Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(16,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.65508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.15759792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.500000 + 1.98116i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.31 |
Dual form | 45.4.e.b.16.2 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0874923 | + | 0.151541i | 0.0309332 | + | 0.0535779i | 0.881078 | − | 0.472972i | \(-0.156819\pi\) |
−0.850144 | + | 0.526550i | \(0.823485\pi\) | |||||||
\(3\) | 5.19394 | − | 0.151541i | 0.999575 | − | 0.0291641i | ||||
\(4\) | 3.98469 | − | 6.90169i | 0.498086 | − | 0.862711i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.477395 | + | 0.773837i | 0.0324826 | + | 0.0526529i | ||||
\(7\) | −4.23186 | − | 7.32979i | −0.228499 | − | 0.395772i | 0.728865 | − | 0.684658i | \(-0.240048\pi\) |
−0.957363 | + | 0.288886i | \(0.906715\pi\) | |||||||
\(8\) | 2.79440 | 0.123496 | ||||||||
\(9\) | 26.9541 | − | 1.57419i | 0.998299 | − | 0.0583034i | ||||
\(10\) | −0.874923 | −0.0276675 | ||||||||
\(11\) | 15.7541 | + | 27.2870i | 0.431823 | + | 0.747939i | 0.997030 | − | 0.0770098i | \(-0.0245373\pi\) |
−0.565208 | + | 0.824949i | \(0.691204\pi\) | |||||||
\(12\) | 19.6504 | − | 36.4508i | 0.472714 | − | 0.876870i | ||||
\(13\) | −13.4348 | + | 23.2697i | −0.286626 | + | 0.496451i | −0.973002 | − | 0.230796i | \(-0.925867\pi\) |
0.686376 | + | 0.727247i | \(0.259200\pi\) | |||||||
\(14\) | 0.740510 | − | 1.28260i | 0.0141364 | − | 0.0244850i | ||||
\(15\) | −12.3287 | + | 22.8693i | −0.212216 | + | 0.393655i | ||||
\(16\) | −31.6330 | − | 54.7900i | −0.494266 | − | 0.856094i | ||||
\(17\) | −44.3307 | −0.632457 | −0.316229 | − | 0.948683i | \(-0.602417\pi\) | ||||
−0.316229 | + | 0.948683i | \(0.602417\pi\) | |||||||
\(18\) | 2.59683 | + | 3.94692i | 0.0340044 | + | 0.0516832i | ||||
\(19\) | −90.2082 | −1.08922 | −0.544610 | − | 0.838689i | \(-0.683322\pi\) | ||||
−0.544610 | + | 0.838689i | \(0.683322\pi\) | |||||||
\(20\) | 19.9235 | + | 34.5084i | 0.222751 | + | 0.385816i | ||||
\(21\) | −23.0908 | − | 37.4292i | −0.239944 | − | 0.388939i | ||||
\(22\) | −2.75673 | + | 4.77480i | −0.0267153 | + | 0.0462723i | ||||
\(23\) | −97.1287 | + | 168.232i | −0.880553 | + | 1.52516i | −0.0298265 | + | 0.999555i | \(0.509495\pi\) |
−0.850727 | + | 0.525608i | \(0.823838\pi\) | |||||||
\(24\) | 14.5139 | − | 0.423466i | 0.123443 | − | 0.00360165i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −4.70176 | −0.0354650 | ||||||||
\(27\) | 139.759 | − | 12.2609i | 0.996174 | − | 0.0873931i | ||||
\(28\) | −67.4506 | −0.455248 | ||||||||
\(29\) | −1.87186 | − | 3.24215i | −0.0119860 | − | 0.0207604i | 0.859970 | − | 0.510344i | \(-0.170482\pi\) |
−0.871956 | + | 0.489584i | \(0.837149\pi\) | |||||||
\(30\) | −4.54430 | + | 0.132587i | −0.0276557 | + | 0.000806898i | ||||
\(31\) | 125.832 | − | 217.947i | 0.729035 | − | 1.26273i | −0.228257 | − | 0.973601i | \(-0.573303\pi\) |
0.957292 | − | 0.289124i | \(-0.0933641\pi\) | |||||||
\(32\) | 16.7129 | − | 28.9476i | 0.0923265 | − | 0.159914i | ||||
\(33\) | 85.9611 | + | 139.339i | 0.453452 | + | 0.735027i | ||||
\(34\) | −3.87859 | − | 6.71792i | −0.0195639 | − | 0.0338857i | ||||
\(35\) | 42.3186 | 0.204376 | ||||||||
\(36\) | 96.5390 | − | 192.301i | 0.446940 | − | 0.890283i | ||||
\(37\) | −62.2293 | −0.276498 | −0.138249 | − | 0.990397i | \(-0.544147\pi\) | ||||
−0.138249 | + | 0.990397i | \(0.544147\pi\) | |||||||
\(38\) | −7.89252 | − | 13.6703i | −0.0336931 | − | 0.0583581i | ||||
\(39\) | −66.2532 | + | 122.898i | −0.272026 | + | 0.504599i | ||||
\(40\) | −6.98599 | + | 12.1001i | −0.0276145 | + | 0.0478298i | ||||
\(41\) | 102.173 | − | 176.969i | 0.389188 | − | 0.674094i | −0.603152 | − | 0.797626i | \(-0.706089\pi\) |
0.992341 | + | 0.123532i | \(0.0394223\pi\) | |||||||
\(42\) | 3.65180 | − | 6.77397i | 0.0134163 | − | 0.0248868i | ||||
\(43\) | 263.831 | + | 456.968i | 0.935669 | + | 1.62063i | 0.773436 | + | 0.633874i | \(0.218536\pi\) |
0.162233 | + | 0.986752i | \(0.448130\pi\) | |||||||
\(44\) | 251.101 | 0.860340 | ||||||||
\(45\) | −60.5687 | + | 120.650i | −0.200646 | + | 0.399677i | ||||
\(46\) | −33.9920 | −0.108953 | ||||||||
\(47\) | −77.8637 | − | 134.864i | −0.241651 | − | 0.418551i | 0.719534 | − | 0.694457i | \(-0.244355\pi\) |
−0.961185 | + | 0.275906i | \(0.911022\pi\) | |||||||
\(48\) | −172.603 | − | 279.782i | −0.519023 | − | 0.841315i | ||||
\(49\) | 135.683 | − | 235.009i | 0.395577 | − | 0.685159i | ||||
\(50\) | 2.18731 | − | 3.78853i | 0.00618664 | − | 0.0107156i | ||||
\(51\) | −230.251 | + | 6.71792i | −0.632188 | + | 0.0184450i | ||||
\(52\) | 107.067 | + | 185.445i | 0.285529 | + | 0.494551i | ||||
\(53\) | −141.694 | −0.367230 | −0.183615 | − | 0.982998i | \(-0.558780\pi\) | ||||
−0.183615 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(54\) | 14.0859 | + | 20.1065i | 0.0354972 | + | 0.0506695i | ||||
\(55\) | −157.541 | −0.386234 | ||||||||
\(56\) | −11.8255 | − | 20.4823i | −0.0282187 | − | 0.0488762i | ||||
\(57\) | −468.536 | + | 13.6703i | −1.08876 | + | 0.0317661i | ||||
\(58\) | 0.327546 | − | 0.567326i | 0.000741533 | − | 0.00128437i | ||||
\(59\) | 246.923 | − | 427.683i | 0.544857 | − | 0.943721i | −0.453758 | − | 0.891125i | \(-0.649917\pi\) |
0.998616 | − | 0.0525961i | \(-0.0167496\pi\) | |||||||
\(60\) | 108.711 | + | 176.216i | 0.233908 | + | 0.379156i | ||||
\(61\) | 379.742 | + | 657.732i | 0.797065 | + | 1.38056i | 0.921520 | + | 0.388331i | \(0.126948\pi\) |
−0.124455 | + | 0.992225i | \(0.539718\pi\) | |||||||
\(62\) | 44.0373 | 0.0902055 | ||||||||
\(63\) | −125.604 | − | 190.906i | −0.251185 | − | 0.381776i | ||||
\(64\) | −500.280 | −0.977108 | ||||||||
\(65\) | −67.1739 | − | 116.349i | −0.128183 | − | 0.222020i | ||||
\(66\) | −13.5947 | + | 25.2178i | −0.0253545 | + | 0.0470317i | ||||
\(67\) | 271.795 | − | 470.763i | 0.495598 | − | 0.858401i | −0.504389 | − | 0.863476i | \(-0.668282\pi\) |
0.999987 | + | 0.00507574i | \(0.00161566\pi\) | |||||||
\(68\) | −176.644 | + | 305.956i | −0.315018 | + | 0.545627i | ||||
\(69\) | −478.987 | + | 888.505i | −0.835699 | + | 1.55019i | ||||
\(70\) | 3.70255 | + | 6.41300i | 0.00632199 | + | 0.0109500i | ||||
\(71\) | −928.207 | −1.55152 | −0.775760 | − | 0.631028i | \(-0.782633\pi\) | ||||
−0.775760 | + | 0.631028i | \(0.782633\pi\) | |||||||
\(72\) | 75.3203 | − | 4.39891i | 0.123286 | − | 0.00720024i | ||||
\(73\) | 608.739 | 0.975993 | 0.487997 | − | 0.872845i | \(-0.337728\pi\) | ||||
0.487997 | + | 0.872845i | \(0.337728\pi\) | |||||||
\(74\) | −5.44459 | − | 9.43030i | −0.00855298 | − | 0.0148142i | ||||
\(75\) | −68.2052 | − | 110.558i | −0.105009 | − | 0.170215i | ||||
\(76\) | −359.452 | + | 622.589i | −0.542526 | + | 0.939682i | ||||
\(77\) | 133.338 | − | 230.949i | 0.197342 | − | 0.341806i | ||||
\(78\) | −24.4207 | + | 0.712510i | −0.0354500 | + | 0.00103431i | ||||
\(79\) | −307.420 | − | 532.467i | −0.437816 | − | 0.758319i | 0.559705 | − | 0.828692i | \(-0.310915\pi\) |
−0.997521 | + | 0.0703726i | \(0.977581\pi\) | |||||||
\(80\) | 316.330 | 0.442085 | ||||||||
\(81\) | 724.044 | − | 84.8617i | 0.993201 | − | 0.116408i | ||||
\(82\) | 35.7573 | 0.0481553 | ||||||||
\(83\) | −537.655 | − | 931.246i | −0.711028 | − | 1.23154i | −0.964472 | − | 0.264186i | \(-0.914897\pi\) |
0.253444 | − | 0.967350i | \(-0.418437\pi\) | |||||||
\(84\) | −350.334 | + | 10.2215i | −0.455055 | + | 0.0132769i | ||||
\(85\) | 110.827 | − | 191.957i | 0.141422 | − | 0.244950i | ||||
\(86\) | −46.1663 | + | 79.9623i | −0.0578865 | + | 0.100262i | ||||
\(87\) | −10.2136 | − | 16.5559i | −0.0125864 | − | 0.0204020i | ||||
\(88\) | 44.0233 | + | 76.2506i | 0.0533284 | + | 0.0923675i | ||||
\(89\) | 1505.15 | 1.79265 | 0.896324 | − | 0.443400i | \(-0.146228\pi\) | ||||
0.896324 | + | 0.443400i | \(0.146228\pi\) | |||||||
\(90\) | −23.5827 | + | 1.37730i | −0.0276204 | + | 0.00161311i | ||||
\(91\) | 227.416 | 0.261975 | ||||||||
\(92\) | 774.055 | + | 1340.70i | 0.877183 | + | 1.51933i | ||||
\(93\) | 620.536 | − | 1151.07i | 0.691898 | − | 1.28345i | ||||
\(94\) | 13.6249 | − | 23.5991i | 0.0149501 | − | 0.0258943i | ||||
\(95\) | 225.521 | − | 390.613i | 0.243557 | − | 0.421853i | ||||
\(96\) | 82.4190 | − | 152.885i | 0.0876234 | − | 0.162539i | ||||
\(97\) | 166.369 | + | 288.160i | 0.174147 | + | 0.301631i | 0.939866 | − | 0.341544i | \(-0.110950\pi\) |
−0.765719 | + | 0.643175i | \(0.777617\pi\) | |||||||
\(98\) | 47.4848 | 0.0489458 | ||||||||
\(99\) | 467.593 | + | 710.695i | 0.474695 | + | 0.721490i | ||||
\(100\) | −199.235 | −0.199235 | ||||||||
\(101\) | 247.493 | + | 428.670i | 0.243826 | + | 0.422319i | 0.961801 | − | 0.273750i | \(-0.0882640\pi\) |
−0.717975 | + | 0.696069i | \(0.754931\pi\) | |||||||
\(102\) | −21.1632 | − | 34.3047i | −0.0205438 | − | 0.0333007i | ||||
\(103\) | 315.015 | − | 545.622i | 0.301353 | − | 0.521959i | −0.675090 | − | 0.737736i | \(-0.735895\pi\) |
0.976443 | + | 0.215777i | \(0.0692284\pi\) | |||||||
\(104\) | −37.5421 | + | 65.0248i | −0.0353972 | + | 0.0613097i | ||||
\(105\) | 219.800 | − | 6.41300i | 0.204289 | − | 0.00596043i | ||||
\(106\) | −12.3971 | − | 21.4725i | −0.0113596 | − | 0.0196754i | ||||
\(107\) | −1561.00 | −1.41035 | −0.705175 | − | 0.709034i | \(-0.749131\pi\) | ||||
−0.705175 | + | 0.709034i | \(0.749131\pi\) | |||||||
\(108\) | 472.277 | − | 1013.43i | 0.420786 | − | 0.902939i | ||||
\(109\) | −936.140 | −0.822623 | −0.411311 | − | 0.911495i | \(-0.634929\pi\) | ||||
−0.411311 | + | 0.911495i | \(0.634929\pi\) | |||||||
\(110\) | −13.7837 | − | 23.8740i | −0.0119475 | − | 0.0206936i | ||||
\(111\) | −323.215 | + | 9.43030i | −0.276381 | + | 0.00806382i | ||||
\(112\) | −267.733 | + | 463.727i | −0.225878 | + | 0.391233i | ||||
\(113\) | −677.490 | + | 1173.45i | −0.564008 | + | 0.976890i | 0.433134 | + | 0.901330i | \(0.357408\pi\) |
−0.997141 | + | 0.0755602i | \(0.975925\pi\) | |||||||
\(114\) | −43.0649 | − | 69.8065i | −0.0353807 | − | 0.0573506i | ||||
\(115\) | −485.643 | − | 841.159i | −0.393795 | − | 0.682074i | ||||
\(116\) | −29.8351 | −0.0238803 | ||||||||
\(117\) | −325.491 | + | 648.363i | −0.257194 | + | 0.512318i | ||||
\(118\) | 86.4153 | 0.0674167 | ||||||||
\(119\) | 187.601 | + | 324.935i | 0.144516 | + | 0.250309i | ||||
\(120\) | −34.4512 | + | 63.9058i | −0.0262079 | + | 0.0486148i | ||||
\(121\) | 169.115 | − | 292.915i | 0.127058 | − | 0.220071i | ||||
\(122\) | −66.4490 | + | 115.093i | −0.0493115 | + | 0.0854101i | ||||
\(123\) | 503.862 | − | 934.648i | 0.369363 | − | 0.685157i | ||||
\(124\) | −1002.80 | − | 1736.90i | −0.726244 | − | 1.25789i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 17.9407 | − | 35.7370i | 0.0126848 | − | 0.0252675i | ||||
\(127\) | −1182.37 | −0.826126 | −0.413063 | − | 0.910702i | \(-0.635541\pi\) | ||||
−0.413063 | + | 0.910702i | \(0.635541\pi\) | |||||||
\(128\) | −177.474 | − | 307.393i | −0.122552 | − | 0.212266i | ||||
\(129\) | 1439.57 | + | 2333.48i | 0.982535 | + | 1.59265i | ||||
\(130\) | 11.7544 | − | 20.3592i | 0.00793022 | − | 0.0137356i | ||||
\(131\) | −1126.87 | + | 1951.80i | −0.751569 | + | 1.30176i | 0.195494 | + | 0.980705i | \(0.437369\pi\) |
−0.947062 | + | 0.321050i | \(0.895964\pi\) | |||||||
\(132\) | 1304.21 | − | 38.0522i | 0.859974 | − | 0.0250910i | ||||
\(133\) | 381.748 | + | 661.207i | 0.248885 | + | 0.431082i | ||||
\(134\) | 95.1199 | 0.0613217 | ||||||||
\(135\) | −296.307 | + | 635.828i | −0.188904 | + | 0.405358i | ||||
\(136\) | −123.877 | −0.0781059 | ||||||||
\(137\) | −236.856 | − | 410.246i | −0.147708 | − | 0.255837i | 0.782672 | − | 0.622434i | \(-0.213856\pi\) |
−0.930380 | + | 0.366597i | \(0.880523\pi\) | |||||||
\(138\) | −176.553 | + | 5.15119i | −0.108907 | + | 0.00317753i | ||||
\(139\) | 68.5193 | − | 118.679i | 0.0418110 | − | 0.0724188i | −0.844363 | − | 0.535772i | \(-0.820021\pi\) |
0.886174 | + | 0.463353i | \(0.153354\pi\) | |||||||
\(140\) | 168.626 | − | 292.069i | 0.101797 | − | 0.176317i | ||||
\(141\) | −424.857 | − | 688.675i | −0.253755 | − | 0.411326i | ||||
\(142\) | −81.2110 | − | 140.662i | −0.0479935 | − | 0.0831272i | ||||
\(143\) | −846.613 | −0.495086 | ||||||||
\(144\) | −938.889 | − | 1427.02i | −0.543339 | − | 0.825820i | ||||
\(145\) | 18.7186 | 0.0107206 | ||||||||
\(146\) | 53.2600 | + | 92.2490i | 0.0301906 | + | 0.0522917i | ||||
\(147\) | 669.115 | − | 1241.19i | 0.375426 | − | 0.696404i | ||||
\(148\) | −247.965 | + | 429.487i | −0.137720 | + | 0.238538i | ||||
\(149\) | 71.5553 | − | 123.937i | 0.0393426 | − | 0.0681433i | −0.845684 | − | 0.533685i | \(-0.820807\pi\) |
0.885026 | + | 0.465541i | \(0.154140\pi\) | |||||||
\(150\) | 10.7866 | − | 20.0089i | 0.00587150 | − | 0.0108914i | ||||
\(151\) | −108.421 | − | 187.790i | −0.0584314 | − | 0.101206i | 0.835330 | − | 0.549749i | \(-0.185277\pi\) |
−0.893761 | + | 0.448543i | \(0.851943\pi\) | |||||||
\(152\) | −252.077 | −0.134514 | ||||||||
\(153\) | −1194.89 | + | 69.7850i | −0.631381 | + | 0.0368744i | ||||
\(154\) | 46.6644 | 0.0244177 | ||||||||
\(155\) | 629.159 | + | 1089.74i | 0.326034 | + | 0.564708i | ||||
\(156\) | 584.202 | + | 946.967i | 0.299831 | + | 0.486013i | ||||
\(157\) | −674.215 | + | 1167.78i | −0.342728 | + | 0.593622i | −0.984938 | − | 0.172906i | \(-0.944684\pi\) |
0.642211 | + | 0.766528i | \(0.278017\pi\) | |||||||
\(158\) | 53.7938 | − | 93.1736i | 0.0270861 | − | 0.0469145i | ||||
\(159\) | −735.951 | + | 21.4725i | −0.367074 | + | 0.0107099i | ||||
\(160\) | 83.5644 | + | 144.738i | 0.0412897 | + | 0.0715158i | ||||
\(161\) | 1644.14 | 0.804822 | ||||||||
\(162\) | 76.2083 | + | 102.298i | 0.0369598 | + | 0.0496127i | ||||
\(163\) | 1039.85 | 0.499676 | 0.249838 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249838 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(164\) | −814.254 | − | 1410.33i | −0.387699 | − | 0.671514i | ||||
\(165\) | −818.261 | + | 23.8740i | −0.386070 | + | 0.0112642i | ||||
\(166\) | 94.0813 | − | 162.954i | 0.0439887 | − | 0.0761907i | ||||
\(167\) | 1663.52 | − | 2881.31i | 0.770822 | − | 1.33510i | −0.166291 | − | 0.986077i | \(-0.553179\pi\) |
0.937113 | − | 0.349026i | \(-0.113487\pi\) | |||||||
\(168\) | −64.5248 | − | 104.592i | −0.0296321 | − | 0.0480324i | ||||
\(169\) | 737.513 | + | 1277.41i | 0.335691 | + | 0.581434i | ||||
\(170\) | 38.7859 | 0.0174985 | ||||||||
\(171\) | −2431.48 | + | 142.005i | −1.08737 | + | 0.0635052i | ||||
\(172\) | 4205.13 | 1.86418 | ||||||||
\(173\) | 597.127 | + | 1034.25i | 0.262420 | + | 0.454525i | 0.966885 | − | 0.255214i | \(-0.0821460\pi\) |
−0.704464 | + | 0.709740i | \(0.748813\pi\) | |||||||
\(174\) | 1.61528 | − | 2.99630i | 0.000703760 | − | 0.00130545i | ||||
\(175\) | −105.796 | + | 183.245i | −0.0456998 | + | 0.0791543i | ||||
\(176\) | 996.702 | − | 1726.34i | 0.426871 | − | 0.739362i | ||||
\(177\) | 1217.69 | − | 2258.78i | 0.517103 | − | 0.959210i | ||||
\(178\) | 131.689 | + | 228.092i | 0.0554523 | + | 0.0960463i | ||||
\(179\) | 2323.70 | 0.970288 | 0.485144 | − | 0.874434i | \(-0.338767\pi\) | ||||
0.485144 | + | 0.874434i | \(0.338767\pi\) | |||||||
\(180\) | 591.341 | + | 898.779i | 0.244866 | + | 0.372173i | ||||
\(181\) | 2527.12 | 1.03779 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) | ||||
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(182\) | 19.8972 | + | 34.4629i | 0.00810372 | + | 0.0140361i | ||||
\(183\) | 2072.03 | + | 3358.68i | 0.836988 | + | 1.35672i | ||||
\(184\) | −271.416 | + | 470.106i | −0.108745 | + | 0.188352i | ||||
\(185\) | 155.573 | − | 269.461i | 0.0618269 | − | 0.107087i | ||||
\(186\) | 228.727 | − | 6.67346i | 0.0901671 | − | 0.00263076i | ||||
\(187\) | −698.391 | − | 1209.65i | −0.273109 | − | 0.473039i | ||||
\(188\) | −1241.05 | −0.481452 | ||||||||
\(189\) | −681.311 | − | 972.520i | −0.262212 | − | 0.374288i | ||||
\(190\) | 78.9252 | 0.0301360 | ||||||||
\(191\) | −1194.43 | − | 2068.82i | −0.452493 | − | 0.783741i | 0.546047 | − | 0.837754i | \(-0.316132\pi\) |
−0.998540 | + | 0.0540134i | \(0.982799\pi\) | |||||||
\(192\) | −2598.42 | + | 75.8129i | −0.976693 | + | 0.0284965i | ||||
\(193\) | −1773.99 | + | 3072.64i | −0.661629 | + | 1.14597i | 0.318559 | + | 0.947903i | \(0.396801\pi\) |
−0.980188 | + | 0.198072i | \(0.936532\pi\) | |||||||
\(194\) | −29.1120 | + | 50.4235i | −0.0107738 | + | 0.0186608i | ||||
\(195\) | −366.529 | − | 594.128i | −0.134604 | − | 0.218187i | ||||
\(196\) | −1081.31 | − | 1872.88i | −0.394063 | − | 0.682536i | ||||
\(197\) | −1239.26 | −0.448192 | −0.224096 | − | 0.974567i | \(-0.571943\pi\) | ||||
−0.224096 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(198\) | −66.7887 | + | 133.040i | −0.0239720 | + | 0.0477512i | ||||
\(199\) | 516.657 | 0.184044 | 0.0920222 | − | 0.995757i | \(-0.470667\pi\) | ||||
0.0920222 | + | 0.995757i | \(0.470667\pi\) | |||||||
\(200\) | −34.9299 | − | 60.5004i | −0.0123496 | − | 0.0213901i | ||||
\(201\) | 1340.35 | − | 2486.30i | 0.470353 | − | 0.872489i | ||||
\(202\) | −43.3074 | + | 75.0107i | −0.0150847 | + | 0.0261274i | ||||
\(203\) | −15.8429 | + | 27.4406i | −0.00547759 | + | 0.00948746i | ||||
\(204\) | −871.114 | + | 1615.89i | −0.298971 | + | 0.554583i | ||||
\(205\) | 510.864 | + | 884.843i | 0.174050 | + | 0.301464i | ||||
\(206\) | 110.246 | 0.0372873 | ||||||||
\(207\) | −2353.18 | + | 4687.43i | −0.790133 | + | 1.57391i | ||||
\(208\) | 1699.93 | 0.566678 | ||||||||
\(209\) | −1421.15 | − | 2461.51i | −0.470350 | − | 0.814670i | ||||
\(210\) | 20.2027 | + | 32.7477i | 0.00663865 | + | 0.0107610i | ||||
\(211\) | 8.92159 | − | 15.4527i | 0.00291084 | − | 0.00504173i | −0.864566 | − | 0.502519i | \(-0.832407\pi\) |
0.867477 | + | 0.497477i | \(0.165740\pi\) | |||||||
\(212\) | −564.607 | + | 977.928i | −0.182912 | + | 0.316813i | ||||
\(213\) | −4821.05 | + | 140.662i | −1.55086 | + | 0.0452487i | ||||
\(214\) | −136.575 | − | 236.555i | −0.0436266 | − | 0.0755635i | ||||
\(215\) | −2638.31 | −0.836888 | ||||||||
\(216\) | 390.543 | − | 34.2618i | 0.123024 | − | 0.0107927i | ||||
\(217\) | −2130.01 | −0.666334 | ||||||||
\(218\) | −81.9050 | − | 141.864i | −0.0254464 | − | 0.0440744i | ||||
\(219\) | 3161.76 | − | 92.2490i | 0.975578 | − | 0.0284640i | ||||
\(220\) | −627.753 | + | 1087.30i | −0.192378 | + | 0.333208i | ||||
\(221\) | 595.573 | − | 1031.56i | 0.181279 | − | 0.313984i | ||||
\(222\) | −29.7079 | − | 48.1554i | −0.00898138 | − | 0.0145584i | ||||
\(223\) | −494.777 | − | 856.978i | −0.148577 | − | 0.257343i | 0.782125 | − | 0.623122i | \(-0.214136\pi\) |
−0.930702 | + | 0.365779i | \(0.880803\pi\) | |||||||
\(224\) | −282.906 | −0.0843860 | ||||||||
\(225\) | −371.008 | − | 563.895i | −0.109928 | − | 0.167080i | ||||
\(226\) | −237.101 | −0.0697863 | ||||||||
\(227\) | 1713.57 | + | 2967.98i | 0.501028 | + | 0.867806i | 0.999999 | + | 0.00118754i | \(0.000378004\pi\) |
−0.498971 | + | 0.866619i | \(0.666289\pi\) | |||||||
\(228\) | −1772.62 | + | 3288.16i | −0.514890 | + | 0.955104i | ||||
\(229\) | −549.805 | + | 952.290i | −0.158656 | + | 0.274800i | −0.934384 | − | 0.356267i | \(-0.884049\pi\) |
0.775728 | + | 0.631067i | \(0.217383\pi\) | |||||||
\(230\) | 84.9801 | − | 147.190i | 0.0243627 | − | 0.0421974i | ||||
\(231\) | 657.554 | − | 1219.74i | 0.187290 | − | 0.347416i | ||||
\(232\) | −5.23071 | − | 9.05985i | −0.00148023 | − | 0.00256383i | ||||
\(233\) | 4459.91 | 1.25399 | 0.626993 | − | 0.779025i | \(-0.284285\pi\) | ||||
0.626993 | + | 0.779025i | \(0.284285\pi\) | |||||||
\(234\) | −126.732 | + | 7.40147i | −0.0354047 | + | 0.00206773i | ||||
\(235\) | 778.637 | 0.216139 | ||||||||
\(236\) | −1967.82 | − | 3408.37i | −0.542772 | − | 0.940109i | ||||
\(237\) | −1677.41 | − | 2719.02i | −0.459745 | − | 0.745228i | ||||
\(238\) | −32.8273 | + | 56.8586i | −0.00894067 | + | 0.0154857i | ||||
\(239\) | −3272.23 | + | 5667.66i | −0.885618 | + | 1.53394i | −0.0406148 | + | 0.999175i | \(0.512932\pi\) |
−0.845003 | + | 0.534761i | \(0.820402\pi\) | |||||||
\(240\) | 1643.00 | − | 47.9371i | 0.441897 | − | 0.0128930i | ||||
\(241\) | 105.162 | + | 182.147i | 0.0281083 | + | 0.0486851i | 0.879737 | − | 0.475460i | \(-0.157718\pi\) |
−0.851629 | + | 0.524145i | \(0.824385\pi\) | |||||||
\(242\) | 59.1849 | 0.0157213 | ||||||||
\(243\) | 3747.78 | − | 550.489i | 0.989384 | − | 0.145325i | ||||
\(244\) | 6052.61 | 1.58803 | ||||||||
\(245\) | 678.414 | + | 1175.05i | 0.176907 | + | 0.306412i | ||||
\(246\) | 185.722 | − | 5.41871i | 0.0481349 | − | 0.00140441i | ||||
\(247\) | 1211.93 | − | 2099.12i | 0.312199 | − | 0.540744i | ||||
\(248\) | 351.624 | − | 609.031i | 0.0900329 | − | 0.155942i | ||||
\(249\) | −2933.67 | − | 4755.36i | −0.746642 | − | 1.21028i | ||||
\(250\) | 10.9365 | + | 18.9426i | 0.00276675 | + | 0.00479215i | ||||
\(251\) | 816.143 | 0.205237 | 0.102618 | − | 0.994721i | \(-0.467278\pi\) | ||||
0.102618 | + | 0.994721i | \(0.467278\pi\) | |||||||
\(252\) | −1818.07 | + | 106.180i | −0.454474 | + | 0.0265425i | ||||
\(253\) | −6120.71 | −1.52097 | ||||||||
\(254\) | −103.448 | − | 179.177i | −0.0255547 | − | 0.0442621i | ||||
\(255\) | 546.538 | − | 1013.81i | 0.134218 | − | 0.248970i | ||||
\(256\) | −1970.06 | + | 3412.25i | −0.480972 | + | 0.833069i | ||||
\(257\) | 2086.17 | − | 3613.36i | 0.506350 | − | 0.877023i | −0.493623 | − | 0.869676i | \(-0.664328\pi\) |
0.999973 | − | 0.00734758i | \(-0.00233883\pi\) | |||||||
\(258\) | −227.667 | + | 422.316i | −0.0549378 | + | 0.101908i | ||||
\(259\) | 263.346 | + | 456.128i | 0.0631795 | + | 0.109430i | ||||
\(260\) | −1070.67 | −0.255385 | ||||||||
\(261\) | −55.5579 | − | 84.4425i | −0.0131760 | − | 0.0200263i | ||||
\(262\) | −394.371 | −0.0929937 | ||||||||
\(263\) | 1408.52 | + | 2439.64i | 0.330241 | + | 0.571994i | 0.982559 | − | 0.185951i | \(-0.0595367\pi\) |
−0.652318 | + | 0.757945i | \(0.726203\pi\) | |||||||
\(264\) | 240.209 | + | 389.370i | 0.0559995 | + | 0.0907729i | ||||
\(265\) | 354.235 | − | 613.554i | 0.0821151 | − | 0.142228i | ||||
\(266\) | −66.8001 | + | 115.701i | −0.0153976 | + | 0.0266695i | ||||
\(267\) | 7817.66 | − | 228.092i | 1.79189 | − | 0.0522810i | ||||
\(268\) | −2166.04 | − | 3751.69i | −0.493701 | − | 0.855115i | ||||
\(269\) | −102.610 | −0.0232573 | −0.0116287 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116287 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(270\) | −122.279 | + | 10.7274i | −0.0275616 | + | 0.00241795i | ||||
\(271\) | −3337.27 | −0.748061 | −0.374031 | − | 0.927416i | \(-0.622025\pi\) | ||||
−0.374031 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(272\) | 1402.31 | + | 2428.88i | 0.312602 | + | 0.541443i | ||||
\(273\) | 1181.19 | − | 34.4629i | 0.261863 | − | 0.00764026i | ||||
\(274\) | 41.4461 | − | 71.7867i | 0.00913814 | − | 0.0158277i | ||||
\(275\) | 393.853 | − | 682.174i | 0.0863645 | − | 0.149588i | ||||
\(276\) | 4223.57 | + | 6846.23i | 0.921120 | + | 1.49310i | ||||
\(277\) | −316.941 | − | 548.959i | −0.0687479 | − | 0.119075i | 0.829603 | − | 0.558354i | \(-0.188567\pi\) |
−0.898350 | + | 0.439280i | \(0.855234\pi\) | |||||||
\(278\) | 23.9796 | 0.00517339 | ||||||||
\(279\) | 3048.59 | − | 6072.65i | 0.654173 | − | 1.30308i | ||||
\(280\) | 118.255 | 0.0252396 | ||||||||
\(281\) | 3101.20 | + | 5371.44i | 0.658370 | + | 1.14033i | 0.981037 | + | 0.193818i | \(0.0620872\pi\) |
−0.322667 | + | 0.946513i | \(0.604579\pi\) | |||||||
\(282\) | 67.1909 | − | 124.637i | 0.0141885 | − | 0.0263193i | ||||
\(283\) | 3740.06 | − | 6477.98i | 0.785596 | − | 1.36069i | −0.143047 | − | 0.989716i | \(-0.545690\pi\) |
0.928642 | − | 0.370976i | \(-0.120977\pi\) | |||||||
\(284\) | −3698.62 | + | 6406.19i | −0.772791 | + | 1.33851i | ||||
\(285\) | 1112.15 | − | 2063.00i | 0.231150 | − | 0.428777i | ||||
\(286\) | −74.0722 | − | 128.297i | −0.0153146 | − | 0.0265257i | ||||
\(287\) | −1729.52 | −0.355716 | ||||||||
\(288\) | 404.911 | − | 806.564i | 0.0828459 | − | 0.165025i | ||||
\(289\) | −2947.79 | −0.599998 | ||||||||
\(290\) | 1.63773 | + | 2.83663i | 0.000331623 | + | 0.000574389i | ||||
\(291\) | 907.780 | + | 1471.47i | 0.182869 | + | 0.296424i | ||||
\(292\) | 2425.64 | − | 4201.33i | 0.486129 | − | 0.842000i | ||||
\(293\) | 2418.26 | − | 4188.54i | 0.482171 | − | 0.835144i | −0.517620 | − | 0.855611i | \(-0.673182\pi\) |
0.999791 | + | 0.0204666i | \(0.00651519\pi\) | |||||||
\(294\) | 246.633 | − | 7.19590i | 0.0489250 | − | 0.00142746i | ||||
\(295\) | 1234.61 | + | 2138.41i | 0.243668 | + | 0.422045i | ||||
\(296\) | −173.893 | −0.0341464 | ||||||||
\(297\) | 2536.35 | + | 3620.45i | 0.495535 | + | 0.707339i | ||||
\(298\) | 25.0422 | 0.00486796 | ||||||||
\(299\) | −2609.81 | − | 4520.31i | −0.504779 | − | 0.874303i | ||||
\(300\) | −1034.81 | + | 30.1922i | −0.199150 | + | 0.00581050i | ||||
\(301\) | 2232.99 | − | 3867.65i | 0.427599 | − | 0.740623i | ||||
\(302\) | 18.9719 | − | 32.8604i | 0.00361494 | − | 0.00626126i | ||||
\(303\) | 1350.42 | + | 2188.98i | 0.256039 | + | 0.415029i | ||||
\(304\) | 2853.56 | + | 4942.51i | 0.538365 | + | 0.932475i | ||||
\(305\) | −3797.42 | −0.712916 | ||||||||
\(306\) | −115.119 | − | 174.970i | −0.0215063 | − | 0.0326874i | ||||
\(307\) | −5611.86 | −1.04328 | −0.521638 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521638 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(308\) | −1062.63 | − | 1840.52i | −0.196587 | − | 0.340498i | ||||
\(309\) | 1553.49 | − | 2881.67i | 0.286002 | − | 0.530525i | ||||
\(310\) | −110.093 | + | 190.687i | −0.0201706 | + | 0.0349364i | ||||
\(311\) | −5460.70 | + | 9458.21i | −0.995653 | + | 1.72452i | −0.417163 | + | 0.908831i | \(0.636976\pi\) |
−0.578489 | + | 0.815690i | \(0.696358\pi\) | |||||||
\(312\) | −185.138 | + | 343.424i | −0.0335941 | + | 0.0623159i | ||||
\(313\) | −2490.36 | − | 4313.44i | −0.449724 | − | 0.778946i | 0.548643 | − | 0.836056i | \(-0.315144\pi\) |
−0.998368 | + | 0.0571109i | \(0.981811\pi\) | |||||||
\(314\) | −235.955 | −0.0424067 | ||||||||
\(315\) | 1140.66 | − | 66.6175i | 0.204028 | − | 0.0119158i | ||||
\(316\) | −4899.89 | −0.872280 | ||||||||
\(317\) | 1878.06 | + | 3252.90i | 0.332752 | + | 0.576344i | 0.983050 | − | 0.183335i | \(-0.0586894\pi\) |
−0.650298 | + | 0.759679i | \(0.725356\pi\) | |||||||
\(318\) | −67.6440 | − | 109.648i | −0.0119286 | − | 0.0193357i | ||||
\(319\) | 58.9789 | − | 102.154i | 0.0103517 | − | 0.0179296i | ||||
\(320\) | 1250.70 | − | 2166.27i | 0.218488 | − | 0.378432i | ||||
\(321\) | −8107.73 | + | 236.555i | −1.40975 | + | 0.0411316i | ||||
\(322\) | 143.849 | + | 249.155i | 0.0248957 | + | 0.0431206i | ||||
\(323\) | 3998.99 | 0.688885 | ||||||||
\(324\) | 2299.40 | − | 5335.27i | 0.394273 | − | 0.914827i | ||||
\(325\) | 671.739 | 0.114650 | ||||||||
\(326\) | 90.9788 | + | 157.580i | 0.0154566 | + | 0.0267716i | ||||
\(327\) | −4862.25 | + | 141.864i | −0.822273 | + | 0.0239911i | ||||
\(328\) | 285.511 | − | 494.520i | 0.0480632 | − | 0.0832479i | ||||
\(329\) | −659.016 | + | 1141.45i | −0.110434 | + | 0.191277i | ||||
\(330\) | −75.2094 | − | 121.911i | −0.0125459 | − | 0.0203364i | ||||
\(331\) | 453.477 | + | 785.445i | 0.0753031 | + | 0.130429i | 0.901218 | − | 0.433366i | \(-0.142674\pi\) |
−0.825915 | + | 0.563795i | \(0.809341\pi\) | |||||||
\(332\) | −8569.55 | −1.41661 | ||||||||
\(333\) | −1677.33 | + | 97.9609i | −0.276028 | + | 0.0161208i | ||||
\(334\) | 582.182 | 0.0953759 | ||||||||
\(335\) | 1358.98 | + | 2353.81i | 0.221638 | + | 0.383888i | ||||
\(336\) | −1320.32 | + | 2449.14i | −0.214372 | + | 0.397654i | ||||
\(337\) | −4939.35 | + | 8555.20i | −0.798408 | + | 1.38288i | 0.122245 | + | 0.992500i | \(0.460991\pi\) |
−0.920653 | + | 0.390383i | \(0.872343\pi\) | |||||||
\(338\) | −129.053 | + | 223.527i | −0.0207680 | + | 0.0359712i | ||||
\(339\) | −3341.02 | + | 6197.48i | −0.535278 | + | 0.992923i | ||||
\(340\) | −883.220 | − | 1529.78i | −0.140880 | − | 0.244012i | ||||
\(341\) | 7929.49 | 1.25925 | ||||||||
\(342\) | −234.255 | − | 356.045i | −0.0370382 | − | 0.0562944i | ||||
\(343\) | −5199.81 | −0.818553 | ||||||||
\(344\) | 737.247 | + | 1276.95i | 0.115551 | + | 0.200141i | ||||
\(345\) | −2649.87 | − | 4295.34i | −0.413520 | − | 0.670299i | ||||
\(346\) | −104.488 | + | 180.979i | −0.0162350 | + | 0.0281199i | ||||
\(347\) | 1754.86 | − | 3039.50i | 0.271486 | − | 0.470228i | −0.697757 | − | 0.716335i | \(-0.745818\pi\) |
0.969243 | + | 0.246107i | \(0.0791516\pi\) | |||||||
\(348\) | −154.962 | + | 4.52124i | −0.0238702 | + | 0.000696448i | ||||
\(349\) | 5196.48 | + | 9000.57i | 0.797024 | + | 1.38049i | 0.921546 | + | 0.388269i | \(0.126927\pi\) |
−0.124522 | + | 0.992217i | \(0.539740\pi\) | |||||||
\(350\) | −37.0255 | −0.00565456 | ||||||||
\(351\) | −1592.33 | + | 3416.88i | −0.242143 | + | 0.519600i | ||||
\(352\) | 1053.19 | 0.159475 | ||||||||
\(353\) | −4042.70 | − | 7002.16i | −0.609550 | − | 1.05577i | −0.991315 | − | 0.131512i | \(-0.958017\pi\) |
0.381765 | − | 0.924259i | \(-0.375316\pi\) | |||||||
\(354\) | 448.836 | − | 13.0955i | 0.0673881 | − | 0.00196615i | ||||
\(355\) | 2320.52 | − | 4019.26i | 0.346930 | − | 0.600901i | ||||
\(356\) | 5997.56 | − | 10388.1i | 0.892893 | − | 1.54654i | ||||
\(357\) | 1023.63 | + | 1659.26i | 0.151754 | + | 0.245987i | ||||
\(358\) | 203.306 | + | 352.136i | 0.0300141 | + | 0.0519860i | ||||
\(359\) | −8189.49 | −1.20397 | −0.601984 | − | 0.798508i | \(-0.705623\pi\) | ||||
−0.601984 | + | 0.798508i | \(0.705623\pi\) | |||||||
\(360\) | −169.253 | + | 337.144i | −0.0247789 | + | 0.0493585i | ||||
\(361\) | 1278.52 | 0.186400 | ||||||||
\(362\) | 221.103 | + | 382.962i | 0.0321020 | + | 0.0556024i | ||||
\(363\) | 833.983 | − | 1547.01i | 0.120586 | − | 0.223683i | ||||
\(364\) | 906.184 | − | 1569.56i | 0.130486 | − | 0.226008i | ||||
\(365\) | −1521.85 | + | 2635.92i | −0.218239 | + | 0.378001i | ||||
\(366\) | −327.691 | + | 607.856i | −0.0467996 | + | 0.0868119i | ||||
\(367\) | 4497.33 | + | 7789.60i | 0.639669 | + | 1.10794i | 0.985505 | + | 0.169645i | \(0.0542621\pi\) |
−0.345836 | + | 0.938295i | \(0.612405\pi\) | |||||||
\(368\) | 12289.9 | 1.74091 | ||||||||
\(369\) | 2475.39 | − | 4930.86i | 0.349224 | − | 0.695638i | ||||
\(370\) | 54.4459 | 0.00765001 | ||||||||
\(371\) | 599.629 | + | 1038.59i | 0.0839116 | + | 0.145339i | ||||
\(372\) | −5471.71 | − | 8869.42i | −0.762621 | − | 1.23618i | ||||
\(373\) | 464.934 | − | 805.288i | 0.0645398 | − | 0.111786i | −0.831950 | − | 0.554851i | \(-0.812775\pi\) |
0.896490 | + | 0.443064i | \(0.146109\pi\) | |||||||
\(374\) | 122.208 | − | 211.670i | 0.0168963 | − | 0.0292652i | ||||
\(375\) | 649.243 | − | 18.9426i | 0.0894047 | − | 0.00260852i | ||||
\(376\) | −217.582 | − | 376.863i | −0.0298429 | − | 0.0516894i | ||||
\(377\) | 100.592 | 0.0137420 | ||||||||
\(378\) | 87.7673 | − | 188.335i | 0.0119425 | − | 0.0256267i | ||||
\(379\) | 3449.71 | 0.467546 | 0.233773 | − | 0.972291i | \(-0.424893\pi\) | ||||
0.233773 | + | 0.972291i | \(0.424893\pi\) | |||||||
\(380\) | −1797.26 | − | 3112.94i | −0.242625 | − | 0.420238i | ||||
\(381\) | −6141.14 | + | 179.177i | −0.825775 | + | 0.0240932i | ||||
\(382\) | 209.007 | − | 362.012i | 0.0279941 | − | 0.0484872i | ||||
\(383\) | 2673.07 | − | 4629.89i | 0.356625 | − | 0.617692i | −0.630770 | − | 0.775970i | \(-0.717261\pi\) |
0.987395 | + | 0.158278i | \(0.0505941\pi\) | |||||||
\(384\) | −968.370 | − | 1569.69i | −0.128690 | − | 0.208601i | ||||
\(385\) | 666.692 | + | 1154.75i | 0.0882540 | + | 0.152860i | ||||
\(386\) | −620.841 | −0.0818652 | ||||||||
\(387\) | 7830.66 | + | 11901.8i | 1.02857 | + | 1.56332i | ||||
\(388\) | 2651.72 | 0.346960 | ||||||||
\(389\) | −3861.72 | − | 6688.70i | −0.503334 | − | 0.871801i | −0.999993 | − | 0.00385448i | \(-0.998773\pi\) |
0.496658 | − | 0.867946i | \(-0.334560\pi\) | |||||||
\(390\) | 57.9664 | − | 107.526i | 0.00752627 | − | 0.0139610i | ||||
\(391\) | 4305.78 | − | 7457.83i | 0.556912 | − | 0.964600i | ||||
\(392\) | 379.151 | − | 656.709i | 0.0488521 | − | 0.0846144i | ||||
\(393\) | −5557.14 | + | 10308.3i | −0.713284 | + | 1.32312i | ||||
\(394\) | −108.426 | − | 187.799i | −0.0138640 | − | 0.0240132i | ||||
\(395\) | 3074.20 | 0.391594 | ||||||||
\(396\) | 6768.20 | − | 395.282i | 0.858876 | − | 0.0501607i | ||||
\(397\) | 7125.03 | 0.900744 | 0.450372 | − | 0.892841i | \(-0.351291\pi\) | ||||
0.450372 | + | 0.892841i | \(0.351291\pi\) | |||||||
\(398\) | 45.2035 | + | 78.2948i | 0.00569308 | + | 0.00986071i | ||||
\(399\) | 2082.98 | + | 3376.42i | 0.261352 | + | 0.423640i | ||||
\(400\) | −790.826 | + | 1369.75i | −0.0988532 | + | 0.171219i | ||||
\(401\) | 896.547 | − | 1552.86i | 0.111649 | − | 0.193382i | −0.804786 | − | 0.593565i | \(-0.797720\pi\) |
0.916435 | + | 0.400183i | \(0.131053\pi\) | |||||||
\(402\) | 494.047 | − | 14.4146i | 0.0612956 | − | 0.00178839i | ||||
\(403\) | 3381.05 | + | 5856.15i | 0.417921 | + | 0.723860i | ||||
\(404\) | 3944.73 | 0.485786 | ||||||||
\(405\) | −1442.65 | + | 3347.36i | −0.177002 | + | 0.410695i | ||||
\(406\) | −5.54451 | −0.000677757 | ||||||||
\(407\) | −980.369 | − | 1698.05i | −0.119398 | − | 0.206804i | ||||
\(408\) | −643.412 | + | 18.7725i | −0.0780727 | + | 0.00227789i | ||||
\(409\) | −1569.87 | + | 2719.09i | −0.189792 | + | 0.328729i | −0.945181 | − | 0.326548i | \(-0.894115\pi\) |
0.755389 | + | 0.655277i | \(0.227448\pi\) | |||||||
\(410\) | −89.3934 | + | 154.834i | −0.0107679 | + | 0.0186505i | ||||
\(411\) | −1292.38 | − | 2094.90i | −0.155106 | − | 0.251420i | ||||
\(412\) | −2510.48 | − | 4348.27i | −0.300200 | − | 0.519961i | ||||
\(413\) | −4179.77 | −0.497997 | ||||||||
\(414\) | −916.224 | + | 53.5100i | −0.108768 | + | 0.00635235i | ||||
\(415\) | 5376.55 | 0.635962 | ||||||||
\(416\) | 449.068 | + | 777.808i | 0.0529263 | + | 0.0916711i | ||||
\(417\) | 337.900 | − | 626.795i | 0.0396812 | − | 0.0736074i | ||||
\(418\) | 248.680 | − | 430.726i | 0.0290989 | − | 0.0504007i | ||||
\(419\) | −1228.70 | + | 2128.17i | −0.143260 | + | 0.248133i | −0.928722 | − | 0.370776i | \(-0.879092\pi\) |
0.785463 | + | 0.618909i | \(0.212425\pi\) | |||||||
\(420\) | 831.575 | − | 1542.55i | 0.0966112 | − | 0.179211i | ||||
\(421\) | 1339.33 | + | 2319.80i | 0.155048 | + | 0.268551i | 0.933076 | − | 0.359678i | \(-0.117113\pi\) |
−0.778029 | + | 0.628229i | \(0.783780\pi\) | |||||||
\(422\) | 3.12228 | 0.000360167 | ||||||||
\(423\) | −2311.04 | − | 3512.56i | −0.265643 | − | 0.403750i | ||||
\(424\) | −395.949 | −0.0453514 | ||||||||
\(425\) | 554.134 | + | 959.787i | 0.0632457 | + | 0.109545i | ||||
\(426\) | −443.121 | − | 718.281i | −0.0503974 | − | 0.0816921i | ||||
\(427\) | 3214.03 | − | 5566.86i | 0.364257 | − | 0.630911i | ||||
\(428\) | −6220.09 | + | 10773.5i | −0.702476 | + | 1.21672i | ||||
\(429\) | −4397.26 | + | 128.297i | −0.494876 | + | 0.0144388i | ||||
\(430\) | −230.831 | − | 399.812i | −0.0258876 | − | 0.0448387i | ||||
\(431\) | −9472.42 | −1.05863 | −0.529316 | − | 0.848425i | \(-0.677551\pi\) | ||||
−0.529316 | + | 0.848425i | \(0.677551\pi\) | |||||||
\(432\) | −5092.79 | − | 7269.57i | −0.567192 | − | 0.809623i | ||||
\(433\) | −4238.21 | −0.470382 | −0.235191 | − | 0.971949i | \(-0.575572\pi\) | ||||
−0.235191 | + | 0.971949i | \(0.575572\pi\) | |||||||
\(434\) | −186.360 | − | 322.784i | −0.0206119 | − | 0.0357008i | ||||
\(435\) | 97.2231 | − | 2.83663i | 0.0107161 | − | 0.000312658i | ||||
\(436\) | −3730.23 | + | 6460.94i | −0.409737 | + | 0.709686i | ||||
\(437\) | 8761.80 | − | 15175.9i | 0.959116 | − | 1.66124i | ||||
\(438\) | 290.609 | + | 471.065i | 0.0317028 | + | 0.0513889i | ||||
\(439\) | −2429.47 | − | 4207.96i | −0.264128 | − | 0.457483i | 0.703207 | − | 0.710985i | \(-0.251751\pi\) |
−0.967335 | + | 0.253503i | \(0.918417\pi\) | |||||||
\(440\) | −440.233 | −0.0476984 | ||||||||
\(441\) | 3287.25 | − | 6548.05i | 0.354957 | − | 0.707057i | ||||
\(442\) | 208.432 | 0.0224301 | ||||||||
\(443\) | −1167.88 | − | 2022.82i | −0.125254 | − | 0.216946i | 0.796578 | − | 0.604535i | \(-0.206641\pi\) |
−0.921832 | + | 0.387589i | \(0.873308\pi\) | |||||||
\(444\) | −1222.83 | + | 2268.31i | −0.130705 | + | 0.242453i | ||||
\(445\) | −3762.88 | + | 6517.49i | −0.400848 | + | 0.694289i | ||||
\(446\) | 86.5783 | − | 149.958i | 0.00919193 | − | 0.0159209i | ||||
\(447\) | 352.873 | − | 654.568i | 0.0373385 | − | 0.0692617i | ||||
\(448\) | 2117.11 | + | 3666.94i | 0.223268 | + | 0.386712i | ||||
\(449\) | 13290.5 | 1.39692 | 0.698460 | − | 0.715649i | \(-0.253869\pi\) | ||||
0.698460 | + | 0.715649i | \(0.253869\pi\) | |||||||
\(450\) | 52.9930 | − | 105.559i | 0.00555136 | − | 0.0110580i | ||||
\(451\) | 6438.58 | 0.672241 | ||||||||
\(452\) | 5399.17 | + | 9351.64i | 0.561849 | + | 0.973151i | ||||
\(453\) | −591.588 | − | 958.941i | −0.0613582 | − | 0.0994591i | ||||
\(454\) | −299.848 | + | 519.351i | −0.0309968 | + | 0.0536880i | ||||
\(455\) | −568.541 | + | 984.742i | −0.0585794 | + | 0.101462i | ||||
\(456\) | −1309.28 | + | 38.2001i | −0.134457 | + | 0.00392299i | ||||
\(457\) | −2587.31 | − | 4481.35i | −0.264834 | − | 0.458706i | 0.702686 | − | 0.711500i | \(-0.251984\pi\) |
−0.967520 | + | 0.252794i | \(0.918650\pi\) | |||||||
\(458\) | −192.415 | −0.0196309 | ||||||||
\(459\) | −6195.63 | + | 543.534i | −0.630037 | + | 0.0552724i | ||||
\(460\) | −7740.55 | −0.784576 | ||||||||
\(461\) | −3170.44 | − | 5491.37i | −0.320309 | − | 0.554791i | 0.660243 | − | 0.751052i | \(-0.270453\pi\) |
−0.980552 | + | 0.196261i | \(0.937120\pi\) | |||||||
\(462\) | 242.372 | − | 7.07157i | 0.0244073 | − | 0.000712119i | ||||
\(463\) | −1591.40 | + | 2756.38i | −0.159737 | + | 0.276673i | −0.934774 | − | 0.355243i | \(-0.884398\pi\) |
0.775036 | + | 0.631916i | \(0.217731\pi\) | |||||||
\(464\) | −118.425 | + | 205.118i | −0.0118486 | + | 0.0205223i | ||||
\(465\) | 3432.96 | + | 5564.68i | 0.342365 | + | 0.554959i | ||||
\(466\) | 390.208 | + | 675.860i | 0.0387898 | + | 0.0671859i | ||||
\(467\) | −8576.23 | −0.849808 | −0.424904 | − | 0.905238i | \(-0.639692\pi\) | ||||
−0.424904 | + | 0.905238i | \(0.639692\pi\) | |||||||
\(468\) | 3177.82 | + | 4829.96i | 0.313877 | + | 0.477062i | ||||
\(469\) | −4600.79 | −0.452974 | ||||||||
\(470\) | 68.1247 | + | 117.995i | 0.00668587 | + | 0.0115803i | ||||
\(471\) | −3324.87 | + | 6167.53i | −0.325269 | + | 0.603365i | ||||
\(472\) | 690.000 | − | 1195.11i | 0.0672877 | − | 0.116546i | ||||
\(473\) | −8312.84 | + | 14398.3i | −0.808086 | + | 1.39965i | ||||
\(474\) | 265.282 | − | 492.090i | 0.0257064 | − | 0.0476845i | ||||
\(475\) | 1127.60 | + | 1953.06i | 0.108922 | + | 0.188658i | ||||
\(476\) | 2990.13 | 0.287925 | ||||||||
\(477\) | −3819.23 | + | 223.054i | −0.366605 | + | 0.0214107i | ||||
\(478\) | −1145.18 | −0.109580 | ||||||||
\(479\) | −1458.82 | − | 2526.76i | −0.139155 | − | 0.241024i | 0.788022 | − | 0.615647i | \(-0.211105\pi\) |
−0.927177 | + | 0.374623i | \(0.877772\pi\) | |||||||
\(480\) | 455.962 | + | 739.096i | 0.0433578 | + | 0.0702812i | ||||
\(481\) | 836.037 | − | 1448.06i | 0.0792516 | − | 0.137268i | ||||
\(482\) | −18.4018 | + | 31.8729i | −0.00173896 | + | 0.00301197i | ||||
\(483\) | 8539.56 | − | 249.155i | 0.804479 | − | 0.0234719i | ||||
\(484\) | −1347.74 | − | 2334.35i | −0.126572 | − | 0.219229i | ||||
\(485\) | −1663.69 | −0.155761 | ||||||||
\(486\) | 411.324 | + | 519.779i | 0.0383910 | + | 0.0485137i | ||||
\(487\) | −14061.0 | −1.30834 | −0.654172 | − | 0.756346i | \(-0.726983\pi\) | ||||
−0.654172 | + | 0.756346i | \(0.726983\pi\) | |||||||
\(488\) | 1061.15 | + | 1837.96i | 0.0984343 | + | 0.170493i | ||||
\(489\) | 5400.92 | − | 157.580i | 0.499464 | − | 0.0145726i | ||||
\(490\) | −118.712 | + | 205.615i | −0.0109446 | + | 0.0189566i | ||||
\(491\) | 466.331 | − | 807.709i | 0.0428620 | − | 0.0742391i | −0.843799 | − | 0.536660i | \(-0.819686\pi\) |
0.886661 | + | 0.462421i | \(0.153019\pi\) | |||||||
\(492\) | −4442.91 | − | 7201.78i | −0.407118 | − | 0.659921i | ||||
\(493\) | 82.9806 | + | 143.727i | 0.00758065 | + | 0.0131301i | ||||
\(494\) | 424.137 | 0.0386292 | ||||||||
\(495\) | −4246.38 | + | 248.000i | −0.385577 | + | 0.0225187i | ||||
\(496\) | −15921.8 | −1.44135 | ||||||||
\(497\) | 3928.04 | + | 6803.57i | 0.354521 | + | 0.614048i | ||||
\(498\) | 463.959 | − | 860.629i | 0.0417480 | − | 0.0774412i | ||||
\(499\) | 7215.39 | − | 12497.4i | 0.647305 | − | 1.12117i | −0.336459 | − | 0.941698i | \(-0.609229\pi\) |
0.983764 | − | 0.179467i | \(-0.0574374\pi\) | |||||||
\(500\) | 498.086 | − | 862.711i | 0.0445502 | − | 0.0771632i | ||||
\(501\) | 8203.60 | − | 15217.4i | 0.731557 | − | 1.35701i | ||||
\(502\) | 71.4062 | + | 123.679i | 0.00634864 | + | 0.0109962i | ||||
\(503\) | −3230.55 | −0.286368 | −0.143184 | − | 0.989696i | \(-0.545734\pi\) | ||||
−0.143184 | + | 0.989696i | \(0.545734\pi\) | |||||||
\(504\) | −350.988 | − | 533.467i | −0.0310203 | − | 0.0471478i | ||||
\(505\) | −2474.93 | −0.218085 | ||||||||
\(506\) | −535.515 | − | 927.539i | −0.0470485 | − | 0.0814904i | ||||
\(507\) | 4024.18 | + | 6523.03i | 0.352505 | + | 0.571397i | ||||
\(508\) | −4711.36 | + | 8160.32i | −0.411482 | + | 0.712708i | ||||
\(509\) | 180.378 | − | 312.424i | 0.0157075 | − | 0.0272062i | −0.858065 | − | 0.513541i | \(-0.828333\pi\) |
0.873772 | + | 0.486335i | \(0.161667\pi\) | |||||||
\(510\) | 201.452 | − | 5.87766i | 0.0174911 | − | 0.000510328i | ||||
\(511\) | −2576.10 | − | 4461.93i | −0.223013 | − | 0.386270i | ||||
\(512\) | −3529.04 | −0.304615 | ||||||||
\(513\) | −12607.4 | + | 1106.03i | −1.08505 | + | 0.0951903i | ||||
\(514\) | 730.096 | 0.0626521 | ||||||||
\(515\) | 1575.08 | + | 2728.11i | 0.134769 | + | 0.233427i | ||||
\(516\) | 21841.2 | − | 637.250i | 1.86338 | − | 0.0543670i | ||||
\(517\) | 2453.35 | − | 4249.33i | 0.208701 | − | 0.361480i | ||||
\(518\) | −46.0814 | + | 79.8154i | −0.00390869 | + | 0.00677005i | ||||
\(519\) | 3258.18 | + | 5281.37i | 0.275565 | + | 0.446679i | ||||
\(520\) | −187.710 | − | 325.124i | −0.0158301 | − | 0.0274185i | ||||
\(521\) | −11698.8 | −0.983747 | −0.491873 | − | 0.870667i | \(-0.663688\pi\) | ||||
−0.491873 | + | 0.870667i | \(0.663688\pi\) | |||||||
\(522\) | 7.93562 | − | 15.8074i | 0.000665388 | − | 0.00132542i | ||||
\(523\) | 18557.3 | 1.55154 | 0.775770 | − | 0.631015i | \(-0.217362\pi\) | ||||
0.775770 | + | 0.631015i | \(0.217362\pi\) | |||||||
\(524\) | 8980.49 | + | 15554.7i | 0.748692 | + | 1.29677i | ||||
\(525\) | −521.731 | + | 967.795i | −0.0433719 | + | 0.0804534i | ||||
\(526\) | −246.470 | + | 426.899i | −0.0204308 | + | 0.0353872i | ||||
\(527\) | −5578.21 | + | 9661.75i | −0.461083 | + | 0.798619i | ||||
\(528\) | 4915.20 | − | 9117.54i | 0.405126 | − | 0.751496i | ||||
\(529\) | −12784.5 | − | 22143.3i | −1.05075 | − | 1.81995i | ||||
\(530\) | 123.971 | 0.0101603 | ||||||||
\(531\) | 5982.32 | − | 11916.5i | 0.488909 | − | 0.973883i | ||||
\(532\) | 6084.59 | 0.495866 | ||||||||
\(533\) | 2745.34 | + | 4755.07i | 0.223103 | + | 0.386426i | ||||
\(534\) | 718.551 | + | 1164.74i | 0.0582298 | + | 0.0943882i | ||||
\(535\) | 3902.50 | − | 6759.32i | 0.315364 | − | 0.546226i | ||||
\(536\) | 759.503 | − | 1315.50i | 0.0612044 | − | 0.106009i | ||||
\(537\) | 12069.2 | − | 352.136i | 0.969875 | − | 0.0282976i | ||||
\(538\) | −8.97756 | − | 15.5496i | −0.000719424 | − | 0.00124608i | ||||
\(539\) | 8550.26 | 0.683276 | ||||||||
\(540\) | 3207.59 | + | 4578.60i | 0.255616 | + | 0.364873i | ||||
\(541\) | 22755.3 | 1.80837 | 0.904185 | − | 0.427140i | \(-0.140479\pi\) | ||||
0.904185 | + | 0.427140i | \(0.140479\pi\) | |||||||
\(542\) | −291.985 | − | 505.733i | −0.0231399 | − | 0.0400795i | ||||
\(543\) | 13125.7 | − | 382.962i | 1.03734 | − | 0.0302661i | ||||
\(544\) | −740.893 | + | 1283.26i | −0.0583925 | + | 0.101139i | ||||
\(545\) | 2340.35 | − | 4053.60i | 0.183944 | − | 0.318601i | ||||
\(546\) | 108.567 | + | 175.983i | 0.00850962 | + | 0.0137937i | ||||
\(547\) | −2899.05 | − | 5021.30i | −0.226608 | − | 0.392496i | 0.730193 | − | 0.683241i | \(-0.239430\pi\) |
−0.956801 | + | 0.290745i | \(0.906097\pi\) | |||||||
\(548\) | −3775.18 | −0.294284 | ||||||||
\(549\) | 11271.0 | + | 17130.8i | 0.876200 | + | 1.33174i | ||||
\(550\) | 137.837 | 0.0106861 | ||||||||
\(551\) | 168.857 | + | 292.468i | 0.0130554 | + | 0.0226127i | ||||
\(552\) | −1338.48 | + | 2482.84i | −0.103205 | + | 0.191443i | ||||
\(553\) | −2601.92 | + | 4506.65i | −0.200081 | + | 0.346550i | ||||
\(554\) | 55.4599 | − | 96.0593i | 0.00425318 | − | 0.00736673i | ||||
\(555\) | 767.204 | − | 1423.14i | 0.0586775 | − | 0.108845i | ||||
\(556\) | −546.056 | − | 945.797i | −0.0416510 | − | 0.0721416i | ||||
\(557\) | 15740.3 | 1.19738 | 0.598688 | − | 0.800982i | \(-0.295689\pi\) | ||||
0.598688 | + | 0.800982i | \(0.295689\pi\) | |||||||
\(558\) | 1186.98 | − | 69.3231i | 0.0900521 | − | 0.00525929i | ||||
\(559\) | −14178.0 | −1.07275 | ||||||||
\(560\) | −1338.66 | − | 2318.64i | −0.101016 | − | 0.174965i | ||||
\(561\) | −3810.72 | − | 6177.01i | −0.286789 | − | 0.464873i | ||||
\(562\) | −542.662 | + | 939.919i | −0.0407310 | + | 0.0705482i | ||||
\(563\) | −1909.56 | + | 3307.45i | −0.142946 | + | 0.247589i | −0.928605 | − | 0.371071i | \(-0.878991\pi\) |
0.785659 | + | 0.618660i | \(0.212324\pi\) | |||||||
\(564\) | −6445.94 | + | 188.070i | −0.481247 | + | 0.0140411i | ||||
\(565\) | −3387.45 | − | 5867.23i | −0.252232 | − | 0.436878i | ||||
\(566\) | 1308.91 | 0.0972040 | ||||||||
\(567\) | −3686.07 | − | 4947.97i | −0.273016 | − | 0.366482i | ||||
\(568\) | −2593.78 | −0.191607 | ||||||||
\(569\) | −4445.56 | − | 7699.93i | −0.327535 | − | 0.567308i | 0.654487 | − | 0.756073i | \(-0.272885\pi\) |
−0.982022 | + | 0.188766i | \(0.939551\pi\) | |||||||
\(570\) | 409.933 | − | 11.9604i | 0.0301232 | − | 0.000878889i | ||||
\(571\) | −4193.31 | + | 7263.03i | −0.307329 | + | 0.532309i | −0.977777 | − | 0.209647i | \(-0.932768\pi\) |
0.670448 | + | 0.741956i | \(0.266102\pi\) | |||||||
\(572\) | −3373.49 | + | 5843.06i | −0.246596 | + | 0.427116i | ||||
\(573\) | −6517.33 | − | 10564.3i | −0.475158 | − | 0.770211i | ||||
\(574\) | −151.320 | − | 262.094i | −0.0110034 | − | 0.0190585i | ||||
\(575\) | 4856.43 | 0.352221 | ||||||||
\(576\) | −13484.6 | + | 787.536i | −0.975446 | + | 0.0569687i | ||||
\(577\) | 16922.3 | 1.22095 | 0.610473 | − | 0.792037i | \(-0.290979\pi\) | ||||
0.610473 | + | 0.792037i | \(0.290979\pi\) | |||||||
\(578\) | −257.909 | − | 446.711i | −0.0185599 | − | 0.0321466i | ||||
\(579\) | −8748.35 | + | 16227.9i | −0.627926 | + | 1.16478i | ||||
\(580\) | 74.5877 | − | 129.190i | 0.00533980 | − | 0.00924880i | ||||
\(581\) | −4550.56 | + | 7881.80i | −0.324938 | + | 0.562809i | ||||
\(582\) | −143.565 | + | 266.309i | −0.0102250 | + | 0.0189671i | ||||
\(583\) | −2232.27 | − | 3866.40i | −0.158578 | − | 0.274666i | ||||
\(584\) | 1701.06 | 0.120531 | ||||||||
\(585\) | −1993.77 | − | 3030.32i | −0.140909 | − | 0.214168i | ||||
\(586\) | 846.315 | 0.0596603 | ||||||||
\(587\) | −7619.29 | − | 13197.0i | −0.535744 | − | 0.927936i | −0.999127 | − | 0.0417777i | \(-0.986698\pi\) |
0.463383 | − | 0.886158i | \(-0.346635\pi\) | |||||||
\(588\) | −5900.07 | − | 9563.77i | −0.413800 | − | 0.670754i | ||||
\(589\) | −11351.1 | + | 19660.6i | −0.794079 | + | 1.37539i | ||||
\(590\) | −216.038 | + | 374.189i | −0.0150748 | + | 0.0261104i | ||||
\(591\) | −6436.66 | + | 187.799i | −0.448002 | + | 0.0130711i | ||||
\(592\) | 1968.50 | + | 3409.55i | 0.136664 | + | 0.236709i | ||||
\(593\) | −16960.2 | −1.17449 | −0.587245 | − | 0.809409i | \(-0.699787\pi\) | ||||
−0.587245 | + | 0.809409i | \(0.699787\pi\) | |||||||
\(594\) | −326.735 | + | 701.123i | −0.0225692 | + | 0.0484300i | ||||
\(595\) | −1876.01 | −0.129259 | ||||||||
\(596\) | −570.252 | − | 987.705i | −0.0391920 | − | 0.0678825i | ||||
\(597\) | 2683.49 | − | 78.2948i | 0.183966 | − | 0.00536749i | ||||
\(598\) | 456.676 | − | 790.986i | 0.0312289 | − | 0.0540900i | ||||
\(599\) | 12456.1 | − | 21574.5i | 0.849651 | − | 1.47164i | −0.0318690 | − | 0.999492i | \(-0.510146\pi\) |
0.881520 | − | 0.472147i | \(-0.156521\pi\) | |||||||
\(600\) | −190.592 | − | 308.942i | −0.0129682 | − | 0.0210209i | ||||
\(601\) | 2175.63 | + | 3768.31i | 0.147664 | + | 0.255761i | 0.930364 | − | 0.366638i | \(-0.119491\pi\) |
−0.782700 | + | 0.622399i | \(0.786158\pi\) | |||||||
\(602\) | 781.476 | 0.0529080 | ||||||||
\(603\) | 6584.91 | − | 13116.8i | 0.444707 | − | 0.885835i | ||||
\(604\) | −1728.09 | −0.116416 | ||||||||
\(605\) | 845.573 | + | 1464.58i | 0.0568222 | + | 0.0984190i | ||||
\(606\) | −213.569 | + | 396.164i | −0.0143163 | + | 0.0265562i | ||||
\(607\) | −13911.8 | + | 24096.0i | −0.930254 | + | 1.61125i | −0.147369 | + | 0.989082i | \(0.547081\pi\) |
−0.782885 | + | 0.622166i | \(0.786253\pi\) | |||||||
\(608\) | −1507.64 | + | 2611.31i | −0.100564 | + | 0.174182i | ||||
\(609\) | −78.1285 | + | 144.926i | −0.00519856 | + | 0.00964317i | ||||
\(610\) | −332.245 | − | 575.465i | −0.0220528 | − | 0.0381965i | ||||
\(611\) | 4184.33 | 0.277054 | ||||||||
\(612\) | −4279.64 | + | 8524.84i | −0.282670 | + | 0.563066i | ||||
\(613\) | 20034.6 | 1.32005 | 0.660024 | − | 0.751244i | \(-0.270546\pi\) | ||||
0.660024 | + | 0.751244i | \(0.270546\pi\) | |||||||
\(614\) | −490.994 | − | 850.427i | −0.0322719 | − | 0.0558965i | ||||
\(615\) | 2787.49 | + | 4518.40i | 0.182768 | + | 0.296260i | ||||
\(616\) | 372.600 | − | 645.363i | 0.0243709 | − | 0.0422117i | ||||
\(617\) | −3776.95 | + | 6541.86i | −0.246441 | + | 0.426848i | −0.962536 | − | 0.271155i | \(-0.912595\pi\) |
0.716095 | + | 0.698003i | \(0.245928\pi\) | |||||||
\(618\) | 572.609 | − | 16.7067i | 0.0372714 | − | 0.00108745i | ||||
\(619\) | −6192.54 | − | 10725.8i | −0.402099 | − | 0.696456i | 0.591880 | − | 0.806026i | \(-0.298386\pi\) |
−0.993979 | + | 0.109570i | \(0.965053\pi\) | |||||||
\(620\) | 10028.0 | 0.649573 | ||||||||
\(621\) | −11512.0 | + | 24702.8i | −0.743896 | + | 1.59628i | ||||
\(622\) | −1911.08 | −0.123195 | ||||||||
\(623\) | −6369.58 | − | 11032.4i | −0.409618 | − | 0.709479i | ||||
\(624\) | 8829.35 | − | 257.610i | 0.566437 | − | 0.0165267i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 435.775 | − | 754.785i | 0.0278228 | − | 0.0481906i | ||||
\(627\) | −7754.40 | − | 12569.6i | −0.493909 | − | 0.800606i | ||||
\(628\) | 5373.08 | + | 9306.45i | 0.341416 | + | 0.591350i | ||||
\(629\) | 2758.67 | 0.174873 | ||||||||
\(630\) | 109.894 | + | 167.028i | 0.00694966 | + | 0.0105628i | ||||
\(631\) | −1325.17 | −0.0836043 | −0.0418022 | − | 0.999126i | \(-0.513310\pi\) | ||||
−0.0418022 | + | 0.999126i | \(0.513310\pi\) | |||||||
\(632\) | −859.053 | − | 1487.92i | −0.0540685 | − | 0.0936494i | ||||
\(633\) | 43.9965 | − | 81.6122i | 0.00276257 | − | 0.00512447i | ||||
\(634\) | −328.632 | + | 569.207i | −0.0205862 | + | 0.0356563i | ||||
\(635\) | 2955.91 | − | 5119.79i | 0.184727 | − | 0.319957i | ||||
\(636\) | −2784.34 | + | 5164.86i | −0.173595 | + | 0.322013i | ||||
\(637\) | 3645.74 | + | 6314.60i | 0.226765 | + | 0.392769i | ||||
\(638\) | 20.6408 | 0.00128084 | ||||||||
\(639\) | −25019.0 | + | 1461.18i | −1.54888 | + | 0.0904589i | ||||
\(640\) | 1774.74 | 0.109613 | ||||||||
\(641\) | 11255.8 | + | 19495.6i | 0.693568 | + | 1.20129i | 0.970661 | + | 0.240451i | \(0.0772955\pi\) |
−0.277094 | + | 0.960843i | \(0.589371\pi\) | |||||||
\(642\) | −745.212 | − | 1207.96i | −0.0458118 | − | 0.0742590i | ||||
\(643\) | −2807.31 | + | 4862.40i | −0.172176 | + | 0.298218i | −0.939180 | − | 0.343424i | \(-0.888413\pi\) |
0.767004 | + | 0.641642i | \(0.221747\pi\) | |||||||
\(644\) | 6551.38 | − | 11347.3i | 0.400871 | − | 0.694328i | ||||
\(645\) | −13703.2 | + | 399.812i | −0.836532 | + | 0.0244071i | ||||
\(646\) | 349.881 | + | 606.012i | 0.0213094 | + | 0.0369090i | ||||
\(647\) | −11753.6 | −0.714188 | −0.357094 | − | 0.934068i | \(-0.616232\pi\) | ||||
−0.357094 | + | 0.934068i | \(0.616232\pi\) | |||||||
\(648\) | 2023.27 | − | 237.137i | 0.122656 | − | 0.0143760i | ||||
\(649\) | 15560.2 | 0.941127 | ||||||||
\(650\) | 58.7720 | + | 101.796i | 0.00354650 | + | 0.00614273i | ||||
\(651\) | −11063.2 | + | 322.784i | −0.666051 | + | 0.0194330i | ||||
\(652\) | 4143.48 | − | 7176.71i | 0.248882 | − | 0.431076i | ||||
\(653\) | 12929.1 | − | 22393.9i | 0.774816 | − | 1.34202i | −0.160082 | − | 0.987104i | \(-0.551176\pi\) |
0.934898 | − | 0.354916i | \(-0.115491\pi\) | |||||||
\(654\) | −446.908 | − | 724.420i | −0.0267209 | − | 0.0433135i | ||||
\(655\) | −5634.37 | − | 9759.02i | −0.336112 | − | 0.582163i | ||||
\(656\) | −12928.1 | −0.769450 | ||||||||
\(657\) | 16408.0 | − | 958.272i | 0.974333 | − | 0.0569037i | ||||
\(658\) | −230.635 | −0.0136643 | ||||||||
\(659\) | 8847.75 | + | 15324.8i | 0.523004 | + | 0.905869i | 0.999642 | + | 0.0267695i | \(0.00852201\pi\) |
−0.476638 | + | 0.879100i | \(0.658145\pi\) | |||||||
\(660\) | −3095.74 | + | 5742.51i | −0.182578 | + | 0.338677i | ||||
\(661\) | −3115.05 | + | 5395.42i | −0.183300 | + | 0.317485i | −0.943002 | − | 0.332786i | \(-0.892011\pi\) |
0.759702 | + | 0.650271i | \(0.225345\pi\) | |||||||
\(662\) | −79.3515 | + | 137.441i | −0.00465873 | + | 0.00806916i | ||||
\(663\) | 2937.05 | − | 5448.13i | 0.172044 | − | 0.319137i | ||||
\(664\) | −1502.42 | − | 2602.27i | −0.0878091 | − | 0.152090i | ||||
\(665\) | −3817.48 | −0.222610 | ||||||||
\(666\) | −161.599 | − | 245.614i | −0.00940214 | − | 0.0142903i | ||||
\(667\) | 727.243 | 0.0422174 | ||||||||
\(668\) | −13257.2 | − | 22962.2i | −0.767872 | − | 1.32999i | ||||
\(669\) | −2699.71 | − | 4376.12i | −0.156019 | − | 0.252901i | ||||
\(670\) | −237.800 | + | 411.881i | −0.0137120 | + | 0.0237498i | ||||
\(671\) | −11965.0 | + | 20724.0i | −0.688381 | + | 1.19231i | ||||
\(672\) | −1469.40 | + | 42.8719i | −0.0843501 | + | 0.00246104i | ||||
\(673\) | 3025.84 | + | 5240.91i | 0.173310 | + | 0.300182i | 0.939575 | − | 0.342343i | \(-0.111220\pi\) |
−0.766265 | + | 0.642524i | \(0.777887\pi\) | |||||||
\(674\) | −1728.62 | −0.0987892 | ||||||||
\(675\) | −2012.45 | − | 2872.62i | −0.114754 | − | 0.163803i | ||||
\(676\) | 11755.0 | 0.668812 | ||||||||
\(677\) | −14049.3 | − | 24334.1i | −0.797576 | − | 1.38144i | −0.921190 | − | 0.389112i | \(-0.872782\pi\) |
0.123614 | − | 0.992330i | \(-0.460551\pi\) | |||||||
\(678\) | −1231.49 | + | 35.9305i | −0.0697566 | + | 0.00203525i | ||||
\(679\) | 1408.10 | − | 2438.90i | 0.0795846 | − | 0.137845i | ||||
\(680\) | 309.694 | − | 536.405i | 0.0174650 | − | 0.0302503i | ||||
\(681\) | 9349.93 | + | 15155.9i | 0.526124 | + | 0.852825i | ||||
\(682\) | 693.769 | + | 1201.64i | 0.0389528 | + | 0.0674682i | ||||
\(683\) | −8335.71 | −0.466994 | −0.233497 | − | 0.972358i | \(-0.575017\pi\) | ||||
−0.233497 | + | 0.972358i | \(0.575017\pi\) | |||||||
\(684\) | −8708.61 | + | 17347.1i | −0.486816 | + | 0.969714i | ||||
\(685\) | 2368.56 | 0.132114 | ||||||||
\(686\) | −454.944 | − | 787.986i | −0.0253205 | − | 0.0438563i | ||||
\(687\) | −2711.34 | + | 5029.46i | −0.150574 | + | 0.279310i | ||||
\(688\) | 16691.5 | − | 28910.6i | 0.924939 | − | 1.60204i | ||||
\(689\) | 1903.63 | − | 3297.18i | 0.105258 | − | 0.182312i | ||||
\(690\) | 419.076 | − | 777.374i | 0.0231217 | − | 0.0428900i | ||||
\(691\) | 8442.55 | + | 14622.9i | 0.464790 | + | 0.805039i | 0.999192 | − | 0.0401909i | \(-0.0127966\pi\) |
−0.534402 | + | 0.845230i | \(0.679463\pi\) | |||||||
\(692\) | 9517.46 | 0.522832 | ||||||||
\(693\) | 3230.46 | − | 6434.92i | 0.177078 | − | 0.352731i | ||||
\(694\) | 614.146 | 0.0335917 | ||||||||
\(695\) | 342.596 | + | 593.394i | 0.0186984 | + | 0.0323867i | ||||
\(696\) | −28.5409 | − | 46.2637i | −0.00155437 | − | 0.00251957i | ||||
\(697\) | −4529.39 | + | 7845.14i | −0.246145 | + | 0.426335i | ||||
\(698\) | −909.305 | + | 1574.96i | −0.0493090 | + | 0.0854057i | ||||
\(699\) | 23164.5 | − | 675.860i | 1.25345 | − | 0.0365714i | ||||
\(700\) | 843.132 | + | 1460.35i | 0.0455248 | + | 0.0788514i | ||||
\(701\) | 16875.2 | 0.909226 | 0.454613 | − | 0.890689i | \(-0.349778\pi\) | ||||
0.454613 | + | 0.890689i | \(0.349778\pi\) | |||||||
\(702\) | −657.115 | + | 57.6479i | −0.0353293 | + | 0.00309940i | ||||
\(703\) | 5613.59 | 0.301167 | ||||||||
\(704\) | −7881.47 | − | 13651.1i | −0.421938 | − | 0.730817i | ||||
\(705\) | 4044.19 | − | 117.995i | 0.216047 | − | 0.00630350i | ||||
\(706\) | 707.410 | − | 1225.27i | 0.0377106 | − | 0.0653168i | ||||
\(707\) | 2094.71 | − | 3628.14i | 0.111428 | − | 0.192999i | ||||
\(708\) | −10737.3 | − | 17404.6i | −0.569959 | − | 0.923879i | ||||
\(709\) | 9503.71 | + | 16460.9i | 0.503412 | + | 0.871936i | 0.999992 | + | 0.00394482i | \(0.00125568\pi\) |
−0.496580 | + | 0.867991i | \(0.665411\pi\) | |||||||
\(710\) | 812.110 | 0.0429267 | ||||||||
\(711\) | −9124.43 | − | 13868.2i | −0.481284 | − | 0.731503i | ||||
\(712\) | 4205.99 | 0.221385 | ||||||||
\(713\) | 24443.8 | + | 42337.9i | 1.28391 | + | 2.22379i | ||||
\(714\) | −161.887 | + | 300.295i | −0.00848524 | + | 0.0157398i | ||||
\(715\) | 2116.53 | − | 3665.94i | 0.110705 | − | 0.191746i | ||||
\(716\) | 9259.23 | − | 16037.4i | 0.483287 | − | 0.837078i | ||||
\(717\) | −16136.9 | + | 29933.4i | −0.840506 | + | 1.55911i | ||||
\(718\) | −716.517 | − | 1241.04i | −0.0372426 | − | 0.0645061i | ||||
\(719\) | 17588.1 | 0.912275 | 0.456138 | − | 0.889909i | \(-0.349233\pi\) | ||||
0.456138 | + | 0.889909i | \(0.349233\pi\) | |||||||
\(720\) | 8526.39 | − | 497.965i | 0.441333 | − | 0.0257751i | ||||
\(721\) | −5332.40 | −0.275435 | ||||||||
\(722\) | 111.861 | + | 193.748i | 0.00576596 | + | 0.00998693i | ||||
\(723\) | 573.810 | + | 930.123i | 0.0295162 | + | 0.0478446i | ||||
\(724\) | 10069.8 | − | 17441.4i | 0.516907 | − | 0.895309i | ||||
\(725\) | −46.7964 | + | 81.0537i | −0.00239721 | + | 0.00415208i | ||||
\(726\) | 307.403 | − | 8.96895i | 0.0157146 | − | 0.000458497i | ||||
\(727\) | −2802.69 | − | 4854.40i | −0.142979 | − | 0.247648i | 0.785638 | − | 0.618687i | \(-0.212335\pi\) |
−0.928617 | + | 0.371039i | \(0.879002\pi\) | |||||||
\(728\) | 635.491 | 0.0323528 | ||||||||
\(729\) | 19382.3 | − | 3427.15i | 0.984725 | − | 0.174117i | ||||
\(730\) | −532.600 | −0.0270033 | ||||||||
\(731\) | −11695.8 | − | 20257.7i | −0.591771 | − | 1.02498i | ||||
\(732\) | 31436.9 | − | 917.220i | 1.58735 | − | 0.0463134i | ||||
\(733\) | −7460.04 | + | 12921.2i | −0.375911 | + | 0.651097i | −0.990463 | − | 0.137779i | \(-0.956004\pi\) |
0.614552 | + | 0.788877i | \(0.289337\pi\) | |||||||
\(734\) | −786.963 | + | 1363.06i | −0.0395740 | + | 0.0685443i | ||||
\(735\) | 3701.71 | + | 6000.32i | 0.185768 | + | 0.301123i | ||||
\(736\) | 3246.60 | + | 5623.27i | 0.162597 | + | 0.281626i | ||||
\(737\) | 17127.6 | 0.856042 | ||||||||
\(738\) | 963.806 | − | 56.2889i | 0.0480734 | − | 0.00280762i | ||||
\(739\) | −27418.8 | −1.36484 | −0.682421 | − | 0.730959i | \(-0.739073\pi\) | ||||
−0.682421 | + | 0.730959i | \(0.739073\pi\) | |||||||
\(740\) | −1239.82 | − | 2147.44i | −0.0615903 | − | 0.106677i | ||||
\(741\) | 5976.58 | − | 11086.4i | 0.296296 | − | 0.549619i | ||||
\(742\) | −104.926 | + | 181.737i | −0.00519131 | + | 0.00899161i | ||||
\(743\) | 12272.1 | − | 21255.9i | 0.605948 | − | 1.04953i | −0.385953 | − | 0.922518i | \(-0.626127\pi\) |
0.991901 | − | 0.127014i | \(-0.0405394\pi\) | |||||||
\(744\) | 1734.02 | − | 3216.56i | 0.0854467 | − | 0.158501i | ||||
\(745\) | 357.777 | + | 619.687i | 0.0175945 | + | 0.0304746i | ||||
\(746\) | 162.712 | 0.00798569 | ||||||||
\(747\) | −15957.9 | − | 24254.5i | −0.781621 | − | 1.18799i | ||||
\(748\) | −11131.5 | −0.544128 | ||||||||
\(749\) | 6605.92 | + | 11441.8i | 0.322263 | + | 0.558176i | ||||
\(750\) | 59.6743 | + | 96.7296i | 0.00290533 | + | 0.00470942i | ||||
\(751\) | −767.283 | + | 1328.97i | −0.0372817 | + | 0.0645738i | −0.884064 | − | 0.467365i | \(-0.845203\pi\) |
0.846782 | + | 0.531939i | \(0.178537\pi\) | |||||||
\(752\) | −4926.13 | + | 8532.30i | −0.238880 | + | 0.413752i | ||||
\(753\) | 4239.00 | − | 123.679i | 0.205150 | − | 0.00598555i | ||||
\(754\) | 8.80102 | + | 15.2438i | 0.000425085 | + | 0.000736269i | ||||
\(755\) | 1084.21 | 0.0522627 | ||||||||
\(756\) | −9426.85 | + | 827.005i | −0.453507 | + | 0.0397856i | ||||
\(757\) | −18051.1 | −0.866681 | −0.433341 | − | 0.901230i | \(-0.642665\pi\) | ||||
−0.433341 | + | 0.901230i | \(0.642665\pi\) | |||||||
\(758\) | 301.823 | + | 522.773i | 0.0144627 | + | 0.0250501i | ||||
\(759\) | −31790.6 | + | 927.539i | −1.52032 | + | 0.0443578i | ||||
\(760\) | 630.194 | − | 1091.53i | 0.0300783 | − | 0.0520972i | ||||
\(761\) | −6462.29 | + | 11193.0i | −0.307829 | + | 0.533176i | −0.977887 | − | 0.209133i | \(-0.932936\pi\) |
0.670058 | + | 0.742309i | \(0.266269\pi\) | |||||||
\(762\) | −564.455 | − | 914.958i | −0.0268347 | − | 0.0434980i | ||||
\(763\) | 3961.61 | + | 6861.71i | 0.187968 | + | 0.325571i | ||||
\(764\) | −19037.8 | −0.901522 | ||||||||
\(765\) | 2685.05 | − | 5348.50i | 0.126900 | − | 0.252778i | ||||
\(766\) | 935.491 | 0.0441262 | ||||||||
\(767\) | 6634.70 | + | 11491.6i | 0.312341 | + | 0.540990i | ||||
\(768\) | −9715.30 | + | 18021.6i | −0.456472 | + | 0.846741i | ||||
\(769\) | 1686.16 | − | 2920.51i | 0.0790695 | − | 0.136952i | −0.823779 | − | 0.566911i | \(-0.808138\pi\) |
0.902849 | + | 0.429958i | \(0.141472\pi\) | |||||||
\(770\) | −116.661 | + | 202.063i | −0.00545996 | + | 0.00945692i | ||||
\(771\) | 10287.9 | − | 19083.7i | 0.480557 | − | 0.891418i | ||||
\(772\) | 14137.6 | + | 24487.0i | 0.659097 | + | 1.14159i | ||||
\(773\) | −27152.6 | −1.26341 | −0.631703 | − | 0.775211i | \(-0.717644\pi\) | ||||
−0.631703 | + | 0.775211i | \(0.717644\pi\) | |||||||
\(774\) | −1118.49 | + | 2227.99i | −0.0519424 | + | 0.103467i | ||||
\(775\) | −6291.59 | −0.291614 | ||||||||
\(776\) | 464.901 | + | 805.232i | 0.0215064 | + | 0.0372502i | ||||
\(777\) | 1436.92 | + | 2329.19i | 0.0663441 | + | 0.107541i | ||||
\(778\) | 675.742 | − | 1170.42i | 0.0311395 | − | 0.0539352i | ||||
\(779\) | −9216.83 | + | 15964.0i | −0.423912 | + | 0.734236i | ||||
\(780\) | −5560.99 | + | 162.250i | −0.255276 | + | 0.00744807i | ||||
\(781\) | −14623.1 | − | 25327.9i | −0.669982 | − | 1.16044i | ||||
\(782\) | 1506.89 | 0.0689083 | ||||||||
\(783\) | −301.361 | − | 430.170i | −0.0137545 | − | 0.0196335i | ||||
\(784\) | −17168.2 | −0.782080 | ||||||||
\(785\) | −3371.08 | − | 5838.88i | −0.153272 | − | 0.265476i | ||||
\(786\) | −2048.34 | + | 59.7635i | −0.0929541 | + | 0.00271208i | ||||
\(787\) | 12606.0 | − | 21834.3i | 0.570974 | − | 0.988957i | −0.425492 | − | 0.904962i | \(-0.639899\pi\) |
0.996466 | − | 0.0839943i | \(-0.0267677\pi\) | |||||||
\(788\) | −4938.08 | + | 8553.01i | −0.223238 | + | 0.386660i | ||||
\(789\) | 7685.50 | + | 12457.9i | 0.346782 | + | 0.562120i | ||||
\(790\) | 268.969 | + | 465.868i | 0.0121133 | + | 0.0209808i | ||||
\(791\) | 11468.2 | 0.515500 | ||||||||
\(792\) | 1306.64 | + | 1985.96i | 0.0586230 | + | 0.0891011i | ||||
\(793\) | −20407.0 | −0.913838 | ||||||||
\(794\) | 623.386 | + | 1079.74i | 0.0278629 | + | 0.0482599i | ||||
\(795\) | 1746.90 | − | 3240.44i | 0.0779322 | − | 0.144562i | ||||
\(796\) | 2058.72 | − | 3565.80i | 0.0916700 | − | 0.158777i | ||||
\(797\) | −19588.5 | + | 33928.2i | −0.870588 | + | 1.50790i | −0.00919851 | + | 0.999958i | \(0.502928\pi\) |
−0.861390 | + | 0.507945i | \(0.830405\pi\) | |||||||
\(798\) | −329.422 | + | 611.068i | −0.0146133 | + | 0.0271072i | ||||
\(799\) | 3451.75 | + | 5978.61i | 0.152834 | + | 0.264716i | ||||
\(800\) | −835.644 | −0.0369306 | ||||||||
\(801\) | 40569.9 | − | 2369.40i | 1.78960 | − | 0.104517i | ||||
\(802\) | 313.764 | 0.0138147 | ||||||||
\(803\) | 9590.16 | + | 16610.6i | 0.421456 | + | 0.729983i | ||||
\(804\) | −11818.8 | − | 19157.8i | −0.518430 | − | 0.840353i | ||||
\(805\) | −4110.35 | + | 7119.33i | −0.179964 | + | 0.311706i | ||||
\(806\) | −591.631 | + | 1024.74i | −0.0258552 | + | 0.0447826i | ||||
\(807\) | −532.949 | + | 15.5496i | −0.0232474 | + | 0.000678279i | ||||
\(808\) | 691.593 | + | 1197.87i | 0.0301116 | + | 0.0521548i | ||||
\(809\) | −36739.0 | −1.59663 | −0.798316 | − | 0.602239i | \(-0.794275\pi\) | ||||
−0.798316 | + | 0.602239i | \(0.794275\pi\) | |||||||
\(810\) | −633.483 | + | 74.2475i | −0.0274794 | + | 0.00322073i | ||||
\(811\) | −29660.0 | −1.28422 | −0.642111 | − | 0.766611i | \(-0.721941\pi\) | ||||
−0.642111 | + | 0.766611i | \(0.721941\pi\) | |||||||
\(812\) | 126.258 | + | 218.685i | 0.00545662 | + | 0.00945115i | ||||
\(813\) | −17333.6 | + | 505.733i | −0.747743 | + | 0.0218165i | ||||
\(814\) | 171.549 | − | 297.132i | 0.00738674 | − | 0.0127942i | ||||
\(815\) | −2599.62 | + | 4502.68i | −0.111731 | + | 0.193524i | ||||
\(816\) | 7651.61 | + | 12402.9i | 0.328260 | + | 0.532096i | ||||
\(817\) | −23799.7 | − | 41222.2i | −1.01915 | − | 1.76522i | ||||
\(818\) | −549.405 | −0.0234835 | ||||||||
\(819\) | 6129.80 | − | 357.997i | 0.261529 | − | 0.0152740i | ||||
\(820\) | 8142.54 | 0.346768 | ||||||||
\(821\) | −10056.6 | − | 17418.6i | −0.427501 | − | 0.740453i | 0.569149 | − | 0.822234i | \(-0.307273\pi\) |
−0.996650 | + | 0.0817808i | \(0.973939\pi\) | |||||||
\(822\) | 204.390 | − | 379.137i | 0.00867265 | − | 0.0160875i | ||||
\(823\) | −2687.02 | + | 4654.06i | −0.113808 | + | 0.197121i | −0.917303 | − | 0.398191i | \(-0.869638\pi\) |
0.803495 | + | 0.595312i | \(0.202971\pi\) | |||||||
\(824\) | 880.277 | − | 1524.68i | 0.0372159 | − | 0.0644598i | ||||
\(825\) | 1942.27 | − | 3602.86i | 0.0819652 | − | 0.152043i | ||||
\(826\) | −365.697 | − | 633.406i | −0.0154046 | − | 0.0266816i | ||||
\(827\) | 27865.2 | 1.17167 | 0.585833 | − | 0.810432i | \(-0.300767\pi\) | ||||
0.585833 | + | 0.810432i | \(0.300767\pi\) | |||||||
\(828\) | 22974.5 | + | 34918.9i | 0.964273 | + | 1.46560i | ||||
\(829\) | 24363.1 | 1.02070 | 0.510352 | − | 0.859965i | \(-0.329515\pi\) | ||||
0.510352 | + | 0.859965i | \(0.329515\pi\) | |||||||
\(830\) | 470.407 | + | 814.768i | 0.0196724 | + | 0.0340735i | ||||
\(831\) | −1729.36 | − | 2803.23i | −0.0721913 | − | 0.117019i | ||||
\(832\) | 6721.15 | − | 11641.4i | 0.280065 | − | 0.485086i | ||||
\(833\) | −6014.91 | + | 10418.1i | −0.250185 | + | 0.433333i | ||||
\(834\) | 124.549 | − | 3.63390i | 0.00517119 | − | 0.000150877i | ||||
\(835\) | 8317.61 | + | 14406.5i | 0.344722 | + | 0.597076i | ||||
\(836\) | −22651.4 | −0.937099 | ||||||||
\(837\) | 14914.0 | − | 32003.0i | 0.615892 | − | 1.32161i | ||||
\(838\) | −430.007 | −0.0177259 | ||||||||
\(839\) | 17765.3 | + | 30770.4i | 0.731020 | + | 1.26616i | 0.956448 | + | 0.291903i | \(0.0942886\pi\) |
−0.225428 | + | 0.974260i | \(0.572378\pi\) | |||||||
\(840\) | 614.209 | − | 17.9205i | 0.0252288 | − | 0.000736089i | ||||
\(841\) | 12187.5 | − | 21109.4i | 0.499713 | − | 0.865528i | ||||
\(842\) | −234.363 | + | 405.928i | −0.00959226 | + | 0.0166143i | ||||
\(843\) | 16921.4 | + | 27429.0i | 0.691347 | + | 1.12065i | ||||
\(844\) | −71.0996 | − | 123.148i | −0.00289970 | − | 0.00502243i | ||||
\(845\) | −7375.13 | −0.300251 | ||||||||
\(846\) | 330.098 | − | 657.540i | 0.0134149 | − | 0.0267219i | ||||
\(847\) | −2862.68 | −0.116131 | ||||||||
\(848\) | 4482.22 | + | 7763.42i | 0.181509 | + | 0.314383i | ||||
\(849\) | 18444.0 | − | 34213.0i | 0.745578 | − | 1.38302i | ||||
\(850\) | −96.9648 | + | 167.948i | −0.00391278 | + | 0.00677714i | ||||
\(851\) | 6044.25 | − | 10468.9i | 0.243471 | − | 0.421705i | ||||
\(852\) | −18239.6 | + | 33833.9i | −0.733426 | + | 1.36048i | ||||
\(853\) | −17223.8 | − | 29832.4i | −0.691360 | − | 1.19747i | −0.971392 | − | 0.237480i | \(-0.923679\pi\) |
0.280032 | − | 0.959991i | \(-0.409655\pi\) | |||||||
\(854\) | 1124.81 | 0.0450705 | ||||||||
\(855\) | 5463.80 | − | 10883.6i | 0.218547 | − | 0.435336i | ||||
\(856\) | −4362.05 | −0.174173 | ||||||||
\(857\) | −10003.4 | − | 17326.4i | −0.398729 | − | 0.690618i | 0.594841 | − | 0.803844i | \(-0.297215\pi\) |
−0.993569 | + | 0.113225i | \(0.963882\pi\) | |||||||
\(858\) | −404.169 | − | 655.141i | −0.0160817 | − | 0.0260678i | ||||
\(859\) | −893.190 | + | 1547.05i | −0.0354776 | + | 0.0614490i | −0.883219 | − | 0.468961i | \(-0.844629\pi\) |
0.847741 | + | 0.530410i | \(0.177962\pi\) | |||||||
\(860\) | −10512.8 | + | 18208.8i | −0.416842 | + | 0.721992i | ||||
\(861\) | −8983.04 | + | 262.094i | −0.355565 | + | 0.0103741i | ||||
\(862\) | −828.764 | − | 1435.46i | −0.0327469 | − | 0.0567192i | ||||
\(863\) | 12151.9 | 0.479322 | 0.239661 | − | 0.970857i | \(-0.422964\pi\) | ||||
0.239661 | + | 0.970857i | \(0.422964\pi\) | |||||||
\(864\) | 1980.86 | − | 4250.61i | 0.0779978 | − | 0.167371i | ||||
\(865\) | −5971.27 | −0.234716 | ||||||||
\(866\) | −370.811 | − | 642.263i | −0.0145504 | − | 0.0252021i | ||||
\(867\) | −15310.7 | + | 446.711i | −0.599743 | + | 0.0174984i | ||||
\(868\) | −8487.43 | + | 14700.7i | −0.331892 | + | 0.574854i | ||||
\(869\) | 9686.27 | − | 16777.1i | 0.378118 | − | 0.654919i | ||||
\(870\) | 8.93614 | + | 14.4851i | 0.000348234 | + | 0.000564473i | ||||
\(871\) | 7303.02 | + | 12649.2i | 0.284102 | + | 0.492080i | ||||
\(872\) | −2615.94 | −0.101591 | ||||||||
\(873\) | 4937.94 | + | 7505.18i | 0.191436 | + | 0.290964i | ||||
\(874\) | 3066.36 | 0.118674 | ||||||||
\(875\) | −528.982 | − | 916.224i | −0.0204376 | − | 0.0353989i | ||||
\(876\) | 11961.9 | − | 22189.0i | 0.461366 | − | 0.855819i | ||||
\(877\) | 9436.64 | − | 16344.7i | 0.363344 | − | 0.629330i | −0.625165 | − | 0.780493i | \(-0.714968\pi\) |
0.988509 | + | 0.151163i | \(0.0483017\pi\) | |||||||
\(878\) | 425.119 | − | 736.328i | 0.0163406 | − | 0.0283028i | ||||
\(879\) | 11925.5 | − | 22121.5i | 0.457609 | − | 0.848851i | ||||
\(880\) | 4983.51 | + | 8631.69i | 0.190902 | + | 0.330653i | ||||
\(881\) | 23587.2 | 0.902014 | 0.451007 | − | 0.892520i | \(-0.351065\pi\) | ||||
0.451007 | + | 0.892520i | \(0.351065\pi\) | |||||||
\(882\) | 1279.91 | − | 74.7502i | 0.0488625 | − | 0.00285371i | ||||
\(883\) | −29504.5 | −1.12447 | −0.562234 | − | 0.826978i | \(-0.690058\pi\) | ||||
−0.562234 | + | 0.826978i | \(0.690058\pi\) | |||||||
\(884\) | −4746.35 | − | 8220.92i | −0.180585 | − | 0.312782i | ||||
\(885\) | 6736.57 | + | 10919.7i | 0.255873 | + | 0.414759i | ||||
\(886\) | 204.360 | − | 353.963i | 0.00774901 | − | 0.0134217i | ||||
\(887\) | −1238.02 | + | 2144.31i | −0.0468643 | + | 0.0811714i | −0.888506 | − | 0.458865i | \(-0.848256\pi\) |
0.841642 | + | 0.540036i | \(0.181590\pi\) | |||||||
\(888\) | −903.192 | + | 26.3520i | −0.0341319 | + | 0.000995850i | ||||
\(889\) | 5003.60 | + | 8666.49i | 0.188769 | + | 0.326957i | ||||
\(890\) | −1316.89 | −0.0495981 | ||||||||
\(891\) | 13722.3 | + | 18420.0i | 0.515953 | + | 0.692586i | ||||
\(892\) | −7886.13 | −0.296017 | ||||||||
\(893\) | 7023.94 | + | 12165.8i | 0.263211 | + | 0.455894i | ||||
\(894\) | 130.068 | − | 3.79492i | 0.00486589 | − | 0.000141970i | ||||
\(895\) | −5809.25 | + | 10061.9i | −0.216963 | + | 0.375791i | ||||
\(896\) | −1502.09 | + | 2601.69i | −0.0560058 | + | 0.0970048i | ||||
\(897\) | −14240.2 | − | 23082.8i | −0.530063 | − | 0.859210i | ||||
\(898\) | 1162.82 | + | 2014.06i | 0.0432112 | + | 0.0748440i | ||||
\(899\) | −942.157 | −0.0349529 | ||||||||
\(900\) | −5370.18 | + | 313.633i | −0.198896 | + | 0.0116160i | ||||
\(901\) | 6281.40 | 0.232257 | ||||||||
\(902\) | 563.326 | + | 975.709i | 0.0207946 | + | 0.0360173i | ||||
\(903\) | 11011.9 | − | 20426.7i | 0.405817 | − | 0.752778i | ||||
\(904\) | −1893.17 | + | 3279.07i | −0.0696527 | + | 0.120642i | ||||
\(905\) | −6317.80 | + | 10942.7i | −0.232056 | + | 0.401933i | ||||
\(906\) | 93.5595 | − | 173.550i | 0.00343080 | − | 0.00636403i | ||||
\(907\) | 13375.5 | + | 23167.1i | 0.489666 | + | 0.848126i | 0.999929 | − | 0.0118922i | \(-0.00378549\pi\) |
−0.510264 | + | 0.860018i | \(0.670452\pi\) | |||||||
\(908\) | 27312.1 | 0.998221 | ||||||||
\(909\) | 7345.75 | + | 11164.8i | 0.268034 | + | 0.407385i | ||||
\(910\) | −198.972 | −0.00724819 | ||||||||
\(911\) | −6334.11 | − | 10971.0i | −0.230360 | − | 0.398996i | 0.727554 | − | 0.686051i | \(-0.240657\pi\) |
−0.957914 | + | 0.287055i | \(0.907324\pi\) | |||||||
\(912\) | 15570.2 | + | 25238.7i | 0.565330 | + | 0.916377i | ||||
\(913\) | 16940.6 | − | 29341.9i | 0.614076 | − | 1.06361i | ||||
\(914\) | 452.739 | − | 784.167i | 0.0163843 | − | 0.0283785i | ||||
\(915\) | −19723.6 | + | 575.465i | −0.712613 | + | 0.0207916i | ||||
\(916\) | 4381.61 | + | 7589.16i | 0.158048 | + | 0.273748i | ||||
\(917\) | 19075.1 | 0.686930 | ||||||||
\(918\) | −624.437 | − | 891.337i | −0.0224504 | − | 0.0320463i | ||||
\(919\) | 46565.5 | 1.67144 | 0.835721 | − | 0.549155i | \(-0.185050\pi\) | ||||
0.835721 | + | 0.549155i | \(0.185050\pi\) | |||||||
\(920\) | −1357.08 | − | 2350.53i | −0.0486322 | − | 0.0842334i | ||||
\(921\) | −29147.7 | + | 850.427i | −1.04283 | + | 0.0304262i | ||||
\(922\) | 554.779 | − | 960.905i | 0.0198163 | − | 0.0343229i | ||||
\(923\) | 12470.3 | − | 21599.1i | 0.444706 | − | 0.770253i | ||||
\(924\) | −5798.13 | − | 9398.53i | −0.206433 | − | 0.334620i | ||||
\(925\) | 777.866 | + | 1347.30i | 0.0276498 | + | 0.0478909i | ||||
\(926\) | −556.940 | −0.0197648 | ||||||||
\(927\) | 7632.03 | − | 15202.6i | 0.270408 | − | 0.538641i | ||||
\(928\) | −125.136 | −0.00442651 | ||||||||
\(929\) | −2305.46 | − | 3993.17i | −0.0814205 | − | 0.141024i | 0.822440 | − | 0.568852i | \(-0.192612\pi\) |
−0.903860 | + | 0.427828i | \(0.859279\pi\) | |||||||
\(930\) | −542.921 | + | 1007.10i | −0.0191431 | + | 0.0355098i | ||||
\(931\) | −12239.7 | + | 21199.8i | −0.430870 | + | 0.746289i | ||||
\(932\) | 17771.4 | − | 30780.9i | 0.624593 | − | 1.08183i | ||||
\(933\) | −26929.3 | + | 49952.9i | −0.944935 | + | 1.75283i | ||||
\(934\) | −750.354 | − | 1299.65i | −0.0262873 | − | 0.0455309i | ||||
\(935\) | 6983.91 | 0.244276 | ||||||||
\(936\) | −909.551 | + | 1811.78i | −0.0317624 | + | 0.0632692i | ||||
\(937\) | −6625.43 | −0.230996 | −0.115498 | − | 0.993308i | \(-0.536846\pi\) | ||||
−0.115498 | + | 0.993308i | \(0.536846\pi\) | |||||||
\(938\) | −402.534 | − | 697.209i | −0.0140119 | − | 0.0242694i | ||||
\(939\) | −13588.5 | − | 22026.4i | −0.472250 | − | 0.765498i | ||||
\(940\) | 3102.63 | − | 5373.91i | 0.107656 | − | 0.186465i | ||||
\(941\) | 21721.3 | − | 37622.4i | 0.752491 | − | 1.30335i | −0.194121 | − | 0.980978i | \(-0.562185\pi\) |
0.946612 | − | 0.322375i | \(-0.104481\pi\) | |||||||
\(942\) | −1225.53 | + | 35.7568i | −0.0423886 | + | 0.00123675i | ||||
\(943\) | 19847.8 | + | 34377.4i | 0.685402 | + | 1.18715i | ||||
\(944\) | −31243.7 | −1.07722 | ||||||||
\(945\) | 5914.42 | − | 518.864i | 0.203594 | − | 0.0178610i | ||||
\(946\) | −2909.24 | −0.0999868 | ||||||||
\(947\) | −16461.2 | − | 28511.7i | −0.564855 | − | 0.978357i | −0.997063 | − | 0.0765835i | \(-0.975599\pi\) |
0.432208 | − | 0.901774i | \(-0.357735\pi\) | |||||||
\(948\) | −25449.8 | + | 742.536i | −0.871909 | + | 0.0254393i | ||||
\(949\) | −8178.28 | + | 14165.2i | −0.279745 | + | 0.484533i | ||||
\(950\) | −197.313 | + | 341.756i | −0.00673861 | + | 0.0116716i | ||||
\(951\) | 10247.5 | + | 16610.8i | 0.349419 | + | 0.566394i | ||||
\(952\) | 524.232 | + | 907.996i | 0.0178471 | + | 0.0309121i | ||||
\(953\) | 20253.5 | 0.688430 | 0.344215 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344215 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(954\) | −367.955 | − | 559.255i | −0.0124874 | − | 0.0189796i | ||||
\(955\) | 11944.3 | 0.404722 | ||||||||
\(956\) | 26077.6 | + | 45167.8i | 0.882229 | + | 1.52806i | ||||
\(957\) | 290.853 | − | 539.522i | 0.00982437 | − | 0.0182239i | ||||
\(958\) | 255.272 | − | 442.144i | 0.00860904 | − | 0.0149113i | ||||
\(959\) | −2004.68 | + | 3472.20i | −0.0675020 | + | 0.116917i | ||||
\(960\) | 6167.78 | − | 11441.0i | 0.207359 | − | 0.384644i | ||||
\(961\) | −16771.8 | − | 29049.7i | −0.562983 | − | 0.975116i | ||||
\(962\) | 292.587 | 0.00980602 | ||||||||
\(963\) | −42075.3 | + | 2457.31i | −1.40795 | + | 0.0822282i | ||||
\(964\) | 1676.16 | 0.0560015 | ||||||||
\(965\) | −8869.93 | − | 15363.2i | −0.295889 | − | 0.512496i | ||||
\(966\) | 784.903 | + | 1272.30i | 0.0261427 | + | 0.0423762i | ||||
\(967\) | −1618.56 | + | 2803.43i | −0.0538257 | + | 0.0932289i | −0.891683 | − | 0.452661i | \(-0.850475\pi\) |
0.837857 | + | 0.545890i | \(0.183808\pi\) | |||||||
\(968\) | 472.573 | − | 818.521i | 0.0156912 | − | 0.0271780i | ||||
\(969\) | 20770.5 | − | 606.012i | 0.688592 | − | 0.0200907i | ||||
\(970\) | −145.560 | − | 252.118i | −0.00481820 | − | 0.00834537i | ||||
\(971\) | −1731.06 | −0.0572114 | −0.0286057 | − | 0.999591i | \(-0.509107\pi\) | ||||
−0.0286057 | + | 0.999591i | \(0.509107\pi\) | |||||||
\(972\) | 11134.4 | − | 28059.5i | 0.367425 | − | 0.925936i | ||||
\(973\) | −1159.86 | −0.0382151 | ||||||||
\(974\) | −1230.23 | − | 2130.81i | −0.0404712 | − | 0.0700982i | ||||
\(975\) | 3488.97 | − | 101.796i | 0.114602 | − | 0.00334368i | ||||
\(976\) | 24024.8 | − | 41612.1i | 0.787924 | − | 1.36472i | ||||
\(977\) | −17273.4 | + | 29918.5i | −0.565636 | + | 0.979710i | 0.431354 | + | 0.902183i | \(0.358036\pi\) |
−0.996990 | + | 0.0775275i | \(0.975297\pi\) | |||||||
\(978\) | 496.418 | + | 804.674i | 0.0162308 | + | 0.0263094i | ||||
\(979\) | 23712.3 | + | 41071.0i | 0.774106 | + | 1.34079i | ||||
\(980\) | 10813.1 | 0.352460 | ||||||||
\(981\) | −25232.8 | + | 1473.66i | −0.821224 | + | 0.0479617i | ||||
\(982\) | 163.201 | 0.00530343 | ||||||||
\(983\) | −10226.6 | − | 17713.0i | −0.331818 | − | 0.574726i | 0.651050 | − | 0.759035i | \(-0.274329\pi\) |
−0.982868 | + | 0.184309i | \(0.940995\pi\) | |||||||
\(984\) | 1407.99 | − | 2611.78i | 0.0456149 | − | 0.0846142i | ||||
\(985\) | 3098.16 | − | 5366.17i | 0.100219 | − | 0.173584i | ||||
\(986\) | −14.5203 | + | 25.1500i | −0.000468987 | + | 0.000812310i | ||||
\(987\) | −3249.91 | + | 6028.49i | −0.104808 | + | 0.194416i | ||||
\(988\) | −9658.31 | − | 16728.7i | −0.311004 | − | 0.538675i | ||||
\(989\) | −102502. | −3.29563 | ||||||||
\(990\) | −409.108 | − | 621.803i | −0.0131336 | − | 0.0199618i | ||||
\(991\) | −5387.77 | −0.172703 | −0.0863513 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863513 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(992\) | −4206.03 | − | 7285.05i | −0.134618 | − | 0.233166i | ||||
\(993\) | 2474.36 | + | 4010.84i | 0.0790750 | + | 0.128177i | ||||
\(994\) | −687.347 | + | 1190.52i | −0.0219329 | + | 0.0379889i | ||||
\(995\) | −1291.64 | + | 2237.19i | −0.0411536 | + | 0.0712801i | ||||
\(996\) | −44509.8 | + | 1298.64i | −1.41601 | + | 0.0413142i | ||||
\(997\) | 10922.4 | + | 18918.2i | 0.346958 | + | 0.600949i | 0.985707 | − | 0.168466i | \(-0.0538813\pi\) |
−0.638750 | + | 0.769415i | \(0.720548\pi\) | |||||||
\(998\) | 2525.16 | 0.0800929 | ||||||||
\(999\) | −8697.13 | + | 762.988i | −0.275440 | + | 0.0241640i |
(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 | 45.4.e.b.31.2 | yes | 6 | |
3.2 | odd | 2 | 135.4.e.b.91.2 | 6 | |||
5.2 | odd | 4 | 225.4.k.c.49.3 | 12 | |||
5.3 | odd | 4 | 225.4.k.c.49.4 | 12 | |||
5.4 | even | 2 | 225.4.e.c.76.2 | 6 | |||
9.2 | odd | 6 | 135.4.e.b.46.2 | 6 | |||
9.4 | even | 3 | 405.4.a.h.1.2 | 3 | |||
9.5 | odd | 6 | 405.4.a.j.1.2 | 3 | |||
9.7 | even | 3 | inner | 45.4.e.b.16.2 | ✓ | 6 | |
45.4 | even | 6 | 2025.4.a.s.1.2 | 3 | |||
45.7 | odd | 12 | 225.4.k.c.124.4 | 12 | |||
45.14 | odd | 6 | 2025.4.a.q.1.2 | 3 | |||
45.34 | even | 6 | 225.4.e.c.151.2 | 6 | |||
45.43 | odd | 12 | 225.4.k.c.124.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.2 | ✓ | 6 | 9.7 | even | 3 | inner | |
45.4.e.b.31.2 | yes | 6 | 1.1 | even | 1 | trivial | |
135.4.e.b.46.2 | 6 | 9.2 | odd | 6 | |||
135.4.e.b.91.2 | 6 | 3.2 | odd | 2 | |||
225.4.e.c.76.2 | 6 | 5.4 | even | 2 | |||
225.4.e.c.151.2 | 6 | 45.34 | even | 6 | |||
225.4.k.c.49.3 | 12 | 5.2 | odd | 4 | |||
225.4.k.c.49.4 | 12 | 5.3 | odd | 4 | |||
225.4.k.c.124.3 | 12 | 45.43 | odd | 12 | |||
225.4.k.c.124.4 | 12 | 45.7 | odd | 12 | |||
405.4.a.h.1.2 | 3 | 9.4 | even | 3 | |||
405.4.a.j.1.2 | 3 | 9.5 | odd | 6 | |||
2025.4.a.q.1.2 | 3 | 45.14 | odd | 6 | |||
2025.4.a.s.1.2 | 3 | 45.4 | even | 6 |