Properties

Label 126.8.g.j.109.3
Level $126$
Weight $8$
Character 126.109
Analytic conductor $39.361$
Analytic rank $0$
Dimension $6$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,8,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, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(39.3605132110\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(-0.389676 + 0.674939i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.8.g.j.37.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 + 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(6.21726 + 10.7686i) q^{5} +(-879.593 - 223.290i) q^{7} -512.000 q^{8} +(-49.7381 + 86.1488i) q^{10} +(-3361.57 + 5822.41i) q^{11} +7231.99 q^{13} +(-1971.37 - 6987.16i) q^{14} +(-2048.00 - 3547.24i) q^{16} +(7665.42 - 13276.9i) q^{17} +(-9457.32 - 16380.6i) q^{19} -795.809 q^{20} -53785.1 q^{22} +(-23860.2 - 41327.2i) q^{23} +(38985.2 - 67524.3i) q^{25} +(28928.0 + 50104.7i) q^{26} +(40523.0 - 41606.7i) q^{28} +67449.4 q^{29} +(-54888.1 + 95068.9i) q^{31} +(16384.0 - 28377.9i) q^{32} +122647. q^{34} +(-3064.13 - 10860.2i) q^{35} +(-304625. - 527626. i) q^{37} +(75658.5 - 131044. i) q^{38} +(-3183.24 - 5513.53i) q^{40} +808859. q^{41} -334949. q^{43} +(-215140. - 372634. i) q^{44} +(190882. - 330617. i) q^{46} +(-382587. - 662661. i) q^{47} +(723826. + 392809. i) q^{49} +623763. q^{50} +(-231424. + 400838. i) q^{52} +(622359. - 1.07796e6i) q^{53} -83598.9 q^{55} +(450352. + 114325. i) q^{56} +(269798. + 467303. i) q^{58} +(1.02330e6 - 1.77240e6i) q^{59} +(-70471.7 - 122061. i) q^{61} -878209. q^{62} +262144. q^{64} +(44963.1 + 77878.4i) q^{65} +(-1.46662e6 + 2.54027e6i) q^{67} +(490587. + 849721. i) q^{68} +(62985.4 - 64669.9i) q^{70} +615326. q^{71} +(711328. - 1.23206e6i) q^{73} +(2.43700e6 - 4.22101e6i) q^{74} +1.21054e6 q^{76} +(4.25690e6 - 4.37075e6i) q^{77} +(1.19370e6 + 2.06754e6i) q^{79} +(25465.9 - 44108.2i) q^{80} +(3.23544e6 + 5.60394e6i) q^{82} +7.53432e6 q^{83} +190631. q^{85} +(-1.33980e6 - 2.32060e6i) q^{86} +(1.72112e6 - 2.98107e6i) q^{88} +(-2.67757e6 - 4.63769e6i) q^{89} +(-6.36121e6 - 1.61483e6i) q^{91} +3.05411e6 q^{92} +(3.06070e6 - 5.30129e6i) q^{94} +(117597. - 203684. i) q^{95} -1.58174e7 q^{97} +(173842. + 6.58605e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 + 6.92820i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −32.0000 + 55.4256i −0.250000 + 0.433013i
\(5\) 6.21726 + 10.7686i 0.0222435 + 0.0385269i 0.876933 0.480613i \(-0.159586\pi\)
−0.854689 + 0.519140i \(0.826252\pi\)
\(6\) 0 0
\(7\) −879.593 223.290i −0.969257 0.246052i
\(8\) −512.000 −0.353553
\(9\) 0 0
\(10\) −49.7381 + 86.1488i −0.0157286 + 0.0272427i
\(11\) −3361.57 + 5822.41i −0.761496 + 1.31895i 0.180584 + 0.983560i \(0.442201\pi\)
−0.942079 + 0.335390i \(0.891132\pi\)
\(12\) 0 0
\(13\) 7231.99 0.912969 0.456485 0.889731i \(-0.349108\pi\)
0.456485 + 0.889731i \(0.349108\pi\)
\(14\) −1971.37 6987.16i −0.192009 0.680539i
\(15\) 0 0
\(16\) −2048.00 3547.24i −0.125000 0.216506i
\(17\) 7665.42 13276.9i 0.378412 0.655428i −0.612420 0.790533i \(-0.709804\pi\)
0.990831 + 0.135105i \(0.0431370\pi\)
\(18\) 0 0
\(19\) −9457.32 16380.6i −0.316323 0.547887i 0.663395 0.748269i \(-0.269115\pi\)
−0.979718 + 0.200382i \(0.935782\pi\)
\(20\) −795.809 −0.0222435
\(21\) 0 0
\(22\) −53785.1 −1.07692
\(23\) −23860.2 41327.2i −0.408910 0.708253i 0.585858 0.810414i \(-0.300758\pi\)
−0.994768 + 0.102161i \(0.967424\pi\)
\(24\) 0 0
\(25\) 38985.2 67524.3i 0.499010 0.864311i
\(26\) 28928.0 + 50104.7i 0.322783 + 0.559077i
\(27\) 0 0
\(28\) 40523.0 41606.7i 0.348858 0.358188i
\(29\) 67449.4 0.513553 0.256776 0.966471i \(-0.417340\pi\)
0.256776 + 0.966471i \(0.417340\pi\)
\(30\) 0 0
\(31\) −54888.1 + 95068.9i −0.330912 + 0.573156i −0.982691 0.185253i \(-0.940690\pi\)
0.651779 + 0.758409i \(0.274023\pi\)
\(32\) 16384.0 28377.9i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 122647. 0.535155
\(35\) −3064.13 10860.2i −0.0120801 0.0428155i
\(36\) 0 0
\(37\) −304625. 527626.i −0.988688 1.71246i −0.624235 0.781237i \(-0.714589\pi\)
−0.364454 0.931222i \(-0.618744\pi\)
\(38\) 75658.5 131044.i 0.223674 0.387415i
\(39\) 0 0
\(40\) −3183.24 5513.53i −0.00786428 0.0136213i
\(41\) 808859. 1.83286 0.916430 0.400195i \(-0.131057\pi\)
0.916430 + 0.400195i \(0.131057\pi\)
\(42\) 0 0
\(43\) −334949. −0.642450 −0.321225 0.947003i \(-0.604095\pi\)
−0.321225 + 0.947003i \(0.604095\pi\)
\(44\) −215140. 372634.i −0.380748 0.659475i
\(45\) 0 0
\(46\) 190882. 330617.i 0.289143 0.500810i
\(47\) −382587. 662661.i −0.537512 0.930998i −0.999037 0.0438710i \(-0.986031\pi\)
0.461525 0.887127i \(-0.347302\pi\)
\(48\) 0 0
\(49\) 723826. + 392809.i 0.878917 + 0.476975i
\(50\) 623763. 0.705707
\(51\) 0 0
\(52\) −231424. + 400838.i −0.228242 + 0.395327i
\(53\) 622359. 1.07796e6i 0.574216 0.994572i −0.421910 0.906638i \(-0.638640\pi\)
0.996126 0.0879342i \(-0.0280265\pi\)
\(54\) 0 0
\(55\) −83598.9 −0.0677534
\(56\) 450352. + 114325.i 0.342684 + 0.0869924i
\(57\) 0 0
\(58\) 269798. + 467303.i 0.181568 + 0.314486i
\(59\) 1.02330e6 1.77240e6i 0.648665 1.12352i −0.334777 0.942297i \(-0.608661\pi\)
0.983442 0.181223i \(-0.0580056\pi\)
\(60\) 0 0
\(61\) −70471.7 122061.i −0.0397521 0.0688527i 0.845465 0.534031i \(-0.179323\pi\)
−0.885217 + 0.465178i \(0.845990\pi\)
\(62\) −878209. −0.467980
\(63\) 0 0
\(64\) 262144. 0.125000
\(65\) 44963.1 + 77878.4i 0.0203077 + 0.0351739i
\(66\) 0 0
\(67\) −1.46662e6 + 2.54027e6i −0.595740 + 1.03185i 0.397702 + 0.917515i \(0.369808\pi\)
−0.993442 + 0.114338i \(0.963525\pi\)
\(68\) 490587. + 849721.i 0.189206 + 0.327714i
\(69\) 0 0
\(70\) 62985.4 64669.9i 0.0219481 0.0225351i
\(71\) 615326. 0.204033 0.102017 0.994783i \(-0.467470\pi\)
0.102017 + 0.994783i \(0.467470\pi\)
\(72\) 0 0
\(73\) 711328. 1.23206e6i 0.214013 0.370681i −0.738954 0.673756i \(-0.764680\pi\)
0.952967 + 0.303075i \(0.0980132\pi\)
\(74\) 2.43700e6 4.22101e6i 0.699108 1.21089i
\(75\) 0 0
\(76\) 1.21054e6 0.316323
\(77\) 4.25690e6 4.37075e6i 1.06261 1.09103i
\(78\) 0 0
\(79\) 1.19370e6 + 2.06754e6i 0.272395 + 0.471802i 0.969475 0.245192i \(-0.0788509\pi\)
−0.697079 + 0.716994i \(0.745518\pi\)
\(80\) 25465.9 44108.2i 0.00556088 0.00963173i
\(81\) 0 0
\(82\) 3.23544e6 + 5.60394e6i 0.648014 + 1.12239i
\(83\) 7.53432e6 1.44634 0.723171 0.690669i \(-0.242684\pi\)
0.723171 + 0.690669i \(0.242684\pi\)
\(84\) 0 0
\(85\) 190631. 0.0336689
\(86\) −1.33980e6 2.32060e6i −0.227140 0.393419i
\(87\) 0 0
\(88\) 1.72112e6 2.98107e6i 0.269229 0.466319i
\(89\) −2.67757e6 4.63769e6i −0.402602 0.697327i 0.591437 0.806351i \(-0.298561\pi\)
−0.994039 + 0.109024i \(0.965227\pi\)
\(90\) 0 0
\(91\) −6.36121e6 1.61483e6i −0.884901 0.224638i
\(92\) 3.05411e6 0.408910
\(93\) 0 0
\(94\) 3.06070e6 5.30129e6i 0.380078 0.658315i
\(95\) 117597. 203684.i 0.0140723 0.0243739i
\(96\) 0 0
\(97\) −1.58174e7 −1.75969 −0.879843 0.475265i \(-0.842352\pi\)
−0.879843 + 0.475265i \(0.842352\pi\)
\(98\) 173842. + 6.58605e6i 0.0186580 + 0.706861i
\(99\) 0 0
\(100\) 2.49505e6 + 4.32156e6i 0.249505 + 0.432156i
\(101\) −5.82603e6 + 1.00910e7i −0.562662 + 0.974559i 0.434601 + 0.900623i \(0.356889\pi\)
−0.997263 + 0.0739362i \(0.976444\pi\)
\(102\) 0 0
\(103\) −3.58003e6 6.20080e6i −0.322817 0.559136i 0.658251 0.752799i \(-0.271297\pi\)
−0.981068 + 0.193663i \(0.937963\pi\)
\(104\) −3.70278e6 −0.322783
\(105\) 0 0
\(106\) 9.95775e6 0.812065
\(107\) −2.91738e6 5.05305e6i −0.230224 0.398759i 0.727650 0.685948i \(-0.240612\pi\)
−0.957874 + 0.287189i \(0.907279\pi\)
\(108\) 0 0
\(109\) 4.66490e6 8.07985e6i 0.345024 0.597600i −0.640334 0.768097i \(-0.721204\pi\)
0.985358 + 0.170497i \(0.0545373\pi\)
\(110\) −334396. 579190.i −0.0239545 0.0414903i
\(111\) 0 0
\(112\) 1.00934e6 + 3.57743e6i 0.0678853 + 0.240607i
\(113\) −8.84372e6 −0.576581 −0.288290 0.957543i \(-0.593087\pi\)
−0.288290 + 0.957543i \(0.593087\pi\)
\(114\) 0 0
\(115\) 296691. 513883.i 0.0181912 0.0315081i
\(116\) −2.15838e6 + 3.73842e6i −0.128388 + 0.222375i
\(117\) 0 0
\(118\) 1.63728e7 0.917350
\(119\) −9.70705e6 + 9.96665e6i −0.528047 + 0.542169i
\(120\) 0 0
\(121\) −1.28567e7 2.22684e7i −0.659752 1.14272i
\(122\) 563773. 976484.i 0.0281090 0.0486862i
\(123\) 0 0
\(124\) −3.51284e6 6.08441e6i −0.165456 0.286578i
\(125\) 1.94097e6 0.0888861
\(126\) 0 0
\(127\) −2.22621e7 −0.964393 −0.482196 0.876063i \(-0.660161\pi\)
−0.482196 + 0.876063i \(0.660161\pi\)
\(128\) 1.04858e6 + 1.81619e6i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −359705. + 623027.i −0.0143597 + 0.0248717i
\(131\) 5.45088e6 + 9.44120e6i 0.211844 + 0.366925i 0.952292 0.305189i \(-0.0987197\pi\)
−0.740447 + 0.672114i \(0.765386\pi\)
\(132\) 0 0
\(133\) 4.66098e6 + 1.65199e7i 0.171789 + 0.608875i
\(134\) −2.34660e7 −0.842504
\(135\) 0 0
\(136\) −3.92469e6 + 6.79777e6i −0.133789 + 0.231729i
\(137\) −1.60629e7 + 2.78218e7i −0.533706 + 0.924406i 0.465519 + 0.885038i \(0.345868\pi\)
−0.999225 + 0.0393678i \(0.987466\pi\)
\(138\) 0 0
\(139\) −1.89050e7 −0.597070 −0.298535 0.954399i \(-0.596498\pi\)
−0.298535 + 0.954399i \(0.596498\pi\)
\(140\) 699988. + 177696.i 0.0215597 + 0.00547306i
\(141\) 0 0
\(142\) 2.46131e6 + 4.26311e6i 0.0721367 + 0.124944i
\(143\) −2.43108e7 + 4.21076e7i −0.695222 + 1.20416i
\(144\) 0 0
\(145\) 419350. + 726336.i 0.0114232 + 0.0197856i
\(146\) 1.13813e7 0.302660
\(147\) 0 0
\(148\) 3.89920e7 0.988688
\(149\) −2.77312e6 4.80319e6i −0.0686779 0.118954i 0.829642 0.558296i \(-0.188545\pi\)
−0.898320 + 0.439343i \(0.855211\pi\)
\(150\) 0 0
\(151\) 1.13319e7 1.96275e7i 0.267845 0.463922i −0.700460 0.713692i \(-0.747022\pi\)
0.968305 + 0.249770i \(0.0803550\pi\)
\(152\) 4.84215e6 + 8.38684e6i 0.111837 + 0.193707i
\(153\) 0 0
\(154\) 4.73090e7 + 1.20097e7i 1.04381 + 0.264978i
\(155\) −1.36501e6 −0.0294426
\(156\) 0 0
\(157\) −3.25062e7 + 5.63025e7i −0.670375 + 1.16112i 0.307423 + 0.951573i \(0.400533\pi\)
−0.977798 + 0.209551i \(0.932800\pi\)
\(158\) −9.54958e6 + 1.65404e7i −0.192612 + 0.333615i
\(159\) 0 0
\(160\) 407454. 0.00786428
\(161\) 1.17594e7 + 4.16789e7i 0.222072 + 0.787092i
\(162\) 0 0
\(163\) −1.74670e7 3.02537e7i −0.315908 0.547170i 0.663722 0.747980i \(-0.268976\pi\)
−0.979630 + 0.200810i \(0.935643\pi\)
\(164\) −2.58835e7 + 4.48315e7i −0.458215 + 0.793652i
\(165\) 0 0
\(166\) 3.01373e7 + 5.21993e7i 0.511359 + 0.885700i
\(167\) −8.89524e7 −1.47792 −0.738959 0.673751i \(-0.764682\pi\)
−0.738959 + 0.673751i \(0.764682\pi\)
\(168\) 0 0
\(169\) −1.04468e7 −0.166487
\(170\) 762526. + 1.32073e6i 0.0119037 + 0.0206179i
\(171\) 0 0
\(172\) 1.07184e7 1.85648e7i 0.160612 0.278189i
\(173\) −1.53819e7 2.66422e7i −0.225865 0.391209i 0.730714 0.682684i \(-0.239187\pi\)
−0.956578 + 0.291475i \(0.905854\pi\)
\(174\) 0 0
\(175\) −4.93686e7 + 5.06889e7i −0.696335 + 0.714957i
\(176\) 2.75380e7 0.380748
\(177\) 0 0
\(178\) 2.14206e7 3.71015e7i 0.284683 0.493085i
\(179\) 5.15359e7 8.92628e7i 0.671621 1.16328i −0.305823 0.952088i \(-0.598932\pi\)
0.977444 0.211194i \(-0.0677351\pi\)
\(180\) 0 0
\(181\) −6.25682e7 −0.784294 −0.392147 0.919903i \(-0.628268\pi\)
−0.392147 + 0.919903i \(0.628268\pi\)
\(182\) −1.42570e7 5.05311e7i −0.175298 0.621311i
\(183\) 0 0
\(184\) 1.22164e7 + 2.11595e7i 0.144571 + 0.250405i
\(185\) 3.78786e6 6.56077e6i 0.0439838 0.0761822i
\(186\) 0 0
\(187\) 5.15356e7 + 8.92623e7i 0.576318 + 0.998212i
\(188\) 4.89712e7 0.537512
\(189\) 0 0
\(190\) 1.88155e6 0.0199012
\(191\) 3.95503e7 + 6.85031e7i 0.410707 + 0.711366i 0.994967 0.100201i \(-0.0319484\pi\)
−0.584260 + 0.811567i \(0.698615\pi\)
\(192\) 0 0
\(193\) 2.81447e7 4.87480e7i 0.281803 0.488097i −0.690026 0.723785i \(-0.742401\pi\)
0.971829 + 0.235687i \(0.0757342\pi\)
\(194\) −6.32697e7 1.09586e8i −0.622143 1.07758i
\(195\) 0 0
\(196\) −4.49341e7 + 2.75486e7i −0.426265 + 0.261339i
\(197\) 4.91598e7 0.458119 0.229059 0.973412i \(-0.426435\pi\)
0.229059 + 0.973412i \(0.426435\pi\)
\(198\) 0 0
\(199\) 8.35475e7 1.44709e8i 0.751533 1.30169i −0.195547 0.980694i \(-0.562648\pi\)
0.947080 0.320998i \(-0.104018\pi\)
\(200\) −1.99604e7 + 3.45725e7i −0.176427 + 0.305580i
\(201\) 0 0
\(202\) −9.32164e7 −0.795724
\(203\) −5.93280e7 1.50608e7i −0.497764 0.126361i
\(204\) 0 0
\(205\) 5.02888e6 + 8.71028e6i 0.0407693 + 0.0706145i
\(206\) 2.86403e7 4.96064e7i 0.228266 0.395369i
\(207\) 0 0
\(208\) −1.48111e7 2.56536e7i −0.114121 0.197664i
\(209\) 1.27166e8 0.963513
\(210\) 0 0
\(211\) 7.06109e7 0.517467 0.258734 0.965949i \(-0.416695\pi\)
0.258734 + 0.965949i \(0.416695\pi\)
\(212\) 3.98310e7 + 6.89893e7i 0.287108 + 0.497286i
\(213\) 0 0
\(214\) 2.33390e7 4.04244e7i 0.162793 0.281965i
\(215\) −2.08246e6 3.60693e6i −0.0142904 0.0247516i
\(216\) 0 0
\(217\) 6.95071e7 7.13660e7i 0.461764 0.474114i
\(218\) 7.46384e7 0.487938
\(219\) 0 0
\(220\) 2.67517e6 4.63352e6i 0.0169384 0.0293381i
\(221\) 5.54362e7 9.60183e7i 0.345478 0.598386i
\(222\) 0 0
\(223\) −2.49891e8 −1.50898 −0.754489 0.656313i \(-0.772115\pi\)
−0.754489 + 0.656313i \(0.772115\pi\)
\(224\) −2.07478e7 + 2.13026e7i −0.123340 + 0.126638i
\(225\) 0 0
\(226\) −3.53749e7 6.12711e7i −0.203852 0.353082i
\(227\) 1.62335e8 2.81173e8i 0.921133 1.59545i 0.123468 0.992349i \(-0.460598\pi\)
0.797665 0.603101i \(-0.206068\pi\)
\(228\) 0 0
\(229\) 1.05242e7 + 1.82284e7i 0.0579115 + 0.100306i 0.893528 0.449008i \(-0.148223\pi\)
−0.835616 + 0.549314i \(0.814889\pi\)
\(230\) 4.74705e6 0.0257262
\(231\) 0 0
\(232\) −3.45341e7 −0.181568
\(233\) −8.17424e7 1.41582e8i −0.423352 0.733267i 0.572913 0.819616i \(-0.305813\pi\)
−0.996265 + 0.0863491i \(0.972480\pi\)
\(234\) 0 0
\(235\) 4.75729e6 8.23987e6i 0.0239123 0.0414174i
\(236\) 6.54911e7 + 1.13434e8i 0.324332 + 0.561760i
\(237\) 0 0
\(238\) −1.07879e8 2.73858e7i −0.518703 0.131676i
\(239\) 3.18177e8 1.50757 0.753784 0.657123i \(-0.228227\pi\)
0.753784 + 0.657123i \(0.228227\pi\)
\(240\) 0 0
\(241\) 6.47859e7 1.12213e8i 0.298141 0.516395i −0.677570 0.735458i \(-0.736967\pi\)
0.975711 + 0.219064i \(0.0703003\pi\)
\(242\) 1.02854e8 1.78148e8i 0.466515 0.808027i
\(243\) 0 0
\(244\) 9.02038e6 0.0397521
\(245\) 270206. + 1.02368e7i 0.00117385 + 0.0444716i
\(246\) 0 0
\(247\) −6.83952e7 1.18464e8i −0.288793 0.500204i
\(248\) 2.81027e7 4.86753e7i 0.116995 0.202641i
\(249\) 0 0
\(250\) 7.76388e6 + 1.34474e7i 0.0314260 + 0.0544314i
\(251\) 7.94873e7 0.317278 0.158639 0.987337i \(-0.449289\pi\)
0.158639 + 0.987337i \(0.449289\pi\)
\(252\) 0 0
\(253\) 3.20831e8 1.24553
\(254\) −8.90486e7 1.54237e8i −0.340964 0.590567i
\(255\) 0 0
\(256\) −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
\(257\) −2.14513e8 3.71547e8i −0.788293 1.36536i −0.927012 0.375032i \(-0.877632\pi\)
0.138719 0.990332i \(-0.455702\pi\)
\(258\) 0 0
\(259\) 1.50132e8 + 5.32116e8i 0.536939 + 1.90308i
\(260\) −5.75528e6 −0.0203077
\(261\) 0 0
\(262\) −4.36070e7 + 7.55296e7i −0.149797 + 0.259455i
\(263\) −2.12061e7 + 3.67300e7i −0.0718812 + 0.124502i −0.899726 0.436456i \(-0.856234\pi\)
0.827845 + 0.560958i \(0.189567\pi\)
\(264\) 0 0
\(265\) 1.54775e7 0.0510904
\(266\) −9.58097e7 + 9.83720e7i −0.312121 + 0.320469i
\(267\) 0 0
\(268\) −9.38639e7 1.62577e8i −0.297870 0.515926i
\(269\) −2.60097e8 + 4.50501e8i −0.814709 + 1.41112i 0.0948278 + 0.995494i \(0.469770\pi\)
−0.909537 + 0.415624i \(0.863563\pi\)
\(270\) 0 0
\(271\) 8.71406e7 + 1.50932e8i 0.265967 + 0.460668i 0.967817 0.251657i \(-0.0809754\pi\)
−0.701850 + 0.712325i \(0.747642\pi\)
\(272\) −6.27951e7 −0.189206
\(273\) 0 0
\(274\) −2.57006e8 −0.754774
\(275\) 2.62103e8 + 4.53975e8i 0.759989 + 1.31634i
\(276\) 0 0
\(277\) 3.38413e8 5.86149e8i 0.956683 1.65702i 0.226216 0.974077i \(-0.427365\pi\)
0.730468 0.682947i \(-0.239302\pi\)
\(278\) −7.56200e7 1.30978e8i −0.211096 0.365629i
\(279\) 0 0
\(280\) 1.56884e6 + 5.56045e6i 0.00427095 + 0.0151376i
\(281\) 3.51245e8 0.944360 0.472180 0.881502i \(-0.343467\pi\)
0.472180 + 0.881502i \(0.343467\pi\)
\(282\) 0 0
\(283\) −3.24140e8 + 5.61428e8i −0.850121 + 1.47245i 0.0309780 + 0.999520i \(0.490138\pi\)
−0.881099 + 0.472932i \(0.843196\pi\)
\(284\) −1.96904e7 + 3.41048e7i −0.0510083 + 0.0883490i
\(285\) 0 0
\(286\) −3.88973e8 −0.983193
\(287\) −7.11467e8 1.80610e8i −1.77651 0.450979i
\(288\) 0 0
\(289\) 8.76521e7 + 1.51818e8i 0.213609 + 0.369982i
\(290\) −3.35480e6 + 5.81069e6i −0.00807744 + 0.0139905i
\(291\) 0 0
\(292\) 4.55250e7 + 7.88516e7i 0.107006 + 0.185341i
\(293\) −6.35015e6 −0.0147485 −0.00737424 0.999973i \(-0.502347\pi\)
−0.00737424 + 0.999973i \(0.502347\pi\)
\(294\) 0 0
\(295\) 2.54484e7 0.0577144
\(296\) 1.55968e8 + 2.70144e8i 0.349554 + 0.605445i
\(297\) 0 0
\(298\) 2.21850e7 3.84255e7i 0.0485626 0.0841129i
\(299\) −1.72557e8 2.98878e8i −0.373322 0.646613i
\(300\) 0 0
\(301\) 2.94619e8 + 7.47908e7i 0.622699 + 0.158076i
\(302\) 1.81311e8 0.378791
\(303\) 0 0
\(304\) −3.87372e7 + 6.70947e7i −0.0790807 + 0.136972i
\(305\) 876281. 1.51776e6i 0.00176845 0.00306305i
\(306\) 0 0
\(307\) 8.05452e8 1.58875 0.794375 0.607428i \(-0.207798\pi\)
0.794375 + 0.607428i \(0.207798\pi\)
\(308\) 1.06031e8 + 3.75805e8i 0.206778 + 0.732884i
\(309\) 0 0
\(310\) −5.46005e6 9.45709e6i −0.0104095 0.0180298i
\(311\) −2.12401e8 + 3.67889e8i −0.400401 + 0.693514i −0.993774 0.111413i \(-0.964462\pi\)
0.593374 + 0.804927i \(0.297796\pi\)
\(312\) 0 0
\(313\) 2.08578e8 + 3.61268e8i 0.384472 + 0.665924i 0.991696 0.128606i \(-0.0410503\pi\)
−0.607224 + 0.794531i \(0.707717\pi\)
\(314\) −5.20100e8 −0.948054
\(315\) 0 0
\(316\) −1.52793e8 −0.272395
\(317\) 2.13997e8 + 3.70654e8i 0.377312 + 0.653523i 0.990670 0.136282i \(-0.0435152\pi\)
−0.613358 + 0.789805i \(0.710182\pi\)
\(318\) 0 0
\(319\) −2.26736e8 + 3.92718e8i −0.391068 + 0.677350i
\(320\) 1.62982e6 + 2.82292e6i 0.00278044 + 0.00481587i
\(321\) 0 0
\(322\) −2.41722e8 + 2.48187e8i −0.403479 + 0.414270i
\(323\) −2.89977e8 −0.478801
\(324\) 0 0
\(325\) 2.81941e8 4.88335e8i 0.455581 0.789090i
\(326\) 1.39736e8 2.42030e8i 0.223381 0.386907i
\(327\) 0 0
\(328\) −4.14136e8 −0.648014
\(329\) 1.88556e8 + 6.68300e8i 0.291913 + 1.03463i
\(330\) 0 0
\(331\) −1.32553e8 2.29588e8i −0.200905 0.347978i 0.747915 0.663794i \(-0.231055\pi\)
−0.948820 + 0.315816i \(0.897722\pi\)
\(332\) −2.41098e8 + 4.17595e8i −0.361586 + 0.626284i
\(333\) 0 0
\(334\) −3.55810e8 6.16281e8i −0.522523 0.905036i
\(335\) −3.64735e7 −0.0530055
\(336\) 0 0
\(337\) 2.17646e8 0.309775 0.154887 0.987932i \(-0.450499\pi\)
0.154887 + 0.987932i \(0.450499\pi\)
\(338\) −4.17874e7 7.23778e7i −0.0588622 0.101952i
\(339\) 0 0
\(340\) −6.10021e6 + 1.05659e7i −0.00841721 + 0.0145790i
\(341\) −3.69020e8 6.39161e8i −0.503976 0.872911i
\(342\) 0 0
\(343\) −5.48962e8 5.07136e8i −0.734536 0.678570i
\(344\) 1.71494e8 0.227140
\(345\) 0 0
\(346\) 1.23055e8 2.13138e8i 0.159710 0.276626i
\(347\) −3.24979e8 + 5.62880e8i −0.417544 + 0.723207i −0.995692 0.0927250i \(-0.970442\pi\)
0.578148 + 0.815932i \(0.303776\pi\)
\(348\) 0 0
\(349\) −7.11539e8 −0.896003 −0.448002 0.894033i \(-0.647864\pi\)
−0.448002 + 0.894033i \(0.647864\pi\)
\(350\) −5.48658e8 1.39280e8i −0.684012 0.173641i
\(351\) 0 0
\(352\) 1.10152e8 + 1.90789e8i 0.134615 + 0.233160i
\(353\) −7.74200e8 + 1.34095e9i −0.936788 + 1.62257i −0.165375 + 0.986231i \(0.552884\pi\)
−0.771413 + 0.636335i \(0.780450\pi\)
\(354\) 0 0
\(355\) 3.82564e6 + 6.62621e6i 0.00453842 + 0.00786078i
\(356\) 3.42729e8 0.402602
\(357\) 0 0
\(358\) 8.24575e8 0.949816
\(359\) 8.43823e7 + 1.46154e8i 0.0962544 + 0.166718i 0.910131 0.414320i \(-0.135980\pi\)
−0.813877 + 0.581037i \(0.802647\pi\)
\(360\) 0 0
\(361\) 2.68054e8 4.64284e8i 0.299880 0.519407i
\(362\) −2.50273e8 4.33486e8i −0.277290 0.480280i
\(363\) 0 0
\(364\) 2.93062e8 3.00899e8i 0.318496 0.327014i
\(365\) 1.76900e7 0.0190416
\(366\) 0 0
\(367\) 1.71858e8 2.97666e8i 0.181484 0.314339i −0.760902 0.648867i \(-0.775243\pi\)
0.942386 + 0.334527i \(0.108577\pi\)
\(368\) −9.77316e7 + 1.69276e8i −0.102227 + 0.177063i
\(369\) 0 0
\(370\) 6.06058e7 0.0622025
\(371\) −7.88120e8 + 8.09198e8i −0.801279 + 0.822709i
\(372\) 0 0
\(373\) 6.96771e7 + 1.20684e8i 0.0695199 + 0.120412i 0.898690 0.438584i \(-0.144520\pi\)
−0.829170 + 0.558996i \(0.811187\pi\)
\(374\) −4.12285e8 + 7.14099e8i −0.407518 + 0.705842i
\(375\) 0 0
\(376\) 1.95885e8 + 3.39282e8i 0.190039 + 0.329158i
\(377\) 4.87793e8 0.468858
\(378\) 0 0
\(379\) −7.74462e8 −0.730740 −0.365370 0.930862i \(-0.619057\pi\)
−0.365370 + 0.930862i \(0.619057\pi\)
\(380\) 7.52621e6 + 1.30358e7i 0.00703613 + 0.0121869i
\(381\) 0 0
\(382\) −3.16402e8 + 5.48024e8i −0.290414 + 0.503012i
\(383\) −6.53115e8 1.13123e9i −0.594011 1.02886i −0.993686 0.112200i \(-0.964210\pi\)
0.399675 0.916657i \(-0.369123\pi\)
\(384\) 0 0
\(385\) 7.35331e7 + 1.86668e7i 0.0656705 + 0.0166709i
\(386\) 4.50315e8 0.398530
\(387\) 0 0
\(388\) 5.06158e8 8.76691e8i 0.439921 0.761966i
\(389\) 1.10694e9 1.91728e9i 0.953455 1.65143i 0.215591 0.976484i \(-0.430832\pi\)
0.737864 0.674949i \(-0.235834\pi\)
\(390\) 0 0
\(391\) −7.31595e8 −0.618945
\(392\) −3.70599e8 2.01118e8i −0.310744 0.168636i
\(393\) 0 0
\(394\) 1.96639e8 + 3.40589e8i 0.161969 + 0.280539i
\(395\) −1.48430e7 + 2.57089e7i −0.0121181 + 0.0209891i
\(396\) 0 0
\(397\) −5.85561e8 1.01422e9i −0.469684 0.813516i 0.529715 0.848176i \(-0.322299\pi\)
−0.999399 + 0.0346591i \(0.988965\pi\)
\(398\) 1.33676e9 1.06283
\(399\) 0 0
\(400\) −3.19367e8 −0.249505
\(401\) −7.49819e8 1.29872e9i −0.580699 1.00580i −0.995397 0.0958406i \(-0.969446\pi\)
0.414698 0.909959i \(-0.363887\pi\)
\(402\) 0 0
\(403\) −3.96950e8 + 6.87538e8i −0.302112 + 0.523274i
\(404\) −3.72866e8 6.45822e8i −0.281331 0.487280i
\(405\) 0 0
\(406\) −1.32968e8 4.71280e8i −0.0986066 0.349492i
\(407\) 4.09607e9 3.01153
\(408\) 0 0
\(409\) 3.74802e7 6.49176e7i 0.0270876 0.0469171i −0.852164 0.523275i \(-0.824710\pi\)
0.879251 + 0.476358i \(0.158043\pi\)
\(410\) −4.02311e7 + 6.96823e7i −0.0288282 + 0.0499320i
\(411\) 0 0
\(412\) 4.58244e8 0.322817
\(413\) −1.29585e9 + 1.33050e9i −0.905167 + 0.929374i
\(414\) 0 0
\(415\) 4.68428e7 + 8.11342e7i 0.0321718 + 0.0557231i
\(416\) 1.18489e8 2.05229e8i 0.0806958 0.139769i
\(417\) 0 0
\(418\) 5.08663e8 + 8.81029e8i 0.340653 + 0.590029i
\(419\) 8.47037e7 0.0562540 0.0281270 0.999604i \(-0.491046\pi\)
0.0281270 + 0.999604i \(0.491046\pi\)
\(420\) 0 0
\(421\) −6.03152e8 −0.393949 −0.196974 0.980409i \(-0.563112\pi\)
−0.196974 + 0.980409i \(0.563112\pi\)
\(422\) 2.82443e8 + 4.89206e8i 0.182952 + 0.316883i
\(423\) 0 0
\(424\) −3.18648e8 + 5.51914e8i −0.203016 + 0.351634i
\(425\) −5.97675e8 1.03520e9i −0.377663 0.654131i
\(426\) 0 0
\(427\) 3.47315e7 + 1.23099e8i 0.0215887 + 0.0765170i
\(428\) 3.73425e8 0.230224
\(429\) 0 0
\(430\) 1.66597e7 2.88555e7i 0.0101048 0.0175020i
\(431\) 1.30326e9 2.25732e9i 0.784081 1.35807i −0.145465 0.989363i \(-0.546468\pi\)
0.929546 0.368705i \(-0.120199\pi\)
\(432\) 0 0
\(433\) 3.09676e9 1.83316 0.916579 0.399854i \(-0.130939\pi\)
0.916579 + 0.399854i \(0.130939\pi\)
\(434\) 7.72467e8 + 1.96095e8i 0.453592 + 0.115147i
\(435\) 0 0
\(436\) 2.98554e8 + 5.17110e8i 0.172512 + 0.298800i
\(437\) −4.51308e8 + 7.81688e8i −0.258695 + 0.448073i
\(438\) 0 0
\(439\) 3.02299e8 + 5.23597e8i 0.170534 + 0.295374i 0.938607 0.344989i \(-0.112117\pi\)
−0.768073 + 0.640363i \(0.778784\pi\)
\(440\) 4.28026e7 0.0239545
\(441\) 0 0
\(442\) 8.86979e8 0.488580
\(443\) 1.08327e9 + 1.87628e9i 0.592003 + 1.02538i 0.993962 + 0.109722i \(0.0349960\pi\)
−0.401959 + 0.915658i \(0.631671\pi\)
\(444\) 0 0
\(445\) 3.32943e7 5.76674e7i 0.0179106 0.0310220i
\(446\) −9.99562e8 1.73129e9i −0.533504 0.924056i
\(447\) 0 0
\(448\) −2.30580e8 5.85342e7i −0.121157 0.0307565i
\(449\) 1.01304e9 0.528161 0.264080 0.964501i \(-0.414932\pi\)
0.264080 + 0.964501i \(0.414932\pi\)
\(450\) 0 0
\(451\) −2.71903e9 + 4.70951e9i −1.39572 + 2.41745i
\(452\) 2.82999e8 4.90169e8i 0.144145 0.249667i
\(453\) 0 0
\(454\) 2.59736e9 1.30268
\(455\) −2.21598e7 7.85412e7i −0.0110287 0.0390893i
\(456\) 0 0
\(457\) −8.04203e8 1.39292e9i −0.394148 0.682684i 0.598844 0.800865i \(-0.295627\pi\)
−0.992992 + 0.118182i \(0.962293\pi\)
\(458\) −8.41936e7 + 1.45828e8i −0.0409496 + 0.0709268i
\(459\) 0 0
\(460\) 1.89882e7 + 3.28885e7i 0.00909560 + 0.0157540i
\(461\) 2.98355e9 1.41834 0.709169 0.705039i \(-0.249070\pi\)
0.709169 + 0.705039i \(0.249070\pi\)
\(462\) 0 0
\(463\) −2.83402e9 −1.32700 −0.663499 0.748178i \(-0.730929\pi\)
−0.663499 + 0.748178i \(0.730929\pi\)
\(464\) −1.38136e8 2.39259e8i −0.0641941 0.111187i
\(465\) 0 0
\(466\) 6.53939e8 1.13266e9i 0.299355 0.518498i
\(467\) −2.15916e9 3.73977e9i −0.981014 1.69917i −0.658460 0.752616i \(-0.728792\pi\)
−0.322555 0.946551i \(-0.604542\pi\)
\(468\) 0 0
\(469\) 1.85725e9 1.90692e9i 0.831314 0.853547i
\(470\) 7.61166e7 0.0338171
\(471\) 0 0
\(472\) −5.23929e8 + 9.07471e8i −0.229338 + 0.397224i
\(473\) 1.12595e9 1.95021e9i 0.489223 0.847359i
\(474\) 0 0
\(475\) −1.47478e9 −0.631393
\(476\) −2.41782e8 8.56952e8i −0.102754 0.364194i
\(477\) 0 0
\(478\) 1.27271e9 + 2.20440e9i 0.533006 + 0.923193i
\(479\) −4.10161e8 + 7.10420e8i −0.170522 + 0.295353i −0.938602 0.345001i \(-0.887879\pi\)
0.768081 + 0.640353i \(0.221212\pi\)
\(480\) 0 0
\(481\) −2.20304e9 3.81578e9i −0.902642 1.56342i
\(482\) 1.03657e9 0.421634
\(483\) 0 0
\(484\) 1.64566e9 0.659752
\(485\) −9.83410e7 1.70332e8i −0.0391416 0.0677953i
\(486\) 0 0
\(487\) −2.16713e9 + 3.75359e9i −0.850226 + 1.47263i 0.0307785 + 0.999526i \(0.490201\pi\)
−0.881004 + 0.473108i \(0.843132\pi\)
\(488\) 3.60815e7 + 6.24950e7i 0.0140545 + 0.0243431i
\(489\) 0 0
\(490\) −6.98417e7 + 4.28192e7i −0.0268181 + 0.0164419i
\(491\) 1.79725e9 0.685208 0.342604 0.939480i \(-0.388691\pi\)
0.342604 + 0.939480i \(0.388691\pi\)
\(492\) 0 0
\(493\) 5.17028e8 8.95518e8i 0.194334 0.336597i
\(494\) 5.47162e8 9.47712e8i 0.204207 0.353697i
\(495\) 0 0
\(496\) 4.49643e8 0.165456
\(497\) −5.41237e8 1.37396e8i −0.197761 0.0502028i
\(498\) 0 0
\(499\) −4.07065e8 7.05058e8i −0.146660 0.254023i 0.783331 0.621605i \(-0.213519\pi\)
−0.929991 + 0.367582i \(0.880186\pi\)
\(500\) −6.21110e7 + 1.07579e8i −0.0222215 + 0.0384888i
\(501\) 0 0
\(502\) 3.17949e8 + 5.50704e8i 0.112175 + 0.194292i
\(503\) −3.03176e9 −1.06220 −0.531101 0.847309i \(-0.678221\pi\)
−0.531101 + 0.847309i \(0.678221\pi\)
\(504\) 0 0
\(505\) −1.44888e8 −0.0500624
\(506\) 1.28333e9 + 2.22279e9i 0.440362 + 0.762730i
\(507\) 0 0
\(508\) 7.12388e8 1.23389e9i 0.241098 0.417594i
\(509\) −1.34515e9 2.32986e9i −0.452124 0.783101i 0.546394 0.837528i \(-0.316000\pi\)
−0.998518 + 0.0544271i \(0.982667\pi\)
\(510\) 0 0
\(511\) −9.00786e8 + 9.24876e8i −0.298640 + 0.306627i
\(512\) −1.34218e8 −0.0441942
\(513\) 0 0
\(514\) 1.71610e9 2.97238e9i 0.557407 0.965458i
\(515\) 4.45160e7 7.71039e7i 0.0143612 0.0248743i
\(516\) 0 0
\(517\) 5.14437e9 1.63725
\(518\) −3.08608e9 + 3.16861e9i −0.975557 + 1.00165i
\(519\) 0 0
\(520\) −2.30211e7 3.98738e7i −0.00717984 0.0124359i
\(521\) −1.84690e9 + 3.19892e9i −0.572152 + 0.990996i 0.424193 + 0.905572i \(0.360558\pi\)
−0.996345 + 0.0854238i \(0.972776\pi\)
\(522\) 0 0
\(523\) −1.36893e9 2.37105e9i −0.418432 0.724745i 0.577350 0.816497i \(-0.304087\pi\)
−0.995782 + 0.0917518i \(0.970753\pi\)
\(524\) −6.97712e8 −0.211844
\(525\) 0 0
\(526\) −3.39297e8 −0.101655
\(527\) 8.41480e8 + 1.45749e9i 0.250442 + 0.433778i
\(528\) 0 0
\(529\) 5.63790e8 9.76512e8i 0.165585 0.286802i
\(530\) 6.19099e7 + 1.07231e8i 0.0180632 + 0.0312864i
\(531\) 0 0
\(532\) −1.06478e9 2.70301e8i −0.306598 0.0778317i
\(533\) 5.84966e9 1.67334
\(534\) 0 0
\(535\) 3.62762e7 6.28322e7i 0.0102420 0.0177396i
\(536\) 7.50912e8 1.30062e9i 0.210626 0.364815i
\(537\) 0 0
\(538\) −4.16155e9 −1.15217
\(539\) −4.72028e9 + 2.89395e9i −1.29840 + 0.796033i
\(540\) 0 0
\(541\) −1.26385e9 2.18905e9i −0.343167 0.594382i 0.641852 0.766828i \(-0.278166\pi\)
−0.985019 + 0.172446i \(0.944833\pi\)
\(542\) −6.97124e8 + 1.20745e9i −0.188067 + 0.325742i
\(543\) 0 0
\(544\) −2.51180e8 4.35057e8i −0.0668944 0.115864i
\(545\) 1.16012e8 0.0306982
\(546\) 0 0
\(547\) 1.49324e8 0.0390098 0.0195049 0.999810i \(-0.493791\pi\)
0.0195049 + 0.999810i \(0.493791\pi\)
\(548\) −1.02803e9 1.78059e9i −0.266853 0.462203i
\(549\) 0 0
\(550\) −2.09682e9 + 3.63180e9i −0.537393 + 0.930792i
\(551\) −6.37890e8 1.10486e9i −0.162448 0.281369i
\(552\) 0 0
\(553\) −5.88306e8 2.08514e9i −0.147933 0.524321i
\(554\) 5.41461e9 1.35295
\(555\) 0 0
\(556\) 6.04960e8 1.04782e9i 0.149267 0.258539i
\(557\) −2.77646e9 + 4.80896e9i −0.680766 + 1.17912i 0.293982 + 0.955811i \(0.405019\pi\)
−0.974748 + 0.223310i \(0.928314\pi\)
\(558\) 0 0
\(559\) −2.42235e9 −0.586537
\(560\) −3.22486e7 + 3.31110e7i −0.00775983 + 0.00796736i
\(561\) 0 0
\(562\) 1.40498e9 + 2.43350e9i 0.333882 + 0.578300i
\(563\) −1.41867e9 + 2.45721e9i −0.335045 + 0.580315i −0.983493 0.180944i \(-0.942085\pi\)
0.648449 + 0.761258i \(0.275418\pi\)
\(564\) 0 0
\(565\) −5.49837e7 9.52345e7i −0.0128252 0.0222139i
\(566\) −5.18625e9 −1.20225
\(567\) 0 0
\(568\) −3.15047e8 −0.0721367
\(569\) 4.10087e9 + 7.10291e9i 0.933217 + 1.61638i 0.777782 + 0.628534i \(0.216345\pi\)
0.155435 + 0.987846i \(0.450322\pi\)
\(570\) 0 0
\(571\) −2.70322e7 + 4.68211e7i −0.00607651 + 0.0105248i −0.869048 0.494728i \(-0.835268\pi\)
0.862971 + 0.505253i \(0.168601\pi\)
\(572\) −1.55589e9 2.69489e9i −0.347611 0.602080i
\(573\) 0 0
\(574\) −1.59456e9 5.65163e9i −0.351925 1.24733i
\(575\) −3.72079e9 −0.816201
\(576\) 0 0
\(577\) 7.27103e8 1.25938e9i 0.157573 0.272924i −0.776420 0.630216i \(-0.782967\pi\)
0.933993 + 0.357292i \(0.116300\pi\)
\(578\) −7.01217e8 + 1.21454e9i −0.151044 + 0.261617i
\(579\) 0 0
\(580\) −5.36768e7 −0.0114232
\(581\) −6.62714e9 1.68234e9i −1.40188 0.355875i
\(582\) 0 0
\(583\) 4.18421e9 + 7.24726e9i 0.874527 + 1.51472i
\(584\) −3.64200e8 + 6.30813e8i −0.0756650 + 0.131056i
\(585\) 0 0
\(586\) −2.54006e7 4.39951e7i −0.00521437 0.00903156i
\(587\) 7.30976e9 1.49166 0.745830 0.666137i \(-0.232053\pi\)
0.745830 + 0.666137i \(0.232053\pi\)
\(588\) 0 0
\(589\) 2.07638e9 0.418699
\(590\) 1.01794e8 + 1.76312e8i 0.0204051 + 0.0353427i
\(591\) 0 0
\(592\) −1.24774e9 + 2.16116e9i −0.247172 + 0.428115i
\(593\) −2.16461e9 3.74922e9i −0.426274 0.738329i 0.570264 0.821461i \(-0.306841\pi\)
−0.996538 + 0.0831327i \(0.973507\pi\)
\(594\) 0 0
\(595\) −1.67678e8 4.25661e7i −0.0326338 0.00828428i
\(596\) 3.54959e8 0.0686779
\(597\) 0 0
\(598\) 1.38046e9 2.39102e9i 0.263979 0.457224i
\(599\) −1.44898e9 + 2.50970e9i −0.275466 + 0.477121i −0.970253 0.242095i \(-0.922165\pi\)
0.694787 + 0.719216i \(0.255499\pi\)
\(600\) 0 0
\(601\) 7.87385e9 1.47954 0.739770 0.672860i \(-0.234935\pi\)
0.739770 + 0.672860i \(0.234935\pi\)
\(602\) 6.60310e8 + 2.34034e9i 0.123356 + 0.437212i
\(603\) 0 0
\(604\) 7.25243e8 + 1.25616e9i 0.133923 + 0.231961i
\(605\) 1.59867e8 2.76897e8i 0.0293504 0.0508364i
\(606\) 0 0
\(607\) 1.80092e9 + 3.11928e9i 0.326838 + 0.566101i 0.981883 0.189490i \(-0.0606834\pi\)
−0.655044 + 0.755591i \(0.727350\pi\)
\(608\) −6.19795e8 −0.111837
\(609\) 0 0
\(610\) 1.40205e7 0.00250097
\(611\) −2.76687e9 4.79236e9i −0.490732 0.849973i
\(612\) 0 0
\(613\) 1.97224e9 3.41602e9i 0.345819 0.598976i −0.639683 0.768639i \(-0.720934\pi\)
0.985502 + 0.169663i \(0.0542678\pi\)
\(614\) 3.22181e9 + 5.58034e9i 0.561708 + 0.972907i
\(615\) 0 0
\(616\) −2.17953e9 + 2.23782e9i −0.375691 + 0.385738i
\(617\) −4.54305e9 −0.778663 −0.389331 0.921098i \(-0.627294\pi\)
−0.389331 + 0.921098i \(0.627294\pi\)
\(618\) 0 0
\(619\) −3.82703e9 + 6.62860e9i −0.648551 + 1.12332i 0.334918 + 0.942247i \(0.391291\pi\)
−0.983469 + 0.181076i \(0.942042\pi\)
\(620\) 4.36804e7 7.56567e7i 0.00736064 0.0127490i
\(621\) 0 0
\(622\) −3.39841e9 −0.566252
\(623\) 1.31962e9 + 4.67716e9i 0.218646 + 0.774950i
\(624\) 0 0
\(625\) −3.03365e9 5.25444e9i −0.497033 0.860887i
\(626\) −1.66863e9 + 2.89015e9i −0.271862 + 0.470880i
\(627\) 0 0
\(628\) −2.08040e9 3.60336e9i −0.335188 0.580562i
\(629\) −9.34031e9 −1.49652
\(630\) 0 0
\(631\) −7.11407e9 −1.12724 −0.563619 0.826035i \(-0.690591\pi\)
−0.563619 + 0.826035i \(0.690591\pi\)
\(632\) −6.11173e8 1.05858e9i −0.0963062 0.166807i
\(633\) 0 0
\(634\) −1.71198e9 + 2.96523e9i −0.266800 + 0.462111i
\(635\) −1.38409e8 2.39732e8i −0.0214515 0.0371551i
\(636\) 0 0
\(637\) 5.23470e9 + 2.84079e9i 0.802424 + 0.435463i
\(638\) −3.62777e9 −0.553054
\(639\) 0 0
\(640\) −1.30385e7 + 2.25834e7i −0.00196607 + 0.00340533i
\(641\) 1.99141e9 3.44923e9i 0.298647 0.517271i −0.677180 0.735818i \(-0.736798\pi\)
0.975827 + 0.218546i \(0.0701314\pi\)
\(642\) 0 0
\(643\) 3.89465e9 0.577737 0.288869 0.957369i \(-0.406721\pi\)
0.288869 + 0.957369i \(0.406721\pi\)
\(644\) −2.68638e9 6.81953e8i −0.396339 0.100613i
\(645\) 0 0
\(646\) −1.15991e9 2.00902e9i −0.169282 0.293204i
\(647\) −2.55065e9 + 4.41786e9i −0.370243 + 0.641279i −0.989603 0.143828i \(-0.954059\pi\)
0.619360 + 0.785107i \(0.287392\pi\)
\(648\) 0 0
\(649\) 6.87977e9 + 1.19161e10i 0.987911 + 1.71111i
\(650\) 4.51105e9 0.644289
\(651\) 0 0
\(652\) 2.23577e9 0.315908
\(653\) 4.67227e9 + 8.09262e9i 0.656647 + 1.13735i 0.981478 + 0.191574i \(0.0613593\pi\)
−0.324831 + 0.945772i \(0.605307\pi\)
\(654\) 0 0
\(655\) −6.77790e7 + 1.17397e8i −0.00942433 + 0.0163234i
\(656\) −1.65654e9 2.86922e9i −0.229108 0.396826i
\(657\) 0 0
\(658\) −3.87590e9 + 3.97955e9i −0.530373 + 0.544557i
\(659\) 1.00669e10 1.37024 0.685120 0.728430i \(-0.259750\pi\)
0.685120 + 0.728430i \(0.259750\pi\)
\(660\) 0 0
\(661\) −7.51511e8 + 1.30166e9i −0.101212 + 0.175304i −0.912184 0.409781i \(-0.865605\pi\)
0.810973 + 0.585084i \(0.198939\pi\)
\(662\) 1.06042e9 1.83671e9i 0.142062 0.246058i
\(663\) 0 0
\(664\) −3.85757e9 −0.511359
\(665\) −1.48918e8 + 1.52901e8i −0.0196369 + 0.0201620i
\(666\) 0 0
\(667\) −1.60936e9 2.78749e9i −0.209997 0.363725i
\(668\) 2.84648e9 4.93024e9i 0.369479 0.639957i
\(669\) 0 0
\(670\) −1.45894e8 2.52696e8i −0.0187403 0.0324591i
\(671\) 9.47581e8 0.121084
\(672\) 0 0
\(673\) 3.90495e9 0.493814 0.246907 0.969039i \(-0.420586\pi\)
0.246907 + 0.969039i \(0.420586\pi\)
\(674\) 8.70584e8 + 1.50790e9i 0.109522 + 0.189697i
\(675\) 0 0
\(676\) 3.34299e8 5.79023e8i 0.0416219 0.0720912i
\(677\) −3.20795e9 5.55633e9i −0.397344 0.688220i 0.596053 0.802945i \(-0.296735\pi\)
−0.993397 + 0.114725i \(0.963401\pi\)
\(678\) 0 0
\(679\) 1.39129e10 + 3.53188e9i 1.70559 + 0.432974i
\(680\) −9.76033e7 −0.0119037
\(681\) 0 0
\(682\) 2.95216e9 5.11329e9i 0.356365 0.617242i
\(683\) 4.58428e9 7.94021e9i 0.550553 0.953585i −0.447682 0.894193i \(-0.647750\pi\)
0.998235 0.0593923i \(-0.0189163\pi\)
\(684\) 0 0
\(685\) −3.99469e8 −0.0474860
\(686\) 1.31769e9 5.83186e9i 0.155840 0.689720i
\(687\) 0 0
\(688\) 6.85976e8 + 1.18814e9i 0.0803062 + 0.139094i
\(689\) 4.50090e9 7.79578e9i 0.524242 0.908013i
\(690\) 0 0
\(691\) −4.12922e9 7.15202e9i −0.476096 0.824623i 0.523529 0.852008i \(-0.324615\pi\)
−0.999625 + 0.0273851i \(0.991282\pi\)
\(692\) 1.96888e9 0.225865
\(693\) 0 0
\(694\) −5.19966e9 −0.590496
\(695\) −1.17537e8 2.03581e8i −0.0132809 0.0230033i
\(696\) 0 0
\(697\) 6.20024e9 1.07391e10i 0.693576 1.20131i
\(698\) −2.84615e9 4.92969e9i −0.316785 0.548688i
\(699\) 0 0
\(700\) −1.22967e9 4.35833e9i −0.135502 0.480261i
\(701\) 1.35693e10 1.48779 0.743897 0.668294i \(-0.232975\pi\)
0.743897 + 0.668294i \(0.232975\pi\)
\(702\) 0 0
\(703\) −5.76187e9 + 9.97985e9i −0.625489 + 1.08338i
\(704\) −8.81215e8 + 1.52631e9i −0.0951870 + 0.164869i
\(705\) 0 0
\(706\) −1.23872e10 −1.32482
\(707\) 7.37775e9 7.57506e9i 0.785156 0.806154i
\(708\) 0 0
\(709\) −3.01524e9 5.22255e9i −0.317731 0.550327i 0.662283 0.749254i \(-0.269588\pi\)
−0.980014 + 0.198927i \(0.936254\pi\)
\(710\) −3.06051e7 + 5.30096e7i −0.00320915 + 0.00555841i
\(711\) 0 0
\(712\) 1.37092e9 + 2.37450e9i 0.142341 + 0.246542i
\(713\) 5.23857e9 0.541252
\(714\) 0 0
\(715\) −6.04587e8 −0.0618568
\(716\) 3.29830e9 + 5.71282e9i 0.335811 + 0.581641i
\(717\) 0 0
\(718\) −6.75058e8 + 1.16923e9i −0.0680621 + 0.117887i
\(719\) −4.88166e8 8.45527e8i −0.0489797 0.0848353i 0.840496 0.541818i \(-0.182264\pi\)
−0.889476 + 0.456982i \(0.848930\pi\)
\(720\) 0 0
\(721\) 1.76440e9 + 6.25357e9i 0.175316 + 0.621376i
\(722\) 4.28887e9 0.424094
\(723\) 0 0
\(724\) 2.00218e9 3.46788e9i 0.196074 0.339609i
\(725\) 2.62953e9 4.55447e9i 0.256268 0.443869i
\(726\) 0 0
\(727\) 1.25379e10 1.21019 0.605095 0.796153i \(-0.293135\pi\)
0.605095 + 0.796153i \(0.293135\pi\)
\(728\) 3.25694e9 + 8.26794e8i 0.312860 + 0.0794214i
\(729\) 0 0
\(730\) 7.07602e7 + 1.22560e8i 0.00673223 + 0.0116606i
\(731\) −2.56752e9 + 4.44708e9i −0.243111 + 0.421080i
\(732\) 0 0
\(733\) −6.39843e9 1.10824e10i −0.600080 1.03937i −0.992808 0.119715i \(-0.961802\pi\)
0.392728 0.919655i \(-0.371531\pi\)
\(734\) 2.74972e9 0.256657
\(735\) 0 0
\(736\) −1.56371e9 −0.144571
\(737\) −9.86031e9 1.70786e10i −0.907307 1.57150i
\(738\) 0 0
\(739\) 2.26030e9 3.91495e9i 0.206020 0.356838i −0.744437 0.667693i \(-0.767282\pi\)
0.950457 + 0.310855i \(0.100615\pi\)
\(740\) 2.42423e8 + 4.19889e8i 0.0219919 + 0.0380911i
\(741\) 0 0
\(742\) −8.75877e9 2.22347e9i −0.787099 0.199810i
\(743\) −1.42321e10 −1.27294 −0.636469 0.771303i \(-0.719606\pi\)
−0.636469 + 0.771303i \(0.719606\pi\)
\(744\) 0 0
\(745\) 3.44824e7 5.97253e7i 0.00305528 0.00529190i
\(746\) −5.57417e8 + 9.65474e8i −0.0491580 + 0.0851442i
\(747\) 0 0
\(748\) −6.59656e9 −0.576318
\(749\) 1.43781e9 + 5.09605e9i 0.125030 + 0.443147i
\(750\) 0 0
\(751\) −7.44123e9 1.28886e10i −0.641069 1.11036i −0.985194 0.171441i \(-0.945158\pi\)
0.344125 0.938924i \(-0.388175\pi\)
\(752\) −1.56708e9 + 2.71426e9i −0.134378 + 0.232750i
\(753\) 0 0
\(754\) 1.95117e9 + 3.37953e9i 0.165766 + 0.287116i
\(755\) 2.81814e8 0.0238313
\(756\) 0 0
\(757\) 1.24473e10 1.04289 0.521445 0.853285i \(-0.325393\pi\)
0.521445 + 0.853285i \(0.325393\pi\)
\(758\) −3.09785e9 5.36563e9i −0.258356 0.447485i
\(759\) 0 0
\(760\) −6.02097e7 + 1.04286e8i −0.00497530 + 0.00861747i
\(761\) 1.15160e10 + 1.99463e10i 0.947230 + 1.64065i 0.751223 + 0.660049i \(0.229464\pi\)
0.196007 + 0.980602i \(0.437202\pi\)
\(762\) 0 0
\(763\) −5.90737e9 + 6.06535e9i −0.481458 + 0.494334i
\(764\) −5.06243e9 −0.410707
\(765\) 0 0
\(766\) 5.22492e9 9.04983e9i 0.420029 0.727511i
\(767\) 7.40048e9 1.28180e10i 0.592211 1.02574i
\(768\) 0 0
\(769\) −1.08864e10 −0.863265 −0.431632 0.902050i \(-0.642062\pi\)
−0.431632 + 0.902050i \(0.642062\pi\)
\(770\) 1.64805e8 + 5.84119e8i 0.0130092 + 0.0461088i
\(771\) 0 0
\(772\) 1.80126e9 + 3.11987e9i 0.140902 + 0.244049i
\(773\) 7.34907e9 1.27290e10i 0.572275 0.991209i −0.424057 0.905635i \(-0.639395\pi\)
0.996332 0.0855732i \(-0.0272722\pi\)
\(774\) 0 0
\(775\) 4.27964e9 + 7.41256e9i 0.330257 + 0.572021i
\(776\) 8.09853e9 0.622143
\(777\) 0 0
\(778\) 1.77110e10 1.34839
\(779\) −7.64964e9 1.32496e10i −0.579775 1.00420i
\(780\) 0 0
\(781\) −2.06846e9 + 3.58268e9i −0.155371 + 0.269110i
\(782\) −2.92638e9 5.06864e9i −0.218830 0.379025i
\(783\) 0 0
\(784\) −8.90073e7 3.37206e9i −0.00659659 0.249913i
\(785\) −8.08398e8 −0.0596460
\(786\) 0 0
\(787\) 4.29872e8 7.44560e8i 0.0314360 0.0544488i −0.849879 0.526977i \(-0.823325\pi\)
0.881315 + 0.472528i \(0.156659\pi\)
\(788\) −1.57311e9 + 2.72471e9i −0.114530 + 0.198371i
\(789\) 0 0
\(790\) −2.37489e8 −0.0171375
\(791\) 7.77888e9 + 1.97472e9i 0.558855 + 0.141869i
\(792\) 0 0
\(793\) −5.09651e8 8.82741e8i −0.0362925 0.0628604i
\(794\) 4.68449e9 8.11378e9i 0.332117 0.575243i
\(795\) 0 0
\(796\) 5.34704e9 + 9.26135e9i 0.375766 + 0.650846i
\(797\) −4.31200e9 −0.301699 −0.150850 0.988557i \(-0.548201\pi\)
−0.150850 + 0.988557i \(0.548201\pi\)
\(798\) 0 0
\(799\) −1.17308e10 −0.813603
\(800\) −1.27747e9 2.21264e9i −0.0882134 0.152790i
\(801\) 0 0
\(802\) 5.99855e9 1.03898e10i 0.410616 0.711208i
\(803\) 4.78236e9 + 8.28329e9i 0.325940 + 0.564545i
\(804\) 0 0
\(805\) −3.75712e8 + 3.85760e8i −0.0253846 + 0.0260634i
\(806\) −6.35120e9 −0.427251
\(807\) 0 0
\(808\) 2.98293e9 5.16658e9i 0.198931 0.344559i
\(809\) −9.94355e9 + 1.72227e10i −0.660270 + 1.14362i 0.320275 + 0.947325i \(0.396225\pi\)
−0.980545 + 0.196296i \(0.937108\pi\)
\(810\) 0 0
\(811\) −2.58957e10 −1.70473 −0.852363 0.522950i \(-0.824831\pi\)
−0.852363 + 0.522950i \(0.824831\pi\)
\(812\) 2.73325e9 2.80635e9i 0.179157 0.183948i
\(813\) 0 0
\(814\) 1.63843e10 + 2.83784e10i 1.06474 + 1.84418i
\(815\) 2.17193e8 3.76190e8i 0.0140538 0.0243420i
\(816\) 0 0
\(817\) 3.16772e9 + 5.48665e9i 0.203221 + 0.351990i
\(818\) 5.99683e8 0.0383076
\(819\) 0 0
\(820\) −6.43697e8 −0.0407693
\(821\) 1.06287e9 + 1.84094e9i 0.0670314 + 0.116102i 0.897593 0.440825i \(-0.145314\pi\)
−0.830562 + 0.556926i \(0.811981\pi\)
\(822\) 0 0
\(823\) 7.58631e9 1.31399e10i 0.474385 0.821660i −0.525184 0.850988i \(-0.676004\pi\)
0.999570 + 0.0293289i \(0.00933701\pi\)
\(824\) 1.83298e9 + 3.17481e9i 0.114133 + 0.197684i
\(825\) 0 0
\(826\) −1.44014e10 3.65588e9i −0.889148 0.225716i
\(827\) −1.94463e10 −1.19555 −0.597776 0.801663i \(-0.703949\pi\)
−0.597776 + 0.801663i \(0.703949\pi\)
\(828\) 0 0
\(829\) 1.84579e9 3.19701e9i 0.112523 0.194896i −0.804264 0.594273i \(-0.797440\pi\)
0.916787 + 0.399376i \(0.130773\pi\)
\(830\) −3.74743e8 + 6.49073e8i −0.0227489 + 0.0394022i
\(831\) 0 0
\(832\) 1.89582e9 0.114121
\(833\) 1.07637e10 6.59911e9i 0.645215 0.395574i
\(834\) 0 0
\(835\) −5.53040e8 9.57894e8i −0.0328741 0.0569396i
\(836\) −4.06930e9 + 7.04823e9i −0.240878 + 0.417214i
\(837\) 0 0
\(838\) 3.38815e8 + 5.86844e8i 0.0198888 + 0.0344484i
\(839\) 9.94899e9 0.581584 0.290792 0.956786i \(-0.406081\pi\)
0.290792 + 0.956786i \(0.406081\pi\)
\(840\) 0 0
\(841\) −1.27005e10 −0.736264
\(842\) −2.41261e9 4.17876e9i −0.139282 0.241243i
\(843\) 0 0
\(844\) −2.25955e9 + 3.91365e9i −0.129367 + 0.224070i
\(845\) −6.49507e7 1.12498e8i −0.00370327 0.00641425i
\(846\) 0 0
\(847\) 6.33634e9 + 2.24580e10i 0.358300 + 1.26993i
\(848\) −5.09837e9 −0.287108
\(849\) 0 0
\(850\) 4.78140e9 8.28163e9i 0.267048 0.462541i
\(851\) −1.45369e10 + 2.51786e10i −0.808569 + 1.40048i
\(852\) 0 0
\(853\) 3.15287e9 0.173934 0.0869669 0.996211i \(-0.472283\pi\)
0.0869669 + 0.996211i \(0.472283\pi\)
\(854\) −7.13931e8 + 7.33024e8i −0.0392242 + 0.0402732i
\(855\) 0 0
\(856\) 1.49370e9 + 2.58716e9i 0.0813963 + 0.140983i
\(857\) 8.54798e7 1.48055e8i 0.00463907 0.00803510i −0.863697 0.504012i \(-0.831857\pi\)
0.868336 + 0.495977i \(0.165190\pi\)
\(858\) 0 0
\(859\) 9.17292e9 + 1.58880e10i 0.493778 + 0.855248i 0.999974 0.00717006i \(-0.00228232\pi\)
−0.506197 + 0.862418i \(0.668949\pi\)
\(860\) 2.66555e8 0.0142904
\(861\) 0 0
\(862\) 2.08522e10 1.10886
\(863\) 1.05965e10 + 1.83536e10i 0.561208 + 0.972040i 0.997391 + 0.0721827i \(0.0229965\pi\)
−0.436184 + 0.899858i \(0.643670\pi\)
\(864\) 0 0
\(865\) 1.91266e8 3.31283e8i 0.0100481 0.0174037i
\(866\) 1.23870e10 + 2.14550e10i 0.648119 + 1.12258i
\(867\) 0 0
\(868\) 1.73128e9 + 6.13619e9i 0.0898562 + 0.318478i
\(869\) −1.60508e10 −0.829711
\(870\) 0 0
\(871\) −1.06066e10 + 1.83712e10i −0.543893 + 0.942049i
\(872\) −2.38843e9 + 4.13688e9i −0.121985 + 0.211283i
\(873\) 0 0
\(874\) −7.22092e9 −0.365850
\(875\) −1.70726e9 4.33400e8i −0.0861534 0.0218706i
\(876\) 0 0
\(877\) −1.29471e10 2.24251e10i −0.648148 1.12263i −0.983565 0.180556i \(-0.942210\pi\)
0.335417 0.942070i \(-0.391123\pi\)
\(878\) −2.41839e9 + 4.18878e9i −0.120586 + 0.208861i
\(879\) 0 0
\(880\) 1.71211e8 + 2.96545e8i 0.00846918 + 0.0146690i
\(881\) −2.45497e10 −1.20957 −0.604785 0.796389i \(-0.706741\pi\)
−0.604785 + 0.796389i \(0.706741\pi\)
\(882\) 0 0
\(883\) 2.01403e10 0.984473 0.492237 0.870461i \(-0.336179\pi\)
0.492237 + 0.870461i \(0.336179\pi\)
\(884\) 3.54792e9 + 6.14517e9i 0.172739 + 0.299193i
\(885\) 0 0
\(886\) −8.66617e9 + 1.50102e10i −0.418609 + 0.725053i
\(887\) 7.24531e8 + 1.25492e9i 0.0348597 + 0.0603788i 0.882929 0.469507i \(-0.155568\pi\)
−0.848069 + 0.529886i \(0.822235\pi\)
\(888\) 0 0
\(889\) 1.95816e10 + 4.97092e9i 0.934744 + 0.237291i
\(890\) 5.32709e8 0.0253294
\(891\) 0 0
\(892\) 7.99650e9 1.38503e10i 0.377244 0.653407i
\(893\) −7.23650e9 + 1.25340e10i −0.340054 + 0.588992i
\(894\) 0 0
\(895\) 1.28165e9 0.0597569
\(896\) −5.16784e8 1.83164e9i −0.0240011 0.0850673i
\(897\) 0 0
\(898\) 4.05218e9 + 7.01858e9i 0.186733 + 0.323431i
\(899\) −3.70217e9 + 6.41234e9i −0.169941 + 0.294346i
\(900\) 0 0
\(901\) −9.54129e9 1.65260e10i −0.434580 0.752715i
\(902\) −4.35046e10 −1.97384
\(903\) 0 0
\(904\) 4.52798e9 0.203852
\(905\) −3.89003e8 6.73773e8i −0.0174455 0.0302164i
\(906\) 0 0
\(907\) 1.54863e9 2.68231e9i 0.0689165 0.119367i −0.829508 0.558495i \(-0.811379\pi\)
0.898425 + 0.439128i \(0.144712\pi\)
\(908\) 1.03895e10 + 1.79951e10i 0.460567 + 0.797725i
\(909\) 0 0
\(910\) 4.55510e8 4.67692e8i 0.0200379 0.0205738i
\(911\) −2.29298e10 −1.00481 −0.502406 0.864632i \(-0.667552\pi\)
−0.502406 + 0.864632i \(0.667552\pi\)
\(912\) 0 0
\(913\) −2.53271e10 + 4.38679e10i −1.10138 + 1.90765i
\(914\) 6.43362e9 1.11434e10i 0.278705 0.482730i
\(915\) 0 0
\(916\) −1.34710e9 −0.0579115
\(917\) −2.68643e9 9.52154e9i −0.115049 0.407769i
\(918\) 0 0
\(919\) −2.23880e10 3.87772e10i −0.951506 1.64806i −0.742168 0.670213i \(-0.766203\pi\)
−0.209338 0.977843i \(-0.567131\pi\)
\(920\) −1.51906e8 + 2.63108e8i −0.00643156 + 0.0111398i
\(921\) 0 0
\(922\) 1.19342e10 + 2.06706e10i 0.501458 + 0.868551i
\(923\) 4.45003e9 0.186276
\(924\) 0 0
\(925\) −4.75034e10 −1.97346
\(926\) −1.13361e10 1.96347e10i −0.469164 0.812616i
\(927\) 0 0
\(928\) 1.10509e9 1.91407e9i 0.0453921 0.0786214i
\(929\) 1.49225e10 + 2.58466e10i 0.610644 + 1.05767i 0.991132 + 0.132880i \(0.0424226\pi\)
−0.380488 + 0.924786i \(0.624244\pi\)
\(930\) 0 0
\(931\) −4.11020e8 1.55716e10i −0.0166932 0.632425i
\(932\) 1.04630e10 0.423352
\(933\) 0 0
\(934\) 1.72733e10 2.99182e10i 0.693682 1.20149i
\(935\) −6.40821e8 + 1.10993e9i −0.0256387 + 0.0444075i
\(936\) 0 0
\(937\) 1.43090e10 0.568227 0.284113 0.958791i \(-0.408301\pi\)
0.284113 + 0.958791i \(0.408301\pi\)
\(938\) 2.06405e10 + 5.23972e9i 0.816603 + 0.207300i
\(939\) 0 0
\(940\) 3.04466e8 + 5.27351e8i 0.0119562 + 0.0207087i
\(941\) −3.30316e9 + 5.72124e9i −0.129231 + 0.223834i −0.923379 0.383890i \(-0.874584\pi\)
0.794148 + 0.607724i \(0.207917\pi\)
\(942\) 0 0
\(943\) −1.92996e10 3.34279e10i −0.749475 1.29813i
\(944\) −8.38286e9 −0.324332
\(945\) 0 0
\(946\) 1.80153e10 0.691866
\(947\) −9.94687e9 1.72285e10i −0.380594 0.659208i 0.610553 0.791975i \(-0.290947\pi\)
−0.991147 + 0.132767i \(0.957614\pi\)
\(948\) 0 0
\(949\) 5.14432e9 8.91022e9i 0.195387 0.338421i
\(950\) −5.89912e9 1.02176e10i −0.223231 0.386648i
\(951\) 0 0
\(952\) 4.97001e9 5.10293e9i 0.186693 0.191686i
\(953\) −4.15702e10 −1.55581 −0.777905 0.628382i \(-0.783717\pi\)
−0.777905 + 0.628382i \(0.783717\pi\)
\(954\) 0 0
\(955\) −4.91788e8 + 8.51802e8i −0.0182712 + 0.0316466i
\(956\) −1.01817e10 + 1.76352e10i −0.376892 + 0.652796i
\(957\) 0 0
\(958\) −6.56258e9 −0.241154
\(959\) 2.03411e10 2.08851e10i 0.744750 0.764667i
\(960\) 0 0
\(961\) 7.73091e9 + 1.33903e10i 0.280995 + 0.486698i
\(962\) 1.76244e10 3.05263e10i 0.638264 1.10551i
\(963\) 0 0
\(964\) 4.14630e9 + 7.18160e9i 0.149070 + 0.258197i
\(965\) 6.99931e8 0.0250732
\(966\) 0 0
\(967\) −2.38376e10 −0.847755 −0.423877 0.905720i \(-0.639331\pi\)
−0.423877 + 0.905720i \(0.639331\pi\)
\(968\) 6.58263e9 + 1.14014e10i 0.233257 + 0.404014i
\(969\) 0 0
\(970\) 7.86728e8 1.36265e9i 0.0276773 0.0479385i
\(971\) 2.49541e10 + 4.32218e10i 0.874732 + 1.51508i 0.857047 + 0.515237i \(0.172296\pi\)
0.0176850 + 0.999844i \(0.494370\pi\)
\(972\) 0 0
\(973\) 1.66287e10 + 4.22130e9i 0.578714 + 0.146910i
\(974\) −3.46741e10 −1.20240
\(975\) 0 0
\(976\) −2.88652e8 + 4.99960e8i −0.00993803 + 0.0172132i
\(977\) −1.06421e10 + 1.84327e10i −0.365087 + 0.632350i −0.988790 0.149312i \(-0.952294\pi\)
0.623703 + 0.781662i \(0.285628\pi\)
\(978\) 0 0
\(979\) 3.60034e10 1.22632
\(980\) −5.76027e8 3.12601e8i −0.0195502 0.0106096i
\(981\) 0 0
\(982\) 7.18899e9 + 1.24517e10i 0.242258 + 0.419603i
\(983\) 2.02849e10 3.51344e10i 0.681138 1.17977i −0.293496 0.955960i \(-0.594819\pi\)
0.974634 0.223805i \(-0.0718479\pi\)
\(984\) 0 0
\(985\) 3.05639e8 + 5.29382e8i 0.0101902 + 0.0176499i
\(986\) 8.27244e9 0.274830
\(987\) 0 0
\(988\) 8.75459e9 0.288793
\(989\) 7.99197e9 + 1.38425e10i 0.262704 + 0.455017i
\(990\) 0 0
\(991\) 1.53510e10 2.65888e10i 0.501048 0.867841i −0.498951 0.866630i \(-0.666281\pi\)
0.999999 0.00121109i \(-0.000385502\pi\)
\(992\) 1.79857e9 + 3.11522e9i 0.0584975 + 0.101321i
\(993\) 0 0
\(994\) −1.21304e9 4.29938e9i −0.0391762 0.138853i
\(995\) 2.07775e9 0.0668670
\(996\) 0 0
\(997\) −1.94876e10 + 3.37534e10i −0.622765 + 1.07866i 0.366203 + 0.930535i \(0.380657\pi\)
−0.988968 + 0.148126i \(0.952676\pi\)
\(998\) 3.25652e9 5.64046e9i 0.103704 0.179621i
\(999\) 0 0
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 126.8.g.j.109.3 yes 6
3.2 odd 2 126.8.g.i.109.1 yes 6
7.2 even 3 inner 126.8.g.j.37.3 yes 6
21.2 odd 6 126.8.g.i.37.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.8.g.i.37.1 6 21.2 odd 6
126.8.g.i.109.1 yes 6 3.2 odd 2
126.8.g.j.37.3 yes 6 7.2 even 3 inner
126.8.g.j.109.3 yes 6 1.1 even 1 trivial