Properties

Label 55.6.e.b.43.10
Level $55$
Weight $6$
Character 55.43
Analytic conductor $8.821$
Analytic rank $0$
Dimension $52$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,6,Mod(32,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.32");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 55.e (of order \(4\), 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: \(8.82111008971\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.10
Character \(\chi\) \(=\) 55.43
Dual form 55.6.e.b.32.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.88475 - 2.88475i) q^{2} +(5.55436 + 5.55436i) q^{3} -15.3564i q^{4} +(-11.0950 - 54.7896i) q^{5} -32.0459i q^{6} +(103.743 + 103.743i) q^{7} +(-136.612 + 136.612i) q^{8} -181.298i q^{9} +(-126.048 + 190.061i) q^{10} +(-271.739 - 295.311i) q^{11} +(85.2950 - 85.2950i) q^{12} +(-40.9640 + 40.9640i) q^{13} -598.545i q^{14} +(242.696 - 365.947i) q^{15} +296.775 q^{16} +(-752.091 - 752.091i) q^{17} +(-523.000 + 523.000i) q^{18} -2333.79 q^{19} +(-841.372 + 170.379i) q^{20} +1152.45i q^{21} +(-67.9994 + 1635.80i) q^{22} +(-1568.23 - 1568.23i) q^{23} -1517.58 q^{24} +(-2878.80 + 1215.78i) q^{25} +236.342 q^{26} +(2356.70 - 2356.70i) q^{27} +(1593.12 - 1593.12i) q^{28} +477.232 q^{29} +(-1755.78 + 355.548i) q^{30} +8126.11 q^{31} +(3515.44 + 3515.44i) q^{32} +(130.928 - 3149.60i) q^{33} +4339.19i q^{34} +(4533.01 - 6835.06i) q^{35} -2784.09 q^{36} +(-971.434 + 971.434i) q^{37} +(6732.40 + 6732.40i) q^{38} -455.058 q^{39} +(9000.59 + 5969.19i) q^{40} -2223.10i q^{41} +(3324.53 - 3324.53i) q^{42} +(10296.0 - 10296.0i) q^{43} +(-4534.92 + 4172.94i) q^{44} +(-9933.26 + 2011.50i) q^{45} +9047.93i q^{46} +(3963.20 - 3963.20i) q^{47} +(1648.40 + 1648.40i) q^{48} +4718.17i q^{49} +(11811.9 + 4797.42i) q^{50} -8354.77i q^{51} +(629.061 + 629.061i) q^{52} +(11691.1 + 11691.1i) q^{53} -13597.0 q^{54} +(-13165.1 + 18165.0i) q^{55} -28344.9 q^{56} +(-12962.7 - 12962.7i) q^{57} +(-1376.69 - 1376.69i) q^{58} -2379.92i q^{59} +(-5619.63 - 3726.94i) q^{60} +34132.7i q^{61} +(-23441.8 - 23441.8i) q^{62} +(18808.4 - 18808.4i) q^{63} -29779.2i q^{64} +(2698.90 + 1789.91i) q^{65} +(-9463.52 + 8708.13i) q^{66} +(31275.3 - 31275.3i) q^{67} +(-11549.4 + 11549.4i) q^{68} -17421.1i q^{69} +(-32794.0 + 6640.83i) q^{70} +34239.7 q^{71} +(24767.4 + 24767.4i) q^{72} +(-6013.88 + 6013.88i) q^{73} +5604.69 q^{74} +(-22742.8 - 9237.05i) q^{75} +35838.6i q^{76} +(2445.43 - 58827.5i) q^{77} +(1312.73 + 1312.73i) q^{78} -97400.0 q^{79} +(-3292.71 - 16260.2i) q^{80} -17875.5 q^{81} +(-6413.09 + 6413.09i) q^{82} +(58184.5 - 58184.5i) q^{83} +17697.5 q^{84} +(-32862.4 + 49551.2i) q^{85} -59403.1 q^{86} +(2650.72 + 2650.72i) q^{87} +(77465.6 + 3220.21i) q^{88} -109220. i q^{89} +(34457.6 + 22852.3i) q^{90} -8499.46 q^{91} +(-24082.4 + 24082.4i) q^{92} +(45135.4 + 45135.4i) q^{93} -22865.7 q^{94} +(25893.3 + 127867. i) q^{95} +39052.1i q^{96} +(-36525.4 + 36525.4i) q^{97} +(13610.8 - 13610.8i) q^{98} +(-53539.4 + 49265.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.88475 2.88475i −0.509957 0.509957i 0.404556 0.914513i \(-0.367426\pi\)
−0.914513 + 0.404556i \(0.867426\pi\)
\(3\) 5.55436 + 5.55436i 0.356312 + 0.356312i 0.862452 0.506139i \(-0.168928\pi\)
−0.506139 + 0.862452i \(0.668928\pi\)
\(4\) 15.3564i 0.479888i
\(5\) −11.0950 54.7896i −0.198473 0.980106i
\(6\) 32.0459i 0.363408i
\(7\) 103.743 + 103.743i 0.800227 + 0.800227i 0.983131 0.182904i \(-0.0585497\pi\)
−0.182904 + 0.983131i \(0.558550\pi\)
\(8\) −136.612 + 136.612i −0.754679 + 0.754679i
\(9\) 181.298i 0.746083i
\(10\) −126.048 + 190.061i −0.398599 + 0.601025i
\(11\) −271.739 295.311i −0.677128 0.735865i
\(12\) 85.2950 85.2950i 0.170990 0.170990i
\(13\) −40.9640 + 40.9640i −0.0672271 + 0.0672271i −0.739921 0.672694i \(-0.765137\pi\)
0.672694 + 0.739921i \(0.265137\pi\)
\(14\) 598.545i 0.816163i
\(15\) 242.696 365.947i 0.278506 0.419942i
\(16\) 296.775 0.289820
\(17\) −752.091 752.091i −0.631173 0.631173i 0.317190 0.948362i \(-0.397261\pi\)
−0.948362 + 0.317190i \(0.897261\pi\)
\(18\) −523.000 + 523.000i −0.380470 + 0.380470i
\(19\) −2333.79 −1.48312 −0.741562 0.670884i \(-0.765915\pi\)
−0.741562 + 0.670884i \(0.765915\pi\)
\(20\) −841.372 + 170.379i −0.470341 + 0.0952447i
\(21\) 1152.45i 0.570262i
\(22\) −67.9994 + 1635.80i −0.0299536 + 0.720566i
\(23\) −1568.23 1568.23i −0.618146 0.618146i 0.326910 0.945056i \(-0.393993\pi\)
−0.945056 + 0.326910i \(0.893993\pi\)
\(24\) −1517.58 −0.537803
\(25\) −2878.80 + 1215.78i −0.921217 + 0.389049i
\(26\) 236.342 0.0685659
\(27\) 2356.70 2356.70i 0.622151 0.622151i
\(28\) 1593.12 1593.12i 0.384019 0.384019i
\(29\) 477.232 0.105374 0.0526871 0.998611i \(-0.483221\pi\)
0.0526871 + 0.998611i \(0.483221\pi\)
\(30\) −1755.78 + 355.548i −0.356178 + 0.0721266i
\(31\) 8126.11 1.51872 0.759362 0.650669i \(-0.225511\pi\)
0.759362 + 0.650669i \(0.225511\pi\)
\(32\) 3515.44 + 3515.44i 0.606884 + 0.606884i
\(33\) 130.928 3149.60i 0.0209289 0.503467i
\(34\) 4339.19i 0.643742i
\(35\) 4533.01 6835.06i 0.625484 0.943131i
\(36\) −2784.09 −0.358036
\(37\) −971.434 + 971.434i −0.116657 + 0.116657i −0.763025 0.646369i \(-0.776287\pi\)
0.646369 + 0.763025i \(0.276287\pi\)
\(38\) 6732.40 + 6732.40i 0.756330 + 0.756330i
\(39\) −455.058 −0.0479077
\(40\) 9000.59 + 5969.19i 0.889449 + 0.589883i
\(41\) 2223.10i 0.206538i −0.994653 0.103269i \(-0.967070\pi\)
0.994653 0.103269i \(-0.0329302\pi\)
\(42\) 3324.53 3324.53i 0.290809 0.290809i
\(43\) 10296.0 10296.0i 0.849179 0.849179i −0.140852 0.990031i \(-0.544984\pi\)
0.990031 + 0.140852i \(0.0449840\pi\)
\(44\) −4534.92 + 4172.94i −0.353133 + 0.324945i
\(45\) −9933.26 + 2011.50i −0.731241 + 0.148077i
\(46\) 9047.93i 0.630456i
\(47\) 3963.20 3963.20i 0.261698 0.261698i −0.564045 0.825744i \(-0.690756\pi\)
0.825744 + 0.564045i \(0.190756\pi\)
\(48\) 1648.40 + 1648.40i 0.103266 + 0.103266i
\(49\) 4718.17i 0.280727i
\(50\) 11811.9 + 4797.42i 0.668179 + 0.271383i
\(51\) 8354.77i 0.449789i
\(52\) 629.061 + 629.061i 0.0322615 + 0.0322615i
\(53\) 11691.1 + 11691.1i 0.571697 + 0.571697i 0.932602 0.360906i \(-0.117532\pi\)
−0.360906 + 0.932602i \(0.617532\pi\)
\(54\) −13597.0 −0.634540
\(55\) −13165.1 + 18165.0i −0.586835 + 0.809707i
\(56\) −28344.9 −1.20783
\(57\) −12962.7 12962.7i −0.528456 0.528456i
\(58\) −1376.69 1376.69i −0.0537363 0.0537363i
\(59\) 2379.92i 0.0890087i −0.999009 0.0445043i \(-0.985829\pi\)
0.999009 0.0445043i \(-0.0141709\pi\)
\(60\) −5619.63 3726.94i −0.201525 0.133652i
\(61\) 34132.7i 1.17448i 0.809413 + 0.587240i \(0.199786\pi\)
−0.809413 + 0.587240i \(0.800214\pi\)
\(62\) −23441.8 23441.8i −0.774484 0.774484i
\(63\) 18808.4 18808.4i 0.597036 0.597036i
\(64\) 29779.2i 0.908789i
\(65\) 2698.90 + 1789.91i 0.0792325 + 0.0525470i
\(66\) −9463.52 + 8708.13i −0.267419 + 0.246074i
\(67\) 31275.3 31275.3i 0.851167 0.851167i −0.139110 0.990277i \(-0.544424\pi\)
0.990277 + 0.139110i \(0.0444240\pi\)
\(68\) −11549.4 + 11549.4i −0.302892 + 0.302892i
\(69\) 17421.1i 0.440506i
\(70\) −32794.0 + 6640.83i −0.799926 + 0.161986i
\(71\) 34239.7 0.806091 0.403046 0.915180i \(-0.367952\pi\)
0.403046 + 0.915180i \(0.367952\pi\)
\(72\) 24767.4 + 24767.4i 0.563053 + 0.563053i
\(73\) −6013.88 + 6013.88i −0.132083 + 0.132083i −0.770058 0.637974i \(-0.779773\pi\)
0.637974 + 0.770058i \(0.279773\pi\)
\(74\) 5604.69 0.118980
\(75\) −22742.8 9237.05i −0.466864 0.189618i
\(76\) 35838.6i 0.711734i
\(77\) 2445.43 58827.5i 0.0470033 1.13072i
\(78\) 1312.73 + 1312.73i 0.0244309 + 0.0244309i
\(79\) −97400.0 −1.75587 −0.877933 0.478784i \(-0.841078\pi\)
−0.877933 + 0.478784i \(0.841078\pi\)
\(80\) −3292.71 16260.2i −0.0575213 0.284054i
\(81\) −17875.5 −0.302723
\(82\) −6413.09 + 6413.09i −0.105325 + 0.105325i
\(83\) 58184.5 58184.5i 0.927069 0.927069i −0.0704462 0.997516i \(-0.522442\pi\)
0.997516 + 0.0704462i \(0.0224423\pi\)
\(84\) 17697.5 0.273662
\(85\) −32862.4 + 49551.2i −0.493346 + 0.743887i
\(86\) −59403.1 −0.866090
\(87\) 2650.72 + 2650.72i 0.0375461 + 0.0375461i
\(88\) 77465.6 + 3220.21i 1.06636 + 0.0443279i
\(89\) 109220.i 1.46159i −0.682596 0.730796i \(-0.739149\pi\)
0.682596 0.730796i \(-0.260851\pi\)
\(90\) 34457.6 + 22852.3i 0.448414 + 0.297388i
\(91\) −8499.46 −0.107594
\(92\) −24082.4 + 24082.4i −0.296641 + 0.296641i
\(93\) 45135.4 + 45135.4i 0.541140 + 0.541140i
\(94\) −22865.7 −0.266910
\(95\) 25893.3 + 127867.i 0.294360 + 1.45362i
\(96\) 39052.1i 0.432480i
\(97\) −36525.4 + 36525.4i −0.394154 + 0.394154i −0.876165 0.482011i \(-0.839906\pi\)
0.482011 + 0.876165i \(0.339906\pi\)
\(98\) 13610.8 13610.8i 0.143158 0.143158i
\(99\) −53539.4 + 49265.8i −0.549017 + 0.505194i
\(100\) 18670.0 + 44208.1i 0.186700 + 0.442081i
\(101\) 152382.i 1.48638i −0.669080 0.743190i \(-0.733312\pi\)
0.669080 0.743190i \(-0.266688\pi\)
\(102\) −24101.4 + 24101.4i −0.229373 + 0.229373i
\(103\) 76493.8 + 76493.8i 0.710450 + 0.710450i 0.966629 0.256180i \(-0.0824639\pi\)
−0.256180 + 0.966629i \(0.582464\pi\)
\(104\) 11192.3i 0.101470i
\(105\) 63142.3 12786.4i 0.558917 0.113181i
\(106\) 67451.8i 0.583081i
\(107\) −160384. 160384.i −1.35426 1.35426i −0.880831 0.473431i \(-0.843015\pi\)
−0.473431 0.880831i \(-0.656985\pi\)
\(108\) −36190.5 36190.5i −0.298563 0.298563i
\(109\) 230522. 1.85843 0.929214 0.369543i \(-0.120486\pi\)
0.929214 + 0.369543i \(0.120486\pi\)
\(110\) 90379.3 14423.5i 0.712176 0.113655i
\(111\) −10791.4 −0.0831323
\(112\) 30788.3 + 30788.3i 0.231922 + 0.231922i
\(113\) 117467. + 117467.i 0.865409 + 0.865409i 0.991960 0.126551i \(-0.0403908\pi\)
−0.126551 + 0.991960i \(0.540391\pi\)
\(114\) 74788.4i 0.538979i
\(115\) −68523.4 + 103322.i −0.483164 + 0.728534i
\(116\) 7328.56i 0.0505678i
\(117\) 7426.71 + 7426.71i 0.0501570 + 0.0501570i
\(118\) −6865.48 + 6865.48i −0.0453906 + 0.0453906i
\(119\) 156048.i 1.01016i
\(120\) 16837.5 + 83147.6i 0.106739 + 0.527104i
\(121\) −13366.5 + 160495.i −0.0829956 + 0.996550i
\(122\) 98464.3 98464.3i 0.598934 0.598934i
\(123\) 12347.9 12347.9i 0.0735919 0.0735919i
\(124\) 124788.i 0.728817i
\(125\) 98552.2 + 144240.i 0.564146 + 0.825675i
\(126\) −108515. −0.608925
\(127\) 131960. + 131960.i 0.725992 + 0.725992i 0.969819 0.243827i \(-0.0784029\pi\)
−0.243827 + 0.969819i \(0.578403\pi\)
\(128\) 26588.7 26588.7i 0.143440 0.143440i
\(129\) 114376. 0.605146
\(130\) −2622.21 12949.1i −0.0136085 0.0672018i
\(131\) 5606.55i 0.0285442i −0.999898 0.0142721i \(-0.995457\pi\)
0.999898 0.0142721i \(-0.00454310\pi\)
\(132\) −48366.6 2010.58i −0.241608 0.0100435i
\(133\) −242114. 242114.i −1.18684 1.18684i
\(134\) −180443. −0.868117
\(135\) −155270. 102975.i −0.733254 0.486294i
\(136\) 205489. 0.952666
\(137\) −51214.1 + 51214.1i −0.233125 + 0.233125i −0.813996 0.580871i \(-0.802712\pi\)
0.580871 + 0.813996i \(0.302712\pi\)
\(138\) −50255.4 + 50255.4i −0.224639 + 0.224639i
\(139\) 29167.4 0.128044 0.0640222 0.997948i \(-0.479607\pi\)
0.0640222 + 0.997948i \(0.479607\pi\)
\(140\) −104962. 69610.8i −0.452597 0.300162i
\(141\) 44026.0 0.186493
\(142\) −98773.1 98773.1i −0.411072 0.411072i
\(143\) 23228.7 + 965.606i 0.0949915 + 0.00394875i
\(144\) 53804.8i 0.216230i
\(145\) −5294.87 26147.3i −0.0209139 0.103278i
\(146\) 34697.1 0.134714
\(147\) −26206.4 + 26206.4i −0.100026 + 0.100026i
\(148\) 14917.7 + 14917.7i 0.0559821 + 0.0559821i
\(149\) −313510. −1.15687 −0.578436 0.815728i \(-0.696337\pi\)
−0.578436 + 0.815728i \(0.696337\pi\)
\(150\) 38960.7 + 92253.9i 0.141383 + 0.334778i
\(151\) 173899.i 0.620662i 0.950629 + 0.310331i \(0.100440\pi\)
−0.950629 + 0.310331i \(0.899560\pi\)
\(152\) 318823. 318823.i 1.11928 1.11928i
\(153\) −136353. + 136353.i −0.470907 + 0.470907i
\(154\) −176757. + 162648.i −0.600586 + 0.552646i
\(155\) −90158.9 445227.i −0.301425 1.48851i
\(156\) 6988.06i 0.0229903i
\(157\) −161370. + 161370.i −0.522484 + 0.522484i −0.918321 0.395837i \(-0.870455\pi\)
0.395837 + 0.918321i \(0.370455\pi\)
\(158\) 280975. + 280975.i 0.895416 + 0.895416i
\(159\) 129873.i 0.407405i
\(160\) 153606. 231614.i 0.474361 0.715260i
\(161\) 325386.i 0.989314i
\(162\) 51566.3 + 51566.3i 0.154376 + 0.154376i
\(163\) −442373. 442373.i −1.30413 1.30413i −0.925585 0.378540i \(-0.876426\pi\)
−0.378540 0.925585i \(-0.623574\pi\)
\(164\) −34138.8 −0.0991149
\(165\) −174018. + 27771.3i −0.497605 + 0.0794119i
\(166\) −335696. −0.945531
\(167\) 197052. + 197052.i 0.546751 + 0.546751i 0.925500 0.378749i \(-0.123646\pi\)
−0.378749 + 0.925500i \(0.623646\pi\)
\(168\) −157438. 157438.i −0.430364 0.430364i
\(169\) 367937.i 0.990961i
\(170\) 237743. 48143.2i 0.630935 0.127765i
\(171\) 423112.i 1.10653i
\(172\) −158110. 158110.i −0.407511 0.407511i
\(173\) 38967.4 38967.4i 0.0989888 0.0989888i −0.655878 0.754867i \(-0.727701\pi\)
0.754867 + 0.655878i \(0.227701\pi\)
\(174\) 15293.3i 0.0382938i
\(175\) −424784. 172527.i −1.04851 0.425856i
\(176\) −80645.5 87641.1i −0.196245 0.213268i
\(177\) 13218.9 13218.9i 0.0317149 0.0317149i
\(178\) −315072. + 315072.i −0.745349 + 0.745349i
\(179\) 334650.i 0.780653i 0.920676 + 0.390327i \(0.127638\pi\)
−0.920676 + 0.390327i \(0.872362\pi\)
\(180\) 30889.4 + 152539.i 0.0710604 + 0.350914i
\(181\) 102496. 0.232547 0.116273 0.993217i \(-0.462905\pi\)
0.116273 + 0.993217i \(0.462905\pi\)
\(182\) 24518.8 + 24518.8i 0.0548683 + 0.0548683i
\(183\) −189585. + 189585.i −0.418482 + 0.418482i
\(184\) 428477. 0.933003
\(185\) 64002.5 + 42446.5i 0.137489 + 0.0911827i
\(186\) 260409.i 0.551916i
\(187\) −17728.3 + 426474.i −0.0370735 + 0.891843i
\(188\) −60860.5 60860.5i −0.125586 0.125586i
\(189\) 488983. 0.995724
\(190\) 294170. 443562.i 0.591173 0.891395i
\(191\) 565974. 1.12257 0.561284 0.827623i \(-0.310307\pi\)
0.561284 + 0.827623i \(0.310307\pi\)
\(192\) 165404. 165404.i 0.323813 0.323813i
\(193\) 364829. 364829.i 0.705011 0.705011i −0.260471 0.965482i \(-0.583878\pi\)
0.965482 + 0.260471i \(0.0838779\pi\)
\(194\) 210734. 0.402003
\(195\) 5048.85 + 24932.5i 0.00950837 + 0.0469546i
\(196\) 72454.2 0.134717
\(197\) 235641. + 235641.i 0.432598 + 0.432598i 0.889511 0.456913i \(-0.151045\pi\)
−0.456913 + 0.889511i \(0.651045\pi\)
\(198\) 296568. + 12328.2i 0.537602 + 0.0223479i
\(199\) 767403.i 1.37370i −0.726801 0.686848i \(-0.758994\pi\)
0.726801 0.686848i \(-0.241006\pi\)
\(200\) 227189. 559367.i 0.401616 0.988830i
\(201\) 347429. 0.606563
\(202\) −439584. + 439584.i −0.757990 + 0.757990i
\(203\) 49509.4 + 49509.4i 0.0843233 + 0.0843233i
\(204\) −128299. −0.215848
\(205\) −121803. + 24665.2i −0.202429 + 0.0409921i
\(206\) 441331.i 0.724597i
\(207\) −284318. + 284318.i −0.461188 + 0.461188i
\(208\) −12157.1 + 12157.1i −0.0194837 + 0.0194837i
\(209\) 634182. + 689195.i 1.00427 + 1.09138i
\(210\) −219036. 145264.i −0.342741 0.227306i
\(211\) 218175.i 0.337364i 0.985671 + 0.168682i \(0.0539511\pi\)
−0.985671 + 0.168682i \(0.946049\pi\)
\(212\) 179533. 179533.i 0.274350 0.274350i
\(213\) 190180. + 190180.i 0.287220 + 0.287220i
\(214\) 925338.i 1.38123i
\(215\) −678351. 449882.i −1.00082 0.663747i
\(216\) 643906.i 0.939049i
\(217\) 843027. + 843027.i 1.21532 + 1.21532i
\(218\) −664998. 664998.i −0.947718 0.947718i
\(219\) −66806.5 −0.0941258
\(220\) 278949. + 202168.i 0.388568 + 0.281615i
\(221\) 61617.4 0.0848638
\(222\) 31130.5 + 31130.5i 0.0423939 + 0.0423939i
\(223\) 34654.9 + 34654.9i 0.0466661 + 0.0466661i 0.730055 0.683389i \(-0.239495\pi\)
−0.683389 + 0.730055i \(0.739495\pi\)
\(224\) 729405.i 0.971289i
\(225\) 220418. + 521922.i 0.290263 + 0.687304i
\(226\) 677729.i 0.882642i
\(227\) −136425. 136425.i −0.175724 0.175724i 0.613765 0.789489i \(-0.289654\pi\)
−0.789489 + 0.613765i \(0.789654\pi\)
\(228\) −199061. + 199061.i −0.253600 + 0.253600i
\(229\) 582233.i 0.733682i −0.930284 0.366841i \(-0.880439\pi\)
0.930284 0.366841i \(-0.119561\pi\)
\(230\) 495732. 100386.i 0.617913 0.125128i
\(231\) 340332. 313166.i 0.419636 0.386140i
\(232\) −65195.3 + 65195.3i −0.0795237 + 0.0795237i
\(233\) 283442. 283442.i 0.342038 0.342038i −0.515095 0.857133i \(-0.672243\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(234\) 42848.4i 0.0511558i
\(235\) −261113. 173170.i −0.308432 0.204552i
\(236\) −36547.0 −0.0427142
\(237\) −540995. 540995.i −0.625637 0.625637i
\(238\) −450160. + 450160.i −0.515139 + 0.515139i
\(239\) −1.58918e6 −1.79960 −0.899802 0.436298i \(-0.856289\pi\)
−0.899802 + 0.436298i \(0.856289\pi\)
\(240\) 72026.1 108604.i 0.0807164 0.121708i
\(241\) 519927.i 0.576633i −0.957535 0.288317i \(-0.906904\pi\)
0.957535 0.288317i \(-0.0930956\pi\)
\(242\) 501548. 424430.i 0.550522 0.465873i
\(243\) −671966. 671966.i −0.730015 0.730015i
\(244\) 524156. 0.563619
\(245\) 258507. 52347.9i 0.275142 0.0557166i
\(246\) −71241.2 −0.0750574
\(247\) 95601.5 95601.5i 0.0997062 0.0997062i
\(248\) −1.11012e6 + 1.11012e6i −1.14615 + 1.14615i
\(249\) 646356. 0.660653
\(250\) 131797. 700394.i 0.133369 0.708749i
\(251\) −70673.7 −0.0708066 −0.0354033 0.999373i \(-0.511272\pi\)
−0.0354033 + 0.999373i \(0.511272\pi\)
\(252\) −288829. 288829.i −0.286510 0.286510i
\(253\) −36966.4 + 889267.i −0.0363083 + 0.873436i
\(254\) 761342.i 0.740449i
\(255\) −457755. + 92695.9i −0.440841 + 0.0892709i
\(256\) −1.10634e6 −1.05509
\(257\) −1.20806e6 + 1.20806e6i −1.14092 + 1.14092i −0.152640 + 0.988282i \(0.548777\pi\)
−0.988282 + 0.152640i \(0.951223\pi\)
\(258\) −329946. 329946.i −0.308598 0.308598i
\(259\) −201559. −0.186703
\(260\) 27486.6 41445.4i 0.0252167 0.0380227i
\(261\) 86521.2i 0.0786179i
\(262\) −16173.5 + 16173.5i −0.0145563 + 0.0145563i
\(263\) −893794. + 893794.i −0.796798 + 0.796798i −0.982589 0.185792i \(-0.940515\pi\)
0.185792 + 0.982589i \(0.440515\pi\)
\(264\) 412386. + 448158.i 0.364161 + 0.395751i
\(265\) 510839. 770263.i 0.446857 0.673790i
\(266\) 1.39688e6i 1.21047i
\(267\) 606646. 606646.i 0.520784 0.520784i
\(268\) −480277. 480277.i −0.408465 0.408465i
\(269\) 969842.i 0.817184i −0.912717 0.408592i \(-0.866020\pi\)
0.912717 0.408592i \(-0.133980\pi\)
\(270\) 150858. + 744975.i 0.125939 + 0.621917i
\(271\) 1.10341e6i 0.912669i −0.889808 0.456334i \(-0.849162\pi\)
0.889808 0.456334i \(-0.150838\pi\)
\(272\) −223202. 223202.i −0.182926 0.182926i
\(273\) −47209.0 47209.0i −0.0383370 0.0383370i
\(274\) 295480. 0.237767
\(275\) 1.14132e6 + 519769.i 0.910069 + 0.414456i
\(276\) −267525. −0.211394
\(277\) 170236. + 170236.i 0.133307 + 0.133307i 0.770612 0.637305i \(-0.219951\pi\)
−0.637305 + 0.770612i \(0.719951\pi\)
\(278\) −84140.6 84140.6i −0.0652971 0.0652971i
\(279\) 1.47325e6i 1.13309i
\(280\) 314486. + 1.55301e6i 0.239721 + 1.18380i
\(281\) 14924.1i 0.0112751i −0.999984 0.00563756i \(-0.998205\pi\)
0.999984 0.00563756i \(-0.00179450\pi\)
\(282\) −127004. 127004.i −0.0951032 0.0951032i
\(283\) 66100.1 66100.1i 0.0490610 0.0490610i −0.682151 0.731212i \(-0.738955\pi\)
0.731212 + 0.682151i \(0.238955\pi\)
\(284\) 525799.i 0.386833i
\(285\) −566401. + 854043.i −0.413059 + 0.622827i
\(286\) −64223.5 69794.5i −0.0464279 0.0504552i
\(287\) 230631. 230631.i 0.165277 0.165277i
\(288\) 637344. 637344.i 0.452785 0.452785i
\(289\) 288575.i 0.203242i
\(290\) −60154.2 + 90702.9i −0.0420021 + 0.0633325i
\(291\) −405751. −0.280884
\(292\) 92351.7 + 92351.7i 0.0633852 + 0.0633852i
\(293\) 1.59914e6 1.59914e6i 1.08822 1.08822i 0.0925065 0.995712i \(-0.470512\pi\)
0.995712 0.0925065i \(-0.0294879\pi\)
\(294\) 151198. 0.102018
\(295\) −130395. + 26405.1i −0.0872380 + 0.0176658i
\(296\) 265418.i 0.176076i
\(297\) −1.33637e6 55552.3i −0.879095 0.0365436i
\(298\) 904398. + 904398.i 0.589955 + 0.589955i
\(299\) 128482. 0.0831123
\(300\) −141848. + 349247.i −0.0909955 + 0.224042i
\(301\) 2.13628e6 1.35907
\(302\) 501656. 501656.i 0.316511 0.316511i
\(303\) 846384. 846384.i 0.529616 0.529616i
\(304\) −692611. −0.429839
\(305\) 1.87012e6 378701.i 1.15112 0.233102i
\(306\) 786688. 0.480285
\(307\) −1.02898e6 1.02898e6i −0.623107 0.623107i 0.323218 0.946325i \(-0.395235\pi\)
−0.946325 + 0.323218i \(0.895235\pi\)
\(308\) −903379. 37553.0i −0.542617 0.0225563i
\(309\) 849748.i 0.506284i
\(310\) −1.02428e6 + 1.54445e6i −0.605362 + 0.912790i
\(311\) −1.96307e6 −1.15089 −0.575446 0.817840i \(-0.695171\pi\)
−0.575446 + 0.817840i \(0.695171\pi\)
\(312\) 62166.2 62166.2i 0.0361549 0.0361549i
\(313\) 1.41211e6 + 1.41211e6i 0.814719 + 0.814719i 0.985337 0.170618i \(-0.0545764\pi\)
−0.170618 + 0.985337i \(0.554576\pi\)
\(314\) 931023. 0.532889
\(315\) −1.23918e6 821826.i −0.703654 0.466663i
\(316\) 1.49571e6i 0.842619i
\(317\) −527387. + 527387.i −0.294769 + 0.294769i −0.838961 0.544192i \(-0.816836\pi\)
0.544192 + 0.838961i \(0.316836\pi\)
\(318\) 374652. 374652.i 0.207759 0.207759i
\(319\) −129683. 140932.i −0.0713518 0.0775412i
\(320\) −1.63159e6 + 330399.i −0.890709 + 0.180370i
\(321\) 1.78167e6i 0.965081i
\(322\) −938658. + 938658.i −0.504508 + 0.504508i
\(323\) 1.75522e6 + 1.75522e6i 0.936108 + 0.936108i
\(324\) 274503.i 0.145273i
\(325\) 68124.3 167731.i 0.0357761 0.0880854i
\(326\) 2.55227e6i 1.33010i
\(327\) 1.28040e6 + 1.28040e6i 0.662181 + 0.662181i
\(328\) 303701. + 303701.i 0.155870 + 0.155870i
\(329\) 822307. 0.418836
\(330\) 582112. + 421886.i 0.294254 + 0.213260i
\(331\) 103664. 0.0520067 0.0260034 0.999662i \(-0.491722\pi\)
0.0260034 + 0.999662i \(0.491722\pi\)
\(332\) −893506. 893506.i −0.444889 0.444889i
\(333\) 176119. + 176119.i 0.0870355 + 0.0870355i
\(334\) 1.13689e6i 0.557639i
\(335\) −2.06056e6 1.36656e6i −1.00317 0.665301i
\(336\) 342019.i 0.165273i
\(337\) 1.47688e6 + 1.47688e6i 0.708387 + 0.708387i 0.966196 0.257809i \(-0.0830006\pi\)
−0.257809 + 0.966196i \(0.583001\pi\)
\(338\) 1.06141e6 1.06141e6i 0.505347 0.505347i
\(339\) 1.30491e6i 0.616712i
\(340\) 760929. + 504648.i 0.356982 + 0.236751i
\(341\) −2.20818e6 2.39973e6i −1.02837 1.11758i
\(342\) 1.22057e6 1.22057e6i 0.564285 0.564285i
\(343\) 1.25413e6 1.25413e6i 0.575582 0.575582i
\(344\) 2.81312e6i 1.28172i
\(345\) −954493. + 193286.i −0.431743 + 0.0874284i
\(346\) −224823. −0.100960
\(347\) 1.35556e6 + 1.35556e6i 0.604358 + 0.604358i 0.941466 0.337108i \(-0.109449\pi\)
−0.337108 + 0.941466i \(0.609449\pi\)
\(348\) 40705.5 40705.5i 0.0180179 0.0180179i
\(349\) −3.89080e6 −1.70992 −0.854960 0.518695i \(-0.826418\pi\)
−0.854960 + 0.518695i \(0.826418\pi\)
\(350\) 727697. + 1.72309e6i 0.317527 + 0.751863i
\(351\) 193080.i 0.0836508i
\(352\) 82866.2 1.99343e6i 0.0356468 0.857522i
\(353\) 2.14991e6 + 2.14991e6i 0.918299 + 0.918299i 0.996906 0.0786071i \(-0.0250473\pi\)
−0.0786071 + 0.996906i \(0.525047\pi\)
\(354\) −76266.7 −0.0323465
\(355\) −379888. 1.87598e6i −0.159987 0.790055i
\(356\) −1.67722e6 −0.701401
\(357\) 866748. 866748.i 0.359933 0.359933i
\(358\) 965382. 965382.i 0.398100 0.398100i
\(359\) −2.36885e6 −0.970067 −0.485033 0.874496i \(-0.661193\pi\)
−0.485033 + 0.874496i \(0.661193\pi\)
\(360\) 1.08220e6 1.63179e6i 0.440101 0.663603i
\(361\) 2.97048e6 1.19966
\(362\) −295675. 295675.i −0.118589 0.118589i
\(363\) −965692. + 817206.i −0.384655 + 0.325511i
\(364\) 130521.i 0.0516330i
\(365\) 396222. + 262774.i 0.155671 + 0.103241i
\(366\) 1.09381e6 0.426816
\(367\) 2.46073e6 2.46073e6i 0.953672 0.953672i −0.0453010 0.998973i \(-0.514425\pi\)
0.998973 + 0.0453010i \(0.0144247\pi\)
\(368\) −465413. 465413.i −0.179151 0.179151i
\(369\) −403044. −0.154094
\(370\) −62183.9 307079.i −0.0236142 0.116613i
\(371\) 2.42574e6i 0.914974i
\(372\) 693117. 693117.i 0.259687 0.259687i
\(373\) 2.21059e6 2.21059e6i 0.822690 0.822690i −0.163803 0.986493i \(-0.552376\pi\)
0.986493 + 0.163803i \(0.0523760\pi\)
\(374\) 1.28141e6 1.17913e6i 0.473707 0.435895i
\(375\) −253764. + 1.34855e6i −0.0931862 + 0.495210i
\(376\) 1.08284e6i 0.394996i
\(377\) −19549.3 + 19549.3i −0.00708400 + 0.00708400i
\(378\) −1.41059e6 1.41059e6i −0.507776 0.507776i
\(379\) 1.51410e6i 0.541447i −0.962657 0.270724i \(-0.912737\pi\)
0.962657 0.270724i \(-0.0872630\pi\)
\(380\) 1.96359e6 397628.i 0.697575 0.141260i
\(381\) 1.46590e6i 0.517360i
\(382\) −1.63269e6 1.63269e6i −0.572462 0.572462i
\(383\) −1.34885e6 1.34885e6i −0.469857 0.469857i 0.432011 0.901868i \(-0.357804\pi\)
−0.901868 + 0.432011i \(0.857804\pi\)
\(384\) 295366. 0.102219
\(385\) −3.25027e6 + 518704.i −1.11755 + 0.178348i
\(386\) −2.10488e6 −0.719050
\(387\) −1.86665e6 1.86665e6i −0.633558 0.633558i
\(388\) 560900. + 560900.i 0.189150 + 0.189150i
\(389\) 1.61439e6i 0.540921i −0.962731 0.270461i \(-0.912824\pi\)
0.962731 0.270461i \(-0.0871760\pi\)
\(390\) 57359.3 86488.6i 0.0190960 0.0287937i
\(391\) 2.35891e6i 0.780313i
\(392\) −644557. 644557.i −0.211859 0.211859i
\(393\) 31140.8 31140.8i 0.0101707 0.0101707i
\(394\) 1.35953e6i 0.441213i
\(395\) 1.08065e6 + 5.33651e6i 0.348491 + 1.72094i
\(396\) 756546. + 822173.i 0.242436 + 0.263466i
\(397\) −1.63341e6 + 1.63341e6i −0.520137 + 0.520137i −0.917613 0.397476i \(-0.869886\pi\)
0.397476 + 0.917613i \(0.369886\pi\)
\(398\) −2.21377e6 + 2.21377e6i −0.700526 + 0.700526i
\(399\) 2.68958e6i 0.845769i
\(400\) −854358. + 360813.i −0.266987 + 0.112754i
\(401\) −3.39398e6 −1.05402 −0.527010 0.849859i \(-0.676687\pi\)
−0.527010 + 0.849859i \(0.676687\pi\)
\(402\) −1.00225e6 1.00225e6i −0.309321 0.309321i
\(403\) −332879. + 332879.i −0.102099 + 0.102099i
\(404\) −2.34004e6 −0.713296
\(405\) 198328. + 979391.i 0.0600822 + 0.296701i
\(406\) 285645.i 0.0860025i
\(407\) 550852. + 22898.7i 0.164835 + 0.00685211i
\(408\) 1.14136e6 + 1.14136e6i 0.339446 + 0.339446i
\(409\) −4.46788e6 −1.32067 −0.660333 0.750973i \(-0.729585\pi\)
−0.660333 + 0.750973i \(0.729585\pi\)
\(410\) 422524. + 280218.i 0.124134 + 0.0823258i
\(411\) −568923. −0.166130
\(412\) 1.17467e6 1.17467e6i 0.340936 0.340936i
\(413\) 246900. 246900.i 0.0712271 0.0712271i
\(414\) 1.64037e6 0.470372
\(415\) −3.83346e6 2.54235e6i −1.09262 0.724629i
\(416\) −288014. −0.0815981
\(417\) 162006. + 162006.i 0.0456238 + 0.0456238i
\(418\) 158696. 3.81761e6i 0.0444249 1.06869i
\(419\) 3.51858e6i 0.979112i 0.871972 + 0.489556i \(0.162841\pi\)
−0.871972 + 0.489556i \(0.837159\pi\)
\(420\) −196353. 969640.i −0.0543144 0.268218i
\(421\) 5.31362e6 1.46112 0.730559 0.682849i \(-0.239259\pi\)
0.730559 + 0.682849i \(0.239259\pi\)
\(422\) 629381. 629381.i 0.172041 0.172041i
\(423\) −718520. 718520.i −0.195249 0.195249i
\(424\) −3.19428e6 −0.862895
\(425\) 3.07950e6 + 1.25075e6i 0.827004 + 0.335890i
\(426\) 1.09724e6i 0.292940i
\(427\) −3.54102e6 + 3.54102e6i −0.939851 + 0.939851i
\(428\) −2.46293e6 + 2.46293e6i −0.649894 + 0.649894i
\(429\) 123657. + 134384.i 0.0324396 + 0.0352536i
\(430\) 659075. + 3.25467e6i 0.171895 + 0.848860i
\(431\) 1.57613e6i 0.408694i −0.978898 0.204347i \(-0.934493\pi\)
0.978898 0.204347i \(-0.0655071\pi\)
\(432\) 699412. 699412.i 0.180312 0.180312i
\(433\) −3.29284e6 3.29284e6i −0.844017 0.844017i 0.145361 0.989379i \(-0.453566\pi\)
−0.989379 + 0.145361i \(0.953566\pi\)
\(434\) 4.86385e6i 1.23953i
\(435\) 115822. 174641.i 0.0293473 0.0442511i
\(436\) 3.53999e6i 0.891837i
\(437\) 3.65993e6 + 3.65993e6i 0.916788 + 0.916788i
\(438\) 192720. + 192720.i 0.0480001 + 0.0480001i
\(439\) 4.51196e6 1.11739 0.558694 0.829374i \(-0.311302\pi\)
0.558694 + 0.829374i \(0.311302\pi\)
\(440\) −683044. 4.28004e6i −0.168197 1.05394i
\(441\) 855396. 0.209445
\(442\) −177751. 177751.i −0.0432769 0.0432769i
\(443\) 4.03065e6 + 4.03065e6i 0.975812 + 0.975812i 0.999714 0.0239020i \(-0.00760897\pi\)
−0.0239020 + 0.999714i \(0.507609\pi\)
\(444\) 165717.i 0.0398942i
\(445\) −5.98411e6 + 1.21179e6i −1.43252 + 0.290086i
\(446\) 199941.i 0.0475954i
\(447\) −1.74135e6 1.74135e6i −0.412208 0.412208i
\(448\) 3.08938e6 3.08938e6i 0.727237 0.727237i
\(449\) 7.25561e6i 1.69847i 0.528014 + 0.849235i \(0.322937\pi\)
−0.528014 + 0.849235i \(0.677063\pi\)
\(450\) 869763. 2.14147e6i 0.202474 0.498517i
\(451\) −656506. + 604103.i −0.151984 + 0.139852i
\(452\) 1.80388e6 1.80388e6i 0.415299 0.415299i
\(453\) −965899. + 965899.i −0.221150 + 0.221150i
\(454\) 787107.i 0.179223i
\(455\) 94301.2 + 465682.i 0.0213545 + 0.105453i
\(456\) 3.54171e6 0.797629
\(457\) 3.32290e6 + 3.32290e6i 0.744265 + 0.744265i 0.973396 0.229131i \(-0.0735884\pi\)
−0.229131 + 0.973396i \(0.573588\pi\)
\(458\) −1.67960e6 + 1.67960e6i −0.374146 + 0.374146i
\(459\) −3.54491e6 −0.785369
\(460\) 1.58666e6 + 1.05227e6i 0.349615 + 0.231864i
\(461\) 748252.i 0.163982i −0.996633 0.0819909i \(-0.973872\pi\)
0.996633 0.0819909i \(-0.0261278\pi\)
\(462\) −1.88518e6 78366.0i −0.410911 0.0170814i
\(463\) 4.39822e6 + 4.39822e6i 0.953509 + 0.953509i 0.998966 0.0454573i \(-0.0144745\pi\)
−0.0454573 + 0.998966i \(0.514475\pi\)
\(464\) 141631. 0.0305395
\(465\) 1.97217e6 2.97372e6i 0.422973 0.637776i
\(466\) −1.63532e6 −0.348850
\(467\) −694029. + 694029.i −0.147260 + 0.147260i −0.776893 0.629633i \(-0.783205\pi\)
0.629633 + 0.776893i \(0.283205\pi\)
\(468\) 114048. 114048.i 0.0240697 0.0240697i
\(469\) 6.48919e6 1.36225
\(470\) 253694. + 1.25280e6i 0.0529743 + 0.261600i
\(471\) −1.79261e6 −0.372335
\(472\) 325124. + 325124.i 0.0671730 + 0.0671730i
\(473\) −5.83838e6 242699.i −1.19988 0.0498786i
\(474\) 3.12127e6i 0.638095i
\(475\) 6.71852e6 2.83737e6i 1.36628 0.577008i
\(476\) −2.39634e6 −0.484765
\(477\) 2.11958e6 2.11958e6i 0.426533 0.426533i
\(478\) 4.58438e6 + 4.58438e6i 0.917721 + 0.917721i
\(479\) 4.12849e6 0.822153 0.411076 0.911601i \(-0.365153\pi\)
0.411076 + 0.911601i \(0.365153\pi\)
\(480\) 2.13965e6 433281.i 0.423877 0.0858355i
\(481\) 79587.8i 0.0156850i
\(482\) −1.49986e6 + 1.49986e6i −0.294058 + 0.294058i
\(483\) 1.80731e6 1.80731e6i 0.352505 0.352505i
\(484\) 2.46463e6 + 205262.i 0.478232 + 0.0398286i
\(485\) 2.40646e6 + 1.59597e6i 0.464542 + 0.308084i
\(486\) 3.87691e6i 0.744552i
\(487\) −2.14733e6 + 2.14733e6i −0.410277 + 0.410277i −0.881835 0.471558i \(-0.843692\pi\)
0.471558 + 0.881835i \(0.343692\pi\)
\(488\) −4.66292e6 4.66292e6i −0.886356 0.886356i
\(489\) 4.91419e6i 0.929352i
\(490\) −896739. 594717.i −0.168724 0.111897i
\(491\) 8.67245e6i 1.62345i −0.584042 0.811723i \(-0.698530\pi\)
0.584042 0.811723i \(-0.301470\pi\)
\(492\) −189619. 189619.i −0.0353159 0.0353159i
\(493\) −358922. 358922.i −0.0665093 0.0665093i
\(494\) −551573. −0.101692
\(495\) 3.29327e6 + 2.38680e6i 0.604108 + 0.437828i
\(496\) 2.41163e6 0.440156
\(497\) 3.55213e6 + 3.55213e6i 0.645056 + 0.645056i
\(498\) −1.86458e6 1.86458e6i −0.336904 0.336904i
\(499\) 5.93754e6i 1.06747i −0.845652 0.533735i \(-0.820788\pi\)
0.845652 0.533735i \(-0.179212\pi\)
\(500\) 2.21500e6 1.51341e6i 0.396232 0.270727i
\(501\) 2.18899e6i 0.389628i
\(502\) 203876. + 203876.i 0.0361083 + 0.0361083i
\(503\) 977755. 977755.i 0.172310 0.172310i −0.615684 0.787993i \(-0.711120\pi\)
0.787993 + 0.615684i \(0.211120\pi\)
\(504\) 5.13889e6i 0.901141i
\(505\) −8.34895e6 + 1.69067e6i −1.45681 + 0.295006i
\(506\) 2.67195e6 2.45868e6i 0.463930 0.426899i
\(507\) −2.04365e6 + 2.04365e6i −0.353092 + 0.353092i
\(508\) 2.02643e6 2.02643e6i 0.348395 0.348395i
\(509\) 5.91467e6i 1.01190i 0.862564 + 0.505948i \(0.168857\pi\)
−0.862564 + 0.505948i \(0.831143\pi\)
\(510\) 1.58791e6 + 1.05310e6i 0.270334 + 0.179286i
\(511\) −1.24779e6 −0.211393
\(512\) 2.34067e6 + 2.34067e6i 0.394608 + 0.394608i
\(513\) −5.50005e6 + 5.50005e6i −0.922728 + 0.922728i
\(514\) 6.96991e6 1.16364
\(515\) 3.34237e6 5.03976e6i 0.555311 0.837321i
\(516\) 1.75640e6i 0.290402i
\(517\) −2.24733e6 93420.6i −0.369778 0.0153715i
\(518\) 581447. + 581447.i 0.0952107 + 0.0952107i
\(519\) 432878. 0.0705419
\(520\) −613223. + 124178.i −0.0994512 + 0.0201390i
\(521\) −3.44763e6 −0.556451 −0.278225 0.960516i \(-0.589746\pi\)
−0.278225 + 0.960516i \(0.589746\pi\)
\(522\) −249592. + 249592.i −0.0400917 + 0.0400917i
\(523\) 179722. 179722.i 0.0287308 0.0287308i −0.692595 0.721326i \(-0.743533\pi\)
0.721326 + 0.692595i \(0.243533\pi\)
\(524\) −86096.6 −0.0136980
\(525\) −1.40112e6 3.31768e6i −0.221860 0.525335i
\(526\) 5.15675e6 0.812665
\(527\) −6.11158e6 6.11158e6i −0.958577 0.958577i
\(528\) 38856.1 934725.i 0.00606560 0.145915i
\(529\) 1.51763e6i 0.235791i
\(530\) −3.69566e6 + 748376.i −0.571482 + 0.115726i
\(531\) −431475. −0.0664079
\(532\) −3.71800e6 + 3.71800e6i −0.569549 + 0.569549i
\(533\) 91067.1 + 91067.1i 0.0138849 + 0.0138849i
\(534\) −3.50005e6 −0.531154
\(535\) −7.00794e6 + 1.05669e7i −1.05854 + 1.59610i
\(536\) 8.54514e6i 1.28472i
\(537\) −1.85877e6 + 1.85877e6i −0.278156 + 0.278156i
\(538\) −2.79775e6 + 2.79775e6i −0.416729 + 0.416729i
\(539\) 1.39333e6 1.28211e6i 0.206577 0.190088i
\(540\) −1.58133e6 + 2.38440e6i −0.233367 + 0.351880i
\(541\) 1.06366e7i 1.56247i −0.624237 0.781235i \(-0.714590\pi\)
0.624237 0.781235i \(-0.285410\pi\)
\(542\) −3.18306e6 + 3.18306e6i −0.465422 + 0.465422i
\(543\) 569299. + 569299.i 0.0828592 + 0.0828592i
\(544\) 5.28787e6i 0.766097i
\(545\) −2.55763e6 1.26302e7i −0.368847 1.82146i
\(546\) 272373.i 0.0391005i
\(547\) 2.27156e6 + 2.27156e6i 0.324606 + 0.324606i 0.850531 0.525925i \(-0.176281\pi\)
−0.525925 + 0.850531i \(0.676281\pi\)
\(548\) 786465. + 786465.i 0.111874 + 0.111874i
\(549\) 6.18819e6 0.876260
\(550\) −1.79301e6 4.79182e6i −0.252741 0.675451i
\(551\) −1.11376e6 −0.156283
\(552\) 2.37992e6 + 2.37992e6i 0.332441 + 0.332441i
\(553\) −1.01046e7 1.01046e7i −1.40509 1.40509i
\(554\) 982178.i 0.135962i
\(555\) 119730. + 591256.i 0.0164995 + 0.0814785i
\(556\) 447906.i 0.0614469i
\(557\) −3.46671e6 3.46671e6i −0.473456 0.473456i 0.429575 0.903031i \(-0.358663\pi\)
−0.903031 + 0.429575i \(0.858663\pi\)
\(558\) −4.24996e6 + 4.24996e6i −0.577829 + 0.577829i
\(559\) 843535.i 0.114176i
\(560\) 1.34529e6 2.02848e6i 0.181278 0.273338i
\(561\) −2.46726e6 + 2.27032e6i −0.330984 + 0.304565i
\(562\) −43052.2 + 43052.2i −0.00574983 + 0.00574983i
\(563\) −3.54634e6 + 3.54634e6i −0.471530 + 0.471530i −0.902409 0.430880i \(-0.858203\pi\)
0.430880 + 0.902409i \(0.358203\pi\)
\(564\) 676082.i 0.0894956i
\(565\) 5.13270e6 7.73929e6i 0.676433 1.01995i
\(566\) −381365. −0.0500379
\(567\) −1.85445e6 1.85445e6i −0.242247 0.242247i
\(568\) −4.67754e6 + 4.67754e6i −0.608340 + 0.608340i
\(569\) 3.69527e6 0.478482 0.239241 0.970960i \(-0.423101\pi\)
0.239241 + 0.970960i \(0.423101\pi\)
\(570\) 4.09763e6 829774.i 0.528257 0.106973i
\(571\) 57926.4i 0.00743509i 0.999993 + 0.00371754i \(0.00118333\pi\)
−0.999993 + 0.00371754i \(0.998817\pi\)
\(572\) 14828.2 356709.i 0.00189496 0.0455853i
\(573\) 3.14362e6 + 3.14362e6i 0.399985 + 0.399985i
\(574\) −1.33062e6 −0.168568
\(575\) 6.42126e6 + 2.60801e6i 0.809935 + 0.328958i
\(576\) −5.39891e6 −0.678032
\(577\) −4.07236e6 + 4.07236e6i −0.509222 + 0.509222i −0.914288 0.405066i \(-0.867249\pi\)
0.405066 + 0.914288i \(0.367249\pi\)
\(578\) −832467. + 832467.i −0.103645 + 0.103645i
\(579\) 4.05278e6 0.502408
\(580\) −401529. + 81310.2i −0.0495618 + 0.0100363i
\(581\) 1.20725e7 1.48373
\(582\) 1.17049e6 + 1.17049e6i 0.143239 + 0.143239i
\(583\) 275583. 6.62945e6i 0.0335800 0.807804i
\(584\) 1.64313e6i 0.199361i
\(585\) 324507. 489305.i 0.0392044 0.0591140i
\(586\) −9.22622e6 −1.10989
\(587\) 9.28769e6 9.28769e6i 1.11253 1.11253i 0.119725 0.992807i \(-0.461799\pi\)
0.992807 0.119725i \(-0.0382013\pi\)
\(588\) 402437. + 402437.i 0.0480014 + 0.0480014i
\(589\) −1.89646e7 −2.25246
\(590\) 452329. + 299985.i 0.0534964 + 0.0354788i
\(591\) 2.61767e6i 0.308280i
\(592\) −288298. + 288298.i −0.0338094 + 0.0338094i
\(593\) −8.14113e6 + 8.14113e6i −0.950710 + 0.950710i −0.998841 0.0481307i \(-0.984674\pi\)
0.0481307 + 0.998841i \(0.484674\pi\)
\(594\) 3.69484e6 + 4.01535e6i 0.429665 + 0.466936i
\(595\) −8.54982e6 + 1.73135e6i −0.990067 + 0.200490i
\(596\) 4.81439e6i 0.555169i
\(597\) 4.26243e6 4.26243e6i 0.489465 0.489465i
\(598\) −370640. 370640.i −0.0423837 0.0423837i
\(599\) 9.35621e6i 1.06545i 0.846288 + 0.532725i \(0.178832\pi\)
−0.846288 + 0.532725i \(0.821168\pi\)
\(600\) 4.36881e6 1.84504e6i 0.495433 0.209232i
\(601\) 3.08695e6i 0.348612i −0.984692 0.174306i \(-0.944232\pi\)
0.984692 0.174306i \(-0.0557682\pi\)
\(602\) −6.16265e6 6.16265e6i −0.693068 0.693068i
\(603\) −5.67016e6 5.67016e6i −0.635042 0.635042i
\(604\) 2.67047e6 0.297848
\(605\) 8.94178e6 1.04834e6i 0.993197 0.116443i
\(606\) −4.88322e6 −0.540162
\(607\) 8.54411e6 + 8.54411e6i 0.941229 + 0.941229i 0.998366 0.0571376i \(-0.0181974\pi\)
−0.0571376 + 0.998366i \(0.518197\pi\)
\(608\) −8.20431e6 8.20431e6i −0.900084 0.900084i
\(609\) 549986.i 0.0600908i
\(610\) −6.48728e6 4.30236e6i −0.705892 0.468147i
\(611\) 324697.i 0.0351864i
\(612\) 2.09389e6 + 2.09389e6i 0.225983 + 0.225983i
\(613\) −795336. + 795336.i −0.0854868 + 0.0854868i −0.748557 0.663070i \(-0.769253\pi\)
0.663070 + 0.748557i \(0.269253\pi\)
\(614\) 5.93673e6i 0.635516i
\(615\) −813536. 539537.i −0.0867339 0.0575219i
\(616\) 7.70243e6 + 8.37058e6i 0.817855 + 0.888800i
\(617\) 8.54656e6 8.54656e6i 0.903813 0.903813i −0.0919506 0.995764i \(-0.529310\pi\)
0.995764 + 0.0919506i \(0.0293102\pi\)
\(618\) 2.45131e6 2.45131e6i 0.258183 0.258183i
\(619\) 1.12492e7i 1.18003i 0.807392 + 0.590016i \(0.200879\pi\)
−0.807392 + 0.590016i \(0.799121\pi\)
\(620\) −6.83709e6 + 1.38452e6i −0.714318 + 0.144650i
\(621\) −7.39172e6 −0.769160
\(622\) 5.66297e6 + 5.66297e6i 0.586905 + 0.586905i
\(623\) 1.13308e7 1.13308e7i 1.16961 1.16961i
\(624\) −135050. −0.0138846
\(625\) 6.80940e6 6.99997e6i 0.697282 0.716797i
\(626\) 8.14718e6i 0.830944i
\(627\) −305557. + 7.35051e6i −0.0310402 + 0.746704i
\(628\) 2.47806e6 + 2.47806e6i 0.250734 + 0.250734i
\(629\) 1.46121e6 0.147261
\(630\) 1.20397e6 + 5.94550e6i 0.120855 + 0.596811i
\(631\) 1.09646e7 1.09628 0.548139 0.836387i \(-0.315337\pi\)
0.548139 + 0.836387i \(0.315337\pi\)
\(632\) 1.33060e7 1.33060e7i 1.32512 1.32512i
\(633\) −1.21182e6 + 1.21182e6i −0.120207 + 0.120207i
\(634\) 3.04276e6 0.300639
\(635\) 5.76593e6 8.69410e6i 0.567460 0.855639i
\(636\) 1.99439e6 0.195509
\(637\) −193275. 193275.i −0.0188724 0.0188724i
\(638\) −32451.5 + 780655.i −0.00315633 + 0.0759290i
\(639\) 6.20760e6i 0.601411i
\(640\) −1.75178e6 1.16178e6i −0.169056 0.112118i
\(641\) 1.14621e7 1.10184 0.550922 0.834557i \(-0.314276\pi\)
0.550922 + 0.834557i \(0.314276\pi\)
\(642\) −5.13966e6 + 5.13966e6i −0.492149 + 0.492149i
\(643\) 1.26161e7 + 1.26161e7i 1.20337 + 1.20337i 0.973135 + 0.230235i \(0.0739496\pi\)
0.230235 + 0.973135i \(0.426050\pi\)
\(644\) −4.99676e6 −0.474760
\(645\) −1.26900e6 6.26661e6i −0.120105 0.593108i
\(646\) 1.01268e7i 0.954749i
\(647\) −1.04760e7 + 1.04760e7i −0.983863 + 0.983863i −0.999872 0.0160092i \(-0.994904\pi\)
0.0160092 + 0.999872i \(0.494904\pi\)
\(648\) 2.44200e6 2.44200e6i 0.228459 0.228459i
\(649\) −702817. + 646718.i −0.0654984 + 0.0602703i
\(650\) −680383. + 287340.i −0.0631640 + 0.0266755i
\(651\) 9.36495e6i 0.866070i
\(652\) −6.79326e6 + 6.79326e6i −0.625834 + 0.625834i
\(653\) 7.16606e6 + 7.16606e6i 0.657654 + 0.657654i 0.954824 0.297170i \(-0.0960429\pi\)
−0.297170 + 0.954824i \(0.596043\pi\)
\(654\) 7.38728e6i 0.675367i
\(655\) −307181. + 62204.5i −0.0279764 + 0.00566524i
\(656\) 659761.i 0.0598587i
\(657\) 1.09031e6 + 1.09031e6i 0.0985451 + 0.0985451i
\(658\) −2.37215e6 2.37215e6i −0.213588 0.213588i
\(659\) 3.23080e6 0.289799 0.144900 0.989446i \(-0.453714\pi\)
0.144900 + 0.989446i \(0.453714\pi\)
\(660\) 426467. + 2.67229e6i 0.0381088 + 0.238795i
\(661\) −933367. −0.0830900 −0.0415450 0.999137i \(-0.513228\pi\)
−0.0415450 + 0.999137i \(0.513228\pi\)
\(662\) −299046. 299046.i −0.0265212 0.0265212i
\(663\) 342245. + 342245.i 0.0302380 + 0.0302380i
\(664\) 1.58973e7i 1.39928i
\(665\) −1.05791e7 + 1.59516e7i −0.927672 + 1.39878i
\(666\) 1.01612e6i 0.0887687i
\(667\) −748410. 748410.i −0.0651366 0.0651366i
\(668\) 3.02601e6 3.02601e6i 0.262379 0.262379i
\(669\) 384971.i 0.0332554i
\(670\) 2.00201e6 + 9.88641e6i 0.172298 + 0.850847i
\(671\) 1.00798e7 9.27519e6i 0.864260 0.795274i
\(672\) −4.05138e6 + 4.05138e6i −0.346082 + 0.346082i
\(673\) 1.28117e6 1.28117e6i 0.109036 0.109036i −0.650484 0.759520i \(-0.725434\pi\)
0.759520 + 0.650484i \(0.225434\pi\)
\(674\) 8.52086e6i 0.722493i
\(675\) −3.91926e6 + 9.64972e6i −0.331089 + 0.815183i
\(676\) 5.65019e6 0.475550
\(677\) −9.10030e6 9.10030e6i −0.763105 0.763105i 0.213778 0.976882i \(-0.431423\pi\)
−0.976882 + 0.213778i \(0.931423\pi\)
\(678\) 3.76435e6 3.76435e6i 0.314496 0.314496i
\(679\) −7.57851e6 −0.630825
\(680\) −2.27989e6 1.12586e7i −0.189078 0.933714i
\(681\) 1.51551e6i 0.125225i
\(682\) −552571. + 1.32927e7i −0.0454912 + 1.09434i
\(683\) −2.56185e6 2.56185e6i −0.210136 0.210136i 0.594189 0.804325i \(-0.297473\pi\)
−0.804325 + 0.594189i \(0.797473\pi\)
\(684\) 6.49748e6 0.531012
\(685\) 3.37422e6 + 2.23778e6i 0.274756 + 0.182218i
\(686\) −7.23571e6 −0.587044
\(687\) 3.23393e6 3.23393e6i 0.261420 0.261420i
\(688\) 3.05561e6 3.05561e6i 0.246109 0.246109i
\(689\) −957829. −0.0768670
\(690\) 3.31106e6 + 2.19589e6i 0.264755 + 0.175585i
\(691\) −1.42077e7 −1.13195 −0.565977 0.824421i \(-0.691501\pi\)
−0.565977 + 0.824421i \(0.691501\pi\)
\(692\) −598399. 598399.i −0.0475035 0.0475035i
\(693\) −1.06653e7 443352.i −0.843608 0.0350684i
\(694\) 7.82089e6i 0.616393i
\(695\) −323611. 1.59807e6i −0.0254133 0.125497i
\(696\) −724237. −0.0566705
\(697\) −1.67197e6 + 1.67197e6i −0.130361 + 0.130361i
\(698\) 1.12240e7 + 1.12240e7i 0.871985 + 0.871985i
\(699\) 3.14868e6 0.243745
\(700\) −2.64940e6 + 6.52315e6i −0.204363 + 0.503167i
\(701\) 5.09542e6i 0.391638i 0.980640 + 0.195819i \(0.0627365\pi\)
−0.980640 + 0.195819i \(0.937264\pi\)
\(702\) 556989. 556989.i 0.0426583 0.0426583i
\(703\) 2.26712e6 2.26712e6i 0.173016 0.173016i
\(704\) −8.79413e6 + 8.09217e6i −0.668746 + 0.615366i
\(705\) −488467. 2.41217e6i −0.0370137 0.182783i
\(706\) 1.24039e7i 0.936585i
\(707\) 1.58085e7 1.58085e7i 1.18944 1.18944i
\(708\) −202995. 202995.i −0.0152196 0.0152196i
\(709\) 1.06450e7i 0.795298i −0.917538 0.397649i \(-0.869826\pi\)
0.917538 0.397649i \(-0.130174\pi\)
\(710\) −4.31586e6 + 6.50762e6i −0.321308 + 0.484481i
\(711\) 1.76584e7i 1.31002i
\(712\) 1.49207e7 + 1.49207e7i 1.10303 + 1.10303i
\(713\) −1.27436e7 1.27436e7i −0.938793 0.938793i
\(714\) −5.00071e6 −0.367101
\(715\) −204816. 1.28340e6i −0.0149830 0.0938855i
\(716\) 5.13902e6 0.374626
\(717\) −8.82685e6 8.82685e6i −0.641221 0.641221i
\(718\) 6.83355e6 + 6.83355e6i 0.494692 + 0.494692i
\(719\) 1.91481e6i 0.138135i −0.997612 0.0690675i \(-0.977998\pi\)
0.997612 0.0690675i \(-0.0220024\pi\)
\(720\) −2.94795e6 + 596963.i −0.211928 + 0.0429157i
\(721\) 1.58714e7i 1.13704i
\(722\) −8.56909e6 8.56909e6i −0.611775 0.611775i
\(723\) 2.88786e6 2.88786e6i 0.205462 0.205462i
\(724\) 1.57397e6i 0.111596i
\(725\) −1.37386e6 + 580207.i −0.0970725 + 0.0409957i
\(726\) 5.14322e6 + 428343.i 0.362154 + 0.0301613i
\(727\) 2.86558e6 2.86558e6i 0.201084 0.201084i −0.599380 0.800464i \(-0.704586\pi\)
0.800464 + 0.599380i \(0.204586\pi\)
\(728\) 1.16112e6 1.16112e6i 0.0811989 0.0811989i
\(729\) 3.12094e6i 0.217504i
\(730\) −384963. 1.90104e6i −0.0267370 0.132034i
\(731\) −1.54871e7 −1.07196
\(732\) 2.91135e6 + 2.91135e6i 0.200824 + 0.200824i
\(733\) −3.71404e6 + 3.71404e6i −0.255321 + 0.255321i −0.823148 0.567827i \(-0.807784\pi\)
0.567827 + 0.823148i \(0.307784\pi\)
\(734\) −1.41972e7 −0.972664
\(735\) 1.72660e6 + 1.14508e6i 0.117889 + 0.0781840i
\(736\) 1.10261e7i 0.750285i
\(737\) −1.77347e7 737223.i −1.20269 0.0499954i
\(738\) 1.16268e6 + 1.16268e6i 0.0785814 + 0.0785814i
\(739\) −361202. −0.0243298 −0.0121649 0.999926i \(-0.503872\pi\)
−0.0121649 + 0.999926i \(0.503872\pi\)
\(740\) 651826. 982849.i 0.0437575 0.0659793i
\(741\) 1.06201e6 0.0710531
\(742\) 6.99765e6 6.99765e6i 0.466597 0.466597i
\(743\) 1.41219e7 1.41219e7i 0.938471 0.938471i −0.0597430 0.998214i \(-0.519028\pi\)
0.998214 + 0.0597430i \(0.0190281\pi\)
\(744\) −1.23320e7 −0.816774
\(745\) 3.47838e6 + 1.71771e7i 0.229608 + 1.13386i
\(746\) −1.27540e7 −0.839073
\(747\) −1.05487e7 1.05487e7i −0.691671 0.691671i
\(748\) 6.54911e6 + 272243.i 0.427985 + 0.0177911i
\(749\) 3.32775e7i 2.16743i
\(750\) 4.62229e6 3.15819e6i 0.300057 0.205015i
\(751\) 1.69707e7 1.09800 0.548998 0.835824i \(-0.315009\pi\)
0.548998 + 0.835824i \(0.315009\pi\)
\(752\) 1.17618e6 1.17618e6i 0.0758453 0.0758453i
\(753\) −392547. 392547.i −0.0252293 0.0252293i
\(754\) 112790. 0.00722507
\(755\) 9.52787e6 1.92941e6i 0.608315 0.123184i
\(756\) 7.50902e6i 0.477836i
\(757\) 8.98692e6 8.98692e6i 0.569995 0.569995i −0.362132 0.932127i \(-0.617951\pi\)
0.932127 + 0.362132i \(0.117951\pi\)
\(758\) −4.36780e6 + 4.36780e6i −0.276115 + 0.276115i
\(759\) −5.14464e6 + 4.73399e6i −0.324153 + 0.298279i
\(760\) −2.10055e7 1.39308e7i −1.31916 0.874870i
\(761\) 2.69339e7i 1.68592i 0.537973 + 0.842962i \(0.319190\pi\)
−0.537973 + 0.842962i \(0.680810\pi\)
\(762\) 4.22877e6 4.22877e6i 0.263831 0.263831i
\(763\) 2.39150e7 + 2.39150e7i 1.48716 + 1.48716i
\(764\) 8.69133e6i 0.538707i
\(765\) 8.98354e6 + 5.95789e6i 0.555001 + 0.368077i
\(766\) 7.78218e6i 0.479214i
\(767\) 97491.2 + 97491.2i 0.00598380 + 0.00598380i
\(768\) −6.14500e6 6.14500e6i −0.375940 0.375940i
\(769\) −202443. −0.0123449 −0.00617243 0.999981i \(-0.501965\pi\)
−0.00617243 + 0.999981i \(0.501965\pi\)
\(770\) 1.08725e7 + 7.87988e6i 0.660852 + 0.478953i
\(771\) −1.34200e7 −0.813049
\(772\) −5.60246e6 5.60246e6i −0.338326 0.338326i
\(773\) −1.15495e7 1.15495e7i −0.695208 0.695208i 0.268165 0.963373i \(-0.413583\pi\)
−0.963373 + 0.268165i \(0.913583\pi\)
\(774\) 1.07697e7i 0.646175i
\(775\) −2.33935e7 + 9.87955e6i −1.39907 + 0.590858i
\(776\) 9.97959e6i 0.594920i
\(777\) −1.11953e6 1.11953e6i −0.0665247 0.0665247i
\(778\) −4.65711e6 + 4.65711e6i −0.275847 + 0.275847i
\(779\) 5.18825e6i 0.306321i
\(780\) 382873. 77532.3i 0.0225330 0.00456295i
\(781\) −9.30427e6 1.01114e7i −0.545827 0.593175i
\(782\) 6.80486e6 6.80486e6i 0.397926 0.397926i
\(783\) 1.12469e6 1.12469e6i 0.0655586 0.0655586i
\(784\) 1.40024e6i 0.0813601i
\(785\) 1.06318e7 + 7.05099e6i 0.615789 + 0.408391i
\(786\) −179667. −0.0103732
\(787\) 4.00932e6 + 4.00932e6i 0.230746 + 0.230746i 0.813004 0.582258i \(-0.197831\pi\)
−0.582258 + 0.813004i \(0.697831\pi\)
\(788\) 3.61860e6 3.61860e6i 0.207599 0.207599i
\(789\) −9.92891e6 −0.567818
\(790\) 1.22771e7 1.85119e7i 0.699887 1.05532i
\(791\) 2.43728e7i 1.38505i
\(792\) 583818. 1.40444e7i 0.0330723 0.795590i
\(793\) −1.39821e6 1.39821e6i −0.0789569 0.0789569i
\(794\) 9.42394e6 0.530495
\(795\) 7.11570e6 1.44094e6i 0.399300 0.0808588i
\(796\) −1.17846e7 −0.659220
\(797\) −3.11217e6 + 3.11217e6i −0.173547 + 0.173547i −0.788536 0.614989i \(-0.789160\pi\)
0.614989 + 0.788536i \(0.289160\pi\)
\(798\) −7.75876e6 + 7.75876e6i −0.431306 + 0.431306i
\(799\) −5.96137e6 −0.330354
\(800\) −1.43943e7 5.84628e6i −0.795179 0.322964i
\(801\) −1.98014e7 −1.09047
\(802\) 9.79080e6 + 9.79080e6i 0.537505 + 0.537505i
\(803\) 3.41018e6 + 141759.i 0.186633 + 0.00775824i
\(804\) 5.33526e6i 0.291082i
\(805\) −1.78278e7 + 3.61015e6i −0.969633 + 0.196352i
\(806\) 1.92054e6 0.104133
\(807\) 5.38685e6 5.38685e6i 0.291173 0.291173i
\(808\) 2.08171e7 + 2.08171e7i 1.12174 + 1.12174i
\(809\) 3.41033e7 1.83200 0.915998 0.401182i \(-0.131400\pi\)
0.915998 + 0.401182i \(0.131400\pi\)
\(810\) 2.25317e6 3.39743e6i 0.120665 0.181944i
\(811\) 1.41485e7i 0.755367i −0.925935 0.377683i \(-0.876721\pi\)
0.925935 0.377683i \(-0.123279\pi\)
\(812\) 760286. 760286.i 0.0404657 0.0404657i
\(813\) 6.12873e6 6.12873e6i 0.325195 0.325195i
\(814\) −1.52302e6 1.65513e6i −0.0805644 0.0875530i
\(815\) −1.93293e7 + 2.91455e7i −1.01935 + 1.53701i
\(816\) 2.47949e6i 0.130358i
\(817\) −2.40288e7 + 2.40288e7i −1.25944 + 1.25944i
\(818\) 1.28887e7 + 1.28887e7i 0.673483 + 0.673483i
\(819\) 1.54094e6i 0.0802740i
\(820\) 378769. + 1.87045e6i 0.0196716 + 0.0971432i
\(821\) 426503.i 0.0220833i −0.999939 0.0110416i \(-0.996485\pi\)
0.999939 0.0110416i \(-0.00351474\pi\)
\(822\) 1.64120e6 + 1.64120e6i 0.0847193 + 0.0847193i
\(823\) −1.23191e7 1.23191e7i −0.633985 0.633985i 0.315080 0.949065i \(-0.397969\pi\)
−0.949065 + 0.315080i \(0.897969\pi\)
\(824\) −2.08999e7 −1.07232
\(825\) 3.45230e6 + 9.22627e6i 0.176593 + 0.471945i
\(826\) −1.42449e6 −0.0726456
\(827\) −2.45123e7 2.45123e7i −1.24630 1.24630i −0.957344 0.288951i \(-0.906693\pi\)
−0.288951 0.957344i \(-0.593307\pi\)
\(828\) 4.36610e6 + 4.36610e6i 0.221319 + 0.221319i
\(829\) 3.31255e6i 0.167408i 0.996491 + 0.0837039i \(0.0266750\pi\)
−0.996491 + 0.0837039i \(0.973325\pi\)
\(830\) 3.72453e6 + 1.83926e7i 0.187662 + 0.926721i
\(831\) 1.89111e6i 0.0949978i
\(832\) 1.21988e6 + 1.21988e6i 0.0610952 + 0.0610952i
\(833\) 3.54850e6 3.54850e6i 0.177187 0.177187i
\(834\) 934695.i 0.0465323i
\(835\) 8.61011e6 1.29827e7i 0.427359 0.644389i
\(836\) 1.05836e7 9.73877e6i 0.523740 0.481935i
\(837\) 1.91509e7 1.91509e7i 0.944875 0.944875i
\(838\) 1.01502e7 1.01502e7i 0.499305 0.499305i
\(839\) 7.51942e6i 0.368790i −0.982852 0.184395i \(-0.940967\pi\)
0.982852 0.184395i \(-0.0590326\pi\)
\(840\) −6.87920e6 + 1.03727e7i −0.336387 + 0.507219i
\(841\) −2.02834e7 −0.988896
\(842\) −1.53285e7 1.53285e7i −0.745108 0.745108i
\(843\) 82893.7 82893.7i 0.00401747 0.00401747i
\(844\) 3.35039e6 0.161897
\(845\) 2.01591e7 4.08225e6i 0.971247 0.196679i
\(846\) 4.14550e6i 0.199137i
\(847\) −1.80369e7 + 1.52636e7i −0.863882 + 0.731051i
\(848\) 3.46963e6 + 3.46963e6i 0.165689 + 0.165689i
\(849\) 734287. 0.0349620
\(850\) −5.27549e6 1.24917e7i −0.250447 0.593026i
\(851\) 3.04687e6 0.144222
\(852\) 2.92048e6 2.92048e6i 0.137834 0.137834i
\(853\) −4.14004e6 + 4.14004e6i −0.194820 + 0.194820i −0.797775 0.602955i \(-0.793990\pi\)
0.602955 + 0.797775i \(0.293990\pi\)
\(854\) 2.04299e7 0.958567
\(855\) 2.31821e7 4.69441e6i 1.08452 0.219617i
\(856\) 4.38207e7 2.04407
\(857\) 2.93533e7 + 2.93533e7i 1.36523 + 1.36523i 0.867108 + 0.498120i \(0.165976\pi\)
0.498120 + 0.867108i \(0.334024\pi\)
\(858\) 30943.7 744384.i 0.00143501 0.0345206i
\(859\) 3.26018e7i 1.50750i −0.657160 0.753751i \(-0.728242\pi\)
0.657160 0.753751i \(-0.271758\pi\)
\(860\) −6.90858e6 + 1.04170e7i −0.318524 + 0.480284i
\(861\) 2.56201e6 0.117780
\(862\) −4.54674e6 + 4.54674e6i −0.208417 + 0.208417i
\(863\) 1.82172e7 + 1.82172e7i 0.832636 + 0.832636i 0.987877 0.155241i \(-0.0496153\pi\)
−0.155241 + 0.987877i \(0.549615\pi\)
\(864\) 1.65697e7 0.755146
\(865\) −2.56735e6 1.70267e6i −0.116666 0.0773730i
\(866\) 1.89981e7i 0.860825i
\(867\) 1.60285e6 1.60285e6i 0.0724177 0.0724177i
\(868\) 1.29459e7 1.29459e7i 0.583219 0.583219i
\(869\) 2.64674e7 + 2.87633e7i 1.18895 + 1.29208i
\(870\) −837915. + 169679.i −0.0375320 + 0.00760028i
\(871\) 2.56233e6i 0.114443i
\(872\) −3.14919e7 + 3.14919e7i −1.40252 + 1.40252i
\(873\) 6.62199e6 + 6.62199e6i 0.294072 + 0.294072i
\(874\) 2.11160e7i 0.935044i
\(875\) −4.73974e6 + 2.51879e7i −0.209283 + 1.11217i
\(876\) 1.02591e6i 0.0451698i
\(877\) −2.48426e7 2.48426e7i −1.09068 1.09068i −0.995456 0.0952252i \(-0.969643\pi\)
−0.0952252 0.995456i \(-0.530357\pi\)
\(878\) −1.30159e7 1.30159e7i −0.569820 0.569820i
\(879\) 1.77643e7 0.775491
\(880\) −3.90706e6 + 5.39091e6i −0.170076 + 0.234669i
\(881\) −2.11393e7 −0.917597 −0.458798 0.888540i \(-0.651720\pi\)
−0.458798 + 0.888540i \(0.651720\pi\)
\(882\) −2.46761e6 2.46761e6i −0.106808 0.106808i
\(883\) −1.39827e7 1.39827e7i −0.603516 0.603516i 0.337728 0.941244i \(-0.390342\pi\)
−0.941244 + 0.337728i \(0.890342\pi\)
\(884\) 946222.i 0.0407251i
\(885\) −870924. 577597.i −0.0373785 0.0247894i
\(886\) 2.32549e7i 0.995244i
\(887\) 2.11639e7 + 2.11639e7i 0.903205 + 0.903205i 0.995712 0.0925066i \(-0.0294879\pi\)
−0.0925066 + 0.995712i \(0.529488\pi\)
\(888\) 1.47423e6 1.47423e6i 0.0627382 0.0627382i
\(889\) 2.73797e7i 1.16192i
\(890\) 2.07584e7 + 1.37670e7i 0.878453 + 0.582590i
\(891\) 4.85747e6 + 5.27883e6i 0.204982 + 0.222763i
\(892\) 532174. 532174.i 0.0223945 0.0223945i
\(893\) −9.24927e6 + 9.24927e6i −0.388131 + 0.388131i
\(894\) 1.00467e7i 0.420416i
\(895\) 1.83353e7 3.71293e6i 0.765123 0.154938i
\(896\) 5.51677e6 0.229570
\(897\) 713637. + 713637.i 0.0296139 + 0.0296139i
\(898\) 2.09306e7 2.09306e7i 0.866147 0.866147i
\(899\) 3.87804e6 0.160034
\(900\) 8.01485e6 3.38483e6i 0.329829 0.139294i
\(901\) 1.75855e7i 0.721679i
\(902\) 3.63655e6 + 151170.i 0.148824 + 0.00618654i
\(903\) 1.18657e7 + 1.18657e7i 0.484254 + 0.484254i
\(904\) −3.20948e7 −1.30621
\(905\) −1.13719e6 5.61571e6i −0.0461541 0.227920i
\(906\) 5.57276e6 0.225554
\(907\) 1.80897e7 1.80897e7i 0.730152 0.730152i −0.240498 0.970650i \(-0.577311\pi\)
0.970650 + 0.240498i \(0.0773107\pi\)
\(908\) −2.09501e6 + 2.09501e6i −0.0843277 + 0.0843277i
\(909\) −2.76266e7 −1.10896
\(910\) 1.07134e6 1.61541e6i 0.0428869 0.0646666i
\(911\) −5.34182e6 −0.213252 −0.106626 0.994299i \(-0.534005\pi\)
−0.106626 + 0.994299i \(0.534005\pi\)
\(912\) −3.84701e6 3.84701e6i −0.153157 0.153157i
\(913\) −3.29936e7 1.37153e6i −1.30994 0.0544537i
\(914\) 1.91715e7i 0.759086i
\(915\) 1.24907e7 + 8.28386e6i 0.493214 + 0.327100i
\(916\) −8.94101e6 −0.352085
\(917\) 581640. 581640.i 0.0228418 0.0228418i
\(918\) 1.02262e7 + 1.02262e7i 0.400504 + 0.400504i
\(919\) −2.14327e6 −0.0837121 −0.0418561 0.999124i \(-0.513327\pi\)
−0.0418561 + 0.999124i \(0.513327\pi\)
\(920\) −4.75394e6 2.34761e7i −0.185176 0.914443i
\(921\) 1.14307e7i 0.444042i
\(922\) −2.15852e6 + 2.15852e6i −0.0836237 + 0.0836237i
\(923\) −1.40260e6 + 1.40260e6i −0.0541912 + 0.0541912i
\(924\) −4.80911e6 5.22627e6i −0.185304 0.201378i
\(925\) 1.61552e6 3.97762e6i 0.0620809 0.152851i
\(926\) 2.53756e7i 0.972497i
\(927\) 1.38682e7 1.38682e7i 0.530054 0.530054i
\(928\) 1.67768e6 + 1.67768e6i 0.0639498 + 0.0639498i
\(929\) 1.07564e7i 0.408909i 0.978876 + 0.204454i \(0.0655420\pi\)
−0.978876 + 0.204454i \(0.934458\pi\)
\(930\) −1.42677e7 + 2.88922e6i −0.540937 + 0.109540i
\(931\) 1.10112e7i 0.416353i
\(932\) −4.35266e6 4.35266e6i −0.164140 0.164140i
\(933\) −1.09036e7 1.09036e7i −0.410077 0.410077i
\(934\) 4.00420e6 0.150193
\(935\) 2.35630e7 3.76038e6i 0.881459 0.140670i
\(936\) −2.02915e6 −0.0757049
\(937\) 2.67520e7 + 2.67520e7i 0.995424 + 0.995424i 0.999990 0.00456603i \(-0.00145342\pi\)
−0.00456603 + 0.999990i \(0.501453\pi\)
\(938\) −1.87197e7 1.87197e7i −0.694691 0.694691i
\(939\) 1.56867e7i 0.580589i
\(940\) −2.65928e6 + 4.00977e6i −0.0981621 + 0.148013i
\(941\) 1.84090e7i 0.677730i 0.940835 + 0.338865i \(0.110043\pi\)
−0.940835 + 0.338865i \(0.889957\pi\)
\(942\) 5.17124e6 + 5.17124e6i 0.189875 + 0.189875i
\(943\) −3.48634e6 + 3.48634e6i −0.127670 + 0.127670i
\(944\) 706302.i 0.0257965i
\(945\) −5.42524e6 2.67912e7i −0.197624 0.975916i
\(946\) 1.61421e7 + 1.75424e7i 0.586453 + 0.637325i
\(947\) 1.48200e7 1.48200e7i 0.537000 0.537000i −0.385647 0.922646i \(-0.626022\pi\)
0.922646 + 0.385647i \(0.126022\pi\)
\(948\) −8.30774e6 + 8.30774e6i −0.300235 + 0.300235i
\(949\) 492706.i 0.0177592i
\(950\) −2.75664e7 1.11962e7i −0.990993 0.402495i
\(951\) −5.85860e6 −0.210059
\(952\) 2.13180e7 + 2.13180e7i 0.762349 + 0.762349i
\(953\) −2.44828e7 + 2.44828e7i −0.873230 + 0.873230i −0.992823 0.119593i \(-0.961841\pi\)
0.119593 + 0.992823i \(0.461841\pi\)
\(954\) −1.22289e7 −0.435027
\(955\) −6.27946e6 3.10095e7i −0.222799 1.10024i
\(956\) 2.44040e7i 0.863609i
\(957\) 62482.7 1.50309e6i 0.00220536 0.0530524i
\(958\) −1.19097e7 1.19097e7i −0.419262 0.419262i
\(959\) −1.06262e7 −0.373105
\(960\) −1.08976e7 7.22728e6i −0.381639 0.253103i
\(961\) 3.74046e7 1.30652
\(962\) −229591. + 229591.i −0.00799866 + 0.00799866i
\(963\) −2.90774e7 + 2.90774e7i −1.01039 + 1.01039i
\(964\) −7.98421e6 −0.276719
\(965\) −2.40366e7 1.59411e7i −0.830911 0.551060i
\(966\) −1.04273e7 −0.359525
\(967\) −1.53148e7 1.53148e7i −0.526679 0.526679i 0.392901 0.919581i \(-0.371471\pi\)
−0.919581 + 0.392901i \(0.871471\pi\)
\(968\) −2.00995e7 2.37515e7i −0.689440 0.814710i
\(969\) 1.94983e7i 0.667094i
\(970\) −2.33808e6 1.15460e7i −0.0797867 0.394006i
\(971\) 2.59371e7 0.882823 0.441412 0.897305i \(-0.354478\pi\)
0.441412 + 0.897305i \(0.354478\pi\)
\(972\) −1.03190e7 + 1.03190e7i −0.350325 + 0.350325i
\(973\) 3.02591e6 + 3.02591e6i 0.102465 + 0.102465i
\(974\) 1.23891e7 0.418447
\(975\) 1.31002e6 553249.i 0.0441334 0.0186384i
\(976\) 1.01297e7i 0.340388i
\(977\) −2.89552e7 + 2.89552e7i −0.970488 + 0.970488i −0.999577 0.0290887i \(-0.990739\pi\)
0.0290887 + 0.999577i \(0.490739\pi\)
\(978\) −1.41762e7 + 1.41762e7i −0.473929 + 0.473929i
\(979\) −3.22538e7 + 2.96793e7i −1.07554 + 0.989685i
\(980\) −803877. 3.96974e6i −0.0267377 0.132037i
\(981\) 4.17932e7i 1.38654i
\(982\) −2.50179e7 + 2.50179e7i −0.827888 + 0.827888i
\(983\) −3.40565e7 3.40565e7i −1.12413 1.12413i −0.991114 0.133014i \(-0.957535\pi\)
−0.133014 0.991114i \(-0.542465\pi\)
\(984\) 3.37373e6i 0.111077i
\(985\) 1.02962e7 1.55251e7i 0.338133 0.509851i
\(986\) 2.07080e6i 0.0678337i
\(987\) 4.56739e6 + 4.56739e6i 0.149236 + 0.149236i
\(988\) −1.46810e6 1.46810e6i −0.0478478 0.0478478i
\(989\) −3.22932e7 −1.04983
\(990\) −2.61495e6 1.63856e7i −0.0847960 0.531342i
\(991\) −1.26497e7 −0.409162 −0.204581 0.978850i \(-0.565583\pi\)
−0.204581 + 0.978850i \(0.565583\pi\)
\(992\) 2.85669e7 + 2.85669e7i 0.921688 + 0.921688i
\(993\) 575789. + 575789.i 0.0185306 + 0.0185306i
\(994\) 2.04940e7i 0.657902i
\(995\) −4.20457e7 + 8.51430e6i −1.34637 + 0.272641i
\(996\) 9.92570e6i 0.317039i
\(997\) 1.08845e7 + 1.08845e7i 0.346793 + 0.346793i 0.858913 0.512121i \(-0.171140\pi\)
−0.512121 + 0.858913i \(0.671140\pi\)
\(998\) −1.71283e7 + 1.71283e7i −0.544363 + 0.544363i
\(999\) 4.57877e6i 0.145156i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 55.6.e.b.43.10 yes 52
5.2 odd 4 inner 55.6.e.b.32.17 yes 52
11.10 odd 2 inner 55.6.e.b.43.17 yes 52
55.32 even 4 inner 55.6.e.b.32.10 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.6.e.b.32.10 52 55.32 even 4 inner
55.6.e.b.32.17 yes 52 5.2 odd 4 inner
55.6.e.b.43.10 yes 52 1.1 even 1 trivial
55.6.e.b.43.17 yes 52 11.10 odd 2 inner