Properties

Label 126.6.g.h.109.2
Level $126$
Weight $6$
Character 126.109
Analytic conductor $20.208$
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] = [126,6,Mod(37,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(20.2083612964\)
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 109.2
Root \(-24.2462 - 41.9956i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.6.g.h.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(11.2462 + 19.4789i) q^{5} +(-96.4847 - 86.5893i) q^{7} -64.0000 q^{8} +O(q^{10})\) \(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(11.2462 + 19.4789i) q^{5} +(-96.4847 - 86.5893i) q^{7} -64.0000 q^{8} +(-44.9847 + 77.9158i) q^{10} +(170.231 - 294.849i) q^{11} -728.416 q^{13} +(106.985 - 507.411i) q^{14} +(-128.000 - 221.703i) q^{16} +(404.923 - 701.348i) q^{17} +(-513.101 - 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(711.015 + 1231.51i) q^{23} +(1309.55 - 2268.20i) q^{25} +(-1456.83 - 2523.31i) q^{26} +(1971.69 - 644.217i) q^{28} -5218.03 q^{29} +(3518.87 - 6094.87i) q^{31} +(512.000 - 886.810i) q^{32} +3239.39 q^{34} +(601.584 - 2853.22i) q^{35} +(-6396.05 - 11078.3i) q^{37} +(2052.40 - 3554.87i) q^{38} +(-719.755 - 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(2723.69 + 4717.58i) q^{44} +(-2844.06 + 4926.06i) q^{46} +(4656.60 + 8065.46i) q^{47} +(1811.59 + 16709.1i) q^{49} +10476.4 q^{50} +(5827.33 - 10093.2i) q^{52} +(17821.4 - 30867.6i) q^{53} +7657.78 q^{55} +(6175.02 + 5541.71i) q^{56} +(-10436.1 - 18075.8i) q^{58} +(-15188.1 + 26306.5i) q^{59} +(-16093.1 - 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(-8191.89 - 14188.8i) q^{65} +(-10675.5 + 18490.6i) q^{67} +(6478.78 + 11221.6i) q^{68} +(11087.0 - 3622.49i) q^{70} -61153.7 q^{71} +(-20633.9 + 35739.0i) q^{73} +(25584.2 - 44313.2i) q^{74} +16419.2 q^{76} +(-41955.4 + 13708.2i) q^{77} +(17500.2 + 30311.3i) q^{79} +(2879.02 - 4986.61i) q^{80} +(-2347.01 - 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(7328.33 + 12693.0i) q^{86} +(-10894.8 + 18870.3i) q^{88} +(38996.3 + 67543.6i) q^{89} +(70281.0 + 63073.0i) q^{91} -22752.5 q^{92} +(-18626.4 + 32261.9i) q^{94} +(11540.8 - 19989.3i) q^{95} -161765. q^{97} +(-54258.8 + 39693.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8} + 212 q^{10} + 191 q^{11} - 758 q^{13} + 36 q^{14} - 512 q^{16} - 340 q^{17} + 1769 q^{19} + 1696 q^{20} + 1528 q^{22} + 3236 q^{23} + 45 q^{25} - 1516 q^{26} + 48 q^{28} - 8918 q^{29} - 1994 q^{31} + 2048 q^{32} - 2720 q^{34} + 4562 q^{35} - 20587 q^{37} - 7076 q^{38} + 3392 q^{40} - 17628 q^{41} + 31706 q^{43} + 3056 q^{44} - 12944 q^{46} + 33912 q^{47} + 9598 q^{49} + 360 q^{50} + 6064 q^{52} + 49239 q^{53} + 37882 q^{55} - 384 q^{56} - 17836 q^{58} - 56735 q^{59} - 67508 q^{61} - 15952 q^{62} + 16384 q^{64} - 42762 q^{65} - 75723 q^{67} - 5440 q^{68} + 95692 q^{70} + 17984 q^{71} + 3201 q^{73} + 82348 q^{74} - 56608 q^{76} - 120299 q^{77} - 26612 q^{79} - 13568 q^{80} - 35256 q^{82} + 1898 q^{83} + 210040 q^{85} + 63412 q^{86} - 12224 q^{88} + 176562 q^{89} + 210085 q^{91} - 103552 q^{92} - 135648 q^{94} + 234098 q^{95} - 258846 q^{97} - 211156 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) 11.2462 + 19.4789i 0.201178 + 0.348450i 0.948908 0.315552i \(-0.102190\pi\)
−0.747730 + 0.664002i \(0.768856\pi\)
\(6\) 0 0
\(7\) −96.4847 86.5893i −0.744241 0.667912i
\(8\) −64.0000 −0.353553
\(9\) 0 0
\(10\) −44.9847 + 77.9158i −0.142254 + 0.246391i
\(11\) 170.231 294.849i 0.424186 0.734712i −0.572158 0.820144i \(-0.693894\pi\)
0.996344 + 0.0854314i \(0.0272268\pi\)
\(12\) 0 0
\(13\) −728.416 −1.19542 −0.597711 0.801712i \(-0.703923\pi\)
−0.597711 + 0.801712i \(0.703923\pi\)
\(14\) 106.985 507.411i 0.145882 0.691895i
\(15\) 0 0
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) 404.923 701.348i 0.339821 0.588588i −0.644578 0.764539i \(-0.722967\pi\)
0.984399 + 0.175951i \(0.0563001\pi\)
\(18\) 0 0
\(19\) −513.101 888.717i −0.326076 0.564780i 0.655654 0.755062i \(-0.272393\pi\)
−0.981730 + 0.190282i \(0.939060\pi\)
\(20\) −359.878 −0.201178
\(21\) 0 0
\(22\) 1361.85 0.599890
\(23\) 711.015 + 1231.51i 0.280259 + 0.485423i 0.971448 0.237251i \(-0.0762464\pi\)
−0.691190 + 0.722674i \(0.742913\pi\)
\(24\) 0 0
\(25\) 1309.55 2268.20i 0.419055 0.725825i
\(26\) −1456.83 2523.31i −0.422645 0.732043i
\(27\) 0 0
\(28\) 1971.69 644.217i 0.475274 0.155288i
\(29\) −5218.03 −1.15216 −0.576079 0.817394i \(-0.695418\pi\)
−0.576079 + 0.817394i \(0.695418\pi\)
\(30\) 0 0
\(31\) 3518.87 6094.87i 0.657657 1.13909i −0.323564 0.946206i \(-0.604881\pi\)
0.981221 0.192889i \(-0.0617856\pi\)
\(32\) 512.000 886.810i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3239.39 0.480580
\(35\) 601.584 2853.22i 0.0830092 0.393699i
\(36\) 0 0
\(37\) −6396.05 11078.3i −0.768082 1.33036i −0.938601 0.345004i \(-0.887878\pi\)
0.170519 0.985354i \(-0.445456\pi\)
\(38\) 2052.40 3554.87i 0.230570 0.399360i
\(39\) 0 0
\(40\) −719.755 1246.65i −0.0711270 0.123196i
\(41\) −1173.51 −0.109025 −0.0545124 0.998513i \(-0.517360\pi\)
−0.0545124 + 0.998513i \(0.517360\pi\)
\(42\) 0 0
\(43\) 3664.17 0.302207 0.151103 0.988518i \(-0.451717\pi\)
0.151103 + 0.988518i \(0.451717\pi\)
\(44\) 2723.69 + 4717.58i 0.212093 + 0.367356i
\(45\) 0 0
\(46\) −2844.06 + 4926.06i −0.198173 + 0.343246i
\(47\) 4656.60 + 8065.46i 0.307485 + 0.532580i 0.977812 0.209487i \(-0.0671793\pi\)
−0.670326 + 0.742066i \(0.733846\pi\)
\(48\) 0 0
\(49\) 1811.59 + 16709.1i 0.107788 + 0.994174i
\(50\) 10476.4 0.592633
\(51\) 0 0
\(52\) 5827.33 10093.2i 0.298855 0.517633i
\(53\) 17821.4 30867.6i 0.871469 1.50943i 0.0109916 0.999940i \(-0.496501\pi\)
0.860477 0.509489i \(-0.170165\pi\)
\(54\) 0 0
\(55\) 7657.78 0.341347
\(56\) 6175.02 + 5541.71i 0.263129 + 0.236142i
\(57\) 0 0
\(58\) −10436.1 18075.8i −0.407349 0.705549i
\(59\) −15188.1 + 26306.5i −0.568033 + 0.983861i 0.428728 + 0.903434i \(0.358962\pi\)
−0.996760 + 0.0804276i \(0.974371\pi\)
\(60\) 0 0
\(61\) −16093.1 27874.1i −0.553753 0.959128i −0.997999 0.0632231i \(-0.979862\pi\)
0.444247 0.895904i \(-0.353471\pi\)
\(62\) 28151.0 0.930067
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −8191.89 14188.8i −0.240492 0.416544i
\(66\) 0 0
\(67\) −10675.5 + 18490.6i −0.290538 + 0.503226i −0.973937 0.226819i \(-0.927168\pi\)
0.683399 + 0.730045i \(0.260501\pi\)
\(68\) 6478.78 + 11221.6i 0.169911 + 0.294294i
\(69\) 0 0
\(70\) 11087.0 3622.49i 0.270439 0.0883612i
\(71\) −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 −0.998582 0.0532401i \(-0.983045\pi\)
0.545398 + 0.838177i \(0.316378\pi\)
\(74\) 25584.2 44313.2i 0.543116 0.940705i
\(75\) 0 0
\(76\) 16419.2 0.326076
\(77\) −41955.4 + 13708.2i −0.806419 + 0.263484i
\(78\) 0 0
\(79\) 17500.2 + 30311.3i 0.315483 + 0.546433i 0.979540 0.201249i \(-0.0645001\pi\)
−0.664057 + 0.747682i \(0.731167\pi\)
\(80\) 2879.02 4986.61i 0.0502944 0.0871125i
\(81\) 0 0
\(82\) −2347.01 4065.14i −0.0385461 0.0667638i
\(83\) −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
\(86\) 7328.33 + 12693.0i 0.106846 + 0.185063i
\(87\) 0 0
\(88\) −10894.8 + 18870.3i −0.149972 + 0.259760i
\(89\) 38996.3 + 67543.6i 0.521853 + 0.903876i 0.999677 + 0.0254206i \(0.00809249\pi\)
−0.477824 + 0.878456i \(0.658574\pi\)
\(90\) 0 0
\(91\) 70281.0 + 63073.0i 0.889681 + 0.798436i
\(92\) −22752.5 −0.280259
\(93\) 0 0
\(94\) −18626.4 + 32261.9i −0.217425 + 0.376591i
\(95\) 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 \(0.837713\pi\)
\(98\) −54258.8 + 39693.7i −0.570696 + 0.417500i
\(99\) 0 0
\(100\) 20952.8 + 36291.2i 0.209528 + 0.362912i
\(101\) −32927.2 + 57031.6i −0.321182 + 0.556304i −0.980732 0.195357i \(-0.937414\pi\)
0.659550 + 0.751661i \(0.270747\pi\)
\(102\) 0 0
\(103\) −65099.0 112755.i −0.604619 1.04723i −0.992112 0.125358i \(-0.959992\pi\)
0.387493 0.921873i \(-0.373341\pi\)
\(104\) 46618.6 0.422645
\(105\) 0 0
\(106\) 142571. 1.23244
\(107\) 1295.48 + 2243.83i 0.0109388 + 0.0189466i 0.871443 0.490497i \(-0.163185\pi\)
−0.860504 + 0.509443i \(0.829851\pi\)
\(108\) 0 0
\(109\) −55326.9 + 95828.9i −0.446036 + 0.772557i −0.998124 0.0612291i \(-0.980498\pi\)
0.552088 + 0.833786i \(0.313831\pi\)
\(110\) 15315.6 + 26527.3i 0.120684 + 0.209032i
\(111\) 0 0
\(112\) −6847.02 + 32474.3i −0.0515771 + 0.244622i
\(113\) 193910. 1.42858 0.714291 0.699849i \(-0.246749\pi\)
0.714291 + 0.699849i \(0.246749\pi\)
\(114\) 0 0
\(115\) −15992.4 + 27699.7i −0.112764 + 0.195312i
\(116\) 41744.3 72303.2i 0.288039 0.498899i
\(117\) 0 0
\(118\) −121505. −0.803319
\(119\) −99798.1 + 32607.3i −0.646033 + 0.211080i
\(120\) 0 0
\(121\) 22568.4 + 39089.6i 0.140132 + 0.242716i
\(122\) 64372.5 111496.i 0.391562 0.678206i
\(123\) 0 0
\(124\) 56302.0 + 97517.9i 0.328828 + 0.569547i
\(125\) 129198. 0.739573
\(126\) 0 0
\(127\) 27429.2 0.150905 0.0754526 0.997149i \(-0.475960\pi\)
0.0754526 + 0.997149i \(0.475960\pi\)
\(128\) 8192.00 + 14189.0i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 32767.6 56755.1i 0.170054 0.294541i
\(131\) 75188.0 + 130229.i 0.382798 + 0.663026i 0.991461 0.130403i \(-0.0416271\pi\)
−0.608663 + 0.793429i \(0.708294\pi\)
\(132\) 0 0
\(133\) −27447.0 + 130177.i −0.134544 + 0.638122i
\(134\) −85404.3 −0.410883
\(135\) 0 0
\(136\) −25915.1 + 44886.3i −0.120145 + 0.208097i
\(137\) 48051.0 83226.8i 0.218726 0.378845i −0.735693 0.677316i \(-0.763143\pi\)
0.954419 + 0.298471i \(0.0964765\pi\)
\(138\) 0 0
\(139\) 100854. 0.442749 0.221375 0.975189i \(-0.428946\pi\)
0.221375 + 0.975189i \(0.428946\pi\)
\(140\) 34722.7 + 31161.5i 0.149725 + 0.134369i
\(141\) 0 0
\(142\) −122307. 211843.i −0.509017 0.881643i
\(143\) −123999. + 214772.i −0.507081 + 0.878291i
\(144\) 0 0
\(145\) −58682.9 101642.i −0.231788 0.401469i
\(146\) −165071. −0.640898
\(147\) 0 0
\(148\) 204674. 0.768082
\(149\) −180472. 312587.i −0.665954 1.15347i −0.979026 0.203737i \(-0.934691\pi\)
0.313071 0.949730i \(-0.398642\pi\)
\(150\) 0 0
\(151\) 217028. 375903.i 0.774592 1.34163i −0.160431 0.987047i \(-0.551288\pi\)
0.935023 0.354586i \(-0.115378\pi\)
\(152\) 32838.4 + 56877.9i 0.115285 + 0.199680i
\(153\) 0 0
\(154\) −131397. 117921.i −0.446462 0.400674i
\(155\) 158295. 0.529223
\(156\) 0 0
\(157\) 255798. 443055.i 0.828225 1.43453i −0.0712046 0.997462i \(-0.522684\pi\)
0.899430 0.437066i \(-0.143982\pi\)
\(158\) −70000.9 + 121245.i −0.223080 + 0.386386i
\(159\) 0 0
\(160\) 23032.2 0.0711270
\(161\) 38033.9 180389.i 0.115639 0.548459i
\(162\) 0 0
\(163\) 125635. + 217606.i 0.370374 + 0.641507i 0.989623 0.143688i \(-0.0458962\pi\)
−0.619249 + 0.785195i \(0.712563\pi\)
\(164\) 9388.04 16260.6i 0.0272562 0.0472091i
\(165\) 0 0
\(166\) −172386. 298581.i −0.485547 0.840993i
\(167\) −419277. −1.16335 −0.581674 0.813422i \(-0.697602\pi\)
−0.581674 + 0.813422i \(0.697602\pi\)
\(168\) 0 0
\(169\) 159297. 0.429032
\(170\) 36430.7 + 63099.8i 0.0966819 + 0.167458i
\(171\) 0 0
\(172\) −29313.3 + 50772.2i −0.0755517 + 0.130859i
\(173\) −230688. 399564.i −0.586017 1.01501i −0.994748 0.102356i \(-0.967362\pi\)
0.408731 0.912655i \(-0.365971\pi\)
\(174\) 0 0
\(175\) −322753. + 105454.i −0.796665 + 0.260296i
\(176\) −87158.2 −0.212093
\(177\) 0 0
\(178\) −155985. + 270174.i −0.369006 + 0.639137i
\(179\) 370853. 642336.i 0.865105 1.49841i −0.00183697 0.999998i \(-0.500585\pi\)
0.866942 0.498408i \(-0.166082\pi\)
\(180\) 0 0
\(181\) 301371. 0.683762 0.341881 0.939743i \(-0.388936\pi\)
0.341881 + 0.939743i \(0.388936\pi\)
\(182\) −77929.3 + 369606.i −0.174390 + 0.827106i
\(183\) 0 0
\(184\) −45505.0 78816.9i −0.0990865 0.171623i
\(185\) 143862. 249177.i 0.309042 0.535277i
\(186\) 0 0
\(187\) −137861. 238782.i −0.288295 0.499342i
\(188\) −149011. −0.307485
\(189\) 0 0
\(190\) 92326.7 0.185542
\(191\) 131591. + 227923.i 0.261002 + 0.452069i 0.966508 0.256635i \(-0.0826138\pi\)
−0.705507 + 0.708703i \(0.749280\pi\)
\(192\) 0 0
\(193\) 415563. 719777.i 0.803053 1.39093i −0.114545 0.993418i \(-0.536541\pi\)
0.917598 0.397510i \(-0.130126\pi\)
\(194\) −323531. 560372.i −0.617179 1.06899i
\(195\) 0 0
\(196\) −246021. 108570.i −0.457437 0.201870i
\(197\) 1.05421e6 1.93536 0.967681 0.252178i \(-0.0811470\pi\)
0.967681 + 0.252178i \(0.0811470\pi\)
\(198\) 0 0
\(199\) −349284. + 604977.i −0.625239 + 1.08295i 0.363256 + 0.931689i \(0.381665\pi\)
−0.988495 + 0.151256i \(0.951668\pi\)
\(200\) −83811.0 + 145165.i −0.148158 + 0.256618i
\(201\) 0 0
\(202\) −263418. −0.454220
\(203\) 503460. + 451826.i 0.857482 + 0.769539i
\(204\) 0 0
\(205\) −13197.4 22858.6i −0.0219334 0.0379897i
\(206\) 260396. 451019.i 0.427530 0.740504i
\(207\) 0 0
\(208\) 93237.2 + 161492.i 0.149428 + 0.258816i
\(209\) −349382. −0.553268
\(210\) 0 0
\(211\) −99693.6 −0.154156 −0.0770781 0.997025i \(-0.524559\pi\)
−0.0770781 + 0.997025i \(0.524559\pi\)
\(212\) 285142. + 493881.i 0.435734 + 0.754714i
\(213\) 0 0
\(214\) −5181.90 + 8975.32i −0.00773490 + 0.0133972i
\(215\) 41207.8 + 71374.1i 0.0607972 + 0.105304i
\(216\) 0 0
\(217\) −867267. + 283365.i −1.25027 + 0.408504i
\(218\) −442615. −0.630790
\(219\) 0 0
\(220\) −61262.3 + 106109.i −0.0853368 + 0.147808i
\(221\) −294953. + 510873.i −0.406230 + 0.703610i
\(222\) 0 0
\(223\) 526194. 0.708572 0.354286 0.935137i \(-0.384724\pi\)
0.354286 + 0.935137i \(0.384724\pi\)
\(224\) −126188. + 41229.9i −0.168035 + 0.0549025i
\(225\) 0 0
\(226\) 387821. + 671725.i 0.505080 + 0.874824i
\(227\) −490802. + 850095.i −0.632182 + 1.09497i 0.354923 + 0.934896i \(0.384507\pi\)
−0.987105 + 0.160076i \(0.948826\pi\)
\(228\) 0 0
\(229\) 42540.5 + 73682.3i 0.0536061 + 0.0928484i 0.891583 0.452857i \(-0.149595\pi\)
−0.837977 + 0.545705i \(0.816262\pi\)
\(230\) −127939. −0.159472
\(231\) 0 0
\(232\) 333954. 0.407349
\(233\) 56561.4 + 97967.3i 0.0682544 + 0.118220i 0.898133 0.439724i \(-0.144924\pi\)
−0.829879 + 0.557944i \(0.811590\pi\)
\(234\) 0 0
\(235\) −104738. + 181411.i −0.123718 + 0.214286i
\(236\) −243009. 420905.i −0.284016 0.491931i
\(237\) 0 0
\(238\) −312551. 280496.i −0.357667 0.320985i
\(239\) 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 −0.974432 0.224683i \(-0.927865\pi\)
0.681797 + 0.731542i \(0.261199\pi\)
\(242\) −90273.6 + 156358.i −0.0990883 + 0.171626i
\(243\) 0 0
\(244\) 514980. 0.553753
\(245\) −305102. + 223201.i −0.324735 + 0.237564i
\(246\) 0 0
\(247\) 373751. + 647355.i 0.389798 + 0.675150i
\(248\) −225208. + 390071.i −0.232517 + 0.402731i
\(249\) 0 0
\(250\) 258396. + 447556.i 0.261479 + 0.452894i
\(251\) 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
\(254\) 54858.5 + 95017.7i 0.0533531 + 0.0924102i
\(255\) 0 0
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −597462. 1.03483e6i −0.564257 0.977322i −0.997118 0.0758617i \(-0.975829\pi\)
0.432861 0.901461i \(-0.357504\pi\)
\(258\) 0 0
\(259\) −342140. + 1.62272e6i −0.316923 + 1.50312i
\(260\) 262140. 0.240492
\(261\) 0 0
\(262\) −300752. + 520917.i −0.270679 + 0.468830i
\(263\) −1.06115e6 + 1.83797e6i −0.945993 + 1.63851i −0.192244 + 0.981347i \(0.561576\pi\)
−0.753750 + 0.657161i \(0.771757\pi\)
\(264\) 0 0
\(265\) 801690. 0.701280
\(266\) −505839. + 165274.i −0.438337 + 0.143219i
\(267\) 0 0
\(268\) −170809. 295849.i −0.145269 0.251613i
\(269\) 77488.3 134214.i 0.0652913 0.113088i −0.831532 0.555477i \(-0.812536\pi\)
0.896823 + 0.442389i \(0.145869\pi\)
\(270\) 0 0
\(271\) −979439. 1.69644e6i −0.810129 1.40318i −0.912773 0.408466i \(-0.866064\pi\)
0.102645 0.994718i \(-0.467270\pi\)
\(272\) −207321. −0.169911
\(273\) 0 0
\(274\) 384408. 0.309326
\(275\) −445851. 772236.i −0.355515 0.615770i
\(276\) 0 0
\(277\) 874763. 1.51513e6i 0.685001 1.18646i −0.288436 0.957499i \(-0.593135\pi\)
0.973437 0.228957i \(-0.0735315\pi\)
\(278\) 201709. + 349370.i 0.156536 + 0.271128i
\(279\) 0 0
\(280\) −38501.4 + 182606.i −0.0293482 + 0.139194i
\(281\) −1.40665e6 −1.06272 −0.531361 0.847145i \(-0.678319\pi\)
−0.531361 + 0.847145i \(0.678319\pi\)
\(282\) 0 0
\(283\) −978536. + 1.69487e6i −0.726291 + 1.25797i 0.232150 + 0.972680i \(0.425424\pi\)
−0.958441 + 0.285292i \(0.907909\pi\)
\(284\) 489230. 847371.i 0.359929 0.623416i
\(285\) 0 0
\(286\) −991991. −0.717121
\(287\) 113225. + 101613.i 0.0811407 + 0.0728189i
\(288\) 0 0
\(289\) 382002. + 661648.i 0.269043 + 0.465996i
\(290\) 234732. 406567.i 0.163899 0.283882i
\(291\) 0 0
\(292\) −330142. 571823.i −0.226592 0.392469i
\(293\) 1.26998e6 0.864229 0.432114 0.901819i \(-0.357768\pi\)
0.432114 + 0.901819i \(0.357768\pi\)
\(294\) 0 0
\(295\) −683232. −0.457102
\(296\) 409348. + 709011.i 0.271558 + 0.470353i
\(297\) 0 0
\(298\) 721888. 1.25035e6i 0.470901 0.815624i
\(299\) −517915. 897055.i −0.335027 0.580285i
\(300\) 0 0
\(301\) −353536. 317277.i −0.224914 0.201847i
\(302\) 1.73622e6 1.09544
\(303\) 0 0
\(304\) −131354. + 227511.i −0.0815190 + 0.141195i
\(305\) 361972. 626954.i 0.222805 0.385910i
\(306\) 0 0
\(307\) −41854.4 −0.0253451 −0.0126726 0.999920i \(-0.504034\pi\)
−0.0126726 + 0.999920i \(0.504034\pi\)
\(308\) 145697. 691017.i 0.0875131 0.415061i
\(309\) 0 0
\(310\) 316591. + 548351.i 0.187109 + 0.324082i
\(311\) −1.14595e6 + 1.98484e6i −0.671837 + 1.16366i 0.305546 + 0.952177i \(0.401161\pi\)
−0.977383 + 0.211478i \(0.932172\pi\)
\(312\) 0 0
\(313\) −1.13575e6 1.96717e6i −0.655271 1.13496i −0.981826 0.189785i \(-0.939221\pi\)
0.326555 0.945178i \(-0.394112\pi\)
\(314\) 2.04639e6 1.17129
\(315\) 0 0
\(316\) −560007. −0.315483
\(317\) −992372. 1.71884e6i −0.554659 0.960698i −0.997930 0.0643100i \(-0.979515\pi\)
0.443271 0.896388i \(-0.353818\pi\)
\(318\) 0 0
\(319\) −888270. + 1.53853e6i −0.488729 + 0.846504i
\(320\) 46064.3 + 79785.8i 0.0251472 + 0.0435562i
\(321\) 0 0
\(322\) 700952. 229024.i 0.376746 0.123095i
\(323\) −831066. −0.443230
\(324\) 0 0
\(325\) −953895. + 1.65219e6i −0.500947 + 0.867666i
\(326\) −502539. + 870423.i −0.261894 + 0.453614i
\(327\) 0 0
\(328\) 75104.3 0.0385461
\(329\) 249092. 1.18141e6i 0.126873 0.601740i
\(330\) 0 0
\(331\) −319230. 552923.i −0.160153 0.277393i 0.774771 0.632242i \(-0.217865\pi\)
−0.934923 + 0.354850i \(0.884532\pi\)
\(332\) 689544. 1.19432e6i 0.343334 0.594672i
\(333\) 0 0
\(334\) −838553. 1.45242e6i −0.411305 0.712402i
\(335\) −480236. −0.233799
\(336\) 0 0
\(337\) 2.72026e6 1.30478 0.652388 0.757886i \(-0.273767\pi\)
0.652388 + 0.757886i \(0.273767\pi\)
\(338\) 318593. + 551820.i 0.151686 + 0.262727i
\(339\) 0 0
\(340\) −145723. + 252399.i −0.0683645 + 0.118411i
\(341\) −1.19804e6 2.07507e6i −0.557938 0.966377i
\(342\) 0 0
\(343\) 1.27204e6 1.76903e6i 0.583800 0.811897i
\(344\) −234507. −0.106846
\(345\) 0 0
\(346\) 922753. 1.59825e6i 0.414376 0.717721i
\(347\) 1.31038e6 2.26965e6i 0.584217 1.01189i −0.410755 0.911746i \(-0.634735\pi\)
0.994973 0.100148i \(-0.0319317\pi\)
\(348\) 0 0
\(349\) 575592. 0.252960 0.126480 0.991969i \(-0.459632\pi\)
0.126480 + 0.991969i \(0.459632\pi\)
\(350\) −1.01081e6 907142.i −0.441062 0.395827i
\(351\) 0 0
\(352\) −174316. 301925.i −0.0749862 0.129880i
\(353\) −1.29486e6 + 2.24276e6i −0.553077 + 0.957957i 0.444974 + 0.895544i \(0.353213\pi\)
−0.998050 + 0.0624135i \(0.980120\pi\)
\(354\) 0 0
\(355\) −687746. 1.19121e6i −0.289639 0.501669i
\(356\) −1.24788e6 −0.521853
\(357\) 0 0
\(358\) 2.96682e6 1.22344
\(359\) 1.43389e6 + 2.48358e6i 0.587193 + 1.01705i 0.994598 + 0.103801i \(0.0331005\pi\)
−0.407405 + 0.913248i \(0.633566\pi\)
\(360\) 0 0
\(361\) 711505. 1.23236e6i 0.287349 0.497703i
\(362\) 602742. + 1.04398e6i 0.241746 + 0.418717i
\(363\) 0 0
\(364\) −1.43621e6 + 469258.i −0.568153 + 0.185634i
\(365\) −928210. −0.364682
\(366\) 0 0
\(367\) 977255. 1.69265e6i 0.378741 0.655999i −0.612138 0.790751i \(-0.709690\pi\)
0.990879 + 0.134752i \(0.0430237\pi\)
\(368\) 182020. 315268.i 0.0700647 0.121356i
\(369\) 0 0
\(370\) 1.15090e6 0.437052
\(371\) −4.39229e6 + 1.43510e6i −1.65675 + 0.541314i
\(372\) 0 0
\(373\) −1.10555e6 1.91486e6i −0.411439 0.712633i 0.583608 0.812035i \(-0.301640\pi\)
−0.995047 + 0.0994020i \(0.968307\pi\)
\(374\) 551444. 955129.i 0.203855 0.353088i
\(375\) 0 0
\(376\) −298022. 516190.i −0.108712 0.188295i
\(377\) 3.80090e6 1.37731
\(378\) 0 0
\(379\) 3.81232e6 1.36330 0.681649 0.731679i \(-0.261263\pi\)
0.681649 + 0.731679i \(0.261263\pi\)
\(380\) 184653. + 319829.i 0.0655992 + 0.113621i
\(381\) 0 0
\(382\) −526365. + 911691.i −0.184556 + 0.319661i
\(383\) 1.90303e6 + 3.29614e6i 0.662901 + 1.14818i 0.979850 + 0.199735i \(0.0640082\pi\)
−0.316949 + 0.948442i \(0.602658\pi\)
\(384\) 0 0
\(385\) −738859. 663082.i −0.254044 0.227990i
\(386\) 3.32451e6 1.13569
\(387\) 0 0
\(388\) 1.29412e6 2.24149e6i 0.436411 0.755887i
\(389\) 1.53762e6 2.66324e6i 0.515200 0.892352i −0.484645 0.874711i \(-0.661051\pi\)
0.999844 0.0176410i \(-0.00561558\pi\)
\(390\) 0 0
\(391\) 1.15163e6 0.380952
\(392\) −115942. 1.06938e6i −0.0381088 0.351494i
\(393\) 0 0
\(394\) 2.10842e6 + 3.65190e6i 0.684254 + 1.18516i
\(395\) −393621. + 681772.i −0.126936 + 0.219860i
\(396\) 0 0
\(397\) −1.09566e6 1.89774e6i −0.348900 0.604312i 0.637154 0.770736i \(-0.280111\pi\)
−0.986054 + 0.166424i \(0.946778\pi\)
\(398\) −2.79427e6 −0.884221
\(399\) 0 0
\(400\) −670488. −0.209528
\(401\) 888340. + 1.53865e6i 0.275879 + 0.477836i 0.970356 0.241678i \(-0.0776978\pi\)
−0.694478 + 0.719514i \(0.744365\pi\)
\(402\) 0 0
\(403\) −2.56320e6 + 4.43960e6i −0.786177 + 1.36170i
\(404\) −526835. 912505.i −0.160591 0.278152i
\(405\) 0 0
\(406\) −558250. + 2.64769e6i −0.168079 + 0.797172i
\(407\) −4.35522e6 −1.30324
\(408\) 0 0
\(409\) −1.18059e6 + 2.04484e6i −0.348973 + 0.604438i −0.986067 0.166347i \(-0.946803\pi\)
0.637095 + 0.770786i \(0.280136\pi\)
\(410\) 52789.8 91434.6i 0.0155092 0.0268628i
\(411\) 0 0
\(412\) 2.08317e6 0.604619
\(413\) 3.74328e6 1.22305e6i 1.07989 0.352834i
\(414\) 0 0
\(415\) −969341. 1.67895e6i −0.276284 0.478539i
\(416\) −372949. + 645966.i −0.105661 + 0.183011i
\(417\) 0 0
\(418\) −698765. 1.21030e6i −0.195610 0.338806i
\(419\) 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 \(0.628523\pi\)
\(422\) −199387. 345349.i −0.0545025 0.0944010i
\(423\) 0 0
\(424\) −1.14057e6 + 1.97552e6i −0.308111 + 0.533664i
\(425\) −1.06053e6 1.83690e6i −0.284808 0.493301i
\(426\) 0 0
\(427\) −860859. + 4.08292e6i −0.228487 + 1.08368i
\(428\) −41455.2 −0.0109388
\(429\) 0 0
\(430\) −164831. + 285496.i −0.0429901 + 0.0744611i
\(431\) −44193.1 + 76544.7i −0.0114594 + 0.0198482i −0.871698 0.490043i \(-0.836981\pi\)
0.860239 + 0.509891i \(0.170314\pi\)
\(432\) 0 0
\(433\) −3.09418e6 −0.793097 −0.396549 0.918014i \(-0.629792\pi\)
−0.396549 + 0.918014i \(0.629792\pi\)
\(434\) −2.71614e6 2.43757e6i −0.692194 0.621203i
\(435\) 0 0
\(436\) −885230. 1.53326e6i −0.223018 0.386278i
\(437\) 729645. 1.26378e6i 0.182771 0.316569i
\(438\) 0 0
\(439\) −242589. 420177.i −0.0600773 0.104057i 0.834422 0.551125i \(-0.185801\pi\)
−0.894500 + 0.447068i \(0.852468\pi\)
\(440\) −490098. −0.120684
\(441\) 0 0
\(442\) −2.35962e6 −0.574495
\(443\) 637598. + 1.10435e6i 0.154361 + 0.267361i 0.932826 0.360327i \(-0.117335\pi\)
−0.778465 + 0.627688i \(0.784001\pi\)
\(444\) 0 0
\(445\) −877118. + 1.51921e6i −0.209970 + 0.363679i
\(446\) 1.05239e6 + 1.82279e6i 0.250518 + 0.433910i
\(447\) 0 0
\(448\) −395201. 354670.i −0.0930301 0.0834890i
\(449\) 3.79144e6 0.887541 0.443770 0.896141i \(-0.353641\pi\)
0.443770 + 0.896141i \(0.353641\pi\)
\(450\) 0 0
\(451\) −199767. + 346006.i −0.0462468 + 0.0801019i
\(452\) −1.55128e6 + 2.68690e6i −0.357145 + 0.618594i
\(453\) 0 0
\(454\) −3.92642e6 −0.894040
\(455\) −438203. + 2.07833e6i −0.0992310 + 0.470637i
\(456\) 0 0
\(457\) −851404. 1.47467e6i −0.190698 0.330298i 0.754784 0.655973i \(-0.227742\pi\)
−0.945482 + 0.325675i \(0.894408\pi\)
\(458\) −170162. + 294729.i −0.0379052 + 0.0656537i
\(459\) 0 0
\(460\) −255878. 443194.i −0.0563818 0.0976562i
\(461\) −4.55537e6 −0.998323 −0.499161 0.866509i \(-0.666358\pi\)
−0.499161 + 0.866509i \(0.666358\pi\)
\(462\) 0 0
\(463\) 5.82647e6 1.26314 0.631572 0.775317i \(-0.282410\pi\)
0.631572 + 0.775317i \(0.282410\pi\)
\(464\) 667908. + 1.15685e6i 0.144020 + 0.249449i
\(465\) 0 0
\(466\) −226246. + 391869.i −0.0482631 + 0.0835942i
\(467\) −1.77131e6 3.06799e6i −0.375839 0.650972i 0.614614 0.788828i \(-0.289312\pi\)
−0.990452 + 0.137857i \(0.955979\pi\)
\(468\) 0 0
\(469\) 2.63111e6 859670.i 0.552341 0.180468i
\(470\) −837902. −0.174964
\(471\) 0 0
\(472\) 972038. 1.68362e6i 0.200830 0.347847i
\(473\) 623754. 1.08037e6i 0.128192 0.222035i
\(474\) 0 0
\(475\) −2.68772e6 −0.546575
\(476\) 346565. 1.64370e6i 0.0701079 0.332511i
\(477\) 0 0
\(478\) 1.79020e6 + 3.10072e6i 0.358370 + 0.620715i
\(479\) −2.11771e6 + 3.66798e6i −0.421723 + 0.730446i −0.996108 0.0881390i \(-0.971908\pi\)
0.574385 + 0.818585i \(0.305241\pi\)
\(480\) 0 0
\(481\) 4.65899e6 + 8.06960e6i 0.918182 + 1.59034i
\(482\) −2.11086e6 −0.413849
\(483\) 0 0
\(484\) −722189. −0.140132
\(485\) −1.81924e6 3.15102e6i −0.351185 0.608270i
\(486\) 0 0
\(487\) 2.82740e6 4.89719e6i 0.540212 0.935675i −0.458679 0.888602i \(-0.651677\pi\)
0.998891 0.0470729i \(-0.0149893\pi\)
\(488\) 1.02996e6 + 1.78394e6i 0.195781 + 0.339103i
\(489\) 0 0
\(490\) −1.38339e6 610501.i −0.260289 0.114867i
\(491\) −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
\(494\) −1.49500e6 + 2.58942e6i −0.275629 + 0.477403i
\(495\) 0 0
\(496\) −1.80166e6 −0.328828
\(497\) 5.90040e6 + 5.29526e6i 1.07150 + 0.961604i
\(498\) 0 0
\(499\) 3.61884e6 + 6.26802e6i 0.650607 + 1.12688i 0.982976 + 0.183734i \(0.0588187\pi\)
−0.332369 + 0.943149i \(0.607848\pi\)
\(500\) −1.03359e6 + 1.79022e6i −0.184893 + 0.320245i
\(501\) 0 0
\(502\) 2.38585e6 + 4.13242e6i 0.422556 + 0.731888i
\(503\) 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
\(506\) 968294. + 1.67713e6i 0.168124 + 0.291200i
\(507\) 0 0
\(508\) −219434. + 380071.i −0.0377263 + 0.0653439i
\(509\) 917439. + 1.58905e6i 0.156958 + 0.271859i 0.933770 0.357873i \(-0.116498\pi\)
−0.776812 + 0.629732i \(0.783165\pi\)
\(510\) 0 0
\(511\) 5.08547e6 1.66159e6i 0.861546 0.281495i
\(512\) −262144. −0.0441942
\(513\) 0 0
\(514\) 2.38985e6 4.13934e6i 0.398990 0.691071i
\(515\) 1.46423e6 2.53612e6i 0.243272 0.421359i
\(516\) 0 0
\(517\) 3.17079e6 0.521724
\(518\) −6.30553e6 + 2.06022e6i −1.03252 + 0.337357i
\(519\) 0 0
\(520\) 524281. + 908081.i 0.0850268 + 0.147271i
\(521\) 2.65520e6 4.59894e6i 0.428551 0.742273i −0.568193 0.822895i \(-0.692357\pi\)
0.996745 + 0.0806224i \(0.0256908\pi\)
\(522\) 0 0
\(523\) 1.49418e6 + 2.58799e6i 0.238862 + 0.413722i 0.960388 0.278666i \(-0.0898922\pi\)
−0.721526 + 0.692388i \(0.756559\pi\)
\(524\) −2.40601e6 −0.382798
\(525\) 0 0
\(526\) −8.48921e6 −1.33784
\(527\) −2.84975e6 4.93591e6i −0.446972 0.774178i
\(528\) 0 0
\(529\) 2.20709e6 3.82279e6i 0.342910 0.593937i
\(530\) 1.60338e6 + 2.77713e6i 0.247940 + 0.429445i
\(531\) 0 0
\(532\) −1.58420e6 1.42173e6i −0.242679 0.217790i
\(533\) 854800. 0.130331
\(534\) 0 0
\(535\) −29138.3 + 50469.0i −0.00440128 + 0.00762325i
\(536\) 683235. 1.18340e6i 0.102721 0.177917i
\(537\) 0 0
\(538\) 619907. 0.0923359
\(539\) 5.23504e6 + 2.31026e6i 0.776154 + 0.342522i
\(540\) 0 0
\(541\) −1.08416e6 1.87782e6i −0.159258 0.275843i 0.775343 0.631540i \(-0.217577\pi\)
−0.934601 + 0.355697i \(0.884243\pi\)
\(542\) 3.91775e6 6.78575e6i 0.572848 0.992201i
\(543\) 0 0
\(544\) −414642. 718180.i −0.0600725 0.104049i
\(545\) −2.48886e6 −0.358930
\(546\) 0 0
\(547\) −9.13272e6 −1.30506 −0.652532 0.757761i \(-0.726293\pi\)
−0.652532 + 0.757761i \(0.726293\pi\)
\(548\) 768816. + 1.33163e6i 0.109363 + 0.189423i
\(549\) 0 0
\(550\) 1.78340e6 3.08894e6i 0.251387 0.435415i
\(551\) 2.67738e6 + 4.63735e6i 0.375691 + 0.650715i
\(552\) 0 0
\(553\) 936128. 4.43991e6i 0.130173 0.617392i
\(554\) 6.99810e6 0.968737
\(555\) 0 0
\(556\) −806835. + 1.39748e6i −0.110687 + 0.191716i
\(557\) −4.61014e6 + 7.98500e6i −0.629617 + 1.09053i 0.358012 + 0.933717i \(0.383455\pi\)
−0.987629 + 0.156811i \(0.949879\pi\)
\(558\) 0 0
\(559\) −2.66904e6 −0.361264
\(560\) −709568. + 231839.i −0.0956146 + 0.0312404i
\(561\) 0 0
\(562\) −2.81330e6 4.87277e6i −0.375729 0.650782i
\(563\) 4.24638e6 7.35495e6i 0.564610 0.977933i −0.432476 0.901645i \(-0.642360\pi\)
0.997086 0.0762872i \(-0.0243066\pi\)
\(564\) 0 0
\(565\) 2.18075e6 + 3.77717e6i 0.287399 + 0.497789i
\(566\) −7.82828e6 −1.02713
\(567\) 0 0
\(568\) 3.91384e6 0.509017
\(569\) −2.35456e6 4.07822e6i −0.304880 0.528068i 0.672355 0.740229i \(-0.265283\pi\)
−0.977235 + 0.212162i \(0.931950\pi\)
\(570\) 0 0
\(571\) 864035. 1.49655e6i 0.110902 0.192089i −0.805232 0.592960i \(-0.797959\pi\)
0.916134 + 0.400871i \(0.131293\pi\)
\(572\) −1.98398e6 3.43636e6i −0.253541 0.439145i
\(573\) 0 0
\(574\) −125547. + 595450.i −0.0159048 + 0.0754337i
\(575\) 3.72443e6 0.469776
\(576\) 0 0
\(577\) −1.19249e6 + 2.06546e6i −0.149113 + 0.258272i −0.930900 0.365274i \(-0.880975\pi\)
0.781787 + 0.623546i \(0.214309\pi\)
\(578\) −1.52801e6 + 2.64659e6i −0.190242 + 0.329509i
\(579\) 0 0
\(580\) 1.87785e6 0.231788
\(581\) 8.31630e6 + 7.46339e6i 1.02209 + 0.917267i
\(582\) 0 0
\(583\) −6.06750e6 1.05092e7i −0.739330 1.28056i
\(584\) 1.32057e6 2.28729e6i 0.160225 0.277517i
\(585\) 0 0
\(586\) 2.53997e6 + 4.39935e6i 0.305551 + 0.529230i
\(587\) 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
\(590\) −1.36646e6 2.36678e6i −0.161610 0.279917i
\(591\) 0 0
\(592\) −1.63739e6 + 2.83604e6i −0.192021 + 0.332589i
\(593\) 567341. + 982664.i 0.0662533 + 0.114754i 0.897249 0.441524i \(-0.145562\pi\)
−0.830996 + 0.556278i \(0.812229\pi\)
\(594\) 0 0
\(595\) −1.75750e6 1.57725e6i −0.203518 0.182646i
\(596\) 5.77511e6 0.665954
\(597\) 0 0
\(598\) 2.07166e6 3.58822e6i 0.236900 0.410323i
\(599\) 3.80933e6 6.59795e6i 0.433792 0.751349i −0.563404 0.826181i \(-0.690509\pi\)
0.997196 + 0.0748320i \(0.0238420\pi\)
\(600\) 0 0
\(601\) 9.78414e6 1.10493 0.552467 0.833535i \(-0.313686\pi\)
0.552467 + 0.833535i \(0.313686\pi\)
\(602\) 392010. 1.85924e6i 0.0440865 0.209095i
\(603\) 0 0
\(604\) 3.47245e6 + 6.01445e6i 0.387296 + 0.670817i
\(605\) −507616. + 879217.i −0.0563829 + 0.0976580i
\(606\) 0 0
\(607\) −926673. 1.60504e6i −0.102083 0.176813i 0.810460 0.585795i \(-0.199217\pi\)
−0.912543 + 0.408981i \(0.865884\pi\)
\(608\) −1.05083e6 −0.115285
\(609\) 0 0
\(610\) 2.89578e6 0.315094
\(611\) −3.39194e6 5.87501e6i −0.367574 0.636657i
\(612\) 0 0
\(613\) 3.56048e6 6.16694e6i 0.382699 0.662855i −0.608748 0.793364i \(-0.708328\pi\)
0.991447 + 0.130509i \(0.0416612\pi\)
\(614\) −83708.7 144988.i −0.00896086 0.0155207i
\(615\) 0 0
\(616\) 2.68515e6 877325.i 0.285112 0.0931555i
\(617\) 2.75212e6 0.291041 0.145521 0.989355i \(-0.453514\pi\)
0.145521 + 0.989355i \(0.453514\pi\)
\(618\) 0 0
\(619\) 6.51660e6 1.12871e7i 0.683588 1.18401i −0.290291 0.956939i \(-0.593752\pi\)
0.973878 0.227070i \(-0.0729147\pi\)
\(620\) −1.26636e6 + 2.19341e6i −0.132306 + 0.229160i
\(621\) 0 0
\(622\) −9.16758e6 −0.950120
\(623\) 2.08600e6 9.89358e6i 0.215325 1.02125i
\(624\) 0 0
\(625\) −2.63935e6 4.57149e6i −0.270269 0.468120i
\(626\) 4.54299e6 7.86869e6i 0.463347 0.802540i
\(627\) 0 0
\(628\) 4.09277e6 + 7.08889e6i 0.414112 + 0.717264i
\(629\) −1.03597e7 −1.04404
\(630\) 0 0
\(631\) −4.40820e6 −0.440745 −0.220373 0.975416i \(-0.570727\pi\)
−0.220373 + 0.975416i \(0.570727\pi\)
\(632\) −1.12001e6 1.93992e6i −0.111540 0.193193i
\(633\) 0 0
\(634\) 3.96949e6 6.87535e6i 0.392203 0.679316i
\(635\) 308474. + 534293.i 0.0303588 + 0.0525829i
\(636\) 0 0
\(637\) −1.31959e6 1.21712e7i −0.128852 1.18846i
\(638\) −7.10616e6 −0.691168
\(639\) 0 0
\(640\) −184257. + 319143.i −0.0177818 + 0.0307989i
\(641\) −3.99195e6 + 6.91426e6i −0.383742 + 0.664661i −0.991594 0.129389i \(-0.958698\pi\)
0.607851 + 0.794051i \(0.292032\pi\)
\(642\) 0 0
\(643\) 1.52102e6 0.145080 0.0725398 0.997366i \(-0.476890\pi\)
0.0725398 + 0.997366i \(0.476890\pi\)
\(644\) 2.19527e6 + 1.97012e6i 0.208580 + 0.187188i
\(645\) 0 0
\(646\) −1.66213e6 2.87890e6i −0.156706 0.271422i
\(647\) −6.26247e6 + 1.08469e7i −0.588146 + 1.01870i 0.406329 + 0.913727i \(0.366809\pi\)
−0.994475 + 0.104972i \(0.966525\pi\)
\(648\) 0 0
\(649\) 5.17096e6 + 8.95637e6i 0.481903 + 0.834681i
\(650\) −7.63116e6 −0.708447
\(651\) 0 0
\(652\) −4.02031e6 −0.370374
\(653\) −8.53702e6 1.47865e7i −0.783471 1.35701i −0.929908 0.367792i \(-0.880114\pi\)
0.146436 0.989220i \(-0.453220\pi\)
\(654\) 0 0
\(655\) −1.69115e6 + 2.92916e6i −0.154021 + 0.266772i
\(656\) 150209. + 260169.i 0.0136281 + 0.0236046i
\(657\) 0 0
\(658\) 4.59069e6 1.49993e6i 0.413346 0.135054i
\(659\) 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 −0.802339 0.596868i \(-0.796412\pi\)
0.918073 + 0.396412i \(0.129745\pi\)
\(662\) 1.27692e6 2.21169e6i 0.113245 0.196146i
\(663\) 0 0
\(664\) 5.51635e6 0.485547
\(665\) −2.84438e6 + 929350.i −0.249421 + 0.0814940i
\(666\) 0 0
\(667\) −3.71010e6 6.42608e6i −0.322902 0.559283i
\(668\) 3.35421e6 5.80967e6i 0.290837 0.503744i
\(669\) 0 0
\(670\) −960472. 1.66359e6i −0.0826604 0.143172i
\(671\) −1.09582e7 −0.939577
\(672\) 0 0
\(673\) −1.44746e7 −1.23188 −0.615942 0.787792i \(-0.711224\pi\)
−0.615942 + 0.787792i \(0.711224\pi\)
\(674\) 5.44052e6 + 9.42326e6i 0.461308 + 0.799008i
\(675\) 0 0
\(676\) −1.27437e6 + 2.20728e6i −0.107258 + 0.185776i
\(677\) −1.64423e6 2.84788e6i −0.137876 0.238809i 0.788816 0.614629i \(-0.210694\pi\)
−0.926693 + 0.375820i \(0.877361\pi\)
\(678\) 0 0
\(679\) 1.56079e7 + 1.40071e7i 1.29918 + 1.16594i
\(680\) −1.16578e6 −0.0966819
\(681\) 0 0
\(682\) 4.79217e6 8.30027e6i 0.394522 0.683332i
\(683\) 4.40943e6 7.63736e6i 0.361685 0.626458i −0.626553 0.779379i \(-0.715535\pi\)
0.988238 + 0.152921i \(0.0488681\pi\)
\(684\) 0 0
\(685\) 2.16156e6 0.176011
\(686\) 8.67219e6 + 868394.i 0.703588 + 0.0704541i
\(687\) 0 0
\(688\) −469013. 812355.i −0.0377758 0.0654297i
\(689\) −1.29814e7 + 2.24844e7i −1.04177 + 1.80440i
\(690\) 0 0
\(691\) 4.29808e6 + 7.44450e6i 0.342436 + 0.593117i 0.984885 0.173212i \(-0.0554146\pi\)
−0.642448 + 0.766329i \(0.722081\pi\)
\(692\) 7.38202e6 0.586017
\(693\) 0 0
\(694\) 1.04831e7 0.826208
\(695\) 1.13423e6 + 1.96454e6i 0.0890713 + 0.154276i
\(696\) 0 0
\(697\) −475180. + 823035.i −0.0370490 + 0.0641707i
\(698\) 1.15118e6 + 1.99391e6i 0.0894348 + 0.154906i
\(699\) 0 0
\(700\) 1.12081e6 5.31583e6i 0.0864545 0.410040i
\(701\) −2.06437e7 −1.58669 −0.793347 0.608770i \(-0.791663\pi\)
−0.793347 + 0.608770i \(0.791663\pi\)
\(702\) 0 0
\(703\) −6.56364e6 + 1.13686e7i −0.500906 + 0.867595i
\(704\) 697266. 1.20770e6i 0.0530233 0.0918390i
\(705\) 0 0
\(706\) −1.03589e7 −0.782169
\(707\) 8.11530e6 2.65153e6i 0.610599 0.199503i
\(708\) 0 0
\(709\) 213441. + 369691.i 0.0159464 + 0.0276200i 0.873888 0.486126i \(-0.161591\pi\)
−0.857942 + 0.513746i \(0.828257\pi\)
\(710\) 2.75098e6 4.76484e6i 0.204806 0.354734i
\(711\) 0 0
\(712\) −2.49576e6 4.32279e6i −0.184503 0.319569i
\(713\) 1.00079e7 0.737257
\(714\) 0 0
\(715\) −5.57805e6 −0.408054
\(716\) 5.93365e6 + 1.02774e7i 0.432553 + 0.749203i
\(717\) 0 0
\(718\) −5.73558e6 + 9.93431e6i −0.415208 + 0.719162i
\(719\) 1.90362e6 + 3.29716e6i 0.137328 + 0.237858i 0.926484 0.376334i \(-0.122815\pi\)
−0.789157 + 0.614192i \(0.789482\pi\)
\(720\) 0 0
\(721\) −3.48230e6 + 1.65160e7i −0.249476 + 1.18322i
\(722\) 5.69204e6 0.406373
\(723\) 0 0
\(724\) −2.41097e6 + 4.17592e6i −0.170940 + 0.296077i
\(725\) −6.83326e6 + 1.18356e7i −0.482817 + 0.836264i
\(726\) 0 0
\(727\) −2.22044e7 −1.55813 −0.779065 0.626943i \(-0.784306\pi\)
−0.779065 + 0.626943i \(0.784306\pi\)
\(728\) −4.49798e6 4.03667e6i −0.314550 0.282290i
\(729\) 0 0
\(730\) −1.85642e6 3.21541e6i −0.128934 0.223321i
\(731\) 1.48371e6 2.56986e6i 0.102696 0.177875i
\(732\) 0 0
\(733\) 1.45286e7 + 2.51643e7i 0.998766 + 1.72991i 0.542401 + 0.840120i \(0.317515\pi\)
0.456365 + 0.889793i \(0.349151\pi\)
\(734\) 7.81804e6 0.535621
\(735\) 0 0
\(736\) 1.45616e6 0.0990865
\(737\) 3.63461e6 + 6.29533e6i 0.246484 + 0.426923i
\(738\) 0 0
\(739\) −1.06761e7 + 1.84916e7i −0.719122 + 1.24556i 0.242226 + 0.970220i \(0.422123\pi\)
−0.961348 + 0.275337i \(0.911211\pi\)
\(740\) 2.30180e6 + 3.98683e6i 0.154521 + 0.267638i
\(741\) 0 0
\(742\) −1.37559e7 1.23451e7i −0.917234 0.823163i
\(743\) −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
\(746\) 4.42219e6 7.65946e6i 0.290931 0.503908i
\(747\) 0 0
\(748\) 4.41155e6 0.288295
\(749\) 69298.0 328669.i 0.00451353 0.0214069i
\(750\) 0 0
\(751\) −2.83456e6 4.90960e6i −0.183394 0.317648i 0.759640 0.650344i \(-0.225375\pi\)
−0.943034 + 0.332696i \(0.892042\pi\)
\(752\) 1.19209e6 2.06476e6i 0.0768713 0.133145i
\(753\) 0 0
\(754\) 7.60180e6 + 1.31667e7i 0.486954 + 0.843429i
\(755\) 9.76293e6 0.623323
\(756\) 0 0
\(757\) −1.91706e7 −1.21590 −0.607949 0.793976i \(-0.708007\pi\)
−0.607949 + 0.793976i \(0.708007\pi\)
\(758\) 7.62463e6 + 1.32063e7i 0.481999 + 0.834846i
\(759\) 0 0
\(760\) −738614. + 1.27932e6i −0.0463856 + 0.0803423i
\(761\) 7.31680e6 + 1.26731e7i 0.457993 + 0.793268i 0.998855 0.0478438i \(-0.0152350\pi\)
−0.540861 + 0.841112i \(0.681902\pi\)
\(762\) 0 0
\(763\) 1.36360e7 4.45531e6i 0.847958 0.277056i
\(764\) −4.21092e6 −0.261002
\(765\) 0 0
\(766\) −7.61212e6 + 1.31846e7i −0.468742 + 0.811884i
\(767\) 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 \(0.340740\pi\)
\(770\) 819266. 3.88565e6i 0.0497964 0.236176i
\(771\) 0 0
\(772\) 6.64902e6 + 1.15164e7i 0.401526 + 0.695464i
\(773\) 2.02452e6 3.50658e6i 0.121864 0.211074i −0.798639 0.601810i \(-0.794446\pi\)
0.920503 + 0.390736i \(0.127780\pi\)
\(774\) 0 0
\(775\) −9.21626e6 1.59630e7i