Properties

Label 5.21.c.a.2.1
Level $5$
Weight $21$
Character 5.2
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 2.1
Root \(1286.49i\) of defining polynomial
Character \(\chi\) \(=\) 5.2
Dual form 5.21.c.a.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1286.49 - 1286.49i) q^{2} +(59231.4 - 59231.4i) q^{3} +2.26156e6i q^{4} +(2.84523e6 - 9.34195e6i) q^{5} -1.52402e8 q^{6} +(-2.38026e8 - 2.38026e8i) q^{7} +(1.56049e9 - 1.56049e9i) q^{8} -3.52992e9i q^{9} +O(q^{10})\) \(q+(-1286.49 - 1286.49i) q^{2} +(59231.4 - 59231.4i) q^{3} +2.26156e6i q^{4} +(2.84523e6 - 9.34195e6i) q^{5} -1.52402e8 q^{6} +(-2.38026e8 - 2.38026e8i) q^{7} +(1.56049e9 - 1.56049e9i) q^{8} -3.52992e9i q^{9} +(-1.56787e10 + 8.35799e9i) q^{10} -2.64802e10 q^{11} +(1.33955e11 + 1.33955e11i) q^{12} +(1.86588e10 - 1.86588e10i) q^{13} +6.12438e11i q^{14} +(-3.84810e11 - 7.21863e11i) q^{15} -1.64372e12 q^{16} +(2.00052e12 + 2.00052e12i) q^{17} +(-4.54122e12 + 4.54122e12i) q^{18} -5.99288e12i q^{19} +(2.11274e13 + 6.43466e12i) q^{20} -2.81972e13 q^{21} +(3.40667e13 + 3.40667e13i) q^{22} +(-4.08127e12 + 4.08127e12i) q^{23} -1.84860e14i q^{24} +(-7.91767e13 - 5.31601e13i) q^{25} -4.80088e13 q^{26} +(-2.55507e12 - 2.55507e12i) q^{27} +(5.38310e14 - 5.38310e14i) q^{28} +4.65510e14i q^{29} +(-4.33618e14 + 1.42373e15i) q^{30} -1.10651e14 q^{31} +(4.78335e14 + 4.78335e14i) q^{32} +(-1.56846e15 + 1.56846e15i) q^{33} -5.14731e15i q^{34} +(-2.90087e15 + 1.54639e15i) q^{35} +7.98312e15 q^{36} +(1.51125e14 + 1.51125e14i) q^{37} +(-7.70980e15 + 7.70980e15i) q^{38} -2.21037e15i q^{39} +(-1.01381e16 - 1.90180e16i) q^{40} +6.70503e15 q^{41} +(3.62755e16 + 3.62755e16i) q^{42} +(8.19546e15 - 8.19546e15i) q^{43} -5.98866e16i q^{44} +(-3.29764e16 - 1.00434e16i) q^{45} +1.05011e16 q^{46} +(-5.57252e16 - 5.57252e16i) q^{47} +(-9.73595e16 + 9.73595e16i) q^{48} +3.35205e16i q^{49} +(3.34703e16 + 1.70250e17i) q^{50} +2.36987e17 q^{51} +(4.21979e16 + 4.21979e16i) q^{52} +(8.91509e16 - 8.91509e16i) q^{53} +6.57415e15i q^{54} +(-7.53424e16 + 2.47377e17i) q^{55} -7.42876e17 q^{56} +(-3.54966e17 - 3.54966e17i) q^{57} +(5.98876e17 - 5.98876e17i) q^{58} +4.26601e16i q^{59} +(1.63254e18 - 8.70269e17i) q^{60} -1.01319e18 q^{61} +(1.42352e17 + 1.42352e17i) q^{62} +(-8.40213e17 + 8.40213e17i) q^{63} +4.92812e17i q^{64} +(-1.21221e17 - 2.27398e17i) q^{65} +4.03563e18 q^{66} +(-1.19643e18 - 1.19643e18i) q^{67} +(-4.52429e18 + 4.52429e18i) q^{68} +4.83479e17i q^{69} +(5.72137e18 + 1.74253e18i) q^{70} -4.52528e18 q^{71} +(-5.50842e18 - 5.50842e18i) q^{72} +(3.34929e18 - 3.34929e18i) q^{73} -3.88842e17i q^{74} +(-7.83849e18 + 1.54100e18i) q^{75} +1.35532e19 q^{76} +(6.30299e18 + 6.30299e18i) q^{77} +(-2.84363e18 + 2.84363e18i) q^{78} -9.80914e18i q^{79} +(-4.67675e18 + 1.53555e19i) q^{80} +1.20054e19 q^{81} +(-8.62598e18 - 8.62598e18i) q^{82} +(-1.34022e19 + 1.34022e19i) q^{83} -6.37696e19i q^{84} +(2.43807e19 - 1.29968e19i) q^{85} -2.10868e19 q^{86} +(2.75728e19 + 2.75728e19i) q^{87} +(-4.13222e19 + 4.13222e19i) q^{88} -4.73439e19i q^{89} +(2.95031e19 + 5.53447e19i) q^{90} -8.88255e18 q^{91} +(-9.23003e18 - 9.23003e18i) q^{92} +(-6.55400e18 + 6.55400e18i) q^{93} +1.43380e20i q^{94} +(-5.59852e19 - 1.70511e19i) q^{95} +5.66648e19 q^{96} +(-1.75542e19 - 1.75542e19i) q^{97} +(4.31240e19 - 4.31240e19i) q^{98} +9.34732e19i 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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1286.49 1286.49i −1.25634 1.25634i −0.952827 0.303515i \(-0.901840\pi\)
−0.303515 0.952827i \(-0.598160\pi\)
\(3\) 59231.4 59231.4i 1.00309 1.00309i 0.00309291 0.999995i \(-0.499015\pi\)
0.999995 0.00309291i \(-0.000984506\pi\)
\(4\) 2.26156e6i 2.15679i
\(5\) 2.84523e6 9.34195e6i 0.291352 0.956616i
\(6\) −1.52402e8 −2.52044
\(7\) −2.38026e8 2.38026e8i −0.842644 0.842644i 0.146558 0.989202i \(-0.453180\pi\)
−0.989202 + 0.146558i \(0.953180\pi\)
\(8\) 1.56049e9 1.56049e9i 1.45332 1.45332i
\(9\) 3.52992e9i 1.01237i
\(10\) −1.56787e10 + 8.35799e9i −1.56787 + 0.835799i
\(11\) −2.64802e10 −1.02093 −0.510464 0.859899i \(-0.670526\pi\)
−0.510464 + 0.859899i \(0.670526\pi\)
\(12\) 1.33955e11 + 1.33955e11i 2.16345 + 2.16345i
\(13\) 1.86588e10 1.86588e10i 0.135347 0.135347i −0.636187 0.771535i \(-0.719489\pi\)
0.771535 + 0.636187i \(0.219489\pi\)
\(14\) 6.12438e11i 2.11730i
\(15\) −3.84810e11 7.21863e11i −0.667319 1.25182i
\(16\) −1.64372e12 −1.49495
\(17\) 2.00052e12 + 2.00052e12i 0.992324 + 0.992324i 0.999971 0.00764641i \(-0.00243395\pi\)
−0.00764641 + 0.999971i \(0.502434\pi\)
\(18\) −4.54122e12 + 4.54122e12i −1.27188 + 1.27188i
\(19\) 5.99288e12i 0.977461i −0.872435 0.488731i \(-0.837460\pi\)
0.872435 0.488731i \(-0.162540\pi\)
\(20\) 2.11274e13 + 6.43466e12i 2.06322 + 0.628385i
\(21\) −2.81972e13 −1.69049
\(22\) 3.40667e13 + 3.40667e13i 1.28263 + 1.28263i
\(23\) −4.08127e12 + 4.08127e12i −0.0985184 + 0.0985184i −0.754648 0.656130i \(-0.772192\pi\)
0.656130 + 0.754648i \(0.272192\pi\)
\(24\) 1.84860e14i 2.91562i
\(25\) −7.91767e13 5.31601e13i −0.830228 0.557424i
\(26\) −4.80088e13 −0.340085
\(27\) −2.55507e12 2.55507e12i −0.0124098 0.0124098i
\(28\) 5.38310e14 5.38310e14i 1.81741 1.81741i
\(29\) 4.65510e14i 1.10649i 0.833017 + 0.553247i \(0.186611\pi\)
−0.833017 + 0.553247i \(0.813389\pi\)
\(30\) −4.33618e14 + 1.42373e15i −0.734336 + 2.41110i
\(31\) −1.10651e14 −0.135001 −0.0675007 0.997719i \(-0.521502\pi\)
−0.0675007 + 0.997719i \(0.521502\pi\)
\(32\) 4.78335e14 + 4.78335e14i 0.424847 + 0.424847i
\(33\) −1.56846e15 + 1.56846e15i −1.02408 + 1.02408i
\(34\) 5.14731e15i 2.49340i
\(35\) −2.90087e15 + 1.54639e15i −1.05159 + 0.560581i
\(36\) 7.98312e15 2.18347
\(37\) 1.51125e14 + 1.51125e14i 0.0314281 + 0.0314281i 0.722646 0.691218i \(-0.242926\pi\)
−0.691218 + 0.722646i \(0.742926\pi\)
\(38\) −7.70980e15 + 7.70980e15i −1.22803 + 1.22803i
\(39\) 2.21037e15i 0.271531i
\(40\) −1.01381e16 1.90180e16i −0.966844 1.81370i
\(41\) 6.70503e15 0.499530 0.249765 0.968306i \(-0.419647\pi\)
0.249765 + 0.968306i \(0.419647\pi\)
\(42\) 3.62755e16 + 3.62755e16i 2.12384 + 2.12384i
\(43\) 8.19546e15 8.19546e15i 0.379218 0.379218i −0.491602 0.870820i \(-0.663589\pi\)
0.870820 + 0.491602i \(0.163589\pi\)
\(44\) 5.98866e16i 2.20193i
\(45\) −3.29764e16 1.00434e16i −0.968451 0.294956i
\(46\) 1.05011e16 0.247545
\(47\) −5.57252e16 5.57252e16i −1.05943 1.05943i −0.998119 0.0613137i \(-0.980471\pi\)
−0.0613137 0.998119i \(-0.519529\pi\)
\(48\) −9.73595e16 + 9.73595e16i −1.49957 + 1.49957i
\(49\) 3.35205e16i 0.420098i
\(50\) 3.34703e16 + 1.70250e17i 0.342736 + 1.74336i
\(51\) 2.36987e17 1.99078
\(52\) 4.21979e16 + 4.21979e16i 0.291916 + 0.291916i
\(53\) 8.91509e16 8.91509e16i 0.509761 0.509761i −0.404692 0.914453i \(-0.632621\pi\)
0.914453 + 0.404692i \(0.132621\pi\)
\(54\) 6.57415e15i 0.0311819i
\(55\) −7.53424e16 + 2.47377e17i −0.297449 + 0.976636i
\(56\) −7.42876e17 −2.44927
\(57\) −3.54966e17 3.54966e17i −0.980480 0.980480i
\(58\) 5.98876e17 5.98876e17i 1.39013 1.39013i
\(59\) 4.26601e16i 0.0834645i 0.999129 + 0.0417323i \(0.0132876\pi\)
−0.999129 + 0.0417323i \(0.986712\pi\)
\(60\) 1.63254e18 8.70269e17i 2.69992 1.43927i
\(61\) −1.01319e18 −1.42034 −0.710168 0.704032i \(-0.751381\pi\)
−0.710168 + 0.704032i \(0.751381\pi\)
\(62\) 1.42352e17 + 1.42352e17i 0.169608 + 0.169608i
\(63\) −8.40213e17 + 8.40213e17i −0.853069 + 0.853069i
\(64\) 4.92812e17i 0.427446i
\(65\) −1.21221e17 2.27398e17i −0.0900417 0.168909i
\(66\) 4.03563e18 2.57319
\(67\) −1.19643e18 1.19643e18i −0.656355 0.656355i 0.298160 0.954516i \(-0.403627\pi\)
−0.954516 + 0.298160i \(0.903627\pi\)
\(68\) −4.52429e18 + 4.52429e18i −2.14023 + 2.14023i
\(69\) 4.83479e17i 0.197645i
\(70\) 5.72137e18 + 1.74253e18i 2.02544 + 0.616879i
\(71\) −4.52528e18 −1.39015 −0.695075 0.718937i \(-0.744629\pi\)
−0.695075 + 0.718937i \(0.744629\pi\)
\(72\) −5.50842e18 5.50842e18i −1.47130 1.47130i
\(73\) 3.34929e18 3.34929e18i 0.779335 0.779335i −0.200383 0.979718i \(-0.564219\pi\)
0.979718 + 0.200383i \(0.0642186\pi\)
\(74\) 3.88842e17i 0.0789689i
\(75\) −7.83849e18 + 1.54100e18i −1.39194 + 0.273647i
\(76\) 1.35532e19 2.10818
\(77\) 6.30299e18 + 6.30299e18i 0.860279 + 0.860279i
\(78\) −2.84363e18 + 2.84363e18i −0.341135 + 0.341135i
\(79\) 9.80914e18i 1.03600i −0.855381 0.518000i \(-0.826677\pi\)
0.855381 0.518000i \(-0.173323\pi\)
\(80\) −4.67675e18 + 1.53555e19i −0.435557 + 1.43009i
\(81\) 1.20054e19 0.987475
\(82\) −8.62598e18 8.62598e18i −0.627581 0.627581i
\(83\) −1.34022e19 + 1.34022e19i −0.863763 + 0.863763i −0.991773 0.128010i \(-0.959141\pi\)
0.128010 + 0.991773i \(0.459141\pi\)
\(84\) 6.37696e19i 3.64604i
\(85\) 2.43807e19 1.29968e19i 1.23839 0.660158i
\(86\) −2.10868e19 −0.952854
\(87\) 2.75728e19 + 2.75728e19i 1.10991 + 1.10991i
\(88\) −4.13222e19 + 4.13222e19i −1.48374 + 1.48374i
\(89\) 4.73439e19i 1.51832i −0.650903 0.759161i \(-0.725609\pi\)
0.650903 0.759161i \(-0.274391\pi\)
\(90\) 2.95031e19 + 5.53447e19i 0.846139 + 1.58727i
\(91\) −8.88255e18 −0.228099
\(92\) −9.23003e18 9.23003e18i −0.212483 0.212483i
\(93\) −6.55400e18 + 6.55400e18i −0.135418 + 0.135418i
\(94\) 1.43380e20i 2.66202i
\(95\) −5.59852e19 1.70511e19i −0.935055 0.284785i
\(96\) 5.66648e19 0.852317
\(97\) −1.75542e19 1.75542e19i −0.238047 0.238047i 0.577994 0.816041i \(-0.303836\pi\)
−0.816041 + 0.577994i \(0.803836\pi\)
\(98\) 4.31240e19 4.31240e19i 0.527786 0.527786i
\(99\) 9.34732e19i 1.03356i
\(100\) 1.20225e20 1.79063e20i 1.20225 1.79063i
\(101\) 1.27364e20 1.15301 0.576506 0.817093i \(-0.304416\pi\)
0.576506 + 0.817093i \(0.304416\pi\)
\(102\) −3.04882e20 3.04882e20i −2.50110 2.50110i
\(103\) 3.91228e19 3.91228e19i 0.291110 0.291110i −0.546409 0.837519i \(-0.684005\pi\)
0.837519 + 0.546409i \(0.184005\pi\)
\(104\) 5.82338e19i 0.393407i
\(105\) −8.02276e19 + 2.63417e20i −0.492528 + 1.61715i
\(106\) −2.29384e20 −1.28087
\(107\) 9.32958e19 + 9.32958e19i 0.474269 + 0.474269i 0.903293 0.429024i \(-0.141143\pi\)
−0.429024 + 0.903293i \(0.641143\pi\)
\(108\) 5.77843e18 5.77843e18i 0.0267653 0.0267653i
\(109\) 8.91537e19i 0.376595i −0.982112 0.188297i \(-0.939703\pi\)
0.982112 0.188297i \(-0.0602969\pi\)
\(110\) 4.15177e20 2.21322e20i 1.60069 0.853291i
\(111\) 1.79026e19 0.0630503
\(112\) 3.91247e20 + 3.91247e20i 1.25971 + 1.25971i
\(113\) 1.21796e20 1.21796e20i 0.358796 0.358796i −0.504573 0.863369i \(-0.668350\pi\)
0.863369 + 0.504573i \(0.168350\pi\)
\(114\) 9.13324e20i 2.46364i
\(115\) 2.65149e19 + 4.97392e19i 0.0655407 + 0.122948i
\(116\) −1.05278e21 −2.38647
\(117\) −6.58640e19 6.58640e19i −0.137022 0.137022i
\(118\) 5.48820e19 5.48820e19i 0.104860 0.104860i
\(119\) 9.52352e20i 1.67235i
\(120\) −1.72696e21 5.25970e20i −2.78913 0.849472i
\(121\) 2.84529e19 0.0422935
\(122\) 1.30346e21 + 1.30346e21i 1.78443 + 1.78443i
\(123\) 3.97148e20 3.97148e20i 0.501073 0.501073i
\(124\) 2.50243e20i 0.291169i
\(125\) −7.21895e20 + 5.88413e20i −0.775129 + 0.631803i
\(126\) 2.16186e21 2.14349
\(127\) 7.06445e20 + 7.06445e20i 0.647204 + 0.647204i 0.952316 0.305112i \(-0.0986940\pi\)
−0.305112 + 0.952316i \(0.598694\pi\)
\(128\) 1.13557e21 1.13557e21i 0.961865 0.961865i
\(129\) 9.70856e20i 0.760778i
\(130\) −1.36596e20 + 4.48496e20i −0.0990844 + 0.325331i
\(131\) −1.37131e21 −0.921343 −0.460672 0.887571i \(-0.652391\pi\)
−0.460672 + 0.887571i \(0.652391\pi\)
\(132\) −3.54716e21 3.54716e21i −2.20873 2.20873i
\(133\) −1.42646e21 + 1.42646e21i −0.823652 + 0.823652i
\(134\) 3.07840e21i 1.64921i
\(135\) −3.11391e19 + 1.65995e19i −0.0154870 + 0.00825579i
\(136\) 6.24360e21 2.88434
\(137\) 1.04913e20 + 1.04913e20i 0.0450427 + 0.0450427i 0.729269 0.684227i \(-0.239860\pi\)
−0.684227 + 0.729269i \(0.739860\pi\)
\(138\) 6.21992e20 6.21992e20i 0.248310 0.248310i
\(139\) 1.71087e21i 0.635434i −0.948186 0.317717i \(-0.897084\pi\)
0.948186 0.317717i \(-0.102916\pi\)
\(140\) −3.49725e21 6.56048e21i −1.20905 2.26806i
\(141\) −6.60136e21 −2.12541
\(142\) 5.82174e21 + 5.82174e21i 1.74650 + 1.74650i
\(143\) −4.94089e20 + 4.94089e20i −0.138180 + 0.138180i
\(144\) 5.80219e21i 1.51345i
\(145\) 4.34877e21 + 1.32448e21i 1.05849 + 0.322379i
\(146\) −8.61768e21 −1.95822
\(147\) 1.98547e21 + 1.98547e21i 0.421395 + 0.421395i
\(148\) −3.41777e20 + 3.41777e20i −0.0677838 + 0.0677838i
\(149\) 6.18077e21i 1.14599i 0.819560 + 0.572994i \(0.194218\pi\)
−0.819560 + 0.572994i \(0.805782\pi\)
\(150\) 1.20667e22 + 8.10168e21i 2.09254 + 1.40495i
\(151\) −1.28013e21 −0.207724 −0.103862 0.994592i \(-0.533120\pi\)
−0.103862 + 0.994592i \(0.533120\pi\)
\(152\) −9.35185e21 9.35185e21i −1.42057 1.42057i
\(153\) 7.06168e21 7.06168e21i 1.00460 1.00460i
\(154\) 1.62175e22i 2.16161i
\(155\) −3.14828e20 + 1.03370e21i −0.0393329 + 0.129144i
\(156\) 4.99888e21 0.585634
\(157\) −8.25482e21 8.25482e21i −0.907216 0.907216i 0.0888303 0.996047i \(-0.471687\pi\)
−0.996047 + 0.0888303i \(0.971687\pi\)
\(158\) −1.26194e22 + 1.26194e22i −1.30157 + 1.30157i
\(159\) 1.05611e22i 1.02267i
\(160\) 5.82955e21 3.10761e21i 0.530195 0.282635i
\(161\) 1.94290e21 0.166032
\(162\) −1.54449e22 1.54449e22i −1.24061 1.24061i
\(163\) 1.65197e22 1.65197e22i 1.24774 1.24774i 0.291031 0.956714i \(-0.406002\pi\)
0.956714 0.291031i \(-0.0939984\pi\)
\(164\) 1.51638e22i 1.07738i
\(165\) 1.01898e22 + 1.91151e22i 0.681284 + 1.27802i
\(166\) 3.44837e22 2.17036
\(167\) 1.72661e22 + 1.72661e22i 1.02336 + 1.02336i 0.999720 + 0.0236440i \(0.00752682\pi\)
0.0236440 + 0.999720i \(0.492473\pi\)
\(168\) −4.40016e22 + 4.40016e22i −2.45683 + 2.45683i
\(169\) 1.83087e22i 0.963362i
\(170\) −4.80860e22 1.46453e22i −2.38522 0.726456i
\(171\) −2.11544e22 −0.989554
\(172\) 1.85345e22 + 1.85345e22i 0.817893 + 0.817893i
\(173\) 2.99421e22 2.99421e22i 1.24687 1.24687i 0.289773 0.957095i \(-0.406420\pi\)
0.957095 0.289773i \(-0.0935799\pi\)
\(174\) 7.09444e22i 2.78885i
\(175\) 6.19265e21 + 3.14996e22i 0.229877 + 1.16930i
\(176\) 4.35260e22 1.52624
\(177\) 2.52682e21 + 2.52682e21i 0.0837223 + 0.0837223i
\(178\) −6.09076e22 + 6.09076e22i −1.90753 + 1.90753i
\(179\) 2.64440e22i 0.783063i −0.920165 0.391531i \(-0.871945\pi\)
0.920165 0.391531i \(-0.128055\pi\)
\(180\) 2.27138e22 7.45779e22i 0.636159 2.08874i
\(181\) −2.29061e22 −0.606968 −0.303484 0.952837i \(-0.598150\pi\)
−0.303484 + 0.952837i \(0.598150\pi\)
\(182\) 1.14273e22 + 1.14273e22i 0.286571 + 0.286571i
\(183\) −6.00124e22 + 6.00124e22i −1.42472 + 1.42472i
\(184\) 1.27376e22i 0.286358i
\(185\) 1.84178e21 9.81815e20i 0.0392213 0.0209080i
\(186\) 1.68634e22 0.340263
\(187\) −5.29742e22 5.29742e22i −1.01309 1.01309i
\(188\) 1.26026e23 1.26026e23i 2.28497 2.28497i
\(189\) 1.21634e21i 0.0209141i
\(190\) 5.00884e22 + 9.39608e22i 0.816961 + 1.53254i
\(191\) −1.43936e22 −0.222759 −0.111379 0.993778i \(-0.535527\pi\)
−0.111379 + 0.993778i \(0.535527\pi\)
\(192\) 2.91899e22 + 2.91899e22i 0.428766 + 0.428766i
\(193\) 1.94187e22 1.94187e22i 0.270798 0.270798i −0.558623 0.829422i \(-0.688670\pi\)
0.829422 + 0.558623i \(0.188670\pi\)
\(194\) 4.51667e22i 0.598137i
\(195\) −2.06492e22 6.28901e21i −0.259750 0.0791109i
\(196\) −7.58086e22 −0.906062
\(197\) 6.12299e22 + 6.12299e22i 0.695506 + 0.695506i 0.963438 0.267932i \(-0.0863401\pi\)
−0.267932 + 0.963438i \(0.586340\pi\)
\(198\) 1.20253e23 1.20253e23i 1.29850 1.29850i
\(199\) 6.79895e22i 0.698089i −0.937106 0.349045i \(-0.886506\pi\)
0.937106 0.349045i \(-0.113494\pi\)
\(200\) −2.06511e23 + 4.05989e22i −2.01671 + 0.396473i
\(201\) −1.41732e23 −1.31676
\(202\) −1.63853e23 1.63853e23i −1.44858 1.44858i
\(203\) 1.10803e23 1.10803e23i 0.932380 0.932380i
\(204\) 5.35960e23i 4.29369i
\(205\) 1.90774e22 6.26380e22i 0.145539 0.477859i
\(206\) −1.00662e23 −0.731468
\(207\) 1.44066e22 + 1.44066e22i 0.0997372 + 0.0997372i
\(208\) −3.06697e22 + 3.06697e22i −0.202338 + 0.202338i
\(209\) 1.58693e23i 0.997917i
\(210\) 4.42097e23 2.35672e23i 2.65048 1.41291i
\(211\) 2.19229e23 1.25336 0.626678 0.779278i \(-0.284414\pi\)
0.626678 + 0.779278i \(0.284414\pi\)
\(212\) 2.01620e23 + 2.01620e23i 1.09945 + 1.09945i
\(213\) −2.68038e23 + 2.68038e23i −1.39444 + 1.39444i
\(214\) 2.40049e23i 1.19169i
\(215\) −5.32436e22 9.98795e22i −0.252280 0.473251i
\(216\) −7.97433e21 −0.0360709
\(217\) 2.63378e22 + 2.63378e22i 0.113758 + 0.113758i
\(218\) −1.14696e23 + 1.14696e23i −0.473132 + 0.473132i
\(219\) 3.96766e23i 1.56348i
\(220\) −5.59458e23 1.70391e23i −2.10640 0.641535i
\(221\) 7.46545e22 0.268617
\(222\) −2.30316e22 2.30316e22i −0.0792128 0.0792128i
\(223\) 2.11342e23 2.11342e23i 0.694924 0.694924i −0.268387 0.963311i \(-0.586491\pi\)
0.963311 + 0.268387i \(0.0864906\pi\)
\(224\) 2.27712e23i 0.715989i
\(225\) −1.87651e23 + 2.79488e23i −0.564320 + 0.840499i
\(226\) −3.13379e23 −0.901542
\(227\) −7.69430e22 7.69430e22i −0.211793 0.211793i 0.593236 0.805029i \(-0.297850\pi\)
−0.805029 + 0.593236i \(0.797850\pi\)
\(228\) 8.02777e23 8.02777e23i 2.11469 2.11469i
\(229\) 9.53460e22i 0.240407i 0.992749 + 0.120204i \(0.0383548\pi\)
−0.992749 + 0.120204i \(0.961645\pi\)
\(230\) 2.98780e22 9.81004e22i 0.0721228 0.236806i
\(231\) 7.46669e23 1.72587
\(232\) 7.26425e23 + 7.26425e23i 1.60809 + 1.60809i
\(233\) −5.12339e23 + 5.12339e23i −1.08642 + 1.08642i −0.0905279 + 0.995894i \(0.528855\pi\)
−0.995894 + 0.0905279i \(0.971145\pi\)
\(234\) 1.69467e23i 0.344292i
\(235\) −6.79134e23 + 3.62031e23i −1.32214 + 0.704802i
\(236\) −9.64783e22 −0.180015
\(237\) −5.81008e23 5.81008e23i −1.03920 1.03920i
\(238\) −1.22519e24 + 1.22519e24i −2.10105 + 2.10105i
\(239\) 3.51188e23i 0.577512i 0.957403 + 0.288756i \(0.0932416\pi\)
−0.957403 + 0.288756i \(0.906758\pi\)
\(240\) 6.32518e23 + 1.18654e24i 0.997609 + 1.87141i
\(241\) 5.29836e23 0.801624 0.400812 0.916160i \(-0.368728\pi\)
0.400812 + 0.916160i \(0.368728\pi\)
\(242\) −3.66045e22 3.66045e22i −0.0531351 0.0531351i
\(243\) 7.20005e23 7.20005e23i 1.00293 1.00293i
\(244\) 2.29138e24i 3.06337i
\(245\) 3.13147e23 + 9.53737e22i 0.401872 + 0.122396i
\(246\) −1.02186e24 −1.25904
\(247\) −1.11820e23 1.11820e23i −0.132297 0.132297i
\(248\) −1.72670e23 + 1.72670e23i −0.196201 + 0.196201i
\(249\) 1.58766e24i 1.73286i
\(250\) 1.68570e24 + 1.71724e23i 1.76759 + 0.180066i
\(251\) 6.18463e23 0.623127 0.311564 0.950225i \(-0.399147\pi\)
0.311564 + 0.950225i \(0.399147\pi\)
\(252\) −1.90019e24 1.90019e24i −1.83989 1.83989i
\(253\) 1.08073e23 1.08073e23i 0.100580 0.100580i
\(254\) 1.81767e24i 1.62622i
\(255\) 6.74283e23 2.21392e24i 0.580017 1.90441i
\(256\) −2.40506e24 −1.98942
\(257\) 1.39844e24 + 1.39844e24i 1.11253 + 1.11253i 0.992807 + 0.119723i \(0.0382006\pi\)
0.119723 + 0.992807i \(0.461799\pi\)
\(258\) −1.24900e24 + 1.24900e24i −0.955797 + 0.955797i
\(259\) 7.19432e22i 0.0529654i
\(260\) 5.14274e23 2.74148e23i 0.364301 0.194201i
\(261\) 1.64321e24 1.12018
\(262\) 1.76418e24 + 1.76418e24i 1.15752 + 1.15752i
\(263\) −9.89553e23 + 9.89553e23i −0.625002 + 0.625002i −0.946806 0.321804i \(-0.895711\pi\)
0.321804 + 0.946806i \(0.395711\pi\)
\(264\) 4.89514e24i 2.97664i
\(265\) −5.79188e23 1.08650e24i −0.339126 0.636166i
\(266\) 3.67027e24 2.06958
\(267\) −2.80424e24 2.80424e24i −1.52301 1.52301i
\(268\) 2.70579e24 2.70579e24i 1.41562 1.41562i
\(269\) 6.03707e23i 0.304301i 0.988357 + 0.152150i \(0.0486198\pi\)
−0.988357 + 0.152150i \(0.951380\pi\)
\(270\) 6.14154e22 + 1.87050e22i 0.0298291 + 0.00908489i
\(271\) −3.36780e24 −1.57635 −0.788177 0.615449i \(-0.788975\pi\)
−0.788177 + 0.615449i \(0.788975\pi\)
\(272\) −3.28829e24 3.28829e24i −1.48348 1.48348i
\(273\) −5.26125e23 + 5.26125e23i −0.228804 + 0.228804i
\(274\) 2.69940e23i 0.113178i
\(275\) 2.09662e24 + 1.40769e24i 0.847603 + 0.569089i
\(276\) −1.09341e24 −0.426279
\(277\) −1.99675e24 1.99675e24i −0.750803 0.750803i 0.223826 0.974629i \(-0.428145\pi\)
−0.974629 + 0.223826i \(0.928145\pi\)
\(278\) −2.20103e24 + 2.20103e24i −0.798322 + 0.798322i
\(279\) 3.90589e23i 0.136672i
\(280\) −2.11366e24 + 6.93991e24i −0.713599 + 2.34301i
\(281\) 2.53470e24 0.825778 0.412889 0.910781i \(-0.364520\pi\)
0.412889 + 0.910781i \(0.364520\pi\)
\(282\) 8.49261e24 + 8.49261e24i 2.67024 + 2.67024i
\(283\) 1.97158e24 1.97158e24i 0.598342 0.598342i −0.341529 0.939871i \(-0.610945\pi\)
0.939871 + 0.341529i \(0.110945\pi\)
\(284\) 1.02342e25i 2.99826i
\(285\) −4.32604e24 + 2.30612e24i −1.22361 + 0.652278i
\(286\) 1.27128e24 0.347202
\(287\) −1.59597e24 1.59597e24i −0.420926 0.420926i
\(288\) 1.68848e24 1.68848e24i 0.430103 0.430103i
\(289\) 3.93993e24i 0.969415i
\(290\) −3.89073e24 7.29861e24i −0.924806 1.73484i
\(291\) −2.07951e24 −0.477565
\(292\) 7.57461e24 + 7.57461e24i 1.68086 + 1.68086i
\(293\) −3.02579e24 + 3.02579e24i −0.648878 + 0.648878i −0.952722 0.303844i \(-0.901730\pi\)
0.303844 + 0.952722i \(0.401730\pi\)
\(294\) 5.10858e24i 1.05883i
\(295\) 3.98529e23 + 1.21378e23i 0.0798435 + 0.0243175i
\(296\) 4.71658e23 0.0913504
\(297\) 6.76587e22 + 6.76587e22i 0.0126695 + 0.0126695i
\(298\) 7.95152e24 7.95152e24i 1.43975 1.43975i
\(299\) 1.52303e23i 0.0266684i
\(300\) −3.48507e24 1.77272e25i −0.590199 3.00212i
\(301\) −3.90146e24 −0.639091
\(302\) 1.64689e24 + 1.64689e24i 0.260972 + 0.260972i
\(303\) 7.54396e24 7.54396e24i 1.15657 1.15657i
\(304\) 9.85059e24i 1.46126i
\(305\) −2.88275e24 + 9.46514e24i −0.413818 + 1.35872i
\(306\) −1.81696e25 −2.52424
\(307\) 4.93037e23 + 4.93037e23i 0.0662973 + 0.0662973i 0.739478 0.673181i \(-0.235072\pi\)
−0.673181 + 0.739478i \(0.735072\pi\)
\(308\) −1.42546e25 + 1.42546e25i −1.85544 + 1.85544i
\(309\) 4.63459e24i 0.584018i
\(310\) 1.73487e24 9.24820e23i 0.211665 0.112834i
\(311\) 1.51891e25 1.79444 0.897218 0.441588i \(-0.145585\pi\)
0.897218 + 0.441588i \(0.145585\pi\)
\(312\) −3.44927e24 3.44927e24i −0.394622 0.394622i
\(313\) 5.78929e24 5.78929e24i 0.641479 0.641479i −0.309440 0.950919i \(-0.600142\pi\)
0.950919 + 0.309440i \(0.100142\pi\)
\(314\) 2.12395e25i 2.27955i
\(315\) 5.45863e24 + 1.02398e25i 0.567516 + 1.06460i
\(316\) 2.21839e25 2.23443
\(317\) −6.71778e24 6.71778e24i −0.655591 0.655591i 0.298743 0.954334i \(-0.403433\pi\)
−0.954334 + 0.298743i \(0.903433\pi\)
\(318\) −1.35867e25 + 1.35867e25i −1.28482 + 1.28482i
\(319\) 1.23268e25i 1.12965i
\(320\) 4.60382e24 + 1.40216e24i 0.408902 + 0.124537i
\(321\) 1.10521e25 0.951466
\(322\) −2.49953e24 2.49953e24i −0.208593 0.208593i
\(323\) 1.19889e25 1.19889e25i 0.969959 0.969959i
\(324\) 2.71509e25i 2.12978i
\(325\) −2.46924e24 + 4.85439e23i −0.187815 + 0.0369234i
\(326\) −4.25050e25 −3.13519
\(327\) −5.28069e24 5.28069e24i −0.377758 0.377758i
\(328\) 1.04631e25 1.04631e25i 0.725979 0.725979i
\(329\) 2.65281e25i 1.78545i
\(330\) 1.14823e25 3.77007e25i 0.749704 2.46155i
\(331\) −2.32303e25 −1.47155 −0.735776 0.677225i \(-0.763182\pi\)
−0.735776 + 0.677225i \(0.763182\pi\)
\(332\) −3.03098e25 3.03098e25i −1.86295 1.86295i
\(333\) 5.33458e23 5.33458e23i 0.0318169 0.0318169i
\(334\) 4.44255e25i 2.57139i
\(335\) −1.45811e25 + 7.77287e24i −0.819110 + 0.436650i
\(336\) 4.63482e25 2.52720
\(337\) 1.80258e25 + 1.80258e25i 0.954105 + 0.954105i 0.998992 0.0448872i \(-0.0142928\pi\)
−0.0448872 + 0.998992i \(0.514293\pi\)
\(338\) 2.35540e25 2.35540e25i 1.21031 1.21031i
\(339\) 1.44283e25i 0.719809i
\(340\) 2.93931e25 + 5.51384e25i 1.42382 + 2.67094i
\(341\) 2.93006e24 0.137827
\(342\) 2.72150e25 + 2.72150e25i 1.24322 + 1.24322i
\(343\) −1.10139e25 + 1.10139e25i −0.488651 + 0.488651i
\(344\) 2.55779e25i 1.10225i
\(345\) 4.51663e24 + 1.37561e24i 0.189071 + 0.0575843i
\(346\) −7.70406e25 −3.13299
\(347\) 3.26396e25 + 3.26396e25i 1.28958 + 1.28958i 0.935039 + 0.354544i \(0.115364\pi\)
0.354544 + 0.935039i \(0.384636\pi\)
\(348\) −6.23574e25 + 6.23574e25i −2.39384 + 2.39384i
\(349\) 2.58898e25i 0.965772i −0.875683 0.482886i \(-0.839589\pi\)
0.875683 0.482886i \(-0.160411\pi\)
\(350\) 3.25572e25 4.84909e25i 1.18023 1.75784i
\(351\) −9.53488e22 −0.00335926
\(352\) −1.26664e25 1.26664e25i −0.433738 0.433738i
\(353\) −1.27154e25 + 1.27154e25i −0.423235 + 0.423235i −0.886316 0.463081i \(-0.846744\pi\)
0.463081 + 0.886316i \(0.346744\pi\)
\(354\) 6.50147e24i 0.210368i
\(355\) −1.28755e25 + 4.22749e25i −0.405023 + 1.32984i
\(356\) 1.07071e26 3.27470
\(357\) −5.64091e25 5.64091e25i −1.67752 1.67752i
\(358\) −3.40200e25 + 3.40200e25i −0.983794 + 0.983794i
\(359\) 1.64035e25i 0.461310i −0.973036 0.230655i \(-0.925913\pi\)
0.973036 0.230655i \(-0.0740868\pi\)
\(360\) −6.71321e25 + 3.57867e25i −1.83614 + 0.978805i
\(361\) 1.67537e24 0.0445696
\(362\) 2.94686e25 + 2.94686e25i 0.762559 + 0.762559i
\(363\) 1.68531e24 1.68531e24i 0.0424241 0.0424241i
\(364\) 2.00884e25i 0.491962i
\(365\) −2.17594e25 4.08184e25i −0.518463 0.972585i
\(366\) 1.54411e26 3.57988
\(367\) −2.08553e25 2.08553e25i −0.470495 0.470495i 0.431580 0.902075i \(-0.357956\pi\)
−0.902075 + 0.431580i \(0.857956\pi\)
\(368\) 6.70845e24 6.70845e24i 0.147280 0.147280i
\(369\) 2.36682e25i 0.505710i
\(370\) −3.63254e24 1.10635e24i −0.0755429 0.0230077i
\(371\) −4.24405e25 −0.859095
\(372\) −1.48223e25 1.48223e25i −0.292069 0.292069i
\(373\) 5.98463e25 5.98463e25i 1.14802 1.14802i 0.161077 0.986942i \(-0.448503\pi\)
0.986942 0.161077i \(-0.0514967\pi\)
\(374\) 1.36302e26i 2.54558i
\(375\) −7.90634e24 + 7.76113e25i −0.143768 + 1.41128i
\(376\) −1.73918e26 −3.07939
\(377\) 8.68584e24 + 8.68584e24i 0.149761 + 0.149761i
\(378\) 1.56482e24 1.56482e24i 0.0262752 0.0262752i
\(379\) 8.22219e25i 1.34461i 0.740276 + 0.672303i \(0.234695\pi\)
−0.740276 + 0.672303i \(0.765305\pi\)
\(380\) 3.85621e25 1.26614e26i 0.614221 2.01672i
\(381\) 8.36874e25 1.29841
\(382\) 1.85172e25 + 1.85172e25i 0.279861 + 0.279861i
\(383\) 5.06387e25 5.06387e25i 0.745581 0.745581i −0.228065 0.973646i \(-0.573240\pi\)
0.973646 + 0.228065i \(0.0732399\pi\)
\(384\) 1.34523e26i 1.92967i
\(385\) 7.68157e25 4.09487e25i 1.07360 0.572313i
\(386\) −4.99640e25 −0.680431
\(387\) −2.89293e25 2.89293e25i −0.383909 0.383909i
\(388\) 3.96998e25 3.96998e25i 0.513418 0.513418i
\(389\) 3.29273e25i 0.415011i 0.978234 + 0.207506i \(0.0665345\pi\)
−0.978234 + 0.207506i \(0.933465\pi\)
\(390\) 1.84742e25 + 3.46558e25i 0.226945 + 0.425726i
\(391\) −1.63293e25 −0.195524
\(392\) 5.23086e25 + 5.23086e25i 0.610537 + 0.610537i
\(393\) −8.12243e25 + 8.12243e25i −0.924188 + 0.924188i
\(394\) 1.57544e26i 1.74759i
\(395\) −9.16365e25 2.79093e25i −0.991054 0.301841i
\(396\) −2.11395e26 −2.22917
\(397\) −9.96917e25 9.96917e25i −1.02507 1.02507i −0.999678 0.0253931i \(-0.991916\pi\)
−0.0253931 0.999678i \(-0.508084\pi\)
\(398\) −8.74681e25 + 8.74681e25i −0.877039 + 0.877039i
\(399\) 1.68982e26i 1.65239i
\(400\) 1.30144e26 + 8.73800e25i 1.24115 + 0.833321i
\(401\) 1.33713e26 1.24374 0.621868 0.783122i \(-0.286374\pi\)
0.621868 + 0.783122i \(0.286374\pi\)
\(402\) 1.82338e26 + 1.82338e26i 1.65431 + 1.65431i
\(403\) −2.06461e24 + 2.06461e24i −0.0182721 + 0.0182721i
\(404\) 2.88042e26i 2.48680i
\(405\) 3.41581e25 1.12154e26i 0.287703 0.944635i
\(406\) −2.85096e26 −2.34278
\(407\) −4.00182e24 4.00182e24i −0.0320858 0.0320858i
\(408\) 3.69817e26 3.69817e26i 2.89324 2.89324i
\(409\) 1.78296e26i 1.36115i 0.732676 + 0.680577i \(0.238271\pi\)
−0.732676 + 0.680577i \(0.761729\pi\)
\(410\) −1.05126e26 + 5.60406e25i −0.783201 + 0.417507i
\(411\) 1.24283e25 0.0903635
\(412\) 8.84784e25 + 8.84784e25i 0.627863 + 0.627863i
\(413\) 1.01542e25 1.01542e25i 0.0703309 0.0703309i
\(414\) 3.70679e25i 0.250608i
\(415\) 8.70702e25 + 1.63335e26i 0.574631 + 1.07795i
\(416\) 1.78503e25 0.115004
\(417\) −1.01337e26 1.01337e26i −0.637396 0.637396i
\(418\) 2.04157e26 2.04157e26i 1.25373 1.25373i
\(419\) 2.35922e26i 1.41458i −0.706924 0.707290i \(-0.749918\pi\)
0.706924 0.707290i \(-0.250082\pi\)
\(420\) −5.95733e26 1.81439e26i −3.48786 1.06228i
\(421\) 1.00758e26 0.576051 0.288025 0.957623i \(-0.407001\pi\)
0.288025 + 0.957623i \(0.407001\pi\)
\(422\) −2.82037e26 2.82037e26i −1.57464 1.57464i
\(423\) −1.96706e26 + 1.96706e26i −1.07254 + 1.07254i
\(424\) 2.78239e26i 1.48170i
\(425\) −5.20469e25 2.64742e26i −0.270711 1.37700i
\(426\) 6.89659e26 3.50379
\(427\) 2.41165e26 + 2.41165e26i 1.19684 + 1.19684i
\(428\) −2.10994e26 + 2.10994e26i −1.02290 + 1.02290i
\(429\) 5.85311e25i 0.277213i
\(430\) −5.99969e25 + 1.96992e26i −0.277616 + 0.911515i
\(431\) −5.63826e25 −0.254902 −0.127451 0.991845i \(-0.540679\pi\)
−0.127451 + 0.991845i \(0.540679\pi\)
\(432\) 4.19980e24 + 4.19980e24i 0.0185520 + 0.0185520i
\(433\) −3.60490e25 + 3.60490e25i −0.155602 + 0.155602i −0.780614 0.625013i \(-0.785094\pi\)
0.625013 + 0.780614i \(0.285094\pi\)
\(434\) 6.77669e25i 0.285838i
\(435\) 3.36035e26 1.79133e26i 1.38513 0.738384i
\(436\) 2.01626e26 0.812236
\(437\) 2.44586e25 + 2.44586e25i 0.0962979 + 0.0962979i
\(438\) −5.10437e26 + 5.10437e26i −1.96427 + 1.96427i
\(439\) 2.47680e26i 0.931636i −0.884881 0.465818i \(-0.845760\pi\)
0.884881 0.465818i \(-0.154240\pi\)
\(440\) 2.68459e26 + 5.03602e26i 0.987077 + 1.85166i
\(441\) 1.18325e26 0.425295
\(442\) −9.60426e25 9.60426e25i −0.337475 0.337475i
\(443\) 6.46778e25 6.46778e25i 0.222187 0.222187i −0.587232 0.809419i \(-0.699782\pi\)
0.809419 + 0.587232i \(0.199782\pi\)
\(444\) 4.04879e25i 0.135986i
\(445\) −4.42284e26 1.34704e26i −1.45245 0.442366i
\(446\) −5.43781e26 −1.74612
\(447\) 3.66095e26 + 3.66095e26i 1.14953 + 1.14953i
\(448\) 1.17302e26 1.17302e26i 0.360185 0.360185i
\(449\) 1.35248e26i 0.406131i −0.979165 0.203066i \(-0.934910\pi\)
0.979165 0.203066i \(-0.0650905\pi\)
\(450\) 6.00971e26 1.18148e26i 1.76493 0.346976i
\(451\) −1.77551e26 −0.509984
\(452\) 2.75448e26 + 2.75448e26i 0.773848 + 0.773848i
\(453\) −7.58241e25 + 7.58241e25i −0.208365 + 0.208365i
\(454\) 1.97973e26i 0.532168i
\(455\) −2.52729e25 + 8.29804e25i −0.0664571 + 0.218203i
\(456\) −1.10785e27 −2.84991
\(457\) 1.50945e26 + 1.50945e26i 0.379889 + 0.379889i 0.871062 0.491173i \(-0.163432\pi\)
−0.491173 + 0.871062i \(0.663432\pi\)
\(458\) 1.22662e26 1.22662e26i 0.302034 0.302034i
\(459\) 1.02229e25i 0.0246291i
\(460\) −1.12488e26 + 5.99649e25i −0.265172 + 0.141358i
\(461\) 1.32819e26 0.306374 0.153187 0.988197i \(-0.451046\pi\)
0.153187 + 0.988197i \(0.451046\pi\)
\(462\) −9.60585e26 9.60585e26i −2.16828 2.16828i
\(463\) 1.91477e26 1.91477e26i 0.422967 0.422967i −0.463257 0.886224i \(-0.653319\pi\)
0.886224 + 0.463257i \(0.153319\pi\)
\(464\) 7.65166e26i 1.65415i
\(465\) 4.25795e25 + 7.98749e25i 0.0900889 + 0.168998i
\(466\) 1.31824e27 2.72983
\(467\) −6.02296e26 6.02296e26i −1.22079 1.22079i −0.967352 0.253438i \(-0.918439\pi\)
−0.253438 0.967352i \(-0.581561\pi\)
\(468\) 1.48955e26 1.48955e26i 0.295527 0.295527i
\(469\) 5.69563e26i 1.10615i
\(470\) 1.33945e27 + 4.07950e26i 2.54653 + 0.775584i
\(471\) −9.77888e26 −1.82004
\(472\) 6.65708e25 + 6.65708e25i 0.121301 + 0.121301i
\(473\) −2.17018e26 + 2.17018e26i −0.387154 + 0.387154i
\(474\) 1.49493e27i 2.61118i
\(475\) −3.18582e26 + 4.74497e26i −0.544860 + 0.811516i
\(476\) 2.15380e27 3.60691
\(477\) −3.14696e26 3.14696e26i −0.516068 0.516068i
\(478\) 4.51802e26 4.51802e26i 0.725552 0.725552i
\(479\) 5.87413e26i 0.923822i −0.886926 0.461911i \(-0.847164\pi\)
0.886926 0.461911i \(-0.152836\pi\)
\(480\) 1.61225e26 5.29360e26i 0.248324 0.815340i
\(481\) 5.63960e24 0.00850742
\(482\) −6.81630e26 6.81630e26i −1.00711 1.00711i
\(483\) 1.15080e26 1.15080e26i 0.166545 0.166545i
\(484\) 6.43480e25i 0.0912181i
\(485\) −2.13936e26 + 1.14045e26i −0.297075 + 0.158364i
\(486\) −1.85256e27 −2.52006
\(487\) 1.69794e26 + 1.69794e26i 0.226273 + 0.226273i 0.811134 0.584861i \(-0.198851\pi\)
−0.584861 + 0.811134i \(0.698851\pi\)
\(488\) −1.58107e27 + 1.58107e27i −2.06421 + 2.06421i
\(489\) 1.95697e27i 2.50320i
\(490\) −2.80164e26 5.25560e26i −0.351117 0.658660i
\(491\) −7.03307e26 −0.863634 −0.431817 0.901961i \(-0.642127\pi\)
−0.431817 + 0.901961i \(0.642127\pi\)
\(492\) 8.98173e26 + 8.98173e26i 1.08071 + 1.08071i
\(493\) −9.31262e26 + 9.31262e26i −1.09800 + 1.09800i
\(494\) 2.87711e26i 0.332420i
\(495\) 8.73222e26 + 2.65953e26i 0.988718 + 0.301129i
\(496\) 1.81879e26 0.201820
\(497\) 1.07713e27 + 1.07713e27i 1.17140 + 1.17140i
\(498\) 2.04251e27 2.04251e27i 2.17707 2.17707i
\(499\) 1.55018e27i 1.61949i 0.586783 + 0.809744i \(0.300394\pi\)
−0.586783 + 0.809744i \(0.699606\pi\)
\(500\) −1.33073e27 1.63261e27i −1.36267 1.67179i
\(501\) 2.04539e27 2.05305
\(502\) −7.95650e26 7.95650e26i −0.782861 0.782861i
\(503\) 7.37100e26 7.37100e26i 0.710962 0.710962i −0.255774 0.966737i \(-0.582330\pi\)
0.966737 + 0.255774i \(0.0823303\pi\)
\(504\) 2.62229e27i 2.47957i
\(505\) 3.62381e26 1.18983e27i 0.335932 1.10299i
\(506\) −2.78071e26 −0.252726
\(507\) 1.08445e27 + 1.08445e27i 0.966337 + 0.966337i
\(508\) −1.59767e27 + 1.59767e27i −1.39588 + 1.39588i
\(509\) 4.37786e26i 0.375046i 0.982260 + 0.187523i \(0.0600459\pi\)
−0.982260 + 0.187523i \(0.939954\pi\)
\(510\) −3.71566e27 + 1.98074e27i −3.12129 + 1.66389i
\(511\) −1.59444e27 −1.31340
\(512\) 1.90336e27 + 1.90336e27i 1.53752 + 1.53752i
\(513\) −1.53122e25 + 1.53122e25i −0.0121301 + 0.0121301i
\(514\) 3.59816e27i 2.79544i
\(515\) −2.54170e26 4.76796e26i −0.193665 0.363296i
\(516\) 2.19565e27 1.64084
\(517\) 1.47562e27 + 1.47562e27i 1.08160 + 1.08160i
\(518\) −9.25545e25 + 9.25545e25i −0.0665427 + 0.0665427i
\(519\) 3.54702e27i 2.50144i
\(520\) −5.44017e26 1.65689e26i −0.376339 0.114620i
\(521\) −2.74417e27 −1.86223 −0.931117 0.364721i \(-0.881164\pi\)
−0.931117 + 0.364721i \(0.881164\pi\)
\(522\) −2.11398e27 2.11398e27i −1.40733 1.40733i
\(523\) 1.64898e27 1.64898e27i 1.07696 1.07696i 0.0801793 0.996780i \(-0.474451\pi\)
0.996780 0.0801793i \(-0.0255493\pi\)
\(524\) 3.10129e27i 1.98714i
\(525\) 2.23256e27 + 1.49897e27i 1.40349 + 0.942320i
\(526\) 2.54611e27 1.57043
\(527\) −2.21359e26 2.21359e26i −0.133965 0.133965i
\(528\) 2.57810e27 2.57810e27i 1.53095 1.53095i
\(529\) 1.68284e27i 0.980588i
\(530\) −6.52651e26 + 2.14290e27i −0.373184 + 1.22530i
\(531\) 1.50587e26 0.0844971
\(532\) −3.22602e27 3.22602e27i −1.77644 1.77644i
\(533\) 1.25108e26 1.25108e26i 0.0676101 0.0676101i
\(534\) 7.21528e27i 3.82684i
\(535\) 1.13701e27 6.06117e26i 0.591872 0.315514i
\(536\) −3.73404e27 −1.90779
\(537\) −1.56631e27 1.56631e27i −0.785481 0.785481i
\(538\) 7.76665e26 7.76665e26i 0.382306 0.382306i
\(539\) 8.87632e26i 0.428889i
\(540\) −3.75408e25 7.04228e25i −0.0178060 0.0334022i
\(541\) −2.06020e27 −0.959263 −0.479631 0.877470i \(-0.659230\pi\)
−0.479631 + 0.877470i \(0.659230\pi\)
\(542\) 4.33266e27 + 4.33266e27i 1.98044 + 1.98044i
\(543\) −1.35676e27 + 1.35676e27i −0.608842 + 0.608842i
\(544\) 1.91384e27i 0.843171i
\(545\) −8.32870e26 2.53663e26i −0.360257 0.109722i
\(546\) 1.35371e27 0.574911
\(547\) 4.14511e26 + 4.14511e26i 0.172847 + 0.172847i 0.788229 0.615382i \(-0.210998\pi\)
−0.615382 + 0.788229i \(0.710998\pi\)
\(548\) −2.37267e26 + 2.37267e26i −0.0971476 + 0.0971476i
\(549\) 3.57647e27i 1.43791i
\(550\) −8.86301e26 4.50827e27i −0.349909 1.77985i
\(551\) 2.78974e27 1.08155
\(552\) 7.54465e26 + 7.54465e26i 0.287242 + 0.287242i
\(553\) −2.33483e27 + 2.33483e27i −0.872979 + 0.872979i
\(554\) 5.13761e27i 1.88653i
\(555\) 5.09372e25 1.67246e26i 0.0183698 0.0603149i
\(556\) 3.86924e27 1.37050
\(557\) 6.05596e26 + 6.05596e26i 0.210684 + 0.210684i 0.804558 0.593874i \(-0.202402\pi\)
−0.593874 + 0.804558i \(0.702402\pi\)
\(558\) 5.02491e26 5.02491e26i 0.171706 0.171706i
\(559\) 3.05834e26i 0.102652i
\(560\) 4.76820e27 2.54182e27i 1.57208 0.838041i
\(561\) −6.27547e27 −2.03244
\(562\) −3.26087e27 3.26087e27i −1.03746 1.03746i
\(563\) 2.05402e27 2.05402e27i 0.641978 0.641978i −0.309063 0.951042i \(-0.600015\pi\)
0.951042 + 0.309063i \(0.100015\pi\)
\(564\) 1.49294e28i 4.58406i
\(565\) −7.91273e26 1.48435e27i −0.238694 0.447766i
\(566\) −5.07285e27 −1.50344
\(567\) −2.85760e27 2.85760e27i −0.832090 0.832090i
\(568\) −7.06166e27 + 7.06166e27i −2.02034 + 2.02034i
\(569\) 2.67189e27i 0.751097i 0.926803 + 0.375548i \(0.122546\pi\)
−0.926803 + 0.375548i \(0.877454\pi\)
\(570\) 8.53223e27 + 2.59862e27i 2.35675 + 0.717785i
\(571\) 2.12903e27 0.577857 0.288929 0.957351i \(-0.406701\pi\)
0.288929 + 0.957351i \(0.406701\pi\)
\(572\) −1.11741e27 1.11741e27i −0.298025 0.298025i
\(573\) −8.52551e26 + 8.52551e26i −0.223447 + 0.223447i
\(574\) 4.10641e27i 1.05765i
\(575\) 5.40102e26 1.06181e26i 0.136709 0.0268763i
\(576\) 1.73959e27 0.432734
\(577\) −1.47017e27 1.47017e27i −0.359427 0.359427i 0.504175 0.863602i \(-0.331797\pi\)
−0.863602 + 0.504175i \(0.831797\pi\)
\(578\) 5.06869e27 5.06869e27i 1.21792 1.21792i
\(579\) 2.30039e27i 0.543270i
\(580\) −2.99540e27 + 9.83499e27i −0.695303 + 2.28294i
\(581\) 6.38014e27 1.45569
\(582\) 2.67528e27 + 2.67528e27i 0.599984 + 0.599984i
\(583\) −2.36074e27 + 2.36074e27i −0.520430 + 0.520430i
\(584\) 1.04531e28i 2.26525i
\(585\) −8.02697e26 + 4.27900e26i −0.170999 + 0.0911557i
\(586\) 7.78532e27 1.63042
\(587\) 4.17034e26 + 4.17034e26i 0.0858600 + 0.0858600i 0.748732 0.662872i \(-0.230663\pi\)
−0.662872 + 0.748732i \(0.730663\pi\)
\(588\) −4.49025e27 + 4.49025e27i −0.908860 + 0.908860i
\(589\) 6.63118e26i 0.131959i
\(590\) −3.56553e26 6.68857e26i −0.0697596 0.130862i
\(591\) 7.25346e27 1.39531
\(592\) −2.48406e26 2.48406e26i −0.0469835 0.0469835i
\(593\) 5.98664e27 5.98664e27i 1.11336 1.11336i 0.120669 0.992693i \(-0.461496\pi\)
0.992693 0.120669i \(-0.0385040\pi\)
\(594\) 1.74085e26i 0.0318344i
\(595\) −8.89682e27 2.70966e27i −1.59980 0.487243i
\(596\) −1.39782e28 −2.47165
\(597\) −4.02711e27 4.02711e27i −0.700245 0.700245i
\(598\) 1.95937e26 1.95937e26i 0.0335046 0.0335046i
\(599\) 4.93475e27i 0.829846i 0.909857 + 0.414923i \(0.136191\pi\)
−0.909857 + 0.414923i \(0.863809\pi\)
\(600\) −9.82718e27 + 1.46366e28i −1.62524 + 2.42063i
\(601\) 8.84404e27 1.43849 0.719244 0.694758i \(-0.244488\pi\)
0.719244 + 0.694758i \(0.244488\pi\)
\(602\) 5.01921e27 + 5.01921e27i 0.802917 + 0.802917i
\(603\) −4.22330e27 + 4.22330e27i −0.664475 + 0.664475i
\(604\) 2.89510e27i 0.448016i
\(605\) 8.09552e25 2.65806e26i 0.0123223 0.0404586i
\(606\) −1.94105e28 −2.90610
\(607\) −2.47176e27 2.47176e27i −0.364015 0.364015i 0.501274 0.865289i \(-0.332865\pi\)
−0.865289 + 0.501274i \(0.832865\pi\)
\(608\) 2.86660e27 2.86660e27i 0.415271 0.415271i
\(609\) 1.31261e28i 1.87052i
\(610\) 1.58855e28 8.46821e27i 2.22691 1.18712i
\(611\) −2.07953e27 −0.286783
\(612\) 1.59704e28 + 1.59704e28i 2.16671 + 2.16671i
\(613\) −3.58716e27 + 3.58716e27i −0.478791 + 0.478791i −0.904745 0.425954i \(-0.859939\pi\)
0.425954 + 0.904745i \(0.359939\pi\)
\(614\) 1.26858e27i 0.166584i
\(615\) −2.58016e27 4.84011e27i −0.333346 0.625323i
\(616\) 1.96715e28 2.50053
\(617\) 8.29805e27 + 8.29805e27i 1.03783 + 1.03783i 0.999256 + 0.0385691i \(0.0122800\pi\)
0.0385691 + 0.999256i \(0.487720\pi\)
\(618\) −5.96237e27 + 5.96237e27i −0.733726 + 0.733726i
\(619\) 4.81099e27i 0.582543i 0.956640 + 0.291271i \(0.0940783\pi\)
−0.956640 + 0.291271i \(0.905922\pi\)
\(620\) −2.33776e27 7.12001e26i −0.278537 0.0848328i
\(621\) 2.08558e25 0.00244518
\(622\) −1.95407e28 1.95407e28i −2.25442 2.25442i
\(623\) −1.12691e28 + 1.12691e28i −1.27941 + 1.27941i
\(624\) 3.63322e27i 0.405925i
\(625\) 3.44296e27 + 8.41808e27i 0.378558 + 0.925578i
\(626\) −1.48958e28 −1.61183
\(627\) 9.39959e27 + 9.39959e27i 1.00100 + 1.00100i
\(628\) 1.86687e28 1.86687e28i 1.95667 1.95667i
\(629\) 6.04656e26i 0.0623738i
\(630\) 6.15099e27 2.01960e28i 0.624510 2.05050i
\(631\) 2.89091e26 0.0288895 0.0144448 0.999896i \(-0.495402\pi\)
0.0144448 + 0.999896i \(0.495402\pi\)
\(632\) −1.53071e28 1.53071e28i −1.50564 1.50564i
\(633\) 1.29853e28 1.29853e28i 1.25723 1.25723i
\(634\) 1.72848e28i 1.64729i
\(635\) 8.60958e27 4.58958e27i 0.807690 0.430562i
\(636\) 2.38844e28 2.20569
\(637\) 6.25452e26 + 6.25452e26i 0.0568591 + 0.0568591i
\(638\) −1.58584e28 + 1.58584e28i −1.41923 + 1.41923i
\(639\) 1.59739e28i 1.40735i
\(640\) −7.37748e27 1.38394e28i −0.639894 1.20038i
\(641\) −7.88928e27 −0.673686 −0.336843 0.941561i \(-0.609359\pi\)
−0.336843 + 0.941561i \(0.609359\pi\)
\(642\) −1.42184e28 1.42184e28i −1.19537 1.19537i
\(643\) 1.35996e27 1.35996e27i 0.112569 0.112569i −0.648579 0.761147i \(-0.724636\pi\)
0.761147 + 0.648579i \(0.224636\pi\)
\(644\) 4.39398e27i 0.358096i
\(645\) −9.06969e27 2.76231e27i −0.727772 0.221654i
\(646\) −3.08472e28 −2.43720
\(647\) −1.13173e28 1.13173e28i −0.880444 0.880444i 0.113136 0.993580i \(-0.463911\pi\)
−0.993580 + 0.113136i \(0.963911\pi\)
\(648\) 1.87343e28 1.87343e28i 1.43512 1.43512i
\(649\) 1.12965e27i 0.0852112i
\(650\) 3.80118e27 + 2.55215e27i 0.282348 + 0.189571i
\(651\) 3.12005e27 0.228219
\(652\) 3.73602e28 + 3.73602e28i 2.69112 + 2.69112i
\(653\) 6.02418e27 6.02418e27i 0.427333 0.427333i −0.460386 0.887719i \(-0.652289\pi\)
0.887719 + 0.460386i \(0.152289\pi\)
\(654\) 1.35872e28i 0.949186i
\(655\) −3.90168e27 + 1.28107e28i −0.268435 + 0.881372i
\(656\) −1.10212e28 −0.746773
\(657\) −1.18227e28 1.18227e28i −0.788976 0.788976i
\(658\) 3.41283e28 3.41283e28i 2.24313 2.24313i
\(659\) 2.19924e26i 0.0142370i −0.999975 0.00711851i \(-0.997734\pi\)
0.999975 0.00711851i \(-0.00226591\pi\)
\(660\) −4.32299e28 + 2.30449e28i −2.75642 + 1.46939i
\(661\) 6.20388e27 0.389627 0.194813 0.980840i \(-0.437590\pi\)
0.194813 + 0.980840i \(0.437590\pi\)
\(662\) 2.98857e28 + 2.98857e28i 1.84877 + 1.84877i
\(663\) 4.42189e27 4.42189e27i 0.269446 0.269446i
\(664\) 4.18280e28i 2.51065i
\(665\) 9.26732e27 + 1.73846e28i 0.547946 + 1.02789i
\(666\) −1.37258e27 −0.0799459
\(667\) −1.89987e27 1.89987e27i −0.109010 0.109010i
\(668\) −3.90483e28 + 3.90483e28i −2.20718 + 2.20718i
\(669\) 2.50362e28i 1.39414i
\(670\) 2.87583e28 + 8.75876e27i 1.57766 + 0.480501i
\(671\) 2.68294e28 1.45006
\(672\) −1.34877e28 1.34877e28i −0.718200 0.718200i
\(673\) −4.47258e26 + 4.47258e26i −0.0234643 + 0.0234643i −0.718742 0.695277i \(-0.755282\pi\)
0.695277 + 0.718742i \(0.255282\pi\)
\(674\) 4.63802e28i 2.39736i
\(675\) 6.64743e25 + 3.38129e26i 0.00338545 + 0.0172205i
\(676\) −4.14061e28 −2.07777
\(677\) −2.32780e28 2.32780e28i −1.15096 1.15096i −0.986361 0.164597i \(-0.947368\pi\)
−0.164597 0.986361i \(-0.552632\pi\)
\(678\) −1.85619e28 + 1.85619e28i −0.904326 + 0.904326i
\(679\) 8.35670e27i 0.401178i
\(680\) 1.77645e28 5.83274e28i 0.840356 2.75920i
\(681\) −9.11488e27 −0.424893
\(682\) −3.76951e27 3.76951e27i −0.173157 0.173157i
\(683\) 4.46628e27 4.46628e27i 0.202180 0.202180i −0.598753 0.800934i \(-0.704337\pi\)
0.800934 + 0.598753i \(0.204337\pi\)
\(684\) 4.78419e28i 2.13426i
\(685\) 1.27860e27 6.81591e26i 0.0562118 0.0299653i
\(686\) 2.83386e28 1.22783
\(687\) 5.64747e27 + 5.64747e27i 0.241150 + 0.241150i
\(688\) −1.34710e28 + 1.34710e28i −0.566912 + 0.566912i
\(689\) 3.32689e27i 0.137990i
\(690\) −4.04091e27 7.58033e27i −0.165192 0.309883i
\(691\) −8.29432e27 −0.334195 −0.167098 0.985940i \(-0.553440\pi\)
−0.167098 + 0.985940i \(0.553440\pi\)
\(692\) 6.77157e28 + 6.77157e28i 2.68923 + 2.68923i
\(693\) 2.22490e28 2.22490e28i 0.870922 0.870922i
\(694\) 8.39812e28i 3.24032i
\(695\) −1.59829e28 4.86784e27i −0.607866 0.185135i
\(696\) 8.60543e28 3.22612
\(697\) 1.34135e28 + 1.34135e28i 0.495696 + 0.495696i
\(698\) −3.33071e28 + 3.33071e28i −1.21334 + 1.21334i
\(699\) 6.06931e28i 2.17955i
\(700\) −7.12382e28 + 1.40050e28i −2.52193 + 0.495797i
\(701\) −4.44091e28 −1.54986 −0.774929 0.632049i \(-0.782214\pi\)
−0.774929 + 0.632049i \(0.782214\pi\)
\(702\) 1.22666e26 + 1.22666e26i 0.00422038 + 0.00422038i
\(703\) 9.05672e26 9.05672e26i 0.0307198 0.0307198i
\(704\) 1.30498e28i 0.436391i
\(705\) −1.87824e28 + 6.16696e28i −0.619241 + 2.03320i
\(706\) 3.27165e28 1.06346
\(707\) −3.03160e28 3.03160e28i −0.971579 0.971579i
\(708\) −5.71454e27 + 5.71454e27i −0.180571 + 0.180571i
\(709\) 8.23820e27i 0.256667i −0.991731 0.128333i \(-0.959037\pi\)
0.991731 0.128333i \(-0.0409628\pi\)
\(710\) 7.09506e28 3.78222e28i 2.17958 1.16189i
\(711\) −3.46255e28 −1.04882
\(712\) −7.38798e28 7.38798e28i −2.20661 2.20661i
\(713\) 4.51597e26 4.51597e26i 0.0133001 0.0133001i
\(714\) 1.45140e29i 4.21507i
\(715\) 3.20996e27 + 6.02155e27i 0.0919261 + 0.172444i
\(716\) 5.98046e28 1.68890
\(717\) 2.08014e28 + 2.08014e28i 0.579295 + 0.579295i
\(718\) −2.11030e28 + 2.11030e28i −0.579563 + 0.579563i
\(719\) 9.86614e27i 0.267214i −0.991034 0.133607i \(-0.957344\pi\)
0.991034 0.133607i \(-0.0426559\pi\)
\(720\) 5.42038e28 + 1.65086e28i 1.44779 + 0.440945i
\(721\) −1.86245e28 −0.490604
\(722\) −2.15535e27 2.15535e27i −0.0559946 0.0559946i
\(723\) 3.13829e28 3.13829e28i 0.804100 0.804100i
\(724\) 5.18035e28i 1.30910i
\(725\) 2.47465e28 3.68575e28i 0.616786 0.918642i
\(726\) −4.33627e27 −0.106598
\(727\) −2.04991e28 2.04991e28i −0.497040 0.497040i 0.413475 0.910515i \(-0.364315\pi\)
−0.910515 + 0.413475i \(0.864315\pi\)
\(728\) −1.38612e28 + 1.38612e28i −0.331502 + 0.331502i
\(729\) 4.34335e28i 1.02459i
\(730\) −2.45193e28 + 8.05060e28i −0.570531 + 1.87327i
\(731\) 3.27903e28 0.752614
\(732\) −1.35722e29 1.35722e29i −3.07283 3.07283i
\(733\) −3.34359e28 + 3.34359e28i −0.746748 + 0.746748i −0.973867 0.227119i \(-0.927069\pi\)
0.227119 + 0.973867i \(0.427069\pi\)
\(734\) 5.36603e28i 1.18220i
\(735\) 2.41973e28 1.28990e28i 0.525887 0.280339i
\(736\) −3.90443e27 −0.0837104
\(737\) 3.16817e28 + 3.16817e28i 0.670091 + 0.670091i
\(738\) −3.04490e28 + 3.04490e28i −0.635345 + 0.635345i
\(739\) 1.03645e28i 0.213356i −0.994294 0.106678i \(-0.965979\pi\)
0.994294 0.106678i \(-0.0340214\pi\)
\(740\) 2.22043e27 + 4.16530e27i 0.0450941 + 0.0845920i
\(741\) −1.32465e28 −0.265411
\(742\) 5.45994e28 + 5.45994e28i 1.07932 + 1.07932i
\(743\) −2.84193e28 + 2.84193e28i −0.554275 + 0.554275i −0.927672 0.373397i \(-0.878193\pi\)
0.373397 + 0.927672i \(0.378193\pi\)
\(744\) 2.04550e28i 0.393613i
\(745\) 5.77405e28 + 1.75857e28i 1.09627 + 0.333886i
\(746\) −1.53984e29 −2.88461
\(747\) 4.73086e28 + 4.73086e28i 0.874449 + 0.874449i
\(748\) 1.19804e29 1.19804e29i 2.18502 2.18502i
\(749\) 4.44137e28i 0.799279i
\(750\) 1.10018e29 8.96750e28i 1.95367 1.59242i
\(751\) −5.17262e28 −0.906381 −0.453191 0.891414i \(-0.649714\pi\)
−0.453191 + 0.891414i \(0.649714\pi\)
\(752\) 9.15964e28 + 9.15964e28i 1.58380 + 1.58380i
\(753\) 3.66324e28 3.66324e28i 0.625052 0.625052i
\(754\) 2.23486e28i 0.376302i
\(755\) −3.64228e27 + 1.19590e28i −0.0605207 + 0.198712i
\(756\) −2.75083e27 −0.0451072
\(757\) 2.90311e28 + 2.90311e28i 0.469791 + 0.469791i 0.901847 0.432056i \(-0.142212\pi\)
−0.432056 + 0.901847i \(0.642212\pi\)
\(758\) 1.05778e29 1.05778e29i 1.68929 1.68929i
\(759\) 1.28026e28i 0.201781i
\(760\) −1.13973e29 + 6.07564e28i −1.77282 + 0.945052i
\(761\) 5.55850e28 0.853318 0.426659 0.904413i \(-0.359690\pi\)
0.426659 + 0.904413i \(0.359690\pi\)
\(762\) −1.07663e29 1.07663e29i −1.63124 1.63124i
\(763\) −2.12209e28 + 2.12209e28i −0.317335 + 0.317335i
\(764\) 3.25519e28i 0.480444i
\(765\) −4.58777e28 8.60620e28i −0.668325 1.25371i
\(766\) −1.30293e29 −1.87341
\(767\) 7.95986e26 + 7.95986e26i 0.0112967 + 0.0112967i
\(768\) −1.42455e29 + 1.42455e29i −1.99556 + 1.99556i
\(769\) 8.46303e28i 1.17021i 0.810959 + 0.585103i \(0.198946\pi\)
−0.810959 + 0.585103i \(0.801054\pi\)
\(770\) −1.51503e29 4.61426e28i −2.06783 0.629788i
\(771\) 1.65663e29 2.23193
\(772\) 4.39164e28 + 4.39164e28i 0.584055 + 0.584055i
\(773\) 1.26889e27 1.26889e27i 0.0166583 0.0166583i −0.698729 0.715387i \(-0.746250\pi\)
0.715387 + 0.698729i \(0.246250\pi\)
\(774\) 7.44348e28i 0.964642i
\(775\) 8.76098e27 + 5.88221e27i 0.112082 + 0.0752529i
\(776\) −5.47863e28 −0.691919
\(777\) −4.26130e27 4.26130e27i −0.0531290 0.0531290i
\(778\) 4.23607e28 4.23607e28i 0.521396 0.521396i
\(779\) 4.01824e28i 0.488272i
\(780\) 1.42230e28 4.66993e28i 0.170626 0.560227i
\(781\) 1.19830e29 1.41924
\(782\) 2.10076e28 + 2.10076e28i 0.245645 + 0.245645i
\(783\) 1.18941e27 1.18941e27i 0.0137313 0.0137313i
\(784\) 5.50983e28i 0.628025i
\(785\) −1.00603e29 + 5.36292e28i −1.13218 + 0.603539i
\(786\) 2.08989e29 2.32219
\(787\) −7.82439e27 7.82439e27i −0.0858427 0.0858427i 0.662882 0.748724i \(-0.269333\pi\)
−0.748724 + 0.662882i \(0.769333\pi\)
\(788\) −1.38475e29 + 1.38475e29i −1.50006 + 1.50006i
\(789\) 1.17225e29i 1.25386i
\(790\) 8.19847e28 + 1.53795e29i 0.865888 + 1.62432i
\(791\) −5.79812e28 −0.604675
\(792\) 1.45864e29 + 1.45864e29i 1.50209 + 1.50209i
\(793\) −1.89048e28 + 1.89048e28i −0.192239 + 0.192239i
\(794\) 2.56505e29i 2.57568i
\(795\) −9.86609e28 3.00487e28i −0.978304 0.297957i
\(796\) 1.53762e29 1.50563
\(797\) −9.35158e28 9.35158e28i −0.904278 0.904278i 0.0915249 0.995803i \(-0.470826\pi\)
−0.995803 + 0.0915249i \(0.970826\pi\)
\(798\) 2.17395e29 2.17395e29i 2.07597 2.07597i
\(799\) 2.22959e29i 2.10260i
\(800\) −1.24447e28 6.33013e28i −0.115900 0.589539i
\(801\) −1.67120e29 −1.53711
\(802\) −1.72020e29 1.72020e29i −1.56256 1.56256i
\(803\) −8.86900e28 + 8.86900e28i −0.795644 + 0.795644i
\(804\) 3.20536e29i 2.83998i
\(805\) 5.52800e27 1.81505e28i 0.0483737 0.158829i
\(806\) 5.31222e27 0.0459119
\(807\) 3.57584e28 + 3.57584e28i 0.305241 + 0.305241i
\(808\) 1.98751e29 1.98751e29i 1.67570 1.67570i
\(809\) 7.84858e28i 0.653590i 0.945095 + 0.326795i \(0.105969\pi\)
−0.945095 + 0.326795i \(0.894031\pi\)
\(810\) −1.88229e29 + 1.00341e29i −1.54824 + 0.825331i
\(811\) 7.38021e27 0.0599598 0.0299799 0.999551i \(-0.490456\pi\)
0.0299799 + 0.999551i \(0.490456\pi\)
\(812\) 2.50588e29 + 2.50588e29i 2.01095 + 2.01095i
\(813\) −1.99480e29 + 1.99480e29i −1.58122 + 1.58122i
\(814\) 1.02966e28i 0.0806215i
\(815\) −1.07324e29 2.01328e29i −0.830080 1.55715i
\(816\) −3.89539e29 −2.97611
\(817\) −4.91144e28 4.91144e28i −0.370671 0.370671i
\(818\) 2.29376e29 2.29376e29i 1.71008 1.71008i
\(819\) 3.13547e28i 0.230921i
\(820\) 1.41660e29 + 4.31445e28i 1.03064 + 0.313897i
\(821\) 1.98234e29 1.42478 0.712389 0.701785i \(-0.247613\pi\)
0.712389 + 0.701785i \(0.247613\pi\)
\(822\) −1.59889e28 1.59889e28i −0.113527 0.113527i
\(823\) 9.57142e28 9.57142e28i 0.671395 0.671395i −0.286643 0.958037i \(-0.592539\pi\)
0.958037 + 0.286643i \(0.0925393\pi\)
\(824\) 1.22102e29i 0.846154i
\(825\) 2.07565e29 4.08061e28i 1.42107 0.279374i
\(826\) −2.61267e28 −0.176719
\(827\) 8.77185e28 + 8.77185e28i 0.586187 + 0.586187i 0.936597 0.350410i \(-0.113958\pi\)
−0.350410 + 0.936597i \(0.613958\pi\)
\(828\) −3.25813e28 + 3.25813e28i −0.215112 + 0.215112i
\(829\) 2.13178e29i 1.39058i 0.718728 + 0.695291i \(0.244724\pi\)
−0.718728 + 0.695291i \(0.755276\pi\)
\(830\) 9.81140e28 3.22145e29i 0.632339 2.07620i
\(831\) −2.36540e29 −1.50624
\(832\) 9.19526e27 + 9.19526e27i 0.0578537 + 0.0578537i
\(833\) −6.70585e28 + 6.70585e28i −0.416873 + 0.416873i
\(834\) 2.60740e29i 1.60157i
\(835\) 2.10426e29 1.12173e29i 1.27713 0.680808i
\(836\) −3.58893e29 −2.15230
\(837\) 2.82720e26 + 2.82720e26i 0.00167534 + 0.00167534i
\(838\) −3.03512e29 + 3.03512e29i −1.77720 + 1.77720i
\(839\) 6.36044e28i 0.368017i −0.982925 0.184008i \(-0.941093\pi\)
0.982925 0.184008i \(-0.0589073\pi\)
\(840\) 2.85866e29 + 5.36255e29i 1.63444 + 3.06605i
\(841\) −3.97048e28 −0.224328
\(842\) −1.29625e29 1.29625e29i −0.723717 0.723717i
\(843\) 1.50134e29 1.50134e29i 0.828328 0.828328i
\(844\) 4.95800e29i 2.70322i
\(845\) 1.71039e29 + 5.20924e28i 0.921568 + 0.280677i
\(846\) 5.06121e29 2.69495
\(847\) −6.77254e27 6.77254e27i −0.0356383 0.0356383i
\(848\) −1.46539e29 + 1.46539e29i −0.762068 + 0.762068i
\(849\) 2.33558e29i 1.20038i
\(850\) −2.73631e29 + 4.07547e29i −1.38988 + 2.07009i
\(851\) −1.23356e27 −0.00619249
\(852\) −6.06184e29 6.06184e29i −3.00752 3.00752i
\(853\) −1.38791e29 + 1.38791e29i −0.680568 + 0.680568i −0.960128 0.279560i \(-0.909811\pi\)
0.279560 + 0.960128i \(0.409811\pi\)
\(854\) 6.20514e29i 3.00727i
\(855\) −6.01892e28 + 1.97623e29i −0.288308 + 0.946623i
\(856\) 2.91175e29 1.37853
\(857\) 7.58343e27 + 7.58343e27i 0.0354860 + 0.0354860i 0.724627 0.689141i \(-0.242012\pi\)
−0.689141 + 0.724627i \(0.742012\pi\)
\(858\) 7.52999e28 7.52999e28i 0.348274 0.348274i
\(859\) 1.12132e29i 0.512622i −0.966594 0.256311i \(-0.917493\pi\)
0.966594 0.256311i \(-0.0825071\pi\)
\(860\) 2.25883e29 1.20413e29i 1.02070 0.544115i
\(861\) −1.89063e29 −0.844452
\(862\) 7.25359e28 + 7.25359e28i 0.320244 + 0.320244i
\(863\) 1.95303e29 1.95303e29i 0.852319 0.852319i −0.138100 0.990418i \(-0.544099\pi\)
0.990418 + 0.138100i \(0.0440994\pi\)
\(864\) 2.44435e27i 0.0105445i
\(865\) −1.94525e29 3.64909e29i −0.829497 1.55605i
\(866\) 9.27536e28 0.390977
\(867\) 2.33367e29 + 2.33367e29i 0.972409 + 0.972409i
\(868\) −5.95645e28 + 5.95645e28i −0.245352 + 0.245352i
\(869\) 2.59748e29i 1.05768i
\(870\) −6.62759e29 2.01853e29i −2.66786 0.812538i
\(871\) −4.46478e28 −0.177672
\(872\) −1.39124e29 1.39124e29i −0.547314 0.547314i
\(873\) −6.19648e28 + 6.19648e28i −0.240992 + 0.240992i
\(874\) 6.29316e28i 0.241966i
\(875\) 3.11887e29 + 3.17723e28i 1.18554 + 0.120772i
\(876\) 8.97309e29 3.37210
\(877\) 4.06067e28 + 4.06067e28i 0.150870 + 0.150870i 0.778506 0.627637i \(-0.215978\pi\)
−0.627637 + 0.778506i \(0.715978\pi\)
\(878\) −3.18639e29 + 3.18639e29i −1.17045 + 1.17045i
\(879\) 3.58443e29i 1.30176i
\(880\) 1.23842e29 4.06618e29i 0.444672 1.46002i
\(881\) 1.52098e29 0.539962 0.269981 0.962866i \(-0.412983\pi\)
0.269981 + 0.962866i \(0.412983\pi\)
\(882\) −1.52224e29 1.52224e29i −0.534316 0.534316i
\(883\) 2.56486e29 2.56486e29i 0.890137 0.890137i −0.104399 0.994536i \(-0.533292\pi\)
0.994536 + 0.104399i \(0.0332918\pi\)
\(884\) 1.68835e29i 0.579350i
\(885\) 3.07948e28 1.64160e28i 0.104483 0.0556974i
\(886\) −1.66415e29 −0.558285
\(887\) 6.78026e28 + 6.78026e28i 0.224911 + 0.224911i 0.810563 0.585652i \(-0.199161\pi\)
−0.585652 + 0.810563i \(0.699161\pi\)
\(888\) 2.79370e28 2.79370e28i 0.0916325 0.0916325i
\(889\) 3.36305e29i 1.09072i
\(890\) 3.95700e29 + 7.42293e29i 1.26901 + 2.38054i
\(891\) −3.17906e29 −1.00814
\(892\) 4.77962e29 + 4.77962e29i 1.49881 + 1.49881i
\(893\) −3.33955e29 + 3.33955e29i −1.03555 + 1.03555i
\(894\) 9.41959e29i 2.88840i
\(895\) −2.47038e29 7.52393e28i −0.749090 0.228147i
\(896\) −5.40590e29 −1.62102
\(897\) 9.02112e27 + 9.02112e27i 0.0267507 + 0.0267507i
\(898\) −1.73995e29 + 1.73995e29i −0.510239 + 0.510239i
\(899\) 5.15091e28i 0.149378i
\(900\) −6.32077e29 4.24383e29i −1.81278 1.21712i
\(901\) 3.56696e29 1.01170
\(902\) 2.28418e29 + 2.28418e29i 0.640715 + 0.640715i
\(903\) −2.31089e29 + 2.31089e29i −0.641065 + 0.641065i
\(904\) 3.80123e29i 1.04289i
\(905\) −6.51732e28 + 2.13988e29i −0.176841 + 0.580635i
\(906\) 1.95095e29 0.523556
\(907\) −3.21925e29 3.21925e29i −0.854442 0.854442i 0.136235 0.990677i \(-0.456500\pi\)
−0.990677 + 0.136235i \(0.956500\pi\)
\(908\) 1.74011e29 1.74011e29i 0.456792 0.456792i
\(909\) 4.49586e29i 1.16728i
\(910\) 1.39267e29 7.42403e28i 0.357631 0.190645i
\(911\) −5.89230e29 −1.49658 −0.748292 0.663370i \(-0.769126\pi\)
−0.748292 + 0.663370i \(0.769126\pi\)
\(912\) 5.83464e29 + 5.83464e29i 1.46577 + 1.46577i
\(913\) 3.54893e29 3.54893e29i 0.881840 0.881840i
\(914\) 3.88379e29i 0.954540i
\(915\) 3.89884e29 + 7.31382e29i 0.947817 + 1.77801i
\(916\) −2.15630e29 −0.518508
\(917\) 3.26407e29 + 3.26407e29i 0.776364 + 0.776364i
\(918\) −1.31517e28 + 1.31517e28i −0.0309425 + 0.0309425i
\(919\) 5.18713e29i 1.20718i 0.797295 + 0.603590i \(0.206264\pi\)
−0.797295 + 0.603590i \(0.793736\pi\)
\(920\) 1.18994e29 + 3.62414e28i 0.273935 + 0.0834309i
\(921\) 5.84065e28 0.133004
\(922\) −1.70871e29 1.70871e29i −0.384910 0.384910i
\(923\) −8.44361e28 + 8.44361e28i −0.188153 + 0.188153i
\(924\) 1.68863e30i 3.72234i
\(925\) −3.93176e27 1.99994e28i −0.00857373 0.0436113i
\(926\) −4.92667e29 −1.06278
\(927\) −1.38100e29 1.38100e29i −0.294712 0.294712i
\(928\) −2.22670e29 + 2.22670e29i −0.470090 + 0.470090i
\(929\) 9.59557e28i 0.200407i 0.994967 + 0.100204i \(0.0319495\pi\)
−0.994967 + 0.100204i \(0.968051\pi\)
\(930\) 4.79802e28 1.57537e29i 0.0991363 0.325501i
\(931\) 2.00885e29 0.410629
\(932\) −1.15868e30 1.15868e30i −2.34318 2.34318i
\(933\) 8.99671e29 8.99671e29i 1.79998 1.79998i
\(934\) 1.54970e30i 3.06746i
\(935\) −6.45607e29 + 3.44159e29i −1.26431 + 0.673973i
\(936\) −2.05561e29 −0.398274
\(937\) −2.24886e29 2.24886e29i −0.431089 0.431089i 0.457910 0.888999i \(-0.348598\pi\)
−0.888999 + 0.457910i \(0.848598\pi\)
\(938\) 7.32739e29 7.32739e29i 1.38970 1.38970i
\(939\) 6.85815e29i 1.28692i
\(940\) −8.18754e29 1.53590e30i −1.52011 2.85157i
\(941\) 9.61795e29 1.76679 0.883397 0.468625i \(-0.155250\pi\)
0.883397 + 0.468625i \(0.155250\pi\)
\(942\) 1.25805e30 + 1.25805e30i 2.28659 + 2.28659i
\(943\) −2.73650e28 + 2.73650e28i −0.0492129 + 0.0492129i
\(944\) 7.01211e28i 0.124775i
\(945\) 1.13630e28 + 3.46078e27i 0.0200067 + 0.00609335i
\(946\) 5.58384e29 0.972795
\(947\) 5.36645e29 + 5.36645e29i 0.925097 + 0.925097i 0.997384 0.0722867i \(-0.0230297\pi\)
−0.0722867 + 0.997384i \(0.523030\pi\)
\(948\) 1.31398e30 1.31398e30i 2.24133 2.24133i
\(949\) 1.24987e29i 0.210962i
\(950\) 1.02029e30 2.00583e29i 1.70407 0.335011i
\(951\) −7.95806e29 −1.31523
\(952\) −1.48614e30 1.48614e30i −2.43047 2.43047i
\(953\) −3.99557e29 + 3.99557e29i −0.646621 + 0.646621i −0.952175 0.305554i \(-0.901158\pi\)
0.305554 + 0.952175i \(0.401158\pi\)
\(954\) 8.09708e29i 1.29672i
\(955\) −4.09531e28 + 1.34464e29i −0.0649012 + 0.213095i
\(956\) −7.94232e29 −1.24557
\(957\) −7.30134e29 7.30134e29i −1.13314 1.13314i
\(958\) −7.55703e29 + 7.55703e29i −1.16064 + 1.16064i
\(959\) 4.99441e28i 0.0759099i
\(960\) 3.55743e29 1.89639e29i 0.535086 0.285243i
\(961\) −6.59547e29 −0.981775
\(962\) −7.25532e27 7.25532e27i −0.0106882 0.0106882i
\(963\) 3.29327e29 3.29327e29i 0.480136 0.480136i
\(964\) 1.19825e30i 1.72893i
\(965\) −1.26158e29 2.36659e29i −0.180153 0.337948i
\(966\) −2.96101e29 −0.418474
\(967\) −4.84629e29 4.84629e29i −0.677867 0.677867i 0.281650 0.959517i \(-0.409118\pi\)
−0.959517 + 0.281650i \(0.909118\pi\)
\(968\) 4.44006e28 4.44006e28i 0.0614661 0.0614661i
\(969\) 1.42023e30i 1.94591i
\(970\) 4.21945e29 + 1.28510e29i 0.572188 + 0.174268i
\(971\) −1.49540e29 −0.200709 −0.100354 0.994952i \(-0.531998\pi\)
−0.100354 + 0.994952i \(0.531998\pi\)
\(972\) 1.62833e30 + 1.62833e30i 2.16312 + 2.16312i
\(973\) −4.07233e29 + 4.07233e29i −0.535444 + 0.535444i
\(974\) 4.36877e29i 0.568552i
\(975\) −1.17503e29 + 1.75010e29i −0.151358 + 0.225432i
\(976\) 1.66539e30 2.12333
\(977\) 1.07442e29 + 1.07442e29i 0.135590 + 0.135590i 0.771644 0.636054i \(-0.219435\pi\)
−0.636054 + 0.771644i \(0.719435\pi\)
\(978\) −2.51763e30 + 2.51763e30i −3.14487 + 3.14487i
\(979\) 1.25368e30i 1.55010i
\(980\) −2.15693e29 + 7.08201e29i −0.263983 + 0.866754i
\(981\) −3.14706e29 −0.381254
\(982\) 9.04800e29 + 9.04800e29i 1.08502 + 1.08502i
\(983\) 2.34164e29 2.34164e29i 0.277962 0.277962i −0.554333 0.832295i \(-0.687027\pi\)
0.832295 + 0.554333i \(0.187027\pi\)
\(984\) 1.23949e30i 1.45644i
\(985\) 7.46220e29 3.97793e29i 0.867970 0.462696i
\(986\) 2.39612e30 2.75893
\(987\) 1.57130e30 + 1.57130e30i 1.79096 + 1.79096i
\(988\) 2.52887e29 2.52887e29i 0.285336 0.285336i
\(989\) 6.68958e28i 0.0747198i
\(990\) −7.81248e29 1.46554e30i −0.863847 1.62049i
\(991\) 4.79836e29 0.525238 0.262619 0.964900i \(-0.415414\pi\)
0.262619 + 0.964900i \(0.415414\pi\)
\(992\) −5.29282e28 5.29282e28i −0.0573549 0.0573549i
\(993\) −1.37596e30 + 1.37596e30i −1.47610 + 1.47610i
\(994\) 2.77145e30i 2.94336i
\(995\) −6.35155e29 1.93446e29i −0.667803 0.203390i
\(996\) −3.59058e30 −3.73742
\(997\) −9.92132e28 9.92132e28i −0.102239 0.102239i 0.654137 0.756376i \(-0.273032\pi\)
−0.756376 + 0.654137i \(0.773032\pi\)
\(998\) 1.99430e30 1.99430e30i 2.03463 2.03463i
\(999\) 7.72267e26i 0.000780032i
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.2.1 18
3.2 odd 2 45.21.g.a.37.9 18
5.2 odd 4 25.21.c.b.18.9 18
5.3 odd 4 inner 5.21.c.a.3.1 yes 18
5.4 even 2 25.21.c.b.7.9 18
15.8 even 4 45.21.g.a.28.9 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.21.c.a.2.1 18 1.1 even 1 trivial
5.21.c.a.3.1 yes 18 5.3 odd 4 inner
25.21.c.b.7.9 18 5.4 even 2
25.21.c.b.18.9 18 5.2 odd 4
45.21.g.a.28.9 18 15.8 even 4
45.21.g.a.37.9 18 3.2 odd 2