Properties

Label 3.43.b.b.2.2
Level $3$
Weight $43$
Character 3.2
Analytic conductor $33.518$
Analytic rank $0$
Dimension $12$
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] = [3,43,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, 43, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 43);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 43 \)
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: \(33.5183121516\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.2
Root \(-103520. i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.43.b.b.2.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.72673e6i q^{2} +(-8.44421e9 - 6.17368e9i) q^{3} -9.49045e12 q^{4} -9.25532e14i q^{5} +(-2.30076e16 + 3.14693e16i) q^{6} +7.62151e16 q^{7} +1.89780e19i q^{8} +(3.31903e19 + 1.04264e20i) q^{9} +O(q^{10})\) \(q-3.72673e6i q^{2} +(-8.44421e9 - 6.17368e9i) q^{3} -9.49045e12 q^{4} -9.25532e14i q^{5} +(-2.30076e16 + 3.14693e16i) q^{6} +7.62151e16 q^{7} +1.89780e19i q^{8} +(3.31903e19 + 1.04264e20i) q^{9} -3.44920e21 q^{10} +2.76672e21i q^{11} +(8.01393e22 + 5.85910e22i) q^{12} -4.84047e22 q^{13} -2.84033e23i q^{14} +(-5.71394e24 + 7.81538e24i) q^{15} +2.89863e25 q^{16} +6.14895e25i q^{17} +(3.88562e26 - 1.23691e26i) q^{18} +4.90280e26 q^{19} +8.78371e27i q^{20} +(-6.43576e26 - 4.70528e26i) q^{21} +1.03108e28 q^{22} -2.38969e28i q^{23} +(1.17164e29 - 1.60254e29i) q^{24} -6.29235e29 q^{25} +1.80391e29i q^{26} +(3.63425e29 - 1.08533e30i) q^{27} -7.23315e29 q^{28} -3.61235e30i q^{29} +(2.91258e31 + 2.12943e31i) q^{30} -1.89712e31 q^{31} -2.45581e31i q^{32} +(1.70808e31 - 2.33627e31i) q^{33} +2.29155e32 q^{34} -7.05395e31i q^{35} +(-3.14991e32 - 9.89509e32i) q^{36} +2.49339e32 q^{37} -1.82714e33i q^{38} +(4.08739e32 + 2.98835e32i) q^{39} +1.75647e34 q^{40} +5.17484e33i q^{41} +(-1.75353e33 + 2.39843e33i) q^{42} -2.37160e34 q^{43} -2.62574e34i q^{44} +(9.64994e34 - 3.07187e34i) q^{45} -8.90572e34 q^{46} -9.55888e34i q^{47} +(-2.44767e35 - 1.78952e35i) q^{48} -3.06165e35 q^{49} +2.34499e36i q^{50} +(3.79617e35 - 5.19231e35i) q^{51} +4.59382e35 q^{52} -4.75877e35i q^{53} +(-4.04473e36 - 1.35438e36i) q^{54} +2.56068e36 q^{55} +1.44641e36i q^{56} +(-4.14003e36 - 3.02683e36i) q^{57} -1.34623e37 q^{58} +1.88111e37i q^{59} +(5.42278e37 - 7.41715e37i) q^{60} +3.45997e37 q^{61} +7.07005e37i q^{62} +(2.52960e36 + 7.94646e36i) q^{63} +3.59620e37 q^{64} +4.48001e37i q^{65} +(-8.70666e37 - 6.36556e37i) q^{66} -6.89699e37 q^{67} -5.83563e38i q^{68} +(-1.47532e38 + 2.01790e38i) q^{69} -2.62881e38 q^{70} +1.00119e39i q^{71} +(-1.97871e39 + 6.29885e38i) q^{72} +1.07589e39 q^{73} -9.29217e38i q^{74} +(5.31339e39 + 3.88470e39i) q^{75} -4.65298e39 q^{76} +2.10866e38i q^{77} +(1.11368e39 - 1.52326e39i) q^{78} -8.81067e38 q^{79} -2.68278e40i q^{80} +(-9.76932e39 + 6.92109e39i) q^{81} +1.92852e40 q^{82} -2.06470e40i q^{83} +(6.10782e39 + 4.46552e39i) q^{84} +5.69105e40 q^{85} +8.83830e40i q^{86} +(-2.23015e40 + 3.05035e40i) q^{87} -5.25067e40 q^{88} +9.55931e40i q^{89} +(-1.14480e41 - 3.59627e41i) q^{90} -3.68917e39 q^{91} +2.26792e41i q^{92} +(1.60197e41 + 1.17122e41i) q^{93} -3.56233e41 q^{94} -4.53770e41i q^{95} +(-1.51614e41 + 2.07373e41i) q^{96} -8.45265e41 q^{97} +1.14099e42i q^{98} +(-2.88468e41 + 9.18282e40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.72673e6i 1.77704i −0.458836 0.888521i \(-0.651734\pi\)
0.458836 0.888521i \(-0.348266\pi\)
\(3\) −8.44421e9 6.17368e9i −0.807258 0.590198i
\(4\) −9.49045e12 −2.15788
\(5\) 9.25532e14i 1.94098i −0.241140 0.970490i \(-0.577521\pi\)
0.241140 0.970490i \(-0.422479\pi\)
\(6\) −2.30076e16 + 3.14693e16i −1.04881 + 1.43453i
\(7\) 7.62151e16 0.136453 0.0682263 0.997670i \(-0.478266\pi\)
0.0682263 + 0.997670i \(0.478266\pi\)
\(8\) 1.89780e19i 2.05760i
\(9\) 3.31903e19 + 1.04264e20i 0.303332 + 0.952885i
\(10\) −3.44920e21 −3.44920
\(11\) 2.76672e21i 0.373868i 0.982372 + 0.186934i \(0.0598551\pi\)
−0.982372 + 0.186934i \(0.940145\pi\)
\(12\) 8.01393e22 + 5.85910e22i 1.74196 + 1.27358i
\(13\) −4.84047e22 −0.195919 −0.0979596 0.995190i \(-0.531232\pi\)
−0.0979596 + 0.995190i \(0.531232\pi\)
\(14\) 2.84033e23i 0.242482i
\(15\) −5.71394e24 + 7.81538e24i −1.14556 + 1.56687i
\(16\) 2.89863e25 1.49856
\(17\) 6.14895e25i 0.889967i 0.895539 + 0.444984i \(0.146790\pi\)
−0.895539 + 0.444984i \(0.853210\pi\)
\(18\) 3.88562e26 1.23691e26i 1.69332 0.539034i
\(19\) 4.90280e26 0.686465 0.343233 0.939250i \(-0.388478\pi\)
0.343233 + 0.939250i \(0.388478\pi\)
\(20\) 8.78371e27i 4.18840i
\(21\) −6.43576e26 4.70528e26i −0.110153 0.0805341i
\(22\) 1.03108e28 0.664379
\(23\) 2.38969e28i 0.605420i −0.953083 0.302710i \(-0.902109\pi\)
0.953083 0.302710i \(-0.0978914\pi\)
\(24\) 1.17164e29 1.60254e29i 1.21439 1.66101i
\(25\) −6.29235e29 −2.76741
\(26\) 1.80391e29i 0.348157i
\(27\) 3.63425e29 1.08533e30i 0.317523 0.948250i
\(28\) −7.23315e29 −0.294448
\(29\) 3.61235e30i 0.703773i −0.936043 0.351886i \(-0.885540\pi\)
0.936043 0.351886i \(-0.114460\pi\)
\(30\) 2.91258e31 + 2.12943e31i 2.78440 + 2.03571i
\(31\) −1.89712e31 −0.910960 −0.455480 0.890246i \(-0.650532\pi\)
−0.455480 + 0.890246i \(0.650532\pi\)
\(32\) 2.45581e31i 0.605403i
\(33\) 1.70808e31 2.33627e31i 0.220656 0.301808i
\(34\) 2.29155e32 1.58151
\(35\) 7.05395e31i 0.264852i
\(36\) −3.14991e32 9.89509e32i −0.654554 2.05621i
\(37\) 2.49339e32 0.291443 0.145721 0.989326i \(-0.453450\pi\)
0.145721 + 0.989326i \(0.453450\pi\)
\(38\) 1.82714e33i 1.21988i
\(39\) 4.08739e32 + 2.98835e32i 0.158157 + 0.115631i
\(40\) 1.75647e34 3.99376
\(41\) 5.17484e33i 0.700545i 0.936648 + 0.350273i \(0.113911\pi\)
−0.936648 + 0.350273i \(0.886089\pi\)
\(42\) −1.75353e33 + 2.39843e33i −0.143112 + 0.195746i
\(43\) −2.37160e34 −1.18087 −0.590437 0.807084i \(-0.701045\pi\)
−0.590437 + 0.807084i \(0.701045\pi\)
\(44\) 2.62574e34i 0.806762i
\(45\) 9.64994e34 3.07187e34i 1.84953 0.588762i
\(46\) −8.90572e34 −1.07586
\(47\) 9.55888e34i 0.735109i −0.930002 0.367555i \(-0.880195\pi\)
0.930002 0.367555i \(-0.119805\pi\)
\(48\) −2.44767e35 1.78952e35i −1.20972 0.884446i
\(49\) −3.06165e35 −0.981381
\(50\) 2.34499e36i 4.91780i
\(51\) 3.79617e35 5.19231e35i 0.525257 0.718433i
\(52\) 4.59382e35 0.422770
\(53\) 4.75877e35i 0.293563i −0.989169 0.146781i \(-0.953109\pi\)
0.989169 0.146781i \(-0.0468914\pi\)
\(54\) −4.04473e36 1.35438e36i −1.68508 0.564252i
\(55\) 2.56068e36 0.725671
\(56\) 1.44641e36i 0.280765i
\(57\) −4.14003e36 3.02683e36i −0.554155 0.405151i
\(58\) −1.34623e37 −1.25063
\(59\) 1.88111e37i 1.22045i 0.792227 + 0.610227i \(0.208922\pi\)
−0.792227 + 0.610227i \(0.791078\pi\)
\(60\) 5.42278e37 7.41715e37i 2.47198 3.38112i
\(61\) 3.45997e37 1.11467 0.557335 0.830288i \(-0.311824\pi\)
0.557335 + 0.830288i \(0.311824\pi\)
\(62\) 7.07005e37i 1.61881i
\(63\) 2.52960e36 + 7.94646e36i 0.0413905 + 0.130024i
\(64\) 3.59620e37 0.422731
\(65\) 4.48001e37i 0.380275i
\(66\) −8.70666e37 6.36556e37i −0.536326 0.392115i
\(67\) −6.89699e37 −0.309805 −0.154903 0.987930i \(-0.549506\pi\)
−0.154903 + 0.987930i \(0.549506\pi\)
\(68\) 5.83563e38i 1.92044i
\(69\) −1.47532e38 + 2.01790e38i −0.357318 + 0.488731i
\(70\) −2.62881e38 −0.470653
\(71\) 1.00119e39i 1.33074i 0.746514 + 0.665370i \(0.231726\pi\)
−0.746514 + 0.665370i \(0.768274\pi\)
\(72\) −1.97871e39 + 6.29885e38i −1.96065 + 0.624136i
\(73\) 1.07589e39 0.797971 0.398986 0.916957i \(-0.369362\pi\)
0.398986 + 0.916957i \(0.369362\pi\)
\(74\) 9.29217e38i 0.517906i
\(75\) 5.31339e39 + 3.88470e39i 2.23401 + 1.63332i
\(76\) −4.65298e39 −1.48131
\(77\) 2.10866e38i 0.0510153i
\(78\) 1.11368e39 1.52326e39i 0.205481 0.281052i
\(79\) −8.81067e38 −0.124406 −0.0622028 0.998064i \(-0.519813\pi\)
−0.0622028 + 0.998064i \(0.519813\pi\)
\(80\) 2.68278e40i 2.90867i
\(81\) −9.76932e39 + 6.92109e39i −0.815979 + 0.578082i
\(82\) 1.92852e40 1.24490
\(83\) 2.06470e40i 1.03328i −0.856204 0.516638i \(-0.827183\pi\)
0.856204 0.516638i \(-0.172817\pi\)
\(84\) 6.10782e39 + 4.46552e39i 0.237696 + 0.173783i
\(85\) 5.69105e40 1.72741
\(86\) 8.83830e40i 2.09846i
\(87\) −2.23015e40 + 3.05035e40i −0.415365 + 0.568127i
\(88\) −5.25067e40 −0.769270
\(89\) 9.55931e40i 1.10468i 0.833619 + 0.552340i \(0.186265\pi\)
−0.833619 + 0.552340i \(0.813735\pi\)
\(90\) −1.14480e41 3.59627e41i −1.04625 3.28669i
\(91\) −3.68917e39 −0.0267337
\(92\) 2.26792e41i 1.30642i
\(93\) 1.60197e41 + 1.17122e41i 0.735380 + 0.537647i
\(94\) −3.56233e41 −1.30632
\(95\) 4.53770e41i 1.33242i
\(96\) −1.51614e41 + 2.07373e41i −0.357308 + 0.488717i
\(97\) −8.45265e41 −1.60246 −0.801229 0.598358i \(-0.795820\pi\)
−0.801229 + 0.598358i \(0.795820\pi\)
\(98\) 1.14099e42i 1.74395i
\(99\) −2.88468e41 + 9.18282e40i −0.356253 + 0.113406i
\(100\) 5.97172e42 5.97172
\(101\) 1.25810e42i 1.02086i −0.859920 0.510429i \(-0.829487\pi\)
0.859920 0.510429i \(-0.170513\pi\)
\(102\) −1.93503e42 1.41473e42i −1.27669 0.933403i
\(103\) −1.49136e42 −0.801679 −0.400840 0.916148i \(-0.631282\pi\)
−0.400840 + 0.916148i \(0.631282\pi\)
\(104\) 9.18623e41i 0.403123i
\(105\) −4.35488e41 + 5.95650e41i −0.156315 + 0.213804i
\(106\) −1.77346e42 −0.521673
\(107\) 5.91303e42i 1.42807i −0.700108 0.714037i \(-0.746865\pi\)
0.700108 0.714037i \(-0.253135\pi\)
\(108\) −3.44906e42 + 1.03003e43i −0.685176 + 2.04621i
\(109\) 8.08579e42 1.32363 0.661814 0.749668i \(-0.269787\pi\)
0.661814 + 0.749668i \(0.269787\pi\)
\(110\) 9.54297e42i 1.28955i
\(111\) −2.10547e42 1.53934e42i −0.235270 0.172009i
\(112\) 2.20919e42 0.204482
\(113\) 1.58175e43i 1.21476i 0.794411 + 0.607381i \(0.207780\pi\)
−0.794411 + 0.607381i \(0.792220\pi\)
\(114\) −1.12802e43 + 1.54287e43i −0.719969 + 0.984756i
\(115\) −2.21173e43 −1.17511
\(116\) 3.42829e43i 1.51866i
\(117\) −1.60657e42 5.04685e42i −0.0594286 0.186688i
\(118\) 7.01037e43 2.16880
\(119\) 4.68643e42i 0.121438i
\(120\) −1.48320e44 1.08439e44i −3.22399 2.35711i
\(121\) 4.71090e43 0.860223
\(122\) 1.28944e44i 1.98081i
\(123\) 3.19478e43 4.36975e43i 0.413461 0.565521i
\(124\) 1.80045e44 1.96574
\(125\) 3.71936e44i 3.43050i
\(126\) 2.96143e43 9.42714e42i 0.231057 0.0735527i
\(127\) −1.40045e44 −0.925531 −0.462765 0.886481i \(-0.653143\pi\)
−0.462765 + 0.886481i \(0.653143\pi\)
\(128\) 2.42028e44i 1.35661i
\(129\) 2.00263e44 + 1.46415e44i 0.953270 + 0.696950i
\(130\) 1.66958e44 0.675765
\(131\) 1.97668e44i 0.681146i −0.940218 0.340573i \(-0.889379\pi\)
0.940218 0.340573i \(-0.110621\pi\)
\(132\) −1.62105e44 + 2.21723e44i −0.476149 + 0.651265i
\(133\) 3.73667e43 0.0936700
\(134\) 2.57032e44i 0.550537i
\(135\) −1.00451e45 3.36361e44i −1.84054 0.616306i
\(136\) −1.16695e45 −1.83119
\(137\) 8.24366e44i 1.10914i −0.832136 0.554572i \(-0.812882\pi\)
0.832136 0.554572i \(-0.187118\pi\)
\(138\) 7.52018e44 + 5.49811e44i 0.868495 + 0.634969i
\(139\) −6.92426e43 −0.0687168 −0.0343584 0.999410i \(-0.510939\pi\)
−0.0343584 + 0.999410i \(0.510939\pi\)
\(140\) 6.69451e44i 0.571518i
\(141\) −5.90135e44 + 8.07171e44i −0.433860 + 0.593423i
\(142\) 3.73118e45 2.36478
\(143\) 1.33922e44i 0.0732480i
\(144\) 9.62065e44 + 3.02222e45i 0.454561 + 1.42795i
\(145\) −3.34335e45 −1.36601
\(146\) 4.00954e45i 1.41803i
\(147\) 2.58532e45 + 1.89016e45i 0.792228 + 0.579209i
\(148\) −2.36633e45 −0.628898
\(149\) 1.73231e45i 0.399681i −0.979828 0.199841i \(-0.935958\pi\)
0.979828 0.199841i \(-0.0640425\pi\)
\(150\) 1.44772e46 1.98016e46i 2.90247 3.96993i
\(151\) −9.40484e45 −1.63997 −0.819985 0.572386i \(-0.806018\pi\)
−0.819985 + 0.572386i \(0.806018\pi\)
\(152\) 9.30453e45i 1.41247i
\(153\) −6.41113e45 + 2.04086e45i −0.848036 + 0.269956i
\(154\) 7.85838e44 0.0906563
\(155\) 1.75584e46i 1.76816i
\(156\) −3.87912e45 2.83608e45i −0.341284 0.249518i
\(157\) 5.32848e45 0.409931 0.204966 0.978769i \(-0.434292\pi\)
0.204966 + 0.978769i \(0.434292\pi\)
\(158\) 3.28350e45i 0.221074i
\(159\) −2.93791e45 + 4.01840e45i −0.173260 + 0.236981i
\(160\) −2.27293e46 −1.17508
\(161\) 1.82130e45i 0.0826112i
\(162\) 2.57930e46 + 3.64076e46i 1.02728 + 1.45003i
\(163\) 2.85126e46 0.997922 0.498961 0.866624i \(-0.333715\pi\)
0.498961 + 0.866624i \(0.333715\pi\)
\(164\) 4.91116e46i 1.51169i
\(165\) −2.16230e46 1.58089e46i −0.585804 0.428290i
\(166\) −7.69457e46 −1.83618
\(167\) 7.75663e46i 1.63165i 0.578298 + 0.815826i \(0.303717\pi\)
−0.578298 + 0.815826i \(0.696283\pi\)
\(168\) 8.92966e45 1.22138e46i 0.165707 0.226650i
\(169\) −5.86979e46 −0.961616
\(170\) 2.12090e47i 3.06968i
\(171\) 1.62726e46 + 5.11184e46i 0.208227 + 0.654122i
\(172\) 2.25075e47 2.54818
\(173\) 5.71829e45i 0.0573189i −0.999589 0.0286595i \(-0.990876\pi\)
0.999589 0.0286595i \(-0.00912384\pi\)
\(174\) 1.13678e47 + 8.31117e46i 1.00958 + 0.738122i
\(175\) −4.79572e46 −0.377620
\(176\) 8.01970e46i 0.560263i
\(177\) 1.16134e47 1.58845e47i 0.720310 0.985222i
\(178\) 3.56249e47 1.96306
\(179\) 1.13886e47i 0.557900i 0.960306 + 0.278950i \(0.0899864\pi\)
−0.960306 + 0.278950i \(0.910014\pi\)
\(180\) −9.15822e47 + 2.91534e47i −3.99106 + 1.27048i
\(181\) −1.93929e47 −0.752302 −0.376151 0.926558i \(-0.622753\pi\)
−0.376151 + 0.926558i \(0.622753\pi\)
\(182\) 1.37485e46i 0.0475069i
\(183\) −2.92167e47 2.13608e47i −0.899826 0.657876i
\(184\) 4.53515e47 1.24571
\(185\) 2.30771e47i 0.565685i
\(186\) 4.36482e47 5.97010e47i 0.955421 1.30680i
\(187\) −1.70124e47 −0.332730
\(188\) 9.07180e47i 1.58628i
\(189\) 2.76984e46 8.27186e46i 0.0433269 0.129391i
\(190\) −1.69108e48 −2.36776
\(191\) 1.43772e46i 0.0180291i −0.999959 0.00901455i \(-0.997131\pi\)
0.999959 0.00901455i \(-0.00286946\pi\)
\(192\) −3.03671e47 2.22018e47i −0.341253 0.249495i
\(193\) 1.62529e48 1.63767 0.818836 0.574027i \(-0.194620\pi\)
0.818836 + 0.574027i \(0.194620\pi\)
\(194\) 3.15007e48i 2.84763i
\(195\) 2.76581e47 3.78301e47i 0.224438 0.306981i
\(196\) 2.90564e48 2.11770
\(197\) 4.19882e47i 0.275003i −0.990502 0.137501i \(-0.956093\pi\)
0.990502 0.137501i \(-0.0439071\pi\)
\(198\) 3.42219e47 + 1.07504e48i 0.201528 + 0.633077i
\(199\) −2.81109e47 −0.148923 −0.0744613 0.997224i \(-0.523724\pi\)
−0.0744613 + 0.997224i \(0.523724\pi\)
\(200\) 1.19416e49i 5.69420i
\(201\) 5.82397e47 + 4.25798e47i 0.250093 + 0.182847i
\(202\) −4.68859e48 −1.81411
\(203\) 2.75316e47i 0.0960317i
\(204\) −3.60273e48 + 4.92773e48i −1.13344 + 1.55029i
\(205\) 4.78948e48 1.35975
\(206\) 5.55789e48i 1.42462i
\(207\) 2.49158e48 7.93146e47i 0.576896 0.183644i
\(208\) −1.40307e48 −0.293596
\(209\) 1.35647e48i 0.256648i
\(210\) 2.21982e48 + 1.62295e48i 0.379939 + 0.277779i
\(211\) −3.62991e48 −0.562295 −0.281147 0.959665i \(-0.590715\pi\)
−0.281147 + 0.959665i \(0.590715\pi\)
\(212\) 4.51628e48i 0.633473i
\(213\) 6.18106e48 8.45430e48i 0.785400 1.07425i
\(214\) −2.20362e49 −2.53775
\(215\) 2.19499e49i 2.29205i
\(216\) 2.05974e49 + 6.89707e48i 1.95112 + 0.653335i
\(217\) −1.44589e48 −0.124303
\(218\) 3.01335e49i 2.35214i
\(219\) −9.08503e48 6.64219e48i −0.644169 0.470961i
\(220\) −2.43020e49 −1.56591
\(221\) 2.97638e48i 0.174362i
\(222\) −5.73669e48 + 7.84650e48i −0.305667 + 0.418084i
\(223\) 3.36955e49 1.63369 0.816845 0.576857i \(-0.195721\pi\)
0.816845 + 0.576857i \(0.195721\pi\)
\(224\) 1.87169e48i 0.0826088i
\(225\) −2.08845e49 6.56064e49i −0.839444 2.63702i
\(226\) 5.89476e49 2.15868
\(227\) 2.59547e49i 0.866309i 0.901320 + 0.433154i \(0.142599\pi\)
−0.901320 + 0.433154i \(0.857401\pi\)
\(228\) 3.92907e49 + 2.87260e49i 1.19580 + 0.874265i
\(229\) −4.49974e49 −1.24923 −0.624615 0.780933i \(-0.714744\pi\)
−0.624615 + 0.780933i \(0.714744\pi\)
\(230\) 8.24253e49i 2.08822i
\(231\) 1.30182e48 1.78059e48i 0.0301091 0.0411825i
\(232\) 6.85552e49 1.44808
\(233\) 3.61477e49i 0.697601i −0.937197 0.348800i \(-0.886589\pi\)
0.937197 0.348800i \(-0.113411\pi\)
\(234\) −1.88082e49 + 5.98724e48i −0.331753 + 0.105607i
\(235\) −8.84704e49 −1.42683
\(236\) 1.78525e50i 2.63359i
\(237\) 7.43991e48 + 5.43943e48i 0.100428 + 0.0734240i
\(238\) 1.74650e49 0.215801
\(239\) 7.67891e49i 0.868848i 0.900709 + 0.434424i \(0.143048\pi\)
−0.900709 + 0.434424i \(0.856952\pi\)
\(240\) −1.65626e50 + 2.26539e50i −1.71669 + 2.34805i
\(241\) 4.55318e49 0.432471 0.216236 0.976341i \(-0.430622\pi\)
0.216236 + 0.976341i \(0.430622\pi\)
\(242\) 1.75562e50i 1.52865i
\(243\) 1.25223e50 + 1.86954e48i 0.999889 + 0.0149281i
\(244\) −3.28367e50 −2.40532
\(245\) 2.83365e50i 1.90484i
\(246\) −1.62849e50 1.19061e50i −1.00495 0.734737i
\(247\) −2.37319e49 −0.134492
\(248\) 3.60035e50i 1.87439i
\(249\) −1.27468e50 + 1.74347e50i −0.609838 + 0.834121i
\(250\) 1.38610e51 6.09614
\(251\) 1.16717e50i 0.472048i 0.971747 + 0.236024i \(0.0758444\pi\)
−0.971747 + 0.236024i \(0.924156\pi\)
\(252\) −2.40071e49 7.54155e49i −0.0893156 0.280575i
\(253\) 6.61160e49 0.226347
\(254\) 5.21911e50i 1.64471i
\(255\) −4.80564e50 3.51347e50i −1.39447 1.01951i
\(256\) −7.43810e50 −1.98803
\(257\) 2.35428e50i 0.579778i 0.957060 + 0.289889i \(0.0936184\pi\)
−0.957060 + 0.289889i \(0.906382\pi\)
\(258\) 5.45648e50 7.46324e50i 1.23851 1.69400i
\(259\) 1.90034e49 0.0397681
\(260\) 4.25173e50i 0.820588i
\(261\) 3.76637e50 1.19895e50i 0.670614 0.213477i
\(262\) −7.36656e50 −1.21043
\(263\) 2.93238e50i 0.444784i −0.974957 0.222392i \(-0.928614\pi\)
0.974957 0.222392i \(-0.0713864\pi\)
\(264\) 4.43378e50 + 3.24160e50i 0.621000 + 0.454022i
\(265\) −4.40439e50 −0.569800
\(266\) 1.39256e50i 0.166456i
\(267\) 5.90161e50 8.07208e50i 0.651980 0.891762i
\(268\) 6.54555e50 0.668522
\(269\) 9.44885e50i 0.892444i 0.894922 + 0.446222i \(0.147231\pi\)
−0.894922 + 0.446222i \(0.852769\pi\)
\(270\) −1.25353e51 + 3.74353e51i −1.09520 + 3.27071i
\(271\) −1.90890e50 −0.154322 −0.0771611 0.997019i \(-0.524586\pi\)
−0.0771611 + 0.997019i \(0.524586\pi\)
\(272\) 1.78236e51i 1.33367i
\(273\) 3.11521e49 + 2.27757e49i 0.0215810 + 0.0157782i
\(274\) −3.07219e51 −1.97100
\(275\) 1.74092e51i 1.03464i
\(276\) 1.40014e51 1.91508e51i 0.771048 1.05462i
\(277\) 8.93871e50 0.456247 0.228123 0.973632i \(-0.426741\pi\)
0.228123 + 0.973632i \(0.426741\pi\)
\(278\) 2.58048e50i 0.122113i
\(279\) −6.29660e50 1.97801e51i −0.276324 0.868040i
\(280\) 1.33870e51 0.544959
\(281\) 2.69788e51i 1.01904i −0.860460 0.509519i \(-0.829823\pi\)
0.860460 0.509519i \(-0.170177\pi\)
\(282\) 3.00811e51 + 2.19927e51i 1.05454 + 0.770987i
\(283\) −6.26675e50 −0.203952 −0.101976 0.994787i \(-0.532516\pi\)
−0.101976 + 0.994787i \(0.532516\pi\)
\(284\) 9.50179e51i 2.87157i
\(285\) −2.80143e51 + 3.83173e51i −0.786389 + 1.07560i
\(286\) −4.99091e50 −0.130165
\(287\) 3.94401e50i 0.0955913i
\(288\) 2.56051e51 8.15090e50i 0.576879 0.183638i
\(289\) 9.92731e50 0.207959
\(290\) 1.24597e52i 2.42746i
\(291\) 7.13759e51 + 5.21840e51i 1.29360 + 0.945767i
\(292\) −1.02107e52 −1.72192
\(293\) 8.06847e50i 0.126640i −0.997993 0.0633200i \(-0.979831\pi\)
0.997993 0.0633200i \(-0.0201689\pi\)
\(294\) 7.04412e51 9.63478e51i 1.02928 1.40782i
\(295\) 1.74102e52 2.36888
\(296\) 4.73194e51i 0.599671i
\(297\) 3.00280e51 + 1.00549e51i 0.354521 + 0.118712i
\(298\) −6.45585e51 −0.710251
\(299\) 1.15672e51i 0.118613i
\(300\) −5.04265e52 3.68675e52i −4.82072 3.52450i
\(301\) −1.80752e51 −0.161133
\(302\) 3.50493e52i 2.91429i
\(303\) −7.76709e51 + 1.06236e52i −0.602509 + 0.824096i
\(304\) 1.42114e52 1.02871
\(305\) 3.20231e52i 2.16355i
\(306\) 7.60572e51 + 2.38925e52i 0.479723 + 1.50700i
\(307\) −2.81133e52 −1.65579 −0.827896 0.560881i \(-0.810462\pi\)
−0.827896 + 0.560881i \(0.810462\pi\)
\(308\) 2.00121e51i 0.110085i
\(309\) 1.25934e52 + 9.20718e51i 0.647162 + 0.473150i
\(310\) 6.54355e52 3.14209
\(311\) 1.39156e49i 0.000624500i 1.00000 0.000312250i \(9.93923e-5\pi\)
−1.00000 0.000312250i \(0.999901\pi\)
\(312\) −5.67129e51 + 7.75705e51i −0.237922 + 0.325424i
\(313\) −1.83072e52 −0.718110 −0.359055 0.933316i \(-0.616901\pi\)
−0.359055 + 0.933316i \(0.616901\pi\)
\(314\) 1.98578e52i 0.728465i
\(315\) 7.35470e51 2.34123e51i 0.252373 0.0803382i
\(316\) 8.36172e51 0.268452
\(317\) 1.45252e52i 0.436394i −0.975905 0.218197i \(-0.929983\pi\)
0.975905 0.218197i \(-0.0700175\pi\)
\(318\) 1.49755e52 + 1.09488e52i 0.421125 + 0.307891i
\(319\) 9.99437e51 0.263118
\(320\) 3.32840e52i 0.820513i
\(321\) −3.65052e52 + 4.99309e52i −0.842847 + 1.15282i
\(322\) −6.78750e51 −0.146804
\(323\) 3.01471e52i 0.610932i
\(324\) 9.27152e52 6.56842e52i 1.76078 1.24743i
\(325\) 3.04579e52 0.542188
\(326\) 1.06259e53i 1.77335i
\(327\) −6.82781e52 4.99191e52i −1.06851 0.781203i
\(328\) −9.82081e52 −1.44144
\(329\) 7.28530e51i 0.100308i
\(330\) −5.89153e52 + 8.05829e52i −0.761088 + 1.04100i
\(331\) −1.47798e53 −1.79176 −0.895881 0.444294i \(-0.853455\pi\)
−0.895881 + 0.444294i \(0.853455\pi\)
\(332\) 1.95949e53i 2.22968i
\(333\) 8.27562e51 + 2.59970e52i 0.0884040 + 0.277711i
\(334\) 2.89069e53 2.89951
\(335\) 6.38339e52i 0.601326i
\(336\) −1.86549e52 1.36389e52i −0.165070 0.120685i
\(337\) 1.02469e53 0.851851 0.425926 0.904758i \(-0.359949\pi\)
0.425926 + 0.904758i \(0.359949\pi\)
\(338\) 2.18751e53i 1.70883i
\(339\) 9.76524e52 1.33567e53i 0.716950 0.980627i
\(340\) −5.40106e53 −3.72754
\(341\) 5.24880e52i 0.340579i
\(342\) 1.90504e53 6.06434e52i 1.16240 0.370028i
\(343\) −4.71114e52 −0.270365
\(344\) 4.50081e53i 2.42976i
\(345\) 1.86763e53 + 1.36545e53i 0.948617 + 0.693547i
\(346\) −2.13105e52 −0.101858
\(347\) 3.43095e53i 1.54346i 0.635949 + 0.771731i \(0.280609\pi\)
−0.635949 + 0.771731i \(0.719391\pi\)
\(348\) 2.11651e53 2.89492e53i 0.896308 1.22595i
\(349\) −2.94558e53 −1.17446 −0.587228 0.809421i \(-0.699781\pi\)
−0.587228 + 0.809421i \(0.699781\pi\)
\(350\) 1.78723e53i 0.671046i
\(351\) −1.75915e52 + 5.25351e52i −0.0622089 + 0.185780i
\(352\) 6.79452e52 0.226341
\(353\) 2.46186e53i 0.772671i −0.922358 0.386335i \(-0.873741\pi\)
0.922358 0.386335i \(-0.126259\pi\)
\(354\) −5.91971e53 4.32798e53i −1.75078 1.28002i
\(355\) 9.26638e53 2.58294
\(356\) 9.07221e53i 2.38376i
\(357\) 2.89325e52 3.95732e52i 0.0716727 0.0980322i
\(358\) 4.24422e53 0.991412
\(359\) 4.66209e53i 1.02706i 0.858071 + 0.513531i \(0.171663\pi\)
−0.858071 + 0.513531i \(0.828337\pi\)
\(360\) 5.82979e53 + 1.83136e54i 1.21144 + 3.80559i
\(361\) −2.69721e53 −0.528765
\(362\) 7.22720e53i 1.33687i
\(363\) −3.97798e53 2.90836e53i −0.694422 0.507702i
\(364\) 3.50118e52 0.0576880
\(365\) 9.95769e53i 1.54885i
\(366\) −7.96057e53 + 1.08883e54i −1.16907 + 1.59903i
\(367\) −5.40062e53 −0.748955 −0.374478 0.927236i \(-0.622178\pi\)
−0.374478 + 0.927236i \(0.622178\pi\)
\(368\) 6.92683e53i 0.907257i
\(369\) −5.39548e53 + 1.71755e53i −0.667539 + 0.212498i
\(370\) −8.60019e53 −1.00525
\(371\) 3.62690e52i 0.0400574i
\(372\) −1.52034e54 1.11154e54i −1.58686 1.16018i
\(373\) 5.62332e53 0.554763 0.277381 0.960760i \(-0.410533\pi\)
0.277381 + 0.960760i \(0.410533\pi\)
\(374\) 6.34006e53i 0.591276i
\(375\) 2.29621e54 3.14070e54i 2.02467 2.76930i
\(376\) 1.81408e54 1.51256
\(377\) 1.74855e53i 0.137883i
\(378\) −3.08269e53 1.03225e53i −0.229934 0.0769937i
\(379\) −1.60530e54 −1.13274 −0.566372 0.824150i \(-0.691653\pi\)
−0.566372 + 0.824150i \(0.691653\pi\)
\(380\) 4.30648e54i 2.87519i
\(381\) 1.18257e54 + 8.64596e53i 0.747142 + 0.546246i
\(382\) −5.35799e52 −0.0320384
\(383\) 2.05660e54i 1.16406i 0.813168 + 0.582029i \(0.197741\pi\)
−0.813168 + 0.582029i \(0.802259\pi\)
\(384\) −1.49420e54 + 2.04374e54i −0.800671 + 1.09514i
\(385\) 1.95163e53 0.0990197
\(386\) 6.05701e54i 2.91021i
\(387\) −7.87141e53 2.47272e54i −0.358197 1.12524i
\(388\) 8.02194e54 3.45791
\(389\) 2.66324e54i 1.08760i 0.839215 + 0.543800i \(0.183015\pi\)
−0.839215 + 0.543800i \(0.816985\pi\)
\(390\) −1.40982e54 1.03074e54i −0.545517 0.398835i
\(391\) 1.46941e54 0.538804
\(392\) 5.81039e54i 2.01929i
\(393\) −1.22034e54 + 1.66915e54i −0.402011 + 0.549861i
\(394\) −1.56479e54 −0.488691
\(395\) 8.15456e53i 0.241469i
\(396\) 2.73769e54 8.71491e53i 0.768751 0.244717i
\(397\) −2.65478e54 −0.707013 −0.353507 0.935432i \(-0.615011\pi\)
−0.353507 + 0.935432i \(0.615011\pi\)
\(398\) 1.04762e54i 0.264642i
\(399\) −3.15532e53 2.30690e53i −0.0756159 0.0552839i
\(400\) −1.82392e55 −4.14712
\(401\) 2.41130e54i 0.520260i −0.965574 0.260130i \(-0.916235\pi\)
0.965574 0.260130i \(-0.0837654\pi\)
\(402\) 1.58683e54 2.17043e54i 0.324926 0.444426i
\(403\) 9.18295e53 0.178475
\(404\) 1.19399e55i 2.20289i
\(405\) 6.40569e54 + 9.04182e54i 1.12205 + 1.58380i
\(406\) −1.02603e54 −0.170652
\(407\) 6.89849e53i 0.108961i
\(408\) 9.85395e54 + 7.20436e54i 1.47825 + 1.08077i
\(409\) 8.57205e53 0.122150 0.0610752 0.998133i \(-0.480547\pi\)
0.0610752 + 0.998133i \(0.480547\pi\)
\(410\) 1.78491e55i 2.41632i
\(411\) −5.08937e54 + 6.96112e54i −0.654615 + 0.895366i
\(412\) 1.41537e55 1.72993
\(413\) 1.43369e54i 0.166534i
\(414\) −2.95584e54 9.28543e54i −0.326342 1.02517i
\(415\) −1.91094e55 −2.00557
\(416\) 1.18873e54i 0.118610i
\(417\) 5.84699e53 + 4.27482e53i 0.0554722 + 0.0405565i
\(418\) 5.05518e54 0.456073
\(419\) 8.87392e54i 0.761414i −0.924696 0.380707i \(-0.875681\pi\)
0.924696 0.380707i \(-0.124319\pi\)
\(420\) 4.13298e54 5.65298e54i 0.337309 0.461363i
\(421\) −6.71691e54 −0.521489 −0.260745 0.965408i \(-0.583968\pi\)
−0.260745 + 0.965408i \(0.583968\pi\)
\(422\) 1.35277e55i 0.999222i
\(423\) 9.96644e54 3.17262e54i 0.700474 0.222982i
\(424\) 9.03117e54 0.604034
\(425\) 3.86914e55i 2.46290i
\(426\) −3.15069e55 2.30351e55i −1.90899 1.39569i
\(427\) 2.63702e54 0.152100
\(428\) 5.61173e55i 3.08161i
\(429\) −8.26792e53 + 1.13087e54i −0.0432308 + 0.0591300i
\(430\) 8.18012e55 4.07307
\(431\) 1.57059e55i 0.744799i 0.928072 + 0.372400i \(0.121465\pi\)
−0.928072 + 0.372400i \(0.878535\pi\)
\(432\) 1.05343e55 3.14597e55i 0.475827 1.42101i
\(433\) −3.31327e55 −1.42564 −0.712822 0.701345i \(-0.752583\pi\)
−0.712822 + 0.701345i \(0.752583\pi\)
\(434\) 5.38844e54i 0.220891i
\(435\) 2.82319e55 + 2.06408e55i 1.10272 + 0.806216i
\(436\) −7.67378e55 −2.85623
\(437\) 1.17162e55i 0.415600i
\(438\) −2.47536e55 + 3.38574e55i −0.836918 + 1.14472i
\(439\) −9.41508e54 −0.303437 −0.151719 0.988424i \(-0.548481\pi\)
−0.151719 + 0.988424i \(0.548481\pi\)
\(440\) 4.85966e55i 1.49314i
\(441\) −1.01617e55 3.19219e55i −0.297684 0.935143i
\(442\) −1.10922e55 −0.309848
\(443\) 4.31274e55i 1.14888i 0.818546 + 0.574440i \(0.194780\pi\)
−0.818546 + 0.574440i \(0.805220\pi\)
\(444\) 1.99818e55 + 1.46090e55i 0.507683 + 0.371174i
\(445\) 8.84745e55 2.14416
\(446\) 1.25574e56i 2.90313i
\(447\) −1.06947e55 + 1.46280e55i −0.235891 + 0.322646i
\(448\) 2.74085e54 0.0576828
\(449\) 4.04251e55i 0.811853i −0.913906 0.405927i \(-0.866949\pi\)
0.913906 0.405927i \(-0.133051\pi\)
\(450\) −2.44497e56 + 7.78309e55i −4.68609 + 1.49173i
\(451\) −1.43173e55 −0.261912
\(452\) 1.50115e56i 2.62131i
\(453\) 7.94165e55 + 5.80625e55i 1.32388 + 0.967907i
\(454\) 9.67260e55 1.53947
\(455\) 3.41444e54i 0.0518896i
\(456\) 5.74432e55 7.85693e55i 0.833636 1.14023i
\(457\) −9.40516e55 −1.30355 −0.651773 0.758414i \(-0.725974\pi\)
−0.651773 + 0.758414i \(0.725974\pi\)
\(458\) 1.67693e56i 2.21993i
\(459\) 6.67365e55 + 2.23468e55i 0.843912 + 0.282585i
\(460\) 2.09903e56 2.53574
\(461\) 1.25903e56i 1.45317i 0.687078 + 0.726584i \(0.258893\pi\)
−0.687078 + 0.726584i \(0.741107\pi\)
\(462\) −6.63578e54 4.85152e54i −0.0731831 0.0535052i
\(463\) 5.75276e55 0.606283 0.303142 0.952946i \(-0.401964\pi\)
0.303142 + 0.952946i \(0.401964\pi\)
\(464\) 1.04709e56i 1.05464i
\(465\) 1.08400e56 1.48267e56i 1.04356 1.42736i
\(466\) −1.34713e56 −1.23967
\(467\) 1.88059e56i 1.65440i −0.561911 0.827198i \(-0.689934\pi\)
0.561911 0.827198i \(-0.310066\pi\)
\(468\) 1.52470e55 + 4.78969e55i 0.128240 + 0.402851i
\(469\) −5.25655e54 −0.0422738
\(470\) 3.29705e56i 2.53554i
\(471\) −4.49948e55 3.28964e55i −0.330920 0.241941i
\(472\) −3.56996e56 −2.51120
\(473\) 6.56154e55i 0.441491i
\(474\) 2.02713e55 2.77265e55i 0.130477 0.178464i
\(475\) −3.08501e56 −1.89973
\(476\) 4.44763e55i 0.262049i
\(477\) 4.96166e55 1.57945e55i 0.279732 0.0890471i
\(478\) 2.86172e56 1.54398
\(479\) 1.69047e56i 0.872896i −0.899729 0.436448i \(-0.856236\pi\)
0.899729 0.436448i \(-0.143764\pi\)
\(480\) 1.91931e56 + 1.40323e56i 0.948590 + 0.693527i
\(481\) −1.20692e55 −0.0570992
\(482\) 1.69685e56i 0.768519i
\(483\) −1.12441e55 + 1.53795e55i −0.0487570 + 0.0666886i
\(484\) −4.47085e56 −1.85625
\(485\) 7.82320e56i 3.11034i
\(486\) 6.96727e54 4.66671e56i 0.0265278 1.77684i
\(487\) −5.61969e55 −0.204929 −0.102465 0.994737i \(-0.532673\pi\)
−0.102465 + 0.994737i \(0.532673\pi\)
\(488\) 6.56633e56i 2.29354i
\(489\) −2.40766e56 1.76027e56i −0.805581 0.588972i
\(490\) 1.05602e57 3.38498
\(491\) 3.11506e56i 0.956655i −0.878182 0.478327i \(-0.841243\pi\)
0.878182 0.478327i \(-0.158757\pi\)
\(492\) −3.03199e56 + 4.14708e56i −0.892197 + 1.22033i
\(493\) 2.22122e56 0.626335
\(494\) 8.84421e55i 0.238997i
\(495\) 8.49899e55 + 2.66986e56i 0.220119 + 0.691481i
\(496\) −5.49905e56 −1.36513
\(497\) 7.63061e55i 0.181583i
\(498\) 6.49745e56 + 4.75038e56i 1.48227 + 1.08371i
\(499\) −5.54023e56 −1.21176 −0.605879 0.795557i \(-0.707179\pi\)
−0.605879 + 0.795557i \(0.707179\pi\)
\(500\) 3.52983e57i 7.40260i
\(501\) 4.78870e56 6.54986e56i 0.962998 1.31716i
\(502\) 4.34973e56 0.838849
\(503\) 6.48555e56i 1.19955i 0.800168 + 0.599776i \(0.204744\pi\)
−0.800168 + 0.599776i \(0.795256\pi\)
\(504\) −1.50808e56 + 4.80067e55i −0.267536 + 0.0851650i
\(505\) −1.16441e57 −1.98147
\(506\) 2.46396e56i 0.402229i
\(507\) 4.95657e56 + 3.62382e56i 0.776272 + 0.567544i
\(508\) 1.32909e57 1.99718
\(509\) 3.07619e56i 0.443548i 0.975098 + 0.221774i \(0.0711847\pi\)
−0.975098 + 0.221774i \(0.928815\pi\)
\(510\) −1.30938e57 + 1.79093e57i −1.81172 + 2.47802i
\(511\) 8.19989e55 0.108885
\(512\) 1.70753e57i 2.17620i
\(513\) 1.78180e56 5.32116e56i 0.217969 0.650941i
\(514\) 8.77374e56 1.03029
\(515\) 1.38030e57i 1.55604i
\(516\) −1.90058e57 1.38954e57i −2.05704 1.50393i
\(517\) 2.64467e56 0.274834
\(518\) 7.08203e55i 0.0706696i
\(519\) −3.53029e55 + 4.82864e55i −0.0338295 + 0.0462712i
\(520\) −8.50215e56 −0.782453
\(521\) 8.69046e56i 0.768158i −0.923300 0.384079i \(-0.874519\pi\)
0.923300 0.384079i \(-0.125481\pi\)
\(522\) −4.46817e56 1.40362e57i −0.379358 1.19171i
\(523\) 2.09639e57 1.70977 0.854884 0.518820i \(-0.173628\pi\)
0.854884 + 0.518820i \(0.173628\pi\)
\(524\) 1.87596e57i 1.46983i
\(525\) 4.04961e56 + 2.96072e56i 0.304837 + 0.222871i
\(526\) −1.09282e57 −0.790399
\(527\) 1.16653e57i 0.810724i
\(528\) 4.95111e56 6.77200e56i 0.330666 0.452277i
\(529\) 9.86944e56 0.633466
\(530\) 1.64139e57i 1.01256i
\(531\) −1.96131e57 + 6.24346e56i −1.16295 + 0.370203i
\(532\) −3.54627e56 −0.202128
\(533\) 2.50487e56i 0.137250i
\(534\) −3.00824e57 2.19937e57i −1.58470 1.15860i
\(535\) −5.47270e57 −2.77186
\(536\) 1.30891e57i 0.637455i
\(537\) 7.03095e56 9.61676e56i 0.329272 0.450370i
\(538\) 3.52133e57 1.58591
\(539\) 8.47071e56i 0.366907i
\(540\) 9.53323e57 + 3.19222e57i 3.97165 + 1.32991i
\(541\) 3.23852e57 1.29779 0.648895 0.760878i \(-0.275232\pi\)
0.648895 + 0.760878i \(0.275232\pi\)
\(542\) 7.11395e56i 0.274237i
\(543\) 1.63758e57 + 1.19726e57i 0.607302 + 0.444007i
\(544\) 1.51006e57 0.538789
\(545\) 7.48366e57i 2.56914i
\(546\) 8.48790e55 1.16095e56i 0.0280385 0.0383503i
\(547\) −1.51432e57 −0.481376 −0.240688 0.970602i \(-0.577373\pi\)
−0.240688 + 0.970602i \(0.577373\pi\)
\(548\) 7.82360e57i 2.39340i
\(549\) 1.14838e57 + 3.60750e57i 0.338115 + 1.06215i
\(550\) −6.48792e57 −1.83861
\(551\) 1.77107e57i 0.483116i
\(552\) −3.82957e57 2.79986e57i −1.00561 0.735216i
\(553\) −6.71506e55 −0.0169755
\(554\) 3.33121e57i 0.810769i
\(555\) −1.42470e57 + 1.94868e57i −0.333866 + 0.456654i
\(556\) 6.57144e56 0.148282
\(557\) 2.75915e56i 0.0599536i −0.999551 0.0299768i \(-0.990457\pi\)
0.999551 0.0299768i \(-0.00954335\pi\)
\(558\) −7.37149e57 + 2.34657e57i −1.54254 + 0.491039i
\(559\) 1.14796e57 0.231356
\(560\) 2.04468e57i 0.396896i
\(561\) 1.43656e57 + 1.05029e57i 0.268599 + 0.196377i
\(562\) −1.00543e58 −1.81087
\(563\) 3.66567e57i 0.636030i 0.948086 + 0.318015i \(0.103016\pi\)
−0.948086 + 0.318015i \(0.896984\pi\)
\(564\) 5.60064e57 7.66042e57i 0.936217 1.28053i
\(565\) 1.46396e58 2.35783
\(566\) 2.33544e57i 0.362430i
\(567\) −7.44569e56 + 5.27491e56i −0.111343 + 0.0788808i
\(568\) −1.90007e58 −2.73813
\(569\) 6.88329e57i 0.955957i −0.878372 0.477979i \(-0.841370\pi\)
0.878372 0.477979i \(-0.158630\pi\)
\(570\) 1.42798e58 + 1.04402e58i 1.91139 + 1.39745i
\(571\) −6.60942e57 −0.852717 −0.426359 0.904554i \(-0.640204\pi\)
−0.426359 + 0.904554i \(0.640204\pi\)
\(572\) 1.27098e57i 0.158060i
\(573\) −8.87603e55 + 1.21404e56i −0.0106407 + 0.0145541i
\(574\) 1.46983e57 0.169870
\(575\) 1.50368e58i 1.67544i
\(576\) 1.19359e57 + 3.74953e57i 0.128228 + 0.402814i
\(577\) 1.34069e57 0.138879 0.0694393 0.997586i \(-0.477879\pi\)
0.0694393 + 0.997586i \(0.477879\pi\)
\(578\) 3.69964e57i 0.369551i
\(579\) −1.37243e58 1.00340e58i −1.32202 0.966551i
\(580\) 3.17299e58 2.94768
\(581\) 1.57361e57i 0.140993i
\(582\) 1.94475e58 2.65999e58i 1.68067 2.29878i
\(583\) 1.31662e57 0.109754
\(584\) 2.04182e58i 1.64190i
\(585\) −4.67102e57 + 1.48693e57i −0.362359 + 0.115350i
\(586\) −3.00690e57 −0.225045
\(587\) 2.55179e58i 1.84266i 0.388783 + 0.921329i \(0.372896\pi\)
−0.388783 + 0.921329i \(0.627104\pi\)
\(588\) −2.45358e58 1.79385e58i −1.70953 1.24986i
\(589\) −9.30120e57 −0.625342
\(590\) 6.48832e58i 4.20959i
\(591\) −2.59222e57 + 3.54557e57i −0.162306 + 0.221998i
\(592\) 7.22741e57 0.436744
\(593\) 1.87124e57i 0.109139i −0.998510 0.0545697i \(-0.982621\pi\)
0.998510 0.0545697i \(-0.0173787\pi\)
\(594\) 3.74720e57 1.11906e58i 0.210956 0.629998i
\(595\) 4.33744e57 0.235710
\(596\) 1.64404e58i 0.862464i
\(597\) 2.37374e57 + 1.73548e57i 0.120219 + 0.0878938i
\(598\) 4.31079e57 0.210781
\(599\) 3.92182e57i 0.185150i 0.995706 + 0.0925752i \(0.0295099\pi\)
−0.995706 + 0.0925752i \(0.970490\pi\)
\(600\) −7.37237e58 + 1.00837e59i −3.36071 + 4.59669i
\(601\) 7.48410e57 0.329440 0.164720 0.986340i \(-0.447328\pi\)
0.164720 + 0.986340i \(0.447328\pi\)
\(602\) 6.73611e57i 0.286341i
\(603\) −2.28913e57 7.19106e57i −0.0939740 0.295209i
\(604\) 8.92562e58 3.53885
\(605\) 4.36008e58i 1.66968i
\(606\) 3.95914e58 + 2.89458e58i 1.46445 + 1.07068i
\(607\) −2.11459e58 −0.755552 −0.377776 0.925897i \(-0.623311\pi\)
−0.377776 + 0.925897i \(0.623311\pi\)
\(608\) 1.20403e58i 0.415588i
\(609\) −1.69971e57 + 2.32482e57i −0.0566777 + 0.0775224i
\(610\) −1.19342e59 −3.84472
\(611\) 4.62694e57i 0.144022i
\(612\) 6.08445e58 1.93686e58i 1.82996 0.582532i
\(613\) −7.77952e57 −0.226091 −0.113045 0.993590i \(-0.536061\pi\)
−0.113045 + 0.993590i \(0.536061\pi\)
\(614\) 1.04771e59i 2.94241i
\(615\) −4.04434e58 2.95687e58i −1.09767 0.802519i
\(616\) −4.00180e57 −0.104969
\(617\) 4.12643e57i 0.104613i −0.998631 0.0523065i \(-0.983343\pi\)
0.998631 0.0523065i \(-0.0166573\pi\)
\(618\) 3.43126e58 4.69320e58i 0.840807 1.15003i
\(619\) −5.35791e58 −1.26909 −0.634544 0.772887i \(-0.718812\pi\)
−0.634544 + 0.772887i \(0.718812\pi\)
\(620\) 1.66637e59i 3.81546i
\(621\) −2.59360e58 8.68472e57i −0.574090 0.192235i
\(622\) 5.18595e55 0.00110976
\(623\) 7.28564e57i 0.150737i
\(624\) 1.18478e58 + 8.66213e57i 0.237008 + 0.173280i
\(625\) 2.01167e59 3.89113
\(626\) 6.82260e58i 1.27611i
\(627\) 8.37439e57 1.14543e58i 0.151473 0.207181i
\(628\) −5.05697e58 −0.884581
\(629\) 1.53317e58i 0.259374i
\(630\) −8.72511e57 2.74090e58i −0.142764 0.448478i
\(631\) 7.12248e58 1.12724 0.563618 0.826036i \(-0.309409\pi\)
0.563618 + 0.826036i \(0.309409\pi\)
\(632\) 1.67209e58i 0.255977i
\(633\) 3.06517e58 + 2.24099e58i 0.453917 + 0.331865i
\(634\) −5.41316e58 −0.775490
\(635\) 1.29616e59i 1.79644i
\(636\) 2.78821e58 3.81364e58i 0.373874 0.511376i
\(637\) 1.48198e58 0.192271
\(638\) 3.72463e58i 0.467572i
\(639\) −1.04388e59 + 3.32300e58i −1.26804 + 0.403657i
\(640\) −2.24005e59 −2.63316
\(641\) 1.15105e59i 1.30941i 0.755883 + 0.654707i \(0.227208\pi\)
−0.755883 + 0.654707i \(0.772792\pi\)
\(642\) 1.86079e59 + 1.36045e59i 2.04862 + 1.49777i
\(643\) −8.15086e57 −0.0868506 −0.0434253 0.999057i \(-0.513827\pi\)
−0.0434253 + 0.999057i \(0.513827\pi\)
\(644\) 1.72850e58i 0.178265i
\(645\) 1.35512e59 1.85349e59i 1.35277 1.85028i
\(646\) 1.12350e59 1.08565
\(647\) 3.63923e58i 0.340424i −0.985407 0.170212i \(-0.945555\pi\)
0.985407 0.170212i \(-0.0544452\pi\)
\(648\) −1.31348e59 1.85402e59i −1.18946 1.67896i
\(649\) −5.20449e58 −0.456289
\(650\) 1.13508e59i 0.963491i
\(651\) 1.22094e58 + 8.92647e57i 0.100345 + 0.0733633i
\(652\) −2.70597e59 −2.15339
\(653\) 2.30345e59i 1.77501i −0.460796 0.887506i \(-0.652436\pi\)
0.460796 0.887506i \(-0.347564\pi\)
\(654\) −1.86035e59 + 2.54454e59i −1.38823 + 1.89879i
\(655\) −1.82948e59 −1.32209
\(656\) 1.50000e59i 1.04981i
\(657\) 3.57091e58 + 1.12176e59i 0.242050 + 0.760375i
\(658\) −2.71503e58 −0.178251
\(659\) 1.39143e59i 0.884848i −0.896806 0.442424i \(-0.854119\pi\)
0.896806 0.442424i \(-0.145881\pi\)
\(660\) 2.05211e59 + 1.50033e59i 1.26409 + 0.924196i
\(661\) 1.94176e59 1.15868 0.579341 0.815085i \(-0.303310\pi\)
0.579341 + 0.815085i \(0.303310\pi\)
\(662\) 5.50802e59i 3.18404i
\(663\) −1.83752e58 + 2.51332e58i −0.102908 + 0.140755i
\(664\) 3.91838e59 2.12607
\(665\) 3.45841e58i 0.181812i
\(666\) 9.68835e58 3.08410e58i 0.493505 0.157098i
\(667\) −8.63241e58 −0.426078
\(668\) 7.36139e59i 3.52090i
\(669\) −2.84532e59 2.08025e59i −1.31881 0.964201i
\(670\) 2.37891e59 1.06858
\(671\) 9.57277e58i 0.416739i
\(672\) −1.15552e58 + 1.58050e58i −0.0487556 + 0.0666867i
\(673\) 4.25186e59 1.73885 0.869426 0.494064i \(-0.164489\pi\)
0.869426 + 0.494064i \(0.164489\pi\)
\(674\) 3.81873e59i 1.51378i
\(675\) −2.28680e59 + 6.82928e59i −0.878716 + 2.62419i
\(676\) 5.57069e59 2.07505
\(677\) 5.18811e59i 1.87347i −0.350039 0.936735i \(-0.613832\pi\)
0.350039 0.936735i \(-0.386168\pi\)
\(678\) −4.97766e59 3.63924e59i −1.74262 1.27405i
\(679\) −6.44219e58 −0.218660
\(680\) 1.08005e60i 3.55431i
\(681\) 1.60236e59 2.19167e59i 0.511294 0.699335i
\(682\) −1.95608e59 −0.605223
\(683\) 1.31944e59i 0.395872i 0.980215 + 0.197936i \(0.0634237\pi\)
−0.980215 + 0.197936i \(0.936576\pi\)
\(684\) −1.54434e59 4.85137e59i −0.449329 1.41152i
\(685\) −7.62977e59 −2.15283
\(686\) 1.75571e59i 0.480449i
\(687\) 3.79967e59 + 2.77800e59i 1.00845 + 0.737293i
\(688\) −6.87439e59 −1.76961
\(689\) 2.30347e58i 0.0575146i
\(690\) 5.08867e59 6.96016e59i 1.23246 1.68573i
\(691\) −2.84007e59 −0.667252 −0.333626 0.942705i \(-0.608272\pi\)
−0.333626 + 0.942705i \(0.608272\pi\)
\(692\) 5.42691e58i 0.123687i
\(693\) −2.19856e58 + 6.99870e57i −0.0486117 + 0.0154746i
\(694\) 1.27862e60 2.74280
\(695\) 6.40863e58i 0.133378i
\(696\) −5.78894e59 4.23238e59i −1.16898 0.854654i
\(697\) −3.18199e59 −0.623462
\(698\) 1.09774e60i 2.08706i
\(699\) −2.23165e59 + 3.05239e59i −0.411723 + 0.563144i
\(700\) 4.55135e59 0.814857
\(701\) 6.37124e59i 1.10700i 0.832851 + 0.553498i \(0.186707\pi\)
−0.832851 + 0.553498i \(0.813293\pi\)
\(702\) 1.95784e59 + 6.55586e58i 0.330140 + 0.110548i
\(703\) 1.22246e59 0.200065
\(704\) 9.94967e58i 0.158046i
\(705\) 7.47063e59 + 5.46188e59i 1.15182 + 0.842114i
\(706\) −9.17468e59 −1.37307
\(707\) 9.58860e58i 0.139299i
\(708\) −1.10216e60 + 1.50751e60i −1.55434 + 2.12599i
\(709\) 9.34454e59 1.27934 0.639672 0.768648i \(-0.279070\pi\)
0.639672 + 0.768648i \(0.279070\pi\)
\(710\) 3.45332e60i 4.58999i
\(711\) −2.92429e58 9.18633e58i −0.0377363 0.118544i
\(712\) −1.81416e60 −2.27299
\(713\) 4.53353e59i 0.551513i
\(714\) −1.47478e59 1.07824e59i −0.174207 0.127365i
\(715\) −1.23949e59 −0.142173
\(716\) 1.08083e60i 1.20388i
\(717\) 4.74071e59 6.48423e59i 0.512792 0.701385i
\(718\) 1.73743e60 1.82513
\(719\) 1.54952e60i 1.58085i −0.612560 0.790424i \(-0.709860\pi\)
0.612560 0.790424i \(-0.290140\pi\)
\(720\) 2.79716e60 8.90422e59i 2.77163 0.882294i
\(721\) −1.13664e59 −0.109391
\(722\) 1.00518e60i 0.939638i
\(723\) −3.84480e59 2.81099e59i −0.349116 0.255244i
\(724\) 1.84047e60 1.62338
\(725\) 2.27302e60i 1.94762i
\(726\) −1.08387e60 + 1.48248e60i −0.902207 + 1.23402i
\(727\) −1.51238e60 −1.22304 −0.611518 0.791230i \(-0.709441\pi\)
−0.611518 + 0.791230i \(0.709441\pi\)
\(728\) 7.00129e58i 0.0550072i
\(729\) −1.04587e60 7.88872e59i −0.798358 0.602183i
\(730\) −3.71096e60 −2.75236
\(731\) 1.45828e60i 1.05094i
\(732\) 2.77280e60 + 2.02723e60i 1.94172 + 1.41962i
\(733\) 2.51815e59 0.171355 0.0856776 0.996323i \(-0.472694\pi\)
0.0856776 + 0.996323i \(0.472694\pi\)
\(734\) 2.01266e60i 1.33093i
\(735\) 1.74941e60 2.39279e60i 1.12423 1.53770i
\(736\) −5.86861e59 −0.366523
\(737\) 1.90820e59i 0.115826i
\(738\) 6.40083e59 + 2.01075e60i 0.377618 + 1.18624i
\(739\) 6.64821e59 0.381217 0.190608 0.981666i \(-0.438954\pi\)
0.190608 + 0.981666i \(0.438954\pi\)
\(740\) 2.19012e60i 1.22068i
\(741\) 2.00397e59 + 1.46513e59i 0.108570 + 0.0793768i
\(742\) −1.35165e59 −0.0711837
\(743\) 9.10560e59i 0.466169i −0.972456 0.233085i \(-0.925118\pi\)
0.972456 0.233085i \(-0.0748819\pi\)
\(744\) −2.22274e60 + 3.04021e60i −1.10626 + 1.51312i
\(745\) −1.60331e60 −0.775774
\(746\) 2.09566e60i 0.985836i
\(747\) 2.15273e60 6.85280e59i 0.984594 0.313426i
\(748\) 1.61455e60 0.717991
\(749\) 4.50662e59i 0.194865i
\(750\) −1.17045e61 8.55735e60i −4.92116 3.59793i
\(751\) −2.23704e59 −0.0914607 −0.0457303 0.998954i \(-0.514561\pi\)
−0.0457303 + 0.998954i \(0.514561\pi\)
\(752\) 2.77077e60i 1.10160i
\(753\) 7.20574e59 9.85583e59i 0.278602 0.381065i
\(754\) 6.51636e59 0.245023
\(755\) 8.70448e60i 3.18315i
\(756\) −2.62871e59 + 7.85036e59i −0.0934941 + 0.279211i
\(757\) 4.53142e58 0.0156755 0.00783774 0.999969i \(-0.497505\pi\)
0.00783774 + 0.999969i \(0.497505\pi\)
\(758\) 5.98250e60i 2.01293i
\(759\) −5.58297e59 4.08179e59i −0.182721 0.133590i
\(760\) 8.61163e60 2.74157
\(761\) 5.57015e60i 1.72500i −0.506057 0.862500i \(-0.668898\pi\)
0.506057 0.862500i \(-0.331102\pi\)
\(762\) 3.22211e60 4.40713e60i 0.970703 1.32770i
\(763\) 6.16259e59 0.180613
\(764\) 1.36446e59i 0.0389046i
\(765\) 1.88888e60 + 5.93370e60i 0.523979 + 1.64602i
\(766\) 7.66437e60 2.06858
\(767\) 9.10544e59i 0.239110i
\(768\) 6.28089e60 + 4.59204e60i 1.60485 + 1.17333i
\(769\) −5.85974e60 −1.45688 −0.728442 0.685107i \(-0.759755\pi\)
−0.728442 + 0.685107i \(0.759755\pi\)
\(770\) 7.27318e59i 0.175962i
\(771\) 1.45346e60 1.98800e60i 0.342184 0.468031i
\(772\) −1.54247e61 −3.53390
\(773\) 1.90869e60i 0.425565i 0.977100 + 0.212782i \(0.0682526\pi\)
−0.977100 + 0.212782i \(0.931747\pi\)
\(774\) −9.21514e60 + 2.93346e60i −1.99959 + 0.636531i
\(775\) 1.19373e61 2.52100
\(776\) 1.60414e61i 3.29721i
\(777\) −1.60468e59 1.17321e59i −0.0321032 0.0234711i
\(778\) 9.92517e60 1.93271
\(779\) 2.53712e60i 0.480900i
\(780\) −2.62488e60 + 3.59025e60i −0.484309 + 0.662426i
\(781\) −2.77002e60 −0.497521
\(782\) 5.47609e60i 0.957477i
\(783\) −3.92060e60 1.31282e60i −0.667353 0.223464i
\(784\) −8.87459e60 −1.47066
\(785\) 4.93168e60i 0.795668i
\(786\) 6.22048e60 + 4.54788e60i 0.977126 + 0.714391i
\(787\) −8.42104e60 −1.28794 −0.643971 0.765050i \(-0.722714\pi\)
−0.643971 + 0.765050i \(0.722714\pi\)
\(788\) 3.98487e60i 0.593422i
\(789\) −1.81036e60 + 2.47616e60i −0.262511 + 0.359055i
\(790\) 3.03898e60 0.429100
\(791\) 1.20553e60i 0.165758i
\(792\) −1.74271e60 5.47454e60i −0.233344 0.733026i
\(793\) −1.67479e60 −0.218385
\(794\) 9.89363e60i 1.25639i
\(795\) 3.71916e60 + 2.71913e60i 0.459976 + 0.336295i
\(796\) 2.66785e60 0.321357
\(797\) 1.46593e60i 0.171984i 0.996296 + 0.0859920i \(0.0274059\pi\)
−0.996296 + 0.0859920i \(0.972594\pi\)
\(798\) −8.59720e59 + 1.17590e60i −0.0982418 + 0.134373i
\(799\) 5.87771e60 0.654223
\(800\) 1.54528e61i 1.67540i
\(801\) −9.96689e60 + 3.17277e60i −1.05263 + 0.335085i
\(802\) −8.98627e60 −0.924523
\(803\) 2.97668e60i 0.298336i
\(804\) −5.52720e60 4.04102e60i −0.539670 0.394561i
\(805\) −1.68567e60 −0.160347
\(806\) 3.42223e60i 0.317157i
\(807\) 5.83342e60 7.97881e60i 0.526719 0.720433i
\(808\) 2.38761e61 2.10051
\(809\) 1.47552e61i 1.26481i 0.774638 + 0.632405i \(0.217932\pi\)
−0.774638 + 0.632405i \(0.782068\pi\)
\(810\) 3.36964e61 2.38722e61i 2.81448 1.99392i
\(811\) −2.01099e61 −1.63671 −0.818355 0.574713i \(-0.805114\pi\)
−0.818355 + 0.574713i \(0.805114\pi\)
\(812\) 2.61287e60i 0.207225i
\(813\) 1.61192e60 + 1.17849e60i 0.124578 + 0.0910807i
\(814\) 2.57088e60 0.193629
\(815\) 2.63893e61i 1.93695i
\(816\) 1.10037e61 1.50506e61i 0.787128 1.07661i
\(817\) −1.16275e61 −0.810629
\(818\) 3.19457e60i 0.217067i
\(819\) −1.22445e59 3.84646e59i −0.00810920 0.0254741i
\(820\) −4.54543e61 −2.93416
\(821\) 7.93309e60i 0.499156i −0.968355 0.249578i \(-0.919708\pi\)
0.968355 0.249578i \(-0.0802919\pi\)
\(822\) 2.59422e61 + 1.89667e61i 1.59110 + 1.16328i
\(823\) 5.15535e60 0.308221 0.154110 0.988054i \(-0.450749\pi\)
0.154110 + 0.988054i \(0.450749\pi\)
\(824\) 2.83030e61i 1.64953i
\(825\) −1.07479e61 + 1.47007e61i −0.610645 + 0.835226i
\(826\) 5.34296e60 0.295938
\(827\) 2.66521e60i 0.143918i 0.997408 + 0.0719590i \(0.0229251\pi\)
−0.997408 + 0.0719590i \(0.977075\pi\)
\(828\) −2.36462e61 + 7.52730e60i −1.24487 + 0.396280i
\(829\) 1.95335e61 1.00262 0.501309 0.865268i \(-0.332852\pi\)
0.501309 + 0.865268i \(0.332852\pi\)
\(830\) 7.12157e61i 3.56398i
\(831\) −7.54803e60 5.51847e60i −0.368309 0.269276i
\(832\) −1.74073e60 −0.0828212
\(833\) 1.88259e61i 0.873396i
\(834\) 1.59311e60 2.17901e60i 0.0720706 0.0985764i
\(835\) 7.17901e61 3.16700
\(836\) 1.28735e61i 0.553814i
\(837\) −6.89460e60 + 2.05900e61i −0.289251 + 0.863818i
\(838\) −3.30707e61 −1.35307
\(839\) 4.52741e61i 1.80655i −0.429067 0.903273i \(-0.641157\pi\)
0.429067 0.903273i \(-0.358843\pi\)
\(840\) −1.13042e61 8.26468e60i −0.439922 0.321633i
\(841\) 1.32970e61 0.504704
\(842\) 2.50321e61i 0.926708i
\(843\) −1.66559e61 + 2.27815e61i −0.601434 + 0.822627i
\(844\) 3.44495e61 1.21336
\(845\) 5.43267e61i 1.86648i
\(846\) −1.18235e61 3.71422e61i −0.396249 1.24477i
\(847\) 3.59041e60 0.117380
\(848\) 1.37939e61i 0.439921i
\(849\) 5.29177e60 + 3.86889e60i 0.164642 + 0.120372i
\(850\) −1.44192e62 −4.37668
\(851\) 5.95842e60i 0.176445i
\(852\) −5.86610e61 + 8.02351e61i −1.69480 + 2.31810i
\(853\) −5.96149e61 −1.68045 −0.840224 0.542240i \(-0.817576\pi\)
−0.840224 + 0.542240i \(0.817576\pi\)
\(854\) 9.82746e60i 0.270287i
\(855\) 4.73117e61 1.50608e61i 1.26964 0.404165i
\(856\) 1.12217e62 2.93840
\(857\) 6.42053e59i 0.0164049i 0.999966 + 0.00820245i \(0.00261095\pi\)
−0.999966 + 0.00820245i \(0.997389\pi\)
\(858\) 4.21443e60 + 3.08123e60i 0.105077 + 0.0768229i
\(859\) 5.24704e61 1.27661 0.638304 0.769784i \(-0.279636\pi\)
0.638304 + 0.769784i \(0.279636\pi\)
\(860\) 2.08314e62i 4.94597i
\(861\) 2.43491e60 3.33041e60i 0.0564178 0.0771669i
\(862\) 5.85315e61 1.32354
\(863\) 4.07881e60i 0.0900132i −0.998987 0.0450066i \(-0.985669\pi\)
0.998987 0.0450066i \(-0.0143309\pi\)
\(864\) −2.66536e61 8.92501e60i −0.574074 0.192230i
\(865\) −5.29246e60 −0.111255
\(866\) 1.23477e62i 2.53343i
\(867\) −8.38283e60 6.12880e60i −0.167876 0.122737i
\(868\) 1.37222e61 0.268230
\(869\) 2.43766e60i 0.0465113i
\(870\) 7.69225e61 1.05213e62i 1.43268 1.95958i
\(871\) 3.33847e60 0.0606968
\(872\) 1.53452e62i 2.72349i
\(873\) −2.80546e61 8.81305e61i −0.486077 1.52696i
\(874\) −4.36630e61 −0.738539
\(875\) 2.83471e61i 0.468101i
\(876\) 8.62209e61 + 6.30374e61i 1.39004 + 1.01628i
\(877\) 3.47453e61 0.546895 0.273448 0.961887i \(-0.411836\pi\)
0.273448 + 0.961887i \(0.411836\pi\)
\(878\) 3.50874e61i 0.539221i
\(879\) −4.98121e60 + 6.81318e60i −0.0747427 + 0.102231i
\(880\) 7.42248e61 1.08746
\(881\) 1.23936e62i 1.77298i 0.462745 + 0.886491i \(0.346864\pi\)
−0.462745 + 0.886491i \(0.653136\pi\)
\(882\) −1.18964e62 + 3.78699e61i −1.66179 + 0.528998i
\(883\) −8.10245e61 −1.10520 −0.552601 0.833446i \(-0.686365\pi\)
−0.552601 + 0.833446i \(0.686365\pi\)
\(884\) 2.82472e61i 0.376251i
\(885\) −1.47016e62 1.07485e62i −1.91230 1.39811i
\(886\) 1.60724e62 2.04161
\(887\) 5.84393e61i 0.724952i −0.931993 0.362476i \(-0.881932\pi\)
0.931993 0.362476i \(-0.118068\pi\)
\(888\) 2.92135e61 3.99575e61i 0.353925 0.484090i
\(889\) −1.06736e61 −0.126291
\(890\) 3.29720e62i 3.81027i
\(891\) −1.91487e61 2.70290e61i −0.216126 0.305069i
\(892\) −3.19785e62 −3.52530
\(893\) 4.68653e61i 0.504627i
\(894\) 5.45145e61 + 3.98563e61i 0.573356 + 0.419189i
\(895\) 1.05405e62 1.08287
\(896\) 1.84462e61i 0.185114i
\(897\) 7.14123e60 9.76760e60i 0.0700054 0.0957517i
\(898\) −1.50653e62 −1.44270
\(899\) 6.85307e61i 0.641109i
\(900\) 1.98203e62 + 6.22634e62i 1.81142 + 5.69036i
\(901\) 2.92614e61 0.261261
\(902\) 5.33568e61i 0.465428i
\(903\) 1.52630e61 + 1.11590e61i 0.130076 + 0.0951006i
\(904\) −3.00185e62 −2.49949
\(905\) 1.79487e62i 1.46020i
\(906\) 2.16383e62 2.95963e62i 1.72001 2.35259i
\(907\) −6.42901e61 −0.499334 −0.249667 0.968332i \(-0.580321\pi\)
−0.249667 + 0.968332i \(0.580321\pi\)
\(908\) 2.46321e62i 1.86939i
\(909\) 1.31174e62 4.17567e61i 0.972760 0.309659i
\(910\) 1.27247e61 0.0922100
\(911\) 5.51019e61i 0.390194i −0.980784 0.195097i \(-0.937498\pi\)
0.980784 0.195097i \(-0.0625021\pi\)
\(912\) −1.20004e62 8.77367e61i −0.830433 0.607141i
\(913\) 5.71244e61 0.386309
\(914\) 3.50505e62i 2.31645i
\(915\) −1.97701e62 + 2.70410e62i −1.27692 + 1.74655i
\(916\) 4.27045e62 2.69568
\(917\) 1.50653e61i 0.0929442i
\(918\) 8.32805e61 2.48709e62i 0.502166 1.49967i
\(919\) −1.73999e62 −1.02546 −0.512732 0.858549i \(-0.671366\pi\)
−0.512732 + 0.858549i \(0.671366\pi\)
\(920\) 4.19742e62i 2.41790i
\(921\) 2.37395e62 + 1.73563e62i 1.33665 + 0.977246i
\(922\) 4.69205e62 2.58234
\(923\) 4.84625e61i 0.260718i
\(924\) −1.23548e61 + 1.68986e61i −0.0649718 + 0.0888669i
\(925\) −1.56893e62 −0.806540
\(926\) 2.14390e62i 1.07739i
\(927\) −4.94987e61 1.55495e62i −0.243175 0.763908i
\(928\) −8.87124e61 −0.426066
\(929\) 1.95586e60i 0.00918351i 0.999989 + 0.00459175i \(0.00146161\pi\)
−0.999989 + 0.00459175i \(0.998538\pi\)
\(930\) −5.52551e62 4.03978e62i −2.53648 1.85445i
\(931\) −1.50106e62 −0.673684
\(932\) 3.43058e62i 1.50534i
\(933\) 8.59102e58 1.17506e59i 0.000368579 0.000504133i
\(934\) −7.00844e62 −2.93993
\(935\) 1.57455e62i 0.645823i
\(936\) 9.57790e61 3.04894e61i 0.384130 0.122280i
\(937\) 4.26896e62 1.67414 0.837069 0.547098i \(-0.184268\pi\)
0.837069 + 0.547098i \(0.184268\pi\)
\(938\) 1.95897e61i 0.0751223i
\(939\) 1.54590e62 + 1.13023e62i 0.579701 + 0.423827i
\(940\) 8.39624e62 3.07893
\(941\) 2.64347e62i 0.947965i −0.880534 0.473983i \(-0.842816\pi\)
0.880534 0.473983i \(-0.157184\pi\)
\(942\) −1.22596e62 + 1.67683e62i −0.429939 + 0.588059i
\(943\) 1.23663e62 0.424124
\(944\) 5.45264e62i 1.82892i
\(945\) −7.65586e61 2.56358e61i −0.251146 0.0840967i
\(946\) −2.44531e62 −0.784548
\(947\) 2.63301e62i 0.826235i 0.910678 + 0.413117i \(0.135560\pi\)
−0.910678 + 0.413117i \(0.864440\pi\)
\(948\) −7.06081e61 5.16226e61i −0.216710 0.158440i
\(949\) −5.20780e61 −0.156338
\(950\) 1.14970e63i 3.37590i
\(951\) −8.96741e61 + 1.22654e62i −0.257559 + 0.352282i
\(952\) −8.89390e61 −0.249871
\(953\) 4.85271e62i 1.33362i −0.745227 0.666811i \(-0.767659\pi\)
0.745227 0.666811i \(-0.232341\pi\)
\(954\) −5.88618e61 1.84908e62i −0.158240 0.497095i
\(955\) −1.33066e61 −0.0349941
\(956\) 7.28763e62i 1.87487i
\(957\) −8.43945e61 6.17020e61i −0.212404 0.155292i
\(958\) −6.29993e62 −1.55117
\(959\) 6.28291e61i 0.151346i
\(960\) −2.05485e62 + 2.81057e62i −0.484265 + 0.662366i
\(961\) −7.37953e61 −0.170152
\(962\) 4.49784e61i 0.101468i
\(963\) 6.16514e62 1.96255e62i 1.36079 0.433181i
\(964\) −4.32117e62 −0.933220
\(965\) 1.50426e63i 3.17869i
\(966\) 5.73151e61 + 4.19039e61i 0.118508 + 0.0866432i
\(967\) −4.76466e62 −0.963998 −0.481999 0.876172i \(-0.660089\pi\)
−0.481999 + 0.876172i \(0.660089\pi\)
\(968\) 8.94033e62i 1.76999i
\(969\) 1.86119e62 2.54568e62i 0.360571 0.493180i
\(970\) 2.91549e63 5.52720
\(971\) 6.87992e61i 0.127638i −0.997961 0.0638189i \(-0.979672\pi\)
0.997961 0.0638189i \(-0.0203280\pi\)
\(972\) −1.18842e63 1.77428e61i −2.15764 0.0322129i
\(973\) −5.27733e60 −0.00937659
\(974\) 2.09430e62i 0.364168i
\(975\) −2.57193e62 1.88038e62i −0.437686 0.319998i
\(976\) 1.00292e63 1.67040
\(977\) 3.25635e62i 0.530818i 0.964136 + 0.265409i \(0.0855070\pi\)
−0.964136 + 0.265409i \(0.914493\pi\)
\(978\) −6.56006e62 + 8.97269e62i −1.04663 + 1.43155i
\(979\) −2.64479e62 −0.413005
\(980\) 2.68926e63i 4.11041i
\(981\) 2.68370e62 + 8.43055e62i 0.401499 + 1.26127i
\(982\) −1.16090e63 −1.70002
\(983\) 8.96354e62i 1.28486i 0.766344 + 0.642430i \(0.222074\pi\)
−0.766344 + 0.642430i \(0.777926\pi\)
\(984\) 8.29290e62 + 6.06305e62i 1.16361 + 0.850735i
\(985\) −3.88614e62 −0.533775
\(986\) 8.27788e62i 1.11302i
\(987\) −4.49771e61 + 6.15186e61i −0.0592014 + 0.0809742i
\(988\) 2.25226e62 0.290217
\(989\) 5.66738e62i 0.714925i
\(990\) 9.94986e62 3.16734e62i 1.22879 0.391161i
\(991\) 1.51607e62 0.183304 0.0916522 0.995791i \(-0.470785\pi\)
0.0916522 + 0.995791i \(0.470785\pi\)
\(992\) 4.65896e62i 0.551498i
\(993\) 1.24804e63 + 9.12457e62i 1.44642 + 1.05749i
\(994\) 2.84372e62 0.322681
\(995\) 2.60175e62i 0.289056i
\(996\) 1.20973e63 1.65463e63i 1.31596 1.79993i
\(997\) 1.51339e63 1.61195 0.805975 0.591949i \(-0.201641\pi\)
0.805975 + 0.591949i \(0.201641\pi\)
\(998\) 2.06469e63i 2.15335i
\(999\) 9.06158e61 2.70615e62i 0.0925398 0.276361i
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 3.43.b.b.2.2 12
3.2 odd 2 inner 3.43.b.b.2.11 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.43.b.b.2.2 12 1.1 even 1 trivial
3.43.b.b.2.11 yes 12 3.2 odd 2 inner