Properties

Label 72.14.d.c.37.6
Level $72$
Weight $14$
Character 72.37
Analytic conductor $77.206$
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] = [72,14,Mod(37,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.37");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 72.d (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: \(77.2062688454\)
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: \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} + \cdots + 31\!\cdots\!68 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.6
Root \(1.33949 + 44.8086i\) of defining polynomial
Character \(\chi\) \(=\) 72.37
Dual form 72.14.d.c.37.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12.6790 + 89.6172i) q^{2} +(-7870.49 - 2272.51i) q^{4} -45531.7i q^{5} -249036. q^{7} +(303446. - 676518. i) q^{8} +O(q^{10})\) \(q+(-12.6790 + 89.6172i) q^{2} +(-7870.49 - 2272.51i) q^{4} -45531.7i q^{5} -249036. q^{7} +(303446. - 676518. i) q^{8} +(4.08042e6 + 577295. i) q^{10} -5.28836e6i q^{11} +1.17535e7i q^{13} +(3.15752e6 - 2.23179e7i) q^{14} +(5.67803e7 + 3.57715e7i) q^{16} +1.22707e8 q^{17} -5.19560e7i q^{19} +(-1.03471e8 + 3.58356e8i) q^{20} +(4.73928e8 + 6.70510e7i) q^{22} +1.22082e9 q^{23} -8.52431e8 q^{25} +(-1.05331e9 - 1.49022e8i) q^{26} +(1.96003e9 + 5.65936e8i) q^{28} -4.04054e9i q^{29} +1.61058e9 q^{31} +(-3.92566e9 + 4.63494e9i) q^{32} +(-1.55580e9 + 1.09967e10i) q^{34} +1.13390e10i q^{35} +4.09023e9i q^{37} +(4.65615e9 + 6.58749e8i) q^{38} +(-3.08030e10 - 1.38164e10i) q^{40} -4.23280e10 q^{41} -7.66300e10i q^{43} +(-1.20178e10 + 4.16220e10i) q^{44} +(-1.54787e10 + 1.09406e11i) q^{46} -6.09947e10 q^{47} -3.48703e10 q^{49} +(1.08079e10 - 7.63924e10i) q^{50} +(2.67098e10 - 9.25055e10i) q^{52} -2.24645e11i q^{53} -2.40788e11 q^{55} +(-7.55688e10 + 1.68477e11i) q^{56} +(3.62102e11 + 5.12299e10i) q^{58} +4.64215e11i q^{59} -4.58331e10i q^{61} +(-2.04205e10 + 1.44336e11i) q^{62} +(-3.65597e11 - 4.10573e11i) q^{64} +5.35155e11 q^{65} +8.92905e11i q^{67} +(-9.65764e11 - 2.78853e11i) q^{68} +(-1.01617e12 - 1.43767e11i) q^{70} -1.53438e12 q^{71} +8.01210e11 q^{73} +(-3.66555e11 - 5.18599e10i) q^{74} +(-1.18070e11 + 4.08919e11i) q^{76} +1.31699e12i q^{77} +5.92669e10 q^{79} +(1.62874e12 - 2.58530e12i) q^{80} +(5.36676e11 - 3.79332e12i) q^{82} -4.57014e12i q^{83} -5.58705e12i q^{85} +(6.86736e12 + 9.71590e11i) q^{86} +(-3.57767e12 - 1.60473e12i) q^{88} +5.17348e12 q^{89} -2.92703e12i q^{91} +(-9.60841e12 - 2.77431e12i) q^{92} +(7.73351e11 - 5.46618e12i) q^{94} -2.36564e12 q^{95} -3.32642e12 q^{97} +(4.42119e11 - 3.12498e12i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 110 q^{2} - 4716 q^{4} + 586960 q^{7} + 270712 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 110 q^{2} - 4716 q^{4} + 586960 q^{7} + 270712 q^{8} - 4542088 q^{10} - 1408688 q^{14} + 56624912 q^{16} - 217326004 q^{17} - 21655184 q^{20} - 177987876 q^{22} + 78679952 q^{23} - 3076402574 q^{25} - 3734872040 q^{26} - 1653812448 q^{28} + 648233792 q^{31} + 11298380000 q^{32} - 6096822724 q^{34} + 18764968628 q^{38} + 7466802592 q^{40} - 59324640356 q^{41} - 13325704392 q^{44} - 55046867440 q^{46} + 10176534816 q^{47} + 182708552058 q^{49} - 326454435302 q^{50} - 53296499536 q^{52} - 123010753008 q^{55} + 462152447680 q^{56} + 766482705096 q^{58} + 1665308528960 q^{62} - 2180548996032 q^{64} - 1577231990240 q^{65} - 2338280915304 q^{68} - 6070110714688 q^{70} - 726361179984 q^{71} - 633240365532 q^{73} - 7528513982264 q^{74} + 10338420845032 q^{76} + 5445103565344 q^{79} + 15406871881920 q^{80} + 12273334206796 q^{82} + 26794541719396 q^{86} - 27677491769136 q^{88} - 5506344808004 q^{89} - 33971694298464 q^{92} - 45356008560096 q^{94} + 14214732035504 q^{95} + 1361133320788 q^{97} - 54325451514942 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.6790 + 89.6172i −0.140084 + 0.990140i
\(3\) 0 0
\(4\) −7870.49 2272.51i −0.960753 0.277406i
\(5\) 45531.7i 1.30319i −0.758566 0.651596i \(-0.774100\pi\)
0.758566 0.651596i \(-0.225900\pi\)
\(6\) 0 0
\(7\) −249036. −0.800063 −0.400032 0.916501i \(-0.631001\pi\)
−0.400032 + 0.916501i \(0.631001\pi\)
\(8\) 303446. 676518.i 0.409257 0.912419i
\(9\) 0 0
\(10\) 4.08042e6 + 577295.i 1.29034 + 0.182557i
\(11\) 5.28836e6i 0.900054i −0.893015 0.450027i \(-0.851414\pi\)
0.893015 0.450027i \(-0.148586\pi\)
\(12\) 0 0
\(13\) 1.17535e7i 0.675358i 0.941261 + 0.337679i \(0.109642\pi\)
−0.941261 + 0.337679i \(0.890358\pi\)
\(14\) 3.15752e6 2.23179e7i 0.112076 0.792174i
\(15\) 0 0
\(16\) 5.67803e7 + 3.57715e7i 0.846092 + 0.533037i
\(17\) 1.22707e8 1.23297 0.616483 0.787368i \(-0.288557\pi\)
0.616483 + 0.787368i \(0.288557\pi\)
\(18\) 0 0
\(19\) 5.19560e7i 0.253359i −0.991944 0.126680i \(-0.959568\pi\)
0.991944 0.126680i \(-0.0404320\pi\)
\(20\) −1.03471e8 + 3.58356e8i −0.361513 + 1.25205i
\(21\) 0 0
\(22\) 4.73928e8 + 6.70510e7i 0.891179 + 0.126083i
\(23\) 1.22082e9 1.71957 0.859784 0.510659i \(-0.170598\pi\)
0.859784 + 0.510659i \(0.170598\pi\)
\(24\) 0 0
\(25\) −8.52431e8 −0.698311
\(26\) −1.05331e9 1.49022e8i −0.668699 0.0946070i
\(27\) 0 0
\(28\) 1.96003e9 + 5.65936e8i 0.768663 + 0.221942i
\(29\) 4.04054e9i 1.26140i −0.776027 0.630699i \(-0.782768\pi\)
0.776027 0.630699i \(-0.217232\pi\)
\(30\) 0 0
\(31\) 1.61058e9 0.325935 0.162967 0.986631i \(-0.447893\pi\)
0.162967 + 0.986631i \(0.447893\pi\)
\(32\) −3.92566e9 + 4.63494e9i −0.646305 + 0.763079i
\(33\) 0 0
\(34\) −1.55580e9 + 1.09967e10i −0.172719 + 1.22081i
\(35\) 1.13390e10i 1.04264i
\(36\) 0 0
\(37\) 4.09023e9i 0.262081i 0.991377 + 0.131041i \(0.0418318\pi\)
−0.991377 + 0.131041i \(0.958168\pi\)
\(38\) 4.65615e9 + 6.58749e8i 0.250861 + 0.0354917i
\(39\) 0 0
\(40\) −3.08030e10 1.38164e10i −1.18906 0.533341i
\(41\) −4.23280e10 −1.39166 −0.695830 0.718207i \(-0.744963\pi\)
−0.695830 + 0.718207i \(0.744963\pi\)
\(42\) 0 0
\(43\) 7.66300e10i 1.84865i −0.381611 0.924323i \(-0.624631\pi\)
0.381611 0.924323i \(-0.375369\pi\)
\(44\) −1.20178e10 + 4.16220e10i −0.249680 + 0.864729i
\(45\) 0 0
\(46\) −1.54787e10 + 1.09406e11i −0.240884 + 1.70261i
\(47\) −6.09947e10 −0.825384 −0.412692 0.910871i \(-0.635411\pi\)
−0.412692 + 0.910871i \(0.635411\pi\)
\(48\) 0 0
\(49\) −3.48703e10 −0.359899
\(50\) 1.08079e10 7.63924e10i 0.0978224 0.691426i
\(51\) 0 0
\(52\) 2.67098e10 9.25055e10i 0.187348 0.648852i
\(53\) 2.24645e11i 1.39220i −0.717943 0.696102i \(-0.754916\pi\)
0.717943 0.696102i \(-0.245084\pi\)
\(54\) 0 0
\(55\) −2.40788e11 −1.17294
\(56\) −7.55688e10 + 1.68477e11i −0.327431 + 0.729993i
\(57\) 0 0
\(58\) 3.62102e11 + 5.12299e10i 1.24896 + 0.176702i
\(59\) 4.64215e11i 1.43279i 0.697697 + 0.716393i \(0.254208\pi\)
−0.697697 + 0.716393i \(0.745792\pi\)
\(60\) 0 0
\(61\) 4.58331e10i 0.113903i −0.998377 0.0569515i \(-0.981862\pi\)
0.998377 0.0569515i \(-0.0181381\pi\)
\(62\) −2.04205e10 + 1.44336e11i −0.0456583 + 0.322721i
\(63\) 0 0
\(64\) −3.65597e11 4.10573e11i −0.665018 0.746828i
\(65\) 5.35155e11 0.880121
\(66\) 0 0
\(67\) 8.92905e11i 1.20592i 0.797771 + 0.602961i \(0.206012\pi\)
−0.797771 + 0.602961i \(0.793988\pi\)
\(68\) −9.65764e11 2.78853e11i −1.18458 0.342032i
\(69\) 0 0
\(70\) −1.01617e12 1.43767e11i −1.03236 0.146057i
\(71\) −1.53438e12 −1.42152 −0.710762 0.703432i \(-0.751650\pi\)
−0.710762 + 0.703432i \(0.751650\pi\)
\(72\) 0 0
\(73\) 8.01210e11 0.619652 0.309826 0.950793i \(-0.399729\pi\)
0.309826 + 0.950793i \(0.399729\pi\)
\(74\) −3.66555e11 5.18599e10i −0.259497 0.0367135i
\(75\) 0 0
\(76\) −1.18070e11 + 4.08919e11i −0.0702834 + 0.243416i
\(77\) 1.31699e12i 0.720100i
\(78\) 0 0
\(79\) 5.92669e10 0.0274306 0.0137153 0.999906i \(-0.495634\pi\)
0.0137153 + 0.999906i \(0.495634\pi\)
\(80\) 1.62874e12 2.58530e12i 0.694650 1.10262i
\(81\) 0 0
\(82\) 5.36676e11 3.79332e12i 0.194950 1.37794i
\(83\) 4.57014e12i 1.53434i −0.641444 0.767170i \(-0.721664\pi\)
0.641444 0.767170i \(-0.278336\pi\)
\(84\) 0 0
\(85\) 5.58705e12i 1.60679i
\(86\) 6.86736e12 + 9.71590e11i 1.83042 + 0.258966i
\(87\) 0 0
\(88\) −3.57767e12 1.60473e12i −0.821227 0.368353i
\(89\) 5.17348e12 1.10344 0.551719 0.834030i \(-0.313972\pi\)
0.551719 + 0.834030i \(0.313972\pi\)
\(90\) 0 0
\(91\) 2.92703e12i 0.540329i
\(92\) −9.60841e12 2.77431e12i −1.65208 0.477018i
\(93\) 0 0
\(94\) 7.73351e11 5.46618e12i 0.115623 0.817246i
\(95\) −2.36564e12 −0.330176
\(96\) 0 0
\(97\) −3.32642e12 −0.405472 −0.202736 0.979233i \(-0.564983\pi\)
−0.202736 + 0.979233i \(0.564983\pi\)
\(98\) 4.42119e11 3.12498e12i 0.0504162 0.356350i
\(99\) 0 0
\(100\) 6.70904e12 + 1.93716e12i 0.670904 + 0.193716i
\(101\) 1.04951e13i 0.983783i −0.870657 0.491891i \(-0.836306\pi\)
0.870657 0.491891i \(-0.163694\pi\)
\(102\) 0 0
\(103\) −1.41996e13 −1.17175 −0.585873 0.810403i \(-0.699248\pi\)
−0.585873 + 0.810403i \(0.699248\pi\)
\(104\) 7.95143e12 + 3.56654e12i 0.616210 + 0.276395i
\(105\) 0 0
\(106\) 2.01320e13 + 2.84826e12i 1.37848 + 0.195026i
\(107\) 1.68471e12i 0.108525i 0.998527 + 0.0542625i \(0.0172808\pi\)
−0.998527 + 0.0542625i \(0.982719\pi\)
\(108\) 0 0
\(109\) 1.19613e12i 0.0683133i 0.999416 + 0.0341566i \(0.0108745\pi\)
−0.999416 + 0.0341566i \(0.989125\pi\)
\(110\) 3.05294e12 2.15787e13i 0.164311 1.16138i
\(111\) 0 0
\(112\) −1.41403e13 8.90838e12i −0.676927 0.426463i
\(113\) −1.04130e13 −0.470506 −0.235253 0.971934i \(-0.575592\pi\)
−0.235253 + 0.971934i \(0.575592\pi\)
\(114\) 0 0
\(115\) 5.55858e13i 2.24093i
\(116\) −9.18216e12 + 3.18010e13i −0.349919 + 1.21189i
\(117\) 0 0
\(118\) −4.16017e13 5.88578e12i −1.41866 0.200711i
\(119\) −3.05584e13 −0.986451
\(120\) 0 0
\(121\) 6.55596e12 0.189903
\(122\) 4.10744e12 + 5.81117e11i 0.112780 + 0.0159560i
\(123\) 0 0
\(124\) −1.26760e13 3.66005e12i −0.313143 0.0904162i
\(125\) 1.67681e13i 0.393159i
\(126\) 0 0
\(127\) 2.30936e12 0.0488391 0.0244195 0.999702i \(-0.492226\pi\)
0.0244195 + 0.999702i \(0.492226\pi\)
\(128\) 4.14298e13 2.75582e13i 0.832622 0.553842i
\(129\) 0 0
\(130\) −6.78522e12 + 4.79591e13i −0.123291 + 0.871443i
\(131\) 2.94834e13i 0.509699i 0.966981 + 0.254850i \(0.0820259\pi\)
−0.966981 + 0.254850i \(0.917974\pi\)
\(132\) 0 0
\(133\) 1.29389e13i 0.202704i
\(134\) −8.00196e13 1.13211e13i −1.19403 0.168931i
\(135\) 0 0
\(136\) 3.72349e13 8.30135e13i 0.504600 1.12498i
\(137\) −7.84391e13 −1.01356 −0.506779 0.862076i \(-0.669164\pi\)
−0.506779 + 0.862076i \(0.669164\pi\)
\(138\) 0 0
\(139\) 9.83230e13i 1.15627i 0.815941 + 0.578135i \(0.196219\pi\)
−0.815941 + 0.578135i \(0.803781\pi\)
\(140\) 2.57680e13 8.92435e13i 0.289233 1.00172i
\(141\) 0 0
\(142\) 1.94544e13 1.37507e14i 0.199133 1.40751i
\(143\) 6.21565e13 0.607859
\(144\) 0 0
\(145\) −1.83972e14 −1.64384
\(146\) −1.01585e13 + 7.18022e13i −0.0868034 + 0.613542i
\(147\) 0 0
\(148\) 9.29507e12 3.21921e13i 0.0727029 0.251795i
\(149\) 1.46382e14i 1.09591i 0.836507 + 0.547957i \(0.184594\pi\)
−0.836507 + 0.547957i \(0.815406\pi\)
\(150\) 0 0
\(151\) 5.37629e12 0.0369090 0.0184545 0.999830i \(-0.494125\pi\)
0.0184545 + 0.999830i \(0.494125\pi\)
\(152\) −3.51492e13 1.57658e13i −0.231170 0.103689i
\(153\) 0 0
\(154\) −1.18025e14 1.66981e13i −0.713000 0.100875i
\(155\) 7.33323e13i 0.424756i
\(156\) 0 0
\(157\) 1.49568e14i 0.797060i −0.917155 0.398530i \(-0.869521\pi\)
0.917155 0.398530i \(-0.130479\pi\)
\(158\) −7.51444e11 + 5.31133e12i −0.00384260 + 0.0271602i
\(159\) 0 0
\(160\) 2.11037e14 + 1.78742e14i 0.994439 + 0.842260i
\(161\) −3.04027e14 −1.37576
\(162\) 0 0
\(163\) 3.22488e14i 1.34677i 0.739291 + 0.673386i \(0.235161\pi\)
−0.739291 + 0.673386i \(0.764839\pi\)
\(164\) 3.33142e14 + 9.61909e13i 1.33704 + 0.386055i
\(165\) 0 0
\(166\) 4.09563e14 + 5.79447e13i 1.51921 + 0.214937i
\(167\) −1.29327e14 −0.461351 −0.230675 0.973031i \(-0.574094\pi\)
−0.230675 + 0.973031i \(0.574094\pi\)
\(168\) 0 0
\(169\) 1.64731e14 0.543892
\(170\) 5.00696e14 + 7.08381e13i 1.59095 + 0.225086i
\(171\) 0 0
\(172\) −1.74142e14 + 6.03115e14i −0.512825 + 1.77609i
\(173\) 4.84488e13i 0.137399i 0.997637 + 0.0686995i \(0.0218850\pi\)
−0.997637 + 0.0686995i \(0.978115\pi\)
\(174\) 0 0
\(175\) 2.12286e14 0.558693
\(176\) 1.89173e14 3.00275e14i 0.479762 0.761528i
\(177\) 0 0
\(178\) −6.55945e13 + 4.63633e14i −0.154574 + 1.09256i
\(179\) 1.35115e14i 0.307014i 0.988148 + 0.153507i \(0.0490567\pi\)
−0.988148 + 0.153507i \(0.950943\pi\)
\(180\) 0 0
\(181\) 2.37822e14i 0.502738i 0.967891 + 0.251369i \(0.0808808\pi\)
−0.967891 + 0.251369i \(0.919119\pi\)
\(182\) 2.62312e14 + 3.71118e13i 0.535001 + 0.0756916i
\(183\) 0 0
\(184\) 3.70451e14 8.25904e14i 0.703745 1.56897i
\(185\) 1.86235e14 0.341542
\(186\) 0 0
\(187\) 6.48919e14i 1.10974i
\(188\) 4.80058e14 + 1.38611e14i 0.792990 + 0.228966i
\(189\) 0 0
\(190\) 2.99939e13 2.12002e14i 0.0462525 0.326921i
\(191\) −2.46109e14 −0.366784 −0.183392 0.983040i \(-0.558708\pi\)
−0.183392 + 0.983040i \(0.558708\pi\)
\(192\) 0 0
\(193\) −1.27091e14 −0.177008 −0.0885039 0.996076i \(-0.528209\pi\)
−0.0885039 + 0.996076i \(0.528209\pi\)
\(194\) 4.21756e13 2.98104e14i 0.0568002 0.401473i
\(195\) 0 0
\(196\) 2.74446e14 + 7.92430e13i 0.345774 + 0.0998381i
\(197\) 4.31897e14i 0.526442i −0.964736 0.263221i \(-0.915215\pi\)
0.964736 0.263221i \(-0.0847848\pi\)
\(198\) 0 0
\(199\) −1.16464e15 −1.32937 −0.664687 0.747122i \(-0.731435\pi\)
−0.664687 + 0.747122i \(0.731435\pi\)
\(200\) −2.58666e14 + 5.76685e14i −0.285789 + 0.637153i
\(201\) 0 0
\(202\) 9.40545e14 + 1.33068e14i 0.974082 + 0.137812i
\(203\) 1.00624e15i 1.00920i
\(204\) 0 0
\(205\) 1.92727e15i 1.81360i
\(206\) 1.80036e14 1.27253e15i 0.164143 1.16019i
\(207\) 0 0
\(208\) −4.20439e14 + 6.67365e14i −0.359991 + 0.571415i
\(209\) −2.74762e14 −0.228037
\(210\) 0 0
\(211\) 1.10642e15i 0.863146i 0.902078 + 0.431573i \(0.142041\pi\)
−0.902078 + 0.431573i \(0.857959\pi\)
\(212\) −5.10507e14 + 1.76806e15i −0.386205 + 1.33756i
\(213\) 0 0
\(214\) −1.50979e14 2.13604e13i −0.107455 0.0152026i
\(215\) −3.48909e15 −2.40914
\(216\) 0 0
\(217\) −4.01091e14 −0.260768
\(218\) −1.07194e14 1.51657e13i −0.0676397 0.00956962i
\(219\) 0 0
\(220\) 1.89512e15 + 5.47193e14i 1.12691 + 0.325381i
\(221\) 1.44223e15i 0.832694i
\(222\) 0 0
\(223\) −6.47353e14 −0.352500 −0.176250 0.984345i \(-0.556397\pi\)
−0.176250 + 0.984345i \(0.556397\pi\)
\(224\) 9.77629e14 1.15427e15i 0.517085 0.610511i
\(225\) 0 0
\(226\) 1.32026e14 9.33183e14i 0.0659105 0.465867i
\(227\) 2.07784e15i 1.00796i 0.863715 + 0.503981i \(0.168132\pi\)
−0.863715 + 0.503981i \(0.831868\pi\)
\(228\) 0 0
\(229\) 2.11802e15i 0.970509i −0.874373 0.485254i \(-0.838727\pi\)
0.874373 0.485254i \(-0.161273\pi\)
\(230\) 4.98144e15 + 7.04771e14i 2.21883 + 0.313919i
\(231\) 0 0
\(232\) −2.73350e15 1.22608e15i −1.15092 0.516236i
\(233\) −3.45947e15 −1.41643 −0.708217 0.705995i \(-0.750500\pi\)
−0.708217 + 0.705995i \(0.750500\pi\)
\(234\) 0 0
\(235\) 2.77719e15i 1.07563i
\(236\) 1.05493e15 3.65360e15i 0.397463 1.37655i
\(237\) 0 0
\(238\) 3.87449e14 2.73856e15i 0.138186 0.976724i
\(239\) −7.67582e14 −0.266402 −0.133201 0.991089i \(-0.542526\pi\)
−0.133201 + 0.991089i \(0.542526\pi\)
\(240\) 0 0
\(241\) 3.34399e14 0.109940 0.0549698 0.998488i \(-0.482494\pi\)
0.0549698 + 0.998488i \(0.482494\pi\)
\(242\) −8.31229e13 + 5.87527e14i −0.0266024 + 0.188030i
\(243\) 0 0
\(244\) −1.04156e14 + 3.60729e14i −0.0315974 + 0.109433i
\(245\) 1.58770e15i 0.469018i
\(246\) 0 0
\(247\) 6.10663e14 0.171108
\(248\) 4.88723e14 1.08959e15i 0.133391 0.297389i
\(249\) 0 0
\(250\) 1.50271e15 + 2.12602e14i 0.389282 + 0.0550753i
\(251\) 6.50564e15i 1.64214i −0.570825 0.821071i \(-0.693377\pi\)
0.570825 0.821071i \(-0.306623\pi\)
\(252\) 0 0
\(253\) 6.45611e15i 1.54770i
\(254\) −2.92803e13 + 2.06958e14i −0.00684158 + 0.0483575i
\(255\) 0 0
\(256\) 1.94440e15 + 4.06223e15i 0.431743 + 0.901997i
\(257\) −1.04460e14 −0.0226143 −0.0113072 0.999936i \(-0.503599\pi\)
−0.0113072 + 0.999936i \(0.503599\pi\)
\(258\) 0 0
\(259\) 1.01861e15i 0.209682i
\(260\) −4.21193e15 1.21614e15i −0.845579 0.244151i
\(261\) 0 0
\(262\) −2.64222e15 3.73819e14i −0.504673 0.0714008i
\(263\) 4.31849e14 0.0804673 0.0402337 0.999190i \(-0.487190\pi\)
0.0402337 + 0.999190i \(0.487190\pi\)
\(264\) 0 0
\(265\) −1.02284e16 −1.81431
\(266\) −1.15955e15 1.64052e14i −0.200705 0.0283956i
\(267\) 0 0
\(268\) 2.02913e15 7.02760e15i 0.334530 1.15859i
\(269\) 6.51041e15i 1.04765i −0.851824 0.523827i \(-0.824504\pi\)
0.851824 0.523827i \(-0.175496\pi\)
\(270\) 0 0
\(271\) −7.50666e15 −1.15119 −0.575594 0.817735i \(-0.695229\pi\)
−0.575594 + 0.817735i \(0.695229\pi\)
\(272\) 6.96734e15 + 4.38941e15i 1.04320 + 0.657217i
\(273\) 0 0
\(274\) 9.94527e14 7.02949e15i 0.141984 1.00356i
\(275\) 4.50796e15i 0.628518i
\(276\) 0 0
\(277\) 9.31932e15i 1.23955i −0.784778 0.619777i \(-0.787223\pi\)
0.784778 0.619777i \(-0.212777\pi\)
\(278\) −8.81143e15 1.24663e15i −1.14487 0.161975i
\(279\) 0 0
\(280\) 7.67104e15 + 3.44077e15i 0.951321 + 0.426706i
\(281\) −7.70003e15 −0.933042 −0.466521 0.884510i \(-0.654493\pi\)
−0.466521 + 0.884510i \(0.654493\pi\)
\(282\) 0 0
\(283\) 5.78501e15i 0.669410i −0.942323 0.334705i \(-0.891363\pi\)
0.942323 0.334705i \(-0.108637\pi\)
\(284\) 1.20763e16 + 3.48690e15i 1.36573 + 0.394339i
\(285\) 0 0
\(286\) −7.88081e14 + 5.57029e15i −0.0851514 + 0.601865i
\(287\) 1.05412e16 1.11342
\(288\) 0 0
\(289\) 5.15243e15 0.520206
\(290\) 2.33258e15 1.64871e16i 0.230277 1.62764i
\(291\) 0 0
\(292\) −6.30591e15 1.82076e15i −0.595332 0.171895i
\(293\) 1.41861e16i 1.30985i −0.755693 0.654926i \(-0.772700\pi\)
0.755693 0.654926i \(-0.227300\pi\)
\(294\) 0 0
\(295\) 2.11365e16 1.86720
\(296\) 2.76711e15 + 1.24116e15i 0.239128 + 0.107259i
\(297\) 0 0
\(298\) −1.31183e16 1.85597e15i −1.08511 0.153520i
\(299\) 1.43488e16i 1.16132i
\(300\) 0 0
\(301\) 1.90836e16i 1.47903i
\(302\) −6.81658e13 + 4.81808e14i −0.00517037 + 0.0365451i
\(303\) 0 0
\(304\) 1.85854e15 2.95007e15i 0.135050 0.214365i
\(305\) −2.08686e15 −0.148438
\(306\) 0 0
\(307\) 9.07714e15i 0.618799i 0.950932 + 0.309400i \(0.100128\pi\)
−0.950932 + 0.309400i \(0.899872\pi\)
\(308\) 2.99287e15 1.03654e16i 0.199760 0.691838i
\(309\) 0 0
\(310\) 6.57184e15 + 9.29779e14i 0.420568 + 0.0595016i
\(311\) −1.48689e16 −0.931827 −0.465914 0.884830i \(-0.654274\pi\)
−0.465914 + 0.884830i \(0.654274\pi\)
\(312\) 0 0
\(313\) 9.98994e15 0.600516 0.300258 0.953858i \(-0.402927\pi\)
0.300258 + 0.953858i \(0.402927\pi\)
\(314\) 1.34039e16 + 1.89637e15i 0.789200 + 0.111656i
\(315\) 0 0
\(316\) −4.66459e14 1.34685e14i −0.0263541 0.00760942i
\(317\) 2.22336e16i 1.23062i 0.788284 + 0.615311i \(0.210970\pi\)
−0.788284 + 0.615311i \(0.789030\pi\)
\(318\) 0 0
\(319\) −2.13678e16 −1.13533
\(320\) −1.86941e16 + 1.66463e16i −0.973260 + 0.866646i
\(321\) 0 0
\(322\) 3.85475e15 2.72460e16i 0.192723 1.36220i
\(323\) 6.37536e15i 0.312384i
\(324\) 0 0
\(325\) 1.00190e16i 0.471610i
\(326\) −2.89005e16 4.08881e15i −1.33349 0.188661i
\(327\) 0 0
\(328\) −1.28443e16 + 2.86357e16i −0.569546 + 1.26978i
\(329\) 1.51899e16 0.660360
\(330\) 0 0
\(331\) 2.73268e16i 1.14211i 0.820913 + 0.571053i \(0.193465\pi\)
−0.820913 + 0.571053i \(0.806535\pi\)
\(332\) −1.03857e16 + 3.59692e16i −0.425635 + 1.47412i
\(333\) 0 0
\(334\) 1.63973e15 1.15899e16i 0.0646280 0.456802i
\(335\) 4.06555e16 1.57155
\(336\) 0 0
\(337\) −1.93018e16 −0.717801 −0.358900 0.933376i \(-0.616848\pi\)
−0.358900 + 0.933376i \(0.616848\pi\)
\(338\) −2.08862e15 + 1.47628e16i −0.0761906 + 0.538529i
\(339\) 0 0
\(340\) −1.26966e16 + 4.39728e16i −0.445734 + 1.54373i
\(341\) 8.51732e15i 0.293359i
\(342\) 0 0
\(343\) 3.28128e16 1.08801
\(344\) −5.18416e16 2.32530e16i −1.68674 0.756571i
\(345\) 0 0
\(346\) −4.34185e15 6.14281e14i −0.136044 0.0192474i
\(347\) 7.29553e15i 0.224344i −0.993689 0.112172i \(-0.964219\pi\)
0.993689 0.112172i \(-0.0357808\pi\)
\(348\) 0 0
\(349\) 5.37690e16i 1.59282i −0.604758 0.796409i \(-0.706730\pi\)
0.604758 0.796409i \(-0.293270\pi\)
\(350\) −2.69156e15 + 1.90244e16i −0.0782641 + 0.553184i
\(351\) 0 0
\(352\) 2.45112e16 + 2.07603e16i 0.686812 + 0.581710i
\(353\) 4.64817e16 1.27863 0.639317 0.768943i \(-0.279217\pi\)
0.639317 + 0.768943i \(0.279217\pi\)
\(354\) 0 0
\(355\) 6.98630e16i 1.85252i
\(356\) −4.07178e16 1.17568e16i −1.06013 0.306100i
\(357\) 0 0
\(358\) −1.21086e16 1.71311e15i −0.303986 0.0430077i
\(359\) −4.50239e16 −1.11002 −0.555008 0.831845i \(-0.687285\pi\)
−0.555008 + 0.831845i \(0.687285\pi\)
\(360\) 0 0
\(361\) 3.93536e16 0.935809
\(362\) −2.13130e16 3.01534e15i −0.497781 0.0704257i
\(363\) 0 0
\(364\) −6.65170e15 + 2.30372e16i −0.149890 + 0.519123i
\(365\) 3.64804e16i 0.807526i
\(366\) 0 0
\(367\) −1.88578e16 −0.402868 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(368\) 6.93182e16 + 4.36704e16i 1.45491 + 0.916593i
\(369\) 0 0
\(370\) −2.36127e15 + 1.66898e16i −0.0478447 + 0.338175i
\(371\) 5.59445e16i 1.11385i
\(372\) 0 0
\(373\) 7.72158e16i 1.48456i −0.670088 0.742282i \(-0.733744\pi\)
0.670088 0.742282i \(-0.266256\pi\)
\(374\) 5.81543e16 + 8.22763e15i 1.09879 + 0.155457i
\(375\) 0 0
\(376\) −1.85086e16 + 4.12640e16i −0.337794 + 0.753097i
\(377\) 4.74903e16 0.851895
\(378\) 0 0
\(379\) 2.71019e16i 0.469726i 0.972028 + 0.234863i \(0.0754642\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(380\) 1.86188e16 + 5.37594e15i 0.317218 + 0.0915928i
\(381\) 0 0
\(382\) 3.12041e15 2.20556e16i 0.0513806 0.363167i
\(383\) 7.57350e16 1.22604 0.613020 0.790067i \(-0.289955\pi\)
0.613020 + 0.790067i \(0.289955\pi\)
\(384\) 0 0
\(385\) 5.99648e16 0.938429
\(386\) 1.61138e15 1.13895e16i 0.0247960 0.175262i
\(387\) 0 0
\(388\) 2.61805e16 + 7.55931e15i 0.389558 + 0.112480i
\(389\) 4.92786e16i 0.721085i −0.932743 0.360542i \(-0.882592\pi\)
0.932743 0.360542i \(-0.117408\pi\)
\(390\) 0 0
\(391\) 1.49803e17 2.12017
\(392\) −1.05812e16 + 2.35904e16i −0.147291 + 0.328379i
\(393\) 0 0
\(394\) 3.87054e16 + 5.47602e15i 0.521251 + 0.0737462i
\(395\) 2.69852e15i 0.0357474i
\(396\) 0 0
\(397\) 3.19333e16i 0.409361i 0.978829 + 0.204680i \(0.0656155\pi\)
−0.978829 + 0.204680i \(0.934385\pi\)
\(398\) 1.47665e16 1.04372e17i 0.186224 1.31627i
\(399\) 0 0
\(400\) −4.84012e16 3.04927e16i −0.590835 0.372226i
\(401\) 4.73693e16 0.568930 0.284465 0.958686i \(-0.408184\pi\)
0.284465 + 0.958686i \(0.408184\pi\)
\(402\) 0 0
\(403\) 1.89299e16i 0.220123i
\(404\) −2.38503e16 + 8.26019e16i −0.272907 + 0.945172i
\(405\) 0 0
\(406\) −9.01762e16 1.27581e16i −0.999247 0.141373i
\(407\) 2.16306e16 0.235887
\(408\) 0 0
\(409\) −6.85823e16 −0.724453 −0.362227 0.932090i \(-0.617983\pi\)
−0.362227 + 0.932090i \(0.617983\pi\)
\(410\) −1.72716e17 2.44358e16i −1.79572 0.254057i
\(411\) 0 0
\(412\) 1.11758e17 + 3.22687e16i 1.12576 + 0.325049i
\(413\) 1.15606e17i 1.14632i
\(414\) 0 0
\(415\) −2.08086e17 −1.99954
\(416\) −5.44766e16 4.61401e16i −0.515351 0.436487i
\(417\) 0 0
\(418\) 3.48370e15 2.46234e16i 0.0319444 0.225789i
\(419\) 8.53203e16i 0.770302i 0.922853 + 0.385151i \(0.125851\pi\)
−0.922853 + 0.385151i \(0.874149\pi\)
\(420\) 0 0
\(421\) 8.55909e16i 0.749193i −0.927188 0.374597i \(-0.877781\pi\)
0.927188 0.374597i \(-0.122219\pi\)
\(422\) −9.91543e16 1.40283e16i −0.854635 0.120913i
\(423\) 0 0
\(424\) −1.51976e17 6.81674e16i −1.27027 0.569769i
\(425\) −1.04599e17 −0.860994
\(426\) 0 0
\(427\) 1.14141e16i 0.0911297i
\(428\) 3.82851e15 1.32595e16i 0.0301055 0.104266i
\(429\) 0 0
\(430\) 4.42381e16 3.12683e17i 0.337483 2.38539i
\(431\) 2.15111e17 1.61644 0.808220 0.588880i \(-0.200431\pi\)
0.808220 + 0.588880i \(0.200431\pi\)
\(432\) 0 0
\(433\) −6.08494e16 −0.443696 −0.221848 0.975081i \(-0.571209\pi\)
−0.221848 + 0.975081i \(0.571209\pi\)
\(434\) 5.08543e15 3.59447e16i 0.0365295 0.258197i
\(435\) 0 0
\(436\) 2.71821e15 9.41411e15i 0.0189505 0.0656322i
\(437\) 6.34287e16i 0.435669i
\(438\) 0 0
\(439\) 2.01095e17 1.34086 0.670428 0.741975i \(-0.266111\pi\)
0.670428 + 0.741975i \(0.266111\pi\)
\(440\) −7.30660e16 + 1.62897e17i −0.480035 + 1.07022i
\(441\) 0 0
\(442\) −1.29249e17 1.82860e16i −0.824483 0.116647i
\(443\) 7.60262e16i 0.477902i 0.971032 + 0.238951i \(0.0768036\pi\)
−0.971032 + 0.238951i \(0.923196\pi\)
\(444\) 0 0
\(445\) 2.35557e17i 1.43799i
\(446\) 8.20777e15 5.80139e16i 0.0493797 0.349024i
\(447\) 0 0
\(448\) 9.10468e16 + 1.02247e17i 0.532056 + 0.597509i
\(449\) −8.77575e16 −0.505455 −0.252728 0.967537i \(-0.581328\pi\)
−0.252728 + 0.967537i \(0.581328\pi\)
\(450\) 0 0
\(451\) 2.23846e17i 1.25257i
\(452\) 8.19553e16 + 2.36636e16i 0.452040 + 0.130521i
\(453\) 0 0
\(454\) −1.86210e17 2.63449e16i −0.998023 0.141200i
\(455\) −1.33273e17 −0.704153
\(456\) 0 0
\(457\) −8.19691e16 −0.420916 −0.210458 0.977603i \(-0.567495\pi\)
−0.210458 + 0.977603i \(0.567495\pi\)
\(458\) 1.89811e17 + 2.68543e16i 0.960939 + 0.135953i
\(459\) 0 0
\(460\) −1.26319e17 + 4.37487e17i −0.621646 + 2.15298i
\(461\) 1.34599e17i 0.653110i 0.945178 + 0.326555i \(0.105888\pi\)
−0.945178 + 0.326555i \(0.894112\pi\)
\(462\) 0 0
\(463\) 1.44197e17 0.680269 0.340135 0.940377i \(-0.389527\pi\)
0.340135 + 0.940377i \(0.389527\pi\)
\(464\) 1.44536e17 2.29423e17i 0.672372 1.06726i
\(465\) 0 0
\(466\) 4.38626e16 3.10028e17i 0.198420 1.40247i
\(467\) 3.32854e17i 1.48489i −0.669908 0.742444i \(-0.733667\pi\)
0.669908 0.742444i \(-0.266333\pi\)
\(468\) 0 0
\(469\) 2.22365e17i 0.964813i
\(470\) −2.48884e17 3.52120e16i −1.06503 0.150679i
\(471\) 0 0
\(472\) 3.14050e17 + 1.40864e17i 1.30730 + 0.586378i
\(473\) −4.05247e17 −1.66388
\(474\) 0 0
\(475\) 4.42889e16i 0.176924i
\(476\) 2.40510e17 + 6.94443e16i 0.947736 + 0.273647i
\(477\) 0 0
\(478\) 9.73215e15 6.87885e16i 0.0373188 0.263776i
\(479\) −1.65749e17 −0.627004 −0.313502 0.949588i \(-0.601502\pi\)
−0.313502 + 0.949588i \(0.601502\pi\)
\(480\) 0 0
\(481\) −4.80743e16 −0.176999
\(482\) −4.23984e15 + 2.99679e16i −0.0154008 + 0.108856i
\(483\) 0 0
\(484\) −5.15986e16 1.48985e16i −0.182450 0.0526802i
\(485\) 1.51457e17i 0.528408i
\(486\) 0 0
\(487\) −4.13371e17 −1.40411 −0.702056 0.712122i \(-0.747734\pi\)
−0.702056 + 0.712122i \(0.747734\pi\)
\(488\) −3.10069e16 1.39079e16i −0.103927 0.0466156i
\(489\) 0 0
\(490\) −1.42285e17 2.01304e16i −0.464393 0.0657020i
\(491\) 2.41125e17i 0.776626i 0.921527 + 0.388313i \(0.126942\pi\)
−0.921527 + 0.388313i \(0.873058\pi\)
\(492\) 0 0
\(493\) 4.95802e17i 1.55526i
\(494\) −7.74258e15 + 5.47259e16i −0.0239696 + 0.169421i
\(495\) 0 0
\(496\) 9.14491e16 + 5.76128e16i 0.275771 + 0.173735i
\(497\) 3.82116e17 1.13731
\(498\) 0 0
\(499\) 2.61865e17i 0.759319i 0.925126 + 0.379660i \(0.123959\pi\)
−0.925126 + 0.379660i \(0.876041\pi\)
\(500\) −3.81056e16 + 1.31973e17i −0.109065 + 0.377728i
\(501\) 0 0
\(502\) 5.83017e17 + 8.24849e16i 1.62595 + 0.230038i
\(503\) −4.41721e17 −1.21606 −0.608031 0.793913i \(-0.708040\pi\)
−0.608031 + 0.793913i \(0.708040\pi\)
\(504\) 0 0
\(505\) −4.77861e17 −1.28206
\(506\) 5.78579e17 + 8.18569e16i 1.53244 + 0.216809i
\(507\) 0 0
\(508\) −1.81758e16 5.24804e15i −0.0469223 0.0135482i
\(509\) 6.01276e17i 1.53253i −0.642527 0.766263i \(-0.722114\pi\)
0.642527 0.766263i \(-0.277886\pi\)
\(510\) 0 0
\(511\) −1.99530e17 −0.495761
\(512\) −3.88699e17 + 1.22747e17i −0.953583 + 0.301131i
\(513\) 0 0
\(514\) 1.32444e15 9.36139e15i 0.00316791 0.0223913i
\(515\) 6.46531e17i 1.52701i
\(516\) 0 0
\(517\) 3.22562e17i 0.742890i
\(518\) 9.12852e16 + 1.29150e16i 0.207614 + 0.0293731i
\(519\) 0 0
\(520\) 1.62390e17 3.62042e17i 0.360196 0.803040i
\(521\) 1.78457e16 0.0390921 0.0195460 0.999809i \(-0.493778\pi\)
0.0195460 + 0.999809i \(0.493778\pi\)
\(522\) 0 0
\(523\) 3.35491e17i 0.716836i 0.933561 + 0.358418i \(0.116684\pi\)
−0.933561 + 0.358418i \(0.883316\pi\)
\(524\) 6.70012e16 2.32049e17i 0.141394 0.489695i
\(525\) 0 0
\(526\) −5.47540e15 + 3.87011e16i −0.0112722 + 0.0796739i
\(527\) 1.97629e17 0.401867
\(528\) 0 0
\(529\) 9.86354e17 1.95691
\(530\) 1.29686e17 9.16644e17i 0.254156 1.79642i
\(531\) 0 0
\(532\) 2.94037e16 1.01835e17i 0.0562312 0.194748i
\(533\) 4.97501e17i 0.939869i
\(534\) 0 0
\(535\) 7.67075e16 0.141429
\(536\) 6.04066e17 + 2.70948e17i 1.10031 + 0.493531i
\(537\) 0 0
\(538\) 5.83444e17 + 8.25453e16i 1.03732 + 0.146760i
\(539\) 1.84406e17i 0.323929i
\(540\) 0 0
\(541\) 2.18609e17i 0.374874i 0.982277 + 0.187437i \(0.0600181\pi\)
−0.982277 + 0.187437i \(0.939982\pi\)
\(542\) 9.51768e16 6.72726e17i 0.161263 1.13984i
\(543\) 0 0
\(544\) −4.81706e17 + 5.68740e17i −0.796873 + 0.940851i
\(545\) 5.44617e16 0.0890254
\(546\) 0 0
\(547\) 5.87423e17i 0.937633i 0.883296 + 0.468817i \(0.155319\pi\)
−0.883296 + 0.468817i \(0.844681\pi\)
\(548\) 6.17354e17 + 1.78254e17i 0.973779 + 0.281167i
\(549\) 0 0
\(550\) −4.03991e17 5.71563e16i −0.622320 0.0880454i
\(551\) −2.09930e17 −0.319587
\(552\) 0 0
\(553\) −1.47596e16 −0.0219462
\(554\) 8.35171e17 + 1.18159e17i 1.22733 + 0.173642i
\(555\) 0 0
\(556\) 2.23440e17 7.73850e17i 0.320756 1.11089i
\(557\) 6.63373e17i 0.941237i 0.882337 + 0.470619i \(0.155969\pi\)
−0.882337 + 0.470619i \(0.844031\pi\)
\(558\) 0 0
\(559\) 9.00667e17 1.24850
\(560\) −4.05613e17 + 6.43832e17i −0.555764 + 0.882166i
\(561\) 0 0
\(562\) 9.76285e16 6.90055e17i 0.130705 0.923842i
\(563\) 1.15064e18i 1.52277i 0.648298 + 0.761387i \(0.275481\pi\)
−0.648298 + 0.761387i \(0.724519\pi\)
\(564\) 0 0
\(565\) 4.74121e17i 0.613160i
\(566\) 5.18436e17 + 7.33480e16i 0.662809 + 0.0937737i
\(567\) 0 0
\(568\) −4.65602e17 + 1.03804e18i −0.581769 + 1.29703i
\(569\) −8.26006e17 −1.02036 −0.510180 0.860068i \(-0.670421\pi\)
−0.510180 + 0.860068i \(0.670421\pi\)
\(570\) 0 0
\(571\) 3.74515e17i 0.452204i −0.974104 0.226102i \(-0.927402\pi\)
0.974104 0.226102i \(-0.0725983\pi\)
\(572\) −4.89202e17 1.41251e17i −0.584002 0.168624i
\(573\) 0 0
\(574\) −1.33652e17 + 9.44672e17i −0.155972 + 1.10244i
\(575\) −1.04066e18 −1.20079
\(576\) 0 0
\(577\) −1.13319e18 −1.27838 −0.639189 0.769050i \(-0.720730\pi\)
−0.639189 + 0.769050i \(0.720730\pi\)
\(578\) −6.53275e16 + 4.61746e17i −0.0728727 + 0.515077i
\(579\) 0 0
\(580\) 1.44795e18 + 4.18079e17i 1.57933 + 0.456012i
\(581\) 1.13813e18i 1.22757i
\(582\) 0 0
\(583\) −1.18800e18 −1.25306
\(584\) 2.43124e17 5.42033e17i 0.253597 0.565382i
\(585\) 0 0
\(586\) 1.27132e18 + 1.79865e17i 1.29694 + 0.183490i
\(587\) 1.80779e18i 1.82390i −0.410301 0.911950i \(-0.634576\pi\)
0.410301 0.911950i \(-0.365424\pi\)
\(588\) 0 0
\(589\) 8.36792e16i 0.0825787i
\(590\) −2.67989e17 + 1.89419e18i −0.261565 + 1.84879i
\(591\) 0 0
\(592\) −1.46314e17 + 2.32244e17i −0.139699 + 0.221745i
\(593\) −4.84457e17 −0.457509 −0.228755 0.973484i \(-0.573465\pi\)
−0.228755 + 0.973484i \(0.573465\pi\)
\(594\) 0 0
\(595\) 1.39138e18i 1.28554i
\(596\) 3.32654e17 1.15210e18i 0.304013 1.05290i
\(597\) 0 0
\(598\) −1.28590e18 1.81928e17i −1.14987 0.162683i
\(599\) 1.07468e18 0.950620 0.475310 0.879818i \(-0.342336\pi\)
0.475310 + 0.879818i \(0.342336\pi\)
\(600\) 0 0
\(601\) 3.25263e17 0.281547 0.140774 0.990042i \(-0.455041\pi\)
0.140774 + 0.990042i \(0.455041\pi\)
\(602\) −1.71022e18 2.41960e17i −1.46445 0.207189i
\(603\) 0 0
\(604\) −4.23140e16 1.22177e16i −0.0354604 0.0102388i
\(605\) 2.98504e17i 0.247480i
\(606\) 0 0
\(607\) −4.02710e16 −0.0326788 −0.0163394 0.999867i \(-0.505201\pi\)
−0.0163394 + 0.999867i \(0.505201\pi\)
\(608\) 2.40813e17 + 2.03961e17i 0.193333 + 0.163748i
\(609\) 0 0
\(610\) 2.64592e16 1.87018e17i 0.0207938 0.146974i
\(611\) 7.16899e17i 0.557430i
\(612\) 0 0
\(613\) 8.13502e17i 0.619250i −0.950859 0.309625i \(-0.899797\pi\)
0.950859 0.309625i \(-0.100203\pi\)
\(614\) −8.13468e17 1.15089e17i −0.612698 0.0866840i
\(615\) 0 0
\(616\) 8.90968e17 + 3.99635e17i 0.657033 + 0.294706i
\(617\) 4.37374e17 0.319153 0.159577 0.987186i \(-0.448987\pi\)
0.159577 + 0.987186i \(0.448987\pi\)
\(618\) 0 0
\(619\) 2.59586e18i 1.85478i −0.374099 0.927389i \(-0.622048\pi\)
0.374099 0.927389i \(-0.377952\pi\)
\(620\) −1.66648e17 + 5.77161e17i −0.117830 + 0.408085i
\(621\) 0 0
\(622\) 1.88522e17 1.33251e18i 0.130534 0.922639i
\(623\) −1.28838e18 −0.882820
\(624\) 0 0
\(625\) −1.80404e18 −1.21067
\(626\) −1.26662e17 + 8.95270e17i −0.0841228 + 0.594595i
\(627\) 0 0
\(628\) −3.39895e17 + 1.17717e18i −0.221109 + 0.765777i
\(629\) 5.01899e17i 0.323137i
\(630\) 0 0
\(631\) 2.52029e16 0.0158950 0.00794748 0.999968i \(-0.497470\pi\)
0.00794748 + 0.999968i \(0.497470\pi\)
\(632\) 1.79843e16 4.00951e16i 0.0112262 0.0250283i
\(633\) 0 0
\(634\) −1.99251e18 2.81899e17i −1.21849 0.172391i
\(635\) 1.05149e17i 0.0636467i
\(636\) 0 0
\(637\) 4.09846e17i 0.243061i
\(638\) 2.70922e17 1.91492e18i 0.159041 1.12413i
\(639\) 0 0
\(640\) −1.25477e18 1.88637e18i −0.721762 1.08507i
\(641\) −5.97617e17 −0.340287 −0.170144 0.985419i \(-0.554423\pi\)
−0.170144 + 0.985419i \(0.554423\pi\)
\(642\) 0 0
\(643\) 2.19754e17i 0.122621i 0.998119 + 0.0613106i \(0.0195280\pi\)
−0.998119 + 0.0613106i \(0.980472\pi\)
\(644\) 2.39284e18 + 6.90903e17i 1.32177 + 0.381645i
\(645\) 0 0
\(646\) 5.71342e17 + 8.08331e16i 0.309304 + 0.0437600i
\(647\) 3.20518e18 1.71781 0.858905 0.512135i \(-0.171145\pi\)
0.858905 + 0.512135i \(0.171145\pi\)
\(648\) 0 0
\(649\) 2.45494e18 1.28959
\(650\) 8.97876e17 + 1.27031e17i 0.466960 + 0.0660651i
\(651\) 0 0
\(652\) 7.32856e17 2.53814e18i 0.373602 1.29391i
\(653\) 2.61177e17i 0.131826i −0.997825 0.0659128i \(-0.979004\pi\)
0.997825 0.0659128i \(-0.0209959\pi\)
\(654\) 0 0
\(655\) 1.34243e18 0.664236
\(656\) −2.40340e18 1.51414e18i −1.17747 0.741806i
\(657\) 0 0
\(658\) −1.92592e17 + 1.36127e18i −0.0925060 + 0.653848i
\(659\) 2.06165e17i 0.0980529i −0.998797 0.0490265i \(-0.984388\pi\)
0.998797 0.0490265i \(-0.0156119\pi\)
\(660\) 0 0
\(661\) 1.46618e18i 0.683718i 0.939751 + 0.341859i \(0.111057\pi\)
−0.939751 + 0.341859i \(0.888943\pi\)
\(662\) −2.44895e18 3.46475e17i −1.13084 0.159991i
\(663\) 0 0
\(664\) −3.09178e18 1.38679e18i −1.39996 0.627939i
\(665\) 5.89129e17 0.264162
\(666\) 0 0
\(667\) 4.93275e18i 2.16906i
\(668\) 1.01786e18 + 2.93896e17i 0.443244 + 0.127981i
\(669\) 0 0
\(670\) −5.15470e17 + 3.64343e18i −0.220149 + 1.55605i
\(671\) −2.42382e17 −0.102519
\(672\) 0 0
\(673\) 2.71250e18 1.12531 0.562655 0.826692i \(-0.309780\pi\)
0.562655 + 0.826692i \(0.309780\pi\)
\(674\) 2.44727e17 1.72977e18i 0.100553 0.710723i
\(675\) 0 0
\(676\) −1.29652e18 3.74353e17i −0.522546 0.150879i
\(677\) 3.72209e18i 1.48580i −0.669402 0.742901i \(-0.733450\pi\)
0.669402 0.742901i \(-0.266550\pi\)
\(678\) 0 0
\(679\) 8.28396e17 0.324403
\(680\) −3.77974e18 1.69537e18i −1.46607 0.657591i
\(681\) 0 0
\(682\) 7.63298e17 + 1.07991e17i 0.290466 + 0.0410950i
\(683\) 8.34945e17i 0.314719i −0.987541 0.157360i \(-0.949702\pi\)
0.987541 0.157360i \(-0.0502982\pi\)
\(684\) 0 0
\(685\) 3.57146e18i 1.32086i
\(686\) −4.16032e17 + 2.94059e18i −0.152412 + 1.07728i
\(687\) 0 0
\(688\) 2.74117e18 4.35107e18i 0.985397 1.56412i
\(689\) 2.64035e18 0.940235
\(690\) 0 0
\(691\) 9.77059e17i 0.341439i 0.985320 + 0.170720i \(0.0546092\pi\)
−0.985320 + 0.170720i \(0.945391\pi\)
\(692\) 1.10100e17 3.81316e17i 0.0381153 0.132006i
\(693\) 0 0
\(694\) 6.53805e17 + 9.24999e16i 0.222132 + 0.0314271i
\(695\) 4.47681e18 1.50684
\(696\) 0 0
\(697\) −5.19395e18 −1.71587
\(698\) 4.81862e18 + 6.81735e17i 1.57711 + 0.223129i
\(699\) 0 0
\(700\) −1.67079e18 4.82421e17i −0.536766 0.154985i
\(701\) 1.70397e18i 0.542370i 0.962527 + 0.271185i \(0.0874156\pi\)
−0.962527 + 0.271185i \(0.912584\pi\)
\(702\) 0 0
\(703\) 2.12512e17 0.0664008
\(704\) −2.17126e18 + 1.93341e18i −0.672185 + 0.598552i
\(705\) 0 0
\(706\) −5.89340e17 + 4.16556e18i −0.179116 + 1.26603i
\(707\) 2.61366e18i 0.787088i
\(708\) 0 0
\(709\) 5.77024e17i 0.170605i 0.996355 + 0.0853027i \(0.0271857\pi\)
−0.996355 + 0.0853027i \(0.972814\pi\)
\(710\) −6.26093e18 8.85792e17i −1.83425 0.259509i
\(711\) 0 0
\(712\) 1.56987e18 3.49995e18i 0.451590 1.00680i
\(713\) 1.96622e18 0.560467
\(714\) 0 0
\(715\) 2.83009e18i 0.792157i
\(716\) 3.07049e17 1.06342e18i 0.0851673 0.294964i
\(717\) 0 0
\(718\) 5.70857e17 4.03491e18i 0.155496 1.09907i
\(719\) −2.65402e18 −0.716417 −0.358209 0.933642i \(-0.616612\pi\)
−0.358209 + 0.933642i \(0.616612\pi\)
\(720\) 0 0
\(721\) 3.53620e18 0.937471
\(722\) −4.98963e17 + 3.52676e18i −0.131092 + 0.926582i
\(723\) 0 0
\(724\) 5.40454e17 1.87178e18i 0.139463 0.483007i
\(725\) 3.44428e18i 0.880848i
\(726\) 0 0
\(727\) −6.78102e18 −1.70342 −0.851710 0.524014i \(-0.824434\pi\)
−0.851710 + 0.524014i \(0.824434\pi\)
\(728\) −1.98019e18 8.88195e17i −0.493007 0.221133i
\(729\) 0 0
\(730\) 3.26927e18 + 4.62534e17i 0.799563 + 0.113122i
\(731\) 9.40303e18i 2.27932i
\(732\) 0 0
\(733\) 3.94118e17i 0.0938535i −0.998898 0.0469267i \(-0.985057\pi\)
0.998898 0.0469267i \(-0.0149427\pi\)
\(734\) 2.39098e17 1.68999e18i 0.0564354 0.398895i
\(735\) 0 0
\(736\) −4.79250e18 + 5.65841e18i −1.11137 + 1.31217i
\(737\) 4.72200e18 1.08539
\(738\) 0 0
\(739\) 2.42319e18i 0.547266i −0.961834 0.273633i \(-0.911775\pi\)
0.961834 0.273633i \(-0.0882253\pi\)
\(740\) −1.46576e18 4.23220e17i −0.328138 0.0947459i
\(741\) 0 0
\(742\) −5.01359e18 7.09319e17i −1.10287 0.156033i
\(743\) −2.76079e18 −0.602013 −0.301006 0.953622i \(-0.597323\pi\)
−0.301006 + 0.953622i \(0.597323\pi\)
\(744\) 0 0
\(745\) 6.66501e18 1.42819
\(746\) 6.91986e18 + 9.79017e17i 1.46992 + 0.207964i
\(747\) 0 0
\(748\) −1.47467e18 + 5.10731e18i −0.307847 + 1.06618i
\(749\) 4.19552e17i 0.0868269i
\(750\) 0 0
\(751\) 7.34720e18 1.49438 0.747192 0.664608i \(-0.231402\pi\)
0.747192 + 0.664608i \(0.231402\pi\)
\(752\) −3.46330e18 2.18187e18i −0.698351 0.439960i
\(753\) 0 0
\(754\) −6.02128e17 + 4.25595e18i −0.119337 + 0.843495i
\(755\) 2.44791e17i 0.0480995i
\(756\) 0 0
\(757\) 1.26012e18i 0.243382i −0.992568 0.121691i \(-0.961168\pi\)
0.992568 0.121691i \(-0.0388317\pi\)
\(758\) −2.42880e18 3.43624e17i −0.465095 0.0658012i
\(759\) 0 0
\(760\) −7.17844e17 + 1.60040e18i −0.135127 + 0.301259i
\(761\) 3.58935e18 0.669908 0.334954 0.942235i \(-0.391279\pi\)
0.334954 + 0.942235i \(0.391279\pi\)
\(762\) 0 0
\(763\) 2.97878e17i 0.0546550i
\(764\) 1.93700e18 + 5.59284e17i 0.352389 + 0.101748i
\(765\) 0 0
\(766\) −9.60242e17 + 6.78716e18i −0.171749 + 1.21395i
\(767\) −5.45614e18 −0.967644
\(768\) 0 0
\(769\) −4.46415e17 −0.0778426 −0.0389213 0.999242i \(-0.512392\pi\)
−0.0389213 + 0.999242i \(0.512392\pi\)
\(770\) −7.60292e17 + 5.37388e18i −0.131459 + 0.929176i
\(771\) 0 0
\(772\) 1.00027e18 + 2.88815e17i 0.170061 + 0.0491030i
\(773\) 6.26507e18i 1.05623i 0.849172 + 0.528116i \(0.177101\pi\)
−0.849172 + 0.528116i \(0.822899\pi\)
\(774\) 0 0
\(775\) −1.37291e18 −0.227604
\(776\) −1.00939e18 + 2.25038e18i −0.165942 + 0.369960i
\(777\) 0 0
\(778\) 4.41621e18 + 6.24803e17i 0.713975 + 0.101013i
\(779\) 2.19920e18i 0.352590i
\(780\) 0 0
\(781\) 8.11437e18i 1.27945i
\(782\) −1.89934e18 + 1.34249e19i −0.297002 + 2.09926i
\(783\) 0 0
\(784\) −1.97994e18 1.24736e18i −0.304508 0.191839i
\(785\) −6.81008e18 −1.03872
\(786\) 0 0
\(787\) 1.07781e16i 0.00161698i −1.00000 0.000808492i \(-0.999743\pi\)
1.00000 0.000808492i \(-0.000257351\pi\)
\(788\) −9.81491e17 + 3.39924e18i −0.146038 + 0.505780i
\(789\) 0 0
\(790\) 2.41834e17 + 3.42145e16i 0.0353949 + 0.00500765i
\(791\) 2.59320e18 0.376435
\(792\) 0 0
\(793\) 5.38698e17 0.0769254
\(794\) −2.86178e18 4.04882e17i −0.405324 0.0573449i
\(795\) 0 0
\(796\) 9.16629e18 + 2.64666e18i 1.27720 + 0.368776i
\(797\) 8.45030e18i 1.16787i 0.811802 + 0.583933i \(0.198487\pi\)
−0.811802 + 0.583933i \(0.801513\pi\)
\(798\) 0 0
\(799\) −7.48448e18 −1.01767
\(800\) 3.34635e18 3.95097e18i 0.451322 0.532867i
\(801\) 0 0
\(802\) −6.00594e17 + 4.24511e18i −0.0796981 + 0.563320i
\(803\) 4.23709e18i 0.557720i
\(804\) 0 0
\(805\) 1.38428e19i 1.79288i
\(806\) −1.69644e18 2.40011e17i −0.217952 0.0308357i
\(807\) 0 0
\(808\) −7.10015e18 3.18470e18i −0.897622 0.402620i
\(809\) 1.02697e18 0.128794 0.0643968 0.997924i \(-0.479488\pi\)
0.0643968 + 0.997924i \(0.479488\pi\)
\(810\) 0 0
\(811\) 6.09641e18i 0.752382i −0.926542 0.376191i \(-0.877234\pi\)
0.926542 0.376191i \(-0.122766\pi\)
\(812\) 2.28668e18 7.91958e18i 0.279957 0.969590i
\(813\) 0 0
\(814\) −2.74254e17 + 1.93847e18i −0.0330441 + 0.233561i
\(815\) 1.46834e19 1.75510
\(816\) 0 0
\(817\) −3.98139e18 −0.468372
\(818\) 8.69553e17 6.14615e18i 0.101484 0.717310i
\(819\) 0 0
\(820\) 4.37973e18 1.51685e19i 0.503104 1.74242i
\(821\) 4.75938e18i 0.542400i −0.962523 0.271200i \(-0.912579\pi\)
0.962523 0.271200i \(-0.0874205\pi\)
\(822\) 0 0
\(823\) 1.35115e19 1.51567 0.757835 0.652446i \(-0.226257\pi\)
0.757835 + 0.652446i \(0.226257\pi\)
\(824\) −4.30880e18 + 9.60627e18i −0.479545 + 1.06912i
\(825\) 0 0
\(826\) 1.03603e19 + 1.46577e18i 1.13502 + 0.160581i
\(827\) 3.80345e18i 0.413420i 0.978402 + 0.206710i \(0.0662757\pi\)
−0.978402 + 0.206710i \(0.933724\pi\)
\(828\) 0 0
\(829\) 1.29267e19i 1.38319i 0.722284 + 0.691597i \(0.243093\pi\)
−0.722284 + 0.691597i \(0.756907\pi\)
\(830\) 2.63832e18 1.86481e19i 0.280104 1.97982i
\(831\) 0 0
\(832\) 4.82565e18 4.29703e18i 0.504376 0.449125i
\(833\) −4.27882e18 −0.443743
\(834\) 0 0
\(835\) 5.88846e18i 0.601229i
\(836\) 2.16251e18 + 6.24399e17i 0.219087 + 0.0632589i
\(837\) 0 0
\(838\) −7.64617e18 1.08177e18i −0.762707 0.107907i
\(839\) −4.18489e18 −0.414220 −0.207110 0.978318i \(-0.566406\pi\)
−0.207110 + 0.978318i \(0.566406\pi\)
\(840\) 0 0
\(841\) −6.06532e18 −0.591125
\(842\) 7.67041e18 + 1.08520e18i 0.741806 + 0.104950i
\(843\) 0 0
\(844\) 2.51435e18 8.70806e18i 0.239442 0.829270i
\(845\) 7.50049e18i 0.708796i
\(846\) 0 0
\(847\) −1.63267e18 −0.151934
\(848\) 8.03587e18 1.27554e19i 0.742096 1.17793i
\(849\) 0 0
\(850\) 1.32621e18 9.37389e18i 0.120612 0.852505i
\(851\) 4.99341e18i 0.450666i
\(852\) 0 0
\(853\) 5.09953e18i 0.453275i −0.973979 0.226637i \(-0.927227\pi\)
0.973979 0.226637i \(-0.0727732\pi\)
\(854\) −1.02290e18 1.44719e17i −0.0902311 0.0127658i
\(855\) 0 0
\(856\) 1.13973e18 + 5.11217e17i 0.0990203 + 0.0444146i
\(857\) −8.40331e18 −0.724562 −0.362281 0.932069i \(-0.618002\pi\)
−0.362281 + 0.932069i \(0.618002\pi\)
\(858\) 0 0
\(859\) 2.21269e19i 1.87917i −0.342317 0.939584i \(-0.611212\pi\)
0.342317 0.939584i \(-0.388788\pi\)
\(860\) 2.74608e19 + 7.92899e18i 2.31459 + 0.668310i
\(861\) 0 0
\(862\) −2.72738e18 + 1.92776e19i −0.226438 + 1.60050i
\(863\) 6.01097e18 0.495307 0.247653 0.968849i \(-0.420341\pi\)
0.247653 + 0.968849i \(0.420341\pi\)
\(864\) 0 0
\(865\) 2.20596e18 0.179057
\(866\) 7.71508e17 5.45316e18i 0.0621548 0.439321i
\(867\) 0 0
\(868\) 3.15678e18 + 9.11484e17i 0.250534 + 0.0723387i
\(869\) 3.13425e17i 0.0246891i
\(870\) 0 0
\(871\) −1.04947e19 −0.814428
\(872\) 8.09202e17 + 3.62960e17i 0.0623304 + 0.0279577i
\(873\) 0 0
\(874\) 5.68430e18 + 8.04211e17i 0.431373 + 0.0610303i
\(875\) 4.17585e18i 0.314552i
\(876\) 0 0
\(877\) 1.14586e19i 0.850421i −0.905094 0.425211i \(-0.860200\pi\)
0.905094 0.425211i \(-0.139800\pi\)
\(878\) −2.54968e18 + 1.80216e19i −0.187833 + 1.32763i
\(879\) 0 0
\(880\) −1.36720e19 8.61335e18i −0.992418 0.625222i
\(881\) −2.52139e19 −1.81676 −0.908378 0.418149i \(-0.862679\pi\)
−0.908378 + 0.418149i \(0.862679\pi\)
\(882\) 0 0
\(883\) 8.81682e18i 0.625990i 0.949755 + 0.312995i \(0.101332\pi\)
−0.949755 + 0.312995i \(0.898668\pi\)
\(884\) 3.27748e18 1.13511e19i 0.230994 0.800013i
\(885\) 0 0
\(886\) −6.81326e18 9.63935e17i −0.473190 0.0669466i
\(887\) −2.63061e19 −1.81365 −0.906823 0.421512i \(-0.861499\pi\)
−0.906823 + 0.421512i \(0.861499\pi\)
\(888\) 0 0
\(889\) −5.75113e17 −0.0390743
\(890\) 2.11100e19 + 2.98663e18i 1.42381 + 0.201440i
\(891\) 0 0
\(892\) 5.09498e18 + 1.47111e18i 0.338666 + 0.0977856i
\(893\) 3.16904e18i 0.209119i
\(894\) 0 0
\(895\) 6.15199e18 0.400098
\(896\) −1.03175e19 + 6.86297e18i −0.666150 + 0.443108i
\(897\) 0 0
\(898\) 1.11267e18 7.86458e18i 0.0708063 0.500471i
\(899\) 6.50760e18i 0.411134i
\(900\) 0 0
\(901\) 2.75655e19i 1.71654i
\(902\) −2.00604e19 2.83814e18i −1.24022 0.175465i
\(903\) 0 0
\(904\) −3.15977e18 + 7.04457e18i −0.192558 + 0.429299i
\(905\) 1.08285e19 0.655165
\(906\) 0 0
\(907\) 1.16508e19i 0.694877i 0.937703 + 0.347439i \(0.112948\pi\)
−0.937703 + 0.347439i \(0.887052\pi\)
\(908\) 4.72191e18 1.63536e19i 0.279615 0.968403i
\(909\) 0 0
\(910\) 1.68976e18 1.19435e19i 0.0986407 0.697209i
\(911\) −6.57470e18 −0.381071 −0.190536 0.981680i \(-0.561023\pi\)
−0.190536 + 0.981680i \(0.561023\pi\)
\(912\) 0 0
\(913\) −2.41685e19 −1.38099
\(914\) 1.03928e18 7.34584e18i 0.0589636 0.416765i
\(915\) 0 0
\(916\) −4.81322e18 + 1.66698e19i −0.269225 + 0.932419i
\(917\) 7.34241e18i 0.407791i
\(918\) 0 0
\(919\) −7.15001e18 −0.391522 −0.195761 0.980652i \(-0.562718\pi\)
−0.195761 + 0.980652i \(0.562718\pi\)
\(920\) −3.76048e19 1.68673e19i −2.04467 0.917115i
\(921\) 0 0
\(922\) −1.20624e19 1.70658e18i −0.646670 0.0914904i
\(923\) 1.80343e19i 0.960038i
\(924\) 0 0
\(925\) 3.48663e18i 0.183014i
\(926\) −1.82828e18 + 1.29226e19i −0.0952950 + 0.673562i
\(927\) 0 0
\(928\) 1.87277e19 + 1.58618e19i 0.962547 + 0.815248i
\(929\) 1.97713e19 1.00910 0.504550 0.863383i \(-0.331658\pi\)
0.504550 + 0.863383i \(0.331658\pi\)
\(930\) 0 0
\(931\) 1.81172e18i 0.0911838i
\(932\) 2.72277e19 + 7.86168e18i 1.36084 + 0.392927i
\(933\) 0 0
\(934\) 2.98294e19 + 4.22024e18i 1.47025 + 0.208009i
\(935\) −2.95464e19 −1.44620
\(936\) 0 0
\(937\) 2.48380e19 1.19897 0.599487 0.800384i \(-0.295371\pi\)
0.599487 + 0.800384i \(0.295371\pi\)
\(938\) 1.99277e19 + 2.81936e18i 0.955300 + 0.135155i
\(939\) 0 0
\(940\) 6.31119e18 2.18579e19i 0.298387 1.03342i
\(941\) 3.79177e19i 1.78036i 0.455605 + 0.890182i \(0.349423\pi\)
−0.455605 + 0.890182i \(0.650577\pi\)
\(942\) 0 0
\(943\) −5.16747e19 −2.39305
\(944\) −1.66057e19 + 2.63583e19i −0.763728 + 1.21227i
\(945\) 0 0
\(946\) 5.13812e18 3.63171e19i 0.233083 1.64747i
\(947\) 3.17492e18i 0.143040i −0.997439 0.0715200i \(-0.977215\pi\)
0.997439 0.0715200i \(-0.0227850\pi\)
\(948\) 0 0
\(949\) 9.41699e18i 0.418487i
\(950\) −3.96904e18 5.61538e17i −0.175179 0.0247842i
\(951\) 0 0
\(952\) −9.27282e18 + 2.06733e19i −0.403712 + 0.900057i
\(953\) 8.65721e17 0.0374347 0.0187173 0.999825i \(-0.494042\pi\)
0.0187173 + 0.999825i \(0.494042\pi\)
\(954\) 0 0
\(955\) 1.12057e19i 0.477990i
\(956\) 6.04124e18 + 1.74434e18i 0.255947 + 0.0739016i
\(957\) 0 0
\(958\) 2.10153e18 1.48540e19i 0.0878334 0.620821i
\(959\) 1.95341e19 0.810911
\(960\) 0 0
\(961\) −2.18236e19 −0.893766
\(962\) 6.09533e17 4.30828e18i 0.0247947 0.175253i
\(963\) 0 0
\(964\) −2.63188e18 7.59925e17i −0.105625 0.0304979i
\(965\) 5.78667e18i 0.230675i
\(966\) 0 0
\(967\) 3.62918e19 1.42737 0.713685 0.700467i \(-0.247025\pi\)
0.713685 + 0.700467i \(0.247025\pi\)
\(968\) 1.98938e18 4.43523e18i 0.0777190 0.173271i
\(969\) 0 0
\(970\) −1.35732e19 1.92032e18i −0.523197 0.0740216i
\(971\) 1.43624e19i 0.549923i 0.961455 + 0.274962i \(0.0886652\pi\)
−0.961455 + 0.274962i \(0.911335\pi\)
\(972\) 0 0
\(973\) 2.44859e19i 0.925088i
\(974\) 5.24112e18 3.70451e19i 0.196694 1.39027i
\(975\) 0 0
\(976\) 1.63952e18 2.60242e18i 0.0607146 0.0963725i
\(977\) −3.27934e19 −1.20635 −0.603173 0.797610i \(-0.706097\pi\)
−0.603173 + 0.797610i \(0.706097\pi\)
\(978\) 0 0
\(979\) 2.73592e19i 0.993154i
\(980\) 3.60807e18 1.24960e19i 0.130108 0.450610i
\(981\) 0 0
\(982\) −2.16089e19 3.05722e18i −0.768969 0.108793i
\(983\) −2.04182e19 −0.721806 −0.360903 0.932603i \(-0.617531\pi\)
−0.360903 + 0.932603i \(0.617531\pi\)
\(984\) 0 0
\(985\) −1.96650e19 −0.686055
\(986\) 4.44324e19 + 6.28626e18i 1.53993 + 0.217868i
\(987\) 0 0
\(988\) −4.80621e18 1.38774e18i −0.164393 0.0474665i
\(989\) 9.35511e19i 3.17887i
\(990\) 0 0
\(991\) 3.13618e18 0.105177 0.0525887 0.998616i \(-0.483253\pi\)
0.0525887 + 0.998616i \(0.483253\pi\)
\(992\) −6.32258e18 + 7.46494e18i −0.210653 + 0.248714i
\(993\) 0 0
\(994\) −4.84484e18 + 3.42442e19i −0.159319 + 1.12610i
\(995\) 5.30280e19i 1.73243i
\(996\) 0 0
\(997\) 3.08455e19i 0.994658i 0.867562 + 0.497329i \(0.165686\pi\)
−0.867562 + 0.497329i \(0.834314\pi\)
\(998\) −2.34676e19 3.32018e18i −0.751832 0.106369i
\(999\) 0 0
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 72.14.d.c.37.6 10
3.2 odd 2 8.14.b.b.5.5 10
8.5 even 2 inner 72.14.d.c.37.5 10
12.11 even 2 32.14.b.b.17.5 10
24.5 odd 2 8.14.b.b.5.6 yes 10
24.11 even 2 32.14.b.b.17.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.14.b.b.5.5 10 3.2 odd 2
8.14.b.b.5.6 yes 10 24.5 odd 2
32.14.b.b.17.5 10 12.11 even 2
32.14.b.b.17.6 10 24.11 even 2
72.14.d.c.37.5 10 8.5 even 2 inner
72.14.d.c.37.6 10 1.1 even 1 trivial