Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(36,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.q (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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(0.759479 + 1.19298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.43 |
Dual form | 91.2.q.a.36.2 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20027 | − | 0.692976i | −0.848719 | − | 0.490008i | 0.0114993 | − | 0.999934i | \(-0.496340\pi\) |
−0.860218 | + | 0.509926i | \(0.829673\pi\) | |||||||
\(3\) | 1.41289 | − | 2.44719i | 0.815731 | − | 1.41289i | −0.0930713 | − | 0.995659i | \(-0.529668\pi\) |
0.908802 | − | 0.417228i | \(-0.136998\pi\) | |||||||
\(4\) | −0.0395678 | − | 0.0685334i | −0.0197839 | − | 0.0342667i | ||||
\(5\) | 0.518957i | 0.232085i | 0.993244 | + | 0.116042i | \(0.0370208\pi\) | ||||
−0.993244 | + | 0.116042i | \(0.962979\pi\) | |||||||
\(6\) | −3.39169 | + | 1.95819i | −1.38465 | + | 0.799429i | ||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | 2.88158i | 1.01879i | ||||||||
\(9\) | −2.49250 | − | 4.31714i | −0.830833 | − | 1.43905i | ||||
\(10\) | 0.359625 | − | 0.622889i | 0.113723 | − | 0.196975i | ||||
\(11\) | 1.40656 | + | 0.812080i | 0.424095 | + | 0.244851i | 0.696828 | − | 0.717239i | \(-0.254594\pi\) |
−0.272733 | + | 0.962090i | \(0.587928\pi\) | |||||||
\(12\) | −0.223619 | −0.0645533 | ||||||||
\(13\) | 1.42641 | − | 3.31140i | 0.395616 | − | 0.918416i | ||||
\(14\) | 1.38595 | 0.370411 | ||||||||
\(15\) | 1.26999 | + | 0.733228i | 0.327909 | + | 0.189319i | ||||
\(16\) | 1.91773 | − | 3.32161i | 0.479433 | − | 0.830403i | ||||
\(17\) | 0.974127 | + | 1.68724i | 0.236260 | + | 0.409215i | 0.959638 | − | 0.281237i | \(-0.0907448\pi\) |
−0.723378 | + | 0.690452i | \(0.757411\pi\) | |||||||
\(18\) | 6.90897i | 1.62846i | ||||||||
\(19\) | 2.15740 | − | 1.24558i | 0.494942 | − | 0.285755i | −0.231680 | − | 0.972792i | \(-0.574422\pi\) |
0.726622 | + | 0.687037i | \(0.241089\pi\) | |||||||
\(20\) | 0.0355659 | − | 0.0205340i | 0.00795277 | − | 0.00459154i | ||||
\(21\) | 2.82577i | 0.616634i | ||||||||
\(22\) | −1.12550 | − | 1.94943i | −0.239958 | − | 0.415620i | ||||
\(23\) | −4.57029 | + | 7.91598i | −0.952971 | + | 1.65059i | −0.214028 | + | 0.976828i | \(0.568658\pi\) |
−0.738943 | + | 0.673767i | \(0.764675\pi\) | |||||||
\(24\) | 7.05179 | + | 4.07135i | 1.43944 | + | 0.831061i | ||||
\(25\) | 4.73068 | 0.946137 | ||||||||
\(26\) | −4.00680 | + | 2.98610i | −0.785798 | + | 0.585622i | ||||
\(27\) | −5.60916 | −1.07948 | ||||||||
\(28\) | 0.0685334 | + | 0.0395678i | 0.0129516 | + | 0.00747761i | ||||
\(29\) | 2.61498 | − | 4.52928i | 0.485589 | − | 0.841065i | −0.514274 | − | 0.857626i | \(-0.671938\pi\) |
0.999863 | + | 0.0165608i | \(0.00527172\pi\) | |||||||
\(30\) | −1.01622 | − | 1.76014i | −0.185535 | − | 0.321357i | ||||
\(31\) | 5.79391i | 1.04062i | 0.853978 | + | 0.520308i | \(0.174183\pi\) | ||||
−0.853978 | + | 0.520308i | \(0.825817\pi\) | |||||||
\(32\) | 0.387453 | − | 0.223696i | 0.0684926 | − | 0.0395442i | ||||
\(33\) | 3.97463 | − | 2.29475i | 0.691894 | − | 0.399465i | ||||
\(34\) | − | 2.70019i | − | 0.463078i | ||||||
\(35\) | −0.259479 | − | 0.449430i | −0.0438599 | − | 0.0759675i | ||||
\(36\) | −0.197245 | + | 0.341639i | −0.0328742 | + | 0.0569398i | ||||
\(37\) | −8.85879 | − | 5.11463i | −1.45638 | − | 0.840840i | −0.457546 | − | 0.889186i | \(-0.651272\pi\) |
−0.998831 | + | 0.0483462i | \(0.984605\pi\) | |||||||
\(38\) | −3.45262 | −0.560089 | ||||||||
\(39\) | −6.08826 | − | 8.16934i | −0.974902 | − | 1.30814i | ||||
\(40\) | −1.49542 | −0.236446 | ||||||||
\(41\) | 3.64513 | + | 2.10452i | 0.569273 | + | 0.328670i | 0.756859 | − | 0.653578i | \(-0.226733\pi\) |
−0.187586 | + | 0.982248i | \(0.560066\pi\) | |||||||
\(42\) | 1.95819 | − | 3.39169i | 0.302156 | − | 0.523349i | ||||
\(43\) | −0.498655 | − | 0.863697i | −0.0760442 | − | 0.131712i | 0.825496 | − | 0.564408i | \(-0.190896\pi\) |
−0.901540 | + | 0.432696i | \(0.857562\pi\) | |||||||
\(44\) | − | 0.128529i | − | 0.0193764i | ||||||
\(45\) | 2.24041 | − | 1.29350i | 0.333980 | − | 0.192824i | ||||
\(46\) | 10.9712 | − | 6.33421i | 1.61761 | − | 0.933928i | ||||
\(47\) | 4.51725i | 0.658909i | 0.944171 | + | 0.329455i | \(0.106865\pi\) | ||||
−0.944171 | + | 0.329455i | \(0.893135\pi\) | |||||||
\(48\) | −5.41908 | − | 9.38612i | −0.782177 | − | 1.35477i | ||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | −5.67810 | − | 3.27825i | −0.803004 | − | 0.463615i | ||||
\(51\) | 5.50532 | 0.770899 | ||||||||
\(52\) | −0.283381 | + | 0.0332676i | −0.0392979 | + | 0.00461339i | ||||
\(53\) | −8.89651 | −1.22203 | −0.611015 | − | 0.791619i | \(-0.709238\pi\) | ||||
−0.611015 | + | 0.791619i | \(0.709238\pi\) | |||||||
\(54\) | 6.73251 | + | 3.88701i | 0.916178 | + | 0.528956i | ||||
\(55\) | −0.421434 | + | 0.729946i | −0.0568262 | + | 0.0984259i | ||||
\(56\) | −1.44079 | − | 2.49552i | −0.192534 | − | 0.333478i | ||||
\(57\) | − | 7.03944i | − | 0.932397i | ||||||
\(58\) | −6.27736 | + | 3.62424i | −0.824258 | + | 0.475886i | ||||
\(59\) | −5.37392 | + | 3.10263i | −0.699624 | + | 0.403928i | −0.807207 | − | 0.590268i | \(-0.799022\pi\) |
0.107583 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(60\) | − | 0.116049i | − | 0.0149818i | ||||||
\(61\) | 6.73536 | + | 11.6660i | 0.862375 | + | 1.49368i | 0.869630 | + | 0.493703i | \(0.164357\pi\) |
−0.00725571 | + | 0.999974i | \(0.502310\pi\) | |||||||
\(62\) | 4.01504 | − | 6.95426i | 0.509911 | − | 0.883191i | ||||
\(63\) | 4.31714 | + | 2.49250i | 0.543908 | + | 0.314025i | ||||
\(64\) | −8.29100 | −1.03637 | ||||||||
\(65\) | 1.71847 | + | 0.740247i | 0.213150 | + | 0.0918164i | ||||
\(66\) | −6.36084 | −0.782965 | ||||||||
\(67\) | −7.25094 | − | 4.18633i | −0.885843 | − | 0.511442i | −0.0132624 | − | 0.999912i | \(-0.504222\pi\) |
−0.872580 | + | 0.488470i | \(0.837555\pi\) | |||||||
\(68\) | 0.0770880 | − | 0.133520i | 0.00934830 | − | 0.0161917i | ||||
\(69\) | 12.9146 | + | 22.3688i | 1.55474 | + | 2.69288i | ||||
\(70\) | 0.719250i | 0.0859668i | ||||||||
\(71\) | −4.50168 | + | 2.59905i | −0.534251 | + | 0.308450i | −0.742746 | − | 0.669573i | \(-0.766477\pi\) |
0.208495 | + | 0.978023i | \(0.433144\pi\) | |||||||
\(72\) | 12.4402 | − | 7.18234i | 1.46609 | − | 0.846447i | ||||
\(73\) | 11.8395i | 1.38571i | 0.721076 | + | 0.692856i | \(0.243648\pi\) | ||||
−0.721076 | + | 0.692856i | \(0.756352\pi\) | |||||||
\(74\) | 7.08863 | + | 12.2779i | 0.824037 | + | 1.42727i | ||||
\(75\) | 6.68392 | − | 11.5769i | 0.771793 | − | 1.33678i | ||||
\(76\) | −0.170727 | − | 0.0985694i | −0.0195838 | − | 0.0113067i | ||||
\(77\) | −1.62416 | −0.185090 | ||||||||
\(78\) | 1.64640 | + | 14.0244i | 0.186418 | + | 1.58795i | ||||
\(79\) | 0.982310 | 0.110518 | 0.0552592 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552592 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(80\) | 1.72377 | + | 0.995221i | 0.192724 | + | 0.111269i | ||||
\(81\) | −0.447609 | + | 0.775281i | −0.0497343 | + | 0.0861423i | ||||
\(82\) | −2.91676 | − | 5.05197i | −0.322102 | − | 0.557897i | ||||
\(83\) | − | 8.91851i | − | 0.978934i | −0.872022 | − | 0.489467i | \(-0.837191\pi\) | ||
0.872022 | − | 0.489467i | \(-0.162809\pi\) | |||||||
\(84\) | 0.193660 | − | 0.111810i | 0.0211300 | − | 0.0121994i | ||||
\(85\) | −0.875603 | + | 0.505530i | −0.0949725 | + | 0.0548324i | ||||
\(86\) | 1.38223i | 0.149049i | ||||||||
\(87\) | −7.38934 | − | 12.7987i | −0.792220 | − | 1.37217i | ||||
\(88\) | −2.34008 | + | 4.05313i | −0.249453 | + | 0.432065i | ||||
\(89\) | −10.4087 | − | 6.00949i | −1.10332 | − | 0.637005i | −0.166233 | − | 0.986087i | \(-0.553160\pi\) |
−0.937092 | + | 0.349082i | \(0.886494\pi\) | |||||||
\(90\) | −3.58546 | −0.377941 | ||||||||
\(91\) | 0.420388 | + | 3.58096i | 0.0440686 | + | 0.375387i | ||||
\(92\) | 0.723345 | 0.0754139 | ||||||||
\(93\) | 14.1788 | + | 8.18614i | 1.47027 | + | 0.848863i | ||||
\(94\) | 3.13035 | − | 5.42193i | 0.322871 | − | 0.559229i | ||||
\(95\) | 0.646401 | + | 1.11960i | 0.0663194 | + | 0.114869i | ||||
\(96\) | − | 1.26423i | − | 0.129030i | ||||||
\(97\) | 3.82981 | − | 2.21114i | 0.388858 | − | 0.224507i | −0.292807 | − | 0.956172i | \(-0.594589\pi\) |
0.681665 | + | 0.731664i | \(0.261256\pi\) | |||||||
\(98\) | −1.20027 | + | 0.692976i | −0.121246 | + | 0.0700012i | ||||
\(99\) | − | 8.09643i | − | 0.813722i | ||||||
\(100\) | −0.187183 | − | 0.324210i | −0.0187183 | − | 0.0324210i | ||||
\(101\) | 9.15132 | − | 15.8506i | 0.910591 | − | 1.57719i | 0.0973594 | − | 0.995249i | \(-0.468960\pi\) |
0.813231 | − | 0.581940i | \(-0.197706\pi\) | |||||||
\(102\) | −6.60787 | − | 3.81506i | −0.654277 | − | 0.377747i | ||||
\(103\) | −5.02046 | −0.494680 | −0.247340 | − | 0.968929i | \(-0.579556\pi\) | ||||
−0.247340 | + | 0.968929i | \(0.579556\pi\) | |||||||
\(104\) | 9.54206 | + | 4.11033i | 0.935676 | + | 0.403051i | ||||
\(105\) | −1.46646 | −0.143111 | ||||||||
\(106\) | 10.6782 | + | 6.16507i | 1.03716 | + | 0.598804i | ||||
\(107\) | −3.07228 | + | 5.32134i | −0.297008 | + | 0.514434i | −0.975450 | − | 0.220221i | \(-0.929322\pi\) |
0.678442 | + | 0.734654i | \(0.262656\pi\) | |||||||
\(108\) | 0.221942 | + | 0.384415i | 0.0213564 | + | 0.0369903i | ||||
\(109\) | 11.8962i | 1.13945i | 0.821834 | + | 0.569727i | \(0.192951\pi\) | ||||
−0.821834 | + | 0.569727i | \(0.807049\pi\) | |||||||
\(110\) | 1.01167 | − | 0.584088i | 0.0964590 | − | 0.0556906i | ||||
\(111\) | −25.0330 | + | 14.4528i | −2.37602 | + | 1.37180i | ||||
\(112\) | 3.83547i | 0.362418i | ||||||||
\(113\) | −1.77806 | − | 3.07969i | −0.167266 | − | 0.289713i | 0.770192 | − | 0.637812i | \(-0.220161\pi\) |
−0.937458 | + | 0.348099i | \(0.886827\pi\) | |||||||
\(114\) | −4.87817 | + | 8.44923i | −0.456882 | + | 0.791343i | ||||
\(115\) | −4.10805 | − | 2.37178i | −0.383078 | − | 0.221170i | ||||
\(116\) | −0.413875 | −0.0384274 | ||||||||
\(117\) | −17.8511 | + | 2.09563i | −1.65033 | + | 0.193741i | ||||
\(118\) | 8.60020 | 0.791713 | ||||||||
\(119\) | −1.68724 | − | 0.974127i | −0.154669 | − | 0.0892980i | ||||
\(120\) | −2.11286 | + | 3.65957i | −0.192877 | + | 0.334072i | ||||
\(121\) | −4.18105 | − | 7.24180i | −0.380096 | − | 0.658345i | ||||
\(122\) | − | 18.6698i | − | 1.69028i | ||||||
\(123\) | 10.3003 | − | 5.94689i | 0.928748 | − | 0.536213i | ||||
\(124\) | 0.397076 | − | 0.229252i | 0.0356585 | − | 0.0205874i | ||||
\(125\) | 5.04981i | 0.451668i | ||||||||
\(126\) | −3.45449 | − | 5.98335i | −0.307750 | − | 0.533039i | ||||
\(127\) | −0.711749 | + | 1.23279i | −0.0631575 | + | 0.109392i | −0.895875 | − | 0.444306i | \(-0.853450\pi\) |
0.832718 | + | 0.553698i | \(0.186784\pi\) | |||||||
\(128\) | 9.17653 | + | 5.29807i | 0.811098 | + | 0.468288i | ||||
\(129\) | −2.81818 | −0.248127 | ||||||||
\(130\) | −1.54966 | − | 2.07936i | −0.135914 | − | 0.182372i | ||||
\(131\) | 8.67374 | 0.757828 | 0.378914 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378914 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(132\) | −0.314535 | − | 0.181597i | −0.0273767 | − | 0.0158060i | ||||
\(133\) | −1.24558 | + | 2.15740i | −0.108005 | + | 0.187071i | ||||
\(134\) | 5.80205 | + | 10.0495i | 0.501221 | + | 0.868141i | ||||
\(135\) | − | 2.91091i | − | 0.250531i | ||||||
\(136\) | −4.86191 | + | 2.80703i | −0.416906 | + | 0.240701i | ||||
\(137\) | 7.37667 | − | 4.25892i | 0.630231 | − | 0.363864i | −0.150611 | − | 0.988593i | \(-0.548124\pi\) |
0.780842 | + | 0.624729i | \(0.214791\pi\) | |||||||
\(138\) | − | 35.7981i | − | 3.04733i | ||||||
\(139\) | 2.51922 | + | 4.36342i | 0.213677 | + | 0.370100i | 0.952863 | − | 0.303402i | \(-0.0981225\pi\) |
−0.739185 | + | 0.673502i | \(0.764789\pi\) | |||||||
\(140\) | −0.0205340 | + | 0.0355659i | −0.00173544 | + | 0.00300587i | ||||
\(141\) | 11.0546 | + | 6.38237i | 0.930964 | + | 0.537493i | ||||
\(142\) | 7.20431 | 0.604572 | ||||||||
\(143\) | 4.69546 | − | 3.49933i | 0.392654 | − | 0.292628i | ||||
\(144\) | −19.1198 | −1.59332 | ||||||||
\(145\) | 2.35050 | + | 1.35706i | 0.195198 | + | 0.112698i | ||||
\(146\) | 8.20451 | − | 14.2106i | 0.679010 | − | 1.17608i | ||||
\(147\) | −1.41289 | − | 2.44719i | −0.116533 | − | 0.201841i | ||||
\(148\) | 0.809498i | 0.0665403i | ||||||||
\(149\) | 2.91409 | − | 1.68245i | 0.238732 | − | 0.137832i | −0.375862 | − | 0.926676i | \(-0.622653\pi\) |
0.614594 | + | 0.788844i | \(0.289320\pi\) | |||||||
\(150\) | −16.0450 | + | 9.26360i | −1.31007 | + | 0.756370i | ||||
\(151\) | − | 12.6566i | − | 1.02998i | −0.857196 | − | 0.514991i | \(-0.827795\pi\) | ||
0.857196 | − | 0.514991i | \(-0.172205\pi\) | |||||||
\(152\) | 3.58924 | + | 6.21674i | 0.291125 | + | 0.504244i | ||||
\(153\) | 4.85602 | − | 8.41087i | 0.392586 | − | 0.679979i | ||||
\(154\) | 1.94943 | + | 1.12550i | 0.157090 | + | 0.0906957i | ||||
\(155\) | −3.00679 | −0.241511 | ||||||||
\(156\) | −0.318973 | + | 0.740492i | −0.0255383 | + | 0.0592868i | ||||
\(157\) | 10.3691 | 0.827547 | 0.413773 | − | 0.910380i | \(-0.364211\pi\) | ||||
0.413773 | + | 0.910380i | \(0.364211\pi\) | |||||||
\(158\) | −1.17904 | − | 0.680717i | −0.0937992 | − | 0.0541550i | ||||
\(159\) | −12.5698 | + | 21.7715i | −0.996847 | + | 1.72659i | ||||
\(160\) | 0.116089 | + | 0.201071i | 0.00917761 | + | 0.0158961i | ||||
\(161\) | − | 9.14058i | − | 0.720379i | ||||||
\(162\) | 1.07450 | − | 0.620364i | 0.0844209 | − | 0.0487404i | ||||
\(163\) | 13.6428 | − | 7.87669i | 1.06859 | − | 0.616950i | 0.140794 | − | 0.990039i | \(-0.455035\pi\) |
0.927796 | + | 0.373089i | \(0.121701\pi\) | |||||||
\(164\) | − | 0.333084i | − | 0.0260095i | ||||||
\(165\) | 1.19088 | + | 2.06266i | 0.0927098 | + | 0.160578i | ||||
\(166\) | −6.18032 | + | 10.7046i | −0.479686 | + | 0.830840i | ||||
\(167\) | −14.2016 | − | 8.19930i | −1.09895 | − | 0.634481i | −0.163007 | − | 0.986625i | \(-0.552119\pi\) |
−0.935946 | + | 0.352144i | \(0.885453\pi\) | |||||||
\(168\) | −8.14270 | −0.628223 | ||||||||
\(169\) | −8.93069 | − | 9.44684i | −0.686976 | − | 0.726680i | ||||
\(170\) | 1.40128 | 0.107473 | ||||||||
\(171\) | −10.7547 | − | 6.20920i | −0.822429 | − | 0.474830i | ||||
\(172\) | −0.0394614 | + | 0.0683491i | −0.00300890 | + | 0.00521157i | ||||
\(173\) | −0.150677 | − | 0.260981i | −0.0114558 | − | 0.0198420i | 0.860241 | − | 0.509888i | \(-0.170313\pi\) |
−0.871696 | + | 0.490046i | \(0.836980\pi\) | |||||||
\(174\) | 20.4825i | 1.55278i | ||||||||
\(175\) | −4.09689 | + | 2.36534i | −0.309696 | + | 0.178803i | ||||
\(176\) | 5.39483 | − | 3.11470i | 0.406650 | − | 0.234780i | ||||
\(177\) | 17.5347i | 1.31799i | ||||||||
\(178\) | 8.32887 | + | 14.4260i | 0.624275 | + | 1.08128i | ||||
\(179\) | −4.90791 | + | 8.50075i | −0.366834 | + | 0.635376i | −0.989069 | − | 0.147455i | \(-0.952892\pi\) |
0.622234 | + | 0.782831i | \(0.286225\pi\) | |||||||
\(180\) | −0.177296 | − | 0.102362i | −0.0132149 | − | 0.00762960i | ||||
\(181\) | 12.4320 | 0.924062 | 0.462031 | − | 0.886864i | \(-0.347121\pi\) | ||||
0.462031 | + | 0.886864i | \(0.347121\pi\) | |||||||
\(182\) | 1.97694 | − | 4.58944i | 0.146541 | − | 0.340192i | ||||
\(183\) | 38.0652 | 2.81386 | ||||||||
\(184\) | −22.8105 | − | 13.1697i | −1.68162 | − | 0.970881i | ||||
\(185\) | 2.65427 | − | 4.59733i | 0.195146 | − | 0.338003i | ||||
\(186\) | −11.3456 | − | 19.6512i | −0.831900 | − | 1.44089i | ||||
\(187\) | 3.16427i | 0.231395i | ||||||||
\(188\) | 0.309583 | − | 0.178738i | 0.0225786 | − | 0.0130358i | ||||
\(189\) | 4.85767 | − | 2.80458i | 0.353344 | − | 0.204003i | ||||
\(190\) | − | 1.79176i | − | 0.129988i | ||||||
\(191\) | 6.12346 | + | 10.6061i | 0.443078 | + | 0.767434i | 0.997916 | − | 0.0645248i | \(-0.0205531\pi\) |
−0.554838 | + | 0.831958i | \(0.687220\pi\) | |||||||
\(192\) | −11.7142 | + | 20.2897i | −0.845403 | + | 1.46428i | ||||
\(193\) | −10.0752 | − | 5.81692i | −0.725229 | − | 0.418711i | 0.0914452 | − | 0.995810i | \(-0.470851\pi\) |
−0.816674 | + | 0.577099i | \(0.804185\pi\) | |||||||
\(194\) | −6.12908 | −0.440042 | ||||||||
\(195\) | 4.23953 | − | 3.15955i | 0.303599 | − | 0.226260i | ||||
\(196\) | −0.0791355 | −0.00565254 | ||||||||
\(197\) | −1.55984 | − | 0.900572i | −0.111134 | − | 0.0641631i | 0.443403 | − | 0.896322i | \(-0.353771\pi\) |
−0.554537 | + | 0.832159i | \(0.687104\pi\) | |||||||
\(198\) | −5.61064 | + | 9.71791i | −0.398731 | + | 0.690622i | ||||
\(199\) | 3.29657 | + | 5.70982i | 0.233687 | + | 0.404759i | 0.958890 | − | 0.283777i | \(-0.0915874\pi\) |
−0.725203 | + | 0.688535i | \(0.758254\pi\) | |||||||
\(200\) | 13.6319i | 0.963918i | ||||||||
\(201\) | −20.4895 | + | 11.8296i | −1.44522 | + | 0.834397i | ||||
\(202\) | −21.9681 | + | 12.6833i | −1.54567 | + | 0.892394i | ||||
\(203\) | 5.22996i | 0.367071i | ||||||||
\(204\) | −0.217833 | − | 0.377298i | −0.0152514 | − | 0.0264162i | ||||
\(205\) | −1.09215 | + | 1.89166i | −0.0762793 | + | 0.132120i | ||||
\(206\) | 6.02590 | + | 3.47906i | 0.419845 | + | 0.242397i | ||||
\(207\) | 45.5658 | 3.16704 | ||||||||
\(208\) | −8.26369 | − | 11.0884i | −0.572984 | − | 0.768840i | ||||
\(209\) | 4.04603 | 0.279870 | ||||||||
\(210\) | 1.76014 | + | 1.01622i | 0.121461 | + | 0.0701258i | ||||
\(211\) | −5.35996 | + | 9.28373i | −0.368995 | + | 0.639118i | −0.989409 | − | 0.145157i | \(-0.953631\pi\) |
0.620414 | + | 0.784275i | \(0.286965\pi\) | |||||||
\(212\) | 0.352015 | + | 0.609708i | 0.0241765 | + | 0.0418749i | ||||
\(213\) | 14.6886i | 1.00645i | ||||||||
\(214\) | 7.37513 | − | 4.25803i | 0.504154 | − | 0.291073i | ||||
\(215\) | 0.448221 | − | 0.258781i | 0.0305684 | − | 0.0176487i | ||||
\(216\) | − | 16.1633i | − | 1.09977i | ||||||
\(217\) | −2.89695 | − | 5.01767i | −0.196658 | − | 0.340622i | ||||
\(218\) | 8.24382 | − | 14.2787i | 0.558342 | − | 0.967076i | ||||
\(219\) | 28.9736 | + | 16.7279i | 1.95785 | + | 1.13037i | ||||
\(220\) | 0.0667009 | 0.00449697 | ||||||||
\(221\) | 6.97662 | − | 0.819021i | 0.469298 | − | 0.0550933i | ||||
\(222\) | 40.0617 | 2.68877 | ||||||||
\(223\) | −11.1612 | − | 6.44392i | −0.747409 | − | 0.431517i | 0.0773480 | − | 0.997004i | \(-0.475355\pi\) |
−0.824757 | + | 0.565487i | \(0.808688\pi\) | |||||||
\(224\) | −0.223696 | + | 0.387453i | −0.0149463 | + | 0.0258878i | ||||
\(225\) | −11.7912 | − | 20.4230i | −0.786082 | − | 1.36153i | ||||
\(226\) | 4.92862i | 0.327847i | ||||||||
\(227\) | −0.605486 | + | 0.349577i | −0.0401875 | + | 0.0232023i | −0.519959 | − | 0.854191i | \(-0.674053\pi\) |
0.479772 | + | 0.877393i | \(0.340720\pi\) | |||||||
\(228\) | −0.482437 | + | 0.278535i | −0.0319502 | + | 0.0184464i | ||||
\(229\) | − | 18.2868i | − | 1.20843i | −0.796822 | − | 0.604214i | \(-0.793487\pi\) | ||
0.796822 | − | 0.604214i | \(-0.206513\pi\) | |||||||
\(230\) | 3.28718 | + | 5.69356i | 0.216750 | + | 0.375422i | ||||
\(231\) | −2.29475 | + | 3.97463i | −0.150984 | + | 0.261511i | ||||
\(232\) | 13.0515 | + | 7.53528i | 0.856872 | + | 0.494715i | ||||
\(233\) | −26.7796 | −1.75439 | −0.877194 | − | 0.480137i | \(-0.840587\pi\) | ||||
−0.877194 | + | 0.480137i | \(0.840587\pi\) | |||||||
\(234\) | 22.8783 | + | 9.85505i | 1.49560 | + | 0.644245i | ||||
\(235\) | −2.34426 | −0.152923 | ||||||||
\(236\) | 0.425268 | + | 0.245528i | 0.0276826 | + | 0.0159825i | ||||
\(237\) | 1.38789 | − | 2.40390i | 0.0901533 | − | 0.156150i | ||||
\(238\) | 1.35009 | + | 2.33843i | 0.0875135 | + | 0.151578i | ||||
\(239\) | − | 16.6177i | − | 1.07491i | −0.843293 | − | 0.537454i | \(-0.819386\pi\) | ||
0.843293 | − | 0.537454i | \(-0.180614\pi\) | |||||||
\(240\) | 4.87099 | − | 2.81227i | 0.314421 | − | 0.181531i | ||||
\(241\) | 15.0800 | − | 8.70643i | 0.971387 | − | 0.560830i | 0.0717279 | − | 0.997424i | \(-0.477149\pi\) |
0.899659 | + | 0.436594i | \(0.143815\pi\) | |||||||
\(242\) | 11.5895i | 0.745000i | ||||||||
\(243\) | −7.14890 | − | 12.3823i | −0.458602 | − | 0.794322i | ||||
\(244\) | 0.533007 | − | 0.923194i | 0.0341222 | − | 0.0591015i | ||||
\(245\) | 0.449430 | + | 0.259479i | 0.0287130 | + | 0.0165775i | ||||
\(246\) | −16.4842 | −1.05099 | ||||||||
\(247\) | −1.04725 | − | 8.92073i | −0.0666350 | − | 0.567612i | ||||
\(248\) | −16.6956 | −1.06017 | ||||||||
\(249\) | −21.8253 | − | 12.6008i | −1.38312 | − | 0.798546i | ||||
\(250\) | 3.49940 | − | 6.06113i | 0.221321 | − | 0.383340i | ||||
\(251\) | −3.22491 | − | 5.58571i | −0.203554 | − | 0.352567i | 0.746117 | − | 0.665815i | \(-0.231916\pi\) |
−0.949671 | + | 0.313249i | \(0.898583\pi\) | |||||||
\(252\) | − | 0.394491i | − | 0.0248506i | ||||||
\(253\) | −12.8568 | + | 7.42288i | −0.808300 | + | 0.466672i | ||||
\(254\) | 1.70858 | − | 0.986451i | 0.107206 | − | 0.0618954i | ||||
\(255\) | 2.85703i | 0.178914i | ||||||||
\(256\) | 0.948120 | + | 1.64219i | 0.0592575 | + | 0.102637i | ||||
\(257\) | −1.83578 | + | 3.17966i | −0.114513 | + | 0.198342i | −0.917585 | − | 0.397540i | \(-0.869864\pi\) |
0.803072 | + | 0.595882i | \(0.203197\pi\) | |||||||
\(258\) | 3.38257 | + | 1.95293i | 0.210590 | + | 0.121584i | ||||
\(259\) | 10.2293 | 0.635615 | ||||||||
\(260\) | −0.0172645 | − | 0.147063i | −0.00107070 | − | 0.00912044i | ||||
\(261\) | −26.0713 | −1.61377 | ||||||||
\(262\) | −10.4108 | − | 6.01070i | −0.643183 | − | 0.371342i | ||||
\(263\) | −9.15964 | + | 15.8650i | −0.564807 | + | 0.978275i | 0.432260 | + | 0.901749i | \(0.357716\pi\) |
−0.997068 | + | 0.0765263i | \(0.975617\pi\) | |||||||
\(264\) | 6.61252 | + | 11.4532i | 0.406973 | + | 0.704897i | ||||
\(265\) | − | 4.61690i | − | 0.283614i | ||||||
\(266\) | 2.99006 | − | 1.72631i | 0.183332 | − | 0.105847i | ||||
\(267\) | −29.4128 | + | 16.9815i | −1.80003 | + | 1.03925i | ||||
\(268\) | 0.662575i | 0.0404732i | ||||||||
\(269\) | −13.7715 | − | 23.8529i | −0.839661 | − | 1.45434i | −0.890178 | − | 0.455613i | \(-0.849420\pi\) |
0.0505171 | − | 0.998723i | \(-0.483913\pi\) | |||||||
\(270\) | −2.01719 | + | 3.49388i | −0.122762 | + | 0.212631i | ||||
\(271\) | 5.64582 | + | 3.25961i | 0.342959 | + | 0.198007i | 0.661580 | − | 0.749875i | \(-0.269886\pi\) |
−0.318621 | + | 0.947882i | \(0.603220\pi\) | |||||||
\(272\) | 7.47246 | 0.453084 | ||||||||
\(273\) | 9.35726 | + | 4.03072i | 0.566327 | + | 0.243950i | ||||
\(274\) | −11.8053 | −0.713186 | ||||||||
\(275\) | 6.65401 | + | 3.84169i | 0.401252 | + | 0.231663i | ||||
\(276\) | 1.02200 | − | 1.77016i | 0.0615174 | − | 0.106551i | ||||
\(277\) | 2.72093 | + | 4.71279i | 0.163485 | + | 0.283164i | 0.936116 | − | 0.351691i | \(-0.114393\pi\) |
−0.772631 | + | 0.634855i | \(0.781060\pi\) | |||||||
\(278\) | − | 6.98304i | − | 0.418815i | ||||||
\(279\) | 25.0131 | − | 14.4413i | 1.49749 | − | 0.864579i | ||||
\(280\) | 1.29507 | − | 0.747709i | 0.0773952 | − | 0.0446842i | ||||
\(281\) | − | 3.54237i | − | 0.211320i | −0.994402 | − | 0.105660i | \(-0.966304\pi\) | ||
0.994402 | − | 0.105660i | \(-0.0336955\pi\) | |||||||
\(282\) | −8.84566 | − | 15.3211i | −0.526752 | − | 0.912360i | ||||
\(283\) | −7.06956 | + | 12.2448i | −0.420242 | + | 0.727880i | −0.995963 | − | 0.0897658i | \(-0.971388\pi\) |
0.575721 | + | 0.817646i | \(0.304721\pi\) | |||||||
\(284\) | 0.356243 | + | 0.205677i | 0.0211391 | + | 0.0122047i | ||||
\(285\) | 3.65317 | 0.216395 | ||||||||
\(286\) | −8.06077 | + | 0.946296i | −0.476643 | + | 0.0559556i | ||||
\(287\) | −4.20903 | −0.248451 | ||||||||
\(288\) | −1.93145 | − | 1.11512i | −0.113812 | − | 0.0657093i | ||||
\(289\) | 6.60215 | − | 11.4353i | 0.388362 | − | 0.672663i | ||||
\(290\) | −1.88082 | − | 3.25768i | −0.110446 | − | 0.191298i | ||||
\(291\) | − | 12.4964i | − | 0.732551i | ||||||
\(292\) | 0.811403 | − | 0.468464i | 0.0474838 | − | 0.0274148i | ||||
\(293\) | −7.23071 | + | 4.17465i | −0.422423 | + | 0.243886i | −0.696113 | − | 0.717932i | \(-0.745089\pi\) |
0.273691 | + | 0.961818i | \(0.411756\pi\) | |||||||
\(294\) | 3.91639i | 0.228408i | ||||||||
\(295\) | −1.61013 | − | 2.78883i | −0.0937455 | − | 0.162372i | ||||
\(296\) | 14.7382 | − | 25.5274i | 0.856642 | − | 1.48375i | ||||
\(297\) | −7.88964 | − | 4.55508i | −0.457803 | − | 0.264313i | ||||
\(298\) | −4.66359 | −0.270155 | ||||||||
\(299\) | 19.6938 | + | 26.4255i | 1.13892 | + | 1.52823i | ||||
\(300\) | −1.05787 | −0.0610762 | ||||||||
\(301\) | 0.863697 | + | 0.498655i | 0.0497826 | + | 0.0287420i | ||||
\(302\) | −8.77074 | + | 15.1914i | −0.504699 | + | 0.874165i | ||||
\(303\) | −25.8596 | − | 44.7901i | −1.48559 | − | 2.57312i | ||||
\(304\) | − | 9.55474i | − | 0.548002i | ||||||
\(305\) | −6.05415 | + | 3.49536i | −0.346659 | + | 0.200144i | ||||
\(306\) | −11.6571 | + | 6.73021i | −0.666390 | + | 0.384741i | ||||
\(307\) | 8.33362i | 0.475625i | 0.971311 | + | 0.237813i | \(0.0764304\pi\) | ||||
−0.971311 | + | 0.237813i | \(0.923570\pi\) | |||||||
\(308\) | 0.0642644 | + | 0.111309i | 0.00366180 | + | 0.00634243i | ||||
\(309\) | −7.09334 | + | 12.2860i | −0.403526 | + | 0.698927i | ||||
\(310\) | 3.60896 | + | 2.08363i | 0.204975 | + | 0.118342i | ||||
\(311\) | 14.6227 | 0.829176 | 0.414588 | − | 0.910009i | \(-0.363926\pi\) | ||||
0.414588 | + | 0.910009i | \(0.363926\pi\) | |||||||
\(312\) | 23.5406 | − | 17.5438i | 1.33273 | − | 0.993224i | ||||
\(313\) | 17.1328 | 0.968404 | 0.484202 | − | 0.874956i | \(-0.339110\pi\) | ||||
0.484202 | + | 0.874956i | \(0.339110\pi\) | |||||||
\(314\) | −12.4458 | − | 7.18556i | −0.702355 | − | 0.405505i | ||||
\(315\) | −1.29350 | + | 2.24041i | −0.0728805 | + | 0.126233i | ||||
\(316\) | −0.0388678 | − | 0.0673210i | −0.00218649 | − | 0.00378710i | ||||
\(317\) | − | 14.0000i | − | 0.786320i | −0.919470 | − | 0.393160i | \(-0.871382\pi\) | ||
0.919470 | − | 0.393160i | \(-0.128618\pi\) | |||||||
\(318\) | 30.1742 | − | 17.4211i | 1.69209 | − | 0.976926i | ||||
\(319\) | 7.35627 | − | 4.24714i | 0.411872 | − | 0.237794i | ||||
\(320\) | − | 4.30267i | − | 0.240527i | ||||||
\(321\) | 8.68157 | + | 15.0369i | 0.484558 | + | 0.839279i | ||||
\(322\) | −6.33421 | + | 10.9712i | −0.352991 | + | 0.611399i | ||||
\(323\) | 4.20317 | + | 2.42670i | 0.233871 | + | 0.135025i | ||||
\(324\) | 0.0708435 | 0.00393575 | ||||||||
\(325\) | 6.74791 | − | 15.6652i | 0.374307 | − | 0.868947i | ||||
\(326\) | −21.8334 | −1.20924 | ||||||||
\(327\) | 29.1124 | + | 16.8081i | 1.60992 | + | 0.929487i | ||||
\(328\) | −6.06434 | + | 10.5037i | −0.334847 | + | 0.579972i | ||||
\(329\) | −2.25863 | − | 3.91206i | −0.124522 | − | 0.215679i | ||||
\(330\) | − | 3.30100i | − | 0.181714i | ||||||
\(331\) | 5.99286 | − | 3.45998i | 0.329397 | − | 0.190178i | −0.326176 | − | 0.945309i | \(-0.605760\pi\) |
0.655574 | + | 0.755131i | \(0.272427\pi\) | |||||||
\(332\) | −0.611216 | + | 0.352886i | −0.0335448 | + | 0.0193671i | ||||
\(333\) | 50.9928i | 2.79439i | ||||||||
\(334\) | 11.3638 | + | 19.6827i | 0.621801 | + | 1.07699i | ||||
\(335\) | 2.17253 | − | 3.76292i | 0.118698 | − | 0.205591i | ||||
\(336\) | 9.38612 | + | 5.41908i | 0.512055 | + | 0.295635i | ||||
\(337\) | 11.1559 | 0.607703 | 0.303852 | − | 0.952719i | \(-0.401727\pi\) | ||||
0.303852 | + | 0.952719i | \(0.401727\pi\) | |||||||
\(338\) | 4.17280 | + | 17.5275i | 0.226970 | + | 0.953371i | ||||
\(339\) | −10.0488 | −0.545776 | ||||||||
\(340\) | 0.0692913 | + | 0.0400054i | 0.00375785 | + | 0.00216960i | ||||
\(341\) | −4.70512 | + | 8.14950i | −0.254796 | + | 0.441320i | ||||
\(342\) | 8.60566 | + | 14.9054i | 0.465341 | + | 0.805994i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 2.48881 | − | 1.43692i | 0.134188 | − | 0.0774734i | ||||
\(345\) | −11.6084 | + | 6.70213i | −0.624977 | + | 0.360830i | ||||
\(346\) | 0.417663i | 0.0224537i | ||||||||
\(347\) | 2.46255 | + | 4.26527i | 0.132197 | + | 0.228971i | 0.924523 | − | 0.381126i | \(-0.124464\pi\) |
−0.792326 | + | 0.610097i | \(0.791130\pi\) | |||||||
\(348\) | −0.584759 | + | 1.01283i | −0.0313464 | + | 0.0542935i | ||||
\(349\) | 1.31926 | + | 0.761675i | 0.0706183 | + | 0.0407715i | 0.534893 | − | 0.844920i | \(-0.320352\pi\) |
−0.464275 | + | 0.885691i | \(0.653685\pi\) | |||||||
\(350\) | 6.55650 | 0.350460 | ||||||||
\(351\) | −8.00098 | + | 18.5741i | −0.427061 | + | 0.991415i | ||||
\(352\) | 0.726636 | 0.0387298 | ||||||||
\(353\) | 15.5261 | + | 8.96401i | 0.826372 | + | 0.477106i | 0.852609 | − | 0.522550i | \(-0.175019\pi\) |
−0.0262367 | + | 0.999656i | \(0.508352\pi\) | |||||||
\(354\) | 12.1511 | − | 21.0463i | 0.645824 | − | 1.11860i | ||||
\(355\) | −1.34879 | − | 2.33618i | −0.0715865 | − | 0.123991i | ||||
\(356\) | 0.951129i | 0.0504097i | ||||||||
\(357\) | −4.76775 | + | 2.75266i | −0.252336 | + | 0.145686i | ||||
\(358\) | 11.7816 | − | 6.80213i | 0.622679 | − | 0.359504i | ||||
\(359\) | 20.0014i | 1.05563i | 0.849359 | + | 0.527816i | \(0.176989\pi\) | ||||
−0.849359 | + | 0.527816i | \(0.823011\pi\) | |||||||
\(360\) | 3.72733 | + | 6.45592i | 0.196447 | + | 0.340257i | ||||
\(361\) | −6.39707 | + | 11.0801i | −0.336688 | + | 0.583161i | ||||
\(362\) | −14.9217 | − | 8.61507i | −0.784269 | − | 0.452798i | ||||
\(363\) | −23.6294 | −1.24022 | ||||||||
\(364\) | 0.228782 | − | 0.170501i | 0.0119914 | − | 0.00893669i | ||||
\(365\) | −6.14421 | −0.321602 | ||||||||
\(366\) | −45.6885 | − | 26.3783i | −2.38818 | − | 1.37882i | ||||
\(367\) | −13.7078 | + | 23.7427i | −0.715544 | + | 1.23936i | 0.247206 | + | 0.968963i | \(0.420488\pi\) |
−0.962749 | + | 0.270395i | \(0.912846\pi\) | |||||||
\(368\) | 17.5292 | + | 30.3615i | 0.913772 | + | 1.58270i | ||||
\(369\) | − | 20.9820i | − | 1.09228i | ||||||
\(370\) | −6.37169 | + | 3.67870i | −0.331248 | + | 0.191246i | ||||
\(371\) | 7.70460 | − | 4.44825i | 0.400003 | − | 0.230942i | ||||
\(372\) | − | 1.29563i | − | 0.0671752i | ||||||
\(373\) | 7.94643 | + | 13.7636i | 0.411451 | + | 0.712653i | 0.995049 | − | 0.0993893i | \(-0.0316889\pi\) |
−0.583598 | + | 0.812043i | \(0.698356\pi\) | |||||||
\(374\) | 2.19277 | − | 3.79798i | 0.113385 | − | 0.196389i | ||||
\(375\) | 12.3578 | + | 7.13481i | 0.638156 | + | 0.368440i | ||||
\(376\) | −13.0168 | −0.671292 | ||||||||
\(377\) | −11.2682 | − | 15.1199i | −0.580341 | − | 0.778712i | ||||
\(378\) | −7.77403 | −0.399853 | ||||||||
\(379\) | 7.60284 | + | 4.38950i | 0.390532 | + | 0.225474i | 0.682390 | − | 0.730988i | \(-0.260940\pi\) |
−0.291859 | + | 0.956461i | \(0.594274\pi\) | |||||||
\(380\) | 0.0511533 | − | 0.0886001i | 0.00262411 | − | 0.00454509i | ||||
\(381\) | 2.01124 | + | 3.48357i | 0.103039 | + | 0.178469i | ||||
\(382\) | − | 16.9736i | − | 0.868447i | ||||||
\(383\) | 6.89562 | − | 3.98119i | 0.352349 | − | 0.203429i | −0.313370 | − | 0.949631i | \(-0.601458\pi\) |
0.665720 | + | 0.746202i | \(0.268125\pi\) | |||||||
\(384\) | 25.9308 | − | 14.9712i | 1.32328 | − | 0.763994i | ||||
\(385\) | − | 0.842869i | − | 0.0429566i | ||||||
\(386\) | 8.06198 | + | 13.9638i | 0.410344 | + | 0.710736i | ||||
\(387\) | −2.48580 | + | 4.30553i | −0.126360 | + | 0.218862i | ||||
\(388\) | −0.303074 | − | 0.174980i | −0.0153863 | − | 0.00888326i | ||||
\(389\) | −32.0434 | −1.62467 | −0.812333 | − | 0.583194i | \(-0.801803\pi\) | ||||
−0.812333 | + | 0.583194i | \(0.801803\pi\) | |||||||
\(390\) | −7.27808 | + | 0.854411i | −0.368540 | + | 0.0432648i | ||||
\(391\) | −17.8082 | −0.900598 | ||||||||
\(392\) | 2.49552 | + | 1.44079i | 0.126043 | + | 0.0727710i | ||||
\(393\) | 12.2550 | − | 21.2263i | 0.618184 | − | 1.07073i | ||||
\(394\) | 1.24815 | + | 2.16186i | 0.0628809 | + | 0.108913i | ||||
\(395\) | 0.509777i | 0.0256496i | ||||||||
\(396\) | −0.554876 | + | 0.320358i | −0.0278836 | + | 0.0160986i | ||||
\(397\) | 5.57251 | − | 3.21729i | 0.279676 | − | 0.161471i | −0.353601 | − | 0.935396i | \(-0.615043\pi\) |
0.633277 | + | 0.773925i | \(0.281710\pi\) | |||||||
\(398\) | − | 9.13777i | − | 0.458035i | ||||||
\(399\) | 3.51972 | + | 6.09633i | 0.176206 | + | 0.305198i | ||||
\(400\) | 9.07219 | − | 15.7135i | 0.453609 | − | 0.785675i | ||||
\(401\) | −0.462092 | − | 0.266789i | −0.0230758 | − | 0.0133228i | 0.488418 | − | 0.872610i | \(-0.337574\pi\) |
−0.511494 | + | 0.859287i | \(0.670908\pi\) | |||||||
\(402\) | 32.7906 | 1.63545 | ||||||||
\(403\) | 19.1859 | + | 8.26451i | 0.955719 | + | 0.411685i | ||||
\(404\) | −1.44839 | −0.0720601 | ||||||||
\(405\) | −0.402337 | − | 0.232290i | −0.0199923 | − | 0.0115426i | ||||
\(406\) | 3.62424 | − | 6.27736i | 0.179868 | − | 0.311540i | ||||
\(407\) | −8.30697 | − | 14.3881i | −0.411761 | − | 0.713191i | ||||
\(408\) | 15.8640i | 0.785387i | ||||||||
\(409\) | −34.4269 | + | 19.8764i | −1.70230 | + | 0.982824i | −0.758877 | + | 0.651234i | \(0.774252\pi\) |
−0.943424 | + | 0.331590i | \(0.892415\pi\) | |||||||
\(410\) | 2.62176 | − | 1.51367i | 0.129479 | − | 0.0747550i | ||||
\(411\) | − | 24.0695i | − | 1.18726i | ||||||
\(412\) | 0.198648 | + | 0.344069i | 0.00978670 | + | 0.0169511i | ||||
\(413\) | 3.10263 | − | 5.37392i | 0.152671 | − | 0.264433i | ||||
\(414\) | −54.6913 | − | 31.5760i | −2.68793 | − | 1.55188i | ||||
\(415\) | 4.62832 | 0.227195 | ||||||||
\(416\) | −0.188078 | − | 1.60209i | −0.00922128 | − | 0.0785490i | ||||
\(417\) | 14.2375 | 0.697213 | ||||||||
\(418\) | −4.85633 | − | 2.80380i | −0.237531 | − | 0.137139i | ||||
\(419\) | −11.9088 | + | 20.6266i | −0.581783 | + | 1.00768i | 0.413485 | + | 0.910511i | \(0.364311\pi\) |
−0.995268 | + | 0.0971665i | \(0.969022\pi\) | |||||||
\(420\) | 0.0580244 | + | 0.100501i | 0.00283130 | + | 0.00490395i | ||||
\(421\) | 23.2419i | 1.13274i | 0.824151 | + | 0.566370i | \(0.191653\pi\) | ||||
−0.824151 | + | 0.566370i | \(0.808347\pi\) | |||||||
\(422\) | 12.8668 | − | 7.42865i | 0.626346 | − | 0.361621i | ||||
\(423\) | 19.5016 | − | 11.2593i | 0.948200 | − | 0.547444i | ||||
\(424\) | − | 25.6360i | − | 1.24500i | ||||||
\(425\) | 4.60828 | + | 7.98178i | 0.223535 | + | 0.387173i | ||||
\(426\) | 10.1789 | − | 17.6303i | 0.493168 | − | 0.854192i | ||||
\(427\) | −11.6660 | − | 6.73536i | −0.564557 | − | 0.325947i | ||||
\(428\) | 0.486253 | 0.0235039 | ||||||||
\(429\) | −1.92937 | − | 16.4348i | −0.0931510 | − | 0.793482i | ||||
\(430\) | −0.717316 | −0.0345920 | ||||||||
\(431\) | −2.34424 | − | 1.35345i | −0.112918 | − | 0.0651932i | 0.442477 | − | 0.896780i | \(-0.354100\pi\) |
−0.555395 | + | 0.831586i | \(0.687433\pi\) | |||||||
\(432\) | −10.7569 | + | 18.6314i | −0.517540 | + | 0.896406i | ||||
\(433\) | −2.90945 | − | 5.03932i | −0.139819 | − | 0.242174i | 0.787609 | − | 0.616176i | \(-0.211319\pi\) |
−0.927428 | + | 0.374002i | \(0.877985\pi\) | |||||||
\(434\) | 8.03008i | 0.385456i | ||||||||
\(435\) | 6.64198 | − | 3.83475i | 0.318459 | − | 0.183862i | ||||
\(436\) | 0.815290 | − | 0.470708i | 0.0390453 | − | 0.0225428i | ||||
\(437\) | 22.7706i | 1.08927i | ||||||||
\(438\) | −23.1841 | − | 40.1560i | −1.10778 | − | 1.91873i | ||||
\(439\) | 19.0851 | − | 33.0563i | 0.910882 | − | 1.57769i | 0.0980599 | − | 0.995181i | \(-0.468736\pi\) |
0.812822 | − | 0.582513i | \(-0.197930\pi\) | |||||||
\(440\) | −2.10340 | − | 1.21440i | −0.100276 | − | 0.0578942i | ||||
\(441\) | −4.98500 | −0.237381 | ||||||||
\(442\) | −8.94139 | − | 3.85158i | −0.425298 | − | 0.183201i | ||||
\(443\) | −31.6740 | −1.50488 | −0.752440 | − | 0.658661i | \(-0.771123\pi\) | ||||
−0.752440 | + | 0.658661i | \(0.771123\pi\) | |||||||
\(444\) | 1.98100 | + | 1.14373i | 0.0940139 | + | 0.0542790i | ||||
\(445\) | 3.11867 | − | 5.40169i | 0.147839 | − | 0.256065i | ||||
\(446\) | 8.93097 | + | 15.4689i | 0.422894 | + | 0.732473i | ||||
\(447\) | − | 9.50845i | − | 0.449734i | ||||||
\(448\) | 7.18021 | − | 4.14550i | 0.339233 | − | 0.195856i | ||||
\(449\) | 27.1975 | − | 15.7025i | 1.28353 | − | 0.741045i | 0.306036 | − | 0.952020i | \(-0.400997\pi\) |
0.977491 | + | 0.210975i | \(0.0676638\pi\) | |||||||
\(450\) | 32.6842i | 1.54075i | ||||||||
\(451\) | 3.41807 | + | 5.92027i | 0.160951 | + | 0.278775i | ||||
\(452\) | −0.140708 | + | 0.243713i | −0.00661834 | + | 0.0114633i | ||||
\(453\) | −30.9732 | − | 17.8824i | −1.45525 | − | 0.840187i | ||||
\(454\) | 0.968995 | 0.0454772 | ||||||||
\(455\) | −1.85836 | + | 0.218163i | −0.0871215 | + | 0.0102276i | ||||
\(456\) | 20.2847 | 0.949920 | ||||||||
\(457\) | 27.5640 | + | 15.9141i | 1.28939 | + | 0.744429i | 0.978545 | − | 0.206032i | \(-0.0660551\pi\) |
0.310844 | + | 0.950461i | \(0.399388\pi\) | |||||||
\(458\) | −12.6723 | + | 21.9491i | −0.592140 | + | 1.02562i | ||||
\(459\) | −5.46403 | − | 9.46398i | −0.255039 | − | 0.441741i | ||||
\(460\) | 0.375385i | 0.0175024i | ||||||||
\(461\) | 1.01005 | − | 0.583153i | 0.0470427 | − | 0.0271601i | −0.476294 | − | 0.879286i | \(-0.658020\pi\) |
0.523337 | + | 0.852126i | \(0.324687\pi\) | |||||||
\(462\) | 5.50865 | − | 3.18042i | 0.256286 | − | 0.147967i | ||||
\(463\) | − | 20.3441i | − | 0.945469i | −0.881205 | − | 0.472734i | \(-0.843267\pi\) | ||
0.881205 | − | 0.472734i | \(-0.156733\pi\) | |||||||
\(464\) | −10.0297 | − | 17.3719i | −0.465615 | − | 0.806470i | ||||
\(465\) | −4.24825 | + | 7.35819i | −0.197008 | + | 0.341228i | ||||
\(466\) | 32.1427 | + | 18.5576i | 1.48898 | + | 0.859664i | ||||
\(467\) | 1.56939 | 0.0726229 | 0.0363114 | − | 0.999341i | \(-0.488439\pi\) | ||||
0.0363114 | + | 0.999341i | \(0.488439\pi\) | |||||||
\(468\) | 0.849948 | + | 1.14048i | 0.0392889 | + | 0.0527185i | ||||
\(469\) | 8.37266 | 0.386614 | ||||||||
\(470\) | 2.81375 | + | 1.62452i | 0.129788 | + | 0.0749334i | ||||
\(471\) | 14.6504 | − | 25.3753i | 0.675055 | − | 1.16923i | ||||
\(472\) | −8.94049 | − | 15.4854i | −0.411519 | − | 0.712773i | ||||
\(473\) | − | 1.61979i | − | 0.0744781i | ||||||
\(474\) | −3.33169 | + | 1.92355i | −0.153030 | + | 0.0883517i | ||||
\(475\) | 10.2060 | − | 5.89243i | 0.468283 | − | 0.270363i | ||||
\(476\) | 0.154176i | 0.00706665i | ||||||||
\(477\) | 22.1745 | + | 38.4074i | 1.01530 | + | 1.75856i | ||||
\(478\) | −11.5157 | + | 19.9457i | −0.526714 | + | 0.912295i | ||||
\(479\) | 6.68501 | + | 3.85959i | 0.305446 | + | 0.176349i | 0.644887 | − | 0.764278i | \(-0.276905\pi\) |
−0.339441 | + | 0.940627i | \(0.610238\pi\) | |||||||
\(480\) | 0.656080 | 0.0299458 | ||||||||
\(481\) | −29.5729 | + | 22.0394i | −1.34841 | + | 1.00491i | ||||
\(482\) | −24.1334 | −1.09925 | ||||||||
\(483\) | −22.3688 | − | 12.9146i | −1.01781 | − | 0.587635i | ||||
\(484\) | −0.330870 | + | 0.573083i | −0.0150395 | + | 0.0260492i | ||||
\(485\) | 1.14749 | + | 1.98751i | 0.0521047 | + | 0.0902481i | ||||
\(486\) | 19.8161i | 0.898875i | ||||||||
\(487\) | −0.0659739 | + | 0.0380900i | −0.00298956 | + | 0.00172602i | −0.501494 | − | 0.865161i | \(-0.667216\pi\) |
0.498504 | + | 0.866887i | \(0.333883\pi\) | |||||||
\(488\) | −33.6165 | + | 19.4085i | −1.52175 | + | 0.878582i | ||||
\(489\) | − | 44.5155i | − | 2.01306i | ||||||
\(490\) | −0.359625 | − | 0.622889i | −0.0162462 | − | 0.0281392i | ||||
\(491\) | 0.893574 | − | 1.54772i | 0.0403264 | − | 0.0698474i | −0.845158 | − | 0.534517i | \(-0.820494\pi\) |
0.885484 | + | 0.464670i | \(0.153827\pi\) | |||||||
\(492\) | −0.815121 | − | 0.470610i | −0.0367485 | − | 0.0212167i | ||||
\(493\) | 10.1893 | 0.458902 | ||||||||
\(494\) | −4.92487 | + | 11.4330i | −0.221580 | + | 0.514395i | ||||
\(495\) | 4.20170 | 0.188852 | ||||||||
\(496\) | 19.2451 | + | 11.1112i | 0.864131 | + | 0.498906i | ||||
\(497\) | 2.59905 | − | 4.50168i | 0.116583 | − | 0.201928i | ||||
\(498\) | 17.4642 | + | 30.2488i | 0.782589 | + | 1.35548i | ||||
\(499\) | 8.33493i | 0.373123i | 0.982443 | + | 0.186561i | \(0.0597343\pi\) | ||||
−0.982443 | + | 0.186561i | \(0.940266\pi\) | |||||||
\(500\) | 0.346080 | − | 0.199810i | 0.0154772 | − | 0.00893576i | ||||
\(501\) | −40.1305 | + | 23.1694i | −1.79290 | + | 1.03513i | ||||
\(502\) | 8.93914i | 0.398973i | ||||||||
\(503\) | −0.720238 | − | 1.24749i | −0.0321138 | − | 0.0556228i | 0.849522 | − | 0.527554i | \(-0.176891\pi\) |
−0.881636 | + | 0.471931i | \(0.843557\pi\) | |||||||
\(504\) | −7.18234 | + | 12.4402i | −0.319927 | + | 0.554130i | ||||
\(505\) | 8.22576 | + | 4.74914i | 0.366041 | + | 0.211334i | ||||
\(506\) | 20.5755 | 0.914693 | ||||||||
\(507\) | −35.7363 | + | 8.50779i | −1.58710 | + | 0.377844i | ||||
\(508\) | 0.112649 | 0.00499801 | ||||||||
\(509\) | 12.8394 | + | 7.41282i | 0.569096 | + | 0.328568i | 0.756788 | − | 0.653660i | \(-0.226767\pi\) |
−0.187692 | + | 0.982228i | \(0.560101\pi\) | |||||||
\(510\) | 1.97985 | − | 3.42920i | 0.0876693 | − | 0.151848i | ||||
\(511\) | −5.91976 | − | 10.2533i | −0.261875 | − | 0.453581i | ||||
\(512\) | − | 23.8204i | − | 1.05272i | ||||||
\(513\) | −12.1012 | + | 6.98664i | −0.534282 | + | 0.308468i | ||||
\(514\) | 4.40686 | − | 2.54430i | 0.194378 | − | 0.112224i | ||||
\(515\) | − | 2.60540i | − | 0.114808i | ||||||
\(516\) | 0.111509 | + | 0.193139i | 0.00490891 | + | 0.00850248i | ||||
\(517\) | −3.66837 | + | 6.35380i | −0.161335 | + | 0.279440i | ||||
\(518\) | −12.2779 | − | 7.08863i | −0.539459 | − | 0.311457i | ||||
\(519\) | −0.851561 | −0.0373794 | ||||||||
\(520\) | −2.13308 | + | 4.95192i | −0.0935419 | + | 0.217156i | ||||
\(521\) | −0.334388 | −0.0146498 | −0.00732489 | − | 0.999973i | \(-0.502332\pi\) | ||||
−0.00732489 | + | 0.999973i | \(0.502332\pi\) | |||||||
\(522\) | 31.2926 | + | 18.0668i | 1.36964 | + | 0.790763i | ||||
\(523\) | 16.2533 | − | 28.1515i | 0.710705 | − | 1.23098i | −0.253887 | − | 0.967234i | \(-0.581709\pi\) |
0.964593 | − | 0.263744i | \(-0.0849574\pi\) | |||||||
\(524\) | −0.343201 | − | 0.594441i | −0.0149928 | − | 0.0259683i | ||||
\(525\) | 13.3678i | 0.583420i | ||||||||
\(526\) | 21.9881 | − | 12.6948i | 0.958726 | − | 0.553521i | ||||
\(527\) | −9.77570 | + | 5.64400i | −0.425836 | + | 0.245857i | ||||
\(528\) | − | 17.6029i | − | 0.766068i | ||||||
\(529\) | −30.2751 | − | 52.4380i | −1.31631 | − | 2.27991i | ||||
\(530\) | −3.19941 | + | 5.54153i | −0.138973 | + | 0.240709i | ||||
\(531\) | 26.7890 | + | 15.4666i | 1.16254 | + | 0.671194i | ||||
\(532\) | 0.197139 | 0.00854706 | ||||||||
\(533\) | 12.1683 | − | 9.06855i | 0.527070 | − | 0.392803i | ||||
\(534\) | 47.0710 | 2.03696 | ||||||||
\(535\) | −2.76155 | − | 1.59438i | −0.119392 | − | 0.0689311i | ||||
\(536\) | 12.0633 | − | 20.8942i | 0.521053 | − | 0.902491i | ||||
\(537\) | 13.8686 | + | 24.0212i | 0.598476 | + | 1.03659i | ||||
\(538\) | 38.1732i | 1.64576i | ||||||||
\(539\) | 1.40656 | − | 0.812080i | 0.0605850 | − | 0.0349787i | ||||
\(540\) | −0.199495 | + | 0.115178i | −0.00858488 | + | 0.00495649i | ||||
\(541\) | − | 10.6015i | − | 0.455796i | −0.973685 | − | 0.227898i | \(-0.926815\pi\) | ||
0.973685 | − | 0.227898i | \(-0.0731852\pi\) | |||||||
\(542\) | −4.51767 | − | 7.82483i | −0.194051 | − | 0.336105i | ||||
\(543\) | 17.5650 | − | 30.4235i | 0.753786 | − | 1.30560i | ||||
\(544\) | 0.754856 | + | 0.435816i | 0.0323642 | + | 0.0186855i | ||||
\(545\) | −6.17364 | −0.264450 | ||||||||
\(546\) | −8.43804 | − | 11.3223i | −0.361115 | − | 0.484550i | ||||
\(547\) | 10.2327 | 0.437519 | 0.218760 | − | 0.975779i | \(-0.429799\pi\) | ||||
0.218760 | + | 0.975779i | \(0.429799\pi\) | |||||||
\(548\) | −0.583756 | − | 0.337032i | −0.0249368 | − | 0.0143973i | ||||
\(549\) | 33.5758 | − | 58.1549i | 1.43298 | − | 2.48199i | ||||
\(550\) | −5.32440 | − | 9.22214i | −0.227033 | − | 0.393233i | ||||
\(551\) | − | 13.0286i | − | 0.555038i | ||||||
\(552\) | −64.4574 | + | 37.2145i | −2.74349 | + | 1.58396i | ||||
\(553\) | −0.850705 | + | 0.491155i | −0.0361757 | + | 0.0208860i | ||||
\(554\) | − | 7.54216i | − | 0.320436i | ||||||
\(555\) | −7.50037 | − | 12.9910i | −0.318373 | − | 0.551438i | ||||
\(556\) | 0.199360 | − | 0.345301i | 0.00845474 | − | 0.0146440i | ||||
\(557\) | 27.7067 | + | 15.9965i | 1.17397 | + | 0.677793i | 0.954612 | − | 0.297851i | \(-0.0962700\pi\) |
0.219359 | + | 0.975644i | \(0.429603\pi\) | |||||||
\(558\) | −40.0300 | −1.69460 | ||||||||
\(559\) | −3.57133 | + | 0.419257i | −0.151051 | + | 0.0177327i | ||||
\(560\) | −1.99044 | −0.0841115 | ||||||||
\(561\) | 7.74359 | + | 4.47076i | 0.326934 | + | 0.188756i | ||||
\(562\) | −2.45478 | + | 4.25180i | −0.103549 | + | 0.179351i | ||||
\(563\) | 5.39566 | + | 9.34556i | 0.227400 | + | 0.393868i | 0.957037 | − | 0.289967i | \(-0.0936442\pi\) |
−0.729637 | + | 0.683835i | \(0.760311\pi\) | |||||||
\(564\) | − | 1.01014i | − | 0.0425348i | ||||||
\(565\) | 1.59823 | − | 0.922737i | 0.0672380 | − | 0.0388199i | ||||
\(566\) | 16.9708 | − | 9.79808i | 0.713335 | − | 0.411844i | ||||
\(567\) | − | 0.895217i | − | 0.0375956i | ||||||
\(568\) | −7.48937 | − | 12.9720i | −0.314247 | − | 0.544292i | ||||
\(569\) | −12.3007 | + | 21.3054i | −0.515672 | + | 0.893170i | 0.484163 | + | 0.874978i | \(0.339124\pi\) |
−0.999835 | + | 0.0181917i | \(0.994209\pi\) | |||||||
\(570\) | −4.38479 | − | 2.53156i | −0.183659 | − | 0.106035i | ||||
\(571\) | −16.5724 | −0.693534 | −0.346767 | − | 0.937951i | \(-0.612721\pi\) | ||||
−0.346767 | + | 0.937951i | \(0.612721\pi\) | |||||||
\(572\) | −0.425610 | − | 0.183335i | −0.0177956 | − | 0.00766563i | ||||
\(573\) | 34.6070 | 1.44573 | ||||||||
\(574\) | 5.05197 | + | 2.91676i | 0.210865 | + | 0.121743i | ||||
\(575\) | −21.6206 | + | 37.4480i | −0.901641 | + | 1.56169i | ||||
\(576\) | 20.6653 | + | 35.7934i | 0.861054 | + | 1.49139i | ||||
\(577\) | 14.6611i | 0.610348i | 0.952297 | + | 0.305174i | \(0.0987147\pi\) | ||||
−0.952297 | + | 0.305174i | \(0.901285\pi\) | |||||||
\(578\) | −15.8487 | + | 9.15027i | −0.659221 | + | 0.380601i | ||||
\(579\) | −28.4702 | + | 16.4373i | −1.18318 | + | 0.683111i | ||||
\(580\) | − | 0.214784i | − | 0.00891840i | ||||||
\(581\) | 4.45926 | + | 7.72366i | 0.185001 | + | 0.320431i | ||||
\(582\) | −8.65969 | + | 14.9990i | −0.358956 | + | 0.621730i | ||||
\(583\) | −12.5135 | − | 7.22467i | −0.518256 | − | 0.299215i | ||||
\(584\) | −34.1166 | −1.41175 | ||||||||
\(585\) | −1.08754 | − | 9.26394i | −0.0449644 | − | 0.383017i | ||||
\(586\) | 11.5717 | 0.478024 | ||||||||
\(587\) | 30.5998 | + | 17.6668i | 1.26299 | + | 0.729186i | 0.973652 | − | 0.228041i | \(-0.0732320\pi\) |
0.289336 | + | 0.957227i | \(0.406565\pi\) | |||||||
\(588\) | −0.111810 | + | 0.193660i | −0.00461095 | + | 0.00798640i | ||||
\(589\) | 7.21676 | + | 12.4998i | 0.297362 | + | 0.515045i | ||||
\(590\) | 4.46313i | 0.183744i | ||||||||
\(591\) | −4.40775 | + | 2.54481i | −0.181310 | + | 0.104680i | ||||
\(592\) | −33.9776 | + | 19.6170i | −1.39647 | + | 0.806253i | ||||
\(593\) | − | 16.4294i | − | 0.674675i | −0.941384 | − | 0.337338i | \(-0.890474\pi\) | ||
0.941384 | − | 0.337338i | \(-0.109526\pi\) | |||||||
\(594\) | 6.31313 | + | 10.9347i | 0.259031 | + | 0.448655i | ||||
\(595\) | 0.505530 | − | 0.875603i | 0.0207247 | − | 0.0358962i | ||||
\(596\) | −0.230608 | − | 0.133142i | −0.00944608 | − | 0.00545370i | ||||
\(597\) | 18.6307 | 0.762504 | ||||||||
\(598\) | −5.32564 | − | 45.3651i | −0.217782 | − | 1.85512i | ||||
\(599\) | 12.0819 | 0.493653 | 0.246826 | − | 0.969060i | \(-0.420612\pi\) | ||||
0.246826 | + | 0.969060i | \(0.420612\pi\) | |||||||
\(600\) | 33.3598 | + | 19.2603i | 1.36191 | + | 0.786297i | ||||
\(601\) | −3.90743 | + | 6.76787i | −0.159387 | + | 0.276067i | −0.934648 | − | 0.355574i | \(-0.884285\pi\) |
0.775261 | + | 0.631642i | \(0.217619\pi\) | |||||||
\(602\) | −0.691113 | − | 1.19704i | −0.0281677 | − | 0.0487878i | ||||
\(603\) | 41.7377i | 1.69969i | ||||||||
\(604\) | −0.867401 | + | 0.500794i | −0.0352941 | + | 0.0203770i | ||||
\(605\) | 3.75818 | − | 2.16979i | 0.152792 | − | 0.0882144i | ||||
\(606\) | 71.6803i | 2.91181i | ||||||||
\(607\) | −17.7825 | − | 30.8001i | −0.721768 | − | 1.25014i | −0.960291 | − | 0.279002i | \(-0.909996\pi\) |
0.238523 | − | 0.971137i | \(-0.423337\pi\) | |||||||
\(608\) | 0.557261 | − | 0.965205i | 0.0225999 | − | 0.0391442i | ||||
\(609\) | 12.7987 | + | 7.38934i | 0.518630 | + | 0.299431i | ||||
\(610\) | 9.68882 | 0.392289 | ||||||||
\(611\) | 14.9584 | + | 6.44347i | 0.605153 | + | 0.260675i | ||||
\(612\) | −0.768568 | −0.0310675 | ||||||||
\(613\) | −10.3376 | − | 5.96839i | −0.417530 | − | 0.241061i | 0.276490 | − | 0.961017i | \(-0.410829\pi\) |
−0.694020 | + | 0.719956i | \(0.744162\pi\) | |||||||
\(614\) | 5.77500 | − | 10.0026i | 0.233060 | − | 0.403672i | ||||
\(615\) | 3.08618 | + | 5.34542i | 0.124447 | + | 0.215548i | ||||
\(616\) | − | 4.68015i | − | 0.188569i | ||||||
\(617\) | −20.4124 | + | 11.7851i | −0.821772 | + | 0.474450i | −0.851027 | − | 0.525122i | \(-0.824020\pi\) |
0.0292550 | + | 0.999572i | \(0.490687\pi\) | |||||||
\(618\) | 17.0278 | − | 9.83103i | 0.684960 | − | 0.395462i | ||||
\(619\) | − | 28.5571i | − | 1.14781i | −0.818923 | − | 0.573904i | \(-0.805428\pi\) | ||
0.818923 | − | 0.573904i | \(-0.194572\pi\) | |||||||
\(620\) | 0.118972 | + | 0.206066i | 0.00477803 | + | 0.00827579i | ||||
\(621\) | 25.6355 | − | 44.4020i | 1.02872 | − | 1.78179i | ||||
\(622\) | −17.5512 | − | 10.1332i | −0.703738 | − | 0.406303i | ||||
\(623\) | 12.0190 | 0.481530 | ||||||||
\(624\) | −38.8110 | + | 4.55623i | −1.55368 | + | 0.182395i | ||||
\(625\) | 21.0328 | 0.841311 | ||||||||
\(626\) | −20.5640 | − | 11.8726i | −0.821903 | − | 0.474526i | ||||
\(627\) | 5.71659 | − | 9.90142i | 0.228298 | − | 0.395425i | ||||
\(628\) | −0.410283 | − | 0.710632i | −0.0163721 | − | 0.0283573i | ||||
\(629\) | − | 19.9292i | − | 0.794628i | ||||||
\(630\) | 3.10510 | − | 1.79273i | 0.123710 | − | 0.0714241i | ||||
\(631\) | −38.9646 | + | 22.4962i | −1.55116 | + | 0.895561i | −0.553109 | + | 0.833109i | \(0.686559\pi\) |
−0.998048 | + | 0.0624526i | \(0.980108\pi\) | |||||||
\(632\) | 2.83061i | 0.112596i | ||||||||
\(633\) | 15.1460 | + | 26.2337i | 0.602001 | + | 1.04270i | ||||
\(634\) | −9.70169 | + | 16.8038i | −0.385303 | + | 0.667365i | ||||
\(635\) | −0.639763 | − | 0.369367i | −0.0253882 | − | 0.0146579i | ||||
\(636\) | 1.98943 | 0.0788860 | ||||||||
\(637\) | −2.15455 | − | 2.89101i | −0.0853662 | − | 0.114546i | ||||
\(638\) | −11.7727 | −0.466085 | ||||||||
\(639\) | 22.4409 | + | 12.9562i | 0.887747 | + | 0.512541i | ||||
\(640\) | −2.74947 | + | 4.76222i | −0.108682 | + | 0.188243i | ||||
\(641\) | −1.26650 | − | 2.19364i | −0.0500238 | − | 0.0866437i | 0.839929 | − | 0.542696i | \(-0.182596\pi\) |
−0.889953 | + | 0.456052i | \(0.849263\pi\) | |||||||
\(642\) | − | 24.0645i | − | 0.949749i | ||||||
\(643\) | 15.9150 | − | 9.18853i | 0.627627 | − | 0.362360i | −0.152206 | − | 0.988349i | \(-0.548638\pi\) |
0.779832 | + | 0.625988i | \(0.215304\pi\) | |||||||
\(644\) | −0.626435 | + | 0.361672i | −0.0246850 | + | 0.0142519i | ||||
\(645\) | − | 1.46251i | − | 0.0575863i | ||||||
\(646\) | −3.36329 | − | 5.82539i | −0.132327 | − | 0.229197i | ||||
\(647\) | 10.4643 | − | 18.1248i | 0.411396 | − | 0.712558i | −0.583647 | − | 0.812008i | \(-0.698375\pi\) |
0.995043 | + | 0.0994494i | \(0.0317081\pi\) | |||||||
\(648\) | −2.23404 | − | 1.28982i | −0.0877612 | − | 0.0506690i | ||||
\(649\) | −10.0783 | −0.395609 | ||||||||
\(650\) | −18.9549 | + | 14.1263i | −0.743473 | + | 0.554079i | ||||
\(651\) | −16.3723 | −0.641680 | ||||||||
\(652\) | −1.07963 | − | 0.623326i | −0.0422817 | − | 0.0244113i | ||||
\(653\) | 24.0580 | − | 41.6696i | 0.941461 | − | 1.63066i | 0.178775 | − | 0.983890i | \(-0.442786\pi\) |
0.762686 | − | 0.646769i | \(-0.223880\pi\) | |||||||
\(654\) | −23.2952 | − | 40.3484i | −0.910913 | − | 1.57775i | ||||
\(655\) | 4.50130i | 0.175880i | ||||||||
\(656\) | 13.9808 | − | 8.07180i | 0.545857 | − | 0.315151i | ||||
\(657\) | 51.1129 | − | 29.5100i | 1.99410 | − | 1.15130i | ||||
\(658\) | 6.26070i | 0.244068i | ||||||||
\(659\) | 1.10819 | + | 1.91944i | 0.0431690 | + | 0.0747708i | 0.886803 | − | 0.462148i | \(-0.152921\pi\) |
−0.843634 | + | 0.536919i | \(0.819588\pi\) | |||||||
\(660\) | 0.0942408 | − | 0.163230i | 0.00366832 | − | 0.00635371i | ||||
\(661\) | −0.552034 | − | 0.318717i | −0.0214716 | − | 0.0123966i | 0.489226 | − | 0.872157i | \(-0.337279\pi\) |
−0.510697 | + | 0.859761i | \(0.670613\pi\) | |||||||
\(662\) | −9.59073 | −0.372754 | ||||||||
\(663\) | 7.85287 | − | 18.2303i | 0.304980 | − | 0.708006i | ||||
\(664\) | 25.6994 | 0.997331 | ||||||||
\(665\) | −1.11960 | − | 0.646401i | −0.0434162 | − | 0.0250664i | ||||
\(666\) | 35.3368 | − | 61.2052i | 1.36927 | − | 2.37165i | ||||
\(667\) | 23.9024 | + | 41.4002i | 0.925506 | + | 1.60302i | ||||
\(668\) | 1.29771i | 0.0502100i | ||||||||
\(669\) | −31.5390 | + | 18.2091i | −1.21937 | + | 0.704003i | ||||
\(670\) | −5.21523 | + | 3.01102i | −0.201482 | + | 0.116326i | ||||
\(671\) | 21.8786i | 0.844614i | ||||||||
\(672\) | 0.632114 | + | 1.09485i | 0.0243843 | + | 0.0422349i | ||||
\(673\) | 7.70343 | − | 13.3427i | 0.296945 | − | 0.514324i | −0.678490 | − | 0.734609i | \(-0.737365\pi\) |
0.975436 | + | 0.220285i | \(0.0706988\pi\) | |||||||
\(674\) | −13.3901 | − | 7.73081i | −0.515769 | − | 0.297780i | ||||
\(675\) | −26.5352 | −1.02134 | ||||||||
\(676\) | −0.294057 | + | 0.985841i | −0.0113099 | + | 0.0379170i | ||||
\(677\) | −11.6812 | −0.448945 | −0.224473 | − | 0.974480i | \(-0.572066\pi\) | ||||
−0.224473 | + | 0.974480i | \(0.572066\pi\) | |||||||
\(678\) | 12.0613 | + | 6.96358i | 0.463210 | + | 0.267435i | ||||
\(679\) | −2.21114 | + | 3.82981i | −0.0848559 | + | 0.146975i | ||||
\(680\) | −1.45673 | − | 2.52312i | −0.0558629 | − | 0.0967574i | ||||
\(681\) | 1.97565i | 0.0757072i | ||||||||
\(682\) | 11.2948 | − | 6.52107i | 0.432501 | − | 0.249705i | ||||
\(683\) | 19.8419 | − | 11.4557i | 0.759227 | − | 0.438340i | −0.0697909 | − | 0.997562i | \(-0.522233\pi\) |
0.829018 | + | 0.559221i | \(0.188900\pi\) | |||||||
\(684\) | 0.982737i | 0.0375759i | ||||||||
\(685\) | 2.21020 | + | 3.82817i | 0.0844473 | + | 0.146267i | ||||
\(686\) | 0.692976 | − | 1.20027i | 0.0264580 | − | 0.0458265i | ||||
\(687\) | −44.7514 | − | 25.8372i | −1.70737 | − | 0.985752i | ||||
\(688\) | −3.82515 | −0.145833 | ||||||||
\(689\) | −12.6901 | + | 29.4599i | −0.483454 | + | 1.12233i | ||||
\(690\) | 18.5777 | 0.707239 | ||||||||
\(691\) | −40.9046 | − | 23.6163i | −1.55608 | − | 0.898405i | −0.997625 | − | 0.0688729i | \(-0.978060\pi\) |
−0.558458 | − | 0.829533i | \(-0.688607\pi\) | |||||||
\(692\) | −0.0119239 | + | 0.0206529i | −0.000453280 | + | 0.000785104i | ||||
\(693\) | 4.04822 | + | 7.01172i | 0.153779 | + | 0.266353i | ||||
\(694\) | − | 6.82596i | − | 0.259110i | ||||||
\(695\) | −2.26443 | + | 1.30737i | −0.0858946 | + | 0.0495913i | ||||
\(696\) | 36.8805 | − | 21.2930i | 1.39795 | − | 0.807109i | ||||
\(697\) | 8.20026i | 0.310607i | ||||||||
\(698\) | −1.05565 | − | 1.82843i | −0.0399568 | − | 0.0692071i | ||||
\(699\) | −37.8365 | + | 65.5347i | −1.43111 | + | 2.47875i | ||||
\(700\) | 0.324210 | + | 0.187183i | 0.0122540 | + | 0.00707484i | ||||
\(701\) | 12.2098 | 0.461158 | 0.230579 | − | 0.973054i | \(-0.425938\pi\) | ||||
0.230579 | + | 0.973054i | \(0.425938\pi\) | |||||||
\(702\) | 22.4748 | − | 16.7495i | 0.848256 | − | 0.632169i | ||||
\(703\) | −25.4827 | −0.961097 | ||||||||
\(704\) | −11.6618 | − | 6.73295i | −0.439521 | − | 0.253758i | ||||
\(705\) | −3.31218 | + | 5.73686i | −0.124744 | + | 0.216063i | ||||
\(706\) | −12.4237 | − | 21.5185i | −0.467572 | − | 0.809858i | ||||
\(707\) | 18.3026i | 0.688342i | ||||||||
\(708\) | 1.20171 | − | 0.693808i | 0.0451630 | − | 0.0260749i | ||||
\(709\) | −15.4910 | + | 8.94374i | −0.581777 | + | 0.335889i | −0.761839 | − | 0.647766i | \(-0.775703\pi\) |
0.180062 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(710\) | 3.73873i | 0.140312i | ||||||||
\(711\) | −2.44841 | − | 4.24076i | −0.0918224 | − | 0.159041i | ||||
\(712\) | 17.3169 | − | 29.9937i | 0.648977 | − | 1.12406i | ||||
\(713\) | −45.8644 | − | 26.4798i | −1.71764 | − | 0.991678i | ||||
\(714\) | 7.63012 | 0.285550 | ||||||||
\(715\) | 1.81600 | + | 2.43674i | 0.0679146 | + | 0.0911290i | ||||
\(716\) | 0.776780 | 0.0290296 | ||||||||
\(717\) | −40.6667 | − | 23.4789i | −1.51872 | − | 0.876836i | ||||
\(718\) | 13.8605 | − | 24.0070i | 0.517268 | − | 0.895935i | ||||
\(719\) | 4.56317 | + | 7.90364i | 0.170178 | + | 0.294756i | 0.938482 | − | 0.345329i | \(-0.112233\pi\) |
−0.768304 | + | 0.640085i | \(0.778899\pi\) | |||||||
\(720\) | − | 9.92235i | − | 0.369784i | ||||||
\(721\) | 4.34784 | − | 2.51023i | 0.161922 | − | 0.0934858i | ||||
\(722\) | 15.3564 | − | 8.86604i | 0.571507 | − | 0.329960i | ||||
\(723\) | − | 49.2048i | − | 1.82995i | ||||||
\(724\) | −0.491906 | − | 0.852006i | −0.0182815 | − | 0.0316646i | ||||
\(725\) | 12.3706 | − | 21.4266i | 0.459434 | − | 0.795763i | ||||
\(726\) | 28.3617 | + | 16.3746i | 1.05260 | + | 0.607719i | ||||
\(727\) | 33.6859 | 1.24934 | 0.624670 | − | 0.780889i | \(-0.285233\pi\) | ||||
0.624670 | + | 0.780889i | \(0.285233\pi\) | |||||||
\(728\) | −10.3188 | + | 1.21138i | −0.382441 | + | 0.0448968i | ||||
\(729\) | −43.0880 | −1.59585 | ||||||||
\(730\) | 7.37471 | + | 4.25779i | 0.272950 | + | 0.157588i | ||||
\(731\) | 0.971507 | − | 1.68270i | 0.0359325 | − | 0.0622369i | ||||
\(732\) | −1.50616 | − | 2.60874i | −0.0556691 | − | 0.0964218i | ||||
\(733\) | 46.4344i | 1.71509i | 0.514406 | + | 0.857547i | \(0.328013\pi\) | ||||
−0.514406 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(734\) | 32.9062 | − | 18.9984i | 1.21459 | − | 0.701245i | ||||
\(735\) | 1.26999 | − | 0.733228i | 0.0468442 | − | 0.0270455i | ||||
\(736\) | 4.08942i | 0.150738i | ||||||||
\(737\) | −6.79927 | − | 11.7767i | −0.250454 | − | 0.433799i | ||||
\(738\) | −14.5400 | + | 25.1841i | −0.535226 | + | 0.927039i | ||||
\(739\) | −1.60237 | − | 0.925127i | −0.0589440 | − | 0.0340314i | 0.470238 | − | 0.882539i | \(-0.344168\pi\) |
−0.529182 | + | 0.848508i | \(0.677501\pi\) | |||||||
\(740\) | −0.420095 | −0.0154430 | ||||||||
\(741\) | −23.3104 | − | 10.0412i | −0.856328 | − | 0.368871i | ||||
\(742\) | −12.3301 | −0.452654 | ||||||||
\(743\) | 28.7095 | + | 16.5755i | 1.05325 | + | 0.608094i | 0.923558 | − | 0.383460i | \(-0.125268\pi\) |
0.129693 | + | 0.991554i | \(0.458601\pi\) | |||||||
\(744\) | −23.5890 | + | 40.8574i | −0.864816 | + | 1.49791i | ||||
\(745\) | 0.873120 | + | 1.51229i | 0.0319886 | + | 0.0554059i | ||||
\(746\) | − | 22.0268i | − | 0.806457i | ||||||
\(747\) | −38.5024 | + | 22.2294i | −1.40873 | + | 0.813331i | ||||
\(748\) | 0.216858 | − | 0.125203i | 0.00792913 | − | 0.00457788i | ||||
\(749\) | − | 6.14456i | − | 0.224517i | ||||||
\(750\) | −9.88850 | − | 17.1274i | −0.361077 | − | 0.625404i | ||||
\(751\) | −10.3871 | + | 17.9910i | −0.379032 | + | 0.656503i | −0.990922 | − | 0.134441i | \(-0.957076\pi\) |
0.611890 | + | 0.790943i | \(0.290410\pi\) | |||||||
\(752\) | 15.0046 | + | 8.66289i | 0.547160 | + | 0.315903i | ||||
\(753\) | −18.2257 | −0.664182 | ||||||||
\(754\) | 3.04717 | + | 25.9565i | 0.110971 | + | 0.945280i | ||||
\(755\) | 6.56824 | 0.239043 | ||||||||
\(756\) | −0.384415 | − | 0.221942i | −0.0139810 | − | 0.00807195i | ||||
\(757\) | −21.8075 | + | 37.7717i | −0.792607 | + | 1.37283i | 0.131741 | + | 0.991284i | \(0.457943\pi\) |
−0.924348 | + | 0.381551i | \(0.875390\pi\) | |||||||
\(758\) | −6.08364 | − | 10.5372i | −0.220968 | − | 0.382727i | ||||
\(759\) | 41.9508i | 1.52272i | ||||||||
\(760\) | −3.22622 | + | 1.86266i | −0.117027 | + | 0.0675657i | ||||
\(761\) | 10.7302 | − | 6.19511i | 0.388971 | − | 0.224573i | −0.292743 | − | 0.956191i | \(-0.594568\pi\) |
0.681714 | + | 0.731619i | \(0.261235\pi\) | |||||||
\(762\) | − | 5.57497i | − | 0.201960i | ||||||
\(763\) | −5.94812 | − | 10.3025i | −0.215337 | − | 0.372974i | ||||
\(764\) | 0.484583 | − | 0.839323i | 0.0175316 | − | 0.0303656i | ||||
\(765\) | 4.36488 | + | 2.52007i | 0.157813 | + | 0.0911132i | ||||
\(766\) | −11.0355 | −0.398728 | ||||||||
\(767\) | 2.60862 | + | 22.2208i | 0.0941917 | + | 0.802347i | ||||
\(768\) | 5.35835 | 0.193353 | ||||||||
\(769\) | −4.80955 | − | 2.77680i | −0.173437 | − | 0.100134i | 0.410769 | − | 0.911740i | \(-0.365260\pi\) |
−0.584205 | + | 0.811606i | \(0.698594\pi\) | |||||||
\(770\) | −0.584088 | + | 1.01167i | −0.0210491 | + | 0.0364581i | ||||
\(771\) | 5.18750 | + | 8.98501i | 0.186823 | + | 0.323587i | ||||
\(772\) | 0.920651i | 0.0331349i | ||||||||
\(773\) | 37.9355 | − | 21.9021i | 1.36445 | − | 0.787764i | 0.374235 | − | 0.927334i | \(-0.377905\pi\) |
0.990212 | + | 0.139570i | \(0.0445721\pi\) | |||||||
\(774\) | 5.96726 | − | 3.44520i | 0.214489 | − | 0.123835i | ||||
\(775\) | 27.4092i | 0.984566i | ||||||||
\(776\) | 6.37159 | + | 11.0359i | 0.228727 | + | 0.396166i | ||||
\(777\) | 14.4528 | − | 25.0330i | 0.518491 | − | 0.898052i | ||||
\(778\) | 38.4608 | + | 22.2053i | 1.37889 | + | 0.796100i | ||||
\(779\) | 10.4853 | 0.375677 | ||||||||
\(780\) | −0.384283 | − | 0.165534i | −0.0137596 | − | 0.00592705i | ||||
\(781\) | −8.44253 | −0.302098 | ||||||||
\(782\) | 21.3746 | + | 12.3406i | 0.764354 | + | 0.441300i | ||||
\(783\) | −14.6678 | + | 25.4054i | −0.524185 | + | 0.907916i | ||||
\(784\) | −1.91773 | − | 3.32161i | −0.0684905 | − | 0.118629i | ||||
\(785\) | 5.38113i | 0.192061i | ||||||||
\(786\) | −29.4187 | + | 16.9849i | −1.04933 | + | 0.605830i | ||||
\(787\) | 21.4782 | − | 12.4005i | 0.765616 | − | 0.442029i | −0.0656923 | − | 0.997840i | \(-0.520926\pi\) |
0.831309 | + | 0.555811i | \(0.187592\pi\) | |||||||
\(788\) | 0.142535i | 0.00507758i | ||||||||
\(789\) | 25.8831 | + | 44.8308i | 0.921462 | + | 1.59602i | ||||
\(790\) | 0.353263 | − | 0.611870i | 0.0125685 | − | 0.0217693i | ||||
\(791\) | 3.07969 | + | 1.77806i | 0.109501 | + | 0.0632206i | ||||
\(792\) | 23.3305 | 0.829015 | ||||||||
\(793\) | 48.2381 | − | 5.66293i | 1.71299 | − | 0.201096i | ||||
\(794\) | −8.91801 | −0.316489 | ||||||||
\(795\) | −11.2985 | − | 6.52316i | −0.400715 | − | 0.231353i | ||||
\(796\) | 0.260876 | − | 0.451850i | 0.00924649 | − | 0.0160154i | ||||
\(797\) | −8.23575 | − | 14.2647i | −0.291725 | − | 0.505283i | 0.682492 | − | 0.730893i | \(-0.260896\pi\) |
−0.974218 | + | 0.225610i | \(0.927563\pi\) | |||||||
\(798\) | − | 9.75633i | − | 0.345370i | ||||||
\(799\) | −7.62168 | + | 4.40038i | −0.269636 | + | 0.155674i | ||||
\(800\) | 1.83292 | − | 1.05823i | 0.0648034 | − | 0.0374142i | ||||
\(801\) | 59.9146i | 2.11698i | ||||||||
\(802\) | 0.369756 | + | 0.640437i | 0.0130566 | + | 0.0226146i | ||||
\(803\) | −9.61464 | + | 16.6530i | −0.339293 | + | 0.587673i | ||||
\(804\) | 1.62145 | + | 0.936144i | 0.0571841 | + | 0.0330152i | ||||
\(805\) | 4.74357 | 0.167189 | ||||||||
\(806\) | −17.3012 | − | 23.2150i | −0.609408 | − | 0.817715i | ||||
\(807\) | −77.8301 | −2.73975 | ||||||||
\(808\) | 45.6747 | + | 26.3703i | 1.60683 | + | 0.927704i | ||||
\(809\) | −0.690968 | + | 1.19679i | −0.0242932 | + | 0.0420770i | −0.877916 | − | 0.478814i | \(-0.841067\pi\) |
0.853623 | + | 0.520891i | \(0.174400\pi\) | |||||||
\(810\) | 0.321942 | + | 0.557621i | 0.0113119 | + | 0.0195928i | ||||
\(811\) | − | 6.83571i | − | 0.240034i | −0.992772 | − | 0.120017i | \(-0.961705\pi\) | ||
0.992772 | − | 0.120017i | \(-0.0382950\pi\) | |||||||
\(812\) | 0.358427 | − | 0.206938i | 0.0125783 | − | 0.00726209i | ||||
\(813\) | 15.9538 | − | 9.21093i | 0.559524 | − | 0.323041i | ||||
\(814\) | 23.0261i | 0.807066i | ||||||||
\(815\) | 4.08767 | + | 7.08004i | 0.143185 | + | 0.248003i | ||||
\(816\) | 10.5577 | − | 18.2865i | 0.369595 | − | 0.640157i | ||||
\(817\) | −2.15160 | − | 1.24223i | −0.0752750 | − | 0.0434601i | ||||
\(818\) | 55.0954 | 1.92637 | ||||||||
\(819\) | 14.4117 | − | 10.7404i | 0.503585 | − | 0.375300i | ||||
\(820\) | 0.172856 | 0.00603640 | ||||||||
\(821\) | −9.13009 | − | 5.27126i | −0.318642 | − | 0.183968i | 0.332145 | − | 0.943228i | \(-0.392228\pi\) |
−0.650787 | + | 0.759260i | \(0.725561\pi\) | |||||||
\(822\) | −16.6796 | + | 28.8899i | −0.581767 | + | 1.00765i | ||||
\(823\) | 7.41652 | + | 12.8458i | 0.258524 | + | 0.447776i | 0.965847 | − | 0.259114i | \(-0.0834307\pi\) |
−0.707323 | + | 0.706891i | \(0.750097\pi\) | |||||||
\(824\) | − | 14.4669i | − | 0.503977i | ||||||
\(825\) | 18.8027 | − | 10.8558i | 0.654627 | − | 0.377949i | ||||
\(826\) | −7.44799 | + | 4.30010i | −0.259149 | + | 0.149620i | ||||
\(827\) | − | 55.6758i | − | 1.93604i | −0.250879 | − | 0.968018i | \(-0.580720\pi\) | ||
0.250879 | − | 0.968018i | \(-0.419280\pi\) | |||||||
\(828\) | −1.80294 | − | 3.12278i | −0.0626564 | − | 0.108524i | ||||
\(829\) | −0.0232424 | + | 0.0402570i | −0.000807242 | + | 0.00139818i | −0.866429 | − | 0.499301i | \(-0.833590\pi\) |
0.865622 | + | 0.500699i | \(0.166924\pi\) | |||||||
\(830\) | −5.55524 | − | 3.20732i | −0.192825 | − | 0.111328i | ||||
\(831\) | 15.3775 | 0.533438 | ||||||||
\(832\) | −11.8264 | + | 27.4548i | −0.410006 | + | 0.951823i | ||||
\(833\) | 1.94825 | 0.0675030 | ||||||||
\(834\) | −17.0888 | − | 9.86624i | −0.591738 | − | 0.341640i | ||||
\(835\) | 4.25508 | − | 7.37002i | 0.147253 | − | 0.255050i | ||||
\(836\) | −0.160092 | − | 0.277288i | −0.00553691 | − | 0.00959022i | ||||
\(837\) | − | 32.4990i | − | 1.12333i | ||||||
\(838\) | 28.5875 | − | 16.5050i | 0.987540 | − | 0.570157i | ||||
\(839\) | 22.1248 | − | 12.7738i | 0.763833 | − | 0.440999i | −0.0668370 | − | 0.997764i | \(-0.521291\pi\) |
0.830670 | + | 0.556765i | \(0.187957\pi\) | |||||||
\(840\) | − | 4.22571i | − | 0.145801i | ||||||
\(841\) | 0.823775 | + | 1.42682i | 0.0284060 | + | 0.0492007i | ||||
\(842\) | 16.1061 | − | 27.8965i | 0.555052 | − | 0.961378i | ||||
\(843\) | −8.66886 | − | 5.00497i | −0.298572 | − | 0.172380i | ||||
\(844\) | 0.848327 | 0.0292006 | ||||||||
\(845\) | 4.90250 | − | 4.63464i | 0.168651 | − | 0.159437i | ||||
\(846\) | −31.2096 | −1.07301 | ||||||||
\(847\) | 7.24180 | + | 4.18105i | 0.248831 | + | 0.143663i | ||||
\(848\) | −17.0611 | + | 29.5507i | −0.585881 | + | 1.01478i | ||||
\(849\) | 19.9770 | + | 34.6012i | 0.685609 | + | 1.18751i | ||||
\(850\) | − | 12.7737i | − | 0.438135i | ||||||
\(851\) | 80.9745 | − | 46.7507i | 2.77577 | − | 1.60259i | ||||
\(852\) | 1.00666 | − | 0.581197i | 0.0344877 | − | 0.0199115i | ||||
\(853\) | 22.6671i | 0.776105i | 0.921637 | + | 0.388053i | \(0.126852\pi\) | ||||
−0.921637 | + | 0.388053i | \(0.873148\pi\) | |||||||
\(854\) | 9.33489 | + | 16.1685i | 0.319433 | + | 0.553275i | ||||
\(855\) | 3.22231 | − | 5.58120i | 0.110201 | − | 0.190873i | ||||
\(856\) | −15.3339 | − | 8.85303i | −0.524102 | − | 0.302590i | ||||
\(857\) | 37.0535 | 1.26572 | 0.632862 | − | 0.774264i | \(-0.281880\pi\) | ||||
0.632862 | + | 0.774264i | \(0.281880\pi\) | |||||||
\(858\) | −9.07319 | + | 21.0633i | −0.309754 | + | 0.719088i | ||||
\(859\) | −4.24339 | −0.144782 | −0.0723912 | − | 0.997376i | \(-0.523063\pi\) | ||||
−0.0723912 | + | 0.997376i | \(0.523063\pi\) | |||||||
\(860\) | −0.0354702 | − | 0.0204788i | −0.00120953 | − | 0.000698320i | ||||
\(861\) | −5.94689 | + | 10.3003i | −0.202669 | + | 0.351034i | ||||
\(862\) | 1.87581 | + | 3.24900i | 0.0638904 | + | 0.110661i | ||||
\(863\) | − | 7.50051i | − | 0.255320i | −0.991818 | − | 0.127660i | \(-0.959253\pi\) | ||
0.991818 | − | 0.127660i | \(-0.0407467\pi\) | |||||||
\(864\) | −2.17328 | + | 1.25475i | −0.0739366 | + | 0.0426873i | ||||
\(865\) | 0.135438 | − | 0.0781951i | 0.00460503 | − | 0.00265871i | ||||
\(866\) | 8.06472i | 0.274050i | ||||||||
\(867\) | −18.6562 | − | 32.3135i | −0.633598 | − | 1.09742i | ||||
\(868\) | −0.229252 | + | 0.397076i | −0.00778132 | + | 0.0134776i | ||||
\(869\) | 1.38168 | + | 0.797714i | 0.0468703 | + | 0.0270606i | ||||
\(870\) | −10.6296 | −0.360376 | ||||||||
\(871\) | −24.2054 | + | 18.0393i | −0.820170 | + | 0.611238i | ||||
\(872\) | −34.2800 | −1.16087 | ||||||||
\(873\) | −19.0916 | − | 11.0225i | −0.646153 | − | 0.373057i | ||||
\(874\) | 15.7795 | − | 27.3309i | 0.533749 | − | 0.924481i | ||||
\(875\) | −2.52490 | − | 4.37326i | −0.0853573 | − | 0.147843i | ||||
\(876\) | − | 2.64755i | − | 0.0894523i | ||||||
\(877\) | −24.4996 | + | 14.1448i | −0.827291 | + | 0.477637i | −0.852924 | − | 0.522035i | \(-0.825173\pi\) |
0.0256330 | + | 0.999671i | \(0.491840\pi\) | |||||||
\(878\) | −45.8145 | + | 26.4510i | −1.54617 | + | 0.892679i | ||||
\(879\) | 23.5933i | 0.795781i | ||||||||
\(880\) | 1.61640 | + | 2.79968i | 0.0544888 | + | 0.0943773i | ||||
\(881\) | −19.7860 | + | 34.2704i | −0.666609 | + | 1.15460i | 0.312238 | + | 0.950004i | \(0.398921\pi\) |
−0.978846 | + | 0.204596i | \(0.934412\pi\) | |||||||
\(882\) | 5.98335 | + | 3.45449i | 0.201470 | + | 0.116319i | ||||
\(883\) | −28.3609 | −0.954419 | −0.477209 | − | 0.878790i | \(-0.658352\pi\) | ||||
−0.477209 | + | 0.878790i | \(0.658352\pi\) | |||||||
\(884\) | −0.332179 | − | 0.445724i | −0.0111724 | − | 0.0149913i | ||||
\(885\) | −9.09974 | −0.305884 | ||||||||
\(886\) | 38.0174 | + | 21.9494i | 1.27722 | + | 0.737403i | ||||
\(887\) | 21.8593 | − | 37.8614i | 0.733963 | − | 1.27126i | −0.221214 | − | 0.975225i | \(-0.571002\pi\) |
0.955177 | − | 0.296036i | \(-0.0956648\pi\) | |||||||
\(888\) | −41.6469 | − | 72.1345i | −1.39758 | − | 2.42068i | ||||
\(889\) | − | 1.42350i | − | 0.0477426i | ||||||
\(890\) | −7.48649 | + | 4.32233i | −0.250948 | + | 0.144885i | ||||
\(891\) | −1.25918 | + | 0.726988i | −0.0421841 | + | 0.0243550i | ||||
\(892\) | 1.01989i | 0.0341483i | ||||||||
\(893\) | 5.62659 | + | 9.74554i | 0.188287 | + | 0.326122i | ||||
\(894\) | −6.58913 | + | 11.4127i | −0.220374 | + | 0.381698i | ||||
\(895\) | −4.41152 | − | 2.54699i | −0.147461 | − | 0.0851366i | ||||
\(896\) | −10.5961 | −0.353992 | ||||||||
\(897\) | 92.4934 | − | 10.8583i | 3.08826 | − | 0.362547i | ||||
\(898\) | −43.5257 | −1.45247 | ||||||||
\(899\) | 26.2422 | + | 15.1509i | 0.875227 | + | 0.505312i | ||||
\(900\) | −0.933105 | + | 1.61619i | −0.0311035 | + | 0.0538728i | ||||
\(901\) | −8.66632 | − | 15.0105i | −0.288717 | − | 0.500073i | ||||
\(902\) | − | 9.47456i | − | 0.315468i | ||||||
\(903\) | 2.44061 | − | 1.40909i | 0.0812185 | − | 0.0468915i | ||||
\(904\) | 8.87439 | − | 5.12363i | 0.295158 | − | 0.170409i | ||||
\(905\) | 6.45167i | 0.214461i | ||||||||
\(906\) | 24.7841 | + | 42.9274i | 0.823397 | + | 1.42617i | ||||
\(907\) | −18.3493 | + | 31.7818i | −0.609277 | + | 1.05530i | 0.382083 | + | 0.924128i | \(0.375207\pi\) |
−0.991360 | + | 0.131171i | \(0.958126\pi\) | |||||||
\(908\) | 0.0479154 | + | 0.0276640i | 0.00159013 | + | 0.000918062i | ||||
\(909\) | −91.2387 | −3.02620 | ||||||||
\(910\) | 2.38172 | + | 1.02595i | 0.0789533 | + | 0.0340098i | ||||
\(911\) | −35.5211 | −1.17686 | −0.588432 | − | 0.808546i | \(-0.700255\pi\) | ||||
−0.588432 | + | 0.808546i | \(0.700255\pi\) | |||||||
\(912\) | −23.3823 | − | 13.4998i | −0.774265 | − | 0.447022i | ||||
\(913\) | 7.24254 | − | 12.5444i | 0.239693 | − | 0.415161i | ||||
\(914\) | −22.0562 | − | 38.2024i | −0.729553 | − | 1.26362i | ||||
\(915\) | 19.7542i | 0.653054i | ||||||||
\(916\) | −1.25326 | + | 0.723569i | −0.0414088 | + | 0.0239074i | ||||
\(917\) | −7.51168 | + | 4.33687i | −0.248057 | + | 0.143216i | ||||
\(918\) | 15.1458i | 0.499885i | ||||||||
\(919\) | −10.9667 | − | 18.9949i | −0.361758 | − | 0.626583i | 0.626492 | − | 0.779428i | \(-0.284490\pi\) |
−0.988250 | + | 0.152844i | \(0.951157\pi\) | |||||||
\(920\) | 6.83449 | − | 11.8377i | 0.225327 | − | 0.390277i | ||||
\(921\) | 20.3940 | + | 11.7745i | 0.672005 | + | 0.387982i | ||||
\(922\) | −1.61644 | −0.0532348 | ||||||||
\(923\) | 2.18521 | + | 18.6142i | 0.0719272 | + | 0.612693i | ||||
\(924\) | 0.363193 | 0.0119482 | ||||||||
\(925\) | −41.9082 | − | 24.1957i | −1.37793 | − | 0.795549i | ||||
\(926\) | −14.0980 | + | 24.4184i | −0.463287 | + | 0.802437i | ||||
\(927\) | 12.5135 | + | 21.6740i | 0.410997 | + | 0.711867i | ||||
\(928\) | − | 2.33984i | − | 0.0768090i | ||||||
\(929\) | −13.4383 | + | 7.75858i | −0.440895 | + | 0.254551i | −0.703977 | − | 0.710223i | \(-0.748594\pi\) |
0.263082 | + | 0.964773i | \(0.415261\pi\) | |||||||
\(930\) | 10.1981 | − | 5.88788i | 0.334409 | − | 0.193071i | ||||
\(931\) | − | 2.49115i | − | 0.0816443i | ||||||
\(932\) | 1.05961 | + | 1.83529i | 0.0347086 | + | 0.0601171i | ||||
\(933\) | 20.6602 | − | 35.7845i | 0.676385 | − | 1.17153i | ||||
\(934\) | −1.88370 | − | 1.08755i | −0.0616364 | − | 0.0355858i | ||||
\(935\) | −1.64212 | −0.0537031 | ||||||||
\(936\) | −6.03874 | − | 51.4394i | −0.197382 | − | 1.68135i | ||||
\(937\) | 40.8110 | 1.33324 | 0.666618 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666618 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(938\) | −10.0495 | − | 5.80205i | −0.328126 | − | 0.189444i | ||||
\(939\) | 24.2067 | − | 41.9273i | 0.789957 | − | 1.36825i | ||||
\(940\) | 0.0927572 | + | 0.160660i | 0.00302541 | + | 0.00524016i | ||||
\(941\) | − | 51.5936i | − | 1.68190i | −0.541109 | − | 0.840952i | \(-0.681996\pi\) | ||
0.541109 | − | 0.840952i | \(-0.318004\pi\) | |||||||
\(942\) | −35.1689 | + | 20.3048i | −1.14586 | + | 0.661565i | ||||
\(943\) | −33.3186 | + | 19.2365i | −1.08500 | + | 0.626427i | ||||
\(944\) | 23.8001i | 0.774627i | ||||||||
\(945\) | 1.45546 | + | 2.52092i | 0.0473460 | + | 0.0820057i | ||||
\(946\) | −1.12248 | + | 1.94419i | −0.0364949 | + | 0.0632110i | ||||
\(947\) | −4.31462 | − | 2.49105i | −0.140206 | − | 0.0809482i | 0.428256 | − | 0.903657i | \(-0.359128\pi\) |
−0.568462 | + | 0.822709i | \(0.692461\pi\) | |||||||
\(948\) | −0.219663 | −0.00713433 | ||||||||
\(949\) | 39.2054 | + | 16.8881i | 1.27266 | + | 0.548210i | ||||
\(950\) | −16.3333 | −0.529921 | ||||||||
\(951\) | −34.2608 | − | 19.7805i | −1.11098 | − | 0.641426i | ||||
\(952\) | 2.80703 | − | 4.86191i | 0.0909763 | − | 0.157576i | ||||
\(953\) | 15.1163 | + | 26.1822i | 0.489664 | + | 0.848123i | 0.999929 | − | 0.0118941i | \(-0.00378608\pi\) |
−0.510265 | + | 0.860017i | \(0.670453\pi\) | |||||||
\(954\) | − | 61.4657i | − | 1.99003i | ||||||
\(955\) | −5.50413 | + | 3.17781i | −0.178110 | + | 0.102832i | ||||
\(956\) | −1.13887 | + | 0.657525i | −0.0368336 | + | 0.0212659i | ||||
\(957\) | − | 24.0029i | − | 0.775904i | ||||||
\(958\) | −5.34921 | − | 9.26511i | −0.172825 | − | 0.299342i | ||||
\(959\) | −4.25892 | + | 7.37667i | −0.137528 | + | 0.238205i | ||||
\(960\) | −10.5295 | − | 6.07919i | −0.339837 | − | 0.196205i | ||||
\(961\) | −2.56939 | −0.0828835 | ||||||||
\(962\) | 50.7682 | − | 5.95995i | 1.63683 | − | 0.192156i | ||||
\(963\) | 30.6306 | 0.987058 | ||||||||
\(964\) | −1.19336 | − | 0.688988i | −0.0384356 | − | 0.0221908i | ||||
\(965\) | 3.01873 | − | 5.22860i | 0.0971764 | − | 0.168315i | ||||
\(966\) | 17.8990 | + | 31.0020i | 0.575892 | + | 0.997474i | ||||
\(967\) | − | 29.9990i | − | 0.964703i | −0.875978 | − | 0.482352i | \(-0.839783\pi\) | ||
0.875978 | − | 0.482352i | \(-0.160217\pi\) | |||||||
\(968\) | 20.8678 | − | 12.0481i | 0.670718 | − | 0.387239i | ||||
\(969\) | 11.8772 | − | 6.85731i | 0.381551 | − | 0.220288i | ||||
\(970\) | − | 3.18073i | − | 0.102127i | ||||||
\(971\) | −22.0620 | − | 38.2125i | −0.708003 | − | 1.22630i | −0.965597 | − | 0.260044i | \(-0.916263\pi\) |
0.257594 | − | 0.966253i | \(-0.417070\pi\) | |||||||
\(972\) | −0.565732 | + | 0.979876i | −0.0181459 | + | 0.0314295i | ||||
\(973\) | −4.36342 | − | 2.51922i | −0.139885 | − | 0.0807625i | ||||
\(974\) | 0.105582 | 0.00338306 | ||||||||
\(975\) | −28.8016 | − | 38.6465i | −0.922391 | − | 1.23768i | ||||
\(976\) | 51.6665 | 1.65380 | ||||||||
\(977\) | −12.9925 | − | 7.50121i | −0.415666 | − | 0.239985i | 0.277555 | − | 0.960710i | \(-0.410476\pi\) |
−0.693221 | + | 0.720725i | \(0.743809\pi\) | |||||||
\(978\) | −30.8482 | + | 53.4306i | −0.986417 | + | 1.70852i | ||||
\(979\) | −9.76037 | − | 16.9055i | −0.311943 | − | 0.540301i | ||||
\(980\) | − | 0.0410679i | − | 0.00131187i | ||||||
\(981\) | 51.3577 | − | 29.6514i | 1.63973 | − | 0.946696i | ||||
\(982\) | −2.14506 | + | 1.23845i | −0.0684516 | + | 0.0395206i | ||||
\(983\) | 6.01856i | 0.191962i | 0.995383 | + | 0.0959812i | \(0.0305989\pi\) | ||||
−0.995383 | + | 0.0959812i | \(0.969401\pi\) | |||||||
\(984\) | 17.1364 | + | 29.6812i | 0.546290 | + | 0.946202i | ||||
\(985\) | 0.467358 | − | 0.809488i | 0.0148913 | − | 0.0257924i | ||||
\(986\) | −12.2299 | − | 7.06093i | −0.389479 | − | 0.224866i | ||||
\(987\) | −12.7647 | −0.406306 | ||||||||
\(988\) | −0.569930 | + | 0.424745i | −0.0181319 | + | 0.0135129i | ||||
\(989\) | 9.11600 | 0.289872 | ||||||||
\(990\) | −5.04318 | − | 2.91168i | −0.160283 | − | 0.0925392i | ||||
\(991\) | −16.9200 | + | 29.3063i | −0.537482 | + | 0.930946i | 0.461557 | + | 0.887111i | \(0.347291\pi\) |
−0.999039 | + | 0.0438356i | \(0.986042\pi\) | |||||||
\(992\) | 1.29607 | + | 2.24487i | 0.0411504 | + | 0.0712746i | ||||
\(993\) | − | 19.5542i | − | 0.620535i | ||||||
\(994\) | −6.23912 | + | 3.60215i | −0.197893 | + | 0.114253i | ||||
\(995\) | −2.96315 | + | 1.71078i | −0.0939382 | + | 0.0542353i | ||||
\(996\) | 1.99435i | 0.0631934i | ||||||||
\(997\) | −13.1608 | − | 22.7951i | −0.416805 | − | 0.721928i | 0.578811 | − | 0.815462i | \(-0.303517\pi\) |
−0.995616 | + | 0.0935340i | \(0.970184\pi\) | |||||||
\(998\) | 5.77591 | − | 10.0042i | 0.182833 | − | 0.316676i | ||||
\(999\) | 49.6904 | + | 28.6888i | 1.57213 | + | 0.907672i |
(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 | 91.2.q.a.43.2 | yes | 12 | |
3.2 | odd | 2 | 819.2.ct.a.316.5 | 12 | |||
4.3 | odd | 2 | 1456.2.cc.c.225.1 | 12 | |||
7.2 | even | 3 | 637.2.k.h.459.5 | 12 | |||
7.3 | odd | 6 | 637.2.u.i.30.5 | 12 | |||
7.4 | even | 3 | 637.2.u.h.30.5 | 12 | |||
7.5 | odd | 6 | 637.2.k.g.459.5 | 12 | |||
7.6 | odd | 2 | 637.2.q.h.589.2 | 12 | |||
13.4 | even | 6 | 1183.2.c.i.337.3 | 12 | |||
13.6 | odd | 12 | 1183.2.a.m.1.6 | 6 | |||
13.7 | odd | 12 | 1183.2.a.p.1.1 | 6 | |||
13.9 | even | 3 | 1183.2.c.i.337.10 | 12 | |||
13.10 | even | 6 | inner | 91.2.q.a.36.2 | ✓ | 12 | |
39.23 | odd | 6 | 819.2.ct.a.127.5 | 12 | |||
52.23 | odd | 6 | 1456.2.cc.c.673.1 | 12 | |||
91.6 | even | 12 | 8281.2.a.by.1.6 | 6 | |||
91.10 | odd | 6 | 637.2.k.g.569.2 | 12 | |||
91.20 | even | 12 | 8281.2.a.ch.1.1 | 6 | |||
91.23 | even | 6 | 637.2.u.h.361.5 | 12 | |||
91.62 | odd | 6 | 637.2.q.h.491.2 | 12 | |||
91.75 | odd | 6 | 637.2.u.i.361.5 | 12 | |||
91.88 | even | 6 | 637.2.k.h.569.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.2 | ✓ | 12 | 13.10 | even | 6 | inner | |
91.2.q.a.43.2 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.k.g.459.5 | 12 | 7.5 | odd | 6 | |||
637.2.k.g.569.2 | 12 | 91.10 | odd | 6 | |||
637.2.k.h.459.5 | 12 | 7.2 | even | 3 | |||
637.2.k.h.569.2 | 12 | 91.88 | even | 6 | |||
637.2.q.h.491.2 | 12 | 91.62 | odd | 6 | |||
637.2.q.h.589.2 | 12 | 7.6 | odd | 2 | |||
637.2.u.h.30.5 | 12 | 7.4 | even | 3 | |||
637.2.u.h.361.5 | 12 | 91.23 | even | 6 | |||
637.2.u.i.30.5 | 12 | 7.3 | odd | 6 | |||
637.2.u.i.361.5 | 12 | 91.75 | odd | 6 | |||
819.2.ct.a.127.5 | 12 | 39.23 | odd | 6 | |||
819.2.ct.a.316.5 | 12 | 3.2 | odd | 2 | |||
1183.2.a.m.1.6 | 6 | 13.6 | odd | 12 | |||
1183.2.a.p.1.1 | 6 | 13.7 | odd | 12 | |||
1183.2.c.i.337.3 | 12 | 13.4 | even | 6 | |||
1183.2.c.i.337.10 | 12 | 13.9 | even | 3 | |||
1456.2.cc.c.225.1 | 12 | 4.3 | odd | 2 | |||
1456.2.cc.c.673.1 | 12 | 52.23 | odd | 6 | |||
8281.2.a.by.1.6 | 6 | 91.6 | even | 12 | |||
8281.2.a.ch.1.1 | 6 | 91.20 | even | 12 |