.568521 | + | 0.984707i | 0.428191 | + | 0.903688i | \(0.359151\pi\) |
−0.996713 | + | 0.0810193i | \(0.974182\pi\) | |||||||
\(654\) | 2.63105e7 | + | 4.55712e7i | 2.40539 | + | 4.16625i | ||||
\(655\) | −6.85474e6 | −0.624292 | ||||||||
\(656\) | −3.35436e7 | −3.04334 | ||||||||
\(657\) | −3.48130e6 | − | 6.02979e6i | −0.314650 | − | 0.544991i | ||||
\(658\) | 456847. | 0.0411345 | ||||||||
\(659\) | −8.99670e6 | + | 1.55827e7i | −0.806993 | + | 1.39775i | 0.107945 | + | 0.994157i | \(0.465573\pi\) |
−0.914938 | + | 0.403595i | \(0.867760\pi\) | |||||||
\(660\) | 8.63880e7 | 7.71958 | ||||||||
\(661\) | 5.90741e6 | − | 1.02319e7i | 0.525889 | − | 0.910866i | −0.473657 | − | 0.880710i | \(-0.657066\pi\) |
0.999545 | − | 0.0301561i | \(-0.00960044\pi\) | |||||||
\(662\) | 672402. | − | 1.16463e6i | 0.0596326 | − | 0.103287i | ||||
\(663\) | −213978. | + | 370620.i | −0.0189054 | + | 0.0327450i | ||||
\(664\) | −1.15627e7 | − | 2.00272e7i | −1.01775 | − | 1.76279i | ||||
\(665\) | −7.22067e6 | −0.633174 | ||||||||
\(666\) | −3.81876e7 | + | 2.31075e7i | −3.33608 | + | 2.01868i | ||||
\(667\) | 615202. | 0.0535431 | ||||||||
\(668\) | 5.83359e6 | + | 1.01041e7i | 0.505818 | + | 0.876103i | ||||
\(669\) | −1.92455e7 | + | 3.33342e7i | −1.66251 | + | 2.87955i | ||||
\(670\) | 1.13217e7 | − | 1.96098e7i | 0.974374 | − | 1.68766i | ||||
\(671\) | 751898. | − | 1.30233e6i | 0.0644692 | − | 0.111664i | ||||
\(672\) | −1.25282e7 | −1.07020 | ||||||||
\(673\) | 2.11460e6 | − | 3.66260e6i | 0.179966 | − | 0.311711i | −0.761902 | − | 0.647692i | \(-0.775734\pi\) |
0.941869 | + | 0.335981i | \(0.109068\pi\) | |||||||
\(674\) | 2.66284e7 | 2.25785 | ||||||||
\(675\) | 5.61102e6 | + | 9.71857e6i | 0.474004 | + | 0.821000i | ||||
\(676\) | −2.75191e7 | −2.31616 | ||||||||
\(677\) | 4.96316e6 | 0.416185 | 0.208092 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208092 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(678\) | 3.93852e6 | + | 6.82172e6i | 0.329048 | + | 0.569927i | ||||
\(679\) | −965113. | + | 1.67162e6i | −0.0803348 | + | 0.139144i | ||||
\(680\) | 4.48899e7 | 3.72286 | ||||||||
\(681\) | −1.66092e7 | − | 2.87680e7i | −1.37240 | − | 2.37707i | ||||
\(682\) | −8.78828e6 | − | 1.52217e7i | −0.723507 | − | 1.25315i | ||||
\(683\) | 477051. | + | 826276.i | 0.0391303 | + | 0.0677756i | 0.884927 | − | 0.465729i | \(-0.154208\pi\) |
−0.845797 | + | 0.533505i | \(0.820875\pi\) | |||||||
\(684\) | 3.50972e7 | − | 6.07902e7i | 2.86835 | − | 4.96813i | ||||
\(685\) | 4.10994e6 | − | 7.11863e6i | 0.334664 | − | 0.579656i | ||||
\(686\) | 9.10594e6 | + | 1.57719e7i | 0.738779 | + | 1.27960i | ||||
\(687\) | 1.07209e7 | + | 1.85692e7i | 0.866643 | + | 1.50107i | ||||
\(688\) | 1.57757e7 | + | 2.73244e7i | 1.27063 | + | 2.20079i | ||||
\(689\) | 166118. | 0.0133312 | ||||||||
\(690\) | −1.99502e7 | + | 3.45547e7i | −1.59523 | + | 2.76303i | ||||
\(691\) | −5.87931e6 | − | 1.01833e7i | −0.468416 | − | 0.811319i | 0.530933 | − | 0.847414i | \(-0.321842\pi\) |
−0.999348 | + | 0.0360944i | \(0.988508\pi\) | |||||||
\(692\) | 8.69302e6 | 0.690089 | ||||||||
\(693\) | −1.89691e7 | −1.50042 | ||||||||
\(694\) | −1.17920e6 | − | 2.04243e6i | −0.0929367 | − | 0.160971i | ||||
\(695\) | −2.26346e6 | −0.177751 | ||||||||
\(696\) | −1.78293e6 | + | 3.08812e6i | −0.139512 | + | 0.241641i | ||||
\(697\) | −2.43801e7 | −1.90088 | ||||||||
\(698\) | −1.17212e7 | + | 2.03017e7i | −0.910610 | + | 1.57722i | ||||
\(699\) | 1.19564e7 | − | 2.07091e7i | 0.925565 | − | 1.60313i | ||||
\(700\) | −3.18032e6 | + | 5.50848e6i | −0.245316 | + | 0.424900i | ||||
\(701\) | −6.71611e6 | − | 1.16326e7i | −0.516205 | − | 0.894094i | −0.999823 | − | 0.0188145i | \(-0.994011\pi\) |
0.483618 | − | 0.875279i | \(-0.339323\pi\) | |||||||
\(702\) | 800946. | 0.0613423 | ||||||||
\(703\) | 1.29654e7 | − | 7.84544e6i | 0.989459 | − | 0.598727i | ||||
\(704\) | −7.82607e6 | −0.595131 | ||||||||
\(705\) | 708612. | + | 1.22735e6i | 0.0536952 | + | 0.0930029i | ||||
\(706\) | 1.21653e7 | − | 2.10710e7i | 0.918569 | − | 1.59101i | ||||
\(707\) | 3.12320e6 | − | 5.40955e6i | 0.234991 | − | 0.407017i | ||||
\(708\) | 3.46077e7 | − | 5.99423e7i | 2.59472 | − | 4.49418i | ||||
\(709\) | 1.65823e7 | 1.23888 | 0.619438 | − | 0.785045i | \(-0.287360\pi\) | ||||
0.619438 | + | 0.785045i | \(0.287360\pi\) | |||||||
\(710\) | 4.62631e6 | − | 8.01300e6i | 0.344420 | − | 0.596554i | ||||
\(711\) | 1.63750e7 | 1.21481 | ||||||||
\(712\) | −6.26945e6 | − | 1.08590e7i | −0.463478 | − | 0.802768i | ||||
\(713\) | 5.67057e6 | 0.417737 | ||||||||
\(714\) | −2.54424e7 | −1.86772 | ||||||||
\(715\) | −214024. | − | 370700.i | −0.0156566 | − | 0.0271180i | ||||
\(716\) | −2.65430e6 | + | 4.59739e6i | −0.193494 | + | 0.335142i | ||||
\(717\) | −2.98492e7 | −2.16838 | ||||||||
\(718\) | −1.37766e7 | − | 2.38618e7i | −0.997314 | − | 1.72740i | ||||
\(719\) | 4.32789e6 | + | 7.49613e6i | 0.312215 | + | 0.540773i | 0.978842 | − | 0.204619i | \(-0.0655956\pi\) |
−0.666626 | + | 0.745392i | \(0.732262\pi\) | |||||||
\(720\) | −3.70102e7 | − | 6.41035e7i | −2.66066 | − | 4.60840i | ||||
\(721\) | 570457. | − | 988060.i | 0.0408681 | − | 0.0707856i | ||||
\(722\) | −4.30479e6 | + | 7.45611e6i | −0.307333 | + | 0.532316i | ||||
\(723\) | −1.41594e7 | − | 2.45249e7i | −1.00740 | − | 1.74486i | ||||
\(724\) | 1.97278e7 | + | 3.41695e7i | 1.39872 | + | 2.42266i | ||||
\(725\) | 217776. | + | 377199.i | 0.0153874 | + | 0.0266518i | ||||
\(726\) | −6.44712e7 | −4.53967 | ||||||||
\(727\) | 1.80950e6 | − | 3.13415e6i | 0.126976 | − | 0.219930i | −0.795527 | − | 0.605918i | \(-0.792806\pi\) |
0.922504 | + | 0.385988i | \(0.126139\pi\) | |||||||
\(728\) | 129013. | + | 223457.i | 0.00902205 | + | 0.0156266i | ||||
\(729\) | −7.09507e6 | −0.494468 | ||||||||
\(730\) | 9.34065e6 | 0.648739 | ||||||||
\(731\) | 1.14661e7 | + | 1.98599e7i | 0.793638 | + | 1.37462i | ||||
\(732\) | −4.94762e6 | −0.341286 | ||||||||
\(733\) | −9.69365e6 | + | 1.67899e7i | −0.666389 | + | 1.15422i | 0.312518 | + | 0.949912i | \(0.398827\pi\) |
−0.978907 | + | 0.204307i | \(0.934506\pi\) | |||||||
\(734\) | −4.20840e7 | −2.88321 | ||||||||
\(735\) | −1.25192e7 | + | 2.16838e7i | −0.854785 | + | 1.48053i | ||||
\(736\) | 8.01079e6 | − | 1.38751e7i | 0.545106 | − | 0.944151i | ||||
\(737\) | −1.00982e7 | + | 1.74906e7i | −0.684820 | + | 1.18614i | ||||
\(738\) | 4.28087e7 | + | 7.41469e7i | 2.89329 | + | 5.01132i | ||||
\(739\) | 1.50944e7 | 1.01673 | 0.508363 | − | 0.861143i | \(-0.330251\pi\) | ||||
0.508363 | + | 0.861143i | \(0.330251\pi\) | |||||||
\(740\) | −860156. | − | 4.18172e7i | −0.0577428 | − | 2.80721i | ||||
\(741\) | −510258. | −0.0341385 | ||||||||
\(742\) | 4.93794e6 | + | 8.55277e6i | 0.329258 | + | 0.570292i | ||||
\(743\) | 1.09683e7 | − | 1.89977e7i | 0.728899 | − | 1.26249i | −0.228450 | − | 0.973556i | \(-0.573366\pi\) |
0.957349 | − | 0.288935i | \(-0.0933011\pi\) | |||||||
\(744\) | −1.64340e7 | + | 2.84645e7i | −1.08846 | + | 1.88526i | ||||
\(745\) | −1.70219e7 | + | 2.94828e7i | −1.12362 | + | 1.94616i | ||||
\(746\) | 3.71732e7 | 2.44559 | ||||||||
\(747\) | −1.38576e7 | + | 2.40021e7i | −0.908631 | + | 1.57380i | ||||
\(748\) | −7.04450e7 | −4.60358 | ||||||||
\(749\) | −4.92166e6 | − | 8.52456e6i | −0.320558 | − | 0.555223i | ||||
\(750\) | 3.20112e7 | 2.07801 | ||||||||
\(751\) | 1.46693e7 | 0.949092 | 0.474546 | − | 0.880231i | \(-0.342612\pi\) | ||||
0.474546 | + | 0.880231i | \(0.342612\pi\) | |||||||
\(752\) | −795022. | − | 1.37702e6i | −0.0512666 | − | 0.0887963i | ||||
\(753\) | −580591. | + | 1.00561e6i | −0.0373150 | + | 0.0646314i | ||||
\(754\) | 31086.5 | 0.00199133 | ||||||||
\(755\) | 9.68024e6 | + | 1.67667e7i | 0.618043 | + | 1.07048i | ||||
\(756\) | 1.66304e7 | + | 2.88046e7i | 1.05827 | + | 1.83298i | ||||
\(757\) | 9.97401e6 | + | 1.72755e7i | 0.632601 | + | 1.09570i | 0.987018 | + | 0.160610i | \(0.0513461\pi\) |
−0.354417 | + | 0.935088i | \(0.615321\pi\) | |||||||
\(758\) | −1.70780e7 | + | 2.95799e7i | −1.07960 | + | 1.86992i | ||||
\(759\) | 1.77943e7 | − | 3.08206e7i | 1.12118 | − | 1.94194i | ||||
\(760\) | 2.67614e7 | + | 4.63522e7i | 1.68064 | + | 2.91096i | ||||
\(761\) | 3.03841e6 | + | 5.26268e6i | 0.190189 | + | 0.329417i | 0.945313 | − | 0.326165i | \(-0.105757\pi\) |
−0.755124 | + | 0.655582i | \(0.772423\pi\) | |||||||
\(762\) | −9.76822e6 | − | 1.69191e7i | −0.609436 | − | 1.05557i | ||||
\(763\) | 1.08275e7 | 0.673310 | ||||||||
\(764\) | 3.46715e7 | − | 6.00528e7i | 2.14901 | − | 3.72220i | ||||
\(765\) | −2.68997e7 | − | 4.65916e7i | −1.66186 | − | 2.87842i | ||||
\(766\) | 1.61339e7 | 0.993498 | ||||||||
\(767\) | −342958. | −0.0210500 | ||||||||
\(768\) | −2.23874e7 | − | 3.87760e7i | −1.36962 | − | 2.37225i | ||||
\(769\) | 5.25100e6 | 0.320204 | 0.160102 | − | 0.987100i | \(-0.448818\pi\) | ||||
0.160102 | + | 0.987100i | \(0.448818\pi\) | |||||||
\(770\) | 1.27239e7 | − | 2.20385e7i | 0.773383 | − | 1.33954i | ||||
\(771\) | −9.39108e6 | −0.568957 | ||||||||
\(772\) | 1.79581e7 | − | 3.11044e7i | 1.08447 | − | 1.87836i | ||||
\(773\) | −1.10307e7 | + | 1.91057e7i | −0.663977 | + | 1.15004i | 0.315585 | + | 0.948897i | \(0.397799\pi\) |
−0.979562 | + | 0.201145i | \(0.935534\pi\) | |||||||
\(774\) | 4.02664e7 | − | 6.97434e7i | 2.41596 | − | 4.18457i | ||||
\(775\) | 2.00733e6 | + | 3.47680e6i | 0.120051 | + | 0.207934i | ||||
\(776\) | 1.43077e7 | 0.852935 | ||||||||
\(777\) | 277088. | + | 1.34709e7i | 0.0164651 | + | 0.800465i | ||||
\(778\) | 2.20558e7 | 1.30639 | ||||||||
\(779\) | −1.45344e7 | − | 2.51743e7i | −0.858129 | − | 1.48632i | ||||
\(780\) | −704158. | + | 1.21964e6i | −0.0414413 | + | 0.0717784i | ||||
\(781\) | −4.12636e6 | + | 7.14707e6i | −0.242069 | + | 0.419276i | ||||
\(782\) | 1.62684e7 | − | 2.81776e7i | 0.951320 | − | 1.64774i | ||||
\(783\) | 2.27756e6 | 0.132760 | ||||||||
\(784\) | 1.40458e7 | − | 2.43280e7i | 0.816123 | − | 1.41357i | ||||
\(785\) | 2.81866e6 | 0.163256 | ||||||||
\(786\) | −1.43990e7 | − | 2.49398e7i | −0.831335 | − | 1.43991i | ||||
\(787\) | 1.26169e7 | 0.726135 | 0.363068 | − | 0.931763i | \(-0.381729\pi\) | ||||
0.363068 | + | 0.931763i | \(0.381729\pi\) | |||||||
\(788\) | −4.96078e7 | −2.84600 | ||||||||
\(789\) | −323953. | − | 561103.i | −0.0185263 | − | 0.0320886i | ||||
\(790\) | −1.09839e7 | + | 1.90247e7i | −0.626167 | + | 1.08455i | ||||
\(791\) | 1.62080e6 | 0.0921062 | ||||||||
\(792\) | 7.03037e7 | + | 1.21770e8i | 3.98258 | + | 6.89804i | ||||
\(793\) | 12257.6 | + | 21230.8i | 0.000692185 | + | 0.00119890i | ||||
\(794\) | −1.40007e6 | − | 2.42499e6i | −0.0788132 | − | 0.136508i | ||||
\(795\) | −1.53184e7 | + | 2.65323e7i | −0.859599 | + | 1.48887i | ||||
\(796\) | 1.87759e7 | − | 3.25207e7i | 1.05031 | − | 1.81919i | ||||
\(797\) | 1.33189e7 | + | 2.30691e7i | 0.742717 | + | 1.28642i | 0.951254 | + | 0.308409i | \(0.0997966\pi\) |
−0.208537 | + | 0.978015i | \(0.566870\pi\) | |||||||
\(798\) | −1.51677e7 | − | 2.62712e7i | −0.843163 | − | 1.46040i | ||||
\(799\) | −577837. | − | 1.00084e6i | −0.0320212 | − | 0.0554624i | ||||
\(800\) | 1.13430e7 | 0.626618 | ||||||||
\(801\) | −7.51378e6 | + | 1.30142e7i | −0.413787 | + | 0.716700i | ||||
\(802\) | −1.65220e6 | − | 2.86170e6i | −0.0907042 | − | 0.157104i | ||||
\(803\) | −8.33124e6 | −0.455954 | ||||||||
\(804\) | 6.64482e7 | 3.62529 | ||||||||
\(805\) | 4.10501e6 | + | 7.11008e6i | 0.223267 | + | 0.386710i | ||||
\(806\) | 286537. | 0.0155361 | ||||||||
\(807\) | −3.78055e6 | + | 6.54811e6i | −0.204349 | + | 0.353942i | ||||
\(808\) | −4.63012e7 | −2.49496 | ||||||||
\(809\) | −7.55653e6 | + | 1.30883e7i | −0.405930 | + | 0.703091i | −0.994429 | − | 0.105406i | \(-0.966386\pi\) |
0.588499 | + | 0.808498i | \(0.299719\pi\) | |||||||
\(810\) | −2.97372e7 | + | 5.15063e7i | −1.59253 | + | 2.75834i | ||||
\(811\) | 1.09636e7 | − | 1.89895e7i | 0.585331 | − | 1.01382i | −0.409503 | − | 0.912309i | \(-0.634298\pi\) |
0.994834 | − | 0.101514i | \(-0.0323686\pi\) | |||||||
\(812\) | 645461. | + | 1.11797e6i | 0.0343542 | + | 0.0595032i | ||||
\(813\) | 1.19432e7 | 0.633713 | ||||||||
\(814\) | 1.09835e6 | + | 5.33971e7i | 0.0581004 | + | 2.82460i | ||||
\(815\) | −2.53085e7 | −1.33467 | ||||||||
\(816\) | 4.42757e7 | + | 7.66878e7i | 2.32777 | + | 4.03182i | ||||
\(817\) | −1.36712e7 | + | 2.36792e7i | −0.716558 | + | 1.24111i | ||||
\(818\) | −3.01160e7 | + | 5.21625e7i | −1.57367 | + | 2.72568i | ||||
\(819\) | 154619. | − | 267808.i | 0.00805476 | − | 0.0139513i | ||||
\(820\) | −8.02300e7 | −4.16680 | ||||||||
\(821\) | 1.17227e7 | − | 2.03043e7i | 0.606973 | − | 1.05131i | −0.384763 | − | 0.923015i | \(-0.625717\pi\) |
0.991736 | − | 0.128293i | \(-0.0409499\pi\) | |||||||
\(822\) | 3.45332e7 | 1.78262 | ||||||||
\(823\) | −3.99662e6 | − | 6.92235e6i | −0.205681 | − | 0.356249i | 0.744669 | − | 0.667434i | \(-0.232607\pi\) |
−0.950349 | + | 0.311185i | \(0.899274\pi\) | |||||||
\(824\) | −8.45697e6 | −0.433907 | ||||||||
\(825\) | 2.51960e7 | 1.28884 | ||||||||
\(826\) | −1.01946e7 | − | 1.76576e7i | −0.519901 | − | 0.900495i | ||||
\(827\) | −1.67372e7 | + | 2.89896e7i | −0.850977 | + | 1.47394i | 0.0293504 | + | 0.999569i | \(0.490656\pi\) |
−0.880327 | + | 0.474366i | \(0.842677\pi\) | |||||||
\(828\) | −7.98123e7 | −4.04570 | ||||||||
\(829\) | −3.20542e6 | − | 5.55196e6i | −0.161994 | − | 0.280582i | 0.773590 | − | 0.633687i | \(-0.218459\pi\) |
−0.935584 | + | 0.353105i | \(0.885126\pi\) | |||||||
\(830\) | −1.85906e7 | − | 3.21999e7i | −0.936697 | − | 1.62241i | ||||
\(831\) | −3.11572e7 | − | 5.39659e7i | −1.56515 | − | 2.71092i | ||||
\(832\) | 63791.1 | − | 110489.i | 0.00319486 | − | 0.00553366i | ||||
\(833\) | 1.02087e7 | − | 1.76821e7i | 0.509753 | − | 0.882918i | ||||
\(834\) | −4.75461e6 | − | 8.23523e6i | −0.236701 | − | 0.409978i | ||||
\(835\) | 5.33091e6 | + | 9.23340e6i | 0.264597 | + | 0.458295i | ||||
\(836\) | −4.19963e7 | − | 7.27397e7i | −2.07824 | − | 3.59961i | ||||
\(837\) | 2.09932e7 | 1.03578 | ||||||||
\(838\) | 9.45796e6 | − | 1.63817e7i | 0.465251 | − | 0.805839i | ||||
\(839\) | −1.59594e7 | − | 2.76424e7i | −0.782727 | − | 1.35572i | −0.930347 | − | 0.366679i | \(-0.880495\pi\) |
0.147620 | − | 0.989044i | \(-0.452839\pi\) | |||||||
\(840\) | −4.75872e7 | −2.32698 | ||||||||
\(841\) | −2.04228e7 | −0.995690 | ||||||||
\(842\) | −7.64174e6 | − | 1.32359e7i | −0.371460 | − | 0.643387i | ||||
\(843\) | 5.09829e7 | 2.47090 | ||||||||
\(844\) | −3.04827e7 | + | 5.27976e7i | −1.47298 | + | 2.55128i | ||||
\(845\) | −2.51478e7 | −1.21160 | ||||||||
\(846\) | −2.02923e6 | + | 3.51473e6i | −0.0974778 | + | 0.168837i | ||||
\(847\) | −6.63289e6 | + | 1.14885e7i | −0.317683 | + | 0.550243i | ||||
\(848\) | 1.71864e7 | − | 2.97677e7i | 0.820719 | − | 1.42153i | ||||
\(849\) | −9.91074e6 | − | 1.71659e7i | −0.471886 | − | 0.817330i | ||||
\(850\) | 2.30354e7 | 1.09358 | ||||||||
\(851\) | −1.50962e7 | − | 8.30665e6i | −0.714570 | − | 0.393189i | ||||
\(852\) | 2.71522e7 | 1.28146 | ||||||||
\(853\) | 5.64006e6 | + | 9.76887e6i | 0.265406 | + | 0.459697i | 0.967670 | − | 0.252220i | \(-0.0811606\pi\) |
−0.702264 | + | 0.711917i | \(0.747827\pi\) | |||||||
\(854\) | −728726. | + | 1.26219e6i | −0.0341916 | + | 0.0592216i | ||||
\(855\) | 3.20729e7 | − | 5.55519e7i | 1.50045 | − | 2.59886i | ||||
\(856\) | −3.64816e7 | + | 6.31879e7i | −1.70172 | + | 2.94747i | ||||
\(857\) | 9.31400e6 | 0.433196 | 0.216598 | − | 0.976261i | \(-0.430504\pi\) | ||||
0.216598 | + | 0.976261i | \(0.430504\pi\) | |||||||
\(858\) | 899153. | − | 1.55738e6i | 0.0416980 | − | 0.0722231i | ||||
\(859\) | 3.11166e7 | 1.43883 | 0.719416 | − | 0.694580i | \(-0.244410\pi\) | ||||
0.719416 | + | 0.694580i | \(0.244410\pi\) | |||||||
\(860\) | 3.77326e7 | + | 6.53548e7i | 1.73969 | + | 3.01322i | ||||
\(861\) | 2.58451e7 | 1.18815 | ||||||||
\(862\) | 5.54302e7 | 2.54084 | ||||||||
\(863\) | 5.90254e6 | + | 1.02235e7i | 0.269782 | + | 0.467275i | 0.968805 | − | 0.247823i | \(-0.0797152\pi\) |
−0.699024 | + | 0.715098i | \(0.746382\pi\) | |||||||
\(864\) | 2.96571e7 | − | 5.13675e7i | 1.35159 | − | 2.34102i | ||||
\(865\) | 7.94394e6 | 0.360990 | ||||||||
\(866\) | 3.29224e7 | + | 5.70233e7i | 1.49175 | + | 2.58379i | ||||
\(867\) | 1.25669e7 | + | 2.17666e7i | 0.567782 | + | 0.983428i | ||||
\(868\) | 5.94948e6 | + | 1.03048e7i | 0.268028 | + | 0.464237i | ||||
\(869\) | 9.79694e6 | − | 1.69688e7i | 0.440090 | − | 0.762258i | ||||
\(870\) | −2.86661e6 | + | 4.96511e6i | −0.128401 | + | 0.222398i | ||||
\(871\) | −164623. | − | 285136.i | −0.00735269 | − | 0.0127352i | ||||
\(872\) | −4.01290e7 | − | 6.95055e7i | −1.78718 | − | 3.09548i | ||||
\(873\) | −8.57371e6 | − | 1.48501e7i | −0.380744 | − | 0.659468i | ||||
\(874\) | 3.87940e7 | 1.71785 | ||||||||
\(875\) | 3.29336e6 | − | 5.70426e6i | 0.145418 | − | 0.251872i | ||||
\(876\) | 1.37053e7 | + | 2.37382e7i | 0.603431 | + | 1.04517i | ||||
\(877\) | 1.64532e7 | 0.722358 | 0.361179 | − | 0.932497i | \(-0.382374\pi\) | ||||
0.361179 | + | 0.932497i | \(0.382374\pi\) | |||||||
\(878\) | −2.30985e7 | −1.01123 | ||||||||
\(879\) | 3.86938e7 | + | 6.70195e7i | 1.68915 | + | 2.92570i | ||||
\(880\) | −8.85705e7 | −3.85552 | ||||||||
\(881\) | 7.06547e6 | − | 1.22378e7i | 0.306691 | − | 0.531205i | −0.670945 | − | 0.741507i | \(-0.734111\pi\) |
0.977636 | + | 0.210302i | \(0.0674447\pi\) | |||||||
\(882\) | −7.17016e7 | −3.10354 | ||||||||
\(883\) | −1.34256e7 | + | 2.32539e7i | −0.579472 | + | 1.00368i | 0.416068 | + | 0.909334i | \(0.363408\pi\) |
−0.995540 | + | 0.0943418i | \(0.969925\pi\) | |||||||
\(884\) | 574204. | − | 994551.i | 0.0247136 | − | 0.0428052i | ||||
\(885\) | 3.16256e7 | − | 5.47771e7i | 1.35731 | − | 2.35093i | ||||
\(886\) | 2.99586e7 | + | 5.18899e7i | 1.28215 | + | 2.22074i | ||||
\(887\) | 6.60614e6 | 0.281928 | 0.140964 | − | 0.990015i | \(-0.454980\pi\) | ||||
0.140964 | + | 0.990015i | \(0.454980\pi\) | |||||||
\(888\) | 8.54475e7 | − | 5.17048e7i | 3.63636 | − | 2.20038i | ||||
\(889\) | −4.01987e6 | −0.170592 | ||||||||
\(890\) | −1.00801e7 | − | 1.74592e7i | −0.426568 | − | 0.738838i | ||||
\(891\) | 2.65236e7 | − | 4.59402e7i | 1.11928 | − | 1.93865i | ||||
\(892\) | 5.16448e7 | − | 8.94514e7i | 2.17327 | − | 3.76422i | ||||
\(893\) | 688963. | − | 1.19332e6i | 0.0289113 | − | 0.0500758i | ||||
\(894\) | −1.43024e8 | −5.98503 | ||||||||
\(895\) | −2.42558e6 | + | 4.20123e6i | −0.101218 | + | 0.175315i | ||||
\(896\) | −6.92616e6 | −0.288219 | ||||||||
\(897\) | 290086. | + | 502443.i | 0.0120377 | + | 0.0208500i | ||||
\(898\) | −4.98087e7 | −2.06117 | ||||||||
\(899\) | 814794. | 0.0336239 | ||||||||
\(900\) | −2.82528e7 | − | 4.89354e7i | −1.16267 | − | 2.01380i | ||||
\(901\) | 1.24914e7 | − | 2.16357e7i | 0.512623 | − | 0.887889i | ||||
\(902\) | 1.02447e8 | 4.19261 | ||||||||
\(903\) | −1.21551e7 | − | 2.10532e7i | −0.496064 | − | 0.859209i | ||||
\(904\) | −6.00706e6 | − | 1.04045e7i | −0.244479 | − | 0.423450i | ||||
\(905\) | 1.80278e7 | + | 3.12251e7i | 0.731681 | + | 1.26731i | ||||
\(906\) | −4.06685e7 | + | 7.04398e7i | −1.64603 | + | 2.85100i | ||||
\(907\) | −1.27218e7 | + | 2.20347e7i | −0.513486 | + | 0.889384i | 0.486391 | + | 0.873741i | \(0.338313\pi\) |
−0.999878 | + | 0.0156431i | \(0.995020\pi\) | |||||||
\(908\) | 4.45704e7 | + | 7.71983e7i | 1.79404 | + | 3.10737i | ||||
\(909\) | 2.77454e7 | + | 4.80565e7i | 1.11373 | + | 1.92904i | ||||
\(910\) | 207428. | + | 359276.i | 0.00830356 | + | 0.0143822i | ||||
\(911\) | −3.35547e7 | −1.33955 | −0.669773 | − | 0.742566i | \(-0.733609\pi\) | ||||
−0.669773 | + | 0.742566i | \(0.733609\pi\) | |||||||
\(912\) | −5.27906e7 | + | 9.14360e7i | −2.10169 | + | 3.64024i | ||||
\(913\) | 1.65816e7 | + | 2.87202e7i | 0.658340 | + | 1.14028i | ||||
\(914\) | 1.42650e7 | 0.564814 | ||||||||
\(915\) | −4.52129e6 | −0.178529 | ||||||||
\(916\) | −2.87693e7 | − | 4.98300e7i | −1.13290 | − | 1.96224i | ||||
\(917\) | −5.92556e6 | −0.232705 | ||||||||
\(918\) | 6.02277e7 | − | 1.04317e8i | 2.35879 | − | 4.08555i | ||||
\(919\) | 1.85292e6 | 0.0723715 | 0.0361857 | − | 0.999345i | \(-0.488479\pi\) | ||||
0.0361857 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(920\) | 3.04282e7 | − | 5.27032e7i | 1.18524 | − | 2.05290i | ||||
\(921\) | 4.27026e6 | − | 7.39631e6i | 0.165884 | − | 0.287320i | ||||
\(922\) | 1.74359e7 | − | 3.01998e7i | 0.675485 | − | 1.16997i | ||||
\(923\) | −67268.8 | − | 116513.i | −0.00259902 | − | 0.00450164i | ||||
\(924\) | 7.46779e7 | 2.87748 | ||||||||
\(925\) | −250874. | − | 1.21964e7i | −0.00964054 | − | 0.468683i | ||||
\(926\) | 7.59232e6 | 0.290969 | ||||||||
\(927\) | 5.06773e6 | + | 8.77757e6i | 0.193693 | + | 0.335486i | ||||
\(928\) | 1.15106e6 | − | 1.99369e6i | 0.0438759 | − | 0.0759954i | ||||
\(929\) | 6.43982e6 | − | 1.11541e7i | 0.244813 | − | 0.424029i | −0.717266 | − | 0.696800i | \(-0.754607\pi\) |
0.962079 | + | 0.272771i | \(0.0879401\pi\) | |||||||
\(930\) | −2.64227e7 | + | 4.57655e7i | −1.00177 | + | 1.73512i | ||||
\(931\) | 2.43440e7 | 0.920489 | ||||||||
\(932\) | −3.20847e7 | + | 5.55723e7i | −1.20992 | + | 2.09565i | ||||
\(933\) | −4.45427e7 | −1.67522 | ||||||||
\(934\) | −3.59107e7 | − | 6.21991e7i | −1.34697 | − | 2.33301i | ||||
\(935\) | −6.43747e7 | −2.40817 | ||||||||
\(936\) | −2.29221e6 | −0.0855194 | ||||||||
\(937\) | −5.82182e6 | − | 1.00837e7i | −0.216625 | − | 0.375206i | 0.737149 | − | 0.675731i | \(-0.236172\pi\) |
−0.953774 | + | 0.300524i | \(0.902838\pi\) | |||||||
\(938\) | 9.78703e6 | − | 1.69516e7i | 0.363198 | − | 0.629078i | ||||
\(939\) | −8.47984e7 | −3.13851 | ||||||||
\(940\) | −1.90154e6 | − | 3.29357e6i | −0.0701919 | − | 0.121576i | ||||
\(941\) | 2.03437e6 | + | 3.52362e6i | 0.0748953 | + | 0.129723i | 0.901041 | − | 0.433734i | \(-0.142804\pi\) |
−0.826145 | + | 0.563457i | \(0.809471\pi\) | |||||||
\(942\) | 5.92086e6 | + | 1.02552e7i | 0.217399 | + | 0.376546i | ||||
\(943\) | −1.65258e7 | + | 2.86236e7i | −0.605179 | + | 1.04820i | ||||
\(944\) | −3.54820e7 | + | 6.14567e7i | −1.29592 | + | 2.24460i | ||||
\(945\) | 1.51973e7 | + | 2.63225e7i | 0.553589 | + | 0.958844i | ||||
\(946\) | −4.81815e7 | − | 8.34528e7i | −1.75046 | − | 3.03189i | ||||
\(947\) | −1.13362e7 | − | 1.96348e7i | −0.410763 | − | 0.711462i | 0.584211 | − | 0.811602i | \(-0.301404\pi\) |
−0.994973 | + | 0.100140i | \(0.968071\pi\) | |||||||
\(948\) | −6.44657e7 | −2.32974 | ||||||||
\(949\) | 67908.8 | − | 117622.i | 0.00244771 | − | 0.00423957i | ||||
\(950\) | 1.37327e7 | + | 2.37858e7i | 0.493683 | + | 0.855084i | ||||
\(951\) | −2.60976e7 | −0.935728 | ||||||||
\(952\) | 3.88049e7 | 1.38770 | ||||||||
\(953\) | −9.24432e6 | − | 1.60116e7i | −0.329718 | − | 0.571089i | 0.652738 | − | 0.757584i | \(-0.273620\pi\) |
−0.982456 | + | 0.186495i | \(0.940287\pi\) | |||||||
\(954\) | −8.77338e7 | −3.12102 | ||||||||
\(955\) | 3.16839e7 | − | 5.48781e7i | 1.12416 | − | 1.94711i | ||||
\(956\) | 8.00996e7 | 2.83456 | ||||||||
\(957\) | 2.55682e6 | − | 4.42855e6i | 0.0902445 | − | 0.156308i | ||||
\(958\) | 1.00835e7 | − | 1.74651e7i | 0.354974 | − | 0.614832i | ||||
\(959\) | 3.55283e6 | − | 6.15368e6i | 0.124746 | − | 0.216067i | ||||
\(960\) | 1.17649e7 | + | 2.03774e7i | 0.412011 | + | 0.713624i | ||||
\(961\) | −2.11189e7 | −0.737670 | ||||||||
\(962\) | −762820. | − | 419739.i | −0.0265757 | − | 0.0146232i | ||||
\(963\) | 8.74444e7 | 3.03855 | ||||||||
\(964\) | 3.79965e7 | + | 6.58119e7i | 1.31690 | + | 2.28093i | ||||
\(965\) | 1.64107e7 | − | 2.84242e7i | 0.567295 | − | 0.982583i | ||||
\(966\) | −1.72459e7 | + | 2.98708e7i | −0.594624 | + | 1.02992i | ||||
\(967\) | 2.09259e6 | − | 3.62447e6i | 0.0719644 | − | 0.124646i | −0.827798 | − | 0.561027i | \(-0.810407\pi\) |
0.899762 | + | 0.436381i | \(0.143740\pi\) | |||||||
\(968\) | 9.83319e7 | 3.37292 | ||||||||
\(969\) | −3.83692e7 | + | 6.64574e7i | −1.31272 | + | 2.27370i | ||||
\(970\) | 2.30040e7 | 0.785009 | ||||||||
\(971\) | 2.15145e7 | + | 3.72641e7i | 0.732289 | + | 1.26836i | 0.955903 | + | 0.293684i | \(0.0948812\pi\) |
−0.223614 | + | 0.974678i | \(0.571785\pi\) | |||||||
\(972\) | −3.65248e7 | −1.24000 | ||||||||
\(973\) | −1.95665e6 | −0.0662567 | ||||||||
\(974\) | 4.56126e7 | + | 7.90034e7i | 1.54059 | + | 2.66838i | ||||
\(975\) | −205376. | + | 355721.i | −0.00691890 | + | 0.0119839i | ||||
\(976\) | 5.07262e6 | 0.170454 | ||||||||
\(977\) | 2.36821e6 | + | 4.10186e6i | 0.0793750 | + | 0.137482i | 0.902980 | − | 0.429682i | \(-0.141374\pi\) |
−0.823605 | + | 0.567163i | \(0.808041\pi\) | |||||||
\(978\) | −5.31629e7 | − | 9.20808e7i | −1.77730 | − | 3.07838i | ||||
\(979\) | 8.99076e6 | + | 1.55724e7i | 0.299805 | + | 0.519278i | ||||
\(980\) | 3.35949e7 | − | 5.81881e7i | 1.11740 | − | 1.93539i | ||||
\(981\) | −4.80936e7 | + | 8.33006e7i | −1.59557 | + | 2.76360i | ||||
\(982\) | −2.81972e7 | − | 4.88389e7i | −0.933097 | − | 1.61617i | ||||
\(983\) | −1.22973e7 | − | 2.12995e7i | −0.405906 | − | 0.703051i | 0.588520 | − | 0.808483i | \(-0.299711\pi\) |
−0.994427 | + | 0.105432i | \(0.966377\pi\) | |||||||
\(984\) | −9.57876e7 | − | 1.65909e8i | −3.15371 | − | 5.46239i | ||||
\(985\) | −4.53331e7 | −1.48876 | ||||||||
\(986\) | 2.33757e6 | − | 4.04879e6i | 0.0765724 | − | 0.132627i | ||||
\(987\) | 612558. | + | 1.06098e6i | 0.0200149 | + | 0.0346669i | ||||
\(988\) | 1.36926e6 | 0.0446267 | ||||||||
\(989\) | 3.10887e7 | 1.01068 | ||||||||
\(990\) | 1.13035e8 | + | 1.95782e8i | 3.66542 | + | 6.34870i | ||||
\(991\) | −9.08498e6 | −0.293860 | −0.146930 | − | 0.989147i | \(-0.546939\pi\) | ||||
−0.146930 | + | 0.989147i | \(0.546939\pi\) | |||||||
\(992\) | 1.06098e7 | − | 1.83766e7i | 0.342315 | − | 0.592907i | ||||
\(993\) | 3.60632e6 | 0.116062 | ||||||||
\(994\) | 3.99920e6 | − | 6.92682e6i | 0.128383 | − | 0.222366i | ||||
\(995\) | 1.71579e7 | − | 2.97184e7i | 0.549424 | − | 0.951630i | ||||
\(996\) | 5.45551e7 | − | 9.44921e7i | 1.74256 | − | 3.01820i | ||||
\(997\) | −4.72014e6 | − | 8.17552e6i | −0.150389 | − | 0.260482i | 0.780981 | − | 0.624554i | \(-0.214719\pi\) |
−0.931371 | + | 0.364073i | \(0.881386\pi\) | |||||||
\(998\) | −1.21034e7 | −0.384664 | ||||||||
\(999\) | −5.58884e7 | − | 3.07524e7i | −1.77177 | − | 0.974910i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 37.6.c.a.26.2 | yes | 30 | |
37.10 | even | 3 | inner | 37.6.c.a.10.2 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.c.a.10.2 | ✓ | 30 | 37.10 | even | 3 | inner | |
37.6.c.a.26.2 | yes | 30 | 1.1 | even | 1 | trivial |