Properties

Label 81.8.c.c.55.1
Level $81$
Weight $8$
Character 81.55
Analytic conductor $25.303$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,8,Mod(28,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.28");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 81.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(25.3031870642\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 81.55
Dual form 81.8.c.c.28.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.00000 - 5.19615i) q^{2} +(46.0000 + 79.6743i) q^{4} +(195.000 + 337.750i) q^{5} +(32.0000 - 55.4256i) q^{7} +1320.00 q^{8} +2340.00 q^{10} +(-474.000 + 820.992i) q^{11} +(2549.00 + 4415.00i) q^{13} +(-192.000 - 332.554i) q^{14} +(-1928.00 + 3339.39i) q^{16} -28386.0 q^{17} -8620.00 q^{19} +(-17940.0 + 31073.0i) q^{20} +(2844.00 + 4925.95i) q^{22} +(-7644.00 - 13239.8i) q^{23} +(-36987.5 + 64064.2i) q^{25} +30588.0 q^{26} +5888.00 q^{28} +(18255.0 - 31618.6i) q^{29} +(138404. + 239723. i) q^{31} +(96048.0 + 166360. i) q^{32} +(-85158.0 + 147498. i) q^{34} +24960.0 q^{35} +268526. q^{37} +(-25860.0 + 44790.8i) q^{38} +(257400. + 445830. i) q^{40} +(-314859. - 545352. i) q^{41} +(-342886. + 593896. i) q^{43} -87216.0 q^{44} -91728.0 q^{46} +(291648. - 505149. i) q^{47} +(409724. + 709662. i) q^{49} +(221925. + 384385. i) q^{50} +(-234508. + 406180. i) q^{52} +428058. q^{53} -369720. q^{55} +(42240.0 - 73161.8i) q^{56} +(-109530. - 189712. i) q^{58} +(653190. + 1.13136e6i) q^{59} +(-150331. + 260381. i) q^{61} +1.66085e6 q^{62} +659008. q^{64} +(-994110. + 1.72185e6i) q^{65} +(253622. + 439286. i) q^{67} +(-1.30576e6 - 2.26164e6i) q^{68} +(74880.0 - 129696. i) q^{70} -5.56063e6 q^{71} +1.36908e6 q^{73} +(805578. - 1.39530e6i) q^{74} +(-396520. - 686793. i) q^{76} +(30336.0 + 52543.5i) q^{77} +(3.45686e6 - 5.98746e6i) q^{79} -1.50384e6 q^{80} -3.77831e6 q^{82} +(-2.18837e6 + 3.79037e6i) q^{83} +(-5.53527e6 - 9.58737e6i) q^{85} +(2.05732e6 + 3.56338e6i) q^{86} +(-625680. + 1.08371e6i) q^{88} +8.52831e6 q^{89} +326272. q^{91} +(703248. - 1.21806e6i) q^{92} +(-1.74989e6 - 3.03089e6i) q^{94} +(-1.68090e6 - 2.91140e6i) q^{95} +(4.41341e6 - 7.64425e6i) q^{97} +4.91668e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{2} + 92 q^{4} + 390 q^{5} + 64 q^{7} + 2640 q^{8} + 4680 q^{10} - 948 q^{11} + 5098 q^{13} - 384 q^{14} - 3856 q^{16} - 56772 q^{17} - 17240 q^{19} - 35880 q^{20} + 5688 q^{22} - 15288 q^{23}+ \cdots + 9833364 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 5.19615i 0.265165 0.459279i −0.702442 0.711741i \(-0.747907\pi\)
0.967607 + 0.252462i \(0.0812402\pi\)
\(3\) 0 0
\(4\) 46.0000 + 79.6743i 0.359375 + 0.622456i
\(5\) 195.000 + 337.750i 0.697653 + 1.20837i 0.969278 + 0.245968i \(0.0791057\pi\)
−0.271625 + 0.962403i \(0.587561\pi\)
\(6\) 0 0
\(7\) 32.0000 55.4256i 0.0352620 0.0610756i −0.847856 0.530227i \(-0.822107\pi\)
0.883118 + 0.469151i \(0.155440\pi\)
\(8\) 1320.00 0.911505
\(9\) 0 0
\(10\) 2340.00 0.739973
\(11\) −474.000 + 820.992i −0.107375 + 0.185979i −0.914706 0.404120i \(-0.867578\pi\)
0.807331 + 0.590099i \(0.200911\pi\)
\(12\) 0 0
\(13\) 2549.00 + 4415.00i 0.321787 + 0.557351i 0.980857 0.194731i \(-0.0623833\pi\)
−0.659070 + 0.752082i \(0.729050\pi\)
\(14\) −192.000 332.554i −0.0187005 0.0323902i
\(15\) 0 0
\(16\) −1928.00 + 3339.39i −0.117676 + 0.203820i
\(17\) −28386.0 −1.40131 −0.700653 0.713502i \(-0.747108\pi\)
−0.700653 + 0.713502i \(0.747108\pi\)
\(18\) 0 0
\(19\) −8620.00 −0.288317 −0.144158 0.989555i \(-0.546047\pi\)
−0.144158 + 0.989555i \(0.546047\pi\)
\(20\) −17940.0 + 31073.0i −0.501438 + 0.868517i
\(21\) 0 0
\(22\) 2844.00 + 4925.95i 0.0569443 + 0.0986304i
\(23\) −7644.00 13239.8i −0.131001 0.226900i 0.793062 0.609141i \(-0.208486\pi\)
−0.924063 + 0.382241i \(0.875152\pi\)
\(24\) 0 0
\(25\) −36987.5 + 64064.2i −0.473440 + 0.820022i
\(26\) 30588.0 0.341306
\(27\) 0 0
\(28\) 5888.00 0.0506891
\(29\) 18255.0 31618.6i 0.138992 0.240741i −0.788124 0.615517i \(-0.788947\pi\)
0.927115 + 0.374776i \(0.122281\pi\)
\(30\) 0 0
\(31\) 138404. + 239723.i 0.834416 + 1.44525i 0.894505 + 0.447058i \(0.147528\pi\)
−0.0600887 + 0.998193i \(0.519138\pi\)
\(32\) 96048.0 + 166360.i 0.518159 + 0.897478i
\(33\) 0 0
\(34\) −85158.0 + 147498.i −0.371577 + 0.643591i
\(35\) 24960.0 0.0984026
\(36\) 0 0
\(37\) 268526. 0.871526 0.435763 0.900061i \(-0.356479\pi\)
0.435763 + 0.900061i \(0.356479\pi\)
\(38\) −25860.0 + 44790.8i −0.0764515 + 0.132418i
\(39\) 0 0
\(40\) 257400. + 445830.i 0.635914 + 1.10144i
\(41\) −314859. 545352.i −0.713465 1.23576i −0.963549 0.267533i \(-0.913791\pi\)
0.250084 0.968224i \(-0.419542\pi\)
\(42\) 0 0
\(43\) −342886. + 593896.i −0.657673 + 1.13912i 0.323543 + 0.946213i \(0.395126\pi\)
−0.981216 + 0.192910i \(0.938207\pi\)
\(44\) −87216.0 −0.154352
\(45\) 0 0
\(46\) −91728.0 −0.138947
\(47\) 291648. 505149.i 0.409748 0.709704i −0.585114 0.810951i \(-0.698950\pi\)
0.994861 + 0.101248i \(0.0322834\pi\)
\(48\) 0 0
\(49\) 409724. + 709662.i 0.497513 + 0.861718i
\(50\) 221925. + 384385.i 0.251079 + 0.434882i
\(51\) 0 0
\(52\) −234508. + 406180.i −0.231284 + 0.400596i
\(53\) 428058. 0.394945 0.197473 0.980308i \(-0.436727\pi\)
0.197473 + 0.980308i \(0.436727\pi\)
\(54\) 0 0
\(55\) −369720. −0.299643
\(56\) 42240.0 73161.8i 0.0321415 0.0556707i
\(57\) 0 0
\(58\) −109530. 189712.i −0.0737115 0.127672i
\(59\) 653190. + 1.13136e6i 0.414054 + 0.717163i 0.995329 0.0965444i \(-0.0307790\pi\)
−0.581274 + 0.813708i \(0.697446\pi\)
\(60\) 0 0
\(61\) −150331. + 260381.i −0.0847997 + 0.146877i −0.905306 0.424760i \(-0.860358\pi\)
0.820506 + 0.571638i \(0.193692\pi\)
\(62\) 1.66085e6 0.885032
\(63\) 0 0
\(64\) 659008. 0.314240
\(65\) −994110. + 1.72185e6i −0.448991 + 0.777675i
\(66\) 0 0
\(67\) 253622. + 439286.i 0.103021 + 0.178437i 0.912928 0.408121i \(-0.133816\pi\)
−0.809907 + 0.586558i \(0.800482\pi\)
\(68\) −1.30576e6 2.26164e6i −0.503594 0.872251i
\(69\) 0 0
\(70\) 74880.0 129696.i 0.0260929 0.0451943i
\(71\) −5.56063e6 −1.84383 −0.921913 0.387397i \(-0.873374\pi\)
−0.921913 + 0.387397i \(0.873374\pi\)
\(72\) 0 0
\(73\) 1.36908e6 0.411907 0.205954 0.978562i \(-0.433970\pi\)
0.205954 + 0.978562i \(0.433970\pi\)
\(74\) 805578. 1.39530e6i 0.231098 0.400274i
\(75\) 0 0
\(76\) −396520. 686793.i −0.103614 0.179464i
\(77\) 30336.0 + 52543.5i 0.00757253 + 0.0131160i
\(78\) 0 0
\(79\) 3.45686e6 5.98746e6i 0.788836 1.36630i −0.137844 0.990454i \(-0.544017\pi\)
0.926680 0.375851i \(-0.122649\pi\)
\(80\) −1.50384e6 −0.328388
\(81\) 0 0
\(82\) −3.77831e6 −0.756744
\(83\) −2.18837e6 + 3.79037e6i −0.420096 + 0.727627i −0.995948 0.0899264i \(-0.971337\pi\)
0.575853 + 0.817553i \(0.304670\pi\)
\(84\) 0 0
\(85\) −5.53527e6 9.58737e6i −0.977626 1.69330i
\(86\) 2.05732e6 + 3.56338e6i 0.348784 + 0.604111i
\(87\) 0 0
\(88\) −625680. + 1.08371e6i −0.0978730 + 0.169521i
\(89\) 8.52831e6 1.28232 0.641162 0.767405i \(-0.278453\pi\)
0.641162 + 0.767405i \(0.278453\pi\)
\(90\) 0 0
\(91\) 326272. 0.0453874
\(92\) 703248. 1.21806e6i 0.0941567 0.163084i
\(93\) 0 0
\(94\) −1.74989e6 3.03089e6i −0.217302 0.376377i
\(95\) −1.68090e6 2.91140e6i −0.201145 0.348393i
\(96\) 0 0
\(97\) 4.41341e6 7.64425e6i 0.490990 0.850420i −0.508956 0.860793i \(-0.669968\pi\)
0.999946 + 0.0103725i \(0.00330171\pi\)
\(98\) 4.91668e6 0.527692
\(99\) 0 0
\(100\) −6.80570e6 −0.680570
\(101\) 5.99321e6 1.03805e7i 0.578808 1.00253i −0.416808 0.908995i \(-0.636851\pi\)
0.995616 0.0935309i \(-0.0298154\pi\)
\(102\) 0 0
\(103\) −3.60470e6 6.24352e6i −0.325041 0.562988i 0.656480 0.754344i \(-0.272045\pi\)
−0.981521 + 0.191356i \(0.938711\pi\)
\(104\) 3.36468e6 + 5.82780e6i 0.293310 + 0.508028i
\(105\) 0 0
\(106\) 1.28417e6 2.22425e6i 0.104726 0.181390i
\(107\) −1.14261e7 −0.901683 −0.450842 0.892604i \(-0.648876\pi\)
−0.450842 + 0.892604i \(0.648876\pi\)
\(108\) 0 0
\(109\) 4.02095e6 0.297397 0.148698 0.988883i \(-0.452492\pi\)
0.148698 + 0.988883i \(0.452492\pi\)
\(110\) −1.10916e6 + 1.92112e6i −0.0794547 + 0.137620i
\(111\) 0 0
\(112\) 123392. + 213721.i 0.00829896 + 0.0143742i
\(113\) −8.85316e6 1.53341e7i −0.577197 0.999734i −0.995799 0.0915642i \(-0.970813\pi\)
0.418603 0.908169i \(-0.362520\pi\)
\(114\) 0 0
\(115\) 2.98116e6 5.16352e6i 0.182786 0.316595i
\(116\) 3.35892e6 0.199801
\(117\) 0 0
\(118\) 7.83828e6 0.439171
\(119\) −908352. + 1.57331e6i −0.0494128 + 0.0855855i
\(120\) 0 0
\(121\) 9.29423e6 + 1.60981e7i 0.476941 + 0.826086i
\(122\) 901986. + 1.56229e6i 0.0449718 + 0.0778935i
\(123\) 0 0
\(124\) −1.27332e7 + 2.20545e7i −0.599737 + 1.03877i
\(125\) 1.61850e6 0.0741187
\(126\) 0 0
\(127\) 1.67883e7 0.727267 0.363633 0.931542i \(-0.381536\pi\)
0.363633 + 0.931542i \(0.381536\pi\)
\(128\) −1.03171e7 + 1.78698e7i −0.434834 + 0.753155i
\(129\) 0 0
\(130\) 5.96466e6 + 1.03311e7i 0.238113 + 0.412425i
\(131\) 8.41339e6 + 1.45724e7i 0.326980 + 0.566346i 0.981911 0.189343i \(-0.0606357\pi\)
−0.654931 + 0.755689i \(0.727302\pi\)
\(132\) 0 0
\(133\) −275840. + 477769.i −0.0101666 + 0.0176091i
\(134\) 3.04346e6 0.109270
\(135\) 0 0
\(136\) −3.74695e7 −1.27730
\(137\) 1.40225e7 2.42876e7i 0.465910 0.806980i −0.533332 0.845906i \(-0.679060\pi\)
0.999242 + 0.0389262i \(0.0123937\pi\)
\(138\) 0 0
\(139\) 5.91365e6 + 1.02427e7i 0.186769 + 0.323493i 0.944171 0.329456i \(-0.106865\pi\)
−0.757402 + 0.652948i \(0.773532\pi\)
\(140\) 1.14816e6 + 1.98867e6i 0.0353634 + 0.0612512i
\(141\) 0 0
\(142\) −1.66819e7 + 2.88939e7i −0.488918 + 0.846831i
\(143\) −4.83290e6 −0.138208
\(144\) 0 0
\(145\) 1.42389e7 0.387872
\(146\) 4.10725e6 7.11396e6i 0.109223 0.189180i
\(147\) 0 0
\(148\) 1.23522e7 + 2.13946e7i 0.313205 + 0.542486i
\(149\) 1.03923e7 + 1.80000e7i 0.257371 + 0.445780i 0.965537 0.260266i \(-0.0838103\pi\)
−0.708165 + 0.706046i \(0.750477\pi\)
\(150\) 0 0
\(151\) −38056.0 + 65914.9i −0.000899505 + 0.00155799i −0.866475 0.499221i \(-0.833620\pi\)
0.865575 + 0.500779i \(0.166953\pi\)
\(152\) −1.13784e7 −0.262802
\(153\) 0 0
\(154\) 364032. 0.00803188
\(155\) −5.39776e7 + 9.34919e7i −1.16427 + 2.01657i
\(156\) 0 0
\(157\) 1.60912e7 + 2.78708e7i 0.331849 + 0.574780i 0.982874 0.184276i \(-0.0589942\pi\)
−0.651025 + 0.759056i \(0.725661\pi\)
\(158\) −2.07412e7 3.59247e7i −0.418344 0.724593i
\(159\) 0 0
\(160\) −3.74587e7 + 6.48804e7i −0.722991 + 1.25226i
\(161\) −978432. −0.0184774
\(162\) 0 0
\(163\) 5.83435e7 1.05520 0.527601 0.849492i \(-0.323092\pi\)
0.527601 + 0.849492i \(0.323092\pi\)
\(164\) 2.89670e7 5.01724e7i 0.512803 0.888201i
\(165\) 0 0
\(166\) 1.31302e7 + 2.27422e7i 0.222789 + 0.385883i
\(167\) −1.29183e7 2.23751e7i −0.214633 0.371755i 0.738526 0.674225i \(-0.235522\pi\)
−0.953159 + 0.302470i \(0.902189\pi\)
\(168\) 0 0
\(169\) 1.83795e7 3.18342e7i 0.292907 0.507329i
\(170\) −6.64232e7 −1.03693
\(171\) 0 0
\(172\) −6.30910e7 −0.945405
\(173\) 3.17600e7 5.50100e7i 0.466358 0.807756i −0.532904 0.846176i \(-0.678899\pi\)
0.999262 + 0.0384200i \(0.0122325\pi\)
\(174\) 0 0
\(175\) 2.36720e6 + 4.10011e6i 0.0333889 + 0.0578312i
\(176\) −1.82774e6 3.16575e6i −0.0252709 0.0437705i
\(177\) 0 0
\(178\) 2.55849e7 4.43144e7i 0.340028 0.588945i
\(179\) 8.09559e7 1.05503 0.527513 0.849547i \(-0.323125\pi\)
0.527513 + 0.849547i \(0.323125\pi\)
\(180\) 0 0
\(181\) 6.45032e7 0.808549 0.404274 0.914638i \(-0.367524\pi\)
0.404274 + 0.914638i \(0.367524\pi\)
\(182\) 978816. 1.69536e6i 0.0120351 0.0208455i
\(183\) 0 0
\(184\) −1.00901e7 1.74765e7i −0.119408 0.206820i
\(185\) 5.23626e7 + 9.06946e7i 0.608023 + 1.05313i
\(186\) 0 0
\(187\) 1.34550e7 2.33047e7i 0.150465 0.260614i
\(188\) 5.36632e7 0.589012
\(189\) 0 0
\(190\) −2.01708e7 −0.213346
\(191\) 2.84137e7 4.92140e7i 0.295060 0.511060i −0.679939 0.733269i \(-0.737994\pi\)
0.974999 + 0.222209i \(0.0713269\pi\)
\(192\) 0 0
\(193\) −5.81885e7 1.00785e8i −0.582621 1.00913i −0.995167 0.0981931i \(-0.968694\pi\)
0.412546 0.910937i \(-0.364640\pi\)
\(194\) −2.64804e7 4.58655e7i −0.260387 0.451003i
\(195\) 0 0
\(196\) −3.76946e7 + 6.52889e7i −0.357588 + 0.619360i
\(197\) 1.18816e8 1.10724 0.553622 0.832768i \(-0.313245\pi\)
0.553622 + 0.832768i \(0.313245\pi\)
\(198\) 0 0
\(199\) −9.50106e7 −0.854646 −0.427323 0.904099i \(-0.640543\pi\)
−0.427323 + 0.904099i \(0.640543\pi\)
\(200\) −4.88235e7 + 8.45648e7i −0.431543 + 0.747454i
\(201\) 0 0
\(202\) −3.59593e7 6.22833e7i −0.306959 0.531669i
\(203\) −1.16832e6 2.02359e6i −0.00980225 0.0169780i
\(204\) 0 0
\(205\) 1.22795e8 2.12687e8i 0.995502 1.72426i
\(206\) −4.32564e7 −0.344758
\(207\) 0 0
\(208\) −1.96579e7 −0.151466
\(209\) 4.08588e6 7.07695e6i 0.0309581 0.0536209i
\(210\) 0 0
\(211\) −8.96232e7 1.55232e8i −0.656798 1.13761i −0.981440 0.191770i \(-0.938577\pi\)
0.324642 0.945837i \(-0.394756\pi\)
\(212\) 1.96907e7 + 3.41052e7i 0.141934 + 0.245836i
\(213\) 0 0
\(214\) −3.42782e7 + 5.93716e7i −0.239095 + 0.414124i
\(215\) −2.67451e8 −1.83531
\(216\) 0 0
\(217\) 1.77157e7 0.117693
\(218\) 1.20628e7 2.08935e7i 0.0788592 0.136588i
\(219\) 0 0
\(220\) −1.70071e7 2.94572e7i −0.107684 0.186514i
\(221\) −7.23559e7 1.25324e8i −0.450922 0.781019i
\(222\) 0 0
\(223\) 1.03268e8 1.78866e8i 0.623592 1.08009i −0.365219 0.930922i \(-0.619006\pi\)
0.988811 0.149172i \(-0.0476607\pi\)
\(224\) 1.22941e7 0.0730853
\(225\) 0 0
\(226\) −1.06238e8 −0.612209
\(227\) 2.16977e7 3.75815e7i 0.123118 0.213247i −0.797877 0.602820i \(-0.794044\pi\)
0.920996 + 0.389572i \(0.127377\pi\)
\(228\) 0 0
\(229\) 1.80965e7 + 3.13441e7i 0.0995799 + 0.172477i 0.911511 0.411276i \(-0.134917\pi\)
−0.811931 + 0.583753i \(0.801583\pi\)
\(230\) −1.78870e7 3.09811e7i −0.0969369 0.167900i
\(231\) 0 0
\(232\) 2.40966e7 4.17365e7i 0.126692 0.219436i
\(233\) −9.22347e7 −0.477693 −0.238846 0.971057i \(-0.576769\pi\)
−0.238846 + 0.971057i \(0.576769\pi\)
\(234\) 0 0
\(235\) 2.27485e8 1.14345
\(236\) −6.00935e7 + 1.04085e8i −0.297602 + 0.515461i
\(237\) 0 0
\(238\) 5.45011e6 + 9.43987e6i 0.0262051 + 0.0453886i
\(239\) 2.49234e7 + 4.31686e7i 0.118090 + 0.204539i 0.919011 0.394232i \(-0.128989\pi\)
−0.800920 + 0.598771i \(0.795656\pi\)
\(240\) 0 0
\(241\) −9.96870e7 + 1.72663e8i −0.458753 + 0.794583i −0.998895 0.0469902i \(-0.985037\pi\)
0.540142 + 0.841574i \(0.318370\pi\)
\(242\) 1.11531e8 0.505872
\(243\) 0 0
\(244\) −2.76609e7 −0.121900
\(245\) −1.59792e8 + 2.76768e8i −0.694183 + 1.20236i
\(246\) 0 0
\(247\) −2.19724e7 3.80573e7i −0.0927765 0.160694i
\(248\) 1.82693e8 + 3.16434e8i 0.760574 + 1.31735i
\(249\) 0 0
\(250\) 4.85550e6 8.40997e6i 0.0196537 0.0340412i
\(251\) 3.94678e8 1.57538 0.787689 0.616073i \(-0.211277\pi\)
0.787689 + 0.616073i \(0.211277\pi\)
\(252\) 0 0
\(253\) 1.44930e7 0.0562649
\(254\) 5.03649e7 8.72345e7i 0.192846 0.334018i
\(255\) 0 0
\(256\) 1.04079e8 + 1.80271e8i 0.387725 + 0.671560i
\(257\) −7.14427e7 1.23742e8i −0.262538 0.454729i 0.704378 0.709825i \(-0.251226\pi\)
−0.966916 + 0.255096i \(0.917893\pi\)
\(258\) 0 0
\(259\) 8.59283e6 1.48832e7i 0.0307317 0.0532289i
\(260\) −1.82916e8 −0.645425
\(261\) 0 0
\(262\) 1.00961e8 0.346815
\(263\) 2.20120e8 3.81260e8i 0.746131 1.29234i −0.203533 0.979068i \(-0.565243\pi\)
0.949664 0.313269i \(-0.101424\pi\)
\(264\) 0 0
\(265\) 8.34713e7 + 1.44577e8i 0.275535 + 0.477241i
\(266\) 1.65504e6 + 2.86661e6i 0.00539166 + 0.00933863i
\(267\) 0 0
\(268\) −2.33332e7 + 4.04143e7i −0.0740462 + 0.128252i
\(269\) −2.75405e8 −0.862657 −0.431329 0.902195i \(-0.641955\pi\)
−0.431329 + 0.902195i \(0.641955\pi\)
\(270\) 0 0
\(271\) −4.24670e8 −1.29616 −0.648080 0.761572i \(-0.724428\pi\)
−0.648080 + 0.761572i \(0.724428\pi\)
\(272\) 5.47282e7 9.47920e7i 0.164900 0.285615i
\(273\) 0 0
\(274\) −8.41347e7 1.45726e8i −0.247086 0.427966i
\(275\) −3.50642e7 6.07329e7i −0.101671 0.176100i
\(276\) 0 0
\(277\) −2.58079e8 + 4.47006e8i −0.729581 + 1.26367i 0.227479 + 0.973783i \(0.426952\pi\)
−0.957060 + 0.289889i \(0.906382\pi\)
\(278\) 7.09638e7 0.198098
\(279\) 0 0
\(280\) 3.29472e7 0.0896944
\(281\) −1.55521e8 + 2.69371e8i −0.418137 + 0.724234i −0.995752 0.0920753i \(-0.970650\pi\)
0.577616 + 0.816309i \(0.303983\pi\)
\(282\) 0 0
\(283\) 2.97154e8 + 5.14686e8i 0.779344 + 1.34986i 0.932320 + 0.361634i \(0.117781\pi\)
−0.152976 + 0.988230i \(0.548886\pi\)
\(284\) −2.55789e8 4.43040e8i −0.662625 1.14770i
\(285\) 0 0
\(286\) −1.44987e7 + 2.51125e7i −0.0366478 + 0.0634759i
\(287\) −4.03020e7 −0.100633
\(288\) 0 0
\(289\) 3.95426e8 0.963658
\(290\) 4.27167e7 7.39875e7i 0.102850 0.178142i
\(291\) 0 0
\(292\) 6.29778e7 + 1.09081e8i 0.148029 + 0.256394i
\(293\) 5.77574e7 + 1.00039e8i 0.134144 + 0.232344i 0.925270 0.379309i \(-0.123838\pi\)
−0.791126 + 0.611653i \(0.790505\pi\)
\(294\) 0 0
\(295\) −2.54744e8 + 4.41230e8i −0.577733 + 1.00066i
\(296\) 3.54454e8 0.794400
\(297\) 0 0
\(298\) 1.24708e8 0.272984
\(299\) 3.89691e7 6.74965e7i 0.0843085 0.146027i
\(300\) 0 0
\(301\) 2.19447e7 + 3.80093e7i 0.0463817 + 0.0803355i
\(302\) 228336. + 395490.i 0.000477035 + 0.000826249i
\(303\) 0 0
\(304\) 1.66194e7 2.87856e7i 0.0339279 0.0587648i
\(305\) −1.17258e8 −0.236643
\(306\) 0 0
\(307\) −2.60600e8 −0.514032 −0.257016 0.966407i \(-0.582739\pi\)
−0.257016 + 0.966407i \(0.582739\pi\)
\(308\) −2.79091e6 + 4.83400e6i −0.00544275 + 0.00942712i
\(309\) 0 0
\(310\) 3.23865e8 + 5.60951e8i 0.617445 + 1.06945i
\(311\) 2.88397e8 + 4.99519e8i 0.543663 + 0.941652i 0.998690 + 0.0511744i \(0.0162964\pi\)
−0.455027 + 0.890478i \(0.650370\pi\)
\(312\) 0 0
\(313\) 2.30037e8 3.98436e8i 0.424026 0.734435i −0.572303 0.820043i \(-0.693950\pi\)
0.996329 + 0.0856073i \(0.0272831\pi\)
\(314\) 1.93095e8 0.351979
\(315\) 0 0
\(316\) 6.36062e8 1.13395
\(317\) 3.12781e7 5.41752e7i 0.0551483 0.0955197i −0.837133 0.546999i \(-0.815770\pi\)
0.892282 + 0.451479i \(0.149103\pi\)
\(318\) 0 0
\(319\) 1.73057e7 + 2.99744e7i 0.0298485 + 0.0516992i
\(320\) 1.28507e8 + 2.22580e8i 0.219230 + 0.379718i
\(321\) 0 0
\(322\) −2.93530e6 + 5.08408e6i −0.00489955 + 0.00848627i
\(323\) 2.44687e8 0.404020
\(324\) 0 0
\(325\) −3.77125e8 −0.609387
\(326\) 1.75030e8 3.03162e8i 0.279803 0.484633i
\(327\) 0 0
\(328\) −4.15614e8 7.19864e8i −0.650327 1.12640i
\(329\) −1.86655e7 3.23295e7i −0.0288970 0.0500511i
\(330\) 0 0
\(331\) −3.42118e8 + 5.92566e8i −0.518535 + 0.898128i 0.481233 + 0.876593i \(0.340189\pi\)
−0.999768 + 0.0215359i \(0.993144\pi\)
\(332\) −4.02661e8 −0.603888
\(333\) 0 0
\(334\) −1.55019e8 −0.227652
\(335\) −9.89126e7 + 1.71322e8i −0.143746 + 0.248975i
\(336\) 0 0
\(337\) 3.13156e8 + 5.42403e8i 0.445714 + 0.772000i 0.998102 0.0615875i \(-0.0196163\pi\)
−0.552387 + 0.833588i \(0.686283\pi\)
\(338\) −1.10277e8 1.91005e8i −0.155337 0.269052i
\(339\) 0 0
\(340\) 5.09245e8 8.82038e8i 0.702668 1.21706i
\(341\) −2.62414e8 −0.358382
\(342\) 0 0
\(343\) 1.05151e8 0.140697
\(344\) −4.52610e8 + 7.83943e8i −0.599472 + 1.03832i
\(345\) 0 0
\(346\) −1.90560e8 3.30060e8i −0.247324 0.428377i
\(347\) −6.26698e8 1.08547e9i −0.805203 1.39465i −0.916154 0.400826i \(-0.868723\pi\)
0.110952 0.993826i \(-0.464610\pi\)
\(348\) 0 0
\(349\) −1.32675e8 + 2.29800e8i −0.167071 + 0.289375i −0.937389 0.348285i \(-0.886764\pi\)
0.770318 + 0.637660i \(0.220098\pi\)
\(350\) 2.84064e7 0.0354142
\(351\) 0 0
\(352\) −1.82107e8 −0.222550
\(353\) −2.84818e8 + 4.93319e8i −0.344632 + 0.596920i −0.985287 0.170909i \(-0.945330\pi\)
0.640655 + 0.767829i \(0.278663\pi\)
\(354\) 0 0
\(355\) −1.08432e9 1.87810e9i −1.28635 2.22803i
\(356\) 3.92302e8 + 6.79487e8i 0.460835 + 0.798190i
\(357\) 0 0
\(358\) 2.42868e8 4.20659e8i 0.279756 0.484551i
\(359\) −9.32541e8 −1.06374 −0.531872 0.846825i \(-0.678511\pi\)
−0.531872 + 0.846825i \(0.678511\pi\)
\(360\) 0 0
\(361\) −8.19567e8 −0.916874
\(362\) 1.93510e8 3.35168e8i 0.214399 0.371350i
\(363\) 0 0
\(364\) 1.50085e7 + 2.59955e7i 0.0163111 + 0.0282516i
\(365\) 2.66971e8 + 4.62407e8i 0.287368 + 0.497737i
\(366\) 0 0
\(367\) 4.26282e8 7.38343e8i 0.450159 0.779699i −0.548236 0.836323i \(-0.684701\pi\)
0.998396 + 0.0566249i \(0.0180339\pi\)
\(368\) 5.89505e7 0.0616624
\(369\) 0 0
\(370\) 6.28351e8 0.644906
\(371\) 1.36979e7 2.37254e7i 0.0139266 0.0241215i
\(372\) 0 0
\(373\) −1.90592e8 3.30115e8i −0.190162 0.329370i 0.755142 0.655561i \(-0.227568\pi\)
−0.945304 + 0.326192i \(0.894235\pi\)
\(374\) −8.07298e7 1.39828e8i −0.0797964 0.138211i
\(375\) 0 0
\(376\) 3.84975e8 6.66797e8i 0.373487 0.646898i
\(377\) 1.86128e8 0.178903
\(378\) 0 0
\(379\) −1.48353e9 −1.39978 −0.699889 0.714251i \(-0.746767\pi\)
−0.699889 + 0.714251i \(0.746767\pi\)
\(380\) 1.54643e8 2.67849e8i 0.144573 0.250408i
\(381\) 0 0
\(382\) −1.70482e8 2.95284e8i −0.156479 0.271030i
\(383\) −3.80965e8 6.59851e8i −0.346489 0.600136i 0.639134 0.769095i \(-0.279293\pi\)
−0.985623 + 0.168959i \(0.945959\pi\)
\(384\) 0 0
\(385\) −1.18310e7 + 2.04920e7i −0.0105660 + 0.0183008i
\(386\) −6.98262e8 −0.617963
\(387\) 0 0
\(388\) 8.12067e8 0.705799
\(389\) 8.04509e8 1.39345e9i 0.692959 1.20024i −0.277905 0.960608i \(-0.589640\pi\)
0.970864 0.239631i \(-0.0770265\pi\)
\(390\) 0 0
\(391\) 2.16983e8 + 3.75825e8i 0.183572 + 0.317956i
\(392\) 5.40835e8 + 9.36754e8i 0.453486 + 0.785460i
\(393\) 0 0
\(394\) 3.56448e8 6.17386e8i 0.293602 0.508534i
\(395\) 2.69635e9 2.20134
\(396\) 0 0
\(397\) 1.88016e9 1.50809 0.754046 0.656822i \(-0.228100\pi\)
0.754046 + 0.656822i \(0.228100\pi\)
\(398\) −2.85032e8 + 4.93690e8i −0.226622 + 0.392521i
\(399\) 0 0
\(400\) −1.42624e8 2.47032e8i −0.111425 0.192993i
\(401\) 1.34296e8 + 2.32608e8i 0.104006 + 0.180144i 0.913332 0.407217i \(-0.133501\pi\)
−0.809326 + 0.587360i \(0.800167\pi\)
\(402\) 0 0
\(403\) −7.05584e8 + 1.22211e9i −0.537008 + 0.930125i
\(404\) 1.10275e9 0.832037
\(405\) 0 0
\(406\) −1.40198e7 −0.0103969
\(407\) −1.27281e8 + 2.20458e8i −0.0935803 + 0.162086i
\(408\) 0 0
\(409\) −4.49739e7 7.78971e7i −0.0325034 0.0562976i 0.849316 0.527885i \(-0.177015\pi\)
−0.881820 + 0.471587i \(0.843681\pi\)
\(410\) −7.36770e8 1.27612e9i −0.527945 0.914427i
\(411\) 0 0
\(412\) 3.31632e8 5.74404e8i 0.233623 0.404647i
\(413\) 8.36083e7 0.0584015
\(414\) 0 0
\(415\) −1.70693e9 −1.17232
\(416\) −4.89653e8 + 8.48103e8i −0.333474 + 0.577593i
\(417\) 0 0
\(418\) −2.45153e7 4.24617e7i −0.0164180 0.0284368i
\(419\) 8.45271e8 + 1.46405e9i 0.561367 + 0.972317i 0.997377 + 0.0723749i \(0.0230578\pi\)
−0.436010 + 0.899942i \(0.643609\pi\)
\(420\) 0 0
\(421\) 5.66664e8 9.81490e8i 0.370116 0.641060i −0.619467 0.785023i \(-0.712651\pi\)
0.989583 + 0.143963i \(0.0459845\pi\)
\(422\) −1.07548e9 −0.696639
\(423\) 0 0
\(424\) 5.65037e8 0.359995
\(425\) 1.04993e9 1.81853e9i 0.663434 1.14910i
\(426\) 0 0
\(427\) 9.62118e6 + 1.66644e7i 0.00598041 + 0.0103584i
\(428\) −5.25599e8 9.10365e8i −0.324042 0.561258i
\(429\) 0 0
\(430\) −8.02353e8 + 1.38972e9i −0.486660 + 0.842921i
\(431\) −2.19943e9 −1.32324 −0.661621 0.749839i \(-0.730131\pi\)
−0.661621 + 0.749839i \(0.730131\pi\)
\(432\) 0 0
\(433\) −1.51738e8 −0.0898227 −0.0449114 0.998991i \(-0.514301\pi\)
−0.0449114 + 0.998991i \(0.514301\pi\)
\(434\) 5.31471e7 9.20535e7i 0.0312080 0.0540538i
\(435\) 0 0
\(436\) 1.84964e8 + 3.20367e8i 0.106877 + 0.185116i
\(437\) 6.58913e7 + 1.14127e8i 0.0377696 + 0.0654189i
\(438\) 0 0
\(439\) −4.95381e8 + 8.58026e8i −0.279456 + 0.484032i −0.971250 0.238063i \(-0.923488\pi\)
0.691793 + 0.722095i \(0.256821\pi\)
\(440\) −4.88030e8 −0.273126
\(441\) 0 0
\(442\) −8.68271e8 −0.478275
\(443\) −8.86878e8 + 1.53612e9i −0.484675 + 0.839482i −0.999845 0.0176059i \(-0.994396\pi\)
0.515170 + 0.857088i \(0.327729\pi\)
\(444\) 0 0
\(445\) 1.66302e9 + 2.88044e9i 0.894618 + 1.54952i
\(446\) −6.19611e8 1.07320e9i −0.330710 0.572806i
\(447\) 0 0
\(448\) 2.10883e7 3.65259e7i 0.0110807 0.0191924i
\(449\) 2.77010e8 0.144422 0.0722110 0.997389i \(-0.476994\pi\)
0.0722110 + 0.997389i \(0.476994\pi\)
\(450\) 0 0
\(451\) 5.96973e8 0.306434
\(452\) 8.14491e8 1.41074e9i 0.414860 0.718559i
\(453\) 0 0
\(454\) −1.30186e8 2.25489e8i −0.0652934 0.113092i
\(455\) 6.36230e7 + 1.10198e8i 0.0316646 + 0.0548448i
\(456\) 0 0
\(457\) −1.47379e9 + 2.55268e9i −0.722320 + 1.25109i 0.237748 + 0.971327i \(0.423591\pi\)
−0.960068 + 0.279768i \(0.909742\pi\)
\(458\) 2.17159e8 0.105620
\(459\) 0 0
\(460\) 5.48533e8 0.262755
\(461\) −1.38344e9 + 2.39618e9i −0.657667 + 1.13911i 0.323551 + 0.946211i \(0.395123\pi\)
−0.981218 + 0.192902i \(0.938210\pi\)
\(462\) 0 0
\(463\) −2.31776e8 4.01449e8i −0.108527 0.187973i 0.806647 0.591034i \(-0.201280\pi\)
−0.915174 + 0.403060i \(0.867947\pi\)
\(464\) 7.03913e7 + 1.21921e8i 0.0327119 + 0.0566587i
\(465\) 0 0
\(466\) −2.76704e8 + 4.79265e8i −0.126667 + 0.219394i
\(467\) 4.17922e8 0.189883 0.0949415 0.995483i \(-0.469734\pi\)
0.0949415 + 0.995483i \(0.469734\pi\)
\(468\) 0 0
\(469\) 3.24636e7 0.0145309
\(470\) 6.82456e8 1.18205e9i 0.303202 0.525162i
\(471\) 0 0
\(472\) 8.62211e8 + 1.49339e9i 0.377413 + 0.653698i
\(473\) −3.25056e8 5.63013e8i −0.141236 0.244627i
\(474\) 0 0
\(475\) 3.18832e8 5.52234e8i 0.136501 0.236426i
\(476\) −1.67137e8 −0.0710310
\(477\) 0 0
\(478\) 2.99081e8 0.125254
\(479\) −7.54864e8 + 1.30746e9i −0.313830 + 0.543570i −0.979188 0.202955i \(-0.934946\pi\)
0.665358 + 0.746524i \(0.268279\pi\)
\(480\) 0 0
\(481\) 6.84473e8 + 1.18554e9i 0.280445 + 0.485746i
\(482\) 5.98122e8 + 1.03598e9i 0.243290 + 0.421392i
\(483\) 0 0
\(484\) −8.55069e8 + 1.48102e9i −0.342801 + 0.593750i
\(485\) 3.44246e9 1.37016
\(486\) 0 0
\(487\) 9.29460e8 0.364653 0.182326 0.983238i \(-0.441637\pi\)
0.182326 + 0.983238i \(0.441637\pi\)
\(488\) −1.98437e8 + 3.43703e8i −0.0772953 + 0.133879i
\(489\) 0 0
\(490\) 9.58753e8 + 1.66061e9i 0.368146 + 0.637648i
\(491\) 2.56401e9 + 4.44100e9i 0.977541 + 1.69315i 0.671280 + 0.741204i \(0.265745\pi\)
0.306262 + 0.951947i \(0.400922\pi\)
\(492\) 0 0
\(493\) −5.18186e8 + 8.97525e8i −0.194770 + 0.337351i
\(494\) −2.63669e8 −0.0984043
\(495\) 0 0
\(496\) −1.06737e9 −0.392762
\(497\) −1.77940e8 + 3.08202e8i −0.0650170 + 0.112613i
\(498\) 0 0
\(499\) 2.05325e8 + 3.55633e8i 0.0739757 + 0.128130i 0.900640 0.434565i \(-0.143098\pi\)
−0.826665 + 0.562695i \(0.809765\pi\)
\(500\) 7.44510e7 + 1.28953e8i 0.0266364 + 0.0461356i
\(501\) 0 0
\(502\) 1.18403e9 2.05081e9i 0.417735 0.723538i
\(503\) −5.02041e9 −1.75894 −0.879470 0.475954i \(-0.842103\pi\)
−0.879470 + 0.475954i \(0.842103\pi\)
\(504\) 0 0
\(505\) 4.67470e9 1.61523
\(506\) 4.34791e7 7.53080e7i 0.0149195 0.0258413i
\(507\) 0 0
\(508\) 7.72262e8 + 1.33760e9i 0.261361 + 0.452691i
\(509\) −1.62463e9 2.81394e9i −0.546062 0.945807i −0.998539 0.0540314i \(-0.982793\pi\)
0.452477 0.891776i \(-0.350540\pi\)
\(510\) 0 0
\(511\) 4.38106e7 7.58822e7i 0.0145247 0.0251575i
\(512\) −1.39223e9 −0.458423
\(513\) 0 0
\(514\) −8.57312e8 −0.278463
\(515\) 1.40583e9 2.43497e9i 0.453532 0.785540i
\(516\) 0 0
\(517\) 2.76482e8 + 4.78881e8i 0.0879935 + 0.152409i
\(518\) −5.15570e7 8.92993e7i −0.0162980 0.0282289i
\(519\) 0 0
\(520\) −1.31223e9 + 2.27284e9i −0.409258 + 0.708855i
\(521\) 2.10950e9 0.653503 0.326752 0.945110i \(-0.394046\pi\)
0.326752 + 0.945110i \(0.394046\pi\)
\(522\) 0 0
\(523\) −5.28911e9 −1.61669 −0.808345 0.588709i \(-0.799636\pi\)
−0.808345 + 0.588709i \(0.799636\pi\)
\(524\) −7.74032e8 + 1.34066e9i −0.235017 + 0.407061i
\(525\) 0 0
\(526\) −1.32072e9 2.28756e9i −0.395696 0.685365i
\(527\) −3.92874e9 6.80477e9i −1.16927 2.02524i
\(528\) 0 0
\(529\) 1.58555e9 2.74626e9i 0.465678 0.806577i
\(530\) 1.00166e9 0.292249
\(531\) 0 0
\(532\) −5.07546e7 −0.0146145
\(533\) 1.60515e9 2.78020e9i 0.459167 0.795301i
\(534\) 0 0
\(535\) −2.22808e9 3.85916e9i −0.629062 1.08957i
\(536\) 3.34781e8 + 5.79858e8i 0.0939040 + 0.162646i
\(537\) 0 0
\(538\) −8.26214e8 + 1.43104e9i −0.228747 + 0.396201i
\(539\) −7.76836e8 −0.213682
\(540\) 0 0
\(541\) 3.04614e9 0.827101 0.413551 0.910481i \(-0.364288\pi\)
0.413551 + 0.910481i \(0.364288\pi\)
\(542\) −1.27401e9 + 2.20665e9i −0.343696 + 0.595300i
\(543\) 0 0
\(544\) −2.72642e9 4.72230e9i −0.726100 1.25764i
\(545\) 7.84085e8 + 1.35808e9i 0.207480 + 0.359365i
\(546\) 0 0
\(547\) 2.42768e9 4.20487e9i 0.634215 1.09849i −0.352466 0.935825i \(-0.614657\pi\)
0.986681 0.162668i \(-0.0520100\pi\)
\(548\) 2.58013e9 0.669746
\(549\) 0 0
\(550\) −4.20770e8 −0.107839
\(551\) −1.57358e8 + 2.72552e8i −0.0400736 + 0.0694095i
\(552\) 0 0
\(553\) −2.21239e8 3.83197e8i −0.0556319 0.0963573i
\(554\) 1.54847e9 + 2.68204e9i 0.386919 + 0.670163i
\(555\) 0 0
\(556\) −5.44056e8 + 9.42332e8i −0.134240 + 0.232510i
\(557\) −1.27762e9 −0.313263 −0.156631 0.987657i \(-0.550063\pi\)
−0.156631 + 0.987657i \(0.550063\pi\)
\(558\) 0 0
\(559\) −3.49607e9 −0.846522
\(560\) −4.81229e7 + 8.33513e7i −0.0115796 + 0.0200565i
\(561\) 0 0
\(562\) 9.33129e8 + 1.61623e9i 0.221750 + 0.384083i
\(563\) 2.35632e9 + 4.08127e9i 0.556487 + 0.963865i 0.997786 + 0.0665042i \(0.0211846\pi\)
−0.441299 + 0.897360i \(0.645482\pi\)
\(564\) 0 0
\(565\) 3.45273e9 5.98031e9i 0.805366 1.39493i
\(566\) 3.56585e9 0.826619
\(567\) 0 0
\(568\) −7.34003e9 −1.68066
\(569\) 2.28900e9 3.96466e9i 0.520898 0.902222i −0.478807 0.877920i \(-0.658931\pi\)
0.999705 0.0243013i \(-0.00773611\pi\)
\(570\) 0 0
\(571\) −2.47560e9 4.28786e9i −0.556485 0.963860i −0.997786 0.0665012i \(-0.978816\pi\)
0.441301 0.897359i \(-0.354517\pi\)
\(572\) −2.22314e8 3.85058e8i −0.0496684 0.0860281i
\(573\) 0 0
\(574\) −1.20906e8 + 2.09415e8i −0.0266843 + 0.0462186i
\(575\) 1.13093e9 0.248084
\(576\) 0 0
\(577\) 8.51847e9 1.84606 0.923031 0.384725i \(-0.125704\pi\)
0.923031 + 0.384725i \(0.125704\pi\)
\(578\) 1.18628e9 2.05470e9i 0.255529 0.442588i
\(579\) 0 0
\(580\) 6.54989e8 + 1.13447e9i 0.139392 + 0.241433i
\(581\) 1.40056e8 + 2.42584e8i 0.0296268 + 0.0513152i
\(582\) 0 0
\(583\) −2.02899e8 + 3.51432e8i −0.0424073 + 0.0734517i
\(584\) 1.80719e9 0.375455
\(585\) 0 0
\(586\) 6.93088e8 0.142281
\(587\) −2.81124e8 + 4.86921e8i −0.0573673 + 0.0993630i −0.893283 0.449495i \(-0.851604\pi\)
0.835916 + 0.548858i \(0.184937\pi\)
\(588\) 0 0
\(589\) −1.19304e9 2.06641e9i −0.240576 0.416690i
\(590\) 1.52846e9 + 2.64738e9i 0.306389 + 0.530682i
\(591\) 0 0
\(592\) −5.17718e8 + 8.96714e8i −0.102557 + 0.177635i
\(593\) −3.62110e9 −0.713099 −0.356549 0.934277i \(-0.616047\pi\)
−0.356549 + 0.934277i \(0.616047\pi\)
\(594\) 0 0
\(595\) −7.08515e8 −0.137892
\(596\) −9.56093e8 + 1.65600e9i −0.184986 + 0.320405i
\(597\) 0 0
\(598\) −2.33815e8 4.04979e8i −0.0447113 0.0774423i
\(599\) −3.74052e9 6.47877e9i −0.711112 1.23168i −0.964440 0.264301i \(-0.914859\pi\)
0.253328 0.967380i \(-0.418475\pi\)
\(600\) 0 0
\(601\) 2.90635e9 5.03395e9i 0.546119 0.945906i −0.452416 0.891807i \(-0.649438\pi\)
0.998536 0.0540994i \(-0.0172288\pi\)
\(602\) 2.63336e8 0.0491953
\(603\) 0 0
\(604\) −7.00230e6 −0.00129304
\(605\) −3.62475e9 + 6.27825e9i −0.665479 + 1.15264i
\(606\) 0 0
\(607\) −1.92026e9 3.32598e9i −0.348497 0.603614i 0.637486 0.770462i \(-0.279974\pi\)
−0.985983 + 0.166848i \(0.946641\pi\)
\(608\) −8.27934e8 1.43402e9i −0.149394 0.258758i
\(609\) 0 0
\(610\) −3.51775e8 + 6.09291e8i −0.0627495 + 0.108685i
\(611\) 2.97364e9 0.527405
\(612\) 0 0
\(613\) 1.70484e9 0.298932 0.149466 0.988767i \(-0.452245\pi\)
0.149466 + 0.988767i \(0.452245\pi\)
\(614\) −7.81799e8 + 1.35412e9i −0.136303 + 0.236084i
\(615\) 0 0
\(616\) 4.00435e7 + 6.93574e7i 0.00690239 + 0.0119553i
\(617\) −1.40405e9 2.43188e9i −0.240649 0.416816i 0.720251 0.693714i \(-0.244027\pi\)
−0.960899 + 0.276898i \(0.910693\pi\)
\(618\) 0 0
\(619\) 1.27183e9 2.20287e9i 0.215532 0.373312i −0.737905 0.674904i \(-0.764185\pi\)
0.953437 + 0.301593i \(0.0975182\pi\)
\(620\) −9.93187e9 −1.67363
\(621\) 0 0
\(622\) 3.46077e9 0.576642
\(623\) 2.72906e8 4.72687e8i 0.0452173 0.0783187i
\(624\) 0 0
\(625\) 3.20526e9 + 5.55167e9i 0.525149 + 0.909585i
\(626\) −1.38022e9 2.39062e9i −0.224874 0.389493i
\(627\) 0 0
\(628\) −1.48039e9 + 2.56412e9i −0.238517 + 0.413123i
\(629\) −7.62238e9 −1.22127
\(630\) 0 0
\(631\) −1.51146e8 −0.0239494 −0.0119747 0.999928i \(-0.503812\pi\)
−0.0119747 + 0.999928i \(0.503812\pi\)
\(632\) 4.56306e9 7.90344e9i 0.719028 1.24539i
\(633\) 0 0
\(634\) −1.87668e8 3.25051e8i −0.0292468 0.0506570i
\(635\) 3.27372e9 + 5.67025e9i 0.507380 + 0.878808i
\(636\) 0 0
\(637\) −2.08877e9 + 3.61786e9i −0.320186 + 0.554579i
\(638\) 2.07669e8 0.0316591
\(639\) 0 0
\(640\) −8.04735e9 −1.21345
\(641\) −6.18126e9 + 1.07062e10i −0.926987 + 1.60559i −0.138653 + 0.990341i \(0.544277\pi\)
−0.788334 + 0.615247i \(0.789056\pi\)
\(642\) 0 0
\(643\) −1.43372e9 2.48328e9i −0.212680 0.368372i 0.739873 0.672747i \(-0.234886\pi\)
−0.952552 + 0.304375i \(0.901552\pi\)
\(644\) −4.50079e7 7.79559e7i −0.00664030 0.0115013i
\(645\) 0 0
\(646\) 7.34062e8 1.27143e9i 0.107132 0.185558i
\(647\) 4.10640e9 0.596068 0.298034 0.954555i \(-0.403669\pi\)
0.298034 + 0.954555i \(0.403669\pi\)
\(648\) 0 0
\(649\) −1.23845e9 −0.177837
\(650\) −1.13137e9 + 1.95960e9i −0.161588 + 0.279879i
\(651\) 0 0
\(652\) 2.68380e9 + 4.64848e9i 0.379213 + 0.656817i
\(653\) 3.45550e9 + 5.98510e9i 0.485640 + 0.841153i 0.999864 0.0165027i \(-0.00525320\pi\)
−0.514224 + 0.857656i \(0.671920\pi\)
\(654\) 0 0
\(655\) −3.28122e9 + 5.68324e9i −0.456237 + 0.790226i
\(656\) 2.42819e9 0.335830
\(657\) 0 0
\(658\) −2.23986e8 −0.0306499
\(659\) 1.71222e9 2.96565e9i 0.233056 0.403665i −0.725650 0.688064i \(-0.758461\pi\)
0.958706 + 0.284399i \(0.0917941\pi\)
\(660\) 0 0
\(661\) 3.38219e9 + 5.85812e9i 0.455504 + 0.788956i 0.998717 0.0506388i \(-0.0161257\pi\)
−0.543213 + 0.839595i \(0.682792\pi\)
\(662\) 2.05271e9 + 3.55539e9i 0.274995 + 0.476305i
\(663\) 0 0
\(664\) −2.88865e9 + 5.00329e9i −0.382919 + 0.663236i
\(665\) −2.15155e8 −0.0283711
\(666\) 0 0
\(667\) −5.58165e8 −0.0728320
\(668\) 1.18848e9 2.05851e9i 0.154267 0.267199i
\(669\) 0 0
\(670\) 5.93475e8 + 1.02793e9i 0.0762326 + 0.132039i
\(671\) −1.42514e8 2.46841e8i −0.0182108 0.0315420i
\(672\) 0 0
\(673\) 8.74796e8 1.51519e9i 0.110625 0.191608i −0.805397 0.592735i \(-0.798048\pi\)
0.916023 + 0.401127i \(0.131381\pi\)
\(674\) 3.75788e9 0.472752
\(675\) 0 0
\(676\) 3.38182e9 0.421053
\(677\) 4.15006e9 7.18811e9i 0.514036 0.890337i −0.485831 0.874053i \(-0.661483\pi\)
0.999867 0.0162840i \(-0.00518358\pi\)
\(678\) 0 0
\(679\) −2.82458e8 4.89232e8i −0.0346266 0.0599750i
\(680\) −7.30656e9 1.26553e10i −0.891110 1.54345i
\(681\) 0 0
\(682\) −7.87242e8 + 1.36354e9i −0.0950305 + 0.164598i
\(683\) 1.21232e10 1.45594 0.727969 0.685610i \(-0.240464\pi\)
0.727969 + 0.685610i \(0.240464\pi\)
\(684\) 0 0
\(685\) 1.09375e10 1.30017
\(686\) 3.15454e8 5.46382e8i 0.0373080 0.0646193i
\(687\) 0 0
\(688\) −1.32217e9 2.29006e9i −0.154784 0.268094i
\(689\) 1.09112e9 + 1.88988e9i 0.127088 + 0.220123i
\(690\) 0 0
\(691\) −4.10923e9 + 7.11739e9i −0.473791 + 0.820631i −0.999550 0.0300033i \(-0.990448\pi\)
0.525758 + 0.850634i \(0.323782\pi\)
\(692\) 5.84385e9 0.670390
\(693\) 0 0
\(694\) −7.52038e9 −0.854046
\(695\) −2.30632e9 + 3.99467e9i −0.260599 + 0.451371i
\(696\) 0 0
\(697\) 8.93759e9 + 1.54804e10i 0.999783 + 1.73167i
\(698\) 7.96051e8 + 1.37880e9i 0.0886027 + 0.153464i
\(699\) 0 0
\(700\) −2.17782e8 + 3.77210e8i −0.0239983 + 0.0415662i
\(701\) −4.72231e9 −0.517775 −0.258888 0.965907i \(-0.583356\pi\)
−0.258888 + 0.965907i \(0.583356\pi\)
\(702\) 0 0
\(703\) −2.31469e9 −0.251275
\(704\) −3.12370e8 + 5.41040e8i −0.0337415 + 0.0584420i
\(705\) 0 0
\(706\) 1.70891e9 + 2.95991e9i 0.182769 + 0.316565i
\(707\) −3.83566e8 6.64355e8i −0.0408199 0.0707021i
\(708\) 0 0
\(709\) −1.39487e9 + 2.41599e9i −0.146985 + 0.254585i −0.930112 0.367277i \(-0.880290\pi\)
0.783127 + 0.621862i \(0.213624\pi\)
\(710\) −1.30119e10 −1.36438
\(711\) 0 0
\(712\) 1.12574e10 1.16885
\(713\) 2.11592e9 3.66488e9i 0.218618 0.378658i
\(714\) 0 0
\(715\) −9.42416e8 1.63231e9i −0.0964210 0.167006i
\(716\) 3.72397e9 + 6.45011e9i 0.379150 + 0.656707i
\(717\) 0 0
\(718\) −2.79762e9 + 4.84562e9i −0.282068 + 0.488556i
\(719\) −1.51985e9 −0.152493 −0.0762463 0.997089i \(-0.524294\pi\)
−0.0762463 + 0.997089i \(0.524294\pi\)
\(720\) 0 0
\(721\) −4.61401e8 −0.0458464
\(722\) −2.45870e9 + 4.25860e9i −0.243123 + 0.421101i
\(723\) 0 0
\(724\) 2.96715e9 + 5.13925e9i 0.290572 + 0.503286i
\(725\) 1.35041e9 + 2.33899e9i 0.131608 + 0.227953i
\(726\) 0 0
\(727\) 4.05880e9 7.03005e9i 0.391767 0.678560i −0.600916 0.799312i \(-0.705197\pi\)
0.992683 + 0.120752i \(0.0385307\pi\)
\(728\) 4.30679e8 0.0413708
\(729\) 0 0
\(730\) 3.20365e9 0.304800
\(731\) 9.73316e9 1.68583e10i 0.921601 1.59626i
\(732\) 0 0
\(733\) 5.16203e9 + 8.94090e9i 0.484124 + 0.838528i 0.999834 0.0182357i \(-0.00580493\pi\)
−0.515709 + 0.856764i \(0.672472\pi\)
\(734\) −2.55769e9 4.43006e9i −0.238733 0.413498i
\(735\) 0 0
\(736\) 1.46838e9 2.54331e9i 0.135758 0.235140i
\(737\) −4.80867e8 −0.0442475
\(738\) 0 0
\(739\) −1.35365e10 −1.23382 −0.616908 0.787035i \(-0.711615\pi\)
−0.616908 + 0.787035i \(0.711615\pi\)
\(740\) −4.81736e9 + 8.34391e9i −0.437016 + 0.756935i
\(741\) 0 0
\(742\) −8.21871e7 1.42352e8i −0.00738567 0.0127924i
\(743\) −8.59680e9 1.48901e10i −0.768910 1.33179i −0.938154 0.346218i \(-0.887466\pi\)
0.169244 0.985574i \(-0.445868\pi\)
\(744\) 0 0
\(745\) −4.05300e9 + 7.02001e9i −0.359112 + 0.622000i
\(746\) −2.28710e9 −0.201697
\(747\) 0 0
\(748\) 2.47571e9 0.216294
\(749\) −3.65634e8 + 6.33297e8i −0.0317951 + 0.0550708i
\(750\) 0 0
\(751\) −5.62392e9 9.74092e9i −0.484506 0.839190i 0.515335 0.856989i \(-0.327667\pi\)
−0.999842 + 0.0177991i \(0.994334\pi\)
\(752\) 1.12459e9 + 1.94786e9i 0.0964348 + 0.167030i
\(753\) 0 0
\(754\) 5.58384e8 9.67149e8i 0.0474387 0.0821663i
\(755\) −2.96837e7 −0.00251017
\(756\) 0 0
\(757\) 1.63068e10 1.36626 0.683131 0.730296i \(-0.260618\pi\)
0.683131 + 0.730296i \(0.260618\pi\)
\(758\) −4.45059e9 + 7.70865e9i −0.371172 + 0.642889i
\(759\) 0 0
\(760\) −2.21879e9 3.84305e9i −0.183345 0.317562i
\(761\) 3.07035e9 + 5.31800e9i 0.252546 + 0.437423i 0.964226 0.265081i \(-0.0853986\pi\)
−0.711680 + 0.702504i \(0.752065\pi\)
\(762\) 0 0
\(763\) 1.28670e8 2.22864e8i 0.0104868 0.0181637i
\(764\) 5.22812e9 0.424149
\(765\) 0 0
\(766\) −4.57158e9 −0.367507
\(767\) −3.32996e9 + 5.76766e9i −0.266474 + 0.461547i
\(768\) 0 0
\(769\) −1.22534e10 2.12236e10i −0.971664 1.68297i −0.690532 0.723302i \(-0.742624\pi\)
−0.281132 0.959669i \(-0.590710\pi\)
\(770\) 7.09862e7 + 1.22952e8i 0.00560346 + 0.00970549i
\(771\) 0 0
\(772\) 5.35334e9 9.27226e9i 0.418759 0.725312i
\(773\) 1.01722e10 0.792110 0.396055 0.918227i \(-0.370379\pi\)
0.396055 + 0.918227i \(0.370379\pi\)
\(774\) 0 0
\(775\) −2.04769e10 −1.58018
\(776\) 5.82570e9 1.00904e10i 0.447540 0.775162i
\(777\) 0 0
\(778\) −4.82705e9 8.36070e9i −0.367497 0.636523i
\(779\) 2.71408e9 + 4.70093e9i 0.205704 + 0.356289i
\(780\) 0 0
\(781\) 2.63574e9 4.56523e9i 0.197981 0.342913i
\(782\) 2.60379e9 0.194707
\(783\) 0 0
\(784\) −3.15979e9 −0.234181
\(785\) −6.27558e9 + 1.08696e10i −0.463031 + 0.801994i
\(786\) 0 0
\(787\) 4.89567e9 + 8.47956e9i 0.358015 + 0.620100i 0.987629 0.156808i \(-0.0501204\pi\)
−0.629614 + 0.776908i \(0.716787\pi\)
\(788\) 5.46554e9 + 9.46659e9i 0.397916 + 0.689211i
\(789\) 0 0
\(790\) 8.08905e9 1.40106e10i 0.583718 1.01103i
\(791\) −1.13320e9 −0.0814124
\(792\) 0 0
\(793\) −1.53277e9 −0.109150
\(794\) 5.64047e9 9.76959e9i 0.399893 0.692635i
\(795\) 0 0
\(796\) −4.37049e9 7.56991e9i −0.307139 0.531980i
\(797\) −4.87891e9 8.45052e9i −0.341365 0.591261i 0.643322 0.765596i \(-0.277556\pi\)
−0.984686 + 0.174335i \(0.944222\pi\)
\(798\) 0 0
\(799\) −8.27872e9 + 1.43392e10i −0.574182 + 0.994512i
\(800\) −1.42103e10 −0.981270
\(801\) 0 0
\(802\) 1.61155e9 0.110315
\(803\) −6.48945e8 + 1.12401e9i −0.0442286 + 0.0766062i
\(804\) 0 0
\(805\) −1.90794e8 3.30465e8i −0.0128908 0.0223275i
\(806\) 4.23350e9 + 7.33264e9i 0.284792 + 0.493273i
\(807\) 0 0
\(808\) 7.91104e9 1.37023e10i 0.527587 0.913807i
\(809\) 2.78706e9 0.185066 0.0925330 0.995710i \(-0.470504\pi\)
0.0925330 + 0.995710i \(0.470504\pi\)
\(810\) 0 0
\(811\) −7.99983e9 −0.526633 −0.263316 0.964710i \(-0.584816\pi\)
−0.263316 + 0.964710i \(0.584816\pi\)
\(812\) 1.07485e8 1.86170e8i 0.00704537 0.0122029i
\(813\) 0 0
\(814\) 7.63688e8 + 1.32275e9i 0.0496284 + 0.0859590i
\(815\) 1.13770e10 + 1.97055e10i 0.736165 + 1.27508i
\(816\) 0 0
\(817\) 2.95568e9 5.11938e9i 0.189618 0.328428i
\(818\) −5.39687e8 −0.0344751
\(819\) 0 0
\(820\) 2.25943e10 1.43103
\(821\) −5.12009e9 + 8.86826e9i −0.322906 + 0.559290i −0.981086 0.193570i \(-0.937993\pi\)
0.658180 + 0.752861i \(0.271327\pi\)
\(822\) 0 0
\(823\) −1.39341e10 2.41346e10i −0.871324 1.50918i −0.860627 0.509236i \(-0.829928\pi\)
−0.0106973 0.999943i \(-0.503405\pi\)
\(824\) −4.75820e9 8.24144e9i −0.296277 0.513166i
\(825\) 0 0
\(826\) 2.50825e8 4.34442e8i 0.0154860 0.0268226i
\(827\) −2.35125e10 −1.44554 −0.722769 0.691090i \(-0.757131\pi\)
−0.722769 + 0.691090i \(0.757131\pi\)
\(828\) 0 0
\(829\) −1.28598e10 −0.783960 −0.391980 0.919974i \(-0.628210\pi\)
−0.391980 + 0.919974i \(0.628210\pi\)
\(830\) −5.12080e9 + 8.86948e9i −0.310859 + 0.538424i
\(831\) 0 0
\(832\) 1.67981e9 + 2.90952e9i 0.101118 + 0.175142i
\(833\) −1.16304e10 2.01445e10i −0.697168 1.20753i
\(834\) 0 0
\(835\) 5.03812e9 8.72628e9i 0.299479 0.518712i
\(836\) 7.51802e8 0.0445022
\(837\) 0 0
\(838\) 1.01433e10 0.595420
\(839\) −3.99916e9 + 6.92675e9i −0.233777 + 0.404914i −0.958917 0.283688i \(-0.908442\pi\)
0.725139 + 0.688602i \(0.241775\pi\)
\(840\) 0 0
\(841\) 7.95845e9 + 1.37844e10i 0.461363 + 0.799103i
\(842\) −3.39998e9 5.88894e9i −0.196284 0.339973i
\(843\) 0 0
\(844\) 8.24533e9 1.42813e10i 0.472074 0.817655i
\(845\) 1.43360e10 0.817389
\(846\) 0 0
\(847\) 1.18966e9 0.0672716
\(848\) −8.25296e8 + 1.42945e9i −0.0464755 + 0.0804979i
\(849\) 0 0
\(850\) −6.29956e9 1.09112e10i −0.351839 0.609403i
\(851\) −2.05261e9 3.55523e9i −0.114170 0.197749i
\(852\) 0 0
\(853\) −2.10414e9 + 3.64447e9i −0.116079 + 0.201054i −0.918210 0.396093i \(-0.870366\pi\)
0.802132 + 0.597147i \(0.203699\pi\)
\(854\) 1.15454e8 0.00634318
\(855\) 0 0
\(856\) −1.50824e10 −0.821888
\(857\) 1.59653e10 2.76528e10i 0.866453 1.50074i 0.000855933 1.00000i \(-0.499728\pi\)
0.865597 0.500741i \(-0.166939\pi\)
\(858\) 0 0
\(859\) −1.09001e10 1.88795e10i −0.586752 1.01628i −0.994655 0.103259i \(-0.967073\pi\)
0.407903 0.913025i \(-0.366260\pi\)
\(860\) −1.23027e10 2.13090e10i −0.659565 1.14240i
\(861\) 0 0
\(862\) −6.59828e9 + 1.14286e10i −0.350877 + 0.607737i
\(863\) −1.04728e10 −0.554657 −0.277329 0.960775i \(-0.589449\pi\)
−0.277329 + 0.960775i \(0.589449\pi\)
\(864\) 0 0
\(865\) 2.47728e10 1.30142
\(866\) −4.55214e8 + 7.88453e8i −0.0238178 + 0.0412537i
\(867\) 0 0
\(868\) 8.14923e8 + 1.41149e9i 0.0422958 + 0.0732585i
\(869\) 3.27710e9 + 5.67611e9i 0.169403 + 0.293414i
\(870\) 0 0
\(871\) −1.29296e9 + 2.23948e9i −0.0663015 + 0.114838i
\(872\) 5.30765e9 0.271078
\(873\) 0 0
\(874\) 7.90695e8 0.0400608
\(875\) 5.17920e7 8.97064e7i 0.00261357 0.00452684i
\(876\) 0 0
\(877\) 8.88935e9 + 1.53968e10i 0.445012 + 0.770783i 0.998053 0.0623707i \(-0.0198661\pi\)
−0.553041 + 0.833154i \(0.686533\pi\)
\(878\) 2.97229e9 + 5.14815e9i 0.148204 + 0.256697i
\(879\) 0 0
\(880\) 7.12820e8 1.23464e9i 0.0352607 0.0610733i
\(881\) 7.64253e9 0.376549 0.188274 0.982116i \(-0.439711\pi\)
0.188274 + 0.982116i \(0.439711\pi\)
\(882\) 0 0
\(883\) −2.76375e10 −1.35094 −0.675472 0.737386i \(-0.736060\pi\)
−0.675472 + 0.737386i \(0.736060\pi\)
\(884\) 6.65674e9 1.15298e10i 0.324100 0.561358i
\(885\) 0 0
\(886\) 5.32127e9 + 9.21671e9i 0.257038 + 0.445203i
\(887\) 1.61544e10 + 2.79802e10i 0.777243 + 1.34622i 0.933525 + 0.358512i \(0.116716\pi\)
−0.156282 + 0.987713i \(0.549951\pi\)
\(888\) 0 0
\(889\) 5.37225e8 9.30502e8i 0.0256449 0.0444182i
\(890\) 1.99562e10 0.948886
\(891\) 0 0
\(892\) 1.90014e10 0.896414
\(893\) −2.51401e9 + 4.35439e9i −0.118137 + 0.204619i
\(894\) 0 0
\(895\) 1.57864e10 + 2.73428e10i 0.736042 + 1.27486i
\(896\) 6.60296e8 + 1.14367e9i 0.0306662 + 0.0531155i
\(897\) 0 0
\(898\) 8.31031e8 1.43939e9i 0.0382957 0.0663301i
\(899\) 1.01063e10 0.463908
\(900\) 0 0
\(901\) −1.21509e10 −0.553439
\(902\) 1.79092e9 3.10196e9i 0.0812555 0.140739i
\(903\) 0 0
\(904\) −1.16862e10 2.02410e10i −0.526117 0.911262i
\(905\) 1.25781e10 + 2.17859e10i 0.564087 + 0.977027i
\(906\) 0 0
\(907\) −1.13571e10 + 1.96711e10i −0.505409 + 0.875394i 0.494572 + 0.869137i \(0.335325\pi\)
−0.999980 + 0.00625673i \(0.998008\pi\)
\(908\) 3.99238e9 0.176983
\(909\) 0 0
\(910\) 7.63476e8 0.0335854
\(911\) 3.75463e9 6.50320e9i 0.164533 0.284979i −0.771957 0.635675i \(-0.780722\pi\)
0.936489 + 0.350696i \(0.114055\pi\)
\(912\) 0 0
\(913\) −2.07458e9 3.59328e9i −0.0902157 0.156258i
\(914\) 8.84275e9 + 1.53161e10i 0.383068 + 0.663493i
\(915\) 0 0
\(916\) −1.66488e9 + 2.88366e9i −0.0715730 + 0.123968i
\(917\) 1.07691e9 0.0461199
\(918\) 0 0
\(919\) −2.49374e10 −1.05986 −0.529928 0.848043i \(-0.677781\pi\)
−0.529928 + 0.848043i \(0.677781\pi\)
\(920\) 3.93513e9 6.81585e9i 0.166610 0.288577i
\(921\) 0 0
\(922\) 8.30062e9 + 1.43771e10i 0.348781 + 0.604106i
\(923\) −1.41741e10 2.45502e10i −0.593319 1.02766i
\(924\) 0 0
\(925\) −9.93211e9 + 1.72029e10i −0.412615 + 0.714671i
\(926\) −2.78132e9 −0.115110
\(927\) 0 0
\(928\) 7.01342e9 0.288079
\(929\) −4.33103e9 + 7.50156e9i −0.177229 + 0.306970i −0.940931 0.338600i \(-0.890047\pi\)
0.763701 + 0.645570i \(0.223380\pi\)
\(930\) 0 0
\(931\) −3.53182e9 6.11729e9i −0.143441 0.248448i
\(932\) −4.24280e9 7.34874e9i −0.171671 0.297343i
\(933\) 0 0
\(934\) 1.25377e9 2.17159e9i 0.0503503 0.0872093i
\(935\) 1.04949e10 0.419891
\(936\) 0 0
\(937\) 2.82655e10 1.12245 0.561226 0.827663i \(-0.310330\pi\)
0.561226 + 0.827663i \(0.310330\pi\)
\(938\) 9.73908e7 1.68686e8i 0.00385308 0.00667373i
\(939\) 0 0
\(940\) 1.04643e10 + 1.81248e10i 0.410926 + 0.711745i
\(941\) −2.33541e10 4.04505e10i −0.913691 1.58256i −0.808807 0.588074i \(-0.799886\pi\)
−0.104884 0.994484i \(-0.533447\pi\)
\(942\) 0 0
\(943\) −4.81356e9 + 8.33734e9i −0.186929 + 0.323770i
\(944\) −5.03740e9 −0.194897
\(945\) 0 0
\(946\) −3.90067e9 −0.149803
\(947\) −2.33696e10 + 4.04774e10i −0.894184 + 1.54877i −0.0593718 + 0.998236i \(0.518910\pi\)
−0.834812 + 0.550535i \(0.814424\pi\)
\(948\) 0 0
\(949\) 3.48979e9 + 6.04449e9i 0.132546 + 0.229577i
\(950\) −1.91299e9 3.31340e9i −0.0723904 0.125384i
\(951\) 0 0
\(952\) −1.19902e9 + 2.07677e9i −0.0450400 + 0.0780116i
\(953\) −3.82420e10 −1.43125 −0.715625 0.698484i \(-0.753858\pi\)
−0.715625 + 0.698484i \(0.753858\pi\)
\(954\) 0 0
\(955\) 2.21627e10 0.823399
\(956\) −2.29295e9 + 3.97151e9i −0.0848775 + 0.147012i
\(957\) 0 0
\(958\) 4.52919e9 + 7.84478e9i 0.166434 + 0.288271i
\(959\) −8.97437e8 1.55441e9i −0.0328578 0.0569114i
\(960\) 0 0
\(961\) −2.45550e10 + 4.25306e10i −0.892501 + 1.54586i
\(962\) 8.21367e9 0.297457
\(963\) 0 0
\(964\) −1.83424e10 −0.659457
\(965\) 2.26935e10 3.93063e10i 0.812935 1.40805i
\(966\) 0 0
\(967\) 2.45006e10 + 4.24363e10i 0.871333 + 1.50919i 0.860618 + 0.509250i \(0.170077\pi\)
0.0107146 + 0.999943i \(0.496589\pi\)
\(968\) 1.22684e10 + 2.12495e10i 0.434734 + 0.752982i
\(969\) 0 0
\(970\) 1.03274e10 1.78875e10i 0.363320 0.629288i
\(971\) −2.72929e10 −0.956713 −0.478357 0.878166i \(-0.658767\pi\)
−0.478357 + 0.878166i \(0.658767\pi\)
\(972\) 0 0
\(973\) 7.56947e8 0.0263433
\(974\) 2.78838e9 4.82962e9i 0.0966931 0.167477i
\(975\) 0 0
\(976\) −5.79676e8 1.00403e9i −0.0199577 0.0345678i
\(977\) 1.97241e9 + 3.41631e9i 0.0676653 + 0.117200i 0.897873 0.440254i \(-0.145112\pi\)
−0.830208 + 0.557454i \(0.811778\pi\)
\(978\) 0 0
\(979\) −4.04242e9 + 7.00167e9i −0.137690 + 0.238486i
\(980\) −2.94018e10 −0.997889
\(981\) 0 0
\(982\) 3.07682e10 1.03684
\(983\) 2.37160e8 4.10774e8i 0.00796351 0.0137932i −0.862016 0.506881i \(-0.830798\pi\)
0.869980 + 0.493088i \(0.164132\pi\)
\(984\) 0 0
\(985\) 2.31691e10 + 4.01301e10i 0.772472 + 1.33796i
\(986\) 3.10912e9 + 5.38515e9i 0.103292 + 0.178908i
\(987\) 0 0
\(988\) 2.02146e9 3.50127e9i 0.0666831 0.115498i
\(989\) 1.04841e10 0.344622
\(990\) 0 0
\(991\) 1.22197e10 0.398843 0.199421 0.979914i \(-0.436094\pi\)
0.199421 + 0.979914i \(0.436094\pi\)
\(992\) −2.65869e10 + 4.60498e10i −0.864721 + 1.49774i
\(993\) 0 0
\(994\) 1.06764e9 + 1.84921e9i 0.0344805 + 0.0597219i
\(995\) −1.85271e10 3.20898e10i −0.596247 1.03273i
\(996\) 0 0
\(997\) 1.80345e10 3.12367e10i 0.576330 0.998233i −0.419566 0.907725i \(-0.637818\pi\)
0.995896 0.0905079i \(-0.0288490\pi\)
\(998\) 2.46390e9 0.0784631
\(999\) 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 81.8.c.c.55.1 2
3.2 odd 2 81.8.c.a.55.1 2
9.2 odd 6 3.8.a.a.1.1 1
9.4 even 3 inner 81.8.c.c.28.1 2
9.5 odd 6 81.8.c.a.28.1 2
9.7 even 3 9.8.a.a.1.1 1
36.7 odd 6 144.8.a.b.1.1 1
36.11 even 6 48.8.a.g.1.1 1
45.2 even 12 75.8.b.c.49.2 2
45.7 odd 12 225.8.b.f.199.1 2
45.29 odd 6 75.8.a.a.1.1 1
45.34 even 6 225.8.a.i.1.1 1
45.38 even 12 75.8.b.c.49.1 2
45.43 odd 12 225.8.b.f.199.2 2
63.2 odd 6 147.8.e.b.67.1 2
63.11 odd 6 147.8.e.b.79.1 2
63.20 even 6 147.8.a.b.1.1 1
63.34 odd 6 441.8.a.a.1.1 1
63.38 even 6 147.8.e.a.79.1 2
63.47 even 6 147.8.e.a.67.1 2
72.11 even 6 192.8.a.a.1.1 1
72.29 odd 6 192.8.a.i.1.1 1
72.43 odd 6 576.8.a.x.1.1 1
72.61 even 6 576.8.a.w.1.1 1
99.65 even 6 363.8.a.b.1.1 1
117.38 odd 6 507.8.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.8.a.a.1.1 1 9.2 odd 6
9.8.a.a.1.1 1 9.7 even 3
48.8.a.g.1.1 1 36.11 even 6
75.8.a.a.1.1 1 45.29 odd 6
75.8.b.c.49.1 2 45.38 even 12
75.8.b.c.49.2 2 45.2 even 12
81.8.c.a.28.1 2 9.5 odd 6
81.8.c.a.55.1 2 3.2 odd 2
81.8.c.c.28.1 2 9.4 even 3 inner
81.8.c.c.55.1 2 1.1 even 1 trivial
144.8.a.b.1.1 1 36.7 odd 6
147.8.a.b.1.1 1 63.20 even 6
147.8.e.a.67.1 2 63.47 even 6
147.8.e.a.79.1 2 63.38 even 6
147.8.e.b.67.1 2 63.2 odd 6
147.8.e.b.79.1 2 63.11 odd 6
192.8.a.a.1.1 1 72.11 even 6
192.8.a.i.1.1 1 72.29 odd 6
225.8.a.i.1.1 1 45.34 even 6
225.8.b.f.199.1 2 45.7 odd 12
225.8.b.f.199.2 2 45.43 odd 12
363.8.a.b.1.1 1 99.65 even 6
441.8.a.a.1.1 1 63.34 odd 6
507.8.a.a.1.1 1 117.38 odd 6
576.8.a.w.1.1 1 72.61 even 6
576.8.a.x.1.1 1 72.43 odd 6