Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(37,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.ca (of order \(12\), degree \(4\), 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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Character | \(\chi\) | \(=\) | 315.37 |
Dual form | 315.3.ca.b.298.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.41166 | + | 0.914152i | −1.70583 | + | 0.457076i | −0.974397 | − | 0.224836i | \(-0.927815\pi\) |
−0.731435 | + | 0.681912i | \(0.761149\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.33966 | − | 4.23756i | 1.83492 | − | 1.05939i | ||||
\(5\) | 4.98672 | − | 0.364163i | 0.997344 | − | 0.0728326i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.35750 | − | 2.92953i | −0.908215 | − | 0.418505i | ||||
\(8\) | −11.1766 | + | 11.1766i | −1.39708 | + | 1.39708i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −16.6801 | + | 5.80102i | −1.66801 | + | 0.580102i | ||||
\(11\) | −8.72135 | − | 15.1058i | −0.792850 | − | 1.37326i | −0.924195 | − | 0.381920i | \(-0.875263\pi\) |
0.131345 | − | 0.991337i | \(-0.458070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.72144 | + | 8.72144i | −0.670880 | + | 0.670880i | −0.957919 | − | 0.287039i | \(-0.907329\pi\) |
0.287039 | + | 0.957919i | \(0.407329\pi\) | |||||||
\(14\) | 24.3677 | + | 4.18286i | 1.74055 | + | 0.298776i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.9636 | − | 18.9894i | 0.685222 | − | 1.18684i | ||||
\(17\) | −3.02215 | + | 11.2788i | −0.177774 | + | 0.663461i | 0.818289 | + | 0.574807i | \(0.194923\pi\) |
−0.996063 | + | 0.0886535i | \(0.971744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12903 | − | 1.80655i | −0.164686 | − | 0.0950814i | 0.415392 | − | 0.909643i | \(-0.363644\pi\) |
−0.580078 | + | 0.814561i | \(0.696978\pi\) | |||||||
\(20\) | 35.0577 | − | 23.8044i | 1.75288 | − | 1.19022i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 43.5633 | + | 43.5633i | 1.98015 | + | 1.98015i | ||||
\(23\) | 6.21349 | + | 23.1890i | 0.270152 | + | 1.00822i | 0.959021 | + | 0.283334i | \(0.0914406\pi\) |
−0.688870 | + | 0.724885i | \(0.741893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.7348 | − | 3.63196i | 0.989391 | − | 0.145278i | ||||
\(26\) | 21.7819 | − | 37.7273i | 0.837765 | − | 1.45105i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −59.0760 | + | 5.43848i | −2.10986 | + | 0.194231i | ||||
\(29\) | 46.5831i | 1.60631i | 0.595767 | + | 0.803157i | \(0.296848\pi\) | ||||
−0.595767 | + | 0.803157i | \(0.703152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.10507 | − | 1.91403i | −0.0356474 | − | 0.0617430i | 0.847651 | − | 0.530554i | \(-0.178016\pi\) |
−0.883299 | + | 0.468811i | \(0.844683\pi\) | |||||||
\(32\) | −3.68097 | + | 13.7376i | −0.115030 | + | 0.429300i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 41.2423i | − | 1.21301i | ||||||
\(35\) | −32.7699 | − | 12.2936i | −0.936283 | − | 0.351246i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −29.3791 | + | 7.87211i | −0.794030 | + | 0.212760i | −0.632961 | − | 0.774183i | \(-0.718161\pi\) |
−0.161069 | + | 0.986943i | \(0.551494\pi\) | |||||||
\(38\) | 12.3266 | + | 3.30292i | 0.324386 | + | 0.0869188i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −51.6647 | + | 59.8049i | −1.29162 | + | 1.49512i | ||||
\(41\) | −29.9435 | −0.730329 | −0.365165 | − | 0.930943i | \(-0.618987\pi\) | ||||
−0.365165 | + | 0.930943i | \(0.618987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.6771 | + | 19.6771i | −0.457608 | + | 0.457608i | −0.897869 | − | 0.440262i | \(-0.854886\pi\) |
0.440262 | + | 0.897869i | \(0.354886\pi\) | |||||||
\(44\) | −128.024 | − | 73.9145i | −2.90963 | − | 1.67987i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −42.3966 | − | 73.4331i | −0.921666 | − | 1.59637i | ||||
\(47\) | −79.1503 | + | 21.2083i | −1.68405 | + | 0.451240i | −0.968844 | − | 0.247674i | \(-0.920334\pi\) |
−0.715206 | + | 0.698913i | \(0.753667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.8357 | + | 37.2490i | 0.649707 | + | 0.760185i | ||||
\(50\) | −81.0665 | + | 35.0024i | −1.62133 | + | 0.700047i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −27.0549 | + | 100.970i | −0.520286 | + | 1.94173i | ||||
\(53\) | −1.63190 | − | 0.437265i | −0.0307905 | − | 0.00825028i | 0.243391 | − | 0.969928i | \(-0.421740\pi\) |
−0.274181 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −48.9919 | − | 72.1526i | −0.890763 | − | 1.31186i | ||||
\(56\) | 103.798 | − | 38.3132i | 1.85353 | − | 0.684164i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −42.5841 | − | 158.926i | −0.734208 | − | 2.74010i | ||||
\(59\) | 76.5567 | − | 44.2000i | 1.29757 | − | 0.749153i | 0.317587 | − | 0.948229i | \(-0.397127\pi\) |
0.979984 | + | 0.199076i | \(0.0637941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.4309 | + | 40.5836i | −0.384114 | + | 0.665305i | −0.991646 | − | 0.128990i | \(-0.958826\pi\) |
0.607532 | + | 0.794295i | \(0.292160\pi\) | |||||||
\(62\) | 5.51984 | + | 5.51984i | 0.0890296 | + | 0.0890296i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 37.4755i | 0.585554i | ||||||||
\(65\) | −40.3154 | + | 46.6674i | −0.620236 | + | 0.717960i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.01836 | − | 11.2647i | 0.0450501 | − | 0.168129i | −0.939736 | − | 0.341902i | \(-0.888929\pi\) |
0.984786 | + | 0.173772i | \(0.0555957\pi\) | |||||||
\(68\) | 25.6131 | + | 95.5894i | 0.376663 | + | 1.40573i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 123.038 | + | 11.9849i | 1.75769 | + | 0.171213i | ||||
\(71\) | −67.1402 | −0.945636 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.6525 | − | 4.72997i | −0.241815 | − | 0.0647941i | 0.135876 | − | 0.990726i | \(-0.456615\pi\) |
−0.377691 | + | 0.925932i | \(0.623282\pi\) | |||||||
\(74\) | 93.0353 | − | 53.7140i | 1.25723 | − | 0.725865i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30.6214 | −0.402913 | ||||||||
\(77\) | 11.1930 | + | 121.585i | 0.145363 | + | 1.57902i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.4021 | + | 11.2018i | 0.245596 | + | 0.141795i | 0.617746 | − | 0.786378i | \(-0.288046\pi\) |
−0.372150 | + | 0.928173i | \(0.621379\pi\) | |||||||
\(80\) | 47.7569 | − | 98.6876i | 0.596962 | − | 1.23359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 102.157 | − | 27.3729i | 1.24582 | − | 0.333816i | ||||
\(83\) | −52.4430 | + | 52.4430i | −0.631844 | + | 0.631844i | −0.948530 | − | 0.316686i | \(-0.897430\pi\) |
0.316686 | + | 0.948530i | \(0.397430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9633 | + | 57.3450i | −0.128980 | + | 0.674647i | ||||
\(86\) | 49.1438 | − | 85.1196i | 0.571440 | − | 0.989763i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 266.308 | + | 71.3570i | 3.02623 | + | 0.810875i | ||||
\(89\) | −44.2757 | − | 25.5626i | −0.497480 | − | 0.287220i | 0.230192 | − | 0.973145i | \(-0.426065\pi\) |
−0.727672 | + | 0.685925i | \(0.759398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 80.9964 | − | 29.8968i | 0.890070 | − | 0.328536i | ||||
\(92\) | 143.870 | + | 143.870i | 1.56380 | + | 1.56380i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 250.647 | − | 144.711i | 2.66645 | − | 1.53948i | ||||
\(95\) | −16.2615 | − | 7.86926i | −0.171173 | − | 0.0828343i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.15031 | + | 9.15031i | 0.0943331 | + | 0.0943331i | 0.752698 | − | 0.658365i | \(-0.228752\pi\) |
−0.658365 | + | 0.752698i | \(0.728752\pi\) | |||||||
\(98\) | −142.664 | − | 97.9785i | −1.45575 | − | 0.999781i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 166.154 | − | 131.472i | 1.66154 | − | 1.31472i | ||||
\(101\) | −42.1642 | − | 73.0305i | −0.417467 | − | 0.723074i | 0.578217 | − | 0.815883i | \(-0.303749\pi\) |
−0.995684 | + | 0.0928089i | \(0.970415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −30.3411 | − | 113.235i | −0.294574 | − | 1.09937i | −0.941555 | − | 0.336859i | \(-0.890635\pi\) |
0.646981 | − | 0.762506i | \(-0.276031\pi\) | |||||||
\(104\) | − | 194.953i | − | 1.87455i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.96720 | 0.0562944 | ||||||||
\(107\) | 138.045 | − | 36.9890i | 1.29014 | − | 0.345691i | 0.452425 | − | 0.891802i | \(-0.350559\pi\) |
0.837713 | + | 0.546111i | \(0.183892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −140.724 | + | 81.2472i | −1.29105 | + | 0.745387i | −0.978840 | − | 0.204627i | \(-0.934402\pi\) |
−0.312208 | + | 0.950014i | \(0.601069\pi\) | |||||||
\(110\) | 233.102 | + | 201.374i | 2.11911 | + | 1.83067i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −125.331 | + | 88.6073i | −1.11903 | + | 0.791136i | ||||
\(113\) | 3.09464 | − | 3.09464i | 0.0273862 | − | 0.0273862i | −0.693281 | − | 0.720667i | \(-0.743836\pi\) |
0.720667 | + | 0.693281i | \(0.243836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.4295 | + | 113.375i | 0.342865 | + | 0.985866i | ||||
\(116\) | 197.399 | + | 341.904i | 1.70171 | + | 2.94745i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −220.780 | + | 220.780i | −1.87102 | + | 1.87102i | ||||
\(119\) | 52.2551 | − | 62.8517i | 0.439118 | − | 0.528166i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −91.6240 | + | 158.697i | −0.757223 | + | 1.31155i | ||||
\(122\) | 42.8389 | − | 159.877i | 0.351139 | − | 1.31047i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.2217 | − | 9.36558i | −0.130820 | − | 0.0755289i | ||||
\(125\) | 122.023 | − | 27.1191i | 0.976182 | − | 0.216953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.674 | − | 117.674i | −0.926571 | − | 0.926571i | 0.0709120 | − | 0.997483i | \(-0.477409\pi\) |
−0.997483 | + | 0.0709120i | \(0.977409\pi\) | |||||||
\(128\) | −48.9822 | − | 182.804i | −0.382673 | − | 1.42816i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 94.8813 | − | 196.068i | 0.729856 | − | 1.50821i | ||||
\(131\) | −81.6255 | + | 141.379i | −0.623095 | + | 1.07923i | 0.365811 | + | 0.930689i | \(0.380792\pi\) |
−0.988906 | + | 0.148543i | \(0.952542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6005 | + | 20.6517i | 0.109778 | + | 0.155276i | ||||
\(134\) | 41.1905i | 0.307392i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −92.2820 | − | 159.837i | −0.678544 | − | 1.17527i | ||||
\(137\) | 38.2623 | − | 142.797i | 0.279287 | − | 1.04231i | −0.673627 | − | 0.739072i | \(-0.735265\pi\) |
0.952914 | − | 0.303241i | \(-0.0980688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 101.553i | − | 0.730596i | −0.930891 | − | 0.365298i | \(-0.880967\pi\) | ||
0.930891 | − | 0.365298i | \(-0.119033\pi\) | |||||||
\(140\) | −292.615 | + | 48.6335i | −2.09011 | + | 0.347382i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 229.060 | − | 61.3763i | 1.61310 | − | 0.432228i | ||||
\(143\) | 207.807 | + | 55.6818i | 1.45320 | + | 0.389383i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.9639 | + | 232.297i | 0.116992 | + | 1.60205i | ||||
\(146\) | 64.5483 | 0.442112 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −182.274 | + | 182.274i | −1.23158 | + | 1.23158i | ||||
\(149\) | −91.7653 | − | 52.9807i | −0.615874 | − | 0.355575i | 0.159387 | − | 0.987216i | \(-0.449048\pi\) |
−0.775261 | + | 0.631641i | \(0.782382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 80.5845 | + | 139.576i | 0.533672 | + | 0.924347i | 0.999226 | + | 0.0393279i | \(0.0125217\pi\) |
−0.465554 | + | 0.885019i | \(0.654145\pi\) | |||||||
\(152\) | 55.1632 | − | 14.7809i | 0.362916 | − | 0.0972429i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −149.334 | − | 404.574i | −0.969699 | − | 2.62711i | ||||
\(155\) | −6.20769 | − | 9.14233i | −0.0400496 | − | 0.0589828i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −35.5563 | + | 132.698i | −0.226473 | + | 0.845210i | 0.755336 | + | 0.655338i | \(0.227474\pi\) |
−0.981809 | + | 0.189872i | \(0.939193\pi\) | |||||||
\(158\) | −76.4335 | − | 20.4803i | −0.483756 | − | 0.129622i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.3533 | + | 69.8460i | −0.0834579 | + | 0.436537i | ||||
\(161\) | 28.4309 | − | 165.627i | 0.176589 | − | 1.02874i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −48.8824 | − | 182.431i | −0.299892 | − | 1.11921i | −0.937254 | − | 0.348647i | \(-0.886641\pi\) |
0.637362 | − | 0.770564i | \(-0.280025\pi\) | |||||||
\(164\) | −219.775 | + | 126.887i | −1.34009 | + | 0.773703i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 130.977 | − | 226.859i | 0.789018 | − | 1.36662i | ||||
\(167\) | 114.153 | + | 114.153i | 0.683552 | + | 0.683552i | 0.960799 | − | 0.277247i | \(-0.0894220\pi\) |
−0.277247 | + | 0.960799i | \(0.589422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8729i | 0.0998396i | ||||||||
\(170\) | −15.0189 | − | 205.664i | −0.0883466 | − | 1.20979i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −61.0406 | + | 227.807i | −0.354887 | + | 1.32446i | ||||
\(173\) | −53.9511 | − | 201.348i | −0.311856 | − | 1.16386i | −0.926881 | − | 0.375355i | \(-0.877521\pi\) |
0.615025 | − | 0.788508i | \(-0.289146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −167.891 | − | 49.3712i | −0.959379 | − | 0.282121i | ||||
\(176\) | −382.468 | −2.17312 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 174.422 | + | 46.7362i | 0.979899 | + | 0.262563i | ||||
\(179\) | 102.967 | − | 59.4481i | 0.575235 | − | 0.332112i | −0.184002 | − | 0.982926i | \(-0.558905\pi\) |
0.759238 | + | 0.650814i | \(0.225572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.13381 | −0.0117890 | −0.00589449 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589449 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(182\) | −249.002 | + | 176.041i | −1.36814 | + | 0.967257i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −328.622 | − | 189.730i | −1.78599 | − | 1.03114i | ||||
\(185\) | −143.639 | + | 49.9548i | −0.776426 | + | 0.270026i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 196.733 | − | 52.7146i | 1.05205 | − | 0.281896i | ||||
\(188\) | −491.066 | + | 491.066i | −2.61205 | + | 2.61205i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 62.6724 | + | 11.9818i | 0.329855 | + | 0.0630621i | ||||
\(191\) | −85.4671 | + | 148.033i | −0.447472 | + | 0.775044i | −0.998221 | − | 0.0596272i | \(-0.981009\pi\) |
0.550749 | + | 0.834671i | \(0.314342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 80.0626 | + | 21.4527i | 0.414832 | + | 0.111154i | 0.460197 | − | 0.887817i | \(-0.347779\pi\) |
−0.0453656 | + | 0.998970i | \(0.514445\pi\) | |||||||
\(194\) | −39.5825 | − | 22.8530i | −0.204034 | − | 0.117799i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 391.508 | + | 138.490i | 1.99749 | + | 0.706582i | ||||
\(197\) | −32.0391 | − | 32.0391i | −0.162635 | − | 0.162635i | 0.621098 | − | 0.783733i | \(-0.286687\pi\) |
−0.783733 | + | 0.621098i | \(0.786687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0307 | − | 12.7194i | 0.110707 | − | 0.0639167i | −0.443624 | − | 0.896213i | \(-0.646307\pi\) |
0.554331 | + | 0.832296i | \(0.312974\pi\) | |||||||
\(200\) | −235.859 | + | 317.045i | −1.17929 | + | 1.58522i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 210.611 | + | 210.611i | 1.04263 | + | 1.04263i | ||||
\(203\) | 136.467 | − | 296.152i | 0.672250 | − | 1.45888i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −149.320 | + | 10.9043i | −0.728390 | + | 0.0531918i | ||||
\(206\) | 207.027 | + | 358.582i | 1.00499 | + | 1.74069i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 69.9973 | + | 261.233i | 0.336525 | + | 1.25593i | ||||
\(209\) | 63.0221i | 0.301541i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.996 | 0.663487 | 0.331744 | − | 0.943370i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943370i | \(0.392363\pi\) | |||||||
\(212\) | −13.8305 | + | 3.70587i | −0.0652382 | + | 0.0174805i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −437.148 | + | 252.388i | −2.04275 | + | 1.17938i | ||||
\(215\) | −90.9587 | + | 105.290i | −0.423064 | + | 0.489721i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41824 | + | 15.4058i | 0.00653568 | + | 0.0709945i | ||||
\(218\) | 405.831 | − | 405.831i | 1.86161 | − | 1.86161i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −665.335 | − | 321.969i | −3.02425 | − | 1.46350i | ||||
\(221\) | −72.0102 | − | 124.725i | −0.325838 | − | 0.564368i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 132.643 | − | 132.643i | 0.594809 | − | 0.594809i | −0.344117 | − | 0.938927i | \(-0.611822\pi\) |
0.938927 | + | 0.344117i | \(0.111822\pi\) | |||||||
\(224\) | 63.6465 | − | 76.5532i | 0.284136 | − | 0.341755i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.72888 | + | 13.3868i | −0.0341986 | + | 0.0592337i | ||||
\(227\) | −63.5422 | + | 237.143i | −0.279922 | + | 1.04468i | 0.672549 | + | 0.740052i | \(0.265199\pi\) |
−0.952471 | + | 0.304629i | \(0.901467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 217.561 | + | 125.609i | 0.950047 | + | 0.548510i | 0.893096 | − | 0.449867i | \(-0.148529\pi\) |
0.0569516 | + | 0.998377i | \(0.481862\pi\) | |||||||
\(230\) | −238.162 | − | 350.751i | −1.03549 | − | 1.52501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −520.643 | − | 520.643i | −2.24415 | − | 2.24415i | ||||
\(233\) | 76.4808 | + | 285.430i | 0.328244 | + | 1.22502i | 0.911010 | + | 0.412383i | \(0.135304\pi\) |
−0.582767 | + | 0.812640i | \(0.698030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −386.977 | + | 134.583i | −1.64671 | + | 0.572695i | ||||
\(236\) | 374.600 | − | 648.827i | 1.58729 | − | 2.74927i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −120.821 | + | 262.198i | −0.507650 | + | 1.10167i | ||||
\(239\) | 100.831i | 0.421885i | 0.977498 | + | 0.210943i | \(0.0676533\pi\) | ||||
−0.977498 | + | 0.210943i | \(0.932347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −179.672 | − | 311.201i | −0.745527 | − | 1.29129i | −0.949948 | − | 0.312408i | \(-0.898865\pi\) |
0.204421 | − | 0.978883i | \(-0.434469\pi\) | |||||||
\(242\) | 167.517 | − | 625.181i | 0.692217 | − | 2.58339i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 397.160i | 1.62770i | ||||||||
\(245\) | 172.320 | + | 174.157i | 0.703348 | + | 0.710846i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.0453 | − | 11.5340i | 0.174273 | − | 0.0466962i | ||||
\(248\) | 33.7434 | + | 9.04153i | 0.136062 | + | 0.0364578i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −391.510 | + | 204.068i | −1.56604 | + | 0.816274i | ||||
\(251\) | −17.4715 | −0.0696075 | −0.0348038 | − | 0.999394i | \(-0.511081\pi\) | ||||
−0.0348038 | + | 0.999394i | \(0.511081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 296.100 | − | 296.100i | 1.17035 | − | 1.17035i | ||||
\(254\) | 509.038 | + | 293.893i | 2.00409 | + | 1.15706i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 259.270 | + | 449.070i | 1.01278 | + | 1.75418i | ||||
\(257\) | −77.1706 | + | 20.6778i | −0.300275 | + | 0.0804583i | −0.405811 | − | 0.913957i | \(-0.633011\pi\) |
0.105536 | + | 0.994415i | \(0.466344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 209.839 | + | 36.0202i | 0.810191 | + | 0.139074i | ||||
\(260\) | −98.1454 | + | 513.362i | −0.377482 | + | 1.97447i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 149.236 | − | 556.957i | 0.569604 | − | 2.12579i | ||||
\(263\) | −167.452 | − | 44.8686i | −0.636699 | − | 0.170603i | −0.0739911 | − | 0.997259i | \(-0.523574\pi\) |
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.29704 | − | 1.58624i | −0.0313096 | − | 0.00598582i | ||||
\(266\) | −68.6907 | − | 57.1096i | −0.258236 | − | 0.214698i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.5809 | − | 95.4694i | −0.0954513 | − | 0.356229i | ||||
\(269\) | 160.485 | − | 92.6559i | 0.596597 | − | 0.344446i | −0.171104 | − | 0.985253i | \(-0.554734\pi\) |
0.767702 | + | 0.640807i | \(0.221400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −182.223 | + | 315.620i | −0.672410 | + | 1.16465i | 0.304808 | + | 0.952414i | \(0.401408\pi\) |
−0.977219 | + | 0.212235i | \(0.931926\pi\) | |||||||
\(272\) | 181.045 | + | 181.045i | 0.665607 | + | 0.665607i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 522.152i | 1.90567i | ||||||||
\(275\) | −270.584 | − | 341.964i | −0.983943 | − | 1.24350i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 125.143 | − | 467.038i | 0.451778 | − | 1.68606i | −0.245613 | − | 0.969368i | \(-0.578989\pi\) |
0.697391 | − | 0.716691i | \(-0.254344\pi\) | |||||||
\(278\) | 92.8347 | + | 346.464i | 0.333938 | + | 1.24627i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 503.659 | − | 228.856i | 1.79878 | − | 0.817345i | ||||
\(281\) | 472.914 | 1.68297 | 0.841484 | − | 0.540282i | \(-0.181682\pi\) | ||||
0.841484 | + | 0.540282i | \(0.181682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −239.837 | − | 64.2640i | −0.847479 | − | 0.227081i | −0.191154 | − | 0.981560i | \(-0.561223\pi\) |
−0.656324 | + | 0.754479i | \(0.727890\pi\) | |||||||
\(284\) | −492.786 | + | 284.510i | −1.73516 | + | 1.00180i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −759.870 | −2.65689 | ||||||||
\(287\) | 190.366 | + | 87.7205i | 0.663296 | + | 0.305646i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 132.203 | + | 76.3272i | 0.457449 | + | 0.264108i | ||||
\(290\) | −270.230 | − | 777.011i | −0.931827 | − | 2.67935i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −149.607 | + | 40.0871i | −0.512353 | + | 0.137284i | ||||
\(293\) | −61.1515 | + | 61.1515i | −0.208708 | + | 0.208708i | −0.803718 | − | 0.595010i | \(-0.797148\pi\) |
0.595010 | + | 0.803718i | \(0.297148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 365.671 | − | 248.292i | 1.23956 | − | 0.841669i | ||||
\(296\) | 240.376 | − | 416.344i | 0.812082 | − | 1.40657i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 361.505 | + | 96.8649i | 1.21310 | + | 0.325050i | ||||
\(299\) | −256.433 | − | 148.051i | −0.857634 | − | 0.495155i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 182.742 | − | 67.4526i | 0.607117 | − | 0.224095i | ||||
\(302\) | −402.521 | − | 402.521i | −1.33285 | − | 1.33285i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −68.6106 | + | 39.6123i | −0.225693 | + | 0.130304i | ||||
\(305\) | −102.065 | + | 210.912i | −0.334638 | + | 0.691514i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −36.7448 | − | 36.7448i | −0.119690 | − | 0.119690i | 0.644725 | − | 0.764415i | \(-0.276972\pi\) |
−0.764415 | + | 0.644725i | \(0.776972\pi\) | |||||||
\(308\) | 597.375 | + | 844.961i | 1.93953 | + | 2.74338i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.5360 | + | 25.5158i | 0.0952775 | + | 0.0823089i | ||||
\(311\) | 44.4761 | + | 77.0348i | 0.143010 | + | 0.247700i | 0.928629 | − | 0.371010i | \(-0.120989\pi\) |
−0.785619 | + | 0.618711i | \(0.787655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 47.5609 | + | 177.500i | 0.151952 | + | 0.567092i | 0.999347 | + | 0.0361293i | \(0.0115028\pi\) |
−0.847395 | + | 0.530962i | \(0.821831\pi\) | |||||||
\(314\) | − | 485.224i | − | 1.54530i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 189.873 | 0.600864 | ||||||||
\(317\) | 356.038 | − | 95.4002i | 1.12315 | − | 0.300947i | 0.350992 | − | 0.936378i | \(-0.385844\pi\) |
0.772157 | + | 0.635431i | \(0.219178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 703.676 | − | 406.268i | 2.20588 | − | 1.27357i | ||||
\(320\) | 13.6472 | + | 186.880i | 0.0426475 | + | 0.583999i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 54.4118 | + | 591.054i | 0.168981 | + | 1.83557i | ||||
\(323\) | 29.8321 | − | 29.8321i | 0.0923596 | − | 0.0923596i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −184.047 | + | 247.399i | −0.566298 | + | 0.761227i | ||||
\(326\) | 333.540 | + | 577.709i | 1.02313 | + | 1.77211i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 334.668 | − | 334.668i | 1.02033 | − | 1.02033i | ||||
\(329\) | 565.329 | + | 97.0420i | 1.71832 | + | 0.294961i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 224.992 | − | 389.697i | 0.679734 | − | 1.17733i | −0.295327 | − | 0.955396i | \(-0.595429\pi\) |
0.975061 | − | 0.221937i | \(-0.0712381\pi\) | |||||||
\(332\) | −162.684 | + | 607.145i | −0.490012 | + | 1.82875i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −493.805 | − | 285.099i | −1.47846 | − | 0.853589i | ||||
\(335\) | 10.9495 | − | 57.2729i | 0.0326852 | − | 0.170964i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.37231 | − | 9.37231i | −0.0278110 | − | 0.0278110i | 0.693065 | − | 0.720876i | \(-0.256260\pi\) |
−0.720876 | + | 0.693065i | \(0.756260\pi\) | |||||||
\(338\) | −15.4244 | − | 57.5646i | −0.0456343 | − | 0.170309i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 162.536 | + | 467.350i | 0.478046 | + | 1.37456i | ||||
\(341\) | −19.2754 | + | 33.3859i | −0.0565260 | + | 0.0979060i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −93.2729 | − | 330.074i | −0.271933 | − | 0.962316i | ||||
\(344\) | − | 439.849i | − | 1.27863i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 368.126 | + | 637.613i | 1.06395 | + | 1.84281i | ||||
\(347\) | 101.459 | − | 378.650i | 0.292389 | − | 1.09121i | −0.650880 | − | 0.759180i | \(-0.725600\pi\) |
0.943269 | − | 0.332029i | \(-0.107733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 480.726i | 1.37744i | 0.725028 | + | 0.688720i | \(0.241827\pi\) | ||||
−0.725028 | + | 0.688720i | \(0.758173\pi\) | |||||||
\(350\) | 617.921 | + | 14.9596i | 1.76549 | + | 0.0427416i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 239.621 | − | 64.2062i | 0.680741 | − | 0.182404i | ||||
\(353\) | −535.395 | − | 143.459i | −1.51670 | − | 0.406398i | −0.598045 | − | 0.801462i | \(-0.704056\pi\) |
−0.918654 | + | 0.395064i | \(0.870722\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −334.809 | + | 24.4500i | −0.943125 | + | 0.0688732i | ||||
\(356\) | −433.292 | −1.21711 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −296.944 | + | 296.944i | −0.829454 | + | 0.829454i | ||||
\(359\) | 87.7247 | + | 50.6479i | 0.244359 | + | 0.141080i | 0.617178 | − | 0.786823i | \(-0.288276\pi\) |
−0.372820 | + | 0.927904i | \(0.621609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −173.973 | − | 301.330i | −0.481919 | − | 0.834708i | ||||
\(362\) | 7.27983 | − | 1.95062i | 0.0201100 | − | 0.00538846i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 467.797 | − | 562.659i | 1.28516 | − | 1.54577i | ||||
\(365\) | −89.7506 | − | 17.1587i | −0.245892 | − | 0.0470100i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −78.8661 | + | 294.332i | −0.214894 | + | 0.801996i | 0.771310 | + | 0.636460i | \(0.219602\pi\) |
−0.986204 | + | 0.165536i | \(0.947065\pi\) | |||||||
\(368\) | 508.469 | + | 136.244i | 1.38171 | + | 0.370228i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 444.381 | − | 301.737i | 1.20103 | − | 0.815505i | ||||
\(371\) | 9.09379 | + | 7.56061i | 0.0245116 | + | 0.0203790i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7530 | + | 103.576i | 0.0744048 | + | 0.277682i | 0.993098 | − | 0.117290i | \(-0.0374208\pi\) |
−0.918693 | + | 0.394973i | \(0.870754\pi\) | |||||||
\(374\) | −622.999 | + | 359.689i | −1.66577 | + | 0.961734i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 647.598 | − | 1121.67i | 1.72234 | − | 2.98317i | ||||
\(377\) | −406.272 | − | 406.272i | −1.07764 | − | 1.07764i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 5.00789e-5i | 0 | 1.32134e-7i | 1.00000 | 6.60672e-8i | \(2.10298e-8\pi\) | |||
−1.00000 | 6.60672e-8i | \(1.00000\pi\) | ||||||||
\(380\) | −152.700 | + | 11.1512i | −0.401843 | + | 0.0293452i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 156.260 | − | 583.170i | 0.409057 | − | 1.52662i | ||||
\(383\) | −48.7638 | − | 181.989i | −0.127321 | − | 0.475167i | 0.872591 | − | 0.488451i | \(-0.162438\pi\) |
−0.999912 | + | 0.0132843i | \(0.995771\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 100.093 | + | 602.234i | 0.259982 | + | 1.56424i | ||||
\(386\) | −292.757 | −0.758439 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 105.935 | + | 28.3852i | 0.273029 | + | 0.0731578i | ||||
\(389\) | −182.547 | + | 105.394i | −0.469273 | + | 0.270935i | −0.715935 | − | 0.698166i | \(-0.754000\pi\) |
0.246662 | + | 0.969102i | \(0.420666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −280.324 | −0.716940 | ||||||||
\(392\) | −772.135 | − | 60.5035i | −1.96973 | − | 0.154346i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 138.595 | + | 80.0181i | 0.351765 | + | 0.203092i | ||||
\(395\) | 100.832 | + | 48.7947i | 0.255271 | + | 0.123531i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −242.295 | + | 64.9229i | −0.610316 | + | 0.163534i | −0.550722 | − | 0.834689i | \(-0.685647\pi\) |
−0.0595944 | + | 0.998223i | \(0.518981\pi\) | |||||||
\(398\) | −63.5338 | + | 63.5338i | −0.159633 | + | 0.159633i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 202.212 | − | 509.519i | 0.505530 | − | 1.27380i | ||||
\(401\) | −172.876 | + | 299.430i | −0.431113 | + | 0.746709i | −0.996969 | − | 0.0777947i | \(-0.975212\pi\) |
0.565857 | + | 0.824503i | \(0.308545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.3309 | + | 7.05535i | 0.0653373 | + | 0.0175071i | ||||
\(404\) | −618.942 | − | 357.346i | −1.53203 | − | 0.884520i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −194.851 | + | 1135.12i | −0.479928 | + | 2.79587i | ||||
\(407\) | 375.141 | + | 375.141i | 0.921721 | + | 0.921721i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −98.4923 | + | 56.8646i | −0.240812 | + | 0.139033i | −0.615550 | − | 0.788098i | \(-0.711066\pi\) |
0.374738 | + | 0.927131i | \(0.377733\pi\) | |||||||
\(410\) | 499.461 | − | 173.703i | 1.21820 | − | 0.423666i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −702.532 | − | 702.532i | −1.70518 | − | 1.70518i | ||||
\(413\) | −616.195 | + | 56.7263i | −1.49200 | + | 0.137352i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −242.421 | + | 280.617i | −0.584147 | + | 0.676185i | ||||
\(416\) | −87.7081 | − | 151.915i | −0.210837 | − | 0.365180i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −57.6118 | − | 215.010i | −0.137827 | − | 0.514378i | ||||
\(419\) | 220.394i | 0.526000i | 0.964796 | + | 0.263000i | \(0.0847120\pi\) | ||||
−0.964796 | + | 0.263000i | \(0.915288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −611.981 | −1.45364 | −0.726818 | − | 0.686830i | \(-0.759002\pi\) | ||||
−0.726818 | + | 0.686830i | \(0.759002\pi\) | |||||||
\(422\) | −477.618 | + | 127.977i | −1.13180 | + | 0.303264i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.1263 | − | 13.3520i | 0.0545431 | − | 0.0314905i | ||||
\(425\) | −33.7880 | + | 289.956i | −0.0795012 | + | 0.682249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 267.853 | − | 189.368i | 0.627291 | − | 0.443486i | ||||
\(428\) | 856.459 | − | 856.459i | 2.00107 | − | 2.00107i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 214.069 | − | 442.364i | 0.497835 | − | 1.02875i | ||||
\(431\) | −362.392 | − | 627.681i | −0.840816 | − | 1.45634i | −0.889206 | − | 0.457508i | \(-0.848742\pi\) |
0.0483893 | − | 0.998829i | \(-0.484591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −152.433 | + | 152.433i | −0.352038 | + | 0.352038i | −0.860867 | − | 0.508829i | \(-0.830078\pi\) |
0.508829 | + | 0.860867i | \(0.330078\pi\) | |||||||
\(434\) | −18.9218 | − | 51.2629i | −0.0435987 | − | 0.118117i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −688.579 | + | 1192.65i | −1.57931 | + | 2.73545i | ||||
\(437\) | 22.4499 | − | 83.7842i | 0.0513728 | − | 0.191726i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −719.426 | − | 415.361i | −1.63878 | − | 0.946152i | −0.981253 | − | 0.192723i | \(-0.938268\pi\) |
−0.657530 | − | 0.753428i | \(-0.728399\pi\) | |||||||
\(440\) | 1353.99 | + | 258.858i | 3.07725 | + | 0.588313i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 359.692 | + | 359.692i | 0.813783 | + | 0.813783i | ||||
\(443\) | 86.1258 | + | 321.426i | 0.194415 | + | 0.725566i | 0.992418 | + | 0.122912i | \(0.0392234\pi\) |
−0.798003 | + | 0.602654i | \(0.794110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −230.100 | − | 111.350i | −0.517078 | − | 0.250225i | ||||
\(446\) | −331.276 | + | 573.787i | −0.742771 | + | 1.28652i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 109.786 | − | 238.250i | 0.245057 | − | 0.531809i | ||||
\(449\) | − | 20.5616i | − | 0.0457943i | −0.999738 | − | 0.0228971i | \(-0.992711\pi\) | ||
0.999738 | − | 0.0228971i | \(-0.00728902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 261.148 | + | 452.321i | 0.579042 | + | 1.00293i | ||||
\(452\) | 9.59989 | − | 35.8273i | 0.0212387 | − | 0.0792639i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 867.138i | − | 1.91000i | ||||||
\(455\) | 393.019 | − | 178.583i | 0.863778 | − | 0.392490i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 521.445 | − | 139.721i | 1.14102 | − | 0.305734i | 0.361657 | − | 0.932311i | \(-0.382211\pi\) |
0.779360 | + | 0.626577i | \(0.215545\pi\) | |||||||
\(458\) | −857.070 | − | 229.651i | −1.87133 | − | 0.501422i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 769.831 | + | 665.047i | 1.67355 | + | 1.44575i | ||||
\(461\) | −650.544 | −1.41116 | −0.705579 | − | 0.708632i | \(-0.749313\pi\) | ||||
−0.705579 | + | 0.708632i | \(0.749313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 229.971 | − | 229.971i | 0.496697 | − | 0.496697i | −0.413711 | − | 0.910408i | \(-0.635768\pi\) |
0.910408 | + | 0.413711i | \(0.135768\pi\) | |||||||
\(464\) | 884.587 | + | 510.717i | 1.90644 | + | 1.10068i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −521.854 | − | 903.877i | −1.11986 | − | 1.93965i | ||||
\(467\) | −564.037 | + | 151.133i | −1.20779 | + | 0.323626i | −0.805894 | − | 0.592060i | \(-0.798315\pi\) |
−0.401895 | + | 0.915686i | \(0.631648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52.1895 | + | 62.7728i | −0.111278 | + | 0.133844i | ||||
\(470\) | 1197.21 | − | 812.909i | 2.54725 | − | 1.72959i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −361.639 | + | 1349.66i | −0.766184 | + | 2.85944i | ||||
\(473\) | 468.851 | + | 125.628i | 0.991228 | + | 0.265599i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −83.9571 | − | 33.3200i | −0.176752 | − | 0.0701473i | ||||
\(476\) | 117.197 | − | 682.744i | 0.246212 | − | 1.43434i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −92.1745 | − | 344.000i | −0.192834 | − | 0.719665i | ||||
\(479\) | −255.740 | + | 147.651i | −0.533904 | + | 0.308249i | −0.742605 | − | 0.669730i | \(-0.766410\pi\) |
0.208701 | + | 0.977980i | \(0.433076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 187.572 | − | 324.885i | 0.389963 | − | 0.675436i | ||||
\(482\) | 897.465 | + | 897.465i | 1.86196 | + | 1.86196i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1553.05i | 3.20878i | ||||||||
\(485\) | 48.9622 | + | 42.2978i | 0.100953 | + | 0.0872120i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.56814 | + | 31.9767i | −0.0175937 | + | 0.0656606i | −0.974165 | − | 0.225839i | \(-0.927488\pi\) |
0.956571 | + | 0.291500i | \(0.0941543\pi\) | |||||||
\(488\) | −191.709 | − | 715.468i | −0.392846 | − | 1.46612i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −747.105 | − | 436.639i | −1.52470 | − | 0.891099i | ||||
\(491\) | −602.433 | −1.22695 | −0.613476 | − | 0.789713i | \(-0.710229\pi\) | ||||
−0.613476 | + | 0.789713i | \(0.710229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −525.403 | − | 140.781i | −1.06573 | − | 0.285561i | ||||
\(494\) | −136.312 | + | 78.7000i | −0.275936 | + | 0.159312i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48.4619 | −0.0977055 | ||||||||
\(497\) | 426.844 | + | 196.689i | 0.858841 | + | 0.395754i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 712.187 | + | 411.181i | 1.42723 | + | 0.824010i | 0.996901 | − | 0.0786631i | \(-0.0250651\pi\) |
0.430326 | + | 0.902673i | \(0.358398\pi\) | |||||||
\(500\) | 780.688 | − | 716.123i | 1.56138 | − | 1.43225i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 59.6068 | − | 15.9716i | 0.118739 | − | 0.0318159i | ||||
\(503\) | 494.995 | − | 494.995i | 0.984086 | − | 0.984086i | −0.0157893 | − | 0.999875i | \(-0.505026\pi\) |
0.999875 | + | 0.0157893i | \(0.00502609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −236.856 | − | 348.828i | −0.469022 | − | 0.690749i | ||||
\(506\) | −739.512 | + | 1280.87i | −1.46149 | + | 2.53137i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1362.34 | − | 365.039i | −2.68178 | − | 0.718580i | ||||
\(509\) | 503.114 | + | 290.473i | 0.988437 | + | 0.570674i | 0.904807 | − | 0.425823i | \(-0.140015\pi\) |
0.0836299 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 98.3692 | + | 81.7844i | 0.192503 | + | 0.160048i | ||||
\(512\) | −759.774 | − | 759.774i | −1.48393 | − | 1.48393i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 244.377 | − | 141.091i | 0.475442 | − | 0.274497i | ||||
\(515\) | −192.539 | − | 553.621i | −0.373861 | − | 1.07499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1010.67 | + | 1010.67i | 1.95487 | + | 1.95487i | ||||
\(518\) | −748.829 | + | 68.9365i | −1.44562 | + | 0.133082i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −70.9947 | − | 972.176i | −0.136528 | − | 1.86957i | ||||
\(521\) | 274.035 | + | 474.643i | 0.525979 | + | 0.911023i | 0.999542 | + | 0.0302629i | \(0.00963445\pi\) |
−0.473563 | + | 0.880760i | \(0.657032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 60.8889 | + | 227.240i | 0.116422 | + | 0.434494i | 0.999389 | − | 0.0349409i | \(-0.0111243\pi\) |
−0.882967 | + | 0.469435i | \(0.844458\pi\) | |||||||
\(524\) | 1383.57i | 2.64040i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 612.306 | 1.16408 | ||||||||
\(527\) | 24.9278 | − | 6.67937i | 0.0473013 | − | 0.0126743i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −40.9971 | + | 23.6697i | −0.0774992 | + | 0.0447442i | ||||
\(530\) | 29.7568 | − | 2.17304i | 0.0561449 | − | 0.00410007i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 194.675 | + | 89.7064i | 0.365931 | + | 0.168621i | ||||
\(533\) | 261.151 | − | 261.151i | 0.489964 | − | 0.489964i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 674.921 | − | 234.725i | 1.26153 | − | 0.438737i | ||||
\(536\) | 92.1661 | + | 159.636i | 0.171952 | + | 0.297829i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −462.818 | + | 462.818i | −0.860256 | + | 0.860256i | ||||
\(539\) | 285.028 | − | 805.766i | 0.528808 | − | 1.49493i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 261.735 | − | 453.339i | 0.483799 | − | 0.837965i | −0.516028 | − | 0.856572i | \(-0.672590\pi\) |
0.999827 | + | 0.0186072i | \(0.00592319\pi\) | |||||||
\(542\) | 333.159 | − | 1243.37i | 0.614685 | − | 2.29404i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −143.819 | − | 83.0342i | −0.264374 | − | 0.152636i | ||||
\(545\) | −672.165 | + | 456.404i | −1.23333 | + | 0.837438i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −201.681 | − | 201.681i | −0.368703 | − | 0.368703i | 0.498301 | − | 0.867004i | \(-0.333958\pi\) |
−0.867004 | + | 0.498301i | \(0.833958\pi\) | |||||||
\(548\) | −324.277 | − | 1210.22i | −0.591747 | − | 2.20843i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1235.75 | + | 919.309i | 2.24682 | + | 1.67147i | ||||
\(551\) | 84.1545 | − | 145.760i | 0.152731 | − | 0.264537i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −90.5327 | − | 128.054i | −0.163712 | − | 0.231563i | ||||
\(554\) | 1707.78i | 3.08263i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −430.336 | − | 745.364i | −0.773985 | − | 1.34058i | ||||
\(557\) | −178.472 | + | 666.065i | −0.320416 | + | 1.19581i | 0.598425 | + | 0.801179i | \(0.295793\pi\) |
−0.918841 | + | 0.394629i | \(0.870873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 343.226i | − | 0.614000i | ||||||
\(560\) | −592.723 | + | 487.501i | −1.05843 | + | 0.870537i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1613.42 | + | 432.315i | −2.87086 | + | 0.769244i | ||||
\(563\) | 739.166 | + | 198.059i | 1.31291 | + | 0.351792i | 0.846315 | − | 0.532682i | \(-0.178816\pi\) |
0.466590 | + | 0.884474i | \(0.345483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.3051 | − | 16.5590i | 0.0253188 | − | 0.0293080i | ||||
\(566\) | 876.988 | 1.54945 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 750.402 | − | 750.402i | 1.32113 | − | 1.32113i | ||||
\(569\) | 116.121 | + | 67.0425i | 0.204079 | + | 0.117825i | 0.598557 | − | 0.801080i | \(-0.295741\pi\) |
−0.394478 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −286.520 | − | 496.267i | −0.501786 | − | 0.869119i | −0.999998 | − | 0.00206333i | \(-0.999343\pi\) |
0.498212 | − | 0.867055i | \(-0.333990\pi\) | |||||||
\(572\) | 1761.19 | − | 471.910i | 3.07901 | − | 0.825017i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −729.654 | − | 125.249i | −1.27117 | − | 0.218205i | ||||
\(575\) | 237.911 | + | 551.009i | 0.413758 | + | 0.958276i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −178.653 | + | 666.742i | −0.309624 | + | 1.15553i | 0.619268 | + | 0.785180i | \(0.287430\pi\) |
−0.928891 | + | 0.370352i | \(0.879237\pi\) | |||||||
\(578\) | −520.805 | − | 139.549i | −0.901048 | − | 0.241435i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1108.88 | + | 1633.10i | 1.91186 | + | 2.81568i | ||||
\(581\) | 487.040 | − | 179.773i | 0.838280 | − | 0.309420i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.62709 | + | 28.4647i | 0.0130825 | + | 0.0488245i | ||||
\(584\) | 250.161 | − | 144.430i | 0.428358 | − | 0.247312i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 152.726 | − | 264.530i | 0.260625 | − | 0.451416i | ||||
\(587\) | −688.633 | − | 688.633i | −1.17314 | − | 1.17314i | −0.981457 | − | 0.191682i | \(-0.938606\pi\) |
−0.191682 | − | 0.981457i | \(-0.561394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.98542i | 0.0135576i | ||||||||
\(590\) | −1020.57 | + | 1181.37i | −1.72978 | + | 2.00232i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −172.613 | + | 644.199i | −0.291576 | + | 1.08817i | ||||
\(593\) | 100.681 | + | 375.748i | 0.169783 | + | 0.633640i | 0.997382 | + | 0.0723188i | \(0.0230399\pi\) |
−0.827598 | + | 0.561321i | \(0.810293\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 237.693 | − | 332.453i | 0.399484 | − | 0.558745i | ||||
\(596\) | −898.035 | −1.50677 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1010.20 | + | 270.683i | 1.68930 | + | 0.452647i | ||||
\(599\) | −223.139 | + | 128.830i | −0.372520 | + | 0.215074i | −0.674559 | − | 0.738221i | \(-0.735666\pi\) |
0.302039 | + | 0.953296i | \(0.402333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 91.8404 | 0.152813 | 0.0764064 | − | 0.997077i | \(-0.475655\pi\) | ||||
0.0764064 | + | 0.997077i | \(0.475655\pi\) | |||||||
\(602\) | −561.793 | + | 397.180i | −0.933211 | + | 0.659767i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1182.93 | + | 682.963i | 1.95849 | + | 1.13073i | ||||
\(605\) | −399.112 | + | 824.746i | −0.659689 | + | 1.36322i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 759.412 | − | 203.484i | 1.25109 | − | 0.335229i | 0.428333 | − | 0.903621i | \(-0.359101\pi\) |
0.822757 | + | 0.568393i | \(0.192435\pi\) | |||||||
\(608\) | 36.3355 | − | 36.3355i | 0.0597623 | − | 0.0597623i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 155.404 | − | 812.862i | 0.254761 | − | 1.33256i | ||||
\(611\) | 505.338 | − | 875.272i | 0.827068 | − | 1.43252i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 407.928 | + | 109.304i | 0.665461 | + | 0.178310i | 0.575709 | − | 0.817654i | \(-0.304726\pi\) |
0.0897518 | + | 0.995964i | \(0.471393\pi\) | |||||||
\(614\) | 158.951 | + | 91.7706i | 0.258878 | + | 0.149464i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1484.01 | − | 1233.81i | −2.40911 | − | 2.00294i | ||||
\(617\) | −174.640 | − | 174.640i | −0.283047 | − | 0.283047i | 0.551276 | − | 0.834323i | \(-0.314141\pi\) |
−0.834323 | + | 0.551276i | \(0.814141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 408.198 | − | 235.673i | 0.659448 | − | 0.380732i | −0.132619 | − | 0.991167i | \(-0.542339\pi\) |
0.792066 | + | 0.610435i | \(0.209005\pi\) | |||||||
\(620\) | −84.3035 | − | 40.7962i | −0.135973 | − | 0.0658003i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −222.159 | − | 222.159i | −0.357169 | − | 0.357169i | ||||
\(623\) | 206.597 | + | 292.222i | 0.331616 | + | 0.469056i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 598.618 | − | 179.671i | 0.957788 | − | 0.287474i | ||||
\(626\) | −324.524 | − | 562.091i | −0.518408 | − | 0.897909i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 301.344 | + | 1124.63i | 0.479847 | + | 1.79081i | ||||
\(629\) | − | 355.153i | − | 0.564631i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −670.413 | −1.06246 | −0.531230 | − | 0.847227i | \(-0.678270\pi\) | ||||
−0.531230 | + | 0.847227i | \(0.678270\pi\) | |||||||
\(632\) | −342.049 | + | 91.6516i | −0.541216 | + | 0.145018i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1127.47 | + | 650.947i | −1.77835 | + | 1.02673i | ||||
\(635\) | −629.662 | − | 543.957i | −0.991594 | − | 0.856625i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −602.518 | − | 47.2125i | −0.945868 | − | 0.0741170i | ||||
\(638\) | −2029.32 | + | 2029.32i | −3.18075 | + | 3.18075i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −310.831 | − | 893.755i | −0.485673 | − | 1.39649i | ||||
\(641\) | −617.665 | − | 1069.83i | −0.963596 | − | 1.66900i | −0.713341 | − | 0.700818i | \(-0.752819\pi\) |
−0.250256 | − | 0.968180i | \(-0.580515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −504.796 | + | 504.796i | −0.785064 | + | 0.785064i | −0.980680 | − | 0.195617i | \(-0.937329\pi\) |
0.195617 | + | 0.980680i | \(0.437329\pi\) | |||||||
\(644\) | −493.181 | − | 1336.12i | −0.765809 | − | 2.07473i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −74.5061 | + | 129.048i | −0.115334 | + | 0.199765i | ||||
\(647\) | −27.8251 | + | 103.845i | −0.0430064 | + | 0.160502i | −0.984090 | − | 0.177673i | \(-0.943143\pi\) |
0.941083 | + | 0.338175i | \(0.109810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1335.36 | − | 770.968i | −2.05756 | − | 1.18793i | ||||
\(650\) | 401.746 | − | 1012.29i | 0.618071 | − | 1.55737i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1131.84 | − | 1131.84i | −1.73596 | − | 1.73596i | ||||
\(653\) | −79.6877 | − | 297.399i | −0.122033 | − | 0.455434i | 0.877683 | − | 0.479241i | \(-0.159088\pi\) |
−0.999717 | + | 0.0238067i | \(0.992421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −355.558 | + | 734.745i | −0.542837 | + | 1.12175i | ||||
\(656\) | −328.287 | + | 568.610i | −0.500438 | + | 0.866784i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2017.42 | + | 185.722i | −3.06599 | + | 0.282252i | ||||
\(659\) | − | 590.013i | − | 0.895315i | −0.894205 | − | 0.447658i | \(-0.852258\pi\) | ||
0.894205 | − | 0.447658i | \(-0.147742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.19346 | − | 2.06714i | −0.00180554 | − | 0.00312729i | 0.865121 | − | 0.501563i | \(-0.167241\pi\) |
−0.866927 | + | 0.498436i | \(0.833908\pi\) | |||||||
\(662\) | −411.354 | + | 1535.19i | −0.621380 | + | 2.31902i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1172.27i | − | 1.76547i | ||||||
\(665\) | 80.3291 | + | 97.6674i | 0.120796 | + | 0.146868i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1080.22 | + | 289.444i | −1.61952 | + | 0.433948i | ||||
\(668\) | 1321.58 | + | 354.115i | 1.97841 | + | 0.530113i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.0001 | + | 205.405i | 0.0223882 | + | 0.306575i | ||||
\(671\) | 817.398 | 1.21818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.3354 | + | 50.3354i | −0.0747925 | + | 0.0747925i | −0.743513 | − | 0.668721i | \(-0.766842\pi\) |
0.668721 | + | 0.743513i | \(0.266842\pi\) | |||||||
\(674\) | 40.5429 | + | 23.4075i | 0.0601527 | + | 0.0347292i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 71.4998 | + | 123.841i | 0.105769 | + | 0.183197i | ||||
\(677\) | 500.800 | − | 134.189i | 0.739734 | − | 0.198211i | 0.130774 | − | 0.991412i | \(-0.458254\pi\) |
0.608960 | + | 0.793201i | \(0.291587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.3670 | − | 84.9793i | −0.0461958 | − | 0.125154i | ||||
\(680\) | −518.391 | − | 763.457i | −0.762340 | − | 1.12273i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.2413 | − | 131.522i | 0.0516734 | − | 0.192848i | ||||
\(683\) | 97.0866 | + | 26.0143i | 0.142147 | + | 0.0380883i | 0.329191 | − | 0.944263i | \(-0.393224\pi\) |
−0.187044 | + | 0.982352i | \(0.559891\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 138.802 | − | 726.022i | 0.202631 | − | 1.05989i | ||||
\(686\) | 619.954 | + | 1040.84i | 0.903723 | + | 1.51726i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 157.926 | + | 589.389i | 0.229544 | + | 0.856670i | ||||
\(689\) | 18.0461 | − | 10.4189i | 0.0261917 | − | 0.0151218i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.723424 | − | 1.25301i | 0.00104692 | − | 0.00181332i | −0.865501 | − | 0.500906i | \(-0.833000\pi\) |
0.866548 | + | 0.499093i | \(0.166333\pi\) | |||||||
\(692\) | −1249.21 | − | 1249.21i | −1.80521 | − | 1.80521i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1384.57i | 1.99506i | ||||||||
\(695\) | −36.9818 | − | 506.416i | −0.0532112 | − | 0.728655i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 90.4939 | − | 337.728i | 0.129833 | − | 0.484545i | ||||
\(698\) | −439.457 | − | 1640.08i | −0.629595 | − | 2.34968i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1441.48 | + | 349.081i | −2.05926 | + | 0.498687i | ||||
\(701\) | 230.081 | 0.328218 | 0.164109 | − | 0.986442i | \(-0.447525\pi\) | ||||
0.164109 | + | 0.986442i | \(0.447525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.149 | + | 28.4427i | 0.150995 | + | 0.0404590i | ||||
\(704\) | 566.098 | − | 326.837i | 0.804117 | − | 0.464257i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1957.73 | 2.77299 | ||||||||
\(707\) | 54.1135 | + | 587.813i | 0.0765396 | + | 0.831419i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 383.431 | + | 221.374i | 0.540805 | + | 0.312234i | 0.745405 | − | 0.666612i | \(-0.232256\pi\) |
−0.204600 | + | 0.978846i | \(0.565589\pi\) | |||||||
\(710\) | 1119.91 | − | 389.482i | 1.57733 | − | 0.548566i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 780.559 | − | 209.150i | 1.09629 | − | 0.293750i | ||||
\(713\) | 37.5183 | − | 37.5183i | 0.0526203 | − | 0.0526203i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1056.55 | + | 201.994i | 1.47770 | + | 0.282509i | ||||
\(716\) | 503.829 | − | 872.658i | 0.703672 | − | 1.21880i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −345.587 | − | 92.5998i | −0.481319 | − | 0.128969i | ||||
\(719\) | 446.525 | + | 257.801i | 0.621036 | + | 0.358555i | 0.777272 | − | 0.629164i | \(-0.216603\pi\) |
−0.156236 | + | 0.987720i | \(0.549936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −138.831 | + | 808.775i | −0.192553 | + | 1.12174i | ||||
\(722\) | 868.998 | + | 868.998i | 1.20360 | + | 1.20360i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.6614 | + | 9.04213i | −0.0216318 | + | 0.0124891i | ||||
\(725\) | 169.188 | + | 1152.22i | 0.233363 | + | 1.58927i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −829.146 | − | 829.146i | −1.14050 | − | 1.14050i | −0.988358 | − | 0.152145i | \(-0.951382\pi\) |
−0.152145 | − | 0.988358i | \(-0.548618\pi\) | |||||||
\(728\) | −571.121 | + | 1239.41i | −0.784507 | + | 1.70249i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 321.884 | − | 23.5061i | 0.440937 | − | 0.0322001i | ||||
\(731\) | −162.468 | − | 281.402i | −0.222254 | − | 0.384956i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 266.886 | + | 996.034i | 0.364102 | + | 1.35885i | 0.868635 | + | 0.495453i | \(0.164998\pi\) |
−0.504533 | + | 0.863392i | \(0.668335\pi\) | |||||||
\(734\) | − | 1076.26i | − | 1.46629i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −341.433 | −0.463904 | ||||||||
\(737\) | −196.486 | + | 52.6484i | −0.266603 | + | 0.0714360i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −287.660 | + | 166.081i | −0.389256 | + | 0.224737i | −0.681838 | − | 0.731503i | \(-0.738819\pi\) |
0.292582 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(740\) | −842.574 | + | 975.329i | −1.13861 | + | 1.31801i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.9365 | − | 17.4811i | −0.0511274 | − | 0.0235595i | ||||
\(743\) | 764.980 | − | 764.980i | 1.02958 | − | 1.02958i | 0.0300340 | − | 0.999549i | \(-0.490438\pi\) |
0.999549 | − | 0.0300340i | \(-0.00956155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −476.902 | − | 230.783i | −0.640136 | − | 0.309775i | ||||
\(746\) | −189.368 | − | 327.994i | −0.253844 | − | 0.439671i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1220.58 | − | 1220.58i | 1.63179 | − | 1.63179i | ||||
\(749\) | −985.980 | − | 169.249i | −1.31640 | − | 0.225967i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −66.3561 | + | 114.932i | −0.0883570 | + | 0.153039i | −0.906817 | − | 0.421525i | \(-0.861495\pi\) |
0.818460 | + | 0.574564i | \(0.194828\pi\) | |||||||
\(752\) | −465.036 | + | 1735.54i | −0.618399 | + | 2.30790i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1757.46 | + | 1014.67i | 2.33084 | + | 1.34571i | ||||
\(755\) | 452.681 | + | 666.683i | 0.599577 | + | 0.883024i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 705.876 | + | 705.876i | 0.932465 | + | 0.932465i | 0.997859 | − | 0.0653945i | \(-0.0208306\pi\) |
−0.0653945 | + | 0.997859i | \(0.520831\pi\) | |||||||
\(758\) | −4.57797e−5 | 0 | 0.000170852i | −6.03954e−8 | 0 | 2.25399e-7i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 269.701 | − | 93.7968i | 0.354869 | − | 0.123417i | ||||
\(761\) | 21.9538 | − | 38.0250i | 0.0288486 | − | 0.0499672i | −0.851241 | − | 0.524776i | \(-0.824149\pi\) |
0.880089 | + | 0.474808i | \(0.157483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1132.67 | − | 104.273i | 1.48450 | − | 0.136661i | ||||
\(764\) | 1448.69i | 1.89619i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 332.731 | + | 576.308i | 0.434375 | + | 0.752360i | ||||
\(767\) | −282.197 | + | 1053.17i | −0.367923 | + | 1.37311i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 317.954i | 0.413464i | 0.978398 | + | 0.206732i | \(0.0662829\pi\) | ||||
−0.978398 | + | 0.206732i | \(0.933717\pi\) | |||||||
\(770\) | −892.017 | − | 1963.12i | −1.15846 | − | 2.54950i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 678.539 | − | 181.814i | 0.878937 | − | 0.235510i | ||||
\(773\) | 681.538 | + | 182.617i | 0.881679 | + | 0.236245i | 0.671131 | − | 0.741339i | \(-0.265809\pi\) |
0.210547 | + | 0.977584i | \(0.432475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.2853 | − | 43.3296i | −0.0442391 | − | 0.0559092i | ||||
\(776\) | −204.540 | −0.263582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 526.444 | − | 526.444i | 0.676663 | − | 0.676663i | ||||
\(779\) | 93.6941 | + | 54.0943i | 0.120275 | + | 0.0694407i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 585.553 | + | 1014.21i | 0.749748 | + | 1.29860i | ||||
\(782\) | 956.369 | − | 256.258i | 1.22298 | − | 0.327696i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1056.37 | − | 196.159i | 1.34741 | − | 0.250203i | ||||
\(785\) | −128.986 | + | 674.676i | −0.164313 | + | 0.859460i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −81.4498 | + | 303.975i | −0.103494 | + | 0.386245i | −0.998170 | − | 0.0604708i | \(-0.980740\pi\) |
0.894676 | + | 0.446716i | \(0.147406\pi\) | |||||||
\(788\) | −370.924 | − | 99.3888i | −0.470716 | − | 0.126128i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −388.611 | − | 74.2952i | −0.491912 | − | 0.0940446i | ||||
\(791\) | −28.7400 | + | 10.6083i | −0.0363337 | + | 0.0134113i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −149.596 | − | 558.299i | −0.188645 | − | 0.704034i | ||||
\(794\) | 767.281 | − | 442.990i | 0.966349 | − | 0.557922i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 107.799 | − | 186.713i | 0.135425 | − | 0.234564i | ||||
\(797\) | −298.666 | − | 298.666i | −0.374738 | − | 0.374738i | 0.494461 | − | 0.869200i | \(-0.335365\pi\) |
−0.869200 | + | 0.494461i | \(0.835365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 956.818i | − | 1.19752i | ||||||
\(800\) | −41.1537 | + | 353.165i | −0.0514421 | + | 0.441456i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 316.070 | − | 1179.59i | 0.394102 | − | 1.47081i | ||||
\(803\) | 82.5035 | + | 307.907i | 0.102744 | + | 0.383446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.4615 | − | 836.289i | 0.101194 | − | 1.03887i | ||||
\(806\) | −96.2819 | −0.119456 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1287.49 | + | 344.982i | 1.59343 | + | 0.426958i | ||||
\(809\) | 1146.88 | − | 662.154i | 1.41766 | − | 0.818485i | 0.421564 | − | 0.906798i | \(-0.361481\pi\) |
0.996093 | + | 0.0883137i | \(0.0281478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 238.488 | 0.294067 | 0.147033 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147033 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(812\) | −253.341 | − | 2751.94i | −0.311997 | − | 3.38909i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1622.79 | − | 936.917i | −1.99360 | − | 1.15100i | ||||
\(815\) | −310.197 | − | 891.933i | −0.380610 | − | 1.09440i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 97.1180 | − | 26.0227i | 0.118871 | − | 0.0318515i | ||||
\(818\) | 284.040 | − | 284.040i | 0.347237 | − | 0.347237i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1049.75 | + | 712.786i | −1.28018 | + | 0.869251i | ||||
\(821\) | −276.005 | + | 478.055i | −0.336182 | + | 0.582284i | −0.983711 | − | 0.179756i | \(-0.942469\pi\) |
0.647529 | + | 0.762041i | \(0.275802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −700.442 | − | 187.683i | −0.851084 | − | 0.228047i | −0.193194 | − | 0.981161i | \(-0.561885\pi\) |
−0.657891 | + | 0.753113i | \(0.728551\pi\) | |||||||
\(824\) | 1604.70 | + | 926.472i | 1.94745 | + | 1.12436i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2050.39 | − | 756.827i | 2.48231 | − | 0.916255i | ||||
\(827\) | −403.921 | − | 403.921i | −0.488417 | − | 0.488417i | 0.419389 | − | 0.907807i | \(-0.362244\pi\) |
−0.907807 | + | 0.419389i | \(0.862244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 292.544 | − | 168.900i | 0.352887 | − | 0.203740i | −0.313069 | − | 0.949730i | \(-0.601357\pi\) |
0.665956 | + | 0.745991i | \(0.268024\pi\) | |||||||
\(830\) | 570.532 | − | 1178.98i | 0.687388 | − | 1.42046i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −326.840 | − | 326.840i | −0.392837 | − | 0.392837i | ||||
\(833\) | −516.338 | + | 246.497i | −0.619854 | + | 0.295914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 610.820 | + | 527.679i | 0.731521 | + | 0.631951i | ||||
\(836\) | 267.060 | + | 462.561i | 0.319449 | + | 0.553303i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −201.474 | − | 751.910i | −0.240422 | − | 0.897268i | ||||
\(839\) | 1419.09i | 1.69141i | 0.533649 | + | 0.845706i | \(0.320820\pi\) | ||||
−0.533649 | + | 0.845706i | \(0.679180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1328.99 | −1.58025 | ||||||||
\(842\) | 2087.87 | − | 559.444i | 2.47966 | − | 0.664423i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1027.52 | − | 593.240i | 1.21744 | − | 0.702891i | ||||
\(845\) | 6.14448 | + | 84.1404i | 0.00727158 | + | 0.0995744i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1047.41 | − | 740.504i | 1.23661 | − | 0.874266i | ||||
\(848\) | −26.1948 | + | 26.1948i | −0.0308901 | + | 0.0308901i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −149.790 | − | 1020.12i | −0.176224 | − | 1.20014i | ||||
\(851\) | −365.094 | − | 632.361i | −0.429017 | − | 0.743080i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −104.379 | + | 104.379i | −0.122367 | + | 0.122367i | −0.765638 | − | 0.643271i | \(-0.777577\pi\) |
0.643271 | + | 0.765638i | \(0.277577\pi\) | |||||||
\(854\) | −740.713 | + | 890.920i | −0.867346 | + | 1.04323i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1129.46 | + | 1956.29i | −1.31947 | + | 2.28539i | ||||
\(857\) | −306.801 | + | 1145.00i | −0.357995 | + | 1.33605i | 0.518679 | + | 0.854969i | \(0.326424\pi\) |
−0.876674 | + | 0.481085i | \(0.840243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −70.8786 | − | 40.9218i | −0.0825129 | − | 0.0476388i | 0.458176 | − | 0.888862i | \(-0.348503\pi\) |
−0.540689 | + | 0.841223i | \(0.681836\pi\) | |||||||
\(860\) | −221.434 | + | 1158.24i | −0.257481 | + | 1.34679i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1810.15 | + | 1810.15i | 2.09995 | + | 2.09995i | ||||
\(863\) | 148.450 | + | 554.024i | 0.172016 | + | 0.641974i | 0.997041 | + | 0.0768766i | \(0.0244948\pi\) |
−0.825024 | + | 0.565097i | \(0.808839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −342.363 | − | 984.420i | −0.395795 | − | 1.13806i | ||||
\(866\) | 380.702 | − | 659.395i | 0.439609 | − | 0.761426i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 75.6924 | + | 107.064i | 0.0872033 | + | 0.123345i | ||||
\(869\) | − | 390.779i | − | 0.449688i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.9197 | + | 124.569i | 0.0825714 | + | 0.143018i | ||||
\(872\) | 664.754 | − | 2480.90i | 0.762333 | − | 2.84506i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 306.366i | 0.350533i | ||||||||
\(875\) | −855.206 | − | 185.060i | −0.977379 | − | 0.211498i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1061.54 | + | 284.440i | −1.21043 | + | 0.324333i | −0.806929 | − | 0.590648i | \(-0.798872\pi\) |
−0.403497 | + | 0.914981i | \(0.632206\pi\) | |||||||
\(878\) | 2834.14 | + | 759.406i | 3.22795 | + | 0.864927i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1907.26 | + | 139.281i | −2.16734 | + | 0.158274i | ||||
\(881\) | 791.292 | 0.898175 | 0.449087 | − | 0.893488i | \(-0.351749\pi\) | ||||
0.449087 | + | 0.893488i | \(0.351749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −364.152 | + | 364.152i | −0.412403 | + | 0.412403i | −0.882575 | − | 0.470172i | \(-0.844192\pi\) |
0.470172 | + | 0.882575i | \(0.344192\pi\) | |||||||
\(884\) | −1057.06 | − | 610.294i | −1.19577 | − | 0.690378i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −587.664 | − | 1017.86i | −0.663278 | − | 1.14883i | ||||
\(887\) | −651.280 | + | 174.510i | −0.734250 | + | 0.196742i | −0.606521 | − | 0.795067i | \(-0.707435\pi\) |
−0.127729 | + | 0.991809i | \(0.540769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 403.384 | + | 1092.85i | 0.453751 | + | 1.22930i | ||||
\(890\) | 886.813 | + | 169.542i | 0.996420 | + | 0.190497i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 411.471 | − | 1535.63i | 0.461291 | − | 1.72156i | ||||
\(893\) | 285.977 | + | 76.6274i | 0.320243 | + | 0.0858090i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 491.819 | − | 333.948i | 0.549519 | − | 0.373126i | ||||
\(896\) | −224.126 | + | 1305.67i | −0.250141 | + | 1.45722i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.7965 | + | 70.1493i | 0.0209315 | + | 0.0781173i | ||||
\(899\) | 89.1617 | − | 51.4775i | 0.0991787 | − | 0.0572609i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.86368 | − | 17.0844i | 0.0109475 | − | 0.0189616i | ||||
\(902\) | −1304.44 | − | 1304.44i | −1.44616 | − | 1.44616i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 69.1753i | 0.0765213i | ||||||||
\(905\) | −10.6407 | + | 0.777054i | −0.0117577 | + | 0.000858623i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −254.987 | + | 951.626i | −0.281133 | + | 1.04920i | 0.670486 | + | 0.741922i | \(0.266086\pi\) |
−0.951619 | + | 0.307280i | \(0.900581\pi\) | |||||||
\(908\) | 538.528 | + | 2009.81i | 0.593092 | + | 2.21345i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1177.60 | + | 968.544i | −1.29406 | + | 1.06433i | ||||
\(911\) | −395.990 | −0.434676 | −0.217338 | − | 0.976096i | \(-0.569737\pi\) | ||||
−0.217338 | + | 0.976096i | \(0.569737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1249.57 | + | 334.821i | 1.36864 | + | 0.366726i | ||||
\(914\) | −1651.27 | + | 953.359i | −1.80664 | + | 1.04306i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2129.10 | 2.32434 | ||||||||
\(917\) | 933.110 | − | 659.696i | 1.01757 | − | 0.719406i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −967.833 | − | 558.779i | −1.05314 | − | 0.608029i | −0.129612 | − | 0.991565i | \(-0.541373\pi\) |
−0.923526 | + | 0.383536i | \(0.874706\pi\) | |||||||
\(920\) | −1707.84 | − | 826.458i | −1.85634 | − | 0.898324i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2219.43 | − | 594.696i | 2.40720 | − | 0.645006i | ||||
\(923\) | 585.559 | − | 585.559i | 0.634409 | − | 0.634409i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −698.095 | + | 301.419i | −0.754697 | + | 0.325858i | ||||
\(926\) | −574.354 | + | 994.811i | −0.620253 | + | 1.07431i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −639.939 | − | 171.471i | −0.689590 | − | 0.184775i | ||||
\(929\) | −724.522 | − | 418.303i | −0.779894 | − | 0.450272i | 0.0564987 | − | 0.998403i | \(-0.482006\pi\) |
−0.836393 | + | 0.548131i | \(0.815340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.3226 | − | 174.066i | −0.0347181 | − | 0.186967i | ||||
\(932\) | 1770.87 | + | 1770.87i | 1.90008 | + | 1.90008i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1786.15 | − | 1031.23i | 1.91236 | − | 1.10410i | ||||
\(935\) | 961.858 | − | 334.516i | 1.02873 | − | 0.357771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −406.918 | − | 406.918i | −0.434277 | − | 0.434277i | 0.455803 | − | 0.890081i | \(-0.349352\pi\) |
−0.890081 | + | 0.455803i | \(0.849352\pi\) | |||||||
\(938\) | 120.669 | − | 261.869i | 0.128645 | − | 0.279178i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2269.98 | + | 2627.64i | −2.41487 | + | 2.79536i | ||||
\(941\) | −75.9717 | − | 131.587i | −0.0807350 | − | 0.139837i | 0.822831 | − | 0.568286i | \(-0.192393\pi\) |
−0.903566 | + | 0.428449i | \(0.859060\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −186.054 | − | 694.361i | −0.197300 | − | 0.736332i | ||||
\(944\) | − | 1938.36i | − | 2.05335i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1714.40 | −1.81227 | ||||||||
\(947\) | −532.138 | + | 142.586i | −0.561920 | + | 0.150566i | −0.528588 | − | 0.848878i | \(-0.677278\pi\) |
−0.0333318 | + | 0.999444i | \(0.510612\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 195.207 | − | 112.703i | 0.205698 | − | 0.118760i | ||||
\(950\) | 316.893 | + | 36.9270i | 0.333571 | + | 0.0388705i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 118.435 | + | 1286.51i | 0.124406 | + | 1.35137i | ||||
\(953\) | −12.6759 | + | 12.6759i | −0.0133010 | + | 0.0133010i | −0.713726 | − | 0.700425i | \(-0.752994\pi\) |
0.700425 | + | 0.713726i | \(0.252994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −372.292 | + | 769.325i | −0.389835 | + | 0.805576i | ||||
\(956\) | 427.275 | + | 740.063i | 0.446941 | + | 0.774124i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 737.522 | − | 737.522i | 0.769856 | − | 0.769856i | ||||
\(959\) | −661.581 | + | 795.741i | −0.689865 | + | 0.829761i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 478.058 | − | 828.020i | 0.497459 | − | 0.861623i | ||||
\(962\) | −342.939 | + | 1279.87i | −0.356485 | + | 1.33042i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2637.46 | − | 1522.74i | −2.73596 | − | 1.57961i | ||||
\(965\) | 407.062 | + | 77.8228i | 0.421826 | + | 0.0806454i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −674.724 | − | 674.724i | −0.697750 | − | 0.697750i | 0.266175 | − | 0.963925i | \(-0.414240\pi\) |
−0.963925 | + | 0.266175i | \(0.914240\pi\) | |||||||
\(968\) | −749.656 | − | 2797.75i | −0.774438 | − | 2.89024i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −205.709 | − | 99.5470i | −0.212071 | − | 0.102626i | ||||
\(971\) | −876.594 | + | 1518.30i | −0.902774 | + | 1.56365i | −0.0788965 | + | 0.996883i | \(0.525140\pi\) |
−0.823878 | + | 0.566768i | \(0.808194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −297.502 | + | 645.622i | −0.305758 | + | 0.663538i | ||||
\(974\) | − | 116.926i | − | 0.120048i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 513.773 | + | 889.881i | 0.526407 | + | 0.911763i | ||||
\(977\) | 320.764 | − | 1197.11i | 0.328315 | − | 1.22529i | −0.582621 | − | 0.812744i | \(-0.697973\pi\) |
0.910937 | − | 0.412546i | \(-0.135360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 891.762i | 0.910891i | ||||||||
\(980\) | 2002.77 | + | 548.038i | 2.04365 | + | 0.559223i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2055.30 | − | 550.716i | 2.09297 | − | 0.560810i | ||||
\(983\) | −1036.06 | − | 277.611i | −1.05398 | − | 0.282412i | −0.310083 | − | 0.950710i | \(-0.600357\pi\) |
−0.743894 | + | 0.668297i | \(0.767023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −171.438 | − | 148.103i | −0.174048 | − | 0.150358i | ||||
\(986\) | 1921.19 | 1.94847 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 267.062 | − | 267.062i | 0.270306 | − | 0.270306i | ||||
\(989\) | −578.558 | − | 334.030i | −0.584992 | − | 0.337746i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 128.143 | + | 221.951i | 0.129307 | + | 0.223966i | 0.923408 | − | 0.383819i | \(-0.125391\pi\) |
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(992\) | 30.3619 | − | 8.13546i | 0.0306068 | − | 0.00820106i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1636.05 | − | 280.838i | −1.64593 | − | 0.282533i | ||||
\(995\) | 105.229 | − | 71.4510i | 0.105758 | − | 0.0718101i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −374.016 | + | 1395.85i | −0.375141 | + | 1.40005i | 0.477997 | + | 0.878362i | \(0.341363\pi\) |
−0.853138 | + | 0.521685i | \(0.825304\pi\) | |||||||
\(998\) | −2805.62 | − | 751.764i | −2.81124 | − | 0.753271i | ||||
\(999\) | 0 | 0 |
(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 | 315.3.ca.b.37.2 | 64 | ||
3.2 | odd | 2 | 105.3.v.a.37.15 | ✓ | 64 | ||
5.3 | odd | 4 | inner | 315.3.ca.b.163.15 | 64 | ||
7.4 | even | 3 | inner | 315.3.ca.b.172.15 | 64 | ||
15.8 | even | 4 | 105.3.v.a.58.2 | yes | 64 | ||
21.11 | odd | 6 | 105.3.v.a.67.2 | yes | 64 | ||
35.18 | odd | 12 | inner | 315.3.ca.b.298.2 | 64 | ||
105.53 | even | 12 | 105.3.v.a.88.15 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.15 | ✓ | 64 | 3.2 | odd | 2 | ||
105.3.v.a.58.2 | yes | 64 | 15.8 | even | 4 | ||
105.3.v.a.67.2 | yes | 64 | 21.11 | odd | 6 | ||
105.3.v.a.88.15 | yes | 64 | 105.53 | even | 12 | ||
315.3.ca.b.37.2 | 64 | 1.1 | even | 1 | trivial | ||
315.3.ca.b.163.15 | 64 | 5.3 | odd | 4 | inner | ||
315.3.ca.b.172.15 | 64 | 7.4 | even | 3 | inner | ||
315.3.ca.b.298.2 | 64 | 35.18 | odd | 12 | inner |