Properties

Label 4.21.b.b.3.5
Level $4$
Weight $21$
Character 4.3
Analytic conductor $10.141$
Analytic rank $0$
Dimension $8$
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] = [4,21,Mod(3,4)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 21, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4.3");
 
S:= CuspForms(chi, 21);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 4.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: \(10.1405506041\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3 x^{7} + 41744 x^{6} - 12461904 x^{5} + 2339673984 x^{4} - 888904297728 x^{3} + 163438296621056 x^{2} + \cdots + 18\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{56}\cdot 3^{5}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.5
Root \(77.2239 - 239.948i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.21.b.b.3.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(356.896 - 959.792i) q^{2} -46975.6i q^{3} +(-793827. - 685091. i) q^{4} -4.32154e6 q^{5} +(-4.50868e7 - 1.67654e7i) q^{6} -1.10972e8i q^{7} +(-9.40859e8 + 5.17403e8i) q^{8} +1.28008e9 q^{9} +O(q^{10})\) \(q+(356.896 - 959.792i) q^{2} -46975.6i q^{3} +(-793827. - 685091. i) q^{4} -4.32154e6 q^{5} +(-4.50868e7 - 1.67654e7i) q^{6} -1.10972e8i q^{7} +(-9.40859e8 + 5.17403e8i) q^{8} +1.28008e9 q^{9} +(-1.54234e9 + 4.14778e9i) q^{10} +2.26825e10i q^{11} +(-3.21826e10 + 3.72905e10i) q^{12} -2.51114e11 q^{13} +(-1.06510e11 - 3.96053e10i) q^{14} +2.03007e11i q^{15} +(1.60811e11 + 1.08769e12i) q^{16} +1.40803e12 q^{17} +(4.56853e11 - 1.22861e12i) q^{18} -1.01893e13i q^{19} +(3.43056e12 + 2.96065e12i) q^{20} -5.21296e12 q^{21} +(2.17705e13 + 8.09530e12i) q^{22} -4.06234e13i q^{23} +(2.43053e13 + 4.41974e13i) q^{24} -7.66917e13 q^{25} +(-8.96217e13 + 2.41018e14i) q^{26} -2.23926e14i q^{27} +(-7.60257e13 + 8.80923e13i) q^{28} -2.78623e14 q^{29} +(1.94845e14 + 7.24523e13i) q^{30} -5.16079e14i q^{31} +(1.10135e15 + 2.33846e14i) q^{32} +1.06553e15 q^{33} +(5.02520e14 - 1.35142e15i) q^{34} +4.79568e14i q^{35} +(-1.01616e15 - 8.76969e14i) q^{36} +8.25764e14 q^{37} +(-9.77960e15 - 3.63651e15i) q^{38} +1.17963e16i q^{39} +(4.06596e15 - 2.23598e15i) q^{40} -2.23881e14 q^{41} +(-1.86048e15 + 5.00336e15i) q^{42} +2.43150e16i q^{43} +(1.55396e16 - 1.80060e16i) q^{44} -5.53190e15 q^{45} +(-3.89900e16 - 1.44983e16i) q^{46} -7.49929e16i q^{47} +(5.10948e16 - 7.55420e15i) q^{48} +6.74776e16 q^{49} +(-2.73709e16 + 7.36081e16i) q^{50} -6.61431e16i q^{51} +(1.99341e17 + 1.72036e17i) q^{52} -1.39239e17 q^{53} +(-2.14923e17 - 7.99183e16i) q^{54} -9.80236e16i q^{55} +(5.74171e16 + 1.04409e17i) q^{56} -4.78648e17 q^{57} +(-9.94394e16 + 2.67420e17i) q^{58} +1.92225e17i q^{59} +(1.39078e17 - 1.61153e17i) q^{60} +9.81172e17 q^{61} +(-4.95329e17 - 1.84186e17i) q^{62} -1.42052e17i q^{63} +(6.17510e17 - 9.73607e17i) q^{64} +1.08520e18 q^{65} +(3.80282e17 - 1.02268e18i) q^{66} +2.38323e18i q^{67} +(-1.11773e18 - 9.64630e17i) q^{68} -1.90831e18 q^{69} +(4.60286e17 + 1.71156e17i) q^{70} -6.63259e17i q^{71} +(-1.20437e18 + 6.62315e17i) q^{72} -6.58097e17 q^{73} +(2.94712e17 - 7.92562e17i) q^{74} +3.60264e18i q^{75} +(-6.98059e18 + 8.08853e18i) q^{76} +2.51712e18 q^{77} +(1.13220e19 + 4.21003e18i) q^{78} -1.44666e19i q^{79} +(-6.94952e17 - 4.70049e18i) q^{80} -6.05573e18 q^{81} +(-7.99022e16 + 2.14880e17i) q^{82} -1.67166e19i q^{83} +(4.13819e18 + 3.57135e18i) q^{84} -6.08486e18 q^{85} +(2.33373e19 + 8.67790e18i) q^{86} +1.30885e19i q^{87} +(-1.17360e19 - 2.13411e19i) q^{88} +3.01212e19 q^{89} +(-1.97431e18 + 5.30947e18i) q^{90} +2.78666e19i q^{91} +(-2.78307e19 + 3.22479e19i) q^{92} -2.42431e19 q^{93} +(-7.19776e19 - 2.67646e19i) q^{94} +4.40334e19i q^{95} +(1.09851e19 - 5.17365e19i) q^{96} -3.28404e19 q^{97} +(2.40824e19 - 6.47645e19i) q^{98} +2.90354e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 396 q^{2} - 1316080 q^{4} + 18568080 q^{5} + 99460608 q^{6} + 2177274816 q^{8} - 10411362168 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 396 q^{2} - 1316080 q^{4} + 18568080 q^{5} + 99460608 q^{6} + 2177274816 q^{8} - 10411362168 q^{9} - 18158047400 q^{10} - 41779799040 q^{12} - 43179394928 q^{13} - 200556776448 q^{14} - 1029373411072 q^{16} - 2434881831408 q^{17} + 5206289577036 q^{18} + 20485893906720 q^{20} + 33281721747456 q^{21} - 31324969489920 q^{22} - 47563142934528 q^{24} - 277943780989800 q^{25} + 132190787676888 q^{26} + 385881741772800 q^{28} + 100761472221840 q^{29} - 10\!\cdots\!40 q^{30}+ \cdots - 19\!\cdots\!84 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 356.896 959.792i 0.348531 0.937297i
\(3\) 46975.6i 0.795536i −0.917486 0.397768i \(-0.869785\pi\)
0.917486 0.397768i \(-0.130215\pi\)
\(4\) −793827. 685091.i −0.757052 0.653354i
\(5\) −4.32154e6 −0.442526 −0.221263 0.975214i \(-0.571018\pi\)
−0.221263 + 0.975214i \(0.571018\pi\)
\(6\) −4.50868e7 1.67654e7i −0.745654 0.277269i
\(7\) 1.10972e8i 0.392854i −0.980518 0.196427i \(-0.937066\pi\)
0.980518 0.196427i \(-0.0629339\pi\)
\(8\) −9.40859e8 + 5.17403e8i −0.876243 + 0.481869i
\(9\) 1.28008e9 0.367122
\(10\) −1.54234e9 + 4.14778e9i −0.154234 + 0.414778i
\(11\) 2.26825e10i 0.874510i 0.899337 + 0.437255i \(0.144049\pi\)
−0.899337 + 0.437255i \(0.855951\pi\)
\(12\) −3.21826e10 + 3.72905e10i −0.519767 + 0.602263i
\(13\) −2.51114e11 −1.82154 −0.910769 0.412916i \(-0.864510\pi\)
−0.910769 + 0.412916i \(0.864510\pi\)
\(14\) −1.06510e11 3.96053e10i −0.368221 0.136922i
\(15\) 2.03007e11i 0.352045i
\(16\) 1.60811e11 + 1.08769e12i 0.146257 + 0.989247i
\(17\) 1.40803e12 0.698430 0.349215 0.937043i \(-0.386448\pi\)
0.349215 + 0.937043i \(0.386448\pi\)
\(18\) 4.56853e11 1.22861e12i 0.127953 0.344102i
\(19\) 1.01893e13i 1.66191i −0.556339 0.830956i \(-0.687794\pi\)
0.556339 0.830956i \(-0.312206\pi\)
\(20\) 3.43056e12 + 2.96065e12i 0.335015 + 0.289126i
\(21\) −5.21296e12 −0.312530
\(22\) 2.17705e13 + 8.09530e12i 0.819676 + 0.304794i
\(23\) 4.06234e13i 0.980613i −0.871550 0.490307i \(-0.836885\pi\)
0.871550 0.490307i \(-0.163115\pi\)
\(24\) 2.43053e13 + 4.41974e13i 0.383344 + 0.697083i
\(25\) −7.66917e13 −0.804171
\(26\) −8.96217e13 + 2.41018e14i −0.634862 + 1.70732i
\(27\) 2.23926e14i 1.08760i
\(28\) −7.60257e13 + 8.80923e13i −0.256673 + 0.297411i
\(29\) −2.78623e14 −0.662273 −0.331137 0.943583i \(-0.607432\pi\)
−0.331137 + 0.943583i \(0.607432\pi\)
\(30\) 1.94845e14 + 7.24523e13i 0.329971 + 0.122699i
\(31\) 5.16079e14i 0.629650i −0.949150 0.314825i \(-0.898054\pi\)
0.949150 0.314825i \(-0.101946\pi\)
\(32\) 1.10135e15 + 2.33846e14i 0.978193 + 0.207697i
\(33\) 1.06553e15 0.695705
\(34\) 5.02520e14 1.35142e15i 0.243424 0.654637i
\(35\) 4.79568e14i 0.173848i
\(36\) −1.01616e15 8.76969e14i −0.277931 0.239861i
\(37\) 8.25764e14 0.171727 0.0858636 0.996307i \(-0.472635\pi\)
0.0858636 + 0.996307i \(0.472635\pi\)
\(38\) −9.77960e15 3.63651e15i −1.55770 0.579227i
\(39\) 1.17963e16i 1.44910i
\(40\) 4.06596e15 2.23598e15i 0.387760 0.213240i
\(41\) −2.23881e14 −0.0166793 −0.00833967 0.999965i \(-0.502655\pi\)
−0.00833967 + 0.999965i \(0.502655\pi\)
\(42\) −1.86048e15 + 5.00336e15i −0.108926 + 0.292933i
\(43\) 2.43150e16i 1.12509i 0.826765 + 0.562547i \(0.190179\pi\)
−0.826765 + 0.562547i \(0.809821\pi\)
\(44\) 1.55396e16 1.80060e16i 0.571365 0.662050i
\(45\) −5.53190e15 −0.162461
\(46\) −3.89900e16 1.44983e16i −0.919126 0.341774i
\(47\) 7.49929e16i 1.42574i −0.701295 0.712872i \(-0.747394\pi\)
0.701295 0.712872i \(-0.252606\pi\)
\(48\) 5.10948e16 7.55420e15i 0.786982 0.116353i
\(49\) 6.74776e16 0.845666
\(50\) −2.73709e16 + 7.36081e16i −0.280278 + 0.753747i
\(51\) 6.61431e16i 0.555626i
\(52\) 1.99341e17 + 1.72036e17i 1.37900 + 1.19011i
\(53\) −1.39239e17 −0.796162 −0.398081 0.917350i \(-0.630324\pi\)
−0.398081 + 0.917350i \(0.630324\pi\)
\(54\) −2.14923e17 7.99183e16i −1.01940 0.379061i
\(55\) 9.80236e16i 0.386993i
\(56\) 5.74171e16 + 1.04409e17i 0.189304 + 0.344236i
\(57\) −4.78648e17 −1.32211
\(58\) −9.94394e16 + 2.67420e17i −0.230823 + 0.620747i
\(59\) 1.92225e17i 0.376089i 0.982160 + 0.188045i \(0.0602150\pi\)
−0.982160 + 0.188045i \(0.939785\pi\)
\(60\) 1.39078e17 1.61153e17i 0.230010 0.266517i
\(61\) 9.81172e17 1.37546 0.687728 0.725969i \(-0.258608\pi\)
0.687728 + 0.725969i \(0.258608\pi\)
\(62\) −4.95329e17 1.84186e17i −0.590169 0.219452i
\(63\) 1.42052e17i 0.144225i
\(64\) 6.17510e17 9.73607e17i 0.535604 0.844469i
\(65\) 1.08520e18 0.806078
\(66\) 3.80282e17 1.02268e18i 0.242475 0.652082i
\(67\) 2.38323e18i 1.30743i 0.756740 + 0.653716i \(0.226791\pi\)
−0.756740 + 0.653716i \(0.773209\pi\)
\(68\) −1.11773e18 9.64630e17i −0.528748 0.456322i
\(69\) −1.90831e18 −0.780113
\(70\) 4.60286e17 + 1.71156e17i 0.162947 + 0.0605915i
\(71\) 6.63259e17i 0.203751i −0.994797 0.101875i \(-0.967516\pi\)
0.994797 0.101875i \(-0.0324843\pi\)
\(72\) −1.20437e18 + 6.62315e17i −0.321688 + 0.176905i
\(73\) −6.58097e17 −0.153130 −0.0765652 0.997065i \(-0.524395\pi\)
−0.0765652 + 0.997065i \(0.524395\pi\)
\(74\) 2.94712e17 7.92562e17i 0.0598522 0.160959i
\(75\) 3.60264e18i 0.639747i
\(76\) −6.98059e18 + 8.08853e18i −1.08582 + 1.25815i
\(77\) 2.51712e18 0.343555
\(78\) 1.13220e19 + 4.21003e18i 1.35824 + 0.505056i
\(79\) 1.44666e19i 1.52790i −0.645274 0.763951i \(-0.723257\pi\)
0.645274 0.763951i \(-0.276743\pi\)
\(80\) −6.94952e17 4.70049e18i −0.0647224 0.437767i
\(81\) −6.05573e18 −0.498099
\(82\) −7.99022e16 + 2.14880e17i −0.00581327 + 0.0156335i
\(83\) 1.67166e19i 1.07737i −0.842506 0.538687i \(-0.818921\pi\)
0.842506 0.538687i \(-0.181079\pi\)
\(84\) 4.13819e18 + 3.57135e18i 0.236601 + 0.204193i
\(85\) −6.08486e18 −0.309073
\(86\) 2.33373e19 + 8.67790e18i 1.05455 + 0.392130i
\(87\) 1.30885e19i 0.526862i
\(88\) −1.17360e19 2.13411e19i −0.421400 0.766284i
\(89\) 3.01212e19 0.965989 0.482994 0.875623i \(-0.339549\pi\)
0.482994 + 0.875623i \(0.339549\pi\)
\(90\) −1.97431e18 + 5.30947e18i −0.0566227 + 0.152274i
\(91\) 2.78666e19i 0.715599i
\(92\) −2.78307e19 + 3.22479e19i −0.640688 + 0.742376i
\(93\) −2.42431e19 −0.500909
\(94\) −7.19776e19 2.67646e19i −1.33635 0.496916i
\(95\) 4.40334e19i 0.735439i
\(96\) 1.09851e19 5.17365e19i 0.165230 0.778188i
\(97\) −3.28404e19 −0.445339 −0.222669 0.974894i \(-0.571477\pi\)
−0.222669 + 0.974894i \(0.571477\pi\)
\(98\) 2.40824e19 6.47645e19i 0.294741 0.792640i
\(99\) 2.90354e19i 0.321052i
\(100\) 6.08800e19 + 5.25408e19i 0.608800 + 0.525408i
\(101\) 1.20372e20 1.08971 0.544857 0.838529i \(-0.316584\pi\)
0.544857 + 0.838529i \(0.316584\pi\)
\(102\) −6.34837e19 2.36062e19i −0.520787 0.193653i
\(103\) 5.38576e19i 0.400751i 0.979719 + 0.200375i \(0.0642162\pi\)
−0.979719 + 0.200375i \(0.935784\pi\)
\(104\) 2.36263e20 1.29927e20i 1.59611 0.877743i
\(105\) 2.25280e19 0.138303
\(106\) −4.96937e19 + 1.33640e20i −0.277487 + 0.746240i
\(107\) 3.68120e20i 1.87134i −0.352883 0.935668i \(-0.614798\pi\)
0.352883 0.935668i \(-0.385202\pi\)
\(108\) −1.53410e20 + 1.77759e20i −0.710585 + 0.823367i
\(109\) −1.32963e20 −0.561651 −0.280826 0.959759i \(-0.590608\pi\)
−0.280826 + 0.959759i \(0.590608\pi\)
\(110\) −9.40823e19 3.49842e19i −0.362728 0.134879i
\(111\) 3.87908e19i 0.136615i
\(112\) 1.20703e20 1.78455e19i 0.388630 0.0574576i
\(113\) −1.19742e20 −0.352746 −0.176373 0.984323i \(-0.556436\pi\)
−0.176373 + 0.984323i \(0.556436\pi\)
\(114\) −1.70827e20 + 4.59403e20i −0.460796 + 1.23921i
\(115\) 1.75556e20i 0.433947i
\(116\) 2.21179e20 + 1.90882e20i 0.501375 + 0.432699i
\(117\) −3.21445e20 −0.668727
\(118\) 1.84497e20 + 6.86044e19i 0.352507 + 0.131079i
\(119\) 1.56251e20i 0.274381i
\(120\) −1.05036e20 1.91001e20i −0.169640 0.308477i
\(121\) 1.58252e20 0.235232
\(122\) 3.50176e20 9.41721e20i 0.479389 1.28921i
\(123\) 1.05170e19i 0.0132690i
\(124\) −3.53561e20 + 4.09677e20i −0.411384 + 0.476678i
\(125\) 7.43561e20 0.798392
\(126\) −1.36340e20 5.06977e19i −0.135182 0.0502670i
\(127\) 5.31218e20i 0.486671i 0.969942 + 0.243336i \(0.0782416\pi\)
−0.969942 + 0.243336i \(0.921758\pi\)
\(128\) −7.14074e20 9.40157e20i −0.604844 0.796344i
\(129\) 1.14221e21 0.895054
\(130\) 3.87304e20 1.04157e21i 0.280943 0.755534i
\(131\) 6.40485e20i 0.430325i 0.976578 + 0.215162i \(0.0690281\pi\)
−0.976578 + 0.215162i \(0.930972\pi\)
\(132\) −8.45844e20 7.29983e20i −0.526685 0.454542i
\(133\) −1.13072e21 −0.652889
\(134\) 2.28741e21 + 8.50566e20i 1.22545 + 0.455680i
\(135\) 9.67706e20i 0.481289i
\(136\) −1.32476e21 + 7.28519e20i −0.611995 + 0.336552i
\(137\) −1.07755e20 −0.0462630 −0.0231315 0.999732i \(-0.507364\pi\)
−0.0231315 + 0.999732i \(0.507364\pi\)
\(138\) −6.81067e20 + 1.83158e21i −0.271894 + 0.731198i
\(139\) 1.98580e21i 0.737542i 0.929520 + 0.368771i \(0.120221\pi\)
−0.929520 + 0.368771i \(0.879779\pi\)
\(140\) 3.28548e20 3.80694e20i 0.113584 0.131612i
\(141\) −3.52284e21 −1.13423
\(142\) −6.36591e20 2.36714e20i −0.190975 0.0710135i
\(143\) 5.69592e21i 1.59295i
\(144\) 2.05850e20 + 1.39232e21i 0.0536941 + 0.363174i
\(145\) 1.20408e21 0.293073
\(146\) −2.34872e20 + 6.31637e20i −0.0533707 + 0.143529i
\(147\) 3.16980e21i 0.672758i
\(148\) −6.55514e20 5.65724e20i −0.130006 0.112199i
\(149\) 4.30326e21 0.797875 0.398938 0.916978i \(-0.369379\pi\)
0.398938 + 0.916978i \(0.369379\pi\)
\(150\) 3.45779e21 + 1.28577e21i 0.599633 + 0.222972i
\(151\) 4.36918e21i 0.708974i −0.935061 0.354487i \(-0.884656\pi\)
0.935061 0.354487i \(-0.115344\pi\)
\(152\) 5.27197e21 + 9.58668e21i 0.800824 + 1.45624i
\(153\) 1.80239e21 0.256409
\(154\) 8.98349e20 2.41591e21i 0.119740 0.322013i
\(155\) 2.23026e21i 0.278636i
\(156\) 8.08152e21 9.36419e21i 0.946775 1.09704i
\(157\) −7.25176e21 −0.796980 −0.398490 0.917173i \(-0.630466\pi\)
−0.398490 + 0.917173i \(0.630466\pi\)
\(158\) −1.38849e22 5.16307e21i −1.43210 0.532521i
\(159\) 6.54082e21i 0.633375i
\(160\) −4.75952e21 1.01057e21i −0.432876 0.0919112i
\(161\) −4.50804e21 −0.385238
\(162\) −2.16126e21 + 5.81224e21i −0.173603 + 0.466867i
\(163\) 7.20508e21i 0.544206i 0.962268 + 0.272103i \(0.0877191\pi\)
−0.962268 + 0.272103i \(0.912281\pi\)
\(164\) 1.77723e20 + 1.53379e20i 0.0126271 + 0.0108975i
\(165\) −4.60472e21 −0.307867
\(166\) −1.60444e22 5.96607e21i −1.00982 0.375498i
\(167\) 2.22940e22i 1.32137i 0.750665 + 0.660683i \(0.229733\pi\)
−0.750665 + 0.660683i \(0.770267\pi\)
\(168\) 4.90466e21 2.69720e21i 0.273852 0.150598i
\(169\) 4.40535e22 2.31800
\(170\) −2.17166e21 + 5.84020e21i −0.107722 + 0.289694i
\(171\) 1.30431e22i 0.610124i
\(172\) 1.66580e22 1.93019e22i 0.735085 0.851756i
\(173\) −2.89860e22 −1.20705 −0.603527 0.797343i \(-0.706238\pi\)
−0.603527 + 0.797343i \(0.706238\pi\)
\(174\) 1.25622e22 + 4.67123e21i 0.493827 + 0.183628i
\(175\) 8.51060e21i 0.315922i
\(176\) −2.46715e22 + 3.64761e21i −0.865106 + 0.127903i
\(177\) 9.02991e21 0.299193
\(178\) 1.07501e22 2.89101e22i 0.336677 0.905419i
\(179\) 3.34229e22i 0.989724i −0.868972 0.494862i \(-0.835219\pi\)
0.868972 0.494862i \(-0.164781\pi\)
\(180\) 4.39137e21 + 3.78986e21i 0.122991 + 0.106145i
\(181\) −1.78015e22 −0.471705 −0.235853 0.971789i \(-0.575788\pi\)
−0.235853 + 0.971789i \(0.575788\pi\)
\(182\) 2.67461e22 + 9.94546e21i 0.670729 + 0.249408i
\(183\) 4.60912e22i 1.09423i
\(184\) 2.10187e22 + 3.82209e22i 0.472527 + 0.859256i
\(185\) −3.56857e21 −0.0759937
\(186\) −8.65227e21 + 2.32684e22i −0.174582 + 0.469501i
\(187\) 3.19377e22i 0.610784i
\(188\) −5.13770e22 + 5.95314e22i −0.931515 + 1.07936i
\(189\) −2.48495e22 −0.427266
\(190\) 4.22630e22 + 1.57153e22i 0.689325 + 0.256323i
\(191\) 7.50141e21i 0.116094i −0.998314 0.0580469i \(-0.981513\pi\)
0.998314 0.0580469i \(-0.0184873\pi\)
\(192\) −4.57358e22 2.90079e22i −0.671806 0.426093i
\(193\) 6.42333e22 0.895751 0.447876 0.894096i \(-0.352181\pi\)
0.447876 + 0.894096i \(0.352181\pi\)
\(194\) −1.17206e22 + 3.15199e22i −0.155214 + 0.417415i
\(195\) 5.09780e22i 0.641264i
\(196\) −5.35655e22 4.62283e22i −0.640213 0.552519i
\(197\) −1.51037e23 −1.71562 −0.857809 0.513968i \(-0.828175\pi\)
−0.857809 + 0.513968i \(0.828175\pi\)
\(198\) 2.78679e22 + 1.03626e22i 0.300921 + 0.111897i
\(199\) 9.57591e22i 0.983217i 0.870816 + 0.491608i \(0.163591\pi\)
−0.870816 + 0.491608i \(0.836409\pi\)
\(200\) 7.21561e22 3.96805e22i 0.704649 0.387505i
\(201\) 1.11954e23 1.04011
\(202\) 4.29603e22 1.15532e23i 0.379799 1.02139i
\(203\) 3.09193e22i 0.260177i
\(204\) −4.53141e22 + 5.25062e22i −0.363021 + 0.420638i
\(205\) 9.67512e20 0.00738104
\(206\) 5.16921e22 + 1.92215e22i 0.375623 + 0.139674i
\(207\) 5.20010e22i 0.360005i
\(208\) −4.03820e22 2.73134e23i −0.266412 1.80195i
\(209\) 2.31119e23 1.45336
\(210\) 8.04015e21 2.16222e22i 0.0482027 0.129631i
\(211\) 2.46315e23i 1.40821i 0.710097 + 0.704104i \(0.248651\pi\)
−0.710097 + 0.704104i \(0.751349\pi\)
\(212\) 1.10531e23 + 9.53912e22i 0.602736 + 0.520175i
\(213\) −3.11570e22 −0.162091
\(214\) −3.53319e23 1.31380e23i −1.75400 0.652218i
\(215\) 1.05078e23i 0.497884i
\(216\) 1.15860e23 + 2.10683e23i 0.524079 + 0.952998i
\(217\) −5.72701e22 −0.247361
\(218\) −4.74540e22 + 1.27617e23i −0.195753 + 0.526434i
\(219\) 3.09145e22i 0.121821i
\(220\) −6.71551e22 + 7.78138e22i −0.252844 + 0.292974i
\(221\) −3.53577e23 −1.27222
\(222\) −3.72311e22 1.38443e22i −0.128049 0.0476146i
\(223\) 3.80877e21i 0.0125238i −0.999980 0.00626189i \(-0.998007\pi\)
0.999980 0.00626189i \(-0.00199324\pi\)
\(224\) 2.59503e22 1.22218e23i 0.0815946 0.384287i
\(225\) −9.81712e22 −0.295229
\(226\) −4.27354e22 + 1.14927e23i −0.122943 + 0.330628i
\(227\) 4.40164e23i 1.21159i −0.795621 0.605795i \(-0.792855\pi\)
0.795621 0.605795i \(-0.207145\pi\)
\(228\) 3.79964e23 + 3.27918e23i 1.00091 + 0.863806i
\(229\) −1.47692e23 −0.372395 −0.186197 0.982512i \(-0.559616\pi\)
−0.186197 + 0.982512i \(0.559616\pi\)
\(230\) 1.68497e23 + 6.26550e22i 0.406737 + 0.151244i
\(231\) 1.18243e23i 0.273311i
\(232\) 2.62145e23 1.44160e23i 0.580312 0.319129i
\(233\) 9.21685e23 1.95445 0.977223 0.212216i \(-0.0680682\pi\)
0.977223 + 0.212216i \(0.0680682\pi\)
\(234\) −1.14722e23 + 3.08521e23i −0.233072 + 0.626796i
\(235\) 3.24085e23i 0.630928i
\(236\) 1.31692e23 1.52594e23i 0.245719 0.284719i
\(237\) −6.79577e23 −1.21550
\(238\) −1.49969e23 5.57655e22i −0.257177 0.0956303i
\(239\) 1.05038e24i 1.72730i −0.504092 0.863650i \(-0.668173\pi\)
0.504092 0.863650i \(-0.331827\pi\)
\(240\) −2.20808e23 + 3.26458e22i −0.348260 + 0.0514890i
\(241\) 6.62860e23 1.00289 0.501443 0.865191i \(-0.332803\pi\)
0.501443 + 0.865191i \(0.332803\pi\)
\(242\) 5.64795e22 1.51889e23i 0.0819855 0.220482i
\(243\) 4.96311e23i 0.691339i
\(244\) −7.78881e23 6.72192e23i −1.04129 0.898660i
\(245\) −2.91607e23 −0.374229
\(246\) 1.00941e22 + 3.75346e21i 0.0124370 + 0.00462467i
\(247\) 2.55868e24i 3.02723i
\(248\) 2.67021e23 + 4.85558e23i 0.303409 + 0.551727i
\(249\) −7.85271e23 −0.857090
\(250\) 2.65374e23 7.13664e23i 0.278264 0.748331i
\(251\) 7.10595e23i 0.715954i 0.933730 + 0.357977i \(0.116533\pi\)
−0.933730 + 0.357977i \(0.883467\pi\)
\(252\) −9.73186e22 + 1.12765e23i −0.0942303 + 0.109186i
\(253\) 9.21442e23 0.857556
\(254\) 5.09859e23 + 1.89589e23i 0.456156 + 0.169620i
\(255\) 2.85840e23i 0.245879i
\(256\) −1.15721e24 + 3.49825e23i −0.957218 + 0.289368i
\(257\) −1.74157e23 −0.138551 −0.0692757 0.997598i \(-0.522069\pi\)
−0.0692757 + 0.997598i \(0.522069\pi\)
\(258\) 4.07650e23 1.09629e24i 0.311954 0.838931i
\(259\) 9.16364e22i 0.0674637i
\(260\) −8.61462e23 7.43462e23i −0.610243 0.526654i
\(261\) −3.56658e23 −0.243135
\(262\) 6.14733e23 + 2.28586e23i 0.403342 + 0.149981i
\(263\) 1.12925e24i 0.713236i −0.934250 0.356618i \(-0.883930\pi\)
0.934250 0.356618i \(-0.116070\pi\)
\(264\) −1.00251e24 + 5.51307e23i −0.609607 + 0.335239i
\(265\) 6.01726e23 0.352322
\(266\) −4.03550e23 + 1.08526e24i −0.227552 + 0.611951i
\(267\) 1.41496e24i 0.768479i
\(268\) 1.63273e24 1.89188e24i 0.854216 0.989794i
\(269\) 6.44605e23 0.324916 0.162458 0.986715i \(-0.448058\pi\)
0.162458 + 0.986715i \(0.448058\pi\)
\(270\) 9.28797e23 + 3.45370e23i 0.451111 + 0.167744i
\(271\) 1.50436e23i 0.0704139i −0.999380 0.0352069i \(-0.988791\pi\)
0.999380 0.0352069i \(-0.0112090\pi\)
\(272\) 2.26427e23 + 1.53150e24i 0.102150 + 0.690920i
\(273\) 1.30905e24 0.569285
\(274\) −3.84574e22 + 1.03423e23i −0.0161241 + 0.0433621i
\(275\) 1.73956e24i 0.703256i
\(276\) 1.51487e24 + 1.30737e24i 0.590587 + 0.509690i
\(277\) −1.30317e24 −0.490007 −0.245003 0.969522i \(-0.578789\pi\)
−0.245003 + 0.969522i \(0.578789\pi\)
\(278\) 1.90595e24 + 7.08722e23i 0.691296 + 0.257056i
\(279\) 6.60620e23i 0.231158i
\(280\) −2.48130e23 4.51206e23i −0.0837721 0.152333i
\(281\) −5.88408e24 −1.91697 −0.958484 0.285145i \(-0.907958\pi\)
−0.958484 + 0.285145i \(0.907958\pi\)
\(282\) −1.25728e24 + 3.38119e24i −0.395314 + 1.06311i
\(283\) 1.13806e24i 0.345382i 0.984976 + 0.172691i \(0.0552463\pi\)
−0.984976 + 0.172691i \(0.944754\pi\)
\(284\) −4.54393e23 + 5.26513e23i −0.133121 + 0.154250i
\(285\) 2.06850e24 0.585068
\(286\) −5.46690e24 2.03285e24i −1.49307 0.555194i
\(287\) 2.48445e22i 0.00655255i
\(288\) 1.40981e24 + 2.99340e23i 0.359116 + 0.0762501i
\(289\) −2.08168e24 −0.512196
\(290\) 4.29731e23 1.15567e24i 0.102145 0.274696i
\(291\) 1.54270e24i 0.354283i
\(292\) 5.22415e23 + 4.50857e23i 0.115928 + 0.100048i
\(293\) 4.07125e24 0.873075 0.436537 0.899686i \(-0.356205\pi\)
0.436537 + 0.899686i \(0.356205\pi\)
\(294\) −3.04235e24 1.13129e24i −0.630574 0.234477i
\(295\) 8.30710e23i 0.166429i
\(296\) −7.76928e23 + 4.27253e23i −0.150475 + 0.0827500i
\(297\) 5.07922e24 0.951113
\(298\) 1.53582e24 4.13024e24i 0.278084 0.747846i
\(299\) 1.02011e25i 1.78622i
\(300\) 2.46814e24 2.85987e24i 0.417981 0.484322i
\(301\) 2.69827e24 0.441998
\(302\) −4.19350e24 1.55934e24i −0.664519 0.247099i
\(303\) 5.65456e24i 0.866907i
\(304\) 1.10828e25 1.63855e24i 1.64404 0.243066i
\(305\) −4.24017e24 −0.608675
\(306\) 6.43263e23 1.72992e24i 0.0893665 0.240331i
\(307\) 3.43457e24i 0.461837i −0.972973 0.230918i \(-0.925827\pi\)
0.972973 0.230918i \(-0.0741730\pi\)
\(308\) −1.99816e24 1.72446e24i −0.260089 0.224463i
\(309\) 2.52999e24 0.318812
\(310\) 2.14058e24 + 7.95969e23i 0.261165 + 0.0971134i
\(311\) 9.90915e24i 1.17067i 0.810793 + 0.585333i \(0.199036\pi\)
−0.810793 + 0.585333i \(0.800964\pi\)
\(312\) −6.10342e24 1.10986e25i −0.698276 1.26976i
\(313\) −4.23818e24 −0.469609 −0.234804 0.972043i \(-0.575445\pi\)
−0.234804 + 0.972043i \(0.575445\pi\)
\(314\) −2.58812e24 + 6.96019e24i −0.277772 + 0.747007i
\(315\) 6.13884e23i 0.0638235i
\(316\) −9.91094e24 + 1.14840e25i −0.998261 + 1.15670i
\(317\) 1.28467e24 0.125371 0.0626855 0.998033i \(-0.480033\pi\)
0.0626855 + 0.998033i \(0.480033\pi\)
\(318\) 6.27783e24 + 2.33439e24i 0.593661 + 0.220751i
\(319\) 6.31988e24i 0.579165i
\(320\) −2.66859e24 + 4.20748e24i −0.237019 + 0.373699i
\(321\) −1.72927e25 −1.48872
\(322\) −1.60890e24 + 4.32678e24i −0.134267 + 0.361083i
\(323\) 1.43468e25i 1.16073i
\(324\) 4.80720e24 + 4.14873e24i 0.377087 + 0.325435i
\(325\) 1.92584e25 1.46483
\(326\) 6.91538e24 + 2.57146e24i 0.510082 + 0.189672i
\(327\) 6.24603e24i 0.446814i
\(328\) 2.10641e23 1.15837e23i 0.0146152 0.00803726i
\(329\) −8.32208e24 −0.560109
\(330\) −1.64340e24 + 4.41957e24i −0.107301 + 0.288563i
\(331\) 6.47947e24i 0.410449i −0.978715 0.205225i \(-0.934207\pi\)
0.978715 0.205225i \(-0.0657925\pi\)
\(332\) −1.14524e25 + 1.32701e25i −0.703906 + 0.815628i
\(333\) 1.05704e24 0.0630448
\(334\) 2.13976e25 + 7.95663e24i 1.23851 + 0.460537i
\(335\) 1.02992e25i 0.578572i
\(336\) −8.38302e23 5.67008e24i −0.0457096 0.309169i
\(337\) −1.56644e25 −0.829117 −0.414559 0.910023i \(-0.636064\pi\)
−0.414559 + 0.910023i \(0.636064\pi\)
\(338\) 1.57225e25 4.22822e25i 0.807895 2.17266i
\(339\) 5.62496e24i 0.280622i
\(340\) 4.83033e24 + 4.16869e24i 0.233985 + 0.201934i
\(341\) 1.17060e25 0.550635
\(342\) −1.25186e25 4.65501e24i −0.571868 0.212647i
\(343\) 1.63428e25i 0.725078i
\(344\) −1.25806e25 2.28770e25i −0.542148 0.985857i
\(345\) 8.24683e24 0.345220
\(346\) −1.03450e25 + 2.78205e25i −0.420696 + 1.13137i
\(347\) 7.41553e24i 0.292987i 0.989212 + 0.146493i \(0.0467987\pi\)
−0.989212 + 0.146493i \(0.953201\pi\)
\(348\) 8.96681e24 1.03900e25i 0.344228 0.398862i
\(349\) 5.41785e24 0.202103 0.101051 0.994881i \(-0.467779\pi\)
0.101051 + 0.994881i \(0.467779\pi\)
\(350\) 8.16841e24 + 3.03740e24i 0.296113 + 0.110109i
\(351\) 5.62311e25i 1.98110i
\(352\) −5.30422e24 + 2.49814e25i −0.181633 + 0.855440i
\(353\) 3.91060e25 1.30166 0.650828 0.759225i \(-0.274422\pi\)
0.650828 + 0.759225i \(0.274422\pi\)
\(354\) 3.22274e24 8.66684e24i 0.104278 0.280432i
\(355\) 2.86630e24i 0.0901650i
\(356\) −2.39110e25 2.06358e25i −0.731304 0.631133i
\(357\) −7.34001e24 −0.218280
\(358\) −3.20791e25 1.19285e25i −0.927665 0.344949i
\(359\) 3.06864e25i 0.862980i 0.902118 + 0.431490i \(0.142012\pi\)
−0.902118 + 0.431490i \(0.857988\pi\)
\(360\) 5.20474e24 2.86222e24i 0.142355 0.0782849i
\(361\) −6.62316e25 −1.76195
\(362\) −6.35327e24 + 1.70857e25i −0.164404 + 0.442128i
\(363\) 7.43399e24i 0.187135i
\(364\) 1.90912e25 2.21212e25i 0.467540 0.541746i
\(365\) 2.84399e24 0.0677642
\(366\) −4.42379e25 1.64497e25i −1.02561 0.381371i
\(367\) 3.23632e25i 0.730113i −0.930985 0.365057i \(-0.881050\pi\)
0.930985 0.365057i \(-0.118950\pi\)
\(368\) 4.41856e25 6.53269e24i 0.970068 0.143421i
\(369\) −2.86585e23 −0.00612336
\(370\) −1.27361e24 + 3.42509e24i −0.0264861 + 0.0712287i
\(371\) 1.54515e25i 0.312776i
\(372\) 1.92449e25 + 1.66088e25i 0.379215 + 0.327271i
\(373\) −6.42747e24 −0.123297 −0.0616484 0.998098i \(-0.519636\pi\)
−0.0616484 + 0.998098i \(0.519636\pi\)
\(374\) 3.06536e25 + 1.13984e25i 0.572486 + 0.212877i
\(375\) 3.49292e25i 0.635150i
\(376\) 3.88015e25 + 7.05577e25i 0.687022 + 1.24930i
\(377\) 6.99663e25 1.20636
\(378\) −8.86866e24 + 2.38503e25i −0.148916 + 0.400476i
\(379\) 7.60895e25i 1.24432i −0.782889 0.622161i \(-0.786255\pi\)
0.782889 0.622161i \(-0.213745\pi\)
\(380\) 3.01669e25 3.49549e25i 0.480502 0.556766i
\(381\) 2.49543e25 0.387165
\(382\) −7.19980e24 2.67722e24i −0.108814 0.0404623i
\(383\) 4.45029e25i 0.655241i −0.944809 0.327620i \(-0.893753\pi\)
0.944809 0.327620i \(-0.106247\pi\)
\(384\) −4.41645e25 + 3.35441e25i −0.633521 + 0.481175i
\(385\) −1.08778e25 −0.152032
\(386\) 2.29246e25 6.16507e25i 0.312197 0.839585i
\(387\) 3.11250e25i 0.413047i
\(388\) 2.60696e25 + 2.24986e25i 0.337145 + 0.290964i
\(389\) −9.57190e25 −1.20643 −0.603215 0.797579i \(-0.706114\pi\)
−0.603215 + 0.797579i \(0.706114\pi\)
\(390\) −4.89283e25 1.81938e25i −0.601055 0.223500i
\(391\) 5.71990e25i 0.684890i
\(392\) −6.34869e25 + 3.49131e25i −0.741009 + 0.407500i
\(393\) 3.00872e25 0.342339
\(394\) −5.39044e25 + 1.44964e26i −0.597946 + 1.60804i
\(395\) 6.25180e25i 0.676136i
\(396\) 1.98919e25 2.30491e25i 0.209761 0.243053i
\(397\) −1.10405e26 −1.13523 −0.567616 0.823294i \(-0.692134\pi\)
−0.567616 + 0.823294i \(0.692134\pi\)
\(398\) 9.19088e25 + 3.41760e25i 0.921566 + 0.342681i
\(399\) 5.31164e25i 0.519397i
\(400\) −1.23329e25 8.34167e25i −0.117615 0.795523i
\(401\) 2.17511e24 0.0202319 0.0101160 0.999949i \(-0.496780\pi\)
0.0101160 + 0.999949i \(0.496780\pi\)
\(402\) 3.99559e25 1.07453e26i 0.362510 0.974891i
\(403\) 1.29595e26i 1.14693i
\(404\) −9.55547e25 8.24660e25i −0.824971 0.711969i
\(405\) 2.61701e25 0.220422
\(406\) 2.96761e25 + 1.10349e25i 0.243863 + 0.0906797i
\(407\) 1.87304e25i 0.150177i
\(408\) 3.42226e25 + 6.22313e25i 0.267739 + 0.486864i
\(409\) 1.56984e26 1.19846 0.599228 0.800578i \(-0.295474\pi\)
0.599228 + 0.800578i \(0.295474\pi\)
\(410\) 3.45301e23 9.28611e23i 0.00257252 0.00691823i
\(411\) 5.06188e24i 0.0368039i
\(412\) 3.68974e25 4.27536e25i 0.261832 0.303389i
\(413\) 2.13316e25 0.147748
\(414\) −4.99101e25 1.85589e25i −0.337431 0.125473i
\(415\) 7.22414e25i 0.476766i
\(416\) −2.76564e26 5.87221e25i −1.78182 0.378328i
\(417\) 9.32841e25 0.586742
\(418\) 8.24854e25 2.21826e26i 0.506540 1.36223i
\(419\) 8.81451e25i 0.528516i −0.964452 0.264258i \(-0.914873\pi\)
0.964452 0.264258i \(-0.0851270\pi\)
\(420\) −1.78834e25 1.54338e25i −0.104702 0.0903605i
\(421\) 9.14206e25 0.522665 0.261332 0.965249i \(-0.415838\pi\)
0.261332 + 0.965249i \(0.415838\pi\)
\(422\) 2.36411e26 + 8.79088e25i 1.31991 + 0.490804i
\(423\) 9.59965e25i 0.523422i
\(424\) 1.31004e26 7.20425e25i 0.697631 0.383646i
\(425\) −1.07984e26 −0.561657
\(426\) −1.11198e25 + 2.99042e25i −0.0564938 + 0.151928i
\(427\) 1.08882e26i 0.540354i
\(428\) −2.52196e26 + 2.92224e26i −1.22264 + 1.41670i
\(429\) −2.67569e26 −1.26725
\(430\) −1.00853e26 3.75019e25i −0.466665 0.173528i
\(431\) 2.07549e26i 0.938315i 0.883114 + 0.469158i \(0.155442\pi\)
−0.883114 + 0.469158i \(0.844558\pi\)
\(432\) 2.43562e26 3.60098e25i 1.07590 0.159068i
\(433\) 2.42954e26 1.04869 0.524343 0.851507i \(-0.324311\pi\)
0.524343 + 0.851507i \(0.324311\pi\)
\(434\) −2.04395e25 + 5.49674e25i −0.0862128 + 0.231851i
\(435\) 5.65625e25i 0.233150i
\(436\) 1.05550e26 + 9.10920e25i 0.425200 + 0.366957i
\(437\) −4.13923e26 −1.62969
\(438\) 2.96715e25 + 1.10333e25i 0.114182 + 0.0424583i
\(439\) 5.15067e25i 0.193740i −0.995297 0.0968699i \(-0.969117\pi\)
0.995297 0.0968699i \(-0.0308831\pi\)
\(440\) 5.07177e25 + 9.22264e25i 0.186480 + 0.339100i
\(441\) 8.63764e25 0.310462
\(442\) −1.26190e26 + 3.39360e26i −0.443407 + 1.19245i
\(443\) 1.24024e26i 0.426059i −0.977046 0.213029i \(-0.931667\pi\)
0.977046 0.213029i \(-0.0683330\pi\)
\(444\) −2.65752e25 + 3.07932e25i −0.0892581 + 0.103425i
\(445\) −1.30170e26 −0.427475
\(446\) −3.65562e24 1.35933e24i −0.0117385 0.00436493i
\(447\) 2.02148e26i 0.634739i
\(448\) −1.08043e26 6.85260e25i −0.331753 0.210414i
\(449\) 2.51952e26 0.756579 0.378289 0.925687i \(-0.376512\pi\)
0.378289 + 0.925687i \(0.376512\pi\)
\(450\) −3.50369e25 + 9.42239e25i −0.102896 + 0.276717i
\(451\) 5.07820e24i 0.0145863i
\(452\) 9.50545e25 + 8.20342e25i 0.267047 + 0.230468i
\(453\) −2.05245e26 −0.564014
\(454\) −4.22466e26 1.57092e26i −1.13562 0.422276i
\(455\) 1.20427e26i 0.316671i
\(456\) 4.50340e26 2.47654e26i 1.15849 0.637084i
\(457\) 2.63098e25 0.0662150 0.0331075 0.999452i \(-0.489460\pi\)
0.0331075 + 0.999452i \(0.489460\pi\)
\(458\) −5.27108e25 + 1.41754e26i −0.129791 + 0.349045i
\(459\) 3.15295e26i 0.759609i
\(460\) 1.20272e26 1.39361e26i 0.283521 0.328520i
\(461\) 5.55492e26 1.28135 0.640677 0.767811i \(-0.278654\pi\)
0.640677 + 0.767811i \(0.278654\pi\)
\(462\) −1.13489e26 4.22005e25i −0.256173 0.0952572i
\(463\) 6.62902e26i 1.46433i 0.681126 + 0.732166i \(0.261491\pi\)
−0.681126 + 0.732166i \(0.738509\pi\)
\(464\) −4.48057e25 3.03055e26i −0.0968620 0.655151i
\(465\) 1.04768e26 0.221665
\(466\) 3.28946e26 8.84627e26i 0.681185 1.83190i
\(467\) 1.84071e26i 0.373092i 0.982446 + 0.186546i \(0.0597294\pi\)
−0.982446 + 0.186546i \(0.940271\pi\)
\(468\) 2.55172e26 + 2.20219e26i 0.506261 + 0.436915i
\(469\) 2.64471e26 0.513630
\(470\) 3.11054e26 + 1.15664e26i 0.591367 + 0.219898i
\(471\) 3.40656e26i 0.634026i
\(472\) −9.94581e25 1.80857e26i −0.181226 0.329546i
\(473\) −5.51525e26 −0.983907
\(474\) −2.42538e26 + 6.52253e26i −0.423640 + 1.13929i
\(475\) 7.81434e26i 1.33646i
\(476\) −1.07047e26 + 1.24037e26i −0.179268 + 0.207721i
\(477\) −1.78236e26 −0.292288
\(478\) −1.00815e27 3.74876e26i −1.61899 0.602018i
\(479\) 6.01355e26i 0.945749i −0.881130 0.472874i \(-0.843216\pi\)
0.881130 0.472874i \(-0.156784\pi\)
\(480\) −4.74724e25 + 2.23581e26i −0.0731187 + 0.344368i
\(481\) −2.07361e26 −0.312807
\(482\) 2.36572e26 6.36208e26i 0.349537 0.940002i
\(483\) 2.11768e26i 0.306471i
\(484\) −1.25625e26 1.08417e26i −0.178083 0.153690i
\(485\) 1.41921e26 0.197074
\(486\) −4.76355e26 1.77131e26i −0.647990 0.240953i
\(487\) 2.56966e26i 0.342441i −0.985233 0.171220i \(-0.945229\pi\)
0.985233 0.171220i \(-0.0547710\pi\)
\(488\) −9.23144e26 + 5.07661e26i −1.20523 + 0.662790i
\(489\) 3.38463e26 0.432935
\(490\) −1.04073e26 + 2.79882e26i −0.130430 + 0.350764i
\(491\) 1.07454e26i 0.131949i −0.997821 0.0659744i \(-0.978984\pi\)
0.997821 0.0659744i \(-0.0210156\pi\)
\(492\) 7.20508e24 8.34865e24i 0.00866937 0.0100454i
\(493\) −3.92310e26 −0.462551
\(494\) 2.45580e27 + 9.13181e26i 2.83742 + 1.05508i
\(495\) 1.25478e26i 0.142074i
\(496\) 5.61333e26 8.29912e25i 0.622879 0.0920906i
\(497\) −7.36029e25 −0.0800444
\(498\) −2.80260e26 + 7.53698e26i −0.298722 + 0.803348i
\(499\) 4.56847e26i 0.477271i 0.971109 + 0.238636i \(0.0767001\pi\)
−0.971109 + 0.238636i \(0.923300\pi\)
\(500\) −5.90259e26 5.09407e26i −0.604425 0.521633i
\(501\) 1.04727e27 1.05119
\(502\) 6.82024e26 + 2.53608e26i 0.671062 + 0.249532i
\(503\) 1.36768e27i 1.31918i −0.751626 0.659590i \(-0.770730\pi\)
0.751626 0.659590i \(-0.229270\pi\)
\(504\) 7.34981e25 + 1.33651e26i 0.0694978 + 0.126377i
\(505\) −5.20194e26 −0.482227
\(506\) 3.28859e26 8.84393e26i 0.298885 0.803785i
\(507\) 2.06944e27i 1.84405i
\(508\) 3.63933e26 4.21695e26i 0.317969 0.368436i
\(509\) −2.65638e26 −0.227569 −0.113784 0.993505i \(-0.536297\pi\)
−0.113784 + 0.993505i \(0.536297\pi\)
\(510\) 2.74347e26 + 1.02015e26i 0.230462 + 0.0856964i
\(511\) 7.30301e25i 0.0601580i
\(512\) −7.72425e25 + 1.23553e27i −0.0623960 + 0.998051i
\(513\) −2.28165e27 −1.80749
\(514\) −6.21560e25 + 1.67155e26i −0.0482894 + 0.129864i
\(515\) 2.32748e26i 0.177343i
\(516\) −9.06718e26 7.82519e26i −0.677603 0.584787i
\(517\) 1.70103e27 1.24683
\(518\) −8.79519e25 3.27046e25i −0.0632336 0.0235132i
\(519\) 1.36163e27i 0.960255i
\(520\) −1.02102e27 + 5.61487e26i −0.706320 + 0.388424i
\(521\) 6.73621e26 0.457129 0.228564 0.973529i \(-0.426597\pi\)
0.228564 + 0.973529i \(0.426597\pi\)
\(522\) −1.27290e26 + 3.42318e26i −0.0847401 + 0.227890i
\(523\) 2.31489e27i 1.51187i 0.654648 + 0.755934i \(0.272817\pi\)
−0.654648 + 0.755934i \(0.727183\pi\)
\(524\) 4.38791e26 5.08435e26i 0.281154 0.325778i
\(525\) 3.99791e26 0.251327
\(526\) −1.08385e27 4.03025e26i −0.668514 0.248585i
\(527\) 7.26655e26i 0.439766i
\(528\) 1.71349e26 + 1.15896e27i 0.101752 + 0.688224i
\(529\) 6.58969e25 0.0383980
\(530\) 2.14753e26 5.77532e26i 0.122795 0.330231i
\(531\) 2.46063e26i 0.138071i
\(532\) 8.97597e26 + 7.74648e26i 0.494271 + 0.426568i
\(533\) 5.62198e25 0.0303821
\(534\) −1.35807e27 5.04994e26i −0.720293 0.267839i
\(535\) 1.59085e27i 0.828114i
\(536\) −1.23309e27 2.24229e27i −0.630011 1.14563i
\(537\) −1.57006e27 −0.787361
\(538\) 2.30057e26 6.18687e26i 0.113243 0.304543i
\(539\) 1.53056e27i 0.739543i
\(540\) 6.62967e26 7.68191e26i 0.314452 0.364361i
\(541\) 2.78485e26 0.129667 0.0648333 0.997896i \(-0.479348\pi\)
0.0648333 + 0.997896i \(0.479348\pi\)
\(542\) −1.44387e26 5.36899e25i −0.0659987 0.0245414i
\(543\) 8.36236e26i 0.375258i
\(544\) 1.55073e27 + 3.29262e26i 0.683199 + 0.145062i
\(545\) 5.74606e26 0.248545
\(546\) 4.67194e26 1.25642e27i 0.198413 0.533589i
\(547\) 3.92778e27i 1.63785i −0.573901 0.818924i \(-0.694571\pi\)
0.573901 0.818924i \(-0.305429\pi\)
\(548\) 8.55392e25 + 7.38223e25i 0.0350235 + 0.0302261i
\(549\) 1.25597e27 0.504960
\(550\) −1.66962e27 6.20843e26i −0.659160 0.245106i
\(551\) 2.83897e27i 1.10064i
\(552\) 1.79545e27 9.87365e26i 0.683569 0.375913i
\(553\) −1.60538e27 −0.600243
\(554\) −4.65094e26 + 1.25077e27i −0.170783 + 0.459282i
\(555\) 1.67636e26i 0.0604557i
\(556\) 1.36045e27 1.57638e27i 0.481876 0.558358i
\(557\) 3.16206e27 1.10007 0.550033 0.835143i \(-0.314615\pi\)
0.550033 + 0.835143i \(0.314615\pi\)
\(558\) −6.34058e26 2.35772e26i −0.216664 0.0805658i
\(559\) 6.10584e27i 2.04940i
\(560\) −5.21621e26 + 7.71199e25i −0.171979 + 0.0254265i
\(561\) 1.50029e27 0.485901
\(562\) −2.10000e27 + 5.64749e27i −0.668123 + 1.79677i
\(563\) 8.24040e26i 0.257552i −0.991674 0.128776i \(-0.958895\pi\)
0.991674 0.128776i \(-0.0411048\pi\)
\(564\) 2.79652e27 + 2.41346e27i 0.858672 + 0.741054i
\(565\) 5.17470e26 0.156099
\(566\) 1.09230e27 + 4.06168e26i 0.323726 + 0.120376i
\(567\) 6.72014e26i 0.195681i
\(568\) 3.43172e26 + 6.24033e26i 0.0981813 + 0.178535i
\(569\) −6.59416e27 −1.85369 −0.926844 0.375446i \(-0.877489\pi\)
−0.926844 + 0.375446i \(0.877489\pi\)
\(570\) 7.38238e26 1.98533e27i 0.203914 0.548383i
\(571\) 7.51186e25i 0.0203886i −0.999948 0.0101943i \(-0.996755\pi\)
0.999948 0.0101943i \(-0.00324500\pi\)
\(572\) −3.90222e27 + 4.52157e27i −1.04076 + 1.20595i
\(573\) −3.52383e26 −0.0923569
\(574\) 2.38455e25 + 8.86688e24i 0.00614169 + 0.00228377i
\(575\) 3.11548e27i 0.788580i
\(576\) 7.90459e26 1.24629e27i 0.196632 0.310023i
\(577\) −2.15646e27 −0.527209 −0.263605 0.964631i \(-0.584911\pi\)
−0.263605 + 0.964631i \(0.584911\pi\)
\(578\) −7.42943e26 + 1.99798e27i −0.178516 + 0.480080i
\(579\) 3.01740e27i 0.712603i
\(580\) −9.55832e26 8.24906e26i −0.221872 0.191480i
\(581\) −1.85507e27 −0.423251
\(582\) 1.48067e27 + 5.50581e26i 0.332069 + 0.123479i
\(583\) 3.15829e27i 0.696252i
\(584\) 6.19177e26 3.40502e26i 0.134180 0.0737888i
\(585\) 1.38914e27 0.295929
\(586\) 1.45301e27 3.90755e27i 0.304293 0.818330i
\(587\) 2.34361e25i 0.00482508i −0.999997 0.00241254i \(-0.999232\pi\)
0.999997 0.00241254i \(-0.000767936\pi\)
\(588\) −2.17160e27 + 2.51627e27i −0.439549 + 0.509313i
\(589\) −5.25848e27 −1.04642
\(590\) −7.97310e26 2.96477e26i −0.155994 0.0580057i
\(591\) 7.09505e27i 1.36484i
\(592\) 1.32792e26 + 8.98174e26i 0.0251163 + 0.169880i
\(593\) 7.67293e27 1.42697 0.713484 0.700672i \(-0.247116\pi\)
0.713484 + 0.700672i \(0.247116\pi\)
\(594\) 1.81275e27 4.87499e27i 0.331492 0.891476i
\(595\) 6.75247e26i 0.121421i
\(596\) −3.41604e27 2.94813e27i −0.604033 0.521295i
\(597\) 4.49834e27 0.782185
\(598\) 9.79096e27 + 3.64073e27i 1.67422 + 0.622554i
\(599\) 3.68287e27i 0.619324i −0.950847 0.309662i \(-0.899784\pi\)
0.950847 0.309662i \(-0.100216\pi\)
\(600\) −1.86402e27 3.38958e27i −0.308274 0.560574i
\(601\) 8.99774e27 1.46349 0.731743 0.681581i \(-0.238707\pi\)
0.731743 + 0.681581i \(0.238707\pi\)
\(602\) 9.63001e26 2.58978e27i 0.154050 0.414284i
\(603\) 3.05072e27i 0.479987i
\(604\) −2.99329e27 + 3.46837e27i −0.463211 + 0.536730i
\(605\) −6.83893e26 −0.104096
\(606\) −5.42720e27 2.01809e27i −0.812550 0.302144i
\(607\) 7.57570e27i 1.11567i −0.829952 0.557835i \(-0.811632\pi\)
0.829952 0.557835i \(-0.188368\pi\)
\(608\) 2.38272e27 1.12219e28i 0.345174 1.62567i
\(609\) 1.45245e27 0.206980
\(610\) −1.51330e27 + 4.06969e27i −0.212142 + 0.570509i
\(611\) 1.88318e28i 2.59705i
\(612\) −1.43078e27 1.23480e27i −0.194115 0.167526i
\(613\) −2.13003e25 −0.00284302 −0.00142151 0.999999i \(-0.500452\pi\)
−0.00142151 + 0.999999i \(0.500452\pi\)
\(614\) −3.29647e27 1.22578e27i −0.432878 0.160964i
\(615\) 4.54495e25i 0.00587189i
\(616\) −2.36825e27 + 1.30237e27i −0.301038 + 0.165549i
\(617\) −1.43698e28 −1.79721 −0.898605 0.438759i \(-0.855418\pi\)
−0.898605 + 0.438759i \(0.855418\pi\)
\(618\) 9.02943e26 2.42827e27i 0.111116 0.298822i
\(619\) 1.69027e25i 0.00204667i 0.999999 + 0.00102334i \(0.000325738\pi\)
−0.999999 + 0.00102334i \(0.999674\pi\)
\(620\) 1.52793e27 1.77044e27i 0.182048 0.210942i
\(621\) −9.09664e27 −1.06651
\(622\) 9.51073e27 + 3.53653e27i 1.09726 + 0.408013i
\(623\) 3.34260e27i 0.379493i
\(624\) −1.28307e28 + 1.89697e27i −1.43352 + 0.211941i
\(625\) 4.10056e27 0.450862
\(626\) −1.51259e27 + 4.06778e27i −0.163673 + 0.440163i
\(627\) 1.08570e28i 1.15620i
\(628\) 5.75665e27 + 4.96812e27i 0.603355 + 0.520710i
\(629\) 1.16270e27 0.119939
\(630\) 5.89201e26 + 2.19092e26i 0.0598216 + 0.0222445i
\(631\) 1.22788e28i 1.22706i 0.789673 + 0.613528i \(0.210250\pi\)
−0.789673 + 0.613528i \(0.789750\pi\)
\(632\) 7.48506e27 + 1.36110e28i 0.736249 + 1.33881i
\(633\) 1.15708e28 1.12028
\(634\) 4.58491e26 1.23301e27i 0.0436957 0.117510i
\(635\) 2.29568e27i 0.215365i
\(636\) 4.48106e27 5.19228e27i 0.413818 0.479498i
\(637\) −1.69446e28 −1.54041
\(638\) −6.06577e27 2.25554e27i −0.542849 0.201857i
\(639\) 8.49021e26i 0.0748014i
\(640\) 3.08590e27 + 4.06293e27i 0.267659 + 0.352403i
\(641\) 1.84865e28 1.57861 0.789306 0.614000i \(-0.210441\pi\)
0.789306 + 0.614000i \(0.210441\pi\)
\(642\) −6.17168e27 + 1.65974e28i −0.518863 + 1.39537i
\(643\) 1.89929e28i 1.57211i −0.618159 0.786053i \(-0.712121\pi\)
0.618159 0.786053i \(-0.287879\pi\)
\(644\) 3.57861e27 + 3.08842e27i 0.291645 + 0.251697i
\(645\) −4.93611e27 −0.396084
\(646\) −1.37700e28 5.12032e27i −1.08795 0.404550i
\(647\) 1.85495e28i 1.44308i −0.692375 0.721538i \(-0.743436\pi\)
0.692375 0.721538i \(-0.256564\pi\)
\(648\) 5.69758e27 3.13325e27i 0.436456 0.240019i
\(649\) −4.36016e27 −0.328894
\(650\) 6.87324e27 1.84841e28i 0.510538 1.37298i
\(651\) 2.69030e27i 0.196784i
\(652\) 4.93614e27 5.71959e27i 0.355559 0.411992i
\(653\) 7.10570e26 0.0504052 0.0252026 0.999682i \(-0.491977\pi\)
0.0252026 + 0.999682i \(0.491977\pi\)
\(654\) 5.99490e27 + 2.22918e27i 0.418798 + 0.155729i
\(655\) 2.76788e27i 0.190430i
\(656\) −3.60026e25 2.43513e26i −0.00243947 0.0165000i
\(657\) −8.42414e26 −0.0562176
\(658\) −2.97011e27 + 7.98747e27i −0.195215 + 0.524989i
\(659\) 7.25237e26i 0.0469490i −0.999724 0.0234745i \(-0.992527\pi\)
0.999724 0.0234745i \(-0.00747284\pi\)
\(660\) 3.65535e27 + 3.15465e27i 0.233072 + 0.201146i
\(661\) −1.64602e27 −0.103376 −0.0516880 0.998663i \(-0.516460\pi\)
−0.0516880 + 0.998663i \(0.516460\pi\)
\(662\) −6.21895e27 2.31250e27i −0.384713 0.143054i
\(663\) 1.66095e28i 1.01209i
\(664\) 8.64921e27 + 1.57279e28i 0.519153 + 0.944041i
\(665\) 4.88646e27 0.288920
\(666\) 3.77253e26 1.01454e27i 0.0219731 0.0590917i
\(667\) 1.13186e28i 0.649434i
\(668\) 1.52734e28 1.76976e28i 0.863320 1.00034i
\(669\) −1.78919e26 −0.00996313
\(670\) −9.88514e27 3.67576e27i −0.542294 0.201650i
\(671\) 2.22555e28i 1.20285i
\(672\) −5.74128e27 1.21903e27i −0.305715 0.0649115i
\(673\) 4.79262e27 0.251433 0.125716 0.992066i \(-0.459877\pi\)
0.125716 + 0.992066i \(0.459877\pi\)
\(674\) −5.59057e27 + 1.50346e28i −0.288973 + 0.777129i
\(675\) 1.71733e28i 0.874612i
\(676\) −3.49709e28 3.01807e28i −1.75485 1.51447i
\(677\) −9.21148e26 −0.0455452 −0.0227726 0.999741i \(-0.507249\pi\)
−0.0227726 + 0.999741i \(0.507249\pi\)
\(678\) 5.39879e27 + 2.00752e27i 0.263026 + 0.0978055i
\(679\) 3.64435e27i 0.174953i
\(680\) 5.72500e27 3.14833e27i 0.270823 0.148933i
\(681\) −2.06770e28 −0.963863
\(682\) 4.17781e27 1.12353e28i 0.191913 0.516109i
\(683\) 3.26558e28i 1.47827i −0.673558 0.739135i \(-0.735235\pi\)
0.673558 0.739135i \(-0.264765\pi\)
\(684\) −8.93569e27 + 1.03539e28i −0.398627 + 0.461896i
\(685\) 4.65669e26 0.0204726
\(686\) −1.56857e28 5.83266e27i −0.679613 0.252712i
\(687\) 6.93795e27i 0.296254i
\(688\) −2.64471e28 + 3.91012e27i −1.11300 + 0.164553i
\(689\) 3.49648e28 1.45024
\(690\) 2.94326e27 7.91525e27i 0.120320 0.323574i
\(691\) 4.19194e28i 1.68902i 0.535541 + 0.844509i \(0.320108\pi\)
−0.535541 + 0.844509i \(0.679892\pi\)
\(692\) 2.30098e28 + 1.98580e28i 0.913803 + 0.788634i
\(693\) 3.22210e27 0.126127
\(694\) 7.11737e27 + 2.64657e27i 0.274616 + 0.102115i
\(695\) 8.58170e27i 0.326381i
\(696\) −6.77203e27 1.23144e28i −0.253879 0.461659i
\(697\) −3.15232e26 −0.0116494
\(698\) 1.93361e27 5.20001e27i 0.0704391 0.189430i
\(699\) 4.32967e28i 1.55483i
\(700\) 5.83054e27 6.75595e27i 0.206409 0.239170i
\(701\) −3.11179e28 −1.08600 −0.543000 0.839732i \(-0.682712\pi\)
−0.543000 + 0.839732i \(0.682712\pi\)
\(702\) 5.39702e28 + 2.00686e28i 1.85688 + 0.690473i
\(703\) 8.41395e27i 0.285395i
\(704\) 2.20839e28 + 1.40067e28i 0.738497 + 0.468392i
\(705\) 1.52241e28 0.501926
\(706\) 1.39568e28 3.75336e28i 0.453667 1.22004i
\(707\) 1.33579e28i 0.428099i
\(708\) −7.16819e27 6.18632e27i −0.226504 0.195479i
\(709\) 3.43808e28 1.07116 0.535580 0.844485i \(-0.320093\pi\)
0.535580 + 0.844485i \(0.320093\pi\)
\(710\) 2.75105e27 + 1.02297e27i 0.0845114 + 0.0314253i
\(711\) 1.85183e28i 0.560926i
\(712\) −2.83398e28 + 1.55848e28i −0.846441 + 0.465480i
\(713\) −2.09649e28 −0.617443
\(714\) −2.61962e27 + 7.04488e27i −0.0760774 + 0.204593i
\(715\) 2.46151e28i 0.704923i
\(716\) −2.28978e28 + 2.65320e28i −0.646640 + 0.749273i
\(717\) −4.93423e28 −1.37413
\(718\) 2.94525e28 + 1.09518e28i 0.808869 + 0.300775i
\(719\) 8.43616e27i 0.228484i −0.993453 0.114242i \(-0.963556\pi\)
0.993453 0.114242i \(-0.0364439\pi\)
\(720\) −8.89591e26 6.01698e27i −0.0237610 0.160714i
\(721\) 5.97666e27 0.157437
\(722\) −2.36378e28 + 6.35686e28i −0.614094 + 1.65147i
\(723\) 3.11383e28i 0.797832i
\(724\) 1.41313e28 + 1.21956e28i 0.357105 + 0.308190i
\(725\) 2.13681e28 0.532581
\(726\) −7.13509e27 2.65316e27i −0.175401 0.0652224i
\(727\) 4.05297e28i 0.982718i −0.870957 0.491359i \(-0.836500\pi\)
0.870957 0.491359i \(-0.163500\pi\)
\(728\) −1.44183e28 2.62185e28i −0.344825 0.627039i
\(729\) −4.44295e28 −1.04808
\(730\) 1.01501e27 2.72964e27i 0.0236179 0.0635152i
\(731\) 3.42362e28i 0.785800i
\(732\) −3.15767e28 + 3.65884e28i −0.714916 + 0.828386i
\(733\) 1.18252e28 0.264101 0.132050 0.991243i \(-0.457844\pi\)
0.132050 + 0.991243i \(0.457844\pi\)
\(734\) −3.10619e28 1.15503e28i −0.684333 0.254467i
\(735\) 1.36984e28i 0.297713i
\(736\) 9.49961e27 4.47405e28i 0.203670 0.959229i
\(737\) −5.40578e28 −1.14336
\(738\) −1.02281e26 + 2.75062e26i −0.00213418 + 0.00573941i
\(739\) 5.26424e28i 1.08366i 0.840490 + 0.541828i \(0.182267\pi\)
−0.840490 + 0.541828i \(0.817733\pi\)
\(740\) 2.83283e27 + 2.44480e27i 0.0575312 + 0.0496508i
\(741\) 1.20195e29 2.40827
\(742\) 1.48303e28 + 5.51459e27i 0.293164 + 0.109012i
\(743\) 1.23546e28i 0.240957i 0.992716 + 0.120478i \(0.0384428\pi\)
−0.992716 + 0.120478i \(0.961557\pi\)
\(744\) 2.28094e28 1.25435e28i 0.438918 0.241373i
\(745\) −1.85967e28 −0.353080
\(746\) −2.29394e27 + 6.16904e27i −0.0429728 + 0.115566i
\(747\) 2.13985e28i 0.395528i
\(748\) 2.18803e28 2.53530e28i 0.399058 0.462396i
\(749\) −4.08509e28 −0.735162
\(750\) −3.35248e28 1.24661e28i −0.595324 0.221369i
\(751\) 6.50823e28i 1.14042i 0.821500 + 0.570208i \(0.193138\pi\)
−0.821500 + 0.570208i \(0.806862\pi\)
\(752\) 8.15688e28 1.20597e28i 1.41041 0.208525i
\(753\) 3.33807e28 0.569567
\(754\) 2.49707e28 6.71531e28i 0.420452 1.13071i
\(755\) 1.88816e28i 0.313739i
\(756\) 1.97262e28 + 1.70241e28i 0.323463 + 0.279156i
\(757\) 8.59189e28 1.39037 0.695184 0.718832i \(-0.255323\pi\)
0.695184 + 0.718832i \(0.255323\pi\)
\(758\) −7.30301e28 2.71560e28i −1.16630 0.433685i
\(759\) 4.32853e28i 0.682217i
\(760\) −2.27830e28 4.14292e28i −0.354385 0.644423i
\(761\) −5.28034e28 −0.810616 −0.405308 0.914180i \(-0.632836\pi\)
−0.405308 + 0.914180i \(0.632836\pi\)
\(762\) 8.90608e27 2.39509e28i 0.134939 0.362888i
\(763\) 1.47552e28i 0.220647i
\(764\) −5.13915e27 + 5.95482e27i −0.0758504 + 0.0878891i
\(765\) −7.78908e27 −0.113468
\(766\) −4.27136e28 1.58829e28i −0.614156 0.228372i
\(767\) 4.82706e28i 0.685061i
\(768\) 1.64332e28 + 5.43604e28i 0.230203 + 0.761502i
\(769\) −7.68587e26 −0.0106275 −0.00531373 0.999986i \(-0.501691\pi\)
−0.00531373 + 0.999986i \(0.501691\pi\)
\(770\) −3.88225e27 + 1.04405e28i −0.0529879 + 0.142499i
\(771\) 8.18116e27i 0.110223i
\(772\) −5.09902e28 4.40057e28i −0.678131 0.585243i
\(773\) 1.94609e28 0.255486 0.127743 0.991807i \(-0.459227\pi\)
0.127743 + 0.991807i \(0.459227\pi\)
\(774\) 2.98735e28 + 1.11084e28i 0.387148 + 0.143960i
\(775\) 3.95790e28i 0.506346i
\(776\) 3.08981e28 1.69917e28i 0.390225 0.214595i
\(777\) −4.30468e27 −0.0536699
\(778\) −3.41617e28 + 9.18703e28i −0.420478 + 1.13078i
\(779\) 2.28119e27i 0.0277196i
\(780\) −3.49246e28 + 4.04677e28i −0.418972 + 0.485470i
\(781\) 1.50444e28 0.178182
\(782\) −5.48991e28 2.04141e28i −0.641945 0.238705i
\(783\) 6.23910e28i 0.720285i
\(784\) 1.08511e28 + 7.33946e28i 0.123684 + 0.836572i
\(785\) 3.13388e28 0.352684
\(786\) 1.07380e28 2.88775e28i 0.119316 0.320873i
\(787\) 1.09776e29i 1.20437i −0.798356 0.602186i \(-0.794297\pi\)
0.798356 0.602186i \(-0.205703\pi\)
\(788\) 1.19897e29 + 1.03474e29i 1.29881 + 1.12091i
\(789\) −5.30473e28 −0.567405
\(790\) 6.00043e28 + 2.23124e28i 0.633741 + 0.235654i
\(791\) 1.32880e28i 0.138578i
\(792\) −1.50230e28 2.73182e28i −0.154705 0.281320i
\(793\) −2.46386e29 −2.50544
\(794\) −3.94031e28 + 1.05966e29i −0.395663 + 1.06405i
\(795\) 2.82664e28i 0.280285i
\(796\) 6.56037e28 7.60161e28i 0.642389 0.744347i
\(797\) 4.82089e28 0.466170 0.233085 0.972456i \(-0.425118\pi\)
0.233085 + 0.972456i \(0.425118\pi\)
\(798\) 5.09807e28 + 1.89570e28i 0.486829 + 0.181026i
\(799\) 1.05592e29i 0.995782i
\(800\) −8.44642e28 1.79340e28i −0.786635 0.167024i
\(801\) 3.85574e28 0.354636
\(802\) 7.76287e26 2.08765e27i 0.00705145 0.0189633i
\(803\) 1.49273e28i 0.133914i
\(804\) −8.88721e28 7.66987e28i −0.787417 0.679559i
\(805\) 1.94817e28 0.170478
\(806\) 1.24384e29 + 4.62518e28i 1.07502 + 0.399741i
\(807\) 3.02807e28i 0.258483i
\(808\) −1.13253e29 + 6.22810e28i −0.954854 + 0.525100i
\(809\) −5.78152e28 −0.481456 −0.240728 0.970593i \(-0.577386\pi\)
−0.240728 + 0.970593i \(0.577386\pi\)
\(810\) 9.33998e27 2.51178e28i 0.0768238 0.206601i
\(811\) 7.59855e28i 0.617337i −0.951170 0.308668i \(-0.900117\pi\)
0.951170 0.308668i \(-0.0998833\pi\)
\(812\) 2.11825e28 2.45445e28i 0.169988 0.196967i
\(813\) −7.06681e27 −0.0560168
\(814\) 1.79773e28 + 6.68481e27i 0.140761 + 0.0523414i
\(815\) 3.11371e28i 0.240825i
\(816\) 7.19431e28 1.06365e28i 0.549652 0.0812642i
\(817\) 2.47752e29 1.86981
\(818\) 5.60269e28 1.50672e29i 0.417699 1.12331i
\(819\) 3.56713e28i 0.262712i
\(820\) −7.68037e26 6.62834e26i −0.00558784 0.00482243i
\(821\) 2.52919e29 1.81782 0.908908 0.416997i \(-0.136917\pi\)
0.908908 + 0.416997i \(0.136917\pi\)
\(822\) 4.85835e27 + 1.80656e27i 0.0344962 + 0.0128273i
\(823\) 2.11620e29i 1.48443i 0.670163 + 0.742214i \(0.266224\pi\)
−0.670163 + 0.742214i \(0.733776\pi\)
\(824\) −2.78661e28 5.06724e28i −0.193110 0.351155i
\(825\) −8.17171e28 −0.559466
\(826\) 7.61314e27 2.04739e28i 0.0514948 0.138484i
\(827\) 5.82890e28i 0.389521i 0.980851 + 0.194761i \(0.0623930\pi\)
−0.980851 + 0.194761i \(0.937607\pi\)
\(828\) −3.56254e28 + 4.12798e28i −0.235211 + 0.272542i
\(829\) −1.85843e29 −1.21228 −0.606138 0.795359i \(-0.707282\pi\)
−0.606138 + 0.795359i \(0.707282\pi\)
\(830\) 6.93367e28 + 2.57826e28i 0.446871 + 0.166168i
\(831\) 6.12170e28i 0.389818i
\(832\) −1.55066e29 + 2.44487e29i −0.975623 + 1.53823i
\(833\) 9.50105e28 0.590638
\(834\) 3.32927e28 8.95333e28i 0.204498 0.549951i
\(835\) 9.63444e28i 0.584739i
\(836\) −1.83469e29 1.58338e29i −1.10027 0.949558i
\(837\) −1.15564e29 −0.684804
\(838\) −8.46010e28 3.14586e28i −0.495377 0.184204i
\(839\) 1.00427e29i 0.581071i 0.956864 + 0.290536i \(0.0938335\pi\)
−0.956864 + 0.290536i \(0.906167\pi\)
\(840\) −2.11957e28 + 1.16561e28i −0.121187 + 0.0666437i
\(841\) −9.93638e28 −0.561394
\(842\) 3.26276e28 8.77448e28i 0.182165 0.489892i
\(843\) 2.76408e29i 1.52502i
\(844\) 1.68748e29 1.95532e29i 0.920058 1.06609i
\(845\) −1.90379e29 −1.02577
\(846\) −9.21367e28 3.42607e28i −0.490602 0.182429i
\(847\) 1.75615e28i 0.0924117i
\(848\) −2.23911e28 1.51448e29i −0.116444 0.787600i
\(849\) 5.34610e28 0.274764
\(850\) −3.85391e28 + 1.03642e29i −0.195755 + 0.526440i
\(851\) 3.35453e28i 0.168398i
\(852\) 2.47333e28 + 2.13454e28i 0.122712 + 0.105903i
\(853\) 7.73820e28 0.379446 0.189723 0.981838i \(-0.439241\pi\)
0.189723 + 0.981838i \(0.439241\pi\)
\(854\) −1.04504e29 3.88596e28i −0.506472 0.188330i
\(855\) 5.63661e28i 0.269996i
\(856\) 1.90466e29 + 3.46349e29i 0.901739 + 1.63974i
\(857\) 8.40785e28 0.393439 0.196719 0.980460i \(-0.436971\pi\)
0.196719 + 0.980460i \(0.436971\pi\)
\(858\) −9.54943e28 + 2.56811e29i −0.441677 + 1.18779i
\(859\) 1.74941e28i 0.0799759i 0.999200 + 0.0399880i \(0.0127320\pi\)
−0.999200 + 0.0399880i \(0.987268\pi\)
\(860\) −7.19881e28 + 8.34139e28i −0.325294 + 0.376924i
\(861\) 1.16708e27 0.00521279
\(862\) 1.99204e29 + 7.40735e28i 0.879480 + 0.327032i
\(863\) 2.78339e29i 1.21469i −0.794437 0.607346i \(-0.792234\pi\)
0.794437 0.607346i \(-0.207766\pi\)
\(864\) 5.23642e28 2.46621e29i 0.225890 1.06388i
\(865\) 1.25264e29 0.534153
\(866\) 8.67092e28 2.33185e29i 0.365499 0.982930i
\(867\) 9.77883e28i 0.407470i
\(868\) 4.54626e28 + 3.92353e28i 0.187265 + 0.161614i
\(869\) 3.28139e29 1.33617
\(870\) −5.42882e28 2.01869e28i −0.218531 0.0812600i
\(871\) 5.98465e29i 2.38154i
\(872\) 1.25100e29 6.87956e28i 0.492143 0.270642i
\(873\) −4.20381e28 −0.163494
\(874\) −1.47727e29 + 3.97280e29i −0.567998 + 1.52751i
\(875\) 8.25141e28i 0.313652i
\(876\) 2.11793e28 2.45408e28i 0.0795921 0.0922248i
\(877\) −3.40612e29 −1.26550 −0.632752 0.774355i \(-0.718075\pi\)
−0.632752 + 0.774355i \(0.718075\pi\)
\(878\) −4.94358e28 1.83825e28i −0.181592 0.0675243i
\(879\) 1.91249e29i 0.694562i
\(880\) 1.06619e29 1.57633e28i 0.382832 0.0566004i
\(881\) −2.52780e28 −0.0897394 −0.0448697 0.998993i \(-0.514287\pi\)
−0.0448697 + 0.998993i \(0.514287\pi\)
\(882\) 3.08273e28 8.29034e28i 0.108206 0.290996i
\(883\) 8.39810e28i 0.291457i −0.989325 0.145728i \(-0.953447\pi\)
0.989325 0.145728i \(-0.0465526\pi\)
\(884\) 2.80679e29 + 2.42232e29i 0.963135 + 0.831208i
\(885\) −3.90231e28 −0.132400
\(886\) −1.19038e29 4.42637e28i −0.399344 0.148495i
\(887\) 4.81109e29i 1.59591i 0.602720 + 0.797953i \(0.294084\pi\)
−0.602720 + 0.797953i \(0.705916\pi\)
\(888\) 2.00705e28 + 3.64967e28i 0.0658306 + 0.119708i
\(889\) 5.89501e28 0.191191
\(890\) −4.64571e28 + 1.24936e29i −0.148988 + 0.400671i
\(891\) 1.37359e29i 0.435593i
\(892\) −2.60935e27 + 3.02350e27i −0.00818247 + 0.00948116i
\(893\) −7.64124e29 −2.36946
\(894\) −1.94020e29 7.21459e28i −0.594939 0.221226i
\(895\) 1.44439e29i 0.437978i
\(896\) −1.04331e29 + 7.92419e28i −0.312847 + 0.237616i
\(897\) 4.79204e29 1.42101
\(898\) 8.99205e28 2.41821e29i 0.263691 0.709139i
\(899\) 1.43791e29i 0.417000i
\(900\) 7.79309e28 + 6.72562e28i 0.223504 + 0.192889i
\(901\) −1.96052e29 −0.556063
\(902\) −4.87401e27 1.81239e27i −0.0136717 0.00508376i
\(903\) 1.26753e29i 0.351626i
\(904\) 1.12660e29 6.19549e28i 0.309091 0.169977i
\(905\) 7.69299e28 0.208742
\(906\) −7.32510e28 + 1.96992e29i −0.196576 + 0.528649i
\(907\) 4.31861e28i 0.114623i 0.998356 + 0.0573115i \(0.0182528\pi\)
−0.998356 + 0.0573115i \(0.981747\pi\)
\(908\) −3.01552e29 + 3.49414e29i −0.791597 + 0.917237i
\(909\) 1.54085e29 0.400058
\(910\) −1.15585e29 4.29797e28i −0.296815 0.110370i
\(911\) 2.79697e29i 0.710402i 0.934790 + 0.355201i \(0.115588\pi\)
−0.934790 + 0.355201i \(0.884412\pi\)
\(912\) −7.69719e28 5.20620e29i −0.193368 1.30789i
\(913\) 3.79174e29 0.942174
\(914\) 9.38987e27 2.52520e28i 0.0230780 0.0620631i
\(915\) 1.99185e29i 0.484223i
\(916\) 1.17242e29 + 1.01183e29i 0.281922 + 0.243306i
\(917\) 7.10757e28 0.169055
\(918\) −3.02618e29 1.12527e29i −0.711980 0.264747i
\(919\) 3.42266e29i 0.796541i 0.917268 + 0.398270i \(0.130389\pi\)
−0.917268 + 0.398270i \(0.869611\pi\)
\(920\) −9.08330e28 1.65173e29i −0.209105 0.380243i
\(921\) −1.61341e29 −0.367408
\(922\) 1.98253e29 5.33157e29i 0.446591 1.20101i
\(923\) 1.66554e29i 0.371140i
\(924\) −8.10074e28 + 9.38647e28i −0.178569 + 0.206910i
\(925\) −6.33293e28 −0.138098
\(926\) 6.36249e29 + 2.36587e29i 1.37251 + 0.510365i
\(927\) 6.89418e28i 0.147124i
\(928\) −3.06861e29 6.51549e28i −0.647831 0.137552i
\(929\) 5.60736e29 1.17112 0.585560 0.810629i \(-0.300875\pi\)
0.585560 + 0.810629i \(0.300875\pi\)
\(930\) 3.73911e28 1.00555e29i 0.0772572 0.207766i
\(931\) 6.87548e29i 1.40542i
\(932\) −7.31659e29 6.31439e29i −1.47962 1.27694i
\(933\) 4.65489e29 0.931307
\(934\) 1.76670e29 + 6.56941e28i 0.349698 + 0.130034i
\(935\) 1.38020e29i 0.270288i
\(936\) 3.02435e29 1.66317e29i 0.585967 0.322239i
\(937\) −5.90326e29 −1.13161 −0.565804 0.824540i \(-0.691434\pi\)
−0.565804 + 0.824540i \(0.691434\pi\)
\(938\) 9.43887e28 2.53838e29i 0.179016 0.481424i
\(939\) 1.99091e29i 0.373591i
\(940\) 2.22028e29 2.57267e29i 0.412220 0.477646i
\(941\) −5.80808e29 −1.06693 −0.533466 0.845822i \(-0.679111\pi\)
−0.533466 + 0.845822i \(0.679111\pi\)
\(942\) 3.26959e29 + 1.21579e29i 0.594271 + 0.220978i
\(943\) 9.09481e27i 0.0163560i
\(944\) −2.09081e29 + 3.09120e28i −0.372045 + 0.0550056i
\(945\) 1.07388e29 0.189076
\(946\) −1.96837e29 + 5.29350e29i −0.342922 + 0.922213i
\(947\) 1.14663e28i 0.0197661i −0.999951 0.00988307i \(-0.996854\pi\)
0.999951 0.00988307i \(-0.00314593\pi\)
\(948\) 5.39467e29 + 4.65573e29i 0.920198 + 0.794153i
\(949\) 1.65258e29 0.278933
\(950\) 7.50014e29 + 2.78890e29i 1.25266 + 0.465798i
\(951\) 6.03480e28i 0.0997372i
\(952\) 8.08450e28 + 1.47011e29i 0.132216 + 0.240425i
\(953\) 4.04399e28 0.0654457 0.0327228 0.999464i \(-0.489582\pi\)
0.0327228 + 0.999464i \(0.489582\pi\)
\(954\) −6.36116e28 + 1.71070e29i −0.101872 + 0.273961i
\(955\) 3.24177e28i 0.0513745i
\(956\) −7.19607e29 + 8.33821e29i −1.12854 + 1.30766i
\(957\) −2.96880e29 −0.460747
\(958\) −5.77176e29 2.14621e29i −0.886448 0.329623i
\(959\) 1.19578e28i 0.0181746i
\(960\) 1.97649e29 + 1.25359e29i 0.297291 + 0.188557i
\(961\) 4.05453e29 0.603541
\(962\) −7.40064e28 + 1.99024e29i −0.109023 + 0.293194i
\(963\) 4.71221e29i 0.687008i
\(964\) −5.26196e29 4.54120e29i −0.759237 0.655239i
\(965\) −2.77587e29 −0.396393
\(966\) 2.03253e29 + 7.55791e28i 0.287254 + 0.106815i
\(967\) 1.79373e29i 0.250895i 0.992100 + 0.125448i \(0.0400367\pi\)
−0.992100 + 0.125448i \(0.959963\pi\)
\(968\) −1.48893e29 + 8.18801e28i −0.206120 + 0.113351i
\(969\) −6.73951e29 −0.923402
\(970\) 5.06510e28 1.36215e29i 0.0686863 0.184717i
\(971\) 7.65855e29i 1.02791i −0.857818 0.513954i \(-0.828180\pi\)
0.857818 0.513954i \(-0.171820\pi\)
\(972\) −3.40018e29 + 3.93985e29i −0.451689 + 0.523380i
\(973\) 2.20367e29 0.289747
\(974\) −2.46634e29 9.17100e28i −0.320969 0.119351i
\(975\) 9.04675e29i 1.16532i
\(976\) 1.57783e29 + 1.06721e30i 0.201170 + 1.36067i
\(977\) −9.46713e29 −1.19474 −0.597369 0.801967i \(-0.703787\pi\)
−0.597369 + 0.801967i \(0.703787\pi\)
\(978\) 1.20796e29 3.24854e29i 0.150891 0.405789i
\(979\) 6.83225e29i 0.844767i
\(980\) 2.31486e29 + 1.99778e29i 0.283311 + 0.244504i
\(981\) −1.70203e29 −0.206195
\(982\) −1.03133e29 3.83497e28i −0.123675 0.0459883i
\(983\) 1.69036e29i 0.200652i −0.994955 0.100326i \(-0.968011\pi\)
0.994955 0.100326i \(-0.0319885\pi\)
\(984\) −5.44151e27 9.89498e27i −0.00639394 0.0116269i
\(985\) 6.52712e29 0.759205
\(986\) −1.40014e29 + 3.76536e29i −0.161213 + 0.433548i
\(987\) 3.90935e29i 0.445587i
\(988\) 1.75293e30 2.03115e30i 1.97786 2.29178i
\(989\) 9.87756e29 1.10328
\(990\) −1.20432e29 4.47824e28i −0.133165 0.0495171i
\(991\) 6.84335e29i 0.749087i 0.927209 + 0.374543i \(0.122201\pi\)
−0.927209 + 0.374543i \(0.877799\pi\)
\(992\) 1.20683e29 5.68382e29i 0.130776 0.615919i
\(993\) −3.04377e29 −0.326527
\(994\) −2.62686e28 + 7.06435e28i −0.0278979 + 0.0750254i
\(995\) 4.13827e29i 0.435099i
\(996\) 6.23370e29 + 5.37983e29i 0.648862 + 0.559983i
\(997\) 1.75083e30 1.80423 0.902114 0.431497i \(-0.142015\pi\)
0.902114 + 0.431497i \(0.142015\pi\)
\(998\) 4.38478e29 + 1.63047e29i 0.447345 + 0.166344i
\(999\) 1.84910e29i 0.186770i
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 4.21.b.b.3.5 8
3.2 odd 2 36.21.d.b.19.4 8
4.3 odd 2 inner 4.21.b.b.3.6 yes 8
8.3 odd 2 64.21.c.d.63.3 8
8.5 even 2 64.21.c.d.63.6 8
12.11 even 2 36.21.d.b.19.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.21.b.b.3.5 8 1.1 even 1 trivial
4.21.b.b.3.6 yes 8 4.3 odd 2 inner
36.21.d.b.19.3 8 12.11 even 2
36.21.d.b.19.4 8 3.2 odd 2
64.21.c.d.63.3 8 8.3 odd 2
64.21.c.d.63.6 8 8.5 even 2