Properties

Label 336.6.q.f.193.2
Level $336$
Weight $6$
Character 336.193
Analytic conductor $53.889$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,6,Mod(193,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.193");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), 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: \(53.8889634572\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{9601})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.2
Root \(24.7462 + 42.8616i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.6.q.f.289.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 + 7.79423i) q^{3} +(37.7462 + 65.3783i) q^{5} +(-99.4847 - 83.1252i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 + 7.79423i) q^{3} +(37.7462 + 65.3783i) q^{5} +(-99.4847 - 83.1252i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(-74.7309 + 129.438i) q^{11} +349.416 q^{13} -679.431 q^{15} +(574.923 - 995.797i) q^{17} +(-1397.60 - 2420.72i) q^{19} +(1095.58 - 401.343i) q^{21} +(906.985 + 1570.94i) q^{23} +(-1287.05 + 2229.23i) q^{25} +729.000 q^{27} -759.033 q^{29} +(4515.87 - 7821.72i) q^{31} +(-672.578 - 1164.94i) q^{33} +(1679.42 - 9641.80i) q^{35} +(-3897.45 - 6750.57i) q^{37} +(-1572.37 + 2723.43i) q^{39} +7640.49 q^{41} -12188.8 q^{43} +(3057.44 - 5295.64i) q^{45} +(12299.4 + 21303.2i) q^{47} +(2987.41 + 16539.4i) q^{49} +(5174.31 + 8962.17i) q^{51} +(-6798.11 + 11774.7i) q^{53} -11283.2 q^{55} +25156.8 q^{57} +(-13179.4 + 22827.4i) q^{59} +(-17660.9 - 30589.5i) q^{61} +(-1801.94 + 10345.2i) q^{63} +(13189.1 + 22844.2i) q^{65} +(27186.0 - 47087.5i) q^{67} -16325.7 q^{69} +70145.7 q^{71} +(22234.4 - 38511.1i) q^{73} +(-11583.4 - 20063.1i) q^{75} +(18194.1 - 6665.05i) q^{77} +(30806.2 + 53357.9i) q^{79} +(-3280.50 + 5681.99i) q^{81} +87142.0 q^{83} +86804.6 q^{85} +(3415.65 - 5916.08i) q^{87} +(-49284.7 - 85363.6i) q^{89} +(-34761.5 - 29045.3i) q^{91} +(40642.9 + 70395.5i) q^{93} +(105508. - 182745. i) q^{95} +32342.3 q^{97} +12106.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9} + 191 q^{11} - 758 q^{13} - 954 q^{15} + 340 q^{17} - 1769 q^{19} - 27 q^{21} + 3236 q^{23} + 45 q^{25} + 2916 q^{27} + 8918 q^{29} + 1994 q^{31} + 1719 q^{33} + 4562 q^{35} - 20587 q^{37} + 3411 q^{39} + 17628 q^{41} - 31706 q^{43} + 4293 q^{45} + 33912 q^{47} + 9598 q^{49} + 3060 q^{51} - 49239 q^{53} - 37882 q^{55} + 31842 q^{57} - 56735 q^{59} - 67508 q^{61} + 729 q^{63} + 42762 q^{65} + 75723 q^{67} - 58248 q^{69} + 17984 q^{71} + 3201 q^{73} + 405 q^{75} + 120299 q^{77} + 26612 q^{79} - 13122 q^{81} + 1898 q^{83} + 210040 q^{85} - 40131 q^{87} - 176562 q^{89} - 210085 q^{91} + 17946 q^{93} + 234098 q^{95} - 258846 q^{97} - 30942 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 37.7462 + 65.3783i 0.675224 + 1.16952i 0.976403 + 0.215955i \(0.0692864\pi\)
−0.301179 + 0.953568i \(0.597380\pi\)
\(6\) 0 0
\(7\) −99.4847 83.1252i −0.767381 0.641191i
\(8\) 0 0
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 0 0
\(11\) −74.7309 + 129.438i −0.186217 + 0.322537i −0.943986 0.329986i \(-0.892956\pi\)
0.757769 + 0.652523i \(0.226289\pi\)
\(12\) 0 0
\(13\) 349.416 0.573435 0.286717 0.958015i \(-0.407436\pi\)
0.286717 + 0.958015i \(0.407436\pi\)
\(14\) 0 0
\(15\) −679.431 −0.779682
\(16\) 0 0
\(17\) 574.923 995.797i 0.482489 0.835696i −0.517309 0.855799i \(-0.673066\pi\)
0.999798 + 0.0201029i \(0.00639938\pi\)
\(18\) 0 0
\(19\) −1397.60 2420.72i −0.888176 1.53837i −0.842029 0.539432i \(-0.818639\pi\)
−0.0461468 0.998935i \(-0.514694\pi\)
\(20\) 0 0
\(21\) 1095.58 401.343i 0.542119 0.198595i
\(22\) 0 0
\(23\) 906.985 + 1570.94i 0.357504 + 0.619214i 0.987543 0.157349i \(-0.0502947\pi\)
−0.630040 + 0.776563i \(0.716961\pi\)
\(24\) 0 0
\(25\) −1287.05 + 2229.23i −0.411855 + 0.713354i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −759.033 −0.167597 −0.0837984 0.996483i \(-0.526705\pi\)
−0.0837984 + 0.996483i \(0.526705\pi\)
\(30\) 0 0
\(31\) 4515.87 7821.72i 0.843990 1.46183i −0.0425050 0.999096i \(-0.513534\pi\)
0.886495 0.462738i \(-0.153133\pi\)
\(32\) 0 0
\(33\) −672.578 1164.94i −0.107512 0.186217i
\(34\) 0 0
\(35\) 1679.42 9641.80i 0.231733 1.33042i
\(36\) 0 0
\(37\) −3897.45 6750.57i −0.468032 0.810655i 0.531300 0.847183i \(-0.321704\pi\)
−0.999333 + 0.0365280i \(0.988370\pi\)
\(38\) 0 0
\(39\) −1572.37 + 2723.43i −0.165536 + 0.286717i
\(40\) 0 0
\(41\) 7640.49 0.709842 0.354921 0.934896i \(-0.384508\pi\)
0.354921 + 0.934896i \(0.384508\pi\)
\(42\) 0 0
\(43\) −12188.8 −1.00529 −0.502645 0.864493i \(-0.667640\pi\)
−0.502645 + 0.864493i \(0.667640\pi\)
\(44\) 0 0
\(45\) 3057.44 5295.64i 0.225075 0.389841i
\(46\) 0 0
\(47\) 12299.4 + 21303.2i 0.812156 + 1.40670i 0.911352 + 0.411627i \(0.135039\pi\)
−0.0991964 + 0.995068i \(0.531627\pi\)
\(48\) 0 0
\(49\) 2987.41 + 16539.4i 0.177748 + 0.984076i
\(50\) 0 0
\(51\) 5174.31 + 8962.17i 0.278565 + 0.482489i
\(52\) 0 0
\(53\) −6798.11 + 11774.7i −0.332429 + 0.575783i −0.982988 0.183672i \(-0.941201\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(54\) 0 0
\(55\) −11283.2 −0.502952
\(56\) 0 0
\(57\) 25156.8 1.02558
\(58\) 0 0
\(59\) −13179.4 + 22827.4i −0.492908 + 0.853742i −0.999967 0.00816991i \(-0.997399\pi\)
0.507059 + 0.861912i \(0.330733\pi\)
\(60\) 0 0
\(61\) −17660.9 30589.5i −0.607698 1.05256i −0.991619 0.129198i \(-0.958760\pi\)
0.383921 0.923366i \(-0.374573\pi\)
\(62\) 0 0
\(63\) −1801.94 + 10345.2i −0.0571991 + 0.328389i
\(64\) 0 0
\(65\) 13189.1 + 22844.2i 0.387197 + 0.670645i
\(66\) 0 0
\(67\) 27186.0 47087.5i 0.739874 1.28150i −0.212678 0.977122i \(-0.568219\pi\)
0.952552 0.304377i \(-0.0984482\pi\)
\(68\) 0 0
\(69\) −16325.7 −0.412810
\(70\) 0 0
\(71\) 70145.7 1.65141 0.825706 0.564101i \(-0.190777\pi\)
0.825706 + 0.564101i \(0.190777\pi\)
\(72\) 0 0
\(73\) 22234.4 38511.1i 0.488335 0.845822i −0.511574 0.859239i \(-0.670938\pi\)
0.999910 + 0.0134170i \(0.00427090\pi\)
\(74\) 0 0
\(75\) −11583.4 20063.1i −0.237785 0.411855i
\(76\) 0 0
\(77\) 18194.1 6665.05i 0.349707 0.128108i
\(78\) 0 0
\(79\) 30806.2 + 53357.9i 0.555355 + 0.961903i 0.997876 + 0.0651450i \(0.0207510\pi\)
−0.442521 + 0.896758i \(0.645916\pi\)
\(80\) 0 0
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 87142.0 1.38846 0.694228 0.719755i \(-0.255746\pi\)
0.694228 + 0.719755i \(0.255746\pi\)
\(84\) 0 0
\(85\) 86804.6 1.30315
\(86\) 0 0
\(87\) 3415.65 5916.08i 0.0483810 0.0837984i
\(88\) 0 0
\(89\) −49284.7 85363.6i −0.659534 1.14235i −0.980736 0.195336i \(-0.937420\pi\)
0.321203 0.947010i \(-0.395913\pi\)
\(90\) 0 0
\(91\) −34761.5 29045.3i −0.440043 0.367681i
\(92\) 0 0
\(93\) 40642.9 + 70395.5i 0.487278 + 0.843990i
\(94\) 0 0
\(95\) 105508. 182745.i 1.19944 2.07748i
\(96\) 0 0
\(97\) 32342.3 0.349013 0.174507 0.984656i \(-0.444167\pi\)
0.174507 + 0.984656i \(0.444167\pi\)
\(98\) 0 0
\(99\) 12106.4 0.124144
\(100\) 0 0
\(101\) −15673.2 + 27146.8i −0.152881 + 0.264798i −0.932286 0.361723i \(-0.882189\pi\)
0.779404 + 0.626521i \(0.215522\pi\)
\(102\) 0 0
\(103\) 49666.5 + 86024.8i 0.461286 + 0.798970i 0.999025 0.0441406i \(-0.0140549\pi\)
−0.537740 + 0.843111i \(0.680722\pi\)
\(104\) 0 0
\(105\) 67593.0 + 56477.8i 0.598313 + 0.499925i
\(106\) 0 0
\(107\) −72634.0 125806.i −0.613310 1.06228i −0.990678 0.136221i \(-0.956504\pi\)
0.377368 0.926063i \(-0.376829\pi\)
\(108\) 0 0
\(109\) 90425.4 156621.i 0.728994 1.26265i −0.228315 0.973587i \(-0.573321\pi\)
0.957309 0.289067i \(-0.0933452\pi\)
\(110\) 0 0
\(111\) 70154.0 0.540437
\(112\) 0 0
\(113\) 197832. 1.45748 0.728738 0.684793i \(-0.240107\pi\)
0.728738 + 0.684793i \(0.240107\pi\)
\(114\) 0 0
\(115\) −68470.4 + 118594.i −0.482790 + 0.836217i
\(116\) 0 0
\(117\) −14151.3 24510.8i −0.0955725 0.165536i
\(118\) 0 0
\(119\) −139972. + 51275.9i −0.906094 + 0.331930i
\(120\) 0 0
\(121\) 69356.1 + 120128.i 0.430647 + 0.745902i
\(122\) 0 0
\(123\) −34382.2 + 59551.8i −0.204914 + 0.354921i
\(124\) 0 0
\(125\) 41589.2 0.238070
\(126\) 0 0
\(127\) 33517.2 0.184399 0.0921996 0.995741i \(-0.470610\pi\)
0.0921996 + 0.995741i \(0.470610\pi\)
\(128\) 0 0
\(129\) 54849.8 95002.6i 0.290202 0.502645i
\(130\) 0 0
\(131\) −5404.45 9360.79i −0.0275153 0.0476578i 0.851940 0.523640i \(-0.175426\pi\)
−0.879455 + 0.475982i \(0.842093\pi\)
\(132\) 0 0
\(133\) −62182.5 + 357000.i −0.304817 + 1.75000i
\(134\) 0 0
\(135\) 27517.0 + 47660.8i 0.129947 + 0.225075i
\(136\) 0 0
\(137\) 9466.01 16395.6i 0.0430889 0.0746322i −0.843677 0.536852i \(-0.819613\pi\)
0.886766 + 0.462220i \(0.152947\pi\)
\(138\) 0 0
\(139\) 168897. 0.741457 0.370729 0.928741i \(-0.379108\pi\)
0.370729 + 0.928741i \(0.379108\pi\)
\(140\) 0 0
\(141\) −221389. −0.937797
\(142\) 0 0
\(143\) −26112.1 + 45227.6i −0.106783 + 0.184954i
\(144\) 0 0
\(145\) −28650.6 49624.3i −0.113165 0.196008i
\(146\) 0 0
\(147\) −142355. 51142.6i −0.543349 0.195204i
\(148\) 0 0
\(149\) −132001. 228633.i −0.487093 0.843670i 0.512797 0.858510i \(-0.328609\pi\)
−0.999890 + 0.0148402i \(0.995276\pi\)
\(150\) 0 0
\(151\) 139587. 241772.i 0.498200 0.862908i −0.501798 0.864985i \(-0.667328\pi\)
0.999998 + 0.00207707i \(0.000661153\pi\)
\(152\) 0 0
\(153\) −93137.6 −0.321660
\(154\) 0 0
\(155\) 681828. 2.27953
\(156\) 0 0
\(157\) −94301.2 + 163334.i −0.305329 + 0.528845i −0.977334 0.211701i \(-0.932100\pi\)
0.672006 + 0.740546i \(0.265433\pi\)
\(158\) 0 0
\(159\) −61183.0 105972.i −0.191928 0.332429i
\(160\) 0 0
\(161\) 40353.9 231678.i 0.122693 0.704402i
\(162\) 0 0
\(163\) 44858.7 + 77697.5i 0.132244 + 0.229054i 0.924541 0.381081i \(-0.124448\pi\)
−0.792297 + 0.610136i \(0.791115\pi\)
\(164\) 0 0
\(165\) 50774.5 87944.0i 0.145190 0.251476i
\(166\) 0 0
\(167\) −529411. −1.46893 −0.734467 0.678645i \(-0.762568\pi\)
−0.734467 + 0.678645i \(0.762568\pi\)
\(168\) 0 0
\(169\) −249202. −0.671172
\(170\) 0 0
\(171\) −113206. + 196078.i −0.296059 + 0.512789i
\(172\) 0 0
\(173\) −16919.2 29304.8i −0.0429797 0.0744430i 0.843735 0.536759i \(-0.180352\pi\)
−0.886715 + 0.462316i \(0.847018\pi\)
\(174\) 0 0
\(175\) 313347. 114788.i 0.773446 0.283337i
\(176\) 0 0
\(177\) −118615. 205447.i −0.284581 0.492908i
\(178\) 0 0
\(179\) −123872. + 214552.i −0.288962 + 0.500496i −0.973562 0.228422i \(-0.926643\pi\)
0.684601 + 0.728918i \(0.259977\pi\)
\(180\) 0 0
\(181\) 369470. 0.838268 0.419134 0.907924i \(-0.362334\pi\)
0.419134 + 0.907924i \(0.362334\pi\)
\(182\) 0 0
\(183\) 317896. 0.701709
\(184\) 0 0
\(185\) 294227. 509617.i 0.632053 1.09475i
\(186\) 0 0
\(187\) 85929.1 + 148833.i 0.179695 + 0.311241i
\(188\) 0 0
\(189\) −72524.3 60598.3i −0.147683 0.123397i
\(190\) 0 0
\(191\) −242612. 420217.i −0.481204 0.833470i 0.518563 0.855039i \(-0.326467\pi\)
−0.999767 + 0.0215693i \(0.993134\pi\)
\(192\) 0 0
\(193\) 165409. 286496.i 0.319643 0.553637i −0.660771 0.750588i \(-0.729770\pi\)
0.980413 + 0.196950i \(0.0631038\pi\)
\(194\) 0 0
\(195\) −237404. −0.447097
\(196\) 0 0
\(197\) −161963. −0.297337 −0.148669 0.988887i \(-0.547499\pi\)
−0.148669 + 0.988887i \(0.547499\pi\)
\(198\) 0 0
\(199\) 27698.1 47974.5i 0.0495813 0.0858773i −0.840170 0.542324i \(-0.817545\pi\)
0.889751 + 0.456446i \(0.150878\pi\)
\(200\) 0 0
\(201\) 244674. + 423787.i 0.427166 + 0.739874i
\(202\) 0 0
\(203\) 75512.2 + 63094.8i 0.128611 + 0.107462i
\(204\) 0 0
\(205\) 288399. + 499522.i 0.479303 + 0.830176i
\(206\) 0 0
\(207\) 73465.8 127246.i 0.119168 0.206405i
\(208\) 0 0
\(209\) 417776. 0.661572
\(210\) 0 0
\(211\) −481748. −0.744926 −0.372463 0.928047i \(-0.621487\pi\)
−0.372463 + 0.928047i \(0.621487\pi\)
\(212\) 0 0
\(213\) −315656. + 546732.i −0.476722 + 0.825706i
\(214\) 0 0
\(215\) −460082. 796885.i −0.678795 1.17571i
\(216\) 0 0
\(217\) −1.09944e6 + 402759.i −1.58498 + 0.580625i
\(218\) 0 0
\(219\) 200110. + 346600.i 0.281941 + 0.488335i
\(220\) 0 0
\(221\) 200887. 347947.i 0.276676 0.479217i
\(222\) 0 0
\(223\) −638779. −0.860178 −0.430089 0.902787i \(-0.641518\pi\)
−0.430089 + 0.902787i \(0.641518\pi\)
\(224\) 0 0
\(225\) 208502. 0.274570
\(226\) 0 0
\(227\) −262841. + 455254.i −0.338554 + 0.586394i −0.984161 0.177277i \(-0.943271\pi\)
0.645607 + 0.763670i \(0.276605\pi\)
\(228\) 0 0
\(229\) −466343. 807730.i −0.587647 1.01784i −0.994540 0.104359i \(-0.966721\pi\)
0.406892 0.913476i \(-0.366612\pi\)
\(230\) 0 0
\(231\) −29924.6 + 171802.i −0.0368976 + 0.211835i
\(232\) 0 0
\(233\) 353896. + 612967.i 0.427058 + 0.739685i 0.996610 0.0822696i \(-0.0262168\pi\)
−0.569553 + 0.821955i \(0.692884\pi\)
\(234\) 0 0
\(235\) −928511. + 1.60823e6i −1.09677 + 1.89967i
\(236\) 0 0
\(237\) −554512. −0.641269
\(238\) 0 0
\(239\) 500614. 0.566902 0.283451 0.958987i \(-0.408521\pi\)
0.283451 + 0.958987i \(0.408521\pi\)
\(240\) 0 0
\(241\) −604109. + 1.04635e6i −0.669997 + 1.16047i 0.307907 + 0.951416i \(0.400371\pi\)
−0.977904 + 0.209052i \(0.932962\pi\)
\(242\) 0 0
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) −968552. + 819609.i −1.03088 + 0.872352i
\(246\) 0 0
\(247\) −488344. 845836.i −0.509311 0.882153i
\(248\) 0 0
\(249\) −392139. + 679204.i −0.400813 + 0.694228i
\(250\) 0 0
\(251\) −97826.7 −0.0980106 −0.0490053 0.998799i \(-0.515605\pi\)
−0.0490053 + 0.998799i \(0.515605\pi\)
\(252\) 0 0
\(253\) −271119. −0.266292
\(254\) 0 0
\(255\) −390621. + 676575.i −0.376188 + 0.651577i
\(256\) 0 0
\(257\) 553956. + 959481.i 0.523170 + 0.906157i 0.999636 + 0.0269643i \(0.00858403\pi\)
−0.476466 + 0.879193i \(0.658083\pi\)
\(258\) 0 0
\(259\) −173406. + 995555.i −0.160626 + 0.922180i
\(260\) 0 0
\(261\) 30740.8 + 53244.7i 0.0279328 + 0.0483810i
\(262\) 0 0
\(263\) 753427. 1.30497e6i 0.671663 1.16336i −0.305769 0.952106i \(-0.598913\pi\)
0.977432 0.211249i \(-0.0677532\pi\)
\(264\) 0 0
\(265\) −1.02641e6 −0.897856
\(266\) 0 0
\(267\) 887125. 0.761564
\(268\) 0 0
\(269\) 1.06751e6 1.84898e6i 0.899481 1.55795i 0.0713221 0.997453i \(-0.477278\pi\)
0.828159 0.560493i \(-0.189388\pi\)
\(270\) 0 0
\(271\) 614299. + 1.06400e6i 0.508108 + 0.880070i 0.999956 + 0.00938828i \(0.00298843\pi\)
−0.491847 + 0.870681i \(0.663678\pi\)
\(272\) 0 0
\(273\) 382812. 140236.i 0.310870 0.113881i
\(274\) 0 0
\(275\) −192364. 333185.i −0.153388 0.265677i
\(276\) 0 0
\(277\) 923412. 1.59940e6i 0.723097 1.25244i −0.236656 0.971593i \(-0.576051\pi\)
0.959753 0.280847i \(-0.0906152\pi\)
\(278\) 0 0
\(279\) −731571. −0.562660
\(280\) 0 0
\(281\) −2.28326e6 −1.72500 −0.862500 0.506056i \(-0.831103\pi\)
−0.862500 + 0.506056i \(0.831103\pi\)
\(282\) 0 0
\(283\) 668463. 1.15781e6i 0.496148 0.859354i −0.503842 0.863796i \(-0.668081\pi\)
0.999990 + 0.00444218i \(0.00141400\pi\)
\(284\) 0 0
\(285\) 949573. + 1.64471e6i 0.692495 + 1.19944i
\(286\) 0 0
\(287\) −760112. 635118.i −0.544720 0.455145i
\(288\) 0 0
\(289\) 48854.5 + 84618.5i 0.0344081 + 0.0595965i
\(290\) 0 0
\(291\) −145541. + 252084.i −0.100751 + 0.174507i
\(292\) 0 0
\(293\) −2.23033e6 −1.51775 −0.758875 0.651236i \(-0.774251\pi\)
−0.758875 + 0.651236i \(0.774251\pi\)
\(294\) 0 0
\(295\) −1.98989e6 −1.33129
\(296\) 0 0
\(297\) −54478.8 + 94360.1i −0.0358374 + 0.0620722i
\(298\) 0 0
\(299\) 316915. + 548913.i 0.205005 + 0.355079i
\(300\) 0 0
\(301\) 1.21260e6 + 1.01320e6i 0.771440 + 0.644583i
\(302\) 0 0
\(303\) −141059. 244321.i −0.0882661 0.152881i
\(304\) 0 0
\(305\) 1.33326e6 2.30928e6i 0.820664 1.42143i
\(306\) 0 0
\(307\) −1.77782e6 −1.07657 −0.538284 0.842763i \(-0.680927\pi\)
−0.538284 + 0.842763i \(0.680927\pi\)
\(308\) 0 0
\(309\) −893996. −0.532647
\(310\) 0 0
\(311\) 701358. 1.21479e6i 0.411187 0.712196i −0.583833 0.811874i \(-0.698448\pi\)
0.995020 + 0.0996776i \(0.0317811\pi\)
\(312\) 0 0
\(313\) −609472. 1.05564e6i −0.351636 0.609051i 0.634900 0.772594i \(-0.281041\pi\)
−0.986536 + 0.163543i \(0.947708\pi\)
\(314\) 0 0
\(315\) −744370. + 272685.i −0.422681 + 0.154841i
\(316\) 0 0
\(317\) −1.34001e6 2.32096e6i −0.748961 1.29724i −0.948321 0.317312i \(-0.897220\pi\)
0.199361 0.979926i \(-0.436113\pi\)
\(318\) 0 0
\(319\) 56723.2 98247.5i 0.0312093 0.0540561i
\(320\) 0 0
\(321\) 1.30741e6 0.708190
\(322\) 0 0
\(323\) −3.21405e6 −1.71414
\(324\) 0 0
\(325\) −449715. + 778929.i −0.236172 + 0.409062i
\(326\) 0 0
\(327\) 813828. + 1.40959e6i 0.420885 + 0.728994i
\(328\) 0 0
\(329\) 547229. 3.14173e6i 0.278727 1.60022i
\(330\) 0 0
\(331\) 71280.1 + 123461.i 0.0357601 + 0.0619383i 0.883352 0.468711i \(-0.155281\pi\)
−0.847591 + 0.530649i \(0.821948\pi\)
\(332\) 0 0
\(333\) −315693. + 546796.i −0.156011 + 0.270218i
\(334\) 0 0
\(335\) 4.10466e6 1.99832
\(336\) 0 0
\(337\) −1.21206e6 −0.581367 −0.290683 0.956819i \(-0.593883\pi\)
−0.290683 + 0.956819i \(0.593883\pi\)
\(338\) 0 0
\(339\) −890246. + 1.54195e6i −0.420737 + 0.728738i
\(340\) 0 0
\(341\) 674950. + 1.16905e6i 0.314330 + 0.544435i
\(342\) 0 0
\(343\) 1.07764e6 1.89374e6i 0.494580 0.869132i
\(344\) 0 0
\(345\) −616234. 1.06735e6i −0.278739 0.482790i
\(346\) 0 0
\(347\) 1.73426e6 3.00383e6i 0.773199 1.33922i −0.162602 0.986692i \(-0.551989\pi\)
0.935801 0.352529i \(-0.114678\pi\)
\(348\) 0 0
\(349\) 1.01692e6 0.446911 0.223456 0.974714i \(-0.428266\pi\)
0.223456 + 0.974714i \(0.428266\pi\)
\(350\) 0 0
\(351\) 254724. 0.110358
\(352\) 0 0
\(353\) −781927. + 1.35434e6i −0.333987 + 0.578483i −0.983290 0.182048i \(-0.941728\pi\)
0.649303 + 0.760530i \(0.275061\pi\)
\(354\) 0 0
\(355\) 2.64773e6 + 4.58601e6i 1.11507 + 1.93136i
\(356\) 0 0
\(357\) 230217. 1.32171e6i 0.0956021 0.548867i
\(358\) 0 0
\(359\) 24776.6 + 42914.3i 0.0101462 + 0.0175738i 0.871054 0.491187i \(-0.163437\pi\)
−0.860908 + 0.508761i \(0.830104\pi\)
\(360\) 0 0
\(361\) −2.66853e6 + 4.62202e6i −1.07771 + 1.86666i
\(362\) 0 0
\(363\) −1.24841e6 −0.497268
\(364\) 0 0
\(365\) 3.35705e6 1.31894
\(366\) 0 0
\(367\) 1.77416e6 3.07293e6i 0.687585 1.19093i −0.285032 0.958518i \(-0.592004\pi\)
0.972617 0.232414i \(-0.0746626\pi\)
\(368\) 0 0
\(369\) −309440. 535966.i −0.118307 0.204914i
\(370\) 0 0
\(371\) 1.65508e6 606306.i 0.624287 0.228695i
\(372\) 0 0
\(373\) 1.12787e6 + 1.95352e6i 0.419745 + 0.727020i 0.995914 0.0903112i \(-0.0287862\pi\)
−0.576169 + 0.817331i \(0.695453\pi\)
\(374\) 0 0
\(375\) −187151. + 324155.i −0.0687250 + 0.119035i
\(376\) 0 0
\(377\) −265218. −0.0961059
\(378\) 0 0
\(379\) −4.39503e6 −1.57168 −0.785840 0.618430i \(-0.787769\pi\)
−0.785840 + 0.618430i \(0.787769\pi\)
\(380\) 0 0
\(381\) −150828. + 261241.i −0.0532315 + 0.0921996i
\(382\) 0 0
\(383\) −613904. 1.06331e6i −0.213847 0.370394i 0.739068 0.673631i \(-0.235266\pi\)
−0.952915 + 0.303237i \(0.901933\pi\)
\(384\) 0 0
\(385\) 1.12251e6 + 937919.i 0.385956 + 0.322488i
\(386\) 0 0
\(387\) 493648. + 855023.i 0.167548 + 0.290202i
\(388\) 0 0
\(389\) −1.02712e6 + 1.77903e6i −0.344150 + 0.596086i −0.985199 0.171415i \(-0.945166\pi\)
0.641049 + 0.767500i \(0.278500\pi\)
\(390\) 0 0
\(391\) 2.08579e6 0.689967
\(392\) 0 0
\(393\) 97280.2 0.0317719
\(394\) 0 0
\(395\) −2.32563e6 + 4.02812e6i −0.749978 + 1.29900i
\(396\) 0 0
\(397\) 1.90184e6 + 3.29408e6i 0.605615 + 1.04896i 0.991954 + 0.126599i \(0.0404062\pi\)
−0.386339 + 0.922357i \(0.626260\pi\)
\(398\) 0 0
\(399\) −2.50272e6 2.09116e6i −0.787009 0.657591i
\(400\) 0 0
\(401\) −592622. 1.02645e6i −0.184042 0.318770i 0.759211 0.650844i \(-0.225585\pi\)
−0.943253 + 0.332074i \(0.892252\pi\)
\(402\) 0 0
\(403\) 1.57792e6 2.73303e6i 0.483974 0.838267i
\(404\) 0 0
\(405\) −495305. −0.150050
\(406\) 0 0
\(407\) 1.16504e6 0.348621
\(408\) 0 0
\(409\) 2.15197e6 3.72731e6i 0.636102 1.10176i −0.350178 0.936683i \(-0.613879\pi\)
0.986280 0.165079i \(-0.0527878\pi\)
\(410\) 0 0
\(411\) 85194.1 + 147560.i 0.0248774 + 0.0430889i
\(412\) 0 0
\(413\) 3.20868e6 1.17544e6i 0.925660 0.339097i
\(414\) 0 0
\(415\) 3.28928e6 + 5.69719e6i 0.937519 + 1.62383i
\(416\) 0 0
\(417\) −760038. + 1.31643e6i −0.214040 + 0.370729i
\(418\) 0 0
\(419\) 113725. 0.0316461 0.0158230 0.999875i \(-0.494963\pi\)
0.0158230 + 0.999875i \(0.494963\pi\)
\(420\) 0 0
\(421\) 443417. 0.121929 0.0609645 0.998140i \(-0.480582\pi\)
0.0609645 + 0.998140i \(0.480582\pi\)
\(422\) 0 0
\(423\) 996252. 1.72556e6i 0.270719 0.468898i
\(424\) 0 0
\(425\) 1.47991e6 + 2.56327e6i 0.397431 + 0.688371i
\(426\) 0 0
\(427\) −785774. + 4.51125e6i −0.208559 + 1.19737i
\(428\) 0 0
\(429\) −235009. 407048.i −0.0616512 0.106783i
\(430\) 0 0
\(431\) 2.31655e6 4.01239e6i 0.600688 1.04042i −0.392029 0.919953i \(-0.628227\pi\)
0.992717 0.120469i \(-0.0384399\pi\)
\(432\) 0 0
\(433\) 6.57955e6 1.68646 0.843231 0.537552i \(-0.180651\pi\)
0.843231 + 0.537552i \(0.180651\pi\)
\(434\) 0 0
\(435\) 515711. 0.130672
\(436\) 0 0
\(437\) 2.53520e6 4.39110e6i 0.635052 1.09994i
\(438\) 0 0
\(439\) −910348. 1.57677e6i −0.225448 0.390487i 0.731006 0.682371i \(-0.239051\pi\)
−0.956454 + 0.291884i \(0.905718\pi\)
\(440\) 0 0
\(441\) 1.03921e6 879405.i 0.254454 0.215324i
\(442\) 0 0
\(443\) −1.03495e6 1.79259e6i −0.250559 0.433982i 0.713121 0.701041i \(-0.247281\pi\)
−0.963680 + 0.267060i \(0.913948\pi\)
\(444\) 0 0
\(445\) 3.72062e6 6.44430e6i 0.890666 1.54268i
\(446\) 0 0
\(447\) 2.37602e6 0.562447
\(448\) 0 0
\(449\) 5.72581e6 1.34036 0.670180 0.742199i \(-0.266217\pi\)
0.670180 + 0.742199i \(0.266217\pi\)
\(450\) 0 0
\(451\) −570981. + 988968.i −0.132184 + 0.228950i
\(452\) 0 0
\(453\) 1.25629e6 + 2.17595e6i 0.287636 + 0.498200i
\(454\) 0 0
\(455\) 586814. 3.36900e6i 0.132884 0.762908i
\(456\) 0 0
\(457\) −159338. 275982.i −0.0356886 0.0618144i 0.847629 0.530589i \(-0.178029\pi\)
−0.883318 + 0.468774i \(0.844696\pi\)
\(458\) 0 0
\(459\) 419119. 725936.i 0.0928551 0.160830i
\(460\) 0 0
\(461\) −3.42470e6 −0.750535 −0.375267 0.926917i \(-0.622449\pi\)
−0.375267 + 0.926917i \(0.622449\pi\)
\(462\) 0 0
\(463\) −3.82945e6 −0.830201 −0.415101 0.909775i \(-0.636254\pi\)
−0.415101 + 0.909775i \(0.636254\pi\)
\(464\) 0 0
\(465\) −3.06822e6 + 5.31432e6i −0.658044 + 1.13977i
\(466\) 0 0
\(467\) 1.42231e6 + 2.46351e6i 0.301788 + 0.522712i 0.976541 0.215332i \(-0.0690832\pi\)
−0.674753 + 0.738044i \(0.735750\pi\)
\(468\) 0 0
\(469\) −6.61874e6 + 2.42464e6i −1.38945 + 0.508998i
\(470\) 0 0
\(471\) −848710. 1.47001e6i −0.176282 0.305329i
\(472\) 0 0
\(473\) 910882. 1.57769e6i 0.187202 0.324243i
\(474\) 0 0
\(475\) 7.19511e6 1.46320
\(476\) 0 0
\(477\) 1.10129e6 0.221619
\(478\) 0 0
\(479\) 651827. 1.12900e6i 0.129806 0.224830i −0.793796 0.608185i \(-0.791898\pi\)
0.923601 + 0.383355i \(0.125231\pi\)
\(480\) 0 0
\(481\) −1.36183e6 2.35876e6i −0.268386 0.464858i
\(482\) 0 0
\(483\) 1.62416e6 + 1.35708e6i 0.316782 + 0.264690i
\(484\) 0 0
\(485\) 1.22080e6 + 2.11449e6i 0.235662 + 0.408179i
\(486\) 0 0
\(487\) 3.11812e6 5.40074e6i 0.595759 1.03188i −0.397681 0.917524i \(-0.630185\pi\)
0.993439 0.114360i \(-0.0364818\pi\)
\(488\) 0 0
\(489\) −807456. −0.152703
\(490\) 0 0
\(491\) 3.93928e6 0.737417 0.368709 0.929545i \(-0.379800\pi\)
0.368709 + 0.929545i \(0.379800\pi\)
\(492\) 0 0
\(493\) −436386. + 755843.i −0.0808637 + 0.140060i
\(494\) 0 0
\(495\) 456970. + 791496.i 0.0838253 + 0.145190i
\(496\) 0 0
\(497\) −6.97843e6 5.83088e6i −1.26726 1.05887i
\(498\) 0 0
\(499\) 3.98785e6 + 6.90717e6i 0.716948 + 1.24179i 0.962203 + 0.272333i \(0.0877951\pi\)
−0.245255 + 0.969459i \(0.578872\pi\)
\(500\) 0 0
\(501\) 2.38235e6 4.12635e6i 0.424045 0.734467i
\(502\) 0 0
\(503\) 2.70777e6 0.477190 0.238595 0.971119i \(-0.423313\pi\)
0.238595 + 0.971119i \(0.423313\pi\)
\(504\) 0 0
\(505\) −2.36641e6 −0.412917
\(506\) 0 0
\(507\) 1.12141e6 1.94233e6i 0.193751 0.335586i
\(508\) 0 0
\(509\) −1.95025e6 3.37793e6i −0.333653 0.577904i 0.649572 0.760300i \(-0.274948\pi\)
−0.983225 + 0.182396i \(0.941615\pi\)
\(510\) 0 0
\(511\) −5.41323e6 + 1.98303e6i −0.917073 + 0.335951i
\(512\) 0 0
\(513\) −1.01885e6 1.76470e6i −0.170930 0.296059i
\(514\) 0 0
\(515\) −3.74944e6 + 6.49422e6i −0.622943 + 1.07897i
\(516\) 0 0
\(517\) −3.67658e6 −0.604947
\(518\) 0 0
\(519\) 304545. 0.0496287
\(520\) 0 0
\(521\) −3.50032e6 + 6.06273e6i −0.564954 + 0.978529i 0.432100 + 0.901826i \(0.357773\pi\)
−0.997054 + 0.0767034i \(0.975561\pi\)
\(522\) 0 0
\(523\) −1.05604e6 1.82911e6i −0.168821 0.292406i 0.769185 0.639026i \(-0.220663\pi\)
−0.938005 + 0.346620i \(0.887329\pi\)
\(524\) 0 0
\(525\) −515374. + 2.95884e6i −0.0816064 + 0.468515i
\(526\) 0 0
\(527\) −5.19256e6 8.99378e6i −0.814433 1.41064i
\(528\) 0 0
\(529\) 1.57293e6 2.72439e6i 0.244382 0.423283i
\(530\) 0 0
\(531\) 2.13506e6 0.328605
\(532\) 0 0
\(533\) 2.66971e6 0.407048
\(534\) 0 0
\(535\) 5.48331e6 9.49737e6i 0.828244 1.43456i
\(536\) 0 0
\(537\) −1.11485e6 1.93097e6i −0.166832 0.288962i
\(538\) 0 0
\(539\) −2.36407e6 849318.i −0.350500 0.125921i
\(540\) 0 0
\(541\) −2.85283e6 4.94125e6i −0.419067 0.725845i 0.576779 0.816900i \(-0.304309\pi\)
−0.995846 + 0.0910551i \(0.970976\pi\)
\(542\) 0 0
\(543\) −1.66262e6 + 2.87974e6i −0.241987 + 0.419134i
\(544\) 0 0
\(545\) 1.36528e7 1.96894
\(546\) 0 0
\(547\) −2.28054e6 −0.325888 −0.162944 0.986635i \(-0.552099\pi\)
−0.162944 + 0.986635i \(0.552099\pi\)
\(548\) 0 0
\(549\) −1.43053e6 + 2.47775e6i −0.202566 + 0.350855i
\(550\) 0 0
\(551\) 1.06083e6 + 1.83740e6i 0.148855 + 0.257825i
\(552\) 0 0
\(553\) 1.37064e6 7.86907e6i 0.190595 1.09424i
\(554\) 0 0
\(555\) 2.64805e6 + 4.58655e6i 0.364916 + 0.632053i
\(556\) 0 0
\(557\) 3.36970e6 5.83650e6i 0.460208 0.797103i −0.538763 0.842457i \(-0.681108\pi\)
0.998971 + 0.0453541i \(0.0144416\pi\)
\(558\) 0 0
\(559\) −4.25897e6 −0.576468
\(560\) 0 0
\(561\) −1.54672e6 −0.207494
\(562\) 0 0
\(563\) −4.83410e6 + 8.37291e6i −0.642754 + 1.11328i 0.342061 + 0.939678i \(0.388875\pi\)
−0.984815 + 0.173605i \(0.944458\pi\)
\(564\) 0 0
\(565\) 7.46742e6 + 1.29339e7i 0.984123 + 1.70455i
\(566\) 0 0
\(567\) 798676. 292579.i 0.104331 0.0382196i
\(568\) 0 0
\(569\) 6.97934e6 + 1.20886e7i 0.903719 + 1.56529i 0.822627 + 0.568581i \(0.192507\pi\)
0.0810922 + 0.996707i \(0.474159\pi\)
\(570\) 0 0
\(571\) −1.17920e6 + 2.04244e6i −0.151355 + 0.262155i −0.931726 0.363162i \(-0.881697\pi\)
0.780371 + 0.625317i \(0.215030\pi\)
\(572\) 0 0
\(573\) 4.36702e6 0.555647
\(574\) 0 0
\(575\) −4.66933e6 −0.588959
\(576\) 0 0
\(577\) −2.50549e6 + 4.33963e6i −0.313295 + 0.542642i −0.979074 0.203507i \(-0.934766\pi\)
0.665779 + 0.746149i \(0.268099\pi\)
\(578\) 0 0
\(579\) 1.48868e6 + 2.57846e6i 0.184546 + 0.319643i
\(580\) 0 0
\(581\) −8.66929e6 7.24369e6i −1.06547 0.890266i
\(582\) 0 0
\(583\) −1.01606e6 1.75986e6i −0.123807 0.214441i
\(584\) 0 0
\(585\) 1.06832e6 1.85038e6i 0.129066 0.223548i
\(586\) 0 0
\(587\) −3.95106e6 −0.473280 −0.236640 0.971597i \(-0.576046\pi\)
−0.236640 + 0.971597i \(0.576046\pi\)
\(588\) 0 0
\(589\) −2.52455e7 −2.99845
\(590\) 0 0
\(591\) 728832. 1.26237e6i 0.0858339 0.148669i
\(592\) 0 0
\(593\) 1.26840e6 + 2.19694e6i 0.148122 + 0.256555i 0.930533 0.366207i \(-0.119344\pi\)
−0.782411 + 0.622762i \(0.786010\pi\)
\(594\) 0 0
\(595\) −8.63573e6 7.21565e6i −1.00002 0.835571i
\(596\) 0 0
\(597\) 249283. + 431771.i 0.0286258 + 0.0495813i
\(598\) 0 0
\(599\) 3.58857e6 6.21558e6i 0.408652 0.707807i −0.586087 0.810248i \(-0.699332\pi\)
0.994739 + 0.102442i \(0.0326655\pi\)
\(600\) 0 0
\(601\) 1.12527e7 1.27078 0.635392 0.772190i \(-0.280838\pi\)
0.635392 + 0.772190i \(0.280838\pi\)
\(602\) 0 0
\(603\) −4.40413e6 −0.493249
\(604\) 0 0
\(605\) −5.23585e6 + 9.06877e6i −0.581566 + 1.00730i
\(606\) 0 0
\(607\) −7.01851e6 1.21564e7i −0.773167 1.33916i −0.935819 0.352481i \(-0.885338\pi\)
0.162652 0.986684i \(-0.447995\pi\)
\(608\) 0 0
\(609\) −831580. + 304633.i −0.0908575 + 0.0332838i
\(610\) 0 0
\(611\) 4.29761e6 + 7.44367e6i 0.465719 + 0.806648i
\(612\) 0 0
\(613\) 3.81436e6 6.60667e6i 0.409988 0.710119i −0.584900 0.811105i \(-0.698866\pi\)
0.994888 + 0.100986i \(0.0321997\pi\)
\(614\) 0 0
\(615\) −5.19119e6 −0.553451
\(616\) 0 0
\(617\) −4.41080e6 −0.466450 −0.233225 0.972423i \(-0.574928\pi\)
−0.233225 + 0.972423i \(0.574928\pi\)
\(618\) 0 0
\(619\) −4.52178e6 + 7.83195e6i −0.474332 + 0.821567i −0.999568 0.0293895i \(-0.990644\pi\)
0.525236 + 0.850957i \(0.323977\pi\)
\(620\) 0 0
\(621\) 661192. + 1.14522e6i 0.0688016 + 0.119168i
\(622\) 0 0
\(623\) −2.19279e6 + 1.25892e7i −0.226348 + 1.29950i
\(624\) 0 0
\(625\) 5.59185e6 + 9.68538e6i 0.572606 + 0.991782i
\(626\) 0 0
\(627\) −1.87999e6 + 3.25624e6i −0.190980 + 0.330786i
\(628\) 0 0
\(629\) −8.96293e6 −0.903282
\(630\) 0 0
\(631\) 7.33039e6 0.732916 0.366458 0.930435i \(-0.380570\pi\)
0.366458 + 0.930435i \(0.380570\pi\)
\(632\) 0 0
\(633\) 2.16786e6 3.75485e6i 0.215042 0.372463i
\(634\) 0 0
\(635\) 1.26515e6 + 2.19130e6i 0.124511 + 0.215659i
\(636\) 0 0
\(637\) 1.04385e6 + 5.77912e6i 0.101927 + 0.564304i
\(638\) 0 0
\(639\) −2.84090e6 4.92059e6i −0.275235 0.476722i
\(640\) 0 0
\(641\) −1.84412e6 + 3.19411e6i −0.177273 + 0.307047i −0.940946 0.338558i \(-0.890061\pi\)
0.763672 + 0.645604i \(0.223394\pi\)
\(642\) 0 0
\(643\) 1.17584e7 1.12155 0.560776 0.827968i \(-0.310503\pi\)
0.560776 + 0.827968i \(0.310503\pi\)
\(644\) 0 0
\(645\) 8.28147e6 0.783806
\(646\) 0 0
\(647\) −4.97025e6 + 8.60873e6i −0.466786 + 0.808497i −0.999280 0.0379368i \(-0.987921\pi\)
0.532494 + 0.846434i \(0.321255\pi\)
\(648\) 0 0
\(649\) −1.96982e6 3.41182e6i −0.183575 0.317962i
\(650\) 0 0
\(651\) 1.80830e6 1.03817e7i 0.167231 0.960101i
\(652\) 0 0
\(653\) 513100. + 888714.i 0.0470889 + 0.0815604i 0.888609 0.458665i \(-0.151672\pi\)
−0.841520 + 0.540226i \(0.818339\pi\)
\(654\) 0 0
\(655\) 407995. 706668.i 0.0371579 0.0643594i
\(656\) 0 0
\(657\) −3.60197e6 −0.325557
\(658\) 0 0
\(659\) −1.00207e7 −0.898846 −0.449423 0.893319i \(-0.648370\pi\)
−0.449423 + 0.893319i \(0.648370\pi\)
\(660\) 0 0
\(661\) −1.31413e6 + 2.27614e6i −0.116986 + 0.202626i −0.918572 0.395254i \(-0.870657\pi\)
0.801586 + 0.597880i \(0.203990\pi\)
\(662\) 0 0
\(663\) 1.80799e6 + 3.13152e6i 0.159739 + 0.276676i
\(664\) 0 0
\(665\) −2.56872e7 + 9.40999e6i −2.25249 + 0.825154i
\(666\) 0 0
\(667\) −688431. 1.19240e6i −0.0599165 0.103778i
\(668\) 0 0
\(669\) 2.87450e6 4.97879e6i 0.248312 0.430089i
\(670\) 0 0
\(671\) 5.27925e6 0.452654
\(672\) 0 0
\(673\) −1.50220e7 −1.27847 −0.639233 0.769013i \(-0.720748\pi\)
−0.639233 + 0.769013i \(0.720748\pi\)
\(674\) 0 0
\(675\) −938257. + 1.62511e6i −0.0792616 + 0.137285i
\(676\) 0 0
\(677\) 3.01655e6 + 5.22482e6i 0.252953 + 0.438127i 0.964337 0.264676i \(-0.0852650\pi\)
−0.711385 + 0.702803i \(0.751932\pi\)
\(678\) 0 0
\(679\) −3.21757e6 2.68846e6i −0.267826 0.223784i
\(680\) 0 0
\(681\) −2.36557e6 4.09729e6i −0.195465 0.338554i
\(682\) 0 0
\(683\) 5.53601e6 9.58865e6i 0.454093 0.786513i −0.544542 0.838734i \(-0.683297\pi\)
0.998636 + 0.0522205i \(0.0166299\pi\)
\(684\) 0 0
\(685\) 1.42922e6 0.116379
\(686\) 0 0
\(687\) 8.39417e6 0.678557
\(688\) 0 0
\(689\) −2.37537e6 + 4.11426e6i −0.190626 + 0.330174i
\(690\) 0 0
\(691\) −5.27739e6 9.14071e6i −0.420460 0.728257i 0.575525 0.817784i \(-0.304798\pi\)
−0.995984 + 0.0895269i \(0.971464\pi\)
\(692\) 0 0
\(693\) −1.20440e6 1.00635e6i −0.0952661 0.0796003i
\(694\) 0 0
\(695\) 6.37523e6 + 1.10422e7i 0.500650 + 0.867151i
\(696\) 0 0
\(697\) 4.39270e6 7.60838e6i 0.342491 0.593212i
\(698\) 0 0
\(699\) −6.37014e6 −0.493124
\(700\) 0 0
\(701\) −7.20675e6 −0.553917 −0.276958 0.960882i \(-0.589326\pi\)
−0.276958 + 0.960882i \(0.589326\pi\)
\(702\) 0 0
\(703\) −1.08941e7 + 1.88692e7i −0.831390 + 1.44001i
\(704\) 0 0
\(705\) −8.35660e6 1.44741e7i −0.633223 1.09677i
\(706\) 0 0
\(707\) 3.81583e6 1.39785e6i 0.287104 0.105175i
\(708\) 0 0
\(709\) −1.34687e6 2.33284e6i −0.100626 0.174289i 0.811317 0.584607i \(-0.198751\pi\)
−0.911943 + 0.410318i \(0.865418\pi\)
\(710\) 0 0
\(711\) 2.49530e6 4.32199e6i 0.185118 0.320634i
\(712\) 0 0
\(713\) 1.63833e7 1.20692
\(714\) 0 0
\(715\) −3.94253e6 −0.288410
\(716\) 0 0
\(717\) −2.25276e6 + 3.90190e6i −0.163651 + 0.283451i
\(718\) 0 0
\(719\) 3.46275e6 + 5.99766e6i 0.249804 + 0.432673i 0.963471 0.267812i \(-0.0863005\pi\)
−0.713667 + 0.700485i \(0.752967\pi\)
\(720\) 0 0
\(721\) 2.20978e6 1.26867e7i 0.158311 0.908887i
\(722\) 0 0
\(723\) −5.43698e6 9.41713e6i −0.386823 0.669997i
\(724\) 0 0
\(725\) 976911. 1.69206e6i 0.0690256 0.119556i
\(726\) 0 0
\(727\) −4.11366e6 −0.288664 −0.144332 0.989529i \(-0.546103\pi\)
−0.144332 + 0.989529i \(0.546103\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −7.00765e6 + 1.21376e7i −0.485041 + 0.840116i
\(732\) 0 0
\(733\) −3.96019e6 6.85925e6i −0.272243 0.471538i 0.697193 0.716883i \(-0.254432\pi\)
−0.969436 + 0.245345i \(0.921099\pi\)
\(734\) 0 0
\(735\) −2.02974e6 1.12374e7i −0.138587 0.767266i
\(736\) 0 0
\(737\) 4.06326e6 + 7.03777e6i 0.275554 + 0.477273i
\(738\) 0 0
\(739\) 8.02050e6 1.38919e7i 0.540245 0.935731i −0.458645 0.888620i \(-0.651665\pi\)
0.998890 0.0471115i \(-0.0150016\pi\)
\(740\) 0 0
\(741\) 8.79019e6 0.588102
\(742\) 0 0
\(743\) −1.53453e7 −1.01977 −0.509887 0.860241i \(-0.670313\pi\)
−0.509887 + 0.860241i \(0.670313\pi\)
\(744\) 0 0
\(745\) 9.96507e6 1.72600e7i 0.657794 1.13933i
\(746\) 0 0
\(747\) −3.52925e6 6.11284e6i −0.231409 0.400813i
\(748\) 0 0
\(749\) −3.23166e6 + 1.85535e7i −0.210485 + 1.20843i
\(750\) 0 0
\(751\) 1.12488e7 + 1.94835e7i 0.727790 + 1.26057i 0.957815 + 0.287385i \(0.0927860\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(752\) 0 0
\(753\) 440220. 762483.i 0.0282932 0.0490053i
\(754\) 0 0
\(755\) 2.10756e7 1.34559
\(756\) 0 0
\(757\) 2.30349e7 1.46099 0.730494 0.682919i \(-0.239290\pi\)
0.730494 + 0.682919i \(0.239290\pi\)
\(758\) 0 0
\(759\) 1.22004e6 2.11316e6i 0.0768720 0.133146i
\(760\) 0 0
\(761\) −2.70368e6 4.68290e6i −0.169236 0.293126i 0.768915 0.639351i \(-0.220797\pi\)
−0.938152 + 0.346225i \(0.887463\pi\)
\(762\) 0 0
\(763\) −2.20151e7 + 8.06480e6i −1.36902 + 0.501513i
\(764\) 0 0
\(765\) −3.51559e6 6.08918e6i −0.217192 0.376188i
\(766\) 0 0
\(767\) −4.60509e6 + 7.97626e6i −0.282651 + 0.489565i
\(768\) 0 0
\(769\) −7.93100e6 −0.483629 −0.241814 0.970323i \(-0.577742\pi\)
−0.241814 + 0.970323i \(0.577742\pi\)
\(770\) 0 0
\(771\) −9.97122e6 −0.604105
\(772\) 0 0
\(773\) −134790. + 233462.i −0.00811349 + 0.0140530i −0.870054 0.492957i \(-0.835916\pi\)
0.861940 + 0.507010i \(0.169249\pi\)
\(774\) 0 0
\(775\) 1.16243e7 + 2.01338e7i 0.695203 + 1.20413i
\(776\) 0 0
\(777\) −6.97925e6 5.83157e6i −0.414721 0.346523i
\(778\) 0 0
\(779\) −1.06784e7 1.84955e7i −0.630465 1.09200i
\(780\) 0 0
\(781\) −5.24205e6 + 9.07950e6i −0.307520 + 0.532641i