Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,6,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.1329671342\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.20 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.6.d.a.137.18 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | −14.2654 | + | 6.28478i | −0.915126 | + | 0.403169i | ||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 46.4212 | 0.830408 | 0.415204 | − | 0.909728i | \(-0.363710\pi\) | ||||
0.415204 | + | 0.909728i | \(0.363710\pi\) | |||||||
\(6\) | −25.1391 | − | 57.0616i | −0.285083 | − | 0.647092i | ||||
\(7\) | 104.982i | 0.809786i | 0.914364 | + | 0.404893i | \(0.132691\pi\) | ||||
−0.914364 | + | 0.404893i | \(0.867309\pi\) | |||||||
\(8\) | − | 64.0000i | − | 0.353553i | ||||||
\(9\) | 164.003 | − | 179.310i | 0.674910 | − | 0.737900i | ||||
\(10\) | 185.685i | 0.587187i | ||||||||
\(11\) | −578.520 | −1.44157 | −0.720786 | − | 0.693157i | \(-0.756219\pi\) | ||||
−0.720786 | + | 0.693157i | \(0.756219\pi\) | |||||||
\(12\) | 228.246 | − | 100.556i | 0.457563 | − | 0.201584i | ||||
\(13\) | −661.326 | −1.08532 | −0.542660 | − | 0.839953i | \(-0.682583\pi\) | ||||
−0.542660 | + | 0.839953i | \(0.682583\pi\) | |||||||
\(14\) | −419.928 | −0.572605 | ||||||||
\(15\) | −662.217 | + | 291.747i | −0.759928 | + | 0.334795i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −54.6274 | −0.0458446 | −0.0229223 | − | 0.999737i | \(-0.507297\pi\) | ||||
−0.0229223 | + | 0.999737i | \(0.507297\pi\) | |||||||
\(18\) | 717.239 | + | 656.013i | 0.521774 | + | 0.477234i | ||||
\(19\) | − | 1057.69i | − | 0.672164i | −0.941833 | − | 0.336082i | \(-0.890898\pi\) | ||
0.941833 | − | 0.336082i | \(-0.109102\pi\) | |||||||
\(20\) | −742.740 | −0.415204 | ||||||||
\(21\) | −659.789 | − | 1497.61i | −0.326480 | − | 0.741056i | ||||
\(22\) | − | 2314.08i | − | 1.01935i | ||||||
\(23\) | 2390.00 | − | 851.011i | 0.942061 | − | 0.335441i | ||||
\(24\) | 402.226 | + | 912.985i | 0.142542 | + | 0.323546i | ||||
\(25\) | −970.068 | −0.310422 | ||||||||
\(26\) | − | 2645.31i | − | 0.767436i | ||||||
\(27\) | −1212.65 | + | 3588.65i | −0.320130 | + | 0.947374i | ||||
\(28\) | − | 1679.71i | − | 0.404893i | ||||||
\(29\) | − | 2907.49i | − | 0.641983i | −0.947082 | − | 0.320991i | \(-0.895984\pi\) | ||
0.947082 | − | 0.320991i | \(-0.104016\pi\) | |||||||
\(30\) | −1166.99 | − | 2648.87i | −0.236736 | − | 0.537350i | ||||
\(31\) | 8286.18 | 1.54864 | 0.774319 | − | 0.632795i | \(-0.218093\pi\) | ||||
0.774319 | + | 0.632795i | \(0.218093\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | 8252.82 | − | 3635.87i | 1.31922 | − | 0.581197i | ||||
\(34\) | − | 218.510i | − | 0.0324170i | ||||||
\(35\) | 4873.40i | 0.672453i | ||||||||
\(36\) | −2624.05 | + | 2868.95i | −0.337455 | + | 0.368950i | ||||
\(37\) | − | 12502.0i | − | 1.50133i | −0.660683 | − | 0.750665i | \(-0.729733\pi\) | ||
0.660683 | − | 0.750665i | \(-0.270267\pi\) | |||||||
\(38\) | 4230.77 | 0.475291 | ||||||||
\(39\) | 9434.08 | − | 4156.29i | 0.993203 | − | 0.437567i | ||||
\(40\) | − | 2970.96i | − | 0.293594i | ||||||
\(41\) | − | 7396.71i | − | 0.687193i | −0.939117 | − | 0.343597i | \(-0.888355\pi\) | ||
0.939117 | − | 0.343597i | \(-0.111645\pi\) | |||||||
\(42\) | 5990.45 | − | 2639.16i | 0.524006 | − | 0.230856i | ||||
\(43\) | − | 3072.54i | − | 0.253412i | −0.991940 | − | 0.126706i | \(-0.959560\pi\) | ||
0.991940 | − | 0.126706i | \(-0.0404405\pi\) | |||||||
\(44\) | 9256.32 | 0.720786 | ||||||||
\(45\) | 7613.23 | − | 8323.78i | 0.560451 | − | 0.612758i | ||||
\(46\) | 3404.04 | + | 9560.02i | 0.237192 | + | 0.666138i | ||||
\(47\) | 22036.7i | 1.45513i | 0.686039 | + | 0.727564i | \(0.259348\pi\) | ||||
−0.686039 | + | 0.727564i | \(0.740652\pi\) | |||||||
\(48\) | −3651.94 | + | 1608.90i | −0.228781 | + | 0.100792i | ||||
\(49\) | 5785.76 | 0.344247 | ||||||||
\(50\) | − | 3880.27i | − | 0.219501i | ||||||
\(51\) | 779.281 | − | 343.321i | 0.0419536 | − | 0.0184831i | ||||
\(52\) | 10581.2 | 0.542660 | ||||||||
\(53\) | −24688.7 | −1.20728 | −0.603642 | − | 0.797256i | \(-0.706284\pi\) | ||||
−0.603642 | + | 0.797256i | \(0.706284\pi\) | |||||||
\(54\) | −14354.6 | − | 4850.60i | −0.669894 | − | 0.226366i | ||||
\(55\) | −26855.6 | −1.19709 | ||||||||
\(56\) | 6718.85 | 0.286302 | ||||||||
\(57\) | 6647.35 | + | 15088.4i | 0.270995 | + | 0.615114i | ||||
\(58\) | 11630.0 | 0.453950 | ||||||||
\(59\) | − | 8214.34i | − | 0.307215i | −0.988132 | − | 0.153608i | \(-0.950911\pi\) | ||
0.988132 | − | 0.153608i | \(-0.0490892\pi\) | |||||||
\(60\) | 10595.5 | − | 4667.95i | 0.379964 | − | 0.167397i | ||||
\(61\) | − | 55044.6i | − | 1.89404i | −0.321170 | − | 0.947021i | \(-0.604076\pi\) | ||
0.321170 | − | 0.947021i | \(-0.395924\pi\) | |||||||
\(62\) | 33144.7i | 1.09505i | ||||||||
\(63\) | 18824.3 | + | 17217.4i | 0.597541 | + | 0.546533i | ||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | −30699.6 | −0.901258 | ||||||||
\(66\) | 14543.5 | + | 33011.3i | 0.410968 | + | 0.932830i | ||||
\(67\) | − | 6618.24i | − | 0.180117i | −0.995936 | − | 0.0900587i | \(-0.971295\pi\) | ||
0.995936 | − | 0.0900587i | \(-0.0287055\pi\) | |||||||
\(68\) | 874.038 | 0.0229223 | ||||||||
\(69\) | −28746.0 | + | 27160.7i | −0.726866 | + | 0.686780i | ||||
\(70\) | −19493.6 | −0.475496 | ||||||||
\(71\) | − | 20997.9i | − | 0.494345i | −0.968971 | − | 0.247173i | \(-0.920498\pi\) | ||
0.968971 | − | 0.247173i | \(-0.0795015\pi\) | |||||||
\(72\) | −11475.8 | − | 10496.2i | −0.260887 | − | 0.238617i | ||||
\(73\) | 48703.2 | 1.06967 | 0.534835 | − | 0.844956i | \(-0.320374\pi\) | ||||
0.534835 | + | 0.844956i | \(0.320374\pi\) | |||||||
\(74\) | 50008.1 | 1.06160 | ||||||||
\(75\) | 13838.4 | − | 6096.66i | 0.284075 | − | 0.125152i | ||||
\(76\) | 16923.1i | 0.336082i | ||||||||
\(77\) | − | 60734.2i | − | 1.16737i | ||||||
\(78\) | 16625.2 | + | 37736.3i | 0.309406 | + | 0.702301i | ||||
\(79\) | − | 44636.7i | − | 0.804683i | −0.915490 | − | 0.402341i | \(-0.868196\pi\) | ||
0.915490 | − | 0.402341i | \(-0.131804\pi\) | |||||||
\(80\) | 11883.8 | 0.207602 | ||||||||
\(81\) | −5254.93 | − | 58814.7i | −0.0889926 | − | 0.996032i | ||||
\(82\) | 29586.8 | 0.485919 | ||||||||
\(83\) | −62926.6 | −1.00263 | −0.501313 | − | 0.865266i | \(-0.667150\pi\) | ||||
−0.501313 | + | 0.865266i | \(0.667150\pi\) | |||||||
\(84\) | 10556.6 | + | 23961.8i | 0.163240 | + | 0.370528i | ||||
\(85\) | −2535.87 | −0.0380697 | ||||||||
\(86\) | 12290.2 | 0.179189 | ||||||||
\(87\) | 18272.9 | + | 41476.5i | 0.258827 | + | 0.587495i | ||||
\(88\) | 37025.3i | 0.509673i | ||||||||
\(89\) | −114278. | −1.52928 | −0.764640 | − | 0.644458i | \(-0.777083\pi\) | ||||
−0.764640 | + | 0.644458i | \(0.777083\pi\) | |||||||
\(90\) | 33295.1 | + | 30452.9i | 0.433286 | + | 0.396299i | ||||
\(91\) | − | 69427.4i | − | 0.878876i | ||||||
\(92\) | −38240.1 | + | 13616.2i | −0.471031 | + | 0.167720i | ||||
\(93\) | −118206. | + | 52076.8i | −1.41720 | + | 0.624362i | ||||
\(94\) | −88146.7 | −1.02893 | ||||||||
\(95\) | − | 49099.4i | − | 0.558170i | ||||||
\(96\) | −6435.61 | − | 14607.8i | −0.0712708 | − | 0.161773i | ||||
\(97\) | − | 81715.9i | − | 0.881815i | −0.897553 | − | 0.440907i | \(-0.854657\pi\) | ||
0.897553 | − | 0.440907i | \(-0.145343\pi\) | |||||||
\(98\) | 23143.0i | 0.243419i | ||||||||
\(99\) | −94879.1 | + | 103734.i | −0.972932 | + | 1.06374i | ||||
\(100\) | 15521.1 | 0.155211 | ||||||||
\(101\) | 36061.1i | 0.351751i | 0.984412 | + | 0.175876i | \(0.0562756\pi\) | ||||
−0.984412 | + | 0.175876i | \(0.943724\pi\) | |||||||
\(102\) | 1373.28 | + | 3117.13i | 0.0130695 | + | 0.0296657i | ||||
\(103\) | 151498.i | 1.40707i | 0.710662 | + | 0.703534i | \(0.248396\pi\) | ||||
−0.710662 | + | 0.703534i | \(0.751604\pi\) | |||||||
\(104\) | 42324.9i | 0.383718i | ||||||||
\(105\) | −30628.2 | − | 69521.0i | −0.271112 | − | 0.615379i | ||||
\(106\) | − | 98755.0i | − | 0.853679i | ||||||
\(107\) | 19393.7 | 0.163757 | 0.0818786 | − | 0.996642i | \(-0.473908\pi\) | ||||
0.0818786 | + | 0.996642i | \(0.473908\pi\) | |||||||
\(108\) | 19402.4 | − | 57418.4i | 0.160065 | − | 0.473687i | ||||
\(109\) | 134089.i | 1.08100i | 0.841342 | + | 0.540502i | \(0.181766\pi\) | ||||
−0.841342 | + | 0.540502i | \(0.818234\pi\) | |||||||
\(110\) | − | 107422.i | − | 0.846474i | ||||||
\(111\) | 78572.5 | + | 178346.i | 0.605289 | + | 1.37391i | ||||
\(112\) | 26875.4i | 0.202446i | ||||||||
\(113\) | −27811.4 | −0.204893 | −0.102446 | − | 0.994739i | \(-0.532667\pi\) | ||||
−0.102446 | + | 0.994739i | \(0.532667\pi\) | |||||||
\(114\) | −60353.6 | + | 26589.4i | −0.434951 | + | 0.191623i | ||||
\(115\) | 110947. | − | 39505.0i | 0.782296 | − | 0.278553i | ||||
\(116\) | 46519.8i | 0.320991i | ||||||||
\(117\) | −108460. | + | 118582.i | −0.732493 | + | 0.800857i | ||||
\(118\) | 32857.4 | 0.217234 | ||||||||
\(119\) | − | 5734.90i | − | 0.0371243i | ||||||
\(120\) | 18671.8 | + | 42381.9i | 0.118368 | + | 0.268675i | ||||
\(121\) | 173634. | 1.07813 | ||||||||
\(122\) | 220178. | 1.33929 | ||||||||
\(123\) | 46486.7 | + | 105517.i | 0.277055 | + | 0.628868i | ||||
\(124\) | −132579. | −0.774319 | ||||||||
\(125\) | −190098. | −1.08819 | ||||||||
\(126\) | −68869.6 | + | 75297.2i | −0.386457 | + | 0.422525i | ||||
\(127\) | −266793. | −1.46779 | −0.733897 | − | 0.679261i | \(-0.762300\pi\) | ||||
−0.733897 | + | 0.679261i | \(0.762300\pi\) | |||||||
\(128\) | − | 16384.0i | − | 0.0883883i | ||||||
\(129\) | 19310.3 | + | 43831.1i | 0.102168 | + | 0.231904i | ||||
\(130\) | − | 122798.i | − | 0.637286i | ||||||
\(131\) | − | 159200.i | − | 0.810520i | −0.914202 | − | 0.405260i | \(-0.867181\pi\) | ||
0.914202 | − | 0.405260i | \(-0.132819\pi\) | |||||||
\(132\) | −132045. | + | 58173.9i | −0.659610 | + | 0.290598i | ||||
\(133\) | 111039. | 0.544309 | ||||||||
\(134\) | 26473.0 | 0.127362 | ||||||||
\(135\) | −56292.7 | + | 166589.i | −0.265838 | + | 0.786707i | ||||
\(136\) | 3496.15i | 0.0162085i | ||||||||
\(137\) | −1507.05 | −0.00686003 | −0.00343001 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343001 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(138\) | −108643. | − | 114984.i | −0.485627 | − | 0.513972i | ||||
\(139\) | 87208.8 | 0.382845 | 0.191423 | − | 0.981508i | \(-0.438690\pi\) | ||||
0.191423 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(140\) | − | 77974.4i | − | 0.336226i | ||||||
\(141\) | −138496. | − | 314362.i | −0.586662 | − | 1.33163i | ||||
\(142\) | 83991.7 | 0.349555 | ||||||||
\(143\) | 382590. | 1.56457 | ||||||||
\(144\) | 41984.8 | − | 45903.3i | 0.168728 | − | 0.184475i | ||||
\(145\) | − | 134969.i | − | 0.533108i | ||||||
\(146\) | 194813.i | 0.756372i | ||||||||
\(147\) | −82536.2 | + | 36362.2i | −0.315029 | + | 0.138790i | ||||
\(148\) | 200032.i | 0.750665i | ||||||||
\(149\) | −172655. | −0.637107 | −0.318553 | − | 0.947905i | \(-0.603197\pi\) | ||||
−0.318553 | + | 0.947905i | \(0.603197\pi\) | |||||||
\(150\) | 24386.7 | + | 55353.6i | 0.0884961 | + | 0.200871i | ||||
\(151\) | −218207. | −0.778802 | −0.389401 | − | 0.921068i | \(-0.627318\pi\) | ||||
−0.389401 | + | 0.921068i | \(0.627318\pi\) | |||||||
\(152\) | −67692.3 | −0.237646 | ||||||||
\(153\) | −8959.06 | + | 9795.22i | −0.0309410 | + | 0.0338287i | ||||
\(154\) | 242937. | 0.825452 | ||||||||
\(155\) | 384655. | 1.28600 | ||||||||
\(156\) | −150945. | + | 66500.6i | −0.496602 | + | 0.218783i | ||||
\(157\) | − | 495612.i | − | 1.60470i | −0.596856 | − | 0.802348i | \(-0.703584\pi\) | ||
0.596856 | − | 0.802348i | \(-0.296416\pi\) | |||||||
\(158\) | 178547. | 0.568997 | ||||||||
\(159\) | 352195. | − | 155163.i | 1.10482 | − | 0.486739i | ||||
\(160\) | 47535.4i | 0.146797i | ||||||||
\(161\) | 89340.9 | + | 250908.i | 0.271635 | + | 0.762868i | ||||
\(162\) | 235259. | − | 21019.7i | 0.704301 | − | 0.0629273i | ||||
\(163\) | −5266.61 | −0.0155261 | −0.00776304 | − | 0.999970i | \(-0.502471\pi\) | ||||
−0.00776304 | + | 0.999970i | \(0.502471\pi\) | |||||||
\(164\) | 118347.i | 0.343597i | ||||||||
\(165\) | 383106. | − | 168782.i | 1.09549 | − | 0.482631i | ||||
\(166\) | − | 251706.i | − | 0.708964i | ||||||
\(167\) | 307465.i | 0.853109i | 0.904462 | + | 0.426554i | \(0.140273\pi\) | ||||
−0.904462 | + | 0.426554i | \(0.859727\pi\) | |||||||
\(168\) | −95847.1 | + | 42226.5i | −0.262003 | + | 0.115428i | ||||
\(169\) | 66059.5 | 0.177917 | ||||||||
\(170\) | − | 10143.5i | − | 0.0269194i | ||||||
\(171\) | −189654. | − | 173465.i | −0.495989 | − | 0.453650i | ||||
\(172\) | 49160.7i | 0.126706i | ||||||||
\(173\) | 678994.i | 1.72485i | 0.506186 | + | 0.862424i | \(0.331055\pi\) | ||||
−0.506186 | + | 0.862424i | \(0.668945\pi\) | |||||||
\(174\) | −165906. | + | 73091.7i | −0.415422 | + | 0.183019i | ||||
\(175\) | − | 101840.i | − | 0.251375i | ||||||
\(176\) | −148101. | −0.360393 | ||||||||
\(177\) | 51625.3 | + | 117181.i | 0.123860 | + | 0.281141i | ||||
\(178\) | − | 457111.i | − | 1.08136i | ||||||
\(179\) | 86085.4i | 0.200815i | 0.994946 | + | 0.100408i | \(0.0320147\pi\) | ||||
−0.994946 | + | 0.100408i | \(0.967985\pi\) | |||||||
\(180\) | −121812. | + | 133180.i | −0.280226 | + | 0.306379i | ||||
\(181\) | − | 716990.i | − | 1.62673i | −0.581751 | − | 0.813367i | \(-0.697632\pi\) | ||
0.581751 | − | 0.813367i | \(-0.302368\pi\) | |||||||
\(182\) | 277710. | 0.621459 | ||||||||
\(183\) | 345943. | + | 785233.i | 0.763619 | + | 1.73329i | ||||
\(184\) | −54464.7 | − | 152960.i | −0.118596 | − | 0.333069i | ||||
\(185\) | − | 580360.i | − | 1.24672i | ||||||
\(186\) | −208307. | − | 472822.i | −0.441491 | − | 1.00211i | ||||
\(187\) | 31603.0 | 0.0660883 | ||||||||
\(188\) | − | 352587.i | − | 0.727564i | ||||||
\(189\) | −376744. | − | 127306.i | −0.767170 | − | 0.259236i | ||||
\(190\) | 196397. | 0.394686 | ||||||||
\(191\) | −598502. | −1.18709 | −0.593543 | − | 0.804802i | \(-0.702271\pi\) | ||||
−0.593543 | + | 0.804802i | \(0.702271\pi\) | |||||||
\(192\) | 58431.1 | − | 25742.4i | 0.114391 | − | 0.0503961i | ||||
\(193\) | 698278. | 1.34938 | 0.674691 | − | 0.738100i | \(-0.264277\pi\) | ||||
0.674691 | + | 0.738100i | \(0.264277\pi\) | |||||||
\(194\) | 326864. | 0.623537 | ||||||||
\(195\) | 437942. | − | 192940.i | 0.824764 | − | 0.363359i | ||||
\(196\) | −92572.2 | −0.172124 | ||||||||
\(197\) | − | 774477.i | − | 1.42181i | −0.703286 | − | 0.710907i | \(-0.748285\pi\) | ||
0.703286 | − | 0.710907i | \(-0.251715\pi\) | |||||||
\(198\) | −414937. | − | 379516.i | −0.752175 | − | 0.687967i | ||||
\(199\) | − | 830422.i | − | 1.48650i | −0.669011 | − | 0.743252i | \(-0.733282\pi\) | ||
0.669011 | − | 0.743252i | \(-0.266718\pi\) | |||||||
\(200\) | 62084.4i | 0.109751i | ||||||||
\(201\) | 41594.2 | + | 94411.8i | 0.0726177 | + | 0.164830i | ||||
\(202\) | −144244. | −0.248726 | ||||||||
\(203\) | 305234. | 0.519868 | ||||||||
\(204\) | −12468.5 | + | 5493.14i | −0.0209768 | + | 0.00924155i | ||||
\(205\) | − | 343364.i | − | 0.570651i | ||||||
\(206\) | −605993. | −0.994947 | ||||||||
\(207\) | 239374. | − | 568120.i | 0.388285 | − | 0.921539i | ||||
\(208\) | −169300. | −0.271330 | ||||||||
\(209\) | 611896.i | 0.968973i | ||||||||
\(210\) | 278084. | − | 122513.i | 0.435139 | − | 0.191705i | ||||
\(211\) | 336475. | 0.520291 | 0.260146 | − | 0.965569i | \(-0.416229\pi\) | ||||
0.260146 | + | 0.965569i | \(0.416229\pi\) | |||||||
\(212\) | 395020. | 0.603642 | ||||||||
\(213\) | 131967. | + | 299544.i | 0.199305 | + | 0.452388i | ||||
\(214\) | 77574.6i | 0.115794i | ||||||||
\(215\) | − | 142631.i | − | 0.210435i | ||||||
\(216\) | 229673. | + | 77609.5i | 0.334947 | + | 0.113183i | ||||
\(217\) | 869900.i | 1.25406i | ||||||||
\(218\) | −536357. | −0.764386 | ||||||||
\(219\) | −694770. | + | 306089.i | −0.978883 | + | 0.431258i | ||||
\(220\) | 429690. | 0.598547 | ||||||||
\(221\) | 36126.5 | 0.0497560 | ||||||||
\(222\) | −713386. | + | 314290.i | −0.971498 | + | 0.428004i | ||||
\(223\) | −748144. | −1.00745 | −0.503724 | − | 0.863864i | \(-0.668037\pi\) | ||||
−0.503724 | + | 0.863864i | \(0.668037\pi\) | |||||||
\(224\) | −107502. | −0.143151 | ||||||||
\(225\) | −159094. | + | 173943.i | −0.209507 | + | 0.229060i | ||||
\(226\) | − | 111246.i | − | 0.144881i | ||||||
\(227\) | −204240. | −0.263073 | −0.131536 | − | 0.991311i | \(-0.541991\pi\) | ||||
−0.131536 | + | 0.991311i | \(0.541991\pi\) | |||||||
\(228\) | −106358. | − | 241414.i | −0.135498 | − | 0.307557i | ||||
\(229\) | 868528.i | 1.09445i | 0.836986 | + | 0.547224i | \(0.184315\pi\) | ||||
−0.836986 | + | 0.547224i | \(0.815685\pi\) | |||||||
\(230\) | 158020. | + | 443788.i | 0.196966 | + | 0.553167i | ||||
\(231\) | 381701. | + | 866398.i | 0.470645 | + | 1.06829i | ||||
\(232\) | −186079. | −0.226975 | ||||||||
\(233\) | − | 1.37882e6i | − | 1.66387i | −0.554874 | − | 0.831934i | \(-0.687234\pi\) | ||
0.554874 | − | 0.831934i | \(-0.312766\pi\) | |||||||
\(234\) | −474329. | − | 433838.i | −0.566291 | − | 0.517951i | ||||
\(235\) | 1.02297e6i | 1.20835i | ||||||||
\(236\) | 131429.i | 0.153608i | ||||||||
\(237\) | 280532. | + | 636761.i | 0.324423 | + | 0.736386i | ||||
\(238\) | 22939.6 | 0.0262508 | ||||||||
\(239\) | − | 440130.i | − | 0.498410i | −0.968451 | − | 0.249205i | \(-0.919831\pi\) | ||
0.968451 | − | 0.249205i | \(-0.0801692\pi\) | |||||||
\(240\) | −169528. | + | 74687.3i | −0.189982 | + | 0.0836987i | ||||
\(241\) | 632523.i | 0.701510i | 0.936467 | + | 0.350755i | \(0.114075\pi\) | ||||
−0.936467 | + | 0.350755i | \(0.885925\pi\) | |||||||
\(242\) | 694537.i | 0.762355i | ||||||||
\(243\) | 444601. | + | 805989.i | 0.483008 | + | 0.875616i | ||||
\(244\) | 880713.i | 0.947021i | ||||||||
\(245\) | 268582. | 0.285866 | ||||||||
\(246\) | −422068. | + | 185947.i | −0.444677 | + | 0.195907i | ||||
\(247\) | 699479.i | 0.729512i | ||||||||
\(248\) | − | 530315.i | − | 0.547526i | ||||||
\(249\) | 897673. | − | 395480.i | 0.917529 | − | 0.404227i | ||||
\(250\) | − | 760393.i | − | 0.769463i | ||||||
\(251\) | −373263. | −0.373965 | −0.186983 | − | 0.982363i | \(-0.559871\pi\) | ||||
−0.186983 | + | 0.982363i | \(0.559871\pi\) | |||||||
\(252\) | −301189. | − | 275478.i | −0.298770 | − | 0.273266i | ||||
\(253\) | −1.38267e6 | + | 492327.i | −1.35805 | + | 0.483562i | ||||
\(254\) | − | 1.06717e6i | − | 1.03789i | ||||||
\(255\) | 36175.2 | − | 15937.4i | 0.0348386 | − | 0.0153485i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 850287.i | 0.803032i | 0.915852 | + | 0.401516i | \(0.131517\pi\) | ||||
−0.915852 | + | 0.401516i | \(0.868483\pi\) | |||||||
\(258\) | −175324. | + | 77241.0i | −0.163981 | + | 0.0722435i | ||||
\(259\) | 1.31249e6 | 1.21576 | ||||||||
\(260\) | 491193. | 0.450629 | ||||||||
\(261\) | −521341. | − | 476838.i | −0.473719 | − | 0.433281i | ||||
\(262\) | 636798. | 0.573124 | ||||||||
\(263\) | −150995. | −0.134609 | −0.0673046 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673046 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(264\) | −232696. | − | 528180.i | −0.205484 | − | 0.466415i | ||||
\(265\) | −1.14608e6 | −1.00254 | ||||||||
\(266\) | 444155.i | 0.384884i | ||||||||
\(267\) | 1.63022e6 | − | 718211.i | 1.39948 | − | 0.616558i | ||||
\(268\) | 105892.i | 0.0900587i | ||||||||
\(269\) | 643301.i | 0.542043i | 0.962573 | + | 0.271021i | \(0.0873614\pi\) | ||||
−0.962573 | + | 0.271021i | \(0.912639\pi\) | |||||||
\(270\) | −666358. | − | 225171.i | −0.556286 | − | 0.187976i | ||||
\(271\) | −1.65146e6 | −1.36598 | −0.682992 | − | 0.730426i | \(-0.739322\pi\) | ||||
−0.682992 | + | 0.730426i | \(0.739322\pi\) | |||||||
\(272\) | −13984.6 | −0.0114611 | ||||||||
\(273\) | 436336. | + | 990410.i | 0.354335 | + | 0.804282i | ||||
\(274\) | − | 6028.19i | − | 0.00485077i | ||||||
\(275\) | 561204. | 0.447496 | ||||||||
\(276\) | 459935. | − | 434571.i | 0.363433 | − | 0.343390i | ||||
\(277\) | 396745. | 0.310679 | 0.155340 | − | 0.987861i | \(-0.450353\pi\) | ||||
0.155340 | + | 0.987861i | \(0.450353\pi\) | |||||||
\(278\) | 348835.i | 0.270712i | ||||||||
\(279\) | 1.35896e6 | − | 1.48579e6i | 1.04519 | − | 1.14274i | ||||
\(280\) | 311898. | 0.237748 | ||||||||
\(281\) | −1.45610e6 | −1.10008 | −0.550040 | − | 0.835138i | \(-0.685388\pi\) | ||||
−0.550040 | + | 0.835138i | \(0.685388\pi\) | |||||||
\(282\) | 1.25745e6 | − | 553982.i | 0.941602 | − | 0.414833i | ||||
\(283\) | 1.56195e6i | 1.15931i | 0.814860 | + | 0.579657i | \(0.196814\pi\) | ||||
−0.814860 | + | 0.579657i | \(0.803186\pi\) | |||||||
\(284\) | 335967.i | 0.247173i | ||||||||
\(285\) | 308578. | + | 700422.i | 0.225037 | + | 0.510796i | ||||
\(286\) | 1.53036e6i | 1.10632i | ||||||||
\(287\) | 776522. | 0.556479 | ||||||||
\(288\) | 183613. | + | 167939.i | 0.130444 | + | 0.119308i | ||||
\(289\) | −1.41687e6 | −0.997898 | ||||||||
\(290\) | 539877. | 0.376964 | ||||||||
\(291\) | 513566. | + | 1.16571e6i | 0.355520 | + | 0.806971i | ||||
\(292\) | −779251. | −0.534835 | ||||||||
\(293\) | −2.07699e6 | −1.41340 | −0.706699 | − | 0.707514i | \(-0.749817\pi\) | ||||
−0.706699 | + | 0.707514i | \(0.749817\pi\) | |||||||
\(294\) | −145449. | − | 330145.i | −0.0981391 | − | 0.222759i | ||||
\(295\) | − | 381320.i | − | 0.255114i | ||||||
\(296\) | −800130. | −0.530800 | ||||||||
\(297\) | 701542. | − | 2.07610e6i | 0.461490 | − | 1.36571i | ||||
\(298\) | − | 690618.i | − | 0.450503i | ||||||
\(299\) | −1.58057e6 | + | 562796.i | −1.02244 | + | 0.364060i | ||||
\(300\) | −221415. | + | 97546.6i | −0.142038 | + | 0.0625762i | ||||
\(301\) | 322562. | 0.205209 | ||||||||
\(302\) | − | 872829.i | − | 0.550696i | ||||||
\(303\) | −226636. | − | 514426.i | −0.141815 | − | 0.321896i | ||||
\(304\) | − | 270769.i | − | 0.168041i | ||||||
\(305\) | − | 2.55524e6i | − | 1.57283i | ||||||
\(306\) | −39180.9 | − | 35836.3i | −0.0239205 | − | 0.0218786i | ||||
\(307\) | 280461. | 0.169835 | 0.0849173 | − | 0.996388i | \(-0.472937\pi\) | ||||
0.0849173 | + | 0.996388i | \(0.472937\pi\) | |||||||
\(308\) | 971748.i | 0.583683i | ||||||||
\(309\) | −952133. | − | 2.16118e6i | −0.567285 | − | 1.28764i | ||||
\(310\) | 1.53862e6i | 0.909341i | ||||||||
\(311\) | 903873.i | 0.529915i | 0.964260 | + | 0.264958i | \(0.0853580\pi\) | ||||
−0.964260 | + | 0.264958i | \(0.914642\pi\) | |||||||
\(312\) | −266002. | − | 603781.i | −0.154703 | − | 0.351150i | ||||
\(313\) | 1.86380e6i | 1.07532i | 0.843160 | + | 0.537662i | \(0.180692\pi\) | ||||
−0.843160 | + | 0.537662i | \(0.819308\pi\) | |||||||
\(314\) | 1.98245e6 | 1.13469 | ||||||||
\(315\) | 873848. | + | 799253.i | 0.496203 | + | 0.453845i | ||||
\(316\) | 714188.i | 0.402341i | ||||||||
\(317\) | − | 361175.i | − | 0.201869i | −0.994893 | − | 0.100935i | \(-0.967817\pi\) | ||
0.994893 | − | 0.100935i | \(-0.0321833\pi\) | |||||||
\(318\) | 620653. | + | 1.40878e6i | 0.344176 | + | 0.781223i | ||||
\(319\) | 1.68204e6i | 0.925465i | ||||||||
\(320\) | −190141. | −0.103801 | ||||||||
\(321\) | −276658. | + | 121885.i | −0.149858 | + | 0.0660217i | ||||
\(322\) | −1.00363e6 | + | 357364.i | −0.539429 | + | 0.192075i | ||||
\(323\) | 57778.9i | 0.0308151i | ||||||||
\(324\) | 84078.8 | + | 941035.i | 0.0444963 | + | 0.498016i | ||||
\(325\) | 641532. | 0.336907 | ||||||||
\(326\) | − | 21066.4i | − | 0.0109786i | ||||||
\(327\) | −842721. | − | 1.91284e6i | −0.435827 | − | 0.989255i | ||||
\(328\) | −473389. | −0.242960 | ||||||||
\(329\) | −2.31346e6 | −1.17834 | ||||||||
\(330\) | 675126. | + | 1.53242e6i | 0.341272 | + | 0.774630i | ||||
\(331\) | 1.10475e6 | 0.554237 | 0.277118 | − | 0.960836i | \(-0.410621\pi\) | ||||
0.277118 | + | 0.960836i | \(0.410621\pi\) | |||||||
\(332\) | 1.00683e6 | 0.501313 | ||||||||
\(333\) | −2.24174e6 | − | 2.05037e6i | −1.10783 | − | 1.01326i | ||||
\(334\) | −1.22986e6 | −0.603239 | ||||||||
\(335\) | − | 307227.i | − | 0.149571i | ||||||
\(336\) | −168906. | − | 383388.i | −0.0816200 | − | 0.185264i | ||||
\(337\) | − | 1.82818e6i | − | 0.876888i | −0.898758 | − | 0.438444i | \(-0.855530\pi\) | ||
0.898758 | − | 0.438444i | \(-0.144470\pi\) | |||||||
\(338\) | 264238.i | 0.125807i | ||||||||
\(339\) | 396741. | − | 174789.i | 0.187503 | − | 0.0826064i | ||||
\(340\) | 40573.9 | 0.0190349 | ||||||||
\(341\) | −4.79372e6 | −2.23247 | ||||||||
\(342\) | 693859. | − | 758617.i | 0.320779 | − | 0.350718i | ||||
\(343\) | 2.37184e6i | 1.08855i | ||||||||
\(344\) | −196643. | −0.0895946 | ||||||||
\(345\) | −1.33442e6 | + | 1.26083e6i | −0.603595 | + | 0.570308i | ||||
\(346\) | −2.71598e6 | −1.21965 | ||||||||
\(347\) | 1.53933e6i | 0.686289i | 0.939283 | + | 0.343145i | \(0.111492\pi\) | ||||
−0.939283 | + | 0.343145i | \(0.888508\pi\) | |||||||
\(348\) | −292367. | − | 663624.i | −0.129414 | − | 0.293747i | ||||
\(349\) | 2.65317e6 | 1.16601 | 0.583005 | − | 0.812469i | \(-0.301877\pi\) | ||||
0.583005 | + | 0.812469i | \(0.301877\pi\) | |||||||
\(350\) | 407359. | 0.177749 | ||||||||
\(351\) | 801957. | − | 2.37327e6i | 0.347443 | − | 1.02820i | ||||
\(352\) | − | 592404.i | − | 0.254837i | ||||||
\(353\) | − | 2.13691e6i | − | 0.912745i | −0.889789 | − | 0.456372i | \(-0.849148\pi\) | ||
0.889789 | − | 0.456372i | \(-0.150852\pi\) | |||||||
\(354\) | −468723. | + | 206501.i | −0.198796 | + | 0.0875819i | ||||
\(355\) | − | 974750.i | − | 0.410509i | ||||||
\(356\) | 1.82845e6 | 0.764640 | ||||||||
\(357\) | 36042.6 | + | 81810.6i | 0.0149674 | + | 0.0339734i | ||||
\(358\) | −344342. | −0.141998 | ||||||||
\(359\) | −904914. | −0.370571 | −0.185285 | − | 0.982685i | \(-0.559321\pi\) | ||||
−0.185285 | + | 0.982685i | \(0.559321\pi\) | |||||||
\(360\) | −532722. | − | 487247.i | −0.216643 | − | 0.198149i | ||||
\(361\) | 1.35739e6 | 0.548196 | ||||||||
\(362\) | 2.86796e6 | 1.15027 | ||||||||
\(363\) | −2.47696e6 | + | 1.09125e6i | −0.986627 | + | 0.434669i | ||||
\(364\) | 1.11084e6i | 0.439438i | ||||||||
\(365\) | 2.26086e6 | 0.888264 | ||||||||
\(366\) | −3.14093e6 | + | 1.38377e6i | −1.22562 | + | 0.539960i | ||||
\(367\) | − | 4.85024e6i | − | 1.87974i | −0.341533 | − | 0.939870i | \(-0.610946\pi\) | ||
0.341533 | − | 0.939870i | \(-0.389054\pi\) | |||||||
\(368\) | 611841. | − | 217859.i | 0.235515 | − | 0.0838601i | ||||
\(369\) | −1.32630e6 | − | 1.21308e6i | −0.507080 | − | 0.463794i | ||||
\(370\) | 2.32144e6 | 0.881562 | ||||||||
\(371\) | − | 2.59188e6i | − | 0.977641i | ||||||
\(372\) | 1.89129e6 | − | 833228.i | 0.708599 | − | 0.312181i | ||||
\(373\) | − | 773061.i | − | 0.287701i | −0.989599 | − | 0.143851i | \(-0.954052\pi\) | ||
0.989599 | − | 0.143851i | \(-0.0459485\pi\) | |||||||
\(374\) | 126412.i | 0.0467315i | ||||||||
\(375\) | 2.71183e6 | − | 1.19472e6i | 0.995826 | − | 0.438722i | ||||
\(376\) | 1.41035e6 | 0.514466 | ||||||||
\(377\) | 1.92280e6i | 0.696756i | ||||||||
\(378\) | 509226. | − | 1.50697e6i | 0.183308 | − | 0.542471i | ||||
\(379\) | 554583.i | 0.198321i | 0.995071 | + | 0.0991605i | \(0.0316157\pi\) | ||||
−0.995071 | + | 0.0991605i | \(0.968384\pi\) | |||||||
\(380\) | 785590.i | 0.279085i | ||||||||
\(381\) | 3.80591e6 | − | 1.67673e6i | 1.34322 | − | 0.591768i | ||||
\(382\) | − | 2.39401e6i | − | 0.839397i | ||||||
\(383\) | 3.81249e6 | 1.32804 | 0.664021 | − | 0.747714i | \(-0.268848\pi\) | ||||
0.664021 | + | 0.747714i | \(0.268848\pi\) | |||||||
\(384\) | 102970. | + | 233724.i | 0.0356354 | + | 0.0808864i | ||||
\(385\) | − | 2.81936e6i | − | 0.969390i | ||||||
\(386\) | 2.79311e6i | 0.954157i | ||||||||
\(387\) | −550937. | − | 503907.i | −0.186993 | − | 0.171030i | ||||
\(388\) | 1.30745e6i | 0.440907i | ||||||||
\(389\) | −328921. | −0.110209 | −0.0551046 | − | 0.998481i | \(-0.517549\pi\) | ||||
−0.0551046 | + | 0.998481i | \(0.517549\pi\) | |||||||
\(390\) | 771760. | + | 1.75177e6i | 0.256934 | + | 0.583197i | ||||
\(391\) | −130560. | + | 46488.5i | −0.0431884 | + | 0.0153781i | ||||
\(392\) | − | 370289.i | − | 0.121710i | ||||||
\(393\) | 1.00053e6 | + | 2.27104e6i | 0.326776 | + | 0.741727i | ||||
\(394\) | 3.09791e6 | 1.00537 | ||||||||
\(395\) | − | 2.07209e6i | − | 0.668215i | ||||||
\(396\) | 1.51807e6 | − | 1.65975e6i | 0.486466 | − | 0.531868i | ||||
\(397\) | 3.79002e6 | 1.20688 | 0.603442 | − | 0.797407i | \(-0.293795\pi\) | ||||
0.603442 | + | 0.797407i | \(0.293795\pi\) | |||||||
\(398\) | 3.32169e6 | 1.05112 | ||||||||
\(399\) | −1.58401e6 | + | 697853.i | −0.498111 | + | 0.219448i | ||||
\(400\) | −248337. | −0.0776055 | ||||||||
\(401\) | 3.33202e6 | 1.03478 | 0.517388 | − | 0.855751i | \(-0.326904\pi\) | ||||
0.517388 | + | 0.855751i | \(0.326904\pi\) | |||||||
\(402\) | −377647. | + | 166377.i | −0.116552 | + | 0.0513484i | ||||
\(403\) | −5.47987e6 | −1.68077 | ||||||||
\(404\) | − | 576977.i | − | 0.175876i | ||||||
\(405\) | −243940. | − | 2.73025e6i | −0.0739002 | − | 0.827114i | ||||
\(406\) | 1.22094e6i | 0.367602i | ||||||||
\(407\) | 7.23267e6i | 2.16428i | ||||||||
\(408\) | −21972.5 | − | 49874.0i | −0.00653476 | − | 0.0148328i | ||||
\(409\) | −633448. | −0.187242 | −0.0936209 | − | 0.995608i | \(-0.529844\pi\) | ||||
−0.0936209 | + | 0.995608i | \(0.529844\pi\) | |||||||
\(410\) | 1.37346e6 | 0.403511 | ||||||||
\(411\) | 21498.6 | − | 9471.46i | 0.00627779 | − | 0.00276575i | ||||
\(412\) | − | 2.42397e6i | − | 0.703534i | ||||||
\(413\) | 862359. | 0.248778 | ||||||||
\(414\) | 2.27248e6 | + | 957495.i | 0.651627 | + | 0.274559i | ||||
\(415\) | −2.92113e6 | −0.832589 | ||||||||
\(416\) | − | 677198.i | − | 0.191859i | ||||||
\(417\) | −1.24407e6 | + | 548088.i | −0.350351 | + | 0.154351i | ||||
\(418\) | −2.44758e6 | −0.685167 | ||||||||
\(419\) | 4.56704e6 | 1.27086 | 0.635432 | − | 0.772157i | \(-0.280822\pi\) | ||||
0.635432 | + | 0.772157i | \(0.280822\pi\) | |||||||
\(420\) | 490052. | + | 1.11234e6i | 0.135556 | + | 0.307689i | ||||
\(421\) | − | 4.87938e6i | − | 1.34171i | −0.741588 | − | 0.670856i | \(-0.765927\pi\) | ||
0.741588 | − | 0.670856i | \(-0.234073\pi\) | |||||||
\(422\) | 1.34590e6i | 0.367902i | ||||||||
\(423\) | 3.95139e6 | + | 3.61408e6i | 1.07374 | + | 0.982081i | ||||
\(424\) | 1.58008e6i | 0.426839i | ||||||||
\(425\) | 52992.3 | 0.0142312 | ||||||||
\(426\) | −1.19818e6 | + | 527869.i | −0.319887 | + | 0.140930i | ||||
\(427\) | 5.77869e6 | 1.53377 | ||||||||
\(428\) | −310299. | −0.0818786 | ||||||||
\(429\) | −5.45781e6 | + | 2.40450e6i | −1.43178 | + | 0.630784i | ||||
\(430\) | 570525. | 0.148800 | ||||||||
\(431\) | 1.78523e6 | 0.462916 | 0.231458 | − | 0.972845i | \(-0.425650\pi\) | ||||
0.231458 | + | 0.972845i | \(0.425650\pi\) | |||||||
\(432\) | −310438. | + | 918694.i | −0.0800324 | + | 0.236843i | ||||
\(433\) | − | 862750.i | − | 0.221139i | −0.993868 | − | 0.110570i | \(-0.964733\pi\) | ||
0.993868 | − | 0.110570i | \(-0.0352675\pi\) | |||||||
\(434\) | −3.47960e6 | −0.886758 | ||||||||
\(435\) | 848252. | + | 1.92539e6i | 0.214932 | + | 0.487861i | ||||
\(436\) | − | 2.14543e6i | − | 0.540502i | ||||||
\(437\) | −900107. | − | 2.52789e6i | −0.225471 | − | 0.633219i | ||||
\(438\) | −1.22435e6 | − | 2.77908e6i | −0.304945 | − | 0.692175i | ||||
\(439\) | −2.38229e6 | −0.589974 | −0.294987 | − | 0.955501i | \(-0.595315\pi\) | ||||
−0.294987 | + | 0.955501i | \(0.595315\pi\) | |||||||
\(440\) | 1.71876e6i | 0.423237i | ||||||||
\(441\) | 948883. | − | 1.03744e6i | 0.232336 | − | 0.254020i | ||||
\(442\) | 144506.i | 0.0351828i | ||||||||
\(443\) | − | 3.65237e6i | − | 0.884231i | −0.896958 | − | 0.442115i | \(-0.854228\pi\) | ||
0.896958 | − | 0.442115i | \(-0.145772\pi\) | |||||||
\(444\) | −1.25716e6 | − | 2.85354e6i | −0.302645 | − | 0.686953i | ||||
\(445\) | −5.30492e6 | −1.26993 | ||||||||
\(446\) | − | 2.99258e6i | − | 0.712374i | ||||||
\(447\) | 2.46299e6 | − | 1.08509e6i | 0.583033 | − | 0.256861i | ||||
\(448\) | − | 430007.i | − | 0.101223i | ||||||
\(449\) | 3.44781e6i | 0.807099i | 0.914958 | + | 0.403550i | \(0.132224\pi\) | ||||
−0.914958 | + | 0.403550i | \(0.867776\pi\) | |||||||
\(450\) | −695771. | − | 636377.i | −0.161970 | − | 0.148144i | ||||
\(451\) | 4.27914e6i | 0.990639i | ||||||||
\(452\) | 444983. | 0.102446 | ||||||||
\(453\) | 3.11281e6 | − | 1.37138e6i | 0.712702 | − | 0.313988i | ||||
\(454\) | − | 816959.i | − | 0.186020i | ||||||
\(455\) | − | 3.22291e6i | − | 0.729826i | ||||||
\(456\) | 965657. | − | 425431.i | 0.217476 | − | 0.0958113i | ||||
\(457\) | 2.09933e6i | 0.470208i | 0.971970 | + | 0.235104i | \(0.0755431\pi\) | ||||
−0.971970 | + | 0.235104i | \(0.924457\pi\) | |||||||
\(458\) | −3.47411e6 | −0.773891 | ||||||||
\(459\) | 66243.9 | − | 196038.i | 0.0146762 | − | 0.0434320i | ||||
\(460\) | −1.77515e6 | + | 632080.i | −0.391148 | + | 0.139276i | ||||
\(461\) | − | 1.55911e6i | − | 0.341684i | −0.985298 | − | 0.170842i | \(-0.945351\pi\) | ||
0.985298 | − | 0.170842i | \(-0.0546487\pi\) | |||||||
\(462\) | −3.46559e6 | + | 1.52680e6i | −0.755392 | + | 0.332796i | ||||
\(463\) | −4.79193e6 | −1.03886 | −0.519432 | − | 0.854512i | \(-0.673856\pi\) | ||||
−0.519432 | + | 0.854512i | \(0.673856\pi\) | |||||||
\(464\) | − | 744318.i | − | 0.160496i | ||||||
\(465\) | −5.48725e6 | + | 2.41747e6i | −1.17685 | + | 0.518476i | ||||
\(466\) | 5.51530e6 | 1.17653 | ||||||||
\(467\) | −4.43239e6 | −0.940473 | −0.470236 | − | 0.882541i | \(-0.655831\pi\) | ||||
−0.470236 | + | 0.882541i | \(0.655831\pi\) | |||||||
\(468\) | 1.73535e6 | − | 1.89732e6i | 0.366246 | − | 0.400428i | ||||
\(469\) | 694797. | 0.145856 | ||||||||
\(470\) | −4.09188e6 | −0.854433 | ||||||||
\(471\) | 3.11481e6 | + | 7.07011e6i | 0.646963 | + | 1.46850i | ||||
\(472\) | −525718. | −0.108617 | ||||||||
\(473\) | 1.77753e6i | 0.365312i | ||||||||
\(474\) | −2.54704e6 | + | 1.12213e6i | −0.520704 | + | 0.229402i | ||||
\(475\) | 1.02603e6i | 0.208654i | ||||||||
\(476\) | 91758.4i | 0.0185621i | ||||||||
\(477\) | −4.04903e6 | + | 4.42693e6i | −0.814808 | + | 0.890855i | ||||
\(478\) | 1.76052e6 | 0.352429 | ||||||||
\(479\) | −3.19416e6 | −0.636090 | −0.318045 | − | 0.948076i | \(-0.603026\pi\) | ||||
−0.318045 | + | 0.948076i | \(0.603026\pi\) | |||||||
\(480\) | −298749. | − | 678111.i | −0.0591839 | − | 0.134338i | ||||
\(481\) | 8.26792e6i | 1.62942i | ||||||||
\(482\) | −2.53009e6 | −0.496042 | ||||||||
\(483\) | −2.85138e6 | − | 3.01781e6i | −0.556144 | − | 0.588605i | ||||
\(484\) | −2.77815e6 | −0.539066 | ||||||||
\(485\) | − | 3.79335e6i | − | 0.732266i | ||||||
\(486\) | −3.22396e6 | + | 1.77840e6i | −0.619154 | + | 0.341539i | ||||
\(487\) | 4.87872e6 | 0.932145 | 0.466072 | − | 0.884747i | \(-0.345669\pi\) | ||||
0.466072 | + | 0.884747i | \(0.345669\pi\) | |||||||
\(488\) | −3.52285e6 | −0.669645 | ||||||||
\(489\) | 75130.2 | − | 33099.4i | 0.0142083 | − | 0.00625963i | ||||
\(490\) | 1.07433e6i | 0.202138i | ||||||||
\(491\) | 7.58791e6i | 1.42043i | 0.703987 | + | 0.710213i | \(0.251401\pi\) | ||||
−0.703987 | + | 0.710213i | \(0.748599\pi\) | |||||||
\(492\) | −743787. | − | 1.68827e6i | −0.138527 | − | 0.314434i | ||||
\(493\) | 158829.i | 0.0294314i | ||||||||
\(494\) | −2.79792e6 | −0.515843 | ||||||||
\(495\) | −4.40441e6 | + | 4.81547e6i | −0.807931 | + | 0.883336i | ||||
\(496\) | 2.12126e6 | 0.387159 | ||||||||
\(497\) | 2.20441e6 | 0.400314 | ||||||||
\(498\) | 1.58192e6 | + | 3.59069e6i | 0.285832 | + | 0.648791i | ||||
\(499\) | 6.67031e6 | 1.19921 | 0.599604 | − | 0.800297i | \(-0.295325\pi\) | ||||
0.599604 | + | 0.800297i | \(0.295325\pi\) | |||||||
\(500\) | 3.04157e6 | 0.544093 | ||||||||
\(501\) | −1.93235e6 | − | 4.38611e6i | −0.343947 | − | 0.780702i | ||||
\(502\) | − | 1.49305e6i | − | 0.264433i | ||||||
\(503\) | 7.71176e6 | 1.35904 | 0.679522 | − | 0.733655i | \(-0.262187\pi\) | ||||
0.679522 | + | 0.733655i | \(0.262187\pi\) | |||||||
\(504\) | 1.10191e6 | − | 1.20476e6i | 0.193228 | − | 0.211263i | ||||
\(505\) | 1.67400e6i | 0.292097i | ||||||||
\(506\) | −1.96931e6 | − | 5.53066e6i | −0.341930 | − | 0.960287i | ||||
\(507\) | −942365. | + | 415169.i | −0.162817 | + | 0.0717307i | ||||
\(508\) | 4.26869e6 | 0.733897 | ||||||||
\(509\) | − | 6.01246e6i | − | 1.02863i | −0.857602 | − | 0.514313i | \(-0.828047\pi\) | ||
0.857602 | − | 0.514313i | \(-0.171953\pi\) | |||||||
\(510\) | 63749.5 | + | 144701.i | 0.0108530 | + | 0.0246346i | ||||
\(511\) | 5.11296e6i | 0.866204i | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | 3.79568e6 | + | 1.28261e6i | 0.636790 | + | 0.215179i | ||||
\(514\) | −3.40115e6 | −0.567829 | ||||||||
\(515\) | 7.03274e6i | 1.16844i | ||||||||
\(516\) | −308964. | − | 701297.i | −0.0510839 | − | 0.115952i | ||||
\(517\) | − | 1.27487e7i | − | 2.09767i | ||||||
\(518\) | 5.24996e6i | 0.859669i | ||||||||
\(519\) | −4.26733e6 | − | 9.68613e6i | −0.695405 | − | 1.57845i | ||||
\(520\) | 1.96477e6i | 0.318643i | ||||||||
\(521\) | −1.04577e7 | −1.68788 | −0.843941 | − | 0.536436i | \(-0.819770\pi\) | ||||
−0.843941 | + | 0.536436i | \(0.819770\pi\) | |||||||
\(522\) | 1.90735e6 | − | 2.08536e6i | 0.306376 | − | 0.334970i | ||||
\(523\) | − | 3.52422e6i | − | 0.563390i | −0.959504 | − | 0.281695i | \(-0.909103\pi\) | ||
0.959504 | − | 0.281695i | \(-0.0908966\pi\) | |||||||
\(524\) | 2.54719e6i | 0.405260i | ||||||||
\(525\) | 640040. | + | 1.45279e6i | 0.101347 | + | 0.230040i | ||||
\(526\) | − | 603982.i | − | 0.0951830i | ||||||
\(527\) | −452652. | −0.0709967 | ||||||||
\(528\) | 2.11272e6 | − | 930782.i | 0.329805 | − | 0.145299i | ||||
\(529\) | 4.98790e6 | − | 4.06784e6i | 0.774959 | − | 0.632011i | ||||
\(530\) | − | 4.58433e6i | − | 0.708902i | ||||||
\(531\) | −1.47291e6 | − | 1.34718e6i | −0.226694 | − | 0.207343i | ||||
\(532\) | −1.77662e6 | −0.272154 | ||||||||
\(533\) | 4.89164e6i | 0.745824i | ||||||||
\(534\) | 2.87284e6 | + | 6.52088e6i | 0.435972 | + | 0.989584i | ||||
\(535\) | 900278. | 0.135985 | ||||||||
\(536\) | −423567. | −0.0636811 | ||||||||
\(537\) | −541028. | − | 1.22804e6i | −0.0809625 | − | 0.183771i | ||||
\(538\) | −2.57320e6 | −0.383282 | ||||||||
\(539\) | −3.34718e6 | −0.496257 | ||||||||
\(540\) | 900683. | − | 2.66543e6i | 0.132919 | − | 0.393354i | ||||
\(541\) | −1.09709e7 | −1.61157 | −0.805786 | − | 0.592206i | \(-0.798257\pi\) | ||||
−0.805786 | + | 0.592206i | \(0.798257\pi\) | |||||||
\(542\) | − | 6.60585e6i | − | 0.965897i | ||||||
\(543\) | 4.50612e6 | + | 1.02281e7i | 0.655848 | + | 1.48867i | ||||
\(544\) | − | 55938.4i | − | 0.00810426i | ||||||
\(545\) | 6.22459e6i | 0.897676i | ||||||||
\(546\) | −3.96164e6 | + | 1.74534e6i | −0.568713 | + | 0.250553i | ||||
\(547\) | −9.00106e6 | −1.28625 | −0.643125 | − | 0.765761i | \(-0.722362\pi\) | ||||
−0.643125 | + | 0.765761i | \(0.722362\pi\) | |||||||
\(548\) | 24112.8 | 0.00343001 | ||||||||
\(549\) | −9.87002e6 | − | 9.02748e6i | −1.39761 | − | 1.27831i | ||||
\(550\) | 2.24482e6i | 0.316427i | ||||||||
\(551\) | −3.07523e6 | −0.431517 | ||||||||
\(552\) | 1.73828e6 | + | 1.83974e6i | 0.242813 | + | 0.256986i | ||||
\(553\) | 4.68606e6 | 0.651621 | ||||||||
\(554\) | 1.58698e6i | 0.219683i | ||||||||
\(555\) | 3.64743e6 | + | 8.27906e6i | 0.502637 | + | 1.14090i | ||||
\(556\) | −1.39534e6 | −0.191423 | ||||||||
\(557\) | 4.16338e6 | 0.568601 | 0.284300 | − | 0.958735i | \(-0.408239\pi\) | ||||
0.284300 | + | 0.958735i | \(0.408239\pi\) | |||||||
\(558\) | 5.94317e6 | + | 5.43584e6i | 0.808039 | + | 0.739062i | ||||
\(559\) | 2.03195e6i | 0.275033i | ||||||||
\(560\) | 1.24759e6i | 0.168113i | ||||||||
\(561\) | −450830. | + | 198618.i | −0.0604791 | + | 0.0266447i | ||||
\(562\) | − | 5.82439e6i | − | 0.777875i | ||||||
\(563\) | 1.15019e7 | 1.52932 | 0.764661 | − | 0.644432i | \(-0.222906\pi\) | ||||
0.764661 | + | 0.644432i | \(0.222906\pi\) | |||||||
\(564\) | 2.21593e6 | + | 5.02979e6i | 0.293331 | + | 0.665813i | ||||
\(565\) | −1.29104e6 | −0.170145 | ||||||||
\(566\) | −6.24780e6 | −0.819759 | ||||||||
\(567\) | 6.17449e6 | − | 551673.i | 0.806573 | − | 0.0720650i | ||||
\(568\) | −1.34387e6 | −0.174778 | ||||||||
\(569\) | 6.25524e6 | 0.809960 | 0.404980 | − | 0.914326i | \(-0.367279\pi\) | ||||
0.404980 | + | 0.914326i | \(0.367279\pi\) | |||||||
\(570\) | −2.80169e6 | + | 1.23431e6i | −0.361187 | + | 0.159125i | ||||
\(571\) | 507892.i | 0.0651900i | 0.999469 | + | 0.0325950i | \(0.0103771\pi\) | ||||
−0.999469 | + | 0.0325950i | \(0.989623\pi\) | |||||||
\(572\) | −6.12145e6 | −0.782283 | ||||||||
\(573\) | 8.53787e6 | − | 3.76145e6i | 1.08633 | − | 0.478596i | ||||
\(574\) | 3.10609e6i | 0.393490i | ||||||||
\(575\) | −2.31847e6 | + | 825539.i | −0.292436 | + | 0.104128i | ||||
\(576\) | −671757. | + | 734452.i | −0.0843638 | + | 0.0922375i | ||||
\(577\) | 1.06418e7 | 1.33068 | 0.665340 | − | 0.746540i | \(-0.268287\pi\) | ||||
0.665340 | + | 0.746540i | \(0.268287\pi\) | |||||||
\(578\) | − | 5.66749e6i | − | 0.705621i | ||||||
\(579\) | −9.96121e6 | + | 4.38852e6i | −1.23485 | + | 0.544029i | ||||
\(580\) | 2.15951e6i | 0.266554i | ||||||||
\(581\) | − | 6.60617e6i | − | 0.811912i | ||||||
\(582\) | −4.66284e6 | + | 2.05427e6i | −0.570615 | + | 0.251391i | ||||
\(583\) | 1.42829e7 | 1.74039 | ||||||||
\(584\) | − | 3.11700e6i | − | 0.378186i | ||||||
\(585\) | −5.03483e6 | + | 5.50473e6i | −0.608268 | + | 0.665038i | ||||
\(586\) | − | 8.30795e6i | − | 0.999424i | ||||||
\(587\) | − | 1.39325e7i | − | 1.66892i | −0.551070 | − | 0.834459i | \(-0.685780\pi\) | ||
0.551070 | − | 0.834459i | \(-0.314220\pi\) | |||||||
\(588\) | 1.32058e6 | − | 581795.i | 0.157515 | − | 0.0693948i | ||||
\(589\) | − | 8.76422e6i | − | 1.04094i | ||||||
\(590\) | 1.52528e6 | 0.180393 | ||||||||
\(591\) | 4.86741e6 | + | 1.10482e7i | 0.573231 | + | 1.30114i | ||||
\(592\) | − | 3.20052e6i | − | 0.375333i | ||||||
\(593\) | 1.47891e7i | 1.72705i | 0.504304 | + | 0.863526i | \(0.331749\pi\) | ||||
−0.504304 | + | 0.863526i | \(0.668251\pi\) | |||||||
\(594\) | 8.30442e6 | + | 2.80617e6i | 0.965702 | + | 0.326323i | ||||
\(595\) | − | 266221.i | − | 0.0308283i | ||||||
\(596\) | 2.76247e6 | 0.318553 | ||||||||
\(597\) | 5.21902e6 | + | 1.18463e7i | 0.599312 | + | 1.36034i | ||||
\(598\) | −2.25118e6 | − | 6.32229e6i | −0.257429 | − | 0.722972i | ||||
\(599\) | − | 706139.i | − | 0.0804125i | −0.999191 | − | 0.0402062i | \(-0.987199\pi\) | ||
0.999191 | − | 0.0402062i | \(-0.0128015\pi\) | |||||||
\(600\) | −390186. | − | 885658.i | −0.0442480 | − | 0.100436i | ||||
\(601\) | −1.60096e7 | −1.80798 | −0.903991 | − | 0.427551i | \(-0.859377\pi\) | ||||
−0.903991 | + | 0.427551i | \(0.859377\pi\) | |||||||
\(602\) | 1.29025e6i | 0.145105i | ||||||||
\(603\) | −1.18671e6 | − | 1.08541e6i | −0.132909 | − | 0.121563i | ||||
\(604\) | 3.49132e6 | 0.389401 | ||||||||
\(605\) | 8.06032e6 | 0.895290 | ||||||||
\(606\) | 2.05770e6 | − | 906544.i | 0.227615 | − | 0.100278i | ||||
\(607\) | 6.76123e6 | 0.744825 | 0.372413 | − | 0.928067i | \(-0.378531\pi\) | ||||
0.372413 | + | 0.928067i | \(0.378531\pi\) | |||||||
\(608\) | 1.08308e6 | 0.118823 | ||||||||
\(609\) | −4.35429e6 | + | 1.91833e6i | −0.475745 | + | 0.209595i | ||||
\(610\) | 1.02209e7 | 1.11216 | ||||||||
\(611\) | − | 1.45734e7i | − | 1.57928i | ||||||
\(612\) | 143345. | − | 156724.i | 0.0154705 | − | 0.0169144i | ||||
\(613\) | 3.11552e6i | 0.334872i | 0.985883 | + | 0.167436i | \(0.0535488\pi\) | ||||
−0.985883 | + | 0.167436i | \(0.946451\pi\) | |||||||
\(614\) | 1.12184e6i | 0.120091i | ||||||||
\(615\) | 2.15797e6 | + | 4.89823e6i | 0.230069 | + | 0.522218i | ||||
\(616\) | −3.88699e6 | −0.412726 | ||||||||
\(617\) | 1.74682e7 | 1.84729 | 0.923645 | − | 0.383248i | \(-0.125195\pi\) | ||||
0.923645 | + | 0.383248i | \(0.125195\pi\) | |||||||
\(618\) | 8.64474e6 | − | 3.80853e6i | 0.910501 | − | 0.401131i | ||||
\(619\) | − | 4.52333e6i | − | 0.474495i | −0.971449 | − | 0.237247i | \(-0.923755\pi\) | ||
0.971449 | − | 0.237247i | \(-0.0762452\pi\) | |||||||
\(620\) | −6.15447e6 | −0.643001 | ||||||||
\(621\) | 155741. | + | 9.60886e6i | 0.0162059 | + | 0.999869i | ||||
\(622\) | −3.61549e6 | −0.374707 | ||||||||
\(623\) | − | 1.19971e7i | − | 1.23839i | ||||||
\(624\) | 2.41513e6 | − | 1.06401e6i | 0.248301 | − | 0.109392i | ||||
\(625\) | −5.79313e6 | −0.593216 | ||||||||
\(626\) | −7.45522e6 | −0.760369 | ||||||||
\(627\) | −3.84563e6 | − | 8.72893e6i | −0.390659 | − | 0.886732i | ||||
\(628\) | 7.92980e6i | 0.802348i | ||||||||
\(629\) | 682953.i | 0.0688279i | ||||||||
\(630\) | −3.19701e6 | + | 3.49539e6i | −0.320917 | + | 0.350868i | ||||
\(631\) | 7.95471e6i | 0.795336i | 0.917529 | + | 0.397668i | \(0.130180\pi\) | ||||
−0.917529 | + | 0.397668i | \(0.869820\pi\) | |||||||
\(632\) | −2.85675e6 | −0.284498 | ||||||||
\(633\) | −4.79995e6 | + | 2.11467e6i | −0.476132 | + | 0.209765i | ||||
\(634\) | 1.44470e6 | 0.142743 | ||||||||
\(635\) | −1.23849e7 | −1.21887 | ||||||||
\(636\) | −5.63512e6 | + | 2.48261e6i | −0.552408 | + | 0.243369i | ||||
\(637\) | −3.82628e6 | −0.373618 | ||||||||
\(638\) | −6.72816e6 | −0.654402 | ||||||||
\(639\) | −3.76513e6 | − | 3.44373e6i | −0.364777 | − | 0.333639i | ||||
\(640\) | − | 760566.i | − | 0.0733984i | ||||||
\(641\) | 2.60477e6 | 0.250394 | 0.125197 | − | 0.992132i | \(-0.460044\pi\) | ||||
0.125197 | + | 0.992132i | \(0.460044\pi\) | |||||||
\(642\) | −487539. | − | 1.10663e6i | −0.0466844 | − | 0.105966i | ||||
\(643\) | − | 1.12007e7i | − | 1.06836i | −0.845371 | − | 0.534179i | \(-0.820621\pi\) | ||
0.845371 | − | 0.534179i | \(-0.179379\pi\) | |||||||
\(644\) | −1.42945e6 | − | 4.01452e6i | −0.135817 | − | 0.381434i | ||||
\(645\) | 896406. | + | 2.03469e6i | 0.0848409 | + | 0.192575i | ||||
\(646\) | −231116. | −0.0217895 | ||||||||
\(647\) | 6.03514e6i | 0.566796i | 0.959002 | + | 0.283398i | \(0.0914618\pi\) | ||||
−0.959002 | + | 0.283398i | \(0.908538\pi\) | |||||||
\(648\) | −3.76414e6 | + | 336315.i | −0.352151 | + | 0.0314636i | ||||
\(649\) | 4.75216e6i | 0.442873i | ||||||||
\(650\) | 2.56613e6i | 0.238229i | ||||||||
\(651\) | −5.46713e6 | − | 1.24095e7i | −0.505600 | − | 1.14763i | ||||
\(652\) | 84265.7 | 0.00776304 | ||||||||
\(653\) | 2.16366e7i | 1.98566i | 0.119515 | + | 0.992832i | \(0.461866\pi\) | ||||
−0.119515 | + | 0.992832i | \(0.538134\pi\) | |||||||
\(654\) | 7.65134e6 | − | 3.37088e6i | 0.699509 | − | 0.308176i | ||||
\(655\) | − | 7.39024e6i | − | 0.673062i | ||||||
\(656\) | − | 1.89356e6i | − | 0.171798i | ||||||
\(657\) | 7.98748e6 | − | 8.73295e6i | 0.721932 | − | 0.789310i | ||||
\(658\) | − | 9.25382e6i | − | 0.833214i | ||||||
\(659\) | −2.95605e6 | −0.265154 | −0.132577 | − | 0.991173i | \(-0.542325\pi\) | ||||
−0.132577 | + | 0.991173i | \(0.542325\pi\) | |||||||
\(660\) | −6.12970e6 | + | 2.70050e6i | −0.547746 | + | 0.241315i | ||||
\(661\) | − | 9.44325e6i | − | 0.840655i | −0.907372 | − | 0.420328i | \(-0.861915\pi\) | ||
0.907372 | − | 0.420328i | \(-0.138085\pi\) | |||||||
\(662\) | 4.41901e6i | 0.391905i | ||||||||
\(663\) | −515359. | + | 227047.i | −0.0455330 | + | 0.0200601i | ||||
\(664\) | 4.02730e6i | 0.354482i | ||||||||
\(665\) | 5.15455e6 | 0.451998 | ||||||||
\(666\) | 8.20149e6 | − | 8.96694e6i | 0.716485 | − | 0.783355i | ||||
\(667\) | −2.47431e6 | − | 6.94892e6i | −0.215347 | − | 0.604787i | ||||
\(668\) | − | 4.91944e6i | − | 0.426554i | ||||||
\(669\) | 1.06726e7 | − | 4.70192e6i | 0.921942 | − | 0.406172i | ||||
\(670\) | 1.22891e6 | 0.105763 | ||||||||
\(671\) | 3.18444e7i | 2.73040i | ||||||||
\(672\) | 1.53355e6 | − | 675624.i | 0.131001 | − | 0.0577141i | ||||
\(673\) | 1.77229e7 | 1.50833 | 0.754165 | − | 0.656685i | \(-0.228042\pi\) | ||||
0.754165 | + | 0.656685i | \(0.228042\pi\) | |||||||
\(674\) | 7.31272e6 | 0.620053 | ||||||||
\(675\) | 1.17635e6 | − | 3.48123e6i | 0.0993752 | − | 0.294086i | ||||
\(676\) | −1.05695e6 | −0.0889587 | ||||||||
\(677\) | −2.80472e6 | −0.235189 | −0.117595 | − | 0.993062i | \(-0.537518\pi\) | ||||
−0.117595 | + | 0.993062i | \(0.537518\pi\) | |||||||
\(678\) | 699154. | + | 1.58696e6i | 0.0584115 | + | 0.132585i | ||||
\(679\) | 8.57871e6 | 0.714081 | ||||||||
\(680\) | 162296.i | 0.0134597i | ||||||||
\(681\) | 2.91356e6 | − | 1.28360e6i | 0.240744 | − | 0.106063i | ||||
\(682\) | − | 1.91749e7i | − | 1.57860i | ||||||
\(683\) | − | 6.08512e6i | − | 0.499135i | −0.968357 | − | 0.249567i | \(-0.919712\pi\) | ||
0.968357 | − | 0.249567i | \(-0.0802884\pi\) | |||||||
\(684\) | 3.03447e6 | + | 2.77544e6i | 0.247995 | + | 0.226825i | ||||
\(685\) | −69959.1 | −0.00569662 | ||||||||
\(686\) | −9.48734e6 | −0.769723 | ||||||||
\(687\) | −5.45850e6 | − | 1.23899e7i | −0.441247 | − | 1.00156i | ||||
\(688\) | − | 786571.i | − | 0.0633530i | ||||||
\(689\) | 1.63273e7 | 1.31029 | ||||||||
\(690\) | −5.04333e6 | − | 5.33769e6i | −0.403268 | − | 0.426806i | ||||
\(691\) | 1.21419e7 | 0.967368 | 0.483684 | − | 0.875243i | \(-0.339298\pi\) | ||||
0.483684 | + | 0.875243i | \(0.339298\pi\) | |||||||
\(692\) | − | 1.08639e7i | − | 0.862424i | ||||||
\(693\) | −1.08902e7 | − | 9.96061e6i | −0.861399 | − | 0.787867i | ||||
\(694\) | −6.15731e6 | −0.485280 | ||||||||
\(695\) | 4.04834e6 | 0.317918 | ||||||||
\(696\) | 2.65450e6 | − | 1.16947e6i | 0.207711 | − | 0.0915093i | ||||
\(697\) | 404063.i | 0.0315041i | ||||||||
\(698\) | 1.06127e7i | 0.824493i | ||||||||
\(699\) | 8.66560e6 | + | 1.96695e7i | 0.670820 | + | 1.52265i | ||||
\(700\) | 1.62944e6i | 0.125688i | ||||||||
\(701\) | −1.31040e7 | −1.00718 | −0.503590 | − | 0.863943i | \(-0.667988\pi\) | ||||
−0.503590 | + | 0.863943i | \(0.667988\pi\) | |||||||
\(702\) | 9.49307e6 | + | 3.20783e6i | 0.727049 | + | 0.245679i | ||||
\(703\) | −1.32233e7 | −1.00914 | ||||||||
\(704\) | 2.36962e6 | 0.180197 | ||||||||
\(705\) | −6.42914e6 | − | 1.45931e7i | −0.487169 | − | 1.10579i | ||||
\(706\) | 8.54764e6 | 0.645408 | ||||||||
\(707\) | −3.78577e6 | −0.284843 | ||||||||
\(708\) | −826005. | − | 1.87489e6i | −0.0619298 | − | 0.140570i | ||||
\(709\) | − | 151796.i | − | 0.0113408i | −0.999984 | − | 0.00567040i | \(-0.998195\pi\) | ||
0.999984 | − | 0.00567040i | \(-0.00180495\pi\) | |||||||
\(710\) | 3.89900e6 | 0.290273 | ||||||||
\(711\) | −8.00380e6 | − | 7.32057e6i | −0.593775 | − | 0.543089i | ||||
\(712\) | 7.31378e6i | 0.540682i | ||||||||
\(713\) | 1.98040e7 | − | 7.05163e6i | 1.45891 | − | 0.519476i | ||||
\(714\) | −327242. | + | 144170.i | −0.0240228 | + | 0.0105835i | ||||
\(715\) | 1.77603e7 | 1.29923 | ||||||||
\(716\) | − | 1.37737e6i | − | 0.100408i | ||||||
\(717\) | 2.76612e6 | + | 6.27863e6i | 0.200943 | + | 0.456108i | ||||
\(718\) | − | 3.61966e6i | − | 0.262033i | ||||||
\(719\) | − | 2.13306e7i | − | 1.53879i | −0.638771 | − | 0.769397i | \(-0.720557\pi\) | ||
0.638771 | − | 0.769397i | \(-0.279443\pi\) | |||||||
\(720\) | 1.94899e6 | − | 2.13089e6i | 0.140113 | − | 0.153190i | ||||
\(721\) | −1.59046e7 | −1.13942 | ||||||||
\(722\) | 5.42955e6i | 0.387633i | ||||||||
\(723\) | −3.97526e6 | − | 9.02319e6i | −0.282827 | − | 0.641969i | ||||
\(724\) | 1.14718e7i | 0.813367i | ||||||||
\(725\) | 2.82046e6i | 0.199285i | ||||||||
\(726\) | −4.36501e6 | − | 9.90785e6i | −0.307358 | − | 0.697651i | ||||
\(727\) | − | 1.67210e7i | − | 1.17335i | −0.809824 | − | 0.586673i | \(-0.800438\pi\) | ||
0.809824 | − | 0.586673i | \(-0.199562\pi\) | |||||||
\(728\) | −4.44335e6 | −0.310730 | ||||||||
\(729\) | −1.14079e7 | − | 8.70354e6i | −0.795034 | − | 0.606565i | ||||
\(730\) | 9.04345e6i | 0.628097i | ||||||||
\(731\) | 167845.i | 0.0116176i | ||||||||
\(732\) | −5.53508e6 | − | 1.25637e7i | −0.381809 | − | 0.866644i | ||||
\(733\) | 1.85430e7i | 1.27473i | 0.770561 | + | 0.637366i | \(0.219976\pi\) | ||||
−0.770561 | + | 0.637366i | \(0.780024\pi\) | |||||||
\(734\) | 1.94009e7 | 1.32918 | ||||||||
\(735\) | −3.83143e6 | + | 1.68798e6i | −0.261603 | + | 0.115252i | ||||
\(736\) | 871435. | + | 2.44737e6i | 0.0592981 | + | 0.166534i | ||||
\(737\) | 3.82878e6i | 0.259652i | ||||||||
\(738\) | 4.85234e6 | − | 5.30521e6i | 0.327952 | − | 0.358560i | ||||
\(739\) | −7.00315e6 | −0.471718 | −0.235859 | − | 0.971787i | \(-0.575790\pi\) | ||||
−0.235859 | + | 0.971787i | \(0.575790\pi\) | |||||||
\(740\) | 9.28576e6i | 0.623359i | ||||||||
\(741\) | −4.39607e6 | − | 9.97835e6i | −0.294116 | − | 0.667595i | ||||
\(742\) | 1.03675e7 | 0.691297 | ||||||||
\(743\) | −1.90312e7 | −1.26472 | −0.632361 | − | 0.774674i | \(-0.717914\pi\) | ||||
−0.632361 | + | 0.774674i | \(0.717914\pi\) | |||||||
\(744\) | 3.33291e6 | + | 7.56516e6i | 0.220745 | + | 0.501055i | ||||
\(745\) | −8.01484e6 | −0.529059 | ||||||||
\(746\) | 3.09224e6 | 0.203435 | ||||||||
\(747\) | −1.03202e7 | + | 1.12833e7i | −0.676683 | + | 0.739838i | ||||
\(748\) | −505649. | −0.0330442 | ||||||||
\(749\) | 2.03599e6i | 0.132608i | ||||||||
\(750\) | 4.77890e6 | + | 1.08473e7i | 0.310223 | + | 0.704156i | ||||
\(751\) | 2.27683e7i | 1.47309i | 0.676386 | + | 0.736547i | \(0.263545\pi\) | ||||
−0.676386 | + | 0.736547i | \(0.736455\pi\) | |||||||
\(752\) | 5.64139e6i | 0.363782i | ||||||||
\(753\) | 5.32475e6 | − | 2.34588e6i | 0.342225 | − | 0.150771i | ||||
\(754\) | −7.69120e6 | −0.492681 | ||||||||
\(755\) | −1.01295e7 | −0.646724 | ||||||||
\(756\) | 6.02790e6 | + | 2.03690e6i | 0.383585 | + | 0.129618i | ||||
\(757\) | 1.17215e7i | 0.743435i | 0.928346 | + | 0.371717i | \(0.121231\pi\) | ||||
−0.928346 | + | 0.371717i | \(0.878769\pi\) | |||||||
\(758\) | −2.21833e6 | −0.140234 | ||||||||
\(759\) | 1.66301e7 | − | 1.57130e7i | 1.04783 | − | 0.990043i | ||||
\(760\) | −3.14236e6 | −0.197343 | ||||||||
\(761\) | − | 2.42582e7i | − | 1.51844i | −0.650834 | − | 0.759220i | \(-0.725581\pi\) | ||
0.650834 | − | 0.759220i | \(-0.274419\pi\) | |||||||
\(762\) | 6.70693e6 | + | 1.52236e7i | 0.418443 | + | 0.949797i | ||||
\(763\) | −1.40770e7 | −0.875382 | ||||||||
\(764\) | 9.57604e6 | 0.593543 | ||||||||
\(765\) | −415891. | + | 454706.i | −0.0256937 | + | 0.0280917i | ||||
\(766\) | 1.52500e7i | 0.939068i | ||||||||
\(767\) | 5.43236e6i | 0.333426i | ||||||||
\(768\) | −934897. | + | 411879.i | −0.0571954 | + | 0.0251980i | ||||
\(769\) | − | 2.96832e6i | − | 0.181007i | −0.995896 | − | 0.0905033i | \(-0.971152\pi\) | ||
0.995896 | − | 0.0905033i | \(-0.0288476\pi\) | |||||||
\(770\) | 1.12774e7 | 0.685462 | ||||||||
\(771\) | −5.34386e6 | − | 1.21297e7i | −0.323757 | − | 0.734875i | ||||
\(772\) | −1.11724e7 | −0.674691 | ||||||||
\(773\) | 1.40122e7 | 0.843448 | 0.421724 | − | 0.906724i | \(-0.361425\pi\) | ||||
0.421724 | + | 0.906724i | \(0.361425\pi\) | |||||||
\(774\) | 2.01563e6 | − | 2.20375e6i | 0.120937 | − | 0.132224i | ||||
\(775\) | −8.03816e6 | −0.480731 | ||||||||
\(776\) | −5.22982e6 | −0.311769 | ||||||||
\(777\) | −1.87232e7 | + | 8.24870e6i | −1.11257 | + | 0.490155i | ||||
\(778\) | − | 1.31568e6i | − | 0.0779296i | ||||||
\(779\) | −7.82344e6 | −0.461906 | ||||||||
\(780\) | −7.00707e6 | + | 3.08704e6i | −0.412382 | + | 0.181679i | ||||
\(781\) | 1.21477e7i | 0.712635i | ||||||||
\(782\) | −185954. | − | 522239.i | −0.0108740 | − | 0.0305388i | ||||
\(783\) | 1.04340e7 | + | 3.52577e6i | 0.608198 | + | 0.205518i | ||||
\(784\) | 1.48115e6 | 0.0860618 | ||||||||
\(785\) | − | 2.30069e7i | − | 1.33255i | ||||||
\(786\) | −9.08418e6 | + | 4.00213e6i | −0.524480 | + | 0.231066i | ||||
\(787\) | − | 2.78881e7i | − | 1.60503i | −0.596633 | − | 0.802514i | \(-0.703495\pi\) | ||
0.596633 | − | 0.802514i | \(-0.296505\pi\) | |||||||
\(788\) | 1.23916e7i | 0.710907i | ||||||||
\(789\) | 2.15401e6 | − | 948973.i | 0.123184 | − | 0.0542702i | ||||
\(790\) | 8.28837e6 | 0.472500 | ||||||||
\(791\) | − | 2.91970e6i | − | 0.165919i | ||||||
\(792\) | 6.63899e6 | + | 6.07226e6i | 0.376088 | + | 0.343983i | ||||
\(793\) | 3.64024e7i | 2.05564i | ||||||||
\(794\) | 1.51601e7i | 0.853396i | ||||||||
\(795\) | 1.63493e7 | − | 7.20287e6i | 0.917449 | − | 0.404192i | ||||
\(796\) | 1.32868e7i | 0.743252i | ||||||||
\(797\) | 1.98565e7 | 1.10728 | 0.553640 | − | 0.832756i | \(-0.313238\pi\) | ||||
0.553640 | + | 0.832756i | \(0.313238\pi\) | |||||||
\(798\) | −2.79141e6 | − | 6.33604e6i | −0.155173 | − | 0.352217i | ||||
\(799\) | − | 1.20381e6i | − | 0.0667098i | ||||||
\(800\) | − | 993350.i | − | 0.0548753i | ||||||
\(801\) | −1.87419e7 | + | 2.04911e7i | −1.03213 | + | 1.12846i | ||||
\(802\) | 1.33281e7i | 0.731697i | ||||||||
\(803\) | −2.81758e7 | −1.54201 | ||||||||
\(804\) | −665507. | − | 1.51059e6i | −0.0363088 | − | 0.0824150i | ||||
\(805\) | 4.14732e6 | + | 1.16474e7i | 0.225568 | + | 0.633492i | ||||
\(806\) | − | 2.19195e7i | − | 1.18848i | ||||||
\(807\) | −4.04300e6 | − | 9.17694e6i | −0.218535 | − | 0.496037i | ||||
\(808\) | 2.30791e6 | 0.124363 | ||||||||
\(809\) | 2.73543e7i | 1.46945i | 0.678366 | + | 0.734724i | \(0.262689\pi\) | ||||
−0.678366 | + | 0.734724i | \(0.737311\pi\) | |||||||
\(810\) | 1.09210e7 | − | 975761.i | 0.584858 | − | 0.0522553i | ||||
\(811\) | −1.89733e7 | −1.01295 | −0.506477 | − | 0.862253i | \(-0.669053\pi\) | ||||
−0.506477 | + | 0.862253i | \(0.669053\pi\) | |||||||
\(812\) | −4.88375e6 | −0.259934 | ||||||||
\(813\) | 2.35588e7 | − | 1.03791e7i | 1.25005 | − | 0.550722i | ||||
\(814\) | −2.89307e7 | −1.53038 | ||||||||
\(815\) | −244482. | −0.0128930 | ||||||||
\(816\) | 199496. | − | 87890.2i | 0.0104884 | − | 0.00462078i | ||||
\(817\) | −3.24980e6 | −0.170334 | ||||||||
\(818\) | − | 2.53379e6i | − | 0.132400i | ||||||
\(819\) | −1.24490e7 | − | 1.13863e7i | −0.648522 | − | 0.593162i | ||||
\(820\) | 5.49383e6i | 0.285326i | ||||||||
\(821\) | 2.29178e7i | 1.18663i | 0.804971 | + | 0.593314i | \(0.202181\pi\) | ||||
−0.804971 | + | 0.593314i | \(0.797819\pi\) | |||||||
\(822\) | 37885.8 | + | 85994.6i | 0.00195568 | + | 0.00443907i | ||||
\(823\) | −1.77229e7 | −0.912083 | −0.456041 | − | 0.889959i | \(-0.650733\pi\) | ||||
−0.456041 | + | 0.889959i | \(0.650733\pi\) | |||||||
\(824\) | 9.69589e6 | 0.497473 | ||||||||
\(825\) | −8.00580e6 | + | 3.52704e6i | −0.409515 | + | 0.180416i | ||||
\(826\) | 3.44943e6i | 0.175913i | ||||||||
\(827\) | −3.39229e7 | −1.72476 | −0.862380 | − | 0.506261i | \(-0.831027\pi\) | ||||
−0.862380 | + | 0.506261i | \(0.831027\pi\) | |||||||
\(828\) | −3.82998e6 | + | 9.08991e6i | −0.194143 | + | 0.460770i | ||||
\(829\) | 2.43200e7 | 1.22907 | 0.614537 | − | 0.788888i | \(-0.289343\pi\) | ||||
0.614537 | + | 0.788888i | \(0.289343\pi\) | |||||||
\(830\) | − | 1.16845e7i | − | 0.588730i | ||||||
\(831\) | −5.65973e6 | + | 2.49345e6i | −0.284311 | + | 0.125256i | ||||
\(832\) | 2.70879e6 | 0.135665 | ||||||||
\(833\) | −316061. | −0.0157819 | ||||||||
\(834\) | −2.19235e6 | − | 4.97627e6i | −0.109143 | − | 0.247736i | ||||
\(835\) | 1.42729e7i | 0.708429i | ||||||||
\(836\) | − | 9.79033e6i | − | 0.484486i | ||||||
\(837\) | −1.00482e7 | + | 2.97362e7i | −0.495765 | + | 1.46714i | ||||
\(838\) | 1.82681e7i | 0.898637i | ||||||||
\(839\) | −1.32599e6 | −0.0650334 | −0.0325167 | − | 0.999471i | \(-0.510352\pi\) | ||||
−0.0325167 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(840\) | −4.44934e6 | + | 1.96021e6i | −0.217569 | + | 0.0958525i | ||||
\(841\) | 1.20576e7 | 0.587858 | ||||||||
\(842\) | 1.95175e7 | 0.948733 | ||||||||
\(843\) | 2.07718e7 | − | 9.15125e6i | 1.00671 | − | 0.443518i | ||||
\(844\) | −5.38360e6 | −0.260146 | ||||||||
\(845\) | 3.06656e6 | 0.147744 | ||||||||
\(846\) | −1.44563e7 | + | 1.58056e7i | −0.694436 | + | 0.759248i | ||||
\(847\) | 1.82285e7i | 0.873056i | ||||||||
\(848\) | −6.32032e6 | −0.301821 | ||||||||
\(849\) | −9.81651e6 | − | 2.22818e7i | −0.467399 | − | 1.06092i | ||||
\(850\) | 211969.i | 0.0100630i | ||||||||
\(851\) | −1.06394e7 | − | 2.98799e7i | −0.503607 | − | 1.41435i | ||||
\(852\) | −2.11148e6 | − | 4.79270e6i | −0.0996523 | − | 0.226194i | ||||
\(853\) | 1.55445e7 | 0.731485 | 0.365743 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365743 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(854\) | 2.31148e7i | 1.08454i | ||||||||
\(855\) | −8.80399e6 | − | 8.05245e6i | −0.411874 | − | 0.376715i | ||||
\(856\) | − | 1.24119e6i | − | 0.0578969i | ||||||
\(857\) | 1.41982e6i | 0.0660360i | 0.999455 | + | 0.0330180i | \(0.0105119\pi\) | ||||
−0.999455 | + | 0.0330180i | \(0.989488\pi\) | |||||||
\(858\) | −9.61798e6 | − | 2.18312e7i | −0.446032 | − | 1.01242i | ||||
\(859\) | −6.46087e6 | −0.298750 | −0.149375 | − | 0.988781i | \(-0.547726\pi\) | ||||
−0.149375 | + | 0.988781i | \(0.547726\pi\) | |||||||
\(860\) | 2.28210e6i | 0.105218i | ||||||||
\(861\) | −1.10774e7 | + | 4.88027e6i | −0.509249 | + | 0.224355i | ||||
\(862\) | 7.14094e6i | 0.327331i | ||||||||
\(863\) | 4.23625e7i | 1.93622i | 0.250523 | + | 0.968111i | \(0.419397\pi\) | ||||
−0.250523 | + | 0.968111i | \(0.580603\pi\) | |||||||
\(864\) | −3.67477e6 | − | 1.24175e6i | −0.167474 | − | 0.0565914i | ||||
\(865\) | 3.15198e7i | 1.43233i | ||||||||
\(866\) | 3.45100e6 | 0.156369 | ||||||||
\(867\) | 2.02123e7 | − | 8.90473e6i | 0.913202 | − | 0.402321i | ||||
\(868\) | − | 1.39184e7i | − | 0.627032i | ||||||
\(869\) | 2.58232e7i | 1.16001i | ||||||||
\(870\) | −7.70156e6 | + | 3.39301e6i | −0.344970 | + | 0.151980i | ||||
\(871\) | 4.37682e6i | 0.195485i | ||||||||
\(872\) | 8.58171e6 | 0.382193 | ||||||||
\(873\) | −1.46525e7 | − | 1.34017e7i | −0.650691 | − | 0.595146i | ||||
\(874\) | 1.01116e7 | − | 3.60043e6i | 0.447754 | − | 0.159432i | ||||
\(875\) | − | 1.99569e7i | − | 0.881197i | ||||||
\(876\) | 1.11163e7 | − | 4.89742e6i | 0.489442 | − | 0.215629i | ||||
\(877\) | −2.08726e7 | −0.916383 | −0.458191 | − | 0.888854i | \(-0.651503\pi\) | ||||
−0.458191 | + | 0.888854i | \(0.651503\pi\) | |||||||
\(878\) | − | 9.52915e6i | − | 0.417174i | ||||||
\(879\) | 2.96290e7 | − | 1.30534e7i | 1.29344 | − | 0.569838i | ||||
\(880\) | −6.87504e6 | −0.299274 | ||||||||
\(881\) | 2.34455e7 | 1.01770 | 0.508851 | − | 0.860855i | \(-0.330070\pi\) | ||||
0.508851 | + | 0.860855i | \(0.330070\pi\) | |||||||
\(882\) | 4.14977e6 | + | 3.79553e6i | 0.179619 | + | 0.164286i | ||||
\(883\) | −3.76556e7 | −1.62528 | −0.812639 | − | 0.582767i | \(-0.801970\pi\) | ||||
−0.812639 | + | 0.582767i | \(0.801970\pi\) | |||||||
\(884\) | −578025. | −0.0248780 | ||||||||
\(885\) | 2.39651e6 | + | 5.43968e6i | 0.102854 | + | 0.233461i | ||||
\(886\) | 1.46095e7 | 0.625246 | ||||||||
\(887\) | − | 3.76988e7i | − | 1.60886i | −0.594046 | − | 0.804431i | \(-0.702470\pi\) | ||
0.594046 | − | 0.804431i | \(-0.297530\pi\) | |||||||
\(888\) | 1.14142e7 | − | 5.02864e6i | 0.485749 | − | 0.214002i | ||||
\(889\) | − | 2.80085e7i | − | 1.18860i | ||||||
\(890\) | − | 2.12197e7i | − | 0.897974i | ||||||
\(891\) | 3.04008e6 | + | 3.40255e7i | 0.128289 | + | 1.43585i | ||||
\(892\) | 1.19703e7 | 0.503724 | ||||||||
\(893\) | 2.33080e7 | 0.978085 | ||||||||
\(894\) | 4.34038e6 | + | 9.85194e6i | 0.181628 | + | 0.412266i | ||||
\(895\) | 3.99619e6i | 0.166759i | ||||||||
\(896\) | 1.72003e6 | 0.0715756 | ||||||||
\(897\) | 1.90105e7 | − | 1.79621e7i | 0.788881 | − | 0.745375i | ||||
\(898\) | −1.37912e7 | −0.570706 | ||||||||
\(899\) | − | 2.40920e7i | − | 0.994199i | ||||||
\(900\) | 2.54551e6 | − | 2.78308e6i | 0.104753 | − | 0.114530i | ||||
\(901\) | 1.34868e6 | 0.0553474 | ||||||||
\(902\) | −1.71166e7 | −0.700488 | ||||||||
\(903\) | −4.60148e6 | + | 2.02723e6i | −0.187792 | + | 0.0827340i | ||||
\(904\) | 1.77993e6i | 0.0724406i | ||||||||
\(905\) | − | 3.32836e7i | − | 1.35085i | ||||||
\(906\) | 5.48554e6 | + | 1.24513e7i | 0.222023 | + | 0.503956i | ||||
\(907\) | − | 7.81724e6i | − | 0.315526i | −0.987477 | − | 0.157763i | \(-0.949572\pi\) | ||
0.987477 | − | 0.157763i | \(-0.0504282\pi\) | |||||||
\(908\) | 3.26784e6 | 0.131536 | ||||||||
\(909\) | 6.46610e6 | + | 5.91413e6i | 0.259557 | + | 0.237400i | ||||
\(910\) | 1.28916e7 | 0.516065 | ||||||||
\(911\) | −1.13258e7 | −0.452140 | −0.226070 | − | 0.974111i | \(-0.572588\pi\) | ||||
−0.226070 | + | 0.974111i | \(0.572588\pi\) | |||||||
\(912\) | 1.70172e6 | + | 3.86263e6i | 0.0677488 | + | 0.153779i | ||||
\(913\) | 3.64043e7 | 1.44536 | ||||||||
\(914\) | −8.39732e6 | −0.332487 | ||||||||
\(915\) | 1.60591e7 | + | 3.64515e7i | 0.634115 | + | 1.43934i | ||||
\(916\) | − | 1.38964e7i | − | 0.547224i | ||||||
\(917\) | 1.67131e7 | 0.656347 | ||||||||
\(918\) | 784154. | + | 264975.i | 0.0307110 | + | 0.0103776i | ||||
\(919\) | − | 5.35114e6i | − | 0.209005i | −0.994525 | − | 0.104503i | \(-0.966675\pi\) | ||
0.994525 | − | 0.104503i | \(-0.0333251\pi\) | |||||||
\(920\) | −2.52832e6 | − | 7.10061e6i | −0.0984832 | − | 0.276583i | ||||
\(921\) | −4.00089e6 | + | 1.76263e6i | −0.155420 | + | 0.0684720i | ||||
\(922\) | 6.23644e6 | 0.241607 | ||||||||
\(923\) | 1.38865e7i | 0.536523i | ||||||||
\(924\) | −6.10722e6 | − | 1.38624e7i | −0.235323 | − | 0.534143i | ||||
\(925\) | 1.21278e7i | 0.466046i | ||||||||
\(926\) | − | 1.91677e7i | − | 0.734587i | ||||||
\(927\) | 2.71651e7 | + | 2.48462e7i | 1.03827 | + | 0.949644i | ||||
\(928\) | 2.97727e6 | 0.113488 | ||||||||
\(929\) | 3.42386e7i | 1.30160i | 0.759250 | + | 0.650799i | \(0.225566\pi\) | ||||
−0.759250 | + | 0.650799i | \(0.774434\pi\) | |||||||
\(930\) | −9.66987e6 | − | 2.19490e7i | −0.366618 | − | 0.832161i | ||||
\(931\) | − | 6.11955e6i | − | 0.231390i | ||||||
\(932\) | 2.20612e7i | 0.831934i | ||||||||
\(933\) | −5.68064e6 | − | 1.28941e7i | −0.213645 | − | 0.484939i | ||||
\(934\) | − | 1.77296e7i | − | 0.665015i | ||||||
\(935\) | 1.46705e6 | 0.0548803 | ||||||||
\(936\) | 7.58926e6 | + | 6.94141e6i | 0.283146 | + | 0.258975i | ||||
\(937\) | − | 3.00322e6i | − | 0.111747i | −0.998438 | − | 0.0558737i | \(-0.982206\pi\) | ||
0.998438 | − | 0.0558737i | \(-0.0177944\pi\) | |||||||
\(938\) | 2.77919e6i | 0.103136i | ||||||||
\(939\) | −1.17136e7 | − | 2.65879e7i | −0.433537 | − | 0.984057i | ||||
\(940\) | − | 1.63675e7i | − | 0.604176i | ||||||
\(941\) | −1.38304e7 | −0.509169 | −0.254585 | − | 0.967050i | \(-0.581939\pi\) | ||||
−0.254585 | + | 0.967050i | \(0.581939\pi\) | |||||||
\(942\) | −2.82804e7 | + | 1.24592e7i | −1.03839 | + | 0.457472i | ||||
\(943\) | −6.29468e6 | − | 1.76782e7i | −0.230513 | − | 0.647378i | ||||
\(944\) | − | 2.10287e6i | − | 0.0768038i | ||||||
\(945\) | −1.74889e7 | − | 5.90972e6i | −0.637064 | − | 0.215272i | ||||
\(946\) | −7.11011e6 | −0.258314 | ||||||||
\(947\) | 2.76242e7i | 1.00096i | 0.865749 | + | 0.500478i | \(0.166843\pi\) | ||||
−0.865749 | + | 0.500478i | \(0.833157\pi\) | |||||||
\(948\) | −4.48851e6 | − | 1.01882e7i | −0.162211 | − | 0.368193i | ||||
\(949\) | −3.22087e7 | −1.16093 | ||||||||
\(950\) | −4.10413e6 | −0.147541 | ||||||||
\(951\) | 2.26991e6 | + | 5.15231e6i | 0.0813873 | + | 0.184736i | ||||
\(952\) | −367033. | −0.0131254 | ||||||||
\(953\) | 1.42475e7 | 0.508167 | 0.254083 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254083 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(954\) | −1.77077e7 | − | 1.61961e7i | −0.629929 | − | 0.576156i | ||||
\(955\) | −2.77832e7 | −0.985767 | ||||||||
\(956\) | 7.04208e6i | 0.249205i | ||||||||
\(957\) | −1.05713e7 | − | 2.39950e7i | −0.373118 | − | 0.846917i | ||||
\(958\) | − | 1.27767e7i | − | 0.449783i | ||||||
\(959\) | − | 158213.i | − | 0.00555515i | ||||||
\(960\) | 2.71244e6 | − | 1.19500e6i | 0.0949910 | − | 0.0418493i | ||||
\(961\) | 4.00316e7 | 1.39828 | ||||||||
\(962\) | −3.30717e7 | −1.15218 | ||||||||
\(963\) | 3.18062e6 | − | 3.47747e6i | 0.110521 | − | 0.120836i | ||||
\(964\) | − | 1.01204e7i | − | 0.350755i | ||||||
\(965\) | 3.24149e7 | 1.12054 | ||||||||
\(966\) | 1.20712e7 | − | 1.14055e7i | 0.416207 | − | 0.393254i | ||||
\(967\) | 4.31861e7 | 1.48517 | 0.742587 | − | 0.669749i | \(-0.233598\pi\) | ||||
0.742587 | + | 0.669749i | \(0.233598\pi\) | |||||||
\(968\) | − | 1.11126e7i | − | 0.381177i | ||||||
\(969\) | −363128. | − | 824239.i | −0.0124237 | − | 0.0281997i | ||||
\(970\) | 1.51734e7 | 0.517791 | ||||||||
\(971\) | −5.09861e7 | −1.73542 | −0.867708 | − | 0.497075i | \(-0.834407\pi\) | ||||
−0.867708 | + | 0.497075i | \(0.834407\pi\) | |||||||
\(972\) | −7.11361e6 | − | 1.28958e7i | −0.241504 | − | 0.437808i | ||||
\(973\) | 9.15536e6i | 0.310023i | ||||||||
\(974\) | 1.95149e7i | 0.659126i | ||||||||
\(975\) | −9.15170e6 | + | 4.03188e6i | −0.308312 | + | 0.135830i | ||||
\(976\) | − | 1.40914e7i | − | 0.473511i | ||||||
\(977\) | −2.83114e7 | −0.948909 | −0.474455 | − | 0.880280i | \(-0.657355\pi\) | ||||
−0.474455 | + | 0.880280i | \(0.657355\pi\) | |||||||
\(978\) | 132398. | + | 300521.i | 0.00442623 | + | 0.0100468i | ||||
\(979\) | 6.61120e7 | 2.20457 | ||||||||
\(980\) | −4.29732e6 | −0.142933 | ||||||||
\(981\) | 2.40435e7 | + | 2.19911e7i | 0.797673 | + | 0.729581i | ||||
\(982\) | −3.03516e7 | −1.00439 | ||||||||
\(983\) | −1.34774e7 | −0.444860 | −0.222430 | − | 0.974949i | \(-0.571399\pi\) | ||||
−0.222430 | + | 0.974949i | \(0.571399\pi\) | |||||||
\(984\) | 6.75309e6 | − | 2.97515e6i | 0.222339 | − | 0.0979537i | ||||
\(985\) | − | 3.59522e7i | − | 1.18069i | ||||||
\(986\) | −635314. | −0.0208112 | ||||||||
\(987\) | 3.30024e7 | − | 1.45396e7i | 1.07833 | − | 0.475071i | ||||
\(988\) | − | 1.11917e7i | − | 0.364756i | ||||||
\(989\) | −2.61477e6 | − | 7.34339e6i | −0.0850046 | − | 0.238730i | ||||
\(990\) | −1.92619e7 | − | 1.76176e7i | −0.624613 | − | 0.571294i | ||||
\(991\) | 1.18912e7 | 0.384630 | 0.192315 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192315 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(992\) | 8.48504e6i | 0.273763i | ||||||||
\(993\) | −1.57598e7 | + | 6.94313e6i | −0.507197 | + | 0.223451i | ||||
\(994\) | 8.81762e6i | 0.283065i | ||||||||
\(995\) | − | 3.85492e7i | − | 1.23441i | ||||||
\(996\) | −1.43628e7 | + | 6.32767e6i | −0.458765 | + | 0.202114i | ||||
\(997\) | −3.41726e7 | −1.08878 | −0.544390 | − | 0.838832i | \(-0.683239\pi\) | ||||
−0.544390 | + | 0.838832i | \(0.683239\pi\) | |||||||
\(998\) | 2.66812e7i | 0.847969i | ||||||||
\(999\) | 4.48654e7 | + | 1.51606e7i | 1.42232 | + | 0.480620i |
(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 | 138.6.d.a.137.20 | yes | 40 | |
3.2 | odd | 2 | inner | 138.6.d.a.137.17 | ✓ | 40 | |
23.22 | odd | 2 | inner | 138.6.d.a.137.19 | yes | 40 | |
69.68 | even | 2 | inner | 138.6.d.a.137.18 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.6.d.a.137.17 | ✓ | 40 | 3.2 | odd | 2 | inner | |
138.6.d.a.137.18 | yes | 40 | 69.68 | even | 2 | inner | |
138.6.d.a.137.19 | yes | 40 | 23.22 | odd | 2 | inner | |
138.6.d.a.137.20 | yes | 40 | 1.1 | even | 1 | trivial |