Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,4,Mod(11,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.e (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: | \(2.18307067021\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 82 x^{14} + 2679 x^{12} + 44392 x^{10} + 392767 x^{8} + 1779258 x^{6} + 3438825 x^{4} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.8 | ||
Root | \(4.53054i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.27 |
Dual form | 37.4.e.a.11.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.92356 | + | 2.26527i | 1.38719 | + | 0.800894i | 0.992998 | − | 0.118134i | \(-0.0376912\pi\) |
0.394192 | + | 0.919028i | \(0.371025\pi\) | |||||||
\(3\) | −0.409472 | − | 0.709227i | −0.0788030 | − | 0.136491i | 0.823931 | − | 0.566690i | \(-0.191776\pi\) |
−0.902734 | + | 0.430200i | \(0.858443\pi\) | |||||||
\(4\) | 6.26291 | + | 10.8477i | 0.782863 | + | 1.35596i | ||||
\(5\) | −2.10394 | + | 1.21471i | −0.188182 | + | 0.108647i | −0.591131 | − | 0.806575i | \(-0.701318\pi\) |
0.402949 | + | 0.915222i | \(0.367985\pi\) | |||||||
\(6\) | − | 3.71026i | − | 0.252451i | ||||||
\(7\) | −2.25379 | − | 3.90368i | −0.121693 | − | 0.210779i | 0.798742 | − | 0.601673i | \(-0.205499\pi\) |
−0.920436 | + | 0.390894i | \(0.872166\pi\) | |||||||
\(8\) | 20.5044i | 0.906174i | ||||||||
\(9\) | 13.1647 | − | 22.8019i | 0.487580 | − | 0.844514i | ||||
\(10\) | −11.0066 | −0.348059 | ||||||||
\(11\) | −32.7176 | −0.896793 | −0.448396 | − | 0.893835i | \(-0.648005\pi\) | ||||
−0.448396 | + | 0.893835i | \(0.648005\pi\) | |||||||
\(12\) | 5.12897 | − | 8.88364i | 0.123384 | − | 0.213707i | ||||
\(13\) | −26.6656 | + | 15.3954i | −0.568902 | + | 0.328455i | −0.756711 | − | 0.653750i | \(-0.773195\pi\) |
0.187809 | + | 0.982206i | \(0.439861\pi\) | |||||||
\(14\) | − | 20.4218i | − | 0.389854i | ||||||
\(15\) | 1.72301 | + | 0.994779i | 0.0296586 | + | 0.0171234i | ||||
\(16\) | 3.65526 | − | 6.33109i | 0.0571134 | − | 0.0989233i | ||||
\(17\) | 32.5573 | + | 18.7970i | 0.464488 | + | 0.268172i | 0.713930 | − | 0.700217i | \(-0.246914\pi\) |
−0.249441 | + | 0.968390i | \(0.580247\pi\) | |||||||
\(18\) | 103.305 | − | 59.6431i | 1.35273 | − | 0.781000i | ||||
\(19\) | 18.0514 | − | 10.4220i | 0.217962 | − | 0.125840i | −0.387044 | − | 0.922061i | \(-0.626504\pi\) |
0.605006 | + | 0.796221i | \(0.293171\pi\) | |||||||
\(20\) | −26.3535 | − | 15.2152i | −0.294641 | − | 0.170111i | ||||
\(21\) | −1.84573 | + | 3.19690i | −0.0191796 | + | 0.0332200i | ||||
\(22\) | −128.370 | − | 74.1142i | −1.24402 | − | 0.718236i | ||||
\(23\) | 70.9376i | 0.643109i | 0.946891 | + | 0.321555i | \(0.104205\pi\) | ||||
−0.946891 | + | 0.321555i | \(0.895795\pi\) | |||||||
\(24\) | 14.5423 | − | 8.39598i | 0.123684 | − | 0.0714092i | ||||
\(25\) | −59.5490 | + | 103.142i | −0.476392 | + | 0.825135i | ||||
\(26\) | −139.499 | −1.05223 | ||||||||
\(27\) | −43.6738 | −0.311297 | ||||||||
\(28\) | 28.2306 | − | 48.8968i | 0.190538 | − | 0.330022i | ||||
\(29\) | − | 160.432i | − | 1.02729i | −0.858002 | − | 0.513647i | \(-0.828294\pi\) | ||
0.858002 | − | 0.513647i | \(-0.171706\pi\) | |||||||
\(30\) | 4.50689 | + | 7.80616i | 0.0274280 | + | 0.0475068i | ||||
\(31\) | 304.782i | 1.76582i | 0.469539 | + | 0.882912i | \(0.344420\pi\) | ||||
−0.469539 | + | 0.882912i | \(0.655580\pi\) | |||||||
\(32\) | 170.742 | − | 98.5778i | 0.943224 | − | 0.544571i | ||||
\(33\) | 13.3969 | + | 23.2042i | 0.0706699 | + | 0.122404i | ||||
\(34\) | 85.1604 | + | 147.502i | 0.429556 | + | 0.744012i | ||||
\(35\) | 9.48367 | + | 5.47540i | 0.0458009 | + | 0.0264432i | ||||
\(36\) | 329.796 | 1.52683 | ||||||||
\(37\) | 134.674 | + | 180.322i | 0.598386 | + | 0.801208i | ||||
\(38\) | 94.4344 | 0.403139 | ||||||||
\(39\) | 21.8377 | + | 12.6080i | 0.0896622 | + | 0.0517665i | ||||
\(40\) | −24.9069 | − | 43.1399i | −0.0984530 | − | 0.170526i | ||||
\(41\) | 77.7201 | + | 134.615i | 0.296045 | + | 0.512765i | 0.975227 | − | 0.221205i | \(-0.0709988\pi\) |
−0.679182 | + | 0.733969i | \(0.737665\pi\) | |||||||
\(42\) | −14.4837 | + | 8.36215i | −0.0532114 | + | 0.0307216i | ||||
\(43\) | − | 255.312i | − | 0.905459i | −0.891648 | − | 0.452730i | \(-0.850450\pi\) | ||
0.891648 | − | 0.452730i | \(-0.149550\pi\) | |||||||
\(44\) | −204.907 | − | 354.910i | −0.702066 | − | 1.21601i | ||||
\(45\) | 63.9649i | 0.211896i | ||||||||
\(46\) | −160.693 | + | 278.328i | −0.515063 | + | 0.892115i | ||||
\(47\) | −474.197 | −1.47167 | −0.735837 | − | 0.677158i | \(-0.763211\pi\) | ||||
−0.735837 | + | 0.677158i | \(0.763211\pi\) | |||||||
\(48\) | −5.98690 | −0.0180028 | ||||||||
\(49\) | 161.341 | − | 279.451i | 0.470381 | − | 0.814725i | ||||
\(50\) | −467.288 | + | 269.789i | −1.32169 | + | 0.763079i | ||||
\(51\) | − | 30.7873i | − | 0.0845311i | ||||||
\(52\) | −334.009 | − | 192.840i | −0.890744 | − | 0.514271i | ||||
\(53\) | 232.452 | − | 402.618i | 0.602447 | − | 1.04347i | −0.390002 | − | 0.920814i | \(-0.627526\pi\) |
0.992449 | − | 0.122655i | \(-0.0391410\pi\) | |||||||
\(54\) | −171.357 | − | 98.9329i | −0.431828 | − | 0.249316i | ||||
\(55\) | 68.8357 | − | 39.7423i | 0.168760 | − | 0.0974337i | ||||
\(56\) | 80.0426 | − | 46.2126i | 0.191002 | − | 0.110275i | ||||
\(57\) | −14.7831 | − | 8.53502i | −0.0343521 | − | 0.0198332i | ||||
\(58\) | 363.422 | − | 629.466i | 0.822753 | − | 1.42505i | ||||
\(59\) | −262.062 | − | 151.301i | −0.578263 | − | 0.333860i | 0.182180 | − | 0.983265i | \(-0.441685\pi\) |
−0.760443 | + | 0.649405i | \(0.775018\pi\) | |||||||
\(60\) | 24.9208i | 0.0536211i | ||||||||
\(61\) | 105.715 | − | 61.0347i | 0.221893 | − | 0.128110i | −0.384934 | − | 0.922944i | \(-0.625776\pi\) |
0.606826 | + | 0.794834i | \(0.292442\pi\) | |||||||
\(62\) | −690.415 | + | 1195.83i | −1.41424 | + | 2.44953i | ||||
\(63\) | −118.682 | −0.237341 | ||||||||
\(64\) | 834.738 | 1.63035 | ||||||||
\(65\) | 37.4019 | − | 64.7820i | 0.0713713 | − | 0.123619i | ||||
\(66\) | 121.391i | 0.226397i | ||||||||
\(67\) | −217.869 | − | 377.361i | −0.397269 | − | 0.688089i | 0.596119 | − | 0.802896i | \(-0.296709\pi\) |
−0.993388 | + | 0.114807i | \(0.963375\pi\) | |||||||
\(68\) | 470.894i | 0.839769i | ||||||||
\(69\) | 50.3108 | − | 29.0470i | 0.0877785 | − | 0.0506789i | ||||
\(70\) | 24.8065 | + | 42.9662i | 0.0423564 | + | 0.0733634i | ||||
\(71\) | −225.618 | − | 390.782i | −0.377126 | − | 0.653201i | 0.613517 | − | 0.789682i | \(-0.289754\pi\) |
−0.990643 | + | 0.136480i | \(0.956421\pi\) | |||||||
\(72\) | 467.538 | + | 269.933i | 0.765277 | + | 0.441833i | ||||
\(73\) | 1130.10 | 1.81189 | 0.905943 | − | 0.423400i | \(-0.139163\pi\) | ||||
0.905943 | + | 0.423400i | \(0.139163\pi\) | |||||||
\(74\) | 119.925 | + | 1012.58i | 0.188392 | + | 1.59067i | ||||
\(75\) | 97.5346 | 0.150164 | ||||||||
\(76\) | 226.108 | + | 130.544i | 0.341269 | + | 0.197032i | ||||
\(77\) | 73.7386 | + | 127.719i | 0.109134 | + | 0.189025i | ||||
\(78\) | 57.1210 | + | 98.9365i | 0.0829190 | + | 0.143620i | ||||
\(79\) | 518.771 | − | 299.512i | 0.738813 | − | 0.426554i | −0.0828243 | − | 0.996564i | \(-0.526394\pi\) |
0.821638 | + | 0.570010i | \(0.193061\pi\) | |||||||
\(80\) | 17.7603i | 0.0248208i | ||||||||
\(81\) | −337.563 | − | 584.676i | −0.463049 | − | 0.802025i | ||||
\(82\) | 704.229i | 0.948403i | ||||||||
\(83\) | −529.637 | + | 917.358i | −0.700424 | + | 1.21317i | 0.267893 | + | 0.963449i | \(0.413673\pi\) |
−0.968318 | + | 0.249722i | \(0.919661\pi\) | |||||||
\(84\) | −46.2385 | −0.0600600 | ||||||||
\(85\) | −91.3313 | −0.116544 | ||||||||
\(86\) | 578.351 | − | 1001.73i | 0.725177 | − | 1.25604i | ||||
\(87\) | −113.783 | + | 65.6925i | −0.140216 | + | 0.0809538i | ||||
\(88\) | − | 670.854i | − | 0.812651i | ||||||
\(89\) | −452.440 | − | 261.216i | −0.538860 | − | 0.311111i | 0.205757 | − | 0.978603i | \(-0.434034\pi\) |
−0.744617 | + | 0.667492i | \(0.767368\pi\) | |||||||
\(90\) | −144.898 | + | 250.971i | −0.169706 | + | 0.293940i | ||||
\(91\) | 120.198 | + | 69.3961i | 0.138463 | + | 0.0799416i | ||||
\(92\) | −769.508 | + | 444.276i | −0.872030 | + | 0.503467i | ||||
\(93\) | 216.160 | − | 124.800i | 0.241019 | − | 0.139152i | ||||
\(94\) | −1860.54 | − | 1074.18i | −2.04149 | − | 1.17866i | ||||
\(95\) | −25.3193 | + | 43.8544i | −0.0273443 | + | 0.0473617i | ||||
\(96\) | −139.828 | − | 80.7298i | −0.148658 | − | 0.0858276i | ||||
\(97\) | 380.432i | 0.398217i | 0.979977 | + | 0.199108i | \(0.0638046\pi\) | ||||
−0.979977 | + | 0.199108i | \(0.936195\pi\) | |||||||
\(98\) | 1266.06 | − | 730.962i | 1.30502 | − | 0.753452i | ||||
\(99\) | −430.716 | + | 746.022i | −0.437258 | + | 0.757354i | ||||
\(100\) | −1491.80 | −1.49180 | ||||||||
\(101\) | −348.298 | −0.343138 | −0.171569 | − | 0.985172i | \(-0.554884\pi\) | ||||
−0.171569 | + | 0.985172i | \(0.554884\pi\) | |||||||
\(102\) | 69.7416 | − | 120.796i | 0.0677005 | − | 0.117261i | ||||
\(103\) | 962.548i | 0.920803i | 0.887711 | + | 0.460401i | \(0.152295\pi\) | ||||
−0.887711 | + | 0.460401i | \(0.847705\pi\) | |||||||
\(104\) | −315.674 | − | 546.763i | −0.297638 | − | 0.515524i | ||||
\(105\) | − | 8.96809i | − | 0.00833520i | ||||||
\(106\) | 1824.08 | − | 1053.13i | 1.67142 | − | 0.964993i | ||||
\(107\) | −332.270 | − | 575.509i | −0.300204 | − | 0.519968i | 0.675978 | − | 0.736922i | \(-0.263721\pi\) |
−0.976182 | + | 0.216954i | \(0.930388\pi\) | |||||||
\(108\) | −273.525 | − | 473.759i | −0.243703 | − | 0.422106i | ||||
\(109\) | 1732.93 | + | 1000.51i | 1.52280 | + | 0.879187i | 0.999637 | + | 0.0269514i | \(0.00857993\pi\) |
0.523159 | + | 0.852235i | \(0.324753\pi\) | |||||||
\(110\) | 360.109 | 0.312136 | ||||||||
\(111\) | 72.7436 | − | 169.351i | 0.0622029 | − | 0.144812i | ||||
\(112\) | −32.9527 | −0.0278013 | ||||||||
\(113\) | 584.630 | + | 337.536i | 0.486703 | + | 0.280998i | 0.723206 | − | 0.690633i | \(-0.242668\pi\) |
−0.236503 | + | 0.971631i | \(0.576001\pi\) | |||||||
\(114\) | −38.6683 | − | 66.9754i | −0.0317686 | − | 0.0550248i | ||||
\(115\) | −86.1685 | − | 149.248i | −0.0698718 | − | 0.121021i | ||||
\(116\) | 1740.32 | − | 1004.77i | 1.39297 | − | 0.804230i | ||||
\(117\) | 810.702i | 0.640594i | ||||||||
\(118\) | −685.477 | − | 1187.28i | −0.534774 | − | 0.926255i | ||||
\(119\) | − | 169.458i | − | 0.130539i | ||||||
\(120\) | −20.3973 | + | 35.3292i | −0.0155168 | + | 0.0268758i | ||||
\(121\) | −260.560 | −0.195763 | ||||||||
\(122\) | 553.041 | 0.410410 | ||||||||
\(123\) | 63.6485 | − | 110.242i | 0.0466584 | − | 0.0808148i | ||||
\(124\) | −3306.18 | + | 1908.82i | −2.39438 | + | 1.38240i | ||||
\(125\) | − | 593.016i | − | 0.424327i | ||||||
\(126\) | −465.655 | − | 268.846i | −0.329237 | − | 0.190085i | ||||
\(127\) | −1181.86 | + | 2047.04i | −0.825772 | + | 1.43028i | 0.0755553 | + | 0.997142i | \(0.475927\pi\) |
−0.901328 | + | 0.433138i | \(0.857406\pi\) | |||||||
\(128\) | 1909.21 | + | 1102.29i | 1.31838 | + | 0.761165i | ||||
\(129\) | −181.074 | + | 104.543i | −0.123587 | + | 0.0713528i | ||||
\(130\) | 293.498 | − | 169.451i | 0.198011 | − | 0.114322i | ||||
\(131\) | −1736.08 | − | 1002.32i | −1.15788 | − | 0.668500i | −0.207082 | − | 0.978324i | \(-0.566397\pi\) |
−0.950794 | + | 0.309823i | \(0.899730\pi\) | |||||||
\(132\) | −167.808 | + | 290.651i | −0.110650 | + | 0.191651i | ||||
\(133\) | −81.3682 | − | 46.9779i | −0.0530490 | − | 0.0306278i | ||||
\(134\) | − | 1974.13i | − | 1.27268i | ||||||
\(135\) | 91.8868 | − | 53.0509i | 0.0585804 | − | 0.0338214i | ||||
\(136\) | −385.420 | + | 667.567i | −0.243011 | + | 0.420907i | ||||
\(137\) | 1002.93 | 0.625443 | 0.312722 | − | 0.949845i | \(-0.398759\pi\) | ||||
0.312722 | + | 0.949845i | \(0.398759\pi\) | |||||||
\(138\) | 263.197 | 0.162354 | ||||||||
\(139\) | −270.024 | + | 467.695i | −0.164771 | + | 0.285391i | −0.936574 | − | 0.350471i | \(-0.886022\pi\) |
0.771803 | + | 0.635861i | \(0.219355\pi\) | |||||||
\(140\) | 137.168i | 0.0828056i | ||||||||
\(141\) | 194.170 | + | 336.313i | 0.115972 | + | 0.200870i | ||||
\(142\) | − | 2044.34i | − | 1.20815i | ||||||
\(143\) | 872.436 | − | 503.701i | 0.510187 | − | 0.294557i | ||||
\(144\) | −96.2404 | − | 166.693i | −0.0556947 | − | 0.0964661i | ||||
\(145\) | 194.878 | + | 337.539i | 0.111612 | + | 0.193318i | ||||
\(146\) | 4434.00 | + | 2559.97i | 2.51343 | + | 1.45113i | ||||
\(147\) | −264.258 | −0.148270 | ||||||||
\(148\) | −1112.62 | + | 2590.24i | −0.617951 | + | 1.43862i | ||||
\(149\) | −2395.51 | −1.31710 | −0.658550 | − | 0.752537i | \(-0.728830\pi\) | ||||
−0.658550 | + | 0.752537i | \(0.728830\pi\) | |||||||
\(150\) | 382.683 | + | 220.942i | 0.208306 | + | 0.120266i | ||||
\(151\) | 40.1213 | + | 69.4922i | 0.0216227 | + | 0.0374516i | 0.876634 | − | 0.481157i | \(-0.159783\pi\) |
−0.855012 | + | 0.518609i | \(0.826450\pi\) | |||||||
\(152\) | 213.696 | + | 370.133i | 0.114033 | + | 0.197511i | ||||
\(153\) | 857.211 | − | 494.911i | 0.452951 | − | 0.261511i | ||||
\(154\) | 668.152i | 0.349618i | ||||||||
\(155\) | −370.222 | − | 641.243i | −0.191851 | − | 0.332296i | ||||
\(156\) | 315.851i | 0.162104i | ||||||||
\(157\) | 869.272 | − | 1505.62i | 0.441882 | − | 0.765362i | −0.555947 | − | 0.831218i | \(-0.687644\pi\) |
0.997829 | + | 0.0658555i | \(0.0209776\pi\) | |||||||
\(158\) | 2713.91 | 1.36650 | ||||||||
\(159\) | −380.730 | −0.189899 | ||||||||
\(160\) | −239.487 | + | 414.803i | −0.118332 | + | 0.204957i | ||||
\(161\) | 276.918 | − | 159.879i | 0.135554 | − | 0.0782621i | ||||
\(162\) | − | 3058.68i | − | 1.48341i | ||||||
\(163\) | 869.525 | + | 502.020i | 0.417831 | + | 0.241235i | 0.694149 | − | 0.719831i | \(-0.255781\pi\) |
−0.276318 | + | 0.961066i | \(0.589114\pi\) | |||||||
\(164\) | −973.508 | + | 1686.16i | −0.463526 | + | 0.802850i | ||||
\(165\) | −56.3726 | − | 32.5467i | −0.0265976 | − | 0.0153561i | ||||
\(166\) | −4156.13 | + | 2399.54i | −1.94324 | + | 1.12193i | ||||
\(167\) | 2165.28 | − | 1250.12i | 1.00332 | − | 0.579266i | 0.0940895 | − | 0.995564i | \(-0.470006\pi\) |
0.909228 | + | 0.416298i | \(0.136673\pi\) | |||||||
\(168\) | −65.5504 | − | 37.8455i | −0.0301031 | − | 0.0173800i | ||||
\(169\) | −624.462 | + | 1081.60i | −0.284234 | + | 0.492308i | ||||
\(170\) | −358.344 | − | 206.890i | −0.161669 | − | 0.0933397i | ||||
\(171\) | − | 548.808i | − | 0.245429i | ||||||
\(172\) | 2769.54 | − | 1599.00i | 1.22777 | − | 0.708851i | ||||
\(173\) | −547.969 | + | 949.110i | −0.240817 | + | 0.417107i | −0.960947 | − | 0.276732i | \(-0.910749\pi\) |
0.720130 | + | 0.693839i | \(0.244082\pi\) | |||||||
\(174\) | −595.245 | −0.259342 | ||||||||
\(175\) | 536.844 | 0.231895 | ||||||||
\(176\) | −119.591 | + | 207.138i | −0.0512189 | + | 0.0887137i | ||||
\(177\) | 247.815i | 0.105237i | ||||||||
\(178\) | −1183.45 | − | 2049.80i | −0.498334 | − | 0.863140i | ||||
\(179\) | − | 1607.60i | − | 0.671273i | −0.941992 | − | 0.335637i | \(-0.891049\pi\) | ||
0.941992 | − | 0.335637i | \(-0.108951\pi\) | |||||||
\(180\) | −693.871 | + | 400.606i | −0.287323 | + | 0.165886i | ||||
\(181\) | −1417.49 | − | 2455.16i | −0.582106 | − | 1.00824i | −0.995229 | − | 0.0975617i | \(-0.968896\pi\) |
0.413124 | − | 0.910675i | \(-0.364438\pi\) | |||||||
\(182\) | 314.402 | + | 544.560i | 0.128050 | + | 0.221788i | ||||
\(183\) | −86.5749 | − | 49.9841i | −0.0349716 | − | 0.0201909i | ||||
\(184\) | −1454.53 | −0.582769 | ||||||||
\(185\) | −502.384 | − | 215.796i | −0.199654 | − | 0.0857601i | ||||
\(186\) | 1130.82 | 0.445785 | ||||||||
\(187\) | −1065.20 | − | 614.991i | −0.416550 | − | 0.240495i | ||||
\(188\) | −2969.85 | − | 5143.93i | −1.15212 | − | 1.99553i | ||||
\(189\) | 98.4315 | + | 170.488i | 0.0378827 | + | 0.0656148i | ||||
\(190\) | −198.684 | + | 114.710i | −0.0758635 | + | 0.0437998i | ||||
\(191\) | 2966.83i | 1.12394i | 0.827158 | + | 0.561969i | \(0.189956\pi\) | ||||
−0.827158 | + | 0.561969i | \(0.810044\pi\) | |||||||
\(192\) | −341.802 | − | 592.018i | −0.128476 | − | 0.222527i | ||||
\(193\) | − | 2640.30i | − | 0.984730i | −0.870389 | − | 0.492365i | \(-0.836133\pi\) | ||
0.870389 | − | 0.492365i | \(-0.163867\pi\) | |||||||
\(194\) | −861.782 | + | 1492.65i | −0.318930 | + | 0.552402i | ||||
\(195\) | −61.2601 | −0.0224971 | ||||||||
\(196\) | 4041.85 | 1.47298 | ||||||||
\(197\) | 388.864 | − | 673.532i | 0.140637 | − | 0.243590i | −0.787100 | − | 0.616825i | \(-0.788418\pi\) |
0.927736 | + | 0.373236i | \(0.121752\pi\) | |||||||
\(198\) | −3379.88 | + | 1951.38i | −1.21312 | + | 0.700396i | ||||
\(199\) | 1516.30i | 0.540140i | 0.962841 | + | 0.270070i | \(0.0870469\pi\) | ||||
−0.962841 | + | 0.270070i | \(0.912953\pi\) | |||||||
\(200\) | −2114.86 | − | 1221.02i | −0.747716 | − | 0.431694i | ||||
\(201\) | −178.423 | + | 309.038i | −0.0626119 | + | 0.108447i | ||||
\(202\) | −1366.57 | − | 788.989i | −0.475998 | − | 0.274817i | ||||
\(203\) | −626.276 | + | 361.581i | −0.216532 | + | 0.125015i | ||||
\(204\) | 333.971 | − | 192.818i | 0.114621 | − | 0.0661763i | ||||
\(205\) | −327.036 | − | 188.815i | −0.111421 | − | 0.0643287i | ||||
\(206\) | −2180.43 | + | 3776.62i | −0.737466 | + | 1.27733i | ||||
\(207\) | 1617.51 | + | 933.870i | 0.543115 | + | 0.313567i | ||||
\(208\) | 225.097i | 0.0750368i | ||||||||
\(209\) | −590.598 | + | 340.982i | −0.195467 | + | 0.112853i | ||||
\(210\) | 20.3152 | − | 35.1869i | 0.00667562 | − | 0.0115625i | ||||
\(211\) | 318.584 | 0.103944 | 0.0519720 | − | 0.998649i | \(-0.483449\pi\) | ||||
0.0519720 | + | 0.998649i | \(0.483449\pi\) | |||||||
\(212\) | 5823.30 | 1.88654 | ||||||||
\(213\) | −184.769 | + | 320.029i | −0.0594373 | + | 0.102948i | ||||
\(214\) | − | 3010.73i | − | 0.961726i | ||||||
\(215\) | 310.130 | + | 537.161i | 0.0983753 | + | 0.170391i | ||||
\(216\) | − | 895.503i | − | 0.282089i | ||||||
\(217\) | 1189.77 | − | 686.916i | 0.372198 | − | 0.214889i | ||||
\(218\) | 4532.85 | + | 7851.12i | 1.40827 | + | 2.43920i | ||||
\(219\) | −462.743 | − | 801.494i | −0.142782 | − | 0.247306i | ||||
\(220\) | 862.223 | + | 497.805i | 0.264232 | + | 0.152555i | ||||
\(221\) | −1157.55 | −0.352331 | ||||||||
\(222\) | 669.040 | − | 499.676i | 0.202266 | − | 0.151063i | ||||
\(223\) | 4752.81 | 1.42723 | 0.713613 | − | 0.700540i | \(-0.247057\pi\) | ||||
0.713613 | + | 0.700540i | \(0.247057\pi\) | |||||||
\(224\) | −769.633 | − | 444.348i | −0.229568 | − | 0.132541i | ||||
\(225\) | 1567.88 | + | 2715.66i | 0.464558 | + | 0.804639i | ||||
\(226\) | 1529.22 | + | 2648.69i | 0.450099 | + | 0.779595i | ||||
\(227\) | 4064.12 | − | 2346.42i | 1.18830 | − | 0.686068i | 0.230383 | − | 0.973100i | \(-0.426002\pi\) |
0.957921 | + | 0.287032i | \(0.0926686\pi\) | |||||||
\(228\) | − | 213.816i | − | 0.0621067i | ||||||
\(229\) | 2037.77 | + | 3529.52i | 0.588033 | + | 1.01850i | 0.994490 | + | 0.104834i | \(0.0334310\pi\) |
−0.406456 | + | 0.913670i | \(0.633236\pi\) | |||||||
\(230\) | − | 780.780i | − | 0.223840i | ||||||
\(231\) | 60.3878 | − | 104.595i | 0.0172001 | − | 0.0297915i | ||||
\(232\) | 3289.56 | 0.930907 | ||||||||
\(233\) | 1756.72 | 0.493934 | 0.246967 | − | 0.969024i | \(-0.420566\pi\) | ||||
0.246967 | + | 0.969024i | \(0.420566\pi\) | |||||||
\(234\) | −1836.46 | + | 3180.84i | −0.513048 | + | 0.888625i | ||||
\(235\) | 997.680 | − | 576.011i | 0.276942 | − | 0.159893i | ||||
\(236\) | − | 3790.35i | − | 1.04547i | ||||||
\(237\) | −424.844 | − | 245.284i | −0.116441 | − | 0.0672275i | ||||
\(238\) | 383.867 | − | 664.878i | 0.104548 | − | 0.181083i | ||||
\(239\) | −4571.61 | − | 2639.42i | −1.23729 | − | 0.714352i | −0.268753 | − | 0.963209i | \(-0.586612\pi\) |
−0.968540 | + | 0.248857i | \(0.919945\pi\) | |||||||
\(240\) | 12.5961 | − | 7.27234i | 0.00338780 | − | 0.00195595i | ||||
\(241\) | −6068.51 | + | 3503.66i | −1.62202 | + | 0.936475i | −0.635644 | + | 0.771983i | \(0.719265\pi\) |
−0.986378 | + | 0.164492i | \(0.947401\pi\) | |||||||
\(242\) | −1022.32 | − | 590.239i | −0.271560 | − | 0.156785i | ||||
\(243\) | −866.041 | + | 1500.03i | −0.228628 | + | 0.395995i | ||||
\(244\) | 1324.17 | + | 764.510i | 0.347423 | + | 0.200585i | ||||
\(245\) | 783.928i | 0.204422i | ||||||||
\(246\) | 499.458 | − | 288.362i | 0.129448 | − | 0.0747370i | ||||
\(247\) | −320.902 | + | 555.818i | −0.0826659 | + | 0.143182i | ||||
\(248\) | −6249.38 | −1.60014 | ||||||||
\(249\) | 867.487 | 0.220782 | ||||||||
\(250\) | 1343.34 | − | 2326.74i | 0.339841 | − | 0.588623i | ||||
\(251\) | − | 6033.57i | − | 1.51727i | −0.651514 | − | 0.758637i | \(-0.725866\pi\) | ||
0.651514 | − | 0.758637i | \(-0.274134\pi\) | |||||||
\(252\) | −743.292 | − | 1287.42i | −0.185805 | − | 0.321825i | ||||
\(253\) | − | 2320.91i | − | 0.576736i | ||||||
\(254\) | −9274.21 | + | 5354.46i | −2.29101 | + | 1.32271i | ||||
\(255\) | 37.3976 | + | 64.7746i | 0.00918404 | + | 0.0159072i | ||||
\(256\) | 1655.00 | + | 2866.54i | 0.404052 | + | 0.699839i | ||||
\(257\) | −4351.52 | − | 2512.35i | −1.05619 | − | 0.609791i | −0.131813 | − | 0.991275i | \(-0.542080\pi\) |
−0.924376 | + | 0.381484i | \(0.875413\pi\) | |||||||
\(258\) | −947.275 | −0.228584 | ||||||||
\(259\) | 400.391 | − | 932.132i | 0.0960582 | − | 0.223629i | ||||
\(260\) | 936.978 | 0.223496 | ||||||||
\(261\) | −3658.15 | − | 2112.04i | −0.867563 | − | 0.500888i | ||||
\(262\) | −4541.08 | − | 7865.37i | −1.07080 | − | 1.85467i | ||||
\(263\) | 2987.64 | + | 5174.75i | 0.700479 | + | 1.21327i | 0.968298 | + | 0.249796i | \(0.0803637\pi\) |
−0.267819 | + | 0.963469i | \(0.586303\pi\) | |||||||
\(264\) | −475.787 | + | 274.696i | −0.110919 | + | 0.0640393i | ||||
\(265\) | 1129.44i | 0.261816i | ||||||||
\(266\) | −212.835 | − | 368.642i | −0.0490593 | − | 0.0849732i | ||||
\(267\) | 427.843i | 0.0980658i | ||||||||
\(268\) | 2728.99 | − | 4726.75i | 0.622014 | − | 1.07736i | ||||
\(269\) | −4297.85 | −0.974143 | −0.487071 | − | 0.873362i | \(-0.661935\pi\) | ||||
−0.487071 | + | 0.873362i | \(0.661935\pi\) | |||||||
\(270\) | 480.698 | 0.108350 | ||||||||
\(271\) | 1779.97 | − | 3083.00i | 0.398987 | − | 0.691066i | −0.594614 | − | 0.804011i | \(-0.702695\pi\) |
0.993601 | + | 0.112945i | \(0.0360285\pi\) | |||||||
\(272\) | 238.010 | − | 137.415i | 0.0530570 | − | 0.0306325i | ||||
\(273\) | − | 113.663i | − | 0.0251985i | ||||||
\(274\) | 3935.04 | + | 2271.90i | 0.867608 | + | 0.500914i | ||||
\(275\) | 1948.30 | − | 3374.55i | 0.427225 | − | 0.739975i | ||||
\(276\) | 630.184 | + | 363.837i | 0.137437 | + | 0.0793493i | ||||
\(277\) | 1899.36 | − | 1096.60i | 0.411991 | − | 0.237863i | −0.279654 | − | 0.960101i | \(-0.590220\pi\) |
0.691645 | + | 0.722238i | \(0.256886\pi\) | |||||||
\(278\) | −2118.91 | + | 1223.35i | −0.457136 | + | 0.263928i | ||||
\(279\) | 6949.61 | + | 4012.36i | 1.49126 | + | 0.860981i | ||||
\(280\) | −112.270 | + | 194.457i | −0.0239621 | + | 0.0415036i | ||||
\(281\) | −4107.37 | − | 2371.39i | −0.871975 | − | 0.503435i | −0.00397114 | − | 0.999992i | \(-0.501264\pi\) |
−0.868004 | + | 0.496557i | \(0.834597\pi\) | |||||||
\(282\) | 1759.39i | 0.371526i | ||||||||
\(283\) | −973.615 | + | 562.117i | −0.204507 | + | 0.118072i | −0.598756 | − | 0.800932i | \(-0.704338\pi\) |
0.394249 | + | 0.919004i | \(0.371005\pi\) | |||||||
\(284\) | 2826.05 | − | 4894.86i | 0.590476 | − | 1.02273i | ||||
\(285\) | 41.4703 | 0.00861925 | ||||||||
\(286\) | 4564.08 | 0.943635 | ||||||||
\(287\) | 350.330 | − | 606.789i | 0.0720534 | − | 0.124800i | ||||
\(288\) | − | 5190.98i | − | 1.06209i | ||||||
\(289\) | −1749.85 | − | 3030.83i | −0.356167 | − | 0.616899i | ||||
\(290\) | 1765.81i | 0.357558i | ||||||||
\(291\) | 269.813 | − | 155.776i | 0.0543529 | − | 0.0313807i | ||||
\(292\) | 7077.68 | + | 12258.9i | 1.41846 | + | 2.45684i | ||||
\(293\) | 4576.68 | + | 7927.05i | 0.912535 | + | 1.58056i | 0.810471 | + | 0.585779i | \(0.199211\pi\) |
0.102064 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(294\) | −1036.83 | − | 598.617i | −0.205678 | − | 0.118748i | ||||
\(295\) | 735.148 | 0.145092 | ||||||||
\(296\) | −3697.38 | + | 2761.41i | −0.726034 | + | 0.542242i | ||||
\(297\) | 1428.90 | 0.279169 | ||||||||
\(298\) | −9398.94 | − | 5426.48i | −1.82707 | − | 1.05486i | ||||
\(299\) | −1092.11 | − | 1891.60i | −0.211233 | − | 0.365866i | ||||
\(300\) | 610.850 | + | 1058.02i | 0.117558 | + | 0.203617i | ||||
\(301\) | −996.657 | + | 575.420i | −0.190852 | + | 0.110188i | ||||
\(302\) | 363.543i | 0.0692700i | ||||||||
\(303\) | 142.618 | + | 247.022i | 0.0270403 | + | 0.0468352i | ||||
\(304\) | − | 152.380i | − | 0.0287487i | ||||||
\(305\) | −148.279 | + | 256.826i | −0.0278374 | + | 0.0482159i | ||||
\(306\) | 4484.43 | 0.837771 | ||||||||
\(307\) | −9149.98 | −1.70103 | −0.850517 | − | 0.525948i | \(-0.823711\pi\) | ||||
−0.850517 | + | 0.525948i | \(0.823711\pi\) | |||||||
\(308\) | −923.636 | + | 1599.78i | −0.170873 | + | 0.295962i | ||||
\(309\) | 682.665 | − | 394.137i | 0.125681 | − | 0.0725620i | ||||
\(310\) | − | 3354.61i | − | 0.614610i | ||||||
\(311\) | 4118.11 | + | 2377.59i | 0.750858 | + | 0.433508i | 0.826004 | − | 0.563665i | \(-0.190609\pi\) |
−0.0751460 | + | 0.997173i | \(0.523942\pi\) | |||||||
\(312\) | −258.519 | + | 447.768i | −0.0469095 | + | 0.0812496i | ||||
\(313\) | −4394.77 | − | 2537.32i | −0.793632 | − | 0.458204i | 0.0476074 | − | 0.998866i | \(-0.484840\pi\) |
−0.841240 | + | 0.540662i | \(0.818174\pi\) | |||||||
\(314\) | 6821.29 | − | 3938.28i | 1.22595 | − | 0.707802i | ||||
\(315\) | 249.699 | − | 144.164i | 0.0446632 | − | 0.0257863i | ||||
\(316\) | 6498.03 | + | 3751.64i | 1.15678 | + | 0.667867i | ||||
\(317\) | −4676.83 | + | 8100.50i | −0.828633 | + | 1.43523i | 0.0704775 | + | 0.997513i | \(0.477548\pi\) |
−0.899111 | + | 0.437721i | \(0.855786\pi\) | |||||||
\(318\) | −1493.82 | − | 862.457i | −0.263425 | − | 0.152089i | ||||
\(319\) | 5248.95i | 0.921269i | ||||||||
\(320\) | −1756.24 | + | 1013.96i | −0.306802 | + | 0.177132i | ||||
\(321\) | −272.111 | + | 471.310i | −0.0473139 | + | 0.0819500i | ||||
\(322\) | 1448.67 | 0.250719 | ||||||||
\(323\) | 783.606 | 0.134988 | ||||||||
\(324\) | 4228.25 | − | 7323.54i | 0.725008 | − | 1.25575i | ||||
\(325\) | − | 3667.13i | − | 0.625894i | ||||||
\(326\) | 2274.42 | + | 3939.42i | 0.386407 | + | 0.669277i | ||||
\(327\) | − | 1638.72i | − | 0.277130i | ||||||
\(328\) | −2760.20 | + | 1593.60i | −0.464655 | + | 0.268268i | ||||
\(329\) | 1068.74 | + | 1851.11i | 0.179093 | + | 0.310198i | ||||
\(330\) | −147.454 | − | 255.399i | −0.0245973 | − | 0.0426037i | ||||
\(331\) | −3016.17 | − | 1741.39i | −0.500858 | − | 0.289170i | 0.228210 | − | 0.973612i | \(-0.426713\pi\) |
−0.729068 | + | 0.684442i | \(0.760046\pi\) | |||||||
\(332\) | −13268.3 | −2.19335 | ||||||||
\(333\) | 5884.61 | − | 696.946i | 0.968392 | − | 0.114692i | ||||
\(334\) | 11327.5 | 1.85572 | ||||||||
\(335\) | 916.767 | + | 529.296i | 0.149517 | + | 0.0863239i | ||||
\(336\) | 13.4932 | + | 23.3710i | 0.00219082 | + | 0.00379461i | ||||
\(337\) | 2027.94 | + | 3512.50i | 0.327801 | + | 0.567768i | 0.982075 | − | 0.188489i | \(-0.0603591\pi\) |
−0.654274 | + | 0.756257i | \(0.727026\pi\) | |||||||
\(338\) | −4900.23 | + | 2829.15i | −0.788573 | + | 0.455283i | ||||
\(339\) | − | 552.847i | − | 0.0885739i | ||||||
\(340\) | −571.999 | − | 990.732i | −0.0912383 | − | 0.158029i | ||||
\(341\) | − | 9971.74i | − | 1.58358i | ||||||
\(342\) | 1243.20 | − | 2153.28i | 0.196563 | − | 0.340457i | ||||
\(343\) | −3000.61 | −0.472356 | ||||||||
\(344\) | 5235.02 | 0.820504 | ||||||||
\(345\) | −70.5672 | + | 122.226i | −0.0110122 | + | 0.0190737i | ||||
\(346\) | −4299.98 | + | 2482.60i | −0.668117 | + | 0.385737i | ||||
\(347\) | 9215.60i | 1.42570i | 0.701314 | + | 0.712852i | \(0.252597\pi\) | ||||
−0.701314 | + | 0.712852i | \(0.747403\pi\) | |||||||
\(348\) | −1425.22 | − | 822.852i | −0.219540 | − | 0.126751i | ||||
\(349\) | −2874.65 | + | 4979.05i | −0.440907 | + | 0.763674i | −0.997757 | − | 0.0669394i | \(-0.978677\pi\) |
0.556850 | + | 0.830613i | \(0.312010\pi\) | |||||||
\(350\) | 2106.34 | + | 1216.10i | 0.321682 | + | 0.185723i | ||||
\(351\) | 1164.59 | − | 672.376i | 0.177097 | − | 0.102247i | ||||
\(352\) | −5586.26 | + | 3225.23i | −0.845877 | + | 0.488367i | ||||
\(353\) | −752.631 | − | 434.532i | −0.113480 | − | 0.0655178i | 0.442186 | − | 0.896924i | \(-0.354203\pi\) |
−0.555666 | + | 0.831406i | \(0.687537\pi\) | |||||||
\(354\) | −561.368 | + | 972.318i | −0.0842835 | + | 0.145983i | ||||
\(355\) | 949.372 | + | 548.120i | 0.141936 | + | 0.0819471i | ||||
\(356\) | − | 6543.89i | − | 0.974229i | ||||||
\(357\) | −120.184 | + | 69.3882i | −0.0178174 | + | 0.0102869i | ||||
\(358\) | 3641.66 | − | 6307.53i | 0.537619 | − | 0.931183i | ||||
\(359\) | 2687.83 | 0.395148 | 0.197574 | − | 0.980288i | \(-0.436694\pi\) | ||||
0.197574 | + | 0.980288i | \(0.436694\pi\) | |||||||
\(360\) | −1311.56 | −0.192015 | ||||||||
\(361\) | −3212.26 | + | 5563.81i | −0.468328 | + | 0.811169i | ||||
\(362\) | − | 12844.0i | − | 1.86482i | ||||||
\(363\) | 106.692 | + | 184.796i | 0.0154267 | + | 0.0267198i | ||||
\(364\) | 1738.49i | 0.250334i | ||||||||
\(365\) | −2377.65 | + | 1372.74i | −0.340964 | + | 0.196856i | ||||
\(366\) | −226.455 | − | 392.231i | −0.0323415 | − | 0.0560171i | ||||
\(367\) | 5095.86 | + | 8826.30i | 0.724801 | + | 1.25539i | 0.959056 | + | 0.283217i | \(0.0914016\pi\) |
−0.234255 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(368\) | 449.112 | + | 259.295i | 0.0636185 | + | 0.0367301i | ||||
\(369\) | 4092.64 | 0.577383 | ||||||||
\(370\) | −1482.30 | − | 1984.72i | −0.208273 | − | 0.278867i | ||||
\(371\) | −2095.59 | −0.293255 | ||||||||
\(372\) | 2707.58 | + | 1563.22i | 0.377369 | + | 0.217874i | ||||
\(373\) | 665.867 | + | 1153.32i | 0.0924324 | + | 0.160098i | 0.908534 | − | 0.417811i | \(-0.137202\pi\) |
−0.816102 | + | 0.577908i | \(0.803869\pi\) | |||||||
\(374\) | −2786.24 | − | 4825.91i | −0.385222 | − | 0.667225i | ||||
\(375\) | −420.582 | + | 242.823i | −0.0579168 | + | 0.0334383i | ||||
\(376\) | − | 9723.11i | − | 1.33359i | ||||||
\(377\) | 2469.92 | + | 4278.03i | 0.337420 | + | 0.584429i | ||||
\(378\) | 891.896i | 0.121360i | ||||||||
\(379\) | 3319.35 | − | 5749.28i | 0.449878 | − | 0.779211i | −0.548500 | − | 0.836151i | \(-0.684801\pi\) |
0.998378 | + | 0.0569397i | \(0.0181343\pi\) | |||||||
\(380\) | −634.291 | −0.0856274 | ||||||||
\(381\) | 1935.75 | 0.260293 | ||||||||
\(382\) | −6720.67 | + | 11640.5i | −0.900156 | + | 1.55912i | ||||
\(383\) | 8034.08 | − | 4638.48i | 1.07186 | − | 0.618839i | 0.143171 | − | 0.989698i | \(-0.454270\pi\) |
0.928689 | + | 0.370859i | \(0.120937\pi\) | |||||||
\(384\) | − | 1805.42i | − | 0.239928i | ||||||
\(385\) | −310.283 | − | 179.142i | −0.0410739 | − | 0.0237141i | ||||
\(386\) | 5980.99 | − | 10359.4i | 0.788664 | − | 1.36601i | ||||
\(387\) | −5821.59 | − | 3361.10i | −0.764673 | − | 0.441484i | ||||
\(388\) | −4126.80 | + | 2382.61i | −0.539966 | + | 0.311749i | ||||
\(389\) | 6642.78 | − | 3835.21i | 0.865815 | − | 0.499879i | −0.000140214 | − | 1.00000i | \(-0.500045\pi\) |
0.865955 | + | 0.500121i | \(0.166711\pi\) | |||||||
\(390\) | −240.358 | − | 138.771i | −0.0312077 | − | 0.0180178i | ||||
\(391\) | −1333.41 | + | 2309.54i | −0.172464 | + | 0.298717i | ||||
\(392\) | 5729.96 | + | 3308.20i | 0.738283 | + | 0.426248i | ||||
\(393\) | 1641.70i | 0.210719i | ||||||||
\(394\) | 3051.46 | − | 1761.76i | 0.390179 | − | 0.225270i | ||||
\(395\) | −727.641 | + | 1260.31i | −0.0926875 | + | 0.160539i | ||||
\(396\) | −10790.1 | −1.36925 | ||||||||
\(397\) | −3487.56 | −0.440895 | −0.220448 | − | 0.975399i | \(-0.570752\pi\) | ||||
−0.220448 | + | 0.975399i | \(0.570752\pi\) | |||||||
\(398\) | −3434.84 | + | 5949.31i | −0.432595 | + | 0.749277i | ||||
\(399\) | 76.9446i | 0.00965426i | ||||||||
\(400\) | 435.333 | + | 754.020i | 0.0544167 | + | 0.0942525i | ||||
\(401\) | − | 4165.15i | − | 0.518698i | −0.965784 | − | 0.259349i | \(-0.916492\pi\) | ||
0.965784 | − | 0.259349i | \(-0.0835079\pi\) | |||||||
\(402\) | −1400.11 | + | 808.353i | −0.173709 | + | 0.100291i | ||||
\(403\) | −4692.25 | − | 8127.22i | −0.579995 | − | 1.00458i | ||||
\(404\) | −2181.36 | − | 3778.22i | −0.268630 | − | 0.465281i | ||||
\(405\) | 1420.42 | + | 820.081i | 0.174275 | + | 0.100618i | ||||
\(406\) | −3276.31 | −0.400494 | ||||||||
\(407\) | −4406.21 | − | 5899.69i | −0.536628 | − | 0.718518i | ||||
\(408\) | 631.275 | 0.0765999 | ||||||||
\(409\) | −8004.21 | − | 4621.23i | −0.967684 | − | 0.558693i | −0.0691546 | − | 0.997606i | \(-0.522030\pi\) |
−0.898529 | + | 0.438913i | \(0.855364\pi\) | |||||||
\(410\) | −855.433 | − | 1481.65i | −0.103041 | − | 0.178472i | ||||
\(411\) | −410.670 | − | 711.302i | −0.0492868 | − | 0.0853672i | ||||
\(412\) | −10441.4 | + | 6028.35i | −1.24857 | + | 0.720863i | ||||
\(413\) | 1364.01i | 0.162514i | ||||||||
\(414\) | 4230.94 | + | 7328.20i | 0.502269 | + | 0.869955i | ||||
\(415\) | − | 2573.42i | − | 0.304396i | ||||||
\(416\) | −3035.29 | + | 5257.28i | −0.357735 | + | 0.619614i | ||||
\(417\) | 442.269 | 0.0519376 | ||||||||
\(418\) | −3089.67 | −0.361532 | ||||||||
\(419\) | 4223.99 | − | 7316.17i | 0.492495 | − | 0.853026i | −0.507468 | − | 0.861671i | \(-0.669418\pi\) |
0.999963 | + | 0.00864443i | \(0.00275164\pi\) | |||||||
\(420\) | 97.2829 | − | 56.1663i | 0.0113022 | − | 0.00652532i | ||||
\(421\) | − | 8887.45i | − | 1.02885i | −0.857534 | − | 0.514427i | \(-0.828005\pi\) | ||
0.857534 | − | 0.514427i | \(-0.171995\pi\) | |||||||
\(422\) | 1249.98 | + | 721.678i | 0.144190 | + | 0.0832482i | ||||
\(423\) | −6242.64 | + | 10812.6i | −0.717559 | + | 1.24285i | ||||
\(424\) | 8255.44 | + | 4766.28i | 0.945565 | + | 0.545922i | ||||
\(425\) | −3877.51 | + | 2238.68i | −0.442557 | + | 0.255510i | ||||
\(426\) | −1449.90 | + | 837.102i | −0.164901 | + | 0.0952059i | ||||
\(427\) | −476.520 | − | 275.119i | −0.0540057 | − | 0.0311802i | ||||
\(428\) | 4161.96 | − | 7208.72i | 0.470037 | − | 0.814128i | ||||
\(429\) | −714.476 | − | 412.503i | −0.0804085 | − | 0.0464238i | ||||
\(430\) | 2810.11i | 0.315153i | ||||||||
\(431\) | −6166.79 | + | 3560.40i | −0.689197 | + | 0.397908i | −0.803311 | − | 0.595560i | \(-0.796930\pi\) |
0.114114 | + | 0.993468i | \(0.463597\pi\) | |||||||
\(432\) | −159.639 | + | 276.502i | −0.0177792 | + | 0.0307945i | ||||
\(433\) | 12492.4 | 1.38649 | 0.693243 | − | 0.720704i | \(-0.256181\pi\) | ||||
0.693243 | + | 0.720704i | \(0.256181\pi\) | |||||||
\(434\) | 6224.20 | 0.688413 | ||||||||
\(435\) | 159.595 | − | 276.426i | 0.0175907 | − | 0.0304681i | ||||
\(436\) | 25064.4i | 2.75313i | ||||||||
\(437\) | 739.310 | + | 1280.52i | 0.0809291 | + | 0.140173i | ||||
\(438\) | − | 4192.95i | − | 0.457413i | ||||||
\(439\) | 4814.96 | − | 2779.92i | 0.523474 | − | 0.302228i | −0.214881 | − | 0.976640i | \(-0.568936\pi\) |
0.738355 | + | 0.674412i | \(0.235603\pi\) | |||||||
\(440\) | 814.892 | + | 1411.43i | 0.0882919 | + | 0.152926i | ||||
\(441\) | −4248.00 | − | 7357.75i | −0.458697 | − | 0.794487i | ||||
\(442\) | −4541.71 | − | 2622.16i | −0.488750 | − | 0.282180i | ||||
\(443\) | −2073.34 | −0.222364 | −0.111182 | − | 0.993800i | \(-0.535464\pi\) | ||||
−0.111182 | + | 0.993800i | \(0.535464\pi\) | |||||||
\(444\) | 2292.65 | − | 271.531i | 0.245055 | − | 0.0290232i | ||||
\(445\) | 1269.21 | 0.135205 | ||||||||
\(446\) | 18647.9 | + | 10766.4i | 1.97983 | + | 1.14306i | ||||
\(447\) | 980.895 | + | 1698.96i | 0.103791 | + | 0.179772i | ||||
\(448\) | −1881.32 | − | 3258.55i | −0.198402 | − | 0.343643i | ||||
\(449\) | 14764.2 | − | 8524.10i | 1.55181 | − | 0.895940i | 0.553819 | − | 0.832637i | \(-0.313170\pi\) |
0.997994 | − | 0.0633028i | \(-0.0201634\pi\) | |||||||
\(450\) | 14206.7i | 1.48825i | ||||||||
\(451\) | −2542.81 | − | 4404.28i | −0.265491 | − | 0.459844i | ||||
\(452\) | 8455.84i | 0.879932i | ||||||||
\(453\) | 32.8571 | − | 56.9102i | 0.00340787 | − | 0.00590260i | ||||
\(454\) | 21261.1 | 2.19787 | ||||||||
\(455\) | −337.184 | −0.0347416 | ||||||||
\(456\) | 175.005 | − | 303.118i | 0.0179723 | − | 0.0311290i | ||||
\(457\) | 11907.0 | − | 6874.52i | 1.21879 | − | 0.703669i | 0.254131 | − | 0.967170i | \(-0.418211\pi\) |
0.964659 | + | 0.263501i | \(0.0848774\pi\) | |||||||
\(458\) | 18464.4i | 1.88381i | ||||||||
\(459\) | −1421.90 | − | 820.934i | −0.144594 | − | 0.0834813i | ||||
\(460\) | 1079.33 | − | 1869.46i | 0.109400 | − | 0.189487i | ||||
\(461\) | 3371.76 | + | 1946.69i | 0.340647 | + | 0.196673i | 0.660558 | − | 0.750775i | \(-0.270320\pi\) |
−0.319911 | + | 0.947448i | \(0.603653\pi\) | |||||||
\(462\) | 473.871 | − | 273.589i | 0.0477196 | − | 0.0275509i | ||||
\(463\) | 2810.76 | − | 1622.79i | 0.282132 | − | 0.162889i | −0.352256 | − | 0.935904i | \(-0.614585\pi\) |
0.634388 | + | 0.773015i | \(0.281252\pi\) | |||||||
\(464\) | −1015.71 | − | 586.421i | −0.101623 | − | 0.0586722i | ||||
\(465\) | −303.191 | + | 525.142i | −0.0302369 | + | 0.0523718i | ||||
\(466\) | 6892.61 | + | 3979.45i | 0.685181 | + | 0.395589i | ||||
\(467\) | − | 8371.13i | − | 0.829485i | −0.909939 | − | 0.414743i | \(-0.863872\pi\) | ||
0.909939 | − | 0.414743i | \(-0.136128\pi\) | |||||||
\(468\) | −8794.23 | + | 5077.35i | −0.868619 | + | 0.501497i | ||||
\(469\) | −982.065 | + | 1700.99i | −0.0966898 | + | 0.167472i | ||||
\(470\) | 5219.28 | 0.512229 | ||||||||
\(471\) | −1423.77 | −0.139286 | ||||||||
\(472\) | 3102.34 | − | 5373.42i | 0.302536 | − | 0.524007i | ||||
\(473\) | 8353.20i | 0.812009i | ||||||||
\(474\) | −1111.27 | − | 1924.78i | −0.107684 | − | 0.186514i | ||||
\(475\) | 2482.47i | 0.239797i | ||||||||
\(476\) | 1838.22 | − | 1061.30i | 0.177006 | − | 0.102194i | ||||
\(477\) | −6120.30 | − | 10600.7i | −0.587483 | − | 1.01755i | ||||
\(478\) | −11958.0 | − | 20711.9i | −1.14424 | − | 1.98188i | ||||
\(479\) | 6955.07 | + | 4015.51i | 0.663434 | + | 0.383034i | 0.793584 | − | 0.608460i | \(-0.208213\pi\) |
−0.130150 | + | 0.991494i | \(0.541546\pi\) | |||||||
\(480\) | 392.253 | 0.0372996 | ||||||||
\(481\) | −6367.30 | − | 2735.03i | −0.603584 | − | 0.259265i | ||||
\(482\) | −31746.9 | −3.00007 | ||||||||
\(483\) | −226.780 | − | 130.932i | −0.0213641 | − | 0.0123346i | ||||
\(484\) | −1631.86 | − | 2826.47i | −0.153255 | − | 0.265446i | ||||
\(485\) | −462.114 | − | 800.405i | −0.0432650 | − | 0.0749372i | ||||
\(486\) | −6795.93 | + | 3923.63i | −0.634300 | + | 0.366213i | ||||
\(487\) | 11296.1i | 1.05108i | 0.850768 | + | 0.525541i | \(0.176137\pi\) | ||||
−0.850768 | + | 0.525541i | \(0.823863\pi\) | |||||||
\(488\) | 1251.48 | + | 2167.63i | 0.116090 | + | 0.201073i | ||||
\(489\) | − | 822.254i | − | 0.0760401i | ||||||
\(490\) | −1775.81 | + | 3075.79i | −0.163720 | + | 0.283572i | ||||
\(491\) | −19843.0 | −1.82383 | −0.911915 | − | 0.410380i | \(-0.865396\pi\) | ||||
−0.911915 | + | 0.410380i | \(0.865396\pi\) | |||||||
\(492\) | 1594.50 | 0.146109 | ||||||||
\(493\) | 3015.64 | − | 5223.24i | 0.275492 | − | 0.477166i | ||||
\(494\) | −2518.16 | + | 1453.86i | −0.229347 | + | 0.132413i | ||||
\(495\) | − | 2092.78i | − | 0.190027i | ||||||
\(496\) | 1929.60 | + | 1114.06i | 0.174681 | + | 0.100852i | ||||
\(497\) | −1016.99 | + | 1761.48i | −0.0917873 | + | 0.158980i | ||||
\(498\) | 3403.64 | + | 1965.09i | 0.306267 | + | 0.176823i | ||||
\(499\) | −10579.1 | + | 6107.84i | −0.949068 | + | 0.547944i | −0.892791 | − | 0.450471i | \(-0.851256\pi\) |
−0.0562764 | + | 0.998415i | \(0.517923\pi\) | |||||||
\(500\) | 6432.84 | − | 3714.00i | 0.575371 | − | 0.332190i | ||||
\(501\) | −1773.24 | − | 1023.78i | −0.158129 | − | 0.0912957i | ||||
\(502\) | 13667.7 | − | 23673.1i | 1.21518 | − | 2.10475i | ||||
\(503\) | 1219.71 | + | 704.201i | 0.108120 | + | 0.0624230i | 0.553085 | − | 0.833125i | \(-0.313451\pi\) |
−0.444965 | + | 0.895548i | \(0.646784\pi\) | |||||||
\(504\) | − | 2433.49i | − | 0.215072i | ||||||
\(505\) | 732.797 | − | 423.081i | 0.0645724 | − | 0.0372809i | ||||
\(506\) | 5257.48 | − | 9106.23i | 0.461904 | − | 0.800042i | ||||
\(507\) | 1022.80 | 0.0895939 | ||||||||
\(508\) | −29607.5 | −2.58587 | ||||||||
\(509\) | −4625.31 | + | 8011.28i | −0.402777 | + | 0.697630i | −0.994060 | − | 0.108834i | \(-0.965288\pi\) |
0.591283 | + | 0.806464i | \(0.298622\pi\) | |||||||
\(510\) | 338.863i | 0.0294218i | ||||||||
\(511\) | −2547.00 | − | 4411.53i | −0.220494 | − | 0.381907i | ||||
\(512\) | − | 2640.49i | − | 0.227918i | ||||||
\(513\) | −788.372 | + | 455.167i | −0.0678509 | + | 0.0391737i | ||||
\(514\) | −11382.3 | − | 19714.8i | −0.976756 | − | 1.69179i | ||||
\(515\) | −1169.22 | − | 2025.14i | −0.100042 | − | 0.173278i | ||||
\(516\) | −2268.10 | − | 1309.49i | −0.193503 | − | 0.111719i | ||||
\(517\) | 15514.6 | 1.31979 | ||||||||
\(518\) | 3682.49 | − | 2750.29i | 0.312354 | − | 0.233283i | ||||
\(519\) | 897.512 | 0.0759083 | ||||||||
\(520\) | 1328.31 | + | 766.903i | 0.112020 | + | 0.0646748i | ||||
\(521\) | 9179.92 | + | 15900.1i | 0.771938 | + | 1.33704i | 0.936499 | + | 0.350669i | \(0.114046\pi\) |
−0.164561 | + | 0.986367i | \(0.552621\pi\) | |||||||
\(522\) | −9568.67 | − | 16573.4i | −0.802317 | − | 1.38965i | ||||
\(523\) | 11992.0 | − | 6923.57i | 1.00262 | − | 0.578866i | 0.0936009 | − | 0.995610i | \(-0.470162\pi\) |
0.909024 | + | 0.416744i | \(0.136829\pi\) | |||||||
\(524\) | − | 25109.9i | − | 2.09338i | ||||||
\(525\) | −219.823 | − | 380.744i | −0.0182740 | − | 0.0316515i | ||||
\(526\) | 27071.3i | 2.24404i | ||||||||
\(527\) | −5728.98 | + | 9922.89i | −0.473545 | + | 0.820205i | ||||
\(528\) | 195.877 | 0.0161448 | ||||||||
\(529\) | 7134.86 | 0.586410 | ||||||||
\(530\) | −2558.50 | + | 4431.45i | −0.209687 | + | 0.363188i | ||||
\(531\) | −6899.91 | + | 3983.66i | −0.563899 | + | 0.325567i | ||||
\(532\) | − | 1176.87i | − | 0.0959097i | ||||||
\(533\) | −4144.92 | − | 2393.07i | −0.336841 | − | 0.194475i | ||||
\(534\) | −969.181 | + | 1678.67i | −0.0785404 | + | 0.136036i | ||||
\(535\) | 1398.15 | + | 807.223i | 0.112986 | + | 0.0652324i | ||||
\(536\) | 7737.56 | − | 4467.28i | 0.623529 | − | 0.359995i | ||||
\(537\) | −1140.15 | + | 658.269i | −0.0916225 | + | 0.0528983i | ||||
\(538\) | −16862.9 | − | 9735.79i | −1.35132 | − | 0.780185i | ||||
\(539\) | −5278.68 | + | 9142.95i | −0.421835 | + | 0.730639i | ||||
\(540\) | 1150.96 | + | 664.505i | 0.0917209 | + | 0.0529551i | ||||
\(541\) | 9654.91i | 0.767277i | 0.923483 | + | 0.383638i | \(0.125329\pi\) | ||||
−0.923483 | + | 0.383638i | \(0.874671\pi\) | |||||||
\(542\) | 13967.7 | − | 8064.23i | 1.10694 | − | 0.639093i | ||||
\(543\) | −1160.84 | + | 2010.64i | −0.0917433 | + | 0.158904i | ||||
\(544\) | 7411.85 | 0.584155 | ||||||||
\(545\) | −4861.30 | −0.382083 | ||||||||
\(546\) | 257.478 | − | 445.965i | 0.0201814 | − | 0.0349552i | ||||
\(547\) | 17556.9i | 1.37235i | 0.727434 | + | 0.686177i | \(0.240713\pi\) | ||||
−0.727434 | + | 0.686177i | \(0.759287\pi\) | |||||||
\(548\) | 6281.23 | + | 10879.4i | 0.489637 | + | 0.848075i | ||||
\(549\) | − | 3214.01i | − | 0.249855i | ||||||
\(550\) | 15288.5 | − | 8826.85i | 1.18528 | − | 0.684324i | ||||
\(551\) | −1672.02 | − | 2896.03i | −0.129275 | − | 0.223911i | ||||
\(552\) | 595.590 | + | 1031.59i | 0.0459239 | + | 0.0795426i | ||||
\(553\) | −2338.40 | − | 1350.08i | −0.179817 | − | 0.103818i | ||||
\(554\) | 9936.35 | 0.762012 | ||||||||
\(555\) | 52.6643 | + | 444.666i | 0.00402788 | + | 0.0340091i | ||||
\(556\) | −6764.53 | −0.515971 | ||||||||
\(557\) | 11741.2 | + | 6778.76i | 0.893157 | + | 0.515665i | 0.874974 | − | 0.484170i | \(-0.160878\pi\) |
0.0181834 | + | 0.999835i | \(0.494212\pi\) | |||||||
\(558\) | 18178.2 | + | 31485.5i | 1.37911 | + | 2.38869i | ||||
\(559\) | 3930.64 | + | 6808.06i | 0.297403 | + | 0.515117i | ||||
\(560\) | 69.3305 | − | 40.0280i | 0.00523169 | − | 0.00302052i | ||||
\(561\) | 1007.29i | 0.0758069i | ||||||||
\(562\) | −10743.7 | − | 18608.6i | −0.806397 | − | 1.39672i | ||||
\(563\) | − | 10182.3i | − | 0.762225i | −0.924529 | − | 0.381112i | \(-0.875541\pi\) | ||
0.924529 | − | 0.381112i | \(-0.124459\pi\) | |||||||
\(564\) | −2432.14 | + | 4212.59i | −0.181581 | + | 0.314507i | ||||
\(565\) | −1640.03 | −0.122118 | ||||||||
\(566\) | −5093.39 | −0.378253 | ||||||||
\(567\) | −1521.59 | + | 2635.47i | −0.112700 | + | 0.195202i | ||||
\(568\) | 8012.74 | − | 4626.16i | 0.591914 | − | 0.341742i | ||||
\(569\) | 11455.6i | 0.844014i | 0.906593 | + | 0.422007i | \(0.138674\pi\) | ||||
−0.906593 | + | 0.422007i | \(0.861326\pi\) | |||||||
\(570\) | 162.711 | + | 93.9414i | 0.0119565 | + | 0.00690311i | ||||
\(571\) | 1507.70 | − | 2611.41i | 0.110500 | − | 0.191391i | −0.805472 | − | 0.592634i | \(-0.798088\pi\) |
0.915972 | + | 0.401243i | \(0.131422\pi\) | |||||||
\(572\) | 10928.0 | + | 6309.26i | 0.798813 | + | 0.461195i | ||||
\(573\) | 2104.15 | − | 1214.83i | 0.153407 | − | 0.0885697i | ||||
\(574\) | 2749.08 | − | 1587.18i | 0.199903 | − | 0.115414i | ||||
\(575\) | −7316.64 | − | 4224.26i | −0.530652 | − | 0.306372i | ||||
\(576\) | 10989.0 | − | 19033.6i | 0.794925 | − | 1.37685i | ||||
\(577\) | 4272.25 | + | 2466.58i | 0.308243 | + | 0.177964i | 0.646140 | − | 0.763219i | \(-0.276382\pi\) |
−0.337897 | + | 0.941183i | \(0.609716\pi\) | |||||||
\(578\) | − | 15855.5i | − | 1.14101i | ||||||
\(579\) | −1872.57 | + | 1081.13i | −0.134406 | + | 0.0775996i | ||||
\(580\) | −2441.01 | + | 4227.95i | −0.174754 | + | 0.302683i | ||||
\(581\) | 4774.77 | 0.340948 | ||||||||
\(582\) | 1411.50 | 0.100530 | ||||||||
\(583\) | −7605.26 | + | 13172.7i | −0.540271 | + | 0.935776i | ||||
\(584\) | 23171.9i | 1.64188i | ||||||||
\(585\) | −984.767 | − | 1705.67i | −0.0695985 | − | 0.120548i | ||||
\(586\) | 41469.7i | 2.92338i | ||||||||
\(587\) | 16139.6 | − | 9318.21i | 1.13484 | − | 0.655202i | 0.189695 | − | 0.981843i | \(-0.439250\pi\) |
0.945148 | + | 0.326641i | \(0.105917\pi\) | |||||||
\(588\) | −1655.03 | − | 2866.59i | −0.116075 | − | 0.201048i | ||||
\(589\) | 3176.44 | + | 5501.75i | 0.222212 | + | 0.384882i | ||||
\(590\) | 2884.40 | + | 1665.31i | 0.201269 | + | 0.116203i | ||||
\(591\) | −636.915 | −0.0443303 | ||||||||
\(592\) | 1633.90 | − | 193.512i | 0.113434 | − | 0.0134346i | ||||
\(593\) | −8993.28 | −0.622782 | −0.311391 | − | 0.950282i | \(-0.600795\pi\) | ||||
−0.311391 | + | 0.950282i | \(0.600795\pi\) | |||||||
\(594\) | 5606.38 | + | 3236.84i | 0.387260 | + | 0.223585i | ||||
\(595\) | 205.842 | + | 356.528i | 0.0141827 | + | 0.0245651i | ||||
\(596\) | −15002.9 | − | 25985.7i | −1.03111 | − | 1.78593i | ||||
\(597\) | 1075.40 | − | 620.884i | 0.0737241 | − | 0.0425646i | ||||
\(598\) | − | 9895.74i | − | 0.676700i | ||||||
\(599\) | 1089.49 | + | 1887.06i | 0.0743163 | + | 0.128720i | 0.900789 | − | 0.434258i | \(-0.142989\pi\) |
−0.826472 | + | 0.562977i | \(0.809656\pi\) | |||||||
\(600\) | 1999.89i | 0.136075i | ||||||||
\(601\) | 4244.80 | − | 7352.21i | 0.288102 | − | 0.499007i | −0.685255 | − | 0.728303i | \(-0.740309\pi\) |
0.973357 | + | 0.229297i | \(0.0736426\pi\) | |||||||
\(602\) | −5213.93 | −0.352997 | ||||||||
\(603\) | −11472.7 | −0.774801 | ||||||||
\(604\) | −502.552 | + | 870.446i | −0.0338552 | + | 0.0586390i | ||||
\(605\) | 548.202 | − | 316.504i | 0.0368390 | − | 0.0212690i | ||||
\(606\) | 1292.28i | 0.0866257i | ||||||||
\(607\) | −16530.0 | − | 9543.61i | −1.10533 | − | 0.638160i | −0.167711 | − | 0.985836i | \(-0.553638\pi\) |
−0.937615 | + | 0.347676i | \(0.886971\pi\) | |||||||
\(608\) | 2054.75 | − | 3558.94i | 0.137058 | − | 0.237391i | ||||
\(609\) | 512.885 | + | 296.114i | 0.0341267 | + | 0.0197031i | ||||
\(610\) | −1163.56 | + | 671.784i | −0.0772316 | + | 0.0445897i | ||||
\(611\) | 12644.8 | − | 7300.46i | 0.837238 | − | 0.483380i | ||||
\(612\) | 10737.3 | + | 6199.17i | 0.709197 | + | 0.409455i | ||||
\(613\) | −832.947 | + | 1442.71i | −0.0548816 | + | 0.0950577i | −0.892161 | − | 0.451718i | \(-0.850811\pi\) |
0.837279 | + | 0.546775i | \(0.184145\pi\) | |||||||
\(614\) | −35900.6 | − | 20727.2i | −2.35966 | − | 1.36235i | ||||
\(615\) | 309.257i | 0.0202772i | ||||||||
\(616\) | −2618.80 | + | 1511.96i | −0.171290 | + | 0.0988941i | ||||
\(617\) | −9714.51 | + | 16826.0i | −0.633860 | + | 1.09788i | 0.352896 | + | 0.935663i | \(0.385197\pi\) |
−0.986756 | + | 0.162214i | \(0.948136\pi\) | |||||||
\(618\) | 3571.31 | 0.232458 | ||||||||
\(619\) | −22808.6 | −1.48103 | −0.740513 | − | 0.672042i | \(-0.765417\pi\) | ||||
−0.740513 | + | 0.672042i | \(0.765417\pi\) | |||||||
\(620\) | 4637.33 | − | 8032.09i | 0.300387 | − | 0.520285i | ||||
\(621\) | − | 3098.11i | − | 0.200198i | ||||||
\(622\) | 10771.8 | + | 18657.3i | 0.694388 | + | 1.20272i | ||||
\(623\) | 2354.91i | 0.151440i | ||||||||
\(624\) | 159.645 | − | 92.1709i | 0.0102418 | − | 0.00591312i | ||||
\(625\) | −6723.28 | − | 11645.1i | −0.430290 | − | 0.745284i | ||||
\(626\) | −11495.4 | − | 19910.7i | −0.733946 | − | 1.27123i | ||||
\(627\) | 483.667 | + | 279.245i | 0.0308067 | + | 0.0177863i | ||||
\(628\) | 21776.7 | 1.38373 | ||||||||
\(629\) | 995.124 | + | 8402.25i | 0.0630814 | + | 0.532622i | ||||
\(630\) | 1306.28 | 0.0826085 | ||||||||
\(631\) | −660.581 | − | 381.387i | −0.0416756 | − | 0.0240614i | 0.479017 | − | 0.877805i | \(-0.340993\pi\) |
−0.520693 | + | 0.853744i | \(0.674326\pi\) | |||||||
\(632\) | 6141.32 | + | 10637.1i | 0.386532 | + | 0.669494i | ||||
\(633\) | −130.451 | − | 225.948i | −0.00819110 | − | 0.0141874i | ||||
\(634\) | −36699.7 | + | 21188.6i | −2.29894 | + | 1.32730i | ||||
\(635\) | − | 5742.46i | − | 0.358870i | ||||||
\(636\) | −2384.48 | − | 4130.04i | −0.148665 | − | 0.257495i | ||||
\(637\) | 9935.64i | 0.617998i | ||||||||
\(638\) | −11890.3 | + | 20594.6i | −0.737839 | + | 1.27798i | ||||
\(639\) | −11880.7 | −0.735516 | ||||||||
\(640\) | −5355.82 | −0.330793 | ||||||||
\(641\) | 15355.5 | − | 26596.6i | 0.946189 | − | 1.63885i | 0.192837 | − | 0.981231i | \(-0.438231\pi\) |
0.753352 | − | 0.657617i | \(-0.228436\pi\) | |||||||
\(642\) | −2135.29 | + | 1232.81i | −0.131267 | + | 0.0757868i | ||||
\(643\) | − | 6558.80i | − | 0.402261i | −0.979564 | − | 0.201130i | \(-0.935538\pi\) | ||
0.979564 | − | 0.201130i | \(-0.0644615\pi\) | |||||||
\(644\) | 3468.62 | + | 2002.61i | 0.212240 | + | 0.122537i | ||||
\(645\) | 253.979 | − | 439.905i | 0.0155045 | − | 0.0268546i | ||||
\(646\) | 3074.53 | + | 1775.08i | 0.187253 | + | 0.108111i | ||||
\(647\) | 25070.7 | − | 14474.6i | 1.52338 | − | 0.879526i | 0.523767 | − | 0.851862i | \(-0.324526\pi\) |
0.999617 | − | 0.0276646i | \(-0.00880705\pi\) | |||||||
\(648\) | 11988.4 | − | 6921.52i | 0.726774 | − | 0.419603i | ||||
\(649\) | 8574.03 | + | 4950.22i | 0.518582 | + | 0.299404i | ||||
\(650\) | 8307.03 | − | 14388.2i | 0.501275 | − | 0.868233i | ||||
\(651\) | −974.358 | − | 562.546i | −0.0586607 | − | 0.0338678i | ||||
\(652\) | 12576.4i | 0.755416i | ||||||||
\(653\) | −5129.32 | + | 2961.42i | −0.307390 | + | 0.177472i | −0.645758 | − | 0.763542i | \(-0.723459\pi\) |
0.338368 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(654\) | 3712.15 | − | 6429.63i | 0.221952 | − | 0.384432i | ||||
\(655\) | 4870.13 | 0.290522 | ||||||||
\(656\) | 1136.35 | 0.0676325 | ||||||||
\(657\) | 14877.3 | − | 25768.3i | 0.883440 | − | 1.53016i | ||||
\(658\) | 9683.95i | 0.573738i | ||||||||
\(659\) | 1716.93 | + | 2973.81i | 0.101490 | + | 0.175786i | 0.912299 | − | 0.409525i | \(-0.134306\pi\) |
−0.810809 | + | 0.585311i | \(0.800972\pi\) | |||||||
\(660\) | − | 815.349i | − | 0.0480870i | ||||||
\(661\) | 13213.8 | − | 7629.01i | 0.777547 | − | 0.448917i | −0.0580135 | − | 0.998316i | \(-0.518477\pi\) |
0.835560 | + | 0.549399i | \(0.185143\pi\) | |||||||
\(662\) | −7889.43 | − | 13664.9i | −0.463190 | − | 0.802268i | ||||
\(663\) | 473.984 | + | 820.964i | 0.0277647 | + | 0.0480899i | ||||
\(664\) | −18809.9 | − | 10859.9i | −1.09934 | − | 0.634707i | ||||
\(665\) | 228.258 | 0.0133105 | ||||||||
\(666\) | 24667.4 | + | 10595.7i | 1.43520 | + | 0.616480i | ||||
\(667\) | 11380.7 | 0.660662 | ||||||||
\(668\) | 27121.8 | + | 15658.8i | 1.57092 | + | 0.906972i | ||||
\(669\) | −1946.14 | − | 3370.82i | −0.112470 | − | 0.194803i | ||||
\(670\) | 2398.00 | + | 4153.45i | 0.138273 | + | 0.239495i | ||||
\(671\) | −3458.75 | + | 1996.91i | −0.198992 | + | 0.114888i | ||||
\(672\) | 727.792i | 0.0417785i | ||||||||
\(673\) | −5700.33 | − | 9873.26i | −0.326495 | − | 0.565507i | 0.655318 | − | 0.755353i | \(-0.272534\pi\) |
−0.981814 | + | 0.189846i | \(0.939201\pi\) | |||||||
\(674\) | 18375.3i | 1.05014i | ||||||||
\(675\) | 2600.73 | − | 4504.59i | 0.148299 | − | 0.256862i | ||||
\(676\) | −15643.8 | −0.890065 | ||||||||
\(677\) | −29393.7 | −1.66867 | −0.834337 | − | 0.551255i | \(-0.814149\pi\) | ||||
−0.834337 | + | 0.551255i | \(0.814149\pi\) | |||||||
\(678\) | 1252.35 | − | 2169.13i | 0.0709383 | − | 0.122869i | ||||
\(679\) | 1485.09 | − | 857.414i | 0.0839357 | − | 0.0484603i | ||||
\(680\) | − | 1872.69i | − | 0.105610i | ||||||
\(681\) | −3328.29 | − | 1921.59i | −0.187284 | − | 0.108128i | ||||
\(682\) | 22588.7 | − | 39124.8i | 1.26828 | − | 2.19672i | ||||
\(683\) | 994.066 | + | 573.924i | 0.0556909 | + | 0.0321531i | 0.527587 | − | 0.849501i | \(-0.323097\pi\) |
−0.471896 | + | 0.881654i | \(0.656430\pi\) | |||||||
\(684\) | 5953.28 | − | 3437.13i | 0.332792 | − | 0.192137i | ||||
\(685\) | −2110.09 | + | 1218.26i | −0.117697 | + | 0.0679524i | ||||
\(686\) | −11773.1 | − | 6797.21i | −0.655247 | − | 0.378307i | ||||
\(687\) | 1668.82 | − | 2890.48i | 0.0926775 | − | 0.160522i | ||||
\(688\) | −1616.40 | − | 933.231i | −0.0895710 | − | 0.0517138i | ||||
\(689\) | 14314.8i | 0.791509i | ||||||||
\(690\) | −553.750 | + | 319.708i | −0.0305520 | + | 0.0176392i | ||||
\(691\) | −14632.7 | + | 25344.6i | −0.805578 | + | 1.39530i | 0.110322 | + | 0.993896i | \(0.464812\pi\) |
−0.915900 | + | 0.401406i | \(0.868521\pi\) | |||||||
\(692\) | −13727.5 | −0.754106 | ||||||||
\(693\) | 3882.98 | 0.212846 | ||||||||
\(694\) | −20875.8 | + | 36158.0i | −1.14184 | + | 1.97772i | ||||
\(695\) | − | 1312.00i | − | 0.0716072i | ||||||
\(696\) | −1346.98 | − | 2333.05i | −0.0733582 | − | 0.127060i | ||||
\(697\) | 5843.61i | 0.317564i | ||||||||
\(698\) | −22557.8 | + | 13023.7i | −1.22324 | + | 0.706240i | ||||
\(699\) | −719.329 | − | 1245.91i | −0.0389235 | − | 0.0674174i | ||||
\(700\) | 3362.20 | + | 5823.50i | 0.181542 | + | 0.314440i | ||||
\(701\) | −9142.22 | − | 5278.26i | −0.492577 | − | 0.284390i | 0.233066 | − | 0.972461i | \(-0.425124\pi\) |
−0.725643 | + | 0.688071i | \(0.758458\pi\) | |||||||
\(702\) | 6092.45 | 0.327557 | ||||||||
\(703\) | 4310.36 | + | 1851.49i | 0.231250 | + | 0.0993317i | ||||
\(704\) | −27310.6 | −1.46208 | ||||||||
\(705\) | −817.044 | − | 471.721i | −0.0436478 | − | 0.0252000i | ||||
\(706\) | −1968.66 | − | 3409.83i | −0.104946 | − | 0.181771i | ||||
\(707\) | 784.991 | + | 1359.64i | 0.0417576 | + | 0.0723263i | ||||
\(708\) | −2688.21 | + | 1552.04i | −0.142697 | + | 0.0823860i | ||||
\(709\) | − | 29373.6i | − | 1.55592i | −0.628312 | − | 0.777961i | \(-0.716254\pi\) | ||
0.628312 | − | 0.777961i | \(-0.283746\pi\) | |||||||
\(710\) | 2483.28 | + | 4301.17i | 0.131262 | + | 0.227352i | ||||
\(711\) | − | 15771.9i | − | 0.831917i | ||||||
\(712\) | 5356.08 | − | 9277.00i | 0.281921 | − | 0.488301i | ||||
\(713\) | −21620.5 | −1.13562 | ||||||||
\(714\) | −628.732 | −0.0329548 | ||||||||
\(715\) | −1223.70 | + | 2119.51i | −0.0640053 | + | 0.110860i | ||||
\(716\) | 17438.7 | − | 10068.3i | 0.910219 | − | 0.525515i | ||||
\(717\) | 4323.08i | 0.225172i | ||||||||
\(718\) | 10545.9 | + | 6088.66i | 0.548145 | + | 0.316472i | ||||
\(719\) | 632.900 | − | 1096.21i | 0.0328278 | − | 0.0568594i | −0.849145 | − | 0.528160i | \(-0.822882\pi\) |
0.881973 | + | 0.471301i | \(0.156215\pi\) | |||||||
\(720\) | 404.968 | + | 233.808i | 0.0209615 | + | 0.0121021i | ||||
\(721\) | 3757.48 | − | 2169.38i | 0.194086 | − | 0.112056i | ||||
\(722\) | −25207.1 | + | 14553.3i | −1.29932 | + | 0.750163i | ||||
\(723\) | 4969.77 | + | 2869.30i | 0.255640 | + | 0.147594i | ||||
\(724\) | 17755.2 | − | 30752.9i | 0.911418 | − | 1.57862i | ||||
\(725\) | 16547.3 | + | 9553.57i | 0.847655 | + | 0.489394i | ||||
\(726\) | 966.746i | 0.0494205i | ||||||||
\(727\) | 8076.84 | − | 4663.16i | 0.412040 | − | 0.237892i | −0.279626 | − | 0.960109i | \(-0.590210\pi\) |
0.691666 | + | 0.722218i | \(0.256877\pi\) | |||||||
\(728\) | −1422.92 | + | 2464.58i | −0.0724411 | + | 0.125472i | ||||
\(729\) | −16809.9 | −0.854032 | ||||||||
\(730\) | −12438.5 | −0.630642 | ||||||||
\(731\) | 4799.09 | − | 8312.27i | 0.242819 | − | 0.420575i | ||||
\(732\) | − | 1252.18i | − | 0.0632267i | ||||||
\(733\) | −5559.22 | − | 9628.86i | −0.280129 | − | 0.485198i | 0.691287 | − | 0.722580i | \(-0.257044\pi\) |
−0.971416 | + | 0.237382i | \(0.923711\pi\) | |||||||
\(734\) | 46174.1i | 2.32196i | ||||||||
\(735\) | 555.983 | − | 320.997i | 0.0279017 | − | 0.0161090i | ||||
\(736\) | 6992.88 | + | 12112.0i | 0.350219 | + | 0.606596i | ||||
\(737\) | 7128.16 | + | 12346.3i | 0.356268 | + | 0.617074i | ||||
\(738\) | 16057.7 | + | 9270.93i | 0.800939 | + | 0.462423i | ||||
\(739\) | 35080.4 | 1.74622 | 0.873109 | − | 0.487525i | \(-0.162100\pi\) | ||||
0.873109 | + | 0.487525i | \(0.162100\pi\) | |||||||
\(740\) | −805.504 | − | 6801.20i | −0.0400147 | − | 0.337861i | ||||
\(741\) | 525.601 | 0.0260573 | ||||||||
\(742\) | −8222.19 | − | 4747.08i | −0.406801 | − | 0.234866i | ||||
\(743\) | 985.725 | + | 1707.33i | 0.0486713 | + | 0.0843011i | 0.889335 | − | 0.457257i | \(-0.151168\pi\) |
−0.840663 | + | 0.541558i | \(0.817835\pi\) | |||||||
\(744\) | 2558.95 | + | 4432.22i | 0.126096 | + | 0.218405i | ||||
\(745\) | 5040.00 | − | 2909.85i | 0.247854 | − | 0.143099i | ||||
\(746\) | 6033.47i | 0.296114i | ||||||||
\(747\) | 13945.0 | + | 24153.4i | 0.683026 | + | 1.18304i | ||||
\(748\) | − | 15406.5i | − | 0.753099i | ||||||
\(749\) | −1497.74 | + | 2594.15i | −0.0730655 | + | 0.126553i | ||||
\(750\) | −2200.24 | −0.107122 | ||||||||
\(751\) | 23142.3 | 1.12447 | 0.562233 | − | 0.826979i | \(-0.309943\pi\) | ||||
0.562233 | + | 0.826979i | \(0.309943\pi\) | |||||||
\(752\) | −1733.31 | + | 3002.18i | −0.0840523 | + | 0.145583i | ||||
\(753\) | −4279.17 | + | 2470.58i | −0.207094 | + | 0.119566i | ||||
\(754\) | 22380.2i | 1.08095i | ||||||||
\(755\) | −168.826 | − | 97.4715i | −0.00813800 | − | 0.00469848i | ||||
\(756\) | −1232.93 | + | 2135.51i | −0.0593140 | + | 0.102735i | ||||
\(757\) | −15995.0 | − | 9234.75i | −0.767966 | − | 0.443385i | 0.0641828 | − | 0.997938i | \(-0.479556\pi\) |
−0.832148 | + | 0.554553i | \(0.812889\pi\) | |||||||
\(758\) | 26047.4 | − | 15038.5i | 1.24813 | − | 0.720609i | ||||
\(759\) | −1646.05 | + | 950.347i | −0.0787191 | + | 0.0454485i | ||||
\(760\) | −899.207 | − | 519.157i | −0.0429180 | − | 0.0247787i | ||||
\(761\) | 1141.44 | − | 1977.04i | 0.0543723 | − | 0.0941756i | −0.837558 | − | 0.546348i | \(-0.816018\pi\) |
0.891930 | + | 0.452173i | \(0.149351\pi\) | |||||||
\(762\) | 7595.06 | + | 4385.01i | 0.361076 | + | 0.208467i | ||||
\(763\) | − | 9019.75i | − | 0.427964i | ||||||
\(764\) | −32183.2 | + | 18581.0i | −1.52401 | + | 0.879890i | ||||
\(765\) | −1202.35 | + | 2082.52i | −0.0568247 | + | 0.0984233i | ||||
\(766\) | 42029.6 | 1.98250 | ||||||||
\(767\) | 9317.39 | 0.438633 | ||||||||
\(768\) | 1355.35 | − | 2347.54i | 0.0636810 | − | 0.110299i | ||||
\(769\) | 15675.5i | 0.735077i | 0.930008 | + | 0.367539i | \(0.119799\pi\) | ||||
−0.930008 | + | 0.367539i | \(0.880201\pi\) | |||||||
\(770\) | −811.609 | − | 1405.75i | −0.0379849 | − | 0.0657918i | ||||
\(771\) | 4114.95i | 0.192213i | ||||||||
\(772\) | 28641.1 | − | 16535.9i | 1.33525 | − | 0.770909i | ||||
\(773\) | 8428.66 | + | 14598.9i | 0.392183 | + | 0.679282i | 0.992737 | − | 0.120303i | \(-0.0383865\pi\) |
−0.600554 | + | 0.799584i | \(0.705053\pi\) | |||||||
\(774\) | −15227.6 | − | 26375.0i | −0.707164 | − | 1.22484i | ||||
\(775\) | −31435.8 | − | 18149.5i | −1.45704 | − | 0.841224i | ||||
\(776\) | −7800.53 | −0.360854 | ||||||||
\(777\) | −825.042 | + | 97.7142i | −0.0380929 | + | 0.00451155i | ||||
\(778\) | 34751.1 | 1.60140 | ||||||||
\(779\) | 2805.91 | + | 1620.00i | 0.129053 | + | 0.0745088i | ||||
\(780\) | −383.667 | − | 664.530i | −0.0176121 | − | 0.0305051i | ||||
\(781\) | 7381.68 | + | 12785.4i | 0.338204 | + | 0.585786i | ||||
\(782\) | −10463.4 | + | 6041.08i | −0.478481 | + | 0.276251i | ||||
\(783\) | 7006.68i | 0.319793i | ||||||||
\(784\) | −1179.48 | − | 2042.93i | −0.0537302 | − | 0.0930634i | ||||
\(785\) | 4223.65i | 0.192036i | ||||||||
\(786\) | −3718.89 | + | 6441.30i | −0.168764 | + | 0.292307i | ||||
\(787\) | 9930.93 | 0.449809 | 0.224904 | − | 0.974381i | \(-0.427793\pi\) | ||||
0.224904 | + | 0.974381i | \(0.427793\pi\) | |||||||
\(788\) | 9741.67 | 0.440397 | ||||||||
\(789\) | 2446.71 | − | 4237.83i | 0.110400 | − | 0.191218i | ||||
\(790\) | −5709.89 | + | 3296.61i | −0.257150 | + | 0.148466i | ||||
\(791\) | − | 3042.95i | − | 0.136782i | ||||||
\(792\) | −15296.7 | − | 8831.57i | −0.686295 | − | 0.396232i | ||||
\(793\) | −1879.31 | + | 3255.06i | −0.0841567 | + | 0.145764i | ||||
\(794\) | −13683.6 | − | 7900.26i | −0.611605 | − | 0.353110i | ||||
\(795\) | 801.032 | − | 462.476i | 0.0357355 | − | 0.0206319i | ||||
\(796\) | −16448.4 | + | 9496.47i | −0.732408 | + | 0.422856i | ||||
\(797\) | 10458.3 | + | 6038.08i | 0.464806 | + | 0.268356i | 0.714063 | − | 0.700081i | \(-0.246853\pi\) |
−0.249257 | + | 0.968437i | \(0.580186\pi\) | |||||||
\(798\) | −174.300 | + | 301.897i | −0.00773204 | + | 0.0133923i | ||||
\(799\) | −15438.6 | − | 8913.45i | −0.683576 | − | 0.394663i | ||||
\(800\) | 23480.8i | 1.03772i | ||||||||
\(801\) | −11912.4 | + | 6877.65i | −0.525475 | + | 0.303383i | ||||
\(802\) | 9435.20 | − | 16342.2i | 0.415422 | − | 0.719532i | ||||
\(803\) | −36974.0 | −1.62489 | ||||||||
\(804\) | −4469.79 | −0.196066 | ||||||||
\(805\) | −388.412 | + | 672.749i | −0.0170059 | + | 0.0294550i | ||||
\(806\) | − | 42516.9i | − | 1.85806i | ||||||
\(807\) | 1759.85 | + | 3048.15i | 0.0767653 | + | 0.132961i | ||||
\(808\) | − | 7141.64i | − | 0.310943i | ||||||
\(809\) | −14313.7 | + | 8264.03i | −0.622056 | + | 0.359144i | −0.777669 | − | 0.628674i | \(-0.783598\pi\) |
0.155613 | + | 0.987818i | \(0.450265\pi\) | |||||||
\(810\) | 3715.41 | + | 6435.28i | 0.161168 | + | 0.279151i | ||||
\(811\) | 11245.0 | + | 19476.9i | 0.486887 | + | 0.843313i | 0.999886 | − | 0.0150758i | \(-0.00479896\pi\) |
−0.512999 | + | 0.858389i | \(0.671466\pi\) | |||||||
\(812\) | −7844.62 | − | 4529.09i | −0.339030 | − | 0.195739i | ||||
\(813\) | −2915.39 | −0.125765 | ||||||||
\(814\) | −3923.66 | − | 33129.1i | −0.168948 | − | 1.42650i | ||||
\(815\) | −2439.23 | −0.104838 | ||||||||
\(816\) | −194.917 | − | 112.536i | −0.00836209 | − | 0.00482786i | ||||
\(817\) | −2660.86 | − | 4608.74i | −0.113943 | − | 0.197356i | ||||
\(818\) | −20936.7 | − | 36263.4i | −0.894908 | − | 1.55003i | ||||
\(819\) | 3164.72 | − | 1827.15i | 0.135024 | − | 0.0779559i | ||||
\(820\) | − | 4730.11i | − | 0.201442i | ||||||
\(821\) | 3388.73 | + | 5869.45i | 0.144053 | + | 0.249507i | 0.929019 | − | 0.370031i | \(-0.120653\pi\) |
−0.784966 | + | 0.619539i | \(0.787320\pi\) | |||||||
\(822\) | − | 3721.12i | − | 0.157894i | ||||||
\(823\) | 1065.37 | − | 1845.28i | 0.0451233 | − | 0.0781559i | −0.842582 | − | 0.538569i | \(-0.818965\pi\) |
0.887705 | + | 0.460413i | \(0.152299\pi\) | |||||||
\(824\) | −19736.5 | −0.834408 | ||||||||
\(825\) | −3191.10 | −0.134666 | ||||||||
\(826\) | −3089.85 | + | 5351.77i | −0.130157 | + | 0.225438i | ||||
\(827\) | 27273.2 | − | 15746.2i | 1.14677 | − | 0.662089i | 0.198674 | − | 0.980066i | \(-0.436337\pi\) |
0.948099 | + | 0.317977i | \(0.103003\pi\) | |||||||
\(828\) | 23395.0i | 0.981922i | ||||||||
\(829\) | −10359.4 | − | 5980.98i | −0.434012 | − | 0.250577i | 0.267042 | − | 0.963685i | \(-0.413954\pi\) |
−0.701054 | + | 0.713108i | \(0.747287\pi\) | |||||||
\(830\) | 5829.49 | − | 10097.0i | 0.243789 | − | 0.422254i | ||||
\(831\) | −1555.47 | − | 898.051i | −0.0649322 | − | 0.0374886i | ||||
\(832\) | −22258.8 | + | 12851.1i | −0.927507 | + | 0.535497i | ||||
\(833\) | 10505.6 | − | 6065.43i | 0.436973 | − | 0.252287i | ||||
\(834\) | 1735.27 | + | 1001.86i | 0.0720473 | + | 0.0415965i | ||||
\(835\) | −3037.07 | + | 5260.36i | −0.125871 | + | 0.218015i | ||||
\(836\) | −7397.72 | − | 4271.08i | −0.306047 | − | 0.176696i | ||||
\(837\) | − | 13311.0i | − | 0.549696i | ||||||
\(838\) | 33146.2 | − | 19137.0i | 1.36637 | − | 0.788873i | ||||
\(839\) | 18221.8 | − | 31561.1i | 0.749804 | − | 1.29870i | −0.198112 | − | 0.980179i | \(-0.563481\pi\) |
0.947916 | − | 0.318520i | \(-0.103186\pi\) | |||||||
\(840\) | 183.885 | 0.00755315 | ||||||||
\(841\) | −1349.49 | −0.0553319 | ||||||||
\(842\) | 20132.5 | − | 34870.5i | 0.824004 | − | 1.42722i | ||||
\(843\) | 3884.07i | 0.158689i | ||||||||
\(844\) | 1995.26 | + | 3455.89i | 0.0813740 | + | 0.140944i | ||||
\(845\) | − | 3034.16i | − | 0.123524i | ||||||
\(846\) | −48986.8 | + | 28282.5i | −1.99078 | + | 1.14938i | ||||
\(847\) | 587.248 | + | 1017.14i | 0.0238230 | + | 0.0412626i | ||||
\(848\) | −1699.34 | − | 2943.35i | −0.0688156 | − | 0.119192i | ||||
\(849\) | 797.336 | + | 460.342i | 0.0322315 | + | 0.0186088i | ||||
\(850\) | −20284.9 | −0.818547 | ||||||||
\(851\) | −12791.6 | + | 9553.46i | −0.515264 | + | 0.384828i | ||||
\(852\) | −4628.75 | −0.186125 | ||||||||
\(853\) | −35007.0 | − | 20211.3i | −1.40518 | − | 0.811280i | −0.410260 | − | 0.911969i | \(-0.634562\pi\) |
−0.994918 | + | 0.100688i | \(0.967895\pi\) | |||||||
\(854\) | −1246.44 | − | 2158.90i | −0.0499441 | − | 0.0865057i | ||||
\(855\) | 666.641 | + | 1154.66i | 0.0266651 | + | 0.0461853i | ||||
\(856\) | 11800.5 | − | 6813.00i | 0.471182 | − | 0.272037i | ||||
\(857\) | 15436.4i | 0.615281i | 0.951503 | + | 0.307641i | \(0.0995395\pi\) | ||||
−0.951503 | + | 0.307641i | \(0.900461\pi\) | |||||||
\(858\) | −1868.86 | − | 3236.96i | −0.0743612 | − | 0.128797i | ||||
\(859\) | 17860.3i | 0.709413i | 0.934978 | + | 0.354707i | \(0.115419\pi\) | ||||
−0.934978 | + | 0.354707i | \(0.884581\pi\) | |||||||
\(860\) | −3884.63 | + | 6728.37i | −0.154029 | + | 0.266786i | ||||
\(861\) | −573.801 | −0.0227121 | ||||||||
\(862\) | −32261.1 | −1.27473 | ||||||||
\(863\) | 5991.90 | − | 10378.3i | 0.236346 | − | 0.409364i | −0.723317 | − | 0.690516i | \(-0.757383\pi\) |
0.959663 | + | 0.281153i | \(0.0907167\pi\) | |||||||
\(864\) | −7456.94 | + | 4305.26i | −0.293623 | + | 0.169523i | ||||
\(865\) | − | 2662.49i | − | 0.104656i | ||||||
\(866\) | 49014.9 | + | 28298.7i | 1.92332 | + | 1.11043i | ||||
\(867\) | −1433.03 | + | 2482.08i | −0.0561340 | + | 0.0972270i | ||||
\(868\) | 14902.9 | + | 8604.18i | 0.582761 | + | 0.336457i | ||||
\(869\) | −16972.9 | + | 9799.32i | −0.662563 | + | 0.382531i | ||||
\(870\) | 1252.36 | − | 723.050i | 0.0488034 | − | 0.0281766i | ||||
\(871\) | 11619.3 | + | 6708.38i | 0.452013 | + | 0.260970i | ||||
\(872\) | −20514.8 | + | 35532.7i | −0.796696 | + | 1.37992i | ||||
\(873\) | 8674.56 | + | 5008.26i | 0.336300 | + | 0.194163i | ||||
\(874\) | 6698.95i | 0.259263i | ||||||||
\(875\) | −2314.94 | + | 1336.53i | −0.0894393 | + | 0.0516378i | ||||
\(876\) | 5796.23 | − | 10039.4i | 0.223558 | − | 0.387213i | ||||
\(877\) | −10079.1 | −0.388080 | −0.194040 | − | 0.980994i | \(-0.562159\pi\) | ||||
−0.194040 | + | 0.980994i | \(0.562159\pi\) | |||||||
\(878\) | 25189.1 | 0.968211 | ||||||||
\(879\) | 3748.05 | − | 6491.81i | 0.143821 | − | 0.249105i | ||||
\(880\) | − | 581.073i | − | 0.0222591i | ||||||
\(881\) | −5334.60 | − | 9239.80i | −0.204004 | − | 0.353345i | 0.745811 | − | 0.666157i | \(-0.232062\pi\) |
−0.949815 | + | 0.312813i | \(0.898729\pi\) | |||||||
\(882\) | − | 38491.5i | − | 1.46947i | ||||||
\(883\) | −3460.76 | + | 1998.07i | −0.131896 | + | 0.0761499i | −0.564496 | − | 0.825436i | \(-0.690929\pi\) |
0.432600 | + | 0.901586i | \(0.357596\pi\) | |||||||
\(884\) | −7249.62 | − | 12556.7i | −0.275827 | − | 0.477746i | ||||
\(885\) | −301.023 | − | 521.387i | −0.0114336 | − | 0.0198036i | ||||
\(886\) | −8134.87 | − | 4696.67i | −0.308461 | − | 0.178090i | ||||
\(887\) | −34570.3 | −1.30863 | −0.654317 | − | 0.756220i | \(-0.727044\pi\) | ||||
−0.654317 | + | 0.756220i | \(0.727044\pi\) | |||||||
\(888\) | 3472.44 | + | 1491.56i | 0.131225 | + | 0.0563667i | ||||
\(889\) | 10654.7 | 0.401964 | ||||||||
\(890\) | 4979.81 | + | 2875.10i | 0.187555 | + | 0.108285i | ||||
\(891\) | 11044.2 | + | 19129.2i | 0.415259 | + | 0.719250i | ||||
\(892\) | 29766.4 | + | 51556.9i | 1.11732 | + | 1.93526i | ||||
\(893\) | −8559.91 | + | 4942.07i | −0.320769 | + | 0.185196i | ||||
\(894\) | 8887.97i | 0.332504i | ||||||||
\(895\) | 1952.77 | + | 3382.29i | 0.0729317 | + | 0.126321i | ||||
\(896\) | − | 9937.28i | − | 0.370515i | ||||||
\(897\) | −894.381 | + | 1549.11i | −0.0332915 | + | 0.0576626i | ||||
\(898\) | 77237.6 | 2.87021 | ||||||||
\(899\) | 48896.9 | 1.81402 | ||||||||
\(900\) | −19639.0 | + | 34015.8i | −0.727371 | + | 1.25984i | ||||
\(901\) | 15136.0 | − | 8738.77i | 0.559659 | − | 0.323120i | ||||
\(902\) | − | 23040.7i | − | 0.850521i | ||||||
\(903\) | 816.207 | + | 471.237i | 0.0300794 | + | 0.0173663i | ||||
\(904\) | −6920.98 | + | 11987.5i | −0.254633 | + | 0.441037i | ||||
\(905\) | 5964.61 | + | 3443.67i | 0.219083 | + | 0.126488i | ||||
\(906\) | 257.834 | − | 148.861i | 0.00945471 | − | 0.00545868i | ||||
\(907\) | −10121.1 | + | 5843.42i | −0.370524 | + | 0.213922i | −0.673687 | − | 0.739016i | \(-0.735291\pi\) |
0.303163 | + | 0.952939i | \(0.401957\pi\) | |||||||
\(908\) | 50906.4 | + | 29390.8i | 1.86056 | + | 1.07419i | ||||
\(909\) | −4585.23 | + | 7941.85i | −0.167307 | + | 0.289785i | ||||
\(910\) | −1322.96 | − | 763.814i | −0.0481932 | − | 0.0278244i | ||||
\(911\) | − | 17546.6i | − | 0.638140i | −0.947731 | − | 0.319070i | \(-0.896630\pi\) | ||
0.947731 | − | 0.319070i | \(-0.103370\pi\) | |||||||
\(912\) | −108.072 | + | 62.3954i | −0.00392393 | + | 0.00226548i | ||||
\(913\) | 17328.4 | − | 30013.7i | 0.628136 | − | 1.08796i | ||||
\(914\) | 62290.6 | 2.25426 | ||||||||
\(915\) | 242.864 | 0.00877469 | ||||||||
\(916\) | −25524.7 | + | 44210.1i | −0.920700 | + | 1.59470i | ||||
\(917\) | 9036.12i | 0.325408i | ||||||||
\(918\) | −3719.27 | − | 6441.97i | −0.133719 | − | 0.231609i | ||||
\(919\) | − | 33284.5i | − | 1.19473i | −0.801971 | − | 0.597363i | \(-0.796215\pi\) | ||
0.801971 | − | 0.597363i | \(-0.203785\pi\) | |||||||
\(920\) | 3060.24 | − | 1766.83i | 0.109667 | − | 0.0633160i | ||||
\(921\) | 3746.66 | + | 6489.41i | 0.134046 | + | 0.232175i | ||||
\(922\) | 8819.54 | + | 15275.9i | 0.315028 | + | 0.545645i | ||||
\(923\) | 12032.5 | + | 6946.97i | 0.429095 | + | 0.247738i | ||||
\(924\) | 1512.81 | 0.0538613 | ||||||||
\(925\) | −26618.4 | + | 3152.56i | −0.946171 | + | 0.112060i | ||||
\(926\) | 14704.3 | 0.521828 | ||||||||
\(927\) | 21947.9 | + | 12671.6i | 0.777631 | + | 0.448965i | ||||
\(928\) | −15815.1 | − | 27392.5i | −0.559434 | − | 0.968968i | ||||
\(929\) | −6474.46 | − | 11214.1i | −0.228654 | − | 0.396041i | 0.728755 | − | 0.684774i | \(-0.240099\pi\) |
−0.957410 | + | 0.288733i | \(0.906766\pi\) | |||||||
\(930\) | −2379.18 | + | 1373.62i | −0.0838886 | + | 0.0484331i | ||||
\(931\) | − | 6725.96i | − | 0.236772i | ||||||
\(932\) | 11002.2 | + | 19056.3i | 0.386683 | + | 0.669755i | ||||
\(933\) | − | 3894.23i | − | 0.136647i | ||||||
\(934\) | 18962.9 | − | 32844.7i | 0.664330 | − | 1.15065i | ||||
\(935\) | 2988.14 | 0.104516 | ||||||||
\(936\) | −16623.0 | −0.580489 | ||||||||
\(937\) | −12678.3 | + | 21959.4i | −0.442030 | + | 0.765618i | −0.997840 | − | 0.0656914i | \(-0.979075\pi\) |
0.555810 | + | 0.831309i | \(0.312408\pi\) | |||||||
\(938\) | −7706.39 | + | 4449.29i | −0.268254 | + | 0.154877i | ||||
\(939\) | 4155.85i | 0.144431i | ||||||||
\(940\) | 12496.8 | + | 7215.00i | 0.433616 | + | 0.250348i | ||||
\(941\) | −22283.6 | + | 38596.4i | −0.771971 | + | 1.33709i | 0.164510 | + | 0.986375i | \(0.447396\pi\) |
−0.936481 | + | 0.350718i | \(0.885938\pi\) | |||||||
\(942\) | −5586.26 | − | 3225.23i | −0.193217 | − | 0.111554i | ||||
\(943\) | −9549.28 | + | 5513.28i | −0.329764 | + | 0.190389i | ||||
\(944\) | −1915.81 | + | 1106.09i | −0.0660531 | + | 0.0381358i | ||||
\(945\) | −414.187 | − | 239.131i | −0.0142577 | − | 0.00823168i | ||||
\(946\) | −18922.3 | + | 32774.3i | −0.650334 | + | 1.12641i | ||||
\(947\) | 15796.8 | + | 9120.26i | 0.542055 | + | 0.312955i | 0.745911 | − | 0.666045i | \(-0.232014\pi\) |
−0.203857 | + | 0.979001i | \(0.565348\pi\) | |||||||
\(948\) | − | 6144.76i | − | 0.210520i | ||||||
\(949\) | −30134.7 | + | 17398.3i | −1.03078 | + | 0.595124i | ||||
\(950\) | −5623.47 | + | 9740.14i | −0.192052 | + | 0.332644i | ||||
\(951\) | 7660.12 | 0.261195 | ||||||||
\(952\) | 3474.62 | 0.118291 | ||||||||
\(953\) | 1553.55 | − | 2690.83i | 0.0528064 | − | 0.0914634i | −0.838414 | − | 0.545034i | \(-0.816517\pi\) |
0.891220 | + | 0.453571i | \(0.149850\pi\) | |||||||
\(954\) | − | 55456.6i | − | 1.88205i | ||||||
\(955\) | −3603.83 | − | 6242.02i | −0.122112 | − | 0.211505i | ||||
\(956\) | − | 66121.8i | − | 2.23696i | ||||||
\(957\) | 3722.70 | − | 2149.30i | 0.125745 | − | 0.0725988i | ||||
\(958\) | 18192.4 | + | 31510.2i | 0.613539 | + | 1.06268i | ||||
\(959\) | −2260.38 | − | 3915.10i | −0.0761122 | − | 0.131830i | ||||
\(960\) | 1438.26 | + | 830.380i | 0.0483538 | + | 0.0279171i | ||||
\(961\) | −63101.3 | −2.11813 | ||||||||
\(962\) | −18786.9 | − | 25154.7i | −0.629641 | − | 0.843057i | ||||
\(963\) | −17496.9 | −0.585493 | ||||||||
\(964\) | −76013.1 | − | 43886.2i | −2.53964 | − | 1.46626i | ||||
\(965\) | 3207.19 | + | 5555.02i | 0.106988 | + | 0.185308i | ||||
\(966\) | −593.191 | − | 1027.44i | −0.0197574 | − | 0.0342208i | ||||
\(967\) | −14896.1 | + | 8600.29i | −0.495375 | + | 0.286005i | −0.726801 | − | 0.686848i | \(-0.758994\pi\) |
0.231427 | + | 0.972852i | \(0.425661\pi\) | |||||||
\(968\) | − | 5342.62i | − | 0.177395i | ||||||
\(969\) | −320.865 | − | 555.754i | −0.0106374 | − | 0.0184246i | ||||
\(970\) | − | 4187.26i | − | 0.138603i | ||||||
\(971\) | 27292.9 | − | 47272.7i | 0.902029 | − | 1.56236i | 0.0771737 | − | 0.997018i | \(-0.475410\pi\) |
0.824856 | − | 0.565343i | \(-0.191256\pi\) | |||||||
\(972\) | −21695.7 | −0.715937 | ||||||||
\(973\) | 2434.31 | 0.0802059 | ||||||||
\(974\) | −25588.8 | + | 44321.1i | −0.841806 | + | 1.45805i | ||||
\(975\) | −2600.82 | + | 1501.59i | −0.0854287 | + | 0.0493223i | ||||
\(976\) | − | 892.390i | − | 0.0292671i | ||||||
\(977\) | −9078.06 | − | 5241.22i | −0.297270 | − | 0.171629i | 0.343946 | − | 0.938990i | \(-0.388236\pi\) |
−0.641216 | + | 0.767360i | \(0.721570\pi\) | |||||||
\(978\) | 1862.63 | − | 3226.16i | 0.0609001 | − | 0.105482i | ||||
\(979\) | 14802.7 | + | 8546.36i | 0.483246 | + | 0.279002i | ||||
\(980\) | −8503.80 | + | 4909.67i | −0.277188 | + | 0.160034i | ||||
\(981\) | 45626.9 | − | 26342.7i | 1.48497 | − | 0.857348i | ||||
\(982\) | −77855.1 | − | 44949.7i | −2.53000 | − | 1.46069i | ||||
\(983\) | −17994.4 | + | 31167.2i | −0.583858 | + | 1.01127i | 0.411158 | + | 0.911564i | \(0.365124\pi\) |
−0.995017 | + | 0.0997084i | \(0.968209\pi\) | |||||||
\(984\) | 2260.45 | + | 1305.07i | 0.0732323 | + | 0.0422807i | ||||
\(985\) | 1889.42i | 0.0611188i | ||||||||
\(986\) | 23664.1 | − | 13662.5i | 0.764319 | − | 0.441280i | ||||
\(987\) | 875.239 | − | 1515.96i | 0.0282261 | − | 0.0488890i | ||||
\(988\) | −8039.11 | −0.258864 | ||||||||
\(989\) | 18111.2 | 0.582309 | ||||||||
\(990\) | 4740.71 | − | 8211.15i | 0.152192 | − | 0.263603i | ||||
\(991\) | 33474.4i | 1.07301i | 0.843899 | + | 0.536503i | \(0.180255\pi\) | ||||
−0.843899 | + | 0.536503i | \(0.819745\pi\) | |||||||
\(992\) | 30044.8 | + | 52039.1i | 0.961616 | + | 1.66557i | ||||
\(993\) | 2852.20i | 0.0911499i | ||||||||
\(994\) | −7980.47 | + | 4607.52i | −0.254653 | + | 0.147024i | ||||
\(995\) | −1841.87 | − | 3190.21i | −0.0586845 | − | 0.101645i | ||||
\(996\) | 5432.99 | + | 9410.21i | 0.172842 | + | 0.299371i | ||||
\(997\) | −16758.8 | − | 9675.70i | −0.532354 | − | 0.307354i | 0.209621 | − | 0.977783i | \(-0.432777\pi\) |
−0.741974 | + | 0.670428i | \(0.766110\pi\) | |||||||
\(998\) | −55343.6 | −1.75538 | ||||||||
\(999\) | −5881.72 | − | 7875.32i | −0.186276 | − | 0.249414i |
(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 | 37.4.e.a.27.8 | yes | 16 | |
3.2 | odd | 2 | 333.4.s.c.64.1 | 16 | |||
37.11 | even | 6 | inner | 37.4.e.a.11.8 | ✓ | 16 | |
37.14 | odd | 12 | 1369.4.a.g.1.15 | 16 | |||
37.23 | odd | 12 | 1369.4.a.g.1.2 | 16 | |||
111.11 | odd | 6 | 333.4.s.c.307.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.4.e.a.11.8 | ✓ | 16 | 37.11 | even | 6 | inner | |
37.4.e.a.27.8 | yes | 16 | 1.1 | even | 1 | trivial | |
333.4.s.c.64.1 | 16 | 3.2 | odd | 2 | |||
333.4.s.c.307.1 | 16 | 111.11 | odd | 6 | |||
1369.4.a.g.1.2 | 16 | 37.23 | odd | 12 | |||
1369.4.a.g.1.15 | 16 | 37.14 | odd | 12 |