Properties

Label 294.6.e.u.79.2
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 79.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.6.e.u.67.2

$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

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

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 \(-0.649393\pi\)
0.998528 0.0542389i \(-0.0172732\pi\)
\(6\) 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 \(-0.490970\pi\)
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 0.867210 + 0.497943i \(0.165911\pi\)
−0.00237330 + 0.999997i \(0.500755\pi\)
\(18\) −162.000 280.592i −0.117851 0.204124i
\(19\) −226.119 + 391.650i −0.143699 + 0.248894i −0.928887 0.370364i \(-0.879233\pi\)
0.785188 + 0.619258i \(0.212566\pi\)
\(20\) −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 0.999953 0.00965788i \(-0.00307425\pi\)
−0.508341 + 0.861156i \(0.669741\pi\)
\(32\) −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 \(-0.607405\pi\)
−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 −0.161351 0.986897i \(-0.551585\pi\)
0.935353 0.353714i \(-0.115082\pi\)
\(48\) 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 \(0.143267\pi\)
−0.0734457 + 0.997299i \(0.523400\pi\)
\(60\) 4397.12 + 7616.03i 0.157685 + 0.273118i
\(61\) −9690.24 + 16784.0i −0.333434 + 0.577524i −0.983183 0.182624i \(-0.941541\pi\)
0.649749 + 0.760149i \(0.274874\pi\)
\(62\) −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 0.994556 0.104199i \(-0.0332278\pi\)
−0.587517 + 0.809212i \(0.699895\pi\)
\(74\) 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 \(-0.516011\pi\)
−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 −0.640712 0.767781i \(-0.721361\pi\)
0.985274 + 0.170983i \(0.0546942\pi\)
\(90\) −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 0.659923 0.751333i \(-0.270589\pi\)
−0.980635 + 0.195844i \(0.937255\pi\)
\(102\) 37098.7 + 64256.8i 0.353068 + 0.611532i
\(103\) −85005.1 + 147233.i −0.789499 + 1.36745i 0.136774 + 0.990602i \(0.456326\pi\)
−0.926274 + 0.376851i \(0.877007\pi\)
\(104\) 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 −0.840354 0.542038i \(-0.817653\pi\)
0.889596 + 0.456749i \(0.150986\pi\)
\(132\) −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 \(-0.198298\pi\)
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 −0.0538086 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 0.994095 0.108509i \(-0.0346076\pi\)
−0.591019 + 0.806658i \(0.701274\pi\)
\(158\) −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 \(-0.270524\pi\)
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 −0.626611 0.779332i \(-0.715559\pi\)
0.988227 + 0.152995i \(0.0488920\pi\)
\(174\) −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 \(-0.358250\pi\)
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 −0.946204 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 0.927169 0.374642i \(-0.122235\pi\)
−0.788035 + 0.615631i \(0.788901\pi\)
\(200\) −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 −0.999886 0.0150727i \(-0.995202\pi\)
0.486890 0.873463i \(-0.338131\pi\)
\(228\) −32561.1 56397.5i −0.0414823 0.0718494i
\(229\) −193522. + 335191.i −0.243861 + 0.422380i −0.961811 0.273715i \(-0.911747\pi\)
0.717950 + 0.696095i \(0.245081\pi\)
\(230\) −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 0.946372 0.323080i \(-0.104718\pi\)
−0.752981 + 0.658042i \(0.771385\pi\)
\(242\) 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 0.221728 + 0.975109i \(0.428830\pi\)
−0.955333 + 0.295532i \(0.904503\pi\)
\(258\) 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 0.899697 0.436515i \(-0.143788\pi\)
−0.827882 + 0.560903i \(0.810454\pi\)
\(270\) 89041.6 + 154225.i 0.0743333 + 0.128749i
\(271\) −1.11372e6 + 1.92901e6i −0.921194 + 1.59555i −0.123623 + 0.992329i \(0.539451\pi\)
−0.797571 + 0.603225i \(0.793882\pi\)
\(272\) −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 \(0.0825861\pi\)
−0.261086 + 0.965316i \(0.584081\pi\)
\(284\) −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 0.830266 0.557368i \(-0.188189\pi\)
−0.897828 + 0.440347i \(0.854855\pi\)
\(312\) −9954.89 17242.4i −0.00578962 0.0100279i
\(313\) −221289. + 383283.i −0.127673 + 0.221136i −0.922775 0.385340i \(-0.874084\pi\)
0.795102 + 0.606476i \(0.207417\pi\)
\(314\) −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 \(-0.633256\pi\)
−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 0.999863 0.0165411i \(-0.00526543\pi\)
−0.514257 + 0.857636i \(0.671932\pi\)
\(354\) 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 0.989203 0.146555i \(-0.0468185\pi\)
−0.621522 + 0.783397i \(0.713485\pi\)
\(368\) −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 \(-0.611943\pi\)
0.985258 0.171074i \(-0.0547236\pi\)
\(384\) 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 −0.898455 0.439065i \(-0.855310\pi\)
0.829469 + 0.558553i \(0.188643\pi\)
\(398\) −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 \(0.0997320\pi\)
−0.208735 + 0.977972i \(0.566935\pi\)
\(410\) −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 0.850293 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 \(-0.596525\pi\)
−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 −0.993253 0.115970i \(-0.963002\pi\)
0.597059 + 0.802197i \(0.296336\pi\)
\(440\) 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 \(-0.488398\pi\)
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 −0.808691 0.588233i \(-0.799824\pi\)
0.913771 + 0.406231i \(0.133157\pi\)
\(468\) 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 \(0.0403419\pi\)
−0.386525 + 0.922279i \(0.626325\pi\)
\(480\) 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 \(-0.608497\pi\)
−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 −0.227162 0.973857i \(-0.572945\pi\)
0.956966 0.290200i \(-0.0937220\pi\)
\(510\) 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 0.708080 0.706132i \(-0.249561\pi\)
−0.965568 + 0.260150i \(0.916228\pi\)
\(522\) 771965. + 1.33708e6i 0.124000 + 0.214774i
\(523\) −4.80339e6 + 8.31971e6i −0.767880 + 1.33001i 0.170830 + 0.985301i \(0.445355\pi\)
−0.938710 + 0.344707i \(0.887978\pi\)
\(524\) −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 0.999930 0.0118029i \(-0.00375708\pi\)
−0.510187 + 0.860064i \(0.670424\pi\)
\(564\) 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 \(-0.880717\pi\)
0.148311 0.988941i \(-0.452616\pi\)
\(578\) −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 0.445534 + 0.895265i \(0.353014\pi\)
−0.998089 + 0.0617892i \(0.980319\pi\)
\(594\) −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 \(-0.753182\pi\)
−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 −0.934316 0.356445i \(-0.883989\pi\)
0.775848 + 0.630919i \(0.217322\pi\)
\(608\) 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 0.910587 0.413317i \(-0.135630\pi\)
−0.813236 + 0.581933i \(0.802296\pi\)
\(620\) −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 \(-0.652712\pi\)
−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 0.903679 0.428211i \(-0.140856\pi\)
−0.822681 + 0.568504i \(0.807523\pi\)
\(648\) −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 \(-0.895554\pi\)
0.194230 0.980956i \(-0.437779\pi\)
\(662\) 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 −0.822160 0.569256i \(-0.807231\pi\)
0.904070 + 0.427384i \(0.140565\pi\)
\(678\) 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 \(-0.636229\pi\)
0.995432 0.0954768i \(-0.0304376\pi\)
\(692\) −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 \(0.342109\pi\)
−0.999620 + 0.0275667i \(0.991224\pi\)
\(720\) −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 −0.689584 0.724206i \(-0.742207\pi\)
0.971973 + 0.235094i \(0.0755399\pi\)
\(734\) −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 −0.848596 0.529041i \(-0.822552\pi\)
0.882461 + 0.470386i \(0.155885\pi\)
\(762\) 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