Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(19,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Character | \(\chi\) | \(=\) | 105.19 |
Dual form | 105.3.r.a.94.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.95153 | − | 1.70407i | −1.47577 | − | 0.852033i | −0.476139 | − | 0.879370i | \(-0.657964\pi\) |
−0.999626 | + | 0.0273367i | \(0.991297\pi\) | |||||||
\(3\) | −0.866025 | − | 1.50000i | −0.288675 | − | 0.500000i | ||||
\(4\) | 3.80769 | + | 6.59511i | 0.951922 | + | 1.64878i | ||||
\(5\) | −3.57204 | − | 3.49865i | −0.714407 | − | 0.699730i | ||||
\(6\) | 5.90306i | 0.983843i | ||||||||
\(7\) | −5.14807 | + | 4.74314i | −0.735438 | + | 0.677592i | ||||
\(8\) | − | 12.3217i | − | 1.54021i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 4.58104 | + | 16.4134i | 0.458104 | + | 1.64134i | ||||
\(11\) | 0.694658 | + | 1.20318i | 0.0631508 | + | 0.109380i | 0.895872 | − | 0.444312i | \(-0.146552\pi\) |
−0.832721 | + | 0.553692i | \(0.813218\pi\) | |||||||
\(12\) | 6.59511 | − | 11.4231i | 0.549592 | − | 0.951922i | ||||
\(13\) | 3.78639 | 0.291261 | 0.145630 | − | 0.989339i | \(-0.453479\pi\) | ||||
0.145630 | + | 0.989339i | \(0.453479\pi\) | |||||||
\(14\) | 23.2773 | − | 5.22688i | 1.66266 | − | 0.373349i | ||||
\(15\) | −2.15450 | + | 8.38798i | −0.143633 | + | 0.559198i | ||||
\(16\) | −5.76621 | + | 9.98737i | −0.360388 | + | 0.624211i | ||||
\(17\) | 15.8536 | + | 27.4592i | 0.932563 | + | 1.61525i | 0.778922 | + | 0.627121i | \(0.215767\pi\) |
0.153641 | + | 0.988127i | \(0.450900\pi\) | |||||||
\(18\) | 8.85459 | − | 5.11220i | 0.491922 | − | 0.284011i | ||||
\(19\) | 12.8335 | + | 7.40942i | 0.675447 | + | 0.389970i | 0.798137 | − | 0.602475i | \(-0.205819\pi\) |
−0.122690 | + | 0.992445i | \(0.539152\pi\) | |||||||
\(20\) | 9.47278 | − | 36.8797i | 0.473639 | − | 1.84399i | ||||
\(21\) | 11.5731 | + | 3.61442i | 0.551099 | + | 0.172115i | ||||
\(22\) | − | 4.73498i | − | 0.215226i | ||||||
\(23\) | −19.5874 | − | 11.3088i | −0.851625 | − | 0.491686i | 0.00957359 | − | 0.999954i | \(-0.496953\pi\) |
−0.861199 | + | 0.508268i | \(0.830286\pi\) | |||||||
\(24\) | −18.4825 | + | 10.6709i | −0.770105 | + | 0.444620i | ||||
\(25\) | 0.518893 | + | 24.9946i | 0.0207557 | + | 0.999785i | ||||
\(26\) | −11.1756 | − | 6.45226i | −0.429833 | − | 0.248164i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −50.8838 | − | 15.8916i | −1.81728 | − | 0.567559i | ||||
\(29\) | −42.9485 | −1.48098 | −0.740492 | − | 0.672065i | \(-0.765407\pi\) | ||||
−0.740492 | + | 0.672065i | \(0.765407\pi\) | |||||||
\(30\) | 20.6527 | − | 21.0859i | 0.688425 | − | 0.702865i | ||||
\(31\) | −28.0131 | + | 16.1734i | −0.903649 | + | 0.521722i | −0.878382 | − | 0.477959i | \(-0.841377\pi\) |
−0.0252666 | + | 0.999681i | \(0.508043\pi\) | |||||||
\(32\) | −8.64524 | + | 4.99133i | −0.270164 | + | 0.155979i | ||||
\(33\) | 1.20318 | − | 2.08398i | 0.0364601 | − | 0.0631508i | ||||
\(34\) | − | 108.062i | − | 3.17830i | ||||||
\(35\) | 34.9837 | + | 1.06860i | 0.999534 | + | 0.0305314i | ||||
\(36\) | −22.8461 | −0.634615 | ||||||||
\(37\) | −7.29321 | − | 4.21074i | −0.197114 | − | 0.113804i | 0.398195 | − | 0.917301i | \(-0.369637\pi\) |
−0.595309 | + | 0.803497i | \(0.702970\pi\) | |||||||
\(38\) | −25.2523 | − | 43.7383i | −0.664534 | − | 1.15101i | ||||
\(39\) | −3.27911 | − | 5.67959i | −0.0840798 | − | 0.145630i | ||||
\(40\) | −43.1092 | + | 44.0135i | −1.07773 | + | 1.10034i | ||||
\(41\) | 46.3613i | 1.13076i | 0.824829 | + | 0.565382i | \(0.191271\pi\) | ||||
−0.824829 | + | 0.565382i | \(0.808729\pi\) | |||||||
\(42\) | −27.9991 | − | 30.3893i | −0.666644 | − | 0.723556i | ||||
\(43\) | 9.92743i | 0.230871i | 0.993315 | + | 0.115435i | \(0.0368263\pi\) | ||||
−0.993315 | + | 0.115435i | \(0.963174\pi\) | |||||||
\(44\) | −5.29008 | + | 9.16269i | −0.120229 | + | 0.208243i | ||||
\(45\) | 14.4478 | − | 4.03245i | 0.321063 | − | 0.0896100i | ||||
\(46\) | 38.5418 | + | 66.7564i | 0.837866 | + | 1.45123i | ||||
\(47\) | −27.2811 | + | 47.2522i | −0.580448 | + | 1.00537i | 0.414978 | + | 0.909832i | \(0.363789\pi\) |
−0.995426 | + | 0.0955345i | \(0.969544\pi\) | |||||||
\(48\) | 19.9747 | 0.416141 | ||||||||
\(49\) | 4.00517 | − | 48.8360i | 0.0817381 | − | 0.996654i | ||||
\(50\) | 41.0610 | − | 74.6566i | 0.821219 | − | 1.49313i | ||||
\(51\) | 27.4592 | − | 47.5607i | 0.538416 | − | 0.932563i | ||||
\(52\) | 14.4174 | + | 24.9717i | 0.277258 | + | 0.480224i | ||||
\(53\) | 74.4321 | − | 42.9734i | 1.40438 | − | 0.810819i | 0.409542 | − | 0.912291i | \(-0.365689\pi\) |
0.994838 | + | 0.101472i | \(0.0323553\pi\) | |||||||
\(54\) | −15.3366 | − | 8.85459i | −0.284011 | − | 0.163974i | ||||
\(55\) | 1.72817 | − | 6.72818i | 0.0314213 | − | 0.122331i | ||||
\(56\) | 58.4435 | + | 63.4328i | 1.04363 | + | 1.13273i | ||||
\(57\) | − | 25.6670i | − | 0.450298i | ||||||
\(58\) | 126.764 | + | 73.1872i | 2.18558 | + | 1.26185i | ||||
\(59\) | −80.4509 | + | 46.4483i | −1.36357 | + | 0.787260i | −0.990098 | − | 0.140380i | \(-0.955168\pi\) |
−0.373477 | + | 0.927640i | \(0.621834\pi\) | |||||||
\(60\) | −63.5233 | + | 17.7296i | −1.05872 | + | 0.295494i | ||||
\(61\) | 1.41863 | + | 0.819048i | 0.0232563 | + | 0.0134270i | 0.511583 | − | 0.859234i | \(-0.329059\pi\) |
−0.488327 | + | 0.872661i | \(0.662393\pi\) | |||||||
\(62\) | 110.242 | 1.77810 | ||||||||
\(63\) | −4.60095 | − | 20.4898i | −0.0730310 | − | 0.325235i | ||||
\(64\) | 80.1519 | 1.25237 | ||||||||
\(65\) | −13.5251 | − | 13.2473i | −0.208079 | − | 0.203804i | ||||
\(66\) | −7.10247 | + | 4.10061i | −0.107613 | + | 0.0621305i | ||||
\(67\) | −37.9034 | + | 21.8835i | −0.565722 | + | 0.326620i | −0.755439 | − | 0.655219i | \(-0.772576\pi\) |
0.189717 | + | 0.981839i | \(0.439243\pi\) | |||||||
\(68\) | −120.731 | + | 209.112i | −1.77545 | + | 3.07518i | ||||
\(69\) | 39.1748i | 0.567750i | ||||||||
\(70\) | −101.434 | − | 62.7685i | −1.44906 | − | 0.896693i | ||||
\(71\) | −60.9268 | −0.858124 | −0.429062 | − | 0.903275i | \(-0.641156\pi\) | ||||
−0.429062 | + | 0.903275i | \(0.641156\pi\) | |||||||
\(72\) | 32.0127 | + | 18.4825i | 0.444620 | + | 0.256702i | ||||
\(73\) | −32.3243 | − | 55.9872i | −0.442798 | − | 0.766949i | 0.555098 | − | 0.831785i | \(-0.312681\pi\) |
−0.997896 | + | 0.0648364i | \(0.979347\pi\) | |||||||
\(74\) | 14.3508 | + | 24.8563i | 0.193929 | + | 0.335895i | ||||
\(75\) | 37.0425 | − | 22.4243i | 0.493901 | − | 0.298991i | ||||
\(76\) | 112.851i | 1.48488i | ||||||||
\(77\) | −9.28302 | − | 2.89920i | −0.120559 | − | 0.0376520i | ||||
\(78\) | 22.3513i | 0.286555i | ||||||||
\(79\) | 0.744936 | − | 1.29027i | 0.00942957 | − | 0.0163325i | −0.861272 | − | 0.508144i | \(-0.830332\pi\) |
0.870702 | + | 0.491812i | \(0.163665\pi\) | |||||||
\(80\) | 55.5395 | − | 15.5013i | 0.694243 | − | 0.193766i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 79.0028 | − | 136.837i | 0.963449 | − | 1.66874i | ||||
\(83\) | 13.6731 | 0.164736 | 0.0823681 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823681 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(84\) | 20.2292 | + | 90.0882i | 0.240824 | + | 1.07248i | ||||
\(85\) | 39.4406 | − | 153.551i | 0.464007 | − | 1.80649i | ||||
\(86\) | 16.9170 | − | 29.3011i | 0.196709 | − | 0.340711i | ||||
\(87\) | 37.1945 | + | 64.4228i | 0.427523 | + | 0.740492i | ||||
\(88\) | 14.8252 | − | 8.55936i | 0.168469 | − | 0.0972654i | ||||
\(89\) | 110.062 | + | 63.5444i | 1.23665 | + | 0.713982i | 0.968409 | − | 0.249369i | \(-0.0802232\pi\) |
0.268244 | + | 0.963351i | \(0.413557\pi\) | |||||||
\(90\) | −49.5147 | − | 12.7181i | −0.550164 | − | 0.141313i | ||||
\(91\) | −19.4926 | + | 17.9594i | −0.214204 | + | 0.197356i | ||||
\(92\) | − | 172.241i | − | 1.87219i | ||||||
\(93\) | 48.5201 | + | 28.0131i | 0.521722 | + | 0.301216i | ||||
\(94\) | 161.042 | − | 92.9775i | 1.71321 | − | 0.989123i | ||||
\(95\) | −19.9187 | − | 71.3666i | −0.209671 | − | 0.751228i | ||||
\(96\) | 14.9740 | + | 8.64524i | 0.155979 | + | 0.0900546i | ||||
\(97\) | −119.276 | −1.22965 | −0.614824 | − | 0.788664i | \(-0.710773\pi\) | ||||
−0.614824 | + | 0.788664i | \(0.710773\pi\) | |||||||
\(98\) | −95.0412 | + | 137.316i | −0.969809 | + | 1.40118i | ||||
\(99\) | −4.16795 | −0.0421005 | ||||||||
\(100\) | −162.866 | + | 98.5938i | −1.62866 | + | 0.985938i | ||||
\(101\) | 103.691 | − | 59.8659i | 1.02664 | − | 0.592732i | 0.110621 | − | 0.993863i | \(-0.464716\pi\) |
0.916021 | + | 0.401131i | \(0.131383\pi\) | |||||||
\(102\) | −162.093 | + | 93.5846i | −1.58915 | + | 0.917496i | ||||
\(103\) | 31.1886 | − | 54.0203i | 0.302802 | − | 0.524469i | −0.673967 | − | 0.738761i | \(-0.735411\pi\) |
0.976770 | + | 0.214292i | \(0.0687445\pi\) | |||||||
\(104\) | − | 46.6547i | − | 0.448603i | ||||||
\(105\) | −28.6939 | − | 53.4010i | −0.273275 | − | 0.508581i | ||||
\(106\) | −292.918 | −2.76338 | ||||||||
\(107\) | −104.206 | − | 60.1634i | −0.973888 | − | 0.562275i | −0.0734689 | − | 0.997298i | \(-0.523407\pi\) |
−0.900419 | + | 0.435023i | \(0.856740\pi\) | |||||||
\(108\) | 19.7853 | + | 34.2692i | 0.183197 | + | 0.317307i | ||||
\(109\) | 32.5298 | + | 56.3433i | 0.298439 | + | 0.516911i | 0.975779 | − | 0.218759i | \(-0.0702009\pi\) |
−0.677340 | + | 0.735670i | \(0.736868\pi\) | |||||||
\(110\) | −16.5660 | + | 16.9135i | −0.150600 | + | 0.153759i | ||||
\(111\) | 14.5864i | 0.131409i | ||||||||
\(112\) | −17.6867 | − | 78.7656i | −0.157917 | − | 0.703265i | ||||
\(113\) | 133.463i | 1.18109i | 0.807005 | + | 0.590545i | \(0.201087\pi\) | ||||
−0.807005 | + | 0.590545i | \(0.798913\pi\) | |||||||
\(114\) | −43.7383 | + | 75.7569i | −0.383669 | + | 0.664534i | ||||
\(115\) | 30.4014 | + | 108.925i | 0.264360 | + | 0.947172i | ||||
\(116\) | −163.535 | − | 283.250i | −1.40978 | − | 2.44181i | ||||
\(117\) | −5.67959 | + | 9.83733i | −0.0485435 | + | 0.0840798i | ||||
\(118\) | 316.604 | 2.68309 | ||||||||
\(119\) | −211.858 | − | 66.1660i | −1.78032 | − | 0.556017i | ||||
\(120\) | 103.354 | + | 26.5471i | 0.861283 | + | 0.221226i | ||||
\(121\) | 59.5349 | − | 103.117i | 0.492024 | − | 0.852211i | ||||
\(122\) | −2.79143 | − | 4.83489i | −0.0228805 | − | 0.0396303i | ||||
\(123\) | 69.5420 | − | 40.1501i | 0.565382 | − | 0.326424i | ||||
\(124\) | −213.330 | − | 123.166i | −1.72041 | − | 0.993277i | ||||
\(125\) | 85.5939 | − | 91.0971i | 0.684751 | − | 0.728777i | ||||
\(126\) | −21.3361 | + | 68.3165i | −0.169334 | + | 0.542195i | ||||
\(127\) | 187.969i | 1.48007i | 0.672570 | + | 0.740034i | \(0.265191\pi\) | ||||
−0.672570 | + | 0.740034i | \(0.734809\pi\) | |||||||
\(128\) | −201.990 | − | 116.619i | −1.57805 | − | 0.911086i | ||||
\(129\) | 14.8912 | − | 8.59741i | 0.115435 | − | 0.0666466i | ||||
\(130\) | 17.3456 | + | 62.1474i | 0.133428 | + | 0.478057i | ||||
\(131\) | 61.6992 | + | 35.6220i | 0.470986 | + | 0.271924i | 0.716652 | − | 0.697431i | \(-0.245673\pi\) |
−0.245666 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(132\) | 18.3254 | 0.138829 | ||||||||
\(133\) | −101.212 | + | 22.7269i | −0.760990 | + | 0.170879i | ||||
\(134\) | 149.164 | 1.11316 | ||||||||
\(135\) | −18.5608 | − | 18.1795i | −0.137488 | − | 0.134663i | ||||
\(136\) | 338.343 | − | 195.343i | 2.48782 | − | 1.43634i | ||||
\(137\) | 32.8928 | − | 18.9907i | 0.240093 | − | 0.138618i | −0.375126 | − | 0.926974i | \(-0.622401\pi\) |
0.615220 | + | 0.788356i | \(0.289067\pi\) | |||||||
\(138\) | 66.7564 | − | 115.626i | 0.483742 | − | 0.837866i | ||||
\(139\) | 98.4179i | 0.708042i | 0.935237 | + | 0.354021i | \(0.115186\pi\) | ||||
−0.935237 | + | 0.354021i | \(0.884814\pi\) | |||||||
\(140\) | 126.159 | + | 234.790i | 0.901139 | + | 1.67707i | ||||
\(141\) | 94.5044 | 0.670244 | ||||||||
\(142\) | 179.827 | + | 103.823i | 1.26639 | + | 0.731150i | ||||
\(143\) | 2.63025 | + | 4.55572i | 0.0183933 | + | 0.0318582i | ||||
\(144\) | −17.2986 | − | 29.9621i | −0.120129 | − | 0.208070i | ||||
\(145\) | 153.414 | + | 150.262i | 1.05803 | + | 1.03629i | ||||
\(146\) | 220.331i | 1.50911i | ||||||||
\(147\) | −76.7226 | + | 36.2855i | −0.521923 | + | 0.246840i | ||||
\(148\) | − | 64.1327i | − | 0.433329i | ||||||
\(149\) | 89.3441 | − | 154.748i | 0.599625 | − | 1.03858i | −0.393252 | − | 0.919431i | \(-0.628650\pi\) |
0.992876 | − | 0.119149i | \(-0.0380167\pi\) | |||||||
\(150\) | −147.545 | + | 3.06306i | −0.983631 | + | 0.0204204i | ||||
\(151\) | −120.777 | − | 209.191i | −0.799846 | − | 1.38537i | −0.919716 | − | 0.392584i | \(-0.871581\pi\) |
0.119870 | − | 0.992790i | \(-0.461752\pi\) | |||||||
\(152\) | 91.2965 | − | 158.130i | 0.600635 | − | 1.04033i | ||||
\(153\) | −95.1215 | −0.621709 | ||||||||
\(154\) | 22.4587 | + | 24.3760i | 0.145836 | + | 0.158286i | ||||
\(155\) | 156.649 | + | 40.2362i | 1.01064 | + | 0.259588i | ||||
\(156\) | 24.9717 | − | 43.2522i | 0.160075 | − | 0.277258i | ||||
\(157\) | 20.6624 | + | 35.7883i | 0.131607 | + | 0.227951i | 0.924296 | − | 0.381676i | \(-0.124653\pi\) |
−0.792689 | + | 0.609626i | \(0.791320\pi\) | |||||||
\(158\) | −4.39740 | + | 2.53884i | −0.0278317 | + | 0.0160686i | ||||
\(159\) | −128.920 | − | 74.4321i | −0.810819 | − | 0.468127i | ||||
\(160\) | 48.3440 | + | 12.4174i | 0.302150 | + | 0.0776090i | ||||
\(161\) | 154.476 | − | 34.6874i | 0.959480 | − | 0.215450i | ||||
\(162\) | 30.6732i | 0.189341i | ||||||||
\(163\) | −60.5120 | − | 34.9366i | −0.371239 | − | 0.214335i | 0.302760 | − | 0.953067i | \(-0.402092\pi\) |
−0.674000 | + | 0.738732i | \(0.735425\pi\) | |||||||
\(164\) | −305.758 | + | 176.529i | −1.86438 | + | 1.07640i | ||||
\(165\) | −11.5889 | + | 3.23452i | −0.0702359 | + | 0.0196031i | ||||
\(166\) | −40.3566 | − | 23.2999i | −0.243112 | − | 0.140361i | ||||
\(167\) | 32.7058 | 0.195843 | 0.0979217 | − | 0.995194i | \(-0.468781\pi\) | ||||
0.0979217 | + | 0.995194i | \(0.468781\pi\) | |||||||
\(168\) | 44.5357 | − | 142.600i | 0.265093 | − | 0.848808i | ||||
\(169\) | −154.663 | −0.915167 | ||||||||
\(170\) | −378.072 | + | 386.002i | −2.22395 | + | 2.27060i | ||||
\(171\) | −38.5005 | + | 22.2283i | −0.225149 | + | 0.129990i | ||||
\(172\) | −65.4725 | + | 37.8006i | −0.380654 | + | 0.219771i | ||||
\(173\) | −12.4244 | + | 21.5197i | −0.0718173 | + | 0.124391i | −0.899698 | − | 0.436513i | \(-0.856213\pi\) |
0.827881 | + | 0.560904i | \(0.189547\pi\) | |||||||
\(174\) | − | 253.528i | − | 1.45706i | ||||||
\(175\) | −121.224 | − | 126.213i | −0.692711 | − | 0.721216i | ||||
\(176\) | −16.0222 | −0.0910352 | ||||||||
\(177\) | 139.345 | + | 80.4509i | 0.787260 | + | 0.454525i | ||||
\(178\) | −216.568 | − | 375.106i | −1.21667 | − | 2.10734i | ||||
\(179\) | 70.0625 | + | 121.352i | 0.391411 | + | 0.677943i | 0.992636 | − | 0.121136i | \(-0.0386539\pi\) |
−0.601225 | + | 0.799080i | \(0.705321\pi\) | |||||||
\(180\) | 81.6072 | + | 79.9306i | 0.453373 | + | 0.444059i | ||||
\(181\) | 281.086i | 1.55296i | 0.630142 | + | 0.776480i | \(0.282997\pi\) | ||||
−0.630142 | + | 0.776480i | \(0.717003\pi\) | |||||||
\(182\) | 88.1370 | − | 19.7910i | 0.484269 | − | 0.108742i | ||||
\(183\) | − | 2.83727i | − | 0.0155042i | ||||||
\(184\) | −139.343 | + | 241.349i | −0.757300 | + | 1.31168i | ||||
\(185\) | 11.3197 | + | 40.5573i | 0.0611877 | + | 0.219229i | ||||
\(186\) | −95.4724 | − | 165.363i | −0.513293 | − | 0.889049i | ||||
\(187\) | −22.0256 | + | 38.1495i | −0.117784 | + | 0.204008i | ||||
\(188\) | −415.511 | −2.21017 | ||||||||
\(189\) | −26.7501 | + | 24.6461i | −0.141535 | + | 0.130403i | ||||
\(190\) | −62.8227 | + | 244.584i | −0.330646 | + | 1.28728i | ||||
\(191\) | 51.1878 | − | 88.6599i | 0.267999 | − | 0.464188i | −0.700346 | − | 0.713804i | \(-0.746971\pi\) |
0.968345 | + | 0.249616i | \(0.0803043\pi\) | |||||||
\(192\) | −69.4136 | − | 120.228i | −0.361529 | − | 0.626187i | ||||
\(193\) | −2.32270 | + | 1.34101i | −0.0120347 | + | 0.00694825i | −0.506005 | − | 0.862530i | \(-0.668878\pi\) |
0.493971 | + | 0.869479i | \(0.335545\pi\) | |||||||
\(194\) | 352.047 | + | 203.254i | 1.81467 | + | 1.04770i | ||||
\(195\) | −8.15778 | + | 31.7602i | −0.0418348 | + | 0.162873i | ||||
\(196\) | 337.329 | − | 159.538i | 1.72107 | − | 0.813969i | ||||
\(197\) | 32.0387i | 0.162633i | 0.996688 | + | 0.0813164i | \(0.0259124\pi\) | ||||
−0.996688 | + | 0.0813164i | \(0.974088\pi\) | |||||||
\(198\) | 12.3018 | + | 7.10247i | 0.0621305 | + | 0.0358710i | ||||
\(199\) | 14.1309 | − | 8.15845i | 0.0710093 | − | 0.0409973i | −0.464075 | − | 0.885796i | \(-0.653613\pi\) |
0.535084 | + | 0.844799i | \(0.320280\pi\) | |||||||
\(200\) | 307.976 | − | 6.39363i | 1.53988 | − | 0.0319682i | ||||
\(201\) | 65.6506 | + | 37.9034i | 0.326620 | + | 0.188574i | ||||
\(202\) | −408.062 | −2.02011 | ||||||||
\(203\) | 221.102 | − | 203.711i | 1.08917 | − | 1.00350i | ||||
\(204\) | 418.224 | 2.05012 | ||||||||
\(205\) | 162.202 | − | 165.604i | 0.791230 | − | 0.807826i | ||||
\(206\) | −184.108 | + | 106.295i | −0.893730 | + | 0.515995i | ||||
\(207\) | 58.7621 | − | 33.9263i | 0.283875 | − | 0.163895i | ||||
\(208\) | −21.8331 | + | 37.8161i | −0.104967 | + | 0.181808i | ||||
\(209\) | 20.5881i | 0.0985075i | ||||||||
\(210\) | −6.30799 | + | 206.511i | −0.0300381 | + | 0.983385i | ||||
\(211\) | −311.474 | −1.47618 | −0.738091 | − | 0.674701i | \(-0.764272\pi\) | ||||
−0.738091 | + | 0.674701i | \(0.764272\pi\) | |||||||
\(212\) | 566.829 | + | 327.259i | 2.67372 | + | 1.54367i | ||||
\(213\) | 52.7642 | + | 91.3902i | 0.247719 | + | 0.429062i | ||||
\(214\) | 205.045 | + | 355.148i | 0.958154 | + | 1.65957i | ||||
\(215\) | 34.7326 | − | 35.4612i | 0.161547 | − | 0.164936i | ||||
\(216\) | − | 64.0253i | − | 0.296414i | ||||||
\(217\) | 67.5007 | − | 216.132i | 0.311063 | − | 0.995999i | ||||
\(218\) | − | 221.732i | − | 1.01712i | ||||||
\(219\) | −55.9872 | + | 96.9728i | −0.255650 | + | 0.442798i | ||||
\(220\) | 50.9534 | − | 14.2213i | 0.231606 | − | 0.0646424i | ||||
\(221\) | 60.0278 | + | 103.971i | 0.271619 | + | 0.470458i | ||||
\(222\) | 24.8563 | − | 43.0523i | 0.111965 | − | 0.193929i | ||||
\(223\) | −111.515 | −0.500068 | −0.250034 | − | 0.968237i | \(-0.580442\pi\) | ||||
−0.250034 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(224\) | 20.8317 | − | 66.7013i | 0.0929985 | − | 0.297774i | ||||
\(225\) | −65.7163 | − | 36.1438i | −0.292072 | − | 0.160639i | ||||
\(226\) | 227.430 | − | 393.920i | 1.00633 | − | 1.74301i | ||||
\(227\) | −42.6365 | − | 73.8486i | −0.187826 | − | 0.325324i | 0.756699 | − | 0.653763i | \(-0.226811\pi\) |
−0.944525 | + | 0.328439i | \(0.893477\pi\) | |||||||
\(228\) | 169.277 | − | 97.7319i | 0.742441 | − | 0.428649i | ||||
\(229\) | −60.4219 | − | 34.8846i | −0.263851 | − | 0.152334i | 0.362239 | − | 0.932085i | \(-0.382012\pi\) |
−0.626090 | + | 0.779751i | \(0.715346\pi\) | |||||||
\(230\) | 95.8845 | − | 373.301i | 0.416889 | − | 1.62305i | ||||
\(231\) | 3.69053 | + | 16.4353i | 0.0159763 | + | 0.0711485i | ||||
\(232\) | 529.198i | 2.28103i | ||||||||
\(233\) | −150.319 | − | 86.7866i | −0.645145 | − | 0.372475i | 0.141449 | − | 0.989946i | \(-0.454824\pi\) |
−0.786594 | + | 0.617471i | \(0.788157\pi\) | |||||||
\(234\) | 33.5269 | − | 19.3568i | 0.143278 | − | 0.0827213i | ||||
\(235\) | 262.768 | − | 73.3397i | 1.11816 | − | 0.312084i | ||||
\(236\) | −612.664 | − | 353.722i | −2.59603 | − | 1.49882i | ||||
\(237\) | −2.58053 | −0.0108883 | ||||||||
\(238\) | 512.555 | + | 556.311i | 2.15359 | + | 2.33744i | ||||
\(239\) | −108.916 | −0.455717 | −0.227858 | − | 0.973694i | \(-0.573172\pi\) | ||||
−0.227858 | + | 0.973694i | \(0.573172\pi\) | |||||||
\(240\) | −71.3505 | − | 69.8847i | −0.297294 | − | 0.291186i | ||||
\(241\) | −89.8157 | + | 51.8551i | −0.372679 | + | 0.215167i | −0.674628 | − | 0.738158i | \(-0.735696\pi\) |
0.301949 | + | 0.953324i | \(0.402363\pi\) | |||||||
\(242\) | −351.438 | + | 202.903i | −1.45222 | + | 0.838442i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 12.4747i | 0.0511259i | ||||||||
\(245\) | −185.167 | + | 160.431i | −0.755783 | + | 0.654822i | ||||
\(246\) | −273.674 | −1.11249 | ||||||||
\(247\) | 48.5926 | + | 28.0550i | 0.196731 | + | 0.113583i | ||||
\(248\) | 199.283 | + | 345.169i | 0.803561 | + | 1.39181i | ||||
\(249\) | −11.8413 | − | 20.5097i | −0.0475553 | − | 0.0823681i | ||||
\(250\) | −407.869 | + | 123.018i | −1.63147 | + | 0.492073i | ||||
\(251\) | − | 231.368i | − | 0.921787i | −0.887456 | − | 0.460893i | \(-0.847529\pi\) | ||
0.887456 | − | 0.460893i | \(-0.152471\pi\) | |||||||
\(252\) | 117.613 | − | 108.362i | 0.466720 | − | 0.430010i | ||||
\(253\) | − | 31.4230i | − | 0.124201i | ||||||
\(254\) | 320.311 | − | 554.795i | 1.26107 | − | 2.18423i | ||||
\(255\) | −264.484 | + | 73.8185i | −1.03719 | + | 0.289485i | ||||
\(256\) | 237.149 | + | 410.754i | 0.926364 | + | 1.60451i | ||||
\(257\) | 46.1522 | − | 79.9380i | 0.179581 | − | 0.311043i | −0.762156 | − | 0.647393i | \(-0.775859\pi\) |
0.941737 | + | 0.336350i | \(0.109193\pi\) | |||||||
\(258\) | −58.6022 | −0.227140 | ||||||||
\(259\) | 57.5181 | − | 12.9156i | 0.222078 | − | 0.0498672i | ||||
\(260\) | 35.8676 | − | 139.641i | 0.137952 | − | 0.537081i | ||||
\(261\) | 64.4228 | − | 111.584i | 0.246831 | − | 0.427523i | ||||
\(262\) | −121.405 | − | 210.279i | −0.463377 | − | 0.802592i | ||||
\(263\) | −130.580 | + | 75.3906i | −0.496503 | + | 0.286656i | −0.727268 | − | 0.686353i | \(-0.759210\pi\) |
0.230765 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(264\) | −25.6781 | − | 14.8252i | −0.0972654 | − | 0.0561562i | ||||
\(265\) | −416.223 | − | 106.909i | −1.57065 | − | 0.403432i | ||||
\(266\) | 337.457 | + | 105.392i | 1.26864 | + | 0.396211i | ||||
\(267\) | − | 220.124i | − | 0.824435i | ||||||
\(268\) | −288.649 | − | 166.651i | −1.07705 | − | 0.621833i | ||||
\(269\) | −95.5538 | + | 55.1680i | −0.355219 | + | 0.205086i | −0.666981 | − | 0.745074i | \(-0.732414\pi\) |
0.311763 | + | 0.950160i | \(0.399081\pi\) | |||||||
\(270\) | 23.8038 | + | 85.2863i | 0.0881622 | + | 0.315875i | ||||
\(271\) | −85.9659 | − | 49.6324i | −0.317217 | − | 0.183145i | 0.332934 | − | 0.942950i | \(-0.391961\pi\) |
−0.650152 | + | 0.759805i | \(0.725295\pi\) | |||||||
\(272\) | −365.660 | −1.34434 | ||||||||
\(273\) | 43.8202 | + | 13.6856i | 0.160513 | + | 0.0501304i | ||||
\(274\) | −129.445 | −0.472428 | ||||||||
\(275\) | −29.7127 | + | 17.9870i | −0.108046 | + | 0.0654074i | ||||
\(276\) | −258.362 | + | 149.165i | −0.936093 | + | 0.540454i | ||||
\(277\) | 337.139 | − | 194.648i | 1.21711 | − | 0.702699i | 0.252811 | − | 0.967516i | \(-0.418645\pi\) |
0.964299 | + | 0.264817i | \(0.0853115\pi\) | |||||||
\(278\) | 167.711 | − | 290.483i | 0.603276 | − | 1.04490i | ||||
\(279\) | − | 97.0403i | − | 0.347815i | ||||||
\(280\) | 13.1669 | − | 431.058i | 0.0470247 | − | 1.53949i | ||||
\(281\) | 307.374 | 1.09386 | 0.546928 | − | 0.837180i | \(-0.315797\pi\) | ||||
0.546928 | + | 0.837180i | \(0.315797\pi\) | |||||||
\(282\) | −278.933 | − | 161.042i | −0.989123 | − | 0.571070i | ||||
\(283\) | 224.540 | + | 388.915i | 0.793428 | + | 1.37426i | 0.923833 | + | 0.382796i | \(0.125039\pi\) |
−0.130405 | + | 0.991461i | \(0.541628\pi\) | |||||||
\(284\) | −231.990 | − | 401.819i | −0.816867 | − | 1.41486i | ||||
\(285\) | −89.7998 | + | 91.6834i | −0.315087 | + | 0.321696i | ||||
\(286\) | − | 17.9285i | − | 0.0626870i | ||||||
\(287\) | −219.898 | − | 238.671i | −0.766197 | − | 0.831607i | ||||
\(288\) | − | 29.9480i | − | 0.103986i | ||||||
\(289\) | −358.172 | + | 620.372i | −1.23935 | + | 2.14662i | ||||
\(290\) | −196.749 | − | 704.930i | −0.678445 | − | 2.43079i | ||||
\(291\) | 103.296 | + | 178.914i | 0.354969 | + | 0.614824i | ||||
\(292\) | 246.161 | − | 426.364i | 0.843018 | − | 1.46015i | ||||
\(293\) | −73.8439 | −0.252027 | −0.126013 | − | 0.992029i | \(-0.540218\pi\) | ||||
−0.126013 | + | 0.992029i | \(0.540218\pi\) | |||||||
\(294\) | 288.282 | + | 23.6427i | 0.980551 | + | 0.0804175i | ||||
\(295\) | 449.880 | + | 115.554i | 1.52502 | + | 0.391710i | ||||
\(296\) | −51.8834 | + | 89.8646i | −0.175282 | + | 0.303597i | ||||
\(297\) | 3.60955 | + | 6.25193i | 0.0121534 | + | 0.0210503i | ||||
\(298\) | −527.403 | + | 304.496i | −1.76981 | + | 1.02180i | ||||
\(299\) | −74.1655 | − | 42.8195i | −0.248045 | − | 0.143209i | ||||
\(300\) | 288.937 | + | 158.915i | 0.963124 | + | 0.529716i | ||||
\(301\) | −47.0873 | − | 51.1071i | −0.156436 | − | 0.169791i | ||||
\(302\) | 823.246i | 2.72598i | ||||||||
\(303\) | −179.598 | − | 103.691i | −0.592732 | − | 0.342214i | ||||
\(304\) | −148.001 | + | 85.4486i | −0.486847 | + | 0.281081i | ||||
\(305\) | −2.20185 | − | 7.88897i | −0.00721917 | − | 0.0258655i | ||||
\(306\) | 280.754 | + | 162.093i | 0.917496 | + | 0.529717i | ||||
\(307\) | 162.912 | 0.530659 | 0.265330 | − | 0.964158i | \(-0.414519\pi\) | ||||
0.265330 | + | 0.964158i | \(0.414519\pi\) | |||||||
\(308\) | −16.2263 | − | 72.2618i | −0.0526827 | − | 0.234616i | ||||
\(309\) | −108.041 | −0.349646 | ||||||||
\(310\) | −393.789 | − | 385.698i | −1.27029 | − | 1.24419i | ||||
\(311\) | 34.3514 | − | 19.8328i | 0.110455 | − | 0.0637711i | −0.443755 | − | 0.896148i | \(-0.646354\pi\) |
0.554210 | + | 0.832377i | \(0.313021\pi\) | |||||||
\(312\) | −69.9820 | + | 40.4041i | −0.224301 | + | 0.129500i | ||||
\(313\) | 74.1316 | − | 128.400i | 0.236842 | − | 0.410222i | −0.722964 | − | 0.690885i | \(-0.757221\pi\) |
0.959806 | + | 0.280663i | \(0.0905543\pi\) | |||||||
\(314\) | − | 140.840i | − | 0.448536i | ||||||
\(315\) | −55.2518 | + | 89.2874i | −0.175403 | + | 0.283452i | ||||
\(316\) | 11.3459 | 0.0359049 | ||||||||
\(317\) | −44.9762 | − | 25.9670i | −0.141881 | − | 0.0819149i | 0.427379 | − | 0.904072i | \(-0.359437\pi\) |
−0.569260 | + | 0.822158i | \(0.692770\pi\) | |||||||
\(318\) | 253.675 | + | 439.377i | 0.797719 | + | 1.38169i | ||||
\(319\) | −29.8346 | − | 51.6750i | −0.0935253 | − | 0.161991i | ||||
\(320\) | −286.306 | − | 280.424i | −0.894705 | − | 0.876324i | ||||
\(321\) | 208.412i | 0.649259i | ||||||||
\(322\) | −515.051 | − | 160.857i | −1.59954 | − | 0.499556i | ||||
\(323\) | 469.863i | 1.45469i | ||||||||
\(324\) | 34.2692 | − | 59.3560i | 0.105769 | − | 0.183197i | ||||
\(325\) | 1.96473 | + | 94.6394i | 0.00604533 | + | 0.291198i | ||||
\(326\) | 119.069 | + | 206.233i | 0.365241 | + | 0.632617i | ||||
\(327\) | 56.3433 | − | 97.5894i | 0.172304 | − | 0.298439i | ||||
\(328\) | 571.249 | 1.74161 | ||||||||
\(329\) | −83.6792 | − | 372.656i | −0.254344 | − | 1.13269i | ||||
\(330\) | 39.7169 | + | 10.2015i | 0.120354 | + | 0.0309137i | ||||
\(331\) | −193.516 | + | 335.179i | −0.584639 | + | 1.01262i | 0.410281 | + | 0.911959i | \(0.365431\pi\) |
−0.994920 | + | 0.100666i | \(0.967903\pi\) | |||||||
\(332\) | 52.0629 | + | 90.1756i | 0.156816 | + | 0.271613i | ||||
\(333\) | 21.8796 | − | 12.6322i | 0.0657046 | − | 0.0379346i | ||||
\(334\) | −96.5323 | − | 55.7329i | −0.289019 | − | 0.166865i | ||||
\(335\) | 211.955 | + | 54.4419i | 0.632702 | + | 0.162513i | ||||
\(336\) | −102.831 | + | 94.7431i | −0.306046 | + | 0.281974i | ||||
\(337\) | − | 574.984i | − | 1.70618i | −0.521761 | − | 0.853092i | \(-0.674725\pi\) | ||
0.521761 | − | 0.853092i | \(-0.325275\pi\) | |||||||
\(338\) | 456.493 | + | 263.556i | 1.35057 | + | 0.779753i | ||||
\(339\) | 200.195 | − | 115.582i | 0.590545 | − | 0.340951i | ||||
\(340\) | 1162.87 | − | 324.561i | 3.42019 | − | 0.954591i | ||||
\(341\) | −38.9191 | − | 22.4699i | −0.114132 | − | 0.0658943i | ||||
\(342\) | 151.514 | 0.443023 | ||||||||
\(343\) | 211.017 | + | 270.408i | 0.615211 | + | 0.788362i | ||||
\(344\) | 122.323 | 0.355589 | ||||||||
\(345\) | 137.059 | − | 139.934i | 0.397272 | − | 0.405605i | ||||
\(346\) | 73.3419 | − | 42.3440i | 0.211971 | − | 0.122381i | ||||
\(347\) | −21.1805 | + | 12.2286i | −0.0610389 | + | 0.0352408i | −0.530209 | − | 0.847867i | \(-0.677886\pi\) |
0.469170 | + | 0.883108i | \(0.344553\pi\) | |||||||
\(348\) | −283.250 | + | 490.604i | −0.813937 | + | 1.40978i | ||||
\(349\) | − | 162.352i | − | 0.465193i | −0.972573 | − | 0.232597i | \(-0.925278\pi\) | ||
0.972573 | − | 0.232597i | \(-0.0747222\pi\) | |||||||
\(350\) | 142.722 | + | 579.095i | 0.407778 | + | 1.65456i | ||||
\(351\) | 19.6747 | 0.0560532 | ||||||||
\(352\) | −12.0110 | − | 6.93454i | −0.0341221 | − | 0.0197004i | ||||
\(353\) | 195.326 | + | 338.314i | 0.553331 | + | 0.958397i | 0.998031 | + | 0.0627175i | \(0.0199767\pi\) |
−0.444701 | + | 0.895679i | \(0.646690\pi\) | |||||||
\(354\) | −274.187 | − | 474.906i | −0.774541 | − | 1.34154i | ||||
\(355\) | 217.633 | + | 213.162i | 0.613050 | + | 0.600455i | ||||
\(356\) | 967.828i | 2.71862i | ||||||||
\(357\) | 84.2256 | + | 375.089i | 0.235926 | + | 1.05067i | ||||
\(358\) | − | 477.565i | − | 1.33398i | ||||||
\(359\) | −168.035 | + | 291.044i | −0.468063 | + | 0.810709i | −0.999334 | − | 0.0364931i | \(-0.988381\pi\) |
0.531271 | + | 0.847202i | \(0.321715\pi\) | |||||||
\(360\) | −49.6865 | − | 178.021i | −0.138018 | − | 0.494504i | ||||
\(361\) | −70.7009 | − | 122.458i | −0.195847 | − | 0.339218i | ||||
\(362\) | 478.989 | − | 829.633i | 1.32317 | − | 2.29180i | ||||
\(363\) | −206.235 | −0.568140 | ||||||||
\(364\) | −192.666 | − | 60.1720i | −0.529302 | − | 0.165308i | ||||
\(365\) | −80.4164 | + | 313.080i | −0.220319 | + | 0.857753i | ||||
\(366\) | −4.83489 | + | 8.37428i | −0.0132101 | + | 0.0228805i | ||||
\(367\) | 174.508 | + | 302.258i | 0.475500 | + | 0.823590i | 0.999606 | − | 0.0280628i | \(-0.00893385\pi\) |
−0.524106 | + | 0.851653i | \(0.675601\pi\) | |||||||
\(368\) | 225.890 | − | 130.418i | 0.613832 | − | 0.354396i | ||||
\(369\) | −120.450 | − | 69.5420i | −0.326424 | − | 0.188461i | ||||
\(370\) | 35.7019 | − | 138.996i | 0.0964916 | − | 0.375664i | ||||
\(371\) | −179.352 | + | 574.272i | −0.483430 | + | 1.54790i | ||||
\(372\) | 426.661i | 1.14694i | ||||||||
\(373\) | 142.361 | + | 82.1924i | 0.381666 | + | 0.220355i | 0.678543 | − | 0.734561i | \(-0.262612\pi\) |
−0.296877 | + | 0.954916i | \(0.595945\pi\) | |||||||
\(374\) | 130.019 | − | 75.0663i | 0.347644 | − | 0.200712i | ||||
\(375\) | −210.772 | − | 49.4985i | −0.562059 | − | 0.131996i | ||||
\(376\) | 582.226 | + | 336.149i | 1.54847 | + | 0.894012i | ||||
\(377\) | −162.620 | −0.431353 | ||||||||
\(378\) | 120.952 | − | 27.1597i | 0.319980 | − | 0.0718510i | ||||
\(379\) | 172.731 | 0.455755 | 0.227878 | − | 0.973690i | \(-0.426821\pi\) | ||||
0.227878 | + | 0.973690i | \(0.426821\pi\) | |||||||
\(380\) | 394.826 | − | 403.108i | 1.03902 | − | 1.06081i | ||||
\(381\) | 281.953 | − | 162.786i | 0.740034 | − | 0.427259i | ||||
\(382\) | −302.165 | + | 174.455i | −0.791007 | + | 0.456688i | ||||
\(383\) | −111.180 | + | 192.569i | −0.290287 | + | 0.502791i | −0.973877 | − | 0.227074i | \(-0.927084\pi\) |
0.683591 | + | 0.729866i | \(0.260417\pi\) | |||||||
\(384\) | 403.980i | 1.05203i | ||||||||
\(385\) | 23.0160 | + | 42.8341i | 0.0597818 | + | 0.111257i | ||||
\(386\) | 9.14070 | 0.0236806 | ||||||||
\(387\) | −25.7922 | − | 14.8912i | −0.0666466 | − | 0.0384784i | ||||
\(388\) | −454.165 | − | 786.638i | −1.17053 | − | 2.02742i | ||||
\(389\) | 242.996 | + | 420.881i | 0.624668 | + | 1.08196i | 0.988605 | + | 0.150533i | \(0.0480991\pi\) |
−0.363937 | + | 0.931424i | \(0.618568\pi\) | |||||||
\(390\) | 78.1994 | − | 79.8396i | 0.200511 | − | 0.204717i | ||||
\(391\) | − | 717.139i | − | 1.83411i | ||||||
\(392\) | −601.742 | − | 49.3504i | −1.53506 | − | 0.125894i | ||||
\(393\) | − | 123.398i | − | 0.313991i | ||||||
\(394\) | 54.5960 | − | 94.5631i | 0.138569 | − | 0.240008i | ||||
\(395\) | −7.17513 | + | 2.00261i | −0.0181649 | + | 0.00506990i | ||||
\(396\) | −15.8702 | − | 27.4881i | −0.0400764 | − | 0.0694143i | ||||
\(397\) | −197.795 | + | 342.591i | −0.498224 | + | 0.862949i | −0.999998 | − | 0.00204967i | \(-0.999348\pi\) |
0.501774 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(398\) | −55.6102 | −0.139724 | ||||||||
\(399\) | 121.742 | + | 132.135i | 0.305118 | + | 0.331166i | ||||
\(400\) | −252.623 | − | 138.942i | −0.631557 | − | 0.347355i | ||||
\(401\) | −189.425 | + | 328.093i | −0.472380 | + | 0.818187i | −0.999500 | − | 0.0316039i | \(-0.989939\pi\) |
0.527120 | + | 0.849791i | \(0.323272\pi\) | |||||||
\(402\) | −129.180 | − | 223.746i | −0.321343 | − | 0.556582i | ||||
\(403\) | −106.069 | + | 61.2387i | −0.263198 | + | 0.151957i | ||||
\(404\) | 789.644 | + | 455.901i | 1.95456 | + | 1.12847i | ||||
\(405\) | −11.1951 | + | 43.5852i | −0.0276423 | + | 0.107618i | ||||
\(406\) | −999.726 | + | 224.487i | −2.46238 | + | 0.552924i | ||||
\(407\) | − | 11.7001i | − | 0.0287472i | ||||||
\(408\) | −586.028 | − | 338.343i | −1.43634 | − | 0.829273i | ||||
\(409\) | 674.493 | − | 389.419i | 1.64913 | − | 0.952124i | 0.671707 | − | 0.740817i | \(-0.265562\pi\) |
0.977420 | − | 0.211306i | \(-0.0677718\pi\) | |||||||
\(410\) | −760.945 | + | 212.383i | −1.85596 | + | 0.518008i | ||||
\(411\) | −56.9720 | − | 32.8928i | −0.138618 | − | 0.0800311i | ||||
\(412\) | 475.026 | 1.15298 | ||||||||
\(413\) | 193.855 | − | 620.709i | 0.469383 | − | 1.50293i | ||||
\(414\) | −231.251 | −0.558577 | ||||||||
\(415\) | −48.8408 | − | 47.8374i | −0.117689 | − | 0.115271i | ||||
\(416\) | −32.7342 | + | 18.8991i | −0.0786881 | + | 0.0454306i | ||||
\(417\) | 147.627 | − | 85.2324i | 0.354021 | − | 0.204394i | ||||
\(418\) | 35.0834 | − | 60.7663i | 0.0839317 | − | 0.145374i | ||||
\(419\) | 350.942i | 0.837571i | 0.908085 | + | 0.418785i | \(0.137544\pi\) | ||||
−0.908085 | + | 0.418785i | \(0.862456\pi\) | |||||||
\(420\) | 242.928 | − | 392.573i | 0.578400 | − | 0.934698i | ||||
\(421\) | 175.760 | 0.417482 | 0.208741 | − | 0.977971i | \(-0.433063\pi\) | ||||
0.208741 | + | 0.977971i | \(0.433063\pi\) | |||||||
\(422\) | 919.326 | + | 530.773i | 2.17850 | + | 1.25776i | ||||
\(423\) | −81.8432 | − | 141.757i | −0.193483 | − | 0.335122i | ||||
\(424\) | −529.505 | − | 917.129i | −1.24883 | − | 2.16304i | ||||
\(425\) | −678.106 | + | 410.502i | −1.59554 | + | 0.965888i | ||||
\(426\) | − | 359.655i | − | 0.844260i | ||||||
\(427\) | −11.1881 | + | 2.51227i | −0.0262016 | + | 0.00588353i | ||||
\(428\) | − | 916.334i | − | 2.14097i | ||||||
\(429\) | 4.55572 | − | 7.89074i | 0.0106194 | − | 0.0183933i | ||||
\(430\) | −162.943 | + | 45.4780i | −0.378936 | + | 0.105763i | ||||
\(431\) | −427.661 | − | 740.730i | −0.992252 | − | 1.71863i | −0.603720 | − | 0.797196i | \(-0.706316\pi\) |
−0.388532 | − | 0.921435i | \(-0.627018\pi\) | |||||||
\(432\) | −29.9621 | + | 51.8959i | −0.0693568 | + | 0.120129i | ||||
\(433\) | −67.4511 | −0.155776 | −0.0778881 | − | 0.996962i | \(-0.524818\pi\) | ||||
−0.0778881 | + | 0.996962i | \(0.524818\pi\) | |||||||
\(434\) | −567.533 | + | 522.894i | −1.30768 | + | 1.20482i | ||||
\(435\) | 92.5327 | − | 360.251i | 0.212719 | − | 0.828164i | ||||
\(436\) | −247.727 | + | 429.075i | −0.568180 | + | 0.984117i | ||||
\(437\) | −167.583 | − | 290.262i | −0.383485 | − | 0.664216i | ||||
\(438\) | 330.496 | − | 190.812i | 0.754557 | − | 0.435644i | ||||
\(439\) | 242.742 | + | 140.147i | 0.552944 | + | 0.319242i | 0.750308 | − | 0.661088i | \(-0.229905\pi\) |
−0.197365 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(440\) | −82.9025 | − | 21.2940i | −0.188415 | − | 0.0483954i | ||||
\(441\) | 120.872 | + | 83.6598i | 0.274086 | + | 0.189705i | ||||
\(442\) | − | 409.166i | − | 0.925715i | ||||||
\(443\) | −400.585 | − | 231.278i | −0.904256 | − | 0.522072i | −0.0256772 | − | 0.999670i | \(-0.508174\pi\) |
−0.878578 | + | 0.477598i | \(0.841508\pi\) | |||||||
\(444\) | −96.1991 | + | 55.5406i | −0.216665 | + | 0.125091i | ||||
\(445\) | −170.826 | − | 612.052i | −0.383879 | − | 1.37540i | ||||
\(446\) | 329.140 | + | 190.029i | 0.737983 | + | 0.426074i | ||||
\(447\) | −309.497 | −0.692387 | ||||||||
\(448\) | −412.628 | + | 380.172i | −0.921044 | + | 0.848599i | ||||
\(449\) | −502.561 | −1.11929 | −0.559644 | − | 0.828733i | \(-0.689062\pi\) | ||||
−0.559644 | + | 0.828733i | \(0.689062\pi\) | |||||||
\(450\) | 132.372 | + | 218.664i | 0.294160 | + | 0.485921i | ||||
\(451\) | −55.7812 | + | 32.2053i | −0.123683 | + | 0.0714086i | ||||
\(452\) | −880.203 | + | 508.186i | −1.94735 | + | 1.12430i | ||||
\(453\) | −209.191 | + | 362.330i | −0.461791 | + | 0.799846i | ||||
\(454\) | 290.622i | 0.640136i | ||||||||
\(455\) | 132.462 | + | 4.04613i | 0.291125 | + | 0.00889259i | ||||
\(456\) | −316.260 | −0.693553 | ||||||||
\(457\) | 540.918 | + | 312.299i | 1.18363 | + | 0.683368i | 0.956851 | − | 0.290579i | \(-0.0938479\pi\) |
0.226777 | + | 0.973947i | \(0.427181\pi\) | |||||||
\(458\) | 118.891 | + | 205.926i | 0.259588 | + | 0.449620i | ||||
\(459\) | 82.3776 | + | 142.682i | 0.179472 | + | 0.310854i | ||||
\(460\) | −602.612 | + | 615.252i | −1.31003 | + | 1.33750i | ||||
\(461\) | 68.1722i | 0.147879i | 0.997263 | + | 0.0739395i | \(0.0235572\pi\) | ||||
−0.997263 | + | 0.0739395i | \(0.976443\pi\) | |||||||
\(462\) | 17.1142 | − | 54.7982i | 0.0370437 | − | 0.118611i | ||||
\(463\) | − | 231.353i | − | 0.499682i | −0.968287 | − | 0.249841i | \(-0.919622\pi\) | ||
0.968287 | − | 0.249841i | \(-0.0803784\pi\) | |||||||
\(464\) | 247.650 | − | 428.943i | 0.533729 | − | 0.924446i | ||||
\(465\) | −75.3076 | − | 269.819i | −0.161952 | − | 0.580256i | ||||
\(466\) | 295.780 | + | 512.306i | 0.634721 | + | 1.09937i | ||||
\(467\) | 246.131 | − | 426.312i | 0.527048 | − | 0.912873i | −0.472456 | − | 0.881355i | \(-0.656632\pi\) |
0.999503 | − | 0.0315188i | \(-0.0100344\pi\) | |||||||
\(468\) | −86.5044 | −0.184838 | ||||||||
\(469\) | 91.3324 | − | 292.439i | 0.194739 | − | 0.623538i | ||||
\(470\) | −900.543 | − | 231.310i | −1.91605 | − | 0.492149i | ||||
\(471\) | 35.7883 | − | 61.9871i | 0.0759836 | − | 0.131607i | ||||
\(472\) | 572.322 | + | 991.290i | 1.21255 | + | 2.10019i | ||||
\(473\) | −11.9445 | + | 6.89618i | −0.0252527 | + | 0.0145797i | ||||
\(474\) | 7.61653 | + | 4.39740i | 0.0160686 | + | 0.00927722i | ||||
\(475\) | −178.536 | + | 324.613i | −0.375866 | + | 0.683396i | ||||
\(476\) | −370.318 | − | 1649.17i | −0.777979 | − | 3.46464i | ||||
\(477\) | 257.841i | 0.540546i | ||||||||
\(478\) | 321.470 | + | 185.601i | 0.672531 | + | 0.388286i | ||||
\(479\) | 621.354 | − | 358.739i | 1.29719 | − | 0.748933i | 0.317272 | − | 0.948335i | \(-0.397233\pi\) |
0.979918 | + | 0.199401i | \(0.0638998\pi\) | |||||||
\(480\) | −23.2410 | − | 83.2699i | −0.0484187 | − | 0.173479i | ||||
\(481\) | −27.6150 | − | 15.9435i | −0.0574116 | − | 0.0331466i | ||||
\(482\) | 353.458 | 0.733316 | ||||||||
\(483\) | −185.812 | − | 201.674i | −0.384703 | − | 0.417545i | ||||
\(484\) | 906.761 | 1.87347 | ||||||||
\(485\) | 426.058 | + | 417.305i | 0.878470 | + | 0.860422i | ||||
\(486\) | 46.0098 | − | 26.5638i | 0.0946704 | − | 0.0546580i | ||||
\(487\) | 347.225 | − | 200.471i | 0.712988 | − | 0.411644i | −0.0991784 | − | 0.995070i | \(-0.531621\pi\) |
0.812166 | + | 0.583426i | \(0.198288\pi\) | |||||||
\(488\) | 10.0921 | − | 17.4799i | 0.0206804 | − | 0.0358196i | ||||
\(489\) | 121.024i | 0.247493i | ||||||||
\(490\) | 819.911 | − | 157.982i | 1.67329 | − | 0.322411i | ||||
\(491\) | 894.115 | 1.82101 | 0.910505 | − | 0.413499i | \(-0.135693\pi\) | ||||
0.910505 | + | 0.413499i | \(0.135693\pi\) | |||||||
\(492\) | 529.588 | + | 305.758i | 1.07640 | + | 0.621459i | ||||
\(493\) | −680.888 | − | 1179.33i | −1.38111 | − | 2.39216i | ||||
\(494\) | −95.6151 | − | 165.610i | −0.193553 | − | 0.335243i | ||||
\(495\) | 14.8881 | + | 14.5822i | 0.0300769 | + | 0.0294590i | ||||
\(496\) | − | 373.037i | − | 0.752090i | ||||||
\(497\) | 313.655 | − | 288.985i | 0.631097 | − | 0.581458i | ||||
\(498\) | 80.7132i | 0.162075i | ||||||||
\(499\) | 261.273 | − | 452.538i | 0.523593 | − | 0.906890i | −0.476030 | − | 0.879429i | \(-0.657925\pi\) |
0.999623 | − | 0.0274608i | \(-0.00874213\pi\) | |||||||
\(500\) | 926.710 | + | 217.632i | 1.85342 | + | 0.435263i | ||||
\(501\) | −28.3241 | − | 49.0588i | −0.0565351 | − | 0.0979217i | ||||
\(502\) | −394.267 | + | 682.891i | −0.785393 | + | 1.36034i | ||||
\(503\) | 849.283 | 1.68844 | 0.844218 | − | 0.536000i | \(-0.180065\pi\) | ||||
0.844218 | + | 0.536000i | \(0.180065\pi\) | |||||||
\(504\) | −252.469 | + | 56.6914i | −0.500930 | + | 0.112483i | ||||
\(505\) | −579.837 | − | 148.935i | −1.14819 | − | 0.294920i | ||||
\(506\) | −53.5468 | + | 92.7458i | −0.105824 | + | 0.183292i | ||||
\(507\) | 133.942 | + | 231.995i | 0.264186 | + | 0.457584i | ||||
\(508\) | −1239.67 | + | 715.726i | −2.44030 | + | 1.40891i | ||||
\(509\) | −589.645 | − | 340.432i | −1.15844 | − | 0.668824i | −0.207509 | − | 0.978233i | \(-0.566536\pi\) |
−0.950929 | + | 0.309409i | \(0.899869\pi\) | |||||||
\(510\) | 906.423 | + | 232.820i | 1.77730 | + | 0.456510i | ||||
\(511\) | 431.963 | + | 134.907i | 0.845329 | + | 0.264007i | ||||
\(512\) | − | 683.520i | − | 1.33500i | ||||||
\(513\) | 66.6848 | + | 38.5005i | 0.129990 | + | 0.0750497i | ||||
\(514\) | −272.439 | + | 157.293i | −0.530037 | + | 0.306017i | ||||
\(515\) | −300.405 | + | 83.8444i | −0.583311 | + | 0.162805i | ||||
\(516\) | 113.402 | + | 65.4725i | 0.219771 | + | 0.126885i | ||||
\(517\) | −75.8041 | −0.146623 | ||||||||
\(518\) | −191.775 | − | 59.8939i | −0.370223 | − | 0.115625i | ||||
\(519\) | 43.0393 | 0.0829274 | ||||||||
\(520\) | −163.228 | + | 166.652i | −0.313901 | + | 0.320485i | ||||
\(521\) | −65.5525 | + | 37.8468i | −0.125821 | + | 0.0726425i | −0.561589 | − | 0.827416i | \(-0.689810\pi\) |
0.435769 | + | 0.900059i | \(0.356477\pi\) | |||||||
\(522\) | −380.292 | + | 219.562i | −0.728528 | + | 0.420616i | ||||
\(523\) | 89.4351 | − | 154.906i | 0.171004 | − | 0.296188i | −0.767767 | − | 0.640729i | \(-0.778632\pi\) |
0.938771 | + | 0.344541i | \(0.111966\pi\) | |||||||
\(524\) | 542.550i | 1.03540i | ||||||||
\(525\) | −84.3357 | + | 291.140i | −0.160640 | + | 0.554552i | ||||
\(526\) | 513.882 | 0.976963 | ||||||||
\(527\) | −888.216 | − | 512.812i | −1.68542 | − | 0.973078i | ||||
\(528\) | 13.8756 | + | 24.0333i | 0.0262796 | + | 0.0455176i | ||||
\(529\) | −8.72296 | − | 15.1086i | −0.0164895 | − | 0.0285607i | ||||
\(530\) | 1046.31 | + | 1024.82i | 1.97418 | + | 1.93362i | ||||
\(531\) | − | 278.690i | − | 0.524840i | ||||||
\(532\) | −535.269 | − | 580.965i | −1.00614 | − | 1.09204i | ||||
\(533\) | 175.542i | 0.329347i | ||||||||
\(534\) | −375.106 | + | 649.703i | −0.702446 | + | 1.21667i | ||||
\(535\) | 161.737 | + | 579.486i | 0.302313 | + | 1.08315i | ||||
\(536\) | 269.642 | + | 467.033i | 0.503063 | + | 0.871331i | ||||
\(537\) | 121.352 | − | 210.188i | 0.225981 | − | 0.391411i | ||||
\(538\) | 376.040 | 0.698959 | ||||||||
\(539\) | 61.5409 | − | 29.1054i | 0.114176 | − | 0.0539989i | ||||
\(540\) | 49.2220 | − | 191.633i | 0.0911518 | − | 0.354875i | ||||
\(541\) | −357.392 | + | 619.020i | −0.660613 | + | 1.14422i | 0.319842 | + | 0.947471i | \(0.396370\pi\) |
−0.980455 | + | 0.196744i | \(0.936963\pi\) | |||||||
\(542\) | 169.154 | + | 292.983i | 0.312092 | + | 0.540559i | ||||
\(543\) | 421.629 | − | 243.427i | 0.776480 | − | 0.448301i | ||||
\(544\) | −274.116 | − | 158.261i | −0.503890 | − | 0.290921i | ||||
\(545\) | 80.9278 | − | 315.071i | 0.148491 | − | 0.578111i | ||||
\(546\) | −106.015 | − | 115.066i | −0.194167 | − | 0.210743i | ||||
\(547\) | 422.685i | 0.772734i | 0.922345 | + | 0.386367i | \(0.126270\pi\) | ||||
−0.922345 | + | 0.386367i | \(0.873730\pi\) | |||||||
\(548\) | 250.491 | + | 144.621i | 0.457100 | + | 0.263907i | ||||
\(549\) | −4.25590 | + | 2.45715i | −0.00775210 | + | 0.00447567i | ||||
\(550\) | 118.349 | − | 2.45695i | 0.215180 | − | 0.00446718i | ||||
\(551\) | −551.180 | − | 318.224i | −1.00033 | − | 0.577539i | ||||
\(552\) | 482.699 | 0.874454 | ||||||||
\(553\) | 2.28494 | + | 10.1757i | 0.00413190 | + | 0.0184009i | ||||
\(554\) | −1326.77 | −2.39489 | ||||||||
\(555\) | 51.0328 | − | 52.1033i | 0.0919510 | − | 0.0938798i | ||||
\(556\) | −649.077 | + | 374.745i | −1.16740 | + | 0.674001i | ||||
\(557\) | −427.861 | + | 247.026i | −0.768152 | + | 0.443493i | −0.832215 | − | 0.554453i | \(-0.812928\pi\) |
0.0640629 | + | 0.997946i | \(0.479594\pi\) | |||||||
\(558\) | −165.363 | + | 286.417i | −0.296350 | + | 0.513293i | ||||
\(559\) | 37.5891i | 0.0672436i | ||||||||
\(560\) | −212.396 | + | 343.233i | −0.379278 | + | 0.612917i | ||||
\(561\) | 76.2991 | 0.136005 | ||||||||
\(562\) | −907.222 | − | 523.785i | −1.61427 | − | 0.932002i | ||||
\(563\) | −121.401 | − | 210.272i | −0.215632 | − | 0.373485i | 0.737836 | − | 0.674980i | \(-0.235848\pi\) |
−0.953468 | + | 0.301495i | \(0.902514\pi\) | |||||||
\(564\) | 359.843 | + | 623.267i | 0.638020 | + | 1.10508i | ||||
\(565\) | 466.941 | − | 476.735i | 0.826444 | − | 0.843779i | ||||
\(566\) | − | 1530.52i | − | 2.70411i | ||||||
\(567\) | 60.1354 | + | 18.7811i | 0.106059 | + | 0.0331236i | ||||
\(568\) | 750.721i | 1.32169i | ||||||||
\(569\) | 239.174 | − | 414.262i | 0.420342 | − | 0.728053i | −0.575631 | − | 0.817710i | \(-0.695244\pi\) |
0.995973 | + | 0.0896563i | \(0.0285769\pi\) | |||||||
\(570\) | 421.282 | − | 117.582i | 0.739090 | − | 0.206283i | ||||
\(571\) | −54.1383 | − | 93.7703i | −0.0948131 | − | 0.164221i | 0.814717 | − | 0.579858i | \(-0.196892\pi\) |
−0.909531 | + | 0.415637i | \(0.863559\pi\) | |||||||
\(572\) | −20.0303 | + | 34.6935i | −0.0350180 | + | 0.0606530i | ||||
\(573\) | −177.320 | −0.309459 | ||||||||
\(574\) | 242.325 | + | 1079.17i | 0.422170 | + | 1.88008i | ||||
\(575\) | 272.495 | − | 495.447i | 0.473904 | − | 0.861647i | ||||
\(576\) | −120.228 | + | 208.241i | −0.208729 | + | 0.361529i | ||||
\(577\) | 49.6800 | + | 86.0482i | 0.0861004 | + | 0.149130i | 0.905860 | − | 0.423578i | \(-0.139226\pi\) |
−0.819759 | + | 0.572708i | \(0.805893\pi\) | |||||||
\(578\) | 2114.31 | − | 1220.70i | 3.65798 | − | 2.11193i | ||||
\(579\) | 4.02304 | + | 2.32270i | 0.00694825 | + | 0.00401157i | ||||
\(580\) | −406.842 | + | 1583.93i | −0.701452 | + | 2.73091i | ||||
\(581\) | −70.3901 | + | 64.8535i | −0.121153 | + | 0.111624i | ||||
\(582\) | − | 704.093i | − | 1.20978i | ||||||
\(583\) | 103.410 | + | 59.7037i | 0.177375 | + | 0.102408i | ||||
\(584\) | −689.857 | + | 398.289i | −1.18126 | + | 0.682002i | ||||
\(585\) | 54.7051 | − | 15.2684i | 0.0935129 | − | 0.0260999i | ||||
\(586\) | 217.952 | + | 125.835i | 0.371932 | + | 0.214735i | ||||
\(587\) | 3.32500 | 0.00566440 | 0.00283220 | − | 0.999996i | \(-0.499098\pi\) | ||||
0.00283220 | + | 0.999996i | \(0.499098\pi\) | |||||||
\(588\) | −531.443 | − | 367.830i | −0.903814 | − | 0.625562i | ||||
\(589\) | −479.342 | −0.813823 | ||||||||
\(590\) | −1130.92 | − | 1107.69i | −1.91682 | − | 1.87744i | ||||
\(591\) | 48.0580 | − | 27.7463i | 0.0813164 | − | 0.0469481i | ||||
\(592\) | 84.1085 | − | 48.5600i | 0.142075 | − | 0.0820271i | ||||
\(593\) | −233.891 | + | 405.112i | −0.394421 | + | 0.683157i | −0.993027 | − | 0.117887i | \(-0.962388\pi\) |
0.598606 | + | 0.801043i | \(0.295721\pi\) | |||||||
\(594\) | − | 24.6037i | − | 0.0414203i | ||||||
\(595\) | 525.274 | + | 977.565i | 0.882813 | + | 1.64297i | ||||
\(596\) | 1360.78 | 2.28318 | ||||||||
\(597\) | −24.4754 | − | 14.1309i | −0.0409973 | − | 0.0236698i | ||||
\(598\) | 145.934 | + | 252.766i | 0.244038 | + | 0.422685i | ||||
\(599\) | 264.452 | + | 458.045i | 0.441490 | + | 0.764683i | 0.997800 | − | 0.0662916i | \(-0.0211167\pi\) |
−0.556310 | + | 0.830975i | \(0.687783\pi\) | |||||||
\(600\) | −276.305 | − | 456.426i | −0.460509 | − | 0.760711i | ||||
\(601\) | − | 490.357i | − | 0.815901i | −0.913004 | − | 0.407951i | \(-0.866244\pi\) | ||
0.913004 | − | 0.407951i | \(-0.133756\pi\) | |||||||
\(602\) | 51.8896 | + | 231.084i | 0.0861953 | + | 0.383860i | ||||
\(603\) | − | 131.301i | − | 0.217747i | ||||||
\(604\) | 919.760 | − | 1593.07i | 1.52278 | − | 2.63753i | ||||
\(605\) | −573.433 | + | 160.048i | −0.947823 | + | 0.264541i | ||||
\(606\) | 353.392 | + | 612.093i | 0.583155 | + | 1.01005i | ||||
\(607\) | 49.6685 | − | 86.0283i | 0.0818261 | − | 0.141727i | −0.822208 | − | 0.569187i | \(-0.807258\pi\) |
0.904034 | + | 0.427460i | \(0.140591\pi\) | |||||||
\(608\) | −147.931 | −0.243308 | ||||||||
\(609\) | −497.047 | − | 155.234i | −0.816168 | − | 0.254900i | ||||
\(610\) | −6.94452 | + | 27.0366i | −0.0113845 | + | 0.0443224i | ||||
\(611\) | −103.297 | + | 178.915i | −0.169062 | + | 0.292824i | ||||
\(612\) | −362.193 | − | 627.336i | −0.591818 | − | 1.02506i | ||||
\(613\) | −248.004 | + | 143.185i | −0.404573 | + | 0.233581i | −0.688455 | − | 0.725279i | \(-0.741711\pi\) |
0.283882 | + | 0.958859i | \(0.408378\pi\) | |||||||
\(614\) | −480.841 | − | 277.614i | −0.783128 | − | 0.452139i | ||||
\(615\) | −388.878 | − | 99.8855i | −0.632321 | − | 0.162415i | ||||
\(616\) | −35.7231 | + | 114.382i | −0.0579920 | + | 0.185686i | ||||
\(617\) | 335.855i | 0.544336i | 0.962250 | + | 0.272168i | \(0.0877406\pi\) | ||||
−0.962250 | + | 0.272168i | \(0.912259\pi\) | |||||||
\(618\) | 318.885 | + | 184.108i | 0.515995 | + | 0.297910i | ||||
\(619\) | 539.249 | − | 311.336i | 0.871162 | − | 0.502966i | 0.00342798 | − | 0.999994i | \(-0.498909\pi\) |
0.867734 | + | 0.497028i | \(0.165576\pi\) | |||||||
\(620\) | 331.108 | + | 1186.32i | 0.534045 | + | 1.91342i | ||||
\(621\) | −101.779 | − | 58.7621i | −0.163895 | − | 0.0946250i | ||||
\(622\) | −135.186 | −0.217340 | ||||||||
\(623\) | −868.007 | + | 194.910i | −1.39327 | + | 0.312857i | ||||
\(624\) | 75.6322 | 0.121205 | ||||||||
\(625\) | −624.461 | + | 25.9391i | −0.999138 | + | 0.0415025i | ||||
\(626\) | −437.603 | + | 252.650i | −0.699046 | + | 0.403595i | ||||
\(627\) | 30.8821 | − | 17.8298i | 0.0492537 | − | 0.0284367i | ||||
\(628\) | −157.352 | + | 272.541i | −0.250560 | + | 0.433983i | ||||
\(629\) | − | 267.021i | − | 0.424517i | ||||||
\(630\) | 315.229 | − | 169.382i | 0.500364 | − | 0.268860i | ||||
\(631\) | −342.555 | −0.542876 | −0.271438 | − | 0.962456i | \(-0.587499\pi\) | ||||
−0.271438 | + | 0.962456i | \(0.587499\pi\) | |||||||
\(632\) | −15.8983 | − | 9.17886i | −0.0251555 | − | 0.0145235i | ||||
\(633\) | 269.745 | + | 467.212i | 0.426137 | + | 0.738091i | ||||
\(634\) | 88.4991 | + | 153.285i | 0.139588 | + | 0.241774i | ||||
\(635\) | 657.636 | − | 671.431i | 1.03565 | − | 1.05737i | ||||
\(636\) | − | 1133.66i | − | 1.78248i | ||||||
\(637\) | 15.1651 | − | 184.912i | 0.0238071 | − | 0.290286i | ||||
\(638\) | 203.360i | 0.318747i | ||||||||
\(639\) | 91.3902 | − | 158.293i | 0.143021 | − | 0.247719i | ||||
\(640\) | 313.507 | + | 1123.26i | 0.489854 | + | 1.75509i | ||||
\(641\) | 486.307 | + | 842.309i | 0.758670 | + | 1.31405i | 0.943529 | + | 0.331289i | \(0.107484\pi\) |
−0.184859 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(642\) | 355.148 | − | 615.135i | 0.553190 | − | 0.958154i | ||||
\(643\) | 986.446 | 1.53413 | 0.767065 | − | 0.641569i | \(-0.221716\pi\) | ||||
0.767065 | + | 0.641569i | \(0.221716\pi\) | |||||||
\(644\) | 816.965 | + | 886.709i | 1.26858 | + | 1.37688i | ||||
\(645\) | −83.2711 | − | 21.3887i | −0.129102 | − | 0.0331607i | ||||
\(646\) | 800.679 | − | 1386.82i | 1.23944 | − | 2.14677i | ||||
\(647\) | −40.4977 | − | 70.1440i | −0.0625930 | − | 0.108414i | 0.833031 | − | 0.553227i | \(-0.186604\pi\) |
−0.895624 | + | 0.444812i | \(0.853270\pi\) | |||||||
\(648\) | −96.0380 | + | 55.4476i | −0.148207 | + | 0.0855672i | ||||
\(649\) | −111.772 | − | 64.5315i | −0.172222 | − | 0.0994321i | ||||
\(650\) | 155.473 | − | 282.679i | 0.239189 | − | 0.434891i | ||||
\(651\) | −382.655 | + | 85.9246i | −0.587796 | + | 0.131989i | ||||
\(652\) | − | 532.111i | − | 0.816121i | ||||||
\(653\) | 329.060 | + | 189.983i | 0.503920 | + | 0.290938i | 0.730331 | − | 0.683093i | \(-0.239366\pi\) |
−0.226411 | + | 0.974032i | \(0.572699\pi\) | |||||||
\(654\) | −332.598 | + | 192.025i | −0.508559 | + | 0.293617i | ||||
\(655\) | −95.7627 | − | 343.107i | −0.146203 | − | 0.523828i | ||||
\(656\) | −463.028 | − | 267.329i | −0.705835 | − | 0.407514i | ||||
\(657\) | 193.946 | 0.295199 | ||||||||
\(658\) | −388.048 | + | 1242.50i | −0.589739 | + | 1.88830i | ||||
\(659\) | 409.417 | 0.621269 | 0.310635 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310635 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(660\) | −65.4590 | − | 64.1141i | −0.0991802 | − | 0.0971426i | ||||
\(661\) | −392.365 | + | 226.532i | −0.593592 | + | 0.342711i | −0.766517 | − | 0.642224i | \(-0.778012\pi\) |
0.172924 | + | 0.984935i | \(0.444678\pi\) | |||||||
\(662\) | 1142.33 | − | 659.527i | 1.72558 | − | 0.996264i | ||||
\(663\) | 103.971 | − | 180.084i | 0.156819 | − | 0.271619i | ||||
\(664\) | − | 168.476i | − | 0.253728i | ||||||
\(665\) | 441.045 | + | 272.923i | 0.663226 | + | 0.410410i | ||||
\(666\) | −86.1046 | −0.129286 | ||||||||
\(667\) | 841.249 | + | 485.696i | 1.26124 | + | 0.728179i | ||||
\(668\) | 124.534 | + | 215.699i | 0.186428 | + | 0.322902i | ||||
\(669\) | 96.5749 | + | 167.273i | 0.144357 | + | 0.250034i | ||||
\(670\) | −532.819 | − | 521.873i | −0.795253 | − | 0.778915i | ||||
\(671\) | 2.27584i | 0.00339171i | ||||||||
\(672\) | −118.093 | + | 26.5175i | −0.175733 | + | 0.0394606i | ||||
\(673\) | 1044.13i | 1.55145i | 0.631071 | + | 0.775725i | \(0.282616\pi\) | ||||
−0.631071 | + | 0.775725i | \(0.717384\pi\) | |||||||
\(674\) | −979.811 | + | 1697.08i | −1.45372 | + | 2.51793i | ||||
\(675\) | 2.69625 | + | 129.876i | 0.00399444 | + | 0.192409i | ||||
\(676\) | −588.909 | − | 1020.02i | −0.871168 | − | 1.50891i | ||||
\(677\) | −661.013 | + | 1144.91i | −0.976386 | + | 1.69115i | −0.301102 | + | 0.953592i | \(0.597354\pi\) |
−0.675284 | + | 0.737558i | \(0.735979\pi\) | |||||||
\(678\) | −787.841 | −1.16201 | ||||||||
\(679\) | 614.040 | − | 565.743i | 0.904330 | − | 0.833200i | ||||
\(680\) | −1892.01 | − | 485.974i | −2.78237 | − | 0.714668i | ||||
\(681\) | −73.8486 | + | 127.909i | −0.108441 | + | 0.187826i | ||||
\(682\) | 76.5806 | + | 132.641i | 0.112288 | + | 0.194489i | ||||
\(683\) | 715.045 | − | 412.831i | 1.04692 | − | 0.604438i | 0.125133 | − | 0.992140i | \(-0.460064\pi\) |
0.921785 | + | 0.387702i | \(0.126731\pi\) | |||||||
\(684\) | −293.196 | − | 169.277i | −0.428649 | − | 0.247480i | ||||
\(685\) | −183.936 | − | 47.2450i | −0.268520 | − | 0.0689708i | ||||
\(686\) | −162.031 | − | 1157.71i | −0.236197 | − | 1.68762i | ||||
\(687\) | 120.844i | 0.175901i | ||||||||
\(688\) | −99.1490 | − | 57.2437i | −0.144112 | − | 0.0832031i | ||||
\(689\) | 281.829 | − | 162.714i | 0.409041 | − | 0.236160i | ||||
\(690\) | −642.990 | + | 179.461i | −0.931869 | + | 0.260089i | ||||
\(691\) | −219.857 | − | 126.935i | −0.318173 | − | 0.183697i | 0.332405 | − | 0.943137i | \(-0.392140\pi\) |
−0.650578 | + | 0.759440i | \(0.725473\pi\) | |||||||
\(692\) | −189.233 | −0.273458 | ||||||||
\(693\) | 21.4569 | − | 19.7692i | 0.0309623 | − | 0.0285270i | ||||
\(694\) | 83.3531 | 0.120105 | ||||||||
\(695\) | 344.330 | − | 351.552i | 0.495439 | − | 0.505831i | ||||
\(696\) | 793.797 | − | 458.299i | 1.14051 | − | 0.658476i | ||||
\(697\) | −1273.05 | + | 734.993i | −1.82646 | + | 1.05451i | ||||
\(698\) | −276.659 | + | 479.188i | −0.396360 | + | 0.686516i | ||||
\(699\) | 300.637i | 0.430097i | ||||||||
\(700\) | 370.802 | − | 1280.07i | 0.529717 | − | 1.82867i | ||||
\(701\) | 304.585 | 0.434500 | 0.217250 | − | 0.976116i | \(-0.430291\pi\) | ||||
0.217250 | + | 0.976116i | \(0.430291\pi\) | |||||||
\(702\) | −58.0704 | − | 33.5269i | −0.0827213 | − | 0.0477592i | ||||
\(703\) | −62.3983 | − | 108.077i | −0.0887600 | − | 0.153737i | ||||
\(704\) | 55.6782 | + | 96.4375i | 0.0790884 | + | 0.136985i | ||||
\(705\) | −337.573 | − | 330.638i | −0.478827 | − | 0.468990i | ||||
\(706\) | − | 1331.39i | − | 1.88582i | ||||||
\(707\) | −249.854 | + | 800.014i | −0.353401 | + | 1.13156i | ||||
\(708\) | 1225.33i | 1.73069i | ||||||||
\(709\) | −23.4875 | + | 40.6815i | −0.0331276 | + | 0.0573787i | −0.882114 | − | 0.471036i | \(-0.843880\pi\) |
0.848986 | + | 0.528415i | \(0.177213\pi\) | |||||||
\(710\) | −279.108 | − | 1000.01i | −0.393110 | − | 1.40847i | ||||
\(711\) | 2.23481 | + | 3.87080i | 0.00314319 | + | 0.00544417i | ||||
\(712\) | 782.973 | − | 1356.15i | 1.09968 | − | 1.90470i | ||||
\(713\) | 731.605 | 1.02609 | ||||||||
\(714\) | 390.582 | − | 1250.61i | 0.547033 | − | 1.75156i | ||||
\(715\) | 6.54354 | − | 25.4755i | 0.00915180 | − | 0.0356301i | ||||
\(716\) | −533.552 | + | 924.140i | −0.745185 | + | 1.29070i | ||||
\(717\) | 94.3243 | + | 163.374i | 0.131554 | + | 0.227858i | ||||
\(718\) | 991.918 | − | 572.684i | 1.38150 | − | 0.797611i | ||||
\(719\) | 276.768 | + | 159.792i | 0.384934 | + | 0.222242i | 0.679963 | − | 0.733247i | \(-0.261996\pi\) |
−0.295029 | + | 0.955488i | \(0.595329\pi\) | |||||||
\(720\) | −43.0356 | + | 167.548i | −0.0597717 | + | 0.232705i | ||||
\(721\) | 95.6649 | + | 426.032i | 0.132684 | + | 0.590891i | ||||
\(722\) | 481.916i | 0.667474i | ||||||||
\(723\) | 155.565 | + | 89.8157i | 0.215167 | + | 0.124226i | ||||
\(724\) | −1853.79 | + | 1070.29i | −2.56048 | + | 1.47830i | ||||
\(725\) | −22.2857 | − | 1073.48i | −0.0307389 | − | 1.48067i | ||||
\(726\) | 608.709 | + | 351.438i | 0.838442 | + | 0.484075i | ||||
\(727\) | −1192.80 | −1.64071 | −0.820354 | − | 0.571855i | \(-0.806224\pi\) | ||||
−0.820354 | + | 0.571855i | \(0.806224\pi\) | |||||||
\(728\) | 221.290 | + | 240.181i | 0.303970 | + | 0.329920i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 770.860 | − | 787.029i | 1.05597 | − | 1.07812i | ||||
\(731\) | −272.599 | + | 157.385i | −0.372913 | + | 0.215301i | ||||
\(732\) | 18.7121 | − | 10.8034i | 0.0255630 | − | 0.0147588i | ||||
\(733\) | −17.6644 | + | 30.5956i | −0.0240988 | + | 0.0417403i | −0.877823 | − | 0.478985i | \(-0.841005\pi\) |
0.853725 | + | 0.520725i | \(0.174338\pi\) | |||||||
\(734\) | − | 1189.50i | − | 1.62057i | ||||||
\(735\) | 401.006 | + | 138.813i | 0.545587 | + | 0.188861i | ||||
\(736\) | 225.783 | 0.306771 | ||||||||
\(737\) | −52.6598 | − | 30.4032i | −0.0714516 | − | 0.0412526i | ||||
\(738\) | 237.008 | + | 410.511i | 0.321150 | + | 0.556247i | ||||
\(739\) | 392.667 | + | 680.119i | 0.531349 | + | 0.920324i | 0.999331 | + | 0.0365854i | \(0.0116481\pi\) |
−0.467981 | + | 0.883738i | \(0.655019\pi\) | |||||||
\(740\) | −224.378 | + | 229.084i | −0.303213 | + | 0.309574i | ||||
\(741\) | − | 97.1853i | − | 0.131154i | ||||||
\(742\) | 1507.96 | − | 1389.35i | 2.03229 | − | 1.87244i | ||||
\(743\) | 419.098i | 0.564062i | 0.959405 | + | 0.282031i | \(0.0910082\pi\) | ||||
−0.959405 | + | 0.282031i | \(0.908992\pi\) | |||||||
\(744\) | 345.169 | − | 597.849i | 0.463936 | − | 0.803561i | ||||
\(745\) | −860.551 | + | 240.184i | −1.15510 | + | 0.322394i | ||||
\(746\) | −280.123 | − | 485.187i | −0.375500 | − | 0.650384i | ||||
\(747\) | −20.5097 | + | 35.5238i | −0.0274560 | + | 0.0475553i | ||||
\(748\) | −335.467 | −0.448485 | ||||||||
\(749\) | 821.823 | − | 184.539i | 1.09723 | − | 0.246381i | ||||
\(750\) | 537.752 | + | 505.266i | 0.717002 | + | 0.673688i | ||||
\(751\) | 59.8519 | − | 103.667i | 0.0796963 | − | 0.138038i | −0.823423 | − | 0.567429i | \(-0.807938\pi\) |
0.903119 | + | 0.429391i | \(0.141272\pi\) | |||||||
\(752\) | −314.617 | − | 544.933i | −0.418374 | − | 0.724644i | ||||
\(753\) | −347.053 | + | 200.371i | −0.460893 | + | 0.266097i | ||||
\(754\) | 479.978 | + | 277.115i | 0.636575 | + | 0.367527i | ||||
\(755\) | −300.469 | + | 1169.79i | −0.397972 | + | 1.54940i | ||||
\(756\) | −264.400 | − | 82.5754i | −0.349735 | − | 0.109227i | ||||
\(757\) | − | 995.970i | − | 1.31568i | −0.753157 | − | 0.657840i | \(-0.771470\pi\) | ||
0.753157 | − | 0.657840i | \(-0.228530\pi\) | |||||||
\(758\) | −509.821 | − | 294.346i | −0.672588 | − | 0.388319i | ||||
\(759\) | −47.1344 | + | 27.2131i | −0.0621007 | + | 0.0358539i | ||||
\(760\) | −879.357 | + | 245.432i | −1.15705 | + | 0.322937i | ||||
\(761\) | 237.050 | + | 136.861i | 0.311498 | + | 0.179843i | 0.647596 | − | 0.761983i | \(-0.275774\pi\) |
−0.336099 | + | 0.941827i | \(0.609108\pi\) | |||||||
\(762\) | −1109.59 | −1.45615 | ||||||||
\(763\) | −434.710 | − | 135.765i | −0.569738 | − | 0.177936i | ||||
\(764\) | 779.629 | 1.02046 | ||||||||
\(765\) | 339.777 | + | 332.797i | 0.444153 | + | 0.435028i | ||||
\(766\) | 656.301 | − | 378.916i | 0.856790 | − | 0.494668i | ||||
\(767\) | −304.619 | + | 175.872i | −0.397156 | + | 0.229298i | ||||
\(768\) | 410.754 | − | 711.447i | 0.534836 | − | 0.926364i | ||||
\(769\) | 694.742i | 0.903435i | 0.892161 | + | 0.451718i | \(0.149189\pi\) | ||||
−0.892161 | + | 0.451718i | \(0.850811\pi\) | |||||||
\(770\) | 5.05978 | − | 165.647i | 0.00657115 | − | 0.215126i | ||||
\(771\) | −159.876 | −0.207362 | ||||||||
\(772\) | −17.6882 | − | 10.2123i | −0.0229122 | − | 0.0132284i | ||||
\(773\) | −310.846 | − | 538.402i | −0.402130 | − | 0.696510i | 0.591853 | − | 0.806046i | \(-0.298397\pi\) |
−0.993983 | + | 0.109537i | \(0.965063\pi\) | |||||||
\(774\) | 50.7510 | + | 87.9034i | 0.0655698 | + | 0.113570i | ||||
\(775\) | −418.783 | − | 691.785i | −0.540365 | − | 0.892625i | ||||
\(776\) | 1469.68i | 1.89392i | ||||||||
\(777\) | −69.1855 | − | 75.0919i | −0.0890419 | − | 0.0966434i | ||||
\(778\) | − | 1656.32i | − | 2.12895i | ||||||
\(779\) | −343.511 | + | 594.978i | −0.440964 | + | 0.763771i | ||||
\(780\) | −240.524 | + | 67.1313i | −0.308364 | + | 0.0860657i | ||||
\(781\) | −42.3233 | − | 73.3061i | −0.0541912 | − | 0.0938619i | ||||
\(782\) | −1222.05 | + | 2116.66i | −1.56273 | + | 2.70672i | ||||
\(783\) | −223.167 | −0.285016 | ||||||||
\(784\) | 464.649 | + | 321.600i | 0.592665 | + | 0.410204i | ||||
\(785\) | 51.4039 | − | 200.127i | 0.0654827 | − | 0.254939i | ||||
\(786\) | −210.279 | + | 364.214i | −0.267531 | + | 0.463377i | ||||
\(787\) | −11.6617 | − | 20.1986i | −0.0148179 | − | 0.0256653i | 0.858521 | − | 0.512778i | \(-0.171384\pi\) |
−0.873339 | + | 0.487112i | \(0.838050\pi\) | |||||||
\(788\) | −211.299 | + | 121.993i | −0.268145 | + | 0.154814i | ||||
\(789\) | 226.172 | + | 130.580i | 0.286656 | + | 0.165501i | ||||
\(790\) | 24.5902 | + | 6.31614i | 0.0311268 | + | 0.00799511i | ||||
\(791\) | −633.035 | − | 687.077i | −0.800297 | − | 0.868618i | ||||
\(792\) | 51.3561i | 0.0648436i | ||||||||
\(793\) | 5.37150 | + | 3.10124i | 0.00677365 | + | 0.00391077i | ||||
\(794\) | 1167.60 | − | 674.111i | 1.47052 | − | 0.849007i | ||||
\(795\) | 200.096 | + | 716.921i | 0.251693 | + | 0.901788i | ||||
\(796\) | 107.612 | + | 62.1297i | 0.135191 | + | 0.0780524i | ||||
\(797\) | 140.581 | 0.176388 | 0.0881941 | − | 0.996103i | \(-0.471890\pi\) | ||||
0.0881941 | + | 0.996103i | \(0.471890\pi\) | |||||||
\(798\) | −134.158 | − | 597.458i | −0.168118 | − | 0.748695i | ||||
\(799\) | −1730.01 | −2.16522 | ||||||||
\(800\) | −129.242 | − | 213.494i | −0.161553 | − | 0.266868i | ||||
\(801\) | −330.186 | + | 190.633i | −0.412218 | + | 0.237994i | ||||
\(802\) | 1118.18 | − | 645.584i | 1.39425 | − | 0.804968i | ||||
\(803\) | 44.9086 | − | 77.7840i | 0.0559261 | − | 0.0968668i | ||||
\(804\) | 577.297i | 0.718031i | ||||||||
\(805\) | −673.154 | − | 416.554i | −0.836216 | − | 0.517458i | ||||
\(806\) | 417.420 | 0.517890 | ||||||||
\(807\) | 165.504 | + | 95.5538i | 0.205086 | + | 0.118406i | ||||
\(808\) | −737.648 | − | 1277.64i | −0.912931 | − | 1.58124i | ||||
\(809\) | 92.8993 | + | 160.906i | 0.114832 | + | 0.198895i | 0.917713 | − | 0.397245i | \(-0.130034\pi\) |
−0.802880 | + | 0.596140i | \(0.796700\pi\) | |||||||
\(810\) | 107.315 | − | 109.566i | 0.132487 | − | 0.135266i | ||||
\(811\) | 683.280i | 0.842516i | 0.906941 | + | 0.421258i | \(0.138411\pi\) | ||||
−0.906941 | + | 0.421258i | \(0.861589\pi\) | |||||||
\(812\) | 2185.38 | + | 682.523i | 2.69136 | + | 0.840545i | ||||
\(813\) | 171.932i | 0.211478i | ||||||||
\(814\) | −19.9378 | + | 34.5332i | −0.0244936 | + | 0.0424241i | ||||
\(815\) | 93.9201 | + | 336.505i | 0.115239 | + | 0.412890i | ||||
\(816\) | 316.671 | + | 548.491i | 0.388078 | + | 0.672170i | ||||
\(817\) | −73.5566 | + | 127.404i | −0.0900325 | + | 0.155941i | ||||
\(818\) | −2654.38 | −3.24496 | ||||||||
\(819\) | −17.4210 | − | 77.5823i | −0.0212711 | − | 0.0947281i | ||||
\(820\) | 1709.79 | + | 439.171i | 2.08511 | + | 0.535574i | ||||
\(821\) | 382.762 | − | 662.963i | 0.466214 | − | 0.807507i | −0.533041 | − | 0.846089i | \(-0.678951\pi\) |
0.999255 | + | 0.0385823i | \(0.0122842\pi\) | |||||||
\(822\) | 112.103 | + | 194.168i | 0.136378 | + | 0.236214i | ||||
\(823\) | −1336.87 | + | 771.839i | −1.62438 | + | 0.937836i | −0.638651 | + | 0.769496i | \(0.720507\pi\) |
−0.985729 | + | 0.168340i | \(0.946159\pi\) | |||||||
\(824\) | −665.621 | − | 384.296i | −0.807792 | − | 0.466379i | ||||
\(825\) | 52.7125 | + | 28.9917i | 0.0638939 | + | 0.0351415i | ||||
\(826\) | −1629.90 | + | 1501.70i | −1.97324 | + | 1.81804i | ||||
\(827\) | − | 794.814i | − | 0.961081i | −0.876973 | − | 0.480540i | \(-0.840441\pi\) | ||
0.876973 | − | 0.480540i | \(-0.159559\pi\) | |||||||
\(828\) | 447.496 | + | 258.362i | 0.540454 | + | 0.312031i | ||||
\(829\) | −686.072 | + | 396.104i | −0.827590 | + | 0.477809i | −0.853027 | − | 0.521867i | \(-0.825236\pi\) |
0.0254368 | + | 0.999676i | \(0.491902\pi\) | |||||||
\(830\) | 62.6371 | + | 224.422i | 0.0754663 | + | 0.270388i | ||||
\(831\) | −583.943 | − | 337.139i | −0.702699 | − | 0.405703i | ||||
\(832\) | 303.487 | 0.364768 | ||||||||
\(833\) | 1404.49 | − | 664.247i | 1.68607 | − | 0.797416i | ||||
\(834\) | −580.967 | −0.696603 | ||||||||
\(835\) | −116.826 | − | 114.426i | −0.139912 | − | 0.137038i | ||||
\(836\) | −135.781 | + | 78.3929i | −0.162417 | + | 0.0937714i | ||||
\(837\) | −145.560 | + | 84.0393i | −0.173907 | + | 0.100405i | ||||
\(838\) | 598.029 | − | 1035.82i | 0.713638 | − | 1.23606i | ||||
\(839\) | − | 1167.54i | − | 1.39159i | −0.718241 | − | 0.695795i | \(-0.755052\pi\) | ||
0.718241 | − | 0.695795i | \(-0.244948\pi\) | |||||||
\(840\) | −657.989 | + | 353.557i | −0.783321 | + | 0.420901i | ||||
\(841\) | 1003.58 | 1.19331 | ||||||||
\(842\) | −518.761 | − | 299.507i | −0.616105 | − | 0.355709i | ||||
\(843\) | −266.193 | − | 461.060i | −0.315769 | − | 0.546928i | ||||
\(844\) | −1186.00 | − | 2054.21i | −1.40521 | − | 2.43389i | ||||
\(845\) | 552.463 | + | 541.113i | 0.653802 | + | 0.640370i | ||||
\(846\) | 557.865i | 0.659415i | ||||||||
\(847\) | 182.611 | + | 813.238i | 0.215598 | + | 0.960140i | ||||
\(848\) | 991.176i | 1.16884i | ||||||||
\(849\) | 388.915 | − | 673.620i | 0.458086 | − | 0.793428i | ||||
\(850\) | 2700.97 | − | 56.0728i | 3.17762 | − | 0.0659679i | ||||
\(851\) | 95.2367 | + | 164.955i | 0.111911 | + | 0.193836i | ||||
\(852\) | −401.819 | + | 695.971i | −0.471618 | + | 0.816867i | ||||
\(853\) | 1146.86 | 1.34450 | 0.672251 | − | 0.740324i | \(-0.265328\pi\) | ||||
0.672251 | + | 0.740324i | \(0.265328\pi\) | |||||||
\(854\) | 37.3030 | + | 11.6502i | 0.0436804 | + | 0.0136419i | ||||
\(855\) | 215.294 | + | 55.2995i | 0.251806 | + | 0.0646778i | ||||
\(856\) | −741.314 | + | 1283.99i | −0.866021 | + | 1.49999i | ||||
\(857\) | −107.457 | − | 186.121i | −0.125387 | − | 0.217177i | 0.796497 | − | 0.604643i | \(-0.206684\pi\) |
−0.921884 | + | 0.387465i | \(0.873351\pi\) | |||||||
\(858\) | −26.8927 | + | 15.5265i | −0.0313435 | + | 0.0180962i | ||||
\(859\) | 986.635 | + | 569.634i | 1.14859 | + | 0.663136i | 0.948542 | − | 0.316651i | \(-0.102558\pi\) |
0.200044 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(860\) | 366.121 | + | 94.0404i | 0.425722 | + | 0.109349i | ||||
\(861\) | −167.569 | + | 536.543i | −0.194622 | + | 0.623163i | ||||
\(862\) | 2915.05i | 3.38173i | ||||||||
\(863\) | −471.152 | − | 272.020i | −0.545947 | − | 0.315203i | 0.201539 | − | 0.979481i | \(-0.435406\pi\) |
−0.747486 | + | 0.664278i | \(0.768739\pi\) | |||||||
\(864\) | −44.9220 | + | 25.9357i | −0.0519930 | + | 0.0300182i | ||||
\(865\) | 119.670 | − | 33.4005i | 0.138347 | − | 0.0386133i | ||||
\(866\) | 199.084 | + | 114.941i | 0.229889 | + | 0.132726i | ||||
\(867\) | 1240.74 | 1.43108 | ||||||||
\(868\) | 1682.43 | − | 377.788i | 1.93829 | − | 0.435240i | ||||
\(869\) | 2.06990 | 0.00238194 | ||||||||
\(870\) | −887.005 | + | 905.611i | −1.01955 | + | 1.04093i | ||||
\(871\) | −143.517 | + | 82.8596i | −0.164773 | + | 0.0951316i | ||||
\(872\) | 694.244 | − | 400.822i | 0.796151 | − | 0.459658i | ||||
\(873\) | 178.914 | − | 309.888i | 0.204941 | − | 0.354969i | ||||
\(874\) | 1142.29i | 1.30697i | ||||||||
\(875\) | −8.55638 | + | 874.958i | −0.00977872 | + | 0.999952i | ||||
\(876\) | −852.728 | −0.973433 | ||||||||
\(877\) | 456.068 | + | 263.311i | 0.520032 | + | 0.300241i | 0.736948 | − | 0.675950i | \(-0.236266\pi\) |
−0.216916 | + | 0.976190i | \(0.569600\pi\) | |||||||
\(878\) | −477.641 | − | 827.298i | −0.544010 | − | 0.942253i | ||||
\(879\) | 63.9507 | + | 110.766i | 0.0727539 | + | 0.126013i | ||||
\(880\) | 57.2319 | + | 56.0560i | 0.0650362 | + | 0.0637001i | ||||
\(881\) | 121.399i | 0.137797i | 0.997624 | + | 0.0688983i | \(0.0219484\pi\) | ||||
−0.997624 | + | 0.0688983i | \(0.978052\pi\) | |||||||
\(882\) | −214.195 | − | 452.898i | −0.242852 | − | 0.513490i | ||||
\(883\) | − | 243.586i | − | 0.275862i | −0.990442 | − | 0.137931i | \(-0.955955\pi\) | ||
0.990442 | − | 0.137931i | \(-0.0440453\pi\) | |||||||
\(884\) | −457.135 | + | 791.780i | −0.517120 | + | 0.895679i | ||||
\(885\) | −216.276 | − | 774.893i | −0.244380 | − | 0.875585i | ||||
\(886\) | 788.226 | + | 1365.25i | 0.889646 | + | 1.54091i | ||||
\(887\) | 636.947 | − | 1103.23i | 0.718092 | − | 1.24377i | −0.243663 | − | 0.969860i | \(-0.578349\pi\) |
0.961755 | − | 0.273911i | \(-0.0883175\pi\) | |||||||
\(888\) | 179.729 | 0.202398 | ||||||||
\(889\) | −891.562 | − | 967.675i | −1.00288 | − | 1.08850i | ||||
\(890\) | −538.778 | + | 2097.59i | −0.605368 | + | 2.35684i | ||||
\(891\) | 6.25193 | − | 10.8287i | 0.00701675 | − | 0.0121534i | ||||
\(892\) | −424.615 | − | 735.454i | −0.476025 | − | 0.824500i | ||||
\(893\) | −700.223 | + | 404.274i | −0.784124 | + | 0.452714i | ||||
\(894\) | 913.489 | + | 527.403i | 1.02180 | + | 0.589937i | ||||
\(895\) | 174.302 | − | 678.597i | 0.194751 | − | 0.758209i | ||||
\(896\) | 1593.00 | − | 357.705i | 1.77790 | − | 0.399225i | ||||
\(897\) | 148.331i | 0.165363i | ||||||||
\(898\) | 1483.32 | + | 856.397i | 1.65181 | + | 0.953671i | ||||
\(899\) | 1203.12 | − | 694.623i | 1.33829 | − | 0.772662i | ||||
\(900\) | −11.8547 | − | 571.030i | −0.0131719 | − | 0.634478i | ||||
\(901\) | 2360.03 | + | 1362.57i | 2.61935 | + | 1.51228i | ||||
\(902\) | 219.520 | 0.243370 | ||||||||
\(903\) | −35.8819 | + | 114.891i | −0.0397363 | + | 0.127232i | ||||
\(904\) | 1644.49 | 1.81913 | ||||||||
\(905\) | 983.421 | − | 1004.05i | 1.08665 | − | 1.10945i | ||||
\(906\) | 1234.87 | − | 712.952i | 1.36299 | − | 0.786923i | ||||
\(907\) | 490.555 | − | 283.222i | 0.540854 | − | 0.312262i | −0.204571 | − | 0.978852i | \(-0.565580\pi\) |
0.745425 | + | 0.666589i | \(0.232247\pi\) | |||||||
\(908\) | 324.693 | − | 562.384i | 0.357591 | − | 0.619366i | ||||
\(909\) | 359.195i | 0.395154i | ||||||||
\(910\) | −384.070 | − | 237.666i | −0.422055 | − | 0.261172i | ||||
\(911\) | −1468.26 | −1.61170 | −0.805850 | − | 0.592120i | \(-0.798291\pi\) | ||||
−0.805850 | + | 0.592120i | \(0.798291\pi\) | |||||||
\(912\) | 256.346 | + | 148.001i | 0.281081 | + | 0.162282i | ||||
\(913\) | 9.49814 | + | 16.4513i | 0.0104032 | + | 0.0180189i | ||||
\(914\) | −1064.36 | − | 1843.52i | −1.16450 | − | 2.01698i | ||||
\(915\) | −9.92660 | + | 10.1348i | −0.0108487 | + | 0.0110763i | ||||
\(916\) | − | 531.318i | − | 0.580042i | ||||||
\(917\) | −486.592 | + | 109.263i | −0.530635 | + | 0.119153i | ||||
\(918\) | − | 561.508i | − | 0.611664i | ||||||
\(919\) | −514.213 | + | 890.643i | −0.559535 | + | 0.969143i | 0.438000 | + | 0.898975i | \(0.355687\pi\) |
−0.997535 | + | 0.0701683i | \(0.977646\pi\) | |||||||
\(920\) | 1342.14 | − | 374.596i | 1.45884 | − | 0.407170i | ||||
\(921\) | −141.086 | − | 244.369i | −0.153188 | − | 0.265330i | ||||
\(922\) | 116.170 | − | 201.212i | 0.125998 | − | 0.218235i | ||||
\(923\) | −230.693 | −0.249938 | ||||||||
\(924\) | −94.3403 | + | 86.9199i | −0.102100 | + | 0.0940692i | ||||
\(925\) | 101.461 | − | 184.476i | 0.109688 | − | 0.199434i | ||||
\(926\) | −394.241 | + | 682.845i | −0.425746 | + | 0.737414i | ||||
\(927\) | 93.5659 | + | 162.061i | 0.100934 | + | 0.174823i | ||||
\(928\) | 371.300 | − | 214.370i | 0.400108 | − | 0.231003i | ||||
\(929\) | −551.039 | − | 318.143i | −0.593153 | − | 0.342457i | 0.173190 | − | 0.984888i | \(-0.444593\pi\) |
−0.766343 | + | 0.642431i | \(0.777926\pi\) | |||||||
\(930\) | −237.517 | + | 924.708i | −0.255394 | + | 0.994309i | ||||
\(931\) | 413.247 | − | 597.061i | 0.443874 | − | 0.641312i | ||||
\(932\) | − | 1321.82i | − | 1.41827i | ||||||
\(933\) | −59.4984 | − | 34.3514i | −0.0637711 | − | 0.0368183i | ||||
\(934\) | −1452.93 | + | 838.848i | −1.55560 | + | 0.898124i | ||||
\(935\) | 212.148 | − | 59.2115i | 0.226897 | − | 0.0633278i | ||||
\(936\) | 121.212 | + | 69.9820i | 0.129500 | + | 0.0747671i | ||||
\(937\) | −1396.05 | −1.48991 | −0.744956 | − | 0.667113i | \(-0.767530\pi\) | ||||
−0.744956 | + | 0.667113i | \(0.767530\pi\) | |||||||
\(938\) | −767.906 | + | 707.506i | −0.818663 | + | 0.754271i | ||||
\(939\) | −256.799 | −0.273482 | ||||||||
\(940\) | 1484.22 | + | 1453.73i | 1.57896 | + | 1.54652i | ||||
\(941\) | −334.880 | + | 193.343i | −0.355877 | + | 0.205466i | −0.667271 | − | 0.744815i | \(-0.732538\pi\) |
0.311394 | + | 0.950281i | \(0.399204\pi\) | |||||||
\(942\) | −211.260 | + | 121.971i | −0.224268 | + | 0.129481i | ||||
\(943\) | 524.290 | − | 908.097i | 0.555981 | − | 0.962987i | ||||
\(944\) | − | 1071.32i | − | 1.13488i | ||||||
\(945\) | 181.781 | + | 5.55259i | 0.192360 | + | 0.00587576i | ||||
\(946\) | 47.0062 | 0.0496894 | ||||||||
\(947\) | −499.180 | − | 288.202i | −0.527117 | − | 0.304331i | 0.212725 | − | 0.977112i | \(-0.431766\pi\) |
−0.739842 | + | 0.672781i | \(0.765100\pi\) | |||||||
\(948\) | −9.82587 | − | 17.0189i | −0.0103648 | − | 0.0179524i | ||||
\(949\) | −122.392 | − | 211.990i | −0.128970 | − | 0.223382i | ||||
\(950\) | 1080.12 | − | 653.867i | 1.13697 | − | 0.688281i | ||||
\(951\) | 89.9524i | 0.0945872i | ||||||||
\(952\) | −815.276 | + | 2610.45i | −0.856382 | + | 2.74207i | ||||
\(953\) | − | 1080.91i | − | 1.13421i | −0.823644 | − | 0.567107i | \(-0.808063\pi\) | ||
0.823644 | − | 0.567107i | \(-0.191937\pi\) | |||||||
\(954\) | 439.377 | − | 761.024i | 0.460563 | − | 0.797719i | ||||
\(955\) | −493.035 | + | 137.608i | −0.516267 | + | 0.144092i | ||||
\(956\) | −414.719 | − | 718.315i | −0.433807 | − | 0.751375i | ||||
\(957\) | −51.6750 | + | 89.5037i | −0.0539968 | + | 0.0935253i | ||||
\(958\) | −2445.26 | −2.55246 | ||||||||
\(959\) | −79.2588 | + | 253.780i | −0.0826473 | + | 0.264630i | ||||
\(960\) | −172.687 | + | 672.313i | −0.179883 | + | 0.700326i | ||||
\(961\) | 42.6564 | − | 73.8830i | 0.0443875 | − | 0.0768814i | ||||
\(962\) | 54.3376 | + | 94.1155i | 0.0564840 | + | 0.0978331i | ||||
\(963\) | 312.618 | − | 180.490i | 0.324629 | − | 0.187425i | ||||
\(964\) | −683.980 | − | 394.896i | −0.709523 | − | 0.409643i | ||||
\(965\) | 12.9885 | + | 3.33617i | 0.0134596 | + | 0.00345718i | ||||
\(966\) | 204.762 | + | 911.883i | 0.211969 | + | 0.943978i | ||||
\(967\) | 785.695i | 0.812508i | 0.913760 | + | 0.406254i | \(0.133165\pi\) | ||||
−0.913760 | + | 0.406254i | \(0.866835\pi\) | |||||||
\(968\) | −1270.58 | − | 733.570i | −1.31258 | − | 0.757820i | ||||
\(969\) | 704.795 | − | 406.914i | 0.727343 | − | 0.419932i | ||||
\(970\) | −546.408 | − | 1957.72i | −0.563307 | − | 2.01827i | ||||
\(971\) | −801.304 | − | 462.633i | −0.825236 | − | 0.476450i | 0.0269825 | − | 0.999636i | \(-0.491410\pi\) |
−0.852219 | + | 0.523186i | \(0.824743\pi\) | |||||||
\(972\) | −118.712 | −0.122132 | ||||||||
\(973\) | −466.810 | − | 506.662i | −0.479764 | − | 0.520721i | ||||
\(974\) | −1366.46 | −1.40294 | ||||||||
\(975\) | 140.258 | − | 84.9072i | 0.143854 | − | 0.0870843i | ||||
\(976\) | −16.3603 | + | 9.44562i | −0.0167626 | + | 0.00967789i | ||||
\(977\) | 278.572 | − | 160.834i | 0.285130 | − | 0.164620i | −0.350614 | − | 0.936520i | \(-0.614027\pi\) |
0.635743 | + | 0.771900i | \(0.280694\pi\) | |||||||
\(978\) | 206.233 | − | 357.206i | 0.210872 | − | 0.365241i | ||||
\(979\) | 176.567i | 0.180354i | ||||||||
\(980\) | −1763.12 | − | 610.322i | −1.79910 | − | 0.622778i | ||||
\(981\) | −195.179 | −0.198959 | ||||||||
\(982\) | −2639.01 | − | 1523.63i | −2.68738 | − | 1.55156i | ||||
\(983\) | 713.047 | + | 1235.03i | 0.725379 | + | 1.25639i | 0.958818 | + | 0.284021i | \(0.0916687\pi\) |
−0.233439 | + | 0.972371i | \(0.574998\pi\) | |||||||
\(984\) | −494.716 | − | 856.874i | −0.502761 | − | 0.870807i | ||||
\(985\) | 112.092 | − | 114.443i | 0.113799 | − | 0.116186i | ||||
\(986\) | 4641.11i | 4.70701i | ||||||||
\(987\) | −486.515 | + | 448.248i | −0.492923 | + | 0.454152i | ||||
\(988\) | 427.298i | 0.432488i | ||||||||
\(989\) | 112.267 | − | 194.452i | 0.113516 | − | 0.196615i | ||||
\(990\) | −19.0935 | − | 68.4101i | −0.0192864 | − | 0.0691011i | ||||
\(991\) | −854.919 | − | 1480.76i | −0.862683 | − | 1.49421i | −0.869329 | − | 0.494234i | \(-0.835449\pi\) |
0.00664562 | − | 0.999978i | \(-0.497885\pi\) | |||||||
\(992\) | 161.453 | − | 279.645i | 0.162755 | − | 0.281901i | ||||
\(993\) | 670.358 | 0.675083 | ||||||||
\(994\) | −1418.21 | + | 318.457i | −1.42677 | + | 0.320380i | ||||
\(995\) | −79.0195 | − | 20.2966i | −0.0794166 | − | 0.0203986i | ||||
\(996\) | 90.1756 | − | 156.189i | 0.0905378 | − | 0.156816i | ||||
\(997\) | −687.055 | − | 1190.01i | −0.689122 | − | 1.19359i | −0.972122 | − | 0.234475i | \(-0.924663\pi\) |
0.283000 | − | 0.959120i | \(-0.408670\pi\) | |||||||
\(998\) | −1542.31 | + | 890.453i | −1.54540 | + | 0.892238i | ||||
\(999\) | −37.8967 | − | 21.8796i | −0.0379346 | − | 0.0219015i |
(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.r.a.19.2 | ✓ | 32 | |
3.2 | odd | 2 | 315.3.bi.e.19.15 | 32 | |||
5.2 | odd | 4 | 525.3.o.p.376.8 | 16 | |||
5.3 | odd | 4 | 525.3.o.q.376.1 | 16 | |||
5.4 | even | 2 | inner | 105.3.r.a.19.15 | yes | 32 | |
7.2 | even | 3 | 735.3.e.a.244.6 | 32 | |||
7.3 | odd | 6 | inner | 105.3.r.a.94.15 | yes | 32 | |
7.5 | odd | 6 | 735.3.e.a.244.14 | 32 | |||
15.14 | odd | 2 | 315.3.bi.e.19.2 | 32 | |||
21.17 | even | 6 | 315.3.bi.e.199.2 | 32 | |||
35.3 | even | 12 | 525.3.o.q.451.1 | 16 | |||
35.9 | even | 6 | 735.3.e.a.244.13 | 32 | |||
35.17 | even | 12 | 525.3.o.p.451.8 | 16 | |||
35.19 | odd | 6 | 735.3.e.a.244.5 | 32 | |||
35.24 | odd | 6 | inner | 105.3.r.a.94.2 | yes | 32 | |
105.59 | even | 6 | 315.3.bi.e.199.15 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.r.a.19.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
105.3.r.a.19.15 | yes | 32 | 5.4 | even | 2 | inner | |
105.3.r.a.94.2 | yes | 32 | 35.24 | odd | 6 | inner | |
105.3.r.a.94.15 | yes | 32 | 7.3 | odd | 6 | inner | |
315.3.bi.e.19.2 | 32 | 15.14 | odd | 2 | |||
315.3.bi.e.19.15 | 32 | 3.2 | odd | 2 | |||
315.3.bi.e.199.2 | 32 | 21.17 | even | 6 | |||
315.3.bi.e.199.15 | 32 | 105.59 | even | 6 | |||
525.3.o.p.376.8 | 16 | 5.2 | odd | 4 | |||
525.3.o.p.451.8 | 16 | 35.17 | even | 12 | |||
525.3.o.q.376.1 | 16 | 5.3 | odd | 4 | |||
525.3.o.q.451.1 | 16 | 35.3 | even | 12 | |||
735.3.e.a.244.5 | 32 | 35.19 | odd | 6 | |||
735.3.e.a.244.6 | 32 | 7.2 | even | 3 | |||
735.3.e.a.244.13 | 32 | 35.9 | even | 6 | |||
735.3.e.a.244.14 | 32 | 7.5 | odd | 6 |