Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,4,Mod(41,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.m (of order \(6\), 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: | \(7.43424066072\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.6 | ||
Character | \(\chi\) | \(=\) | 126.41 |
Dual form | 126.4.m.a.83.6 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.111457 | + | 5.19496i | −0.0214499 | + | 0.999770i | ||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 8.24952 | − | 14.2886i | 0.737860 | − | 1.27801i | −0.215598 | − | 0.976482i | \(-0.569170\pi\) |
0.953457 | − | 0.301528i | \(-0.0974967\pi\) | |||||||
\(6\) | −5.00191 | − | 9.10939i | −0.340337 | − | 0.619815i | ||||
\(7\) | −17.4194 | + | 6.29008i | −0.940558 | + | 0.339633i | ||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −26.9752 | − | 1.15803i | −0.999080 | − | 0.0428899i | ||||
\(10\) | 32.9981i | 1.04349i | ||||||||
\(11\) | −36.5379 | + | 21.0952i | −1.00151 | + | 0.578221i | −0.908694 | − | 0.417462i | \(-0.862920\pi\) |
−0.0928143 | + | 0.995683i | \(0.529586\pi\) | |||||||
\(12\) | 17.7729 | + | 10.7760i | 0.427551 | + | 0.259231i | ||||
\(13\) | −39.5847 | − | 22.8542i | −0.844524 | − | 0.487586i | 0.0142753 | − | 0.999898i | \(-0.495456\pi\) |
−0.858800 | + | 0.512312i | \(0.828789\pi\) | |||||||
\(14\) | 23.8812 | − | 28.3141i | 0.455894 | − | 0.540519i | ||||
\(15\) | 73.3091 | + | 44.4485i | 1.26189 | + | 0.765103i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −65.3440 | −0.932251 | −0.466125 | − | 0.884719i | \(-0.654350\pi\) | ||||
−0.466125 | + | 0.884719i | \(0.654350\pi\) | |||||||
\(18\) | 47.8804 | − | 24.9694i | 0.626973 | − | 0.326963i | ||||
\(19\) | − | 161.794i | − | 1.95359i | −0.214183 | − | 0.976794i | \(-0.568709\pi\) | ||
0.214183 | − | 0.976794i | \(-0.431291\pi\) | |||||||
\(20\) | −32.9981 | − | 57.1544i | −0.368930 | − | 0.639005i | ||||
\(21\) | −30.7352 | − | 91.1940i | −0.319379 | − | 0.947627i | ||||
\(22\) | 42.1903 | − | 73.0758i | 0.408864 | − | 0.708174i | ||||
\(23\) | 147.699 | + | 85.2741i | 1.33902 | + | 0.773081i | 0.986662 | − | 0.162785i | \(-0.0520477\pi\) |
0.352355 | + | 0.935867i | \(0.385381\pi\) | |||||||
\(24\) | −41.5597 | − | 0.891656i | −0.353472 | − | 0.00758369i | ||||
\(25\) | −73.6092 | − | 127.495i | −0.588874 | − | 1.01996i | ||||
\(26\) | 91.4169 | 0.689551 | ||||||||
\(27\) | 9.02248 | − | 140.006i | 0.0643102 | − | 0.997930i | ||||
\(28\) | −13.0493 | + | 72.9227i | −0.0880744 | + | 0.492182i | ||||
\(29\) | −171.860 | + | 99.2232i | −1.10047 | + | 0.635355i | −0.936344 | − | 0.351085i | \(-0.885813\pi\) |
−0.164123 | + | 0.986440i | \(0.552480\pi\) | |||||||
\(30\) | −171.424 | − | 3.67787i | −1.04325 | − | 0.0223828i | ||||
\(31\) | −48.4789 | − | 27.9893i | −0.280873 | − | 0.162162i | 0.352945 | − | 0.935644i | \(-0.385180\pi\) |
−0.633819 | + | 0.773482i | \(0.718513\pi\) | |||||||
\(32\) | 27.7128 | + | 16.0000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −105.516 | − | 192.164i | −0.556606 | − | 1.01368i | ||||
\(34\) | 113.179 | − | 65.3440i | 0.570885 | − | 0.329600i | ||||
\(35\) | −53.8252 | + | 300.789i | −0.259946 | + | 1.45264i | ||||
\(36\) | −57.9618 | + | 91.1286i | −0.268342 | + | 0.421892i | ||||
\(37\) | −133.655 | −0.593859 | −0.296929 | − | 0.954899i | \(-0.595963\pi\) | ||||
−0.296929 | + | 0.954899i | \(0.595963\pi\) | |||||||
\(38\) | 161.794 | + | 280.236i | 0.690697 | + | 1.19632i | ||||
\(39\) | 123.139 | − | 203.093i | 0.505589 | − | 0.833871i | ||||
\(40\) | 114.309 | + | 65.9962i | 0.451845 | + | 0.260873i | ||||
\(41\) | −9.23461 | + | 15.9948i | −0.0351757 | + | 0.0609261i | −0.883077 | − | 0.469228i | \(-0.844532\pi\) |
0.847902 | + | 0.530154i | \(0.177866\pi\) | |||||||
\(42\) | 144.429 | + | 127.217i | 0.530616 | + | 0.467383i | ||||
\(43\) | 12.1938 | + | 21.1202i | 0.0432450 | + | 0.0749025i | 0.886838 | − | 0.462081i | \(-0.152897\pi\) |
−0.843593 | + | 0.536983i | \(0.819564\pi\) | |||||||
\(44\) | 168.761i | 0.578221i | ||||||||
\(45\) | −239.079 | + | 375.884i | −0.791994 | + | 1.24519i | ||||
\(46\) | −341.096 | −1.09330 | ||||||||
\(47\) | 61.6110 | + | 106.713i | 0.191210 | + | 0.331186i | 0.945652 | − | 0.325181i | \(-0.105425\pi\) |
−0.754441 | + | 0.656368i | \(0.772092\pi\) | |||||||
\(48\) | 72.8751 | − | 40.0153i | 0.219138 | − | 0.120327i | ||||
\(49\) | 263.870 | − | 219.139i | 0.769300 | − | 0.638888i | ||||
\(50\) | 254.990 | + | 147.218i | 0.721220 | + | 0.416397i | ||||
\(51\) | 7.28305 | − | 339.460i | 0.0199967 | − | 0.932036i | ||||
\(52\) | −158.339 | + | 91.4169i | −0.422262 | + | 0.243793i | ||||
\(53\) | − | 400.837i | − | 1.03885i | −0.854515 | − | 0.519427i | \(-0.826146\pi\) | ||
0.854515 | − | 0.519427i | \(-0.173854\pi\) | |||||||
\(54\) | 124.378 | + | 251.519i | 0.313440 | + | 0.633842i | ||||
\(55\) | 696.100i | 1.70658i | ||||||||
\(56\) | −50.3207 | − | 139.355i | −0.120078 | − | 0.332538i | ||||
\(57\) | 840.514 | + | 18.0331i | 1.95314 | + | 0.0419043i | ||||
\(58\) | 198.446 | − | 343.719i | 0.449264 | − | 0.778148i | ||||
\(59\) | 114.190 | − | 197.783i | 0.251971 | − | 0.436426i | −0.712098 | − | 0.702080i | \(-0.752255\pi\) |
0.964068 | + | 0.265655i | \(0.0855881\pi\) | |||||||
\(60\) | 300.592 | − | 165.053i | 0.646772 | − | 0.355138i | ||||
\(61\) | −212.887 | + | 122.910i | −0.446842 | + | 0.257984i | −0.706496 | − | 0.707718i | \(-0.749725\pi\) |
0.259654 | + | 0.965702i | \(0.416392\pi\) | |||||||
\(62\) | 111.957 | 0.229332 | ||||||||
\(63\) | 477.175 | − | 149.504i | 0.954260 | − | 0.298979i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −653.109 | + | 377.073i | −1.24628 | + | 0.719540i | ||||
\(66\) | 374.923 | + | 227.322i | 0.699241 | + | 0.423960i | ||||
\(67\) | −466.625 | + | 808.218i | −0.850856 | + | 1.47373i | 0.0295817 | + | 0.999562i | \(0.490582\pi\) |
−0.880437 | + | 0.474163i | \(0.842751\pi\) | |||||||
\(68\) | −130.688 | + | 226.358i | −0.233063 | + | 0.403676i | ||||
\(69\) | −459.457 | + | 757.786i | −0.801625 | + | 1.32213i | ||||
\(70\) | −207.561 | − | 574.806i | −0.354403 | − | 0.981464i | ||||
\(71\) | 808.476i | 1.35139i | 0.737183 | + | 0.675693i | \(0.236156\pi\) | ||||
−0.737183 | + | 0.675693i | \(0.763844\pi\) | |||||||
\(72\) | 9.26423 | − | 215.801i | 0.0151639 | − | 0.353228i | ||||
\(73\) | − | 98.0777i | − | 0.157248i | −0.996904 | − | 0.0786241i | \(-0.974947\pi\) | ||
0.996904 | − | 0.0786241i | \(-0.0250527\pi\) | |||||||
\(74\) | 231.498 | − | 133.655i | 0.363663 | − | 0.209961i | ||||
\(75\) | 670.535 | − | 368.186i | 1.03236 | − | 0.566860i | ||||
\(76\) | −560.472 | − | 323.589i | −0.845928 | − | 0.488397i | ||||
\(77\) | 503.777 | − | 597.291i | 0.745594 | − | 0.883996i | ||||
\(78\) | −10.1891 | + | 474.907i | −0.0147908 | + | 0.689392i | ||||
\(79\) | −450.095 | − | 779.587i | −0.641008 | − | 1.11026i | −0.985208 | − | 0.171362i | \(-0.945183\pi\) |
0.344200 | − | 0.938896i | \(-0.388150\pi\) | |||||||
\(80\) | −263.985 | −0.368930 | ||||||||
\(81\) | 726.318 | + | 62.4760i | 0.996321 | + | 0.0857009i | ||||
\(82\) | − | 36.9384i | − | 0.0497459i | ||||||
\(83\) | 605.681 | + | 1049.07i | 0.800989 | + | 1.38735i | 0.918966 | + | 0.394338i | \(0.129026\pi\) |
−0.117976 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(84\) | −377.376 | − | 75.9182i | −0.490179 | − | 0.0986114i | ||||
\(85\) | −539.057 | + | 933.674i | −0.687870 | + | 1.19143i | ||||
\(86\) | −42.2405 | − | 24.3875i | −0.0529640 | − | 0.0305788i | ||||
\(87\) | −496.305 | − | 903.863i | −0.611604 | − | 1.11384i | ||||
\(88\) | −168.761 | − | 292.303i | −0.204432 | − | 0.354087i | ||||
\(89\) | −678.302 | −0.807864 | −0.403932 | − | 0.914789i | \(-0.632357\pi\) | ||||
−0.403932 | + | 0.914789i | \(0.632357\pi\) | |||||||
\(90\) | 38.2127 | − | 890.128i | 0.0447553 | − | 1.04253i | ||||
\(91\) | 833.296 | + | 149.116i | 0.959924 | + | 0.171775i | ||||
\(92\) | 590.796 | − | 341.096i | 0.669508 | − | 0.386541i | ||||
\(93\) | 150.807 | − | 248.726i | 0.168150 | − | 0.277330i | ||||
\(94\) | −213.427 | − | 123.222i | −0.234184 | − | 0.135206i | ||||
\(95\) | −2311.81 | − | 1334.73i | −2.49670 | − | 1.44147i | ||||
\(96\) | −86.2081 | + | 142.184i | −0.0916518 | + | 0.151162i | ||||
\(97\) | 749.281 | − | 432.598i | 0.784309 | − | 0.452821i | −0.0536461 | − | 0.998560i | \(-0.517084\pi\) |
0.837955 | + | 0.545739i | \(0.183751\pi\) | |||||||
\(98\) | −237.897 | + | 643.429i | −0.245217 | + | 0.663226i | ||||
\(99\) | 1010.04 | − | 526.734i | 1.02539 | − | 0.534735i | ||||
\(100\) | −588.874 | −0.588874 | ||||||||
\(101\) | −85.8176 | − | 148.640i | −0.0845463 | − | 0.146438i | 0.820652 | − | 0.571429i | \(-0.193611\pi\) |
−0.905198 | + | 0.424991i | \(0.860277\pi\) | |||||||
\(102\) | 326.845 | + | 595.244i | 0.317279 | + | 0.577823i | ||||
\(103\) | −480.335 | − | 277.322i | −0.459503 | − | 0.265294i | 0.252332 | − | 0.967641i | \(-0.418802\pi\) |
−0.711835 | + | 0.702346i | \(0.752136\pi\) | |||||||
\(104\) | 182.834 | − | 316.677i | 0.172388 | − | 0.298584i | ||||
\(105\) | −1556.58 | − | 313.144i | −1.44673 | − | 0.291045i | ||||
\(106\) | 400.837 | + | 694.271i | 0.367290 | + | 0.636165i | ||||
\(107\) | − | 379.663i | − | 0.343022i | −0.985182 | − | 0.171511i | \(-0.945135\pi\) | ||
0.985182 | − | 0.171511i | \(-0.0548649\pi\) | |||||||
\(108\) | −466.949 | − | 311.266i | −0.416039 | − | 0.277330i | ||||
\(109\) | −701.227 | −0.616196 | −0.308098 | − | 0.951355i | \(-0.599693\pi\) | ||||
−0.308098 | + | 0.951355i | \(0.599693\pi\) | |||||||
\(110\) | −696.100 | − | 1205.68i | −0.603369 | − | 1.04507i | ||||
\(111\) | 14.8968 | − | 694.333i | 0.0127382 | − | 0.593722i | ||||
\(112\) | 226.513 | + | 191.049i | 0.191102 | + | 0.161183i | ||||
\(113\) | 844.466 | + | 487.553i | 0.703015 | + | 0.405886i | 0.808469 | − | 0.588538i | \(-0.200296\pi\) |
−0.105454 | + | 0.994424i | \(0.533630\pi\) | |||||||
\(114\) | −1473.85 | + | 809.280i | −1.21086 | + | 0.664877i | ||||
\(115\) | 2436.89 | − | 1406.94i | 1.97601 | − | 1.14085i | ||||
\(116\) | 793.786i | 0.635355i | ||||||||
\(117\) | 1041.34 | + | 662.336i | 0.822835 | + | 0.523359i | ||||
\(118\) | 456.760i | 0.356340i | ||||||||
\(119\) | 1138.25 | − | 411.019i | 0.876836 | − | 0.316623i | ||||
\(120\) | −355.588 | + | 586.473i | −0.270505 | + | 0.446145i | ||||
\(121\) | 224.513 | − | 388.867i | 0.168680 | − | 0.292162i | ||||
\(122\) | 245.820 | − | 425.774i | 0.182422 | − | 0.315965i | ||||
\(123\) | −82.0631 | − | 49.7561i | −0.0601575 | − | 0.0364745i | ||||
\(124\) | −193.916 | + | 111.957i | −0.140437 | + | 0.0810811i | ||||
\(125\) | −366.583 | −0.262305 | ||||||||
\(126\) | −676.987 | + | 736.123i | −0.478657 | + | 0.520468i | ||||
\(127\) | 1119.91 | 0.782490 | 0.391245 | − | 0.920286i | \(-0.372044\pi\) | ||||
0.391245 | + | 0.920286i | \(0.372044\pi\) | |||||||
\(128\) | 110.851 | − | 64.0000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −111.078 | + | 60.9921i | −0.0758128 | + | 0.0416284i | ||||
\(130\) | 754.146 | − | 1306.22i | 0.508792 | − | 0.881253i | ||||
\(131\) | −810.040 | + | 1403.03i | −0.540256 | + | 0.935751i | 0.458633 | + | 0.888626i | \(0.348339\pi\) |
−0.998889 | + | 0.0471250i | \(0.984994\pi\) | |||||||
\(132\) | −876.708 | − | 18.8096i | −0.578088 | − | 0.0124028i | ||||
\(133\) | 1017.70 | + | 2818.36i | 0.663502 | + | 1.83746i | ||||
\(134\) | − | 1866.50i | − | 1.20329i | ||||||
\(135\) | −1926.05 | − | 1283.90i | −1.22791 | − | 0.818521i | ||||
\(136\) | − | 522.752i | − | 0.329600i | ||||||
\(137\) | 821.304 | − | 474.180i | 0.512181 | − | 0.295708i | −0.221549 | − | 0.975149i | \(-0.571111\pi\) |
0.733730 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(138\) | 38.0176 | − | 1771.98i | 0.0234512 | − | 1.09305i | ||||
\(139\) | −2707.36 | − | 1563.10i | −1.65206 | − | 0.953814i | −0.976226 | − | 0.216756i | \(-0.930452\pi\) |
−0.675829 | − | 0.737058i | \(-0.736214\pi\) | |||||||
\(140\) | 934.312 | + | 788.033i | 0.564027 | + | 0.475721i | ||||
\(141\) | −561.238 | + | 308.173i | −0.335211 | + | 0.184062i | ||||
\(142\) | −808.476 | − | 1400.32i | −0.477787 | − | 0.827552i | ||||
\(143\) | 1928.46 | 1.12773 | ||||||||
\(144\) | 199.755 | + | 383.043i | 0.115599 | + | 0.221668i | ||||
\(145\) | 3274.18i | 1.87521i | ||||||||
\(146\) | 98.0777 | + | 169.875i | 0.0555956 | + | 0.0962945i | ||||
\(147\) | 1109.01 | + | 1395.22i | 0.622240 | + | 0.782827i | ||||
\(148\) | −267.310 | + | 462.995i | −0.148465 | + | 0.257148i | ||||
\(149\) | −1674.91 | − | 967.009i | −0.920898 | − | 0.531681i | −0.0369767 | − | 0.999316i | \(-0.511773\pi\) |
−0.883922 | + | 0.467635i | \(0.845106\pi\) | |||||||
\(150\) | −793.214 | + | 1308.25i | −0.431771 | + | 0.712122i | ||||
\(151\) | 1160.63 | + | 2010.27i | 0.625501 | + | 1.08340i | 0.988444 | + | 0.151588i | \(0.0484387\pi\) |
−0.362943 | + | 0.931811i | \(0.618228\pi\) | |||||||
\(152\) | 1294.35 | 0.690697 | ||||||||
\(153\) | 1762.67 | + | 75.6703i | 0.931393 | + | 0.0399842i | ||||
\(154\) | −275.277 | + | 1538.32i | −0.144042 | + | 0.804942i | ||||
\(155\) | −799.855 | + | 461.797i | −0.414490 | + | 0.239306i | ||||
\(156\) | −457.259 | − | 832.752i | −0.234680 | − | 0.427394i | ||||
\(157\) | −991.971 | − | 572.715i | −0.504254 | − | 0.291131i | 0.226214 | − | 0.974078i | \(-0.427365\pi\) |
−0.730469 | + | 0.682946i | \(0.760698\pi\) | |||||||
\(158\) | 1559.17 | + | 900.190i | 0.785071 | + | 0.453261i | ||||
\(159\) | 2082.33 | + | 44.6761i | 1.03861 | + | 0.0222833i | ||||
\(160\) | 457.235 | − | 263.985i | 0.225922 | − | 0.130436i | ||||
\(161\) | −3109.21 | − | 556.383i | −1.52199 | − | 0.272355i | ||||
\(162\) | −1320.50 | + | 618.106i | −0.640419 | + | 0.299772i | ||||
\(163\) | 1808.95 | 0.869250 | 0.434625 | − | 0.900611i | \(-0.356881\pi\) | ||||
0.434625 | + | 0.900611i | \(0.356881\pi\) | |||||||
\(164\) | 36.9384 | + | 63.9792i | 0.0175878 | + | 0.0304630i | ||||
\(165\) | −3616.21 | − | 77.5852i | −1.70619 | − | 0.0366061i | ||||
\(166\) | −2098.14 | − | 1211.36i | −0.981008 | − | 0.566385i | ||||
\(167\) | 1152.46 | − | 1996.12i | 0.534013 | − | 0.924938i | −0.465197 | − | 0.885207i | \(-0.654017\pi\) |
0.999210 | − | 0.0397312i | \(-0.0126502\pi\) | |||||||
\(168\) | 729.552 | − | 245.882i | 0.335037 | − | 0.112918i | ||||
\(169\) | −53.8688 | − | 93.3034i | −0.0245192 | − | 0.0424686i | ||||
\(170\) | − | 2156.23i | − | 0.972795i | ||||||
\(171\) | −187.362 | + | 4364.43i | −0.0837892 | + | 1.95179i | ||||
\(172\) | 97.5502 | 0.0432450 | ||||||||
\(173\) | −585.924 | − | 1014.85i | −0.257497 | − | 0.445998i | 0.708074 | − | 0.706139i | \(-0.249564\pi\) |
−0.965571 | + | 0.260140i | \(0.916231\pi\) | |||||||
\(174\) | 1763.49 | + | 1069.23i | 0.768332 | + | 0.465852i | ||||
\(175\) | 2084.18 | + | 1757.87i | 0.900281 | + | 0.759330i | ||||
\(176\) | 584.607 | + | 337.523i | 0.250377 | + | 0.144555i | ||||
\(177\) | 1014.75 | + | 615.256i | 0.430921 | + | 0.261274i | ||||
\(178\) | 1174.85 | − | 678.302i | 0.494714 | − | 0.285623i | ||||
\(179\) | − | 534.622i | − | 0.223238i | −0.993751 | − | 0.111619i | \(-0.964396\pi\) | ||
0.993751 | − | 0.111619i | \(-0.0356036\pi\) | |||||||
\(180\) | 823.942 | + | 1579.96i | 0.341183 | + | 0.654241i | ||||
\(181\) | − | 238.167i | − | 0.0978058i | −0.998804 | − | 0.0489029i | \(-0.984428\pi\) | ||
0.998804 | − | 0.0489029i | \(-0.0155725\pi\) | |||||||
\(182\) | −1592.43 | + | 575.020i | −0.648563 | + | 0.234194i | ||||
\(183\) | −614.786 | − | 1119.64i | −0.248340 | − | 0.452273i | ||||
\(184\) | −682.193 | + | 1181.59i | −0.273326 | + | 0.473414i | ||||
\(185\) | −1102.59 | + | 1909.74i | −0.438185 | + | 0.758958i | ||||
\(186\) | −12.4784 | + | 581.613i | −0.00491915 | + | 0.229279i | ||||
\(187\) | 2387.54 | − | 1378.44i | 0.933657 | − | 0.539047i | ||||
\(188\) | 492.888 | 0.191210 | ||||||||
\(189\) | 723.481 | + | 2495.56i | 0.278442 | + | 0.960453i | ||||
\(190\) | 5338.90 | 2.03855 | ||||||||
\(191\) | −273.555 | + | 157.937i | −0.103632 | + | 0.0598321i | −0.550920 | − | 0.834558i | \(-0.685723\pi\) |
0.447288 | + | 0.894390i | \(0.352390\pi\) | |||||||
\(192\) | 7.13325 | − | 332.477i | 0.00268124 | − | 0.124971i | ||||
\(193\) | 680.432 | − | 1178.54i | 0.253775 | − | 0.439551i | −0.710787 | − | 0.703407i | \(-0.751661\pi\) |
0.964562 | + | 0.263856i | \(0.0849944\pi\) | |||||||
\(194\) | −865.195 | + | 1498.56i | −0.320193 | + | 0.554590i | ||||
\(195\) | −1886.08 | − | 3434.90i | −0.692642 | − | 1.26143i | ||||
\(196\) | −231.379 | − | 1352.35i | −0.0843219 | − | 0.492839i | ||||
\(197\) | − | 706.051i | − | 0.255350i | −0.991816 | − | 0.127675i | \(-0.959249\pi\) | ||
0.991816 | − | 0.127675i | \(-0.0407515\pi\) | |||||||
\(198\) | −1222.72 | + | 1922.37i | −0.438861 | + | 0.689986i | ||||
\(199\) | 24.9282i | 0.00887998i | 0.999990 | + | 0.00443999i | \(0.00141330\pi\) | ||||
−0.999990 | + | 0.00443999i | \(0.998587\pi\) | |||||||
\(200\) | 1019.96 | − | 588.874i | 0.360610 | − | 0.208198i | ||||
\(201\) | −4146.65 | − | 2514.18i | −1.45514 | − | 0.882271i | ||||
\(202\) | 297.281 | + | 171.635i | 0.103548 | + | 0.0597832i | ||||
\(203\) | 2369.57 | − | 2809.42i | 0.819266 | − | 0.971343i | ||||
\(204\) | −1161.36 | − | 704.148i | −0.398584 | − | 0.241668i | ||||
\(205\) | 152.362 | + | 263.899i | 0.0519094 | + | 0.0899098i | ||||
\(206\) | 1109.29 | 0.375183 | ||||||||
\(207\) | −3885.45 | − | 2471.32i | −1.30463 | − | 0.829800i | ||||
\(208\) | 731.335i | 0.243793i | ||||||||
\(209\) | 3413.08 | + | 5911.63i | 1.12961 | + | 1.95653i | ||||
\(210\) | 3009.23 | − | 1014.20i | 0.988840 | − | 0.333270i | ||||
\(211\) | 1612.49 | − | 2792.92i | 0.526107 | − | 0.911243i | −0.473431 | − | 0.880831i | \(-0.656985\pi\) |
0.999537 | − | 0.0304125i | \(-0.00968208\pi\) | |||||||
\(212\) | −1388.54 | − | 801.675i | −0.449837 | − | 0.259713i | ||||
\(213\) | −4200.00 | − | 90.1103i | −1.35108 | − | 0.0289871i | ||||
\(214\) | 379.663 | + | 657.595i | 0.121277 | + | 0.210057i | ||||
\(215\) | 402.371 | 0.127635 | ||||||||
\(216\) | 1120.05 | + | 72.1798i | 0.352822 | + | 0.0227371i | ||||
\(217\) | 1020.53 | + | 182.620i | 0.319253 | + | 0.0571293i | ||||
\(218\) | 1214.56 | − | 701.227i | 0.377342 | − | 0.217858i | ||||
\(219\) | 509.509 | + | 10.9314i | 0.157212 | + | 0.00337296i | ||||
\(220\) | 2411.36 | + | 1392.20i | 0.738973 | + | 0.426646i | ||||
\(221\) | 2586.62 | + | 1493.39i | 0.787308 | + | 0.454553i | ||||
\(222\) | 668.531 | + | 1217.52i | 0.202112 | + | 0.368083i | ||||
\(223\) | −3385.12 | + | 1954.40i | −1.01652 | + | 0.586890i | −0.913095 | − | 0.407747i | \(-0.866314\pi\) |
−0.103428 | + | 0.994637i | \(0.532981\pi\) | |||||||
\(224\) | −583.381 | − | 104.394i | −0.174013 | − | 0.0311390i | ||||
\(225\) | 1837.98 | + | 3524.44i | 0.544586 | + | 1.04428i | ||||
\(226\) | −1950.21 | −0.574009 | ||||||||
\(227\) | −943.561 | − | 1634.30i | −0.275887 | − | 0.477850i | 0.694471 | − | 0.719520i | \(-0.255638\pi\) |
−0.970359 | + | 0.241670i | \(0.922305\pi\) | |||||||
\(228\) | 1743.50 | − | 2875.56i | 0.506429 | − | 0.835257i | ||||
\(229\) | −1330.72 | − | 768.290i | −0.384001 | − | 0.221703i | 0.295557 | − | 0.955325i | \(-0.404495\pi\) |
−0.679558 | + | 0.733622i | \(0.737828\pi\) | |||||||
\(230\) | −2813.88 | + | 4873.78i | −0.806704 | + | 1.39725i | ||||
\(231\) | 3046.75 | + | 2683.67i | 0.867799 | + | 0.764385i | ||||
\(232\) | −793.786 | − | 1374.88i | −0.224632 | − | 0.389074i | ||||
\(233\) | − | 4906.62i | − | 1.37959i | −0.724007 | − | 0.689793i | \(-0.757702\pi\) | ||
0.724007 | − | 0.689793i | \(-0.242298\pi\) | |||||||
\(234\) | −2465.99 | − | 105.863i | −0.688917 | − | 0.0295748i | ||||
\(235\) | 2033.05 | 0.564346 | ||||||||
\(236\) | −456.760 | − | 791.131i | −0.125985 | − | 0.218213i | ||||
\(237\) | 4100.09 | − | 2251.33i | 1.12375 | − | 0.617046i | ||||
\(238\) | −1560.49 | + | 1850.16i | −0.425007 | + | 0.503899i | ||||
\(239\) | −2270.06 | − | 1310.62i | −0.614384 | − | 0.354715i | 0.160295 | − | 0.987069i | \(-0.448755\pi\) |
−0.774679 | + | 0.632354i | \(0.782089\pi\) | |||||||
\(240\) | 29.4229 | − | 1371.39i | 0.00791351 | − | 0.368845i | ||||
\(241\) | 3017.49 | − | 1742.15i | 0.806530 | − | 0.465650i | −0.0392193 | − | 0.999231i | \(-0.512487\pi\) |
0.845749 | + | 0.533580i | \(0.179154\pi\) | |||||||
\(242\) | 898.051i | 0.238549i | ||||||||
\(243\) | −405.513 | + | 3766.23i | −0.107052 | + | 0.994253i | ||||
\(244\) | 983.282i | 0.257984i | ||||||||
\(245\) | −954.384 | − | 5578.12i | −0.248871 | − | 1.45458i | ||||
\(246\) | 191.894 | + | 4.11704i | 0.0497345 | + | 0.00106705i | ||||
\(247\) | −3697.68 | + | 6404.58i | −0.952542 | + | 1.64985i | ||||
\(248\) | 223.914 | − | 387.831i | 0.0573330 | − | 0.0993037i | ||||
\(249\) | −5517.38 | + | 3029.56i | −1.40422 | + | 0.771046i | ||||
\(250\) | 634.940 | − | 366.583i | 0.160628 | − | 0.0927389i | ||||
\(251\) | −2998.70 | −0.754089 | −0.377045 | − | 0.926195i | \(-0.623060\pi\) | ||||
−0.377045 | + | 0.926195i | \(0.623060\pi\) | |||||||
\(252\) | 436.453 | − | 1951.99i | 0.109103 | − | 0.487951i | ||||
\(253\) | −7195.49 | −1.78805 | ||||||||
\(254\) | −1939.75 | + | 1119.91i | −0.479176 | + | 0.276652i | ||||
\(255\) | −4790.32 | − | 2904.44i | −1.17640 | − | 0.713268i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.14903 | + | 15.8466i | −0.00222063 | + | 0.00384624i | −0.867134 | − | 0.498076i | \(-0.834040\pi\) |
0.864913 | + | 0.501922i | \(0.167374\pi\) | |||||||
\(258\) | 131.400 | − | 216.719i | 0.0317078 | − | 0.0522959i | ||||
\(259\) | 2328.19 | − | 840.702i | 0.558559 | − | 0.201694i | ||||
\(260\) | 3016.58i | 0.719540i | ||||||||
\(261\) | 4750.84 | − | 2477.54i | 1.12670 | − | 0.587571i | ||||
\(262\) | − | 3240.16i | − | 0.764037i | ||||||
\(263\) | −5374.18 | + | 3102.78i | −1.26002 | + | 0.727475i | −0.973079 | − | 0.230473i | \(-0.925973\pi\) |
−0.286944 | + | 0.957947i | \(0.592639\pi\) | |||||||
\(264\) | 1537.31 | − | 844.129i | 0.358390 | − | 0.196790i | ||||
\(265\) | −5727.40 | − | 3306.72i | −1.32767 | − | 0.766528i | ||||
\(266\) | −4581.06 | − | 3863.84i | −1.05595 | − | 0.890628i | ||||
\(267\) | 75.6015 | − | 3523.75i | 0.0173286 | − | 0.807678i | ||||
\(268\) | 1866.50 | + | 3232.87i | 0.425428 | + | 0.736863i | ||||
\(269\) | 330.596 | 0.0749323 | 0.0374661 | − | 0.999298i | \(-0.488071\pi\) | ||||
0.0374661 | + | 0.999298i | \(0.488071\pi\) | |||||||
\(270\) | 4619.92 | + | 297.724i | 1.04133 | + | 0.0671072i | ||||
\(271\) | 1365.01i | 0.305971i | 0.988228 | + | 0.152986i | \(0.0488888\pi\) | ||||
−0.988228 | + | 0.152986i | \(0.951111\pi\) | |||||||
\(272\) | 522.752 | + | 905.434i | 0.116531 | + | 0.201838i | ||||
\(273\) | −867.526 | + | 4312.31i | −0.192326 | + | 0.956019i | ||||
\(274\) | −948.361 | + | 1642.61i | −0.209097 | + | 0.362167i | ||||
\(275\) | 5379.05 | + | 3105.60i | 1.17952 | + | 0.680999i | ||||
\(276\) | 1706.13 | + | 3107.18i | 0.372091 | + | 0.677645i | ||||
\(277\) | −2448.77 | − | 4241.40i | −0.531165 | − | 0.920004i | −0.999338 | − | 0.0363677i | \(-0.988421\pi\) |
0.468174 | − | 0.883636i | \(-0.344912\pi\) | |||||||
\(278\) | 6252.39 | 1.34890 | ||||||||
\(279\) | 1275.31 | + | 811.156i | 0.273660 | + | 0.174060i | ||||
\(280\) | −2406.31 | − | 430.601i | −0.513587 | − | 0.0919048i | ||||
\(281\) | 2204.08 | − | 1272.53i | 0.467917 | − | 0.270152i | −0.247450 | − | 0.968901i | \(-0.579593\pi\) |
0.715367 | + | 0.698749i | \(0.246259\pi\) | |||||||
\(282\) | 663.921 | − | 1095.01i | 0.140198 | − | 0.231230i | ||||
\(283\) | 540.515 | + | 312.067i | 0.113535 | + | 0.0655492i | 0.555692 | − | 0.831388i | \(-0.312453\pi\) |
−0.442157 | + | 0.896937i | \(0.645787\pi\) | |||||||
\(284\) | 2800.64 | + | 1616.95i | 0.585168 | + | 0.337847i | ||||
\(285\) | 7191.51 | − | 11861.0i | 1.49470 | − | 2.46521i | ||||
\(286\) | −3340.18 | + | 1928.46i | −0.690591 | + | 0.398713i | ||||
\(287\) | 60.2525 | − | 336.706i | 0.0123923 | − | 0.0692513i | ||||
\(288\) | −729.029 | − | 463.695i | −0.149161 | − | 0.0948732i | ||||
\(289\) | −643.156 | −0.130909 | ||||||||
\(290\) | −3274.18 | − | 5671.04i | −0.662987 | − | 1.14833i | ||||
\(291\) | 2163.81 | + | 3940.70i | 0.435894 | + | 0.793842i | ||||
\(292\) | −339.751 | − | 196.155i | −0.0680905 | − | 0.0393121i | ||||
\(293\) | −845.058 | + | 1463.68i | −0.168494 | + | 0.291841i | −0.937891 | − | 0.346931i | \(-0.887224\pi\) |
0.769396 | + | 0.638772i | \(0.220557\pi\) | |||||||
\(294\) | −3316.07 | − | 1307.58i | −0.657814 | − | 0.259386i | ||||
\(295\) | −1884.02 | − | 3263.23i | −0.371838 | − | 0.644042i | ||||
\(296\) | − | 1069.24i | − | 0.209961i | ||||||
\(297\) | 2623.78 | + | 5305.85i | 0.512617 | + | 1.03662i | ||||
\(298\) | 3868.04 | 0.751910 | ||||||||
\(299\) | −3897.75 | − | 6751.09i | −0.753888 | − | 1.30577i | ||||
\(300\) | 65.6341 | − | 3059.17i | 0.0126313 | − | 0.588738i | ||||
\(301\) | −345.256 | − | 291.202i | −0.0661137 | − | 0.0557627i | ||||
\(302\) | −4020.54 | − | 2321.26i | −0.766079 | − | 0.442296i | ||||
\(303\) | 781.746 | − | 429.252i | 0.148218 | − | 0.0813857i | ||||
\(304\) | −2241.89 | + | 1294.35i | −0.422964 | + | 0.244198i | ||||
\(305\) | 4055.80i | 0.761425i | ||||||||
\(306\) | −3128.70 | + | 1631.60i | −0.584496 | + | 0.304812i | ||||
\(307\) | − | 6791.33i | − | 1.26255i | −0.775561 | − | 0.631273i | \(-0.782533\pi\) | ||
0.775561 | − | 0.631273i | \(-0.217467\pi\) | |||||||
\(308\) | −1061.52 | − | 2939.72i | −0.196383 | − | 0.543851i | ||||
\(309\) | 1494.21 | − | 2464.41i | 0.275089 | − | 0.453707i | ||||
\(310\) | 923.594 | − | 1599.71i | 0.169215 | − | 0.293089i | ||||
\(311\) | 2070.08 | − | 3585.49i | 0.377440 | − | 0.653744i | −0.613249 | − | 0.789889i | \(-0.710138\pi\) |
0.990689 | + | 0.136145i | \(0.0434713\pi\) | |||||||
\(312\) | 1624.75 | + | 985.110i | 0.294818 | + | 0.178753i | ||||
\(313\) | −6079.07 | + | 3509.75i | −1.09779 | + | 0.633811i | −0.935641 | − | 0.352954i | \(-0.885177\pi\) |
−0.162153 | + | 0.986766i | \(0.551844\pi\) | |||||||
\(314\) | 2290.86 | 0.411722 | ||||||||
\(315\) | 1800.26 | − | 8051.49i | 0.322011 | − | 1.44016i | ||||
\(316\) | −3600.76 | −0.641008 | ||||||||
\(317\) | 4218.89 | − | 2435.78i | 0.747497 | − | 0.431567i | −0.0772920 | − | 0.997008i | \(-0.524627\pi\) |
0.824789 | + | 0.565441i | \(0.191294\pi\) | |||||||
\(318\) | −3651.38 | + | 2004.95i | −0.643897 | + | 0.353560i | ||||
\(319\) | 4186.26 | − | 7250.82i | 0.734751 | − | 1.27263i | ||||
\(320\) | −527.969 | + | 914.470i | −0.0922325 | + | 0.159751i | ||||
\(321\) | 1972.33 | + | 42.3160i | 0.342943 | + | 0.00735779i | ||||
\(322\) | 5941.69 | − | 2145.52i | 1.02831 | − | 0.371321i | ||||
\(323\) | 10572.3i | 1.82123i | ||||||||
\(324\) | 1669.06 | − | 2391.09i | 0.286190 | − | 0.409994i | ||||
\(325\) | 6729.13i | 1.14851i | ||||||||
\(326\) | −3133.19 | + | 1808.95i | −0.532305 | + | 0.307326i | ||||
\(327\) | 78.1567 | − | 3642.85i | 0.0132174 | − | 0.616054i | ||||
\(328\) | −127.958 | − | 73.8768i | −0.0215406 | − | 0.0124365i | ||||
\(329\) | −1744.46 | − | 1471.34i | −0.292326 | − | 0.246559i | ||||
\(330\) | 6341.05 | − | 3481.83i | 1.05777 | − | 0.580813i | ||||
\(331\) | −3117.40 | − | 5399.50i | −0.517667 | − | 0.896626i | −0.999789 | − | 0.0205218i | \(-0.993467\pi\) |
0.482122 | − | 0.876104i | \(-0.339866\pi\) | |||||||
\(332\) | 4845.45 | 0.800989 | ||||||||
\(333\) | 3605.37 | + | 154.777i | 0.593312 | + | 0.0254706i | ||||
\(334\) | 4609.85i | 0.755209i | ||||||||
\(335\) | 7698.87 | + | 13334.8i | 1.25562 | + | 2.17480i | ||||
\(336\) | −1017.74 | + | 1155.43i | −0.165245 | + | 0.187601i | ||||
\(337\) | −1295.87 | + | 2244.51i | −0.209467 | + | 0.362808i | −0.951547 | − | 0.307504i | \(-0.900506\pi\) |
0.742080 | + | 0.670312i | \(0.233840\pi\) | |||||||
\(338\) | 186.607 | + | 107.738i | 0.0300298 | + | 0.0173377i | ||||
\(339\) | −2626.94 | + | 4332.62i | −0.420872 | + | 0.694147i | ||||
\(340\) | 2156.23 | + | 3734.70i | 0.343935 | + | 0.595713i | ||||
\(341\) | 2361.76 | 0.375063 | ||||||||
\(342\) | −4039.90 | − | 7746.77i | −0.638752 | − | 1.22485i | ||||
\(343\) | −3218.05 | + | 5477.02i | −0.506584 | + | 0.862191i | ||||
\(344\) | −168.962 | + | 97.5502i | −0.0264820 | + | 0.0152894i | ||||
\(345\) | 7037.39 | + | 12816.4i | 1.09820 | + | 2.00003i | ||||
\(346\) | 2029.70 | + | 1171.85i | 0.315368 | + | 0.182078i | ||||
\(347\) | −552.196 | − | 318.811i | −0.0854278 | − | 0.0493218i | 0.456678 | − | 0.889632i | \(-0.349039\pi\) |
−0.542105 | + | 0.840311i | \(0.682373\pi\) | |||||||
\(348\) | −4123.68 | − | 88.4730i | −0.635209 | − | 0.0136283i | ||||
\(349\) | −2436.50 | + | 1406.71i | −0.373704 | + | 0.215758i | −0.675076 | − | 0.737749i | \(-0.735889\pi\) |
0.301371 | + | 0.953507i | \(0.402556\pi\) | |||||||
\(350\) | −5367.78 | − | 960.547i | −0.819771 | − | 0.146695i | ||||
\(351\) | −3556.87 | + | 5335.88i | −0.540889 | + | 0.811419i | ||||
\(352\) | −1350.09 | −0.204432 | ||||||||
\(353\) | 920.770 | + | 1594.82i | 0.138832 | + | 0.240464i | 0.927055 | − | 0.374926i | \(-0.122332\pi\) |
−0.788223 | + | 0.615390i | \(0.788999\pi\) | |||||||
\(354\) | −2372.85 | − | 50.9090i | −0.356258 | − | 0.00764346i | ||||
\(355\) | 11552.0 | + | 6669.54i | 1.72709 | + | 0.997134i | ||||
\(356\) | −1356.60 | + | 2349.71i | −0.201966 | + | 0.349815i | ||||
\(357\) | 2008.36 | + | 5958.99i | 0.297742 | + | 0.883426i | ||||
\(358\) | 534.622 | + | 925.993i | 0.0789264 | + | 0.136705i | ||||
\(359\) | 13045.6i | 1.91789i | 0.283599 | + | 0.958943i | \(0.408471\pi\) | ||||
−0.283599 | + | 0.958943i | \(0.591529\pi\) | |||||||
\(360\) | −3007.07 | − | 1912.63i | −0.440240 | − | 0.280012i | ||||
\(361\) | −19318.4 | −2.81650 | ||||||||
\(362\) | 238.167 | + | 412.518i | 0.0345796 | + | 0.0598936i | ||||
\(363\) | 1995.13 | + | 1209.68i | 0.288476 | + | 0.174908i | ||||
\(364\) | 2183.14 | − | 2588.39i | 0.314362 | − | 0.372716i | ||||
\(365\) | −1401.39 | − | 809.094i | −0.200965 | − | 0.116027i | ||||
\(366\) | 2184.48 | + | 1324.48i | 0.311979 | + | 0.189158i | ||||
\(367\) | 6006.43 | − | 3467.82i | 0.854314 | − | 0.493238i | −0.00779004 | − | 0.999970i | \(-0.502480\pi\) |
0.862104 | + | 0.506731i | \(0.169146\pi\) | |||||||
\(368\) | − | 2728.77i | − | 0.386541i | ||||||
\(369\) | 267.627 | − | 420.768i | 0.0377564 | − | 0.0593613i | ||||
\(370\) | − | 4410.37i | − | 0.619687i | ||||||
\(371\) | 2521.30 | + | 6982.34i | 0.352828 | + | 0.977102i | ||||
\(372\) | −560.000 | − | 1019.86i | −0.0780501 | − | 0.142143i | ||||
\(373\) | 5686.57 | − | 9849.43i | 0.789382 | − | 1.36725i | −0.136964 | − | 0.990576i | \(-0.543735\pi\) |
0.926346 | − | 0.376674i | \(-0.122932\pi\) | |||||||
\(374\) | −2756.89 | + | 4775.07i | −0.381164 | + | 0.660195i | ||||
\(375\) | 40.8582 | − | 1904.38i | 0.00562642 | − | 0.262245i | ||||
\(376\) | −853.707 | + | 492.888i | −0.117092 | + | 0.0676031i | ||||
\(377\) | 9070.68 | 1.23916 | ||||||||
\(378\) | −3748.67 | − | 3598.96i | −0.510082 | − | 0.489711i | ||||
\(379\) | 9779.96 | 1.32549 | 0.662747 | − | 0.748843i | \(-0.269390\pi\) | ||||
0.662747 | + | 0.748843i | \(0.269390\pi\) | |||||||
\(380\) | −9247.25 | + | 5338.90i | −1.24835 | + | 0.720737i | ||||
\(381\) | −124.822 | + | 5817.90i | −0.0167843 | + | 0.782310i | ||||
\(382\) | 315.874 | − | 547.111i | 0.0423077 | − | 0.0732791i | ||||
\(383\) | −4830.39 | + | 8366.47i | −0.644442 | + | 1.11621i | 0.339988 | + | 0.940430i | \(0.389577\pi\) |
−0.984430 | + | 0.175776i | \(0.943756\pi\) | |||||||
\(384\) | 320.122 | + | 583.001i | 0.0425421 | + | 0.0774769i | ||||
\(385\) | −4378.53 | − | 12125.6i | −0.579612 | − | 1.60514i | ||||
\(386\) | 2721.73i | 0.358892i | ||||||||
\(387\) | −304.471 | − | 583.842i | −0.0399926 | − | 0.0766883i | ||||
\(388\) | − | 3460.78i | − | 0.452821i | ||||||
\(389\) | 5033.86 | − | 2906.30i | 0.656110 | − | 0.378805i | −0.134683 | − | 0.990889i | \(-0.543002\pi\) |
0.790793 | + | 0.612083i | \(0.209668\pi\) | |||||||
\(390\) | 6701.69 | + | 4063.34i | 0.870137 | + | 0.527578i | ||||
\(391\) | −9651.25 | − | 5572.15i | −1.24830 | − | 0.720706i | ||||
\(392\) | 1753.11 | + | 2110.96i | 0.225881 | + | 0.271988i | ||||
\(393\) | −7198.40 | − | 4364.50i | −0.923947 | − | 0.560203i | ||||
\(394\) | 706.051 | + | 1222.92i | 0.0902800 | + | 0.156370i | ||||
\(395\) | −14852.3 | −1.89190 | ||||||||
\(396\) | 195.430 | − | 4552.36i | 0.0247999 | − | 0.577689i | ||||
\(397\) | − | 6603.43i | − | 0.834803i | −0.908722 | − | 0.417402i | \(-0.862941\pi\) | ||
0.908722 | − | 0.417402i | \(-0.137059\pi\) | |||||||
\(398\) | −24.9282 | − | 43.1770i | −0.00313955 | − | 0.00543786i | ||||
\(399\) | −14754.7 | + | 4972.78i | −1.85127 | + | 0.623936i | ||||
\(400\) | −1177.75 | + | 2039.92i | −0.147218 | + | 0.254990i | ||||
\(401\) | 12295.6 | + | 7098.88i | 1.53121 | + | 0.884042i | 0.999307 | + | 0.0372347i | \(0.0118549\pi\) |
0.531899 | + | 0.846808i | \(0.321478\pi\) | |||||||
\(402\) | 9696.39 | + | 208.034i | 1.20301 | + | 0.0258105i | ||||
\(403\) | 1279.35 | + | 2215.90i | 0.158136 | + | 0.273900i | ||||
\(404\) | −686.541 | −0.0845463 | ||||||||
\(405\) | 6884.47 | − | 9862.66i | 0.844672 | − | 1.21007i | ||||
\(406\) | −1294.79 | + | 7235.62i | −0.158274 | + | 0.884478i | ||||
\(407\) | 4883.48 | − | 2819.48i | 0.594755 | − | 0.343382i | ||||
\(408\) | 2715.68 | + | 58.2644i | 0.329525 | + | 0.00706990i | ||||
\(409\) | 12573.0 | + | 7259.05i | 1.52004 | + | 0.877597i | 0.999721 | + | 0.0236262i | \(0.00752116\pi\) |
0.520321 | + | 0.853971i | \(0.325812\pi\) | |||||||
\(410\) | −527.798 | − | 304.724i | −0.0635758 | − | 0.0367055i | ||||
\(411\) | 2371.81 | + | 4319.49i | 0.284653 | + | 0.518406i | ||||
\(412\) | −1921.34 | + | 1109.29i | −0.229751 | + | 0.132647i | ||||
\(413\) | −745.048 | + | 4163.52i | −0.0887686 | + | 0.496061i | ||||
\(414\) | 9201.12 | + | 394.999i | 1.09230 | + | 0.0468917i | ||||
\(415\) | 19986.3 | 2.36407 | ||||||||
\(416\) | −731.335 | − | 1266.71i | −0.0861939 | − | 0.149292i | ||||
\(417\) | 8421.98 | − | 13890.4i | 0.989031 | − | 1.63122i | ||||
\(418\) | −11823.3 | − | 6826.16i | −1.38348 | − | 0.798752i | ||||
\(419\) | 709.447 | − | 1228.80i | 0.0827178 | − | 0.143271i | −0.821699 | − | 0.569922i | \(-0.806973\pi\) |
0.904416 | + | 0.426651i | \(0.140307\pi\) | |||||||
\(420\) | −4197.93 | + | 4765.88i | −0.487710 | + | 0.553693i | ||||
\(421\) | −2315.86 | − | 4011.18i | −0.268095 | − | 0.464354i | 0.700275 | − | 0.713873i | \(-0.253061\pi\) |
−0.968370 | + | 0.249519i | \(0.919727\pi\) | |||||||
\(422\) | 6449.97i | 0.744027i | ||||||||
\(423\) | −1538.39 | − | 2949.96i | −0.176830 | − | 0.339082i | ||||
\(424\) | 3206.70 | 0.367290 | ||||||||
\(425\) | 4809.92 | + | 8331.03i | 0.548978 | + | 0.950857i | ||||
\(426\) | 7364.72 | − | 4043.92i | 0.837610 | − | 0.459927i | ||||
\(427\) | 2935.24 | − | 3480.10i | 0.332661 | − | 0.394411i | ||||
\(428\) | −1315.19 | − | 759.325i | −0.148533 | − | 0.0857555i | ||||
\(429\) | −214.940 | + | 10018.2i | −0.0241897 | + | 1.12747i | ||||
\(430\) | −696.927 | + | 402.371i | −0.0781601 | + | 0.0451257i | ||||
\(431\) | − | 7638.31i | − | 0.853653i | −0.904333 | − | 0.426827i | \(-0.859631\pi\) | ||
0.904333 | − | 0.426827i | \(-0.140369\pi\) | |||||||
\(432\) | −2012.16 | + | 995.026i | −0.224097 | + | 0.110818i | ||||
\(433\) | 930.244i | 0.103244i | 0.998667 | + | 0.0516220i | \(0.0164391\pi\) | ||||
−0.998667 | + | 0.0516220i | \(0.983561\pi\) | |||||||
\(434\) | −1950.23 | + | 704.220i | −0.215700 | + | 0.0778886i | ||||
\(435\) | −17009.2 | − | 364.930i | −1.87478 | − | 0.0402231i | ||||
\(436\) | −1402.45 | + | 2429.12i | −0.154049 | + | 0.266821i | ||||
\(437\) | 13796.9 | − | 23896.9i | 1.51028 | − | 2.61588i | ||||
\(438\) | −893.427 | + | 490.575i | −0.0974648 | + | 0.0535173i | ||||
\(439\) | −14238.8 | + | 8220.78i | −1.54802 | + | 0.893751i | −0.549728 | + | 0.835343i | \(0.685269\pi\) |
−0.998293 | + | 0.0584071i | \(0.981398\pi\) | |||||||
\(440\) | −5568.80 | −0.603369 | ||||||||
\(441\) | −7371.70 | + | 5605.73i | −0.795993 | + | 0.605305i | ||||
\(442\) | −5973.55 | −0.642834 | ||||||||
\(443\) | −6731.30 | + | 3886.32i | −0.721927 | + | 0.416805i | −0.815462 | − | 0.578811i | \(-0.803517\pi\) |
0.0935343 | + | 0.995616i | \(0.470184\pi\) | |||||||
\(444\) | −2375.45 | − | 1440.27i | −0.253905 | − | 0.153946i | ||||
\(445\) | −5595.67 | + | 9691.98i | −0.596090 | + | 1.03246i | ||||
\(446\) | 3908.80 | − | 6770.25i | 0.414994 | − | 0.718790i | ||||
\(447\) | 5210.25 | − | 8593.30i | 0.551312 | − | 0.909282i | ||||
\(448\) | 1114.84 | − | 402.565i | 0.117570 | − | 0.0424541i | ||||
\(449\) | − | 12669.0i | − | 1.33160i | −0.746130 | − | 0.665800i | \(-0.768090\pi\) | ||
0.746130 | − | 0.665800i | \(-0.231910\pi\) | |||||||
\(450\) | −6707.91 | − | 4266.52i | −0.702697 | − | 0.446946i | ||||
\(451\) | − | 779.222i | − | 0.0813573i | ||||||
\(452\) | 3377.87 | − | 1950.21i | 0.351508 | − | 0.202943i | ||||
\(453\) | −10572.6 | + | 5805.36i | −1.09657 | + | 0.602118i | ||||
\(454\) | 3268.59 | + | 1887.12i | 0.337891 | + | 0.195082i | ||||
\(455\) | 9004.94 | − | 10676.5i | 0.927820 | − | 1.10005i | ||||
\(456\) | −144.265 | + | 6724.11i | −0.0148154 | + | 0.690538i | ||||
\(457\) | 3159.06 | + | 5471.65i | 0.323358 | + | 0.560072i | 0.981179 | − | 0.193102i | \(-0.0618550\pi\) |
−0.657821 | + | 0.753174i | \(0.728522\pi\) | |||||||
\(458\) | 3073.16 | 0.313535 | ||||||||
\(459\) | −589.565 | + | 9148.54i | −0.0599533 | + | 0.930321i | ||||
\(460\) | − | 11255.5i | − | 1.14085i | ||||||
\(461\) | −1951.76 | − | 3380.55i | −0.197186 | − | 0.341535i | 0.750429 | − | 0.660951i | \(-0.229847\pi\) |
−0.947615 | + | 0.319415i | \(0.896513\pi\) | |||||||
\(462\) | −7960.81 | − | 1601.51i | −0.801667 | − | 0.161275i | ||||
\(463\) | −1503.35 | + | 2603.89i | −0.150900 | + | 0.261367i | −0.931559 | − | 0.363591i | \(-0.881551\pi\) |
0.780658 | + | 0.624958i | \(0.214884\pi\) | |||||||
\(464\) | 2749.76 | + | 1587.57i | 0.275117 | + | 0.158839i | ||||
\(465\) | −2309.86 | − | 4206.68i | −0.230360 | − | 0.419528i | ||||
\(466\) | 4906.62 | + | 8498.52i | 0.487757 | + | 0.844820i | ||||
\(467\) | −5666.92 | −0.561528 | −0.280764 | − | 0.959777i | \(-0.590588\pi\) | ||||
−0.280764 | + | 0.959777i | \(0.590588\pi\) | |||||||
\(468\) | 4377.07 | − | 2282.62i | 0.432330 | − | 0.225458i | ||||
\(469\) | 3044.56 | − | 17013.8i | 0.299754 | − | 1.67510i | ||||
\(470\) | −3521.34 | + | 2033.05i | −0.345590 | + | 0.199526i | ||||
\(471\) | 3085.79 | − | 5089.41i | 0.301881 | − | 0.497894i | ||||
\(472\) | 1582.26 | + | 913.519i | 0.154300 | + | 0.0890850i | ||||
\(473\) | −891.070 | − | 514.460i | −0.0866204 | − | 0.0500103i | ||||
\(474\) | −4850.23 | + | 7999.51i | −0.469996 | + | 0.775168i | ||||
\(475\) | −20627.9 | + | 11909.5i | −1.99258 | + | 1.15042i | ||||
\(476\) | 852.693 | − | 4765.06i | 0.0821074 | − | 0.458837i | ||||
\(477\) | −464.181 | + | 10812.6i | −0.0445564 | + | 1.03790i | ||||
\(478\) | 5242.47 | 0.501643 | ||||||||
\(479\) | −7177.17 | − | 12431.2i | −0.684621 | − | 1.18580i | −0.973556 | − | 0.228450i | \(-0.926634\pi\) |
0.288935 | − | 0.957349i | \(-0.406699\pi\) | |||||||
\(480\) | 1320.43 | + | 2404.74i | 0.125560 | + | 0.228668i | ||||
\(481\) | 5290.70 | + | 3054.59i | 0.501528 | + | 0.289557i | ||||
\(482\) | −3484.30 | + | 6034.98i | −0.329265 | + | 0.570303i | ||||
\(483\) | 3236.93 | − | 16090.2i | 0.304938 | − | 1.51579i | ||||
\(484\) | −898.051 | − | 1555.47i | −0.0843399 | − | 0.146081i | ||||
\(485\) | − | 14274.9i | − | 1.33647i | ||||||
\(486\) | −3063.86 | − | 6928.81i | −0.285966 | − | 0.646702i | ||||
\(487\) | −3209.55 | −0.298642 | −0.149321 | − | 0.988789i | \(-0.547709\pi\) | ||||
−0.149321 | + | 0.988789i | \(0.547709\pi\) | |||||||
\(488\) | −983.282 | − | 1703.09i | −0.0912112 | − | 0.157982i | ||||
\(489\) | −201.620 | + | 9397.41i | −0.0186453 | + | 0.869050i | ||||
\(490\) | 7231.16 | + | 8707.20i | 0.666674 | + | 0.802757i | ||||
\(491\) | −11741.8 | − | 6779.15i | −1.07923 | − | 0.623093i | −0.148541 | − | 0.988906i | \(-0.547458\pi\) |
−0.930688 | + | 0.365813i | \(0.880791\pi\) | |||||||
\(492\) | −336.486 | + | 184.763i | −0.0308333 | + | 0.0169304i | ||||
\(493\) | 11230.0 | − | 6483.65i | 1.02591 | − | 0.592310i | ||||
\(494\) | − | 14790.7i | − | 1.34710i | ||||||
\(495\) | 806.104 | − | 18777.4i | 0.0731953 | − | 1.70501i | ||||
\(496\) | 895.658i | 0.0810811i | ||||||||
\(497\) | −5085.38 | − | 14083.2i | −0.458975 | − | 1.27106i | ||||
\(498\) | 6526.82 | − | 10764.7i | 0.587297 | − | 0.968633i | ||||
\(499\) | −8097.41 | + | 14025.1i | −0.726432 | + | 1.25822i | 0.231949 | + | 0.972728i | \(0.425490\pi\) |
−0.958382 | + | 0.285490i | \(0.907844\pi\) | |||||||
\(500\) | −733.165 | + | 1269.88i | −0.0655763 | + | 0.113581i | ||||
\(501\) | 10241.3 | + | 6209.48i | 0.913271 | + | 0.553730i | ||||
\(502\) | 5193.90 | − | 2998.70i | 0.461783 | − | 0.266611i | ||||
\(503\) | 3233.66 | 0.286644 | 0.143322 | − | 0.989676i | \(-0.454222\pi\) | ||||
0.143322 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(504\) | 1196.03 | + | 3817.40i | 0.105705 | + | 0.337382i | ||||
\(505\) | −2831.82 | −0.249533 | ||||||||
\(506\) | 12462.9 | − | 7195.49i | 1.09495 | − | 0.632171i | ||||
\(507\) | 490.711 | − | 269.447i | 0.0429847 | − | 0.0236027i | ||||
\(508\) | 2239.83 | − | 3879.49i | 0.195623 | − | 0.338828i | ||||
\(509\) | −3720.92 | + | 6444.82i | −0.324021 | + | 0.561221i | −0.981314 | − | 0.192414i | \(-0.938368\pi\) |
0.657292 | + | 0.753636i | \(0.271702\pi\) | |||||||
\(510\) | 11201.5 | + | 240.327i | 0.972571 | + | 0.0208664i | ||||
\(511\) | 616.916 | + | 1708.45i | 0.0534066 | + | 0.147901i | ||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | −22652.1 | − | 1459.79i | −1.94954 | − | 0.125636i | ||||
\(514\) | − | 36.5961i | − | 0.00314044i | ||||||
\(515\) | −7925.07 | + | 4575.54i | −0.678097 | + | 0.391500i | ||||
\(516\) | −10.8726 | + | 506.769i | −0.000927600 | + | 0.0432350i | ||||
\(517\) | −4502.27 | − | 2599.39i | −0.382998 | − | 0.221124i | ||||
\(518\) | −3191.84 | + | 3784.33i | −0.270737 | + | 0.320992i | ||||
\(519\) | 5337.41 | − | 2930.74i | 0.451419 | − | 0.247871i | ||||
\(520\) | −3016.58 | − | 5224.87i | −0.254396 | − | 0.440627i | ||||
\(521\) | −15082.0 | −1.26824 | −0.634121 | − | 0.773234i | \(-0.718638\pi\) | ||||
−0.634121 | + | 0.773234i | \(0.718638\pi\) | |||||||
\(522\) | −5751.16 | + | 9042.08i | −0.482225 | + | 0.758163i | ||||
\(523\) | − | 16623.1i | − | 1.38983i | −0.719093 | − | 0.694913i | \(-0.755443\pi\) | ||
0.719093 | − | 0.694913i | \(-0.244557\pi\) | |||||||
\(524\) | 3240.16 | + | 5612.12i | 0.270128 | + | 0.467875i | ||||
\(525\) | −9364.38 | + | 10631.3i | −0.778467 | + | 0.883787i | ||||
\(526\) | 6205.57 | − | 10748.4i | 0.514402 | − | 0.890971i | ||||
\(527\) | 3167.81 | + | 1828.93i | 0.261844 | + | 0.151176i | ||||
\(528\) | −1818.57 | + | 2999.39i | −0.149893 | + | 0.247219i | ||||
\(529\) | 8459.83 | + | 14652.9i | 0.695310 | + | 1.20431i | ||||
\(530\) | 13226.9 | 1.08403 | ||||||||
\(531\) | −3309.33 | + | 5202.98i | −0.270457 | + | 0.425217i | ||||
\(532\) | 11798.5 | + | 2111.30i | 0.961520 | + | 0.172061i | ||||
\(533\) | 731.098 | − | 422.100i | 0.0594134 | − | 0.0343024i | ||||
\(534\) | 3392.81 | + | 6178.92i | 0.274946 | + | 0.500726i | ||||
\(535\) | −5424.84 | − | 3132.04i | −0.438386 | − | 0.253102i | ||||
\(536\) | −6465.75 | − | 3733.00i | −0.521040 | − | 0.300823i | ||||
\(537\) | 2777.34 | + | 59.5874i | 0.223186 | + | 0.00478843i | ||||
\(538\) | −572.609 | + | 330.596i | −0.0458865 | + | 0.0264926i | ||||
\(539\) | −5018.48 | + | 13573.2i | −0.401041 | + | 1.08468i | ||||
\(540\) | −8299.66 | + | 4104.25i | −0.661408 | + | 0.327072i | ||||
\(541\) | 1812.75 | 0.144060 | 0.0720299 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720299 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(542\) | −1365.01 | − | 2364.26i | −0.108177 | − | 0.187368i | ||||
\(543\) | 1237.27 | + | 26.5454i | 0.0977833 | + | 0.00209792i | ||||
\(544\) | −1810.87 | − | 1045.50i | −0.142721 | − | 0.0824001i | ||||
\(545\) | −5784.79 | + | 10019.5i | −0.454666 | + | 0.787505i | ||||
\(546\) | −2809.72 | − | 8336.67i | −0.220228 | − | 0.653437i | ||||
\(547\) | 8331.58 | + | 14430.7i | 0.651248 | + | 1.12800i | 0.982820 | + | 0.184565i | \(0.0590877\pi\) |
−0.331572 | + | 0.943430i | \(0.607579\pi\) | |||||||
\(548\) | − | 3793.44i | − | 0.295708i | ||||||
\(549\) | 5884.99 | − | 3068.99i | 0.457496 | − | 0.238582i | ||||
\(550\) | −12422.4 | −0.963077 | ||||||||
\(551\) | 16053.8 | + | 27805.9i | 1.24122 | + | 2.14986i | ||||
\(552\) | −6062.29 | − | 3675.66i | −0.467442 | − | 0.283417i | ||||
\(553\) | 12744.0 | + | 10748.8i | 0.979985 | + | 0.826555i | ||||
\(554\) | 8482.80 | + | 4897.55i | 0.650541 | + | 0.375590i | ||||
\(555\) | −9798.15 | − | 5940.77i | −0.749384 | − | 0.454363i | ||||
\(556\) | −10829.5 | + | 6252.39i | −0.826028 | + | 0.476907i | ||||
\(557\) | − | 5558.97i | − | 0.422875i | −0.977392 | − | 0.211437i | \(-0.932186\pi\) | ||
0.977392 | − | 0.211437i | \(-0.0678144\pi\) | |||||||
\(558\) | −3020.06 | − | 129.650i | −0.229121 | − | 0.00983603i | ||||
\(559\) | − | 1114.72i | − | 0.0843426i | ||||||
\(560\) | 4598.45 | − | 1660.49i | 0.347000 | − | 0.125301i | ||||
\(561\) | 6894.85 | + | 12556.8i | 0.518896 | + | 0.945005i | ||||
\(562\) | −2545.06 | + | 4408.17i | −0.191026 | + | 0.330867i | ||||
\(563\) | −9704.90 | + | 16809.4i | −0.726488 | + | 1.25831i | 0.231870 | + | 0.972747i | \(0.425516\pi\) |
−0.958359 | + | 0.285568i | \(0.907818\pi\) | |||||||
\(564\) | −54.9358 | + | 2560.53i | −0.00410144 | + | 0.191166i | ||||
\(565\) | 13932.9 | − | 8044.16i | 1.03745 | − | 0.598974i | ||||
\(566\) | −1248.27 | −0.0927006 | ||||||||
\(567\) | −13045.0 | + | 3480.31i | −0.966205 | + | 0.257776i | ||||
\(568\) | −6467.81 | −0.477787 | ||||||||
\(569\) | 8339.85 | − | 4815.01i | 0.614454 | − | 0.354755i | −0.160252 | − | 0.987076i | \(-0.551231\pi\) |
0.774707 | + | 0.632321i | \(0.217897\pi\) | |||||||
\(570\) | −595.058 | + | 27735.4i | −0.0437267 | + | 2.03808i | ||||
\(571\) | 11113.4 | − | 19249.0i | 0.814504 | − | 1.41076i | −0.0951799 | − | 0.995460i | \(-0.530343\pi\) |
0.909684 | − | 0.415302i | \(-0.136324\pi\) | |||||||
\(572\) | 3856.91 | − | 6680.37i | 0.281933 | − | 0.488322i | ||||
\(573\) | −789.988 | − | 1438.71i | −0.0575955 | − | 0.104892i | ||||
\(574\) | 232.346 | + | 643.445i | 0.0168953 | + | 0.0467889i | ||||
\(575\) | − | 25107.8i | − | 1.82099i | ||||||
\(576\) | 1726.41 | + | 74.1138i | 0.124885 | + | 0.00536124i | ||||
\(577\) | 13671.2i | 0.986378i | 0.869922 | + | 0.493189i | \(0.164169\pi\) | ||||
−0.869922 | + | 0.493189i | \(0.835831\pi\) | |||||||
\(578\) | 1113.98 | − | 643.156i | 0.0801650 | − | 0.0462833i | ||||
\(579\) | 6046.64 | + | 3666.17i | 0.434007 | + | 0.263145i | ||||
\(580\) | 11342.1 | + | 6548.35i | 0.811990 | + | 0.468803i | ||||
\(581\) | −17149.3 | − | 14464.4i | −1.22457 | − | 1.03285i | ||||
\(582\) | −7688.54 | − | 4661.68i | −0.547595 | − | 0.332015i | ||||
\(583\) | 8455.73 | + | 14645.8i | 0.600687 | + | 1.04042i | ||||
\(584\) | 784.621 | 0.0555956 | ||||||||
\(585\) | 18054.4 | − | 9415.28i | 1.27599 | − | 0.665425i | ||||
\(586\) | − | 3380.23i | − | 0.238287i | ||||||
\(587\) | 6314.02 | + | 10936.2i | 0.443965 | + | 0.768970i | 0.997979 | − | 0.0635372i | \(-0.0202382\pi\) |
−0.554015 | + | 0.832507i | \(0.686905\pi\) | |||||||
\(588\) | 7051.18 | − | 1051.28i | 0.494534 | − | 0.0737311i | ||||
\(589\) | −4528.51 | + | 7843.61i | −0.316798 | + | 0.548710i | ||||
\(590\) | 6526.45 | + | 3768.05i | 0.455406 | + | 0.262929i | ||||
\(591\) | 3667.90 | + | 78.6943i | 0.255292 | + | 0.00547724i | ||||
\(592\) | 1069.24 | + | 1851.98i | 0.0742324 | + | 0.128574i | ||||
\(593\) | −26058.7 | −1.80456 | −0.902280 | − | 0.431150i | \(-0.858108\pi\) | ||||
−0.902280 | + | 0.431150i | \(0.858108\pi\) | |||||||
\(594\) | −9850.37 | − | 6566.21i | −0.680413 | − | 0.453561i | ||||
\(595\) | 3517.15 | − | 19654.7i | 0.242335 | − | 1.35423i | ||||
\(596\) | −6699.63 | + | 3868.04i | −0.460449 | + | 0.265840i | ||||
\(597\) | −129.501 | − | 2.77843i | −0.00887794 | − | 0.000190475i | ||||
\(598\) | 13502.2 | + | 7795.49i | 0.923320 | + | 0.533079i | ||||
\(599\) | −6925.41 | − | 3998.39i | −0.472395 | − | 0.272737i | 0.244847 | − | 0.969562i | \(-0.421262\pi\) |
−0.717242 | + | 0.696824i | \(0.754596\pi\) | |||||||
\(600\) | 2945.49 | + | 5364.28i | 0.200415 | + | 0.364993i | ||||
\(601\) | −8015.01 | + | 4627.47i | −0.543992 | + | 0.314074i | −0.746695 | − | 0.665166i | \(-0.768361\pi\) |
0.202703 | + | 0.979240i | \(0.435027\pi\) | |||||||
\(602\) | 889.203 | + | 159.120i | 0.0602013 | + | 0.0107728i | ||||
\(603\) | 13523.2 | − | 21261.4i | 0.913281 | − | 1.43588i | ||||
\(604\) | 9285.03 | 0.625501 | ||||||||
\(605\) | −3704.25 | − | 6415.94i | −0.248924 | − | 0.431149i | ||||
\(606\) | −924.772 | + | 1525.23i | −0.0619906 | + | 0.102241i | ||||
\(607\) | 4856.01 | + | 2803.62i | 0.324710 | + | 0.187472i | 0.653490 | − | 0.756935i | \(-0.273304\pi\) |
−0.328780 | + | 0.944407i | \(0.606637\pi\) | |||||||
\(608\) | 2588.71 | − | 4483.77i | 0.172674 | − | 0.299081i | ||||
\(609\) | 14330.7 | + | 12622.9i | 0.953546 | + | 0.839913i | ||||
\(610\) | −4055.80 | − | 7024.86i | −0.269204 | − | 0.466276i | ||||
\(611\) | − | 5632.29i | − | 0.372926i | ||||||
\(612\) | 3787.46 | − | 5954.71i | 0.250162 | − | 0.393309i | ||||
\(613\) | 86.2923 | 0.00568566 | 0.00284283 | − | 0.999996i | \(-0.499095\pi\) | ||||
0.00284283 | + | 0.999996i | \(0.499095\pi\) | |||||||
\(614\) | 6791.33 | + | 11762.9i | 0.446378 | + | 0.773149i | ||||
\(615\) | −1387.93 | + | 762.101i | −0.0910025 | + | 0.0499689i | ||||
\(616\) | 4778.33 | + | 4030.22i | 0.312540 | + | 0.263607i | ||||
\(617\) | −312.162 | − | 180.227i | −0.0203682 | − | 0.0117596i | 0.489781 | − | 0.871845i | \(-0.337077\pi\) |
−0.510150 | + | 0.860086i | \(0.670410\pi\) | |||||||
\(618\) | −123.638 | + | 5762.69i | −0.00804763 | + | 0.375096i | ||||
\(619\) | −7320.65 | + | 4226.58i | −0.475350 | + | 0.274444i | −0.718477 | − | 0.695551i | \(-0.755160\pi\) |
0.243127 | + | 0.969995i | \(0.421827\pi\) | |||||||
\(620\) | 3694.37i | 0.239306i | ||||||||
\(621\) | 13271.5 | − | 19909.3i | 0.857594 | − | 1.28653i | ||||
\(622\) | 8280.34i | 0.533780i | ||||||||
\(623\) | 11815.6 | − | 4266.58i | 0.759843 | − | 0.274377i | ||||
\(624\) | −3799.25 | − | 81.5124i | −0.243737 | − | 0.00522934i | ||||
\(625\) | 6177.02 | − | 10698.9i | 0.395329 | − | 0.684730i | ||||
\(626\) | 7019.51 | − | 12158.1i | 0.448172 | − | 0.776257i | ||||
\(627\) | −31091.1 | + | 17071.9i | −1.98031 | + | 1.08738i | ||||
\(628\) | −3967.88 | + | 2290.86i | −0.252127 | + | 0.145566i | ||||
\(629\) | 8733.57 | 0.553625 | ||||||||
\(630\) | 4933.34 | + | 15745.8i | 0.311982 | + | 0.995761i | ||||
\(631\) | 6541.89 | 0.412723 | 0.206362 | − | 0.978476i | \(-0.433838\pi\) | ||||
0.206362 | + | 0.978476i | \(0.433838\pi\) | |||||||
\(632\) | 6236.70 | − | 3600.76i | 0.392536 | − | 0.226631i | ||||
\(633\) | 14329.4 | + | 8688.12i | 0.899749 | + | 0.545532i | ||||
\(634\) | −4871.55 | + | 8437.78i | −0.305164 | + | 0.528560i | ||||
\(635\) | 9238.75 | − | 16002.0i | 0.577368 | − | 1.00003i | ||||
\(636\) | 4319.43 | − | 7124.06i | 0.269303 | − | 0.444162i | ||||
\(637\) | −15453.4 | + | 2644.00i | −0.961205 | + | 0.164457i | ||||
\(638\) | 16745.1i | 1.03910i | ||||||||
\(639\) | 936.238 | − | 21808.8i | 0.0579609 | − | 1.35014i | ||||
\(640\) | − | 2111.88i | − | 0.130436i | ||||||
\(641\) | 11151.5 | − | 6438.30i | 0.687139 | − | 0.396720i | −0.115400 | − | 0.993319i | \(-0.536815\pi\) |
0.802539 | + | 0.596599i | \(0.203482\pi\) | |||||||
\(642\) | −3458.49 | + | 1899.04i | −0.212610 | + | 0.116743i | ||||
\(643\) | −3396.70 | − | 1961.09i | −0.208325 | − | 0.120276i | 0.392208 | − | 0.919877i | \(-0.371711\pi\) |
−0.600533 | + | 0.799600i | \(0.705045\pi\) | |||||||
\(644\) | −8145.78 | + | 9657.84i | −0.498430 | + | 0.590951i | ||||
\(645\) | −44.8471 | + | 2090.30i | −0.00273775 | + | 0.127605i | ||||
\(646\) | −10572.3 | − | 18311.7i | −0.643903 | − | 1.11527i | ||||
\(647\) | 1398.46 | 0.0849755 | 0.0424877 | − | 0.999097i | \(-0.486472\pi\) | ||||
0.0424877 | + | 0.999097i | \(0.486472\pi\) | |||||||
\(648\) | −499.808 | + | 5810.54i | −0.0302999 | + | 0.352253i | ||||
\(649\) | 9635.42i | 0.582779i | ||||||||
\(650\) | −6729.13 | − | 11655.2i | −0.406058 | − | 0.703314i | ||||
\(651\) | −1062.45 | + | 5281.24i | −0.0639641 | + | 0.317954i | ||||
\(652\) | 3617.90 | − | 6266.38i | 0.217313 | − | 0.376396i | ||||
\(653\) | −20232.9 | − | 11681.5i | −1.21252 | − | 0.700049i | −0.249212 | − | 0.968449i | \(-0.580172\pi\) |
−0.963307 | + | 0.268400i | \(0.913505\pi\) | |||||||
\(654\) | 3507.47 | + | 6387.75i | 0.209714 | + | 0.381928i | ||||
\(655\) | 13364.9 | + | 23148.7i | 0.797266 | + | 1.38091i | ||||
\(656\) | 295.507 | 0.0175878 | ||||||||
\(657\) | −113.577 | + | 2645.66i | −0.00674437 | + | 0.157104i | ||||
\(658\) | 4492.84 | + | 803.979i | 0.266184 | + | 0.0476328i | ||||
\(659\) | 4429.36 | − | 2557.29i | 0.261826 | − | 0.151165i | −0.363341 | − | 0.931656i | \(-0.618364\pi\) |
0.625167 | + | 0.780491i | \(0.285031\pi\) | |||||||
\(660\) | −7501.19 | + | 12371.8i | −0.442399 | + | 0.729651i | ||||
\(661\) | 10826.3 | + | 6250.57i | 0.637057 | + | 0.367805i | 0.783480 | − | 0.621417i | \(-0.213443\pi\) |
−0.146423 | + | 0.989222i | \(0.546776\pi\) | |||||||
\(662\) | 10799.0 | + | 6234.80i | 0.634010 | + | 0.366046i | ||||
\(663\) | −8046.38 | + | 13270.9i | −0.471336 | + | 0.777377i | ||||
\(664\) | −8392.56 | + | 4845.45i | −0.490504 | + | 0.283192i | ||||
\(665\) | 48665.9 | + | 8708.60i | 2.83787 | + | 0.507827i | ||||
\(666\) | −6399.46 | + | 3337.29i | −0.372333 | + | 0.194170i | ||||
\(667\) | −33844.7 | −1.96472 | ||||||||
\(668\) | −4609.85 | − | 7984.50i | −0.267007 | − | 0.462469i | ||||
\(669\) | −9775.74 | − | 17803.4i | −0.564950 | − | 1.02888i | ||||
\(670\) | −26669.7 | − | 15397.7i | −1.53782 | − | 0.887860i | ||||
\(671\) | 5185.63 | − | 8981.77i | 0.298344 | − | 0.516747i | ||||
\(672\) | 607.346 | − | 3019.01i | 0.0348644 | − | 0.173305i | ||||
\(673\) | 7226.37 | + | 12516.4i | 0.413902 | + | 0.716899i | 0.995312 | − | 0.0967113i | \(-0.0308323\pi\) |
−0.581411 | + | 0.813610i | \(0.697499\pi\) | |||||||
\(674\) | − | 5183.47i | − | 0.296231i | ||||||
\(675\) | −18514.1 | + | 9155.39i | −1.05572 | + | 0.522061i | ||||
\(676\) | −430.950 | −0.0245192 | ||||||||
\(677\) | −7473.87 | − | 12945.1i | −0.424290 | − | 0.734891i | 0.572064 | − | 0.820209i | \(-0.306143\pi\) |
−0.996354 | + | 0.0853175i | \(0.972810\pi\) | |||||||
\(678\) | 217.365 | − | 10131.3i | 0.0123124 | − | 0.573877i | ||||
\(679\) | −10330.9 | + | 12248.6i | −0.583896 | + | 0.692281i | ||||
\(680\) | −7469.39 | − | 4312.46i | −0.421233 | − | 0.243199i | ||||
\(681\) | 8595.26 | − | 4719.61i | 0.483658 | − | 0.265574i | ||||
\(682\) | −4090.68 | + | 2361.76i | −0.229678 | + | 0.132605i | ||||
\(683\) | 31786.1i | 1.78077i | 0.455213 | + | 0.890383i | \(0.349563\pi\) | ||||
−0.455213 | + | 0.890383i | \(0.650437\pi\) | |||||||
\(684\) | 14744.1 | + | 9377.89i | 0.824202 | + | 0.524229i | ||||
\(685\) | − | 15647.0i | − | 0.872763i | ||||||
\(686\) | 96.7988 | − | 12704.5i | 0.00538746 | − | 0.707086i | ||||
\(687\) | 4139.55 | − | 6827.38i | 0.229889 | − | 0.379157i | ||||
\(688\) | 195.100 | − | 337.924i | 0.0108112 | − | 0.0187256i | ||||
\(689\) | −9160.83 | + | 15867.0i | −0.506531 | + | 0.877337i | ||||
\(690\) | −25005.5 | − | 15161.2i | −1.37963 | − | 0.836489i | ||||
\(691\) | 10608.4 | − | 6124.78i | 0.584029 | − | 0.337189i | −0.178704 | − | 0.983903i | \(-0.557191\pi\) |
0.762733 | + | 0.646714i | \(0.223857\pi\) | |||||||
\(692\) | −4687.40 | −0.257497 | ||||||||
\(693\) | −14281.2 | + | 15528.6i | −0.782823 | + | 0.851204i | ||||
\(694\) | 1275.24 | 0.0697515 | ||||||||
\(695\) | −44668.9 | + | 25789.6i | −2.43797 | + | 1.40756i | ||||
\(696\) | 7230.90 | − | 3970.44i | 0.393803 | − | 0.216235i | ||||
\(697\) | 603.427 | − | 1045.17i | 0.0327926 | − | 0.0567984i | ||||
\(698\) | 2813.43 | − | 4873.00i | 0.152564 | − | 0.264249i | ||||
\(699\) | 25489.7 | + | 546.877i | 1.37927 | + | 0.0295920i | ||||
\(700\) | 10257.8 | − | 3704.06i | 0.553870 | − | 0.200001i | ||||
\(701\) | 35354.1i | 1.90486i | 0.304757 | + | 0.952430i | \(0.401425\pi\) | ||||
−0.304757 | + | 0.952430i | \(0.598575\pi\) | |||||||
\(702\) | 824.807 | − | 12798.9i | 0.0443452 | − | 0.688124i | ||||
\(703\) | 21624.6i | 1.16016i | ||||||||
\(704\) | 2338.43 | − | 1350.09i | 0.125189 | − | 0.0722777i | ||||
\(705\) | −226.597 | + | 10561.6i | −0.0121052 | + | 0.564216i | ||||
\(706\) | −3189.64 | − | 1841.54i | −0.170034 | − | 0.0981689i | ||||
\(707\) | 2429.85 | + | 2049.43i | 0.129256 | + | 0.109019i | ||||
\(708\) | 4160.80 | − | 2284.67i | 0.220865 | − | 0.121276i | ||||
\(709\) | −15616.4 | − | 27048.4i | −0.827203 | − | 1.43276i | −0.900224 | − | 0.435427i | \(-0.856597\pi\) |
0.0730207 | − | 0.997330i | \(-0.476736\pi\) | |||||||
\(710\) | −26678.2 | −1.41016 | ||||||||
\(711\) | 11238.6 | + | 21550.7i | 0.592799 | + | 1.13673i | ||||
\(712\) | − | 5426.42i | − | 0.285623i | ||||||
\(713\) | −4773.52 | − | 8267.99i | −0.250729 | − | 0.434276i | ||||
\(714\) | −9437.57 | − | 8312.90i | −0.494667 | − | 0.435718i | ||||
\(715\) | 15908.8 | − | 27554.9i | 0.832107 | − | 1.44125i | ||||
\(716\) | −1851.99 | − | 1069.24i | −0.0966647 | − | 0.0558094i | ||||
\(717\) | 7061.62 | − | 11646.8i | 0.367812 | − | 0.606634i | ||||
\(718\) | −13045.6 | − | 22595.7i | −0.678075 | − | 1.17446i | ||||
\(719\) | −17546.8 | −0.910132 | −0.455066 | − | 0.890458i | \(-0.650384\pi\) | ||||
−0.455066 | + | 0.890458i | \(0.650384\pi\) | |||||||
\(720\) | 7121.03 | + | 305.702i | 0.368590 | + | 0.0158234i | ||||
\(721\) | 10111.5 | + | 1809.42i | 0.522292 | + | 0.0934625i | ||||
\(722\) | 33460.4 | − | 19318.4i | 1.72475 | − | 0.995784i | ||||
\(723\) | 8714.07 | + | 15869.9i | 0.448243 | + | 0.816333i | ||||
\(724\) | −825.036 | − | 476.335i | −0.0423511 | − | 0.0244514i | ||||
\(725\) | 25300.9 | + | 14607.5i | 1.29607 | + | 0.748288i | ||||
\(726\) | −4665.34 | − | 100.094i | −0.238494 | − | 0.00511686i | ||||
\(727\) | 27922.8 | − | 16121.3i | 1.42449 | − | 0.822427i | 0.427807 | − | 0.903870i | \(-0.359286\pi\) |
0.996678 | + | 0.0814430i | \(0.0259529\pi\) | |||||||
\(728\) | −1192.92 | + | 6666.36i | −0.0607318 | + | 0.339385i | ||||
\(729\) | −19520.2 | − | 2526.40i | −0.991728 | − | 0.128354i | ||||
\(730\) | 3236.37 | 0.164087 | ||||||||
\(731\) | −796.791 | − | 1380.08i | −0.0403151 | − | 0.0698279i | ||||
\(732\) | −5108.11 | − | 109.594i | −0.257925 | − | 0.00553374i | ||||
\(733\) | 7458.32 | + | 4306.06i | 0.375825 | + | 0.216982i | 0.676000 | − | 0.736902i | \(-0.263712\pi\) |
−0.300175 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(734\) | −6935.63 | + | 12012.9i | −0.348772 | + | 0.604091i | ||||
\(735\) | 29084.4 | − | 4336.26i | 1.45959 | − | 0.217613i | ||||
\(736\) | 2728.77 | + | 4726.37i | 0.136663 | + | 0.236707i | ||||
\(737\) | − | 39374.1i | − | 1.96793i | ||||||
\(738\) | −42.7757 | + | 996.420i | −0.00213360 | + | 0.0497002i | ||||
\(739\) | 20330.4 | 1.01200 | 0.505999 | − | 0.862534i | \(-0.331124\pi\) | ||||
0.505999 | + | 0.862534i | \(0.331124\pi\) | |||||||
\(740\) | 4410.37 | + | 7638.98i | 0.219092 | + | 0.379479i | ||||
\(741\) | −32859.4 | − | 19923.1i | −1.62904 | − | 0.987712i | ||||
\(742\) | −11349.4 | − | 9572.46i | −0.561520 | − | 0.473607i | ||||
\(743\) | 15779.3 | + | 9110.20i | 0.779122 | + | 0.449826i | 0.836119 | − | 0.548548i | \(-0.184819\pi\) |
−0.0569970 | + | 0.998374i | \(0.518153\pi\) | |||||||
\(744\) | 1989.81 | + | 1206.45i | 0.0980510 | + | 0.0594499i | ||||
\(745\) | −27634.4 | + | 15954.7i | −1.35899 | + | 0.784612i | ||||
\(746\) | 22746.3i | 1.11635i | ||||||||
\(747\) | −15123.5 | − | 29000.2i | −0.740749 | − | 1.42043i | ||||
\(748\) | − | 11027.6i | − | 0.539047i | ||||||
\(749\) | 2388.11 | + | 6613.49i | 0.116501 | + | 0.322632i | ||||
\(750\) | 1833.61 | + | 3339.34i | 0.0892721 | + | 0.162581i | ||||
\(751\) | −9944.27 | + | 17224.0i | −0.483184 | + | 0.836900i | −0.999814 | − | 0.0193093i | \(-0.993853\pi\) |
0.516629 | + | 0.856209i | \(0.327187\pi\) | |||||||
\(752\) | 985.776 | − | 1707.41i | 0.0478026 | − | 0.0827965i | ||||
\(753\) | 334.226 | − | 15578.1i | 0.0161751 | − | 0.753916i | ||||
\(754\) | −15710.9 | + | 9070.68i | −0.758828 | + | 0.438110i | ||||
\(755\) | 38298.5 | 1.84613 | ||||||||
\(756\) | 10091.9 | + | 2484.92i | 0.485499 | + | 0.119544i | ||||
\(757\) | −18149.2 | −0.871394 | −0.435697 | − | 0.900093i | \(-0.643498\pi\) | ||||
−0.435697 | + | 0.900093i | \(0.643498\pi\) | |||||||
\(758\) | −16939.4 | + | 9779.96i | −0.811697 | + | 0.468633i | ||||
\(759\) | 801.987 | − | 37380.2i | 0.0383535 | − | 1.78764i | ||||
\(760\) | 10677.8 | − | 18494.5i | 0.509638 | − | 0.882718i | ||||
\(761\) | −4020.37 | + | 6963.48i | −0.191509 | + | 0.331703i | −0.945750 | − | 0.324894i | \(-0.894671\pi\) |
0.754242 | + | 0.656597i | \(0.228005\pi\) | |||||||
\(762\) | −5601.71 | − | 10201.7i | −0.266310 | − | 0.484999i | ||||
\(763\) | 12214.9 | − | 4410.78i | 0.579568 | − | 0.209280i | ||||
\(764\) | 1263.50i | 0.0598321i | ||||||||
\(765\) | 15622.4 | − | 24561.8i | 0.738337 | − | 1.16083i | ||||
\(766\) | − | 19321.5i | − | 0.911378i | ||||||
\(767\) | −9040.34 | + | 5219.44i | −0.425590 | + | 0.245715i | ||||
\(768\) | −1137.47 | − | 689.665i | −0.0534438 | − | 0.0324038i | ||||
\(769\) | −15453.5 | − | 8922.08i | −0.724665 | − | 0.418385i | 0.0918025 | − | 0.995777i | \(-0.470737\pi\) |
−0.816467 | + | 0.577392i | \(0.804071\pi\) | |||||||
\(770\) | 19709.5 | + | 16623.7i | 0.922442 | + | 0.778021i | ||||
\(771\) | −81.3026 | − | 49.2950i | −0.00379772 | − | 0.00230262i | ||||
\(772\) | −2721.73 | − | 4714.17i | −0.126888 | − | 0.219776i | ||||
\(773\) | 9883.75 | 0.459889 | 0.229944 | − | 0.973204i | \(-0.426146\pi\) | ||||
0.229944 | + | 0.973204i | \(0.426146\pi\) | |||||||
\(774\) | 1111.20 | + | 706.774i | 0.0516038 | + | 0.0328223i | ||||
\(775\) | 8241.08i | 0.381972i | ||||||||
\(776\) | 3460.78 | + | 5994.25i | 0.160096 | + | 0.277295i | ||||
\(777\) | 4107.92 | + | 12188.6i | 0.189666 | + | 0.562757i | ||||
\(778\) | −5812.60 | + | 10067.7i | −0.267856 | + | 0.463940i | ||||
\(779\) | 2587.87 | + | 1494.11i | 0.119024 | + | 0.0687188i | ||||
\(780\) | −15671.0 | − | 336.219i | −0.719375 | − | 0.0154341i | ||||
\(781\) | −17054.9 | − | 29540.0i | −0.781401 | − | 1.35343i | ||||
\(782\) | 22288.6 | 1.01923 | ||||||||
\(783\) | 12341.2 | + | 24956.6i | 0.563268 | + | 1.13905i | ||||
\(784\) | −5147.43 | − | 1903.18i | −0.234486 | − | 0.0866972i | ||||
\(785\) | −16366.6 | + | 9449.25i | −0.744138 | + | 0.429628i | ||||
\(786\) | 16832.5 | + | 361.138i | 0.763862 | + | 0.0163885i | ||||
\(787\) | 7760.64 | + | 4480.61i | 0.351508 | + | 0.202943i | 0.665349 | − | 0.746532i | \(-0.268283\pi\) |
−0.313841 | + | 0.949475i | \(0.601616\pi\) | |||||||
\(788\) | −2445.83 | − | 1412.10i | −0.110570 | − | 0.0638376i | ||||
\(789\) | −15519.8 | − | 28264.5i | −0.700280 | − | 1.27534i | ||||
\(790\) | 25724.9 | − | 14852.3i | 1.15854 | − | 0.668886i | ||||
\(791\) | −17776.8 | − | 3181.11i | −0.799079 | − | 0.142993i | ||||
\(792\) | 4213.87 | + | 8080.36i | 0.189057 | + | 0.362529i | ||||
\(793\) | 11236.1 | 0.503158 | ||||||||
\(794\) | 6603.43 | + | 11437.5i | 0.295147 | + | 0.511210i | ||||
\(795\) | 17816.6 | − | 29385.0i | 0.794830 | − | 1.31092i | ||||
\(796\) | 86.3540 | + | 49.8565i | 0.00384514 | + | 0.00222000i | ||||
\(797\) | −15480.1 | + | 26812.3i | −0.687995 | + | 1.19164i | 0.284491 | + | 0.958679i | \(0.408176\pi\) |
−0.972486 | + | 0.232963i | \(0.925158\pi\) | |||||||
\(798\) | 20583.1 | − | 23367.8i | 0.913073 | − | 1.03660i | ||||
\(799\) | −4025.91 | − | 6973.08i | −0.178256 | − | 0.308748i | ||||
\(800\) | − | 4710.99i | − | 0.208198i | ||||||
\(801\) | 18297.3 | + | 785.493i | 0.807121 | + | 0.0346492i | ||||
\(802\) | −28395.5 | −1.25022 | ||||||||
\(803\) | 2068.97 | + | 3583.55i | 0.0909243 | + | 0.157485i | ||||
\(804\) | −17002.7 | + | 9336.06i | −0.745818 | + | 0.409524i | ||||
\(805\) | −33599.4 | + | 39836.3i | −1.47108 | + | 1.74415i | ||||
\(806\) | −4431.79 | − | 2558.70i | −0.193676 | − | 0.111819i | ||||
\(807\) | −36.8472 | + | 1717.43i | −0.00160729 | + | 0.0749151i | ||||
\(808\) | 1189.12 | − | 686.541i | 0.0517738 | − | 0.0298916i | ||||
\(809\) | 11260.0i | 0.489345i | 0.969606 | + | 0.244673i | \(0.0786805\pi\) | ||||
−0.969606 | + | 0.244673i | \(0.921320\pi\) | |||||||
\(810\) | −2061.59 | + | 23967.1i | −0.0894282 | + | 1.03965i | ||||
\(811\) | 26285.2i | 1.13810i | 0.822304 | + | 0.569049i | \(0.192688\pi\) | ||||
−0.822304 | + | 0.569049i | \(0.807312\pi\) | |||||||
\(812\) | −4992.98 | − | 13827.3i | −0.215787 | − | 0.597588i | ||||
\(813\) | −7091.15 | − | 152.139i | −0.305901 | − | 0.00656305i | ||||
\(814\) | −5638.96 | + | 9766.96i | −0.242808 | + | 0.420555i | ||||
\(815\) | 14923.0 | − | 25847.3i | 0.641385 | − | 1.11091i | ||||
\(816\) | −4761.95 | + | 2614.76i | −0.204291 | + | 0.112175i | ||||
\(817\) | 3417.13 | − | 1972.88i | 0.146328 | − | 0.0844828i | ||||
\(818\) | −29036.2 | −1.24111 | ||||||||
\(819\) | −22305.6 | − | 4987.40i | −0.951674 | − | 0.212788i | ||||
\(820\) | 1218.90 | 0.0519094 | ||||||||
\(821\) | −25195.4 | + | 14546.6i | −1.07104 | + | 0.618367i | −0.928466 | − | 0.371417i | \(-0.878872\pi\) |
−0.142576 | + | 0.989784i | \(0.545539\pi\) | |||||||
\(822\) | −8427.58 | − | 5109.77i | −0.357598 | − | 0.216817i | ||||
\(823\) | 21484.0 | − | 37211.4i | 0.909946 | − | 1.57607i | 0.0958090 | − | 0.995400i | \(-0.469456\pi\) |
0.814137 | − | 0.580673i | \(-0.197210\pi\) | |||||||
\(824\) | 2218.57 | − | 3842.68i | 0.0937957 | − | 0.162459i | ||||
\(825\) | −16733.0 | + | 27597.8i | −0.706143 | + | 1.16465i | ||||
\(826\) | −2873.06 | − | 7956.47i | −0.121025 | − | 0.335159i | ||||
\(827\) | 18283.1i | 0.768762i | 0.923175 | + | 0.384381i | \(0.125585\pi\) | ||||
−0.923175 | + | 0.384381i | \(0.874415\pi\) | |||||||
\(828\) | −16331.8 | + | 8516.97i | −0.685471 | + | 0.357470i | ||||
\(829\) | − | 28273.8i | − | 1.18455i | −0.805737 | − | 0.592273i | \(-0.798231\pi\) | ||
0.805737 | − | 0.592273i | \(-0.201769\pi\) | |||||||
\(830\) | −34617.3 | + | 19986.3i | −1.44769 | + | 0.835825i | ||||
\(831\) | 22306.8 | − | 12248.5i | 0.931186 | − | 0.511308i | ||||
\(832\) | 2533.42 | + | 1462.67i | 0.105566 | + | 0.0609483i | ||||
\(833\) | −17242.3 | + | 14319.4i | −0.717180 | + | 0.595604i | ||||
\(834\) | −696.872 | + | 32480.9i | −0.0289337 | + | 1.34859i | ||||
\(835\) | −19014.5 | − | 32934.1i | −0.788054 | − | 1.36495i | ||||
\(836\) | 27304.6 | 1.12961 | ||||||||
\(837\) | −4356.06 | + | 6534.79i | −0.179890 | + | 0.269863i | ||||
\(838\) | 2837.79i | 0.116981i | ||||||||
\(839\) | −22654.6 | − | 39238.8i | −0.932208 | − | 1.61463i | −0.779539 | − | 0.626354i | \(-0.784547\pi\) |
−0.152669 | − | 0.988277i | \(-0.548787\pi\) | |||||||
\(840\) | 2505.15 | − | 12452.7i | 0.102900 | − | 0.511498i | ||||
\(841\) | 7496.00 | − | 12983.5i | 0.307352 | − | 0.532349i | ||||
\(842\) | 8022.36 | + | 4631.71i | 0.328348 | + | 0.189572i | ||||
\(843\) | 6365.07 | + | 11592.0i | 0.260053 | + | 0.473604i | ||||
\(844\) | −6449.97 | − | 11171.7i | −0.263053 | − | 0.455622i | ||||
\(845\) | −1777.57 | −0.0723670 | ||||||||
\(846\) | 5614.53 | + | 3571.09i | 0.228169 | + | 0.145126i | ||||
\(847\) | −1464.86 | + | 8186.03i | −0.0594254 | + | 0.332084i | ||||
\(848\) | −5554.16 | + | 3206.70i | −0.224918 | + | 0.129857i | ||||
\(849\) | −1681.42 | + | 2773.17i | −0.0679694 | + | 0.112102i | ||||
\(850\) | −16662.1 | − | 9619.85i | −0.672358 | − | 0.388186i | ||||
\(851\) | −19740.7 | − | 11397.3i | −0.795187 | − | 0.459101i | ||||
\(852\) | −8712.15 | + | 14369.0i | −0.350321 | + | 0.577786i | ||||
\(853\) | −9129.40 | + | 5270.86i | −0.366453 | + | 0.211572i | −0.671908 | − | 0.740635i | \(-0.734525\pi\) |
0.305454 | + | 0.952207i | \(0.401192\pi\) | |||||||
\(854\) | −1603.89 | + | 8962.94i | −0.0642670 | + | 0.359140i | ||||
\(855\) | 60815.8 | + | 38681.6i | 2.43258 | + | 1.54723i | ||||
\(856\) | 3037.30 | 0.121277 | ||||||||
\(857\) | −3669.34 | − | 6355.49i | −0.146257 | − | 0.253325i | 0.783584 | − | 0.621286i | \(-0.213389\pi\) |
−0.929841 | + | 0.367961i | \(0.880056\pi\) | |||||||
\(858\) | −9645.96 | − | 17567.0i | −0.383808 | − | 0.698985i | ||||
\(859\) | 18600.0 | + | 10738.7i | 0.738796 | + | 0.426544i | 0.821631 | − | 0.570019i | \(-0.193064\pi\) |
−0.0828357 | + | 0.996563i | \(0.526398\pi\) | |||||||
\(860\) | 804.742 | − | 1393.85i | 0.0319087 | − | 0.0552675i | ||||
\(861\) | 1742.46 | + | 350.537i | 0.0689696 | + | 0.0138749i | ||||
\(862\) | 7638.31 | + | 13229.9i | 0.301812 | + | 0.522754i | ||||
\(863\) | 1403.26i | 0.0553507i | 0.999617 | + | 0.0276754i | \(0.00881047\pi\) | ||||
−0.999617 | + | 0.0276754i | \(0.991190\pi\) | |||||||
\(864\) | 2490.13 | − | 3735.59i | 0.0980508 | − | 0.147092i | ||||
\(865\) | −19334.4 | −0.759987 | ||||||||
\(866\) | −930.244 | − | 1611.23i | −0.0365023 | − | 0.0632238i | ||||
\(867\) | 71.6842 | − | 3341.17i | 0.00280798 | − | 0.130879i | ||||
\(868\) | 2673.67 | − | 3169.97i | 0.104551 | − | 0.123958i | ||||
\(869\) | 32891.1 | + | 18989.7i | 1.28395 | + | 0.741289i | ||||
\(870\) | 29825.7 | − | 16377.1i | 1.16228 | − | 0.638203i | ||||
\(871\) | 36942.4 | − | 21328.7i | 1.43714 | − | 0.829731i | ||||
\(872\) | − | 5609.82i | − | 0.217858i | ||||||
\(873\) | −20712.9 | + | 10801.7i | −0.803009 | + | 0.418765i | ||||
\(874\) | 55187.4i | 2.13586i | ||||||||
\(875\) | 6385.64 | − | 2305.83i | 0.246713 | − | 0.0890874i | ||||
\(876\) | 1056.89 | − | 1743.13i | 0.0407635 | − | 0.0672316i | ||||
\(877\) | −13024.4 | + | 22559.0i | −0.501487 | + | 0.868600i | 0.498512 | + | 0.866883i | \(0.333880\pi\) |
−0.999999 | + | 0.00171749i | \(0.999453\pi\) | |||||||
\(878\) | 16441.6 | − | 28477.6i | 0.631977 | − | 1.09462i | ||||
\(879\) | −7509.58 | − | 4553.18i | −0.288159 | − | 0.174715i | ||||
\(880\) | 9645.45 | − | 5568.80i | 0.369486 | − | 0.213323i | ||||
\(881\) | 25474.5 | 0.974187 | 0.487093 | − | 0.873350i | \(-0.338057\pi\) | ||||
0.487093 | + | 0.873350i | \(0.338057\pi\) | |||||||
\(882\) | 7162.42 | − | 17081.1i | 0.273437 | − | 0.652098i | ||||
\(883\) | 16202.6 | 0.617508 | 0.308754 | − | 0.951142i | \(-0.400088\pi\) | ||||
0.308754 | + | 0.951142i | \(0.400088\pi\) | |||||||
\(884\) | 10346.5 | − | 5973.55i | 0.393654 | − | 0.227276i | ||||
\(885\) | 17162.3 | − | 9423.72i | 0.651870 | − | 0.357938i | ||||
\(886\) | 7772.64 | − | 13462.6i | 0.294726 | − | 0.510480i | ||||
\(887\) | −9778.12 | + | 16936.2i | −0.370144 | + | 0.641107i | −0.989587 | − | 0.143934i | \(-0.954025\pi\) |
0.619444 | + | 0.785041i | \(0.287358\pi\) | |||||||
\(888\) | 5554.66 | + | 119.174i | 0.209913 | + | 0.00450364i | ||||
\(889\) | −19508.2 | + | 7044.35i | −0.735978 | + | 0.265759i | ||||
\(890\) | − | 22382.7i | − | 0.842999i | ||||||
\(891\) | −27856.1 | + | 13039.1i | −1.04738 | + | 0.490264i | ||||
\(892\) | 15635.2i | 0.586890i | ||||||||
\(893\) | 17265.6 | − | 9968.31i | 0.647001 | − | 0.373546i | ||||
\(894\) | −431.119 | + | 20094.3i | −0.0161284 | + | 0.751737i | ||||
\(895\) | −7639.00 | − | 4410.38i | −0.285300 | − | 0.164718i | ||||
\(896\) | −1528.40 | + | 1812.10i | −0.0569867 | + | 0.0675649i | ||||
\(897\) | 35506.1 | − | 19496.2i | 1.32164 | − | 0.725706i | ||||
\(898\) | 12669.0 | + | 21943.4i | 0.470792 | + | 0.815435i | ||||
\(899\) | 11108.8 | 0.412122 | ||||||||
\(900\) | 15885.0 | + | 681.932i | 0.588332 | + | 0.0252568i | ||||
\(901\) | 26192.3i | 0.968472i | ||||||||
\(902\) | 779.222 | + | 1349.65i | 0.0287642 | + | 0.0498210i | ||||
\(903\) | 1551.26 | − | 1761.13i | 0.0571680 | − | 0.0649024i | ||||
\(904\) | −3900.42 | + | 6755.73i | −0.143502 | + | 0.248553i | ||||
\(905\) | −3403.08 | − | 1964.77i | −0.124997 | − | 0.0721669i | ||||
\(906\) | 12507.0 | − | 20627.8i | 0.458626 | − | 0.756416i | ||||
\(907\) | 17714.3 | + | 30682.1i | 0.648504 | + | 1.12324i | 0.983480 | + | 0.181016i | \(0.0579385\pi\) |
−0.334976 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(908\) | −7548.49 | −0.275887 | ||||||||
\(909\) | 2142.81 | + | 4108.98i | 0.0781877 | + | 0.149930i | ||||
\(910\) | −4920.53 | + | 27497.2i | −0.179246 | + | 1.00167i | ||||
\(911\) | −8301.17 | + | 4792.68i | −0.301899 | + | 0.174301i | −0.643296 | − | 0.765618i | \(-0.722433\pi\) |
0.341397 | + | 0.939919i | \(0.389100\pi\) | |||||||
\(912\) | −6474.24 | − | 11790.8i | −0.235070 | − | 0.428105i | ||||
\(913\) | −44260.6 | − | 25553.9i | −1.60440 | − | 0.926298i | ||||
\(914\) | −10943.3 | − | 6318.11i | −0.396031 | − | 0.228648i | ||||
\(915\) | −21069.7 | − | 452.047i | −0.761250 | − | 0.0163325i | ||||
\(916\) | −5322.87 | + | 3073.16i | −0.192000 | + | 0.110852i | ||||
\(917\) | 5285.22 | − | 29535.1i | 0.190331 | − | 1.06362i | ||||
\(918\) | −8127.38 | − | 16435.3i | −0.292204 | − | 0.590899i | ||||
\(919\) | −49145.6 | −1.76405 | −0.882026 | − | 0.471202i | \(-0.843820\pi\) | ||||
−0.882026 | + | 0.471202i | \(0.843820\pi\) | |||||||
\(920\) | 11255.5 | + | 19495.1i | 0.403352 | + | 0.698626i | ||||
\(921\) | 35280.7 | + | 756.941i | 1.26226 | + | 0.0270815i | ||||
\(922\) | 6761.10 | + | 3903.52i | 0.241502 | + | 0.139431i | ||||
\(923\) | 18477.1 | − | 32003.3i | 0.658918 | − | 1.14128i | ||||
\(924\) | 15390.0 | − | 5186.91i | 0.547938 | − | 0.184672i | ||||
\(925\) | 9838.25 | + | 17040.4i | 0.349708 | + | 0.605712i | ||||
\(926\) | − | 6013.42i | − | 0.213405i | ||||||
\(927\) | 12636.0 | + | 8037.03i | 0.447702 | + | 0.284758i | ||||
\(928\) | −6350.29 | −0.224632 | ||||||||
\(929\) | 1073.78 | + | 1859.84i | 0.0379220 | + | 0.0656828i | 0.884363 | − | 0.466799i | \(-0.154593\pi\) |
−0.846441 | + | 0.532482i | \(0.821260\pi\) | |||||||
\(930\) | 8207.49 | + | 4976.33i | 0.289392 | + | 0.175463i | ||||
\(931\) | −35455.4 | − | 42692.6i | −1.24812 | − | 1.50289i | ||||
\(932\) | −16997.0 | − | 9813.24i | −0.597378 | − | 0.344896i | ||||
\(933\) | 18395.7 | + | 11153.6i | 0.645498 | + | 0.391375i | ||||
\(934\) | 9815.39 | − | 5666.92i | 0.343864 | − | 0.198530i | ||||
\(935\) | − | 45486.0i | − | 1.59096i | ||||||
\(936\) | −5298.69 | + | 8330.70i | −0.185035 | + | 0.290916i | ||||
\(937\) | − | 304.033i | − | 0.0106001i | −0.999986 | − | 0.00530007i | \(-0.998313\pi\) | ||
0.999986 | − | 0.00530007i | \(-0.00168707\pi\) | |||||||
\(938\) | 11740.4 | + | 32513.3i | 0.408677 | + | 1.13177i | ||||
\(939\) | −17555.5 | − | 31971.7i | −0.610118 | − | 1.11114i | ||||
\(940\) | 4066.09 | − | 7042.68i | 0.141086 | − | 0.244369i | ||||
\(941\) | −26628.9 | + | 46122.6i | −0.922505 | + | 1.59783i | −0.126980 | + | 0.991905i | \(0.540528\pi\) |
−0.795525 | + | 0.605921i | \(0.792805\pi\) | |||||||
\(942\) | −255.332 | + | 11900.9i | −0.00883139 | + | 0.411627i | ||||
\(943\) | −2727.88 | + | 1574.94i | −0.0942016 | + | 0.0543873i | ||||
\(944\) | −3654.08 | −0.125985 | ||||||||
\(945\) | 41626.5 | + | 10249.7i | 1.43292 | + | 0.352828i | ||||
\(946\) | 2057.84 | 0.0707253 | ||||||||
\(947\) | 31983.1 | − | 18465.5i | 1.09748 | − | 0.633629i | 0.161921 | − | 0.986804i | \(-0.448231\pi\) |
0.935558 | + | 0.353174i | \(0.114898\pi\) | |||||||
\(948\) | 401.330 | − | 18705.8i | 0.0137496 | − | 0.640860i | ||||
\(949\) | −2241.49 | + | 3882.37i | −0.0766721 | + | 0.132800i | ||||
\(950\) | 23819.1 | − | 41255.9i | 0.813467 | − | 1.40897i | ||||
\(951\) | 12183.5 | + | 22188.4i | 0.415434 | + | 0.756582i | ||||
\(952\) | 3288.16 | + | 9106.02i | 0.111943 | + | 0.310008i | ||||
\(953\) | 34392.3i | 1.16902i | 0.811386 | + | 0.584510i | \(0.198713\pi\) | ||||
−0.811386 | + | 0.584510i | \(0.801287\pi\) | |||||||
\(954\) | −10008.7 | − | 19192.2i | −0.339667 | − | 0.651333i | ||||
\(955\) | 5211.63i | 0.176591i | ||||||||
\(956\) | −9080.23 | + | 5242.47i | −0.307192 | + | 0.177357i | ||||
\(957\) | 37201.1 | + | 22555.6i | 1.25657 | + | 0.761880i | ||||
\(958\) | 24862.5 | + | 14354.3i | 0.838486 | + | 0.484100i | ||||
\(959\) | −11324.0 | + | 13426.0i | −0.381304 | + | 0.452084i | ||||
\(960\) | −4691.79 | − | 2844.70i | −0.157736 | − | 0.0956379i | ||||
\(961\) | −13328.7 | − | 23086.0i | −0.447407 | − | 0.774931i | ||||
\(962\) | −12218.3 | −0.409496 | ||||||||
\(963\) | −439.660 | + | 10241.5i | −0.0147122 | + | 0.342707i | ||||
\(964\) | − | 13937.2i | − | 0.465650i | ||||||
\(965\) | −11226.5 | − | 19444.8i | −0.374501 | − | 0.648654i | ||||
\(966\) | 10483.7 | + | 31105.9i | 0.349178 | + | 1.03604i | ||||
\(967\) | −20065.3 | + | 34754.1i | −0.667277 | + | 1.15576i | 0.311385 | + | 0.950284i | \(0.399207\pi\) |
−0.978663 | + | 0.205474i | \(0.934126\pi\) | |||||||
\(968\) | 3110.94 | + | 1796.10i | 0.103295 | + | 0.0596373i | ||||
\(969\) | −54922.6 | − | 1178.36i | −1.82081 | − | 0.0390653i | ||||
\(970\) | 14274.9 | + | 24724.8i | 0.472515 | + | 0.818420i | ||||
\(971\) | 3583.78 | 0.118444 | 0.0592219 | − | 0.998245i | \(-0.481138\pi\) | ||||
0.0592219 | + | 0.998245i | \(0.481138\pi\) | |||||||
\(972\) | 12235.6 | + | 8937.19i | 0.403761 | + | 0.294918i | ||||
\(973\) | 56992.6 | + | 10198.6i | 1.87780 | + | 0.336026i | ||||
\(974\) | 5559.10 | − | 3209.55i | 0.182880 | − | 0.105586i | ||||
\(975\) | −34957.5 | − | 750.008i | −1.14824 | − | 0.0246354i | ||||
\(976\) | 3406.19 | + | 1966.56i | 0.111710 | + | 0.0644961i | ||||
\(977\) | 16070.4 | + | 9278.23i | 0.526240 | + | 0.303825i | 0.739484 | − | 0.673174i | \(-0.235070\pi\) |
−0.213244 | + | 0.976999i | \(0.568403\pi\) | |||||||
\(978\) | −9048.20 | − | 16478.4i | −0.295838 | − | 0.538775i | ||||
\(979\) | 24783.7 | − | 14308.9i | 0.809083 | − | 0.467124i | ||||
\(980\) | −21231.9 | − | 7850.15i | −0.692070 | − | 0.255881i | ||||
\(981\) | 18915.7 | + | 812.041i | 0.615629 | + | 0.0264286i | ||||
\(982\) | 27116.6 | 0.881187 | ||||||||
\(983\) | 24784.7 | + | 42928.3i | 0.804180 | + | 1.39288i | 0.916844 | + | 0.399247i | \(0.130728\pi\) |
−0.112664 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(984\) | 398.049 | − | 656.505i | 0.0128957 | − | 0.0212689i | ||||
\(985\) | −10088.5 | − | 5824.58i | −0.326340 | − | 0.188413i | ||||
\(986\) | −12967.3 | + | 22460.0i | −0.418826 | + | 0.725429i | ||||
\(987\) | 7838.00 | − | 8898.41i | 0.252772 | − | 0.286970i | ||||
\(988\) | 14790.7 | + | 25618.3i | 0.476271 | + | 0.824926i | ||||
\(989\) | 4159.25i | 0.133727i | ||||||||
\(990\) | 17381.2 | + | 33329.5i | 0.557991 | + | 1.06998i | ||||
\(991\) | −36296.8 | −1.16348 | −0.581739 | − | 0.813375i | \(-0.697628\pi\) | ||||
−0.581739 | + | 0.813375i | \(0.697628\pi\) | |||||||
\(992\) | −895.658 | − | 1551.32i | −0.0286665 | − | 0.0496518i | ||||
\(993\) | 28397.6 | − | 15592.9i | 0.907523 | − | 0.498315i | ||||
\(994\) | 22891.3 | + | 19307.4i | 0.730451 | + | 0.616089i | ||||
\(995\) | 356.189 | + | 205.646i | 0.0113487 | + | 0.00655218i | ||||
\(996\) | −540.059 | + | 25171.9i | −0.0171811 | + | 0.800805i | ||||
\(997\) | 925.524 | − | 534.352i | 0.0293998 | − | 0.0169740i | −0.485228 | − | 0.874388i | \(-0.661263\pi\) |
0.514628 | + | 0.857414i | \(0.327930\pi\) | |||||||
\(998\) | − | 32389.6i | − | 1.02733i | ||||||
\(999\) | −1205.90 | + | 18712.5i | −0.0381912 | + | 0.592630i |
(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 | 126.4.m.a.41.6 | ✓ | 48 | |
3.2 | odd | 2 | 378.4.m.a.125.23 | 48 | |||
7.6 | odd | 2 | inner | 126.4.m.a.41.7 | yes | 48 | |
9.2 | odd | 6 | inner | 126.4.m.a.83.7 | yes | 48 | |
9.4 | even | 3 | 1134.4.d.b.1133.41 | 48 | |||
9.5 | odd | 6 | 1134.4.d.b.1133.8 | 48 | |||
9.7 | even | 3 | 378.4.m.a.251.24 | 48 | |||
21.20 | even | 2 | 378.4.m.a.125.24 | 48 | |||
63.13 | odd | 6 | 1134.4.d.b.1133.7 | 48 | |||
63.20 | even | 6 | inner | 126.4.m.a.83.6 | yes | 48 | |
63.34 | odd | 6 | 378.4.m.a.251.23 | 48 | |||
63.41 | even | 6 | 1134.4.d.b.1133.42 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.m.a.41.6 | ✓ | 48 | 1.1 | even | 1 | trivial | |
126.4.m.a.41.7 | yes | 48 | 7.6 | odd | 2 | inner | |
126.4.m.a.83.6 | yes | 48 | 63.20 | even | 6 | inner | |
126.4.m.a.83.7 | yes | 48 | 9.2 | odd | 6 | inner | |
378.4.m.a.125.23 | 48 | 3.2 | odd | 2 | |||
378.4.m.a.125.24 | 48 | 21.20 | even | 2 | |||
378.4.m.a.251.23 | 48 | 63.34 | odd | 6 | |||
378.4.m.a.251.24 | 48 | 9.7 | even | 3 | |||
1134.4.d.b.1133.7 | 48 | 63.13 | odd | 6 | |||
1134.4.d.b.1133.8 | 48 | 9.5 | odd | 6 | |||
1134.4.d.b.1133.41 | 48 | 9.4 | even | 3 | |||
1134.4.d.b.1133.42 | 48 | 63.41 | even | 6 |