Properties

Label 294.6.e.u.67.2
Level $294$
Weight $6$
Character 294.67
Analytic conductor $47.153$
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] = [294,6,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.e (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: \(47.1528430250\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.6.e.u.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(122.142 - 211.556i) q^{10} +(18.2721 - 31.6482i) q^{11} +(-72.0000 - 124.708i) q^{12} +34.5656 q^{13} -549.640 q^{15} +(-128.000 - 221.703i) q^{16} +(1030.52 - 1784.91i) q^{17} +(-162.000 + 280.592i) q^{18} +(-226.119 - 391.650i) q^{19} -977.137 q^{20} -146.177 q^{22} +(-842.124 - 1458.60i) q^{23} +(-288.000 + 498.831i) q^{24} +(-302.338 + 523.664i) q^{25} +(-69.1312 - 119.739i) q^{26} +729.000 q^{27} -4765.22 q^{29} +(1099.28 + 1904.01i) q^{30} +(2630.43 - 4556.04i) q^{31} +(-512.000 + 886.810i) q^{32} +(164.449 + 284.834i) q^{33} -8244.16 q^{34} +1296.00 q^{36} +(6410.98 + 11104.1i) q^{37} +(-904.476 + 1566.60i) q^{38} +(-155.545 + 269.412i) q^{39} +(1954.27 + 3384.90i) q^{40} -7126.74 q^{41} +11141.7 q^{43} +(292.353 + 506.371i) q^{44} +(2473.38 - 4284.02i) q^{45} +(-3368.50 + 5834.41i) q^{46} +(11721.6 + 20302.4i) q^{47} +2304.00 q^{48} +2418.70 q^{50} +(9274.68 + 16064.2i) q^{51} +(-276.525 + 478.955i) q^{52} +(3515.15 - 6088.42i) q^{53} +(-1458.00 - 2525.33i) q^{54} +2231.79 q^{55} +4070.14 q^{57} +(9530.43 + 16507.2i) q^{58} +(22111.4 - 38298.1i) q^{59} +(4397.12 - 7616.03i) q^{60} +(-9690.24 - 16784.0i) q^{61} -21043.5 q^{62} +4096.00 q^{64} +(1055.48 + 1828.14i) q^{65} +(657.795 - 1139.33i) q^{66} +(-10472.0 + 18138.1i) q^{67} +(16488.3 + 28558.6i) q^{68} +15158.2 q^{69} +79843.4 q^{71} +(-2592.00 - 4489.48i) q^{72} +(18532.9 - 32099.9i) q^{73} +(25643.9 - 44416.6i) q^{74} +(-2721.04 - 4712.98i) q^{75} +7235.81 q^{76} +1244.36 q^{78} +(-21036.0 - 36435.4i) q^{79} +(7817.10 - 13539.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(14253.5 + 24687.7i) q^{82} -6311.34 q^{83} +125870. q^{85} +(-22283.4 - 38595.9i) q^{86} +(21443.5 - 37141.2i) q^{87} +(1169.41 - 2025.48i) q^{88} +(25747.9 + 44596.7i) q^{89} -19787.0 q^{90} +26948.0 q^{92} +(23673.9 + 41004.4i) q^{93} +(46886.4 - 81209.6i) q^{94} +(13809.3 - 23918.5i) q^{95} +(-4608.00 - 7981.29i) q^{96} -127357. q^{97} -2960.08 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 1440 q^{13} - 1944 q^{15} - 512 q^{16} + 612 q^{17} - 648 q^{18} + 2088 q^{19} - 3456 q^{20} - 992 q^{22} - 772 q^{23} - 1152 q^{24} + 318 q^{25} + 2880 q^{26} + 2916 q^{27} - 9184 q^{29} + 3888 q^{30} + 9792 q^{31} - 2048 q^{32} + 1116 q^{33} - 4896 q^{34} + 5184 q^{36} + 5992 q^{37} + 8352 q^{38} + 6480 q^{39} + 6912 q^{40} - 40392 q^{41} - 2272 q^{43} + 1984 q^{44} + 8748 q^{45} - 3088 q^{46} + 36936 q^{47} + 9216 q^{48} - 2544 q^{50} + 5508 q^{51} + 11520 q^{52} + 16708 q^{53} - 5832 q^{54} + 12672 q^{55} - 37584 q^{57} + 18368 q^{58} + 74592 q^{59} + 15552 q^{60} - 18648 q^{61} - 78336 q^{62} + 16384 q^{64} - 33300 q^{65} + 4464 q^{66} - 67344 q^{67} + 9792 q^{68} + 13896 q^{69} + 153096 q^{71} - 10368 q^{72} + 47304 q^{73} + 23968 q^{74} + 2862 q^{75} - 66816 q^{76} - 51840 q^{78} - 140656 q^{79} + 27648 q^{80} - 13122 q^{81} + 80784 q^{82} - 188208 q^{83} + 115736 q^{85} + 4544 q^{86} + 41328 q^{87} + 7936 q^{88} - 17604 q^{89} - 69984 q^{90} + 24704 q^{92} + 88128 q^{93} + 147744 q^{94} - 91592 q^{95} - 18432 q^{96} - 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) 30.5355 + 52.8891i 0.546236 + 0.946109i 0.998528 + 0.0542389i \(0.0172732\pi\)
−0.452292 + 0.891870i \(0.649393\pi\)
\(6\) 36.0000 0.408248
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 122.142 211.556i 0.386247 0.669000i
\(11\) 18.2721 31.6482i 0.0455309 0.0788618i −0.842362 0.538912i \(-0.818835\pi\)
0.887893 + 0.460051i \(0.152169\pi\)
\(12\) −72.0000 124.708i −0.144338 0.250000i
\(13\) 34.5656 0.0567264 0.0283632 0.999598i \(-0.490970\pi\)
0.0283632 + 0.999598i \(0.490970\pi\)
\(14\) 0 0
\(15\) −549.640 −0.630739
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) 1030.52 1784.91i 0.864836 1.49794i −0.00237330 0.999997i \(-0.500755\pi\)
0.867210 0.497943i \(-0.165911\pi\)
\(18\) −162.000 + 280.592i −0.117851 + 0.204124i
\(19\) −226.119 391.650i −0.143699 0.248894i 0.785188 0.619258i \(-0.212566\pi\)
−0.928887 + 0.370364i \(0.879233\pi\)
\(20\) −977.137 −0.546236
\(21\) 0 0
\(22\) −146.177 −0.0643904
\(23\) −842.124 1458.60i −0.331938 0.574933i 0.650954 0.759117i \(-0.274369\pi\)
−0.982892 + 0.184184i \(0.941036\pi\)
\(24\) −288.000 + 498.831i −0.102062 + 0.176777i
\(25\) −302.338 + 523.664i −0.0967481 + 0.167573i
\(26\) −69.1312 119.739i −0.0200558 0.0347377i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −4765.22 −1.05217 −0.526087 0.850431i \(-0.676341\pi\)
−0.526087 + 0.850431i \(0.676341\pi\)
\(30\) 1099.28 + 1904.01i 0.223000 + 0.386247i
\(31\) 2630.43 4556.04i 0.491613 0.851498i −0.508341 0.861156i \(-0.669741\pi\)
0.999953 + 0.00965788i \(0.00307425\pi\)
\(32\) −512.000 + 886.810i −0.0883883 + 0.153093i
\(33\) 164.449 + 284.834i 0.0262873 + 0.0455309i
\(34\) −8244.16 −1.22306
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) 6410.98 + 11104.1i 0.769875 + 1.33346i 0.937631 + 0.347633i \(0.113015\pi\)
−0.167756 + 0.985829i \(0.553652\pi\)
\(38\) −904.476 + 1566.60i −0.101610 + 0.175994i
\(39\) −155.545 + 269.412i −0.0163755 + 0.0283632i
\(40\) 1954.27 + 3384.90i 0.193124 + 0.334500i
\(41\) −7126.74 −0.662111 −0.331056 0.943611i \(-0.607405\pi\)
−0.331056 + 0.943611i \(0.607405\pi\)
\(42\) 0 0
\(43\) 11141.7 0.918925 0.459462 0.888197i \(-0.348042\pi\)
0.459462 + 0.888197i \(0.348042\pi\)
\(44\) 292.353 + 506.371i 0.0227654 + 0.0394309i
\(45\) 2473.38 4284.02i 0.182079 0.315370i
\(46\) −3368.50 + 5834.41i −0.234715 + 0.406539i
\(47\) 11721.6 + 20302.4i 0.774002 + 1.34061i 0.935353 + 0.353714i \(0.115082\pi\)
−0.161351 + 0.986897i \(0.551585\pi\)
\(48\) 2304.00 0.144338
\(49\) 0 0
\(50\) 2418.70 0.136822
\(51\) 9274.68 + 16064.2i 0.499313 + 0.864836i
\(52\) −276.525 + 478.955i −0.0141816 + 0.0245633i
\(53\) 3515.15 6088.42i 0.171891 0.297725i −0.767190 0.641420i \(-0.778346\pi\)
0.939081 + 0.343696i \(0.111679\pi\)
\(54\) −1458.00 2525.33i −0.0680414 0.117851i
\(55\) 2231.79 0.0994825
\(56\) 0 0
\(57\) 4070.14 0.165929
\(58\) 9530.43 + 16507.2i 0.372000 + 0.644323i
\(59\) 22111.4 38298.1i 0.826964 1.43234i −0.0734457 0.997299i \(-0.523400\pi\)
0.900409 0.435044i \(-0.143267\pi\)
\(60\) 4397.12 7616.03i 0.157685 0.273118i
\(61\) −9690.24 16784.0i −0.333434 0.577524i 0.649749 0.760149i \(-0.274874\pi\)
−0.983183 + 0.182624i \(0.941541\pi\)
\(62\) −21043.5 −0.695245
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 1055.48 + 1828.14i 0.0309860 + 0.0536694i
\(66\) 657.795 1139.33i 0.0185879 0.0321952i
\(67\) −10472.0 + 18138.1i −0.285000 + 0.493634i −0.972609 0.232447i \(-0.925327\pi\)
0.687609 + 0.726081i \(0.258660\pi\)
\(68\) 16488.3 + 28558.6i 0.432418 + 0.748970i
\(69\) 15158.2 0.383289
\(70\) 0 0
\(71\) 79843.4 1.87972 0.939860 0.341560i \(-0.110955\pi\)
0.939860 + 0.341560i \(0.110955\pi\)
\(72\) −2592.00 4489.48i −0.0589256 0.102062i
\(73\) 18532.9 32099.9i 0.407039 0.705013i −0.587517 0.809212i \(-0.699895\pi\)
0.994556 + 0.104199i \(0.0332278\pi\)
\(74\) 25643.9 44416.6i 0.544384 0.942900i
\(75\) −2721.04 4712.98i −0.0558575 0.0967481i
\(76\) 7235.81 0.143699
\(77\) 0 0
\(78\) 1244.36 0.0231585
\(79\) −21036.0 36435.4i −0.379224 0.656835i 0.611726 0.791070i \(-0.290476\pi\)
−0.990950 + 0.134235i \(0.957142\pi\)
\(80\) 7817.10 13539.6i 0.136559 0.236527i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 14253.5 + 24687.7i 0.234092 + 0.405459i
\(83\) −6311.34 −0.100560 −0.0502801 0.998735i \(-0.516011\pi\)
−0.0502801 + 0.998735i \(0.516011\pi\)
\(84\) 0 0
\(85\) 125870. 1.88962
\(86\) −22283.4 38595.9i −0.324889 0.562724i
\(87\) 21443.5 37141.2i 0.303737 0.526087i
\(88\) 1169.41 2025.48i 0.0160976 0.0278819i
\(89\) 25747.9 + 44596.7i 0.344562 + 0.596798i 0.985274 0.170983i \(-0.0546942\pi\)
−0.640712 + 0.767781i \(0.721361\pi\)
\(90\) −19787.0 −0.257498
\(91\) 0 0
\(92\) 26948.0 0.331938
\(93\) 23673.9 + 41004.4i 0.283833 + 0.491613i
\(94\) 46886.4 81209.6i 0.547302 0.947955i
\(95\) 13809.3 23918.5i 0.156987 0.271909i
\(96\) −4608.00 7981.29i −0.0510310 0.0883883i
\(97\) −127357. −1.37434 −0.687171 0.726496i \(-0.741148\pi\)
−0.687171 + 0.726496i \(0.741148\pi\)
\(98\) 0 0
\(99\) −2960.08 −0.0303539
\(100\) −4837.40 8378.63i −0.0483740 0.0837863i
\(101\) −32879.0 + 56948.0i −0.320712 + 0.555489i −0.980635 0.195844i \(-0.937255\pi\)
0.659923 + 0.751333i \(0.270589\pi\)
\(102\) 37098.7 64256.8i 0.353068 0.611532i
\(103\) −85005.1 147233.i −0.789499 1.36745i −0.926274 0.376851i \(-0.877007\pi\)
0.136774 0.990602i \(-0.456326\pi\)
\(104\) 2212.20 0.0200558
\(105\) 0 0
\(106\) −28121.2 −0.243091
\(107\) 53966.4 + 93472.6i 0.455685 + 0.789269i 0.998727 0.0504363i \(-0.0160612\pi\)
−0.543043 + 0.839705i \(0.682728\pi\)
\(108\) −5832.00 + 10101.3i −0.0481125 + 0.0833333i
\(109\) 111349. 192862.i 0.897679 1.55482i 0.0672244 0.997738i \(-0.478586\pi\)
0.830454 0.557087i \(-0.188081\pi\)
\(110\) −4463.58 7731.15i −0.0351724 0.0609203i
\(111\) −115398. −0.888975
\(112\) 0 0
\(113\) 181055. 1.33387 0.666936 0.745115i \(-0.267605\pi\)
0.666936 + 0.745115i \(0.267605\pi\)
\(114\) −8140.28 14099.4i −0.0586648 0.101610i
\(115\) 51429.4 89078.4i 0.362633 0.628098i
\(116\) 38121.7 66028.8i 0.263044 0.455605i
\(117\) −1399.91 2424.71i −0.00945441 0.0163755i
\(118\) −176891. −1.16950
\(119\) 0 0
\(120\) −35176.9 −0.223000
\(121\) 79857.8 + 138318.i 0.495854 + 0.858844i
\(122\) −38760.9 + 67135.9i −0.235773 + 0.408371i
\(123\) 32070.3 55547.4i 0.191135 0.331056i
\(124\) 42086.9 + 72896.7i 0.245806 + 0.425749i
\(125\) 153919. 0.881083
\(126\) 0 0
\(127\) 91474.7 0.503259 0.251630 0.967824i \(-0.419034\pi\)
0.251630 + 0.967824i \(0.419034\pi\)
\(128\) −8192.00 14189.0i −0.0441942 0.0765466i
\(129\) −50137.6 + 86840.9i −0.265271 + 0.459462i
\(130\) 4221.91 7312.57i 0.0219104 0.0379500i
\(131\) 9671.95 + 16752.3i 0.0492420 + 0.0852896i 0.889596 0.456749i \(-0.150986\pi\)
−0.840354 + 0.542038i \(0.817653\pi\)
\(132\) −5262.36 −0.0262873
\(133\) 0 0
\(134\) 83776.3 0.403050
\(135\) 22260.4 + 38556.2i 0.105123 + 0.182079i
\(136\) 65953.2 114234.i 0.305766 0.529602i
\(137\) 1538.52 2664.79i 0.00700327 0.0121300i −0.862503 0.506053i \(-0.831104\pi\)
0.869506 + 0.493923i \(0.164437\pi\)
\(138\) −30316.5 52509.7i −0.135513 0.234715i
\(139\) 370001. 1.62430 0.812149 0.583450i \(-0.198298\pi\)
0.812149 + 0.583450i \(0.198298\pi\)
\(140\) 0 0
\(141\) −210989. −0.893741
\(142\) −159687. 276586.i −0.664581 1.15109i
\(143\) 631.585 1093.94i 0.00258281 0.00447355i
\(144\) −10368.0 + 17957.9i −0.0416667 + 0.0721688i
\(145\) −145508. 252028.i −0.574736 0.995471i
\(146\) −148263. −0.575641
\(147\) 0 0
\(148\) −205151. −0.769875
\(149\) 227060. + 393279.i 0.837866 + 1.45123i 0.891675 + 0.452676i \(0.149531\pi\)
−0.0538086 + 0.998551i \(0.517136\pi\)
\(150\) −10884.2 + 18851.9i −0.0394972 + 0.0684112i
\(151\) −88795.9 + 153799.i −0.316921 + 0.548923i −0.979844 0.199765i \(-0.935982\pi\)
0.662923 + 0.748687i \(0.269316\pi\)
\(152\) −14471.6 25065.6i −0.0508052 0.0879972i
\(153\) −166944. −0.576558
\(154\) 0 0
\(155\) 321287. 1.07415
\(156\) −2488.72 4310.59i −0.00818776 0.0141816i
\(157\) 124491. 215624.i 0.403076 0.698149i −0.591019 0.806658i \(-0.701274\pi\)
0.994095 + 0.108509i \(0.0346076\pi\)
\(158\) −84144.0 + 145742.i −0.268152 + 0.464452i
\(159\) 31636.3 + 54795.7i 0.0992415 + 0.171891i
\(160\) −62536.8 −0.193124
\(161\) 0 0
\(162\) 26244.0 0.0785674
\(163\) −101124. 175152.i −0.298116 0.516351i 0.677589 0.735441i \(-0.263025\pi\)
−0.975705 + 0.219089i \(0.929691\pi\)
\(164\) 57013.9 98751.0i 0.165528 0.286703i
\(165\) −10043.1 + 17395.1i −0.0287181 + 0.0497413i
\(166\) 12622.7 + 21863.1i 0.0355534 + 0.0615803i
\(167\) 475790. 1.32015 0.660076 0.751199i \(-0.270524\pi\)
0.660076 + 0.751199i \(0.270524\pi\)
\(168\) 0 0
\(169\) −370098. −0.996782
\(170\) −251740. 436026.i −0.668081 1.15715i
\(171\) −18315.6 + 31723.6i −0.0478996 + 0.0829645i
\(172\) −89133.5 + 154384.i −0.229731 + 0.397906i
\(173\) 142352. + 246560.i 0.361616 + 0.626337i 0.988227 0.152995i \(-0.0488920\pi\)
−0.626611 + 0.779332i \(0.715559\pi\)
\(174\) −171548. −0.429548
\(175\) 0 0
\(176\) −9355.30 −0.0227654
\(177\) 199003. + 344683.i 0.477448 + 0.826964i
\(178\) 102992. 178387.i 0.243642 0.422000i
\(179\) −173979. + 301341.i −0.405849 + 0.702952i −0.994420 0.105494i \(-0.966358\pi\)
0.588571 + 0.808446i \(0.299691\pi\)
\(180\) 39574.1 + 68544.3i 0.0910394 + 0.157685i
\(181\) 379706. 0.861492 0.430746 0.902473i \(-0.358250\pi\)
0.430746 + 0.902473i \(0.358250\pi\)
\(182\) 0 0
\(183\) 174424. 0.385016
\(184\) −53895.9 93350.5i −0.117358 0.203269i
\(185\) −391525. + 678142.i −0.841067 + 1.45677i
\(186\) 94695.6 164018.i 0.200700 0.347623i
\(187\) −37659.5 65228.1i −0.0787535 0.136405i
\(188\) −375091. −0.774002
\(189\) 0 0
\(190\) −110475. −0.222013
\(191\) −97246.2 168435.i −0.192881 0.334080i 0.753323 0.657651i \(-0.228450\pi\)
−0.946204 + 0.323571i \(0.895116\pi\)
\(192\) −18432.0 + 31925.2i −0.0360844 + 0.0625000i
\(193\) −438700. + 759851.i −0.847763 + 1.46837i 0.0354361 + 0.999372i \(0.488718\pi\)
−0.883200 + 0.468997i \(0.844615\pi\)
\(194\) 254715. + 441179.i 0.485903 + 0.841609i
\(195\) −18998.6 −0.0357796
\(196\) 0 0
\(197\) −752368. −1.38123 −0.690613 0.723225i \(-0.742659\pi\)
−0.690613 + 0.723225i \(0.742659\pi\)
\(198\) 5920.15 + 10254.0i 0.0107317 + 0.0185879i
\(199\) 77726.4 134626.i 0.139135 0.240989i −0.788035 0.615631i \(-0.788901\pi\)
0.927169 + 0.374642i \(0.122235\pi\)
\(200\) −19349.6 + 33514.5i −0.0342056 + 0.0592458i
\(201\) −94248.4 163243.i −0.164545 0.285000i
\(202\) 263032. 0.453555
\(203\) 0 0
\(204\) −296790. −0.499313
\(205\) −217619. 376927.i −0.361669 0.626430i
\(206\) −340020. + 588932.i −0.558260 + 0.966935i
\(207\) −68212.0 + 118147.i −0.110646 + 0.191644i
\(208\) −4424.39 7663.28i −0.00709080 0.0122816i
\(209\) −16526.7 −0.0261709
\(210\) 0 0
\(211\) 3898.23 0.00602783 0.00301391 0.999995i \(-0.499041\pi\)
0.00301391 + 0.999995i \(0.499041\pi\)
\(212\) 56242.4 + 97414.6i 0.0859457 + 0.148862i
\(213\) −359295. + 622318.i −0.542628 + 0.939860i
\(214\) 215866. 373890.i 0.322218 0.558097i
\(215\) 340217. + 589274.i 0.501950 + 0.869403i
\(216\) 46656.0 0.0680414
\(217\) 0 0
\(218\) −890794. −1.26951
\(219\) 166796. + 288899.i 0.235004 + 0.407039i
\(220\) −17854.3 + 30924.6i −0.0248706 + 0.0430772i
\(221\) 35620.5 61696.5i 0.0490591 0.0849728i
\(222\) 230795. + 399749.i 0.314300 + 0.544384i
\(223\) 782574. 1.05381 0.526906 0.849924i \(-0.323352\pi\)
0.526906 + 0.849924i \(0.323352\pi\)
\(224\) 0 0
\(225\) 48978.7 0.0644987
\(226\) −362110. 627193.i −0.471595 0.816827i
\(227\) −398271. + 689826.i −0.512997 + 0.888536i 0.486890 + 0.873463i \(0.338131\pi\)
−0.999886 + 0.0150727i \(0.995202\pi\)
\(228\) −32561.1 + 56397.5i −0.0414823 + 0.0718494i
\(229\) −193522. 335191.i −0.243861 0.422380i 0.717950 0.696095i \(-0.245081\pi\)
−0.961811 + 0.273715i \(0.911747\pi\)
\(230\) −411435. −0.512840
\(231\) 0 0
\(232\) −304974. −0.372000
\(233\) 191879. + 332345.i 0.231547 + 0.401051i 0.958263 0.285887i \(-0.0922881\pi\)
−0.726717 + 0.686937i \(0.758955\pi\)
\(234\) −5599.62 + 9698.83i −0.00668527 + 0.0115792i
\(235\) −715851. + 1.23989e6i −0.845576 + 1.46458i
\(236\) 353783. + 612769.i 0.413482 + 0.716171i
\(237\) 378648. 0.437890
\(238\) 0 0
\(239\) −465409. −0.527036 −0.263518 0.964654i \(-0.584883\pi\)
−0.263518 + 0.964654i \(0.584883\pi\)
\(240\) 70353.9 + 121856.i 0.0788424 + 0.136559i
\(241\) 174372. 302022.i 0.193390 0.334962i −0.752981 0.658042i \(-0.771385\pi\)
0.946372 + 0.323080i \(0.104718\pi\)
\(242\) 319431. 553271.i 0.350622 0.607294i
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) 310088. 0.333434
\(245\) 0 0
\(246\) −256563. −0.270306
\(247\) −7815.93 13537.6i −0.00815152 0.0141188i
\(248\) 168348. 291587.i 0.173811 0.301050i
\(249\) 28401.0 49192.0i 0.0290292 0.0502801i
\(250\) −307838. 533191.i −0.311510 0.539551i
\(251\) −186543. −0.186894 −0.0934468 0.995624i \(-0.529789\pi\)
−0.0934468 + 0.995624i \(0.529789\pi\)
\(252\) 0 0
\(253\) −61549.4 −0.0604537
\(254\) −182949. 316878.i −0.177929 0.308182i
\(255\) −566414. + 981058.i −0.545486 + 0.944810i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −776774. 1.34541e6i −0.733605 1.27064i −0.955333 0.295532i \(-0.904503\pi\)
0.221728 0.975109i \(-0.428830\pi\)
\(258\) 401101. 0.375149
\(259\) 0 0
\(260\) −33775.3 −0.0309860
\(261\) 192991. + 334271.i 0.175362 + 0.303737i
\(262\) 38687.8 67009.2i 0.0348193 0.0603089i
\(263\) 629798. 1.09084e6i 0.561451 0.972462i −0.435919 0.899986i \(-0.643577\pi\)
0.997370 0.0724759i \(-0.0230901\pi\)
\(264\) 10524.7 + 18229.3i 0.00929396 + 0.0160976i
\(265\) 429348. 0.375573
\(266\) 0 0
\(267\) −463462. −0.397866
\(268\) −167553. 290210.i −0.142500 0.246817i
\(269\) 85230.6 147624.i 0.0718149 0.124387i −0.827882 0.560903i \(-0.810454\pi\)
0.899697 + 0.436515i \(0.143788\pi\)
\(270\) 89041.6 154225.i 0.0743333 0.128749i
\(271\) −1.11372e6 1.92901e6i −0.921194 1.59555i −0.797571 0.603225i \(-0.793882\pi\)
−0.123623 0.992329i \(-0.539451\pi\)
\(272\) −527626. −0.432418
\(273\) 0 0
\(274\) −12308.1 −0.00990412
\(275\) 11048.7 + 19136.9i 0.00881005 + 0.0152595i
\(276\) −121266. + 210039.i −0.0958221 + 0.165969i
\(277\) −991697. + 1.71767e6i −0.776568 + 1.34506i 0.157341 + 0.987544i \(0.449708\pi\)
−0.933909 + 0.357511i \(0.883626\pi\)
\(278\) −740002. 1.28172e6i −0.574276 0.994676i
\(279\) −426130. −0.327742
\(280\) 0 0
\(281\) −1.16687e6 −0.881573 −0.440786 0.897612i \(-0.645300\pi\)
−0.440786 + 0.897612i \(0.645300\pi\)
\(282\) 421978. + 730887.i 0.315985 + 0.547302i
\(283\) 950450. 1.64623e6i 0.705445 1.22187i −0.261086 0.965316i \(-0.584081\pi\)
0.966531 0.256551i \(-0.0825861\pi\)
\(284\) −638747. + 1.10634e6i −0.469930 + 0.813943i
\(285\) 124284. + 215266.i 0.0906364 + 0.156987i
\(286\) −5052.68 −0.00365264
\(287\) 0 0
\(288\) 82944.0 0.0589256
\(289\) −1.41401e6 2.44914e6i −0.995884 1.72492i
\(290\) −582034. + 1.00811e6i −0.406400 + 0.703905i
\(291\) 573108. 992653.i 0.396738 0.687171i
\(292\) 296527. + 513599.i 0.203520 + 0.352506i
\(293\) 1.65009e6 1.12289 0.561445 0.827514i \(-0.310245\pi\)
0.561445 + 0.827514i \(0.310245\pi\)
\(294\) 0 0
\(295\) 2.70073e6 1.80687
\(296\) 410303. + 710665.i 0.272192 + 0.471450i
\(297\) 13320.3 23071.5i 0.00876243 0.0151770i
\(298\) 908240. 1.57312e6i 0.592461 1.02617i
\(299\) −29108.5 50417.4i −0.0188296 0.0326139i
\(300\) 87073.2 0.0558575
\(301\) 0 0
\(302\) 710367. 0.448194
\(303\) −295911. 512532.i −0.185163 0.320712i
\(304\) −57886.5 + 100262.i −0.0359247 + 0.0622234i
\(305\) 591793. 1.02502e6i 0.364267 0.630930i
\(306\) 333888. + 578312.i 0.203844 + 0.353068i
\(307\) 597936. 0.362084 0.181042 0.983475i \(-0.442053\pi\)
0.181042 + 0.983475i \(0.442053\pi\)
\(308\) 0 0
\(309\) 1.53009e6 0.911635
\(310\) −642574. 1.11297e6i −0.379768 0.657778i
\(311\) −115240. + 199602.i −0.0675620 + 0.117021i −0.897828 0.440347i \(-0.854855\pi\)
0.830266 + 0.557368i \(0.188189\pi\)
\(312\) −9954.89 + 17242.4i −0.00578962 + 0.0100279i
\(313\) −221289. 383283.i −0.127673 0.221136i 0.795102 0.606476i \(-0.207417\pi\)
−0.922775 + 0.385340i \(0.874084\pi\)
\(314\) −995925. −0.570036
\(315\) 0 0
\(316\) 673152. 0.379224
\(317\) 631238. + 1.09334e6i 0.352813 + 0.611091i 0.986741 0.162302i \(-0.0518917\pi\)
−0.633928 + 0.773392i \(0.718558\pi\)
\(318\) 126545. 219183.i 0.0701743 0.121546i
\(319\) −87070.4 + 150810.i −0.0479064 + 0.0829764i
\(320\) 125074. + 216634.i 0.0682795 + 0.118264i
\(321\) −971396. −0.526179
\(322\) 0 0
\(323\) −932080. −0.497104
\(324\) −52488.0 90911.9i −0.0277778 0.0481125i
\(325\) −10450.5 + 18100.8i −0.00548817 + 0.00950579i
\(326\) −404496. + 700607.i −0.210800 + 0.365116i
\(327\) 1.00214e6 + 1.73576e6i 0.518275 + 0.897679i
\(328\) −456111. −0.234092
\(329\) 0 0
\(330\) 80344.5 0.0406136
\(331\) 234468. + 406110.i 0.117629 + 0.203739i 0.918827 0.394659i \(-0.129137\pi\)
−0.801199 + 0.598398i \(0.795804\pi\)
\(332\) 50490.7 87452.4i 0.0251400 0.0435438i
\(333\) 519289. 899435.i 0.256625 0.444487i
\(334\) −951580. 1.64818e6i −0.466744 0.808425i
\(335\) −1.27908e6 −0.622708
\(336\) 0 0
\(337\) −2.46798e6 −1.18377 −0.591884 0.806023i \(-0.701616\pi\)
−0.591884 + 0.806023i \(0.701616\pi\)
\(338\) 740196. + 1.28206e6i 0.352416 + 0.610402i
\(339\) −814747. + 1.41118e6i −0.385056 + 0.666936i
\(340\) −1.00696e6 + 1.74410e6i −0.472405 + 0.818229i
\(341\) −96127.0 166497.i −0.0447671 0.0775390i
\(342\) 146525. 0.0677402
\(343\) 0 0
\(344\) 713068. 0.324889
\(345\) 462865. + 801705.i 0.209366 + 0.362633i
\(346\) 569406. 986241.i 0.255701 0.442887i
\(347\) 2.14125e6 3.70875e6i 0.954648 1.65350i 0.219477 0.975618i \(-0.429565\pi\)
0.735171 0.677882i \(-0.237102\pi\)
\(348\) 343096. + 594259.i 0.151868 + 0.263044i
\(349\) −1.84999e6 −0.813028 −0.406514 0.913645i \(-0.633256\pi\)
−0.406514 + 0.913645i \(0.633256\pi\)
\(350\) 0 0
\(351\) 25198.3 0.0109170
\(352\) 18710.6 + 32407.7i 0.00804880 + 0.0139409i
\(353\) 1.13690e6 1.96916e6i 0.485607 0.841095i −0.514257 0.857636i \(-0.671932\pi\)
0.999863 + 0.0165411i \(0.00526543\pi\)
\(354\) 796011. 1.37873e6i 0.337606 0.584752i
\(355\) 2.43806e6 + 4.22284e6i 1.02677 + 1.77842i
\(356\) −823933. −0.344562
\(357\) 0 0
\(358\) 1.39183e6 0.573958
\(359\) 2.19996e6 + 3.81044e6i 0.900905 + 1.56041i 0.826322 + 0.563198i \(0.190429\pi\)
0.0745823 + 0.997215i \(0.476238\pi\)
\(360\) 158296. 274177.i 0.0643746 0.111500i
\(361\) 1.13579e6 1.96725e6i 0.458701 0.794494i
\(362\) −759412. 1.31534e6i −0.304583 0.527554i
\(363\) −1.43744e6 −0.572563
\(364\) 0 0
\(365\) 2.26365e6 0.889359
\(366\) −348849. 604223.i −0.136124 0.235773i
\(367\) 948716. 1.64322e6i 0.367681 0.636842i −0.621522 0.783397i \(-0.713485\pi\)
0.989203 + 0.146555i \(0.0468185\pi\)
\(368\) −215584. + 373402.i −0.0829844 + 0.143733i
\(369\) 288633. + 499927.i 0.110352 + 0.191135i
\(370\) 3.13220e6 1.18945
\(371\) 0 0
\(372\) −757565. −0.283833
\(373\) −2.28130e6 3.95133e6i −0.849005 1.47052i −0.882097 0.471067i \(-0.843869\pi\)
0.0330929 0.999452i \(-0.489464\pi\)
\(374\) −150638. + 260912.i −0.0556872 + 0.0964530i
\(375\) −692635. + 1.19968e6i −0.254347 + 0.440542i
\(376\) 750183. + 1.29935e6i 0.273651 + 0.473978i
\(377\) −164713. −0.0596861
\(378\) 0 0
\(379\) 4.99400e6 1.78587 0.892936 0.450184i \(-0.148642\pi\)
0.892936 + 0.450184i \(0.148642\pi\)
\(380\) 220949. + 382695.i 0.0784935 + 0.135955i
\(381\) −411636. + 712975.i −0.145278 + 0.251630i
\(382\) −388985. + 673742.i −0.136387 + 0.236230i
\(383\) 1.83954e6 + 3.18617e6i 0.640783 + 1.10987i 0.985258 + 0.171074i \(0.0547236\pi\)
−0.344475 + 0.938796i \(0.611943\pi\)
\(384\) 147456. 0.0510310
\(385\) 0 0
\(386\) 3.50960e6 1.19892
\(387\) −451238. 781568.i −0.153154 0.265271i
\(388\) 1.01886e6 1.76472e6i 0.343585 0.595107i
\(389\) −128617. + 222771.i −0.0430947 + 0.0746422i −0.886768 0.462214i \(-0.847055\pi\)
0.843673 + 0.536857i \(0.180388\pi\)
\(390\) 37997.2 + 65813.1i 0.0126500 + 0.0219104i
\(391\) −3.47130e6 −1.14829
\(392\) 0 0
\(393\) −174095. −0.0568598
\(394\) 1.50474e6 + 2.60628e6i 0.488337 + 0.845825i
\(395\) 1.28469e6 2.22515e6i 0.414292 0.717574i
\(396\) 23680.6 41016.0i 0.00758848 0.0131436i
\(397\) −216640. 375232.i −0.0689862 0.119488i 0.829469 0.558553i \(-0.188643\pi\)
−0.898455 + 0.439065i \(0.855310\pi\)
\(398\) −621811. −0.196766
\(399\) 0 0
\(400\) 154797. 0.0483740
\(401\) 569122. + 985748.i 0.176744 + 0.306129i 0.940763 0.339064i \(-0.110110\pi\)
−0.764020 + 0.645193i \(0.776777\pi\)
\(402\) −376993. + 652972.i −0.116351 + 0.201525i
\(403\) 90922.5 157482.i 0.0278874 0.0483025i
\(404\) −526063. 911169.i −0.160356 0.277744i
\(405\) −400687. −0.121386
\(406\) 0 0
\(407\) 468568. 0.140212
\(408\) 593579. + 1.02811e6i 0.176534 + 0.305766i
\(409\) 2.51219e6 4.35124e6i 0.742581 1.28619i −0.208735 0.977972i \(-0.566935\pi\)
0.951316 0.308216i \(-0.0997320\pi\)
\(410\) −870475. + 1.50771e6i −0.255739 + 0.442953i
\(411\) 13846.7 + 23983.1i 0.00404334 + 0.00700327i
\(412\) 2.72016e6 0.789499
\(413\) 0 0
\(414\) 545696. 0.156477
\(415\) −192720. 333801.i −0.0549296 0.0951409i
\(416\) −17697.6 + 30653.1i −0.00501396 + 0.00868443i
\(417\) −1.66500e6 + 2.88387e6i −0.468895 + 0.812149i
\(418\) 33053.3 + 57250.0i 0.00925282 + 0.0160264i
\(419\) −2.57295e6 −0.715974 −0.357987 0.933727i \(-0.616537\pi\)
−0.357987 + 0.933727i \(0.616537\pi\)
\(420\) 0 0
\(421\) 336425. 0.0925089 0.0462545 0.998930i \(-0.485271\pi\)
0.0462545 + 0.998930i \(0.485271\pi\)
\(422\) −7796.45 13503.9i −0.00213116 0.00369128i
\(423\) 949450. 1.64450e6i 0.258001 0.446871i
\(424\) 224969. 389659.i 0.0607728 0.105262i
\(425\) 623130. + 1.07929e6i 0.167342 + 0.289846i
\(426\) 2.87436e6 0.767392
\(427\) 0 0
\(428\) −1.72693e6 −0.455685
\(429\) 5684.27 + 9845.44i 0.00149118 + 0.00258281i
\(430\) 1.36087e6 2.35710e6i 0.354932 0.614761i
\(431\) −118205. + 204737.i −0.0306509 + 0.0530889i −0.880944 0.473221i \(-0.843091\pi\)
0.850293 + 0.526310i \(0.176425\pi\)
\(432\) −93312.0 161621.i −0.0240563 0.0416667i
\(433\) −2.33004e6 −0.597232 −0.298616 0.954373i \(-0.596525\pi\)
−0.298616 + 0.954373i \(0.596525\pi\)
\(434\) 0 0
\(435\) 2.61915e6 0.663648
\(436\) 1.78159e6 + 3.08580e6i 0.448839 + 0.777412i
\(437\) −380840. + 659635.i −0.0953980 + 0.165234i
\(438\) 667185. 1.15560e6i 0.166173 0.287820i
\(439\) −1.59981e6 2.77095e6i −0.396193 0.686227i 0.597059 0.802197i \(-0.296336\pi\)
−0.993253 + 0.115970i \(0.963002\pi\)
\(440\) 142835. 0.0351724
\(441\) 0 0
\(442\) −284964. −0.0693800
\(443\) −566202. 980690.i −0.137076 0.237423i 0.789313 0.613992i \(-0.210437\pi\)
−0.926389 + 0.376569i \(0.877104\pi\)
\(444\) 923181. 1.59900e6i 0.222244 0.384937i
\(445\) −1.57245e6 + 2.72357e6i −0.376424 + 0.651986i
\(446\) −1.56515e6 2.71091e6i −0.372579 0.645325i
\(447\) −4.08708e6 −0.967485
\(448\) 0 0
\(449\) −8.23687e6 −1.92817 −0.964087 0.265585i \(-0.914435\pi\)
−0.964087 + 0.265585i \(0.914435\pi\)
\(450\) −97957.4 169667.i −0.0228037 0.0394972i
\(451\) −130220. + 225548.i −0.0301465 + 0.0522153i
\(452\) −1.44844e6 + 2.50877e6i −0.333468 + 0.577584i
\(453\) −799163. 1.38419e6i −0.182974 0.316921i
\(454\) 3.18617e6 0.725487
\(455\) 0 0
\(456\) 260489. 0.0586648
\(457\) 182566. + 316214.i 0.0408912 + 0.0708256i 0.885747 0.464169i \(-0.153647\pi\)
−0.844855 + 0.534995i \(0.820314\pi\)
\(458\) −774090. + 1.34076e6i −0.172436 + 0.298668i
\(459\) 751249. 1.30120e6i 0.166438 0.288279i
\(460\) 822871. + 1.42525e6i 0.181316 + 0.314049i
\(461\) 332567. 0.0728832 0.0364416 0.999336i \(-0.488398\pi\)
0.0364416 + 0.999336i \(0.488398\pi\)
\(462\) 0 0
\(463\) 1.69992e6 0.368533 0.184266 0.982876i \(-0.441009\pi\)
0.184266 + 0.982876i \(0.441009\pi\)
\(464\) 609948. + 1.05646e6i 0.131522 + 0.227802i
\(465\) −1.44579e6 + 2.50418e6i −0.310079 + 0.537073i
\(466\) 767518. 1.32938e6i 0.163728 0.283586i
\(467\) 495233. + 857768.i 0.105079 + 0.182003i 0.913771 0.406231i \(-0.133157\pi\)
−0.808691 + 0.588233i \(0.799824\pi\)
\(468\) 44797.0 0.00945441
\(469\) 0 0
\(470\) 5.72681e6 1.19583
\(471\) 1.12042e6 + 1.94062e6i 0.232716 + 0.403076i
\(472\) 1.41513e6 2.45108e6i 0.292376 0.506410i
\(473\) 203582. 352614.i 0.0418395 0.0724681i
\(474\) −757296. 1.31168e6i −0.154817 0.268152i
\(475\) 273457. 0.0556103
\(476\) 0 0
\(477\) −569454. −0.114594
\(478\) 930819. + 1.61223e6i 0.186335 + 0.322742i
\(479\) 3.04033e6 5.26600e6i 0.605454 1.04868i −0.386525 0.922279i \(-0.626325\pi\)
0.991980 0.126399i \(-0.0403419\pi\)
\(480\) 281415. 487426.i 0.0557500 0.0965618i
\(481\) 221599. + 383821.i 0.0436722 + 0.0756425i
\(482\) −1.39498e6 −0.273495
\(483\) 0 0
\(484\) −2.55545e6 −0.495854
\(485\) −3.88893e6 6.73582e6i −0.750715 1.30028i
\(486\) −118098. + 204552.i −0.0226805 + 0.0392837i
\(487\) 3.35549e6 5.81188e6i 0.641112 1.11044i −0.344073 0.938943i \(-0.611807\pi\)
0.985185 0.171495i \(-0.0548598\pi\)
\(488\) −620175. 1.07417e6i −0.117887 0.204186i
\(489\) 1.82023e6 0.344234
\(490\) 0 0
\(491\) −914042. −0.171105 −0.0855525 0.996334i \(-0.527266\pi\)
−0.0855525 + 0.996334i \(0.527266\pi\)
\(492\) 513125. + 888759.i 0.0955676 + 0.165528i
\(493\) −4.91065e6 + 8.50549e6i −0.909959 + 1.57609i
\(494\) −31263.7 + 54150.4i −0.00576399 + 0.00998353i
\(495\) −90387.5 156556.i −0.0165804 0.0287181i
\(496\) −1.34678e6 −0.245806
\(497\) 0 0
\(498\) −227208. −0.0410535
\(499\) 3.87746e6 + 6.71596e6i 0.697101 + 1.20742i 0.969467 + 0.245221i \(0.0788606\pi\)
−0.272366 + 0.962194i \(0.587806\pi\)
\(500\) −1.23135e6 + 2.13276e6i −0.220271 + 0.381520i
\(501\) −2.14106e6 + 3.70842e6i −0.381095 + 0.660076i
\(502\) 373086. + 646204.i 0.0660769 + 0.114449i
\(503\) −3.79381e6 −0.668584 −0.334292 0.942470i \(-0.608497\pi\)
−0.334292 + 0.942470i \(0.608497\pi\)
\(504\) 0 0
\(505\) −4.01591e6 −0.700737
\(506\) 123099. + 213213.i 0.0213736 + 0.0370202i
\(507\) 1.66544e6 2.88463e6i 0.287746 0.498391i
\(508\) −731798. + 1.26751e6i −0.125815 + 0.217918i
\(509\) 4.26580e6 + 7.38858e6i 0.729804 + 1.26406i 0.956966 + 0.290200i \(0.0937220\pi\)
−0.227162 + 0.973857i \(0.572945\pi\)
\(510\) 4.53131e6 0.771434
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) −164841. 285513.i −0.0276548 0.0478996i
\(514\) −3.10710e6 + 5.38165e6i −0.518737 + 0.898478i
\(515\) 5.19135e6 8.99168e6i 0.862506 1.49390i
\(516\) −802202. 1.38945e6i −0.132635 0.229731i
\(517\) 856712. 0.140964
\(518\) 0 0
\(519\) −2.56233e6 −0.417558
\(520\) 67550.6 + 117001.i 0.0109552 + 0.0189750i
\(521\) −1.59533e6 + 2.76320e6i −0.257488 + 0.445982i −0.965568 0.260150i \(-0.916228\pi\)
0.708080 + 0.706132i \(0.249561\pi\)
\(522\) 771965. 1.33708e6i 0.124000 0.214774i
\(523\) −4.80339e6 8.31971e6i −0.767880 1.33001i −0.938710 0.344707i \(-0.887978\pi\)
0.170830 0.985301i \(-0.445355\pi\)
\(524\) −309502. −0.0492420
\(525\) 0 0
\(526\) −5.03838e6 −0.794012
\(527\) −5.42143e6 9.39019e6i −0.850329 1.47281i
\(528\) 42098.9 72917.4i 0.00657182 0.0113827i
\(529\) 1.79983e6 3.11739e6i 0.279635 0.484342i
\(530\) −858695. 1.48730e6i −0.132785 0.229991i
\(531\) −3.58205e6 −0.551309
\(532\) 0 0
\(533\) −246340. −0.0375592
\(534\) 926925. + 1.60548e6i 0.140667 + 0.243642i
\(535\) −3.29579e6 + 5.70847e6i −0.497823 + 0.862254i
\(536\) −670210. + 1.16084e6i −0.100763 + 0.174526i
\(537\) −1.56581e6 2.71207e6i −0.234317 0.405849i
\(538\) −681844. −0.101562
\(539\) 0 0
\(540\) −712333. −0.105123
\(541\) −5.11832e6 8.86519e6i −0.751855 1.30225i −0.946923 0.321462i \(-0.895826\pi\)
0.195067 0.980790i \(-0.437508\pi\)
\(542\) −4.45486e6 + 7.71605e6i −0.651382 + 1.12823i
\(543\) −1.70868e6 + 2.95952e6i −0.248691 + 0.430746i
\(544\) 1.05525e6 + 1.82775e6i 0.152883 + 0.264801i
\(545\) 1.36004e7 1.96138
\(546\) 0 0
\(547\) −9.27757e6 −1.32576 −0.662882 0.748724i \(-0.730667\pi\)
−0.662882 + 0.748724i \(0.730667\pi\)
\(548\) 24616.3 + 42636.7i 0.00350164 + 0.00606501i
\(549\) −784909. + 1.35950e6i −0.111145 + 0.192508i
\(550\) 44194.7 76547.5i 0.00622965 0.0107901i
\(551\) 1.07751e6 + 1.86630e6i 0.151196 + 0.261879i
\(552\) 970127. 0.135513
\(553\) 0 0
\(554\) 7.93357e6 1.09823
\(555\) −3.52373e6 6.10327e6i −0.485590 0.841067i
\(556\) −2.96001e6 + 5.12688e6i −0.406075 + 0.703342i
\(557\) −310049. + 537021.i −0.0423441 + 0.0733421i −0.886421 0.462881i \(-0.846816\pi\)
0.844077 + 0.536223i \(0.180149\pi\)
\(558\) 852260. + 1.47616e6i 0.115874 + 0.200700i
\(559\) 385119. 0.0521273
\(560\) 0 0
\(561\) 677870. 0.0909368
\(562\) 2.33375e6 + 4.04217e6i 0.311683 + 0.539851i
\(563\) 3.68332e6 6.37970e6i 0.489744 0.848261i −0.510187 0.860064i \(-0.670424\pi\)
0.999930 + 0.0118029i \(0.00375708\pi\)
\(564\) 1.68791e6 2.92355e6i 0.223435 0.387001i
\(565\) 5.52861e6 + 9.57583e6i 0.728610 + 1.26199i
\(566\) −7.60360e6 −0.997650
\(567\) 0 0
\(568\) 5.10998e6 0.664581
\(569\) −1.84111e6 3.18890e6i −0.238396 0.412914i 0.721858 0.692041i \(-0.243288\pi\)
−0.960254 + 0.279127i \(0.909955\pi\)
\(570\) 497136. 861064.i 0.0640896 0.111007i
\(571\) −5.16600e6 + 8.94777e6i −0.663077 + 1.14848i 0.316726 + 0.948517i \(0.397416\pi\)
−0.979803 + 0.199966i \(0.935917\pi\)
\(572\) 10105.4 + 17503.0i 0.00129140 + 0.00223678i
\(573\) 1.75043e6 0.222720
\(574\) 0 0
\(575\) 1.01842e6 0.128457
\(576\) −165888. 287326.i −0.0208333 0.0360844i
\(577\) −6.25617e6 + 1.08360e7i −0.782292 + 1.35497i 0.148311 + 0.988941i \(0.452616\pi\)
−0.930603 + 0.366029i \(0.880717\pi\)
\(578\) −5.65605e6 + 9.79657e6i −0.704196 + 1.21970i
\(579\) −3.94830e6 6.83866e6i −0.489456 0.847763i
\(580\) 4.65627e6 0.574736
\(581\) 0 0
\(582\) −4.58487e6 −0.561073
\(583\) −128458. 222496.i −0.0156527 0.0271113i
\(584\) 1.18611e6 2.05440e6i 0.143910 0.249260i
\(585\) 85493.8 148080.i 0.0103287 0.0178898i
\(586\) −3.30017e6 5.71607e6i −0.397002 0.687627i
\(587\) 1.60865e7 1.92694 0.963468 0.267823i \(-0.0863042\pi\)
0.963468 + 0.267823i \(0.0863042\pi\)
\(588\) 0 0
\(589\) −2.37916e6 −0.282577
\(590\) −5.40147e6 9.35562e6i −0.638825 1.10648i
\(591\) 3.38566e6 5.86413e6i 0.398726 0.690613i
\(592\) 1.64121e6 2.84266e6i 0.192469 0.333365i
\(593\) −4.73165e6 8.19546e6i −0.552556 0.957054i −0.998089 0.0617892i \(-0.980319\pi\)
0.445534 0.895265i \(-0.353014\pi\)
\(594\) −106563. −0.0123919
\(595\) 0 0
\(596\) −7.26592e6 −0.837866
\(597\) 699538. + 1.21163e6i 0.0803295 + 0.139135i
\(598\) −116434. + 201670.i −0.0133146 + 0.0230615i
\(599\) −2.50749e6 + 4.34310e6i −0.285544 + 0.494576i −0.972741 0.231895i \(-0.925507\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(600\) −174146. 301631.i −0.0197486 0.0342056i
\(601\) −1.26473e7 −1.42828 −0.714139 0.700004i \(-0.753182\pi\)
−0.714139 + 0.700004i \(0.753182\pi\)
\(602\) 0 0
\(603\) 1.69647e6 0.190000
\(604\) −1.42073e6 2.46078e6i −0.158460 0.274461i
\(605\) −4.87700e6 + 8.44721e6i −0.541707 + 0.938264i
\(606\) −1.18364e6 + 2.05013e6i −0.130930 + 0.226777i
\(607\) −1.43851e6 2.49157e6i −0.158468 0.274475i 0.775848 0.630919i \(-0.217322\pi\)
−0.934316 + 0.356445i \(0.883989\pi\)
\(608\) 463092. 0.0508052
\(609\) 0 0
\(610\) −4.73434e6 −0.515152
\(611\) 405164. + 701765.i 0.0439064 + 0.0760481i
\(612\) 1.33555e6 2.31325e6i 0.144139 0.249657i
\(613\) 1.86291e6 3.22666e6i 0.200236 0.346818i −0.748369 0.663283i \(-0.769163\pi\)
0.948604 + 0.316465i \(0.102496\pi\)
\(614\) −1.19587e6 2.07131e6i −0.128016 0.221730i
\(615\) 3.91714e6 0.417620
\(616\) 0 0
\(617\) −1.15861e7 −1.22525 −0.612625 0.790374i \(-0.709886\pi\)
−0.612625 + 0.790374i \(0.709886\pi\)
\(618\) −3.06018e6 5.30039e6i −0.322312 0.558260i
\(619\) 928039. 1.60741e6i 0.0973508 0.168617i −0.813236 0.581933i \(-0.802296\pi\)
0.910587 + 0.413317i \(0.135630\pi\)
\(620\) −2.57029e6 + 4.45188e6i −0.268537 + 0.465119i
\(621\) −613908. 1.06332e6i −0.0638814 0.110646i
\(622\) 921921. 0.0955471
\(623\) 0 0
\(624\) 79639.1 0.00818776
\(625\) 5.64480e6 + 9.77708e6i 0.578028 + 1.00117i
\(626\) −885155. + 1.53313e6i −0.0902783 + 0.156367i
\(627\) 74369.9 128813.i 0.00755490 0.0130855i
\(628\) 1.99185e6 + 3.44998e6i 0.201538 + 0.349074i
\(629\) 2.64266e7 2.66326
\(630\) 0 0
\(631\) 8.92135e6 0.891984 0.445992 0.895037i \(-0.352851\pi\)
0.445992 + 0.895037i \(0.352851\pi\)
\(632\) −1.34630e6 2.33187e6i −0.134076 0.232226i
\(633\) −17542.0 + 30383.7i −0.00174008 + 0.00301391i
\(634\) 2.52495e6 4.37335e6i 0.249477 0.432106i
\(635\) 2.79323e6 + 4.83802e6i 0.274898 + 0.476138i
\(636\) −1.01236e6 −0.0992415
\(637\) 0 0
\(638\) 696563. 0.0677499
\(639\) −3.23366e6 5.60086e6i −0.313287 0.542628i
\(640\) 500294. 866535.i 0.0482809 0.0836250i
\(641\) −6.59332e6 + 1.14200e7i −0.633810 + 1.09779i 0.352956 + 0.935640i \(0.385177\pi\)
−0.986766 + 0.162151i \(0.948157\pi\)
\(642\) 1.94279e6 + 3.36501e6i 0.186032 + 0.322218i
\(643\) −9.67813e6 −0.923132 −0.461566 0.887106i \(-0.652712\pi\)
−0.461566 + 0.887106i \(0.652712\pi\)
\(644\) 0 0
\(645\) −6.12391e6 −0.579602
\(646\) 1.86416e6 + 3.22882e6i 0.175753 + 0.304413i
\(647\) 862455. 1.49382e6i 0.0809982 0.140293i −0.822681 0.568504i \(-0.807523\pi\)
0.903679 + 0.428211i \(0.140856\pi\)
\(648\) −209952. + 363648.i −0.0196419 + 0.0340207i
\(649\) −808043. 1.39957e6i −0.0753048 0.130432i
\(650\) 83603.8 0.00776145
\(651\) 0 0
\(652\) 3.23596e6 0.298116
\(653\) −298755. 517459.i −0.0274178 0.0474890i 0.851991 0.523557i \(-0.175395\pi\)
−0.879409 + 0.476068i \(0.842062\pi\)
\(654\) 4.00857e6 6.94305e6i 0.366476 0.634755i
\(655\) −590676. + 1.02308e6i −0.0537955 + 0.0931766i
\(656\) 912222. + 1.58002e6i 0.0827639 + 0.143351i
\(657\) −3.00233e6 −0.271360
\(658\) 0 0
\(659\) 1.47605e7 1.32400 0.662001 0.749503i \(-0.269707\pi\)
0.662001 + 0.749503i \(0.269707\pi\)
\(660\) −160689. 278321.i −0.0143591 0.0248706i
\(661\) −8.45206e6 + 1.46394e7i −0.752418 + 1.30323i 0.194230 + 0.980956i \(0.437779\pi\)
−0.946648 + 0.322270i \(0.895554\pi\)
\(662\) 937871. 1.62444e6i 0.0831760 0.144065i
\(663\) 320585. + 555269.i 0.0283243 + 0.0490591i
\(664\) −403925. −0.0355534
\(665\) 0 0
\(666\) −4.15431e6 −0.362922
\(667\) 4.01290e6 + 6.95055e6i 0.349256 + 0.604930i
\(668\) −3.80632e6 + 6.59274e6i −0.330038 + 0.571643i
\(669\) −3.52158e6 + 6.09956e6i −0.304209 + 0.526906i
\(670\) 2.55815e6 + 4.43085e6i 0.220161 + 0.381329i
\(671\) −708243. −0.0607262
\(672\) 0 0
\(673\) −1.58960e7 −1.35285 −0.676425 0.736512i \(-0.736472\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(674\) 4.93596e6 + 8.54933e6i 0.418525 + 0.724907i
\(675\) −220404. + 381751.i −0.0186192 + 0.0322494i
\(676\) 2.96079e6 5.12823e6i 0.249196 0.431619i
\(677\) 976806. + 1.69188e6i 0.0819099 + 0.141872i 0.904070 0.427384i \(-0.140565\pi\)
−0.822160 + 0.569256i \(0.807231\pi\)
\(678\) 6.51798e6 0.544551
\(679\) 0 0
\(680\) 8.05567e6 0.668081
\(681\) −3.58444e6 6.20844e6i −0.296179 0.512997i
\(682\) −384508. + 665987.i −0.0316551 + 0.0548283i
\(683\) 4.61985e6 8.00182e6i 0.378945 0.656352i −0.611964 0.790886i \(-0.709620\pi\)
0.990909 + 0.134534i \(0.0429536\pi\)
\(684\) −293050. 507578.i −0.0239498 0.0414823i
\(685\) 187918. 0.0153018
\(686\) 0 0
\(687\) 3.48340e6 0.281587
\(688\) −1.42614e6 2.47014e6i −0.114866 0.198953i
\(689\) 121503. 210450.i 0.00975078 0.0168889i
\(690\) 1.85146e6 3.20682e6i 0.148044 0.256420i
\(691\) 7.28490e6 + 1.26178e7i 0.580401 + 1.00528i 0.995432 + 0.0954768i \(0.0304376\pi\)
−0.415030 + 0.909808i \(0.636229\pi\)
\(692\) −4.55525e6 −0.361616
\(693\) 0 0
\(694\) −1.71300e7 −1.35008
\(695\) 1.12982e7 + 1.95690e7i 0.887251 + 1.53676i
\(696\) 1.37238e6 2.37704e6i 0.107387 0.186000i
\(697\) −7.34424e6 + 1.27206e7i −0.572618 + 0.991804i
\(698\) 3.69998e6 + 6.40855e6i 0.287449 + 0.497876i
\(699\) −3.45383e6 −0.267367
\(700\) 0 0
\(701\) −3.70190e6 −0.284531 −0.142266 0.989829i \(-0.545439\pi\)
−0.142266 + 0.989829i \(0.545439\pi\)
\(702\) −50396.6 87289.5i −0.00385975 0.00668527i
\(703\) 2.89929e6 5.02171e6i 0.221260 0.383234i
\(704\) 74842.4 129631.i 0.00569136 0.00985773i
\(705\) −6.44266e6 1.11590e7i −0.488194 0.845576i
\(706\) −9.09518e6 −0.686751
\(707\) 0 0
\(708\) −6.36809e6 −0.477448
\(709\) 1.26468e7 + 2.19049e7i 0.944857 + 1.63654i 0.756038 + 0.654528i \(0.227133\pi\)
0.188819 + 0.982012i \(0.439534\pi\)
\(710\) 9.75224e6 1.68914e7i 0.726037 1.25753i
\(711\) −1.70392e6 + 2.95127e6i −0.126408 + 0.218945i
\(712\) 1.64787e6 + 2.85419e6i 0.121821 + 0.211000i
\(713\) −8.86061e6 −0.652739
\(714\) 0 0
\(715\) 77143.1 0.00564329
\(716\) −2.78367e6 4.82145e6i −0.202925 0.351476i
\(717\) 2.09434e6 3.62751e6i 0.152142 0.263518i
\(718\) 8.79984e6 1.52418e7i 0.637036 1.10338i
\(719\) −7.25924e6 1.25734e7i −0.523683 0.907046i −0.999620 0.0275667i \(-0.991224\pi\)
0.475937 0.879480i \(-0.342109\pi\)
\(720\) −1.26637e6 −0.0910394
\(721\) 0 0
\(722\) −9.08632e6 −0.648702
\(723\) 1.56935e6 + 2.71819e6i 0.111654 + 0.193390i
\(724\) −3.03765e6 + 5.26136e6i −0.215373 + 0.373037i
\(725\) 1.44070e6 2.49537e6i 0.101796 0.176316i
\(726\) 2.87488e6 + 4.97944e6i 0.202431 + 0.350622i
\(727\) −1.42855e7 −1.00244 −0.501222 0.865319i \(-0.667116\pi\)
−0.501222 + 0.865319i \(0.667116\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −4.52730e6 7.84151e6i −0.314436 0.544619i
\(731\) 1.14817e7 1.98869e7i 0.794719 1.37649i
\(732\) −1.39539e6 + 2.41689e6i −0.0962541 + 0.166717i
\(733\) 4.10778e6 + 7.11488e6i 0.282389 + 0.489112i 0.971973 0.235094i \(-0.0755399\pi\)
−0.689584 + 0.724206i \(0.742207\pi\)
\(734\) −7.58973e6 −0.519979
\(735\) 0 0
\(736\) 1.72467e6 0.117358
\(737\) 382692. + 662842.i 0.0259526 + 0.0449512i
\(738\) 1.15453e6 1.99971e6i 0.0780306 0.135153i
\(739\) 1.71948e6 2.97822e6i 0.115821 0.200607i −0.802287 0.596939i \(-0.796384\pi\)
0.918107 + 0.396332i \(0.129717\pi\)
\(740\) −6.26440e6 1.08503e7i −0.420533 0.728385i
\(741\) 140687. 0.00941256
\(742\) 0 0
\(743\) 1.53588e6 0.102067 0.0510334 0.998697i \(-0.483748\pi\)
0.0510334 + 0.998697i \(0.483748\pi\)
\(744\) 1.51513e6 + 2.62428e6i 0.100350 + 0.173811i
\(745\) −1.38668e7 + 2.40180e7i −0.915346 + 1.58543i
\(746\) −9.12519e6 + 1.58053e7i −0.600337 + 1.03981i
\(747\) 255609. + 442728.i 0.0167600 + 0.0290292i
\(748\) 1.20510e6 0.0787535
\(749\) 0 0
\(750\) 5.54108e6 0.359701
\(751\) 1.00573e7 + 1.74197e7i 0.650700 + 1.12704i 0.982953 + 0.183855i \(0.0588576\pi\)
−0.332254 + 0.943190i \(0.607809\pi\)
\(752\) 3.00073e6 5.19742e6i 0.193501 0.335153i
\(753\) 839443. 1.45396e6i 0.0539515 0.0934468i
\(754\) 329425. + 570581.i 0.0211022 + 0.0365501i
\(755\) −1.08457e7 −0.692454
\(756\) 0 0
\(757\) 202045. 0.0128147 0.00640733 0.999979i \(-0.497960\pi\)
0.00640733 + 0.999979i \(0.497960\pi\)
\(758\) −9.98799e6 1.72997e7i −0.631401 1.09362i
\(759\) 276972. 479730.i 0.0174515 0.0302268i
\(760\) 883797. 1.53078e6i 0.0555033 0.0961345i
\(761\) 541011. + 937058.i 0.0338645 + 0.0586550i 0.882461 0.470386i \(-0.155885\pi\)
−0.848596 + 0.529041i \(0.822552\pi\)
\(762\) 3.29309e6 0.205455
\(763\) 0 0
\(764\) 3.11188e6 0.192881
\(765\) −5.09773e6 8.82953e6i −0.314937 0.545486i
\(766\) 7.35814e6 1.27447e7i 0.453102 0.784796i
\(767\) 764294. 1.32380e6i 0.0469107 0.0812517i
\(768\) −294912. 510803.i −0.0180422 0.0312500i
\(769\) 1.19305e7