Properties

Label 126.6.g.h.109.1
Level $126$
Weight $6$
Character 126.109
Analytic conductor $20.208$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(20.2083612964\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{9601})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(24.7462 + 42.8616i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.6.g.h.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-37.7462 - 65.3783i) q^{5} +(99.4847 + 83.1252i) q^{7} -64.0000 q^{8} +O(q^{10})\) \(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-37.7462 - 65.3783i) q^{5} +(99.4847 + 83.1252i) q^{7} -64.0000 q^{8} +(150.985 - 261.513i) q^{10} +(-74.7309 + 129.438i) q^{11} +349.416 q^{13} +(-88.9847 + 510.875i) q^{14} +(-128.000 - 221.703i) q^{16} +(-574.923 + 995.797i) q^{17} +(1397.60 + 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(906.985 + 1570.94i) q^{23} +(-1287.05 + 2229.23i) q^{25} +(698.832 + 1210.41i) q^{26} +(-1947.69 + 713.499i) q^{28} +759.033 q^{29} +(-4515.87 + 7821.72i) q^{31} +(512.000 - 886.810i) q^{32} -4599.39 q^{34} +(1679.42 - 9641.80i) q^{35} +(-3897.45 - 6750.57i) q^{37} +(-5590.40 + 9682.86i) q^{38} +(2415.76 + 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(-1195.69 - 2071.00i) q^{44} +(-3627.94 + 6283.77i) q^{46} +(12299.4 + 21303.2i) q^{47} +(2987.41 + 16539.4i) q^{49} -10296.4 q^{50} +(-2795.33 + 4841.65i) q^{52} +(6798.11 - 11774.7i) q^{53} +11283.2 q^{55} +(-6367.02 - 5320.01i) q^{56} +(1518.07 + 2629.37i) q^{58} +(-13179.4 + 22827.4i) q^{59} +(-17660.9 - 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(-13189.1 - 22844.2i) q^{65} +(-27186.0 + 47087.5i) q^{67} +(-9198.78 - 15932.7i) q^{68} +(36759.0 - 13465.9i) q^{70} +70145.7 q^{71} +(22234.4 - 38511.1i) q^{73} +(15589.8 - 27002.3i) q^{74} -44723.2 q^{76} +(-18194.1 + 6665.05i) q^{77} +(-30806.2 - 53357.9i) q^{79} +(-9663.02 + 16736.8i) q^{80} +(-15281.0 - 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(24377.7 + 42223.4i) q^{86} +(4782.78 - 8284.01i) q^{88} +(49284.7 + 85363.6i) q^{89} +(34761.5 + 29045.3i) q^{91} -29023.5 q^{92} +(-49197.6 + 85212.8i) q^{94} +(105508. - 182745. i) q^{95} +32342.3 q^{97} +(-51319.2 + 43427.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 32 q^{4} - 53 q^{5} + 6 q^{7} - 256 q^{8} + 212 q^{10} + 191 q^{11} - 758 q^{13} + 36 q^{14} - 512 q^{16} - 340 q^{17} + 1769 q^{19} + 1696 q^{20} + 1528 q^{22} + 3236 q^{23} + 45 q^{25} - 1516 q^{26} + 48 q^{28} - 8918 q^{29} - 1994 q^{31} + 2048 q^{32} - 2720 q^{34} + 4562 q^{35} - 20587 q^{37} - 7076 q^{38} + 3392 q^{40} - 17628 q^{41} + 31706 q^{43} + 3056 q^{44} - 12944 q^{46} + 33912 q^{47} + 9598 q^{49} + 360 q^{50} + 6064 q^{52} + 49239 q^{53} + 37882 q^{55} - 384 q^{56} - 17836 q^{58} - 56735 q^{59} - 67508 q^{61} - 15952 q^{62} + 16384 q^{64} - 42762 q^{65} - 75723 q^{67} - 5440 q^{68} + 95692 q^{70} + 17984 q^{71} + 3201 q^{73} + 82348 q^{74} - 56608 q^{76} - 120299 q^{77} - 26612 q^{79} - 13568 q^{80} - 35256 q^{82} + 1898 q^{83} + 210040 q^{85} + 63412 q^{86} - 12224 q^{88} + 176562 q^{89} + 210085 q^{91} - 103552 q^{92} - 135648 q^{94} + 234098 q^{95} - 258846 q^{97} - 211156 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) −37.7462 65.3783i −0.675224 1.16952i −0.976403 0.215955i \(-0.930714\pi\)
0.301179 0.953568i \(-0.402620\pi\)
\(6\) 0 0
\(7\) 99.4847 + 83.1252i 0.767381 + 0.641191i
\(8\) −64.0000 −0.353553
\(9\) 0 0
\(10\) 150.985 261.513i 0.477456 0.826977i
\(11\) −74.7309 + 129.438i −0.186217 + 0.322537i −0.943986 0.329986i \(-0.892956\pi\)
0.757769 + 0.652523i \(0.226289\pi\)
\(12\) 0 0
\(13\) 349.416 0.573435 0.286717 0.958015i \(-0.407436\pi\)
0.286717 + 0.958015i \(0.407436\pi\)
\(14\) −88.9847 + 510.875i −0.121338 + 0.696618i
\(15\) 0 0
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) −574.923 + 995.797i −0.482489 + 0.835696i −0.999798 0.0201029i \(-0.993601\pi\)
0.517309 + 0.855799i \(0.326934\pi\)
\(18\) 0 0
\(19\) 1397.60 + 2420.72i 0.888176 + 1.53837i 0.842029 + 0.539432i \(0.181361\pi\)
0.0461468 + 0.998935i \(0.485306\pi\)
\(20\) 1207.88 0.675224
\(21\) 0 0
\(22\) −597.847 −0.263350
\(23\) 906.985 + 1570.94i 0.357504 + 0.619214i 0.987543 0.157349i \(-0.0502947\pi\)
−0.630040 + 0.776563i \(0.716961\pi\)
\(24\) 0 0
\(25\) −1287.05 + 2229.23i −0.411855 + 0.713354i
\(26\) 698.832 + 1210.41i 0.202740 + 0.351156i
\(27\) 0 0
\(28\) −1947.69 + 713.499i −0.469489 + 0.171988i
\(29\) 759.033 0.167597 0.0837984 0.996483i \(-0.473295\pi\)
0.0837984 + 0.996483i \(0.473295\pi\)
\(30\) 0 0
\(31\) −4515.87 + 7821.72i −0.843990 + 1.46183i 0.0425050 + 0.999096i \(0.486466\pi\)
−0.886495 + 0.462738i \(0.846867\pi\)
\(32\) 512.000 886.810i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −4599.39 −0.682343
\(35\) 1679.42 9641.80i 0.231733 1.33042i
\(36\) 0 0
\(37\) −3897.45 6750.57i −0.468032 0.810655i 0.531300 0.847183i \(-0.321704\pi\)
−0.999333 + 0.0365280i \(0.988370\pi\)
\(38\) −5590.40 + 9682.86i −0.628035 + 1.08779i
\(39\) 0 0
\(40\) 2415.76 + 4184.21i 0.238728 + 0.413489i
\(41\) −7640.49 −0.709842 −0.354921 0.934896i \(-0.615492\pi\)
−0.354921 + 0.934896i \(0.615492\pi\)
\(42\) 0 0
\(43\) 12188.8 1.00529 0.502645 0.864493i \(-0.332360\pi\)
0.502645 + 0.864493i \(0.332360\pi\)
\(44\) −1195.69 2071.00i −0.0931083 0.161268i
\(45\) 0 0
\(46\) −3627.94 + 6283.77i −0.252793 + 0.437851i
\(47\) 12299.4 + 21303.2i 0.812156 + 1.40670i 0.911352 + 0.411627i \(0.135039\pi\)
−0.0991964 + 0.995068i \(0.531627\pi\)
\(48\) 0 0
\(49\) 2987.41 + 16539.4i 0.177748 + 0.984076i
\(50\) −10296.4 −0.582451
\(51\) 0 0
\(52\) −2795.33 + 4841.65i −0.143359 + 0.248305i
\(53\) 6798.11 11774.7i 0.332429 0.575783i −0.650559 0.759456i \(-0.725465\pi\)
0.982988 + 0.183672i \(0.0587986\pi\)
\(54\) 0 0
\(55\) 11283.2 0.502952
\(56\) −6367.02 5320.01i −0.271310 0.226695i
\(57\) 0 0
\(58\) 1518.07 + 2629.37i 0.0592544 + 0.102632i
\(59\) −13179.4 + 22827.4i −0.492908 + 0.853742i −0.999967 0.00816991i \(-0.997399\pi\)
0.507059 + 0.861912i \(0.330733\pi\)
\(60\) 0 0
\(61\) −17660.9 30589.5i −0.607698 1.05256i −0.991619 0.129198i \(-0.958760\pi\)
0.383921 0.923366i \(-0.374573\pi\)
\(62\) −36127.0 −1.19358
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −13189.1 22844.2i −0.387197 0.670645i
\(66\) 0 0
\(67\) −27186.0 + 47087.5i −0.739874 + 1.28150i 0.212678 + 0.977122i \(0.431781\pi\)
−0.952552 + 0.304377i \(0.901552\pi\)
\(68\) −9198.78 15932.7i −0.241245 0.417848i
\(69\) 0 0
\(70\) 36759.0 13465.9i 0.896641 0.328467i
\(71\) 70145.7 1.65141 0.825706 0.564101i \(-0.190777\pi\)
0.825706 + 0.564101i \(0.190777\pi\)
\(72\) 0 0
\(73\) 22234.4 38511.1i 0.488335 0.845822i −0.511574 0.859239i \(-0.670938\pi\)
0.999910 + 0.0134170i \(0.00427090\pi\)
\(74\) 15589.8 27002.3i 0.330949 0.573220i
\(75\) 0 0
\(76\) −44723.2 −0.888176
\(77\) −18194.1 + 6665.05i −0.349707 + 0.128108i
\(78\) 0 0
\(79\) −30806.2 53357.9i −0.555355 0.961903i −0.997876 0.0651450i \(-0.979249\pi\)
0.442521 0.896758i \(-0.354084\pi\)
\(80\) −9663.02 + 16736.8i −0.168806 + 0.292381i
\(81\) 0 0
\(82\) −15281.0 26467.5i −0.250967 0.434688i
\(83\) 87142.0 1.38846 0.694228 0.719755i \(-0.255746\pi\)
0.694228 + 0.719755i \(0.255746\pi\)
\(84\) 0 0
\(85\) 86804.6 1.30315
\(86\) 24377.7 + 42223.4i 0.355423 + 0.615611i
\(87\) 0 0
\(88\) 4782.78 8284.01i 0.0658375 0.114034i
\(89\) 49284.7 + 85363.6i 0.659534 + 1.14235i 0.980736 + 0.195336i \(0.0625796\pi\)
−0.321203 + 0.947010i \(0.604087\pi\)
\(90\) 0 0
\(91\) 34761.5 + 29045.3i 0.440043 + 0.367681i
\(92\) −29023.5 −0.357504
\(93\) 0 0
\(94\) −49197.6 + 85212.8i −0.574281 + 0.994684i
\(95\) 105508. 182745.i 1.19944 2.07748i
\(96\) 0 0
\(97\) 32342.3 0.349013 0.174507 0.984656i \(-0.444167\pi\)
0.174507 + 0.984656i \(0.444167\pi\)
\(98\) −51319.2 + 43427.4i −0.539778 + 0.456771i
\(99\) 0 0
\(100\) −20592.8 35667.7i −0.205928 0.356677i
\(101\) 15673.2 27146.8i 0.152881 0.264798i −0.779404 0.626521i \(-0.784478\pi\)
0.932286 + 0.361723i \(0.117811\pi\)
\(102\) 0 0
\(103\) −49666.5 86024.8i −0.461286 0.798970i 0.537740 0.843111i \(-0.319278\pi\)
−0.999025 + 0.0441406i \(0.985945\pi\)
\(104\) −22362.6 −0.202740
\(105\) 0 0
\(106\) 54384.9 0.470125
\(107\) −72634.0 125806.i −0.613310 1.06228i −0.990678 0.136221i \(-0.956504\pi\)
0.377368 0.926063i \(-0.376829\pi\)
\(108\) 0 0
\(109\) 90425.4 156621.i 0.728994 1.26265i −0.228315 0.973587i \(-0.573321\pi\)
0.957309 0.289067i \(-0.0933452\pi\)
\(110\) 22566.4 + 39086.2i 0.177820 + 0.307994i
\(111\) 0 0
\(112\) 5695.02 32696.0i 0.0428993 0.246292i
\(113\) −197832. −1.45748 −0.728738 0.684793i \(-0.759893\pi\)
−0.728738 + 0.684793i \(0.759893\pi\)
\(114\) 0 0
\(115\) 68470.4 118594.i 0.482790 0.836217i
\(116\) −6072.27 + 10517.5i −0.0418992 + 0.0725715i
\(117\) 0 0
\(118\) −105435. −0.697077
\(119\) −139972. + 51275.9i −0.906094 + 0.331930i
\(120\) 0 0
\(121\) 69356.1 + 120128.i 0.430647 + 0.745902i
\(122\) 70643.5 122358.i 0.429707 0.744275i
\(123\) 0 0
\(124\) −72254.0 125148.i −0.421995 0.730917i
\(125\) −41589.2 −0.238070
\(126\) 0 0
\(127\) −33517.2 −0.184399 −0.0921996 0.995741i \(-0.529390\pi\)
−0.0921996 + 0.995741i \(0.529390\pi\)
\(128\) 8192.00 + 14189.0i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 52756.4 91376.8i 0.273790 0.474218i
\(131\) −5404.45 9360.79i −0.0275153 0.0476578i 0.851940 0.523640i \(-0.175426\pi\)
−0.879455 + 0.475982i \(0.842093\pi\)
\(132\) 0 0
\(133\) −62182.5 + 357000.i −0.304817 + 1.75000i
\(134\) −217488. −1.04634
\(135\) 0 0
\(136\) 36795.1 63731.0i 0.170586 0.295463i
\(137\) −9466.01 + 16395.6i −0.0430889 + 0.0746322i −0.886766 0.462220i \(-0.847053\pi\)
0.843677 + 0.536852i \(0.180387\pi\)
\(138\) 0 0
\(139\) −168897. −0.741457 −0.370729 0.928741i \(-0.620892\pi\)
−0.370729 + 0.928741i \(0.620892\pi\)
\(140\) 120165. + 100405.i 0.518154 + 0.432948i
\(141\) 0 0
\(142\) 140291. + 242992.i 0.583862 + 1.01128i
\(143\) −26112.1 + 45227.6i −0.106783 + 0.184954i
\(144\) 0 0
\(145\) −28650.6 49624.3i −0.113165 0.196008i
\(146\) 177875. 0.690611
\(147\) 0 0
\(148\) 124718. 0.468032
\(149\) 132001. + 228633.i 0.487093 + 0.843670i 0.999890 0.0148402i \(-0.00472395\pi\)
−0.512797 + 0.858510i \(0.671391\pi\)
\(150\) 0 0
\(151\) −139587. + 241772.i −0.498200 + 0.862908i −0.999998 0.00207707i \(-0.999339\pi\)
0.501798 + 0.864985i \(0.332672\pi\)
\(152\) −89446.4 154926.i −0.314018 0.543895i
\(153\) 0 0
\(154\) −59476.6 49696.1i −0.202090 0.168858i
\(155\) 681828. 2.27953
\(156\) 0 0
\(157\) −94301.2 + 163334.i −0.305329 + 0.528845i −0.977334 0.211701i \(-0.932100\pi\)
0.672006 + 0.740546i \(0.265433\pi\)
\(158\) 123225. 213432.i 0.392695 0.680168i
\(159\) 0 0
\(160\) −77304.2 −0.238728
\(161\) −40353.9 + 231678.i −0.122693 + 0.704402i
\(162\) 0 0
\(163\) −44858.7 77697.5i −0.132244 0.229054i 0.792297 0.610136i \(-0.208885\pi\)
−0.924541 + 0.381081i \(0.875552\pi\)
\(164\) 61124.0 105870.i 0.177461 0.307371i
\(165\) 0 0
\(166\) 174284. + 301869.i 0.490893 + 0.850252i
\(167\) −529411. −1.46893 −0.734467 0.678645i \(-0.762568\pi\)
−0.734467 + 0.678645i \(0.762568\pi\)
\(168\) 0 0
\(169\) −249202. −0.671172
\(170\) 173609. + 300700.i 0.460734 + 0.798015i
\(171\) 0 0
\(172\) −97510.7 + 168893.i −0.251322 + 0.435303i
\(173\) 16919.2 + 29304.8i 0.0429797 + 0.0744430i 0.886715 0.462316i \(-0.152982\pi\)
−0.843735 + 0.536759i \(0.819648\pi\)
\(174\) 0 0
\(175\) −313347. + 114788.i −0.773446 + 0.283337i
\(176\) 38262.2 0.0931083
\(177\) 0 0
\(178\) −197139. + 341454.i −0.466361 + 0.807761i
\(179\) −123872. + 214552.i −0.288962 + 0.500496i −0.973562 0.228422i \(-0.926643\pi\)
0.684601 + 0.728918i \(0.259977\pi\)
\(180\) 0 0
\(181\) 369470. 0.838268 0.419134 0.907924i \(-0.362334\pi\)
0.419134 + 0.907924i \(0.362334\pi\)
\(182\) −31092.7 + 178508.i −0.0695792 + 0.399465i
\(183\) 0 0
\(184\) −58047.0 100540.i −0.126397 0.218925i
\(185\) −294227. + 509617.i −0.632053 + 1.09475i
\(186\) 0 0
\(187\) −85929.1 148833.i −0.179695 0.311241i
\(188\) −393581. −0.812156
\(189\) 0 0
\(190\) 844065. 1.69626
\(191\) −242612. 420217.i −0.481204 0.833470i 0.518563 0.855039i \(-0.326467\pi\)
−0.999767 + 0.0215693i \(0.993134\pi\)
\(192\) 0 0
\(193\) 165409. 286496.i 0.319643 0.553637i −0.660771 0.750588i \(-0.729770\pi\)
0.980413 + 0.196950i \(0.0631038\pi\)
\(194\) 64684.7 + 112037.i 0.123395 + 0.213726i
\(195\) 0 0
\(196\) −253075. 90920.2i −0.470554 0.169052i
\(197\) 161963. 0.297337 0.148669 0.988887i \(-0.452501\pi\)
0.148669 + 0.988887i \(0.452501\pi\)
\(198\) 0 0
\(199\) −27698.1 + 47974.5i −0.0495813 + 0.0858773i −0.889751 0.456446i \(-0.849122\pi\)
0.840170 + 0.542324i \(0.182455\pi\)
\(200\) 82371.0 142671.i 0.145613 0.252209i
\(201\) 0 0
\(202\) 125386. 0.216207
\(203\) 75512.2 + 63094.8i 0.128611 + 0.107462i
\(204\) 0 0
\(205\) 288399. + 499522.i 0.479303 + 0.830176i
\(206\) 198666. 344099.i 0.326178 0.564957i
\(207\) 0 0
\(208\) −44725.2 77466.4i −0.0716794 0.124152i
\(209\) −417776. −0.661572
\(210\) 0 0
\(211\) 481748. 0.744926 0.372463 0.928047i \(-0.378513\pi\)
0.372463 + 0.928047i \(0.378513\pi\)
\(212\) 108770. + 188395.i 0.166214 + 0.287892i
\(213\) 0 0
\(214\) 290536. 503223.i 0.433676 0.751149i
\(215\) −460082. 796885.i −0.678795 1.17571i
\(216\) 0 0
\(217\) −1.09944e6 + 402759.i −1.58498 + 0.580625i
\(218\) 723403. 1.03095
\(219\) 0 0
\(220\) −90265.7 + 156345.i −0.125738 + 0.217784i
\(221\) −200887. + 347947.i −0.276676 + 0.479217i
\(222\) 0 0
\(223\) 638779. 0.860178 0.430089 0.902787i \(-0.358482\pi\)
0.430089 + 0.902787i \(0.358482\pi\)
\(224\) 124652. 45663.9i 0.165990 0.0608070i
\(225\) 0 0
\(226\) −395665. 685312.i −0.515295 0.892518i
\(227\) −262841. + 455254.i −0.338554 + 0.586394i −0.984161 0.177277i \(-0.943271\pi\)
0.645607 + 0.763670i \(0.276605\pi\)
\(228\) 0 0
\(229\) −466343. 807730.i −0.587647 1.01784i −0.994540 0.104359i \(-0.966721\pi\)
0.406892 0.913476i \(-0.366612\pi\)
\(230\) 547763. 0.682768
\(231\) 0 0
\(232\) −48578.1 −0.0592544
\(233\) −353896. 612967.i −0.427058 0.739685i 0.569553 0.821955i \(-0.307116\pi\)
−0.996610 + 0.0822696i \(0.973783\pi\)
\(234\) 0 0
\(235\) 928511. 1.60823e6i 1.09677 1.89967i
\(236\) −210871. 365238.i −0.246454 0.426871i
\(237\) 0 0
\(238\) −457569. 382325.i −0.523617 0.437512i
\(239\) 500614. 0.566902 0.283451 0.958987i \(-0.408521\pi\)
0.283451 + 0.958987i \(0.408521\pi\)
\(240\) 0 0
\(241\) −604109. + 1.04635e6i −0.669997 + 1.16047i 0.307907 + 0.951416i \(0.400371\pi\)
−0.977904 + 0.209052i \(0.932962\pi\)
\(242\) −277424. + 480513.i −0.304513 + 0.527432i
\(243\) 0 0
\(244\) 565148. 0.607698
\(245\) 968552. 819609.i 1.03088 0.872352i
\(246\) 0 0
\(247\) 488344. + 845836.i 0.509311 + 0.882153i
\(248\) 289016. 500590.i 0.298396 0.516836i
\(249\) 0 0
\(250\) −83178.3 144069.i −0.0841705 0.145788i
\(251\) −97826.7 −0.0980106 −0.0490053 0.998799i \(-0.515605\pi\)
−0.0490053 + 0.998799i \(0.515605\pi\)
\(252\) 0 0
\(253\) −271119. −0.266292
\(254\) −67034.5 116107.i −0.0651949 0.112921i
\(255\) 0 0
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −553956. 959481.i −0.523170 0.906157i −0.999636 0.0269643i \(-0.991416\pi\)
0.476466 0.879193i \(-0.341917\pi\)
\(258\) 0 0
\(259\) 173406. 995555.i 0.160626 0.922180i
\(260\) 422052. 0.387197
\(261\) 0 0
\(262\) 21617.8 37443.2i 0.0194562 0.0336992i
\(263\) 753427. 1.30497e6i 0.671663 1.16336i −0.305769 0.952106i \(-0.598913\pi\)
0.977432 0.211249i \(-0.0677532\pi\)
\(264\) 0 0
\(265\) −1.02641e6 −0.897856
\(266\) −1.36105e6 + 498593.i −1.17942 + 0.432058i
\(267\) 0 0
\(268\) −434975. 753399.i −0.369937 0.640750i
\(269\) −1.06751e6 + 1.84898e6i −0.899481 + 1.55795i −0.0713221 + 0.997453i \(0.522722\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(270\) 0 0
\(271\) −614299. 1.06400e6i −0.508108 0.880070i −0.999956 0.00938828i \(-0.997012\pi\)
0.491847 0.870681i \(-0.336322\pi\)
\(272\) 294361. 0.241245
\(273\) 0 0
\(274\) −75728.1 −0.0609369
\(275\) −192364. 333185.i −0.153388 0.265677i
\(276\) 0 0
\(277\) 923412. 1.59940e6i 0.723097 1.25244i −0.236656 0.971593i \(-0.576051\pi\)
0.959753 0.280847i \(-0.0906152\pi\)
\(278\) −337795. 585078.i −0.262145 0.454048i
\(279\) 0 0
\(280\) −107483. + 617075.i −0.0819300 + 0.470374i
\(281\) 2.28326e6 1.72500 0.862500 0.506056i \(-0.168897\pi\)
0.862500 + 0.506056i \(0.168897\pi\)
\(282\) 0 0
\(283\) −668463. + 1.15781e6i −0.496148 + 0.859354i −0.999990 0.00444218i \(-0.998586\pi\)
0.503842 + 0.863796i \(0.331919\pi\)
\(284\) −561166. + 971968.i −0.412853 + 0.715082i
\(285\) 0 0
\(286\) −208897. −0.151014
\(287\) −760112. 635118.i −0.544720 0.455145i
\(288\) 0 0
\(289\) 48854.5 + 84618.5i 0.0344081 + 0.0595965i
\(290\) 114602. 198497.i 0.0800200 0.138599i
\(291\) 0 0
\(292\) 355750. + 616178.i 0.244168 + 0.422911i
\(293\) 2.23033e6 1.51775 0.758875 0.651236i \(-0.225749\pi\)
0.758875 + 0.651236i \(0.225749\pi\)
\(294\) 0 0
\(295\) 1.98989e6 1.33129
\(296\) 249436. + 432037.i 0.165474 + 0.286610i
\(297\) 0 0
\(298\) −528004. + 914530.i −0.344427 + 0.596565i
\(299\) 316915. + 548913.i 0.205005 + 0.355079i
\(300\) 0 0
\(301\) 1.21260e6 + 1.01320e6i 0.771440 + 0.644583i
\(302\) −1.11670e6 −0.704561
\(303\) 0 0
\(304\) 357786. 619703.i 0.222044 0.384592i
\(305\) −1.33326e6 + 2.30928e6i −0.820664 + 1.42143i
\(306\) 0 0
\(307\) 1.77782e6 1.07657 0.538284 0.842763i \(-0.319073\pi\)
0.538284 + 0.842763i \(0.319073\pi\)
\(308\) 53199.2 305425.i 0.0319542 0.183454i
\(309\) 0 0
\(310\) 1.36366e6 + 2.36192e6i 0.805936 + 1.39592i
\(311\) 701358. 1.21479e6i 0.411187 0.712196i −0.583833 0.811874i \(-0.698448\pi\)
0.995020 + 0.0996776i \(0.0317811\pi\)
\(312\) 0 0
\(313\) −609472. 1.05564e6i −0.351636 0.609051i 0.634900 0.772594i \(-0.281041\pi\)
−0.986536 + 0.163543i \(0.947708\pi\)
\(314\) −754409. −0.431800
\(315\) 0 0
\(316\) 985799. 0.555355
\(317\) 1.34001e6 + 2.32096e6i 0.748961 + 1.29724i 0.948321 + 0.317312i \(0.102780\pi\)
−0.199361 + 0.979926i \(0.563887\pi\)
\(318\) 0 0
\(319\) −56723.2 + 98247.5i −0.0312093 + 0.0540561i
\(320\) −154608. 267789.i −0.0844030 0.146190i
\(321\) 0 0
\(322\) −883264. + 323566.i −0.474735 + 0.173910i
\(323\) −3.21405e6 −1.71414
\(324\) 0 0
\(325\) −449715. + 778929.i −0.236172 + 0.409062i
\(326\) 179435. 310790.i 0.0935110 0.161966i
\(327\) 0 0
\(328\) 488992. 0.250967
\(329\) −547229. + 3.14173e6i −0.278727 + 1.60022i
\(330\) 0 0
\(331\) −71280.1 123461.i −0.0357601 0.0619383i 0.847591 0.530649i \(-0.178052\pi\)
−0.883352 + 0.468711i \(0.844719\pi\)
\(332\) −697136. + 1.20747e6i −0.347114 + 0.601219i
\(333\) 0 0
\(334\) −1.05882e6 1.83393e6i −0.519346 0.899534i
\(335\) 4.10466e6 1.99832
\(336\) 0 0
\(337\) −1.21206e6 −0.581367 −0.290683 0.956819i \(-0.593883\pi\)
−0.290683 + 0.956819i \(0.593883\pi\)
\(338\) −498403. 863260.i −0.237295 0.411007i
\(339\) 0 0
\(340\) −694437. + 1.20280e6i −0.325788 + 0.564282i
\(341\) −674950. 1.16905e6i −0.314330 0.544435i
\(342\) 0 0
\(343\) −1.07764e6 + 1.89374e6i −0.494580 + 0.869132i
\(344\) −780085. −0.355423
\(345\) 0 0
\(346\) −67676.6 + 117219.i −0.0303912 + 0.0526392i
\(347\) 1.73426e6 3.00383e6i 0.773199 1.33922i −0.162602 0.986692i \(-0.551989\pi\)
0.935801 0.352529i \(-0.114678\pi\)
\(348\) 0 0
\(349\) 1.01692e6 0.446911 0.223456 0.974714i \(-0.428266\pi\)
0.223456 + 0.974714i \(0.428266\pi\)
\(350\) −1.02433e6 855888.i −0.446962 0.373462i
\(351\) 0 0
\(352\) 76524.4 + 132544.i 0.0329187 + 0.0570169i
\(353\) 781927. 1.35434e6i 0.333987 0.578483i −0.649303 0.760530i \(-0.724939\pi\)
0.983290 + 0.182048i \(0.0582725\pi\)
\(354\) 0 0
\(355\) −2.64773e6 4.58601e6i −1.11507 1.93136i
\(356\) −1.57711e6 −0.659534
\(357\) 0 0
\(358\) −990975. −0.408653
\(359\) 24776.6 + 42914.3i 0.0101462 + 0.0175738i 0.871054 0.491187i \(-0.163437\pi\)
−0.860908 + 0.508761i \(0.830104\pi\)
\(360\) 0 0
\(361\) −2.66853e6 + 4.62202e6i −1.07771 + 1.86666i
\(362\) 738940. + 1.27988e6i 0.296373 + 0.513332i
\(363\) 0 0
\(364\) −680555. + 249308.i −0.269222 + 0.0986239i
\(365\) −3.35705e6 −1.31894
\(366\) 0 0
\(367\) −1.77416e6 + 3.07293e6i −0.687585 + 1.19093i 0.285032 + 0.958518i \(0.407996\pi\)
−0.972617 + 0.232414i \(0.925337\pi\)
\(368\) 232188. 402162.i 0.0893759 0.154804i
\(369\) 0 0
\(370\) −2.35382e6 −0.893858
\(371\) 1.65508e6 606306.i 0.624287 0.228695i
\(372\) 0 0
\(373\) 1.12787e6 + 1.95352e6i 0.419745 + 0.727020i 0.995914 0.0903112i \(-0.0287862\pi\)
−0.576169 + 0.817331i \(0.695453\pi\)
\(374\) 343716. 595334.i 0.127064 0.220081i
\(375\) 0 0
\(376\) −787162. 1.36340e6i −0.287140 0.497342i
\(377\) 265218. 0.0961059
\(378\) 0 0
\(379\) 4.39503e6 1.57168 0.785840 0.618430i \(-0.212231\pi\)
0.785840 + 0.618430i \(0.212231\pi\)
\(380\) 1.68813e6 + 2.92393e6i 0.599718 + 1.03874i
\(381\) 0 0
\(382\) 970449. 1.68087e6i 0.340263 0.589352i
\(383\) −613904. 1.06331e6i −0.213847 0.370394i 0.739068 0.673631i \(-0.235266\pi\)
−0.952915 + 0.303237i \(0.901933\pi\)
\(384\) 0 0
\(385\) 1.12251e6 + 937919.i 0.385956 + 0.322488i
\(386\) 1.32327e6 0.452043
\(387\) 0 0
\(388\) −258739. + 448149.i −0.0872533 + 0.151127i
\(389\) 1.02712e6 1.77903e6i 0.344150 0.596086i −0.641049 0.767500i \(-0.721500\pi\)
0.985199 + 0.171415i \(0.0548337\pi\)
\(390\) 0 0
\(391\) −2.08579e6 −0.689967
\(392\) −191194. 1.05852e6i −0.0628434 0.347923i
\(393\) 0 0
\(394\) 323925. + 561055.i 0.105125 + 0.182081i
\(395\) −2.32563e6 + 4.02812e6i −0.749978 + 1.29900i
\(396\) 0 0
\(397\) 1.90184e6 + 3.29408e6i 0.605615 + 1.04896i 0.991954 + 0.126599i \(0.0404062\pi\)
−0.386339 + 0.922357i \(0.626260\pi\)
\(398\) −221585. −0.0701185
\(399\) 0 0
\(400\) 658968. 0.205928
\(401\) 592622. + 1.02645e6i 0.184042 + 0.318770i 0.943253 0.332074i \(-0.107748\pi\)
−0.759211 + 0.650844i \(0.774415\pi\)
\(402\) 0 0
\(403\) −1.57792e6 + 2.73303e6i −0.483974 + 0.838267i
\(404\) 250771. + 434349.i 0.0764406 + 0.132399i
\(405\) 0 0
\(406\) −67542.3 + 387771.i −0.0203358 + 0.116751i
\(407\) 1.16504e6 0.348621
\(408\) 0 0
\(409\) 2.15197e6 3.72731e6i 0.636102 1.10176i −0.350178 0.936683i \(-0.613879\pi\)
0.986280 0.165079i \(-0.0527878\pi\)
\(410\) −1.15360e6 + 1.99809e6i −0.338918 + 0.587023i
\(411\) 0 0
\(412\) 1.58933e6 0.461286
\(413\) −3.20868e6 + 1.17544e6i −0.925660 + 0.339097i
\(414\) 0 0
\(415\) −3.28928e6 5.69719e6i −0.937519 1.62383i
\(416\) 178901. 309865.i 0.0506850 0.0877889i
\(417\) 0 0
\(418\) −835551. 1.44722e6i −0.233901 0.405129i
\(419\) 113725. 0.0316461 0.0158230 0.999875i \(-0.494963\pi\)
0.0158230 + 0.999875i \(0.494963\pi\)
\(420\) 0 0
\(421\) 443417. 0.121929 0.0609645 0.998140i \(-0.480582\pi\)
0.0609645 + 0.998140i \(0.480582\pi\)
\(422\) 963495. + 1.66882e6i 0.263371 + 0.456172i
\(423\) 0 0
\(424\) −435079. + 753579.i −0.117531 + 0.203570i
\(425\) −1.47991e6 2.56327e6i −0.397431 0.688371i
\(426\) 0 0
\(427\) 785774. 4.51125e6i 0.208559 1.19737i
\(428\) 2.32429e6 0.613310
\(429\) 0 0
\(430\) 1.84033e6 3.18754e6i 0.479981 0.831351i
\(431\) 2.31655e6 4.01239e6i 0.600688 1.04042i −0.392029 0.919953i \(-0.628227\pi\)
0.992717 0.120469i \(-0.0384399\pi\)
\(432\) 0 0
\(433\) 6.57955e6 1.68646 0.843231 0.537552i \(-0.180651\pi\)
0.843231 + 0.537552i \(0.180651\pi\)
\(434\) −3.59408e6 3.00306e6i −0.915933 0.765314i
\(435\) 0 0
\(436\) 1.44681e6 + 2.50594e6i 0.364497 + 0.631327i
\(437\) −2.53520e6 + 4.39110e6i −0.635052 + 1.09994i
\(438\) 0 0
\(439\) 910348. + 1.57677e6i 0.225448 + 0.390487i 0.956454 0.291884i \(-0.0942822\pi\)
−0.731006 + 0.682371i \(0.760949\pi\)
\(440\) −722126. −0.177820
\(441\) 0 0
\(442\) −1.60710e6 −0.391279
\(443\) −1.03495e6 1.79259e6i −0.250559 0.433982i 0.713121 0.701041i \(-0.247281\pi\)
−0.963680 + 0.267060i \(0.913948\pi\)
\(444\) 0 0
\(445\) 3.72062e6 6.44430e6i 0.890666 1.54268i
\(446\) 1.27756e6 + 2.21279e6i 0.304119 + 0.526749i
\(447\) 0 0
\(448\) 407489. + 340481.i 0.0959227 + 0.0801489i
\(449\) −5.72581e6 −1.34036 −0.670180 0.742199i \(-0.733783\pi\)
−0.670180 + 0.742199i \(0.733783\pi\)
\(450\) 0 0
\(451\) 570981. 988968.i 0.132184 0.228950i
\(452\) 1.58266e6 2.74125e6i 0.364369 0.631105i
\(453\) 0 0
\(454\) −2.10273e6 −0.478788
\(455\) 586814. 3.36900e6i 0.132884 0.762908i
\(456\) 0 0
\(457\) −159338. 275982.i −0.0356886 0.0618144i 0.847629 0.530589i \(-0.178029\pi\)
−0.883318 + 0.468774i \(0.844696\pi\)
\(458\) 1.86537e6 3.23092e6i 0.415529 0.719718i
\(459\) 0 0
\(460\) 1.09553e6 + 1.89751e6i 0.241395 + 0.418108i
\(461\) 3.42470e6 0.750535 0.375267 0.926917i \(-0.377551\pi\)
0.375267 + 0.926917i \(0.377551\pi\)
\(462\) 0 0
\(463\) 3.82945e6 0.830201 0.415101 0.909775i \(-0.363746\pi\)
0.415101 + 0.909775i \(0.363746\pi\)
\(464\) −97156.2 168280.i −0.0209496 0.0362858i
\(465\) 0 0
\(466\) 1.41559e6 2.45187e6i 0.301975 0.523037i
\(467\) 1.42231e6 + 2.46351e6i 0.301788 + 0.522712i 0.976541 0.215332i \(-0.0690832\pi\)
−0.674753 + 0.738044i \(0.735750\pi\)
\(468\) 0 0
\(469\) −6.61874e6 + 2.42464e6i −1.38945 + 0.508998i
\(470\) 7.42809e6 1.55107
\(471\) 0 0
\(472\) 843482. 1.46095e6i 0.174269 0.301843i
\(473\) −910882. + 1.57769e6i −0.187202 + 0.324243i
\(474\) 0 0
\(475\) −7.19511e6 −1.46320
\(476\) 409275. 2.34971e6i 0.0827938 0.475333i
\(477\) 0 0
\(478\) 1.00123e6 + 1.73418e6i 0.200430 + 0.347155i
\(479\) 651827. 1.12900e6i 0.129806 0.224830i −0.793796 0.608185i \(-0.791898\pi\)
0.923601 + 0.383355i \(0.125231\pi\)
\(480\) 0 0
\(481\) −1.36183e6 2.35876e6i −0.268386 0.464858i
\(482\) −4.83287e6 −0.947519
\(483\) 0 0
\(484\) −2.21940e6 −0.430647
\(485\) −1.22080e6 2.11449e6i −0.235662 0.408179i
\(486\) 0 0
\(487\) −3.11812e6 + 5.40074e6i −0.595759 + 1.03188i 0.397681 + 0.917524i \(0.369815\pi\)
−0.993439 + 0.114360i \(0.963518\pi\)
\(488\) 1.13030e6 + 1.95773e6i 0.214854 + 0.372137i
\(489\) 0 0
\(490\) 4.77631e6 + 1.71594e6i 0.898675 + 0.322859i
\(491\) 3.93928e6 0.737417 0.368709 0.929545i \(-0.379800\pi\)
0.368709 + 0.929545i \(0.379800\pi\)
\(492\) 0 0
\(493\) −436386. + 755843.i −0.0808637 + 0.140060i
\(494\) −1.95338e6 + 3.38335e6i −0.360137 + 0.623776i
\(495\) 0 0
\(496\) 2.31213e6 0.421995
\(497\) 6.97843e6 + 5.83088e6i 1.26726 + 1.05887i
\(498\) 0 0
\(499\) −3.98785e6 6.90717e6i −0.716948 1.24179i −0.962203 0.272333i \(-0.912205\pi\)
0.245255 0.969459i \(-0.421128\pi\)
\(500\) 332713. 576276.i 0.0595176 0.103087i
\(501\) 0 0
\(502\) −195653. 338882.i −0.0346520 0.0600190i
\(503\) 2.70777e6 0.477190 0.238595 0.971119i \(-0.423313\pi\)
0.238595 + 0.971119i \(0.423313\pi\)
\(504\) 0 0
\(505\) −2.36641e6 −0.412917
\(506\) −542238. 939184.i −0.0941486 0.163070i
\(507\) 0 0
\(508\) 268138. 464428.i 0.0460998 0.0798472i
\(509\) 1.95025e6 + 3.37793e6i 0.333653 + 0.577904i 0.983225 0.182396i \(-0.0583852\pi\)
−0.649572 + 0.760300i \(0.725052\pi\)
\(510\) 0 0
\(511\) 5.41323e6 1.98303e6i 0.917073 0.335951i
\(512\) −262144. −0.0441942
\(513\) 0 0
\(514\) 2.21583e6 3.83792e6i 0.369937 0.640750i
\(515\) −3.74944e6 + 6.49422e6i −0.622943 + 1.07897i
\(516\) 0 0
\(517\) −3.67658e6 −0.604947
\(518\) 3.79551e6 1.39041e6i 0.621507 0.227677i
\(519\) 0 0
\(520\) 844103. + 1.46203e6i 0.136895 + 0.237109i
\(521\) 3.50032e6 6.06273e6i 0.564954 0.978529i −0.432100 0.901826i \(-0.642227\pi\)
0.997054 0.0767034i \(-0.0244394\pi\)
\(522\) 0 0
\(523\) 1.05604e6 + 1.82911e6i 0.168821 + 0.292406i 0.938005 0.346620i \(-0.112671\pi\)
−0.769185 + 0.639026i \(0.779337\pi\)
\(524\) 172943. 0.0275153
\(525\) 0 0
\(526\) 6.02741e6 0.949875
\(527\) −5.19256e6 8.99378e6i −0.814433 1.41064i
\(528\) 0 0
\(529\) 1.57293e6 2.72439e6i 0.244382 0.423283i
\(530\) −2.05282e6 3.55559e6i −0.317440 0.549822i
\(531\) 0 0
\(532\) −4.44928e6 3.71763e6i −0.681570 0.569491i
\(533\) −2.66971e6 −0.407048
\(534\) 0 0
\(535\) −5.48331e6 + 9.49737e6i −0.828244 + 1.43456i
\(536\) 1.73990e6 3.01360e6i 0.261585 0.453078i
\(537\) 0 0
\(538\) −8.54009e6 −1.27206
\(539\) −2.36407e6 849318.i −0.350500 0.125921i
\(540\) 0 0
\(541\) −2.85283e6 4.94125e6i −0.419067 0.725845i 0.576779 0.816900i \(-0.304309\pi\)
−0.995846 + 0.0910551i \(0.970976\pi\)
\(542\) 2.45720e6 4.25599e6i 0.359287 0.622303i
\(543\) 0 0
\(544\) 588722. + 1.01970e6i 0.0852929 + 0.147732i
\(545\) −1.36528e7 −1.96894
\(546\) 0 0
\(547\) 2.28054e6 0.325888 0.162944 0.986635i \(-0.447901\pi\)
0.162944 + 0.986635i \(0.447901\pi\)
\(548\) −151456. 262330.i −0.0215445 0.0373161i
\(549\) 0 0
\(550\) 769457. 1.33274e6i 0.108462 0.187862i
\(551\) 1.06083e6 + 1.83740e6i 0.148855 + 0.257825i
\(552\) 0 0
\(553\) 1.37064e6 7.86907e6i 0.190595 1.09424i
\(554\) 7.38730e6 1.02261
\(555\) 0 0
\(556\) 1.35118e6 2.34031e6i 0.185364 0.321060i
\(557\) −3.36970e6 + 5.83650e6i −0.460208 + 0.797103i −0.998971 0.0453541i \(-0.985558\pi\)
0.538763 + 0.842457i \(0.318892\pi\)
\(558\) 0 0
\(559\) 4.25897e6 0.576468
\(560\) −2.35258e6 + 861819.i −0.317010 + 0.116130i
\(561\) 0 0
\(562\) 4.56652e6 + 7.90944e6i 0.609880 + 1.05634i
\(563\) −4.83410e6 + 8.37291e6i −0.642754 + 1.11328i 0.342061 + 0.939678i \(0.388875\pi\)
−0.984815 + 0.173605i \(0.944458\pi\)
\(564\) 0 0
\(565\) 7.46742e6 + 1.29339e7i 0.984123 + 1.70455i
\(566\) −5.34770e6 −0.701659
\(567\) 0 0
\(568\) −4.48933e6 −0.583862
\(569\) −6.97934e6 1.20886e7i −0.903719 1.56529i −0.822627 0.568581i \(-0.807493\pi\)
−0.0810922 0.996707i \(-0.525841\pi\)
\(570\) 0 0
\(571\) 1.17920e6 2.04244e6i 0.151355 0.262155i −0.780371 0.625317i \(-0.784970\pi\)
0.931726 + 0.363162i \(0.118303\pi\)
\(572\) −417794. 723641.i −0.0533915 0.0924769i
\(573\) 0 0
\(574\) 679887. 3.90334e6i 0.0861305 0.494489i
\(575\) −4.66933e6 −0.588959
\(576\) 0 0
\(577\) −2.50549e6 + 4.33963e6i −0.313295 + 0.542642i −0.979074 0.203507i \(-0.934766\pi\)
0.665779 + 0.746149i \(0.268099\pi\)
\(578\) −195418. + 338474.i −0.0243302 + 0.0421411i
\(579\) 0 0
\(580\) 916819. 0.113165
\(581\) 8.66929e6 + 7.24369e6i 1.06547 + 0.890266i
\(582\) 0 0
\(583\) 1.01606e6 + 1.75986e6i 0.123807 + 0.214441i
\(584\) −1.42300e6 + 2.46471e6i −0.172653 + 0.299043i
\(585\) 0 0
\(586\) 4.46066e6 + 7.72609e6i 0.536606 + 0.929428i
\(587\) −3.95106e6 −0.473280 −0.236640 0.971597i \(-0.576046\pi\)
−0.236640 + 0.971597i \(0.576046\pi\)
\(588\) 0 0
\(589\) −2.52455e7 −2.99845
\(590\) 3.97978e6 + 6.89318e6i 0.470683 + 0.815247i
\(591\) 0 0
\(592\) −997746. + 1.72815e6i −0.117008 + 0.202664i
\(593\) −1.26840e6 2.19694e6i −0.148122 0.256555i 0.782411 0.622762i \(-0.213990\pi\)
−0.930533 + 0.366207i \(0.880656\pi\)
\(594\) 0 0
\(595\) 8.63573e6 + 7.21565e6i 1.00002 + 0.835571i
\(596\) −4.22403e6 −0.487093
\(597\) 0 0
\(598\) −1.26766e6 + 2.19565e6i −0.144960 + 0.251079i
\(599\) 3.58857e6 6.21558e6i 0.408652 0.707807i −0.586087 0.810248i \(-0.699332\pi\)
0.994739 + 0.102442i \(0.0326655\pi\)
\(600\) 0 0
\(601\) 1.12527e7 1.27078 0.635392 0.772190i \(-0.280838\pi\)
0.635392 + 0.772190i \(0.280838\pi\)
\(602\) −1.08462e6 + 6.22698e6i −0.121979 + 0.700303i
\(603\) 0 0
\(604\) −2.23340e6 3.86836e6i −0.249100 0.431454i
\(605\) 5.23585e6 9.06877e6i 0.581566 1.00730i
\(606\) 0 0
\(607\) 7.01851e6 + 1.21564e7i 0.773167 + 1.33916i 0.935819 + 0.352481i \(0.114662\pi\)
−0.162652 + 0.986684i \(0.552005\pi\)
\(608\) 2.86229e6 0.314018
\(609\) 0 0
\(610\) −1.06661e7 −1.16059
\(611\) 4.29761e6 + 7.44367e6i 0.465719 + 0.806648i
\(612\) 0 0
\(613\) 3.81436e6 6.60667e6i 0.409988 0.710119i −0.584900 0.811105i \(-0.698866\pi\)
0.994888 + 0.100986i \(0.0321997\pi\)
\(614\) 3.55564e6 + 6.15855e6i 0.380624 + 0.659261i
\(615\) 0 0
\(616\) 1.16442e6 426563.i 0.123640 0.0452930i
\(617\) 4.41080e6 0.466450 0.233225 0.972423i \(-0.425072\pi\)
0.233225 + 0.972423i \(0.425072\pi\)
\(618\) 0 0
\(619\) 4.52178e6 7.83195e6i 0.474332 0.821567i −0.525236 0.850957i \(-0.676023\pi\)
0.999568 + 0.0293895i \(0.00935632\pi\)
\(620\) −5.45462e6 + 9.44768e6i −0.569883 + 0.987065i
\(621\) 0 0
\(622\) 5.61087e6 0.581506
\(623\) −2.19279e6 + 1.25892e7i −0.226348 + 1.29950i
\(624\) 0 0
\(625\) 5.59185e6 + 9.68538e6i 0.572606 + 0.991782i
\(626\) 2.43789e6 4.22255e6i 0.248644 0.430664i
\(627\) 0 0
\(628\) −1.50882e6 2.61335e6i −0.152664 0.264423i
\(629\) 8.96293e6 0.903282
\(630\) 0 0
\(631\) −7.33039e6 −0.732916 −0.366458 0.930435i \(-0.619430\pi\)
−0.366458 + 0.930435i \(0.619430\pi\)
\(632\) 1.97160e6 + 3.41491e6i 0.196348 + 0.340084i
\(633\) 0 0
\(634\) −5.36003e6 + 9.28384e6i −0.529595 + 0.917286i
\(635\) 1.26515e6 + 2.19130e6i 0.124511 + 0.215659i
\(636\) 0 0
\(637\) 1.04385e6 + 5.77912e6i 0.101927 + 0.564304i
\(638\) −453786. −0.0441366
\(639\) 0 0
\(640\) 618433. 1.07116e6i 0.0596819 0.103372i
\(641\) 1.84412e6 3.19411e6i 0.177273 0.307047i −0.763672 0.645604i \(-0.776606\pi\)
0.940946 + 0.338558i \(0.109939\pi\)
\(642\) 0 0
\(643\) −1.17584e7 −1.12155 −0.560776 0.827968i \(-0.689497\pi\)
−0.560776 + 0.827968i \(0.689497\pi\)
\(644\) −2.88739e6 2.41258e6i −0.274342 0.229228i
\(645\) 0 0
\(646\) −6.42811e6 1.11338e7i −0.606041 1.04969i
\(647\) −4.97025e6 + 8.60873e6i −0.466786 + 0.808497i −0.999280 0.0379368i \(-0.987921\pi\)
0.532494 + 0.846434i \(0.321255\pi\)
\(648\) 0 0
\(649\) −1.96982e6 3.41182e6i −0.183575 0.317962i
\(650\) −3.59772e6 −0.333998
\(651\) 0 0
\(652\) 1.43548e6 0.132244
\(653\) −513100. 888714.i −0.0470889 0.0815604i 0.841520 0.540226i \(-0.181661\pi\)
−0.888609 + 0.458665i \(0.848328\pi\)
\(654\) 0 0
\(655\) −407995. + 706668.i −0.0371579 + 0.0643594i
\(656\) 977983. + 1.69392e6i 0.0887303 + 0.153685i
\(657\) 0 0
\(658\) −1.19777e7 + 4.38781e6i −1.07847 + 0.395078i
\(659\) −1.00207e7 −0.898846 −0.449423 0.893319i \(-0.648370\pi\)
−0.449423 + 0.893319i \(0.648370\pi\)
\(660\) 0 0
\(661\) −1.31413e6 + 2.27614e6i −0.116986 + 0.202626i −0.918572 0.395254i \(-0.870657\pi\)
0.801586 + 0.597880i \(0.203990\pi\)
\(662\) 285120. 493843.i 0.0252862 0.0437970i
\(663\) 0 0
\(664\) −5.57709e6 −0.490893
\(665\) 2.56872e7 9.40999e6i 2.25249 0.825154i
\(666\) 0 0
\(667\) 688431. + 1.19240e6i 0.0599165 + 0.103778i
\(668\) 4.23529e6 7.33574e6i 0.367233 0.636067i
\(669\) 0 0
\(670\) 8.20933e6 + 1.42190e7i 0.706514 + 1.22372i
\(671\) 5.27925e6 0.452654
\(672\) 0 0
\(673\) −1.50220e7 −1.27847 −0.639233 0.769013i \(-0.720748\pi\)
−0.639233 + 0.769013i \(0.720748\pi\)
\(674\) −2.42412e6 4.19871e6i −0.205544 0.356013i
\(675\) 0 0
\(676\) 1.99361e6 3.45304e6i 0.167793 0.290626i
\(677\) −3.01655e6 5.22482e6i −0.252953 0.438127i 0.711385 0.702803i \(-0.248068\pi\)
−0.964337 + 0.264676i \(0.914735\pi\)
\(678\) 0 0
\(679\) 3.21757e6 + 2.68846e6i 0.267826 + 0.223784i
\(680\) −5.55550e6 −0.460734
\(681\) 0 0
\(682\) 2.69980e6 4.67619e6i 0.222265 0.384974i
\(683\) 5.53601e6 9.58865e6i 0.454093 0.786513i −0.544542 0.838734i \(-0.683297\pi\)
0.998636 + 0.0522205i \(0.0166299\pi\)
\(684\) 0 0
\(685\) 1.42922e6 0.116379
\(686\) −8.71539e6 + 54443.0i −0.707093 + 0.00441705i
\(687\) 0 0
\(688\) −1.56017e6 2.70230e6i −0.125661 0.217652i
\(689\) 2.37537e6 4.11426e6i 0.190626 0.330174i
\(690\) 0 0
\(691\) 5.27739e6 + 9.14071e6i 0.420460 + 0.728257i 0.995984 0.0895269i \(-0.0285355\pi\)
−0.575525 + 0.817784i \(0.695202\pi\)
\(692\) −541413. −0.0429797
\(693\) 0 0
\(694\) 1.38741e7 1.09347
\(695\) 6.37523e6 + 1.10422e7i 0.500650 + 0.867151i
\(696\) 0 0
\(697\) 4.39270e6 7.60838e6i 0.342491 0.593212i
\(698\) 2.03383e6 + 3.52270e6i 0.158007 + 0.273676i
\(699\) 0 0
\(700\) 916220. 5.26017e6i 0.0706732 0.405746i
\(701\) 7.20675e6 0.553917 0.276958 0.960882i \(-0.410674\pi\)
0.276958 + 0.960882i \(0.410674\pi\)
\(702\) 0 0
\(703\) 1.08941e7 1.88692e7i 0.831390 1.44001i
\(704\) −306098. + 530177.i −0.0232771 + 0.0403171i
\(705\) 0 0
\(706\) 6.25542e6 0.472329
\(707\) 3.81583e6 1.39785e6i 0.287104 0.105175i
\(708\) 0 0
\(709\) −1.34687e6 2.33284e6i −0.100626 0.174289i 0.811317 0.584607i \(-0.198751\pi\)
−0.911943 + 0.410318i \(0.865418\pi\)
\(710\) 1.05909e7 1.83440e7i 0.788476 1.36568i
\(711\) 0 0
\(712\) −3.15422e6 5.46327e6i −0.233180 0.403880i
\(713\) −1.63833e7 −1.20692
\(714\) 0 0
\(715\) 3.94253e6 0.288410
\(716\) −1.98195e6 3.43284e6i −0.144481 0.250248i
\(717\) 0 0
\(718\) −99106.3 + 171657.i −0.00717447 + 0.0124266i
\(719\) 3.46275e6 + 5.99766e6i 0.249804 + 0.432673i 0.963471 0.267812i \(-0.0863005\pi\)
−0.713667 + 0.700485i \(0.752967\pi\)
\(720\) 0 0
\(721\) 2.20978e6 1.26867e7i 0.158311 0.908887i
\(722\) −2.13482e7 −1.52412
\(723\) 0 0
\(724\) −2.95576e6 + 5.11953e6i −0.209567 + 0.362981i
\(725\) −976911. + 1.69206e6i −0.0690256 + 0.119556i
\(726\) 0 0
\(727\) 4.11366e6 0.288664 0.144332 0.989529i \(-0.453897\pi\)
0.144332 + 0.989529i \(0.453897\pi\)
\(728\) −2.22474e6 1.85890e6i −0.155579 0.129995i
\(729\) 0 0
\(730\) −6.71411e6 1.16292e7i −0.466317 0.807685i
\(731\) −7.00765e6 + 1.21376e7i −0.485041 + 0.840116i
\(732\) 0 0
\(733\) −3.96019e6 6.85925e6i −0.272243 0.471538i 0.697193 0.716883i \(-0.254432\pi\)
−0.969436 + 0.245345i \(0.921099\pi\)
\(734\) −1.41932e7 −0.972392
\(735\) 0 0
\(736\) 1.85750e6 0.126397
\(737\) −4.06326e6 7.03777e6i −0.275554 0.477273i
\(738\) 0 0
\(739\) −8.02050e6 + 1.38919e7i −0.540245 + 0.935731i 0.458645 + 0.888620i \(0.348335\pi\)
−0.998890 + 0.0471115i \(0.984998\pi\)
\(740\) −4.70764e6 8.15387e6i −0.316027 0.547374i
\(741\) 0 0
\(742\) 5.41046e6 + 4.52075e6i 0.360765 + 0.301440i
\(743\) −1.53453e7 −1.01977 −0.509887 0.860241i \(-0.670313\pi\)
−0.509887 + 0.860241i \(0.670313\pi\)
\(744\) 0 0
\(745\) 9.96507e6 1.72600e7i 0.657794 1.13933i
\(746\) −4.51147e6 + 7.81409e6i −0.296805 + 0.514081i
\(747\) 0 0
\(748\) 2.74973e6 0.179695
\(749\) 3.23166e6 1.85535e7i 0.210485 1.20843i
\(750\) 0 0
\(751\) −1.12488e7 1.94835e7i −0.727790 1.26057i −0.957815 0.287385i \(-0.907214\pi\)
0.230025 0.973185i \(-0.426119\pi\)
\(752\) 3.14865e6 5.45362e6i 0.203039 0.351674i
\(753\) 0 0
\(754\) 530436. + 918743.i 0.0339786 + 0.0588526i
\(755\) 2.10756e7 1.34559
\(756\) 0 0
\(757\) 2.30349e7 1.46099 0.730494 0.682919i \(-0.239290\pi\)
0.730494 + 0.682919i \(0.239290\pi\)
\(758\) 8.79006e6 + 1.52248e7i 0.555673 + 0.962453i
\(759\) 0 0
\(760\) −6.75252e6 + 1.16957e7i −0.424065 + 0.734501i
\(761\) 2.70368e6 + 4.68290e6i 0.169236 + 0.293126i 0.938152 0.346225i \(-0.112537\pi\)
−0.768915 + 0.639351i \(0.779203\pi\)
\(762\) 0 0
\(763\) 2.20151e7 8.06480e6i 1.36902 0.501513i
\(764\) 7.76359e6 0.481204
\(765\) 0 0
\(766\) 2.45562e6 4.25325e6i 0.151213 0.261908i
\(767\) −4.60509e6 + 7.97626e6i −0.282651 + 0.489565i
\(768\) 0 0
\(769\) −7.93100e6 −0.483629 −0.241814 0.970323i \(-0.577742\pi\)
−0.241814 + 0.970323i \(0.577742\pi\)
\(770\) −1.00403e6 + 5.76432e6i −0.0610269 + 0.350365i
\(771\) 0 0
\(772\) 2.64654e6 + 4.58394e6i 0.159821 + 0.276819i
\(773\) 134790. 233462.i 0.00811349 0.0140530i −0.861940 0.507010i \(-0.830751\pi\)
0.870054 + 0.492957i \(0.164084\pi\)
\(774\) 0 0
\(775\) −1.16243e7 2.01338e7i