Properties

Label 5.21.c.a.3.5
Level $5$
Weight $21$
Character 5.3
Analytic conductor $12.676$
Analytic rank $0$
Dimension $18$
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] = [5,21,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
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("5.2");
 
S:= CuspForms(chi, 21);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), 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: \(12.6756882551\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{16}\cdot 5^{32} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.5
Root \(3.77310i\) of defining polynomial
Character \(\chi\) \(=\) 5.3
Dual form 5.21.c.a.2.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.77310 - 3.77310i) q^{2} +(38858.9 + 38858.9i) q^{3} +1.04855e6i q^{4} +(-8.90462e6 + 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 - 4.46902e7i) q^{7} +(7.91266e6 + 7.91266e6i) q^{8} -4.66753e8i q^{9} +O(q^{10})\) \(q+(3.77310 - 3.77310i) q^{2} +(38858.9 + 38858.9i) q^{3} +1.04855e6i q^{4} +(-8.90462e6 + 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 - 4.46902e7i) q^{7} +(7.91266e6 + 7.91266e6i) q^{8} -4.66753e8i q^{9} +(-1.84702e7 + 4.87259e7i) q^{10} -1.60852e10 q^{11} +(-4.07454e10 + 4.07454e10i) q^{12} +(-3.76718e10 - 3.76718e10i) q^{13} -3.37242e8i q^{14} +(-5.01824e11 - 1.90223e11i) q^{15} -1.09942e12 q^{16} +(-2.08022e12 + 2.08022e12i) q^{17} +(-1.76111e9 - 1.76111e9i) q^{18} +2.99942e11i q^{19} +(-4.20404e12 - 9.33691e12i) q^{20} +3.47323e12 q^{21} +(-6.06910e10 + 6.06910e10i) q^{22} +(4.11357e13 + 4.11357e13i) q^{23} +6.14955e11i q^{24} +(6.32170e13 - 7.14042e13i) q^{25} -2.84279e11 q^{26} +(1.53630e14 - 1.53630e14i) q^{27} +(4.68598e13 + 4.68598e13i) q^{28} +3.65291e14i q^{29} +(-2.61117e12 + 1.17570e12i) q^{30} -1.33214e15 q^{31} +(-1.24453e13 + 1.24453e13i) q^{32} +(-6.25053e14 - 6.25053e14i) q^{33} +1.56978e13i q^{34} +(-2.18769e14 + 5.77130e14i) q^{35} +4.89412e14 q^{36} +(-1.48105e15 + 1.48105e15i) q^{37} +(1.13171e12 + 1.13171e12i) q^{38} -2.92777e15i q^{39} +(-1.02184e14 - 3.87343e13i) q^{40} +2.38548e16 q^{41} +(1.31048e13 - 1.31048e13i) q^{42} +(5.02697e15 + 5.02697e15i) q^{43} -1.68661e16i q^{44} +(1.87139e15 + 4.15625e15i) q^{45} +3.10419e14 q^{46} +(-1.96675e16 + 1.96675e16i) q^{47} +(-4.27224e16 - 4.27224e16i) q^{48} +7.57978e16i q^{49} +(-3.08912e13 - 5.07940e14i) q^{50} -1.61670e17 q^{51} +(3.95006e16 - 3.95006e16i) q^{52} +(-6.48453e15 - 6.48453e15i) q^{53} -1.15932e15i q^{54} +(1.43232e17 - 6.44918e16i) q^{55} +7.07237e14 q^{56} +(-1.16554e16 + 1.16554e16i) q^{57} +(1.37828e15 + 1.37828e15i) q^{58} +5.84951e17i q^{59} +(1.99458e17 - 5.26187e17i) q^{60} +9.66810e17 q^{61} +(-5.02630e15 + 5.02630e15i) q^{62} +(-2.08593e16 - 2.08593e16i) q^{63} -1.15273e18i q^{64} +(4.86494e17 + 1.84412e17i) q^{65} -4.71678e15 q^{66} +(-2.23353e18 + 2.23353e18i) q^{67} +(-2.18121e18 - 2.18121e18i) q^{68} +3.19698e18i q^{69} +(1.35213e15 + 3.00301e15i) q^{70} +1.33306e18 q^{71} +(3.69326e15 - 3.69326e15i) q^{72} +(-4.76853e18 - 4.76853e18i) q^{73} +1.11763e16i q^{74} +(5.23123e18 - 3.18146e17i) q^{75} -3.14504e17 q^{76} +(-7.18850e17 + 7.18850e17i) q^{77} +(-1.10468e16 - 1.10468e16i) q^{78} +1.15172e19i q^{79} +(9.78993e18 - 4.40801e18i) q^{80} +1.03123e19 q^{81} +(9.00068e16 - 9.00068e16i) q^{82} +(-6.54386e18 - 6.54386e18i) q^{83} +3.64184e18i q^{84} +(1.01831e19 - 2.68640e19i) q^{85} +3.79345e16 q^{86} +(-1.41948e19 + 1.41948e19i) q^{87} +(-1.27277e17 - 1.27277e17i) q^{88} +2.48209e19i q^{89} +(2.27429e16 + 8.62101e15i) q^{90} -3.36712e18 q^{91} +(-4.31328e19 + 4.31328e19i) q^{92} +(-5.17655e19 - 5.17655e19i) q^{93} +1.48415e17i q^{94} +(-1.20259e18 - 2.67087e18i) q^{95} -9.67219e17 q^{96} +(4.02655e19 - 4.02655e19i) q^{97} +(2.85993e17 + 2.85993e17i) q^{98} +7.50780e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.77310 3.77310i 0.00368467 0.00368467i −0.705262 0.708947i \(-0.749171\pi\)
0.708947 + 0.705262i \(0.249171\pi\)
\(3\) 38858.9 + 38858.9i 0.658079 + 0.658079i 0.954925 0.296846i \(-0.0959348\pi\)
−0.296846 + 0.954925i \(0.595935\pi\)
\(4\) 1.04855e6i 0.999973i
\(5\) −8.90462e6 + 4.00939e6i −0.911833 + 0.410562i
\(6\) 293237. 0.00484961
\(7\) 4.46902e7 4.46902e7i 0.158209 0.158209i −0.623563 0.781773i \(-0.714316\pi\)
0.781773 + 0.623563i \(0.214316\pi\)
\(8\) 7.91266e6 + 7.91266e6i 0.00736924 + 0.00736924i
\(9\) 4.66753e8i 0.133863i
\(10\) −1.84702e7 + 4.87259e7i −0.00184702 + 0.00487259i
\(11\) −1.60852e10 −0.620153 −0.310077 0.950712i \(-0.600355\pi\)
−0.310077 + 0.950712i \(0.600355\pi\)
\(12\) −4.07454e10 + 4.07454e10i −0.658061 + 0.658061i
\(13\) −3.76718e10 3.76718e10i −0.273264 0.273264i 0.557149 0.830413i \(-0.311895\pi\)
−0.830413 + 0.557149i \(0.811895\pi\)
\(14\) 3.37242e8i 0.00116590i
\(15\) −5.01824e11 1.90223e11i −0.870240 0.329876i
\(16\) −1.09942e12 −0.999919
\(17\) −2.08022e12 + 2.08022e12i −1.03186 + 1.03186i −0.0323821 + 0.999476i \(0.510309\pi\)
−0.999476 + 0.0323821i \(0.989691\pi\)
\(18\) −1.76111e9 1.76111e9i −0.000493242 0.000493242i
\(19\) 2.99942e11i 0.0489217i 0.999701 + 0.0244609i \(0.00778691\pi\)
−0.999701 + 0.0244609i \(0.992213\pi\)
\(20\) −4.20404e12 9.33691e12i −0.410551 0.911808i
\(21\) 3.47323e12 0.208229
\(22\) −6.06910e10 + 6.06910e10i −0.00228506 + 0.00228506i
\(23\) 4.11357e13 + 4.11357e13i 0.992981 + 0.992981i 0.999976 0.00699448i \(-0.00222643\pi\)
−0.00699448 + 0.999976i \(0.502226\pi\)
\(24\) 6.14955e11i 0.00969909i
\(25\) 6.32170e13 7.14042e13i 0.662878 0.748727i
\(26\) −2.84279e11 −0.00201378
\(27\) 1.53630e14 1.53630e14i 0.746172 0.746172i
\(28\) 4.68598e13 + 4.68598e13i 0.158205 + 0.158205i
\(29\) 3.65291e14i 0.868279i 0.900846 + 0.434140i \(0.142948\pi\)
−0.900846 + 0.434140i \(0.857052\pi\)
\(30\) −2.61117e12 + 1.17570e12i −0.00442203 + 0.00199106i
\(31\) −1.33214e15 −1.62530 −0.812649 0.582754i \(-0.801975\pi\)
−0.812649 + 0.582754i \(0.801975\pi\)
\(32\) −1.24453e13 + 1.24453e13i −0.0110536 + 0.0110536i
\(33\) −6.25053e14 6.25053e14i −0.408110 0.408110i
\(34\) 1.56978e13i 0.00760411i
\(35\) −2.18769e14 + 5.77130e14i −0.0793058 + 0.209215i
\(36\) 4.89412e14 0.133860
\(37\) −1.48105e15 + 1.48105e15i −0.308002 + 0.308002i −0.844134 0.536132i \(-0.819885\pi\)
0.536132 + 0.844134i \(0.319885\pi\)
\(38\) 1.13171e12 + 1.13171e12i 0.000180260 + 0.000180260i
\(39\) 2.92777e15i 0.359659i
\(40\) −1.02184e14 3.87343e13i −0.00974504 0.00369399i
\(41\) 2.38548e16 1.77721 0.888603 0.458676i \(-0.151676\pi\)
0.888603 + 0.458676i \(0.151676\pi\)
\(42\) 1.31048e13 1.31048e13i 0.000767254 0.000767254i
\(43\) 5.02697e15 + 5.02697e15i 0.232606 + 0.232606i 0.813780 0.581173i \(-0.197406\pi\)
−0.581173 + 0.813780i \(0.697406\pi\)
\(44\) 1.68661e16i 0.620136i
\(45\) 1.87139e15 + 4.15625e15i 0.0549592 + 0.122061i
\(46\) 3.10419e14 0.00731762
\(47\) −1.96675e16 + 1.96675e16i −0.373913 + 0.373913i −0.868900 0.494987i \(-0.835173\pi\)
0.494987 + 0.868900i \(0.335173\pi\)
\(48\) −4.27224e16 4.27224e16i −0.658026 0.658026i
\(49\) 7.57978e16i 0.949940i
\(50\) −3.08912e13 5.07940e14i −0.000316326 0.00520130i
\(51\) −1.61670e17 −1.35809
\(52\) 3.95006e16 3.95006e16i 0.273257 0.273257i
\(53\) −6.48453e15 6.48453e15i −0.0370783 0.0370783i 0.688325 0.725403i \(-0.258347\pi\)
−0.725403 + 0.688325i \(0.758347\pi\)
\(54\) 1.15932e15i 0.00549880i
\(55\) 1.43232e17 6.44918e16i 0.565476 0.254611i
\(56\) 7.07237e14 0.00233177
\(57\) −1.16554e16 + 1.16554e16i −0.0321944 + 0.0321944i
\(58\) 1.37828e15 + 1.37828e15i 0.00319932 + 0.00319932i
\(59\) 5.84951e17i 1.14446i 0.820094 + 0.572229i \(0.193921\pi\)
−0.820094 + 0.572229i \(0.806079\pi\)
\(60\) 1.99458e17 5.26187e17i 0.329867 0.870217i
\(61\) 9.66810e17 1.35532 0.677662 0.735374i \(-0.262993\pi\)
0.677662 + 0.735374i \(0.262993\pi\)
\(62\) −5.02630e15 + 5.02630e15i −0.00598869 + 0.00598869i
\(63\) −2.08593e16 2.08593e16i −0.0211784 0.0211784i
\(64\) 1.15273e18i 0.999837i
\(65\) 4.86494e17 + 1.84412e17i 0.361363 + 0.136979i
\(66\) −4.71678e15 −0.00300750
\(67\) −2.23353e18 + 2.23353e18i −1.22530 + 1.22530i −0.259581 + 0.965721i \(0.583584\pi\)
−0.965721 + 0.259581i \(0.916416\pi\)
\(68\) −2.18121e18 2.18121e18i −1.03183 1.03183i
\(69\) 3.19698e18i 1.30692i
\(70\) 1.35213e15 + 3.00301e15i 0.000478673 + 0.00106310i
\(71\) 1.33306e18 0.409513 0.204757 0.978813i \(-0.434360\pi\)
0.204757 + 0.978813i \(0.434360\pi\)
\(72\) 3.69326e15 3.69326e15i 0.000986471 0.000986471i
\(73\) −4.76853e18 4.76853e18i −1.10957 1.10957i −0.993206 0.116367i \(-0.962875\pi\)
−0.116367 0.993206i \(-0.537125\pi\)
\(74\) 1.11763e16i 0.00226977i
\(75\) 5.23123e18 3.18146e17i 0.928948 0.0564956i
\(76\) −3.14504e17 −0.0489204
\(77\) −7.18850e17 + 7.18850e17i −0.0981141 + 0.0981141i
\(78\) −1.10468e16 1.10468e16i −0.00132522 0.00132522i
\(79\) 1.15172e19i 1.21639i 0.793786 + 0.608197i \(0.208107\pi\)
−0.793786 + 0.608197i \(0.791893\pi\)
\(80\) 9.78993e18 4.40801e18i 0.911759 0.410528i
\(81\) 1.03123e19 0.848217
\(82\) 9.00068e16 9.00068e16i 0.00654842 0.00654842i
\(83\) −6.54386e18 6.54386e18i −0.421748 0.421748i 0.464057 0.885805i \(-0.346393\pi\)
−0.885805 + 0.464057i \(0.846393\pi\)
\(84\) 3.64184e18i 0.208223i
\(85\) 1.01831e19 2.68640e19i 0.517240 1.36452i
\(86\) 3.79345e16 0.00171415
\(87\) −1.41948e19 + 1.41948e19i −0.571397 + 0.571397i
\(88\) −1.27277e17 1.27277e17i −0.00457006 0.00457006i
\(89\) 2.48209e19i 0.796008i 0.917384 + 0.398004i \(0.130297\pi\)
−0.917384 + 0.398004i \(0.869703\pi\)
\(90\) 2.27429e16 + 8.62101e15i 0.000652261 + 0.000247248i
\(91\) −3.36712e18 −0.0864659
\(92\) −4.31328e19 + 4.31328e19i −0.992954 + 0.992954i
\(93\) −5.17655e19 5.17655e19i −1.06957 1.06957i
\(94\) 1.48415e17i 0.00275549i
\(95\) −1.20259e18 2.67087e18i −0.0200854 0.0446084i
\(96\) −9.67219e17 −0.0145483
\(97\) 4.02655e19 4.02655e19i 0.546030 0.546030i −0.379260 0.925290i \(-0.623822\pi\)
0.925290 + 0.379260i \(0.123822\pi\)
\(98\) 2.85993e17 + 2.85993e17i 0.00350021 + 0.00350021i
\(99\) 7.50780e18i 0.0830158i
\(100\) 7.48707e19 + 6.62860e19i 0.748707 + 0.662860i
\(101\) 1.10526e20 1.00058 0.500288 0.865859i \(-0.333228\pi\)
0.500288 + 0.865859i \(0.333228\pi\)
\(102\) −6.09998e17 + 6.09998e17i −0.00500411 + 0.00500411i
\(103\) −5.79262e19 5.79262e19i −0.431025 0.431025i 0.457952 0.888977i \(-0.348583\pi\)
−0.888977 + 0.457952i \(0.848583\pi\)
\(104\) 5.96168e17i 0.00402750i
\(105\) −3.09278e19 + 1.39255e19i −0.189870 + 0.0854907i
\(106\) −4.89336e16 −0.000273243
\(107\) 8.04515e19 8.04515e19i 0.408975 0.408975i −0.472406 0.881381i \(-0.656614\pi\)
0.881381 + 0.472406i \(0.156614\pi\)
\(108\) 1.61089e20 + 1.61089e20i 0.746152 + 0.746152i
\(109\) 1.45257e20i 0.613581i −0.951777 0.306790i \(-0.900745\pi\)
0.951777 0.306790i \(-0.0992551\pi\)
\(110\) 2.97096e17 7.83765e17i 0.00114543 0.00302175i
\(111\) −1.15104e20 −0.405379
\(112\) −4.91334e19 + 4.91334e19i −0.158196 + 0.158196i
\(113\) 1.43712e20 + 1.43712e20i 0.423359 + 0.423359i 0.886358 0.463000i \(-0.153227\pi\)
−0.463000 + 0.886358i \(0.653227\pi\)
\(114\) 8.79543e16i 0.000237251i
\(115\) −5.31227e20 2.01369e20i −1.31311 0.497753i
\(116\) −3.83025e20 −0.868256
\(117\) −1.75834e19 + 1.75834e19i −0.0365800 + 0.0365800i
\(118\) 2.20708e18 + 2.20708e18i 0.00421695 + 0.00421695i
\(119\) 1.85931e20i 0.326499i
\(120\) −2.46560e18 5.47594e18i −0.00398207 0.00884395i
\(121\) −4.14017e20 −0.615410
\(122\) 3.64787e18 3.64787e18i 0.00499392 0.00499392i
\(123\) 9.26973e20 + 9.26973e20i 1.16954 + 1.16954i
\(124\) 1.39681e21i 1.62525i
\(125\) −2.76636e20 + 8.89289e20i −0.297035 + 0.954867i
\(126\) −1.57408e17 −0.000156071
\(127\) 1.28344e21 1.28344e21i 1.17582 1.17582i 0.195016 0.980800i \(-0.437524\pi\)
0.980800 0.195016i \(-0.0624760\pi\)
\(128\) −1.73992e19 1.73992e19i −0.0147377 0.0147377i
\(129\) 3.90685e20i 0.306147i
\(130\) 2.53139e18 1.13979e18i 0.00183623 0.000826779i
\(131\) 9.63942e20 0.647647 0.323823 0.946118i \(-0.395032\pi\)
0.323823 + 0.946118i \(0.395032\pi\)
\(132\) 6.55398e20 6.55398e20i 0.408099 0.408099i
\(133\) 1.34045e19 + 1.34045e19i 0.00773987 + 0.00773987i
\(134\) 1.68547e19i 0.00902967i
\(135\) −7.52054e20 + 1.98398e21i −0.374034 + 0.986734i
\(136\) −3.29201e19 −0.0152080
\(137\) −1.38810e21 + 1.38810e21i −0.595958 + 0.595958i −0.939234 0.343276i \(-0.888463\pi\)
0.343276 + 0.939234i \(0.388463\pi\)
\(138\) 1.20625e19 + 1.20625e19i 0.00481557 + 0.00481557i
\(139\) 2.98122e21i 1.10725i −0.832766 0.553626i \(-0.813244\pi\)
0.832766 0.553626i \(-0.186756\pi\)
\(140\) −6.05148e20 2.29389e20i −0.209210 0.0793036i
\(141\) −1.52852e21 −0.492129
\(142\) 5.02979e18 5.02979e18i 0.00150892 0.00150892i
\(143\) 6.05957e20 + 6.05957e20i 0.169466 + 0.169466i
\(144\) 5.13158e20i 0.133852i
\(145\) −1.46460e21 3.25278e21i −0.356482 0.791726i
\(146\) −3.59843e19 −0.00817682
\(147\) −2.94542e21 + 2.94542e21i −0.625136 + 0.625136i
\(148\) −1.55295e21 1.55295e21i −0.307993 0.307993i
\(149\) 5.77191e21i 1.07018i 0.844795 + 0.535090i \(0.179722\pi\)
−0.844795 + 0.535090i \(0.820278\pi\)
\(150\) 1.85376e19 2.09384e19i 0.00321470 0.00363104i
\(151\) −2.64955e20 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(152\) −2.37334e18 + 2.37334e18i −0.000360516 + 0.000360516i
\(153\) 9.70948e20 + 9.70948e20i 0.138128 + 0.138128i
\(154\) 5.42459e18i 0.000723036i
\(155\) 1.18622e22 5.34107e21i 1.48200 0.667285i
\(156\) 3.06990e21 0.359649
\(157\) 6.41131e21 6.41131e21i 0.704612 0.704612i −0.260785 0.965397i \(-0.583981\pi\)
0.965397 + 0.260785i \(0.0839813\pi\)
\(158\) 4.34554e19 + 4.34554e19i 0.00448201 + 0.00448201i
\(159\) 5.03964e20i 0.0488009i
\(160\) 6.09223e19 1.60718e20i 0.00554086 0.0146172i
\(161\) 3.67673e21 0.314198
\(162\) 3.89095e19 3.89095e19i 0.00312540 0.00312540i
\(163\) −1.36800e22 1.36800e22i −1.03326 1.03326i −0.999428 0.0338306i \(-0.989229\pi\)
−0.0338306 0.999428i \(-0.510771\pi\)
\(164\) 2.50129e22i 1.77716i
\(165\) 8.07194e21 + 3.05977e21i 0.539682 + 0.204574i
\(166\) −4.93813e19 −0.00310801
\(167\) −1.38963e22 + 1.38963e22i −0.823634 + 0.823634i −0.986627 0.162993i \(-0.947885\pi\)
0.162993 + 0.986627i \(0.447885\pi\)
\(168\) 2.74825e19 + 2.74825e19i 0.00153449 + 0.00153449i
\(169\) 1.61666e22i 0.850654i
\(170\) −6.29385e19 1.39783e20i −0.00312196 0.00693368i
\(171\) 1.39999e20 0.00654883
\(172\) −5.27101e21 + 5.27101e21i −0.232600 + 0.232600i
\(173\) −2.74845e22 2.74845e22i −1.14453 1.14453i −0.987612 0.156915i \(-0.949845\pi\)
−0.156915 0.987612i \(-0.550155\pi\)
\(174\) 1.07117e20i 0.00421082i
\(175\) −3.65888e20 6.01625e21i −0.0135821 0.223329i
\(176\) 1.76844e22 0.620103
\(177\) −2.27306e22 + 2.27306e22i −0.753144 + 0.753144i
\(178\) 9.36518e19 + 9.36518e19i 0.00293303 + 0.00293303i
\(179\) 7.43674e21i 0.220218i 0.993920 + 0.110109i \(0.0351200\pi\)
−0.993920 + 0.110109i \(0.964880\pi\)
\(180\) −4.35803e21 + 1.96225e21i −0.122058 + 0.0549577i
\(181\) 9.99277e21 0.264789 0.132395 0.991197i \(-0.457733\pi\)
0.132395 + 0.991197i \(0.457733\pi\)
\(182\) −1.27045e19 + 1.27045e19i −0.000318598 + 0.000318598i
\(183\) 3.75692e22 + 3.75692e22i 0.891910 + 0.891910i
\(184\) 6.50986e20i 0.0146350i
\(185\) 7.25009e21 1.91263e22i 0.154392 0.407300i
\(186\) −3.90633e20 −0.00788206
\(187\) 3.34607e22 3.34607e22i 0.639910 0.639910i
\(188\) −2.06223e22 2.06223e22i −0.373903 0.373903i
\(189\) 1.37315e22i 0.236103i
\(190\) −1.46150e19 5.53999e18i −0.000238375 9.03593e-5i
\(191\) 1.85330e22 0.286822 0.143411 0.989663i \(-0.454193\pi\)
0.143411 + 0.989663i \(0.454193\pi\)
\(192\) 4.47940e22 4.47940e22i 0.657972 0.657972i
\(193\) 5.77240e22 + 5.77240e22i 0.804976 + 0.804976i 0.983869 0.178892i \(-0.0572514\pi\)
−0.178892 + 0.983869i \(0.557251\pi\)
\(194\) 3.03852e20i 0.00402388i
\(195\) 1.17386e22 + 2.60707e22i 0.147662 + 0.327949i
\(196\) −7.94776e22 −0.949914
\(197\) 3.85613e21 3.85613e21i 0.0438015 0.0438015i −0.684867 0.728668i \(-0.740140\pi\)
0.728668 + 0.684867i \(0.240140\pi\)
\(198\) 2.83277e19 + 2.83277e19i 0.000305886 + 0.000305886i
\(199\) 5.84096e22i 0.599727i 0.953982 + 0.299863i \(0.0969411\pi\)
−0.953982 + 0.299863i \(0.903059\pi\)
\(200\) 1.06521e21 6.47827e19i 0.0104025 0.000632643i
\(201\) −1.73585e23 −1.61269
\(202\) 4.17025e20 4.17025e20i 0.00368679 0.00368679i
\(203\) 1.63250e22 + 1.63250e22i 0.137370 + 0.137370i
\(204\) 1.69519e23i 1.35805i
\(205\) −2.12418e23 + 9.56434e22i −1.62052 + 0.729653i
\(206\) −4.37123e20 −0.00317637
\(207\) 1.92002e22 1.92002e22i 0.132924 0.132924i
\(208\) 4.14172e22 + 4.14172e22i 0.273242 + 0.273242i
\(209\) 4.82463e21i 0.0303390i
\(210\) −6.41512e19 + 1.69236e20i −0.000384602 + 0.00101461i
\(211\) 1.97241e23 1.12765 0.563824 0.825895i \(-0.309330\pi\)
0.563824 + 0.825895i \(0.309330\pi\)
\(212\) 6.79934e21 6.79934e21i 0.0370773 0.0370773i
\(213\) 5.18015e22 + 5.18015e22i 0.269492 + 0.269492i
\(214\) 6.07104e20i 0.00301387i
\(215\) −6.49183e22 2.46081e22i −0.307597 0.116599i
\(216\) 2.43125e21 0.0109974
\(217\) −5.95336e22 + 5.95336e22i −0.257137 + 0.257137i
\(218\) −5.48069e20 5.48069e20i −0.00226084 0.00226084i
\(219\) 3.70600e23i 1.46037i
\(220\) 6.76227e22 + 1.50186e23i 0.254604 + 0.565461i
\(221\) 1.56731e23 0.563939
\(222\) −4.34300e20 + 4.34300e20i −0.00149369 + 0.00149369i
\(223\) 2.39987e23 + 2.39987e23i 0.789112 + 0.789112i 0.981349 0.192237i \(-0.0615741\pi\)
−0.192237 + 0.981349i \(0.561574\pi\)
\(224\) 1.11236e21i 0.00349757i
\(225\) −3.33281e22 2.95067e22i −0.100227 0.0887351i
\(226\) 1.08448e21 0.00311987
\(227\) 3.10473e23 3.10473e23i 0.854605 0.854605i −0.136092 0.990696i \(-0.543454\pi\)
0.990696 + 0.136092i \(0.0434542\pi\)
\(228\) −1.22213e22 1.22213e22i −0.0321935 0.0321935i
\(229\) 4.24623e23i 1.07065i 0.844645 + 0.535327i \(0.179811\pi\)
−0.844645 + 0.535327i \(0.820189\pi\)
\(230\) −2.76416e21 + 1.24459e21i −0.00667244 + 0.00300433i
\(231\) −5.58675e22 −0.129134
\(232\) −2.89043e21 + 2.89043e21i −0.00639856 + 0.00639856i
\(233\) −4.79808e23 4.79808e23i −1.01744 1.01744i −0.999845 0.0175940i \(-0.994399\pi\)
−0.0175940 0.999845i \(-0.505601\pi\)
\(234\) 1.32688e20i 0.000269571i
\(235\) 9.62768e22 2.53986e23i 0.187432 0.494460i
\(236\) −6.13349e23 −1.14443
\(237\) −4.47544e23 + 4.47544e23i −0.800484 + 0.800484i
\(238\) 7.01536e20 + 7.01536e20i 0.00120304 + 0.00120304i
\(239\) 1.58870e23i 0.261254i 0.991432 + 0.130627i \(0.0416991\pi\)
−0.991432 + 0.130627i \(0.958301\pi\)
\(240\) 5.51717e23 + 2.09136e23i 0.870170 + 0.329849i
\(241\) −3.90298e23 −0.590509 −0.295254 0.955419i \(-0.595404\pi\)
−0.295254 + 0.955419i \(0.595404\pi\)
\(242\) −1.56213e21 + 1.56213e21i −0.00226758 + 0.00226758i
\(243\) −1.34949e23 1.34949e23i −0.187978 0.187978i
\(244\) 1.01375e24i 1.35529i
\(245\) −3.03903e23 6.74951e23i −0.390009 0.866186i
\(246\) 6.99513e21 0.00861876
\(247\) 1.12994e22 1.12994e22i 0.0133685 0.0133685i
\(248\) −1.05408e22 1.05408e22i −0.0119772 0.0119772i
\(249\) 5.08575e23i 0.555087i
\(250\) 2.31160e21 + 4.39915e21i 0.00242389 + 0.00461285i
\(251\) 1.59459e24 1.60661 0.803307 0.595565i \(-0.203072\pi\)
0.803307 + 0.595565i \(0.203072\pi\)
\(252\) 2.18720e22 2.18720e22i 0.0211779 0.0211779i
\(253\) −6.61676e23 6.61676e23i −0.615800 0.615800i
\(254\) 9.68513e21i 0.00866499i
\(255\) 1.43961e24 6.48199e23i 1.23835 0.557579i
\(256\) 1.20860e24 0.999728
\(257\) −9.80272e23 + 9.80272e23i −0.779858 + 0.779858i −0.979806 0.199948i \(-0.935923\pi\)
0.199948 + 0.979806i \(0.435923\pi\)
\(258\) 1.47409e21 + 1.47409e21i 0.00112805 + 0.00112805i
\(259\) 1.32377e23i 0.0974575i
\(260\) −1.93365e23 + 5.10112e23i −0.136976 + 0.361353i
\(261\) 1.70501e23 0.116231
\(262\) 3.63705e21 3.63705e21i 0.00238636 0.00238636i
\(263\) 7.09161e23 + 7.09161e23i 0.447907 + 0.447907i 0.894658 0.446752i \(-0.147419\pi\)
−0.446752 + 0.894658i \(0.647419\pi\)
\(264\) 9.89166e21i 0.00601492i
\(265\) 8.37413e22 + 3.17432e22i 0.0490321 + 0.0185863i
\(266\) 1.01153e20 5.70378e−5
\(267\) −9.64513e23 + 9.64513e23i −0.523836 + 0.523836i
\(268\) −2.34196e24 2.34196e24i −1.22527 1.22527i
\(269\) 3.36094e23i 0.169409i 0.996406 + 0.0847047i \(0.0269947\pi\)
−0.996406 + 0.0847047i \(0.973005\pi\)
\(270\) 4.64819e21 + 1.03233e22i 0.00225759 + 0.00501398i
\(271\) 8.77461e23 0.410710 0.205355 0.978688i \(-0.434165\pi\)
0.205355 + 0.978688i \(0.434165\pi\)
\(272\) 2.28704e24 2.28704e24i 1.03177 1.03177i
\(273\) −1.30843e23 1.30843e23i −0.0569014 0.0569014i
\(274\) 1.04749e22i 0.00439182i
\(275\) −1.01686e24 + 1.14855e24i −0.411086 + 0.464326i
\(276\) −3.35219e24 −1.30688
\(277\) −1.37066e24 + 1.37066e24i −0.515385 + 0.515385i −0.916172 0.400786i \(-0.868737\pi\)
0.400786 + 0.916172i \(0.368737\pi\)
\(278\) −1.12485e22 1.12485e22i −0.00407986 0.00407986i
\(279\) 6.21780e23i 0.217568i
\(280\) −6.29768e21 + 2.83559e21i −0.00212618 + 0.000957334i
\(281\) −3.31689e24 −1.08061 −0.540304 0.841470i \(-0.681691\pi\)
−0.540304 + 0.841470i \(0.681691\pi\)
\(282\) −5.76724e21 + 5.76724e21i −0.00181333 + 0.00181333i
\(283\) 2.37935e24 + 2.37935e24i 0.722094 + 0.722094i 0.969031 0.246937i \(-0.0794242\pi\)
−0.246937 + 0.969031i \(0.579424\pi\)
\(284\) 1.39778e24i 0.409502i
\(285\) 5.70560e22 1.50518e23i 0.0161381 0.0425737i
\(286\) 4.57268e21 0.00124885
\(287\) 1.06608e24 1.06608e24i 0.281171 0.281171i
\(288\) 5.80886e21 + 5.80886e21i 0.00147967 + 0.00147967i
\(289\) 4.59039e24i 1.12946i
\(290\) −1.77991e22 6.74700e21i −0.00423077 0.00160373i
\(291\) 3.12935e24 0.718662
\(292\) 5.00003e24 5.00003e24i 1.10954 1.10954i
\(293\) 5.85441e24 + 5.85441e24i 1.25547 + 1.25547i 0.953232 + 0.302240i \(0.0977343\pi\)
0.302240 + 0.953232i \(0.402266\pi\)
\(294\) 2.22268e22i 0.00460684i
\(295\) −2.34530e24 5.20877e24i −0.469870 1.04355i
\(296\) −2.34381e22 −0.00453948
\(297\) −2.47117e24 + 2.47117e24i −0.462741 + 0.462741i
\(298\) 2.17780e22 + 2.17780e22i 0.00394326 + 0.00394326i
\(299\) 3.09931e24i 0.542692i
\(300\) 3.33592e23 + 5.48520e24i 0.0564940 + 0.928923i
\(301\) 4.49313e23 0.0736010
\(302\) −9.99701e20 + 9.99701e20i −0.000158417 + 0.000158417i
\(303\) 4.29491e24 + 4.29491e24i 0.658458 + 0.658458i
\(304\) 3.29763e23i 0.0489177i
\(305\) −8.60908e24 + 3.87632e24i −1.23583 + 0.556444i
\(306\) 7.32697e21 0.00101791
\(307\) 1.15304e24 1.15304e24i 0.155046 0.155046i −0.625321 0.780367i \(-0.715032\pi\)
0.780367 + 0.625321i \(0.215032\pi\)
\(308\) −7.53749e23 7.53749e23i −0.0981114 0.0981114i
\(309\) 4.50190e24i 0.567298i
\(310\) 2.46049e22 6.49097e22i 0.00300196 0.00791941i
\(311\) −2.21080e23 −0.0261183 −0.0130592 0.999915i \(-0.504157\pi\)
−0.0130592 + 0.999915i \(0.504157\pi\)
\(312\) 2.31664e22 2.31664e22i 0.00265041 0.00265041i
\(313\) −6.86614e24 6.86614e24i −0.760798 0.760798i 0.215668 0.976467i \(-0.430807\pi\)
−0.976467 + 0.215668i \(0.930807\pi\)
\(314\) 4.83810e22i 0.00519253i
\(315\) 2.69377e23 + 1.02111e23i 0.0280062 + 0.0106161i
\(316\) −1.20763e25 −1.21636
\(317\) −3.58531e24 + 3.58531e24i −0.349892 + 0.349892i −0.860069 0.510177i \(-0.829580\pi\)
0.510177 + 0.860069i \(0.329580\pi\)
\(318\) −1.90151e21 1.90151e21i −0.000179815 0.000179815i
\(319\) 5.87578e24i 0.538466i
\(320\) 4.62176e24 + 1.02647e25i 0.410495 + 0.911684i
\(321\) 6.25252e24 0.538276
\(322\) 1.38727e22 1.38727e22i 0.00115772 0.00115772i
\(323\) −6.23946e23 6.23946e23i −0.0504803 0.0504803i
\(324\) 1.08130e25i 0.848194i
\(325\) −5.07142e24 + 3.08427e23i −0.385741 + 0.0234595i
\(326\) −1.03232e23 −0.00761443
\(327\) 5.64453e24 5.64453e24i 0.403785 0.403785i
\(328\) 1.88755e23 + 1.88755e23i 0.0130967 + 0.0130967i
\(329\) 1.75789e24i 0.118313i
\(330\) 4.20011e22 1.89114e22i 0.00274234 0.00123477i
\(331\) 6.60953e24 0.418688 0.209344 0.977842i \(-0.432867\pi\)
0.209344 + 0.977842i \(0.432867\pi\)
\(332\) 6.86155e24 6.86155e24i 0.421737 0.421737i
\(333\) 6.91285e23 + 6.91285e23i 0.0412302 + 0.0412302i
\(334\) 1.04864e23i 0.00606964i
\(335\) 1.09336e25 2.88438e25i 0.614209 1.62033i
\(336\) −3.81854e24 −0.208212
\(337\) −7.50720e24 + 7.50720e24i −0.397355 + 0.397355i −0.877299 0.479944i \(-0.840657\pi\)
0.479944 + 0.877299i \(0.340657\pi\)
\(338\) −6.09984e22 6.09984e22i −0.00313438 0.00313438i
\(339\) 1.11690e25i 0.557207i
\(340\) 2.81681e25 + 1.06775e25i 1.36449 + 0.517226i
\(341\) 2.14277e25 1.00793
\(342\) 5.28230e20 5.28230e20i 2.41303e−5 2.41303e-5i
\(343\) 6.95336e24 + 6.95336e24i 0.308499 + 0.308499i
\(344\) 7.95534e22i 0.00342826i
\(345\) −1.28180e25 2.84679e25i −0.536572 1.19169i
\(346\) −2.07403e23 −0.00843441
\(347\) −2.47822e25 + 2.47822e25i −0.979141 + 0.979141i −0.999787 0.0206460i \(-0.993428\pi\)
0.0206460 + 0.999787i \(0.493428\pi\)
\(348\) −1.48840e25 1.48840e25i −0.571381 0.571381i
\(349\) 1.86774e25i 0.696725i 0.937360 + 0.348363i \(0.113262\pi\)
−0.937360 + 0.348363i \(0.886738\pi\)
\(350\) −2.40805e22 2.13194e22i −0.000872940 0.000772849i
\(351\) −1.15750e25 −0.407804
\(352\) 2.00184e23 2.00184e23i 0.00685493 0.00685493i
\(353\) −1.93968e25 1.93968e25i −0.645631 0.645631i 0.306303 0.951934i \(-0.400908\pi\)
−0.951934 + 0.306303i \(0.900908\pi\)
\(354\) 1.71530e23i 0.00555017i
\(355\) −1.18704e25 + 5.34478e24i −0.373407 + 0.168130i
\(356\) −2.60259e25 −0.795986
\(357\) −7.22507e24 + 7.22507e24i −0.214862 + 0.214862i
\(358\) 2.80596e22 + 2.80596e22i 0.000811430 + 0.000811430i
\(359\) 1.14804e25i 0.322859i 0.986884 + 0.161430i \(0.0516105\pi\)
−0.986884 + 0.161430i \(0.948389\pi\)
\(360\) −1.80793e22 + 4.76947e22i −0.000494490 + 0.00130450i
\(361\) 3.75000e25 0.997607
\(362\) 3.77038e22 3.77038e22i 0.000975661 0.000975661i
\(363\) −1.60883e25 1.60883e25i −0.404988 0.404988i
\(364\) 3.53058e24i 0.0864635i
\(365\) 6.15809e25 + 2.33430e25i 1.46729 + 0.556197i
\(366\) 2.83505e23 0.00657279
\(367\) −3.13881e25 + 3.13881e25i −0.708117 + 0.708117i −0.966139 0.258022i \(-0.916929\pi\)
0.258022 + 0.966139i \(0.416929\pi\)
\(368\) −4.52255e25 4.52255e25i −0.992900 0.992900i
\(369\) 1.11343e25i 0.237903i
\(370\) −4.48103e22 9.95209e22i −0.000931881 0.00206965i
\(371\) −5.79590e23 −0.0117323
\(372\) 5.42786e25 5.42786e25i 1.06955 1.06955i
\(373\) 3.66873e25 + 3.66873e25i 0.703765 + 0.703765i 0.965217 0.261452i \(-0.0842013\pi\)
−0.261452 + 0.965217i \(0.584201\pi\)
\(374\) 2.52501e23i 0.00471571i
\(375\) −4.53066e25 + 2.38070e25i −0.823851 + 0.432905i
\(376\) −3.11244e23 −0.00551091
\(377\) 1.37612e25 1.37612e25i 0.237270 0.237270i
\(378\) −5.18105e22 5.18105e22i −0.000869961 0.000869961i
\(379\) 2.11918e25i 0.346558i 0.984873 + 0.173279i \(0.0554362\pi\)
−0.984873 + 0.173279i \(0.944564\pi\)
\(380\) 2.80054e24 1.26097e24i 0.0446072 0.0200848i
\(381\) 9.97464e25 1.54756
\(382\) 6.99269e22 6.99269e22i 0.00105684 0.00105684i
\(383\) 2.94906e25 + 2.94906e25i 0.434207 + 0.434207i 0.890057 0.455850i \(-0.150665\pi\)
−0.455850 + 0.890057i \(0.650665\pi\)
\(384\) 1.35223e24i 0.0193971i
\(385\) 3.51893e24 9.28324e24i 0.0491817 0.129745i
\(386\) 4.35597e23 0.00593215
\(387\) 2.34635e24 2.34635e24i 0.0311375 0.0311375i
\(388\) 4.22203e25 + 4.22203e25i 0.546015 + 0.546015i
\(389\) 1.10150e26i 1.38831i −0.719825 0.694156i \(-0.755778\pi\)
0.719825 0.694156i \(-0.244222\pi\)
\(390\) 1.42658e23 + 5.40764e22i 0.00175247 + 0.000664296i
\(391\) −1.71143e26 −2.04923
\(392\) −5.99763e23 + 5.99763e23i −0.00700033 + 0.00700033i
\(393\) 3.74578e25 + 3.74578e25i 0.426203 + 0.426203i
\(394\) 2.90991e22i 0.000322788i
\(395\) −4.61768e25 1.02556e26i −0.499405 1.10915i
\(396\) −7.87229e24 −0.0830136
\(397\) −2.67646e25 + 2.67646e25i −0.275204 + 0.275204i −0.831191 0.555987i \(-0.812341\pi\)
0.555987 + 0.831191i \(0.312341\pi\)
\(398\) 2.20385e23 + 2.20385e23i 0.00220979 + 0.00220979i
\(399\) 1.04177e24i 0.0101869i
\(400\) −6.95021e25 + 7.85034e25i −0.662824 + 0.748666i
\(401\) −5.13198e25 −0.477355 −0.238677 0.971099i \(-0.576714\pi\)
−0.238677 + 0.971099i \(0.576714\pi\)
\(402\) −6.54954e23 + 6.54954e23i −0.00594224 + 0.00594224i
\(403\) 5.01841e25 + 5.01841e25i 0.444135 + 0.444135i
\(404\) 1.15892e26i 1.00055i
\(405\) −9.18275e25 + 4.13462e25i −0.773432 + 0.348246i
\(406\) 1.23191e23 0.00101233
\(407\) 2.38230e25 2.38230e25i 0.191008 0.191008i
\(408\) −1.27924e24 1.27924e24i −0.0100081 0.0100081i
\(409\) 1.45081e26i 1.10759i −0.832654 0.553794i \(-0.813180\pi\)
0.832654 0.553794i \(-0.186820\pi\)
\(410\) −4.40603e23 + 1.16235e24i −0.00328253 + 0.00865960i
\(411\) −1.07880e26 −0.784375
\(412\) 6.07384e25 6.07384e25i 0.431014 0.431014i
\(413\) 2.61416e25 + 2.61416e25i 0.181064 + 0.181064i
\(414\) 1.44889e23i 0.000979561i
\(415\) 8.45075e25 + 3.20337e25i 0.557717 + 0.211410i
\(416\) 9.37670e23 0.00604111
\(417\) 1.15847e26 1.15847e26i 0.728659 0.728659i
\(418\) −1.82038e22 1.82038e22i −0.000111789 0.000111789i
\(419\) 9.76407e25i 0.585451i −0.956196 0.292726i \(-0.905438\pi\)
0.956196 0.292726i \(-0.0945622\pi\)
\(420\) −1.46016e25 3.24292e25i −0.0854884 0.189865i
\(421\) 2.34366e26 1.33990 0.669952 0.742404i \(-0.266315\pi\)
0.669952 + 0.742404i \(0.266315\pi\)
\(422\) 7.44212e23 7.44212e23i 0.00415501 0.00415501i
\(423\) 9.17986e24 + 9.17986e24i 0.0500532 + 0.0500532i
\(424\) 1.02620e23i 0.000546478i
\(425\) 1.70312e25 + 2.80042e26i 0.0885841 + 1.45658i
\(426\) 3.90904e23 0.00198598
\(427\) 4.32070e25 4.32070e25i 0.214425 0.214425i
\(428\) 8.43573e25 + 8.43573e25i 0.408964 + 0.408964i
\(429\) 4.70937e25i 0.223044i
\(430\) −3.37792e23 + 1.52094e23i −0.00156302 + 0.000703766i
\(431\) −1.95945e25 −0.0885853 −0.0442926 0.999019i \(-0.514103\pi\)
−0.0442926 + 0.999019i \(0.514103\pi\)
\(432\) −1.68904e26 + 1.68904e26i −0.746111 + 0.746111i
\(433\) −2.06182e26 2.06182e26i −0.889965 0.889965i 0.104555 0.994519i \(-0.466658\pi\)
−0.994519 + 0.104555i \(0.966658\pi\)
\(434\) 4.49253e23i 0.00189493i
\(435\) 6.94869e25 1.83312e26i 0.286425 0.755612i
\(436\) 1.52309e26 0.613564
\(437\) −1.23383e25 + 1.23383e25i −0.0485783 + 0.0485783i
\(438\) −1.39831e24 1.39831e24i −0.00538100 0.00538100i
\(439\) 7.67531e24i 0.0288702i −0.999896 0.0144351i \(-0.995405\pi\)
0.999896 0.0144351i \(-0.00459500\pi\)
\(440\) 1.64365e24 + 6.23048e23i 0.00604342 + 0.00229084i
\(441\) 3.53788e25 0.127162
\(442\) 5.91362e23 5.91362e23i 0.00207793 0.00207793i
\(443\) −6.26585e25 6.26585e25i −0.215250 0.215250i 0.591243 0.806493i \(-0.298637\pi\)
−0.806493 + 0.591243i \(0.798637\pi\)
\(444\) 1.20692e26i 0.405368i
\(445\) −9.95167e25 2.21021e26i −0.326810 0.725826i
\(446\) 1.81099e24 0.00581523
\(447\) −2.24290e26 + 2.24290e26i −0.704263 + 0.704263i
\(448\) −5.15159e25 5.15159e25i −0.158184 0.158184i
\(449\) 3.72189e26i 1.11763i 0.829291 + 0.558817i \(0.188745\pi\)
−0.829291 + 0.558817i \(0.811255\pi\)
\(450\) −2.37082e23 + 1.44186e22i −0.000696264 + 4.23444e-5i
\(451\) −3.83709e26 −1.10214
\(452\) −1.50689e26 + 1.50689e26i −0.423347 + 0.423347i
\(453\) −1.02958e25 1.02958e25i −0.0282931 0.0282931i
\(454\) 2.34289e24i 0.00629787i
\(455\) 2.99829e25 1.35001e25i 0.0788424 0.0354996i
\(456\) −1.84451e23 −0.000474496
\(457\) −1.07465e26 + 1.07465e26i −0.270461 + 0.270461i −0.829286 0.558825i \(-0.811252\pi\)
0.558825 + 0.829286i \(0.311252\pi\)
\(458\) 1.60215e24 + 1.60215e24i 0.00394500 + 0.00394500i
\(459\) 6.39169e26i 1.53989i
\(460\) 2.11145e26 5.57017e26i 0.497739 1.31308i
\(461\) 1.93725e26 0.446865 0.223433 0.974719i \(-0.428274\pi\)
0.223433 + 0.974719i \(0.428274\pi\)
\(462\) −2.10794e23 + 2.10794e23i −0.000475815 + 0.000475815i
\(463\) −2.75418e26 2.75418e26i −0.608391 0.608391i 0.334135 0.942525i \(-0.391556\pi\)
−0.942525 + 0.334135i \(0.891556\pi\)
\(464\) 4.01609e26i 0.868209i
\(465\) 6.68501e26 + 2.53404e26i 1.41440 + 0.536147i
\(466\) −3.62073e24 −0.00749786
\(467\) 5.17420e26 5.17420e26i 1.04876 1.04876i 0.0500079 0.998749i \(-0.484075\pi\)
0.998749 0.0500079i \(-0.0159246\pi\)
\(468\) −1.84370e25 1.84370e25i −0.0365790 0.0365790i
\(469\) 1.99634e26i 0.387709i
\(470\) −5.95054e23 1.32158e24i −0.00113130 0.00251255i
\(471\) 4.98273e26 0.927381
\(472\) −4.62852e24 + 4.62852e24i −0.00843378 + 0.00843378i
\(473\) −8.08597e25 8.08597e25i −0.144252 0.144252i
\(474\) 3.37726e24i 0.00589904i
\(475\) 2.14171e25 + 1.89614e25i 0.0366290 + 0.0324291i
\(476\) −1.94957e26 −0.326490
\(477\) −3.02667e24 + 3.02667e24i −0.00496343 + 0.00496343i
\(478\) 5.99433e23 + 5.99433e23i 0.000962636 + 0.000962636i
\(479\) 7.65347e26i 1.20366i 0.798625 + 0.601829i \(0.205561\pi\)
−0.798625 + 0.601829i \(0.794439\pi\)
\(480\) 8.61271e24 3.87796e24i 0.0132656 0.00597298i
\(481\) 1.11588e26 0.168332
\(482\) −1.47264e24 + 1.47264e24i −0.00217583 + 0.00217583i
\(483\) 1.42874e26 + 1.42874e26i 0.206767 + 0.206767i
\(484\) 4.34116e26i 0.615393i
\(485\) −1.97109e26 + 5.19990e26i −0.273709 + 0.722067i
\(486\) −1.01835e24 −0.00138527
\(487\) 1.26890e25 1.26890e25i 0.0169097 0.0169097i −0.698601 0.715511i \(-0.746194\pi\)
0.715511 + 0.698601i \(0.246194\pi\)
\(488\) 7.65004e24 + 7.65004e24i 0.00998770 + 0.00998770i
\(489\) 1.06318e27i 1.35993i
\(490\) −3.69332e24 1.40000e24i −0.00462866 0.00175456i
\(491\) −5.45011e26 −0.669253 −0.334626 0.942351i \(-0.608610\pi\)
−0.334626 + 0.942351i \(0.608610\pi\)
\(492\) −9.71976e26 + 9.71976e26i −1.16951 + 1.16951i
\(493\) −7.59886e26 7.59886e26i −0.895941 0.895941i
\(494\) 8.52673e22i 9.85174e-5i
\(495\) −3.01017e25 6.68541e25i −0.0340831 0.0756965i
\(496\) 1.46458e27 1.62517
\(497\) 5.95750e25 5.95750e25i 0.0647888 0.0647888i
\(498\) −1.91890e24 1.91890e24i −0.00204531 0.00204531i
\(499\) 3.36680e26i 0.351732i 0.984414 + 0.175866i \(0.0562725\pi\)
−0.984414 + 0.175866i \(0.943727\pi\)
\(500\) −9.32462e26 2.90066e26i −0.954841 0.297027i
\(501\) −1.07999e27 −1.08403
\(502\) 6.01655e24 6.01655e24i 0.00591984 0.00591984i
\(503\) 4.74966e26 + 4.74966e26i 0.458123 + 0.458123i 0.898039 0.439916i \(-0.144992\pi\)
−0.439916 + 0.898039i \(0.644992\pi\)
\(504\) 3.30105e23i 0.000312138i
\(505\) −9.84190e26 + 4.43141e26i −0.912358 + 0.410798i
\(506\) −4.99314e24 −0.00453804
\(507\) 6.28218e26 6.28218e26i 0.559797 0.559797i
\(508\) 1.34575e27 + 1.34575e27i 1.17578 + 1.17578i
\(509\) 6.84432e26i 0.586344i −0.956060 0.293172i \(-0.905289\pi\)
0.956060 0.293172i \(-0.0947108\pi\)
\(510\) 2.98608e24 7.87752e24i 0.00250841 0.00661740i
\(511\) −4.26214e26 −0.351090
\(512\) 2.28045e25 2.28045e25i 0.0184214 0.0184214i
\(513\) 4.60802e25 + 4.60802e25i 0.0365040 + 0.0365040i
\(514\) 7.39734e24i 0.00574704i
\(515\) 7.48060e26 + 2.83562e26i 0.569986 + 0.216061i
\(516\) −4.09652e26 −0.306138
\(517\) 3.16355e26 3.16355e26i 0.231883 0.231883i
\(518\) 4.99472e23 + 4.99472e23i 0.000359099 + 0.000359099i
\(519\) 2.13603e27i 1.50638i
\(520\) 2.39027e24 + 5.30865e24i 0.00165354 + 0.00367240i
\(521\) −3.25861e26 −0.221134 −0.110567 0.993869i \(-0.535267\pi\)
−0.110567 + 0.993869i \(0.535267\pi\)
\(522\) 6.43317e23 6.43317e23i 0.000428272 0.000428272i
\(523\) 1.32995e27 + 1.32995e27i 0.868596 + 0.868596i 0.992317 0.123721i \(-0.0394829\pi\)
−0.123721 + 0.992317i \(0.539483\pi\)
\(524\) 1.01074e27i 0.647629i
\(525\) 2.19567e26 2.48003e26i 0.138030 0.155906i
\(526\) 5.35147e24 0.00330078
\(527\) 2.77114e27 2.77114e27i 1.67708 1.67708i
\(528\) 6.87197e26 + 6.87197e26i 0.408077 + 0.408077i
\(529\) 1.66814e27i 0.972023i
\(530\) 4.35735e23 1.96194e23i 0.000249152 0.000112183i
\(531\) 2.73028e26 0.153201
\(532\) −1.40552e25 + 1.40552e25i −0.00773966 + 0.00773966i
\(533\) −8.98654e26 8.98654e26i −0.485647 0.485647i
\(534\) 7.27842e24i 0.00386033i
\(535\) −3.93828e26 + 1.03895e27i −0.205007 + 0.540826i
\(536\) −3.53463e25 −0.0180591
\(537\) −2.88984e26 + 2.88984e26i −0.144921 + 0.144921i
\(538\) 1.26812e24 + 1.26812e24i 0.000624218 + 0.000624218i
\(539\) 1.21922e27i 0.589108i
\(540\) −2.08030e27 7.88565e26i −0.986707 0.374024i
\(541\) −3.00958e27 −1.40130 −0.700652 0.713503i \(-0.747108\pi\)
−0.700652 + 0.713503i \(0.747108\pi\)
\(542\) 3.31075e24 3.31075e24i 0.00151333 0.00151333i
\(543\) 3.88308e26 + 3.88308e26i 0.174252 + 0.174252i
\(544\) 5.17777e25i 0.0228115i
\(545\) 5.82392e26 + 1.29346e27i 0.251913 + 0.559483i
\(546\) −9.87365e23 −0.000419326
\(547\) −2.39169e27 + 2.39169e27i −0.997311 + 0.997311i −0.999996 0.00268498i \(-0.999145\pi\)
0.00268498 + 0.999996i \(0.499145\pi\)
\(548\) −1.45549e27 1.45549e27i −0.595942 0.595942i
\(549\) 4.51261e26i 0.181428i
\(550\) 4.96891e23 + 8.17030e24i 0.000196171 + 0.00322560i
\(551\) −1.09566e26 −0.0424777
\(552\) −2.52966e25 + 2.52966e25i −0.00963101 + 0.00963101i
\(553\) 5.14704e26 + 5.14704e26i 0.192445 + 0.192445i
\(554\) 1.03433e25i 0.00379805i
\(555\) 1.02496e27 4.61498e26i 0.369638 0.166433i
\(556\) 3.12595e27 1.10722
\(557\) −1.94071e27 + 1.94071e27i −0.675162 + 0.675162i −0.958901 0.283739i \(-0.908425\pi\)
0.283739 + 0.958901i \(0.408425\pi\)
\(558\) 2.34604e24 + 2.34604e24i 0.000801666 + 0.000801666i
\(559\) 3.78749e26i 0.127126i
\(560\) 2.40519e26 6.34509e26i 0.0792993 0.209198i
\(561\) 2.60049e27 0.842223
\(562\) −1.25150e25 + 1.25150e25i −0.00398168 + 0.00398168i
\(563\) −3.04528e27 3.04528e27i −0.951794 0.951794i 0.0470961 0.998890i \(-0.485003\pi\)
−0.998890 + 0.0470961i \(0.985003\pi\)
\(564\) 1.60272e27i 0.492115i
\(565\) −1.85590e27 7.03502e26i −0.559847 0.212217i
\(566\) 1.79551e25 0.00532136
\(567\) 4.60861e26 4.60861e26i 0.134196 0.134196i
\(568\) 1.05481e25 + 1.05481e25i 0.00301780 + 0.00301780i
\(569\) 3.26586e27i 0.918068i 0.888419 + 0.459034i \(0.151804\pi\)
−0.888419 + 0.459034i \(0.848196\pi\)
\(570\) −3.52643e23 7.83199e23i −9.74063e−5 0.000216333i
\(571\) 3.57523e27 0.970383 0.485191 0.874408i \(-0.338750\pi\)
0.485191 + 0.874408i \(0.338750\pi\)
\(572\) −6.35375e26 + 6.35375e26i −0.169461 + 0.169461i
\(573\) 7.20173e26 + 7.20173e26i 0.188752 + 0.188752i
\(574\) 8.04484e24i 0.00207204i
\(575\) 5.53774e27 3.36787e26i 1.40170 0.0852466i
\(576\) −5.38042e26 −0.133842
\(577\) 2.63542e26 2.63542e26i 0.0644306 0.0644306i −0.674157 0.738588i \(-0.735493\pi\)
0.738588 + 0.674157i \(0.235493\pi\)
\(578\) −1.73200e25 1.73200e25i −0.00416169 0.00416169i
\(579\) 4.48618e27i 1.05948i
\(580\) 3.41069e27 1.53570e27i 0.791704 0.356473i
\(581\) −5.84893e26 −0.133449
\(582\) 1.18074e25 1.18074e25i 0.00264803 0.00264803i
\(583\) 1.04305e26 + 1.04305e26i 0.0229942 + 0.0229942i
\(584\) 7.54636e25i 0.0163534i
\(585\) 8.60747e25 2.27072e26i 0.0183365 0.0483732i
\(586\) 4.41786e25 0.00925200
\(587\) 1.83539e27 1.83539e27i 0.377873 0.377873i −0.492461 0.870334i \(-0.663903\pi\)
0.870334 + 0.492461i \(0.163903\pi\)
\(588\) −3.08842e27 3.08842e27i −0.625119 0.625119i
\(589\) 3.99565e26i 0.0795124i
\(590\) −2.85023e25 1.08042e25i −0.00557647 0.00211383i
\(591\) 2.99690e26 0.0576497
\(592\) 1.62830e27 1.62830e27i 0.307977 0.307977i
\(593\) −2.89387e27 2.89387e27i −0.538185 0.538185i 0.384811 0.922996i \(-0.374267\pi\)
−0.922996 + 0.384811i \(0.874267\pi\)
\(594\) 1.86479e25i 0.00341010i
\(595\) −7.45470e26 1.65564e27i −0.134048 0.297713i
\(596\) −6.05212e27 −1.07015
\(597\) −2.26973e27 + 2.26973e27i −0.394668 + 0.394668i
\(598\) −1.16940e25 1.16940e25i −0.00199964 0.00199964i
\(599\) 7.86676e27i 1.32290i 0.749988 + 0.661451i \(0.230059\pi\)
−0.749988 + 0.661451i \(0.769941\pi\)
\(600\) 4.39104e25 + 3.88756e25i 0.00726197 + 0.00642931i
\(601\) −4.80387e27 −0.781351 −0.390676 0.920528i \(-0.627759\pi\)
−0.390676 + 0.920528i \(0.627759\pi\)
\(602\) 1.69530e24 1.69530e24i 0.000271195 0.000271195i
\(603\) 1.04250e27 + 1.04250e27i 0.164023 + 0.164023i
\(604\) 2.77817e26i 0.0429922i
\(605\) 3.68666e27 1.65996e27i 0.561151 0.252664i
\(606\) 3.24103e25 0.00485240
\(607\) −8.30490e27 + 8.30490e27i −1.22306 + 1.22306i −0.256520 + 0.966539i \(0.582576\pi\)
−0.966539 + 0.256520i \(0.917424\pi\)
\(608\) −3.73286e24 3.73286e24i −0.000540762 0.000540762i
\(609\) 1.26874e27i 0.180801i
\(610\) −1.78572e25 + 4.71087e25i −0.00250331 + 0.00660393i
\(611\) 1.48182e27 0.204354
\(612\) −1.01808e27 + 1.01808e27i −0.138124 + 0.138124i
\(613\) −2.69070e26 2.69070e26i −0.0359138 0.0359138i 0.688922 0.724836i \(-0.258084\pi\)
−0.724836 + 0.688922i \(0.758084\pi\)
\(614\) 8.70106e24i 0.00114259i
\(615\) −1.19709e28 4.53774e27i −1.54660 0.586258i
\(616\) −1.13760e25 −0.00144605
\(617\) 7.68618e27 7.68618e27i 0.961300 0.961300i −0.0379785 0.999279i \(-0.512092\pi\)
0.999279 + 0.0379785i \(0.0120918\pi\)
\(618\) −1.69861e25 1.69861e25i −0.00209030 0.00209030i
\(619\) 1.64811e28i 1.99563i −0.0660814 0.997814i \(-0.521050\pi\)
0.0660814 0.997814i \(-0.478950\pi\)
\(620\) 5.60037e27 + 1.24381e28i 0.667267 + 1.48196i
\(621\) 1.26394e28 1.48187
\(622\) −8.34158e23 + 8.34158e23i −9.62375e−5 + 9.62375e-5i
\(623\) 1.10925e27 + 1.10925e27i 0.125936 + 0.125936i
\(624\) 3.21885e27i 0.359629i
\(625\) −1.10217e27 9.02792e27i −0.121185 0.992630i
\(626\) −5.18133e25 −0.00560658
\(627\) 1.87480e26 1.87480e26i 0.0199654 0.0199654i
\(628\) 6.72256e27 + 6.72256e27i 0.704593 + 0.704593i
\(629\) 6.16183e27i 0.635628i
\(630\) 1.40166e24 6.31112e23i 0.000142311 6.40768e-5i
\(631\) 4.08536e27 0.408260 0.204130 0.978944i \(-0.434563\pi\)
0.204130 + 0.978944i \(0.434563\pi\)
\(632\) −9.11313e25 + 9.11313e25i −0.00896390 + 0.00896390i
\(633\) 7.66458e27 + 7.66458e27i 0.742081 + 0.742081i
\(634\) 2.70555e25i 0.00257847i
\(635\) −6.28274e27 + 1.65744e28i −0.589403 + 1.55489i
\(636\) 5.28430e26 0.0487996
\(637\) 2.85544e27 2.85544e27i 0.259584 0.259584i
\(638\) −2.21699e25 2.21699e25i −0.00198407 0.00198407i
\(639\) 6.22212e26i 0.0548188i
\(640\) 2.24693e26 + 8.51729e25i 0.0194890 + 0.00738757i
\(641\) −2.99650e27 −0.255878 −0.127939 0.991782i \(-0.540836\pi\)
−0.127939 + 0.991782i \(0.540836\pi\)
\(642\) 2.35914e25 2.35914e25i 0.00198337 0.00198337i
\(643\) −1.09767e28 1.09767e28i −0.908577 0.908577i 0.0875802 0.996157i \(-0.472087\pi\)
−0.996157 + 0.0875802i \(0.972087\pi\)
\(644\) 3.85523e27i 0.314189i
\(645\) −1.56641e27 3.47890e27i −0.125692 0.279155i
\(646\) −4.70842e24 −0.000372006
\(647\) 2.13474e27 2.13474e27i 0.166074 0.166074i −0.619177 0.785251i \(-0.712534\pi\)
0.785251 + 0.619177i \(0.212534\pi\)
\(648\) 8.15981e25 + 8.15981e25i 0.00625072 + 0.00625072i
\(649\) 9.40905e27i 0.709739i
\(650\) −1.79713e25 + 2.02987e25i −0.00133489 + 0.00150777i
\(651\) −4.62683e27 −0.338434
\(652\) 1.43441e28 1.43441e28i 1.03323 1.03323i
\(653\) 1.51870e28 + 1.51870e28i 1.07731 + 1.07731i 0.996750 + 0.0805577i \(0.0256701\pi\)
0.0805577 + 0.996750i \(0.474330\pi\)
\(654\) 4.25948e25i 0.00297563i
\(655\) −8.58354e27 + 3.86482e27i −0.590545 + 0.265899i
\(656\) −2.62265e28 −1.77706
\(657\) −2.22573e27 + 2.22573e27i −0.148531 + 0.148531i
\(658\) 6.63270e24 + 6.63270e24i 0.000435945 + 0.000435945i
\(659\) 7.70752e27i 0.498954i −0.968381 0.249477i \(-0.919741\pi\)
0.968381 0.249477i \(-0.0802587\pi\)
\(660\) −3.20832e27 + 8.46381e27i −0.204568 + 0.539668i
\(661\) −1.06771e28 −0.670561 −0.335280 0.942118i \(-0.608831\pi\)
−0.335280 + 0.942118i \(0.608831\pi\)
\(662\) 2.49384e25 2.49384e25i 0.00154273 0.00154273i
\(663\) 6.09040e27 + 6.09040e27i 0.371117 + 0.371117i
\(664\) 1.03559e26i 0.00621593i
\(665\) −1.73106e26 6.56180e25i −0.0102352 0.00387977i
\(666\) 5.21658e24 0.000303839
\(667\) −1.50265e28 + 1.50265e28i −0.862185 + 0.862185i
\(668\) −1.45709e28 1.45709e28i −0.823612 0.823612i
\(669\) 1.86513e28i 1.03860i
\(670\) −6.75769e25 1.50084e26i −0.00370724 0.00823355i
\(671\) −1.55513e28 −0.840508
\(672\) −4.32252e25 + 4.32252e25i −0.00230168 + 0.00230168i
\(673\) 1.34303e28 + 1.34303e28i 0.704590 + 0.704590i 0.965392 0.260802i \(-0.0839871\pi\)
−0.260802 + 0.965392i \(0.583987\pi\)
\(674\) 5.66509e25i 0.00292825i
\(675\) −1.25780e27 2.06819e28i −0.0640582 1.05330i
\(676\) 1.69515e28 0.850630
\(677\) 1.97993e28 1.97993e28i 0.978955 0.978955i −0.0208277 0.999783i \(-0.506630\pi\)
0.999783 + 0.0208277i \(0.00663015\pi\)
\(678\) 4.21417e25 + 4.21417e25i 0.00205312 + 0.00205312i
\(679\) 3.59895e27i 0.172774i
\(680\) 2.93141e26 1.31990e26i 0.0138672 0.00624383i
\(681\) 2.41293e28 1.12480
\(682\) 8.08490e25 8.08490e25i 0.00371390 0.00371390i
\(683\) 6.17987e27 + 6.17987e27i 0.279752 + 0.279752i 0.833010 0.553258i \(-0.186616\pi\)
−0.553258 + 0.833010i \(0.686616\pi\)
\(684\) 1.46795e26i 0.00654865i
\(685\) 6.79507e27 1.79260e28i 0.298736 0.788091i
\(686\) 5.24715e25 0.00227343
\(687\) −1.65004e28 + 1.65004e28i −0.704575 + 0.704575i
\(688\) −5.52676e27 5.52676e27i −0.232587 0.232587i
\(689\) 4.88567e26i 0.0202643i
\(690\) −1.55776e26 5.90488e25i −0.00636808 0.00241391i
\(691\) 2.87344e28 1.15777 0.578884 0.815410i \(-0.303489\pi\)
0.578884 + 0.815410i \(0.303489\pi\)
\(692\) 2.88188e28 2.88188e28i 1.14450 1.14450i
\(693\) 3.35525e26 + 3.35525e26i 0.0131339 + 0.0131339i
\(694\) 1.87012e26i 0.00721562i
\(695\) 1.19529e28 + 2.65466e28i 0.454595 + 1.00963i
\(696\) −2.24638e26 −0.00842152
\(697\) −4.96233e28 + 4.96233e28i −1.83382 + 1.83382i
\(698\) 7.04716e25 + 7.04716e25i 0.00256720 + 0.00256720i
\(699\) 3.72897e28i 1.33911i
\(700\) 6.30833e27 3.83651e26i 0.223323 0.0135818i
\(701\) 1.27524e27 0.0445053 0.0222527 0.999752i \(-0.492916\pi\)
0.0222527 + 0.999752i \(0.492916\pi\)
\(702\) −4.36738e25 + 4.36738e25i −0.00150262 + 0.00150262i
\(703\) −4.44230e26 4.44230e26i −0.0150680 0.0150680i
\(704\) 1.85419e28i 0.620052i
\(705\) 1.36108e28 6.12842e27i 0.448739 0.202049i
\(706\) −1.46373e26 −0.00475787
\(707\) 4.93942e27 4.93942e27i 0.158300 0.158300i
\(708\) −2.38341e28 2.38341e28i −0.753123 0.753123i
\(709\) 3.99111e28i 1.24346i 0.783232 + 0.621729i \(0.213570\pi\)
−0.783232 + 0.621729i \(0.786430\pi\)
\(710\) −2.46220e25 + 6.49548e25i −0.000756378 + 0.00199539i
\(711\) 5.37566e27 0.162831
\(712\) −1.96399e26 + 1.96399e26i −0.00586598 + 0.00586598i
\(713\) −5.47986e28 5.47986e28i −1.61389 1.61389i
\(714\) 5.45219e25i 0.00158339i
\(715\) −7.82534e27 2.96630e27i −0.224100 0.0849482i
\(716\) −7.79778e27 −0.220212
\(717\) −6.17352e27 + 6.17352e27i −0.171926 + 0.171926i
\(718\) 4.33168e25 + 4.33168e25i 0.00118963 + 0.00118963i
\(719\) 3.78806e28i 1.02595i 0.858402 + 0.512977i \(0.171457\pi\)
−0.858402 + 0.512977i \(0.828543\pi\)
\(720\) −2.05745e27 4.56948e27i −0.0549547 0.122051i
\(721\) −5.17747e27 −0.136384
\(722\) 1.41491e26 1.41491e26i 0.00367585 0.00367585i
\(723\) −1.51666e28 1.51666e28i −0.388601 0.388601i
\(724\) 1.04779e28i 0.264782i
\(725\) 2.60833e28 + 2.30926e28i 0.650104 + 0.575563i
\(726\) −1.21405e26 −0.00298450
\(727\) −6.81066e26 + 6.81066e26i −0.0165137 + 0.0165137i −0.715315 0.698802i \(-0.753717\pi\)
0.698802 + 0.715315i \(0.253717\pi\)
\(728\) −2.66429e25 2.66429e25i −0.000637188 0.000637188i
\(729\) 4.64448e28i 1.09563i
\(730\) 3.20427e26 1.44275e26i 0.00745590 0.00335709i
\(731\) −2.09144e28 −0.480033
\(732\) −3.93931e28 + 3.93931e28i −0.891886 + 0.891886i
\(733\) 3.19735e28 + 3.19735e28i 0.714087 + 0.714087i 0.967388 0.253301i \(-0.0815163\pi\)
−0.253301 + 0.967388i \(0.581516\pi\)
\(734\) 2.36861e26i 0.00521835i
\(735\) 1.44185e28 3.80372e28i 0.313362 0.826676i
\(736\) −1.02389e27 −0.0219521
\(737\) 3.59267e28 3.59267e28i 0.759875 0.759875i
\(738\) −4.20109e25 4.20109e25i −0.000876594 0.000876594i
\(739\) 5.44973e28i 1.12184i 0.827871 + 0.560919i \(0.189552\pi\)
−0.827871 + 0.560919i \(0.810448\pi\)
\(740\) 2.00549e28 + 7.60206e27i 0.407289 + 0.154388i
\(741\) 8.78162e26 0.0175951
\(742\) −2.18685e24 + 2.18685e24i −4.32295e−5 + 4.32295e-5i
\(743\) −3.02473e28 3.02473e28i −0.589928 0.589928i 0.347684 0.937612i \(-0.386968\pi\)
−0.937612 + 0.347684i \(0.886968\pi\)
\(744\) 8.19206e26i 0.0157639i
\(745\) −2.31419e28 5.13967e28i −0.439375 0.975825i
\(746\) 2.76850e26 0.00518628
\(747\) −3.05436e27 + 3.05436e27i −0.0564566 + 0.0564566i
\(748\) 3.50851e28 + 3.50851e28i 0.639893 + 0.639893i
\(749\) 7.19079e27i 0.129407i
\(750\) −8.11199e25 + 2.60773e26i −0.00144051 + 0.00463073i
\(751\) 7.71306e28 1.35153 0.675767 0.737115i \(-0.263812\pi\)
0.675767 + 0.737115i \(0.263812\pi\)
\(752\) 2.16229e28 2.16229e28i 0.373882 0.373882i
\(753\) 6.19640e28 + 6.19640e28i 1.05728 + 1.05728i
\(754\) 1.03845e26i 0.00174852i
\(755\) 2.35932e27 1.06231e27i 0.0392028 0.0176514i
\(756\) 1.43982e28 0.236096
\(757\) 7.96584e27 7.96584e27i 0.128906 0.128906i −0.639710 0.768616i \(-0.720946\pi\)
0.768616 + 0.639710i \(0.220946\pi\)
\(758\) 7.99588e25 + 7.99588e25i 0.00127695 + 0.00127695i
\(759\) 5.14240e28i 0.810491i
\(760\) 1.16180e25 3.06494e25i 0.000180716 0.000476744i
\(761\) −4.63585e28 −0.711677 −0.355839 0.934547i \(-0.615805\pi\)
−0.355839 + 0.934547i \(0.615805\pi\)
\(762\) 3.76354e26 3.76354e26i 0.00570225 0.00570225i
\(763\) −6.49156e27 6.49156e27i −0.0970742 0.0970742i
\(764\) 1.94327e28i 0.286814i
\(765\) −1.25388e28 4.75301e27i −0.182660 0.0692395i
\(766\) 2.22542e26 0.00319982
\(767\) 2.20362e28 2.20362e28i 0.312739 0.312739i
\(768\) 4.69648e28 + 4.69648e28i 0.657901 + 0.657901i
\(769\) 5.21119e28i 0.720565i −0.932843 0.360283i \(-0.882680\pi\)
0.932843 0.360283i \(-0.117320\pi\)
\(770\) −2.17493e25 4.83039e25i −0.000296851 0.000659288i
\(771\) −7.61847e28 −1.02642
\(772\) −6.05263e28 + 6.05263e28i −0.804955 + 0.804955i
\(773\) −8.28103e28 8.28103e28i −1.08715 1.08715i −0.995821 0.0913294i \(-0.970888\pi\)
−0.0913294 0.995821i \(-0.529112\pi\)
\(774\) 1.77060e25i 0.000229463i
\(775\) −8.42139e28 + 9.51204e28i −1.07737 + 1.21690i
\(776\) 6.37215e26 0.00804765
\(777\) −5.14403e27 + 5.14403e27i −0.0641348 + 0.0641348i
\(778\) −4.15606e26 4.15606e26i −0.00511547 0.00511547i
\(779\) 7.15508e27i 0.0869440i
\(780\) −2.73363e28 + 1.23085e28i −0.327940 + 0.147658i
\(781\) −2.14426e28 −0.253961
\(782\) −6.45739e26 + 6.45739e26i −0.00755074 + 0.00755074i
\(783\) 5.61198e28 + 5.61198e28i 0.647886 + 0.647886i
\(784\) 8.33338e28i 0.949862i
\(785\) −3.13848e28 + 8.27957e28i −0.353202 + 0.931775i
\(786\) 2.82664e26 0.00314083
\(787\) 8.66634e28 8.66634e28i 0.950798 0.950798i −0.0480469 0.998845i \(-0.515300\pi\)
0.998845 + 0.0480469i \(0.0152997\pi\)
\(788\) 4.04333e27 + 4.04333e27i 0.0438003 + 0.0438003i
\(789\) 5.51145e28i 0.589516i
\(790\) −5.61183e26 2.12724e26i −0.00592699 0.00224670i
\(791\) 1.28450e28 0.133959
\(792\) −5.94067e25 + 5.94067e25i −0.000611763 + 0.000611763i
\(793\) −3.64215e28 3.64215e28i −0.370361 0.370361i
\(794\) 2.01971e26i 0.00202808i
\(795\) 2.02059e27 + 4.48760e27i 0.0200358 + 0.0444983i
\(796\) −6.12452e28 −0.599710
\(797\) 5.24123e28 5.24123e28i 0.506815 0.506815i −0.406732 0.913547i \(-0.633332\pi\)
0.913547 + 0.406732i \(0.133332\pi\)
\(798\) 3.93070e24 + 3.93070e24i 3.75354e−5 + 3.75354e-5i
\(799\) 8.18254e28i 0.771650i
\(800\) 1.01892e26 + 1.67540e27i 0.000948943 + 0.0156033i
\(801\) 1.15852e28 0.106556
\(802\) −1.93635e26 + 1.93635e26i −0.00175889 + 0.00175889i
\(803\) 7.67027e28 + 7.67027e28i 0.688106 + 0.688106i
\(804\) 1.82012e29i 1.61265i
\(805\) −3.27399e28 + 1.47415e28i −0.286496 + 0.128998i
\(806\) 3.78699e26 0.00327299
\(807\) −1.30602e28 + 1.30602e28i −0.111485 + 0.111485i
\(808\) 8.74553e26 + 8.74553e26i 0.00737348 + 0.00737348i
\(809\) 2.16772e29i 1.80517i 0.430509 + 0.902586i \(0.358334\pi\)
−0.430509 + 0.902586i \(0.641666\pi\)
\(810\) −1.90471e26 + 5.02478e26i −0.00156667 + 0.00413301i
\(811\) 6.24252e28 0.507167 0.253584 0.967313i \(-0.418391\pi\)
0.253584 + 0.967313i \(0.418391\pi\)
\(812\) −1.71175e28 + 1.71175e28i −0.137366 + 0.137366i
\(813\) 3.40972e28 + 3.40972e28i 0.270279 + 0.270279i
\(814\) 1.79773e26i 0.00140761i
\(815\) 1.76663e29 + 6.69665e28i 1.36638 + 0.517942i
\(816\) 1.77744e29 1.35798
\(817\) −1.50780e27 + 1.50780e27i −0.0113795 + 0.0113795i
\(818\) −5.47406e26 5.47406e26i −0.00408109 0.00408109i
\(819\) 1.57161e27i 0.0115746i
\(820\) −1.00287e29 2.22731e29i −0.729633 1.62047i
\(821\) −1.45291e29 −1.04425 −0.522127 0.852868i \(-0.674861\pi\)
−0.522127 + 0.852868i \(0.674861\pi\)
\(822\) −4.07043e26 + 4.07043e26i −0.00289016 + 0.00289016i
\(823\) 1.58958e29 + 1.58958e29i 1.11502 + 1.11502i 0.992461 + 0.122560i \(0.0391103\pi\)
0.122560 + 0.992461i \(0.460890\pi\)
\(824\) 9.16701e26i 0.00635266i
\(825\) −8.41453e28 + 5.11744e27i −0.576090 + 0.0350359i
\(826\) 1.97270e26 0.00133432
\(827\) 1.28860e29 1.28860e29i 0.861122 0.861122i −0.130347 0.991468i \(-0.541609\pi\)
0.991468 + 0.130347i \(0.0416090\pi\)
\(828\) 2.01323e28 + 2.01323e28i 0.132920 + 0.132920i
\(829\) 1.27029e29i 0.828624i −0.910135 0.414312i \(-0.864022\pi\)
0.910135 0.414312i \(-0.135978\pi\)
\(830\) 4.39722e26 1.97989e26i 0.00283398 0.00127603i
\(831\) −1.06525e29 −0.678329
\(832\) −4.34255e28 + 4.34255e28i −0.273220 + 0.273220i
\(833\) −1.57676e29 1.57676e29i −0.980202 0.980202i
\(834\) 8.74205e26i 0.00536974i
\(835\) 6.80255e28 1.79457e29i 0.412864 1.08917i
\(836\) 5.05885e27 0.0303381
\(837\) −2.04657e29 + 2.04657e29i −1.21275 + 1.21275i
\(838\) −3.68408e26 3.68408e26i −0.00215719 0.00215719i
\(839\) 1.51592e29i 0.877114i 0.898703 + 0.438557i \(0.144510\pi\)
−0.898703 + 0.438557i \(0.855490\pi\)
\(840\) −3.54909e26 1.34533e26i −0.00202920 0.000769194i
\(841\) 4.35568e28 0.246091
\(842\) 8.84287e26 8.84287e26i 0.00493710 0.00493710i
\(843\) −1.28891e29 1.28891e29i −0.711125 0.711125i
\(844\) 2.06817e29i 1.12762i
\(845\) 6.48184e28 + 1.43958e29i 0.349246 + 0.775654i
\(846\) 6.92731e25 0.000368859
\(847\) −1.85025e28 + 1.85025e28i −0.0973636 + 0.0973636i
\(848\) 7.12923e27 + 7.12923e27i 0.0370753 + 0.0370753i
\(849\) 1.84918e29i 0.950390i
\(850\) 1.12089e27 + 9.92365e26i 0.00569341 + 0.00504060i
\(851\) −1.21848e29 −0.611680
\(852\) −5.43163e28 + 5.43163e28i −0.269485 + 0.269485i
\(853\) −2.18327e29 2.18327e29i −1.07058 1.07058i −0.997313 0.0732623i \(-0.976659\pi\)
−0.0732623 0.997313i \(-0.523341\pi\)
\(854\) 3.26049e26i 0.00158017i
\(855\) −1.24664e27 + 5.61310e26i −0.00597143 + 0.00268870i
\(856\) 1.27317e27 0.00602767
\(857\) −4.94404e28 + 4.94404e28i −0.231352 + 0.231352i −0.813257 0.581905i \(-0.802308\pi\)
0.581905 + 0.813257i \(0.302308\pi\)
\(858\) 1.77689e26 + 1.77689e26i 0.000821842 + 0.000821842i
\(859\) 2.18722e29i 0.999910i −0.866052 0.499955i \(-0.833350\pi\)
0.866052 0.499955i \(-0.166650\pi\)
\(860\) 2.58028e28 6.80699e28i 0.116596 0.307589i
\(861\) 8.28533e28 0.370065
\(862\) −7.39321e25 + 7.39321e25i −0.000326408 + 0.000326408i
\(863\) −3.26266e28 3.26266e28i −0.142385 0.142385i 0.632321 0.774706i \(-0.282102\pi\)
−0.774706 + 0.632321i \(0.782102\pi\)
\(864\) 3.82394e27i 0.0164958i
\(865\) 3.54935e29 + 1.34543e29i 1.51352 + 0.573718i
\(866\) −1.55589e27 −0.00655845
\(867\) 1.78378e29 1.78378e29i 0.743275 0.743275i
\(868\) −6.24239e28 6.24239e28i −0.257130 0.257130i
\(869\) 1.85255e29i 0.754351i
\(870\) −4.29474e26 9.53837e26i −0.00172880 0.00383956i
\(871\) 1.68282e29 0.669662
\(872\) 1.14937e27 1.14937e27i 0.00452162 0.00452162i
\(873\) −1.87940e28 1.87940e28i −0.0730934 0.0730934i
\(874\) 9.31077e25i 0.000357990i
\(875\) 2.73796e28 + 5.21054e28i 0.104075 + 0.198063i
\(876\) 3.88592e29 1.46033
\(877\) −6.53451e28 + 6.53451e28i −0.242782 + 0.242782i −0.818000 0.575218i \(-0.804917\pi\)
0.575218 + 0.818000i \(0.304917\pi\)
\(878\) −2.89597e25 2.89597e25i −0.000106377 0.000106377i
\(879\) 4.54992e29i 1.65240i
\(880\) −1.57473e29 + 7.09037e28i −0.565430 + 0.254590i
\(881\) 1.64158e29 0.582779 0.291390 0.956604i \(-0.405882\pi\)
0.291390 + 0.956604i \(0.405882\pi\)
\(882\) 1.33488e26 1.33488e26i 0.000468550 0.000468550i
\(883\) −3.18805e28 3.18805e28i −0.110642 0.110642i 0.649619 0.760260i \(-0.274929\pi\)
−0.760260 + 0.649619i \(0.774929\pi\)
\(884\) 1.64340e29i 0.563924i
\(885\) 1.11271e29 2.93543e29i 0.377529 0.995953i
\(886\) −4.72834e26 −0.00158625
\(887\) −3.31815e28 + 3.31815e28i −0.110068 + 0.110068i −0.759996 0.649928i \(-0.774799\pi\)
0.649928 + 0.759996i \(0.274799\pi\)
\(888\) −9.10781e26 9.10781e26i −0.00298734 0.00298734i
\(889\) 1.14715e29i 0.372050i
\(890\) −1.20942e27 4.58447e26i −0.00387862 0.00147024i
\(891\) −1.65876e29 −0.526025
\(892\) −2.51637e29 + 2.51637e29i −0.789091 + 0.789091i
\(893\) −5.89911e27 5.89911e27i −0.0182925 0.0182925i
\(894\) 1.69254e27i 0.00518996i
\(895\) −2.98168e28 6.62214e28i −0.0904130 0.200802i
\(896\) −1.55515e27 −0.00466328
\(897\) 1.20436e29 1.20436e29i 0.357134 0.357134i
\(898\) 1.40431e27 + 1.40431e27i 0.00411811 + 0.00411811i
\(899\) 4.86619e29i 1.41121i
\(900\) 3.09392e28 3.49461e28i 0.0887327 0.100224i
\(901\) 2.69785e28 0.0765190
\(902\) −1.44777e27 + 1.44777e27i −0.00406102 + 0.00406102i
\(903\) 1.74598e28 + 1.74598e28i 0.0484353 + 0.0484353i
\(904\) 2.27429e27i 0.00623966i
\(905\) −8.89818e28 + 4.00649e28i −0.241443 + 0.108712i
\(906\) −7.76946e25 −0.000208501
\(907\) −5.55720e28 + 5.55720e28i −0.147497 + 0.147497i −0.776999 0.629502i \(-0.783259\pi\)
0.629502 + 0.776999i \(0.283259\pi\)
\(908\) 3.25546e29 + 3.25546e29i 0.854581 + 0.854581i
\(909\) 5.15882e28i 0.133940i
\(910\) 6.21913e25 1.64066e26i 0.000159704 0.000421312i
\(911\) −6.81980e29 −1.73216 −0.866080 0.499906i \(-0.833368\pi\)
−0.866080 + 0.499906i \(0.833368\pi\)
\(912\) 1.28142e28 1.28142e28i 0.0321917 0.0321917i
\(913\) 1.05259e29 + 1.05259e29i 0.261548 + 0.261548i
\(914\) 8.10953e26i 0.00199312i
\(915\) −4.85169e29 1.83910e29i −1.17946 0.447089i
\(916\) −4.45238e29 −1.07062
\(917\) 4.30788e28 4.30788e28i 0.102464 0.102464i
\(918\) 2.41165e27 + 2.41165e27i 0.00567397 + 0.00567397i
\(919\) 6.49458e29i 1.51146i 0.654885 + 0.755728i \(0.272717\pi\)
−0.654885 + 0.755728i \(0.727283\pi\)
\(920\) −2.61006e27 5.79678e27i −0.00600858 0.0133447i
\(921\) 8.96117e28 0.204065
\(922\) 7.30944e26 7.30944e26i 0.00164655 0.00164655i
\(923\) −5.02189e28 5.02189e28i −0.111905 0.111905i
\(924\) 5.85797e28i 0.129130i
\(925\) 1.21257e28 + 1.99381e29i 0.0264417 + 0.434777i
\(926\) −2.07836e27 −0.00448344
\(927\) −2.70372e28 + 2.70372e28i −0.0576985 + 0.0576985i
\(928\) −4.54615e27 4.54615e27i −0.00959762 0.00959762i
\(929\) 2.76287e29i 0.577037i −0.957474 0.288518i \(-0.906837\pi\)
0.957474 0.288518i \(-0.0931627\pi\)
\(930\) 3.47844e27 1.56620e27i 0.00718712 0.00323607i
\(931\) −2.27350e28 −0.0464727
\(932\) 5.03102e29 5.03102e29i 1.01741 1.01741i
\(933\) −8.59093e27 8.59093e27i −0.0171879 0.0171879i
\(934\) 3.90456e27i 0.00772865i
\(935\) −1.63798e29 + 4.32112e29i −0.320768 + 0.846213i
\(936\) −2.78263e26 −0.000539134
\(937\) 2.92472e29 2.92472e29i 0.560646 0.560646i −0.368845 0.929491i \(-0.620247\pi\)
0.929491 + 0.368845i \(0.120247\pi\)
\(938\) 7.53238e26 + 7.53238e26i 0.00142858 + 0.00142858i
\(939\) 5.33622e29i 1.00133i
\(940\) 2.66317e29 + 1.00951e29i 0.494447 + 0.187427i
\(941\) 4.28555e29 0.787246 0.393623 0.919272i \(-0.371222\pi\)
0.393623 + 0.919272i \(0.371222\pi\)
\(942\) 1.88003e27 1.88003e27i 0.00341709 0.00341709i
\(943\) 9.81287e29 + 9.81287e29i 1.76473 + 1.76473i
\(944\) 6.43108e29i 1.14436i
\(945\) 5.50551e28 + 1.22274e29i 0.0969348 + 0.215286i
\(946\) −6.10183e26 −0.00106304
\(947\) 1.53144e29 1.53144e29i 0.263998 0.263998i −0.562678 0.826676i \(-0.690229\pi\)
0.826676 + 0.562678i \(0.190229\pi\)
\(948\) −4.69271e29 4.69271e29i −0.800462 0.800462i
\(949\) 3.59278e29i 0.606413i
\(950\) 1.52353e26 9.26558e24i 0.000254457 1.54752e-5i
\(951\) −2.78642e29 −0.460513
\(952\) −1.47121e27 + 1.47121e27i −0.00240605 + 0.00240605i
\(953\) 1.42012e29 + 1.42012e29i 0.229825 + 0.229825i 0.812620 0.582795i \(-0.198041\pi\)
−0.582795 + 0.812620i \(0.698041\pi\)
\(954\) 2.28399e25i 3.65772e-5i
\(955\) −1.65029e29 + 7.43061e28i −0.261534 + 0.117758i
\(956\) −1.66583e29 −0.261247
\(957\) 2.28326e29 2.28326e29i 0.354354 0.354354i
\(958\) 2.88773e27 + 2.88773e27i 0.00443509 + 0.00443509i
\(959\) 1.24069e29i 0.188572i
\(960\) −2.19277e29 + 5.78470e29i −0.329822 + 0.870099i
\(961\) 1.10281e30 1.64159
\(962\) 4.21032e26 4.21032e26i 0.000620246 0.000620246i
\(963\) −3.75510e28 3.75510e28i −0.0547467 0.0547467i
\(964\) 4.09246e29i 0.590492i
\(965\) −7.45448e29 2.82572e29i −1.06450 0.403511i
\(966\) 1.07816e27 0.00152374
\(967\) −5.27619e29 + 5.27619e29i −0.737999 + 0.737999i −0.972191 0.234191i \(-0.924756\pi\)
0.234191 + 0.972191i \(0.424756\pi\)
\(968\) −3.27598e27 3.27598e27i −0.00453510 0.00453510i
\(969\) 4.84917e28i 0.0664400i
\(970\) 1.21826e27 + 2.70569e27i 0.00165205 + 0.00366910i
\(971\) 1.97947e29 0.265679 0.132840 0.991138i \(-0.457590\pi\)
0.132840 + 0.991138i \(0.457590\pi\)
\(972\) 1.41500e29 1.41500e29i 0.187973 0.187973i
\(973\) −1.33231e29 1.33231e29i −0.175177 0.175177i
\(974\) 9.57535e25i 0.000124614i
\(975\) −2.09055e29 1.85085e29i −0.269286 0.238410i
\(976\) −1.06293e30 −1.35521
\(977\) −9.76815e29 + 9.76815e29i −1.23273 + 1.23273i −0.269813 + 0.962913i \(0.586962\pi\)
−0.962913 + 0.269813i \(0.913038\pi\)
\(978\) −4.01148e27 4.01148e27i −0.00501090 0.00501090i
\(979\) 3.99249e29i 0.493647i
\(980\) 7.07718e29 3.18657e29i 0.866163 0.389998i
\(981\) −6.77991e28 −0.0821360
\(982\) −2.05638e27 + 2.05638e27i −0.00246598 + 0.00246598i
\(983\) −1.45347e29 1.45347e29i −0.172532 0.172532i 0.615559 0.788091i \(-0.288930\pi\)
−0.788091 + 0.615559i \(0.788930\pi\)
\(984\) 1.46697e28i 0.0172373i
\(985\) −1.88766e28 + 4.97981e28i −0.0219564 + 0.0579229i
\(986\) −5.73426e27 −0.00660249
\(987\) −6.83097e28 + 6.83097e28i −0.0778594 + 0.0778594i
\(988\) 1.18479e28 + 1.18479e28i 0.0133682 + 0.0133682i
\(989\) 4.13576e29i 0.461947i
\(990\) −3.65824e26 1.38670e26i −0.000404502 0.000153332i
\(991\) −3.82280e29 −0.418452 −0.209226 0.977867i \(-0.567094\pi\)
−0.209226 + 0.977867i \(0.567094\pi\)
\(992\) 1.65788e28 1.65788e28i 0.0179654 0.0179654i
\(993\) 2.56839e29 + 2.56839e29i 0.275530 + 0.275530i
\(994\) 4.49565e26i 0.000477451i
\(995\) −2.34187e29 5.20115e29i −0.246225 0.546850i
\(996\) 5.33265e29 0.555072
\(997\) 2.89012e29 2.89012e29i 0.297827 0.297827i −0.542335 0.840162i \(-0.682460\pi\)
0.840162 + 0.542335i \(0.182460\pi\)
\(998\) 1.27033e27 + 1.27033e27i 0.00129602 + 0.00129602i
\(999\) 4.55069e29i 0.459645i
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 5.21.c.a.3.5 yes 18
3.2 odd 2 45.21.g.a.28.5 18
5.2 odd 4 inner 5.21.c.a.2.5 18
5.3 odd 4 25.21.c.b.7.5 18
5.4 even 2 25.21.c.b.18.5 18
15.2 even 4 45.21.g.a.37.5 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.21.c.a.2.5 18 5.2 odd 4 inner
5.21.c.a.3.5 yes 18 1.1 even 1 trivial
25.21.c.b.7.5 18 5.3 odd 4
25.21.c.b.18.5 18 5.4 even 2
45.21.g.a.28.5 18 3.2 odd 2
45.21.g.a.37.5 18 15.2 even 4