Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(146,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 146.4 | ||
Character | \(\chi\) | \(=\) | 441.146 |
Dual form | 441.2.o.e.293.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05485 | − | 1.18637i | −1.45300 | − | 0.838890i | −0.454350 | − | 0.890823i | \(-0.650129\pi\) |
−0.998651 | + | 0.0519328i | \(0.983462\pi\) | |||||||
\(3\) | 1.27902 | + | 1.16795i | 0.738445 | + | 0.674314i | ||||
\(4\) | 1.81495 | + | 3.14358i | 0.907474 | + | 1.57179i | ||||
\(5\) | 1.71774 | + | 2.97522i | 0.768198 | + | 1.33056i | 0.938539 | + | 0.345172i | \(0.112180\pi\) |
−0.170342 | + | 0.985385i | \(0.554487\pi\) | |||||||
\(6\) | −1.24259 | − | 3.91735i | −0.507285 | − | 1.59925i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 3.86732i | − | 1.36730i | ||||||
\(9\) | 0.271802 | + | 2.98766i | 0.0906007 | + | 0.995887i | ||||
\(10\) | − | 8.15151i | − | 2.57773i | ||||||
\(11\) | 0.271895 | + | 0.156979i | 0.0819795 | + | 0.0473309i | 0.540429 | − | 0.841389i | \(-0.318262\pi\) |
−0.458450 | + | 0.888720i | \(0.651595\pi\) | |||||||
\(12\) | −1.35017 | + | 6.14048i | −0.389762 | + | 1.77260i | ||||
\(13\) | 5.09882 | − | 2.94381i | 1.41416 | − | 0.816465i | 0.418383 | − | 0.908271i | \(-0.362597\pi\) |
0.995777 | + | 0.0918054i | \(0.0292638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.27786 | + | 5.81160i | −0.329942 | + | 1.50055i | ||||
\(16\) | −0.958178 | + | 1.65961i | −0.239545 | + | 0.414903i | ||||
\(17\) | −0.953423 | −0.231239 | −0.115620 | − | 0.993294i | \(-0.536885\pi\) | ||||
−0.115620 | + | 0.993294i | \(0.536885\pi\) | |||||||
\(18\) | 2.98596 | − | 6.46167i | 0.703797 | − | 1.52303i | ||||
\(19\) | − | 1.26109i | − | 0.289314i | −0.989482 | − | 0.144657i | \(-0.953792\pi\) | ||
0.989482 | − | 0.144657i | \(-0.0462079\pi\) | |||||||
\(20\) | −6.23523 | + | 10.7997i | −1.39424 | + | 2.41489i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.372470 | − | 0.645137i | −0.0794108 | − | 0.137544i | ||||
\(23\) | −5.91336 | + | 3.41408i | −1.23302 | + | 0.711884i | −0.967658 | − | 0.252265i | \(-0.918825\pi\) |
−0.265362 | + | 0.964149i | \(0.585491\pi\) | |||||||
\(24\) | 4.51682 | − | 4.94639i | 0.921993 | − | 1.00968i | ||||
\(25\) | −3.40128 | + | 5.89118i | −0.680255 | + | 1.17824i | ||||
\(26\) | −13.9698 | −2.73970 | ||||||||
\(27\) | −3.14179 | + | 4.13874i | −0.604637 | + | 0.796501i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43518 | + | 1.98330i | 0.637897 | + | 0.368290i | 0.783804 | − | 0.621008i | \(-0.213277\pi\) |
−0.145907 | + | 0.989298i | \(0.546610\pi\) | |||||||
\(30\) | 9.52053 | − | 10.4260i | 1.73820 | − | 1.90351i | ||||
\(31\) | −4.53388 | + | 2.61764i | −0.814309 | + | 0.470141i | −0.848450 | − | 0.529276i | \(-0.822464\pi\) |
0.0341412 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(32\) | −2.76057 | + | 1.59381i | −0.488004 | + | 0.281749i | ||||
\(33\) | 0.164418 | + | 0.518338i | 0.0286214 | + | 0.0902311i | ||||
\(34\) | 1.95915 | + | 1.13111i | 0.335991 | + | 0.193984i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.89866 | + | 6.27688i | −1.48311 | + | 1.04615i | ||||
\(37\) | 5.37604 | 0.883816 | 0.441908 | − | 0.897060i | \(-0.354302\pi\) | ||||
0.441908 | + | 0.897060i | \(0.354302\pi\) | |||||||
\(38\) | −1.49612 | + | 2.59136i | −0.242703 | + | 0.420374i | ||||
\(39\) | 9.95973 | + | 2.18996i | 1.59483 | + | 0.350673i | ||||
\(40\) | 11.5061 | − | 6.64306i | 1.81928 | − | 1.05036i | ||||
\(41\) | −0.0699627 | − | 0.121179i | −0.0109263 | − | 0.0189250i | 0.860511 | − | 0.509433i | \(-0.170145\pi\) |
−0.871437 | + | 0.490508i | \(0.836811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44078 | − | 2.49550i | 0.219716 | − | 0.380560i | −0.735005 | − | 0.678062i | \(-0.762820\pi\) |
0.954721 | + | 0.297502i | \(0.0961535\pi\) | |||||||
\(44\) | 1.13963i | 0.171806i | ||||||||
\(45\) | −8.42206 | + | 5.94070i | −1.25549 | + | 0.885588i | ||||
\(46\) | 16.2014 | 2.38877 | ||||||||
\(47\) | 1.00695 | − | 1.74409i | 0.146879 | − | 0.254402i | −0.783193 | − | 0.621778i | \(-0.786411\pi\) |
0.930072 | + | 0.367376i | \(0.119744\pi\) | |||||||
\(48\) | −3.16387 | + | 1.00358i | −0.456666 | + | 0.144855i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.9783 | − | 8.07035i | 1.97682 | − | 1.14132i | ||||
\(51\) | −1.21945 | − | 1.11355i | −0.170757 | − | 0.155928i | ||||
\(52\) | 18.5082 | + | 10.6857i | 2.56663 | + | 1.48184i | ||||
\(53\) | − | 11.9799i | − | 1.64557i | −0.568351 | − | 0.822786i | \(-0.692418\pi\) | ||
0.568351 | − | 0.822786i | \(-0.307582\pi\) | |||||||
\(54\) | 11.3660 | − | 4.77718i | 1.54672 | − | 0.650092i | ||||
\(55\) | 1.07860i | 0.145438i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.47289 | − | 1.61297i | 0.195089 | − | 0.213643i | ||||
\(58\) | −4.70586 | − | 8.15079i | −0.617910 | − | 1.07025i | ||||
\(59\) | −0.824459 | − | 1.42801i | −0.107335 | − | 0.185910i | 0.807355 | − | 0.590067i | \(-0.200899\pi\) |
−0.914690 | + | 0.404156i | \(0.867565\pi\) | |||||||
\(60\) | −20.5885 | + | 6.53070i | −2.65796 | + | 0.843109i | ||||
\(61\) | −2.57423 | − | 1.48623i | −0.329597 | − | 0.190293i | 0.326065 | − | 0.945347i | \(-0.394277\pi\) |
−0.655662 | + | 0.755055i | \(0.727610\pi\) | |||||||
\(62\) | 12.4219 | 1.57759 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.3961 | 1.42452 | ||||||||
\(65\) | 17.5169 | + | 10.1134i | 2.17271 | + | 1.25441i | ||||
\(66\) | 0.277087 | − | 1.26017i | 0.0341071 | − | 0.155116i | ||||
\(67\) | 0.934059 | + | 1.61784i | 0.114113 | + | 0.197650i | 0.917425 | − | 0.397909i | \(-0.130264\pi\) |
−0.803312 | + | 0.595559i | \(0.796931\pi\) | |||||||
\(68\) | −1.73041 | − | 2.99717i | −0.209844 | − | 0.363460i | ||||
\(69\) | −11.5508 | − | 2.53980i | −1.39055 | − | 0.305756i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9981i | 1.30524i | 0.757686 | + | 0.652619i | \(0.226330\pi\) | ||||
−0.757686 | + | 0.652619i | \(0.773670\pi\) | |||||||
\(72\) | 11.5542 | − | 1.05115i | 1.36168 | − | 0.123879i | ||||
\(73\) | 0.409520i | 0.0479307i | 0.999713 | + | 0.0239653i | \(0.00762914\pi\) | ||||
−0.999713 | + | 0.0239653i | \(0.992371\pi\) | |||||||
\(74\) | −11.0470 | − | 6.37798i | −1.28419 | − | 0.741425i | ||||
\(75\) | −11.2309 | + | 3.56245i | −1.29683 | + | 0.411357i | ||||
\(76\) | 3.96435 | − | 2.28882i | 0.454742 | − | 0.262545i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17.8677 | − | 16.3160i | −2.02312 | − | 1.84742i | ||||
\(79\) | −5.23325 | + | 9.06426i | −0.588787 | + | 1.01981i | 0.405605 | + | 0.914049i | \(0.367061\pi\) |
−0.994392 | + | 0.105760i | \(0.966272\pi\) | |||||||
\(80\) | −6.58361 | −0.736070 | ||||||||
\(81\) | −8.85225 | + | 1.62411i | −0.983583 | + | 0.180456i | ||||
\(82\) | 0.332007i | 0.0366640i | ||||||||
\(83\) | 4.00094 | − | 6.92984i | 0.439161 | − | 0.760649i | −0.558464 | − | 0.829529i | \(-0.688609\pi\) |
0.997625 | + | 0.0688800i | \(0.0219426\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.63774 | − | 2.83664i | −0.177637 | − | 0.307677i | ||||
\(86\) | −5.92117 | + | 3.41859i | −0.638496 | + | 0.368636i | ||||
\(87\) | 2.07729 | + | 6.54880i | 0.222708 | + | 0.702105i | ||||
\(88\) | 0.607087 | − | 1.05151i | 0.0647157 | − | 0.112091i | ||||
\(89\) | 2.11862 | 0.224574 | 0.112287 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112287 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(90\) | 24.3540 | − | 2.21560i | 2.56713 | − | 0.233545i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.4649 | − | 12.3927i | −2.23787 | − | 1.29203i | ||||
\(93\) | −8.85620 | − | 1.94731i | −0.918345 | − | 0.201927i | ||||
\(94\) | −4.13828 | + | 2.38924i | −0.426831 | + | 0.246431i | ||||
\(95\) | 3.75202 | − | 2.16623i | 0.384949 | − | 0.222251i | ||||
\(96\) | −5.39232 | − | 1.18567i | −0.550351 | − | 0.121012i | ||||
\(97\) | −10.5054 | − | 6.06531i | −1.06666 | − | 0.615839i | −0.139396 | − | 0.990237i | \(-0.544516\pi\) |
−0.927268 | + | 0.374398i | \(0.877850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.395098 | + | 0.854998i | −0.0397088 | + | 0.0859305i | ||||
\(100\) | −24.6926 | −2.46926 | ||||||||
\(101\) | 6.26039 | − | 10.8433i | 0.622932 | − | 1.07895i | −0.366005 | − | 0.930613i | \(-0.619275\pi\) |
0.988937 | − | 0.148337i | \(-0.0473920\pi\) | |||||||
\(102\) | 1.18471 | + | 3.73490i | 0.117304 | + | 0.369810i | ||||
\(103\) | 15.6040 | − | 9.00897i | 1.53751 | − | 0.887680i | 0.538523 | − | 0.842611i | \(-0.318983\pi\) |
0.998984 | − | 0.0450689i | \(-0.0143507\pi\) | |||||||
\(104\) | −11.3847 | − | 19.7188i | −1.11636 | − | 1.93359i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.2127 | + | 24.6170i | −1.38046 | + | 2.39102i | ||||
\(107\) | 3.59816i | 0.347848i | 0.984759 | + | 0.173924i | \(0.0556447\pi\) | ||||
−0.984759 | + | 0.173924i | \(0.944355\pi\) | |||||||
\(108\) | −18.7127 | − | 2.36487i | −1.80063 | − | 0.227560i | ||||
\(109\) | −6.56218 | −0.628543 | −0.314271 | − | 0.949333i | \(-0.601760\pi\) | ||||
−0.314271 | + | 0.949333i | \(0.601760\pi\) | |||||||
\(110\) | 1.27961 | − | 2.21636i | 0.122006 | − | 0.211321i | ||||
\(111\) | 6.87609 | + | 6.27893i | 0.652649 | + | 0.595970i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.87912 | + | 1.08491i | −0.176773 | + | 0.102060i | −0.585775 | − | 0.810473i | \(-0.699210\pi\) |
0.409003 | + | 0.912533i | \(0.365877\pi\) | |||||||
\(114\) | −4.94014 | + | 1.56702i | −0.462687 | + | 0.146765i | ||||
\(115\) | −20.3152 | − | 11.7290i | −1.89441 | − | 1.09374i | ||||
\(116\) | 14.3984i | 1.33685i | ||||||||
\(117\) | 10.1810 | + | 14.4334i | 0.941231 | + | 1.33437i | ||||
\(118\) | 3.91246i | 0.360171i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 22.4753 | + | 4.94190i | 2.05171 | + | 0.451132i | ||||
\(121\) | −5.45072 | − | 9.44092i | −0.495520 | − | 0.858265i | ||||
\(122\) | 3.52645 | + | 6.10798i | 0.319269 | + | 0.552991i | ||||
\(123\) | 0.0520466 | − | 0.236703i | 0.00469288 | − | 0.0213428i | ||||
\(124\) | −16.4575 | − | 9.50175i | −1.47793 | − | 0.853282i | ||||
\(125\) | −6.19265 | −0.553887 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.34967 | 0.208499 | 0.104250 | − | 0.994551i | \(-0.466756\pi\) | ||||
0.104250 | + | 0.994551i | \(0.466756\pi\) | |||||||
\(128\) | −17.8962 | − | 10.3324i | −1.58182 | − | 0.913263i | ||||
\(129\) | 4.75740 | − | 1.50905i | 0.418865 | − | 0.132865i | ||||
\(130\) | −23.9965 | − | 41.5631i | −2.10463 | − | 3.64533i | ||||
\(131\) | −4.74594 | − | 8.22021i | −0.414655 | − | 0.718203i | 0.580737 | − | 0.814091i | \(-0.302764\pi\) |
−0.995392 | + | 0.0958879i | \(0.969431\pi\) | |||||||
\(132\) | −1.33103 | + | 1.45762i | −0.115851 | + | 0.126869i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 4.43256i | − | 0.382915i | ||||||
\(135\) | −17.7104 | − | 2.23821i | −1.52427 | − | 0.192635i | ||||
\(136\) | 3.68719i | 0.316174i | ||||||||
\(137\) | 8.85456 | + | 5.11218i | 0.756496 | + | 0.436763i | 0.828036 | − | 0.560674i | \(-0.189458\pi\) |
−0.0715401 | + | 0.997438i | \(0.522791\pi\) | |||||||
\(138\) | 20.7220 | + | 18.9224i | 1.76398 | + | 1.61078i | ||||
\(139\) | −4.56556 | + | 2.63593i | −0.387246 | + | 0.223577i | −0.680966 | − | 0.732315i | \(-0.738440\pi\) |
0.293720 | + | 0.955891i | \(0.405107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.32492 | − | 1.05467i | 0.280009 | − | 0.0888192i | ||||
\(142\) | 13.0479 | − | 22.5996i | 1.09495 | − | 1.89651i | ||||
\(143\) | 1.84846 | 0.154576 | ||||||||
\(144\) | −5.21880 | − | 2.41163i | −0.434900 | − | 0.200969i | ||||
\(145\) | 13.6272i | 1.13168i | ||||||||
\(146\) | 0.485842 | − | 0.841504i | 0.0402086 | − | 0.0696433i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.75724 | + | 16.9000i | 0.802040 | + | 1.38917i | ||||
\(149\) | 15.8151 | − | 9.13086i | 1.29562 | − | 0.748029i | 0.315979 | − | 0.948766i | \(-0.397667\pi\) |
0.979645 | + | 0.200737i | \(0.0643338\pi\) | |||||||
\(150\) | 27.3042 | + | 6.00369i | 2.22938 | + | 0.490199i | ||||
\(151\) | −11.5551 | + | 20.0140i | −0.940340 | + | 1.62872i | −0.175517 | + | 0.984476i | \(0.556160\pi\) |
−0.764823 | + | 0.644240i | \(0.777174\pi\) | |||||||
\(152\) | −4.87705 | −0.395581 | ||||||||
\(153\) | −0.259142 | − | 2.84851i | −0.0209504 | − | 0.230288i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5761 | − | 8.99285i | −1.25110 | − | 0.722323i | ||||
\(156\) | 11.1921 | + | 35.2839i | 0.896084 | + | 2.82497i | ||||
\(157\) | 5.65459 | − | 3.26468i | 0.451286 | − | 0.260550i | −0.257087 | − | 0.966388i | \(-0.582763\pi\) |
0.708373 | + | 0.705838i | \(0.249430\pi\) | |||||||
\(158\) | 21.5071 | − | 12.4172i | 1.71102 | − | 0.987855i | ||||
\(159\) | 13.9919 | − | 15.3226i | 1.10963 | − | 1.21516i | ||||
\(160\) | −9.48388 | − | 5.47552i | −0.749767 | − | 0.432878i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 20.1169 | + | 7.16474i | 1.58053 | + | 0.562915i | ||||
\(163\) | 24.5246 | 1.92091 | 0.960457 | − | 0.278428i | \(-0.0898133\pi\) | ||||
0.960457 | + | 0.278428i | \(0.0898133\pi\) | |||||||
\(164\) | 0.253957 | − | 0.439867i | 0.0198307 | − | 0.0343478i | ||||
\(165\) | −1.25974 | + | 1.37955i | −0.0980708 | + | 0.107398i | ||||
\(166\) | −16.4427 | + | 9.49320i | −1.27620 | + | 0.736815i | ||||
\(167\) | −6.99871 | − | 12.1221i | −0.541576 | − | 0.938037i | −0.998814 | − | 0.0486928i | \(-0.984494\pi\) |
0.457238 | − | 0.889345i | \(-0.348839\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8320 | − | 18.7616i | 0.833232 | − | 1.44320i | ||||
\(170\) | 7.77184i | 0.596073i | ||||||||
\(171\) | 3.76772 | − | 0.342767i | 0.288124 | − | 0.0262121i | ||||
\(172\) | 10.4597 | 0.797548 | ||||||||
\(173\) | 5.44974 | − | 9.43923i | 0.414336 | − | 0.717651i | −0.581022 | − | 0.813888i | \(-0.697347\pi\) |
0.995359 | + | 0.0962363i | \(0.0306805\pi\) | |||||||
\(174\) | 3.50078 | − | 15.9212i | 0.265394 | − | 1.20699i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.521048 | + | 0.300827i | −0.0392755 | + | 0.0226757i | ||||
\(177\) | 0.613331 | − | 2.78938i | 0.0461008 | − | 0.209662i | ||||
\(178\) | −4.35346 | − | 2.51347i | −0.326306 | − | 0.188393i | ||||
\(179\) | − | 1.59945i | − | 0.119549i | −0.998212 | − | 0.0597743i | \(-0.980962\pi\) | ||
0.998212 | − | 0.0597743i | \(-0.0190381\pi\) | |||||||
\(180\) | −33.9607 | − | 15.6934i | −2.53128 | − | 1.16971i | ||||
\(181\) | 17.5088i | 1.30142i | 0.759326 | + | 0.650710i | \(0.225529\pi\) | ||||
−0.759326 | + | 0.650710i | \(0.774471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.55666 | − | 4.90749i | −0.115072 | − | 0.362772i | ||||
\(184\) | 13.2033 | + | 22.8688i | 0.973363 | + | 1.68591i | ||||
\(185\) | 9.23466 | + | 15.9949i | 0.678946 | + | 1.17597i | ||||
\(186\) | 15.8880 | + | 14.5082i | 1.16496 | + | 1.06379i | ||||
\(187\) | −0.259231 | − | 0.149667i | −0.0189569 | − | 0.0109447i | ||||
\(188\) | 7.31027 | 0.533156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.2798 | −0.745775 | ||||||||
\(191\) | −13.9107 | − | 8.03138i | −1.00655 | − | 0.581130i | −0.0963679 | − | 0.995346i | \(-0.530723\pi\) |
−0.910179 | + | 0.414216i | \(0.864056\pi\) | |||||||
\(192\) | 14.5759 | + | 13.3101i | 1.05193 | + | 0.960571i | ||||
\(193\) | 5.44196 | + | 9.42575i | 0.391721 | + | 0.678480i | 0.992677 | − | 0.120802i | \(-0.0385467\pi\) |
−0.600956 | + | 0.799282i | \(0.705213\pi\) | |||||||
\(194\) | 14.3914 | + | 24.9267i | 1.03324 | + | 1.78963i | ||||
\(195\) | 10.5927 | + | 33.3941i | 0.758556 | + | 2.39140i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.50777i | − | 0.463660i | −0.972756 | − | 0.231830i | \(-0.925529\pi\) | ||
0.972756 | − | 0.231830i | \(-0.0744712\pi\) | |||||||
\(198\) | 1.82621 | − | 1.28816i | 0.129783 | − | 0.0915458i | ||||
\(199\) | − | 17.8074i | − | 1.26234i | −0.775646 | − | 0.631168i | \(-0.782576\pi\) | ||
0.775646 | − | 0.631168i | \(-0.217424\pi\) | |||||||
\(200\) | 22.7831 | + | 13.1538i | 1.61101 | + | 0.930116i | ||||
\(201\) | −0.694864 | + | 3.16018i | −0.0490119 | + | 0.222902i | ||||
\(202\) | −25.7284 | + | 14.8543i | −1.81024 | + | 1.04514i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.28729 | − | 5.85448i | 0.0901282 | − | 0.409895i | ||||
\(205\) | 0.240356 | − | 0.416308i | 0.0167872 | − | 0.0290762i | ||||
\(206\) | −42.7519 | −2.97866 | ||||||||
\(207\) | −11.8074 | − | 16.7392i | −0.820669 | − | 1.16345i | ||||
\(208\) | 11.2828i | 0.782319i | ||||||||
\(209\) | 0.197965 | − | 0.342885i | 0.0136935 | − | 0.0237178i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.282402 | − | 0.489135i | −0.0194414 | − | 0.0336735i | 0.856141 | − | 0.516742i | \(-0.172855\pi\) |
−0.875582 | + | 0.483069i | \(0.839522\pi\) | |||||||
\(212\) | 37.6600 | − | 21.7430i | 2.58650 | − | 1.49331i | ||||
\(213\) | −12.8452 | + | 14.0669i | −0.880141 | + | 0.963846i | ||||
\(214\) | 4.26875 | − | 7.39370i | 0.291806 | − | 0.505423i | ||||
\(215\) | 9.89953 | 0.675143 | ||||||||
\(216\) | 16.0058 | + | 12.1503i | 1.08906 | + | 0.826723i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.4843 | + | 7.78518i | 0.913273 | + | 0.527279i | ||||
\(219\) | −0.478298 | + | 0.523786i | −0.0323204 | + | 0.0353942i | ||||
\(220\) | −3.39066 | + | 1.95760i | −0.228598 | + | 0.131981i | ||||
\(221\) | −4.86134 | + | 2.80670i | −0.327009 | + | 0.188799i | ||||
\(222\) | −6.68021 | − | 21.0599i | −0.448347 | − | 1.41345i | ||||
\(223\) | 7.61261 | + | 4.39514i | 0.509778 | + | 0.294321i | 0.732742 | − | 0.680506i | \(-0.238240\pi\) |
−0.222964 | + | 0.974827i | \(0.571573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.5253 | − | 8.56063i | −1.23502 | − | 0.570709i | ||||
\(226\) | 5.14842 | 0.342468 | ||||||||
\(227\) | 8.45329 | − | 14.6415i | 0.561065 | − | 0.971793i | −0.436339 | − | 0.899782i | \(-0.643725\pi\) |
0.997404 | − | 0.0720104i | \(-0.0229415\pi\) | |||||||
\(228\) | 7.74371 | + | 1.70269i | 0.512839 | + | 0.112764i | ||||
\(229\) | −16.9410 | + | 9.78088i | −1.11949 | + | 0.646339i | −0.941271 | − | 0.337652i | \(-0.890367\pi\) |
−0.178221 | + | 0.983991i | \(0.557034\pi\) | |||||||
\(230\) | 27.8299 | + | 48.2028i | 1.83505 | + | 3.17840i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.67007 | − | 13.2849i | 0.503565 | − | 0.872200i | ||||
\(233\) | 19.7368i | 1.29300i | 0.762914 | + | 0.646500i | \(0.223768\pi\) | ||||
−0.762914 | + | 0.646500i | \(0.776232\pi\) | |||||||
\(234\) | −3.79702 | − | 41.7370i | −0.248219 | − | 2.72843i | ||||
\(235\) | 6.91874 | 0.451329 | ||||||||
\(236\) | 2.99270 | − | 5.18351i | 0.194808 | − | 0.337418i | ||||
\(237\) | −17.2800 | + | 5.48124i | −1.12246 | + | 0.356045i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9761 | + | 9.80118i | −1.09809 | + | 0.633985i | −0.935720 | − | 0.352744i | \(-0.885249\pi\) |
−0.162375 | + | 0.986729i | \(0.551915\pi\) | |||||||
\(240\) | −8.42060 | − | 7.68931i | −0.543547 | − | 0.496343i | ||||
\(241\) | 13.8166 | + | 7.97702i | 0.890006 | + | 0.513845i | 0.873945 | − | 0.486026i | \(-0.161554\pi\) |
0.0160617 | + | 0.999871i | \(0.494887\pi\) | |||||||
\(242\) | 25.8663i | 1.66275i | ||||||||
\(243\) | −13.2191 | − | 8.26168i | −0.848006 | − | 0.529987i | ||||
\(244\) | − | 10.7897i | − | 0.690743i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.387766 | + | 0.424644i | −0.0247230 | + | 0.0270743i | ||||
\(247\) | −3.71241 | − | 6.43008i | −0.236215 | − | 0.409136i | ||||
\(248\) | 10.1232 | + | 17.5340i | 0.642826 | + | 1.11341i | ||||
\(249\) | 13.2110 | − | 4.19054i | 0.837212 | − | 0.265565i | ||||
\(250\) | 12.7250 | + | 7.34677i | 0.804798 | + | 0.464651i | ||||
\(251\) | −0.976065 | −0.0616087 | −0.0308044 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308044 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14375 | −0.134776 | ||||||||
\(254\) | −4.82822 | − | 2.78758i | −0.302950 | − | 0.174908i | ||||
\(255\) | 1.21834 | − | 5.54092i | 0.0762956 | − | 0.346986i | ||||
\(256\) | 13.1200 | + | 22.7244i | 0.819998 | + | 1.42028i | ||||
\(257\) | −6.11947 | − | 10.5992i | −0.381722 | − | 0.661162i | 0.609587 | − | 0.792720i | \(-0.291335\pi\) |
−0.991309 | + | 0.131558i | \(0.958002\pi\) | |||||||
\(258\) | −11.5660 | − | 2.54315i | −0.720071 | − | 0.158330i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 73.4212i | 4.55339i | ||||||||
\(261\) | −4.99175 | + | 10.8022i | −0.308981 | + | 0.668641i | ||||
\(262\) | 22.5218i | 1.39140i | ||||||||
\(263\) | −3.64436 | − | 2.10407i | −0.224721 | − | 0.129743i | 0.383413 | − | 0.923577i | \(-0.374748\pi\) |
−0.608134 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(264\) | 2.00458 | − | 0.635855i | 0.123373 | − | 0.0391342i | ||||
\(265\) | 35.6429 | − | 20.5785i | 2.18953 | − | 1.26413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.70977 | + | 2.47444i | 0.165835 | + | 0.151433i | ||||
\(268\) | −3.39054 | + | 5.87258i | −0.207110 | + | 0.358725i | ||||
\(269\) | 21.6597 | 1.32062 | 0.660309 | − | 0.750994i | \(-0.270425\pi\) | ||||
0.660309 | + | 0.750994i | \(0.270425\pi\) | |||||||
\(270\) | 33.7370 | + | 25.6103i | 2.05317 | + | 1.55859i | ||||
\(271\) | − | 20.6677i | − | 1.25547i | −0.778426 | − | 0.627736i | \(-0.783982\pi\) | ||
0.778426 | − | 0.627736i | \(-0.216018\pi\) | |||||||
\(272\) | 0.913549 | − | 1.58231i | 0.0553921 | − | 0.0959419i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.1299 | − | 21.0096i | −0.732793 | − | 1.26923i | ||||
\(275\) | −1.84958 | + | 1.06786i | −0.111534 | + | 0.0643942i | ||||
\(276\) | −12.9800 | − | 40.9204i | −0.781304 | − | 2.46312i | ||||
\(277\) | 13.9448 | − | 24.1532i | 0.837864 | − | 1.45122i | −0.0538127 | − | 0.998551i | \(-0.517137\pi\) |
0.891677 | − | 0.452672i | \(-0.149529\pi\) | |||||||
\(278\) | 12.5087 | 0.750225 | ||||||||
\(279\) | −9.05293 | − | 12.8342i | −0.541985 | − | 0.768365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7176 | + | 9.65190i | 0.997287 | + | 0.575784i | 0.907444 | − | 0.420172i | \(-0.138030\pi\) |
0.0898425 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(282\) | −8.08346 | − | 1.77740i | −0.481363 | − | 0.105843i | ||||
\(283\) | 15.2703 | − | 8.81631i | 0.907725 | − | 0.524075i | 0.0280263 | − | 0.999607i | \(-0.491078\pi\) |
0.879698 | + | 0.475532i | \(0.157744\pi\) | |||||||
\(284\) | −34.5735 | + | 19.9610i | −2.05156 | + | 1.18447i | ||||
\(285\) | 7.32896 | + | 1.61150i | 0.434130 | + | 0.0954570i | ||||
\(286\) | −3.79832 | − | 2.19296i | −0.224599 | − | 0.129672i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.51210 | − | 7.81444i | −0.324804 | − | 0.460470i | ||||
\(289\) | −16.0910 | −0.946528 | ||||||||
\(290\) | 16.1669 | − | 28.0019i | 0.949354 | − | 1.64433i | ||||
\(291\) | −6.35273 | − | 20.0275i | −0.372404 | − | 1.17403i | ||||
\(292\) | −1.28736 | + | 0.743258i | −0.0753371 | + | 0.0434959i | ||||
\(293\) | −14.1138 | − | 24.4458i | −0.824536 | − | 1.42814i | −0.902273 | − | 0.431165i | \(-0.858103\pi\) |
0.0777369 | − | 0.996974i | \(-0.475231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.83242 | − | 4.90589i | 0.164910 | − | 0.285632i | ||||
\(296\) | − | 20.7909i | − | 1.20845i | ||||||
\(297\) | −1.50393 | + | 0.632109i | −0.0872669 | + | 0.0366787i | ||||
\(298\) | −43.3303 | −2.51006 | ||||||||
\(299\) | −20.1008 | + | 34.8156i | −1.16246 | + | 2.01344i | ||||
\(300\) | −31.5824 | − | 28.8396i | −1.82341 | − | 1.66505i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 47.4880 | − | 27.4172i | 2.73263 | − | 1.57768i | ||||
\(303\) | 20.6716 | − | 6.55705i | 1.18755 | − | 0.376693i | ||||
\(304\) | 2.09292 | + | 1.20835i | 0.120037 | + | 0.0693036i | ||||
\(305\) | − | 10.2119i | − | 0.584730i | ||||||
\(306\) | −2.84688 | + | 6.16070i | −0.162746 | + | 0.352184i | ||||
\(307\) | 8.56651i | 0.488917i | 0.969660 | + | 0.244458i | \(0.0786102\pi\) | ||||
−0.969660 | + | 0.244458i | \(0.921390\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.4799 | + | 6.70194i | 1.73394 | + | 0.381260i | ||||
\(310\) | 21.3377 | + | 36.9580i | 1.21190 | + | 2.09907i | ||||
\(311\) | −9.67914 | − | 16.7648i | −0.548854 | − | 0.950642i | −0.998353 | − | 0.0573619i | \(-0.981731\pi\) |
0.449500 | − | 0.893280i | \(-0.351602\pi\) | |||||||
\(312\) | 8.46926 | − | 38.5175i | 0.479477 | − | 2.18062i | ||||
\(313\) | 22.9507 | + | 13.2506i | 1.29725 | + | 0.748967i | 0.979928 | − | 0.199352i | \(-0.0638836\pi\) |
0.317321 | + | 0.948318i | \(0.397217\pi\) | |||||||
\(314\) | −15.4925 | −0.874291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −37.9923 | −2.13724 | ||||||||
\(317\) | −7.50458 | − | 4.33277i | −0.421499 | − | 0.243353i | 0.274219 | − | 0.961667i | \(-0.411581\pi\) |
−0.695719 | + | 0.718314i | \(0.744914\pi\) | |||||||
\(318\) | −46.9297 | + | 14.8862i | −2.63169 | + | 0.834774i | ||||
\(319\) | 0.622673 | + | 1.07850i | 0.0348630 | + | 0.0603844i | ||||
\(320\) | 19.5756 | + | 33.9059i | 1.09431 | + | 1.89540i | ||||
\(321\) | −4.20246 | + | 4.60214i | −0.234559 | + | 0.256866i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20235i | 0.0669008i | ||||||||
\(324\) | −21.1719 | − | 24.8801i | −1.17622 | − | 1.38223i | ||||
\(325\) | 40.0508i | 2.22162i | ||||||||
\(326\) | −50.3944 | − | 29.0952i | −2.79109 | − | 1.61144i | ||||
\(327\) | −8.39318 | − | 7.66428i | −0.464144 | − | 0.423835i | ||||
\(328\) | −0.468638 | + | 0.270568i | −0.0258762 | + | 0.0149396i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.22524 | − | 1.34025i | 0.232592 | − | 0.0737784i | ||||
\(331\) | −9.66912 | + | 16.7474i | −0.531463 | + | 0.920521i | 0.467863 | + | 0.883801i | \(0.345024\pi\) |
−0.999326 | + | 0.0367197i | \(0.988309\pi\) | |||||||
\(332\) | 29.0460 | 1.59411 | ||||||||
\(333\) | 1.46122 | + | 16.0618i | 0.0800744 | + | 0.880181i | ||||
\(334\) | 33.2122i | 1.81729i | ||||||||
\(335\) | −3.20894 | + | 5.55805i | −0.175323 | + | 0.303669i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4451 | − | 21.5556i | −0.677930 | − | 1.17421i | −0.975603 | − | 0.219542i | \(-0.929544\pi\) |
0.297673 | − | 0.954668i | \(-0.403790\pi\) | |||||||
\(338\) | −44.5164 | + | 25.7015i | −2.42137 | + | 1.39798i | ||||
\(339\) | −3.67055 | − | 0.807085i | −0.199357 | − | 0.0438348i | ||||
\(340\) | 5.94481 | − | 10.2967i | 0.322403 | − | 0.558418i | ||||
\(341\) | −1.64365 | −0.0890088 | ||||||||
\(342\) | −8.14875 | − | 3.76557i | −0.440634 | − | 0.203619i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.65090 | − | 5.57195i | −0.520341 | − | 0.300419i | ||||
\(345\) | −12.2848 | − | 38.7288i | −0.661392 | − | 2.08509i | ||||
\(346\) | −22.3968 | + | 12.9308i | −1.20406 | + | 0.695165i | ||||
\(347\) | 5.01728 | − | 2.89673i | 0.269342 | − | 0.155505i | −0.359247 | − | 0.933243i | \(-0.616966\pi\) |
0.628588 | + | 0.777738i | \(0.283633\pi\) | |||||||
\(348\) | −16.8165 | + | 18.4158i | −0.901460 | + | 0.987193i | ||||
\(349\) | 13.3430 | + | 7.70360i | 0.714236 | + | 0.412364i | 0.812627 | − | 0.582784i | \(-0.198037\pi\) |
−0.0983918 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.83577 | + | 30.3515i | −0.204738 | + | 1.62004i | ||||
\(352\) | −1.00078 | −0.0533417 | ||||||||
\(353\) | −8.87263 | + | 15.3679i | −0.472243 | + | 0.817948i | −0.999496 | − | 0.0317602i | \(-0.989889\pi\) |
0.527253 | + | 0.849708i | \(0.323222\pi\) | |||||||
\(354\) | −4.56954 | + | 5.00412i | −0.242868 | + | 0.265966i | ||||
\(355\) | −32.7218 | + | 18.8920i | −1.73669 | + | 1.00268i | ||||
\(356\) | 3.84519 | + | 6.66007i | 0.203795 | + | 0.352983i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.89754 | + | 3.28664i | −0.100288 | + | 0.173704i | ||||
\(359\) | − | 22.9197i | − | 1.20966i | −0.796356 | − | 0.604828i | \(-0.793242\pi\) | ||
0.796356 | − | 0.604828i | \(-0.206758\pi\) | |||||||
\(360\) | 22.9746 | + | 32.5708i | 1.21087 | + | 1.71663i | ||||
\(361\) | 17.4096 | 0.916297 | ||||||||
\(362\) | 20.7719 | − | 35.9781i | 1.09175 | − | 1.89096i | ||||
\(363\) | 4.05489 | − | 18.4413i | 0.212827 | − | 0.967917i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.21841 | + | 0.703450i | −0.0637745 | + | 0.0368203i | ||||
\(366\) | −2.62339 | + | 11.9310i | −0.137127 | + | 0.623641i | ||||
\(367\) | −4.33253 | − | 2.50139i | −0.226156 | − | 0.130571i | 0.382641 | − | 0.923897i | \(-0.375014\pi\) |
−0.608797 | + | 0.793326i | \(0.708348\pi\) | |||||||
\(368\) | − | 13.0852i | − | 0.682112i | ||||||
\(369\) | 0.343026 | − | 0.241961i | 0.0178572 | − | 0.0125960i | ||||
\(370\) | − | 43.8229i | − | 2.27824i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.95201 | − | 31.3745i | −0.515988 | − | 1.62669i | ||||
\(373\) | −4.76280 | − | 8.24941i | −0.246608 | − | 0.427138i | 0.715974 | − | 0.698127i | \(-0.245983\pi\) |
−0.962583 | + | 0.270988i | \(0.912649\pi\) | |||||||
\(374\) | 0.355121 | + | 0.615088i | 0.0183629 | + | 0.0318055i | ||||
\(375\) | −7.92054 | − | 7.23268i | −0.409015 | − | 0.373494i | ||||
\(376\) | −6.74497 | − | 3.89421i | −0.347845 | − | 0.200828i | ||||
\(377\) | 23.3538 | 1.20278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.8369 | −0.710756 | −0.355378 | − | 0.934723i | \(-0.615648\pi\) | ||||
−0.355378 | + | 0.934723i | \(0.615648\pi\) | |||||||
\(380\) | 13.6194 | + | 7.86319i | 0.698663 | + | 0.403373i | ||||
\(381\) | 3.00528 | + | 2.74429i | 0.153965 | + | 0.140594i | ||||
\(382\) | 19.0564 | + | 33.0066i | 0.975009 | + | 1.68876i | ||||
\(383\) | −10.6160 | − | 18.3874i | −0.542452 | − | 0.939554i | −0.998763 | − | 0.0497336i | \(-0.984163\pi\) |
0.456311 | − | 0.889821i | \(-0.349171\pi\) | |||||||
\(384\) | −10.8220 | − | 34.1172i | −0.552259 | − | 1.74104i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 25.8247i | − | 1.31444i | ||||||
\(387\) | 7.84731 | + | 3.62627i | 0.398901 | + | 0.184334i | ||||
\(388\) | − | 44.0329i | − | 2.23543i | ||||||
\(389\) | −3.91419 | − | 2.25986i | −0.198457 | − | 0.114579i | 0.397478 | − | 0.917612i | \(-0.369885\pi\) |
−0.595936 | + | 0.803032i | \(0.703219\pi\) | |||||||
\(390\) | 17.8514 | − | 81.1868i | 0.903943 | − | 4.11106i | ||||
\(391\) | 5.63793 | − | 3.25506i | 0.285122 | − | 0.164616i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.53060 | − | 16.0568i | 0.178095 | − | 0.809961i | ||||
\(394\) | −7.72063 | + | 13.3725i | −0.388960 | + | 0.673698i | ||||
\(395\) | −35.9575 | −1.80922 | ||||||||
\(396\) | −3.40484 | + | 0.309755i | −0.171100 | + | 0.0155658i | ||||
\(397\) | − | 15.6843i | − | 0.787171i | −0.919288 | − | 0.393586i | \(-0.871235\pi\) | ||
0.919288 | − | 0.393586i | \(-0.128765\pi\) | |||||||
\(398\) | −21.1262 | + | 36.5917i | −1.05896 | + | 1.83417i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.51806 | − | 11.2896i | −0.325903 | − | 0.564480i | ||||
\(401\) | 9.34292 | − | 5.39414i | 0.466563 | − | 0.269370i | −0.248237 | − | 0.968699i | \(-0.579851\pi\) |
0.714800 | + | 0.699329i | \(0.246518\pi\) | |||||||
\(402\) | 5.17699 | − | 5.66934i | 0.258205 | − | 0.282761i | ||||
\(403\) | −15.4116 | + | 26.6937i | −0.767708 | + | 1.32971i | ||||
\(404\) | 45.4491 | 2.26118 | ||||||||
\(405\) | −20.0379 | − | 23.5476i | −0.995693 | − | 1.17009i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.46172 | + | 0.843925i | 0.0724548 | + | 0.0418318i | ||||
\(408\) | −4.30645 | + | 4.71601i | −0.213201 | + | 0.233477i | ||||
\(409\) | 16.9860 | − | 9.80689i | 0.839906 | − | 0.484920i | −0.0173265 | − | 0.999850i | \(-0.505515\pi\) |
0.857232 | + | 0.514930i | \(0.172182\pi\) | |||||||
\(410\) | −0.987791 | + | 0.570302i | −0.0487835 | + | 0.0281652i | ||||
\(411\) | 5.35444 | + | 16.8803i | 0.264115 | + | 0.832642i | ||||
\(412\) | 56.6409 | + | 32.7016i | 2.79050 | + | 1.61109i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.40358 | + | 48.4044i | 0.216424 | + | 2.37895i | ||||
\(415\) | 27.4904 | 1.34945 | ||||||||
\(416\) | −9.38376 | + | 16.2532i | −0.460077 | + | 0.796876i | ||||
\(417\) | −8.91808 | − | 1.96092i | −0.436720 | − | 0.0960266i | ||||
\(418\) | −0.813576 | + | 0.469718i | −0.0397933 | + | 0.0229747i | ||||
\(419\) | 8.83829 | + | 15.3084i | 0.431779 | + | 0.747862i | 0.997027 | − | 0.0770586i | \(-0.0245528\pi\) |
−0.565248 | + | 0.824921i | \(0.691220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9507 | + | 29.3594i | −0.826124 | + | 1.43089i | 0.0749327 | + | 0.997189i | \(0.476126\pi\) |
−0.901057 | + | 0.433701i | \(0.857208\pi\) | |||||||
\(422\) | 1.34014i | 0.0652368i | ||||||||
\(423\) | 5.48445 | + | 2.53439i | 0.266663 | + | 0.123226i | ||||
\(424\) | −46.3303 | −2.25000 | ||||||||
\(425\) | 3.24286 | − | 5.61679i | 0.157302 | − | 0.272454i | ||||
\(426\) | 43.0836 | − | 13.6662i | 2.08741 | − | 0.662128i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.3111 | + | 6.53048i | −0.546744 | + | 0.315663i | ||||
\(429\) | 2.36422 | + | 2.15890i | 0.114146 | + | 0.104233i | ||||
\(430\) | −20.3421 | − | 11.7445i | −0.980983 | − | 0.566371i | ||||
\(431\) | 14.1239i | 0.680324i | 0.940367 | + | 0.340162i | \(0.110482\pi\) | ||||
−0.940367 | + | 0.340162i | \(0.889518\pi\) | |||||||
\(432\) | −3.85832 | − | 9.17980i | −0.185633 | − | 0.441664i | ||||
\(433\) | − | 9.10088i | − | 0.437360i | −0.975797 | − | 0.218680i | \(-0.929825\pi\) | ||
0.975797 | − | 0.218680i | \(-0.0701752\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.9159 | + | 17.4295i | −0.763107 | + | 0.835682i | ||||
\(436\) | −11.9100 | − | 20.6288i | −0.570387 | − | 0.987938i | ||||
\(437\) | 4.30546 | + | 7.45728i | 0.205958 | + | 0.356730i | ||||
\(438\) | 1.60424 | − | 0.508865i | 0.0766533 | − | 0.0243145i | ||||
\(439\) | 10.1520 | + | 5.86126i | 0.484529 | + | 0.279743i | 0.722302 | − | 0.691578i | \(-0.243084\pi\) |
−0.237773 | + | 0.971321i | \(0.576417\pi\) | |||||||
\(440\) | 4.17128 | 0.198858 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.3191 | 0.633526 | ||||||||
\(443\) | −6.17796 | − | 3.56685i | −0.293524 | − | 0.169466i | 0.346006 | − | 0.938232i | \(-0.387538\pi\) |
−0.639530 | + | 0.768766i | \(0.720871\pi\) | |||||||
\(444\) | −7.25860 | + | 33.0115i | −0.344478 | + | 1.56666i | ||||
\(445\) | 3.63925 | + | 6.30337i | 0.172517 | + | 0.298808i | ||||
\(446\) | −10.4285 | − | 18.0628i | −0.493805 | − | 0.855296i | ||||
\(447\) | 30.8922 | + | 6.79262i | 1.46115 | + | 0.321280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.17445i | 0.149811i | 0.997191 | + | 0.0749057i | \(0.0238656\pi\) | ||||
−0.997191 | + | 0.0749057i | \(0.976134\pi\) | |||||||
\(450\) | 27.9108 | + | 39.5688i | 1.31573 | + | 1.86529i | ||||
\(451\) | − | 0.0439306i | − | 0.00206861i | ||||||
\(452\) | −6.82100 | − | 3.93811i | −0.320833 | − | 0.185233i | ||||
\(453\) | −38.1545 | + | 12.1027i | −1.79266 | + | 0.568632i | ||||
\(454\) | −34.7406 | + | 20.0575i | −1.63045 | + | 0.941344i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.23786 | − | 5.69613i | −0.292114 | − | 0.266746i | ||||
\(457\) | −12.0745 | + | 20.9137i | −0.564821 | + | 0.978299i | 0.432245 | + | 0.901756i | \(0.357722\pi\) |
−0.997066 | + | 0.0765431i | \(0.975612\pi\) | |||||||
\(458\) | 46.4150 | 2.16883 | ||||||||
\(459\) | 2.99545 | − | 3.94597i | 0.139816 | − | 0.184182i | ||||
\(460\) | − | 85.1502i | − | 3.97015i | ||||||
\(461\) | −6.87281 | + | 11.9041i | −0.320099 | + | 0.554427i | −0.980508 | − | 0.196478i | \(-0.937049\pi\) |
0.660409 | + | 0.750906i | \(0.270383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3157 | + | 17.8673i | 0.479411 | + | 0.830364i | 0.999721 | − | 0.0236135i | \(-0.00751711\pi\) |
−0.520310 | + | 0.853977i | \(0.674184\pi\) | |||||||
\(464\) | −6.58303 | + | 3.80071i | −0.305610 | + | 0.176444i | ||||
\(465\) | −9.41899 | − | 29.6941i | −0.436795 | − | 1.37703i | ||||
\(466\) | 23.4151 | − | 40.5562i | 1.08469 | − | 1.87873i | ||||
\(467\) | 0.931788 | 0.0431180 | 0.0215590 | − | 0.999768i | \(-0.493137\pi\) | ||||
0.0215590 | + | 0.999768i | \(0.493137\pi\) | |||||||
\(468\) | −26.8947 | + | 58.2007i | −1.24321 | + | 2.69033i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14.2170 | − | 8.20819i | −0.655781 | − | 0.378615i | ||||
\(471\) | 11.0453 | + | 2.42866i | 0.508942 | + | 0.111907i | ||||
\(472\) | −5.52256 | + | 3.18845i | −0.254196 | + | 0.146760i | ||||
\(473\) | 0.783481 | − | 0.452343i | 0.0360245 | − | 0.0207987i | ||||
\(474\) | 42.0107 | + | 9.23736i | 1.92962 | + | 0.424286i | ||||
\(475\) | 7.42932 | + | 4.28932i | 0.340881 | + | 0.196808i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.7920 | − | 3.25617i | 1.63880 | − | 0.149090i | ||||
\(478\) | 46.5113 | 2.12738 | ||||||||
\(479\) | −16.2031 | + | 28.0647i | −0.740340 | + | 1.28231i | 0.212000 | + | 0.977270i | \(0.432002\pi\) |
−0.952340 | + | 0.305037i | \(0.901331\pi\) | |||||||
\(480\) | −5.73499 | − | 18.0800i | −0.261765 | − | 0.825235i | ||||
\(481\) | 27.4115 | − | 15.8260i | 1.24986 | − | 0.721605i | ||||
\(482\) | −18.9274 | − | 32.7832i | −0.862120 | − | 1.49324i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7855 | − | 34.2695i | 0.899342 | − | 1.55771i | ||||
\(485\) | − | 41.6746i | − | 1.89234i | ||||||
\(486\) | 17.3619 | + | 32.6593i | 0.787552 | + | 1.48146i | ||||
\(487\) | −34.3733 | −1.55760 | −0.778802 | − | 0.627270i | \(-0.784172\pi\) | ||||
−0.778802 | + | 0.627270i | \(0.784172\pi\) | |||||||
\(488\) | −5.74774 | + | 9.95538i | −0.260188 | + | 0.450659i | ||||
\(489\) | 31.3675 | + | 28.6434i | 1.41849 | + | 1.29530i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.31048 | + | 4.22071i | −0.329917 | + | 0.190478i | −0.655804 | − | 0.754931i | \(-0.727670\pi\) |
0.325887 | + | 0.945409i | \(0.394337\pi\) | |||||||
\(492\) | 0.838558 | − | 0.265992i | 0.0378051 | − | 0.0119918i | ||||
\(493\) | −3.27518 | − | 1.89093i | −0.147507 | − | 0.0851631i | ||||
\(494\) | 17.6172i | 0.792634i | ||||||||
\(495\) | −3.22248 | + | 0.293165i | −0.144840 | + | 0.0131768i | ||||
\(496\) | − | 10.0326i | − | 0.450479i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −32.1182 | − | 7.06217i | −1.43925 | − | 0.316464i | ||||
\(499\) | 5.70400 | + | 9.87961i | 0.255346 | + | 0.442272i | 0.964989 | − | 0.262289i | \(-0.0844773\pi\) |
−0.709643 | + | 0.704561i | \(0.751144\pi\) | |||||||
\(500\) | −11.2393 | − | 19.4671i | −0.502638 | − | 0.870595i | ||||
\(501\) | 5.20647 | − | 23.6786i | 0.232608 | − | 1.05788i | ||||
\(502\) | 2.00567 | + | 1.15797i | 0.0895175 | + | 0.0516830i | ||||
\(503\) | 32.8028 | 1.46261 | 0.731303 | − | 0.682053i | \(-0.238913\pi\) | ||||
0.731303 | + | 0.682053i | \(0.238913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0149 | 1.91414 | ||||||||
\(506\) | 4.40509 | + | 2.54328i | 0.195830 | + | 0.113063i | ||||
\(507\) | 35.7669 | − | 11.3453i | 1.58847 | − | 0.503863i | ||||
\(508\) | 4.26453 | + | 7.38638i | 0.189208 | + | 0.327717i | ||||
\(509\) | 9.75828 | + | 16.9018i | 0.432528 | + | 0.749160i | 0.997090 | − | 0.0762300i | \(-0.0242883\pi\) |
−0.564562 | + | 0.825390i | \(0.690955\pi\) | |||||||
\(510\) | −9.07710 | + | 9.94037i | −0.401941 | + | 0.440167i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 20.9310i | − | 0.925027i | ||||||
\(513\) | 5.21933 | + | 3.96208i | 0.230439 | + | 0.174930i | ||||
\(514\) | 29.0398i | 1.28089i | ||||||||
\(515\) | 53.6073 | + | 30.9502i | 2.36222 | + | 1.36383i | ||||
\(516\) | 13.3783 | + | 12.2164i | 0.588945 | + | 0.537798i | ||||
\(517\) | 0.547571 | − | 0.316140i | 0.0240821 | − | 0.0139038i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.9949 | − | 5.70799i | 0.789887 | − | 0.250553i | ||||
\(520\) | 39.1118 | − | 67.7436i | 1.71517 | − | 2.97075i | ||||
\(521\) | −19.8622 | −0.870177 | −0.435088 | − | 0.900388i | \(-0.643283\pi\) | ||||
−0.435088 | + | 0.900388i | \(0.643283\pi\) | |||||||
\(522\) | 23.0727 | − | 16.2749i | 1.00987 | − | 0.712334i | ||||
\(523\) | − | 7.75356i | − | 0.339039i | −0.985527 | − | 0.169520i | \(-0.945778\pi\) | ||
0.985527 | − | 0.169520i | \(-0.0542216\pi\) | |||||||
\(524\) | 17.2273 | − | 29.8385i | 0.752577 | − | 1.30350i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.99242 | + | 8.64713i | 0.217680 | + | 0.377033i | ||||
\(527\) | 4.32271 | − | 2.49572i | 0.188300 | − | 0.108715i | ||||
\(528\) | −1.01778 | − | 0.223791i | −0.0442933 | − | 0.00973926i | ||||
\(529\) | 11.8118 | − | 20.4587i | 0.513559 | − | 0.889509i | ||||
\(530\) | −97.6547 | −4.24185 | ||||||||
\(531\) | 4.04231 | − | 2.85134i | 0.175421 | − | 0.123738i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.713455 | − | 0.411913i | −0.0309032 | − | 0.0178419i | ||||
\(534\) | −2.63258 | − | 8.29940i | −0.113923 | − | 0.359150i | ||||
\(535\) | −10.7053 | + | 6.18072i | −0.462831 | + | 0.267216i | ||||
\(536\) | 6.25670 | − | 3.61231i | 0.270248 | − | 0.156028i | ||||
\(537\) | 1.86807 | − | 2.04574i | 0.0806134 | − | 0.0882801i | ||||
\(538\) | −44.5076 | − | 25.6965i | −1.91886 | − | 1.10785i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −25.1075 | − | 59.7364i | −1.08046 | − | 2.57065i | ||||
\(541\) | −18.0923 | −0.777850 | −0.388925 | − | 0.921269i | \(-0.627153\pi\) | ||||
−0.388925 | + | 0.921269i | \(0.627153\pi\) | |||||||
\(542\) | −24.5195 | + | 42.4691i | −1.05320 | + | 1.82420i | ||||
\(543\) | −20.4494 | + | 22.3942i | −0.877566 | + | 0.961027i | ||||
\(544\) | 2.63199 | − | 1.51958i | 0.112846 | − | 0.0651514i | ||||
\(545\) | −11.2721 | − | 19.5239i | −0.482845 | − | 0.836313i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.46839 | − | 6.00743i | 0.148298 | − | 0.256859i | −0.782301 | − | 0.622901i | \(-0.785954\pi\) |
0.930598 | + | 0.366042i | \(0.119287\pi\) | |||||||
\(548\) | 37.1134i | 1.58541i | ||||||||
\(549\) | 3.74068 | − | 8.09490i | 0.159648 | − | 0.345482i | ||||
\(550\) | 5.06749 | 0.216079 | ||||||||
\(551\) | 2.50113 | − | 4.33208i | 0.106552 | − | 0.184553i | ||||
\(552\) | −9.82221 | + | 44.6706i | −0.418061 | + | 1.90131i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −57.3092 | + | 33.0875i | −2.43483 | + | 1.40575i | ||||
\(555\) | −6.86984 | + | 31.2434i | −0.291608 | + | 1.32621i | ||||
\(556\) | −16.5725 | − | 9.56815i | −0.702831 | − | 0.405780i | ||||
\(557\) | − | 15.8186i | − | 0.670257i | −0.942172 | − | 0.335128i | \(-0.891220\pi\) | ||
0.942172 | − | 0.335128i | \(-0.108780\pi\) | |||||||
\(558\) | 3.37631 | + | 37.1126i | 0.142931 | + | 1.57110i | ||||
\(559\) | − | 16.9655i | − | 0.717563i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.156759 | − | 0.494196i | −0.00661839 | − | 0.0208650i | ||||
\(562\) | −22.9014 | − | 39.6665i | −0.966039 | − | 1.67323i | ||||
\(563\) | 16.0561 | + | 27.8101i | 0.676686 | + | 1.17205i | 0.975973 | + | 0.217891i | \(0.0699178\pi\) |
−0.299287 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(564\) | 9.35000 | + | 8.53800i | 0.393706 | + | 0.359515i | ||||
\(565\) | −6.45568 | − | 3.72719i | −0.271593 | − | 0.156804i | ||||
\(566\) | −41.8376 | −1.75857 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.5333 | 1.78466 | ||||||||
\(569\) | 31.3107 | + | 18.0772i | 1.31261 | + | 0.757837i | 0.982528 | − | 0.186114i | \(-0.0595894\pi\) |
0.330084 | + | 0.943951i | \(0.392923\pi\) | |||||||
\(570\) | −13.1481 | − | 12.0063i | −0.550714 | − | 0.502887i | ||||
\(571\) | −14.1792 | − | 24.5590i | −0.593380 | − | 1.02776i | −0.993773 | − | 0.111421i | \(-0.964460\pi\) |
0.400393 | − | 0.916343i | \(-0.368873\pi\) | |||||||
\(572\) | 3.35486 | + | 5.81079i | 0.140274 | + | 0.242961i | ||||
\(573\) | −8.41196 | − | 26.5193i | −0.351415 | − | 1.10786i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 46.4489i | − | 1.93705i | ||||||
\(576\) | 3.09749 | + | 34.0478i | 0.129062 | + | 1.41866i | ||||
\(577\) | 41.9836i | 1.74780i | 0.486105 | + | 0.873901i | \(0.338417\pi\) | ||||
−0.486105 | + | 0.873901i | \(0.661583\pi\) | |||||||
\(578\) | 33.0646 | + | 19.0899i | 1.37531 | + | 0.794034i | ||||
\(579\) | −4.04838 | + | 18.4117i | −0.168245 | + | 0.765163i | ||||
\(580\) | −42.8383 | + | 24.7327i | −1.77876 | + | 1.02697i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.7060 | + | 48.6902i | −0.443780 | + | 2.01827i | ||||
\(583\) | 1.88060 | − | 3.25729i | 0.0778864 | − | 0.134903i | ||||
\(584\) | 1.58375 | 0.0655359 | ||||||||
\(585\) | −25.4543 | + | 55.0835i | −1.05241 | + | 2.27742i | ||||
\(586\) | 66.9767i | 2.76678i | ||||||||
\(587\) | −9.79227 | + | 16.9607i | −0.404170 | + | 0.700043i | −0.994225 | − | 0.107320i | \(-0.965773\pi\) |
0.590054 | + | 0.807364i | \(0.299106\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.30108 | + | 5.71764i | 0.136019 | + | 0.235591i | ||||
\(590\) | −11.6404 | + | 6.72059i | −0.479228 | + | 0.276682i | ||||
\(591\) | 7.60073 | − | 8.32359i | 0.312652 | − | 0.342387i | ||||
\(592\) | −5.15121 | + | 8.92216i | −0.211713 | + | 0.366698i | ||||
\(593\) | −19.9275 | −0.818324 | −0.409162 | − | 0.912462i | \(-0.634179\pi\) | ||||
−0.409162 | + | 0.912462i | \(0.634179\pi\) | |||||||
\(594\) | 3.84027 | + | 0.485327i | 0.157568 | + | 0.0199132i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 57.4072 | + | 33.1441i | 2.35149 | + | 1.35763i | ||||
\(597\) | 20.7981 | − | 22.7761i | 0.851211 | − | 0.932165i | ||||
\(598\) | 82.6083 | − | 47.6939i | 3.37810 | − | 1.95035i | ||||
\(599\) | 0.0267639 | − | 0.0154521i | 0.00109354 | − | 0.000631357i | −0.499453 | − | 0.866341i | \(-0.666466\pi\) |
0.500547 | + | 0.865710i | \(0.333132\pi\) | |||||||
\(600\) | 13.7772 | + | 43.4335i | 0.562450 | + | 1.77317i | ||||
\(601\) | −25.8633 | − | 14.9322i | −1.05499 | − | 0.609097i | −0.130945 | − | 0.991390i | \(-0.541801\pi\) |
−0.924041 | + | 0.382293i | \(0.875135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.57967 | + | 3.23038i | −0.186499 | + | 0.131551i | ||||
\(604\) | −83.8876 | −3.41334 | ||||||||
\(605\) | 18.7258 | − | 32.4341i | 0.761314 | − | 1.31863i | ||||
\(606\) | −50.2562 | − | 11.0504i | −2.04152 | − | 0.448891i | ||||
\(607\) | −27.1898 | + | 15.6980i | −1.10360 | + | 0.637163i | −0.937164 | − | 0.348889i | \(-0.886559\pi\) |
−0.166435 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(608\) | 2.00994 | + | 3.48133i | 0.0815140 | + | 0.141186i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1151 | + | 20.9839i | −0.490524 | + | 0.849613i | ||||
\(611\) | − | 11.8571i | − | 0.479687i | ||||||
\(612\) | 8.48419 | − | 5.98453i | 0.342953 | − | 0.241910i | ||||
\(613\) | −4.46292 | −0.180256 | −0.0901278 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901278 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(614\) | 10.1631 | − | 17.6029i | 0.410148 | − | 0.710396i | ||||
\(615\) | 0.793646 | − | 0.251745i | 0.0320029 | − | 0.0101514i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9685 | − | 15.5703i | 1.08571 | − | 0.626835i | 0.153279 | − | 0.988183i | \(-0.451017\pi\) |
0.932431 | + | 0.361348i | \(0.117683\pi\) | |||||||
\(618\) | −54.6807 | − | 49.9319i | −2.19958 | − | 2.00856i | ||||
\(619\) | −1.13493 | − | 0.655252i | −0.0456167 | − | 0.0263368i | 0.477018 | − | 0.878893i | \(-0.341718\pi\) |
−0.522635 | + | 0.852557i | \(0.675051\pi\) | |||||||
\(620\) | − | 65.2862i | − | 2.62196i | ||||||
\(621\) | 4.44853 | − | 35.2001i | 0.178513 | − | 1.41253i | ||||
\(622\) | 45.9322i | 1.84171i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.1777 | + | 14.4309i | −0.527529 | + | 0.577699i | ||||
\(625\) | 6.36901 | + | 11.0315i | 0.254761 | + | 0.441258i | ||||
\(626\) | −31.4402 | − | 54.4560i | −1.25660 | − | 2.17650i | ||||
\(627\) | 0.653672 | − | 0.207346i | 0.0261052 | − | 0.00828058i | ||||
\(628\) | 20.5256 | + | 11.8505i | 0.819060 | + | 0.472884i | ||||
\(629\) | −5.12565 | −0.204373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8892 | −1.15006 | −0.575030 | − | 0.818132i | \(-0.695010\pi\) | ||||
−0.575030 | + | 0.818132i | \(0.695010\pi\) | |||||||
\(632\) | 35.0544 | + | 20.2387i | 1.39439 | + | 0.805051i | ||||
\(633\) | 0.210085 | − | 0.955447i | 0.00835011 | − | 0.0379756i | ||||
\(634\) | 10.2805 | + | 17.8064i | 0.408293 | + | 0.707183i | ||||
\(635\) | 4.03612 | + | 6.99077i | 0.160169 | + | 0.277420i | ||||
\(636\) | 73.5626 | + | 16.1750i | 2.91695 | + | 0.641382i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.95488i | − | 0.116985i | ||||||
\(639\) | −32.8587 | + | 2.98932i | −1.29987 | + | 0.118255i | ||||
\(640\) | − | 70.9936i | − | 2.80627i | ||||||
\(641\) | 2.41325 | + | 1.39329i | 0.0953176 | + | 0.0550316i | 0.546901 | − | 0.837197i | \(-0.315807\pi\) |
−0.451584 | + | 0.892229i | \(0.649141\pi\) | |||||||
\(642\) | 14.0953 | − | 4.47104i | 0.556296 | − | 0.176458i | ||||
\(643\) | 0.324584 | − | 0.187399i | 0.0128004 | − | 0.00739029i | −0.493586 | − | 0.869697i | \(-0.664314\pi\) |
0.506387 | + | 0.862307i | \(0.330981\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.6617 | + | 11.5621i | 0.498555 | + | 0.455258i | ||||
\(646\) | 1.42644 | − | 2.47066i | 0.0561224 | − | 0.0972069i | ||||
\(647\) | −50.3216 | −1.97834 | −0.989172 | − | 0.146758i | \(-0.953116\pi\) | ||||
−0.989172 | + | 0.146758i | \(0.953116\pi\) | |||||||
\(648\) | 6.28094 | + | 34.2345i | 0.246738 | + | 1.34486i | ||||
\(649\) | − | 0.517690i | − | 0.0203211i | ||||||
\(650\) | 47.5151 | − | 82.2986i | 1.86370 | − | 3.22802i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 44.5109 | + | 77.0951i | 1.74318 | + | 3.01928i | ||||
\(653\) | −25.0515 | + | 14.4635i | −0.980342 | + | 0.566000i | −0.902373 | − | 0.430955i | \(-0.858177\pi\) |
−0.0779684 | + | 0.996956i | \(0.524843\pi\) | |||||||
\(654\) | 8.15409 | + | 25.7064i | 0.318850 | + | 1.00520i | ||||
\(655\) | 16.3046 | − | 28.2404i | 0.637074 | − | 1.10344i | ||||
\(656\) | 0.268147 | 0.0104694 | ||||||||
\(657\) | −1.22351 | + | 0.111308i | −0.0477336 | + | 0.00434255i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8449 | − | 13.1895i | −0.889910 | − | 0.513790i | −0.0159971 | − | 0.999872i | \(-0.505092\pi\) |
−0.873913 | + | 0.486082i | \(0.838426\pi\) | |||||||
\(660\) | −6.62310 | − | 1.45629i | −0.257804 | − | 0.0566861i | ||||
\(661\) | −10.0533 | + | 5.80428i | −0.391028 | + | 0.225760i | −0.682606 | − | 0.730787i | \(-0.739153\pi\) |
0.291577 | + | 0.956547i | \(0.405820\pi\) | |||||||
\(662\) | 39.7373 | − | 22.9423i | 1.54443 | − | 0.891678i | ||||
\(663\) | −9.49584 | − | 2.08795i | −0.368788 | − | 0.0810894i | ||||
\(664\) | −26.7999 | − | 15.4729i | −1.04004 | − | 0.600466i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.0527 | − | 34.7382i | 0.622028 | − | 1.34608i | ||||
\(667\) | −27.0846 | −1.04872 | ||||||||
\(668\) | 25.4046 | − | 44.0020i | 0.982933 | − | 1.70249i | ||||
\(669\) | 4.60342 | + | 14.5126i | 0.177978 | + | 0.561090i | ||||
\(670\) | 13.1878 | − | 7.61399i | 0.509490 | − | 0.294154i | ||||
\(671\) | −0.466614 | − | 0.808199i | −0.0180134 | − | 0.0312002i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7692 | + | 23.8490i | −0.530764 | + | 0.919310i | 0.468592 | + | 0.883415i | \(0.344761\pi\) |
−0.999356 | + | 0.0358949i | \(0.988572\pi\) | |||||||
\(674\) | 59.0582i | 2.27484i | ||||||||
\(675\) | −13.6960 | − | 32.5859i | −0.527159 | − | 1.25423i | ||||
\(676\) | 78.6382 | 3.02454 | ||||||||
\(677\) | −2.31563 | + | 4.01080i | −0.0889970 | + | 0.154147i | −0.907087 | − | 0.420942i | \(-0.861700\pi\) |
0.818090 | + | 0.575090i | \(0.195033\pi\) | |||||||
\(678\) | 6.58495 | + | 6.01307i | 0.252893 | + | 0.230931i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.9702 | + | 6.33365i | −0.420688 | + | 0.242884i | ||||
\(681\) | 27.9125 | − | 8.85387i | 1.06961 | − | 0.339281i | ||||
\(682\) | 3.37747 | + | 1.94998i | 0.129330 | + | 0.0746686i | ||||
\(683\) | − | 13.8792i | − | 0.531072i | −0.964101 | − | 0.265536i | \(-0.914451\pi\) | ||
0.964101 | − | 0.265536i | \(-0.0855490\pi\) | |||||||
\(684\) | 7.91573 | + | 11.2220i | 0.302665 | + | 0.429085i | ||||
\(685\) | 35.1257i | 1.34208i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.0915 | − | 7.27619i | −1.26252 | − | 0.277604i | ||||
\(688\) | 2.76104 | + | 4.78227i | 0.105264 | + | 0.182322i | ||||
\(689\) | −35.2667 | − | 61.0837i | −1.34355 | − | 2.32710i | ||||
\(690\) | −20.7032 | + | 94.1563i | −0.788157 | + | 3.58447i | ||||
\(691\) | 19.6168 | + | 11.3258i | 0.746258 | + | 0.430852i | 0.824340 | − | 0.566095i | \(-0.191546\pi\) |
−0.0780825 | + | 0.996947i | \(0.524880\pi\) | |||||||
\(692\) | 39.5640 | 1.50400 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.7464 | −0.521805 | ||||||||
\(695\) | −15.6849 | − | 9.05569i | −0.594963 | − | 0.343502i | ||||
\(696\) | 25.3263 | − | 8.03353i | 0.959991 | − | 0.304510i | ||||
\(697\) | 0.0667040 | + | 0.115535i | 0.00252660 | + | 0.00437619i | ||||
\(698\) | −18.2786 | − | 31.6595i | −0.691856 | − | 1.19833i | ||||
\(699\) | −23.0515 | + | 25.2438i | −0.871888 | + | 0.954809i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.3485i | − | 0.617474i | −0.951147 | − | 0.308737i | \(-0.900094\pi\) | ||
0.951147 | − | 0.308737i | \(-0.0999063\pi\) | |||||||
\(702\) | 43.8901 | − | 57.8173i | 1.65653 | − | 2.18217i | ||||
\(703\) | − | 6.77968i | − | 0.255701i | ||||||
\(704\) | 3.09855 | + | 1.78895i | 0.116781 | + | 0.0674236i | ||||
\(705\) | 8.84923 | + | 8.08072i | 0.333281 | + | 0.304337i | ||||
\(706\) | 36.4639 | − | 21.0525i | 1.37234 | − | 0.792320i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.88180 | − | 3.13452i | 0.371381 | − | 0.117802i | ||||
\(709\) | −7.65356 | + | 13.2564i | −0.287435 | + | 0.497853i | −0.973197 | − | 0.229974i | \(-0.926136\pi\) |
0.685761 | + | 0.727826i | \(0.259469\pi\) | |||||||
\(710\) | 89.6514 | 3.36456 | ||||||||
\(711\) | −28.5034 | − | 13.1715i | −1.06896 | − | 0.493970i | ||||
\(712\) | − | 8.19340i | − | 0.307061i | ||||||
\(713\) | 17.8736 | − | 30.9580i | 0.669372 | − | 1.15939i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.17518 | + | 5.49957i | 0.118745 | + | 0.205672i | ||||
\(716\) | 5.02801 | − | 2.90292i | 0.187906 | − | 0.108487i | ||||
\(717\) | −33.1601 | − | 7.29128i | −1.23839 | − | 0.272298i | ||||
\(718\) | −27.1913 | + | 47.0966i | −1.01477 | + | 1.75763i | ||||
\(719\) | 14.9272 | 0.556690 | 0.278345 | − | 0.960481i | \(-0.410214\pi\) | ||||
0.278345 | + | 0.960481i | \(0.410214\pi\) | |||||||
\(720\) | −1.78944 | − | 19.6696i | −0.0666885 | − | 0.733043i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.7743 | − | 20.6543i | −1.33138 | − | 0.768673i | ||||
\(723\) | 8.35503 | + | 26.3399i | 0.310727 | + | 0.979590i | ||||
\(724\) | −55.0404 | + | 31.7776i | −2.04556 | + | 1.18101i | ||||
\(725\) | −23.3680 | + | 13.4915i | −0.867866 | + | 0.501063i | ||||
\(726\) | −30.2104 | + | 33.0836i | −1.12121 | + | 1.22785i | ||||
\(727\) | 4.62968 | + | 2.67295i | 0.171705 | + | 0.0991341i | 0.583390 | − | 0.812192i | \(-0.301726\pi\) |
−0.411684 | + | 0.911326i | \(0.635059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.25834 | − | 26.0061i | −0.268827 | − | 0.963188i | ||||
\(730\) | 3.33821 | 0.123553 | ||||||||
\(731\) | −1.37367 | + | 2.37927i | −0.0508070 | + | 0.0880004i | ||||
\(732\) | 12.6018 | − | 13.8003i | 0.465778 | − | 0.510075i | ||||
\(733\) | −16.4099 | + | 9.47428i | −0.606115 | + | 0.349941i | −0.771443 | − | 0.636298i | \(-0.780465\pi\) |
0.165328 | + | 0.986239i | \(0.447132\pi\) | |||||||
\(734\) | 5.93514 | + | 10.2800i | 0.219070 | + | 0.379440i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.8828 | − | 18.8496i | 0.401145 | − | 0.694804i | ||||
\(737\) | 0.586509i | 0.0216044i | ||||||||
\(738\) | −0.991923 | + | 0.0902400i | −0.0365132 | + | 0.00332178i | ||||
\(739\) | 45.6861 | 1.68059 | 0.840295 | − | 0.542130i | \(-0.182382\pi\) | ||||
0.840295 | + | 0.542130i | \(0.182382\pi\) | |||||||
\(740\) | −33.5209 | + | 58.0598i | −1.23225 | + | 2.13432i | ||||
\(741\) | 2.76173 | − | 12.5601i | 0.101455 | − | 0.461408i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.0448 | + | 14.4596i | −0.918804 | + | 0.530472i | −0.883253 | − | 0.468896i | \(-0.844652\pi\) |
−0.0355508 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(744\) | −7.53087 | + | 34.2498i | −0.276095 | + | 1.25566i | ||||
\(745\) | 54.3326 | + | 31.3689i | 1.99059 | + | 1.14927i | ||||
\(746\) | 22.6018i | 0.827510i | ||||||||
\(747\) | 21.7915 | + | 10.0699i | 0.797309 | + | 0.368439i | ||||
\(748\) | − | 1.08655i | − | 0.0397283i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.69491 | + | 24.2588i | 0.280979 | + | 0.885806i | ||||
\(751\) | −22.1007 | − | 38.2795i | −0.806465 | − | 1.39684i | −0.915297 | − | 0.402779i | \(-0.868044\pi\) |
0.108832 | − | 0.994060i | \(-0.465289\pi\) | |||||||
\(752\) | 1.92968 | + | 3.34230i | 0.0703682 | + | 0.121881i | ||||
\(753\) | −1.24841 | − | 1.13999i | −0.0454946 | − | 0.0415436i | ||||
\(754\) | −47.9887 | − | 27.7063i | −1.74765 | − | 1.00900i | ||||
\(755\) | −79.3947 | −2.88947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.5029 | −0.999611 | −0.499805 | − | 0.866138i | \(-0.666595\pi\) | ||||
−0.499805 | + | 0.866138i | \(0.666595\pi\) | |||||||
\(758\) | 28.4329 | + | 16.4157i | 1.03273 | + | 0.596246i | ||||
\(759\) | −2.74191 | − | 2.50379i | −0.0995249 | − | 0.0908816i | ||||
\(760\) | −8.37751 | − | 14.5103i | −0.303884 | − | 0.526343i | ||||
\(761\) | −2.54651 | − | 4.41069i | −0.0923109 | − | 0.159887i | 0.816172 | − | 0.577809i | \(-0.196092\pi\) |
−0.908483 | + | 0.417921i | \(0.862759\pi\) | |||||||
\(762\) | −2.91967 | − | 9.20448i | −0.105769 | − | 0.333443i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 58.3061i | − | 2.10944i | ||||||
\(765\) | 8.02979 | − | 5.66401i | 0.290317 | − | 0.204783i | ||||
\(766\) | 50.3780i | 1.82023i | ||||||||
\(767\) | −8.40755 | − | 4.85410i | −0.303579 | − | 0.175271i | ||||
\(768\) | −9.76019 | + | 44.3885i | −0.352191 | + | 1.60173i | ||||
\(769\) | −33.4505 | + | 19.3126i | −1.20626 | + | 0.696432i | −0.961939 | − | 0.273264i | \(-0.911897\pi\) |
−0.244316 | + | 0.969696i | \(0.578564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.55239 | − | 20.7039i | 0.163950 | − | 0.745632i | ||||
\(772\) | −19.7537 | + | 34.2145i | −0.710953 | + | 1.23141i | ||||
\(773\) | 34.3507 | 1.23551 | 0.617754 | − | 0.786371i | \(-0.288043\pi\) | ||||
0.617754 | + | 0.786371i | \(0.288043\pi\) | |||||||
\(774\) | −11.8230 | − | 16.7613i | −0.424968 | − | 0.602472i | ||||
\(775\) | − | 35.6132i | − | 1.27926i | ||||||
\(776\) | −23.4565 | + | 40.6279i | −0.842040 | + | 1.45846i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.36206 | + | 9.28736i | 0.192239 | + | 0.332968i | ||||
\(779\) | −0.152818 | + | 0.0882293i | −0.00547526 | + | 0.00316114i | ||||
\(780\) | −85.7521 | + | 93.9075i | −3.07042 | + | 3.36243i | ||||
\(781\) | −1.72647 | + | 2.99034i | −0.0617781 | + | 0.107003i | ||||
\(782\) | −15.4468 | −0.552377 | ||||||||
\(783\) | −19.0010 | + | 7.98620i | −0.679040 | + | 0.285404i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.4263 | + | 11.2158i | 0.693353 | + | 0.400308i | ||||
\(786\) | −26.3042 | + | 28.8059i | −0.938240 | + | 1.02747i | ||||
\(787\) | 20.3343 | − | 11.7400i | 0.724839 | − | 0.418486i | −0.0916921 | − | 0.995787i | \(-0.529228\pi\) |
0.816531 | + | 0.577301i | \(0.195894\pi\) | |||||||
\(788\) | 20.4577 | − | 11.8113i | 0.728776 | − | 0.420759i | ||||
\(789\) | −2.20378 | − | 6.94758i | −0.0784567 | − | 0.247340i | ||||
\(790\) | 73.8874 | + | 42.6589i | 2.62880 | + | 1.51774i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.30655 | + | 1.52797i | 0.117493 | + | 0.0542940i | ||||
\(793\) | −17.5007 | −0.621470 | ||||||||
\(794\) | −18.6074 | + | 32.2289i | −0.660350 | + | 1.14376i | ||||
\(795\) | 69.6227 | + | 15.3087i | 2.46926 | + | 0.542944i | ||||
\(796\) | 55.9791 | − | 32.3196i | 1.98413 | − | 1.14554i | ||||
\(797\) | 5.82399 | + | 10.0875i | 0.206296 | + | 0.357316i | 0.950545 | − | 0.310587i | \(-0.100526\pi\) |
−0.744249 | + | 0.667903i | \(0.767192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.960052 | + | 1.66286i | −0.0339642 | + | 0.0588277i | ||||
\(800\) | − | 21.6840i | − | 0.766645i | ||||||
\(801\) | 0.575846 | + | 6.32973i | 0.0203465 | + | 0.223650i | ||||
\(802\) | −25.5978 | −0.903889 | ||||||||
\(803\) | −0.0642859 | + | 0.111347i | −0.00226860 | + | 0.00392933i | ||||
\(804\) | −11.1954 | + | 3.55120i | −0.394833 | + | 0.125241i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 63.3373 | − | 36.5678i | 2.23096 | − | 1.28805i | ||||
\(807\) | 27.7033 | + | 25.2974i | 0.975203 | + | 0.890512i | ||||
\(808\) | −41.9346 | − | 24.2109i | −1.47525 | − | 0.851738i | ||||
\(809\) | 15.9029i | 0.559117i | 0.960129 | + | 0.279559i | \(0.0901881\pi\) | ||||
−0.960129 | + | 0.279559i | \(0.909812\pi\) | |||||||
\(810\) | 13.2389 | + | 72.1592i | 0.465168 | + | 2.53542i | ||||
\(811\) | − | 3.56109i | − | 0.125047i | −0.998044 | − | 0.0625233i | \(-0.980085\pi\) | ||
0.998044 | − | 0.0625233i | \(-0.0199148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.1388 | − | 26.4345i | 0.846583 | − | 0.927097i | ||||
\(814\) | −2.00241 | − | 3.46828i | −0.0701846 | − | 0.121563i | ||||
\(815\) | 42.1269 | + | 72.9660i | 1.47564 | + | 2.55589i | ||||
\(816\) | 3.01651 | − | 0.956840i | 0.105599 | − | 0.0334961i | ||||
\(817\) | −3.14705 | − | 1.81695i | −0.110101 | − | 0.0635671i | ||||
\(818\) | −46.5384 | −1.62718 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.74493 | 0.0609357 | ||||||||
\(821\) | −0.113440 | − | 0.0654949i | −0.00395910 | − | 0.00228579i | 0.498019 | − | 0.867166i | \(-0.334061\pi\) |
−0.501978 | + | 0.864880i | \(0.667394\pi\) | |||||||
\(822\) | 9.02365 | − | 41.0388i | 0.314736 | − | 1.43139i | ||||
\(823\) | −23.0144 | − | 39.8621i | −0.802231 | − | 1.38950i | −0.918145 | − | 0.396245i | \(-0.870313\pi\) |
0.115914 | − | 0.993259i | \(-0.463020\pi\) | |||||||
\(824\) | −34.8406 | − | 60.3456i | −1.21373 | − | 2.10224i | ||||
\(825\) | −3.61286 | − | 0.794399i | −0.125784 | − | 0.0276574i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.5836i | 1.41123i | 0.708595 | + | 0.705615i | \(0.249329\pi\) | ||||
−0.708595 | + | 0.705615i | \(0.750671\pi\) | |||||||
\(828\) | 31.1911 | − | 67.4981i | 1.08397 | − | 2.34572i | ||||
\(829\) | − | 30.1296i | − | 1.04645i | −0.852196 | − | 0.523223i | \(-0.824730\pi\) | ||
0.852196 | − | 0.523223i | \(-0.175270\pi\) | |||||||
\(830\) | −56.4887 | − | 32.6137i | −1.96075 | − | 1.13204i | ||||
\(831\) | 46.0454 | − | 14.6056i | 1.59730 | − | 0.506664i | ||||
\(832\) | 58.1068 | − | 33.5480i | 2.01449 | − | 1.16307i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.9990 | + | 14.6095i | 0.553999 | + | 0.505887i | ||||
\(835\) | 24.0439 | − | 41.6453i | 0.832075 | − | 1.44120i | ||||
\(836\) | 1.43718 | 0.0497060 | ||||||||
\(837\) | 3.41077 | − | 26.9886i | 0.117893 | − | 0.932863i | ||||
\(838\) | − | 41.9419i | − | 1.44886i | ||||||
\(839\) | −5.81551 | + | 10.0728i | −0.200774 | + | 0.347750i | −0.948778 | − | 0.315944i | \(-0.897679\pi\) |
0.748004 | + | 0.663694i | \(0.231012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.63302 | − | 11.4887i | −0.228725 | − | 0.396163i | ||||
\(842\) | 69.6622 | − | 40.2195i | 2.40072 | − | 1.38606i | ||||
\(843\) | 10.1093 | + | 31.8702i | 0.348182 | + | 1.09767i | ||||
\(844\) | 1.02509 | − | 1.77551i | 0.0352851 | − | 0.0611156i | ||||
\(845\) | 74.4264 | 2.56035 | ||||||||
\(846\) | −8.26302 | − | 11.7144i | −0.284089 | − | 0.402749i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.8821 | + | 11.4789i | 0.682754 | + | 0.394188i | ||||
\(849\) | 29.8280 | + | 6.55862i | 1.02370 | + | 0.225091i | ||||
\(850\) | −13.3272 | + | 7.69446i | −0.457119 | + | 0.263918i | ||||
\(851\) | −31.7905 | + | 18.3542i | −1.08976 | + | 0.629175i | ||||
\(852\) | −67.5338 | − | 14.8494i | −2.31367 | − | 0.508732i | ||||
\(853\) | −20.6854 | − | 11.9427i | −0.708254 | − | 0.408911i | 0.102160 | − | 0.994768i | \(-0.467425\pi\) |
−0.810414 | + | 0.585857i | \(0.800758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.49177 | + | 10.6210i | 0.256213 | + | 0.363230i | ||||
\(856\) | 13.9153 | 0.475614 | ||||||||
\(857\) | 17.3362 | − | 30.0271i | 0.592193 | − | 1.02571i | −0.401744 | − | 0.915752i | \(-0.631596\pi\) |
0.993936 | − | 0.109956i | \(-0.0350709\pi\) | |||||||
\(858\) | −2.29688 | − | 7.24108i | −0.0784141 | − | 0.247206i | ||||
\(859\) | 26.3932 | − | 15.2381i | 0.900525 | − | 0.519918i | 0.0231546 | − | 0.999732i | \(-0.492629\pi\) |
0.877371 | + | 0.479813i | \(0.159296\pi\) | |||||||
\(860\) | 17.9671 | + | 31.1200i | 0.612674 | + | 1.06118i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.7562 | − | 29.0225i | 0.570717 | − | 0.988512i | ||||
\(863\) | 33.4052i | 1.13713i | 0.822639 | + | 0.568564i | \(0.192501\pi\) | ||||
−0.822639 | + | 0.568564i | \(0.807499\pi\) | |||||||
\(864\) | 2.07673 | − | 16.4327i | 0.0706519 | − | 0.559051i | ||||
\(865\) | 37.4450 | 1.27317 | ||||||||
\(866\) | −10.7970 | + | 18.7010i | −0.366898 | + | 0.635485i | ||||
\(867\) | −20.5807 | − | 18.7934i | −0.698959 | − | 0.638258i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.84579 | + | 1.64302i | −0.0965369 | + | 0.0557356i | ||||
\(870\) | 53.3826 | − | 16.9330i | 1.80984 | − | 0.574083i | ||||
\(871\) | 9.52520 | + | 5.49938i | 0.322749 | + | 0.186339i | ||||
\(872\) | 25.3781i | 0.859410i | ||||||||
\(873\) | 15.2657 | − | 33.0352i | 0.516666 | − | 1.11807i | ||||
\(874\) | − | 20.4315i | − | 0.691106i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.51465 | − | 0.552924i | −0.0849621 | − | 0.0186816i | ||||
\(877\) | 27.7600 | + | 48.0817i | 0.937389 | + | 1.62360i | 0.770318 | + | 0.637660i | \(0.220097\pi\) |
0.167070 | + | 0.985945i | \(0.446569\pi\) | |||||||
\(878\) | −13.9073 | − | 24.0881i | −0.469347 | − | 0.812933i | ||||
\(879\) | 10.4995 | − | 47.7509i | 0.354140 | − | 1.61060i | ||||
\(880\) | −1.79005 | − | 1.03349i | −0.0603426 | − | 0.0348388i | ||||
\(881\) | 19.9850 | 0.673313 | 0.336656 | − | 0.941628i | \(-0.390704\pi\) | ||||
0.336656 | + | 0.941628i | \(0.390704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5837 | 1.19749 | 0.598743 | − | 0.800941i | \(-0.295667\pi\) | ||||
0.598743 | + | 0.800941i | \(0.295667\pi\) | |||||||
\(884\) | −17.6462 | − | 10.1880i | −0.593504 | − | 0.342660i | ||||
\(885\) | 9.35255 | − | 2.96664i | 0.314382 | − | 0.0997224i | ||||
\(886\) | 8.46321 | + | 14.6587i | 0.284327 | + | 0.492469i | ||||
\(887\) | −17.8317 | − | 30.8853i | −0.598729 | − | 1.03703i | −0.993009 | − | 0.118038i | \(-0.962339\pi\) |
0.394280 | − | 0.918990i | \(-0.370994\pi\) | |||||||
\(888\) | 24.2827 | − | 26.5920i | 0.814872 | − | 0.892370i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 17.2700i | − | 0.578892i | ||||||
\(891\) | −2.66183 | − | 0.948028i | −0.0891748 | − | 0.0317601i | ||||
\(892\) | 31.9078i | 1.06835i | ||||||||
\(893\) | −2.19946 | − | 1.26986i | −0.0736021 | − | 0.0424942i | ||||
\(894\) | −55.4205 | − | 50.6075i | −1.85354 | − | 1.69257i | ||||
\(895\) | 4.75872 | − | 2.74745i | 0.159066 | − | 0.0918370i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −66.3721 | + | 21.0533i | −2.21610 | + | 0.702949i | ||||
\(898\) | 3.76607 | − | 6.52302i | 0.125675 | − | 0.217676i | ||||
\(899\) | −20.7663 | −0.692594 | ||||||||
\(900\) | −6.71149 | − | 73.7730i | −0.223716 | − | 2.45910i | ||||
\(901\) | 11.4220i | 0.380521i | ||||||||
\(902\) | −0.0521180 | + | 0.0902710i | −0.00173534 | + | 0.00300569i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.19569 | + | 7.26715i | 0.139547 | + | 0.241702i | ||||
\(905\) | −52.0925 | + | 30.0756i | −1.73161 | + | 0.999748i | ||||
\(906\) | 92.7602 | + | 20.3962i | 3.08175 | + | 0.677619i | ||||
\(907\) | −18.6215 | + | 32.2533i | −0.618315 | + | 1.07095i | 0.371478 | + | 0.928442i | \(0.378851\pi\) |
−0.989793 | + | 0.142512i | \(0.954482\pi\) | |||||||
\(908\) | 61.3692 | 2.03661 | ||||||||
\(909\) | 34.0977 | + | 15.7567i | 1.13095 | + | 0.522616i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8068 | − | 10.8581i | −0.623098 | − | 0.359746i | 0.154976 | − | 0.987918i | \(-0.450470\pi\) |
−0.778074 | + | 0.628172i | \(0.783803\pi\) | |||||||
\(912\) | 1.26561 | + | 3.98993i | 0.0419086 | + | 0.132120i | ||||
\(913\) | 2.17567 | − | 1.25613i | 0.0720043 | − | 0.0415717i | ||||
\(914\) | 49.6227 | − | 28.6497i | 1.64137 | − | 0.947647i | ||||
\(915\) | 11.9269 | − | 13.0612i | 0.394292 | − | 0.431790i | ||||
\(916\) | −61.4940 | − | 35.5036i | −2.03182 | − | 1.17307i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10.8366 | + | 4.55468i | −0.357661 | + | 0.150327i | ||||
\(919\) | 34.2046 | 1.12831 | 0.564153 | − | 0.825671i | \(-0.309203\pi\) | ||||
0.564153 | + | 0.825671i | \(0.309203\pi\) | |||||||
\(920\) | −45.3598 | + | 78.5656i | −1.49547 | + | 2.59023i | ||||
\(921\) | −10.0052 | + | 10.9568i | −0.329684 | + | 0.361038i | ||||
\(922\) | 28.2452 | − | 16.3074i | 0.930208 | − | 0.537056i | ||||
\(923\) | 32.3764 | + | 56.0776i | 1.06568 | + | 1.84582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.2854 | + | 31.6713i | −0.601221 | + | 1.04135i | ||||
\(926\) | − | 48.9529i | − | 1.60869i | ||||||
\(927\) | 31.1569 | + | 44.1708i | 1.02333 | + | 1.45076i | ||||
\(928\) | −12.6441 | −0.415062 | ||||||||
\(929\) | −23.4757 | + | 40.6611i | −0.770213 | + | 1.33405i | 0.167233 | + | 0.985917i | \(0.446517\pi\) |
−0.937446 | + | 0.348131i | \(0.886816\pi\) | |||||||
\(930\) | −15.8735 | + | 72.1914i | −0.520513 | + | 2.36725i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −62.0442 | + | 35.8213i | −2.03233 | + | 1.17336i | ||||
\(933\) | 7.20050 | − | 32.7472i | 0.235734 | − | 1.07210i | ||||
\(934\) | −1.91469 | − | 1.10545i | −0.0626505 | − | 0.0361713i | ||||
\(935\) | − | 1.02836i | − | 0.0336309i | ||||||
\(936\) | 55.8187 | − | 39.3731i | 1.82449 | − | 1.28695i | ||||
\(937\) | 28.8826i | 0.943555i | 0.881718 | + | 0.471777i | \(0.156387\pi\) | ||||
−0.881718 | + | 0.471777i | \(0.843613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8785 | + | 43.7530i | 0.452907 | + | 1.42782i | ||||
\(940\) | 12.5572 | + | 21.7496i | 0.409569 | + | 0.709395i | ||||
\(941\) | −0.727044 | − | 1.25928i | −0.0237009 | − | 0.0410512i | 0.853932 | − | 0.520385i | \(-0.174212\pi\) |
−0.877633 | + | 0.479334i | \(0.840878\pi\) | |||||||
\(942\) | −19.8152 | − | 18.0944i | −0.645615 | − | 0.589547i | ||||
\(943\) | 0.827428 | + | 0.477716i | 0.0269448 | + | 0.0155566i | ||||
\(944\) | 3.15992 | 0.102847 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.14658 | −0.0697914 | ||||||||
\(947\) | −36.9596 | − | 21.3386i | −1.20102 | − | 0.693412i | −0.240241 | − | 0.970713i | \(-0.577227\pi\) |
−0.960783 | + | 0.277301i | \(0.910560\pi\) | |||||||
\(948\) | −48.5931 | − | 44.3730i | −1.57823 | − | 1.44117i | ||||
\(949\) | 1.20555 | + | 2.08807i | 0.0391338 | + | 0.0677817i | ||||
\(950\) | −10.1774 | − | 17.6279i | −0.330200 | − | 0.571923i | ||||
\(951\) | −4.53809 | − | 14.3067i | −0.147158 | − | 0.463926i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8171i | 0.350401i | 0.984533 | + | 0.175200i | \(0.0560574\pi\) | ||||
−0.984533 | + | 0.175200i | \(0.943943\pi\) | |||||||
\(954\) | −77.4104 | − | 35.7716i | −2.50625 | − | 1.15815i | ||||
\(955\) | − | 55.1833i | − | 1.78569i | ||||||
\(956\) | −61.6216 | − | 35.5773i | −1.99299 | − | 1.15065i | ||||
\(957\) | −0.463218 | + | 2.10668i | −0.0149737 | + | 0.0680992i | ||||
\(958\) | 66.5902 | − | 38.4458i | 2.15143 | − | 1.24213i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −14.5627 | + | 66.2298i | −0.470008 | + | 2.13756i | ||||
\(961\) | −1.79596 | + | 3.11070i | −0.0579342 | + | 0.100345i | ||||
\(962\) | −75.1022 | −2.42139 | ||||||||
\(963\) | −10.7501 | + | 0.977988i | −0.346417 | + | 0.0315152i | ||||
\(964\) | 57.9115i | 1.86521i | ||||||||
\(965\) | −18.6958 | + | 32.3820i | −0.601838 | + | 1.04241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4942 | − | 38.9611i | −0.723365 | − | 1.25290i | −0.959643 | − | 0.281219i | \(-0.909261\pi\) |
0.236279 | − | 0.971685i | \(-0.424072\pi\) | |||||||
\(968\) | −36.5111 | + | 21.0797i | −1.17351 | + | 0.677526i | ||||
\(969\) | −1.40429 | + | 1.53784i | −0.0451121 | + | 0.0494025i | ||||
\(970\) | −49.4415 | + | 85.6351i | −1.58747 | + | 2.74958i | ||||
\(971\) | −6.80343 | −0.218332 | −0.109166 | − | 0.994024i | \(-0.534818\pi\) | ||||
−0.109166 | + | 0.994024i | \(0.534818\pi\) | |||||||
\(972\) | 1.97930 | − | 56.5499i | 0.0634860 | − | 1.81384i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 70.6321 | + | 40.7795i | 2.26320 | + | 1.30666i | ||||
\(975\) | −46.7772 | + | 51.2259i | −1.49807 | + | 1.64054i | ||||
\(976\) | 4.93315 | − | 2.84815i | 0.157906 | − | 0.0911672i | ||||
\(977\) | −29.2645 | + | 16.8959i | −0.936254 | + | 0.540546i | −0.888784 | − | 0.458326i | \(-0.848449\pi\) |
−0.0474698 | + | 0.998873i | \(0.515116\pi\) | |||||||
\(978\) | −30.4740 | − | 96.0715i | −0.974451 | − | 3.07203i | ||||
\(979\) | 0.576044 | + | 0.332579i | 0.0184104 | + | 0.0106293i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.78361 | − | 19.6056i | −0.0569464 | − | 0.625958i | ||||
\(982\) | 20.0293 | 0.639160 | ||||||||
\(983\) | −23.4913 | + | 40.6881i | −0.749256 | + | 1.29775i | 0.198923 | + | 0.980015i | \(0.436256\pi\) |
−0.948180 | + | 0.317735i | \(0.897078\pi\) | |||||||
\(984\) | −0.915408 | − | 0.201281i | −0.0291821 | − | 0.00641660i | ||||
\(985\) | 19.3620 | − | 11.1787i | 0.616926 | − | 0.356182i | ||||
\(986\) | 4.48668 | + | 7.77116i | 0.142885 | + | 0.247484i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.4757 | − | 23.3405i | 0.428718 | − | 0.742562i | ||||
\(989\) | 19.6757i | 0.625651i | ||||||||
\(990\) | 6.96953 | + | 3.22064i | 0.221506 | + | 0.102359i | ||||
\(991\) | 0.600897 | 0.0190881 | 0.00954406 | − | 0.999954i | \(-0.496962\pi\) | ||||
0.00954406 | + | 0.999954i | \(0.496962\pi\) | |||||||
\(992\) | 8.34405 | − | 14.4523i | 0.264924 | − | 0.458861i | ||||
\(993\) | −31.9271 | + | 10.1273i | −1.01318 | + | 0.321381i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.9810 | − | 30.5886i | 1.67961 | − | 0.969723i | ||||
\(996\) | 37.1505 | + | 33.9242i | 1.17716 | + | 1.07493i | ||||
\(997\) | −41.9387 | − | 24.2133i | −1.32821 | − | 0.766844i | −0.343189 | − | 0.939266i | \(-0.611507\pi\) |
−0.985023 | + | 0.172423i | \(0.944841\pi\) | |||||||
\(998\) | − | 27.0682i | − | 0.856829i | ||||||
\(999\) | −16.8904 | + | 22.2501i | −0.534388 | + | 0.703960i |
(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 | 441.2.o.e.146.4 | yes | 48 | |
3.2 | odd | 2 | 1323.2.o.e.440.22 | 48 | |||
7.2 | even | 3 | 441.2.i.d.227.21 | 48 | |||
7.3 | odd | 6 | 441.2.s.d.362.21 | 48 | |||
7.4 | even | 3 | 441.2.s.d.362.22 | 48 | |||
7.5 | odd | 6 | 441.2.i.d.227.22 | 48 | |||
7.6 | odd | 2 | inner | 441.2.o.e.146.3 | ✓ | 48 | |
9.4 | even | 3 | 1323.2.o.e.881.21 | 48 | |||
9.5 | odd | 6 | inner | 441.2.o.e.293.3 | yes | 48 | |
21.2 | odd | 6 | 1323.2.i.d.521.4 | 48 | |||
21.5 | even | 6 | 1323.2.i.d.521.24 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.656.4 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.656.3 | 48 | |||
21.20 | even | 2 | 1323.2.o.e.440.21 | 48 | |||
63.4 | even | 3 | 1323.2.i.d.1097.24 | 48 | |||
63.5 | even | 6 | 441.2.s.d.374.22 | 48 | |||
63.13 | odd | 6 | 1323.2.o.e.881.22 | 48 | |||
63.23 | odd | 6 | 441.2.s.d.374.21 | 48 | |||
63.31 | odd | 6 | 1323.2.i.d.1097.4 | 48 | |||
63.32 | odd | 6 | 441.2.i.d.68.4 | 48 | |||
63.40 | odd | 6 | 1323.2.s.d.962.4 | 48 | |||
63.41 | even | 6 | inner | 441.2.o.e.293.4 | yes | 48 | |
63.58 | even | 3 | 1323.2.s.d.962.3 | 48 | |||
63.59 | even | 6 | 441.2.i.d.68.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.3 | 48 | 63.59 | even | 6 | |||
441.2.i.d.68.4 | 48 | 63.32 | odd | 6 | |||
441.2.i.d.227.21 | 48 | 7.2 | even | 3 | |||
441.2.i.d.227.22 | 48 | 7.5 | odd | 6 | |||
441.2.o.e.146.3 | ✓ | 48 | 7.6 | odd | 2 | inner | |
441.2.o.e.146.4 | yes | 48 | 1.1 | even | 1 | trivial | |
441.2.o.e.293.3 | yes | 48 | 9.5 | odd | 6 | inner | |
441.2.o.e.293.4 | yes | 48 | 63.41 | even | 6 | inner | |
441.2.s.d.362.21 | 48 | 7.3 | odd | 6 | |||
441.2.s.d.362.22 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.21 | 48 | 63.23 | odd | 6 | |||
441.2.s.d.374.22 | 48 | 63.5 | even | 6 | |||
1323.2.i.d.521.4 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.24 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.1097.4 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.1097.24 | 48 | 63.4 | even | 3 | |||
1323.2.o.e.440.21 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.440.22 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.881.21 | 48 | 9.4 | even | 3 | |||
1323.2.o.e.881.22 | 48 | 63.13 | odd | 6 | |||
1323.2.s.d.656.3 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.656.4 | 48 | 21.11 | odd | 6 | |||
1323.2.s.d.962.3 | 48 | 63.58 | even | 3 | |||
1323.2.s.d.962.4 | 48 | 63.40 | odd | 6 |