Properties

Label 3.37.b.b.2.4
Level $3$
Weight $37$
Character 3.2
Analytic conductor $24.627$
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] = [3,37,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, 37, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 37);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 37 \)
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: \(24.6273775978\)
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: \( x^{10} + 1732091138 x^{8} + \cdots + 87\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{44}\cdot 3^{71}\cdot 5^{4}\cdot 7^{2}\cdot 13 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.4
Root \(-10236.4i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.37.b.b.2.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-184256. i q^{2} +(7.73223e7 + 3.79626e8i) q^{3} +3.47692e10 q^{4} -1.78906e12i q^{5} +(6.99484e13 - 1.42471e13i) q^{6} -1.12077e15 q^{7} -1.90684e16i q^{8} +(-1.38137e17 + 5.87071e16i) q^{9} +O(q^{10})\) \(q-184256. i q^{2} +(7.73223e7 + 3.79626e8i) q^{3} +3.47692e10 q^{4} -1.78906e12i q^{5} +(6.99484e13 - 1.42471e13i) q^{6} -1.12077e15 q^{7} -1.90684e16i q^{8} +(-1.38137e17 + 5.87071e16i) q^{9} -3.29645e17 q^{10} -3.23174e18i q^{11} +(2.68843e18 + 1.31993e19i) q^{12} +1.98159e20 q^{13} +2.06509e20i q^{14} +(6.79173e20 - 1.38334e20i) q^{15} -1.12415e21 q^{16} -9.74924e21i q^{17} +(1.08171e22 + 2.54526e22i) q^{18} -4.96441e22 q^{19} -6.22041e22i q^{20} +(-8.66605e22 - 4.25473e23i) q^{21} -5.95467e23 q^{22} -1.29913e24i q^{23} +(7.23886e24 - 1.47441e24i) q^{24} +1.13512e25 q^{25} -3.65119e25i q^{26} +(-3.29678e25 - 4.79011e25i) q^{27} -3.89682e25 q^{28} -3.60149e26i q^{29} +(-2.54889e25 - 1.25142e26i) q^{30} +7.63484e26 q^{31} -1.10324e27i q^{32} +(1.22685e27 - 2.49885e26i) q^{33} -1.79636e27 q^{34} +2.00512e27i q^{35} +(-4.80292e27 + 2.04120e27i) q^{36} -3.30211e27 q^{37} +9.14724e27i q^{38} +(1.53221e28 + 7.52261e28i) q^{39} -3.41145e28 q^{40} +1.75258e28i q^{41} +(-7.83960e28 + 1.59677e28i) q^{42} +2.19776e29 q^{43} -1.12365e29i q^{44} +(1.05030e29 + 2.47135e29i) q^{45} -2.39373e29 q^{46} -2.28804e30i q^{47} +(-8.69219e28 - 4.26757e29i) q^{48} -1.39561e30 q^{49} -2.09153e30i q^{50} +(3.70107e30 - 7.53834e29i) q^{51} +6.88981e30 q^{52} +8.49778e30i q^{53} +(-8.82606e30 + 6.07452e30i) q^{54} -5.78176e30 q^{55} +2.13713e31i q^{56} +(-3.83860e30 - 1.88462e31i) q^{57} -6.63597e31 q^{58} +1.12146e32i q^{59} +(2.36143e31 - 4.80976e30i) q^{60} +1.74183e32 q^{61} -1.40677e32i q^{62} +(1.54820e32 - 6.57972e31i) q^{63} -2.80530e32 q^{64} -3.54517e32i q^{65} +(-4.60429e31 - 2.26055e32i) q^{66} -2.93948e32 q^{67} -3.38973e32i q^{68} +(4.93184e32 - 1.00452e32i) q^{69} +3.69456e32 q^{70} +3.75606e32i q^{71} +(1.11945e33 + 2.63406e33i) q^{72} -2.87128e33 q^{73} +6.08433e32i q^{74} +(8.77700e32 + 4.30921e33i) q^{75} -1.72609e33 q^{76} +3.62203e33i q^{77} +(1.38609e34 - 2.82319e33i) q^{78} -2.55540e34 q^{79} +2.01117e33i q^{80} +(1.56353e34 - 1.62193e34i) q^{81} +3.22923e33 q^{82} -2.12898e34i q^{83} +(-3.01311e33 - 1.47934e34i) q^{84} -1.74420e34 q^{85} -4.04951e34i q^{86} +(1.36722e35 - 2.78476e34i) q^{87} -6.16241e34 q^{88} +1.66287e35i q^{89} +(4.55362e34 - 1.93525e34i) q^{90} -2.22090e35 q^{91} -4.51697e34i q^{92} +(5.90344e34 + 2.89838e35i) q^{93} -4.21585e35 q^{94} +8.88162e34i q^{95} +(4.18818e35 - 8.53051e34i) q^{96} +3.09990e35 q^{97} +2.57149e35i q^{98} +(1.89726e35 + 4.46423e35i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 69\!\cdots\!78 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 29\!\cdots\!20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 184256.i 0.702881i −0.936210 0.351441i \(-0.885692\pi\)
0.936210 0.351441i \(-0.114308\pi\)
\(3\) 7.73223e7 + 3.79626e8i 0.199582 + 0.979881i
\(4\) 3.47692e10 0.505958
\(5\) 1.78906e12i 0.468991i −0.972117 0.234495i \(-0.924656\pi\)
0.972117 0.234495i \(-0.0753438\pi\)
\(6\) 6.99484e13 1.42471e13i 0.688740 0.140283i
\(7\) −1.12077e15 −0.688258 −0.344129 0.938922i \(-0.611826\pi\)
−0.344129 + 0.938922i \(0.611826\pi\)
\(8\) 1.90684e16i 1.05851i
\(9\) −1.38137e17 + 5.87071e16i −0.920334 + 0.391134i
\(10\) −3.29645e17 −0.329645
\(11\) 3.23174e18i 0.581256i −0.956836 0.290628i \(-0.906136\pi\)
0.956836 0.290628i \(-0.0938643\pi\)
\(12\) 2.68843e18 + 1.31993e19i 0.100980 + 0.495779i
\(13\) 1.98159e20 1.76211 0.881054 0.473016i \(-0.156835\pi\)
0.881054 + 0.473016i \(0.156835\pi\)
\(14\) 2.06509e20i 0.483764i
\(15\) 6.79173e20 1.38334e20i 0.459555 0.0936023i
\(16\) −1.12415e21 −0.238048
\(17\) 9.74924e21i 0.693251i −0.938004 0.346625i \(-0.887328\pi\)
0.938004 0.346625i \(-0.112672\pi\)
\(18\) 1.08171e22 + 2.54526e22i 0.274921 + 0.646885i
\(19\) −4.96441e22 −0.476764 −0.238382 0.971171i \(-0.576617\pi\)
−0.238382 + 0.971171i \(0.576617\pi\)
\(20\) 6.22041e22i 0.237290i
\(21\) −8.66605e22 4.25473e23i −0.137364 0.674411i
\(22\) −5.95467e23 −0.408554
\(23\) 1.29913e24i 0.400453i −0.979750 0.200227i \(-0.935832\pi\)
0.979750 0.200227i \(-0.0641678\pi\)
\(24\) 7.23886e24 1.47441e24i 1.03721 0.211260i
\(25\) 1.13512e25 0.780048
\(26\) 3.65119e25i 1.23855i
\(27\) −3.29678e25 4.79011e25i −0.566947 0.823754i
\(28\) −3.89682e25 −0.348230
\(29\) 3.60149e26i 1.71127i −0.517579 0.855635i \(-0.673167\pi\)
0.517579 0.855635i \(-0.326833\pi\)
\(30\) −2.54889e25 1.25142e26i −0.0657913 0.323013i
\(31\) 7.63484e26 1.09217 0.546084 0.837730i \(-0.316118\pi\)
0.546084 + 0.837730i \(0.316118\pi\)
\(32\) 1.10324e27i 0.891190i
\(33\) 1.22685e27 2.49885e26i 0.569562 0.116009i
\(34\) −1.79636e27 −0.487273
\(35\) 2.00512e27i 0.322787i
\(36\) −4.80292e27 + 2.04120e27i −0.465650 + 0.197897i
\(37\) −3.30211e27 −0.195506 −0.0977530 0.995211i \(-0.531166\pi\)
−0.0977530 + 0.995211i \(0.531166\pi\)
\(38\) 9.14724e27i 0.335108i
\(39\) 1.53221e28 + 7.52261e28i 0.351686 + 1.72666i
\(40\) −3.41145e28 −0.496431
\(41\) 1.75258e28i 0.163519i 0.996652 + 0.0817595i \(0.0260539\pi\)
−0.996652 + 0.0817595i \(0.973946\pi\)
\(42\) −7.83960e28 + 1.59677e28i −0.474031 + 0.0965508i
\(43\) 2.19776e29 0.870059 0.435030 0.900416i \(-0.356738\pi\)
0.435030 + 0.900416i \(0.356738\pi\)
\(44\) 1.12365e29i 0.294091i
\(45\) 1.05030e29 + 2.47135e29i 0.183438 + 0.431628i
\(46\) −2.39373e29 −0.281471
\(47\) 2.28804e30i 1.82685i −0.407010 0.913424i \(-0.633429\pi\)
0.407010 0.913424i \(-0.366571\pi\)
\(48\) −8.69219e28 4.26757e29i −0.0475102 0.233259i
\(49\) −1.39561e30 −0.526300
\(50\) 2.09153e30i 0.548281i
\(51\) 3.70107e30 7.53834e29i 0.679303 0.138361i
\(52\) 6.88981e30 0.891553
\(53\) 8.49778e30i 0.780440i 0.920722 + 0.390220i \(0.127601\pi\)
−0.920722 + 0.390220i \(0.872399\pi\)
\(54\) −8.82606e30 + 6.07452e30i −0.579001 + 0.398497i
\(55\) −5.78176e30 −0.272604
\(56\) 2.13713e31i 0.728528i
\(57\) −3.83860e30 1.88462e31i −0.0951537 0.467172i
\(58\) −6.63597e31 −1.20282
\(59\) 1.12146e32i 1.49433i 0.664638 + 0.747166i \(0.268586\pi\)
−0.664638 + 0.747166i \(0.731414\pi\)
\(60\) 2.36143e31 4.80976e30i 0.232516 0.0473589i
\(61\) 1.74183e32 1.27371 0.636854 0.770985i \(-0.280236\pi\)
0.636854 + 0.770985i \(0.280236\pi\)
\(62\) 1.40677e32i 0.767664i
\(63\) 1.54820e32 6.57972e31i 0.633427 0.269201i
\(64\) −2.80530e32 −0.864449
\(65\) 3.54517e32i 0.826412i
\(66\) −4.60429e31 2.26055e32i −0.0815402 0.400334i
\(67\) −2.93948e32 −0.397123 −0.198561 0.980088i \(-0.563627\pi\)
−0.198561 + 0.980088i \(0.563627\pi\)
\(68\) 3.38973e32i 0.350756i
\(69\) 4.93184e32 1.00452e32i 0.392397 0.0799234i
\(70\) 3.69456e32 0.226881
\(71\) 3.75606e32i 0.178683i 0.996001 + 0.0893413i \(0.0284762\pi\)
−0.996001 + 0.0893413i \(0.971524\pi\)
\(72\) 1.11945e33 + 2.63406e33i 0.414019 + 0.974182i
\(73\) −2.87128e33 −0.828446 −0.414223 0.910175i \(-0.635947\pi\)
−0.414223 + 0.910175i \(0.635947\pi\)
\(74\) 6.08433e32i 0.137417i
\(75\) 8.77700e32 + 4.30921e33i 0.155684 + 0.764354i
\(76\) −1.72609e33 −0.241223
\(77\) 3.62203e33i 0.400055i
\(78\) 1.38609e34 2.82319e33i 1.21363 0.247193i
\(79\) −2.55540e34 −1.77898 −0.889491 0.456953i \(-0.848941\pi\)
−0.889491 + 0.456953i \(0.848941\pi\)
\(80\) 2.01117e33i 0.111642i
\(81\) 1.56353e34 1.62193e34i 0.694028 0.719948i
\(82\) 3.22923e33 0.114934
\(83\) 2.12898e34i 0.609209i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985243\pi\)
\(84\) −3.01311e33 1.47934e34i −0.0695006 0.341224i
\(85\) −1.74420e34 −0.325128
\(86\) 4.04951e34i 0.611548i
\(87\) 1.36722e35 2.78476e34i 1.67684 0.341540i
\(88\) −6.16241e34 −0.615265
\(89\) 1.66287e35i 1.35468i 0.735670 + 0.677340i \(0.236867\pi\)
−0.735670 + 0.677340i \(0.763133\pi\)
\(90\) 4.55362e34 1.93525e34i 0.303383 0.128935i
\(91\) −2.22090e35 −1.21279
\(92\) 4.51697e34i 0.202613i
\(93\) 5.90344e34 + 2.89838e35i 0.217978 + 1.07019i
\(94\) −4.21585e35 −1.28406
\(95\) 8.88162e34i 0.223598i
\(96\) 4.18818e35 8.53051e34i 0.873260 0.177866i
\(97\) 3.09990e35 0.536360 0.268180 0.963369i \(-0.413578\pi\)
0.268180 + 0.963369i \(0.413578\pi\)
\(98\) 2.57149e35i 0.369926i
\(99\) 1.89726e35 + 4.46423e35i 0.227349 + 0.534950i
\(100\) 3.94671e35 0.394671
\(101\) 1.10326e36i 0.922347i −0.887310 0.461174i \(-0.847429\pi\)
0.887310 0.461174i \(-0.152571\pi\)
\(102\) −1.38899e35 6.81944e35i −0.0972511 0.477469i
\(103\) −1.74073e36 −1.02249 −0.511247 0.859434i \(-0.670816\pi\)
−0.511247 + 0.859434i \(0.670816\pi\)
\(104\) 3.77857e36i 1.86521i
\(105\) −7.61196e35 + 1.55041e35i −0.316293 + 0.0644226i
\(106\) 1.56577e36 0.548557
\(107\) 4.62581e36i 1.36861i 0.729196 + 0.684305i \(0.239894\pi\)
−0.729196 + 0.684305i \(0.760106\pi\)
\(108\) −1.14626e36 1.66548e36i −0.286852 0.416785i
\(109\) 4.26215e36 0.903550 0.451775 0.892132i \(-0.350791\pi\)
0.451775 + 0.892132i \(0.350791\pi\)
\(110\) 1.06533e36i 0.191608i
\(111\) −2.55327e35 1.25357e36i −0.0390196 0.191573i
\(112\) 1.25991e36 0.163839
\(113\) 1.56660e37i 1.73598i 0.496578 + 0.867992i \(0.334590\pi\)
−0.496578 + 0.867992i \(0.665410\pi\)
\(114\) −3.47253e36 + 7.07285e35i −0.328366 + 0.0668817i
\(115\) −2.32422e36 −0.187809
\(116\) 1.25221e37i 0.865831i
\(117\) −2.73731e37 + 1.16333e37i −1.62173 + 0.689220i
\(118\) 2.06636e37 1.05034
\(119\) 1.09267e37i 0.477136i
\(120\) −2.63781e36 1.29507e37i −0.0990789 0.486443i
\(121\) 2.04686e37 0.662141
\(122\) 3.20943e37i 0.895265i
\(123\) −6.65325e36 + 1.35513e36i −0.160229 + 0.0326355i
\(124\) 2.65457e37 0.552591
\(125\) 4.63421e37i 0.834826i
\(126\) −1.21235e37 2.85265e37i −0.189217 0.445224i
\(127\) 1.49422e36 0.0202277 0.0101138 0.999949i \(-0.496781\pi\)
0.0101138 + 0.999949i \(0.496781\pi\)
\(128\) 2.41248e37i 0.283585i
\(129\) 1.69936e37 + 8.34328e37i 0.173649 + 0.852554i
\(130\) −6.53219e37 −0.580869
\(131\) 3.94725e37i 0.305781i 0.988243 + 0.152891i \(0.0488582\pi\)
−0.988243 + 0.152891i \(0.951142\pi\)
\(132\) 4.26566e37 8.68831e36i 0.288175 0.0586955i
\(133\) 5.56396e37 0.328137
\(134\) 5.41618e37i 0.279130i
\(135\) −8.56978e37 + 5.89814e37i −0.386333 + 0.265893i
\(136\) −1.85903e38 −0.733813
\(137\) 4.00656e38i 1.38612i 0.720878 + 0.693062i \(0.243739\pi\)
−0.720878 + 0.693062i \(0.756261\pi\)
\(138\) −1.85089e37 9.08721e37i −0.0561767 0.275808i
\(139\) −1.96149e38 −0.522781 −0.261390 0.965233i \(-0.584181\pi\)
−0.261390 + 0.965233i \(0.584181\pi\)
\(140\) 6.97164e37i 0.163317i
\(141\) 8.68600e38 1.76917e38i 1.79009 0.364607i
\(142\) 6.92077e37 0.125593
\(143\) 6.40396e38i 1.02424i
\(144\) 1.55287e38 6.59957e37i 0.219084 0.0931088i
\(145\) −6.44328e38 −0.802570
\(146\) 5.29051e38i 0.582299i
\(147\) −1.07912e38 5.29809e38i −0.105040 0.515712i
\(148\) −1.14812e38 −0.0989178
\(149\) 2.06248e39i 1.57412i −0.616878 0.787059i \(-0.711603\pi\)
0.616878 0.787059i \(-0.288397\pi\)
\(150\) 7.93997e38 1.61722e38i 0.537250 0.109427i
\(151\) −1.90467e39 −1.14350 −0.571749 0.820428i \(-0.693735\pi\)
−0.571749 + 0.820428i \(0.693735\pi\)
\(152\) 9.46635e38i 0.504659i
\(153\) 5.72350e38 + 1.34673e39i 0.271154 + 0.638022i
\(154\) 6.67381e38 0.281191
\(155\) 1.36592e39i 0.512217i
\(156\) 5.32736e38 + 2.61555e39i 0.177938 + 0.873616i
\(157\) 4.18282e39 1.24530 0.622651 0.782499i \(-0.286055\pi\)
0.622651 + 0.782499i \(0.286055\pi\)
\(158\) 4.70848e39i 1.25041i
\(159\) −3.22598e39 + 6.57068e38i −0.764739 + 0.155762i
\(160\) −1.97376e39 −0.417960
\(161\) 1.45603e39i 0.275615i
\(162\) −2.98850e39 2.88091e39i −0.506038 0.487819i
\(163\) −8.81419e38 −0.133600 −0.0667999 0.997766i \(-0.521279\pi\)
−0.0667999 + 0.997766i \(0.521279\pi\)
\(164\) 6.09357e38i 0.0827338i
\(165\) −4.47059e38 2.19491e39i −0.0544069 0.267119i
\(166\) −3.92278e39 −0.428201
\(167\) 1.25263e40i 1.22723i −0.789604 0.613617i \(-0.789714\pi\)
0.789604 0.613617i \(-0.210286\pi\)
\(168\) −8.11310e39 + 1.65248e39i −0.713871 + 0.145401i
\(169\) 2.66206e40 2.10502
\(170\) 3.21379e39i 0.228526i
\(171\) 6.85770e39 2.91447e39i 0.438782 0.186479i
\(172\) 7.64144e39 0.440214
\(173\) 1.13842e39i 0.0590842i 0.999564 + 0.0295421i \(0.00940491\pi\)
−0.999564 + 0.0295421i \(0.990595\pi\)
\(174\) −5.13109e39 2.51919e40i −0.240062 1.17862i
\(175\) −1.27221e40 −0.536874
\(176\) 3.63296e39i 0.138367i
\(177\) −4.25735e40 + 8.67138e39i −1.46427 + 0.298242i
\(178\) 3.06393e40 0.952179
\(179\) 7.98758e38i 0.0224420i −0.999937 0.0112210i \(-0.996428\pi\)
0.999937 0.0112210i \(-0.00357182\pi\)
\(180\) 3.65182e39 + 8.59269e39i 0.0928121 + 0.218386i
\(181\) −2.00135e40 −0.460372 −0.230186 0.973147i \(-0.573933\pi\)
−0.230186 + 0.973147i \(0.573933\pi\)
\(182\) 4.09214e40i 0.852444i
\(183\) 1.34683e40 + 6.61245e40i 0.254210 + 1.24808i
\(184\) −2.47724e40 −0.423884
\(185\) 5.90766e39i 0.0916905i
\(186\) 5.34045e40 1.08774e40i 0.752220 0.153212i
\(187\) −3.15070e40 −0.402956
\(188\) 7.95533e40i 0.924308i
\(189\) 3.69493e40 + 5.36861e40i 0.390206 + 0.566956i
\(190\) 1.63649e40 0.157163
\(191\) 7.86625e39i 0.0687333i 0.999409 + 0.0343666i \(0.0109414\pi\)
−0.999409 + 0.0343666i \(0.989059\pi\)
\(192\) −2.16912e40 1.06496e41i −0.172529 0.847057i
\(193\) −8.42492e40 −0.610287 −0.305143 0.952306i \(-0.598704\pi\)
−0.305143 + 0.952306i \(0.598704\pi\)
\(194\) 5.71175e40i 0.376997i
\(195\) 1.34584e41 2.74121e40i 0.809786 0.164937i
\(196\) −4.85241e40 −0.266286
\(197\) 2.05769e40i 0.103036i −0.998672 0.0515180i \(-0.983594\pi\)
0.998672 0.0515180i \(-0.0164059\pi\)
\(198\) 8.22561e40 3.49582e40i 0.376006 0.159799i
\(199\) −2.79071e40 −0.116509 −0.0582544 0.998302i \(-0.518553\pi\)
−0.0582544 + 0.998302i \(0.518553\pi\)
\(200\) 2.16449e41i 0.825688i
\(201\) −2.27288e40 1.11590e41i −0.0792587 0.389133i
\(202\) −2.03283e41 −0.648300
\(203\) 4.03644e41i 1.17780i
\(204\) 1.28683e41 2.62102e40i 0.343699 0.0700047i
\(205\) 3.13547e40 0.0766889
\(206\) 3.20740e41i 0.718692i
\(207\) 7.62682e40 + 1.79458e41i 0.156631 + 0.368551i
\(208\) −2.22760e41 −0.419467
\(209\) 1.60437e41i 0.277122i
\(210\) 2.85672e40 + 1.40255e41i 0.0452814 + 0.222316i
\(211\) 2.27251e41 0.330690 0.165345 0.986236i \(-0.447126\pi\)
0.165345 + 0.986236i \(0.447126\pi\)
\(212\) 2.95461e41i 0.394870i
\(213\) −1.42590e41 + 2.90427e40i −0.175088 + 0.0356619i
\(214\) 8.52334e41 0.961970
\(215\) 3.93193e41i 0.408050i
\(216\) −9.13398e41 + 6.28644e41i −0.871952 + 0.600119i
\(217\) −8.55690e41 −0.751694
\(218\) 7.85328e41i 0.635088i
\(219\) −2.22014e41 1.09001e42i −0.165343 0.811779i
\(220\) −2.01027e41 −0.137926
\(221\) 1.93190e42i 1.22158i
\(222\) −2.30977e41 + 4.70455e40i −0.134653 + 0.0274261i
\(223\) 2.70449e42 1.45411 0.727056 0.686578i \(-0.240888\pi\)
0.727056 + 0.686578i \(0.240888\pi\)
\(224\) 1.23648e42i 0.613369i
\(225\) −1.56802e42 + 6.66396e41i −0.717904 + 0.305103i
\(226\) 2.88655e42 1.22019
\(227\) 2.11376e42i 0.825257i −0.910899 0.412629i \(-0.864611\pi\)
0.910899 0.412629i \(-0.135389\pi\)
\(228\) −1.33465e41 6.55267e41i −0.0481438 0.236369i
\(229\) 2.93053e42 0.977030 0.488515 0.872556i \(-0.337539\pi\)
0.488515 + 0.872556i \(0.337539\pi\)
\(230\) 4.28252e41i 0.132007i
\(231\) −1.37502e42 + 2.80064e41i −0.392006 + 0.0798439i
\(232\) −6.86748e42 −1.81140
\(233\) 3.38086e42i 0.825316i 0.910886 + 0.412658i \(0.135399\pi\)
−0.910886 + 0.412658i \(0.864601\pi\)
\(234\) 2.14351e42 + 5.04365e42i 0.484440 + 1.13988i
\(235\) −4.09344e42 −0.856775
\(236\) 3.89922e42i 0.756069i
\(237\) −1.97590e42 9.70097e42i −0.355053 1.74319i
\(238\) 2.01330e42 0.335370
\(239\) 6.94508e42i 1.07279i 0.843967 + 0.536396i \(0.180215\pi\)
−0.843967 + 0.536396i \(0.819785\pi\)
\(240\) −7.63493e41 + 1.55508e41i −0.109396 + 0.0222819i
\(241\) 2.49680e42 0.331954 0.165977 0.986130i \(-0.446922\pi\)
0.165977 + 0.986130i \(0.446922\pi\)
\(242\) 3.77146e42i 0.465406i
\(243\) 7.36622e42 + 4.68147e42i 0.843979 + 0.536376i
\(244\) 6.05621e42 0.644443
\(245\) 2.49682e42i 0.246830i
\(246\) 2.49692e41 + 1.22590e42i 0.0229389 + 0.112622i
\(247\) −9.83741e42 −0.840109
\(248\) 1.45584e43i 1.15607i
\(249\) 8.08217e42 1.64618e42i 0.596952 0.121587i
\(250\) −8.53882e42 −0.586783
\(251\) 2.20823e43i 1.41227i −0.708077 0.706136i \(-0.750437\pi\)
0.708077 0.706136i \(-0.249563\pi\)
\(252\) 5.38296e42 2.28771e42i 0.320488 0.136205i
\(253\) −4.19845e42 −0.232766
\(254\) 2.75318e41i 0.0142177i
\(255\) −1.34865e42 6.62142e42i −0.0648899 0.318587i
\(256\) −2.37230e43 −1.06378
\(257\) 2.21794e43i 0.927157i 0.886056 + 0.463579i \(0.153435\pi\)
−0.886056 + 0.463579i \(0.846565\pi\)
\(258\) 1.53730e43 3.13118e42i 0.599244 0.122054i
\(259\) 3.70090e42 0.134559
\(260\) 1.23263e43i 0.418130i
\(261\) 2.11433e43 + 4.97500e43i 0.669336 + 1.57494i
\(262\) 7.27304e42 0.214928
\(263\) 3.11959e43i 0.860785i 0.902642 + 0.430392i \(0.141625\pi\)
−0.902642 + 0.430392i \(0.858375\pi\)
\(264\) −4.76492e42 2.33941e43i −0.122796 0.602887i
\(265\) 1.52030e43 0.366019
\(266\) 1.02519e43i 0.230641i
\(267\) −6.31267e43 + 1.28577e43i −1.32743 + 0.270370i
\(268\) −1.02203e43 −0.200927
\(269\) 4.50123e43i 0.827543i 0.910381 + 0.413771i \(0.135789\pi\)
−0.910381 + 0.413771i \(0.864211\pi\)
\(270\) 1.08677e43 + 1.57903e43i 0.186891 + 0.271546i
\(271\) −3.68709e42 −0.0593248 −0.0296624 0.999560i \(-0.509443\pi\)
−0.0296624 + 0.999560i \(0.509443\pi\)
\(272\) 1.09596e43i 0.165027i
\(273\) −1.71725e43 8.43112e43i −0.242051 1.18839i
\(274\) 7.38234e43 0.974280
\(275\) 3.66841e43i 0.453408i
\(276\) 1.71476e43 3.49263e42i 0.198536 0.0404379i
\(277\) −1.53564e43 −0.166592 −0.0832960 0.996525i \(-0.526545\pi\)
−0.0832960 + 0.996525i \(0.526545\pi\)
\(278\) 3.61416e43i 0.367453i
\(279\) −1.05466e44 + 4.48220e43i −1.00516 + 0.427184i
\(280\) 3.82345e43 0.341673
\(281\) 1.68902e44i 1.41554i −0.706445 0.707768i \(-0.749702\pi\)
0.706445 0.707768i \(-0.250298\pi\)
\(282\) −3.25980e43 1.60045e44i −0.256275 1.25822i
\(283\) 1.87568e44 1.38357 0.691786 0.722102i \(-0.256824\pi\)
0.691786 + 0.722102i \(0.256824\pi\)
\(284\) 1.30595e43i 0.0904059i
\(285\) −3.37170e43 + 6.86748e42i −0.219099 + 0.0446262i
\(286\) −1.17997e44 −0.719916
\(287\) 1.96424e43i 0.112543i
\(288\) 6.47680e43 + 1.52398e44i 0.348575 + 0.820192i
\(289\) 1.02723e44 0.519403
\(290\) 1.18721e44i 0.564111i
\(291\) 2.39691e43 + 1.17680e44i 0.107048 + 0.525569i
\(292\) −9.98321e43 −0.419159
\(293\) 6.94199e43i 0.274073i 0.990566 + 0.137037i \(0.0437578\pi\)
−0.990566 + 0.137037i \(0.956242\pi\)
\(294\) −9.76204e43 + 1.98834e43i −0.362484 + 0.0738308i
\(295\) 2.00635e44 0.700828
\(296\) 6.29659e43i 0.206945i
\(297\) −1.54804e44 + 1.06543e44i −0.478812 + 0.329542i
\(298\) −3.80025e44 −1.10642
\(299\) 2.57434e44i 0.705642i
\(300\) 3.05169e43 + 1.49828e44i 0.0787695 + 0.386731i
\(301\) −2.46319e44 −0.598826
\(302\) 3.50948e44i 0.803744i
\(303\) 4.18827e44 8.53069e43i 0.903791 0.184084i
\(304\) 5.58075e43 0.113493
\(305\) 3.11624e44i 0.597357i
\(306\) 2.48144e44 1.05459e44i 0.448454 0.190589i
\(307\) 1.59238e44 0.271366 0.135683 0.990752i \(-0.456677\pi\)
0.135683 + 0.990752i \(0.456677\pi\)
\(308\) 1.25935e44i 0.202411i
\(309\) −1.34597e44 6.60825e44i −0.204072 1.00192i
\(310\) −2.51678e44 −0.360027
\(311\) 2.11490e44i 0.285498i 0.989759 + 0.142749i \(0.0455942\pi\)
−0.989759 + 0.142749i \(0.954406\pi\)
\(312\) 1.43444e45 2.92168e44i 1.82768 0.372263i
\(313\) −6.34982e43 −0.0763771 −0.0381885 0.999271i \(-0.512159\pi\)
−0.0381885 + 0.999271i \(0.512159\pi\)
\(314\) 7.70709e44i 0.875300i
\(315\) −1.17715e44 2.76982e44i −0.126253 0.297072i
\(316\) −8.88492e44 −0.900090
\(317\) 2.83676e44i 0.271491i −0.990744 0.135745i \(-0.956657\pi\)
0.990744 0.135745i \(-0.0433429\pi\)
\(318\) 1.21069e44 + 5.94406e44i 0.109482 + 0.537520i
\(319\) −1.16391e45 −0.994687
\(320\) 5.01884e44i 0.405418i
\(321\) −1.75608e45 + 3.57678e44i −1.34108 + 0.273151i
\(322\) 2.68282e44 0.193725
\(323\) 4.83993e44i 0.330517i
\(324\) 5.43628e44 5.63931e44i 0.351149 0.364263i
\(325\) 2.24933e45 1.37453
\(326\) 1.62407e44i 0.0939047i
\(327\) 3.29560e44 + 1.61802e45i 0.180333 + 0.885371i
\(328\) 3.34189e44 0.173086
\(329\) 2.56437e45i 1.25734i
\(330\) −4.04425e44 + 8.23734e43i −0.187753 + 0.0382416i
\(331\) 7.89685e44 0.347176 0.173588 0.984818i \(-0.444464\pi\)
0.173588 + 0.984818i \(0.444464\pi\)
\(332\) 7.40230e44i 0.308234i
\(333\) 4.56144e44 1.93857e44i 0.179931 0.0764691i
\(334\) −2.30805e45 −0.862599
\(335\) 5.25891e44i 0.186247i
\(336\) 9.74195e43 + 4.78296e44i 0.0326993 + 0.160542i
\(337\) 1.86680e45 0.593963 0.296982 0.954883i \(-0.404020\pi\)
0.296982 + 0.954883i \(0.404020\pi\)
\(338\) 4.90500e45i 1.47958i
\(339\) −5.94722e45 + 1.21133e45i −1.70106 + 0.346472i
\(340\) −6.06443e44 −0.164501
\(341\) 2.46738e45i 0.634830i
\(342\) −5.37008e44 1.26357e45i −0.131072 0.308411i
\(343\) 4.53613e45 1.05049
\(344\) 4.19079e45i 0.920966i
\(345\) −1.79714e44 8.82334e44i −0.0374833 0.184030i
\(346\) 2.09760e44 0.0415291
\(347\) 5.41382e45i 1.01759i 0.860887 + 0.508796i \(0.169909\pi\)
−0.860887 + 0.508796i \(0.830091\pi\)
\(348\) 4.75371e45 9.68238e44i 0.848412 0.172805i
\(349\) 6.88573e45 1.16706 0.583529 0.812092i \(-0.301672\pi\)
0.583529 + 0.812092i \(0.301672\pi\)
\(350\) 2.34412e45i 0.377359i
\(351\) −6.53286e45 9.49201e45i −0.999022 1.45154i
\(352\) −3.56538e45 −0.518010
\(353\) 1.50986e45i 0.208446i 0.994554 + 0.104223i \(0.0332355\pi\)
−0.994554 + 0.104223i \(0.966764\pi\)
\(354\) 1.59775e45 + 7.84442e45i 0.209629 + 1.02921i
\(355\) 6.71981e44 0.0838005
\(356\) 5.78165e45i 0.685412i
\(357\) −4.14804e45 + 8.44874e44i −0.467536 + 0.0952279i
\(358\) −1.47176e44 −0.0157740
\(359\) 1.29291e44i 0.0131785i −0.999978 0.00658927i \(-0.997903\pi\)
0.999978 0.00658927i \(-0.00209744\pi\)
\(360\) 4.71248e45 2.00276e45i 0.456882 0.194171i
\(361\) −8.37796e45 −0.772696
\(362\) 3.68761e45i 0.323587i
\(363\) 1.58268e45 + 7.77040e45i 0.132152 + 0.648819i
\(364\) −7.72189e45 −0.613619
\(365\) 5.13689e45i 0.388534i
\(366\) 1.21838e46 2.48161e45i 0.877253 0.178679i
\(367\) −9.17946e45 −0.629257 −0.314628 0.949215i \(-0.601880\pi\)
−0.314628 + 0.949215i \(0.601880\pi\)
\(368\) 1.46042e45i 0.0953272i
\(369\) −1.02889e45 2.42096e45i −0.0639579 0.150492i
\(370\) 1.08852e45 0.0644475
\(371\) 9.52405e45i 0.537145i
\(372\) 2.05258e45 + 1.00774e46i 0.110288 + 0.541474i
\(373\) 1.89617e46 0.970773 0.485387 0.874300i \(-0.338679\pi\)
0.485387 + 0.874300i \(0.338679\pi\)
\(374\) 5.80535e45i 0.283230i
\(375\) 1.75927e46 3.58328e45i 0.818030 0.166617i
\(376\) −4.36293e46 −1.93374
\(377\) 7.13667e46i 3.01544i
\(378\) 9.89198e45 6.80814e45i 0.398502 0.274269i
\(379\) 1.40641e46 0.540266 0.270133 0.962823i \(-0.412932\pi\)
0.270133 + 0.962823i \(0.412932\pi\)
\(380\) 3.08807e45i 0.113131i
\(381\) 1.15536e44 + 5.67243e44i 0.00403709 + 0.0198207i
\(382\) 1.44940e45 0.0483113
\(383\) 3.65569e46i 1.16250i 0.813727 + 0.581248i \(0.197435\pi\)
−0.813727 + 0.581248i \(0.802565\pi\)
\(384\) 9.15839e45 1.86538e45i 0.277880 0.0565986i
\(385\) 6.48003e45 0.187622
\(386\) 1.55234e46i 0.428959i
\(387\) −3.03593e46 + 1.29024e46i −0.800745 + 0.340310i
\(388\) 1.07781e46 0.271376
\(389\) 2.13748e46i 0.513819i −0.966435 0.256910i \(-0.917296\pi\)
0.966435 0.256910i \(-0.0827042\pi\)
\(390\) −5.05084e45 2.47979e46i −0.115931 0.569183i
\(391\) −1.26655e46 −0.277614
\(392\) 2.66120e46i 0.557094i
\(393\) −1.49848e46 + 3.05210e45i −0.299629 + 0.0610286i
\(394\) −3.79143e45 −0.0724220
\(395\) 4.57176e46i 0.834326i
\(396\) 6.59662e45 + 1.55218e46i 0.115029 + 0.270662i
\(397\) −3.23014e46 −0.538260 −0.269130 0.963104i \(-0.586736\pi\)
−0.269130 + 0.963104i \(0.586736\pi\)
\(398\) 5.14205e45i 0.0818919i
\(399\) 4.30219e45 + 2.11223e46i 0.0654903 + 0.321535i
\(400\) −1.27604e46 −0.185689
\(401\) 5.33934e46i 0.742829i 0.928467 + 0.371414i \(0.121127\pi\)
−0.928467 + 0.371414i \(0.878873\pi\)
\(402\) −2.05612e46 + 4.18791e45i −0.273514 + 0.0557095i
\(403\) 1.51291e47 1.92452
\(404\) 3.83596e46i 0.466669i
\(405\) −2.90172e46 2.79725e46i −0.337649 0.325493i
\(406\) 7.43739e46 0.827851
\(407\) 1.06715e46i 0.113639i
\(408\) −1.43744e46 7.05735e46i −0.146456 0.719049i
\(409\) 2.82102e46 0.275035 0.137517 0.990499i \(-0.456088\pi\)
0.137517 + 0.990499i \(0.456088\pi\)
\(410\) 5.77728e45i 0.0539032i
\(411\) −1.52100e47 + 3.09797e46i −1.35824 + 0.276646i
\(412\) −6.05237e46 −0.517339
\(413\) 1.25690e47i 1.02849i
\(414\) 3.30663e46 1.40529e46i 0.259047 0.110093i
\(415\) −3.80887e46 −0.285713
\(416\) 2.18616e47i 1.57037i
\(417\) −1.51667e46 7.44633e46i −0.104338 0.512263i
\(418\) 2.95615e46 0.194784
\(419\) 1.53626e47i 0.969647i 0.874612 + 0.484823i \(0.161116\pi\)
−0.874612 + 0.484823i \(0.838884\pi\)
\(420\) −2.64662e46 + 5.39064e45i −0.160031 + 0.0325951i
\(421\) 1.84762e46 0.107037 0.0535186 0.998567i \(-0.482956\pi\)
0.0535186 + 0.998567i \(0.482956\pi\)
\(422\) 4.18723e46i 0.232436i
\(423\) 1.34324e47 + 3.16063e47i 0.714542 + 1.68131i
\(424\) 1.62039e47 0.826104
\(425\) 1.10665e47i 0.540769i
\(426\) 5.35130e45 + 2.62730e46i 0.0250661 + 0.123066i
\(427\) −1.95219e47 −0.876640
\(428\) 1.60836e47i 0.692460i
\(429\) 2.43111e47 4.95169e46i 1.00363 0.204420i
\(430\) −7.24481e46 −0.286810
\(431\) 2.20596e47i 0.837542i 0.908092 + 0.418771i \(0.137539\pi\)
−0.908092 + 0.418771i \(0.862461\pi\)
\(432\) 3.70608e46 + 5.38480e46i 0.134961 + 0.196093i
\(433\) −2.44161e47 −0.852893 −0.426447 0.904513i \(-0.640235\pi\)
−0.426447 + 0.904513i \(0.640235\pi\)
\(434\) 1.57666e47i 0.528351i
\(435\) −4.98209e46 2.44604e47i −0.160179 0.786423i
\(436\) 1.48192e47 0.457158
\(437\) 6.44942e46i 0.190922i
\(438\) −2.00842e47 + 4.09075e46i −0.570584 + 0.116217i
\(439\) −4.59501e47 −1.25292 −0.626462 0.779452i \(-0.715498\pi\)
−0.626462 + 0.779452i \(0.715498\pi\)
\(440\) 1.10249e47i 0.288554i
\(441\) 1.92785e47 8.19321e46i 0.484372 0.205854i
\(442\) −3.55964e47 −0.858627
\(443\) 1.36833e47i 0.316900i 0.987367 + 0.158450i \(0.0506497\pi\)
−0.987367 + 0.158450i \(0.949350\pi\)
\(444\) −8.87749e45 4.35854e46i −0.0197423 0.0969277i
\(445\) 2.97496e47 0.635333
\(446\) 4.98319e47i 1.02207i
\(447\) 7.82972e47 1.59476e47i 1.54245 0.314166i
\(448\) 3.14409e47 0.594964
\(449\) 8.45639e47i 1.53727i −0.639687 0.768636i \(-0.720936\pi\)
0.639687 0.768636i \(-0.279064\pi\)
\(450\) 1.22787e47 + 2.88917e47i 0.214451 + 0.504601i
\(451\) 5.66388e46 0.0950465
\(452\) 5.44694e47i 0.878336i
\(453\) −1.47274e47 7.23064e47i −0.228222 1.12049i
\(454\) −3.89472e47 −0.580058
\(455\) 3.97332e47i 0.568785i
\(456\) −3.59367e47 + 7.31960e46i −0.494506 + 0.100721i
\(457\) 7.90122e47 1.04521 0.522604 0.852576i \(-0.324961\pi\)
0.522604 + 0.852576i \(0.324961\pi\)
\(458\) 5.39968e47i 0.686736i
\(459\) −4.66999e47 + 3.21411e47i −0.571068 + 0.393037i
\(460\) −8.08112e46 −0.0950234
\(461\) 5.44752e47i 0.616003i −0.951386 0.308001i \(-0.900340\pi\)
0.951386 0.308001i \(-0.0996601\pi\)
\(462\) 5.16035e46 + 2.53355e47i 0.0561208 + 0.275534i
\(463\) −1.52156e48 −1.59159 −0.795796 0.605565i \(-0.792947\pi\)
−0.795796 + 0.605565i \(0.792947\pi\)
\(464\) 4.04862e47i 0.407365i
\(465\) 5.18538e47 1.05616e47i 0.501911 0.102229i
\(466\) 6.22943e47 0.580099
\(467\) 6.18890e47i 0.554511i 0.960796 + 0.277255i \(0.0894248\pi\)
−0.960796 + 0.277255i \(0.910575\pi\)
\(468\) −9.51739e47 + 4.04481e47i −0.820526 + 0.348717i
\(469\) 3.29448e47 0.273323
\(470\) 7.54241e47i 0.602211i
\(471\) 3.23425e47 + 1.58791e48i 0.248541 + 1.22025i
\(472\) 2.13844e48 1.58176
\(473\) 7.10259e47i 0.505727i
\(474\) −1.78746e48 + 3.64071e47i −1.22526 + 0.249560i
\(475\) −5.63520e47 −0.371898
\(476\) 3.79911e47i 0.241411i
\(477\) −4.98880e47 1.17386e48i −0.305257 0.718266i
\(478\) 1.27967e48 0.754045
\(479\) 7.48459e47i 0.424746i 0.977189 + 0.212373i \(0.0681191\pi\)
−0.977189 + 0.212373i \(0.931881\pi\)
\(480\) −1.52616e47 7.49290e47i −0.0834174 0.409551i
\(481\) −6.54341e47 −0.344503
\(482\) 4.60051e47i 0.233324i
\(483\) −5.52745e47 + 1.12583e47i −0.270070 + 0.0550080i
\(484\) 7.11675e47 0.335016
\(485\) 5.54590e47i 0.251548i
\(486\) 8.62590e47 1.35727e48i 0.377009 0.593217i
\(487\) 1.72017e48 0.724519 0.362260 0.932077i \(-0.382005\pi\)
0.362260 + 0.932077i \(0.382005\pi\)
\(488\) 3.32140e48i 1.34823i
\(489\) −6.81534e46 3.34610e47i −0.0266642 0.130912i
\(490\) 4.60054e47 0.173492
\(491\) 7.68862e47i 0.279500i 0.990187 + 0.139750i \(0.0446299\pi\)
−0.990187 + 0.139750i \(0.955370\pi\)
\(492\) −2.31328e47 + 4.71169e46i −0.0810693 + 0.0165122i
\(493\) −3.51118e48 −1.18634
\(494\) 1.81260e48i 0.590497i
\(495\) 7.98676e47 3.39431e47i 0.250887 0.106625i
\(496\) −8.58271e47 −0.259989
\(497\) 4.20968e47i 0.122980i
\(498\) −3.03318e47 1.48919e48i −0.0854615 0.419587i
\(499\) 1.27440e48 0.346336 0.173168 0.984892i \(-0.444600\pi\)
0.173168 + 0.984892i \(0.444600\pi\)
\(500\) 1.61128e48i 0.422387i
\(501\) 4.75532e48 9.68564e47i 1.20254 0.244934i
\(502\) −4.06881e48 −0.992659
\(503\) 7.16188e48i 1.68579i 0.538078 + 0.842895i \(0.319151\pi\)
−0.538078 + 0.842895i \(0.680849\pi\)
\(504\) −1.25465e48 2.95217e48i −0.284952 0.670489i
\(505\) −1.97380e48 −0.432572
\(506\) 7.73590e47i 0.163607i
\(507\) 2.05837e48 + 1.01059e49i 0.420126 + 2.06267i
\(508\) 5.19526e46 0.0102344
\(509\) 5.76516e48i 1.09620i −0.836411 0.548102i \(-0.815350\pi\)
0.836411 0.548102i \(-0.184650\pi\)
\(510\) −1.22004e48 + 2.48497e47i −0.223929 + 0.0456099i
\(511\) 3.21805e48 0.570185
\(512\) 2.71326e48i 0.464122i
\(513\) 1.63666e48 + 2.37801e48i 0.270300 + 0.392736i
\(514\) 4.08669e48 0.651681
\(515\) 3.11426e48i 0.479540i
\(516\) 5.90854e47 + 2.90089e48i 0.0878589 + 0.431357i
\(517\) −7.39435e48 −1.06187
\(518\) 6.81913e47i 0.0945787i
\(519\) −4.32172e47 + 8.80250e46i −0.0578955 + 0.0117922i
\(520\) −6.76008e48 −0.874765
\(521\) 9.10339e48i 1.13795i −0.822354 0.568977i \(-0.807340\pi\)
0.822354 0.568977i \(-0.192660\pi\)
\(522\) 9.16674e48 3.89579e48i 1.10700 0.470464i
\(523\) −1.20984e49 −1.41155 −0.705777 0.708434i \(-0.749402\pi\)
−0.705777 + 0.708434i \(0.749402\pi\)
\(524\) 1.37243e48i 0.154713i
\(525\) −9.83700e47 4.82963e48i −0.107151 0.526073i
\(526\) 5.74804e48 0.605029
\(527\) 7.44339e48i 0.757146i
\(528\) −1.37917e48 + 2.80909e47i −0.135583 + 0.0276156i
\(529\) 8.83677e48 0.839637
\(530\) 2.80125e48i 0.257268i
\(531\) −6.58376e48 1.54915e49i −0.584484 1.37528i
\(532\) 1.93454e48 0.166023
\(533\) 3.47289e48i 0.288138i
\(534\) 2.36910e48 + 1.16315e49i 0.190038 + 0.933022i
\(535\) 8.27584e48 0.641866
\(536\) 5.60513e48i 0.420358i
\(537\) 3.03229e47 6.17618e46i 0.0219904 0.00447902i
\(538\) 8.29379e48 0.581664
\(539\) 4.51023e48i 0.305915i
\(540\) −2.97964e48 + 2.05073e48i −0.195468 + 0.134531i
\(541\) 1.75620e49 1.11435 0.557176 0.830395i \(-0.311885\pi\)
0.557176 + 0.830395i \(0.311885\pi\)
\(542\) 6.79368e47i 0.0416983i
\(543\) −1.54749e48 7.59764e48i −0.0918821 0.451109i
\(544\) −1.07558e49 −0.617818
\(545\) 7.62524e48i 0.423756i
\(546\) −1.55348e49 + 3.16414e48i −0.835294 + 0.170133i
\(547\) −1.84394e49 −0.959346 −0.479673 0.877447i \(-0.659245\pi\)
−0.479673 + 0.877447i \(0.659245\pi\)
\(548\) 1.39305e49i 0.701320i
\(549\) −2.40612e49 + 1.02258e49i −1.17224 + 0.498190i
\(550\) −6.75926e48 −0.318692
\(551\) 1.78793e49i 0.815872i
\(552\) −1.91546e48 9.40423e48i −0.0845997 0.415355i
\(553\) 2.86402e49 1.22440
\(554\) 2.82951e48i 0.117094i
\(555\) −2.24270e48 + 4.56794e47i −0.0898458 + 0.0182998i
\(556\) −6.81994e48 −0.264505
\(557\) 2.17422e49i 0.816414i 0.912889 + 0.408207i \(0.133846\pi\)
−0.912889 + 0.408207i \(0.866154\pi\)
\(558\) 8.25872e48 + 1.94327e49i 0.300260 + 0.706507i
\(559\) 4.35506e49 1.53314
\(560\) 2.25406e48i 0.0768388i
\(561\) −2.43619e48 1.19609e49i −0.0804230 0.394849i
\(562\) −3.11212e49 −0.994953
\(563\) 4.38124e49i 1.35658i −0.734794 0.678291i \(-0.762721\pi\)
0.734794 0.678291i \(-0.237279\pi\)
\(564\) 3.02005e49 6.15125e48i 0.905712 0.184476i
\(565\) 2.80274e49 0.814161
\(566\) 3.45605e49i 0.972487i
\(567\) −1.75236e49 + 1.81781e49i −0.477671 + 0.495510i
\(568\) 7.16221e48 0.189137
\(569\) 6.29187e48i 0.160975i −0.996756 0.0804876i \(-0.974352\pi\)
0.996756 0.0804876i \(-0.0256477\pi\)
\(570\) 1.26537e48 + 6.21255e48i 0.0313669 + 0.154001i
\(571\) −4.24109e49 −1.01866 −0.509328 0.860573i \(-0.670106\pi\)
−0.509328 + 0.860573i \(0.670106\pi\)
\(572\) 2.22661e49i 0.518221i
\(573\) −2.98623e48 + 6.08236e47i −0.0673504 + 0.0137180i
\(574\) −3.61923e48 −0.0791046
\(575\) 1.47467e49i 0.312373i
\(576\) 3.87516e49 1.64691e49i 0.795581 0.338115i
\(577\) −5.07984e49 −1.01085 −0.505423 0.862872i \(-0.668664\pi\)
−0.505423 + 0.862872i \(0.668664\pi\)
\(578\) 1.89273e49i 0.365079i
\(579\) −6.51434e48 3.19832e49i −0.121803 0.598008i
\(580\) −2.24028e49 −0.406067
\(581\) 2.38610e49i 0.419293i
\(582\) 2.16833e49 4.41646e48i 0.369412 0.0752420i
\(583\) 2.74626e49 0.453636
\(584\) 5.47508e49i 0.876918i
\(585\) 2.08127e49 + 4.89720e49i 0.323238 + 0.760575i
\(586\) 1.27910e49 0.192641
\(587\) 6.76227e49i 0.987658i 0.869559 + 0.493829i \(0.164403\pi\)
−0.869559 + 0.493829i \(0.835597\pi\)
\(588\) −3.75200e48 1.84210e49i −0.0531460 0.260929i
\(589\) −3.79025e49 −0.520706
\(590\) 3.69683e49i 0.492599i
\(591\) 7.81154e48 1.59106e48i 0.100963 0.0205642i
\(592\) 3.71207e48 0.0465398
\(593\) 1.09064e50i 1.32647i 0.748412 + 0.663234i \(0.230816\pi\)
−0.748412 + 0.663234i \(0.769184\pi\)
\(594\) 1.96313e49 + 2.85235e49i 0.231629 + 0.336548i
\(595\) 1.95484e49 0.223772
\(596\) 7.17108e49i 0.796438i
\(597\) −2.15784e48 1.05942e49i −0.0232531 0.114165i
\(598\) −4.74337e49 −0.495982
\(599\) 8.77311e49i 0.890165i 0.895490 + 0.445083i \(0.146826\pi\)
−0.895490 + 0.445083i \(0.853174\pi\)
\(600\) 8.21697e49 1.67363e49i 0.809076 0.164793i
\(601\) −1.55745e50 −1.48825 −0.744123 0.668042i \(-0.767132\pi\)
−0.744123 + 0.668042i \(0.767132\pi\)
\(602\) 4.53857e49i 0.420903i
\(603\) 4.06052e49 1.72569e49i 0.365485 0.155328i
\(604\) −6.62240e49 −0.578562
\(605\) 3.66194e49i 0.310538i
\(606\) −1.57183e49 7.71715e49i −0.129389 0.635257i
\(607\) 2.05418e50 1.64151 0.820754 0.571282i \(-0.193554\pi\)
0.820754 + 0.571282i \(0.193554\pi\)
\(608\) 5.47694e49i 0.424887i
\(609\) −1.53234e50 + 3.12107e49i −1.15410 + 0.235067i
\(610\) −5.74186e49 −0.419871
\(611\) 4.53395e50i 3.21910i
\(612\) 1.99001e49 + 4.68248e49i 0.137193 + 0.322812i
\(613\) 2.44687e50 1.63803 0.819017 0.573769i \(-0.194519\pi\)
0.819017 + 0.573769i \(0.194519\pi\)
\(614\) 2.93406e49i 0.190738i
\(615\) 2.42441e48 + 1.19030e49i 0.0153058 + 0.0751460i
\(616\) 6.90664e49 0.423462
\(617\) 1.86269e50i 1.10920i 0.832118 + 0.554598i \(0.187128\pi\)
−0.832118 + 0.554598i \(0.812872\pi\)
\(618\) −1.21761e50 + 2.48003e49i −0.704232 + 0.143438i
\(619\) −1.39441e50 −0.783356 −0.391678 0.920102i \(-0.628105\pi\)
−0.391678 + 0.920102i \(0.628105\pi\)
\(620\) 4.74918e49i 0.259160i
\(621\) −6.22298e49 + 4.28295e49i −0.329875 + 0.227036i
\(622\) 3.89684e49 0.200671
\(623\) 1.86369e50i 0.932370i
\(624\) −1.72243e49 8.45655e49i −0.0837181 0.411027i
\(625\) 8.22728e49 0.388522
\(626\) 1.16999e49i 0.0536840i
\(627\) −6.09060e49 + 1.24054e49i −0.271547 + 0.0553087i
\(628\) 1.45433e50 0.630071
\(629\) 3.21930e49i 0.135535i
\(630\) −5.10356e49 + 2.16897e49i −0.208806 + 0.0887408i
\(631\) 3.02076e50 1.20112 0.600561 0.799579i \(-0.294944\pi\)
0.600561 + 0.799579i \(0.294944\pi\)
\(632\) 4.87274e50i 1.88307i
\(633\) 1.75716e49 + 8.62703e49i 0.0659999 + 0.324037i
\(634\) −5.22690e49 −0.190826
\(635\) 2.67324e48i 0.00948660i
\(636\) −1.12165e50 + 2.28457e49i −0.386926 + 0.0788092i
\(637\) −2.76551e50 −0.927398
\(638\) 2.14457e50i 0.699147i
\(639\) −2.20507e49 5.18851e49i −0.0698888 0.164448i
\(640\) −4.31606e49 −0.132999
\(641\) 1.72071e50i 0.515542i −0.966206 0.257771i \(-0.917012\pi\)
0.966206 0.257771i \(-0.0829880\pi\)
\(642\) 6.59044e49 + 3.23568e50i 0.191992 + 0.942616i
\(643\) −4.34040e50 −1.22951 −0.614755 0.788718i \(-0.710745\pi\)
−0.614755 + 0.788718i \(0.710745\pi\)
\(644\) 5.06248e49i 0.139450i
\(645\) 1.49266e50 3.04026e49i 0.399840 0.0814395i
\(646\) 8.91786e49 0.232314
\(647\) 9.80395e49i 0.248384i −0.992258 0.124192i \(-0.960366\pi\)
0.992258 0.124192i \(-0.0396339\pi\)
\(648\) −3.09276e50 2.98141e50i −0.762072 0.734636i
\(649\) 3.62426e50 0.868590
\(650\) 4.14454e50i 0.966130i
\(651\) −6.61639e49 3.24842e50i −0.150025 0.736571i
\(652\) −3.06462e49 −0.0675959
\(653\) 5.13701e50i 1.10223i 0.834428 + 0.551116i \(0.185798\pi\)
−0.834428 + 0.551116i \(0.814202\pi\)
\(654\) 2.98131e50 6.07234e49i 0.622311 0.126752i
\(655\) 7.06185e49 0.143409
\(656\) 1.97016e49i 0.0389254i
\(657\) 3.96631e50 1.68565e50i 0.762447 0.324034i
\(658\) 4.72500e50 0.883763
\(659\) 1.24566e50i 0.226705i −0.993555 0.113352i \(-0.963841\pi\)
0.993555 0.113352i \(-0.0361589\pi\)
\(660\) −1.55439e49 7.63152e49i −0.0275276 0.135151i
\(661\) −5.32566e50 −0.917799 −0.458899 0.888488i \(-0.651756\pi\)
−0.458899 + 0.888488i \(0.651756\pi\)
\(662\) 1.45504e50i 0.244024i
\(663\) 7.33398e50 1.49379e50i 1.19701 0.243806i
\(664\) −4.05963e50 −0.644854
\(665\) 9.95425e49i 0.153893i
\(666\) −3.57194e49 8.40472e49i −0.0537487 0.126470i
\(667\) −4.67881e50 −0.685284
\(668\) 4.35530e50i 0.620929i
\(669\) 2.09117e50 + 1.02669e51i 0.290215 + 1.42486i
\(670\) 9.68986e49 0.130909
\(671\) 5.62915e50i 0.740350i
\(672\) −4.69399e50 + 9.56073e49i −0.601029 + 0.122418i
\(673\) −1.36851e51 −1.70600 −0.852998 0.521915i \(-0.825218\pi\)
−0.852998 + 0.521915i \(0.825218\pi\)
\(674\) 3.43969e50i 0.417486i
\(675\) −3.74224e50 5.43734e50i −0.442246 0.642567i
\(676\) 9.25576e50 1.06505
\(677\) 1.36362e51i 1.52790i 0.645274 + 0.763951i \(0.276743\pi\)
−0.645274 + 0.763951i \(0.723257\pi\)
\(678\) 2.23195e50 + 1.09581e51i 0.243529 + 1.19564i
\(679\) −3.47427e50 −0.369154
\(680\) 3.32590e50i 0.344151i
\(681\) 8.02437e50 1.63441e50i 0.808654 0.164707i
\(682\) −4.54630e50 −0.446210
\(683\) 3.17270e50i 0.303289i 0.988435 + 0.151644i \(0.0484568\pi\)
−0.988435 + 0.151644i \(0.951543\pi\)
\(684\) 2.38437e50 1.01334e50i 0.222005 0.0943504i
\(685\) 7.16797e50 0.650079
\(686\) 8.35810e50i 0.738369i
\(687\) 2.26596e50 + 1.11251e51i 0.194998 + 0.957373i
\(688\) −2.47062e50 −0.207116
\(689\) 1.68391e51i 1.37522i
\(690\) −1.62575e50 + 3.31134e49i −0.129351 + 0.0263463i
\(691\) 6.64077e50 0.514770 0.257385 0.966309i \(-0.417139\pi\)
0.257385 + 0.966309i \(0.417139\pi\)
\(692\) 3.95818e49i 0.0298941i
\(693\) −2.12639e50 5.00337e50i −0.156475 0.368184i
\(694\) 9.97529e50 0.715246
\(695\) 3.50922e50i 0.245179i
\(696\) −5.31009e50 2.60707e51i −0.361523 1.77495i
\(697\) 1.70863e50 0.113360
\(698\) 1.26874e51i 0.820303i
\(699\) −1.28346e51 + 2.61416e50i −0.808711 + 0.164718i
\(700\) −4.42336e50 −0.271636
\(701\) 3.03202e51i 1.81471i −0.420366 0.907355i \(-0.638098\pi\)
0.420366 0.907355i \(-0.361902\pi\)
\(702\) −1.74896e51 + 1.20372e51i −1.02026 + 0.702194i
\(703\) 1.63930e50 0.0932102
\(704\) 9.06598e50i 0.502466i
\(705\) −3.16514e50 1.55397e51i −0.170997 0.839537i
\(706\) 2.78201e50 0.146513
\(707\) 1.23650e51i 0.634813i
\(708\) −1.48024e51 + 3.01497e50i −0.740858 + 0.150898i
\(709\) 8.48005e50 0.413777 0.206888 0.978365i \(-0.433666\pi\)
0.206888 + 0.978365i \(0.433666\pi\)
\(710\) 1.23817e50i 0.0589018i
\(711\) 3.52996e51 1.50020e51i 1.63726 0.695820i
\(712\) 3.17082e51 1.43394
\(713\) 9.91865e50i 0.437362i
\(714\) 1.55673e50 + 7.64302e50i 0.0669339 + 0.328622i
\(715\) −1.14571e51 −0.480357
\(716\) 2.77722e49i 0.0113547i
\(717\) −2.63653e51 + 5.37010e50i −1.05121 + 0.214110i
\(718\) −2.38226e49 −0.00926295
\(719\) 2.60399e51i 0.987460i 0.869615 + 0.493730i \(0.164367\pi\)
−0.869615 + 0.493730i \(0.835633\pi\)
\(720\) −1.18070e50 2.77817e50i −0.0436671 0.102748i
\(721\) 1.95095e51 0.703740
\(722\) 1.54369e51i 0.543114i
\(723\) 1.93059e50 + 9.47851e50i 0.0662521 + 0.325275i
\(724\) −6.95853e50 −0.232929
\(725\) 4.08812e51i 1.33487i
\(726\) 1.43174e51 2.91618e50i 0.456043 0.0928869i
\(727\) −4.00585e51 −1.24473 −0.622365 0.782727i \(-0.713828\pi\)
−0.622365 + 0.782727i \(0.713828\pi\)
\(728\) 4.23490e51i 1.28375i
\(729\) −1.20764e51 + 3.15839e51i −0.357141 + 0.934050i
\(730\) 9.46503e50 0.273093
\(731\) 2.14265e51i 0.603169i
\(732\) 4.68280e50 + 2.29910e51i 0.128619 + 0.631477i
\(733\) −2.72371e51 −0.729943 −0.364971 0.931019i \(-0.618921\pi\)
−0.364971 + 0.931019i \(0.618921\pi\)
\(734\) 1.69137e51i 0.442293i
\(735\) −9.47858e50 + 1.93060e50i −0.241864 + 0.0492629i
\(736\) −1.43325e51 −0.356880
\(737\) 9.49964e50i 0.230830i
\(738\) −4.46077e50 + 1.89579e50i −0.105778 + 0.0449548i
\(739\) 7.29458e51 1.68811 0.844054 0.536258i \(-0.180163\pi\)
0.844054 + 0.536258i \(0.180163\pi\)
\(740\) 2.05404e50i 0.0463916i
\(741\) −7.60652e50 3.73454e51i −0.167671 0.823207i
\(742\) −1.75486e51 −0.377549
\(743\) 2.66881e51i 0.560426i −0.959938 0.280213i \(-0.909595\pi\)
0.959938 0.280213i \(-0.0904051\pi\)
\(744\) 5.52676e51 1.12569e51i 1.13281 0.230731i
\(745\) −3.68990e51 −0.738247
\(746\) 3.49380e51i 0.682338i
\(747\) 1.24986e51 + 2.94091e51i 0.238282 + 0.560676i
\(748\) −1.09547e51 −0.203879
\(749\) 5.18447e51i 0.941958i
\(750\) −6.60241e50 3.24156e51i −0.117112 0.574978i
\(751\) −7.60412e50 −0.131683 −0.0658416 0.997830i \(-0.520973\pi\)
−0.0658416 + 0.997830i \(0.520973\pi\)
\(752\) 2.57210e51i 0.434878i
\(753\) 8.38303e51 1.70746e51i 1.38386 0.281865i
\(754\) −1.31497e52 −2.11950
\(755\) 3.40757e51i 0.536290i
\(756\) 1.28470e51 + 1.86662e51i 0.197428 + 0.286856i
\(757\) 9.95443e51 1.49379 0.746897 0.664940i \(-0.231543\pi\)
0.746897 + 0.664940i \(0.231543\pi\)
\(758\) 2.59140e51i 0.379743i
\(759\) −3.24634e50 1.59384e51i −0.0464560 0.228083i
\(760\) 1.69358e51 0.236680
\(761\) 1.02462e52i 1.39842i −0.714915 0.699211i \(-0.753535\pi\)
0.714915 0.699211i \(-0.246465\pi\)
\(762\) 1.04518e50 2.12882e49i 0.0139316 0.00283760i
\(763\) −4.77689e51 −0.621876
\(764\) 2.73503e50i 0.0347762i
\(765\) 2.40938e51 1.02397e51i 0.299226 0.127169i
\(766\) 6.73583e51 0.817096
\(767\) 2.22227e52i 2.63317i
\(768\) −1.83432e51 9.00586e51i −0.212311 1.04237i
\(769\) −1.00804e52 −1.13974 −0.569869 0.821735i \(-0.693006\pi\)
−0.569869 + 0.821735i \(0.693006\pi\)
\(770\) 1.19398e51i 0.131876i
\(771\) −8.41988e51 + 1.71496e51i −0.908504 + 0.185044i
\(772\) −2.92927e51 −0.308780
\(773\) 1.35607e52i 1.39654i 0.715835 + 0.698269i \(0.246046\pi\)
−0.715835 + 0.698269i \(0.753954\pi\)
\(774\) 2.37735e51 + 5.59388e51i 0.239197 + 0.562828i
\(775\) 8.66645e51 0.851943
\(776\) 5.91101e51i 0.567742i
\(777\) 2.86162e50 + 1.40496e51i 0.0268555 + 0.131851i
\(778\) −3.93845e51 −0.361154
\(779\) 8.70053e50i 0.0779599i
\(780\) 4.67937e51 9.53096e50i 0.409718 0.0834514i
\(781\) 1.21386e51 0.103860
\(782\) 2.33370e51i 0.195130i
\(783\) −1.72515e52 + 1.18733e52i −1.40967 + 0.970200i
\(784\) 1.56887e51 0.125285
\(785\) 7.48330e51i 0.584035i
\(786\) 5.62368e50 + 2.76104e51i 0.0428958 + 0.210604i
\(787\) 2.46972e51 0.184121 0.0920603 0.995753i \(-0.470655\pi\)
0.0920603 + 0.995753i \(0.470655\pi\)
\(788\) 7.15443e50i 0.0521319i
\(789\) −1.18428e52 + 2.41214e51i −0.843467 + 0.171798i
\(790\) 8.42375e51 0.586432
\(791\) 1.75580e52i 1.19481i
\(792\) 8.51258e51 3.61777e51i 0.566249 0.240651i
\(793\) 3.45159e52 2.24441
\(794\) 5.95172e51i 0.378333i
\(795\) 1.17553e51 + 5.77146e51i 0.0730510 + 0.358655i
\(796\) −9.70306e50 −0.0589486
\(797\) 1.49302e51i 0.0886780i −0.999017 0.0443390i \(-0.985882\pi\)
0.999017 0.0443390i \(-0.0141182\pi\)
\(798\) 3.89190e51 7.92704e50i 0.226001 0.0460319i
\(799\) −2.23067e52 −1.26646
\(800\) 1.25231e52i 0.695171i
\(801\) −9.76220e51 2.29703e52i −0.529862 1.24676i
\(802\) 9.83805e51 0.522120
\(803\) 9.27923e51i 0.481540i
\(804\) −7.90261e50 3.87991e51i −0.0401016 0.196885i
\(805\) 2.60491e51 0.129261
\(806\) 2.78763e52i 1.35271i
\(807\) −1.70878e52 + 3.48046e51i −0.810893 + 0.165163i
\(808\) −2.10375e52 −0.976313
\(809\) 4.45901e51i 0.202379i 0.994867 + 0.101189i \(0.0322648\pi\)
−0.994867 + 0.101189i \(0.967735\pi\)
\(810\) −5.15411e51 + 5.34660e51i −0.228783 + 0.237327i
\(811\) 1.44695e52 0.628172 0.314086 0.949395i \(-0.398302\pi\)
0.314086 + 0.949395i \(0.398302\pi\)
\(812\) 1.40344e52i 0.595916i
\(813\) −2.85094e50 1.39971e51i −0.0118402 0.0581312i
\(814\) 1.96630e51 0.0798748
\(815\) 1.57691e51i 0.0626570i
\(816\) −4.16056e51 + 8.47423e50i −0.161707 + 0.0329365i
\(817\) −1.09106e52 −0.414813
\(818\) 5.19791e51i 0.193317i
\(819\) 3.06789e52 1.30383e52i 1.11617 0.474362i
\(820\) 1.09018e51 0.0388014
\(821\) 2.38829e51i 0.0831591i 0.999135 + 0.0415795i \(0.0132390\pi\)
−0.999135 + 0.0415795i \(0.986761\pi\)
\(822\) 5.70819e51 + 2.80253e52i 0.194449 + 0.954678i
\(823\) 2.69269e52 0.897407 0.448703 0.893681i \(-0.351886\pi\)
0.448703 + 0.893681i \(0.351886\pi\)
\(824\) 3.31929e52i 1.08232i
\(825\) 1.39262e52 2.83650e51i 0.444286 0.0904922i
\(826\) −2.31591e52 −0.722904
\(827\) 4.62393e52i 1.41225i 0.708086 + 0.706127i \(0.249559\pi\)
−0.708086 + 0.706127i \(0.750441\pi\)
\(828\) 2.65178e51 + 6.23961e51i 0.0792487 + 0.186471i
\(829\) 3.34053e52 0.976862 0.488431 0.872602i \(-0.337569\pi\)
0.488431 + 0.872602i \(0.337569\pi\)
\(830\) 7.01808e51i 0.200823i
\(831\) −1.18739e51 5.82969e51i −0.0332488 0.163240i
\(832\) −5.55893e52 −1.52325
\(833\) 1.36061e52i 0.364858i
\(834\) −1.37203e52 + 2.79456e51i −0.360060 + 0.0733371i
\(835\) −2.24103e52 −0.575561
\(836\) 5.57826e51i 0.140212i
\(837\) −2.51704e52 3.65717e52i −0.619202 0.899678i
\(838\) 2.83066e52 0.681546
\(839\) 6.10331e52i 1.43830i −0.694854 0.719151i \(-0.744531\pi\)
0.694854 0.719151i \(-0.255469\pi\)
\(840\) 2.95638e51 + 1.45148e52i 0.0681919 + 0.334799i
\(841\) −8.54153e52 −1.92845
\(842\) 3.40435e51i 0.0752344i
\(843\) 6.41196e52 1.30599e52i 1.38706 0.282516i
\(844\) 7.90132e51 0.167315
\(845\) 4.76258e52i 0.987236i
\(846\) 5.82366e52 2.47501e52i 1.18176 0.502238i
\(847\) −2.29405e52 −0.455724
\(848\) 9.55278e51i 0.185782i
\(849\) 1.45032e52 + 7.12056e52i 0.276137 + 1.35574i
\(850\) −2.03908e52 −0.380096
\(851\) 4.28987e51i 0.0782910i
\(852\) −4.95773e51 + 1.00979e51i −0.0885870 + 0.0180434i
\(853\) −7.25447e51 −0.126918 −0.0634590 0.997984i \(-0.520213\pi\)
−0.0634590 + 0.997984i \(0.520213\pi\)
\(854\) 3.59704e52i 0.616174i
\(855\) −5.21415e51 1.22688e52i −0.0874567 0.205785i
\(856\) 8.82069e52 1.44869
\(857\) 8.42381e52i 1.35473i −0.735646 0.677366i \(-0.763121\pi\)
0.735646 0.677366i \(-0.236879\pi\)
\(858\) −9.12380e51 4.47947e52i −0.143683 0.705432i
\(859\) 2.60858e52 0.402279 0.201140 0.979563i \(-0.435536\pi\)
0.201140 + 0.979563i \(0.435536\pi\)
\(860\) 1.36710e52i 0.206456i
\(861\) 7.45676e51 1.51879e51i 0.110279 0.0224617i
\(862\) 4.06461e52 0.588692
\(863\) 4.81527e52i 0.683009i −0.939880 0.341505i \(-0.889064\pi\)
0.939880 0.341505i \(-0.110936\pi\)
\(864\) −5.28464e52 + 3.63714e52i −0.734121 + 0.505258i
\(865\) 2.03669e51 0.0277099
\(866\) 4.49882e52i 0.599482i
\(867\) 7.94275e51 + 3.89962e52i 0.103664 + 0.508954i
\(868\) −2.97516e52 −0.380326
\(869\) 8.25839e52i 1.03404i
\(870\) −4.50697e52 + 9.17981e51i −0.552762 + 0.112587i
\(871\) −5.82484e52 −0.699773
\(872\) 8.12725e52i 0.956416i
\(873\) −4.28211e52 + 1.81986e52i −0.493630 + 0.209789i
\(874\) 1.18835e52 0.134195
\(875\) 5.19389e52i 0.574576i
\(876\) −7.71925e51 3.78989e52i −0.0836568 0.410726i
\(877\) −1.85957e52 −0.197433 −0.0987165 0.995116i \(-0.531474\pi\)
−0.0987165 + 0.995116i \(0.531474\pi\)
\(878\) 8.46658e52i 0.880656i
\(879\) −2.63536e52 + 5.36771e51i −0.268559 + 0.0547002i
\(880\) 6.49957e51 0.0648928
\(881\) 1.62346e53i 1.58809i 0.607859 + 0.794045i \(0.292029\pi\)
−0.607859 + 0.794045i \(0.707971\pi\)
\(882\) −1.50965e52 3.55218e52i −0.144691 0.340456i
\(883\) 1.35375e53 1.27130 0.635648 0.771979i \(-0.280733\pi\)
0.635648 + 0.771979i \(0.280733\pi\)
\(884\) 6.71704e52i 0.618070i
\(885\) 1.55136e52 + 7.61664e52i 0.139873 + 0.686728i
\(886\) 2.52123e52 0.222743
\(887\) 8.73319e51i 0.0756045i 0.999285 + 0.0378022i \(0.0120357\pi\)
−0.999285 + 0.0378022i \(0.987964\pi\)
\(888\) −2.39035e52 + 4.86867e51i −0.202781 + 0.0413026i
\(889\) −1.67467e51 −0.0139219
\(890\) 5.48155e52i 0.446563i
\(891\) −5.24164e52 5.05293e52i −0.418474 0.403408i
\(892\) 9.40329e52 0.735720
\(893\) 1.13588e53i 0.870975i
\(894\) −2.93844e52 1.44267e53i −0.220822 1.08416i
\(895\) −1.42902e51 −0.0105251
\(896\) 2.70383e52i 0.195180i
\(897\) 9.77286e52 1.99054e52i 0.691445 0.140834i
\(898\) −1.55814e53 −1.08052
\(899\) 2.74968e53i 1.86899i
\(900\) −5.45188e52 + 2.31700e52i −0.363229 + 0.154369i
\(901\) 8.28469e52 0.541041
\(902\) 1.04360e52i 0.0668064i
\(903\) −1.90459e52 9.35090e52i −0.119515 0.586778i
\(904\) 2.98726e53 1.83756
\(905\) 3.58053e52i 0.215910i
\(906\) −1.33229e53 + 2.71361e52i −0.787573 + 0.160413i
\(907\) −2.38299e53 −1.38099 −0.690497 0.723335i \(-0.742608\pi\)
−0.690497 + 0.723335i \(0.742608\pi\)
\(908\) 7.34936e52i 0.417546i
\(909\) 6.47694e52 + 1.52402e53i 0.360761 + 0.848867i
\(910\) 7.32108e52 0.399788
\(911\) 6.66896e52i 0.357048i −0.983936 0.178524i \(-0.942868\pi\)
0.983936 0.178524i \(-0.0571323\pi\)
\(912\) 4.31517e51 + 2.11860e52i 0.0226512 + 0.111209i
\(913\) −6.88031e52 −0.354107
\(914\) 1.45585e53i 0.734657i
\(915\) 1.18301e53 2.40955e52i 0.585339 0.119222i
\(916\) 1.01892e53 0.494336
\(917\) 4.42395e52i 0.210457i
\(918\) 5.92220e52 + 8.60475e52i 0.276258 + 0.401393i
\(919\) −2.05261e53 −0.938915 −0.469458 0.882955i \(-0.655551\pi\)
−0.469458 + 0.882955i \(0.655551\pi\)
\(920\) 4.43192e52i 0.198797i
\(921\) 1.23127e52 + 6.04509e52i 0.0541600 + 0.265907i
\(922\) −1.00374e53 −0.432977
\(923\) 7.44295e52i 0.314858i
\(924\) −4.78082e52 + 9.73760e51i −0.198339 + 0.0403977i
\(925\) −3.74828e52 −0.152504
\(926\) 2.80357e53i 1.11870i
\(927\) 2.40459e53 1.02193e53i 0.941036 0.399932i
\(928\) −3.97331e53 −1.52507
\(929\) 1.08375e53i 0.407986i 0.978972 + 0.203993i \(0.0653920\pi\)
−0.978972 + 0.203993i \(0.934608\pi\)
\(930\) −1.94604e52 9.55437e52i −0.0718551 0.352784i
\(931\) 6.92837e52 0.250921
\(932\) 1.17550e53i 0.417575i
\(933\) −8.02873e52 + 1.63529e52i −0.279755 + 0.0569805i
\(934\) 1.14034e53 0.389755
\(935\) 5.63678e52i 0.188983i
\(936\) 2.21829e53 + 5.21961e53i 0.729546 + 1.71661i
\(937\) 1.55713e53 0.502356 0.251178 0.967941i \(-0.419182\pi\)
0.251178 + 0.967941i \(0.419182\pi\)
\(938\) 6.07029e52i 0.192114i
\(939\) −4.90983e51 2.41056e52i −0.0152435 0.0748405i
\(940\) −1.42325e53 −0.433492
\(941\) 5.05546e52i 0.151059i 0.997144 + 0.0755296i \(0.0240647\pi\)
−0.997144 + 0.0755296i \(0.975935\pi\)
\(942\) 2.92581e53 5.95930e52i 0.857690 0.174694i
\(943\) 2.27683e52 0.0654817
\(944\) 1.26069e53i 0.355723i
\(945\) 9.60475e52 6.61045e52i 0.265897 0.183003i
\(946\) −1.30870e53 −0.355466
\(947\) 4.18557e53i 1.11546i −0.830022 0.557731i \(-0.811672\pi\)
0.830022 0.557731i \(-0.188328\pi\)
\(948\) −6.87003e52 3.37295e53i −0.179642 0.881981i
\(949\) −5.68969e53 −1.45981
\(950\) 1.03832e53i 0.261400i
\(951\) 1.07691e53 2.19345e52i 0.266029 0.0541848i
\(952\) 2.08354e53 0.505053
\(953\) 3.25845e52i 0.0775066i 0.999249 + 0.0387533i \(0.0123386\pi\)
−0.999249 + 0.0387533i \(0.987661\pi\)
\(954\) −2.16291e53 + 9.19217e52i −0.504855 + 0.214559i
\(955\) 1.40732e52 0.0322353
\(956\) 2.41475e53i 0.542788i
\(957\) −8.99961e52 4.41850e53i −0.198522 0.974675i
\(958\) 1.37908e53 0.298546
\(959\) 4.49043e53i 0.954011i
\(960\) −1.90528e53 + 3.88068e52i −0.397262 + 0.0809144i
\(961\) 9.42318e52 0.192831
\(962\) 1.20566e53i 0.242144i
\(963\) −2.71568e53 6.38996e53i −0.535310 1.25958i
\(964\) 8.68118e52 0.167955
\(965\) 1.50727e53i 0.286219i
\(966\) 2.07442e52 + 1.01847e53i 0.0386641 + 0.189827i
\(967\) 8.75276e53 1.60129 0.800643 0.599142i \(-0.204492\pi\)
0.800643 + 0.599142i \(0.204492\pi\)
\(968\) 3.90303e53i 0.700883i
\(969\) −1.83736e53 + 3.74235e52i −0.323867 + 0.0659654i
\(970\) −1.02187e53 −0.176808
\(971\) 6.79262e53i 1.15370i 0.816852 + 0.576848i \(0.195717\pi\)
−0.816852 + 0.576848i \(0.804283\pi\)
\(972\) 2.56117e53 + 1.62771e53i 0.427018 + 0.271384i
\(973\) 2.19838e53 0.359808
\(974\) 3.16952e53i 0.509251i
\(975\) 1.73924e53 + 8.53906e53i 0.274332 + 1.34687i
\(976\) −1.95808e53 −0.303204
\(977\) 3.90925e53i 0.594280i −0.954834 0.297140i \(-0.903967\pi\)
0.954834 0.297140i \(-0.0960327\pi\)
\(978\) −6.16538e52 + 1.25577e52i −0.0920154 + 0.0187417i
\(979\) 5.37394e53 0.787417
\(980\) 8.68124e52i 0.124886i
\(981\) −5.88762e53 + 2.50219e53i −0.831567 + 0.353409i
\(982\) 1.41668e53 0.196455
\(983\) 8.03195e53i 1.09360i 0.837264 + 0.546799i \(0.184154\pi\)
−0.837264 + 0.546799i \(0.815846\pi\)
\(984\) 2.58403e52 + 1.26867e53i 0.0345450 + 0.169604i
\(985\) −3.68133e52 −0.0483229
\(986\) 6.46957e53i 0.833856i
\(987\) −9.73500e53 + 1.98283e53i −1.23205 + 0.250944i
\(988\) −3.42039e53 −0.425060
\(989\) 2.85518e53i 0.348418i
\(990\) −6.25422e52 1.47161e53i −0.0749445 0.176343i
\(991\) −1.24081e54 −1.46009 −0.730045 0.683399i \(-0.760501\pi\)
−0.730045 + 0.683399i \(0.760501\pi\)
\(992\) 8.42306e53i 0.973329i
\(993\) 6.10603e52 + 2.99785e53i 0.0692903 + 0.340191i
\(994\) −7.75659e52 −0.0864402
\(995\) 4.99274e52i 0.0546416i
\(996\) 2.81010e53 5.72363e52i 0.302033 0.0615181i
\(997\) 1.37750e54 1.45405 0.727024 0.686612i \(-0.240903\pi\)
0.727024 + 0.686612i \(0.240903\pi\)
\(998\) 2.34817e53i 0.243433i
\(999\) 1.08863e53 + 1.58174e53i 0.110842 + 0.161049i
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 3.37.b.b.2.4 10
3.2 odd 2 inner 3.37.b.b.2.7 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.37.b.b.2.4 10 1.1 even 1 trivial
3.37.b.b.2.7 yes 10 3.2 odd 2 inner