Properties

Label 29.15.c.a.12.15
Level $29$
Weight $15$
Character 29.12
Analytic conductor $36.055$
Analytic rank $0$
Dimension $68$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,15,Mod(12,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.12");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 29.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: \(36.0554007641\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 12.15
Character \(\chi\) \(=\) 29.12
Dual form 29.15.c.a.17.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-48.4316 - 48.4316i) q^{2} +(2910.35 + 2910.35i) q^{3} -11692.8i q^{4} -56568.4i q^{5} -281906. i q^{6} +166969. q^{7} +(-1.35980e6 + 1.35980e6i) q^{8} +1.21573e7i q^{9} +O(q^{10})\) \(q+(-48.4316 - 48.4316i) q^{2} +(2910.35 + 2910.35i) q^{3} -11692.8i q^{4} -56568.4i q^{5} -281906. i q^{6} +166969. q^{7} +(-1.35980e6 + 1.35980e6i) q^{8} +1.21573e7i q^{9} +(-2.73969e6 + 2.73969e6i) q^{10} +(8.97417e6 + 8.97417e6i) q^{11} +(3.40301e7 - 3.40301e7i) q^{12} -5.10364e7i q^{13} +(-8.08659e6 - 8.08659e6i) q^{14} +(1.64634e8 - 1.64634e8i) q^{15} -5.98597e7 q^{16} +(5.50123e8 + 5.50123e8i) q^{17} +(5.88798e8 - 5.88798e8i) q^{18} +(-3.93948e8 - 3.93948e8i) q^{19} -6.61441e8 q^{20} +(4.85940e8 + 4.85940e8i) q^{21} -8.69266e8i q^{22} +2.69461e9 q^{23} -7.91500e9 q^{24} +2.90354e9 q^{25} +(-2.47177e9 + 2.47177e9i) q^{26} +(-2.14620e10 + 2.14620e10i) q^{27} -1.95233e9i q^{28} +(1.70785e10 - 2.42557e9i) q^{29} -1.59469e10 q^{30} +(-1.63564e10 - 1.63564e10i) q^{31} +(2.51781e10 + 2.51781e10i) q^{32} +5.22360e10i q^{33} -5.32867e10i q^{34} -9.44519e9i q^{35} +1.42153e11 q^{36} +(1.82791e10 - 1.82791e10i) q^{37} +3.81591e10i q^{38} +(1.48534e11 - 1.48534e11i) q^{39} +(7.69218e10 + 7.69218e10i) q^{40} +(1.65641e11 - 1.65641e11i) q^{41} -4.70696e10i q^{42} +(3.51242e11 + 3.51242e11i) q^{43} +(1.04933e11 - 1.04933e11i) q^{44} +6.87720e11 q^{45} +(-1.30504e11 - 1.30504e11i) q^{46} +(-1.60441e11 + 1.60441e11i) q^{47} +(-1.74213e11 - 1.74213e11i) q^{48} -6.50344e11 q^{49} +(-1.40623e11 - 1.40623e11i) q^{50} +3.20211e12i q^{51} -5.96757e11 q^{52} +1.48615e11 q^{53} +2.07887e12 q^{54} +(5.07654e11 - 5.07654e11i) q^{55} +(-2.27045e11 + 2.27045e11i) q^{56} -2.29306e12i q^{57} +(-9.44612e11 - 7.09664e11i) q^{58} +2.18073e12 q^{59} +(-1.92503e12 - 1.92503e12i) q^{60} +(4.21207e12 + 4.21207e12i) q^{61} +1.58433e12i q^{62} +2.02990e12i q^{63} -1.45809e12i q^{64} -2.88705e12 q^{65} +(2.52987e12 - 2.52987e12i) q^{66} -1.29909e12i q^{67} +(6.43247e12 - 6.43247e12i) q^{68} +(7.84225e12 + 7.84225e12i) q^{69} +(-4.57445e11 + 4.57445e11i) q^{70} -1.80711e12i q^{71} +(-1.65316e13 - 1.65316e13i) q^{72} +(-3.74645e12 + 3.74645e12i) q^{73} -1.77057e12 q^{74} +(8.45031e12 + 8.45031e12i) q^{75} +(-4.60635e12 + 4.60635e12i) q^{76} +(1.49841e12 + 1.49841e12i) q^{77} -1.43875e13 q^{78} +(6.34597e12 + 6.34597e12i) q^{79} +3.38617e12i q^{80} -6.67757e13 q^{81} -1.60445e13 q^{82} -3.51297e13 q^{83} +(5.68198e12 - 5.68198e12i) q^{84} +(3.11196e13 - 3.11196e13i) q^{85} -3.40224e13i q^{86} +(5.67637e13 + 4.26452e13i) q^{87} -2.44062e13 q^{88} +(1.49288e13 + 1.49288e13i) q^{89} +(-3.33074e13 - 3.33074e13i) q^{90} -8.52153e12i q^{91} -3.15074e13i q^{92} -9.52055e13i q^{93} +1.55408e13 q^{94} +(-2.22850e13 + 2.22850e13i) q^{95} +1.46554e14i q^{96} +(4.05437e13 - 4.05437e13i) q^{97} +(3.14972e13 + 3.14972e13i) q^{98} +(-1.09102e14 + 1.09102e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8} + 23502846 q^{10} - 2993734 q^{11} - 76269906 q^{12} - 3845224 q^{14} + 277690070 q^{15} - 5490752792 q^{16} + 285786056 q^{17} + 5809842386 q^{18} - 1195066336 q^{19} + 1866268668 q^{20} - 8197524756 q^{21} + 2117392192 q^{23} + 8629372824 q^{24} - 73846917196 q^{25} - 16368356994 q^{26} + 33411191086 q^{27} + 48687460392 q^{29} + 128044102700 q^{30} + 73968522614 q^{31} - 2657032122 q^{32} - 259972090824 q^{36} + 95888936640 q^{37} - 571710579738 q^{39} + 977850700426 q^{40} - 57594847104 q^{41} + 48472463810 q^{43} + 1173476843650 q^{44} - 299491373708 q^{45} + 656204001636 q^{46} + 29961288922 q^{47} + 1808198535114 q^{48} + 9857850529980 q^{49} + 1443642384290 q^{50} - 11263919114280 q^{52} - 1993070689076 q^{53} + 2064324525592 q^{54} + 3054165001846 q^{55} + 8002123380864 q^{56} - 9170547007720 q^{58} - 8402401993912 q^{59} + 4455428077662 q^{60} - 4381209993964 q^{61} - 14884429709724 q^{65} - 5756218265814 q^{66} + 4595908790532 q^{68} + 51089269002600 q^{69} - 65383337180236 q^{70} + 101900024607216 q^{72} + 39493186331224 q^{73} - 152862151734316 q^{74} - 46335428712972 q^{75} + 46232026918072 q^{76} + 63231072283300 q^{77} + 111617680995888 q^{78} - 29034273461086 q^{79} - 345331621902328 q^{81} + 104609665443600 q^{82} - 2994621113016 q^{83} + 269240332456580 q^{84} + 11907997971872 q^{85} - 148747542169982 q^{87} + 186485775340436 q^{88} - 89923791148548 q^{89} + 103388070190448 q^{90} - 920451476162284 q^{94} - 393920660173420 q^{95} - 116095608365672 q^{97} + 24492650399928 q^{98} - 402079041111864 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −48.4316 48.4316i −0.378372 0.378372i 0.492143 0.870514i \(-0.336214\pi\)
−0.870514 + 0.492143i \(0.836214\pi\)
\(3\) 2910.35 + 2910.35i 1.33075 + 1.33075i 0.904699 + 0.426052i \(0.140096\pi\)
0.426052 + 0.904699i \(0.359904\pi\)
\(4\) 11692.8i 0.713670i
\(5\) 56568.4i 0.724075i −0.932164 0.362038i \(-0.882081\pi\)
0.932164 0.362038i \(-0.117919\pi\)
\(6\) 281906.i 1.00704i
\(7\) 166969. 0.202745 0.101373 0.994849i \(-0.467677\pi\)
0.101373 + 0.994849i \(0.467677\pi\)
\(8\) −1.35980e6 + 1.35980e6i −0.648404 + 0.648404i
\(9\) 1.21573e7i 2.54180i
\(10\) −2.73969e6 + 2.73969e6i −0.273969 + 0.273969i
\(11\) 8.97417e6 + 8.97417e6i 0.460517 + 0.460517i 0.898825 0.438308i \(-0.144422\pi\)
−0.438308 + 0.898825i \(0.644422\pi\)
\(12\) 3.40301e7 3.40301e7i 0.949717 0.949717i
\(13\) 5.10364e7i 0.813349i −0.913573 0.406675i \(-0.866688\pi\)
0.913573 0.406675i \(-0.133312\pi\)
\(14\) −8.08659e6 8.08659e6i −0.0767130 0.0767130i
\(15\) 1.64634e8 1.64634e8i 0.963564 0.963564i
\(16\) −5.98597e7 −0.222995
\(17\) 5.50123e8 + 5.50123e8i 1.34066 + 1.34066i 0.895406 + 0.445252i \(0.146886\pi\)
0.445252 + 0.895406i \(0.353114\pi\)
\(18\) 5.88798e8 5.88798e8i 0.961743 0.961743i
\(19\) −3.93948e8 3.93948e8i −0.440721 0.440721i 0.451533 0.892254i \(-0.350877\pi\)
−0.892254 + 0.451533i \(0.850877\pi\)
\(20\) −6.61441e8 −0.516751
\(21\) 4.85940e8 + 4.85940e8i 0.269803 + 0.269803i
\(22\) 8.69266e8i 0.348493i
\(23\) 2.69461e9 0.791408 0.395704 0.918378i \(-0.370501\pi\)
0.395704 + 0.918378i \(0.370501\pi\)
\(24\) −7.91500e9 −1.72573
\(25\) 2.90354e9 0.475715
\(26\) −2.47177e9 + 2.47177e9i −0.307748 + 0.307748i
\(27\) −2.14620e10 + 2.14620e10i −2.05175 + 2.05175i
\(28\) 1.95233e9i 0.144693i
\(29\) 1.70785e10 2.42557e9i 0.990065 0.140614i
\(30\) −1.59469e10 −0.729170
\(31\) −1.63564e10 1.63564e10i −0.594504 0.594504i 0.344341 0.938845i \(-0.388102\pi\)
−0.938845 + 0.344341i \(0.888102\pi\)
\(32\) 2.51781e10 + 2.51781e10i 0.732779 + 0.732779i
\(33\) 5.22360e10i 1.22567i
\(34\) 5.32867e10i 1.01453i
\(35\) 9.44519e9i 0.146803i
\(36\) 1.42153e11 1.81400
\(37\) 1.82791e10 1.82791e10i 0.192549 0.192549i −0.604247 0.796797i \(-0.706526\pi\)
0.796797 + 0.604247i \(0.206526\pi\)
\(38\) 3.81591e10i 0.333513i
\(39\) 1.48534e11 1.48534e11i 1.08236 1.08236i
\(40\) 7.69218e10 + 7.69218e10i 0.469493 + 0.469493i
\(41\) 1.65641e11 1.65641e11i 0.850513 0.850513i −0.139683 0.990196i \(-0.544608\pi\)
0.990196 + 0.139683i \(0.0446084\pi\)
\(42\) 4.70696e10i 0.204172i
\(43\) 3.51242e11 + 3.51242e11i 1.29219 + 1.29219i 0.933428 + 0.358765i \(0.116802\pi\)
0.358765 + 0.933428i \(0.383198\pi\)
\(44\) 1.04933e11 1.04933e11i 0.328657 0.328657i
\(45\) 6.87720e11 1.84045
\(46\) −1.30504e11 1.30504e11i −0.299446 0.299446i
\(47\) −1.60441e11 + 1.60441e11i −0.316686 + 0.316686i −0.847493 0.530807i \(-0.821889\pi\)
0.530807 + 0.847493i \(0.321889\pi\)
\(48\) −1.74213e11 1.74213e11i −0.296751 0.296751i
\(49\) −6.50344e11 −0.958894
\(50\) −1.40623e11 1.40623e11i −0.179997 0.179997i
\(51\) 3.20211e12i 3.56816i
\(52\) −5.96757e11 −0.580463
\(53\) 1.48615e11 0.126512 0.0632560 0.997997i \(-0.479852\pi\)
0.0632560 + 0.997997i \(0.479852\pi\)
\(54\) 2.07887e12 1.55264
\(55\) 5.07654e11 5.07654e11i 0.333449 0.333449i
\(56\) −2.27045e11 + 2.27045e11i −0.131461 + 0.131461i
\(57\) 2.29306e12i 1.17298i
\(58\) −9.44612e11 7.09664e11i −0.427816 0.321408i
\(59\) 2.18073e12 0.876271 0.438136 0.898909i \(-0.355639\pi\)
0.438136 + 0.898909i \(0.355639\pi\)
\(60\) −1.92503e12 1.92503e12i −0.687666 0.687666i
\(61\) 4.21207e12 + 4.21207e12i 1.34025 + 1.34025i 0.895806 + 0.444446i \(0.146600\pi\)
0.444446 + 0.895806i \(0.353400\pi\)
\(62\) 1.58433e12i 0.449887i
\(63\) 2.02990e12i 0.515337i
\(64\) 1.45809e12i 0.331530i
\(65\) −2.88705e12 −0.588926
\(66\) 2.52987e12 2.52987e12i 0.463757 0.463757i
\(67\) 1.29909e12i 0.214346i −0.994240 0.107173i \(-0.965820\pi\)
0.994240 0.107173i \(-0.0341799\pi\)
\(68\) 6.43247e12 6.43247e12i 0.956787 0.956787i
\(69\) 7.84225e12 + 7.84225e12i 1.05317 + 1.05317i
\(70\) −4.57445e11 + 4.57445e11i −0.0555460 + 0.0555460i
\(71\) 1.80711e12i 0.198691i −0.995053 0.0993453i \(-0.968325\pi\)
0.995053 0.0993453i \(-0.0316748\pi\)
\(72\) −1.65316e13 1.65316e13i −1.64811 1.64811i
\(73\) −3.74645e12 + 3.74645e12i −0.339125 + 0.339125i −0.856038 0.516913i \(-0.827081\pi\)
0.516913 + 0.856038i \(0.327081\pi\)
\(74\) −1.77057e12 −0.145710
\(75\) 8.45031e12 + 8.45031e12i 0.633058 + 0.633058i
\(76\) −4.60635e12 + 4.60635e12i −0.314530 + 0.314530i
\(77\) 1.49841e12 + 1.49841e12i 0.0933676 + 0.0933676i
\(78\) −1.43875e13 −0.819072
\(79\) 6.34597e12 + 6.34597e12i 0.330452 + 0.330452i 0.852758 0.522306i \(-0.174928\pi\)
−0.522306 + 0.852758i \(0.674928\pi\)
\(80\) 3.38617e12i 0.161465i
\(81\) −6.67757e13 −2.91893
\(82\) −1.60445e13 −0.643620
\(83\) −3.51297e13 −1.29458 −0.647289 0.762245i \(-0.724097\pi\)
−0.647289 + 0.762245i \(0.724097\pi\)
\(84\) 5.68198e12 5.68198e12i 0.192551 0.192551i
\(85\) 3.11196e13 3.11196e13i 0.970736 0.970736i
\(86\) 3.40224e13i 0.977858i
\(87\) 5.67637e13 + 4.26452e13i 1.50465 + 1.13041i
\(88\) −2.44062e13 −0.597202
\(89\) 1.49288e13 + 1.49288e13i 0.337516 + 0.337516i 0.855432 0.517916i \(-0.173292\pi\)
−0.517916 + 0.855432i \(0.673292\pi\)
\(90\) −3.33074e13 3.33074e13i −0.696374 0.696374i
\(91\) 8.52153e12i 0.164903i
\(92\) 3.15074e13i 0.564804i
\(93\) 9.52055e13i 1.58227i
\(94\) 1.55408e13 0.239650
\(95\) −2.22850e13 + 2.22850e13i −0.319115 + 0.319115i
\(96\) 1.46554e14i 1.95029i
\(97\) 4.05437e13 4.05437e13i 0.501789 0.501789i −0.410204 0.911994i \(-0.634543\pi\)
0.911994 + 0.410204i \(0.134543\pi\)
\(98\) 3.14972e13 + 3.14972e13i 0.362818 + 0.362818i
\(99\) −1.09102e14 + 1.09102e14i −1.17054 + 1.17054i
\(100\) 3.39504e13i 0.339504i
\(101\) −2.26421e13 2.26421e13i −0.211187 0.211187i 0.593584 0.804772i \(-0.297712\pi\)
−0.804772 + 0.593584i \(0.797712\pi\)
\(102\) 1.55083e14 1.55083e14i 1.35009 1.35009i
\(103\) −1.31518e14 −1.06936 −0.534681 0.845054i \(-0.679568\pi\)
−0.534681 + 0.845054i \(0.679568\pi\)
\(104\) 6.93994e13 + 6.93994e13i 0.527379 + 0.527379i
\(105\) 2.74888e13 2.74888e13i 0.195358 0.195358i
\(106\) −7.19766e12 7.19766e12i −0.0478685 0.0478685i
\(107\) −2.04400e14 −1.27290 −0.636451 0.771317i \(-0.719598\pi\)
−0.636451 + 0.771317i \(0.719598\pi\)
\(108\) 2.50950e14 + 2.50950e14i 1.46427 + 1.46427i
\(109\) 3.03290e12i 0.0165910i −0.999966 0.00829551i \(-0.997359\pi\)
0.999966 0.00829551i \(-0.00264057\pi\)
\(110\) −4.91730e13 −0.252335
\(111\) 1.06397e14 0.512470
\(112\) −9.99474e12 −0.0452111
\(113\) −1.56639e14 + 1.56639e14i −0.665809 + 0.665809i −0.956743 0.290934i \(-0.906034\pi\)
0.290934 + 0.956743i \(0.406034\pi\)
\(114\) −1.11056e14 + 1.11056e14i −0.443822 + 0.443822i
\(115\) 1.52429e14i 0.573039i
\(116\) −2.83616e13 1.99695e14i −0.100352 0.706579i
\(117\) 6.20467e14 2.06737
\(118\) −1.05616e14 1.05616e14i −0.331556 0.331556i
\(119\) 9.18538e13 + 9.18538e13i 0.271812 + 0.271812i
\(120\) 4.47739e14i 1.24956i
\(121\) 2.18678e14i 0.575848i
\(122\) 4.07994e14i 1.01423i
\(123\) 9.64147e14 2.26364
\(124\) −1.91251e14 + 1.91251e14i −0.424279 + 0.424279i
\(125\) 5.09514e14i 1.06853i
\(126\) 9.83113e13 9.83113e13i 0.194989 0.194989i
\(127\) −2.15974e14 2.15974e14i −0.405298 0.405298i 0.474797 0.880095i \(-0.342521\pi\)
−0.880095 + 0.474797i \(0.842521\pi\)
\(128\) 3.41900e14 3.41900e14i 0.607337 0.607337i
\(129\) 2.04448e15i 3.43917i
\(130\) 1.39824e14 + 1.39824e14i 0.222833 + 0.222833i
\(131\) 4.42781e14 4.42781e14i 0.668791 0.668791i −0.288646 0.957436i \(-0.593205\pi\)
0.957436 + 0.288646i \(0.0932049\pi\)
\(132\) 6.10784e14 0.874722
\(133\) −6.57773e13 6.57773e13i −0.0893541 0.0893541i
\(134\) −6.29171e13 + 6.29171e13i −0.0811026 + 0.0811026i
\(135\) 1.21407e15 + 1.21407e15i 1.48562 + 1.48562i
\(136\) −1.49612e15 −1.73857
\(137\) −7.95705e14 7.95705e14i −0.878432 0.878432i 0.114940 0.993372i \(-0.463332\pi\)
−0.993372 + 0.114940i \(0.963332\pi\)
\(138\) 7.59625e14i 0.796977i
\(139\) −5.25176e14 −0.523843 −0.261921 0.965089i \(-0.584356\pi\)
−0.261921 + 0.965089i \(0.584356\pi\)
\(140\) −1.10440e14 −0.104769
\(141\) −9.33878e14 −0.842862
\(142\) −8.75213e13 + 8.75213e13i −0.0751788 + 0.0751788i
\(143\) 4.58010e14 4.58010e14i 0.374561 0.374561i
\(144\) 7.27734e14i 0.566807i
\(145\) −1.37211e14 9.66102e14i −0.101815 0.716881i
\(146\) 3.62893e14 0.256630
\(147\) −1.89273e15 1.89273e15i −1.27605 1.27605i
\(148\) −2.13733e14 2.13733e14i −0.137417 0.137417i
\(149\) 2.41822e15i 1.48318i 0.670855 + 0.741588i \(0.265927\pi\)
−0.670855 + 0.741588i \(0.734073\pi\)
\(150\) 8.18523e14i 0.479063i
\(151\) 1.83567e15i 1.02555i −0.858524 0.512773i \(-0.828618\pi\)
0.858524 0.512773i \(-0.171382\pi\)
\(152\) 1.07138e15 0.571531
\(153\) −6.68803e15 + 6.68803e15i −3.40768 + 3.40768i
\(154\) 1.45141e14i 0.0706553i
\(155\) −9.25252e14 + 9.25252e14i −0.430465 + 0.430465i
\(156\) −1.73677e15 1.73677e15i −0.772451 0.772451i
\(157\) −1.33570e15 + 1.33570e15i −0.568082 + 0.568082i −0.931591 0.363509i \(-0.881579\pi\)
0.363509 + 0.931591i \(0.381579\pi\)
\(158\) 6.14690e14i 0.250067i
\(159\) 4.32522e14 + 4.32522e14i 0.168356 + 0.168356i
\(160\) 1.42428e15 1.42428e15i 0.530587 0.530587i
\(161\) 4.49917e14 0.160454
\(162\) 3.23405e15 + 3.23405e15i 1.10444 + 1.10444i
\(163\) −8.81170e13 + 8.81170e13i −0.0288235 + 0.0288235i −0.721372 0.692548i \(-0.756488\pi\)
0.692548 + 0.721372i \(0.256488\pi\)
\(164\) −1.93680e15 1.93680e15i −0.606986 0.606986i
\(165\) 2.95491e15 0.887475
\(166\) 1.70139e15 + 1.70139e15i 0.489831 + 0.489831i
\(167\) 6.74997e15i 1.86332i −0.363336 0.931658i \(-0.618362\pi\)
0.363336 0.931658i \(-0.381638\pi\)
\(168\) −1.32156e15 −0.349883
\(169\) 1.33266e15 0.338463
\(170\) −3.01434e15 −0.734598
\(171\) 4.78936e15 4.78936e15i 1.12022 1.12022i
\(172\) 4.10699e15 4.10699e15i 0.922199 0.922199i
\(173\) 1.81269e15i 0.390841i 0.980720 + 0.195421i \(0.0626072\pi\)
−0.980720 + 0.195421i \(0.937393\pi\)
\(174\) −6.83782e14 4.81452e15i −0.141603 0.997031i
\(175\) 4.84802e14 0.0964490
\(176\) −5.37192e14 5.37192e14i −0.102693 0.102693i
\(177\) 6.34670e15 + 6.34670e15i 1.16610 + 1.16610i
\(178\) 1.44605e15i 0.255413i
\(179\) 7.93134e15i 1.34702i −0.739176 0.673512i \(-0.764785\pi\)
0.739176 0.673512i \(-0.235215\pi\)
\(180\) 8.04135e15i 1.31347i
\(181\) 2.82725e15 0.444236 0.222118 0.975020i \(-0.428703\pi\)
0.222118 + 0.975020i \(0.428703\pi\)
\(182\) −4.12711e14 + 4.12711e14i −0.0623945 + 0.0623945i
\(183\) 2.45172e16i 3.56708i
\(184\) −3.66413e15 + 3.66413e15i −0.513152 + 0.513152i
\(185\) −1.03402e15 1.03402e15i −0.139420 0.139420i
\(186\) −4.61095e15 + 4.61095e15i −0.598687 + 0.598687i
\(187\) 9.87381e15i 1.23479i
\(188\) 1.87600e15 + 1.87600e15i 0.226010 + 0.226010i
\(189\) −3.58350e15 + 3.58350e15i −0.415982 + 0.415982i
\(190\) 2.15860e15 0.241488
\(191\) 1.13864e15 + 1.13864e15i 0.122787 + 0.122787i 0.765830 0.643043i \(-0.222328\pi\)
−0.643043 + 0.765830i \(0.722328\pi\)
\(192\) 4.24354e15 4.24354e15i 0.441184 0.441184i
\(193\) −5.80212e15 5.80212e15i −0.581682 0.581682i 0.353683 0.935365i \(-0.384929\pi\)
−0.935365 + 0.353683i \(0.884929\pi\)
\(194\) −3.92719e15 −0.379725
\(195\) −8.40233e15 8.40233e15i −0.783713 0.783713i
\(196\) 7.60433e15i 0.684334i
\(197\) −2.25726e16 −1.96028 −0.980138 0.198317i \(-0.936452\pi\)
−0.980138 + 0.198317i \(0.936452\pi\)
\(198\) 1.05680e16 0.885798
\(199\) 1.67821e16 1.35792 0.678962 0.734174i \(-0.262430\pi\)
0.678962 + 0.734174i \(0.262430\pi\)
\(200\) −3.94823e15 + 3.94823e15i −0.308456 + 0.308456i
\(201\) 3.78082e15 3.78082e15i 0.285242 0.285242i
\(202\) 2.19319e15i 0.159815i
\(203\) 2.85159e15 4.04996e14i 0.200731 0.0285088i
\(204\) 3.74415e16 2.54649
\(205\) −9.37004e15 9.37004e15i −0.615835 0.615835i
\(206\) 6.36962e15 + 6.36962e15i 0.404616 + 0.404616i
\(207\) 3.27592e16i 2.01160i
\(208\) 3.05503e15i 0.181373i
\(209\) 7.07072e15i 0.405919i
\(210\) −2.66265e15 −0.147836
\(211\) 1.58631e14 1.58631e14i 0.00851946 0.00851946i −0.702834 0.711354i \(-0.748082\pi\)
0.711354 + 0.702834i \(0.248082\pi\)
\(212\) 1.73772e15i 0.0902878i
\(213\) 5.25934e15 5.25934e15i 0.264408 0.264408i
\(214\) 9.89943e15 + 9.89943e15i 0.481630 + 0.481630i
\(215\) 1.98692e16 1.98692e16i 0.935645 0.935645i
\(216\) 5.83681e16i 2.66072i
\(217\) −2.73101e15 2.73101e15i −0.120533 0.120533i
\(218\) −1.46888e14 + 1.46888e14i −0.00627757 + 0.00627757i
\(219\) −2.18070e16 −0.902581
\(220\) −5.93589e15 5.93589e15i −0.237972 0.237972i
\(221\) 2.80763e16 2.80763e16i 1.09042 1.09042i
\(222\) −5.15297e15 5.15297e15i −0.193904 0.193904i
\(223\) 2.97321e16 1.08416 0.542078 0.840328i \(-0.317638\pi\)
0.542078 + 0.840328i \(0.317638\pi\)
\(224\) 4.20397e15 + 4.20397e15i 0.148567 + 0.148567i
\(225\) 3.52992e16i 1.20917i
\(226\) 1.51725e16 0.503846
\(227\) −5.81337e15 −0.187175 −0.0935874 0.995611i \(-0.529833\pi\)
−0.0935874 + 0.995611i \(0.529833\pi\)
\(228\) −2.68122e16 −0.837121
\(229\) −3.68949e16 + 3.68949e16i −1.11717 + 1.11717i −0.125010 + 0.992156i \(0.539896\pi\)
−0.992156 + 0.125010i \(0.960104\pi\)
\(230\) −7.38240e15 + 7.38240e15i −0.216822 + 0.216822i
\(231\) 8.72182e15i 0.248498i
\(232\) −1.99251e16 + 2.65217e16i −0.550787 + 0.733136i
\(233\) −6.60788e16 −1.77244 −0.886219 0.463267i \(-0.846677\pi\)
−0.886219 + 0.463267i \(0.846677\pi\)
\(234\) −3.00502e16 3.00502e16i −0.782233 0.782233i
\(235\) 9.07587e15 + 9.07587e15i 0.229305 + 0.229305i
\(236\) 2.54988e16i 0.625368i
\(237\) 3.69380e16i 0.879498i
\(238\) 8.89724e15i 0.205692i
\(239\) 4.28843e15 0.0962750 0.0481375 0.998841i \(-0.484671\pi\)
0.0481375 + 0.998841i \(0.484671\pi\)
\(240\) −9.85494e15 + 9.85494e15i −0.214870 + 0.214870i
\(241\) 6.57682e16i 1.39282i 0.717642 + 0.696412i \(0.245222\pi\)
−0.717642 + 0.696412i \(0.754778\pi\)
\(242\) −1.05909e16 + 1.05909e16i −0.217885 + 0.217885i
\(243\) −9.16889e16 9.16889e16i −1.83262 1.83262i
\(244\) 4.92507e16 4.92507e16i 0.956497 0.956497i
\(245\) 3.67889e16i 0.694312i
\(246\) −4.66952e16 4.66952e16i −0.856498 0.856498i
\(247\) −2.01057e16 + 2.01057e16i −0.358460 + 0.358460i
\(248\) 4.44828e16 0.770957
\(249\) −1.02240e17 1.02240e17i −1.72276 1.72276i
\(250\) −2.46766e16 + 2.46766e16i −0.404301 + 0.404301i
\(251\) −1.09046e16 1.09046e16i −0.173738 0.173738i 0.614882 0.788619i \(-0.289204\pi\)
−0.788619 + 0.614882i \(0.789204\pi\)
\(252\) 2.37352e16 0.367780
\(253\) 2.41819e16 + 2.41819e16i 0.364457 + 0.364457i
\(254\) 2.09199e16i 0.306707i
\(255\) 1.81138e17 2.58362
\(256\) −5.70068e16 −0.791129
\(257\) −8.72641e16 −1.17843 −0.589215 0.807977i \(-0.700563\pi\)
−0.589215 + 0.807977i \(0.700563\pi\)
\(258\) 9.90172e16 9.90172e16i 1.30129 1.30129i
\(259\) 3.05204e15 3.05204e15i 0.0390384 0.0390384i
\(260\) 3.37576e16i 0.420299i
\(261\) 2.94885e16 + 2.07629e17i 0.357411 + 2.51654i
\(262\) −4.28892e16 −0.506103
\(263\) 1.01258e17 + 1.01258e17i 1.16343 + 1.16343i 0.983720 + 0.179706i \(0.0575148\pi\)
0.179706 + 0.983720i \(0.442485\pi\)
\(264\) −7.10306e16 7.10306e16i −0.794727 0.794727i
\(265\) 8.40691e15i 0.0916042i
\(266\) 6.37139e15i 0.0676181i
\(267\) 8.68961e16i 0.898300i
\(268\) −1.51900e16 −0.152973
\(269\) 1.07766e17 1.07766e17i 1.05734 1.05734i 0.0590915 0.998253i \(-0.481180\pi\)
0.998253 0.0590915i \(-0.0188204\pi\)
\(270\) 1.17599e17i 1.12423i
\(271\) 5.97366e16 5.97366e16i 0.556487 0.556487i −0.371818 0.928306i \(-0.621266\pi\)
0.928306 + 0.371818i \(0.121266\pi\)
\(272\) −3.29302e16 3.29302e16i −0.298960 0.298960i
\(273\) 2.48006e16 2.48006e16i 0.219444 0.219444i
\(274\) 7.70745e16i 0.664747i
\(275\) 2.60568e16 + 2.60568e16i 0.219075 + 0.219075i
\(276\) 9.16976e16 9.16976e16i 0.751614 0.751614i
\(277\) −5.66529e16 −0.452756 −0.226378 0.974040i \(-0.572688\pi\)
−0.226378 + 0.974040i \(0.572688\pi\)
\(278\) 2.54351e16 + 2.54351e16i 0.198207 + 0.198207i
\(279\) 1.98850e17 1.98850e17i 1.51111 1.51111i
\(280\) 1.28436e16 + 1.28436e16i 0.0951875 + 0.0951875i
\(281\) 8.39442e16 0.606801 0.303401 0.952863i \(-0.401878\pi\)
0.303401 + 0.952863i \(0.401878\pi\)
\(282\) 4.52292e16 + 4.52292e16i 0.318915 + 0.318915i
\(283\) 1.22543e15i 0.00842915i 0.999991 + 0.00421458i \(0.00134155\pi\)
−0.999991 + 0.00421458i \(0.998658\pi\)
\(284\) −2.11302e16 −0.141799
\(285\) −1.29714e17 −0.849326
\(286\) −4.43643e16 −0.283447
\(287\) 2.76570e16 2.76570e16i 0.172437 0.172437i
\(288\) −3.06098e17 + 3.06098e17i −1.86257 + 1.86257i
\(289\) 4.36894e17i 2.59472i
\(290\) −4.01445e16 + 5.34352e16i −0.232724 + 0.309771i
\(291\) 2.35993e17 1.33551
\(292\) 4.38063e16 + 4.38063e16i 0.242023 + 0.242023i
\(293\) 2.38824e16 + 2.38824e16i 0.128826 + 0.128826i 0.768580 0.639754i \(-0.220964\pi\)
−0.639754 + 0.768580i \(0.720964\pi\)
\(294\) 1.83336e17i 0.965642i
\(295\) 1.23361e17i 0.634486i
\(296\) 4.97118e16i 0.249699i
\(297\) −3.85207e17 −1.88973
\(298\) 1.17118e17 1.17118e17i 0.561192 0.561192i
\(299\) 1.37523e17i 0.643691i
\(300\) 9.88075e16 9.88075e16i 0.451795 0.451795i
\(301\) 5.86467e16 + 5.86467e16i 0.261986 + 0.261986i
\(302\) −8.89042e16 + 8.89042e16i −0.388037 + 0.388037i
\(303\) 1.31793e17i 0.562075i
\(304\) 2.35816e16 + 2.35816e16i 0.0982785 + 0.0982785i
\(305\) 2.38270e17 2.38270e17i 0.970443 0.970443i
\(306\) 6.47824e17 2.57874
\(307\) −1.74926e17 1.74926e17i −0.680592 0.680592i 0.279542 0.960134i \(-0.409817\pi\)
−0.960134 + 0.279542i \(0.909817\pi\)
\(308\) 1.75206e16 1.75206e16i 0.0666337 0.0666337i
\(309\) −3.82764e17 3.82764e17i −1.42305 1.42305i
\(310\) 8.96228e16 0.325752
\(311\) 8.65927e15 + 8.65927e15i 0.0307722 + 0.0307722i 0.722325 0.691553i \(-0.243073\pi\)
−0.691553 + 0.722325i \(0.743073\pi\)
\(312\) 4.03954e17i 1.40362i
\(313\) −2.01190e17 −0.683589 −0.341795 0.939775i \(-0.611035\pi\)
−0.341795 + 0.939775i \(0.611035\pi\)
\(314\) 1.29380e17 0.429892
\(315\) 1.14828e17 0.373143
\(316\) 7.42019e16 7.42019e16i 0.235834 0.235834i
\(317\) 6.95469e16 6.95469e16i 0.216204 0.216204i −0.590693 0.806897i \(-0.701145\pi\)
0.806897 + 0.590693i \(0.201145\pi\)
\(318\) 4.18954e16i 0.127402i
\(319\) 1.75033e17 + 1.31498e17i 0.520697 + 0.391187i
\(320\) −8.24816e16 −0.240053
\(321\) −5.94877e17 5.94877e17i −1.69392 1.69392i
\(322\) −2.17902e16 2.17902e16i −0.0607113 0.0607113i
\(323\) 4.33440e17i 1.18171i
\(324\) 7.80793e17i 2.08315i
\(325\) 1.48186e17i 0.386923i
\(326\) 8.53529e15 0.0218120
\(327\) 8.82681e15 8.82681e15i 0.0220785 0.0220785i
\(328\) 4.50478e17i 1.10295i
\(329\) −2.67887e16 + 2.67887e16i −0.0642067 + 0.0642067i
\(330\) −1.43111e17 1.43111e17i −0.335795 0.335795i
\(331\) −2.38744e17 + 2.38744e17i −0.548449 + 0.548449i −0.925992 0.377543i \(-0.876769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(332\) 4.10764e17i 0.923901i
\(333\) 2.22225e17 + 2.22225e17i 0.489421 + 0.489421i
\(334\) −3.26912e17 + 3.26912e17i −0.705026 + 0.705026i
\(335\) −7.34875e16 −0.155203
\(336\) −2.90882e16 2.90882e16i −0.0601648 0.0601648i
\(337\) 4.05039e17 4.05039e17i 0.820517 0.820517i −0.165665 0.986182i \(-0.552977\pi\)
0.986182 + 0.165665i \(0.0529771\pi\)
\(338\) −6.45427e16 6.45427e16i −0.128065 0.128065i
\(339\) −9.11747e17 −1.77205
\(340\) −3.63874e17 3.63874e17i −0.692785 0.692785i
\(341\) 2.93570e17i 0.547558i
\(342\) −4.63912e17 −0.847721
\(343\) −2.21830e17 −0.397157
\(344\) −9.55239e17 −1.67573
\(345\) 4.43623e17 4.43623e17i 0.762572 0.762572i
\(346\) 8.77913e16 8.77913e16i 0.147883 0.147883i
\(347\) 4.22004e17i 0.696642i −0.937375 0.348321i \(-0.886752\pi\)
0.937375 0.348321i \(-0.113248\pi\)
\(348\) 4.98640e17 6.63725e17i 0.806738 1.07382i
\(349\) −6.75708e17 −1.07147 −0.535737 0.844385i \(-0.679966\pi\)
−0.535737 + 0.844385i \(0.679966\pi\)
\(350\) −2.34797e16 2.34797e16i −0.0364936 0.0364936i
\(351\) 1.09534e18 + 1.09534e18i 1.66879 + 1.66879i
\(352\) 4.51905e17i 0.674914i
\(353\) 6.14165e17i 0.899212i 0.893227 + 0.449606i \(0.148436\pi\)
−0.893227 + 0.449606i \(0.851564\pi\)
\(354\) 6.14761e17i 0.882437i
\(355\) −1.02225e17 −0.143867
\(356\) 1.74559e17 1.74559e17i 0.240875 0.240875i
\(357\) 5.34654e17i 0.723428i
\(358\) −3.84127e17 + 3.84127e17i −0.509676 + 0.509676i
\(359\) −9.83480e17 9.83480e17i −1.27969 1.27969i −0.940842 0.338847i \(-0.889963\pi\)
−0.338847 0.940842i \(-0.610037\pi\)
\(360\) −9.35163e17 + 9.35163e17i −1.19336 + 1.19336i
\(361\) 4.88616e17i 0.611530i
\(362\) −1.36928e17 1.36928e17i −0.168086 0.168086i
\(363\) 6.36431e17 6.36431e17i 0.766310 0.766310i
\(364\) −9.96402e16 −0.117686
\(365\) 2.11930e17 + 2.11930e17i 0.245552 + 0.245552i
\(366\) 1.18741e18 1.18741e18i 1.34968 1.34968i
\(367\) 1.19902e18 + 1.19902e18i 1.33711 + 1.33711i 0.898851 + 0.438255i \(0.144403\pi\)
0.438255 + 0.898851i \(0.355597\pi\)
\(368\) −1.61298e17 −0.176480
\(369\) 2.01375e18 + 2.01375e18i 2.16183 + 2.16183i
\(370\) 1.00158e17i 0.105505i
\(371\) 2.48142e16 0.0256497
\(372\) −1.11322e18 −1.12922
\(373\) 1.10288e18 1.09791 0.548957 0.835851i \(-0.315025\pi\)
0.548957 + 0.835851i \(0.315025\pi\)
\(374\) 4.78204e17 4.78204e17i 0.467210 0.467210i
\(375\) 1.48287e18 1.48287e18i 1.42195 1.42195i
\(376\) 4.36335e17i 0.410681i
\(377\) −1.23792e17 8.71626e17i −0.114368 0.805268i
\(378\) 3.47108e17 0.314791
\(379\) −1.09964e18 1.09964e18i −0.978986 0.978986i 0.0207973 0.999784i \(-0.493380\pi\)
−0.999784 + 0.0207973i \(0.993380\pi\)
\(380\) 2.60573e17 + 2.60573e17i 0.227743 + 0.227743i
\(381\) 1.25712e18i 1.07870i
\(382\) 1.10292e17i 0.0929180i
\(383\) 6.00651e17i 0.496856i −0.968650 0.248428i \(-0.920086\pi\)
0.968650 0.248428i \(-0.0799140\pi\)
\(384\) 1.99010e18 1.61643
\(385\) 8.47628e16 8.47628e16i 0.0676052 0.0676052i
\(386\) 5.62012e17i 0.440184i
\(387\) −4.27017e18 + 4.27017e18i −3.28449 + 3.28449i
\(388\) −4.74068e17 4.74068e17i −0.358112 0.358112i
\(389\) −6.02713e17 + 6.02713e17i −0.447160 + 0.447160i −0.894409 0.447249i \(-0.852404\pi\)
0.447249 + 0.894409i \(0.352404\pi\)
\(390\) 8.13876e17i 0.593070i
\(391\) 1.48237e18 + 1.48237e18i 1.06101 + 1.06101i
\(392\) 8.84339e17 8.84339e17i 0.621751 0.621751i
\(393\) 2.57730e18 1.77999
\(394\) 1.09322e18 + 1.09322e18i 0.741713 + 0.741713i
\(395\) 3.58981e17 3.58981e17i 0.239272 0.239272i
\(396\) 1.27570e18 + 1.27570e18i 0.835379 + 0.835379i
\(397\) −2.37417e18 −1.52749 −0.763745 0.645518i \(-0.776642\pi\)
−0.763745 + 0.645518i \(0.776642\pi\)
\(398\) −8.12784e17 8.12784e17i −0.513800 0.513800i
\(399\) 3.82870e17i 0.237816i
\(400\) −1.73805e17 −0.106082
\(401\) 1.55954e18 0.935377 0.467689 0.883893i \(-0.345087\pi\)
0.467689 + 0.883893i \(0.345087\pi\)
\(402\) −3.66222e17 −0.215855
\(403\) −8.34770e17 + 8.34770e17i −0.483539 + 0.483539i
\(404\) −2.64749e17 + 2.64749e17i −0.150718 + 0.150718i
\(405\) 3.77739e18i 2.11352i
\(406\) −1.57721e17 1.18492e17i −0.0867378 0.0651639i
\(407\) 3.28079e17 0.177344
\(408\) −4.35423e18 4.35423e18i −2.31361 2.31361i
\(409\) −6.11563e17 6.11563e17i −0.319432 0.319432i 0.529117 0.848549i \(-0.322523\pi\)
−0.848549 + 0.529117i \(0.822523\pi\)
\(410\) 9.07611e17i 0.466029i
\(411\) 4.63156e18i 2.33795i
\(412\) 1.53781e18i 0.763171i
\(413\) 3.64116e17 0.177660
\(414\) 1.58658e18 1.58658e18i 0.761131 0.761131i
\(415\) 1.98723e18i 0.937372i
\(416\) 1.28500e18 1.28500e18i 0.596005 0.596005i
\(417\) −1.52845e18 1.52845e18i −0.697104 0.697104i
\(418\) −3.42446e17 + 3.42446e17i −0.153588 + 0.153588i
\(419\) 2.84591e18i 1.25523i 0.778525 + 0.627614i \(0.215968\pi\)
−0.778525 + 0.627614i \(0.784032\pi\)
\(420\) −3.21420e17 3.21420e17i −0.139421 0.139421i
\(421\) −1.03009e18 + 1.03009e18i −0.439439 + 0.439439i −0.891823 0.452384i \(-0.850574\pi\)
0.452384 + 0.891823i \(0.350574\pi\)
\(422\) −1.53655e16 −0.00644704
\(423\) −1.95053e18 1.95053e18i −0.804952 0.804952i
\(424\) −2.02087e17 + 2.02087e17i −0.0820309 + 0.0820309i
\(425\) 1.59730e18 + 1.59730e18i 0.637771 + 0.637771i
\(426\) −5.09436e17 −0.200089
\(427\) 7.03286e17 + 7.03286e17i 0.271730 + 0.271730i
\(428\) 2.39001e18i 0.908433i
\(429\) 2.66594e18 0.996895
\(430\) −1.92459e18 −0.708043
\(431\) 3.94437e18 1.42770 0.713850 0.700298i \(-0.246950\pi\)
0.713850 + 0.700298i \(0.246950\pi\)
\(432\) 1.28471e18 1.28471e18i 0.457529 0.457529i
\(433\) −3.07603e18 + 3.07603e18i −1.07789 + 1.07789i −0.0811938 + 0.996698i \(0.525873\pi\)
−0.996698 + 0.0811938i \(0.974127\pi\)
\(434\) 2.64534e17i 0.0912124i
\(435\) 2.41237e18 3.21103e18i 0.818500 1.08948i
\(436\) −3.54630e16 −0.0118405
\(437\) −1.06154e18 1.06154e18i −0.348790 0.348790i
\(438\) 1.05615e18 + 1.05615e18i 0.341511 + 0.341511i
\(439\) 3.08389e18i 0.981403i −0.871328 0.490701i \(-0.836741\pi\)
0.871328 0.490701i \(-0.163259\pi\)
\(440\) 1.38062e18i 0.432419i
\(441\) 7.90645e18i 2.43731i
\(442\) −2.71956e18 −0.825169
\(443\) 3.04279e18 3.04279e18i 0.908754 0.908754i −0.0874177 0.996172i \(-0.527861\pi\)
0.996172 + 0.0874177i \(0.0278615\pi\)
\(444\) 1.24408e18i 0.365735i
\(445\) 8.44497e17 8.44497e17i 0.244387 0.244387i
\(446\) −1.43997e18 1.43997e18i −0.410214 0.410214i
\(447\) −7.03788e18 + 7.03788e18i −1.97374 + 1.97374i
\(448\) 2.43456e17i 0.0672162i
\(449\) −3.87645e17 3.87645e17i −0.105368 0.105368i 0.652457 0.757826i \(-0.273738\pi\)
−0.757826 + 0.652457i \(0.773738\pi\)
\(450\) 1.70960e18 1.70960e18i 0.457516 0.457516i
\(451\) 2.97298e18 0.783351
\(452\) 1.83154e18 + 1.83154e18i 0.475168 + 0.475168i
\(453\) 5.34244e18 5.34244e18i 1.36475 1.36475i
\(454\) 2.81551e17 + 2.81551e17i 0.0708216 + 0.0708216i
\(455\) −4.82049e17 −0.119402
\(456\) 3.11810e18 + 3.11810e18i 0.760565 + 0.760565i
\(457\) 7.84237e18i 1.88380i 0.335900 + 0.941898i \(0.390960\pi\)
−0.335900 + 0.941898i \(0.609040\pi\)
\(458\) 3.57375e18 0.845407
\(459\) −2.36135e19 −5.50137
\(460\) −1.78232e18 −0.408961
\(461\) 4.50214e18 4.50214e18i 1.01745 1.01745i 0.0176048 0.999845i \(-0.494396\pi\)
0.999845 0.0176048i \(-0.00560406\pi\)
\(462\) 4.22411e17 4.22411e17i 0.0940246 0.0940246i
\(463\) 6.89151e18i 1.51094i 0.655183 + 0.755470i \(0.272591\pi\)
−0.655183 + 0.755470i \(0.727409\pi\)
\(464\) −1.02231e18 + 1.45194e17i −0.220779 + 0.0313561i
\(465\) −5.38562e18 −1.14568
\(466\) 3.20030e18 + 3.20030e18i 0.670640 + 0.670640i
\(467\) −4.73454e18 4.73454e18i −0.977371 0.977371i 0.0223790 0.999750i \(-0.492876\pi\)
−0.999750 + 0.0223790i \(0.992876\pi\)
\(468\) 7.25498e18i 1.47542i
\(469\) 2.16909e17i 0.0434577i
\(470\) 8.79117e17i 0.173525i
\(471\) −7.77471e18 −1.51195
\(472\) −2.96536e18 + 2.96536e18i −0.568178 + 0.568178i
\(473\) 6.30422e18i 1.19015i
\(474\) 1.78896e18 1.78896e18i 0.332777 0.332777i
\(475\) −1.14384e18 1.14384e18i −0.209658 0.209658i
\(476\) 1.07403e18 1.07403e18i 0.193984 0.193984i
\(477\) 1.80676e18i 0.321568i
\(478\) −2.07696e17 2.07696e17i −0.0364277 0.0364277i
\(479\) −9.73194e17 + 9.73194e17i −0.168210 + 0.168210i −0.786192 0.617982i \(-0.787950\pi\)
0.617982 + 0.786192i \(0.287950\pi\)
\(480\) 8.29033e18 1.41216
\(481\) −9.32898e17 9.32898e17i −0.156610 0.156610i
\(482\) 3.18526e18 3.18526e18i 0.527005 0.527005i
\(483\) 1.30942e18 + 1.30942e18i 0.213525 + 0.213525i
\(484\) −2.55695e18 −0.410965
\(485\) −2.29349e18 2.29349e18i −0.363333 0.363333i
\(486\) 8.88127e18i 1.38682i
\(487\) 1.36458e18 0.210037 0.105019 0.994470i \(-0.466510\pi\)
0.105019 + 0.994470i \(0.466510\pi\)
\(488\) −1.14551e19 −1.73805
\(489\) −5.12903e17 −0.0767138
\(490\) 1.78174e18 1.78174e18i 0.262708 0.262708i
\(491\) 3.18535e18 3.18535e18i 0.463006 0.463006i −0.436634 0.899639i \(-0.643829\pi\)
0.899639 + 0.436634i \(0.143829\pi\)
\(492\) 1.12736e19i 1.61549i
\(493\) 1.07296e19 + 8.06092e18i 1.51585 + 1.13882i
\(494\) 1.94750e18 0.271262
\(495\) 6.17172e18 + 6.17172e18i 0.847559 + 0.847559i
\(496\) 9.79087e17 + 9.79087e17i 0.132571 + 0.132571i
\(497\) 3.01733e17i 0.0402836i
\(498\) 9.90327e18i 1.30369i
\(499\) 1.18259e19i 1.53508i 0.641003 + 0.767538i \(0.278518\pi\)
−0.641003 + 0.767538i \(0.721482\pi\)
\(500\) −5.95763e18 −0.762577
\(501\) 1.96448e19 1.96448e19i 2.47961 2.47961i
\(502\) 1.05625e18i 0.131475i
\(503\) −4.52857e18 + 4.52857e18i −0.555886 + 0.555886i −0.928133 0.372248i \(-0.878587\pi\)
0.372248 + 0.928133i \(0.378587\pi\)
\(504\) −2.76026e18 2.76026e18i −0.334146 0.334146i
\(505\) −1.28083e18 + 1.28083e18i −0.152915 + 0.152915i
\(506\) 2.34233e18i 0.275800i
\(507\) 3.87850e18 + 3.87850e18i 0.450410 + 0.450410i
\(508\) −2.52533e18 + 2.52533e18i −0.289249 + 0.289249i
\(509\) 1.21817e19 1.37621 0.688104 0.725612i \(-0.258443\pi\)
0.688104 + 0.725612i \(0.258443\pi\)
\(510\) −8.77279e18 8.77279e18i −0.977567 0.977567i
\(511\) −6.25542e17 + 6.25542e17i −0.0687559 + 0.0687559i
\(512\) −2.84077e18 2.84077e18i −0.307997 0.307997i
\(513\) 1.69098e19 1.80850
\(514\) 4.22633e18 + 4.22633e18i 0.445884 + 0.445884i
\(515\) 7.43976e18i 0.774298i
\(516\) 2.39056e19 2.45444
\(517\) −2.87965e18 −0.291679
\(518\) −2.95631e17 −0.0295421
\(519\) −5.27556e18 + 5.27556e18i −0.520113 + 0.520113i
\(520\) 3.92581e18 3.92581e18i 0.381862 0.381862i
\(521\) 6.00810e18i 0.576598i 0.957540 + 0.288299i \(0.0930896\pi\)
−0.957540 + 0.288299i \(0.906910\pi\)
\(522\) 8.62762e18 1.14840e19i 0.816953 1.08742i
\(523\) 3.81122e18 0.356084 0.178042 0.984023i \(-0.443024\pi\)
0.178042 + 0.984023i \(0.443024\pi\)
\(524\) −5.17734e18 5.17734e18i −0.477296 0.477296i
\(525\) 1.41094e18 + 1.41094e18i 0.128350 + 0.128350i
\(526\) 9.80816e18i 0.880415i
\(527\) 1.79960e19i 1.59405i
\(528\) 3.12683e18i 0.273317i
\(529\) −4.33193e18 −0.373673
\(530\) −4.07160e17 + 4.07160e17i −0.0346604 + 0.0346604i
\(531\) 2.65119e19i 2.22730i
\(532\) −7.69119e17 + 7.69119e17i −0.0637694 + 0.0637694i
\(533\) −8.45373e18 8.45373e18i −0.691764 0.691764i
\(534\) 4.20851e18 4.20851e18i 0.339891 0.339891i
\(535\) 1.15626e19i 0.921677i
\(536\) 1.76651e18 + 1.76651e18i 0.138983 + 0.138983i
\(537\) 2.30830e19 2.30830e19i 1.79255 1.79255i
\(538\) −1.04386e19 −0.800138
\(539\) −5.83630e18 5.83630e18i −0.441587 0.441587i
\(540\) 1.41958e19 1.41958e19i 1.06024 1.06024i
\(541\) −8.55903e18 8.55903e18i −0.631021 0.631021i 0.317303 0.948324i \(-0.397223\pi\)
−0.948324 + 0.317303i \(0.897223\pi\)
\(542\) −5.78627e18 −0.421118
\(543\) 8.22829e18 + 8.22829e18i 0.591168 + 0.591168i
\(544\) 2.77021e19i 1.96481i
\(545\) −1.71566e17 −0.0120131
\(546\) −2.40227e18 −0.166063
\(547\) −1.38137e19 −0.942754 −0.471377 0.881932i \(-0.656243\pi\)
−0.471377 + 0.881932i \(0.656243\pi\)
\(548\) −9.30399e18 + 9.30399e18i −0.626911 + 0.626911i
\(549\) −5.12075e19 + 5.12075e19i −3.40665 + 3.40665i
\(550\) 2.52395e18i 0.165783i
\(551\) −7.68359e18 5.77249e18i −0.498314 0.374371i
\(552\) −2.13278e19 −1.36576
\(553\) 1.05958e18 + 1.05958e18i 0.0669975 + 0.0669975i
\(554\) 2.74379e18 + 2.74379e18i 0.171310 + 0.171310i
\(555\) 6.01871e18i 0.371067i
\(556\) 6.14076e18i 0.373851i
\(557\) 1.70604e19i 1.02566i −0.858491 0.512829i \(-0.828598\pi\)
0.858491 0.512829i \(-0.171402\pi\)
\(558\) −1.92612e19 −1.14352
\(559\) 1.79262e19 1.79262e19i 1.05100 1.05100i
\(560\) 5.65386e17i 0.0327363i
\(561\) −2.87363e19 + 2.87363e19i −1.64320 + 1.64320i
\(562\) −4.06555e18 4.06555e18i −0.229596 0.229596i
\(563\) 1.29732e19 1.29732e19i 0.723585 0.723585i −0.245748 0.969334i \(-0.579034\pi\)
0.969334 + 0.245748i \(0.0790336\pi\)
\(564\) 1.09196e19i 0.601525i
\(565\) 8.86079e18 + 8.86079e18i 0.482096 + 0.482096i
\(566\) 5.93495e16 5.93495e16i 0.00318935 0.00318935i
\(567\) −1.11495e19 −0.591799
\(568\) 2.45732e18 + 2.45732e18i 0.128832 + 0.128832i
\(569\) 2.15643e18 2.15643e18i 0.111673 0.111673i −0.649062 0.760735i \(-0.724839\pi\)
0.760735 + 0.649062i \(0.224839\pi\)
\(570\) 6.28227e18 + 6.28227e18i 0.321361 + 0.321361i
\(571\) 5.49118e18 0.277468 0.138734 0.990330i \(-0.455697\pi\)
0.138734 + 0.990330i \(0.455697\pi\)
\(572\) −5.35541e18 5.35541e18i −0.267313 0.267313i
\(573\) 6.62766e18i 0.326797i
\(574\) −2.67894e18 −0.130491
\(575\) 7.82388e18 0.376485
\(576\) 1.77264e19 0.842683
\(577\) 2.05903e19 2.05903e19i 0.967011 0.967011i −0.0324616 0.999473i \(-0.510335\pi\)
0.999473 + 0.0324616i \(0.0103347\pi\)
\(578\) 2.11594e19 2.11594e19i 0.981769 0.981769i
\(579\) 3.37724e19i 1.54815i
\(580\) −1.12964e19 + 1.60437e18i −0.511616 + 0.0726622i
\(581\) −5.86559e18 −0.262470
\(582\) −1.14295e19 1.14295e19i −0.505320 0.505320i
\(583\) 1.33370e18 + 1.33370e18i 0.0582609 + 0.0582609i
\(584\) 1.01889e19i 0.439780i
\(585\) 3.50988e19i 1.49693i
\(586\) 2.31332e18i 0.0974882i
\(587\) 2.61272e19 1.08799 0.543997 0.839087i \(-0.316910\pi\)
0.543997 + 0.839087i \(0.316910\pi\)
\(588\) −2.21313e19 + 2.21313e19i −0.910678 + 0.910678i
\(589\) 1.28871e19i 0.524021i
\(590\) −5.97454e18 + 5.97454e18i −0.240071 + 0.240071i
\(591\) −6.56941e19 6.56941e19i −2.60864 2.60864i
\(592\) −1.09418e18 + 1.09418e18i −0.0429375 + 0.0429375i
\(593\) 1.30386e19i 0.505648i 0.967512 + 0.252824i \(0.0813594\pi\)
−0.967512 + 0.252824i \(0.918641\pi\)
\(594\) 1.86562e19 + 1.86562e19i 0.715019 + 0.715019i
\(595\) 5.19602e18 5.19602e18i 0.196812 0.196812i
\(596\) 2.82757e19 1.05850
\(597\) 4.88419e19 + 4.88419e19i 1.80706 + 1.80706i
\(598\) −6.66046e18 + 6.66046e18i −0.243554 + 0.243554i
\(599\) −1.67564e19 1.67564e19i −0.605610 0.605610i 0.336185 0.941796i \(-0.390863\pi\)
−0.941796 + 0.336185i \(0.890863\pi\)
\(600\) −2.29815e19 −0.820955
\(601\) −4.15842e18 4.15842e18i −0.146827 0.146827i 0.629872 0.776699i \(-0.283107\pi\)
−0.776699 + 0.629872i \(0.783107\pi\)
\(602\) 5.68070e18i 0.198256i
\(603\) 1.57935e19 0.544825
\(604\) −2.14640e19 −0.731902
\(605\) −1.23703e19 −0.416957
\(606\) −6.38295e18 + 6.38295e18i −0.212673 + 0.212673i
\(607\) 1.75765e19 1.75765e19i 0.578910 0.578910i −0.355693 0.934603i \(-0.615755\pi\)
0.934603 + 0.355693i \(0.115755\pi\)
\(608\) 1.98377e19i 0.645902i
\(609\) 9.47780e18 + 7.12044e18i 0.305061 + 0.229185i
\(610\) −2.30795e19 −0.734376
\(611\) 8.18832e18 + 8.18832e18i 0.257577 + 0.257577i
\(612\) 7.82016e19 + 7.82016e19i 2.43196 + 2.43196i
\(613\) 6.28825e19i 1.93333i −0.256041 0.966666i \(-0.582418\pi\)
0.256041 0.966666i \(-0.417582\pi\)
\(614\) 1.69439e19i 0.515033i
\(615\) 5.45402e19i 1.63905i
\(616\) −4.07509e18 −0.121080
\(617\) −4.42237e19 + 4.42237e19i −1.29915 + 1.29915i −0.370194 + 0.928955i \(0.620709\pi\)
−0.928955 + 0.370194i \(0.879291\pi\)
\(618\) 3.70757e19i 1.07689i
\(619\) −4.00346e18 + 4.00346e18i −0.114974 + 0.114974i −0.762253 0.647279i \(-0.775907\pi\)
0.647279 + 0.762253i \(0.275907\pi\)
\(620\) 1.08188e19 + 1.08188e19i 0.307210 + 0.307210i
\(621\) −5.78316e19 + 5.78316e19i −1.62377 + 1.62377i
\(622\) 8.38763e17i 0.0232866i
\(623\) 2.49265e18 + 2.49265e18i 0.0684298 + 0.0684298i
\(624\) −8.89121e18 + 8.89121e18i −0.241362 + 0.241362i
\(625\) −1.11006e19 −0.297980
\(626\) 9.74393e18 + 9.74393e18i 0.258651 + 0.258651i
\(627\) 2.05783e19 2.05783e19i 0.540177 0.540177i
\(628\) 1.56180e19 + 1.56180e19i 0.405423 + 0.405423i
\(629\) 2.01115e19 0.516285
\(630\) −5.56131e18 5.56131e18i −0.141187 0.141187i
\(631\) 1.75309e19i 0.440148i −0.975483 0.220074i \(-0.929370\pi\)
0.975483 0.220074i \(-0.0706298\pi\)
\(632\) −1.72585e19 −0.428532
\(633\) 9.23346e17 0.0226745
\(634\) −6.73653e18 −0.163611
\(635\) −1.22173e19 + 1.22173e19i −0.293466 + 0.293466i
\(636\) 5.05738e18 5.05738e18i 0.120151 0.120151i
\(637\) 3.31913e19i 0.779916i
\(638\) −2.10847e18 1.48458e19i −0.0490029 0.345031i
\(639\) 2.19697e19 0.505031
\(640\) −1.93407e19 1.93407e19i −0.439758 0.439758i
\(641\) −1.54209e17 1.54209e17i −0.00346819 0.00346819i 0.705371 0.708839i \(-0.250781\pi\)
−0.708839 + 0.705371i \(0.750781\pi\)
\(642\) 5.76216e19i 1.28186i
\(643\) 2.64698e19i 0.582471i −0.956651 0.291235i \(-0.905934\pi\)
0.956651 0.291235i \(-0.0940663\pi\)
\(644\) 5.26077e18i 0.114511i
\(645\) 1.15653e20 2.49022
\(646\) −2.09922e19 + 2.09922e19i −0.447126 + 0.447126i
\(647\) 1.17468e19i 0.247508i 0.992313 + 0.123754i \(0.0394934\pi\)
−0.992313 + 0.123754i \(0.960507\pi\)
\(648\) 9.08017e19 9.08017e19i 1.89264 1.89264i
\(649\) 1.95703e19 + 1.95703e19i 0.403538 + 0.403538i
\(650\) −7.17689e18 + 7.17689e18i −0.146400 + 0.146400i
\(651\) 1.58964e19i 0.320798i
\(652\) 1.03033e18 + 1.03033e18i 0.0205705 + 0.0205705i
\(653\) 5.41769e19 5.41769e19i 1.07009 1.07009i 0.0727437 0.997351i \(-0.476824\pi\)
0.997351 0.0727437i \(-0.0231755\pi\)
\(654\) −8.54993e17 −0.0167078
\(655\) −2.50474e19 2.50474e19i −0.484255 0.484255i
\(656\) −9.91523e18 + 9.91523e18i −0.189660 + 0.189660i
\(657\) −4.55468e19 4.55468e19i −0.861986 0.861986i
\(658\) 2.59484e18 0.0485880
\(659\) 1.16257e19 + 1.16257e19i 0.215388 + 0.215388i 0.806552 0.591163i \(-0.201331\pi\)
−0.591163 + 0.806552i \(0.701331\pi\)
\(660\) 3.45510e19i 0.633364i
\(661\) −1.00629e20 −1.82521 −0.912606 0.408841i \(-0.865933\pi\)
−0.912606 + 0.408841i \(0.865933\pi\)
\(662\) 2.31255e19 0.415035
\(663\) 1.63424e20 2.90216
\(664\) 4.77695e19 4.77695e19i 0.839409 0.839409i
\(665\) −3.72091e18 + 3.72091e18i −0.0646991 + 0.0646991i
\(666\) 2.15254e19i 0.370366i
\(667\) 4.60198e19 6.53596e18i 0.783545 0.111283i
\(668\) −7.89258e19 −1.32979
\(669\) 8.65310e19 + 8.65310e19i 1.44274 + 1.44274i
\(670\) 3.55911e18 + 3.55911e18i 0.0587244 + 0.0587244i
\(671\) 7.55996e19i 1.23442i
\(672\) 2.44701e19i 0.395412i
\(673\) 4.79193e19i 0.766310i −0.923684 0.383155i \(-0.874837\pi\)
0.923684 0.383155i \(-0.125163\pi\)
\(674\) −3.92333e19 −0.620920
\(675\) −6.23156e19 + 6.23156e19i −0.976047 + 0.976047i
\(676\) 1.55825e19i 0.241551i
\(677\) −3.63672e19 + 3.63672e19i −0.557943 + 0.557943i −0.928721 0.370779i \(-0.879091\pi\)
0.370779 + 0.928721i \(0.379091\pi\)
\(678\) 4.41573e19 + 4.41573e19i 0.670494 + 0.670494i
\(679\) 6.76956e18 6.76956e18i 0.101735 0.101735i
\(680\) 8.46329e19i 1.25886i
\(681\) −1.69190e19 1.69190e19i −0.249083 0.249083i
\(682\) −1.42180e19 + 1.42180e19i −0.207180 + 0.207180i
\(683\) 5.50209e19 0.793565 0.396783 0.917913i \(-0.370127\pi\)
0.396783 + 0.917913i \(0.370127\pi\)
\(684\) −5.60009e19 5.60009e19i −0.799470 0.799470i
\(685\) −4.50117e19 + 4.50117e19i −0.636051 + 0.636051i
\(686\) 1.07436e19 + 1.07436e19i 0.150273 + 0.150273i
\(687\) −2.14754e20 −2.97334
\(688\) −2.10253e19 2.10253e19i −0.288152 0.288152i
\(689\) 7.58478e18i 0.102898i
\(690\) −4.29707e19 −0.577071
\(691\) 1.00668e20 1.33828 0.669140 0.743136i \(-0.266662\pi\)
0.669140 + 0.743136i \(0.266662\pi\)
\(692\) 2.11954e19 0.278932
\(693\) −1.82167e19 + 1.82167e19i −0.237321 + 0.237321i
\(694\) −2.04383e19 + 2.04383e19i −0.263590 + 0.263590i
\(695\) 2.97083e19i 0.379302i
\(696\) −1.35176e20 + 1.91984e19i −1.70858 + 0.242661i
\(697\) 1.82246e20 2.28049
\(698\) 3.27256e19 + 3.27256e19i 0.405415 + 0.405415i
\(699\) −1.92313e20 1.92313e20i −2.35867 2.35867i
\(700\) 5.66867e18i 0.0688328i
\(701\) 2.31238e19i 0.277992i −0.990293 0.138996i \(-0.955612\pi\)
0.990293 0.138996i \(-0.0443875\pi\)
\(702\) 1.06098e20i 1.26284i
\(703\) −1.44020e19 −0.169721
\(704\) 1.30851e19 1.30851e19i 0.152675 0.152675i
\(705\) 5.28279e19i 0.610295i
\(706\) 2.97450e19 2.97450e19i 0.340236 0.340236i
\(707\) −3.78054e18 3.78054e18i −0.0428172 0.0428172i
\(708\) 7.42105e19 7.42105e19i 0.832210 0.832210i
\(709\) 1.19336e20i 1.32510i −0.749017 0.662551i \(-0.769474\pi\)
0.749017 0.662551i \(-0.230526\pi\)
\(710\) 4.95094e18 + 4.95094e18i 0.0544351 + 0.0544351i
\(711\) −7.71500e19 + 7.71500e19i −0.839941 + 0.839941i
\(712\) −4.06004e19 −0.437694
\(713\) −4.40739e19 4.40739e19i −0.470495 0.470495i
\(714\) 2.58941e19 2.58941e19i 0.273724 0.273724i
\(715\) −2.59089e19 2.59089e19i −0.271210 0.271210i
\(716\) −9.27394e19 −0.961331
\(717\) 1.24809e19 + 1.24809e19i 0.128118 + 0.128118i
\(718\) 9.52629e19i 0.968395i
\(719\) 1.14477e20 1.15244 0.576219 0.817296i \(-0.304528\pi\)
0.576219 + 0.817296i \(0.304528\pi\)
\(720\) −4.11667e19 −0.410411
\(721\) −2.19595e19 −0.216808
\(722\) −2.36644e19 + 2.36644e19i −0.231385 + 0.231385i
\(723\) −1.91409e20 + 1.91409e20i −1.85350 + 1.85350i
\(724\) 3.30584e19i 0.317038i
\(725\) 4.95880e19 7.04273e18i 0.470989 0.0668921i
\(726\) −6.16466e19 −0.579900
\(727\) 4.05188e19 + 4.05188e19i 0.377499 + 0.377499i 0.870199 0.492700i \(-0.163990\pi\)
−0.492700 + 0.870199i \(0.663990\pi\)
\(728\) 1.15876e19 + 1.15876e19i 0.106924 + 0.106924i
\(729\) 2.14308e20i 1.95860i
\(730\) 2.05282e19i 0.185820i
\(731\) 3.86453e20i 3.46478i
\(732\) 2.86674e20 2.54572
\(733\) 4.67208e19 4.67208e19i 0.410944 0.410944i −0.471124 0.882067i \(-0.656151\pi\)
0.882067 + 0.471124i \(0.156151\pi\)
\(734\) 1.16141e20i 1.01185i
\(735\) −1.07069e20 + 1.07069e20i −0.923956 + 0.923956i
\(736\) 6.78450e19 + 6.78450e19i 0.579927 + 0.579927i
\(737\) 1.16583e19 1.16583e19i 0.0987102 0.0987102i
\(738\) 1.95058e20i 1.63595i
\(739\) −1.12681e20 1.12681e20i −0.936139 0.936139i 0.0619409 0.998080i \(-0.480271\pi\)
−0.998080 + 0.0619409i \(0.980271\pi\)
\(740\) −1.20905e19 + 1.20905e19i −0.0995000 + 0.0995000i
\(741\) −1.17029e20 −0.954042
\(742\) −1.20179e18 1.20179e18i −0.00970512 0.00970512i
\(743\) 1.86280e19 1.86280e19i 0.149020 0.149020i −0.628660 0.777680i \(-0.716396\pi\)
0.777680 + 0.628660i \(0.216396\pi\)
\(744\) 1.29461e20 + 1.29461e20i 1.02595 + 1.02595i
\(745\) 1.36795e20 1.07393
\(746\) −5.34144e19 5.34144e19i −0.415419 0.415419i
\(747\) 4.27084e20i 3.29055i
\(748\) 1.15452e20 0.881233
\(749\) −3.41286e19 −0.258075
\(750\) −1.43635e20 −1.07605
\(751\) 1.30339e20 1.30339e20i 0.967375 0.967375i −0.0321094 0.999484i \(-0.510223\pi\)
0.999484 + 0.0321094i \(0.0102225\pi\)
\(752\) 9.60393e18 9.60393e18i 0.0706194 0.0706194i
\(753\) 6.34725e19i 0.462403i
\(754\) −3.62187e19 + 4.82096e19i −0.261417 + 0.347964i
\(755\) −1.03841e20 −0.742572
\(756\) 4.19010e19 + 4.19010e19i 0.296874 + 0.296874i
\(757\) 1.07890e20 + 1.07890e20i 0.757374 + 0.757374i 0.975844 0.218469i \(-0.0701064\pi\)
−0.218469 + 0.975844i \(0.570106\pi\)
\(758\) 1.06515e20i 0.740841i
\(759\) 1.40755e20i 0.970003i
\(760\) 6.06064e19i 0.413831i
\(761\) 5.41190e19 0.366149 0.183074 0.983099i \(-0.441395\pi\)
0.183074 + 0.983099i \(0.441395\pi\)
\(762\) −6.08842e19 + 6.08842e19i −0.408150 + 0.408150i
\(763\) 5.06402e17i 0.00336375i
\(764\) 1.33138e19 1.33138e19i 0.0876292 0.0876292i
\(765\) 3.78331e20 + 3.78331e20i 2.46741 + 2.46741i
\(766\) −2.90905e19 + 2.90905e19i −0.187996 + 0.187996i
\(767\) 1.11297e20i 0.712714i
\(768\) −1.65910e20 1.65910e20i −1.05280 1.05280i
\(769\) −1.07417e20 + 1.07417e20i −0.675440 + 0.675440i −0.958965 0.283525i \(-0.908496\pi\)
0.283525 + 0.958965i \(0.408496\pi\)
\(770\) −8.21038e18 −0.0511598
\(771\) −2.53969e20 2.53969e20i −1.56820 1.56820i
\(772\) −6.78429e19 + 6.78429e19i −0.415129 + 0.415129i
\(773\) 6.75970e19 + 6.75970e19i 0.409894 + 0.409894i 0.881701 0.471808i \(-0.156398\pi\)
−0.471808 + 0.881701i \(0.656398\pi\)
\(774\) 4.13622e20 2.48552
\(775\) −4.74912e19 4.74912e19i −0.282814 0.282814i
\(776\) 1.10263e20i 0.650724i
\(777\) 1.77650e19 0.103901
\(778\) 5.83806e19 0.338385
\(779\) −1.30508e20 −0.749678
\(780\) −9.82465e19 + 9.82465e19i −0.559313 + 0.559313i
\(781\) 1.62174e19 1.62174e19i 0.0915004 0.0915004i
\(782\) 1.43587e20i 0.802909i
\(783\) −3.14481e20 + 4.18596e20i −1.74286 + 2.31986i
\(784\) 3.89294e19 0.213828
\(785\) 7.55583e19 + 7.55583e19i 0.411334 + 0.411334i
\(786\) −1.24823e20 1.24823e20i −0.673496 0.673496i
\(787\) 2.28850e20i 1.22385i −0.790916 0.611925i \(-0.790395\pi\)
0.790916 0.611925i \(-0.209605\pi\)
\(788\) 2.63936e20i 1.39899i
\(789\) 5.89393e20i 3.09646i
\(790\) −3.47720e19 −0.181067
\(791\) −2.61539e19 + 2.61539e19i −0.134990 + 0.134990i
\(792\) 2.96714e20i 1.51797i
\(793\) 2.14969e20 2.14969e20i 1.09009 1.09009i
\(794\) 1.14985e20 + 1.14985e20i 0.577959 + 0.577959i
\(795\) 2.44671e19 2.44671e19i 0.121902 0.121902i
\(796\) 1.96229e20i 0.969109i
\(797\) 2.42410e19 + 2.42410e19i 0.118670 + 0.118670i 0.763948 0.645278i \(-0.223258\pi\)
−0.645278 + 0.763948i \(0.723258\pi\)
\(798\) −1.85430e19 + 1.85430e19i −0.0899829 + 0.0899829i
\(799\) −1.76524e20 −0.849136
\(800\) 7.31055e19 + 7.31055e19i 0.348594 + 0.348594i
\(801\) −1.81494e20 + 1.81494e20i −0.857897 + 0.857897i
\(802\) −7.55311e19 7.55311e19i −0.353920 0.353920i
\(803\) −6.72425e19 −0.312346
\(804\) −4.42082e19 4.42082e19i −0.203568 0.203568i
\(805\) 2.54511e19i 0.116181i
\(806\) 8.08584e19 0.365915
\(807\) 6.27275e20 2.81412
\(808\) 6.15776e19 0.273869
\(809\) 6.55444e19 6.55444e19i 0.288999 0.288999i −0.547686 0.836684i \(-0.684491\pi\)
0.836684 + 0.547686i \(0.184491\pi\)
\(810\) 1.82945e20 1.82945e20i 0.799697 0.799697i
\(811\) 1.33538e19i 0.0578705i 0.999581 + 0.0289353i \(0.00921167\pi\)
−0.999581 + 0.0289353i \(0.990788\pi\)
\(812\) −4.73552e18 3.33429e19i −0.0203459 0.143256i
\(813\) 3.47709e20 1.48109
\(814\) −1.58894e19 1.58894e19i −0.0671021 0.0671021i
\(815\) 4.98464e18 + 4.98464e18i 0.0208704 + 0.0208704i
\(816\) 1.91677e20i 0.795681i
\(817\) 2.76742e20i 1.13899i
\(818\) 5.92379e19i 0.241728i
\(819\) 1.03599e20 0.419149
\(820\) −1.09562e20 + 1.09562e20i −0.439503 + 0.439503i
\(821\) 2.44658e20i 0.973099i −0.873653 0.486549i \(-0.838255\pi\)
0.873653 0.486549i \(-0.161745\pi\)
\(822\) −2.24314e20 + 2.24314e20i −0.884613 + 0.884613i
\(823\) 1.16674e20 + 1.16674e20i 0.456219 + 0.456219i 0.897412 0.441193i \(-0.145445\pi\)
−0.441193 + 0.897412i \(0.645445\pi\)
\(824\) 1.78838e20 1.78838e20i 0.693378 0.693378i
\(825\) 1.51669e20i 0.583068i
\(826\) −1.76347e19 1.76347e19i −0.0672214 0.0672214i
\(827\) −2.50337e20 + 2.50337e20i −0.946209 + 0.946209i −0.998625 0.0524161i \(-0.983308\pi\)
0.0524161 + 0.998625i \(0.483308\pi\)
\(828\) 3.83046e20 1.43562
\(829\) 8.18348e19 + 8.18348e19i 0.304128 + 0.304128i 0.842627 0.538498i \(-0.181008\pi\)
−0.538498 + 0.842627i \(0.681008\pi\)
\(830\) 9.62447e19 9.62447e19i 0.354675 0.354675i
\(831\) −1.64880e20 1.64880e20i −0.602505 0.602505i
\(832\) −7.44155e19 −0.269650
\(833\) −3.57770e20 3.57770e20i −1.28555 1.28555i
\(834\) 1.48050e20i 0.527529i
\(835\) −3.81835e20 −1.34918
\(836\) −8.26763e19 −0.289692
\(837\) 7.02079e20 2.43954
\(838\) 1.37832e20 1.37832e20i 0.474942 0.474942i
\(839\) −2.46308e20 + 2.46308e20i −0.841677 + 0.841677i −0.989077 0.147400i \(-0.952910\pi\)
0.147400 + 0.989077i \(0.452910\pi\)
\(840\) 7.47587e19i 0.253342i
\(841\) 2.85791e20 8.28501e19i 0.960456 0.278433i
\(842\) 9.97773e19 0.332542
\(843\) 2.44307e20 + 2.44307e20i 0.807501 + 0.807501i
\(844\) −1.85484e18 1.85484e18i −0.00608008 0.00608008i
\(845\) 7.53862e19i 0.245073i
\(846\) 1.88934e20i 0.609142i
\(847\) 3.65126e19i 0.116750i
\(848\) −8.89606e18 −0.0282115
\(849\) −3.56644e18 + 3.56644e18i −0.0112171 + 0.0112171i
\(850\) 1.54720e20i 0.482629i
\(851\) 4.92549e19 4.92549e19i 0.152385 0.152385i
\(852\) −6.14962e19 6.14962e19i −0.188700 0.188700i
\(853\) −2.30765e20 + 2.30765e20i −0.702306 + 0.702306i −0.964905 0.262599i \(-0.915420\pi\)
0.262599 + 0.964905i \(0.415420\pi\)
\(854\) 6.81225e19i 0.205630i
\(855\) −2.70926e20 2.70926e20i −0.811126 0.811126i
\(856\) 2.77944e20 2.77944e20i 0.825355 0.825355i
\(857\) −3.12364e20 −0.920016 −0.460008 0.887915i \(-0.652153\pi\)
−0.460008 + 0.887915i \(0.652153\pi\)
\(858\) −1.29116e20 1.29116e20i −0.377197 0.377197i
\(859\) 4.37711e19 4.37711e19i 0.126834 0.126834i −0.640840 0.767674i \(-0.721414\pi\)
0.767674 + 0.640840i \(0.221414\pi\)
\(860\) −2.32326e20 2.32326e20i −0.667742 0.667742i
\(861\) 1.60983e20 0.458943
\(862\) −1.91032e20 1.91032e20i −0.540201 0.540201i
\(863\) 6.20342e20i 1.74002i −0.493030 0.870012i \(-0.664111\pi\)
0.493030 0.870012i \(-0.335889\pi\)
\(864\) −1.08074e21 −3.00695
\(865\) 1.02541e20 0.282999
\(866\) 2.97954e20 0.815687
\(867\) −1.27151e21 + 1.27151e21i −3.45293 + 3.45293i
\(868\) −3.19331e19 + 3.19331e19i −0.0860206 + 0.0860206i
\(869\) 1.13900e20i 0.304357i
\(870\) −2.72350e20 + 3.86804e19i −0.721925 + 0.102531i
\(871\) −6.63010e19 −0.174338
\(872\) 4.12415e18 + 4.12415e18i 0.0107577 + 0.0107577i
\(873\) 4.92903e20 + 4.92903e20i 1.27545 + 1.27545i
\(874\) 1.02824e20i 0.263945i
\(875\) 8.50733e19i 0.216639i
\(876\) 2.54984e20i 0.644145i
\(877\) −2.88814e19 −0.0723804 −0.0361902 0.999345i \(-0.511522\pi\)
−0.0361902 + 0.999345i \(0.511522\pi\)
\(878\) −1.49358e20 + 1.49358e20i −0.371335 + 0.371335i
\(879\) 1.39012e20i 0.342871i
\(880\) −3.03880e19 + 3.03880e19i −0.0743574 + 0.0743574i
\(881\) 6.81011e19 + 6.81011e19i 0.165319 + 0.165319i 0.784918 0.619599i \(-0.212705\pi\)
−0.619599 + 0.784918i \(0.712705\pi\)
\(882\) −3.82922e20 + 3.82922e20i −0.922210 + 0.922210i
\(883\) 5.73939e19i 0.137133i 0.997647 + 0.0685663i \(0.0218425\pi\)
−0.997647 + 0.0685663i \(0.978158\pi\)
\(884\) −3.28290e20 3.28290e20i −0.778202 0.778202i
\(885\) 3.59023e20 3.59023e20i 0.844343 0.844343i
\(886\) −2.94734e20 −0.687693
\(887\) 1.49366e20 + 1.49366e20i 0.345770 + 0.345770i 0.858531 0.512761i \(-0.171377\pi\)
−0.512761 + 0.858531i \(0.671377\pi\)
\(888\) −1.44679e20 + 1.44679e20i −0.332288 + 0.332288i
\(889\) −3.60610e19 3.60610e19i −0.0821723 0.0821723i
\(890\) −8.18006e19 −0.184938
\(891\) −5.99257e20 5.99257e20i −1.34422 1.34422i
\(892\) 3.47651e20i 0.773730i
\(893\) 1.26411e20 0.279141
\(894\) 6.81711e20 1.49361
\(895\) −4.48663e20 −0.975347
\(896\) 5.70869e19 5.70869e19i 0.123135 0.123135i
\(897\) 4.00241e20 4.00241e20i 0.856592 0.856592i
\(898\) 3.75485e19i 0.0797367i
\(899\) −3.19015e20 2.39668e20i −0.672192 0.505002i
\(900\) 4.12746e20 0.862949
\(901\) 8.17566e19 + 8.17566e19i 0.169609 + 0.169609i
\(902\) −1.43986e20 1.43986e20i −0.296398 0.296398i
\(903\) 3.41365e20i 0.697276i
\(904\) 4.25995e20i 0.863426i
\(905\) 1.59933e20i 0.321660i
\(906\) −5.17485e20 −1.03276
\(907\) −4.47350e20 + 4.47350e20i −0.885924 + 0.885924i −0.994129 0.108205i \(-0.965490\pi\)
0.108205 + 0.994129i \(0.465490\pi\)
\(908\) 6.79744e19i 0.133581i
\(909\) 2.75268e20 2.75268e20i 0.536795 0.536795i
\(910\) 2.33464e19 + 2.33464e19i 0.0451783 + 0.0451783i
\(911\) 1.97182e19 1.97182e19i 0.0378651 0.0378651i −0.687921 0.725786i \(-0.741476\pi\)
0.725786 + 0.687921i \(0.241476\pi\)
\(912\) 1.37262e20i 0.261569i
\(913\) −3.15260e20 3.15260e20i −0.596175 0.596175i
\(914\) 3.79818e20 3.79818e20i 0.712775 0.712775i
\(915\) 1.38690e21 2.58284
\(916\) 4.31403e20 + 4.31403e20i 0.797287 + 0.797287i
\(917\) 7.39309e19 7.39309e19i 0.135594 0.135594i
\(918\) 1.14364e21 + 1.14364e21i 2.08156 + 2.08156i
\(919\) −2.41948e20 −0.437031 −0.218516 0.975833i \(-0.570122\pi\)
−0.218516 + 0.975833i \(0.570122\pi\)
\(920\) 2.07274e20 + 2.07274e20i 0.371561 + 0.371561i
\(921\) 1.01819e21i 1.81140i
\(922\) −4.36092e20 −0.769948
\(923\) −9.22287e19 −0.161605
\(924\) 1.01982e20 0.177346
\(925\) 5.30739e19 5.30739e19i 0.0915986 0.0915986i
\(926\) 3.33766e20 3.33766e20i 0.571697 0.571697i
\(927\) 1.59891e21i 2.71810i
\(928\) 4.91075e20 + 3.68933e20i 0.828537 + 0.622460i
\(929\) 4.43872e19 0.0743272 0.0371636 0.999309i \(-0.488168\pi\)
0.0371636 + 0.999309i \(0.488168\pi\)
\(930\) 2.60834e20 + 2.60834e20i 0.433494 + 0.433494i
\(931\) 2.56202e20 + 2.56202e20i 0.422605 + 0.422605i
\(932\) 7.72645e20i 1.26494i
\(933\) 5.04030e19i 0.0819002i
\(934\) 4.58602e20i 0.739618i
\(935\) 5.58545e20 0.894081
\(936\) −8.43712e20 + 8.43712e20i −1.34049 + 1.34049i
\(937\) 1.04484e20i 0.164768i 0.996601 + 0.0823840i \(0.0262534\pi\)
−0.996601 + 0.0823840i \(0.973747\pi\)
\(938\) −1.05052e19 + 1.05052e19i −0.0164432 + 0.0164432i
\(939\) −5.85533e20 5.85533e20i −0.909687 0.909687i
\(940\) 1.06122e20 1.06122e20i 0.163648 0.163648i
\(941\) 4.89866e20i 0.749808i 0.927064 + 0.374904i \(0.122324\pi\)
−0.927064 + 0.374904i \(0.877676\pi\)
\(942\) 3.76541e20 + 3.76541e20i 0.572079 + 0.572079i
\(943\) 4.46337e20 4.46337e20i 0.673103 0.673103i
\(944\) −1.30538e20 −0.195404
\(945\) 2.02712e20 + 2.02712e20i 0.301202 + 0.301202i
\(946\) 3.05323e20 3.05323e20i 0.450320 0.450320i
\(947\) 6.25580e20 + 6.25580e20i 0.915868 + 0.915868i 0.996726 0.0808579i \(-0.0257660\pi\)
−0.0808579 + 0.996726i \(0.525766\pi\)
\(948\) 4.31907e20 0.627671
\(949\) 1.91205e20 + 1.91205e20i 0.275827 + 0.275827i
\(950\) 1.10796e20i 0.158657i
\(951\) 4.04812e20 0.575427
\(952\) −2.49806e20 −0.352488
\(953\) −1.10866e21 −1.55291 −0.776456 0.630172i \(-0.782985\pi\)
−0.776456 + 0.630172i \(0.782985\pi\)
\(954\) 8.75043e19 8.75043e19i 0.121672 0.121672i
\(955\) 6.44108e19 6.44108e19i 0.0889068 0.0889068i
\(956\) 5.01437e19i 0.0687086i
\(957\) 1.26702e20 + 8.92112e20i 0.172346 + 1.21349i
\(958\) 9.42666e19 0.127292
\(959\) −1.32858e20 1.32858e20i −0.178098 0.178098i
\(960\) −2.40050e20 2.40050e20i −0.319451 0.319451i
\(961\) 2.21883e20i 0.293131i
\(962\) 9.03634e19i 0.118513i
\(963\) 2.48496e21i 3.23546i
\(964\) 7.69012e20 0.994017
\(965\) −3.28217e20 + 3.28217e20i −0.421181 + 0.421181i
\(966\) 1.26834e20i 0.161583i
\(967\) −6.35002e20 + 6.35002e20i −0.803137 + 0.803137i −0.983585 0.180447i \(-0.942245\pi\)
0.180447 + 0.983585i \(0.442245\pi\)
\(968\) 2.97359e20 + 2.97359e20i 0.373382 + 0.373382i
\(969\) 1.26146e21 1.26146e21i 1.57256 1.57256i
\(970\) 2.22155e20i 0.274950i
\(971\) −7.19881e20 7.19881e20i −0.884557 0.884557i 0.109437 0.993994i \(-0.465095\pi\)
−0.993994 + 0.109437i \(0.965095\pi\)
\(972\) −1.07210e21 + 1.07210e21i −1.30789 + 1.30789i
\(973\) −8.76883e19 −0.106207
\(974\) −6.60887e19 6.60887e19i −0.0794721 0.0794721i
\(975\) 4.31274e20 4.31274e20i 0.514898 0.514898i
\(976\) −2.52133e20 2.52133e20i −0.298869 0.298869i
\(977\) −4.90519e20 −0.577290 −0.288645 0.957436i \(-0.593205\pi\)
−0.288645 + 0.957436i \(0.593205\pi\)
\(978\) 2.48407e19 + 2.48407e19i 0.0290263 + 0.0290263i
\(979\) 2.67947e20i 0.310864i
\(980\) 4.30164e20 0.495509
\(981\) 3.68720e19 0.0421710
\(982\) −3.08543e20 −0.350376
\(983\) −3.40382e20 + 3.40382e20i −0.383789 + 0.383789i −0.872465 0.488676i \(-0.837480\pi\)
0.488676 + 0.872465i \(0.337480\pi\)
\(984\) −1.31105e21 + 1.31105e21i −1.46775 + 1.46775i
\(985\) 1.27689e21i 1.41939i
\(986\) −1.29251e20 9.10056e20i −0.142657 1.00445i
\(987\) −1.55929e20 −0.170886
\(988\) 2.35092e20 + 2.35092e20i 0.255822 + 0.255822i
\(989\) 9.46459e20 + 9.46459e20i 1.02265 + 1.02265i
\(990\) 5.97812e20i 0.641384i
\(991\) 9.41171e20i 1.00266i 0.865257 + 0.501329i \(0.167155\pi\)
−0.865257 + 0.501329i \(0.832845\pi\)
\(992\) 8.23643e20i 0.871279i
\(993\) −1.38966e21 −1.45970
\(994\) −1.46134e19 + 1.46134e19i −0.0152422 + 0.0152422i
\(995\) 9.49337e20i 0.983238i
\(996\) −1.19547e21 + 1.19547e21i −1.22948 + 1.22948i
\(997\) 1.04466e21 + 1.04466e21i 1.06687 + 1.06687i 0.997598 + 0.0692675i \(0.0220662\pi\)
0.0692675 + 0.997598i \(0.477934\pi\)
\(998\) 5.72746e20 5.72746e20i 0.580829 0.580829i
\(999\) 7.84610e20i 0.790124i
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 29.15.c.a.12.15 68
29.17 odd 4 inner 29.15.c.a.17.15 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.15.c.a.12.15 68 1.1 even 1 trivial
29.15.c.a.17.15 yes 68 29.17 odd 4 inner