Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(7,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.11 |
Dual form | 38.4.c.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | −2.50000 | + | 4.33013i | −0.481125 | + | 0.833333i | −0.999765 | − | 0.0216593i | \(-0.993105\pi\) |
0.518640 | + | 0.854993i | \(0.326438\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.134164 | + | 0.232379i | −0.925278 | − | 0.379290i | \(-0.876168\pi\) |
0.791114 | + | 0.611669i | \(0.209502\pi\) | |||||||
\(6\) | −5.00000 | − | 8.66025i | −0.340207 | − | 0.589256i | ||||
\(7\) | −32.0000 | −1.72784 | −0.863919 | − | 0.503631i | \(-0.831997\pi\) | ||||
−0.863919 | + | 0.503631i | \(0.831997\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.0370370 | + | 0.0641500i | ||||
\(10\) | −3.00000 | − | 5.19615i | −0.0948683 | − | 0.164317i | ||||
\(11\) | 4.00000 | 0.109640 | 0.0548202 | − | 0.998496i | \(-0.482541\pi\) | ||||
0.0548202 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(12\) | 20.0000 | 0.481125 | ||||||||
\(13\) | 34.5000 | + | 59.7558i | 0.736044 | + | 1.27487i | 0.954264 | + | 0.298967i | \(0.0966419\pi\) |
−0.218219 | + | 0.975900i | \(0.570025\pi\) | |||||||
\(14\) | 32.0000 | − | 55.4256i | 0.610883 | − | 1.05808i | ||||
\(15\) | −7.50000 | − | 12.9904i | −0.129099 | − | 0.223607i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −9.50000 | + | 16.4545i | −0.135535 | + | 0.234753i | −0.925802 | − | 0.378010i | \(-0.876609\pi\) |
0.790267 | + | 0.612763i | \(0.209942\pi\) | |||||||
\(18\) | −4.00000 | −0.0523783 | ||||||||
\(19\) | 76.0000 | + | 32.9090i | 0.917663 | + | 0.397360i | ||||
\(20\) | 12.0000 | 0.134164 | ||||||||
\(21\) | 80.0000 | − | 138.564i | 0.831306 | − | 1.43986i | ||||
\(22\) | −4.00000 | + | 6.92820i | −0.0387638 | + | 0.0671408i | ||||
\(23\) | −33.5000 | − | 58.0237i | −0.303706 | − | 0.526034i | 0.673267 | − | 0.739400i | \(-0.264891\pi\) |
−0.976972 | + | 0.213366i | \(0.931557\pi\) | |||||||
\(24\) | −20.0000 | + | 34.6410i | −0.170103 | + | 0.294628i | ||||
\(25\) | 58.0000 | + | 100.459i | 0.464000 | + | 0.803672i | ||||
\(26\) | −138.000 | −1.04092 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 64.0000 | + | 110.851i | 0.431959 | + | 0.748176i | ||||
\(29\) | −25.5000 | − | 44.1673i | −0.163284 | − | 0.282816i | 0.772761 | − | 0.634698i | \(-0.218875\pi\) |
−0.936045 | + | 0.351882i | \(0.885542\pi\) | |||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | −132.000 | −0.764771 | −0.382385 | − | 0.924003i | \(-0.624897\pi\) | ||||
−0.382385 | + | 0.924003i | \(0.624897\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −10.0000 | + | 17.3205i | −0.0527508 | + | 0.0913671i | ||||
\(34\) | −19.0000 | − | 32.9090i | −0.0958374 | − | 0.165995i | ||||
\(35\) | 48.0000 | − | 83.1384i | 0.231814 | − | 0.401513i | ||||
\(36\) | 4.00000 | − | 6.92820i | 0.0185185 | − | 0.0320750i | ||||
\(37\) | −14.0000 | −0.0622050 | −0.0311025 | − | 0.999516i | \(-0.509902\pi\) | ||||
−0.0311025 | + | 0.999516i | \(0.509902\pi\) | |||||||
\(38\) | −133.000 | + | 98.7269i | −0.567775 | + | 0.421464i | ||||
\(39\) | −345.000 | −1.41652 | ||||||||
\(40\) | −12.0000 | + | 20.7846i | −0.0474342 | + | 0.0821584i | ||||
\(41\) | 206.500 | − | 357.668i | 0.786582 | − | 1.36240i | −0.141467 | − | 0.989943i | \(-0.545182\pi\) |
0.928049 | − | 0.372458i | \(-0.121485\pi\) | |||||||
\(42\) | 160.000 | + | 277.128i | 0.587822 | + | 1.01814i | ||||
\(43\) | −64.5000 | + | 111.717i | −0.228748 | + | 0.396203i | −0.957437 | − | 0.288641i | \(-0.906796\pi\) |
0.728689 | + | 0.684844i | \(0.240130\pi\) | |||||||
\(44\) | −8.00000 | − | 13.8564i | −0.0274101 | − | 0.0474757i | ||||
\(45\) | −6.00000 | −0.0198762 | ||||||||
\(46\) | 134.000 | 0.429505 | ||||||||
\(47\) | 308.500 | + | 534.338i | 0.957433 | + | 1.65832i | 0.728700 | + | 0.684833i | \(0.240125\pi\) |
0.228733 | + | 0.973489i | \(0.426542\pi\) | |||||||
\(48\) | −40.0000 | − | 69.2820i | −0.120281 | − | 0.208333i | ||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | −232.000 | −0.656195 | ||||||||
\(51\) | −47.5000 | − | 82.2724i | −0.130418 | − | 0.225891i | ||||
\(52\) | 138.000 | − | 239.023i | 0.368022 | − | 0.637433i | ||||
\(53\) | −191.500 | − | 331.688i | −0.496312 | − | 0.859638i | 0.503679 | − | 0.863891i | \(-0.331980\pi\) |
−0.999991 | + | 0.00425305i | \(0.998646\pi\) | |||||||
\(54\) | 145.000 | − | 251.147i | 0.365407 | − | 0.632904i | ||||
\(55\) | −6.00000 | + | 10.3923i | −0.0147098 | + | 0.0254781i | ||||
\(56\) | −256.000 | −0.610883 | ||||||||
\(57\) | −332.500 | + | 246.817i | −0.772644 | + | 0.573539i | ||||
\(58\) | 102.000 | 0.230918 | ||||||||
\(59\) | 299.500 | − | 518.749i | 0.660874 | − | 1.14467i | −0.319512 | − | 0.947582i | \(-0.603519\pi\) |
0.980386 | − | 0.197086i | \(-0.0631477\pi\) | |||||||
\(60\) | −30.0000 | + | 51.9615i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 108.500 | + | 187.928i | 0.227738 | + | 0.394453i | 0.957137 | − | 0.289635i | \(-0.0935338\pi\) |
−0.729400 | + | 0.684088i | \(0.760200\pi\) | |||||||
\(62\) | 132.000 | − | 228.631i | 0.270387 | − | 0.468325i | ||||
\(63\) | −32.0000 | − | 55.4256i | −0.0639940 | − | 0.110841i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −207.000 | −0.395003 | ||||||||
\(66\) | −20.0000 | − | 34.6410i | −0.0373005 | − | 0.0646063i | ||||
\(67\) | 112.500 | + | 194.856i | 0.205135 | + | 0.355305i | 0.950176 | − | 0.311714i | \(-0.100903\pi\) |
−0.745041 | + | 0.667019i | \(0.767570\pi\) | |||||||
\(68\) | 76.0000 | 0.135535 | ||||||||
\(69\) | 335.000 | 0.584482 | ||||||||
\(70\) | 96.0000 | + | 166.277i | 0.163917 | + | 0.283913i | ||||
\(71\) | −350.500 | + | 607.084i | −0.585869 | + | 1.01475i | 0.408898 | + | 0.912580i | \(0.365913\pi\) |
−0.994766 | + | 0.102175i | \(0.967420\pi\) | |||||||
\(72\) | 8.00000 | + | 13.8564i | 0.0130946 | + | 0.0226805i | ||||
\(73\) | −507.500 | + | 879.016i | −0.813676 | + | 1.40933i | 0.0965979 | + | 0.995323i | \(0.469204\pi\) |
−0.910274 | + | 0.414005i | \(0.864129\pi\) | |||||||
\(74\) | 14.0000 | − | 24.2487i | 0.0219928 | − | 0.0380926i | ||||
\(75\) | −580.000 | −0.892968 | ||||||||
\(76\) | −38.0000 | − | 329.090i | −0.0573539 | − | 0.496700i | ||||
\(77\) | −128.000 | −0.189441 | ||||||||
\(78\) | 345.000 | − | 597.558i | 0.500815 | − | 0.867437i | ||||
\(79\) | −174.500 | + | 302.243i | −0.248516 | + | 0.430443i | −0.963114 | − | 0.269092i | \(-0.913276\pi\) |
0.714598 | + | 0.699535i | \(0.246610\pi\) | |||||||
\(80\) | −24.0000 | − | 41.5692i | −0.0335410 | − | 0.0580948i | ||||
\(81\) | 335.500 | − | 581.103i | 0.460219 | − | 0.797124i | ||||
\(82\) | 413.000 | + | 715.337i | 0.556198 | + | 0.963363i | ||||
\(83\) | −592.000 | −0.782897 | −0.391448 | − | 0.920200i | \(-0.628026\pi\) | ||||
−0.391448 | + | 0.920200i | \(0.628026\pi\) | |||||||
\(84\) | −640.000 | −0.831306 | ||||||||
\(85\) | −28.5000 | − | 49.3634i | −0.0363678 | − | 0.0629908i | ||||
\(86\) | −129.000 | − | 223.435i | −0.161749 | − | 0.280158i | ||||
\(87\) | 255.000 | 0.314240 | ||||||||
\(88\) | 32.0000 | 0.0387638 | ||||||||
\(89\) | 674.500 | + | 1168.27i | 0.803335 | + | 1.39142i | 0.917409 | + | 0.397946i | \(0.130277\pi\) |
−0.114074 | + | 0.993472i | \(0.536390\pi\) | |||||||
\(90\) | 6.00000 | − | 10.3923i | 0.00702728 | − | 0.0121716i | ||||
\(91\) | −1104.00 | − | 1912.18i | −1.27177 | − | 2.20276i | ||||
\(92\) | −134.000 | + | 232.095i | −0.151853 | + | 0.263017i | ||||
\(93\) | 330.000 | − | 571.577i | 0.367951 | − | 0.637309i | ||||
\(94\) | −1234.00 | −1.35401 | ||||||||
\(95\) | −199.500 | + | 148.090i | −0.215455 | + | 0.159934i | ||||
\(96\) | 160.000 | 0.170103 | ||||||||
\(97\) | 306.500 | − | 530.874i | 0.320828 | − | 0.555691i | −0.659831 | − | 0.751414i | \(-0.729372\pi\) |
0.980659 | + | 0.195723i | \(0.0627054\pi\) | |||||||
\(98\) | −681.000 | + | 1179.53i | −0.701953 | + | 1.21582i | ||||
\(99\) | 4.00000 | + | 6.92820i | 0.00406076 | + | 0.00703344i | ||||
\(100\) | 232.000 | − | 401.836i | 0.232000 | − | 0.401836i | ||||
\(101\) | −617.500 | − | 1069.54i | −0.608352 | − | 1.05370i | −0.991512 | − | 0.130015i | \(-0.958498\pi\) |
0.383160 | − | 0.923682i | \(-0.374836\pi\) | |||||||
\(102\) | 190.000 | 0.184439 | ||||||||
\(103\) | 1632.00 | 1.56122 | 0.780610 | − | 0.625018i | \(-0.214908\pi\) | ||||
0.780610 | + | 0.625018i | \(0.214908\pi\) | |||||||
\(104\) | 276.000 | + | 478.046i | 0.260231 | + | 0.450733i | ||||
\(105\) | 240.000 | + | 415.692i | 0.223063 | + | 0.386356i | ||||
\(106\) | 766.000 | 0.701891 | ||||||||
\(107\) | 2060.00 | 1.86119 | 0.930597 | − | 0.366046i | \(-0.119289\pi\) | ||||
0.930597 | + | 0.366046i | \(0.119289\pi\) | |||||||
\(108\) | 290.000 | + | 502.295i | 0.258382 | + | 0.447531i | ||||
\(109\) | −527.500 | + | 913.657i | −0.463535 | + | 0.802867i | −0.999134 | − | 0.0416060i | \(-0.986753\pi\) |
0.535599 | + | 0.844473i | \(0.320086\pi\) | |||||||
\(110\) | −12.0000 | − | 20.7846i | −0.0104014 | − | 0.0180158i | ||||
\(111\) | 35.0000 | − | 60.6218i | 0.0299284 | − | 0.0518375i | ||||
\(112\) | 256.000 | − | 443.405i | 0.215980 | − | 0.374088i | ||||
\(113\) | 1006.00 | 0.837491 | 0.418746 | − | 0.908104i | \(-0.362470\pi\) | ||||
0.418746 | + | 0.908104i | \(0.362470\pi\) | |||||||
\(114\) | −95.0000 | − | 822.724i | −0.0780488 | − | 0.675923i | ||||
\(115\) | 201.000 | 0.162986 | ||||||||
\(116\) | −102.000 | + | 176.669i | −0.0816419 | + | 0.141408i | ||||
\(117\) | −69.0000 | + | 119.512i | −0.0545218 | + | 0.0944346i | ||||
\(118\) | 599.000 | + | 1037.50i | 0.467309 | + | 0.809402i | ||||
\(119\) | 304.000 | − | 526.543i | 0.234182 | − | 0.405615i | ||||
\(120\) | −60.0000 | − | 103.923i | −0.0456435 | − | 0.0790569i | ||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | −434.000 | −0.322070 | ||||||||
\(123\) | 1032.50 | + | 1788.34i | 0.756889 | + | 1.31097i | ||||
\(124\) | 264.000 | + | 457.261i | 0.191193 | + | 0.331156i | ||||
\(125\) | −723.000 | −0.517337 | ||||||||
\(126\) | 128.000 | 0.0905012 | ||||||||
\(127\) | −993.500 | − | 1720.79i | −0.694164 | − | 1.20233i | −0.970462 | − | 0.241256i | \(-0.922441\pi\) |
0.276297 | − | 0.961072i | \(-0.410893\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −322.500 | − | 558.586i | −0.220113 | − | 0.381246i | ||||
\(130\) | 207.000 | − | 358.535i | 0.139655 | − | 0.241889i | ||||
\(131\) | 901.500 | − | 1561.44i | 0.601255 | − | 1.04140i | −0.391376 | − | 0.920231i | \(-0.628001\pi\) |
0.992631 | − | 0.121174i | \(-0.0386658\pi\) | |||||||
\(132\) | 80.0000 | 0.0527508 | ||||||||
\(133\) | −2432.00 | − | 1053.09i | −1.58557 | − | 0.686573i | ||||
\(134\) | −450.000 | −0.290105 | ||||||||
\(135\) | 217.500 | − | 376.721i | 0.138662 | − | 0.240170i | ||||
\(136\) | −76.0000 | + | 131.636i | −0.0479187 | + | 0.0829977i | ||||
\(137\) | 334.500 | + | 579.371i | 0.208600 | + | 0.361307i | 0.951274 | − | 0.308347i | \(-0.0997758\pi\) |
−0.742673 | + | 0.669654i | \(0.766443\pi\) | |||||||
\(138\) | −335.000 | + | 580.237i | −0.206646 | + | 0.357921i | ||||
\(139\) | 1362.50 | + | 2359.92i | 0.831408 | + | 1.44004i | 0.896922 | + | 0.442190i | \(0.145798\pi\) |
−0.0655134 | + | 0.997852i | \(0.520869\pi\) | |||||||
\(140\) | −384.000 | −0.231814 | ||||||||
\(141\) | −3085.00 | −1.84258 | ||||||||
\(142\) | −701.000 | − | 1214.17i | −0.414272 | − | 0.717540i | ||||
\(143\) | 138.000 | + | 239.023i | 0.0807003 | + | 0.139777i | ||||
\(144\) | −32.0000 | −0.0185185 | ||||||||
\(145\) | 153.000 | 0.0876273 | ||||||||
\(146\) | −1015.00 | − | 1758.03i | −0.575356 | − | 0.996546i | ||||
\(147\) | −1702.50 | + | 2948.82i | −0.955237 | + | 1.65452i | ||||
\(148\) | 28.0000 | + | 48.4974i | 0.0155513 | + | 0.0269356i | ||||
\(149\) | −35.5000 | + | 61.4878i | −0.0195186 | + | 0.0338072i | −0.875620 | − | 0.483001i | \(-0.839547\pi\) |
0.856101 | + | 0.516808i | \(0.172880\pi\) | |||||||
\(150\) | 580.000 | − | 1004.59i | 0.315712 | − | 0.546829i | ||||
\(151\) | −656.000 | −0.353540 | −0.176770 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176770 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(152\) | 608.000 | + | 263.272i | 0.324443 | + | 0.140488i | ||||
\(153\) | −38.0000 | −0.0200792 | ||||||||
\(154\) | 128.000 | − | 221.703i | 0.0669775 | − | 0.116008i | ||||
\(155\) | 198.000 | − | 342.946i | 0.102605 | − | 0.177717i | ||||
\(156\) | 690.000 | + | 1195.12i | 0.354130 | + | 0.613370i | ||||
\(157\) | 526.500 | − | 911.925i | 0.267639 | − | 0.463564i | −0.700613 | − | 0.713542i | \(-0.747090\pi\) |
0.968252 | + | 0.249978i | \(0.0804233\pi\) | |||||||
\(158\) | −349.000 | − | 604.486i | −0.175728 | − | 0.304369i | ||||
\(159\) | 1915.00 | 0.955153 | ||||||||
\(160\) | 96.0000 | 0.0474342 | ||||||||
\(161\) | 1072.00 | + | 1856.76i | 0.524754 | + | 0.908901i | ||||
\(162\) | 671.000 | + | 1162.21i | 0.325424 | + | 0.563651i | ||||
\(163\) | 68.0000 | 0.0326759 | 0.0163379 | − | 0.999867i | \(-0.494799\pi\) | ||||
0.0163379 | + | 0.999867i | \(0.494799\pi\) | |||||||
\(164\) | −1652.00 | −0.786582 | ||||||||
\(165\) | −30.0000 | − | 51.9615i | −0.0141545 | − | 0.0245164i | ||||
\(166\) | 592.000 | − | 1025.37i | 0.276796 | − | 0.479424i | ||||
\(167\) | 460.500 | + | 797.609i | 0.213381 | + | 0.369586i | 0.952770 | − | 0.303692i | \(-0.0982192\pi\) |
−0.739390 | + | 0.673278i | \(0.764886\pi\) | |||||||
\(168\) | 640.000 | − | 1108.51i | 0.293911 | − | 0.509069i | ||||
\(169\) | −1282.00 | + | 2220.49i | −0.583523 | + | 1.01069i | ||||
\(170\) | 114.000 | 0.0514318 | ||||||||
\(171\) | 19.0000 | + | 164.545i | 0.00849688 | + | 0.0735851i | ||||
\(172\) | 516.000 | 0.228748 | ||||||||
\(173\) | 946.500 | − | 1639.39i | 0.415960 | − | 0.720464i | −0.579569 | − | 0.814923i | \(-0.696779\pi\) |
0.995529 | + | 0.0944596i | \(0.0301123\pi\) | |||||||
\(174\) | −255.000 | + | 441.673i | −0.111101 | + | 0.192432i | ||||
\(175\) | −1856.00 | − | 3214.69i | −0.801717 | − | 1.38861i | ||||
\(176\) | −32.0000 | + | 55.4256i | −0.0137051 | + | 0.0237379i | ||||
\(177\) | 1497.50 | + | 2593.75i | 0.635927 | + | 1.10146i | ||||
\(178\) | −2698.00 | −1.13609 | ||||||||
\(179\) | −20.0000 | −0.00835123 | −0.00417562 | − | 0.999991i | \(-0.501329\pi\) | ||||
−0.00417562 | + | 0.999991i | \(0.501329\pi\) | |||||||
\(180\) | 12.0000 | + | 20.7846i | 0.00496904 | + | 0.00860663i | ||||
\(181\) | −919.500 | − | 1592.62i | −0.377602 | − | 0.654025i | 0.613111 | − | 0.789997i | \(-0.289918\pi\) |
−0.990713 | + | 0.135971i | \(0.956584\pi\) | |||||||
\(182\) | 4416.00 | 1.79855 | ||||||||
\(183\) | −1085.00 | −0.438281 | ||||||||
\(184\) | −268.000 | − | 464.190i | −0.107376 | − | 0.185981i | ||||
\(185\) | 21.0000 | − | 36.3731i | 0.00834568 | − | 0.0144551i | ||||
\(186\) | 660.000 | + | 1143.15i | 0.260180 | + | 0.450646i | ||||
\(187\) | −38.0000 | + | 65.8179i | −0.0148601 | + | 0.0257384i | ||||
\(188\) | 1234.00 | − | 2137.35i | 0.478716 | − | 0.829161i | ||||
\(189\) | 4640.00 | 1.78577 | ||||||||
\(190\) | −57.0000 | − | 493.634i | −0.0217643 | − | 0.188484i | ||||
\(191\) | 2992.00 | 1.13347 | 0.566737 | − | 0.823899i | \(-0.308206\pi\) | ||||
0.566737 | + | 0.823899i | \(0.308206\pi\) | |||||||
\(192\) | −160.000 | + | 277.128i | −0.0601407 | + | 0.104167i | ||||
\(193\) | 696.500 | − | 1206.37i | 0.259768 | − | 0.449931i | −0.706412 | − | 0.707801i | \(-0.749687\pi\) |
0.966180 | + | 0.257870i | \(0.0830207\pi\) | |||||||
\(194\) | 613.000 | + | 1061.75i | 0.226860 | + | 0.392933i | ||||
\(195\) | 517.500 | − | 896.336i | 0.190046 | − | 0.329169i | ||||
\(196\) | −1362.00 | − | 2359.05i | −0.496356 | − | 0.859713i | ||||
\(197\) | −4214.00 | −1.52404 | −0.762018 | − | 0.647556i | \(-0.775791\pi\) | ||||
−0.762018 | + | 0.647556i | \(0.775791\pi\) | |||||||
\(198\) | −16.0000 | −0.00574278 | ||||||||
\(199\) | −383.500 | − | 664.241i | −0.136611 | − | 0.236617i | 0.789601 | − | 0.613621i | \(-0.210288\pi\) |
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(200\) | 464.000 | + | 803.672i | 0.164049 | + | 0.284141i | ||||
\(201\) | −1125.00 | −0.394783 | ||||||||
\(202\) | 2470.00 | 0.860340 | ||||||||
\(203\) | 816.000 | + | 1413.35i | 0.282128 | + | 0.488660i | ||||
\(204\) | −190.000 | + | 329.090i | −0.0652091 | + | 0.112946i | ||||
\(205\) | 619.500 | + | 1073.01i | 0.211062 | + | 0.365571i | ||||
\(206\) | −1632.00 | + | 2826.71i | −0.551975 | + | 0.956049i | ||||
\(207\) | 67.0000 | − | 116.047i | 0.0224967 | − | 0.0389655i | ||||
\(208\) | −1104.00 | −0.368022 | ||||||||
\(209\) | 304.000 | + | 131.636i | 0.100613 | + | 0.0435667i | ||||
\(210\) | −960.000 | −0.315459 | ||||||||
\(211\) | −1182.50 | + | 2048.15i | −0.385814 | + | 0.668249i | −0.991882 | − | 0.127164i | \(-0.959413\pi\) |
0.606068 | + | 0.795413i | \(0.292746\pi\) | |||||||
\(212\) | −766.000 | + | 1326.75i | −0.248156 | + | 0.429819i | ||||
\(213\) | −1752.50 | − | 3035.42i | −0.563753 | − | 0.976448i | ||||
\(214\) | −2060.00 | + | 3568.02i | −0.658031 | + | 1.13974i | ||||
\(215\) | −193.500 | − | 335.152i | −0.0613795 | − | 0.106312i | ||||
\(216\) | −1160.00 | −0.365407 | ||||||||
\(217\) | 4224.00 | 1.32140 | ||||||||
\(218\) | −1055.00 | − | 1827.31i | −0.327769 | − | 0.567712i | ||||
\(219\) | −2537.50 | − | 4395.08i | −0.782961 | − | 1.35613i | ||||
\(220\) | 48.0000 | 0.0147098 | ||||||||
\(221\) | −1311.00 | −0.399038 | ||||||||
\(222\) | 70.0000 | + | 121.244i | 0.0211626 | + | 0.0366547i | ||||
\(223\) | 1219.50 | − | 2112.24i | 0.366205 | − | 0.634286i | −0.622764 | − | 0.782410i | \(-0.713990\pi\) |
0.988969 | + | 0.148124i | \(0.0473235\pi\) | |||||||
\(224\) | 512.000 | + | 886.810i | 0.152721 | + | 0.264520i | ||||
\(225\) | −116.000 | + | 200.918i | −0.0343704 | + | 0.0595312i | ||||
\(226\) | −1006.00 | + | 1742.44i | −0.296098 | + | 0.512857i | ||||
\(227\) | −1708.00 | −0.499401 | −0.249700 | − | 0.968323i | \(-0.580332\pi\) | ||||
−0.249700 | + | 0.968323i | \(0.580332\pi\) | |||||||
\(228\) | 1520.00 | + | 658.179i | 0.441511 | + | 0.191180i | ||||
\(229\) | 4618.00 | 1.33260 | 0.666301 | − | 0.745683i | \(-0.267876\pi\) | ||||
0.666301 | + | 0.745683i | \(0.267876\pi\) | |||||||
\(230\) | −201.000 | + | 348.142i | −0.0576241 | + | 0.0998079i | ||||
\(231\) | 320.000 | − | 554.256i | 0.0911448 | − | 0.157867i | ||||
\(232\) | −204.000 | − | 353.338i | −0.0577296 | − | 0.0999905i | ||||
\(233\) | −1609.50 | + | 2787.74i | −0.452540 | + | 0.783823i | −0.998543 | − | 0.0539608i | \(-0.982815\pi\) |
0.546003 | + | 0.837783i | \(0.316149\pi\) | |||||||
\(234\) | −138.000 | − | 239.023i | −0.0385527 | − | 0.0667753i | ||||
\(235\) | −1851.00 | −0.513812 | ||||||||
\(236\) | −2396.00 | −0.660874 | ||||||||
\(237\) | −872.500 | − | 1511.21i | −0.239135 | − | 0.414194i | ||||
\(238\) | 608.000 | + | 1053.09i | 0.165592 | + | 0.286813i | ||||
\(239\) | −4236.00 | −1.14646 | −0.573230 | − | 0.819394i | \(-0.694310\pi\) | ||||
−0.573230 | + | 0.819394i | \(0.694310\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | 1214.50 | + | 2103.58i | 0.324618 | + | 0.562254i | 0.981435 | − | 0.191796i | \(-0.0614311\pi\) |
−0.656817 | + | 0.754050i | \(0.728098\pi\) | |||||||
\(242\) | 1315.00 | − | 2277.65i | 0.349303 | − | 0.605011i | ||||
\(243\) | −280.000 | − | 484.974i | −0.0739177 | − | 0.128029i | ||||
\(244\) | 434.000 | − | 751.710i | 0.113869 | − | 0.197227i | ||||
\(245\) | −1021.50 | + | 1769.29i | −0.266372 | + | 0.461371i | ||||
\(246\) | −4130.00 | −1.07040 | ||||||||
\(247\) | 655.500 | + | 5676.80i | 0.168860 | + | 1.46237i | ||||
\(248\) | −1056.00 | −0.270387 | ||||||||
\(249\) | 1480.00 | − | 2563.44i | 0.376671 | − | 0.652414i | ||||
\(250\) | 723.000 | − | 1252.27i | 0.182906 | − | 0.316803i | ||||
\(251\) | −121.500 | − | 210.444i | −0.0305538 | − | 0.0529208i | 0.850344 | − | 0.526227i | \(-0.176394\pi\) |
−0.880898 | + | 0.473306i | \(0.843060\pi\) | |||||||
\(252\) | −128.000 | + | 221.703i | −0.0319970 | + | 0.0554204i | ||||
\(253\) | −134.000 | − | 232.095i | −0.0332984 | − | 0.0576746i | ||||
\(254\) | 3974.00 | 0.981697 | ||||||||
\(255\) | 285.000 | 0.0699898 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −523.500 | − | 906.729i | −0.127062 | − | 0.220079i | 0.795475 | − | 0.605987i | \(-0.207222\pi\) |
−0.922537 | + | 0.385908i | \(0.873888\pi\) | |||||||
\(258\) | 1290.00 | 0.311286 | ||||||||
\(259\) | 448.000 | 0.107480 | ||||||||
\(260\) | 414.000 | + | 717.069i | 0.0987507 | + | 0.171041i | ||||
\(261\) | 51.0000 | − | 88.3346i | 0.0120951 | − | 0.0209493i | ||||
\(262\) | 1803.00 | + | 3122.89i | 0.425152 | + | 0.736384i | ||||
\(263\) | −952.500 | + | 1649.78i | −0.223322 | + | 0.386805i | −0.955815 | − | 0.293970i | \(-0.905023\pi\) |
0.732493 | + | 0.680775i | \(0.238357\pi\) | |||||||
\(264\) | −80.0000 | + | 138.564i | −0.0186502 | + | 0.0323031i | ||||
\(265\) | 1149.00 | 0.266349 | ||||||||
\(266\) | 4256.00 | − | 3159.26i | 0.981023 | − | 0.728221i | ||||
\(267\) | −6745.00 | −1.54602 | ||||||||
\(268\) | 450.000 | − | 779.423i | 0.102568 | − | 0.177652i | ||||
\(269\) | 2916.50 | − | 5051.53i | 0.661049 | − | 1.14497i | −0.319292 | − | 0.947657i | \(-0.603445\pi\) |
0.980340 | − | 0.197314i | \(-0.0632217\pi\) | |||||||
\(270\) | 435.000 | + | 753.442i | 0.0980491 | + | 0.169826i | ||||
\(271\) | 1863.50 | − | 3227.68i | 0.417711 | − | 0.723496i | −0.577998 | − | 0.816038i | \(-0.696166\pi\) |
0.995709 | + | 0.0925421i | \(0.0294993\pi\) | |||||||
\(272\) | −152.000 | − | 263.272i | −0.0338837 | − | 0.0586882i | ||||
\(273\) | 11040.0 | 2.44751 | ||||||||
\(274\) | −1338.00 | −0.295006 | ||||||||
\(275\) | 232.000 | + | 401.836i | 0.0508732 | + | 0.0881149i | ||||
\(276\) | −670.000 | − | 1160.47i | −0.146121 | − | 0.253088i | ||||
\(277\) | −5294.00 | −1.14832 | −0.574162 | − | 0.818742i | \(-0.694672\pi\) | ||||
−0.574162 | + | 0.818742i | \(0.694672\pi\) | |||||||
\(278\) | −5450.00 | −1.17579 | ||||||||
\(279\) | −132.000 | − | 228.631i | −0.0283249 | − | 0.0490601i | ||||
\(280\) | 384.000 | − | 665.108i | 0.0819585 | − | 0.141956i | ||||
\(281\) | −687.500 | − | 1190.78i | −0.145953 | − | 0.252798i | 0.783775 | − | 0.621045i | \(-0.213292\pi\) |
−0.929728 | + | 0.368247i | \(0.879958\pi\) | |||||||
\(282\) | 3085.00 | − | 5343.38i | 0.651451 | − | 1.12835i | ||||
\(283\) | 653.500 | − | 1131.90i | 0.137267 | − | 0.237753i | −0.789194 | − | 0.614144i | \(-0.789502\pi\) |
0.926461 | + | 0.376390i | \(0.122835\pi\) | |||||||
\(284\) | 2804.00 | 0.585869 | ||||||||
\(285\) | −142.500 | − | 1234.09i | −0.0296174 | − | 0.256495i | ||||
\(286\) | −552.000 | −0.114127 | ||||||||
\(287\) | −6608.00 | + | 11445.4i | −1.35909 | + | 2.35401i | ||||
\(288\) | 32.0000 | − | 55.4256i | 0.00654729 | − | 0.0113402i | ||||
\(289\) | 2276.00 | + | 3942.15i | 0.463261 | + | 0.802391i | ||||
\(290\) | −153.000 | + | 265.004i | −0.0309809 | + | 0.0536605i | ||||
\(291\) | 1532.50 | + | 2654.37i | 0.308717 | + | 0.534714i | ||||
\(292\) | 4060.00 | 0.813676 | ||||||||
\(293\) | 3818.00 | 0.761263 | 0.380631 | − | 0.924727i | \(-0.375707\pi\) | ||||
0.380631 | + | 0.924727i | \(0.375707\pi\) | |||||||
\(294\) | −3405.00 | − | 5897.63i | −0.675455 | − | 1.16992i | ||||
\(295\) | 898.500 | + | 1556.25i | 0.177331 | + | 0.307147i | ||||
\(296\) | −112.000 | −0.0219928 | ||||||||
\(297\) | −580.000 | −0.113317 | ||||||||
\(298\) | −71.0000 | − | 122.976i | −0.0138017 | − | 0.0239053i | ||||
\(299\) | 2311.50 | − | 4003.64i | 0.447082 | − | 0.774369i | ||||
\(300\) | 1160.00 | + | 2009.18i | 0.223242 | + | 0.386667i | ||||
\(301\) | 2064.00 | − | 3574.95i | 0.395239 | − | 0.684574i | ||||
\(302\) | 656.000 | − | 1136.23i | 0.124995 | − | 0.216498i | ||||
\(303\) | 6175.00 | 1.17077 | ||||||||
\(304\) | −1064.00 | + | 789.815i | −0.200739 | + | 0.149010i | ||||
\(305\) | −651.000 | −0.122217 | ||||||||
\(306\) | 38.0000 | − | 65.8179i | 0.00709907 | − | 0.0122959i | ||||
\(307\) | −436.500 | + | 756.040i | −0.0811478 | + | 0.140552i | −0.903743 | − | 0.428075i | \(-0.859192\pi\) |
0.822595 | + | 0.568627i | \(0.192525\pi\) | |||||||
\(308\) | 256.000 | + | 443.405i | 0.0473602 | + | 0.0820303i | ||||
\(309\) | −4080.00 | + | 7066.77i | −0.751143 | + | 1.30102i | ||||
\(310\) | 396.000 | + | 685.892i | 0.0725525 | + | 0.125665i | ||||
\(311\) | 4180.00 | 0.762142 | 0.381071 | − | 0.924546i | \(-0.375555\pi\) | ||||
0.381071 | + | 0.924546i | \(0.375555\pi\) | |||||||
\(312\) | −2760.00 | −0.500815 | ||||||||
\(313\) | 1582.50 | + | 2740.97i | 0.285777 | + | 0.494980i | 0.972797 | − | 0.231658i | \(-0.0744150\pi\) |
−0.687020 | + | 0.726638i | \(0.741082\pi\) | |||||||
\(314\) | 1053.00 | + | 1823.85i | 0.189249 | + | 0.327789i | ||||
\(315\) | 192.000 | 0.0343428 | ||||||||
\(316\) | 1396.00 | 0.248516 | ||||||||
\(317\) | −2269.50 | − | 3930.89i | −0.402107 | − | 0.696469i | 0.591873 | − | 0.806031i | \(-0.298389\pi\) |
−0.993980 | + | 0.109562i | \(0.965055\pi\) | |||||||
\(318\) | −1915.00 | + | 3316.88i | −0.337698 | + | 0.584910i | ||||
\(319\) | −102.000 | − | 176.669i | −0.0179025 | − | 0.0310081i | ||||
\(320\) | −96.0000 | + | 166.277i | −0.0167705 | + | 0.0290474i | ||||
\(321\) | −5150.00 | + | 8920.06i | −0.895467 | + | 1.55099i | ||||
\(322\) | −4288.00 | −0.742115 | ||||||||
\(323\) | −1263.50 | + | 937.906i | −0.217656 | + | 0.161568i | ||||
\(324\) | −2684.00 | −0.460219 | ||||||||
\(325\) | −4002.00 | + | 6931.67i | −0.683049 | + | 1.18308i | ||||
\(326\) | −68.0000 | + | 117.779i | −0.0115527 | + | 0.0200098i | ||||
\(327\) | −2637.50 | − | 4568.28i | −0.446037 | − | 0.772559i | ||||
\(328\) | 1652.00 | − | 2861.35i | 0.278099 | − | 0.481681i | ||||
\(329\) | −9872.00 | − | 17098.8i | −1.65429 | − | 2.86531i | ||||
\(330\) | 120.000 | 0.0200175 | ||||||||
\(331\) | 3660.00 | 0.607770 | 0.303885 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303885 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(332\) | 1184.00 | + | 2050.75i | 0.195724 | + | 0.339004i | ||||
\(333\) | −14.0000 | − | 24.2487i | −0.00230389 | − | 0.00399045i | ||||
\(334\) | −1842.00 | −0.301766 | ||||||||
\(335\) | −675.000 | −0.110087 | ||||||||
\(336\) | 1280.00 | + | 2217.03i | 0.207827 | + | 0.359966i | ||||
\(337\) | 2586.50 | − | 4479.95i | 0.418088 | − | 0.724150i | −0.577659 | − | 0.816278i | \(-0.696034\pi\) |
0.995747 | + | 0.0921285i | \(0.0293671\pi\) | |||||||
\(338\) | −2564.00 | − | 4440.98i | −0.412613 | − | 0.714667i | ||||
\(339\) | −2515.00 | + | 4356.11i | −0.402938 | + | 0.697909i | ||||
\(340\) | −114.000 | + | 197.454i | −0.0181839 | + | 0.0314954i | ||||
\(341\) | −528.000 | −0.0838499 | ||||||||
\(342\) | −304.000 | − | 131.636i | −0.0480656 | − | 0.0208130i | ||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | −516.000 | + | 893.738i | −0.0808746 | + | 0.140079i | ||||
\(345\) | −502.500 | + | 870.356i | −0.0784165 | + | 0.135821i | ||||
\(346\) | 1893.00 | + | 3278.77i | 0.294128 | + | 0.509445i | ||||
\(347\) | 4295.50 | − | 7440.02i | 0.664538 | − | 1.15101i | −0.314873 | − | 0.949134i | \(-0.601962\pi\) |
0.979410 | − | 0.201879i | \(-0.0647048\pi\) | |||||||
\(348\) | −510.000 | − | 883.346i | −0.0785600 | − | 0.136070i | ||||
\(349\) | 6946.00 | 1.06536 | 0.532680 | − | 0.846317i | \(-0.321185\pi\) | ||||
0.532680 | + | 0.846317i | \(0.321185\pi\) | |||||||
\(350\) | 7424.00 | 1.13380 | ||||||||
\(351\) | −5002.50 | − | 8664.58i | −0.760723 | − | 1.31761i | ||||
\(352\) | −64.0000 | − | 110.851i | −0.00969094 | − | 0.0167852i | ||||
\(353\) | −8226.00 | −1.24030 | −0.620150 | − | 0.784483i | \(-0.712928\pi\) | ||||
−0.620150 | + | 0.784483i | \(0.712928\pi\) | |||||||
\(354\) | −5990.00 | −0.899336 | ||||||||
\(355\) | −1051.50 | − | 1821.25i | −0.157205 | − | 0.272287i | ||||
\(356\) | 2698.00 | − | 4673.07i | 0.401668 | − | 0.695709i | ||||
\(357\) | 1520.00 | + | 2632.72i | 0.225342 | + | 0.390303i | ||||
\(358\) | 20.0000 | − | 34.6410i | 0.00295261 | − | 0.00511406i | ||||
\(359\) | −5692.50 | + | 9859.70i | −0.836876 | + | 1.44951i | 0.0556169 | + | 0.998452i | \(0.482287\pi\) |
−0.892493 | + | 0.451060i | \(0.851046\pi\) | |||||||
\(360\) | −48.0000 | −0.00702728 | ||||||||
\(361\) | 4693.00 | + | 5002.16i | 0.684211 | + | 0.729285i | ||||
\(362\) | 3678.00 | 0.534009 | ||||||||
\(363\) | 3287.50 | − | 5694.12i | 0.475342 | − | 0.823316i | ||||
\(364\) | −4416.00 | + | 7648.74i | −0.635883 | + | 1.10138i | ||||
\(365\) | −1522.50 | − | 2637.05i | −0.218332 | − | 0.378163i | ||||
\(366\) | 1085.00 | − | 1879.28i | 0.154956 | − | 0.268391i | ||||
\(367\) | 1476.50 | + | 2557.37i | 0.210007 | + | 0.363743i | 0.951717 | − | 0.306978i | \(-0.0993179\pi\) |
−0.741709 | + | 0.670722i | \(0.765985\pi\) | |||||||
\(368\) | 1072.00 | 0.151853 | ||||||||
\(369\) | 826.000 | 0.116531 | ||||||||
\(370\) | 42.0000 | + | 72.7461i | 0.00590129 | + | 0.0102213i | ||||
\(371\) | 6128.00 | + | 10614.0i | 0.857547 | + | 1.48531i | ||||
\(372\) | −2640.00 | −0.367951 | ||||||||
\(373\) | 5006.00 | 0.694908 | 0.347454 | − | 0.937697i | \(-0.387046\pi\) | ||||
0.347454 | + | 0.937697i | \(0.387046\pi\) | |||||||
\(374\) | −76.0000 | − | 131.636i | −0.0105077 | − | 0.0181998i | ||||
\(375\) | 1807.50 | − | 3130.68i | 0.248904 | − | 0.431114i | ||||
\(376\) | 2468.00 | + | 4274.70i | 0.338504 | + | 0.586306i | ||||
\(377\) | 1759.50 | − | 3047.54i | 0.240368 | − | 0.416330i | ||||
\(378\) | −4640.00 | + | 8036.72i | −0.631365 | + | 1.09356i | ||||
\(379\) | 6764.00 | 0.916737 | 0.458369 | − | 0.888762i | \(-0.348434\pi\) | ||||
0.458369 | + | 0.888762i | \(0.348434\pi\) | |||||||
\(380\) | 912.000 | + | 394.908i | 0.123117 | + | 0.0533114i | ||||
\(381\) | 9935.00 | 1.33592 | ||||||||
\(382\) | −2992.00 | + | 5182.30i | −0.400744 | + | 0.694108i | ||||
\(383\) | 2481.50 | − | 4298.08i | 0.331067 | − | 0.573425i | −0.651654 | − | 0.758516i | \(-0.725925\pi\) |
0.982721 | + | 0.185091i | \(0.0592580\pi\) | |||||||
\(384\) | −320.000 | − | 554.256i | −0.0425259 | − | 0.0736570i | ||||
\(385\) | 192.000 | − | 332.554i | 0.0254162 | − | 0.0440221i | ||||
\(386\) | 1393.00 | + | 2412.75i | 0.183684 | + | 0.318149i | ||||
\(387\) | −258.000 | −0.0338886 | ||||||||
\(388\) | −2452.00 | −0.320828 | ||||||||
\(389\) | −1811.50 | − | 3137.61i | −0.236110 | − | 0.408954i | 0.723485 | − | 0.690340i | \(-0.242539\pi\) |
−0.959595 | + | 0.281386i | \(0.909206\pi\) | |||||||
\(390\) | 1035.00 | + | 1792.67i | 0.134383 | + | 0.232758i | ||||
\(391\) | 1273.00 | 0.164651 | ||||||||
\(392\) | 5448.00 | 0.701953 | ||||||||
\(393\) | 4507.50 | + | 7807.22i | 0.578558 | + | 1.00209i | ||||
\(394\) | 4214.00 | − | 7298.86i | 0.538828 | − | 0.933278i | ||||
\(395\) | −523.500 | − | 906.729i | −0.0666839 | − | 0.115500i | ||||
\(396\) | 16.0000 | − | 27.7128i | 0.00203038 | − | 0.00351672i | ||||
\(397\) | 3814.50 | − | 6606.91i | 0.482227 | − | 0.835242i | −0.517564 | − | 0.855644i | \(-0.673161\pi\) |
0.999792 | + | 0.0204019i | \(0.00649457\pi\) | |||||||
\(398\) | 1534.00 | 0.193197 | ||||||||
\(399\) | 10640.0 | − | 7898.15i | 1.33500 | − | 0.990983i | ||||
\(400\) | −1856.00 | −0.232000 | ||||||||
\(401\) | 4558.50 | − | 7895.55i | 0.567682 | − | 0.983255i | −0.429112 | − | 0.903251i | \(-0.641174\pi\) |
0.996795 | − | 0.0800035i | \(-0.0254932\pi\) | |||||||
\(402\) | 1125.00 | − | 1948.56i | 0.139577 | − | 0.241754i | ||||
\(403\) | −4554.00 | − | 7887.76i | −0.562905 | − | 0.974981i | ||||
\(404\) | −2470.00 | + | 4278.17i | −0.304176 | + | 0.526848i | ||||
\(405\) | 1006.50 | + | 1743.31i | 0.123490 | + | 0.213891i | ||||
\(406\) | −3264.00 | −0.398989 | ||||||||
\(407\) | −56.0000 | −0.00682019 | ||||||||
\(408\) | −380.000 | − | 658.179i | −0.0461098 | − | 0.0798645i | ||||
\(409\) | −2467.50 | − | 4273.84i | −0.298313 | − | 0.516693i | 0.677437 | − | 0.735581i | \(-0.263091\pi\) |
−0.975750 | + | 0.218887i | \(0.929757\pi\) | |||||||
\(410\) | −2478.00 | −0.298487 | ||||||||
\(411\) | −3345.00 | −0.401452 | ||||||||
\(412\) | −3264.00 | − | 5653.41i | −0.390305 | − | 0.676028i | ||||
\(413\) | −9584.00 | + | 16600.0i | −1.14188 | + | 1.97780i | ||||
\(414\) | 134.000 | + | 232.095i | 0.0159076 | + | 0.0275527i | ||||
\(415\) | 888.000 | − | 1538.06i | 0.105037 | − | 0.181929i | ||||
\(416\) | 1104.00 | − | 1912.18i | 0.130116 | − | 0.225367i | ||||
\(417\) | −13625.0 | −1.60005 | ||||||||
\(418\) | −532.000 | + | 394.908i | −0.0622511 | + | 0.0462095i | ||||
\(419\) | 6516.00 | 0.759731 | 0.379866 | − | 0.925042i | \(-0.375970\pi\) | ||||
0.379866 | + | 0.925042i | \(0.375970\pi\) | |||||||
\(420\) | 960.000 | − | 1662.77i | 0.111531 | − | 0.193178i | ||||
\(421\) | −5457.50 | + | 9452.67i | −0.631787 | + | 1.09429i | 0.355399 | + | 0.934715i | \(0.384345\pi\) |
−0.987186 | + | 0.159572i | \(0.948988\pi\) | |||||||
\(422\) | −2365.00 | − | 4096.30i | −0.272811 | − | 0.472523i | ||||
\(423\) | −617.000 | + | 1068.68i | −0.0709210 | + | 0.122839i | ||||
\(424\) | −1532.00 | − | 2653.50i | −0.175473 | − | 0.303928i | ||||
\(425\) | −2204.00 | −0.251552 | ||||||||
\(426\) | 7010.00 | 0.797267 | ||||||||
\(427\) | −3472.00 | − | 6013.68i | −0.393494 | − | 0.681551i | ||||
\(428\) | −4120.00 | − | 7136.05i | −0.465298 | − | 0.805920i | ||||
\(429\) | −1380.00 | −0.155308 | ||||||||
\(430\) | 774.000 | 0.0868037 | ||||||||
\(431\) | 2754.50 | + | 4770.93i | 0.307841 | + | 0.533197i | 0.977890 | − | 0.209120i | \(-0.0670601\pi\) |
−0.670049 | + | 0.742317i | \(0.733727\pi\) | |||||||
\(432\) | 1160.00 | − | 2009.18i | 0.129191 | − | 0.223765i | ||||
\(433\) | 1876.50 | + | 3250.19i | 0.208265 | + | 0.360726i | 0.951168 | − | 0.308673i | \(-0.0998850\pi\) |
−0.742903 | + | 0.669399i | \(0.766552\pi\) | |||||||
\(434\) | −4224.00 | + | 7316.18i | −0.467185 | + | 0.809189i | ||||
\(435\) | −382.500 | + | 662.509i | −0.0421597 | + | 0.0730227i | ||||
\(436\) | 4220.00 | 0.463535 | ||||||||
\(437\) | −636.500 | − | 5512.25i | −0.0696749 | − | 0.603402i | ||||
\(438\) | 10150.0 | 1.10727 | ||||||||
\(439\) | −3906.50 | + | 6766.26i | −0.424709 | + | 0.735617i | −0.996393 | − | 0.0848566i | \(-0.972957\pi\) |
0.571685 | + | 0.820473i | \(0.306290\pi\) | |||||||
\(440\) | −48.0000 | + | 83.1384i | −0.00520071 | + | 0.00900789i | ||||
\(441\) | 681.000 | + | 1179.53i | 0.0735342 | + | 0.127365i | ||||
\(442\) | 1311.00 | − | 2270.72i | 0.141081 | − | 0.244360i | ||||
\(443\) | 3058.50 | + | 5297.48i | 0.328022 | + | 0.568151i | 0.982119 | − | 0.188260i | \(-0.0602847\pi\) |
−0.654097 | + | 0.756410i | \(0.726951\pi\) | |||||||
\(444\) | −280.000 | −0.0299284 | ||||||||
\(445\) | −4047.00 | −0.431115 | ||||||||
\(446\) | 2439.00 | + | 4224.47i | 0.258946 | + | 0.448508i | ||||
\(447\) | −177.500 | − | 307.439i | −0.0187818 | − | 0.0325310i | ||||
\(448\) | −2048.00 | −0.215980 | ||||||||
\(449\) | −7146.00 | −0.751093 | −0.375546 | − | 0.926804i | \(-0.622545\pi\) | ||||
−0.375546 | + | 0.926804i | \(0.622545\pi\) | |||||||
\(450\) | −232.000 | − | 401.836i | −0.0243035 | − | 0.0420949i | ||||
\(451\) | 826.000 | − | 1430.67i | 0.0862413 | − | 0.149374i | ||||
\(452\) | −2012.00 | − | 3484.89i | −0.209373 | − | 0.362644i | ||||
\(453\) | 1640.00 | − | 2840.56i | 0.170097 | − | 0.294617i | ||||
\(454\) | 1708.00 | − | 2958.34i | 0.176565 | − | 0.305819i | ||||
\(455\) | 6624.00 | 0.682501 | ||||||||
\(456\) | −2660.00 | + | 1974.54i | −0.273171 | + | 0.202777i | ||||
\(457\) | −18118.0 | −1.85454 | −0.927269 | − | 0.374395i | \(-0.877851\pi\) | ||||
−0.927269 | + | 0.374395i | \(0.877851\pi\) | |||||||
\(458\) | −4618.00 | + | 7998.61i | −0.471146 | + | 0.816049i | ||||
\(459\) | 1377.50 | − | 2385.90i | 0.140079 | − | 0.242624i | ||||
\(460\) | −402.000 | − | 696.284i | −0.0407464 | − | 0.0705748i | ||||
\(461\) | −8467.50 | + | 14666.1i | −0.855468 | + | 1.48171i | 0.0207420 | + | 0.999785i | \(0.493397\pi\) |
−0.876210 | + | 0.481929i | \(0.839936\pi\) | |||||||
\(462\) | 640.000 | + | 1108.51i | 0.0644491 | + | 0.111629i | ||||
\(463\) | −7788.00 | −0.781726 | −0.390863 | − | 0.920449i | \(-0.627823\pi\) | ||||
−0.390863 | + | 0.920449i | \(0.627823\pi\) | |||||||
\(464\) | 816.000 | 0.0816419 | ||||||||
\(465\) | 990.000 | + | 1714.73i | 0.0987315 | + | 0.171008i | ||||
\(466\) | −3219.00 | − | 5575.47i | −0.319994 | − | 0.554246i | ||||
\(467\) | 12500.0 | 1.23861 | 0.619305 | − | 0.785150i | \(-0.287414\pi\) | ||||
0.619305 | + | 0.785150i | \(0.287414\pi\) | |||||||
\(468\) | 552.000 | 0.0545218 | ||||||||
\(469\) | −3600.00 | − | 6235.38i | −0.354440 | − | 0.613909i | ||||
\(470\) | 1851.00 | − | 3206.03i | 0.181660 | − | 0.314645i | ||||
\(471\) | 2632.50 | + | 4559.62i | 0.257535 | + | 0.446064i | ||||
\(472\) | 2396.00 | − | 4149.99i | 0.233654 | − | 0.404701i | ||||
\(473\) | −258.000 | + | 446.869i | −0.0250800 | + | 0.0434399i | ||||
\(474\) | 3490.00 | 0.338188 | ||||||||
\(475\) | 1102.00 | + | 9543.60i | 0.106449 | + | 0.921875i | ||||
\(476\) | −2432.00 | −0.234182 | ||||||||
\(477\) | 383.000 | − | 663.375i | 0.0367639 | − | 0.0636769i | ||||
\(478\) | 4236.00 | − | 7336.97i | 0.405335 | − | 0.702061i | ||||
\(479\) | 6052.50 | + | 10483.2i | 0.577340 | + | 0.999982i | 0.995783 | + | 0.0917390i | \(0.0292425\pi\) |
−0.418443 | + | 0.908243i | \(0.637424\pi\) | |||||||
\(480\) | −240.000 | + | 415.692i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | −483.000 | − | 836.581i | −0.0457857 | − | 0.0793031i | ||||
\(482\) | −4858.00 | −0.459078 | ||||||||
\(483\) | −10720.0 | −1.00989 | ||||||||
\(484\) | 2630.00 | + | 4555.29i | 0.246995 | + | 0.427807i | ||||
\(485\) | 919.500 | + | 1592.62i | 0.0860873 | + | 0.149108i | ||||
\(486\) | 1120.00 | 0.104535 | ||||||||
\(487\) | 296.000 | 0.0275422 | 0.0137711 | − | 0.999905i | \(-0.495616\pi\) | ||||
0.0137711 | + | 0.999905i | \(0.495616\pi\) | |||||||
\(488\) | 868.000 | + | 1503.42i | 0.0805174 | + | 0.139460i | ||||
\(489\) | −170.000 | + | 294.449i | −0.0157212 | + | 0.0272299i | ||||
\(490\) | −2043.00 | − | 3538.58i | −0.188354 | − | 0.326238i | ||||
\(491\) | −1606.50 | + | 2782.54i | −0.147659 | + | 0.255752i | −0.930362 | − | 0.366643i | \(-0.880507\pi\) |
0.782703 | + | 0.622395i | \(0.213840\pi\) | |||||||
\(492\) | 4130.00 | − | 7153.37i | 0.378445 | − | 0.655485i | ||||
\(493\) | 969.000 | 0.0885224 | ||||||||
\(494\) | −10488.0 | − | 4541.44i | −0.955217 | − | 0.413621i | ||||
\(495\) | −24.0000 | −0.00217923 | ||||||||
\(496\) | 1056.00 | − | 1829.05i | 0.0955964 | − | 0.165578i | ||||
\(497\) | 11216.0 | − | 19426.7i | 1.01229 | − | 1.75333i | ||||
\(498\) | 2960.00 | + | 5126.87i | 0.266347 | + | 0.461326i | ||||
\(499\) | −1508.50 | + | 2612.80i | −0.135330 | + | 0.234399i | −0.925724 | − | 0.378201i | \(-0.876543\pi\) |
0.790393 | + | 0.612600i | \(0.209876\pi\) | |||||||
\(500\) | 1446.00 | + | 2504.55i | 0.129334 | + | 0.224013i | ||||
\(501\) | −4605.00 | −0.410651 | ||||||||
\(502\) | 486.000 | 0.0432096 | ||||||||
\(503\) | 3638.50 | + | 6302.07i | 0.322530 | + | 0.558639i | 0.981009 | − | 0.193960i | \(-0.0621333\pi\) |
−0.658479 | + | 0.752599i | \(0.728800\pi\) | |||||||
\(504\) | −256.000 | − | 443.405i | −0.0226253 | − | 0.0391882i | ||||
\(505\) | 3705.00 | 0.326476 | ||||||||
\(506\) | 536.000 | 0.0470911 | ||||||||
\(507\) | −6410.00 | − | 11102.4i | −0.561495 | − | 0.972538i | ||||
\(508\) | −3974.00 | + | 6883.17i | −0.347082 | + | 0.601164i | ||||
\(509\) | 5346.50 | + | 9260.41i | 0.465578 | + | 0.806406i | 0.999227 | − | 0.0393005i | \(-0.0125130\pi\) |
−0.533649 | + | 0.845706i | \(0.679180\pi\) | |||||||
\(510\) | −285.000 | + | 493.634i | −0.0247451 | + | 0.0428598i | ||||
\(511\) | 16240.0 | − | 28128.5i | 1.40590 | − | 2.43509i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −11020.0 | − | 4771.80i | −0.948431 | − | 0.410682i | ||||
\(514\) | 2094.00 | 0.179693 | ||||||||
\(515\) | −2448.00 | + | 4240.06i | −0.209460 | + | 0.362795i | ||||
\(516\) | −1290.00 | + | 2234.35i | −0.110056 | + | 0.190623i | ||||
\(517\) | 1234.00 | + | 2137.35i | 0.104973 | + | 0.181819i | ||||
\(518\) | −448.000 | + | 775.959i | −0.0380000 | + | 0.0658179i | ||||
\(519\) | 4732.50 | + | 8196.93i | 0.400258 | + | 0.693266i | ||||
\(520\) | −1656.00 | −0.139655 | ||||||||
\(521\) | −7190.00 | −0.604606 | −0.302303 | − | 0.953212i | \(-0.597755\pi\) | ||||
−0.302303 | + | 0.953212i | \(0.597755\pi\) | |||||||
\(522\) | 102.000 | + | 176.669i | 0.00855253 | + | 0.0148134i | ||||
\(523\) | −4323.50 | − | 7488.52i | −0.361479 | − | 0.626100i | 0.626726 | − | 0.779240i | \(-0.284395\pi\) |
−0.988204 | + | 0.153140i | \(0.951061\pi\) | |||||||
\(524\) | −7212.00 | −0.601255 | ||||||||
\(525\) | 18560.0 | 1.54290 | ||||||||
\(526\) | −1905.00 | − | 3299.56i | −0.157912 | − | 0.273512i | ||||
\(527\) | 1254.00 | − | 2171.99i | 0.103653 | − | 0.179532i | ||||
\(528\) | −160.000 | − | 277.128i | −0.0131877 | − | 0.0228418i | ||||
\(529\) | 3839.00 | − | 6649.34i | 0.315526 | − | 0.546506i | ||||
\(530\) | −1149.00 | + | 1990.13i | −0.0941686 | + | 0.163105i | ||||
\(531\) | 1198.00 | 0.0979073 | ||||||||
\(532\) | 1216.00 | + | 10530.9i | 0.0990983 | + | 0.858216i | ||||
\(533\) | 28497.0 | 2.31584 | ||||||||
\(534\) | 6745.00 | − | 11682.7i | 0.546601 | − | 0.946740i | ||||
\(535\) | −3090.00 | + | 5352.04i | −0.249705 | + | 0.432502i | ||||
\(536\) | 900.000 | + | 1558.85i | 0.0725263 | + | 0.125619i | ||||
\(537\) | 50.0000 | − | 86.6025i | 0.00401799 | − | 0.00695936i | ||||
\(538\) | 5833.00 | + | 10103.1i | 0.467432 | + | 0.809616i | ||||
\(539\) | 2724.00 | 0.217683 | ||||||||
\(540\) | −1740.00 | −0.138662 | ||||||||
\(541\) | −2021.50 | − | 3501.34i | −0.160649 | − | 0.278252i | 0.774453 | − | 0.632632i | \(-0.218025\pi\) |
−0.935102 | + | 0.354380i | \(0.884692\pi\) | |||||||
\(542\) | 3727.00 | + | 6455.35i | 0.295366 | + | 0.511589i | ||||
\(543\) | 9195.00 | 0.726695 | ||||||||
\(544\) | 608.000 | 0.0479187 | ||||||||
\(545\) | −1582.50 | − | 2740.97i | −0.124380 | − | 0.215432i | ||||
\(546\) | −11040.0 | + | 19121.8i | −0.865327 | + | 1.49879i | ||||
\(547\) | 2694.50 | + | 4667.01i | 0.210619 | + | 0.364803i | 0.951908 | − | 0.306383i | \(-0.0991188\pi\) |
−0.741290 | + | 0.671185i | \(0.765785\pi\) | |||||||
\(548\) | 1338.00 | − | 2317.48i | 0.104300 | − | 0.180653i | ||||
\(549\) | −217.000 | + | 375.855i | −0.0168695 | + | 0.0292188i | ||||
\(550\) | −928.000 | −0.0719456 | ||||||||
\(551\) | −484.500 | − | 4195.89i | −0.0374599 | − | 0.324412i | ||||
\(552\) | 2680.00 | 0.206646 | ||||||||
\(553\) | 5584.00 | − | 9671.77i | 0.429396 | − | 0.743735i | ||||
\(554\) | 5294.00 | − | 9169.48i | 0.405994 | − | 0.703202i | ||||
\(555\) | 105.000 | + | 181.865i | 0.00803063 | + | 0.0139095i | ||||
\(556\) | 5450.00 | − | 9439.68i | 0.415704 | − | 0.720021i | ||||
\(557\) | −3363.50 | − | 5825.75i | −0.255864 | − | 0.443169i | 0.709266 | − | 0.704941i | \(-0.249026\pi\) |
−0.965130 | + | 0.261772i | \(0.915693\pi\) | |||||||
\(558\) | 528.000 | 0.0400574 | ||||||||
\(559\) | −8901.00 | −0.673474 | ||||||||
\(560\) | 768.000 | + | 1330.22i | 0.0579534 | + | 0.100378i | ||||
\(561\) | −190.000 | − | 329.090i | −0.0142991 | − | 0.0247668i | ||||
\(562\) | 2750.00 | 0.206409 | ||||||||
\(563\) | −19908.0 | −1.49027 | −0.745135 | − | 0.666914i | \(-0.767615\pi\) | ||||
−0.745135 | + | 0.666914i | \(0.767615\pi\) | |||||||
\(564\) | 6170.00 | + | 10686.8i | 0.460645 | + | 0.797861i | ||||
\(565\) | −1509.00 | + | 2613.66i | −0.112361 | + | 0.194615i | ||||
\(566\) | 1307.00 | + | 2263.79i | 0.0970624 | + | 0.168117i | ||||
\(567\) | −10736.0 | + | 18595.3i | −0.795185 | + | 1.37730i | ||||
\(568\) | −2804.00 | + | 4856.67i | −0.207136 | + | 0.358770i | ||||
\(569\) | −8730.00 | −0.643200 | −0.321600 | − | 0.946876i | \(-0.604221\pi\) | ||||
−0.321600 | + | 0.946876i | \(0.604221\pi\) | |||||||
\(570\) | 2280.00 | + | 987.269i | 0.167542 | + | 0.0725476i | ||||
\(571\) | −4732.00 | −0.346809 | −0.173405 | − | 0.984851i | \(-0.555477\pi\) | ||||
−0.173405 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(572\) | 552.000 | − | 956.092i | 0.0403501 | − | 0.0698885i | ||||
\(573\) | −7480.00 | + | 12955.7i | −0.545343 | + | 0.944562i | ||||
\(574\) | −13216.0 | − | 22890.8i | −0.961019 | − | 1.66453i | ||||
\(575\) | 3886.00 | − | 6730.75i | 0.281839 | − | 0.488159i | ||||
\(576\) | 64.0000 | + | 110.851i | 0.00462963 | + | 0.00801875i | ||||
\(577\) | −23882.0 | −1.72309 | −0.861543 | − | 0.507685i | \(-0.830502\pi\) | ||||
−0.861543 | + | 0.507685i | \(0.830502\pi\) | |||||||
\(578\) | −9104.00 | −0.655150 | ||||||||
\(579\) | 3482.50 | + | 6031.87i | 0.249962 | + | 0.432946i | ||||
\(580\) | −306.000 | − | 530.008i | −0.0219068 | − | 0.0379437i | ||||
\(581\) | 18944.0 | 1.35272 | ||||||||
\(582\) | −6130.00 | −0.436592 | ||||||||
\(583\) | −766.000 | − | 1326.75i | −0.0544159 | − | 0.0942511i | ||||
\(584\) | −4060.00 | + | 7032.13i | −0.287678 | + | 0.498273i | ||||
\(585\) | −207.000 | − | 358.535i | −0.0146297 | − | 0.0253394i | ||||
\(586\) | −3818.00 | + | 6612.97i | −0.269147 | + | 0.466176i | ||||
\(587\) | 8273.50 | − | 14330.1i | 0.581744 | − | 1.00761i | −0.413528 | − | 0.910491i | \(-0.635704\pi\) |
0.995273 | − | 0.0971194i | \(-0.0309629\pi\) | |||||||
\(588\) | 13620.0 | 0.955237 | ||||||||
\(589\) | −10032.0 | − | 4343.98i | −0.701802 | − | 0.303889i | ||||
\(590\) | −3594.00 | −0.250784 | ||||||||
\(591\) | 10535.0 | − | 18247.2i | 0.733252 | − | 1.27003i | ||||
\(592\) | 112.000 | − | 193.990i | 0.00777563 | − | 0.0134678i | ||||
\(593\) | 7514.50 | + | 13015.5i | 0.520377 | + | 0.901319i | 0.999719 | + | 0.0236913i | \(0.00754189\pi\) |
−0.479342 | + | 0.877628i | \(0.659125\pi\) | |||||||
\(594\) | 580.000 | − | 1004.59i | 0.0400634 | − | 0.0693919i | ||||
\(595\) | 912.000 | + | 1579.63i | 0.0628376 | + | 0.108838i | ||||
\(596\) | 284.000 | 0.0195186 | ||||||||
\(597\) | 3835.00 | 0.262908 | ||||||||
\(598\) | 4623.00 | + | 8007.27i | 0.316135 | + | 0.547561i | ||||
\(599\) | −6893.50 | − | 11939.9i | −0.470218 | − | 0.814442i | 0.529202 | − | 0.848496i | \(-0.322491\pi\) |
−0.999420 | + | 0.0340541i | \(0.989158\pi\) | |||||||
\(600\) | −4640.00 | −0.315712 | ||||||||
\(601\) | 11382.0 | 0.772515 | 0.386257 | − | 0.922391i | \(-0.373768\pi\) | ||||
0.386257 | + | 0.922391i | \(0.373768\pi\) | |||||||
\(602\) | 4128.00 | + | 7149.91i | 0.279476 | + | 0.484067i | ||||
\(603\) | −225.000 | + | 389.711i | −0.0151952 | + | 0.0263189i | ||||
\(604\) | 1312.00 | + | 2272.45i | 0.0883850 | + | 0.153087i | ||||
\(605\) | 1972.50 | − | 3416.47i | 0.132551 | − | 0.229586i | ||||
\(606\) | −6175.00 | + | 10695.4i | −0.413931 | + | 0.716950i | ||||
\(607\) | −25312.0 | −1.69256 | −0.846279 | − | 0.532740i | \(-0.821162\pi\) | ||||
−0.846279 | + | 0.532740i | \(0.821162\pi\) | |||||||
\(608\) | −304.000 | − | 2632.72i | −0.0202777 | − | 0.175610i | ||||
\(609\) | −8160.00 | −0.542955 | ||||||||
\(610\) | 651.000 | − | 1127.57i | 0.0432102 | − | 0.0748423i | ||||
\(611\) | −21286.5 | + | 36869.3i | −1.40943 | + | 2.44120i | ||||
\(612\) | 76.0000 | + | 131.636i | 0.00501980 | + | 0.00869455i | ||||
\(613\) | 11748.5 | − | 20349.0i | 0.774090 | − | 1.34076i | −0.161214 | − | 0.986920i | \(-0.551541\pi\) |
0.935304 | − | 0.353844i | \(-0.115126\pi\) | |||||||
\(614\) | −873.000 | − | 1512.08i | −0.0573802 | − | 0.0993853i | ||||
\(615\) | −6195.00 | −0.406189 | ||||||||
\(616\) | −1024.00 | −0.0669775 | ||||||||
\(617\) | 6610.50 | + | 11449.7i | 0.431327 | + | 0.747080i | 0.996988 | − | 0.0775578i | \(-0.0247122\pi\) |
−0.565661 | + | 0.824638i | \(0.691379\pi\) | |||||||
\(618\) | −8160.00 | − | 14133.5i | −0.531138 | − | 0.919958i | ||||
\(619\) | 15316.0 | 0.994511 | 0.497255 | − | 0.867604i | \(-0.334341\pi\) | ||||
0.497255 | + | 0.867604i | \(0.334341\pi\) | |||||||
\(620\) | −1584.00 | −0.102605 | ||||||||
\(621\) | 4857.50 | + | 8413.44i | 0.313889 | + | 0.543671i | ||||
\(622\) | −4180.00 | + | 7239.97i | −0.269458 | + | 0.466715i | ||||
\(623\) | −21584.0 | − | 37384.6i | −1.38803 | − | 2.40414i | ||||
\(624\) | 2760.00 | − | 4780.46i | 0.177065 | − | 0.306685i | ||||
\(625\) | −6165.50 | + | 10679.0i | −0.394592 | + | 0.683453i | ||||
\(626\) | −6330.00 | −0.404150 | ||||||||
\(627\) | −1330.00 | + | 987.269i | −0.0847131 | + | 0.0628831i | ||||
\(628\) | −4212.00 | −0.267639 | ||||||||
\(629\) | 133.000 | − | 230.363i | 0.00843093 | − | 0.0146028i | ||||
\(630\) | −192.000 | + | 332.554i | −0.0121420 | + | 0.0210306i | ||||
\(631\) | 3024.50 | + | 5238.59i | 0.190814 | + | 0.330499i | 0.945520 | − | 0.325564i | \(-0.105554\pi\) |
−0.754706 | + | 0.656063i | \(0.772221\pi\) | |||||||
\(632\) | −1396.00 | + | 2417.94i | −0.0878638 | + | 0.152185i | ||||
\(633\) | −5912.50 | − | 10240.8i | −0.371249 | − | 0.643023i | ||||
\(634\) | 9078.00 | 0.568665 | ||||||||
\(635\) | 5961.00 | 0.372528 | ||||||||
\(636\) | −3830.00 | − | 6633.75i | −0.238788 | − | 0.413594i | ||||
\(637\) | 23494.5 | + | 40693.7i | 1.46136 | + | 2.53115i | ||||
\(638\) | 408.000 | 0.0253180 | ||||||||
\(639\) | −1402.00 | −0.0867954 | ||||||||
\(640\) | −192.000 | − | 332.554i | −0.0118585 | − | 0.0205396i | ||||
\(641\) | 12044.5 | − | 20861.7i | 0.742167 | − | 1.28547i | −0.209339 | − | 0.977843i | \(-0.567131\pi\) |
0.951507 | − | 0.307628i | \(-0.0995353\pi\) | |||||||
\(642\) | −10300.0 | − | 17840.1i | −0.633191 | − | 1.09672i | ||||
\(643\) | −816.500 | + | 1414.22i | −0.0500772 | + | 0.0867362i | −0.889977 | − | 0.456005i | \(-0.849280\pi\) |
0.839900 | + | 0.542741i | \(0.182613\pi\) | |||||||
\(644\) | 4288.00 | − | 7427.03i | 0.262377 | − | 0.454451i | ||||
\(645\) | 1935.00 | 0.118125 | ||||||||
\(646\) | −361.000 | − | 3126.35i | −0.0219866 | − | 0.190410i | ||||
\(647\) | 14592.0 | 0.886663 | 0.443331 | − | 0.896358i | \(-0.353797\pi\) | ||||
0.443331 | + | 0.896358i | \(0.353797\pi\) | |||||||
\(648\) | 2684.00 | − | 4648.82i | 0.162712 | − | 0.281826i | ||||
\(649\) | 1198.00 | − | 2075.00i | 0.0724586 | − | 0.125502i | ||||
\(650\) | −8004.00 | − | 13863.3i | −0.482989 | − | 0.836561i | ||||
\(651\) | −10560.0 | + | 18290.5i | −0.635759 | + | 1.10117i | ||||
\(652\) | −136.000 | − | 235.559i | −0.00816897 | − | 0.0141491i | ||||
\(653\) | −23430.0 | −1.40411 | −0.702057 | − | 0.712121i | \(-0.747735\pi\) | ||||
−0.702057 | + | 0.712121i | \(0.747735\pi\) | |||||||
\(654\) | 10550.0 | 0.630792 | ||||||||
\(655\) | 2704.50 | + | 4684.33i | 0.161334 | + | 0.279438i | ||||
\(656\) | 3304.00 | + | 5722.70i | 0.196646 | + | 0.340600i | ||||
\(657\) | −2030.00 | −0.120545 | ||||||||
\(658\) | 39488.0 | 2.33952 | ||||||||
\(659\) | −2067.50 | − | 3581.02i | −0.122213 | − | 0.211679i | 0.798427 | − | 0.602092i | \(-0.205666\pi\) |
−0.920640 | + | 0.390412i | \(0.872332\pi\) | |||||||
\(660\) | −120.000 | + | 207.846i | −0.00707726 | + | 0.0122582i | ||||
\(661\) | 4142.50 | + | 7175.02i | 0.243759 | + | 0.422203i | 0.961782 | − | 0.273817i | \(-0.0882861\pi\) |
−0.718023 | + | 0.696019i | \(0.754953\pi\) | |||||||
\(662\) | −3660.00 | + | 6339.31i | −0.214879 | + | 0.372181i | ||||
\(663\) | 3277.50 | − | 5676.80i | 0.191987 | − | 0.332532i | ||||
\(664\) | −4736.00 | −0.276796 | ||||||||
\(665\) | 6384.00 | − | 4738.89i | 0.372272 | − | 0.276340i | ||||
\(666\) | 56.0000 | 0.00325819 | ||||||||
\(667\) | −1708.50 | + | 2959.21i | −0.0991805 | + | 0.171786i | ||||
\(668\) | 1842.00 | − | 3190.44i | 0.106690 | − | 0.184793i | ||||
\(669\) | 6097.50 | + | 10561.2i | 0.352381 | + | 0.610342i | ||||
\(670\) | 675.000 | − | 1169.13i | 0.0389217 | − | 0.0674143i | ||||
\(671\) | 434.000 | + | 751.710i | 0.0249693 | + | 0.0432481i | ||||
\(672\) | −5120.00 | −0.293911 | ||||||||
\(673\) | 23990.0 | 1.37407 | 0.687033 | − | 0.726626i | \(-0.258913\pi\) | ||||
0.687033 | + | 0.726626i | \(0.258913\pi\) | |||||||
\(674\) | 5173.00 | + | 8959.90i | 0.295633 | + | 0.512051i | ||||
\(675\) | −8410.00 | − | 14566.5i | −0.479557 | − | 0.830617i | ||||
\(676\) | 10256.0 | 0.583523 | ||||||||
\(677\) | 690.000 | 0.0391711 | 0.0195856 | − | 0.999808i | \(-0.493765\pi\) | ||||
0.0195856 | + | 0.999808i | \(0.493765\pi\) | |||||||
\(678\) | −5030.00 | − | 8712.22i | −0.284920 | − | 0.493496i | ||||
\(679\) | −9808.00 | + | 16988.0i | −0.554339 | + | 0.960144i | ||||
\(680\) | −228.000 | − | 394.908i | −0.0128579 | − | 0.0222706i | ||||
\(681\) | 4270.00 | − | 7395.86i | 0.240274 | − | 0.416167i | ||||
\(682\) | 528.000 | − | 914.523i | 0.0296454 | − | 0.0513473i | ||||
\(683\) | 5760.00 | 0.322694 | 0.161347 | − | 0.986898i | \(-0.448416\pi\) | ||||
0.161347 | + | 0.986898i | \(0.448416\pi\) | |||||||
\(684\) | 532.000 | − | 394.908i | 0.0297391 | − | 0.0220755i | ||||
\(685\) | −2007.00 | −0.111947 | ||||||||
\(686\) | 10816.0 | − | 18733.9i | 0.601978 | − | 1.04266i | ||||
\(687\) | −11545.0 | + | 19996.5i | −0.641149 | + | 1.11050i | ||||
\(688\) | −1032.00 | − | 1787.48i | −0.0571870 | − | 0.0990507i | ||||
\(689\) | 13213.5 | − | 22886.5i | 0.730616 | − | 1.26546i | ||||
\(690\) | −1005.00 | − | 1740.71i | −0.0554488 | − | 0.0960402i | ||||
\(691\) | 4348.00 | 0.239372 | 0.119686 | − | 0.992812i | \(-0.461811\pi\) | ||||
0.119686 | + | 0.992812i | \(0.461811\pi\) | |||||||
\(692\) | −7572.00 | −0.415960 | ||||||||
\(693\) | −128.000 | − | 221.703i | −0.00701633 | − | 0.0121526i | ||||
\(694\) | 8591.00 | + | 14880.0i | 0.469899 | + | 0.813889i | ||||
\(695\) | −8175.00 | −0.446180 | ||||||||
\(696\) | 2040.00 | 0.111101 | ||||||||
\(697\) | 3923.50 | + | 6795.70i | 0.213218 | + | 0.369305i | ||||
\(698\) | −6946.00 | + | 12030.8i | −0.376662 | + | 0.652397i | ||||
\(699\) | −8047.50 | − | 13938.7i | −0.435457 | − | 0.754234i | ||||
\(700\) | −7424.00 | + | 12858.7i | −0.400858 | + | 0.694307i | ||||
\(701\) | 5144.50 | − | 8910.54i | 0.277183 | − | 0.480095i | −0.693501 | − | 0.720456i | \(-0.743933\pi\) |
0.970683 | + | 0.240361i | \(0.0772659\pi\) | |||||||
\(702\) | 20010.0 | 1.07582 | ||||||||
\(703\) | −1064.00 | − | 460.726i | −0.0570832 | − | 0.0247178i | ||||
\(704\) | 256.000 | 0.0137051 | ||||||||
\(705\) | 4627.50 | − | 8015.07i | 0.247208 | − | 0.428177i | ||||
\(706\) | 8226.00 | − | 14247.8i | 0.438512 | − | 0.759525i | ||||
\(707\) | 19760.0 | + | 34225.3i | 1.05113 | + | 1.82062i | ||||
\(708\) | 5990.00 | − | 10375.0i | 0.317963 | − | 0.550729i | ||||
\(709\) | 15372.5 | + | 26626.0i | 0.814283 | + | 1.41038i | 0.909842 | + | 0.414955i | \(0.136203\pi\) |
−0.0955593 | + | 0.995424i | \(0.530464\pi\) | |||||||
\(710\) | 4206.00 | 0.222322 | ||||||||
\(711\) | −698.000 | −0.0368172 | ||||||||
\(712\) | 5396.00 | + | 9346.15i | 0.284022 | + | 0.491940i | ||||
\(713\) | 4422.00 | + | 7659.13i | 0.232265 | + | 0.402295i | ||||
\(714\) | −6080.00 | −0.318681 | ||||||||
\(715\) | −828.000 | −0.0433083 | ||||||||
\(716\) | 40.0000 | + | 69.2820i | 0.00208781 | + | 0.00361619i | ||||
\(717\) | 10590.0 | − | 18342.4i | 0.551591 | − | 0.955384i | ||||
\(718\) | −11385.0 | − | 19719.4i | −0.591761 | − | 1.02496i | ||||
\(719\) | −420.500 | + | 728.327i | −0.0218109 | + | 0.0377775i | −0.876725 | − | 0.480992i | \(-0.840276\pi\) |
0.854914 | + | 0.518770i | \(0.173610\pi\) | |||||||
\(720\) | 48.0000 | − | 83.1384i | 0.00248452 | − | 0.00430331i | ||||
\(721\) | −52224.0 | −2.69754 | ||||||||
\(722\) | −13357.0 | + | 3126.35i | −0.688499 | + | 0.161151i | ||||
\(723\) | −12145.0 | −0.624727 | ||||||||
\(724\) | −3678.00 | + | 6370.48i | −0.188801 | + | 0.327013i | ||||
\(725\) | 2958.00 | − | 5123.41i | 0.151527 | − | 0.262453i | ||||
\(726\) | 6575.00 | + | 11388.2i | 0.336117 | + | 0.582172i | ||||
\(727\) | 135.500 | − | 234.693i | 0.00691254 | − | 0.0119729i | −0.862548 | − | 0.505974i | \(-0.831133\pi\) |
0.869461 | + | 0.494002i | \(0.164466\pi\) | |||||||
\(728\) | −8832.00 | − | 15297.5i | −0.449637 | − | 0.778794i | ||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 6090.00 | 0.308769 | ||||||||
\(731\) | −1225.50 | − | 2122.63i | −0.0620065 | − | 0.107398i | ||||
\(732\) | 2170.00 | + | 3758.55i | 0.109570 | + | 0.189781i | ||||
\(733\) | −8102.00 | −0.408259 | −0.204130 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204130 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(734\) | −5906.00 | −0.296995 | ||||||||
\(735\) | −5107.50 | − | 8846.45i | −0.256317 | − | 0.443954i | ||||
\(736\) | −1072.00 | + | 1856.76i | −0.0536881 | + | 0.0929905i | ||||
\(737\) | 450.000 | + | 779.423i | 0.0224911 | + | 0.0389558i | ||||
\(738\) | −826.000 | + | 1430.67i | −0.0411998 | + | 0.0713602i | ||||
\(739\) | −7824.50 | + | 13552.4i | −0.389484 | + | 0.674607i | −0.992380 | − | 0.123213i | \(-0.960680\pi\) |
0.602896 | + | 0.797820i | \(0.294013\pi\) | |||||||
\(740\) | −168.000 | −0.00834568 | ||||||||
\(741\) | −26220.0 | − | 11353.6i | −1.29989 | − | 0.562867i | ||||
\(742\) | −24512.0 | −1.21275 | ||||||||
\(743\) | 5167.50 | − | 8950.37i | 0.255151 | − | 0.441934i | −0.709786 | − | 0.704418i | \(-0.751208\pi\) |
0.964937 | + | 0.262483i | \(0.0845415\pi\) | |||||||
\(744\) | 2640.00 | − | 4572.61i | 0.130090 | − | 0.225323i | ||||
\(745\) | −106.500 | − | 184.463i | −0.00523739 | − | 0.00907143i | ||||
\(746\) | −5006.00 | + | 8670.65i | −0.245687 | + | 0.425543i | ||||
\(747\) | −592.000 | − | 1025.37i | −0.0289962 | − | 0.0502229i | ||||
\(748\) | 304.000 | 0.0148601 | ||||||||
\(749\) | −65920.0 | −3.21584 | ||||||||
\(750\) | 3615.00 | + | 6261.36i | 0.176002 | + | 0.304844i | ||||
\(751\) | 7334.50 | + | 12703.7i | 0.356378 | + | 0.617264i | 0.987353 | − | 0.158539i | \(-0.0506783\pi\) |
−0.630975 | + | 0.775803i | \(0.717345\pi\) | |||||||
\(752\) | −9872.00 | −0.478716 | ||||||||
\(753\) | 1215.00 | 0.0588009 | ||||||||
\(754\) | 3519.00 | + | 6095.09i | 0.169966 | + | 0.294390i | ||||
\(755\) | 984.000 | − | 1704.34i | 0.0474324 | − | 0.0821552i | ||||
\(756\) | −9280.00 | − | 16073.4i | −0.446442 | − | 0.773261i | ||||
\(757\) | 20718.5 | − | 35885.5i | 0.994751 | − | 1.72296i | 0.408761 | − | 0.912641i | \(-0.365961\pi\) |
0.585990 | − | 0.810318i | \(-0.300706\pi\) | |||||||
\(758\) | −6764.00 | + | 11715.6i | −0.324115 | + | 0.561385i | ||||
\(759\) | 1340.00 | 0.0640829 | ||||||||
\(760\) | −1596.00 | + | 1184.72i | −0.0761750 | + | 0.0565453i | ||||
\(761\) | −34258.0 | −1.63187 | −0.815934 | − | 0.578145i | \(-0.803777\pi\) | ||||
−0.815934 | + | 0.578145i | \(0.803777\pi\) | |||||||
\(762\) | −9935.00 | + | 17207.9i | −0.472319 | + | 0.818081i | ||||
\(763\) | 16880.0 | − | 29237.0i | 0.800914 | − | 1.38722i | ||||
\(764\) | −5984.00 | − | 10364.6i | −0.283368 | − | 0.490809i | ||||
\(765\) | 57.0000 | − | 98.7269i | 0.00269391 | − | 0.00466598i | ||||
\(766\) | 4963.00 | + | 8596.17i | 0.234100 | + | 0.405473i | ||||
\(767\) | 41331.0 | 1.94573 | ||||||||
\(768\) | 1280.00 | 0.0601407 | ||||||||
\(769\) | −3427.50 | − | 5936.60i | −0.160727 | − | 0.278387i | 0.774403 | − | 0.632693i | \(-0.218050\pi\) |
−0.935130 | + | 0.354306i | \(0.884717\pi\) | |||||||
\(770\) | 384.000 | + | 665.108i | 0.0179719 | + | 0.0311283i | ||||
\(771\) | 5235.00 | 0.244532 | ||||||||
\(772\) | −5572.00 | −0.259768 | ||||||||
\(773\) | 14728.5 | + | 25510.5i | 0.685313 | + | 1.18700i | 0.973338 | + | 0.229375i | \(0.0736681\pi\) |
−0.288025 | + | 0.957623i | \(0.592999\pi\) | |||||||
\(774\) | 258.000 | − | 446.869i | 0.0119814 | − | 0.0207524i | ||||
\(775\) | −7656.00 | − | 13260.6i | −0.354854 | − | 0.614625i | ||||
\(776\) | 2452.00 | − | 4246.99i | 0.113430 | − | 0.196467i | ||||
\(777\) | −1120.00 | + | 1939.90i | −0.0517114 | + | 0.0895668i | ||||
\(778\) | 7246.00 | 0.333910 | ||||||||
\(779\) | 27464.5 | − | 20387.1i | 1.26318 | − | 0.937669i | ||||
\(780\) | −4140.00 | −0.190046 | ||||||||
\(781\) | −1402.00 | + | 2428.34i | −0.0642350 | + | 0.111258i | ||||
\(782\) | −1273.00 | + | 2204.90i | −0.0582128 | + | 0.100827i | ||||
\(783\) | 3697.50 | + | 6404.26i | 0.168758 | + | 0.292298i | ||||
\(784\) | −5448.00 | + | 9436.21i | −0.248178 | + | 0.429857i | ||||
\(785\) | 1579.50 | + | 2735.77i | 0.0718150 | + | 0.124387i | ||||
\(786\) | −18030.0 | −0.818205 | ||||||||
\(787\) | 20716.0 | 0.938305 | 0.469152 | − | 0.883117i | \(-0.344560\pi\) | ||||
0.469152 | + | 0.883117i | \(0.344560\pi\) | |||||||
\(788\) | 8428.00 | + | 14597.7i | 0.381009 | + | 0.659927i | ||||
\(789\) | −4762.50 | − | 8248.89i | −0.214892 | − | 0.372203i | ||||
\(790\) | 2094.00 | 0.0943053 | ||||||||
\(791\) | −32192.0 | −1.44705 | ||||||||
\(792\) | 32.0000 | + | 55.4256i | 0.00143570 | + | 0.00248670i | ||||
\(793\) | −7486.50 | + | 12967.0i | −0.335250 | + | 0.580670i | ||||
\(794\) | 7629.00 | + | 13213.8i | 0.340986 | + | 0.590606i | ||||
\(795\) | −2872.50 | + | 4975.32i | −0.128147 | + | 0.221958i | ||||
\(796\) | −1534.00 | + | 2656.97i | −0.0683055 | + | 0.118309i | ||||
\(797\) | 3722.00 | 0.165420 | 0.0827102 | − | 0.996574i | \(-0.473642\pi\) | ||||
0.0827102 | + | 0.996574i | \(0.473642\pi\) | |||||||
\(798\) | 3040.00 | + | 26327.2i | 0.134856 | + | 1.16788i | ||||
\(799\) | −11723.0 | −0.519061 | ||||||||
\(800\) | 1856.00 | − | 3214.69i | 0.0820244 | − | 0.142070i | ||||
\(801\) | −1349.00 | + | 2336.54i | −0.0595063 | + | 0.103068i | ||||
\(802\) | 9117.00 | + | 15791.1i | 0.401412 | + | 0.695266i | ||||
\(803\) | −2030.00 | + | 3516.06i | −0.0892119 | + | 0.154520i | ||||
\(804\) | 2250.00 | + | 3897.11i | 0.0986957 | + | 0.170946i | ||||
\(805\) | −6432.00 | −0.281613 | ||||||||
\(806\) | 18216.0 | 0.796069 | ||||||||
\(807\) | 14582.5 | + | 25257.6i | 0.636095 | + | 1.10175i | ||||
\(808\) | −4940.00 | − | 8556.33i | −0.215085 | − | 0.372538i | ||||
\(809\) | 11358.0 | 0.493604 | 0.246802 | − | 0.969066i | \(-0.420620\pi\) | ||||
0.246802 | + | 0.969066i | \(0.420620\pi\) | |||||||
\(810\) | −4026.00 | −0.174641 | ||||||||
\(811\) | −4239.50 | − | 7343.03i | −0.183562 | − | 0.317939i | 0.759529 | − | 0.650474i | \(-0.225430\pi\) |
−0.943091 | + | 0.332534i | \(0.892096\pi\) | |||||||
\(812\) | 3264.00 | − | 5653.41i | 0.141064 | − | 0.244330i | ||||
\(813\) | 9317.50 | + | 16138.4i | 0.401942 | + | 0.696184i | ||||
\(814\) | 56.0000 | − | 96.9948i | 0.00241130 | − | 0.00417650i | ||||
\(815\) | −102.000 | + | 176.669i | −0.00438393 | + | 0.00759319i | ||||
\(816\) | 1520.00 | 0.0652091 | ||||||||
\(817\) | −8578.50 | + | 6367.88i | −0.367348 | + | 0.272686i | ||||
\(818\) | 9870.00 | 0.421878 | ||||||||
\(819\) | 2208.00 | − | 3824.37i | 0.0942048 | − | 0.163168i | ||||
\(820\) | 2478.00 | − | 4292.02i | 0.105531 | − | 0.182785i | ||||
\(821\) | −6685.50 | − | 11579.6i | −0.284197 | − | 0.492243i | 0.688217 | − | 0.725505i | \(-0.258394\pi\) |
−0.972414 | + | 0.233261i | \(0.925060\pi\) | |||||||
\(822\) | 3345.00 | − | 5793.71i | 0.141935 | − | 0.245838i | ||||
\(823\) | 13292.5 | + | 23023.3i | 0.562998 | + | 0.975141i | 0.997233 | + | 0.0743415i | \(0.0236855\pi\) |
−0.434235 | + | 0.900800i | \(0.642981\pi\) | |||||||
\(824\) | 13056.0 | 0.551975 | ||||||||
\(825\) | −2320.00 | −0.0979055 | ||||||||
\(826\) | −19168.0 | − | 33199.9i | −0.807433 | − | 1.39852i | ||||
\(827\) | −18301.5 | − | 31699.1i | −0.769535 | − | 1.33287i | −0.937815 | − | 0.347135i | \(-0.887155\pi\) |
0.168280 | − | 0.985739i | \(-0.446179\pi\) | |||||||
\(828\) | −536.000 | −0.0224967 | ||||||||
\(829\) | 31238.0 | 1.30873 | 0.654367 | − | 0.756177i | \(-0.272935\pi\) | ||||
0.654367 | + | 0.756177i | \(0.272935\pi\) | |||||||
\(830\) | 1776.00 | + | 3076.12i | 0.0742721 | + | 0.128643i | ||||
\(831\) | 13235.0 | − | 22923.7i | 0.552487 | − | 0.956936i | ||||
\(832\) | 2208.00 | + | 3824.37i | 0.0920056 | + | 0.159358i | ||||
\(833\) | −6469.50 | + | 11205.5i | −0.269094 | + | 0.466084i | ||||
\(834\) | 13625.0 | − | 23599.2i | 0.565702 | − | 0.979824i | ||||
\(835\) | −2763.00 | −0.114512 | ||||||||
\(836\) | −152.000 | − | 1316.36i | −0.00628831 | − | 0.0544584i | ||||
\(837\) | 19140.0 | 0.790412 | ||||||||
\(838\) | −6516.00 | + | 11286.0i | −0.268606 | + | 0.465239i | ||||
\(839\) | −15328.5 | + | 26549.7i | −0.630749 | + | 1.09249i | 0.356650 | + | 0.934238i | \(0.383919\pi\) |
−0.987399 | + | 0.158251i | \(0.949414\pi\) | |||||||
\(840\) | 1920.00 | + | 3325.54i | 0.0788646 | + | 0.136598i | ||||
\(841\) | 10894.0 | − | 18869.0i | 0.446677 | − | 0.773667i | ||||
\(842\) | −10915.0 | − | 18905.3i | −0.446741 | − | 0.773778i | ||||
\(843\) | 6875.00 | 0.280887 | ||||||||
\(844\) | 9460.00 | 0.385814 | ||||||||
\(845\) | −3846.00 | − | 6661.47i | −0.156576 | − | 0.271197i | ||||
\(846\) | −1234.00 | − | 2137.35i | −0.0501487 | − | 0.0868601i | ||||
\(847\) | 42080.0 | 1.70707 | ||||||||
\(848\) | 6128.00 | 0.248156 | ||||||||
\(849\) | 3267.50 | + | 5659.48i | 0.132085 | + | 0.228778i | ||||
\(850\) | 2204.00 | − | 3817.44i | 0.0889371 | − | 0.154044i | ||||
\(851\) | 469.000 | + | 812.332i | 0.0188920 | + | 0.0327219i | ||||
\(852\) | −7010.00 | + | 12141.7i | −0.281876 | + | 0.488224i | ||||
\(853\) | −2221.50 | + | 3847.75i | −0.0891708 | + | 0.154448i | −0.907161 | − | 0.420784i | \(-0.861755\pi\) |
0.817990 | + | 0.575232i | \(0.195088\pi\) | |||||||
\(854\) | 13888.0 | 0.556484 | ||||||||
\(855\) | −456.000 | − | 197.454i | −0.0182396 | − | 0.00789799i | ||||
\(856\) | 16480.0 | 0.658031 | ||||||||
\(857\) | 3484.50 | − | 6035.33i | 0.138889 | − | 0.240564i | −0.788187 | − | 0.615436i | \(-0.788980\pi\) |
0.927077 | + | 0.374872i | \(0.122313\pi\) | |||||||
\(858\) | 1380.00 | − | 2390.23i | 0.0549096 | − | 0.0951062i | ||||
\(859\) | −19659.5 | − | 34051.3i | −0.780877 | − | 1.35252i | −0.931431 | − | 0.363917i | \(-0.881439\pi\) |
0.150554 | − | 0.988602i | \(-0.451894\pi\) | |||||||
\(860\) | −774.000 | + | 1340.61i | −0.0306897 | + | 0.0531562i | ||||
\(861\) | −33040.0 | − | 57227.0i | −1.30778 | − | 2.26514i | ||||
\(862\) | −11018.0 | −0.435353 | ||||||||
\(863\) | 9380.00 | 0.369987 | 0.184994 | − | 0.982740i | \(-0.440774\pi\) | ||||
0.184994 | + | 0.982740i | \(0.440774\pi\) | |||||||
\(864\) | 2320.00 | + | 4018.36i | 0.0913519 | + | 0.158226i | ||||
\(865\) | 2839.50 | + | 4918.16i | 0.111614 | + | 0.193321i | ||||
\(866\) | −7506.00 | −0.294531 | ||||||||
\(867\) | −22760.0 | −0.891546 | ||||||||
\(868\) | −8448.00 | − | 14632.4i | −0.330350 | − | 0.572183i | ||||
\(869\) | −698.000 | + | 1208.97i | −0.0272474 | + | 0.0471940i | ||||
\(870\) | −765.000 | − | 1325.02i | −0.0298114 | − | 0.0516349i | ||||
\(871\) | −7762.50 | + | 13445.0i | −0.301977 | + | 0.523040i | ||||
\(872\) | −4220.00 | + | 7309.25i | −0.163884 | + | 0.283856i | ||||
\(873\) | 1226.00 | 0.0475301 | ||||||||
\(874\) | 10184.0 | + | 4409.80i | 0.394141 | + | 0.170668i | ||||
\(875\) | 23136.0 | 0.893874 | ||||||||
\(876\) | −10150.0 | + | 17580.3i | −0.391480 | + | 0.678064i | ||||
\(877\) | 5124.50 | − | 8875.89i | 0.197311 | − | 0.341753i | −0.750344 | − | 0.661047i | \(-0.770112\pi\) |
0.947656 | + | 0.319294i | \(0.103446\pi\) | |||||||
\(878\) | −7813.00 | − | 13532.5i | −0.300314 | − | 0.520160i | ||||
\(879\) | −9545.00 | + | 16532.4i | −0.366263 | + | 0.634385i | ||||
\(880\) | −96.0000 | − | 166.277i | −0.00367745 | − | 0.00636954i | ||||
\(881\) | −28698.0 | −1.09746 | −0.548729 | − | 0.836000i | \(-0.684888\pi\) | ||||
−0.548729 | + | 0.836000i | \(0.684888\pi\) | |||||||
\(882\) | −2724.00 | −0.103993 | ||||||||
\(883\) | −15889.5 | − | 27521.4i | −0.605577 | − | 1.04889i | −0.991960 | − | 0.126551i | \(-0.959609\pi\) |
0.386383 | − | 0.922338i | \(-0.373724\pi\) | |||||||
\(884\) | 2622.00 | + | 4541.44i | 0.0997595 | + | 0.172789i | ||||
\(885\) | −8985.00 | −0.341274 | ||||||||
\(886\) | −12234.0 | −0.463893 | ||||||||
\(887\) | −1783.50 | − | 3089.11i | −0.0675130 | − | 0.116936i | 0.830293 | − | 0.557327i | \(-0.188173\pi\) |
−0.897806 | + | 0.440391i | \(0.854840\pi\) | |||||||
\(888\) | 280.000 | − | 484.974i | 0.0105813 | − | 0.0183273i | ||||
\(889\) | 31792.0 | + | 55065.4i | 1.19940 | + | 2.07743i | ||||
\(890\) | 4047.00 | − | 7009.61i | 0.152422 | − | 0.264003i | ||||
\(891\) | 1342.00 | − | 2324.41i | 0.0504587 | − | 0.0873970i | ||||
\(892\) | −9756.00 | −0.366205 | ||||||||
\(893\) | 5861.50 | + | 50762.1i | 0.219650 | + | 1.90223i | ||||
\(894\) | 710.000 | 0.0265615 | ||||||||
\(895\) | 30.0000 | − | 51.9615i | 0.00112044 | − | 0.00194065i | ||||
\(896\) | 2048.00 | − | 3547.24i | 0.0763604 | − | 0.132260i | ||||
\(897\) | 11557.5 | + | 20018.2i | 0.430205 | + | 0.745137i | ||||
\(898\) | 7146.00 | − | 12377.2i | 0.265551 | − | 0.459948i | ||||
\(899\) | 3366.00 | + | 5830.08i | 0.124875 | + | 0.216289i | ||||
\(900\) | 928.000 | 0.0343704 | ||||||||
\(901\) | 7277.00 | 0.269070 | ||||||||
\(902\) | 1652.00 | + | 2861.35i | 0.0609818 | + | 0.105624i | ||||
\(903\) | 10320.0 | + | 17874.8i | 0.380319 | + | 0.658732i | ||||
\(904\) | 8048.00 | 0.296098 | ||||||||
\(905\) | 5517.00 | 0.202642 | ||||||||
\(906\) | 3280.00 | + | 5681.13i | 0.120277 | + | 0.208325i | ||||
\(907\) | 15539.5 | − | 26915.2i | 0.568887 | − | 0.985341i | −0.427789 | − | 0.903879i | \(-0.640707\pi\) |
0.996676 | − | 0.0814629i | \(-0.0259592\pi\) | |||||||
\(908\) | 3416.00 | + | 5916.69i | 0.124850 | + | 0.216247i | ||||
\(909\) | 1235.00 | − | 2139.08i | 0.0450631 | − | 0.0780516i | ||||
\(910\) | −6624.00 | + | 11473.1i | −0.241301 | + | 0.417945i | ||||
\(911\) | 32856.0 | 1.19492 | 0.597458 | − | 0.801900i | \(-0.296178\pi\) | ||||
0.597458 | + | 0.801900i | \(0.296178\pi\) | |||||||
\(912\) | −760.000 | − | 6581.79i | −0.0275944 | − | 0.238975i | ||||
\(913\) | −2368.00 | −0.0858372 | ||||||||
\(914\) | 18118.0 | − | 31381.3i | 0.655679 | − | 1.13567i | ||||
\(915\) | 1627.50 | − | 2818.91i | 0.0588016 | − | 0.101847i | ||||
\(916\) | −9236.00 | − | 15997.2i | −0.333151 | − | 0.577034i | ||||
\(917\) | −28848.0 | + | 49966.2i | −1.03887 | + | 1.79938i | ||||
\(918\) | 2755.00 | + | 4771.80i | 0.0990507 | + | 0.171561i | ||||
\(919\) | −7736.00 | −0.277679 | −0.138840 | − | 0.990315i | \(-0.544337\pi\) | ||||
−0.138840 | + | 0.990315i | \(0.544337\pi\) | |||||||
\(920\) | 1608.00 | 0.0576241 | ||||||||
\(921\) | −2182.50 | − | 3780.20i | −0.0780845 | − | 0.135246i | ||||
\(922\) | −16935.0 | − | 29332.3i | −0.604907 | − | 1.04773i | ||||
\(923\) | −48369.0 | −1.72490 | ||||||||
\(924\) | −2560.00 | −0.0911448 | ||||||||
\(925\) | −812.000 | − | 1406.43i | −0.0288631 | − | 0.0499924i | ||||
\(926\) | 7788.00 | − | 13489.2i | 0.276382 | − | 0.478707i | ||||
\(927\) | 1632.00 | + | 2826.71i | 0.0578230 | + | 0.100152i | ||||
\(928\) | −816.000 | + | 1413.35i | −0.0288648 | + | 0.0499953i | ||||
\(929\) | −15259.5 | + | 26430.2i | −0.538911 | + | 0.933421i | 0.460052 | + | 0.887892i | \(0.347831\pi\) |
−0.998963 | + | 0.0455288i | \(0.985503\pi\) | |||||||
\(930\) | −3960.00 | −0.139627 | ||||||||
\(931\) | 51756.0 | + | 22411.0i | 1.82195 | + | 0.788927i | ||||
\(932\) | 12876.0 | 0.452540 | ||||||||
\(933\) | −10450.0 | + | 18099.9i | −0.366686 | + | 0.635118i | ||||
\(934\) | −12500.0 | + | 21650.6i | −0.437915 | + | 0.758491i | ||||
\(935\) | −114.000 | − | 197.454i | −0.00398738 | − | 0.00690634i | ||||
\(936\) | −552.000 | + | 956.092i | −0.0192764 | + | 0.0333877i | ||||
\(937\) | −4703.50 | − | 8146.70i | −0.163988 | − | 0.284035i | 0.772308 | − | 0.635249i | \(-0.219102\pi\) |
−0.936295 | + | 0.351214i | \(0.885769\pi\) | |||||||
\(938\) | 14400.0 | 0.501254 | ||||||||
\(939\) | −15825.0 | −0.549978 | ||||||||
\(940\) | 3702.00 | + | 6412.05i | 0.128453 | + | 0.222487i | ||||
\(941\) | −13407.5 | − | 23222.5i | −0.464476 | − | 0.804496i | 0.534702 | − | 0.845041i | \(-0.320424\pi\) |
−0.999178 | + | 0.0405447i | \(0.987091\pi\) | |||||||
\(942\) | −10530.0 | −0.364210 | ||||||||
\(943\) | −27671.0 | −0.955559 | ||||||||
\(944\) | 4792.00 | + | 8299.99i | 0.165219 | + | 0.286167i | ||||
\(945\) | −6960.00 | + | 12055.1i | −0.239586 | + | 0.414975i | ||||
\(946\) | −516.000 | − | 893.738i | −0.0177343 | − | 0.0307166i | ||||
\(947\) | −8724.50 | + | 15111.3i | −0.299375 | + | 0.518533i | −0.975993 | − | 0.217801i | \(-0.930112\pi\) |
0.676618 | + | 0.736334i | \(0.263445\pi\) | |||||||
\(948\) | −3490.00 | + | 6044.86i | −0.119567 | + | 0.207097i | ||||
\(949\) | −70035.0 | −2.39561 | ||||||||
\(950\) | −17632.0 | − | 7634.88i | −0.602166 | − | 0.260745i | ||||
\(951\) | 22695.0 | 0.773855 | ||||||||
\(952\) | 2432.00 | − | 4212.35i | 0.0827958 | − | 0.143406i | ||||
\(953\) | 19936.5 | − | 34531.0i | 0.677656 | − | 1.17374i | −0.298028 | − | 0.954557i | \(-0.596329\pi\) |
0.975685 | − | 0.219178i | \(-0.0703377\pi\) | |||||||
\(954\) | 766.000 | + | 1326.75i | 0.0259960 | + | 0.0450264i | ||||
\(955\) | −4488.00 | + | 7773.44i | −0.152071 | + | 0.263396i | ||||
\(956\) | 8472.00 | + | 14673.9i | 0.286615 | + | 0.496432i | ||||
\(957\) | 1020.00 | 0.0344534 | ||||||||
\(958\) | −24210.0 | −0.816482 | ||||||||
\(959\) | −10704.0 | − | 18539.9i | −0.360428 | − | 0.624279i | ||||
\(960\) | −480.000 | − | 831.384i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | −12367.0 | −0.415125 | ||||||||
\(962\) | 1932.00 | 0.0647507 | ||||||||
\(963\) | 2060.00 | + | 3568.02i | 0.0689331 | + | 0.119396i | ||||
\(964\) | 4858.00 | − | 8414.30i | 0.162309 | − | 0.281127i | ||||
\(965\) | 2089.50 | + | 3619.12i | 0.0697030 | + | 0.120729i | ||||
\(966\) | 10720.0 | − | 18567.6i | 0.357050 | − | 0.618429i | ||||
\(967\) | 5989.50 | − | 10374.1i | 0.199182 | − | 0.344994i | −0.749081 | − | 0.662478i | \(-0.769505\pi\) |
0.948264 | + | 0.317484i | \(0.102838\pi\) | |||||||
\(968\) | −10520.0 | −0.349303 | ||||||||
\(969\) | −902.500 | − | 7815.88i | −0.0299200 | − | 0.259115i | ||||
\(970\) | −3678.00 | −0.121746 | ||||||||
\(971\) | −9100.50 | + | 15762.5i | −0.300771 | + | 0.520951i | −0.976311 | − | 0.216373i | \(-0.930577\pi\) |
0.675540 | + | 0.737324i | \(0.263911\pi\) | |||||||
\(972\) | −1120.00 | + | 1939.90i | −0.0369589 | + | 0.0640146i | ||||
\(973\) | −43600.0 | − | 75517.4i | −1.43654 | − | 2.48816i | ||||
\(974\) | −296.000 | + | 512.687i | −0.00973763 | + | 0.0168661i | ||||
\(975\) | −20010.0 | − | 34658.3i | −0.657264 | − | 1.13842i | ||||
\(976\) | −3472.00 | −0.113869 | ||||||||
\(977\) | 37398.0 | 1.22463 | 0.612317 | − | 0.790612i | \(-0.290238\pi\) | ||||
0.612317 | + | 0.790612i | \(0.290238\pi\) | |||||||
\(978\) | −340.000 | − | 588.897i | −0.0111166 | − | 0.0192545i | ||||
\(979\) | 2698.00 | + | 4673.07i | 0.0880781 | + | 0.152556i | ||||
\(980\) | 8172.00 | 0.266372 | ||||||||
\(981\) | −2110.00 | −0.0686719 | ||||||||
\(982\) | −3213.00 | − | 5565.08i | −0.104410 | − | 0.180844i | ||||
\(983\) | −22018.5 | + | 38137.2i | −0.714426 | + | 1.23742i | 0.248754 | + | 0.968567i | \(0.419979\pi\) |
−0.963180 | + | 0.268856i | \(0.913354\pi\) | |||||||
\(984\) | 8260.00 | + | 14306.7i | 0.267601 | + | 0.463498i | ||||
\(985\) | 6321.00 | − | 10948.3i | 0.204471 | − | 0.354154i | ||||
\(986\) | −969.000 | + | 1678.36i | −0.0312974 | + | 0.0542087i | ||||
\(987\) | 98720.0 | 3.18368 | ||||||||
\(988\) | 18354.0 | − | 13624.3i | 0.591011 | − | 0.438712i | ||||
\(989\) | 8643.00 | 0.277888 | ||||||||
\(990\) | 24.0000 | − | 41.5692i | 0.000770475 | − | 0.00133450i | ||||
\(991\) | −4914.50 | + | 8512.16i | −0.157532 | + | 0.272853i | −0.933978 | − | 0.357330i | \(-0.883687\pi\) |
0.776446 | + | 0.630184i | \(0.217020\pi\) | |||||||
\(992\) | 2112.00 | + | 3658.09i | 0.0675968 | + | 0.117081i | ||||
\(993\) | −9150.00 | + | 15848.3i | −0.292413 | + | 0.506475i | ||||
\(994\) | 22432.0 | + | 38853.4i | 0.715795 | + | 1.23979i | ||||
\(995\) | 2301.00 | 0.0733132 | ||||||||
\(996\) | −11840.0 | −0.376671 | ||||||||
\(997\) | −19991.5 | − | 34626.3i | −0.635042 | − | 1.09993i | −0.986506 | − | 0.163724i | \(-0.947649\pi\) |
0.351464 | − | 0.936201i | \(-0.385684\pi\) | |||||||
\(998\) | −3017.00 | − | 5225.60i | −0.0956929 | − | 0.165745i | ||||
\(999\) | 2030.00 | 0.0642906 |
(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 | 38.4.c.a.11.1 | yes | 2 | |
3.2 | odd | 2 | 342.4.g.d.163.1 | 2 | |||
4.3 | odd | 2 | 304.4.i.b.49.1 | 2 | |||
19.7 | even | 3 | inner | 38.4.c.a.7.1 | ✓ | 2 | |
19.8 | odd | 6 | 722.4.a.a.1.1 | 1 | |||
19.11 | even | 3 | 722.4.a.e.1.1 | 1 | |||
57.26 | odd | 6 | 342.4.g.d.235.1 | 2 | |||
76.7 | odd | 6 | 304.4.i.b.273.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.c.a.7.1 | ✓ | 2 | 19.7 | even | 3 | inner | |
38.4.c.a.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
304.4.i.b.49.1 | 2 | 4.3 | odd | 2 | |||
304.4.i.b.273.1 | 2 | 76.7 | odd | 6 | |||
342.4.g.d.163.1 | 2 | 3.2 | odd | 2 | |||
342.4.g.d.235.1 | 2 | 57.26 | odd | 6 | |||
722.4.a.a.1.1 | 1 | 19.8 | odd | 6 | |||
722.4.a.e.1.1 | 1 | 19.11 | even | 3 |