Properties

Label 294.6.e.v.79.1
Level $294$
Weight $6$
Character 294.79
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 79.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.6.e.v.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 + 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-30.5355 + 52.8891i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.452292 + 0.891870i \(0.350607\pi\)
−0.998528 + 0.0542389i \(0.982727\pi\)
\(6\) −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 0.887893 0.460051i \(-0.152169\pi\)
−0.842362 + 0.538912i \(0.818835\pi\)
\(12\) 72.0000 124.708i 0.144338 0.250000i
\(13\) −34.5656 −0.0567264 −0.0283632 0.999598i \(-0.509030\pi\)
−0.0283632 + 0.999598i \(0.509030\pi\)
\(14\) 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 −0.867210 0.497943i \(-0.834089\pi\)
0.00237330 0.999997i \(-0.499245\pi\)
\(18\) −162.000 280.592i −0.117851 0.204124i
\(19\) 226.119 391.650i 0.143699 0.248894i −0.785188 0.619258i \(-0.787434\pi\)
0.928887 + 0.370364i \(0.120767\pi\)
\(20\) 977.137 0.546236
\(21\) 0 0
\(22\) −146.177 −0.0643904
\(23\) −842.124 + 1458.60i −0.331938 + 0.574933i −0.982892 0.184184i \(-0.941036\pi\)
0.650954 + 0.759117i \(0.274369\pi\)
\(24\) 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 \(-0.330259\pi\)
−0.999953 + 0.00965788i \(0.996926\pi\)
\(32\) −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 −0.167756 0.985829i \(-0.553652\pi\)
0.937631 0.347633i \(-0.113015\pi\)
\(38\) 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 \(-0.392595\pi\)
0.331056 + 0.943611i \(0.392595\pi\)
\(42\) 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 0.161351 + 0.986897i \(0.448415\pi\)
−0.935353 + 0.353714i \(0.884918\pi\)
\(48\) −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 0.939081 0.343696i \(-0.111679\pi\)
−0.767190 + 0.641420i \(0.778346\pi\)
\(54\) 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 −0.900409 0.435044i \(-0.856733\pi\)
0.0734457 0.997299i \(-0.476600\pi\)
\(60\) 4397.12 + 7616.03i 0.157685 + 0.273118i
\(61\) 9690.24 16784.0i 0.333434 0.577524i −0.649749 0.760149i \(-0.725126\pi\)
0.983183 + 0.182624i \(0.0584593\pi\)
\(62\) 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 0.687609 0.726081i \(-0.258660\pi\)
−0.972609 + 0.232447i \(0.925327\pi\)
\(68\) −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 \(-0.300105\pi\)
−0.994556 + 0.104199i \(0.966772\pi\)
\(74\) 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 −0.990950 0.134235i \(-0.957142\pi\)
0.611726 + 0.791070i \(0.290476\pi\)
\(80\) −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 \(-0.483989\pi\)
0.0502801 + 0.998735i \(0.483989\pi\)
\(84\) 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 \(-0.945306\pi\)
0.640712 + 0.767781i \(0.278639\pi\)
\(90\) 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 \(-0.258852\pi\)
0.687171 + 0.726496i \(0.258852\pi\)
\(98\) 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 \(-0.0627446\pi\)
−0.659923 + 0.751333i \(0.729411\pi\)
\(102\) 37098.7 + 64256.8i 0.353068 + 0.611532i
\(103\) 85005.1 147233.i 0.789499 1.36745i −0.136774 0.990602i \(-0.543674\pi\)
0.926274 0.376851i \(-0.122993\pi\)
\(104\) −2212.20 −0.0200558
\(105\) 0 0
\(106\) −28121.2 −0.243091
\(107\) 53966.4 93472.6i 0.455685 0.789269i −0.543043 0.839705i \(-0.682728\pi\)
0.998727 + 0.0504363i \(0.0160612\pi\)
\(108\) 5832.00 + 10101.3i 0.0481125 + 0.0833333i
\(109\) 111349. + 192862.i 0.897679 + 1.55482i 0.830454 + 0.557087i \(0.188081\pi\)
0.0672244 + 0.997738i \(0.478586\pi\)
\(110\) 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 \(-0.849014\pi\)
0.840354 + 0.542038i \(0.182347\pi\)
\(132\) 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 0.869506 0.493923i \(-0.164437\pi\)
−0.862503 + 0.506053i \(0.831104\pi\)
\(138\) 30316.5 52509.7i 0.135513 0.234715i
\(139\) −370001. −1.62430 −0.812149 0.583450i \(-0.801702\pi\)
−0.812149 + 0.583450i \(0.801702\pi\)
\(140\) 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 −0.0538086 0.998551i \(-0.517136\pi\)
0.891675 0.452676i \(-0.149531\pi\)
\(150\) 10884.2 + 18851.9i 0.0394972 + 0.0684112i
\(151\) −88795.9 153799.i −0.316921 0.548923i 0.662923 0.748687i \(-0.269316\pi\)
−0.979844 + 0.199765i \(0.935982\pi\)
\(152\) 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 \(-0.298726\pi\)
−0.994095 + 0.108509i \(0.965392\pi\)
\(158\) −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 −0.975705 0.219089i \(-0.929691\pi\)
0.677589 + 0.735441i \(0.263025\pi\)
\(164\) −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 \(-0.729476\pi\)
−0.660076 + 0.751199i \(0.729476\pi\)
\(168\) 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 \(-0.951108\pi\)
0.626611 + 0.779332i \(0.284441\pi\)
\(174\) 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 0.588571 0.808446i \(-0.299691\pi\)
−0.994420 + 0.105494i \(0.966358\pi\)
\(180\) −39574.1 + 68544.3i −0.0910394 + 0.157685i
\(181\) −379706. −0.861492 −0.430746 0.902473i \(-0.641750\pi\)
−0.430746 + 0.902473i \(0.641750\pi\)
\(182\) 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 −0.946204 0.323571i \(-0.895116\pi\)
0.753323 + 0.657651i \(0.228450\pi\)
\(192\) 18432.0 + 31925.2i 0.0360844 + 0.0625000i
\(193\) −438700. 759851.i −0.847763 1.46837i −0.883200 0.468997i \(-0.844615\pi\)
0.0354361 0.999372i \(-0.488718\pi\)
\(194\) −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 \(-0.211099\pi\)
−0.927169 + 0.374642i \(0.877765\pi\)
\(200\) −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 \(-0.676648\pi\)
−0.526906 + 0.849924i \(0.676648\pi\)
\(224\) 0 0
\(225\) 48978.7 0.0644987
\(226\) −362110. + 627193.i −0.471595 + 0.816827i
\(227\) 398271. + 689826.i 0.512997 + 0.888536i 0.999886 + 0.0150727i \(0.00479799\pi\)
−0.486890 + 0.873463i \(0.661869\pi\)
\(228\) −32561.1 56397.5i −0.0414823 0.0718494i
\(229\) 193522. 335191.i 0.243861 0.422380i −0.717950 0.696095i \(-0.754919\pi\)
0.961811 + 0.273715i \(0.0882525\pi\)
\(230\) 411435. 0.512840
\(231\) 0 0
\(232\) −304974. −0.372000
\(233\) 191879. 332345.i 0.231547 0.401051i −0.726717 0.686937i \(-0.758955\pi\)
0.958263 + 0.285887i \(0.0922881\pi\)
\(234\) 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 \(-0.228615\pi\)
−0.946372 + 0.323080i \(0.895282\pi\)
\(242\) 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 \(-0.470211\pi\)
0.0934468 + 0.995624i \(0.470211\pi\)
\(252\) 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 −0.221728 0.975109i \(-0.571170\pi\)
0.955333 0.295532i \(-0.0954969\pi\)
\(258\) −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 0.997370 + 0.0724759i \(0.0230901\pi\)
−0.435919 + 0.899986i \(0.643577\pi\)
\(264\) −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 \(-0.189546\pi\)
−0.899697 + 0.436515i \(0.856212\pi\)
\(270\) 89041.6 + 154225.i 0.0743333 + 0.128749i
\(271\) 1.11372e6 1.92901e6i 0.921194 1.59555i 0.123623 0.992329i \(-0.460549\pi\)
0.797571 0.603225i \(-0.206118\pi\)
\(272\) 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 −0.933909 0.357511i \(-0.883626\pi\)
0.157341 0.987544i \(-0.449708\pi\)
\(278\) 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 −0.966531 0.256551i \(-0.917414\pi\)
0.261086 0.965316i \(-0.415919\pi\)
\(284\) −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 \(-0.689755\pi\)
−0.561445 + 0.827514i \(0.689755\pi\)
\(294\) 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 \(-0.557947\pi\)
−0.181042 + 0.983475i \(0.557947\pi\)
\(308\) 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 \(-0.145145\pi\)
−0.830266 + 0.557368i \(0.811811\pi\)
\(312\) −9954.89 17242.4i −0.00578962 0.0100279i
\(313\) 221289. 383283.i 0.127673 0.221136i −0.795102 0.606476i \(-0.792583\pi\)
0.922775 + 0.385340i \(0.125916\pi\)
\(314\) 995925. 0.570036
\(315\) 0 0
\(316\) 673152. 0.379224
\(317\) 631238. 1.09334e6i 0.352813 0.611091i −0.633928 0.773392i \(-0.718558\pi\)
0.986741 + 0.162302i \(0.0518917\pi\)
\(318\) −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 −0.801199 0.598398i \(-0.795804\pi\)
0.918827 + 0.394659i \(0.129137\pi\)
\(332\) −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 0.735171 + 0.677882i \(0.237102\pi\)
0.219477 + 0.975618i \(0.429565\pi\)
\(348\) −343096. + 594259.i −0.151868 + 0.263044i
\(349\) 1.84999e6 0.813028 0.406514 0.913645i \(-0.366744\pi\)
0.406514 + 0.913645i \(0.366744\pi\)
\(350\) 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 \(-0.328068\pi\)
−0.999863 + 0.0165411i \(0.994735\pi\)
\(354\) 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 0.0745823 0.997215i \(-0.476238\pi\)
0.826322 0.563198i \(-0.190429\pi\)
\(360\) −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 \(-0.286515\pi\)
−0.989203 + 0.146555i \(0.953181\pi\)
\(368\) −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 0.0330929 + 0.999452i \(0.489464\pi\)
−0.882097 + 0.471067i \(0.843869\pi\)
\(374\) 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 0.344475 + 0.938796i \(0.388057\pi\)
−0.985258 + 0.171074i \(0.945276\pi\)
\(384\) −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 0.843673 0.536857i \(-0.180388\pi\)
−0.886768 + 0.462214i \(0.847055\pi\)
\(390\) −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 \(-0.811357\pi\)
0.898455 + 0.439065i \(0.144690\pi\)
\(398\) 621811. 0.196766
\(399\) 0 0
\(400\) 154797. 0.0483740
\(401\) 569122. 985748.i 0.176744 0.306129i −0.764020 0.645193i \(-0.776777\pi\)
0.940763 + 0.339064i \(0.110110\pi\)
\(402\) 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 −0.951316 0.308216i \(-0.900268\pi\)
0.208735 0.977972i \(-0.433065\pi\)
\(410\) −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 \(-0.383463\pi\)
0.357987 + 0.933727i \(0.383463\pi\)
\(420\) 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 0.850293 0.526310i \(-0.176425\pi\)
−0.880944 + 0.473221i \(0.843091\pi\)
\(432\) 93312.0 161621.i 0.0240563 0.0416667i
\(433\) 2.33004e6 0.597232 0.298616 0.954373i \(-0.403475\pi\)
0.298616 + 0.954373i \(0.403475\pi\)
\(434\) 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 \(-0.703664\pi\)
0.993253 + 0.115970i \(0.0369976\pi\)
\(440\) −142835. −0.0351724
\(441\) 0 0
\(442\) −284964. −0.0693800
\(443\) −566202. + 980690.i −0.137076 + 0.237423i −0.926389 0.376569i \(-0.877104\pi\)
0.789313 + 0.613992i \(0.210437\pi\)
\(444\) −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 −0.844855 0.534995i \(-0.820314\pi\)
0.885747 + 0.464169i \(0.153647\pi\)
\(458\) 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 \(-0.511602\pi\)
−0.0364416 + 0.999336i \(0.511602\pi\)
\(462\) 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 \(-0.866843\pi\)
0.808691 + 0.588233i \(0.200176\pi\)
\(468\) −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 −0.991980 0.126399i \(-0.959658\pi\)
0.386525 0.922279i \(-0.373675\pi\)
\(480\) 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 0.985185 + 0.171495i \(0.0548598\pi\)
−0.344073 + 0.938943i \(0.611807\pi\)
\(488\) 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 −0.272366 0.962194i \(-0.587806\pi\)
0.969467 0.245221i \(-0.0788606\pi\)
\(500\) 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 \(-0.391503\pi\)
0.334292 + 0.942470i \(0.391503\pi\)
\(504\) 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 0.227162 + 0.973857i \(0.427055\pi\)
−0.956966 + 0.290200i \(0.906278\pi\)
\(510\) −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 \(-0.0837719\pi\)
−0.708080 + 0.706132i \(0.750439\pi\)
\(522\) 771965. + 1.33708e6i 0.124000 + 0.214774i
\(523\) 4.80339e6 8.31971e6i 0.767880 1.33001i −0.170830 0.985301i \(-0.554645\pi\)
0.938710 0.344707i \(-0.112022\pi\)
\(524\) 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 0.195067 + 0.980790i \(0.437508\pi\)
−0.946923 + 0.321462i \(0.895826\pi\)
\(542\) 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 0.844077 0.536223i \(-0.180149\pi\)
−0.886421 + 0.462881i \(0.846816\pi\)
\(558\) −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 \(-0.329576\pi\)
−0.999930 + 0.0118029i \(0.996243\pi\)
\(564\) 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 −0.960254 0.279127i \(-0.909955\pi\)
0.721858 + 0.692041i \(0.243288\pi\)
\(570\) −497136. 861064.i −0.0640896 0.111007i
\(571\) −5.16600e6 8.94777e6i −0.663077 1.14848i −0.979803 0.199966i \(-0.935917\pi\)
0.316726 0.948517i \(-0.397416\pi\)
\(572\) −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 0.930603 + 0.366029i \(0.119283\pi\)
−0.148311 + 0.988941i \(0.547384\pi\)
\(578\) −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 \(-0.913696\pi\)
−0.963468 + 0.267823i \(0.913696\pi\)
\(588\) 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 −0.445534 0.895265i \(-0.646986\pi\)
0.998089 0.0617892i \(-0.0196806\pi\)
\(594\) 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 0.687197 0.726471i \(-0.258841\pi\)
−0.972741 + 0.231895i \(0.925507\pi\)
\(600\) 174146. 301631.i 0.0197486 0.0342056i
\(601\) 1.26473e7 1.42828 0.714139 0.700004i \(-0.246818\pi\)
0.714139 + 0.700004i \(0.246818\pi\)
\(602\) 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 \(-0.782678\pi\)
0.934316 + 0.356445i \(0.116011\pi\)
\(608\) −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 0.948604 0.316465i \(-0.102496\pi\)
−0.748369 + 0.663283i \(0.769163\pi\)
\(614\) 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 \(-0.197704\pi\)
−0.910587 + 0.413317i \(0.864370\pi\)
\(620\) −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 −0.986766 0.162151i \(-0.948157\pi\)
0.352956 0.935640i \(-0.385177\pi\)
\(642\) −1.94279e6 + 3.36501e6i −0.186032 + 0.322218i
\(643\) 9.67813e6 0.923132 0.461566 0.887106i \(-0.347288\pi\)
0.461566 + 0.887106i \(0.347288\pi\)
\(644\) 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 \(-0.192477\pi\)
−0.903679 + 0.428211i \(0.859144\pi\)
\(648\) −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 −0.879409 0.476068i \(-0.842062\pi\)
0.851991 + 0.523557i \(0.175395\pi\)
\(654\) −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 0.946648 + 0.322270i \(0.104446\pi\)
−0.194230 + 0.980956i \(0.562221\pi\)
\(662\) 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 \(-0.859435\pi\)
0.822160 + 0.569256i \(0.192769\pi\)
\(678\) −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 0.990909 0.134534i \(-0.0429536\pi\)
−0.611964 + 0.790886i \(0.709620\pi\)
\(684\) 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 0.415030 + 0.909808i \(0.363771\pi\)
−0.995432 + 0.0954768i \(0.969562\pi\)
\(692\) 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 0.188819 0.982012i \(-0.439534\pi\)
0.756038 0.654528i \(-0.227133\pi\)
\(710\) −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 −0.475937 0.879480i \(-0.657891\pi\)
0.999620 0.0275667i \(-0.00877587\pi\)
\(720\) 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 \(-0.332884\pi\)
0.501222 + 0.865319i \(0.332884\pi\)
\(728\) 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 \(-0.924460\pi\)
0.689584 + 0.724206i \(0.257793\pi\)
\(734\) 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 0.918107 0.396332i \(-0.129717\pi\)
−0.802287 + 0.596939i \(0.796384\pi\)
\(740\) 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 −0.332254 0.943190i \(-0.607809\pi\)
0.982953 0.183855i \(-0.0588576\pi\)
\(752\) −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 \(-0.844115\pi\)
0.848596 + 0.529041i \(0.177448\pi\)
\(762\) −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 −0.727517 −0.363759 0.931493i \(-0.618507\pi\)
−0.363759 + 0.931493i