Properties

Label 20.11.b.a.11.8
Level $20$
Weight $11$
Character 20.11
Analytic conductor $12.707$
Analytic rank $0$
Dimension $20$
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] = [20,11,Mod(11,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.11");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 20.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: \(12.7071450535\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + 95990512 x^{13} + 5401091173 x^{12} - 59241975423 x^{11} + \cdots + 11\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{94}\cdot 3^{4}\cdot 5^{29} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.8
Root \(-8.12576 + 14.6168i\) of defining polynomial
Character \(\chi\) \(=\) 20.11
Dual form 20.11.b.a.11.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-13.0154 + 29.2335i) q^{2} +448.707i q^{3} +(-685.197 - 760.974i) q^{4} -1397.54 q^{5} +(-13117.3 - 5840.12i) q^{6} -19334.7i q^{7} +(31164.1 - 10126.3i) q^{8} -142289. q^{9} +O(q^{10})\) \(q+(-13.0154 + 29.2335i) q^{2} +448.707i q^{3} +(-685.197 - 760.974i) q^{4} -1397.54 q^{5} +(-13117.3 - 5840.12i) q^{6} -19334.7i q^{7} +(31164.1 - 10126.3i) q^{8} -142289. q^{9} +(18189.6 - 40855.1i) q^{10} +207443. i q^{11} +(341455. - 307453. i) q^{12} +65166.8 q^{13} +(565222. + 251650. i) q^{14} -627087. i q^{15} +(-109587. + 1.04283e6i) q^{16} -805200. q^{17} +(1.85196e6 - 4.15961e6i) q^{18} -4.08369e6i q^{19} +(957591. + 1.06349e6i) q^{20} +8.67562e6 q^{21} +(-6.06427e6 - 2.69996e6i) q^{22} +4.40794e6i q^{23} +(4.54374e6 + 1.39835e7i) q^{24} +1.95312e6 q^{25} +(-848174. + 1.90505e6i) q^{26} -3.73504e7i q^{27} +(-1.47132e7 + 1.32481e7i) q^{28} -1.06041e7 q^{29} +(1.83320e7 + 8.16182e6i) q^{30} +2.90491e6i q^{31} +(-2.90594e7 - 1.67766e7i) q^{32} -9.30810e7 q^{33} +(1.04800e7 - 2.35388e7i) q^{34} +2.70211e7i q^{35} +(9.74960e7 + 1.08278e8i) q^{36} -1.45768e7 q^{37} +(1.19381e8 + 5.31510e7i) q^{38} +2.92408e7i q^{39} +(-4.35531e7 + 1.41519e7i) q^{40} -6.38483e7 q^{41} +(-1.12917e8 + 2.53619e8i) q^{42} -2.40099e8i q^{43} +(1.57858e8 - 1.42139e8i) q^{44} +1.98855e8 q^{45} +(-1.28860e8 - 5.73713e7i) q^{46} -1.51193e8i q^{47} +(-4.67927e8 - 4.91727e7i) q^{48} -9.13560e7 q^{49} +(-2.54208e7 + 5.70967e7i) q^{50} -3.61299e8i q^{51} +(-4.46520e7 - 4.95902e7i) q^{52} -3.71821e8 q^{53} +(1.09188e9 + 4.86132e8i) q^{54} -2.89910e8i q^{55} +(-1.95789e8 - 6.02549e8i) q^{56} +1.83238e9 q^{57} +(1.38017e8 - 3.09994e8i) q^{58} +4.69987e8i q^{59} +(-4.77197e8 + 4.29678e8i) q^{60} -7.97019e8 q^{61} +(-8.49209e7 - 3.78088e7i) q^{62} +2.75112e9i q^{63} +(8.68659e8 - 6.31153e8i) q^{64} -9.10733e7 q^{65} +(1.21149e9 - 2.72108e9i) q^{66} -8.39728e8i q^{67} +(5.51720e8 + 6.12736e8i) q^{68} -1.97787e9 q^{69} +(-7.89921e8 - 3.51691e8i) q^{70} +4.87774e8i q^{71} +(-4.43431e9 + 1.44086e9i) q^{72} -3.05750e9 q^{73} +(1.89723e8 - 4.26131e8i) q^{74} +8.76381e8i q^{75} +(-3.10758e9 + 2.79813e9i) q^{76} +4.01084e9 q^{77} +(-8.54811e8 - 3.80582e8i) q^{78} +4.58675e9i q^{79} +(1.53153e8 - 1.45740e9i) q^{80} +8.35737e9 q^{81} +(8.31014e8 - 1.86651e9i) q^{82} -2.95392e8i q^{83} +(-5.94451e9 - 6.60193e9i) q^{84} +1.12530e9 q^{85} +(7.01894e9 + 3.12500e9i) q^{86} -4.75812e9i q^{87} +(2.10062e9 + 6.46476e9i) q^{88} -3.76251e9 q^{89} +(-2.58819e9 + 5.81323e9i) q^{90} -1.25998e9i q^{91} +(3.35433e9 - 3.02030e9i) q^{92} -1.30346e9 q^{93} +(4.41990e9 + 1.96784e9i) q^{94} +5.70713e9i q^{95} +(7.52777e9 - 1.30391e10i) q^{96} -1.37175e10 q^{97} +(1.18904e9 - 2.67066e9i) q^{98} -2.95168e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.0154 + 29.2335i −0.406733 + 0.913547i
\(3\) 448.707i 1.84653i 0.384162 + 0.923266i \(0.374490\pi\)
−0.384162 + 0.923266i \(0.625510\pi\)
\(4\) −685.197 760.974i −0.669137 0.743139i
\(5\) −1397.54 −0.447214
\(6\) −13117.3 5840.12i −1.68689 0.751044i
\(7\) 19334.7i 1.15040i −0.818014 0.575198i \(-0.804925\pi\)
0.818014 0.575198i \(-0.195075\pi\)
\(8\) 31164.1 10126.3i 0.951052 0.309030i
\(9\) −142289. −2.40968
\(10\) 18189.6 40855.1i 0.181896 0.408551i
\(11\) 207443.i 1.28806i 0.765002 + 0.644028i \(0.222738\pi\)
−0.765002 + 0.644028i \(0.777262\pi\)
\(12\) 341455. 307453.i 1.37223 1.23558i
\(13\) 65166.8 0.175513 0.0877565 0.996142i \(-0.472030\pi\)
0.0877565 + 0.996142i \(0.472030\pi\)
\(14\) 565222. + 251650.i 1.05094 + 0.467904i
\(15\) 627087.i 0.825794i
\(16\) −109587. + 1.04283e6i −0.104511 + 0.994524i
\(17\) −805200. −0.567099 −0.283550 0.958958i \(-0.591512\pi\)
−0.283550 + 0.958958i \(0.591512\pi\)
\(18\) 1.85196e6 4.15961e6i 0.980094 2.20135i
\(19\) 4.08369e6i 1.64924i −0.565685 0.824622i \(-0.691388\pi\)
0.565685 0.824622i \(-0.308612\pi\)
\(20\) 957591. + 1.06349e6i 0.299247 + 0.332342i
\(21\) 8.67562e6 2.12424
\(22\) −6.06427e6 2.69996e6i −1.17670 0.523894i
\(23\) 4.40794e6i 0.684851i 0.939545 + 0.342426i \(0.111249\pi\)
−0.939545 + 0.342426i \(0.888751\pi\)
\(24\) 4.54374e6 + 1.39835e7i 0.570633 + 1.75615i
\(25\) 1.95312e6 0.200000
\(26\) −848174. + 1.90505e6i −0.0713869 + 0.160339i
\(27\) 3.73504e7i 2.60301i
\(28\) −1.47132e7 + 1.32481e7i −0.854904 + 0.769773i
\(29\) −1.06041e7 −0.516990 −0.258495 0.966013i \(-0.583227\pi\)
−0.258495 + 0.966013i \(0.583227\pi\)
\(30\) 1.83320e7 + 8.16182e6i 0.754402 + 0.335877i
\(31\) 2.90491e6i 0.101467i 0.998712 + 0.0507335i \(0.0161559\pi\)
−0.998712 + 0.0507335i \(0.983844\pi\)
\(32\) −2.90594e7 1.67766e7i −0.866037 0.499981i
\(33\) −9.30810e7 −2.37843
\(34\) 1.04800e7 2.35388e7i 0.230658 0.518072i
\(35\) 2.70211e7i 0.514473i
\(36\) 9.74960e7 + 1.08278e8i 1.61241 + 1.79073i
\(37\) −1.45768e7 −0.210210 −0.105105 0.994461i \(-0.533518\pi\)
−0.105105 + 0.994461i \(0.533518\pi\)
\(38\) 1.19381e8 + 5.31510e7i 1.50666 + 0.670801i
\(39\) 2.92408e7i 0.324090i
\(40\) −4.35531e7 + 1.41519e7i −0.425324 + 0.138202i
\(41\) −6.38483e7 −0.551099 −0.275550 0.961287i \(-0.588860\pi\)
−0.275550 + 0.961287i \(0.588860\pi\)
\(42\) −1.12917e8 + 2.53619e8i −0.863999 + 1.94060i
\(43\) 2.40099e8i 1.63323i −0.577180 0.816617i \(-0.695847\pi\)
0.577180 0.816617i \(-0.304153\pi\)
\(44\) 1.57858e8 1.42139e8i 0.957204 0.861886i
\(45\) 1.98855e8 1.07764
\(46\) −1.28860e8 5.73713e7i −0.625644 0.278551i
\(47\) 1.51193e8i 0.659238i −0.944114 0.329619i \(-0.893080\pi\)
0.944114 0.329619i \(-0.106920\pi\)
\(48\) −4.67927e8 4.91727e7i −1.83642 0.192982i
\(49\) −9.13560e7 −0.323412
\(50\) −2.54208e7 + 5.70967e7i −0.0813465 + 0.182709i
\(51\) 3.61299e8i 1.04717i
\(52\) −4.46520e7 4.95902e7i −0.117442 0.130431i
\(53\) −3.71821e8 −0.889108 −0.444554 0.895752i \(-0.646638\pi\)
−0.444554 + 0.895752i \(0.646638\pi\)
\(54\) 1.09188e9 + 4.86132e8i 2.37798 + 1.05873i
\(55\) 2.89910e8i 0.576036i
\(56\) −1.95789e8 6.02549e8i −0.355507 1.09409i
\(57\) 1.83238e9 3.04538
\(58\) 1.38017e8 3.09994e8i 0.210277 0.472295i
\(59\) 4.69987e8i 0.657395i 0.944435 + 0.328697i \(0.106610\pi\)
−0.944435 + 0.328697i \(0.893390\pi\)
\(60\) −4.77197e8 + 4.29678e8i −0.613680 + 0.552569i
\(61\) −7.97019e8 −0.943669 −0.471835 0.881687i \(-0.656408\pi\)
−0.471835 + 0.881687i \(0.656408\pi\)
\(62\) −8.49209e7 3.78088e7i −0.0926949 0.0412699i
\(63\) 2.75112e9i 2.77209i
\(64\) 8.68659e8 6.31153e8i 0.809001 0.587807i
\(65\) −9.10733e7 −0.0784918
\(66\) 1.21149e9 2.72108e9i 0.967387 2.17281i
\(67\) 8.39728e8i 0.621963i −0.950416 0.310981i \(-0.899342\pi\)
0.950416 0.310981i \(-0.100658\pi\)
\(68\) 5.51720e8 + 6.12736e8i 0.379467 + 0.421433i
\(69\) −1.97787e9 −1.26460
\(70\) −7.89921e8 3.51691e8i −0.469995 0.209253i
\(71\) 4.87774e8i 0.270350i 0.990822 + 0.135175i \(0.0431597\pi\)
−0.990822 + 0.135175i \(0.956840\pi\)
\(72\) −4.43431e9 + 1.44086e9i −2.29173 + 0.744662i
\(73\) −3.05750e9 −1.47487 −0.737433 0.675421i \(-0.763962\pi\)
−0.737433 + 0.675421i \(0.763962\pi\)
\(74\) 1.89723e8 4.26131e8i 0.0854993 0.192037i
\(75\) 8.76381e8i 0.369306i
\(76\) −3.10758e9 + 2.79813e9i −1.22562 + 1.10357i
\(77\) 4.01084e9 1.48177
\(78\) −8.54811e8 3.80582e8i −0.296072 0.131818i
\(79\) 4.58675e9i 1.49063i 0.666712 + 0.745315i \(0.267701\pi\)
−0.666712 + 0.745315i \(0.732299\pi\)
\(80\) 1.53153e8 1.45740e9i 0.0467386 0.444765i
\(81\) 8.35737e9 2.39687
\(82\) 8.31014e8 1.86651e9i 0.224150 0.503455i
\(83\) 2.95392e8i 0.0749909i −0.999297 0.0374954i \(-0.988062\pi\)
0.999297 0.0374954i \(-0.0119380\pi\)
\(84\) −5.94451e9 6.60193e9i −1.42141 1.57861i
\(85\) 1.12530e9 0.253614
\(86\) 7.01894e9 + 3.12500e9i 1.49204 + 0.664289i
\(87\) 4.75812e9i 0.954639i
\(88\) 2.10062e9 + 6.46476e9i 0.398047 + 1.22501i
\(89\) −3.76251e9 −0.673794 −0.336897 0.941541i \(-0.609377\pi\)
−0.336897 + 0.941541i \(0.609377\pi\)
\(90\) −2.58819e9 + 5.81323e9i −0.438312 + 0.984476i
\(91\) 1.25998e9i 0.201910i
\(92\) 3.35433e9 3.02030e9i 0.508940 0.458260i
\(93\) −1.30346e9 −0.187362
\(94\) 4.41990e9 + 1.96784e9i 0.602245 + 0.268134i
\(95\) 5.70713e9i 0.737564i
\(96\) 7.52777e9 1.30391e10i 0.923230 1.59916i
\(97\) −1.37175e10 −1.59741 −0.798706 0.601721i \(-0.794482\pi\)
−0.798706 + 0.601721i \(0.794482\pi\)
\(98\) 1.18904e9 2.67066e9i 0.131542 0.295452i
\(99\) 2.95168e10i 3.10380i
\(100\) −1.33827e9 1.48628e9i −0.133827 0.148628i
\(101\) 6.29138e9 0.598603 0.299301 0.954159i \(-0.403246\pi\)
0.299301 + 0.954159i \(0.403246\pi\)
\(102\) 1.05620e10 + 4.70246e9i 0.956636 + 0.425917i
\(103\) 1.48493e10i 1.28091i 0.767996 + 0.640455i \(0.221254\pi\)
−0.767996 + 0.640455i \(0.778746\pi\)
\(104\) 2.03086e9 6.59897e8i 0.166922 0.0542387i
\(105\) −1.21246e10 −0.949990
\(106\) 4.83941e9 1.08696e10i 0.361629 0.812242i
\(107\) 7.85004e9i 0.559697i −0.960044 0.279848i \(-0.909716\pi\)
0.960044 0.279848i \(-0.0902842\pi\)
\(108\) −2.84227e10 + 2.55924e10i −1.93440 + 1.74177i
\(109\) 3.49014e9 0.226835 0.113418 0.993547i \(-0.463820\pi\)
0.113418 + 0.993547i \(0.463820\pi\)
\(110\) 8.47508e9 + 3.77330e9i 0.526236 + 0.234293i
\(111\) 6.54071e9i 0.388159i
\(112\) 2.01629e10 + 2.11884e9i 1.14410 + 0.120229i
\(113\) 1.37109e10 0.744171 0.372085 0.928199i \(-0.378643\pi\)
0.372085 + 0.928199i \(0.378643\pi\)
\(114\) −2.38492e10 + 5.35669e10i −1.23865 + 2.78210i
\(115\) 6.16028e9i 0.306275i
\(116\) 7.26587e9 + 8.06942e9i 0.345938 + 0.384196i
\(117\) −9.27252e9 −0.422930
\(118\) −1.37394e10 6.11709e9i −0.600561 0.267384i
\(119\) 1.55683e10i 0.652389i
\(120\) −6.35006e9 1.95426e10i −0.255195 0.785373i
\(121\) −1.70950e10 −0.659086
\(122\) 1.03736e10 2.32997e10i 0.383821 0.862086i
\(123\) 2.86492e10i 1.01762i
\(124\) 2.21057e9 1.99044e9i 0.0754041 0.0678954i
\(125\) −2.72958e9 −0.0894427
\(126\) −8.04249e10 3.58070e10i −2.53243 1.12750i
\(127\) 1.28415e10i 0.388684i 0.980934 + 0.194342i \(0.0622571\pi\)
−0.980934 + 0.194342i \(0.937743\pi\)
\(128\) 7.14484e9 + 3.36087e10i 0.207942 + 0.978141i
\(129\) 1.07734e11 3.01582
\(130\) 1.18536e9 2.66239e9i 0.0319252 0.0717060i
\(131\) 8.76942e9i 0.227308i 0.993520 + 0.113654i \(0.0362555\pi\)
−0.993520 + 0.113654i \(0.963744\pi\)
\(132\) 6.37787e10 + 7.08322e10i 1.59150 + 1.76751i
\(133\) −7.89570e10 −1.89728
\(134\) 2.45482e10 + 1.09294e10i 0.568192 + 0.252973i
\(135\) 5.21988e10i 1.16410i
\(136\) −2.50933e10 + 8.15368e9i −0.539341 + 0.175250i
\(137\) −8.29170e10 −1.71807 −0.859034 0.511918i \(-0.828935\pi\)
−0.859034 + 0.511918i \(0.828935\pi\)
\(138\) 2.57429e10 5.78202e10i 0.514354 1.15527i
\(139\) 2.53373e10i 0.488300i 0.969737 + 0.244150i \(0.0785090\pi\)
−0.969737 + 0.244150i \(0.921491\pi\)
\(140\) 2.05624e10 1.85148e10i 0.382325 0.344253i
\(141\) 6.78414e10 1.21730
\(142\) −1.42594e10 6.34860e9i −0.246978 0.109960i
\(143\) 1.35184e10i 0.226071i
\(144\) 1.55931e10 1.48384e11i 0.251837 2.39648i
\(145\) 1.48196e10 0.231205
\(146\) 3.97947e10 8.93815e10i 0.599876 1.34736i
\(147\) 4.09921e10i 0.597191i
\(148\) 9.98797e9 + 1.10926e10i 0.140659 + 0.156215i
\(149\) −1.13838e11 −1.55009 −0.775045 0.631906i \(-0.782273\pi\)
−0.775045 + 0.631906i \(0.782273\pi\)
\(150\) −2.56197e10 1.14065e10i −0.337379 0.150209i
\(151\) 1.22959e11i 1.56630i 0.621832 + 0.783151i \(0.286389\pi\)
−0.621832 + 0.783151i \(0.713611\pi\)
\(152\) −4.13526e10 1.27264e11i −0.509665 1.56852i
\(153\) 1.14571e11 1.36653
\(154\) −5.22029e10 + 1.17251e11i −0.602686 + 1.35367i
\(155\) 4.05974e9i 0.0453774i
\(156\) 2.22515e10 2.00357e10i 0.240844 0.216861i
\(157\) 1.38471e11 1.45164 0.725822 0.687882i \(-0.241460\pi\)
0.725822 + 0.687882i \(0.241460\pi\)
\(158\) −1.34087e11 5.96986e10i −1.36176 0.606288i
\(159\) 1.66839e11i 1.64177i
\(160\) 4.06117e10 + 2.34460e10i 0.387303 + 0.223598i
\(161\) 8.52262e10 0.787851
\(162\) −1.08775e11 + 2.44315e11i −0.974885 + 2.18965i
\(163\) 1.63012e9i 0.0141671i −0.999975 0.00708354i \(-0.997745\pi\)
0.999975 0.00708354i \(-0.00225478\pi\)
\(164\) 4.37486e10 + 4.85869e10i 0.368761 + 0.409543i
\(165\) 1.30085e11 1.06367
\(166\) 8.63535e9 + 3.84466e9i 0.0685077 + 0.0305012i
\(167\) 2.23725e11i 1.72239i −0.508271 0.861197i \(-0.669715\pi\)
0.508271 0.861197i \(-0.330285\pi\)
\(168\) 2.70368e11 8.78518e10i 2.02027 0.656454i
\(169\) −1.33612e11 −0.969195
\(170\) −1.46463e10 + 3.28965e10i −0.103153 + 0.231689i
\(171\) 5.81064e11i 3.97414i
\(172\) −1.82709e11 + 1.64515e11i −1.21372 + 1.09286i
\(173\) 8.02780e10 0.518043 0.259022 0.965872i \(-0.416600\pi\)
0.259022 + 0.965872i \(0.416600\pi\)
\(174\) 1.39097e11 + 6.19290e10i 0.872108 + 0.388283i
\(175\) 3.77631e10i 0.230079i
\(176\) −2.16328e11 2.27331e10i −1.28100 0.134616i
\(177\) −2.10887e11 −1.21390
\(178\) 4.89707e10 1.09991e11i 0.274054 0.615543i
\(179\) 6.51569e10i 0.354565i 0.984160 + 0.177282i \(0.0567306\pi\)
−0.984160 + 0.177282i \(0.943269\pi\)
\(180\) −1.36255e11 1.51324e11i −0.721089 0.800837i
\(181\) −3.13027e11 −1.61135 −0.805673 0.592360i \(-0.798196\pi\)
−0.805673 + 0.592360i \(0.798196\pi\)
\(182\) 3.68337e10 + 1.63992e10i 0.184454 + 0.0821232i
\(183\) 3.57628e11i 1.74251i
\(184\) 4.46360e10 + 1.37369e11i 0.211639 + 0.651330i
\(185\) 2.03717e10 0.0940088
\(186\) 1.69651e10 3.81046e10i 0.0762062 0.171164i
\(187\) 1.67033e11i 0.730455i
\(188\) −1.15054e11 + 1.03597e11i −0.489905 + 0.441121i
\(189\) −7.22159e11 −2.99450
\(190\) −1.66839e11 7.42808e10i −0.673800 0.299991i
\(191\) 2.53418e11i 0.996942i −0.866906 0.498471i \(-0.833895\pi\)
0.866906 0.498471i \(-0.166105\pi\)
\(192\) 2.83203e11 + 3.89773e11i 1.08540 + 1.49385i
\(193\) −9.09625e9 −0.0339684 −0.0169842 0.999856i \(-0.505407\pi\)
−0.0169842 + 0.999856i \(0.505407\pi\)
\(194\) 1.78540e11 4.01011e11i 0.649720 1.45931i
\(195\) 4.08653e10i 0.144938i
\(196\) 6.25968e10 + 6.95196e10i 0.216407 + 0.240340i
\(197\) 3.36881e11 1.13539 0.567695 0.823239i \(-0.307835\pi\)
0.567695 + 0.823239i \(0.307835\pi\)
\(198\) 8.62880e11 + 3.84174e11i 2.83547 + 1.26242i
\(199\) 3.33901e11i 1.06992i 0.844877 + 0.534961i \(0.179674\pi\)
−0.844877 + 0.534961i \(0.820326\pi\)
\(200\) 6.08674e10 1.97779e10i 0.190210 0.0618059i
\(201\) 3.76792e11 1.14847
\(202\) −8.18851e10 + 1.83919e11i −0.243471 + 0.546852i
\(203\) 2.05027e11i 0.594744i
\(204\) −2.74939e11 + 2.47561e11i −0.778190 + 0.700698i
\(205\) 8.92307e10 0.246459
\(206\) −4.34096e11 1.93270e11i −1.17017 0.520988i
\(207\) 6.27201e11i 1.65027i
\(208\) −7.14146e9 + 6.79581e10i −0.0183430 + 0.174552i
\(209\) 8.47131e11 2.12432
\(210\) 1.57806e11 3.54443e11i 0.386392 0.867861i
\(211\) 3.03506e9i 0.00725696i −0.999993 0.00362848i \(-0.998845\pi\)
0.999993 0.00362848i \(-0.00115498\pi\)
\(212\) 2.54770e11 + 2.82946e11i 0.594935 + 0.660731i
\(213\) −2.18868e11 −0.499211
\(214\) 2.29484e11 + 1.02172e11i 0.511310 + 0.227647i
\(215\) 3.35549e11i 0.730404i
\(216\) −3.78221e11 1.16399e12i −0.804409 2.47560i
\(217\) 5.61657e10 0.116727
\(218\) −4.54258e10 + 1.02029e11i −0.0922613 + 0.207225i
\(219\) 1.37192e12i 2.72339i
\(220\) −2.20614e11 + 1.98645e11i −0.428075 + 0.385447i
\(221\) −5.24723e10 −0.0995333
\(222\) 1.91208e11 + 8.51302e10i 0.354602 + 0.157877i
\(223\) 6.58534e11i 1.19414i −0.802191 0.597068i \(-0.796332\pi\)
0.802191 0.597068i \(-0.203668\pi\)
\(224\) −3.24370e11 + 5.61855e11i −0.575176 + 0.996285i
\(225\) −2.77908e11 −0.481936
\(226\) −1.78453e11 + 4.00817e11i −0.302678 + 0.679835i
\(227\) 8.15148e11i 1.35241i 0.736715 + 0.676203i \(0.236376\pi\)
−0.736715 + 0.676203i \(0.763624\pi\)
\(228\) −1.25554e12 1.39439e12i −2.03778 2.26314i
\(229\) 3.19584e11 0.507467 0.253734 0.967274i \(-0.418341\pi\)
0.253734 + 0.967274i \(0.418341\pi\)
\(230\) 1.80087e11 + 8.01788e10i 0.279797 + 0.124572i
\(231\) 1.79969e12i 2.73614i
\(232\) −3.30466e11 + 1.07380e11i −0.491685 + 0.159765i
\(233\) 4.24100e11 0.617573 0.308786 0.951131i \(-0.400077\pi\)
0.308786 + 0.951131i \(0.400077\pi\)
\(234\) 1.20686e11 2.71068e11i 0.172019 0.386366i
\(235\) 2.11299e11i 0.294820i
\(236\) 3.57648e11 3.22034e11i 0.488535 0.439887i
\(237\) −2.05811e12 −2.75250
\(238\) −4.55116e11 2.02628e11i −0.595988 0.265348i
\(239\) 5.17807e11i 0.664016i 0.943277 + 0.332008i \(0.107726\pi\)
−0.943277 + 0.332008i \(0.892274\pi\)
\(240\) 6.53948e11 + 6.87209e10i 0.821272 + 0.0863044i
\(241\) 7.14203e11 0.878489 0.439244 0.898368i \(-0.355246\pi\)
0.439244 + 0.898368i \(0.355246\pi\)
\(242\) 2.22499e11 4.99747e11i 0.268072 0.602106i
\(243\) 1.54451e12i 1.82288i
\(244\) 5.46115e11 + 6.06511e11i 0.631444 + 0.701277i
\(245\) 1.27674e11 0.144634
\(246\) 8.37516e11 + 3.72882e11i 0.929646 + 0.413900i
\(247\) 2.66121e11i 0.289464i
\(248\) 2.94160e10 + 9.05290e10i 0.0313563 + 0.0965005i
\(249\) 1.32545e11 0.138473
\(250\) 3.55266e10 7.97951e10i 0.0363793 0.0817102i
\(251\) 1.25838e11i 0.126311i −0.998004 0.0631557i \(-0.979884\pi\)
0.998004 0.0631557i \(-0.0201165\pi\)
\(252\) 2.09353e12 1.88506e12i 2.06004 1.85491i
\(253\) −9.14394e11 −0.882126
\(254\) −3.75401e11 1.67138e11i −0.355081 0.158090i
\(255\) 5.04931e11i 0.468307i
\(256\) −1.07549e12 2.28563e11i −0.978155 0.207877i
\(257\) −9.33845e11 −0.832931 −0.416466 0.909151i \(-0.636731\pi\)
−0.416466 + 0.909151i \(0.636731\pi\)
\(258\) −1.40221e12 + 3.14945e12i −1.22663 + 2.75509i
\(259\) 2.81838e11i 0.241825i
\(260\) 6.24031e10 + 6.93045e10i 0.0525218 + 0.0583303i
\(261\) 1.50884e12 1.24578
\(262\) −2.56361e11 1.14138e11i −0.207656 0.0924535i
\(263\) 3.58314e10i 0.0284764i −0.999899 0.0142382i \(-0.995468\pi\)
0.999899 0.0142382i \(-0.00453231\pi\)
\(264\) −2.90078e12 + 9.42564e11i −2.26202 + 0.735007i
\(265\) 5.19636e11 0.397621
\(266\) 1.02766e12 2.30819e12i 0.771687 1.73326i
\(267\) 1.68826e12i 1.24418i
\(268\) −6.39011e11 + 5.75378e11i −0.462205 + 0.416178i
\(269\) 2.26680e12 1.60936 0.804678 0.593711i \(-0.202338\pi\)
0.804678 + 0.593711i \(0.202338\pi\)
\(270\) −1.52595e12 6.79390e11i −1.06346 0.473479i
\(271\) 1.16910e12i 0.799845i −0.916549 0.399922i \(-0.869037\pi\)
0.916549 0.399922i \(-0.130963\pi\)
\(272\) 8.82398e10 8.39690e11i 0.0592680 0.563994i
\(273\) 5.65362e11 0.372832
\(274\) 1.07920e12 2.42395e12i 0.698794 1.56954i
\(275\) 4.05161e11i 0.257611i
\(276\) 1.35523e12 + 1.50511e12i 0.846191 + 0.939773i
\(277\) 5.07340e11 0.311100 0.155550 0.987828i \(-0.450285\pi\)
0.155550 + 0.987828i \(0.450285\pi\)
\(278\) −7.40700e11 3.29777e11i −0.446086 0.198608i
\(279\) 4.13338e11i 0.244503i
\(280\) 2.73623e11 + 8.42087e11i 0.158987 + 0.489291i
\(281\) −3.17014e11 −0.180945 −0.0904727 0.995899i \(-0.528838\pi\)
−0.0904727 + 0.995899i \(0.528838\pi\)
\(282\) −8.82985e11 + 1.98324e12i −0.495117 + 1.11206i
\(283\) 1.42234e12i 0.783558i −0.920059 0.391779i \(-0.871860\pi\)
0.920059 0.391779i \(-0.128140\pi\)
\(284\) 3.71184e11 3.34221e11i 0.200908 0.180902i
\(285\) −2.56083e12 −1.36193
\(286\) −3.95189e11 1.75947e11i −0.206526 0.0919502i
\(287\) 1.23449e12i 0.633983i
\(288\) 4.13483e12 + 2.38712e12i 2.08687 + 1.20479i
\(289\) −1.36765e12 −0.678398
\(290\) −1.92884e11 + 4.33230e11i −0.0940387 + 0.211217i
\(291\) 6.15515e12i 2.94967i
\(292\) 2.09499e12 + 2.32668e12i 0.986887 + 1.09603i
\(293\) −2.22060e12 −1.02833 −0.514165 0.857691i \(-0.671898\pi\)
−0.514165 + 0.857691i \(0.671898\pi\)
\(294\) 1.19834e12 + 5.33530e11i 0.545562 + 0.242897i
\(295\) 6.56827e11i 0.293996i
\(296\) −4.54272e11 + 1.47609e11i −0.199921 + 0.0649611i
\(297\) 7.74806e12 3.35283
\(298\) 1.48166e12 3.32789e12i 0.630472 1.41608i
\(299\) 2.87251e11i 0.120200i
\(300\) 6.66903e11 6.00493e11i 0.274446 0.247117i
\(301\) −4.64225e12 −1.87887
\(302\) −3.59452e12 1.60036e12i −1.43089 0.637066i
\(303\) 2.82299e12i 1.10534i
\(304\) 4.25861e12 + 4.47521e11i 1.64021 + 0.172364i
\(305\) 1.11387e12 0.422022
\(306\) −1.49119e12 + 3.34932e12i −0.555811 + 1.24839i
\(307\) 9.58563e11i 0.351503i 0.984435 + 0.175751i \(0.0562355\pi\)
−0.984435 + 0.175751i \(0.943765\pi\)
\(308\) −2.74822e12 3.05215e12i −0.991510 1.10116i
\(309\) −6.66297e12 −2.36524
\(310\) 1.18681e11 + 5.28393e10i 0.0414544 + 0.0184565i
\(311\) 4.11550e12i 1.41456i 0.706934 + 0.707280i \(0.250078\pi\)
−0.706934 + 0.707280i \(0.749922\pi\)
\(312\) 2.96101e11 + 9.11263e11i 0.100154 + 0.308227i
\(313\) 8.45683e10 0.0281505 0.0140752 0.999901i \(-0.495520\pi\)
0.0140752 + 0.999901i \(0.495520\pi\)
\(314\) −1.80226e12 + 4.04799e12i −0.590431 + 1.32615i
\(315\) 3.84481e12i 1.23971i
\(316\) 3.49040e12 3.14283e12i 1.10775 0.997436i
\(317\) −3.02740e12 −0.945745 −0.472872 0.881131i \(-0.656783\pi\)
−0.472872 + 0.881131i \(0.656783\pi\)
\(318\) 4.87728e12 + 2.17148e12i 1.49983 + 0.667760i
\(319\) 2.19974e12i 0.665912i
\(320\) −1.21399e12 + 8.82063e11i −0.361796 + 0.262875i
\(321\) 3.52237e12 1.03350
\(322\) −1.10926e12 + 2.49146e12i −0.320445 + 0.719739i
\(323\) 3.28819e12i 0.935285i
\(324\) −5.72644e12 6.35974e12i −1.60383 1.78121i
\(325\) 1.27279e11 0.0351026
\(326\) 4.76540e10 + 2.12167e10i 0.0129423 + 0.00576221i
\(327\) 1.56605e12i 0.418859i
\(328\) −1.98977e12 + 6.46546e11i −0.524124 + 0.170306i
\(329\) −2.92327e12 −0.758385
\(330\) −1.69311e12 + 3.80283e12i −0.432628 + 0.971711i
\(331\) 3.58363e12i 0.901951i −0.892536 0.450975i \(-0.851076\pi\)
0.892536 0.450975i \(-0.148924\pi\)
\(332\) −2.24786e11 + 2.02402e11i −0.0557286 + 0.0501792i
\(333\) 2.07412e12 0.506538
\(334\) 6.54028e12 + 2.91188e12i 1.57349 + 0.700554i
\(335\) 1.17355e12i 0.278150i
\(336\) −9.50740e11 + 9.04723e12i −0.222006 + 2.11261i
\(337\) 7.53391e12 1.73329 0.866645 0.498926i \(-0.166272\pi\)
0.866645 + 0.498926i \(0.166272\pi\)
\(338\) 1.73902e12 3.90594e12i 0.394203 0.885406i
\(339\) 6.15216e12i 1.37413i
\(340\) −7.71052e11 8.56325e11i −0.169703 0.188471i
\(341\) −6.02603e11 −0.130695
\(342\) −1.69866e13 7.56281e12i −3.63057 1.61641i
\(343\) 3.69524e12i 0.778344i
\(344\) −2.43131e12 7.48247e12i −0.504718 1.55329i
\(345\) 2.76416e12 0.565546
\(346\) −1.04485e12 + 2.34681e12i −0.210705 + 0.473257i
\(347\) 3.87583e12i 0.770401i 0.922833 + 0.385201i \(0.125868\pi\)
−0.922833 + 0.385201i \(0.874132\pi\)
\(348\) −3.62081e12 + 3.26025e12i −0.709429 + 0.638784i
\(349\) 6.88957e12 1.33065 0.665327 0.746552i \(-0.268292\pi\)
0.665327 + 0.746552i \(0.268292\pi\)
\(350\) 1.10395e12 + 4.91504e11i 0.210188 + 0.0935808i
\(351\) 2.43401e12i 0.456863i
\(352\) 3.48017e12 6.02815e12i 0.644003 1.11550i
\(353\) 1.22636e12 0.223741 0.111870 0.993723i \(-0.464316\pi\)
0.111870 + 0.993723i \(0.464316\pi\)
\(354\) 2.74478e12 6.16496e12i 0.493733 1.10895i
\(355\) 6.81685e11i 0.120904i
\(356\) 2.57806e12 + 2.86317e12i 0.450861 + 0.500723i
\(357\) −6.98561e12 −1.20466
\(358\) −1.90477e12 8.48047e11i −0.323912 0.144213i
\(359\) 1.09523e13i 1.83667i 0.395802 + 0.918336i \(0.370467\pi\)
−0.395802 + 0.918336i \(0.629533\pi\)
\(360\) 6.19713e12 2.01366e12i 1.02489 0.333023i
\(361\) −1.05455e13 −1.72000
\(362\) 4.07419e12 9.15088e12i 0.655387 1.47204i
\(363\) 7.67065e12i 1.21702i
\(364\) −9.58813e11 + 8.63335e11i −0.150047 + 0.135105i
\(365\) 4.27299e12 0.659580
\(366\) 1.04547e13 + 4.65469e12i 1.59187 + 0.708737i
\(367\) 7.38135e12i 1.10868i −0.832291 0.554339i \(-0.812971\pi\)
0.832291 0.554339i \(-0.187029\pi\)
\(368\) −4.59675e12 4.83055e11i −0.681101 0.0715744i
\(369\) 9.08491e12 1.32797
\(370\) −2.65147e11 + 5.95536e11i −0.0382364 + 0.0858814i
\(371\) 7.18905e12i 1.02283i
\(372\) 8.93123e11 + 9.91896e11i 0.125371 + 0.139236i
\(373\) 5.26643e12 0.729411 0.364705 0.931123i \(-0.381170\pi\)
0.364705 + 0.931123i \(0.381170\pi\)
\(374\) 4.88295e12 + 2.17400e12i 0.667305 + 0.297100i
\(375\) 1.22478e12i 0.165159i
\(376\) −1.53102e12 4.71179e12i −0.203724 0.626970i
\(377\) −6.91033e11 −0.0907386
\(378\) 9.39923e12 2.11113e13i 1.21796 2.73562i
\(379\) 6.22868e12i 0.796527i 0.917271 + 0.398263i \(0.130387\pi\)
−0.917271 + 0.398263i \(0.869613\pi\)
\(380\) 4.34298e12 3.91051e12i 0.548112 0.493531i
\(381\) −5.76206e12 −0.717717
\(382\) 7.40828e12 + 3.29834e12i 0.910754 + 0.405489i
\(383\) 3.30387e12i 0.400893i −0.979705 0.200447i \(-0.935761\pi\)
0.979705 0.200447i \(-0.0642394\pi\)
\(384\) −1.50805e13 + 3.20594e12i −1.80617 + 0.383972i
\(385\) −5.60532e12 −0.662670
\(386\) 1.18392e11 2.65915e11i 0.0138161 0.0310318i
\(387\) 3.41635e13i 3.93557i
\(388\) 9.39920e12 + 1.04387e13i 1.06889 + 1.18710i
\(389\) 2.72395e12 0.305809 0.152905 0.988241i \(-0.451137\pi\)
0.152905 + 0.988241i \(0.451137\pi\)
\(390\) 1.19463e12 + 5.31879e11i 0.132407 + 0.0589509i
\(391\) 3.54927e12i 0.388379i
\(392\) −2.84703e12 + 9.25097e11i −0.307582 + 0.0999440i
\(393\) −3.93490e12 −0.419731
\(394\) −4.38465e12 + 9.84820e12i −0.461800 + 1.03723i
\(395\) 6.41018e12i 0.666630i
\(396\) −2.24615e13 + 2.02248e13i −2.30655 + 2.07687i
\(397\) −5.16095e12 −0.523332 −0.261666 0.965158i \(-0.584272\pi\)
−0.261666 + 0.965158i \(0.584272\pi\)
\(398\) −9.76110e12 4.34587e12i −0.977425 0.435172i
\(399\) 3.54286e13i 3.50339i
\(400\) −2.14038e11 + 2.03678e12i −0.0209022 + 0.198905i
\(401\) 6.09489e12 0.587820 0.293910 0.955833i \(-0.405043\pi\)
0.293910 + 0.955833i \(0.405043\pi\)
\(402\) −4.90411e12 + 1.10149e13i −0.467122 + 1.04919i
\(403\) 1.89304e11i 0.0178088i
\(404\) −4.31083e12 4.78758e12i −0.400547 0.444845i
\(405\) −1.16798e13 −1.07191
\(406\) −5.99365e12 2.66851e12i −0.543327 0.241902i
\(407\) 3.02385e12i 0.270762i
\(408\) −3.65862e12 1.12595e13i −0.323606 0.995910i
\(409\) 8.94937e12 0.781944 0.390972 0.920402i \(-0.372139\pi\)
0.390972 + 0.920402i \(0.372139\pi\)
\(410\) −1.16138e12 + 2.60853e12i −0.100243 + 0.225152i
\(411\) 3.72054e13i 3.17247i
\(412\) 1.12999e13 1.01747e13i 0.951894 0.857105i
\(413\) 9.08707e12 0.756264
\(414\) 1.83353e13 + 8.16330e12i 1.50760 + 0.671219i
\(415\) 4.12823e11i 0.0335369i
\(416\) −1.89370e12 1.09327e12i −0.152001 0.0877532i
\(417\) −1.13690e13 −0.901662
\(418\) −1.10258e13 + 2.47646e13i −0.864029 + 1.94066i
\(419\) 1.32772e13i 1.02810i 0.857759 + 0.514052i \(0.171856\pi\)
−0.857759 + 0.514052i \(0.828144\pi\)
\(420\) 8.30770e12 + 9.22647e12i 0.635674 + 0.705975i
\(421\) −1.16418e13 −0.880258 −0.440129 0.897935i \(-0.645067\pi\)
−0.440129 + 0.897935i \(0.645067\pi\)
\(422\) 8.87254e10 + 3.95026e10i 0.00662957 + 0.00295164i
\(423\) 2.15131e13i 1.58855i
\(424\) −1.15875e13 + 3.76516e12i −0.845588 + 0.274761i
\(425\) −1.57266e12 −0.113420
\(426\) 2.84866e12 6.39827e12i 0.203045 0.456052i
\(427\) 1.54101e13i 1.08559i
\(428\) −5.97368e12 + 5.37882e12i −0.415933 + 0.374514i
\(429\) −6.06579e12 −0.417446
\(430\) −9.80927e12 4.36732e12i −0.667259 0.297079i
\(431\) 1.70572e13i 1.14689i 0.819245 + 0.573443i \(0.194393\pi\)
−0.819245 + 0.573443i \(0.805607\pi\)
\(432\) 3.89503e13 + 4.09314e12i 2.58876 + 0.272043i
\(433\) 1.59244e13 1.04622 0.523110 0.852265i \(-0.324772\pi\)
0.523110 + 0.852265i \(0.324772\pi\)
\(434\) −7.31021e11 + 1.64192e12i −0.0474768 + 0.106636i
\(435\) 6.64968e12i 0.426928i
\(436\) −2.39143e12 2.65591e12i −0.151784 0.168570i
\(437\) 1.80007e13 1.12949
\(438\) 4.01061e13 + 1.78562e13i 2.48794 + 1.10769i
\(439\) 6.37376e12i 0.390907i −0.980713 0.195453i \(-0.937382\pi\)
0.980713 0.195453i \(-0.0626178\pi\)
\(440\) −2.93571e12 9.03477e12i −0.178012 0.547840i
\(441\) 1.29990e13 0.779320
\(442\) 6.82950e11 1.53395e12i 0.0404834 0.0909284i
\(443\) 2.35727e13i 1.38163i −0.723032 0.690815i \(-0.757252\pi\)
0.723032 0.690815i \(-0.242748\pi\)
\(444\) −4.97731e12 + 4.48167e12i −0.288456 + 0.259732i
\(445\) 5.25827e12 0.301330
\(446\) 1.92513e13 + 8.57111e12i 1.09090 + 0.485694i
\(447\) 5.10800e13i 2.86229i
\(448\) −1.22032e13 1.67953e13i −0.676211 0.930672i
\(449\) −1.03415e13 −0.566700 −0.283350 0.959017i \(-0.591446\pi\)
−0.283350 + 0.959017i \(0.591446\pi\)
\(450\) 3.61710e12 8.12424e12i 0.196019 0.440271i
\(451\) 1.32449e13i 0.709846i
\(452\) −9.39464e12 1.04336e13i −0.497952 0.553022i
\(453\) −5.51725e13 −2.89222
\(454\) −2.38296e13 1.06095e13i −1.23549 0.550068i
\(455\) 1.76088e12i 0.0902967i
\(456\) 5.71045e13 1.85552e13i 2.89631 0.941113i
\(457\) −3.19521e13 −1.60294 −0.801471 0.598033i \(-0.795949\pi\)
−0.801471 + 0.598033i \(0.795949\pi\)
\(458\) −4.15953e12 + 9.34258e12i −0.206404 + 0.463596i
\(459\) 3.00745e13i 1.47617i
\(460\) −4.68782e12 + 4.22100e12i −0.227605 + 0.204940i
\(461\) 1.06085e13 0.509508 0.254754 0.967006i \(-0.418005\pi\)
0.254754 + 0.967006i \(0.418005\pi\)
\(462\) −5.26114e13 2.34238e13i −2.49960 1.11288i
\(463\) 1.01429e13i 0.476715i −0.971178 0.238357i \(-0.923391\pi\)
0.971178 0.238357i \(-0.0766089\pi\)
\(464\) 1.16207e12 1.10583e13i 0.0540311 0.514159i
\(465\) 1.82163e12 0.0837908
\(466\) −5.51984e12 + 1.23979e13i −0.251187 + 0.564182i
\(467\) 1.20631e13i 0.543094i −0.962425 0.271547i \(-0.912465\pi\)
0.962425 0.271547i \(-0.0875353\pi\)
\(468\) 6.35350e12 + 7.05615e12i 0.282998 + 0.314296i
\(469\) −1.62359e13 −0.715504
\(470\) −6.17700e12 2.75014e12i −0.269332 0.119913i
\(471\) 6.21329e13i 2.68051i
\(472\) 4.75923e12 + 1.46467e13i 0.203154 + 0.625217i
\(473\) 4.98068e13 2.10370
\(474\) 2.67872e13 6.01658e13i 1.11953 2.51454i
\(475\) 7.97596e12i 0.329849i
\(476\) 1.18471e13 1.06674e13i 0.484816 0.436538i
\(477\) 5.29060e13 2.14246
\(478\) −1.51373e13 6.73949e12i −0.606610 0.270077i
\(479\) 1.51493e13i 0.600781i −0.953816 0.300390i \(-0.902883\pi\)
0.953816 0.300390i \(-0.0971169\pi\)
\(480\) −1.05204e13 + 1.82228e13i −0.412881 + 0.715168i
\(481\) −9.49923e11 −0.0368946
\(482\) −9.29566e12 + 2.08787e13i −0.357310 + 0.802541i
\(483\) 3.82416e13i 1.45479i
\(484\) 1.17134e13 + 1.30089e13i 0.441019 + 0.489792i
\(485\) 1.91708e13 0.714385
\(486\) −4.51513e13 2.01024e13i −1.66529 0.741425i
\(487\) 1.23333e13i 0.450232i 0.974332 + 0.225116i \(0.0722761\pi\)
−0.974332 + 0.225116i \(0.927724\pi\)
\(488\) −2.48384e13 + 8.07085e12i −0.897479 + 0.291622i
\(489\) 7.31444e11 0.0261600
\(490\) −1.66173e12 + 3.73236e12i −0.0588275 + 0.132130i
\(491\) 2.24401e13i 0.786353i −0.919463 0.393176i \(-0.871376\pi\)
0.919463 0.393176i \(-0.128624\pi\)
\(492\) −2.18013e13 + 1.96303e13i −0.756235 + 0.680929i
\(493\) 8.53839e12 0.293185
\(494\) 7.77965e12 + 3.46368e12i 0.264439 + 0.117734i
\(495\) 4.12510e13i 1.38806i
\(496\) −3.02934e12 3.18342e11i −0.100911 0.0106044i
\(497\) 9.43098e12 0.311010
\(498\) −1.72513e12 + 3.87474e12i −0.0563215 + 0.126502i
\(499\) 3.09195e13i 0.999378i −0.866205 0.499689i \(-0.833448\pi\)
0.866205 0.499689i \(-0.166552\pi\)
\(500\) 1.87030e12 + 2.07714e12i 0.0598495 + 0.0664684i
\(501\) 1.00387e14 3.18046
\(502\) 3.67868e12 + 1.63784e12i 0.115391 + 0.0513750i
\(503\) 5.50005e13i 1.70815i 0.520147 + 0.854077i \(0.325877\pi\)
−0.520147 + 0.854077i \(0.674123\pi\)
\(504\) 2.78586e13 + 8.57361e13i 0.856657 + 2.63640i
\(505\) −8.79247e12 −0.267703
\(506\) 1.19012e13 2.67310e13i 0.358790 0.805864i
\(507\) 5.99526e13i 1.78965i
\(508\) 9.77203e12 8.79894e12i 0.288846 0.260083i
\(509\) −6.10086e13 −1.78567 −0.892836 0.450381i \(-0.851288\pi\)
−0.892836 + 0.450381i \(0.851288\pi\)
\(510\) −1.47609e13 6.57189e12i −0.427821 0.190476i
\(511\) 5.91159e13i 1.69668i
\(512\) 2.06797e13 2.84656e13i 0.587753 0.809041i
\(513\) −1.52527e14 −4.29300
\(514\) 1.21544e13 2.72996e13i 0.338780 0.760922i
\(515\) 2.07525e13i 0.572840i
\(516\) −7.38191e13 8.19830e13i −2.01800 2.24117i
\(517\) 3.13639e13 0.849135
\(518\) −8.23912e12 3.66825e12i −0.220918 0.0983580i
\(519\) 3.60213e13i 0.956583i
\(520\) −2.83822e12 + 9.22235e11i −0.0746498 + 0.0242563i
\(521\) −5.32796e13 −1.38795 −0.693973 0.720001i \(-0.744141\pi\)
−0.693973 + 0.720001i \(0.744141\pi\)
\(522\) −1.96383e13 + 4.41088e13i −0.506699 + 1.13808i
\(523\) 5.41769e13i 1.38454i 0.721638 + 0.692271i \(0.243390\pi\)
−0.721638 + 0.692271i \(0.756610\pi\)
\(524\) 6.67330e12 6.00878e12i 0.168921 0.152100i
\(525\) 1.69446e13 0.424849
\(526\) 1.04748e12 + 4.66362e11i 0.0260145 + 0.0115823i
\(527\) 2.33904e12i 0.0575419i
\(528\) 1.02005e13 9.70680e13i 0.248572 2.36541i
\(529\) 2.19966e13 0.530978
\(530\) −6.76329e12 + 1.51908e13i −0.161725 + 0.363246i
\(531\) 6.68741e13i 1.58411i
\(532\) 5.41010e13 + 6.00842e13i 1.26954 + 1.40995i
\(533\) −4.16079e12 −0.0967251
\(534\) 4.93539e13 + 2.19735e13i 1.13662 + 0.506050i
\(535\) 1.09708e13i 0.250304i
\(536\) −8.50332e12 2.61693e13i −0.192205 0.591519i
\(537\) −2.92364e13 −0.654715
\(538\) −2.95034e13 + 6.62666e13i −0.654578 + 1.47022i
\(539\) 1.89511e13i 0.416573i
\(540\) 3.97219e13 3.57664e13i 0.865090 0.778945i
\(541\) −8.90533e13 −1.92160 −0.960801 0.277239i \(-0.910581\pi\)
−0.960801 + 0.277239i \(0.910581\pi\)
\(542\) 3.41769e13 + 1.52164e13i 0.730696 + 0.325323i
\(543\) 1.40457e14i 2.97540i
\(544\) 2.33986e13 + 1.35085e13i 0.491129 + 0.283539i
\(545\) −4.87762e12 −0.101444
\(546\) −7.35844e12 + 1.65275e13i −0.151643 + 0.340600i
\(547\) 6.79396e13i 1.38735i 0.720287 + 0.693676i \(0.244010\pi\)
−0.720287 + 0.693676i \(0.755990\pi\)
\(548\) 5.68144e13 + 6.30977e13i 1.14962 + 1.27676i
\(549\) 1.13407e14 2.27394
\(550\) −1.18443e13 5.27335e12i −0.235340 0.104779i
\(551\) 4.33037e13i 0.852643i
\(552\) −6.16386e13 + 2.00285e13i −1.20270 + 0.390799i
\(553\) 8.86836e13 1.71482
\(554\) −6.60326e12 + 1.48313e13i −0.126535 + 0.284205i
\(555\) 9.14092e12i 0.173590i
\(556\) 1.92811e13 1.73611e13i 0.362875 0.326740i
\(557\) −3.38104e13 −0.630630 −0.315315 0.948987i \(-0.602110\pi\)
−0.315315 + 0.948987i \(0.602110\pi\)
\(558\) 1.20833e13 + 5.37977e12i 0.223365 + 0.0994473i
\(559\) 1.56465e13i 0.286654i
\(560\) −2.81785e13 2.96117e12i −0.511656 0.0537680i
\(561\) 7.49488e13 1.34881
\(562\) 4.12608e12 9.26744e12i 0.0735964 0.165302i
\(563\) 8.00894e13i 1.41590i −0.706262 0.707951i \(-0.749620\pi\)
0.706262 0.707951i \(-0.250380\pi\)
\(564\) −4.64847e13 5.16255e13i −0.814543 0.904626i
\(565\) −1.91615e13 −0.332803
\(566\) 4.15800e13 + 1.85124e13i 0.715817 + 0.318699i
\(567\) 1.61587e14i 2.75735i
\(568\) 4.93934e12 + 1.52010e13i 0.0835463 + 0.257117i
\(569\) −2.99622e13 −0.502357 −0.251178 0.967941i \(-0.580818\pi\)
−0.251178 + 0.967941i \(0.580818\pi\)
\(570\) 3.33303e13 7.48620e13i 0.553943 1.24419i
\(571\) 2.15663e13i 0.355300i 0.984094 + 0.177650i \(0.0568495\pi\)
−0.984094 + 0.177650i \(0.943150\pi\)
\(572\) 1.02871e13 9.26274e12i 0.168002 0.151272i
\(573\) 1.13710e14 1.84088
\(574\) −3.60884e13 1.60674e13i −0.579173 0.257861i
\(575\) 8.60926e12i 0.136970i
\(576\) −1.23601e14 + 8.98061e13i −1.94943 + 1.41643i
\(577\) −4.63163e13 −0.724194 −0.362097 0.932141i \(-0.617939\pi\)
−0.362097 + 0.932141i \(0.617939\pi\)
\(578\) 1.78005e13 3.99811e13i 0.275927 0.619749i
\(579\) 4.08155e12i 0.0627238i
\(580\) −1.01544e13 1.12774e13i −0.154708 0.171818i
\(581\) −5.71132e12 −0.0862692
\(582\) 1.79937e14 + 8.01120e13i 2.69466 + 1.19973i
\(583\) 7.71315e13i 1.14522i
\(584\) −9.52842e13 + 3.09611e13i −1.40267 + 0.455777i
\(585\) 1.29587e13 0.189140
\(586\) 2.89021e13 6.49160e13i 0.418256 0.939429i
\(587\) 1.79638e13i 0.257755i −0.991660 0.128878i \(-0.958863\pi\)
0.991660 0.128878i \(-0.0411375\pi\)
\(588\) −3.11939e13 + 2.80876e13i −0.443796 + 0.399603i
\(589\) 1.18628e13 0.167344
\(590\) 1.92014e13 + 8.54890e12i 0.268579 + 0.119578i
\(591\) 1.51161e14i 2.09653i
\(592\) 1.59743e12 1.52012e13i 0.0219692 0.209059i
\(593\) −4.08145e13 −0.556597 −0.278298 0.960495i \(-0.589770\pi\)
−0.278298 + 0.960495i \(0.589770\pi\)
\(594\) −1.00844e14 + 2.26503e14i −1.36370 + 3.06296i
\(595\) 2.17574e13i 0.291757i
\(596\) 7.80016e13 + 8.66280e13i 1.03722 + 1.15193i
\(597\) −1.49824e14 −1.97565
\(598\) −8.39736e12 3.73870e12i −0.109809 0.0488894i
\(599\) 8.40892e13i 1.09045i −0.838289 0.545226i \(-0.816444\pi\)
0.838289 0.545226i \(-0.183556\pi\)
\(600\) 8.87448e12 + 2.73116e13i 0.114127 + 0.351230i
\(601\) −4.22110e13 −0.538336 −0.269168 0.963093i \(-0.586749\pi\)
−0.269168 + 0.963093i \(0.586749\pi\)
\(602\) 6.04209e13 1.35709e14i 0.764196 1.71643i
\(603\) 1.19484e14i 1.49873i
\(604\) 9.35686e13 8.42510e13i 1.16398 1.04807i
\(605\) 2.38910e13 0.294752
\(606\) −8.25258e13 3.67424e13i −1.00978 0.449577i
\(607\) 2.70801e13i 0.328630i 0.986408 + 0.164315i \(0.0525414\pi\)
−0.986408 + 0.164315i \(0.947459\pi\)
\(608\) −6.85103e13 + 1.18669e14i −0.824590 + 1.42830i
\(609\) −9.19969e13 −1.09821
\(610\) −1.44975e13 + 3.25623e13i −0.171650 + 0.385537i
\(611\) 9.85276e12i 0.115705i
\(612\) −7.85037e13 8.71857e13i −0.914394 1.01552i
\(613\) 9.95572e13 1.15019 0.575096 0.818086i \(-0.304965\pi\)
0.575096 + 0.818086i \(0.304965\pi\)
\(614\) −2.80222e13 1.24761e13i −0.321114 0.142968i
\(615\) 4.00384e13i 0.455094i
\(616\) 1.24994e14 4.06149e13i 1.40924 0.457912i
\(617\) −1.74652e14 −1.95320 −0.976600 0.215062i \(-0.931005\pi\)
−0.976600 + 0.215062i \(0.931005\pi\)
\(618\) 8.67215e13 1.94782e14i 0.962020 2.16076i
\(619\) 4.05398e13i 0.446096i −0.974807 0.223048i \(-0.928399\pi\)
0.974807 0.223048i \(-0.0716007\pi\)
\(620\) −3.08936e12 + 2.78172e12i −0.0337217 + 0.0303637i
\(621\) 1.64638e14 1.78268
\(622\) −1.20311e14 5.35651e13i −1.29227 0.575347i
\(623\) 7.27470e13i 0.775131i
\(624\) −3.04933e13 3.20443e12i −0.322316 0.0338709i
\(625\) 3.81470e12 0.0400000
\(626\) −1.10069e12 + 2.47223e12i −0.0114497 + 0.0257168i
\(627\) 3.80114e14i 3.92262i
\(628\) −9.48798e13 1.05373e14i −0.971349 1.07877i
\(629\) 1.17372e13 0.119210
\(630\) 1.12397e14 + 5.00418e13i 1.13254 + 0.504232i
\(631\) 7.81000e13i 0.780737i 0.920659 + 0.390368i \(0.127652\pi\)
−0.920659 + 0.390368i \(0.872348\pi\)
\(632\) 4.64468e13 + 1.42942e14i 0.460649 + 1.41767i
\(633\) 1.36185e12 0.0134002
\(634\) 3.94030e13 8.85016e13i 0.384665 0.863983i
\(635\) 1.79465e13i 0.173825i
\(636\) −1.26960e14 + 1.14317e14i −1.22006 + 1.09857i
\(637\) −5.95337e12 −0.0567631
\(638\) 6.43060e13 + 2.86305e13i 0.608342 + 0.270848i
\(639\) 6.94049e13i 0.651458i
\(640\) −9.98521e12 4.69695e13i −0.0929946 0.437438i
\(641\) −6.92002e13 −0.639466 −0.319733 0.947508i \(-0.603593\pi\)
−0.319733 + 0.947508i \(0.603593\pi\)
\(642\) −4.58452e13 + 1.02971e14i −0.420357 + 0.944149i
\(643\) 9.07760e13i 0.825878i −0.910759 0.412939i \(-0.864502\pi\)
0.910759 0.412939i \(-0.135498\pi\)
\(644\) −5.83967e13 6.48550e13i −0.527180 0.585483i
\(645\) −1.50563e14 −1.34871
\(646\) −9.61252e13 4.27972e13i −0.854427 0.380411i
\(647\) 2.15102e14i 1.89724i −0.316413 0.948621i \(-0.602479\pi\)
0.316413 0.948621i \(-0.397521\pi\)
\(648\) 2.60450e14 8.46291e13i 2.27955 0.740704i
\(649\) −9.74954e13 −0.846760
\(650\) −1.65659e12 + 3.72081e12i −0.0142774 + 0.0320679i
\(651\) 2.52019e13i 0.215541i
\(652\) −1.24048e12 + 1.11695e12i −0.0105281 + 0.00947972i
\(653\) 1.02504e14 0.863330 0.431665 0.902034i \(-0.357926\pi\)
0.431665 + 0.902034i \(0.357926\pi\)
\(654\) −4.57812e13 2.03829e13i −0.382647 0.170363i
\(655\) 1.22556e13i 0.101655i
\(656\) 6.99697e12 6.65831e13i 0.0575958 0.548081i
\(657\) 4.35049e14 3.55395
\(658\) 3.80477e13 8.54575e13i 0.308460 0.692821i
\(659\) 1.36237e14i 1.09615i 0.836430 + 0.548074i \(0.184639\pi\)
−0.836430 + 0.548074i \(0.815361\pi\)
\(660\) −8.91335e13 9.89910e13i −0.711740 0.790453i
\(661\) 9.24829e13 0.732916 0.366458 0.930435i \(-0.380570\pi\)
0.366458 + 0.930435i \(0.380570\pi\)
\(662\) 1.04762e14 + 4.66425e13i 0.823975 + 0.366853i
\(663\) 2.35447e13i 0.183791i
\(664\) −2.99122e12 9.20562e12i −0.0231744 0.0713202i
\(665\) 1.10346e14 0.848491
\(666\) −2.69956e13 + 6.06338e13i −0.206026 + 0.462747i
\(667\) 4.67421e13i 0.354062i
\(668\) −1.70249e14 + 1.53296e14i −1.27998 + 1.15252i
\(669\) 2.95489e14 2.20501
\(670\) −3.43071e13 1.52743e13i −0.254103 0.113133i
\(671\) 1.65336e14i 1.21550i
\(672\) −2.52108e14 1.45547e14i −1.83967 1.06208i
\(673\) 1.84677e13 0.133763 0.0668816 0.997761i \(-0.478695\pi\)
0.0668816 + 0.997761i \(0.478695\pi\)
\(674\) −9.80572e13 + 2.20243e14i −0.704985 + 1.58344i
\(675\) 7.29500e13i 0.520603i
\(676\) 9.15503e13 + 1.01675e14i 0.648525 + 0.720247i
\(677\) 2.46456e14 1.73299 0.866497 0.499183i \(-0.166366\pi\)
0.866497 + 0.499183i \(0.166366\pi\)
\(678\) −1.79849e14 8.00731e13i −1.25534 0.558905i
\(679\) 2.65224e14i 1.83766i
\(680\) 3.50690e13 1.13951e13i 0.241201 0.0783744i
\(681\) −3.65763e14 −2.49726
\(682\) 7.84314e12 1.76162e13i 0.0531580 0.119396i
\(683\) 1.59101e13i 0.107046i −0.998567 0.0535228i \(-0.982955\pi\)
0.998567 0.0535228i \(-0.0170450\pi\)
\(684\) 4.42175e14 3.98143e14i 2.95334 2.65925i
\(685\) 1.15880e14 0.768344
\(686\) 1.08025e14 + 4.80951e13i 0.711054 + 0.316578i
\(687\) 1.43400e14i 0.937055i
\(688\) 2.50384e14 + 2.63119e13i 1.62429 + 0.170691i
\(689\) −2.42304e13 −0.156050
\(690\) −3.59768e13 + 8.08062e13i −0.230026 + 0.516653i
\(691\) 1.99068e14i 1.26360i −0.775130 0.631801i \(-0.782316\pi\)
0.775130 0.631801i \(-0.217684\pi\)
\(692\) −5.50062e13 6.10895e13i −0.346642 0.384978i
\(693\) −5.70699e14 −3.57060
\(694\) −1.13304e14 5.04456e13i −0.703798 0.313347i
\(695\) 3.54100e13i 0.218375i
\(696\) −4.81821e13 1.48282e14i −0.295012 0.907912i
\(697\) 5.14106e13 0.312528
\(698\) −8.96708e13 + 2.01406e14i −0.541220 + 1.21561i
\(699\) 1.90297e14i 1.14037i
\(700\) −2.87368e13 + 2.58752e13i −0.170981 + 0.153955i
\(701\) −2.55726e14 −1.51072 −0.755362 0.655308i \(-0.772539\pi\)
−0.755362 + 0.655308i \(0.772539\pi\)
\(702\) 7.11545e13 + 3.16797e13i 0.417366 + 0.185821i
\(703\) 5.95271e13i 0.346687i
\(704\) 1.30928e14 + 1.80197e14i 0.757128 + 1.04204i
\(705\) −9.48112e13 −0.544395
\(706\) −1.59616e13 + 3.58508e13i −0.0910026 + 0.204398i
\(707\) 1.21642e14i 0.688631i
\(708\) 1.44499e14 + 1.60479e14i 0.812265 + 0.902096i
\(709\) −1.47763e14 −0.824774 −0.412387 0.911009i \(-0.635305\pi\)
−0.412387 + 0.911009i \(0.635305\pi\)
\(710\) 1.99281e13 + 8.87244e12i 0.110452 + 0.0491758i
\(711\) 6.52645e14i 3.59194i
\(712\) −1.17255e14 + 3.81002e13i −0.640814 + 0.208222i
\(713\) −1.28047e13 −0.0694898
\(714\) 9.09208e13 2.04214e14i 0.489973 1.10051i
\(715\) 1.88925e13i 0.101102i
\(716\) 4.95828e13 4.46453e13i 0.263491 0.237252i
\(717\) −2.32344e14 −1.22613
\(718\) −3.20173e14 1.42549e14i −1.67789 0.747034i
\(719\) 1.18505e14i 0.616724i 0.951269 + 0.308362i \(0.0997808\pi\)
−0.951269 + 0.308362i \(0.900219\pi\)
\(720\) −2.17920e13 + 2.07373e14i −0.112625 + 1.07174i
\(721\) 2.87106e14 1.47355
\(722\) 1.37254e14 3.08281e14i 0.699581 1.57130i
\(723\) 3.20468e14i 1.62216i
\(724\) 2.14485e14 + 2.38205e14i 1.07821 + 1.19745i
\(725\) −2.07111e13 −0.103398
\(726\) 2.24240e14 + 9.98368e13i 1.11181 + 0.495003i
\(727\) 6.63470e13i 0.326700i 0.986568 + 0.163350i \(0.0522300\pi\)
−0.986568 + 0.163350i \(0.947770\pi\)
\(728\) −1.27589e13 3.92662e13i −0.0623961 0.192027i
\(729\) −1.99536e14 −0.969135
\(730\) −5.56148e13 + 1.24914e14i −0.268273 + 0.602557i
\(731\) 1.93328e14i 0.926206i
\(732\) −2.72146e14 + 2.45046e14i −1.29493 + 1.16598i
\(733\) 8.24457e13 0.389626 0.194813 0.980840i \(-0.437590\pi\)
0.194813 + 0.980840i \(0.437590\pi\)
\(734\) 2.15783e14 + 9.60716e13i 1.01283 + 0.450936i
\(735\) 5.72882e13i 0.267072i
\(736\) 7.39501e13 1.28092e14i 0.342413 0.593106i
\(737\) 1.74195e14 0.801122
\(738\) −1.18244e14 + 2.65584e14i −0.540129 + 1.21317i
\(739\) 3.99191e14i 1.81117i −0.424169 0.905583i \(-0.639434\pi\)
0.424169 0.905583i \(-0.360566\pi\)
\(740\) −1.39586e13 1.55023e13i −0.0629048 0.0698616i
\(741\) 1.19410e14 0.534504
\(742\) −2.10161e14 9.35687e13i −0.934401 0.416017i
\(743\) 4.95145e13i 0.218669i −0.994005 0.109335i \(-0.965128\pi\)
0.994005 0.109335i \(-0.0348720\pi\)
\(744\) −4.06210e13 + 1.31992e13i −0.178191 + 0.0579004i
\(745\) 1.59094e14 0.693221
\(746\) −6.85449e13 + 1.53956e14i −0.296675 + 0.666351i
\(747\) 4.20311e13i 0.180704i
\(748\) −1.27108e14 + 1.14450e14i −0.542830 + 0.488775i
\(749\) −1.51778e14 −0.643873
\(750\) 3.58046e13 + 1.59411e13i 0.150880 + 0.0671755i
\(751\) 3.40765e14i 1.42645i 0.700936 + 0.713224i \(0.252766\pi\)
−0.700936 + 0.713224i \(0.747234\pi\)
\(752\) 1.57669e14 + 1.65689e13i 0.655628 + 0.0688975i
\(753\) 5.64643e13 0.233238
\(754\) 8.99410e12 2.02013e13i 0.0369063 0.0828940i
\(755\) 1.71840e14i 0.700471i
\(756\) 4.94821e14 + 5.49545e14i 2.00373 + 2.22533i
\(757\) 1.55318e14 0.624801 0.312401 0.949950i \(-0.398867\pi\)
0.312401 + 0.949950i \(0.398867\pi\)
\(758\) −1.82086e14 8.10691e13i −0.727665 0.323973i
\(759\) 4.10295e14i 1.62887i
\(760\) 5.77920e13 + 1.77857e14i 0.227929 + 0.701462i
\(761\) −3.51812e13 −0.137844 −0.0689220 0.997622i \(-0.521956\pi\)
−0.0689220 + 0.997622i \(0.521956\pi\)
\(762\) 7.49958e13 1.68445e14i 0.291919 0.655668i
\(763\) 6.74809e13i 0.260951i
\(764\) −1.92844e14 + 1.73641e14i −0.740866 + 0.667091i
\(765\) −1.60118e14 −0.611129
\(766\) 9.65837e13 + 4.30013e13i 0.366235 + 0.163056i
\(767\) 3.06276e13i 0.115381i
\(768\) 1.02558e14 4.82581e14i 0.383851 1.80619i
\(769\) 3.92216e14 1.45846 0.729229 0.684270i \(-0.239879\pi\)
0.729229 + 0.684270i \(0.239879\pi\)
\(770\) 7.29558e13 1.63863e14i 0.269529 0.605380i
\(771\) 4.19023e14i 1.53803i
\(772\) 6.23272e12 + 6.92201e12i 0.0227295 + 0.0252433i
\(773\) −7.38440e13 −0.267558 −0.133779 0.991011i \(-0.542711\pi\)
−0.133779 + 0.991011i \(0.542711\pi\)
\(774\) −9.98719e14 4.44653e14i −3.59533 1.60072i
\(775\) 5.67366e12i 0.0202934i
\(776\) −4.27494e14 + 1.38908e14i −1.51922 + 0.493648i
\(777\) −1.26463e14 −0.446537
\(778\) −3.54534e13 + 7.96306e13i −0.124383 + 0.279371i
\(779\) 2.60737e14i 0.908897i
\(780\) −3.10974e13 + 2.80007e13i −0.107709 + 0.0969832i
\(781\) −1.01185e14 −0.348226
\(782\) 1.03758e14 + 4.61953e13i 0.354802 + 0.157966i
\(783\) 3.96066e14i 1.34573i
\(784\) 1.00115e13 9.52691e13i 0.0338001 0.321641i
\(785\) −1.93519e14 −0.649195
\(786\) 5.12145e13 1.15031e14i 0.170718 0.383444i
\(787\) 1.87527e14i 0.621142i −0.950550 0.310571i \(-0.899480\pi\)
0.950550 0.310571i \(-0.100520\pi\)
\(788\) −2.30829e14 2.56357e14i −0.759731 0.843752i
\(789\) 1.60778e13 0.0525826
\(790\) 1.87392e14 + 8.34314e13i 0.608998 + 0.271140i
\(791\) 2.65096e14i 0.856092i
\(792\) −2.98896e14 9.19864e14i −0.959166 2.95187i
\(793\) −5.19392e13 −0.165626
\(794\) 6.71721e13 1.50873e14i 0.212856 0.478089i
\(795\) 2.33164e14i 0.734220i
\(796\) 2.54090e14 2.28788e14i 0.795101 0.715925i
\(797\) 1.76065e14 0.547498 0.273749 0.961801i \(-0.411736\pi\)
0.273749 + 0.961801i \(0.411736\pi\)
\(798\) 1.03570e15 + 4.61118e14i 3.20052 + 1.42494i
\(799\) 1.21741e14i 0.373853i
\(800\) −5.67566e13 3.27667e13i −0.173207 0.0999961i
\(801\) 5.35364e14 1.62363
\(802\) −7.93278e13 + 1.78175e14i −0.239086 + 0.537001i
\(803\) 6.34256e14i 1.89971i
\(804\) −2.58176e14 2.86729e14i −0.768487 0.853475i
\(805\) −1.19107e14 −0.352338
\(806\) −5.53402e12 2.46387e12i −0.0162692 0.00724341i
\(807\) 1.01713e15i 2.97173i
\(808\) 1.96065e14 6.37083e13i 0.569303 0.184986i
\(809\) 3.01803e14 0.870925 0.435462 0.900207i \(-0.356585\pi\)
0.435462 + 0.900207i \(0.356585\pi\)
\(810\) 1.52017e14 3.41441e14i 0.435982 0.979243i
\(811\) 1.06911e14i 0.304731i −0.988324 0.152366i \(-0.951311\pi\)
0.988324 0.152366i \(-0.0486891\pi\)
\(812\) 1.56020e14 1.40484e14i 0.441977 0.397965i
\(813\) 5.24584e14 1.47694
\(814\) 8.83977e13 + 3.93567e13i 0.247354 + 0.110128i
\(815\) 2.27816e12i 0.00633571i
\(816\) 3.76775e14 + 3.95938e13i 1.04143 + 0.109440i
\(817\) −9.80490e14 −2.69360
\(818\) −1.16480e14 + 2.61621e14i −0.318042 + 0.714343i
\(819\) 1.79282e14i 0.486537i
\(820\) −6.11406e13 6.79022e13i −0.164915 0.183153i
\(821\) −2.26172e13 −0.0606350 −0.0303175 0.999540i \(-0.509652\pi\)
−0.0303175 + 0.999540i \(0.509652\pi\)
\(822\) 1.08765e15 + 4.84245e14i 2.89820 + 1.29035i
\(823\) 4.19066e14i 1.10990i 0.831884 + 0.554949i \(0.187262\pi\)
−0.831884 + 0.554949i \(0.812738\pi\)
\(824\) 1.50368e14 + 4.62764e14i 0.395839 + 1.21821i
\(825\) −1.81799e14 −0.475687
\(826\) −1.18272e14 + 2.65647e14i −0.307597 + 0.690883i
\(827\) 1.07778e14i 0.278614i −0.990249 0.139307i \(-0.955513\pi\)
0.990249 0.139307i \(-0.0444875\pi\)
\(828\) −4.77284e14 + 4.29756e14i −1.22638 + 1.10426i
\(829\) 1.06061e14 0.270883 0.135441 0.990785i \(-0.456755\pi\)
0.135441 + 0.990785i \(0.456755\pi\)
\(830\) −1.20683e13 5.37307e12i −0.0306376 0.0136406i
\(831\) 2.27647e14i 0.574456i
\(832\) 5.66077e13 4.11302e13i 0.141990 0.103168i
\(833\) 7.35598e13 0.183407
\(834\) 1.47973e14 3.32357e14i 0.366735 0.823711i
\(835\) 3.12666e14i 0.770278i
\(836\) −5.80451e14 6.44645e14i −1.42146 1.57866i
\(837\) 1.08500e14 0.264120
\(838\) −3.88140e14 1.72809e14i −0.939221 0.418163i
\(839\) 6.55176e14i 1.57597i 0.615694 + 0.787985i \(0.288876\pi\)
−0.615694 + 0.787985i \(0.711124\pi\)
\(840\) −3.77851e14 + 1.22777e14i −0.903491 + 0.293575i
\(841\) −3.08261e14 −0.732721
\(842\) 1.51523e14 3.40331e14i 0.358030 0.804157i
\(843\) 1.42247e14i 0.334121i
\(844\) −2.30960e12 + 2.07961e12i −0.00539293 + 0.00485590i
\(845\) 1.86728e14 0.433437
\(846\) −6.28904e14 2.80003e14i −1.45122 0.646116i
\(847\) 3.30527e14i 0.758210i
\(848\) 4.07469e13 3.87747e14i 0.0929213 0.884239i
\(849\) 6.38214e14 1.44686
\(850\) 2.04688e13 4.59743e13i 0.0461315 0.103614i
\(851\) 6.42536e13i 0.143963i
\(852\) 1.49967e14 + 1.66553e14i 0.334040 + 0.370983i
\(853\) −6.23120e14 −1.37983 −0.689917 0.723889i \(-0.742353\pi\)
−0.689917 + 0.723889i \(0.742353\pi\)
\(854\) −4.50493e14 2.00570e14i −0.991741 0.441546i
\(855\) 8.12062e14i 1.77729i
\(856\) −7.94917e13 2.44639e14i −0.172963 0.532301i
\(857\) 4.84964e14 1.04907 0.524537 0.851388i \(-0.324239\pi\)
0.524537 + 0.851388i \(0.324239\pi\)
\(858\) 7.89489e13 1.77324e14i 0.169789 0.381357i
\(859\) 3.76960e14i 0.805991i −0.915202 0.402995i \(-0.867969\pi\)
0.915202 0.402995i \(-0.132031\pi\)
\(860\) 2.55344e14 2.29917e14i 0.542792 0.488741i
\(861\) −5.53924e14 −1.17067
\(862\) −4.98641e14 2.22007e14i −1.04774 0.466476i
\(863\) 4.17983e14i 0.873181i 0.899660 + 0.436591i \(0.143814\pi\)
−0.899660 + 0.436591i \(0.856186\pi\)
\(864\) −6.26612e14 + 1.08538e15i −1.30146 + 2.25431i
\(865\) −1.12192e14 −0.231676
\(866\) −2.07263e14 + 4.65525e14i −0.425532 + 0.955771i
\(867\) 6.13673e14i 1.25268i
\(868\) −3.84845e13 4.27406e13i −0.0781066 0.0867446i
\(869\) −9.51488e14 −1.92001
\(870\) −1.94393e14 8.65485e13i −0.390018 0.173645i
\(871\) 5.47223e13i 0.109163i
\(872\) 1.08767e14 3.53422e13i 0.215732 0.0700989i
\(873\) 1.95185e15 3.84925
\(874\) −2.34286e14 + 5.26222e14i −0.459399 + 1.03184i
\(875\) 5.27756e13i 0.102895i
\(876\) −1.04400e15 + 9.40037e14i −2.02385 + 1.82232i
\(877\) −4.50456e14 −0.868270 −0.434135 0.900848i \(-0.642946\pi\)
−0.434135 + 0.900848i \(0.642946\pi\)
\(878\) 1.86327e14 + 8.29573e13i 0.357112 + 0.158995i
\(879\) 9.96400e14i 1.89884i
\(880\) 3.02328e14 + 3.17705e13i 0.572881 + 0.0602019i
\(881\) −4.00485e14 −0.754583 −0.377292 0.926094i \(-0.623145\pi\)
−0.377292 + 0.926094i \(0.623145\pi\)
\(882\) −1.69187e14 + 3.80005e14i −0.316975 + 0.711945i
\(883\) 1.22465e14i 0.228144i −0.993473 0.114072i \(-0.963611\pi\)
0.993473 0.114072i \(-0.0363894\pi\)
\(884\) 3.59538e13 + 3.99300e13i 0.0666015 + 0.0739671i
\(885\) 2.94723e14 0.542872
\(886\) 6.89114e14 + 3.06810e14i 1.26218 + 0.561954i
\(887\) 1.37787e14i 0.250953i 0.992097 + 0.125476i \(0.0400459\pi\)
−0.992097 + 0.125476i \(0.959954\pi\)
\(888\) −6.62331e13 2.03835e14i −0.119953 0.369160i
\(889\) 2.48286e14 0.447140
\(890\) −6.84387e13 + 1.53718e14i −0.122561 + 0.275279i
\(891\) 1.73367e15i 3.08730i
\(892\) −5.01127e14 + 4.51225e14i −0.887409 + 0.799041i
\(893\) −6.17425e14 −1.08724
\(894\) 1.49325e15 + 6.64829e14i 2.61484 + 1.16419i
\(895\) 9.10596e13i 0.158566i
\(896\) 6.49814e14 1.38143e14i 1.12525 0.239216i
\(897\) −1.28892e14 −0.221954
\(898\) 1.34600e14 3.02319e14i 0.230495 0.517707i
\(899\) 3.08039e13i 0.0524575i
\(900\) 1.90422e14 + 2.11481e14i 0.322481 + 0.358145i
\(901\) 2.99390e14 0.504212
\(902\) 3.87194e14 + 1.72388e14i 0.648478 + 0.288718i
\(903\) 2.08301e15i 3.46939i
\(904\) 4.27287e14 1.38840e14i 0.707745 0.229971i
\(905\) 4.37469e14 0.720616
\(906\) 7.18095e14 1.61289e15i 1.17636 2.64218i
\(907\) 3.75970e14i 0.612516i 0.951949 + 0.306258i \(0.0990770\pi\)
−0.951949 + 0.306258i \(0.900923\pi\)
\(908\) 6.20307e14 5.58537e14i 1.00503 0.904945i
\(909\) −8.95194e14 −1.44244
\(910\) −5.14766e13 2.29186e13i −0.0824903 0.0367266i
\(911\) 3.99006e14i 0.635899i 0.948108 + 0.317949i \(0.102994\pi\)
−0.948108 + 0.317949i \(0.897006\pi\)
\(912\) −2.00806e14 + 1.91087e15i −0.318275 + 3.02870i
\(913\) 6.12769e13 0.0965924
\(914\) 4.15870e14 9.34071e14i 0.651969 1.46436i
\(915\) 4.99801e14i 0.779276i
\(916\) −2.18978e14 2.43196e14i −0.339565 0.377119i
\(917\) 1.69554e14 0.261494
\(918\) −8.79184e14 3.91433e14i −1.34855 0.600405i
\(919\) 2.15850e14i 0.329287i −0.986353 0.164643i \(-0.947353\pi\)
0.986353 0.164643i \(-0.0526473\pi\)
\(920\) −6.23808e13 1.91980e14i −0.0946480 0.291283i
\(921\) −4.30114e14 −0.649061
\(922\) −1.38075e14 + 3.10125e14i −0.207234 + 0.465460i
\(923\) 3.17867e13i 0.0474500i
\(924\) 1.36952e15 1.23314e15i 2.03333 1.83085i
\(925\) −2.84703e13 −0.0420420
\(926\) 2.96514e14 + 1.32015e14i 0.435501 + 0.193895i
\(927\) 2.11289e15i 3.08658i
\(928\) 3.08147e14 + 1.77900e14i 0.447733 + 0.258485i
\(929\) 4.43413e14 0.640811 0.320406 0.947280i \(-0.396181\pi\)
0.320406 + 0.947280i \(0.396181\pi\)
\(930\) −2.37094e13 + 5.32528e13i −0.0340805 + 0.0765469i
\(931\) 3.73069e14i 0.533386i
\(932\) −2.90592e14 3.22729e14i −0.413241 0.458942i
\(933\) −1.84666e15 −2.61203
\(934\) 3.52647e14 + 1.57007e14i 0.496142 + 0.220894i
\(935\) 2.33435e14i 0.326669i
\(936\) −2.88970e14 + 9.38962e13i −0.402229 + 0.130698i
\(937\) −5.87919e14 −0.813991 −0.406996 0.913430i \(-0.633424\pi\)
−0.406996 + 0.913430i \(0.633424\pi\)
\(938\) 2.11317e14 4.74632e14i 0.291019 0.653647i
\(939\) 3.79464e13i 0.0519808i
\(940\) 1.60793e14 1.44781e14i 0.219092 0.197275i
\(941\) 1.28114e15 1.73639 0.868195 0.496224i \(-0.165280\pi\)
0.868195 + 0.496224i \(0.165280\pi\)
\(942\) −1.81636e15 8.08687e14i −2.44877 1.09025i
\(943\) 2.81439e14i 0.377421i
\(944\) −4.90119e14 5.15047e13i −0.653795 0.0687048i
\(945\) 1.00925e15 1.33918
\(946\) −6.48257e14 + 1.45603e15i −0.855641 + 1.92183i
\(947\) 1.43625e15i 1.88574i −0.333166 0.942868i \(-0.608117\pi\)
0.333166 0.942868i \(-0.391883\pi\)
\(948\) 1.41021e15 + 1.56617e15i 1.84180 + 2.04549i
\(949\) −1.99248e14 −0.258858
\(950\) 2.33165e14 + 1.03811e14i 0.301332 + 0.134160i
\(951\) 1.35842e15i 1.74635i
\(952\) 1.57649e14 + 4.85172e14i 0.201608 + 0.620456i
\(953\) −1.10609e15 −1.40711 −0.703554 0.710642i \(-0.748405\pi\)
−0.703554 + 0.710642i \(0.748405\pi\)
\(954\) −6.88596e14 + 1.54663e15i −0.871410 + 1.95724i
\(955\) 3.54162e14i 0.445846i
\(956\) 3.94038e14 3.54800e14i 0.493456 0.444318i
\(957\) 9.87037e14 1.22963
\(958\) 4.42868e14 + 1.97175e14i 0.548841 + 0.244357i
\(959\) 1.60318e15i 1.97646i
\(960\) −3.95788e14 5.44725e14i −0.485407 0.668068i
\(961\) 8.11190e14 0.989704
\(962\) 1.23637e13 2.77696e13i 0.0150062 0.0337050i
\(963\) 1.11697e15i 1.34869i
\(964\) −4.89369e14 5.43490e14i −0.587830 0.652839i
\(965\) 1.27124e13 0.0151911
\(966\) −1.11794e15 4.97732e14i −1.32902 0.591711i
\(967\) 5.03424e14i 0.595390i 0.954661 + 0.297695i \(0.0962179\pi\)
−0.954661 + 0.297695i \(0.903782\pi\)
\(968\) −5.32750e14 + 1.73109e14i −0.626825 + 0.203677i
\(969\) −1.47543e15 −1.72703
\(970\) −2.49517e14 + 5.60430e14i −0.290563 + 0.652624i
\(971\) 1.45819e15i 1.68934i 0.535288 + 0.844670i \(0.320203\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(972\) 1.17533e15 1.05829e15i 1.35465 1.21976i
\(973\) 4.89890e14 0.561739
\(974\) −3.60547e14 1.60524e14i −0.411308 0.183124i
\(975\) 5.71109e13i 0.0648181i
\(976\) 8.73434e13 8.31159e14i 0.0986236 0.938501i
\(977\) 1.28973e15 1.44886 0.724431 0.689348i \(-0.242103\pi\)
0.724431 + 0.689348i \(0.242103\pi\)
\(978\) −9.52007e12 + 2.13827e13i −0.0106401 + 0.0238984i
\(979\) 7.80504e14i 0.867884i
\(980\) −8.74817e13 9.71565e13i −0.0967803 0.107483i
\(981\) −4.96609e14 −0.546600
\(982\) 6.56003e14 + 2.92068e14i 0.718370 + 0.319835i
\(983\) 1.23310e15i 1.34348i 0.740788 + 0.671738i \(0.234452\pi\)
−0.740788 + 0.671738i \(0.765548\pi\)
\(984\) −2.90110e14 8.92825e14i −0.314475 0.967812i
\(985\) −4.70805e14 −0.507762
\(986\) −1.11131e14 + 2.49607e14i −0.119248 + 0.267838i
\(987\) 1.31169e15i 1.40038i
\(988\) −2.02511e14 + 1.82345e14i −0.215112 + 0.193691i
\(989\) 1.05834e15 1.11852
\(990\) −1.20591e15 5.36900e14i −1.26806 0.564569i
\(991\) 7.76053e14i 0.811938i −0.913887 0.405969i \(-0.866934\pi\)
0.913887 0.405969i \(-0.133066\pi\)
\(992\) 4.87345e13 8.44150e13i 0.0507316 0.0878741i
\(993\) 1.60800e15 1.66548
\(994\) −1.22748e14 + 2.75701e14i −0.126498 + 0.284123i
\(995\) 4.66641e14i 0.478484i
\(996\) −9.08190e13 1.00863e14i −0.0926574 0.102905i
\(997\) −4.19236e14 −0.425582 −0.212791 0.977098i \(-0.568255\pi\)
−0.212791 + 0.977098i \(0.568255\pi\)
\(998\) 9.03886e14 + 4.02431e14i 0.912979 + 0.406480i
\(999\) 5.44449e14i 0.547180i
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 20.11.b.a.11.8 yes 20
3.2 odd 2 180.11.c.a.91.13 20
4.3 odd 2 inner 20.11.b.a.11.7 20
5.2 odd 4 100.11.d.c.99.7 40
5.3 odd 4 100.11.d.c.99.34 40
5.4 even 2 100.11.b.e.51.13 20
8.3 odd 2 320.11.b.d.191.20 20
8.5 even 2 320.11.b.d.191.1 20
12.11 even 2 180.11.c.a.91.14 20
20.3 even 4 100.11.d.c.99.8 40
20.7 even 4 100.11.d.c.99.33 40
20.19 odd 2 100.11.b.e.51.14 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.11.b.a.11.7 20 4.3 odd 2 inner
20.11.b.a.11.8 yes 20 1.1 even 1 trivial
100.11.b.e.51.13 20 5.4 even 2
100.11.b.e.51.14 20 20.19 odd 2
100.11.d.c.99.7 40 5.2 odd 4
100.11.d.c.99.8 40 20.3 even 4
100.11.d.c.99.33 40 20.7 even 4
100.11.d.c.99.34 40 5.3 odd 4
180.11.c.a.91.13 20 3.2 odd 2
180.11.c.a.91.14 20 12.11 even 2
320.11.b.d.191.1 20 8.5 even 2
320.11.b.d.191.20 20 8.3 odd 2