Properties

Label 8.16.b.a.5.1
Level $8$
Weight $16$
Character 8.5
Analytic conductor $11.415$
Analytic rank $0$
Dimension $14$
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] = [8,16,Mod(5,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 16, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 16);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.4154804080\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} - 361745089708 x^{8} + 52039630950804 x^{7} + \cdots + 24\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(85.4255 + 19.3112i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.16.b.a.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-176.851 - 38.6225i) q^{2} +4900.64i q^{3} +(29784.6 + 13660.8i) q^{4} +174283. i q^{5} +(189275. - 866683. i) q^{6} +3.39868e6 q^{7} +(-4.73983e6 - 3.56629e6i) q^{8} -9.66732e6 q^{9} +O(q^{10})\) \(q+(-176.851 - 38.6225i) q^{2} +4900.64i q^{3} +(29784.6 + 13660.8i) q^{4} +174283. i q^{5} +(189275. - 866683. i) q^{6} +3.39868e6 q^{7} +(-4.73983e6 - 3.56629e6i) q^{8} -9.66732e6 q^{9} +(6.73124e6 - 3.08221e7i) q^{10} +8.19468e7i q^{11} +(-6.69468e7 + 1.45964e8i) q^{12} +1.80132e8i q^{13} +(-6.01060e8 - 1.31265e8i) q^{14} -8.54097e8 q^{15} +(7.00504e8 + 8.13766e8i) q^{16} -1.02640e9 q^{17} +(1.70968e9 + 3.73376e8i) q^{18} -5.87020e9i q^{19} +(-2.38085e9 + 5.19095e9i) q^{20} +1.66557e10i q^{21} +(3.16499e9 - 1.44924e10i) q^{22} -9.43109e9 q^{23} +(1.74771e10 - 2.32282e10i) q^{24} +1.43006e8 q^{25} +(6.95713e9 - 3.18565e10i) q^{26} +2.29428e10i q^{27} +(1.01228e11 + 4.64288e10i) q^{28} -7.53397e10i q^{29} +(1.51048e11 + 3.29873e10i) q^{30} -1.68086e11 q^{31} +(-9.24553e10 - 1.70971e11i) q^{32} -4.01591e11 q^{33} +(1.81520e11 + 3.96420e10i) q^{34} +5.92332e11i q^{35} +(-2.87937e11 - 1.32064e11i) q^{36} +3.21169e11i q^{37} +(-2.26722e11 + 1.03815e12i) q^{38} -8.82760e11 q^{39} +(6.21544e11 - 8.26071e11i) q^{40} +1.60362e12 q^{41} +(6.43284e11 - 2.94558e12i) q^{42} -1.36491e12i q^{43} +(-1.11946e12 + 2.44075e12i) q^{44} -1.68485e12i q^{45} +(1.66790e12 + 3.64252e11i) q^{46} +1.39788e12 q^{47} +(-3.98797e12 + 3.43292e12i) q^{48} +6.80345e12 q^{49} +(-2.52908e10 - 5.52325e9i) q^{50} -5.03000e12i q^{51} +(-2.46075e12 + 5.36515e12i) q^{52} +2.31639e12i q^{53} +(8.86106e11 - 4.05745e12i) q^{54} -1.42819e13 q^{55} +(-1.61091e13 - 1.21207e13i) q^{56} +2.87677e13 q^{57} +(-2.90980e12 + 1.33239e13i) q^{58} +2.85735e13i q^{59} +(-2.54390e13 - 1.16677e13i) q^{60} -2.15410e13i q^{61} +(2.97261e13 + 6.49188e12i) q^{62} -3.28561e13 q^{63} +(9.74751e12 + 3.38072e13i) q^{64} -3.13939e13 q^{65} +(7.10218e13 + 1.55104e13i) q^{66} +7.75964e12i q^{67} +(-3.05709e13 - 1.40215e13i) q^{68} -4.62183e13i q^{69} +(2.28773e13 - 1.04755e14i) q^{70} -9.37922e13 q^{71} +(4.58214e13 + 3.44765e13i) q^{72} +1.79919e14 q^{73} +(1.24043e13 - 5.67991e13i) q^{74} +7.00821e11i q^{75} +(8.01920e13 - 1.74842e14i) q^{76} +2.78511e14i q^{77} +(1.56117e14 + 3.40944e13i) q^{78} -1.28657e14 q^{79} +(-1.41826e14 + 1.22086e14i) q^{80} -2.51150e14 q^{81} +(-2.83602e14 - 6.19357e13i) q^{82} -2.32762e14i q^{83} +(-2.27531e14 + 4.96083e14i) q^{84} -1.78884e14i q^{85} +(-5.27163e13 + 2.41386e14i) q^{86} +3.69212e14 q^{87} +(2.92246e14 - 3.88413e14i) q^{88} +4.72336e12 q^{89} +(-6.50730e13 + 2.97967e14i) q^{90} +6.12210e14i q^{91} +(-2.80901e14 - 1.28837e14i) q^{92} -8.23726e14i q^{93} +(-2.47216e14 - 5.39895e13i) q^{94} +1.02308e15 q^{95} +(8.37865e14 - 4.53090e14i) q^{96} +4.41963e14 q^{97} +(-1.20320e15 - 2.62766e14i) q^{98} -7.92205e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17} + 526853306 q^{18} - 3449250768 q^{20} + 28367364252 q^{22} - 35548816080 q^{23} + 40155187088 q^{24} - 75899954794 q^{25} + 17666210712 q^{26} + 79863955680 q^{28} - 124878825712 q^{30} - 105758138816 q^{31} - 37651613280 q^{32} - 150458001384 q^{33} + 537472307308 q^{34} + 338679650892 q^{36} + 1649727781164 q^{38} - 2251546247120 q^{39} + 1251083710304 q^{40} - 53229185940 q^{41} - 2437011096800 q^{42} - 3416842360344 q^{44} - 3303531082064 q^{46} + 12527998446432 q^{47} - 6441543679584 q^{48} + 8427385380990 q^{49} + 1179755527374 q^{50} - 2436018627056 q^{52} + 3357642572216 q^{54} - 30557833792176 q^{55} + 7549064859072 q^{56} + 18277230892472 q^{57} - 8014960165320 q^{58} - 53574657402912 q^{60} + 77882578979904 q^{62} + 36142362113776 q^{63} + 76083381630528 q^{64} + 5437123965600 q^{65} - 134116957601160 q^{66} - 69772560247896 q^{68} + 133952399750848 q^{70} - 173249927708016 q^{71} + 163390222317848 q^{72} - 182057837882196 q^{73} + 2072780135688 q^{74} - 248503439494072 q^{76} + 636498768647600 q^{78} - 294370273271392 q^{79} + 766230078246336 q^{80} + 256903428263798 q^{81} - 10\!\cdots\!32 q^{82}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −176.851 38.6225i −0.976973 0.213361i
\(3\) 4900.64i 1.29373i 0.762605 + 0.646864i \(0.223920\pi\)
−0.762605 + 0.646864i \(0.776080\pi\)
\(4\) 29784.6 + 13660.8i 0.908954 + 0.416896i
\(5\) 174283.i 0.997654i 0.866702 + 0.498827i \(0.166236\pi\)
−0.866702 + 0.498827i \(0.833764\pi\)
\(6\) 189275. 866683.i 0.276031 1.26394i
\(7\) 3.39868e6 1.55982 0.779911 0.625891i \(-0.215265\pi\)
0.779911 + 0.625891i \(0.215265\pi\)
\(8\) −4.73983e6 3.56629e6i −0.799075 0.601232i
\(9\) −9.66732e6 −0.673732
\(10\) 6.73124e6 3.08221e7i 0.212860 0.974682i
\(11\) 8.19468e7i 1.26791i 0.773372 + 0.633953i \(0.218569\pi\)
−0.773372 + 0.633953i \(0.781431\pi\)
\(12\) −6.69468e7 + 1.45964e8i −0.539350 + 1.17594i
\(13\) 1.80132e8i 0.796187i 0.917345 + 0.398094i \(0.130328\pi\)
−0.917345 + 0.398094i \(0.869672\pi\)
\(14\) −6.01060e8 1.31265e8i −1.52390 0.332805i
\(15\) −8.54097e8 −1.29069
\(16\) 7.00504e8 + 8.13766e8i 0.652395 + 0.757879i
\(17\) −1.02640e9 −0.606665 −0.303332 0.952885i \(-0.598099\pi\)
−0.303332 + 0.952885i \(0.598099\pi\)
\(18\) 1.70968e9 + 3.73376e8i 0.658218 + 0.143748i
\(19\) 5.87020e9i 1.50661i −0.657671 0.753306i \(-0.728458\pi\)
0.657671 0.753306i \(-0.271542\pi\)
\(20\) −2.38085e9 + 5.19095e9i −0.415918 + 0.906822i
\(21\) 1.66557e10i 2.01798i
\(22\) 3.16499e9 1.44924e10i 0.270521 1.23871i
\(23\) −9.43109e9 −0.577568 −0.288784 0.957394i \(-0.593251\pi\)
−0.288784 + 0.957394i \(0.593251\pi\)
\(24\) 1.74771e10 2.32282e10i 0.777830 1.03379i
\(25\) 1.43006e8 0.00468602
\(26\) 6.95713e9 3.18565e10i 0.169875 0.777854i
\(27\) 2.29428e10i 0.422102i
\(28\) 1.01228e11 + 4.64288e10i 1.41781 + 0.650283i
\(29\) 7.53397e10i 0.811033i −0.914088 0.405517i \(-0.867092\pi\)
0.914088 0.405517i \(-0.132908\pi\)
\(30\) 1.51048e11 + 3.29873e10i 1.26097 + 0.275384i
\(31\) −1.68086e11 −1.09728 −0.548640 0.836059i \(-0.684854\pi\)
−0.548640 + 0.836059i \(0.684854\pi\)
\(32\) −9.24553e10 1.70971e11i −0.475671 0.879623i
\(33\) −4.01591e11 −1.64032
\(34\) 1.81520e11 + 3.96420e10i 0.592696 + 0.129439i
\(35\) 5.92332e11i 1.55616i
\(36\) −2.87937e11 1.32064e11i −0.612391 0.280876i
\(37\) 3.21169e11i 0.556187i 0.960554 + 0.278093i \(0.0897025\pi\)
−0.960554 + 0.278093i \(0.910297\pi\)
\(38\) −2.26722e11 + 1.03815e12i −0.321452 + 1.47192i
\(39\) −8.82760e11 −1.03005
\(40\) 6.21544e11 8.26071e11i 0.599821 0.797200i
\(41\) 1.60362e12 1.28594 0.642972 0.765889i \(-0.277701\pi\)
0.642972 + 0.765889i \(0.277701\pi\)
\(42\) 6.43284e11 2.94558e12i 0.430559 1.97152i
\(43\) 1.36491e12i 0.765758i −0.923799 0.382879i \(-0.874933\pi\)
0.923799 0.382879i \(-0.125067\pi\)
\(44\) −1.11946e12 + 2.44075e12i −0.528585 + 1.15247i
\(45\) 1.68485e12i 0.672152i
\(46\) 1.66790e12 + 3.64252e11i 0.564269 + 0.123231i
\(47\) 1.39788e12 0.402472 0.201236 0.979543i \(-0.435504\pi\)
0.201236 + 0.979543i \(0.435504\pi\)
\(48\) −3.98797e12 + 3.43292e12i −0.980489 + 0.844022i
\(49\) 6.80345e12 1.43304
\(50\) −2.52908e10 5.52325e9i −0.00457812 0.000999814i
\(51\) 5.03000e12i 0.784859i
\(52\) −2.46075e12 + 5.36515e12i −0.331927 + 0.723698i
\(53\) 2.31639e12i 0.270858i 0.990787 + 0.135429i \(0.0432413\pi\)
−0.990787 + 0.135429i \(0.956759\pi\)
\(54\) 8.86106e11 4.05745e12i 0.0900601 0.412383i
\(55\) −1.42819e13 −1.26493
\(56\) −1.61091e13 1.21207e13i −1.24641 0.937814i
\(57\) 2.87677e13 1.94914
\(58\) −2.90980e12 + 1.33239e13i −0.173043 + 0.792358i
\(59\) 2.85735e13i 1.49477i 0.664393 + 0.747384i \(0.268690\pi\)
−0.664393 + 0.747384i \(0.731310\pi\)
\(60\) −2.54390e13 1.16677e13i −1.17318 0.538085i
\(61\) 2.15410e13i 0.877591i −0.898587 0.438795i \(-0.855405\pi\)
0.898587 0.438795i \(-0.144595\pi\)
\(62\) 2.97261e13 + 6.49188e12i 1.07201 + 0.234117i
\(63\) −3.28561e13 −1.05090
\(64\) 9.74751e12 + 3.38072e13i 0.277041 + 0.960858i
\(65\) −3.13939e13 −0.794319
\(66\) 7.10218e13 + 1.55104e13i 1.60255 + 0.349981i
\(67\) 7.75964e12i 0.156416i 0.996937 + 0.0782079i \(0.0249198\pi\)
−0.996937 + 0.0782079i \(0.975080\pi\)
\(68\) −3.05709e13 1.40215e13i −0.551431 0.252916i
\(69\) 4.62183e13i 0.747216i
\(70\) 2.28773e13 1.04755e14i 0.332024 1.52033i
\(71\) −9.37922e13 −1.22385 −0.611926 0.790915i \(-0.709605\pi\)
−0.611926 + 0.790915i \(0.709605\pi\)
\(72\) 4.58214e13 + 3.44765e13i 0.538362 + 0.405069i
\(73\) 1.79919e14 1.90614 0.953072 0.302745i \(-0.0979030\pi\)
0.953072 + 0.302745i \(0.0979030\pi\)
\(74\) 1.24043e13 5.67991e13i 0.118669 0.543380i
\(75\) 7.00821e11i 0.00606244i
\(76\) 8.01920e13 1.74842e14i 0.628100 1.36944i
\(77\) 2.78511e14i 1.97771i
\(78\) 1.56117e14 + 3.40944e13i 1.00633 + 0.219772i
\(79\) −1.28657e14 −0.753753 −0.376876 0.926264i \(-0.623002\pi\)
−0.376876 + 0.926264i \(0.623002\pi\)
\(80\) −1.41826e14 + 1.22086e14i −0.756101 + 0.650865i
\(81\) −2.51150e14 −1.21982
\(82\) −2.83602e14 6.19357e13i −1.25633 0.274370i
\(83\) 2.32762e14i 0.941514i −0.882263 0.470757i \(-0.843981\pi\)
0.882263 0.470757i \(-0.156019\pi\)
\(84\) −2.27531e14 + 4.96083e14i −0.841290 + 1.83426i
\(85\) 1.78884e14i 0.605242i
\(86\) −5.27163e13 + 2.41386e14i −0.163383 + 0.748125i
\(87\) 3.69212e14 1.04926
\(88\) 2.92246e14 3.88413e14i 0.762305 1.01315i
\(89\) 4.72336e12 0.0113195 0.00565974 0.999984i \(-0.498198\pi\)
0.00565974 + 0.999984i \(0.498198\pi\)
\(90\) −6.50730e13 + 2.97967e14i −0.143411 + 0.656674i
\(91\) 6.12210e14i 1.24191i
\(92\) −2.80901e14 1.28837e14i −0.524983 0.240786i
\(93\) 8.23726e14i 1.41958i
\(94\) −2.47216e14 5.39895e13i −0.393204 0.0858717i
\(95\) 1.02308e15 1.50308
\(96\) 8.37865e14 4.53090e14i 1.13799 0.615389i
\(97\) 4.41963e14 0.555390 0.277695 0.960669i \(-0.410430\pi\)
0.277695 + 0.960669i \(0.410430\pi\)
\(98\) −1.20320e15 2.62766e14i −1.40004 0.305755i
\(99\) 7.92205e14i 0.854228i
\(100\) 4.25938e12 + 1.95358e12i 0.00425938 + 0.00195358i
\(101\) 7.48993e14i 0.695132i 0.937655 + 0.347566i \(0.112992\pi\)
−0.937655 + 0.347566i \(0.887008\pi\)
\(102\) −1.94271e14 + 8.89561e14i −0.167458 + 0.766787i
\(103\) 1.47544e15 1.18207 0.591034 0.806647i \(-0.298720\pi\)
0.591034 + 0.806647i \(0.298720\pi\)
\(104\) 6.42402e14 8.53793e14i 0.478693 0.636213i
\(105\) −2.90280e15 −2.01325
\(106\) 8.94646e13 4.09656e14i 0.0577906 0.264621i
\(107\) 5.49539e14i 0.330842i −0.986223 0.165421i \(-0.947102\pi\)
0.986223 0.165421i \(-0.0528982\pi\)
\(108\) −3.13418e14 + 6.83341e14i −0.175973 + 0.383671i
\(109\) 2.46207e15i 1.29003i 0.764168 + 0.645017i \(0.223150\pi\)
−0.764168 + 0.645017i \(0.776850\pi\)
\(110\) 2.52578e15 + 5.51603e14i 1.23580 + 0.269887i
\(111\) −1.57393e15 −0.719555
\(112\) 2.38079e15 + 2.76573e15i 1.01762 + 1.18216i
\(113\) −9.16605e14 −0.366517 −0.183259 0.983065i \(-0.558665\pi\)
−0.183259 + 0.983065i \(0.558665\pi\)
\(114\) −5.08760e15 1.11108e15i −1.90426 0.415871i
\(115\) 1.64368e15i 0.576213i
\(116\) 1.02920e15 2.24396e15i 0.338117 0.737192i
\(117\) 1.74139e15i 0.536417i
\(118\) 1.10358e15 5.05326e15i 0.318925 1.46035i
\(119\) −3.48840e15 −0.946289
\(120\) 4.04827e15 + 3.04596e15i 1.03136 + 0.776006i
\(121\) −2.53803e15 −0.607583
\(122\) −8.31966e14 + 3.80955e15i −0.187244 + 0.857383i
\(123\) 7.85875e15i 1.66366i
\(124\) −5.00636e15 2.29619e15i −0.997378 0.457452i
\(125\) 5.34362e15i 1.00233i
\(126\) 5.81064e15 + 1.26898e15i 1.02670 + 0.224221i
\(127\) 5.63341e15 0.938088 0.469044 0.883175i \(-0.344599\pi\)
0.469044 + 0.883175i \(0.344599\pi\)
\(128\) −4.18141e14 6.35531e15i −0.0656520 0.997843i
\(129\) 6.68894e15 0.990682
\(130\) 5.55205e15 + 1.21251e15i 0.776029 + 0.169477i
\(131\) 2.82994e15i 0.373458i −0.982411 0.186729i \(-0.940211\pi\)
0.982411 0.186729i \(-0.0597887\pi\)
\(132\) −1.19612e16 5.48608e15i −1.49098 0.683845i
\(133\) 1.99509e16i 2.35004i
\(134\) 2.99696e14 1.37230e15i 0.0333730 0.152814i
\(135\) −3.99853e15 −0.421112
\(136\) 4.86495e15 + 3.66043e15i 0.484771 + 0.364746i
\(137\) 1.39509e16 1.31583 0.657913 0.753094i \(-0.271439\pi\)
0.657913 + 0.753094i \(0.271439\pi\)
\(138\) −1.78507e15 + 8.17376e15i −0.159427 + 0.730010i
\(139\) 1.36091e16i 1.15138i −0.817669 0.575689i \(-0.804734\pi\)
0.817669 0.575689i \(-0.195266\pi\)
\(140\) −8.09176e15 + 1.76424e16i −0.648758 + 1.41448i
\(141\) 6.85049e15i 0.520689i
\(142\) 1.65872e16 + 3.62248e15i 1.19567 + 0.261122i
\(143\) −1.47612e16 −1.00949
\(144\) −6.77200e15 7.86693e15i −0.439540 0.510607i
\(145\) 1.31304e16 0.809131
\(146\) −3.18189e16 6.94891e15i −1.86225 0.406697i
\(147\) 3.33412e16i 1.85397i
\(148\) −4.38744e15 + 9.56590e15i −0.231872 + 0.505548i
\(149\) 2.14670e14i 0.0107863i 0.999985 + 0.00539317i \(0.00171671\pi\)
−0.999985 + 0.00539317i \(0.998283\pi\)
\(150\) 2.70674e13 1.23941e14i 0.00129349 0.00592284i
\(151\) −2.98047e15 −0.135506 −0.0677529 0.997702i \(-0.521583\pi\)
−0.0677529 + 0.997702i \(0.521583\pi\)
\(152\) −2.09349e16 + 2.78237e16i −0.905822 + 1.20389i
\(153\) 9.92252e15 0.408730
\(154\) 1.07568e16 4.92549e16i 0.421965 1.93217i
\(155\) 2.92945e16i 1.09471i
\(156\) −2.62927e16 1.20593e16i −0.936268 0.429424i
\(157\) 4.50242e16i 1.52827i 0.645059 + 0.764133i \(0.276833\pi\)
−0.645059 + 0.764133i \(0.723167\pi\)
\(158\) 2.27531e16 + 4.96903e15i 0.736396 + 0.160821i
\(159\) −1.13518e16 −0.350417
\(160\) 2.97973e16 1.61134e16i 0.877560 0.474555i
\(161\) −3.20533e16 −0.900903
\(162\) 4.44161e16 + 9.70001e15i 1.19173 + 0.260261i
\(163\) 2.75686e16i 0.706331i −0.935561 0.353165i \(-0.885105\pi\)
0.935561 0.353165i \(-0.114895\pi\)
\(164\) 4.77632e16 + 2.19068e16i 1.16886 + 0.536105i
\(165\) 6.99905e16i 1.63648i
\(166\) −8.98985e15 + 4.11642e16i −0.200882 + 0.919834i
\(167\) 2.90393e15 0.0620315 0.0310157 0.999519i \(-0.490126\pi\)
0.0310157 + 0.999519i \(0.490126\pi\)
\(168\) 5.93990e16 7.89450e16i 1.21328 1.61252i
\(169\) 1.87384e16 0.366086
\(170\) −6.90893e15 + 3.16358e16i −0.129135 + 0.591305i
\(171\) 5.67491e16i 1.01505i
\(172\) 1.86459e16 4.06534e16i 0.319241 0.696039i
\(173\) 2.57418e16i 0.421982i 0.977488 + 0.210991i \(0.0676690\pi\)
−0.977488 + 0.210991i \(0.932331\pi\)
\(174\) −6.52956e16 1.42599e16i −1.02510 0.223870i
\(175\) 4.86032e14 0.00730936
\(176\) −6.66855e16 + 5.74041e16i −0.960918 + 0.827176i
\(177\) −1.40028e17 −1.93382
\(178\) −8.35332e14 1.82428e14i −0.0110588 0.00241513i
\(179\) 8.37590e16i 1.06325i 0.846981 + 0.531623i \(0.178418\pi\)
−0.846981 + 0.531623i \(0.821582\pi\)
\(180\) 2.30165e16 5.01826e16i 0.280217 0.610955i
\(181\) 3.60190e15i 0.0420671i −0.999779 0.0210336i \(-0.993304\pi\)
0.999779 0.0210336i \(-0.00669568\pi\)
\(182\) 2.36451e16 1.08270e17i 0.264975 1.21331i
\(183\) 1.05565e17 1.13536
\(184\) 4.47017e16 + 3.36340e16i 0.461520 + 0.347252i
\(185\) −5.59743e16 −0.554882
\(186\) −3.18143e16 + 1.45677e17i −0.302883 + 1.38689i
\(187\) 8.41100e16i 0.769194i
\(188\) 4.16352e16 + 1.90962e16i 0.365828 + 0.167789i
\(189\) 7.79751e16i 0.658404i
\(190\) −1.80932e17 3.95137e16i −1.46847 0.320698i
\(191\) 1.83863e17 1.43464 0.717322 0.696742i \(-0.245368\pi\)
0.717322 + 0.696742i \(0.245368\pi\)
\(192\) −1.65677e17 + 4.77690e16i −1.24309 + 0.358416i
\(193\) 7.85347e16 0.566737 0.283369 0.959011i \(-0.408548\pi\)
0.283369 + 0.959011i \(0.408548\pi\)
\(194\) −7.81617e16 1.70697e16i −0.542601 0.118499i
\(195\) 1.53850e17i 1.02763i
\(196\) 2.02638e17 + 9.29410e16i 1.30257 + 0.597429i
\(197\) 7.29349e16i 0.451272i −0.974212 0.225636i \(-0.927554\pi\)
0.974212 0.225636i \(-0.0724460\pi\)
\(198\) −3.05969e16 + 1.40102e17i −0.182259 + 0.834558i
\(199\) −1.32290e17 −0.758802 −0.379401 0.925232i \(-0.623870\pi\)
−0.379401 + 0.925232i \(0.623870\pi\)
\(200\) −6.77824e14 5.10001e14i −0.00374448 0.00281739i
\(201\) −3.80272e16 −0.202359
\(202\) 2.89280e16 1.32460e17i 0.148314 0.679126i
\(203\) 2.56055e17i 1.26507i
\(204\) 6.87141e16 1.49817e17i 0.327205 0.713401i
\(205\) 2.79484e17i 1.28293i
\(206\) −2.60933e17 5.69851e16i −1.15485 0.252207i
\(207\) 9.11734e16 0.389126
\(208\) −1.46585e17 + 1.26183e17i −0.603413 + 0.519429i
\(209\) 4.81044e17 1.91024
\(210\) 5.13364e17 + 1.12113e17i 1.96689 + 0.429549i
\(211\) 1.35103e17i 0.499513i 0.968309 + 0.249756i \(0.0803506\pi\)
−0.968309 + 0.249756i \(0.919649\pi\)
\(212\) −3.16438e16 + 6.89927e16i −0.112920 + 0.246198i
\(213\) 4.59641e17i 1.58333i
\(214\) −2.12245e16 + 9.71866e16i −0.0705887 + 0.323223i
\(215\) 2.37881e17 0.763961
\(216\) 8.18206e16 1.08745e17i 0.253781 0.337291i
\(217\) −5.71269e17 −1.71156
\(218\) 9.50911e16 4.35419e17i 0.275243 1.26033i
\(219\) 8.81717e17i 2.46603i
\(220\) −4.25382e17 1.95103e17i −1.14976 0.527345i
\(221\) 1.84887e17i 0.483019i
\(222\) 2.78352e17 + 6.07891e16i 0.702986 + 0.153525i
\(223\) −6.20180e17 −1.51437 −0.757183 0.653202i \(-0.773425\pi\)
−0.757183 + 0.653202i \(0.773425\pi\)
\(224\) −3.14226e17 5.81074e17i −0.741962 1.37205i
\(225\) −1.38248e15 −0.00315712
\(226\) 1.62103e17 + 3.54016e16i 0.358077 + 0.0782004i
\(227\) 2.33485e17i 0.498960i −0.968380 0.249480i \(-0.919740\pi\)
0.968380 0.249480i \(-0.0802597\pi\)
\(228\) 8.56835e17 + 3.92992e17i 1.77168 + 0.812591i
\(229\) 5.46593e17i 1.09370i 0.837231 + 0.546850i \(0.184173\pi\)
−0.837231 + 0.546850i \(0.815827\pi\)
\(230\) −6.34829e16 + 2.90686e17i −0.122941 + 0.562945i
\(231\) −1.36488e18 −2.55861
\(232\) −2.68683e17 + 3.57097e17i −0.487619 + 0.648076i
\(233\) 8.18025e17 1.43746 0.718732 0.695287i \(-0.244723\pi\)
0.718732 + 0.695287i \(0.244723\pi\)
\(234\) −6.72568e16 + 3.07967e17i −0.114450 + 0.524065i
\(235\) 2.43626e17i 0.401527i
\(236\) −3.90339e17 + 8.51051e17i −0.623163 + 1.35868i
\(237\) 6.30499e17i 0.975151i
\(238\) 6.16927e17 + 1.34730e17i 0.924499 + 0.201901i
\(239\) −1.12195e17 −0.162925 −0.0814625 0.996676i \(-0.525959\pi\)
−0.0814625 + 0.996676i \(0.525959\pi\)
\(240\) −5.98299e17 6.95036e17i −0.842042 0.978189i
\(241\) −4.88568e17 −0.666496 −0.333248 0.942839i \(-0.608145\pi\)
−0.333248 + 0.942839i \(0.608145\pi\)
\(242\) 4.48853e17 + 9.80248e16i 0.593593 + 0.129635i
\(243\) 9.01589e17i 1.15601i
\(244\) 2.94268e17 6.41590e17i 0.365864 0.797690i
\(245\) 1.18573e18i 1.42968i
\(246\) 3.03524e17 1.38983e18i 0.354961 1.62535i
\(247\) 1.05741e18 1.19954
\(248\) 7.96696e17 + 5.99442e17i 0.876809 + 0.659720i
\(249\) 1.14068e18 1.21806
\(250\) 2.06384e17 9.45025e17i 0.213858 0.979249i
\(251\) 7.31956e17i 0.736092i −0.929808 0.368046i \(-0.880027\pi\)
0.929808 0.368046i \(-0.119973\pi\)
\(252\) −9.78606e17 4.48842e17i −0.955221 0.438117i
\(253\) 7.72848e17i 0.732302i
\(254\) −9.96275e17 2.17576e17i −0.916487 0.200151i
\(255\) 8.76644e17 0.783018
\(256\) −1.71509e17 + 1.14009e18i −0.148760 + 0.988873i
\(257\) 7.41815e17 0.624881 0.312440 0.949937i \(-0.398854\pi\)
0.312440 + 0.949937i \(0.398854\pi\)
\(258\) −1.18295e18 2.58343e17i −0.967870 0.211373i
\(259\) 1.09155e18i 0.867552i
\(260\) −9.35055e17 4.28867e17i −0.722000 0.331149i
\(261\) 7.28333e17i 0.546419i
\(262\) −1.09299e17 + 5.00478e17i −0.0796815 + 0.364859i
\(263\) 1.76442e17 0.125007 0.0625036 0.998045i \(-0.480092\pi\)
0.0625036 + 0.998045i \(0.480092\pi\)
\(264\) 1.90347e18 + 1.43219e18i 1.31074 + 0.986215i
\(265\) −4.03707e17 −0.270223
\(266\) −7.70554e17 + 3.52834e18i −0.501408 + 2.29593i
\(267\) 2.31475e16i 0.0146443i
\(268\) −1.06003e17 + 2.31118e17i −0.0652091 + 0.142175i
\(269\) 3.11629e18i 1.86422i −0.362179 0.932108i \(-0.617967\pi\)
0.362179 0.932108i \(-0.382033\pi\)
\(270\) 7.07145e17 + 1.54433e17i 0.411415 + 0.0898489i
\(271\) −4.73577e17 −0.267992 −0.133996 0.990982i \(-0.542781\pi\)
−0.133996 + 0.990982i \(0.542781\pi\)
\(272\) −7.18996e17 8.35248e17i −0.395785 0.459778i
\(273\) −3.00022e18 −1.60669
\(274\) −2.46724e18 5.38819e17i −1.28553 0.280746i
\(275\) 1.17189e16i 0.00594143i
\(276\) 6.31382e17 1.37660e18i 0.311511 0.679185i
\(277\) 4.14576e17i 0.199070i 0.995034 + 0.0995350i \(0.0317355\pi\)
−0.995034 + 0.0995350i \(0.968264\pi\)
\(278\) −5.25616e17 + 2.40678e18i −0.245659 + 1.12486i
\(279\) 1.62494e18 0.739273
\(280\) 2.11243e18 2.80755e18i 0.935614 1.24349i
\(281\) −1.18027e18 −0.508959 −0.254479 0.967078i \(-0.581904\pi\)
−0.254479 + 0.967078i \(0.581904\pi\)
\(282\) 2.64583e17 1.21152e18i 0.111095 0.508699i
\(283\) 8.15996e17i 0.333649i −0.985987 0.166824i \(-0.946649\pi\)
0.985987 0.166824i \(-0.0533513\pi\)
\(284\) −2.79356e18 1.28128e18i −1.11243 0.510219i
\(285\) 5.01373e18i 1.94457i
\(286\) 2.61054e18 + 5.70115e17i 0.986245 + 0.215386i
\(287\) 5.45019e18 2.00584
\(288\) 8.93795e17 + 1.65283e18i 0.320475 + 0.592630i
\(289\) −1.80893e18 −0.631958
\(290\) −2.32213e18 5.07129e17i −0.790499 0.172637i
\(291\) 2.16590e18i 0.718524i
\(292\) 5.35882e18 + 2.45785e18i 1.73260 + 0.794664i
\(293\) 2.76770e17i 0.0872190i −0.999049 0.0436095i \(-0.986114\pi\)
0.999049 0.0436095i \(-0.0138857\pi\)
\(294\) 1.28772e18 5.89644e18i 0.395564 1.81128i
\(295\) −4.97988e18 −1.49126
\(296\) 1.14538e18 1.52229e18i 0.334397 0.444435i
\(297\) −1.88009e18 −0.535185
\(298\) 8.29107e15 3.79646e16i 0.00230138 0.0105380i
\(299\) 1.69884e18i 0.459852i
\(300\) −9.57380e15 + 2.08737e16i −0.00252741 + 0.00551048i
\(301\) 4.63890e18i 1.19444i
\(302\) 5.27100e17 + 1.15113e17i 0.132386 + 0.0289117i
\(303\) −3.67054e18 −0.899312
\(304\) 4.77697e18 4.11210e18i 1.14183 0.982906i
\(305\) 3.75423e18 0.875532
\(306\) −1.75481e18 3.83232e17i −0.399318 0.0872069i
\(307\) 1.17318e18i 0.260512i −0.991480 0.130256i \(-0.958420\pi\)
0.991480 0.130256i \(-0.0415800\pi\)
\(308\) −3.80469e18 + 8.29533e18i −0.824497 + 1.79764i
\(309\) 7.23059e18i 1.52927i
\(310\) −1.13142e18 + 5.18076e18i −0.233568 + 1.06950i
\(311\) 1.01267e18 0.204064 0.102032 0.994781i \(-0.467466\pi\)
0.102032 + 0.994781i \(0.467466\pi\)
\(312\) 4.18413e18 + 3.14818e18i 0.823087 + 0.619298i
\(313\) −2.17123e18 −0.416988 −0.208494 0.978024i \(-0.566856\pi\)
−0.208494 + 0.978024i \(0.566856\pi\)
\(314\) 1.73895e18 7.96259e18i 0.326072 1.49308i
\(315\) 5.72626e18i 1.04844i
\(316\) −3.83199e18 1.75756e18i −0.685127 0.314236i
\(317\) 3.39592e18i 0.592943i −0.955042 0.296471i \(-0.904190\pi\)
0.955042 0.296471i \(-0.0958099\pi\)
\(318\) 2.00757e18 + 4.38433e17i 0.342348 + 0.0747653i
\(319\) 6.17384e18 1.02831
\(320\) −5.89202e18 + 1.69883e18i −0.958604 + 0.276391i
\(321\) 2.69309e18 0.428019
\(322\) 5.66865e18 + 1.23798e18i 0.880158 + 0.192218i
\(323\) 6.02517e18i 0.914008i
\(324\) −7.48039e18 3.43092e18i −1.10876 0.508537i
\(325\) 2.57599e16i 0.00373095i
\(326\) −1.06477e18 + 4.87554e18i −0.150703 + 0.690066i
\(327\) −1.20657e19 −1.66895
\(328\) −7.60087e18 5.71897e18i −1.02757 0.773151i
\(329\) 4.75094e18 0.627784
\(330\) −2.70321e18 + 1.23779e19i −0.349160 + 1.59879i
\(331\) 9.91491e18i 1.25193i 0.779852 + 0.625963i \(0.215294\pi\)
−0.779852 + 0.625963i \(0.784706\pi\)
\(332\) 3.17973e18 6.93273e18i 0.392513 0.855793i
\(333\) 3.10484e18i 0.374721i
\(334\) −5.13563e17 1.12157e17i −0.0606031 0.0132351i
\(335\) −1.35237e18 −0.156049
\(336\) −1.35538e19 + 1.16674e19i −1.52939 + 1.31652i
\(337\) 1.37021e19 1.51203 0.756017 0.654552i \(-0.227143\pi\)
0.756017 + 0.654552i \(0.227143\pi\)
\(338\) −3.31391e18 7.23725e17i −0.357656 0.0781085i
\(339\) 4.49195e18i 0.474173i
\(340\) 2.44370e18 5.32798e18i 0.252323 0.550137i
\(341\) 1.37741e19i 1.39125i
\(342\) 2.19179e18 1.00361e19i 0.216572 0.991679i
\(343\) 6.98732e18 0.675468
\(344\) −4.86767e18 + 6.46944e18i −0.460398 + 0.611898i
\(345\) 8.05507e18 0.745463
\(346\) 9.94212e17 4.55247e18i 0.0900344 0.412265i
\(347\) 8.09568e18i 0.717435i 0.933446 + 0.358717i \(0.116786\pi\)
−0.933446 + 0.358717i \(0.883214\pi\)
\(348\) 1.09968e19 + 5.04375e18i 0.953726 + 0.437431i
\(349\) 6.14623e18i 0.521697i 0.965380 + 0.260848i \(0.0840023\pi\)
−0.965380 + 0.260848i \(0.915998\pi\)
\(350\) −8.59552e16 1.87717e16i −0.00714105 0.00155953i
\(351\) −4.13272e18 −0.336072
\(352\) 1.40105e19 7.57641e18i 1.11528 0.603106i
\(353\) 2.71644e18 0.211685 0.105842 0.994383i \(-0.466246\pi\)
0.105842 + 0.994383i \(0.466246\pi\)
\(354\) 2.47642e19 + 5.40824e18i 1.88929 + 0.412602i
\(355\) 1.63464e19i 1.22098i
\(356\) 1.40684e17 + 6.45252e16i 0.0102889 + 0.00471904i
\(357\) 1.70954e19i 1.22424i
\(358\) 3.23498e18 1.48129e19i 0.226855 1.03876i
\(359\) −1.18069e19 −0.810824 −0.405412 0.914134i \(-0.632872\pi\)
−0.405412 + 0.914134i \(0.632872\pi\)
\(360\) −6.00866e18 + 7.98589e18i −0.404119 + 0.537099i
\(361\) −1.92782e19 −1.26988
\(362\) −1.39114e17 + 6.37001e17i −0.00897548 + 0.0410985i
\(363\) 1.24379e19i 0.786048i
\(364\) −8.36331e18 + 1.82344e19i −0.517747 + 1.12884i
\(365\) 3.13568e19i 1.90167i
\(366\) −1.86692e19 4.07716e18i −1.10922 0.242242i
\(367\) 1.15057e19 0.669756 0.334878 0.942262i \(-0.391305\pi\)
0.334878 + 0.942262i \(0.391305\pi\)
\(368\) −6.60652e18 7.67470e18i −0.376803 0.437727i
\(369\) −1.55027e19 −0.866382
\(370\) 9.89912e18 + 2.16187e18i 0.542105 + 0.118390i
\(371\) 7.87266e18i 0.422490i
\(372\) 1.12528e19 2.45344e19i 0.591818 1.29034i
\(373\) 2.65732e19i 1.36971i 0.728680 + 0.684854i \(0.240134\pi\)
−0.728680 + 0.684854i \(0.759866\pi\)
\(374\) −3.24854e18 + 1.48749e19i −0.164116 + 0.751482i
\(375\) −2.61871e19 −1.29674
\(376\) −6.62570e18 4.98524e18i −0.321605 0.241979i
\(377\) 1.35711e19 0.645734
\(378\) 3.01159e18 1.37900e19i 0.140478 0.643243i
\(379\) 1.87597e19i 0.857891i 0.903330 + 0.428945i \(0.141115\pi\)
−0.903330 + 0.428945i \(0.858885\pi\)
\(380\) 3.04719e19 + 1.39761e19i 1.36623 + 0.626627i
\(381\) 2.76073e19i 1.21363i
\(382\) −3.25164e19 7.10125e18i −1.40161 0.306097i
\(383\) 1.00414e19 0.424428 0.212214 0.977223i \(-0.431933\pi\)
0.212214 + 0.977223i \(0.431933\pi\)
\(384\) 3.11451e19 2.04916e18i 1.29094 0.0849359i
\(385\) −4.85397e19 −1.97307
\(386\) −1.38889e19 3.03320e18i −0.553687 0.120920i
\(387\) 1.31950e19i 0.515915i
\(388\) 1.31637e19 + 6.03759e18i 0.504824 + 0.231540i
\(389\) 5.26344e19i 1.97992i −0.141344 0.989961i \(-0.545142\pi\)
0.141344 0.989961i \(-0.454858\pi\)
\(390\) −5.94207e18 + 2.72086e19i −0.219257 + 1.00397i
\(391\) 9.68006e18 0.350390
\(392\) −3.22472e19 2.42631e19i −1.14511 0.861590i
\(393\) 1.38685e19 0.483154
\(394\) −2.81693e18 + 1.28986e19i −0.0962839 + 0.440881i
\(395\) 2.24227e19i 0.751984i
\(396\) 1.08222e19 2.35955e19i 0.356124 0.776454i
\(397\) 4.83129e19i 1.56003i −0.625758 0.780017i \(-0.715210\pi\)
0.625758 0.780017i \(-0.284790\pi\)
\(398\) 2.33956e19 + 5.10936e18i 0.741330 + 0.161899i
\(399\) 9.77722e19 3.04032
\(400\) 1.00176e17 + 1.16373e17i 0.00305714 + 0.00355144i
\(401\) −2.99975e19 −0.898467 −0.449234 0.893414i \(-0.648303\pi\)
−0.449234 + 0.893414i \(0.648303\pi\)
\(402\) 6.72514e18 + 1.46870e18i 0.197700 + 0.0431756i
\(403\) 3.02775e19i 0.873641i
\(404\) −1.02319e19 + 2.23085e19i −0.289798 + 0.631843i
\(405\) 4.37711e19i 1.21696i
\(406\) −9.88949e18 + 4.52837e19i −0.269916 + 1.23594i
\(407\) −2.63188e19 −0.705192
\(408\) −1.79385e19 + 2.38413e19i −0.471882 + 0.627161i
\(409\) 1.07765e18 0.0278325 0.0139163 0.999903i \(-0.495570\pi\)
0.0139163 + 0.999903i \(0.495570\pi\)
\(410\) 1.07943e19 4.94270e19i 0.273727 1.25339i
\(411\) 6.83684e19i 1.70232i
\(412\) 4.39454e19 + 2.01558e19i 1.07445 + 0.492799i
\(413\) 9.71122e19i 2.33157i
\(414\) −1.61241e19 3.52134e18i −0.380166 0.0830243i
\(415\) 4.05665e19 0.939305
\(416\) 3.07972e19 1.66541e19i 0.700345 0.378723i
\(417\) 6.66931e19 1.48957
\(418\) −8.50732e19 1.85791e19i −1.86625 0.407571i
\(419\) 5.32812e19i 1.14807i −0.818830 0.574036i \(-0.805377\pi\)
0.818830 0.574036i \(-0.194623\pi\)
\(420\) −8.64589e19 3.96547e19i −1.82995 0.839316i
\(421\) 5.14025e19i 1.06873i 0.845253 + 0.534366i \(0.179449\pi\)
−0.845253 + 0.534366i \(0.820551\pi\)
\(422\) 5.21801e18 2.38931e19i 0.106577 0.488011i
\(423\) −1.35137e19 −0.271158
\(424\) 8.26091e18 1.09793e19i 0.162849 0.216436i
\(425\) −1.46781e17 −0.00284285
\(426\) −1.77525e19 + 8.12881e19i −0.337821 + 1.54687i
\(427\) 7.32109e19i 1.36888i
\(428\) 7.50717e18 1.63678e19i 0.137927 0.300720i
\(429\) 7.23393e19i 1.30601i
\(430\) −4.20695e19 9.18755e18i −0.746370 0.163000i
\(431\) −3.85909e19 −0.672829 −0.336415 0.941714i \(-0.609214\pi\)
−0.336415 + 0.941714i \(0.609214\pi\)
\(432\) −1.86700e19 + 1.60715e19i −0.319902 + 0.275377i
\(433\) 3.87254e19 0.652133 0.326067 0.945347i \(-0.394277\pi\)
0.326067 + 0.945347i \(0.394277\pi\)
\(434\) 1.01029e20 + 2.20638e19i 1.67215 + 0.365180i
\(435\) 6.43474e19i 1.04680i
\(436\) −3.36339e19 + 7.33317e19i −0.537810 + 1.17258i
\(437\) 5.53624e19i 0.870171i
\(438\) 3.40541e19 1.55933e20i 0.526155 2.40925i
\(439\) −1.11031e20 −1.68640 −0.843201 0.537599i \(-0.819332\pi\)
−0.843201 + 0.537599i \(0.819332\pi\)
\(440\) 6.76939e19 + 5.09335e19i 1.01077 + 0.760517i
\(441\) −6.57712e19 −0.965486
\(442\) −7.14079e18 + 3.26974e19i −0.103057 + 0.471897i
\(443\) 4.75682e19i 0.674976i −0.941330 0.337488i \(-0.890423\pi\)
0.941330 0.337488i \(-0.109577\pi\)
\(444\) −4.68790e19 2.15013e19i −0.654042 0.299979i
\(445\) 8.23202e17i 0.0112929i
\(446\) 1.09679e20 + 2.39529e19i 1.47950 + 0.323107i
\(447\) −1.05202e18 −0.0139546
\(448\) 3.31287e19 + 1.14900e20i 0.432134 + 1.49877i
\(449\) 2.88459e19 0.370029 0.185015 0.982736i \(-0.440767\pi\)
0.185015 + 0.982736i \(0.440767\pi\)
\(450\) 2.44494e17 + 5.33950e16i 0.00308443 + 0.000673607i
\(451\) 1.31411e20i 1.63046i
\(452\) −2.73007e19 1.25216e19i −0.333147 0.152799i
\(453\) 1.46062e19i 0.175308i
\(454\) −9.01778e18 + 4.12921e19i −0.106459 + 0.487471i
\(455\) −1.06698e20 −1.23900
\(456\) −1.36354e20 1.02594e20i −1.55751 1.17189i
\(457\) −6.84233e19 −0.768834 −0.384417 0.923160i \(-0.625597\pi\)
−0.384417 + 0.923160i \(0.625597\pi\)
\(458\) 2.11108e19 9.66656e19i 0.233353 1.06852i
\(459\) 2.35484e19i 0.256075i
\(460\) 2.24541e19 4.89564e19i 0.240221 0.523752i
\(461\) 1.37605e20i 1.44836i −0.689610 0.724181i \(-0.742218\pi\)
0.689610 0.724181i \(-0.257782\pi\)
\(462\) 2.41380e20 + 5.27150e19i 2.49970 + 0.545908i
\(463\) 1.42820e20 1.45523 0.727615 0.685985i \(-0.240629\pi\)
0.727615 + 0.685985i \(0.240629\pi\)
\(464\) 6.13089e19 5.27758e19i 0.614665 0.529115i
\(465\) 1.43561e20 1.41625
\(466\) −1.44669e20 3.15941e19i −1.40436 0.306699i
\(467\) 1.24349e20i 1.18786i 0.804517 + 0.593930i \(0.202424\pi\)
−0.804517 + 0.593930i \(0.797576\pi\)
\(468\) 2.37889e19 5.18666e19i 0.223630 0.487578i
\(469\) 2.63725e19i 0.243981i
\(470\) 9.40945e18 4.30856e19i 0.0856703 0.392282i
\(471\) −2.20647e20 −1.97716
\(472\) 1.01901e20 1.35433e20i 0.898702 1.19443i
\(473\) 1.11850e20 0.970908
\(474\) −2.43514e19 + 1.11504e20i −0.208059 + 0.952696i
\(475\) 8.39475e17i 0.00706001i
\(476\) −1.03901e20 4.76545e19i −0.860133 0.394504i
\(477\) 2.23932e19i 0.182486i
\(478\) 1.98417e19 + 4.33323e18i 0.159173 + 0.0347618i
\(479\) −2.59178e19 −0.204683 −0.102341 0.994749i \(-0.532633\pi\)
−0.102341 + 0.994749i \(0.532633\pi\)
\(480\) 7.89658e19 + 1.46026e20i 0.613946 + 1.13532i
\(481\) −5.78528e19 −0.442829
\(482\) 8.64039e19 + 1.88697e19i 0.651149 + 0.142204i
\(483\) 1.57081e20i 1.16552i
\(484\) −7.55941e19 3.46716e19i −0.552265 0.253299i
\(485\) 7.70267e19i 0.554087i
\(486\) −3.48216e19 + 1.59447e20i −0.246647 + 1.12939i
\(487\) 2.25603e20 1.57354 0.786770 0.617247i \(-0.211752\pi\)
0.786770 + 0.617247i \(0.211752\pi\)
\(488\) −7.68215e19 + 1.02101e20i −0.527635 + 0.701261i
\(489\) 1.35104e20 0.913800
\(490\) 4.57957e19 2.09697e20i 0.305038 1.39676i
\(491\) 8.41823e19i 0.552217i 0.961126 + 0.276109i \(0.0890449\pi\)
−0.961126 + 0.276109i \(0.910955\pi\)
\(492\) −1.07357e20 + 2.34070e20i −0.693574 + 1.51219i
\(493\) 7.73285e19i 0.492026i
\(494\) −1.87004e20 4.08398e19i −1.17192 0.255936i
\(495\) 1.38068e20 0.852224
\(496\) −1.17745e20 1.36782e20i −0.715861 0.831606i
\(497\) −3.18769e20 −1.90899
\(498\) −2.01731e20 4.40560e19i −1.19001 0.259887i
\(499\) 3.32246e20i 1.93066i −0.261035 0.965329i \(-0.584064\pi\)
0.261035 0.965329i \(-0.415936\pi\)
\(500\) −7.29984e19 + 1.59158e20i −0.417867 + 0.911071i
\(501\) 1.42311e19i 0.0802519i
\(502\) −2.82699e19 + 1.29447e20i −0.157053 + 0.719142i
\(503\) −3.33944e20 −1.82774 −0.913870 0.406007i \(-0.866921\pi\)
−0.913870 + 0.406007i \(0.866921\pi\)
\(504\) 1.55732e20 + 1.17174e20i 0.839749 + 0.631835i
\(505\) −1.30537e20 −0.693502
\(506\) −2.98493e19 + 1.36679e20i −0.156245 + 0.715439i
\(507\) 9.18303e19i 0.473616i
\(508\) 1.67789e20 + 7.69572e19i 0.852679 + 0.391085i
\(509\) 1.32906e20i 0.665521i −0.943011 0.332761i \(-0.892020\pi\)
0.943011 0.332761i \(-0.107980\pi\)
\(510\) −1.55035e20 3.38582e19i −0.764988 0.167066i
\(511\) 6.11487e20 2.97324
\(512\) 7.43648e19 1.95003e20i 0.356322 0.934363i
\(513\) 1.34679e20 0.635944
\(514\) −1.31191e20 2.86507e19i −0.610492 0.133325i
\(515\) 2.57144e20i 1.17929i
\(516\) 1.99227e20 + 9.13765e19i 0.900484 + 0.413011i
\(517\) 1.14552e20i 0.510296i
\(518\) 4.21584e19 1.93042e20i 0.185102 0.847575i
\(519\) −1.26151e20 −0.545929
\(520\) 1.48802e20 + 1.11960e20i 0.634721 + 0.477570i
\(521\) 2.73640e20 1.15053 0.575264 0.817968i \(-0.304899\pi\)
0.575264 + 0.817968i \(0.304899\pi\)
\(522\) 2.81300e19 1.28806e20i 0.116585 0.533837i
\(523\) 3.08487e20i 1.26030i −0.776474 0.630149i \(-0.782994\pi\)
0.776474 0.630149i \(-0.217006\pi\)
\(524\) 3.86594e19 8.42886e19i 0.155693 0.339457i
\(525\) 2.38186e18i 0.00945632i
\(526\) −3.12040e19 6.81464e18i −0.122129 0.0266717i
\(527\) 1.72523e20 0.665682
\(528\) −2.81316e20 3.26801e20i −1.07014 1.24317i
\(529\) −1.77690e20 −0.666415
\(530\) 7.13960e19 + 1.55922e19i 0.264001 + 0.0576550i
\(531\) 2.76229e20i 1.00707i
\(532\) 2.72547e20 5.94231e20i 0.979724 2.13608i
\(533\) 2.88863e20i 1.02385i
\(534\) 8.94013e17 4.09366e18i 0.00312453 0.0143071i
\(535\) 9.57753e19 0.330066
\(536\) 2.76731e19 3.67793e19i 0.0940421 0.124988i
\(537\) −4.10472e20 −1.37555
\(538\) −1.20359e20 + 5.51120e20i −0.397751 + 1.82129i
\(539\) 5.57521e20i 1.81696i
\(540\) −1.19095e20 5.46234e19i −0.382771 0.175560i
\(541\) 5.48913e20i 1.73990i −0.493142 0.869949i \(-0.664152\pi\)
0.493142 0.869949i \(-0.335848\pi\)
\(542\) 8.37527e19 + 1.82907e19i 0.261821 + 0.0571790i
\(543\) 1.76516e19 0.0544234
\(544\) 9.48959e19 + 1.75484e20i 0.288573 + 0.533637i
\(545\) −4.29097e20 −1.28701
\(546\) 5.30592e20 + 1.15876e20i 1.56970 + 0.342806i
\(547\) 3.73838e20i 1.09088i 0.838149 + 0.545442i \(0.183638\pi\)
−0.838149 + 0.545442i \(0.816362\pi\)
\(548\) 4.15523e20 + 1.90581e20i 1.19603 + 0.548563i
\(549\) 2.08244e20i 0.591261i
\(550\) 4.52612e17 2.07250e18i 0.00126767 0.00580462i
\(551\) −4.42259e20 −1.22191
\(552\) −1.64828e20 + 2.19067e20i −0.449250 + 0.597082i
\(553\) −4.37262e20 −1.17572
\(554\) 1.60119e19 7.33182e19i 0.0424738 0.194486i
\(555\) 2.74310e20i 0.717867i
\(556\) 1.85912e20 4.05341e20i 0.480005 1.04655i
\(557\) 9.58954e19i 0.244278i −0.992513 0.122139i \(-0.961025\pi\)
0.992513 0.122139i \(-0.0389753\pi\)
\(558\) −2.87372e20 6.27590e19i −0.722250 0.157732i
\(559\) 2.45864e20 0.609686
\(560\) −4.82020e20 + 4.14931e20i −1.17938 + 1.01523i
\(561\) 4.12193e20 0.995127
\(562\) 2.08731e20 + 4.55848e19i 0.497239 + 0.108592i
\(563\) 5.14407e20i 1.20919i −0.796533 0.604595i \(-0.793335\pi\)
0.796533 0.604595i \(-0.206665\pi\)
\(564\) −9.35835e19 + 2.04039e20i −0.217073 + 0.473282i
\(565\) 1.59749e20i 0.365657i
\(566\) −3.15158e19 + 1.44310e20i −0.0711877 + 0.325966i
\(567\) −8.53577e20 −1.90270
\(568\) 4.44559e20 + 3.34490e20i 0.977950 + 0.735819i
\(569\) 8.71846e20 1.89277 0.946385 0.323041i \(-0.104705\pi\)
0.946385 + 0.323041i \(0.104705\pi\)
\(570\) 1.93642e20 8.86683e20i 0.414896 1.89980i
\(571\) 7.82822e20i 1.65536i 0.561202 + 0.827679i \(0.310339\pi\)
−0.561202 + 0.827679i \(0.689661\pi\)
\(572\) −4.39657e20 2.01651e20i −0.917580 0.420852i
\(573\) 9.01046e20i 1.85604i
\(574\) −9.63871e20 2.10500e20i −1.95966 0.427969i
\(575\) −1.34870e18 −0.00270650
\(576\) −9.42323e19 3.26825e20i −0.186651 0.647361i
\(577\) 5.77728e19 0.112955 0.0564774 0.998404i \(-0.482013\pi\)
0.0564774 + 0.998404i \(0.482013\pi\)
\(578\) 3.19911e20 + 6.98653e19i 0.617406 + 0.134835i
\(579\) 3.84870e20i 0.733204i
\(580\) 3.91085e20 + 1.79373e20i 0.735463 + 0.337323i
\(581\) 7.91084e20i 1.46859i
\(582\) 8.36524e19 3.83042e20i 0.153305 0.701979i
\(583\) −1.89820e20 −0.343423
\(584\) −8.52785e20 6.41643e20i −1.52315 1.14603i
\(585\) 3.03495e20 0.535158
\(586\) −1.06895e19 + 4.89470e19i −0.0186091 + 0.0852107i
\(587\) 1.10291e21i 1.89564i −0.318807 0.947820i \(-0.603282\pi\)
0.318807 0.947820i \(-0.396718\pi\)
\(588\) −4.55470e20 + 9.93056e20i −0.772911 + 1.68517i
\(589\) 9.86696e20i 1.65317i
\(590\) 8.80697e20 + 1.92335e20i 1.45692 + 0.318177i
\(591\) 3.57427e20 0.583824
\(592\) −2.61357e20 + 2.24980e20i −0.421522 + 0.362854i
\(593\) 9.27288e20 1.47674 0.738370 0.674395i \(-0.235596\pi\)
0.738370 + 0.674395i \(0.235596\pi\)
\(594\) 3.32495e20 + 7.26135e19i 0.522862 + 0.114188i
\(595\) 6.07968e20i 0.944069i
\(596\) −2.93257e18 + 6.39386e18i −0.00449678 + 0.00980428i
\(597\) 6.48304e20i 0.981683i
\(598\) −6.56134e19 + 3.00442e20i −0.0981146 + 0.449264i
\(599\) 9.48773e20 1.40107 0.700537 0.713616i \(-0.252944\pi\)
0.700537 + 0.713616i \(0.252944\pi\)
\(600\) 2.49933e18 3.32177e18i 0.00364493 0.00484434i
\(601\) −6.01318e20 −0.866056 −0.433028 0.901380i \(-0.642555\pi\)
−0.433028 + 0.901380i \(0.642555\pi\)
\(602\) −1.79166e20 + 8.20394e20i −0.254848 + 1.16694i
\(603\) 7.50149e19i 0.105382i
\(604\) −8.87722e19 4.07158e19i −0.123169 0.0564918i
\(605\) 4.42335e20i 0.606158i
\(606\) 6.49139e20 + 1.41765e20i 0.878604 + 0.191878i
\(607\) −5.61388e20 −0.750495 −0.375248 0.926925i \(-0.622442\pi\)
−0.375248 + 0.926925i \(0.622442\pi\)
\(608\) −1.00363e21 + 5.42731e20i −1.32525 + 0.716652i
\(609\) 1.25483e21 1.63665
\(610\) −6.63940e20 1.44998e20i −0.855372 0.186804i
\(611\) 2.51802e20i 0.320443i
\(612\) 2.95538e20 + 1.35550e20i 0.371516 + 0.170398i
\(613\) 8.99740e20i 1.11728i −0.829409 0.558642i \(-0.811323\pi\)
0.829409 0.558642i \(-0.188677\pi\)
\(614\) −4.53113e19 + 2.07479e20i −0.0555832 + 0.254514i
\(615\) −1.36965e21 −1.65976
\(616\) 9.93250e20 1.32009e21i 1.18906 1.58033i
\(617\) 1.77760e20 0.210230 0.105115 0.994460i \(-0.466479\pi\)
0.105115 + 0.994460i \(0.466479\pi\)
\(618\) 2.79263e20 1.27874e21i 0.326287 1.49406i
\(619\) 2.01875e20i 0.233025i 0.993189 + 0.116513i \(0.0371716\pi\)
−0.993189 + 0.116513i \(0.962828\pi\)
\(620\) 4.00187e20 8.72524e20i 0.456379 0.995038i
\(621\) 2.16375e20i 0.243793i
\(622\) −1.79093e20 3.91120e19i −0.199365 0.0435393i
\(623\) 1.60532e19 0.0176564
\(624\) −6.18377e20 7.18360e20i −0.672000 0.780653i
\(625\) −9.26938e20 −0.995292
\(626\) 3.83985e20 + 8.38583e19i 0.407386 + 0.0889690i
\(627\) 2.35742e21i 2.47133i
\(628\) −6.15069e20 + 1.34103e21i −0.637128 + 1.38912i
\(629\) 3.29647e20i 0.337419i
\(630\) −2.21162e20 + 1.01270e21i −0.223695 + 1.02429i
\(631\) 8.66955e20 0.866516 0.433258 0.901270i \(-0.357364\pi\)
0.433258 + 0.901270i \(0.357364\pi\)
\(632\) 6.09810e20 + 4.58827e20i 0.602305 + 0.453180i
\(633\) −6.62091e20 −0.646234
\(634\) −1.31159e20 + 6.00572e20i −0.126511 + 0.579289i
\(635\) 9.81808e20i 0.935887i
\(636\) −3.38108e20 1.55075e20i −0.318513 0.146087i
\(637\) 1.22552e21i 1.14097i
\(638\) −1.09185e21 2.38449e20i −1.00463 0.219402i
\(639\) 9.06719e20 0.824548
\(640\) 1.10762e21 7.28749e19i 0.995502 0.0654980i
\(641\) −5.75049e20 −0.510822 −0.255411 0.966833i \(-0.582211\pi\)
−0.255411 + 0.966833i \(0.582211\pi\)
\(642\) −4.76276e20 1.04014e20i −0.418163 0.0913226i
\(643\) 5.75046e20i 0.499023i −0.968372 0.249511i \(-0.919730\pi\)
0.968372 0.249511i \(-0.0802700\pi\)
\(644\) −9.54694e20 4.37875e20i −0.818880 0.375583i
\(645\) 1.16577e21i 0.988358i
\(646\) 2.32707e20 1.06556e21i 0.195014 0.892962i
\(647\) −1.86103e21 −1.54159 −0.770797 0.637080i \(-0.780142\pi\)
−0.770797 + 0.637080i \(0.780142\pi\)
\(648\) 1.19040e21 + 8.95672e20i 0.974725 + 0.733393i
\(649\) −2.34151e21 −1.89522
\(650\) 9.94912e17 4.55567e18i 0.000796039 0.00364504i
\(651\) 2.79958e21i 2.21429i
\(652\) 3.76611e20 8.21121e20i 0.294466 0.642022i
\(653\) 1.47506e21i 1.14015i 0.821593 + 0.570074i \(0.193085\pi\)
−0.821593 + 0.570074i \(0.806915\pi\)
\(654\) 2.13383e21 + 4.66007e20i 1.63052 + 0.356090i
\(655\) 4.93210e20 0.372582
\(656\) 1.12334e21 + 1.30497e21i 0.838944 + 0.974590i
\(657\) −1.73933e21 −1.28423
\(658\) −8.40208e20 1.83493e20i −0.613328 0.133945i
\(659\) 1.67485e21i 1.20875i −0.796701 0.604373i \(-0.793424\pi\)
0.796701 0.604373i \(-0.206576\pi\)
\(660\) 9.56130e20 2.08464e21i 0.682240 1.48748i
\(661\) 1.79249e20i 0.126458i 0.997999 + 0.0632288i \(0.0201398\pi\)
−0.997999 + 0.0632288i \(0.979860\pi\)
\(662\) 3.82938e20 1.75346e21i 0.267112 1.22310i
\(663\) 9.06063e20 0.624895
\(664\) −8.30098e20 + 1.10325e21i −0.566068 + 0.752340i
\(665\) 3.47711e21 2.34453
\(666\) −1.19917e20 + 5.49095e20i −0.0799508 + 0.366092i
\(667\) 7.10536e20i 0.468427i
\(668\) 8.64924e19 + 3.96701e19i 0.0563838 + 0.0258607i
\(669\) 3.03927e21i 1.95918i
\(670\) 2.39169e20 + 5.22320e19i 0.152456 + 0.0332947i
\(671\) 1.76522e21 1.11270
\(672\) 2.84763e21 1.53991e21i 1.77507 0.959897i
\(673\) −1.18737e21 −0.731933 −0.365967 0.930628i \(-0.619262\pi\)
−0.365967 + 0.930628i \(0.619262\pi\)
\(674\) −2.42322e21 5.29207e20i −1.47722 0.322609i
\(675\) 3.28095e18i 0.00197798i
\(676\) 5.58117e20 + 2.55983e20i 0.332755 + 0.152620i
\(677\) 1.27444e21i 0.751455i 0.926730 + 0.375728i \(0.122607\pi\)
−0.926730 + 0.375728i \(0.877393\pi\)
\(678\) −1.73490e20 + 7.94406e20i −0.101170 + 0.463255i
\(679\) 1.50209e21 0.866309
\(680\) −6.37952e20 + 8.47878e20i −0.363891 + 0.483634i
\(681\) 1.14423e21 0.645518
\(682\) −5.31988e20 + 2.43596e21i −0.296838 + 1.35921i
\(683\) 1.00010e21i 0.551937i −0.961167 0.275969i \(-0.911001\pi\)
0.961167 0.275969i \(-0.0889986\pi\)
\(684\) −7.75241e20 + 1.69025e21i −0.423171 + 0.922636i
\(685\) 2.43141e21i 1.31274i
\(686\) −1.23572e21 2.69868e20i −0.659914 0.144119i
\(687\) −2.67865e21 −1.41495
\(688\) 1.11072e21 9.56127e20i 0.580351 0.499577i
\(689\) −4.17255e20 −0.215654
\(690\) −1.42455e21 3.11107e20i −0.728298 0.159053i
\(691\) 1.92165e20i 0.0971827i 0.998819 + 0.0485913i \(0.0154732\pi\)
−0.998819 + 0.0485913i \(0.984527\pi\)
\(692\) −3.51655e20 + 7.66710e20i −0.175922 + 0.383562i
\(693\) 2.69245e21i 1.33244i
\(694\) 3.12675e20 1.43173e21i 0.153073 0.700915i
\(695\) 2.37183e21 1.14868
\(696\) −1.75000e21 1.31672e21i −0.838434 0.630846i
\(697\) −1.64595e21 −0.780138
\(698\) 2.37383e20 1.08697e21i 0.111310 0.509684i
\(699\) 4.00884e21i 1.85969i
\(700\) 1.44763e19 + 6.63960e18i 0.00664387 + 0.00304724i
\(701\) 1.99733e21i 0.906913i −0.891278 0.453456i \(-0.850191\pi\)
0.891278 0.453456i \(-0.149809\pi\)
\(702\) 7.30876e20 + 1.59616e20i 0.328334 + 0.0717047i
\(703\) 1.88533e21 0.837957
\(704\) −2.77039e21 + 7.98777e20i −1.21828 + 0.351262i
\(705\) −1.19392e21 −0.519467
\(706\) −4.80405e20 1.04916e20i −0.206810 0.0451653i
\(707\) 2.54559e21i 1.08428i
\(708\) −4.17069e21 1.91291e21i −1.75776 0.806203i
\(709\) 5.38038e20i 0.224371i 0.993687 + 0.112185i \(0.0357850\pi\)
−0.993687 + 0.112185i \(0.964215\pi\)
\(710\) −6.31338e20 + 2.89088e21i −0.260510 + 1.19287i
\(711\) 1.24376e21 0.507827
\(712\) −2.23879e19 1.68449e19i −0.00904511 0.00680563i
\(713\) 1.58523e21 0.633754
\(714\) −6.60265e20 + 3.02333e21i −0.261205 + 1.19605i
\(715\) 2.57263e21i 1.00712i
\(716\) −1.14422e21 + 2.49473e21i −0.443263 + 0.966442i
\(717\) 5.49825e20i 0.210781i
\(718\) 2.08806e21 + 4.56010e20i 0.792153 + 0.172998i
\(719\) −3.14522e21 −1.18082 −0.590410 0.807103i \(-0.701034\pi\)
−0.590410 + 0.807103i \(0.701034\pi\)
\(720\) 1.37107e21 1.18024e21i 0.509409 0.438509i
\(721\) 5.01454e21 1.84381
\(722\) 3.40936e21 + 7.44570e20i 1.24064 + 0.270942i
\(723\) 2.39430e21i 0.862265i
\(724\) 4.92051e19 1.07281e20i 0.0175376 0.0382371i
\(725\) 1.07740e19i 0.00380052i
\(726\) −4.80384e20 + 2.19966e21i −0.167712 + 0.767948i
\(727\) −2.87779e21 −0.994376 −0.497188 0.867643i \(-0.665634\pi\)
−0.497188 + 0.867643i \(0.665634\pi\)
\(728\) 2.18332e21 2.90177e21i 0.746675 0.992379i
\(729\) 8.14636e20 0.275745
\(730\) 1.21108e21 5.54549e21i 0.405743 1.85788i
\(731\) 1.40094e21i 0.464558i
\(732\) 3.14420e21 + 1.44210e21i 1.03199 + 0.473329i
\(733\) 2.26001e21i 0.734227i −0.930176 0.367114i \(-0.880346\pi\)
0.930176 0.367114i \(-0.119654\pi\)
\(734\) −2.03479e21 4.44377e20i −0.654333 0.142900i
\(735\) −5.81081e21 −1.84962
\(736\) 8.71954e20 + 1.61244e21i 0.274733 + 0.508042i
\(737\) −6.35877e20 −0.198320
\(738\) 2.74167e21 + 5.98752e20i 0.846432 + 0.184852i
\(739\) 5.11782e21i 1.56406i −0.623244 0.782028i \(-0.714186\pi\)
0.623244 0.782028i \(-0.285814\pi\)
\(740\) −1.66717e21 7.64657e20i −0.504363 0.231328i
\(741\) 5.18198e21i 1.55188i
\(742\) 3.04061e20 1.39229e21i 0.0901430 0.412762i
\(743\) 1.70440e21 0.500213 0.250106 0.968218i \(-0.419534\pi\)
0.250106 + 0.968218i \(0.419534\pi\)
\(744\) −2.93765e21 + 3.90432e21i −0.853498 + 1.13435i
\(745\) −3.74133e19 −0.0107610
\(746\) 1.02632e21 4.69951e21i 0.292242 1.33817i
\(747\) 2.25019e21i 0.634328i
\(748\) 1.14901e21 2.50518e21i 0.320674 0.699162i
\(749\) 1.86771e21i 0.516054i
\(750\) 4.63122e21 + 1.01141e21i 1.26688 + 0.276674i
\(751\) −2.99833e21 −0.812045 −0.406023 0.913863i \(-0.633085\pi\)
−0.406023 + 0.913863i \(0.633085\pi\)
\(752\) 9.79219e20 + 1.13755e21i 0.262571 + 0.305025i
\(753\) 3.58705e21 0.952302
\(754\) −2.40006e21 5.24148e20i −0.630865 0.137775i
\(755\) 5.19446e20i 0.135188i
\(756\) −1.06521e21 + 2.32246e21i −0.274486 + 0.598459i
\(757\) 4.05028e21i 1.03339i 0.856168 + 0.516697i \(0.172839\pi\)
−0.856168 + 0.516697i \(0.827161\pi\)
\(758\) 7.24546e20 3.31767e21i 0.183040 0.838136i
\(759\) 3.78744e21 0.947399
\(760\) −4.84920e21 3.64859e21i −1.20107 0.903697i
\(761\) −5.55950e21 −1.36349 −0.681743 0.731592i \(-0.738778\pi\)
−0.681743 + 0.731592i \(0.738778\pi\)
\(762\) 1.06626e21 4.88238e21i 0.258941 1.18568i
\(763\) 8.36778e21i 2.01222i
\(764\) 5.47629e21 + 2.51173e21i 1.30403 + 0.598098i
\(765\) 1.72933e21i 0.407771i
\(766\) −1.77584e21 3.87824e20i −0.414655 0.0905564i
\(767\) −5.14700e21 −1.19011
\(768\) −5.58718e21 8.40503e20i −1.27933 0.192455i
\(769\) 7.86521e21 1.78346 0.891729 0.452570i \(-0.149493\pi\)
0.891729 + 0.452570i \(0.149493\pi\)
\(770\) 8.58430e21 + 1.87472e21i 1.92763 + 0.420975i
\(771\) 3.63536e21i 0.808426i
\(772\) 2.33913e21 + 1.07285e21i 0.515138 + 0.236271i
\(773\) 1.26435e21i 0.275753i −0.990449 0.137876i \(-0.955972\pi\)
0.990449 0.137876i \(-0.0440277\pi\)
\(774\) 5.09625e20 2.33356e21i 0.110076 0.504036i
\(775\) −2.40373e19 −0.00514188
\(776\) −2.09483e21 1.57617e21i −0.443798 0.333918i
\(777\) −5.34929e21 −1.12238
\(778\) −2.03287e21 + 9.30846e21i −0.422438 + 1.93433i
\(779\) 9.41357e21i 1.93742i
\(780\) 2.10172e21 4.58237e21i 0.428416 0.934072i
\(781\) 7.68597e21i 1.55173i
\(782\) −1.71193e21 3.73868e20i −0.342322 0.0747596i
\(783\) 1.72850e21 0.342339
\(784\) 4.76585e21 + 5.53642e21i 0.934910 + 1.08607i
\(785\) −7.84696e21 −1.52468
\(786\) −2.45266e21 5.35635e20i −0.472028 0.103086i
\(787\) 2.89214e21i 0.551327i −0.961254 0.275663i \(-0.911102\pi\)
0.961254 0.275663i \(-0.0888975\pi\)
\(788\) 9.96353e20 2.17234e21i 0.188134 0.410186i
\(789\) 8.64680e20i 0.161725i
\(790\) −8.66018e20 + 3.96547e21i −0.160444 + 0.734669i
\(791\) −3.11525e21 −0.571701
\(792\) −2.82524e21 + 3.75492e21i −0.513589 + 0.682592i
\(793\) 3.88022e21 0.698727
\(794\) −1.86596e21 + 8.54418e21i −0.332850 + 1.52411i
\(795\) 1.97842e21i 0.349595i
\(796\) −3.94020e21 1.80719e21i −0.689716 0.316342i
\(797\) 2.93789e21i 0.509447i 0.967014 + 0.254723i \(0.0819844\pi\)
−0.967014 + 0.254723i \(0.918016\pi\)
\(798\) −1.72911e22 3.77620e21i −2.97031 0.648685i
\(799\) −1.43478e21 −0.244165
\(800\) −1.32217e19 2.44498e19i −0.00222901 0.00412193i
\(801\) −4.56623e19 −0.00762629
\(802\) 5.30509e21 + 1.15858e21i 0.877779 + 0.191698i
\(803\) 1.47438e22i 2.41681i
\(804\) −1.13262e21 5.19483e20i −0.183935 0.0843628i
\(805\) 5.58634e21i 0.898790i
\(806\) −1.16939e21 + 5.35462e21i −0.186401 + 0.853524i
\(807\) 1.52718e22 2.41179
\(808\) 2.67113e21 3.55010e21i 0.417936 0.555463i
\(809\) 7.69701e21 1.19319 0.596593 0.802544i \(-0.296521\pi\)
0.596593 + 0.802544i \(0.296521\pi\)
\(810\) −1.69055e21 + 7.74097e21i −0.259651 + 1.18893i
\(811\) 2.38886e21i 0.363525i −0.983342 0.181762i \(-0.941820\pi\)
0.983342 0.181762i \(-0.0581802\pi\)
\(812\) 3.49793e21 7.62651e21i 0.527401 1.14989i
\(813\) 2.32083e21i 0.346708i
\(814\) 4.65450e21 + 1.01650e21i 0.688954 + 0.150461i
\(815\) 4.80474e21 0.704674
\(816\) 4.09325e21 3.52354e21i 0.594828 0.512039i
\(817\) −8.01231e21 −1.15370
\(818\) −1.90584e20 4.16215e19i −0.0271916 0.00593838i
\(819\) 5.91843e21i 0.836714i
\(820\) −3.81798e21 + 8.32431e21i −0.534848 + 1.16612i
\(821\) 1.33122e22i 1.84789i 0.382525 + 0.923945i \(0.375055\pi\)
−0.382525 + 0.923945i \(0.624945\pi\)
\(822\) 2.64055e21 1.20910e22i 0.363209 1.66312i
\(823\) 1.29945e22 1.77117 0.885584 0.464479i \(-0.153759\pi\)
0.885584 + 0.464479i \(0.153759\pi\)
\(824\) −6.99332e21 5.26185e21i −0.944560 0.710696i
\(825\) −5.74300e19 −0.00768660
\(826\) 3.75071e21 1.71744e22i 0.497466 2.27788i
\(827\) 7.92255e21i 1.04130i −0.853772 0.520648i \(-0.825691\pi\)
0.853772 0.520648i \(-0.174309\pi\)
\(828\) 2.71556e21 + 1.24551e21i 0.353698 + 0.162225i
\(829\) 5.85648e21i 0.755924i −0.925821 0.377962i \(-0.876625\pi\)
0.925821 0.377962i \(-0.123375\pi\)
\(830\) −7.17423e21 1.56678e21i −0.917676 0.200411i
\(831\) −2.03168e21 −0.257542
\(832\) −6.08975e21 + 1.75584e21i −0.765023 + 0.220576i
\(833\) −6.98305e21 −0.869376
\(834\) −1.17947e22 2.57585e21i −1.45527 0.317816i
\(835\) 5.06105e20i 0.0618860i
\(836\) 1.43277e22 + 6.57147e21i 1.73632 + 0.796371i
\(837\) 3.85635e21i 0.463164i
\(838\) −2.05785e21 + 9.42284e21i −0.244954 + 1.12163i
\(839\) 8.12948e21 0.959065 0.479532 0.877524i \(-0.340806\pi\)
0.479532 + 0.877524i \(0.340806\pi\)
\(840\) 1.37588e22 + 1.03522e22i 1.60874 + 1.21043i
\(841\) 2.95312e21 0.342225
\(842\) 1.98529e21 9.09059e21i 0.228026 1.04412i
\(843\) 5.78406e21i 0.658454i
\(844\) −1.84562e21 + 4.02399e21i −0.208245 + 0.454034i
\(845\) 3.26579e21i 0.365227i
\(846\) 2.38992e21 + 5.21933e20i 0.264914 + 0.0578545i
\(847\) −8.62594e21 −0.947721
\(848\) −1.88500e21 + 1.62264e21i −0.205278 + 0.176707i
\(849\) 3.99890e21 0.431651
\(850\) 2.59584e19 + 5.66905e18i 0.00277739 + 0.000606552i
\(851\) 3.02898e21i 0.321236i
\(852\) 6.27909e21 1.36902e22i 0.660085 1.43918i
\(853\) 3.59973e21i 0.375105i −0.982255 0.187552i \(-0.939945\pi\)
0.982255 0.187552i \(-0.0600554\pi\)
\(854\) −2.82759e21 + 1.29474e22i −0.292067 + 1.33736i
\(855\) −9.89041e21 −1.01267
\(856\) −1.95982e21 + 2.60472e21i −0.198912 + 0.264367i
\(857\) −1.21594e22 −1.22336 −0.611681 0.791105i \(-0.709506\pi\)
−0.611681 + 0.791105i \(0.709506\pi\)
\(858\) −2.79392e21 + 1.27933e22i −0.278651 + 1.27593i
\(859\) 1.14000e22i 1.12708i 0.826088 + 0.563541i \(0.190561\pi\)
−0.826088 + 0.563541i \(0.809439\pi\)
\(860\) 7.08519e21 + 3.24966e21i 0.694406 + 0.318492i
\(861\) 2.67094e22i 2.59502i
\(862\) 6.82484e21 + 1.49047e21i 0.657336 + 0.143556i
\(863\) −1.71131e22 −1.63399 −0.816994 0.576647i \(-0.804361\pi\)
−0.816994 + 0.576647i \(0.804361\pi\)
\(864\) 3.92254e21 2.12118e21i 0.371291 0.200782i
\(865\) −4.48636e21 −0.420992
\(866\) −6.84862e21 1.49567e21i −0.637117 0.139140i
\(867\) 8.86491e21i 0.817581i
\(868\) −1.70150e22 7.80402e21i −1.55573 0.713543i
\(869\) 1.05430e22i 0.955687i
\(870\) 2.48526e21 1.13799e22i 0.223345 1.02269i
\(871\) −1.39776e21 −0.124536
\(872\) 8.78045e21 1.16698e22i 0.775610 1.03083i
\(873\) −4.27260e21 −0.374184
\(874\) 2.13823e21 9.79091e21i 0.185660 0.850134i
\(875\) 1.81612e22i 1.56345i
\(876\) −1.20450e22 + 2.62616e22i −1.02808 + 2.24151i
\(877\) 1.57451e22i 1.33244i 0.745755 + 0.666220i \(0.232089\pi\)
−0.745755 + 0.666220i \(0.767911\pi\)
\(878\) 1.96360e22 + 4.28830e21i 1.64757 + 0.359812i
\(879\) 1.35635e21 0.112838
\(880\) −1.00046e22 1.16222e22i −0.825235 0.958664i
\(881\) −6.09608e21 −0.498576 −0.249288 0.968429i \(-0.580197\pi\)
−0.249288 + 0.968429i \(0.580197\pi\)
\(882\) 1.16317e22 + 2.54024e21i 0.943254 + 0.205997i
\(883\) 9.32569e21i 0.749853i 0.927055 + 0.374926i \(0.122332\pi\)
−0.927055 + 0.374926i \(0.877668\pi\)
\(884\) 2.52571e21 5.50678e21i 0.201369 0.439042i
\(885\) 2.44046e22i 1.92929i
\(886\) −1.83720e21 + 8.41248e21i −0.144014 + 0.659434i
\(887\) 5.68335e21 0.441751 0.220875 0.975302i \(-0.429109\pi\)
0.220875 + 0.975302i \(0.429109\pi\)
\(888\) 7.46016e21 + 5.61310e21i 0.574978 + 0.432619i
\(889\) 1.91462e22 1.46325
\(890\) 3.17941e19 1.45584e20i 0.00240947 0.0110329i
\(891\) 2.05809e22i 1.54661i
\(892\) −1.84718e22 8.47218e21i −1.37649 0.631333i
\(893\) 8.20583e21i 0.606368i
\(894\) 1.86051e20 + 4.06315e19i 0.0136333 + 0.00297736i
\(895\) −1.45978e22 −1.06075
\(896\) −1.42113e21 2.15997e22i −0.102405 1.55646i
\(897\) 8.32539e21 0.594924
\(898\) −5.10142e21 1.11410e21i −0.361509 0.0789498i
\(899\) 1.26635e22i 0.889931i
\(900\) −4.11768e19 1.88859e19i −0.00286968 0.00131619i
\(901\) 2.37754e21i 0.164320i
\(902\) 5.07543e21 2.32402e22i 0.347876 1.59291i
\(903\) 2.27335e22 1.54529
\(904\) 4.34455e21 + 3.26888e21i 0.292874 + 0.220362i
\(905\) 6.27751e20 0.0419684
\(906\) −5.64128e20 + 2.58312e21i −0.0374038 + 0.171271i
\(907\) 1.47040e22i 0.966897i 0.875373 + 0.483449i \(0.160616\pi\)
−0.875373 + 0.483449i \(0.839384\pi\)
\(908\) 3.18961e21 6.95427e21i 0.208014 0.453532i
\(909\) 7.24075e21i 0.468333i
\(910\) 1.88696e22 + 4.12093e21i 1.21047 + 0.264353i
\(911\) −2.92800e21 −0.186287 −0.0931437 0.995653i \(-0.529692\pi\)
−0.0931437 + 0.995653i \(0.529692\pi\)
\(912\) 2.01519e22 + 2.34102e22i 1.27161 + 1.47722i
\(913\) 1.90741e22 1.19375
\(914\) 1.21007e22 + 2.64268e21i 0.751130 + 0.164039i
\(915\) 1.83981e22i 1.13270i
\(916\) −7.46693e21 + 1.62801e22i −0.455959 + 0.994123i
\(917\) 9.61805e21i 0.582528i
\(918\) −9.09498e20 + 4.16456e21i −0.0546363 + 0.250178i
\(919\) −2.37414e22 −1.41462 −0.707309 0.706904i \(-0.750091\pi\)
−0.707309 + 0.706904i \(0.750091\pi\)
\(920\) −5.86184e21 + 7.79075e21i −0.346438 + 0.460438i
\(921\) 5.74935e21 0.337032
\(922\) −5.31464e21 + 2.43356e22i −0.309024 + 1.41501i
\(923\) 1.68950e22i 0.974416i
\(924\) −4.06524e22 1.86454e22i −2.32566 1.06668i
\(925\) 4.59291e19i 0.00260630i
\(926\) −2.52579e22 5.51606e21i −1.42172 0.310490i
\(927\) −1.42635e22 −0.796396
\(928\) −1.28809e22 + 6.96555e21i −0.713404 + 0.385785i
\(929\) 2.40850e22 1.32321 0.661606 0.749852i \(-0.269875\pi\)
0.661606 + 0.749852i \(0.269875\pi\)
\(930\) −2.53890e22 5.54470e21i −1.38364 0.302173i
\(931\) 3.99377e22i 2.15904i
\(932\) 2.43646e22 + 1.11749e22i 1.30659 + 0.599273i
\(933\) 4.96275e21i 0.264004i
\(934\) 4.80266e21 2.19912e22i 0.253443 1.16051i
\(935\) 1.46589e22 0.767389
\(936\) −6.21031e21 + 8.25389e21i −0.322511 + 0.428637i
\(937\) 1.45880e22 0.751535 0.375768 0.926714i \(-0.377379\pi\)
0.375768 + 0.926714i \(0.377379\pi\)
\(938\) 1.01857e21 4.66401e21i 0.0520559 0.238363i
\(939\) 1.06404e22i 0.539469i
\(940\) −3.32814e21 + 7.25632e21i −0.167395 + 0.364970i
\(941\) 2.69089e21i 0.134268i −0.997744 0.0671342i \(-0.978614\pi\)
0.997744 0.0671342i \(-0.0213856\pi\)
\(942\) 3.90217e22 + 8.52195e21i 1.93163 + 0.421849i
\(943\) −1.51239e22 −0.742721
\(944\) −2.32522e22 + 2.00159e22i −1.13285 + 0.975179i
\(945\) −1.35897e22 −0.656859
\(946\) −1.97808e22 4.31993e21i −0.948551 0.207154i
\(947\) 2.17487e22i 1.03469i −0.855778 0.517344i \(-0.826921\pi\)
0.855778 0.517344i \(-0.173079\pi\)
\(948\) 8.61315e21 1.87792e22i 0.406536 0.886367i
\(949\) 3.24091e22i 1.51765i
\(950\) −3.24226e19 + 1.48462e20i −0.00150633 + 0.00689745i
\(951\) 1.66421e22 0.767106
\(952\) 1.65344e22 + 1.24406e22i 0.756156 + 0.568939i
\(953\) −2.99084e22 −1.35705 −0.678527 0.734576i \(-0.737381\pi\)
−0.678527 + 0.734576i \(0.737381\pi\)
\(954\) −8.64882e20 + 3.96027e21i −0.0389354 + 0.178284i
\(955\) 3.20442e22i 1.43128i
\(956\) −3.34167e21 1.53267e21i −0.148091 0.0679228i
\(957\) 3.02558e22i 1.33036i
\(958\) 4.58359e21 + 1.00101e21i 0.199970 + 0.0436713i
\(959\) 4.74147e22 2.05245
\(960\) −8.32533e21 2.88746e22i −0.357575 1.24017i
\(961\) 4.78749e21 0.204024
\(962\) 1.02313e22 + 2.23442e21i 0.432632 + 0.0944824i
\(963\) 5.31257e21i 0.222899i
\(964\) −1.45518e22 6.67426e21i −0.605814 0.277860i
\(965\) 1.36873e22i 0.565408i
\(966\) −6.06687e21 + 2.77800e22i −0.248677 + 1.13869i
\(967\) −3.74766e22 −1.52427 −0.762134 0.647420i \(-0.775848\pi\)
−0.762134 + 0.647420i \(0.775848\pi\)
\(968\) 1.20298e22 + 9.05134e21i 0.485505 + 0.365298i
\(969\) −2.95271e22 −1.18248
\(970\) 2.97496e21 1.36223e22i 0.118221 0.541329i
\(971\) 2.48699e22i 0.980687i 0.871529 + 0.490344i \(0.163129\pi\)
−0.871529 + 0.490344i \(0.836871\pi\)
\(972\) 1.23165e22 2.68535e22i 0.481936 1.05076i
\(973\) 4.62529e22i 1.79594i
\(974\) −3.98981e22 8.71334e21i −1.53731 0.335732i
\(975\) −1.26240e20 −0.00482684
\(976\) 1.75293e22 1.50896e22i 0.665107 0.572536i
\(977\) 1.45139e22 0.546481 0.273240 0.961946i \(-0.411905\pi\)
0.273240 + 0.961946i \(0.411905\pi\)
\(978\) −2.38933e22 5.21804e21i −0.892758 0.194969i
\(979\) 3.87064e20i 0.0143520i
\(980\) −1.61980e22 + 3.53164e22i −0.596028 + 1.29951i
\(981\) 2.38016e22i 0.869137i
\(982\) 3.25133e21 1.48877e22i 0.117822 0.539501i
\(983\) 3.45371e21 0.124204 0.0621018 0.998070i \(-0.480220\pi\)
0.0621018 + 0.998070i \(0.480220\pi\)
\(984\) 2.80266e22 3.72491e22i 1.00025 1.32939i
\(985\) 1.27113e22 0.450214
\(986\) 2.98662e21 1.36756e22i 0.104979 0.480696i
\(987\) 2.32826e22i 0.812181i
\(988\) 3.14945e22 + 1.44451e22i 1.09033 + 0.500085i
\(989\) 1.28726e22i 0.442277i
\(990\) −2.44175e22 5.33252e21i −0.832601 0.181831i
\(991\) 3.77091e21 0.127613 0.0638064 0.997962i \(-0.479676\pi\)
0.0638064 + 0.997962i \(0.479676\pi\)
\(992\) 1.55404e22 + 2.87377e22i 0.521945 + 0.965193i
\(993\) −4.85894e22 −1.61965
\(994\) 5.63747e22 + 1.23117e22i 1.86503 + 0.407304i
\(995\) 2.30559e22i 0.757022i
\(996\) 3.39748e22 + 1.55827e22i 1.10716 + 0.507805i
\(997\) 3.32273e22i 1.07469i −0.843364 0.537343i \(-0.819428\pi\)
0.843364 0.537343i \(-0.180572\pi\)
\(998\) −1.28322e22 + 5.87580e22i −0.411927 + 1.88620i
\(999\) −7.36851e21 −0.234768
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 8.16.b.a.5.1 14
3.2 odd 2 72.16.d.b.37.14 14
4.3 odd 2 32.16.b.a.17.3 14
8.3 odd 2 32.16.b.a.17.12 14
8.5 even 2 inner 8.16.b.a.5.2 yes 14
24.5 odd 2 72.16.d.b.37.13 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.16.b.a.5.1 14 1.1 even 1 trivial
8.16.b.a.5.2 yes 14 8.5 even 2 inner
32.16.b.a.17.3 14 4.3 odd 2
32.16.b.a.17.12 14 8.3 odd 2
72.16.d.b.37.13 14 24.5 odd 2
72.16.d.b.37.14 14 3.2 odd 2