Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(699,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.c (of order \(2\), degree \(1\), 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.29960650073923649536.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 699.8 | ||
Root | \(0.281691 - 1.38588i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.699 |
Dual form | 700.2.c.k.699.5 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.736813 | + | 1.20711i | −0.521005 | + | 0.853553i | ||||
\(3\) | 2.79793i | 1.61539i | 0.589602 | + | 0.807694i | \(0.299284\pi\) | ||||
−0.589602 | + | 0.807694i | \(0.700716\pi\) | |||||||
\(4\) | −0.914214 | − | 1.77882i | −0.457107 | − | 0.889412i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.37740 | − | 2.06155i | −1.37882 | − | 0.841625i | ||||
\(7\) | 2.51564 | + | 0.819496i | 0.950821 | + | 0.309740i | ||||
\(8\) | 2.82083 | + | 0.207107i | 0.997316 | + | 0.0732233i | ||||
\(9\) | −4.82843 | −1.60948 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.47363i | − | 0.444315i | −0.975011 | − | 0.222157i | \(-0.928690\pi\) | ||
0.975011 | − | 0.222157i | \(-0.0713099\pi\) | |||||||
\(12\) | 4.97703 | − | 2.55791i | 1.43674 | − | 0.738404i | ||||
\(13\) | −5.83095 | −1.61722 | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | −2.84277 | + | 2.43283i | −0.759763 | + | 0.650200i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.32843 | + | 3.25245i | −0.582107 | + | 0.813112i | ||||
\(17\) | −4.12311 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 3.55765 | − | 5.82843i | 0.838546 | − | 1.37377i | ||||
\(19\) | −5.11582 | −1.17365 | −0.586824 | − | 0.809714i | \(-0.699622\pi\) | ||||
−0.586824 | + | 0.809714i | \(0.699622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.29289 | + | 7.03858i | −0.500350 | + | 1.53594i | ||||
\(22\) | 1.77882 | + | 1.08579i | 0.379246 | + | 0.231490i | ||||
\(23\) | −2.08402 | −0.434549 | −0.217274 | − | 0.976111i | \(-0.569717\pi\) | ||||
−0.217274 | + | 0.976111i | \(0.569717\pi\) | |||||||
\(24\) | −0.579471 | + | 7.89250i | −0.118284 | + | 1.61105i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.29632 | − | 7.03858i | 0.842578 | − | 1.38038i | ||||
\(27\) | − | 5.11582i | − | 0.984539i | ||||||
\(28\) | −0.842091 | − | 5.22407i | −0.159140 | − | 0.987256i | ||||
\(29\) | −8.24264 | −1.53062 | −0.765310 | − | 0.643662i | \(-0.777414\pi\) | ||||
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.95687 | 0.710676 | 0.355338 | − | 0.934738i | \(-0.384366\pi\) | ||||
0.355338 | + | 0.934738i | \(0.384366\pi\) | |||||||
\(32\) | −2.21044 | − | 5.20711i | −0.390754 | − | 0.920495i | ||||
\(33\) | 4.12311 | 0.717741 | ||||||||
\(34\) | 3.03796 | − | 4.97703i | 0.521005 | − | 0.853553i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.41421 | + | 8.58892i | 0.735702 | + | 1.43149i | ||||
\(37\) | 2.24264i | 0.368688i | 0.982862 | + | 0.184344i | \(0.0590160\pi\) | ||||
−0.982862 | + | 0.184344i | \(0.940984\pi\) | |||||||
\(38\) | 3.76940 | − | 6.17534i | 0.611477 | − | 1.00177i | ||||
\(39\) | − | 16.3146i | − | 2.61243i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12311i | 0.643921i | 0.946753 | + | 0.321960i | \(0.104342\pi\) | ||||
−0.946753 | + | 0.321960i | \(0.895658\pi\) | |||||||
\(42\) | −6.80689 | − | 7.95388i | −1.05033 | − | 1.22731i | ||||
\(43\) | −2.94725 | −0.449452 | −0.224726 | − | 0.974422i | \(-0.572149\pi\) | ||||
−0.224726 | + | 0.974422i | \(0.572149\pi\) | |||||||
\(44\) | −2.62132 | + | 1.34721i | −0.395179 | + | 0.203099i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53553 | − | 2.51564i | 0.226402 | − | 0.370910i | ||||
\(47\) | 11.8706i | 1.73151i | 0.500470 | + | 0.865754i | \(0.333161\pi\) | ||||
−0.500470 | + | 0.865754i | \(0.666839\pi\) | |||||||
\(48\) | −9.10013 | − | 6.51478i | −1.31349 | − | 0.940328i | ||||
\(49\) | 5.65685 | + | 4.12311i | 0.808122 | + | 0.589015i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 11.5362i | − | 1.61539i | ||||||
\(52\) | 5.33074 | + | 10.3722i | 0.739240 | + | 1.43837i | ||||
\(53\) | 3.75736i | 0.516113i | 0.966130 | + | 0.258056i | \(0.0830821\pi\) | ||||
−0.966130 | + | 0.258056i | \(0.916918\pi\) | |||||||
\(54\) | 6.17534 | + | 3.76940i | 0.840357 | + | 0.512950i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.92647 | + | 2.83267i | 0.925589 | + | 0.378531i | ||||
\(57\) | − | 14.3137i | − | 1.89590i | ||||||
\(58\) | 6.07328 | − | 9.94975i | 0.797461 | − | 1.30647i | ||||
\(59\) | 5.59587 | 0.728520 | 0.364260 | − | 0.931297i | \(-0.381322\pi\) | ||||
0.364260 | + | 0.931297i | \(0.381322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.6619i | − | 1.49315i | −0.665299 | − | 0.746577i | \(-0.731696\pi\) | ||
0.665299 | − | 0.746577i | \(-0.268304\pi\) | |||||||
\(62\) | −2.91548 | + | 4.77637i | −0.370266 | + | 0.606600i | ||||
\(63\) | −12.1466 | − | 3.95687i | −1.53032 | − | 0.498519i | ||||
\(64\) | 7.91421 | + | 1.16843i | 0.989277 | + | 0.146053i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.03796 | + | 4.97703i | −0.373947 | + | 0.612630i | ||||
\(67\) | 12.7570 | 1.55851 | 0.779256 | − | 0.626706i | \(-0.215597\pi\) | ||||
0.779256 | + | 0.626706i | \(0.215597\pi\) | |||||||
\(68\) | 3.76940 | + | 7.33428i | 0.457107 | + | 0.889412i | ||||
\(69\) | − | 5.83095i | − | 0.701964i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.97852i | 0.946877i | 0.880827 | + | 0.473438i | \(0.156987\pi\) | ||||
−0.880827 | + | 0.473438i | \(0.843013\pi\) | |||||||
\(72\) | −13.6202 | − | 1.00000i | −1.60516 | − | 0.117851i | ||||
\(73\) | 12.3693 | 1.44772 | 0.723860 | − | 0.689947i | \(-0.242366\pi\) | ||||
0.723860 | + | 0.689947i | \(0.242366\pi\) | |||||||
\(74\) | −2.70711 | − | 1.65241i | −0.314695 | − | 0.192088i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.67695 | + | 9.10013i | 0.536483 | + | 1.04386i | ||||
\(77\) | 1.20763 | − | 3.70711i | 0.137622 | − | 0.422464i | ||||
\(78\) | 19.6935 | + | 12.0208i | 2.22985 | + | 1.36109i | ||||
\(79\) | 4.16804i | 0.468941i | 0.972123 | + | 0.234471i | \(0.0753357\pi\) | ||||
−0.972123 | + | 0.234471i | \(0.924664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | −4.97703 | − | 3.03796i | −0.549621 | − | 0.335486i | ||||
\(83\) | 2.79793i | 0.307113i | 0.988140 | + | 0.153557i | \(0.0490727\pi\) | ||||
−0.988140 | + | 0.153557i | \(0.950927\pi\) | |||||||
\(84\) | 14.6166 | − | 2.35611i | 1.59480 | − | 0.257073i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.17157 | − | 3.55765i | 0.234167 | − | 0.383631i | ||||
\(87\) | − | 23.0624i | − | 2.47254i | ||||||
\(88\) | 0.305198 | − | 4.15685i | 0.0325342 | − | 0.443122i | ||||
\(89\) | 12.3693i | 1.31114i | 0.755132 | + | 0.655572i | \(0.227573\pi\) | ||||
−0.755132 | + | 0.655572i | \(0.772427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.6686 | − | 4.77844i | −1.53768 | − | 0.500916i | ||||
\(92\) | 1.90524 | + | 3.70711i | 0.198635 | + | 0.386493i | ||||
\(93\) | 11.0711i | 1.14802i | ||||||||
\(94\) | −14.3291 | − | 8.74643i | −1.47793 | − | 0.902125i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.5691 | − | 6.18466i | 1.48696 | − | 0.631219i | ||||
\(97\) | −8.24621 | −0.837276 | −0.418638 | − | 0.908153i | \(-0.637492\pi\) | ||||
−0.418638 | + | 0.908153i | \(0.637492\pi\) | |||||||
\(98\) | −9.14507 | + | 3.79047i | −0.923792 | + | 0.382895i | ||||
\(99\) | 7.11529i | 0.715114i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.0772i | − | 1.40073i | −0.713785 | − | 0.700365i | \(-0.753021\pi\) | ||
0.713785 | − | 0.700365i | \(-0.246979\pi\) | |||||||
\(102\) | 13.9254 | + | 8.50000i | 1.37882 | + | 0.841625i | ||||
\(103\) | 2.31788i | 0.228388i | 0.993458 | + | 0.114194i | \(0.0364285\pi\) | ||||
−0.993458 | + | 0.114194i | \(0.963571\pi\) | |||||||
\(104\) | −16.4481 | − | 1.20763i | −1.61287 | − | 0.118418i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.53553 | − | 2.76847i | −0.440530 | − | 0.268898i | ||||
\(107\) | −9.80971 | −0.948341 | −0.474170 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474170 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(108\) | −9.10013 | + | 4.67695i | −0.875661 | + | 0.450040i | ||||
\(109\) | 2.82843 | 0.270914 | 0.135457 | − | 0.990783i | \(-0.456750\pi\) | ||||
0.135457 | + | 0.990783i | \(0.456750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.27476 | −0.595574 | ||||||||
\(112\) | −8.52284 | + | 6.27384i | −0.805333 | + | 0.592823i | ||||
\(113\) | 4.31371i | 0.405800i | 0.979200 | + | 0.202900i | \(0.0650366\pi\) | ||||
−0.979200 | + | 0.202900i | \(0.934963\pi\) | |||||||
\(114\) | 17.2782 | + | 10.5465i | 1.61825 | + | 0.987773i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.53553 | + | 14.6622i | 0.699657 | + | 1.36135i | ||||
\(117\) | 28.1543 | 2.60287 | ||||||||
\(118\) | −4.12311 | + | 6.75481i | −0.379563 | + | 0.621830i | ||||
\(119\) | −10.3722 | − | 3.37887i | −0.950821 | − | 0.309740i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.82843 | 0.802584 | ||||||||
\(122\) | 14.0772 | + | 8.59264i | 1.27449 | + | 0.777941i | ||||
\(123\) | −11.5362 | −1.04018 | ||||||||
\(124\) | −3.61743 | − | 7.03858i | −0.324855 | − | 0.632083i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.7261 | − | 11.7467i | 1.22282 | − | 1.04648i | ||||
\(127\) | −2.94725 | −0.261526 | −0.130763 | − | 0.991414i | \(-0.541743\pi\) | ||||
−0.130763 | + | 0.991414i | \(0.541743\pi\) | |||||||
\(128\) | −7.24171 | + | 8.69239i | −0.640083 | + | 0.768306i | ||||
\(129\) | − | 8.24621i | − | 0.726038i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.87385 | −0.775312 | −0.387656 | − | 0.921804i | \(-0.626715\pi\) | ||||
−0.387656 | + | 0.921804i | \(0.626715\pi\) | |||||||
\(132\) | −3.76940 | − | 7.33428i | −0.328084 | − | 0.638367i | ||||
\(133\) | −12.8695 | − | 4.19239i | −1.11593 | − | 0.363526i | ||||
\(134\) | −9.39949 | + | 15.3990i | −0.811993 | + | 1.33027i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.6306 | − | 0.853923i | −0.997316 | − | 0.0732233i | ||||
\(137\) | 13.4853i | 1.15213i | 0.817406 | + | 0.576063i | \(0.195412\pi\) | ||||
−0.817406 | + | 0.576063i | \(0.804588\pi\) | |||||||
\(138\) | 7.03858 | + | 4.29632i | 0.599164 | + | 0.365727i | ||||
\(139\) | 10.7117 | 0.908553 | 0.454276 | − | 0.890861i | \(-0.349898\pi\) | ||||
0.454276 | + | 0.890861i | \(0.349898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.2132 | −2.79706 | ||||||||
\(142\) | −9.63093 | − | 5.87868i | −0.808210 | − | 0.493328i | ||||
\(143\) | 8.59264i | 0.718553i | ||||||||
\(144\) | 11.2426 | − | 15.7042i | 0.936887 | − | 1.30868i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.11387 | + | 14.9311i | −0.754269 | + | 1.23571i | ||||
\(147\) | −11.5362 | + | 15.8275i | −0.951487 | + | 1.30543i | ||||
\(148\) | 3.98926 | − | 2.05025i | 0.327915 | − | 0.168530i | ||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.03127i | − | 0.409439i | −0.978821 | − | 0.204720i | \(-0.934372\pi\) | ||
0.978821 | − | 0.204720i | \(-0.0656283\pi\) | |||||||
\(152\) | −14.4309 | − | 1.05952i | −1.17050 | − | 0.0859384i | ||||
\(153\) | 19.9081 | 1.60948 | ||||||||
\(154\) | 3.58508 | + | 4.18918i | 0.288894 | + | 0.337574i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −29.0208 | + | 14.9150i | −2.32352 | + | 1.19416i | ||||
\(157\) | −10.6615 | −0.850878 | −0.425439 | − | 0.904987i | \(-0.639880\pi\) | ||||
−0.425439 | + | 0.904987i | \(0.639880\pi\) | |||||||
\(158\) | −5.03127 | − | 3.07107i | −0.400267 | − | 0.244321i | ||||
\(159\) | −10.5128 | −0.833722 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.24264 | − | 1.70785i | −0.413178 | − | 0.134597i | ||||
\(162\) | 0.126417 | − | 0.207107i | 0.00993227 | − | 0.0162718i | ||||
\(163\) | 3.20009 | 0.250650 | 0.125325 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125325 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(164\) | 7.33428 | − | 3.76940i | 0.572711 | − | 0.294341i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.37740 | − | 2.06155i | −0.262137 | − | 0.160008i | ||||
\(167\) | − | 0.960099i | − | 0.0742947i | −0.999310 | − | 0.0371473i | \(-0.988173\pi\) | ||
0.999310 | − | 0.0371473i | \(-0.0118271\pi\) | |||||||
\(168\) | −7.92561 | + | 19.3798i | −0.611474 | + | 1.49518i | ||||
\(169\) | 21.0000 | 1.61538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.7013 | 1.88896 | ||||||||
\(172\) | 2.69442 | + | 5.24264i | 0.205447 | + | 0.399748i | ||||
\(173\) | −2.41526 | −0.183629 | −0.0918144 | − | 0.995776i | \(-0.529267\pi\) | ||||
−0.0918144 | + | 0.995776i | \(0.529267\pi\) | |||||||
\(174\) | 27.8387 | + | 16.9926i | 2.11045 | + | 1.28821i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.79289 | + | 3.43123i | 0.361278 | + | 0.258639i | ||||
\(177\) | 15.6569i | 1.17684i | ||||||||
\(178\) | −14.9311 | − | 9.11387i | −1.11913 | − | 0.683114i | ||||
\(179\) | − | 2.69442i | − | 0.201390i | −0.994917 | − | 0.100695i | \(-0.967893\pi\) | ||
0.994917 | − | 0.100695i | \(-0.0321067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.41569i | 0.253886i | 0.991910 | + | 0.126943i | \(0.0405166\pi\) | ||||
−0.991910 | + | 0.126943i | \(0.959483\pi\) | |||||||
\(182\) | 16.5761 | − | 14.1857i | 1.22870 | − | 1.05151i | ||||
\(183\) | 32.6292 | 2.41202 | ||||||||
\(184\) | −5.87868 | − | 0.431615i | −0.433382 | − | 0.0318191i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.3640 | − | 8.15731i | −0.979893 | − | 0.598123i | ||||
\(187\) | 6.07591i | 0.444315i | ||||||||
\(188\) | 21.1157 | − | 10.8523i | 1.54002 | − | 0.791484i | ||||
\(189\) | 4.19239 | − | 12.8695i | 0.304951 | − | 0.936121i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.67371i | − | 0.338178i | −0.985601 | − | 0.169089i | \(-0.945917\pi\) | ||
0.985601 | − | 0.169089i | \(-0.0540825\pi\) | |||||||
\(192\) | −3.26918 | + | 22.1434i | −0.235933 | + | 1.59806i | ||||
\(193\) | − | 14.3137i | − | 1.03032i | −0.857093 | − | 0.515162i | \(-0.827732\pi\) | ||
0.857093 | − | 0.515162i | \(-0.172268\pi\) | |||||||
\(194\) | 6.07591 | − | 9.95406i | 0.436225 | − | 0.714660i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.16270 | − | 13.8319i | 0.154479 | − | 0.987996i | ||||
\(197\) | 14.4853i | 1.03203i | 0.856578 | + | 0.516017i | \(0.172586\pi\) | ||||
−0.856578 | + | 0.516017i | \(0.827414\pi\) | |||||||
\(198\) | −8.58892 | − | 5.24264i | −0.610388 | − | 0.372578i | ||||
\(199\) | 22.1023 | 1.56679 | 0.783394 | − | 0.621526i | \(-0.213487\pi\) | ||||
0.783394 | + | 0.621526i | \(0.213487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.6931i | 2.51760i | ||||||||
\(202\) | 16.9926 | + | 10.3722i | 1.19560 | + | 0.729788i | ||||
\(203\) | −20.7355 | − | 6.75481i | −1.45535 | − | 0.474095i | ||||
\(204\) | −20.5208 | + | 10.5465i | −1.43674 | + | 0.738404i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.79793 | − | 1.70785i | −0.194941 | − | 0.118991i | ||||
\(207\) | 10.0625 | 0.699395 | ||||||||
\(208\) | 13.5769 | − | 18.9649i | 0.941392 | − | 1.31498i | ||||
\(209\) | 7.53880i | 0.521470i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.7668i | 1.77386i | 0.461907 | + | 0.886928i | \(0.347165\pi\) | ||||
−0.461907 | + | 0.886928i | \(0.652835\pi\) | |||||||
\(212\) | 6.68368 | − | 3.43503i | 0.459037 | − | 0.235919i | ||||
\(213\) | −22.3234 | −1.52957 | ||||||||
\(214\) | 7.22792 | − | 11.8414i | 0.494091 | − | 0.809459i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.05952 | − | 14.4309i | 0.0720912 | − | 0.981896i | ||||
\(217\) | 9.95406 | + | 3.24264i | 0.675725 | + | 0.220125i | ||||
\(218\) | −2.08402 | + | 3.41421i | −0.141148 | + | 0.231240i | ||||
\(219\) | 34.6085i | 2.33863i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.0416 | 1.61722 | ||||||||
\(222\) | 4.62332 | − | 7.57430i | 0.310297 | − | 0.508354i | ||||
\(223\) | − | 9.55274i | − | 0.639699i | −0.947468 | − | 0.319849i | \(-0.896368\pi\) | ||
0.947468 | − | 0.319849i | \(-0.103632\pi\) | |||||||
\(224\) | −1.29346 | − | 14.9106i | −0.0864229 | − | 0.996259i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.20711 | − | 3.17840i | −0.346372 | − | 0.211424i | ||||
\(227\) | − | 2.31788i | − | 0.153843i | −0.997037 | − | 0.0769217i | \(-0.975491\pi\) | ||
0.997037 | − | 0.0769217i | \(-0.0245091\pi\) | |||||||
\(228\) | −25.4616 | + | 13.0858i | −1.68623 | + | 0.866627i | ||||
\(229\) | − | 2.41526i | − | 0.159605i | −0.996811 | − | 0.0798024i | \(-0.974571\pi\) | ||
0.996811 | − | 0.0798024i | \(-0.0254289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3722 | + | 3.37887i | 0.682443 | + | 0.222313i | ||||
\(232\) | −23.2511 | − | 1.70711i | −1.52651 | − | 0.112077i | ||||
\(233\) | 23.7990i | 1.55912i | 0.626325 | + | 0.779562i | \(0.284558\pi\) | ||||
−0.626325 | + | 0.779562i | \(0.715442\pi\) | |||||||
\(234\) | −20.7445 | + | 33.9853i | −1.35611 | + | 2.22169i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.11582 | − | 9.95406i | −0.333011 | − | 0.647954i | ||||
\(237\) | −11.6619 | −0.757522 | ||||||||
\(238\) | 11.7210 | − | 10.0308i | 0.759763 | − | 0.650200i | ||||
\(239\) | − | 8.84175i | − | 0.571926i | −0.958241 | − | 0.285963i | \(-0.907687\pi\) | ||
0.958241 | − | 0.285963i | \(-0.0923134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.53880i | 0.485617i | 0.970074 | + | 0.242808i | \(0.0780686\pi\) | ||||
−0.970074 | + | 0.242808i | \(0.921931\pi\) | |||||||
\(242\) | −6.50490 | + | 10.6569i | −0.418151 | + | 0.685049i | ||||
\(243\) | − | 15.8275i | − | 1.01533i | ||||||
\(244\) | −20.7445 | + | 10.6615i | −1.32803 | + | 0.682531i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.50000 | − | 13.9254i | 0.541940 | − | 0.887851i | ||||
\(247\) | 29.8301 | 1.89804 | ||||||||
\(248\) | 11.1617 | + | 0.819496i | 0.708768 | + | 0.0520380i | ||||
\(249\) | −7.82843 | −0.496106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9433 | 1.32193 | 0.660965 | − | 0.750417i | \(-0.270147\pi\) | ||||
0.660965 | + | 0.750417i | \(0.270147\pi\) | |||||||
\(252\) | 4.06598 | + | 25.2240i | 0.256132 | + | 1.58896i | ||||
\(253\) | 3.07107i | 0.193076i | ||||||||
\(254\) | 2.17157 | − | 3.55765i | 0.136257 | − | 0.223227i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.15685 | − | 15.1462i | −0.322303 | − | 0.946636i | ||||
\(257\) | −23.3238 | −1.45490 | −0.727450 | − | 0.686161i | \(-0.759294\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | 9.95406 | + | 6.07591i | 0.619713 | + | 0.378270i | ||||
\(259\) | −1.83783 | + | 5.64167i | −0.114197 | + | 0.350556i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 39.7990 | 2.46350 | ||||||||
\(262\) | 6.53836 | − | 10.7117i | 0.403942 | − | 0.661770i | ||||
\(263\) | 14.7363 | 0.908677 | 0.454338 | − | 0.890829i | \(-0.349876\pi\) | ||||
0.454338 | + | 0.890829i | \(0.349876\pi\) | |||||||
\(264\) | 11.6306 | + | 0.853923i | 0.715814 | + | 0.0525553i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.5431 | − | 12.4459i | 0.891695 | − | 0.763107i | ||||
\(267\) | −34.6085 | −2.11801 | ||||||||
\(268\) | −11.6626 | − | 22.6924i | −0.712406 | − | 1.38616i | ||||
\(269\) | − | 14.0772i | − | 0.858300i | −0.903233 | − | 0.429150i | \(-0.858813\pi\) | ||
0.903233 | − | 0.429150i | \(-0.141187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.23808 | 0.257445 | 0.128723 | − | 0.991681i | \(-0.458912\pi\) | ||||
0.128723 | + | 0.991681i | \(0.458912\pi\) | |||||||
\(272\) | 9.60035 | − | 13.4102i | 0.582107 | − | 0.813112i | ||||
\(273\) | 13.3698 | − | 41.0416i | 0.809174 | − | 2.48395i | ||||
\(274\) | −16.2782 | − | 9.93613i | −0.983400 | − | 0.600264i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.3722 | + | 5.33074i | −0.624335 | + | 0.320873i | ||||
\(277\) | − | 25.8995i | − | 1.55615i | −0.628171 | − | 0.778075i | \(-0.716196\pi\) | ||
0.628171 | − | 0.778075i | \(-0.283804\pi\) | |||||||
\(278\) | −7.89250 | + | 12.9301i | −0.473361 | + | 0.775498i | ||||
\(279\) | −19.1055 | −1.14382 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.970563 | −0.0578989 | −0.0289495 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289495 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(282\) | 24.4719 | − | 40.0919i | 1.45728 | − | 2.38744i | ||||
\(283\) | 12.6319i | 0.750887i | 0.926845 | + | 0.375444i | \(0.122510\pi\) | ||||
−0.926845 | + | 0.375444i | \(0.877490\pi\) | |||||||
\(284\) | 14.1924 | − | 7.29408i | 0.842163 | − | 0.432824i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.3722 | − | 6.33117i | −0.613323 | − | 0.374370i | ||||
\(287\) | −3.37887 | + | 10.3722i | −0.199448 | + | 0.612254i | ||||
\(288\) | 10.6729 | + | 25.1421i | 0.628909 | + | 1.48151i | ||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 23.0723i | − | 1.35252i | ||||||
\(292\) | −11.3082 | − | 22.0028i | −0.661762 | − | 1.28762i | ||||
\(293\) | −16.4924 | −0.963498 | −0.481749 | − | 0.876309i | \(-0.659998\pi\) | ||||
−0.481749 | + | 0.876309i | \(0.659998\pi\) | |||||||
\(294\) | −10.6055 | − | 25.5873i | −0.618524 | − | 1.49228i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.464466 | + | 6.32612i | −0.0269965 | + | 0.367698i | ||||
\(297\) | −7.53880 | −0.437445 | ||||||||
\(298\) | 1.47363 | − | 2.41421i | 0.0853648 | − | 0.139852i | ||||
\(299\) | 12.1518 | 0.702758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.41421 | − | 2.41526i | −0.427348 | − | 0.139213i | ||||
\(302\) | 6.07328 | + | 3.70711i | 0.349478 | + | 0.213320i | ||||
\(303\) | 39.3870 | 2.26272 | ||||||||
\(304\) | 11.9118 | − | 16.6389i | 0.683189 | − | 0.954308i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.6686 | + | 24.0312i | −0.838546 | + | 1.37377i | ||||
\(307\) | 3.75803i | 0.214482i | 0.994233 | + | 0.107241i | \(0.0342017\pi\) | ||||
−0.994233 | + | 0.107241i | \(0.965798\pi\) | |||||||
\(308\) | −7.69832 | + | 1.24093i | −0.438653 | + | 0.0707084i | ||||
\(309\) | −6.48528 | −0.368935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.3835 | −1.26925 | −0.634625 | − | 0.772820i | \(-0.718845\pi\) | ||||
−0.634625 | + | 0.772820i | \(0.718845\pi\) | |||||||
\(312\) | 3.37887 | − | 46.0208i | 0.191291 | − | 2.60542i | ||||
\(313\) | −28.1543 | −1.59138 | −0.795688 | − | 0.605706i | \(-0.792891\pi\) | ||||
−0.795688 | + | 0.605706i | \(0.792891\pi\) | |||||||
\(314\) | 7.85551 | − | 12.8695i | 0.443312 | − | 0.726270i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.41421 | − | 3.81048i | 0.417082 | − | 0.214356i | ||||
\(317\) | 14.3431i | 0.805591i | 0.915290 | + | 0.402796i | \(0.131961\pi\) | ||||
−0.915290 | + | 0.402796i | \(0.868039\pi\) | |||||||
\(318\) | 7.74599 | − | 12.6901i | 0.434374 | − | 0.711627i | ||||
\(319\) | 12.1466i | 0.680077i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 27.4469i | − | 1.53194i | ||||||
\(322\) | 5.92440 | − | 5.07006i | 0.330154 | − | 0.282544i | ||||
\(323\) | 21.0930 | 1.17365 | ||||||||
\(324\) | 0.156854 | + | 0.305198i | 0.00871412 | + | 0.0169554i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.35786 | + | 3.86285i | −0.130590 | + | 0.213943i | ||||
\(327\) | 7.91375i | 0.437631i | ||||||||
\(328\) | −0.853923 | + | 11.6306i | −0.0471500 | + | 0.642192i | ||||
\(329\) | −9.72792 | + | 29.8622i | −0.536318 | + | 1.64635i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1458i | 0.997383i | 0.866779 | + | 0.498692i | \(0.166186\pi\) | ||||
−0.866779 | + | 0.498692i | \(0.833814\pi\) | |||||||
\(332\) | 4.97703 | − | 2.55791i | 0.273150 | − | 0.140383i | ||||
\(333\) | − | 10.8284i | − | 0.593394i | ||||||
\(334\) | 1.15894 | + | 0.707413i | 0.0634145 | + | 0.0387079i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −17.5538 | − | 23.8463i | −0.957638 | − | 1.30092i | ||||
\(337\) | − | 24.7990i | − | 1.35089i | −0.737412 | − | 0.675444i | \(-0.763952\pi\) | ||
0.737412 | − | 0.675444i | \(-0.236048\pi\) | |||||||
\(338\) | −15.4731 | + | 25.3492i | −0.841624 | + | 1.37882i | ||||
\(339\) | −12.0695 | −0.655523 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.83095i | − | 0.315764i | ||||||
\(342\) | −18.2003 | + | 29.8172i | −0.984158 | + | 1.61233i | ||||
\(343\) | 10.8517 | + | 15.0080i | 0.585938 | + | 0.810356i | ||||
\(344\) | −8.31371 | − | 0.610396i | −0.448245 | − | 0.0329103i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.77959 | − | 2.91548i | 0.0956716 | − | 0.156737i | ||||
\(347\) | −31.1556 | −1.67252 | −0.836260 | − | 0.548333i | \(-0.815263\pi\) | ||||
−0.836260 | + | 0.548333i | \(0.815263\pi\) | |||||||
\(348\) | −41.0239 | + | 21.0839i | −2.19911 | + | 1.13022i | ||||
\(349\) | − | 2.41526i | − | 0.129286i | −0.997908 | − | 0.0646429i | \(-0.979409\pi\) | ||
0.997908 | − | 0.0646429i | \(-0.0205908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.8301i | 1.59221i | ||||||||
\(352\) | −7.67333 | + | 3.25736i | −0.408990 | + | 0.173618i | ||||
\(353\) | 11.6619 | 0.620701 | 0.310350 | − | 0.950622i | \(-0.399554\pi\) | ||||
0.310350 | + | 0.950622i | \(0.399554\pi\) | |||||||
\(354\) | −18.8995 | − | 11.5362i | −1.00450 | − | 0.613141i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.0028 | − | 11.3082i | 1.16615 | − | 0.599333i | ||||
\(357\) | 9.45384 | − | 29.0208i | 0.500350 | − | 1.53594i | ||||
\(358\) | 3.25245 | + | 1.98528i | 0.171897 | + | 0.104925i | ||||
\(359\) | − | 22.5667i | − | 1.19102i | −0.803347 | − | 0.595512i | \(-0.796949\pi\) | ||
0.803347 | − | 0.595512i | \(-0.203051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.17157 | 0.377451 | ||||||||
\(362\) | −4.12311 | − | 2.51673i | −0.216706 | − | 0.132276i | ||||
\(363\) | 24.7013i | 1.29648i | ||||||||
\(364\) | 4.91019 | + | 30.4613i | 0.257364 | + | 1.59661i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −24.0416 | + | 39.3870i | −1.25668 | + | 2.05879i | ||||
\(367\) | − | 14.4697i | − | 0.755313i | −0.925946 | − | 0.377656i | \(-0.876730\pi\) | ||
0.925946 | − | 0.377656i | \(-0.123270\pi\) | |||||||
\(368\) | 4.85249 | − | 6.77817i | 0.252954 | − | 0.353337i | ||||
\(369\) | − | 19.9081i | − | 1.03638i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.07914 | + | 9.45215i | −0.159861 | + | 0.490731i | ||||
\(372\) | 19.6935 | − | 10.1213i | 1.02106 | − | 0.524766i | ||||
\(373\) | − | 10.5858i | − | 0.548111i | −0.961714 | − | 0.274056i | \(-0.911635\pi\) | ||
0.961714 | − | 0.274056i | \(-0.0883652\pi\) | |||||||
\(374\) | −7.33428 | − | 4.47681i | −0.379246 | − | 0.231490i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.45849 | + | 33.4851i | −0.126787 | + | 1.72686i | ||||
\(377\) | 48.0624 | 2.47534 | ||||||||
\(378\) | 12.4459 | + | 14.5431i | 0.640148 | + | 0.748016i | ||||
\(379\) | 22.8195i | 1.17216i | 0.810253 | + | 0.586080i | \(0.199329\pi\) | ||||
−0.810253 | + | 0.586080i | \(0.800671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 8.24621i | − | 0.422466i | ||||||
\(382\) | 5.64167 | + | 3.44365i | 0.288653 | + | 0.176193i | ||||
\(383\) | − | 12.5495i | − | 0.641250i | −0.947206 | − | 0.320625i | \(-0.896107\pi\) | ||
0.947206 | − | 0.320625i | \(-0.103893\pi\) | |||||||
\(384\) | −24.3207 | − | 20.2618i | −1.24111 | − | 1.03398i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.2782 | + | 10.5465i | 0.879436 | + | 0.536804i | ||||
\(387\) | 14.2306 | 0.723382 | ||||||||
\(388\) | 7.53880 | + | 14.6686i | 0.382724 | + | 0.744683i | ||||
\(389\) | 15.5563 | 0.788738 | 0.394369 | − | 0.918952i | \(-0.370963\pi\) | ||||
0.394369 | + | 0.918952i | \(0.370963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.59264 | 0.434549 | ||||||||
\(392\) | 15.1031 | + | 12.8022i | 0.762823 | + | 0.646607i | ||||
\(393\) | − | 24.8284i | − | 1.25243i | ||||||
\(394\) | −17.4853 | − | 10.6729i | −0.880896 | − | 0.537695i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.6569 | − | 6.50490i | 0.636031 | − | 0.326883i | ||||
\(397\) | −30.5696 | −1.53424 | −0.767122 | − | 0.641502i | \(-0.778312\pi\) | ||||
−0.767122 | + | 0.641502i | \(0.778312\pi\) | |||||||
\(398\) | −16.2852 | + | 26.6798i | −0.816305 | + | 1.33734i | ||||
\(399\) | 11.7300 | − | 36.0081i | 0.587235 | − | 1.80266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4558 | 1.42102 | 0.710509 | − | 0.703689i | \(-0.248465\pi\) | ||||
0.710509 | + | 0.703689i | \(0.248465\pi\) | |||||||
\(402\) | −43.0854 | − | 26.2992i | −2.14891 | − | 1.31168i | ||||
\(403\) | −23.0723 | −1.14932 | ||||||||
\(404\) | −25.0408 | + | 12.8695i | −1.24583 | + | 0.640283i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.4319 | − | 20.0529i | 1.16291 | − | 0.995210i | ||||
\(407\) | 3.30481 | 0.163814 | ||||||||
\(408\) | 2.38922 | − | 32.5416i | 0.118284 | − | 1.61105i | ||||
\(409\) | 7.53880i | 0.372770i | 0.982477 | + | 0.186385i | \(0.0596771\pi\) | ||||
−0.982477 | + | 0.186385i | \(0.940323\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.7309 | −1.86113 | ||||||||
\(412\) | 4.12311 | − | 2.11904i | 0.203131 | − | 0.104398i | ||||
\(413\) | 14.0772 | + | 4.58579i | 0.692692 | + | 0.225652i | ||||
\(414\) | −7.41421 | + | 12.1466i | −0.364389 | + | 0.596971i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.8890 | + | 30.3624i | 0.631933 | + | 1.48864i | ||||
\(417\) | 29.9706i | 1.46766i | ||||||||
\(418\) | −9.10013 | − | 5.55468i | −0.445102 | − | 0.271688i | ||||
\(419\) | 14.9498 | 0.730344 | 0.365172 | − | 0.930940i | \(-0.381010\pi\) | ||||
0.365172 | + | 0.930940i | \(0.381010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3137 | −1.13624 | −0.568120 | − | 0.822946i | \(-0.692329\pi\) | ||||
−0.568120 | + | 0.822946i | \(0.692329\pi\) | |||||||
\(422\) | −31.1032 | − | 18.9853i | −1.51408 | − | 0.924189i | ||||
\(423\) | − | 57.3164i | − | 2.78682i | ||||||
\(424\) | −0.778175 | + | 10.5989i | −0.0377915 | + | 0.514728i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.4481 | − | 26.9467i | 0.796915 | − | 1.30557i | ||||
\(427\) | 9.55688 | − | 29.3371i | 0.462490 | − | 1.41972i | ||||
\(428\) | 8.96817 | + | 17.4497i | 0.433493 | + | 0.843465i | ||||
\(429\) | −24.0416 | −1.16074 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.1564i | 1.21174i | 0.795564 | + | 0.605870i | \(0.207175\pi\) | ||||
−0.795564 | + | 0.605870i | \(0.792825\pi\) | |||||||
\(432\) | 16.6389 | + | 11.9118i | 0.800541 | + | 0.573107i | ||||
\(433\) | −4.12311 | −0.198144 | −0.0990719 | − | 0.995080i | \(-0.531587\pi\) | ||||
−0.0990719 | + | 0.995080i | \(0.531587\pi\) | |||||||
\(434\) | −11.2485 | + | 9.62639i | −0.539945 | + | 0.462082i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.58579 | − | 5.03127i | −0.123837 | − | 0.240954i | ||||
\(437\) | 10.6615 | 0.510007 | ||||||||
\(438\) | −41.7762 | − | 25.5000i | −1.99614 | − | 1.21844i | ||||
\(439\) | −5.59587 | −0.267076 | −0.133538 | − | 0.991044i | \(-0.542634\pi\) | ||||
−0.133538 | + | 0.991044i | \(0.542634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.3137 | − | 19.9081i | −1.30065 | − | 0.948005i | ||||
\(442\) | −17.7142 | + | 29.0208i | −0.842578 | + | 1.38038i | ||||
\(443\) | 15.7042 | 0.746130 | 0.373065 | − | 0.927805i | \(-0.378307\pi\) | ||||
0.373065 | + | 0.927805i | \(0.378307\pi\) | |||||||
\(444\) | 5.73647 | + | 11.1617i | 0.272241 | + | 0.529710i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.5312 | + | 7.03858i | 0.546017 | + | 0.333286i | ||||
\(447\) | − | 5.59587i | − | 0.264675i | ||||||
\(448\) | 18.9518 | + | 9.42500i | 0.895387 | + | 0.445290i | ||||
\(449\) | 0.656854 | 0.0309989 | 0.0154994 | − | 0.999880i | \(-0.495066\pi\) | ||||
0.0154994 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.07591 | 0.286104 | ||||||||
\(452\) | 7.67333 | − | 3.94365i | 0.360923 | − | 0.185494i | ||||
\(453\) | 14.0772 | 0.661403 | ||||||||
\(454\) | 2.79793 | + | 1.70785i | 0.131313 | + | 0.0801532i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.96447 | − | 40.3766i | 0.138824 | − | 1.89081i | ||||
\(457\) | − | 12.5147i | − | 0.585414i | −0.956202 | − | 0.292707i | \(-0.905444\pi\) | ||
0.956202 | − | 0.292707i | \(-0.0945560\pi\) | |||||||
\(458\) | 2.91548 | + | 1.77959i | 0.136231 | + | 0.0831550i | ||||
\(459\) | 21.0930i | 0.984539i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14.0772i | − | 0.655639i | −0.944740 | − | 0.327819i | \(-0.893686\pi\) | ||
0.944740 | − | 0.327819i | \(-0.106314\pi\) | |||||||
\(462\) | −11.7210 | + | 10.0308i | −0.545313 | + | 0.466675i | ||||
\(463\) | −24.2931 | −1.12900 | −0.564499 | − | 0.825434i | \(-0.690931\pi\) | ||||
−0.564499 | + | 0.825434i | \(0.690931\pi\) | |||||||
\(464\) | 19.1924 | − | 26.8088i | 0.890984 | − | 1.24457i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.7279 | − | 17.5354i | −1.33080 | − | 0.812312i | ||||
\(467\) | − | 30.2972i | − | 1.40199i | −0.713167 | − | 0.700994i | \(-0.752740\pi\) | ||
0.713167 | − | 0.700994i | \(-0.247260\pi\) | |||||||
\(468\) | −25.7391 | − | 50.0816i | −1.18979 | − | 2.31502i | ||||
\(469\) | 32.0919 | + | 10.4543i | 1.48187 | + | 0.482734i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 29.8301i | − | 1.37450i | ||||||
\(472\) | 15.7850 | + | 1.15894i | 0.726564 | + | 0.0533446i | ||||
\(473\) | 4.34315i | 0.199698i | ||||||||
\(474\) | 8.59264 | − | 14.0772i | 0.394673 | − | 0.646586i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.47203 | + | 21.5394i | 0.159140 | + | 0.987256i | ||||
\(477\) | − | 18.1421i | − | 0.830671i | ||||||
\(478\) | 10.6729 | + | 6.51472i | 0.488169 | + | 0.297976i | ||||
\(479\) | −16.7876 | −0.767045 | −0.383522 | − | 0.923532i | \(-0.625289\pi\) | ||||
−0.383522 | + | 0.923532i | \(0.625289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13.0767i | − | 0.596248i | ||||||
\(482\) | −9.10013 | − | 5.55468i | −0.414500 | − | 0.253009i | ||||
\(483\) | 4.77844 | − | 14.6686i | 0.217426 | − | 0.667442i | ||||
\(484\) | −8.07107 | − | 15.7042i | −0.366867 | − | 0.713828i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.1055 | + | 11.6619i | 0.866642 | + | 0.528995i | ||||
\(487\) | 31.4084 | 1.42325 | 0.711626 | − | 0.702559i | \(-0.247959\pi\) | ||||
0.711626 | + | 0.702559i | \(0.247959\pi\) | |||||||
\(488\) | 2.41526 | − | 32.8963i | 0.109334 | − | 1.48915i | ||||
\(489\) | 8.95362i | 0.404897i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.55688i | − | 0.431296i | −0.976471 | − | 0.215648i | \(-0.930814\pi\) | ||
0.976471 | − | 0.215648i | \(-0.0691863\pi\) | |||||||
\(492\) | 10.5465 | + | 20.5208i | 0.475474 | + | 0.925150i | ||||
\(493\) | 33.9853 | 1.53062 | ||||||||
\(494\) | −21.9792 | + | 36.0081i | −0.988890 | + | 1.62008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.21329 | + | 12.8695i | −0.413689 | + | 0.577859i | ||||
\(497\) | −6.53836 | + | 20.0711i | −0.293286 | + | 0.900310i | ||||
\(498\) | 5.76809 | − | 9.44975i | 0.258474 | − | 0.423453i | ||||
\(499\) | 8.84175i | 0.395811i | 0.980221 | + | 0.197906i | \(0.0634140\pi\) | ||||
−0.980221 | + | 0.197906i | \(0.936586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.68629 | 0.120015 | ||||||||
\(502\) | −15.4313 | + | 25.2808i | −0.688733 | + | 1.12834i | ||||
\(503\) | − | 19.3867i | − | 0.864410i | −0.901775 | − | 0.432205i | \(-0.857736\pi\) | ||
0.901775 | − | 0.432205i | \(-0.142264\pi\) | |||||||
\(504\) | −33.4440 | − | 13.6773i | −1.48971 | − | 0.609236i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.70711 | − | 2.26280i | −0.164801 | − | 0.100594i | ||||
\(507\) | 58.7566i | 2.60947i | ||||||||
\(508\) | 2.69442 | + | 5.24264i | 0.119545 | + | 0.232605i | ||||
\(509\) | − | 8.24621i | − | 0.365507i | −0.983159 | − | 0.182753i | \(-0.941499\pi\) | ||
0.983159 | − | 0.182753i | \(-0.0585010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.1167 | + | 10.1366i | 1.37652 | + | 0.448417i | ||||
\(512\) | 22.0827 | + | 4.93503i | 0.975927 | + | 0.218100i | ||||
\(513\) | 26.1716i | 1.15550i | ||||||||
\(514\) | 17.1853 | − | 28.1543i | 0.758010 | − | 1.24183i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.6686 | + | 7.53880i | −0.645747 | + | 0.331877i | ||||
\(517\) | 17.4929 | 0.769335 | ||||||||
\(518\) | −5.45596 | − | 6.37532i | −0.239721 | − | 0.280115i | ||||
\(519\) | − | 6.75773i | − | 0.296632i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8617i | 1.26446i | 0.774782 | + | 0.632228i | \(0.217859\pi\) | ||||
−0.774782 | + | 0.632228i | \(0.782141\pi\) | |||||||
\(522\) | −29.3244 | + | 48.0416i | −1.28349 | + | 2.10273i | ||||
\(523\) | 8.39380i | 0.367035i | 0.983016 | + | 0.183518i | \(0.0587484\pi\) | ||||
−0.983016 | + | 0.183518i | \(0.941252\pi\) | |||||||
\(524\) | 8.11259 | + | 15.7850i | 0.354400 | + | 0.689571i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.8579 | + | 17.7882i | −0.473425 | + | 0.775604i | ||||
\(527\) | −16.3146 | −0.710676 | ||||||||
\(528\) | −9.60035 | + | 13.4102i | −0.417802 | + | 0.583604i | ||||
\(529\) | −18.6569 | −0.811168 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.0192 | −1.17253 | ||||||||
\(532\) | 4.30798 | + | 26.7254i | 0.186775 | + | 1.15869i | ||||
\(533\) | − | 24.0416i | − | 1.04136i | ||||||
\(534\) | 25.5000 | − | 41.7762i | 1.10349 | − | 1.80783i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 35.9853 | + | 2.64205i | 1.55433 | + | 0.114119i | ||||
\(537\) | 7.53880 | 0.325323 | ||||||||
\(538\) | 16.9926 | + | 10.3722i | 0.732605 | + | 0.447179i | ||||
\(539\) | 6.07591 | − | 8.33609i | 0.261708 | − | 0.359061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.75736 | 0.0755548 | 0.0377774 | − | 0.999286i | \(-0.487972\pi\) | ||||
0.0377774 | + | 0.999286i | \(0.487972\pi\) | |||||||
\(542\) | −3.12267 | + | 5.11582i | −0.134130 | + | 0.219743i | ||||
\(543\) | −9.55688 | −0.410125 | ||||||||
\(544\) | 9.11387 | + | 21.4695i | 0.390754 | + | 0.920495i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 39.6906 | + | 46.3787i | 1.69860 | + | 1.98483i | ||||
\(547\) | −9.80971 | −0.419433 | −0.209716 | − | 0.977762i | \(-0.567254\pi\) | ||||
−0.209716 | + | 0.977762i | \(0.567254\pi\) | |||||||
\(548\) | 23.9879 | − | 12.3284i | 1.02471 | − | 0.526644i | ||||
\(549\) | 56.3087i | 2.40319i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.1678 | 1.79641 | ||||||||
\(552\) | 1.20763 | − | 16.4481i | 0.0514001 | − | 0.700080i | ||||
\(553\) | −3.41569 | + | 10.4853i | −0.145250 | + | 0.445880i | ||||
\(554\) | 31.2635 | + | 19.0831i | 1.32826 | + | 0.810762i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.79276 | − | 19.0542i | −0.415306 | − | 0.808078i | ||||
\(557\) | 33.3137i | 1.41155i | 0.708437 | + | 0.705774i | \(0.249400\pi\) | ||||
−0.708437 | + | 0.705774i | \(0.750600\pi\) | |||||||
\(558\) | 14.0772 | − | 23.0624i | 0.595934 | − | 0.976307i | ||||
\(559\) | 17.1853 | 0.726860 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0000 | −0.717741 | ||||||||
\(562\) | 0.715123 | − | 1.17157i | 0.0301656 | − | 0.0494198i | ||||
\(563\) | 37.2509i | 1.56994i | 0.619536 | + | 0.784968i | \(0.287321\pi\) | ||||
−0.619536 | + | 0.784968i | \(0.712679\pi\) | |||||||
\(564\) | 30.3640 | + | 59.0804i | 1.27855 | + | 2.48773i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.2480 | − | 9.30733i | −0.640922 | − | 0.391216i | ||||
\(567\) | −0.431615 | − | 0.140603i | −0.0181261 | − | 0.00590478i | ||||
\(568\) | −1.65241 | + | 22.5061i | −0.0693334 | + | 0.944335i | ||||
\(569\) | −26.3137 | −1.10313 | −0.551564 | − | 0.834133i | \(-0.685969\pi\) | ||||
−0.551564 | + | 0.834133i | \(0.685969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.2931i | − | 1.01664i | −0.861169 | − | 0.508318i | \(-0.830267\pi\) | ||
0.861169 | − | 0.508318i | \(-0.169733\pi\) | |||||||
\(572\) | 15.2848 | − | 7.85551i | 0.639089 | − | 0.328455i | ||||
\(573\) | 13.0767 | 0.546288 | ||||||||
\(574\) | −10.0308 | − | 11.7210i | −0.418678 | − | 0.489227i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −38.2132 | − | 5.64167i | −1.59222 | − | 0.235070i | ||||
\(577\) | 15.7850 | 0.657139 | 0.328569 | − | 0.944480i | \(-0.393434\pi\) | ||||
0.328569 | + | 0.944480i | \(0.393434\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 40.0488 | 1.66437 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.29289 | + | 7.03858i | −0.0951252 | + | 0.292010i | ||||
\(582\) | 27.8508 | + | 17.0000i | 1.15445 | + | 0.704673i | ||||
\(583\) | 5.53694 | 0.229317 | ||||||||
\(584\) | 34.8918 | + | 2.56177i | 1.44383 | + | 0.106007i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1518 | − | 19.9081i | 0.501987 | − | 0.822397i | ||||
\(587\) | 29.8172i | 1.23069i | 0.788260 | + | 0.615343i | \(0.210982\pi\) | ||||
−0.788260 | + | 0.615343i | \(0.789018\pi\) | |||||||
\(588\) | 38.7009 | + | 6.05110i | 1.59600 | + | 0.249543i | ||||
\(589\) | −20.2426 | −0.834083 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.5288 | −1.66713 | ||||||||
\(592\) | −7.29408 | − | 5.22183i | −0.299785 | − | 0.214616i | ||||
\(593\) | 0.707413 | 0.0290500 | 0.0145250 | − | 0.999895i | \(-0.495376\pi\) | ||||
0.0145250 | + | 0.999895i | \(0.495376\pi\) | |||||||
\(594\) | 5.55468 | − | 9.10013i | 0.227911 | − | 0.373383i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.82843 | + | 3.55765i | 0.0748953 | + | 0.145727i | ||||
\(597\) | 61.8406i | 2.53097i | ||||||||
\(598\) | −8.95362 | + | 14.6686i | −0.366141 | + | 0.599842i | ||||
\(599\) | − | 6.75773i | − | 0.276113i | −0.990424 | − | 0.138057i | \(-0.955914\pi\) | ||
0.990424 | − | 0.138057i | \(-0.0440856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.53880i | 0.307514i | 0.988109 | + | 0.153757i | \(0.0491373\pi\) | ||||
−0.988109 | + | 0.153757i | \(0.950863\pi\) | |||||||
\(602\) | 8.37836 | − | 7.17015i | 0.341477 | − | 0.292234i | ||||
\(603\) | −61.5961 | −2.50839 | ||||||||
\(604\) | −8.94975 | + | 4.59966i | −0.364160 | + | 0.187157i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −29.0208 | + | 47.5443i | −1.17889 | + | 1.93135i | ||||
\(607\) | − | 31.6550i | − | 1.28484i | −0.766354 | − | 0.642418i | \(-0.777931\pi\) | ||
0.766354 | − | 0.642418i | \(-0.222069\pi\) | |||||||
\(608\) | 11.3082 | + | 26.6386i | 0.458608 | + | 1.08034i | ||||
\(609\) | 18.8995 | − | 58.0165i | 0.765846 | − | 2.35095i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 69.2170i | − | 2.80022i | ||||||
\(612\) | −18.2003 | − | 35.4130i | −0.735702 | − | 1.43149i | ||||
\(613\) | 45.1127i | 1.82208i | 0.412313 | + | 0.911042i | \(0.364721\pi\) | ||||
−0.412313 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(614\) | −4.53635 | − | 2.76897i | −0.183072 | − | 0.111746i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.17429 | − | 10.2070i | 0.168187 | − | 0.411253i | ||||
\(617\) | − | 22.0000i | − | 0.885687i | −0.896599 | − | 0.442843i | \(-0.853970\pi\) | ||
0.896599 | − | 0.442843i | \(-0.146030\pi\) | |||||||
\(618\) | 4.77844 | − | 7.82843i | 0.192217 | − | 0.314906i | ||||
\(619\) | −20.0656 | −0.806504 | −0.403252 | − | 0.915089i | \(-0.632120\pi\) | ||||
−0.403252 | + | 0.915089i | \(0.632120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.6615i | 0.427830i | ||||||||
\(622\) | 16.4924 | − | 27.0192i | 0.661286 | − | 1.08337i | ||||
\(623\) | −10.1366 | + | 31.1167i | −0.406114 | + | 1.24666i | ||||
\(624\) | 53.0624 | + | 37.9874i | 2.12420 | + | 1.52071i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.7445 | − | 33.9853i | 0.829116 | − | 1.35832i | ||||
\(627\) | −21.0930 | −0.842375 | ||||||||
\(628\) | 9.74686 | + | 18.9649i | 0.388942 | + | 0.756781i | ||||
\(629\) | − | 9.24664i | − | 0.368688i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.25206i | 0.248891i | 0.992226 | + | 0.124445i | \(0.0397152\pi\) | ||||
−0.992226 | + | 0.124445i | \(0.960285\pi\) | |||||||
\(632\) | −0.863230 | + | 11.7574i | −0.0343374 | + | 0.467683i | ||||
\(633\) | −72.0937 | −2.86547 | ||||||||
\(634\) | −17.3137 | − | 10.5682i | −0.687615 | − | 0.419717i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.61098 | + | 18.7005i | 0.381100 | + | 0.741522i | ||||
\(637\) | −32.9848 | − | 24.0416i | −1.30691 | − | 0.952564i | ||||
\(638\) | −14.6622 | − | 8.94975i | −0.580482 | − | 0.354324i | ||||
\(639\) | − | 38.5237i | − | 1.52397i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8284 | −1.05966 | −0.529830 | − | 0.848104i | \(-0.677744\pi\) | ||||
−0.529830 | + | 0.848104i | \(0.677744\pi\) | |||||||
\(642\) | 33.1314 | + | 20.2232i | 1.30759 | + | 0.798148i | ||||
\(643\) | − | 14.8674i | − | 0.586313i | −0.956064 | − | 0.293156i | \(-0.905294\pi\) | ||
0.956064 | − | 0.293156i | \(-0.0947057\pi\) | |||||||
\(644\) | 1.75494 | + | 10.8871i | 0.0691542 | + | 0.429011i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.5416 | + | 25.4616i | −0.611477 | + | 1.00177i | ||||
\(647\) | 21.8210i | 0.857874i | 0.903334 | + | 0.428937i | \(0.141112\pi\) | ||||
−0.903334 | + | 0.428937i | \(0.858888\pi\) | |||||||
\(648\) | −0.483979 | − | 0.0355339i | −0.0190125 | − | 0.00139590i | ||||
\(649\) | − | 8.24621i | − | 0.323692i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.07269 | + | 27.8508i | −0.355587 | + | 1.09156i | ||||
\(652\) | −2.92556 | − | 5.69239i | −0.114574 | − | 0.222931i | ||||
\(653\) | 1.55635i | 0.0609047i | 0.999536 | + | 0.0304523i | \(0.00969477\pi\) | ||||
−0.999536 | + | 0.0304523i | \(0.990305\pi\) | |||||||
\(654\) | −9.55274 | − | 5.83095i | −0.373542 | − | 0.228008i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.4102 | − | 9.60035i | −0.523580 | − | 0.374831i | ||||
\(657\) | −59.7243 | −2.33007 | ||||||||
\(658\) | −28.8792 | − | 33.7455i | −1.12583 | − | 1.31554i | ||||
\(659\) | 29.9348i | 1.16609i | 0.812438 | + | 0.583047i | \(0.198140\pi\) | ||||
−0.812438 | + | 0.583047i | \(0.801860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.8158i | 1.50976i | 0.655863 | + | 0.754880i | \(0.272305\pi\) | ||||
−0.655863 | + | 0.754880i | \(0.727695\pi\) | |||||||
\(662\) | −21.9039 | − | 13.3701i | −0.851320 | − | 0.519642i | ||||
\(663\) | 67.2669i | 2.61243i | ||||||||
\(664\) | −0.579471 | + | 7.89250i | −0.0224878 | + | 0.306289i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.0711 | + | 7.97852i | 0.506494 | + | 0.309162i | ||||
\(667\) | 17.1778 | 0.665129 | ||||||||
\(668\) | −1.70785 | + | 0.877735i | −0.0660786 | + | 0.0339606i | ||||
\(669\) | 26.7279 | 1.03336 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.1853 | −0.663430 | ||||||||
\(672\) | 41.7189 | − | 3.61901i | 1.60934 | − | 0.139606i | ||||
\(673\) | 4.00000i | 0.154189i | 0.997024 | + | 0.0770943i | \(0.0245643\pi\) | ||||
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(674\) | 29.9350 | + | 18.2722i | 1.15305 | + | 0.703819i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.1985 | − | 37.3553i | −0.738403 | − | 1.43674i | ||||
\(677\) | 11.6619 | 0.448203 | 0.224102 | − | 0.974566i | \(-0.428055\pi\) | ||||
0.224102 | + | 0.974566i | \(0.428055\pi\) | |||||||
\(678\) | 8.89294 | − | 14.5691i | 0.341531 | − | 0.559524i | ||||
\(679\) | −20.7445 | − | 6.75773i | −0.796100 | − | 0.259338i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.48528 | 0.248517 | ||||||||
\(682\) | 7.03858 | + | 4.29632i | 0.269521 | + | 0.164515i | ||||
\(683\) | −11.0305 | −0.422070 | −0.211035 | − | 0.977478i | \(-0.567683\pi\) | ||||
−0.211035 | + | 0.977478i | \(0.567683\pi\) | |||||||
\(684\) | −22.5823 | − | 43.9393i | −0.863456 | − | 1.68006i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.1119 | + | 2.04110i | −0.996959 | + | 0.0779295i | ||||
\(687\) | 6.75773 | 0.257824 | ||||||||
\(688\) | 6.86246 | − | 9.58579i | 0.261629 | − | 0.365455i | ||||
\(689\) | − | 21.9090i | − | 0.834666i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0231 | 0.723673 | 0.361837 | − | 0.932241i | \(-0.382150\pi\) | ||||
0.361837 | + | 0.932241i | \(0.382150\pi\) | |||||||
\(692\) | 2.20806 | + | 4.29632i | 0.0839380 | + | 0.163322i | ||||
\(693\) | −5.83095 | + | 17.8995i | −0.221500 | + | 0.679946i | ||||
\(694\) | 22.9558 | − | 37.6081i | 0.871392 | − | 1.42759i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.77637 | − | 65.0551i | 0.181048 | − | 2.46591i | ||||
\(697\) | − | 17.0000i | − | 0.643921i | ||||||
\(698\) | 2.91548 | + | 1.77959i | 0.110352 | + | 0.0673586i | ||||
\(699\) | −66.5880 | −2.51859 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.1716 | −0.421944 | −0.210972 | − | 0.977492i | \(-0.567663\pi\) | ||||
−0.210972 | + | 0.977492i | \(0.567663\pi\) | |||||||
\(702\) | −36.0081 | − | 21.9792i | −1.35904 | − | 0.829551i | ||||
\(703\) | − | 11.4729i | − | 0.432710i | ||||||
\(704\) | 1.72183 | − | 11.6626i | 0.0648937 | − | 0.439550i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.59264 | + | 14.0772i | −0.323388 | + | 0.529801i | ||||
\(707\) | 11.5362 | − | 35.4130i | 0.433862 | − | 1.33184i | ||||
\(708\) | 27.8508 | − | 14.3137i | 1.04670 | − | 0.537942i | ||||
\(709\) | 28.0000 | 1.05156 | 0.525781 | − | 0.850620i | \(-0.323773\pi\) | ||||
0.525781 | + | 0.850620i | \(0.323773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 20.1251i | − | 0.754750i | ||||||
\(712\) | −2.56177 | + | 34.8918i | −0.0960064 | + | 1.30763i | ||||
\(713\) | −8.24621 | −0.308823 | ||||||||
\(714\) | 28.0655 | + | 32.7947i | 1.05033 | + | 1.22731i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.79289 | + | 2.46327i | −0.179119 | + | 0.0920568i | ||||
\(717\) | 24.7386 | 0.923881 | ||||||||
\(718\) | 27.2404 | + | 16.6274i | 1.01660 | + | 0.620530i | ||||
\(719\) | −30.5784 | −1.14038 | −0.570191 | − | 0.821512i | \(-0.693131\pi\) | ||||
−0.570191 | + | 0.821512i | \(0.693131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.89949 | + | 5.83095i | −0.0707409 | + | 0.217156i | ||||
\(722\) | −5.28411 | + | 8.65685i | −0.196654 | + | 0.322175i | ||||
\(723\) | −21.0930 | −0.784459 | ||||||||
\(724\) | 6.07591 | − | 3.12267i | 0.225810 | − | 0.116053i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −29.8172 | − | 18.2003i | −1.10662 | − | 0.675475i | ||||
\(727\) | − | 5.87707i | − | 0.217969i | −0.994043 | − | 0.108984i | \(-0.965240\pi\) | ||
0.994043 | − | 0.108984i | \(-0.0347598\pi\) | |||||||
\(728\) | −40.3879 | − | 16.5171i | −1.49688 | − | 0.612166i | ||||
\(729\) | 43.7696 | 1.62109 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1518 | 0.449452 | ||||||||
\(732\) | −29.8301 | − | 58.0416i | −1.10255 | − | 2.14528i | ||||
\(733\) | 24.7386 | 0.913742 | 0.456871 | − | 0.889533i | \(-0.348970\pi\) | ||||
0.456871 | + | 0.889533i | \(0.348970\pi\) | |||||||
\(734\) | 17.4665 | + | 10.6615i | 0.644700 | + | 0.393522i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.60660 | + | 10.8517i | 0.169802 | + | 0.400000i | ||||
\(737\) | − | 18.7990i | − | 0.692470i | ||||||
\(738\) | 24.0312 | + | 14.6686i | 0.884601 | + | 0.539957i | ||||
\(739\) | 43.1974i | 1.58904i | 0.607236 | + | 0.794522i | \(0.292278\pi\) | ||||
−0.607236 | + | 0.794522i | \(0.707722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 83.4625i | 3.06607i | ||||||||
\(742\) | −9.14101 | − | 10.6813i | −0.335577 | − | 0.392123i | ||||
\(743\) | −20.4827 | −0.751436 | −0.375718 | − | 0.926734i | \(-0.622604\pi\) | ||||
−0.375718 | + | 0.926734i | \(0.622604\pi\) | |||||||
\(744\) | −2.29289 | + | 31.2296i | −0.0840615 | + | 1.14493i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.7782 | + | 7.79974i | 0.467842 | + | 0.285569i | ||||
\(747\) | − | 13.5096i | − | 0.494291i | ||||||
\(748\) | 10.8080 | − | 5.55468i | 0.395179 | − | 0.203099i | ||||
\(749\) | −24.6777 | − | 8.03901i | −0.901702 | − | 0.293739i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.7132i | 1.26670i | 0.773864 | + | 0.633352i | \(0.218322\pi\) | ||||
−0.773864 | + | 0.633352i | \(0.781678\pi\) | |||||||
\(752\) | −38.6086 | − | 27.6399i | −1.40791 | − | 1.00792i | ||||
\(753\) | 58.5980i | 2.13543i | ||||||||
\(754\) | −35.4130 | + | 58.0165i | −1.28967 | + | 2.11284i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −26.7254 | + | 4.30798i | −0.971992 | + | 0.156680i | ||||
\(757\) | − | 15.4142i | − | 0.560239i | −0.959965 | − | 0.280120i | \(-0.909626\pi\) | ||
0.959965 | − | 0.280120i | \(-0.0903741\pi\) | |||||||
\(758\) | −27.5456 | − | 16.8137i | −1.00050 | − | 0.610701i | ||||
\(759\) | −8.59264 | −0.311893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30.8626i | − | 1.11877i | −0.828908 | − | 0.559384i | \(-0.811038\pi\) | ||
0.828908 | − | 0.559384i | \(-0.188962\pi\) | |||||||
\(762\) | 9.95406 | + | 6.07591i | 0.360597 | + | 0.220107i | ||||
\(763\) | 7.11529 | + | 2.31788i | 0.257591 | + | 0.0839130i | ||||
\(764\) | −8.31371 | + | 4.27277i | −0.300779 | + | 0.154583i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.1486 | + | 9.24664i | 0.547341 | + | 0.334095i | ||||
\(767\) | −32.6292 | −1.17817 | ||||||||
\(768\) | 42.3780 | − | 14.4285i | 1.52918 | − | 0.520645i | ||||
\(769\) | − | 17.1998i | − | 0.620242i | −0.950697 | − | 0.310121i | \(-0.899630\pi\) | ||
0.950697 | − | 0.310121i | \(-0.100370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 65.2584i | − | 2.35023i | ||||||
\(772\) | −25.4616 | + | 13.0858i | −0.916382 | + | 0.470968i | ||||
\(773\) | 13.0767 | 0.470337 | 0.235169 | − | 0.971955i | \(-0.424436\pi\) | ||||
0.235169 | + | 0.971955i | \(0.424436\pi\) | |||||||
\(774\) | −10.4853 | + | 17.1778i | −0.376886 | + | 0.617445i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −23.2612 | − | 1.70785i | −0.835028 | − | 0.0613081i | ||||
\(777\) | −15.7850 | − | 5.14214i | −0.566284 | − | 0.184473i | ||||
\(778\) | −11.4621 | + | 18.7782i | −0.410937 | + | 0.673230i | ||||
\(779\) | − | 21.0930i | − | 0.755737i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7574 | 0.420711 | ||||||||
\(782\) | −6.33117 | + | 10.3722i | −0.226402 | + | 0.370910i | ||||
\(783\) | 42.1678i | 1.50696i | ||||||||
\(784\) | −26.5818 | + | 8.79828i | −0.949349 | + | 0.314224i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 29.9706 | + | 18.2939i | 1.06901 | + | 0.652522i | ||||
\(787\) | 39.1711i | 1.39630i | 0.715953 | + | 0.698149i | \(0.245993\pi\) | ||||
−0.715953 | + | 0.698149i | \(0.754007\pi\) | |||||||
\(788\) | 25.7668 | − | 13.2426i | 0.917903 | − | 0.471750i | ||||
\(789\) | 41.2311i | 1.46786i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.53506 | + | 10.8517i | −0.125692 | + | 0.385843i | ||||
\(792\) | −1.47363 | + | 20.0711i | −0.0523630 | + | 0.713194i | ||||
\(793\) | 68.0000i | 2.41475i | ||||||||
\(794\) | 22.5241 | − | 36.9008i | 0.799349 | − | 1.30956i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.2062 | − | 39.3160i | −0.716189 | − | 1.39352i | ||||
\(797\) | −43.2319 | −1.53135 | −0.765677 | − | 0.643226i | \(-0.777596\pi\) | ||||
−0.765677 | + | 0.643226i | \(0.777596\pi\) | |||||||
\(798\) | 34.8228 | + | 40.6906i | 1.23271 | + | 1.44043i | ||||
\(799\) | − | 48.9438i | − | 1.73151i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 59.7243i | − | 2.11026i | ||||||
\(802\) | −20.9666 | + | 34.3492i | −0.740358 | + | 1.21291i | ||||
\(803\) | − | 18.2277i | − | 0.643243i | ||||||
\(804\) | 63.4918 | − | 32.6311i | 2.23918 | − | 1.15081i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.0000 | − | 27.8508i | 0.598799 | − | 0.981002i | ||||
\(807\) | 39.3870 | 1.38649 | ||||||||
\(808\) | 2.91548 | − | 39.7093i | 0.102566 | − | 1.39697i | ||||
\(809\) | 6.82843 | 0.240075 | 0.120037 | − | 0.992769i | \(-0.461699\pi\) | ||||
0.120037 | + | 0.992769i | \(0.461699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0257 | 0.738311 | 0.369156 | − | 0.929368i | \(-0.379647\pi\) | ||||
0.369156 | + | 0.929368i | \(0.379647\pi\) | |||||||
\(812\) | 6.94105 | + | 43.0601i | 0.243583 | + | 1.51111i | ||||
\(813\) | 11.8579i | 0.415873i | ||||||||
\(814\) | −2.43503 | + | 3.98926i | −0.0853477 | + | 0.139824i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 37.5208 | + | 26.8611i | 1.31349 | + | 0.940328i | ||||
\(817\) | 15.0776 | 0.527498 | ||||||||
\(818\) | −9.10013 | − | 5.55468i | −0.318179 | − | 0.194215i | ||||
\(819\) | 70.8261 | + | 23.0723i | 2.47486 | + | 0.806213i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4142 | 0.607760 | 0.303880 | − | 0.952710i | \(-0.401718\pi\) | ||||
0.303880 | + | 0.952710i | \(0.401718\pi\) | |||||||
\(822\) | 27.8006 | − | 45.5452i | 0.969658 | − | 1.58857i | ||||
\(823\) | 19.9770 | 0.696354 | 0.348177 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348177 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(824\) | −0.480049 | + | 6.53836i | −0.0167233 | + | 0.227775i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.9078 | + | 13.6138i | −0.553502 | + | 0.473684i | ||||
\(827\) | 33.5972 | 1.16829 | 0.584144 | − | 0.811650i | \(-0.301430\pi\) | ||||
0.584144 | + | 0.811650i | \(0.301430\pi\) | |||||||
\(828\) | −9.19932 | − | 17.8995i | −0.319698 | − | 0.622050i | ||||
\(829\) | − | 43.2319i | − | 1.50151i | −0.660583 | − | 0.750753i | \(-0.729691\pi\) | ||
0.660583 | − | 0.750753i | \(-0.270309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 72.4650 | 2.51378 | ||||||||
\(832\) | −46.1474 | − | 6.81305i | −1.59987 | − | 0.236200i | ||||
\(833\) | −23.3238 | − | 17.0000i | −0.808122 | − | 0.589015i | ||||
\(834\) | −36.1777 | − | 22.0827i | −1.25273 | − | 0.764661i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.4102 | − | 6.89207i | 0.463801 | − | 0.238367i | ||||
\(837\) | − | 20.2426i | − | 0.699688i | ||||||
\(838\) | −11.0152 | + | 18.0460i | −0.380513 | + | 0.623387i | ||||
\(839\) | 15.5463 | 0.536718 | 0.268359 | − | 0.963319i | \(-0.413519\pi\) | ||||
0.268359 | + | 0.963319i | \(0.413519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | 17.1778 | − | 28.1421i | 0.591987 | − | 0.969842i | ||||
\(843\) | − | 2.71557i | − | 0.0935292i | ||||||
\(844\) | 45.8345 | − | 23.5563i | 1.57769 | − | 0.810842i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 69.1871 | + | 42.2315i | 2.37870 | + | 1.45195i | ||||
\(847\) | 22.2091 | + | 7.23486i | 0.763114 | + | 0.248593i | ||||
\(848\) | −12.2206 | − | 8.74874i | −0.419658 | − | 0.300433i | ||||
\(849\) | −35.3431 | −1.21297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.67371i | − | 0.160213i | ||||||
\(852\) | 20.4083 | + | 39.7093i | 0.699178 | + | 1.36042i | ||||
\(853\) | 31.5700 | 1.08094 | 0.540468 | − | 0.841364i | \(-0.318247\pi\) | ||||
0.540468 | + | 0.841364i | \(0.318247\pi\) | |||||||
\(854\) | 28.3714 | + | 33.1521i | 0.970849 | + | 1.13444i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.6716 | − | 2.03166i | −0.945795 | − | 0.0694406i | ||||
\(857\) | 52.1855 | 1.78262 | 0.891312 | − | 0.453390i | \(-0.149786\pi\) | ||||
0.891312 | + | 0.453390i | \(0.149786\pi\) | |||||||
\(858\) | 17.7142 | − | 29.0208i | 0.604752 | − | 0.990754i | ||||
\(859\) | 37.3332 | 1.27379 | 0.636897 | − | 0.770949i | \(-0.280218\pi\) | ||||
0.636897 | + | 0.770949i | \(0.280218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.0208 | − | 9.45384i | −0.989027 | − | 0.322186i | ||||
\(862\) | −30.3664 | − | 18.5355i | −1.03428 | − | 0.631323i | ||||
\(863\) | −23.0723 | −0.785392 | −0.392696 | − | 0.919668i | \(-0.628457\pi\) | ||||
−0.392696 | + | 0.919668i | \(0.628457\pi\) | |||||||
\(864\) | −26.6386 | + | 11.3082i | −0.906264 | + | 0.384713i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.03796 | − | 4.97703i | 0.103234 | − | 0.169126i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.33205 | − | 20.6710i | −0.113097 | − | 0.701619i | ||||
\(869\) | 6.14214 | 0.208358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.3852 | −2.52045 | ||||||||
\(872\) | 7.97852 | + | 0.585786i | 0.270187 | + | 0.0198372i | ||||
\(873\) | 39.8162 | 1.34758 | ||||||||
\(874\) | −7.85551 | + | 12.8695i | −0.265717 | + | 0.435318i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 61.5624 | − | 31.6396i | 2.08000 | − | 1.06900i | ||||
\(877\) | 28.9706i | 0.978266i | 0.872209 | + | 0.489133i | \(0.162687\pi\) | ||||
−0.872209 | + | 0.489133i | \(0.837313\pi\) | |||||||
\(878\) | 4.12311 | − | 6.75481i | 0.139148 | − | 0.227964i | ||||
\(879\) | − | 46.1447i | − | 1.55642i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6619i | 0.392900i | 0.980514 | + | 0.196450i | \(0.0629413\pi\) | ||||
−0.980514 | + | 0.196450i | \(0.937059\pi\) | |||||||
\(882\) | 44.1563 | − | 18.3020i | 1.48682 | − | 0.616261i | ||||
\(883\) | −45.8919 | −1.54438 | −0.772192 | − | 0.635389i | \(-0.780840\pi\) | ||||
−0.772192 | + | 0.635389i | \(0.780840\pi\) | |||||||
\(884\) | −21.9792 | − | 42.7658i | −0.739240 | − | 1.43837i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.5711 | + | 18.9567i | −0.388738 | + | 0.636862i | ||||
\(887\) | 12.8307i | 0.430813i | 0.976524 | + | 0.215407i | \(0.0691077\pi\) | ||||
−0.976524 | + | 0.215407i | \(0.930892\pi\) | |||||||
\(888\) | −17.7001 | − | 1.29954i | −0.593975 | − | 0.0436099i | ||||
\(889\) | −7.41421 | − | 2.41526i | −0.248665 | − | 0.0810052i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.252834i | 0.00847026i | ||||||||
\(892\) | −16.9926 | + | 8.73324i | −0.568956 | + | 0.292411i | ||||
\(893\) | − | 60.7279i | − | 2.03218i | ||||||
\(894\) | 6.75481 | + | 4.12311i | 0.225915 | + | 0.137897i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.3409 | + | 15.9323i | −0.846580 | + | 0.532262i | ||||
\(897\) | 34.0000i | 1.13523i | ||||||||
\(898\) | −0.483979 | + | 0.792893i | −0.0161506 | + | 0.0264592i | ||||
\(899\) | −32.6151 | −1.08777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.4920i | − | 0.516113i | ||||||
\(902\) | −4.47681 | + | 7.33428i | −0.149062 | + | 0.244205i | ||||
\(903\) | 6.75773 | − | 20.7445i | 0.224883 | − | 0.690333i | ||||
\(904\) | −0.893398 | + | 12.1683i | −0.0297140 | + | 0.404710i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.3722 | + | 16.9926i | −0.344594 | + | 0.564543i | ||||
\(907\) | 20.8402 | 0.691988 | 0.345994 | − | 0.938237i | \(-0.387542\pi\) | ||||
0.345994 | + | 0.938237i | \(0.387542\pi\) | |||||||
\(908\) | −4.12311 | + | 2.11904i | −0.136830 | + | 0.0703228i | ||||
\(909\) | 67.9706i | 2.25444i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.62096i | 0.252494i | 0.991999 | + | 0.126247i | \(0.0402932\pi\) | ||||
−0.991999 | + | 0.126247i | \(0.959707\pi\) | |||||||
\(912\) | 46.5546 | + | 33.3284i | 1.54158 | + | 1.10361i | ||||
\(913\) | 4.12311 | 0.136455 | ||||||||
\(914\) | 15.1066 | + | 9.22101i | 0.499682 | + | 0.305004i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.29632 | + | 2.20806i | −0.141954 | + | 0.0729565i | ||||
\(917\) | −22.3234 | − | 7.27208i | −0.737183 | − | 0.240145i | ||||
\(918\) | −25.4616 | − | 15.5416i | −0.840357 | − | 0.512950i | ||||
\(919\) | 29.6820i | 0.979118i | 0.871970 | + | 0.489559i | \(0.162842\pi\) | ||||
−0.871970 | + | 0.489559i | \(0.837158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5147 | −0.346472 | ||||||||
\(922\) | 16.9926 | + | 10.3722i | 0.559623 | + | 0.341591i | ||||
\(923\) | − | 46.5224i | − | 1.53130i | ||||||
\(924\) | −3.47203 | − | 21.5394i | −0.114221 | − | 0.708594i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.8995 | − | 29.3244i | 0.588214 | − | 0.963660i | ||||
\(927\) | − | 11.1917i | − | 0.367585i | ||||||
\(928\) | 18.2199 | + | 42.9203i | 0.598096 | + | 1.40893i | ||||
\(929\) | 6.83139i | 0.224130i | 0.993701 | + | 0.112065i | \(0.0357466\pi\) | ||||
−0.993701 | + | 0.112065i | \(0.964253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.9394 | − | 21.0930i | −0.948451 | − | 0.691297i | ||||
\(932\) | 42.3342 | − | 21.7574i | 1.38670 | − | 0.712686i | ||||
\(933\) | − | 62.6274i | − | 2.05033i | ||||||
\(934\) | 36.5720 | + | 22.3234i | 1.19667 | + | 0.730443i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 79.4187 | + | 5.83095i | 2.59588 | + | 0.190591i | ||||
\(937\) | 35.6931 | 1.16604 | 0.583022 | − | 0.812457i | \(-0.301870\pi\) | ||||
0.583022 | + | 0.812457i | \(0.301870\pi\) | |||||||
\(938\) | −36.2651 | + | 31.0355i | −1.18410 | + | 1.01334i | ||||
\(939\) | − | 78.7739i | − | 2.57069i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.7386i | 0.806456i | 0.915099 | + | 0.403228i | \(0.132112\pi\) | ||||
−0.915099 | + | 0.403228i | \(0.867888\pi\) | |||||||
\(942\) | 36.0081 | + | 21.9792i | 1.17321 | + | 0.716121i | ||||
\(943\) | − | 8.59264i | − | 0.279815i | ||||||
\(944\) | −13.0296 | + | 18.2003i | −0.424076 | + | 0.592368i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.24264 | − | 3.20009i | −0.170453 | − | 0.104044i | ||||
\(947\) | −39.7445 | −1.29152 | −0.645762 | − | 0.763539i | \(-0.723460\pi\) | ||||
−0.645762 | + | 0.763539i | \(0.723460\pi\) | |||||||
\(948\) | 10.6615 | + | 20.7445i | 0.346268 | + | 0.673749i | ||||
\(949\) | −72.1249 | −2.34127 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.1312 | −1.30134 | ||||||||
\(952\) | −28.5586 | − | 11.6794i | −0.925589 | − | 0.378531i | ||||
\(953\) | − | 19.7696i | − | 0.640399i | −0.947350 | − | 0.320199i | \(-0.896250\pi\) | ||
0.947350 | − | 0.320199i | \(-0.103750\pi\) | |||||||
\(954\) | 21.8995 | + | 13.3674i | 0.709022 | + | 0.432784i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.7279 | + | 8.08325i | −0.508677 | + | 0.261431i | ||||
\(957\) | −33.9853 | −1.09859 | ||||||||
\(958\) | 12.3693 | − | 20.2644i | 0.399634 | − | 0.654714i | ||||
\(959\) | −11.0511 | + | 33.9241i | −0.356860 | + | 1.09547i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3431 | −0.494940 | ||||||||
\(962\) | 15.7850 | + | 9.63510i | 0.508929 | + | 0.310648i | ||||
\(963\) | 47.3655 | 1.52633 | ||||||||
\(964\) | 13.4102 | − | 6.89207i | 0.431913 | − | 0.221979i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.1857 | + | 16.5761i | 0.456417 | + | 0.533326i | ||||
\(967\) | −0.863230 | −0.0277596 | −0.0138798 | − | 0.999904i | \(-0.504418\pi\) | ||||
−0.0138798 | + | 0.999904i | \(0.504418\pi\) | |||||||
\(968\) | 24.9035 | + | 1.82843i | 0.800430 | + | 0.0587679i | ||||
\(969\) | 59.0169i | 1.89590i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.0089 | −1.31604 | −0.658019 | − | 0.753001i | \(-0.728605\pi\) | ||||
−0.658019 | + | 0.753001i | \(0.728605\pi\) | |||||||
\(972\) | −28.1543 | + | 14.4697i | −0.903050 | + | 0.464116i | ||||
\(973\) | 26.9467 | + | 8.77817i | 0.863871 | + | 0.281415i | ||||
\(974\) | −23.1421 | + | 37.9133i | −0.741522 | + | 1.21482i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.9298 | + | 27.1539i | 1.21410 | + | 0.869175i | ||||
\(977\) | − | 49.2843i | − | 1.57674i | −0.615199 | − | 0.788372i | \(-0.710924\pi\) | ||
0.615199 | − | 0.788372i | \(-0.289076\pi\) | |||||||
\(978\) | −10.8080 | − | 6.59715i | −0.345601 | − | 0.210953i | ||||
\(979\) | 18.2277 | 0.582561 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6569 | −0.436030 | ||||||||
\(982\) | 11.5362 | + | 7.04163i | 0.368134 | + | 0.224707i | ||||
\(983\) | − | 33.2940i | − | 1.06191i | −0.847399 | − | 0.530957i | \(-0.821833\pi\) | ||
0.847399 | − | 0.530957i | \(-0.178167\pi\) | |||||||
\(984\) | −32.5416 | − | 2.38922i | −1.03739 | − | 0.0761655i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25.0408 | + | 41.0239i | −0.797461 | + | 1.30647i | ||||
\(987\) | −83.5523 | − | 27.2181i | −2.65950 | − | 0.866361i | ||||
\(988\) | −27.2711 | − | 53.0624i | −0.867608 | − | 1.68814i | ||||
\(989\) | 6.14214 | 0.195309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 9.19932i | − | 0.292226i | −0.989268 | − | 0.146113i | \(-0.953324\pi\) | ||
0.989268 | − | 0.146113i | \(-0.0466763\pi\) | |||||||
\(992\) | −8.74643 | − | 20.6039i | −0.277699 | − | 0.654173i | ||||
\(993\) | −50.7707 | −1.61116 | ||||||||
\(994\) | −19.4104 | − | 22.6811i | −0.615660 | − | 0.719402i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.15685 | + | 13.9254i | 0.226774 | + | 0.441243i | ||||
\(997\) | 14.0772 | 0.445828 | 0.222914 | − | 0.974838i | \(-0.428443\pi\) | ||||
0.222914 | + | 0.974838i | \(0.428443\pi\) | |||||||
\(998\) | −10.6729 | − | 6.51472i | −0.337846 | − | 0.206220i | ||||
\(999\) | 11.4729 | 0.362988 |
(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 | 700.2.c.k.699.8 | 16 | ||
4.3 | odd | 2 | inner | 700.2.c.k.699.11 | 16 | ||
5.2 | odd | 4 | 700.2.g.i.251.2 | yes | 8 | ||
5.3 | odd | 4 | 700.2.g.k.251.7 | yes | 8 | ||
5.4 | even | 2 | inner | 700.2.c.k.699.9 | 16 | ||
7.6 | odd | 2 | inner | 700.2.c.k.699.7 | 16 | ||
20.3 | even | 4 | 700.2.g.k.251.6 | yes | 8 | ||
20.7 | even | 4 | 700.2.g.i.251.3 | yes | 8 | ||
20.19 | odd | 2 | inner | 700.2.c.k.699.6 | 16 | ||
28.27 | even | 2 | inner | 700.2.c.k.699.12 | 16 | ||
35.13 | even | 4 | 700.2.g.k.251.8 | yes | 8 | ||
35.27 | even | 4 | 700.2.g.i.251.1 | ✓ | 8 | ||
35.34 | odd | 2 | inner | 700.2.c.k.699.10 | 16 | ||
140.27 | odd | 4 | 700.2.g.i.251.4 | yes | 8 | ||
140.83 | odd | 4 | 700.2.g.k.251.5 | yes | 8 | ||
140.139 | even | 2 | inner | 700.2.c.k.699.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.c.k.699.5 | 16 | 140.139 | even | 2 | inner | ||
700.2.c.k.699.6 | 16 | 20.19 | odd | 2 | inner | ||
700.2.c.k.699.7 | 16 | 7.6 | odd | 2 | inner | ||
700.2.c.k.699.8 | 16 | 1.1 | even | 1 | trivial | ||
700.2.c.k.699.9 | 16 | 5.4 | even | 2 | inner | ||
700.2.c.k.699.10 | 16 | 35.34 | odd | 2 | inner | ||
700.2.c.k.699.11 | 16 | 4.3 | odd | 2 | inner | ||
700.2.c.k.699.12 | 16 | 28.27 | even | 2 | inner | ||
700.2.g.i.251.1 | ✓ | 8 | 35.27 | even | 4 | ||
700.2.g.i.251.2 | yes | 8 | 5.2 | odd | 4 | ||
700.2.g.i.251.3 | yes | 8 | 20.7 | even | 4 | ||
700.2.g.i.251.4 | yes | 8 | 140.27 | odd | 4 | ||
700.2.g.k.251.5 | yes | 8 | 140.83 | odd | 4 | ||
700.2.g.k.251.6 | yes | 8 | 20.3 | even | 4 | ||
700.2.g.k.251.7 | yes | 8 | 5.3 | odd | 4 | ||
700.2.g.k.251.8 | yes | 8 | 35.13 | even | 4 |