Properties

Label 3.35.b.a.2.2
Level $3$
Weight $35$
Character 3.2
Analytic conductor $21.968$
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] = [3,35,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, 35, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 35);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 35 \)
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: \(21.9676962128\)
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: \( x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.2
Root \(-16987.2i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.35.b.a.2.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-203846. i q^{2} +(-1.15096e8 - 5.85668e7i) q^{3} -2.43733e10 q^{4} -1.79877e11i q^{5} +(-1.19386e13 + 2.34619e13i) q^{6} -2.97937e14 q^{7} +1.46635e15i q^{8} +(9.81704e15 + 1.34816e16i) q^{9} +O(q^{10})\) \(q-203846. i q^{2} +(-1.15096e8 - 5.85668e7i) q^{3} -2.43733e10 q^{4} -1.79877e11i q^{5} +(-1.19386e13 + 2.34619e13i) q^{6} -2.97937e14 q^{7} +1.46635e15i q^{8} +(9.81704e15 + 1.34816e16i) q^{9} -3.66671e16 q^{10} +5.45809e17i q^{11} +(2.80527e18 + 1.42747e18i) q^{12} +6.76117e18 q^{13} +6.07333e19i q^{14} +(-1.05348e19 + 2.07031e19i) q^{15} -1.19820e20 q^{16} -1.38305e21i q^{17} +(2.74817e21 - 2.00116e21i) q^{18} -8.87671e21 q^{19} +4.38419e21i q^{20} +(3.42914e22 + 1.74492e22i) q^{21} +1.11261e23 q^{22} -2.99358e22i q^{23} +(8.58794e22 - 1.68771e23i) q^{24} +5.49721e23 q^{25} -1.37824e24i q^{26} +(-3.40329e23 - 2.12663e24i) q^{27} +7.26171e24 q^{28} +3.17183e24i q^{29} +(4.22024e24 + 2.14748e24i) q^{30} +1.17602e24 q^{31} +4.96166e25i q^{32} +(3.19663e25 - 6.28205e25i) q^{33} -2.81928e26 q^{34} +5.35919e25i q^{35} +(-2.39274e26 - 3.28591e26i) q^{36} +3.74912e26 q^{37} +1.80948e27i q^{38} +(-7.78185e26 - 3.95980e26i) q^{39} +2.63762e26 q^{40} +2.13908e27i q^{41} +(3.55695e27 - 6.99016e27i) q^{42} +4.08388e27 q^{43} -1.33032e28i q^{44} +(2.42503e27 - 1.76586e27i) q^{45} -6.10229e27 q^{46} +4.95016e28i q^{47} +(1.37909e28 + 7.01750e27i) q^{48} +3.46495e28 q^{49} -1.12058e29i q^{50} +(-8.10006e28 + 1.59183e29i) q^{51} -1.64792e29 q^{52} -9.35752e28i q^{53} +(-4.33506e29 + 6.93746e28i) q^{54} +9.81784e28 q^{55} -4.36880e29i q^{56} +(1.02167e30 + 5.19881e29i) q^{57} +6.46565e29 q^{58} +6.32368e29i q^{59} +(2.56768e29 - 5.04603e29i) q^{60} +4.42775e29 q^{61} -2.39727e29i q^{62} +(-2.92486e30 - 4.01667e30i) q^{63} +8.05565e30 q^{64} -1.21618e30i q^{65} +(-1.28057e31 - 6.51620e30i) q^{66} -4.63018e30 q^{67} +3.37094e31i q^{68} +(-1.75324e30 + 3.44549e30i) q^{69} +1.09245e31 q^{70} +2.74044e30i q^{71} +(-1.97688e31 + 1.43952e31i) q^{72} -2.72565e31 q^{73} -7.64242e31i q^{74} +(-6.32707e31 - 3.21954e31i) q^{75} +2.16355e32 q^{76} -1.62617e32i q^{77} +(-8.07189e31 + 1.58630e32i) q^{78} +1.93130e32 q^{79} +2.15529e31i q^{80} +(-8.53797e31 + 2.64699e32i) q^{81} +4.36044e32 q^{82} +2.76431e32i q^{83} +(-8.35794e32 - 4.25295e32i) q^{84} -2.48778e32 q^{85} -8.32483e32i q^{86} +(1.85764e32 - 3.65065e32i) q^{87} -8.00347e32 q^{88} +2.71501e33i q^{89} +(-3.59963e32 - 4.94332e32i) q^{90} -2.01440e33 q^{91} +7.29634e32i q^{92} +(-1.35355e32 - 6.88757e31i) q^{93} +1.00907e34 q^{94} +1.59671e33i q^{95} +(2.90589e33 - 5.71068e33i) q^{96} -1.23468e33 q^{97} -7.06317e33i q^{98} +(-7.35839e33 + 5.35823e33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 203846.i 1.55522i −0.628746 0.777611i \(-0.716432\pi\)
0.628746 0.777611i \(-0.283568\pi\)
\(3\) −1.15096e8 5.85668e7i −0.891249 0.453513i
\(4\) −2.43733e10 −1.41871
\(5\) 1.79877e11i 0.235768i −0.993027 0.117884i \(-0.962389\pi\)
0.993027 0.117884i \(-0.0376111\pi\)
\(6\) −1.19386e13 + 2.34619e13i −0.705313 + 1.38609i
\(7\) −2.97937e14 −1.28073 −0.640365 0.768070i \(-0.721217\pi\)
−0.640365 + 0.768070i \(0.721217\pi\)
\(8\) 1.46635e15i 0.651190i
\(9\) 9.81704e15 + 1.34816e16i 0.588651 + 0.808387i
\(10\) −3.66671e16 −0.366671
\(11\) 5.45809e17i 1.07985i 0.841712 + 0.539927i \(0.181548\pi\)
−0.841712 + 0.539927i \(0.818452\pi\)
\(12\) 2.80527e18 + 1.42747e18i 1.26443 + 0.643405i
\(13\) 6.76117e18 0.781601 0.390800 0.920475i \(-0.372198\pi\)
0.390800 + 0.920475i \(0.372198\pi\)
\(14\) 6.07333e19i 1.99182i
\(15\) −1.05348e19 + 2.07031e19i −0.106924 + 0.210128i
\(16\) −1.19820e20 −0.405968
\(17\) 1.38305e21i 1.67188i −0.548821 0.835940i \(-0.684923\pi\)
0.548821 0.835940i \(-0.315077\pi\)
\(18\) 2.74817e21 2.00116e21i 1.25722 0.915483i
\(19\) −8.87671e21 −1.61972 −0.809862 0.586621i \(-0.800458\pi\)
−0.809862 + 0.586621i \(0.800458\pi\)
\(20\) 4.38419e21i 0.334487i
\(21\) 3.42914e22 + 1.74492e22i 1.14145 + 0.580829i
\(22\) 1.11261e23 1.67941
\(23\) 2.99358e22i 0.212235i −0.994354 0.106118i \(-0.966158\pi\)
0.994354 0.106118i \(-0.0338420\pi\)
\(24\) 8.58794e22 1.68771e23i 0.295323 0.580373i
\(25\) 5.49721e23 0.944413
\(26\) 1.37824e24i 1.21556i
\(27\) −3.40329e23 2.12663e24i −0.158021 0.987436i
\(28\) 7.26171e24 1.81699
\(29\) 3.17183e24i 0.437063i 0.975830 + 0.218532i \(0.0701267\pi\)
−0.975830 + 0.218532i \(0.929873\pi\)
\(30\) 4.22024e24 + 2.14748e24i 0.326796 + 0.166290i
\(31\) 1.17602e24 0.0521514 0.0260757 0.999660i \(-0.491699\pi\)
0.0260757 + 0.999660i \(0.491699\pi\)
\(32\) 4.96166e25i 1.28256i
\(33\) 3.19663e25 6.28205e25i 0.489728 0.962420i
\(34\) −2.81928e26 −2.60014
\(35\) 5.35919e25i 0.301955i
\(36\) −2.39274e26 3.28591e26i −0.835127 1.14687i
\(37\) 3.74912e26 0.821296 0.410648 0.911794i \(-0.365302\pi\)
0.410648 + 0.911794i \(0.365302\pi\)
\(38\) 1.80948e27i 2.51903i
\(39\) −7.78185e26 3.95980e26i −0.696601 0.354466i
\(40\) 2.63762e26 0.153530
\(41\) 2.13908e27i 0.818281i 0.912471 + 0.409140i \(0.134171\pi\)
−0.912471 + 0.409140i \(0.865829\pi\)
\(42\) 3.55695e27 6.99016e27i 0.903317 1.77521i
\(43\) 4.08388e27 0.695200 0.347600 0.937643i \(-0.386997\pi\)
0.347600 + 0.937643i \(0.386997\pi\)
\(44\) 1.33032e28i 1.53200i
\(45\) 2.42503e27 1.76586e27i 0.190592 0.138785i
\(46\) −6.10229e27 −0.330073
\(47\) 4.95016e28i 1.85761i 0.370564 + 0.928807i \(0.379164\pi\)
−0.370564 + 0.928807i \(0.620836\pi\)
\(48\) 1.37909e28 + 7.01750e27i 0.361818 + 0.184112i
\(49\) 3.46495e28 0.640272
\(50\) 1.12058e29i 1.46877i
\(51\) −8.10006e28 + 1.59183e29i −0.758220 + 1.49006i
\(52\) −1.64792e29 −1.10887
\(53\) 9.35752e28i 0.455482i −0.973722 0.227741i \(-0.926866\pi\)
0.973722 0.227741i \(-0.0731339\pi\)
\(54\) −4.33506e29 + 6.93746e28i −1.53568 + 0.245757i
\(55\) 9.81784e28 0.254595
\(56\) 4.36880e29i 0.833999i
\(57\) 1.02167e30 + 5.19881e29i 1.44358 + 0.734566i
\(58\) 6.46565e29 0.679730
\(59\) 6.32368e29i 0.497148i 0.968613 + 0.248574i \(0.0799619\pi\)
−0.968613 + 0.248574i \(0.920038\pi\)
\(60\) 2.56768e29 5.04603e29i 0.151694 0.298111i
\(61\) 4.42775e29 0.197504 0.0987519 0.995112i \(-0.468515\pi\)
0.0987519 + 0.995112i \(0.468515\pi\)
\(62\) 2.39727e29i 0.0811069i
\(63\) −2.92486e30 4.01667e30i −0.753904 1.03533i
\(64\) 8.05565e30 1.58870
\(65\) 1.21618e30i 0.184276i
\(66\) −1.28057e31 6.51620e30i −1.49678 0.761636i
\(67\) −4.63018e30 −0.419108 −0.209554 0.977797i \(-0.567201\pi\)
−0.209554 + 0.977797i \(0.567201\pi\)
\(68\) 3.37094e31i 2.37192i
\(69\) −1.75324e30 + 3.44549e30i −0.0962516 + 0.189155i
\(70\) 1.09245e31 0.469607
\(71\) 2.74044e30i 0.0925611i 0.998928 + 0.0462805i \(0.0147368\pi\)
−0.998928 + 0.0462805i \(0.985263\pi\)
\(72\) −1.97688e31 + 1.43952e31i −0.526414 + 0.383324i
\(73\) −2.72565e31 −0.574092 −0.287046 0.957917i \(-0.592673\pi\)
−0.287046 + 0.957917i \(0.592673\pi\)
\(74\) 7.64242e31i 1.27730i
\(75\) −6.32707e31 3.21954e31i −0.841708 0.428304i
\(76\) 2.16355e32 2.29792
\(77\) 1.62617e32i 1.38300i
\(78\) −8.07189e31 + 1.58630e32i −0.551274 + 1.08337i
\(79\) 1.93130e32 1.06216 0.531080 0.847322i \(-0.321787\pi\)
0.531080 + 0.847322i \(0.321787\pi\)
\(80\) 2.15529e31i 0.0957142i
\(81\) −8.53797e31 + 2.64699e32i −0.306979 + 0.951716i
\(82\) 4.36044e32 1.27261
\(83\) 2.76431e32i 0.656537i 0.944584 + 0.328269i \(0.106465\pi\)
−0.944584 + 0.328269i \(0.893535\pi\)
\(84\) −8.35794e32 4.25295e32i −1.61939 0.824029i
\(85\) −2.48778e32 −0.394176
\(86\) 8.32483e32i 1.08119i
\(87\) 1.85764e32 3.65065e32i 0.198214 0.389532i
\(88\) −8.00347e32 −0.703191
\(89\) 2.71501e33i 1.96853i 0.176706 + 0.984264i \(0.443456\pi\)
−0.176706 + 0.984264i \(0.556544\pi\)
\(90\) −3.59963e32 4.94332e32i −0.215842 0.296412i
\(91\) −2.01440e33 −1.00102
\(92\) 7.29634e32i 0.301101i
\(93\) −1.35355e32 6.88757e31i −0.0464799 0.0236513i
\(94\) 1.00907e34 2.88900
\(95\) 1.59671e33i 0.381879i
\(96\) 2.90589e33 5.71068e33i 0.581658 1.14308i
\(97\) −1.23468e33 −0.207222 −0.103611 0.994618i \(-0.533040\pi\)
−0.103611 + 0.994618i \(0.533040\pi\)
\(98\) 7.06317e33i 0.995764i
\(99\) −7.35839e33 + 5.35823e33i −0.872940 + 0.635658i
\(100\) −1.33985e34 −1.33985
\(101\) 1.60999e34i 1.35944i −0.733473 0.679718i \(-0.762102\pi\)
0.733473 0.679718i \(-0.237898\pi\)
\(102\) 3.24489e34 + 1.65116e34i 2.31738 + 1.17920i
\(103\) −1.43441e34 −0.867841 −0.433920 0.900951i \(-0.642870\pi\)
−0.433920 + 0.900951i \(0.642870\pi\)
\(104\) 9.91424e33i 0.508971i
\(105\) 3.13871e33 6.16822e33i 0.136941 0.269118i
\(106\) −1.90749e34 −0.708375
\(107\) 1.60322e34i 0.507537i 0.967265 + 0.253768i \(0.0816701\pi\)
−0.967265 + 0.253768i \(0.918330\pi\)
\(108\) 8.29493e33 + 5.18331e34i 0.224186 + 1.40089i
\(109\) −5.19945e34 −1.20145 −0.600727 0.799454i \(-0.705122\pi\)
−0.600727 + 0.799454i \(0.705122\pi\)
\(110\) 2.00133e34i 0.395952i
\(111\) −4.31509e34 2.19574e34i −0.731980 0.372469i
\(112\) 3.56990e34 0.519935
\(113\) 1.59663e34i 0.199927i 0.994991 + 0.0999633i \(0.0318725\pi\)
−0.994991 + 0.0999633i \(0.968127\pi\)
\(114\) 1.05976e35 2.08264e35i 1.14241 2.24508i
\(115\) −5.38475e33 −0.0500383
\(116\) 7.73080e34i 0.620067i
\(117\) 6.63747e34 + 9.11515e34i 0.460090 + 0.631836i
\(118\) 1.28906e35 0.773175
\(119\) 4.12061e35i 2.14123i
\(120\) −3.03580e34 1.54477e34i −0.136833 0.0696278i
\(121\) −4.24310e34 −0.166086
\(122\) 9.02578e34i 0.307162i
\(123\) 1.25279e35 2.46200e35i 0.371101 0.729292i
\(124\) −2.86635e34 −0.0739878
\(125\) 2.03584e35i 0.458430i
\(126\) −8.18783e35 + 5.96221e35i −1.61016 + 1.17249i
\(127\) −6.17065e34 −0.106088 −0.0530442 0.998592i \(-0.516892\pi\)
−0.0530442 + 0.998592i \(0.516892\pi\)
\(128\) 7.89704e35i 1.18821i
\(129\) −4.70039e35 2.39180e35i −0.619596 0.315282i
\(130\) −2.47913e35 −0.286591
\(131\) 3.37852e35i 0.342858i 0.985196 + 0.171429i \(0.0548385\pi\)
−0.985196 + 0.171429i \(0.945162\pi\)
\(132\) −7.79124e35 + 1.53114e36i −0.694784 + 1.36540i
\(133\) 2.64470e36 2.07443
\(134\) 9.43843e35i 0.651806i
\(135\) −3.82532e35 + 6.12172e34i −0.232806 + 0.0372563i
\(136\) 2.02803e36 1.08871
\(137\) 2.58108e36i 1.22335i −0.791107 0.611677i \(-0.790495\pi\)
0.791107 0.611677i \(-0.209505\pi\)
\(138\) 7.02350e35 + 3.57392e35i 0.294177 + 0.149692i
\(139\) −2.72993e36 −1.01135 −0.505673 0.862725i \(-0.668756\pi\)
−0.505673 + 0.862725i \(0.668756\pi\)
\(140\) 1.30621e36i 0.428388i
\(141\) 2.89915e36 5.69744e36i 0.842453 1.65560i
\(142\) 5.58628e35 0.143953
\(143\) 3.69031e36i 0.844015i
\(144\) −1.17628e36 1.61537e36i −0.238973 0.328179i
\(145\) 5.70539e35 0.103045
\(146\) 5.55613e36i 0.892841i
\(147\) −3.98803e36 2.02931e36i −0.570642 0.290372i
\(148\) −9.13783e36 −1.16518
\(149\) 1.30238e37i 1.48105i 0.672026 + 0.740527i \(0.265424\pi\)
−0.672026 + 0.740527i \(0.734576\pi\)
\(150\) −6.56290e36 + 1.28975e37i −0.666108 + 1.30904i
\(151\) 1.53327e37 1.38998 0.694992 0.719017i \(-0.255408\pi\)
0.694992 + 0.719017i \(0.255408\pi\)
\(152\) 1.30164e37i 1.05475i
\(153\) 1.86457e37 1.35774e37i 1.35153 0.984154i
\(154\) −3.31488e37 −2.15088
\(155\) 2.11538e35i 0.0122956i
\(156\) 1.89669e37 + 9.65134e36i 0.988277 + 0.502886i
\(157\) −2.25738e37 −1.05514 −0.527570 0.849512i \(-0.676897\pi\)
−0.527570 + 0.849512i \(0.676897\pi\)
\(158\) 3.93688e37i 1.65189i
\(159\) −5.48040e36 + 1.07701e37i −0.206567 + 0.405948i
\(160\) 8.92487e36 0.302386
\(161\) 8.91899e36i 0.271816i
\(162\) 5.39579e37 + 1.74043e37i 1.48013 + 0.477421i
\(163\) 2.51834e37 0.622194 0.311097 0.950378i \(-0.399304\pi\)
0.311097 + 0.950378i \(0.399304\pi\)
\(164\) 5.21365e37i 1.16091i
\(165\) −1.12999e37 5.74999e36i −0.226908 0.115462i
\(166\) 5.63494e37 1.02106
\(167\) 6.73804e37i 1.10244i 0.834361 + 0.551218i \(0.185837\pi\)
−0.834361 + 0.551218i \(0.814163\pi\)
\(168\) −2.55867e37 + 5.02832e37i −0.378230 + 0.743302i
\(169\) −2.91163e37 −0.389100
\(170\) 5.07123e37i 0.613030i
\(171\) −8.71431e37 1.19672e38i −0.953452 1.30936i
\(172\) −9.95377e37 −0.986288
\(173\) 4.60014e37i 0.413036i 0.978443 + 0.206518i \(0.0662131\pi\)
−0.978443 + 0.206518i \(0.933787\pi\)
\(174\) −7.44171e37 3.78672e37i −0.605809 0.308267i
\(175\) −1.63782e38 −1.20954
\(176\) 6.53991e37i 0.438386i
\(177\) 3.70358e37 7.27831e37i 0.225463 0.443083i
\(178\) 5.53444e38 3.06150
\(179\) 7.46180e37i 0.375269i 0.982239 + 0.187634i \(0.0600820\pi\)
−0.982239 + 0.187634i \(0.939918\pi\)
\(180\) −5.91059e37 + 4.30398e37i −0.270395 + 0.196896i
\(181\) −2.13615e38 −0.889396 −0.444698 0.895681i \(-0.646689\pi\)
−0.444698 + 0.895681i \(0.646689\pi\)
\(182\) 4.10628e38i 1.55681i
\(183\) −5.09616e37 2.59319e37i −0.176025 0.0895706i
\(184\) 4.38964e37 0.138206
\(185\) 6.74379e37i 0.193635i
\(186\) −1.40400e37 + 2.75916e37i −0.0367831 + 0.0722865i
\(187\) 7.54880e38 1.80539
\(188\) 1.20652e39i 2.63542i
\(189\) 1.01396e38 + 6.33603e38i 0.202382 + 1.26464i
\(190\) 3.25484e38 0.593906
\(191\) 5.98739e38i 0.999242i −0.866244 0.499621i \(-0.833473\pi\)
0.866244 0.499621i \(-0.166527\pi\)
\(192\) −9.27173e38 4.71793e38i −1.41592 0.720495i
\(193\) −5.27026e38 −0.736814 −0.368407 0.929665i \(-0.620097\pi\)
−0.368407 + 0.929665i \(0.620097\pi\)
\(194\) 2.51685e38i 0.322276i
\(195\) −7.12276e37 + 1.39977e38i −0.0835718 + 0.164236i
\(196\) −8.44524e38 −0.908361
\(197\) 1.44438e39i 1.42480i 0.701772 + 0.712402i \(0.252393\pi\)
−0.701772 + 0.712402i \(0.747607\pi\)
\(198\) 1.09225e39 + 1.49998e39i 0.988588 + 1.35762i
\(199\) 2.12251e38 0.176338 0.0881691 0.996106i \(-0.471898\pi\)
0.0881691 + 0.996106i \(0.471898\pi\)
\(200\) 8.06083e38i 0.614993i
\(201\) 5.32915e38 + 2.71175e38i 0.373530 + 0.190071i
\(202\) −3.28189e39 −2.11422
\(203\) 9.45006e38i 0.559760i
\(204\) 1.97425e39 3.87982e39i 1.07570 2.11397i
\(205\) 3.84771e38 0.192924
\(206\) 2.92398e39i 1.34968i
\(207\) 4.03583e38 2.93881e38i 0.171568 0.124933i
\(208\) −8.10127e38 −0.317305
\(209\) 4.84499e39i 1.74907i
\(210\) −1.25737e39 6.39813e38i −0.418537 0.212973i
\(211\) 2.65596e39 0.815491 0.407745 0.913096i \(-0.366315\pi\)
0.407745 + 0.913096i \(0.366315\pi\)
\(212\) 2.28074e39i 0.646198i
\(213\) 1.60499e38 3.15414e38i 0.0419777 0.0824950i
\(214\) 3.26809e39 0.789332
\(215\) 7.34595e38i 0.163906i
\(216\) 3.11839e39 4.99041e38i 0.643009 0.102902i
\(217\) −3.50380e38 −0.0667919
\(218\) 1.05989e40i 1.86853i
\(219\) 3.13712e39 + 1.59633e39i 0.511660 + 0.260359i
\(220\) −2.39293e39 −0.361197
\(221\) 9.35102e39i 1.30674i
\(222\) −4.47592e39 + 8.79613e39i −0.579271 + 1.13839i
\(223\) −1.51320e40 −1.81432 −0.907160 0.420787i \(-0.861754\pi\)
−0.907160 + 0.420787i \(0.861754\pi\)
\(224\) 1.47826e40i 1.64261i
\(225\) 5.39664e39 + 7.41113e39i 0.555930 + 0.763452i
\(226\) 3.25466e39 0.310930
\(227\) 6.49041e38i 0.0575218i 0.999586 + 0.0287609i \(0.00915614\pi\)
−0.999586 + 0.0287609i \(0.990844\pi\)
\(228\) −2.49016e40 1.26712e40i −2.04802 1.04214i
\(229\) 1.50995e40 1.15282 0.576408 0.817162i \(-0.304454\pi\)
0.576408 + 0.817162i \(0.304454\pi\)
\(230\) 1.09766e39i 0.0778206i
\(231\) −9.52394e39 + 1.87166e40i −0.627210 + 1.23260i
\(232\) −4.65102e39 −0.284611
\(233\) 1.83862e40i 1.04578i 0.852400 + 0.522891i \(0.175147\pi\)
−0.852400 + 0.522891i \(0.824853\pi\)
\(234\) 1.85809e40 1.35302e40i 0.982645 0.715542i
\(235\) 8.90418e39 0.437966
\(236\) 1.54129e40i 0.705310i
\(237\) −2.22285e40 1.13110e40i −0.946649 0.481703i
\(238\) 8.39969e40 3.33008
\(239\) 2.31681e40i 0.855317i 0.903940 + 0.427658i \(0.140661\pi\)
−0.903940 + 0.427658i \(0.859339\pi\)
\(240\) 1.26228e39 2.48066e39i 0.0434076 0.0853052i
\(241\) −2.31568e40 −0.741974 −0.370987 0.928638i \(-0.620980\pi\)
−0.370987 + 0.928638i \(0.620980\pi\)
\(242\) 8.64939e39i 0.258300i
\(243\) 2.53295e40 2.54654e40i 0.705211 0.708997i
\(244\) −1.07919e40 −0.280201
\(245\) 6.23265e39i 0.150956i
\(246\) −5.01869e40 2.55377e40i −1.13421 0.577144i
\(247\) −6.00170e40 −1.26598
\(248\) 1.72446e39i 0.0339605i
\(249\) 1.61897e40 3.18162e40i 0.297748 0.585139i
\(250\) −4.14998e40 −0.712961
\(251\) 1.45158e39i 0.0233016i 0.999932 + 0.0116508i \(0.00370866\pi\)
−0.999932 + 0.0116508i \(0.996291\pi\)
\(252\) 7.12885e40 + 9.78996e40i 1.06957 + 1.46883i
\(253\) 1.63392e40 0.229183
\(254\) 1.25786e40i 0.164991i
\(255\) 2.86334e40 + 1.45701e40i 0.351309 + 0.178764i
\(256\) −2.25829e40 −0.259239
\(257\) 2.58352e40i 0.277555i −0.990324 0.138778i \(-0.955683\pi\)
0.990324 0.138778i \(-0.0443173\pi\)
\(258\) −4.87559e40 + 9.58155e40i −0.490334 + 0.963609i
\(259\) −1.11700e41 −1.05186
\(260\) 2.96422e40i 0.261435i
\(261\) −4.27614e40 + 3.11380e40i −0.353316 + 0.257278i
\(262\) 6.88698e40 0.533221
\(263\) 3.82679e40i 0.277707i 0.990313 + 0.138853i \(0.0443417\pi\)
−0.990313 + 0.138853i \(0.955658\pi\)
\(264\) 9.21169e40 + 4.68738e40i 0.626718 + 0.318906i
\(265\) −1.68320e40 −0.107388
\(266\) 5.39112e41i 3.22620i
\(267\) 1.59009e41 3.12487e41i 0.892753 1.75445i
\(268\) 1.12853e41 0.594594
\(269\) 9.18662e40i 0.454325i 0.973857 + 0.227163i \(0.0729449\pi\)
−0.973857 + 0.227163i \(0.927055\pi\)
\(270\) 1.24789e40 + 7.79776e40i 0.0579417 + 0.362064i
\(271\) 5.88942e40 0.256800 0.128400 0.991722i \(-0.459016\pi\)
0.128400 + 0.991722i \(0.459016\pi\)
\(272\) 1.65717e41i 0.678729i
\(273\) 2.31850e41 + 1.17977e41i 0.892159 + 0.453976i
\(274\) −5.26143e41 −1.90259
\(275\) 3.00043e41i 1.01983i
\(276\) 4.27323e40 8.39781e40i 0.136553 0.268356i
\(277\) 2.24409e41 0.674348 0.337174 0.941442i \(-0.390529\pi\)
0.337174 + 0.941442i \(0.390529\pi\)
\(278\) 5.56485e41i 1.57287i
\(279\) 1.15450e40 + 1.58546e40i 0.0306990 + 0.0421585i
\(280\) −7.85845e40 −0.196630
\(281\) 8.35899e40i 0.196855i 0.995144 + 0.0984275i \(0.0313813\pi\)
−0.995144 + 0.0984275i \(0.968619\pi\)
\(282\) −1.16140e42 5.90980e41i −2.57482 1.31020i
\(283\) 4.36918e41 0.912074 0.456037 0.889961i \(-0.349268\pi\)
0.456037 + 0.889961i \(0.349268\pi\)
\(284\) 6.67936e40i 0.131318i
\(285\) 9.35144e40 1.83776e41i 0.173187 0.340349i
\(286\) 7.52255e41 1.31263
\(287\) 6.37313e41i 1.04800i
\(288\) −6.68912e41 + 4.87089e41i −1.03680 + 0.754980i
\(289\) −1.22849e42 −1.79518
\(290\) 1.16302e41i 0.160259i
\(291\) 1.42107e41 + 7.23113e40i 0.184686 + 0.0939778i
\(292\) 6.64331e41 0.814472
\(293\) 2.32629e41i 0.269100i −0.990907 0.134550i \(-0.957041\pi\)
0.990907 0.134550i \(-0.0429590\pi\)
\(294\) −4.13667e41 + 8.12943e41i −0.451592 + 0.887474i
\(295\) 1.13748e41 0.117212
\(296\) 5.49752e41i 0.534820i
\(297\) 1.16074e42 1.85754e41i 1.06629 0.170640i
\(298\) 2.65485e42 2.30337
\(299\) 2.02401e41i 0.165883i
\(300\) 1.54212e42 + 7.84708e41i 1.19414 + 0.607640i
\(301\) −1.21674e42 −0.890364
\(302\) 3.12550e42i 2.16173i
\(303\) −9.42917e41 + 1.85303e42i −0.616523 + 1.21160i
\(304\) 1.06361e42 0.657555
\(305\) 7.96448e40i 0.0465651i
\(306\) −2.76770e42 3.80085e42i −1.53058 2.10192i
\(307\) −3.20258e42 −1.67551 −0.837756 0.546044i \(-0.816133\pi\)
−0.837756 + 0.546044i \(0.816133\pi\)
\(308\) 3.96351e42i 1.96208i
\(309\) 1.65095e42 + 8.40087e41i 0.773463 + 0.393577i
\(310\) −4.31212e40 −0.0191224
\(311\) 3.41897e42i 1.43538i −0.696360 0.717692i \(-0.745198\pi\)
0.696360 0.717692i \(-0.254802\pi\)
\(312\) 5.80645e41 1.14109e42i 0.230825 0.453620i
\(313\) 4.76701e41 0.179470 0.0897350 0.995966i \(-0.471398\pi\)
0.0897350 + 0.995966i \(0.471398\pi\)
\(314\) 4.60157e42i 1.64097i
\(315\) −7.22506e41 + 5.26114e41i −0.244097 + 0.177746i
\(316\) −4.70722e42 −1.50690
\(317\) 1.47092e42i 0.446254i 0.974789 + 0.223127i \(0.0716265\pi\)
−0.974789 + 0.223127i \(0.928373\pi\)
\(318\) 2.19545e42 + 1.11716e42i 0.631339 + 0.321257i
\(319\) −1.73122e42 −0.471965
\(320\) 1.44902e42i 0.374564i
\(321\) 9.38952e41 1.84524e42i 0.230175 0.452342i
\(322\) 1.81810e42 0.422735
\(323\) 1.22769e43i 2.70798i
\(324\) 2.08098e42 6.45159e42i 0.435515 1.35021i
\(325\) 3.71676e42 0.738154
\(326\) 5.13354e42i 0.967649i
\(327\) 5.98437e42 + 3.04515e42i 1.07080 + 0.544875i
\(328\) −3.13665e42 −0.532857
\(329\) 1.47484e43i 2.37910i
\(330\) −1.17211e42 + 2.30345e42i −0.179569 + 0.352892i
\(331\) −1.30392e43 −1.89746 −0.948732 0.316081i \(-0.897633\pi\)
−0.948732 + 0.316081i \(0.897633\pi\)
\(332\) 6.73754e42i 0.931438i
\(333\) 3.68053e42 + 5.05442e42i 0.483457 + 0.663925i
\(334\) 1.37352e43 1.71453
\(335\) 8.32861e41i 0.0988123i
\(336\) −4.10881e42 2.09077e42i −0.463392 0.235798i
\(337\) 3.57010e42 0.382800 0.191400 0.981512i \(-0.438697\pi\)
0.191400 + 0.981512i \(0.438697\pi\)
\(338\) 5.93523e42i 0.605137i
\(339\) 9.35095e41 1.83766e42i 0.0906694 0.178184i
\(340\) 6.06354e42 0.559222
\(341\) 6.41882e41i 0.0563159i
\(342\) −2.43947e43 + 1.77638e43i −2.03635 + 1.48283i
\(343\) 5.80006e42 0.460715
\(344\) 5.98840e42i 0.452707i
\(345\) 6.19764e41 + 3.15368e41i 0.0445966 + 0.0226930i
\(346\) 9.37720e42 0.642362
\(347\) 2.26027e43i 1.47421i −0.675777 0.737106i \(-0.736192\pi\)
0.675777 0.737106i \(-0.263808\pi\)
\(348\) −4.52768e42 + 8.89785e42i −0.281209 + 0.552634i
\(349\) −1.34307e43 −0.794450 −0.397225 0.917721i \(-0.630027\pi\)
−0.397225 + 0.917721i \(0.630027\pi\)
\(350\) 3.33863e43i 1.88110i
\(351\) −2.30102e42 1.43785e43i −0.123509 0.771781i
\(352\) −2.70812e43 −1.38498
\(353\) 1.97828e43i 0.964088i 0.876147 + 0.482044i \(0.160105\pi\)
−0.876147 + 0.482044i \(0.839895\pi\)
\(354\) −1.48365e43 7.54959e42i −0.689092 0.350645i
\(355\) 4.92941e41 0.0218229
\(356\) 6.61738e43i 2.79277i
\(357\) 2.41331e43 4.74266e43i 0.971076 1.90837i
\(358\) 1.52106e43 0.583626
\(359\) 3.01626e43i 1.10373i 0.833933 + 0.551865i \(0.186084\pi\)
−0.833933 + 0.551865i \(0.813916\pi\)
\(360\) 2.58937e42 + 3.55594e42i 0.0903755 + 0.124112i
\(361\) 4.87614e43 1.62350
\(362\) 4.35445e43i 1.38321i
\(363\) 4.88364e42 + 2.48505e42i 0.148024 + 0.0753221i
\(364\) 4.90977e43 1.42016
\(365\) 4.90281e42i 0.135353i
\(366\) −5.28611e42 + 1.03883e43i −0.139302 + 0.273758i
\(367\) −3.90052e43 −0.981295 −0.490648 0.871358i \(-0.663240\pi\)
−0.490648 + 0.871358i \(0.663240\pi\)
\(368\) 3.58692e42i 0.0861607i
\(369\) −2.88383e43 + 2.09995e43i −0.661488 + 0.481682i
\(370\) −1.37469e43 −0.301146
\(371\) 2.78795e43i 0.583350i
\(372\) 3.29905e42 + 1.67873e42i 0.0659416 + 0.0335544i
\(373\) 4.80844e43 0.918236 0.459118 0.888375i \(-0.348166\pi\)
0.459118 + 0.888375i \(0.348166\pi\)
\(374\) 1.53879e44i 2.80778i
\(375\) −1.19233e43 + 2.34317e43i −0.207904 + 0.408576i
\(376\) −7.25866e43 −1.20966
\(377\) 2.14453e43i 0.341609i
\(378\) 1.29157e44 2.06693e43i 1.96679 0.314749i
\(379\) −1.06583e44 −1.55175 −0.775875 0.630886i \(-0.782691\pi\)
−0.775875 + 0.630886i \(0.782691\pi\)
\(380\) 3.89172e43i 0.541776i
\(381\) 7.10218e42 + 3.61395e42i 0.0945512 + 0.0481125i
\(382\) −1.22051e44 −1.55404
\(383\) 1.75688e42i 0.0213975i −0.999943 0.0106988i \(-0.996594\pi\)
0.999943 0.0106988i \(-0.00340559\pi\)
\(384\) −4.62504e43 + 9.08918e43i −0.538871 + 1.05899i
\(385\) −2.92510e43 −0.326068
\(386\) 1.07432e44i 1.14591i
\(387\) 4.00917e43 + 5.50574e43i 0.409230 + 0.561990i
\(388\) 3.00932e43 0.293988
\(389\) 5.10095e41i 0.00476988i −0.999997 0.00238494i \(-0.999241\pi\)
0.999997 0.00238494i \(-0.000759151\pi\)
\(390\) 2.85338e43 + 1.45195e43i 0.255424 + 0.129973i
\(391\) −4.14026e43 −0.354832
\(392\) 5.08084e43i 0.416939i
\(393\) 1.97869e43 3.88855e43i 0.155491 0.305572i
\(394\) 2.94431e44 2.21589
\(395\) 3.47396e43i 0.250423i
\(396\) 1.79348e44 1.30598e44i 1.23845 0.901815i
\(397\) 7.73555e43 0.511744 0.255872 0.966711i \(-0.417637\pi\)
0.255872 + 0.966711i \(0.417637\pi\)
\(398\) 4.32664e43i 0.274245i
\(399\) −3.04395e44 1.54892e44i −1.84883 0.940782i
\(400\) −6.58678e43 −0.383401
\(401\) 2.78483e44i 1.55362i −0.629737 0.776808i \(-0.716837\pi\)
0.629737 0.776808i \(-0.283163\pi\)
\(402\) 5.52778e43 1.08633e44i 0.295603 0.580921i
\(403\) 7.95127e42 0.0407615
\(404\) 3.92407e44i 1.92865i
\(405\) 4.76132e43 + 1.53578e43i 0.224384 + 0.0723759i
\(406\) −1.92636e44 −0.870551
\(407\) 2.04630e44i 0.886880i
\(408\) −2.33418e44 1.18775e44i −0.970314 0.493745i
\(409\) 2.45834e44 0.980271 0.490136 0.871646i \(-0.336947\pi\)
0.490136 + 0.871646i \(0.336947\pi\)
\(410\) 7.84341e43i 0.300040i
\(411\) −1.51166e44 + 2.97073e44i −0.554808 + 1.09031i
\(412\) 3.49613e44 1.23122
\(413\) 1.88406e44i 0.636713i
\(414\) −5.99065e43 8.22688e43i −0.194298 0.266827i
\(415\) 4.97235e43 0.154790
\(416\) 3.35466e44i 1.00245i
\(417\) 3.14204e44 + 1.59883e44i 0.901362 + 0.458659i
\(418\) −9.87632e44 −2.72018
\(419\) 3.06939e44i 0.811733i 0.913932 + 0.405866i \(0.133030\pi\)
−0.913932 + 0.405866i \(0.866970\pi\)
\(420\) −7.65006e43 + 1.50340e44i −0.194280 + 0.381800i
\(421\) 5.45542e44 1.33055 0.665277 0.746596i \(-0.268313\pi\)
0.665277 + 0.746596i \(0.268313\pi\)
\(422\) 5.41406e44i 1.26827i
\(423\) −6.67361e44 + 4.85959e44i −1.50167 + 1.09349i
\(424\) 1.37214e44 0.296605
\(425\) 7.60290e44i 1.57895i
\(426\) −6.42959e43 3.27170e43i −0.128298 0.0652846i
\(427\) −1.31919e44 −0.252949
\(428\) 3.90756e44i 0.720049i
\(429\) 2.16130e44 4.24740e44i 0.382772 0.752228i
\(430\) −1.49744e44 −0.254910
\(431\) 1.40207e44i 0.229433i 0.993398 + 0.114717i \(0.0365960\pi\)
−0.993398 + 0.114717i \(0.963404\pi\)
\(432\) 4.07783e43 + 2.54814e44i 0.0641513 + 0.400867i
\(433\) 1.02287e45 1.54712 0.773560 0.633723i \(-0.218474\pi\)
0.773560 + 0.633723i \(0.218474\pi\)
\(434\) 7.14235e43i 0.103876i
\(435\) −6.56668e43 3.34146e43i −0.0918392 0.0467325i
\(436\) 1.26728e45 1.70452
\(437\) 2.65732e44i 0.343763i
\(438\) 3.25405e44 6.39489e44i 0.404915 0.795744i
\(439\) −4.46827e44 −0.534863 −0.267432 0.963577i \(-0.586175\pi\)
−0.267432 + 0.963577i \(0.586175\pi\)
\(440\) 1.43964e44i 0.165790i
\(441\) 3.40156e44 + 4.67132e44i 0.376897 + 0.517587i
\(442\) −1.90617e45 −2.03227
\(443\) 4.00047e44i 0.410438i −0.978716 0.205219i \(-0.934209\pi\)
0.978716 0.205219i \(-0.0657907\pi\)
\(444\) 1.05173e45 + 5.35174e44i 1.03847 + 0.528426i
\(445\) 4.88367e44 0.464116
\(446\) 3.08460e45i 2.82167i
\(447\) 7.62762e44 1.49899e45i 0.671678 1.31999i
\(448\) −2.40008e45 −2.03469
\(449\) 3.21986e44i 0.262814i −0.991328 0.131407i \(-0.958051\pi\)
0.991328 0.131407i \(-0.0419495\pi\)
\(450\) 1.51073e45 1.10008e45i 1.18734 0.864594i
\(451\) −1.16753e45 −0.883624
\(452\) 3.89151e44i 0.283638i
\(453\) −1.76473e45 8.97986e44i −1.23882 0.630376i
\(454\) 1.32304e44 0.0894591
\(455\) 3.62344e44i 0.236008i
\(456\) −7.62327e44 + 1.49813e45i −0.478342 + 0.940044i
\(457\) −1.13640e45 −0.686996 −0.343498 0.939153i \(-0.611612\pi\)
−0.343498 + 0.939153i \(0.611612\pi\)
\(458\) 3.07797e45i 1.79288i
\(459\) −2.94123e45 + 4.70690e44i −1.65087 + 0.264192i
\(460\) 1.31244e44 0.0709900
\(461\) 1.29866e45i 0.676985i 0.940969 + 0.338493i \(0.109917\pi\)
−0.940969 + 0.338493i \(0.890083\pi\)
\(462\) 3.81529e45 + 1.94142e45i 1.91697 + 0.975451i
\(463\) 1.91002e45 0.925042 0.462521 0.886608i \(-0.346945\pi\)
0.462521 + 0.886608i \(0.346945\pi\)
\(464\) 3.80050e44i 0.177433i
\(465\) −1.23891e43 + 2.43472e43i −0.00557623 + 0.0109585i
\(466\) 3.74795e45 1.62642
\(467\) 2.71525e45i 1.13612i 0.822988 + 0.568058i \(0.192305\pi\)
−0.822988 + 0.568058i \(0.807695\pi\)
\(468\) −1.61777e45 2.22166e45i −0.652736 0.896393i
\(469\) 1.37950e45 0.536765
\(470\) 1.81508e45i 0.681134i
\(471\) 2.59815e45 + 1.32207e45i 0.940392 + 0.478520i
\(472\) −9.27273e44 −0.323738
\(473\) 2.22902e45i 0.750714i
\(474\) −2.30570e45 + 4.53120e45i −0.749155 + 1.47225i
\(475\) −4.87971e45 −1.52969
\(476\) 1.00433e46i 3.03779i
\(477\) 1.26155e45 9.18632e44i 0.368206 0.268120i
\(478\) 4.72273e45 1.33021
\(479\) 4.10305e45i 1.11533i −0.830066 0.557665i \(-0.811697\pi\)
0.830066 0.557665i \(-0.188303\pi\)
\(480\) −1.02722e45 5.22701e44i −0.269502 0.137136i
\(481\) 2.53484e45 0.641926
\(482\) 4.72042e45i 1.15393i
\(483\) 5.22356e44 1.02654e45i 0.123272 0.242256i
\(484\) 1.03418e45 0.235628
\(485\) 2.22090e44i 0.0488562i
\(486\) −5.19103e45 5.16331e45i −1.10265 1.09676i
\(487\) −2.80093e45 −0.574527 −0.287263 0.957852i \(-0.592746\pi\)
−0.287263 + 0.957852i \(0.592746\pi\)
\(488\) 6.49262e44i 0.128613i
\(489\) −2.89852e45 1.47491e45i −0.554530 0.282173i
\(490\) −1.27050e45 −0.234769
\(491\) 1.01670e46i 1.81471i 0.420365 + 0.907355i \(0.361902\pi\)
−0.420365 + 0.907355i \(0.638098\pi\)
\(492\) −3.05347e45 + 6.00071e45i −0.526486 + 1.03466i
\(493\) 4.38679e45 0.730717
\(494\) 1.22342e46i 1.96887i
\(495\) 9.63821e44 + 1.32360e45i 0.149868 + 0.205811i
\(496\) −1.40911e44 −0.0211718
\(497\) 8.16479e44i 0.118546i
\(498\) −6.48559e45 3.30020e45i −0.910020 0.463065i
\(499\) −8.61330e44 −0.116805 −0.0584023 0.998293i \(-0.518601\pi\)
−0.0584023 + 0.998293i \(0.518601\pi\)
\(500\) 4.96201e45i 0.650381i
\(501\) 3.94625e45 7.75522e45i 0.499970 0.982546i
\(502\) 2.95898e44 0.0362392
\(503\) 1.60755e46i 1.90331i −0.307173 0.951654i \(-0.599383\pi\)
0.307173 0.951654i \(-0.400617\pi\)
\(504\) 5.88985e45 4.28887e45i 0.674194 0.490935i
\(505\) −2.89599e45 −0.320512
\(506\) 3.33069e45i 0.356431i
\(507\) 3.35117e45 + 1.70525e45i 0.346785 + 0.176462i
\(508\) 1.50399e45 0.150509
\(509\) 7.93372e45i 0.767847i −0.923365 0.383923i \(-0.874573\pi\)
0.923365 0.383923i \(-0.125427\pi\)
\(510\) 2.97006e45 5.83679e45i 0.278018 0.546363i
\(511\) 8.12073e45 0.735258
\(512\) 8.96357e45i 0.785040i
\(513\) 3.02100e45 + 1.88775e46i 0.255950 + 1.59937i
\(514\) −5.26641e45 −0.431660
\(515\) 2.58017e45i 0.204609i
\(516\) 1.14564e46 + 5.82960e45i 0.879029 + 0.447295i
\(517\) −2.70184e46 −2.00595
\(518\) 2.27696e46i 1.63587i
\(519\) 2.69416e45 5.29459e45i 0.187317 0.368118i
\(520\) 1.78334e45 0.119999
\(521\) 1.97184e46i 1.28419i −0.766623 0.642097i \(-0.778064\pi\)
0.766623 0.642097i \(-0.221936\pi\)
\(522\) 6.34736e45 + 8.71674e45i 0.400124 + 0.549485i
\(523\) 6.08625e45 0.371382 0.185691 0.982608i \(-0.440548\pi\)
0.185691 + 0.982608i \(0.440548\pi\)
\(524\) 8.23457e45i 0.486418i
\(525\) 1.88507e46 + 9.59220e45i 1.07800 + 0.548542i
\(526\) 7.80075e45 0.431895
\(527\) 1.62649e45i 0.0871908i
\(528\) −3.83022e45 + 7.52718e45i −0.198814 + 0.390711i
\(529\) 1.89990e46 0.954956
\(530\) 3.43113e45i 0.167012i
\(531\) −8.52534e45 + 6.20798e45i −0.401888 + 0.292647i
\(532\) −6.44601e46 −2.94302
\(533\) 1.44627e46i 0.639569i
\(534\) −6.36992e46 3.24134e46i −2.72856 1.38843i
\(535\) 2.88381e45 0.119661
\(536\) 6.78946e45i 0.272919i
\(537\) 4.37014e45 8.58824e45i 0.170189 0.334458i
\(538\) 1.87265e46 0.706576
\(539\) 1.89120e46i 0.691400i
\(540\) 9.32356e45 1.49206e45i 0.330284 0.0528559i
\(541\) −4.44680e46 −1.52649 −0.763245 0.646109i \(-0.776395\pi\)
−0.763245 + 0.646109i \(0.776395\pi\)
\(542\) 1.20054e46i 0.399381i
\(543\) 2.45862e46 + 1.25107e46i 0.792674 + 0.403353i
\(544\) 6.86221e46 2.14429
\(545\) 9.35260e45i 0.283264i
\(546\) 2.40492e46 4.72617e46i 0.706033 1.38750i
\(547\) −6.87329e45 −0.195605 −0.0978026 0.995206i \(-0.531181\pi\)
−0.0978026 + 0.995206i \(0.531181\pi\)
\(548\) 6.29095e46i 1.73559i
\(549\) 4.34674e45 + 5.96932e45i 0.116261 + 0.159660i
\(550\) 6.11625e46 1.58606
\(551\) 2.81554e46i 0.707922i
\(552\) −5.05230e45 2.57087e45i −0.123176 0.0626781i
\(553\) −5.75406e46 −1.36034
\(554\) 4.57449e46i 1.04876i
\(555\) −3.94962e45 + 7.76184e45i −0.0878162 + 0.172577i
\(556\) 6.65374e46 1.43481
\(557\) 7.61000e46i 1.59164i 0.605530 + 0.795822i \(0.292961\pi\)
−0.605530 + 0.795822i \(0.707039\pi\)
\(558\) 3.23190e45 2.35341e45i 0.0655658 0.0477437i
\(559\) 2.76118e46 0.543369
\(560\) 6.42141e45i 0.122584i
\(561\) −8.68837e46 4.42109e46i −1.60905 0.818767i
\(562\) 1.70395e46 0.306153
\(563\) 7.61164e46i 1.32689i −0.748225 0.663446i \(-0.769093\pi\)
0.748225 0.663446i \(-0.230907\pi\)
\(564\) −7.06618e46 + 1.38865e47i −1.19520 + 2.34882i
\(565\) 2.87196e45 0.0471363
\(566\) 8.90639e46i 1.41848i
\(567\) 2.54378e46 7.88637e46i 0.393158 1.21889i
\(568\) −4.01844e45 −0.0602749
\(569\) 5.50884e46i 0.801958i 0.916087 + 0.400979i \(0.131330\pi\)
−0.916087 + 0.400979i \(0.868670\pi\)
\(570\) −3.74619e46 1.90625e46i −0.529319 0.269344i
\(571\) 5.77202e46 0.791615 0.395808 0.918333i \(-0.370465\pi\)
0.395808 + 0.918333i \(0.370465\pi\)
\(572\) 8.99450e46i 1.19741i
\(573\) −3.50662e46 + 6.89126e46i −0.453170 + 0.890574i
\(574\) −1.29914e47 −1.62987
\(575\) 1.64563e46i 0.200438i
\(576\) 7.90826e46 + 1.08603e47i 0.935188 + 1.28428i
\(577\) −8.48789e46 −0.974565 −0.487283 0.873244i \(-0.662012\pi\)
−0.487283 + 0.873244i \(0.662012\pi\)
\(578\) 2.50423e47i 2.79191i
\(579\) 6.06587e46 + 3.08662e46i 0.656685 + 0.334155i
\(580\) −1.39059e46 −0.146192
\(581\) 8.23591e46i 0.840848i
\(582\) 1.47404e46 2.89679e46i 0.146156 0.287228i
\(583\) 5.10742e46 0.491854
\(584\) 3.99676e46i 0.373843i
\(585\) 1.63960e46 1.19393e46i 0.148967 0.108475i
\(586\) −4.74205e46 −0.418511
\(587\) 1.53943e46i 0.131982i 0.997820 + 0.0659908i \(0.0210208\pi\)
−0.997820 + 0.0659908i \(0.978979\pi\)
\(588\) 9.72014e46 + 4.94610e46i 0.809576 + 0.411954i
\(589\) −1.04392e46 −0.0844708
\(590\) 2.31871e46i 0.182290i
\(591\) 8.45926e46 1.66242e47i 0.646168 1.26986i
\(592\) −4.49221e46 −0.333420
\(593\) 1.56245e47i 1.12687i 0.826159 + 0.563437i \(0.190521\pi\)
−0.826159 + 0.563437i \(0.809479\pi\)
\(594\) −3.78653e46 2.36611e47i −0.265382 1.65831i
\(595\) 7.41201e46 0.504833
\(596\) 3.17433e47i 2.10119i
\(597\) −2.44292e46 1.24308e46i −0.157161 0.0799717i
\(598\) −4.12586e46 −0.257985
\(599\) 1.40577e47i 0.854394i 0.904159 + 0.427197i \(0.140499\pi\)
−0.904159 + 0.427197i \(0.859501\pi\)
\(600\) 4.72097e46 9.27771e46i 0.278907 0.548112i
\(601\) 1.86614e47 1.07171 0.535856 0.844309i \(-0.319989\pi\)
0.535856 + 0.844309i \(0.319989\pi\)
\(602\) 2.48028e47i 1.38471i
\(603\) −4.54547e46 6.24223e46i −0.246708 0.338802i
\(604\) −3.73708e47 −1.97199
\(605\) 7.63235e45i 0.0391577i
\(606\) 3.77733e47 + 1.92210e47i 1.88430 + 0.958829i
\(607\) 2.36509e47 1.14720 0.573600 0.819135i \(-0.305546\pi\)
0.573600 + 0.819135i \(0.305546\pi\)
\(608\) 4.40432e47i 2.07739i
\(609\) −5.53460e46 + 1.08767e47i −0.253859 + 0.498886i
\(610\) −1.62353e46 −0.0724190
\(611\) 3.34689e47i 1.45191i
\(612\) −4.54457e47 + 3.30927e47i −1.91743 + 1.39623i
\(613\) −8.98395e46 −0.368671 −0.184336 0.982863i \(-0.559013\pi\)
−0.184336 + 0.982863i \(0.559013\pi\)
\(614\) 6.52833e47i 2.60579i
\(615\) −4.42857e46 2.25348e46i −0.171944 0.0874938i
\(616\) 2.38453e47 0.900598
\(617\) 3.23338e47i 1.18798i −0.804472 0.593990i \(-0.797552\pi\)
0.804472 0.593990i \(-0.202448\pi\)
\(618\) 1.71248e47 3.36539e47i 0.612100 1.20291i
\(619\) −4.05876e47 −1.41141 −0.705703 0.708507i \(-0.749369\pi\)
−0.705703 + 0.708507i \(0.749369\pi\)
\(620\) 5.15589e45i 0.0174439i
\(621\) −6.36625e46 + 1.01880e46i −0.209569 + 0.0335376i
\(622\) −6.96943e47 −2.23234
\(623\) 8.08902e47i 2.52115i
\(624\) 9.32424e46 + 4.74465e46i 0.282798 + 0.143902i
\(625\) 2.83360e47 0.836330
\(626\) 9.71735e46i 0.279116i
\(627\) −2.83756e47 + 5.57640e47i −0.793225 + 1.55885i
\(628\) 5.50197e47 1.49694
\(629\) 5.18520e47i 1.37311i
\(630\) 1.07246e47 + 1.47280e47i 0.276435 + 0.379624i
\(631\) 3.21525e47 0.806705 0.403353 0.915045i \(-0.367845\pi\)
0.403353 + 0.915045i \(0.367845\pi\)
\(632\) 2.83196e47i 0.691668i
\(633\) −3.05690e47 1.55551e47i −0.726806 0.369836i
\(634\) 2.99842e47 0.694024
\(635\) 1.10996e46i 0.0250122i
\(636\) 1.33575e47 2.62504e47i 0.293059 0.575923i
\(637\) 2.34272e47 0.500437
\(638\) 3.52901e47i 0.734009i
\(639\) −3.69456e46 + 2.69030e46i −0.0748252 + 0.0544862i
\(640\) −1.42049e47 −0.280143
\(641\) 8.34203e47i 1.60208i 0.598608 + 0.801042i \(0.295721\pi\)
−0.598608 + 0.801042i \(0.704279\pi\)
\(642\) −3.76144e47 1.91402e47i −0.703492 0.357973i
\(643\) −2.61463e47 −0.476237 −0.238119 0.971236i \(-0.576531\pi\)
−0.238119 + 0.971236i \(0.576531\pi\)
\(644\) 2.17385e47i 0.385629i
\(645\) −4.30229e46 + 8.45491e46i −0.0743335 + 0.146081i
\(646\) 2.50260e48 4.21151
\(647\) 2.68818e47i 0.440642i 0.975427 + 0.220321i \(0.0707105\pi\)
−0.975427 + 0.220321i \(0.929289\pi\)
\(648\) −3.88142e47 1.25196e47i −0.619748 0.199902i
\(649\) −3.45152e47 −0.536847
\(650\) 7.57646e47i 1.14799i
\(651\) 4.03273e46 + 2.05206e46i 0.0595282 + 0.0302910i
\(652\) −6.13803e47 −0.882714
\(653\) 1.04474e47i 0.146381i 0.997318 + 0.0731907i \(0.0233182\pi\)
−0.997318 + 0.0731907i \(0.976682\pi\)
\(654\) 6.20742e47 1.21989e48i 0.847402 1.66532i
\(655\) 6.07718e46 0.0808350
\(656\) 2.56306e47i 0.332196i
\(657\) −2.67578e47 3.67462e47i −0.337940 0.464089i
\(658\) −3.00639e48 −3.70003
\(659\) 3.02504e47i 0.362810i 0.983408 + 0.181405i \(0.0580645\pi\)
−0.983408 + 0.181405i \(0.941936\pi\)
\(660\) 2.75417e47 + 1.40146e47i 0.321917 + 0.163808i
\(661\) −8.00100e47 −0.911422 −0.455711 0.890128i \(-0.650615\pi\)
−0.455711 + 0.890128i \(0.650615\pi\)
\(662\) 2.65798e48i 2.95098i
\(663\) −5.47659e47 + 1.07627e48i −0.592625 + 1.16463i
\(664\) −4.05345e47 −0.427531
\(665\) 4.75720e47i 0.489084i
\(666\) 1.03032e48 7.50260e47i 1.03255 0.751882i
\(667\) 9.49514e46 0.0927603
\(668\) 1.64228e48i 1.56404i
\(669\) 1.74163e48 + 8.86233e47i 1.61701 + 0.822818i
\(670\) 1.69775e47 0.153675
\(671\) 2.41670e47i 0.213275i
\(672\) −8.65771e47 + 1.70142e48i −0.744947 + 1.46398i
\(673\) 1.44286e48 1.21051 0.605255 0.796032i \(-0.293071\pi\)
0.605255 + 0.796032i \(0.293071\pi\)
\(674\) 7.27750e47i 0.595339i
\(675\) −1.87086e47 1.16906e48i −0.149237 0.932548i
\(676\) 7.09659e47 0.552021
\(677\) 4.98678e47i 0.378280i 0.981950 + 0.189140i \(0.0605699\pi\)
−0.981950 + 0.189140i \(0.939430\pi\)
\(678\) −3.74599e47 1.90615e47i −0.277116 0.141011i
\(679\) 3.67857e47 0.265395
\(680\) 3.64795e47i 0.256683i
\(681\) 3.80122e46 7.47020e46i 0.0260869 0.0512662i
\(682\) 1.30845e47 0.0875836
\(683\) 1.74664e48i 1.14039i −0.821511 0.570193i \(-0.806868\pi\)
0.821511 0.570193i \(-0.193132\pi\)
\(684\) 2.12396e48 + 2.91681e48i 1.35267 + 1.85761i
\(685\) −4.64277e47 −0.288428
\(686\) 1.18232e48i 0.716514i
\(687\) −1.73790e48 8.84330e47i −1.02745 0.522817i
\(688\) −4.89333e47 −0.282229
\(689\) 6.32678e47i 0.356005i
\(690\) 6.42864e46 1.26336e47i 0.0352927 0.0693576i
\(691\) −5.10678e47 −0.273540 −0.136770 0.990603i \(-0.543672\pi\)
−0.136770 + 0.990603i \(0.543672\pi\)
\(692\) 1.12121e48i 0.585979i
\(693\) 2.19234e48 1.59642e48i 1.11800 0.814106i
\(694\) −4.60748e48 −2.29273
\(695\) 4.91051e47i 0.238443i
\(696\) 5.35314e47 + 2.72395e47i 0.253660 + 0.129075i
\(697\) 2.95845e48 1.36807
\(698\) 2.73779e48i 1.23554i
\(699\) 1.07682e48 2.11618e48i 0.474276 0.932053i
\(700\) 3.99191e48 1.71599
\(701\) 1.07393e48i 0.450579i −0.974292 0.225289i \(-0.927667\pi\)
0.974292 0.225289i \(-0.0723328\pi\)
\(702\) −2.93101e48 + 4.69053e47i −1.20029 + 0.192084i
\(703\) −3.32798e48 −1.33027
\(704\) 4.39685e48i 1.71556i
\(705\) −1.02484e48 5.21489e47i −0.390337 0.198623i
\(706\) 4.03263e48 1.49937
\(707\) 4.79675e48i 1.74107i
\(708\) −9.02683e47 + 1.77396e48i −0.319867 + 0.628607i
\(709\) −3.47364e48 −1.20171 −0.600854 0.799359i \(-0.705173\pi\)
−0.600854 + 0.799359i \(0.705173\pi\)
\(710\) 1.00484e47i 0.0339395i
\(711\) 1.89597e48 + 2.60371e48i 0.625241 + 0.858636i
\(712\) −3.98116e48 −1.28189
\(713\) 3.52051e46i 0.0110684i
\(714\) −9.66772e48 4.91943e48i −2.96794 1.51024i
\(715\) 6.63801e47 0.198992
\(716\) 1.81869e48i 0.532398i
\(717\) 1.35688e48 2.66656e48i 0.387898 0.762301i
\(718\) 6.14852e48 1.71654
\(719\) 3.13338e48i 0.854321i 0.904176 + 0.427161i \(0.140486\pi\)
−0.904176 + 0.427161i \(0.859514\pi\)
\(720\) −2.90568e47 + 2.11586e47i −0.0773741 + 0.0563423i
\(721\) 4.27363e48 1.11147
\(722\) 9.93981e48i 2.52491i
\(723\) 2.66526e48 + 1.35622e48i 0.661284 + 0.336495i
\(724\) 5.20649e48 1.26180
\(725\) 1.74362e48i 0.412768i
\(726\) 5.06567e47 9.95511e47i 0.117142 0.230210i
\(727\) −6.94524e48 −1.56893 −0.784463 0.620176i \(-0.787061\pi\)
−0.784463 + 0.620176i \(0.787061\pi\)
\(728\) 2.95382e48i 0.651855i
\(729\) −4.40675e48 + 1.44751e48i −0.950059 + 0.312071i
\(730\) 9.99418e47 0.210503
\(731\) 5.64820e48i 1.16229i
\(732\) 1.24210e48 + 6.32045e47i 0.249729 + 0.127075i
\(733\) 5.31469e48 1.04402 0.522012 0.852938i \(-0.325182\pi\)
0.522012 + 0.852938i \(0.325182\pi\)
\(734\) 7.95106e48i 1.52613i
\(735\) −3.65026e47 + 7.17353e47i −0.0684603 + 0.134539i
\(736\) 1.48531e48 0.272205
\(737\) 2.52719e48i 0.452576i
\(738\) 4.28066e48 + 5.87857e48i 0.749122 + 1.02876i
\(739\) −4.01720e48 −0.687017 −0.343509 0.939150i \(-0.611615\pi\)
−0.343509 + 0.939150i \(0.611615\pi\)
\(740\) 1.64368e48i 0.274713i
\(741\) 6.90772e48 + 3.51500e48i 1.12830 + 0.574138i
\(742\) 5.68313e48 0.907238
\(743\) 6.75695e48i 1.05424i 0.849790 + 0.527121i \(0.176729\pi\)
−0.849790 + 0.527121i \(0.823271\pi\)
\(744\) 1.00996e47 1.98478e47i 0.0154015 0.0302672i
\(745\) 2.34268e48 0.349185
\(746\) 9.80181e48i 1.42806i
\(747\) −3.72674e48 + 2.71374e48i −0.530736 + 0.386472i
\(748\) −1.83989e49 −2.56133
\(749\) 4.77657e48i 0.650018i
\(750\) 4.77646e48 + 2.43051e48i 0.635426 + 0.323337i
\(751\) −1.38155e49 −1.79675 −0.898377 0.439226i \(-0.855253\pi\)
−0.898377 + 0.439226i \(0.855253\pi\)
\(752\) 5.93130e48i 0.754131i
\(753\) 8.50142e46 1.67071e47i 0.0105676 0.0207676i
\(754\) 4.37154e48 0.531277
\(755\) 2.75799e48i 0.327714i
\(756\) −2.47137e48 1.54430e49i −0.287122 1.79416i
\(757\) −9.82606e48 −1.11622 −0.558109 0.829767i \(-0.688473\pi\)
−0.558109 + 0.829767i \(0.688473\pi\)
\(758\) 2.17265e49i 2.41332i
\(759\) −1.88058e48 9.56937e47i −0.204260 0.103938i
\(760\) −2.34134e48 −0.248676
\(761\) 8.35952e48i 0.868245i −0.900854 0.434122i \(-0.857059\pi\)
0.900854 0.434122i \(-0.142941\pi\)
\(762\) 7.36689e47 1.44775e48i 0.0748255 0.147048i
\(763\) 1.54911e49 1.53874
\(764\) 1.45933e49i 1.41764i
\(765\) −2.44226e48 3.35393e48i −0.232032 0.318647i
\(766\) −3.58133e47 −0.0332779
\(767\) 4.27555e48i 0.388571i
\(768\) 2.59920e48 + 1.32261e48i 0.231047 + 0.117568i
\(769\) −7.58017e48 −0.659069 −0.329535 0.944144i \(-0.606892\pi\)
−0.329535 + 0.944144i \(0.606892\pi\)
\(770\) 5.96269e48i 0.507107i
\(771\) −1.51309e48 + 2.97353e48i −0.125875 + 0.247371i
\(772\) 1.28454e49 1.04533
\(773\) 6.23870e48i 0.496641i 0.968678 + 0.248320i \(0.0798786\pi\)
−0.968678 + 0.248320i \(0.920121\pi\)
\(774\) 1.12232e49 8.17252e48i 0.874019 0.636443i
\(775\) 6.46482e47 0.0492524
\(776\) 1.81047e48i 0.134941i
\(777\) 1.28562e49 + 6.54192e48i 0.937469 + 0.477032i
\(778\) −1.03981e47 −0.00741822
\(779\) 1.89880e49i 1.32539i
\(780\) 1.73605e48 3.41171e48i 0.118564 0.233004i
\(781\) −1.49576e48 −0.0999525
\(782\) 8.43976e48i 0.551842i
\(783\) 6.74533e48 1.07946e48i 0.431572 0.0690651i
\(784\) −4.15173e48 −0.259930
\(785\) 4.06049e48i 0.248768i
\(786\) −7.92665e48 4.03348e48i −0.475233 0.241823i
\(787\) 3.06475e48 0.179814 0.0899071 0.995950i \(-0.471343\pi\)
0.0899071 + 0.995950i \(0.471343\pi\)
\(788\) 3.52043e49i 2.02139i
\(789\) 2.24123e48 4.40448e48i 0.125944 0.247506i
\(790\) −7.08153e48 −0.389463
\(791\) 4.75695e48i 0.256052i
\(792\) −7.85705e48 1.07900e49i −0.413934 0.568450i
\(793\) 2.99367e48 0.154369
\(794\) 1.57686e49i 0.795875i
\(795\) 1.93730e48 + 9.85796e47i 0.0957095 + 0.0487019i
\(796\) −5.17324e48 −0.250173
\(797\) 5.47474e48i 0.259162i 0.991569 + 0.129581i \(0.0413633\pi\)
−0.991569 + 0.129581i \(0.958637\pi\)
\(798\) −3.15740e49 + 6.20497e49i −1.46312 + 2.87535i
\(799\) 6.84630e49 3.10571
\(800\) 2.72753e49i 1.21127i
\(801\) −3.66027e49 + 2.66534e49i −1.59133 + 1.15878i
\(802\) −5.67676e49 −2.41622
\(803\) 1.48769e49i 0.619936i
\(804\) −1.29889e49 6.60942e48i −0.529931 0.269656i
\(805\) 1.60432e48 0.0640856
\(806\) 1.62083e48i 0.0633932i
\(807\) 5.38031e48 1.05734e49i 0.206043 0.404917i
\(808\) 2.36080e49 0.885252
\(809\) 2.65490e49i 0.974818i 0.873174 + 0.487409i \(0.162058\pi\)
−0.873174 + 0.487409i \(0.837942\pi\)
\(810\) 3.13063e48 9.70576e48i 0.112561 0.348967i
\(811\) 1.59289e49 0.560832 0.280416 0.959879i \(-0.409528\pi\)
0.280416 + 0.959879i \(0.409528\pi\)
\(812\) 2.30329e49i 0.794139i
\(813\) −6.77850e48 3.44925e48i −0.228873 0.116462i
\(814\) 4.17131e49 1.37929
\(815\) 4.52991e48i 0.146693i
\(816\) 9.70553e48 1.90734e49i 0.307813 0.604917i
\(817\) −3.62515e49 −1.12603
\(818\) 5.01123e49i 1.52454i
\(819\) −1.97755e49 2.71574e49i −0.589252 0.809212i
\(820\) −9.37815e48 −0.273704
\(821\) 3.21505e49i 0.919082i 0.888156 + 0.459541i \(0.151986\pi\)
−0.888156 + 0.459541i \(0.848014\pi\)
\(822\) 6.05570e49 + 3.08145e49i 1.69568 + 0.862848i
\(823\) −1.30350e49 −0.357532 −0.178766 0.983892i \(-0.557210\pi\)
−0.178766 + 0.983892i \(0.557210\pi\)
\(824\) 2.10334e49i 0.565129i
\(825\) 1.75725e49 3.45338e49i 0.462506 0.908922i
\(826\) −3.84058e49 −0.990229
\(827\) 1.13125e49i 0.285736i 0.989742 + 0.142868i \(0.0456325\pi\)
−0.989742 + 0.142868i \(0.954367\pi\)
\(828\) −9.83665e48 + 7.16285e48i −0.243406 + 0.177243i
\(829\) −2.88791e49 −0.700094 −0.350047 0.936732i \(-0.613834\pi\)
−0.350047 + 0.936732i \(0.613834\pi\)
\(830\) 1.01359e49i 0.240733i
\(831\) −2.58286e49 1.31429e49i −0.601013 0.305826i
\(832\) 5.44656e49 1.24173
\(833\) 4.79219e49i 1.07046i
\(834\) 3.25916e49 6.40493e49i 0.713317 1.40182i
\(835\) 1.21202e49 0.259919
\(836\) 1.18088e50i 2.48142i
\(837\) −4.00233e47 2.50096e48i −0.00824100 0.0514961i
\(838\) 6.25682e49 1.26242
\(839\) 8.09012e49i 1.59956i 0.600290 + 0.799782i \(0.295052\pi\)
−0.600290 + 0.799782i \(0.704948\pi\)
\(840\) 9.04477e48 + 4.60244e48i 0.175247 + 0.0891745i
\(841\) 4.26057e49 0.808976
\(842\) 1.11207e50i 2.06931i
\(843\) 4.89559e48 9.62088e48i 0.0892764 0.175447i
\(844\) −6.47344e49 −1.15695
\(845\) 5.23734e48i 0.0917374i
\(846\) 9.90608e49 + 1.36039e50i 1.70061 + 2.33543i
\(847\) 1.26418e49 0.212711
\(848\) 1.12122e49i 0.184911i
\(849\) −5.02875e49 2.55889e49i −0.812885 0.413638i
\(850\) −1.54982e50 −2.45561
\(851\) 1.12233e49i 0.174308i
\(852\) −3.91188e48 + 7.68768e48i −0.0595543 + 0.117037i
\(853\) −8.15421e49 −1.21688 −0.608441 0.793599i \(-0.708205\pi\)
−0.608441 + 0.793599i \(0.708205\pi\)
\(854\) 2.68911e49i 0.393392i
\(855\) −2.15263e49 + 1.56750e49i −0.308706 + 0.224794i
\(856\) −2.35088e49 −0.330503
\(857\) 1.28860e48i 0.0177600i 0.999961 + 0.00888001i \(0.00282663\pi\)
−0.999961 + 0.00888001i \(0.997173\pi\)
\(858\) −8.65816e49 4.40571e49i −1.16988 0.595295i
\(859\) −3.27445e48 −0.0433764 −0.0216882 0.999765i \(-0.506904\pi\)
−0.0216882 + 0.999765i \(0.506904\pi\)
\(860\) 1.79045e49i 0.232535i
\(861\) −3.73254e49 + 7.33522e49i −0.475281 + 0.934027i
\(862\) 2.85806e49 0.356819
\(863\) 1.42272e50i 1.74155i −0.491683 0.870774i \(-0.663618\pi\)
0.491683 0.870774i \(-0.336382\pi\)
\(864\) 1.05516e50 1.68860e49i 1.26645 0.202671i
\(865\) 8.27458e48 0.0973806
\(866\) 2.08507e50i 2.40611i
\(867\) 1.41395e50 + 7.19488e49i 1.59996 + 0.814140i
\(868\) 8.53991e48 0.0947584
\(869\) 1.05412e50i 1.14698i
\(870\) −6.81143e48 + 1.33859e49i −0.0726794 + 0.142830i
\(871\) −3.13054e49 −0.327575
\(872\) 7.62422e49i 0.782375i
\(873\) −1.21209e49 1.66455e49i −0.121981 0.167515i
\(874\) 5.41683e49 0.534627
\(875\) 6.06552e49i 0.587126i
\(876\) −7.64619e49 3.89077e49i −0.725898 0.369374i
\(877\) 1.15072e50 1.07146 0.535732 0.844388i \(-0.320036\pi\)
0.535732 + 0.844388i \(0.320036\pi\)
\(878\) 9.10839e49i 0.831831i
\(879\) −1.36243e49 + 2.67747e49i −0.122041 + 0.239836i
\(880\) −1.17638e49 −0.103357
\(881\) 1.73656e50i 1.49658i 0.663373 + 0.748289i \(0.269124\pi\)
−0.663373 + 0.748289i \(0.730876\pi\)
\(882\) 9.52230e49 6.93394e49i 0.804963 0.586158i
\(883\) 1.12242e50 0.930729 0.465364 0.885119i \(-0.345923\pi\)
0.465364 + 0.885119i \(0.345923\pi\)
\(884\) 2.27915e50i 1.85389i
\(885\) −1.30920e49 6.66187e48i −0.104465 0.0531570i
\(886\) −8.15480e49 −0.638322
\(887\) 7.41162e49i 0.569130i −0.958657 0.284565i \(-0.908151\pi\)
0.958657 0.284565i \(-0.0918492\pi\)
\(888\) 3.21972e49 6.32743e49i 0.242548 0.476658i
\(889\) 1.83847e49 0.135871
\(890\) 9.95517e49i 0.721803i
\(891\) −1.44475e50 4.66010e49i −1.02771 0.331493i
\(892\) 3.68817e50 2.57400
\(893\) 4.39411e50i 3.00882i
\(894\) −3.05563e50 1.55486e50i −2.05287 1.04461i
\(895\) 1.34220e49 0.0884763
\(896\) 2.35282e50i 1.52178i
\(897\) −1.18540e49 + 2.32956e49i −0.0752303 + 0.147843i
\(898\) −6.56355e49 −0.408734
\(899\) 3.73014e48i 0.0227934i
\(900\) −1.31534e50 1.80634e50i −0.788705 1.08312i
\(901\) −1.29419e50 −0.761511
\(902\) 2.37997e50i 1.37423i
\(903\) 1.40042e50 + 7.12606e49i 0.793536 + 0.403792i
\(904\) −2.34122e49 −0.130190
\(905\) 3.84243e49i 0.209691i
\(906\) −1.83051e50 + 3.59733e50i −0.980375 + 1.92664i
\(907\) −8.59889e49 −0.451979 −0.225990 0.974130i \(-0.572562\pi\)
−0.225990 + 0.974130i \(0.572562\pi\)
\(908\) 1.58193e49i 0.0816068i
\(909\) 2.17052e50 1.58053e50i 1.09895 0.800234i
\(910\) 7.38624e49 0.367045
\(911\) 4.93285e49i 0.240594i −0.992738 0.120297i \(-0.961615\pi\)
0.992738 0.120297i \(-0.0383847\pi\)
\(912\) −1.22418e50 6.22923e49i −0.586046 0.298210i
\(913\) −1.50879e50 −0.708965
\(914\) 2.31650e50i 1.06843i
\(915\) −4.66454e48 + 9.16681e48i −0.0211179 + 0.0415011i
\(916\) −3.68025e50 −1.63551
\(917\) 1.00659e50i 0.439109i
\(918\) 9.59483e49 + 5.99559e50i 0.410877 + 2.56747i
\(919\) 1.25993e50 0.529643 0.264822 0.964297i \(-0.414687\pi\)
0.264822 + 0.964297i \(0.414687\pi\)
\(920\) 7.89593e48i 0.0325845i
\(921\) 3.68605e50 + 1.87565e50i 1.49330 + 0.759867i
\(922\) 2.64726e50 1.05286
\(923\) 1.85286e49i 0.0723458i
\(924\) 2.32130e50 4.56184e50i 0.889831 1.74871i
\(925\) 2.06097e50 0.775643
\(926\) 3.89350e50i 1.43865i
\(927\) −1.40817e50 1.93381e50i −0.510856 0.701551i
\(928\) −1.57376e50 −0.560560
\(929\) 1.62540e50i 0.568452i −0.958757 0.284226i \(-0.908263\pi\)
0.958757 0.284226i \(-0.0917366\pi\)
\(930\) 4.96309e48 + 2.52547e48i 0.0170428 + 0.00867227i
\(931\) −3.07574e50 −1.03706
\(932\) 4.48132e50i 1.48366i
\(933\) −2.00238e50 + 3.93510e50i −0.650966 + 1.27929i
\(934\) 5.53493e50 1.76691
\(935\) 1.35785e50i 0.425652i
\(936\) −1.33660e50 + 9.73286e49i −0.411445 + 0.299606i
\(937\) −1.89835e50 −0.573856 −0.286928 0.957952i \(-0.592634\pi\)
−0.286928 + 0.957952i \(0.592634\pi\)
\(938\) 2.81206e50i 0.834788i
\(939\) −5.48664e49 2.79188e49i −0.159953 0.0813921i
\(940\) −2.17024e50 −0.621348
\(941\) 3.83489e50i 1.07827i 0.842218 + 0.539137i \(0.181250\pi\)
−0.842218 + 0.539137i \(0.818750\pi\)
\(942\) 2.69499e50 5.29623e50i 0.744204 1.46252i
\(943\) 6.40352e49 0.173668
\(944\) 7.57706e49i 0.201826i
\(945\) 1.13970e50 1.82389e49i 0.298161 0.0477152i
\(946\) 4.54377e50 1.16753
\(947\) 5.14482e50i 1.29844i 0.760602 + 0.649218i \(0.224904\pi\)
−0.760602 + 0.649218i \(0.775096\pi\)
\(948\) 5.41782e50 + 2.75687e50i 1.34302 + 0.683398i
\(949\) −1.84286e50 −0.448711
\(950\) 9.94710e50i 2.37900i
\(951\) 8.61472e49 1.69297e50i 0.202382 0.397724i
\(952\) −6.04226e50 −1.39435
\(953\) 2.02536e50i 0.459116i 0.973295 + 0.229558i \(0.0737281\pi\)
−0.973295 + 0.229558i \(0.926272\pi\)
\(954\) −1.87259e50 2.57161e50i −0.416986 0.572641i
\(955\) −1.07699e50 −0.235589
\(956\) 5.64684e50i 1.21345i
\(957\) 1.99256e50 + 1.01392e50i 0.420638 + 0.214042i
\(958\) −8.36391e50 −1.73458
\(959\) 7.69000e50i 1.56679i
\(960\) −8.48646e49 + 1.66777e50i −0.169870 + 0.333830i
\(961\) −5.07125e50 −0.997280
\(962\) 5.16717e50i 0.998336i
\(963\) −2.16139e50 + 1.57388e50i −0.410286 + 0.298762i
\(964\) 5.64407e50 1.05265
\(965\) 9.47998e49i 0.173717i
\(966\) −2.09256e50 1.06480e50i −0.376762 0.191716i
\(967\) 3.17102e49 0.0560983 0.0280491 0.999607i \(-0.491071\pi\)
0.0280491 + 0.999607i \(0.491071\pi\)
\(968\) 6.22187e49i 0.108153i
\(969\) 7.19019e50 1.41302e51i 1.22811 2.41349i
\(970\) 4.52722e49 0.0759823
\(971\) 2.74349e50i 0.452456i −0.974074 0.226228i \(-0.927361\pi\)
0.974074 0.226228i \(-0.0726395\pi\)
\(972\) −6.17362e50 + 6.20677e50i −1.00049 + 1.00586i
\(973\) 8.13348e50 1.29526
\(974\) 5.70959e50i 0.893516i
\(975\) −4.27784e50 2.17679e50i −0.657880 0.334763i
\(976\) −5.30535e49 −0.0801801
\(977\) 3.91008e50i 0.580735i −0.956915 0.290367i \(-0.906222\pi\)
0.956915 0.290367i \(-0.0937775\pi\)
\(978\) −3.00655e50 + 5.90851e50i −0.438842 + 0.862417i
\(979\) −1.48188e51 −2.12572
\(980\) 1.51910e50i 0.214162i
\(981\) −5.10433e50 7.00970e50i −0.707237 0.971240i
\(982\) 2.07250e51 2.82228
\(983\) 5.78758e50i 0.774618i −0.921950 0.387309i \(-0.873405\pi\)
0.921950 0.387309i \(-0.126595\pi\)
\(984\) 3.61016e50 + 1.83703e50i 0.474908 + 0.241658i
\(985\) 2.59810e50 0.335923
\(986\) 8.94230e50i 1.13643i
\(987\) −8.63764e50 + 1.69748e51i −1.07896 + 2.12037i
\(988\) 1.46281e51 1.79606
\(989\) 1.22254e50i 0.147546i
\(990\) 2.69811e50 1.96471e50i 0.320082 0.233077i
\(991\) 5.62137e50 0.655526 0.327763 0.944760i \(-0.393705\pi\)
0.327763 + 0.944760i \(0.393705\pi\)
\(992\) 5.83501e49i 0.0668872i
\(993\) 1.50076e51 + 7.63661e50i 1.69111 + 0.860525i
\(994\) −1.66436e50 −0.184365
\(995\) 3.81789e49i 0.0415749i
\(996\) −3.94596e50 + 7.75464e50i −0.422419 + 0.830143i
\(997\) 4.10467e50 0.431977 0.215988 0.976396i \(-0.430703\pi\)
0.215988 + 0.976396i \(0.430703\pi\)
\(998\) 1.75579e50i 0.181657i
\(999\) −1.27593e50 7.97300e50i −0.129782 0.810977i
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 3.35.b.a.2.2 10
3.2 odd 2 inner 3.35.b.a.2.9 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.35.b.a.2.2 10 1.1 even 1 trivial
3.35.b.a.2.9 yes 10 3.2 odd 2 inner