Properties

Label 12.17.d.a.7.7
Level $12$
Weight $17$
Character 12.7
Analytic conductor $19.479$
Analytic rank $0$
Dimension $16$
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] = [12,17,Mod(7,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.4789452628\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + 12661863519850 x^{10} + 162120109773543 x^{9} + \cdots + 43\!\cdots\!49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{106}\cdot 3^{51} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.7
Root \(72.8587 + 126.195i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.17.d.a.7.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-119.478 - 226.409i) q^{2} -3788.00i q^{3} +(-36986.2 + 54101.7i) q^{4} -481576. q^{5} +(-857637. + 452581. i) q^{6} +515341. i q^{7} +(1.66681e7 + 1.91007e6i) q^{8} -1.43489e7 q^{9} +O(q^{10})\) \(q+(-119.478 - 226.409i) q^{2} -3788.00i q^{3} +(-36986.2 + 54101.7i) q^{4} -481576. q^{5} +(-857637. + 452581. i) q^{6} +515341. i q^{7} +(1.66681e7 + 1.91007e6i) q^{8} -1.43489e7 q^{9} +(5.75375e7 + 1.09033e8i) q^{10} +1.66130e8i q^{11} +(2.04937e8 + 1.40103e8i) q^{12} -4.92842e8 q^{13} +(1.16678e8 - 6.15717e7i) q^{14} +1.82421e9i q^{15} +(-1.55901e9 - 4.00203e9i) q^{16} +7.46224e9 q^{17} +(1.71437e9 + 3.24872e9i) q^{18} +3.55999e9i q^{19} +(1.78116e10 - 2.60540e10i) q^{20} +1.95211e9 q^{21} +(3.76134e10 - 1.98489e10i) q^{22} -1.41839e11i q^{23} +(7.23532e9 - 6.31388e10i) q^{24} +7.93271e10 q^{25} +(5.88837e10 + 1.11584e11i) q^{26} +5.43536e10i q^{27} +(-2.78808e10 - 1.90605e10i) q^{28} +9.07879e11 q^{29} +(4.13017e11 - 2.17952e11i) q^{30} +1.71098e11i q^{31} +(-7.19828e11 + 8.31128e11i) q^{32} +6.29301e11 q^{33} +(-8.91571e11 - 1.68952e12i) q^{34} -2.48175e11i q^{35} +(5.30711e11 - 7.76300e11i) q^{36} -3.92591e12 q^{37} +(8.06015e11 - 4.25340e11i) q^{38} +1.86688e12i q^{39} +(-8.02696e12 - 9.19841e11i) q^{40} +6.33127e12 q^{41} +(-2.33233e11 - 4.41975e11i) q^{42} +1.38507e13i q^{43} +(-8.98793e12 - 6.14452e12i) q^{44} +6.91008e12 q^{45} +(-3.21136e13 + 1.69466e13i) q^{46} +3.46437e13i q^{47} +(-1.51597e13 + 5.90553e12i) q^{48} +3.29674e13 q^{49} +(-9.47781e12 - 1.79604e13i) q^{50} -2.82669e13i q^{51} +(1.82284e13 - 2.66636e13i) q^{52} +8.06522e13 q^{53} +(1.23061e13 - 6.49404e12i) q^{54} -8.00043e13i q^{55} +(-9.84334e11 + 8.58976e12i) q^{56} +1.34852e13 q^{57} +(-1.08471e14 - 2.05552e14i) q^{58} +1.70599e14i q^{59} +(-9.86926e13 - 6.74704e13i) q^{60} +3.04136e14 q^{61} +(3.87381e13 - 2.04424e13i) q^{62} -7.39457e12i q^{63} +(2.74178e14 + 6.36745e13i) q^{64} +2.37341e14 q^{65} +(-7.51874e13 - 1.42479e14i) q^{66} +3.16979e14i q^{67} +(-2.76000e14 + 4.03719e14i) q^{68} -5.37285e14 q^{69} +(-5.61892e13 + 2.96514e13i) q^{70} -1.80534e14i q^{71} +(-2.39169e14 - 2.74074e13i) q^{72} -1.28620e15 q^{73} +(4.69059e14 + 8.88863e14i) q^{74} -3.00491e14i q^{75} +(-1.92602e14 - 1.31671e14i) q^{76} -8.56137e13 q^{77} +(4.22680e14 - 2.23051e14i) q^{78} -1.91899e15i q^{79} +(7.50783e14 + 1.92728e15i) q^{80} +2.05891e14 q^{81} +(-7.56445e14 - 1.43346e15i) q^{82} +2.98068e15i q^{83} +(-7.22010e13 + 1.05612e14i) q^{84} -3.59363e15 q^{85} +(3.13593e15 - 1.65485e15i) q^{86} -3.43904e15i q^{87} +(-3.17320e14 + 2.76908e15i) q^{88} -8.50551e14 q^{89} +(-8.25601e14 - 1.56451e15i) q^{90} -2.53982e14i q^{91} +(7.67372e15 + 5.24608e15i) q^{92} +6.48118e14 q^{93} +(7.84365e15 - 4.13915e15i) q^{94} -1.71441e15i q^{95} +(3.14831e15 + 2.72671e15i) q^{96} -1.30607e15 q^{97} +(-3.93886e15 - 7.46411e15i) q^{98} -2.38379e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −119.478 226.409i −0.466710 0.884411i
\(3\) 3788.00i 0.577350i
\(4\) −36986.2 + 54101.7i −0.564364 + 0.825526i
\(5\) −481576. −1.23283 −0.616417 0.787420i \(-0.711416\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(6\) −857637. + 452581.i −0.510615 + 0.269455i
\(7\) 515341.i 0.0893943i 0.999001 + 0.0446972i \(0.0142323\pi\)
−0.999001 + 0.0446972i \(0.985768\pi\)
\(8\) 1.66681e7 + 1.91007e6i 0.993498 + 0.113849i
\(9\) −1.43489e7 −0.333333
\(10\) 5.75375e7 + 1.09033e8i 0.575375 + 1.09033i
\(11\) 1.66130e8i 0.775010i 0.921868 + 0.387505i \(0.126663\pi\)
−0.921868 + 0.387505i \(0.873337\pi\)
\(12\) 2.04937e8 + 1.40103e8i 0.476618 + 0.325836i
\(13\) −4.92842e8 −0.604173 −0.302086 0.953281i \(-0.597683\pi\)
−0.302086 + 0.953281i \(0.597683\pi\)
\(14\) 1.16678e8 6.15717e7i 0.0790613 0.0417212i
\(15\) 1.82421e9i 0.711777i
\(16\) −1.55901e9 4.00203e9i −0.362986 0.931795i
\(17\) 7.46224e9 1.06974 0.534869 0.844935i \(-0.320361\pi\)
0.534869 + 0.844935i \(0.320361\pi\)
\(18\) 1.71437e9 + 3.24872e9i 0.155570 + 0.294804i
\(19\) 3.55999e9i 0.209614i 0.994493 + 0.104807i \(0.0334225\pi\)
−0.994493 + 0.104807i \(0.966577\pi\)
\(20\) 1.78116e10 2.60540e10i 0.695767 1.01774i
\(21\) 1.95211e9 0.0516118
\(22\) 3.76134e10 1.98489e10i 0.685427 0.361705i
\(23\) 1.41839e11i 1.81123i −0.424105 0.905613i \(-0.639411\pi\)
0.424105 0.905613i \(-0.360589\pi\)
\(24\) 7.23532e9 6.31388e10i 0.0657306 0.573596i
\(25\) 7.93271e10 0.519878
\(26\) 5.88837e10 + 1.11584e11i 0.281973 + 0.534337i
\(27\) 5.43536e10i 0.192450i
\(28\) −2.78808e10 1.90605e10i −0.0737973 0.0504510i
\(29\) 9.07879e11 1.81486 0.907432 0.420200i \(-0.138040\pi\)
0.907432 + 0.420200i \(0.138040\pi\)
\(30\) 4.13017e11 2.17952e11i 0.629503 0.332193i
\(31\) 1.71098e11i 0.200609i 0.994957 + 0.100305i \(0.0319818\pi\)
−0.994957 + 0.100305i \(0.968018\pi\)
\(32\) −7.19828e11 + 8.31128e11i −0.654680 + 0.755906i
\(33\) 6.29301e11 0.447452
\(34\) −8.91571e11 1.68952e12i −0.499257 0.946088i
\(35\) 2.48175e11i 0.110208i
\(36\) 5.30711e11 7.76300e11i 0.188121 0.275175i
\(37\) −3.92591e12 −1.11770 −0.558852 0.829267i \(-0.688758\pi\)
−0.558852 + 0.829267i \(0.688758\pi\)
\(38\) 8.06015e11 4.25340e11i 0.185385 0.0978289i
\(39\) 1.86688e12i 0.348819i
\(40\) −8.02696e12 9.19841e11i −1.22482 0.140357i
\(41\) 6.33127e12 0.792902 0.396451 0.918056i \(-0.370242\pi\)
0.396451 + 0.918056i \(0.370242\pi\)
\(42\) −2.33233e11 4.41975e11i −0.0240877 0.0456461i
\(43\) 1.38507e13i 1.18502i 0.805564 + 0.592508i \(0.201862\pi\)
−0.805564 + 0.592508i \(0.798138\pi\)
\(44\) −8.98793e12 6.14452e12i −0.639791 0.437388i
\(45\) 6.91008e12 0.410944
\(46\) −3.21136e13 + 1.69466e13i −1.60187 + 0.845317i
\(47\) 3.46437e13i 1.45493i 0.686146 + 0.727464i \(0.259301\pi\)
−0.686146 + 0.727464i \(0.740699\pi\)
\(48\) −1.51597e13 + 5.90553e12i −0.537972 + 0.209570i
\(49\) 3.29674e13 0.992009
\(50\) −9.47781e12 1.79604e13i −0.242632 0.459786i
\(51\) 2.82669e13i 0.617614i
\(52\) 1.82284e13 2.66636e13i 0.340974 0.498760i
\(53\) 8.06522e13 1.29542 0.647708 0.761889i \(-0.275728\pi\)
0.647708 + 0.761889i \(0.275728\pi\)
\(54\) 1.23061e13 6.49404e12i 0.170205 0.0898183i
\(55\) 8.00043e13i 0.955458i
\(56\) −9.84334e11 + 8.58976e12i −0.0101774 + 0.0888131i
\(57\) 1.34852e13 0.121021
\(58\) −1.08471e14 2.05552e14i −0.847014 1.60508i
\(59\) 1.70599e14i 1.16188i 0.813946 + 0.580940i \(0.197315\pi\)
−0.813946 + 0.580940i \(0.802685\pi\)
\(60\) −9.86926e13 6.74704e13i −0.587590 0.401701i
\(61\) 3.04136e14 1.58646 0.793231 0.608921i \(-0.208397\pi\)
0.793231 + 0.608921i \(0.208397\pi\)
\(62\) 3.87381e13 2.04424e13i 0.177421 0.0936263i
\(63\) 7.39457e12i 0.0297981i
\(64\) 2.74178e14 + 6.36745e13i 0.974077 + 0.226217i
\(65\) 2.37341e14 0.744845
\(66\) −7.51874e13 1.42479e14i −0.208830 0.395732i
\(67\) 3.16979e14i 0.780606i 0.920686 + 0.390303i \(0.127630\pi\)
−0.920686 + 0.390303i \(0.872370\pi\)
\(68\) −2.76000e14 + 4.03719e14i −0.603722 + 0.883097i
\(69\) −5.37285e14 −1.04571
\(70\) −5.61892e13 + 2.96514e13i −0.0974694 + 0.0514353i
\(71\) 1.80534e14i 0.279572i −0.990182 0.139786i \(-0.955359\pi\)
0.990182 0.139786i \(-0.0446414\pi\)
\(72\) −2.39169e14 2.74074e13i −0.331166 0.0379496i
\(73\) −1.28620e15 −1.59487 −0.797435 0.603405i \(-0.793810\pi\)
−0.797435 + 0.603405i \(0.793810\pi\)
\(74\) 4.69059e14 + 8.88863e14i 0.521644 + 0.988510i
\(75\) 3.00491e14i 0.300152i
\(76\) −1.92602e14 1.31671e14i −0.173042 0.118299i
\(77\) −8.56137e13 −0.0692815
\(78\) 4.22680e14 2.23051e14i 0.308500 0.162797i
\(79\) 1.91899e15i 1.26490i −0.774602 0.632450i \(-0.782050\pi\)
0.774602 0.632450i \(-0.217950\pi\)
\(80\) 7.50783e14 + 1.92728e15i 0.447501 + 1.14875i
\(81\) 2.05891e14 0.111111
\(82\) −7.56445e14 1.43346e15i −0.370055 0.701251i
\(83\) 2.98068e15i 1.32340i 0.749769 + 0.661700i \(0.230165\pi\)
−0.749769 + 0.661700i \(0.769835\pi\)
\(84\) −7.22010e13 + 1.05612e14i −0.0291279 + 0.0426069i
\(85\) −3.59363e15 −1.31881
\(86\) 3.13593e15 1.65485e15i 1.04804 0.553059i
\(87\) 3.43904e15i 1.04781i
\(88\) −3.17320e14 + 2.76908e15i −0.0882340 + 0.769971i
\(89\) −8.50551e14 −0.216063 −0.108031 0.994147i \(-0.534455\pi\)
−0.108031 + 0.994147i \(0.534455\pi\)
\(90\) −8.25601e14 1.56451e15i −0.191792 0.363444i
\(91\) 2.53982e14i 0.0540096i
\(92\) 7.67372e15 + 5.24608e15i 1.49521 + 1.02219i
\(93\) 6.48118e14 0.115822
\(94\) 7.84365e15 4.13915e15i 1.28675 0.679029i
\(95\) 1.71441e15i 0.258419i
\(96\) 3.14831e15 + 2.72671e15i 0.436423 + 0.377980i
\(97\) −1.30607e15 −0.166645 −0.0833224 0.996523i \(-0.526553\pi\)
−0.0833224 + 0.996523i \(0.526553\pi\)
\(98\) −3.93886e15 7.46411e15i −0.462980 0.877343i
\(99\) 2.38379e15i 0.258337i
\(100\) −2.93400e15 + 4.29173e15i −0.293400 + 0.429173i
\(101\) 1.08578e16 1.00270 0.501350 0.865245i \(-0.332837\pi\)
0.501350 + 0.865245i \(0.332837\pi\)
\(102\) −6.39989e15 + 3.37727e15i −0.546224 + 0.288246i
\(103\) 1.78830e15i 0.141170i 0.997506 + 0.0705851i \(0.0224866\pi\)
−0.997506 + 0.0705851i \(0.977513\pi\)
\(104\) −8.21476e15 9.41361e14i −0.600245 0.0687844i
\(105\) −9.40087e14 −0.0636288
\(106\) −9.63613e15 1.82604e16i −0.604583 1.14568i
\(107\) 1.27220e16i 0.740433i −0.928945 0.370217i \(-0.879283\pi\)
0.928945 0.370217i \(-0.120717\pi\)
\(108\) −2.94062e15 2.01033e15i −0.158873 0.108612i
\(109\) 1.17768e16 0.591037 0.295519 0.955337i \(-0.404508\pi\)
0.295519 + 0.955337i \(0.404508\pi\)
\(110\) −1.81137e16 + 9.55873e15i −0.845017 + 0.445922i
\(111\) 1.48713e16i 0.645307i
\(112\) 2.06241e15 8.03423e14i 0.0832972 0.0324489i
\(113\) −1.61155e16 −0.606201 −0.303100 0.952959i \(-0.598022\pi\)
−0.303100 + 0.952959i \(0.598022\pi\)
\(114\) −1.61119e15 3.05318e15i −0.0564816 0.107032i
\(115\) 6.83061e16i 2.23294i
\(116\) −3.35790e16 + 4.91178e16i −1.02424 + 1.49822i
\(117\) 7.07175e15 0.201391
\(118\) 3.86253e16 2.03828e16i 1.02758 0.542261i
\(119\) 3.84559e15i 0.0956286i
\(120\) −3.48435e15 + 3.04061e16i −0.0810349 + 0.707149i
\(121\) 1.83505e16 0.399359
\(122\) −3.63375e16 6.88592e16i −0.740417 1.40308i
\(123\) 2.39828e16i 0.457782i
\(124\) −9.25668e15 6.32826e15i −0.165608 0.113217i
\(125\) 3.52806e16 0.591910
\(126\) −1.67420e15 + 8.83486e14i −0.0263538 + 0.0139071i
\(127\) 5.34191e16i 0.789345i 0.918822 + 0.394673i \(0.129142\pi\)
−0.918822 + 0.394673i \(0.870858\pi\)
\(128\) −1.83417e16 6.96841e16i −0.254542 0.967062i
\(129\) 5.24664e16 0.684170
\(130\) −2.83569e16 5.37361e16i −0.347626 0.658748i
\(131\) 1.48466e17i 1.71181i −0.517132 0.855905i \(-0.673000\pi\)
0.517132 0.855905i \(-0.327000\pi\)
\(132\) −2.32754e16 + 3.40462e16i −0.252526 + 0.369383i
\(133\) −1.83461e15 −0.0187383
\(134\) 7.17669e16 3.78719e16i 0.690376 0.364316i
\(135\) 2.61754e16i 0.237259i
\(136\) 1.24382e17 + 1.42534e16i 1.06278 + 0.121788i
\(137\) 1.59937e14 0.00128880 0.000644398 1.00000i \(-0.499795\pi\)
0.000644398 1.00000i \(0.499795\pi\)
\(138\) 6.41936e16 + 1.21646e17i 0.488044 + 0.924838i
\(139\) 1.28935e16i 0.0925234i 0.998929 + 0.0462617i \(0.0147308\pi\)
−0.998929 + 0.0462617i \(0.985269\pi\)
\(140\) 1.34267e16 + 9.17906e15i 0.0909798 + 0.0621976i
\(141\) 1.31230e17 0.840003
\(142\) −4.08746e16 + 2.15698e16i −0.247256 + 0.130479i
\(143\) 8.18761e16i 0.468240i
\(144\) 2.23701e16 + 5.74247e16i 0.120995 + 0.310598i
\(145\) −4.37212e17 −2.23742
\(146\) 1.53672e17 + 2.91207e17i 0.744341 + 1.41052i
\(147\) 1.24880e17i 0.572736i
\(148\) 1.45205e17 2.12399e17i 0.630793 0.922694i
\(149\) −1.67950e17 −0.691338 −0.345669 0.938357i \(-0.612348\pi\)
−0.345669 + 0.938357i \(0.612348\pi\)
\(150\) −6.80338e16 + 3.59019e16i −0.265457 + 0.140084i
\(151\) 4.43174e17i 1.63968i 0.572595 + 0.819838i \(0.305937\pi\)
−0.572595 + 0.819838i \(0.694063\pi\)
\(152\) −6.79982e15 + 5.93385e16i −0.0238643 + 0.208251i
\(153\) −1.07075e17 −0.356580
\(154\) 1.02289e16 + 1.93837e16i 0.0323344 + 0.0612733i
\(155\) 8.23966e16i 0.247318i
\(156\) −1.01002e17 6.90489e16i −0.287959 0.196861i
\(157\) −1.71679e17 −0.465071 −0.232536 0.972588i \(-0.574702\pi\)
−0.232536 + 0.972588i \(0.574702\pi\)
\(158\) −4.34477e17 + 2.29276e17i −1.11869 + 0.590341i
\(159\) 3.05510e17i 0.747909i
\(160\) 3.46652e17 4.00251e17i 0.807111 0.931906i
\(161\) 7.30953e16 0.161913
\(162\) −2.45994e16 4.66156e16i −0.0518566 0.0982678i
\(163\) 2.62267e17i 0.526311i 0.964753 + 0.263156i \(0.0847633\pi\)
−0.964753 + 0.263156i \(0.915237\pi\)
\(164\) −2.34169e17 + 3.42532e17i −0.447486 + 0.654561i
\(165\) −3.03056e17 −0.551634
\(166\) 6.74854e17 3.56125e17i 1.17043 0.617644i
\(167\) 4.22305e17i 0.698063i −0.937111 0.349032i \(-0.886511\pi\)
0.937111 0.349032i \(-0.113489\pi\)
\(168\) 3.25380e16 + 3.72865e15i 0.0512763 + 0.00587595i
\(169\) −4.22523e17 −0.634975
\(170\) 4.29359e17 + 8.13631e17i 0.615501 + 1.16637i
\(171\) 5.10820e16i 0.0698714i
\(172\) −7.49347e17 5.12285e17i −0.978262 0.668781i
\(173\) 8.67929e17 1.08172 0.540861 0.841112i \(-0.318099\pi\)
0.540861 + 0.841112i \(0.318099\pi\)
\(174\) −7.78630e17 + 4.10889e17i −0.926696 + 0.489024i
\(175\) 4.08805e16i 0.0464741i
\(176\) 6.64858e17 2.58999e17i 0.722150 0.281318i
\(177\) 6.46230e17 0.670812
\(178\) 1.01622e17 + 1.92573e17i 0.100839 + 0.191088i
\(179\) 9.21178e17i 0.874016i 0.899458 + 0.437008i \(0.143962\pi\)
−0.899458 + 0.437008i \(0.856038\pi\)
\(180\) −2.55577e17 + 3.73847e17i −0.231922 + 0.339245i
\(181\) 1.58908e18 1.37948 0.689741 0.724056i \(-0.257724\pi\)
0.689741 + 0.724056i \(0.257724\pi\)
\(182\) −5.75038e16 + 3.03451e16i −0.0477667 + 0.0252068i
\(183\) 1.15207e18i 0.915944i
\(184\) 2.70922e17 2.36419e18i 0.206206 1.79945i
\(185\) 1.89062e18 1.37794
\(186\) −7.74356e16 1.46740e17i −0.0540552 0.102434i
\(187\) 1.23970e18i 0.829058i
\(188\) −1.87428e18 1.28134e18i −1.20108 0.821109i
\(189\) −2.80106e16 −0.0172039
\(190\) −3.88157e17 + 2.04833e17i −0.228549 + 0.120607i
\(191\) 1.10519e18i 0.623978i 0.950086 + 0.311989i \(0.100995\pi\)
−0.950086 + 0.311989i \(0.899005\pi\)
\(192\) 2.41199e17 1.03859e18i 0.130607 0.562384i
\(193\) −9.46462e17 −0.491637 −0.245819 0.969316i \(-0.579057\pi\)
−0.245819 + 0.969316i \(0.579057\pi\)
\(194\) 1.56046e17 + 2.95706e17i 0.0777748 + 0.147383i
\(195\) 8.99046e17i 0.430036i
\(196\) −1.21934e18 + 1.78359e18i −0.559854 + 0.818929i
\(197\) −1.18890e18 −0.524103 −0.262051 0.965054i \(-0.584399\pi\)
−0.262051 + 0.965054i \(0.584399\pi\)
\(198\) −5.39711e17 + 2.84809e17i −0.228476 + 0.120568i
\(199\) 1.82188e17i 0.0740788i −0.999314 0.0370394i \(-0.988207\pi\)
0.999314 0.0370394i \(-0.0117927\pi\)
\(200\) 1.32223e18 + 1.51520e17i 0.516498 + 0.0591875i
\(201\) 1.20071e18 0.450683
\(202\) −1.29727e18 2.45831e18i −0.467970 0.886799i
\(203\) 4.67867e17i 0.162239i
\(204\) 1.52929e18 + 1.04549e18i 0.509856 + 0.348559i
\(205\) −3.04898e18 −0.977516
\(206\) 4.04888e17 2.13662e17i 0.124852 0.0658855i
\(207\) 2.03523e18i 0.603742i
\(208\) 7.68348e17 + 1.97237e18i 0.219306 + 0.562965i
\(209\) −5.91423e17 −0.162453
\(210\) 1.12319e17 + 2.12844e17i 0.0296962 + 0.0562740i
\(211\) 2.01089e18i 0.511833i 0.966699 + 0.255916i \(0.0823772\pi\)
−0.966699 + 0.255916i \(0.917623\pi\)
\(212\) −2.98302e18 + 4.36342e18i −0.731086 + 1.06940i
\(213\) −6.83863e17 −0.161411
\(214\) −2.88038e18 + 1.52000e18i −0.654847 + 0.345567i
\(215\) 6.67017e18i 1.46093i
\(216\) −1.03819e17 + 9.05973e17i −0.0219102 + 0.191199i
\(217\) −8.81737e16 −0.0179333
\(218\) −1.40706e18 2.66637e18i −0.275843 0.522720i
\(219\) 4.87211e18i 0.920798i
\(220\) 4.32837e18 + 2.95905e18i 0.788756 + 0.539226i
\(221\) −3.67771e18 −0.646307
\(222\) 3.36701e18 1.77679e18i 0.570716 0.301171i
\(223\) 2.03402e18i 0.332595i −0.986076 0.166298i \(-0.946819\pi\)
0.986076 0.166298i \(-0.0531812\pi\)
\(224\) −4.28314e17 3.70957e17i −0.0675737 0.0585247i
\(225\) −1.13826e18 −0.173293
\(226\) 1.92544e18 + 3.64870e18i 0.282920 + 0.536130i
\(227\) 8.31593e18i 1.17952i −0.807580 0.589758i \(-0.799223\pi\)
0.807580 0.589758i \(-0.200777\pi\)
\(228\) −4.98767e17 + 7.29574e17i −0.0682998 + 0.0999058i
\(229\) 7.19478e18 0.951335 0.475667 0.879625i \(-0.342207\pi\)
0.475667 + 0.879625i \(0.342207\pi\)
\(230\) 1.54651e19 8.16106e18i 1.97484 1.04213i
\(231\) 3.24304e17i 0.0399997i
\(232\) 1.51326e19 + 1.73411e18i 1.80306 + 0.206620i
\(233\) −7.76947e18 −0.894425 −0.447212 0.894428i \(-0.647583\pi\)
−0.447212 + 0.894428i \(0.647583\pi\)
\(234\) −8.44916e17 1.60111e18i −0.0939911 0.178112i
\(235\) 1.66836e19i 1.79368i
\(236\) −9.22971e18 6.30982e18i −0.959162 0.655724i
\(237\) −7.26912e18 −0.730290
\(238\) 8.70677e17 4.59463e17i 0.0845749 0.0446308i
\(239\) 1.13707e19i 1.06808i 0.845460 + 0.534038i \(0.179326\pi\)
−0.845460 + 0.534038i \(0.820674\pi\)
\(240\) 7.30052e18 2.84396e18i 0.663230 0.258365i
\(241\) 5.22286e18 0.458957 0.229479 0.973314i \(-0.426298\pi\)
0.229479 + 0.973314i \(0.426298\pi\)
\(242\) −2.19247e18 4.15471e18i −0.186385 0.353198i
\(243\) 7.79915e17i 0.0641500i
\(244\) −1.12488e19 + 1.64543e19i −0.895342 + 1.30967i
\(245\) −1.58763e19 −1.22298
\(246\) −5.42993e18 + 2.86541e18i −0.404868 + 0.213651i
\(247\) 1.75452e18i 0.126643i
\(248\) −3.26808e17 + 2.85188e18i −0.0228391 + 0.199305i
\(249\) 1.12908e19 0.764065
\(250\) −4.21525e18 7.98785e18i −0.276250 0.523492i
\(251\) 1.98339e19i 1.25898i 0.777008 + 0.629491i \(0.216736\pi\)
−0.777008 + 0.629491i \(0.783264\pi\)
\(252\) 4.00059e17 + 2.73497e17i 0.0245991 + 0.0168170i
\(253\) 2.35637e19 1.40372
\(254\) 1.20946e19 6.38239e18i 0.698105 0.368395i
\(255\) 1.36127e19i 0.761415i
\(256\) −1.35857e19 + 1.24784e19i −0.736482 + 0.676457i
\(257\) 2.61741e19 1.37533 0.687665 0.726028i \(-0.258636\pi\)
0.687665 + 0.726028i \(0.258636\pi\)
\(258\) −6.26857e18 1.18789e19i −0.319309 0.605087i
\(259\) 2.02318e18i 0.0999165i
\(260\) −8.77833e18 + 1.28405e19i −0.420364 + 0.614888i
\(261\) −1.30271e19 −0.604954
\(262\) −3.36140e19 + 1.77383e19i −1.51394 + 0.798919i
\(263\) 8.72728e18i 0.381270i 0.981661 + 0.190635i \(0.0610547\pi\)
−0.981661 + 0.190635i \(0.938945\pi\)
\(264\) 1.04893e19 + 1.20201e18i 0.444543 + 0.0509419i
\(265\) −3.88401e19 −1.59703
\(266\) 2.19195e17 + 4.15372e17i 0.00874535 + 0.0165724i
\(267\) 3.22188e18i 0.124744i
\(268\) −1.71491e19 1.17238e19i −0.644411 0.440546i
\(269\) 1.34355e18 0.0490046 0.0245023 0.999700i \(-0.492200\pi\)
0.0245023 + 0.999700i \(0.492200\pi\)
\(270\) −5.92634e18 + 3.12737e18i −0.209834 + 0.110731i
\(271\) 4.73624e19i 1.62809i −0.580799 0.814047i \(-0.697260\pi\)
0.580799 0.814047i \(-0.302740\pi\)
\(272\) −1.16337e19 2.98641e19i −0.388300 0.996777i
\(273\) −9.62081e17 −0.0311825
\(274\) −1.91089e16 3.62112e16i −0.000601494 0.00113983i
\(275\) 1.31786e19i 0.402911i
\(276\) 1.98721e19 2.90680e19i 0.590162 0.863262i
\(277\) 3.65464e19 1.05440 0.527202 0.849740i \(-0.323241\pi\)
0.527202 + 0.849740i \(0.323241\pi\)
\(278\) 2.91920e18 1.54048e18i 0.0818287 0.0431816i
\(279\) 2.45507e18i 0.0668698i
\(280\) 4.74031e17 4.13662e18i 0.0125471 0.109492i
\(281\) 5.34347e19 1.37459 0.687295 0.726379i \(-0.258798\pi\)
0.687295 + 0.726379i \(0.258798\pi\)
\(282\) −1.56791e19 2.97117e19i −0.392038 0.742908i
\(283\) 6.88848e19i 1.67430i 0.546977 + 0.837148i \(0.315779\pi\)
−0.546977 + 0.837148i \(0.684221\pi\)
\(284\) 9.76721e18 + 6.67728e18i 0.230794 + 0.157780i
\(285\) −6.49416e18 −0.149198
\(286\) −1.85375e19 + 9.78236e18i −0.414117 + 0.218532i
\(287\) 3.26276e18i 0.0708810i
\(288\) 1.03287e19 1.19258e19i 0.218227 0.251969i
\(289\) 7.02379e18 0.144341
\(290\) 5.22371e19 + 9.89888e19i 1.04423 + 1.97880i
\(291\) 4.94738e18i 0.0962125i
\(292\) 4.75716e19 6.95855e19i 0.900087 1.31661i
\(293\) 2.18046e19 0.401428 0.200714 0.979650i \(-0.435674\pi\)
0.200714 + 0.979650i \(0.435674\pi\)
\(294\) −2.82740e19 + 1.49204e19i −0.506534 + 0.267302i
\(295\) 8.21565e19i 1.43240i
\(296\) −6.54377e19 7.49875e18i −1.11044 0.127249i
\(297\) −9.02978e18 −0.149151
\(298\) 2.00663e19 + 3.80255e19i 0.322654 + 0.611427i
\(299\) 6.99042e19i 1.09429i
\(300\) 1.62570e19 + 1.11140e19i 0.247783 + 0.169395i
\(301\) −7.13784e18 −0.105934
\(302\) 1.00339e20 5.29493e19i 1.45015 0.765253i
\(303\) 4.11293e19i 0.578909i
\(304\) 1.42472e19 5.55008e18i 0.195317 0.0760870i
\(305\) −1.46465e20 −1.95584
\(306\) 1.27931e19 + 2.42427e19i 0.166419 + 0.315363i
\(307\) 9.64113e19i 1.22186i −0.791685 0.610929i \(-0.790796\pi\)
0.791685 0.610929i \(-0.209204\pi\)
\(308\) 3.16652e18 4.63184e18i 0.0391000 0.0571937i
\(309\) 6.77408e18 0.0815046
\(310\) −1.86553e19 + 9.84455e18i −0.218731 + 0.115426i
\(311\) 1.43879e20i 1.64404i −0.569457 0.822021i \(-0.692846\pi\)
0.569457 0.822021i \(-0.307154\pi\)
\(312\) −3.56587e18 + 3.11175e19i −0.0397127 + 0.346551i
\(313\) −4.88496e19 −0.530282 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(314\) 2.05118e19 + 3.88696e19i 0.217053 + 0.411314i
\(315\) 3.56105e18i 0.0367361i
\(316\) 1.03821e20 + 7.09761e19i 1.04421 + 0.713864i
\(317\) −3.53189e19 −0.346365 −0.173182 0.984890i \(-0.555405\pi\)
−0.173182 + 0.984890i \(0.555405\pi\)
\(318\) −6.91703e19 + 3.65016e19i −0.661458 + 0.349056i
\(319\) 1.50826e20i 1.40654i
\(320\) −1.32038e20 3.06641e19i −1.20087 0.278888i
\(321\) −4.81909e19 −0.427489
\(322\) −8.73326e18 1.65494e19i −0.0755665 0.143198i
\(323\) 2.65655e19i 0.224232i
\(324\) −7.61513e18 + 1.11391e19i −0.0627071 + 0.0917251i
\(325\) −3.90957e19 −0.314096
\(326\) 5.93796e19 3.13350e19i 0.465475 0.245635i
\(327\) 4.46104e19i 0.341236i
\(328\) 1.05530e20 + 1.20931e19i 0.787747 + 0.0902710i
\(329\) −1.78533e19 −0.130062
\(330\) 3.62084e19 + 6.86146e19i 0.257453 + 0.487871i
\(331\) 2.76309e20i 1.91766i 0.283984 + 0.958829i \(0.408344\pi\)
−0.283984 + 0.958829i \(0.591656\pi\)
\(332\) −1.61260e20 1.10244e20i −1.09250 0.746880i
\(333\) 5.63326e19 0.372568
\(334\) −9.56138e19 + 5.04561e19i −0.617375 + 0.325793i
\(335\) 1.52649e20i 0.962357i
\(336\) −3.04336e18 7.81239e18i −0.0187344 0.0480916i
\(337\) −8.73126e19 −0.524853 −0.262426 0.964952i \(-0.584523\pi\)
−0.262426 + 0.964952i \(0.584523\pi\)
\(338\) 5.04821e19 + 9.56630e19i 0.296349 + 0.561579i
\(339\) 6.10455e19i 0.349990i
\(340\) 1.32915e20 1.94421e20i 0.744289 1.08871i
\(341\) −2.84246e19 −0.155474
\(342\) −1.15654e19 + 6.10316e18i −0.0617950 + 0.0326096i
\(343\) 3.41157e19i 0.178074i
\(344\) −2.64558e19 + 2.30866e20i −0.134913 + 1.17731i
\(345\) 2.58743e20 1.28919
\(346\) −1.03698e20 1.96507e20i −0.504850 0.956686i
\(347\) 1.16347e20i 0.553505i −0.960941 0.276752i \(-0.910742\pi\)
0.960941 0.276752i \(-0.0892581\pi\)
\(348\) 1.86058e20 + 1.27197e20i 0.864996 + 0.591348i
\(349\) −9.54017e19 −0.433464 −0.216732 0.976231i \(-0.569540\pi\)
−0.216732 + 0.976231i \(0.569540\pi\)
\(350\) 9.25571e18 4.88430e18i 0.0411022 0.0216899i
\(351\) 2.67878e19i 0.116273i
\(352\) −1.38076e20 1.19585e20i −0.585835 0.507384i
\(353\) 2.98288e20 1.23719 0.618597 0.785709i \(-0.287701\pi\)
0.618597 + 0.785709i \(0.287701\pi\)
\(354\) −7.72100e19 1.46312e20i −0.313074 0.593273i
\(355\) 8.69409e19i 0.344665i
\(356\) 3.14586e19 4.60162e19i 0.121938 0.178366i
\(357\) 1.45671e19 0.0552112
\(358\) 2.08563e20 1.10060e20i 0.772989 0.407912i
\(359\) 2.93045e20i 1.06213i −0.847330 0.531067i \(-0.821791\pi\)
0.847330 0.531067i \(-0.178209\pi\)
\(360\) 1.15178e20 + 1.31987e19i 0.408273 + 0.0467855i
\(361\) 2.75768e20 0.956062
\(362\) −1.89859e20 3.59781e20i −0.643817 1.22003i
\(363\) 6.95114e19i 0.230570i
\(364\) 1.37408e19 + 9.39381e18i 0.0445864 + 0.0304811i
\(365\) 6.19402e20 1.96621
\(366\) −2.60838e20 + 1.37646e20i −0.810071 + 0.427480i
\(367\) 1.76985e20i 0.537784i 0.963170 + 0.268892i \(0.0866575\pi\)
−0.963170 + 0.268892i \(0.913343\pi\)
\(368\) −5.67643e20 + 2.21129e20i −1.68769 + 0.657450i
\(369\) −9.08467e19 −0.264301
\(370\) −2.25887e20 4.28055e20i −0.643100 1.21867i
\(371\) 4.15633e19i 0.115803i
\(372\) −2.39714e19 + 3.50643e19i −0.0653657 + 0.0956140i
\(373\) −1.79144e19 −0.0478114 −0.0239057 0.999714i \(-0.507610\pi\)
−0.0239057 + 0.999714i \(0.507610\pi\)
\(374\) 2.80680e20 1.48117e20i 0.733228 0.386929i
\(375\) 1.33643e20i 0.341740i
\(376\) −6.61718e19 + 5.77446e20i −0.165642 + 1.44547i
\(377\) −4.47441e20 −1.09649
\(378\) 3.34664e18 + 6.34186e18i 0.00802925 + 0.0152154i
\(379\) 7.62685e20i 1.79156i 0.444496 + 0.895781i \(0.353383\pi\)
−0.444496 + 0.895781i \(0.646617\pi\)
\(380\) 9.27522e19 + 6.34093e19i 0.213332 + 0.145843i
\(381\) 2.02351e20 0.455729
\(382\) 2.50225e20 1.32045e20i 0.551853 0.291217i
\(383\) 4.79376e20i 1.03535i 0.855578 + 0.517673i \(0.173202\pi\)
−0.855578 + 0.517673i \(0.826798\pi\)
\(384\) −2.63963e20 + 6.94783e19i −0.558333 + 0.146960i
\(385\) 4.12295e19 0.0854126
\(386\) 1.13081e20 + 2.14288e20i 0.229452 + 0.434809i
\(387\) 1.98743e20i 0.395006i
\(388\) 4.83065e19 7.06605e19i 0.0940484 0.137570i
\(389\) −6.78359e20 −1.29379 −0.646893 0.762581i \(-0.723932\pi\)
−0.646893 + 0.762581i \(0.723932\pi\)
\(390\) −2.03552e20 + 1.07416e20i −0.380329 + 0.200702i
\(391\) 1.05844e21i 1.93754i
\(392\) 5.49504e20 + 6.29698e19i 0.985559 + 0.112939i
\(393\) −5.62387e20 −0.988315
\(394\) 1.42047e20 + 2.69178e20i 0.244604 + 0.463522i
\(395\) 9.24138e20i 1.55941i
\(396\) 1.28967e20 + 8.81672e19i 0.213264 + 0.145796i
\(397\) −7.98038e20 −1.29330 −0.646651 0.762786i \(-0.723831\pi\)
−0.646651 + 0.762786i \(0.723831\pi\)
\(398\) −4.12489e19 + 2.17673e19i −0.0655161 + 0.0345733i
\(399\) 6.94949e18i 0.0108186i
\(400\) −1.23672e20 3.17469e20i −0.188708 0.484419i
\(401\) 2.57175e20 0.384657 0.192328 0.981331i \(-0.438396\pi\)
0.192328 + 0.981331i \(0.438396\pi\)
\(402\) −1.43459e20 2.71853e20i −0.210338 0.398589i
\(403\) 8.43243e19i 0.121203i
\(404\) −4.01589e20 + 5.87425e20i −0.565888 + 0.827755i
\(405\) −9.91521e19 −0.136981
\(406\) 1.05929e20 5.58996e19i 0.143485 0.0757183i
\(407\) 6.52213e20i 0.866232i
\(408\) 5.39917e19 4.71157e20i 0.0703146 0.613598i
\(409\) 6.00294e20 0.766616 0.383308 0.923621i \(-0.374785\pi\)
0.383308 + 0.923621i \(0.374785\pi\)
\(410\) 3.64285e20 + 6.90317e20i 0.456216 + 0.864526i
\(411\) 6.05840e17i 0.000744087i
\(412\) −9.67501e19 6.61424e19i −0.116540 0.0796714i
\(413\) −8.79168e19 −0.103866
\(414\) 4.60795e20 2.43165e20i 0.533956 0.281772i
\(415\) 1.43542e21i 1.63153i
\(416\) 3.54762e20 4.09615e20i 0.395540 0.456698i
\(417\) 4.88404e19 0.0534184
\(418\) 7.06618e19 + 1.33904e20i 0.0758184 + 0.143675i
\(419\) 4.24662e20i 0.447025i 0.974701 + 0.223512i \(0.0717523\pi\)
−0.974701 + 0.223512i \(0.928248\pi\)
\(420\) 3.47702e19 5.08603e19i 0.0359098 0.0525272i
\(421\) −4.73419e20 −0.479721 −0.239861 0.970807i \(-0.577102\pi\)
−0.239861 + 0.970807i \(0.577102\pi\)
\(422\) 4.55283e20 2.40256e20i 0.452670 0.238877i
\(423\) 4.97099e20i 0.484976i
\(424\) 1.34432e21 + 1.54051e20i 1.28699 + 0.147481i
\(425\) 5.91957e20 0.556133
\(426\) 8.17064e19 + 1.54833e20i 0.0753320 + 0.142753i
\(427\) 1.56734e20i 0.141821i
\(428\) 6.88282e20 + 4.70539e20i 0.611247 + 0.417874i
\(429\) −3.10146e20 −0.270339
\(430\) −1.51019e21 + 7.96936e20i −1.29206 + 0.681829i
\(431\) 1.74966e21i 1.46938i −0.678401 0.734692i \(-0.737327\pi\)
0.678401 0.734692i \(-0.262673\pi\)
\(432\) 2.17525e20 8.47380e19i 0.179324 0.0698567i
\(433\) −2.61610e20 −0.211715 −0.105857 0.994381i \(-0.533759\pi\)
−0.105857 + 0.994381i \(0.533759\pi\)
\(434\) 1.05348e19 + 1.99633e19i 0.00836966 + 0.0158604i
\(435\) 1.65616e21i 1.29178i
\(436\) −4.35578e20 + 6.37144e20i −0.333560 + 0.487917i
\(437\) 5.04946e20 0.379658
\(438\) 1.10309e21 5.82109e20i 0.814364 0.429745i
\(439\) 1.05652e20i 0.0765882i −0.999267 0.0382941i \(-0.987808\pi\)
0.999267 0.0382941i \(-0.0121924\pi\)
\(440\) 1.52813e20 1.33352e21i 0.108778 0.949246i
\(441\) −4.73046e20 −0.330670
\(442\) 4.39404e20 + 8.32666e20i 0.301638 + 0.571601i
\(443\) 1.41940e21i 0.956915i 0.878111 + 0.478458i \(0.158804\pi\)
−0.878111 + 0.478458i \(0.841196\pi\)
\(444\) −8.04565e20 5.50034e20i −0.532718 0.364188i
\(445\) 4.09605e20 0.266370
\(446\) −4.60520e20 + 2.43020e20i −0.294151 + 0.155225i
\(447\) 6.36194e20i 0.399144i
\(448\) −3.28140e19 + 1.41295e20i −0.0202225 + 0.0870770i
\(449\) −1.56836e21 −0.949459 −0.474729 0.880132i \(-0.657454\pi\)
−0.474729 + 0.880132i \(0.657454\pi\)
\(450\) 1.35996e20 + 2.57712e20i 0.0808773 + 0.153262i
\(451\) 1.05182e21i 0.614507i
\(452\) 5.96051e20 8.71876e20i 0.342118 0.500435i
\(453\) 1.67874e21 0.946668
\(454\) −1.88280e21 + 9.93568e20i −1.04318 + 0.550492i
\(455\) 1.22311e20i 0.0665849i
\(456\) 2.24774e20 + 2.57577e19i 0.120234 + 0.0137781i
\(457\) 2.87857e21 1.51303 0.756514 0.653977i \(-0.226901\pi\)
0.756514 + 0.653977i \(0.226901\pi\)
\(458\) −8.59615e20 1.62896e21i −0.443997 0.841371i
\(459\) 4.05599e20i 0.205871i
\(460\) −3.69548e21 2.52638e21i −1.84335 1.26019i
\(461\) 3.00691e20 0.147405 0.0737027 0.997280i \(-0.476518\pi\)
0.0737027 + 0.997280i \(0.476518\pi\)
\(462\) 7.34254e19 3.87471e19i 0.0353762 0.0186682i
\(463\) 3.71205e21i 1.75779i −0.477019 0.878893i \(-0.658283\pi\)
0.477019 0.878893i \(-0.341717\pi\)
\(464\) −1.41540e21 3.63336e21i −0.658770 1.69108i
\(465\) −3.12118e20 −0.142789
\(466\) 9.28278e20 + 1.75908e21i 0.417437 + 0.791039i
\(467\) 3.36056e21i 1.48551i 0.669562 + 0.742756i \(0.266482\pi\)
−0.669562 + 0.742756i \(0.733518\pi\)
\(468\) −2.61557e20 + 3.82593e20i −0.113658 + 0.166253i
\(469\) −1.63352e20 −0.0697818
\(470\) −3.77731e21 + 1.99331e21i −1.58635 + 0.837130i
\(471\) 6.50319e20i 0.268509i
\(472\) −3.25856e20 + 2.84357e21i −0.132279 + 1.15433i
\(473\) −2.30102e21 −0.918400
\(474\) 8.68498e20 + 1.64580e21i 0.340833 + 0.645876i
\(475\) 2.82404e20i 0.108974i
\(476\) −2.08053e20 1.42234e20i −0.0789439 0.0539693i
\(477\) −1.15727e21 −0.431805
\(478\) 2.57442e21 1.35854e21i 0.944618 0.498481i
\(479\) 3.81556e20i 0.137681i 0.997628 + 0.0688405i \(0.0219300\pi\)
−0.997628 + 0.0688405i \(0.978070\pi\)
\(480\) −1.51615e21 1.31311e21i −0.538036 0.465986i
\(481\) 1.93486e21 0.675287
\(482\) −6.24015e20 1.18250e21i −0.214200 0.405907i
\(483\) 2.76885e20i 0.0934807i
\(484\) −6.78713e20 + 9.92790e20i −0.225384 + 0.329681i
\(485\) 6.28970e20 0.205445
\(486\) −1.76580e20 + 9.31824e19i −0.0567350 + 0.0299394i
\(487\) 2.20764e21i 0.697746i 0.937170 + 0.348873i \(0.113435\pi\)
−0.937170 + 0.348873i \(0.886565\pi\)
\(488\) 5.06938e21 + 5.80920e20i 1.57615 + 0.180617i
\(489\) 9.93466e20 0.303866
\(490\) 1.89686e21 + 3.59453e21i 0.570777 + 1.08162i
\(491\) 4.03031e21i 1.19313i −0.802567 0.596563i \(-0.796533\pi\)
0.802567 0.596563i \(-0.203467\pi\)
\(492\) 1.29751e21 + 8.87032e20i 0.377911 + 0.258356i
\(493\) 6.77481e21 1.94143
\(494\) −3.97238e20 + 2.09626e20i −0.112005 + 0.0591056i
\(495\) 1.14797e21i 0.318486i
\(496\) 6.84739e20 2.66744e20i 0.186927 0.0728184i
\(497\) 9.30367e19 0.0249921
\(498\) −1.34900e21 2.55634e21i −0.356597 0.675747i
\(499\) 1.41774e20i 0.0368801i 0.999830 + 0.0184400i \(0.00586998\pi\)
−0.999830 + 0.0184400i \(0.994130\pi\)
\(500\) −1.30489e21 + 1.90874e21i −0.334053 + 0.488637i
\(501\) −1.59969e21 −0.403027
\(502\) 4.49059e21 2.36971e21i 1.11346 0.587579i
\(503\) 3.80963e21i 0.929692i −0.885392 0.464846i \(-0.846110\pi\)
0.885392 0.464846i \(-0.153890\pi\)
\(504\) 1.41241e19 1.23254e20i 0.00339248 0.0296044i
\(505\) −5.22885e21 −1.23616
\(506\) −2.81534e21 5.33504e21i −0.655129 1.24146i
\(507\) 1.60051e21i 0.366603i
\(508\) −2.89006e21 1.97577e21i −0.651625 0.445478i
\(509\) −1.24890e21 −0.277196 −0.138598 0.990349i \(-0.544260\pi\)
−0.138598 + 0.990349i \(0.544260\pi\)
\(510\) 3.08203e21 1.62641e21i 0.673403 0.355360i
\(511\) 6.62830e20i 0.142572i
\(512\) 4.44842e21 + 1.58503e21i 0.941989 + 0.335644i
\(513\) −1.93498e20 −0.0403403
\(514\) −3.12722e21 5.92606e21i −0.641880 1.21636i
\(515\) 8.61202e20i 0.174039i
\(516\) −1.94053e21 + 2.83852e21i −0.386121 + 0.564800i
\(517\) −5.75537e21 −1.12758
\(518\) −4.58067e20 + 2.41725e20i −0.0883672 + 0.0466320i
\(519\) 3.28771e21i 0.624532i
\(520\) 3.95603e21 + 4.53337e20i 0.740002 + 0.0847996i
\(521\) 6.64621e21 1.22426 0.612128 0.790759i \(-0.290314\pi\)
0.612128 + 0.790759i \(0.290314\pi\)
\(522\) 1.55644e21 + 2.94945e21i 0.282338 + 0.535028i
\(523\) 4.92052e21i 0.879017i −0.898238 0.439509i \(-0.855153\pi\)
0.898238 0.439509i \(-0.144847\pi\)
\(524\) 8.03224e21 + 5.49118e21i 1.41314 + 0.966085i
\(525\) 1.54855e20 0.0268319
\(526\) 1.97593e21 1.04271e21i 0.337199 0.177942i
\(527\) 1.27677e21i 0.214600i
\(528\) −9.81088e20 2.51848e21i −0.162419 0.416934i
\(529\) −1.39857e22 −2.28054
\(530\) 4.64053e21 + 8.79376e21i 0.745350 + 1.41243i
\(531\) 2.44791e21i 0.387293i
\(532\) 6.78552e19 9.92554e19i 0.0105752 0.0154690i
\(533\) −3.12032e21 −0.479050
\(534\) 7.29464e20 3.84943e20i 0.110325 0.0582192i
\(535\) 6.12661e21i 0.912830i
\(536\) −6.05451e20 + 5.28345e21i −0.0888711 + 0.775531i
\(537\) 3.48942e21 0.504614
\(538\) −1.60525e20 3.04193e20i −0.0228709 0.0433402i
\(539\) 5.47688e21i 0.768817i
\(540\) 1.41613e21 + 9.68126e20i 0.195863 + 0.133900i
\(541\) −6.02561e20 −0.0821150 −0.0410575 0.999157i \(-0.513073\pi\)
−0.0410575 + 0.999157i \(0.513073\pi\)
\(542\) −1.07233e22 + 5.65875e21i −1.43990 + 0.759847i
\(543\) 6.01941e21i 0.796444i
\(544\) −5.37153e21 + 6.20207e21i −0.700336 + 0.808622i
\(545\) −5.67141e21 −0.728651
\(546\) 1.14947e20 + 2.17824e20i 0.0145532 + 0.0275781i
\(547\) 9.62662e21i 1.20109i 0.799591 + 0.600545i \(0.205049\pi\)
−0.799591 + 0.600545i \(0.794951\pi\)
\(548\) −5.91546e18 + 8.65285e18i −0.000727350 + 0.00106393i
\(549\) −4.36402e21 −0.528821
\(550\) 2.98376e21 1.57455e21i 0.356338 0.188042i
\(551\) 3.23204e21i 0.380421i
\(552\) −8.95554e21 1.02625e21i −1.03891 0.119053i
\(553\) 9.88933e20 0.113075
\(554\) −4.36648e21 8.27444e21i −0.492100 0.932525i
\(555\) 7.16168e21i 0.795556i
\(556\) −6.97559e20 4.76881e20i −0.0763805 0.0522169i
\(557\) 8.71078e21 0.940190 0.470095 0.882616i \(-0.344220\pi\)
0.470095 + 0.882616i \(0.344220\pi\)
\(558\) −5.55850e20 + 2.93326e20i −0.0591403 + 0.0312088i
\(559\) 6.82622e21i 0.715955i
\(560\) −9.93205e20 + 3.86909e20i −0.102692 + 0.0400041i
\(561\) 4.69599e21 0.478657
\(562\) −6.38425e21 1.20981e22i −0.641534 1.21570i
\(563\) 5.56357e21i 0.551171i 0.961277 + 0.275585i \(0.0888717\pi\)
−0.961277 + 0.275585i \(0.911128\pi\)
\(564\) −4.85370e21 + 7.09977e21i −0.474068 + 0.693444i
\(565\) 7.76084e21 0.747345
\(566\) 1.55962e22 8.23020e21i 1.48076 0.781410i
\(567\) 1.06104e20i 0.00993270i
\(568\) 3.44833e20 3.00917e21i 0.0318289 0.277754i
\(569\) 7.52487e21 0.684859 0.342429 0.939544i \(-0.388750\pi\)
0.342429 + 0.939544i \(0.388750\pi\)
\(570\) 7.75907e20 + 1.47034e21i 0.0696323 + 0.131953i
\(571\) 8.32216e21i 0.736456i 0.929735 + 0.368228i \(0.120035\pi\)
−0.929735 + 0.368228i \(0.879965\pi\)
\(572\) 4.42963e21 + 3.02828e21i 0.386544 + 0.264258i
\(573\) 4.18645e21 0.360254
\(574\) 7.38718e20 3.89827e20i 0.0626879 0.0330808i
\(575\) 1.12517e22i 0.941616i
\(576\) −3.93416e21 9.13659e20i −0.324692 0.0754057i
\(577\) 2.34802e21 0.191115 0.0955577 0.995424i \(-0.469537\pi\)
0.0955577 + 0.995424i \(0.469537\pi\)
\(578\) −8.39186e20 1.59025e21i −0.0673652 0.127656i
\(579\) 3.58519e21i 0.283847i
\(580\) 1.61708e22 2.36539e22i 1.26272 1.84705i
\(581\) −1.53607e21 −0.118304
\(582\) 1.12013e21 5.91101e20i 0.0850913 0.0449033i
\(583\) 1.33988e22i 1.00396i
\(584\) −2.14385e22 2.45672e21i −1.58450 0.181574i
\(585\) −3.40558e21 −0.248282
\(586\) −2.60516e21 4.93676e21i −0.187350 0.355027i
\(587\) 1.45286e22i 1.03067i −0.856989 0.515335i \(-0.827667\pi\)
0.856989 0.515335i \(-0.172333\pi\)
\(588\) 6.75623e21 + 4.61884e21i 0.472809 + 0.323232i
\(589\) −6.09108e20 −0.0420506
\(590\) −1.86010e22 + 9.81587e21i −1.26683 + 0.668517i
\(591\) 4.50356e21i 0.302591i
\(592\) 6.12055e21 + 1.57116e22i 0.405711 + 1.04147i
\(593\) 1.96426e22 1.28458 0.642289 0.766462i \(-0.277985\pi\)
0.642289 + 0.766462i \(0.277985\pi\)
\(594\) 1.07886e21 + 2.04442e21i 0.0696101 + 0.131911i
\(595\) 1.85194e21i 0.117894i
\(596\) 6.21183e21 9.08638e21i 0.390166 0.570717i
\(597\) −6.90126e20 −0.0427694
\(598\) 1.58270e22 8.35199e21i 0.967805 0.510717i
\(599\) 9.81500e21i 0.592210i 0.955155 + 0.296105i \(0.0956878\pi\)
−0.955155 + 0.296105i \(0.904312\pi\)
\(600\) 5.73957e20 5.00862e21i 0.0341719 0.298200i
\(601\) 2.43315e22 1.42947 0.714733 0.699397i \(-0.246548\pi\)
0.714733 + 0.699397i \(0.246548\pi\)
\(602\) 8.52812e20 + 1.61607e21i 0.0494403 + 0.0936890i
\(603\) 4.54830e21i 0.260202i
\(604\) −2.39764e22 1.63913e22i −1.35360 0.925375i
\(605\) −8.83713e21 −0.492343
\(606\) −9.31205e21 + 4.91404e21i −0.511993 + 0.270183i
\(607\) 8.50789e21i 0.461650i 0.972995 + 0.230825i \(0.0741424\pi\)
−0.972995 + 0.230825i \(0.925858\pi\)
\(608\) −2.95881e21 2.56258e21i −0.158449 0.137230i
\(609\) 1.77228e21 0.0936685
\(610\) 1.74992e22 + 3.31609e22i 0.912811 + 1.72977i
\(611\) 1.70739e22i 0.879028i
\(612\) 3.96029e21 5.79293e21i 0.201241 0.294366i
\(613\) −1.83326e21 −0.0919476 −0.0459738 0.998943i \(-0.514639\pi\)
−0.0459738 + 0.998943i \(0.514639\pi\)
\(614\) −2.18284e22 + 1.15190e22i −1.08063 + 0.570253i
\(615\) 1.15495e22i 0.564369i
\(616\) −1.42702e21 1.63528e20i −0.0688311 0.00788762i
\(617\) −1.27024e22 −0.604789 −0.302394 0.953183i \(-0.597786\pi\)
−0.302394 + 0.953183i \(0.597786\pi\)
\(618\) −8.09351e20 1.53371e21i −0.0380390 0.0720836i
\(619\) 2.22936e22i 1.03432i 0.855889 + 0.517160i \(0.173011\pi\)
−0.855889 + 0.517160i \(0.826989\pi\)
\(620\) 4.45779e21 + 3.04753e21i 0.204167 + 0.139577i
\(621\) 7.70945e21 0.348571
\(622\) −3.25754e22 + 1.71903e22i −1.45401 + 0.767291i
\(623\) 4.38324e20i 0.0193148i
\(624\) 7.47132e21 2.91050e21i 0.325028 0.126617i
\(625\) −2.90946e22 −1.24960
\(626\) 5.83644e21 + 1.10600e22i 0.247488 + 0.468987i
\(627\) 2.24031e21i 0.0937923i
\(628\) 6.34974e21 9.28811e21i 0.262470 0.383928i
\(629\) −2.92961e22 −1.19565
\(630\) 8.06253e20 4.25465e20i 0.0324898 0.0171451i
\(631\) 3.06104e22i 1.21796i −0.793185 0.608981i \(-0.791578\pi\)
0.793185 0.608981i \(-0.208422\pi\)
\(632\) 3.66540e21 3.19860e22i 0.144007 1.25667i
\(633\) 7.61723e21 0.295507
\(634\) 4.21983e21 + 7.99653e21i 0.161652 + 0.306329i
\(635\) 2.57253e22i 0.973131i
\(636\) 1.65286e22 + 1.12996e22i 0.617418 + 0.422093i
\(637\) −1.62477e22 −0.599345
\(638\) 3.41484e22 1.80204e22i 1.24396 0.656445i
\(639\) 2.59047e21i 0.0931906i
\(640\) 8.83292e21 + 3.35582e22i 0.313808 + 1.19223i
\(641\) −2.86248e22 −1.00433 −0.502167 0.864771i \(-0.667464\pi\)
−0.502167 + 0.864771i \(0.667464\pi\)
\(642\) 5.75774e21 + 1.09109e22i 0.199513 + 0.378076i
\(643\) 5.10567e22i 1.74729i −0.486563 0.873646i \(-0.661749\pi\)
0.486563 0.873646i \(-0.338251\pi\)
\(644\) −2.70352e21 + 3.95458e21i −0.0913781 + 0.133664i
\(645\) −2.52666e22 −0.843467
\(646\) 6.01468e21 3.17399e21i 0.198313 0.104651i
\(647\) 3.44255e22i 1.12111i 0.828119 + 0.560553i \(0.189411\pi\)
−0.828119 + 0.560553i \(0.810589\pi\)
\(648\) 3.43182e21 + 3.93266e20i 0.110389 + 0.0126499i
\(649\) −2.83417e22 −0.900469
\(650\) 4.67107e21 + 8.85163e21i 0.146592 + 0.277790i
\(651\) 3.34002e20i 0.0103538i
\(652\) −1.41891e22 9.70025e21i −0.434484 0.297031i
\(653\) 1.62027e22 0.490097 0.245049 0.969511i \(-0.421196\pi\)
0.245049 + 0.969511i \(0.421196\pi\)
\(654\) −1.01002e22 + 5.32995e21i −0.301792 + 0.159258i
\(655\) 7.14975e22i 2.11038i
\(656\) −9.87053e21 2.53379e22i −0.287812 0.738822i
\(657\) 1.84555e22 0.531623
\(658\) 2.13307e21 + 4.04215e21i 0.0607014 + 0.115029i
\(659\) 4.22721e21i 0.118842i 0.998233 + 0.0594210i \(0.0189254\pi\)
−0.998233 + 0.0594210i \(0.981075\pi\)
\(660\) 1.12089e22 1.63958e22i 0.311323 0.455388i
\(661\) 2.30284e22 0.631906 0.315953 0.948775i \(-0.397676\pi\)
0.315953 + 0.948775i \(0.397676\pi\)
\(662\) 6.25589e22 3.30128e22i 1.69600 0.894990i
\(663\) 1.39311e22i 0.373146i
\(664\) −5.69330e21 + 4.96824e22i −0.150667 + 1.31480i
\(665\) 8.83503e20 0.0231012
\(666\) −6.73049e21 1.27542e22i −0.173881 0.329503i
\(667\) 1.28773e23i 3.28713i
\(668\) 2.28474e22 + 1.56195e22i 0.576269 + 0.393962i
\(669\) −7.70485e21 −0.192024
\(670\) −3.45612e22 + 1.82382e22i −0.851119 + 0.449141i
\(671\) 5.05263e22i 1.22952i
\(672\) −1.40518e21 + 1.62245e21i −0.0337892 + 0.0390137i
\(673\) 7.63006e22 1.81304 0.906520 0.422163i \(-0.138729\pi\)
0.906520 + 0.422163i \(0.138729\pi\)
\(674\) 1.04319e22 + 1.97684e22i 0.244954 + 0.464186i
\(675\) 4.31171e21i 0.100051i
\(676\) 1.56275e22 2.28592e22i 0.358357 0.524188i
\(677\) 3.76411e22 0.853008 0.426504 0.904486i \(-0.359745\pi\)
0.426504 + 0.904486i \(0.359745\pi\)
\(678\) 1.38213e22 7.29357e21i 0.309535 0.163344i
\(679\) 6.73070e20i 0.0148971i
\(680\) −5.98991e22 6.86407e21i −1.31023 0.150145i
\(681\) −3.15007e22 −0.680994
\(682\) 3.39610e21 + 6.43558e21i 0.0725614 + 0.137503i
\(683\) 6.54593e21i 0.138231i −0.997609 0.0691155i \(-0.977982\pi\)
0.997609 0.0691155i \(-0.0220177\pi\)
\(684\) 2.76362e21 + 1.88933e21i 0.0576806 + 0.0394329i
\(685\) −7.70217e19 −0.00158887
\(686\) 7.72410e21 4.07606e21i 0.157491 0.0831090i
\(687\) 2.72538e22i 0.549253i
\(688\) 5.54309e22 2.15934e22i 1.10419 0.430145i
\(689\) −3.97488e22 −0.782655
\(690\) −3.09140e22 5.85818e22i −0.601677 1.14017i
\(691\) 1.66502e22i 0.320328i −0.987090 0.160164i \(-0.948798\pi\)
0.987090 0.160164i \(-0.0512024\pi\)
\(692\) −3.21014e22 + 4.69564e22i −0.610485 + 0.892989i
\(693\) 1.22846e21 0.0230938
\(694\) −2.63421e22 + 1.39009e22i −0.489525 + 0.258326i
\(695\) 6.20918e21i 0.114066i
\(696\) 6.56879e21 5.73224e22i 0.119292 1.04100i
\(697\) 4.72454e22 0.848198
\(698\) 1.13984e22 + 2.15998e22i 0.202302 + 0.383360i
\(699\) 2.94307e22i 0.516396i
\(700\) −2.21170e21 1.51201e21i −0.0383656 0.0262283i
\(701\) 4.07553e22 0.698939 0.349470 0.936948i \(-0.386362\pi\)
0.349470 + 0.936948i \(0.386362\pi\)
\(702\) −6.06499e21 + 3.20054e21i −0.102833 + 0.0542658i
\(703\) 1.39762e22i 0.234287i
\(704\) −1.05783e22 + 4.55493e22i −0.175321 + 0.754919i
\(705\) −6.31973e22 −1.03558
\(706\) −3.56387e22 6.75350e22i −0.577410 1.09419i
\(707\) 5.59547e21i 0.0896357i
\(708\) −2.39016e22 + 3.49621e22i −0.378582 + 0.553773i
\(709\) 2.58315e21 0.0404558 0.0202279 0.999795i \(-0.493561\pi\)
0.0202279 + 0.999795i \(0.493561\pi\)
\(710\) 1.96842e22 1.03875e22i 0.304826 0.160859i
\(711\) 2.75354e22i 0.421633i
\(712\) −1.41771e22 1.62461e21i −0.214658 0.0245985i
\(713\) 2.42683e22 0.363349
\(714\) −1.74044e21 3.29812e21i −0.0257676 0.0488294i
\(715\) 3.94295e22i 0.577262i
\(716\) −4.98373e22 3.40709e22i −0.721523 0.493263i
\(717\) 4.30720e22 0.616654
\(718\) −6.63481e22 + 3.50124e22i −0.939362 + 0.495708i
\(719\) 1.13920e23i 1.59503i 0.603299 + 0.797515i \(0.293853\pi\)
−0.603299 + 0.797515i \(0.706147\pi\)
\(720\) −1.07729e22 2.76543e22i −0.149167 0.382916i
\(721\) −9.21584e20 −0.0126198
\(722\) −3.29481e22 6.24364e22i −0.446203 0.845551i
\(723\) 1.97842e22i 0.264979i
\(724\) −5.87738e22 + 8.59716e22i −0.778530 + 1.13880i
\(725\) 7.20194e22 0.943507
\(726\) −1.57380e22 + 8.30506e21i −0.203919 + 0.107609i
\(727\) 1.06494e22i 0.136474i 0.997669 + 0.0682370i \(0.0217374\pi\)
−0.997669 + 0.0682370i \(0.978263\pi\)
\(728\) 4.85122e20 4.23340e21i 0.00614893 0.0536585i
\(729\) −2.95431e21 −0.0370370
\(730\) −7.40047e22 1.40238e23i −0.917648 1.73894i
\(731\) 1.03357e23i 1.26766i
\(732\) 6.23287e22 + 4.26105e22i 0.756136 + 0.516926i
\(733\) −9.85179e22 −1.18218 −0.591089 0.806606i \(-0.701302\pi\)
−0.591089 + 0.806606i \(0.701302\pi\)
\(734\) 4.00710e22 2.11458e22i 0.475622 0.250989i
\(735\) 6.01392e22i 0.706089i
\(736\) 1.17886e23 + 1.02100e23i 1.36912 + 1.18577i
\(737\) −5.26598e22 −0.604978
\(738\) 1.08542e22 + 2.05685e22i 0.123352 + 0.233750i
\(739\) 2.62544e22i 0.295152i 0.989051 + 0.147576i \(0.0471472\pi\)
−0.989051 + 0.147576i \(0.952853\pi\)
\(740\) −6.99270e22 + 1.02286e23i −0.777662 + 1.13753i
\(741\) −6.64610e21 −0.0731175
\(742\) 9.41032e21 4.96589e21i 0.102417 0.0540463i
\(743\) 6.77760e22i 0.729736i −0.931059 0.364868i \(-0.881114\pi\)
0.931059 0.364868i \(-0.118886\pi\)
\(744\) 1.08029e22 + 1.23795e21i 0.115069 + 0.0131862i
\(745\) 8.08807e22 0.852304
\(746\) 2.14037e21 + 4.05598e21i 0.0223140 + 0.0422849i
\(747\) 4.27696e22i 0.441133i
\(748\) −6.70700e22 4.58519e22i −0.684409 0.467891i
\(749\) 6.55617e21 0.0661905
\(750\) −3.02579e22 + 1.59673e22i −0.302238 + 0.159493i
\(751\) 3.55558e22i 0.351391i −0.984445 0.175696i \(-0.943783\pi\)
0.984445 0.175696i \(-0.0562175\pi\)
\(752\) 1.38645e23 5.40100e22i 1.35569 0.528119i
\(753\) 7.51309e22 0.726873
\(754\) 5.34592e22 + 1.01305e23i 0.511743 + 0.969749i
\(755\) 2.13422e23i 2.02145i
\(756\) 1.03601e21 1.51542e21i 0.00970929 0.0142023i
\(757\) −6.10956e22 −0.566556 −0.283278 0.959038i \(-0.591422\pi\)
−0.283278 + 0.959038i \(0.591422\pi\)
\(758\) 1.72679e23 9.11239e22i 1.58448 0.836139i
\(759\) 8.92593e22i 0.810437i
\(760\) 3.27463e21 2.85759e22i 0.0294207 0.256739i
\(761\) −7.31694e22 −0.650508 −0.325254 0.945627i \(-0.605450\pi\)
−0.325254 + 0.945627i \(0.605450\pi\)
\(762\) −2.41765e22 4.58142e22i −0.212693 0.403051i
\(763\) 6.06906e21i 0.0528354i
\(764\) −5.97925e22 4.08767e22i −0.515110 0.352151i
\(765\) 5.15647e22 0.439603
\(766\) 1.08535e23 5.72747e22i 0.915672 0.483206i
\(767\) 8.40786e22i 0.701977i
\(768\) 4.72682e22 + 5.14626e22i 0.390553 + 0.425208i
\(769\) −5.63191e22 −0.460516 −0.230258 0.973130i \(-0.573957\pi\)
−0.230258 + 0.973130i \(0.573957\pi\)
\(770\) −4.92600e21 9.33472e21i −0.0398629 0.0755398i
\(771\) 9.91474e22i 0.794047i
\(772\) 3.50060e22 5.12052e22i 0.277463 0.405859i
\(773\) −1.23390e23 −0.967934 −0.483967 0.875086i \(-0.660804\pi\)
−0.483967 + 0.875086i \(0.660804\pi\)
\(774\) −4.49971e22 + 2.37453e22i −0.349347 + 0.184353i
\(775\) 1.35727e22i 0.104292i
\(776\) −2.17697e22 2.49468e21i −0.165561 0.0189723i
\(777\) −7.66381e21 −0.0576868
\(778\) 8.10487e22 + 1.53587e23i 0.603823 + 1.14424i
\(779\) 2.25393e22i 0.166204i
\(780\) 4.86399e22 + 3.32523e22i 0.355006 + 0.242697i
\(781\) 2.99922e22 0.216671
\(782\) −2.39639e23 + 1.26459e23i −1.71358 + 0.904268i
\(783\) 4.93465e22i 0.349271i
\(784\) −5.13965e22 1.31936e23i −0.360085 0.924348i
\(785\) 8.26763e22 0.573355
\(786\) 6.71927e22 + 1.27330e23i 0.461256 + 0.874076i
\(787\) 4.32717e22i 0.294039i 0.989134 + 0.147020i \(0.0469681\pi\)
−0.989134 + 0.147020i \(0.953032\pi\)
\(788\) 4.39730e22 6.43216e22i 0.295785 0.432660i
\(789\) 3.30589e22 0.220126
\(790\) 2.09233e23 1.10414e23i 1.37916 0.727792i
\(791\) 8.30498e21i 0.0541909i
\(792\) 4.55319e21 3.97333e22i 0.0294113 0.256657i
\(793\) −1.49891e23 −0.958497
\(794\) 9.53478e22 + 1.80683e23i 0.603596 + 1.14381i
\(795\) 1.47126e23i 0.922047i
\(796\) 9.85665e21 + 6.73842e21i 0.0611540 + 0.0418074i
\(797\) 1.00831e23 0.619336 0.309668 0.950845i \(-0.399782\pi\)
0.309668 + 0.950845i \(0.399782\pi\)
\(798\) 1.57343e21 8.30309e20i 0.00956806 0.00504913i
\(799\) 2.58520e23i 1.55639i
\(800\) −5.71019e22 + 6.59309e22i −0.340354 + 0.392979i
\(801\) 1.22045e22 0.0720210
\(802\) −3.07266e22 5.82267e22i −0.179523 0.340194i
\(803\) 2.13677e23i 1.23604i
\(804\) −4.44098e22 + 6.49607e22i −0.254349 + 0.372051i
\(805\) −3.52009e22 −0.199612
\(806\) −1.90918e22 + 1.00749e22i −0.107193 + 0.0565665i
\(807\) 5.08937e21i 0.0282928i
\(808\) 1.80979e23 + 2.07391e22i 0.996181 + 0.114156i
\(809\) −2.78402e23 −1.51735 −0.758673 0.651472i \(-0.774152\pi\)
−0.758673 + 0.651472i \(0.774152\pi\)
\(810\) 1.18465e22 + 2.24489e22i 0.0639306 + 0.121148i
\(811\) 1.53217e23i 0.818731i 0.912371 + 0.409365i \(0.134250\pi\)
−0.912371 + 0.409365i \(0.865750\pi\)
\(812\) −2.53124e22 1.73046e22i −0.133932 0.0915616i
\(813\) −1.79409e23 −0.939980
\(814\) −1.47667e23 + 7.79249e22i −0.766105 + 0.404279i
\(815\) 1.26301e23i 0.648854i
\(816\) −1.13125e23 + 4.40685e22i −0.575489 + 0.224185i
\(817\) −4.93085e22 −0.248396
\(818\) −7.17218e22 1.35912e23i −0.357787 0.678003i
\(819\) 3.64436e21i 0.0180032i
\(820\) 1.12770e23 1.64955e23i 0.551675 0.806965i
\(821\) −6.35989e22 −0.308109 −0.154054 0.988062i \(-0.549233\pi\)
−0.154054 + 0.988062i \(0.549233\pi\)
\(822\) −1.37168e20 + 7.23844e19i −0.000658078 + 0.000347273i
\(823\) 1.19757e22i 0.0568985i 0.999595 + 0.0284492i \(0.00905689\pi\)
−0.999595 + 0.0284492i \(0.990943\pi\)
\(824\) −3.41577e21 + 2.98076e22i −0.0160721 + 0.140252i
\(825\) 4.99206e22 0.232621
\(826\) 1.05041e22 + 1.99052e22i 0.0484750 + 0.0918598i
\(827\) 4.37654e22i 0.200026i −0.994986 0.100013i \(-0.968112\pi\)
0.994986 0.100013i \(-0.0318885\pi\)
\(828\) −1.10109e23 7.52755e22i −0.498405 0.340730i
\(829\) −1.65734e23 −0.742976 −0.371488 0.928438i \(-0.621152\pi\)
−0.371488 + 0.928438i \(0.621152\pi\)
\(830\) −3.24993e23 + 1.71501e23i −1.44294 + 0.761452i
\(831\) 1.38438e23i 0.608760i
\(832\) −1.35127e23 3.13815e22i −0.588511 0.136674i
\(833\) 2.46010e23 1.06119
\(834\) −5.83534e21 1.10579e22i −0.0249309 0.0472438i
\(835\) 2.03372e23i 0.860596i
\(836\) 2.18745e22 3.19970e22i 0.0916827 0.134109i
\(837\) −9.29979e21 −0.0386073
\(838\) 9.61474e22 5.07377e22i 0.395353 0.208631i
\(839\) 4.56435e22i 0.185902i −0.995671 0.0929509i \(-0.970370\pi\)
0.995671 0.0929509i \(-0.0296300\pi\)
\(840\) −1.56695e22 1.79563e21i −0.0632151 0.00724406i
\(841\) 5.73998e23 2.29373
\(842\) 5.65630e22 + 1.07186e23i 0.223890 + 0.424270i
\(843\) 2.02410e23i 0.793619i
\(844\) −1.08792e23 7.43750e22i −0.422531 0.288860i
\(845\) 2.03477e23 0.782818
\(846\) −1.12548e23 + 5.93923e22i −0.428918 + 0.226343i
\(847\) 9.45673e21i 0.0357005i
\(848\) −1.25738e23 3.22772e23i −0.470218 1.20706i
\(849\) 2.60935e23 0.966655
\(850\) −7.07257e22 1.34025e23i −0.259553 0.491850i
\(851\) 5.56847e23i 2.02442i
\(852\) 2.52935e22 3.69981e22i 0.0910945 0.133249i
\(853\) 2.70000e23 0.963322 0.481661 0.876358i \(-0.340034\pi\)
0.481661 + 0.876358i \(0.340034\pi\)
\(854\) 3.54860e22 1.87262e22i 0.125428 0.0661891i
\(855\) 2.45999e22i 0.0861397i
\(856\) 2.42999e22 2.12052e23i 0.0842974 0.735619i
\(857\) 1.22894e23 0.422361 0.211180 0.977447i \(-0.432269\pi\)
0.211180 + 0.977447i \(0.432269\pi\)
\(858\) 3.70555e22 + 7.02199e22i 0.126170 + 0.239090i
\(859\) 3.65955e23i 1.23448i −0.786776 0.617238i \(-0.788252\pi\)
0.786776 0.617238i \(-0.211748\pi\)
\(860\) 3.60867e23 + 2.46704e23i 1.20603 + 0.824496i
\(861\) 1.23593e22 0.0409232
\(862\) −3.96139e23 + 2.09045e23i −1.29954 + 0.685776i
\(863\) 3.30833e23i 1.07528i 0.843174 + 0.537641i \(0.180684\pi\)
−0.843174 + 0.537641i \(0.819316\pi\)
\(864\) −4.51748e22 3.91252e22i −0.145474 0.125993i
\(865\) −4.17973e23 −1.33358
\(866\) 3.12566e22 + 5.92309e22i 0.0988094 + 0.187243i
\(867\) 2.66061e22i 0.0833351i
\(868\) 3.26121e21 4.77034e21i 0.0101209 0.0148044i
\(869\) 3.18802e23 0.980310
\(870\) 3.74969e23 1.97874e23i 1.14246 0.602885i
\(871\) 1.56221e23i 0.471621i
\(872\) 1.96297e23 + 2.24944e22i 0.587194 + 0.0672889i
\(873\) 1.87407e22 0.0555483
\(874\) −6.03297e22 1.14324e23i −0.177190 0.335774i
\(875\) 1.81815e22i 0.0529134i
\(876\) −2.63589e23 1.80201e23i −0.760143 0.519666i
\(877\) −3.85703e23 −1.10219 −0.551094 0.834443i \(-0.685790\pi\)
−0.551094 + 0.834443i \(0.685790\pi\)
\(878\) −2.39206e22 + 1.26231e22i −0.0677354 + 0.0357445i
\(879\) 8.25958e22i 0.231764i
\(880\) −3.20179e23 + 1.24728e23i −0.890291 + 0.346818i
\(881\) 2.31132e23 0.636873 0.318437 0.947944i \(-0.396842\pi\)
0.318437 + 0.947944i \(0.396842\pi\)
\(882\) 5.65184e22 + 1.07102e23i 0.154327 + 0.292448i
\(883\) 6.69705e21i 0.0181217i 0.999959 + 0.00906083i \(0.00288419\pi\)
−0.999959 + 0.00906083i \(0.997116\pi\)
\(884\) 1.36024e23 1.98970e23i 0.364753 0.533543i
\(885\) −3.11208e23 −0.826999
\(886\) 3.21364e23 1.69586e23i 0.846306 0.446602i
\(887\) 1.24237e23i 0.324237i 0.986771 + 0.162119i \(0.0518327\pi\)
−0.986771 + 0.162119i \(0.948167\pi\)
\(888\) −2.84052e22 + 2.47878e23i −0.0734674 + 0.641111i
\(889\) −2.75290e22 −0.0705630
\(890\) −4.89386e22 9.27382e22i −0.124317 0.235580i
\(891\) 3.42048e22i 0.0861122i
\(892\) 1.10044e23 + 7.52305e22i 0.274566 + 0.187705i
\(893\) −1.23331e23 −0.304973
\(894\) 1.44040e23 7.60110e22i 0.353007 0.186284i
\(895\) 4.43617e23i 1.07752i
\(896\) 3.59111e22 9.45222e21i 0.0864498 0.0227546i
\(897\) 2.64797e23 0.631791
\(898\) 1.87384e23 + 3.55092e23i 0.443121 + 0.839711i
\(899\) 1.55336e23i 0.364079i
\(900\) 4.20998e22 6.15816e22i 0.0978002 0.143058i
\(901\) 6.01846e23 1.38576
\(902\) 2.38141e23 1.25668e23i 0.543477 0.286797i
\(903\) 2.70381e22i 0.0611609i
\(904\) −2.68615e23 3.07817e22i −0.602259 0.0690152i
\(905\) −7.65260e23 −1.70067
\(906\) −2.00572e23 3.80082e23i −0.441819 0.837243i
\(907\) 5.42263e23i 1.18400i 0.805938 + 0.592000i \(0.201662\pi\)
−0.805938 + 0.592000i \(0.798338\pi\)
\(908\) 4.49906e23 + 3.07574e23i 0.973721 + 0.665677i
\(909\) −1.55798e23 −0.334233
\(910\) 2.76924e22 1.46135e22i 0.0588884 0.0310758i
\(911\) 7.67160e23i 1.61711i −0.588422 0.808554i \(-0.700251\pi\)
0.588422 0.808554i \(-0.299749\pi\)
\(912\) −2.10237e22 5.39683e22i −0.0439288 0.112766i
\(913\) −4.95182e23 −1.02565
\(914\) −3.43925e23 6.51734e23i −0.706145 1.33814i
\(915\) 5.54807e23i 1.12921i
\(916\) −2.66107e23 + 3.89249e23i −0.536899 + 0.785352i
\(917\) 7.65104e22 0.153026
\(918\) 9.18314e22 4.84601e22i 0.182075 0.0960821i
\(919\) 5.38528e23i 1.05848i −0.848471 0.529242i \(-0.822476\pi\)
0.848471 0.529242i \(-0.177524\pi\)
\(920\) −1.30469e23 + 1.13854e24i −0.254217 + 2.21842i
\(921\) −3.65206e23 −0.705441
\(922\) −3.59259e22 6.80793e22i −0.0687955 0.130367i
\(923\) 8.89750e22i 0.168910i
\(924\) −1.75454e22 1.19948e22i −0.0330208 0.0225744i
\(925\) −3.11431e23 −0.581070
\(926\) −8.40442e23 + 4.43507e23i −1.55461 + 0.820376i
\(927\) 2.56602e22i 0.0470567i
\(928\) −6.53517e23 + 7.54563e23i −1.18815 + 1.37187i
\(929\) −8.87061e22 −0.159892 −0.0799461 0.996799i \(-0.525475\pi\)
−0.0799461 + 0.996799i \(0.525475\pi\)
\(930\) 3.72911e22 + 7.06663e22i 0.0666410 + 0.126284i
\(931\) 1.17364e23i 0.207939i
\(932\) 2.87363e23 4.20341e23i 0.504781 0.738371i
\(933\) −5.45012e23 −0.949189
\(934\) 7.60861e23 4.01512e23i 1.31380 0.693303i
\(935\) 5.97011e23i 1.02209i
\(936\) 1.17873e23 + 1.35075e22i 0.200082 + 0.0229281i
\(937\) 2.88142e23 0.484943 0.242471 0.970159i \(-0.422042\pi\)
0.242471 + 0.970159i \(0.422042\pi\)
\(938\) 1.95169e22 + 3.69844e22i 0.0325678 + 0.0617157i
\(939\) 1.85042e23i 0.306158i
\(940\) 9.02609e23 + 6.17061e23i 1.48073 + 1.01229i
\(941\) −6.32626e23 −1.02904 −0.514518 0.857480i \(-0.672029\pi\)
−0.514518 + 0.857480i \(0.672029\pi\)
\(942\) 1.47238e23 7.76985e22i 0.237472 0.125316i
\(943\) 8.98020e23i 1.43613i
\(944\) 6.82743e23 2.65967e23i 1.08263 0.421746i
\(945\) 1.34892e22 0.0212096
\(946\) 2.74921e23 + 5.20973e23i 0.428626 + 0.812243i
\(947\) 1.24941e24i 1.93155i 0.259378 + 0.965776i \(0.416483\pi\)
−0.259378 + 0.965776i \(0.583517\pi\)
\(948\) 2.68857e23 3.93272e23i 0.412149 0.602873i
\(949\) 6.33893e23 0.963577
\(950\) 6.39388e22 3.37410e22i 0.0963775 0.0508591i
\(951\) 1.33788e23i 0.199974i
\(952\) −7.34534e21 + 6.40989e22i −0.0108872 + 0.0950068i
\(953\) −8.68851e23 −1.27703 −0.638517 0.769608i \(-0.720452\pi\)
−0.638517 + 0.769608i \(0.720452\pi\)
\(954\) 1.38268e23 + 2.62017e23i 0.201528 + 0.381893i
\(955\) 5.32232e23i 0.769261i
\(956\) −6.15171e23 4.20557e23i −0.881724 0.602784i
\(957\) 5.71329e23 0.812065
\(958\) 8.63877e22 4.55874e22i 0.121767 0.0642571i
\(959\) 8.24220e19i 0.000115211i
\(960\) −1.16155e23 + 5.00158e23i −0.161016 + 0.693325i
\(961\) 6.98149e23 0.959756
\(962\) −2.31172e23 4.38069e23i −0.315163 0.597231i
\(963\) 1.82547e23i 0.246811i
\(964\) −1.93174e23 + 2.82565e23i −0.259019 + 0.378881i
\(965\) 4.55793e23 0.606107
\(966\) −6.26892e22 + 3.30815e22i −0.0826753 + 0.0436283i
\(967\) 2.59154e23i 0.338959i 0.985534 + 0.169479i \(0.0542086\pi\)
−0.985534 + 0.169479i \(0.945791\pi\)
\(968\) 3.05868e23 + 3.50506e22i 0.396763 + 0.0454666i
\(969\) 1.00630e23 0.129461
\(970\) −7.51479e22 1.42405e23i −0.0958833 0.181698i
\(971\) 2.71728e23i 0.343859i −0.985109 0.171930i \(-0.945000\pi\)
0.985109 0.171930i \(-0.0550002\pi\)
\(972\) 4.21947e22 + 2.88461e22i 0.0529575 + 0.0362040i
\(973\) −6.64453e21 −0.00827107
\(974\) 4.99830e23 2.63764e23i 0.617094 0.325645i
\(975\) 1.48095e23i 0.181344i
\(976\) −4.74153e23 1.21716e24i −0.575863 1.47826i
\(977\) −5.31693e23 −0.640478 −0.320239 0.947337i \(-0.603763\pi\)
−0.320239 + 0.947337i \(0.603763\pi\)
\(978\) −1.18697e23 2.24930e23i −0.141817 0.268742i
\(979\) 1.41302e23i 0.167451i
\(980\) 5.87202e23 8.58933e23i 0.690207 1.00960i
\(981\) −1.68984e23 −0.197012
\(982\) −9.12498e23 + 4.81532e23i −1.05521 + 0.556843i
\(983\) 5.65847e23i 0.649039i −0.945879 0.324520i \(-0.894797\pi\)
0.945879 0.324520i \(-0.105203\pi\)
\(984\) 4.58087e22 3.99749e23i 0.0521180 0.454806i
\(985\) 5.72546e23 0.646131
\(986\) −8.09438e23 1.53388e24i −0.906084 1.71702i
\(987\) 6.76283e22i 0.0750915i
\(988\) 9.49223e22 + 6.48928e22i 0.104547 + 0.0714729i
\(989\) 1.96457e24 2.14633
\(990\) 2.59912e23 1.37157e23i 0.281672 0.148641i
\(991\) 3.28127e22i 0.0352738i 0.999844 + 0.0176369i \(0.00561429\pi\)
−0.999844 + 0.0176369i \(0.994386\pi\)
\(992\) −1.42204e23 1.23161e23i −0.151642 0.131335i
\(993\) 1.04666e24 1.10716
\(994\) −1.11158e22 2.10644e22i −0.0116641 0.0221033i
\(995\) 8.77371e22i 0.0913268i
\(996\) −4.17604e23 + 6.10852e23i −0.431211 + 0.630756i
\(997\) −4.03691e22 −0.0413511 −0.0206756 0.999786i \(-0.506582\pi\)
−0.0206756 + 0.999786i \(0.506582\pi\)
\(998\) 3.20989e22 1.69388e22i 0.0326171 0.0172123i
\(999\) 2.13388e23i 0.215102i
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 12.17.d.a.7.7 16
3.2 odd 2 36.17.d.d.19.10 16
4.3 odd 2 inner 12.17.d.a.7.8 yes 16
12.11 even 2 36.17.d.d.19.9 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.17.d.a.7.7 16 1.1 even 1 trivial
12.17.d.a.7.8 yes 16 4.3 odd 2 inner
36.17.d.d.19.9 16 12.11 even 2
36.17.d.d.19.10 16 3.2 odd 2