Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(4,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.q (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.19 | ||
Character | \(\chi\) | \(=\) | 105.4 |
Dual form | 105.4.q.b.79.19 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00489 | − | 1.73487i | 1.06239 | − | 0.613371i | 0.136297 | − | 0.990668i | \(-0.456480\pi\) |
0.926092 | + | 0.377297i | \(0.123146\pi\) | |||||||
\(3\) | 2.59808 | + | 1.50000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 2.01958 | − | 3.49802i | 0.252448 | − | 0.437252i | ||||
\(5\) | 1.37289 | − | 11.0957i | 0.122795 | − | 0.992432i | ||||
\(6\) | 10.4092 | 0.708260 | ||||||||
\(7\) | 12.4845 | − | 13.6798i | 0.674101 | − | 0.738639i | ||||
\(8\) | 13.7431i | 0.607366i | ||||||||
\(9\) | 4.50000 | + | 7.79423i | 0.166667 | + | 0.288675i | ||||
\(10\) | −15.1243 | − | 35.7232i | −0.478273 | − | 1.12967i | ||||
\(11\) | 13.2857 | − | 23.0115i | 0.364162 | − | 0.630747i | −0.624479 | − | 0.781041i | \(-0.714689\pi\) |
0.988641 | + | 0.150294i | \(0.0480222\pi\) | |||||||
\(12\) | 10.4940 | − | 6.05874i | 0.252448 | − | 0.145751i | ||||
\(13\) | 8.46682i | 0.180636i | 0.995913 | + | 0.0903182i | \(0.0287884\pi\) | ||||
−0.995913 | + | 0.0903182i | \(0.971212\pi\) | |||||||
\(14\) | 13.7819 | − | 62.7654i | 0.263098 | − | 1.19820i | ||||
\(15\) | 20.2105 | − | 26.7682i | 0.347888 | − | 0.460768i | ||||
\(16\) | 39.9992 | + | 69.2807i | 0.624988 | + | 1.08251i | ||||
\(17\) | −34.8477 | − | 20.1193i | −0.497165 | − | 0.287039i | 0.230377 | − | 0.973102i | \(-0.426004\pi\) |
−0.727542 | + | 0.686063i | \(0.759337\pi\) | |||||||
\(18\) | 27.0440 | + | 15.6139i | 0.354130 | + | 0.204457i | ||||
\(19\) | 50.5336 | + | 87.5268i | 0.610169 | + | 1.05684i | 0.991212 | + | 0.132286i | \(0.0422316\pi\) |
−0.381043 | + | 0.924557i | \(0.624435\pi\) | |||||||
\(20\) | −36.0404 | − | 27.2111i | −0.402944 | − | 0.304229i | ||||
\(21\) | 52.9554 | − | 16.8143i | 0.550277 | − | 0.174723i | ||||
\(22\) | − | 92.1959i | − | 0.893465i | ||||||
\(23\) | −123.891 | + | 71.5282i | −1.12317 | + | 0.648464i | −0.942209 | − | 0.335026i | \(-0.891255\pi\) |
−0.180963 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(24\) | −20.6147 | + | 35.7057i | −0.175331 | + | 0.303683i | ||||
\(25\) | −121.230 | − | 30.4663i | −0.969843 | − | 0.243731i | ||||
\(26\) | 14.6889 | + | 25.4419i | 0.110797 | + | 0.191906i | ||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | −22.6386 | − | 71.2985i | −0.152796 | − | 0.481220i | ||||
\(29\) | −80.4405 | −0.515083 | −0.257542 | − | 0.966267i | \(-0.582912\pi\) | ||||
−0.257542 | + | 0.966267i | \(0.582912\pi\) | |||||||
\(30\) | 14.2907 | − | 115.498i | 0.0869705 | − | 0.702900i | ||||
\(31\) | 20.1857 | − | 34.9627i | 0.116950 | − | 0.202564i | −0.801607 | − | 0.597851i | \(-0.796022\pi\) |
0.918558 | + | 0.395287i | \(0.129355\pi\) | |||||||
\(32\) | 145.172 | + | 83.8148i | 0.801967 | + | 0.463016i | ||||
\(33\) | 69.0344 | − | 39.8570i | 0.364162 | − | 0.210249i | ||||
\(34\) | −139.618 | −0.704244 | ||||||||
\(35\) | −134.647 | − | 157.306i | −0.650273 | − | 0.759701i | ||||
\(36\) | 36.3524 | 0.168298 | ||||||||
\(37\) | −252.167 | + | 145.589i | −1.12043 | + | 0.646883i | −0.941512 | − | 0.336980i | \(-0.890595\pi\) |
−0.178923 | + | 0.983863i | \(0.557261\pi\) | |||||||
\(38\) | 303.696 | + | 175.339i | 1.29647 | + | 0.748519i | ||||
\(39\) | −12.7002 | + | 21.9974i | −0.0521452 | + | 0.0903182i | ||||
\(40\) | 152.490 | + | 18.8677i | 0.602769 | + | 0.0745813i | ||||
\(41\) | −16.7260 | −0.0637111 | −0.0318556 | − | 0.999492i | \(-0.510142\pi\) | ||||
−0.0318556 | + | 0.999492i | \(0.510142\pi\) | |||||||
\(42\) | 129.955 | − | 142.396i | 0.477439 | − | 0.523148i | ||||
\(43\) | 435.792i | 1.54553i | 0.634695 | + | 0.772763i | \(0.281126\pi\) | ||||
−0.634695 | + | 0.772763i | \(0.718874\pi\) | |||||||
\(44\) | −53.6630 | − | 92.9470i | −0.183864 | − | 0.318461i | ||||
\(45\) | 92.6606 | − | 39.2302i | 0.306956 | − | 0.129958i | ||||
\(46\) | −248.185 | + | 429.869i | −0.795497 | + | 1.37784i | ||||
\(47\) | 278.455 | − | 160.766i | 0.864187 | − | 0.498938i | −0.00122547 | − | 0.999999i | \(-0.500390\pi\) |
0.865412 | + | 0.501061i | \(0.167057\pi\) | |||||||
\(48\) | 239.995i | 0.721674i | ||||||||
\(49\) | −31.2731 | − | 341.571i | −0.0911752 | − | 0.995835i | ||||
\(50\) | −417.139 | + | 118.771i | −1.17985 | + | 0.335936i | ||||
\(51\) | −60.3580 | − | 104.543i | −0.165722 | − | 0.287039i | ||||
\(52\) | 29.6171 | + | 17.0994i | 0.0789836 | + | 0.0456012i | ||||
\(53\) | 187.426 | + | 108.210i | 0.485753 | + | 0.280450i | 0.722811 | − | 0.691046i | \(-0.242850\pi\) |
−0.237058 | + | 0.971496i | \(0.576183\pi\) | |||||||
\(54\) | 46.8416 | + | 81.1321i | 0.118043 | + | 0.204457i | ||||
\(55\) | −237.089 | − | 179.006i | −0.581256 | − | 0.438858i | ||||
\(56\) | 188.003 | + | 171.576i | 0.448624 | + | 0.409426i | ||||
\(57\) | 303.202i | 0.704562i | ||||||||
\(58\) | −241.715 | + | 139.554i | −0.547219 | + | 0.315937i | ||||
\(59\) | 246.925 | − | 427.686i | 0.544862 | − | 0.943729i | −0.453753 | − | 0.891127i | \(-0.649915\pi\) |
0.998616 | − | 0.0526020i | \(-0.0167515\pi\) | |||||||
\(60\) | −52.8190 | − | 124.757i | −0.113648 | − | 0.268434i | ||||
\(61\) | 392.971 | + | 680.646i | 0.824833 | + | 1.42865i | 0.902047 | + | 0.431638i | \(0.142064\pi\) |
−0.0772143 | + | 0.997015i | \(0.524603\pi\) | |||||||
\(62\) | − | 140.079i | − | 0.286936i | ||||||
\(63\) | 162.804 | + | 35.7482i | 0.325577 | + | 0.0714897i | ||||
\(64\) | −58.3547 | −0.113974 | ||||||||
\(65\) | 93.9455 | + | 11.6240i | 0.179269 | + | 0.0221812i | ||||
\(66\) | 138.294 | − | 239.532i | 0.257921 | − | 0.446733i | ||||
\(67\) | −629.817 | − | 363.625i | −1.14842 | − | 0.663042i | −0.199921 | − | 0.979812i | \(-0.564068\pi\) |
−0.948502 | + | 0.316770i | \(0.897402\pi\) | |||||||
\(68\) | −140.756 | + | 81.2653i | −0.251016 | + | 0.144924i | ||||
\(69\) | −429.169 | −0.748781 | ||||||||
\(70\) | −677.506 | − | 239.090i | −1.15682 | − | 0.408239i | ||||
\(71\) | 546.448 | 0.913400 | 0.456700 | − | 0.889621i | \(-0.349031\pi\) | ||||
0.456700 | + | 0.889621i | \(0.349031\pi\) | |||||||
\(72\) | −107.117 | + | 61.8440i | −0.175331 | + | 0.101228i | ||||
\(73\) | −288.341 | − | 166.474i | −0.462298 | − | 0.266908i | 0.250712 | − | 0.968062i | \(-0.419335\pi\) |
−0.713010 | + | 0.701154i | \(0.752669\pi\) | |||||||
\(74\) | −505.157 | + | 874.958i | −0.793559 | + | 1.37448i | ||||
\(75\) | −269.266 | − | 260.999i | −0.414562 | − | 0.401835i | ||||
\(76\) | 408.227 | 0.616142 | ||||||||
\(77\) | −148.926 | − | 469.032i | −0.220412 | − | 0.694171i | ||||
\(78\) | 88.1332i | 0.127937i | ||||||||
\(79\) | −385.859 | − | 668.327i | −0.549526 | − | 0.951806i | −0.998307 | − | 0.0581646i | \(-0.981475\pi\) |
0.448781 | − | 0.893642i | \(-0.351858\pi\) | |||||||
\(80\) | 823.634 | − | 348.706i | 1.15106 | − | 0.487332i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −50.2597 | + | 29.0174i | −0.0676860 | + | 0.0390785i | ||||
\(83\) | − | 1025.32i | − | 1.35595i | −0.735084 | − | 0.677976i | \(-0.762857\pi\) | ||
0.735084 | − | 0.677976i | \(-0.237143\pi\) | |||||||
\(84\) | 48.1310 | − | 219.197i | 0.0625181 | − | 0.284718i | ||||
\(85\) | −271.081 | + | 359.039i | −0.345916 | + | 0.458156i | ||||
\(86\) | 756.044 | + | 1309.51i | 0.947980 | + | 1.64195i | ||||
\(87\) | −208.990 | − | 120.661i | −0.257542 | − | 0.148692i | ||||
\(88\) | 316.249 | + | 182.587i | 0.383094 | + | 0.221179i | ||||
\(89\) | 428.219 | + | 741.697i | 0.510012 | + | 0.883367i | 0.999933 | + | 0.0116000i | \(0.00369247\pi\) |
−0.489920 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(90\) | 210.376 | − | 278.637i | 0.246395 | − | 0.326344i | ||||
\(91\) | 115.824 | + | 105.704i | 0.133425 | + | 0.121767i | ||||
\(92\) | 577.828i | 0.654812i | ||||||||
\(93\) | 104.888 | − | 60.5571i | 0.116950 | − | 0.0675213i | ||||
\(94\) | 557.817 | − | 966.167i | 0.612068 | − | 1.06013i | ||||
\(95\) | 1040.55 | − | 440.543i | 1.12377 | − | 0.475776i | ||||
\(96\) | 251.445 | + | 435.515i | 0.267322 | + | 0.463016i | ||||
\(97\) | − | 127.420i | − | 0.133377i | −0.997774 | − | 0.0666883i | \(-0.978757\pi\) | ||
0.997774 | − | 0.0666883i | \(-0.0212433\pi\) | |||||||
\(98\) | −686.556 | − | 972.130i | −0.707680 | − | 1.00204i | ||||
\(99\) | 239.142 | 0.242775 | ||||||||
\(100\) | −351.406 | + | 362.537i | −0.351406 | + | 0.362537i | ||||
\(101\) | 450.729 | − | 780.686i | 0.444052 | − | 0.769121i | −0.553934 | − | 0.832561i | \(-0.686874\pi\) |
0.997986 | + | 0.0634402i | \(0.0202072\pi\) | |||||||
\(102\) | −362.739 | − | 209.427i | −0.352122 | − | 0.203298i | ||||
\(103\) | 321.096 | − | 185.385i | 0.307170 | − | 0.177345i | −0.338489 | − | 0.940970i | \(-0.609916\pi\) |
0.645660 | + | 0.763625i | \(0.276583\pi\) | |||||||
\(104\) | −116.360 | −0.109712 | ||||||||
\(105\) | −113.866 | − | 610.663i | −0.105830 | − | 0.567568i | ||||
\(106\) | 750.926 | 0.688079 | ||||||||
\(107\) | −892.421 | + | 515.240i | −0.806296 | + | 0.465515i | −0.845668 | − | 0.533710i | \(-0.820798\pi\) |
0.0393722 | + | 0.999225i | \(0.487464\pi\) | |||||||
\(108\) | 94.4464 | + | 54.5287i | 0.0841492 | + | 0.0485836i | ||||
\(109\) | 942.880 | − | 1633.12i | 0.828546 | − | 1.43508i | −0.0706330 | − | 0.997502i | \(-0.522502\pi\) |
0.899179 | − | 0.437581i | \(-0.144165\pi\) | |||||||
\(110\) | −1022.98 | − | 126.574i | −0.886703 | − | 0.109713i | ||||
\(111\) | −873.534 | −0.746956 | ||||||||
\(112\) | 1447.12 | + | 317.756i | 1.22089 | + | 0.268081i | ||||
\(113\) | − | 2054.47i | − | 1.71034i | −0.518349 | − | 0.855169i | \(-0.673453\pi\) | ||
0.518349 | − | 0.855169i | \(-0.326547\pi\) | |||||||
\(114\) | 526.017 | + | 911.088i | 0.432158 | + | 0.748519i | ||||
\(115\) | 623.570 | + | 1472.86i | 0.505637 | + | 1.19430i | ||||
\(116\) | −162.456 | + | 281.382i | −0.130032 | + | 0.225221i | ||||
\(117\) | −65.9923 | + | 38.1007i | −0.0521452 | + | 0.0301061i | ||||
\(118\) | − | 1713.54i | − | 1.33681i | ||||||
\(119\) | −710.286 | + | 225.529i | −0.547158 | + | 0.173733i | ||||
\(120\) | 367.879 | + | 277.755i | 0.279855 | + | 0.211295i | ||||
\(121\) | 312.482 | + | 541.235i | 0.234772 | + | 0.406638i | ||||
\(122\) | 2361.67 | + | 1363.51i | 1.75259 | + | 1.01186i | ||||
\(123\) | −43.4553 | − | 25.0889i | −0.0318556 | − | 0.0183918i | ||||
\(124\) | −81.5333 | − | 141.220i | −0.0590476 | − | 0.102273i | ||||
\(125\) | −504.482 | + | 1303.31i | −0.360978 | + | 0.932574i | ||||
\(126\) | 551.226 | − | 175.025i | 0.389739 | − | 0.123749i | ||||
\(127\) | 1203.95i | 0.841206i | 0.907245 | + | 0.420603i | \(0.138181\pi\) | ||||
−0.907245 | + | 0.420603i | \(0.861819\pi\) | |||||||
\(128\) | −1336.72 | + | 771.757i | −0.923052 | + | 0.532924i | ||||
\(129\) | −653.687 | + | 1132.22i | −0.446155 | + | 0.772763i | ||||
\(130\) | 302.462 | − | 128.055i | 0.204059 | − | 0.0863935i | ||||
\(131\) | −1435.56 | − | 2486.46i | −0.957445 | − | 1.65834i | −0.728670 | − | 0.684865i | \(-0.759861\pi\) |
−0.228775 | − | 0.973479i | \(-0.573472\pi\) | |||||||
\(132\) | − | 321.978i | − | 0.212307i | ||||||
\(133\) | 1828.24 | + | 401.441i | 1.19194 | + | 0.261725i | ||||
\(134\) | −2523.37 | −1.62676 | ||||||||
\(135\) | 299.585 | + | 37.0679i | 0.190994 | + | 0.0236318i | ||||
\(136\) | 276.502 | − | 478.916i | 0.174337 | − | 0.301961i | ||||
\(137\) | −1556.12 | − | 898.427i | −0.970427 | − | 0.560276i | −0.0710604 | − | 0.997472i | \(-0.522638\pi\) |
−0.899366 | + | 0.437196i | \(0.855972\pi\) | |||||||
\(138\) | −1289.61 | + | 744.555i | −0.795497 | + | 0.459281i | ||||
\(139\) | −7.88277 | −0.00481013 | −0.00240506 | − | 0.999997i | \(-0.500766\pi\) | ||||
−0.00240506 | + | 0.999997i | \(0.500766\pi\) | |||||||
\(140\) | −822.189 | + | 153.307i | −0.496340 | + | 0.0925486i | ||||
\(141\) | 964.595 | 0.576124 | ||||||||
\(142\) | 1642.02 | − | 948.018i | 0.970387 | − | 0.560253i | ||||
\(143\) | 194.834 | + | 112.487i | 0.113936 | + | 0.0657809i | ||||
\(144\) | −359.993 | + | 623.526i | −0.208329 | + | 0.360837i | ||||
\(145\) | −110.436 | + | 892.546i | −0.0632495 | + | 0.511185i | ||||
\(146\) | −1155.24 | −0.654854 | ||||||||
\(147\) | 431.107 | − | 934.338i | 0.241885 | − | 0.524237i | ||||
\(148\) | 1176.11i | 0.653216i | ||||||||
\(149\) | 1178.71 | + | 2041.59i | 0.648080 | + | 1.12251i | 0.983581 | + | 0.180467i | \(0.0577609\pi\) |
−0.335501 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(150\) | −1261.92 | − | 317.132i | −0.686901 | − | 0.172625i | ||||
\(151\) | −1719.08 | + | 2977.53i | −0.926468 | + | 1.60469i | −0.137286 | + | 0.990532i | \(0.543838\pi\) |
−0.789183 | + | 0.614159i | \(0.789496\pi\) | |||||||
\(152\) | −1202.89 | + | 694.489i | −0.641890 | + | 0.370595i | ||||
\(153\) | − | 362.148i | − | 0.191359i | ||||||
\(154\) | −1261.22 | − | 1151.02i | −0.659948 | − | 0.602286i | ||||
\(155\) | −360.223 | − | 271.975i | −0.186670 | − | 0.140939i | ||||
\(156\) | 51.2982 | + | 88.8512i | 0.0263279 | + | 0.0456012i | ||||
\(157\) | −1030.91 | − | 595.196i | −0.524048 | − | 0.302559i | 0.214541 | − | 0.976715i | \(-0.431174\pi\) |
−0.738589 | + | 0.674156i | \(0.764508\pi\) | |||||||
\(158\) | −2318.93 | − | 1338.83i | −1.16762 | − | 0.674126i | ||||
\(159\) | 324.631 | + | 562.277i | 0.161918 | + | 0.280450i | ||||
\(160\) | 1129.29 | − | 1495.72i | 0.557989 | − | 0.739042i | ||||
\(161\) | −568.224 | + | 2587.79i | −0.278151 | + | 1.26675i | ||||
\(162\) | 281.050i | 0.136305i | ||||||||
\(163\) | −2223.76 | + | 1283.89i | −1.06858 | + | 0.616945i | −0.927793 | − | 0.373095i | \(-0.878297\pi\) |
−0.140787 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(164\) | −33.7794 | + | 58.5077i | −0.0160837 | + | 0.0278578i | ||||
\(165\) | −347.466 | − | 820.706i | −0.163941 | − | 0.387223i | ||||
\(166\) | −1778.81 | − | 3080.99i | −0.831701 | − | 1.44055i | ||||
\(167\) | 2994.69i | 1.38764i | 0.720149 | + | 0.693820i | \(0.244074\pi\) | ||||
−0.720149 | + | 0.693820i | \(0.755926\pi\) | |||||||
\(168\) | 231.081 | + | 727.773i | 0.106121 | + | 0.334220i | ||||
\(169\) | 2125.31 | 0.967371 | ||||||||
\(170\) | −191.680 | + | 1549.16i | −0.0864775 | + | 0.698915i | ||||
\(171\) | −454.802 | + | 787.741i | −0.203390 | + | 0.352281i | ||||
\(172\) | 1524.41 | + | 880.116i | 0.675784 | + | 0.390164i | ||||
\(173\) | 1890.39 | − | 1091.41i | 0.830771 | − | 0.479646i | −0.0233456 | − | 0.999727i | \(-0.507432\pi\) |
0.854117 | + | 0.520082i | \(0.174098\pi\) | |||||||
\(174\) | −837.325 | −0.364813 | ||||||||
\(175\) | −1930.28 | + | 1278.05i | −0.833801 | + | 0.552065i | ||||
\(176\) | 2125.67 | 0.910387 | ||||||||
\(177\) | 1283.06 | − | 740.775i | 0.544862 | − | 0.314576i | ||||
\(178\) | 2573.50 | + | 1485.81i | 1.08366 | + | 0.625653i | ||||
\(179\) | 1057.95 | − | 1832.42i | 0.441760 | − | 0.765150i | −0.556061 | − | 0.831142i | \(-0.687688\pi\) |
0.997820 | + | 0.0659917i | \(0.0210211\pi\) | |||||||
\(180\) | 49.9078 | − | 403.357i | 0.0206661 | − | 0.167025i | ||||
\(181\) | −102.107 | −0.0419314 | −0.0209657 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209657 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(182\) | 531.423 | + | 116.689i | 0.216438 | + | 0.0475251i | ||||
\(183\) | 2357.83i | 0.952435i | ||||||||
\(184\) | −983.021 | − | 1702.64i | −0.393855 | − | 0.682176i | ||||
\(185\) | 1269.22 | + | 2997.86i | 0.504404 | + | 1.19139i | ||||
\(186\) | 210.118 | − | 363.935i | 0.0828312 | − | 0.143468i | ||||
\(187\) | −925.951 | + | 534.598i | −0.362097 | + | 0.209057i | ||||
\(188\) | − | 1298.72i | − | 0.503823i | ||||||
\(189\) | 369.354 | + | 337.082i | 0.142151 | + | 0.129731i | ||||
\(190\) | 2362.45 | − | 3129.01i | 0.902054 | − | 1.19475i | ||||
\(191\) | −374.792 | − | 649.158i | −0.141984 | − | 0.245924i | 0.786260 | − | 0.617896i | \(-0.212015\pi\) |
−0.928244 | + | 0.371973i | \(0.878682\pi\) | |||||||
\(192\) | −151.610 | − | 87.5321i | −0.0569871 | − | 0.0329015i | ||||
\(193\) | 1215.06 | + | 701.516i | 0.453171 | + | 0.261638i | 0.709168 | − | 0.705039i | \(-0.249071\pi\) |
−0.255998 | + | 0.966677i | \(0.582404\pi\) | |||||||
\(194\) | −221.058 | − | 382.883i | −0.0818094 | − | 0.141698i | ||||
\(195\) | 226.642 | + | 171.118i | 0.0832315 | + | 0.0628412i | ||||
\(196\) | −1257.98 | − | 580.437i | −0.458448 | − | 0.211530i | ||||
\(197\) | − | 1258.07i | − | 0.454995i | −0.973779 | − | 0.227498i | \(-0.926946\pi\) | ||
0.973779 | − | 0.227498i | \(-0.0730544\pi\) | |||||||
\(198\) | 718.596 | − | 414.882i | 0.257921 | − | 0.148911i | ||||
\(199\) | 1524.75 | − | 2640.94i | 0.543149 | − | 0.940761i | −0.455572 | − | 0.890199i | \(-0.650565\pi\) |
0.998721 | − | 0.0505624i | \(-0.0161014\pi\) | |||||||
\(200\) | 418.703 | − | 1666.08i | 0.148034 | − | 0.589049i | ||||
\(201\) | −1090.87 | − | 1889.45i | −0.382808 | − | 0.663042i | ||||
\(202\) | − | 3127.84i | − | 1.08947i | ||||||
\(203\) | −1004.26 | + | 1100.41i | −0.347218 | + | 0.380461i | ||||
\(204\) | −487.592 | −0.167344 | ||||||||
\(205\) | −22.9628 | + | 185.587i | −0.00782338 | + | 0.0632289i | ||||
\(206\) | 643.240 | − | 1114.12i | 0.217556 | − | 0.376819i | ||||
\(207\) | −1115.01 | − | 643.754i | −0.374391 | − | 0.216155i | ||||
\(208\) | −586.587 | + | 338.666i | −0.195541 | + | 0.112896i | ||||
\(209\) | 2685.49 | 0.888800 | ||||||||
\(210\) | −1401.58 | − | 1637.43i | −0.460562 | − | 0.538065i | ||||
\(211\) | 4241.89 | 1.38400 | 0.691999 | − | 0.721898i | \(-0.256730\pi\) | ||||
0.691999 | + | 0.721898i | \(0.256730\pi\) | |||||||
\(212\) | 757.043 | − | 437.079i | 0.245254 | − | 0.141598i | ||||
\(213\) | 1419.71 | + | 819.672i | 0.456700 | + | 0.263676i | ||||
\(214\) | −1787.75 | + | 3096.48i | −0.571067 | + | 0.989116i | ||||
\(215\) | 4835.43 | + | 598.292i | 1.53383 | + | 0.189782i | ||||
\(216\) | −371.064 | −0.116888 | ||||||||
\(217\) | −226.273 | − | 712.628i | −0.0707852 | − | 0.222933i | ||||
\(218\) | − | 6543.11i | − | 2.03282i | ||||||
\(219\) | −499.421 | − | 865.022i | −0.154099 | − | 0.266908i | ||||
\(220\) | −1104.99 | + | 467.824i | −0.338628 | + | 0.143367i | ||||
\(221\) | 170.347 | − | 295.049i | 0.0518496 | − | 0.0898061i | ||||
\(222\) | −2624.87 | + | 1515.47i | −0.793559 | + | 0.458161i | ||||
\(223\) | 2842.48i | 0.853573i | 0.904352 | + | 0.426786i | \(0.140354\pi\) | ||||
−0.904352 | + | 0.426786i | \(0.859646\pi\) | |||||||
\(224\) | 2958.97 | − | 939.527i | 0.882609 | − | 0.280245i | ||||
\(225\) | −308.075 | − | 1082.00i | −0.0912815 | − | 0.320591i | ||||
\(226\) | −3564.25 | − | 6173.46i | −1.04907 | − | 1.81705i | ||||
\(227\) | −1164.18 | − | 672.137i | −0.340392 | − | 0.196526i | 0.320053 | − | 0.947400i | \(-0.396299\pi\) |
−0.660446 | + | 0.750874i | \(0.729633\pi\) | |||||||
\(228\) | 1060.60 | + | 612.340i | 0.308071 | + | 0.177865i | ||||
\(229\) | 2688.97 | + | 4657.43i | 0.775947 | + | 1.34398i | 0.934261 | + | 0.356591i | \(0.116061\pi\) |
−0.158313 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(230\) | 4428.98 | + | 3343.95i | 1.26973 | + | 0.958669i | ||||
\(231\) | 316.626 | − | 1441.97i | 0.0901838 | − | 0.410713i | ||||
\(232\) | − | 1105.50i | − | 0.312844i | ||||||
\(233\) | 2020.02 | − | 1166.26i | 0.567964 | − | 0.327914i | −0.188372 | − | 0.982098i | \(-0.560321\pi\) |
0.756336 | + | 0.654184i | \(0.226988\pi\) | |||||||
\(234\) | −132.200 | + | 228.977i | −0.0369324 | + | 0.0639687i | ||||
\(235\) | −1401.53 | − | 3310.37i | −0.389045 | − | 0.918913i | ||||
\(236\) | −997.369 | − | 1727.49i | −0.275098 | − | 0.476484i | ||||
\(237\) | − | 2315.15i | − | 0.634537i | ||||||
\(238\) | −1743.07 | + | 1909.95i | −0.474732 | + | 0.520182i | ||||
\(239\) | −1637.91 | −0.443295 | −0.221647 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221647 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(240\) | 2662.92 | + | 329.486i | 0.716212 | + | 0.0886177i | ||||
\(241\) | −634.373 | + | 1098.77i | −0.169558 | + | 0.293684i | −0.938265 | − | 0.345918i | \(-0.887567\pi\) |
0.768706 | + | 0.639602i | \(0.220901\pi\) | |||||||
\(242\) | 1877.95 | + | 1084.23i | 0.498839 | + | 0.288005i | ||||
\(243\) | −210.444 | + | 121.500i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 3174.55 | 0.832908 | ||||||||
\(245\) | −3832.92 | − | 121.941i | −0.999494 | − | 0.0317980i | ||||
\(246\) | −174.105 | −0.0451240 | ||||||||
\(247\) | −741.073 | + | 427.859i | −0.190904 | + | 0.110219i | ||||
\(248\) | 480.496 | + | 277.414i | 0.123030 | + | 0.0710316i | ||||
\(249\) | 1537.99 | − | 2663.87i | 0.391429 | − | 0.677976i | ||||
\(250\) | 745.171 | + | 4791.52i | 0.188515 | + | 1.21217i | ||||
\(251\) | −7277.29 | −1.83003 | −0.915017 | − | 0.403416i | \(-0.867823\pi\) | ||||
−0.915017 | + | 0.403416i | \(0.867823\pi\) | |||||||
\(252\) | 453.843 | − | 497.294i | 0.113450 | − | 0.124312i | ||||
\(253\) | 3801.20i | 0.944583i | ||||||||
\(254\) | 2088.70 | + | 3617.73i | 0.515971 | + | 0.893688i | ||||
\(255\) | −1242.85 | + | 526.190i | −0.305216 | + | 0.129221i | ||||
\(256\) | −2444.38 | + | 4233.80i | −0.596773 | + | 1.03364i | ||||
\(257\) | 156.196 | − | 90.1797i | 0.0379114 | − | 0.0218882i | −0.480925 | − | 0.876762i | \(-0.659699\pi\) |
0.518836 | + | 0.854874i | \(0.326366\pi\) | |||||||
\(258\) | 4536.26i | 1.09463i | ||||||||
\(259\) | −1156.57 | + | 5267.21i | −0.277473 | + | 1.26366i | ||||
\(260\) | 230.391 | − | 305.147i | 0.0549549 | − | 0.0727863i | ||||
\(261\) | −361.982 | − | 626.971i | −0.0858472 | − | 0.148692i | ||||
\(262\) | −8627.39 | − | 4981.03i | −2.03436 | − | 1.17454i | ||||
\(263\) | 589.122 | + | 340.130i | 0.138125 | + | 0.0797464i | 0.567470 | − | 0.823394i | \(-0.307922\pi\) |
−0.429345 | + | 0.903140i | \(0.641256\pi\) | |||||||
\(264\) | 547.760 | + | 948.748i | 0.127698 | + | 0.221179i | ||||
\(265\) | 1457.99 | − | 1931.07i | 0.337975 | − | 0.447639i | ||||
\(266\) | 6190.10 | − | 1965.47i | 1.42684 | − | 0.453048i | ||||
\(267\) | 2569.31i | 0.588911i | ||||||||
\(268\) | −2543.93 | + | 1468.74i | −0.579833 | + | 0.334767i | ||||
\(269\) | −645.815 | + | 1118.58i | −0.146379 | + | 0.253536i | −0.929887 | − | 0.367846i | \(-0.880095\pi\) |
0.783507 | + | 0.621383i | \(0.213429\pi\) | |||||||
\(270\) | 964.527 | − | 408.357i | 0.217405 | − | 0.0920437i | ||||
\(271\) | −2831.37 | − | 4904.08i | −0.634663 | − | 1.09927i | −0.986586 | − | 0.163240i | \(-0.947806\pi\) |
0.351923 | − | 0.936029i | \(-0.385528\pi\) | |||||||
\(272\) | − | 3219.03i | − | 0.717583i | ||||||
\(273\) | 142.364 | + | 448.364i | 0.0315614 | + | 0.0994001i | ||||
\(274\) | −6234.64 | −1.37463 | ||||||||
\(275\) | −2311.70 | + | 2384.92i | −0.506912 | + | 0.522968i | ||||
\(276\) | −866.742 | + | 1501.24i | −0.189028 | + | 0.327406i | ||||
\(277\) | 1212.47 | + | 700.021i | 0.262998 | + | 0.151842i | 0.625701 | − | 0.780063i | \(-0.284813\pi\) |
−0.362704 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(278\) | −23.6869 | + | 13.6756i | −0.00511023 | + | 0.00295039i | ||||
\(279\) | 363.343 | 0.0779669 | ||||||||
\(280\) | 2161.87 | − | 1850.47i | 0.461416 | − | 0.394954i | ||||
\(281\) | −4965.18 | −1.05408 | −0.527042 | − | 0.849839i | \(-0.676699\pi\) | ||||
−0.527042 | + | 0.849839i | \(0.676699\pi\) | |||||||
\(282\) | 2898.50 | − | 1673.45i | 0.612068 | − | 0.353378i | ||||
\(283\) | −6502.86 | − | 3754.43i | −1.36592 | − | 0.788613i | −0.375514 | − | 0.926817i | \(-0.622534\pi\) |
−0.990404 | + | 0.138204i | \(0.955867\pi\) | |||||||
\(284\) | 1103.60 | − | 1911.48i | 0.230586 | − | 0.399386i | ||||
\(285\) | 3364.24 | + | 416.261i | 0.699230 | + | 0.0865164i | ||||
\(286\) | 780.606 | 0.161392 | ||||||||
\(287\) | −208.816 | + | 228.808i | −0.0429477 | + | 0.0470595i | ||||
\(288\) | 1508.67i | 0.308677i | ||||||||
\(289\) | −1646.92 | − | 2852.56i | −0.335218 | − | 0.580614i | ||||
\(290\) | 1216.61 | + | 2873.59i | 0.246351 | + | 0.581873i | ||||
\(291\) | 191.130 | − | 331.047i | 0.0385025 | − | 0.0666883i | ||||
\(292\) | −1164.65 | + | 672.414i | −0.233412 | + | 0.134760i | ||||
\(293\) | 5927.86i | 1.18194i | 0.806693 | + | 0.590971i | \(0.201255\pi\) | ||||
−0.806693 | + | 0.590971i | \(0.798745\pi\) | |||||||
\(294\) | −325.530 | − | 3555.50i | −0.0645757 | − | 0.705310i | ||||
\(295\) | −4406.49 | − | 3326.98i | −0.869681 | − | 0.656624i | ||||
\(296\) | −2000.85 | − | 3465.57i | −0.392895 | − | 0.680514i | ||||
\(297\) | 621.309 | + | 358.713i | 0.121387 | + | 0.0700830i | ||||
\(298\) | 7083.80 | + | 4089.84i | 1.37703 | + | 0.795026i | ||||
\(299\) | −605.616 | − | 1048.96i | −0.117136 | − | 0.202886i | ||||
\(300\) | −1456.78 | + | 414.788i | −0.280358 | + | 0.0798260i | ||||
\(301\) | 5961.54 | + | 5440.65i | 1.14159 | + | 1.04184i | ||||
\(302\) | 11929.6i | 2.27307i | ||||||||
\(303\) | 2342.06 | − | 1352.19i | 0.444052 | − | 0.256374i | ||||
\(304\) | −4042.61 | + | 7002.01i | −0.762696 | + | 1.32103i | ||||
\(305\) | 8091.77 | − | 3425.85i | 1.51913 | − | 0.643160i | ||||
\(306\) | −628.282 | − | 1088.22i | −0.117374 | − | 0.203298i | ||||
\(307\) | − | 2756.38i | − | 0.512426i | −0.966620 | − | 0.256213i | \(-0.917525\pi\) | ||
0.966620 | − | 0.256213i | \(-0.0824749\pi\) | |||||||
\(308\) | −1941.45 | − | 426.301i | −0.359170 | − | 0.0788661i | ||||
\(309\) | 1112.31 | 0.204780 | ||||||||
\(310\) | −1554.27 | − | 192.312i | −0.284764 | − | 0.0352342i | ||||
\(311\) | 1991.81 | − | 3449.92i | 0.363168 | − | 0.629026i | −0.625312 | − | 0.780375i | \(-0.715028\pi\) |
0.988480 | + | 0.151349i | \(0.0483617\pi\) | |||||||
\(312\) | −302.313 | − | 174.541i | −0.0548562 | − | 0.0316712i | ||||
\(313\) | 7472.28 | − | 4314.12i | 1.34939 | − | 0.779069i | 0.361225 | − | 0.932479i | \(-0.382359\pi\) |
0.988163 | + | 0.153409i | \(0.0490253\pi\) | |||||||
\(314\) | −4130.36 | −0.742325 | ||||||||
\(315\) | 620.164 | − | 1757.35i | 0.110928 | − | 0.314334i | ||||
\(316\) | −3117.09 | −0.554906 | ||||||||
\(317\) | 4544.63 | − | 2623.85i | 0.805211 | − | 0.464889i | −0.0400788 | − | 0.999197i | \(-0.512761\pi\) |
0.845290 | + | 0.534308i | \(0.179428\pi\) | |||||||
\(318\) | 1950.96 | + | 1126.39i | 0.344039 | + | 0.198631i | ||||
\(319\) | −1068.71 | + | 1851.05i | −0.187574 | + | 0.324887i | ||||
\(320\) | −80.1144 | + | 647.488i | −0.0139954 | + | 0.113112i | ||||
\(321\) | −3091.44 | −0.537530 | ||||||||
\(322\) | 2782.04 | + | 8761.83i | 0.481482 | + | 1.51639i | ||||
\(323\) | − | 4066.81i | − | 0.700568i | ||||||
\(324\) | 163.586 | + | 283.339i | 0.0280497 | + | 0.0485836i | ||||
\(325\) | 257.953 | − | 1026.44i | 0.0440266 | − | 0.175189i | ||||
\(326\) | −4454.78 | + | 7715.90i | −0.756832 | + | 1.31087i | ||||
\(327\) | 4899.35 | − | 2828.64i | 0.828546 | − | 0.478361i | ||||
\(328\) | − | 229.867i | − | 0.0386959i | ||||||
\(329\) | 1277.13 | − | 5816.28i | 0.214014 | − | 0.974657i | ||||
\(330\) | −2467.92 | − | 1863.32i | −0.411680 | − | 0.310826i | ||||
\(331\) | −2244.31 | − | 3887.26i | −0.372684 | − | 0.645507i | 0.617294 | − | 0.786733i | \(-0.288229\pi\) |
−0.989977 | + | 0.141225i | \(0.954896\pi\) | |||||||
\(332\) | −3586.60 | − | 2070.73i | −0.592893 | − | 0.342307i | ||||
\(333\) | −2269.51 | − | 1310.30i | −0.373478 | − | 0.215628i | ||||
\(334\) | 5195.41 | + | 8998.71i | 0.851138 | + | 1.47421i | ||||
\(335\) | −4899.35 | + | 6489.06i | −0.799045 | + | 1.05831i | ||||
\(336\) | 3283.09 | + | 2996.23i | 0.533057 | + | 0.486481i | ||||
\(337\) | 5703.77i | 0.921971i | 0.887408 | + | 0.460986i | \(0.152504\pi\) | ||||
−0.887408 | + | 0.460986i | \(0.847496\pi\) | |||||||
\(338\) | 6386.33 | − | 3687.15i | 1.02772 | − | 0.593357i | ||||
\(339\) | 3081.70 | − | 5337.67i | 0.493732 | − | 0.855169i | ||||
\(340\) | 708.456 | + | 1673.35i | 0.113004 | + | 0.266913i | ||||
\(341\) | −536.361 | − | 929.005i | −0.0851777 | − | 0.147532i | ||||
\(342\) | 3156.10i | 0.499013i | ||||||||
\(343\) | −5063.05 | − | 3836.55i | −0.797024 | − | 0.603948i | ||||
\(344\) | −5989.14 | −0.938699 | ||||||||
\(345\) | −589.201 | + | 4761.95i | −0.0919464 | + | 0.743115i | ||||
\(346\) | 3786.94 | − | 6559.16i | 0.588402 | − | 1.01914i | ||||
\(347\) | 3987.06 | + | 2301.93i | 0.616820 | + | 0.356121i | 0.775630 | − | 0.631188i | \(-0.217432\pi\) |
−0.158810 | + | 0.987309i | \(0.550766\pi\) | |||||||
\(348\) | −844.146 | + | 487.368i | −0.130032 | + | 0.0750738i | ||||
\(349\) | 4802.77 | 0.736638 | 0.368319 | − | 0.929700i | \(-0.379933\pi\) | ||||
0.368319 | + | 0.929700i | \(0.379933\pi\) | |||||||
\(350\) | −3583.02 | + | 7189.18i | −0.547201 | + | 1.09794i | ||||
\(351\) | −228.604 | −0.0347635 | ||||||||
\(352\) | 3857.40 | − | 2227.07i | 0.584092 | − | 0.337225i | ||||
\(353\) | −8996.88 | − | 5194.35i | −1.35653 | − | 0.783194i | −0.367377 | − | 0.930072i | \(-0.619744\pi\) |
−0.989155 | + | 0.146878i | \(0.953078\pi\) | |||||||
\(354\) | 2570.30 | − | 4451.89i | 0.385904 | − | 0.668405i | ||||
\(355\) | 750.211 | − | 6063.24i | 0.112161 | − | 0.906488i | ||||
\(356\) | 3459.29 | 0.515005 | ||||||||
\(357\) | −2183.67 | − | 479.487i | −0.323731 | − | 0.0710845i | ||||
\(358\) | − | 7341.65i | − | 1.08385i | ||||||
\(359\) | −2265.55 | − | 3924.04i | −0.333067 | − | 0.576889i | 0.650045 | − | 0.759896i | \(-0.274750\pi\) |
−0.983112 | + | 0.183007i | \(0.941417\pi\) | |||||||
\(360\) | 539.145 | + | 1273.45i | 0.0789318 | + | 0.186435i | ||||
\(361\) | −1677.79 | + | 2906.01i | −0.244611 | + | 0.423679i | ||||
\(362\) | −306.821 | + | 177.143i | −0.0445474 | + | 0.0257195i | ||||
\(363\) | 1874.89i | 0.271092i | ||||||||
\(364\) | 603.671 | − | 191.677i | 0.0869258 | − | 0.0276005i | ||||
\(365\) | −2243.01 | + | 2970.80i | −0.321656 | + | 0.426024i | ||||
\(366\) | 4090.53 | + | 7085.01i | 0.584196 | + | 1.01186i | ||||
\(367\) | −4449.31 | − | 2568.81i | −0.632840 | − | 0.365370i | 0.149011 | − | 0.988836i | \(-0.452391\pi\) |
−0.781851 | + | 0.623465i | \(0.785724\pi\) | |||||||
\(368\) | −9911.05 | − | 5722.15i | −1.40394 | − | 0.810564i | ||||
\(369\) | −75.2668 | − | 130.366i | −0.0106185 | − | 0.0183918i | ||||
\(370\) | 9014.77 | + | 6806.30i | 1.26664 | + | 0.956332i | ||||
\(371\) | 3820.22 | − | 1212.99i | 0.534598 | − | 0.169745i | ||||
\(372\) | − | 489.200i | − | 0.0681823i | ||||||
\(373\) | −4685.97 | + | 2705.44i | −0.650483 | + | 0.375557i | −0.788641 | − | 0.614854i | \(-0.789215\pi\) |
0.138158 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(374\) | −1854.92 | + | 3212.82i | −0.256459 | + | 0.444200i | ||||
\(375\) | −3265.65 | + | 2629.38i | −0.449700 | + | 0.362082i | ||||
\(376\) | 2209.42 | + | 3826.83i | 0.303038 | + | 0.524877i | ||||
\(377\) | − | 681.075i | − | 0.0930428i | ||||||
\(378\) | 1694.66 | + | 372.112i | 0.230593 | + | 0.0506333i | ||||
\(379\) | 1905.38 | 0.258239 | 0.129120 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129120 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(380\) | 560.449 | − | 4529.57i | 0.0756590 | − | 0.611479i | ||||
\(381\) | −1805.92 | + | 3127.95i | −0.242835 | + | 0.420603i | ||||
\(382\) | −2252.42 | − | 1300.43i | −0.301685 | − | 0.174178i | ||||
\(383\) | −4233.89 | + | 2444.44i | −0.564860 | + | 0.326122i | −0.755094 | − | 0.655617i | \(-0.772409\pi\) |
0.190234 | + | 0.981739i | \(0.439075\pi\) | |||||||
\(384\) | −4630.54 | −0.615368 | ||||||||
\(385\) | −5408.71 | + | 1008.52i | −0.715983 | + | 0.133504i | ||||
\(386\) | 4868.17 | 0.641925 | ||||||||
\(387\) | −3396.66 | + | 1961.06i | −0.446155 | + | 0.257588i | ||||
\(388\) | −445.717 | − | 257.335i | −0.0583192 | − | 0.0336706i | ||||
\(389\) | 2266.47 | − | 3925.64i | 0.295410 | − | 0.511665i | −0.679670 | − | 0.733518i | \(-0.737877\pi\) |
0.975080 | + | 0.221853i | \(0.0712104\pi\) | |||||||
\(390\) | 977.902 | + | 120.997i | 0.126969 | + | 0.0157100i | ||||
\(391\) | 5756.40 | 0.744537 | ||||||||
\(392\) | 4694.26 | − | 429.790i | 0.604836 | − | 0.0553767i | ||||
\(393\) | − | 8613.35i | − | 1.10556i | ||||||
\(394\) | −2182.60 | − | 3780.38i | −0.279081 | − | 0.483382i | ||||
\(395\) | −7945.32 | + | 3363.85i | −1.01208 | + | 0.428490i | ||||
\(396\) | 482.967 | − | 836.523i | 0.0612878 | − | 0.106154i | ||||
\(397\) | 1922.70 | − | 1110.07i | 0.243067 | − | 0.140335i | −0.373519 | − | 0.927623i | \(-0.621849\pi\) |
0.616586 | + | 0.787288i | \(0.288515\pi\) | |||||||
\(398\) | − | 10581.0i | − | 1.33261i | ||||||
\(399\) | 4147.73 | + | 3785.33i | 0.520417 | + | 0.474946i | ||||
\(400\) | −2738.39 | − | 9617.56i | −0.342299 | − | 1.20219i | ||||
\(401\) | 4071.07 | + | 7051.30i | 0.506981 | + | 0.878117i | 0.999967 | + | 0.00807997i | \(0.00257196\pi\) |
−0.492986 | + | 0.870037i | \(0.664095\pi\) | |||||||
\(402\) | −6555.92 | − | 3785.06i | −0.813382 | − | 0.469606i | ||||
\(403\) | 296.022 | + | 170.909i | 0.0365904 | + | 0.0211255i | ||||
\(404\) | −1820.57 | − | 3153.32i | −0.224200 | − | 0.388325i | ||||
\(405\) | 722.742 | + | 545.682i | 0.0886749 | + | 0.0669510i | ||||
\(406\) | −1108.63 | + | 5048.88i | −0.135518 | + | 0.617171i | ||||
\(407\) | 7736.99i | 0.942281i | ||||||||
\(408\) | 1436.75 | − | 829.507i | 0.174337 | − | 0.100654i | ||||
\(409\) | 993.077 | − | 1720.06i | 0.120060 | − | 0.207950i | −0.799731 | − | 0.600358i | \(-0.795025\pi\) |
0.919791 | + | 0.392408i | \(0.128358\pi\) | |||||||
\(410\) | 252.969 | + | 597.505i | 0.0304713 | + | 0.0719724i | ||||
\(411\) | −2695.28 | − | 4668.37i | −0.323476 | − | 0.560276i | ||||
\(412\) | − | 1497.60i | − | 0.179081i | ||||||
\(413\) | −2767.92 | − | 8717.34i | −0.329783 | − | 1.03863i | ||||
\(414\) | −4467.33 | −0.530332 | ||||||||
\(415\) | −11376.7 | − | 1407.65i | −1.34569 | − | 0.166504i | ||||
\(416\) | −709.645 | + | 1229.14i | −0.0836375 | + | 0.144864i | ||||
\(417\) | −20.4800 | − | 11.8242i | −0.00240506 | − | 0.00138856i | ||||
\(418\) | 8069.61 | − | 4658.99i | 0.944252 | − | 0.545164i | ||||
\(419\) | 14976.8 | 1.74621 | 0.873107 | − | 0.487529i | \(-0.162102\pi\) | ||||
0.873107 | + | 0.487529i | \(0.162102\pi\) | |||||||
\(420\) | −2366.07 | − | 834.980i | −0.274887 | − | 0.0970068i | ||||
\(421\) | 8004.99 | 0.926697 | 0.463348 | − | 0.886176i | \(-0.346648\pi\) | ||||
0.463348 | + | 0.886176i | \(0.346648\pi\) | |||||||
\(422\) | 12746.4 | − | 7359.15i | 1.47035 | − | 0.848905i | ||||
\(423\) | 2506.09 | + | 1446.89i | 0.288062 | + | 0.166313i | ||||
\(424\) | −1487.15 | + | 2575.82i | −0.170336 | + | 0.295030i | ||||
\(425\) | 3611.64 | + | 3500.76i | 0.412212 | + | 0.399557i | ||||
\(426\) | 5688.11 | 0.646925 | ||||||||
\(427\) | 14217.2 | + | 3121.78i | 1.61128 | + | 0.353802i | ||||
\(428\) | 4162.27i | 0.470072i | ||||||||
\(429\) | 337.462 | + | 584.501i | 0.0379786 | + | 0.0657809i | ||||
\(430\) | 15567.9 | − | 6591.05i | 1.74593 | − | 0.739183i | ||||
\(431\) | −2966.24 | + | 5137.68i | −0.331505 | + | 0.574184i | −0.982807 | − | 0.184635i | \(-0.940890\pi\) |
0.651302 | + | 0.758819i | \(0.274223\pi\) | |||||||
\(432\) | −1870.58 | + | 1079.98i | −0.208329 | + | 0.120279i | ||||
\(433\) | 7966.33i | 0.884151i | 0.896978 | + | 0.442075i | \(0.145758\pi\) | ||||
−0.896978 | + | 0.442075i | \(0.854242\pi\) | |||||||
\(434\) | −1916.25 | − | 1748.82i | −0.211942 | − | 0.193424i | ||||
\(435\) | −1625.74 | + | 2153.25i | −0.179191 | + | 0.237334i | ||||
\(436\) | −3808.44 | − | 6596.42i | −0.418329 | − | 0.724567i | ||||
\(437\) | −12521.3 | − | 7229.16i | −1.37065 | − | 0.791344i | ||||
\(438\) | −3001.41 | − | 1732.87i | −0.327427 | − | 0.189040i | ||||
\(439\) | −4873.43 | − | 8441.03i | −0.529832 | − | 0.917696i | −0.999394 | − | 0.0347966i | \(-0.988922\pi\) |
0.469563 | − | 0.882899i | \(-0.344412\pi\) | |||||||
\(440\) | 2460.10 | − | 3258.34i | 0.266547 | − | 0.353035i | ||||
\(441\) | 2521.56 | − | 1780.82i | 0.272277 | − | 0.192293i | ||||
\(442\) | − | 1182.12i | − | 0.127212i | ||||||
\(443\) | 3808.48 | − | 2198.82i | 0.408456 | − | 0.235822i | −0.281670 | − | 0.959511i | \(-0.590888\pi\) |
0.690126 | + | 0.723689i | \(0.257555\pi\) | |||||||
\(444\) | −1764.17 | + | 3055.64i | −0.188567 | + | 0.326608i | ||||
\(445\) | 8817.56 | − | 3733.13i | 0.939309 | − | 0.397680i | ||||
\(446\) | 4931.35 | + | 8541.35i | 0.523557 | + | 0.906827i | ||||
\(447\) | 7072.27i | 0.748338i | ||||||||
\(448\) | −728.531 | + | 798.280i | −0.0768301 | + | 0.0841857i | ||||
\(449\) | 13617.5 | 1.43129 | 0.715645 | − | 0.698464i | \(-0.246133\pi\) | ||||
0.715645 | + | 0.698464i | \(0.246133\pi\) | |||||||
\(450\) | −2802.86 | − | 2716.81i | −0.293618 | − | 0.284603i | ||||
\(451\) | −222.216 | + | 384.889i | −0.0232012 | + | 0.0401856i | ||||
\(452\) | −7186.57 | − | 4149.17i | −0.747849 | − | 0.431771i | ||||
\(453\) | −8932.60 | + | 5157.24i | −0.926468 | + | 0.534897i | ||||
\(454\) | −4664.30 | −0.482172 | ||||||||
\(455\) | 1331.88 | − | 1140.03i | 0.137230 | − | 0.117463i | ||||
\(456\) | −4166.94 | −0.427927 | ||||||||
\(457\) | 5750.26 | − | 3319.92i | 0.588591 | − | 0.339823i | −0.175949 | − | 0.984399i | \(-0.556299\pi\) |
0.764540 | + | 0.644576i | \(0.222966\pi\) | |||||||
\(458\) | 16160.1 | + | 9330.04i | 1.64872 | + | 0.951887i | ||||
\(459\) | 543.222 | − | 940.888i | 0.0552406 | − | 0.0956795i | ||||
\(460\) | 6411.42 | + | 793.292i | 0.649857 | + | 0.0804075i | ||||
\(461\) | −3346.60 | −0.338106 | −0.169053 | − | 0.985607i | \(-0.554071\pi\) | ||||
−0.169053 | + | 0.985607i | \(0.554071\pi\) | |||||||
\(462\) | −1550.21 | − | 4882.27i | −0.156109 | − | 0.491654i | ||||
\(463\) | 4620.72i | 0.463808i | 0.972739 | + | 0.231904i | \(0.0744955\pi\) | ||||
−0.972739 | + | 0.231904i | \(0.925505\pi\) | |||||||
\(464\) | −3217.56 | − | 5572.97i | −0.321921 | − | 0.557584i | ||||
\(465\) | −527.926 | − | 1246.95i | −0.0526494 | − | 0.124356i | ||||
\(466\) | 4046.62 | − | 7008.95i | 0.402266 | − | 0.696745i | ||||
\(467\) | −11032.0 | + | 6369.32i | −1.09315 | + | 0.631129i | −0.934413 | − | 0.356193i | \(-0.884075\pi\) |
−0.158735 | + | 0.987321i | \(0.550741\pi\) | |||||||
\(468\) | 307.789i | 0.0304008i | ||||||||
\(469\) | −12837.3 | + | 4076.07i | −1.26390 | + | 0.401313i | ||||
\(470\) | −9954.51 | − | 7515.82i | −0.976952 | − | 0.737615i | ||||
\(471\) | −1785.59 | − | 3092.73i | −0.174683 | − | 0.302559i | ||||
\(472\) | 5877.75 | + | 3393.52i | 0.573189 | + | 0.330931i | ||||
\(473\) | 10028.2 | + | 5789.78i | 0.974835 | + | 0.562821i | ||||
\(474\) | −4016.50 | − | 6956.78i | −0.389207 | − | 0.674126i | ||||
\(475\) | −3459.59 | − | 12150.5i | −0.334183 | − | 1.17369i | ||||
\(476\) | −645.575 | + | 2940.06i | −0.0621636 | + | 0.283104i | ||||
\(477\) | 1947.79i | 0.186966i | ||||||||
\(478\) | −4921.74 | + | 2841.57i | −0.470952 | + | 0.271904i | ||||
\(479\) | −6797.08 | + | 11772.9i | −0.648365 | + | 1.12300i | 0.335149 | + | 0.942165i | \(0.391213\pi\) |
−0.983513 | + | 0.180835i | \(0.942120\pi\) | |||||||
\(480\) | 5177.56 | − | 2192.05i | 0.492338 | − | 0.208443i | ||||
\(481\) | −1232.67 | − | 2135.06i | −0.116851 | − | 0.202391i | ||||
\(482\) | 4402.23i | 0.416009i | ||||||||
\(483\) | −5357.98 | + | 5870.94i | −0.504754 | + | 0.553079i | ||||
\(484\) | 2524.33 | 0.237071 | ||||||||
\(485\) | −1413.82 | − | 174.933i | −0.132367 | − | 0.0163779i | ||||
\(486\) | −421.575 | + | 730.189i | −0.0393478 | + | 0.0681523i | ||||
\(487\) | 2197.37 | + | 1268.65i | 0.204461 | + | 0.118046i | 0.598735 | − | 0.800948i | \(-0.295670\pi\) |
−0.394274 | + | 0.918993i | \(0.629004\pi\) | |||||||
\(488\) | −9354.20 | + | 5400.65i | −0.867714 | + | 0.500975i | ||||
\(489\) | −7703.34 | −0.712387 | ||||||||
\(490\) | −11729.1 | + | 6283.21i | −1.08136 | + | 0.579279i | ||||
\(491\) | 19203.4 | 1.76504 | 0.882522 | − | 0.470272i | \(-0.155844\pi\) | ||||
0.882522 | + | 0.470272i | \(0.155844\pi\) | |||||||
\(492\) | −175.523 | + | 101.338i | −0.0160837 | + | 0.00928594i | ||||
\(493\) | 2803.17 | + | 1618.41i | 0.256082 | + | 0.147849i | ||||
\(494\) | −1484.56 | + | 2571.34i | −0.135210 | + | 0.234190i | ||||
\(495\) | 328.315 | − | 2653.46i | 0.0298114 | − | 0.240937i | ||||
\(496\) | 3229.65 | 0.292370 | ||||||||
\(497\) | 6822.14 | − | 7475.29i | 0.615724 | − | 0.674673i | ||||
\(498\) | − | 10672.9i | − | 0.960366i | ||||||
\(499\) | 3253.29 | + | 5634.86i | 0.291858 | + | 0.505513i | 0.974249 | − | 0.225475i | \(-0.0723932\pi\) |
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(500\) | 3540.17 | + | 4396.83i | 0.316642 | + | 0.393264i | ||||
\(501\) | −4492.03 | + | 7780.42i | −0.400577 | + | 0.693820i | ||||
\(502\) | −21867.5 | + | 12625.2i | −1.94421 | + | 1.12249i | ||||
\(503\) | 3373.80i | 0.299066i | 0.988757 | + | 0.149533i | \(0.0477770\pi\) | ||||
−0.988757 | + | 0.149533i | \(0.952223\pi\) | |||||||
\(504\) | −491.292 | + | 2237.43i | −0.0434204 | + | 0.197744i | ||||
\(505\) | −8043.48 | − | 6072.96i | −0.708773 | − | 0.535135i | ||||
\(506\) | 6594.61 | + | 11422.2i | 0.579380 | + | 1.00351i | ||||
\(507\) | 5521.73 | + | 3187.97i | 0.483685 | + | 0.279256i | ||||
\(508\) | 4211.43 | + | 2431.47i | 0.367819 | + | 0.212360i | ||||
\(509\) | −1661.50 | − | 2877.80i | −0.144685 | − | 0.250602i | 0.784570 | − | 0.620040i | \(-0.212884\pi\) |
−0.929255 | + | 0.369438i | \(0.879550\pi\) | |||||||
\(510\) | −2821.75 | + | 3737.33i | −0.244998 | + | 0.324494i | ||||
\(511\) | −5877.12 | + | 1866.10i | −0.508784 | + | 0.161548i | ||||
\(512\) | 4614.69i | 0.398325i | ||||||||
\(513\) | −2363.22 | + | 1364.41i | −0.203390 | + | 0.117427i | ||||
\(514\) | 312.901 | − | 541.960i | 0.0268511 | − | 0.0465075i | ||||
\(515\) | −1616.15 | − | 3817.31i | −0.138284 | − | 0.326623i | ||||
\(516\) | 2640.35 | + | 4573.22i | 0.225261 | + | 0.390164i | ||||
\(517\) | − | 8543.53i | − | 0.726777i | ||||||
\(518\) | 5662.59 | + | 17833.9i | 0.480309 | + | 1.51269i | ||||
\(519\) | 6548.49 | 0.553847 | ||||||||
\(520\) | −159.750 | + | 1291.10i | −0.0134721 | + | 0.108882i | ||||
\(521\) | −7755.66 | + | 13433.2i | −0.652172 | + | 1.12959i | 0.330423 | + | 0.943833i | \(0.392809\pi\) |
−0.982595 | + | 0.185762i | \(0.940525\pi\) | |||||||
\(522\) | −2175.43 | − | 1255.99i | −0.182406 | − | 0.105312i | ||||
\(523\) | 16832.0 | − | 9717.97i | 1.40729 | − | 0.812499i | 0.412164 | − | 0.911110i | \(-0.364773\pi\) |
0.995126 | + | 0.0986106i | \(0.0314398\pi\) | |||||||
\(524\) | −11596.9 | −0.966819 | ||||||||
\(525\) | −6932.08 | + | 425.050i | −0.576268 | + | 0.0353346i | ||||
\(526\) | 2360.33 | 0.195656 | ||||||||
\(527\) | −1406.85 | + | 812.246i | −0.116287 | + | 0.0671385i | ||||
\(528\) | 5522.64 | + | 3188.50i | 0.455194 | + | 0.262806i | ||||
\(529\) | 4149.07 | − | 7186.41i | 0.341010 | − | 0.590647i | ||||
\(530\) | 1030.94 | − | 8332.07i | 0.0844924 | − | 0.682871i | ||||
\(531\) | 4444.65 | 0.363242 | ||||||||
\(532\) | 5096.52 | − | 5584.45i | 0.415342 | − | 0.455107i | ||||
\(533\) | − | 141.616i | − | 0.0115085i | ||||||
\(534\) | 4457.43 | + | 7720.50i | 0.361221 | + | 0.625653i | ||||
\(535\) | 4491.77 | + | 10609.4i | 0.362983 | + | 0.857356i | ||||
\(536\) | 4997.34 | − | 8655.65i | 0.402709 | − | 0.697513i | ||||
\(537\) | 5497.27 | − | 3173.85i | 0.441760 | − | 0.255050i | ||||
\(538\) | 4481.63i | 0.359139i | ||||||||
\(539\) | −8275.54 | − | 3818.36i | −0.661322 | − | 0.305137i | ||||
\(540\) | 734.700 | − | 973.090i | 0.0585490 | − | 0.0775466i | ||||
\(541\) | 7151.98 | + | 12387.6i | 0.568369 | + | 0.984445i | 0.996727 | + | 0.0808355i | \(0.0257589\pi\) |
−0.428358 | + | 0.903609i | \(0.640908\pi\) | |||||||
\(542\) | −17015.9 | − | 9824.16i | −1.34852 | − | 0.778568i | ||||
\(543\) | −265.283 | − | 153.161i | −0.0209657 | − | 0.0121045i | ||||
\(544\) | −3372.60 | − | 5841.51i | −0.265807 | − | 0.460391i | ||||
\(545\) | −16826.1 | − | 12704.0i | −1.32248 | − | 0.998496i | ||||
\(546\) | 1205.64 | + | 1100.30i | 0.0944996 | + | 0.0862428i | ||||
\(547\) | 596.885i | 0.0466562i | 0.999728 | + | 0.0233281i | \(0.00742624\pi\) | ||||
−0.999728 | + | 0.0233281i | \(0.992574\pi\) | |||||||
\(548\) | −6285.43 | + | 3628.89i | −0.489964 | + | 0.282881i | ||||
\(549\) | −3536.74 | + | 6125.81i | −0.274944 | + | 0.476217i | ||||
\(550\) | −2808.87 | + | 11176.9i | −0.217765 | + | 0.866521i | ||||
\(551\) | −4064.95 | − | 7040.69i | −0.314288 | − | 0.544362i | ||||
\(552\) | − | 5898.13i | − | 0.454784i | ||||||
\(553\) | −13959.8 | − | 3065.28i | −1.07348 | − | 0.235713i | ||||
\(554\) | 4857.79 | 0.372541 | ||||||||
\(555\) | −1199.26 | + | 9692.49i | −0.0917223 | + | 0.741303i | ||||
\(556\) | −15.9199 | + | 27.5740i | −0.00121430 | + | 0.00210324i | ||||
\(557\) | −4741.31 | − | 2737.40i | −0.360675 | − | 0.208236i | 0.308702 | − | 0.951159i | \(-0.400105\pi\) |
−0.669377 | + | 0.742923i | \(0.733439\pi\) | |||||||
\(558\) | 1091.80 | − | 630.354i | 0.0828312 | − | 0.0478226i | ||||
\(559\) | −3689.77 | −0.279178 | ||||||||
\(560\) | 5512.46 | − | 15620.6i | 0.415971 | − | 1.17873i | ||||
\(561\) | −3207.59 | −0.241398 | ||||||||
\(562\) | −14919.8 | + | 8613.96i | −1.11985 | + | 0.646545i | ||||
\(563\) | 13236.2 | + | 7641.93i | 0.990835 | + | 0.572059i | 0.905524 | − | 0.424296i | \(-0.139478\pi\) |
0.0853110 | + | 0.996354i | \(0.472812\pi\) | |||||||
\(564\) | 1948.08 | − | 3374.17i | 0.145441 | − | 0.251912i | ||||
\(565\) | −22795.8 | − | 2820.55i | −1.69739 | − | 0.210020i | ||||
\(566\) | −26053.8 | −1.93485 | ||||||||
\(567\) | 453.987 | + | 1429.80i | 0.0336255 | + | 0.105901i | ||||
\(568\) | 7509.90i | 0.554768i | ||||||||
\(569\) | −1060.65 | − | 1837.10i | −0.0781454 | − | 0.135352i | 0.824304 | − | 0.566147i | \(-0.191566\pi\) |
−0.902450 | + | 0.430795i | \(0.858233\pi\) | |||||||
\(570\) | 10831.3 | − | 4585.72i | 0.795921 | − | 0.336973i | ||||
\(571\) | −3615.00 | + | 6261.36i | −0.264944 | + | 0.458896i | −0.967549 | − | 0.252684i | \(-0.918687\pi\) |
0.702605 | + | 0.711580i | \(0.252020\pi\) | |||||||
\(572\) | 786.965 | − | 454.354i | 0.0575256 | − | 0.0332124i | ||||
\(573\) | − | 2248.75i | − | 0.163949i | ||||||
\(574\) | −230.516 | + | 1049.81i | −0.0167623 | + | 0.0763384i | ||||
\(575\) | 17198.5 | − | 4896.90i | 1.24735 | − | 0.355156i | ||||
\(576\) | −262.596 | − | 454.830i | −0.0189957 | − | 0.0329015i | ||||
\(577\) | 11534.0 | + | 6659.17i | 0.832180 | + | 0.480459i | 0.854598 | − | 0.519289i | \(-0.173803\pi\) |
−0.0224187 | + | 0.999749i | \(0.507137\pi\) | |||||||
\(578\) | −9897.66 | − | 5714.41i | −0.712263 | − | 0.411225i | ||||
\(579\) | 2104.55 | + | 3645.18i | 0.151057 | + | 0.261638i | ||||
\(580\) | 2899.11 | + | 2188.87i | 0.207550 | + | 0.156703i | ||||
\(581\) | −14026.2 | − | 12800.7i | −1.00156 | − | 0.914049i | ||||
\(582\) | − | 1326.35i | − | 0.0944653i | ||||||
\(583\) | 4980.16 | − | 2875.29i | 0.353786 | − | 0.204258i | ||||
\(584\) | 2287.87 | − | 3962.70i | 0.162111 | − | 0.280784i | ||||
\(585\) | 332.155 | + | 784.541i | 0.0234751 | + | 0.0554474i | ||||
\(586\) | 10284.1 | + | 17812.6i | 0.724969 | + | 1.25568i | ||||
\(587\) | − | 10809.0i | − | 0.760026i | −0.924981 | − | 0.380013i | \(-0.875919\pi\) | ||
0.924981 | − | 0.380013i | \(-0.124081\pi\) | |||||||
\(588\) | −2397.67 | − | 3394.99i | −0.168161 | − | 0.238107i | ||||
\(589\) | 4080.22 | 0.285438 | ||||||||
\(590\) | −19012.9 | − | 2352.49i | −1.32669 | − | 0.164153i | ||||
\(591\) | 1887.11 | − | 3268.57i | 0.131346 | − | 0.227498i | ||||
\(592\) | −20173.0 | − | 11646.9i | −1.40052 | − | 0.808588i | ||||
\(593\) | −13017.2 | + | 7515.46i | −0.901434 | + | 0.520443i | −0.877665 | − | 0.479274i | \(-0.840900\pi\) |
−0.0237691 | + | 0.999717i | \(0.507567\pi\) | |||||||
\(594\) | 2489.29 | 0.171947 | ||||||||
\(595\) | 1527.27 | + | 8190.76i | 0.105230 | + | 0.564350i | ||||
\(596\) | 9522.02 | 0.654424 | ||||||||
\(597\) | 7922.83 | − | 4574.25i | 0.543149 | − | 0.313587i | ||||
\(598\) | −3639.62 | − | 2101.34i | −0.248888 | − | 0.143696i | ||||
\(599\) | −6994.92 | + | 12115.6i | −0.477136 | + | 0.826424i | −0.999657 | − | 0.0262026i | \(-0.991659\pi\) |
0.522520 | + | 0.852627i | \(0.324992\pi\) | |||||||
\(600\) | 3586.95 | − | 3700.56i | 0.244061 | − | 0.251791i | ||||
\(601\) | 13467.0 | 0.914024 | 0.457012 | − | 0.889461i | \(-0.348920\pi\) | ||||
0.457012 | + | 0.889461i | \(0.348920\pi\) | |||||||
\(602\) | 27352.6 | + | 6006.05i | 1.85184 | + | 0.406625i | ||||
\(603\) | − | 6545.25i | − | 0.442028i | ||||||
\(604\) | 6943.64 | + | 12026.7i | 0.467769 | + | 0.810200i | ||||
\(605\) | 6434.39 | − | 2724.16i | 0.432389 | − | 0.183063i | ||||
\(606\) | 4691.75 | − | 8126.36i | 0.314504 | − | 0.544737i | ||||
\(607\) | 13344.4 | − | 7704.38i | 0.892308 | − | 0.515175i | 0.0176116 | − | 0.999845i | \(-0.494394\pi\) |
0.874697 | + | 0.484670i | \(0.161060\pi\) | |||||||
\(608\) | 16941.9i | 1.13007i | ||||||||
\(609\) | −4259.76 | + | 1352.55i | −0.283439 | + | 0.0899971i | ||||
\(610\) | 18371.5 | − | 24332.5i | 1.21941 | − | 1.61507i | ||||
\(611\) | 1361.17 | + | 2357.62i | 0.0901264 | + | 0.156103i | ||||
\(612\) | −1266.80 | − | 731.387i | −0.0836721 | − | 0.0483081i | ||||
\(613\) | 5811.39 | + | 3355.21i | 0.382903 | + | 0.221069i | 0.679081 | − | 0.734064i | \(-0.262379\pi\) |
−0.296177 | + | 0.955133i | \(0.595712\pi\) | |||||||
\(614\) | −4781.97 | − | 8282.62i | −0.314307 | − | 0.544396i | ||||
\(615\) | −338.039 | + | 447.724i | −0.0221643 | + | 0.0293561i | ||||
\(616\) | 6445.97 | − | 2046.71i | 0.421616 | − | 0.133871i | ||||
\(617\) | 24471.6i | 1.59674i | 0.602166 | + | 0.798371i | \(0.294305\pi\) | ||||
−0.602166 | + | 0.798371i | \(0.705695\pi\) | |||||||
\(618\) | 3342.37 | − | 1929.72i | 0.217556 | − | 0.125606i | ||||
\(619\) | 9445.87 | − | 16360.7i | 0.613346 | − | 1.06235i | −0.377326 | − | 0.926081i | \(-0.623156\pi\) |
0.990672 | − | 0.136267i | \(-0.0435104\pi\) | |||||||
\(620\) | −1678.87 | + | 710.793i | −0.108750 | + | 0.0460421i | ||||
\(621\) | −1931.26 | − | 3345.04i | −0.124797 | − | 0.216155i | ||||
\(622\) | − | 13822.2i | − | 0.891027i | ||||||
\(623\) | 15492.4 | + | 3401.79i | 0.996289 | + | 0.218764i | ||||
\(624\) | −2032.00 | −0.130361 | ||||||||
\(625\) | 13768.6 | + | 7386.89i | 0.881191 | + | 0.472761i | ||||
\(626\) | 14968.9 | − | 25926.9i | 0.955717 | − | 1.65535i | ||||
\(627\) | 6977.11 | + | 4028.24i | 0.444400 | + | 0.256575i | ||||
\(628\) | −4164.01 | + | 2404.09i | −0.264589 | + | 0.152761i | ||||
\(629\) | 11716.6 | 0.742722 | ||||||||
\(630\) | −1185.25 | − | 6356.55i | −0.0749550 | − | 0.401985i | ||||
\(631\) | −24768.0 | −1.56259 | −0.781297 | − | 0.624159i | \(-0.785442\pi\) | ||||
−0.781297 | + | 0.624159i | \(0.785442\pi\) | |||||||
\(632\) | 9184.90 | − | 5302.90i | 0.578095 | − | 0.333763i | ||||
\(633\) | 11020.8 | + | 6362.84i | 0.691999 | + | 0.399526i | ||||
\(634\) | 9104.08 | − | 15768.7i | 0.570299 | − | 0.987786i | ||||
\(635\) | 13358.7 | + | 1652.88i | 0.834840 | + | 0.103296i | ||||
\(636\) | 2622.47 | 0.163503 | ||||||||
\(637\) | 2892.02 | − | 264.784i | 0.179884 | − | 0.0164696i | ||||
\(638\) | 7416.28i | 0.460209i | ||||||||
\(639\) | 2459.02 | + | 4259.14i | 0.152233 | + | 0.263676i | ||||
\(640\) | 6728.04 | + | 15891.4i | 0.415545 | + | 0.981507i | ||||
\(641\) | 7719.40 | − | 13370.4i | 0.475660 | − | 0.823867i | −0.523951 | − | 0.851748i | \(-0.675543\pi\) |
0.999611 | + | 0.0278812i | \(0.00887601\pi\) | |||||||
\(642\) | −9289.43 | + | 5363.26i | −0.571067 | + | 0.329705i | ||||
\(643\) | − | 27970.2i | − | 1.71545i | −0.514107 | − | 0.857726i | \(-0.671877\pi\) | ||
0.514107 | − | 0.857726i | \(-0.328123\pi\) | |||||||
\(644\) | 7904.56 | + | 7213.91i | 0.483670 | + | 0.441410i | ||||
\(645\) | 11665.4 | + | 8807.55i | 0.712129 | + | 0.537669i | ||||
\(646\) | −7055.41 | − | 12220.3i | −0.429708 | − | 0.744276i | ||||
\(647\) | −8548.58 | − | 4935.52i | −0.519442 | − | 0.299900i | 0.217264 | − | 0.976113i | \(-0.430287\pi\) |
−0.736707 | + | 0.676213i | \(0.763620\pi\) | |||||||
\(648\) | −964.053 | − | 556.596i | −0.0584438 | − | 0.0337425i | ||||
\(649\) | −6561.13 | − | 11364.2i | −0.396836 | − | 0.687341i | ||||
\(650\) | −1005.62 | − | 3531.84i | −0.0606823 | − | 0.213123i | ||||
\(651\) | 481.069 | − | 2190.87i | 0.0289625 | − | 0.131900i | ||||
\(652\) | 10371.7i | 0.622985i | ||||||||
\(653\) | −9403.83 | + | 5429.30i | −0.563553 | + | 0.325367i | −0.754570 | − | 0.656219i | \(-0.772155\pi\) |
0.191017 | + | 0.981587i | \(0.438821\pi\) | |||||||
\(654\) | 9814.67 | − | 16999.5i | 0.586826 | − | 1.01641i | ||||
\(655\) | −29559.9 | + | 12514.9i | −1.76336 | + | 0.746564i | ||||
\(656\) | −669.025 | − | 1158.79i | −0.0398187 | − | 0.0689680i | ||||
\(657\) | − | 2996.53i | − | 0.177939i | ||||||
\(658\) | −6252.88 | − | 19693.0i | −0.370460 | − | 1.16673i | ||||
\(659\) | −4519.16 | −0.267134 | −0.133567 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133567 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(660\) | −3572.58 | − | 442.039i | −0.210701 | − | 0.0260702i | ||||
\(661\) | −5891.72 | + | 10204.8i | −0.346689 | + | 0.600483i | −0.985659 | − | 0.168749i | \(-0.946027\pi\) |
0.638970 | + | 0.769231i | \(0.279361\pi\) | |||||||
\(662\) | −13487.8 | − | 7787.19i | −0.791871 | − | 0.457187i | ||||
\(663\) | 885.148 | − | 511.040i | 0.0518496 | − | 0.0299354i | ||||
\(664\) | 14091.2 | 0.823559 | ||||||||
\(665\) | 6964.24 | − | 19734.5i | 0.406108 | − | 1.15078i | ||||
\(666\) | −9092.83 | −0.529039 | ||||||||
\(667\) | 9965.81 | − | 5753.76i | 0.578527 | − | 0.334013i | ||||
\(668\) | 10475.5 | + | 6048.01i | 0.606748 | + | 0.350306i | ||||
\(669\) | −4263.72 | + | 7384.99i | −0.246405 | + | 0.426786i | ||||
\(670\) | −3464.31 | + | 27998.7i | −0.199758 | + | 1.61445i | ||||
\(671\) | 20883.5 | 1.20149 | ||||||||
\(672\) | 9096.91 | + | 1997.49i | 0.522204 | + | 0.114665i | ||||
\(673\) | 11910.6i | 0.682197i | 0.940028 | + | 0.341098i | \(0.110799\pi\) | ||||
−0.940028 | + | 0.341098i | \(0.889201\pi\) | |||||||
\(674\) | 9895.33 | + | 17139.2i | 0.565510 | + | 0.979492i | ||||
\(675\) | 822.591 | − | 3273.22i | 0.0469060 | − | 0.186646i | ||||
\(676\) | 4292.24 | − | 7434.38i | 0.244210 | − | 0.422985i | ||||
\(677\) | 2628.33 | − | 1517.47i | 0.149210 | − | 0.0861463i | −0.423536 | − | 0.905879i | \(-0.639211\pi\) |
0.572746 | + | 0.819733i | \(0.305878\pi\) | |||||||
\(678\) | − | 21385.5i | − | 1.21136i | ||||||
\(679\) | −1743.08 | − | 1590.78i | −0.0985172 | − | 0.0899094i | ||||
\(680\) | −4934.32 | − | 3725.49i | −0.278268 | − | 0.210097i | ||||
\(681\) | −2016.41 | − | 3492.53i | −0.113464 | − | 0.196526i | ||||
\(682\) | −3223.41 | − | 1861.04i | −0.180984 | − | 0.104491i | ||||
\(683\) | 11281.6 | + | 6513.46i | 0.632035 | + | 0.364906i | 0.781540 | − | 0.623855i | \(-0.214435\pi\) |
−0.149505 | + | 0.988761i | \(0.547768\pi\) | |||||||
\(684\) | 1837.02 | + | 3181.81i | 0.102690 | + | 0.177865i | ||||
\(685\) | −12105.1 | + | 16032.9i | −0.675199 | + | 0.894284i | ||||
\(686\) | −21869.9 | − | 2744.65i | −1.21719 | − | 0.152757i | ||||
\(687\) | 16133.8i | 0.895987i | ||||||||
\(688\) | −30192.0 | + | 17431.3i | −1.67305 | + | 0.965935i | ||||
\(689\) | −916.197 | + | 1586.90i | −0.0506594 | + | 0.0877447i | ||||
\(690\) | 6490.90 | + | 15331.3i | 0.358122 | + | 0.845874i | ||||
\(691\) | 2249.56 | + | 3896.35i | 0.123846 | + | 0.214507i | 0.921281 | − | 0.388897i | \(-0.127144\pi\) |
−0.797436 | + | 0.603404i | \(0.793811\pi\) | |||||||
\(692\) | − | 8816.80i | − | 0.484342i | ||||||
\(693\) | 2985.58 | − | 3271.41i | 0.163655 | − | 0.179323i | ||||
\(694\) | 15974.2 | 0.873738 | ||||||||
\(695\) | −10.8221 | + | 87.4650i | −0.000590658 | + | 0.00477372i | ||||
\(696\) | 1658.25 | − | 2872.18i | 0.0903103 | − | 0.156422i | ||||
\(697\) | 582.861 | + | 336.515i | 0.0316750 | + | 0.0182875i | ||||
\(698\) | 14431.8 | − | 8332.21i | 0.782596 | − | 0.451832i | ||||
\(699\) | 6997.54 | 0.378643 | ||||||||
\(700\) | 572.281 | + | 9333.26i | 0.0309003 | + | 0.503949i | ||||
\(701\) | −26886.9 | −1.44865 | −0.724327 | − | 0.689457i | \(-0.757849\pi\) | ||||
−0.724327 | + | 0.689457i | \(0.757849\pi\) | |||||||
\(702\) | −686.930 | + | 396.599i | −0.0369324 | + | 0.0213229i | ||||
\(703\) | −25485.9 | − | 14714.3i | −1.36731 | − | 0.789415i | ||||
\(704\) | −775.282 | + | 1342.83i | −0.0415050 | + | 0.0718888i | ||||
\(705\) | 1324.28 | − | 10702.9i | 0.0707450 | − | 0.571764i | ||||
\(706\) | −36046.2 | −1.92155 | ||||||||
\(707\) | −5052.48 | − | 15912.4i | −0.268767 | − | 0.846459i | ||||
\(708\) | − | 5984.22i | − | 0.317656i | ||||||
\(709\) | −11091.9 | − | 19211.7i | −0.587537 | − | 1.01764i | −0.994554 | − | 0.104223i | \(-0.966764\pi\) |
0.407017 | − | 0.913421i | \(-0.366569\pi\) | |||||||
\(710\) | −8264.65 | − | 19520.9i | −0.436855 | − | 1.03184i | ||||
\(711\) | 3472.73 | − | 6014.95i | 0.183175 | − | 0.317269i | ||||
\(712\) | −10193.2 | + | 5885.06i | −0.536527 | + | 0.309764i | ||||
\(713\) | 5775.39i | 0.303352i | ||||||||
\(714\) | −7393.54 | + | 2347.59i | −0.387530 | + | 0.123048i | ||||
\(715\) | 1515.61 | − | 2007.39i | 0.0792737 | − | 0.104996i | ||||
\(716\) | −4273.23 | − | 7401.46i | −0.223042 | − | 0.386321i | ||||
\(717\) | −4255.41 | − | 2456.86i | −0.221647 | − | 0.127968i | ||||
\(718\) | −13615.5 | − | 7860.88i | −0.707694 | − | 0.408587i | ||||
\(719\) | 9093.48 | + | 15750.4i | 0.471669 | + | 0.816954i | 0.999475 | − | 0.0324111i | \(-0.0103186\pi\) |
−0.527806 | + | 0.849365i | \(0.676985\pi\) | |||||||
\(720\) | 6424.25 | + | 4850.42i | 0.332524 | + | 0.251062i | ||||
\(721\) | 1472.71 | − | 6706.97i | 0.0760701 | − | 0.346437i | ||||
\(722\) | 11643.0i | 0.600150i | ||||||||
\(723\) | −3296.30 | + | 1903.12i | −0.169558 | + | 0.0978946i | ||||
\(724\) | −206.214 | + | 357.173i | −0.0105855 | + | 0.0183346i | ||||
\(725\) | 9751.83 | + | 2450.73i | 0.499550 | + | 0.125542i | ||||
\(726\) | 3252.70 | + | 5633.85i | 0.166280 | + | 0.288005i | ||||
\(727\) | 15799.4i | 0.806009i | 0.915198 | + | 0.403004i | \(0.132034\pi\) | ||||
−0.915198 | + | 0.403004i | \(0.867966\pi\) | |||||||
\(728\) | −1452.71 | + | 1591.79i | −0.0739572 | + | 0.0810378i | ||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −1586.02 | + | 12818.3i | −0.0804125 | + | 0.649898i | ||||
\(731\) | 8767.84 | − | 15186.3i | 0.443626 | − | 0.768382i | ||||
\(732\) | 8247.72 | + | 4761.82i | 0.416454 | + | 0.240440i | ||||
\(733\) | 12603.4 | − | 7276.60i | 0.635087 | − | 0.366668i | −0.147632 | − | 0.989042i | \(-0.547165\pi\) |
0.782720 | + | 0.622375i | \(0.213832\pi\) | |||||||
\(734\) | −17826.3 | −0.896430 | ||||||||
\(735\) | −9775.30 | − | 6066.19i | −0.490568 | − | 0.304428i | ||||
\(736\) | −23980.5 | −1.20100 | ||||||||
\(737\) | −16735.1 | + | 9662.00i | −0.836424 | + | 0.482910i | ||||
\(738\) | −452.337 | − | 261.157i | −0.0225620 | − | 0.0130262i | ||||
\(739\) | −15544.2 | + | 26923.4i | −0.773752 | + | 1.34018i | 0.161741 | + | 0.986833i | \(0.448289\pi\) |
−0.935493 | + | 0.353345i | \(0.885044\pi\) | |||||||
\(740\) | 13049.8 | + | 1614.67i | 0.648273 | + | 0.0802115i | ||||
\(741\) | −2567.15 | −0.127269 | ||||||||
\(742\) | 9374.95 | − | 10272.5i | 0.463835 | − | 0.508242i | ||||
\(743\) | − | 20776.5i | − | 1.02586i | −0.858430 | − | 0.512931i | \(-0.828559\pi\) | ||
0.858430 | − | 0.512931i | \(-0.171441\pi\) | |||||||
\(744\) | 832.243 | + | 1441.49i | 0.0410101 | + | 0.0710316i | ||||
\(745\) | 24271.2 | − | 10275.8i | 1.19359 | − | 0.505337i | ||||
\(746\) | −9387.21 | + | 16259.1i | −0.460711 | + | 0.797975i | ||||
\(747\) | 7991.61 | − | 4613.96i | 0.391429 | − | 0.225992i | ||||
\(748\) | 4318.65i | 0.211104i | ||||||||
\(749\) | −4093.09 | + | 18640.7i | −0.199677 | + | 0.909366i | ||||
\(750\) | −5251.28 | + | 13566.5i | −0.255666 | + | 0.660505i | ||||
\(751\) | 9390.12 | + | 16264.2i | 0.456259 | + | 0.790263i | 0.998760 | − | 0.0497920i | \(-0.0158558\pi\) |
−0.542501 | + | 0.840055i | \(0.682523\pi\) | |||||||
\(752\) | 22275.9 | + | 12861.0i | 1.08021 | + | 0.623661i | ||||
\(753\) | −18906.9 | − | 10915.9i | −0.915017 | − | 0.528285i | ||||
\(754\) | −1181.58 | − | 2046.56i | −0.0570697 | − | 0.0988477i | ||||
\(755\) | 30677.8 | + | 23162.3i | 1.47878 | + | 1.11650i | ||||
\(756\) | 1925.06 | − | 611.242i | 0.0926108 | − | 0.0294056i | ||||
\(757\) | 33774.4i | 1.62160i | 0.585323 | + | 0.810800i | \(0.300968\pi\) | ||||
−0.585323 | + | 0.810800i | \(0.699032\pi\) | |||||||
\(758\) | 5725.46 | − | 3305.59i | 0.274351 | − | 0.158397i | ||||
\(759\) | −5701.80 | + | 9875.81i | −0.272678 | + | 0.472291i | ||||
\(760\) | 6054.43 | + | 14300.4i | 0.288970 | + | 0.682540i | ||||
\(761\) | 14123.3 | + | 24462.2i | 0.672757 | + | 1.16525i | 0.977119 | + | 0.212693i | \(0.0682236\pi\) |
−0.304362 | + | 0.952557i | \(0.598443\pi\) | |||||||
\(762\) | 12532.2i | 0.595792i | ||||||||
\(763\) | −10569.3 | − | 33287.1i | −0.501485 | − | 1.57939i | ||||
\(764\) | −3027.69 | −0.143374 | ||||||||
\(765\) | −4018.30 | − | 497.188i | −0.189911 | − | 0.0234979i | ||||
\(766\) | −8481.58 | + | 14690.5i | −0.400068 | + | 0.692938i | ||||
\(767\) | 3621.14 | + | 2090.67i | 0.170472 | + | 0.0984220i | ||||
\(768\) | −12701.4 | + | 7333.15i | −0.596773 | + | 0.344547i | ||||
\(769\) | −15646.0 | −0.733690 | −0.366845 | − | 0.930282i | \(-0.619562\pi\) | ||||
−0.366845 | + | 0.930282i | \(0.619562\pi\) | |||||||
\(770\) | −14502.9 | + | 12413.9i | −0.678766 | + | 0.580996i | ||||
\(771\) | 541.078 | 0.0252743 | ||||||||
\(772\) | 4907.83 | − | 2833.53i | 0.228804 | − | 0.132100i | ||||
\(773\) | 18128.6 | + | 10466.6i | 0.843521 | + | 0.487007i | 0.858459 | − | 0.512881i | \(-0.171422\pi\) |
−0.0149387 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(774\) | −6804.39 | + | 11785.6i | −0.315993 | + | 0.547317i | ||||
\(775\) | −3512.30 | + | 3623.55i | −0.162794 | + | 0.167951i | ||||
\(776\) | 1751.15 | 0.0810084 | ||||||||
\(777\) | −10905.7 | + | 11949.8i | −0.503524 | + | 0.551731i | ||||
\(778\) | − | 15728.2i | − | 0.724784i | ||||||
\(779\) | −845.223 | − | 1463.97i | −0.0388745 | − | 0.0673326i | ||||
\(780\) | 1056.30 | − | 447.209i | 0.0484890 | − | 0.0205290i | ||||
\(781\) | 7259.93 | − | 12574.6i | 0.332626 | − | 0.576124i | ||||
\(782\) | 17297.4 | − | 9986.64i | 0.790988 | − | 0.456677i | ||||
\(783\) | − | 2171.89i | − | 0.0991279i | ||||||
\(784\) | 22413.4 | − | 15829.2i | 1.02102 | − | 0.721083i | ||||
\(785\) | −8019.46 | + | 10621.6i | −0.364620 | + | 0.482930i | ||||
\(786\) | −14943.1 | − | 25882.2i | −0.678120 | − | 1.17454i | ||||
\(787\) | −21731.7 | − | 12546.8i | −0.984311 | − | 0.568292i | −0.0807424 | − | 0.996735i | \(-0.525729\pi\) |
−0.903569 | + | 0.428443i | \(0.859062\pi\) | |||||||
\(788\) | −4400.77 | − | 2540.78i | −0.198948 | − | 0.114862i | ||||
\(789\) | 1020.39 | + | 1767.37i | 0.0460416 | + | 0.0797464i | ||||
\(790\) | −18039.0 | + | 23892.1i | −0.812402 | + | 1.07600i | ||||
\(791\) | −28104.7 | − | 25649.1i | −1.26332 | − | 1.15294i | ||||
\(792\) | 3286.56i | 0.147453i | ||||||||
\(793\) | −5762.90 | + | 3327.21i | −0.258066 | + | 0.148995i | ||||
\(794\) | 3851.67 | − | 6671.29i | 0.172154 | − | 0.298180i | ||||
\(795\) | 6684.56 | − | 2830.08i | 0.298210 | − | 0.126255i | ||||
\(796\) | −6158.71 | − | 10667.2i | −0.274233 | − | 0.474986i | ||||
\(797\) | − | 23043.6i | − | 1.02415i | −0.858942 | − | 0.512073i | \(-0.828878\pi\) | ||
0.858942 | − | 0.512073i | \(-0.171122\pi\) | |||||||
\(798\) | 19030.6 | + | 4178.70i | 0.844203 | + | 0.185369i | ||||
\(799\) | −12938.0 | −0.572858 | ||||||||
\(800\) | −15045.7 | − | 14583.8i | −0.664931 | − | 0.644517i | ||||
\(801\) | −3853.97 | + | 6675.27i | −0.170004 | + | 0.294456i | ||||
\(802\) | 24466.2 | + | 14125.6i | 1.07722 | + | 0.621935i | ||||
\(803\) | −7661.60 | + | 4423.43i | −0.336702 | + | 0.194395i | ||||
\(804\) | −8812.44 | −0.386556 | ||||||||
\(805\) | 27933.3 | + | 9857.60i | 1.22301 | + | 0.431596i | ||||
\(806\) | 1186.02 | 0.0518310 | ||||||||
\(807\) | −3355.75 | + | 1937.45i | −0.146379 | + | 0.0845122i | ||||
\(808\) | 10729.1 | + | 6194.43i | 0.467138 | + | 0.269702i | ||||
\(809\) | −9265.72 | + | 16048.7i | −0.402676 | + | 0.697456i | −0.994048 | − | 0.108943i | \(-0.965253\pi\) |
0.591371 | + | 0.806399i | \(0.298587\pi\) | |||||||
\(810\) | 3118.45 | + | 385.849i | 0.135273 | + | 0.0167375i | ||||
\(811\) | 20005.9 | 0.866218 | 0.433109 | − | 0.901342i | \(-0.357417\pi\) | ||||
0.433109 | + | 0.901342i | \(0.357417\pi\) | |||||||
\(812\) | 1821.06 | + | 5735.29i | 0.0787028 | + | 0.247868i | ||||
\(813\) | − | 16988.2i | − | 0.732846i | ||||||
\(814\) | 13422.7 | + | 23248.8i | 0.577967 | + | 1.00107i | ||||
\(815\) | 11192.7 | + | 26436.9i | 0.481060 | + | 1.13625i | ||||
\(816\) | 4828.55 | − | 8363.29i | 0.207148 | − | 0.358791i | ||||
\(817\) | −38143.4 | + | 22022.1i | −1.63338 | + | 0.943031i | ||||
\(818\) | − | 6891.46i | − | 0.294565i | ||||||
\(819\) | −302.674 | + | 1378.43i | −0.0129136 | + | 0.0588110i | ||||
\(820\) | 602.810 | + | 455.132i | 0.0256720 | + | 0.0193828i | ||||
\(821\) | 2726.58 | + | 4722.58i | 0.115905 | + | 0.200754i | 0.918141 | − | 0.396253i | \(-0.129690\pi\) |
−0.802236 | + | 0.597007i | \(0.796356\pi\) | |||||||
\(822\) | −16198.1 | − | 9351.95i | −0.687314 | − | 0.396821i | ||||
\(823\) | 24933.9 | + | 14395.6i | 1.05606 | + | 0.609719i | 0.924341 | − | 0.381568i | \(-0.124616\pi\) |
0.131723 | + | 0.991287i | \(0.457949\pi\) | |||||||
\(824\) | 2547.77 | + | 4412.86i | 0.107713 | + | 0.186565i | ||||
\(825\) | −9583.36 | + | 2728.66i | −0.404424 | + | 0.115151i | ||||
\(826\) | −23440.8 | − | 21392.7i | −0.987421 | − | 0.901146i | ||||
\(827\) | − | 17303.1i | − | 0.727556i | −0.931486 | − | 0.363778i | \(-0.881487\pi\) | ||
0.931486 | − | 0.363778i | \(-0.118513\pi\) | |||||||
\(828\) | −4503.72 | + | 2600.23i | −0.189028 | + | 0.109135i | ||||
\(829\) | 19897.6 | − | 34463.6i | 0.833621 | − | 1.44387i | −0.0615270 | − | 0.998105i | \(-0.519597\pi\) |
0.895148 | − | 0.445769i | \(-0.147070\pi\) | |||||||
\(830\) | −36627.9 | + | 15507.3i | −1.53178 | + | 0.648515i | ||||
\(831\) | 2100.06 | + | 3637.41i | 0.0876659 | + | 0.151842i | ||||
\(832\) | − | 494.079i | − | 0.0205879i | ||||||
\(833\) | −5782.39 | + | 12532.2i | −0.240514 | + | 0.521266i | ||||
\(834\) | −82.0537 | −0.00340682 | ||||||||
\(835\) | 33228.2 | + | 4111.36i | 1.37714 | + | 0.170395i | ||||
\(836\) | 5423.56 | − | 9393.89i | 0.224375 | − | 0.388630i | ||||
\(837\) | 943.992 | + | 545.014i | 0.0389834 | + | 0.0225071i | ||||
\(838\) | 45003.6 | − | 25982.8i | 1.85516 | − | 1.07108i | ||||
\(839\) | 11244.8 | 0.462710 | 0.231355 | − | 0.972869i | \(-0.425684\pi\) | ||||
0.231355 | + | 0.972869i | \(0.425684\pi\) | |||||||
\(840\) | 8392.42 | − | 1564.87i | 0.344721 | − | 0.0642774i | ||||
\(841\) | −17918.3 | −0.734689 | ||||||||
\(842\) | 24054.1 | − | 13887.7i | 0.984513 | − | 0.568409i | ||||
\(843\) | −12899.9 | − | 7447.77i | −0.527042 | − | 0.304288i | ||||
\(844\) | 8566.84 | − | 14838.2i | 0.349387 | − | 0.605156i | ||||
\(845\) | 2917.81 | − | 23581.9i | 0.118788 | − | 0.960050i | ||||
\(846\) | 10040.7 | 0.408046 | ||||||||
\(847\) | 11305.2 | + | 2482.37i | 0.458619 | + | 0.100703i | ||||
\(848\) | 17313.3i | 0.701111i | ||||||||
\(849\) | −11263.3 | − | 19508.6i | −0.455306 | − | 0.788613i | ||||
\(850\) | 16926.0 | + | 4253.65i | 0.683007 | + | 0.171646i | ||||
\(851\) | 20827.4 | − | 36074.2i | 0.838961 | − | 1.45312i | ||||
\(852\) | 5734.45 | − | 3310.79i | 0.230586 | − | 0.133129i | ||||
\(853\) | 4171.88i | 0.167459i | 0.996489 | + | 0.0837295i | \(0.0266832\pi\) | ||||
−0.996489 | + | 0.0837295i | \(0.973317\pi\) | |||||||
\(854\) | 48136.9 | − | 15284.4i | 1.92882 | − | 0.612436i | ||||
\(855\) | 8116.17 | + | 6127.84i | 0.324640 | + | 0.245108i | ||||
\(856\) | −7081.00 | − | 12264.7i | −0.282738 | − | 0.489716i | ||||
\(857\) | −23079.8 | − | 13325.1i | −0.919943 | − | 0.531129i | −0.0363261 | − | 0.999340i | \(-0.511565\pi\) |
−0.883617 | + | 0.468211i | \(0.844899\pi\) | |||||||
\(858\) | 2028.07 | + | 1170.91i | 0.0806961 | + | 0.0465899i | ||||
\(859\) | 2088.24 | + | 3616.93i | 0.0829449 | + | 0.143665i | 0.904514 | − | 0.426445i | \(-0.140234\pi\) |
−0.821569 | + | 0.570109i | \(0.806901\pi\) | |||||||
\(860\) | 11858.4 | − | 15706.1i | 0.470194 | − | 0.622760i | ||||
\(861\) | −885.730 | + | 281.236i | −0.0350588 | + | 0.0111318i | ||||
\(862\) | 20584.2i | 0.813343i | ||||||||
\(863\) | −29419.7 | + | 16985.5i | −1.16044 | + | 0.669980i | −0.951409 | − | 0.307929i | \(-0.900364\pi\) |
−0.209031 | + | 0.977909i | \(0.567031\pi\) | |||||||
\(864\) | −2263.00 | + | 3919.63i | −0.0891075 | + | 0.154339i | ||||
\(865\) | −9514.76 | − | 22473.6i | −0.374002 | − | 0.883382i | ||||
\(866\) | 13820.6 | + | 23938.0i | 0.542312 | + | 0.939313i | ||||
\(867\) | − | 9881.55i | − | 0.387076i | ||||||
\(868\) | −2949.76 | − | 647.705i | −0.115347 | − | 0.0253278i | ||||
\(869\) | −20505.6 | −0.800465 | ||||||||
\(870\) | −1149.55 | + | 9290.73i | −0.0447971 | + | 0.362052i | ||||
\(871\) | 3078.74 | − | 5332.54i | 0.119770 | − | 0.207447i | ||||
\(872\) | 22444.1 | + | 12958.1i | 0.871621 | + | 0.503230i | ||||
\(873\) | 993.140 | − | 573.390i | 0.0385025 | − | 0.0222294i | ||||
\(874\) | −50166.7 | −1.94155 | ||||||||
\(875\) | 11530.8 | + | 23172.4i | 0.445500 | + | 0.895282i | ||||
\(876\) | −4034.48 | −0.155608 | ||||||||
\(877\) | 22706.9 | − | 13109.9i | 0.874298 | − | 0.504776i | 0.00552360 | − | 0.999985i | \(-0.498242\pi\) |
0.868774 | + | 0.495209i | \(0.164908\pi\) | |||||||
\(878\) | −29288.3 | − | 16909.6i | −1.12578 | − | 0.649967i | ||||
\(879\) | −8891.78 | + | 15401.0i | −0.341197 | + | 0.590971i | ||||
\(880\) | 2918.30 | − | 23585.8i | 0.111791 | − | 0.903497i | ||||
\(881\) | −30831.5 | −1.17905 | −0.589523 | − | 0.807752i | \(-0.700684\pi\) | ||||
−0.589523 | + | 0.807752i | \(0.700684\pi\) | |||||||
\(882\) | 4487.50 | − | 9725.76i | 0.171317 | − | 0.371296i | ||||
\(883\) | 29303.3i | 1.11680i | 0.829572 | + | 0.558399i | \(0.188584\pi\) | ||||
−0.829572 | + | 0.558399i | \(0.811416\pi\) | |||||||
\(884\) | −688.058 | − | 1191.75i | −0.0261786 | − | 0.0453427i | ||||
\(885\) | −6457.94 | − | 15253.5i | −0.245290 | − | 0.579367i | ||||
\(886\) | 7629.37 | − | 13214.5i | 0.289293 | − | 0.501070i | ||||
\(887\) | −14759.8 | + | 8521.55i | −0.558719 | + | 0.322577i | −0.752631 | − | 0.658442i | \(-0.771216\pi\) |
0.193912 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(888\) | − | 12005.1i | − | 0.453676i | ||||||
\(889\) | 16469.8 | + | 15030.7i | 0.621348 | + | 0.567058i | ||||
\(890\) | 20019.3 | − | 26515.0i | 0.753986 | − | 0.998635i | ||||
\(891\) | 1076.14 | + | 1863.93i | 0.0404624 | + | 0.0700830i | ||||
\(892\) | 9943.05 | + | 5740.62i | 0.373226 | + | 0.215482i | ||||
\(893\) | 28142.6 | + | 16248.1i | 1.05460 | + | 0.608873i | ||||
\(894\) | 12269.5 | + | 21251.4i | 0.459009 | + | 0.795026i | ||||
\(895\) | −18879.6 | − | 14254.4i | −0.705114 | − | 0.532373i | ||||
\(896\) | −6130.88 | + | 27921.1i | −0.228592 | + | 1.04105i | ||||
\(897\) | − | 3633.70i | − | 0.135257i | ||||||
\(898\) | 40919.1 | − | 23624.6i | 1.52059 | − | 0.877911i | ||||
\(899\) | −1623.75 | + | 2812.41i | −0.0602392 | + | 0.104337i | ||||
\(900\) | −4407.02 | − | 1107.53i | −0.163223 | − | 0.0410195i | ||||
\(901\) | −4354.24 | − | 7541.77i | −0.161000 | − | 0.278860i | ||||
\(902\) | 1542.06i | 0.0569236i | ||||||||
\(903\) | 7327.55 | + | 23077.5i | 0.270039 | + | 0.850468i | ||||
\(904\) | 28234.8 | 1.03880 | ||||||||
\(905\) | −140.182 | + | 1132.96i | −0.00514895 | + | 0.0416140i | ||||
\(906\) | −17894.3 | + | 30993.9i | −0.656180 | + | 1.13654i | ||||
\(907\) | −38499.2 | − | 22227.5i | −1.40942 | − | 0.813729i | −0.414088 | − | 0.910237i | \(-0.635900\pi\) |
−0.995332 | + | 0.0965073i | \(0.969233\pi\) | |||||||
\(908\) | −4702.29 | + | 2714.87i | −0.171862 | + | 0.0992249i | ||||
\(909\) | 8113.13 | 0.296035 | ||||||||
\(910\) | 2024.33 | − | 5736.32i | 0.0737429 | − | 0.208964i | ||||
\(911\) | −24316.4 | −0.884344 | −0.442172 | − | 0.896930i | \(-0.645792\pi\) | ||||
−0.442172 | + | 0.896930i | \(0.645792\pi\) | |||||||
\(912\) | −21006.0 | + | 12127.8i | −0.762696 | + | 0.440343i | ||||
\(913\) | −23594.2 | − | 13622.1i | −0.855262 | − | 0.493786i | ||||
\(914\) | 11519.3 | − | 19952.0i | 0.416875 | − | 0.722049i | ||||
\(915\) | 26161.8 | + | 3237.03i | 0.945227 | + | 0.116954i | ||||
\(916\) | 21722.3 | 0.783544 | ||||||||
\(917\) | −51936.5 | − | 11404.2i | −1.87033 | − | 0.410685i | ||||
\(918\) | − | 3769.69i | − | 0.135532i | ||||||
\(919\) | −3038.65 | − | 5263.09i | −0.109070 | − | 0.188915i | 0.806324 | − | 0.591475i | \(-0.201454\pi\) |
−0.915394 | + | 0.402559i | \(0.868121\pi\) | |||||||
\(920\) | −20241.6 | + | 8569.80i | −0.725377 | + | 0.307106i | ||||
\(921\) | 4134.57 | − | 7161.28i | 0.147925 | − | 0.256213i | ||||
\(922\) | −10056.2 | + | 5805.93i | −0.359200 | + | 0.207384i | ||||
\(923\) | 4626.67i | 0.164993i | ||||||||
\(924\) | −4404.59 | − | 4019.74i | −0.156818 | − | 0.143117i | ||||
\(925\) | 35005.9 | − | 9967.18i | 1.24431 | − | 0.354291i | ||||
\(926\) | 8016.37 | + | 13884.8i | 0.284486 | + | 0.492744i | ||||
\(927\) | 2889.87 | + | 1668.47i | 0.102390 | + | 0.0591150i | ||||
\(928\) | −11677.7 | − | 6742.11i | −0.413080 | − | 0.238492i | ||||
\(929\) | −11500.2 | − | 19919.0i | −0.406147 | − | 0.703467i | 0.588307 | − | 0.808638i | \(-0.299795\pi\) |
−0.994454 | + | 0.105170i | \(0.966461\pi\) | |||||||
\(930\) | −3749.66 | − | 2831.05i | −0.132211 | − | 0.0998214i | ||||
\(931\) | 28316.3 | − | 19998.1i | 0.996809 | − | 0.703985i | ||||
\(932\) | − | 9421.39i | − | 0.331124i | ||||||
\(933\) | 10349.8 | − | 5975.44i | 0.363168 | − | 0.209675i | ||||
\(934\) | −22100.0 | + | 38278.2i | −0.774232 | + | 1.34101i | ||||
\(935\) | 4660.53 | + | 11008.0i | 0.163011 | + | 0.385028i | ||||
\(936\) | −523.622 | − | 906.940i | −0.0182854 | − | 0.0316712i | ||||
\(937\) | − | 19259.6i | − | 0.671489i | −0.941953 | − | 0.335744i | \(-0.891012\pi\) | ||
0.941953 | − | 0.335744i | \(-0.108988\pi\) | |||||||
\(938\) | −31503.1 | + | 34519.2i | −1.09660 | + | 1.20159i | ||||
\(939\) | 25884.7 | 0.899592 | ||||||||
\(940\) | −14410.2 | − | 1782.99i | −0.500010 | − | 0.0618668i | ||||
\(941\) | 3051.64 | − | 5285.59i | 0.105718 | − | 0.183109i | −0.808313 | − | 0.588752i | \(-0.799619\pi\) |
0.914031 | + | 0.405644i | \(0.132953\pi\) | |||||||
\(942\) | −10731.0 | − | 6195.55i | −0.371162 | − | 0.214291i | ||||
\(943\) | 2072.19 | − | 1196.38i | 0.0715585 | − | 0.0413143i | ||||
\(944\) | 39507.2 | 1.36213 | ||||||||
\(945\) | 4247.25 | − | 3635.48i | 0.146204 | − | 0.125145i | ||||
\(946\) | 40178.2 | 1.38087 | ||||||||
\(947\) | −17922.5 | + | 10347.6i | −0.614998 | + | 0.355069i | −0.774919 | − | 0.632061i | \(-0.782209\pi\) |
0.159921 | + | 0.987130i | \(0.448876\pi\) | |||||||
\(948\) | −8098.44 | − | 4675.64i | −0.277453 | − | 0.160187i | ||||
\(949\) | 1409.50 | − | 2441.33i | 0.0482132 | − | 0.0835078i | ||||
\(950\) | −31475.2 | − | 30508.9i | −1.07494 | − | 1.04194i | ||||
\(951\) | 15743.1 | 0.536808 | ||||||||
\(952\) | −3099.47 | − | 9761.54i | −0.105519 | − | 0.332325i | ||||
\(953\) | − | 35769.9i | − | 1.21585i | −0.793996 | − | 0.607923i | \(-0.792003\pi\) | ||
0.793996 | − | 0.607923i | \(-0.207997\pi\) | |||||||
\(954\) | 3379.17 | + | 5852.89i | 0.114680 | + | 0.198631i | ||||
\(955\) | −7717.43 | + | 3267.37i | −0.261498 | + | 0.110711i | ||||
\(956\) | −3307.89 | + | 5729.43i | −0.111909 | + | 0.193832i | ||||
\(957\) | −5553.16 | + | 3206.12i | −0.187574 | + | 0.108296i | ||||
\(958\) | 47168.4i | 1.59075i | ||||||||
\(959\) | −31717.7 | + | 10071.0i | −1.06801 | + | 0.339112i | ||||
\(960\) | −1179.38 | + | 1562.05i | −0.0396502 | + | 0.0525157i | ||||
\(961\) | 14080.6 | + | 24388.3i | 0.472645 | + | 0.818646i | ||||
\(962\) | −7408.11 | − | 4277.07i | −0.248282 | − | 0.143346i | ||||
\(963\) | −8031.79 | − | 4637.16i | −0.268765 | − | 0.155172i | ||||
\(964\) | 2562.34 | + | 4438.10i | 0.0856092 | + | 0.148280i | ||||
\(965\) | 9451.97 | − | 12518.9i | 0.315305 | − | 0.417614i | ||||
\(966\) | −5914.78 | + | 26937.0i | −0.197003 | + | 0.897187i | ||||
\(967\) | − | 39785.2i | − | 1.32307i | −0.749915 | − | 0.661534i | \(-0.769906\pi\) | ||
0.749915 | − | 0.661534i | \(-0.230094\pi\) | |||||||
\(968\) | −7438.25 | + | 4294.48i | −0.246978 | + | 0.142593i | ||||
\(969\) | 6100.22 | − | 10565.9i | 0.202236 | − | 0.350284i | ||||
\(970\) | −4551.85 | + | 1927.14i | −0.150671 | + | 0.0637905i | ||||
\(971\) | −1036.55 | − | 1795.36i | −0.0342580 | − | 0.0593365i | 0.848388 | − | 0.529375i | \(-0.177573\pi\) |
−0.882646 | + | 0.470038i | \(0.844240\pi\) | |||||||
\(972\) | 981.516i | 0.0323890i | ||||||||
\(973\) | −98.4126 | + | 107.835i | −0.00324251 | + | 0.00355295i | ||||
\(974\) | 8803.82 | 0.289623 | ||||||||
\(975\) | 2209.83 | − | 2279.83i | 0.0725860 | − | 0.0748850i | ||||
\(976\) | −31437.1 | + | 54450.6i | −1.03102 | + | 1.78578i | ||||
\(977\) | −3040.16 | − | 1755.24i | −0.0995532 | − | 0.0574771i | 0.449397 | − | 0.893332i | \(-0.351639\pi\) |
−0.548950 | + | 0.835855i | \(0.684972\pi\) | |||||||
\(978\) | −23147.7 | + | 13364.3i | −0.756832 | + | 0.436957i | ||||
\(979\) | 22756.7 | 0.742908 | ||||||||
\(980\) | −8167.44 | + | 13161.3i | −0.266224 | + | 0.429004i | ||||
\(981\) | 16971.8 | 0.552364 | ||||||||
\(982\) | 57704.1 | − | 33315.5i | 1.87516 | − | 1.08263i | ||||
\(983\) | 48756.7 | + | 28149.7i | 1.58199 | + | 0.913363i | 0.994569 | + | 0.104083i | \(0.0331908\pi\) |
0.587423 | + | 0.809280i | \(0.300143\pi\) | |||||||
\(984\) | 344.800 | − | 597.211i | 0.0111706 | − | 0.0193480i | ||||
\(985\) | −13959.3 | − | 1727.19i | −0.451552 | − | 0.0558710i | ||||
\(986\) | 11230.9 | 0.362745 | ||||||||
\(987\) | 12042.5 | − | 13195.5i | 0.388366 | − | 0.425548i | ||||
\(988\) | 3456.38i | 0.111298i | ||||||||
\(989\) | −31171.4 | − | 53990.5i | −1.00222 | − | 1.73589i | ||||
\(990\) | −3616.86 | − | 8542.93i | −0.116113 | − | 0.274255i | ||||
\(991\) | 29627.3 | − | 51315.9i | 0.949689 | − | 1.64491i | 0.203609 | − | 0.979052i | \(-0.434733\pi\) |
0.746080 | − | 0.665857i | \(-0.231934\pi\) | |||||||
\(992\) | 5860.78 | − | 3383.72i | 0.187581 | − | 0.108300i | ||||
\(993\) | − | 13465.9i | − | 0.430338i | ||||||
\(994\) | 7531.11 | − | 34298.0i | 0.240314 | − | 1.09443i | ||||
\(995\) | −27209.9 | − | 20543.9i | −0.866946 | − | 0.654559i | ||||
\(996\) | −6212.18 | − | 10759.8i | −0.197631 | − | 0.342307i | ||||
\(997\) | 39165.5 | + | 22612.2i | 1.24412 | + | 0.718291i | 0.969930 | − | 0.243386i | \(-0.0782582\pi\) |
0.274186 | + | 0.961677i | \(0.411591\pi\) | |||||||
\(998\) | 19551.5 | + | 11288.1i | 0.620133 | + | 0.358034i | ||||
\(999\) | −3930.90 | − | 6808.52i | −0.124493 | − | 0.215628i |
(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 | 105.4.q.b.4.19 | yes | 44 | |
5.4 | even | 2 | inner | 105.4.q.b.4.4 | ✓ | 44 | |
7.2 | even | 3 | inner | 105.4.q.b.79.4 | yes | 44 | |
35.9 | even | 6 | inner | 105.4.q.b.79.19 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.q.b.4.4 | ✓ | 44 | 5.4 | even | 2 | inner | |
105.4.q.b.4.19 | yes | 44 | 1.1 | even | 1 | trivial | |
105.4.q.b.79.4 | yes | 44 | 7.2 | even | 3 | inner | |
105.4.q.b.79.19 | yes | 44 | 35.9 | even | 6 | inner |