Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, 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("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.2 | ||
Root | \(0.759479 + 1.19298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.h.491.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | \(0.470332\pi\) |
−0.908802 | + | 0.417228i | \(0.863002\pi\) | |||||||
\(4\) | −0.0395678 | − | 0.0685334i | −0.0197839 | − | 0.0342667i | ||||
\(5\) | − | 0.518957i | − | 0.232085i | −0.993244 | − | 0.116042i | \(-0.962979\pi\) | ||
0.993244 | − | 0.116042i | \(-0.0370208\pi\) | |||||||
\(6\) | 3.39169 | − | 1.95819i | 1.38465 | − | 0.799429i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 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 | 0.723378 | − | 0.690452i | \(-0.242589\pi\) |
−0.959638 | + | 0.281237i | \(0.909255\pi\) | |||||||
\(18\) | 6.90897i | 1.62846i | ||||||||
\(19\) | −2.15740 | + | 1.24558i | −0.494942 | + | 0.285755i | −0.726622 | − | 0.687037i | \(-0.758911\pi\) |
0.231680 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(20\) | −0.0355659 | + | 0.0205340i | −0.00795277 | + | 0.00459154i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −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 | 0 | ||||||||
\(29\) | 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 | \(-0.825817\pi\) | ||
0.853978 | − | 0.520308i | \(-0.174183\pi\) | |||||||
\(32\) | 0.387453 | − | 0.223696i | 0.0684926 | − | 0.0395442i | ||||
\(33\) | −3.97463 | + | 2.29475i | −0.691894 | + | 0.399465i | ||||
\(34\) | 2.70019i | 0.463078i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −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 | 0.187586 | − | 0.982248i | \(-0.439934\pi\) |
−0.756859 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −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 | \(-0.893135\pi\) | ||
0.944171 | − | 0.329455i | \(-0.106865\pi\) | |||||||
\(48\) | 5.41908 | + | 9.38612i | 0.782177 | + | 1.35477i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −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 | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.03944i | − | 0.932397i | ||||||
\(58\) | −6.27736 | + | 3.62424i | −0.824258 | + | 0.475886i | ||||
\(59\) | 5.37392 | − | 3.10263i | 0.699624 | − | 0.403928i | −0.107583 | − | 0.994196i | \(-0.534311\pi\) |
0.807207 | + | 0.590268i | \(0.200978\pi\) | |||||||
\(60\) | − | 0.116049i | − | 0.0149818i | ||||||
\(61\) | −6.73536 | − | 11.6660i | −0.862375 | − | 1.49368i | −0.869630 | − | 0.493703i | \(-0.835643\pi\) |
0.00725571 | − | 0.999974i | \(-0.497690\pi\) | |||||||
\(62\) | −4.01504 | + | 6.95426i | −0.509911 | + | 0.883191i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | 0 | ||||||||
\(71\) | −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 | \(-0.756352\pi\) | ||
0.721076 | − | 0.692856i | \(-0.243648\pi\) | |||||||
\(74\) | 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 | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(0.162809\pi\) | ||||
−0.872022 | + | 0.489467i | \(0.837191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −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 | 0.937092 | − | 0.349082i | \(-0.113506\pi\) |
0.166233 | + | 0.986087i | \(0.446840\pi\) | |||||||
\(90\) | 3.58546 | 0.377941 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | −0.681665 | − | 0.731664i | \(-0.738744\pi\) |
0.292807 | + | 0.956172i | \(0.405411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 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 | \(0.531040\pi\) |
−0.813231 | + | 0.581940i | \(0.802294\pi\) | |||||||
\(102\) | −6.60787 | − | 3.81506i | −0.654277 | − | 0.377747i | ||||
\(103\) | 5.02046 | 0.494680 | 0.247340 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247340 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(104\) | −9.54206 | − | 4.11033i | −0.935676 | − | 0.403051i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −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 | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | \(-0.623702\pi\) | ||||
−0.378914 | + | 0.925432i | \(0.623702\pi\) | |||||||
\(132\) | 0.314535 | + | 0.181597i | 0.0273767 | + | 0.0158060i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | 0.739185 | − | 0.673502i | \(-0.235211\pi\) |
−0.952863 | + | 0.303402i | \(0.901877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 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 | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00679 | −0.241511 | ||||||||
\(156\) | −0.318973 | + | 0.740492i | −0.0255383 | + | 0.0592868i | ||||
\(157\) | −10.3691 | −0.827547 | −0.413773 | − | 0.910380i | \(-0.635789\pi\) | ||||
−0.413773 | + | 0.910380i | \(0.635789\pi\) | |||||||
\(158\) | −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 | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | 0.935946 | − | 0.352144i | \(-0.114547\pi\) |
0.163007 | + | 0.986625i | \(0.447881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −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 | 0.871696 | − | 0.490046i | \(-0.163020\pi\) |
−0.860241 | + | 0.509888i | \(0.829687\pi\) | |||||||
\(174\) | − | 20.4825i | − | 1.55278i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(-0.652879\pi\) | ||||
−0.462031 | + | 0.886864i | \(0.652879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 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 | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 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 | 0 | ||||||||
\(197\) | −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 | 0.725203 | − | 0.688535i | \(-0.241746\pi\) |
−0.958890 | + | 0.283777i | \(0.908413\pi\) | |||||||
\(200\) | 13.6319i | 0.963918i | ||||||||
\(201\) | 20.4895 | − | 11.8296i | 1.44522 | − | 0.834397i | ||||
\(202\) | 21.9681 | − | 12.6833i | 1.54567 | − | 0.892394i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | 0.824757 | − | 0.565487i | \(-0.191312\pi\) |
−0.0773480 | + | 0.997004i | \(0.524645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7912 | − | 20.4230i | −0.786082 | − | 1.36153i | ||||
\(226\) | 4.92862i | 0.327847i | ||||||||
\(227\) | 0.605486 | − | 0.349577i | 0.0401875 | − | 0.0232023i | −0.479772 | − | 0.877393i | \(-0.659280\pi\) |
0.519959 | + | 0.854191i | \(0.325947\pi\) | |||||||
\(228\) | −0.482437 | + | 0.278535i | −0.0319502 | + | 0.0184464i | ||||
\(229\) | 18.2868i | 1.20843i | 0.796822 | + | 0.604214i | \(0.206513\pi\) | ||||
−0.796822 | + | 0.604214i | \(0.793487\pi\) | |||||||
\(230\) | −3.28718 | − | 5.69356i | −0.216750 | − | 0.375422i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 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 | −0.899659 | − | 0.436594i | \(-0.856185\pi\) |
−0.0717279 | + | 0.997424i | \(0.522851\pi\) | |||||||
\(242\) | 11.5895i | 0.745000i | ||||||||
\(243\) | 7.14890 | + | 12.3823i | 0.458602 | + | 0.794322i | ||||
\(244\) | −0.533007 | + | 0.923194i | −0.0341222 | + | 0.0591015i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −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 | 0.949671 | − | 0.313249i | \(-0.101417\pi\) |
−0.746117 | + | 0.665815i | \(0.768084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | −0.803072 | − | 0.595882i | \(-0.796803\pi\) |
0.917585 | + | 0.397540i | \(0.130136\pi\) | |||||||
\(258\) | −3.38257 | − | 1.95293i | −0.210590 | − | 0.121584i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −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 | \(0.150580\pi\) |
−0.0505171 | + | 0.998723i | \(0.516087\pi\) | |||||||
\(270\) | −2.01719 | + | 3.49388i | −0.122762 | + | 0.212631i | ||||
\(271\) | −5.64582 | − | 3.25961i | −0.342959 | − | 0.198007i | 0.318621 | − | 0.947882i | \(-0.396780\pi\) |
−0.661580 | + | 0.749875i | \(0.730114\pi\) | |||||||
\(272\) | −7.47246 | −0.453084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 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 | −0.575721 | − | 0.817646i | \(-0.695279\pi\) |
0.995963 | + | 0.0897658i | \(0.0286119\pi\) | |||||||
\(284\) | 0.356243 | + | 0.205677i | 0.0211391 | + | 0.0122047i | ||||
\(285\) | −3.65317 | −0.216395 | ||||||||
\(286\) | 8.06077 | − | 0.946296i | 0.476643 | − | 0.0559556i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −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 | −0.273691 | − | 0.961818i | \(-0.588244\pi\) |
0.696113 | + | 0.717932i | \(0.254911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −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 | 0 | ||||||||
\(302\) | −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 | \(-0.923570\pi\) | ||
0.971311 | − | 0.237813i | \(-0.0764304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −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 | \(-0.636074\pi\) | ||||
−0.414588 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(312\) | 23.5406 | − | 17.5438i | 1.33273 | − | 0.993224i | ||||
\(313\) | −17.1328 | −0.968404 | −0.484202 | − | 0.874956i | \(-0.660890\pi\) | ||||
−0.484202 | + | 0.874956i | \(0.660890\pi\) | |||||||
\(314\) | 12.4458 | + | 7.18556i | 0.702355 | + | 0.405505i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −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 | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 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 | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 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 | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | 0.464275 | − | 0.885691i | \(-0.346315\pi\) |
−0.534893 | + | 0.844920i | \(0.679648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00098 | + | 18.5741i | −0.427061 | + | 0.991415i | ||||
\(352\) | 0.726636 | 0.0387298 | ||||||||
\(353\) | −15.5261 | − | 8.96401i | −0.826372 | − | 0.477106i | 0.0262367 | − | 0.999656i | \(-0.491648\pi\) |
−0.852609 | + | 0.522550i | \(0.824981\pi\) | |||||||
\(354\) | 12.1511 | − | 21.0463i | 0.645824 | − | 1.11860i | ||||
\(355\) | 1.34879 | + | 2.33618i | 0.0715865 | + | 0.123991i | ||||
\(356\) | − | 0.951129i | − | 0.0504097i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | 0 | ||||||||
\(365\) | −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 | \(-0.579512\pi\) |
0.962749 | − | 0.270395i | \(-0.0871543\pi\) | |||||||
\(368\) | 17.5292 | + | 30.3615i | 0.913772 | + | 1.58270i | ||||
\(369\) | 20.9820i | 1.09228i | ||||||||
\(370\) | 6.37169 | − | 3.67870i | 0.331248 | − | 0.191246i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 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 | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 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 | −0.665720 | − | 0.746202i | \(-0.731875\pi\) |
0.313370 | + | 0.949631i | \(0.398542\pi\) | |||||||
\(384\) | −25.9308 | + | 14.9712i | −1.32328 | + | 0.763994i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 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 | −0.633277 | − | 0.773925i | \(-0.718290\pi\) |
0.353601 | + | 0.935396i | \(0.384957\pi\) | |||||||
\(398\) | 9.13777i | 0.458035i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −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 | \(-0.225748\pi\) |
0.943424 | − | 0.331590i | \(-0.107585\pi\) | |||||||
\(410\) | 2.62176 | − | 1.51367i | 0.129479 | − | 0.0747550i | ||||
\(411\) | 24.0695i | 1.18726i | ||||||||
\(412\) | −0.198648 | − | 0.344069i | −0.00978670 | − | 0.0169511i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −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 | \(-0.635689\pi\) |
0.995268 | − | 0.0971665i | \(-0.0309779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | 0.927428 | − | 0.374002i | \(-0.122015\pi\) |
−0.787609 | + | 0.616176i | \(0.788681\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 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 | \(0.531264\pi\) |
−0.812822 | + | 0.582513i | \(0.802070\pi\) | |||||||
\(440\) | 2.10340 | + | 1.21440i | 0.100276 | + | 0.0578942i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | −0.523337 | − | 0.852126i | \(-0.675313\pi\) |
0.476294 | + | 0.879286i | \(0.341980\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 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 | \(-0.511561\pi\) | ||||
−0.0363114 | + | 0.999341i | \(0.511561\pi\) | |||||||
\(468\) | −0.849948 | − | 1.14048i | −0.0392889 | − | 0.0527185i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | 0 | ||||||||
\(477\) | 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 | 0.339441 | − | 0.940627i | \(-0.389762\pi\) |
−0.644887 | + | 0.764278i | \(0.723095\pi\) | |||||||
\(480\) | 0.656080 | 0.0299458 | ||||||||
\(481\) | 29.5729 | − | 22.0394i | 1.34841 | − | 1.00491i | ||||
\(482\) | 24.1334 | 1.09925 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −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 | 0 | ||||||||
\(491\) | 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 | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | 0.881636 | − | 0.471931i | \(-0.156443\pi\) |
−0.849522 | + | 0.527554i | \(0.823109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 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 | 0.187692 | − | 0.982228i | \(-0.439899\pi\) |
−0.756788 | + | 0.653660i | \(0.773233\pi\) | |||||||
\(510\) | −1.97985 | + | 3.42920i | −0.0876693 | + | 0.151848i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 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 | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.851561 | −0.0373794 | ||||||||
\(520\) | −2.13308 | + | 4.95192i | −0.0935419 | + | 0.217156i | ||||
\(521\) | 0.334388 | 0.0146498 | 0.00732489 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732489 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(522\) | 31.2926 | + | 18.0668i | 1.36964 | + | 0.790763i | ||||
\(523\) | −16.2533 | + | 28.1515i | −0.710705 | + | 1.23098i | 0.253887 | + | 0.967234i | \(0.418291\pi\) |
−0.964593 | + | 0.263744i | \(0.915043\pi\) | |||||||
\(524\) | 0.343201 | + | 0.594441i | 0.0149928 | + | 0.0259683i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | 0 | ||||||||
\(533\) | 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 | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | 0 | ||||||||
\(554\) | − | 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 | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | 0.729637 | − | 0.683835i | \(-0.239689\pi\) |
−0.957037 | + | 0.289967i | \(0.906356\pi\) | |||||||
\(564\) | − | 1.01014i | − | 0.0425348i | ||||||
\(565\) | −1.59823 | + | 0.922737i | −0.0672380 | + | 0.0388199i | ||||
\(566\) | −16.9708 | + | 9.79808i | −0.713335 | + | 0.411844i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −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 | \(-0.901285\pi\) | ||
0.952297 | − | 0.305174i | \(-0.0987147\pi\) | |||||||
\(578\) | −15.8487 | + | 9.15027i | −0.659221 | + | 0.380601i | ||||
\(579\) | 28.4702 | − | 16.4373i | 1.18318 | − | 0.683111i | ||||
\(580\) | 0.214784i | 0.00891840i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −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 | −0.289336 | − | 0.957227i | \(-0.593435\pi\) |
−0.973652 | + | 0.228041i | \(0.926768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 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 | \(0.109526\pi\) | ||||
−0.941384 | + | 0.337338i | \(0.890474\pi\) | |||||||
\(594\) | −6.31313 | − | 10.9347i | −0.259031 | − | 0.448655i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −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 | −0.775261 | − | 0.631642i | \(-0.782381\pi\) |
0.934648 | + | 0.355574i | \(0.115715\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | \(0.0900035\pi\) |
−0.238523 | + | 0.971137i | \(0.576663\pi\) | |||||||
\(608\) | −0.557261 | + | 0.965205i | −0.0225999 | + | 0.0391442i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −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 | \(0.194572\pi\) | ||||
−0.818923 | + | 0.573904i | \(0.805428\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −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 | −0.779832 | − | 0.625988i | \(-0.784696\pi\) |
0.152206 | + | 0.988349i | \(0.451362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.46251i | − | 0.0575863i | ||||||
\(646\) | −3.36329 | − | 5.82539i | −0.132327 | − | 0.229197i | ||||
\(647\) | −10.4643 | + | 18.1248i | −0.411396 | + | 0.712558i | −0.995043 | − | 0.0994494i | \(-0.968292\pi\) |
0.583647 | + | 0.812008i | \(0.301625\pi\) | |||||||
\(648\) | −2.23404 | − | 1.28982i | −0.0877612 | − | 0.0506690i | ||||
\(649\) | 10.0783 | 0.395609 | ||||||||
\(650\) | 18.9549 | − | 14.1263i | 0.743473 | − | 0.554079i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −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 | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | 0.510697 | − | 0.859761i | \(-0.329387\pi\) |
−0.489226 | + | 0.872157i | \(0.662721\pi\) | |||||||
\(662\) | −9.59073 | −0.372754 | ||||||||
\(663\) | −7.85287 | + | 18.2303i | −0.304980 | + | 0.708006i | ||||
\(664\) | −25.6994 | −0.997331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | 0 | ||||||||
\(673\) | 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 | \(-0.427934\pi\) | ||||
0.224473 | + | 0.974480i | \(0.427934\pi\) | |||||||
\(678\) | −12.0613 | − | 6.96358i | −0.463210 | − | 0.267435i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −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 | 0 | ||||||||
\(687\) | −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 | \(0.0219403\pi\) |
0.558458 | + | 0.829533i | \(0.311393\pi\) | |||||||
\(692\) | 0.0119239 | − | 0.0206529i | 0.000453280 | − | 0.000785104i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 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 | 0 | ||||||||
\(701\) | 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 | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 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 | 0.768304 | − | 0.640085i | \(-0.221101\pi\) |
−0.938482 | + | 0.345329i | \(0.887767\pi\) | |||||||
\(720\) | 9.92235i | 0.369784i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | \(-0.714767\pi\) | ||||
−0.624670 | + | 0.780889i | \(0.714767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −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 | \(-0.671987\pi\) | ||
0.514406 | − | 0.857547i | \(-0.328013\pi\) | |||||||
\(734\) | −32.9062 | + | 18.9984i | −1.21459 | + | 0.701245i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −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 | 0 | ||||||||
\(757\) | −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 | −0.681714 | − | 0.731619i | \(-0.738765\pi\) |
0.292743 | + | 0.956191i | \(0.405432\pi\) | |||||||
\(762\) | 5.57497i | 0.201960i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | 0.584205 | − | 0.811606i | \(-0.301406\pi\) |
−0.410769 | + | 0.911740i | \(0.634740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.18750 | + | 8.98501i | 0.186823 | + | 0.323587i | ||||
\(772\) | 0.920651i | 0.0331349i | ||||||||
\(773\) | −37.9355 | + | 21.9021i | −1.36445 | + | 0.787764i | −0.990212 | − | 0.139570i | \(-0.955428\pi\) |
−0.374235 | + | 0.927334i | \(0.622095\pi\) | |||||||
\(774\) | 5.96726 | − | 3.44520i | 0.214489 | − | 0.123835i | ||||
\(775\) | − | 27.4092i | − | 0.984566i | ||||||
\(776\) | −6.37159 | − | 11.0359i | −0.228727 | − | 0.396166i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.38113i | 0.192061i | ||||||||
\(786\) | −29.4187 | + | 16.9849i | −1.04933 | + | 0.605830i | ||||
\(787\) | −21.4782 | + | 12.4005i | −0.765616 | + | 0.442029i | −0.831309 | − | 0.555811i | \(-0.812408\pi\) |
0.0656923 | + | 0.997840i | \(0.479074\pi\) | |||||||
\(788\) | 0.142535i | 0.00507758i | ||||||||
\(789\) | −25.8831 | − | 44.8308i | −0.921462 | − | 1.59602i | ||||
\(790\) | −0.353263 | + | 0.611870i | −0.0125685 | + | 0.0217693i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | 0.974218 | − | 0.225610i | \(-0.0724373\pi\) |
−0.682492 | + | 0.730893i | \(0.739104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −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 | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −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 | \(0.0382950\pi\) | ||||
−0.992772 | + | 0.120017i | \(0.961705\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | −0.865622 | − | 0.500699i | \(-0.833076\pi\) |
0.866429 | + | 0.499301i | \(0.166410\pi\) | |||||||
\(830\) | −5.55524 | − | 3.20732i | −0.192825 | − | 0.111328i | ||||
\(831\) | −15.3775 | −0.533438 | ||||||||
\(832\) | 11.8264 | − | 27.4548i | 0.410006 | − | 0.951823i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | −0.830670 | − | 0.556765i | \(-0.812043\pi\) |
0.0668370 | + | 0.997764i | \(0.478709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −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 | \(-0.873148\pi\) | ||
0.921637 | − | 0.388053i | \(-0.126852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 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 | \(-0.718120\pi\) | ||||
−0.632862 | + | 0.774264i | \(0.718120\pi\) | |||||||
\(858\) | −9.07319 | + | 21.0633i | −0.309754 | + | 0.719088i | ||||
\(859\) | 4.24339 | 0.144782 | 0.0723912 | − | 0.997376i | \(-0.476937\pi\) | ||||
0.0723912 | + | 0.997376i | \(0.476937\pi\) | |||||||
\(860\) | 0.0354702 | + | 0.0204788i | 0.00120953 | + | 0.000698320i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | 0 | ||||||||
\(869\) | 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 | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 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 | \(-0.601079\pi\) |
0.978846 | − | 0.204596i | \(-0.0655882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | \(0.428998\pi\) |
−0.955177 | + | 0.296036i | \(0.904335\pi\) | |||||||
\(888\) | 41.6469 | + | 72.1345i | 1.39758 | + | 2.42068i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −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 | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 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 | 0 | ||||||||
\(925\) | −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 | −0.263082 | − | 0.964773i | \(-0.584739\pi\) |
0.703977 | + | 0.710223i | \(0.251406\pi\) | |||||||
\(930\) | −10.1981 | + | 5.88788i | −0.334409 | + | 0.193071i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.732259\pi\) | ||||
−0.666618 | + | 0.745399i | \(0.732259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 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 | \(0.318004\pi\) | ||||
−0.541109 | + | 0.840952i | \(0.681996\pi\) | |||||||
\(942\) | −35.1689 | + | 20.3048i | −1.14586 | + | 0.661565i | ||||
\(943\) | 33.3186 | − | 19.2365i | 1.08500 | − | 0.626427i | ||||
\(944\) | − | 23.8001i | − | 0.774627i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −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 | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −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 | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 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 | \(0.0837371\pi\) |
−0.257594 | + | 0.966253i | \(0.582930\pi\) | |||||||
\(972\) | 0.565732 | − | 0.979876i | 0.0181459 | − | 0.0314295i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | 0 | ||||||||
\(981\) | 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 | \(-0.969401\pi\) | ||
0.995383 | − | 0.0959812i | \(-0.0305989\pi\) | |||||||
\(984\) | 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 | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.96315 | + | 1.71078i | −0.0939382 | + | 0.0542353i | ||||
\(996\) | 1.99435i | 0.0631934i | ||||||||
\(997\) | 13.1608 | + | 22.7951i | 0.416805 | + | 0.721928i | 0.995616 | − | 0.0935340i | \(-0.0298164\pi\) |
−0.578811 | + | 0.815462i | \(0.696483\pi\) | |||||||
\(998\) | 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 | 637.2.q.h.589.2 | 12 | ||
7.2 | even | 3 | 637.2.k.g.459.5 | 12 | |||
7.3 | odd | 6 | 637.2.u.h.30.5 | 12 | |||
7.4 | even | 3 | 637.2.u.i.30.5 | 12 | |||
7.5 | odd | 6 | 637.2.k.h.459.5 | 12 | |||
7.6 | odd | 2 | 91.2.q.a.43.2 | yes | 12 | ||
13.6 | odd | 12 | 8281.2.a.by.1.6 | 6 | |||
13.7 | odd | 12 | 8281.2.a.ch.1.1 | 6 | |||
13.10 | even | 6 | inner | 637.2.q.h.491.2 | 12 | ||
21.20 | even | 2 | 819.2.ct.a.316.5 | 12 | |||
28.27 | even | 2 | 1456.2.cc.c.225.1 | 12 | |||
91.6 | even | 12 | 1183.2.a.m.1.6 | 6 | |||
91.10 | odd | 6 | 637.2.k.h.569.2 | 12 | |||
91.20 | even | 12 | 1183.2.a.p.1.1 | 6 | |||
91.23 | even | 6 | 637.2.u.i.361.5 | 12 | |||
91.48 | odd | 6 | 1183.2.c.i.337.10 | 12 | |||
91.62 | odd | 6 | 91.2.q.a.36.2 | ✓ | 12 | ||
91.69 | odd | 6 | 1183.2.c.i.337.3 | 12 | |||
91.75 | odd | 6 | 637.2.u.h.361.5 | 12 | |||
91.88 | even | 6 | 637.2.k.g.569.2 | 12 | |||
273.62 | even | 6 | 819.2.ct.a.127.5 | 12 | |||
364.335 | even | 6 | 1456.2.cc.c.673.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.2 | ✓ | 12 | 91.62 | odd | 6 | ||
91.2.q.a.43.2 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.g.459.5 | 12 | 7.2 | even | 3 | |||
637.2.k.g.569.2 | 12 | 91.88 | even | 6 | |||
637.2.k.h.459.5 | 12 | 7.5 | odd | 6 | |||
637.2.k.h.569.2 | 12 | 91.10 | odd | 6 | |||
637.2.q.h.491.2 | 12 | 13.10 | even | 6 | inner | ||
637.2.q.h.589.2 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.h.30.5 | 12 | 7.3 | odd | 6 | |||
637.2.u.h.361.5 | 12 | 91.75 | odd | 6 | |||
637.2.u.i.30.5 | 12 | 7.4 | even | 3 | |||
637.2.u.i.361.5 | 12 | 91.23 | even | 6 | |||
819.2.ct.a.127.5 | 12 | 273.62 | even | 6 | |||
819.2.ct.a.316.5 | 12 | 21.20 | even | 2 | |||
1183.2.a.m.1.6 | 6 | 91.6 | even | 12 | |||
1183.2.a.p.1.1 | 6 | 91.20 | even | 12 | |||
1183.2.c.i.337.3 | 12 | 91.69 | odd | 6 | |||
1183.2.c.i.337.10 | 12 | 91.48 | odd | 6 | |||
1456.2.cc.c.225.1 | 12 | 28.27 | even | 2 | |||
1456.2.cc.c.673.1 | 12 | 364.335 | even | 6 | |||
8281.2.a.by.1.6 | 6 | 13.6 | odd | 12 | |||
8281.2.a.ch.1.1 | 6 | 13.7 | odd | 12 |