Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(4,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.c (of order \(4\), 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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.4 | ||
Root | \(4.93651i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.13 |
Dual form | 17.4.c.a.4.1 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.93651i | 1.39177i | 0.718155 | + | 0.695884i | \(0.244987\pi\) | ||||
−0.718155 | + | 0.695884i | \(0.755013\pi\) | |||||||
\(3\) | −0.299807 | − | 0.299807i | −0.0576979 | − | 0.0576979i | 0.677669 | − | 0.735367i | \(-0.262990\pi\) |
−0.735367 | + | 0.677669i | \(0.762990\pi\) | |||||||
\(4\) | −7.49613 | −0.937016 | ||||||||
\(5\) | 1.37942 | + | 1.37942i | 0.123379 | + | 0.123379i | 0.766100 | − | 0.642721i | \(-0.222195\pi\) |
−0.642721 | + | 0.766100i | \(0.722195\pi\) | |||||||
\(6\) | 1.18019 | − | 1.18019i | 0.0803021 | − | 0.0803021i | ||||
\(7\) | 17.9849 | − | 17.9849i | 0.971093 | − | 0.971093i | −0.0285007 | − | 0.999594i | \(-0.509073\pi\) |
0.999594 | + | 0.0285007i | \(0.00907327\pi\) | |||||||
\(8\) | 1.98349i | 0.0876588i | ||||||||
\(9\) | − | 26.8202i | − | 0.993342i | ||||||
\(10\) | −5.43011 | + | 5.43011i | −0.171715 | + | 0.171715i | ||||
\(11\) | −22.9317 | + | 22.9317i | −0.628560 | + | 0.628560i | −0.947706 | − | 0.319146i | \(-0.896604\pi\) |
0.319146 | + | 0.947706i | \(0.396604\pi\) | |||||||
\(12\) | 2.24739 | + | 2.24739i | 0.0540639 | + | 0.0540639i | ||||
\(13\) | −54.6855 | −1.16669 | −0.583347 | − | 0.812223i | \(-0.698257\pi\) | ||||
−0.583347 | + | 0.812223i | \(0.698257\pi\) | |||||||
\(14\) | 70.7978 | + | 70.7978i | 1.35154 | + | 1.35154i | ||||
\(15\) | − | 0.827121i | − | 0.0142375i | ||||||
\(16\) | −67.7771 | −1.05902 | ||||||||
\(17\) | 58.5003 | − | 38.6098i | 0.834612 | − | 0.550839i | ||||
\(18\) | 105.578 | 1.38250 | ||||||||
\(19\) | 46.1336i | 0.557041i | 0.960430 | + | 0.278521i | \(0.0898441\pi\) | ||||
−0.960430 | + | 0.278521i | \(0.910156\pi\) | |||||||
\(20\) | −10.3403 | − | 10.3403i | −0.115608 | − | 0.115608i | ||||
\(21\) | −10.7840 | −0.112060 | ||||||||
\(22\) | −90.2708 | − | 90.2708i | −0.874809 | − | 0.874809i | ||||
\(23\) | −53.2436 | + | 53.2436i | −0.482698 | + | 0.482698i | −0.905992 | − | 0.423294i | \(-0.860874\pi\) |
0.423294 | + | 0.905992i | \(0.360874\pi\) | |||||||
\(24\) | 0.594665 | − | 0.594665i | 0.00505773 | − | 0.00505773i | ||||
\(25\) | − | 121.194i | − | 0.969555i | ||||||
\(26\) | − | 215.270i | − | 1.62377i | ||||||
\(27\) | −16.1357 | + | 16.1357i | −0.115012 | + | 0.115012i | ||||
\(28\) | −134.817 | + | 134.817i | −0.909930 | + | 0.909930i | ||||
\(29\) | 111.044 | + | 111.044i | 0.711045 | + | 0.711045i | 0.966754 | − | 0.255709i | \(-0.0823088\pi\) |
−0.255709 | + | 0.966754i | \(0.582309\pi\) | |||||||
\(30\) | 3.25597 | 0.0198152 | ||||||||
\(31\) | 178.619 | + | 178.619i | 1.03487 | + | 1.03487i | 0.999370 | + | 0.0354994i | \(0.0113022\pi\) |
0.0354994 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(32\) | − | 250.937i | − | 1.38625i | ||||||
\(33\) | 13.7502 | 0.0725332 | ||||||||
\(34\) | 151.988 | + | 230.287i | 0.766639 | + | 1.16159i | ||||
\(35\) | 49.6175 | 0.239626 | ||||||||
\(36\) | 201.048i | 0.930777i | ||||||||
\(37\) | −159.957 | − | 159.957i | −0.710725 | − | 0.710725i | 0.255962 | − | 0.966687i | \(-0.417608\pi\) |
−0.966687 | + | 0.255962i | \(0.917608\pi\) | |||||||
\(38\) | −181.606 | −0.775272 | ||||||||
\(39\) | 16.3951 | + | 16.3951i | 0.0673158 | + | 0.0673158i | ||||
\(40\) | −2.73608 | + | 2.73608i | −0.0108153 | + | 0.0108153i | ||||
\(41\) | −163.457 | + | 163.457i | −0.622626 | + | 0.622626i | −0.946202 | − | 0.323576i | \(-0.895115\pi\) |
0.323576 | + | 0.946202i | \(0.395115\pi\) | |||||||
\(42\) | − | 42.4513i | − | 0.155962i | ||||||
\(43\) | 119.642i | 0.424309i | 0.977236 | + | 0.212154i | \(0.0680480\pi\) | ||||
−0.977236 | + | 0.212154i | \(0.931952\pi\) | |||||||
\(44\) | 171.899 | − | 171.899i | 0.588971 | − | 0.588971i | ||||
\(45\) | 36.9964 | − | 36.9964i | 0.122558 | − | 0.122558i | ||||
\(46\) | −209.594 | − | 209.594i | −0.671803 | − | 0.671803i | ||||
\(47\) | −188.319 | −0.584451 | −0.292225 | − | 0.956349i | \(-0.594396\pi\) | ||||
−0.292225 | + | 0.956349i | \(0.594396\pi\) | |||||||
\(48\) | 20.3200 | + | 20.3200i | 0.0611031 | + | 0.0611031i | ||||
\(49\) | − | 303.913i | − | 0.886044i | ||||||
\(50\) | 477.083 | 1.34940 | ||||||||
\(51\) | −29.1143 | − | 5.96329i | −0.0799376 | − | 0.0163731i | ||||
\(52\) | 409.930 | 1.09321 | ||||||||
\(53\) | − | 468.212i | − | 1.21347i | −0.794905 | − | 0.606734i | \(-0.792479\pi\) | ||
0.794905 | − | 0.606734i | \(-0.207521\pi\) | |||||||
\(54\) | −63.5183 | − | 63.5183i | −0.160069 | − | 0.160069i | ||||
\(55\) | −63.2650 | −0.155103 | ||||||||
\(56\) | 35.6729 | + | 35.6729i | 0.0851249 | + | 0.0851249i | ||||
\(57\) | 13.8312 | − | 13.8312i | 0.0321401 | − | 0.0321401i | ||||
\(58\) | −437.125 | + | 437.125i | −0.989609 | + | 0.989609i | ||||
\(59\) | 751.217i | 1.65763i | 0.559523 | + | 0.828815i | \(0.310984\pi\) | ||||
−0.559523 | + | 0.828815i | \(0.689016\pi\) | |||||||
\(60\) | 6.20021i | 0.0133407i | ||||||||
\(61\) | 341.681 | − | 341.681i | 0.717177 | − | 0.717177i | −0.250849 | − | 0.968026i | \(-0.580710\pi\) |
0.968026 | + | 0.250849i | \(0.0807099\pi\) | |||||||
\(62\) | −703.136 | + | 703.136i | −1.44030 | + | 1.44030i | ||||
\(63\) | −482.359 | − | 482.359i | −0.964627 | − | 0.964627i | ||||
\(64\) | 445.601 | 0.870315 | ||||||||
\(65\) | −75.4344 | − | 75.4344i | −0.143946 | − | 0.143946i | ||||
\(66\) | 54.1277i | 0.100949i | ||||||||
\(67\) | 533.879 | 0.973487 | 0.486744 | − | 0.873545i | \(-0.338185\pi\) | ||||
0.486744 | + | 0.873545i | \(0.338185\pi\) | |||||||
\(68\) | −438.526 | + | 289.424i | −0.782045 | + | 0.516145i | ||||
\(69\) | 31.9256 | 0.0557013 | ||||||||
\(70\) | 195.320i | 0.333503i | ||||||||
\(71\) | 55.2619 | + | 55.2619i | 0.0923715 | + | 0.0923715i | 0.751783 | − | 0.659411i | \(-0.229194\pi\) |
−0.659411 | + | 0.751783i | \(0.729194\pi\) | |||||||
\(72\) | 53.1977 | 0.0870752 | ||||||||
\(73\) | 270.831 | + | 270.831i | 0.434224 | + | 0.434224i | 0.890062 | − | 0.455839i | \(-0.150661\pi\) |
−0.455839 | + | 0.890062i | \(0.650661\pi\) | |||||||
\(74\) | 629.674 | − | 629.674i | 0.989164 | − | 0.989164i | ||||
\(75\) | −36.3349 | + | 36.3349i | −0.0559413 | + | 0.0559413i | ||||
\(76\) | − | 345.824i | − | 0.521957i | ||||||
\(77\) | 824.848i | 1.22078i | ||||||||
\(78\) | −64.5395 | + | 64.5395i | −0.0936880 | + | 0.0936880i | ||||
\(79\) | 904.285 | − | 904.285i | 1.28785 | − | 1.28785i | 0.351757 | − | 0.936091i | \(-0.385584\pi\) |
0.936091 | − | 0.351757i | \(-0.114416\pi\) | |||||||
\(80\) | −93.4932 | − | 93.4932i | −0.130661 | − | 0.130661i | ||||
\(81\) | −714.471 | −0.980070 | ||||||||
\(82\) | −643.449 | − | 643.449i | −0.866550 | − | 0.866550i | ||||
\(83\) | − | 591.376i | − | 0.782071i | −0.920376 | − | 0.391036i | \(-0.872117\pi\) | ||
0.920376 | − | 0.391036i | \(-0.127883\pi\) | |||||||
\(84\) | 80.8382 | 0.105002 | ||||||||
\(85\) | 133.956 | + | 27.4373i | 0.170936 | + | 0.0350117i | ||||
\(86\) | −470.973 | −0.590539 | ||||||||
\(87\) | − | 66.5834i | − | 0.0820516i | ||||||
\(88\) | −45.4848 | − | 45.4848i | −0.0550989 | − | 0.0550989i | ||||
\(89\) | −609.729 | −0.726192 | −0.363096 | − | 0.931752i | \(-0.618280\pi\) | ||||
−0.363096 | + | 0.931752i | \(0.618280\pi\) | |||||||
\(90\) | 145.637 | + | 145.637i | 0.170572 | + | 0.170572i | ||||
\(91\) | −983.513 | + | 983.513i | −1.13297 | + | 1.13297i | ||||
\(92\) | 399.121 | − | 399.121i | 0.452296 | − | 0.452296i | ||||
\(93\) | − | 107.103i | − | 0.119420i | ||||||
\(94\) | − | 741.321i | − | 0.813420i | ||||||
\(95\) | −63.6378 | + | 63.6378i | −0.0687274 | + | 0.0687274i | ||||
\(96\) | −75.2328 | + | 75.2328i | −0.0799835 | + | 0.0799835i | ||||
\(97\) | 1125.76 | + | 1125.76i | 1.17838 | + | 1.17838i | 0.980156 | + | 0.198226i | \(0.0635182\pi\) |
0.198226 | + | 0.980156i | \(0.436482\pi\) | |||||||
\(98\) | 1196.36 | 1.23317 | ||||||||
\(99\) | 615.033 | + | 615.033i | 0.624375 | + | 0.624375i | ||||
\(100\) | 908.489i | 0.908489i | ||||||||
\(101\) | −666.897 | −0.657017 | −0.328508 | − | 0.944501i | \(-0.606546\pi\) | ||||
−0.328508 | + | 0.944501i | \(0.606546\pi\) | |||||||
\(102\) | 23.4746 | − | 114.609i | 0.0227875 | − | 0.111255i | ||||
\(103\) | −872.373 | −0.834538 | −0.417269 | − | 0.908783i | \(-0.637013\pi\) | ||||
−0.417269 | + | 0.908783i | \(0.637013\pi\) | |||||||
\(104\) | − | 108.468i | − | 0.102271i | ||||||
\(105\) | −14.8757 | − | 14.8757i | −0.0138259 | − | 0.0138259i | ||||
\(106\) | 1843.12 | 1.68887 | ||||||||
\(107\) | −244.890 | − | 244.890i | −0.221256 | − | 0.221256i | 0.587771 | − | 0.809027i | \(-0.300006\pi\) |
−0.809027 | + | 0.587771i | \(0.800006\pi\) | |||||||
\(108\) | 120.955 | − | 120.955i | 0.107768 | − | 0.107768i | ||||
\(109\) | −96.0400 | + | 96.0400i | −0.0843942 | + | 0.0843942i | −0.748044 | − | 0.663649i | \(-0.769007\pi\) |
0.663649 | + | 0.748044i | \(0.269007\pi\) | |||||||
\(110\) | − | 249.043i | − | 0.215867i | ||||||
\(111\) | 95.9128i | 0.0820147i | ||||||||
\(112\) | −1218.96 | + | 1218.96i | −1.02840 | + | 1.02840i | ||||
\(113\) | 626.459 | − | 626.459i | 0.521525 | − | 0.521525i | −0.396507 | − | 0.918032i | \(-0.629778\pi\) |
0.918032 | + | 0.396507i | \(0.129778\pi\) | |||||||
\(114\) | 54.4467 | + | 54.4467i | 0.0447316 | + | 0.0447316i | ||||
\(115\) | −146.891 | −0.119110 | ||||||||
\(116\) | −832.398 | − | 832.398i | −0.666261 | − | 0.666261i | ||||
\(117\) | 1466.68i | 1.15893i | ||||||||
\(118\) | −2957.18 | −2.30703 | ||||||||
\(119\) | 357.727 | − | 1746.51i | 0.275570 | − | 1.34540i | ||||
\(120\) | 1.64059 | 0.00124804 | ||||||||
\(121\) | 279.276i | 0.209824i | ||||||||
\(122\) | 1345.03 | + | 1345.03i | 0.998143 | + | 0.998143i | ||||
\(123\) | 98.0110 | 0.0718484 | ||||||||
\(124\) | −1338.95 | − | 1338.95i | −0.969689 | − | 0.969689i | ||||
\(125\) | 339.606 | − | 339.606i | 0.243002 | − | 0.243002i | ||||
\(126\) | 1898.81 | − | 1898.81i | 1.34254 | − | 1.34254i | ||||
\(127\) | − | 1971.07i | − | 1.37720i | −0.725144 | − | 0.688598i | \(-0.758227\pi\) | ||
0.725144 | − | 0.688598i | \(-0.241773\pi\) | |||||||
\(128\) | − | 253.384i | − | 0.174970i | ||||||
\(129\) | 35.8696 | − | 35.8696i | 0.0244817 | − | 0.0244817i | ||||
\(130\) | 296.949 | − | 296.949i | 0.200339 | − | 0.200339i | ||||
\(131\) | 177.333 | + | 177.333i | 0.118272 | + | 0.118272i | 0.763766 | − | 0.645493i | \(-0.223348\pi\) |
−0.645493 | + | 0.763766i | \(0.723348\pi\) | |||||||
\(132\) | −103.073 | −0.0679648 | ||||||||
\(133\) | 829.709 | + | 829.709i | 0.540939 | + | 0.540939i | ||||
\(134\) | 2101.62i | 1.35487i | ||||||||
\(135\) | −44.5159 | −0.0283801 | ||||||||
\(136\) | 76.5823 | + | 116.035i | 0.0482859 | + | 0.0731611i | ||||
\(137\) | 436.372 | 0.272130 | 0.136065 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136065 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(138\) | 125.676i | 0.0775233i | ||||||||
\(139\) | −59.2009 | − | 59.2009i | −0.0361249 | − | 0.0361249i | 0.688814 | − | 0.724938i | \(-0.258132\pi\) |
−0.724938 | + | 0.688814i | \(0.758132\pi\) | |||||||
\(140\) | −371.940 | −0.224533 | ||||||||
\(141\) | 56.4595 | + | 56.4595i | 0.0337216 | + | 0.0337216i | ||||
\(142\) | −217.539 | + | 217.539i | −0.128560 | + | 0.128560i | ||||
\(143\) | 1254.03 | − | 1254.03i | 0.733338 | − | 0.733338i | ||||
\(144\) | 1817.80i | 1.05197i | ||||||||
\(145\) | 306.353i | 0.175457i | ||||||||
\(146\) | −1066.13 | + | 1066.13i | −0.604339 | + | 0.604339i | ||||
\(147\) | −91.1153 | + | 91.1153i | −0.0511229 | + | 0.0511229i | ||||
\(148\) | 1199.06 | + | 1199.06i | 0.665961 | + | 0.665961i | ||||
\(149\) | −2357.45 | −1.29617 | −0.648085 | − | 0.761568i | \(-0.724430\pi\) | ||||
−0.648085 | + | 0.761568i | \(0.724430\pi\) | |||||||
\(150\) | −143.033 | − | 143.033i | −0.0778573 | − | 0.0778573i | ||||
\(151\) | − | 149.746i | − | 0.0807031i | −0.999186 | − | 0.0403515i | \(-0.987152\pi\) | ||
0.999186 | − | 0.0403515i | \(-0.0128478\pi\) | |||||||
\(152\) | −91.5058 | −0.0488296 | ||||||||
\(153\) | −1035.52 | − | 1568.99i | −0.547171 | − | 0.829055i | ||||
\(154\) | −3247.02 | −1.69904 | ||||||||
\(155\) | 492.783i | 0.255363i | ||||||||
\(156\) | −122.900 | − | 122.900i | −0.0630760 | − | 0.0630760i | ||||
\(157\) | −119.280 | −0.0606343 | −0.0303172 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303172 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(158\) | 3559.73 | + | 3559.73i | 1.79238 | + | 1.79238i | ||||
\(159\) | −140.373 | + | 140.373i | −0.0700146 | + | 0.0700146i | ||||
\(160\) | 346.149 | − | 346.149i | 0.171034 | − | 0.171034i | ||||
\(161\) | 1915.16i | 0.937489i | ||||||||
\(162\) | − | 2812.52i | − | 1.36403i | ||||||
\(163\) | 107.923 | − | 107.923i | 0.0518600 | − | 0.0518600i | −0.680701 | − | 0.732561i | \(-0.738325\pi\) |
0.732561 | + | 0.680701i | \(0.238325\pi\) | |||||||
\(164\) | 1225.29 | − | 1225.29i | 0.583410 | − | 0.583410i | ||||
\(165\) | 18.9673 | + | 18.9673i | 0.00894910 | + | 0.00894910i | ||||
\(166\) | 2327.96 | 1.08846 | ||||||||
\(167\) | −1785.49 | − | 1785.49i | −0.827339 | − | 0.827339i | 0.159809 | − | 0.987148i | \(-0.448912\pi\) |
−0.987148 | + | 0.159809i | \(0.948912\pi\) | |||||||
\(168\) | − | 21.3900i | − | 0.00982306i | ||||||
\(169\) | 793.506 | 0.361177 | ||||||||
\(170\) | −108.007 | + | 527.319i | −0.0487281 | + | 0.237903i | ||||
\(171\) | 1237.31 | 0.553332 | ||||||||
\(172\) | − | 896.854i | − | 0.397584i | ||||||
\(173\) | 232.125 | + | 232.125i | 0.102012 | + | 0.102012i | 0.756271 | − | 0.654259i | \(-0.227019\pi\) |
−0.654259 | + | 0.756271i | \(0.727019\pi\) | |||||||
\(174\) | 262.106 | 0.114197 | ||||||||
\(175\) | −2179.67 | − | 2179.67i | −0.941528 | − | 0.941528i | ||||
\(176\) | 1554.24 | − | 1554.24i | 0.665656 | − | 0.665656i | ||||
\(177\) | 225.220 | − | 225.220i | 0.0956417 | − | 0.0956417i | ||||
\(178\) | − | 2400.20i | − | 1.01069i | ||||||
\(179\) | 4155.11i | 1.73501i | 0.497427 | + | 0.867506i | \(0.334278\pi\) | ||||
−0.497427 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(180\) | −277.330 | + | 277.330i | −0.114839 | + | 0.114839i | ||||
\(181\) | 675.588 | − | 675.588i | 0.277437 | − | 0.277437i | −0.554648 | − | 0.832085i | \(-0.687147\pi\) |
0.832085 | + | 0.554648i | \(0.187147\pi\) | |||||||
\(182\) | −3871.61 | − | 3871.61i | −1.57683 | − | 1.57683i | ||||
\(183\) | −204.877 | −0.0827592 | ||||||||
\(184\) | −105.608 | − | 105.608i | −0.0423128 | − | 0.0423128i | ||||
\(185\) | − | 441.298i | − | 0.175378i | ||||||
\(186\) | 421.611 | 0.166204 | ||||||||
\(187\) | −456.121 | + | 2226.90i | −0.178368 | + | 0.870839i | ||||
\(188\) | 1411.67 | 0.547640 | ||||||||
\(189\) | 580.397i | 0.223374i | ||||||||
\(190\) | −250.511 | − | 250.511i | −0.0956525 | − | 0.0956525i | ||||
\(191\) | −889.758 | −0.337072 | −0.168536 | − | 0.985696i | \(-0.553904\pi\) | ||||
−0.168536 | + | 0.985696i | \(0.553904\pi\) | |||||||
\(192\) | −133.594 | − | 133.594i | −0.0502154 | − | 0.0502154i | ||||
\(193\) | −1224.76 | + | 1224.76i | −0.456789 | + | 0.456789i | −0.897600 | − | 0.440811i | \(-0.854691\pi\) |
0.440811 | + | 0.897600i | \(0.354691\pi\) | |||||||
\(194\) | −4431.55 | + | 4431.55i | −1.64003 | + | 1.64003i | ||||
\(195\) | 45.2316i | 0.0166108i | ||||||||
\(196\) | 2278.17i | 0.830237i | ||||||||
\(197\) | 3142.32 | − | 3142.32i | 1.13645 | − | 1.13645i | 0.147369 | − | 0.989082i | \(-0.452919\pi\) |
0.989082 | − | 0.147369i | \(-0.0470805\pi\) | |||||||
\(198\) | −2421.08 | + | 2421.08i | −0.868985 | + | 0.868985i | ||||
\(199\) | 2205.02 | + | 2205.02i | 0.785478 | + | 0.785478i | 0.980749 | − | 0.195272i | \(-0.0625588\pi\) |
−0.195272 | + | 0.980749i | \(0.562559\pi\) | |||||||
\(200\) | 240.388 | 0.0849901 | ||||||||
\(201\) | −160.061 | − | 160.061i | −0.0561682 | − | 0.0561682i | ||||
\(202\) | − | 2625.25i | − | 0.914415i | ||||||
\(203\) | 3994.22 | 1.38098 | ||||||||
\(204\) | 218.245 | + | 44.7016i | 0.0749028 | + | 0.0153419i | ||||
\(205\) | −450.952 | −0.153638 | ||||||||
\(206\) | − | 3434.11i | − | 1.16148i | ||||||
\(207\) | 1428.01 | + | 1428.01i | 0.479484 | + | 0.479484i | ||||
\(208\) | 3706.42 | 1.23555 | ||||||||
\(209\) | −1057.92 | − | 1057.92i | −0.350134 | − | 0.350134i | ||||
\(210\) | 58.5583 | − | 58.5583i | 0.0192424 | − | 0.0192424i | ||||
\(211\) | −3204.98 | + | 3204.98i | −1.04569 | + | 1.04569i | −0.0467829 | + | 0.998905i | \(0.514897\pi\) |
−0.998905 | + | 0.0467829i | \(0.985103\pi\) | |||||||
\(212\) | 3509.78i | 1.13704i | ||||||||
\(213\) | − | 33.1358i | − | 0.0106593i | ||||||
\(214\) | 964.014 | − | 964.014i | 0.307937 | − | 0.307937i | ||||
\(215\) | −165.037 | + | 165.037i | −0.0523509 | + | 0.0523509i | ||||
\(216\) | −32.0050 | − | 32.0050i | −0.0100818 | − | 0.0100818i | ||||
\(217\) | 6424.89 | 2.00991 | ||||||||
\(218\) | −378.063 | − | 378.063i | −0.117457 | − | 0.117457i | ||||
\(219\) | − | 162.394i | − | 0.0501076i | ||||||
\(220\) | 474.242 | 0.145334 | ||||||||
\(221\) | −3199.12 | + | 2111.40i | −0.973737 | + | 0.642661i | ||||
\(222\) | −377.562 | −0.114145 | ||||||||
\(223\) | − | 123.574i | − | 0.0371082i | −0.999828 | − | 0.0185541i | \(-0.994094\pi\) | ||
0.999828 | − | 0.0185541i | \(-0.00590629\pi\) | |||||||
\(224\) | −4513.08 | − | 4513.08i | −1.34617 | − | 1.34617i | ||||
\(225\) | −3250.46 | −0.963100 | ||||||||
\(226\) | 2466.06 | + | 2466.06i | 0.725841 | + | 0.725841i | ||||
\(227\) | 551.638 | − | 551.638i | 0.161293 | − | 0.161293i | −0.621846 | − | 0.783139i | \(-0.713617\pi\) |
0.783139 | + | 0.621846i | \(0.213617\pi\) | |||||||
\(228\) | −103.680 | + | 103.680i | −0.0301158 | + | 0.0301158i | ||||
\(229\) | − | 2776.64i | − | 0.801247i | −0.916243 | − | 0.400624i | \(-0.868794\pi\) | ||
0.916243 | − | 0.400624i | \(-0.131206\pi\) | |||||||
\(230\) | − | 578.237i | − | 0.165773i | ||||||
\(231\) | 247.295 | − | 247.295i | 0.0704365 | − | 0.0704365i | ||||
\(232\) | −220.255 | + | 220.255i | −0.0623294 | + | 0.0623294i | ||||
\(233\) | −3569.19 | − | 3569.19i | −1.00354 | − | 1.00354i | −0.999994 | − | 0.00354906i | \(-0.998870\pi\) |
−0.00354906 | − | 0.999994i | \(-0.501130\pi\) | |||||||
\(234\) | −5773.60 | −1.61296 | ||||||||
\(235\) | −259.772 | − | 259.772i | −0.0721091 | − | 0.0721091i | ||||
\(236\) | − | 5631.22i | − | 1.55323i | ||||||
\(237\) | −542.222 | −0.148612 | ||||||||
\(238\) | 6875.18 | + | 1408.20i | 1.87249 | + | 0.383529i | ||||
\(239\) | 2254.20 | 0.610092 | 0.305046 | − | 0.952338i | \(-0.401328\pi\) | ||||
0.305046 | + | 0.952338i | \(0.401328\pi\) | |||||||
\(240\) | 56.0599i | 0.0150777i | ||||||||
\(241\) | −1222.67 | − | 1222.67i | −0.326802 | − | 0.326802i | 0.524567 | − | 0.851369i | \(-0.324227\pi\) |
−0.851369 | + | 0.524567i | \(0.824227\pi\) | |||||||
\(242\) | −1099.37 | −0.292027 | ||||||||
\(243\) | 649.867 | + | 649.867i | 0.171560 | + | 0.171560i | ||||
\(244\) | −2561.29 | + | 2561.29i | −0.672006 | + | 0.672006i | ||||
\(245\) | 419.224 | − | 419.224i | 0.109319 | − | 0.109319i | ||||
\(246\) | 385.821i | 0.0999962i | ||||||||
\(247\) | − | 2522.84i | − | 0.649897i | ||||||
\(248\) | −354.290 | + | 354.290i | −0.0907154 | + | 0.0907154i | ||||
\(249\) | −177.299 | + | 177.299i | −0.0451239 | + | 0.0451239i | ||||
\(250\) | 1336.86 | + | 1336.86i | 0.338203 | + | 0.338203i | ||||
\(251\) | −1314.25 | −0.330496 | −0.165248 | − | 0.986252i | \(-0.552842\pi\) | ||||
−0.165248 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(252\) | 3615.83 | + | 3615.83i | 0.903872 | + | 0.903872i | ||||
\(253\) | − | 2441.93i | − | 0.606809i | ||||||
\(254\) | 7759.13 | 1.91674 | ||||||||
\(255\) | −31.9350 | − | 48.3868i | −0.00784254 | − | 0.0118827i | ||||
\(256\) | 4562.26 | 1.11383 | ||||||||
\(257\) | 6039.96i | 1.46600i | 0.680228 | + | 0.733001i | \(0.261881\pi\) | ||||
−0.680228 | + | 0.733001i | \(0.738119\pi\) | |||||||
\(258\) | 141.201 | + | 141.201i | 0.0340729 | + | 0.0340729i | ||||
\(259\) | −5753.64 | −1.38036 | ||||||||
\(260\) | 565.466 | + | 565.466i | 0.134880 | + | 0.134880i | ||||
\(261\) | 2978.22 | − | 2978.22i | 0.706311 | − | 0.706311i | ||||
\(262\) | −698.074 | + | 698.074i | −0.164608 | + | 0.164608i | ||||
\(263\) | 990.368i | 0.232201i | 0.993237 | + | 0.116100i | \(0.0370394\pi\) | ||||
−0.993237 | + | 0.116100i | \(0.962961\pi\) | |||||||
\(264\) | 27.2733i | 0.00635818i | ||||||||
\(265\) | 645.862 | − | 645.862i | 0.149717 | − | 0.149717i | ||||
\(266\) | −3266.16 | + | 3266.16i | −0.752861 | + | 0.752861i | ||||
\(267\) | 182.801 | + | 182.801i | 0.0418998 | + | 0.0418998i | ||||
\(268\) | −4002.02 | −0.912173 | ||||||||
\(269\) | 2397.48 | + | 2397.48i | 0.543409 | + | 0.543409i | 0.924527 | − | 0.381117i | \(-0.124461\pi\) |
−0.381117 | + | 0.924527i | \(0.624461\pi\) | |||||||
\(270\) | − | 175.237i | − | 0.0394985i | ||||||
\(271\) | −3706.24 | −0.830767 | −0.415383 | − | 0.909646i | \(-0.636353\pi\) | ||||
−0.415383 | + | 0.909646i | \(0.636353\pi\) | |||||||
\(272\) | −3964.98 | + | 2616.86i | −0.883868 | + | 0.583348i | ||||
\(273\) | 589.729 | 0.130740 | ||||||||
\(274\) | 1717.79i | 0.378742i | ||||||||
\(275\) | 2779.19 | + | 2779.19i | 0.609424 | + | 0.609424i | ||||
\(276\) | −239.318 | −0.0521930 | ||||||||
\(277\) | −5410.66 | − | 5410.66i | −1.17363 | − | 1.17363i | −0.981338 | − | 0.192290i | \(-0.938409\pi\) |
−0.192290 | − | 0.981338i | \(-0.561591\pi\) | |||||||
\(278\) | 233.045 | − | 233.045i | 0.0502774 | − | 0.0502774i | ||||
\(279\) | 4790.61 | − | 4790.61i | 1.02798 | − | 1.02798i | ||||
\(280\) | 98.4161i | 0.0210053i | ||||||||
\(281\) | − | 3194.87i | − | 0.678256i | −0.940740 | − | 0.339128i | \(-0.889868\pi\) | ||
0.940740 | − | 0.339128i | \(-0.110132\pi\) | |||||||
\(282\) | −222.253 | + | 222.253i | −0.0469326 | + | 0.0469326i | ||||
\(283\) | −4235.43 | + | 4235.43i | −0.889648 | + | 0.889648i | −0.994489 | − | 0.104841i | \(-0.966567\pi\) |
0.104841 | + | 0.994489i | \(0.466567\pi\) | |||||||
\(284\) | −414.250 | − | 414.250i | −0.0865536 | − | 0.0865536i | ||||
\(285\) | 38.1581 | 0.00793085 | ||||||||
\(286\) | 4936.51 | + | 4936.51i | 1.02064 | + | 1.02064i | ||||
\(287\) | 5879.50i | 1.20925i | ||||||||
\(288\) | −6730.20 | −1.37702 | ||||||||
\(289\) | 1931.56 | − | 4517.37i | 0.393153 | − | 0.919473i | ||||
\(290\) | −1205.96 | −0.244195 | ||||||||
\(291\) | − | 675.019i | − | 0.135980i | ||||||
\(292\) | −2030.18 | − | 2030.18i | −0.406875 | − | 0.406875i | ||||
\(293\) | 5372.44 | 1.07120 | 0.535600 | − | 0.844472i | \(-0.320086\pi\) | ||||
0.535600 | + | 0.844472i | \(0.320086\pi\) | |||||||
\(294\) | −358.676 | − | 358.676i | −0.0711511 | − | 0.0711511i | ||||
\(295\) | −1036.25 | + | 1036.25i | −0.204517 | + | 0.204517i | ||||
\(296\) | 317.275 | − | 317.275i | 0.0623014 | − | 0.0623014i | ||||
\(297\) | − | 740.037i | − | 0.144583i | ||||||
\(298\) | − | 9280.11i | − | 1.80397i | ||||||
\(299\) | 2911.65 | − | 2911.65i | 0.563161 | − | 0.563161i | ||||
\(300\) | 272.371 | − | 272.371i | 0.0524179 | − | 0.0524179i | ||||
\(301\) | 2151.75 | + | 2151.75i | 0.412043 | + | 0.412043i | ||||
\(302\) | 589.477 | 0.112320 | ||||||||
\(303\) | 199.940 | + | 199.940i | 0.0379085 | + | 0.0379085i | ||||
\(304\) | − | 3126.80i | − | 0.589916i | ||||||
\(305\) | 942.645 | 0.176970 | ||||||||
\(306\) | 6176.35 | − | 4076.36i | 1.15385 | − | 0.761535i | ||||
\(307\) | 7020.91 | 1.30523 | 0.652613 | − | 0.757692i | \(-0.273673\pi\) | ||||
0.652613 | + | 0.757692i | \(0.273673\pi\) | |||||||
\(308\) | − | 6183.16i | − | 1.14389i | ||||||
\(309\) | 261.544 | + | 261.544i | 0.0481511 | + | 0.0481511i | ||||
\(310\) | −1939.84 | −0.355406 | ||||||||
\(311\) | −725.496 | − | 725.496i | −0.132280 | − | 0.132280i | 0.637867 | − | 0.770147i | \(-0.279817\pi\) |
−0.770147 | + | 0.637867i | \(0.779817\pi\) | |||||||
\(312\) | −32.5196 | + | 32.5196i | −0.00590083 | + | 0.00590083i | ||||
\(313\) | −1761.31 | + | 1761.31i | −0.318067 | + | 0.318067i | −0.848024 | − | 0.529957i | \(-0.822208\pi\) |
0.529957 | + | 0.848024i | \(0.322208\pi\) | |||||||
\(314\) | − | 469.548i | − | 0.0843889i | ||||||
\(315\) | − | 1330.75i | − | 0.238030i | ||||||
\(316\) | −6778.64 | + | 6778.64i | −1.20673 | + | 1.20673i | ||||
\(317\) | −1962.35 | + | 1962.35i | −0.347686 | + | 0.347686i | −0.859247 | − | 0.511561i | \(-0.829067\pi\) |
0.511561 | + | 0.859247i | \(0.329067\pi\) | |||||||
\(318\) | −552.581 | − | 552.581i | −0.0974440 | − | 0.0974440i | ||||
\(319\) | −5092.84 | −0.893869 | ||||||||
\(320\) | 614.673 | + | 614.673i | 0.107379 | + | 0.107379i | ||||
\(321\) | 146.840i | 0.0255321i | ||||||||
\(322\) | −7539.05 | −1.30477 | ||||||||
\(323\) | 1781.21 | + | 2698.83i | 0.306840 | + | 0.464913i | ||||
\(324\) | 5355.77 | 0.918341 | ||||||||
\(325\) | 6627.58i | 1.13117i | ||||||||
\(326\) | 424.840 | + | 424.840i | 0.0721770 | + | 0.0721770i | ||||
\(327\) | 57.5870 | 0.00973873 | ||||||||
\(328\) | −324.215 | − | 324.215i | −0.0545786 | − | 0.0545786i | ||||
\(329\) | −3386.90 | + | 3386.90i | −0.567556 | + | 0.567556i | ||||
\(330\) | −74.6649 | + | 74.6649i | −0.0124551 | + | 0.0124551i | ||||
\(331\) | − | 6017.90i | − | 0.999317i | −0.866222 | − | 0.499659i | \(-0.833459\pi\) | ||
0.866222 | − | 0.499659i | \(-0.166541\pi\) | |||||||
\(332\) | 4433.03i | 0.732813i | ||||||||
\(333\) | −4290.10 | + | 4290.10i | −0.705993 | + | 0.705993i | ||||
\(334\) | 7028.61 | − | 7028.61i | 1.15146 | − | 1.15146i | ||||
\(335\) | 736.444 | + | 736.444i | 0.120108 | + | 0.120108i | ||||
\(336\) | 730.908 | 0.118674 | ||||||||
\(337\) | 335.433 | + | 335.433i | 0.0542202 | + | 0.0542202i | 0.733697 | − | 0.679477i | \(-0.237793\pi\) |
−0.679477 | + | 0.733697i | \(0.737793\pi\) | |||||||
\(338\) | 3123.64i | 0.502674i | ||||||||
\(339\) | −375.634 | −0.0601818 | ||||||||
\(340\) | −1004.15 | − | 205.674i | −0.160170 | − | 0.0328065i | ||||
\(341\) | −8192.07 | −1.30095 | ||||||||
\(342\) | 4870.71i | 0.770110i | ||||||||
\(343\) | 702.976 | + | 702.976i | 0.110662 | + | 0.110662i | ||||
\(344\) | −237.310 | −0.0371944 | ||||||||
\(345\) | 44.0389 | + | 44.0389i | 0.00687239 | + | 0.00687239i | ||||
\(346\) | −913.762 | + | 913.762i | −0.141977 | + | 0.141977i | ||||
\(347\) | 1043.30 | − | 1043.30i | 0.161405 | − | 0.161405i | −0.621784 | − | 0.783189i | \(-0.713592\pi\) |
0.783189 | + | 0.621784i | \(0.213592\pi\) | |||||||
\(348\) | 499.118i | 0.0768837i | ||||||||
\(349\) | 6855.25i | 1.05144i | 0.850657 | + | 0.525721i | \(0.176204\pi\) | ||||
−0.850657 | + | 0.525721i | \(0.823796\pi\) | |||||||
\(350\) | 8580.29 | − | 8580.29i | 1.31039 | − | 1.31039i | ||||
\(351\) | 882.388 | − | 882.388i | 0.134183 | − | 0.134183i | ||||
\(352\) | 5754.41 | + | 5754.41i | 0.871339 | + | 0.871339i | ||||
\(353\) | 7485.74 | 1.12868 | 0.564342 | − | 0.825541i | \(-0.309130\pi\) | ||||
0.564342 | + | 0.825541i | \(0.309130\pi\) | |||||||
\(354\) | 886.582 | + | 886.582i | 0.133111 | + | 0.133111i | ||||
\(355\) | 152.459i | 0.0227935i | ||||||||
\(356\) | 4570.60 | 0.680454 | ||||||||
\(357\) | −630.867 | + | 416.368i | −0.0935266 | + | 0.0617270i | ||||
\(358\) | −16356.6 | −2.41473 | ||||||||
\(359\) | − | 7169.54i | − | 1.05402i | −0.849859 | − | 0.527011i | \(-0.823313\pi\) | ||
0.849859 | − | 0.527011i | \(-0.176687\pi\) | |||||||
\(360\) | 73.3822 | + | 73.3822i | 0.0107433 | + | 0.0107433i | ||||
\(361\) | 4730.69 | 0.689705 | ||||||||
\(362\) | 2659.46 | + | 2659.46i | 0.386127 | + | 0.386127i | ||||
\(363\) | 83.7290 | − | 83.7290i | 0.0121064 | − | 0.0121064i | ||||
\(364\) | 7372.54 | − | 7372.54i | 1.06161 | − | 1.06161i | ||||
\(365\) | 747.180i | 0.107149i | ||||||||
\(366\) | − | 806.500i | − | 0.115182i | ||||||
\(367\) | −4673.13 | + | 4673.13i | −0.664674 | + | 0.664674i | −0.956478 | − | 0.291804i | \(-0.905744\pi\) |
0.291804 | + | 0.956478i | \(0.405744\pi\) | |||||||
\(368\) | 3608.69 | − | 3608.69i | 0.511185 | − | 0.511185i | ||||
\(369\) | 4383.95 | + | 4383.95i | 0.618480 | + | 0.618480i | ||||
\(370\) | 1737.17 | 0.244085 | ||||||||
\(371\) | −8420.74 | − | 8420.74i | −1.17839 | − | 1.17839i | ||||
\(372\) | 802.855i | 0.111898i | ||||||||
\(373\) | −1602.91 | −0.222508 | −0.111254 | − | 0.993792i | \(-0.535487\pi\) | ||||
−0.111254 | + | 0.993792i | \(0.535487\pi\) | |||||||
\(374\) | −8766.21 | − | 1795.53i | −1.21200 | − | 0.248247i | ||||
\(375\) | −203.633 | −0.0280415 | ||||||||
\(376\) | − | 373.530i | − | 0.0512323i | ||||||
\(377\) | −6072.49 | − | 6072.49i | −0.829573 | − | 0.829573i | ||||
\(378\) | −2284.74 | −0.310885 | ||||||||
\(379\) | 1232.54 | + | 1232.54i | 0.167049 | + | 0.167049i | 0.785681 | − | 0.618632i | \(-0.212313\pi\) |
−0.618632 | + | 0.785681i | \(0.712313\pi\) | |||||||
\(380\) | 477.037 | − | 477.037i | 0.0643986 | − | 0.0643986i | ||||
\(381\) | −590.940 | + | 590.940i | −0.0794613 | + | 0.0794613i | ||||
\(382\) | − | 3502.55i | − | 0.469125i | ||||||
\(383\) | − | 1155.24i | − | 0.154125i | −0.997026 | − | 0.0770627i | \(-0.975446\pi\) | ||
0.997026 | − | 0.0770627i | \(-0.0245542\pi\) | |||||||
\(384\) | −75.9662 | + | 75.9662i | −0.0100954 | + | 0.0100954i | ||||
\(385\) | −1137.81 | + | 1137.81i | −0.150619 | + | 0.150619i | ||||
\(386\) | −4821.29 | − | 4821.29i | −0.635744 | − | 0.635744i | ||||
\(387\) | 3208.83 | 0.421484 | ||||||||
\(388\) | −8438.81 | − | 8438.81i | −1.10416 | − | 1.10416i | ||||
\(389\) | − | 3698.95i | − | 0.482119i | −0.970510 | − | 0.241060i | \(-0.922505\pi\) | ||
0.970510 | − | 0.241060i | \(-0.0774949\pi\) | |||||||
\(390\) | −178.055 | −0.0231183 | ||||||||
\(391\) | −1059.04 | + | 5170.49i | −0.136977 | + | 0.668754i | ||||
\(392\) | 602.809 | 0.0776696 | ||||||||
\(393\) | − | 106.332i | − | 0.0136481i | ||||||
\(394\) | 12369.8 | + | 12369.8i | 1.58167 | + | 1.58167i | ||||
\(395\) | 2494.78 | 0.317788 | ||||||||
\(396\) | −4610.37 | − | 4610.37i | −0.585050 | − | 0.585050i | ||||
\(397\) | 9608.12 | − | 9608.12i | 1.21465 | − | 1.21465i | 0.245176 | − | 0.969479i | \(-0.421154\pi\) |
0.969479 | − | 0.245176i | \(-0.0788458\pi\) | |||||||
\(398\) | −8680.11 | + | 8680.11i | −1.09320 | + | 1.09320i | ||||
\(399\) | − | 497.505i | − | 0.0624221i | ||||||
\(400\) | 8214.20i | 1.02678i | ||||||||
\(401\) | −1883.98 | + | 1883.98i | −0.234617 | + | 0.234617i | −0.814617 | − | 0.580000i | \(-0.803053\pi\) |
0.580000 | + | 0.814617i | \(0.303053\pi\) | |||||||
\(402\) | 630.081 | − | 630.081i | 0.0781730 | − | 0.0781730i | ||||
\(403\) | −9767.88 | − | 9767.88i | −1.20738 | − | 1.20738i | ||||
\(404\) | 4999.14 | 0.615635 | ||||||||
\(405\) | −985.558 | − | 985.558i | −0.120920 | − | 0.120920i | ||||
\(406\) | 15723.3i | 1.92201i | ||||||||
\(407\) | 7336.19 | 0.893467 | ||||||||
\(408\) | 11.8282 | − | 57.7480i | 0.00143525 | − | 0.00700724i | ||||
\(409\) | 4145.86 | 0.501222 | 0.250611 | − | 0.968088i | \(-0.419368\pi\) | ||||
0.250611 | + | 0.968088i | \(0.419368\pi\) | |||||||
\(410\) | − | 1775.18i | − | 0.213829i | ||||||
\(411\) | −130.828 | − | 130.828i | −0.0157013 | − | 0.0157013i | ||||
\(412\) | 6539.42 | 0.781976 | ||||||||
\(413\) | 13510.6 | + | 13510.6i | 1.60971 | + | 1.60971i | ||||
\(414\) | −5621.36 | + | 5621.36i | −0.667330 | + | 0.667330i | ||||
\(415\) | 815.757 | − | 815.757i | 0.0964914 | − | 0.0964914i | ||||
\(416\) | 13722.6i | 1.61733i | ||||||||
\(417\) | 35.4977i | 0.00416866i | ||||||||
\(418\) | 4164.52 | − | 4164.52i | 0.487305 | − | 0.487305i | ||||
\(419\) | 10074.5 | − | 10074.5i | 1.17463 | − | 1.17463i | 0.193542 | − | 0.981092i | \(-0.438003\pi\) |
0.981092 | − | 0.193542i | \(-0.0619975\pi\) | |||||||
\(420\) | 111.510 | + | 111.510i | 0.0129551 | + | 0.0129551i | ||||
\(421\) | −3191.61 | −0.369477 | −0.184738 | − | 0.982788i | \(-0.559144\pi\) | ||||
−0.184738 | + | 0.982788i | \(0.559144\pi\) | |||||||
\(422\) | −12616.5 | − | 12616.5i | −1.45535 | − | 1.45535i | ||||
\(423\) | 5050.77i | 0.580560i | ||||||||
\(424\) | 928.695 | 0.106371 | ||||||||
\(425\) | −4679.29 | − | 7089.90i | −0.534069 | − | 0.809202i | ||||
\(426\) | 130.439 | 0.0148352 | ||||||||
\(427\) | − | 12290.2i | − | 1.39289i | ||||||
\(428\) | 1835.73 | + | 1835.73i | 0.207321 | + | 0.207321i | ||||
\(429\) | −751.935 | −0.0846241 | ||||||||
\(430\) | −649.671 | − | 649.671i | −0.0728603 | − | 0.0728603i | ||||
\(431\) | −1159.24 | + | 1159.24i | −0.129556 | + | 0.129556i | −0.768911 | − | 0.639355i | \(-0.779201\pi\) |
0.639355 | + | 0.768911i | \(0.279201\pi\) | |||||||
\(432\) | 1093.63 | − | 1093.63i | 0.121799 | − | 0.121799i | ||||
\(433\) | 16579.9i | 1.84013i | 0.391764 | + | 0.920066i | \(0.371865\pi\) | ||||
−0.391764 | + | 0.920066i | \(0.628135\pi\) | |||||||
\(434\) | 25291.7i | 2.79732i | ||||||||
\(435\) | 91.8467 | − | 91.8467i | 0.0101235 | − | 0.0101235i | ||||
\(436\) | 719.928 | − | 719.928i | 0.0790787 | − | 0.0790787i | ||||
\(437\) | −2456.32 | − | 2456.32i | −0.268883 | − | 0.268883i | ||||
\(438\) | 639.266 | 0.0697382 | ||||||||
\(439\) | 5195.18 | + | 5195.18i | 0.564812 | + | 0.564812i | 0.930670 | − | 0.365859i | \(-0.119225\pi\) |
−0.365859 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(440\) | − | 125.486i | − | 0.0135961i | ||||||
\(441\) | −8151.02 | −0.880144 | ||||||||
\(442\) | −8311.55 | − | 12593.4i | −0.894434 | − | 1.35522i | ||||
\(443\) | −13325.5 | −1.42915 | −0.714575 | − | 0.699559i | \(-0.753380\pi\) | ||||
−0.714575 | + | 0.699559i | \(0.753380\pi\) | |||||||
\(444\) | − | 718.974i | − | 0.0768491i | ||||||
\(445\) | −841.074 | − | 841.074i | −0.0895971 | − | 0.0895971i | ||||
\(446\) | 486.451 | 0.0516460 | ||||||||
\(447\) | 706.779 | + | 706.779i | 0.0747863 | + | 0.0747863i | ||||
\(448\) | 8014.09 | − | 8014.09i | 0.845157 | − | 0.845157i | ||||
\(449\) | −6849.28 | + | 6849.28i | −0.719906 | + | 0.719906i | −0.968586 | − | 0.248680i | \(-0.920003\pi\) |
0.248680 | + | 0.968586i | \(0.420003\pi\) | |||||||
\(450\) | − | 12795.5i | − | 1.34041i | ||||||
\(451\) | − | 7496.67i | − | 0.782715i | ||||||
\(452\) | −4696.02 | + | 4696.02i | −0.488677 | + | 0.488677i | ||||
\(453\) | −44.8949 | + | 44.8949i | −0.00465640 | + | 0.00465640i | ||||
\(454\) | 2171.53 | + | 2171.53i | 0.224482 | + | 0.224482i | ||||
\(455\) | −2713.36 | −0.279570 | ||||||||
\(456\) | 27.4341 | + | 27.4341i | 0.00281736 | + | 0.00281736i | ||||
\(457\) | − | 698.065i | − | 0.0714532i | −0.999362 | − | 0.0357266i | \(-0.988625\pi\) | ||
0.999362 | − | 0.0357266i | \(-0.0113745\pi\) | |||||||
\(458\) | 10930.3 | 1.11515 | ||||||||
\(459\) | −320.946 | + | 1566.94i | −0.0326372 | + | 0.159343i | ||||
\(460\) | 1101.11 | 0.111608 | ||||||||
\(461\) | − | 6505.58i | − | 0.657256i | −0.944459 | − | 0.328628i | \(-0.893414\pi\) | ||
0.944459 | − | 0.328628i | \(-0.106586\pi\) | |||||||
\(462\) | 973.481 | + | 973.481i | 0.0980312 | + | 0.0980312i | ||||
\(463\) | 1181.74 | 0.118618 | 0.0593089 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593089 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(464\) | −7526.22 | − | 7526.22i | −0.753009 | − | 0.753009i | ||||
\(465\) | 147.740 | − | 147.740i | 0.0147339 | − | 0.0147339i | ||||
\(466\) | 14050.2 | − | 14050.2i | 1.39670 | − | 1.39670i | ||||
\(467\) | 2950.96i | 0.292407i | 0.989255 | + | 0.146204i | \(0.0467054\pi\) | ||||
−0.989255 | + | 0.146204i | \(0.953295\pi\) | |||||||
\(468\) | − | 10994.4i | − | 1.08593i | ||||||
\(469\) | 9601.75 | − | 9601.75i | 0.945347 | − | 0.945347i | ||||
\(470\) | 1022.60 | − | 1022.60i | 0.100359 | − | 0.100359i | ||||
\(471\) | 35.7610 | + | 35.7610i | 0.00349847 | + | 0.00349847i | ||||
\(472\) | −1490.03 | −0.145306 | ||||||||
\(473\) | −2743.60 | − | 2743.60i | −0.266704 | − | 0.266704i | ||||
\(474\) | − | 2134.46i | − | 0.206834i | ||||||
\(475\) | 5591.14 | 0.540082 | ||||||||
\(476\) | −2681.57 | + | 13092.1i | −0.258213 | + | 1.26066i | ||||
\(477\) | −12557.5 | −1.20539 | ||||||||
\(478\) | 8873.69i | 0.849107i | ||||||||
\(479\) | 6286.33 | + | 6286.33i | 0.599644 | + | 0.599644i | 0.940218 | − | 0.340573i | \(-0.110621\pi\) |
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(480\) | −207.556 | −0.0197366 | ||||||||
\(481\) | 8747.36 | + | 8747.36i | 0.829200 | + | 0.829200i | ||||
\(482\) | 4813.07 | − | 4813.07i | 0.454832 | − | 0.454832i | ||||
\(483\) | 574.179 | − | 574.179i | 0.0540912 | − | 0.0540912i | ||||
\(484\) | − | 2093.49i | − | 0.196609i | ||||||
\(485\) | 3105.78i | 0.290776i | ||||||||
\(486\) | −2558.21 | + | 2558.21i | −0.238771 | + | 0.238771i | ||||
\(487\) | −5023.62 | + | 5023.62i | −0.467437 | + | 0.467437i | −0.901083 | − | 0.433646i | \(-0.857227\pi\) |
0.433646 | + | 0.901083i | \(0.357227\pi\) | |||||||
\(488\) | 677.722 | + | 677.722i | 0.0628669 | + | 0.0628669i | ||||
\(489\) | −64.7121 | −0.00598442 | ||||||||
\(490\) | 1650.28 | + | 1650.28i | 0.152147 | + | 0.152147i | ||||
\(491\) | − | 7638.33i | − | 0.702063i | −0.936364 | − | 0.351031i | \(-0.885831\pi\) | ||
0.936364 | − | 0.351031i | \(-0.114169\pi\) | |||||||
\(492\) | −734.703 | −0.0673231 | ||||||||
\(493\) | 10783.5 | + | 2208.71i | 0.985118 | + | 0.201775i | ||||
\(494\) | 9931.20 | 0.904505 | ||||||||
\(495\) | 1696.78i | 0.154070i | ||||||||
\(496\) | −12106.3 | − | 12106.3i | −1.09594 | − | 1.09594i | ||||
\(497\) | 1987.76 | 0.179403 | ||||||||
\(498\) | −697.938 | − | 697.938i | −0.0628019 | − | 0.0628019i | ||||
\(499\) | −14285.4 | + | 14285.4i | −1.28156 | + | 1.28156i | −0.341787 | + | 0.939778i | \(0.611032\pi\) |
−0.939778 | + | 0.341787i | \(0.888968\pi\) | |||||||
\(500\) | −2545.73 | + | 2545.73i | −0.227697 | + | 0.227697i | ||||
\(501\) | 1070.61i | 0.0954714i | ||||||||
\(502\) | − | 5173.54i | − | 0.459973i | ||||||
\(503\) | −14474.1 | + | 14474.1i | −1.28304 | + | 1.28304i | −0.344107 | + | 0.938931i | \(0.611818\pi\) |
−0.938931 | + | 0.344107i | \(0.888182\pi\) | |||||||
\(504\) | 956.756 | − | 956.756i | 0.0845581 | − | 0.0845581i | ||||
\(505\) | −919.932 | − | 919.932i | −0.0810623 | − | 0.0810623i | ||||
\(506\) | 9612.68 | 0.844537 | ||||||||
\(507\) | −237.899 | − | 237.899i | −0.0208391 | − | 0.0208391i | ||||
\(508\) | 14775.4i | 1.29045i | ||||||||
\(509\) | −19503.1 | −1.69835 | −0.849173 | − | 0.528116i | \(-0.822899\pi\) | ||||
−0.849173 | + | 0.528116i | \(0.822899\pi\) | |||||||
\(510\) | 190.475 | − | 125.713i | 0.0165380 | − | 0.0109150i | ||||
\(511\) | 9741.73 | 0.843344 | ||||||||
\(512\) | 15932.3i | 1.37523i | ||||||||
\(513\) | −744.398 | − | 744.398i | −0.0640662 | − | 0.0640662i | ||||
\(514\) | −23776.4 | −2.04033 | ||||||||
\(515\) | −1203.37 | − | 1203.37i | −0.102965 | − | 0.102965i | ||||
\(516\) | −268.883 | + | 268.883i | −0.0229398 | + | 0.0229398i | ||||
\(517\) | 4318.48 | − | 4318.48i | 0.367362 | − | 0.367362i | ||||
\(518\) | − | 22649.3i | − | 1.92114i | ||||||
\(519\) | − | 139.185i | − | 0.0117718i | ||||||
\(520\) | 149.624 | − | 149.624i | 0.0126181 | − | 0.0126181i | ||||
\(521\) | 4923.95 | − | 4923.95i | 0.414054 | − | 0.414054i | −0.469094 | − | 0.883148i | \(-0.655420\pi\) |
0.883148 | + | 0.469094i | \(0.155420\pi\) | |||||||
\(522\) | 11723.8 | + | 11723.8i | 0.983020 | + | 0.983020i | ||||
\(523\) | −2507.22 | −0.209623 | −0.104812 | − | 0.994492i | \(-0.533424\pi\) | ||||
−0.104812 | + | 0.994492i | \(0.533424\pi\) | |||||||
\(524\) | −1329.31 | − | 1329.31i | −0.110823 | − | 0.110823i | ||||
\(525\) | 1306.96i | 0.108648i | ||||||||
\(526\) | −3898.60 | −0.323169 | ||||||||
\(527\) | 17345.7 | + | 3552.81i | 1.43376 | + | 0.293668i | ||||
\(528\) | −931.946 | −0.0768139 | ||||||||
\(529\) | 6497.24i | 0.534005i | ||||||||
\(530\) | 2542.44 | + | 2542.44i | 0.208371 | + | 0.208371i | ||||
\(531\) | 20147.8 | 1.64659 | ||||||||
\(532\) | −6219.60 | − | 6219.60i | −0.506868 | − | 0.506868i | ||||
\(533\) | 8938.71 | − | 8938.71i | 0.726414 | − | 0.726414i | ||||
\(534\) | −719.598 | + | 719.598i | −0.0583147 | + | 0.0583147i | ||||
\(535\) | − | 675.614i | − | 0.0545969i | ||||||
\(536\) | 1058.94i | 0.0853348i | ||||||||
\(537\) | 1245.73 | − | 1245.73i | 0.100107 | − | 0.100107i | ||||
\(538\) | −9437.72 | + | 9437.72i | −0.756299 | + | 0.756299i | ||||
\(539\) | 6969.23 | + | 6969.23i | 0.556932 | + | 0.556932i | ||||
\(540\) | 333.697 | 0.0265926 | ||||||||
\(541\) | 13701.0 | + | 13701.0i | 1.08882 | + | 1.08882i | 0.995650 | + | 0.0931705i | \(0.0297002\pi\) |
0.0931705 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(542\) | − | 14589.6i | − | 1.15623i | ||||||
\(543\) | −405.092 | −0.0320150 | ||||||||
\(544\) | −9688.65 | − | 14679.9i | −0.763598 | − | 1.15698i | ||||
\(545\) | −264.960 | −0.0208250 | ||||||||
\(546\) | 2321.47i | 0.181960i | ||||||||
\(547\) | −2090.43 | − | 2090.43i | −0.163401 | − | 0.163401i | 0.620671 | − | 0.784071i | \(-0.286860\pi\) |
−0.784071 | + | 0.620671i | \(0.786860\pi\) | |||||||
\(548\) | −3271.10 | −0.254990 | ||||||||
\(549\) | −9163.97 | − | 9163.97i | −0.712402 | − | 0.712402i | ||||
\(550\) | −10940.3 | + | 10940.3i | −0.848176 | + | 0.848176i | ||||
\(551\) | −5122.85 | + | 5122.85i | −0.396081 | + | 0.396081i | ||||
\(552\) | 63.3242i | 0.00488271i | ||||||||
\(553\) | − | 32526.9i | − | 2.50124i | ||||||
\(554\) | 21299.1 | − | 21299.1i | 1.63342 | − | 1.63342i | ||||
\(555\) | −132.304 | + | 132.304i | −0.0101189 | + | 0.0101189i | ||||
\(556\) | 443.778 | + | 443.778i | 0.0338496 | + | 0.0338496i | ||||
\(557\) | −3920.00 | −0.298197 | −0.149099 | − | 0.988822i | \(-0.547637\pi\) | ||||
−0.149099 | + | 0.988822i | \(0.547637\pi\) | |||||||
\(558\) | 18858.3 | + | 18858.3i | 1.43071 | + | 1.43071i | ||||
\(559\) | − | 6542.70i | − | 0.495039i | ||||||
\(560\) | −3362.93 | −0.253768 | ||||||||
\(561\) | 804.388 | − | 530.891i | 0.0605371 | − | 0.0399541i | ||||
\(562\) | 12576.6 | 0.943975 | ||||||||
\(563\) | − | 20821.5i | − | 1.55865i | −0.626618 | − | 0.779326i | \(-0.715561\pi\) | ||
0.626618 | − | 0.779326i | \(-0.284439\pi\) | |||||||
\(564\) | −423.227 | − | 423.227i | −0.0315977 | − | 0.0315977i | ||||
\(565\) | 1728.30 | 0.128691 | ||||||||
\(566\) | −16672.8 | − | 16672.8i | −1.23818 | − | 1.23818i | ||||
\(567\) | −12849.7 | + | 12849.7i | −0.951739 | + | 0.951739i | ||||
\(568\) | −109.612 | + | 109.612i | −0.00809718 | + | 0.00809718i | ||||
\(569\) | − | 7849.66i | − | 0.578339i | −0.957278 | − | 0.289170i | \(-0.906621\pi\) | ||
0.957278 | − | 0.289170i | \(-0.0933791\pi\) | |||||||
\(570\) | 150.210i | 0.0110379i | ||||||||
\(571\) | −17349.3 | + | 17349.3i | −1.27154 | + | 1.27154i | −0.326254 | + | 0.945282i | \(0.605786\pi\) |
−0.945282 | + | 0.326254i | \(0.894214\pi\) | |||||||
\(572\) | −9400.38 | + | 9400.38i | −0.687149 | + | 0.687149i | ||||
\(573\) | 266.756 | + | 266.756i | 0.0194483 | + | 0.0194483i | ||||
\(574\) | −23144.7 | −1.68300 | ||||||||
\(575\) | 6452.82 | + | 6452.82i | 0.468002 | + | 0.468002i | ||||
\(576\) | − | 11951.1i | − | 0.864521i | ||||||
\(577\) | −7549.37 | −0.544687 | −0.272343 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272343 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(578\) | 17782.7 | + | 7603.62i | 1.27969 | + | 0.547178i | ||||
\(579\) | 734.384 | 0.0527115 | ||||||||
\(580\) | − | 2296.46i | − | 0.164406i | ||||||
\(581\) | −10635.8 | − | 10635.8i | −0.759464 | − | 0.759464i | ||||
\(582\) | 2657.22 | 0.189253 | ||||||||
\(583\) | 10736.9 | + | 10736.9i | 0.762738 | + | 0.762738i | ||||
\(584\) | −537.191 | + | 537.191i | −0.0380636 | + | 0.0380636i | ||||
\(585\) | −2023.17 | + | 2023.17i | −0.142988 | + | 0.142988i | ||||
\(586\) | 21148.7i | 1.49086i | ||||||||
\(587\) | 6451.77i | 0.453651i | 0.973935 | + | 0.226826i | \(0.0728347\pi\) | ||||
−0.973935 | + | 0.226826i | \(0.927165\pi\) | |||||||
\(588\) | 683.012 | − | 683.012i | 0.0479029 | − | 0.0479029i | ||||
\(589\) | −8240.35 | + | 8240.35i | −0.576465 | + | 0.576465i | ||||
\(590\) | −4079.19 | − | 4079.19i | −0.284640 | − | 0.284640i | ||||
\(591\) | −1884.18 | −0.131142 | ||||||||
\(592\) | 10841.4 | + | 10841.4i | 0.752670 | + | 0.752670i | ||||
\(593\) | − | 176.420i | − | 0.0122170i | −0.999981 | − | 0.00610850i | \(-0.998056\pi\) | ||
0.999981 | − | 0.00610850i | \(-0.00194441\pi\) | |||||||
\(594\) | 2913.16 | 0.201227 | ||||||||
\(595\) | 2902.64 | − | 1915.72i | 0.199994 | − | 0.131995i | ||||
\(596\) | 17671.7 | 1.21453 | ||||||||
\(597\) | − | 1322.16i | − | 0.0906408i | ||||||
\(598\) | 11461.8 | + | 11461.8i | 0.783789 | + | 0.783789i | ||||
\(599\) | −11248.7 | −0.767292 | −0.383646 | − | 0.923480i | \(-0.625332\pi\) | ||||
−0.383646 | + | 0.923480i | \(0.625332\pi\) | |||||||
\(600\) | −72.0701 | − | 72.0701i | −0.00490375 | − | 0.00490375i | ||||
\(601\) | 17973.6 | − | 17973.6i | 1.21990 | − | 1.21990i | 0.252228 | − | 0.967668i | \(-0.418837\pi\) |
0.967668 | − | 0.252228i | \(-0.0811632\pi\) | |||||||
\(602\) | −8470.41 | + | 8470.41i | −0.573469 | + | 0.573469i | ||||
\(603\) | − | 14318.7i | − | 0.967006i | ||||||
\(604\) | 1122.52i | 0.0756201i | ||||||||
\(605\) | −385.240 | + | 385.240i | −0.0258880 | + | 0.0258880i | ||||
\(606\) | −787.068 | + | 787.068i | −0.0527598 | + | 0.0527598i | ||||
\(607\) | −13916.2 | − | 13916.2i | −0.930542 | − | 0.930542i | 0.0671975 | − | 0.997740i | \(-0.478594\pi\) |
−0.997740 | + | 0.0671975i | \(0.978594\pi\) | |||||||
\(608\) | 11576.7 | 0.772196 | ||||||||
\(609\) | −1197.50 | − | 1197.50i | −0.0796798 | − | 0.0796798i | ||||
\(610\) | 3710.74i | 0.246300i | ||||||||
\(611\) | 10298.3 | 0.681876 | ||||||||
\(612\) | 7762.43 | + | 11761.4i | 0.512708 | + | 0.776838i | ||||
\(613\) | 3619.34 | 0.238473 | 0.119236 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119236 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(614\) | 27637.9i | 1.81657i | ||||||||
\(615\) | 135.199 | + | 135.199i | 0.00886460 | + | 0.00886460i | ||||
\(616\) | −1636.08 | −0.107012 | ||||||||
\(617\) | 13961.7 | + | 13961.7i | 0.910985 | + | 0.910985i | 0.996350 | − | 0.0853644i | \(-0.0272055\pi\) |
−0.0853644 | + | 0.996350i | \(0.527205\pi\) | |||||||
\(618\) | −1029.57 | + | 1029.57i | −0.0670151 | + | 0.0670151i | ||||
\(619\) | 13220.0 | − | 13220.0i | 0.858409 | − | 0.858409i | −0.132741 | − | 0.991151i | \(-0.542378\pi\) |
0.991151 | + | 0.132741i | \(0.0423780\pi\) | |||||||
\(620\) | − | 3693.96i | − | 0.239279i | ||||||
\(621\) | − | 1718.24i | − | 0.111032i | ||||||
\(622\) | 2855.93 | − | 2855.93i | 0.184103 | − | 0.184103i | ||||
\(623\) | −10965.9 | + | 10965.9i | −0.705200 | + | 0.705200i | ||||
\(624\) | −1111.21 | − | 1111.21i | −0.0712886 | − | 0.0712886i | ||||
\(625\) | −14212.4 | −0.909592 | ||||||||
\(626\) | −6933.41 | − | 6933.41i | −0.442676 | − | 0.442676i | ||||
\(627\) | 634.345i | 0.0404040i | ||||||||
\(628\) | 894.139 | 0.0568153 | ||||||||
\(629\) | −15533.5 | − | 3181.62i | −0.984675 | − | 0.201685i | ||||
\(630\) | 5238.53 | 0.331283 | ||||||||
\(631\) | 10087.2i | 0.636394i | 0.948025 | + | 0.318197i | \(0.103077\pi\) | ||||
−0.948025 | + | 0.318197i | \(0.896923\pi\) | |||||||
\(632\) | 1793.64 | + | 1793.64i | 0.112891 | + | 0.112891i | ||||
\(633\) | 1921.75 | 0.120668 | ||||||||
\(634\) | −7724.81 | − | 7724.81i | −0.483898 | − | 0.483898i | ||||
\(635\) | 2718.93 | − | 2718.93i | 0.169917 | − | 0.169917i | ||||
\(636\) | 1052.26 | − | 1052.26i | 0.0656048 | − | 0.0656048i | ||||
\(637\) | 16619.6i | 1.03374i | ||||||||
\(638\) | − | 20048.0i | − | 1.24406i | ||||||
\(639\) | 1482.14 | − | 1482.14i | 0.0917565 | − | 0.0917565i | ||||
\(640\) | 349.523 | − | 349.523i | 0.0215877 | − | 0.0215877i | ||||
\(641\) | 7258.52 | + | 7258.52i | 0.447261 | + | 0.447261i | 0.894443 | − | 0.447182i | \(-0.147572\pi\) |
−0.447182 | + | 0.894443i | \(0.647572\pi\) | |||||||
\(642\) | −578.036 | −0.0355347 | ||||||||
\(643\) | −5500.06 | − | 5500.06i | −0.337327 | − | 0.337327i | 0.518034 | − | 0.855360i | \(-0.326664\pi\) |
−0.855360 | + | 0.518034i | \(0.826664\pi\) | |||||||
\(644\) | − | 14356.3i | − | 0.878443i | ||||||
\(645\) | 98.9587 | 0.00604108 | ||||||||
\(646\) | −10624.0 | + | 7011.76i | −0.647051 | + | 0.427050i | ||||
\(647\) | 5015.28 | 0.304746 | 0.152373 | − | 0.988323i | \(-0.451308\pi\) | ||||
0.152373 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(648\) | − | 1417.15i | − | 0.0859118i | ||||||
\(649\) | −17226.7 | − | 17226.7i | −1.04192 | − | 1.04192i | ||||
\(650\) | −26089.5 | −1.57433 | ||||||||
\(651\) | −1926.23 | − | 1926.23i | −0.115968 | − | 0.115968i | ||||
\(652\) | −809.004 | + | 809.004i | −0.0485936 | + | 0.0485936i | ||||
\(653\) | −10298.2 | + | 10298.2i | −0.617151 | + | 0.617151i | −0.944800 | − | 0.327649i | \(-0.893744\pi\) |
0.327649 | + | 0.944800i | \(0.393744\pi\) | |||||||
\(654\) | 226.692i | 0.0135541i | ||||||||
\(655\) | 489.235i | 0.0291847i | ||||||||
\(656\) | 11078.6 | − | 11078.6i | 0.659371 | − | 0.659371i | ||||
\(657\) | 7263.75 | − | 7263.75i | 0.431333 | − | 0.431333i | ||||
\(658\) | −13332.6 | − | 13332.6i | −0.789906 | − | 0.789906i | ||||
\(659\) | 6199.21 | 0.366445 | 0.183222 | − | 0.983072i | \(-0.441347\pi\) | ||||
0.183222 | + | 0.983072i | \(0.441347\pi\) | |||||||
\(660\) | −142.181 | − | 142.181i | −0.00838545 | − | 0.00838545i | ||||
\(661\) | − | 15131.8i | − | 0.890406i | −0.895430 | − | 0.445203i | \(-0.853132\pi\) | ||
0.895430 | − | 0.445203i | \(-0.146868\pi\) | |||||||
\(662\) | 23689.6 | 1.39082 | ||||||||
\(663\) | 1592.13 | + | 326.106i | 0.0932628 | + | 0.0191024i | ||||
\(664\) | 1172.99 | 0.0685554 | ||||||||
\(665\) | 2289.04i | 0.133481i | ||||||||
\(666\) | −16888.0 | − | 16888.0i | −0.982578 | − | 0.982578i | ||||
\(667\) | −11824.7 | −0.686440 | ||||||||
\(668\) | 13384.3 | + | 13384.3i | 0.775230 | + | 0.775230i | ||||
\(669\) | −37.0484 | + | 37.0484i | −0.00214107 | + | 0.00214107i | ||||
\(670\) | −2899.02 | + | 2899.02i | −0.167163 | + | 0.167163i | ||||
\(671\) | 15670.6i | 0.901577i | ||||||||
\(672\) | 2706.11i | 0.155343i | ||||||||
\(673\) | 19122.8 | − | 19122.8i | 1.09529 | − | 1.09529i | 0.100337 | − | 0.994953i | \(-0.468008\pi\) |
0.994953 | − | 0.100337i | \(-0.0319922\pi\) | |||||||
\(674\) | −1320.44 | + | 1320.44i | −0.0754619 | + | 0.0754619i | ||||
\(675\) | 1955.55 | + | 1955.55i | 0.111510 | + | 0.111510i | ||||
\(676\) | −5948.22 | −0.338429 | ||||||||
\(677\) | 1889.00 | + | 1889.00i | 0.107238 | + | 0.107238i | 0.758690 | − | 0.651452i | \(-0.225840\pi\) |
−0.651452 | + | 0.758690i | \(0.725840\pi\) | |||||||
\(678\) | − | 1478.69i | − | 0.0837591i | ||||||
\(679\) | 40493.2 | 2.28864 | ||||||||
\(680\) | −54.4217 | + | 265.701i | −0.00306909 | + | 0.0149840i | ||||
\(681\) | −330.770 | −0.0186125 | ||||||||
\(682\) | − | 32248.2i | − | 1.81063i | ||||||
\(683\) | 10455.7 | + | 10455.7i | 0.585763 | + | 0.585763i | 0.936481 | − | 0.350718i | \(-0.114063\pi\) |
−0.350718 | + | 0.936481i | \(0.614063\pi\) | |||||||
\(684\) | −9275.07 | −0.518481 | ||||||||
\(685\) | 601.942 | + | 601.942i | 0.0335752 | + | 0.0335752i | ||||
\(686\) | −2767.27 | + | 2767.27i | −0.154016 | + | 0.154016i | ||||
\(687\) | −832.457 | + | 832.457i | −0.0462303 | + | 0.0462303i | ||||
\(688\) | − | 8109.01i | − | 0.449350i | ||||||
\(689\) | 25604.4i | 1.41575i | ||||||||
\(690\) | −173.360 | + | 173.360i | −0.00956477 | + | 0.00956477i | ||||
\(691\) | −13201.7 | + | 13201.7i | −0.726798 | + | 0.726798i | −0.969981 | − | 0.243182i | \(-0.921809\pi\) |
0.243182 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(692\) | −1740.04 | − | 1740.04i | −0.0955871 | − | 0.0955871i | ||||
\(693\) | 22122.6 | 1.21265 | ||||||||
\(694\) | 4106.98 | + | 4106.98i | 0.224638 | + | 0.224638i | ||||
\(695\) | − | 163.326i | − | 0.00891413i | ||||||
\(696\) | 132.068 | 0.00719255 | ||||||||
\(697\) | −3251.23 | + | 15873.3i | −0.176684 | + | 0.862617i | ||||
\(698\) | −26985.8 | −1.46336 | ||||||||
\(699\) | 2140.14i | 0.115805i | ||||||||
\(700\) | 16339.1 | + | 16339.1i | 0.882227 | + | 0.882227i | ||||
\(701\) | 27668.5 | 1.49076 | 0.745381 | − | 0.666638i | \(-0.232267\pi\) | ||||
0.745381 | + | 0.666638i | \(0.232267\pi\) | |||||||
\(702\) | 3473.53 | + | 3473.53i | 0.186752 | + | 0.186752i | ||||
\(703\) | 7379.42 | − | 7379.42i | 0.395903 | − | 0.395903i | ||||
\(704\) | −10218.4 | + | 10218.4i | −0.547045 | + | 0.547045i | ||||
\(705\) | 155.763i | 0.00832109i | ||||||||
\(706\) | 29467.7i | 1.57087i | ||||||||
\(707\) | −11994.1 | + | 11994.1i | −0.638025 | + | 0.638025i | ||||
\(708\) | −1688.28 | + | 1688.28i | −0.0896178 | + | 0.0896178i | ||||
\(709\) | −7382.12 | − | 7382.12i | −0.391032 | − | 0.391032i | 0.484023 | − | 0.875055i | \(-0.339175\pi\) |
−0.875055 | + | 0.484023i | \(0.839175\pi\) | |||||||
\(710\) | −600.157 | −0.0317232 | ||||||||
\(711\) | −24253.1 | − | 24253.1i | −1.27927 | − | 1.27927i | ||||
\(712\) | − | 1209.39i | − | 0.0636572i | ||||||
\(713\) | −19020.6 | −0.999059 | ||||||||
\(714\) | −1639.04 | − | 2483.41i | −0.0859097 | − | 0.130167i | ||||
\(715\) | 3459.68 | 0.180957 | ||||||||
\(716\) | − | 31147.2i | − | 1.62573i | ||||||
\(717\) | −675.825 | − | 675.825i | −0.0352010 | − | 0.0352010i | ||||
\(718\) | 28223.0 | 1.46695 | ||||||||
\(719\) | −12597.2 | − | 12597.2i | −0.653402 | − | 0.653402i | 0.300409 | − | 0.953811i | \(-0.402877\pi\) |
−0.953811 | + | 0.300409i | \(0.902877\pi\) | |||||||
\(720\) | −2507.51 | + | 2507.51i | −0.129791 | + | 0.129791i | ||||
\(721\) | −15689.5 | + | 15689.5i | −0.810414 | + | 0.810414i | ||||
\(722\) | 18622.4i | 0.959909i | ||||||||
\(723\) | 733.132i | 0.0377116i | ||||||||
\(724\) | −5064.29 | + | 5064.29i | −0.259963 | + | 0.259963i | ||||
\(725\) | 13457.9 | − | 13457.9i | 0.689397 | − | 0.689397i | ||||
\(726\) | 329.600 | + | 329.600i | 0.0168493 | + | 0.0168493i | ||||
\(727\) | −4296.42 | −0.219182 | −0.109591 | − | 0.993977i | \(-0.534954\pi\) | ||||
−0.109591 | + | 0.993977i | \(0.534954\pi\) | |||||||
\(728\) | −1950.79 | − | 1950.79i | −0.0993148 | − | 0.0993148i | ||||
\(729\) | 18901.0i | 0.960273i | ||||||||
\(730\) | −2941.28 | −0.149126 | ||||||||
\(731\) | 4619.37 | + | 6999.11i | 0.233726 | + | 0.354133i | ||||
\(732\) | 1535.78 | 0.0775467 | ||||||||
\(733\) | 28559.1i | 1.43909i | 0.694445 | + | 0.719546i | \(0.255650\pi\) | ||||
−0.694445 | + | 0.719546i | \(0.744350\pi\) | |||||||
\(734\) | −18395.8 | − | 18395.8i | −0.925071 | − | 0.925071i | ||||
\(735\) | −251.373 | −0.0126150 | ||||||||
\(736\) | 13360.8 | + | 13360.8i | 0.669138 | + | 0.669138i | ||||
\(737\) | −12242.7 | + | 12242.7i | −0.611895 | + | 0.611895i | ||||
\(738\) | −17257.5 | + | 17257.5i | −0.860780 | + | 0.860780i | ||||
\(739\) | − | 10646.9i | − | 0.529974i | −0.964252 | − | 0.264987i | \(-0.914632\pi\) | ||
0.964252 | − | 0.264987i | \(-0.0853677\pi\) | |||||||
\(740\) | 3308.03i | 0.164332i | ||||||||
\(741\) | −756.366 | + | 756.366i | −0.0374977 | + | 0.0374977i | ||||
\(742\) | 33148.3 | − | 33148.3i | 1.64005 | − | 1.64005i | ||||
\(743\) | −9874.51 | − | 9874.51i | −0.487565 | − | 0.487565i | 0.419972 | − | 0.907537i | \(-0.362040\pi\) |
−0.907537 | + | 0.419972i | \(0.862040\pi\) | |||||||
\(744\) | 212.437 | 0.0104682 | ||||||||
\(745\) | −3251.91 | − | 3251.91i | −0.159921 | − | 0.159921i | ||||
\(746\) | − | 6309.87i | − | 0.309679i | ||||||
\(747\) | −15860.8 | −0.776864 | ||||||||
\(748\) | 3419.14 | − | 16693.1i | 0.167134 | − | 0.815990i | ||||
\(749\) | −8808.65 | −0.429721 | ||||||||
\(750\) | − | 801.602i | − | 0.0390272i | ||||||
\(751\) | 18922.9 | + | 18922.9i | 0.919449 | + | 0.919449i | 0.996989 | − | 0.0775401i | \(-0.0247066\pi\) |
−0.0775401 | + | 0.996989i | \(0.524707\pi\) | |||||||
\(752\) | 12763.7 | 0.618943 | ||||||||
\(753\) | 394.020 | + | 394.020i | 0.0190689 | + | 0.0190689i | ||||
\(754\) | 23904.4 | − | 23904.4i | 1.15457 | − | 1.15457i | ||||
\(755\) | 206.563 | − | 206.563i | 0.00995709 | − | 0.00995709i | ||||
\(756\) | − | 4350.73i | − | 0.209305i | ||||||
\(757\) | − | 1399.40i | − | 0.0671889i | −0.999436 | − | 0.0335945i | \(-0.989305\pi\) | ||
0.999436 | − | 0.0335945i | \(-0.0106955\pi\) | |||||||
\(758\) | −4851.93 | + | 4851.93i | −0.232493 | + | 0.232493i | ||||
\(759\) | −732.108 | + | 732.108i | −0.0350116 | + | 0.0350116i | ||||
\(760\) | −126.225 | − | 126.225i | −0.00602456 | − | 0.00602456i | ||||
\(761\) | 29282.9 | 1.39488 | 0.697440 | − | 0.716644i | \(-0.254323\pi\) | ||||
0.697440 | + | 0.716644i | \(0.254323\pi\) | |||||||
\(762\) | −2326.24 | − | 2326.24i | −0.110592 | − | 0.110592i | ||||
\(763\) | 3454.54i | 0.163909i | ||||||||
\(764\) | 6669.74 | 0.315841 | ||||||||
\(765\) | 735.875 | − | 3592.73i | 0.0347786 | − | 0.169798i | ||||
\(766\) | 4547.62 | 0.214507 | ||||||||
\(767\) | − | 41080.7i | − | 1.93395i | ||||||
\(768\) | −1367.80 | − | 1367.80i | −0.0642658 | − | 0.0642658i | ||||
\(769\) | −11804.9 | −0.553571 | −0.276786 | − | 0.960932i | \(-0.589269\pi\) | ||||
−0.276786 | + | 0.960932i | \(0.589269\pi\) | |||||||
\(770\) | −4479.02 | − | 4479.02i | −0.209627 | − | 0.209627i | ||||
\(771\) | 1810.82 | − | 1810.82i | 0.0845852 | − | 0.0845852i | ||||
\(772\) | 9180.97 | − | 9180.97i | 0.428019 | − | 0.428019i | ||||
\(773\) | − | 18421.7i | − | 0.857155i | −0.903505 | − | 0.428578i | \(-0.859015\pi\) | ||
0.903505 | − | 0.428578i | \(-0.140985\pi\) | |||||||
\(774\) | 12631.6i | 0.586607i | ||||||||
\(775\) | 21647.6 | − | 21647.6i | 1.00336 | − | 1.00336i | ||||
\(776\) | −2232.93 | + | 2232.93i | −0.103296 | + | 0.103296i | ||||
\(777\) | 1724.98 | + | 1724.98i | 0.0796439 | + | 0.0796439i | ||||
\(778\) | 14561.0 | 0.670998 | ||||||||
\(779\) | −7540.85 | − | 7540.85i | −0.346828 | − | 0.346828i | ||||
\(780\) | − | 339.062i | − | 0.0155646i | ||||||
\(781\) | −2534.49 | −0.116122 | ||||||||
\(782\) | −20353.7 | − | 4168.92i | −0.930750 | − | 0.190640i | ||||
\(783\) | −3583.53 | −0.163557 | ||||||||
\(784\) | 20598.3i | 0.938335i | ||||||||
\(785\) | −164.538 | − | 164.538i | −0.00748102 | − | 0.00748102i | ||||
\(786\) | 418.575 | 0.0189950 | ||||||||
\(787\) | −15833.2 | − | 15833.2i | −0.717143 | − | 0.717143i | 0.250876 | − | 0.968019i | \(-0.419281\pi\) |
−0.968019 | + | 0.250876i | \(0.919281\pi\) | |||||||
\(788\) | −23555.2 | + | 23555.2i | −1.06487 | + | 1.06487i | ||||
\(789\) | 296.919 | − | 296.919i | 0.0133975 | − | 0.0133975i | ||||
\(790\) | 9820.74i | 0.442286i | ||||||||
\(791\) | − | 22533.6i | − | 1.01290i | ||||||
\(792\) | −1219.91 | + | 1219.91i | −0.0547320 | + | 0.0547320i | ||||
\(793\) | −18685.0 | + | 18685.0i | −0.836727 | + | 0.836727i | ||||
\(794\) | 37822.5 | + | 37822.5i | 1.69052 | + | 1.69052i | ||||
\(795\) | −387.268 | −0.0172767 | ||||||||
\(796\) | −16529.2 | − | 16529.2i | −0.736005 | − | 0.736005i | ||||
\(797\) | 13676.1i | 0.607818i | 0.952701 | + | 0.303909i | \(0.0982919\pi\) | ||||
−0.952701 | + | 0.303909i | \(0.901708\pi\) | |||||||
\(798\) | 1958.43 | 0.0868770 | ||||||||
\(799\) | −11016.7 | + | 7270.98i | −0.487790 | + | 0.321938i | ||||
\(800\) | −30412.2 | −1.34404 | ||||||||
\(801\) | 16353.1i | 0.721357i | ||||||||
\(802\) | −7416.29 | − | 7416.29i | −0.326532 | − | 0.326532i | ||||
\(803\) | −12421.2 | −0.545872 | ||||||||
\(804\) | 1199.83 | + | 1199.83i | 0.0526305 | + | 0.0526305i | ||||
\(805\) | −2641.82 | + | 2641.82i | −0.115667 | + | 0.115667i | ||||
\(806\) | 38451.4 | − | 38451.4i | 1.68039 | − | 1.68039i | ||||
\(807\) | − | 1437.56i | − | 0.0627071i | ||||||
\(808\) | − | 1322.79i | − | 0.0575933i | ||||||
\(809\) | −71.3327 | + | 71.3327i | −0.00310003 | + | 0.00310003i | −0.708655 | − | 0.705555i | \(-0.750698\pi\) |
0.705555 | + | 0.708655i | \(0.250698\pi\) | |||||||
\(810\) | 3879.66 | − | 3879.66i | 0.168293 | − | 0.168293i | ||||
\(811\) | 11822.5 | + | 11822.5i | 0.511893 | + | 0.511893i | 0.915106 | − | 0.403213i | \(-0.132107\pi\) |
−0.403213 | + | 0.915106i | \(0.632107\pi\) | |||||||
\(812\) | −29941.2 | −1.29400 | ||||||||
\(813\) | 1111.16 | + | 1111.16i | 0.0479335 | + | 0.0479335i | ||||
\(814\) | 28879.0i | 1.24350i | ||||||||
\(815\) | 297.743 | 0.0127969 | ||||||||
\(816\) | 1973.28 | + | 404.175i | 0.0846552 | + | 0.0173394i | ||||
\(817\) | −5519.54 | −0.236358 | ||||||||
\(818\) | 16320.2i | 0.697584i | ||||||||
\(819\) | 26378.1 | + | 26378.1i | 1.12543 | + | 1.12543i | ||||
\(820\) | 3380.39 | 0.143962 | ||||||||
\(821\) | −3487.82 | − | 3487.82i | −0.148265 | − | 0.148265i | 0.629077 | − | 0.777343i | \(-0.283433\pi\) |
−0.777343 | + | 0.629077i | \(0.783433\pi\) | |||||||
\(822\) | 515.004 | − | 515.004i | 0.0218526 | − | 0.0218526i | ||||
\(823\) | 18792.3 | − | 18792.3i | 0.795939 | − | 0.795939i | −0.186513 | − | 0.982452i | \(-0.559719\pi\) |
0.982452 | + | 0.186513i | \(0.0597187\pi\) | |||||||
\(824\) | − | 1730.35i | − | 0.0731547i | ||||||
\(825\) | − | 1666.44i | − | 0.0703249i | ||||||
\(826\) | −53184.5 | + | 53184.5i | −2.24034 | + | 2.24034i | ||||
\(827\) | 22017.0 | − | 22017.0i | 0.925762 | − | 0.925762i | −0.0716667 | − | 0.997429i | \(-0.522832\pi\) |
0.997429 | + | 0.0716667i | \(0.0228318\pi\) | |||||||
\(828\) | −10704.5 | − | 10704.5i | −0.449284 | − | 0.449284i | ||||
\(829\) | 17274.9 | 0.723742 | 0.361871 | − | 0.932228i | \(-0.382138\pi\) | ||||
0.361871 | + | 0.932228i | \(0.382138\pi\) | |||||||
\(830\) | 3211.24 | + | 3211.24i | 0.134294 | + | 0.134294i | ||||
\(831\) | 3244.31i | 0.135432i | ||||||||
\(832\) | −24367.9 | −1.01539 | ||||||||
\(833\) | −11734.0 | − | 17779.0i | −0.488067 | − | 0.739502i | ||||
\(834\) | −139.737 | −0.00580180 | ||||||||
\(835\) | − | 4925.90i | − | 0.204153i | ||||||
\(836\) | 7930.32 | + | 7930.32i | 0.328081 | + | 0.328081i | ||||
\(837\) | −5764.28 | −0.238044 | ||||||||
\(838\) | 39658.4 | + | 39658.4i | 1.63482 | + | 1.63482i | ||||
\(839\) | 3970.01 | − | 3970.01i | 0.163361 | − | 0.163361i | −0.620693 | − | 0.784054i | \(-0.713149\pi\) |
0.784054 | + | 0.620693i | \(0.213149\pi\) | |||||||
\(840\) | 29.5058 | − | 29.5058i | 0.00121196 | − | 0.00121196i | ||||
\(841\) | 272.434i | 0.0111704i | ||||||||
\(842\) | − | 12563.8i | − | 0.514226i | ||||||
\(843\) | −957.845 | + | 957.845i | −0.0391340 | + | 0.0391340i | ||||
\(844\) | 24025.0 | − | 24025.0i | 0.979827 | − | 0.979827i | ||||
\(845\) | 1094.58 | + | 1094.58i | 0.0445618 | + | 0.0445618i | ||||
\(846\) | −19882.4 | −0.808004 | ||||||||
\(847\) | 5022.76 | + | 5022.76i | 0.203759 | + | 0.203759i | ||||
\(848\) | 31734.0i | 1.28508i | ||||||||
\(849\) | 2539.63 | 0.102662 | ||||||||
\(850\) | 27909.5 | − | 18420.1i | 1.12622 | − | 0.743299i | ||||
\(851\) | 17033.4 | 0.686132 | ||||||||
\(852\) | 248.390i | 0.00998792i | ||||||||
\(853\) | 2686.89 | + | 2686.89i | 0.107851 | + | 0.107851i | 0.758973 | − | 0.651122i | \(-0.225701\pi\) |
−0.651122 | + | 0.758973i | \(0.725701\pi\) | |||||||
\(854\) | 48380.5 | 1.93858 | ||||||||
\(855\) | 1706.78 | + | 1706.78i | 0.0682698 | + | 0.0682698i | ||||
\(856\) | 485.738 | − | 485.738i | 0.0193951 | − | 0.0193951i | ||||
\(857\) | 29847.2 | − | 29847.2i | 1.18969 | − | 1.18969i | 0.212532 | − | 0.977154i | \(-0.431829\pi\) |
0.977154 | − | 0.212532i | \(-0.0681710\pi\) | |||||||
\(858\) | − | 2960.00i | − | 0.117777i | ||||||
\(859\) | 3132.98i | 0.124442i | 0.998062 | + | 0.0622212i | \(0.0198184\pi\) | ||||
−0.998062 | + | 0.0622212i | \(0.980182\pi\) | |||||||
\(860\) | 1237.14 | − | 1237.14i | 0.0490537 | − | 0.0490537i | ||||
\(861\) | 1762.72 | − | 1762.72i | 0.0697715 | − | 0.0697715i | ||||
\(862\) | −4563.37 | − | 4563.37i | −0.180312 | − | 0.180312i | ||||
\(863\) | −31934.9 | −1.25965 | −0.629824 | − | 0.776738i | \(-0.716873\pi\) | ||||
−0.629824 | + | 0.776738i | \(0.716873\pi\) | |||||||
\(864\) | 4049.05 | + | 4049.05i | 0.159434 | + | 0.159434i | ||||
\(865\) | 640.396i | 0.0251724i | ||||||||
\(866\) | −65266.8 | −2.56104 | ||||||||
\(867\) | −1933.44 | + | 775.244i | −0.0757358 | + | 0.0303675i | ||||
\(868\) | −48161.8 | −1.88332 | ||||||||
\(869\) | 41473.5i | 1.61898i | ||||||||
\(870\) | 361.556 | + | 361.556i | 0.0140895 | + | 0.0140895i | ||||
\(871\) | −29195.4 | −1.13576 | ||||||||
\(872\) | −190.495 | − | 190.495i | −0.00739790 | − | 0.00739790i | ||||
\(873\) | 30193.0 | − | 30193.0i | 1.17054 | − | 1.17054i | ||||
\(874\) | 9669.33 | − | 9669.33i | 0.374222 | − | 0.374222i | ||||
\(875\) | − | 12215.6i | − | 0.471956i | ||||||
\(876\) | 1217.33i | 0.0469517i | ||||||||
\(877\) | −10847.5 | + | 10847.5i | −0.417667 | + | 0.417667i | −0.884399 | − | 0.466732i | \(-0.845431\pi\) |
0.466732 | + | 0.884399i | \(0.345431\pi\) | |||||||
\(878\) | −20450.9 | + | 20450.9i | −0.786086 | + | 0.786086i | ||||
\(879\) | −1610.70 | − | 1610.70i | −0.0618060 | − | 0.0618060i | ||||
\(880\) | 4287.91 | 0.164256 | ||||||||
\(881\) | 32730.5 | + | 32730.5i | 1.25167 | + | 1.25167i | 0.954972 | + | 0.296695i | \(0.0958845\pi\) |
0.296695 | + | 0.954972i | \(0.404116\pi\) | |||||||
\(882\) | − | 32086.6i | − | 1.22496i | ||||||
\(883\) | −26455.9 | −1.00828 | −0.504140 | − | 0.863622i | \(-0.668190\pi\) | ||||
−0.504140 | + | 0.863622i | \(0.668190\pi\) | |||||||
\(884\) | 23981.0 | − | 15827.3i | 0.912407 | − | 0.602184i | ||||
\(885\) | 621.348 | 0.0236004 | ||||||||
\(886\) | − | 52456.0i | − | 1.98904i | ||||||
\(887\) | −12749.8 | − | 12749.8i | −0.482633 | − | 0.482633i | 0.423339 | − | 0.905972i | \(-0.360858\pi\) |
−0.905972 | + | 0.423339i | \(0.860858\pi\) | |||||||
\(888\) | −190.242 | −0.00718932 | ||||||||
\(889\) | −35449.4 | − | 35449.4i | −1.33739 | − | 1.33739i | ||||
\(890\) | 3310.90 | − | 3310.90i | 0.124698 | − | 0.124698i | ||||
\(891\) | 16384.0 | − | 16384.0i | 0.616033 | − | 0.616033i | ||||
\(892\) | 926.327i | 0.0347710i | ||||||||
\(893\) | − | 8687.85i | − | 0.325563i | ||||||
\(894\) | −2782.24 | + | 2782.24i | −0.104085 | + | 0.104085i | ||||
\(895\) | −5731.65 | + | 5731.65i | −0.214065 | + | 0.214065i | ||||
\(896\) | −4557.08 | − | 4557.08i | −0.169912 | − | 0.169912i | ||||
\(897\) | −1745.87 | −0.0649864 | ||||||||
\(898\) | −26962.3 | − | 26962.3i | −1.00194 | − | 1.00194i | ||||
\(899\) | 39669.1i | 1.47168i | ||||||||
\(900\) | 24365.9 | 0.902440 | ||||||||
\(901\) | −18077.6 | − | 27390.5i | −0.668425 | − | 1.01277i | ||||
\(902\) | 29510.7 | 1.08936 | ||||||||
\(903\) | − | 1290.22i | − | 0.0475481i | ||||||
\(904\) | 1242.58 | + | 1242.58i | 0.0457163 | + | 0.0457163i | ||||
\(905\) | 1863.84 | 0.0684599 | ||||||||
\(906\) | −176.729 | − | 176.729i | −0.00648062 | − | 0.00648062i | ||||
\(907\) | −32345.3 | + | 32345.3i | −1.18413 | + | 1.18413i | −0.205467 | + | 0.978664i | \(0.565871\pi\) |
−0.978664 | + | 0.205467i | \(0.934129\pi\) | |||||||
\(908\) | −4135.15 | + | 4135.15i | −0.151134 | + | 0.151134i | ||||
\(909\) | 17886.3i | 0.652642i | ||||||||
\(910\) | − | 10681.2i | − | 0.389096i | ||||||
\(911\) | −1203.07 | + | 1203.07i | −0.0437534 | + | 0.0437534i | −0.728645 | − | 0.684892i | \(-0.759850\pi\) |
0.684892 | + | 0.728645i | \(0.259850\pi\) | |||||||
\(912\) | −937.438 | + | 937.438i | −0.0340369 | + | 0.0340369i | ||||
\(913\) | 13561.2 | + | 13561.2i | 0.491579 | + | 0.491579i | ||||
\(914\) | 2747.94 | 0.0994462 | ||||||||
\(915\) | −282.612 | − | 282.612i | −0.0102108 | − | 0.0102108i | ||||
\(916\) | 20814.1i | 0.750782i | ||||||||
\(917\) | 6378.64 | 0.229707 | ||||||||
\(918\) | −6168.27 | − | 1263.41i | −0.221768 | − | 0.0454234i | ||||
\(919\) | 30814.5 | 1.10607 | 0.553035 | − | 0.833158i | \(-0.313470\pi\) | ||||
0.553035 | + | 0.833158i | \(0.313470\pi\) | |||||||
\(920\) | − | 291.357i | − | 0.0104410i | ||||||
\(921\) | −2104.92 | − | 2104.92i | −0.0753088 | − | 0.0753088i | ||||
\(922\) | 25609.3 | 0.914747 | ||||||||
\(923\) | −3022.02 | − | 3022.02i | −0.107769 | − | 0.107769i | ||||
\(924\) | −1853.76 | + | 1853.76i | −0.0660001 | + | 0.0660001i | ||||
\(925\) | −19385.9 | + | 19385.9i | −0.689087 | + | 0.689087i | ||||
\(926\) | 4651.93i | 0.165088i | ||||||||
\(927\) | 23397.2i | 0.828982i | ||||||||
\(928\) | 27865.0 | − | 27865.0i | 0.985684 | − | 0.985684i | ||||
\(929\) | 2894.34 | − | 2894.34i | 0.102218 | − | 0.102218i | −0.654149 | − | 0.756366i | \(-0.726973\pi\) |
0.756366 | + | 0.654149i | \(0.226973\pi\) | |||||||
\(930\) | 581.579 | + | 581.579i | 0.0205062 | + | 0.0205062i | ||||
\(931\) | 14020.6 | 0.493563 | ||||||||
\(932\) | 26755.1 | + | 26755.1i | 0.940336 | + | 0.940336i | ||||
\(933\) | 435.018i | 0.0152646i | ||||||||
\(934\) | −11616.5 | −0.406963 | ||||||||
\(935\) | −3701.02 | + | 2442.65i | −0.129450 | + | 0.0854365i | ||||
\(936\) | −2909.15 | −0.101590 | ||||||||
\(937\) | 16517.3i | 0.575877i | 0.957649 | + | 0.287939i | \(0.0929699\pi\) | ||||
−0.957649 | + | 0.287939i | \(0.907030\pi\) | |||||||
\(938\) | 37797.4 | + | 37797.4i | 1.31570 | + | 1.31570i | ||||
\(939\) | 1056.11 | 0.0367036 | ||||||||
\(940\) | 1947.28 | + | 1947.28i | 0.0675674 | + | 0.0675674i | ||||
\(941\) | −4851.27 | + | 4851.27i | −0.168063 | + | 0.168063i | −0.786127 | − | 0.618065i | \(-0.787917\pi\) |
0.618065 | + | 0.786127i | \(0.287917\pi\) | |||||||
\(942\) | −140.774 | + | 140.774i | −0.00486906 | + | 0.00486906i | ||||
\(943\) | − | 17406.0i | − | 0.601080i | ||||||
\(944\) | − | 50915.3i | − | 1.75546i | ||||||
\(945\) | −800.613 | + | 800.613i | −0.0275597 | + | 0.0275597i | ||||
\(946\) | 10800.2 | − | 10800.2i | 0.371189 | − | 0.371189i | ||||
\(947\) | 23545.8 | + | 23545.8i | 0.807957 | + | 0.807957i | 0.984324 | − | 0.176367i | \(-0.0564347\pi\) |
−0.176367 | + | 0.984324i | \(0.556435\pi\) | |||||||
\(948\) | 4064.57 | 0.139252 | ||||||||
\(949\) | −14810.5 | − | 14810.5i | −0.506607 | − | 0.506607i | ||||
\(950\) | 22009.6i | 0.751669i | ||||||||
\(951\) | 1176.65 | 0.0401215 | ||||||||
\(952\) | 3464.20 | + | 709.550i | 0.117936 | + | 0.0241561i | ||||
\(953\) | −24857.5 | −0.844925 | −0.422462 | − | 0.906380i | \(-0.638834\pi\) | ||||
−0.422462 | + | 0.906380i | \(0.638834\pi\) | |||||||
\(954\) | − | 49432.9i | − | 1.67762i | ||||||
\(955\) | −1227.35 | − | 1227.35i | −0.0415877 | − | 0.0415877i | ||||
\(956\) | −16897.8 | −0.571666 | ||||||||
\(957\) | 1526.87 | + | 1526.87i | 0.0515744 | + | 0.0515744i | ||||
\(958\) | −24746.2 | + | 24746.2i | −0.834565 | + | 0.834565i | ||||
\(959\) | 7848.11 | − | 7848.11i | 0.264264 | − | 0.264264i | ||||
\(960\) | − | 368.566i | − | 0.0123911i | ||||||
\(961\) | 34018.6i | 1.14191i | ||||||||
\(962\) | −34434.1 | + | 34434.1i | −1.15405 | + | 1.15405i | ||||
\(963\) | −6568.01 | + | 6568.01i | −0.219783 | + | 0.219783i | ||||
\(964\) | 9165.31 | + | 9165.31i | 0.306219 | + | 0.306219i | ||||
\(965\) | −3378.93 | −0.112717 | ||||||||
\(966\) | 2260.26 | + | 2260.26i | 0.0752823 | + | 0.0752823i | ||||
\(967\) | − | 15832.2i | − | 0.526504i | −0.964727 | − | 0.263252i | \(-0.915205\pi\) | ||
0.964727 | − | 0.263252i | \(-0.0847951\pi\) | |||||||
\(968\) | −553.943 | −0.0183930 | ||||||||
\(969\) | 275.108 | − | 1343.15i | 0.00912049 | − | 0.0445285i | ||||
\(970\) | −12226.0 | −0.404693 | ||||||||
\(971\) | 39521.9i | 1.30620i | 0.757273 | + | 0.653098i | \(0.226531\pi\) | ||||
−0.757273 | + | 0.653098i | \(0.773469\pi\) | |||||||
\(972\) | −4871.49 | − | 4871.49i | −0.160754 | − | 0.160754i | ||||
\(973\) | −2129.45 | −0.0701612 | ||||||||
\(974\) | −19775.5 | − | 19775.5i | −0.650564 | − | 0.650564i | ||||
\(975\) | 1986.99 | − | 1986.99i | 0.0652664 | − | 0.0652664i | ||||
\(976\) | −23158.2 | + | 23158.2i | −0.759502 | + | 0.759502i | ||||
\(977\) | − | 11587.3i | − | 0.379438i | −0.981838 | − | 0.189719i | \(-0.939242\pi\) | ||
0.981838 | − | 0.189719i | \(-0.0607577\pi\) | |||||||
\(978\) | − | 254.740i | − | 0.00832893i | ||||||
\(979\) | 13982.1 | − | 13982.1i | 0.456455 | − | 0.456455i | ||||
\(980\) | −3142.56 | + | 3142.56i | −0.102434 | + | 0.102434i | ||||
\(981\) | 2575.82 | + | 2575.82i | 0.0838323 | + | 0.0838323i | ||||
\(982\) | 30068.4 | 0.977108 | ||||||||
\(983\) | −22711.9 | − | 22711.9i | −0.736925 | − | 0.736925i | 0.235057 | − | 0.971982i | \(-0.424472\pi\) |
−0.971982 | + | 0.235057i | \(0.924472\pi\) | |||||||
\(984\) | 194.404i | 0.00629815i | ||||||||
\(985\) | 8669.17 | 0.280429 | ||||||||
\(986\) | −8694.61 | + | 42449.3i | −0.280824 | + | 1.37105i | ||||
\(987\) | 2030.83 | 0.0654936 | ||||||||
\(988\) | 18911.5i | 0.608964i | ||||||||
\(989\) | −6370.19 | − | 6370.19i | −0.204813 | − | 0.204813i | ||||
\(990\) | −6679.40 | −0.214429 | ||||||||
\(991\) | −13235.2 | − | 13235.2i | −0.424247 | − | 0.424247i | 0.462416 | − | 0.886663i | \(-0.346983\pi\) |
−0.886663 | + | 0.462416i | \(0.846983\pi\) | |||||||
\(992\) | 44822.2 | − | 44822.2i | 1.43458 | − | 1.43458i | ||||
\(993\) | −1804.21 | + | 1804.21i | −0.0576585 | + | 0.0576585i | ||||
\(994\) | 7824.83i | 0.249687i | ||||||||
\(995\) | 6083.32i | 0.193823i | ||||||||
\(996\) | 1329.05 | − | 1329.05i | 0.0422818 | − | 0.0422818i | ||||
\(997\) | −8210.42 | + | 8210.42i | −0.260809 | + | 0.260809i | −0.825383 | − | 0.564574i | \(-0.809041\pi\) |
0.564574 | + | 0.825383i | \(0.309041\pi\) | |||||||
\(998\) | −56234.5 | − | 56234.5i | −1.78364 | − | 1.78364i | ||||
\(999\) | 5162.05 | 0.163483 |
(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 | 17.4.c.a.13.4 | yes | 8 | |
3.2 | odd | 2 | 153.4.f.a.64.1 | 8 | |||
4.3 | odd | 2 | 272.4.o.e.81.3 | 8 | |||
17.2 | even | 8 | 289.4.a.f.1.1 | 8 | |||
17.4 | even | 4 | inner | 17.4.c.a.4.1 | ✓ | 8 | |
17.8 | even | 8 | 289.4.b.c.288.8 | 8 | |||
17.9 | even | 8 | 289.4.b.c.288.7 | 8 | |||
17.15 | even | 8 | 289.4.a.f.1.2 | 8 | |||
51.38 | odd | 4 | 153.4.f.a.55.4 | 8 | |||
68.55 | odd | 4 | 272.4.o.e.225.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.c.a.4.1 | ✓ | 8 | 17.4 | even | 4 | inner | |
17.4.c.a.13.4 | yes | 8 | 1.1 | even | 1 | trivial | |
153.4.f.a.55.4 | 8 | 51.38 | odd | 4 | |||
153.4.f.a.64.1 | 8 | 3.2 | odd | 2 | |||
272.4.o.e.81.3 | 8 | 4.3 | odd | 2 | |||
272.4.o.e.225.3 | 8 | 68.55 | odd | 4 | |||
289.4.a.f.1.1 | 8 | 17.2 | even | 8 | |||
289.4.a.f.1.2 | 8 | 17.15 | even | 8 | |||
289.4.b.c.288.7 | 8 | 17.9 | even | 8 | |||
289.4.b.c.288.8 | 8 | 17.8 | even | 8 |