Properties

Label 336.6.q.f.289.1
Level $336$
Weight $6$
Character 336.289
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 289.1
Root \(-24.2462 + 41.9956i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.6.q.f.193.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(170.231 + 294.849i) q^{11} -728.416 q^{13} +202.431 q^{15} +(-404.923 - 701.348i) q^{17} +(513.101 - 888.717i) q^{19} +(-1109.08 - 362.372i) q^{21} +(711.015 - 1231.51i) q^{23} +(1309.55 + 2268.20i) q^{25} +729.000 q^{27} +5218.03 q^{29} +(-3518.87 - 6094.87i) q^{31} +(1532.08 - 2653.64i) q^{33} +(601.584 + 2853.22i) q^{35} +(-6396.05 + 11078.3i) q^{37} +(3277.87 + 5677.44i) q^{39} +1173.51 q^{41} -3664.17 q^{43} +(-910.940 - 1577.79i) q^{45} +(4656.60 - 8065.46i) q^{47} +(1811.59 - 16709.1i) q^{49} +(-3644.31 + 6312.13i) q^{51} +(-17821.4 - 30867.6i) q^{53} -7657.78 q^{55} -9235.81 q^{57} +(-15188.1 - 26306.5i) q^{59} +(-16093.1 + 27874.1i) q^{61} +(2166.44 + 10275.1i) q^{63} +(8191.89 - 14188.8i) q^{65} +(10675.5 + 18490.6i) q^{67} -12798.3 q^{69} -61153.7 q^{71} +(-20633.9 - 35739.0i) q^{73} +(11785.9 - 20413.8i) q^{75} +(41955.4 + 13708.2i) q^{77} +(-17500.2 + 30311.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} -86193.0 q^{83} +18215.4 q^{85} +(-23481.1 - 40670.5i) q^{87} +(-38996.3 + 67543.6i) q^{89} +(-70281.0 + 63073.0i) q^{91} +(-31669.9 + 54853.8i) q^{93} +(11540.8 + 19989.3i) q^{95} -161765. q^{97} -27577.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

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

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
\(5\) −11.2462 + 19.4789i −0.201178 + 0.348450i −0.948908 0.315552i \(-0.897810\pi\)
0.747730 + 0.664002i \(0.231144\pi\)
\(6\) 0 0
\(7\) 96.4847 86.5893i 0.744241 0.667912i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 170.231 + 294.849i 0.424186 + 0.734712i 0.996344 0.0854314i \(-0.0272268\pi\)
−0.572158 + 0.820144i \(0.693894\pi\)
\(12\) 0 0
\(13\) −728.416 −1.19542 −0.597711 0.801712i \(-0.703923\pi\)
−0.597711 + 0.801712i \(0.703923\pi\)
\(14\) 0 0
\(15\) 202.431 0.232300
\(16\) 0 0
\(17\) −404.923 701.348i −0.339821 0.588588i 0.644578 0.764539i \(-0.277033\pi\)
−0.984399 + 0.175951i \(0.943700\pi\)
\(18\) 0 0
\(19\) 513.101 888.717i 0.326076 0.564780i −0.655654 0.755062i \(-0.727607\pi\)
0.981730 + 0.190282i \(0.0609402\pi\)
\(20\) 0 0
\(21\) −1109.08 362.372i −0.548800 0.179311i
\(22\) 0 0
\(23\) 711.015 1231.51i 0.280259 0.485423i −0.691190 0.722674i \(-0.742913\pi\)
0.971448 + 0.237251i \(0.0762464\pi\)
\(24\) 0 0
\(25\) 1309.55 + 2268.20i 0.419055 + 0.725825i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 5218.03 1.15216 0.576079 0.817394i \(-0.304582\pi\)
0.576079 + 0.817394i \(0.304582\pi\)
\(30\) 0 0
\(31\) −3518.87 6094.87i −0.657657 1.13909i −0.981221 0.192889i \(-0.938214\pi\)
0.323564 0.946206i \(-0.395119\pi\)
\(32\) 0 0
\(33\) 1532.08 2653.64i 0.244904 0.424186i
\(34\) 0 0
\(35\) 601.584 + 2853.22i 0.0830092 + 0.393699i
\(36\) 0 0
\(37\) −6396.05 + 11078.3i −0.768082 + 1.33036i 0.170519 + 0.985354i \(0.445456\pi\)
−0.938601 + 0.345004i \(0.887878\pi\)
\(38\) 0 0
\(39\) 3277.87 + 5677.44i 0.345088 + 0.597711i
\(40\) 0 0
\(41\) 1173.51 0.109025 0.0545124 0.998513i \(-0.482640\pi\)
0.0545124 + 0.998513i \(0.482640\pi\)
\(42\) 0 0
\(43\) −3664.17 −0.302207 −0.151103 0.988518i \(-0.548283\pi\)
−0.151103 + 0.988518i \(0.548283\pi\)
\(44\) 0 0
\(45\) −910.940 1577.79i −0.0670592 0.116150i
\(46\) 0 0
\(47\) 4656.60 8065.46i 0.307485 0.532580i −0.670326 0.742066i \(-0.733846\pi\)
0.977812 + 0.209487i \(0.0671793\pi\)
\(48\) 0 0
\(49\) 1811.59 16709.1i 0.107788 0.994174i
\(50\) 0 0
\(51\) −3644.31 + 6312.13i −0.196196 + 0.339821i
\(52\) 0 0
\(53\) −17821.4 30867.6i −0.871469 1.50943i −0.860477 0.509489i \(-0.829835\pi\)
−0.0109916 0.999940i \(-0.503499\pi\)
\(54\) 0 0
\(55\) −7657.78 −0.341347
\(56\) 0 0
\(57\) −9235.81 −0.376520
\(58\) 0 0
\(59\) −15188.1 26306.5i −0.568033 0.983861i −0.996760 0.0804276i \(-0.974371\pi\)
0.428728 0.903434i \(-0.358962\pi\)
\(60\) 0 0
\(61\) −16093.1 + 27874.1i −0.553753 + 0.959128i 0.444247 + 0.895904i \(0.353471\pi\)
−0.997999 + 0.0632231i \(0.979862\pi\)
\(62\) 0 0
\(63\) 2166.44 + 10275.1i 0.0687694 + 0.326162i
\(64\) 0 0
\(65\) 8191.89 14188.8i 0.240492 0.416544i
\(66\) 0 0
\(67\) 10675.5 + 18490.6i 0.290538 + 0.503226i 0.973937 0.226819i \(-0.0728324\pi\)
−0.683399 + 0.730045i \(0.739499\pi\)
\(68\) 0 0
\(69\) −12798.3 −0.323615
\(70\) 0 0
\(71\) −61153.7 −1.43972 −0.719859 0.694121i \(-0.755793\pi\)
−0.719859 + 0.694121i \(0.755793\pi\)
\(72\) 0 0
\(73\) −20633.9 35739.0i −0.453184 0.784937i 0.545398 0.838177i \(-0.316378\pi\)
−0.998582 + 0.0532401i \(0.983045\pi\)
\(74\) 0 0
\(75\) 11785.9 20413.8i 0.241942 0.419055i
\(76\) 0 0
\(77\) 41955.4 + 13708.2i 0.806419 + 0.263484i
\(78\) 0 0
\(79\) −17500.2 + 30311.3i −0.315483 + 0.546433i −0.979540 0.201249i \(-0.935500\pi\)
0.664057 + 0.747682i \(0.268833\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −86193.0 −1.37334 −0.686668 0.726972i \(-0.740927\pi\)
−0.686668 + 0.726972i \(0.740927\pi\)
\(84\) 0 0
\(85\) 18215.4 0.273458
\(86\) 0 0
\(87\) −23481.1 40670.5i −0.332599 0.576079i
\(88\) 0 0
\(89\) −38996.3 + 67543.6i −0.521853 + 0.903876i 0.477824 + 0.878456i \(0.341426\pi\)
−0.999677 + 0.0254206i \(0.991908\pi\)
\(90\) 0 0
\(91\) −70281.0 + 63073.0i −0.889681 + 0.798436i
\(92\) 0 0
\(93\) −31669.9 + 54853.8i −0.379698 + 0.657657i
\(94\) 0 0
\(95\) 11540.8 + 19989.3i 0.131198 + 0.227242i
\(96\) 0 0
\(97\) −161765. −1.74565 −0.872823 0.488037i \(-0.837713\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(98\) 0 0
\(99\) −27577.4 −0.282791
\(100\) 0 0
\(101\) 32927.2 + 57031.6i 0.321182 + 0.556304i 0.980732 0.195357i \(-0.0625865\pi\)
−0.659550 + 0.751661i \(0.729253\pi\)
\(102\) 0 0
\(103\) 65099.0 112755.i 0.604619 1.04723i −0.387493 0.921873i \(-0.626659\pi\)
0.992112 0.125358i \(-0.0400078\pi\)
\(104\) 0 0
\(105\) 19531.5 17528.4i 0.172887 0.155156i
\(106\) 0 0
\(107\) 1295.48 2243.83i 0.0109388 0.0189466i −0.860504 0.509443i \(-0.829851\pi\)
0.871443 + 0.490497i \(0.163185\pi\)
\(108\) 0 0
\(109\) −55326.9 95828.9i −0.446036 0.772557i 0.552088 0.833786i \(-0.313831\pi\)
−0.998124 + 0.0612291i \(0.980498\pi\)
\(110\) 0 0
\(111\) 115129. 0.886905
\(112\) 0 0
\(113\) −193910. −1.42858 −0.714291 0.699849i \(-0.753251\pi\)
−0.714291 + 0.699849i \(0.753251\pi\)
\(114\) 0 0
\(115\) 15992.4 + 27699.7i 0.112764 + 0.195312i
\(116\) 0 0
\(117\) 29500.8 51097.0i 0.199237 0.345088i
\(118\) 0 0
\(119\) −99798.1 32607.3i −0.646033 0.211080i
\(120\) 0 0
\(121\) 22568.4 39089.6i 0.140132 0.242716i
\(122\) 0 0
\(123\) −5280.77 9146.57i −0.0314728 0.0545124i
\(124\) 0 0
\(125\) −129198. −0.739573
\(126\) 0 0
\(127\) −27429.2 −0.150905 −0.0754526 0.997149i \(-0.524040\pi\)
−0.0754526 + 0.997149i \(0.524040\pi\)
\(128\) 0 0
\(129\) 16488.7 + 28559.3i 0.0872395 + 0.151103i
\(130\) 0 0
\(131\) 75188.0 130229.i 0.382798 0.663026i −0.608663 0.793429i \(-0.708294\pi\)
0.991461 + 0.130403i \(0.0416271\pi\)
\(132\) 0 0
\(133\) −27447.0 130177.i −0.134544 0.638122i
\(134\) 0 0
\(135\) −8198.46 + 14200.1i −0.0387167 + 0.0670592i
\(136\) 0 0
\(137\) −48051.0 83226.8i −0.218726 0.378845i 0.735693 0.677316i \(-0.236857\pi\)
−0.954419 + 0.298471i \(0.903524\pi\)
\(138\) 0 0
\(139\) −100854. −0.442749 −0.221375 0.975189i \(-0.571054\pi\)
−0.221375 + 0.975189i \(0.571054\pi\)
\(140\) 0 0
\(141\) −83818.7 −0.355053
\(142\) 0 0
\(143\) −123999. 214772.i −0.507081 0.878291i
\(144\) 0 0
\(145\) −58682.9 + 101642.i −0.231788 + 0.401469i
\(146\) 0 0
\(147\) −138387. + 61070.9i −0.528203 + 0.233099i
\(148\) 0 0
\(149\) 180472. 312587.i 0.665954 1.15347i −0.313071 0.949730i \(-0.601358\pi\)
0.979026 0.203737i \(-0.0653087\pi\)
\(150\) 0 0
\(151\) −217028. 375903.i −0.774592 1.34163i −0.935023 0.354586i \(-0.884622\pi\)
0.160431 0.987047i \(-0.448712\pi\)
\(152\) 0 0
\(153\) 65597.6 0.226548
\(154\) 0 0
\(155\) 158295. 0.529223
\(156\) 0 0
\(157\) 255798. + 443055.i 0.828225 + 1.43453i 0.899430 + 0.437066i \(0.143982\pi\)
−0.0712046 + 0.997462i \(0.522684\pi\)
\(158\) 0 0
\(159\) −160393. + 277808.i −0.503143 + 0.871469i
\(160\) 0 0
\(161\) −38033.9 180389.i −0.115639 0.548459i
\(162\) 0 0
\(163\) −125635. + 217606.i −0.370374 + 0.641507i −0.989623 0.143688i \(-0.954104\pi\)
0.619249 + 0.785195i \(0.287437\pi\)
\(164\) 0 0
\(165\) 34460.0 + 59686.5i 0.0985384 + 0.170674i
\(166\) 0 0
\(167\) −419277. −1.16335 −0.581674 0.813422i \(-0.697602\pi\)
−0.581674 + 0.813422i \(0.697602\pi\)
\(168\) 0 0
\(169\) 159297. 0.429032
\(170\) 0 0
\(171\) 41561.2 + 71986.0i 0.108692 + 0.188260i
\(172\) 0 0
\(173\) 230688. 399564.i 0.586017 1.01501i −0.408731 0.912655i \(-0.634029\pi\)
0.994748 0.102356i \(-0.0326381\pi\)
\(174\) 0 0
\(175\) 322753. + 105454.i 0.796665 + 0.260296i
\(176\) 0 0
\(177\) −136693. + 236759.i −0.327954 + 0.568033i
\(178\) 0 0
\(179\) 370853. + 642336.i 0.865105 + 1.49841i 0.866942 + 0.498408i \(0.166082\pi\)
−0.00183697 + 0.999998i \(0.500585\pi\)
\(180\) 0 0
\(181\) 301371. 0.683762 0.341881 0.939743i \(-0.388936\pi\)
0.341881 + 0.939743i \(0.388936\pi\)
\(182\) 0 0
\(183\) 289676. 0.639418
\(184\) 0 0
\(185\) −143862. 249177.i −0.309042 0.535277i
\(186\) 0 0
\(187\) 137861. 238782.i 0.288295 0.499342i
\(188\) 0 0
\(189\) 70337.3 63123.6i 0.143229 0.128540i
\(190\) 0 0
\(191\) 131591. 227923.i 0.261002 0.452069i −0.705507 0.708703i \(-0.749280\pi\)
0.966508 + 0.256635i \(0.0826138\pi\)
\(192\) 0 0
\(193\) 415563. + 719777.i 0.803053 + 1.39093i 0.917598 + 0.397510i \(0.130126\pi\)
−0.114545 + 0.993418i \(0.536541\pi\)
\(194\) 0 0
\(195\) −147454. −0.277696
\(196\) 0 0
\(197\) −1.05421e6 −1.93536 −0.967681 0.252178i \(-0.918853\pi\)
−0.967681 + 0.252178i \(0.918853\pi\)
\(198\) 0 0
\(199\) 349284. + 604977.i 0.625239 + 1.08295i 0.988495 + 0.151256i \(0.0483317\pi\)
−0.363256 + 0.931689i \(0.618335\pi\)
\(200\) 0 0
\(201\) 96079.9 166415.i 0.167742 0.290538i
\(202\) 0 0
\(203\) 503460. 451826.i 0.857482 0.769539i
\(204\) 0 0
\(205\) −13197.4 + 22858.6i −0.0219334 + 0.0379897i
\(206\) 0 0
\(207\) 57592.2 + 99752.7i 0.0934196 + 0.161808i
\(208\) 0 0
\(209\) 349382. 0.553268
\(210\) 0 0
\(211\) 99693.6 0.154156 0.0770781 0.997025i \(-0.475441\pi\)
0.0770781 + 0.997025i \(0.475441\pi\)
\(212\) 0 0
\(213\) 275192. + 476646.i 0.415611 + 0.719859i
\(214\) 0 0
\(215\) 41207.8 71374.1i 0.0607972 0.105304i
\(216\) 0 0
\(217\) −867267. 283365.i −1.25027 0.408504i
\(218\) 0 0
\(219\) −185705. + 321651.i −0.261646 + 0.453184i
\(220\) 0 0
\(221\) 294953. + 510873.i 0.406230 + 0.703610i
\(222\) 0 0
\(223\) −526194. −0.708572 −0.354286 0.935137i \(-0.615276\pi\)
−0.354286 + 0.935137i \(0.615276\pi\)
\(224\) 0 0
\(225\) −212147. −0.279370
\(226\) 0 0
\(227\) −490802. 850095.i −0.632182 1.09497i −0.987105 0.160076i \(-0.948826\pi\)
0.354923 0.934896i \(-0.384507\pi\)
\(228\) 0 0
\(229\) 42540.5 73682.3i 0.0536061 0.0928484i −0.837977 0.545705i \(-0.816262\pi\)
0.891583 + 0.452857i \(0.149595\pi\)
\(230\) 0 0
\(231\) −81954.4 388697.i −0.101051 0.479271i
\(232\) 0 0
\(233\) −56561.4 + 97967.3i −0.0682544 + 0.118220i −0.898133 0.439724i \(-0.855076\pi\)
0.829879 + 0.557944i \(0.188410\pi\)
\(234\) 0 0
\(235\) 104738. + 181411.i 0.123718 + 0.214286i
\(236\) 0 0
\(237\) 315004. 0.364288
\(238\) 0 0
\(239\) 895100. 1.01362 0.506812 0.862057i \(-0.330824\pi\)
0.506812 + 0.862057i \(0.330824\pi\)
\(240\) 0 0
\(241\) −263857. 457014.i −0.292635 0.506859i 0.681797 0.731542i \(-0.261199\pi\)
−0.974432 + 0.224683i \(0.927865\pi\)
\(242\) 0 0
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 305102. + 223201.i 0.324735 + 0.237564i
\(246\) 0 0
\(247\) −373751. + 647355.i −0.389798 + 0.675150i
\(248\) 0 0
\(249\) 387868. + 671808.i 0.396448 + 0.686668i
\(250\) 0 0
\(251\) 1.19293e6 1.19517 0.597584 0.801806i \(-0.296127\pi\)
0.597584 + 0.801806i \(0.296127\pi\)
\(252\) 0 0
\(253\) 484147. 0.475528
\(254\) 0 0
\(255\) −81969.1 141975.i −0.0789405 0.136729i
\(256\) 0 0
\(257\) 597462. 1.03483e6i 0.564257 0.977322i −0.432861 0.901461i \(-0.642496\pi\)
0.997118 0.0758617i \(-0.0241707\pi\)
\(258\) 0 0
\(259\) 342140. + 1.62272e6i 0.316923 + 1.50312i
\(260\) 0 0
\(261\) −211330. + 366035.i −0.192026 + 0.332599i
\(262\) 0 0
\(263\) −1.06115e6 1.83797e6i −0.945993 1.63851i −0.753750 0.657161i \(-0.771757\pi\)
−0.192244 0.981347i \(-0.561576\pi\)
\(264\) 0 0
\(265\) 801690. 0.701280
\(266\) 0 0
\(267\) 701933. 0.602584
\(268\) 0 0
\(269\) −77488.3 134214.i −0.0652913 0.113088i 0.831532 0.555477i \(-0.187464\pi\)
−0.896823 + 0.442389i \(0.854131\pi\)
\(270\) 0 0
\(271\) 979439. 1.69644e6i 0.810129 1.40318i −0.102645 0.994718i \(-0.532730\pi\)
0.912773 0.408466i \(-0.133936\pi\)
\(272\) 0 0
\(273\) 807870. + 263957.i 0.656047 + 0.214352i
\(274\) 0 0
\(275\) −445851. + 772236.i −0.355515 + 0.615770i
\(276\) 0 0
\(277\) 874763. + 1.51513e6i 0.685001 + 1.18646i 0.973437 + 0.228957i \(0.0735315\pi\)
−0.288436 + 0.957499i \(0.593135\pi\)
\(278\) 0 0
\(279\) 570057. 0.438438
\(280\) 0 0
\(281\) 1.40665e6 1.06272 0.531361 0.847145i \(-0.321681\pi\)
0.531361 + 0.847145i \(0.321681\pi\)
\(282\) 0 0
\(283\) 978536. + 1.69487e6i 0.726291 + 1.25797i 0.958441 + 0.285292i \(0.0920907\pi\)
−0.232150 + 0.972680i \(0.574576\pi\)
\(284\) 0 0
\(285\) 103868. 179904.i 0.0757474 0.131198i
\(286\) 0 0
\(287\) 113225. 101613.i 0.0811407 0.0728189i
\(288\) 0 0
\(289\) 382002. 661648.i 0.269043 0.465996i
\(290\) 0 0
\(291\) 727944. + 1.26084e6i 0.503925 + 0.872823i
\(292\) 0 0
\(293\) −1.26998e6 −0.864229 −0.432114 0.901819i \(-0.642232\pi\)
−0.432114 + 0.901819i \(0.642232\pi\)
\(294\) 0 0
\(295\) 683232. 0.457102
\(296\) 0 0
\(297\) 124098. + 214945.i 0.0816347 + 0.141395i
\(298\) 0 0
\(299\) −517915. + 897055.i −0.335027 + 0.580285i
\(300\) 0 0
\(301\) −353536. + 317277.i −0.224914 + 0.201847i
\(302\) 0 0
\(303\) 296345. 513284.i 0.185435 0.321182i
\(304\) 0 0
\(305\) −361972. 626954.i −0.222805 0.385910i
\(306\) 0 0
\(307\) 41854.4 0.0253451 0.0126726 0.999920i \(-0.495966\pi\)
0.0126726 + 0.999920i \(0.495966\pi\)
\(308\) 0 0
\(309\) −1.17178e6 −0.698154
\(310\) 0 0
\(311\) −1.14595e6 1.98484e6i −0.671837 1.16366i −0.977383 0.211478i \(-0.932172\pi\)
0.305546 0.952177i \(-0.401161\pi\)
\(312\) 0 0
\(313\) −1.13575e6 + 1.96717e6i −0.655271 + 1.13496i 0.326555 + 0.945178i \(0.394112\pi\)
−0.981826 + 0.189785i \(0.939221\pi\)
\(314\) 0 0
\(315\) −224512. 73355.4i −0.127486 0.0416539i
\(316\) 0 0
\(317\) 992372. 1.71884e6i 0.554659 0.960698i −0.443271 0.896388i \(-0.646182\pi\)
0.997930 0.0643100i \(-0.0204847\pi\)
\(318\) 0 0
\(319\) 888270. + 1.53853e6i 0.488729 + 0.846504i
\(320\) 0 0
\(321\) −23318.6 −0.0126310
\(322\) 0 0
\(323\) −831066. −0.443230
\(324\) 0 0
\(325\) −953895. 1.65219e6i −0.500947 0.867666i
\(326\) 0 0
\(327\) −497942. + 862460.i −0.257519 + 0.446036i
\(328\) 0 0
\(329\) −249092. 1.18141e6i −0.126873 0.601740i
\(330\) 0 0
\(331\) 319230. 552923.i 0.160153 0.277393i −0.774771 0.632242i \(-0.782135\pi\)
0.934923 + 0.354850i \(0.115468\pi\)
\(332\) 0 0
\(333\) −518080. 897342.i −0.256027 0.443453i
\(334\) 0 0
\(335\) −480236. −0.233799
\(336\) 0 0
\(337\) 2.72026e6 1.30478 0.652388 0.757886i \(-0.273767\pi\)
0.652388 + 0.757886i \(0.273767\pi\)
\(338\) 0 0
\(339\) 872597. + 1.51138e6i 0.412396 + 0.714291i
\(340\) 0 0
\(341\) 1.19804e6 2.07507e6i 0.557938 0.966377i
\(342\) 0 0
\(343\) −1.27204e6 1.76903e6i −0.583800 0.811897i
\(344\) 0 0
\(345\) 143932. 249297.i 0.0651041 0.112764i
\(346\) 0 0
\(347\) 1.31038e6 + 2.26965e6i 0.584217 + 1.01189i 0.994973 + 0.100148i \(0.0319317\pi\)
−0.410755 + 0.911746i \(0.634735\pi\)
\(348\) 0 0
\(349\) 575592. 0.252960 0.126480 0.991969i \(-0.459632\pi\)
0.126480 + 0.991969i \(0.459632\pi\)
\(350\) 0 0
\(351\) −531015. −0.230059
\(352\) 0 0
\(353\) 1.29486e6 + 2.24276e6i 0.553077 + 0.957957i 0.998050 + 0.0624135i \(0.0198797\pi\)
−0.444974 + 0.895544i \(0.646787\pi\)
\(354\) 0 0
\(355\) 687746. 1.19121e6i 0.289639 0.501669i
\(356\) 0 0
\(357\) 194943. + 924582.i 0.0809537 + 0.383950i
\(358\) 0 0
\(359\) 1.43389e6 2.48358e6i 0.587193 1.01705i −0.407405 0.913248i \(-0.633566\pi\)
0.994598 0.103801i \(-0.0331005\pi\)
\(360\) 0 0
\(361\) 711505. + 1.23236e6i 0.287349 + 0.497703i
\(362\) 0 0
\(363\) −406231. −0.161811
\(364\) 0 0
\(365\) 928210. 0.364682
\(366\) 0 0
\(367\) −977255. 1.69265e6i −0.378741 0.655999i 0.612138 0.790751i \(-0.290310\pi\)
−0.990879 + 0.134752i \(0.956976\pi\)
\(368\) 0 0
\(369\) −47527.0 + 82319.1i −0.0181708 + 0.0314728i
\(370\) 0 0
\(371\) −4.39229e6 1.43510e6i −1.65675 0.541314i
\(372\) 0 0
\(373\) −1.10555e6 + 1.91486e6i −0.411439 + 0.712633i −0.995047 0.0994020i \(-0.968307\pi\)
0.583608 + 0.812035i \(0.301640\pi\)
\(374\) 0 0
\(375\) 581392. + 1.00700e6i 0.213496 + 0.369787i
\(376\) 0 0
\(377\) −3.80090e6 −1.37731
\(378\) 0 0
\(379\) −3.81232e6 −1.36330 −0.681649 0.731679i \(-0.738737\pi\)
−0.681649 + 0.731679i \(0.738737\pi\)
\(380\) 0 0
\(381\) 123432. + 213790.i 0.0435626 + 0.0754526i
\(382\) 0 0
\(383\) 1.90303e6 3.29614e6i 0.662901 1.14818i −0.316949 0.948442i \(-0.602658\pi\)
0.979850 0.199735i \(-0.0640082\pi\)
\(384\) 0 0
\(385\) −738859. + 663082.i −0.254044 + 0.227990i
\(386\) 0 0
\(387\) 148399. 257034.i 0.0503678 0.0872395i
\(388\) 0 0
\(389\) −1.53762e6 2.66324e6i −0.515200 0.892352i −0.999844 0.0176410i \(-0.994384\pi\)
0.484645 0.874711i \(-0.338949\pi\)
\(390\) 0 0
\(391\) −1.15163e6 −0.380952
\(392\) 0 0
\(393\) −1.35338e6 −0.442017
\(394\) 0 0
\(395\) −393621. 681772.i −0.126936 0.219860i
\(396\) 0 0
\(397\) −1.09566e6 + 1.89774e6i −0.348900 + 0.604312i −0.986054 0.166424i \(-0.946778\pi\)
0.637154 + 0.770736i \(0.280111\pi\)
\(398\) 0 0
\(399\) −891115. + 799722.i −0.280221 + 0.251482i
\(400\) 0 0
\(401\) −888340. + 1.53865e6i −0.275879 + 0.477836i −0.970356 0.241678i \(-0.922302\pi\)
0.694478 + 0.719514i \(0.255635\pi\)
\(402\) 0 0
\(403\) 2.56320e6 + 4.43960e6i 0.786177 + 1.36170i
\(404\) 0 0
\(405\) 147572. 0.0447061
\(406\) 0 0
\(407\) −4.35522e6 −1.30324
\(408\) 0 0
\(409\) −1.18059e6 2.04484e6i −0.348973 0.604438i 0.637095 0.770786i \(-0.280136\pi\)
−0.986067 + 0.166347i \(0.946803\pi\)
\(410\) 0 0
\(411\) −432459. + 749041.i −0.126282 + 0.218726i
\(412\) 0 0
\(413\) −3.74328e6 1.22305e6i −1.07989 0.352834i
\(414\) 0 0
\(415\) 969341. 1.67895e6i 0.276284 0.478539i
\(416\) 0 0
\(417\) 453845. + 786082.i 0.127811 + 0.221375i
\(418\) 0 0
\(419\) 3.23493e6 0.900181 0.450090 0.892983i \(-0.351392\pi\)
0.450090 + 0.892983i \(0.351392\pi\)
\(420\) 0 0
\(421\) −2.85759e6 −0.785769 −0.392884 0.919588i \(-0.628523\pi\)
−0.392884 + 0.919588i \(0.628523\pi\)
\(422\) 0 0
\(423\) 377184. + 653302.i 0.102495 + 0.177527i
\(424\) 0 0
\(425\) 1.06053e6 1.83690e6i 0.284808 0.493301i
\(426\) 0 0
\(427\) 860859. + 4.08292e6i 0.228487 + 1.08368i
\(428\) 0 0
\(429\) −1.11599e6 + 1.93295e6i −0.292764 + 0.507081i
\(430\) 0 0
\(431\) −44193.1 76544.7i −0.0114594 0.0198482i 0.860239 0.509891i \(-0.170314\pi\)
−0.871698 + 0.490043i \(0.836981\pi\)
\(432\) 0 0
\(433\) −3.09418e6 −0.793097 −0.396549 0.918014i \(-0.629792\pi\)
−0.396549 + 0.918014i \(0.629792\pi\)
\(434\) 0 0
\(435\) 1.05629e6 0.267646
\(436\) 0 0
\(437\) −729645. 1.26378e6i −0.182771 0.316569i
\(438\) 0 0
\(439\) 242589. 420177.i 0.0600773 0.104057i −0.834422 0.551125i \(-0.814199\pi\)
0.894500 + 0.447068i \(0.147532\pi\)
\(440\) 0 0
\(441\) 1.09874e6 + 803797.i 0.269029 + 0.196811i
\(442\) 0 0
\(443\) 637598. 1.10435e6i 0.154361 0.267361i −0.778465 0.627688i \(-0.784001\pi\)
0.932826 + 0.360327i \(0.117335\pi\)
\(444\) 0 0
\(445\) −877118. 1.51921e6i −0.209970 0.363679i
\(446\) 0 0
\(447\) −3.24850e6 −0.768978
\(448\) 0 0
\(449\) −3.79144e6 −0.887541 −0.443770 0.896141i \(-0.646359\pi\)
−0.443770 + 0.896141i \(0.646359\pi\)
\(450\) 0 0
\(451\) 199767. + 346006.i 0.0462468 + 0.0801019i
\(452\) 0 0
\(453\) −1.95325e6 + 3.38313e6i −0.447211 + 0.774592i
\(454\) 0 0
\(455\) −438203. 2.07833e6i −0.0992310 0.470637i
\(456\) 0 0
\(457\) −851404. + 1.47467e6i −0.190698 + 0.330298i −0.945482 0.325675i \(-0.894408\pi\)
0.754784 + 0.655973i \(0.227742\pi\)
\(458\) 0 0
\(459\) −295189. 511283.i −0.0653986 0.113274i
\(460\) 0 0
\(461\) 4.55537e6 0.998323 0.499161 0.866509i \(-0.333642\pi\)
0.499161 + 0.866509i \(0.333642\pi\)
\(462\) 0 0
\(463\) −5.82647e6 −1.26314 −0.631572 0.775317i \(-0.717590\pi\)
−0.631572 + 0.775317i \(0.717590\pi\)
\(464\) 0 0
\(465\) −712329. 1.23379e6i −0.152774 0.264612i
\(466\) 0 0
\(467\) −1.77131e6 + 3.06799e6i −0.375839 + 0.650972i −0.990452 0.137857i \(-0.955979\pi\)
0.614614 + 0.788828i \(0.289312\pi\)
\(468\) 0 0
\(469\) 2.63111e6 + 859670.i 0.552341 + 0.180468i
\(470\) 0 0
\(471\) 2.30218e6 3.98750e6i 0.478176 0.828225i
\(472\) 0 0
\(473\) −623754. 1.08037e6i −0.128192 0.222035i
\(474\) 0 0
\(475\) 2.68772e6 0.546575
\(476\) 0 0
\(477\) 2.88707e6 0.580979
\(478\) 0 0
\(479\) −2.11771e6 3.66798e6i −0.421723 0.730446i 0.574385 0.818585i \(-0.305241\pi\)
−0.996108 + 0.0881390i \(0.971908\pi\)
\(480\) 0 0
\(481\) 4.65899e6 8.06960e6i 0.918182 1.59034i
\(482\) 0 0
\(483\) −1.23484e6 + 1.10819e6i −0.240847 + 0.216146i
\(484\) 0 0
\(485\) 1.81924e6 3.15102e6i 0.351185 0.608270i
\(486\) 0 0
\(487\) −2.82740e6 4.89719e6i −0.540212 0.935675i −0.998891 0.0470729i \(-0.985011\pi\)
0.458679 0.888602i \(-0.348323\pi\)
\(488\) 0 0
\(489\) 2.26142e6 0.427671
\(490\) 0 0
\(491\) −8.33183e6 −1.55968 −0.779842 0.625976i \(-0.784701\pi\)
−0.779842 + 0.625976i \(0.784701\pi\)
\(492\) 0 0
\(493\) −2.11290e6 3.65966e6i −0.391528 0.678146i
\(494\) 0 0
\(495\) 310140. 537179.i 0.0568912 0.0985384i
\(496\) 0 0
\(497\) −5.90040e6 + 5.29526e6i −1.07150 + 0.961604i
\(498\) 0 0
\(499\) −3.61884e6 + 6.26802e6i −0.650607 + 1.12688i 0.332369 + 0.943149i \(0.392152\pi\)
−0.982976 + 0.183734i \(0.941181\pi\)
\(500\) 0 0
\(501\) 1.88674e6 + 3.26794e6i 0.335829 + 0.581674i
\(502\) 0 0
\(503\) 6.16761e6 1.08692 0.543459 0.839436i \(-0.317114\pi\)
0.543459 + 0.839436i \(0.317114\pi\)
\(504\) 0 0
\(505\) −1.48122e6 −0.258459
\(506\) 0 0
\(507\) −716835. 1.24159e6i −0.123851 0.214516i
\(508\) 0 0
\(509\) −917439. + 1.58905e6i −0.156958 + 0.271859i −0.933770 0.357873i \(-0.883502\pi\)
0.776812 + 0.629732i \(0.216835\pi\)
\(510\) 0 0
\(511\) −5.08547e6 1.66159e6i −0.861546 0.281495i
\(512\) 0 0
\(513\) 374050. 647874.i 0.0627533 0.108692i
\(514\) 0 0
\(515\) 1.46423e6 + 2.53612e6i 0.243272 + 0.421359i
\(516\) 0 0
\(517\) 3.17079e6 0.521724
\(518\) 0 0
\(519\) −4.15239e6 −0.676674
\(520\) 0 0
\(521\) −2.65520e6 4.59894e6i −0.428551 0.742273i 0.568193 0.822895i \(-0.307643\pi\)
−0.996745 + 0.0806224i \(0.974309\pi\)
\(522\) 0 0
\(523\) −1.49418e6 + 2.58799e6i −0.238862 + 0.413722i −0.960388 0.278666i \(-0.910108\pi\)
0.721526 + 0.692388i \(0.243441\pi\)
\(524\) 0 0
\(525\) −630457. 2.99016e6i −0.0998291 0.473473i
\(526\) 0 0
\(527\) −2.84975e6 + 4.93591e6i −0.446972 + 0.774178i
\(528\) 0 0
\(529\) 2.20709e6 + 3.82279e6i 0.342910 + 0.593937i
\(530\) 0 0
\(531\) 2.46047e6 0.378688
\(532\) 0 0
\(533\) −854800. −0.130331
\(534\) 0 0
\(535\) 29138.3 + 50469.0i 0.00440128 + 0.00762325i
\(536\) 0 0
\(537\) 3.33768e6 5.78102e6i 0.499469 0.865105i
\(538\) 0 0
\(539\) 5.23504e6 2.31026e6i 0.776154 0.342522i
\(540\) 0 0
\(541\) −1.08416e6 + 1.87782e6i −0.159258 + 0.275843i −0.934601 0.355697i \(-0.884243\pi\)
0.775343 + 0.631540i \(0.217577\pi\)
\(542\) 0 0
\(543\) −1.35617e6 2.34895e6i −0.197385 0.341881i
\(544\) 0 0
\(545\) 2.48886e6 0.358930
\(546\) 0 0
\(547\) 9.13272e6 1.30506 0.652532 0.757761i \(-0.273707\pi\)
0.652532 + 0.757761i \(0.273707\pi\)
\(548\) 0 0
\(549\) −1.30354e6 2.25780e6i −0.184584 0.319709i
\(550\) 0 0
\(551\) 2.67738e6 4.63735e6i 0.375691 0.650715i
\(552\) 0 0
\(553\) 936128. + 4.43991e6i 0.130173 + 0.617392i
\(554\) 0 0
\(555\) −1.29476e6 + 2.24259e6i −0.178426 + 0.309042i
\(556\) 0 0
\(557\) 4.61014e6 + 7.98500e6i 0.629617 + 1.09053i 0.987629 + 0.156811i \(0.0501214\pi\)
−0.358012 + 0.933717i \(0.616545\pi\)
\(558\) 0 0
\(559\) 2.66904e6 0.361264
\(560\) 0 0
\(561\) −2.48150e6 −0.332894
\(562\) 0 0
\(563\) 4.24638e6 + 7.35495e6i 0.564610 + 0.977933i 0.997086 + 0.0762872i \(0.0243066\pi\)
−0.432476 + 0.901645i \(0.642360\pi\)
\(564\) 0 0
\(565\) 2.18075e6 3.77717e6i 0.287399 0.497789i
\(566\) 0 0
\(567\) −808518. 264169.i −0.105617 0.0345084i
\(568\) 0 0
\(569\) 2.35456e6 4.07822e6i 0.304880 0.528068i −0.672355 0.740229i \(-0.734717\pi\)
0.977235 + 0.212162i \(0.0680503\pi\)
\(570\) 0 0
\(571\) −864035. 1.49655e6i −0.110902 0.192089i 0.805232 0.592960i \(-0.202041\pi\)
−0.916134 + 0.400871i \(0.868707\pi\)
\(572\) 0 0
\(573\) −2.36864e6 −0.301379
\(574\) 0 0
\(575\) 3.72443e6 0.469776
\(576\) 0 0
\(577\) −1.19249e6 2.06546e6i −0.149113 0.258272i 0.781787 0.623546i \(-0.214309\pi\)
−0.930900 + 0.365274i \(0.880975\pi\)
\(578\) 0 0
\(579\) 3.74007e6 6.47799e6i 0.463643 0.803053i
\(580\) 0 0
\(581\) −8.31630e6 + 7.46339e6i −1.02209 + 0.917267i
\(582\) 0 0
\(583\) 6.06750e6 1.05092e7i 0.739330 1.28056i
\(584\) 0 0
\(585\) 663543. + 1.14929e6i 0.0801640 + 0.138848i
\(586\) 0 0
\(587\) 3.44904e6 0.413145 0.206573 0.978431i \(-0.433769\pi\)
0.206573 + 0.978431i \(0.433769\pi\)
\(588\) 0 0
\(589\) −7.22214e6 −0.857784
\(590\) 0 0
\(591\) 4.74395e6 + 8.21676e6i 0.558691 + 0.967681i
\(592\) 0 0
\(593\) −567341. + 982664.i −0.0662533 + 0.114754i −0.897249 0.441524i \(-0.854438\pi\)
0.830996 + 0.556278i \(0.187771\pi\)
\(594\) 0 0
\(595\) 1.75750e6 1.57725e6i 0.203518 0.182646i
\(596\) 0 0
\(597\) 3.14355e6 5.44480e6i 0.360982 0.625239i
\(598\) 0 0
\(599\) 3.80933e6 + 6.59795e6i 0.433792 + 0.751349i 0.997196 0.0748320i \(-0.0238420\pi\)
−0.563404 + 0.826181i \(0.690509\pi\)
\(600\) 0 0
\(601\) 9.78414e6 1.10493 0.552467 0.833535i \(-0.313686\pi\)
0.552467 + 0.833535i \(0.313686\pi\)
\(602\) 0 0
\(603\) −1.72944e6 −0.193692
\(604\) 0 0
\(605\) 507616. + 879217.i 0.0563829 + 0.0976580i
\(606\) 0 0
\(607\) 926673. 1.60504e6i 0.102083 0.176813i −0.810460 0.585795i \(-0.800783\pi\)
0.912543 + 0.408981i \(0.134116\pi\)
\(608\) 0 0
\(609\) −5.78720e6 1.89087e6i −0.632304 0.206594i
\(610\) 0 0
\(611\) −3.39194e6 + 5.87501e6i −0.367574 + 0.636657i
\(612\) 0 0
\(613\) 3.56048e6 + 6.16694e6i 0.382699 + 0.662855i 0.991447 0.130509i \(-0.0416612\pi\)
−0.608748 + 0.793364i \(0.708328\pi\)
\(614\) 0 0
\(615\) 237554. 0.0253265
\(616\) 0 0
\(617\) −2.75212e6 −0.291041 −0.145521 0.989355i \(-0.546486\pi\)
−0.145521 + 0.989355i \(0.546486\pi\)
\(618\) 0 0
\(619\) −6.51660e6 1.12871e7i −0.683588 1.18401i −0.973878 0.227070i \(-0.927085\pi\)
0.290291 0.956939i \(-0.406248\pi\)
\(620\) 0 0
\(621\) 518330. 897774.i 0.0539358 0.0934196i
\(622\) 0 0
\(623\) 2.08600e6 + 9.89358e6i 0.215325 + 1.02125i
\(624\) 0 0
\(625\) −2.63935e6 + 4.57149e6i −0.270269 + 0.468120i
\(626\) 0 0
\(627\) −1.57222e6 2.72317e6i −0.159715 0.276634i
\(628\) 0 0
\(629\) 1.03597e7 1.04404
\(630\) 0 0
\(631\) 4.40820e6 0.440745 0.220373 0.975416i \(-0.429273\pi\)
0.220373 + 0.975416i \(0.429273\pi\)
\(632\) 0 0
\(633\) −448621. 777035.i −0.0445011 0.0770781i
\(634\) 0 0
\(635\) 308474. 534293.i 0.0303588 0.0525829i
\(636\) 0 0
\(637\) −1.31959e6 + 1.21712e7i −0.128852 + 1.18846i
\(638\) 0 0
\(639\) 2.47673e6 4.28982e6i 0.239953 0.415611i
\(640\) 0 0
\(641\) 3.99195e6 + 6.91426e6i 0.383742 + 0.664661i 0.991594 0.129389i \(-0.0413017\pi\)
−0.607851 + 0.794051i \(0.707968\pi\)
\(642\) 0 0
\(643\) −1.52102e6 −0.145080 −0.0725398 0.997366i \(-0.523110\pi\)
−0.0725398 + 0.997366i \(0.523110\pi\)
\(644\) 0 0
\(645\) −741741. −0.0702026
\(646\) 0 0
\(647\) −6.26247e6 1.08469e7i −0.588146 1.01870i −0.994475 0.104972i \(-0.966525\pi\)
0.406329 0.913727i \(-0.366809\pi\)
\(648\) 0 0
\(649\) 5.17096e6 8.95637e6i 0.481903 0.834681i
\(650\) 0 0
\(651\) 1.69409e6 + 8.03482e6i 0.156670 + 0.743060i
\(652\) 0 0
\(653\) 8.53702e6 1.47865e7i 0.783471 1.35701i −0.146436 0.989220i \(-0.546780\pi\)
0.929908 0.367792i \(-0.119886\pi\)
\(654\) 0 0
\(655\) 1.69115e6 + 2.92916e6i 0.154021 + 0.266772i
\(656\) 0 0
\(657\) 3.34269e6 0.302122
\(658\) 0 0
\(659\) 2.12585e6 0.190686 0.0953432 0.995444i \(-0.469605\pi\)
0.0953432 + 0.995444i \(0.469605\pi\)
\(660\) 0 0
\(661\) 1.30005e6 + 2.25176e6i 0.115733 + 0.200456i 0.918073 0.396412i \(-0.129745\pi\)
−0.802339 + 0.596868i \(0.796412\pi\)
\(662\) 0 0
\(663\) 2.65457e6 4.59786e6i 0.234537 0.406230i
\(664\) 0 0
\(665\) 2.84438e6 + 929350.i 0.249421 + 0.0814940i
\(666\) 0 0
\(667\) 3.71010e6 6.42608e6i 0.322902 0.559283i
\(668\) 0 0
\(669\) 2.36787e6 + 4.10128e6i 0.204547 + 0.354286i
\(670\) 0 0
\(671\) −1.09582e7 −0.939577
\(672\) 0 0
\(673\) −1.44746e7 −1.23188 −0.615942 0.787792i \(-0.711224\pi\)
−0.615942 + 0.787792i \(0.711224\pi\)
\(674\) 0 0
\(675\) 954660. + 1.65352e6i 0.0806472 + 0.139685i
\(676\) 0 0
\(677\) 1.64423e6 2.84788e6i 0.137876 0.238809i −0.788816 0.614629i \(-0.789306\pi\)
0.926693 + 0.375820i \(0.122639\pi\)
\(678\) 0 0
\(679\) −1.56079e7 + 1.40071e7i −1.29918 + 1.16594i
\(680\) 0 0
\(681\) −4.41722e6 + 7.65085e6i −0.364990 + 0.632182i
\(682\) 0 0
\(683\) 4.40943e6 + 7.63736e6i 0.361685 + 0.626458i 0.988238 0.152921i \(-0.0488681\pi\)
−0.626553 + 0.779379i \(0.715535\pi\)
\(684\) 0 0
\(685\) 2.16156e6 0.176011
\(686\) 0 0
\(687\) −765729. −0.0618989
\(688\) 0 0
\(689\) 1.29814e7 + 2.24844e7i 1.04177 + 1.80440i
\(690\) 0 0
\(691\) −4.29808e6 + 7.44450e6i −0.342436 + 0.593117i −0.984885 0.173212i \(-0.944585\pi\)
0.642448 + 0.766329i \(0.277919\pi\)
\(692\) 0 0
\(693\) −2.66080e6 + 2.38791e6i −0.210464 + 0.188879i
\(694\) 0 0
\(695\) 1.13423e6 1.96454e6i 0.0890713 0.154276i
\(696\) 0 0
\(697\) −475180. 823035.i −0.0370490 0.0641707i
\(698\) 0 0
\(699\) 1.01811e6 0.0788134
\(700\) 0 0
\(701\) 2.06437e7 1.58669 0.793347 0.608770i \(-0.208337\pi\)
0.793347 + 0.608770i \(0.208337\pi\)
\(702\) 0 0
\(703\) 6.56364e6 + 1.13686e7i 0.500906 + 0.867595i
\(704\) 0 0
\(705\) 942640. 1.63270e6i 0.0714288 0.123718i
\(706\) 0 0
\(707\) 8.11530e6 + 2.65153e6i 0.610599 + 0.199503i
\(708\) 0 0
\(709\) 213441. 369691.i 0.0159464 0.0276200i −0.857942 0.513746i \(-0.828257\pi\)
0.873888 + 0.486126i \(0.161591\pi\)
\(710\) 0 0
\(711\) −1.41752e6 2.45521e6i −0.105161 0.182144i
\(712\) 0 0
\(713\) −1.00079e7 −0.737257
\(714\) 0 0
\(715\) 5.57805e6 0.408054
\(716\) 0 0
\(717\) −4.02795e6 6.97662e6i −0.292608 0.506812i
\(718\) 0 0
\(719\) 1.90362e6 3.29716e6i 0.137328 0.237858i −0.789157 0.614192i \(-0.789482\pi\)
0.926484 + 0.376334i \(0.122815\pi\)
\(720\) 0 0
\(721\) −3.48230e6 1.65160e7i −0.249476 1.18322i
\(722\) 0 0
\(723\) −2.37472e6 + 4.11313e6i −0.168953 + 0.292635i
\(724\) 0 0
\(725\) 6.83326e6 + 1.18356e7i 0.482817 + 0.836264i
\(726\) 0 0
\(727\) 2.22044e7 1.55813 0.779065 0.626943i \(-0.215694\pi\)
0.779065 + 0.626943i \(0.215694\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 1.48371e6 + 2.56986e6i 0.102696 + 0.177875i
\(732\) 0 0
\(733\) 1.45286e7 2.51643e7i 0.998766 1.72991i 0.456365 0.889793i \(-0.349151\pi\)
0.542401 0.840120i \(-0.317515\pi\)
\(734\) 0 0
\(735\) 366723. 3.38244e6i 0.0250391 0.230947i
\(736\) 0 0
\(737\) −3.63461e6 + 6.29533e6i −0.246484 + 0.426923i
\(738\) 0 0
\(739\) 1.06761e7 + 1.84916e7i 0.719122 + 1.24556i 0.961348 + 0.275337i \(0.0887893\pi\)
−0.242226 + 0.970220i \(0.577877\pi\)
\(740\) 0 0
\(741\) 6.72751e6 0.450100
\(742\) 0 0
\(743\) −3.91874e6 −0.260420 −0.130210 0.991486i \(-0.541565\pi\)
−0.130210 + 0.991486i \(0.541565\pi\)
\(744\) 0 0
\(745\) 4.05924e6 + 7.03081e6i 0.267950 + 0.464103i
\(746\) 0 0
\(747\) 3.49081e6 6.04627e6i 0.228889 0.396448i
\(748\) 0 0
\(749\) −69298.0 328669.i −0.00451353 0.0214069i
\(750\) 0 0
\(751\) 2.83456e6 4.90960e6i 0.183394 0.317648i −0.759640 0.650344i \(-0.774625\pi\)
0.943034 + 0.332696i \(0.107958\pi\)
\(752\) 0 0
\(753\) −5.36817e6 9.29794e6i −0.345015 0.597584i
\(754\) 0 0
\(755\) 9.76293e6 0.623323
\(756\) 0 0
\(757\) −1.91706e7 −1.21590 −0.607949 0.793976i \(-0.708007\pi\)
−0.607949 + 0.793976i \(0.708007\pi\)
\(758\) 0 0
\(759\) −2.17866e6 3.77355e6i −0.137273 0.237764i
\(760\) 0 0
\(761\) −7.31680e6 + 1.26731e7i −0.457993 + 0.793268i −0.998855 0.0478438i \(-0.984765\pi\)
0.540861 + 0.841112i \(0.318098\pi\)
\(762\) 0 0
\(763\) −1.36360e7 4.45531e6i −0.847958 0.277056i
\(764\) 0 0
\(765\) −737722. + 1.27777e6i −0.0455763 + 0.0789405i
\(766\) 0 0
\(767\) 1.10632e7 + 1.91621e7i 0.679038 + 1.17613i
\(768\) 0 0
\(769\) 1.57337e7 0.959432 0.479716 0.877424i \(-0.340740\pi\)
0.479716 + 0.877424i \(0.340740\pi\)
\(770\) 0 0
\(771\) −1.07543e7 −0.651548
\(772\) 0 0
\(773\) −2.02452e6 3.50658e6i −0.121864 0.211074i 0.798639 0.601810i \(-0.205554\pi\)
−0.920503 + 0.390736i \(0.872220\pi\)
\(774\) 0 0
\(775\) 9.21626e6 1.59630e7i 0.551189 0.954687i
\(776\) 0 0
\(777\) 1.11082e7 9.96894e6i 0.660071 0.592374i
\(778\) 0 0
\(779\) 602126. 1.04291e6i 0.0355504 0.0615750i
\(780\) 0 0
\(781\) −1.04103e7 1.80311e7i −0.610708 1.05778i
\(782\)