Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,3,Mod(6,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.6");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.d (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: | \(1.00817697813\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 6.5 | ||
Root | \(2.02961 - 2.02961i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.6 |
Dual form | 37.3.d.a.31.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.02961 | − | 1.02961i | 0.514807 | − | 0.514807i | −0.401188 | − | 0.915996i | \(-0.631403\pi\) |
0.915996 | + | 0.401188i | \(0.131403\pi\) | |||||||
\(3\) | − | 3.18930i | − | 1.06310i | −0.847027 | − | 0.531549i | \(-0.821610\pi\) | ||
0.847027 | − | 0.531549i | \(-0.178390\pi\) | |||||||
\(4\) | 1.87979i | 0.469947i | ||||||||
\(5\) | −0.460662 | − | 0.460662i | −0.0921325 | − | 0.0921325i | 0.659538 | − | 0.751671i | \(-0.270752\pi\) |
−0.751671 | + | 0.659538i | \(0.770752\pi\) | |||||||
\(6\) | −3.28375 | − | 3.28375i | −0.547291 | − | 0.547291i | ||||
\(7\) | −2.31735 | −0.331050 | −0.165525 | − | 0.986206i | \(-0.552932\pi\) | ||||
−0.165525 | + | 0.986206i | \(0.552932\pi\) | |||||||
\(8\) | 6.05392 | + | 6.05392i | 0.756739 | + | 0.756739i | ||||
\(9\) | −1.17160 | −0.130178 | ||||||||
\(10\) | −0.948609 | −0.0948609 | ||||||||
\(11\) | 17.2954i | 1.57231i | 0.618032 | + | 0.786153i | \(0.287930\pi\) | ||||
−0.618032 | + | 0.786153i | \(0.712070\pi\) | |||||||
\(12\) | 5.99520 | 0.499600 | ||||||||
\(13\) | −10.2742 | − | 10.2742i | −0.790319 | − | 0.790319i | 0.191227 | − | 0.981546i | \(-0.438753\pi\) |
−0.981546 | + | 0.191227i | \(0.938753\pi\) | |||||||
\(14\) | −2.38597 | + | 2.38597i | −0.170427 | + | 0.170427i | ||||
\(15\) | −1.46919 | + | 1.46919i | −0.0979459 | + | 0.0979459i | ||||
\(16\) | 4.94725 | 0.309203 | ||||||||
\(17\) | −12.3100 | − | 12.3100i | −0.724115 | − | 0.724115i | 0.245325 | − | 0.969441i | \(-0.421105\pi\) |
−0.969441 | + | 0.245325i | \(0.921105\pi\) | |||||||
\(18\) | −1.20630 | + | 1.20630i | −0.0670167 | + | 0.0670167i | ||||
\(19\) | 1.47612 | + | 1.47612i | 0.0776906 | + | 0.0776906i | 0.744884 | − | 0.667194i | \(-0.232505\pi\) |
−0.667194 | + | 0.744884i | \(0.732505\pi\) | |||||||
\(20\) | 0.865947 | − | 0.865947i | 0.0432974 | − | 0.0432974i | ||||
\(21\) | 7.39070i | 0.351938i | ||||||||
\(22\) | 17.8076 | + | 17.8076i | 0.809435 | + | 0.809435i | ||||
\(23\) | 5.39671 | + | 5.39671i | 0.234640 | + | 0.234640i | 0.814626 | − | 0.579987i | \(-0.196942\pi\) |
−0.579987 | + | 0.814626i | \(0.696942\pi\) | |||||||
\(24\) | 19.3077 | − | 19.3077i | 0.804488 | − | 0.804488i | ||||
\(25\) | − | 24.5756i | − | 0.983023i | ||||||
\(26\) | −21.1568 | −0.813724 | ||||||||
\(27\) | − | 24.9671i | − | 0.924706i | ||||||
\(28\) | − | 4.35612i | − | 0.155576i | ||||||
\(29\) | 5.59041 | − | 5.59041i | 0.192773 | − | 0.192773i | −0.604120 | − | 0.796893i | \(-0.706475\pi\) |
0.796893 | + | 0.604120i | \(0.206475\pi\) | |||||||
\(30\) | 3.02540i | 0.100847i | ||||||||
\(31\) | −3.08292 | + | 3.08292i | −0.0994491 | + | 0.0994491i | −0.755081 | − | 0.655632i | \(-0.772402\pi\) |
0.655632 | + | 0.755081i | \(0.272402\pi\) | |||||||
\(32\) | −19.1219 | + | 19.1219i | −0.597559 | + | 0.597559i | ||||
\(33\) | 55.1600 | 1.67152 | ||||||||
\(34\) | −25.3490 | −0.745560 | ||||||||
\(35\) | 1.06751 | + | 1.06751i | 0.0305004 | + | 0.0305004i | ||||
\(36\) | − | 2.20236i | − | 0.0611768i | ||||||
\(37\) | 3.81569 | − | 36.8027i | 0.103127 | − | 0.994668i | ||||
\(38\) | 3.03967 | 0.0799914 | ||||||||
\(39\) | −32.7673 | + | 32.7673i | −0.840187 | + | 0.840187i | ||||
\(40\) | − | 5.57762i | − | 0.139441i | ||||||
\(41\) | 65.3467i | 1.59382i | 0.604097 | + | 0.796911i | \(0.293534\pi\) | ||||
−0.604097 | + | 0.796911i | \(0.706466\pi\) | |||||||
\(42\) | 7.60958 | + | 7.60958i | 0.181180 | + | 0.181180i | ||||
\(43\) | 41.3135 | + | 41.3135i | 0.960779 | + | 0.960779i | 0.999259 | − | 0.0384801i | \(-0.0122516\pi\) |
−0.0384801 | + | 0.999259i | \(0.512252\pi\) | |||||||
\(44\) | −32.5116 | −0.738900 | ||||||||
\(45\) | 0.539714 | + | 0.539714i | 0.0119936 | + | 0.0119936i | ||||
\(46\) | 11.1131 | 0.241588 | ||||||||
\(47\) | −52.1282 | −1.10911 | −0.554555 | − | 0.832147i | \(-0.687112\pi\) | ||||
−0.554555 | + | 0.832147i | \(0.687112\pi\) | |||||||
\(48\) | − | 15.7782i | − | 0.328713i | ||||||
\(49\) | −43.6299 | −0.890406 | ||||||||
\(50\) | −25.3034 | − | 25.3034i | −0.506068 | − | 0.506068i | ||||
\(51\) | −39.2601 | + | 39.2601i | −0.769806 | + | 0.769806i | ||||
\(52\) | 19.3132 | − | 19.3132i | 0.371408 | − | 0.371408i | ||||
\(53\) | 63.5869 | 1.19975 | 0.599876 | − | 0.800093i | \(-0.295217\pi\) | ||||
0.599876 | + | 0.800093i | \(0.295217\pi\) | |||||||
\(54\) | −25.7065 | − | 25.7065i | −0.476046 | − | 0.476046i | ||||
\(55\) | 7.96733 | − | 7.96733i | 0.144860 | − | 0.144860i | ||||
\(56\) | −14.0290 | − | 14.0290i | −0.250518 | − | 0.250518i | ||||
\(57\) | 4.70779 | − | 4.70779i | 0.0825927 | − | 0.0825927i | ||||
\(58\) | − | 11.5119i | − | 0.198482i | ||||||
\(59\) | 31.9694 | + | 31.9694i | 0.541853 | + | 0.541853i | 0.924072 | − | 0.382219i | \(-0.124840\pi\) |
−0.382219 | + | 0.924072i | \(0.624840\pi\) | |||||||
\(60\) | −2.76176 | − | 2.76176i | −0.0460294 | − | 0.0460294i | ||||
\(61\) | 83.9349 | − | 83.9349i | 1.37598 | − | 1.37598i | 0.524688 | − | 0.851294i | \(-0.324182\pi\) |
0.851294 | − | 0.524688i | \(-0.175818\pi\) | |||||||
\(62\) | 6.34844i | 0.102394i | ||||||||
\(63\) | 2.71501 | 0.0430954 | ||||||||
\(64\) | 59.1654i | 0.924459i | ||||||||
\(65\) | 9.46583i | 0.145628i | ||||||||
\(66\) | 56.7936 | − | 56.7936i | 0.860509 | − | 0.860509i | ||||
\(67\) | − | 5.14012i | − | 0.0767181i | −0.999264 | − | 0.0383591i | \(-0.987787\pi\) | ||
0.999264 | − | 0.0383591i | \(-0.0122131\pi\) | |||||||
\(68\) | 23.1401 | − | 23.1401i | 0.340296 | − | 0.340296i | ||||
\(69\) | 17.2117 | − | 17.2117i | 0.249445 | − | 0.249445i | ||||
\(70\) | 2.19826 | 0.0314037 | ||||||||
\(71\) | 75.1898 | 1.05901 | 0.529505 | − | 0.848307i | \(-0.322378\pi\) | ||||
0.529505 | + | 0.848307i | \(0.322378\pi\) | |||||||
\(72\) | −7.09279 | − | 7.09279i | −0.0985109 | − | 0.0985109i | ||||
\(73\) | 66.0866i | 0.905296i | 0.891689 | + | 0.452648i | \(0.149521\pi\) | ||||
−0.891689 | + | 0.452648i | \(0.850479\pi\) | |||||||
\(74\) | −33.9639 | − | 41.8213i | −0.458972 | − | 0.565153i | ||||
\(75\) | −78.3788 | −1.04505 | ||||||||
\(76\) | −2.77479 | + | 2.77479i | −0.0365104 | + | 0.0365104i | ||||
\(77\) | − | 40.0794i | − | 0.520511i | ||||||
\(78\) | 67.4754i | 0.865069i | ||||||||
\(79\) | −87.3354 | − | 87.3354i | −1.10551 | − | 1.10551i | −0.993733 | − | 0.111778i | \(-0.964346\pi\) |
−0.111778 | − | 0.993733i | \(-0.535654\pi\) | |||||||
\(80\) | −2.27901 | − | 2.27901i | −0.0284877 | − | 0.0284877i | ||||
\(81\) | −90.1718 | −1.11323 | ||||||||
\(82\) | 67.2819 | + | 67.2819i | 0.820511 | + | 0.820511i | ||||
\(83\) | −74.2334 | −0.894379 | −0.447189 | − | 0.894439i | \(-0.647575\pi\) | ||||
−0.447189 | + | 0.894439i | \(0.647575\pi\) | |||||||
\(84\) | −13.8929 | −0.165392 | ||||||||
\(85\) | 11.3415i | 0.133429i | ||||||||
\(86\) | 85.0740 | 0.989232 | ||||||||
\(87\) | −17.8295 | − | 17.8295i | −0.204936 | − | 0.204936i | ||||
\(88\) | −104.705 | + | 104.705i | −1.18983 | + | 1.18983i | ||||
\(89\) | 57.8946 | − | 57.8946i | 0.650501 | − | 0.650501i | −0.302613 | − | 0.953114i | \(-0.597859\pi\) |
0.953114 | + | 0.302613i | \(0.0978589\pi\) | |||||||
\(90\) | 1.11139 | 0.0123488 | ||||||||
\(91\) | 23.8088 | + | 23.8088i | 0.261635 | + | 0.261635i | ||||
\(92\) | −10.1447 | + | 10.1447i | −0.110268 | + | 0.110268i | ||||
\(93\) | 9.83235 | + | 9.83235i | 0.105724 | + | 0.105724i | ||||
\(94\) | −53.6719 | + | 53.6719i | −0.570978 | + | 0.570978i | ||||
\(95\) | − | 1.35999i | − | 0.0143157i | ||||||
\(96\) | 60.9854 | + | 60.9854i | 0.635264 | + | 0.635264i | ||||
\(97\) | 31.5767 | + | 31.5767i | 0.325533 | + | 0.325533i | 0.850885 | − | 0.525352i | \(-0.176066\pi\) |
−0.525352 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(98\) | −44.9220 | + | 44.9220i | −0.458388 | + | 0.458388i | ||||
\(99\) | − | 20.2633i | − | 0.204680i | ||||||
\(100\) | 46.1969 | 0.461969 | ||||||||
\(101\) | 4.86493i | 0.0481677i | 0.999710 | + | 0.0240838i | \(0.00766686\pi\) | ||||
−0.999710 | + | 0.0240838i | \(0.992333\pi\) | |||||||
\(102\) | 80.8456i | 0.792604i | ||||||||
\(103\) | −31.0988 | + | 31.0988i | −0.301930 | + | 0.301930i | −0.841768 | − | 0.539839i | \(-0.818485\pi\) |
0.539839 | + | 0.841768i | \(0.318485\pi\) | |||||||
\(104\) | − | 124.398i | − | 1.19613i | ||||||
\(105\) | 3.40462 | − | 3.40462i | 0.0324249 | − | 0.0324249i | ||||
\(106\) | 65.4700 | − | 65.4700i | 0.617641 | − | 0.617641i | ||||
\(107\) | 146.876 | 1.37267 | 0.686336 | − | 0.727285i | \(-0.259218\pi\) | ||||
0.686336 | + | 0.727285i | \(0.259218\pi\) | |||||||
\(108\) | 46.9328 | 0.434563 | ||||||||
\(109\) | −94.7493 | − | 94.7493i | −0.869260 | − | 0.869260i | 0.123131 | − | 0.992390i | \(-0.460707\pi\) |
−0.992390 | + | 0.123131i | \(0.960707\pi\) | |||||||
\(110\) | − | 16.4066i | − | 0.149150i | ||||||
\(111\) | −117.375 | − | 12.1694i | −1.05743 | − | 0.109634i | ||||
\(112\) | −11.4645 | −0.102362 | ||||||||
\(113\) | −50.9641 | + | 50.9641i | −0.451010 | + | 0.451010i | −0.895690 | − | 0.444680i | \(-0.853317\pi\) |
0.444680 | + | 0.895690i | \(0.353317\pi\) | |||||||
\(114\) | − | 9.69441i | − | 0.0850387i | ||||||
\(115\) | − | 4.97212i | − | 0.0432358i | ||||||
\(116\) | 10.5088 | + | 10.5088i | 0.0905930 | + | 0.0905930i | ||||
\(117\) | 12.0372 | + | 12.0372i | 0.102882 | + | 0.102882i | ||||
\(118\) | 65.8322 | 0.557900 | ||||||||
\(119\) | 28.5265 | + | 28.5265i | 0.239718 | + | 0.239718i | ||||
\(120\) | −17.7887 | −0.148239 | ||||||||
\(121\) | −178.130 | −1.47215 | ||||||||
\(122\) | − | 172.841i | − | 1.41673i | ||||||
\(123\) | 208.410 | 1.69439 | ||||||||
\(124\) | −5.79524 | − | 5.79524i | −0.0467358 | − | 0.0467358i | ||||
\(125\) | −22.8376 | + | 22.8376i | −0.182701 | + | 0.182701i | ||||
\(126\) | 2.79541 | − | 2.79541i | 0.0221858 | − | 0.0221858i | ||||
\(127\) | −181.574 | −1.42972 | −0.714858 | − | 0.699269i | \(-0.753509\pi\) | ||||
−0.714858 | + | 0.699269i | \(0.753509\pi\) | |||||||
\(128\) | −15.5701 | − | 15.5701i | −0.121641 | − | 0.121641i | ||||
\(129\) | 131.761 | − | 131.761i | 1.02140 | − | 1.02140i | ||||
\(130\) | 9.74616 | + | 9.74616i | 0.0749704 | + | 0.0749704i | ||||
\(131\) | 101.787 | − | 101.787i | 0.776998 | − | 0.776998i | −0.202321 | − | 0.979319i | \(-0.564848\pi\) |
0.979319 | + | 0.202321i | \(0.0648485\pi\) | |||||||
\(132\) | 103.689i | 0.785524i | ||||||||
\(133\) | −3.42068 | − | 3.42068i | −0.0257194 | − | 0.0257194i | ||||
\(134\) | −5.29234 | − | 5.29234i | −0.0394951 | − | 0.0394951i | ||||
\(135\) | −11.5014 | + | 11.5014i | −0.0851955 | + | 0.0851955i | ||||
\(136\) | − | 149.047i | − | 1.09593i | ||||||
\(137\) | −64.4553 | −0.470476 | −0.235238 | − | 0.971938i | \(-0.575587\pi\) | ||||
−0.235238 | + | 0.971938i | \(0.575587\pi\) | |||||||
\(138\) | − | 35.4428i | − | 0.256832i | ||||||
\(139\) | 246.167i | 1.77098i | 0.464655 | + | 0.885492i | \(0.346178\pi\) | ||||
−0.464655 | + | 0.885492i | \(0.653822\pi\) | |||||||
\(140\) | −2.00670 | + | 2.00670i | −0.0143336 | + | 0.0143336i | ||||
\(141\) | 166.252i | 1.17909i | ||||||||
\(142\) | 77.4165 | − | 77.4165i | 0.545186 | − | 0.545186i | ||||
\(143\) | 177.695 | − | 177.695i | 1.24262 | − | 1.24262i | ||||
\(144\) | −5.79621 | −0.0402515 | ||||||||
\(145\) | −5.15059 | −0.0355213 | ||||||||
\(146\) | 68.0437 | + | 68.0437i | 0.466053 | + | 0.466053i | ||||
\(147\) | 139.149i | 0.946589i | ||||||||
\(148\) | 69.1813 | + | 7.17269i | 0.467441 | + | 0.0484641i | ||||
\(149\) | −70.3175 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(150\) | −80.6999 | + | 80.6999i | −0.538000 | + | 0.538000i | ||||
\(151\) | 114.317i | 0.757067i | 0.925588 | + | 0.378533i | \(0.123571\pi\) | ||||
−0.925588 | + | 0.378533i | \(0.876429\pi\) | |||||||
\(152\) | 17.8726i | 0.117583i | ||||||||
\(153\) | 14.4224 | + | 14.4224i | 0.0942640 | + | 0.0942640i | ||||
\(154\) | −41.2663 | − | 41.2663i | −0.267963 | − | 0.267963i | ||||
\(155\) | 2.84037 | 0.0183250 | ||||||||
\(156\) | −61.5956 | − | 61.5956i | −0.394843 | − | 0.394843i | ||||
\(157\) | −43.1093 | −0.274581 | −0.137291 | − | 0.990531i | \(-0.543839\pi\) | ||||
−0.137291 | + | 0.990531i | \(0.543839\pi\) | |||||||
\(158\) | −179.844 | −1.13825 | ||||||||
\(159\) | − | 202.797i | − | 1.27545i | ||||||
\(160\) | 17.6175 | 0.110109 | ||||||||
\(161\) | −12.5060 | − | 12.5060i | −0.0776773 | − | 0.0776773i | ||||
\(162\) | −92.8422 | + | 92.8422i | −0.573100 | + | 0.573100i | ||||
\(163\) | 143.266 | − | 143.266i | 0.878934 | − | 0.878934i | −0.114490 | − | 0.993424i | \(-0.536523\pi\) |
0.993424 | + | 0.114490i | \(0.0365234\pi\) | |||||||
\(164\) | −122.838 | −0.749011 | ||||||||
\(165\) | −25.4102 | − | 25.4102i | −0.154001 | − | 0.154001i | ||||
\(166\) | −76.4318 | + | 76.4318i | −0.460433 | + | 0.460433i | ||||
\(167\) | 109.900 | + | 109.900i | 0.658086 | + | 0.658086i | 0.954927 | − | 0.296841i | \(-0.0959330\pi\) |
−0.296841 | + | 0.954927i | \(0.595933\pi\) | |||||||
\(168\) | −44.7427 | + | 44.7427i | −0.266326 | + | 0.266326i | ||||
\(169\) | 42.1164i | 0.249209i | ||||||||
\(170\) | 11.6773 | + | 11.6773i | 0.0686903 | + | 0.0686903i | ||||
\(171\) | −1.72943 | − | 1.72943i | −0.0101136 | − | 0.0101136i | ||||
\(172\) | −77.6606 | + | 77.6606i | −0.451515 | + | 0.451515i | ||||
\(173\) | 286.598i | 1.65663i | 0.560260 | + | 0.828317i | \(0.310701\pi\) | ||||
−0.560260 | + | 0.828317i | \(0.689299\pi\) | |||||||
\(174\) | −36.7150 | −0.211006 | ||||||||
\(175\) | 56.9501i | 0.325429i | ||||||||
\(176\) | 85.5645i | 0.486162i | ||||||||
\(177\) | 101.960 | − | 101.960i | 0.576043 | − | 0.576043i | ||||
\(178\) | − | 119.218i | − | 0.669765i | ||||||
\(179\) | −116.004 | + | 116.004i | −0.648066 | + | 0.648066i | −0.952525 | − | 0.304459i | \(-0.901524\pi\) |
0.304459 | + | 0.952525i | \(0.401524\pi\) | |||||||
\(180\) | −1.01455 | + | 1.01455i | −0.00563637 | + | 0.00563637i | ||||
\(181\) | 99.6081 | 0.550321 | 0.275160 | − | 0.961398i | \(-0.411269\pi\) | ||||
0.275160 | + | 0.961398i | \(0.411269\pi\) | |||||||
\(182\) | 49.0277 | 0.269383 | ||||||||
\(183\) | −267.693 | − | 267.693i | −1.46280 | − | 1.46280i | ||||
\(184\) | 65.3424i | 0.355122i | ||||||||
\(185\) | −18.7114 | + | 15.1959i | −0.101143 | + | 0.0821399i | ||||
\(186\) | 20.2471 | 0.108855 | ||||||||
\(187\) | 212.905 | − | 212.905i | 1.13853 | − | 1.13853i | ||||
\(188\) | − | 97.9899i | − | 0.521223i | ||||||
\(189\) | 57.8573i | 0.306124i | ||||||||
\(190\) | −1.40026 | − | 1.40026i | −0.00736980 | − | 0.00736980i | ||||
\(191\) | −39.3256 | − | 39.3256i | −0.205893 | − | 0.205893i | 0.596626 | − | 0.802519i | \(-0.296508\pi\) |
−0.802519 | + | 0.596626i | \(0.796508\pi\) | |||||||
\(192\) | 188.696 | 0.982791 | ||||||||
\(193\) | 180.602 | + | 180.602i | 0.935763 | + | 0.935763i | 0.998058 | − | 0.0622950i | \(-0.0198420\pi\) |
−0.0622950 | + | 0.998058i | \(0.519842\pi\) | |||||||
\(194\) | 65.0238 | 0.335174 | ||||||||
\(195\) | 30.1893 | 0.154817 | ||||||||
\(196\) | − | 82.0149i | − | 0.418444i | ||||||
\(197\) | −172.849 | −0.877407 | −0.438704 | − | 0.898632i | \(-0.644562\pi\) | ||||
−0.438704 | + | 0.898632i | \(0.644562\pi\) | |||||||
\(198\) | −20.8634 | − | 20.8634i | −0.105371 | − | 0.105371i | ||||
\(199\) | 149.605 | − | 149.605i | 0.751783 | − | 0.751783i | −0.223029 | − | 0.974812i | \(-0.571595\pi\) |
0.974812 | + | 0.223029i | \(0.0715945\pi\) | |||||||
\(200\) | 148.778 | − | 148.778i | 0.743892 | − | 0.743892i | ||||
\(201\) | −16.3933 | −0.0815589 | ||||||||
\(202\) | 5.00901 | + | 5.00901i | 0.0247971 | + | 0.0247971i | ||||
\(203\) | −12.9549 | + | 12.9549i | −0.0638174 | + | 0.0638174i | ||||
\(204\) | −73.8006 | − | 73.8006i | −0.361768 | − | 0.361768i | ||||
\(205\) | 30.1028 | − | 30.1028i | 0.146843 | − | 0.146843i | ||||
\(206\) | 64.0395i | 0.310871i | ||||||||
\(207\) | −6.32280 | − | 6.32280i | −0.0305449 | − | 0.0305449i | ||||
\(208\) | −50.8288 | − | 50.8288i | −0.244369 | − | 0.244369i | ||||
\(209\) | −25.5301 | + | 25.5301i | −0.122153 | + | 0.122153i | ||||
\(210\) | − | 7.01089i | − | 0.0333852i | ||||||
\(211\) | −108.718 | −0.515249 | −0.257625 | − | 0.966245i | \(-0.582940\pi\) | ||||
−0.257625 | + | 0.966245i | \(0.582940\pi\) | |||||||
\(212\) | 119.530i | 0.563820i | ||||||||
\(213\) | − | 239.802i | − | 1.12583i | ||||||
\(214\) | 151.226 | − | 151.226i | 0.706661 | − | 0.706661i | ||||
\(215\) | − | 38.0632i | − | 0.177038i | ||||||
\(216\) | 151.149 | − | 151.149i | 0.699762 | − | 0.699762i | ||||
\(217\) | 7.14420 | − | 7.14420i | 0.0329226 | − | 0.0329226i | ||||
\(218\) | −195.111 | −0.895003 | ||||||||
\(219\) | 210.770 | 0.962419 | ||||||||
\(220\) | 14.9769 | + | 14.9769i | 0.0680767 | + | 0.0680767i | ||||
\(221\) | 252.949i | 1.14456i | ||||||||
\(222\) | −133.381 | + | 108.321i | −0.600813 | + | 0.487932i | ||||
\(223\) | −21.8699 | −0.0980712 | −0.0490356 | − | 0.998797i | \(-0.515615\pi\) | ||||
−0.0490356 | + | 0.998797i | \(0.515615\pi\) | |||||||
\(224\) | 44.3121 | − | 44.3121i | 0.197822 | − | 0.197822i | ||||
\(225\) | 28.7928i | 0.127968i | ||||||||
\(226\) | 104.947i | 0.464366i | ||||||||
\(227\) | −15.4392 | − | 15.4392i | −0.0680140 | − | 0.0680140i | 0.672282 | − | 0.740296i | \(-0.265314\pi\) |
−0.740296 | + | 0.672282i | \(0.765314\pi\) | |||||||
\(228\) | 8.84964 | + | 8.84964i | 0.0388142 | + | 0.0388142i | ||||
\(229\) | 31.9570 | 0.139550 | 0.0697751 | − | 0.997563i | \(-0.477772\pi\) | ||||
0.0697751 | + | 0.997563i | \(0.477772\pi\) | |||||||
\(230\) | −5.11937 | − | 5.11937i | −0.0222581 | − | 0.0222581i | ||||
\(231\) | −127.825 | −0.553355 | ||||||||
\(232\) | 67.6878 | 0.291758 | ||||||||
\(233\) | − | 3.55985i | − | 0.0152783i | −0.999971 | − | 0.00763915i | \(-0.997568\pi\) | ||
0.999971 | − | 0.00763915i | \(-0.00243164\pi\) | |||||||
\(234\) | 24.7874 | 0.105929 | ||||||||
\(235\) | 24.0135 | + | 24.0135i | 0.102185 | + | 0.102185i | ||||
\(236\) | −60.0956 | + | 60.0956i | −0.254642 | + | 0.254642i | ||||
\(237\) | −278.538 | + | 278.538i | −1.17527 | + | 1.17527i | ||||
\(238\) | 58.7425 | 0.246817 | ||||||||
\(239\) | −13.7258 | − | 13.7258i | −0.0574300 | − | 0.0574300i | 0.677808 | − | 0.735239i | \(-0.262930\pi\) |
−0.735239 | + | 0.677808i | \(0.762930\pi\) | |||||||
\(240\) | −7.26844 | + | 7.26844i | −0.0302852 | + | 0.0302852i | ||||
\(241\) | −82.3328 | − | 82.3328i | −0.341630 | − | 0.341630i | 0.515350 | − | 0.856980i | \(-0.327662\pi\) |
−0.856980 | + | 0.515350i | \(0.827662\pi\) | |||||||
\(242\) | −183.405 | + | 183.405i | −0.757872 | + | 0.757872i | ||||
\(243\) | 62.8808i | 0.258769i | ||||||||
\(244\) | 157.780 | + | 157.780i | 0.646639 | + | 0.646639i | ||||
\(245\) | 20.0987 | + | 20.0987i | 0.0820353 | + | 0.0820353i | ||||
\(246\) | 214.582 | − | 214.582i | 0.872284 | − | 0.872284i | ||||
\(247\) | − | 30.3318i | − | 0.122801i | ||||||
\(248\) | −37.3275 | −0.150514 | ||||||||
\(249\) | 236.752i | 0.950812i | ||||||||
\(250\) | 47.0279i | 0.188111i | ||||||||
\(251\) | −140.696 | + | 140.696i | −0.560540 | + | 0.560540i | −0.929461 | − | 0.368921i | \(-0.879727\pi\) |
0.368921 | + | 0.929461i | \(0.379727\pi\) | |||||||
\(252\) | 5.10364i | 0.0202526i | ||||||||
\(253\) | −93.3381 | + | 93.3381i | −0.368925 | + | 0.368925i | ||||
\(254\) | −186.951 | + | 186.951i | −0.736029 | + | 0.736029i | ||||
\(255\) | 36.1713 | 0.141848 | ||||||||
\(256\) | −268.724 | −1.04970 | ||||||||
\(257\) | −142.782 | − | 142.782i | −0.555571 | − | 0.555571i | 0.372472 | − | 0.928043i | \(-0.378510\pi\) |
−0.928043 | + | 0.372472i | \(0.878510\pi\) | |||||||
\(258\) | − | 271.326i | − | 1.05165i | ||||||
\(259\) | −8.84228 | + | 85.2847i | −0.0341401 | + | 0.329284i | ||||
\(260\) | −17.7937 | −0.0684375 | ||||||||
\(261\) | −6.54975 | + | 6.54975i | −0.0250948 | + | 0.0250948i | ||||
\(262\) | − | 209.602i | − | 0.800009i | ||||||
\(263\) | − | 345.178i | − | 1.31246i | −0.754560 | − | 0.656231i | \(-0.772149\pi\) | ||
0.754560 | − | 0.656231i | \(-0.227851\pi\) | |||||||
\(264\) | 333.934 | + | 333.934i | 1.26490 | + | 1.26490i | ||||
\(265\) | −29.2921 | − | 29.2921i | −0.110536 | − | 0.110536i | ||||
\(266\) | −7.04397 | −0.0264811 | ||||||||
\(267\) | −184.643 | − | 184.643i | −0.691546 | − | 0.691546i | ||||
\(268\) | 9.66232 | 0.0360534 | ||||||||
\(269\) | 175.284 | 0.651613 | 0.325806 | − | 0.945437i | \(-0.394364\pi\) | ||||
0.325806 | + | 0.945437i | \(0.394364\pi\) | |||||||
\(270\) | 23.6840i | 0.0877185i | ||||||||
\(271\) | −426.485 | −1.57374 | −0.786872 | − | 0.617116i | \(-0.788301\pi\) | ||||
−0.786872 | + | 0.617116i | \(0.788301\pi\) | |||||||
\(272\) | −60.9005 | − | 60.9005i | −0.223899 | − | 0.223899i | ||||
\(273\) | 75.9332 | − | 75.9332i | 0.278144 | − | 0.278144i | ||||
\(274\) | −66.3641 | + | 66.3641i | −0.242205 | + | 0.242205i | ||||
\(275\) | 425.044 | 1.54561 | ||||||||
\(276\) | 32.3543 | + | 32.3543i | 0.117226 | + | 0.117226i | ||||
\(277\) | 350.918 | − | 350.918i | 1.26685 | − | 1.26685i | 0.319148 | − | 0.947705i | \(-0.396603\pi\) |
0.947705 | − | 0.319148i | \(-0.103397\pi\) | |||||||
\(278\) | 253.457 | + | 253.457i | 0.911715 | + | 0.911715i | ||||
\(279\) | 3.61196 | − | 3.61196i | 0.0129461 | − | 0.0129461i | ||||
\(280\) | 12.9253i | 0.0461617i | ||||||||
\(281\) | 136.491 | + | 136.491i | 0.485732 | + | 0.485732i | 0.906957 | − | 0.421224i | \(-0.138399\pi\) |
−0.421224 | + | 0.906957i | \(0.638399\pi\) | |||||||
\(282\) | 171.176 | + | 171.176i | 0.607006 | + | 0.607006i | ||||
\(283\) | −129.122 | + | 129.122i | −0.456261 | + | 0.456261i | −0.897426 | − | 0.441165i | \(-0.854565\pi\) |
0.441165 | + | 0.897426i | \(0.354565\pi\) | |||||||
\(284\) | 141.341i | 0.497679i | ||||||||
\(285\) | −4.33740 | −0.0152189 | ||||||||
\(286\) | − | 365.915i | − | 1.27942i | ||||||
\(287\) | − | 151.431i | − | 0.527634i | ||||||
\(288\) | 22.4033 | − | 22.4033i | 0.0777892 | − | 0.0777892i | ||||
\(289\) | 14.0704i | 0.0486864i | ||||||||
\(290\) | −5.30312 | + | 5.30312i | −0.0182866 | + | 0.0182866i | ||||
\(291\) | 100.708 | − | 100.708i | 0.346074 | − | 0.346074i | ||||
\(292\) | −124.229 | −0.425441 | ||||||||
\(293\) | −360.811 | −1.23144 | −0.615719 | − | 0.787966i | \(-0.711134\pi\) | ||||
−0.615719 | + | 0.787966i | \(0.711134\pi\) | |||||||
\(294\) | 143.269 | + | 143.269i | 0.487311 | + | 0.487311i | ||||
\(295\) | − | 29.4542i | − | 0.0998446i | ||||||
\(296\) | 245.900 | − | 199.701i | 0.830745 | − | 0.674665i | ||||
\(297\) | 431.815 | 1.45392 | ||||||||
\(298\) | −72.3999 | + | 72.3999i | −0.242953 | + | 0.242953i | ||||
\(299\) | − | 110.893i | − | 0.370880i | ||||||
\(300\) | − | 147.335i | − | 0.491118i | ||||||
\(301\) | −95.7377 | − | 95.7377i | −0.318066 | − | 0.318066i | ||||
\(302\) | 117.703 | + | 117.703i | 0.389744 | + | 0.389744i | ||||
\(303\) | 15.5157 | 0.0512070 | ||||||||
\(304\) | 7.30274 | + | 7.30274i | 0.0240222 | + | 0.0240222i | ||||
\(305\) | −77.3313 | −0.253545 | ||||||||
\(306\) | 29.6990 | 0.0970556 | ||||||||
\(307\) | 71.7099i | 0.233583i | 0.993156 | + | 0.116791i | \(0.0372609\pi\) | ||||
−0.993156 | + | 0.116791i | \(0.962739\pi\) | |||||||
\(308\) | 75.3407 | 0.244613 | ||||||||
\(309\) | 99.1831 | + | 99.1831i | 0.320981 | + | 0.320981i | ||||
\(310\) | 2.92449 | − | 2.92449i | 0.00943384 | − | 0.00943384i | ||||
\(311\) | −219.160 | + | 219.160i | −0.704693 | + | 0.704693i | −0.965414 | − | 0.260721i | \(-0.916040\pi\) |
0.260721 | + | 0.965414i | \(0.416040\pi\) | |||||||
\(312\) | −396.741 | −1.27161 | ||||||||
\(313\) | −295.783 | − | 295.783i | −0.944995 | − | 0.944995i | 0.0535690 | − | 0.998564i | \(-0.482940\pi\) |
−0.998564 | + | 0.0535690i | \(0.982940\pi\) | |||||||
\(314\) | −44.3860 | + | 44.3860i | −0.141357 | + | 0.141357i | ||||
\(315\) | −1.25070 | − | 1.25070i | −0.00397049 | − | 0.00397049i | ||||
\(316\) | 164.172 | − | 164.172i | 0.519531 | − | 0.519531i | ||||
\(317\) | − | 407.463i | − | 1.28537i | −0.766130 | − | 0.642686i | \(-0.777820\pi\) | ||
0.766130 | − | 0.642686i | \(-0.222180\pi\) | |||||||
\(318\) | −208.803 | − | 208.803i | −0.656613 | − | 0.656613i | ||||
\(319\) | 96.6883 | + | 96.6883i | 0.303098 | + | 0.303098i | ||||
\(320\) | 27.2553 | − | 27.2553i | 0.0851727 | − | 0.0851727i | ||||
\(321\) | − | 468.430i | − | 1.45929i | ||||||
\(322\) | −25.7528 | −0.0799777 | ||||||||
\(323\) | − | 36.3420i | − | 0.112514i | ||||||
\(324\) | − | 169.504i | − | 0.523160i | ||||||
\(325\) | −252.493 | + | 252.493i | −0.776902 | + | 0.776902i | ||||
\(326\) | − | 295.018i | − | 0.904964i | ||||||
\(327\) | −302.184 | + | 302.184i | −0.924109 | + | 0.924109i | ||||
\(328\) | −395.603 | + | 395.603i | −1.20611 | + | 1.20611i | ||||
\(329\) | 120.799 | 0.367170 | ||||||||
\(330\) | −52.3253 | −0.158562 | ||||||||
\(331\) | 438.051 | + | 438.051i | 1.32342 | + | 1.32342i | 0.910990 | + | 0.412428i | \(0.135319\pi\) |
0.412428 | + | 0.910990i | \(0.364681\pi\) | |||||||
\(332\) | − | 139.543i | − | 0.420310i | ||||||
\(333\) | −4.47047 | + | 43.1182i | −0.0134248 | + | 0.129484i | ||||
\(334\) | 226.310 | 0.677575 | ||||||||
\(335\) | −2.36786 | + | 2.36786i | −0.00706823 | + | 0.00706823i | ||||
\(336\) | 36.5637i | 0.108820i | ||||||||
\(337\) | 315.899i | 0.937386i | 0.883361 | + | 0.468693i | \(0.155275\pi\) | ||||
−0.883361 | + | 0.468693i | \(0.844725\pi\) | |||||||
\(338\) | 43.3637 | + | 43.3637i | 0.128295 | + | 0.128295i | ||||
\(339\) | 162.539 | + | 162.539i | 0.479468 | + | 0.479468i | ||||
\(340\) | −21.3196 | −0.0627046 | ||||||||
\(341\) | −53.3203 | − | 53.3203i | −0.156364 | − | 0.156364i | ||||
\(342\) | −3.56129 | −0.0104131 | ||||||||
\(343\) | 214.656 | 0.625818 | ||||||||
\(344\) | 500.217i | 1.45412i | ||||||||
\(345\) | −15.8576 | −0.0459640 | ||||||||
\(346\) | 295.085 | + | 295.085i | 0.852847 | + | 0.852847i | ||||
\(347\) | 246.659 | − | 246.659i | 0.710833 | − | 0.710833i | −0.255876 | − | 0.966709i | \(-0.582364\pi\) |
0.966709 | + | 0.255876i | \(0.0823640\pi\) | |||||||
\(348\) | 33.5156 | − | 33.5156i | 0.0963093 | − | 0.0963093i | ||||
\(349\) | 130.612 | 0.374247 | 0.187124 | − | 0.982336i | \(-0.440084\pi\) | ||||
0.187124 | + | 0.982336i | \(0.440084\pi\) | |||||||
\(350\) | 58.6367 | + | 58.6367i | 0.167533 | + | 0.167533i | ||||
\(351\) | −256.515 | + | 256.515i | −0.730813 | + | 0.730813i | ||||
\(352\) | −330.720 | − | 330.720i | −0.939546 | − | 0.939546i | ||||
\(353\) | −28.0902 | + | 28.0902i | −0.0795757 | + | 0.0795757i | −0.745774 | − | 0.666199i | \(-0.767920\pi\) |
0.666199 | + | 0.745774i | \(0.267920\pi\) | |||||||
\(354\) | − | 209.958i | − | 0.593103i | ||||||
\(355\) | −34.6371 | − | 34.6371i | −0.0975693 | − | 0.0975693i | ||||
\(356\) | 108.829 | + | 108.829i | 0.305701 | + | 0.305701i | ||||
\(357\) | 90.9793 | − | 90.9793i | 0.254844 | − | 0.254844i | ||||
\(358\) | 238.878i | 0.667258i | ||||||||
\(359\) | −105.212 | −0.293071 | −0.146536 | − | 0.989205i | \(-0.546812\pi\) | ||||
−0.146536 | + | 0.989205i | \(0.546812\pi\) | |||||||
\(360\) | 6.53476i | 0.0181521i | ||||||||
\(361\) | − | 356.642i | − | 0.987928i | ||||||
\(362\) | 102.558 | − | 102.558i | 0.283309 | − | 0.283309i | ||||
\(363\) | 568.109i | 1.56504i | ||||||||
\(364\) | −44.7554 | + | 44.7554i | −0.122954 | + | 0.122954i | ||||
\(365\) | 30.4436 | − | 30.4436i | 0.0834072 | − | 0.0834072i | ||||
\(366\) | −551.242 | −1.50613 | ||||||||
\(367\) | 133.934 | 0.364944 | 0.182472 | − | 0.983211i | \(-0.441590\pi\) | ||||
0.182472 | + | 0.983211i | \(0.441590\pi\) | |||||||
\(368\) | 26.6989 | + | 26.6989i | 0.0725513 | + | 0.0725513i | ||||
\(369\) | − | 76.5604i | − | 0.207481i | ||||||
\(370\) | −3.61960 | + | 34.9114i | −0.00978270 | + | 0.0943552i | ||||
\(371\) | −147.353 | −0.397177 | ||||||||
\(372\) | −18.4827 | + | 18.4827i | −0.0496847 | + | 0.0496847i | ||||
\(373\) | 439.758i | 1.17898i | 0.807777 | + | 0.589489i | \(0.200671\pi\) | ||||
−0.807777 | + | 0.589489i | \(0.799329\pi\) | |||||||
\(374\) | − | 438.421i | − | 1.17225i | ||||||
\(375\) | 72.8359 | + | 72.8359i | 0.194229 | + | 0.194229i | ||||
\(376\) | −315.580 | − | 315.580i | −0.839307 | − | 0.839307i | ||||
\(377\) | −114.873 | −0.304704 | ||||||||
\(378\) | 59.5708 | + | 59.5708i | 0.157595 | + | 0.157595i | ||||
\(379\) | 146.226 | 0.385821 | 0.192911 | − | 0.981216i | \(-0.438207\pi\) | ||||
0.192911 | + | 0.981216i | \(0.438207\pi\) | |||||||
\(380\) | 2.55649 | 0.00672760 | ||||||||
\(381\) | 579.093i | 1.51993i | ||||||||
\(382\) | −80.9805 | −0.211991 | ||||||||
\(383\) | −317.388 | − | 317.388i | −0.828690 | − | 0.828690i | 0.158646 | − | 0.987336i | \(-0.449287\pi\) |
−0.987336 | + | 0.158646i | \(0.949287\pi\) | |||||||
\(384\) | −49.6575 | + | 49.6575i | −0.129316 | + | 0.129316i | ||||
\(385\) | −18.4631 | + | 18.4631i | −0.0479560 | + | 0.0479560i | ||||
\(386\) | 371.901 | 0.963475 | ||||||||
\(387\) | −48.4030 | − | 48.4030i | −0.125072 | − | 0.125072i | ||||
\(388\) | −59.3576 | + | 59.3576i | −0.152983 | + | 0.152983i | ||||
\(389\) | 161.952 | + | 161.952i | 0.416328 | + | 0.416328i | 0.883936 | − | 0.467608i | \(-0.154884\pi\) |
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(390\) | 31.0834 | − | 31.0834i | 0.0797010 | − | 0.0797010i | ||||
\(391\) | − | 132.867i | − | 0.339812i | ||||||
\(392\) | −264.132 | − | 264.132i | −0.673805 | − | 0.673805i | ||||
\(393\) | −324.628 | − | 324.628i | −0.826025 | − | 0.826025i | ||||
\(394\) | −177.968 | + | 177.968i | −0.451696 | + | 0.451696i | ||||
\(395\) | 80.4642i | 0.203707i | ||||||||
\(396\) | 38.0907 | 0.0961887 | ||||||||
\(397\) | − | 332.442i | − | 0.837385i | −0.908128 | − | 0.418692i | \(-0.862489\pi\) | ||
0.908128 | − | 0.418692i | \(-0.137511\pi\) | |||||||
\(398\) | − | 308.070i | − | 0.774046i | ||||||
\(399\) | −10.9096 | + | 10.9096i | −0.0273423 | + | 0.0273423i | ||||
\(400\) | − | 121.582i | − | 0.303954i | ||||||
\(401\) | 299.367 | − | 299.367i | 0.746550 | − | 0.746550i | −0.227279 | − | 0.973830i | \(-0.572983\pi\) |
0.973830 | + | 0.227279i | \(0.0729830\pi\) | |||||||
\(402\) | −16.8788 | + | 16.8788i | −0.0419871 | + | 0.0419871i | ||||
\(403\) | 63.3488 | 0.157193 | ||||||||
\(404\) | −9.14504 | −0.0226362 | ||||||||
\(405\) | 41.5387 | + | 41.5387i | 0.102565 | + | 0.102565i | ||||
\(406\) | 26.6772i | 0.0657073i | ||||||||
\(407\) | 636.517 | + | 65.9938i | 1.56392 | + | 0.162147i | ||||
\(408\) | −475.355 | −1.16509 | ||||||||
\(409\) | 98.0164 | − | 98.0164i | 0.239649 | − | 0.239649i | −0.577056 | − | 0.816705i | \(-0.695799\pi\) |
0.816705 | + | 0.577056i | \(0.195799\pi\) | |||||||
\(410\) | − | 61.9885i | − | 0.151191i | ||||||
\(411\) | 205.567i | 0.500163i | ||||||||
\(412\) | −58.4591 | − | 58.4591i | −0.141891 | − | 0.141891i | ||||
\(413\) | −74.0841 | − | 74.0841i | −0.179380 | − | 0.179380i | ||||
\(414\) | −13.0201 | −0.0314495 | ||||||||
\(415\) | 34.1965 | + | 34.1965i | 0.0824013 | + | 0.0824013i | ||||
\(416\) | 392.923 | 0.944525 | ||||||||
\(417\) | 785.098 | 1.88273 | ||||||||
\(418\) | 52.5723i | 0.125771i | ||||||||
\(419\) | 285.321 | 0.680958 | 0.340479 | − | 0.940252i | \(-0.389411\pi\) | ||||
0.340479 | + | 0.940252i | \(0.389411\pi\) | |||||||
\(420\) | 6.39996 | + | 6.39996i | 0.0152380 | + | 0.0152380i | ||||
\(421\) | 515.126 | − | 515.126i | 1.22358 | − | 1.22358i | 0.257227 | − | 0.966351i | \(-0.417191\pi\) |
0.966351 | − | 0.257227i | \(-0.0828087\pi\) | |||||||
\(422\) | −111.937 | + | 111.937i | −0.265254 | + | 0.265254i | ||||
\(423\) | 61.0735 | 0.144382 | ||||||||
\(424\) | 384.949 | + | 384.949i | 0.907900 | + | 0.907900i | ||||
\(425\) | −302.524 | + | 302.524i | −0.711822 | + | 0.711822i | ||||
\(426\) | −246.904 | − | 246.904i | −0.579587 | − | 0.579587i | ||||
\(427\) | −194.506 | + | 194.506i | −0.455518 | + | 0.455518i | ||||
\(428\) | 276.095i | 0.645083i | ||||||||
\(429\) | −566.723 | − | 566.723i | −1.32103 | − | 1.32103i | ||||
\(430\) | −39.1904 | − | 39.1904i | −0.0911404 | − | 0.0911404i | ||||
\(431\) | −200.649 | + | 200.649i | −0.465543 | + | 0.465543i | −0.900467 | − | 0.434924i | \(-0.856775\pi\) |
0.434924 | + | 0.900467i | \(0.356775\pi\) | |||||||
\(432\) | − | 123.518i | − | 0.285922i | ||||||
\(433\) | 764.775 | 1.76622 | 0.883112 | − | 0.469162i | \(-0.155444\pi\) | ||||
0.883112 | + | 0.469162i | \(0.155444\pi\) | |||||||
\(434\) | − | 14.7115i | − | 0.0338976i | ||||||
\(435\) | 16.4267i | 0.0377626i | ||||||||
\(436\) | 178.109 | − | 178.109i | 0.408506 | − | 0.408506i | ||||
\(437\) | 15.9324i | 0.0364586i | ||||||||
\(438\) | 217.012 | − | 217.012i | 0.495460 | − | 0.495460i | ||||
\(439\) | −249.701 | + | 249.701i | −0.568796 | + | 0.568796i | −0.931791 | − | 0.362995i | \(-0.881754\pi\) |
0.362995 | + | 0.931791i | \(0.381754\pi\) | |||||||
\(440\) | 96.4670 | 0.219243 | ||||||||
\(441\) | 51.1169 | 0.115911 | ||||||||
\(442\) | 260.440 | + | 260.440i | 0.589230 | + | 0.589230i | ||||
\(443\) | − | 370.301i | − | 0.835894i | −0.908472 | − | 0.417947i | \(-0.862750\pi\) | ||
0.908472 | − | 0.417947i | \(-0.137250\pi\) | |||||||
\(444\) | 22.8758 | − | 220.640i | 0.0515221 | − | 0.496936i | ||||
\(445\) | −53.3397 | −0.119864 | ||||||||
\(446\) | −22.5175 | + | 22.5175i | −0.0504878 | + | 0.0504878i | ||||
\(447\) | 224.263i | 0.501707i | ||||||||
\(448\) | − | 137.107i | − | 0.306042i | ||||||
\(449\) | −348.300 | − | 348.300i | −0.775724 | − | 0.775724i | 0.203377 | − | 0.979101i | \(-0.434808\pi\) |
−0.979101 | + | 0.203377i | \(0.934808\pi\) | |||||||
\(450\) | 29.6455 | + | 29.6455i | 0.0658789 | + | 0.0658789i | ||||
\(451\) | −1130.20 | −2.50598 | ||||||||
\(452\) | −95.8016 | − | 95.8016i | −0.211951 | − | 0.211951i | ||||
\(453\) | 364.591 | 0.804837 | ||||||||
\(454\) | −31.7928 | −0.0700282 | ||||||||
\(455\) | − | 21.9356i | − | 0.0482101i | ||||||
\(456\) | 57.0011 | 0.125002 | ||||||||
\(457\) | 303.849 | + | 303.849i | 0.664878 | + | 0.664878i | 0.956526 | − | 0.291648i | \(-0.0942035\pi\) |
−0.291648 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(458\) | 32.9034 | − | 32.9034i | 0.0718414 | − | 0.0718414i | ||||
\(459\) | −307.344 | + | 307.344i | −0.669594 | + | 0.669594i | ||||
\(460\) | 9.34653 | 0.0203185 | ||||||||
\(461\) | 344.896 | + | 344.896i | 0.748147 | + | 0.748147i | 0.974131 | − | 0.225984i | \(-0.0725598\pi\) |
−0.225984 | + | 0.974131i | \(0.572560\pi\) | |||||||
\(462\) | −131.610 | + | 131.610i | −0.284871 | + | 0.284871i | ||||
\(463\) | −187.728 | − | 187.728i | −0.405459 | − | 0.405459i | 0.474693 | − | 0.880152i | \(-0.342559\pi\) |
−0.880152 | + | 0.474693i | \(0.842559\pi\) | |||||||
\(464\) | 27.6572 | − | 27.6572i | 0.0596060 | − | 0.0596060i | ||||
\(465\) | − | 9.05879i | − | 0.0194813i | ||||||
\(466\) | −3.66527 | − | 3.66527i | −0.00786538 | − | 0.00786538i | ||||
\(467\) | −623.436 | − | 623.436i | −1.33498 | − | 1.33498i | −0.900851 | − | 0.434129i | \(-0.857056\pi\) |
−0.434129 | − | 0.900851i | \(-0.642944\pi\) | |||||||
\(468\) | −22.6274 | + | 22.6274i | −0.0483492 | + | 0.0483492i | ||||
\(469\) | 11.9114i | 0.0253975i | ||||||||
\(470\) | 49.4493 | 0.105211 | ||||||||
\(471\) | 137.488i | 0.291907i | ||||||||
\(472\) | 387.079i | 0.820084i | ||||||||
\(473\) | −714.532 | + | 714.532i | −1.51064 | + | 1.51064i | ||||
\(474\) | 573.574i | 1.21007i | ||||||||
\(475\) | 36.2765 | − | 36.2765i | 0.0763717 | − | 0.0763717i | ||||
\(476\) | −53.6237 | + | 53.6237i | −0.112655 | + | 0.112655i | ||||
\(477\) | −74.4986 | −0.156181 | ||||||||
\(478\) | −28.2645 | −0.0591308 | ||||||||
\(479\) | 93.9576 | + | 93.9576i | 0.196154 | + | 0.196154i | 0.798349 | − | 0.602195i | \(-0.205707\pi\) |
−0.602195 | + | 0.798349i | \(0.705707\pi\) | |||||||
\(480\) | − | 56.1873i | − | 0.117057i | ||||||
\(481\) | −417.320 | + | 338.914i | −0.867609 | + | 0.704603i | ||||
\(482\) | −169.542 | −0.351747 | ||||||||
\(483\) | −39.8855 | + | 39.8855i | −0.0825786 | + | 0.0825786i | ||||
\(484\) | − | 334.846i | − | 0.691831i | ||||||
\(485\) | − | 29.0924i | − | 0.0599844i | ||||||
\(486\) | 64.7430 | + | 64.7430i | 0.133216 | + | 0.133216i | ||||
\(487\) | 294.207 | + | 294.207i | 0.604121 | + | 0.604121i | 0.941404 | − | 0.337282i | \(-0.109508\pi\) |
−0.337282 | + | 0.941404i | \(0.609508\pi\) | |||||||
\(488\) | 1016.27 | 2.08252 | ||||||||
\(489\) | −456.918 | − | 456.918i | −0.934394 | − | 0.934394i | ||||
\(490\) | 41.3877 | 0.0844648 | ||||||||
\(491\) | 20.4034 | 0.0415549 | 0.0207774 | − | 0.999784i | \(-0.493386\pi\) | ||||
0.0207774 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(492\) | 391.766i | 0.796273i | ||||||||
\(493\) | −137.636 | −0.279180 | ||||||||
\(494\) | −31.2301 | − | 31.2301i | −0.0632187 | − | 0.0632187i | ||||
\(495\) | −9.33455 | + | 9.33455i | −0.0188577 | + | 0.0188577i | ||||
\(496\) | −15.2520 | + | 15.2520i | −0.0307500 | + | 0.0307500i | ||||
\(497\) | −174.241 | −0.350585 | ||||||||
\(498\) | 243.764 | + | 243.764i | 0.489485 | + | 0.489485i | ||||
\(499\) | −203.414 | + | 203.414i | −0.407643 | + | 0.407643i | −0.880916 | − | 0.473273i | \(-0.843073\pi\) |
0.473273 | + | 0.880916i | \(0.343073\pi\) | |||||||
\(500\) | −42.9298 | − | 42.9298i | −0.0858597 | − | 0.0858597i | ||||
\(501\) | 350.505 | − | 350.505i | 0.699611 | − | 0.699611i | ||||
\(502\) | 289.724i | 0.577140i | ||||||||
\(503\) | −328.246 | − | 328.246i | −0.652577 | − | 0.652577i | 0.301036 | − | 0.953613i | \(-0.402668\pi\) |
−0.953613 | + | 0.301036i | \(0.902668\pi\) | |||||||
\(504\) | 16.4364 | + | 16.4364i | 0.0326120 | + | 0.0326120i | ||||
\(505\) | 2.24109 | − | 2.24109i | 0.00443781 | − | 0.00443781i | ||||
\(506\) | 192.205i | 0.379851i | ||||||||
\(507\) | 134.322 | 0.264934 | ||||||||
\(508\) | − | 341.321i | − | 0.671891i | ||||||
\(509\) | − | 234.925i | − | 0.461542i | −0.973008 | − | 0.230771i | \(-0.925875\pi\) | ||
0.973008 | − | 0.230771i | \(-0.0741248\pi\) | |||||||
\(510\) | 37.2425 | − | 37.2425i | 0.0730245 | − | 0.0730245i | ||||
\(511\) | − | 153.146i | − | 0.299698i | ||||||
\(512\) | −214.402 | + | 214.402i | −0.418753 | + | 0.418753i | ||||
\(513\) | 36.8544 | − | 36.8544i | 0.0718410 | − | 0.0718410i | ||||
\(514\) | −294.020 | −0.572024 | ||||||||
\(515\) | 28.6521 | 0.0556351 | ||||||||
\(516\) | 247.683 | + | 247.683i | 0.480005 | + | 0.480005i | ||||
\(517\) | − | 901.576i | − | 1.74386i | ||||||
\(518\) | 78.7062 | + | 96.9145i | 0.151942 | + | 0.187094i | ||||
\(519\) | 914.044 | 1.76116 | ||||||||
\(520\) | −57.3053 | + | 57.3053i | −0.110203 | + | 0.110203i | ||||
\(521\) | 1031.04i | 1.97896i | 0.144678 | + | 0.989479i | \(0.453785\pi\) | ||||
−0.144678 | + | 0.989479i | \(0.546215\pi\) | |||||||
\(522\) | 13.4874i | 0.0258380i | ||||||||
\(523\) | −274.682 | − | 274.682i | −0.525204 | − | 0.525204i | 0.393934 | − | 0.919139i | \(-0.371114\pi\) |
−0.919139 | + | 0.393934i | \(0.871114\pi\) | |||||||
\(524\) | 191.337 | + | 191.337i | 0.365148 | + | 0.365148i | ||||
\(525\) | 181.631 | 0.345963 | ||||||||
\(526\) | −355.400 | − | 355.400i | −0.675666 | − | 0.675666i | ||||
\(527\) | 75.9013 | 0.144025 | ||||||||
\(528\) | 272.891 | 0.516838 | ||||||||
\(529\) | − | 470.751i | − | 0.889889i | ||||||
\(530\) | −60.3191 | −0.113810 | ||||||||
\(531\) | −37.4554 | − | 37.4554i | −0.0705375 | − | 0.0705375i | ||||
\(532\) | 6.43016 | − | 6.43016i | 0.0120868 | − | 0.0120868i | ||||
\(533\) | 671.382 | − | 671.382i | 1.25963 | − | 1.25963i | ||||
\(534\) | −380.222 | −0.712026 | ||||||||
\(535\) | −67.6602 | − | 67.6602i | −0.126468 | − | 0.126468i | ||||
\(536\) | 31.1178 | − | 31.1178i | 0.0580556 | − | 0.0580556i | ||||
\(537\) | 369.970 | + | 369.970i | 0.688958 | + | 0.688958i | ||||
\(538\) | 180.475 | − | 180.475i | 0.335455 | − | 0.335455i | ||||
\(539\) | − | 754.595i | − | 1.39999i | ||||||
\(540\) | −21.6202 | − | 21.6202i | −0.0400373 | − | 0.0400373i | ||||
\(541\) | 175.879 | + | 175.879i | 0.325099 | + | 0.325099i | 0.850719 | − | 0.525620i | \(-0.176167\pi\) |
−0.525620 | + | 0.850719i | \(0.676167\pi\) | |||||||
\(542\) | −439.115 | + | 439.115i | −0.810175 | + | 0.810175i | ||||
\(543\) | − | 317.679i | − | 0.585045i | ||||||
\(544\) | 470.780 | 0.865404 | ||||||||
\(545\) | 87.2949i | 0.160174i | ||||||||
\(546\) | − | 156.364i | − | 0.286381i | ||||||
\(547\) | −292.360 | + | 292.360i | −0.534480 | + | 0.534480i | −0.921902 | − | 0.387423i | \(-0.873365\pi\) |
0.387423 | + | 0.921902i | \(0.373365\pi\) | |||||||
\(548\) | − | 121.162i | − | 0.221099i | ||||||
\(549\) | −98.3385 | + | 98.3385i | −0.179123 | + | 0.179123i | ||||
\(550\) | 437.631 | − | 437.631i | 0.795693 | − | 0.795693i | ||||
\(551\) | 16.5043 | 0.0299533 | ||||||||
\(552\) | 208.396 | 0.377530 | ||||||||
\(553\) | 202.386 | + | 202.386i | 0.365979 | + | 0.365979i | ||||
\(554\) | − | 722.621i | − | 1.30437i | ||||||
\(555\) | 48.4642 | + | 59.6761i | 0.0873228 | + | 0.107524i | ||||
\(556\) | −462.741 | −0.832268 | ||||||||
\(557\) | −327.259 | + | 327.259i | −0.587539 | + | 0.587539i | −0.936964 | − | 0.349425i | \(-0.886377\pi\) |
0.349425 | + | 0.936964i | \(0.386377\pi\) | |||||||
\(558\) | − | 7.43786i | − | 0.0133295i | ||||||
\(559\) | − | 848.923i | − | 1.51865i | ||||||
\(560\) | 5.28126 | + | 5.28126i | 0.00943082 | + | 0.00943082i | ||||
\(561\) | −679.018 | − | 679.018i | −1.21037 | − | 1.21037i | ||||
\(562\) | 281.066 | 0.500117 | ||||||||
\(563\) | −42.5457 | − | 42.5457i | −0.0755696 | − | 0.0755696i | 0.668312 | − | 0.743881i | \(-0.267017\pi\) |
−0.743881 | + | 0.668312i | \(0.767017\pi\) | |||||||
\(564\) | −312.519 | −0.554111 | ||||||||
\(565\) | 46.9545 | 0.0831053 | ||||||||
\(566\) | 265.892i | 0.469773i | ||||||||
\(567\) | 208.959 | 0.368535 | ||||||||
\(568\) | 455.192 | + | 455.192i | 0.801395 | + | 0.801395i | ||||
\(569\) | −641.876 | + | 641.876i | −1.12808 | + | 1.12808i | −0.137587 | + | 0.990490i | \(0.543935\pi\) |
−0.990490 | + | 0.137587i | \(0.956065\pi\) | |||||||
\(570\) | −4.46585 | + | 4.46585i | −0.00783483 | + | 0.00783483i | ||||
\(571\) | 303.084 | 0.530794 | 0.265397 | − | 0.964139i | \(-0.414497\pi\) | ||||
0.265397 | + | 0.964139i | \(0.414497\pi\) | |||||||
\(572\) | 334.029 | + | 334.029i | 0.583967 | + | 0.583967i | ||||
\(573\) | −125.421 | + | 125.421i | −0.218885 | + | 0.218885i | ||||
\(574\) | −155.915 | − | 155.915i | −0.271630 | − | 0.271630i | ||||
\(575\) | 132.627 | − | 132.627i | 0.230656 | − | 0.230656i | ||||
\(576\) | − | 69.3183i | − | 0.120344i | ||||||
\(577\) | 155.193 | + | 155.193i | 0.268965 | + | 0.268965i | 0.828683 | − | 0.559718i | \(-0.189091\pi\) |
−0.559718 | + | 0.828683i | \(0.689091\pi\) | |||||||
\(578\) | 14.4871 | + | 14.4871i | 0.0250641 | + | 0.0250641i | ||||
\(579\) | 575.994 | − | 575.994i | 0.994808 | − | 0.994808i | ||||
\(580\) | − | 9.68200i | − | 0.0166931i | ||||||
\(581\) | 172.025 | 0.296084 | ||||||||
\(582\) | − | 207.380i | − | 0.356323i | ||||||
\(583\) | 1099.76i | 1.88638i | ||||||||
\(584\) | −400.083 | + | 400.083i | −0.685073 | + | 0.685073i | ||||
\(585\) | − | 11.0902i | − | 0.0189576i | ||||||
\(586\) | −371.497 | + | 371.497i | −0.633954 | + | 0.633954i | ||||
\(587\) | −265.166 | + | 265.166i | −0.451730 | + | 0.451730i | −0.895929 | − | 0.444198i | \(-0.853489\pi\) |
0.444198 | + | 0.895929i | \(0.353489\pi\) | |||||||
\(588\) | −261.570 | −0.444847 | ||||||||
\(589\) | −9.10153 | −0.0154525 | ||||||||
\(590\) | −30.3264 | − | 30.3264i | −0.0514007 | − | 0.0514007i | ||||
\(591\) | 551.267i | 0.932770i | ||||||||
\(592\) | 18.8772 | − | 182.072i | 0.0318871 | − | 0.307555i | ||||
\(593\) | 652.633 | 1.10056 | 0.550281 | − | 0.834980i | \(-0.314521\pi\) | ||||
0.550281 | + | 0.834980i | \(0.314521\pi\) | |||||||
\(594\) | 444.603 | − | 444.603i | 0.748489 | − | 0.748489i | ||||
\(595\) | − | 26.2821i | − | 0.0441716i | ||||||
\(596\) | − | 132.182i | − | 0.221782i | ||||||
\(597\) | −477.134 | − | 477.134i | −0.799219 | − | 0.799219i | ||||
\(598\) | −114.177 | − | 114.177i | −0.190932 | − | 0.190932i | ||||
\(599\) | −637.192 | −1.06376 | −0.531880 | − | 0.846820i | \(-0.678514\pi\) | ||||
−0.531880 | + | 0.846820i | \(0.678514\pi\) | |||||||
\(600\) | −474.498 | − | 474.498i | −0.790831 | − | 0.790831i | ||||
\(601\) | 339.622 | 0.565094 | 0.282547 | − | 0.959253i | \(-0.408821\pi\) | ||||
0.282547 | + | 0.959253i | \(0.408821\pi\) | |||||||
\(602\) | −197.146 | −0.327485 | ||||||||
\(603\) | 6.02218i | 0.00998703i | ||||||||
\(604\) | −214.892 | −0.355781 | ||||||||
\(605\) | 82.0577 | + | 82.0577i | 0.135633 | + | 0.135633i | ||||
\(606\) | 15.9752 | − | 15.9752i | 0.0263617 | − | 0.0263617i | ||||
\(607\) | −386.313 | + | 386.313i | −0.636431 | + | 0.636431i | −0.949673 | − | 0.313242i | \(-0.898585\pi\) |
0.313242 | + | 0.949673i | \(0.398585\pi\) | |||||||
\(608\) | −56.4525 | −0.0928495 | ||||||||
\(609\) | 41.3171 | + | 41.3171i | 0.0678441 | + | 0.0678441i | ||||
\(610\) | −79.6215 | + | 79.6215i | −0.130527 | + | 0.130527i | ||||
\(611\) | 535.573 | + | 535.573i | 0.876551 | + | 0.876551i | ||||
\(612\) | −27.1110 | + | 27.1110i | −0.0442991 | + | 0.0442991i | ||||
\(613\) | 289.345i | 0.472015i | 0.971751 | + | 0.236008i | \(0.0758390\pi\) | ||||
−0.971751 | + | 0.236008i | \(0.924161\pi\) | |||||||
\(614\) | 73.8336 | + | 73.8336i | 0.120250 | + | 0.120250i | ||||
\(615\) | −96.0066 | − | 96.0066i | −0.156108 | − | 0.156108i | ||||
\(616\) | 242.637 | − | 242.637i | 0.393891 | − | 0.393891i | ||||
\(617\) | 645.129i | 1.04559i | 0.852459 | + | 0.522795i | \(0.175111\pi\) | ||||
−0.852459 | + | 0.522795i | \(0.824889\pi\) | |||||||
\(618\) | 204.241 | 0.330487 | ||||||||
\(619\) | 304.651i | 0.492166i | 0.969249 | + | 0.246083i | \(0.0791435\pi\) | ||||
−0.969249 | + | 0.246083i | \(0.920856\pi\) | |||||||
\(620\) | 5.33930i | 0.00861177i | ||||||||
\(621\) | 134.740 | − | 134.740i | 0.216973 | − | 0.216973i | ||||
\(622\) | 451.300i | 0.725562i | ||||||||
\(623\) | −134.162 | + | 134.162i | −0.215348 | + | 0.215348i | ||||
\(624\) | −162.108 | + | 162.108i | −0.259789 | + | 0.259789i | ||||
\(625\) | −593.349 | −0.949358 | ||||||||
\(626\) | −609.086 | −0.972981 | ||||||||
\(627\) | 81.4229 | + | 81.4229i | 0.129861 | + | 0.129861i | ||||
\(628\) | − | 81.0363i | − | 0.129039i | ||||||
\(629\) | −500.011 | + | 406.069i | −0.794930 | + | 0.645579i | ||||
\(630\) | −2.57549 | −0.00408807 | ||||||||
\(631\) | 570.848 | − | 570.848i | 0.904673 | − | 0.904673i | −0.0911634 | − | 0.995836i | \(-0.529059\pi\) |
0.995836 | + | 0.0911634i | \(0.0290586\pi\) | |||||||
\(632\) | − | 1057.44i | − | 1.67317i | ||||||
\(633\) | 346.733i | 0.547761i | ||||||||
\(634\) | −419.530 | − | 419.530i | −0.661719 | − | 0.661719i | ||||
\(635\) | 83.6443 | + | 83.6443i | 0.131723 | + | 0.131723i | ||||
\(636\) | 381.216 | 0.599396 | ||||||||
\(637\) | 448.260 | + | 448.260i | 0.703705 | + | 0.703705i | ||||
\(638\) | 199.103 | 0.312074 | ||||||||
\(639\) | −88.0926 | −0.137860 | ||||||||
\(640\) | 14.3451i | 0.0224142i | ||||||||
\(641\) | 142.943 | 0.223000 | 0.111500 | − | 0.993764i | \(-0.464434\pi\) | ||||
0.111500 | + | 0.993764i | \(0.464434\pi\) | |||||||
\(642\) | −482.303 | − | 482.303i | −0.751251 | − | 0.751251i | ||||
\(643\) | 725.814 | − | 725.814i | 1.12879 | − | 1.12879i | 0.138420 | − | 0.990374i | \(-0.455798\pi\) |
0.990374 | − | 0.138420i | \(-0.0442025\pi\) | |||||||
\(644\) | 23.5087 | − | 23.5087i | 0.0365042 | − | 0.0365042i | ||||
\(645\) | −121.395 | −0.188209 | ||||||||
\(646\) | −37.4183 | − | 37.4183i | −0.0579230 | − | 0.0579230i | ||||
\(647\) | 200.699 | − | 200.699i | 0.310200 | − | 0.310200i | −0.534787 | − | 0.844987i | \(-0.679608\pi\) |
0.844987 | + | 0.534787i | \(0.179608\pi\) | |||||||
\(648\) | −545.892 | − | 545.892i | −0.842426 | − | 0.842426i | ||||
\(649\) | −552.922 | + | 552.922i | −0.851960 | + | 0.851960i | ||||
\(650\) | 519.942i | 0.799910i | ||||||||
\(651\) | −22.7850 | − | 22.7850i | −0.0349999 | − | 0.0349999i | ||||
\(652\) | 269.310 | + | 269.310i | 0.413052 | + | 0.413052i | ||||
\(653\) | −441.090 | + | 441.090i | −0.675482 | + | 0.675482i | −0.958975 | − | 0.283492i | \(-0.908507\pi\) |
0.283492 | + | 0.958975i | \(0.408507\pi\) | |||||||
\(654\) | 622.265i | 0.951476i | ||||||||
\(655\) | −93.7787 | −0.143174 | ||||||||
\(656\) | 323.286i | 0.492815i | ||||||||
\(657\) | − | 77.4273i | − | 0.117850i | ||||||
\(658\) | 124.376 | − | 124.376i | 0.189022 | − | 0.189022i | ||||
\(659\) | − | 652.584i | − | 0.990264i | −0.868818 | − | 0.495132i | \(-0.835120\pi\) | ||
0.868818 | − | 0.495132i | \(-0.164880\pi\) | |||||||
\(660\) | 47.7657 | − | 47.7657i | 0.0723723 | − | 0.0723723i | ||||
\(661\) | 182.760 | − | 182.760i | 0.276491 | − | 0.276491i | −0.555216 | − | 0.831706i | \(-0.687364\pi\) |
0.831706 | + | 0.555216i | \(0.187364\pi\) | |||||||
\(662\) | 902.048 | 1.36261 | ||||||||
\(663\) | 806.729 | 1.21679 | ||||||||
\(664\) | −449.403 | − | 449.403i | −0.676812 | − | 0.676812i | ||||
\(665\) | 3.15156i | 0.00473919i | ||||||||
\(666\) | 39.7923 | + | 48.9980i | 0.0597481 | + | 0.0735706i | ||||
\(667\) | 60.3397 | 0.0904643 | ||||||||
\(668\) | −206.589 | + | 206.589i | −0.309266 | + | 0.309266i | ||||
\(669\) | 69.7495i | 0.104259i | ||||||||
\(670\) | 4.87596i | 0.00727756i | ||||||||
\(671\) | 1451.69 | + | 1451.69i | 2.16347 | + | 2.16347i | ||||
\(672\) | −141.324 | − | 141.324i | −0.210304 | − | 0.210304i | ||||
\(673\) | −48.2331 | −0.0716688 | −0.0358344 | − | 0.999358i | \(-0.511409\pi\) | ||||
−0.0358344 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(674\) | 325.254 | + | 325.254i | 0.482573 | + | 0.482573i | ||||
\(675\) | −613.580 | −0.909008 | ||||||||
\(676\) | −79.1699 | −0.117115 | ||||||||
\(677\) | 65.2005i | 0.0963080i | 0.998840 | + | 0.0481540i | \(0.0153338\pi\) | ||||
−0.998840 | + | 0.0481540i | \(0.984666\pi\) | |||||||
\(678\) | 334.706 | 0.493667 | ||||||||
\(679\) | −73.1743 | − | 73.1743i | −0.107768 | − | 0.107768i | ||||
\(680\) | −68.6603 | + | 68.6603i | −0.100971 | + | 0.100971i | ||||
\(681\) | −49.2401 | + | 49.2401i | −0.0723056 | + | 0.0723056i | ||||
\(682\) | −109.799 | −0.160995 | ||||||||
\(683\) | −402.730 | − | 402.730i | −0.589648 | − | 0.589648i | 0.347888 | − | 0.937536i | \(-0.386899\pi\) |
−0.937536 | + | 0.347888i | \(0.886899\pi\) | |||||||
\(684\) | 3.25096 | − | 3.25096i | 0.00475286 | − | 0.00475286i | ||||
\(685\) | 29.6921 | + | 29.6921i | 0.0433462 | + | 0.0433462i | ||||
\(686\) | 221.013 | − | 221.013i | 0.322176 | − | 0.322176i | ||||
\(687\) | − | 101.920i | − | 0.148356i | ||||||
\(688\) | 204.388 | + | 204.388i | 0.297076 | + | 0.297076i | ||||
\(689\) | −653.301 | − | 653.301i | −0.948187 | − | 0.948187i | ||||
\(690\) | −16.3272 | + | 16.3272i | −0.0236626 | + | 0.0236626i | ||||
\(691\) | − | 1143.83i | − | 1.65532i | −0.561227 | − | 0.827662i | \(-0.689671\pi\) | ||
0.561227 | − | 0.827662i | \(-0.310329\pi\) | |||||||
\(692\) | −538.742 | −0.778530 | ||||||||
\(693\) | 46.9571i | 0.0677592i | ||||||||
\(694\) | − | 507.928i | − | 0.731884i | ||||||
\(695\) | 113.400 | − | 113.400i | 0.163165 | − | 0.163165i | ||||
\(696\) | − | 215.876i | − | 0.310167i | ||||||
\(697\) | 804.415 | − | 804.415i | 1.15411 | − | 1.15411i | ||||
\(698\) | 134.480 | − | 134.480i | 0.192665 | − | 0.192665i | ||||
\(699\) | −11.3534 | −0.0162423 | ||||||||
\(700\) | −107.054 | −0.152934 | ||||||||
\(701\) | −798.107 | − | 798.107i | −1.13853 | − | 1.13853i | −0.988715 | − | 0.149811i | \(-0.952133\pi\) |
−0.149811 | − | 0.988715i | \(-0.547867\pi\) | |||||||
\(702\) | 528.224i | 0.752456i | ||||||||
\(703\) | 59.9577 | − | 48.6929i | 0.0852883 | − | 0.0692644i | ||||
\(704\) | −1023.29 | −1.45353 | ||||||||
\(705\) | 76.5861 | − | 76.5861i | 0.108633 | − | 0.108633i | ||||
\(706\) | 57.8442i | 0.0819323i | ||||||||
\(707\) | − | 11.2737i | − | 0.0159459i | ||||||
\(708\) | 191.663 | + | 191.663i | 0.270710 | + | 0.270710i | ||||
\(709\) | 145.383 | + | 145.383i | 0.205054 | + | 0.205054i | 0.802161 | − | 0.597107i | \(-0.203683\pi\) |
−0.597107 | + | 0.802161i | \(0.703683\pi\) | |||||||
\(710\) | −71.3257 | −0.100459 | ||||||||
\(711\) | 102.322 | + | 102.322i | 0.143913 | + | 0.143913i | ||||
\(712\) | 700.977 | 0.984519 | ||||||||
\(713\) | −33.2753 | −0.0466694 | ||||||||
\(714\) | − | 187.347i | − | 0.262391i | ||||||
\(715\) | −163.715 | −0.228972 | ||||||||
\(716\) | −218.063 | − | 218.063i | −0.304557 | − | 0.304557i | ||||
\(717\) | −43.7756 | + | 43.7756i | −0.0610538 | + | 0.0610538i | ||||
\(718\) | −108.328 | + | 108.328i | −0.150875 | + | 0.150875i | ||||
\(719\) | 1231.32 | 1.71254 | 0.856269 | − | 0.516530i | \(-0.172776\pi\) | ||||
0.856269 | + | 0.516530i | \(0.172776\pi\) | |||||||
\(720\) | 2.67010 | + | 2.67010i | 0.00370847 | + | 0.00370847i | ||||
\(721\) | 72.0666 | − | 72.0666i | 0.0999537 | − | 0.0999537i | ||||
\(722\) | −367.204 | − | 367.204i | −0.508593 | − | 0.508593i | ||||
\(723\) | −262.584 | + | 262.584i | −0.363186 | + | 0.363186i | ||||
\(724\) | 187.242i | 0.258621i | ||||||||
\(725\) | −137.388 | − | 137.388i | −0.189500 | − | 0.189500i | ||||
\(726\) | 584.933 | + | 584.933i | 0.805693 | + | 0.805693i | ||||
\(727\) | −26.4537 | + | 26.4537i | −0.0363875 | + | 0.0363875i | −0.725066 | − | 0.688679i | \(-0.758191\pi\) |
0.688679 | + | 0.725066i | \(0.258191\pi\) | |||||||
\(728\) | 288.273i | 0.395979i | ||||||||
\(729\) | −611.001 | −0.838135 | ||||||||
\(730\) | − | 62.6904i | − | 0.0858772i | ||||||
\(731\) | − | 1017.14i | − | 1.39143i | ||||||
\(732\) | 503.206 | − | 503.206i | 0.687441 | − | 0.687441i | ||||
\(733\) | 666.104i | 0.908736i | 0.890814 | + | 0.454368i | \(0.150135\pi\) | ||||
−0.890814 | + | 0.454368i | \(0.849865\pi\) | |||||||
\(734\) | 137.901 | − | 137.901i | 0.187876 | − | 0.187876i | ||||
\(735\) | 64.1005 | − | 64.1005i | 0.0872116 | − | 0.0872116i | ||||
\(736\) | −206.391 | −0.280422 | ||||||||
\(737\) | 88.9002 | 0.120624 | ||||||||
\(738\) | −78.8277 | − | 78.8277i | −0.106813 | − | 0.106813i | ||||
\(739\) | 650.489i | 0.880229i | 0.897942 | + | 0.440114i | \(0.145062\pi\) | ||||
−0.897942 | + | 0.440114i | \(0.854938\pi\) | |||||||
\(740\) | −28.5650 | − | 35.1734i | −0.0386014 | − | 0.0475316i | ||||
\(741\) | −96.7370 | −0.130549 | ||||||||
\(742\) | −151.717 | + | 151.717i | −0.204470 | + | 0.204470i | ||||
\(743\) | − | 68.3034i | − | 0.0919292i | −0.998943 | − | 0.0459646i | \(-0.985364\pi\) | ||
0.998943 | − | 0.0459646i | \(-0.0146361\pi\) | |||||||
\(744\) | 119.048i | 0.160011i | ||||||||
\(745\) | 32.3926 | + | 32.3926i | 0.0434800 | + | 0.0434800i | ||||
\(746\) | 452.782 | + | 452.782i | 0.606946 | + | 0.606946i | ||||
\(747\) | 86.9721 | 0.116429 | ||||||||
\(748\) | 400.217 | + | 400.217i | 0.535049 | + | 0.535049i | ||||
\(749\) | −340.362 | −0.454422 | ||||||||
\(750\) | 149.986 | 0.199981 | ||||||||
\(751\) | − | 484.624i | − | 0.645305i | −0.946518 | − | 0.322652i | \(-0.895426\pi\) | ||
0.946518 | − | 0.322652i | \(-0.104574\pi\) | |||||||
\(752\) | −257.891 | −0.342940 | ||||||||
\(753\) | 448.719 | + | 448.719i | 0.595909 | + | 0.595909i | ||||
\(754\) | −118.275 | + | 118.275i | −0.156864 | + | 0.156864i | ||||
\(755\) | 52.6616 | − | 52.6616i | 0.0697504 | − | 0.0697504i | ||||
\(756\) | −108.760 | −0.143862 | ||||||||
\(757\) | −454.129 | − | 454.129i | −0.599907 | − | 0.599907i | 0.340381 | − | 0.940288i | \(-0.389444\pi\) |
−0.940288 | + | 0.340381i | \(0.889444\pi\) | |||||||
\(758\) | 150.557 | − | 150.557i | 0.198624 | − | 0.198624i | ||||
\(759\) | 297.683 | + | 297.683i | 0.392204 | + | 0.392204i | ||||
\(760\) | 8.23325 | − | 8.23325i | 0.0108332 | − | 0.0108332i | ||||
\(761\) | 124.497i | 0.163596i | 0.996649 | + | 0.0817982i | \(0.0260663\pi\) | ||||
−0.996649 | + | 0.0817982i | \(0.973934\pi\) | |||||||
\(762\) | 596.243 | + | 596.243i | 0.782471 | + | 0.782471i | ||||
\(763\) | 219.567 | + | 219.567i | 0.287768 | + | 0.287768i | ||||
\(764\) | 73.9238 | − | 73.9238i | 0.0967589 | − | 0.0967589i | ||||
\(765\) | − | 13.2877i | − | 0.0173696i | ||||||
\(766\) | −653.575 | −0.853231 | ||||||||
\(767\) | − | 656.916i | − | 0.856475i | ||||||
\(768\) | 857.040i | 1.11594i | ||||||||
\(769\) | 860.893 | − | 860.893i | 1.11950 | − | 1.11950i | 0.127681 | − | 0.991815i | \(-0.459247\pi\) |
0.991815 | − | 0.127681i | \(-0.0407534\pi\) | |||||||
\(770\) | 38.0197i | 0.0493762i | ||||||||
\(771\) | −455.373 | + | 455.373i | −0.590626 | + | 0.590626i | ||||
\(772\) | −339.494 | + | 339.494i | −0.439759 | + | 0.439759i | ||||
\(773\) | 771.283 | 0.997778 | 0.498889 | − | 0.866666i | \(-0.333741\pi\) | ||||
0.498889 | + | 0.866666i | \(0.333741\pi\) | |||||||
\(774\) | −99.6730 | −0.128776 | ||||||||
\(775\) | 75.7646 | + | 75.7646i | 0.0977608 | + | 0.0977608i | ||||
\(776\) | 382.326i | 0.492688i | ||||||||
\(777\) | 271.998 | + | 28.2006i | 0.350062 | + | 0.0362942i | ||||
\(778\) | 333.496 | 0.428657 | ||||||||
\(779\) | −96.4596 | + | 96.4596i | −0.123825 | + | 0.123825i | ||||
\(780\) | 56.7495i | 0.0727558i | ||||||||
\(781\) | 1300.43i | 1.66509i | ||||||||
\(782\) | −136.801 | − | 136.801i | −0.174938 | − | 0.174938i | ||||
\(783\) | −139.576 | − | 139.576i | −0.178258 | − | 0.178258i | ||||
\(784\) | −215.848 | −0.275316 | ||||||||
\(785\) | 19.8588 | + | 19.8588i | 0.0252979 | + | 0.0252979i | ||||
\(786\) | −668.484 | −0.850488 | ||||||||
\(787\) | −623.639 | −0.792425 | −0.396213 | − | 0.918159i | \(-0.629676\pi\) | ||||
−0.396213 | + | 0.918159i | \(0.629676\pi\) | |||||||
\(788\) | − | 324.920i | − | 0.412335i | ||||||
\(789\) | −1100.87 | −1.39528 | ||||||||
\(790\) | 82.8471 | + | 82.8471i | 0.104870 | + | 0.104870i | ||||
\(791\) | 118.101 | − | 118.101i | 0.149307 | − | 0.149307i | ||||
\(792\) | 122.672 | − | 122.672i | 0.154889 | − | 0.154889i | ||||
\(793\) | −1724.72 | −2.17493 | ||||||||
\(794\) | −342.287 | − | 342.287i | −0.431092 | − | 0.431092i | ||||
\(795\) | −93.4211 | + | 93.4211i | −0.117511 | + | 0.117511i | ||||
\(796\) | 281.225 | + | 281.225i | 0.353298 | + | 0.353298i | ||||
\(797\) | −701.754 | + | 701.754i | −0.880495 | + | 0.880495i | −0.993585 | − | 0.113090i | \(-0.963925\pi\) |
0.113090 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(798\) | 22.4653i | 0.0281520i | ||||||||
\(799\) | 641.696 | + | 641.696i | 0.803124 | + | 0.803124i | ||||
\(800\) | 469.932 | + | 469.932i | 0.587415 | + | 0.587415i | ||||
\(801\) | −67.8294 | + | 67.8294i | −0.0846810 | + | 0.0846810i | ||||
\(802\) | − | 616.465i | − | 0.768659i | ||||||
\(803\) | −1142.99 | −1.42340 | ||||||||
\(804\) | − | 30.8160i | − | 0.0383284i | ||||||
\(805\) | 11.5221i | 0.0143132i | ||||||||
\(806\) | 65.2249 | − | 65.2249i | 0.0809242 | − | 0.0809242i | ||||
\(807\) | − | 559.032i | − | 0.692728i | ||||||
\(808\) | −29.4519 | + | 29.4519i | −0.0364504 | + | 0.0364504i | ||||
\(809\) | 132.202 | − | 132.202i | 0.163414 | − | 0.163414i | −0.620663 | − | 0.784077i | \(-0.713137\pi\) |
0.784077 | + | 0.620663i | \(0.213137\pi\) | |||||||
\(810\) | 85.5378 | 0.105602 | ||||||||
\(811\) | −1153.23 | −1.42199 | −0.710995 | − | 0.703198i | \(-0.751755\pi\) | ||||
−0.710995 | + | 0.703198i | \(0.751755\pi\) | |||||||
\(812\) | −24.3525 | − | 24.3525i | −0.0299908 | − | 0.0299908i | ||||
\(813\) | 1360.19i | 1.67305i | ||||||||
\(814\) | 723.315 | − | 587.419i | 0.888594 | − | 0.721645i | ||||
\(815\) | −131.995 | −0.161957 | ||||||||
\(816\) | −194.230 | + | 194.230i | −0.238026 | + | 0.238026i | ||||
\(817\) | 121.968i | 0.149287i | ||||||||
\(818\) | − | 201.838i | − | 0.246746i | ||||||
\(819\) | −27.8944 | − | 27.8944i | −0.0340591 | − | 0.0340591i | ||||
\(820\) | 56.5868 | + | 56.5868i | 0.0690083 | + | 0.0690083i | ||||
\(821\) | 1573.26 | 1.91628 | 0.958138 | − | 0.286307i | \(-0.0924278\pi\) | ||||
0.958138 | + | 0.286307i | \(0.0924278\pi\) | |||||||
\(822\) | 211.655 | + | 211.655i | 0.257487 | + | 0.257487i | ||||
\(823\) | −664.845 | −0.807831 | −0.403915 | − | 0.914796i | \(-0.632351\pi\) | ||||
−0.403915 | + | 0.914796i | \(0.632351\pi\) | |||||||
\(824\) | −376.539 | −0.456964 | ||||||||
\(825\) | − | 1355.59i | − | 1.64314i | ||||||
\(826\) | −152.556 | −0.184693 | ||||||||
\(827\) | −921.316 | − | 921.316i | −1.11405 | − | 1.11405i | −0.992598 | − | 0.121448i | \(-0.961246\pi\) |
−0.121448 | − | 0.992598i | \(-0.538754\pi\) | |||||||
\(828\) | 11.8855 | − | 11.8855i | 0.0143545 | − | 0.0143545i | ||||
\(829\) | −83.2492 | + | 83.2492i | −0.100421 | + | 0.100421i | −0.755532 | − | 0.655111i | \(-0.772622\pi\) |
0.655111 | + | 0.755532i | \(0.272622\pi\) | |||||||
\(830\) | 70.4185 | 0.0848416 | ||||||||
\(831\) | −1119.18 | − | 1119.18i | −1.34679 | − | 1.34679i | ||||
\(832\) | 607.874 | − | 607.874i | 0.730618 | − | 0.730618i | ||||
\(833\) | 537.083 | + | 537.083i | 0.644757 | + | 0.644757i | ||||
\(834\) | 808.349 | − | 808.349i | 0.969243 | − | 0.969243i | ||||
\(835\) | − | 101.254i | − | 0.121262i | ||||||
\(836\) | −47.9911 | − | 47.9911i | −0.0574056 | − | 0.0574056i | ||||
\(837\) | 76.9715 | + | 76.9715i | 0.0919612 | + | 0.0919612i | ||||
\(838\) | 293.771 | − | 293.771i | 0.350562 | − | 0.350562i | ||||
\(839\) | 799.534i | 0.952960i | 0.879185 | + | 0.476480i | \(0.158088\pi\) | ||||
−0.879185 | + | 0.476480i | \(0.841912\pi\) | |||||||
\(840\) | 41.2225 | 0.0490745 | ||||||||
\(841\) | 778.495i | 0.925677i | ||||||||
\(842\) | − | 1060.76i | − | 1.25981i | ||||||
\(843\) | 435.309 | − | 435.309i | 0.516381 | − | 0.516381i | ||||
\(844\) | − | 204.366i | − | 0.242140i | ||||||
\(845\) | 19.4014 | − | 19.4014i | 0.0229603 | − | 0.0229603i | ||||
\(846\) | 62.8822 | − | 62.8822i | 0.0743289 | − | 0.0743289i | ||||
\(847\) | 412.789 | 0.487354 | ||||||||
\(848\) | 314.580 | 0.370967 | ||||||||
\(849\) | 411.808 | + | 411.808i | 0.485050 | + | 0.485050i | ||||
\(850\) | 622.967i | 0.732903i | ||||||||
\(851\) | 219.206 | − | 178.021i | 0.257586 | − | 0.209191i | ||||
\(852\) | 450.777 | 0.529081 | ||||||||
\(853\) | −462.562 | + | 462.562i | −0.542276 | + | 0.542276i | −0.924196 | − | 0.381919i | \(-0.875263\pi\) |
0.381919 | + | 0.924196i | \(0.375263\pi\) | |||||||
\(854\) | 400.533i | 0.469008i | ||||||||
\(855\) | 1.59337i | 0.00186359i | ||||||||
\(856\) | 889.174 | + | 889.174i | 1.03875 | + | 1.03875i | ||||
\(857\) | 325.901 | + | 325.901i | 0.380282 | + | 0.380282i | 0.871204 | − | 0.490922i | \(-0.163340\pi\) |
−0.490922 | + | 0.871204i | \(0.663340\pi\) | |||||||
\(858\) | −1167.01 | −1.36015 | ||||||||
\(859\) | 661.306 | + | 661.306i | 0.769856 | + | 0.769856i | 0.978081 | − | 0.208225i | \(-0.0667687\pi\) |
−0.208225 | + | 0.978081i | \(0.566769\pi\) | |||||||
\(860\) | 71.5506 | 0.0831984 | ||||||||
\(861\) | −482.958 | −0.560927 | ||||||||
\(862\) | 413.182i | 0.479330i | ||||||||
\(863\) | 1231.50 | 1.42699 | 0.713497 | − | 0.700658i | \(-0.247110\pi\) | ||||
0.713497 | + | 0.700658i | \(0.247110\pi\) | |||||||
\(864\) | 477.418 | + | 477.418i | 0.552567 | + | 0.552567i | ||||
\(865\) | 132.025 | − | 132.025i | 0.152630 | − | 0.152630i | ||||
\(866\) | 787.424 | − | 787.424i | 0.909265 | − | 0.909265i | ||||
\(867\) | 44.8745 | 0.0517584 | ||||||||
\(868\) | 13.4296 | + | 13.4296i | 0.0154719 | + | 0.0154719i | ||||
\(869\) | 1510.50 | − | 1510.50i | 1.73820 | − | 1.73820i | ||||
\(870\) | 16.9132 | + | 16.9132i | 0.0194405 | + | 0.0194405i | ||||
\(871\) | −52.8103 | + | 52.8103i | −0.0606318 | + | 0.0606318i | ||||
\(872\) | − | 1147.21i | − | 1.31561i | ||||||
\(873\) | −36.9954 | − | 36.9954i | −0.0423773 | − | 0.0423773i | ||||
\(874\) | 16.4042 | + | 16.4042i | 0.0187691 | + | 0.0187691i | ||||
\(875\) | 52.9226 | − | 52.9226i | 0.0604830 | − | 0.0604830i | ||||
\(876\) | 396.202i | 0.452286i | ||||||||
\(877\) | −63.0445 | −0.0718866 | −0.0359433 | − | 0.999354i | \(-0.511444\pi\) | ||||
−0.0359433 | + | 0.999354i | \(0.511444\pi\) | |||||||
\(878\) | 514.192i | 0.585640i | ||||||||
\(879\) | 1150.73i | 1.30914i | ||||||||
\(880\) | 39.4164 | − | 39.4164i | 0.0447913 | − | 0.0447913i | ||||
\(881\) | − | 1196.99i | − | 1.35867i | −0.733827 | − | 0.679336i | \(-0.762268\pi\) | ||
0.733827 | − | 0.679336i | \(-0.237732\pi\) | |||||||
\(882\) | 52.6307 | − | 52.6307i | 0.0596721 | − | 0.0596721i | ||||
\(883\) | 420.334 | − | 420.334i | 0.476030 | − | 0.476030i | −0.427830 | − | 0.903859i | \(-0.640722\pi\) |
0.903859 | + | 0.427830i | \(0.140722\pi\) | |||||||
\(884\) | −475.490 | −0.537885 | ||||||||
\(885\) | −93.9380 | −0.106145 | ||||||||
\(886\) | −381.267 | − | 381.267i | −0.430324 | − | 0.430324i | ||||
\(887\) | − | 404.749i | − | 0.456312i | −0.973625 | − | 0.228156i | \(-0.926730\pi\) | ||
0.973625 | − | 0.228156i | \(-0.0732696\pi\) | |||||||
\(888\) | −636.904 | − | 784.249i | −0.717235 | − | 0.883163i | ||||
\(889\) | 420.770 | 0.473307 | ||||||||
\(890\) | −54.9193 | + | 54.9193i | −0.0617071 | + | 0.0617071i | ||||
\(891\) | − | 1559.55i | − | 1.75034i | ||||||
\(892\) | − | 41.1107i | − | 0.0460882i | ||||||
\(893\) | −76.9475 | − | 76.9475i | −0.0861674 | − | 0.0861674i | ||||
\(894\) | 230.905 | + | 230.905i | 0.258283 | + | 0.258283i | ||||
\(895\) | 106.877 | 0.119416 | ||||||||
\(896\) | 36.0812 | + | 36.0812i | 0.0402692 | + | 0.0402692i | ||||
\(897\) | −353.671 | −0.394282 | ||||||||
\(898\) | −717.230 | −0.798697 | ||||||||
\(899\) | 34.4696i | 0.0383422i | ||||||||
\(900\) | −54.1244 | −0.0601382 | ||||||||
\(901\) | −782.752 | − | 782.752i | −0.868759 | − | 0.868759i | ||||
\(902\) | −1163.67 | + | 1163.67i | −1.29009 | + | 1.29009i | ||||
\(903\) | −305.336 | + | 305.336i | −0.338135 | + | 0.338135i | ||||
\(904\) | −617.064 | −0.682593 | ||||||||
\(905\) | −45.8857 | − | 45.8857i | −0.0507024 | − | 0.0507024i | ||||
\(906\) | 375.388 | − | 375.388i | 0.414336 | − | 0.414336i | ||||
\(907\) | −268.378 | − | 268.378i | −0.295896 | − | 0.295896i | 0.543508 | − | 0.839404i | \(-0.317096\pi\) |
−0.839404 | + | 0.543508i | \(0.817096\pi\) | |||||||
\(908\) | 29.0224 | − | 29.0224i | 0.0319630 | − | 0.0319630i | ||||
\(909\) | − | 5.69977i | − | 0.00627038i | ||||||
\(910\) | −22.5852 | − | 22.5852i | −0.0248189 | − | 0.0248189i | ||||
\(911\) | 1094.95 | + | 1094.95i | 1.20192 | + | 1.20192i | 0.973581 | + | 0.228342i | \(0.0733305\pi\) |
0.228342 | + | 0.973581i | \(0.426669\pi\) | |||||||
\(912\) | 23.2906 | − | 23.2906i | 0.0255379 | − | 0.0255379i | ||||
\(913\) | − | 1283.89i | − | 1.40624i | ||||||
\(914\) | 625.695 | 0.684568 | ||||||||
\(915\) | 246.632i | 0.269544i | ||||||||
\(916\) | 60.0723i | 0.0655811i | ||||||||
\(917\) | −235.875 | + | 235.875i | −0.257225 | + | 0.257225i | ||||
\(918\) | 632.891i | 0.689424i | ||||||||
\(919\) | −544.251 | + | 544.251i | −0.592221 | + | 0.592221i | −0.938231 | − | 0.346010i | \(-0.887536\pi\) |
0.346010 | + | 0.938231i | \(0.387536\pi\) | |||||||
\(920\) | 30.1008 | − | 30.1008i | 0.0327183 | − | 0.0327183i | ||||
\(921\) | 228.704 | 0.248321 | ||||||||
\(922\) | 710.219 | 0.770303 | ||||||||
\(923\) | −772.511 | − | 772.511i | −0.836957 | − | 0.836957i | ||||
\(924\) | − | 240.284i | − | 0.260047i | ||||||
\(925\) | −904.448 | − | 93.7728i | −0.977782 | − | 0.101376i | ||||
\(926\) | −386.574 | −0.417467 | ||||||||
\(927\) | 36.4354 | − | 36.4354i | 0.0393047 | − | 0.0393047i | ||||
\(928\) | 213.799i | 0.230386i | ||||||||
\(929\) | 811.254i | 0.873255i | 0.899642 | + | 0.436628i | \(0.143827\pi\) | ||||
−0.899642 | + | 0.436628i | \(0.856173\pi\) | |||||||
\(930\) | −9.32706 | − | 9.32706i | −0.0100291 | − | 0.0100291i | ||||
\(931\) | −64.4030 | − | 64.4030i | −0.0691762 | − | 0.0691762i | ||||
\(932\) | 6.69175 | 0.00717999 | ||||||||
\(933\) | 698.965 | + | 698.965i | 0.749158 | + | 0.749158i | ||||
\(934\) | −1283.80 | −1.37451 | ||||||||
\(935\) | −196.155 | −0.209791 | ||||||||
\(936\) | 145.745i | 0.155710i | ||||||||
\(937\) | −734.830 | −0.784237 | −0.392119 | − | 0.919915i | \(-0.628258\pi\) | ||||
−0.392119 | + | 0.919915i | \(0.628258\pi\) | |||||||
\(938\) | 12.2642 | + | 12.2642i | 0.0130748 | + | 0.0130748i | ||||
\(939\) | −943.341 | + | 943.341i | −1.00462 | + | 1.00462i | ||||
\(940\) | −45.1403 | + | 45.1403i | −0.0480215 | + | 0.0480215i | ||||
\(941\) | 1741.80 | 1.85101 | 0.925507 | − | 0.378730i | \(-0.123639\pi\) | ||||
0.925507 | + | 0.378730i | \(0.123639\pi\) | |||||||
\(942\) | 141.560 | + | 141.560i | 0.150276 | + | 0.150276i | ||||
\(943\) | −352.657 | + | 352.657i | −0.373974 | + | 0.373974i | ||||
\(944\) | 158.160 | + | 158.160i | 0.167543 | + | 0.167543i | ||||
\(945\) | 26.6527 | − | 26.6527i | 0.0282039 | − | 0.0282039i | ||||
\(946\) | 1471.39i | 1.55538i | ||||||||
\(947\) | 736.970 | + | 736.970i | 0.778216 | + | 0.778216i | 0.979527 | − | 0.201311i | \(-0.0645203\pi\) |
−0.201311 | + | 0.979527i | \(0.564520\pi\) | |||||||
\(948\) | −523.593 | − | 523.593i | −0.552313 | − | 0.552313i | ||||
\(949\) | 678.984 | − | 678.984i | 0.715473 | − | 0.715473i | ||||
\(950\) | − | 74.7017i | − | 0.0786334i | ||||||
\(951\) | −1299.52 | −1.36648 | ||||||||
\(952\) | 345.393i | 0.362808i | ||||||||
\(953\) | 100.144i | 0.105083i | 0.998619 | + | 0.0525414i | \(0.0167321\pi\) | ||||
−0.998619 | + | 0.0525414i | \(0.983268\pi\) | |||||||
\(954\) | −76.7048 | + | 76.7048i | −0.0804034 | + | 0.0804034i | ||||
\(955\) | 36.2317i | 0.0379389i | ||||||||
\(956\) | 25.8015 | − | 25.8015i | 0.0269891 | − | 0.0269891i | ||||
\(957\) | 308.367 | − | 308.367i | 0.322223 | − | 0.322223i | ||||
\(958\) | 193.480 | 0.201963 | ||||||||
\(959\) | 149.365 | 0.155751 | ||||||||
\(960\) | −86.9251 | − | 86.9251i | −0.0905470 | − | 0.0905470i | ||||
\(961\) | 941.991i | 0.980220i | ||||||||
\(962\) | −80.7279 | + | 778.629i | −0.0839168 | + | 0.809386i | ||||
\(963\) | −172.080 | −0.178692 | ||||||||
\(964\) | 154.768 | − | 154.768i | 0.160548 | − | 0.160548i | ||||
\(965\) | − | 166.393i | − | 0.172428i | ||||||
\(966\) | 82.1333i | 0.0850241i | ||||||||
\(967\) | −121.105 | − | 121.105i | −0.125238 | − | 0.125238i | 0.641710 | − | 0.766948i | \(-0.278225\pi\) |
−0.766948 | + | 0.641710i | \(0.778225\pi\) | |||||||
\(968\) | −1078.38 | − | 1078.38i | −1.11403 | − | 1.11403i | ||||
\(969\) | −115.905 | −0.119613 | ||||||||
\(970\) | −29.9540 | − | 29.9540i | −0.0308804 | − | 0.0308804i | ||||
\(971\) | −127.750 | −0.131565 | −0.0657826 | − | 0.997834i | \(-0.520954\pi\) | ||||
−0.0657826 | + | 0.997834i | \(0.520954\pi\) | |||||||
\(972\) | −118.203 | −0.121608 | ||||||||
\(973\) | − | 570.454i | − | 0.586283i | ||||||
\(974\) | 605.840 | 0.622012 | ||||||||
\(975\) | 805.275 | + | 805.275i | 0.825924 | + | 0.825924i | ||||
\(976\) | 415.247 | − | 415.247i | 0.425458 | − | 0.425458i | ||||
\(977\) | −115.752 | + | 115.752i | −0.118477 | + | 0.118477i | −0.763860 | − | 0.645383i | \(-0.776698\pi\) |
0.645383 | + | 0.763860i | \(0.276698\pi\) | |||||||
\(978\) | −940.900 | −0.962065 | ||||||||
\(979\) | 1001.31 | + | 1001.31i | 1.02279 | + | 1.02279i | ||||
\(980\) | −37.7812 | + | 37.7812i | −0.0385522 | + | 0.0385522i | ||||
\(981\) | 111.009 | + | 111.009i | 0.113159 | + | 0.113159i | ||||
\(982\) | 21.0077 | − | 21.0077i | 0.0213927 | − | 0.0213927i | ||||
\(983\) | 27.4845i | 0.0279598i | 0.999902 | + | 0.0139799i | \(0.00445008\pi\) | ||||
−0.999902 | + | 0.0139799i | \(0.995550\pi\) | |||||||
\(984\) | 1261.70 | + | 1261.70i | 1.28221 | + | 1.28221i | ||||
\(985\) | 79.6251 | + | 79.6251i | 0.0808377 | + | 0.0808377i | ||||
\(986\) | −141.712 | + | 141.712i | −0.143724 | + | 0.143724i | ||||
\(987\) | − | 385.264i | − | 0.390338i | ||||||
\(988\) | 57.0173 | 0.0577098 | ||||||||
\(989\) | 445.914i | 0.450874i | ||||||||
\(990\) | 19.2220i | 0.0194161i | ||||||||
\(991\) | 147.450 | − | 147.450i | 0.148790 | − | 0.148790i | −0.628788 | − | 0.777577i | \(-0.716448\pi\) |
0.777577 | + | 0.628788i | \(0.216448\pi\) | |||||||
\(992\) | − | 117.903i | − | 0.118853i | ||||||
\(993\) | 1397.08 | − | 1397.08i | 1.40692 | − | 1.40692i | ||||
\(994\) | −179.401 | + | 179.401i | −0.180484 | + | 0.180484i | ||||
\(995\) | −137.835 | −0.138527 | ||||||||
\(996\) | −445.044 | −0.446831 | ||||||||
\(997\) | −345.971 | − | 345.971i | −0.347012 | − | 0.347012i | 0.511984 | − | 0.858995i | \(-0.328911\pi\) |
−0.858995 | + | 0.511984i | \(0.828911\pi\) | |||||||
\(998\) | 418.876i | 0.419716i | ||||||||
\(999\) | −918.856 | − | 95.2666i | −0.919776 | − | 0.0953620i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 37.3.d.a.6.5 | ✓ | 12 | |
3.2 | odd | 2 | 333.3.i.a.154.2 | 12 | |||
4.3 | odd | 2 | 592.3.k.e.561.5 | 12 | |||
37.31 | odd | 4 | inner | 37.3.d.a.31.5 | yes | 12 | |
111.68 | even | 4 | 333.3.i.a.253.2 | 12 | |||
148.31 | even | 4 | 592.3.k.e.401.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.3.d.a.6.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
37.3.d.a.31.5 | yes | 12 | 37.31 | odd | 4 | inner | |
333.3.i.a.154.2 | 12 | 3.2 | odd | 2 | |||
333.3.i.a.253.2 | 12 | 111.68 | even | 4 | |||
592.3.k.e.401.2 | 12 | 148.31 | even | 4 | |||
592.3.k.e.561.5 | 12 | 4.3 | odd | 2 |