Properties

Label 6.15.b.a.5.2
Level $6$
Weight $15$
Character 6.5
Analytic conductor $7.460$
Analytic rank $0$
Dimension $4$
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] = [6,15,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 6.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: \(7.45973808911\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-35})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} + 23x^{2} - 22x + 51 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(0.500000 + 4.37225i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.15.b.a.5.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-90.5097i q^{2} +(385.790 + 2152.70i) q^{3} -8192.00 q^{4} -105253. i q^{5} +(194841. - 34917.8i) q^{6} -1.21591e6 q^{7} +741455. i q^{8} +(-4.48530e6 + 1.66099e6i) q^{9} +O(q^{10})\) \(q-90.5097i q^{2} +(385.790 + 2152.70i) q^{3} -8192.00 q^{4} -105253. i q^{5} +(194841. - 34917.8i) q^{6} -1.21591e6 q^{7} +741455. i q^{8} +(-4.48530e6 + 1.66099e6i) q^{9} -9.52637e6 q^{10} -1.71107e7i q^{11} +(-3.16040e6 - 1.76350e7i) q^{12} -6.76914e7 q^{13} +1.10051e8i q^{14} +(2.26578e8 - 4.06054e7i) q^{15} +6.71089e7 q^{16} -1.67802e8i q^{17} +(1.50335e8 + 4.05963e8i) q^{18} +8.08356e8 q^{19} +8.62229e8i q^{20} +(-4.69086e8 - 2.61749e9i) q^{21} -1.54868e9 q^{22} +1.02641e9i q^{23} +(-1.59613e9 + 2.86046e8i) q^{24} -4.97458e9 q^{25} +6.12673e9i q^{26} +(-5.30600e9 - 9.01473e9i) q^{27} +9.96072e9 q^{28} +1.38422e10i q^{29} +(-3.67518e9 - 2.05075e10i) q^{30} +3.15369e10 q^{31} -6.07400e9i q^{32} +(3.68342e10 - 6.60113e9i) q^{33} -1.51877e10 q^{34} +1.27977e11i q^{35} +(3.67436e10 - 1.36068e10i) q^{36} -1.41457e11 q^{37} -7.31641e10i q^{38} +(-2.61147e10 - 1.45720e11i) q^{39} +7.80400e10 q^{40} -7.34964e10i q^{41} +(-2.36908e11 + 4.24568e10i) q^{42} -1.15815e11 q^{43} +1.40170e11i q^{44} +(1.74823e11 + 4.72089e11i) q^{45} +9.29000e10 q^{46} -6.63761e11i q^{47} +(2.58900e10 + 1.44466e11i) q^{48} +8.00210e11 q^{49} +4.50248e11i q^{50} +(3.61228e11 - 6.47365e10i) q^{51} +5.54528e11 q^{52} -1.04506e12i q^{53} +(-8.15920e11 + 4.80244e11i) q^{54} -1.80094e12 q^{55} -9.01542e11i q^{56} +(3.11856e11 + 1.74015e12i) q^{57} +1.25285e12 q^{58} +2.50227e11i q^{59} +(-1.85612e12 + 3.32640e11i) q^{60} -5.74063e12 q^{61} -2.85440e12i q^{62} +(5.45371e12 - 2.01961e12i) q^{63} -5.49756e11 q^{64} +7.12470e12i q^{65} +(-5.97466e11 - 3.33385e12i) q^{66} +4.64817e12 q^{67} +1.37464e12i q^{68} +(-2.20956e12 + 3.95979e11i) q^{69} +1.15832e13 q^{70} -4.07288e12i q^{71} +(-1.23155e12 - 3.32565e12i) q^{72} +4.29948e12 q^{73} +1.28032e13i q^{74} +(-1.91915e12 - 1.07088e13i) q^{75} -6.62205e12 q^{76} +2.08050e13i q^{77} +(-1.31890e13 + 2.36363e12i) q^{78} -1.78802e13 q^{79} -7.06338e12i q^{80} +(1.73590e13 - 1.49000e13i) q^{81} -6.65213e12 q^{82} -5.35709e13i q^{83} +(3.84275e12 + 2.14425e13i) q^{84} -1.76616e13 q^{85} +1.04824e13i q^{86} +(-2.97981e13 + 5.34018e12i) q^{87} +1.26868e13 q^{88} +6.15032e13i q^{89} +(4.27286e13 - 1.58232e13i) q^{90} +8.23066e13 q^{91} -8.40835e12i q^{92} +(1.21667e13 + 6.78897e13i) q^{93} -6.00768e13 q^{94} -8.50816e13i q^{95} +(1.30755e13 - 2.34329e12i) q^{96} +1.58213e12 q^{97} -7.24268e13i q^{98} +(2.84205e13 + 7.67464e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9} - 11735040 q^{10} + 26836992 q^{12} - 248212120 q^{13} + 520179840 q^{15} + 268435456 q^{16} + 908070912 q^{18} - 1252067608 q^{19} - 2512164312 q^{21} + 2708779008 q^{22} - 1962934272 q^{24} - 1010496860 q^{25} - 18844787052 q^{27} + 13550157824 q^{28} - 22159872000 q^{30} + 48544485512 q^{31} + 126848191104 q^{33} - 73181085696 q^{34} + 17642520576 q^{36} - 229361099608 q^{37} + 176113271880 q^{39} + 96133447680 q^{40} - 532172648448 q^{42} - 475123816024 q^{43} + 78358129920 q^{45} + 1407078998016 q^{46} - 219848638464 q^{48} + 546417874380 q^{49} + 330389632512 q^{51} + 2033353687040 q^{52} - 3372586813440 q^{54} - 6195118383360 q^{55} + 6429522003912 q^{57} + 3954244177920 q^{58} - 4261313249280 q^{60} - 8008506933784 q^{61} + 13558362184584 q^{63} - 2199023255552 q^{64} - 12945338929152 q^{66} - 5706498189208 q^{67} + 6766877922048 q^{69} + 26012049530880 q^{70} - 7438916911104 q^{72} + 28135799923400 q^{73} - 21928288537260 q^{75} + 10256937844736 q^{76} - 17912213729280 q^{78} - 80292052723192 q^{79} + 35435631821508 q^{81} + 12944796721152 q^{82} + 20579650043904 q^{84} - 16204620119040 q^{85} - 46328672200320 q^{87} - 22190317633536 q^{88} + 110399597015040 q^{90} + 120737034068560 q^{91} + 53737779031272 q^{93} - 219496277852160 q^{94} + 16080357556224 q^{96} + 178244166574856 q^{97} - 158408610377472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 90.5097i 0.707107i
\(3\) 385.790 + 2152.70i 0.176402 + 0.984318i
\(4\) −8192.00 −0.500000
\(5\) 105253.i 1.34723i −0.739081 0.673616i \(-0.764740\pi\)
0.739081 0.673616i \(-0.235260\pi\)
\(6\) 194841. 34917.8i 0.696018 0.124735i
\(7\) −1.21591e6 −1.47644 −0.738218 0.674562i \(-0.764332\pi\)
−0.738218 + 0.674562i \(0.764332\pi\)
\(8\) 741455.i 0.353553i
\(9\) −4.48530e6 + 1.66099e6i −0.937765 + 0.347271i
\(10\) −9.52637e6 −0.952637
\(11\) 1.71107e7i 0.878047i −0.898476 0.439024i \(-0.855324\pi\)
0.898476 0.439024i \(-0.144676\pi\)
\(12\) −3.16040e6 1.76350e7i −0.0882008 0.492159i
\(13\) −6.76914e7 −1.07877 −0.539387 0.842058i \(-0.681344\pi\)
−0.539387 + 0.842058i \(0.681344\pi\)
\(14\) 1.10051e8i 1.04400i
\(15\) 2.26578e8 4.06054e7i 1.32611 0.237654i
\(16\) 6.71089e7 0.250000
\(17\) 1.67802e8i 0.408936i −0.978873 0.204468i \(-0.934454\pi\)
0.978873 0.204468i \(-0.0655464\pi\)
\(18\) 1.50335e8 + 4.05963e8i 0.245558 + 0.663100i
\(19\) 8.08356e8 0.904331 0.452166 0.891934i \(-0.350652\pi\)
0.452166 + 0.891934i \(0.350652\pi\)
\(20\) 8.62229e8i 0.673616i
\(21\) −4.69086e8 2.61749e9i −0.260446 1.45328i
\(22\) −1.54868e9 −0.620873
\(23\) 1.02641e9i 0.301457i 0.988575 + 0.150729i \(0.0481620\pi\)
−0.988575 + 0.150729i \(0.951838\pi\)
\(24\) −1.59613e9 + 2.86046e8i −0.348009 + 0.0623674i
\(25\) −4.97458e9 −0.815036
\(26\) 6.12673e9i 0.762808i
\(27\) −5.30600e9 9.01473e9i −0.507248 0.861800i
\(28\) 9.96072e9 0.738218
\(29\) 1.38422e10i 0.802451i 0.915979 + 0.401225i \(0.131416\pi\)
−0.915979 + 0.401225i \(0.868584\pi\)
\(30\) −3.67518e9 2.05075e10i −0.168047 0.937698i
\(31\) 3.15369e10 1.14627 0.573136 0.819460i \(-0.305727\pi\)
0.573136 + 0.819460i \(0.305727\pi\)
\(32\) 6.07400e9i 0.176777i
\(33\) 3.68342e10 6.60113e9i 0.864278 0.154889i
\(34\) −1.51877e10 −0.289161
\(35\) 1.27977e11i 1.98910i
\(36\) 3.67436e10 1.36068e10i 0.468882 0.173635i
\(37\) −1.41457e11 −1.49009 −0.745045 0.667014i \(-0.767572\pi\)
−0.745045 + 0.667014i \(0.767572\pi\)
\(38\) 7.31641e10i 0.639459i
\(39\) −2.61147e10 1.45720e11i −0.190297 1.06186i
\(40\) 7.80400e10 0.476319
\(41\) 7.34964e10i 0.377380i −0.982037 0.188690i \(-0.939576\pi\)
0.982037 0.188690i \(-0.0604241\pi\)
\(42\) −2.36908e11 + 4.24568e10i −1.02763 + 0.184163i
\(43\) −1.15815e11 −0.426076 −0.213038 0.977044i \(-0.568336\pi\)
−0.213038 + 0.977044i \(0.568336\pi\)
\(44\) 1.40170e11i 0.439024i
\(45\) 1.74823e11 + 4.72089e11i 0.467854 + 1.26339i
\(46\) 9.29000e10 0.213163
\(47\) 6.63761e11i 1.31017i −0.755556 0.655084i \(-0.772633\pi\)
0.755556 0.655084i \(-0.227367\pi\)
\(48\) 2.58900e10 + 1.44466e11i 0.0441004 + 0.246080i
\(49\) 8.00210e11 1.17986
\(50\) 4.50248e11i 0.576317i
\(51\) 3.61228e11 6.47365e10i 0.402523 0.0721370i
\(52\) 5.54528e11 0.539387
\(53\) 1.04506e12i 0.889635i −0.895621 0.444817i \(-0.853269\pi\)
0.895621 0.444817i \(-0.146731\pi\)
\(54\) −8.15920e11 + 4.80244e11i −0.609385 + 0.358679i
\(55\) −1.80094e12 −1.18293
\(56\) 9.01542e11i 0.521999i
\(57\) 3.11856e11 + 1.74015e12i 0.159526 + 0.890150i
\(58\) 1.25285e12 0.567418
\(59\) 2.50227e11i 0.100547i 0.998735 + 0.0502736i \(0.0160093\pi\)
−0.998735 + 0.0502736i \(0.983991\pi\)
\(60\) −1.85612e12 + 3.32640e11i −0.663053 + 0.118827i
\(61\) −5.74063e12 −1.82663 −0.913315 0.407253i \(-0.866487\pi\)
−0.913315 + 0.407253i \(0.866487\pi\)
\(62\) 2.85440e12i 0.810537i
\(63\) 5.45371e12 2.01961e12i 1.38455 0.512723i
\(64\) −5.49756e11 −0.125000
\(65\) 7.12470e12i 1.45336i
\(66\) −5.97466e11 3.33385e12i −0.109523 0.611137i
\(67\) 4.64817e12 0.766935 0.383467 0.923554i \(-0.374730\pi\)
0.383467 + 0.923554i \(0.374730\pi\)
\(68\) 1.37464e12i 0.204468i
\(69\) −2.20956e12 + 3.95979e11i −0.296730 + 0.0531776i
\(70\) 1.15832e13 1.40651
\(71\) 4.07288e12i 0.447809i −0.974611 0.223904i \(-0.928120\pi\)
0.974611 0.223904i \(-0.0718803\pi\)
\(72\) −1.23155e12 3.32565e12i −0.122779 0.331550i
\(73\) 4.29948e12 0.389185 0.194592 0.980884i \(-0.437662\pi\)
0.194592 + 0.980884i \(0.437662\pi\)
\(74\) 1.28032e13i 1.05365i
\(75\) −1.91915e12 1.07088e13i −0.143774 0.802255i
\(76\) −6.62205e12 −0.452166
\(77\) 2.08050e13i 1.29638i
\(78\) −1.31890e13 + 2.36363e12i −0.750846 + 0.134561i
\(79\) −1.78802e13 −0.931071 −0.465536 0.885029i \(-0.654138\pi\)
−0.465536 + 0.885029i \(0.654138\pi\)
\(80\) 7.06338e12i 0.336808i
\(81\) 1.73590e13 1.49000e13i 0.758806 0.651317i
\(82\) −6.65213e12 −0.266848
\(83\) 5.35709e13i 1.97416i −0.160229 0.987080i \(-0.551223\pi\)
0.160229 0.987080i \(-0.448777\pi\)
\(84\) 3.84275e12 + 2.14425e13i 0.130223 + 0.726641i
\(85\) −1.76616e13 −0.550932
\(86\) 1.04824e13i 0.301281i
\(87\) −2.97981e13 + 5.34018e12i −0.789867 + 0.141554i
\(88\) 1.26868e13 0.310437
\(89\) 6.15032e13i 1.39049i 0.718773 + 0.695245i \(0.244704\pi\)
−0.718773 + 0.695245i \(0.755296\pi\)
\(90\) 4.27286e13 1.58232e13i 0.893350 0.330823i
\(91\) 8.23066e13 1.59274
\(92\) 8.40835e12i 0.150729i
\(93\) 1.21667e13 + 6.78897e13i 0.202204 + 1.12830i
\(94\) −6.00768e13 −0.926429
\(95\) 8.50816e13i 1.21834i
\(96\) 1.30755e13 2.34329e12i 0.174005 0.0311837i
\(97\) 1.58213e12 0.0195812 0.00979061 0.999952i \(-0.496884\pi\)
0.00979061 + 0.999952i \(0.496884\pi\)
\(98\) 7.24268e13i 0.834289i
\(99\) 2.84205e13 + 7.67464e13i 0.304920 + 0.823402i
\(100\) 4.07518e13 0.407518
\(101\) 4.44794e13i 0.414868i −0.978249 0.207434i \(-0.933489\pi\)
0.978249 0.207434i \(-0.0665112\pi\)
\(102\) −5.85928e12 3.26947e13i −0.0510085 0.284627i
\(103\) −5.24487e13 −0.426456 −0.213228 0.977002i \(-0.568398\pi\)
−0.213228 + 0.977002i \(0.568398\pi\)
\(104\) 5.01902e13i 0.381404i
\(105\) −2.75498e14 + 4.93725e13i −1.95791 + 0.350881i
\(106\) −9.45884e13 −0.629067
\(107\) 1.69128e14i 1.05324i 0.850100 + 0.526621i \(0.176541\pi\)
−0.850100 + 0.526621i \(0.823459\pi\)
\(108\) 4.34667e13 + 7.38487e13i 0.253624 + 0.430900i
\(109\) 1.41557e14 0.774363 0.387181 0.922004i \(-0.373449\pi\)
0.387181 + 0.922004i \(0.373449\pi\)
\(110\) 1.63002e14i 0.836460i
\(111\) −5.45728e13 3.04515e14i −0.262854 1.46672i
\(112\) −8.15982e13 −0.369109
\(113\) 1.21295e14i 0.515577i −0.966201 0.257789i \(-0.917006\pi\)
0.966201 0.257789i \(-0.0829938\pi\)
\(114\) 1.57501e14 2.82260e13i 0.629431 0.112802i
\(115\) 1.08032e14 0.406133
\(116\) 1.13395e14i 0.401225i
\(117\) 3.03616e14 1.12435e14i 1.01164 0.374627i
\(118\) 2.26480e13 0.0710976
\(119\) 2.04032e14i 0.603768i
\(120\) 3.01071e13 + 1.67997e14i 0.0840234 + 0.468849i
\(121\) 8.69753e13 0.229033
\(122\) 5.19583e14i 1.29162i
\(123\) 1.58216e14 2.83542e13i 0.371462 0.0665705i
\(124\) −2.58351e14 −0.573136
\(125\) 1.18823e14i 0.249190i
\(126\) −1.82794e14 4.93614e14i −0.362550 0.979025i
\(127\) −1.48696e14 −0.279045 −0.139522 0.990219i \(-0.544557\pi\)
−0.139522 + 0.990219i \(0.544557\pi\)
\(128\) 4.97582e13i 0.0883883i
\(129\) −4.46805e13 2.49316e14i −0.0751605 0.419394i
\(130\) 6.44854e14 1.02768
\(131\) 3.88934e14i 0.587457i 0.955889 + 0.293729i \(0.0948962\pi\)
−0.955889 + 0.293729i \(0.905104\pi\)
\(132\) −3.01746e14 + 5.40764e13i −0.432139 + 0.0774445i
\(133\) −9.82887e14 −1.33519
\(134\) 4.20704e14i 0.542305i
\(135\) −9.48824e14 + 5.58470e14i −1.16105 + 0.683381i
\(136\) 1.24418e14 0.144581
\(137\) 4.99822e14i 0.551787i −0.961188 0.275893i \(-0.911026\pi\)
0.961188 0.275893i \(-0.0889737\pi\)
\(138\) 3.58399e13 + 1.99986e14i 0.0376022 + 0.209820i
\(139\) 2.14174e13 0.0213630 0.0106815 0.999943i \(-0.496600\pi\)
0.0106815 + 0.999943i \(0.496600\pi\)
\(140\) 1.04839e15i 0.994551i
\(141\) 1.42888e15 2.56073e14i 1.28962 0.231116i
\(142\) −3.68635e14 −0.316649
\(143\) 1.15825e15i 0.947214i
\(144\) −3.01003e14 + 1.11467e14i −0.234441 + 0.0868177i
\(145\) 1.45692e15 1.08109
\(146\) 3.89144e14i 0.275195i
\(147\) 3.08713e14 + 1.72262e15i 0.208130 + 1.16136i
\(148\) 1.15882e15 0.745045
\(149\) 8.78713e14i 0.538943i −0.963008 0.269472i \(-0.913151\pi\)
0.963008 0.269472i \(-0.0868491\pi\)
\(150\) −9.69250e14 + 1.73701e14i −0.567280 + 0.101663i
\(151\) −1.91539e14 −0.107008 −0.0535042 0.998568i \(-0.517039\pi\)
−0.0535042 + 0.998568i \(0.517039\pi\)
\(152\) 5.99360e14i 0.319729i
\(153\) 2.78717e14 + 7.52643e14i 0.142011 + 0.383486i
\(154\) 1.88305e15 0.916679
\(155\) 3.31934e15i 1.54430i
\(156\) 2.13932e14 + 1.19374e15i 0.0951487 + 0.530928i
\(157\) −4.31468e15 −1.83506 −0.917531 0.397663i \(-0.869821\pi\)
−0.917531 + 0.397663i \(0.869821\pi\)
\(158\) 1.61833e15i 0.658367i
\(159\) 2.24971e15 4.03176e14i 0.875684 0.156933i
\(160\) −6.39304e14 −0.238159
\(161\) 1.24802e15i 0.445083i
\(162\) −1.34860e15 1.57116e15i −0.460550 0.536557i
\(163\) −1.99493e14 −0.0652550 −0.0326275 0.999468i \(-0.510388\pi\)
−0.0326275 + 0.999468i \(0.510388\pi\)
\(164\) 6.02082e14i 0.188690i
\(165\) −6.94785e14 3.87689e15i −0.208671 1.16438i
\(166\) −4.84868e15 −1.39594
\(167\) 3.20465e15i 0.884638i 0.896858 + 0.442319i \(0.145844\pi\)
−0.896858 + 0.442319i \(0.854156\pi\)
\(168\) 1.94075e15 3.47806e14i 0.513813 0.0920815i
\(169\) 6.44756e14 0.163753
\(170\) 1.59855e15i 0.389568i
\(171\) −3.62572e15 + 1.34267e15i −0.848050 + 0.314048i
\(172\) 9.48760e14 0.213038
\(173\) 3.22827e15i 0.696061i 0.937483 + 0.348031i \(0.113149\pi\)
−0.937483 + 0.348031i \(0.886851\pi\)
\(174\) 4.83338e14 + 2.69702e15i 0.100094 + 0.558520i
\(175\) 6.04864e15 1.20335
\(176\) 1.14828e15i 0.219512i
\(177\) −5.38664e14 + 9.65351e13i −0.0989704 + 0.0177367i
\(178\) 5.56663e15 0.983224
\(179\) 1.26665e15i 0.215122i −0.994198 0.107561i \(-0.965696\pi\)
0.994198 0.107561i \(-0.0343042\pi\)
\(180\) −1.43215e15 3.86736e15i −0.233927 0.631694i
\(181\) 5.69529e15 0.894882 0.447441 0.894314i \(-0.352336\pi\)
0.447441 + 0.894314i \(0.352336\pi\)
\(182\) 7.44954e15i 1.12624i
\(183\) −2.21468e15 1.23579e16i −0.322221 1.79799i
\(184\) −7.61037e14 −0.106581
\(185\) 1.48887e16i 2.00750i
\(186\) 6.14468e15 1.10120e15i 0.797826 0.142980i
\(187\) −2.87121e15 −0.359065
\(188\) 5.43753e15i 0.655084i
\(189\) 6.45161e15 + 1.09611e16i 0.748920 + 1.27239i
\(190\) −7.70070e15 −0.861500
\(191\) 1.27381e15i 0.137363i −0.997639 0.0686816i \(-0.978121\pi\)
0.997639 0.0686816i \(-0.0218792\pi\)
\(192\) −2.12091e14 1.18346e15i −0.0220502 0.123040i
\(193\) −8.57584e15 −0.859757 −0.429878 0.902887i \(-0.641444\pi\)
−0.429878 + 0.902887i \(0.641444\pi\)
\(194\) 1.43198e14i 0.0138460i
\(195\) −1.53374e16 + 2.74864e15i −1.43057 + 0.256375i
\(196\) −6.55532e15 −0.589931
\(197\) 1.19404e16i 1.03695i −0.855094 0.518473i \(-0.826501\pi\)
0.855094 0.518473i \(-0.173499\pi\)
\(198\) 6.94629e15 2.57233e15i 0.582233 0.215611i
\(199\) 7.87496e15 0.637202 0.318601 0.947889i \(-0.396787\pi\)
0.318601 + 0.947889i \(0.396787\pi\)
\(200\) 3.68843e15i 0.288159i
\(201\) 1.79322e15 + 1.00061e16i 0.135289 + 0.754908i
\(202\) −4.02582e15 −0.293356
\(203\) 1.68308e16i 1.18477i
\(204\) −2.95918e15 + 5.30321e14i −0.201262 + 0.0360685i
\(205\) −7.73568e15 −0.508419
\(206\) 4.74712e15i 0.301550i
\(207\) −1.70485e15 4.60376e15i −0.104687 0.282696i
\(208\) −4.54270e15 −0.269693
\(209\) 1.38315e16i 0.794046i
\(210\) 4.46869e15 + 2.49352e16i 0.248110 + 1.38445i
\(211\) 3.57862e16 1.92193 0.960967 0.276664i \(-0.0892290\pi\)
0.960967 + 0.276664i \(0.0892290\pi\)
\(212\) 8.56116e15i 0.444817i
\(213\) 8.76769e15 1.57128e15i 0.440786 0.0789942i
\(214\) 1.53077e16 0.744754
\(215\) 1.21899e16i 0.574023i
\(216\) 6.68402e15 3.93416e15i 0.304692 0.179339i
\(217\) −3.83460e16 −1.69240
\(218\) 1.28122e16i 0.547557i
\(219\) 1.65870e15 + 9.25550e15i 0.0686528 + 0.383082i
\(220\) 1.47533e16 0.591467
\(221\) 1.13588e16i 0.441149i
\(222\) −2.75616e16 + 4.93936e15i −1.03713 + 0.185866i
\(223\) 2.97756e16 1.08574 0.542870 0.839816i \(-0.317337\pi\)
0.542870 + 0.839816i \(0.317337\pi\)
\(224\) 7.38543e15i 0.260999i
\(225\) 2.23125e16 8.26271e15i 0.764312 0.283038i
\(226\) −1.09784e16 −0.364568
\(227\) 4.31388e16i 1.38895i −0.719517 0.694475i \(-0.755637\pi\)
0.719517 0.694475i \(-0.244363\pi\)
\(228\) −2.55473e15 1.42553e16i −0.0797628 0.445075i
\(229\) 1.02466e16 0.310263 0.155131 0.987894i \(-0.450420\pi\)
0.155131 + 0.987894i \(0.450420\pi\)
\(230\) 9.77797e15i 0.287180i
\(231\) −4.47870e16 + 8.02637e15i −1.27605 + 0.228684i
\(232\) −1.02634e16 −0.283709
\(233\) 6.13926e16i 1.64674i 0.567506 + 0.823369i \(0.307908\pi\)
−0.567506 + 0.823369i \(0.692092\pi\)
\(234\) −1.01764e16 2.74802e16i −0.264901 0.715335i
\(235\) −6.98626e16 −1.76510
\(236\) 2.04986e15i 0.0502736i
\(237\) −6.89801e15 3.84908e16i −0.164242 0.916470i
\(238\) 1.84669e16 0.426928
\(239\) 5.98554e16i 1.34375i 0.740665 + 0.671875i \(0.234511\pi\)
−0.740665 + 0.671875i \(0.765489\pi\)
\(240\) 1.52054e16 2.72498e15i 0.331526 0.0594135i
\(241\) −1.53889e16 −0.325902 −0.162951 0.986634i \(-0.552101\pi\)
−0.162951 + 0.986634i \(0.552101\pi\)
\(242\) 7.87211e15i 0.161951i
\(243\) 3.87723e16 + 3.16206e16i 0.774958 + 0.632013i
\(244\) 4.70272e16 0.913315
\(245\) 8.42242e16i 1.58955i
\(246\) −2.56633e15 1.43201e16i −0.0470724 0.262663i
\(247\) −5.47188e16 −0.975569
\(248\) 2.33832e16i 0.405268i
\(249\) 1.15322e17 2.06671e16i 1.94320 0.348245i
\(250\) −1.07546e16 −0.176204
\(251\) 1.01100e17i 1.61078i 0.592746 + 0.805389i \(0.298044\pi\)
−0.592746 + 0.805389i \(0.701956\pi\)
\(252\) −4.46768e16 + 1.65446e16i −0.692275 + 0.256362i
\(253\) 1.75625e16 0.264694
\(254\) 1.34584e16i 0.197314i
\(255\) −6.81368e15 3.80202e16i −0.0971853 0.542292i
\(256\) 4.50360e15 0.0625000
\(257\) 6.12785e16i 0.827515i 0.910387 + 0.413758i \(0.135784\pi\)
−0.910387 + 0.413758i \(0.864216\pi\)
\(258\) −2.25655e16 + 4.04401e15i −0.296557 + 0.0531465i
\(259\) 1.71999e17 2.20002
\(260\) 5.83655e16i 0.726680i
\(261\) −2.29917e16 6.20863e16i −0.278668 0.752510i
\(262\) 3.52022e16 0.415395
\(263\) 1.18188e17i 1.35795i −0.734163 0.678973i \(-0.762425\pi\)
0.734163 0.678973i \(-0.237575\pi\)
\(264\) 4.89444e15 + 2.73109e16i 0.0547615 + 0.305568i
\(265\) −1.09996e17 −1.19855
\(266\) 8.89608e16i 0.944120i
\(267\) −1.32398e17 + 2.37273e16i −1.36868 + 0.245285i
\(268\) −3.80778e16 −0.383467
\(269\) 1.90291e17i 1.86704i −0.358528 0.933519i \(-0.616721\pi\)
0.358528 0.933519i \(-0.383279\pi\)
\(270\) 5.05469e16 + 8.58777e16i 0.483224 + 0.820983i
\(271\) 4.08475e16 0.380523 0.190261 0.981733i \(-0.439066\pi\)
0.190261 + 0.981733i \(0.439066\pi\)
\(272\) 1.12610e16i 0.102234i
\(273\) 3.17531e16 + 1.77182e17i 0.280962 + 1.56776i
\(274\) −4.52387e16 −0.390172
\(275\) 8.51184e16i 0.715640i
\(276\) 1.81007e16 3.24386e15i 0.148365 0.0265888i
\(277\) −1.87884e17 −1.50152 −0.750760 0.660575i \(-0.770313\pi\)
−0.750760 + 0.660575i \(0.770313\pi\)
\(278\) 1.93848e15i 0.0151059i
\(279\) −1.41453e17 + 5.23824e16i −1.07493 + 0.398067i
\(280\) −9.48896e16 −0.703254
\(281\) 1.93819e17i 1.40105i −0.713629 0.700523i \(-0.752950\pi\)
0.713629 0.700523i \(-0.247050\pi\)
\(282\) −2.31771e16 1.29328e17i −0.163424 0.911901i
\(283\) 1.59111e17 1.09445 0.547225 0.836985i \(-0.315684\pi\)
0.547225 + 0.836985i \(0.315684\pi\)
\(284\) 3.33650e16i 0.223904i
\(285\) 1.83155e17 3.28237e16i 1.19924 0.214918i
\(286\) 1.04832e17 0.669782
\(287\) 8.93649e16i 0.557177i
\(288\) 1.00888e16 + 2.72437e16i 0.0613894 + 0.165775i
\(289\) 1.40220e17 0.832771
\(290\) 1.31866e17i 0.764445i
\(291\) 6.10370e14 + 3.40585e15i 0.00345416 + 0.0192741i
\(292\) −3.52213e16 −0.194592
\(293\) 1.38296e17i 0.745997i 0.927832 + 0.372999i \(0.121670\pi\)
−0.927832 + 0.372999i \(0.878330\pi\)
\(294\) 1.55913e17 2.79416e16i 0.821206 0.147170i
\(295\) 2.63370e16 0.135460
\(296\) 1.04884e17i 0.526827i
\(297\) −1.54248e17 + 9.07891e16i −0.756701 + 0.445388i
\(298\) −7.95320e16 −0.381091
\(299\) 6.94792e16i 0.325204i
\(300\) 1.57217e16 + 8.77265e16i 0.0718868 + 0.401127i
\(301\) 1.40821e17 0.629074
\(302\) 1.73361e16i 0.0756664i
\(303\) 9.57511e16 1.71597e16i 0.408362 0.0731834i
\(304\) 5.42479e16 0.226083
\(305\) 6.04216e17i 2.46090i
\(306\) 6.81215e16 2.52266e16i 0.271165 0.100417i
\(307\) −1.59731e17 −0.621469 −0.310735 0.950497i \(-0.600575\pi\)
−0.310735 + 0.950497i \(0.600575\pi\)
\(308\) 1.70434e17i 0.648190i
\(309\) −2.02342e16 1.12907e17i −0.0752276 0.419768i
\(310\) −3.00433e17 −1.09198
\(311\) 1.54506e17i 0.549064i −0.961578 0.274532i \(-0.911477\pi\)
0.961578 0.274532i \(-0.0885229\pi\)
\(312\) 1.08045e17 1.93629e16i 0.375423 0.0672803i
\(313\) −3.11171e17 −1.05728 −0.528639 0.848847i \(-0.677297\pi\)
−0.528639 + 0.848847i \(0.677297\pi\)
\(314\) 3.90520e17i 1.29759i
\(315\) −2.12569e17 5.74017e17i −0.690757 1.86531i
\(316\) 1.46475e17 0.465536
\(317\) 3.75988e17i 1.16885i −0.811448 0.584425i \(-0.801320\pi\)
0.811448 0.584425i \(-0.198680\pi\)
\(318\) −3.64913e16 2.03621e17i −0.110968 0.619202i
\(319\) 2.36849e17 0.704590
\(320\) 5.78632e16i 0.168404i
\(321\) −3.64081e17 + 6.52478e16i −1.03672 + 0.185793i
\(322\) −1.12958e17 −0.314721
\(323\) 1.35644e17i 0.369814i
\(324\) −1.42205e17 + 1.22061e17i −0.379403 + 0.325658i
\(325\) 3.36737e17 0.879239
\(326\) 1.80560e16i 0.0461423i
\(327\) 5.46112e16 + 3.04729e17i 0.136599 + 0.762220i
\(328\) 5.44943e16 0.133424
\(329\) 8.07073e17i 1.93438i
\(330\) −3.50896e17 + 6.28848e16i −0.823343 + 0.147553i
\(331\) −1.08569e17 −0.249407 −0.124703 0.992194i \(-0.539798\pi\)
−0.124703 + 0.992194i \(0.539798\pi\)
\(332\) 4.38853e17i 0.987080i
\(333\) 6.34477e17 2.34958e17i 1.39735 0.517465i
\(334\) 2.90052e17 0.625534
\(335\) 4.89232e17i 1.03324i
\(336\) −3.14798e16 1.75657e17i −0.0651114 0.363321i
\(337\) 1.45112e17 0.293963 0.146982 0.989139i \(-0.453044\pi\)
0.146982 + 0.989139i \(0.453044\pi\)
\(338\) 5.83566e16i 0.115791i
\(339\) 2.61112e17 4.67945e16i 0.507492 0.0909487i
\(340\) 1.44684e17 0.275466
\(341\) 5.39618e17i 1.00648i
\(342\) 1.21524e17 + 3.28163e17i 0.222065 + 0.599662i
\(343\) −1.48325e17 −0.265556
\(344\) 8.58719e16i 0.150641i
\(345\) 4.16778e16 + 2.32562e17i 0.0716426 + 0.399764i
\(346\) 2.92190e17 0.492190
\(347\) 1.27586e17i 0.210619i −0.994439 0.105310i \(-0.966417\pi\)
0.994439 0.105310i \(-0.0335834\pi\)
\(348\) 2.44106e17 4.37468e16i 0.394934 0.0707768i
\(349\) −7.20869e17 −1.14309 −0.571543 0.820572i \(-0.693655\pi\)
−0.571543 + 0.820572i \(0.693655\pi\)
\(350\) 5.47460e17i 0.850896i
\(351\) 3.59171e17 + 6.10220e17i 0.547206 + 0.929687i
\(352\) −1.03930e17 −0.155218
\(353\) 6.22911e17i 0.912018i 0.889975 + 0.456009i \(0.150721\pi\)
−0.889975 + 0.456009i \(0.849279\pi\)
\(354\) 8.73736e15 + 4.87543e16i 0.0125417 + 0.0699827i
\(355\) −4.28680e17 −0.603303
\(356\) 5.03834e17i 0.695245i
\(357\) −4.39221e17 + 7.87136e16i −0.594299 + 0.106506i
\(358\) −1.14644e17 −0.152115
\(359\) 2.75392e17i 0.358336i −0.983819 0.179168i \(-0.942659\pi\)
0.983819 0.179168i \(-0.0573405\pi\)
\(360\) −3.50033e17 + 1.29623e17i −0.446675 + 0.165412i
\(361\) −1.45567e17 −0.182185
\(362\) 5.15478e17i 0.632777i
\(363\) 3.35543e16 + 1.87232e17i 0.0404018 + 0.225442i
\(364\) −6.74256e17 −0.796370
\(365\) 4.52531e17i 0.524322i
\(366\) −1.11851e18 + 2.00450e17i −1.27137 + 0.227844i
\(367\) 4.21095e17 0.469588 0.234794 0.972045i \(-0.424558\pi\)
0.234794 + 0.972045i \(0.424558\pi\)
\(368\) 6.88812e16i 0.0753644i
\(369\) 1.22076e17 + 3.29653e17i 0.131053 + 0.353894i
\(370\) 1.34757e18 1.41952
\(371\) 1.27070e18i 1.31349i
\(372\) −9.96692e16 5.56153e17i −0.101102 0.564148i
\(373\) −7.40270e17 −0.736933 −0.368467 0.929641i \(-0.620117\pi\)
−0.368467 + 0.929641i \(0.620117\pi\)
\(374\) 2.59872e17i 0.253897i
\(375\) 2.55791e17 4.58408e16i 0.245282 0.0439575i
\(376\) 4.92149e17 0.463214
\(377\) 9.36997e17i 0.865663i
\(378\) 9.92085e17 5.83933e17i 0.899717 0.529566i
\(379\) −6.56688e17 −0.584635 −0.292317 0.956321i \(-0.594426\pi\)
−0.292317 + 0.956321i \(0.594426\pi\)
\(380\) 6.96988e17i 0.609172i
\(381\) −5.73656e16 3.20099e17i −0.0492240 0.274669i
\(382\) −1.15292e17 −0.0971304
\(383\) 1.86220e17i 0.154041i 0.997030 + 0.0770203i \(0.0245406\pi\)
−0.997030 + 0.0770203i \(0.975459\pi\)
\(384\) −1.07115e17 + 1.91962e16i −0.0870023 + 0.0155919i
\(385\) 2.18978e18 1.74653
\(386\) 7.76196e17i 0.607940i
\(387\) 5.19467e17 1.92368e17i 0.399559 0.147964i
\(388\) −1.29608e16 −0.00979061
\(389\) 2.31179e18i 1.71514i −0.514364 0.857572i \(-0.671972\pi\)
0.514364 0.857572i \(-0.328028\pi\)
\(390\) 2.48779e17 + 1.38818e18i 0.181284 + 1.01156i
\(391\) 1.72234e17 0.123277
\(392\) 5.93320e17i 0.417145i
\(393\) −8.37259e17 + 1.50047e17i −0.578245 + 0.103628i
\(394\) −1.08072e18 −0.733231
\(395\) 1.88194e18i 1.25437i
\(396\) −2.32821e17 6.28707e17i −0.152460 0.411701i
\(397\) 2.74445e18 1.76572 0.882860 0.469636i \(-0.155615\pi\)
0.882860 + 0.469636i \(0.155615\pi\)
\(398\) 7.12760e17i 0.450570i
\(399\) −3.79188e17 2.11587e18i −0.235529 1.31425i
\(400\) −3.33839e17 −0.203759
\(401\) 1.46184e18i 0.876780i 0.898785 + 0.438390i \(0.144451\pi\)
−0.898785 + 0.438390i \(0.855549\pi\)
\(402\) 9.05652e17 1.62304e17i 0.533800 0.0956635i
\(403\) −2.13478e18 −1.23657
\(404\) 3.64376e17i 0.207434i
\(405\) −1.56827e18 1.82708e18i −0.877475 1.02229i
\(406\) −1.52335e18 −0.837757
\(407\) 2.42042e18i 1.30837i
\(408\) 4.79992e16 + 2.67835e17i 0.0255043 + 0.142313i
\(409\) 2.58787e17 0.135170 0.0675848 0.997714i \(-0.478471\pi\)
0.0675848 + 0.997714i \(0.478471\pi\)
\(410\) 7.00154e17i 0.359506i
\(411\) 1.07597e18 1.92827e17i 0.543134 0.0973361i
\(412\) 4.29660e17 0.213228
\(413\) 3.04253e17i 0.148451i
\(414\) −4.16685e17 + 1.54306e17i −0.199896 + 0.0740251i
\(415\) −5.63847e18 −2.65965
\(416\) 4.11158e17i 0.190702i
\(417\) 8.26261e15 + 4.61052e16i 0.00376847 + 0.0210280i
\(418\) −1.25188e18 −0.561475
\(419\) 4.32339e18i 1.90689i −0.301566 0.953445i \(-0.597509\pi\)
0.301566 0.953445i \(-0.402491\pi\)
\(420\) 2.25688e18 4.04459e17i 0.978955 0.175441i
\(421\) 1.31437e18 0.560715 0.280358 0.959896i \(-0.409547\pi\)
0.280358 + 0.959896i \(0.409547\pi\)
\(422\) 3.23900e18i 1.35901i
\(423\) 1.10250e18 + 2.97717e18i 0.454983 + 1.22863i
\(424\) 7.74868e17 0.314533
\(425\) 8.34746e17i 0.333297i
\(426\) −1.42216e17 7.93561e17i −0.0558574 0.311683i
\(427\) 6.98008e18 2.69690
\(428\) 1.38549e18i 0.526621i
\(429\) −2.49336e18 + 4.46840e17i −0.932360 + 0.167090i
\(430\) 1.10330e18 0.405896
\(431\) 1.87112e18i 0.677268i 0.940918 + 0.338634i \(0.109965\pi\)
−0.940918 + 0.338634i \(0.890035\pi\)
\(432\) −3.56079e17 6.04968e17i −0.126812 0.215450i
\(433\) −2.75784e18 −0.966392 −0.483196 0.875512i \(-0.660524\pi\)
−0.483196 + 0.875512i \(0.660524\pi\)
\(434\) 3.47069e18i 1.19671i
\(435\) 5.62068e17 + 3.13633e18i 0.190706 + 1.06413i
\(436\) −1.15963e18 −0.387181
\(437\) 8.29705e17i 0.272617i
\(438\) 8.37712e17 1.50128e17i 0.270880 0.0485449i
\(439\) 1.83354e18 0.583498 0.291749 0.956495i \(-0.405763\pi\)
0.291749 + 0.956495i \(0.405763\pi\)
\(440\) 1.33532e18i 0.418230i
\(441\) −3.58918e18 + 1.32914e18i −1.10643 + 0.409732i
\(442\) 1.02808e18 0.311940
\(443\) 4.33165e17i 0.129368i 0.997906 + 0.0646841i \(0.0206040\pi\)
−0.997906 + 0.0646841i \(0.979396\pi\)
\(444\) 4.47060e17 + 2.49459e18i 0.131427 + 0.733362i
\(445\) 6.47337e18 1.87331
\(446\) 2.69498e18i 0.767735i
\(447\) 1.89161e18 3.38999e17i 0.530492 0.0950705i
\(448\) 6.68453e17 0.184554
\(449\) 4.16940e18i 1.13331i −0.823955 0.566656i \(-0.808237\pi\)
0.823955 0.566656i \(-0.191763\pi\)
\(450\) −7.47855e17 2.01950e18i −0.200138 0.540450i
\(451\) −1.25757e18 −0.331357
\(452\) 9.93649e17i 0.257789i
\(453\) −7.38939e16 4.12326e17i −0.0188765 0.105330i
\(454\) −3.90448e18 −0.982136
\(455\) 8.66298e18i 2.14579i
\(456\) −1.29024e18 + 2.31227e17i −0.314716 + 0.0564008i
\(457\) −5.74510e18 −1.38002 −0.690008 0.723802i \(-0.742393\pi\)
−0.690008 + 0.723802i \(0.742393\pi\)
\(458\) 9.27412e17i 0.219389i
\(459\) −1.51269e18 + 8.90358e17i −0.352421 + 0.207432i
\(460\) −8.85000e17 −0.203067
\(461\) 8.04024e18i 1.81703i 0.417851 + 0.908515i \(0.362783\pi\)
−0.417851 + 0.908515i \(0.637217\pi\)
\(462\) 7.26464e17 + 4.05366e18i 0.161704 + 0.902304i
\(463\) −5.73855e18 −1.25816 −0.629079 0.777341i \(-0.716568\pi\)
−0.629079 + 0.777341i \(0.716568\pi\)
\(464\) 9.28933e17i 0.200613i
\(465\) 7.14557e18 1.28057e18i 1.52008 0.272416i
\(466\) 5.55663e18 1.16442
\(467\) 2.96692e18i 0.612474i −0.951955 0.306237i \(-0.900930\pi\)
0.951955 0.306237i \(-0.0990700\pi\)
\(468\) −2.48723e18 + 9.21063e17i −0.505818 + 0.187313i
\(469\) −5.65175e18 −1.13233
\(470\) 6.32324e18i 1.24812i
\(471\) −1.66456e18 9.28823e18i −0.323708 1.80629i
\(472\) −1.85532e17 −0.0355488
\(473\) 1.98168e18i 0.374115i
\(474\) −3.48379e18 + 6.24337e17i −0.648042 + 0.116137i
\(475\) −4.02124e18 −0.737062
\(476\) 1.67143e18i 0.301884i
\(477\) 1.73584e18 + 4.68743e18i 0.308944 + 0.834268i
\(478\) 5.41750e18 0.950174
\(479\) 3.00387e18i 0.519198i 0.965716 + 0.259599i \(0.0835904\pi\)
−0.965716 + 0.259599i \(0.916410\pi\)
\(480\) −2.46637e17 1.37623e18i −0.0420117 0.234425i
\(481\) 9.57543e18 1.60747
\(482\) 1.39284e18i 0.230448i
\(483\) 2.68662e18 4.81474e17i 0.438103 0.0785133i
\(484\) −7.12502e17 −0.114517
\(485\) 1.66523e17i 0.0263805i
\(486\) 2.86197e18 3.50927e18i 0.446901 0.547978i
\(487\) 8.00668e18 1.23240 0.616198 0.787592i \(-0.288672\pi\)
0.616198 + 0.787592i \(0.288672\pi\)
\(488\) 4.25642e18i 0.645811i
\(489\) −7.69624e16 4.29449e17i −0.0115111 0.0642317i
\(490\) −7.62310e18 −1.12398
\(491\) 3.66948e18i 0.533377i −0.963783 0.266688i \(-0.914071\pi\)
0.963783 0.266688i \(-0.0859294\pi\)
\(492\) −1.29611e18 + 2.32278e17i −0.185731 + 0.0332852i
\(493\) 2.32275e18 0.328151
\(494\) 4.95258e18i 0.689831i
\(495\) 8.07776e18 2.99133e18i 1.10931 0.410798i
\(496\) 2.11641e18 0.286568
\(497\) 4.95224e18i 0.661161i
\(498\) −1.87058e18 1.04378e19i −0.246246 1.37405i
\(499\) −7.47635e18 −0.970478 −0.485239 0.874382i \(-0.661267\pi\)
−0.485239 + 0.874382i \(0.661267\pi\)
\(500\) 9.73398e17i 0.124595i
\(501\) −6.89867e18 + 1.23632e18i −0.870766 + 0.156052i
\(502\) 9.15054e18 1.13899
\(503\) 1.32965e19i 1.63215i 0.577946 + 0.816075i \(0.303855\pi\)
−0.577946 + 0.816075i \(0.696145\pi\)
\(504\) 1.49745e18 + 4.04369e18i 0.181275 + 0.489512i
\(505\) −4.68158e18 −0.558923
\(506\) 1.58958e18i 0.187167i
\(507\) 2.48741e17 + 1.38797e18i 0.0288862 + 0.161185i
\(508\) 1.21812e18 0.139522
\(509\) 1.68157e18i 0.189973i 0.995479 + 0.0949864i \(0.0302808\pi\)
−0.995479 + 0.0949864i \(0.969719\pi\)
\(510\) −3.44120e18 + 6.16704e17i −0.383458 + 0.0687204i
\(511\) −5.22777e18 −0.574606
\(512\) 4.07619e17i 0.0441942i
\(513\) −4.28913e18 7.28712e18i −0.458720 0.779353i
\(514\) 5.54629e18 0.585142
\(515\) 5.52036e18i 0.574536i
\(516\) 3.66022e17 + 2.04240e18i 0.0375803 + 0.209697i
\(517\) −1.13574e19 −1.15039
\(518\) 1.55676e19i 1.55565i
\(519\) −6.94951e18 + 1.24544e18i −0.685146 + 0.122786i
\(520\) −5.28264e18 −0.513840
\(521\) 1.66764e19i 1.60043i −0.599712 0.800216i \(-0.704718\pi\)
0.599712 0.800216i \(-0.295282\pi\)
\(522\) −5.61941e18 + 2.08097e18i −0.532105 + 0.197048i
\(523\) 8.62761e18 0.806081 0.403040 0.915182i \(-0.367953\pi\)
0.403040 + 0.915182i \(0.367953\pi\)
\(524\) 3.18614e18i 0.293729i
\(525\) 2.33351e18 + 1.30209e19i 0.212273 + 1.18448i
\(526\) −1.06971e19 −0.960213
\(527\) 5.29197e18i 0.468752i
\(528\) 2.47190e18 4.42994e17i 0.216069 0.0387222i
\(529\) 1.05393e19 0.909123
\(530\) 9.95567e18i 0.847499i
\(531\) −4.15623e17 1.12234e18i −0.0349171 0.0942896i
\(532\) 8.05181e18 0.667594
\(533\) 4.97508e18i 0.407108i
\(534\) 2.14755e18 + 1.19833e19i 0.173442 + 0.967806i
\(535\) 1.78011e19 1.41896
\(536\) 3.44641e18i 0.271152i
\(537\) 2.72672e18 4.88662e17i 0.211749 0.0379480i
\(538\) −1.72232e19 −1.32020
\(539\) 1.36921e19i 1.03598i
\(540\) 7.77276e18 4.57498e18i 0.580523 0.341691i
\(541\) −1.62414e19 −1.19741 −0.598704 0.800970i \(-0.704318\pi\)
−0.598704 + 0.800970i \(0.704318\pi\)
\(542\) 3.69709e18i 0.269070i
\(543\) 2.19719e18 + 1.22603e19i 0.157859 + 0.880848i
\(544\) −1.01923e18 −0.0722903
\(545\) 1.48992e19i 1.04325i
\(546\) 1.60367e19 2.87396e18i 1.10858 0.198670i
\(547\) −5.54858e18 −0.378678 −0.189339 0.981912i \(-0.560635\pi\)
−0.189339 + 0.981912i \(0.560635\pi\)
\(548\) 4.09454e18i 0.275893i
\(549\) 2.57485e19 9.53510e18i 1.71295 0.634335i
\(550\) 7.70404e18 0.506034
\(551\) 1.11894e19i 0.725681i
\(552\) −2.93601e17 1.63829e18i −0.0188011 0.104910i
\(553\) 2.17407e19 1.37467
\(554\) 1.70053e19i 1.06173i
\(555\) −3.20510e19 + 5.74392e18i −1.97602 + 0.354126i
\(556\) −1.75451e17 −0.0106815
\(557\) 1.31816e19i 0.792471i −0.918149 0.396235i \(-0.870316\pi\)
0.918149 0.396235i \(-0.129684\pi\)
\(558\) 4.74111e18 + 1.28028e19i 0.281476 + 0.760093i
\(559\) 7.83971e18 0.459640
\(560\) 8.58842e18i 0.497276i
\(561\) −1.10768e18 6.18086e18i −0.0633397 0.353434i
\(562\) −1.75425e19 −0.990690
\(563\) 1.30154e19i 0.725939i 0.931801 + 0.362969i \(0.118237\pi\)
−0.931801 + 0.362969i \(0.881763\pi\)
\(564\) −1.17054e19 + 2.09775e18i −0.644811 + 0.115558i
\(565\) −1.27666e19 −0.694603
\(566\) 1.44011e19i 0.773894i
\(567\) −2.11070e19 + 1.81171e19i −1.12033 + 0.961627i
\(568\) 3.01985e18 0.158324
\(569\) 2.97159e19i 1.53888i −0.638722 0.769438i \(-0.720537\pi\)
0.638722 0.769438i \(-0.279463\pi\)
\(570\) −2.97086e18 1.65773e19i −0.151970 0.847990i
\(571\) 2.21909e19 1.12130 0.560650 0.828053i \(-0.310551\pi\)
0.560650 + 0.828053i \(0.310551\pi\)
\(572\) 9.48834e18i 0.473607i
\(573\) 2.74213e18 4.91423e17i 0.135209 0.0242311i
\(574\) 8.08838e18 0.393984
\(575\) 5.10596e18i 0.245699i
\(576\) 2.46582e18 9.13136e17i 0.117221 0.0434088i
\(577\) −2.98019e19 −1.39963 −0.699814 0.714325i \(-0.746734\pi\)
−0.699814 + 0.714325i \(0.746734\pi\)
\(578\) 1.26913e19i 0.588858i
\(579\) −3.30848e18 1.84612e19i −0.151662 0.846274i
\(580\) −1.19351e19 −0.540544
\(581\) 6.51373e19i 2.91472i
\(582\) 3.08263e17 5.52444e16i 0.0136289 0.00244246i
\(583\) −1.78817e19 −0.781141
\(584\) 3.18787e18i 0.137598i
\(585\) −1.18340e19 3.19564e19i −0.504709 1.36291i
\(586\) 1.25171e19 0.527500
\(587\) 1.02892e19i 0.428465i 0.976783 + 0.214233i \(0.0687251\pi\)
−0.976783 + 0.214233i \(0.931275\pi\)
\(588\) −2.52898e18 1.41117e19i −0.104065 0.580680i
\(589\) 2.54931e19 1.03661
\(590\) 2.38375e18i 0.0957850i
\(591\) 2.57042e19 4.60650e18i 1.02068 0.182919i
\(592\) −9.49302e18 −0.372523
\(593\) 3.60491e19i 1.39802i 0.715114 + 0.699008i \(0.246375\pi\)
−0.715114 + 0.699008i \(0.753625\pi\)
\(594\) 8.21729e18 + 1.39609e19i 0.314937 + 0.535068i
\(595\) 2.14749e19 0.813415
\(596\) 7.19842e18i 0.269472i
\(597\) 3.03809e18 + 1.69525e19i 0.112403 + 0.627209i
\(598\) −6.28854e18 −0.229954
\(599\) 9.79465e18i 0.353998i −0.984211 0.176999i \(-0.943361\pi\)
0.984211 0.176999i \(-0.0566390\pi\)
\(600\) 7.94010e18 1.42296e18i 0.283640 0.0508317i
\(601\) −7.22930e18 −0.255255 −0.127628 0.991822i \(-0.540736\pi\)
−0.127628 + 0.991822i \(0.540736\pi\)
\(602\) 1.27457e19i 0.444822i
\(603\) −2.08484e19 + 7.72054e18i −0.719205 + 0.266334i
\(604\) 1.56909e18 0.0535042
\(605\) 9.15438e18i 0.308561i
\(606\) −1.55312e18 8.66640e18i −0.0517485 0.288756i
\(607\) −6.61848e18 −0.217991 −0.108995 0.994042i \(-0.534763\pi\)
−0.108995 + 0.994042i \(0.534763\pi\)
\(608\) 4.90996e18i 0.159865i
\(609\) 3.62318e19 6.49317e18i 1.16619 0.208995i
\(610\) 5.46874e19 1.74012
\(611\) 4.49310e19i 1.41337i
\(612\) −2.28325e18 6.16565e18i −0.0710057 0.191743i
\(613\) 6.10503e17 0.0187700 0.00938501 0.999956i \(-0.497013\pi\)
0.00938501 + 0.999956i \(0.497013\pi\)
\(614\) 1.44572e19i 0.439445i
\(615\) −2.98435e18 1.66526e19i −0.0896859 0.500446i
\(616\) −1.54260e19 −0.458340
\(617\) 6.35333e19i 1.86640i −0.359353 0.933202i \(-0.617002\pi\)
0.359353 0.933202i \(-0.382998\pi\)
\(618\) −1.02191e19 + 1.83139e18i −0.296821 + 0.0531939i
\(619\) 1.54764e19 0.444462 0.222231 0.974994i \(-0.428666\pi\)
0.222231 + 0.974994i \(0.428666\pi\)
\(620\) 2.71921e19i 0.772148i
\(621\) 9.25281e18 5.44613e18i 0.259796 0.152914i
\(622\) −1.39843e19 −0.388247
\(623\) 7.47823e19i 2.05297i
\(624\) −1.75253e18 9.77908e18i −0.0475744 0.265464i
\(625\) −4.28689e19 −1.15075
\(626\) 2.81640e19i 0.747608i
\(627\) 2.97751e19 5.33606e18i 0.781594 0.140071i
\(628\) 3.53459e19 0.917531
\(629\) 2.37368e19i 0.609351i
\(630\) −5.19541e19 + 1.92395e19i −1.31897 + 0.488439i
\(631\) −5.77423e19 −1.44973 −0.724867 0.688889i \(-0.758099\pi\)
−0.724867 + 0.688889i \(0.758099\pi\)
\(632\) 1.32574e19i 0.329183i
\(633\) 1.38060e19 + 7.70371e19i 0.339032 + 1.89179i
\(634\) −3.40305e19 −0.826502
\(635\) 1.56507e19i 0.375938i
\(636\) −1.84297e19 + 3.30282e18i −0.437842 + 0.0784665i
\(637\) −5.41674e19 −1.27281
\(638\) 2.14371e19i 0.498220i
\(639\) 6.76499e18 + 1.82681e19i 0.155511 + 0.419939i
\(640\) 5.23718e18 0.119080
\(641\) 2.72430e19i 0.612702i −0.951919 0.306351i \(-0.900892\pi\)
0.951919 0.306351i \(-0.0991081\pi\)
\(642\) 5.90555e18 + 3.29529e19i 0.131376 + 0.733075i
\(643\) 5.75196e19 1.26572 0.632862 0.774265i \(-0.281880\pi\)
0.632862 + 0.774265i \(0.281880\pi\)
\(644\) 1.02238e19i 0.222541i
\(645\) −2.62412e19 + 4.70273e18i −0.565022 + 0.101259i
\(646\) −1.22771e19 −0.261498
\(647\) 3.32642e19i 0.700886i −0.936584 0.350443i \(-0.886031\pi\)
0.936584 0.350443i \(-0.113969\pi\)
\(648\) 1.10477e19 + 1.28710e19i 0.230275 + 0.268278i
\(649\) 4.28155e18 0.0882852
\(650\) 3.04779e19i 0.621716i
\(651\) −1.47935e19 8.25477e19i −0.298542 1.66586i
\(652\) 1.63424e18 0.0326275
\(653\) 6.10716e18i 0.120628i −0.998179 0.0603138i \(-0.980790\pi\)
0.998179 0.0603138i \(-0.0192101\pi\)
\(654\) 2.75810e19 4.94284e18i 0.538971 0.0965900i
\(655\) 4.09362e19 0.791442
\(656\) 4.93226e18i 0.0943450i
\(657\) −1.92844e19 + 7.14137e18i −0.364964 + 0.135152i
\(658\) 7.30479e19 1.36781
\(659\) 6.12820e19i 1.13536i −0.823248 0.567682i \(-0.807840\pi\)
0.823248 0.567682i \(-0.192160\pi\)
\(660\) 5.69168e18 + 3.17595e19i 0.104336 + 0.582192i
\(661\) 3.98614e19 0.723006 0.361503 0.932371i \(-0.382264\pi\)
0.361503 + 0.932371i \(0.382264\pi\)
\(662\) 9.82650e18i 0.176357i
\(663\) −2.44521e19 + 4.38211e18i −0.434231 + 0.0778195i
\(664\) 3.97204e19 0.697971
\(665\) 1.03451e20i 1.79881i
\(666\) −2.12660e19 5.74263e19i −0.365903 0.988079i
\(667\) −1.42078e19 −0.241905
\(668\) 2.62525e19i 0.442319i
\(669\) 1.14871e19 + 6.40980e19i 0.191526 + 1.06871i
\(670\) −4.42802e19 −0.730611
\(671\) 9.82259e19i 1.60387i
\(672\) −1.58986e19 + 2.84923e18i −0.256907 + 0.0460407i
\(673\) 4.02925e19 0.644346 0.322173 0.946681i \(-0.395587\pi\)
0.322173 + 0.946681i \(0.395587\pi\)
\(674\) 1.31340e19i 0.207863i
\(675\) 2.63951e19 + 4.48445e19i 0.413425 + 0.702398i
\(676\) −5.28184e18 −0.0818763
\(677\) 3.44241e19i 0.528132i −0.964505 0.264066i \(-0.914936\pi\)
0.964505 0.264066i \(-0.0850636\pi\)
\(678\) −4.23535e18 2.36332e19i −0.0643104 0.358851i
\(679\) −1.92372e18 −0.0289104
\(680\) 1.30953e19i 0.194784i
\(681\) 9.28650e19 1.66425e19i 1.36717 0.245013i
\(682\) −4.88406e19 −0.711690
\(683\) 5.94502e19i 0.857450i −0.903435 0.428725i \(-0.858963\pi\)
0.903435 0.428725i \(-0.141037\pi\)
\(684\) 2.97019e19 1.09991e19i 0.424025 0.157024i
\(685\) −5.26075e19 −0.743385
\(686\) 1.34249e19i 0.187776i
\(687\) 3.95302e18 + 2.20578e19i 0.0547308 + 0.305397i
\(688\) −7.77224e18 −0.106519
\(689\) 7.07419e19i 0.959715i
\(690\) 2.10491e19 3.77225e18i 0.282676 0.0506590i
\(691\) −5.55637e19 −0.738661 −0.369330 0.929298i \(-0.620413\pi\)
−0.369330 + 0.929298i \(0.620413\pi\)
\(692\) 2.64460e19i 0.348031i
\(693\) −3.45568e19 9.33166e19i −0.450195 1.21570i
\(694\) −1.15478e19 −0.148930
\(695\) 2.25423e18i 0.0287809i
\(696\) −3.95950e18 2.20940e19i −0.0500468 0.279260i
\(697\) −1.23329e19 −0.154324
\(698\) 6.52456e19i 0.808283i
\(699\) −1.32160e20 + 2.36847e19i −1.62091 + 0.290487i
\(700\) −4.95504e19 −0.601674
\(701\) 4.00549e18i 0.0481537i −0.999710 0.0240768i \(-0.992335\pi\)
0.999710 0.0240768i \(-0.00766464\pi\)
\(702\) 5.52308e19 3.25084e19i 0.657388 0.386933i
\(703\) −1.14348e20 −1.34754
\(704\) 9.40668e18i 0.109756i
\(705\) −2.69523e19 1.50393e20i −0.311367 1.73742i
\(706\) 5.63795e19 0.644894
\(707\) 5.40829e19i 0.612526i
\(708\) 4.41274e18 7.90816e17i 0.0494852 0.00886835i
\(709\) 9.29590e19 1.03221 0.516105 0.856525i \(-0.327381\pi\)
0.516105 + 0.856525i \(0.327381\pi\)
\(710\) 3.87997e19i 0.426599i
\(711\) 8.01981e19 2.96988e19i 0.873126 0.323334i
\(712\) −4.56019e19 −0.491612
\(713\) 3.23698e19i 0.345552i
\(714\) 7.12435e18 + 3.97537e19i 0.0753108 + 0.420233i
\(715\) 1.21908e20 1.27612
\(716\) 1.03764e19i 0.107561i
\(717\) −1.28851e20 + 2.30917e19i −1.32268 + 0.237040i
\(718\) −2.49256e19 −0.253382
\(719\) 2.28421e19i 0.229950i −0.993368 0.114975i \(-0.963321\pi\)
0.993368 0.114975i \(-0.0366788\pi\)
\(720\) 1.17322e19 + 3.16814e19i 0.116964 + 0.315847i
\(721\) 6.37728e19 0.629635
\(722\) 1.31752e19i 0.128824i
\(723\) −5.93688e18 3.31277e19i −0.0574897 0.320792i
\(724\) −4.66558e19 −0.447441
\(725\) 6.88591e19i 0.654026i
\(726\) 1.69463e19 3.03698e18i 0.159411 0.0285684i
\(727\) 1.42048e20 1.32341 0.661704 0.749765i \(-0.269834\pi\)
0.661704 + 0.749765i \(0.269834\pi\)
\(728\) 6.10267e19i 0.563119i
\(729\) −5.31118e19 + 9.56643e19i −0.485398 + 0.874293i
\(730\) −4.09584e19 −0.370752
\(731\) 1.94341e19i 0.174238i
\(732\) 1.81427e19 + 1.01236e20i 0.161110 + 0.898993i
\(733\) 9.48876e19 0.834606 0.417303 0.908767i \(-0.362975\pi\)
0.417303 + 0.908767i \(0.362975\pi\)
\(734\) 3.81131e19i 0.332049i
\(735\) 1.81310e20 3.24929e19i 1.56462 0.280399i
\(736\) 6.23442e18 0.0532907
\(737\) 7.95332e19i 0.673405i
\(738\) 2.98368e19 1.10491e19i 0.250241 0.0926685i
\(739\) −6.97379e19 −0.579372 −0.289686 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(740\) 1.21968e20i 1.00375i
\(741\) −2.11100e19 1.17793e20i −0.172092 0.960270i
\(742\) 1.15011e20 0.928777
\(743\) 1.38432e20i 1.10743i 0.832706 + 0.553715i \(0.186790\pi\)
−0.832706 + 0.553715i \(0.813210\pi\)
\(744\) −5.03372e19 + 9.02103e18i −0.398913 + 0.0714900i
\(745\) −9.24868e19 −0.726082
\(746\) 6.70016e19i 0.521091i
\(747\) 8.89805e19 + 2.40282e20i 0.685568 + 1.85130i
\(748\) 2.35209e19 0.179532
\(749\) 2.05644e20i 1.55504i
\(750\) −4.14903e18 2.31515e19i −0.0310827 0.173441i
\(751\) −1.65143e20 −1.22569 −0.612843 0.790204i \(-0.709974\pi\)
−0.612843 + 0.790204i \(0.709974\pi\)
\(752\) 4.45443e19i 0.327542i
\(753\) −2.17639e20 + 3.90035e19i −1.58552 + 0.284144i
\(754\) −8.48073e19 −0.612116
\(755\) 2.01600e19i 0.144165i
\(756\) −5.28515e19 8.97932e19i −0.374460 0.636196i
\(757\) 2.40098e20 1.68545 0.842727 0.538342i \(-0.180949\pi\)
0.842727 + 0.538342i \(0.180949\pi\)
\(758\) 5.94366e19i 0.413399i
\(759\) 6.77546e18 + 3.78070e19i 0.0466924 + 0.260543i
\(760\) 6.30842e19 0.430750
\(761\) 8.81020e19i 0.596064i −0.954556 0.298032i \(-0.903670\pi\)
0.954556 0.298032i \(-0.0963303\pi\)
\(762\) −2.89720e19 + 5.19214e18i −0.194220 + 0.0348066i
\(763\) −1.72120e20 −1.14330
\(764\) 1.04350e19i 0.0686816i
\(765\) 7.92176e19 2.93357e19i 0.516644 0.191322i
\(766\) 1.68547e19 0.108923
\(767\) 1.69382e19i 0.108468i
\(768\) 1.73745e18 + 9.69492e18i 0.0110251 + 0.0615199i
\(769\) −1.32173e20 −0.831107 −0.415554 0.909569i \(-0.636412\pi\)
−0.415554 + 0.909569i \(0.636412\pi\)
\(770\) 1.98196e20i 1.23498i
\(771\) −1.31914e20 + 2.36406e19i −0.814538 + 0.145975i
\(772\) 7.02533e19 0.429878
\(773\) 7.12550e19i 0.432075i −0.976385 0.216037i \(-0.930687\pi\)
0.976385 0.216037i \(-0.0693133\pi\)
\(774\) −1.74111e19 4.70168e19i −0.104626 0.282531i
\(775\) −1.56883e20 −0.934253
\(776\) 1.17308e18i 0.00692301i
\(777\) 6.63555e19 + 3.70263e20i 0.388088 + 2.16552i
\(778\) −2.09239e20 −1.21279
\(779\) 5.94113e19i 0.341277i
\(780\) 1.25644e20 2.25169e19i 0.715284 0.128187i
\(781\) −6.96896e19 −0.393197
\(782\) 1.55888e19i 0.0871698i
\(783\) 1.24784e20 7.34465e19i 0.691552 0.407042i
\(784\) 5.37012e19 0.294966
\(785\) 4.54131e20i 2.47226i
\(786\) 1.35807e19 + 7.57800e19i 0.0732764 + 0.408881i
\(787\) −3.27593e19 −0.175191 −0.0875956 0.996156i \(-0.527918\pi\)
−0.0875956 + 0.996156i \(0.527918\pi\)
\(788\) 9.78159e19i 0.518473i
\(789\) 2.54424e20 4.55958e19i 1.33665 0.239544i
\(790\) 1.70334e20 0.886973
\(791\) 1.47484e20i 0.761217i
\(792\) −5.69040e19 + 2.10726e19i −0.291116 + 0.107806i
\(793\) 3.88592e20 1.97052
\(794\) 2.48399e20i 1.24855i
\(795\) −4.24353e19 2.36788e20i −0.211425 1.17975i
\(796\) −6.45117e19 −0.318601
\(797\) 2.83169e20i 1.38624i −0.720823 0.693120i \(-0.756236\pi\)
0.720823 0.693120i \(-0.243764\pi\)
\(798\) −1.91506e20 + 3.43202e19i −0.929315 + 0.166544i
\(799\) −1.11381e20 −0.535775
\(800\) 3.02156e19i 0.144079i
\(801\) −1.02156e20 2.75860e20i −0.482876 1.30395i
\(802\) 1.32311e20 0.619977
\(803\) 7.35669e19i 0.341722i
\(804\) −1.46901e19 8.19703e19i −0.0676443 0.377454i
\(805\) −1.31357e20 −0.599630
\(806\) 1.93218e20i 0.874386i
\(807\) 4.09641e20 7.34126e19i 1.83776 0.329349i
\(808\) 3.29795e19 0.146678
\(809\) 4.13602e19i 0.182366i 0.995834 + 0.0911829i \(0.0290648\pi\)
−0.995834 + 0.0911829i \(0.970935\pi\)
\(810\) −1.65369e20 + 1.41943e20i −0.722867 + 0.620469i
\(811\) 4.31837e20 1.87143 0.935716 0.352755i \(-0.114755\pi\)
0.935716 + 0.352755i \(0.114755\pi\)
\(812\) 1.37878e20i 0.592384i
\(813\) 1.57586e19 + 8.79326e19i 0.0671248 + 0.374555i
\(814\) 2.19072e20 0.925157
\(815\) 2.09971e19i 0.0879137i
\(816\) 2.42416e19 4.34439e18i 0.100631 0.0180342i
\(817\) −9.36201e19 −0.385314
\(818\) 2.34227e19i 0.0955793i
\(819\) −3.69170e20 + 1.36710e20i −1.49362 + 0.553112i
\(820\) 6.33707e19 0.254209
\(821\) 3.79271e20i 1.50851i 0.656584 + 0.754253i \(0.272001\pi\)
−0.656584 + 0.754253i \(0.727999\pi\)
\(822\) −1.74527e19 9.73856e19i −0.0688270 0.384054i
\(823\) −3.22818e20 −1.26229 −0.631144 0.775665i \(-0.717414\pi\)
−0.631144 + 0.775665i \(0.717414\pi\)
\(824\) 3.88884e19i 0.150775i
\(825\) −1.83235e20 + 3.28379e19i −0.704417 + 0.126240i
\(826\) −2.75378e19 −0.104971
\(827\) 2.75227e20i 1.04029i −0.854079 0.520143i \(-0.825879\pi\)
0.854079 0.520143i \(-0.174121\pi\)
\(828\) 1.39661e19 + 3.77140e19i 0.0523437 + 0.141348i
\(829\) −4.31769e20 −1.60461 −0.802305 0.596914i \(-0.796393\pi\)
−0.802305 + 0.596914i \(0.796393\pi\)
\(830\) 5.10336e20i 1.88066i
\(831\) −7.24838e19 4.04458e20i −0.264871 1.47797i
\(832\) 3.72138e19 0.134847
\(833\) 1.34277e20i 0.482488i
\(834\) 4.17297e18 7.47846e17i 0.0148690 0.00266471i
\(835\) 3.37298e20 1.19181
\(836\) 1.13308e20i 0.397023i
\(837\) −1.67335e20 2.84297e20i −0.581445 0.987857i
\(838\) −3.91308e20 −1.34838
\(839\) 2.03774e20i 0.696331i 0.937433 + 0.348165i \(0.113195\pi\)
−0.937433 + 0.348165i \(0.886805\pi\)
\(840\) −3.66075e19 2.04269e20i −0.124055 0.692226i
\(841\) 1.05952e20 0.356073
\(842\) 1.18963e20i 0.396486i
\(843\) 4.17235e20 7.47736e19i 1.37908 0.247147i
\(844\) −2.93160e20 −0.960967
\(845\) 6.78622e19i 0.220613i
\(846\) 2.69463e20 9.97867e19i 0.868772 0.321722i
\(847\) −1.05754e20 −0.338153
\(848\) 7.01331e19i 0.222409i
\(849\) 6.13837e19 + 3.42520e20i 0.193063 + 1.07729i
\(850\) 7.55526e19 0.235677
\(851\) 1.45193e20i 0.449199i
\(852\) −7.18250e19 + 1.28719e19i −0.220393 + 0.0394971i
\(853\) 2.99936e19 0.0912821 0.0456411 0.998958i \(-0.485467\pi\)
0.0456411 + 0.998958i \(0.485467\pi\)
\(854\) 6.31765e20i 1.90700i
\(855\) 1.41319e20 + 3.81616e20i 0.423096 + 1.14252i
\(856\) −1.25400e20 −0.372377
\(857\) 2.29562e20i 0.676137i 0.941121 + 0.338069i \(0.109774\pi\)
−0.941121 + 0.338069i \(0.890226\pi\)
\(858\) 4.04433e19 + 2.25673e20i 0.118151 + 0.659278i
\(859\) 6.64441e18 0.0192533 0.00962663 0.999954i \(-0.496936\pi\)
0.00962663 + 0.999954i \(0.496936\pi\)
\(860\) 9.98594e19i 0.287012i
\(861\) −1.92376e20 + 3.44761e19i −0.548440 + 0.0982870i
\(862\) 1.69354e20 0.478901
\(863\) 4.95257e20i 1.38917i −0.719411 0.694584i \(-0.755588\pi\)
0.719411 0.694584i \(-0.244412\pi\)
\(864\) −5.47555e19 + 3.22286e19i −0.152346 + 0.0896697i
\(865\) 3.39784e20 0.937756
\(866\) 2.49611e20i 0.683342i
\(867\) 5.40956e19 + 3.01853e20i 0.146902 + 0.819712i
\(868\) 3.14131e20 0.846199
\(869\) 3.05942e20i 0.817524i
\(870\) 2.83868e20 5.08725e19i 0.752457 0.134849i
\(871\) −3.14641e20 −0.827349
\(872\) 1.04958e20i 0.273779i
\(873\) −7.09632e18 + 2.62789e18i −0.0183626 + 0.00679998i
\(874\) 7.50963e19 0.192770
\(875\) 1.44478e20i 0.367913i
\(876\) −1.35880e19 7.58211e19i −0.0343264 0.191541i
\(877\) 3.41085e20 0.854803 0.427401 0.904062i \(-0.359429\pi\)
0.427401 + 0.904062i \(0.359429\pi\)
\(878\) 1.65953e20i 0.412595i
\(879\) −2.97711e20 + 5.33534e19i −0.734299 + 0.131595i
\(880\) −1.20859e20 −0.295733
\(881\) 7.47892e20i 1.81555i 0.419461 + 0.907773i \(0.362219\pi\)
−0.419461 + 0.907773i \(0.637781\pi\)
\(882\) 1.20300e20 + 3.24856e20i 0.289724 + 0.782367i
\(883\) 1.47899e20 0.353379 0.176690 0.984267i \(-0.443461\pi\)
0.176690 + 0.984267i \(0.443461\pi\)
\(884\) 9.30511e19i 0.220575i
\(885\) 1.01606e19 + 5.66958e19i 0.0238954 + 0.133336i
\(886\) 3.92057e19 0.0914772
\(887\) 6.65945e20i 1.54160i −0.637074 0.770802i \(-0.719856\pi\)
0.637074 0.770802i \(-0.280144\pi\)
\(888\) 2.25784e20 4.04633e19i 0.518565 0.0929331i
\(889\) 1.80801e20 0.411992
\(890\) 5.85902e20i 1.32463i
\(891\) −2.54949e20 2.97025e20i −0.571887 0.666267i
\(892\) −2.43922e20 −0.542870
\(893\) 5.36556e20i 1.18483i
\(894\) −3.06827e19 1.71209e20i −0.0672250 0.375114i
\(895\) −1.33318e20 −0.289820
\(896\) 6.05014e19i 0.130500i
\(897\) 1.49568e20 2.68044e19i 0.320105 0.0573666i
\(898\) −3.77371e20 −0.801372
\(899\) 4.36540e20i 0.919827i
\(900\) −1.82784e20 + 6.76881e19i −0.382156 + 0.141519i
\(901\) −1.75364e20 −0.363804
\(902\) 1.13822e20i 0.234305i
\(903\) 5.43274e19 + 3.03146e20i 0.110970 + 0.619209i
\(904\) 8.99348e19 0.182284
\(905\) 5.99443e20i 1.20561i
\(906\) −3.73195e19 + 6.68811e18i −0.0744798 + 0.0133477i
\(907\) 4.65845e20 0.922551 0.461276 0.887257i \(-0.347392\pi\)
0.461276 + 0.887257i \(0.347392\pi\)
\(908\) 3.53393e20i 0.694475i
\(909\) 7.38797e19 + 1.99504e20i 0.144071 + 0.389048i
\(910\) −7.84083e20 −1.51730
\(911\) 8.03939e19i 0.154381i −0.997016 0.0771906i \(-0.975405\pi\)
0.997016 0.0771906i \(-0.0245950\pi\)
\(912\) 2.09283e19 + 1.16780e20i 0.0398814 + 0.222537i
\(913\) −9.16633e20 −1.73341
\(914\) 5.19987e20i 0.975818i
\(915\) −1.30070e21 + 2.33101e20i −2.42231 + 0.434106i
\(916\) −8.39398e19 −0.155131
\(917\) 4.72908e20i 0.867343i
\(918\) 8.05860e19 + 1.36913e20i 0.146677 + 0.249199i
\(919\) 4.27284e20 0.771807 0.385903 0.922539i \(-0.373890\pi\)
0.385903 + 0.922539i \(0.373890\pi\)
\(920\) 8.01011e19i 0.143590i
\(921\) −6.16225e19 3.43853e20i −0.109628 0.611723i
\(922\) 7.27719e20 1.28483
\(923\) 2.75699e20i 0.483084i
\(924\) 3.66895e20 6.57520e19i 0.638025 0.114342i
\(925\) 7.03690e20 1.21448
\(926\) 5.19394e20i 0.889652i
\(927\) 2.35248e20 8.71165e19i 0.399916 0.148096i
\(928\) 8.40774e19 0.141855
\(929\) 2.96529e20i 0.496543i −0.968691 0.248271i \(-0.920138\pi\)
0.968691 0.248271i \(-0.0798624\pi\)
\(930\) −1.15904e20 6.46743e20i −0.192627 1.07486i
\(931\) 6.46855e20 1.06699
\(932\) 5.02928e20i 0.823369i
\(933\) 3.32606e20 5.96070e19i 0.540454 0.0968558i
\(934\) −2.68535e20 −0.433085
\(935\) 3.02202e20i 0.483744i
\(936\) 8.33651e19 + 2.25118e20i 0.132450 + 0.357667i
\(937\) −9.58472e20 −1.51148 −0.755740 0.654872i \(-0.772723\pi\)
−0.755740 + 0.654872i \(0.772723\pi\)
\(938\) 5.11538e20i 0.800678i
\(939\) −1.20047e20 6.69859e20i −0.186505 1.04070i
\(940\) 5.72314e20 0.882551
\(941\) 3.90634e20i 0.597920i 0.954266 + 0.298960i \(0.0966397\pi\)
−0.954266 + 0.298960i \(0.903360\pi\)
\(942\) −8.40674e20 + 1.50659e20i −1.27724 + 0.228896i
\(943\) 7.54374e19 0.113764
\(944\) 1.67924e19i 0.0251368i
\(945\) 1.15368e21 6.79048e20i 1.71421 1.00897i
\(946\) 1.79361e20 0.264539
\(947\) 1.28178e21i 1.87656i 0.345873 + 0.938281i \(0.387583\pi\)
−0.345873 + 0.938281i \(0.612417\pi\)
\(948\) 5.65085e19 + 3.15317e20i 0.0821212 + 0.458235i
\(949\) −2.91038e20 −0.419842
\(950\) 3.63961e20i 0.521182i
\(951\) 8.09390e20 1.45052e20i 1.15052 0.206187i
\(952\) −1.51281e20 −0.213464
\(953\) 9.39108e20i 1.31542i −0.753270 0.657711i \(-0.771525\pi\)
0.753270 0.657711i \(-0.228475\pi\)
\(954\) 4.24257e20 1.57110e20i 0.589917 0.218457i
\(955\) −1.34071e20 −0.185060
\(956\) 4.90336e20i 0.671875i
\(957\) 9.13740e19 + 5.09865e20i 0.124291 + 0.693540i
\(958\) 2.71880e20 0.367129
\(959\) 6.07738e20i 0.814678i
\(960\) −1.24562e20 + 2.23231e19i −0.165763 + 0.0297068i
\(961\) 2.37635e20 0.313940
\(962\) 8.66669e20i 1.13665i
\(963\) −2.80918e20 7.58588e20i −0.365760 0.987693i
\(964\) 1.26066e20 0.162951
\(965\) 9.02629e20i 1.15829i
\(966\) −4.35781e19 2.43165e20i −0.0555173 0.309786i
\(967\) −1.52276e21 −1.92596 −0.962978 0.269580i \(-0.913115\pi\)
−0.962978 + 0.269580i \(0.913115\pi\)
\(968\) 6.44883e19i 0.0809755i
\(969\) 2.92001e20 5.23301e19i 0.364014 0.0652357i
\(970\) −1.50719e19 −0.0186538
\(971\) 1.35292e20i 0.166240i −0.996540 0.0831201i \(-0.973511\pi\)
0.996540 0.0831201i \(-0.0264885\pi\)
\(972\) −3.17623e20 2.59036e20i −0.387479 0.316007i
\(973\) −2.60416e19 −0.0315411
\(974\) 7.24682e20i 0.871435i
\(975\) 1.29910e20 + 7.24895e20i 0.155099 + 0.865451i
\(976\) −3.85247e20 −0.456658
\(977\) 4.13780e20i 0.486976i −0.969904 0.243488i \(-0.921708\pi\)
0.969904 0.243488i \(-0.0782917\pi\)
\(978\) −3.88693e19 + 6.96584e18i −0.0454187 + 0.00813957i
\(979\) 1.05236e21 1.22092
\(980\) 6.89964e20i 0.794775i
\(981\) −6.34924e20 + 2.35123e20i −0.726170 + 0.268914i
\(982\) −3.32123e20 −0.377154
\(983\) 1.09669e21i 1.23655i 0.785963 + 0.618273i \(0.212168\pi\)
−0.785963 + 0.618273i \(0.787832\pi\)
\(984\) 2.10234e19 + 1.17310e20i 0.0235362 + 0.131332i
\(985\) −1.25676e21 −1.39701
\(986\) 2.10231e20i 0.232038i
\(987\) −1.73739e21 + 3.11361e20i −1.90404 + 0.341228i
\(988\) 4.48256e20 0.487784
\(989\) 1.18874e20i 0.128444i
\(990\) −2.70745e20 7.31115e20i −0.290478 0.784403i
\(991\) 9.67265e20 1.03046 0.515229 0.857053i \(-0.327707\pi\)
0.515229 + 0.857053i \(0.327707\pi\)
\(992\) 1.91555e20i 0.202634i
\(993\) −4.18847e19 2.33716e20i −0.0439957 0.245496i
\(994\) 4.48226e20 0.467511
\(995\) 8.28860e20i 0.858459i
\(996\) −9.44720e20 + 1.69305e20i −0.971601 + 0.174123i
\(997\) −8.31286e20 −0.848954 −0.424477 0.905439i \(-0.639542\pi\)
−0.424477 + 0.905439i \(0.639542\pi\)
\(998\) 6.76682e20i 0.686232i
\(999\) 7.50571e20 + 1.27520e21i 0.755846 + 1.28416i
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 6.15.b.a.5.2 4
3.2 odd 2 inner 6.15.b.a.5.4 yes 4
4.3 odd 2 48.15.e.d.17.1 4
5.2 odd 4 150.15.b.a.149.7 8
5.3 odd 4 150.15.b.a.149.2 8
5.4 even 2 150.15.d.a.101.3 4
12.11 even 2 48.15.e.d.17.2 4
15.2 even 4 150.15.b.a.149.1 8
15.8 even 4 150.15.b.a.149.8 8
15.14 odd 2 150.15.d.a.101.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.15.b.a.5.2 4 1.1 even 1 trivial
6.15.b.a.5.4 yes 4 3.2 odd 2 inner
48.15.e.d.17.1 4 4.3 odd 2
48.15.e.d.17.2 4 12.11 even 2
150.15.b.a.149.1 8 15.2 even 4
150.15.b.a.149.2 8 5.3 odd 4
150.15.b.a.149.7 8 5.2 odd 4
150.15.b.a.149.8 8 15.8 even 4
150.15.d.a.101.1 4 15.14 odd 2
150.15.d.a.101.3 4 5.4 even 2