Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (of order \(6\), degree \(2\), not 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 | 459.5 | ||
Root | \(0.759479 + 1.19298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.g.569.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38595i | 0.980016i | 0.871718 | + | 0.490008i | \(0.163006\pi\) | ||||
−0.871718 | + | 0.490008i | \(0.836994\pi\) | |||||||
\(3\) | −1.41289 | − | 2.44719i | −0.815731 | − | 1.41289i | −0.908802 | − | 0.417228i | \(-0.863002\pi\) |
0.0930713 | − | 0.995659i | \(-0.470332\pi\) | |||||||
\(4\) | 0.0791355 | 0.0395678 | ||||||||
\(5\) | −0.449430 | + | 0.259479i | −0.200991 | + | 0.116042i | −0.597118 | − | 0.802154i | \(-0.703687\pi\) |
0.396127 | + | 0.918196i | \(0.370354\pi\) | |||||||
\(6\) | 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 | \(-0.745406\pi\) |
0.272733 | + | 0.962090i | \(0.412072\pi\) | |||||||
\(12\) | −0.111810 | − | 0.193660i | −0.0322766 | − | 0.0559048i | ||||
\(13\) | −1.42641 | + | 3.31140i | −0.395616 | + | 0.918416i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.26999 | + | 0.733228i | 0.327909 | + | 0.189319i | ||||
\(16\) | −3.83547 | −0.958867 | ||||||||
\(17\) | 1.94825 | 0.472521 | 0.236260 | − | 0.971690i | \(-0.424078\pi\) | ||||
0.236260 | + | 0.971690i | \(0.424078\pi\) | |||||||
\(18\) | −5.98335 | − | 3.45449i | −1.41029 | − | 0.814230i | ||||
\(19\) | 2.15740 | + | 1.24558i | 0.494942 | + | 0.285755i | 0.726622 | − | 0.687037i | \(-0.241089\pi\) |
−0.231680 | + | 0.972792i | \(0.574422\pi\) | |||||||
\(20\) | −0.0355659 | + | 0.0205340i | −0.00795277 | + | 0.00459154i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.12550 | − | 1.94943i | −0.239958 | − | 0.415620i | ||||
\(23\) | 9.14058 | 1.90594 | 0.952971 | − | 0.303060i | \(-0.0980083\pi\) | ||||
0.952971 | + | 0.303060i | \(0.0980083\pi\) | |||||||
\(24\) | 7.05179 | − | 4.07135i | 1.43944 | − | 0.831061i | ||||
\(25\) | −2.36534 | + | 4.09689i | −0.473068 | + | 0.819378i | ||||
\(26\) | −4.58944 | − | 1.97694i | −0.900063 | − | 0.387710i | ||||
\(27\) | 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 | ||||
\(31\) | 5.01767 | + | 2.89695i | 0.901201 | + | 0.520308i | 0.877590 | − | 0.479413i | \(-0.159150\pi\) |
0.0236111 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(32\) | 0.447392i | 0.0790885i | ||||||||
\(33\) | 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 | ||||
\(37\) | 10.2293i | 1.68168i | 0.541284 | + | 0.840840i | \(0.317938\pi\) | ||||
−0.541284 | + | 0.840840i | \(0.682062\pi\) | |||||||
\(38\) | −1.72631 | + | 2.99006i | −0.280045 | + | 0.485052i | ||||
\(39\) | 10.1190 | − | 1.18792i | 1.62033 | − | 0.190219i | ||||
\(40\) | −0.747709 | − | 1.29507i | −0.118223 | − | 0.204769i | ||||
\(41\) | −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 | \(0.857562\pi\) | |||||||
\(44\) | −0.111309 | + | 0.0642644i | −0.0167805 | + | 0.00968822i | ||||
\(45\) | − | 2.58700i | − | 0.385647i | ||||||
\(46\) | 12.6684i | 1.86786i | ||||||||
\(47\) | −3.91206 | + | 2.25863i | −0.570632 | + | 0.329455i | −0.757402 | − | 0.652949i | \(-0.773532\pi\) |
0.186770 | + | 0.982404i | \(0.440198\pi\) | |||||||
\(48\) | 5.41908 | + | 9.38612i | 0.782177 | + | 1.35477i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.67810 | − | 3.27825i | −0.803004 | − | 0.463615i | ||||
\(51\) | −2.75266 | − | 4.76775i | −0.385450 | − | 0.667618i | ||||
\(52\) | −0.112880 | + | 0.262049i | −0.0156536 | + | 0.0363397i | ||||
\(53\) | 4.44825 | − | 7.70460i | 0.611015 | − | 1.05831i | −0.380055 | − | 0.924964i | \(-0.624095\pi\) |
0.991070 | − | 0.133344i | \(-0.0425717\pi\) | |||||||
\(54\) | 7.77403i | 1.05791i | ||||||||
\(55\) | 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 | ||||
\(59\) | 6.20526i | 0.807856i | 0.914791 | + | 0.403928i | \(0.132355\pi\) | ||||
−0.914791 | + | 0.403928i | \(0.867645\pi\) | |||||||
\(60\) | 0.100501 | + | 0.0580244i | 0.0129746 | + | 0.00749091i | ||||
\(61\) | −6.73536 | + | 11.6660i | −0.862375 | + | 1.49368i | 0.00725571 | + | 0.999974i | \(0.497690\pi\) |
−0.869630 | + | 0.493703i | \(0.835643\pi\) | |||||||
\(62\) | −4.01504 | + | 6.95426i | −0.509911 | + | 0.883191i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.29100 | −1.03637 | ||||||||
\(65\) | −0.218163 | − | 1.85836i | −0.0270598 | − | 0.230502i | ||||
\(66\) | −3.18042 | + | 5.50865i | −0.391483 | + | 0.678068i | ||||
\(67\) | 7.25094 | − | 4.18633i | 0.885843 | − | 0.511442i | 0.0132624 | − | 0.999912i | \(-0.495778\pi\) |
0.872580 | + | 0.488470i | \(0.162445\pi\) | |||||||
\(68\) | 0.154176 | 0.0186966 | ||||||||
\(69\) | −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 | ||||
\(73\) | 10.2533 | + | 5.91976i | 1.20006 | + | 0.692856i | 0.960569 | − | 0.278042i | \(-0.0896855\pi\) |
0.239493 | + | 0.970898i | \(0.423019\pi\) | |||||||
\(74\) | −14.1773 | −1.64807 | ||||||||
\(75\) | 13.3678 | 1.54359 | ||||||||
\(76\) | 0.170727 | + | 0.0985694i | 0.0195838 | + | 0.0113067i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.64640 | + | 14.0244i | 0.186418 | + | 1.58795i | ||||
\(79\) | −0.491155 | − | 0.850705i | −0.0552592 | − | 0.0957118i | 0.837073 | − | 0.547092i | \(-0.184265\pi\) |
−0.892332 | + | 0.451380i | \(0.850932\pi\) | |||||||
\(80\) | 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 | ||||
\(86\) | 1.19704 | − | 0.691113i | 0.129080 | − | 0.0745246i | ||||
\(87\) | −14.7787 | −1.58444 | ||||||||
\(88\) | −2.34008 | − | 4.05313i | −0.249453 | − | 0.432065i | ||||
\(89\) | − | 12.0190i | − | 1.27401i | −0.770860 | − | 0.637005i | \(-0.780173\pi\) | ||
0.770860 | − | 0.637005i | \(-0.219827\pi\) | |||||||
\(90\) | 3.58546 | 0.377941 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.723345 | 0.0754139 | ||||||||
\(93\) | − | 16.3723i | − | 1.69773i | ||||||
\(94\) | −3.13035 | − | 5.42193i | −0.322871 | − | 0.559229i | ||||
\(95\) | −1.29280 | −0.132639 | ||||||||
\(96\) | 1.09485 | − | 0.632114i | 0.111743 | − | 0.0645149i | ||||
\(97\) | −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 | −0.813231 | − | 0.581940i | \(-0.802294\pi\) |
−0.0973594 | − | 0.995249i | \(-0.531040\pi\) | |||||||
\(102\) | 6.60787 | − | 3.81506i | 0.654277 | − | 0.377747i | ||||
\(103\) | −2.51023 | − | 4.34784i | −0.247340 | − | 0.428406i | 0.715447 | − | 0.698667i | \(-0.246223\pi\) |
−0.962787 | + | 0.270262i | \(0.912890\pi\) | |||||||
\(104\) | −9.54206 | − | 4.11033i | −0.935676 | − | 0.403051i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6782 | + | 6.16507i | 1.03716 | + | 0.598804i | ||||
\(107\) | 6.14456 | 0.594017 | 0.297008 | − | 0.954875i | \(-0.404011\pi\) | ||||
0.297008 | + | 0.954875i | \(0.404011\pi\) | |||||||
\(108\) | 0.443884 | 0.0427127 | ||||||||
\(109\) | −10.3025 | − | 5.94812i | −0.986796 | − | 0.569727i | −0.0824809 | − | 0.996593i | \(-0.526284\pi\) |
−0.904315 | + | 0.426866i | \(0.859618\pi\) | |||||||
\(110\) | 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 | \(0.886827\pi\) | |||||||
\(114\) | 9.75633 | 0.913764 | ||||||||
\(115\) | −4.10805 | + | 2.37178i | −0.383078 | + | 0.221170i | ||||
\(116\) | 0.206938 | − | 0.358427i | 0.0192137 | − | 0.0332791i | ||||
\(117\) | −10.7404 | − | 14.4117i | −0.992951 | − | 1.33236i | ||||
\(118\) | −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 | ||||
\(122\) | −16.1685 | − | 9.33489i | −1.46383 | − | 0.845141i | ||||
\(123\) | 11.8938i | 1.07243i | ||||||||
\(124\) | 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 | \(0.186784\pi\) | |||||||
\(128\) | − | 10.5961i | − | 0.936576i | ||||||
\(129\) | −1.40909 | + | 2.44061i | −0.124063 | + | 0.214884i | ||||
\(130\) | 2.57560 | − | 0.302364i | 0.225895 | − | 0.0265190i | ||||
\(131\) | 4.33687 | + | 7.51168i | 0.378914 | + | 0.656298i | 0.990905 | − | 0.134567i | \(-0.0429643\pi\) |
−0.611990 | + | 0.790865i | \(0.709631\pi\) | |||||||
\(132\) | 0.314535 | + | 0.181597i | 0.0273767 | + | 0.0158060i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.80205 | + | 10.0495i | 0.501221 | + | 0.868141i | ||||
\(135\) | −2.52092 | + | 1.45546i | −0.216967 | + | 0.125266i | ||||
\(136\) | 5.61405i | 0.481401i | ||||||||
\(137\) | 8.51784i | 0.727728i | 0.931452 | + | 0.363864i | \(0.118543\pi\) | ||||
−0.931452 | + | 0.363864i | \(0.881457\pi\) | |||||||
\(138\) | 31.0020 | − | 17.8990i | 2.63907 | − | 1.52367i | ||||
\(139\) | −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 | ||||
\(142\) | −3.60215 | − | 6.23912i | −0.302286 | − | 0.523575i | ||||
\(143\) | −0.682776 | − | 5.81605i | −0.0570966 | − | 0.486363i | ||||
\(144\) | 9.55990 | − | 16.5582i | 0.796658 | − | 1.37985i | ||||
\(145\) | 2.71412i | 0.225396i | ||||||||
\(146\) | −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 | \(-0.377347\pi\) |
−0.614594 | + | 0.788844i | \(0.710680\pi\) | |||||||
\(150\) | 18.5272i | 1.51274i | ||||||||
\(151\) | 10.9610 | + | 6.32831i | 0.891990 | + | 0.514991i | 0.874593 | − | 0.484858i | \(-0.161129\pi\) |
0.0173971 | + | 0.999849i | \(0.494462\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | 0.800771 | − | 0.0940067i | 0.0641130 | − | 0.00752656i | ||||
\(157\) | 5.18457 | − | 8.97993i | 0.413773 | − | 0.716677i | −0.581525 | − | 0.813528i | \(-0.697544\pi\) |
0.995299 | + | 0.0968517i | \(0.0308772\pi\) | |||||||
\(158\) | 1.17904 | − | 0.680717i | 0.0937992 | − | 0.0541550i | ||||
\(159\) | −25.1395 | −1.99369 | ||||||||
\(160\) | −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 | \(-0.544965\pi\) |
−0.927796 | + | 0.373089i | \(0.878299\pi\) | |||||||
\(164\) | −0.288459 | − | 0.166542i | −0.0225249 | − | 0.0130047i | ||||
\(165\) | −2.38176 | −0.185420 | ||||||||
\(166\) | −12.3606 | −0.959371 | ||||||||
\(167\) | 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 | ||||
\(170\) | −0.700640 | − | 1.21354i | −0.0537367 | − | 0.0930746i | ||||
\(171\) | −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 | \(-0.829687\pi\) |
0.871696 | + | 0.490046i | \(0.163020\pi\) | |||||||
\(174\) | − | 20.4825i | − | 1.55278i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.39483 | − | 3.11470i | 0.406650 | − | 0.234780i | ||||
\(177\) | 15.1855 | − | 8.76734i | 1.14141 | − | 0.658993i | ||||
\(178\) | 16.6577 | 1.24855 | ||||||||
\(179\) | −4.90791 | − | 8.50075i | −0.366834 | − | 0.635376i | 0.622234 | − | 0.782831i | \(-0.286225\pi\) |
−0.989069 | + | 0.147455i | \(0.952892\pi\) | |||||||
\(180\) | − | 0.204724i | − | 0.0152592i | ||||||
\(181\) | −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 | ||||||||
\(184\) | 26.3393i | 1.94176i | ||||||||
\(185\) | −2.65427 | − | 4.59733i | −0.195146 | − | 0.338003i | ||||
\(186\) | 22.6912 | 1.66380 | ||||||||
\(187\) | −2.74034 | + | 1.58214i | −0.200394 | + | 0.115697i | ||||
\(188\) | −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 | −0.554838 | − | 0.831958i | \(-0.687220\pi\) |
0.997916 | + | 0.0645248i | \(0.0205531\pi\) | |||||||
\(192\) | 11.7142 | + | 20.2897i | 0.845403 | + | 1.46428i | ||||
\(193\) | 10.0752 | − | 5.81692i | 0.725229 | − | 0.418711i | −0.0914452 | − | 0.995810i | \(-0.529149\pi\) |
0.816674 | + | 0.577099i | \(0.195815\pi\) | |||||||
\(194\) | −3.06454 | − | 5.30794i | −0.220021 | − | 0.381088i | ||||
\(195\) | −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 | \(0.687104\pi\) | |||||||
\(198\) | 11.2213 | 0.797461 | ||||||||
\(199\) | 6.59313 | 0.467375 | 0.233687 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233687 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(200\) | −11.8055 | − | 6.81593i | −0.834777 | − | 0.481959i | ||||
\(201\) | −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 | ||||
\(205\) | 2.18431 | 0.152559 | ||||||||
\(206\) | 6.02590 | − | 3.47906i | 0.419845 | − | 0.242397i | ||||
\(207\) | −22.7829 | + | 39.4611i | −1.58352 | + | 2.74274i | ||||
\(208\) | 5.47096 | − | 12.7007i | 0.379343 | − | 0.880638i | ||||
\(209\) | −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 | ||||
\(213\) | 12.7207 | + | 7.34432i | 0.871610 | + | 0.503224i | ||||
\(214\) | 8.51607i | 0.582146i | ||||||||
\(215\) | 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 | ||||
\(219\) | − | 33.4558i | − | 2.26074i | ||||||
\(220\) | 0.0333504 | − | 0.0577647i | 0.00224849 | − | 0.00389449i | ||||
\(221\) | −2.77901 | + | 6.45144i | −0.186937 | + | 0.433971i | ||||
\(222\) | 20.0309 | + | 34.6945i | 1.34438 | + | 2.32854i | ||||
\(223\) | 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 | ||||
\(226\) | 4.26831 | − | 2.46431i | 0.283924 | − | 0.163923i | ||||
\(227\) | 0.699155i | 0.0464045i | 0.999731 | + | 0.0232023i | \(0.00738617\pi\) | ||||
−0.999731 | + | 0.0232023i | \(0.992614\pi\) | |||||||
\(228\) | − | 0.557070i | − | 0.0368929i | ||||||
\(229\) | 15.8369 | − | 9.14342i | 1.04653 | − | 0.604214i | 0.124854 | − | 0.992175i | \(-0.460154\pi\) |
0.921676 | + | 0.387961i | \(0.126820\pi\) | |||||||
\(230\) | −3.28718 | − | 5.69356i | −0.216750 | − | 0.375422i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.0515 | + | 7.53528i | 0.856872 | + | 0.494715i | ||||
\(233\) | 13.3898 | + | 23.1918i | 0.877194 | + | 1.51934i | 0.854407 | + | 0.519604i | \(0.173920\pi\) |
0.0227864 | + | 0.999740i | \(0.492746\pi\) | |||||||
\(234\) | 19.9739 | − | 14.8857i | 1.30573 | − | 0.973109i | ||||
\(235\) | 1.17213 | − | 2.03019i | 0.0764614 | − | 0.132435i | ||||
\(236\) | 0.491057i | 0.0319651i | ||||||||
\(237\) | −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 | ||||
\(241\) | − | 17.4129i | − | 1.12166i | −0.827931 | − | 0.560830i | \(-0.810482\pi\) | ||
0.827931 | − | 0.560830i | \(-0.189518\pi\) | |||||||
\(242\) | −10.0368 | − | 5.79474i | −0.645189 | − | 0.372500i | ||||
\(243\) | 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 | ||||||||
\(247\) | −7.20195 | + | 5.36731i | −0.458249 | + | 0.341514i | ||||
\(248\) | −8.34782 | + | 14.4588i | −0.530087 | + | 0.918137i | ||||
\(249\) | 21.8253 | − | 12.6008i | 1.38312 | − | 0.798546i | ||||
\(250\) | 6.99879 | 0.442642 | ||||||||
\(251\) | 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 | ||||
\(255\) | 2.47426 | + | 1.42851i | 0.154944 | + | 0.0894570i | ||||
\(256\) | −1.89624 | −0.118515 | ||||||||
\(257\) | −3.67156 | −0.229025 | −0.114513 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114513 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(258\) | −3.38257 | − | 1.95293i | −0.210590 | − | 0.121584i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0172645 | − | 0.147063i | −0.00107070 | − | 0.00912044i | ||||
\(261\) | 13.0357 | + | 22.5784i | 0.806887 | + | 1.39757i | ||||
\(262\) | −10.4108 | + | 6.01070i | −0.643183 | + | 0.371342i | ||||
\(263\) | −9.15964 | − | 15.8650i | −0.564807 | − | 0.978275i | −0.997068 | − | 0.0765263i | \(-0.975617\pi\) |
0.432260 | − | 0.901749i | \(-0.357716\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | 0.573807 | − | 0.331287i | 0.0350508 | − | 0.0202366i | ||||
\(269\) | −27.5429 | −1.67932 | −0.839661 | − | 0.543111i | \(-0.817246\pi\) | ||||
−0.839661 | + | 0.543111i | \(0.817246\pi\) | |||||||
\(270\) | −2.01719 | − | 3.49388i | −0.122762 | − | 0.212631i | ||||
\(271\) | 6.51923i | 0.396015i | 0.980201 | + | 0.198007i | \(0.0634470\pi\) | ||||
−0.980201 | + | 0.198007i | \(0.936553\pi\) | |||||||
\(272\) | −7.47246 | −0.453084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8053 | −0.713186 | ||||||||
\(275\) | − | 7.68338i | − | 0.463325i | ||||||
\(276\) | −1.02200 | − | 1.77016i | −0.0615174 | − | 0.106551i | ||||
\(277\) | −5.44186 | −0.326970 | −0.163485 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163485 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(278\) | 6.04749 | − | 3.49152i | 0.362704 | − | 0.209407i | ||||
\(279\) | −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 | 0.995963 | − | 0.0897658i | \(-0.0286119\pi\) |
−0.575721 | + | 0.817646i | \(0.695279\pi\) | |||||||
\(284\) | −0.356243 | + | 0.205677i | −0.0211391 | + | 0.0122047i | ||||
\(285\) | 1.82658 | + | 3.16374i | 0.108197 | + | 0.187404i | ||||
\(286\) | 8.06077 | − | 0.946296i | 0.476643 | − | 0.0559556i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.93145 | − | 1.11512i | −0.113812 | − | 0.0657093i | ||||
\(289\) | −13.2043 | −0.776724 | ||||||||
\(290\) | −3.76165 | −0.220891 | ||||||||
\(291\) | 10.8222 | + | 6.24819i | 0.634407 | + | 0.366275i | ||||
\(292\) | 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 | ||||
\(296\) | −29.4765 | −1.71328 | ||||||||
\(297\) | −7.88964 | + | 4.55508i | −0.457803 | + | 0.264313i | ||||
\(298\) | 2.33180 | − | 4.03879i | 0.135077 | − | 0.233961i | ||||
\(299\) | −13.0382 | + | 30.2681i | −0.754021 | + | 1.75045i | ||||
\(300\) | 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 | ||||
\(304\) | −8.27465 | − | 4.77737i | −0.474584 | − | 0.274001i | ||||
\(305\) | − | 6.99073i | − | 0.400288i | ||||||
\(306\) | −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 | ||||
\(310\) | − | 4.16727i | − | 0.236685i | ||||||
\(311\) | 7.31134 | − | 12.6636i | 0.414588 | − | 0.718088i | −0.580797 | − | 0.814048i | \(-0.697259\pi\) |
0.995385 | + | 0.0959606i | \(0.0305923\pi\) | |||||||
\(312\) | 3.42309 | + | 29.1587i | 0.193794 | + | 1.65079i | ||||
\(313\) | 8.56641 | + | 14.8375i | 0.484202 | + | 0.838663i | 0.999835 | − | 0.0181467i | \(-0.00577661\pi\) |
−0.515633 | + | 0.856809i | \(0.672443\pi\) | |||||||
\(314\) | 12.4458 | + | 7.18556i | 0.702355 | + | 0.405505i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0388678 | − | 0.0673210i | −0.00218649 | − | 0.00378710i | ||||
\(317\) | −12.1244 | + | 7.00002i | −0.680973 | + | 0.393160i | −0.800222 | − | 0.599704i | \(-0.795285\pi\) |
0.119248 | + | 0.992864i | \(0.461952\pi\) | |||||||
\(318\) | − | 34.8422i | − | 1.95385i | ||||||
\(319\) | 8.49428i | 0.475589i | ||||||||
\(320\) | 3.72622 | − | 2.15134i | 0.208302 | − | 0.120263i | ||||
\(321\) | −8.68157 | − | 15.0369i | −0.484558 | − | 0.839279i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.20317 | + | 2.42670i | 0.233871 | + | 0.135025i | ||||
\(324\) | −0.0354217 | − | 0.0613523i | −0.00196787 | − | 0.00340846i | ||||
\(325\) | −10.1925 | − | 13.6764i | −0.565377 | − | 0.758633i | ||||
\(326\) | 10.9167 | − | 18.9083i | 0.604621 | − | 1.04724i | ||||
\(327\) | 33.6161i | 1.85897i | ||||||||
\(328\) | 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 | \(-0.394240\pi\) |
−0.655574 | + | 0.755131i | \(0.727573\pi\) | |||||||
\(332\) | 0.705771i | 0.0387342i | ||||||||
\(333\) | −44.1611 | − | 25.4964i | −2.42001 | − | 1.39719i | ||||
\(334\) | −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 | \(0.401727\pi\) | |||||||
\(338\) | 13.0929 | − | 12.3775i | 0.712158 | − | 0.673248i | ||||
\(339\) | −5.02440 | + | 8.70251i | −0.272888 | + | 0.472656i | ||||
\(340\) | −0.0692913 | + | 0.0400054i | −0.00375785 | + | 0.00216960i | ||||
\(341\) | −9.41023 | −0.509593 | ||||||||
\(342\) | −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 | ||||
\(346\) | 0.361707 | + | 0.208832i | 0.0194455 | + | 0.0112269i | ||||
\(347\) | −4.92511 | −0.264393 | −0.132197 | − | 0.991223i | \(-0.542203\pi\) | ||||
−0.132197 | + | 0.991223i | \(0.542203\pi\) | |||||||
\(348\) | −1.16952 | −0.0626928 | ||||||||
\(349\) | −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 | ||||
\(352\) | −0.363318 | − | 0.629285i | −0.0193649 | − | 0.0335410i | ||||
\(353\) | 15.5261 | − | 8.96401i | 0.826372 | − | 0.477106i | −0.0262367 | − | 0.999656i | \(-0.508352\pi\) |
0.852609 | + | 0.522550i | \(0.175019\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | 17.3217 | − | 10.0007i | 0.914204 | − | 0.527816i | 0.0324227 | − | 0.999474i | \(-0.489678\pi\) |
0.881781 | + | 0.471658i | \(0.156344\pi\) | |||||||
\(360\) | 7.45466 | 0.392895 | ||||||||
\(361\) | −6.39707 | − | 11.0801i | −0.336688 | − | 0.583161i | ||||
\(362\) | − | 17.2301i | − | 0.905596i | ||||||
\(363\) | 23.6294 | 1.24022 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.14421 | −0.321602 | ||||||||
\(366\) | 52.7566i | 2.75763i | ||||||||
\(367\) | 13.7078 | + | 23.7427i | 0.715544 | + | 1.23936i | 0.962749 | + | 0.270395i | \(0.0871543\pi\) |
−0.247206 | + | 0.968963i | \(0.579512\pi\) | |||||||
\(368\) | −35.0584 | −1.82754 | ||||||||
\(369\) | 18.1710 | − | 10.4910i | 0.945942 | − | 0.546140i | ||||
\(370\) | 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 | −0.583598 | − | 0.812043i | \(-0.698356\pi\) |
0.995049 | + | 0.0993893i | \(0.0316889\pi\) | |||||||
\(374\) | −2.19277 | − | 3.79798i | −0.113385 | − | 0.196389i | ||||
\(375\) | −12.3578 | + | 7.13481i | −0.638156 | + | 0.368440i | ||||
\(376\) | −6.50842 | − | 11.2729i | −0.335646 | − | 0.581356i | ||||
\(377\) | 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 | \(0.594274\pi\) | |||||||
\(380\) | −0.102307 | −0.00524822 | ||||||||
\(381\) | 4.02249 | 0.206078 | ||||||||
\(382\) | 14.6996 | + | 8.48682i | 0.752098 | + | 0.434224i | ||||
\(383\) | 6.89562 | + | 3.98119i | 0.352349 | + | 0.203429i | 0.665720 | − | 0.746202i | \(-0.268125\pi\) |
−0.313370 | + | 0.949631i | \(0.601458\pi\) | |||||||
\(384\) | −25.9308 | + | 14.9712i | −1.32328 | + | 0.763994i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.06198 | + | 13.9638i | 0.410344 | + | 0.710736i | ||||
\(387\) | 4.97159 | 0.252720 | ||||||||
\(388\) | −0.303074 | + | 0.174980i | −0.0153863 | + | 0.00888326i | ||||
\(389\) | 16.0217 | − | 27.7504i | 0.812333 | − | 1.40700i | −0.0988938 | − | 0.995098i | \(-0.531530\pi\) |
0.911227 | − | 0.411904i | \(-0.135136\pi\) | |||||||
\(390\) | −4.37898 | − | 5.87579i | −0.221738 | − | 0.297532i | ||||
\(391\) | 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 | ||||
\(395\) | 0.441479 | + | 0.254888i | 0.0222132 | + | 0.0128248i | ||||
\(396\) | − | 0.640716i | − | 0.0321972i | ||||||
\(397\) | 5.57251 | + | 3.21729i | 0.279676 | + | 0.161471i | 0.633277 | − | 0.773925i | \(-0.281710\pi\) |
−0.353601 | + | 0.935396i | \(0.615043\pi\) | |||||||
\(398\) | 9.13777i | 0.458035i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.07219 | − | 15.7135i | 0.453609 | − | 0.785675i | ||||
\(401\) | 0.533577i | 0.0266456i | 0.999911 | + | 0.0133228i | \(0.00424090\pi\) | ||||
−0.999911 | + | 0.0133228i | \(0.995759\pi\) | |||||||
\(402\) | 16.3953 | − | 28.3975i | 0.817723 | − | 1.41634i | ||||
\(403\) | −16.7502 | + | 12.4832i | −0.834389 | + | 0.621835i | ||||
\(404\) | −0.724195 | − | 1.25434i | −0.0360301 | − | 0.0624059i | ||||
\(405\) | 0.402337 | + | 0.232290i | 0.0199923 | + | 0.0115426i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.30697 | − | 14.3881i | −0.411761 | − | 0.713191i | ||||
\(408\) | 13.7387 | − | 7.93202i | 0.680165 | − | 0.392694i | ||||
\(409\) | 39.7528i | 1.96565i | 0.184547 | + | 0.982824i | \(0.440918\pi\) | ||||
−0.184547 | + | 0.982824i | \(0.559082\pi\) | |||||||
\(410\) | 3.02735i | 0.149510i | ||||||||
\(411\) | 20.8448 | − | 12.0347i | 1.02820 | − | 0.593630i | ||||
\(412\) | −0.198648 | − | 0.344069i | −0.00978670 | − | 0.0169511i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −54.6913 | − | 31.5760i | −2.68793 | − | 1.55188i | ||||
\(415\) | −2.31416 | − | 4.00825i | −0.113598 | − | 0.196757i | ||||
\(416\) | −1.48149 | − | 0.638166i | −0.0726361 | − | 0.0312887i | ||||
\(417\) | −7.11875 | + | 12.3300i | −0.348607 | + | 0.603804i | ||||
\(418\) | − | 5.60761i | − | 0.274277i | ||||||
\(419\) | 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 | ||||
\(423\) | − | 22.5185i | − | 1.09489i | ||||||
\(424\) | 22.2014 | + | 12.8180i | 1.07820 | + | 0.622498i | ||||
\(425\) | −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 | ||||||||
\(429\) | −13.2683 | + | 9.88831i | −0.640600 | + | 0.477412i | ||||
\(430\) | −0.358658 | + | 0.621214i | −0.0172960 | + | 0.0299576i | ||||
\(431\) | 2.34424 | − | 1.35345i | 0.112918 | − | 0.0651932i | −0.442477 | − | 0.896780i | \(-0.645900\pi\) |
0.555395 | + | 0.831586i | \(0.312567\pi\) | |||||||
\(432\) | −21.5137 | −1.03508 | ||||||||
\(433\) | 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 | ||||
\(437\) | 19.7199 | + | 11.3853i | 0.943332 | + | 0.544633i | ||||
\(438\) | 46.3682 | 2.21556 | ||||||||
\(439\) | 38.1702 | 1.82176 | 0.910882 | − | 0.412668i | \(-0.135403\pi\) | ||||
0.910882 | + | 0.412668i | \(0.135403\pi\) | |||||||
\(440\) | 2.10340 | + | 1.21440i | 0.100276 | + | 0.0578942i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.94139 | − | 3.85158i | −0.425298 | − | 0.183201i | ||||
\(443\) | 15.8370 | + | 27.4305i | 0.752440 | + | 1.30326i | 0.946637 | + | 0.322301i | \(0.104456\pi\) |
−0.194198 | + | 0.980962i | \(0.562210\pi\) | |||||||
\(444\) | 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 | \(0.0676638\pi\) | |||||||
\(450\) | 28.3053 | − | 16.3421i | 1.33433 | − | 0.770373i | ||||
\(451\) | 6.83614 | 0.321901 | ||||||||
\(452\) | −0.140708 | − | 0.243713i | −0.00661834 | − | 0.0114633i | ||||
\(453\) | − | 35.7648i | − | 1.68037i | ||||||
\(454\) | −0.968995 | −0.0454772 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.2847 | 0.949920 | ||||||||
\(457\) | − | 31.8281i | − | 1.48886i | −0.667702 | − | 0.744429i | \(-0.732722\pi\) | ||
0.667702 | − | 0.744429i | \(-0.267278\pi\) | |||||||
\(458\) | 12.6723 | + | 21.9491i | 0.592140 | + | 1.02562i | ||||
\(459\) | 10.9281 | 0.510078 | ||||||||
\(460\) | −0.325093 | + | 0.187692i | −0.0151575 | + | 0.00875121i | ||||
\(461\) | −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 | ||||
\(467\) | 0.784697 | + | 1.35913i | 0.0363114 | + | 0.0628932i | 0.883610 | − | 0.468224i | \(-0.155106\pi\) |
−0.847299 | + | 0.531117i | \(0.821773\pi\) | |||||||
\(468\) | −0.849948 | − | 1.14048i | −0.0392889 | − | 0.0527185i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.81375 | + | 1.62452i | 0.129788 | + | 0.0749334i | ||||
\(471\) | −29.3008 | −1.35011 | ||||||||
\(472\) | −17.8810 | −0.823039 | ||||||||
\(473\) | 1.40278 | + | 0.809896i | 0.0644999 | + | 0.0372391i | ||||
\(474\) | −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 | ||||
\(478\) | 23.0313 | 1.05343 | ||||||||
\(479\) | 6.68501 | − | 3.85959i | 0.305446 | − | 0.176349i | −0.339441 | − | 0.940627i | \(-0.610238\pi\) |
0.644887 | + | 0.764278i | \(0.276905\pi\) | |||||||
\(480\) | −0.328040 | + | 0.568182i | −0.0149729 | + | 0.0259338i | ||||
\(481\) | −33.8731 | − | 14.5911i | −1.54448 | − | 0.665299i | ||||
\(482\) | 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 | ||||
\(486\) | 17.1612 | + | 9.90803i | 0.778448 | + | 0.449437i | ||||
\(487\) | − | 0.0761801i | − | 0.00345205i | −0.999999 | − | 0.00172602i | \(-0.999451\pi\) | ||
0.999999 | − | 0.00172602i | \(-0.000549411\pi\) | |||||||
\(488\) | −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 | \(0.153827\pi\) | |||||||
\(492\) | 0.941220i | 0.0424335i | ||||||||
\(493\) | 5.09464 | − | 8.82418i | 0.229451 | − | 0.397421i | ||||
\(494\) | −7.43884 | − | 9.98156i | −0.334689 | − | 0.449092i | ||||
\(495\) | 2.10085 | + | 3.63878i | 0.0944262 | + | 0.163551i | ||||
\(496\) | −19.2451 | − | 11.1112i | −0.864131 | − | 0.498906i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.4642 | + | 30.2488i | 0.782589 | + | 1.35548i | ||||
\(499\) | 7.21826 | − | 4.16747i | 0.323134 | − | 0.186561i | −0.329655 | − | 0.944102i | \(-0.606932\pi\) |
0.652789 | + | 0.757540i | \(0.273599\pi\) | |||||||
\(500\) | − | 0.399619i | − | 0.0178715i | ||||||
\(501\) | − | 46.3387i | − | 2.07026i | ||||||
\(502\) | −7.74152 | + | 4.46957i | −0.345521 | + | 0.199487i | ||||
\(503\) | 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 | ||||
\(506\) | −10.2878 | − | 17.8189i | −0.457347 | − | 0.792148i | ||||
\(507\) | −10.5002 | + | 35.2024i | −0.466329 | + | 1.56339i | ||||
\(508\) | −0.0563247 | + | 0.0975572i | −0.00249900 | + | 0.00432840i | ||||
\(509\) | 14.8256i | 0.657135i | 0.944480 | + | 0.328568i | \(0.106566\pi\) | ||||
−0.944480 | + | 0.328568i | \(0.893434\pi\) | |||||||
\(510\) | −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 | ||||
\(514\) | − | 5.08860i | − | 0.224449i | ||||||
\(515\) | 2.25634 | + | 1.30270i | 0.0994264 | + | 0.0574038i | ||||
\(516\) | −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 | ||||||||
\(520\) | 5.35503 | − | 0.628655i | 0.234834 | − | 0.0275683i | ||||
\(521\) | −0.167194 | + | 0.289588i | −0.00732489 | + | 0.0126871i | −0.869665 | − | 0.493643i | \(-0.835665\pi\) |
0.862340 | + | 0.506330i | \(0.168998\pi\) | |||||||
\(522\) | −31.2926 | + | 18.0668i | −1.36964 | + | 0.790763i | ||||
\(523\) | 32.5065 | 1.42141 | 0.710705 | − | 0.703490i | \(-0.248376\pi\) | ||||
0.710705 | + | 0.703490i | \(0.248376\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | −15.2446 | − | 8.80145i | −0.663434 | − | 0.383034i | ||||
\(529\) | 60.5502 | 2.63262 | ||||||||
\(530\) | −6.39881 | −0.277947 | ||||||||
\(531\) | −26.7890 | − | 15.4666i | −1.16254 | − | 0.671194i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1683 | − | 9.06855i | 0.527070 | − | 0.392803i | ||||
\(534\) | −23.5355 | − | 40.7647i | −1.01848 | − | 1.76406i | ||||
\(535\) | −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 | ||||
\(541\) | −9.18120 | + | 5.30077i | −0.394731 | + | 0.227898i | −0.684208 | − | 0.729287i | \(-0.739852\pi\) |
0.289477 | + | 0.957185i | \(0.406519\pi\) | |||||||
\(542\) | −9.03534 | −0.388101 | ||||||||
\(543\) | 17.5650 | + | 30.4235i | 0.753786 | + | 1.30560i | ||||
\(544\) | 0.871633i | 0.0373709i | ||||||||
\(545\) | 6.17364 | 0.264450 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2327 | 0.437519 | 0.218760 | − | 0.975779i | \(-0.429799\pi\) | ||||
0.218760 | + | 0.975779i | \(0.429799\pi\) | |||||||
\(548\) | 0.674064i | 0.0287946i | ||||||||
\(549\) | −33.5758 | − | 58.1549i | −1.43298 | − | 2.48199i | ||||
\(550\) | 10.6488 | 0.454067 | ||||||||
\(551\) | 11.2831 | − | 6.51432i | 0.480677 | − | 0.277519i | ||||
\(552\) | 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 | \(-0.903730\pi\) |
−0.219359 | + | 0.975644i | \(0.570397\pi\) | |||||||
\(558\) | −20.0150 | − | 34.6670i | −0.847302 | − | 1.46757i | ||||
\(559\) | 3.57133 | − | 0.419257i | 0.151051 | − | 0.0177327i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.74359 | + | 4.47076i | 0.326934 | + | 0.188756i | ||||
\(562\) | 4.90956 | 0.207097 | ||||||||
\(563\) | 10.7913 | 0.454800 | 0.227400 | − | 0.973801i | \(-0.426978\pi\) | ||||
0.227400 | + | 0.973801i | \(0.426978\pi\) | |||||||
\(564\) | 0.874811 | + | 0.505072i | 0.0368362 | + | 0.0212674i | ||||
\(565\) | 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 | ||||
\(569\) | 24.6014 | 1.03134 | 0.515672 | − | 0.856786i | \(-0.327542\pi\) | ||||
0.515672 | + | 0.856786i | \(0.327542\pi\) | |||||||
\(570\) | −4.38479 | + | 2.53156i | −0.183659 | + | 0.106035i | ||||
\(571\) | 8.28621 | − | 14.3521i | 0.346767 | − | 0.600618i | −0.638906 | − | 0.769285i | \(-0.720613\pi\) |
0.985673 | + | 0.168667i | \(0.0539461\pi\) | |||||||
\(572\) | −0.0540319 | − | 0.460256i | −0.00225919 | − | 0.0192443i | ||||
\(573\) | −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 | ||||
\(577\) | 12.6969 | + | 7.33053i | 0.528577 | + | 0.305174i | 0.740437 | − | 0.672126i | \(-0.234619\pi\) |
−0.211860 | + | 0.977300i | \(0.567952\pi\) | |||||||
\(578\) | − | 18.3005i | − | 0.761202i | ||||||
\(579\) | −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 | ||||
\(583\) | 14.4493i | 0.598431i | ||||||||
\(584\) | −17.0583 | + | 29.5458i | −0.705877 | + | 1.22262i | ||||
\(585\) | 8.56658 | + | 3.69013i | 0.354185 | + | 0.152568i | ||||
\(586\) | 5.78587 | + | 10.0214i | 0.239012 | + | 0.413981i | ||||
\(587\) | −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 | ||||
\(590\) | 3.86519 | − | 2.23157i | 0.159127 | − | 0.0918722i | ||||
\(591\) | 5.08963i | 0.209359i | ||||||||
\(592\) | − | 39.2340i | − | 1.61251i | ||||||
\(593\) | 14.2283 | − | 8.21471i | 0.584286 | − | 0.337338i | −0.178549 | − | 0.983931i | \(-0.557140\pi\) |
0.762835 | + | 0.646593i | \(0.223807\pi\) | |||||||
\(594\) | −6.31313 | − | 10.9347i | −0.259031 | − | 0.448655i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.230608 | − | 0.133142i | −0.00944608 | − | 0.00545370i | ||||
\(597\) | −9.31535 | − | 16.1347i | −0.381252 | − | 0.660348i | ||||
\(598\) | −41.9501 | − | 18.0704i | −1.71547 | − | 0.738953i | ||||
\(599\) | −6.04094 | + | 10.4632i | −0.246826 | + | 0.427516i | −0.962644 | − | 0.270772i | \(-0.912721\pi\) |
0.715817 | + | 0.698288i | \(0.246054\pi\) | |||||||
\(600\) | 38.5206i | 1.57259i | ||||||||
\(601\) | 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 | ||||
\(605\) | − | 4.33957i | − | 0.176429i | ||||||
\(606\) | −62.0770 | − | 35.8401i | −2.52170 | − | 1.45591i | ||||
\(607\) | 17.7825 | − | 30.8001i | 0.721768 | − | 1.25014i | −0.238523 | − | 0.971137i | \(-0.576663\pi\) |
0.960291 | − | 0.279002i | \(-0.0900035\pi\) | |||||||
\(608\) | −0.557261 | + | 0.965205i | −0.0225999 | + | 0.0391442i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.68882 | 0.392289 | ||||||||
\(611\) | −1.89900 | − | 16.1761i | −0.0768252 | − | 0.654415i | ||||
\(612\) | −0.384284 | + | 0.665599i | −0.0155338 | + | 0.0269052i | ||||
\(613\) | 10.3376 | − | 5.96839i | 0.417530 | − | 0.241061i | −0.276490 | − | 0.961017i | \(-0.589171\pi\) |
0.694020 | + | 0.719956i | \(0.255838\pi\) | |||||||
\(614\) | 11.5500 | 0.466120 | ||||||||
\(615\) | −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 | ||||
\(619\) | −24.7312 | − | 14.2786i | −0.994031 | − | 0.573904i | −0.0875541 | − | 0.996160i | \(-0.527905\pi\) |
−0.906477 | + | 0.422256i | \(0.861238\pi\) | |||||||
\(620\) | −0.237944 | −0.00955606 | ||||||||
\(621\) | 51.2710 | 2.05743 | ||||||||
\(622\) | 17.5512 | + | 10.1332i | 0.703738 | + | 0.406303i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −38.8110 | + | 4.55623i | −1.55368 | + | 0.182395i | ||||
\(625\) | −10.5164 | − | 18.2149i | −0.420656 | − | 0.728597i | ||||
\(626\) | −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 | \(0.980108\pi\) | |||||||
\(632\) | 2.45138 | − | 1.41530i | 0.0975106 | − | 0.0562978i | ||||
\(633\) | 30.2921 | 1.20400 | ||||||||
\(634\) | −9.70169 | − | 16.8038i | −0.385303 | − | 0.667365i | ||||
\(635\) | − | 0.738735i | − | 0.0293158i | ||||||
\(636\) | −1.98943 | −0.0788860 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7727 | −0.466085 | ||||||||
\(639\) | − | 25.9125i | − | 1.02508i | ||||||
\(640\) | 2.74947 | + | 4.76222i | 0.108682 | + | 0.188243i | ||||
\(641\) | 2.53300 | 0.100048 | 0.0500238 | − | 0.998748i | \(-0.484070\pi\) | ||||
0.0500238 | + | 0.998748i | \(0.484070\pi\) | |||||||
\(642\) | 20.8405 | − | 12.0322i | 0.822507 | − | 0.474875i | ||||
\(643\) | −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 | 0.583647 | − | 0.812008i | \(-0.301625\pi\) |
−0.995043 | + | 0.0994494i | \(0.968292\pi\) | |||||||
\(648\) | 2.23404 | − | 1.28982i | 0.0877612 | − | 0.0506690i | ||||
\(649\) | −5.03917 | − | 8.72810i | −0.197805 | − | 0.342608i | ||||
\(650\) | 18.9549 | − | 14.1263i | 0.743473 | − | 0.554079i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.07963 | − | 0.623326i | −0.0422817 | − | 0.0244113i | ||||
\(653\) | −48.1160 | −1.88292 | −0.941461 | − | 0.337121i | \(-0.890547\pi\) | ||||
−0.941461 | + | 0.337121i | \(0.890547\pi\) | |||||||
\(654\) | −46.5903 | −1.82183 | ||||||||
\(655\) | −3.89824 | − | 2.25065i | −0.152317 | − | 0.0879401i | ||||
\(656\) | 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 | \(0.819588\pi\) | |||||||
\(660\) | −0.188482 | −0.00733664 | ||||||||
\(661\) | −0.552034 | + | 0.318717i | −0.0214716 | + | 0.0123966i | −0.510697 | − | 0.859761i | \(-0.670613\pi\) |
0.489226 | + | 0.872157i | \(0.337279\pi\) | |||||||
\(662\) | 4.79537 | − | 8.30582i | 0.186377 | − | 0.322815i | ||||
\(663\) | 19.7143 | − | 2.31437i | 0.765642 | − | 0.0898827i | ||||
\(664\) | −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 | ||||
\(668\) | 1.12385 | + | 0.648856i | 0.0434831 | + | 0.0251050i | ||||
\(669\) | − | 36.4181i | − | 1.40801i | ||||||
\(670\) | −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 | \(0.0706988\pi\) | |||||||
\(674\) | 15.4616i | 0.595559i | ||||||||
\(675\) | −13.2676 | + | 22.9801i | −0.510669 | + | 0.884505i | ||||
\(676\) | −0.706735 | − | 0.747581i | −0.0271821 | − | 0.0287531i | ||||
\(677\) | −5.84060 | − | 10.1162i | −0.224473 | − | 0.388798i | 0.731689 | − | 0.681639i | \(-0.238733\pi\) |
−0.956161 | + | 0.292841i | \(0.905399\pi\) | |||||||
\(678\) | −12.0613 | − | 6.96358i | −0.463210 | − | 0.267435i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.45673 | − | 2.52312i | −0.0558629 | − | 0.0967574i | ||||
\(681\) | 1.71097 | − | 0.987826i | 0.0655643 | − | 0.0378536i | ||||
\(682\) | − | 13.0421i | − | 0.499409i | ||||||
\(683\) | 22.9114i | 0.876680i | 0.898809 | + | 0.438340i | \(0.144433\pi\) | ||||
−0.898809 | + | 0.438340i | \(0.855567\pi\) | |||||||
\(684\) | −0.851075 | + | 0.491369i | −0.0325417 | + | 0.0187879i | ||||
\(685\) | −2.21020 | − | 3.82817i | −0.0844473 | − | 0.146267i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44.7514 | − | 25.8372i | −1.70737 | − | 0.985752i | ||||
\(688\) | 1.91258 | + | 3.31268i | 0.0729163 | + | 0.126295i | ||||
\(689\) | 19.1679 | + | 25.7199i | 0.730240 | + | 0.979849i | ||||
\(690\) | −9.28883 | + | 16.0887i | −0.353620 | + | 0.612487i | ||||
\(691\) | − | 47.2325i | − | 1.79681i | −0.439167 | − | 0.898405i | \(-0.644726\pi\) | ||
0.439167 | − | 0.898405i | \(-0.355274\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | − | 42.5860i | − | 1.61422i | ||||||
\(697\) | −7.10163 | − | 4.10013i | −0.268994 | − | 0.155303i | ||||
\(698\) | 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 | \(0.425938\pi\) | |||||||
\(702\) | −25.7429 | − | 11.0890i | −0.971603 | − | 0.418527i | ||||
\(703\) | −12.7413 | + | 22.0686i | −0.480548 | + | 0.832334i | ||||
\(704\) | 11.6618 | − | 6.73295i | 0.439521 | − | 0.253758i | ||||
\(705\) | −6.62435 | −0.249488 | ||||||||
\(706\) | 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 | \(-0.224297\pi\) |
−0.180062 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(710\) | 3.23783 | + | 1.86936i | 0.121514 | + | 0.0701560i | ||||
\(711\) | 4.89681 | 0.183645 | ||||||||
\(712\) | 34.6337 | 1.29795 | ||||||||
\(713\) | 45.8644 | + | 26.4798i | 1.71764 | + | 0.991678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.81600 | + | 2.43674i | 0.0679146 | + | 0.0911290i | ||||
\(716\) | −0.388390 | − | 0.672711i | −0.0145148 | − | 0.0251404i | ||||
\(717\) | −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 | \(-0.887767\pi\) |
0.768304 | + | 0.640085i | \(0.221101\pi\) | |||||||
\(720\) | 9.92235i | 0.369784i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.3564 | − | 8.86604i | 0.571507 | − | 0.329960i | ||||
\(723\) | −42.6126 | + | 24.6024i | −1.58478 | + | 0.914973i | ||||
\(724\) | −0.983812 | −0.0365631 | ||||||||
\(725\) | 12.3706 | + | 21.4266i | 0.459434 | + | 0.795763i | ||||
\(726\) | 32.7493i | 1.21544i | ||||||||
\(727\) | −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 | ||||||||
\(730\) | − | 8.51558i | − | 0.315176i | ||||||
\(731\) | −0.971507 | − | 1.68270i | −0.0359325 | − | 0.0622369i | ||||
\(732\) | 3.01231 | 0.111338 | ||||||||
\(733\) | −40.2134 | + | 23.2172i | −1.48532 | + | 0.857547i | −0.999860 | − | 0.0167147i | \(-0.994679\pi\) |
−0.485455 | + | 0.874262i | \(0.661346\pi\) | |||||||
\(734\) | −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 | \(-0.655832\pi\) |
0.529182 | + | 0.848508i | \(0.322499\pi\) | |||||||
\(740\) | −0.210047 | − | 0.363813i | −0.00772149 | − | 0.0133740i | ||||
\(741\) | 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 | \(0.458601\pi\) | |||||||
\(744\) | 47.1781 | 1.72963 | ||||||||
\(745\) | 1.74624 | 0.0639773 | ||||||||
\(746\) | 19.0757 | + | 11.0134i | 0.698412 | + | 0.403228i | ||||
\(747\) | −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 | ||||
\(751\) | 20.7743 | 0.758064 | 0.379032 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379032 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(752\) | 15.0046 | − | 8.66289i | 0.547160 | − | 0.315903i | ||||
\(753\) | 9.11286 | − | 15.7839i | 0.332091 | − | 0.575199i | ||||
\(754\) | −20.9554 | + | 15.6172i | −0.763150 | + | 0.568744i | ||||
\(755\) | −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 | ||||
\(759\) | 36.3304 | + | 20.9754i | 1.31871 | + | 0.761358i | ||||
\(760\) | − | 3.72532i | − | 0.135131i | ||||||
\(761\) | 10.7302 | + | 6.19511i | 0.388971 | + | 0.224573i | 0.681714 | − | 0.731619i | \(-0.261235\pi\) |
−0.292743 | + | 0.956191i | \(0.594568\pi\) | |||||||
\(762\) | 5.57497i | 0.201960i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.484583 | − | 0.839323i | 0.0175316 | − | 0.0303656i | ||||
\(765\) | − | 5.04013i | − | 0.182226i | ||||||
\(766\) | −5.51773 | + | 9.55700i | −0.199364 | + | 0.345308i | ||||
\(767\) | −20.5481 | − | 8.85127i | −0.741948 | − | 0.319601i | ||||
\(768\) | 2.67917 | + | 4.64046i | 0.0966763 | + | 0.167448i | ||||
\(769\) | 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 | ||||
\(772\) | 0.797307 | − | 0.460325i | 0.0286957 | − | 0.0165675i | ||||
\(773\) | − | 43.8042i | − | 1.57553i | −0.615977 | − | 0.787764i | \(-0.711239\pi\) | ||
0.615977 | − | 0.787764i | \(-0.288761\pi\) | |||||||
\(774\) | 6.89039i | 0.247670i | ||||||||
\(775\) | −23.7370 | + | 13.7046i | −0.852659 | + | 0.492283i | ||||
\(776\) | −6.37159 | − | 11.0359i | −0.228727 | − | 0.396166i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.4608 | + | 22.2053i | 1.37889 | + | 0.796100i | ||||
\(779\) | −5.24267 | − | 9.08058i | −0.187838 | − | 0.325346i | ||||
\(780\) | −0.335498 | + | 0.250032i | −0.0120128 | + | 0.00895260i | ||||
\(781\) | 4.22127 | − | 7.31145i | 0.151049 | − | 0.261624i | ||||
\(782\) | 24.6813i | 0.882600i | ||||||||
\(783\) | 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 | ||||
\(787\) | − | 24.8009i | − | 0.884057i | −0.897001 | − | 0.442029i | \(-0.854259\pi\) | ||
0.897001 | − | 0.442029i | \(-0.145741\pi\) | |||||||
\(788\) | −0.123439 | − | 0.0712673i | −0.00439732 | − | 0.00253879i | ||||
\(789\) | −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 | ||||||||
\(793\) | −29.0233 | − | 38.9440i | −1.03065 | − | 1.38294i | ||||
\(794\) | −4.45901 | + | 7.72323i | −0.158244 | + | 0.274087i | ||||
\(795\) | 11.2985 | − | 6.52316i | 0.400715 | − | 0.231353i | ||||
\(796\) | 0.521751 | 0.0184930 | ||||||||
\(797\) | 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 | ||||
\(801\) | 51.8876 | + | 29.9573i | 1.83336 | + | 1.05849i | ||||
\(802\) | −0.739513 | −0.0261131 | ||||||||
\(803\) | −19.2293 | −0.678587 | ||||||||
\(804\) | −1.62145 | − | 0.936144i | −0.0571841 | − | 0.0330152i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.3012 | − | 23.2150i | −0.609408 | − | 0.817715i | ||||
\(807\) | 38.9151 | + | 67.4028i | 1.36987 | + | 2.37269i | ||||
\(808\) | 45.6747 | − | 26.3703i | 1.60683 | − | 0.927704i | ||||
\(809\) | −0.690968 | − | 1.19679i | −0.0242932 | − | 0.0420770i | 0.853623 | − | 0.520891i | \(-0.174400\pi\) |
−0.877916 | + | 0.478814i | \(0.841067\pi\) | |||||||
\(810\) | −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 | ||||
\(814\) | 19.9412 | − | 11.5131i | 0.698939 | − | 0.403533i | ||||
\(815\) | 8.17533 | 0.286369 | ||||||||
\(816\) | 10.5577 | + | 18.2865i | 0.369595 | + | 0.640157i | ||||
\(817\) | − | 2.48446i | − | 0.0869201i | ||||||
\(818\) | −55.0954 | −1.92637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.172856 | 0.00603640 | ||||||||
\(821\) | 10.5425i | 0.367936i | 0.982932 | + | 0.183968i | \(0.0588943\pi\) | ||||
−0.982932 | + | 0.183968i | \(0.941106\pi\) | |||||||
\(822\) | 16.6796 | + | 28.8899i | 0.581767 | + | 1.00765i | ||||
\(823\) | −14.8330 | −0.517047 | −0.258524 | − | 0.966005i | \(-0.583236\pi\) | ||||
−0.258524 | + | 0.966005i | \(0.583236\pi\) | |||||||
\(824\) | 12.5287 | − | 7.23343i | 0.436457 | − | 0.251988i | ||||
\(825\) | −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 | 0.866429 | − | 0.499301i | \(-0.166410\pi\) |
−0.865622 | + | 0.500699i | \(0.833076\pi\) | |||||||
\(830\) | 5.55524 | − | 3.20732i | 0.192825 | − | 0.111328i | ||||
\(831\) | 7.68873 | + | 13.3173i | 0.266719 | + | 0.461971i | ||||
\(832\) | 11.8264 | − | 27.4548i | 0.410006 | − | 0.951823i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.0888 | − | 9.86624i | −0.591738 | − | 0.341640i | ||||
\(835\) | −8.51016 | −0.294506 | ||||||||
\(836\) | −0.320185 | −0.0110738 | ||||||||
\(837\) | 28.1449 | + | 16.2495i | 0.972831 | + | 0.561664i | ||||
\(838\) | 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 | ||||
\(842\) | −32.2121 | −1.11010 | ||||||||
\(843\) | −8.66886 | + | 5.00497i | −0.298572 | + | 0.172380i | ||||
\(844\) | −0.424164 | + | 0.734673i | −0.0146003 | + | 0.0252885i | ||||
\(845\) | 6.46497 | + | 1.92837i | 0.222402 | + | 0.0663380i | ||||
\(846\) | 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 | ||||
\(850\) | −11.0624 | − | 6.38686i | −0.379436 | − | 0.219068i | ||||
\(851\) | 93.5013i | 3.20518i | ||||||||
\(852\) | 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 | ||||
\(856\) | 17.7061i | 0.605181i | ||||||||
\(857\) | 18.5268 | − | 32.0893i | 0.632862 | − | 1.09615i | −0.354101 | − | 0.935207i | \(-0.615213\pi\) |
0.986964 | − | 0.160943i | \(-0.0514534\pi\) | |||||||
\(858\) | −13.7047 | − | 18.3892i | −0.467872 | − | 0.627798i | ||||
\(859\) | −2.12169 | − | 3.67488i | −0.0723912 | − | 0.125385i | 0.827558 | − | 0.561381i | \(-0.189730\pi\) |
−0.899949 | + | 0.435996i | \(0.856396\pi\) | |||||||
\(860\) | 0.0354702 | + | 0.0204788i | 0.00120953 | + | 0.000698320i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.87581 | + | 3.24900i | 0.0638904 | + | 0.110661i | ||||
\(863\) | −6.49563 | + | 3.75025i | −0.221114 | + | 0.127660i | −0.606466 | − | 0.795110i | \(-0.707413\pi\) |
0.385352 | + | 0.922770i | \(0.374080\pi\) | |||||||
\(864\) | 2.50949i | 0.0853746i | ||||||||
\(865\) | 0.156390i | 0.00531743i | ||||||||
\(866\) | −6.98425 | + | 4.03236i | −0.237335 | + | 0.137025i | ||||
\(867\) | 18.6562 | + | 32.3135i | 0.633598 | + | 1.09742i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.38168 | + | 0.797714i | 0.0468703 | + | 0.0270606i | ||||
\(870\) | 5.31478 | + | 9.20547i | 0.180188 | + | 0.312095i | ||||
\(871\) | 3.51976 | + | 29.9822i | 0.119263 | + | 1.01591i | ||||
\(872\) | 17.1400 | − | 29.6874i | 0.580434 | − | 1.00534i | ||||
\(873\) | − | 22.0451i | − | 0.746113i | ||||||
\(874\) | −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 | \(-0.174827\pi\) |
−0.0256330 | + | 0.999671i | \(0.508160\pi\) | |||||||
\(878\) | 52.9021i | 1.78536i | ||||||||
\(879\) | −20.4324 | − | 11.7966i | −0.689166 | − | 0.397890i | ||||
\(880\) | −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 | \(0.658352\pi\) | |||||||
\(884\) | −0.219919 | + | 0.510538i | −0.00739667 | + | 0.0171713i | ||||
\(885\) | −4.54987 | + | 7.88061i | −0.152942 | + | 0.264904i | ||||
\(886\) | −38.0174 | + | 21.9494i | −1.27722 | + | 0.737403i | ||||
\(887\) | 43.7186 | 1.46793 | 0.733963 | − | 0.679189i | \(-0.237669\pi\) | ||||
0.733963 | + | 0.679189i | \(0.237669\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 0.883247 | + | 0.509943i | 0.0295733 | + | 0.0170742i | ||||
\(893\) | −11.2532 | −0.376573 | ||||||||
\(894\) | −13.1783 | −0.440747 | ||||||||
\(895\) | 4.41152 | + | 2.54699i | 0.147461 | + | 0.0851366i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 92.4934 | − | 10.8583i | 3.08826 | − | 0.362547i | ||||
\(898\) | 21.7629 | + | 37.6944i | 0.726236 | + | 1.25788i | ||||
\(899\) | 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 | ||||
\(905\) | 5.58731 | − | 3.22583i | 0.185728 | − | 0.107230i | ||||
\(906\) | 49.5683 | 1.64679 | ||||||||
\(907\) | −18.3493 | − | 31.7818i | −0.609277 | − | 1.05530i | −0.991360 | − | 0.131171i | \(-0.958126\pi\) |
0.382083 | − | 0.924128i | \(-0.375207\pi\) | |||||||
\(908\) | 0.0553280i | 0.00183612i | ||||||||
\(909\) | 91.2387 | 3.02620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.5211 | −1.17686 | −0.588432 | − | 0.808546i | \(-0.700255\pi\) | ||||
−0.588432 | + | 0.808546i | \(0.700255\pi\) | |||||||
\(912\) | 26.9995i | 0.894044i | ||||||||
\(913\) | −7.24254 | − | 12.5444i | −0.239693 | − | 0.415161i | ||||
\(914\) | 44.1123 | 1.45911 | ||||||||
\(915\) | −17.1077 | + | 9.87711i | −0.565562 | + | 0.326527i | ||||
\(916\) | 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 | −0.988250 | − | 0.152844i | \(-0.951157\pi\) |
0.626492 | + | 0.779428i | \(0.284490\pi\) | |||||||
\(920\) | −6.83449 | − | 11.8377i | −0.225327 | − | 0.390277i | ||||
\(921\) | −20.3940 | + | 11.7745i | −0.672005 | + | 0.387982i | ||||
\(922\) | −0.808222 | − | 1.39988i | −0.0266174 | − | 0.0461026i | ||||
\(923\) | −2.18521 | − | 18.6142i | −0.0719272 | − | 0.612693i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.9082 | − | 24.1957i | −1.37793 | − | 0.795549i | ||||
\(926\) | 28.1959 | 0.926575 | ||||||||
\(927\) | 25.0270 | 0.821993 | ||||||||
\(928\) | 2.02636 | + | 1.16992i | 0.0665186 | + | 0.0384045i | ||||
\(929\) | −13.4383 | − | 7.75858i | −0.440895 | − | 0.254551i | 0.263082 | − | 0.964773i | \(-0.415261\pi\) |
−0.703977 | + | 0.710223i | \(0.748594\pi\) | |||||||
\(930\) | −10.1981 | + | 5.88788i | −0.334409 | + | 0.193071i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.05961 | + | 1.83529i | 0.0347086 | + | 0.0601171i | ||||
\(933\) | −41.3204 | −1.35277 | ||||||||
\(934\) | −1.88370 | + | 1.08755i | −0.0616364 | + | 0.0355858i | ||||
\(935\) | 0.821061 | − | 1.42212i | 0.0268516 | − | 0.0465083i | ||||
\(936\) | 41.5284 | − | 30.9494i | 1.35740 | − | 1.01161i | ||||
\(937\) | −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 | ||||
\(941\) | −44.6814 | − | 25.7968i | −1.45657 | − | 0.840952i | −0.457731 | − | 0.889091i | \(-0.651338\pi\) |
−0.998841 | + | 0.0481384i | \(0.984671\pi\) | |||||||
\(942\) | − | 40.6096i | − | 1.32313i | ||||||
\(943\) | −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 | ||||
\(947\) | 4.98209i | 0.161896i | 0.996718 | + | 0.0809482i | \(0.0257948\pi\) | ||||
−0.996718 | + | 0.0809482i | \(0.974205\pi\) | |||||||
\(948\) | −0.109832 | + | 0.190234i | −0.00356717 | + | 0.00617851i | ||||
\(949\) | −34.2282 | + | 25.5088i | −1.11109 | + | 0.828051i | ||||
\(950\) | −8.16663 | − | 14.1450i | −0.264961 | − | 0.458925i | ||||
\(951\) | 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 | \(0.670453\pi\) | |||||||
\(954\) | −53.2309 | + | 30.7329i | −1.72341 | + | 0.995013i | ||||
\(955\) | 6.35562i | 0.205663i | ||||||||
\(956\) | − | 1.31505i | − | 0.0425317i | ||||||
\(957\) | 20.7871 | − | 12.0015i | 0.671953 | − | 0.387952i | ||||
\(958\) | 5.34921 | + | 9.26511i | 0.172825 | + | 0.299342i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.5295 | − | 6.07919i | −0.339837 | − | 0.196205i | ||||
\(961\) | 1.28469 | + | 2.22516i | 0.0414418 | + | 0.0717792i | ||||
\(962\) | 20.2226 | − | 46.9465i | 0.652004 | − | 1.51362i | ||||
\(963\) | −15.3153 | + | 26.5269i | −0.493529 | + | 0.854817i | ||||
\(964\) | − | 1.37798i | − | 0.0443816i | ||||||
\(965\) | −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 | ||||
\(969\) | − | 13.7146i | − | 0.440577i | ||||||
\(970\) | 2.75459 | + | 1.59036i | 0.0884446 | + | 0.0510635i | ||||
\(971\) | 22.0620 | − | 38.2125i | 0.708003 | − | 1.22630i | −0.257594 | − | 0.966253i | \(-0.582930\pi\) |
0.965597 | − | 0.260044i | \(-0.0837371\pi\) | |||||||
\(972\) | 0.565732 | − | 0.979876i | 0.0181459 | − | 0.0314295i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.105582 | 0.00338306 | ||||||||
\(975\) | −19.0681 | + | 44.2662i | −0.610667 | + | 1.41765i | ||||
\(976\) | 25.8333 | − | 44.7445i | 0.826902 | − | 1.43224i | ||||
\(977\) | 12.9925 | − | 7.50121i | 0.415666 | − | 0.239985i | −0.277555 | − | 0.960710i | \(-0.589524\pi\) |
0.693221 | + | 0.720725i | \(0.256191\pi\) | |||||||
\(978\) | −61.6964 | −1.97283 | ||||||||
\(979\) | 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 | ||||
\(983\) | 5.21223 | + | 3.00928i | 0.166244 | + | 0.0959812i | 0.580814 | − | 0.814037i | \(-0.302734\pi\) |
−0.414569 | + | 0.910018i | \(0.636068\pi\) | |||||||
\(984\) | −34.2729 | −1.09258 | ||||||||
\(985\) | 0.934717 | 0.0297825 | ||||||||
\(986\) | 12.2299 | + | 7.06093i | 0.389479 | + | 0.224866i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.569930 | + | 0.424745i | −0.0181319 | + | 0.0135129i | ||||
\(989\) | −4.55800 | − | 7.89469i | −0.144936 | − | 0.251036i | ||||
\(990\) | −5.04318 | + | 2.91168i | −0.160283 | + | 0.0925392i | ||||
\(991\) | −16.9200 | − | 29.3063i | −0.537482 | − | 0.930946i | −0.999039 | − | 0.0438356i | \(-0.986042\pi\) |
0.461557 | − | 0.887111i | \(-0.347291\pi\) | |||||||
\(992\) | −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 | ||||
\(996\) | 1.72716 | − | 0.997175i | 0.0547271 | − | 0.0315967i | ||||
\(997\) | −26.3215 | −0.833610 | −0.416805 | − | 0.908996i | \(-0.636850\pi\) | ||||
−0.416805 | + | 0.908996i | \(0.636850\pi\) | |||||||
\(998\) | 5.77591 | + | 10.0042i | 0.182833 | + | 0.316676i | ||||
\(999\) | 57.3775i | 1.81534i |
(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.k.g.459.5 | 12 | ||
7.2 | even | 3 | 637.2.u.i.30.5 | 12 | |||
7.3 | odd | 6 | 91.2.q.a.43.2 | yes | 12 | ||
7.4 | even | 3 | 637.2.q.h.589.2 | 12 | |||
7.5 | odd | 6 | 637.2.u.h.30.5 | 12 | |||
7.6 | odd | 2 | 637.2.k.h.459.5 | 12 | |||
13.10 | even | 6 | 637.2.u.i.361.5 | 12 | |||
21.17 | even | 6 | 819.2.ct.a.316.5 | 12 | |||
28.3 | even | 6 | 1456.2.cc.c.225.1 | 12 | |||
91.10 | odd | 6 | 91.2.q.a.36.2 | ✓ | 12 | ||
91.17 | odd | 6 | 1183.2.c.i.337.3 | 12 | |||
91.23 | even | 6 | inner | 637.2.k.g.569.2 | 12 | ||
91.32 | odd | 12 | 8281.2.a.by.1.6 | 6 | |||
91.45 | even | 12 | 1183.2.a.m.1.6 | 6 | |||
91.46 | odd | 12 | 8281.2.a.ch.1.1 | 6 | |||
91.59 | even | 12 | 1183.2.a.p.1.1 | 6 | |||
91.62 | odd | 6 | 637.2.u.h.361.5 | 12 | |||
91.75 | odd | 6 | 637.2.k.h.569.2 | 12 | |||
91.87 | odd | 6 | 1183.2.c.i.337.10 | 12 | |||
91.88 | even | 6 | 637.2.q.h.491.2 | 12 | |||
273.101 | even | 6 | 819.2.ct.a.127.5 | 12 | |||
364.283 | 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 | 91.10 | odd | 6 | ||
91.2.q.a.43.2 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.g.459.5 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.g.569.2 | 12 | 91.23 | even | 6 | inner | ||
637.2.k.h.459.5 | 12 | 7.6 | odd | 2 | |||
637.2.k.h.569.2 | 12 | 91.75 | odd | 6 | |||
637.2.q.h.491.2 | 12 | 91.88 | even | 6 | |||
637.2.q.h.589.2 | 12 | 7.4 | even | 3 | |||
637.2.u.h.30.5 | 12 | 7.5 | odd | 6 | |||
637.2.u.h.361.5 | 12 | 91.62 | odd | 6 | |||
637.2.u.i.30.5 | 12 | 7.2 | even | 3 | |||
637.2.u.i.361.5 | 12 | 13.10 | even | 6 | |||
819.2.ct.a.127.5 | 12 | 273.101 | even | 6 | |||
819.2.ct.a.316.5 | 12 | 21.17 | even | 6 | |||
1183.2.a.m.1.6 | 6 | 91.45 | even | 12 | |||
1183.2.a.p.1.1 | 6 | 91.59 | even | 12 | |||
1183.2.c.i.337.3 | 12 | 91.17 | odd | 6 | |||
1183.2.c.i.337.10 | 12 | 91.87 | odd | 6 | |||
1456.2.cc.c.225.1 | 12 | 28.3 | even | 6 | |||
1456.2.cc.c.673.1 | 12 | 364.283 | even | 6 | |||
8281.2.a.by.1.6 | 6 | 91.32 | odd | 12 | |||
8281.2.a.ch.1.1 | 6 | 91.46 | odd | 12 |