Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(37,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.v (of order \(12\), degree \(4\), 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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 58.2 | ||
Character | \(\chi\) | \(=\) | 105.58 |
Dual form | 105.3.v.a.67.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.914152 | − | 3.41166i | −0.457076 | − | 1.70583i | −0.681912 | − | 0.731435i | \(-0.738851\pi\) |
0.224836 | − | 0.974397i | \(-0.427815\pi\) | |||||||
\(3\) | −0.448288 | + | 1.67303i | −0.149429 | + | 0.557678i | ||||
\(4\) | −7.33966 | + | 4.23756i | −1.83492 | + | 1.05939i | ||||
\(5\) | 2.17799 | + | 4.50071i | 0.435597 | + | 0.900142i | ||||
\(6\) | 6.11763 | 1.01960 | ||||||||
\(7\) | −2.92953 | + | 6.35750i | −0.418505 | + | 0.908215i | ||||
\(8\) | 11.1766 | + | 11.1766i | 1.39708 | + | 1.39708i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 13.3639 | − | 11.5449i | 1.33639 | − | 1.15449i | ||||
\(11\) | 8.72135 | + | 15.1058i | 0.792850 | + | 1.37326i | 0.924195 | + | 0.381920i | \(0.124737\pi\) |
−0.131345 | + | 0.991337i | \(0.541930\pi\) | |||||||
\(12\) | −3.79929 | − | 14.1791i | −0.316608 | − | 1.18160i | ||||
\(13\) | −8.72144 | − | 8.72144i | −0.670880 | − | 0.670880i | 0.287039 | − | 0.957919i | \(-0.407329\pi\) |
−0.957919 | + | 0.287039i | \(0.907329\pi\) | |||||||
\(14\) | 24.3677 | + | 4.18286i | 1.74055 | + | 0.298776i | ||||
\(15\) | −8.50620 | + | 1.62623i | −0.567080 | + | 0.108415i | ||||
\(16\) | 10.9636 | − | 18.9894i | 0.685222 | − | 1.18684i | ||||
\(17\) | −11.2788 | − | 3.02215i | −0.663461 | − | 0.177774i | −0.0886535 | − | 0.996063i | \(-0.528256\pi\) |
−0.574807 | + | 0.818289i | \(0.694923\pi\) | |||||||
\(18\) | −2.74246 | + | 10.2350i | −0.152359 | + | 0.568610i | ||||
\(19\) | 3.12903 | + | 1.80655i | 0.164686 | + | 0.0950814i | 0.580078 | − | 0.814561i | \(-0.303022\pi\) |
−0.415392 | + | 0.909643i | \(0.636356\pi\) | |||||||
\(20\) | −35.0577 | − | 23.8044i | −1.75288 | − | 1.19022i | ||||
\(21\) | −9.32303 | − | 7.75120i | −0.443954 | − | 0.369105i | ||||
\(22\) | 43.5633 | − | 43.5633i | 1.98015 | − | 1.98015i | ||||
\(23\) | 23.1890 | − | 6.21349i | 1.00822 | − | 0.270152i | 0.283334 | − | 0.959021i | \(-0.408559\pi\) |
0.724885 | + | 0.688870i | \(0.241893\pi\) | |||||||
\(24\) | −23.7092 | + | 13.6885i | −0.987885 | + | 0.570356i | ||||
\(25\) | −15.5128 | + | 19.6050i | −0.620510 | + | 0.784198i | ||||
\(26\) | −21.7819 | + | 37.7273i | −0.837765 | + | 1.45105i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −5.43848 | − | 59.0760i | −0.194231 | − | 2.10986i | ||||
\(29\) | 46.5831i | 1.60631i | 0.595767 | + | 0.803157i | \(0.296848\pi\) | ||||
−0.595767 | + | 0.803157i | \(0.703152\pi\) | |||||||
\(30\) | 13.3241 | + | 27.5337i | 0.444137 | + | 0.917788i | ||||
\(31\) | −1.10507 | − | 1.91403i | −0.0356474 | − | 0.0617430i | 0.847651 | − | 0.530554i | \(-0.178016\pi\) |
−0.883299 | + | 0.468811i | \(0.844683\pi\) | |||||||
\(32\) | −13.7376 | − | 3.68097i | −0.429300 | − | 0.115030i | ||||
\(33\) | −29.1822 | + | 7.81935i | −0.884310 | + | 0.236950i | ||||
\(34\) | 41.2423i | 1.21301i | ||||||||
\(35\) | −34.9937 | + | 0.661568i | −0.999821 | + | 0.0189019i | ||||
\(36\) | 25.4253 | 0.706260 | ||||||||
\(37\) | 7.87211 | + | 29.3791i | 0.212760 | + | 0.794030i | 0.986943 | + | 0.161069i | \(0.0514942\pi\) |
−0.774183 | + | 0.632961i | \(0.781839\pi\) | |||||||
\(38\) | 3.30292 | − | 12.3266i | 0.0869188 | − | 0.324386i | ||||
\(39\) | 18.5010 | − | 10.6815i | 0.474384 | − | 0.273886i | ||||
\(40\) | −25.9602 | + | 74.6454i | −0.649006 | + | 1.86614i | ||||
\(41\) | 29.9435 | 0.730329 | 0.365165 | − | 0.930943i | \(-0.381013\pi\) | ||||
0.365165 | + | 0.930943i | \(0.381013\pi\) | |||||||
\(42\) | −17.9218 | + | 38.8928i | −0.426709 | + | 0.926019i | ||||
\(43\) | −19.6771 | − | 19.6771i | −0.457608 | − | 0.457608i | 0.440262 | − | 0.897869i | \(-0.354886\pi\) |
−0.897869 | + | 0.440262i | \(0.854886\pi\) | |||||||
\(44\) | −128.024 | − | 73.9145i | −2.90963 | − | 1.67987i | ||||
\(45\) | 1.09249 | − | 14.9602i | 0.0242775 | − | 0.332448i | ||||
\(46\) | −42.3966 | − | 73.4331i | −0.921666 | − | 1.59637i | ||||
\(47\) | −21.2083 | − | 79.1503i | −0.451240 | − | 1.68405i | −0.698913 | − | 0.715206i | \(-0.746333\pi\) |
0.247674 | − | 0.968844i | \(-0.420334\pi\) | |||||||
\(48\) | 26.8551 | + | 26.8551i | 0.559482 | + | 0.559482i | ||||
\(49\) | −31.8357 | − | 37.2490i | −0.649707 | − | 0.760185i | ||||
\(50\) | 81.0665 | + | 35.0024i | 1.62133 | + | 0.700047i | ||||
\(51\) | 10.1123 | − | 17.5151i | 0.198281 | − | 0.343433i | ||||
\(52\) | 100.970 | + | 27.0549i | 1.94173 | + | 0.520286i | ||||
\(53\) | −0.437265 | + | 1.63190i | −0.00825028 | + | 0.0307905i | −0.969928 | − | 0.243391i | \(-0.921740\pi\) |
0.961678 | + | 0.274181i | \(0.0884069\pi\) | |||||||
\(54\) | −15.8941 | − | 9.17644i | −0.294334 | − | 0.169934i | ||||
\(55\) | −48.9919 | + | 72.1526i | −0.890763 | + | 1.31186i | ||||
\(56\) | −103.798 | + | 38.3132i | −1.85353 | + | 0.684164i | ||||
\(57\) | −4.42512 | + | 4.42512i | −0.0776336 | + | 0.0776336i | ||||
\(58\) | 158.926 | − | 42.5841i | 2.74010 | − | 0.734208i | ||||
\(59\) | 76.5567 | − | 44.2000i | 1.29757 | − | 0.749153i | 0.317587 | − | 0.948229i | \(-0.397127\pi\) |
0.979984 | + | 0.199076i | \(0.0637941\pi\) | |||||||
\(60\) | 55.5414 | − | 47.9815i | 0.925690 | − | 0.799691i | ||||
\(61\) | −23.4309 | + | 40.5836i | −0.384114 | + | 0.665305i | −0.991646 | − | 0.128990i | \(-0.958826\pi\) |
0.607532 | + | 0.794295i | \(0.292160\pi\) | |||||||
\(62\) | −5.51984 | + | 5.51984i | −0.0890296 | + | 0.0890296i | ||||
\(63\) | 17.1474 | − | 12.1230i | 0.272181 | − | 0.192428i | ||||
\(64\) | − | 37.4755i | − | 0.585554i | ||||||
\(65\) | 20.2575 | − | 58.2478i | 0.311654 | − | 0.896121i | ||||
\(66\) | 53.3540 | + | 92.4118i | 0.808394 | + | 1.40018i | ||||
\(67\) | −11.2647 | − | 3.01836i | −0.168129 | − | 0.0450501i | 0.173772 | − | 0.984786i | \(-0.444404\pi\) |
−0.341902 | + | 0.939736i | \(0.611071\pi\) | |||||||
\(68\) | 95.5894 | − | 25.6131i | 1.40573 | − | 0.376663i | ||||
\(69\) | 41.5815i | 0.602630i | ||||||||
\(70\) | 34.2467 | + | 118.782i | 0.489238 | + | 1.69689i | ||||
\(71\) | 67.1402 | 0.945636 | 0.472818 | − | 0.881160i | \(-0.343237\pi\) | ||||
0.472818 | + | 0.881160i | \(0.343237\pi\) | |||||||
\(72\) | −12.2728 | − | 45.8027i | −0.170456 | − | 0.636149i | ||||
\(73\) | 4.72997 | − | 17.6525i | 0.0647941 | − | 0.241815i | −0.925932 | − | 0.377691i | \(-0.876718\pi\) |
0.990726 | + | 0.135876i | \(0.0433848\pi\) | |||||||
\(74\) | 93.0353 | − | 53.7140i | 1.25723 | − | 0.725865i | ||||
\(75\) | −25.8456 | − | 34.7420i | −0.344607 | − | 0.463227i | ||||
\(76\) | −30.6214 | −0.402913 | ||||||||
\(77\) | −121.585 | + | 11.1930i | −1.57902 | + | 0.145363i | ||||
\(78\) | −53.3545 | − | 53.3545i | −0.684032 | − | 0.684032i | ||||
\(79\) | −19.4021 | − | 11.2018i | −0.245596 | − | 0.141795i | 0.372150 | − | 0.928173i | \(-0.378621\pi\) |
−0.617746 | + | 0.786378i | \(0.711954\pi\) | |||||||
\(80\) | 109.344 | + | 7.98505i | 1.36680 | + | 0.0998131i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −27.3729 | − | 102.157i | −0.333816 | − | 1.24582i | ||||
\(83\) | 52.4430 | + | 52.4430i | 0.631844 | + | 0.631844i | 0.948530 | − | 0.316686i | \(-0.102570\pi\) |
−0.316686 | + | 0.948530i | \(0.602570\pi\) | |||||||
\(84\) | 101.274 | + | 17.3843i | 1.20564 | + | 0.206956i | ||||
\(85\) | −10.9633 | − | 57.3450i | −0.128980 | − | 0.674647i | ||||
\(86\) | −49.1438 | + | 85.1196i | −0.571440 | + | 0.989763i | ||||
\(87\) | −77.9351 | − | 20.8826i | −0.895805 | − | 0.240030i | ||||
\(88\) | −71.3570 | + | 266.308i | −0.810875 | + | 3.02623i | ||||
\(89\) | −44.2757 | − | 25.5626i | −0.497480 | − | 0.287220i | 0.230192 | − | 0.973145i | \(-0.426065\pi\) |
−0.727672 | + | 0.685925i | \(0.759398\pi\) | |||||||
\(90\) | −52.0377 | + | 9.94866i | −0.578197 | + | 0.110541i | ||||
\(91\) | 80.9964 | − | 29.8968i | 0.890070 | − | 0.328536i | ||||
\(92\) | −143.870 | + | 143.870i | −1.56380 | + | 1.56380i | ||||
\(93\) | 3.69763 | − | 0.990777i | 0.0397595 | − | 0.0106535i | ||||
\(94\) | −250.647 | + | 144.711i | −2.66645 | + | 1.53948i | ||||
\(95\) | −1.31575 | + | 18.0175i | −0.0138501 | + | 0.189658i | ||||
\(96\) | 12.3168 | − | 21.3333i | 0.128300 | − | 0.222222i | ||||
\(97\) | 9.15031 | − | 9.15031i | 0.0943331 | − | 0.0943331i | −0.658365 | − | 0.752698i | \(-0.728752\pi\) |
0.752698 | + | 0.658365i | \(0.228752\pi\) | |||||||
\(98\) | −97.9785 | + | 142.664i | −0.999781 | + | 1.45575i | ||||
\(99\) | − | 52.3281i | − | 0.528567i | ||||||
\(100\) | 30.7813 | − | 209.630i | 0.307813 | − | 2.09630i | ||||
\(101\) | 42.1642 | + | 73.0305i | 0.417467 | + | 0.723074i | 0.995684 | − | 0.0928089i | \(-0.0295846\pi\) |
−0.578217 | + | 0.815883i | \(0.696251\pi\) | |||||||
\(102\) | −68.9997 | − | 18.4884i | −0.676468 | − | 0.181259i | ||||
\(103\) | 113.235 | − | 30.3411i | 1.09937 | − | 0.294574i | 0.336859 | − | 0.941555i | \(-0.390635\pi\) |
0.762506 | + | 0.646981i | \(0.223969\pi\) | |||||||
\(104\) | − | 194.953i | − | 1.87455i | ||||||
\(105\) | 14.5804 | − | 58.8423i | 0.138861 | − | 0.560402i | ||||
\(106\) | 5.96720 | 0.0562944 | ||||||||
\(107\) | 36.9890 | + | 138.045i | 0.345691 | + | 1.29014i | 0.891802 | + | 0.452425i | \(0.149441\pi\) |
−0.546111 | + | 0.837713i | \(0.683892\pi\) | |||||||
\(108\) | −11.3979 | + | 42.5374i | −0.105536 | + | 0.393865i | ||||
\(109\) | 140.724 | − | 81.2472i | 1.29105 | − | 0.745387i | 0.312208 | − | 0.950014i | \(-0.398931\pi\) |
0.978840 | + | 0.204627i | \(0.0655980\pi\) | |||||||
\(110\) | 290.946 | + | 101.186i | 2.64497 | + | 0.919869i | ||||
\(111\) | −52.6812 | −0.474605 | ||||||||
\(112\) | 88.6073 | + | 125.331i | 0.791136 | + | 1.11903i | ||||
\(113\) | −3.09464 | − | 3.09464i | −0.0273862 | − | 0.0273862i | 0.693281 | − | 0.720667i | \(-0.256164\pi\) |
−0.720667 | + | 0.693281i | \(0.756164\pi\) | |||||||
\(114\) | 19.1422 | + | 11.0518i | 0.167914 | + | 0.0969454i | ||||
\(115\) | 78.4705 | + | 90.8343i | 0.682352 | + | 0.789863i | ||||
\(116\) | −197.399 | − | 341.904i | −1.70171 | − | 2.94745i | ||||
\(117\) | 9.57681 | + | 35.7411i | 0.0818531 | + | 0.305480i | ||||
\(118\) | −220.780 | − | 220.780i | −1.87102 | − | 1.87102i | ||||
\(119\) | 52.2551 | − | 62.8517i | 0.439118 | − | 0.528166i | ||||
\(120\) | −113.247 | − | 76.8950i | −0.943721 | − | 0.640791i | ||||
\(121\) | −91.6240 | + | 158.697i | −0.757223 | + | 1.31155i | ||||
\(122\) | 159.877 | + | 42.8389i | 1.31047 | + | 0.351139i | ||||
\(123\) | −13.4233 | + | 50.0965i | −0.109133 | + | 0.407288i | ||||
\(124\) | 16.2217 | + | 9.36558i | 0.130820 | + | 0.0755289i | ||||
\(125\) | −122.023 | − | 27.1191i | −0.976182 | − | 0.216953i | ||||
\(126\) | −57.0348 | − | 47.4189i | −0.452657 | − | 0.376341i | ||||
\(127\) | −117.674 | + | 117.674i | −0.926571 | + | 0.926571i | −0.997483 | − | 0.0709120i | \(-0.977409\pi\) |
0.0709120 | + | 0.997483i | \(0.477409\pi\) | |||||||
\(128\) | −182.804 | + | 48.9822i | −1.42816 | + | 0.382673i | ||||
\(129\) | 41.7415 | − | 24.0995i | 0.323578 | − | 0.186818i | ||||
\(130\) | −217.240 | − | 15.8643i | −1.67108 | − | 0.122033i | ||||
\(131\) | 81.6255 | − | 141.379i | 0.623095 | − | 1.07923i | −0.365811 | − | 0.930689i | \(-0.619208\pi\) |
0.988906 | − | 0.148543i | \(-0.0474584\pi\) | |||||||
\(132\) | 181.053 | − | 181.053i | 1.37161 | − | 1.37161i | ||||
\(133\) | −20.6517 | + | 14.6005i | −0.155276 | + | 0.109778i | ||||
\(134\) | 41.1905i | 0.307392i | ||||||||
\(135\) | 24.5391 | + | 8.53423i | 0.181771 | + | 0.0632165i | ||||
\(136\) | −92.2820 | − | 159.837i | −0.678544 | − | 1.17527i | ||||
\(137\) | 142.797 | + | 38.2623i | 1.04231 | + | 0.279287i | 0.739072 | − | 0.673627i | \(-0.235265\pi\) |
0.303241 | + | 0.952914i | \(0.401931\pi\) | |||||||
\(138\) | 141.862 | − | 38.0118i | 1.02798 | − | 0.275448i | ||||
\(139\) | 101.553i | 0.730596i | 0.930891 | + | 0.365298i | \(0.119033\pi\) | ||||
−0.930891 | + | 0.365298i | \(0.880967\pi\) | |||||||
\(140\) | 254.039 | − | 153.144i | 1.81456 | − | 1.09388i | ||||
\(141\) | 141.929 | 1.00659 | ||||||||
\(142\) | −61.3763 | − | 229.060i | −0.432228 | − | 1.61310i | ||||
\(143\) | 55.6818 | − | 207.807i | 0.389383 | − | 1.45320i | ||||
\(144\) | −56.9683 | + | 32.8907i | −0.395613 | + | 0.228407i | ||||
\(145\) | −209.657 | + | 101.457i | −1.44591 | + | 0.699706i | ||||
\(146\) | −64.5483 | −0.442112 | ||||||||
\(147\) | 76.5904 | − | 36.5638i | 0.521023 | − | 0.248733i | ||||
\(148\) | −182.274 | − | 182.274i | −1.23158 | − | 1.23158i | ||||
\(149\) | −91.7653 | − | 52.9807i | −0.615874 | − | 0.355575i | 0.159387 | − | 0.987216i | \(-0.449048\pi\) |
−0.775261 | + | 0.631641i | \(0.782382\pi\) | |||||||
\(150\) | −94.9012 | + | 119.936i | −0.632675 | + | 0.799572i | ||||
\(151\) | 80.5845 | + | 139.576i | 0.533672 | + | 0.924347i | 0.999226 | + | 0.0393279i | \(0.0125217\pi\) |
−0.465554 | + | 0.885019i | \(0.654145\pi\) | |||||||
\(152\) | 14.7809 | + | 55.1632i | 0.0972429 | + | 0.362916i | ||||
\(153\) | 24.7700 | + | 24.7700i | 0.161896 | + | 0.161896i | ||||
\(154\) | 149.334 | + | 404.574i | 0.969699 | + | 2.62711i | ||||
\(155\) | 6.20769 | − | 9.14233i | 0.0400496 | − | 0.0589828i | ||||
\(156\) | −90.5273 | + | 156.798i | −0.580303 | + | 1.00511i | ||||
\(157\) | 132.698 | + | 35.5563i | 0.845210 | + | 0.226473i | 0.655338 | − | 0.755336i | \(-0.272526\pi\) |
0.189872 | + | 0.981809i | \(0.439193\pi\) | |||||||
\(158\) | −20.4803 | + | 76.4335i | −0.129622 | + | 0.483756i | ||||
\(159\) | −2.53419 | − | 1.46312i | −0.0159383 | − | 0.00920200i | ||||
\(160\) | −13.3533 | − | 69.8460i | −0.0834579 | − | 0.436537i | ||||
\(161\) | −28.4309 | + | 165.627i | −0.176589 | + | 1.02874i | ||||
\(162\) | 22.4776 | − | 22.4776i | 0.138751 | − | 0.138751i | ||||
\(163\) | 182.431 | − | 48.8824i | 1.11921 | − | 0.299892i | 0.348647 | − | 0.937254i | \(-0.386641\pi\) |
0.770564 | + | 0.637362i | \(0.219975\pi\) | |||||||
\(164\) | −219.775 | + | 126.887i | −1.34009 | + | 0.773703i | ||||
\(165\) | −98.7511 | − | 114.310i | −0.598491 | − | 0.692789i | ||||
\(166\) | 130.977 | − | 226.859i | 0.789018 | − | 1.36662i | ||||
\(167\) | −114.153 | + | 114.153i | −0.683552 | + | 0.683552i | −0.960799 | − | 0.277247i | \(-0.910578\pi\) |
0.277247 | + | 0.960799i | \(0.410578\pi\) | |||||||
\(168\) | −17.5679 | − | 190.833i | −0.104571 | − | 1.13591i | ||||
\(169\) | − | 16.8729i | − | 0.0998396i | ||||||
\(170\) | −185.620 | + | 89.8251i | −1.09188 | + | 0.528383i | ||||
\(171\) | −5.41964 | − | 9.38709i | −0.0316938 | − | 0.0548952i | ||||
\(172\) | 227.807 | + | 61.0406i | 1.32446 | + | 0.354887i | ||||
\(173\) | −201.348 | + | 53.9511i | −1.16386 | + | 0.311856i | −0.788508 | − | 0.615025i | \(-0.789146\pi\) |
−0.375355 | + | 0.926881i | \(0.622479\pi\) | |||||||
\(174\) | 284.978i | 1.63780i | ||||||||
\(175\) | −79.1934 | − | 156.056i | −0.452534 | − | 0.891747i | ||||
\(176\) | 382.468 | 2.17312 | ||||||||
\(177\) | 39.6287 | + | 147.896i | 0.223891 | + | 0.835572i | ||||
\(178\) | −46.7362 | + | 174.422i | −0.262563 | + | 0.979899i | ||||
\(179\) | 102.967 | − | 59.4481i | 0.575235 | − | 0.332112i | −0.184002 | − | 0.982926i | \(-0.558905\pi\) |
0.759238 | + | 0.650814i | \(0.225572\pi\) | |||||||
\(180\) | 55.3760 | + | 114.432i | 0.307645 | + | 0.635734i | ||||
\(181\) | −2.13381 | −0.0117890 | −0.00589449 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589449 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(182\) | −176.041 | − | 249.002i | −0.967257 | − | 1.36814i | ||||
\(183\) | −57.3939 | − | 57.3939i | −0.313628 | − | 0.313628i | ||||
\(184\) | 328.622 | + | 189.730i | 1.78599 | + | 1.03114i | ||||
\(185\) | −115.082 | + | 99.4174i | −0.622062 | + | 0.537391i | ||||
\(186\) | −6.76039 | − | 11.7093i | −0.0363462 | − | 0.0629535i | ||||
\(187\) | −52.7146 | − | 196.733i | −0.281896 | − | 1.05205i | ||||
\(188\) | 491.066 | + | 491.066i | 2.61205 | + | 2.61205i | ||||
\(189\) | 12.5952 | + | 34.1227i | 0.0666410 | + | 0.180544i | ||||
\(190\) | 62.6724 | − | 11.9818i | 0.329855 | − | 0.0630621i | ||||
\(191\) | 85.4671 | − | 148.033i | 0.447472 | − | 0.775044i | −0.550749 | − | 0.834671i | \(-0.685658\pi\) |
0.998221 | + | 0.0596272i | \(0.0189912\pi\) | |||||||
\(192\) | 62.6977 | + | 16.7998i | 0.326551 | + | 0.0874990i | ||||
\(193\) | −21.4527 | + | 80.0626i | −0.111154 | + | 0.414832i | −0.998970 | − | 0.0453656i | \(-0.985555\pi\) |
0.887817 | + | 0.460197i | \(0.152221\pi\) | |||||||
\(194\) | −39.5825 | − | 22.8530i | −0.204034 | − | 0.117799i | ||||
\(195\) | 88.3694 | + | 60.0032i | 0.453176 | + | 0.307709i | ||||
\(196\) | 391.508 | + | 138.490i | 1.99749 | + | 0.706582i | ||||
\(197\) | 32.0391 | − | 32.0391i | 0.162635 | − | 0.162635i | −0.621098 | − | 0.783733i | \(-0.713313\pi\) |
0.783733 | + | 0.621098i | \(0.213313\pi\) | |||||||
\(198\) | −178.526 | + | 47.8359i | −0.901646 | + | 0.241595i | ||||
\(199\) | −22.0307 | + | 12.7194i | −0.110707 | + | 0.0639167i | −0.554331 | − | 0.832296i | \(-0.687026\pi\) |
0.443624 | + | 0.896213i | \(0.353693\pi\) | |||||||
\(200\) | −392.498 | + | 45.7371i | −1.96249 | + | 0.228686i | ||||
\(201\) | 10.0996 | − | 17.4931i | 0.0502469 | − | 0.0870302i | ||||
\(202\) | 210.611 | − | 210.611i | 1.04263 | − | 1.04263i | ||||
\(203\) | −296.152 | − | 136.467i | −1.45888 | − | 0.672250i | ||||
\(204\) | 171.406i | 0.840227i | ||||||||
\(205\) | 65.2165 | + | 134.767i | 0.318129 | + | 0.657400i | ||||
\(206\) | −207.027 | − | 358.582i | −1.00499 | − | 1.74069i | ||||
\(207\) | −69.5671 | − | 18.6405i | −0.336073 | − | 0.0900505i | ||||
\(208\) | −261.233 | + | 69.9973i | −1.25593 | + | 0.336525i | ||||
\(209\) | 63.0221i | 0.301541i | ||||||||
\(210\) | −214.079 | + | 4.04722i | −1.01942 | + | 0.0192725i | ||||
\(211\) | 139.996 | 0.663487 | 0.331744 | − | 0.943370i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943370i | \(0.392363\pi\) | |||||||
\(212\) | −3.70587 | − | 13.8305i | −0.0174805 | − | 0.0652382i | ||||
\(213\) | −30.0981 | + | 112.328i | −0.141306 | + | 0.527360i | ||||
\(214\) | 437.148 | − | 252.388i | 2.04275 | − | 1.17938i | ||||
\(215\) | 45.7045 | − | 131.418i | 0.212579 | − | 0.611244i | ||||
\(216\) | 82.1312 | 0.380237 | ||||||||
\(217\) | 15.4058 | − | 1.41824i | 0.0709945 | − | 0.00653568i | ||||
\(218\) | −405.831 | − | 405.831i | −1.86161 | − | 1.86161i | ||||
\(219\) | 27.4128 | + | 15.8268i | 0.125173 | + | 0.0722685i | ||||
\(220\) | 53.8339 | − | 737.182i | 0.244699 | − | 3.35083i | ||||
\(221\) | 72.0102 | + | 124.725i | 0.325838 | + | 0.564368i | ||||
\(222\) | 48.1586 | + | 179.730i | 0.216931 | + | 0.809597i | ||||
\(223\) | 132.643 | + | 132.643i | 0.594809 | + | 0.594809i | 0.938927 | − | 0.344117i | \(-0.111822\pi\) |
−0.344117 | + | 0.938927i | \(0.611822\pi\) | |||||||
\(224\) | 63.6465 | − | 76.5532i | 0.284136 | − | 0.341755i | ||||
\(225\) | 69.7108 | − | 27.6660i | 0.309826 | − | 0.122960i | ||||
\(226\) | −7.72888 | + | 13.3868i | −0.0341986 | + | 0.0592337i | ||||
\(227\) | −237.143 | − | 63.5422i | −1.04468 | − | 0.279922i | −0.304629 | − | 0.952471i | \(-0.598533\pi\) |
−0.740052 | + | 0.672549i | \(0.765199\pi\) | |||||||
\(228\) | 13.7272 | − | 51.2305i | 0.0602069 | − | 0.224695i | ||||
\(229\) | −217.561 | − | 125.609i | −0.950047 | − | 0.548510i | −0.0569516 | − | 0.998377i | \(-0.518138\pi\) |
−0.893096 | + | 0.449867i | \(0.851471\pi\) | |||||||
\(230\) | 238.162 | − | 350.751i | 1.03549 | − | 1.52501i | ||||
\(231\) | 35.7788 | − | 208.433i | 0.154886 | − | 0.902308i | ||||
\(232\) | −520.643 | + | 520.643i | −2.24415 | + | 2.24415i | ||||
\(233\) | 285.430 | − | 76.4808i | 1.22502 | − | 0.328244i | 0.412383 | − | 0.911010i | \(-0.364696\pi\) |
0.812640 | + | 0.582767i | \(0.198030\pi\) | |||||||
\(234\) | 113.182 | − | 65.3457i | 0.483684 | − | 0.279255i | ||||
\(235\) | 310.041 | − | 267.841i | 1.31932 | − | 1.13975i | ||||
\(236\) | −374.600 | + | 648.827i | −1.58729 | + | 2.74927i | ||||
\(237\) | 27.4387 | − | 27.4387i | 0.115775 | − | 0.115775i | ||||
\(238\) | −262.198 | − | 120.821i | −1.10167 | − | 0.507650i | ||||
\(239\) | 100.831i | 0.421885i | 0.977498 | + | 0.210943i | \(0.0676533\pi\) | ||||
−0.977498 | + | 0.210943i | \(0.932347\pi\) | |||||||
\(240\) | −62.3770 | + | 179.357i | −0.259904 | + | 0.747321i | ||||
\(241\) | −179.672 | − | 311.201i | −0.745527 | − | 1.29129i | −0.949948 | − | 0.312408i | \(-0.898865\pi\) |
0.204421 | − | 0.978883i | \(-0.434469\pi\) | |||||||
\(242\) | 625.181 | + | 167.517i | 2.58339 | + | 0.692217i | ||||
\(243\) | −15.0573 | + | 4.03459i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | − | 397.160i | − | 1.62770i | ||||||
\(245\) | 98.3095 | − | 224.411i | 0.401263 | − | 0.915963i | ||||
\(246\) | 183.183 | 0.744647 | ||||||||
\(247\) | −11.5340 | − | 43.0453i | −0.0466962 | − | 0.174273i | ||||
\(248\) | 9.04153 | − | 33.7434i | 0.0364578 | − | 0.136062i | ||||
\(249\) | −111.248 | + | 64.2293i | −0.446781 | + | 0.257949i | ||||
\(250\) | 19.0263 | + | 441.091i | 0.0761051 | + | 1.76437i | ||||
\(251\) | 17.4715 | 0.0696075 | 0.0348038 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348038 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(252\) | −74.4844 | + | 161.642i | −0.295573 | + | 0.641435i | ||||
\(253\) | 296.100 | + | 296.100i | 1.17035 | + | 1.17035i | ||||
\(254\) | 509.038 | + | 293.893i | 2.00409 | + | 1.15706i | ||||
\(255\) | 100.855 | + | 7.36507i | 0.395509 | + | 0.0288826i | ||||
\(256\) | 259.270 | + | 449.070i | 1.01278 | + | 1.75418i | ||||
\(257\) | −20.6778 | − | 77.1706i | −0.0804583 | − | 0.300275i | 0.913957 | − | 0.405811i | \(-0.133011\pi\) |
−0.994415 | + | 0.105536i | \(0.966344\pi\) | |||||||
\(258\) | −120.377 | − | 120.377i | −0.466579 | − | 0.466579i | ||||
\(259\) | −209.839 | − | 36.0202i | −0.810191 | − | 0.139074i | ||||
\(260\) | 98.1454 | + | 513.362i | 0.377482 | + | 1.97447i | ||||
\(261\) | 69.8747 | − | 121.026i | 0.267719 | − | 0.463703i | ||||
\(262\) | −556.957 | − | 149.236i | −2.12579 | − | 0.569604i | ||||
\(263\) | −44.8686 | + | 167.452i | −0.170603 | + | 0.636699i | 0.826656 | + | 0.562708i | \(0.190240\pi\) |
−0.997259 | + | 0.0739911i | \(0.976426\pi\) | |||||||
\(264\) | −413.553 | − | 238.765i | −1.56649 | − | 0.904414i | ||||
\(265\) | −8.29704 | + | 1.58624i | −0.0313096 | + | 0.00598582i | ||||
\(266\) | 68.6907 | + | 57.1096i | 0.258236 | + | 0.214698i | ||||
\(267\) | 62.6154 | − | 62.6154i | 0.234514 | − | 0.234514i | ||||
\(268\) | 95.4694 | − | 25.5809i | 0.356229 | − | 0.0954513i | ||||
\(269\) | 160.485 | − | 92.6559i | 0.596597 | − | 0.344446i | −0.171104 | − | 0.985253i | \(-0.554734\pi\) |
0.767702 | + | 0.640807i | \(0.221400\pi\) | |||||||
\(270\) | 6.68344 | − | 91.5207i | 0.0247535 | − | 0.338965i | ||||
\(271\) | −182.223 | + | 315.620i | −0.672410 | + | 1.16465i | 0.304808 | + | 0.952414i | \(0.401408\pi\) |
−0.977219 | + | 0.212235i | \(0.931926\pi\) | |||||||
\(272\) | −181.045 | + | 181.045i | −0.665607 | + | 0.665607i | ||||
\(273\) | 13.7087 | + | 148.912i | 0.0502149 | + | 0.545465i | ||||
\(274\) | − | 522.152i | − | 1.90567i | ||||||
\(275\) | −431.441 | − | 63.3512i | −1.56888 | − | 0.230368i | ||||
\(276\) | −176.204 | − | 305.194i | −0.638420 | − | 1.10578i | ||||
\(277\) | −467.038 | − | 125.143i | −1.68606 | − | 0.451778i | −0.716691 | − | 0.697391i | \(-0.754344\pi\) |
−0.969368 | + | 0.245613i | \(0.921011\pi\) | |||||||
\(278\) | 346.464 | − | 92.8347i | 1.24627 | − | 0.333938i | ||||
\(279\) | 6.63041i | 0.0237649i | ||||||||
\(280\) | −398.507 | − | 383.719i | −1.42324 | − | 1.37042i | ||||
\(281\) | −472.914 | −1.68297 | −0.841484 | − | 0.540282i | \(-0.818318\pi\) | ||||
−0.841484 | + | 0.540282i | \(0.818318\pi\) | |||||||
\(282\) | −129.744 | − | 484.212i | −0.460086 | − | 1.71706i | ||||
\(283\) | 64.2640 | − | 239.837i | 0.227081 | − | 0.847479i | −0.754479 | − | 0.656324i | \(-0.772110\pi\) |
0.981560 | − | 0.191154i | \(-0.0612231\pi\) | |||||||
\(284\) | −492.786 | + | 284.510i | −1.73516 | + | 1.00180i | ||||
\(285\) | −29.5540 | − | 10.2783i | −0.103698 | − | 0.0360643i | ||||
\(286\) | −759.870 | −2.65689 | ||||||||
\(287\) | −87.7205 | + | 190.366i | −0.305646 | + | 0.663296i | ||||
\(288\) | 30.1698 | + | 30.1698i | 0.104756 | + | 0.104756i | ||||
\(289\) | −132.203 | − | 76.3272i | −0.457449 | − | 0.264108i | ||||
\(290\) | 537.797 | + | 622.531i | 1.85447 | + | 2.14666i | ||||
\(291\) | 11.2068 | + | 19.4107i | 0.0385113 | + | 0.0667036i | ||||
\(292\) | 40.0871 | + | 149.607i | 0.137284 | + | 0.512353i | ||||
\(293\) | 61.1515 | + | 61.1515i | 0.208708 | + | 0.208708i | 0.803718 | − | 0.595010i | \(-0.202852\pi\) |
−0.595010 | + | 0.803718i | \(0.702852\pi\) | |||||||
\(294\) | −194.759 | − | 227.876i | −0.662444 | − | 0.775087i | ||||
\(295\) | 365.671 | + | 248.292i | 1.23956 | + | 0.841669i | ||||
\(296\) | −240.376 | + | 416.344i | −0.812082 | + | 1.40657i | ||||
\(297\) | 87.5467 | + | 23.4581i | 0.294770 | + | 0.0789834i | ||||
\(298\) | −96.8649 | + | 361.505i | −0.325050 | + | 1.21310i | ||||
\(299\) | −256.433 | − | 148.051i | −0.857634 | − | 0.495155i | ||||
\(300\) | 336.919 | + | 145.473i | 1.12306 | + | 0.484909i | ||||
\(301\) | 182.742 | − | 67.4526i | 0.607117 | − | 0.224095i | ||||
\(302\) | 402.521 | − | 402.521i | 1.33285 | − | 1.33285i | ||||
\(303\) | −141.084 | + | 37.8034i | −0.465624 | + | 0.124764i | ||||
\(304\) | 68.6106 | − | 39.6123i | 0.225693 | − | 0.130304i | ||||
\(305\) | −233.687 | − | 17.0654i | −0.766187 | − | 0.0559521i | ||||
\(306\) | 61.8634 | − | 107.151i | 0.202168 | − | 0.350165i | ||||
\(307\) | −36.7448 | + | 36.7448i | −0.119690 | + | 0.119690i | −0.764415 | − | 0.644725i | \(-0.776972\pi\) |
0.644725 | + | 0.764415i | \(0.276972\pi\) | |||||||
\(308\) | 844.961 | − | 597.375i | 2.74338 | − | 1.93953i | ||||
\(309\) | 203.047i | 0.657110i | ||||||||
\(310\) | −36.8653 | − | 12.8211i | −0.118920 | − | 0.0413582i | ||||
\(311\) | −44.4761 | − | 77.0348i | −0.143010 | − | 0.247700i | 0.785619 | − | 0.618711i | \(-0.212345\pi\) |
−0.928629 | + | 0.371010i | \(0.879011\pi\) | |||||||
\(312\) | 326.163 | + | 87.3950i | 1.04539 | + | 0.280112i | ||||
\(313\) | −177.500 | + | 47.5609i | −0.567092 | + | 0.151952i | −0.530962 | − | 0.847395i | \(-0.678169\pi\) |
−0.0361293 | + | 0.999347i | \(0.511503\pi\) | |||||||
\(314\) | − | 485.224i | − | 1.54530i | ||||||
\(315\) | 91.9088 | + | 50.7718i | 0.291774 | + | 0.161180i | ||||
\(316\) | 189.873 | 0.600864 | ||||||||
\(317\) | 95.4002 | + | 356.038i | 0.300947 | + | 1.12315i | 0.936378 | + | 0.350992i | \(0.114156\pi\) |
−0.635431 | + | 0.772157i | \(0.719178\pi\) | |||||||
\(318\) | −2.67502 | + | 9.98333i | −0.00841203 | + | 0.0313941i | ||||
\(319\) | −703.676 | + | 406.268i | −2.20588 | + | 1.27357i | ||||
\(320\) | 168.666 | − | 81.6211i | 0.527082 | − | 0.255066i | ||||
\(321\) | −247.535 | −0.771137 | ||||||||
\(322\) | 591.054 | − | 54.4118i | 1.83557 | − | 0.168981i | ||||
\(323\) | −29.8321 | − | 29.8321i | −0.0923596 | − | 0.0923596i | ||||
\(324\) | −66.0570 | − | 38.1380i | −0.203880 | − | 0.117710i | ||||
\(325\) | 306.277 | − | 35.6899i | 0.942391 | − | 0.109815i | ||||
\(326\) | −333.540 | − | 577.709i | −1.02313 | − | 1.77211i | ||||
\(327\) | 72.8442 | + | 271.858i | 0.222765 | + | 0.831371i | ||||
\(328\) | 334.668 | + | 334.668i | 1.02033 | + | 1.02033i | ||||
\(329\) | 565.329 | + | 97.0420i | 1.71832 | + | 0.294961i | ||||
\(330\) | −299.714 | + | 441.402i | −0.908225 | + | 1.33758i | ||||
\(331\) | 224.992 | − | 389.697i | 0.679734 | − | 1.17733i | −0.295327 | − | 0.955396i | \(-0.595429\pi\) |
0.975061 | − | 0.221937i | \(-0.0712381\pi\) | |||||||
\(332\) | −607.145 | − | 162.684i | −1.82875 | − | 0.490012i | ||||
\(333\) | 23.6163 | − | 88.1374i | 0.0709199 | − | 0.264677i | ||||
\(334\) | 493.805 | + | 285.099i | 1.47846 | + | 0.853589i | ||||
\(335\) | −10.9495 | − | 57.2729i | −0.0326852 | − | 0.170964i | ||||
\(336\) | −249.404 | + | 92.0585i | −0.742275 | + | 0.273984i | ||||
\(337\) | −9.37231 | + | 9.37231i | −0.0278110 | + | 0.0278110i | −0.720876 | − | 0.693065i | \(-0.756260\pi\) |
0.693065 | + | 0.720876i | \(0.256260\pi\) | |||||||
\(338\) | −57.5646 | + | 15.4244i | −0.170309 | + | 0.0456343i | ||||
\(339\) | 6.56471 | − | 3.79014i | 0.0193649 | − | 0.0111804i | ||||
\(340\) | 323.470 | + | 374.435i | 0.951381 | + | 1.10128i | ||||
\(341\) | 19.2754 | − | 33.3859i | 0.0565260 | − | 0.0979060i | ||||
\(342\) | −27.0712 | + | 27.0712i | −0.0791556 | + | 0.0791556i | ||||
\(343\) | 330.074 | − | 93.2729i | 0.962316 | − | 0.271933i | ||||
\(344\) | − | 439.849i | − | 1.27863i | ||||||
\(345\) | −187.146 | + | 90.5638i | −0.542452 | + | 0.262504i | ||||
\(346\) | 368.126 | + | 637.613i | 1.06395 | + | 1.84281i | ||||
\(347\) | 378.650 | + | 101.459i | 1.09121 | + | 0.292389i | 0.759180 | − | 0.650880i | \(-0.225600\pi\) |
0.332029 | + | 0.943269i | \(0.392267\pi\) | |||||||
\(348\) | 660.509 | − | 176.983i | 1.89801 | − | 0.508571i | ||||
\(349\) | − | 480.726i | − | 1.37744i | −0.725028 | − | 0.688720i | \(-0.758173\pi\) | ||
0.725028 | − | 0.688720i | \(-0.241827\pi\) | |||||||
\(350\) | −460.015 | + | 412.840i | −1.31433 | + | 1.17954i | ||||
\(351\) | −64.0893 | −0.182590 | ||||||||
\(352\) | −64.2062 | − | 239.621i | −0.182404 | − | 0.680741i | ||||
\(353\) | −143.459 | + | 535.395i | −0.406398 | + | 1.51670i | 0.395064 | + | 0.918654i | \(0.370722\pi\) |
−0.801462 | + | 0.598045i | \(0.795944\pi\) | |||||||
\(354\) | 468.345 | − | 270.399i | 1.32301 | − | 0.763840i | ||||
\(355\) | 146.230 | + | 302.178i | 0.411917 | + | 0.851207i | ||||
\(356\) | 433.292 | 1.21711 | ||||||||
\(357\) | 81.7276 | + | 115.600i | 0.228929 | + | 0.323810i | ||||
\(358\) | −296.944 | − | 296.944i | −0.829454 | − | 0.829454i | ||||
\(359\) | 87.7247 | + | 50.6479i | 0.244359 | + | 0.141080i | 0.617178 | − | 0.786823i | \(-0.288276\pi\) |
−0.372820 | + | 0.927904i | \(0.621609\pi\) | |||||||
\(360\) | 179.415 | − | 154.994i | 0.498374 | − | 0.430539i | ||||
\(361\) | −173.973 | − | 301.330i | −0.481919 | − | 0.834708i | ||||
\(362\) | 1.95062 | + | 7.27983i | 0.00538846 | + | 0.0201100i | ||||
\(363\) | −224.432 | − | 224.432i | −0.618270 | − | 0.618270i | ||||
\(364\) | −467.797 | + | 562.659i | −1.28516 | + | 1.54577i | ||||
\(365\) | 89.7506 | − | 17.1587i | 0.245892 | − | 0.0470100i | ||||
\(366\) | −143.342 | + | 248.275i | −0.391644 | + | 0.678348i | ||||
\(367\) | 294.332 | + | 78.8661i | 0.801996 | + | 0.214894i | 0.636460 | − | 0.771310i | \(-0.280398\pi\) |
0.165536 | + | 0.986204i | \(0.447065\pi\) | |||||||
\(368\) | 136.244 | − | 508.469i | 0.370228 | − | 1.38171i | ||||
\(369\) | −77.7955 | − | 44.9153i | −0.210828 | − | 0.121722i | ||||
\(370\) | 444.381 | + | 301.737i | 1.20103 | + | 0.815505i | ||||
\(371\) | −9.09379 | − | 7.56061i | −0.0245116 | − | 0.0203790i | ||||
\(372\) | −22.9409 | + | 22.9409i | −0.0616691 | + | 0.0616691i | ||||
\(373\) | −103.576 | + | 27.7530i | −0.277682 | + | 0.0744048i | −0.394973 | − | 0.918693i | \(-0.629246\pi\) |
0.117290 | + | 0.993098i | \(0.462579\pi\) | |||||||
\(374\) | −622.999 | + | 359.689i | −1.66577 | + | 0.961734i | ||||
\(375\) | 100.072 | − | 191.991i | 0.266860 | − | 0.511976i | ||||
\(376\) | 647.598 | − | 1121.67i | 1.72234 | − | 2.98317i | ||||
\(377\) | 406.272 | − | 406.272i | 1.07764 | − | 1.07764i | ||||
\(378\) | 104.901 | − | 74.1638i | 0.277517 | − | 0.196201i | ||||
\(379\) | 0 | 5.00789e-5i | 0 | 1.32134e-7i | −1.00000 | 6.60672e-8i | \(-1.00000\pi\) | |||
1.00000 | 6.60672e-8i | \(-2.10298e-8\pi\) | ||||||||
\(380\) | −66.6929 | − | 137.818i | −0.175508 | − | 0.362679i | ||||
\(381\) | −144.121 | − | 249.625i | −0.378271 | − | 0.655184i | ||||
\(382\) | −583.170 | − | 156.260i | −1.52662 | − | 0.409057i | ||||
\(383\) | −181.989 | + | 48.7638i | −0.475167 | + | 0.127321i | −0.488451 | − | 0.872591i | \(-0.662438\pi\) |
0.0132843 | + | 0.999912i | \(0.495771\pi\) | |||||||
\(384\) | − | 327.795i | − | 0.853633i | ||||||
\(385\) | −315.186 | − | 522.840i | −0.818666 | − | 1.35803i | ||||
\(386\) | 292.757 | 0.758439 | ||||||||
\(387\) | 21.6070 | + | 80.6384i | 0.0558320 | + | 0.208368i | ||||
\(388\) | −28.3852 | + | 105.935i | −0.0731578 | + | 0.273029i | ||||
\(389\) | −182.547 | + | 105.394i | −0.469273 | + | 0.270935i | −0.715935 | − | 0.698166i | \(-0.754000\pi\) |
0.246662 | + | 0.969102i | \(0.420666\pi\) | |||||||
\(390\) | 123.928 | − | 356.339i | 0.317763 | − | 0.913689i | ||||
\(391\) | −280.324 | −0.716940 | ||||||||
\(392\) | 60.5035 | − | 772.135i | 0.154346 | − | 1.96973i | ||||
\(393\) | 199.941 | + | 199.941i | 0.508755 | + | 0.508755i | ||||
\(394\) | −138.595 | − | 80.0181i | −0.351765 | − | 0.203092i | ||||
\(395\) | 8.15856 | − | 111.720i | 0.0206546 | − | 0.282837i | ||||
\(396\) | 221.743 | + | 384.071i | 0.559958 | + | 0.969876i | ||||
\(397\) | 64.9229 | + | 242.295i | 0.163534 | + | 0.610316i | 0.998223 | + | 0.0595944i | \(0.0189807\pi\) |
−0.834689 | + | 0.550722i | \(0.814353\pi\) | |||||||
\(398\) | 63.5338 | + | 63.5338i | 0.159633 | + | 0.159633i | ||||
\(399\) | −15.1692 | − | 41.0962i | −0.0380179 | − | 0.102998i | ||||
\(400\) | 202.212 | + | 509.519i | 0.505530 | + | 1.27380i | ||||
\(401\) | 172.876 | − | 299.430i | 0.431113 | − | 0.746709i | −0.565857 | − | 0.824503i | \(-0.691455\pi\) |
0.996969 | + | 0.0777947i | \(0.0247879\pi\) | |||||||
\(402\) | −68.9130 | − | 18.4652i | −0.171425 | − | 0.0459333i | ||||
\(403\) | −7.05535 | + | 26.3309i | −0.0175071 | + | 0.0653373i | ||||
\(404\) | −618.942 | − | 357.346i | −1.53203 | − | 0.884520i | ||||
\(405\) | −25.2786 | + | 37.2289i | −0.0624163 | + | 0.0919232i | ||||
\(406\) | −194.851 | + | 1135.12i | −0.479928 | + | 2.79587i | ||||
\(407\) | −375.141 | + | 375.141i | −0.921721 | + | 0.921721i | ||||
\(408\) | 308.782 | − | 82.7378i | 0.756818 | − | 0.202789i | ||||
\(409\) | 98.4923 | − | 56.8646i | 0.240812 | − | 0.139033i | −0.374738 | − | 0.927131i | \(-0.622267\pi\) |
0.615550 | + | 0.788098i | \(0.288934\pi\) | |||||||
\(410\) | 400.162 | − | 345.694i | 0.976004 | − | 0.843157i | ||||
\(411\) | −128.028 | + | 221.751i | −0.311504 | + | 0.539541i | ||||
\(412\) | −702.532 | + | 702.532i | −1.70518 | + | 1.70518i | ||||
\(413\) | 56.7263 | + | 616.195i | 0.137352 | + | 1.49200i | ||||
\(414\) | 254.380i | 0.614444i | ||||||||
\(415\) | −121.811 | + | 350.251i | −0.293520 | + | 0.843978i | ||||
\(416\) | 87.7081 | + | 151.915i | 0.210837 | + | 0.365180i | ||||
\(417\) | −169.901 | − | 45.5249i | −0.407437 | − | 0.109172i | ||||
\(418\) | 215.010 | − | 57.6118i | 0.514378 | − | 0.137827i | ||||
\(419\) | 220.394i | 0.526000i | 0.964796 | + | 0.263000i | \(0.0847120\pi\) | ||||
−0.964796 | + | 0.263000i | \(0.915288\pi\) | |||||||
\(420\) | 142.332 | + | 493.668i | 0.338885 | + | 1.17540i | ||||
\(421\) | −611.981 | −1.45364 | −0.726818 | − | 0.686830i | \(-0.759002\pi\) | ||||
−0.726818 | + | 0.686830i | \(0.759002\pi\) | |||||||
\(422\) | −127.977 | − | 477.618i | −0.303264 | − | 1.13180i | ||||
\(423\) | −63.6248 | + | 237.451i | −0.150413 | + | 0.561350i | ||||
\(424\) | −23.1263 | + | 13.3520i | −0.0545431 | + | 0.0314905i | ||||
\(425\) | 234.215 | − | 174.239i | 0.551094 | − | 0.409974i | ||||
\(426\) | 410.739 | 0.964175 | ||||||||
\(427\) | −189.368 | − | 267.853i | −0.443486 | − | 0.627291i | ||||
\(428\) | −856.459 | − | 856.459i | −2.00107 | − | 2.00107i | ||||
\(429\) | 322.707 | + | 186.315i | 0.752231 | + | 0.434301i | ||||
\(430\) | −490.133 | − | 35.7928i | −1.13984 | − | 0.0832390i | ||||
\(431\) | 362.392 | + | 627.681i | 0.840816 | + | 1.45634i | 0.889206 | + | 0.457508i | \(0.151258\pi\) |
−0.0483893 | + | 0.998829i | \(0.515409\pi\) | |||||||
\(432\) | −29.4890 | − | 110.054i | −0.0682615 | − | 0.254755i | ||||
\(433\) | −152.433 | − | 152.433i | −0.352038 | − | 0.352038i | 0.508829 | − | 0.860867i | \(-0.330078\pi\) |
−0.860867 | + | 0.508829i | \(0.830078\pi\) | |||||||
\(434\) | −18.9218 | − | 51.2629i | −0.0435987 | − | 0.118117i | ||||
\(435\) | −75.7548 | − | 396.245i | −0.174149 | − | 0.910908i | ||||
\(436\) | −688.579 | + | 1192.65i | −1.57931 | + | 2.73545i | ||||
\(437\) | 83.7842 | + | 22.4499i | 0.191726 | + | 0.0513728i | ||||
\(438\) | 28.9362 | − | 107.991i | 0.0660644 | − | 0.246556i | ||||
\(439\) | 719.426 | + | 415.361i | 1.63878 | + | 0.946152i | 0.981253 | + | 0.192723i | \(0.0617320\pi\) |
0.657530 | + | 0.753428i | \(0.271601\pi\) | |||||||
\(440\) | −1353.99 | + | 258.858i | −3.07725 | + | 0.588313i | ||||
\(441\) | 26.8379 | + | 144.529i | 0.0608569 | + | 0.327731i | ||||
\(442\) | 359.692 | − | 359.692i | 0.813783 | − | 0.813783i | ||||
\(443\) | 321.426 | − | 86.1258i | 0.725566 | − | 0.194415i | 0.122912 | − | 0.992418i | \(-0.460777\pi\) |
0.602654 | + | 0.798003i | \(0.294110\pi\) | |||||||
\(444\) | 386.662 | − | 223.240i | 0.870861 | − | 0.502792i | ||||
\(445\) | 18.6179 | − | 254.947i | 0.0418380 | − | 0.572915i | ||||
\(446\) | 331.276 | − | 573.787i | 0.742771 | − | 1.28652i | ||||
\(447\) | 129.776 | − | 129.776i | 0.290326 | − | 0.290326i | ||||
\(448\) | 238.250 | + | 109.786i | 0.531809 | + | 0.245057i | ||||
\(449\) | − | 20.5616i | − | 0.0457943i | −0.999738 | − | 0.0228971i | \(-0.992711\pi\) | ||
0.999738 | − | 0.0228971i | \(-0.00728902\pi\) | |||||||
\(450\) | −158.113 | − | 212.539i | −0.351363 | − | 0.472308i | ||||
\(451\) | 261.148 | + | 452.321i | 0.579042 | + | 1.00293i | ||||
\(452\) | 35.8273 | + | 9.59989i | 0.0792639 | + | 0.0212387i | ||||
\(453\) | −269.641 | + | 72.2501i | −0.595234 | + | 0.159492i | ||||
\(454\) | 867.138i | 1.91000i | ||||||||
\(455\) | 310.966 | + | 299.426i | 0.683441 | + | 0.658079i | ||||
\(456\) | −98.9159 | −0.216921 | ||||||||
\(457\) | −139.721 | − | 521.445i | −0.305734 | − | 1.14102i | −0.932311 | − | 0.361657i | \(-0.882211\pi\) |
0.626577 | − | 0.779360i | \(-0.284455\pi\) | |||||||
\(458\) | −229.651 | + | 857.070i | −0.501422 | + | 1.87133i | ||||
\(459\) | −52.5452 | + | 30.3370i | −0.114478 | + | 0.0660936i | ||||
\(460\) | −960.863 | − | 334.170i | −2.08883 | − | 0.726456i | ||||
\(461\) | 650.544 | 1.41116 | 0.705579 | − | 0.708632i | \(-0.250687\pi\) | ||||
0.705579 | + | 0.708632i | \(0.250687\pi\) | |||||||
\(462\) | −743.811 | + | 68.4744i | −1.60998 | + | 0.148213i | ||||
\(463\) | 229.971 | + | 229.971i | 0.496697 | + | 0.496697i | 0.910408 | − | 0.413711i | \(-0.135768\pi\) |
−0.413711 | + | 0.910408i | \(0.635768\pi\) | |||||||
\(464\) | 884.587 | + | 510.717i | 1.90644 | + | 1.10068i | ||||
\(465\) | 12.5126 | + | 14.4841i | 0.0269088 | + | 0.0311485i | ||||
\(466\) | −521.854 | − | 903.877i | −1.11986 | − | 1.93965i | ||||
\(467\) | −151.133 | − | 564.037i | −0.323626 | − | 1.20779i | −0.915686 | − | 0.401895i | \(-0.868352\pi\) |
0.592060 | − | 0.805894i | \(-0.298315\pi\) | |||||||
\(468\) | −221.746 | − | 221.746i | −0.473816 | − | 0.473816i | ||||
\(469\) | 52.1895 | − | 62.7728i | 0.111278 | − | 0.133844i | ||||
\(470\) | −1197.21 | − | 812.909i | −2.54725 | − | 1.72959i | ||||
\(471\) | −118.974 | + | 206.069i | −0.252598 | + | 0.437513i | ||||
\(472\) | 1349.66 | + | 361.639i | 2.85944 | + | 0.766184i | ||||
\(473\) | 125.628 | − | 468.851i | 0.265599 | − | 0.991228i | ||||
\(474\) | −118.695 | − | 68.5284i | −0.250411 | − | 0.144575i | ||||
\(475\) | −83.9571 | + | 33.3200i | −0.176752 | + | 0.0701473i | ||||
\(476\) | −117.197 | + | 682.744i | −0.246212 | + | 1.43434i | ||||
\(477\) | 3.58389 | − | 3.58389i | 0.00751340 | − | 0.00751340i | ||||
\(478\) | 344.000 | − | 92.1745i | 0.719665 | − | 0.192834i | ||||
\(479\) | −255.740 | + | 147.651i | −0.533904 | + | 0.308249i | −0.742605 | − | 0.669730i | \(-0.766410\pi\) |
0.208701 | + | 0.977980i | \(0.433076\pi\) | |||||||
\(480\) | 122.841 | + | 8.97064i | 0.255918 | + | 0.0186888i | ||||
\(481\) | 187.572 | − | 324.885i | 0.389963 | − | 0.675436i | ||||
\(482\) | −897.465 | + | 897.465i | −1.86196 | + | 1.86196i | ||||
\(483\) | −264.354 | − | 121.814i | −0.547317 | − | 0.252204i | ||||
\(484\) | − | 1553.05i | − | 3.20878i | ||||||
\(485\) | 61.1121 | + | 21.2536i | 0.126004 | + | 0.0438219i | ||||
\(486\) | 27.5293 | + | 47.6822i | 0.0566447 | + | 0.0981115i | ||||
\(487\) | 31.9767 | + | 8.56814i | 0.0656606 | + | 0.0175937i | 0.291500 | − | 0.956571i | \(-0.405846\pi\) |
−0.225839 | + | 0.974165i | \(0.572512\pi\) | |||||||
\(488\) | −715.468 | + | 191.709i | −1.46612 | + | 0.392846i | ||||
\(489\) | 327.127i | 0.668972i | ||||||||
\(490\) | −855.484 | − | 130.253i | −1.74589 | − | 0.265822i | ||||
\(491\) | 602.433 | 1.22695 | 0.613476 | − | 0.789713i | \(-0.289771\pi\) | ||||
0.613476 | + | 0.789713i | \(0.289771\pi\) | |||||||
\(492\) | −113.764 | − | 424.573i | −0.231228 | − | 0.862954i | ||||
\(493\) | 140.781 | − | 525.403i | 0.285561 | − | 1.06573i | ||||
\(494\) | −136.312 | + | 78.7000i | −0.275936 | + | 0.159312i | ||||
\(495\) | 235.514 | − | 113.970i | 0.475785 | − | 0.230242i | ||||
\(496\) | −48.4619 | −0.0977055 | ||||||||
\(497\) | −196.689 | + | 426.844i | −0.395754 | + | 0.858841i | ||||
\(498\) | 320.827 | + | 320.827i | 0.644231 | + | 0.644231i | ||||
\(499\) | −712.187 | − | 411.181i | −1.42723 | − | 0.824010i | −0.430326 | − | 0.902673i | \(-0.641602\pi\) |
−0.996901 | + | 0.0786631i | \(0.974935\pi\) | |||||||
\(500\) | 1010.52 | − | 318.034i | 2.02105 | − | 0.636067i | ||||
\(501\) | −139.808 | − | 242.155i | −0.279059 | − | 0.483344i | ||||
\(502\) | −15.9716 | − | 59.6068i | −0.0318159 | − | 0.118739i | ||||
\(503\) | −494.995 | − | 494.995i | −0.984086 | − | 0.984086i | 0.0157893 | − | 0.999875i | \(-0.494974\pi\) |
−0.999875 | + | 0.0157893i | \(0.994974\pi\) | |||||||
\(504\) | 327.145 | + | 56.1563i | 0.649097 | + | 0.111421i | ||||
\(505\) | −236.856 | + | 348.828i | −0.469022 | + | 0.690749i | ||||
\(506\) | 739.512 | − | 1280.87i | 1.46149 | − | 2.53137i | ||||
\(507\) | 28.2289 | + | 7.56391i | 0.0556783 | + | 0.0149190i | ||||
\(508\) | 365.039 | − | 1362.34i | 0.718580 | − | 2.68178i | ||||
\(509\) | 503.114 | + | 290.473i | 0.988437 | + | 0.570674i | 0.904807 | − | 0.425823i | \(-0.140015\pi\) |
0.0836299 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(510\) | −67.0694 | − | 350.815i | −0.131509 | − | 0.687873i | ||||
\(511\) | 98.3692 | + | 81.7844i | 0.192503 | + | 0.160048i | ||||
\(512\) | 759.774 | − | 759.774i | 1.48393 | − | 1.48393i | ||||
\(513\) | 18.1345 | − | 4.85911i | 0.0353498 | − | 0.00947196i | ||||
\(514\) | −244.377 | + | 141.091i | −0.475442 | + | 0.274497i | ||||
\(515\) | 383.180 | + | 443.554i | 0.744039 | + | 0.861269i | ||||
\(516\) | −204.246 | + | 353.764i | −0.395825 | + | 0.685589i | ||||
\(517\) | 1010.67 | − | 1010.67i | 1.95487 | − | 1.95487i | ||||
\(518\) | 68.9365 | + | 748.829i | 0.133082 | + | 1.44562i | ||||
\(519\) | − | 361.048i | − | 0.695660i | ||||||
\(520\) | 877.426 | − | 424.605i | 1.68736 | − | 0.816548i | ||||
\(521\) | −274.035 | − | 474.643i | −0.525979 | − | 0.911023i | −0.999542 | − | 0.0302629i | \(-0.990366\pi\) |
0.473563 | − | 0.880760i | \(-0.342968\pi\) | |||||||
\(522\) | −476.778 | − | 127.752i | −0.913367 | − | 0.244736i | ||||
\(523\) | −227.240 | + | 60.8889i | −0.434494 | + | 0.116422i | −0.469435 | − | 0.882967i | \(-0.655542\pi\) |
0.0349409 | + | 0.999389i | \(0.488876\pi\) | |||||||
\(524\) | 1383.57i | 2.64040i | ||||||||
\(525\) | 296.588 | − | 62.5353i | 0.564929 | − | 0.119115i | ||||
\(526\) | 612.306 | 1.16408 | ||||||||
\(527\) | 6.67937 | + | 24.9278i | 0.0126743 | + | 0.0473013i | ||||
\(528\) | −171.456 | + | 639.882i | −0.324727 | + | 1.21190i | ||||
\(529\) | 40.9971 | − | 23.6697i | 0.0774992 | − | 0.0447442i | ||||
\(530\) | 12.9965 | + | 26.8566i | 0.0245217 | + | 0.0506729i | ||||
\(531\) | −265.200 | −0.499435 | ||||||||
\(532\) | 89.7064 | − | 194.675i | 0.168621 | − | 0.365931i | ||||
\(533\) | −261.151 | − | 261.151i | −0.489964 | − | 0.489964i | ||||
\(534\) | −270.862 | − | 156.382i | −0.507233 | − | 0.292851i | ||||
\(535\) | −540.738 | + | 467.136i | −1.01072 | + | 0.873152i | ||||
\(536\) | −92.1661 | − | 159.636i | −0.171952 | − | 0.297829i | ||||
\(537\) | 53.2997 | + | 198.917i | 0.0992546 | + | 0.370423i | ||||
\(538\) | −462.818 | − | 462.818i | −0.860256 | − | 0.860256i | ||||
\(539\) | 285.028 | − | 805.766i | 0.528808 | − | 1.49493i | ||||
\(540\) | −216.273 | + | 41.3474i | −0.400506 | + | 0.0765693i | ||||
\(541\) | 261.735 | − | 453.339i | 0.483799 | − | 0.837965i | −0.516028 | − | 0.856572i | \(-0.672590\pi\) |
0.999827 | + | 0.0186072i | \(0.00592319\pi\) | |||||||
\(542\) | 1243.37 | + | 333.159i | 2.29404 | + | 0.614685i | ||||
\(543\) | 0.956559 | − | 3.56993i | 0.00176162 | − | 0.00657445i | ||||
\(544\) | 143.819 | + | 83.0342i | 0.264374 | + | 0.152636i | ||||
\(545\) | 672.165 | + | 456.404i | 1.23333 | + | 0.837438i | ||||
\(546\) | 495.505 | − | 182.898i | 0.907519 | − | 0.334977i | ||||
\(547\) | −201.681 | + | 201.681i | −0.368703 | + | 0.368703i | −0.867004 | − | 0.498301i | \(-0.833958\pi\) |
0.498301 | + | 0.867004i | \(0.333958\pi\) | |||||||
\(548\) | −1210.22 | + | 324.277i | −2.20843 | + | 0.591747i | ||||
\(549\) | 121.751 | − | 70.2928i | 0.221768 | − | 0.128038i | ||||
\(550\) | 178.270 | + | 1529.84i | 0.324127 | + | 2.78154i | ||||
\(551\) | −84.1545 | + | 145.760i | −0.152731 | + | 0.264537i | ||||
\(552\) | −464.741 | + | 464.741i | −0.841923 | + | 0.841923i | ||||
\(553\) | 128.054 | − | 90.5327i | 0.231563 | − | 0.163712i | ||||
\(554\) | 1707.78i | 3.08263i | ||||||||
\(555\) | −114.739 | − | 237.103i | −0.206737 | − | 0.427212i | ||||
\(556\) | −430.336 | − | 745.364i | −0.773985 | − | 1.34058i | ||||
\(557\) | −666.065 | − | 178.472i | −1.19581 | − | 0.320416i | −0.394629 | − | 0.918841i | \(-0.629127\pi\) |
−0.801179 | + | 0.598425i | \(0.795793\pi\) | |||||||
\(558\) | 22.6207 | − | 6.06120i | 0.0405389 | − | 0.0108624i | ||||
\(559\) | 343.226i | 0.614000i | ||||||||
\(560\) | −371.093 | + | 671.765i | −0.662666 | + | 1.19958i | ||||
\(561\) | 352.773 | 0.628828 | ||||||||
\(562\) | 432.315 | + | 1613.42i | 0.769244 | + | 2.87086i | ||||
\(563\) | 198.059 | − | 739.166i | 0.351792 | − | 1.31291i | −0.532682 | − | 0.846315i | \(-0.678816\pi\) |
0.884474 | − | 0.466590i | \(-0.154517\pi\) | |||||||
\(564\) | −1041.71 | + | 601.430i | −1.84700 | + | 1.06637i | ||||
\(565\) | 7.18798 | − | 20.6681i | 0.0127221 | − | 0.0365808i | ||||
\(566\) | −876.988 | −1.54945 | ||||||||
\(567\) | −62.7347 | + | 5.77530i | −0.110643 | + | 0.0101857i | ||||
\(568\) | 750.402 | + | 750.402i | 1.32113 | + | 1.32113i | ||||
\(569\) | 116.121 | + | 67.0425i | 0.204079 | + | 0.117825i | 0.598557 | − | 0.801080i | \(-0.295741\pi\) |
−0.394478 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(570\) | −8.04930 | + | 110.224i | −0.0141216 | + | 0.193376i | ||||
\(571\) | −286.520 | − | 496.267i | −0.501786 | − | 0.869119i | −0.999998 | − | 0.00206333i | \(-0.999343\pi\) |
0.498212 | − | 0.867055i | \(-0.333990\pi\) | |||||||
\(572\) | 471.910 | + | 1761.19i | 0.825017 | + | 3.07901i | ||||
\(573\) | 209.351 | + | 209.351i | 0.365359 | + | 0.365359i | ||||
\(574\) | 729.654 | + | 125.249i | 1.27117 | + | 0.218205i | ||||
\(575\) | −237.911 | + | 551.009i | −0.413758 | + | 0.958276i | ||||
\(576\) | −56.2132 | + | 97.3642i | −0.0975924 | + | 0.169035i | ||||
\(577\) | 666.742 | + | 178.653i | 1.15553 | + | 0.309624i | 0.785180 | − | 0.619268i | \(-0.212570\pi\) |
0.370352 | + | 0.928891i | \(0.379237\pi\) | |||||||
\(578\) | −139.549 | + | 520.805i | −0.241435 | + | 0.901048i | ||||
\(579\) | −124.330 | − | 71.7821i | −0.214733 | − | 0.123976i | ||||
\(580\) | 1108.88 | − | 1633.10i | 1.91186 | − | 2.81568i | ||||
\(581\) | −487.040 | + | 179.773i | −0.838280 | + | 0.309420i | ||||
\(582\) | 55.9782 | − | 55.9782i | 0.0961824 | − | 0.0961824i | ||||
\(583\) | −28.4647 | + | 7.62709i | −0.0488245 | + | 0.0130825i | ||||
\(584\) | 250.161 | − | 144.430i | 0.428358 | − | 0.247312i | ||||
\(585\) | −140.002 | + | 120.946i | −0.239320 | + | 0.206745i | ||||
\(586\) | 152.726 | − | 264.530i | 0.260625 | − | 0.451416i | ||||
\(587\) | 688.633 | − | 688.633i | 1.17314 | − | 1.17314i | 0.191682 | − | 0.981457i | \(-0.438606\pi\) |
0.981457 | − | 0.191682i | \(-0.0613942\pi\) | |||||||
\(588\) | −407.207 | + | 592.922i | −0.692528 | + | 1.00837i | ||||
\(589\) | − | 7.98542i | − | 0.0135576i | ||||||
\(590\) | 512.811 | − | 1474.52i | 0.869171 | − | 2.49919i | ||||
\(591\) | 39.2398 | + | 67.9653i | 0.0663955 | + | 0.115000i | ||||
\(592\) | 644.199 | + | 172.613i | 1.08817 | + | 0.291576i | ||||
\(593\) | 375.748 | − | 100.681i | 0.633640 | − | 0.169783i | 0.0723188 | − | 0.997382i | \(-0.476960\pi\) |
0.561321 | + | 0.827598i | \(0.310293\pi\) | |||||||
\(594\) | − | 320.124i | − | 0.538929i | ||||||
\(595\) | 396.688 | + | 98.2948i | 0.666703 | + | 0.165201i | ||||
\(596\) | 898.035 | 1.50677 | ||||||||
\(597\) | −11.4039 | − | 42.5600i | −0.0191021 | − | 0.0712898i | ||||
\(598\) | −270.683 | + | 1010.20i | −0.452647 | + | 1.68930i | ||||
\(599\) | −223.139 | + | 128.830i | −0.372520 | + | 0.215074i | −0.674559 | − | 0.738221i | \(-0.735666\pi\) |
0.302039 | + | 0.953296i | \(0.402333\pi\) | |||||||
\(600\) | 99.4325 | − | 677.166i | 0.165721 | − | 1.12861i | ||||
\(601\) | 91.8404 | 0.152813 | 0.0764064 | − | 0.997077i | \(-0.475655\pi\) | ||||
0.0764064 | + | 0.997077i | \(0.475655\pi\) | |||||||
\(602\) | −397.180 | − | 561.793i | −0.659767 | − | 0.933211i | ||||
\(603\) | 24.7389 | + | 24.7389i | 0.0410264 | + | 0.0410264i | ||||
\(604\) | −1182.93 | − | 682.963i | −1.95849 | − | 1.13073i | ||||
\(605\) | −913.807 | − | 66.7322i | −1.51042 | − | 0.110301i | ||||
\(606\) | 257.945 | + | 446.773i | 0.425651 | + | 0.737250i | ||||
\(607\) | −203.484 | − | 759.412i | −0.335229 | − | 1.25109i | −0.903621 | − | 0.428333i | \(-0.859101\pi\) |
0.568393 | − | 0.822757i | \(-0.307565\pi\) | |||||||
\(608\) | −36.3355 | − | 36.3355i | −0.0597623 | − | 0.0597623i | ||||
\(609\) | 361.075 | − | 434.296i | 0.592898 | − | 0.713130i | ||||
\(610\) | 155.404 | + | 812.862i | 0.254761 | + | 1.33256i | ||||
\(611\) | −505.338 | + | 875.272i | −0.827068 | + | 1.43252i | ||||
\(612\) | −286.768 | − | 76.8393i | −0.468576 | − | 0.125554i | ||||
\(613\) | −109.304 | + | 407.928i | −0.178310 | + | 0.665461i | 0.817654 | + | 0.575709i | \(0.195274\pi\) |
−0.995964 | + | 0.0897518i | \(0.971393\pi\) | |||||||
\(614\) | 158.951 | + | 91.7706i | 0.258878 | + | 0.149464i | ||||
\(615\) | −254.705 | + | 48.6950i | −0.414155 | + | 0.0791789i | ||||
\(616\) | −1484.01 | − | 1233.81i | −2.40911 | − | 2.00294i | ||||
\(617\) | 174.640 | − | 174.640i | 0.283047 | − | 0.283047i | −0.551276 | − | 0.834323i | \(-0.685859\pi\) |
0.834323 | + | 0.551276i | \(0.185859\pi\) | |||||||
\(618\) | 692.727 | − | 185.616i | 1.12092 | − | 0.300349i | ||||
\(619\) | −408.198 | + | 235.673i | −0.659448 | + | 0.380732i | −0.792066 | − | 0.610435i | \(-0.790995\pi\) |
0.132619 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(620\) | −6.82120 | + | 93.4071i | −0.0110019 | + | 0.150657i | ||||
\(621\) | 62.3722 | − | 108.032i | 0.100438 | − | 0.173964i | ||||
\(622\) | −222.159 | + | 222.159i | −0.357169 | + | 0.357169i | ||||
\(623\) | 292.222 | − | 206.597i | 0.469056 | − | 0.331616i | ||||
\(624\) | − | 468.431i | − | 0.750690i | ||||||
\(625\) | −143.709 | − | 608.254i | −0.229934 | − | 0.973206i | ||||
\(626\) | 324.524 | + | 562.091i | 0.518408 | + | 0.897909i | ||||
\(627\) | −105.438 | − | 28.2520i | −0.168163 | − | 0.0450591i | ||||
\(628\) | −1124.63 | + | 301.344i | −1.79081 | + | 0.479847i | ||||
\(629\) | − | 355.153i | − | 0.564631i | ||||||
\(630\) | 89.1977 | − | 359.975i | 0.141584 | − | 0.571389i | ||||
\(631\) | −670.413 | −1.06246 | −0.531230 | − | 0.847227i | \(-0.678270\pi\) | ||||
−0.531230 | + | 0.847227i | \(0.678270\pi\) | |||||||
\(632\) | −91.6516 | − | 342.049i | −0.145018 | − | 0.541216i | ||||
\(633\) | −62.7584 | + | 234.218i | −0.0991444 | + | 0.370012i | ||||
\(634\) | 1127.47 | − | 650.947i | 1.77835 | − | 1.02673i | ||||
\(635\) | −785.912 | − | 273.325i | −1.23766 | − | 0.430433i | ||||
\(636\) | 24.8002 | 0.0389940 | ||||||||
\(637\) | −47.2125 | + | 602.518i | −0.0741170 | + | 0.945868i | ||||
\(638\) | 2029.32 | + | 2029.32i | 3.18075 | + | 3.18075i | ||||
\(639\) | −174.435 | − | 100.710i | −0.272982 | − | 0.157606i | ||||
\(640\) | −618.599 | − | 716.065i | −0.966561 | − | 1.11885i | ||||
\(641\) | 617.665 | + | 1069.83i | 0.963596 | + | 1.66900i | 0.713341 | + | 0.700818i | \(0.247181\pi\) |
0.250256 | + | 0.968180i | \(0.419485\pi\) | |||||||
\(642\) | 226.285 | + | 844.506i | 0.352468 | + | 1.31543i | ||||
\(643\) | −504.796 | − | 504.796i | −0.785064 | − | 0.785064i | 0.195617 | − | 0.980680i | \(-0.437329\pi\) |
−0.980680 | + | 0.195617i | \(0.937329\pi\) | |||||||
\(644\) | −493.181 | − | 1336.12i | −0.765809 | − | 2.07473i | ||||
\(645\) | 199.377 | + | 135.378i | 0.309112 | + | 0.209888i | ||||
\(646\) | −74.5061 | + | 129.048i | −0.115334 | + | 0.199765i | ||||
\(647\) | −103.845 | − | 27.8251i | −0.160502 | − | 0.0430064i | 0.177673 | − | 0.984090i | \(-0.443143\pi\) |
−0.338175 | + | 0.941083i | \(0.609810\pi\) | |||||||
\(648\) | −36.8184 | + | 137.408i | −0.0568186 | + | 0.212050i | ||||
\(649\) | 1335.36 | + | 770.968i | 2.05756 | + | 1.18793i | ||||
\(650\) | −401.746 | − | 1012.29i | −0.618071 | − | 1.55737i | ||||
\(651\) | −4.53347 | + | 26.4102i | −0.00696385 | + | 0.0405687i | ||||
\(652\) | −1131.84 | + | 1131.84i | −1.73596 | + | 1.73596i | ||||
\(653\) | −297.399 | + | 79.6877i | −0.455434 | + | 0.122033i | −0.479241 | − | 0.877683i | \(-0.659088\pi\) |
0.0238067 | + | 0.999717i | \(0.492421\pi\) | |||||||
\(654\) | 860.898 | − | 497.040i | 1.31636 | − | 0.760000i | ||||
\(655\) | 814.087 | + | 59.4500i | 1.24288 | + | 0.0907633i | ||||
\(656\) | 328.287 | − | 568.610i | 0.500438 | − | 0.866784i | ||||
\(657\) | −38.7676 | + | 38.7676i | −0.0590070 | + | 0.0590070i | ||||
\(658\) | −185.722 | − | 2017.42i | −0.282252 | − | 3.06599i | ||||
\(659\) | − | 590.013i | − | 0.895315i | −0.894205 | − | 0.447658i | \(-0.852258\pi\) | ||
0.894205 | − | 0.447658i | \(-0.147742\pi\) | |||||||
\(660\) | 1209.20 | + | 420.535i | 1.83212 | + | 0.637175i | ||||
\(661\) | −1.19346 | − | 2.06714i | −0.00180554 | − | 0.00312729i | 0.865121 | − | 0.501563i | \(-0.167241\pi\) |
−0.866927 | + | 0.498436i | \(0.833908\pi\) | |||||||
\(662\) | −1535.19 | − | 411.354i | −2.31902 | − | 0.621380i | ||||
\(663\) | −240.951 | + | 64.5625i | −0.363425 | + | 0.0973794i | ||||
\(664\) | 1172.27i | 1.76547i | ||||||||
\(665\) | −110.692 | − | 61.1477i | −0.166454 | − | 0.0919515i | ||||
\(666\) | −322.284 | −0.483910 | ||||||||
\(667\) | 289.444 | + | 1080.22i | 0.433948 | + | 1.61952i | ||||
\(668\) | 354.115 | − | 1321.58i | 0.530113 | − | 1.97841i | ||||
\(669\) | −281.377 | + | 162.453i | −0.420594 | + | 0.242830i | ||||
\(670\) | −185.386 | + | 89.7123i | −0.276696 | + | 0.133899i | ||||
\(671\) | −817.398 | −1.21818 | ||||||||
\(672\) | 99.5440 | + | 140.801i | 0.148131 | + | 0.209525i | ||||
\(673\) | −50.3354 | − | 50.3354i | −0.0747925 | − | 0.0747925i | 0.668721 | − | 0.743513i | \(-0.266842\pi\) |
−0.743513 | + | 0.668721i | \(0.766842\pi\) | |||||||
\(674\) | 40.5429 | + | 23.4075i | 0.0601527 | + | 0.0347292i | ||||
\(675\) | 15.0357 | + | 129.031i | 0.0222751 | + | 0.191157i | ||||
\(676\) | 71.4998 | + | 123.841i | 0.105769 | + | 0.183197i | ||||
\(677\) | 134.189 | + | 500.800i | 0.198211 | + | 0.739734i | 0.991412 | + | 0.130774i | \(0.0417463\pi\) |
−0.793201 | + | 0.608960i | \(0.791587\pi\) | |||||||
\(678\) | −18.9318 | − | 18.9318i | −0.0279230 | − | 0.0279230i | ||||
\(679\) | 31.3670 | + | 84.9793i | 0.0461958 | + | 0.125154i | ||||
\(680\) | 518.391 | − | 763.457i | 0.762340 | − | 1.12273i | ||||
\(681\) | 212.616 | − | 368.262i | 0.312212 | − | 0.540767i | ||||
\(682\) | −131.522 | − | 35.2413i | −0.192848 | − | 0.0516734i | ||||
\(683\) | 26.0143 | − | 97.0866i | 0.0380883 | − | 0.142147i | −0.944263 | − | 0.329191i | \(-0.893224\pi\) |
0.982352 | + | 0.187044i | \(0.0598906\pi\) | |||||||
\(684\) | 79.5566 | + | 45.9321i | 0.116311 | + | 0.0671521i | ||||
\(685\) | 138.802 | + | 726.022i | 0.202631 | + | 1.05989i | ||||
\(686\) | −619.954 | − | 1040.84i | −0.903723 | − | 1.51726i | ||||
\(687\) | 307.677 | − | 307.677i | 0.447857 | − | 0.447857i | ||||
\(688\) | −589.389 | + | 157.926i | −0.856670 | + | 0.229544i | ||||
\(689\) | 18.0461 | − | 10.4189i | 0.0261917 | − | 0.0151218i | ||||
\(690\) | 480.053 | + | 555.690i | 0.695729 | + | 0.805348i | ||||
\(691\) | 0.723424 | − | 1.25301i | 0.00104692 | − | 0.00181332i | −0.865501 | − | 0.500906i | \(-0.833000\pi\) |
0.866548 | + | 0.499093i | \(0.166333\pi\) | |||||||
\(692\) | 1249.21 | − | 1249.21i | 1.80521 | − | 1.80521i | ||||
\(693\) | 332.676 | + | 153.297i | 0.480052 | + | 0.221208i | ||||
\(694\) | − | 1384.57i | − | 1.99506i | ||||||
\(695\) | −457.060 | + | 221.181i | −0.657640 | + | 0.318245i | ||||
\(696\) | −637.655 | − | 1104.45i | −0.916171 | − | 1.58685i | ||||
\(697\) | −337.728 | − | 90.4939i | −0.484545 | − | 0.129833i | ||||
\(698\) | −1640.08 | + | 439.457i | −2.34968 | + | 0.629595i | ||||
\(699\) | 511.820i | 0.732217i | ||||||||
\(700\) | 1242.55 | + | 809.810i | 1.77507 | + | 1.15687i | ||||
\(701\) | −230.081 | −0.328218 | −0.164109 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164109 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(702\) | 58.5873 | + | 218.651i | 0.0834577 | + | 0.311469i | ||||
\(703\) | −28.4427 | + | 106.149i | −0.0404590 | + | 0.150995i | ||||
\(704\) | 566.098 | − | 326.837i | 0.804117 | − | 0.464257i | ||||
\(705\) | 309.118 | + | 638.779i | 0.438466 | + | 0.906069i | ||||
\(706\) | 1957.73 | 2.77299 | ||||||||
\(707\) | −587.813 | + | 54.1135i | −0.831419 | + | 0.0765396i | ||||
\(708\) | −917.580 | − | 917.580i | −1.29602 | − | 1.29602i | ||||
\(709\) | −383.431 | − | 221.374i | −0.540805 | − | 0.312234i | 0.204600 | − | 0.978846i | \(-0.434411\pi\) |
−0.745405 | + | 0.666612i | \(0.767744\pi\) | |||||||
\(710\) | 897.254 | − | 775.126i | 1.26374 | − | 1.09173i | ||||
\(711\) | 33.6054 | + | 58.2062i | 0.0472649 | + | 0.0818653i | ||||
\(712\) | −209.150 | − | 780.559i | −0.293750 | − | 1.09629i | ||||
\(713\) | −37.5183 | − | 37.5183i | −0.0526203 | − | 0.0526203i | ||||
\(714\) | 319.677 | − | 384.503i | 0.447727 | − | 0.538520i | ||||
\(715\) | 1056.55 | − | 201.994i | 1.47770 | − | 0.282509i | ||||
\(716\) | −503.829 | + | 872.658i | −0.703672 | + | 1.21880i | ||||
\(717\) | −168.693 | − | 45.2011i | −0.235276 | − | 0.0630420i | ||||
\(718\) | 92.5998 | − | 345.587i | 0.128969 | − | 0.481319i | ||||
\(719\) | 446.525 | + | 257.801i | 0.621036 | + | 0.358555i | 0.777272 | − | 0.629164i | \(-0.216603\pi\) |
−0.156236 | + | 0.987720i | \(0.549936\pi\) | |||||||
\(720\) | −272.108 | − | 184.762i | −0.377927 | − | 0.256614i | ||||
\(721\) | −138.831 | + | 808.775i | −0.192553 | + | 1.12174i | ||||
\(722\) | −868.998 | + | 868.998i | −1.20360 | + | 1.20360i | ||||
\(723\) | 601.194 | − | 161.090i | 0.831527 | − | 0.222807i | ||||
\(724\) | 15.6614 | − | 9.04213i | 0.0216318 | − | 0.0124891i | ||||
\(725\) | −913.260 | − | 722.632i | −1.25967 | − | 0.996734i | ||||
\(726\) | −560.522 | + | 970.852i | −0.772068 | + | 1.33726i | ||||
\(727\) | −829.146 | + | 829.146i | −1.14050 | + | 1.14050i | −0.152145 | + | 0.988358i | \(0.548618\pi\) |
−0.988358 | + | 0.152145i | \(0.951382\pi\) | |||||||
\(728\) | 1239.41 | + | 571.121i | 1.70249 | + | 0.784507i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −140.585 | − | 290.513i | −0.192583 | − | 0.397963i | ||||
\(731\) | 162.468 | + | 281.402i | 0.222254 | + | 0.384956i | ||||
\(732\) | 664.462 | + | 178.042i | 0.907734 | + | 0.243227i | ||||
\(733\) | −996.034 | + | 266.886i | −1.35885 | + | 0.364102i | −0.863392 | − | 0.504533i | \(-0.831665\pi\) |
−0.495453 | + | 0.868635i | \(0.664998\pi\) | |||||||
\(734\) | − | 1076.26i | − | 1.46629i | ||||||
\(735\) | 331.376 | + | 265.076i | 0.450851 | + | 0.360647i | ||||
\(736\) | −341.433 | −0.463904 | ||||||||
\(737\) | −52.6484 | − | 196.486i | −0.0714360 | − | 0.266603i | ||||
\(738\) | −82.1188 | + | 306.471i | −0.111272 | + | 0.415273i | ||||
\(739\) | 287.660 | − | 166.081i | 0.389256 | − | 0.224737i | −0.292582 | − | 0.956241i | \(-0.594514\pi\) |
0.681838 | + | 0.731503i | \(0.261181\pi\) | |||||||
\(740\) | 423.373 | − | 1217.36i | 0.572126 | − | 1.64507i | ||||
\(741\) | 77.1868 | 0.104166 | ||||||||
\(742\) | −17.4811 | + | 37.9365i | −0.0235595 | + | 0.0511274i | ||||
\(743\) | −764.980 | − | 764.980i | −1.02958 | − | 1.02958i | −0.999549 | − | 0.0300340i | \(-0.990438\pi\) |
−0.0300340 | − | 0.999549i | \(-0.509562\pi\) | |||||||
\(744\) | 52.4007 | + | 30.2535i | 0.0704310 | + | 0.0406634i | ||||
\(745\) | 38.5873 | − | 528.400i | 0.0517950 | − | 0.709262i | ||||
\(746\) | 189.368 | + | 327.994i | 0.253844 | + | 0.439671i | ||||
\(747\) | −57.5865 | − | 214.916i | −0.0770903 | − | 0.287705i | ||||
\(748\) | 1220.58 | + | 1220.58i | 1.63179 | + | 1.63179i | ||||
\(749\) | −985.980 | − | 169.249i | −1.31640 | − | 0.225967i | ||||
\(750\) | −746.490 | − | 165.904i | −0.995320 | − | 0.221206i | ||||
\(751\) | −66.3561 | + | 114.932i | −0.0883570 | + | 0.153039i | −0.906817 | − | 0.421525i | \(-0.861495\pi\) |
0.818460 | + | 0.574564i | \(0.194828\pi\) | |||||||
\(752\) | −1735.54 | − | 465.036i | −2.30790 | − | 0.618399i | ||||
\(753\) | −7.83225 | + | 29.2304i | −0.0104014 | + | 0.0388185i | ||||
\(754\) | −1757.46 | − | 1014.67i | −2.33084 | − | 1.34571i | ||||
\(755\) | −452.681 | + | 666.683i | −0.599577 | + | 0.883024i | ||||
\(756\) | −237.041 | − | 197.077i | −0.313547 | − | 0.260684i | ||||
\(757\) | 705.876 | − | 705.876i | 0.932465 | − | 0.932465i | −0.0653945 | − | 0.997859i | \(-0.520831\pi\) |
0.997859 | + | 0.0653945i | \(0.0208306\pi\) | |||||||
\(758\) | −0.000170852 | 0 | 4.57797e-5i | −2.25399e−7 | 0 | 6.03954e-8i | ||||
\(759\) | −628.122 | + | 362.647i | −0.827566 | + | 0.477795i | ||||
\(760\) | −216.081 | + | 186.669i | −0.284317 | + | 0.245617i | ||||
\(761\) | −21.9538 | + | 38.0250i | −0.0288486 | + | 0.0499672i | −0.880089 | − | 0.474808i | \(-0.842517\pi\) |
0.851241 | + | 0.524776i | \(0.175851\pi\) | |||||||
\(762\) | −719.888 | + | 719.888i | −0.944735 | + | 0.944735i | ||||
\(763\) | 104.273 | + | 1132.67i | 0.136661 | + | 1.48450i | ||||
\(764\) | 1448.69i | 1.89619i | ||||||||
\(765\) | −57.5339 | + | 165.432i | −0.0752078 | + | 0.216250i | ||||
\(766\) | 332.731 | + | 576.308i | 0.434375 | + | 0.752360i | ||||
\(767\) | −1053.17 | − | 282.197i | −1.37311 | − | 0.367923i | ||||
\(768\) | −867.536 | + | 232.456i | −1.12960 | + | 0.302676i | ||||
\(769\) | − | 317.954i | − | 0.413464i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) | ||
0.978398 | − | 0.206732i | \(-0.0662829\pi\) | |||||||
\(770\) | −1495.62 | + | 1553.26i | −1.94237 | + | 2.01723i | ||||
\(771\) | 138.378 | 0.179479 | ||||||||
\(772\) | −181.814 | − | 678.539i | −0.235510 | − | 0.878937i | ||||
\(773\) | 182.617 | − | 681.538i | 0.236245 | − | 0.881679i | −0.741339 | − | 0.671131i | \(-0.765809\pi\) |
0.977584 | − | 0.210547i | \(-0.0675247\pi\) | |||||||
\(774\) | 255.359 | − | 147.432i | 0.329921 | − | 0.190480i | ||||
\(775\) | 54.6672 | + | 8.02713i | 0.0705383 | + | 0.0103576i | ||||
\(776\) | 204.540 | 0.263582 | ||||||||
\(777\) | 154.331 | − | 334.921i | 0.198625 | − | 0.431044i | ||||
\(778\) | 526.444 | + | 526.444i | 0.676663 | + | 0.676663i | ||||
\(779\) | 93.6941 | + | 54.0943i | 0.120275 | + | 0.0694407i | ||||
\(780\) | −902.869 | − | 65.9334i | −1.15752 | − | 0.0845300i | ||||
\(781\) | 585.553 | + | 1014.21i | 0.749748 | + | 1.29860i | ||||
\(782\) | 256.258 | + | 956.369i | 0.327696 | + | 1.22298i | ||||
\(783\) | 171.157 | + | 171.157i | 0.218592 | + | 0.218592i | ||||
\(784\) | −1056.37 | + | 196.159i | −1.34741 | + | 0.250203i | ||||
\(785\) | 128.986 | + | 674.676i | 0.164313 | + | 0.859460i | ||||
\(786\) | 499.354 | − | 864.907i | 0.635311 | − | 1.10039i | ||||
\(787\) | 303.975 | + | 81.4498i | 0.386245 | + | 0.103494i | 0.446716 | − | 0.894676i | \(-0.352594\pi\) |
−0.0604708 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(788\) | −99.3888 | + | 370.924i | −0.126128 | + | 0.470716i | ||||
\(789\) | −260.038 | − | 150.133i | −0.329580 | − | 0.190283i | ||||
\(790\) | −388.611 | + | 74.2952i | −0.491912 | + | 0.0940446i | ||||
\(791\) | 28.7400 | − | 10.6083i | 0.0363337 | − | 0.0134113i | ||||
\(792\) | 584.853 | − | 584.853i | 0.738451 | − | 0.738451i | ||||
\(793\) | 558.299 | − | 149.596i | 0.704034 | − | 0.188645i | ||||
\(794\) | 767.281 | − | 442.990i | 0.966349 | − | 0.557922i | ||||
\(795\) | 1.06563 | − | 14.5923i | 0.00134041 | − | 0.0183551i | ||||
\(796\) | 107.799 | − | 186.713i | 0.135425 | − | 0.234564i | ||||
\(797\) | 298.666 | − | 298.666i | 0.374738 | − | 0.374738i | −0.494461 | − | 0.869200i | \(-0.664635\pi\) |
0.869200 | + | 0.494461i | \(0.164635\pi\) | |||||||
\(798\) | −126.339 | + | 89.3202i | −0.158320 | + | 0.111930i | ||||
\(799\) | 956.818i | 1.19752i | ||||||||
\(800\) | 285.273 | − | 212.223i | 0.356591 | − | 0.265278i | ||||
\(801\) | 76.6878 | + | 132.827i | 0.0957401 | + | 0.165827i | ||||
\(802\) | −1179.59 | − | 316.070i | −1.47081 | − | 0.394102i | ||||
\(803\) | 307.907 | − | 82.5035i | 0.383446 | − | 0.102744i | ||||
\(804\) | 171.191i | 0.212924i | ||||||||
\(805\) | −807.361 | + | 232.774i | −1.00293 | + | 0.289161i | ||||
\(806\) | 96.2819 | 0.119456 | ||||||||
\(807\) | 83.0730 | + | 310.033i | 0.102940 | + | 0.384179i | ||||
\(808\) | −344.982 | + | 1287.49i | −0.426958 | + | 1.59343i | ||||
\(809\) | 1146.88 | − | 662.154i | 1.41766 | − | 0.818485i | 0.421564 | − | 0.906798i | \(-0.361481\pi\) |
0.996093 | + | 0.0883137i | \(0.0281478\pi\) | |||||||
\(810\) | 150.121 | + | 52.2092i | 0.185335 | + | 0.0644558i | ||||
\(811\) | 238.488 | 0.294067 | 0.147033 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147033 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(812\) | 2751.94 | − | 253.341i | 3.38909 | − | 0.311997i | ||||
\(813\) | −446.354 | − | 446.354i | −0.549021 | − | 0.549021i | ||||
\(814\) | 1622.79 | + | 936.917i | 1.99360 | + | 1.15100i | ||||
\(815\) | 617.338 | + | 714.606i | 0.757470 | + | 0.876817i | ||||
\(816\) | −221.734 | − | 384.055i | −0.271733 | − | 0.470655i | ||||
\(817\) | −26.0227 | − | 97.1180i | −0.0318515 | − | 0.118871i | ||||
\(818\) | −284.040 | − | 284.040i | −0.347237 | − | 0.347237i | ||||
\(819\) | −255.280 | − | 43.8203i | −0.311697 | − | 0.0535047i | ||||
\(820\) | −1049.75 | − | 712.786i | −1.28018 | − | 0.869251i | ||||
\(821\) | 276.005 | − | 478.055i | 0.336182 | − | 0.582284i | −0.647529 | − | 0.762041i | \(-0.724198\pi\) |
0.983711 | + | 0.179756i | \(0.0575310\pi\) | |||||||
\(822\) | 873.578 | + | 234.074i | 1.06275 | + | 0.284762i | ||||
\(823\) | 187.683 | − | 700.442i | 0.228047 | − | 0.851084i | −0.753113 | − | 0.657891i | \(-0.771449\pi\) |
0.981161 | − | 0.193194i | \(-0.0618845\pi\) | |||||||
\(824\) | 1604.70 | + | 926.472i | 1.94745 | + | 1.12436i | ||||
\(825\) | 299.399 | − | 693.416i | 0.362907 | − | 0.840504i | ||||
\(826\) | 2050.39 | − | 756.827i | 2.48231 | − | 0.916255i | ||||
\(827\) | 403.921 | − | 403.921i | 0.488417 | − | 0.488417i | −0.419389 | − | 0.907807i | \(-0.637756\pi\) |
0.907807 | + | 0.419389i | \(0.137756\pi\) | |||||||
\(828\) | 589.590 | − | 157.980i | 0.712065 | − | 0.190797i | ||||
\(829\) | −292.544 | + | 168.900i | −0.352887 | + | 0.203740i | −0.665956 | − | 0.745991i | \(-0.731976\pi\) |
0.313069 | + | 0.949730i | \(0.398643\pi\) | |||||||
\(830\) | 1306.29 | + | 95.3940i | 1.57385 | + | 0.114933i | ||||
\(831\) | 418.735 | − | 725.270i | 0.503893 | − | 0.872768i | ||||
\(832\) | −326.840 | + | 326.840i | −0.392837 | + | 0.392837i | ||||
\(833\) | 246.497 | + | 516.338i | 0.295914 | + | 0.619854i | ||||
\(834\) | 621.262i | 0.744919i | ||||||||
\(835\) | −762.394 | − | 265.146i | −0.913046 | − | 0.317540i | ||||
\(836\) | −267.060 | − | 462.561i | −0.319449 | − | 0.553303i | ||||
\(837\) | −11.0929 | − | 2.97233i | −0.0132532 | − | 0.00355117i | ||||
\(838\) | 751.910 | − | 201.474i | 0.897268 | − | 0.240422i | ||||
\(839\) | 1419.09i | 1.69141i | 0.533649 | + | 0.845706i | \(0.320820\pi\) | ||||
−0.533649 | + | 0.845706i | \(0.679180\pi\) | |||||||
\(840\) | 820.619 | − | 494.699i | 0.976928 | − | 0.588927i | ||||
\(841\) | −1328.99 | −1.58025 | ||||||||
\(842\) | 559.444 | + | 2087.87i | 0.664423 | + | 2.47966i | ||||
\(843\) | 212.002 | − | 791.201i | 0.251485 | − | 0.938553i | ||||
\(844\) | −1027.52 | + | 593.240i | −1.21744 | + | 0.702891i | ||||
\(845\) | 75.9399 | − | 36.7489i | 0.0898698 | − | 0.0434898i | ||||
\(846\) | 868.265 | 1.02632 | ||||||||
\(847\) | −740.504 | − | 1047.41i | −0.874266 | − | 1.23661i | ||||
\(848\) | 26.1948 | + | 26.1948i | 0.0308901 | + | 0.0308901i | ||||
\(849\) | 372.446 | + | 215.032i | 0.438687 | + | 0.253276i | ||||
\(850\) | −808.553 | − | 639.782i | −0.951239 | − | 0.752684i | ||||
\(851\) | 365.094 | + | 632.361i | 0.429017 | + | 0.743080i | ||||
\(852\) | −255.085 | − | 951.990i | −0.299396 | − | 1.11736i | ||||
\(853\) | −104.379 | − | 104.379i | −0.122367 | − | 0.122367i | 0.643271 | − | 0.765638i | \(-0.277577\pi\) |
−0.765638 | + | 0.643271i | \(0.777577\pi\) | |||||||
\(854\) | −740.713 | + | 890.920i | −0.867346 | + | 1.04323i | ||||
\(855\) | 30.4447 | − | 44.8372i | 0.0356078 | − | 0.0524411i | ||||
\(856\) | −1129.46 | + | 1956.29i | −1.31947 | + | 2.28539i | ||||
\(857\) | −1145.00 | − | 306.801i | −1.33605 | − | 0.357995i | −0.481085 | − | 0.876674i | \(-0.659757\pi\) |
−0.854969 | + | 0.518679i | \(0.826424\pi\) | |||||||
\(858\) | 340.641 | − | 1271.29i | 0.397017 | − | 1.48169i | ||||
\(859\) | 70.8786 | + | 40.9218i | 0.0825129 | + | 0.0476388i | 0.540689 | − | 0.841223i | \(-0.318164\pi\) |
−0.458176 | + | 0.888862i | \(0.651497\pi\) | |||||||
\(860\) | 221.434 | + | 1158.24i | 0.257481 | + | 1.34679i | ||||
\(861\) | −279.164 | − | 232.098i | −0.324233 | − | 0.269568i | ||||
\(862\) | 1810.15 | − | 1810.15i | 2.09995 | − | 2.09995i | ||||
\(863\) | 554.024 | − | 148.450i | 0.641974 | − | 0.172016i | 0.0768766 | − | 0.997041i | \(-0.475505\pi\) |
0.565097 | + | 0.825024i | \(0.308839\pi\) | |||||||
\(864\) | −63.9999 | + | 36.9503i | −0.0740739 | + | 0.0427666i | ||||
\(865\) | −681.352 | − | 788.705i | −0.787690 | − | 0.911798i | ||||
\(866\) | −380.702 | + | 659.395i | −0.439609 | + | 0.761426i | ||||
\(867\) | 186.963 | − | 186.963i | 0.215643 | − | 0.215643i | ||||
\(868\) | −107.064 | + | 75.6924i | −0.123345 | + | 0.0872033i | ||||
\(869\) | − | 390.779i | − | 0.449688i | ||||||
\(870\) | −1282.60 | + | 620.678i | −1.47426 | + | 0.713423i | ||||
\(871\) | 71.9197 | + | 124.569i | 0.0825714 | + | 0.143018i | ||||
\(872\) | 2480.90 | + | 664.754i | 2.84506 | + | 0.762333i | ||||
\(873\) | −37.4987 | + | 10.0477i | −0.0429538 | + | 0.0115094i | ||||
\(874\) | − | 306.366i | − | 0.350533i | ||||||
\(875\) | 529.879 | − | 696.314i | 0.605576 | − | 0.795787i | ||||
\(876\) | −268.268 | −0.306242 | ||||||||
\(877\) | 284.440 | + | 1061.54i | 0.324333 | + | 1.21043i | 0.914981 | + | 0.403497i | \(0.132206\pi\) |
−0.590648 | + | 0.806929i | \(0.701128\pi\) | |||||||
\(878\) | 759.406 | − | 2834.14i | 0.864927 | − | 3.22795i | ||||
\(879\) | −129.722 | + | 74.8950i | −0.147579 | + | 0.0852047i | ||||
\(880\) | 833.010 | + | 1721.38i | 0.946603 | + | 1.95611i | ||||
\(881\) | −791.292 | −0.898175 | −0.449087 | − | 0.893488i | \(-0.648251\pi\) | ||||
−0.449087 | + | 0.893488i | \(0.648251\pi\) | |||||||
\(882\) | 468.551 | − | 223.684i | 0.531237 | − | 0.253610i | ||||
\(883\) | −364.152 | − | 364.152i | −0.412403 | − | 0.412403i | 0.470172 | − | 0.882575i | \(-0.344192\pi\) |
−0.882575 | + | 0.470172i | \(0.844192\pi\) | |||||||
\(884\) | −1057.06 | − | 610.294i | −1.19577 | − | 0.690378i | ||||
\(885\) | −579.327 | + | 500.473i | −0.654607 | + | 0.565506i | ||||
\(886\) | −587.664 | − | 1017.86i | −0.663278 | − | 1.14883i | ||||
\(887\) | −174.510 | − | 651.280i | −0.196742 | − | 0.734250i | −0.991809 | − | 0.127729i | \(-0.959231\pi\) |
0.795067 | − | 0.606521i | \(-0.207435\pi\) | |||||||
\(888\) | −588.799 | − | 588.799i | −0.663062 | − | 0.663062i | ||||
\(889\) | −403.384 | − | 1092.85i | −0.453751 | − | 1.22930i | ||||
\(890\) | −886.813 | + | 169.542i | −0.996420 | + | 0.190497i | ||||
\(891\) | −78.4922 | + | 135.952i | −0.0880945 | + | 0.152584i | ||||
\(892\) | −1535.63 | − | 411.471i | −1.72156 | − | 0.461291i | ||||
\(893\) | 76.6274 | − | 285.977i | 0.0858090 | − | 0.320243i | ||||
\(894\) | −561.386 | − | 324.116i | −0.627948 | − | 0.362546i | ||||
\(895\) | 491.819 | + | 333.948i | 0.549519 | + | 0.373126i | ||||
\(896\) | 224.126 | − | 1305.67i | 0.250141 | − | 1.45722i | ||||
\(897\) | 362.650 | − | 362.650i | 0.404292 | − | 0.404292i | ||||
\(898\) | −70.1493 | + | 18.7965i | −0.0781173 | + | 0.0209315i | ||||
\(899\) | 89.1617 | − | 51.4775i | 0.0991787 | − | 0.0572609i | ||||
\(900\) | −394.417 | + | 498.463i | −0.438241 | + | 0.553848i | ||||
\(901\) | 9.86368 | − | 17.0844i | 0.0109475 | − | 0.0189616i | ||||
\(902\) | 1304.44 | − | 1304.44i | 1.44616 | − | 1.44616i | ||||
\(903\) | 30.9292 | + | 335.972i | 0.0342516 | + | 0.372062i | ||||
\(904\) | − | 69.1753i | − | 0.0765213i | ||||||
\(905\) | −4.64740 | − | 9.60364i | −0.00513525 | − | 0.0106118i | ||||
\(906\) | 492.986 | + | 853.876i | 0.544134 | + | 0.942468i | ||||
\(907\) | 951.626 | + | 254.987i | 1.04920 | + | 0.281133i | 0.741922 | − | 0.670486i | \(-0.233914\pi\) |
0.307280 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(908\) | 2009.81 | − | 538.528i | 2.21345 | − | 0.593092i | ||||
\(909\) | − | 252.985i | − | 0.278311i | ||||||
\(910\) | 737.271 | − | 1334.63i | 0.810188 | − | 1.46663i | ||||
\(911\) | 395.990 | 0.434676 | 0.217338 | − | 0.976096i | \(-0.430263\pi\) | ||||
0.217338 | + | 0.976096i | \(0.430263\pi\) | |||||||
\(912\) | 35.5154 | + | 132.545i | 0.0389424 | + | 0.145335i | ||||
\(913\) | −334.821 | + | 1249.57i | −0.366726 | + | 1.36864i | ||||
\(914\) | −1651.27 | + | 953.359i | −1.80664 | + | 1.04306i | ||||
\(915\) | 133.310 | − | 383.316i | 0.145694 | − | 0.418925i | ||||
\(916\) | 2129.10 | 2.32434 | ||||||||
\(917\) | 659.696 | + | 933.110i | 0.719406 | + | 1.01757i | ||||
\(918\) | 151.534 | + | 151.534i | 0.165070 | + | 0.165070i | ||||
\(919\) | 967.833 | + | 558.779i | 1.05314 | + | 0.608029i | 0.923526 | − | 0.383536i | \(-0.125294\pi\) |
0.129612 | + | 0.991565i | \(0.458627\pi\) | |||||||
\(920\) | −138.185 | + | 1892.26i | −0.150201 | + | 2.05680i | ||||
\(921\) | −45.0031 | − | 77.9476i | −0.0488633 | − | 0.0846336i | ||||
\(922\) | −594.696 | − | 2219.43i | −0.645006 | − | 2.40720i | ||||
\(923\) | −585.559 | − | 585.559i | −0.634409 | − | 0.634409i | ||||
\(924\) | 620.643 | + | 1681.44i | 0.671691 | + | 1.81974i | ||||
\(925\) | −698.095 | − | 301.419i | −0.754697 | − | 0.325858i | ||||
\(926\) | 574.354 | − | 994.811i | 0.620253 | − | 1.07431i | ||||
\(927\) | −339.704 | − | 91.0234i | −0.366455 | − | 0.0981914i | ||||
\(928\) | 171.471 | − | 639.939i | 0.184775 | − | 0.689590i | ||||
\(929\) | −724.522 | − | 418.303i | −0.779894 | − | 0.450272i | 0.0564987 | − | 0.998403i | \(-0.482006\pi\) |
−0.836393 | + | 0.548131i | \(0.815340\pi\) | |||||||
\(930\) | 37.9763 | − | 55.9293i | 0.0408347 | − | 0.0601391i | ||||
\(931\) | −32.3226 | − | 174.066i | −0.0347181 | − | 0.186967i | ||||
\(932\) | −1770.87 | + | 1770.87i | −1.90008 | + | 1.90008i | ||||
\(933\) | 148.820 | − | 39.8762i | 0.159507 | − | 0.0427397i | ||||
\(934\) | −1786.15 | + | 1031.23i | −1.91236 | + | 1.10410i | ||||
\(935\) | 770.628 | − | 665.736i | 0.824201 | − | 0.712017i | ||||
\(936\) | −292.429 | + | 506.503i | −0.312425 | + | 0.541135i | ||||
\(937\) | −406.918 | + | 406.918i | −0.434277 | + | 0.434277i | −0.890081 | − | 0.455803i | \(-0.849352\pi\) |
0.455803 | + | 0.890081i | \(0.349352\pi\) | |||||||
\(938\) | −261.869 | − | 120.669i | −0.279178 | − | 0.128645i | ||||
\(939\) | − | 318.284i | − | 0.338960i | ||||||
\(940\) | −1140.61 | + | 3279.68i | −1.21341 | + | 3.48902i | ||||
\(941\) | 75.9717 | + | 131.587i | 0.0807350 | + | 0.139837i | 0.903566 | − | 0.428449i | \(-0.140940\pi\) |
−0.822831 | + | 0.568286i | \(0.807607\pi\) | |||||||
\(942\) | 811.796 | + | 217.520i | 0.861780 | + | 0.230913i | ||||
\(943\) | 694.361 | − | 186.054i | 0.736332 | − | 0.197300i | ||||
\(944\) | − | 1938.36i | − | 2.05335i | ||||||
\(945\) | −126.144 | + | 131.006i | −0.133486 | + | 0.138631i | ||||
\(946\) | −1714.40 | −1.81227 | ||||||||
\(947\) | −142.586 | − | 532.138i | −0.150566 | − | 0.561920i | −0.999444 | − | 0.0333318i | \(-0.989388\pi\) |
0.848878 | − | 0.528588i | \(-0.177278\pi\) | |||||||
\(948\) | −85.1177 | + | 317.664i | −0.0897866 | + | 0.335088i | ||||
\(949\) | −195.207 | + | 112.703i | −0.205698 | + | 0.118760i | ||||
\(950\) | 190.426 | + | 255.974i | 0.200449 | + | 0.269446i | ||||
\(951\) | −638.431 | −0.671326 | ||||||||
\(952\) | 1286.51 | − | 118.435i | 1.35137 | − | 0.124406i | ||||
\(953\) | 12.6759 | + | 12.6759i | 0.0133010 | + | 0.0133010i | 0.713726 | − | 0.700425i | \(-0.247006\pi\) |
−0.700425 | + | 0.713726i | \(0.747006\pi\) | |||||||
\(954\) | −15.5032 | − | 8.95080i | −0.0162508 | − | 0.00938240i | ||||
\(955\) | 852.401 | + | 62.2479i | 0.892567 | + | 0.0651811i | ||||
\(956\) | −427.275 | − | 740.063i | −0.446941 | − | 0.774124i | ||||
\(957\) | −364.250 | − | 1359.40i | −0.380616 | − | 1.42048i | ||||
\(958\) | 737.522 | + | 737.522i | 0.769856 | + | 0.769856i | ||||
\(959\) | −661.581 | + | 795.741i | −0.689865 | + | 0.829761i | ||||
\(960\) | 60.9437 | + | 318.774i | 0.0634830 | + | 0.332056i | ||||
\(961\) | 478.058 | − | 828.020i | 0.497459 | − | 0.861623i | ||||
\(962\) | −1279.87 | − | 342.939i | −1.33042 | − | 0.356485i | ||||
\(963\) | 110.967 | − | 414.134i | 0.115230 | − | 0.430046i | ||||
\(964\) | 2637.46 | + | 1522.74i | 2.73596 | + | 1.57961i | ||||
\(965\) | −407.062 | + | 77.8228i | −0.421826 | + | 0.0806454i | ||||
\(966\) | −173.929 | + | 1013.24i | −0.180051 | + | 1.04891i | ||||
\(967\) | −674.724 | + | 674.724i | −0.697750 | + | 0.697750i | −0.963925 | − | 0.266175i | \(-0.914240\pi\) |
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(968\) | −2797.75 | + | 749.656i | −2.89024 | + | 0.774438i | ||||
\(969\) | 63.2835 | − | 36.5368i | 0.0653081 | − | 0.0377056i | ||||
\(970\) | 16.6444 | − | 227.923i | 0.0171592 | − | 0.234972i | ||||
\(971\) | 876.594 | − | 1518.30i | 0.902774 | − | 1.56365i | 0.0788965 | − | 0.996883i | \(-0.474860\pi\) |
0.823878 | − | 0.566768i | \(-0.191806\pi\) | |||||||
\(972\) | 93.4187 | − | 93.4187i | 0.0961098 | − | 0.0961098i | ||||
\(973\) | −645.622 | − | 297.502i | −0.663538 | − | 0.305758i | ||||
\(974\) | − | 116.926i | − | 0.120048i | ||||||
\(975\) | −77.5899 | + | 528.411i | −0.0795794 | + | 0.541960i | ||||
\(976\) | 513.773 | + | 889.881i | 0.526407 | + | 0.911763i | ||||
\(977\) | 1197.11 | + | 320.764i | 1.22529 | + | 0.328315i | 0.812744 | − | 0.582621i | \(-0.197973\pi\) |
0.412546 | + | 0.910937i | \(0.364640\pi\) | |||||||
\(978\) | 1116.05 | − | 299.044i | 1.14115 | − | 0.305771i | ||||
\(979\) | − | 891.762i | − | 0.910891i | ||||||
\(980\) | 229.395 | + | 2063.69i | 0.234077 | + | 2.10581i | ||||
\(981\) | −487.483 | −0.496925 | ||||||||
\(982\) | −550.716 | − | 2055.30i | −0.560810 | − | 2.09297i | ||||
\(983\) | −277.611 | + | 1036.06i | −0.282412 | + | 1.05398i | 0.668297 | + | 0.743894i | \(0.267023\pi\) |
−0.950710 | + | 0.310083i | \(0.899643\pi\) | |||||||
\(984\) | −709.938 | + | 409.883i | −0.721482 | + | 0.416548i | ||||
\(985\) | 213.980 | + | 74.4180i | 0.217238 | + | 0.0755513i | ||||
\(986\) | −1921.19 | −1.94847 | ||||||||
\(987\) | −415.784 | + | 902.311i | −0.421261 | + | 0.914195i | ||||
\(988\) | 267.062 | + | 267.062i | 0.270306 | + | 0.270306i | ||||
\(989\) | −578.558 | − | 334.030i | −0.584992 | − | 0.337746i | ||||
\(990\) | −604.122 | − | 699.307i | −0.610224 | − | 0.706371i | ||||
\(991\) | 128.143 | + | 221.951i | 0.129307 | + | 0.223966i | 0.923408 | − | 0.383819i | \(-0.125391\pi\) |
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(992\) | 8.13546 | + | 30.3619i | 0.00820106 | + | 0.0306068i | ||||
\(993\) | 551.115 | + | 551.115i | 0.555000 | + | 0.555000i | ||||
\(994\) | 1636.05 | + | 280.838i | 1.64593 | + | 0.282533i | ||||
\(995\) | −105.229 | − | 71.4510i | −0.105758 | − | 0.0718101i | ||||
\(996\) | 544.351 | − | 942.844i | 0.546537 | − | 0.946630i | ||||
\(997\) | 1395.85 | + | 374.016i | 1.40005 | + | 0.375141i | 0.878362 | − | 0.477997i | \(-0.158637\pi\) |
0.521685 | + | 0.853138i | \(0.325304\pi\) | |||||||
\(998\) | −751.764 | + | 2805.62i | −0.753271 | + | 2.81124i | ||||
\(999\) | 136.870 | + | 79.0218i | 0.137007 | + | 0.0791009i |
(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 | 105.3.v.a.58.2 | yes | 64 | |
3.2 | odd | 2 | 315.3.ca.b.163.15 | 64 | |||
5.2 | odd | 4 | inner | 105.3.v.a.37.15 | ✓ | 64 | |
7.4 | even | 3 | inner | 105.3.v.a.88.15 | yes | 64 | |
15.2 | even | 4 | 315.3.ca.b.37.2 | 64 | |||
21.11 | odd | 6 | 315.3.ca.b.298.2 | 64 | |||
35.32 | odd | 12 | inner | 105.3.v.a.67.2 | yes | 64 | |
105.32 | even | 12 | 315.3.ca.b.172.15 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.15 | ✓ | 64 | 5.2 | odd | 4 | inner | |
105.3.v.a.58.2 | yes | 64 | 1.1 | even | 1 | trivial | |
105.3.v.a.67.2 | yes | 64 | 35.32 | odd | 12 | inner | |
105.3.v.a.88.15 | yes | 64 | 7.4 | even | 3 | inner | |
315.3.ca.b.37.2 | 64 | 15.2 | even | 4 | |||
315.3.ca.b.163.15 | 64 | 3.2 | odd | 2 | |||
315.3.ca.b.172.15 | 64 | 105.32 | even | 12 | |||
315.3.ca.b.298.2 | 64 | 21.11 | odd | 6 |