Properties

Label 3.33.b.a.2.9
Level $3$
Weight $33$
Character 3.2
Analytic conductor $19.460$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,33,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 33, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 33);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), 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: \(19.4599965427\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{45}\cdot 3^{61}\cdot 5^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.9
Root \(17303.1i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.33.b.a.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+103819. i q^{2} +(-2.32547e7 - 3.62248e7i) q^{3} -6.48340e9 q^{4} -2.49832e11i q^{5} +(3.76082e12 - 2.41428e12i) q^{6} -3.04380e13 q^{7} -2.27200e14i q^{8} +(-7.71458e14 + 1.68480e15i) q^{9} +O(q^{10})\) \(q+103819. i q^{2} +(-2.32547e7 - 3.62248e7i) q^{3} -6.48340e9 q^{4} -2.49832e11i q^{5} +(3.76082e12 - 2.41428e12i) q^{6} -3.04380e13 q^{7} -2.27200e14i q^{8} +(-7.71458e14 + 1.68480e15i) q^{9} +2.59372e16 q^{10} +4.78234e16i q^{11} +(1.50769e17 + 2.34860e17i) q^{12} +5.67246e17 q^{13} -3.16003e18i q^{14} +(-9.05011e18 + 5.80976e18i) q^{15} -4.25830e18 q^{16} +9.91887e18i q^{17} +(-1.74914e20 - 8.00919e19i) q^{18} +3.55318e20 q^{19} +1.61976e21i q^{20} +(7.07826e20 + 1.10261e21i) q^{21} -4.96497e21 q^{22} +3.07553e20i q^{23} +(-8.23029e21 + 5.28347e21i) q^{24} -3.91328e22 q^{25} +5.88909e22i q^{26} +(7.89715e22 - 1.12335e22i) q^{27} +1.97341e23 q^{28} +3.31674e23i q^{29} +(-6.03163e23 - 9.39573e23i) q^{30} +3.59216e23 q^{31} -1.41791e24i q^{32} +(1.73239e24 - 1.11212e24i) q^{33} -1.02977e24 q^{34} +7.60436e24i q^{35} +(5.00167e24 - 1.09232e25i) q^{36} +3.31930e24 q^{37} +3.68887e25i q^{38} +(-1.31911e25 - 2.05484e25i) q^{39} -5.67618e25 q^{40} +3.35484e25i q^{41} +(-1.14472e26 + 7.34857e25i) q^{42} +1.34260e26 q^{43} -3.10058e26i q^{44} +(4.20915e26 + 1.92735e26i) q^{45} -3.19298e25 q^{46} -9.71468e23i q^{47} +(9.90254e25 + 1.54256e26i) q^{48} -1.77959e26 q^{49} -4.06272e27i q^{50} +(3.59310e26 - 2.30660e26i) q^{51} -3.67768e27 q^{52} +5.82182e27i q^{53} +(1.16625e27 + 8.19873e27i) q^{54} +1.19478e28 q^{55} +6.91551e27i q^{56} +(-8.26280e27 - 1.28713e28i) q^{57} -3.44340e28 q^{58} +1.32634e28i q^{59} +(5.86755e28 - 3.76670e28i) q^{60} -6.55279e28 q^{61} +3.72934e28i q^{62} +(2.34816e28 - 5.12817e28i) q^{63} +1.28917e29 q^{64} -1.41716e29i q^{65} +(1.15459e29 + 1.79855e29i) q^{66} -8.95668e28 q^{67} -6.43080e28i q^{68} +(1.11410e28 - 7.15205e27i) q^{69} -7.89477e29 q^{70} +4.59368e28i q^{71} +(3.82786e29 + 1.75275e29i) q^{72} +2.56589e28 q^{73} +3.44606e29i q^{74} +(9.10022e29 + 1.41758e30i) q^{75} -2.30366e30 q^{76} -1.45565e30i q^{77} +(2.13331e30 - 1.36949e30i) q^{78} +3.75026e30 q^{79} +1.06386e30i q^{80} +(-2.24339e30 - 2.59950e30i) q^{81} -3.48296e30 q^{82} -1.44084e30i q^{83} +(-4.58911e30 - 7.14866e30i) q^{84} +2.47805e30 q^{85} +1.39387e31i q^{86} +(1.20148e31 - 7.71297e30i) q^{87} +1.08655e31 q^{88} +4.42071e30i q^{89} +(-2.00095e31 + 4.36990e31i) q^{90} -1.72658e31 q^{91} -1.99399e30i q^{92} +(-8.35346e30 - 1.30125e31i) q^{93} +1.00857e29 q^{94} -8.87696e31i q^{95} +(-5.13635e31 + 3.29731e31i) q^{96} +7.67762e31 q^{97} -1.84755e31i q^{98} +(-8.05726e31 - 3.68937e31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 103819.i 1.58415i 0.610423 + 0.792075i \(0.290999\pi\)
−0.610423 + 0.792075i \(0.709001\pi\)
\(3\) −2.32547e7 3.62248e7i −0.540220 0.841524i
\(4\) −6.48340e9 −1.50953
\(5\) 2.49832e11i 1.63730i −0.574295 0.818648i \(-0.694724\pi\)
0.574295 0.818648i \(-0.305276\pi\)
\(6\) 3.76082e12 2.41428e12i 1.33310 0.855790i
\(7\) −3.04380e13 −0.915897 −0.457949 0.888979i \(-0.651416\pi\)
−0.457949 + 0.888979i \(0.651416\pi\)
\(8\) 2.27200e14i 0.807177i
\(9\) −7.71458e14 + 1.68480e15i −0.416324 + 0.909216i
\(10\) 2.59372e16 2.59372
\(11\) 4.78234e16i 1.04078i 0.853930 + 0.520388i \(0.174213\pi\)
−0.853930 + 0.520388i \(0.825787\pi\)
\(12\) 1.50769e17 + 2.34860e17i 0.815480 + 1.27031i
\(13\) 5.67246e17 0.852468 0.426234 0.904613i \(-0.359840\pi\)
0.426234 + 0.904613i \(0.359840\pi\)
\(14\) 3.16003e18i 1.45092i
\(15\) −9.05011e18 + 5.80976e18i −1.37782 + 0.884501i
\(16\) −4.25830e18 −0.230843
\(17\) 9.91887e18i 0.203835i 0.994793 + 0.101918i \(0.0324978\pi\)
−0.994793 + 0.101918i \(0.967502\pi\)
\(18\) −1.74914e20 8.00919e19i −1.44034 0.659521i
\(19\) 3.55318e20 1.23185 0.615927 0.787803i \(-0.288782\pi\)
0.615927 + 0.787803i \(0.288782\pi\)
\(20\) 1.61976e21i 2.47155i
\(21\) 7.07826e20 + 1.10261e21i 0.494786 + 0.770749i
\(22\) −4.96497e21 −1.64875
\(23\) 3.07553e20i 0.0501504i 0.999686 + 0.0250752i \(0.00798252\pi\)
−0.999686 + 0.0250752i \(0.992017\pi\)
\(24\) −8.23029e21 + 5.28347e21i −0.679259 + 0.436053i
\(25\) −3.91328e22 −1.68074
\(26\) 5.88909e22i 1.35044i
\(27\) 7.89715e22 1.12335e22i 0.990034 0.140830i
\(28\) 1.97341e23 1.38258
\(29\) 3.31674e23i 1.32539i 0.748890 + 0.662694i \(0.230587\pi\)
−0.748890 + 0.662694i \(0.769413\pi\)
\(30\) −6.03163e23 9.39573e23i −1.40118 2.18268i
\(31\) 3.59216e23 0.493820 0.246910 0.969038i \(-0.420585\pi\)
0.246910 + 0.969038i \(0.420585\pi\)
\(32\) 1.41791e24i 1.17287i
\(33\) 1.73239e24 1.11212e24i 0.875838 0.562248i
\(34\) −1.02977e24 −0.322906
\(35\) 7.60436e24i 1.49960i
\(36\) 5.00167e24 1.09232e25i 0.628456 1.37249i
\(37\) 3.31930e24 0.269041 0.134520 0.990911i \(-0.457051\pi\)
0.134520 + 0.990911i \(0.457051\pi\)
\(38\) 3.68887e25i 1.95144i
\(39\) −1.31911e25 2.05484e25i −0.460520 0.717372i
\(40\) −5.67618e25 −1.32159
\(41\) 3.35484e25i 0.526175i 0.964772 + 0.263087i \(0.0847408\pi\)
−0.964772 + 0.263087i \(0.915259\pi\)
\(42\) −1.14472e26 + 7.34857e25i −1.22098 + 0.783816i
\(43\) 1.34260e26 0.982767 0.491384 0.870943i \(-0.336491\pi\)
0.491384 + 0.870943i \(0.336491\pi\)
\(44\) 3.10058e26i 1.57109i
\(45\) 4.20915e26 + 1.92735e26i 1.48866 + 0.681647i
\(46\) −3.19298e25 −0.0794457
\(47\) 9.71468e23i 0.00171342i −1.00000 0.000856708i \(-0.999727\pi\)
1.00000 0.000856708i \(-0.000272699\pi\)
\(48\) 9.90254e25 + 1.54256e26i 0.124706 + 0.194260i
\(49\) −1.77959e26 −0.161132
\(50\) 4.06272e27i 2.66255i
\(51\) 3.59310e26 2.30660e26i 0.171532 0.110116i
\(52\) −3.67768e27 −1.28683
\(53\) 5.82182e27i 1.50191i 0.660351 + 0.750957i \(0.270408\pi\)
−0.660351 + 0.750957i \(0.729592\pi\)
\(54\) 1.16625e27 + 8.19873e27i 0.223096 + 1.56836i
\(55\) 1.19478e28 1.70406
\(56\) 6.91551e27i 0.739292i
\(57\) −8.26280e27 1.28713e28i −0.665472 1.03663i
\(58\) −3.44340e28 −2.09961
\(59\) 1.32634e28i 0.615208i 0.951514 + 0.307604i \(0.0995272\pi\)
−0.951514 + 0.307604i \(0.900473\pi\)
\(60\) 5.86755e28 3.76670e28i 2.07987 1.33518i
\(61\) −6.55279e28 −1.78299 −0.891494 0.453032i \(-0.850342\pi\)
−0.891494 + 0.453032i \(0.850342\pi\)
\(62\) 3.72934e28i 0.782285i
\(63\) 2.34816e28 5.12817e28i 0.381310 0.832749i
\(64\) 1.28917e29 1.62716
\(65\) 1.41716e29i 1.39574i
\(66\) 1.15459e29 + 1.79855e29i 0.890686 + 1.38746i
\(67\) −8.95668e28 −0.543188 −0.271594 0.962412i \(-0.587551\pi\)
−0.271594 + 0.962412i \(0.587551\pi\)
\(68\) 6.43080e28i 0.307696i
\(69\) 1.11410e28 7.15205e27i 0.0422027 0.0270922i
\(70\) −7.89477e29 −2.37559
\(71\) 4.59368e28i 0.110161i 0.998482 + 0.0550805i \(0.0175415\pi\)
−0.998482 + 0.0550805i \(0.982458\pi\)
\(72\) 3.82786e29 + 1.75275e29i 0.733899 + 0.336048i
\(73\) 2.56589e28 0.0394524 0.0197262 0.999805i \(-0.493721\pi\)
0.0197262 + 0.999805i \(0.493721\pi\)
\(74\) 3.44606e29i 0.426201i
\(75\) 9.10022e29 + 1.41758e30i 0.907970 + 1.41438i
\(76\) −2.30366e30 −1.85952
\(77\) 1.45565e30i 0.953244i
\(78\) 2.13331e30 1.36949e30i 1.13642 0.729533i
\(79\) 3.75026e30 1.62940 0.814700 0.579883i \(-0.196902\pi\)
0.814700 + 0.579883i \(0.196902\pi\)
\(80\) 1.06386e30i 0.377958i
\(81\) −2.24339e30 2.59950e30i −0.653348 0.757058i
\(82\) −3.48296e30 −0.833540
\(83\) 1.44084e30i 0.284032i −0.989864 0.142016i \(-0.954642\pi\)
0.989864 0.142016i \(-0.0453585\pi\)
\(84\) −4.58911e30 7.14866e30i −0.746896 1.16347i
\(85\) 2.47805e30 0.333739
\(86\) 1.39387e31i 1.55685i
\(87\) 1.20148e31 7.71297e30i 1.11535 0.716001i
\(88\) 1.08655e31 0.840091
\(89\) 4.42071e30i 0.285268i 0.989776 + 0.142634i \(0.0455571\pi\)
−0.989776 + 0.142634i \(0.954443\pi\)
\(90\) −2.00095e31 + 4.36990e31i −1.07983 + 2.35826i
\(91\) −1.72658e31 −0.780773
\(92\) 1.99399e30i 0.0757036i
\(93\) −8.35346e30 1.30125e31i −0.266771 0.415561i
\(94\) 1.00857e29 0.00271431
\(95\) 8.87696e31i 2.01691i
\(96\) −5.13635e31 + 3.29731e31i −0.986995 + 0.633606i
\(97\) 7.67762e31 1.24991 0.624955 0.780661i \(-0.285117\pi\)
0.624955 + 0.780661i \(0.285117\pi\)
\(98\) 1.84755e31i 0.255257i
\(99\) −8.05726e31 3.68937e31i −0.946291 0.433301i
\(100\) 2.53713e32 2.53713
\(101\) 1.25779e32i 1.07267i 0.844006 + 0.536334i \(0.180191\pi\)
−0.844006 + 0.536334i \(0.819809\pi\)
\(102\) 2.39469e31 + 3.73031e31i 0.174440 + 0.271733i
\(103\) −5.21843e31 −0.325195 −0.162598 0.986692i \(-0.551987\pi\)
−0.162598 + 0.986692i \(0.551987\pi\)
\(104\) 1.28878e32i 0.688093i
\(105\) 2.75467e32 1.76837e32i 1.26195 0.810112i
\(106\) −6.04415e32 −2.37926
\(107\) 1.50915e32i 0.511200i −0.966783 0.255600i \(-0.917727\pi\)
0.966783 0.255600i \(-0.0822731\pi\)
\(108\) −5.12003e32 + 7.28312e31i −1.49449 + 0.212587i
\(109\) 2.44952e32 0.616961 0.308481 0.951231i \(-0.400180\pi\)
0.308481 + 0.951231i \(0.400180\pi\)
\(110\) 1.24041e33i 2.69949i
\(111\) −7.71893e31 1.20241e32i −0.145341 0.226404i
\(112\) 1.29614e32 0.211428
\(113\) 7.51269e32i 1.06302i 0.847053 + 0.531509i \(0.178375\pi\)
−0.847053 + 0.531509i \(0.821625\pi\)
\(114\) 1.33629e33 8.57835e32i 1.64218 1.05421i
\(115\) 7.68364e31 0.0821110
\(116\) 2.15037e33i 2.00072i
\(117\) −4.37606e32 + 9.55694e32i −0.354903 + 0.775077i
\(118\) −1.37699e33 −0.974582
\(119\) 3.01910e32i 0.186692i
\(120\) 1.31998e33 + 2.05619e33i 0.713949 + 1.11215i
\(121\) −1.75699e32 −0.0832153
\(122\) 6.80303e33i 2.82452i
\(123\) 1.21529e33 7.80158e32i 0.442789 0.284250i
\(124\) −2.32894e33 −0.745437
\(125\) 3.95977e33i 1.11458i
\(126\) 5.32401e33 + 2.43783e33i 1.31920 + 0.604053i
\(127\) −5.93082e33 −1.29496 −0.647479 0.762084i \(-0.724176\pi\)
−0.647479 + 0.762084i \(0.724176\pi\)
\(128\) 7.29410e33i 1.40479i
\(129\) −3.12217e33 4.86354e33i −0.530911 0.827022i
\(130\) 1.47128e34 2.21107
\(131\) 6.98819e33i 0.929018i 0.885568 + 0.464509i \(0.153769\pi\)
−0.885568 + 0.464509i \(0.846231\pi\)
\(132\) −1.12318e34 + 7.21031e33i −1.32211 + 0.848732i
\(133\) −1.08151e34 −1.12825
\(134\) 9.29872e33i 0.860491i
\(135\) −2.80648e33 1.97296e34i −0.230580 1.62098i
\(136\) 2.25357e33 0.164531
\(137\) 2.45169e34i 1.59198i 0.605312 + 0.795989i \(0.293048\pi\)
−0.605312 + 0.795989i \(0.706952\pi\)
\(138\) 7.42518e32 + 1.15665e33i 0.0429182 + 0.0668555i
\(139\) 1.85811e34 0.956828 0.478414 0.878134i \(-0.341212\pi\)
0.478414 + 0.878134i \(0.341212\pi\)
\(140\) 4.93021e34i 2.26369i
\(141\) −3.51913e31 + 2.25912e31i −0.00144188 + 0.000925622i
\(142\) −4.76911e33 −0.174512
\(143\) 2.71276e34i 0.887228i
\(144\) 3.28509e33 7.17436e33i 0.0961054 0.209886i
\(145\) 8.28626e34 2.17005
\(146\) 2.66388e33i 0.0624985i
\(147\) 4.13838e33 + 6.44653e33i 0.0870468 + 0.135596i
\(148\) −2.15203e34 −0.406126
\(149\) 1.74564e34i 0.295784i −0.989004 0.147892i \(-0.952751\pi\)
0.989004 0.147892i \(-0.0472488\pi\)
\(150\) −1.47172e35 + 9.44775e34i −2.24060 + 1.43836i
\(151\) −1.31115e35 −1.79482 −0.897410 0.441197i \(-0.854554\pi\)
−0.897410 + 0.441197i \(0.854554\pi\)
\(152\) 8.07282e34i 0.994324i
\(153\) −1.67113e34 7.65199e33i −0.185330 0.0848617i
\(154\) 1.51124e35 1.51008
\(155\) 8.97435e34i 0.808530i
\(156\) 8.55234e34 + 1.33223e35i 0.695170 + 1.08290i
\(157\) 5.79275e34 0.425099 0.212549 0.977150i \(-0.431823\pi\)
0.212549 + 0.977150i \(0.431823\pi\)
\(158\) 3.89348e35i 2.58121i
\(159\) 2.10895e35 1.35385e35i 1.26390 0.811364i
\(160\) −3.54239e35 −1.92033
\(161\) 9.36127e33i 0.0459326i
\(162\) 2.69877e35 2.32906e35i 1.19929 1.03500i
\(163\) −3.16517e34 −0.127466 −0.0637332 0.997967i \(-0.520301\pi\)
−0.0637332 + 0.997967i \(0.520301\pi\)
\(164\) 2.17508e35i 0.794278i
\(165\) −2.77843e35 4.32807e35i −0.920567 1.43401i
\(166\) 1.49587e35 0.449950
\(167\) 5.63562e34i 0.153985i −0.997032 0.0769925i \(-0.975468\pi\)
0.997032 0.0769925i \(-0.0245317\pi\)
\(168\) 2.50513e35 1.60818e35i 0.622131 0.399380i
\(169\) −1.21011e35 −0.273299
\(170\) 2.57268e35i 0.528693i
\(171\) −2.74112e35 + 5.98638e35i −0.512851 + 1.12002i
\(172\) −8.70459e35 −1.48352
\(173\) 1.61709e34i 0.0251186i 0.999921 + 0.0125593i \(0.00399786\pi\)
−0.999921 + 0.0125593i \(0.996002\pi\)
\(174\) 8.00752e35 + 1.24737e36i 1.13425 + 1.76687i
\(175\) 1.19112e36 1.53939
\(176\) 2.03646e35i 0.240256i
\(177\) 4.80464e35 3.08436e35i 0.517712 0.332348i
\(178\) −4.58954e35 −0.451907
\(179\) 8.90367e35i 0.801532i 0.916180 + 0.400766i \(0.131256\pi\)
−0.916180 + 0.400766i \(0.868744\pi\)
\(180\) −2.72896e36 1.24957e36i −2.24718 1.02897i
\(181\) −1.19270e36 −0.898826 −0.449413 0.893324i \(-0.648367\pi\)
−0.449413 + 0.893324i \(0.648367\pi\)
\(182\) 1.79252e36i 1.23686i
\(183\) 1.52383e36 + 2.37374e36i 0.963206 + 1.50043i
\(184\) 6.98760e34 0.0404802
\(185\) 8.29265e35i 0.440500i
\(186\) 1.35095e36 8.67247e35i 0.658311 0.422606i
\(187\) −4.74354e35 −0.212147
\(188\) 6.29841e33i 0.00258646i
\(189\) −2.40373e36 + 3.41925e35i −0.906769 + 0.128986i
\(190\) 9.21596e36 3.19509
\(191\) 3.89653e36i 1.24207i −0.783784 0.621033i \(-0.786713\pi\)
0.783784 0.621033i \(-0.213287\pi\)
\(192\) −2.99792e36 4.66998e36i −0.879022 1.36929i
\(193\) 1.90013e36 0.512703 0.256351 0.966584i \(-0.417480\pi\)
0.256351 + 0.966584i \(0.417480\pi\)
\(194\) 7.97082e36i 1.98005i
\(195\) −5.13364e36 + 3.29556e36i −1.17455 + 0.754008i
\(196\) 1.15378e36 0.243234
\(197\) 3.35666e36i 0.652300i 0.945318 + 0.326150i \(0.105752\pi\)
−0.945318 + 0.326150i \(0.894248\pi\)
\(198\) 3.83027e36 8.36496e36i 0.686413 1.49907i
\(199\) −7.69959e36 −1.27297 −0.636485 0.771289i \(-0.719612\pi\)
−0.636485 + 0.771289i \(0.719612\pi\)
\(200\) 8.89098e36i 1.35666i
\(201\) 2.08285e36 + 3.24454e36i 0.293441 + 0.457105i
\(202\) −1.30582e37 −1.69927
\(203\) 1.00955e37i 1.21392i
\(204\) −2.32955e36 + 1.49546e36i −0.258934 + 0.166224i
\(205\) 8.38145e36 0.861504
\(206\) 5.41772e36i 0.515158i
\(207\) −5.18163e35 2.37264e35i −0.0455975 0.0208788i
\(208\) −2.41550e36 −0.196786
\(209\) 1.69925e37i 1.28208i
\(210\) 1.83590e37 + 2.85987e37i 1.28334 + 1.99911i
\(211\) 6.84634e36 0.443546 0.221773 0.975098i \(-0.428816\pi\)
0.221773 + 0.975098i \(0.428816\pi\)
\(212\) 3.77452e37i 2.26719i
\(213\) 1.66405e36 1.06825e36i 0.0927030 0.0595111i
\(214\) 1.56678e37 0.809818
\(215\) 3.35424e37i 1.60908i
\(216\) −2.55225e36 1.79423e37i −0.113675 0.799133i
\(217\) −1.09338e37 −0.452288
\(218\) 2.54307e37i 0.977359i
\(219\) −5.96691e35 9.29491e35i −0.0213130 0.0332001i
\(220\) −7.74623e37 −2.57233
\(221\) 5.62644e36i 0.173763i
\(222\) 1.24833e37 8.01370e36i 0.358659 0.230243i
\(223\) 5.43018e37 1.45190 0.725950 0.687748i \(-0.241401\pi\)
0.725950 + 0.687748i \(0.241401\pi\)
\(224\) 4.31583e37i 1.07423i
\(225\) 3.01893e37 6.59308e37i 0.699734 1.52816i
\(226\) −7.79960e37 −1.68398
\(227\) 4.49436e37i 0.904178i 0.891973 + 0.452089i \(0.149321\pi\)
−0.891973 + 0.452089i \(0.850679\pi\)
\(228\) 5.35710e37 + 8.34499e37i 1.00455 + 1.56483i
\(229\) 2.48444e37 0.434372 0.217186 0.976130i \(-0.430312\pi\)
0.217186 + 0.976130i \(0.430312\pi\)
\(230\) 7.97707e36i 0.130076i
\(231\) −5.27305e37 + 3.38506e37i −0.802178 + 0.514962i
\(232\) 7.53563e37 1.06982
\(233\) 8.15150e37i 1.08030i 0.841570 + 0.540148i \(0.181632\pi\)
−0.841570 + 0.540148i \(0.818368\pi\)
\(234\) −9.92191e37 4.54318e37i −1.22784 0.562220i
\(235\) −2.42704e35 −0.00280537
\(236\) 8.59917e37i 0.928677i
\(237\) −8.72111e37 1.35852e38i −0.880234 1.37118i
\(238\) 3.13440e37 0.295749
\(239\) 1.65146e38i 1.45714i −0.684971 0.728570i \(-0.740185\pi\)
0.684971 0.728570i \(-0.259815\pi\)
\(240\) 3.85381e37 2.47397e37i 0.318061 0.204180i
\(241\) −1.04519e38 −0.807092 −0.403546 0.914959i \(-0.632222\pi\)
−0.403546 + 0.914959i \(0.632222\pi\)
\(242\) 1.82409e37i 0.131826i
\(243\) −4.19970e37 + 1.41717e38i −0.284130 + 0.958786i
\(244\) 4.24843e38 2.69148
\(245\) 4.44597e37i 0.263821i
\(246\) 8.09951e37 + 1.26170e38i 0.450295 + 0.701444i
\(247\) 2.01552e38 1.05012
\(248\) 8.16139e37i 0.398600i
\(249\) −5.21943e37 + 3.35064e37i −0.239020 + 0.153440i
\(250\) −4.11099e38 −1.76566
\(251\) 5.56329e37i 0.224157i 0.993699 + 0.112079i \(0.0357508\pi\)
−0.993699 + 0.112079i \(0.964249\pi\)
\(252\) −1.52240e38 + 3.32480e38i −0.575601 + 1.25706i
\(253\) −1.47082e37 −0.0521953
\(254\) 6.15731e38i 2.05141i
\(255\) −5.76263e37 8.97669e37i −0.180293 0.280849i
\(256\) −2.03573e38 −0.598247
\(257\) 4.70854e38i 1.30004i 0.759917 + 0.650020i \(0.225239\pi\)
−0.759917 + 0.650020i \(0.774761\pi\)
\(258\) 5.04927e38 3.24140e38i 1.31013 0.841043i
\(259\) −1.01033e38 −0.246414
\(260\) 9.18801e38i 2.10692i
\(261\) −5.58802e38 2.55872e38i −1.20506 0.551791i
\(262\) −7.25506e38 −1.47170
\(263\) 8.36358e38i 1.59625i 0.602494 + 0.798124i \(0.294174\pi\)
−0.602494 + 0.798124i \(0.705826\pi\)
\(264\) −2.52674e38 3.93600e38i −0.453834 0.706957i
\(265\) 1.45448e39 2.45908
\(266\) 1.12282e39i 1.78732i
\(267\) 1.60140e38 1.02802e38i 0.240059 0.154107i
\(268\) 5.80697e38 0.819960
\(269\) 1.11243e38i 0.147992i −0.997259 0.0739960i \(-0.976425\pi\)
0.997259 0.0739960i \(-0.0235752\pi\)
\(270\) 2.04830e39 2.91366e38i 2.56788 0.365274i
\(271\) −6.87434e38 −0.812311 −0.406156 0.913804i \(-0.633131\pi\)
−0.406156 + 0.913804i \(0.633131\pi\)
\(272\) 4.22375e37i 0.0470539i
\(273\) 4.01511e38 + 6.25451e38i 0.421789 + 0.657039i
\(274\) −2.54532e39 −2.52193
\(275\) 1.87146e39i 1.74928i
\(276\) −7.22318e37 + 4.63695e37i −0.0637064 + 0.0408966i
\(277\) −1.52657e39 −1.27070 −0.635348 0.772226i \(-0.719143\pi\)
−0.635348 + 0.772226i \(0.719143\pi\)
\(278\) 1.92907e39i 1.51576i
\(279\) −2.77120e38 + 6.05206e38i −0.205589 + 0.448989i
\(280\) 1.72771e39 1.21044
\(281\) 1.62418e39i 1.07481i −0.843324 0.537405i \(-0.819405\pi\)
0.843324 0.537405i \(-0.180595\pi\)
\(282\) −2.34539e36 3.65352e36i −0.00146632 0.00228416i
\(283\) 2.63488e39 1.55661 0.778303 0.627889i \(-0.216081\pi\)
0.778303 + 0.627889i \(0.216081\pi\)
\(284\) 2.97827e38i 0.166292i
\(285\) −3.21566e39 + 2.06431e39i −1.69728 + 1.08958i
\(286\) −2.81636e39 −1.40550
\(287\) 1.02114e39i 0.481922i
\(288\) 2.38889e39 + 1.09386e39i 1.06639 + 0.488293i
\(289\) 2.26953e39 0.958451
\(290\) 8.60270e39i 3.43769i
\(291\) −1.78541e39 2.78121e39i −0.675227 1.05183i
\(292\) −1.66357e38 −0.0595547
\(293\) 5.48987e39i 1.86072i −0.366651 0.930359i \(-0.619496\pi\)
0.366651 0.930359i \(-0.380504\pi\)
\(294\) −6.69271e38 + 4.29642e38i −0.214805 + 0.137895i
\(295\) 3.31361e39 1.00728
\(296\) 7.54145e38i 0.217164i
\(297\) 5.37224e38 + 3.77668e39i 0.146572 + 1.03040i
\(298\) 1.81231e39 0.468567
\(299\) 1.74458e38i 0.0427516i
\(300\) −5.90003e39 9.19073e39i −1.37061 2.13506i
\(301\) −4.08659e39 −0.900114
\(302\) 1.36122e40i 2.84327i
\(303\) 4.55631e39 2.92495e39i 0.902675 0.579476i
\(304\) −1.51305e39 −0.284364
\(305\) 1.63709e40i 2.91928i
\(306\) 7.94421e38 1.73495e39i 0.134434 0.293591i
\(307\) 4.15729e39 0.667724 0.333862 0.942622i \(-0.391648\pi\)
0.333862 + 0.942622i \(0.391648\pi\)
\(308\) 9.43753e39i 1.43895i
\(309\) 1.21353e39 + 1.89037e39i 0.175677 + 0.273660i
\(310\) 9.31707e39 1.28083
\(311\) 4.12881e39i 0.539087i −0.962988 0.269543i \(-0.913127\pi\)
0.962988 0.269543i \(-0.0868728\pi\)
\(312\) −4.66860e39 + 2.99703e39i −0.579046 + 0.371721i
\(313\) 1.51328e40 1.78324 0.891618 0.452788i \(-0.149570\pi\)
0.891618 + 0.452788i \(0.149570\pi\)
\(314\) 6.01397e39i 0.673421i
\(315\) −1.28118e40 5.86645e39i −1.36346 0.624318i
\(316\) −2.43144e40 −2.45963
\(317\) 1.30044e39i 0.125067i −0.998043 0.0625336i \(-0.980082\pi\)
0.998043 0.0625336i \(-0.0199181\pi\)
\(318\) 1.40555e40 + 2.18948e40i 1.28532 + 2.00220i
\(319\) −1.58618e40 −1.37943
\(320\) 3.22074e40i 2.66414i
\(321\) −5.46686e39 + 3.50948e39i −0.430187 + 0.276161i
\(322\) 9.71877e38 0.0727641
\(323\) 3.52435e39i 0.251095i
\(324\) 1.45448e40 + 1.68536e40i 0.986250 + 1.14280i
\(325\) −2.21979e40 −1.43278
\(326\) 3.28605e39i 0.201926i
\(327\) −5.69630e39 8.87336e39i −0.333295 0.519187i
\(328\) 7.62220e39 0.424716
\(329\) 2.95695e37i 0.00156931i
\(330\) 4.49335e40 2.88453e40i 2.27168 1.45832i
\(331\) 3.01231e40 1.45095 0.725475 0.688249i \(-0.241620\pi\)
0.725475 + 0.688249i \(0.241620\pi\)
\(332\) 9.34156e39i 0.428756i
\(333\) −2.56070e39 + 5.59234e39i −0.112008 + 0.244616i
\(334\) 5.85084e39 0.243935
\(335\) 2.23766e40i 0.889360i
\(336\) −3.01413e39 4.69524e39i −0.114218 0.177922i
\(337\) −4.23569e40 −1.53054 −0.765272 0.643707i \(-0.777396\pi\)
−0.765272 + 0.643707i \(0.777396\pi\)
\(338\) 1.25632e40i 0.432947i
\(339\) 2.72146e40 1.74705e40i 0.894555 0.574264i
\(340\) −1.60662e40 −0.503790
\(341\) 1.71789e40i 0.513956i
\(342\) −6.21499e40 2.84580e40i −1.77428 0.812433i
\(343\) 3.90332e40 1.06348
\(344\) 3.05039e40i 0.793268i
\(345\) −1.78681e39 2.78339e39i −0.0443580 0.0690984i
\(346\) −1.67884e39 −0.0397917
\(347\) 1.86252e40i 0.421530i −0.977537 0.210765i \(-0.932405\pi\)
0.977537 0.210765i \(-0.0675954\pi\)
\(348\) −7.78969e40 + 5.00063e40i −1.68365 + 1.08083i
\(349\) −2.35818e40 −0.486822 −0.243411 0.969923i \(-0.578266\pi\)
−0.243411 + 0.969923i \(0.578266\pi\)
\(350\) 1.23661e41i 2.43862i
\(351\) 4.47963e40 6.37216e39i 0.843972 0.120053i
\(352\) 6.78092e40 1.22069
\(353\) 4.50171e40i 0.774430i 0.921989 + 0.387215i \(0.126563\pi\)
−0.921989 + 0.387215i \(0.873437\pi\)
\(354\) 3.20215e40 + 4.98812e40i 0.526489 + 0.820134i
\(355\) 1.14765e40 0.180366
\(356\) 2.86612e40i 0.430621i
\(357\) −1.09366e40 + 7.02083e39i −0.157106 + 0.100855i
\(358\) −9.24370e40 −1.26975
\(359\) 9.66820e40i 1.27009i −0.772475 0.635045i \(-0.780981\pi\)
0.772475 0.635045i \(-0.219019\pi\)
\(360\) 4.37893e40 9.56321e40i 0.550210 1.20161i
\(361\) 4.30521e40 0.517463
\(362\) 1.23825e41i 1.42388i
\(363\) 4.08583e39 + 6.36467e39i 0.0449546 + 0.0700277i
\(364\) 1.11941e41 1.17860
\(365\) 6.41042e39i 0.0645952i
\(366\) −2.46439e41 + 1.58202e41i −2.37690 + 1.52586i
\(367\) 7.40639e40 0.683832 0.341916 0.939730i \(-0.388924\pi\)
0.341916 + 0.939730i \(0.388924\pi\)
\(368\) 1.30965e39i 0.0115768i
\(369\) −5.65222e40 2.58812e40i −0.478407 0.219059i
\(370\) 8.60934e40 0.697818
\(371\) 1.77204e41i 1.37560i
\(372\) 5.41588e40 + 8.43654e40i 0.402700 + 0.627303i
\(373\) −8.48695e40 −0.604519 −0.302260 0.953226i \(-0.597741\pi\)
−0.302260 + 0.953226i \(0.597741\pi\)
\(374\) 4.92469e40i 0.336073i
\(375\) 1.43442e41 9.20832e40i 0.937942 0.602116i
\(376\) −2.20718e38 −0.00138303
\(377\) 1.88141e41i 1.12985i
\(378\) −3.54983e40 2.49553e41i −0.204333 1.43646i
\(379\) −2.86987e41 −1.58356 −0.791781 0.610805i \(-0.790846\pi\)
−0.791781 + 0.610805i \(0.790846\pi\)
\(380\) 5.75528e41i 3.04459i
\(381\) 1.37920e41 + 2.14843e41i 0.699562 + 1.08974i
\(382\) 4.04534e41 1.96762
\(383\) 2.93471e41i 1.36894i −0.729041 0.684470i \(-0.760034\pi\)
0.729041 0.684470i \(-0.239966\pi\)
\(384\) 2.64228e41 1.69622e41i 1.18217 0.758897i
\(385\) −3.63666e41 −1.56074
\(386\) 1.97269e41i 0.812199i
\(387\) −1.03576e41 + 2.26200e41i −0.409150 + 0.893548i
\(388\) −4.97770e41 −1.88678
\(389\) 5.36936e41i 1.95312i 0.215245 + 0.976560i \(0.430945\pi\)
−0.215245 + 0.976560i \(0.569055\pi\)
\(390\) −3.42142e41 5.32969e41i −1.19446 1.86066i
\(391\) −3.05058e39 −0.0102224
\(392\) 4.04323e40i 0.130062i
\(393\) 2.53146e41 1.62508e41i 0.781790 0.501874i
\(394\) −3.48485e41 −1.03334
\(395\) 9.36933e41i 2.66781i
\(396\) 5.22384e41 + 2.39197e41i 1.42846 + 0.654082i
\(397\) 4.82964e41 1.26843 0.634216 0.773156i \(-0.281323\pi\)
0.634216 + 0.773156i \(0.281323\pi\)
\(398\) 7.99363e41i 2.01658i
\(399\) 2.51503e41 + 3.91777e41i 0.609504 + 0.949450i
\(400\) 1.66639e41 0.387987
\(401\) 6.81584e41i 1.52479i 0.647114 + 0.762394i \(0.275976\pi\)
−0.647114 + 0.762394i \(0.724024\pi\)
\(402\) −3.36845e41 + 2.16239e41i −0.724124 + 0.464855i
\(403\) 2.03764e41 0.420965
\(404\) 8.15473e41i 1.61923i
\(405\) −6.49437e41 + 5.60470e41i −1.23953 + 1.06972i
\(406\) 1.04810e42 1.92303
\(407\) 1.58740e41i 0.280011i
\(408\) −5.24061e40 8.16352e40i −0.0888831 0.138457i
\(409\) −9.34417e41 −1.52394 −0.761970 0.647613i \(-0.775767\pi\)
−0.761970 + 0.647613i \(0.775767\pi\)
\(410\) 8.70153e41i 1.36475i
\(411\) 8.88121e41 5.70134e41i 1.33969 0.860018i
\(412\) 3.38331e41 0.490893
\(413\) 4.03710e41i 0.563467i
\(414\) 2.46325e40 5.37952e40i 0.0330752 0.0722333i
\(415\) −3.59968e41 −0.465045
\(416\) 8.04303e41i 0.999831i
\(417\) −4.32097e41 6.73096e41i −0.516898 0.805194i
\(418\) −1.76414e42 −2.03101
\(419\) 1.19503e42i 1.32421i 0.749412 + 0.662104i \(0.230336\pi\)
−0.749412 + 0.662104i \(0.769664\pi\)
\(420\) −1.78596e42 + 1.14651e42i −1.90495 + 1.22289i
\(421\) −1.01400e41 −0.104118 −0.0520590 0.998644i \(-0.516578\pi\)
−0.0520590 + 0.998644i \(0.516578\pi\)
\(422\) 7.10779e41i 0.702644i
\(423\) 1.63673e39 + 7.49447e38i 0.00155787 + 0.000713337i
\(424\) 1.32272e42 1.21231
\(425\) 3.88153e41i 0.342595i
\(426\) 1.10904e41 + 1.72760e41i 0.0942746 + 0.146856i
\(427\) 1.99453e42 1.63303
\(428\) 9.78440e41i 0.771674i
\(429\) 9.82694e41 6.30845e41i 0.746624 0.479298i
\(430\) 3.48233e42 2.54903
\(431\) 1.23004e42i 0.867524i 0.901028 + 0.433762i \(0.142814\pi\)
−0.901028 + 0.433762i \(0.857186\pi\)
\(432\) −3.36284e41 + 4.78356e40i −0.228542 + 0.0325096i
\(433\) −1.88664e42 −1.23561 −0.617806 0.786330i \(-0.711978\pi\)
−0.617806 + 0.786330i \(0.711978\pi\)
\(434\) 1.13513e42i 0.716493i
\(435\) −1.92694e42 3.00168e42i −1.17231 1.82615i
\(436\) −1.58812e42 −0.931323
\(437\) 1.09279e41i 0.0617779i
\(438\) 9.64987e40 6.19478e40i 0.0525940 0.0337629i
\(439\) 8.54191e41 0.448872 0.224436 0.974489i \(-0.427946\pi\)
0.224436 + 0.974489i \(0.427946\pi\)
\(440\) 2.71454e42i 1.37548i
\(441\) 1.37288e41 2.99824e41i 0.0670832 0.146504i
\(442\) −5.84131e41 −0.275267
\(443\) 2.00522e42i 0.911384i −0.890137 0.455692i \(-0.849392\pi\)
0.890137 0.455692i \(-0.150608\pi\)
\(444\) 5.00449e41 + 7.79570e41i 0.219398 + 0.341765i
\(445\) 1.10443e42 0.467068
\(446\) 5.63755e42i 2.30003i
\(447\) −6.32356e41 + 4.05944e41i −0.248909 + 0.159789i
\(448\) −3.92395e42 −1.49031
\(449\) 3.93631e42i 1.44261i −0.692619 0.721304i \(-0.743543\pi\)
0.692619 0.721304i \(-0.256457\pi\)
\(450\) 6.84486e42 + 3.13422e42i 2.42083 + 1.10848i
\(451\) −1.60440e42 −0.547630
\(452\) 4.87078e42i 1.60466i
\(453\) 3.04904e42 + 4.74962e42i 0.969598 + 1.51038i
\(454\) −4.66599e42 −1.43235
\(455\) 4.31355e42i 1.27836i
\(456\) −2.92437e42 + 1.87731e42i −0.836747 + 0.537154i
\(457\) 4.01009e42 1.10789 0.553943 0.832554i \(-0.313122\pi\)
0.553943 + 0.832554i \(0.313122\pi\)
\(458\) 2.57932e42i 0.688110i
\(459\) 1.11424e41 + 7.83308e41i 0.0287061 + 0.201804i
\(460\) −4.98161e41 −0.123949
\(461\) 1.44532e42i 0.347335i 0.984804 + 0.173668i \(0.0555619\pi\)
−0.984804 + 0.173668i \(0.944438\pi\)
\(462\) −3.51433e42 5.47443e42i −0.815777 1.27077i
\(463\) 4.37917e42 0.981964 0.490982 0.871170i \(-0.336638\pi\)
0.490982 + 0.871170i \(0.336638\pi\)
\(464\) 1.41236e42i 0.305956i
\(465\) −3.25094e42 + 2.08696e42i −0.680397 + 0.436784i
\(466\) −8.46280e42 −1.71135
\(467\) 4.22719e42i 0.826002i −0.910731 0.413001i \(-0.864481\pi\)
0.910731 0.413001i \(-0.135519\pi\)
\(468\) 2.83718e42 6.19614e42i 0.535738 1.17000i
\(469\) 2.72623e42 0.497504
\(470\) 2.51972e40i 0.00444413i
\(471\) −1.34709e42 2.09841e42i −0.229647 0.357731i
\(472\) 3.01344e42 0.496582
\(473\) 6.42076e42i 1.02284i
\(474\) 1.41041e43 9.05416e42i 2.17215 1.39442i
\(475\) −1.39046e43 −2.07043
\(476\) 1.95740e42i 0.281818i
\(477\) −9.80859e42 4.49129e42i −1.36556 0.625284i
\(478\) 1.71453e43 2.30833
\(479\) 1.09686e43i 1.42818i 0.700054 + 0.714090i \(0.253159\pi\)
−0.700054 + 0.714090i \(0.746841\pi\)
\(480\) 8.23771e42 + 1.28322e43i 1.03740 + 1.61600i
\(481\) 1.88286e42 0.229349
\(482\) 1.08511e43i 1.27856i
\(483\) −3.39111e41 + 2.17694e41i −0.0386534 + 0.0248137i
\(484\) 1.13913e42 0.125616
\(485\) 1.91811e43i 2.04647i
\(486\) −1.47129e43 4.36008e42i −1.51886 0.450105i
\(487\) 9.98519e42 0.997454 0.498727 0.866759i \(-0.333801\pi\)
0.498727 + 0.866759i \(0.333801\pi\)
\(488\) 1.48879e43i 1.43919i
\(489\) 7.36052e41 + 1.14658e42i 0.0688599 + 0.107266i
\(490\) −4.61576e42 −0.417932
\(491\) 4.39197e42i 0.384907i −0.981306 0.192453i \(-0.938356\pi\)
0.981306 0.192453i \(-0.0616444\pi\)
\(492\) −7.87918e42 + 5.05807e42i −0.668404 + 0.429085i
\(493\) −3.28983e42 −0.270161
\(494\) 2.09250e43i 1.66354i
\(495\) −9.21722e42 + 2.01296e43i −0.709442 + 1.54936i
\(496\) −1.52965e42 −0.113995
\(497\) 1.39822e42i 0.100896i
\(498\) −3.47860e42 5.41876e42i −0.243072 0.378643i
\(499\) −9.63135e42 −0.651746 −0.325873 0.945414i \(-0.605658\pi\)
−0.325873 + 0.945414i \(0.605658\pi\)
\(500\) 2.56727e43i 1.68249i
\(501\) −2.04150e42 + 1.31055e42i −0.129582 + 0.0831858i
\(502\) −5.77575e42 −0.355099
\(503\) 2.08881e42i 0.124397i 0.998064 + 0.0621986i \(0.0198112\pi\)
−0.998064 + 0.0621986i \(0.980189\pi\)
\(504\) −1.16512e43 5.33502e42i −0.672176 0.307785i
\(505\) 3.14235e43 1.75627
\(506\) 1.52699e42i 0.0826852i
\(507\) 2.81408e42 + 4.38361e42i 0.147642 + 0.229988i
\(508\) 3.84519e43 1.95478
\(509\) 1.42164e43i 0.700335i −0.936687 0.350167i \(-0.886125\pi\)
0.936687 0.350167i \(-0.113875\pi\)
\(510\) 9.31950e42 5.98270e42i 0.444908 0.285611i
\(511\) −7.81006e41 −0.0361343
\(512\) 1.01932e43i 0.457079i
\(513\) 2.80600e43 3.99146e42i 1.21958 0.173482i
\(514\) −4.88836e43 −2.05946
\(515\) 1.30373e43i 0.532441i
\(516\) 2.02423e43 + 3.15323e43i 0.801427 + 1.24842i
\(517\) 4.64589e40 0.00178328
\(518\) 1.04891e43i 0.390357i
\(519\) 5.85788e41 3.76049e41i 0.0211379 0.0135696i
\(520\) −3.21979e43 −1.12661
\(521\) 4.58192e42i 0.155469i −0.996974 0.0777345i \(-0.975231\pi\)
0.996974 0.0777345i \(-0.0247686\pi\)
\(522\) 2.65644e43 5.80142e43i 0.874121 1.90900i
\(523\) 1.51005e43 0.481907 0.240953 0.970537i \(-0.422540\pi\)
0.240953 + 0.970537i \(0.422540\pi\)
\(524\) 4.53072e43i 1.40238i
\(525\) −2.76992e43 4.31482e43i −0.831607 1.29543i
\(526\) −8.68297e43 −2.52870
\(527\) 3.56302e42i 0.100658i
\(528\) −7.37705e42 + 4.73573e42i −0.202181 + 0.129791i
\(529\) 3.75143e43 0.997485
\(530\) 1.51002e44i 3.89555i
\(531\) −2.23461e43 1.02321e43i −0.559357 0.256126i
\(532\) 7.01188e43 1.70313
\(533\) 1.90302e43i 0.448547i
\(534\) 1.06728e43 + 1.66255e43i 0.244129 + 0.380290i
\(535\) −3.77033e43 −0.836987
\(536\) 2.03496e43i 0.438449i
\(537\) 3.22534e43 2.07052e43i 0.674508 0.433004i
\(538\) 1.15492e43 0.234442
\(539\) 8.51059e42i 0.167702i
\(540\) 1.81955e43 + 1.27915e44i 0.348069 + 2.44692i
\(541\) −5.59972e43 −1.03994 −0.519972 0.854183i \(-0.674058\pi\)
−0.519972 + 0.854183i \(0.674058\pi\)
\(542\) 7.13687e43i 1.28682i
\(543\) 2.77360e43 + 4.32055e43i 0.485564 + 0.756383i
\(544\) 1.40641e43 0.239072
\(545\) 6.11969e43i 1.01015i
\(546\) −6.49337e43 + 4.16845e43i −1.04085 + 0.668178i
\(547\) −8.07963e43 −1.25775 −0.628875 0.777506i \(-0.716484\pi\)
−0.628875 + 0.777506i \(0.716484\pi\)
\(548\) 1.58953e44i 2.40314i
\(549\) 5.05520e43 1.10401e44i 0.742302 1.62112i
\(550\) 1.94293e44 2.77112
\(551\) 1.17849e44i 1.63268i
\(552\) −1.62495e42 2.53125e42i −0.0218682 0.0340651i
\(553\) −1.14150e44 −1.49236
\(554\) 1.58487e44i 2.01297i
\(555\) −3.00400e43 + 1.92843e43i −0.370691 + 0.237967i
\(556\) −1.20468e44 −1.44436
\(557\) 6.48513e43i 0.755501i 0.925907 + 0.377751i \(0.123302\pi\)
−0.925907 + 0.377751i \(0.876698\pi\)
\(558\) −6.28318e43 2.87703e43i −0.711266 0.325684i
\(559\) 7.61584e43 0.837777
\(560\) 3.23816e43i 0.346171i
\(561\) 1.10310e43 + 1.71834e43i 0.114606 + 0.178527i
\(562\) 1.68620e44 1.70266
\(563\) 1.87769e41i 0.00184285i 1.00000 0.000921424i \(0.000293298\pi\)
−1.00000 0.000921424i \(0.999707\pi\)
\(564\) 2.28159e41 1.46468e41i 0.00217657 0.00139726i
\(565\) 1.87691e44 1.74048
\(566\) 2.73551e44i 2.46590i
\(567\) 6.82842e43 + 7.91234e43i 0.598400 + 0.693387i
\(568\) 1.04369e43 0.0889194
\(569\) 1.01006e44i 0.836661i 0.908295 + 0.418330i \(0.137385\pi\)
−0.908295 + 0.418330i \(0.862615\pi\)
\(570\) −2.14314e44 3.33847e44i −1.72605 2.68874i
\(571\) 1.16891e44 0.915385 0.457692 0.889111i \(-0.348676\pi\)
0.457692 + 0.889111i \(0.348676\pi\)
\(572\) 1.75879e44i 1.33930i
\(573\) −1.41151e44 + 9.06128e43i −1.04523 + 0.670989i
\(574\) 1.06014e44 0.763437
\(575\) 1.20354e43i 0.0842898i
\(576\) −9.94536e43 + 2.17198e44i −0.677425 + 1.47944i
\(577\) −2.29862e44 −1.52284 −0.761421 0.648258i \(-0.775498\pi\)
−0.761421 + 0.648258i \(0.775498\pi\)
\(578\) 2.35620e44i 1.51833i
\(579\) −4.41869e43 6.88318e43i −0.276972 0.431452i
\(580\) −5.37231e44 −3.27577
\(581\) 4.38563e43i 0.260144i
\(582\) 2.88742e44 1.85359e44i 1.66626 1.06966i
\(583\) −2.78419e44 −1.56316
\(584\) 5.82972e42i 0.0318451i
\(585\) 2.38763e44 + 1.09328e44i 1.26903 + 0.581082i
\(586\) 5.69953e44 2.94766
\(587\) 3.36020e44i 1.69105i −0.533937 0.845524i \(-0.679288\pi\)
0.533937 0.845524i \(-0.320712\pi\)
\(588\) −2.68307e43 4.17954e43i −0.131400 0.204687i
\(589\) 1.27636e44 0.608314
\(590\) 3.44016e44i 1.59568i
\(591\) 1.21594e44 7.80581e43i 0.548926 0.352386i
\(592\) −1.41345e43 −0.0621061
\(593\) 2.81908e44i 1.20568i −0.797862 0.602840i \(-0.794036\pi\)
0.797862 0.602840i \(-0.205964\pi\)
\(594\) −3.92091e44 + 5.57740e43i −1.63231 + 0.232193i
\(595\) −7.54267e43 −0.305671
\(596\) 1.13177e44i 0.446496i
\(597\) 1.79052e44 + 2.78916e44i 0.687684 + 1.07123i
\(598\) −1.81120e43 −0.0677249
\(599\) 1.15173e44i 0.419296i −0.977777 0.209648i \(-0.932768\pi\)
0.977777 0.209648i \(-0.0672318\pi\)
\(600\) 3.22074e44 2.06757e44i 1.14166 0.732893i
\(601\) −3.44390e44 −1.18866 −0.594332 0.804220i \(-0.702583\pi\)
−0.594332 + 0.804220i \(0.702583\pi\)
\(602\) 4.24266e44i 1.42592i
\(603\) 6.90970e43 1.50902e44i 0.226142 0.493875i
\(604\) 8.50070e44 2.70934
\(605\) 4.38952e43i 0.136248i
\(606\) 3.03665e44 + 4.73031e44i 0.917978 + 1.42997i
\(607\) 9.80874e43 0.288798 0.144399 0.989520i \(-0.453875\pi\)
0.144399 + 0.989520i \(0.453875\pi\)
\(608\) 5.03808e44i 1.44480i
\(609\) −3.65707e44 + 2.34767e44i −1.02154 + 0.655784i
\(610\) −1.69961e45 −4.62458
\(611\) 5.51062e41i 0.00146063i
\(612\) 1.08346e44 + 4.96109e43i 0.279762 + 0.128101i
\(613\) 4.37991e44 1.10179 0.550893 0.834576i \(-0.314287\pi\)
0.550893 + 0.834576i \(0.314287\pi\)
\(614\) 4.31606e44i 1.05777i
\(615\) −1.94908e44 3.03617e44i −0.465402 0.724976i
\(616\) −3.30723e44 −0.769437
\(617\) 5.00298e43i 0.113414i −0.998391 0.0567069i \(-0.981940\pi\)
0.998391 0.0567069i \(-0.0180601\pi\)
\(618\) −1.96256e44 + 1.25987e44i −0.433518 + 0.278299i
\(619\) 1.56567e44 0.337015 0.168508 0.985700i \(-0.446105\pi\)
0.168508 + 0.985700i \(0.446105\pi\)
\(620\) 5.81843e44i 1.22050i
\(621\) 3.45489e42 + 2.42879e43i 0.00706267 + 0.0496506i
\(622\) 4.28649e44 0.853995
\(623\) 1.34558e44i 0.261276i
\(624\) 5.61718e43 + 8.75012e43i 0.106308 + 0.165600i
\(625\) 7.81436e43 0.144149
\(626\) 1.57107e45i 2.82492i
\(627\) 6.15550e44 3.95155e44i 1.07890 0.692607i
\(628\) −3.75567e44 −0.641701
\(629\) 3.29237e43i 0.0548401i
\(630\) 6.09048e44 1.33011e45i 0.989014 2.15992i
\(631\) 7.55460e43 0.119603 0.0598015 0.998210i \(-0.480953\pi\)
0.0598015 + 0.998210i \(0.480953\pi\)
\(632\) 8.52059e44i 1.31521i
\(633\) −1.59210e44 2.48007e44i −0.239613 0.373255i
\(634\) 1.35011e44 0.198125
\(635\) 1.48171e45i 2.12023i
\(636\) −1.36731e45 + 8.77753e44i −1.90789 + 1.22478i
\(637\) −1.00946e44 −0.137360
\(638\) 1.64675e45i 2.18523i
\(639\) −7.73942e43 3.54383e43i −0.100160 0.0458627i
\(640\) 1.82230e45 2.30006
\(641\) 5.20543e44i 0.640808i −0.947281 0.320404i \(-0.896181\pi\)
0.947281 0.320404i \(-0.103819\pi\)
\(642\) −3.64350e44 5.67563e44i −0.437480 0.681481i
\(643\) 7.31934e44 0.857229 0.428614 0.903488i \(-0.359002\pi\)
0.428614 + 0.903488i \(0.359002\pi\)
\(644\) 6.06928e43i 0.0693368i
\(645\) −1.21507e45 + 7.80017e44i −1.35408 + 0.869258i
\(646\) −3.65894e44 −0.397773
\(647\) 9.70518e44i 1.02928i −0.857405 0.514642i \(-0.827925\pi\)
0.857405 0.514642i \(-0.172075\pi\)
\(648\) −5.90606e44 + 5.09699e44i −0.611080 + 0.527368i
\(649\) −6.34300e44 −0.640294
\(650\) 2.30456e45i 2.26974i
\(651\) 2.54262e44 + 3.96075e44i 0.244335 + 0.380611i
\(652\) 2.05211e44 0.192415
\(653\) 1.23878e45i 1.13340i 0.823923 + 0.566702i \(0.191781\pi\)
−0.823923 + 0.566702i \(0.808219\pi\)
\(654\) 9.21223e44 5.91383e44i 0.822471 0.527989i
\(655\) 1.74587e45 1.52108
\(656\) 1.42859e44i 0.121464i
\(657\) −1.97948e43 + 4.32301e43i −0.0164250 + 0.0358707i
\(658\) −3.06987e42 −0.00248603
\(659\) 2.31547e43i 0.0183009i 0.999958 + 0.00915045i \(0.00291272\pi\)
−0.999958 + 0.00915045i \(0.997087\pi\)
\(660\) 1.80136e45 + 2.80606e45i 1.38963 + 2.16468i
\(661\) −2.39852e45 −1.80601 −0.903004 0.429632i \(-0.858643\pi\)
−0.903004 + 0.429632i \(0.858643\pi\)
\(662\) 3.12735e45i 2.29852i
\(663\) 2.03817e44 1.30841e44i 0.146226 0.0938703i
\(664\) −3.27360e44 −0.229264
\(665\) 2.70196e45i 1.84728i
\(666\) −5.80590e44 2.65849e44i −0.387509 0.177438i
\(667\) −1.02007e44 −0.0664687
\(668\) 3.65380e44i 0.232445i
\(669\) −1.26277e45 1.96707e45i −0.784345 1.22181i
\(670\) −2.32312e45 −1.40888
\(671\) 3.13376e45i 1.85569i
\(672\) 1.56340e45 1.00363e45i 0.903986 0.580318i
\(673\) 7.52414e44 0.424831 0.212415 0.977179i \(-0.431867\pi\)
0.212415 + 0.977179i \(0.431867\pi\)
\(674\) 4.39745e45i 2.42461i
\(675\) −3.09038e45 + 4.39598e44i −1.66399 + 0.236699i
\(676\) 7.84563e44 0.412554
\(677\) 1.36007e44i 0.0698464i 0.999390 + 0.0349232i \(0.0111187\pi\)
−0.999390 + 0.0349232i \(0.988881\pi\)
\(678\) 1.81377e45 + 2.82539e45i 0.909720 + 1.41711i
\(679\) −2.33691e45 −1.14479
\(680\) 5.63013e44i 0.269387i
\(681\) 1.62807e45 1.04515e45i 0.760887 0.488455i
\(682\) −1.78350e45 −0.814184
\(683\) 2.47049e45i 1.10167i 0.834614 + 0.550835i \(0.185691\pi\)
−0.834614 + 0.550835i \(0.814309\pi\)
\(684\) 1.77718e45 3.88120e45i 0.774165 1.69071i
\(685\) 6.12510e45 2.60654
\(686\) 4.05239e45i 1.68471i
\(687\) −5.77750e44 8.99986e44i −0.234656 0.365534i
\(688\) −5.71718e44 −0.226865
\(689\) 3.30241e45i 1.28033i
\(690\) 2.88968e44 1.85504e44i 0.109462 0.0702698i
\(691\) −2.79704e43 −0.0103526 −0.00517631 0.999987i \(-0.501648\pi\)
−0.00517631 + 0.999987i \(0.501648\pi\)
\(692\) 1.04842e44i 0.0379174i
\(693\) 2.45247e45 + 1.12297e45i 0.866705 + 0.396859i
\(694\) 1.93364e45 0.667767
\(695\) 4.64214e45i 1.56661i
\(696\) −1.75239e45 2.72977e45i −0.577940 0.900282i
\(697\) −3.32762e44 −0.107253
\(698\) 2.44824e45i 0.771199i
\(699\) 2.95287e45 1.89561e45i 0.909095 0.583598i
\(700\) −7.72252e45 −2.32375
\(701\) 1.62599e45i 0.478224i −0.970992 0.239112i \(-0.923144\pi\)
0.970992 0.239112i \(-0.0768562\pi\)
\(702\) 6.61551e44 + 4.65070e45i 0.190182 + 1.33698i
\(703\) 1.17940e45 0.331419
\(704\) 6.16522e45i 1.69350i
\(705\) 5.64400e42 + 8.79190e42i 0.00151552 + 0.00236079i
\(706\) −4.67362e45 −1.22681
\(707\) 3.82844e45i 0.982453i
\(708\) −3.11504e45 + 1.99971e45i −0.781504 + 0.501690i
\(709\) −3.85475e45 −0.945488 −0.472744 0.881200i \(-0.656736\pi\)
−0.472744 + 0.881200i \(0.656736\pi\)
\(710\) 1.19148e45i 0.285727i
\(711\) −2.89316e45 + 6.31842e45i −0.678359 + 1.48148i
\(712\) 1.00439e45 0.230262
\(713\) 1.10478e44i 0.0247652i
\(714\) −7.28895e44 1.13543e45i −0.159769 0.248880i
\(715\) 6.77734e45 1.45266
\(716\) 5.77260e45i 1.20994i
\(717\) −5.98239e45 + 3.84042e45i −1.22622 + 0.787177i
\(718\) 1.00374e46 2.01201
\(719\) 2.74164e45i 0.537462i 0.963215 + 0.268731i \(0.0866043\pi\)
−0.963215 + 0.268731i \(0.913396\pi\)
\(720\) −1.79238e45 8.20721e44i −0.343645 0.157353i
\(721\) 1.58838e45 0.297845
\(722\) 4.46962e45i 0.819739i
\(723\) 2.43056e45 + 3.78619e45i 0.436007 + 0.679187i
\(724\) 7.73277e45 1.35681
\(725\) 1.29793e46i 2.22763i
\(726\) −6.60773e44 + 4.24186e44i −0.110934 + 0.0712148i
\(727\) −2.80128e45 −0.460050 −0.230025 0.973185i \(-0.573881\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(728\) 3.92280e45i 0.630222i
\(729\) 6.11030e45 1.77425e45i 0.960334 0.278853i
\(730\) 6.65522e44 0.102329
\(731\) 1.33171e45i 0.200323i
\(732\) −9.87960e45 1.53899e46i −1.45399 2.26495i
\(733\) −1.89755e45 −0.273231 −0.136616 0.990624i \(-0.543622\pi\)
−0.136616 + 0.990624i \(0.543622\pi\)
\(734\) 7.68923e45i 1.08329i
\(735\) 1.61055e45 1.03390e45i 0.222012 0.142521i
\(736\) 4.36082e44 0.0588197
\(737\) 4.28339e45i 0.565337i
\(738\) 2.68695e45 5.86807e45i 0.347023 0.757868i
\(739\) −1.43939e46 −1.81915 −0.909573 0.415544i \(-0.863591\pi\)
−0.909573 + 0.415544i \(0.863591\pi\)
\(740\) 5.37646e45i 0.664949i
\(741\) −4.68704e45 7.30121e45i −0.567293 0.883697i
\(742\) 1.83972e46 2.17916
\(743\) 2.04644e45i 0.237234i 0.992940 + 0.118617i \(0.0378461\pi\)
−0.992940 + 0.118617i \(0.962154\pi\)
\(744\) −2.95645e45 + 1.89791e45i −0.335432 + 0.215332i
\(745\) −4.36117e45 −0.484286
\(746\) 8.81105e45i 0.957650i
\(747\) 2.42753e45 + 1.11155e45i 0.258247 + 0.118250i
\(748\) 3.07543e45 0.320243
\(749\) 4.59353e45i 0.468207i
\(750\) 9.55998e45 + 1.48920e46i 0.953842 + 1.48584i
\(751\) −5.69616e45 −0.556344 −0.278172 0.960531i \(-0.589729\pi\)
−0.278172 + 0.960531i \(0.589729\pi\)
\(752\) 4.13680e42i 0.000395530i
\(753\) 2.01529e45 1.29373e45i 0.188633 0.121094i
\(754\) −1.95325e46 −1.78985
\(755\) 3.27567e46i 2.93865i
\(756\) 1.55843e46 2.21683e45i 1.36880 0.194708i
\(757\) 1.09110e46 0.938272 0.469136 0.883126i \(-0.344565\pi\)
0.469136 + 0.883126i \(0.344565\pi\)
\(758\) 2.97947e46i 2.50860i
\(759\) 3.42035e44 + 5.32803e44i 0.0281970 + 0.0439236i
\(760\) −2.01685e46 −1.62800
\(761\) 5.51472e45i 0.435882i −0.975962 0.217941i \(-0.930066\pi\)
0.975962 0.217941i \(-0.0699341\pi\)
\(762\) −2.23048e46 + 1.43187e46i −1.72631 + 1.10821i
\(763\) −7.45585e45 −0.565073
\(764\) 2.52628e46i 1.87494i
\(765\) −1.91171e45 + 4.17501e45i −0.138944 + 0.303441i
\(766\) 3.04678e46 2.16861
\(767\) 7.52360e45i 0.524445i
\(768\) 4.73403e45 + 7.37440e45i 0.323185 + 0.503439i
\(769\) 2.37357e46 1.58702 0.793508 0.608560i \(-0.208253\pi\)
0.793508 + 0.608560i \(0.208253\pi\)
\(770\) 3.77555e46i 2.47245i
\(771\) 1.70566e46 1.09496e46i 1.09401 0.702308i
\(772\) −1.23193e46 −0.773942
\(773\) 4.02656e45i 0.247778i −0.992296 0.123889i \(-0.960463\pi\)
0.992296 0.123889i \(-0.0395366\pi\)
\(774\) −2.34839e46 1.07531e46i −1.41551 0.648155i
\(775\) −1.40571e46 −0.829983
\(776\) 1.74436e46i 1.00890i
\(777\) 2.34948e45 + 3.65989e45i 0.133118 + 0.207363i
\(778\) −5.57441e46 −3.09404
\(779\) 1.19203e46i 0.648170i
\(780\) 3.32834e46 2.13665e46i 1.77302 1.13820i
\(781\) −2.19686e45 −0.114653
\(782\) 3.16707e44i 0.0161939i
\(783\) 3.72586e45 + 2.61928e46i 0.186654 + 1.31218i
\(784\) 7.57801e44 0.0371962
\(785\) 1.44721e46i 0.696013i
\(786\) 1.68714e46 + 2.62813e46i 0.795044 + 1.23847i
\(787\) −5.78760e45 −0.267241 −0.133620 0.991033i \(-0.542660\pi\)
−0.133620 + 0.991033i \(0.542660\pi\)
\(788\) 2.17626e46i 0.984669i
\(789\) 3.02969e46 1.94493e46i 1.34328 0.862325i
\(790\) 9.72714e46 4.22621
\(791\) 2.28671e46i 0.973615i
\(792\) −8.38226e45 + 1.83061e46i −0.349750 + 0.763824i
\(793\) −3.71704e46 −1.51994
\(794\) 5.01408e46i 2.00939i
\(795\) −3.38234e46 5.26882e46i −1.32844 2.06937i
\(796\) 4.99195e46 1.92159
\(797\) 1.60304e46i 0.604797i 0.953182 + 0.302399i \(0.0977874\pi\)
−0.953182 + 0.302399i \(0.902213\pi\)
\(798\) −4.06738e46 + 2.61107e46i −1.50407 + 0.965546i
\(799\) 9.63587e42 0.000349255
\(800\) 5.54868e46i 1.97129i
\(801\) −7.44800e45 3.41039e45i −0.259370 0.118764i
\(802\) −7.07613e46 −2.41549
\(803\) 1.22710e45i 0.0410611i
\(804\) −1.35039e46 2.10356e46i −0.442959 0.690016i
\(805\) −2.33874e45 −0.0752053
\(806\) 2.11545e46i 0.666873i
\(807\) −4.02978e45 + 2.58693e45i −0.124539 + 0.0799482i
\(808\) 2.85769e46 0.865833
\(809\) 3.31969e46i 0.986102i −0.870000 0.493051i \(-0.835882\pi\)
0.870000 0.493051i \(-0.164118\pi\)
\(810\) −5.81874e46 6.74238e46i −1.69460 1.96360i
\(811\) 1.78101e46 0.508549 0.254275 0.967132i \(-0.418163\pi\)
0.254275 + 0.967132i \(0.418163\pi\)
\(812\) 6.54529e46i 1.83245i
\(813\) 1.59861e46 + 2.49022e46i 0.438827 + 0.683579i
\(814\) −1.64802e46 −0.443580
\(815\) 7.90761e45i 0.208700i
\(816\) −1.53005e45 + 9.82220e44i −0.0395970 + 0.0254195i
\(817\) 4.77049e46 1.21063
\(818\) 9.70101e46i 2.41415i
\(819\) 1.33198e46 2.90894e46i 0.325055 0.709891i
\(820\) −5.43403e46 −1.30047
\(821\) 1.00347e46i 0.235514i −0.993042 0.117757i \(-0.962430\pi\)
0.993042 0.117757i \(-0.0375703\pi\)
\(822\) 5.91906e46 + 9.22038e46i 1.36240 + 2.12227i
\(823\) 2.83736e46 0.640497 0.320249 0.947334i \(-0.396234\pi\)
0.320249 + 0.947334i \(0.396234\pi\)
\(824\) 1.18563e46i 0.262490i
\(825\) −6.77935e46 + 4.35203e46i −1.47206 + 0.944994i
\(826\) 4.19127e46 0.892617
\(827\) 3.50954e45i 0.0733098i 0.999328 + 0.0366549i \(0.0116702\pi\)
−0.999328 + 0.0366549i \(0.988330\pi\)
\(828\) 3.35946e45 + 1.53828e45i 0.0688310 + 0.0315173i
\(829\) 1.92501e46 0.386866 0.193433 0.981113i \(-0.438038\pi\)
0.193433 + 0.981113i \(0.438038\pi\)
\(830\) 3.73715e46i 0.736701i
\(831\) 3.55000e46 + 5.52999e46i 0.686455 + 1.06932i
\(832\) 7.31274e46 1.38710
\(833\) 1.76515e45i 0.0328444i
\(834\) 6.98801e46 4.48599e46i 1.27555 0.818844i
\(835\) −1.40796e46 −0.252119
\(836\) 1.10169e47i 1.93535i
\(837\) 2.83678e46 4.03525e45i 0.488898 0.0695446i
\(838\) −1.24067e47 −2.09775
\(839\) 2.15724e46i 0.357855i −0.983862 0.178928i \(-0.942737\pi\)
0.983862 0.178928i \(-0.0572628\pi\)
\(840\) −4.01775e46 6.25861e46i −0.653904 1.01861i
\(841\) −4.73841e46 −0.756653
\(842\) 1.05273e46i 0.164939i
\(843\) −5.88355e46 + 3.77697e46i −0.904478 + 0.580634i
\(844\) −4.43875e46 −0.669548
\(845\) 3.02324e46i 0.447472i
\(846\) −7.78067e43 + 1.69923e44i −0.00113003 + 0.00246789i
\(847\) 5.34792e45 0.0762167
\(848\) 2.47910e46i 0.346706i
\(849\) −6.12735e46 9.54483e46i −0.840910 1.30992i
\(850\) 4.02976e46 0.542721
\(851\) 1.02086e45i 0.0134925i
\(852\) −1.07887e46 + 6.92587e45i −0.139938 + 0.0898341i
\(853\) 8.01950e46 1.02085 0.510426 0.859922i \(-0.329488\pi\)
0.510426 + 0.859922i \(0.329488\pi\)
\(854\) 2.07070e47i 2.58697i
\(855\) 1.49559e47 + 6.84820e46i 1.83381 + 0.839689i
\(856\) −3.42879e46 −0.412629
\(857\) 1.07502e47i 1.26976i 0.772610 + 0.634880i \(0.218951\pi\)
−0.772610 + 0.634880i \(0.781049\pi\)
\(858\) 6.54936e46 + 1.02022e47i 0.759281 + 1.18276i
\(859\) −6.14759e46 −0.699543 −0.349772 0.936835i \(-0.613741\pi\)
−0.349772 + 0.936835i \(0.613741\pi\)
\(860\) 2.17468e47i 2.42896i
\(861\) −3.69908e46 + 2.37464e46i −0.405549 + 0.260344i
\(862\) −1.27701e47 −1.37429
\(863\) 1.62772e47i 1.71952i −0.510698 0.859760i \(-0.670613\pi\)
0.510698 0.859760i \(-0.329387\pi\)
\(864\) −1.59281e46 1.11974e47i −0.165175 1.16118i
\(865\) 4.04000e45 0.0411267
\(866\) 1.95869e47i 1.95740i
\(867\) −5.27772e46 8.22133e46i −0.517775 0.806559i
\(868\) 7.08881e46 0.682744
\(869\) 1.79350e47i 1.69584i
\(870\) 3.11631e47 2.00053e47i 2.89290 1.85711i
\(871\) −5.08064e46 −0.463050
\(872\) 5.56533e46i 0.497997i
\(873\) −5.92296e46 + 1.29352e47i −0.520368 + 1.13644i
\(874\) −1.13452e46 −0.0978655
\(875\) 1.20527e47i 1.02084i
\(876\) 3.86859e45 + 6.02626e45i 0.0321726 + 0.0501167i
\(877\) −1.21911e47 −0.995520 −0.497760 0.867315i \(-0.665844\pi\)
−0.497760 + 0.867315i \(0.665844\pi\)
\(878\) 8.86812e46i 0.711081i
\(879\) −1.98870e47 + 1.27665e47i −1.56584 + 1.00520i
\(880\) −5.08773e46 −0.393370
\(881\) 1.52849e47i 1.16051i −0.814435 0.580254i \(-0.802953\pi\)
0.814435 0.580254i \(-0.197047\pi\)
\(882\) 3.11274e46 + 1.42530e46i 0.232084 + 0.106270i
\(883\) 1.12145e47 0.821121 0.410561 0.911833i \(-0.365333\pi\)
0.410561 + 0.911833i \(0.365333\pi\)
\(884\) 3.64785e46i 0.262301i
\(885\) −7.70571e46 1.20035e47i −0.544152 0.847649i
\(886\) 2.08179e47 1.44377
\(887\) 4.57609e46i 0.311685i −0.987782 0.155843i \(-0.950191\pi\)
0.987782 0.155843i \(-0.0498093\pi\)
\(888\) −2.73188e46 + 1.75374e46i −0.182749 + 0.117316i
\(889\) 1.80522e47 1.18605
\(890\) 1.14661e47i 0.739906i
\(891\) 1.24317e47 1.07287e47i 0.787928 0.679989i
\(892\) −3.52060e47 −2.19169
\(893\) 3.45180e44i 0.00211068i
\(894\) −4.21446e46 6.56505e46i −0.253129 0.394310i
\(895\) 2.22442e47 1.31235
\(896\) 2.22017e47i 1.28665i
\(897\) 6.31971e45 4.05697e45i 0.0359765 0.0230953i
\(898\) 4.08664e47 2.28531
\(899\) 1.19142e47i 0.654503i
\(900\) −1.95729e47 + 4.27455e47i −1.05627 + 2.30680i
\(901\) −5.77459e46 −0.306143
\(902\) 1.66567e47i 0.867529i
\(903\) 9.50325e46 + 1.48036e47i 0.486260 + 0.757467i
\(904\) 1.70689e47 0.858044
\(905\) 2.97975e47i 1.47164i
\(906\) −4.93100e47 + 3.16548e47i −2.39268 + 1.53599i
\(907\) 1.96956e46 0.0938970 0.0469485 0.998897i \(-0.485050\pi\)
0.0469485 + 0.998897i \(0.485050\pi\)
\(908\) 2.91387e47i 1.36489i
\(909\) −2.11911e47 9.70329e46i −0.975286 0.446578i
\(910\) −4.47828e47 −2.02511
\(911\) 2.69386e46i 0.119696i −0.998207 0.0598481i \(-0.980938\pi\)
0.998207 0.0598481i \(-0.0190616\pi\)
\(912\) 3.51855e46 + 5.48099e46i 0.153619 + 0.239299i
\(913\) 6.89060e46 0.295614
\(914\) 4.16324e47i 1.75506i
\(915\) 5.93034e47 3.80701e47i 2.45665 1.57705i
\(916\) −1.61076e47 −0.655698
\(917\) 2.12706e47i 0.850885i
\(918\) −8.13222e46 + 1.15679e46i −0.319688 + 0.0454748i
\(919\) −2.40970e47 −0.930924 −0.465462 0.885068i \(-0.654112\pi\)
−0.465462 + 0.885068i \(0.654112\pi\)
\(920\) 1.74572e46i 0.0662782i
\(921\) −9.66767e46 1.50597e47i −0.360718 0.561905i
\(922\) −1.50052e47 −0.550232
\(923\) 2.60575e46i 0.0939086i
\(924\) 3.41873e47 2.19467e47i 1.21091 0.777352i
\(925\) −1.29893e47 −0.452188
\(926\) 4.54640e47i 1.55558i
\(927\) 4.02580e46 8.79199e46i 0.135387 0.295673i
\(928\) 4.70283e47 1.55450
\(929\) 3.65634e47i 1.18794i 0.804486 + 0.593971i \(0.202441\pi\)
−0.804486 + 0.593971i \(0.797559\pi\)
\(930\) −2.16666e47 3.37509e47i −0.691932 1.07785i
\(931\) −6.32319e46 −0.198491
\(932\) 5.28494e47i 1.63074i
\(933\) −1.49566e47 + 9.60143e46i −0.453654 + 0.291226i
\(934\) 4.38862e47 1.30851
\(935\) 1.18509e47i 0.347348i
\(936\) 2.17134e47 + 9.94243e46i 0.625625 + 0.286470i
\(937\) 5.54359e47 1.57021 0.785104 0.619364i \(-0.212609\pi\)
0.785104 + 0.619364i \(0.212609\pi\)
\(938\) 2.83034e47i 0.788122i
\(939\) −3.51908e47 5.48182e47i −0.963340 1.50064i
\(940\) 1.57354e45 0.00423480
\(941\) 2.48801e47i 0.658291i −0.944279 0.329146i \(-0.893239\pi\)
0.944279 0.329146i \(-0.106761\pi\)
\(942\) 2.17855e47 1.39853e47i 0.566700 0.363795i
\(943\) −1.03179e46 −0.0263879
\(944\) 5.64794e46i 0.142016i
\(945\) 8.54236e46 + 6.00528e47i 0.211188 + 1.48465i
\(946\) −6.66596e47 −1.62033
\(947\) 1.57355e47i 0.376080i 0.982161 + 0.188040i \(0.0602134\pi\)
−0.982161 + 0.188040i \(0.939787\pi\)
\(948\) 5.65424e47 + 8.80785e47i 1.32874 + 2.06984i
\(949\) 1.45549e46 0.0336319
\(950\) 1.44356e48i 3.27987i
\(951\) −4.71084e46 + 3.02414e46i −0.105247 + 0.0675638i
\(952\) −6.85941e46 −0.150694
\(953\) 9.60355e46i 0.207465i 0.994605 + 0.103733i \(0.0330786\pi\)
−0.994605 + 0.103733i \(0.966921\pi\)
\(954\) 4.66281e47 1.01832e48i 0.990544 2.16326i
\(955\) −9.73478e47 −2.03363
\(956\) 1.07071e48i 2.19960i
\(957\) 3.68860e47 + 5.74590e47i 0.745197 + 1.16082i
\(958\) −1.13875e48 −2.26245
\(959\) 7.46245e47i 1.45809i
\(960\) −1.16671e48 + 7.48974e47i −2.24193 + 1.43922i
\(961\) −4.00108e47 −0.756142
\(962\) 1.95476e47i 0.363323i
\(963\) 2.54260e47 + 1.16424e47i 0.464792 + 0.212825i
\(964\) 6.77639e47 1.21833
\(965\) 4.74712e47i 0.839447i
\(966\) −2.26007e46 3.52061e46i −0.0393086 0.0612327i
\(967\) −2.92514e47 −0.500407 −0.250203 0.968193i \(-0.580498\pi\)
−0.250203 + 0.968193i \(0.580498\pi\)
\(968\) 3.99188e46i 0.0671695i
\(969\) 1.27669e47 8.19577e46i 0.211303 0.135647i
\(970\) 1.99136e48 3.24192
\(971\) 1.19954e48i 1.92092i 0.278423 + 0.960459i \(0.410188\pi\)
−0.278423 + 0.960459i \(0.589812\pi\)
\(972\) 2.72283e47 9.18807e47i 0.428904 1.44732i
\(973\) −5.65570e47 −0.876356
\(974\) 1.03665e48i 1.58012i
\(975\) 5.16206e47 + 8.04116e47i 0.774015 + 1.20572i
\(976\) 2.79037e47 0.411590
\(977\) 3.06016e47i 0.444049i −0.975041 0.222024i \(-0.928734\pi\)
0.975041 0.222024i \(-0.0712664\pi\)
\(978\) −1.19037e47 + 7.64161e46i −0.169926 + 0.109084i
\(979\) −2.11414e47 −0.296900
\(980\) 2.88250e47i 0.398247i
\(981\) −1.88970e47 + 4.12695e47i −0.256856 + 0.560951i
\(982\) 4.55970e47 0.609751
\(983\) 1.51512e48i 1.99338i −0.0813053 0.996689i \(-0.525909\pi\)
0.0813053 0.996689i \(-0.474091\pi\)
\(984\) −1.77252e47 2.76113e47i −0.229440 0.357409i
\(985\) 8.38600e47 1.06801
\(986\) 3.41546e47i 0.427976i
\(987\) 1.07115e45 6.87630e44i 0.00132061 0.000847775i
\(988\) −1.30674e48 −1.58518
\(989\) 4.12920e46i 0.0492861i
\(990\) −2.08983e48 9.56922e47i −2.45442 1.12386i
\(991\) 3.37053e47 0.389511 0.194756 0.980852i \(-0.437609\pi\)
0.194756 + 0.980852i \(0.437609\pi\)
\(992\) 5.09336e47i 0.579185i
\(993\) −7.00504e47 1.09121e48i −0.783832 1.22101i
\(994\) 1.45162e47 0.159835
\(995\) 1.92360e48i 2.08423i
\(996\) 3.38397e47 2.17235e47i 0.360808 0.231623i
\(997\) 1.52934e48 1.60466 0.802329 0.596882i \(-0.203594\pi\)
0.802329 + 0.596882i \(0.203594\pi\)
\(998\) 9.99916e47i 1.03246i
\(999\) 2.62130e47 3.72873e46i 0.266360 0.0378890i
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 3.33.b.a.2.9 yes 10
3.2 odd 2 inner 3.33.b.a.2.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.33.b.a.2.2 10 3.2 odd 2 inner
3.33.b.a.2.9 yes 10 1.1 even 1 trivial