Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.8 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.8 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35784 | −0.416812 | −0.208406 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208406 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(3\) | −4.70904 | − | 8.15629i | −0.302085 | − | 0.523227i | 0.674523 | − | 0.738254i | \(-0.264349\pi\) |
−0.976608 | + | 0.215027i | \(0.931016\pi\) | |||||||
\(4\) | −26.4406 | −0.826268 | ||||||||
\(5\) | 15.5528 | + | 26.9382i | 0.278216 | + | 0.481885i | 0.970942 | − | 0.239317i | \(-0.0769235\pi\) |
−0.692725 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(6\) | 11.1032 | + | 19.2313i | 0.125913 | + | 0.218087i | ||||
\(7\) | −36.1175 | + | 62.5573i | −0.278594 | + | 0.482540i | −0.971036 | − | 0.238935i | \(-0.923202\pi\) |
0.692441 | + | 0.721474i | \(0.256535\pi\) | |||||||
\(8\) | 137.794 | 0.761210 | ||||||||
\(9\) | 77.1499 | − | 133.628i | 0.317489 | − | 0.549908i | ||||
\(10\) | −36.6710 | − | 63.5160i | −0.115964 | − | 0.200855i | ||||
\(11\) | 785.739 | 1.95793 | 0.978963 | − | 0.204037i | \(-0.0654063\pi\) | ||||
0.978963 | + | 0.204037i | \(0.0654063\pi\) | |||||||
\(12\) | 124.510 | + | 215.657i | 0.249603 | + | 0.432325i | ||||
\(13\) | −374.054 | + | 647.881i | −0.613870 | + | 1.06325i | 0.376712 | + | 0.926330i | \(0.377055\pi\) |
−0.990582 | + | 0.136923i | \(0.956279\pi\) | |||||||
\(14\) | 85.1594 | − | 147.500i | 0.116121 | − | 0.201128i | ||||
\(15\) | 146.477 | − | 253.706i | 0.168090 | − | 0.291140i | ||||
\(16\) | 521.202 | 0.508986 | ||||||||
\(17\) | 198.545 | − | 343.889i | 0.166623 | − | 0.288600i | −0.770607 | − | 0.637310i | \(-0.780047\pi\) |
0.937231 | + | 0.348710i | \(0.113380\pi\) | |||||||
\(18\) | −181.907 | + | 315.073i | −0.132333 | + | 0.229208i | ||||
\(19\) | 1247.23 | + | 2160.26i | 0.792614 | + | 1.37285i | 0.924343 | + | 0.381562i | \(0.124614\pi\) |
−0.131729 | + | 0.991286i | \(0.542053\pi\) | |||||||
\(20\) | −411.224 | − | 712.261i | −0.229881 | − | 0.398166i | ||||
\(21\) | 680.315 | 0.336637 | ||||||||
\(22\) | −1852.65 | −0.816087 | ||||||||
\(23\) | 628.566 | + | 1088.71i | 0.247760 | + | 0.429133i | 0.962904 | − | 0.269844i | \(-0.0869722\pi\) |
−0.715144 | + | 0.698977i | \(0.753639\pi\) | |||||||
\(24\) | −648.876 | − | 1123.89i | −0.229950 | − | 0.398285i | ||||
\(25\) | 1078.72 | − | 1868.40i | 0.345191 | − | 0.597889i | ||||
\(26\) | 881.961 | − | 1527.60i | 0.255868 | − | 0.443177i | ||||
\(27\) | −3741.80 | −0.987805 | ||||||||
\(28\) | 954.967 | − | 1654.05i | 0.230194 | − | 0.398707i | ||||
\(29\) | −2011.40 | + | 3483.85i | −0.444123 | + | 0.769244i | −0.997991 | − | 0.0633608i | \(-0.979818\pi\) |
0.553867 | + | 0.832605i | \(0.313151\pi\) | |||||||
\(30\) | −345.370 | + | 598.199i | −0.0700619 | + | 0.121351i | ||||
\(31\) | −3397.41 | − | 5884.48i | −0.634956 | − | 1.09978i | −0.986525 | − | 0.163614i | \(-0.947685\pi\) |
0.351569 | − | 0.936162i | \(-0.385648\pi\) | |||||||
\(32\) | −5638.31 | −0.973362 | ||||||||
\(33\) | −3700.07 | − | 6408.72i | −0.591460 | − | 1.02444i | ||||
\(34\) | −468.137 | + | 810.838i | −0.0694506 | + | 0.120292i | ||||
\(35\) | −2246.91 | −0.310038 | ||||||||
\(36\) | −2039.89 | + | 3533.19i | −0.262331 | + | 0.454371i | ||||
\(37\) | 5808.25 | + | 10060.2i | 0.697495 | + | 1.20810i | 0.969332 | + | 0.245754i | \(0.0790356\pi\) |
−0.271837 | + | 0.962343i | \(0.587631\pi\) | |||||||
\(38\) | −2940.77 | − | 5093.56i | −0.330371 | − | 0.572219i | ||||
\(39\) | 7045.74 | 0.741763 | ||||||||
\(40\) | 2143.07 | + | 3711.91i | 0.211781 | + | 0.366815i | ||||
\(41\) | 18171.5 | 1.68823 | 0.844113 | − | 0.536166i | \(-0.180128\pi\) | ||||
0.844113 | + | 0.536166i | \(0.180128\pi\) | |||||||
\(42\) | −1604.08 | −0.140314 | ||||||||
\(43\) | −11480.7 | − | 3898.98i | −0.946885 | − | 0.321573i | ||||
\(44\) | −20775.4 | −1.61777 | ||||||||
\(45\) | 4799.58 | 0.353323 | ||||||||
\(46\) | −1482.06 | − | 2567.01i | −0.103269 | − | 0.178868i | ||||
\(47\) | 17311.6 | 1.14312 | 0.571560 | − | 0.820560i | \(-0.306338\pi\) | ||||
0.571560 | + | 0.820560i | \(0.306338\pi\) | |||||||
\(48\) | −2454.36 | − | 4251.08i | −0.153757 | − | 0.266315i | ||||
\(49\) | 5794.55 | + | 10036.5i | 0.344770 | + | 0.597160i | ||||
\(50\) | −2543.46 | + | 4405.40i | −0.143880 | + | 0.249207i | ||||
\(51\) | −3739.82 | −0.201338 | ||||||||
\(52\) | 9890.21 | − | 17130.3i | 0.507221 | − | 0.878532i | ||||
\(53\) | 10053.7 | + | 17413.5i | 0.491626 | + | 0.851521i | 0.999954 | − | 0.00964287i | \(-0.00306947\pi\) |
−0.508328 | + | 0.861164i | \(0.669736\pi\) | |||||||
\(54\) | 8822.58 | 0.411729 | ||||||||
\(55\) | 12220.4 | + | 21166.4i | 0.544727 | + | 0.943495i | ||||
\(56\) | −4976.76 | + | 8620.01i | −0.212069 | + | 0.367314i | ||||
\(57\) | 11746.5 | − | 20345.5i | 0.478874 | − | 0.829433i | ||||
\(58\) | 4742.57 | − | 8214.37i | 0.185116 | − | 0.320630i | ||||
\(59\) | −27080.7 | −1.01281 | −0.506407 | − | 0.862294i | \(-0.669027\pi\) | ||||
−0.506407 | + | 0.862294i | \(0.669027\pi\) | |||||||
\(60\) | −3872.94 | + | 6708.13i | −0.138887 | + | 0.240560i | ||||
\(61\) | 23684.1 | − | 41022.1i | 0.814953 | − | 1.41154i | −0.0944089 | − | 0.995534i | \(-0.530096\pi\) |
0.909362 | − | 0.416006i | \(-0.136571\pi\) | |||||||
\(62\) | 8010.56 | + | 13874.7i | 0.264657 | + | 0.458400i | ||||
\(63\) | 5572.92 | + | 9652.58i | 0.176901 | + | 0.306402i | ||||
\(64\) | −3384.21 | −0.103278 | ||||||||
\(65\) | −23270.3 | −0.683154 | ||||||||
\(66\) | 8724.20 | + | 15110.8i | 0.246528 | + | 0.426998i | ||||
\(67\) | 18579.1 | + | 32179.9i | 0.505635 | + | 0.875785i | 0.999979 | + | 0.00651894i | \(0.00207506\pi\) |
−0.494344 | + | 0.869266i | \(0.664592\pi\) | |||||||
\(68\) | −5249.64 | + | 9092.63i | −0.137676 | + | 0.238461i | ||||
\(69\) | 5919.89 | − | 10253.5i | 0.149689 | − | 0.259269i | ||||
\(70\) | 5297.85 | 0.129227 | ||||||||
\(71\) | −25191.9 | + | 43633.6i | −0.593082 | + | 1.02725i | 0.400732 | + | 0.916195i | \(0.368756\pi\) |
−0.993814 | + | 0.111053i | \(0.964578\pi\) | |||||||
\(72\) | 10630.8 | − | 18413.0i | 0.241676 | − | 0.418595i | ||||
\(73\) | 17654.3 | − | 30578.2i | 0.387743 | − | 0.671590i | −0.604403 | − | 0.796679i | \(-0.706588\pi\) |
0.992146 | + | 0.125089i | \(0.0399216\pi\) | |||||||
\(74\) | −13695.0 | − | 23720.4i | −0.290724 | − | 0.503549i | ||||
\(75\) | −20319.0 | −0.417109 | ||||||||
\(76\) | −32977.4 | − | 57118.6i | −0.654911 | − | 1.13434i | ||||
\(77\) | −28378.9 | + | 49153.7i | −0.545467 | + | 0.944777i | ||||
\(78\) | −16612.8 | −0.309176 | ||||||||
\(79\) | 4905.21 | − | 8496.08i | 0.0884281 | − | 0.153162i | −0.818419 | − | 0.574622i | \(-0.805149\pi\) |
0.906847 | + | 0.421460i | \(0.138482\pi\) | |||||||
\(80\) | 8106.13 | + | 14040.2i | 0.141608 | + | 0.245273i | ||||
\(81\) | −1127.14 | − | 1952.26i | −0.0190882 | − | 0.0330618i | ||||
\(82\) | −42845.5 | −0.703672 | ||||||||
\(83\) | −24391.4 | − | 42247.2i | −0.388635 | − | 0.673136i | 0.603631 | − | 0.797264i | \(-0.293720\pi\) |
−0.992266 | + | 0.124128i | \(0.960387\pi\) | |||||||
\(84\) | −17987.9 | −0.278152 | ||||||||
\(85\) | 12351.7 | 0.185429 | ||||||||
\(86\) | 27069.7 | + | 9193.18i | 0.394673 | + | 0.134035i | ||||
\(87\) | 37887.0 | 0.536652 | ||||||||
\(88\) | 108270. | 1.49039 | ||||||||
\(89\) | −36792.6 | − | 63726.6i | −0.492363 | − | 0.852797i | 0.507599 | − | 0.861594i | \(-0.330533\pi\) |
−0.999961 | + | 0.00879659i | \(0.997200\pi\) | |||||||
\(90\) | −11316.7 | −0.147269 | ||||||||
\(91\) | −27019.8 | − | 46799.6i | −0.342041 | − | 0.592433i | ||||
\(92\) | −16619.7 | − | 28786.1i | −0.204716 | − | 0.354579i | ||||
\(93\) | −31997.1 | + | 55420.5i | −0.383621 | + | 0.664451i | ||||
\(94\) | −40818.0 | −0.476466 | ||||||||
\(95\) | −38795.7 | + | 67196.1i | −0.441036 | + | 0.763897i | ||||
\(96\) | 26551.0 | + | 45987.7i | 0.294038 | + | 0.509289i | ||||
\(97\) | −14665.7 | −0.158261 | −0.0791305 | − | 0.996864i | \(-0.525214\pi\) | ||||
−0.0791305 | + | 0.996864i | \(0.525214\pi\) | |||||||
\(98\) | −13662.7 | − | 23664.4i | −0.143704 | − | 0.248903i | ||||
\(99\) | 60619.7 | − | 104996.i | 0.621621 | − | 1.07668i | ||||
\(100\) | −28522.1 | + | 49401.7i | −0.285221 | + | 0.494017i | ||||
\(101\) | −24764.9 | + | 42894.1i | −0.241565 | + | 0.418402i | −0.961160 | − | 0.275991i | \(-0.910994\pi\) |
0.719596 | + | 0.694393i | \(0.244327\pi\) | |||||||
\(102\) | 8817.91 | 0.0839199 | ||||||||
\(103\) | 19879.4 | − | 34432.1i | 0.184633 | − | 0.319794i | −0.758820 | − | 0.651301i | \(-0.774224\pi\) |
0.943453 | + | 0.331507i | \(0.107557\pi\) | |||||||
\(104\) | −51542.3 | + | 89273.9i | −0.467284 | + | 0.809359i | ||||
\(105\) | 10580.8 | + | 18326.4i | 0.0936578 | + | 0.162220i | ||||
\(106\) | −23705.0 | − | 41058.2i | −0.204915 | − | 0.354924i | ||||
\(107\) | −118895. | −1.00394 | −0.501968 | − | 0.864886i | \(-0.667390\pi\) | ||||
−0.501968 | + | 0.864886i | \(0.667390\pi\) | |||||||
\(108\) | 98935.3 | 0.816192 | ||||||||
\(109\) | 26664.4 | + | 46184.1i | 0.214964 | + | 0.372328i | 0.953261 | − | 0.302147i | \(-0.0977033\pi\) |
−0.738298 | + | 0.674475i | \(0.764370\pi\) | |||||||
\(110\) | −28813.8 | − | 49907.0i | −0.227049 | − | 0.393260i | ||||
\(111\) | 54702.6 | − | 94747.7i | 0.421406 | − | 0.729896i | ||||
\(112\) | −18824.5 | + | 32605.0i | −0.141801 | + | 0.245606i | ||||
\(113\) | −15529.6 | −0.114410 | −0.0572052 | − | 0.998362i | \(-0.518219\pi\) | ||||
−0.0572052 | + | 0.998362i | \(0.518219\pi\) | |||||||
\(114\) | −27696.4 | + | 47971.5i | −0.199600 | + | 0.345718i | ||||
\(115\) | −19551.9 | + | 33864.9i | −0.137862 | + | 0.238784i | ||||
\(116\) | 53182.6 | − | 92114.9i | 0.366965 | − | 0.635602i | ||||
\(117\) | 57716.5 | + | 99967.9i | 0.389794 | + | 0.675143i | ||||
\(118\) | 63852.1 | 0.422153 | ||||||||
\(119\) | 14341.9 | + | 24840.8i | 0.0928407 | + | 0.160805i | ||||
\(120\) | 20183.6 | − | 34959.1i | 0.127952 | − | 0.221619i | ||||
\(121\) | 456334. | 2.83348 | ||||||||
\(122\) | −55843.4 | + | 96723.7i | −0.339682 | + | 0.588347i | ||||
\(123\) | −85570.2 | − | 148212.i | −0.509987 | − | 0.883324i | ||||
\(124\) | 89829.4 | + | 155589.i | 0.524644 | + | 0.908709i | ||||
\(125\) | 164313. | 0.940584 | ||||||||
\(126\) | −13140.1 | − | 22759.3i | −0.0737346 | − | 0.127712i | ||||
\(127\) | −155519. | −0.855604 | −0.427802 | − | 0.903872i | \(-0.640712\pi\) | ||||
−0.427802 | + | 0.903872i | \(0.640712\pi\) | |||||||
\(128\) | 188405. | 1.01641 | ||||||||
\(129\) | 22261.9 | + | 112000.i | 0.117784 | + | 0.592578i | ||||
\(130\) | 54867.7 | 0.284747 | ||||||||
\(131\) | 87048.1 | 0.443181 | 0.221591 | − | 0.975140i | \(-0.428875\pi\) | ||||
0.221591 | + | 0.975140i | \(0.428875\pi\) | |||||||
\(132\) | 97832.1 | + | 169450.i | 0.488705 | + | 0.846461i | ||||
\(133\) | −180187. | −0.883271 | ||||||||
\(134\) | −43806.6 | − | 75875.2i | −0.210755 | − | 0.365038i | ||||
\(135\) | −58195.3 | − | 100797.i | −0.274823 | − | 0.476008i | ||||
\(136\) | 27358.2 | − | 47385.8i | 0.126835 | − | 0.219685i | ||||
\(137\) | −157426. | −0.716596 | −0.358298 | − | 0.933607i | \(-0.616643\pi\) | ||||
−0.358298 | + | 0.933607i | \(0.616643\pi\) | |||||||
\(138\) | −13958.2 | + | 24176.3i | −0.0623923 | + | 0.108067i | ||||
\(139\) | −59373.3 | − | 102838.i | −0.260648 | − | 0.451455i | 0.705766 | − | 0.708445i | \(-0.250603\pi\) |
−0.966414 | + | 0.256989i | \(0.917269\pi\) | |||||||
\(140\) | 59409.5 | 0.256174 | ||||||||
\(141\) | −81520.9 | − | 141198.i | −0.345320 | − | 0.598111i | ||||
\(142\) | 59398.5 | − | 102881.i | 0.247204 | − | 0.428169i | ||||
\(143\) | −293909. | + | 509065.i | −1.20191 | + | 2.08177i | ||||
\(144\) | 40210.7 | − | 69647.0i | 0.161598 | − | 0.279896i | ||||
\(145\) | −125131. | −0.494249 | ||||||||
\(146\) | −41626.1 | + | 72098.5i | −0.161616 | + | 0.279927i | ||||
\(147\) | 54573.6 | − | 94524.2i | 0.208300 | − | 0.360786i | ||||
\(148\) | −153574. | − | 265997.i | −0.576318 | − | 0.998212i | ||||
\(149\) | −50677.4 | − | 87775.9i | −0.187003 | − | 0.323899i | 0.757247 | − | 0.653129i | \(-0.226544\pi\) |
−0.944250 | + | 0.329230i | \(0.893211\pi\) | |||||||
\(150\) | 47909.0 | 0.173856 | ||||||||
\(151\) | −273662. | −0.976724 | −0.488362 | − | 0.872641i | \(-0.662405\pi\) | ||||
−0.488362 | + | 0.872641i | \(0.662405\pi\) | |||||||
\(152\) | 171860. | + | 297671.i | 0.603346 | + | 1.04503i | ||||
\(153\) | −30635.4 | − | 53062.1i | −0.105802 | − | 0.183255i | ||||
\(154\) | 66913.0 | − | 115897.i | 0.227357 | − | 0.393794i | ||||
\(155\) | 105678. | − | 183040.i | 0.353310 | − | 0.611951i | ||||
\(156\) | −186293. | −0.612895 | ||||||||
\(157\) | −85576.5 | + | 148223.i | −0.277080 | + | 0.479917i | −0.970658 | − | 0.240465i | \(-0.922700\pi\) |
0.693578 | + | 0.720382i | \(0.256033\pi\) | |||||||
\(158\) | −11565.7 | + | 20032.4i | −0.0368579 | + | 0.0638397i | ||||
\(159\) | 94686.2 | − | 164001.i | 0.297026 | − | 0.514463i | ||||
\(160\) | −87691.3 | − | 151886.i | −0.270805 | − | 0.469048i | ||||
\(161\) | −90808.9 | −0.276098 | ||||||||
\(162\) | 2657.62 | + | 4603.14i | 0.00795620 | + | 0.0137805i | ||||
\(163\) | −195306. | + | 338280.i | −0.575767 | + | 0.997258i | 0.420191 | + | 0.907436i | \(0.361963\pi\) |
−0.995958 | + | 0.0898219i | \(0.971370\pi\) | |||||||
\(164\) | −480464. | −1.39493 | ||||||||
\(165\) | 115093. | − | 199346.i | 0.329108 | − | 0.570031i | ||||
\(166\) | 57511.2 | + | 99612.3i | 0.161988 | + | 0.280571i | ||||
\(167\) | −324947. | − | 562825.i | −0.901616 | − | 1.56164i | −0.825397 | − | 0.564553i | \(-0.809049\pi\) |
−0.0762185 | − | 0.997091i | \(-0.524285\pi\) | |||||||
\(168\) | 93743.1 | 0.256251 | ||||||||
\(169\) | −94186.5 | − | 163136.i | −0.253672 | − | 0.439372i | ||||
\(170\) | −29123.3 | −0.0772891 | ||||||||
\(171\) | 384894. | 1.00659 | ||||||||
\(172\) | 303556. | + | 103091.i | 0.782381 | + | 0.265705i | ||||
\(173\) | 113478. | 0.288269 | 0.144135 | − | 0.989558i | \(-0.453960\pi\) | ||||
0.144135 | + | 0.989558i | \(0.453960\pi\) | |||||||
\(174\) | −89331.7 | −0.223683 | ||||||||
\(175\) | 77921.5 | + | 134964.i | 0.192337 | + | 0.333137i | ||||
\(176\) | 409529. | 0.996558 | ||||||||
\(177\) | 127524. | + | 220878.i | 0.305956 | + | 0.529931i | ||||
\(178\) | 86751.1 | + | 150257.i | 0.205223 | + | 0.355456i | ||||
\(179\) | −55577.1 | + | 96262.3i | −0.129647 | + | 0.224556i | −0.923540 | − | 0.383502i | \(-0.874718\pi\) |
0.793893 | + | 0.608058i | \(0.208051\pi\) | |||||||
\(180\) | −126904. | −0.291939 | ||||||||
\(181\) | 31209.6 | − | 54056.6i | 0.0708095 | − | 0.122646i | −0.828447 | − | 0.560068i | \(-0.810775\pi\) |
0.899256 | + | 0.437422i | \(0.144108\pi\) | |||||||
\(182\) | 63708.4 | + | 110346.i | 0.142567 | + | 0.246933i | ||||
\(183\) | −446118. | −0.984740 | ||||||||
\(184\) | 86612.5 | + | 150017.i | 0.188598 | + | 0.326661i | ||||
\(185\) | −180669. | + | 312928.i | −0.388109 | + | 0.672225i | ||||
\(186\) | 75444.1 | − | 130673.i | 0.159898 | − | 0.276951i | ||||
\(187\) | 156004. | − | 270207.i | 0.326236 | − | 0.565058i | ||||
\(188\) | −457728. | −0.944524 | ||||||||
\(189\) | 135144. | − | 234077.i | 0.275197 | − | 0.476655i | ||||
\(190\) | 91474.1 | − | 158438.i | 0.183829 | − | 0.318401i | ||||
\(191\) | 80509.0 | + | 139446.i | 0.159684 | + | 0.276581i | 0.934755 | − | 0.355294i | \(-0.115619\pi\) |
−0.775071 | + | 0.631874i | \(0.782286\pi\) | |||||||
\(192\) | 15936.4 | + | 27602.6i | 0.0311987 | + | 0.0540377i | ||||
\(193\) | 386516. | 0.746919 | 0.373460 | − | 0.927646i | \(-0.378171\pi\) | ||||
0.373460 | + | 0.927646i | \(0.378171\pi\) | |||||||
\(194\) | 34579.5 | 0.0659651 | ||||||||
\(195\) | 109581. | + | 189799.i | 0.206371 | + | 0.357444i | ||||
\(196\) | −153211. | − | 265370.i | −0.284873 | − | 0.493414i | ||||
\(197\) | −164469. | + | 284868.i | −0.301938 | + | 0.522972i | −0.976575 | − | 0.215178i | \(-0.930967\pi\) |
0.674637 | + | 0.738150i | \(0.264300\pi\) | |||||||
\(198\) | −142932. | + | 247565.i | −0.259099 | + | 0.448772i | ||||
\(199\) | 309184. | 0.553457 | 0.276729 | − | 0.960948i | \(-0.410750\pi\) | ||||
0.276729 | + | 0.960948i | \(0.410750\pi\) | |||||||
\(200\) | 148641. | − | 257454.i | 0.262763 | − | 0.455119i | ||||
\(201\) | 174979. | − | 303073.i | 0.305489 | − | 0.529123i | ||||
\(202\) | 58391.8 | − | 101138.i | 0.100687 | − | 0.174395i | ||||
\(203\) | −145293. | − | 251656.i | −0.247460 | − | 0.428614i | ||||
\(204\) | 98882.9 | 0.166359 | ||||||||
\(205\) | 282616. | + | 489506.i | 0.469692 | + | 0.813530i | ||||
\(206\) | −46872.5 | + | 81185.6i | −0.0769573 | + | 0.133294i | ||||
\(207\) | 193975. | 0.314645 | ||||||||
\(208\) | −194958. | + | 337677.i | −0.312451 | + | 0.541182i | ||||
\(209\) | 979995. | + | 1.69740e6i | 1.55188 | + | 2.68793i | ||||
\(210\) | −24947.8 | − | 43210.9i | −0.0390377 | − | 0.0676153i | ||||
\(211\) | 146655. | 0.226772 | 0.113386 | − | 0.993551i | \(-0.463830\pi\) | ||||
0.113386 | + | 0.993551i | \(0.463830\pi\) | |||||||
\(212\) | −265825. | − | 460422.i | −0.406215 | − | 0.703584i | ||||
\(213\) | 474518. | 0.716645 | ||||||||
\(214\) | 280337. | 0.418452 | ||||||||
\(215\) | −73525.3 | − | 369909.i | −0.108478 | − | 0.545756i | ||||
\(216\) | −515597. | −0.751927 | ||||||||
\(217\) | 490823. | 0.707580 | ||||||||
\(218\) | −62870.4 | − | 108895.i | −0.0895994 | − | 0.155191i | ||||
\(219\) | −332539. | −0.468525 | ||||||||
\(220\) | −323114. | − | 559651.i | −0.450090 | − | 0.779579i | ||||
\(221\) | 148533. | + | 257267.i | 0.204570 | + | 0.354326i | ||||
\(222\) | −128980. | + | 223400.i | −0.175647 | + | 0.304229i | ||||
\(223\) | −794062. | −1.06928 | −0.534641 | − | 0.845079i | \(-0.679553\pi\) | ||||
−0.534641 | + | 0.845079i | \(0.679553\pi\) | |||||||
\(224\) | 203642. | − | 352718.i | 0.271173 | − | 0.469686i | ||||
\(225\) | −166447. | − | 288294.i | −0.219189 | − | 0.379647i | ||||
\(226\) | 36616.5 | 0.0476876 | ||||||||
\(227\) | −18433.1 | − | 31927.0i | −0.0237429 | − | 0.0411239i | 0.853910 | − | 0.520421i | \(-0.174225\pi\) |
−0.877653 | + | 0.479297i | \(0.840892\pi\) | |||||||
\(228\) | −310584. | + | 537947.i | −0.395678 | + | 0.685334i | ||||
\(229\) | 217075. | − | 375985.i | 0.273540 | − | 0.473786i | −0.696226 | − | 0.717823i | \(-0.745139\pi\) |
0.969766 | + | 0.244037i | \(0.0784720\pi\) | |||||||
\(230\) | 46100.3 | − | 79848.0i | 0.0574624 | − | 0.0995279i | ||||
\(231\) | 534549. | 0.659110 | ||||||||
\(232\) | −277158. | + | 480052.i | −0.338071 | + | 0.585556i | ||||
\(233\) | 677907. | − | 1.17417e6i | 0.818051 | − | 1.41691i | −0.0890646 | − | 0.996026i | \(-0.528388\pi\) |
0.907116 | − | 0.420881i | \(-0.138279\pi\) | |||||||
\(234\) | −136086. | − | 235709.i | −0.162471 | − | 0.281408i | ||||
\(235\) | 269243. | + | 466342.i | 0.318035 | + | 0.550852i | ||||
\(236\) | 716029. | 0.836856 | ||||||||
\(237\) | −92395.4 | −0.106851 | ||||||||
\(238\) | −33815.9 | − | 58570.8i | −0.0386971 | − | 0.0670253i | ||||
\(239\) | −460249. | − | 797175.i | −0.521193 | − | 0.902733i | −0.999696 | − | 0.0246469i | \(-0.992154\pi\) |
0.478503 | − | 0.878086i | \(-0.341179\pi\) | |||||||
\(240\) | 76344.2 | − | 132232.i | 0.0855555 | − | 0.148186i | ||||
\(241\) | 524551. | − | 908549.i | 0.581761 | − | 1.00764i | −0.413509 | − | 0.910500i | \(-0.635697\pi\) |
0.995271 | − | 0.0971404i | \(-0.0309696\pi\) | |||||||
\(242\) | −1.07596e6 | −1.18103 | ||||||||
\(243\) | −465244. | + | 805827.i | −0.505435 | + | 0.875439i | ||||
\(244\) | −626221. | + | 1.08465e6i | −0.673369 | + | 1.16631i | ||||
\(245\) | −180243. | + | 312189.i | −0.191841 | + | 0.332279i | ||||
\(246\) | 201761. | + | 349460.i | 0.212569 | + | 0.368180i | ||||
\(247\) | −1.86612e6 | −1.94625 | ||||||||
\(248\) | −468142. | − | 810845.i | −0.483335 | − | 0.837160i | ||||
\(249\) | −229720. | + | 397888.i | −0.234802 | + | 0.406689i | ||||
\(250\) | −387425. | −0.392047 | ||||||||
\(251\) | 583378. | − | 1.01044e6i | 0.584475 | − | 1.01234i | −0.410466 | − | 0.911876i | \(-0.634634\pi\) |
0.994941 | − | 0.100464i | \(-0.0320328\pi\) | |||||||
\(252\) | −147351. | − | 255220.i | −0.146168 | − | 0.253170i | ||||
\(253\) | 493889. | + | 855440.i | 0.485096 | + | 0.840211i | ||||
\(254\) | 366689. | 0.356626 | ||||||||
\(255\) | −58164.5 | − | 100744.i | −0.0560154 | − | 0.0970216i | ||||
\(256\) | −335936. | −0.320374 | ||||||||
\(257\) | −234774. | −0.221726 | −0.110863 | − | 0.993836i | \(-0.535361\pi\) | ||||
−0.110863 | + | 0.993836i | \(0.535361\pi\) | |||||||
\(258\) | −52490.0 | − | 264079.i | −0.0490939 | − | 0.246993i | ||||
\(259\) | −839118. | −0.777273 | ||||||||
\(260\) | 615280. | 0.564468 | ||||||||
\(261\) | 310359. | + | 537557.i | 0.282009 | + | 0.488454i | ||||
\(262\) | −205246. | −0.184723 | ||||||||
\(263\) | 1.07763e6 | + | 1.86652e6i | 0.960686 | + | 1.66396i | 0.720783 | + | 0.693160i | \(0.243782\pi\) |
0.239903 | + | 0.970797i | \(0.422884\pi\) | |||||||
\(264\) | −509847. | − | 883081.i | −0.450225 | − | 0.779813i | ||||
\(265\) | −312724. | + | 541655.i | −0.273557 | + | 0.473814i | ||||
\(266\) | 424853. | 0.368158 | ||||||||
\(267\) | −346515. | + | 600182.i | −0.297471 | + | 0.515234i | ||||
\(268\) | −491241. | − | 850855.i | −0.417790 | − | 0.723633i | ||||
\(269\) | −374180. | −0.315282 | −0.157641 | − | 0.987496i | \(-0.550389\pi\) | ||||
−0.157641 | + | 0.987496i | \(0.550389\pi\) | |||||||
\(270\) | 137216. | + | 237664.i | 0.114550 | + | 0.198406i | ||||
\(271\) | 1.00118e6 | − | 1.73410e6i | 0.828112 | − | 1.43433i | −0.0714049 | − | 0.997447i | \(-0.522748\pi\) |
0.899517 | − | 0.436885i | \(-0.143918\pi\) | |||||||
\(272\) | 103482. | − | 179236.i | 0.0848091 | − | 0.146894i | ||||
\(273\) | −254474. | + | 440763.i | −0.206651 | + | 0.357930i | ||||
\(274\) | 371185. | 0.298686 | ||||||||
\(275\) | 847594. | − | 1.46808e6i | 0.675859 | − | 1.17062i | ||||
\(276\) | −156525. | + | 271110.i | −0.123683 | + | 0.214226i | ||||
\(277\) | 66019.1 | + | 114348.i | 0.0516976 | + | 0.0895428i | 0.890716 | − | 0.454560i | \(-0.150203\pi\) |
−0.839019 | + | 0.544103i | \(0.816870\pi\) | |||||||
\(278\) | 139993. | + | 242475.i | 0.108641 | + | 0.188172i | ||||
\(279\) | −1.04844e6 | −0.806367 | ||||||||
\(280\) | −309610. | −0.236004 | ||||||||
\(281\) | −700236. | − | 1.21285e6i | −0.529028 | − | 0.916304i | −0.999427 | − | 0.0338498i | \(-0.989223\pi\) |
0.470399 | − | 0.882454i | \(-0.344110\pi\) | |||||||
\(282\) | 192214. | + | 332924.i | 0.143933 | + | 0.249300i | ||||
\(283\) | 289462. | − | 501362.i | 0.214845 | − | 0.372122i | −0.738380 | − | 0.674385i | \(-0.764409\pi\) |
0.953225 | + | 0.302263i | \(0.0977421\pi\) | |||||||
\(284\) | 666088. | − | 1.15370e6i | 0.490045 | − | 0.848782i | ||||
\(285\) | 730761. | 0.532922 | ||||||||
\(286\) | 692991. | − | 1.20030e6i | 0.500971 | − | 0.867707i | ||||
\(287\) | −656308. | + | 1.13676e6i | −0.470330 | + | 0.814636i | ||||
\(288\) | −434995. | + | 753434.i | −0.309032 | + | 0.535259i | ||||
\(289\) | 631089. | + | 1.09308e6i | 0.444473 | + | 0.769850i | ||||
\(290\) | 295040. | 0.206009 | ||||||||
\(291\) | 69061.4 | + | 119618.i | 0.0478083 | + | 0.0828064i | ||||
\(292\) | −466790. | + | 808504.i | −0.320379 | + | 0.554913i | ||||
\(293\) | 357984. | 0.243610 | 0.121805 | − | 0.992554i | \(-0.461132\pi\) | ||||
0.121805 | + | 0.992554i | \(0.461132\pi\) | |||||||
\(294\) | −128676. | + | 222873.i | −0.0868219 | + | 0.150380i | ||||
\(295\) | −421180. | − | 729505.i | −0.281781 | − | 0.488060i | ||||
\(296\) | 800341. | + | 1.38623e6i | 0.530941 | + | 0.919616i | ||||
\(297\) | −2.94008e6 | −1.93405 | ||||||||
\(298\) | 119489. | + | 206962.i | 0.0779451 | + | 0.135005i | ||||
\(299\) | −940471. | −0.608370 | ||||||||
\(300\) | 537246. | 0.344643 | ||||||||
\(301\) | 658563. | − | 577380.i | 0.418968 | − | 0.367321i | ||||
\(302\) | 645252. | 0.407110 | ||||||||
\(303\) | 466476. | 0.291892 | ||||||||
\(304\) | 650058. | + | 1.12593e6i | 0.403430 | + | 0.698761i | ||||
\(305\) | 1.47341e6 | 0.906932 | ||||||||
\(306\) | 72233.5 | + | 125112.i | 0.0440996 | + | 0.0763828i | ||||
\(307\) | 27911.1 | + | 48343.5i | 0.0169017 | + | 0.0292747i | 0.874353 | − | 0.485291i | \(-0.161286\pi\) |
−0.857451 | + | 0.514566i | \(0.827953\pi\) | |||||||
\(308\) | 750354. | − | 1.29965e6i | 0.450702 | − | 0.780639i | ||||
\(309\) | −374451. | −0.223100 | ||||||||
\(310\) | −249173. | + | 431580.i | −0.147264 | + | 0.255068i | ||||
\(311\) | 245116. | + | 424553.i | 0.143704 | + | 0.248903i | 0.928889 | − | 0.370359i | \(-0.120765\pi\) |
−0.785184 | + | 0.619262i | \(0.787432\pi\) | |||||||
\(312\) | 970859. | 0.564638 | ||||||||
\(313\) | −1.08613e6 | − | 1.88123e6i | −0.626644 | − | 1.08538i | −0.988221 | − | 0.153036i | \(-0.951095\pi\) |
0.361577 | − | 0.932342i | \(-0.382239\pi\) | |||||||
\(314\) | 201776. | − | 349486.i | 0.115490 | − | 0.200035i | ||||
\(315\) | −173349. | + | 300249.i | −0.0984337 | + | 0.170492i | ||||
\(316\) | −129697. | + | 224641.i | −0.0730653 | + | 0.126553i | ||||
\(317\) | 853939. | 0.477286 | 0.238643 | − | 0.971107i | \(-0.423297\pi\) | ||||
0.238643 | + | 0.971107i | \(0.423297\pi\) | |||||||
\(318\) | −223255. | + | 386689.i | −0.123804 | + | 0.214434i | ||||
\(319\) | −1.58043e6 | + | 2.73739e6i | −0.869561 | + | 1.50612i | ||||
\(320\) | −52633.7 | − | 91164.3i | −0.0287336 | − | 0.0497680i | ||||
\(321\) | 559883. | + | 969746.i | 0.303274 | + | 0.525286i | ||||
\(322\) | 214113. | 0.115081 | ||||||||
\(323\) | 990522. | 0.528272 | ||||||||
\(324\) | 29802.2 | + | 51619.0i | 0.0157720 | + | 0.0273179i | ||||
\(325\) | 807002. | + | 1.39777e6i | 0.423805 | + | 0.734052i | ||||
\(326\) | 460501. | − | 797612.i | 0.239987 | − | 0.415669i | ||||
\(327\) | 251127. | − | 434965.i | 0.129875 | − | 0.224950i | ||||
\(328\) | 2.50391e6 | 1.28509 | ||||||||
\(329\) | −625251. | + | 1.08297e6i | −0.318467 | + | 0.551601i | ||||
\(330\) | −271371. | + | 470028.i | −0.137176 | + | 0.237596i | ||||
\(331\) | 896639. | − | 1.55303e6i | 0.449829 | − | 0.779127i | −0.548545 | − | 0.836121i | \(-0.684818\pi\) |
0.998375 | + | 0.0569935i | \(0.0181514\pi\) | |||||||
\(332\) | 644924. | + | 1.11704e6i | 0.321117 | + | 0.556191i | ||||
\(333\) | 1.79243e6 | 0.885789 | ||||||||
\(334\) | 766174. | + | 1.32705e6i | 0.375804 | + | 0.650912i | ||||
\(335\) | −577912. | + | 1.00097e6i | −0.281352 | + | 0.487315i | ||||
\(336\) | 354581. | 0.171344 | ||||||||
\(337\) | 1.47938e6 | − | 2.56236e6i | 0.709584 | − | 1.22904i | −0.255427 | − | 0.966828i | \(-0.582216\pi\) |
0.965011 | − | 0.262208i | \(-0.0844506\pi\) | |||||||
\(338\) | 222077. | + | 384649.i | 0.105733 | + | 0.183136i | ||||
\(339\) | 73129.7 | + | 126664.i | 0.0345617 | + | 0.0598626i | ||||
\(340\) | −326585. | −0.153214 | ||||||||
\(341\) | −2.66947e6 | − | 4.62367e6i | −1.24320 | − | 2.15328i | ||||
\(342\) | −907520. | −0.419557 | ||||||||
\(343\) | −2.05119e6 | −0.941393 | ||||||||
\(344\) | −1.58197e6 | − | 537255.i | −0.720778 | − | 0.244785i | ||||
\(345\) | 368282. | 0.166584 | ||||||||
\(346\) | −267564. | −0.120154 | ||||||||
\(347\) | 340583. | + | 589907.i | 0.151845 | + | 0.263002i | 0.931906 | − | 0.362701i | \(-0.118145\pi\) |
−0.780061 | + | 0.625703i | \(0.784812\pi\) | |||||||
\(348\) | −1.00176e6 | −0.443418 | ||||||||
\(349\) | 898075. | + | 1.55551e6i | 0.394683 | + | 0.683612i | 0.993061 | − | 0.117603i | \(-0.0375209\pi\) |
−0.598377 | + | 0.801214i | \(0.704188\pi\) | |||||||
\(350\) | −183727. | − | 318224.i | −0.0801683 | − | 0.138855i | ||||
\(351\) | 1.39964e6 | − | 2.42424e6i | 0.606383 | − | 1.05029i | ||||
\(352\) | −4.43024e6 | −1.90577 | ||||||||
\(353\) | 445.726 | − | 772.021i | 0.000190384 | − | 0.000329756i | −0.865930 | − | 0.500165i | \(-0.833273\pi\) |
0.866121 | + | 0.499835i | \(0.166606\pi\) | |||||||
\(354\) | −300682. | − | 520796.i | −0.127526 | − | 0.220882i | ||||
\(355\) | −1.56721e6 | −0.660020 | ||||||||
\(356\) | 972816. | + | 1.68497e6i | 0.406823 | + | 0.704639i | ||||
\(357\) | 135073. | − | 233953.i | 0.0560916 | − | 0.0971534i | ||||
\(358\) | 131042. | − | 226972.i | 0.0540385 | − | 0.0935974i | ||||
\(359\) | −7293.51 | + | 12632.7i | −0.00298676 | + | 0.00517322i | −0.867515 | − | 0.497411i | \(-0.834284\pi\) |
0.864528 | + | 0.502584i | \(0.167617\pi\) | |||||||
\(360\) | 661352. | 0.268953 | ||||||||
\(361\) | −1.87310e6 | + | 3.24431e6i | −0.756474 | + | 1.31025i | ||||
\(362\) | −73587.3 | + | 127457.i | −0.0295142 | + | 0.0511201i | ||||
\(363\) | −2.14889e6 | − | 3.72200e6i | −0.855950 | − | 1.48255i | ||||
\(364\) | 714419. | + | 1.23741e6i | 0.282618 | + | 0.489508i | ||||
\(365\) | 1.09829e6 | 0.431505 | ||||||||
\(366\) | 1.05188e6 | 0.410451 | ||||||||
\(367\) | 219283. | + | 379809.i | 0.0849845 | + | 0.147197i | 0.905385 | − | 0.424592i | \(-0.139583\pi\) |
−0.820400 | + | 0.571790i | \(0.806249\pi\) | |||||||
\(368\) | 327610. | + | 567437.i | 0.126107 | + | 0.218423i | ||||
\(369\) | 1.40193e6 | − | 2.42821e6i | 0.535993 | − | 0.928368i | ||||
\(370\) | 425989. | − | 737834.i | 0.161768 | − | 0.280191i | ||||
\(371\) | −1.45245e6 | −0.547857 | ||||||||
\(372\) | 846020. | − | 1.46535e6i | 0.316974 | − | 0.549015i | ||||
\(373\) | −1.84218e6 | + | 3.19074e6i | −0.685582 | + | 1.18746i | 0.287672 | + | 0.957729i | \(0.407119\pi\) |
−0.973254 | + | 0.229733i | \(0.926215\pi\) | |||||||
\(374\) | −367834. | + | 637106.i | −0.135979 | + | 0.235523i | ||||
\(375\) | −773758. | − | 1.34019e6i | −0.284136 | − | 0.492139i | ||||
\(376\) | 2.38543e6 | 0.870155 | ||||||||
\(377\) | −1.50475e6 | − | 2.60630e6i | −0.545267 | − | 0.944431i | ||||
\(378\) | −318649. | + | 551917.i | −0.114705 | + | 0.198675i | ||||
\(379\) | −4.33977e6 | −1.55192 | −0.775959 | − | 0.630784i | \(-0.782734\pi\) | ||||
−0.775959 | + | 0.630784i | \(0.782734\pi\) | |||||||
\(380\) | 1.02578e6 | − | 1.77670e6i | 0.364414 | − | 0.631184i | ||||
\(381\) | 732343. | + | 1.26846e6i | 0.258465 | + | 0.447675i | ||||
\(382\) | −189828. | − | 328791.i | −0.0665581 | − | 0.115282i | ||||
\(383\) | 826932. | 0.288053 | 0.144027 | − | 0.989574i | \(-0.453995\pi\) | ||||
0.144027 | + | 0.989574i | \(0.453995\pi\) | |||||||
\(384\) | −887209. | − | 1.53669e6i | −0.307042 | − | 0.531812i | ||||
\(385\) | −1.76548e6 | −0.607031 | ||||||||
\(386\) | −911343. | −0.311325 | ||||||||
\(387\) | −1.40675e6 | + | 1.23333e6i | −0.477461 | + | 0.418603i | ||||
\(388\) | 387770. | 0.130766 | ||||||||
\(389\) | −2.23266e6 | −0.748080 | −0.374040 | − | 0.927413i | \(-0.622028\pi\) | ||||
−0.374040 | + | 0.927413i | \(0.622028\pi\) | |||||||
\(390\) | −258374. | − | 447517.i | −0.0860177 | − | 0.148987i | ||||
\(391\) | 499194. | 0.165131 | ||||||||
\(392\) | 798453. | + | 1.38296e6i | 0.262443 | + | 0.454564i | ||||
\(393\) | −409913. | − | 709990.i | −0.133878 | − | 0.231884i | ||||
\(394\) | 387791. | − | 671674.i | 0.125851 | − | 0.217981i | ||||
\(395\) | 305159. | 0.0984085 | ||||||||
\(396\) | −1.60282e6 | + | 2.77616e6i | −0.513625 | + | 0.889625i | ||||
\(397\) | −1.86790e6 | − | 3.23529e6i | −0.594808 | − | 1.03024i | −0.993574 | − | 0.113184i | \(-0.963895\pi\) |
0.398766 | − | 0.917053i | \(-0.369438\pi\) | |||||||
\(398\) | −729007. | −0.230687 | ||||||||
\(399\) | 848507. | + | 1.46966e6i | 0.266823 | + | 0.462151i | ||||
\(400\) | 562233. | − | 973816.i | 0.175698 | − | 0.304317i | ||||
\(401\) | −894571. | + | 1.54944e6i | −0.277814 | + | 0.481188i | −0.970841 | − | 0.239724i | \(-0.922943\pi\) |
0.693027 | + | 0.720911i | \(0.256276\pi\) | |||||||
\(402\) | −412574. | + | 714598.i | −0.127332 | + | 0.220545i | ||||
\(403\) | 5.08326e6 | 1.55912 | ||||||||
\(404\) | 654798. | − | 1.13414e6i | 0.199597 | − | 0.345712i | ||||
\(405\) | 35060.3 | − | 60726.2i | 0.0106213 | − | 0.0183966i | ||||
\(406\) | 342579. | + | 593365.i | 0.103144 | + | 0.178651i | ||||
\(407\) | 4.56377e6 | + | 7.90468e6i | 1.36564 | + | 2.36537i | ||||
\(408\) | −515324. | −0.153260 | ||||||||
\(409\) | −531028. | −0.156967 | −0.0784836 | − | 0.996915i | \(-0.525008\pi\) | ||||
−0.0784836 | + | 0.996915i | \(0.525008\pi\) | |||||||
\(410\) | −666366. | − | 1.15418e6i | −0.195773 | − | 0.339089i | ||||
\(411\) | 741324. | + | 1.28401e6i | 0.216473 | + | 0.374942i | ||||
\(412\) | −525622. | + | 910405.i | −0.152557 | + | 0.264236i | ||||
\(413\) | 978087. | − | 1.69410e6i | 0.282164 | − | 0.488723i | ||||
\(414\) | −457364. | −0.131148 | ||||||||
\(415\) | 758708. | − | 1.31412e6i | 0.216249 | − | 0.374555i | ||||
\(416\) | 2.10903e6 | − | 3.65295e6i | 0.597517 | − | 1.03493i | ||||
\(417\) | −559182. | + | 968532.i | −0.157476 | + | 0.272756i | ||||
\(418\) | −2.31067e6 | − | 4.00221e6i | −0.646842 | − | 1.12036i | ||||
\(419\) | −4.56915e6 | −1.27145 | −0.635726 | − | 0.771915i | \(-0.719299\pi\) | ||||
−0.635726 | + | 0.771915i | \(0.719299\pi\) | |||||||
\(420\) | −279762. | − | 484561.i | −0.0773864 | − | 0.134037i | ||||
\(421\) | 1.50987e6 | − | 2.61516e6i | 0.415177 | − | 0.719107i | −0.580270 | − | 0.814424i | \(-0.697053\pi\) |
0.995447 | + | 0.0953168i | \(0.0303864\pi\) | |||||||
\(422\) | −345789. | −0.0945214 | ||||||||
\(423\) | 1.33559e6 | − | 2.31330e6i | 0.362929 | − | 0.628611i | ||||
\(424\) | 1.38533e6 | + | 2.39947e6i | 0.374231 | + | 0.648186i | ||||
\(425\) | −428350. | − | 741923.i | −0.115034 | − | 0.199245i | ||||
\(426\) | −1.11884e6 | −0.298706 | ||||||||
\(427\) | 1.71082e6 | + | 2.96323e6i | 0.454083 | + | 0.786494i | ||||
\(428\) | 3.14366e6 | 0.829519 | ||||||||
\(429\) | 5.53611e6 | 1.45232 | ||||||||
\(430\) | 173361. | + | 872187.i | 0.0452148 | + | 0.227478i | ||||
\(431\) | −453602. | −0.117620 | −0.0588101 | − | 0.998269i | \(-0.518731\pi\) | ||||
−0.0588101 | + | 0.998269i | \(0.518731\pi\) | |||||||
\(432\) | −1.95023e6 | −0.502779 | ||||||||
\(433\) | 2.91468e6 | + | 5.04838e6i | 0.747087 | + | 1.29399i | 0.949213 | + | 0.314634i | \(0.101882\pi\) |
−0.202126 | + | 0.979360i | \(0.564785\pi\) | |||||||
\(434\) | −1.15728e6 | −0.294928 | ||||||||
\(435\) | 589248. | + | 1.02061e6i | 0.149305 | + | 0.258604i | ||||
\(436\) | −705021. | − | 1.22113e6i | −0.177618 | − | 0.307643i | ||||
\(437\) | −1.56793e6 | + | 2.71574e6i | −0.392756 | + | 0.680274i | ||||
\(438\) | 784076. | 0.195287 | ||||||||
\(439\) | 3.31046e6 | − | 5.73388e6i | 0.819835 | − | 1.42000i | −0.0859683 | − | 0.996298i | \(-0.527398\pi\) |
0.905803 | − | 0.423698i | \(-0.139268\pi\) | |||||||
\(440\) | 1.68390e6 | + | 2.91659e6i | 0.414652 | + | 0.718198i | ||||
\(441\) | 1.78820e6 | 0.437844 | ||||||||
\(442\) | −350217. | − | 606594.i | −0.0852672 | − | 0.147687i | ||||
\(443\) | −1.63844e6 | + | 2.83786e6i | −0.396662 | + | 0.687039i | −0.993312 | − | 0.115463i | \(-0.963165\pi\) |
0.596650 | + | 0.802502i | \(0.296498\pi\) | |||||||
\(444\) | −1.44637e6 | + | 2.50518e6i | −0.348194 | + | 0.603090i | ||||
\(445\) | 1.14445e6 | − | 1.98225e6i | 0.273967 | − | 0.474524i | ||||
\(446\) | 1.87228e6 | 0.445690 | ||||||||
\(447\) | −477284. | + | 826680.i | −0.112982 | + | 0.195690i | ||||
\(448\) | 122229. | − | 211707.i | 0.0287726 | − | 0.0498356i | ||||
\(449\) | 1.03947e6 | + | 1.80042e6i | 0.243331 | + | 0.421462i | 0.961661 | − | 0.274241i | \(-0.0884265\pi\) |
−0.718330 | + | 0.695703i | \(0.755093\pi\) | |||||||
\(450\) | 392456. | + | 679753.i | 0.0913607 | + | 0.158241i | ||||
\(451\) | 1.42780e7 | 3.30542 | ||||||||
\(452\) | 410613. | 0.0945336 | ||||||||
\(453\) | 1.28868e6 | + | 2.23207e6i | 0.295054 | + | 0.511048i | ||||
\(454\) | 43462.3 | + | 75278.9i | 0.00989631 | + | 0.0171409i | ||||
\(455\) | 840465. | − | 1.45573e6i | 0.190323 | − | 0.329649i | ||||
\(456\) | 1.61859e6 | − | 2.80348e6i | 0.364523 | − | 0.631373i | ||||
\(457\) | −7.10479e6 | −1.59133 | −0.795665 | − | 0.605736i | \(-0.792879\pi\) | ||||
−0.795665 | + | 0.605736i | \(0.792879\pi\) | |||||||
\(458\) | −511829. | + | 886514.i | −0.114015 | + | 0.197479i | ||||
\(459\) | −742915. | + | 1.28677e6i | −0.164591 | + | 0.285081i | ||||
\(460\) | 516963. | − | 895406.i | 0.113911 | − | 0.197299i | ||||
\(461\) | −386731. | − | 669838.i | −0.0847534 | − | 0.146797i | 0.820533 | − | 0.571600i | \(-0.193677\pi\) |
−0.905286 | + | 0.424802i | \(0.860344\pi\) | |||||||
\(462\) | −1.26038e6 | −0.274725 | ||||||||
\(463\) | −1.35158e6 | − | 2.34100e6i | −0.293014 | − | 0.507516i | 0.681507 | − | 0.731812i | \(-0.261325\pi\) |
−0.974521 | + | 0.224296i | \(0.927992\pi\) | |||||||
\(464\) | −1.04835e6 | + | 1.81579e6i | −0.226053 | + | 0.391535i | ||||
\(465\) | −1.99057e6 | −0.426919 | ||||||||
\(466\) | −1.59840e6 | + | 2.76851e6i | −0.340974 | + | 0.590583i | ||||
\(467\) | 1.45585e6 | + | 2.52161e6i | 0.308905 | + | 0.535039i | 0.978123 | − | 0.208027i | \(-0.0667043\pi\) |
−0.669218 | + | 0.743066i | \(0.733371\pi\) | |||||||
\(468\) | −1.52606e6 | − | 2.64321e6i | −0.322074 | − | 0.557849i | ||||
\(469\) | −2.68412e6 | −0.563468 | ||||||||
\(470\) | −634833. | − | 1.09956e6i | −0.132561 | − | 0.229602i | ||||
\(471\) | 1.61193e6 | 0.334807 | ||||||||
\(472\) | −3.73155e6 | −0.770965 | ||||||||
\(473\) | −9.02083e6 | − | 3.06358e6i | −1.85393 | − | 0.629616i | ||||
\(474\) | 217854. | 0.0445369 | ||||||||
\(475\) | 5.38165e6 | 1.09441 | ||||||||
\(476\) | −379207. | − | 656806.i | −0.0767113 | − | 0.132868i | ||||
\(477\) | 3.10256e6 | 0.624344 | ||||||||
\(478\) | 1.08520e6 | + | 1.87962e6i | 0.217239 | + | 0.376270i | ||||
\(479\) | −2.26063e6 | − | 3.91553e6i | −0.450185 | − | 0.779743i | 0.548212 | − | 0.836339i | \(-0.315309\pi\) |
−0.998397 | + | 0.0565964i | \(0.981975\pi\) | |||||||
\(480\) | −825884. | + | 1.43047e6i | −0.163612 | + | 0.283385i | ||||
\(481\) | −8.69041e6 | −1.71268 | ||||||||
\(482\) | −1.23681e6 | + | 2.14222e6i | −0.242485 | + | 0.419996i | ||||
\(483\) | 427623. | + | 740664.i | 0.0834052 | + | 0.144462i | ||||
\(484\) | −1.20657e7 | −2.34121 | ||||||||
\(485\) | −228092. | − | 395068.i | −0.0440308 | − | 0.0762636i | ||||
\(486\) | 1.09697e6 | − | 1.90001e6i | 0.210671 | − | 0.364893i | ||||
\(487\) | −2.41774e6 | + | 4.18764e6i | −0.461941 | + | 0.800105i | −0.999058 | − | 0.0434028i | \(-0.986180\pi\) |
0.537117 | + | 0.843508i | \(0.319513\pi\) | |||||||
\(488\) | 3.26352e6 | − | 5.65259e6i | 0.620350 | − | 1.07448i | ||||
\(489\) | 3.67882e6 | 0.695722 | ||||||||
\(490\) | 424984. | − | 736094.i | 0.0799618 | − | 0.138498i | ||||
\(491\) | 3.77568e6 | − | 6.53967e6i | 0.706792 | − | 1.22420i | −0.259249 | − | 0.965810i | \(-0.583475\pi\) |
0.966041 | − | 0.258389i | \(-0.0831916\pi\) | |||||||
\(492\) | 2.26252e6 | + | 3.91881e6i | 0.421386 | + | 0.729862i | ||||
\(493\) | 798706. | + | 1.38340e6i | 0.148003 | + | 0.256348i | ||||
\(494\) | 4.40003e6 | 0.811219 | ||||||||
\(495\) | 3.77121e6 | 0.691780 | ||||||||
\(496\) | −1.77074e6 | − | 3.06701e6i | −0.323184 | − | 0.559771i | ||||
\(497\) | −1.81974e6 | − | 3.15187e6i | −0.330459 | − | 0.572371i | ||||
\(498\) | 541645. | − | 938157.i | 0.0978682 | − | 0.169513i | ||||
\(499\) | 4.16824e6 | − | 7.21960e6i | 0.749379 | − | 1.29796i | −0.198742 | − | 0.980052i | \(-0.563686\pi\) |
0.948121 | − | 0.317910i | \(-0.102981\pi\) | |||||||
\(500\) | −4.34454e6 | −0.777174 | ||||||||
\(501\) | −3.06038e6 | + | 5.30073e6i | −0.544729 | + | 0.943498i | ||||
\(502\) | −1.37551e6 | + | 2.38246e6i | −0.243616 | + | 0.421955i | ||||
\(503\) | −5.50014e6 | + | 9.52651e6i | −0.969289 | + | 1.67886i | −0.271669 | + | 0.962391i | \(0.587576\pi\) |
−0.697620 | + | 0.716468i | \(0.745758\pi\) | |||||||
\(504\) | 767914. | + | 1.33007e6i | 0.134659 | + | 0.233237i | ||||
\(505\) | −1.54065e6 | −0.268829 | ||||||||
\(506\) | −1.16451e6 | − | 2.01699e6i | −0.202194 | − | 0.350210i | ||||
\(507\) | −887056. | + | 1.53643e6i | −0.153261 | + | 0.265456i | ||||
\(508\) | 4.11200e6 | 0.706958 | ||||||||
\(509\) | −525773. | + | 910665.i | −0.0899505 | + | 0.155799i | −0.907490 | − | 0.420074i | \(-0.862004\pi\) |
0.817540 | + | 0.575873i | \(0.195338\pi\) | |||||||
\(510\) | 137143. | + | 237538.i | 0.0233479 | + | 0.0404397i | ||||
\(511\) | 1.27526e6 | + | 2.20881e6i | 0.216046 | + | 0.374202i | ||||
\(512\) | −5.23689e6 | −0.882874 | ||||||||
\(513\) | −4.66688e6 | − | 8.08327e6i | −0.782948 | − | 1.35611i | ||||
\(514\) | 553560. | 0.0924180 | ||||||||
\(515\) | 1.23672e6 | 0.205472 | ||||||||
\(516\) | −588616. | − | 2.96135e6i | −0.0973213 | − | 0.489628i | ||||
\(517\) | 1.36024e7 | 2.23815 | ||||||||
\(518\) | 1.97851e6 | 0.323977 | ||||||||
\(519\) | −534374. | − | 925563.i | −0.0870818 | − | 0.150830i | ||||
\(520\) | −3.20650e6 | −0.520024 | ||||||||
\(521\) | −286252. | − | 495803.i | −0.0462013 | − | 0.0800230i | 0.842000 | − | 0.539478i | \(-0.181378\pi\) |
−0.888201 | + | 0.459455i | \(0.848045\pi\) | |||||||
\(522\) | −731777. | − | 1.26748e6i | −0.117545 | − | 0.203593i | ||||
\(523\) | 2.93659e6 | − | 5.08632e6i | 0.469450 | − | 0.813111i | −0.529940 | − | 0.848035i | \(-0.677786\pi\) |
0.999390 | + | 0.0349242i | \(0.0111190\pi\) | |||||||
\(524\) | −2.30160e6 | −0.366186 | ||||||||
\(525\) | 733871. | − | 1.27110e6i | 0.116204 | − | 0.201271i | ||||
\(526\) | −2.54089e6 | − | 4.40095e6i | −0.400425 | − | 0.693557i | ||||
\(527\) | −2.69815e6 | −0.423194 | ||||||||
\(528\) | −1.92849e6 | − | 3.34024e6i | −0.301045 | − | 0.521426i | ||||
\(529\) | 2.42798e6 | − | 4.20539e6i | 0.377230 | − | 0.653381i | ||||
\(530\) | 737355. | − | 1.27714e6i | 0.114022 | − | 0.197491i | ||||
\(531\) | −2.08927e6 | + | 3.61873e6i | −0.321558 | + | 0.556954i | ||||
\(532\) | 4.76424e6 | 0.729819 | ||||||||
\(533\) | −6.79711e6 | + | 1.17729e7i | −1.03635 | + | 1.79501i | ||||
\(534\) | 817029. | − | 1.41514e6i | 0.123989 | − | 0.214756i | ||||
\(535\) | −1.84915e6 | − | 3.20283e6i | −0.279311 | − | 0.483781i | ||||
\(536\) | 2.56008e6 | + | 4.43419e6i | 0.384894 | + | 0.666657i | ||||
\(537\) | 1.04686e6 | 0.156658 | ||||||||
\(538\) | 882258. | 0.131413 | ||||||||
\(539\) | 4.55301e6 | + | 7.88604e6i | 0.675035 | + | 1.16919i | ||||
\(540\) | 1.53872e6 | + | 2.66514e6i | 0.227078 | + | 0.393310i | ||||
\(541\) | 163410. | − | 283035.i | 0.0240042 | − | 0.0415764i | −0.853774 | − | 0.520644i | \(-0.825692\pi\) |
0.877778 | + | 0.479068i | \(0.159025\pi\) | |||||||
\(542\) | −2.36063e6 | + | 4.08873e6i | −0.345167 | + | 0.597847i | ||||
\(543\) | −587868. | −0.0855619 | ||||||||
\(544\) | −1.11946e6 | + | 1.93896e6i | −0.162185 | + | 0.280912i | ||||
\(545\) | −829409. | + | 1.43658e6i | −0.119613 | + | 0.207175i | ||||
\(546\) | 600011. | − | 1.03925e6i | 0.0861346 | − | 0.149190i | ||||
\(547\) | −691457. | − | 1.19764e6i | −0.0988090 | − | 0.171142i | 0.812383 | − | 0.583124i | \(-0.198170\pi\) |
−0.911192 | + | 0.411982i | \(0.864837\pi\) | |||||||
\(548\) | 4.16243e6 | 0.592100 | ||||||||
\(549\) | −3.65445e6 | − | 6.32970e6i | −0.517478 | − | 0.896298i | ||||
\(550\) | −1.99850e6 | + | 3.46150e6i | −0.281706 | + | 0.487929i | ||||
\(551\) | −1.00347e7 | −1.40807 | ||||||||
\(552\) | 815723. | − | 1.41287e6i | 0.113945 | − | 0.197358i | ||||
\(553\) | 354328. | + | 613714.i | 0.0492711 | + | 0.0853401i | ||||
\(554\) | −155663. | − | 269616.i | −0.0215482 | − | 0.0373225i | ||||
\(555\) | 3.40311e6 | 0.468968 | ||||||||
\(556\) | 1.56986e6 | + | 2.71908e6i | 0.215365 | + | 0.373023i | ||||
\(557\) | −9.53674e6 | −1.30245 | −0.651226 | − | 0.758883i | \(-0.725745\pi\) | ||||
−0.651226 | + | 0.758883i | \(0.725745\pi\) | |||||||
\(558\) | 2.47205e6 | 0.336103 | ||||||||
\(559\) | 6.82047e6 | − | 5.97970e6i | 0.923177 | − | 0.809375i | ||||
\(560\) | −1.17109e6 | −0.157805 | ||||||||
\(561\) | −2.93852e6 | −0.394204 | ||||||||
\(562\) | 1.65105e6 | + | 2.85970e6i | 0.220505 | + | 0.381926i | ||||
\(563\) | −5.53863e6 | −0.736430 | −0.368215 | − | 0.929741i | \(-0.620031\pi\) | ||||
−0.368215 | + | 0.929741i | \(0.620031\pi\) | |||||||
\(564\) | 2.15546e6 | + | 3.73337e6i | 0.285327 | + | 0.494200i | ||||
\(565\) | −241529. | − | 418340.i | −0.0318308 | − | 0.0551326i | ||||
\(566\) | −682506. | + | 1.18213e6i | −0.0895499 | + | 0.155105i | ||||
\(567\) | 162838. | 0.0212715 | ||||||||
\(568\) | −3.47128e6 | + | 6.01244e6i | −0.451460 | + | 0.781952i | ||||
\(569\) | 4.21862e6 | + | 7.30687e6i | 0.546248 | + | 0.946130i | 0.998527 | + | 0.0542531i | \(0.0172778\pi\) |
−0.452279 | + | 0.891876i | \(0.649389\pi\) | |||||||
\(570\) | −1.72302e6 | −0.222128 | ||||||||
\(571\) | −1.00713e6 | − | 1.74439e6i | −0.129269 | − | 0.223900i | 0.794125 | − | 0.607755i | \(-0.207930\pi\) |
−0.923393 | + | 0.383855i | \(0.874596\pi\) | |||||||
\(572\) | 7.77112e6 | − | 1.34600e7i | 0.993101 | − | 1.72010i | ||||
\(573\) | 758240. | − | 1.31331e6i | 0.0964762 | − | 0.167102i | ||||
\(574\) | 1.54747e6 | − | 2.68030e6i | 0.196039 | − | 0.339550i | ||||
\(575\) | 2.71220e6 | 0.342099 | ||||||||
\(576\) | −261091. | + | 452223.i | −0.0327896 | + | 0.0567932i | ||||
\(577\) | 3.63995e6 | − | 6.30458e6i | 0.455152 | − | 0.788346i | −0.543545 | − | 0.839380i | \(-0.682918\pi\) |
0.998697 | + | 0.0510342i | \(0.0162517\pi\) | |||||||
\(578\) | −1.48801e6 | − | 2.57731e6i | −0.185262 | − | 0.320883i | ||||
\(579\) | −1.82012e6 | − | 3.15254e6i | −0.225633 | − | 0.390808i | ||||
\(580\) | 3.30854e6 | 0.408382 | ||||||||
\(581\) | 3.52383e6 | 0.433086 | ||||||||
\(582\) | −162836. | − | 282040.i | −0.0199271 | − | 0.0345147i | ||||
\(583\) | 7.89955e6 | + | 1.36824e7i | 0.962567 | + | 1.66722i | ||||
\(584\) | 2.43265e6 | − | 4.21348e6i | 0.295154 | − | 0.511221i | ||||
\(585\) | −1.79530e6 | + | 3.10955e6i | −0.216894 | + | 0.375672i | ||||
\(586\) | −844070. | −0.101539 | ||||||||
\(587\) | −2.18347e6 | + | 3.78187e6i | −0.261548 | + | 0.453014i | −0.966653 | − | 0.256088i | \(-0.917566\pi\) |
0.705106 | + | 0.709102i | \(0.250900\pi\) | |||||||
\(588\) | −1.44296e6 | + | 2.49927e6i | −0.172112 | + | 0.298106i | ||||
\(589\) | 8.47468e6 | − | 1.46786e7i | 1.00655 | − | 1.74340i | ||||
\(590\) | 993076. | + | 1.72006e6i | 0.117450 | + | 0.203429i | ||||
\(591\) | 3.09796e6 | 0.364844 | ||||||||
\(592\) | 3.02727e6 | + | 5.24339e6i | 0.355016 | + | 0.614905i | ||||
\(593\) | −2.44473e6 | + | 4.23439e6i | −0.285492 | + | 0.494486i | −0.972728 | − | 0.231947i | \(-0.925490\pi\) |
0.687237 | + | 0.726434i | \(0.258824\pi\) | |||||||
\(594\) | 6.93224e6 | 0.806135 | ||||||||
\(595\) | −446111. | + | 772687.i | −0.0516596 | + | 0.0894770i | ||||
\(596\) | 1.33994e6 | + | 2.32084e6i | 0.154515 | + | 0.267627i | ||||
\(597\) | −1.45596e6 | − | 2.52179e6i | −0.167191 | − | 0.289583i | ||||
\(598\) | 2.21748e6 | 0.253576 | ||||||||
\(599\) | −100075. | − | 173334.i | −0.0113961 | − | 0.0197387i | 0.860271 | − | 0.509837i | \(-0.170294\pi\) |
−0.871667 | + | 0.490098i | \(0.836961\pi\) | |||||||
\(600\) | −2.79983e6 | −0.317507 | ||||||||
\(601\) | −3.52160e6 | −0.397699 | −0.198849 | − | 0.980030i | \(-0.563720\pi\) | ||||
−0.198849 | + | 0.980030i | \(0.563720\pi\) | |||||||
\(602\) | −1.55279e6 | + | 1.36137e6i | −0.174631 | + | 0.153104i | ||||
\(603\) | 5.73350e6 | 0.642135 | ||||||||
\(604\) | 7.23578e6 | 0.807036 | ||||||||
\(605\) | 7.09725e6 | + | 1.22928e7i | 0.788319 | + | 1.36541i | ||||
\(606\) | −1.09988e6 | −0.121664 | ||||||||
\(607\) | −869571. | − | 1.50614e6i | −0.0957929 | − | 0.165918i | 0.814146 | − | 0.580660i | \(-0.197205\pi\) |
−0.909939 | + | 0.414742i | \(0.863872\pi\) | |||||||
\(608\) | −7.03226e6 | − | 1.21802e7i | −0.771500 | − | 1.33628i | ||||
\(609\) | −1.36838e6 | + | 2.37011e6i | −0.149508 | + | 0.258956i | ||||
\(610\) | −3.47408e6 | −0.378020 | ||||||||
\(611\) | −6.47547e6 | + | 1.12158e7i | −0.701727 | + | 1.21543i | ||||
\(612\) | 810018. | + | 1.40299e6i | 0.0874210 | + | 0.151418i | ||||
\(613\) | 3.79841e6 | 0.408273 | 0.204136 | − | 0.978942i | \(-0.434561\pi\) | ||||
0.204136 | + | 0.978942i | \(0.434561\pi\) | |||||||
\(614\) | −65810.0 | − | 113986.i | −0.00704484 | − | 0.0122020i | ||||
\(615\) | 2.66170e6 | − | 4.61021e6i | 0.283774 | − | 0.491510i | ||||
\(616\) | −3.91043e6 | + | 6.77307e6i | −0.415215 | + | 0.719174i | ||||
\(617\) | 8.10025e6 | − | 1.40300e7i | 0.856615 | − | 1.48370i | −0.0185241 | − | 0.999828i | \(-0.505897\pi\) |
0.875139 | − | 0.483872i | \(-0.160770\pi\) | |||||||
\(618\) | 882898. | 0.0929906 | ||||||||
\(619\) | −6.36414e6 | + | 1.10230e7i | −0.667595 | + | 1.15631i | 0.310980 | + | 0.950417i | \(0.399343\pi\) |
−0.978575 | + | 0.205892i | \(0.933990\pi\) | |||||||
\(620\) | −2.79419e6 | + | 4.83968e6i | −0.291929 | + | 0.505635i | ||||
\(621\) | −2.35197e6 | − | 4.07373e6i | −0.244739 | − | 0.423900i | ||||
\(622\) | −577945. | − | 1.00103e6i | −0.0598977 | − | 0.103746i | ||||
\(623\) | 5.31542e6 | 0.548678 | ||||||||
\(624\) | 3.67226e6 | 0.377547 | ||||||||
\(625\) | −815485. | − | 1.41246e6i | −0.0835057 | − | 0.144636i | ||||
\(626\) | 2.56092e6 | + | 4.43565e6i | 0.261193 | + | 0.452399i | ||||
\(627\) | 9.22967e6 | − | 1.59863e7i | 0.937599 | − | 1.62397i | ||||
\(628\) | 2.26269e6 | − | 3.91910e6i | 0.228942 | − | 0.396540i | ||||
\(629\) | 4.61279e6 | 0.464876 | ||||||||
\(630\) | 408729. | − | 707939.i | 0.0410283 | − | 0.0710632i | ||||
\(631\) | −5.58801e6 | + | 9.67872e6i | −0.558707 | + | 0.967708i | 0.438898 | + | 0.898537i | \(0.355369\pi\) |
−0.997605 | + | 0.0691716i | \(0.977964\pi\) | |||||||
\(632\) | 675908. | − | 1.17071e6i | 0.0673124 | − | 0.116588i | ||||
\(633\) | −690603. | − | 1.19616e6i | −0.0685045 | − | 0.118653i | ||||
\(634\) | −2.01346e6 | −0.198938 | ||||||||
\(635\) | −2.41874e6 | − | 4.18939e6i | −0.238043 | − | 0.412303i | ||||
\(636\) | −2.50356e6 | + | 4.33629e6i | −0.245423 | + | 0.425085i | ||||
\(637\) | −8.66991e6 | −0.846576 | ||||||||
\(638\) | 3.72642e6 | − | 6.45435e6i | 0.362443 | − | 0.627770i | ||||
\(639\) | 3.88710e6 | + | 6.73266e6i | 0.376594 | + | 0.652281i | ||||
\(640\) | 2.93022e6 | + | 5.07530e6i | 0.282782 | + | 0.489792i | ||||
\(641\) | −1.39604e7 | −1.34200 | −0.671002 | − | 0.741456i | \(-0.734136\pi\) | ||||
−0.671002 | + | 0.741456i | \(0.734136\pi\) | |||||||
\(642\) | −1.32012e6 | − | 2.28651e6i | −0.126408 | − | 0.218945i | ||||
\(643\) | −1.15185e7 | −1.09867 | −0.549337 | − | 0.835601i | \(-0.685120\pi\) | ||||
−0.549337 | + | 0.835601i | \(0.685120\pi\) | |||||||
\(644\) | 2.40104e6 | 0.228131 | ||||||||
\(645\) | −2.67085e6 | + | 2.34161e6i | −0.252785 | + | 0.221623i | ||||
\(646\) | −2.33550e6 | −0.220190 | ||||||||
\(647\) | 7.86031e6 | 0.738209 | 0.369104 | − | 0.929388i | \(-0.379665\pi\) | ||||
0.369104 | + | 0.929388i | \(0.379665\pi\) | |||||||
\(648\) | −155313. | − | 269010.i | −0.0145302 | − | 0.0251670i | ||||
\(649\) | −2.12784e7 | −1.98302 | ||||||||
\(650\) | −1.90278e6 | − | 3.29572e6i | −0.176647 | − | 0.305962i | ||||
\(651\) | −2.31131e6 | − | 4.00330e6i | −0.213749 | − | 0.370225i | ||||
\(652\) | 5.16400e6 | − | 8.94432e6i | 0.475738 | − | 0.824002i | ||||
\(653\) | −1.39211e7 | −1.27758 | −0.638792 | − | 0.769379i | \(-0.720566\pi\) | ||||
−0.638792 | + | 0.769379i | \(0.720566\pi\) | |||||||
\(654\) | −592119. | + | 1.02558e6i | −0.0541333 | + | 0.0937616i | ||||
\(655\) | 1.35384e6 | + | 2.34492e6i | 0.123300 | + | 0.213562i | ||||
\(656\) | 9.47101e6 | 0.859284 | ||||||||
\(657\) | −2.72406e6 | − | 4.71820e6i | −0.246208 | − | 0.426445i | ||||
\(658\) | 1.47424e6 | − | 2.55347e6i | 0.132741 | − | 0.229914i | ||||
\(659\) | −6.30343e6 | + | 1.09179e7i | −0.565410 | + | 0.979319i | 0.431601 | + | 0.902064i | \(0.357949\pi\) |
−0.997011 | + | 0.0772545i | \(0.975385\pi\) | |||||||
\(660\) | −3.04312e6 | + | 5.27083e6i | −0.271931 | + | 0.470998i | ||||
\(661\) | −111996. | −0.00997012 | −0.00498506 | − | 0.999988i | \(-0.501587\pi\) | ||||
−0.00498506 | + | 0.999988i | \(0.501587\pi\) | |||||||
\(662\) | −2.11414e6 | + | 3.66179e6i | −0.187494 | + | 0.324750i | ||||
\(663\) | 1.39889e6 | − | 2.42296e6i | 0.123595 | − | 0.214073i | ||||
\(664\) | −3.36099e6 | − | 5.82140e6i | −0.295833 | − | 0.512398i | ||||
\(665\) | −2.80240e6 | − | 4.85391e6i | −0.245740 | − | 0.425635i | ||||
\(666\) | −4.22626e6 | −0.369207 | ||||||||
\(667\) | −5.05719e6 | −0.440144 | ||||||||
\(668\) | 8.59178e6 | + | 1.48814e7i | 0.744976 | + | 1.29034i | ||||
\(669\) | 3.73927e6 | + | 6.47661e6i | 0.323014 | + | 0.559477i | ||||
\(670\) | 1.36263e6 | − | 2.36014e6i | 0.117271 | − | 0.203119i | ||||
\(671\) | 1.86095e7 | − | 3.22326e7i | 1.59562 | − | 2.76369i | ||||
\(672\) | −3.83583e6 | −0.327669 | ||||||||
\(673\) | 6.26611e6 | − | 1.08532e7i | 0.533286 | − | 0.923678i | −0.465958 | − | 0.884807i | \(-0.654290\pi\) |
0.999244 | − | 0.0388717i | \(-0.0123764\pi\) | |||||||
\(674\) | −3.48814e6 | + | 6.04163e6i | −0.295763 | + | 0.512277i | ||||
\(675\) | −4.03637e6 | + | 6.99119e6i | −0.340982 | + | 0.590598i | ||||
\(676\) | 2.49035e6 | + | 4.31341e6i | 0.209601 | + | 0.363039i | ||||
\(677\) | 1.27948e7 | 1.07291 | 0.536455 | − | 0.843929i | \(-0.319763\pi\) | ||||
0.536455 | + | 0.843929i | \(0.319763\pi\) | |||||||
\(678\) | −172428. | − | 298655.i | −0.0144057 | − | 0.0249514i | ||||
\(679\) | 529689. | − | 917448.i | 0.0440906 | − | 0.0763672i | ||||
\(680\) | 1.70198e6 | 0.141151 | ||||||||
\(681\) | −173604. | + | 300691.i | −0.0143447 | + | 0.0248458i | ||||
\(682\) | 6.29420e6 | + | 1.09019e7i | 0.518179 | + | 0.897512i | ||||
\(683\) | −1.94779e6 | − | 3.37367e6i | −0.159768 | − | 0.276727i | 0.775017 | − | 0.631941i | \(-0.217741\pi\) |
−0.934785 | + | 0.355214i | \(0.884408\pi\) | |||||||
\(684\) | −1.01768e7 | −0.831710 | ||||||||
\(685\) | −2.44841e6 | − | 4.24076e6i | −0.199369 | − | 0.345317i | ||||
\(686\) | 4.83639e6 | 0.392384 | ||||||||
\(687\) | −4.08886e6 | −0.330530 | ||||||||
\(688\) | −5.98376e6 | − | 2.03215e6i | −0.481952 | − | 0.163676i | ||||
\(689\) | −1.50425e7 | −1.20718 | ||||||||
\(690\) | −868352. | −0.0694342 | ||||||||
\(691\) | 284444. | + | 492671.i | 0.0226622 | + | 0.0392520i | 0.877134 | − | 0.480246i | \(-0.159452\pi\) |
−0.854472 | + | 0.519498i | \(0.826119\pi\) | |||||||
\(692\) | −3.00043e6 | −0.238187 | ||||||||
\(693\) | 4.37886e6 | + | 7.58441e6i | 0.346360 | + | 0.599913i | ||||
\(694\) | −803041. | − | 1.39091e6i | −0.0632906 | − | 0.109623i | ||||
\(695\) | 1.84684e6 | − | 3.19882e6i | 0.145033 | − | 0.251204i | ||||
\(696\) | 5.22060e6 | 0.408505 | ||||||||
\(697\) | 3.60785e6 | − | 6.24898e6i | 0.281298 | − | 0.487222i | ||||
\(698\) | −2.11752e6 | − | 3.66765e6i | −0.164509 | − | 0.284937i | ||||
\(699\) | −1.27692e7 | −0.988484 | ||||||||
\(700\) | −2.06029e6 | − | 3.56853e6i | −0.158922 | − | 0.275260i | ||||
\(701\) | 6.57247e6 | − | 1.13839e7i | 0.505166 | − | 0.874973i | −0.494816 | − | 0.868998i | \(-0.664765\pi\) |
0.999982 | − | 0.00597517i | \(-0.00190197\pi\) | |||||||
\(702\) | −3.30012e6 | + | 5.71598e6i | −0.252748 | + | 0.437772i | ||||
\(703\) | −1.44884e7 | + | 2.50947e7i | −1.10569 | + | 1.91511i | ||||
\(704\) | −2.65910e6 | −0.202210 | ||||||||
\(705\) | 2.53575e6 | − | 4.39205e6i | 0.192147 | − | 0.332808i | ||||
\(706\) | −1050.95 | + | 1820.30i | −7.93545e−5 | + | 0.000137446i | ||||
\(707\) | −1.78889e6 | − | 3.09845e6i | −0.134597 | − | 0.233129i | ||||
\(708\) | −3.37181e6 | − | 5.84015e6i | −0.252802 | − | 0.437865i | ||||
\(709\) | 1.54954e7 | 1.15767 | 0.578836 | − | 0.815444i | \(-0.303507\pi\) | ||||
0.578836 | + | 0.815444i | \(0.303507\pi\) | |||||||
\(710\) | 3.69524e6 | 0.275104 | ||||||||
\(711\) | −756874. | − | 1.31094e6i | −0.0561500 | − | 0.0972546i | ||||
\(712\) | −5.06979e6 | − | 8.78113e6i | −0.374791 | − | 0.649158i | ||||
\(713\) | 4.27099e6 | − | 7.39758e6i | 0.314633 | − | 0.544961i | ||||
\(714\) | −318481. | + | 551625.i | −0.0233796 | + | 0.0404947i | ||||
\(715\) | −1.82844e7 | −1.33757 | ||||||||
\(716\) | 1.46949e6 | − | 2.54523e6i | 0.107123 | − | 0.185543i | ||||
\(717\) | −4.33467e6 | + | 7.50786e6i | −0.314889 | + | 0.545404i | ||||
\(718\) | 17197.0 | − | 29786.0i | 0.00124492 | − | 0.00215626i | ||||
\(719\) | −6.63582e6 | − | 1.14936e7i | −0.478710 | − | 0.829150i | 0.520992 | − | 0.853562i | \(-0.325562\pi\) |
−0.999702 | + | 0.0244114i | \(0.992229\pi\) | |||||||
\(720\) | 2.50155e6 | 0.179836 | ||||||||
\(721\) | 1.43599e6 | + | 2.48720e6i | 0.102876 | + | 0.178186i | ||||
\(722\) | 4.41649e6 | − | 7.64958e6i | 0.315307 | − | 0.546128i | ||||
\(723\) | −9.88052e6 | −0.702966 | ||||||||
\(724\) | −825199. | + | 1.42929e6i | −0.0585076 | + | 0.101338i | ||||
\(725\) | 4.33949e6 | + | 7.51621e6i | 0.306615 | + | 0.531073i | ||||
\(726\) | 5.06676e6 | + | 8.77588e6i | 0.356770 | + | 0.617944i | ||||
\(727\) | 7.27001e6 | 0.510151 | 0.255076 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255076 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(728\) | −3.72316e6 | − | 6.44870e6i | −0.260365 | − | 0.450966i | ||||
\(729\) | 8.21562e6 | 0.572561 | ||||||||
\(730\) | −2.58960e6 | −0.179856 | ||||||||
\(731\) | −3.62025e6 | + | 3.17397e6i | −0.250579 | + | 0.219690i | ||||
\(732\) | 1.17956e7 | 0.813659 | ||||||||
\(733\) | 1.00580e7 | 0.691438 | 0.345719 | − | 0.938338i | \(-0.387635\pi\) | ||||
0.345719 | + | 0.938338i | \(0.387635\pi\) | |||||||
\(734\) | −517035. | − | 895531.i | −0.0354225 | − | 0.0613536i | ||||
\(735\) | 3.39508e6 | 0.231810 | ||||||||
\(736\) | −3.54405e6 | − | 6.13848e6i | −0.241160 | − | 0.417702i | ||||
\(737\) | 1.45983e7 | + | 2.52850e7i | 0.989996 | + | 1.71472i | ||||
\(738\) | −3.30552e6 | + | 5.72534e6i | −0.223408 | + | 0.386955i | ||||
\(739\) | 7.58208e6 | 0.510713 | 0.255357 | − | 0.966847i | \(-0.417807\pi\) | ||||
0.255357 | + | 0.966847i | \(0.417807\pi\) | |||||||
\(740\) | 4.77699e6 | − | 8.27398e6i | 0.320682 | − | 0.555438i | ||||
\(741\) | 8.78765e6 | + | 1.52206e7i | 0.587932 | + | 1.01833i | ||||
\(742\) | 3.42466e6 | 0.228353 | ||||||||
\(743\) | 3.36685e6 | + | 5.83156e6i | 0.223744 | + | 0.387536i | 0.955942 | − | 0.293556i | \(-0.0948386\pi\) |
−0.732198 | + | 0.681092i | \(0.761505\pi\) | |||||||
\(744\) | −4.40899e6 | + | 7.63660e6i | −0.292016 | + | 0.505787i | ||||
\(745\) | 1.57635e6 | − | 2.73031e6i | 0.104055 | − | 0.180228i | ||||
\(746\) | 4.34356e6 | − | 7.52327e6i | 0.285759 | − | 0.494948i | ||||
\(747\) | −7.52719e6 | −0.493550 | ||||||||
\(748\) | −4.12484e6 | + | 7.14443e6i | −0.269559 | + | 0.466889i | ||||
\(749\) | 4.29420e6 | − | 7.43778e6i | 0.279691 | − | 0.484438i | ||||
\(750\) | 1.82440e6 | + | 3.15995e6i | 0.118431 | + | 0.205129i | ||||
\(751\) | 6.84753e6 | + | 1.18603e7i | 0.443031 | + | 0.767352i | 0.997913 | − | 0.0645774i | \(-0.0205699\pi\) |
−0.554882 | + | 0.831929i | \(0.687237\pi\) | |||||||
\(752\) | 9.02283e6 | 0.581833 | ||||||||
\(753\) | −1.09886e7 | −0.706244 | ||||||||
\(754\) | 3.54795e6 | + | 6.14524e6i | 0.227274 | + | 0.393650i | ||||
\(755\) | −4.25620e6 | − | 7.37195e6i | −0.271741 | − | 0.470668i | ||||
\(756\) | −3.57330e6 | + | 6.18913e6i | −0.227386 | + | 0.393845i | ||||
\(757\) | −254645. | + | 441058.i | −0.0161508 | + | 0.0279741i | −0.873988 | − | 0.485948i | \(-0.838475\pi\) |
0.857837 | + | 0.513922i | \(0.171808\pi\) | |||||||
\(758\) | 1.02325e7 | 0.646858 | ||||||||
\(759\) | 4.65148e6 | − | 8.05660e6i | 0.293081 | − | 0.507630i | ||||
\(760\) | −5.34580e6 | + | 9.25920e6i | −0.335721 | + | 0.581486i | ||||
\(761\) | −2.37927e6 | + | 4.12102e6i | −0.148930 | + | 0.257955i | −0.930832 | − | 0.365446i | \(-0.880916\pi\) |
0.781902 | + | 0.623401i | \(0.214250\pi\) | |||||||
\(762\) | −1.72675e6 | − | 2.99082e6i | −0.107731 | − | 0.186596i | ||||
\(763\) | −3.85220e6 | −0.239551 | ||||||||
\(764\) | −2.12870e6 | − | 3.68702e6i | −0.131942 | − | 0.228530i | ||||
\(765\) | 952930. | − | 1.65052e6i | 0.0588718 | − | 0.101969i | ||||
\(766\) | −1.94978e6 | −0.120064 | ||||||||
\(767\) | 1.01296e7 | − | 1.75451e7i | 0.621736 | − | 1.07688i | ||||
\(768\) | 1.58194e6 | + | 2.73999e6i | 0.0967801 | + | 0.167628i | ||||
\(769\) | −6.90091e6 | − | 1.19527e7i | −0.420814 | − | 0.728871i | 0.575205 | − | 0.818009i | \(-0.304922\pi\) |
−0.996019 | + | 0.0891377i | \(0.971589\pi\) | |||||||
\(770\) | 4.16273e6 | 0.253018 | ||||||||
\(771\) | 1.10556e6 | + | 1.91488e6i | 0.0669801 | + | 0.116013i | ||||
\(772\) | −1.02197e7 | −0.617156 | ||||||||
\(773\) | 2.81246e7 | 1.69293 | 0.846463 | − | 0.532447i | \(-0.178727\pi\) | ||||
0.846463 | + | 0.532447i | \(0.178727\pi\) | |||||||
\(774\) | 3.31689e6 | − | 2.90800e6i | 0.199011 | − | 0.174479i | ||||
\(775\) | −1.46595e7 | −0.876725 | ||||||||
\(776\) | −2.02084e6 | −0.120470 | ||||||||
\(777\) | 3.95144e6 | + | 6.84410e6i | 0.234803 | + | 0.406690i | ||||
\(778\) | 5.26425e6 | 0.311808 | ||||||||
\(779\) | 2.26640e7 | + | 3.92551e7i | 1.33811 | + | 2.31768i | ||||
\(780\) | −2.89738e6 | − | 5.01841e6i | −0.170517 | − | 0.295345i | ||||
\(781\) | −1.97942e7 | + | 3.42846e7i | −1.16121 | + | 2.01128i | ||||
\(782\) | −1.17702e6 | −0.0688284 | ||||||||
\(783\) | 7.52626e6 | − | 1.30359e7i | 0.438707 | − | 0.759863i | ||||
\(784\) | 3.02013e6 | + | 5.23103e6i | 0.175483 | + | 0.303946i | ||||
\(785\) | −5.32380e6 | −0.308353 | ||||||||
\(786\) | 966511. | + | 1.67405e6i | 0.0558021 | + | 0.0966520i | ||||
\(787\) | 1.36896e7 | − | 2.37111e7i | 0.787871 | − | 1.36463i | −0.139398 | − | 0.990236i | \(-0.544517\pi\) |
0.927269 | − | 0.374396i | \(-0.122150\pi\) | |||||||
\(788\) | 4.34865e6 | − | 7.53208e6i | 0.249482 | − | 0.432115i | ||||
\(789\) | 1.01492e7 | − | 1.75790e7i | 0.580418 | − | 1.00531i | ||||
\(790\) | −719516. | −0.0410178 | ||||||||
\(791\) | 560892. | − | 971493.i | 0.0318741 | − | 0.0552076i | ||||
\(792\) | 8.35301e6 | − | 1.44678e7i | 0.473184 | − | 0.819579i | ||||
\(793\) | 1.77183e7 | + | 3.06890e7i | 1.00055 | + | 1.73300i | ||||
\(794\) | 4.40421e6 | + | 7.62831e6i | 0.247923 | + | 0.429415i | ||||
\(795\) | 5.89053e6 | 0.330549 | ||||||||
\(796\) | −8.17500e6 | −0.457304 | ||||||||
\(797\) | −1.29354e6 | − | 2.24048e6i | −0.0721333 | − | 0.124938i | 0.827703 | − | 0.561167i | \(-0.189647\pi\) |
−0.899836 | + | 0.436228i | \(0.856314\pi\) | |||||||
\(798\) | −2.00065e6 | − | 3.46522e6i | −0.111215 | − | 0.192630i | ||||
\(799\) | 3.43712e6 | − | 5.95327e6i | 0.190471 | − | 0.329905i | ||||
\(800\) | −6.08218e6 | + | 1.05346e7i | −0.335996 | + | 0.581962i | ||||
\(801\) | −1.13542e7 | −0.625279 | ||||||||
\(802\) | 2.10926e6 | − | 3.65334e6i | 0.115796 | − | 0.200565i | ||||
\(803\) | 1.38717e7 | − | 2.40264e7i | 0.759172 | − | 1.31492i | ||||
\(804\) | −4.62655e6 | + | 8.01342e6i | −0.252416 | + | 0.437198i | ||||
\(805\) | −1.41233e6 | − | 2.44623e6i | −0.0768151 | − | 0.133048i | ||||
\(806\) | −1.19855e7 | −0.649860 | ||||||||
\(807\) | 1.76203e6 | + | 3.05192e6i | 0.0952421 | + | 0.164964i | ||||
\(808\) | −3.41245e6 | + | 5.91054e6i | −0.183881 | + | 0.318492i | ||||
\(809\) | 971190. | 0.0521715 | 0.0260857 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260857 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(810\) | −82666.7 | + | 143183.i | −0.00442709 | + | 0.00766794i | ||||
\(811\) | 9.97266e6 | + | 1.72731e7i | 0.532425 | + | 0.922188i | 0.999283 | + | 0.0378554i | \(0.0120526\pi\) |
−0.466858 | + | 0.884332i | \(0.654614\pi\) | |||||||
\(812\) | 3.84164e6 | + | 6.65392e6i | 0.204469 | + | 0.354150i | ||||
\(813\) | −1.88584e7 | −1.00064 | ||||||||
\(814\) | −1.07607e7 | − | 1.86380e7i | −0.569217 | − | 0.985913i | ||||
\(815\) | −1.21502e7 | −0.640751 | ||||||||
\(816\) | −1.94920e6 | −0.102478 | ||||||||
\(817\) | −5.89624e6 | − | 2.96642e7i | −0.309044 | − | 1.55481i | ||||
\(818\) | 1.25208e6 | 0.0654258 | ||||||||
\(819\) | −8.33830e6 | −0.434378 | ||||||||
\(820\) | −7.47254e6 | − | 1.29428e7i | −0.388091 | − | 0.672194i | ||||
\(821\) | −2.34166e7 | −1.21245 | −0.606227 | − | 0.795292i | \(-0.707318\pi\) | ||||
−0.606227 | + | 0.795292i | \(0.707318\pi\) | |||||||
\(822\) | −1.74793e6 | − | 3.02750e6i | −0.0902285 | − | 0.156280i | ||||
\(823\) | −1.06666e7 | − | 1.84751e7i | −0.548943 | − | 0.950796i | −0.998347 | − | 0.0574681i | \(-0.981697\pi\) |
0.449405 | − | 0.893328i | \(-0.351636\pi\) | |||||||
\(824\) | 2.73926e6 | − | 4.74453e6i | 0.140545 | − | 0.243431i | ||||
\(825\) | −1.59654e7 | −0.816668 | ||||||||
\(826\) | −2.30618e6 | + | 3.99441e6i | −0.117609 | + | 0.203706i | ||||
\(827\) | −6.22611e6 | − | 1.07839e7i | −0.316558 | − | 0.548294i | 0.663210 | − | 0.748434i | \(-0.269194\pi\) |
−0.979767 | + | 0.200139i | \(0.935860\pi\) | |||||||
\(828\) | −5.12882e6 | −0.259981 | ||||||||
\(829\) | 1.69617e7 | + | 2.93784e7i | 0.857199 | + | 1.48471i | 0.874590 | + | 0.484864i | \(0.161131\pi\) |
−0.0173903 | + | 0.999849i | \(0.505536\pi\) | |||||||
\(830\) | −1.78892e6 | + | 3.09849e6i | −0.0901353 | + | 0.156119i | ||||
\(831\) | 621773. | − | 1.07694e6i | 0.0312341 | − | 0.0540991i | ||||
\(832\) | 1.26588e6 | − | 2.19256e6i | 0.0633991 | − | 0.109810i | ||||
\(833\) | 4.60191e6 | 0.229787 | ||||||||
\(834\) | 1.31846e6 | − | 2.28365e6i | 0.0656377 | − | 0.113688i | ||||
\(835\) | 1.01076e7 | − | 1.75070e7i | 0.501688 | − | 0.868949i | ||||
\(836\) | −2.59116e7 | − | 4.48803e7i | −1.28227 | − | 2.22095i | ||||
\(837\) | 1.27124e7 | + | 2.20186e7i | 0.627212 | + | 1.08636i | ||||
\(838\) | 1.07733e7 | 0.529956 | ||||||||
\(839\) | −381374. | −0.0187045 | −0.00935226 | − | 0.999956i | \(-0.502977\pi\) | ||||
−0.00935226 | + | 0.999956i | \(0.502977\pi\) | |||||||
\(840\) | 1.45796e6 | + | 2.52527e6i | 0.0712933 | + | 0.123484i | ||||
\(841\) | 2.16411e6 | + | 3.74835e6i | 0.105509 | + | 0.182747i | ||||
\(842\) | −3.56003e6 | + | 6.16615e6i | −0.173051 | + | 0.299732i | ||||
\(843\) | −6.59488e6 | + | 1.14227e7i | −0.319623 | + | 0.553603i | ||||
\(844\) | −3.87764e6 | −0.187375 | ||||||||
\(845\) | 2.92972e6 | − | 5.07443e6i | 0.141151 | − | 0.244481i | ||||
\(846\) | −3.14911e6 | + | 5.45441e6i | −0.151273 | + | 0.262012i | ||||
\(847\) | −1.64816e7 | + | 2.85470e7i | −0.789390 | + | 1.36726i | ||||
\(848\) | 5.23999e6 | + | 9.07593e6i | 0.250231 | + | 0.433413i | ||||
\(849\) | −5.45235e6 | −0.259606 | ||||||||
\(850\) | 1.00998e6 | + | 1.74934e6i | 0.0479475 | + | 0.0830475i | ||||
\(851\) | −7.30175e6 | + | 1.26470e7i | −0.345623 | + | 0.598637i | ||||
\(852\) | −1.25465e7 | −0.592141 | ||||||||
\(853\) | 160333. | − | 277704.i | 0.00754482 | − | 0.0130680i | −0.862228 | − | 0.506520i | \(-0.830932\pi\) |
0.869773 | + | 0.493452i | \(0.164265\pi\) | |||||||
\(854\) | −4.03385e6 | − | 6.98683e6i | −0.189267 | − | 0.327820i | ||||
\(855\) | 5.98616e6 | + | 1.03683e7i | 0.280049 | + | 0.485058i | ||||
\(856\) | −1.63830e7 | −0.764206 | ||||||||
\(857\) | −6.03271e6 | − | 1.04490e7i | −0.280583 | − | 0.485983i | 0.690946 | − | 0.722907i | \(-0.257194\pi\) |
−0.971528 | + | 0.236923i | \(0.923861\pi\) | |||||||
\(858\) | −1.30533e7 | −0.605343 | ||||||||
\(859\) | −759379. | −0.0351136 | −0.0175568 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175568 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(860\) | 1.94405e6 | + | 9.78060e6i | 0.0896316 | + | 0.450941i | ||||
\(861\) | 1.23623e7 | 0.568319 | ||||||||
\(862\) | 1.06952e6 | 0.0490255 | ||||||||
\(863\) | −8.53763e6 | − | 1.47876e7i | −0.390221 | − | 0.675882i | 0.602258 | − | 0.798302i | \(-0.294268\pi\) |
−0.992478 | + | 0.122420i | \(0.960935\pi\) | |||||||
\(864\) | 2.10974e7 | 0.961492 | ||||||||
\(865\) | 1.76490e6 | + | 3.05690e6i | 0.0802011 | + | 0.138912i | ||||
\(866\) | −6.87236e6 | − | 1.19033e7i | −0.311395 | − | 0.539352i | ||||
\(867\) | 5.94364e6 | − | 1.02947e7i | 0.268537 | − | 0.465120i | ||||
\(868\) | −1.29776e7 | −0.584651 | ||||||||
\(869\) | 3.85422e6 | − | 6.67570e6i | 0.173136 | − | 0.299880i | ||||
\(870\) | −1.38936e6 | − | 2.40643e6i | −0.0622322 | − | 0.107789i | ||||
\(871\) | −2.77983e7 | −1.24158 | ||||||||
\(872\) | 3.67418e6 | + | 6.36387e6i | 0.163633 | + | 0.283420i | ||||
\(873\) | −1.13146e6 | + | 1.95974e6i | −0.0502462 | + | 0.0870289i | ||||
\(874\) | 3.69694e6 | − | 6.40328e6i | 0.163706 | − | 0.283546i | ||||
\(875\) | −5.93458e6 | + | 1.02790e7i | −0.262041 | + | 0.453869i | ||||
\(876\) | 8.79253e6 | 0.387127 | ||||||||
\(877\) | 2.23854e7 | − | 3.87727e7i | 0.982804 | − | 1.70227i | 0.331487 | − | 0.943460i | \(-0.392450\pi\) |
0.651316 | − | 0.758806i | \(-0.274217\pi\) | |||||||
\(878\) | −7.80554e6 | + | 1.35196e7i | −0.341717 | + | 0.591871i | ||||
\(879\) | −1.68576e6 | − | 2.91982e6i | −0.0735908 | − | 0.127463i | ||||
\(880\) | 6.36930e6 | + | 1.10320e7i | 0.277259 | + | 0.480226i | ||||
\(881\) | −1.72138e7 | −0.747202 | −0.373601 | − | 0.927590i | \(-0.621877\pi\) | ||||
−0.373601 | + | 0.927590i | \(0.621877\pi\) | |||||||
\(882\) | −4.21629e6 | −0.182498 | ||||||||
\(883\) | 3.32656e6 | + | 5.76177e6i | 0.143580 | + | 0.248688i | 0.928842 | − | 0.370476i | \(-0.120805\pi\) |
−0.785262 | + | 0.619163i | \(0.787472\pi\) | |||||||
\(884\) | −3.92730e6 | − | 6.80228e6i | −0.169030 | − | 0.292768i | ||||
\(885\) | −3.96670e6 | + | 6.87053e6i | −0.170244 | + | 0.294871i | ||||
\(886\) | 3.86318e6 | − | 6.69123e6i | 0.165334 | − | 0.286366i | ||||
\(887\) | 7.44897e6 | 0.317897 | 0.158949 | − | 0.987287i | \(-0.449190\pi\) | ||||
0.158949 | + | 0.987287i | \(0.449190\pi\) | |||||||
\(888\) | 7.53768e6 | − | 1.30556e7i | 0.320778 | − | 0.555604i | ||||
\(889\) | 5.61694e6 | − | 9.72882e6i | 0.238367 | − | 0.412863i | ||||
\(890\) | −2.69844e6 | + | 4.67383e6i | −0.114193 | + | 0.197787i | ||||
\(891\) | −885638. | − | 1.53397e6i | −0.0373733 | − | 0.0647325i | ||||
\(892\) | 2.09955e7 | 0.883514 | ||||||||
\(893\) | 2.15915e7 | + | 3.73975e7i | 0.906054 | + | 1.56933i | ||||
\(894\) | 1.12536e6 | − | 1.94918e6i | 0.0470921 | − | 0.0815659i | ||||
\(895\) | −3.45751e6 | −0.144280 | ||||||||
\(896\) | −6.80473e6 | + | 1.17861e7i | −0.283166 | + | 0.490458i | ||||
\(897\) | 4.42872e6 | + | 7.67076e6i | 0.183779 | + | 0.318315i | ||||
\(898\) | −2.45092e6 | − | 4.24511e6i | −0.101423 | − | 0.175670i | ||||
\(899\) | 2.73342e7 | 1.12799 | ||||||||
\(900\) | 4.40095e6 | + | 7.62267e6i | 0.181109 | + | 0.313690i | ||||
\(901\) | 7.98441e6 | 0.327665 | ||||||||
\(902\) | −3.36653e7 | −1.37774 | ||||||||
\(903\) | −7.81049e6 | − | 2.65253e6i | −0.318756 | − | 0.108253i | ||||
\(904\) | −2.13989e6 | −0.0870904 | ||||||||
\(905\) | 1.94158e6 | 0.0788014 | ||||||||
\(906\) | −3.03852e6 | − | 5.26287e6i | −0.122982 | − | 0.213011i | ||||
\(907\) | 2.91117e7 | 1.17503 | 0.587515 | − | 0.809213i | \(-0.300106\pi\) | ||||
0.587515 | + | 0.809213i | \(0.300106\pi\) | |||||||
\(908\) | 487381. | + | 844169.i | 0.0196180 | + | 0.0339793i | ||||
\(909\) | 3.82122e6 | + | 6.61855e6i | 0.153388 | + | 0.265676i | ||||
\(910\) | −1.98168e6 | + | 3.43238e6i | −0.0793288 | + | 0.137402i | ||||
\(911\) | 2.00574e7 | 0.800715 | 0.400358 | − | 0.916359i | \(-0.368886\pi\) | ||||
0.400358 | + | 0.916359i | \(0.368886\pi\) | |||||||
\(912\) | 6.12229e6 | − | 1.06041e7i | 0.243740 | − | 0.422170i | ||||
\(913\) | −1.91653e7 | − | 3.31953e7i | −0.760919 | − | 1.31795i | ||||
\(914\) | 1.67520e7 | 0.663286 | ||||||||
\(915\) | −6.93836e6 | − | 1.20176e7i | −0.273971 | − | 0.474531i | ||||
\(916\) | −5.73959e6 | + | 9.94126e6i | −0.226018 | + | 0.391474i | ||||
\(917\) | −3.14396e6 | + | 5.44550e6i | −0.123468 | + | 0.213852i | ||||
\(918\) | 1.75168e6 | − | 3.03399e6i | 0.0686037 | − | 0.118825i | ||||
\(919\) | 6.60703e6 | 0.258058 | 0.129029 | − | 0.991641i | \(-0.458814\pi\) | ||||
0.129029 | + | 0.991641i | \(0.458814\pi\) | |||||||
\(920\) | −2.69413e6 | + | 4.66637e6i | −0.104942 | + | 0.181765i | ||||
\(921\) | 262869. | − | 455302.i | 0.0102115 | − | 0.0176869i | ||||
\(922\) | 911852. | + | 1.57937e6i | 0.0353262 | + | 0.0611868i | ||||
\(923\) | −1.88463e7 | − | 3.26427e7i | −0.728150 | − | 1.26119i | ||||
\(924\) | −1.41338e7 | −0.544601 | ||||||||
\(925\) | 2.50620e7 | 0.963078 | ||||||||
\(926\) | 3.18681e6 | + | 5.51972e6i | 0.122132 | + | 0.211539i | ||||
\(927\) | −3.06739e6 | − | 5.31287e6i | −0.117238 | − | 0.203063i | ||||
\(928\) | 1.13409e7 | − | 1.96430e7i | 0.432293 | − | 0.748753i | ||||
\(929\) | 7.58813e6 | − | 1.31430e7i | 0.288467 | − | 0.499639i | −0.684977 | − | 0.728564i | \(-0.740188\pi\) |
0.973444 | + | 0.228925i | \(0.0735212\pi\) | |||||||
\(930\) | 4.69345e6 | 0.177945 | ||||||||
\(931\) | −1.44543e7 | + | 2.50355e7i | −0.546540 | + | 0.946634i | ||||
\(932\) | −1.79243e7 | + | 3.10457e7i | −0.675930 | + | 1.17074i | ||||
\(933\) | 2.30852e6 | − | 3.99847e6i | 0.0868219 | − | 0.150380i | ||||
\(934\) | −3.43267e6 | − | 5.94555e6i | −0.128755 | − | 0.223010i | ||||
\(935\) | 9.70518e6 | 0.363057 | ||||||||
\(936\) | 7.95297e6 | + | 1.37749e7i | 0.296715 | + | 0.513926i | ||||
\(937\) | 2.73730e6 | − | 4.74114e6i | 0.101853 | − | 0.176414i | −0.810595 | − | 0.585607i | \(-0.800856\pi\) |
0.912448 | + | 0.409193i | \(0.134190\pi\) | |||||||
\(938\) | 6.32873e6 | 0.234860 | ||||||||
\(939\) | −1.02293e7 | + | 1.77176e7i | −0.378599 | + | 0.655753i | ||||
\(940\) | −7.11894e6 | − | 1.23304e7i | −0.262782 | − | 0.455152i | ||||
\(941\) | −3.29319e6 | − | 5.70397e6i | −0.121239 | − | 0.209992i | 0.799018 | − | 0.601308i | \(-0.205353\pi\) |
−0.920257 | + | 0.391316i | \(0.872020\pi\) | |||||||
\(942\) | −3.80068e6 | −0.139552 | ||||||||
\(943\) | 1.14220e7 | + | 1.97834e7i | 0.418275 | + | 0.724473i | ||||
\(944\) | −1.41145e7 | −0.515509 | ||||||||
\(945\) | 8.40748e6 | 0.306257 | ||||||||
\(946\) | 2.12697e7 | + | 7.22343e6i | 0.772740 | + | 0.262431i | ||||
\(947\) | 1.91206e7 | 0.692831 | 0.346415 | − | 0.938081i | \(-0.387399\pi\) | ||||
0.346415 | + | 0.938081i | \(0.387399\pi\) | |||||||
\(948\) | 2.44299e6 | 0.0882877 | ||||||||
\(949\) | 1.32073e7 | + | 2.28758e7i | 0.476047 | + | 0.824537i | ||||
\(950\) | −1.26891e7 | −0.456165 | ||||||||
\(951\) | −4.02123e6 | − | 6.96498e6i | −0.144181 | − | 0.249729i | ||||
\(952\) | 1.97622e6 | + | 3.42291e6i | 0.0706713 | + | 0.122406i | ||||
\(953\) | −6.72804e6 | + | 1.16533e7i | −0.239970 | + | 0.415640i | −0.960705 | − | 0.277570i | \(-0.910471\pi\) |
0.720736 | + | 0.693210i | \(0.243804\pi\) | |||||||
\(954\) | −7.31534e6 | −0.260234 | ||||||||
\(955\) | −2.50427e6 | + | 4.33753e6i | −0.0888533 | + | 0.153898i | ||||
\(956\) | 1.21693e7 | + | 2.10778e7i | 0.430645 | + | 0.745899i | ||||
\(957\) | 2.97693e7 | 1.05072 | ||||||||
\(958\) | 5.33021e6 | + | 9.23220e6i | 0.187642 | + | 0.325006i | ||||
\(959\) | 5.68582e6 | − | 9.84814e6i | 0.199640 | − | 0.345786i | ||||
\(960\) | −495709. | + | 858593.i | −0.0173600 | + | 0.0300683i | ||||
\(961\) | −8.77018e6 | + | 1.51904e7i | −0.306338 | + | 0.530592i | ||||
\(962\) | 2.04906e7 | 0.713867 | ||||||||
\(963\) | −9.17277e6 | + | 1.58877e7i | −0.318739 | + | 0.552072i | ||||
\(964\) | −1.38694e7 | + | 2.40225e7i | −0.480691 | + | 0.832581i | ||||
\(965\) | 6.01138e6 | + | 1.04120e7i | 0.207805 | + | 0.359929i | ||||
\(966\) | −1.00827e6 | − | 1.74637e6i | −0.0347643 | − | 0.0602135i | ||||
\(967\) | −4.26507e7 | −1.46676 | −0.733382 | − | 0.679817i | \(-0.762059\pi\) | ||||
−0.733382 | + | 0.679817i | \(0.762059\pi\) | |||||||
\(968\) | 6.28800e7 | 2.15687 | ||||||||
\(969\) | −4.66441e6 | − | 8.07899e6i | −0.159583 | − | 0.276406i | ||||
\(970\) | 537806. | + | 931508.i | 0.0183526 | + | 0.0317876i | ||||
\(971\) | −2.01049e7 | + | 3.48227e7i | −0.684310 | + | 1.18526i | 0.289343 | + | 0.957226i | \(0.406563\pi\) |
−0.973653 | + | 0.228035i | \(0.926770\pi\) | |||||||
\(972\) | 1.23013e7 | − | 2.13065e7i | 0.417625 | − | 0.723347i | ||||
\(973\) | 8.57765e6 | 0.290460 | ||||||||
\(974\) | 5.70064e6 | − | 9.87380e6i | 0.192542 | − | 0.333493i | ||||
\(975\) | 7.60041e6 | − | 1.31643e7i | 0.256050 | − | 0.443492i | ||||
\(976\) | 1.23442e7 | − | 2.13808e7i | 0.414800 | − | 0.718455i | ||||
\(977\) | 2.08409e7 | + | 3.60974e7i | 0.698521 | + | 1.20987i | 0.968979 | + | 0.247142i | \(0.0794913\pi\) |
−0.270459 | + | 0.962732i | \(0.587175\pi\) | |||||||
\(978\) | −8.67407e6 | −0.289985 | ||||||||
\(979\) | −2.89093e7 | − | 5.00724e7i | −0.964010 | − | 1.66971i | ||||
\(980\) | 4.76572e6 | − | 8.25447e6i | 0.158512 | − | 0.274552i | ||||
\(981\) | 8.22862e6 | 0.272995 | ||||||||
\(982\) | −8.90246e6 | + | 1.54195e7i | −0.294599 | + | 0.510261i | ||||
\(983\) | −2.38251e7 | − | 4.12663e7i | −0.786414 | − | 1.36211i | −0.928151 | − | 0.372204i | \(-0.878602\pi\) |
0.141737 | − | 0.989904i | \(-0.454731\pi\) | |||||||
\(984\) | −1.17910e7 | − | 2.04227e7i | −0.388208 | − | 0.672395i | ||||
\(985\) | −1.02318e7 | −0.336016 | ||||||||
\(986\) | −1.88322e6 | − | 3.26184e6i | −0.0616893 | − | 0.106849i | ||||
\(987\) | 1.17773e7 | 0.384816 | ||||||||
\(988\) | 4.93414e7 | 1.60812 | ||||||||
\(989\) | −2.97153e6 | − | 1.49499e7i | −0.0966027 | − | 0.486013i | ||||
\(990\) | −8.89193e6 | −0.288342 | ||||||||
\(991\) | −3.40171e7 | −1.10031 | −0.550153 | − | 0.835064i | \(-0.685431\pi\) | ||||
−0.550153 | + | 0.835064i | \(0.685431\pi\) | |||||||
\(992\) | 1.91556e7 | + | 3.31786e7i | 0.618042 | + | 1.07048i | ||||
\(993\) | −1.68892e7 | −0.543547 | ||||||||
\(994\) | 4.29065e6 | + | 7.43163e6i | 0.137739 | + | 0.238571i | ||||
\(995\) | 4.80866e6 | + | 8.32884e6i | 0.153981 | + | 0.266702i | ||||
\(996\) | 6.07394e6 | − | 1.05204e7i | 0.194009 | − | 0.336034i | ||||
\(997\) | −1.36706e7 | −0.435560 | −0.217780 | − | 0.975998i | \(-0.569882\pi\) | ||||
−0.217780 | + | 0.975998i | \(0.569882\pi\) | |||||||
\(998\) | −9.82806e6 | + | 1.70227e7i | −0.312350 | + | 0.541006i | ||||
\(999\) | −2.17333e7 | − | 3.76432e7i | −0.688989 | − | 1.19336i |
(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 | 43.6.c.a.36.8 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.8 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.8 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.8 | yes | 34 | 1.1 | even | 1 | trivial |