Properties

Label 8.16.b.a.5.10
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 5.10
Root \(-53.8860 - 74.8506i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.16.b.a.5.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(101.772 + 149.701i) q^{2} +3583.46i q^{3} +(-12052.9 + 30470.8i) q^{4} +82632.2i q^{5} +(-536448. + 364695. i) q^{6} -153730. q^{7} +(-5.78817e6 + 1.29673e6i) q^{8} +1.50775e6 q^{9} +O(q^{10})\) \(q+(101.772 + 149.701i) q^{2} +3583.46i q^{3} +(-12052.9 + 30470.8i) q^{4} +82632.2i q^{5} +(-536448. + 364695. i) q^{6} -153730. q^{7} +(-5.78817e6 + 1.29673e6i) q^{8} +1.50775e6 q^{9} +(-1.23701e7 + 8.40964e6i) q^{10} -2.04333e7i q^{11} +(-1.09191e8 - 4.31912e7i) q^{12} -7.09837e7i q^{13} +(-1.56454e7 - 2.30136e7i) q^{14} -2.96109e8 q^{15} +(-7.83195e8 - 7.34525e8i) q^{16} -2.71566e9 q^{17} +(1.53447e8 + 2.25712e8i) q^{18} +4.09857e9i q^{19} +(-2.51787e9 - 9.95961e8i) q^{20} -5.50885e8i q^{21} +(3.05889e9 - 2.07953e9i) q^{22} +2.81564e10 q^{23} +(-4.64677e9 - 2.07416e10i) q^{24} +2.36895e10 q^{25} +(1.06264e10 - 7.22415e9i) q^{26} +5.68216e10i q^{27} +(1.85290e9 - 4.68428e9i) q^{28} +1.54113e11i q^{29} +(-3.01356e10 - 4.43279e10i) q^{30} -7.02050e10 q^{31} +(3.02521e10 - 1.91999e11i) q^{32} +7.32217e10 q^{33} +(-2.76378e11 - 4.06538e11i) q^{34} -1.27031e10i q^{35} +(-1.81728e10 + 4.59423e10i) q^{36} +4.56880e11i q^{37} +(-6.13561e11 + 4.17119e11i) q^{38} +2.54367e11 q^{39} +(-1.07152e11 - 4.78289e11i) q^{40} -4.22953e11 q^{41} +(8.24682e10 - 5.60646e10i) q^{42} -9.06774e11i q^{43} +(6.22618e11 + 2.46281e11i) q^{44} +1.24589e11i q^{45} +(2.86553e12 + 4.21505e12i) q^{46} +3.38491e12 q^{47} +(2.63214e12 - 2.80654e12i) q^{48} -4.72393e12 q^{49} +(2.41093e12 + 3.54635e12i) q^{50} -9.73146e12i q^{51} +(2.16293e12 + 8.55563e11i) q^{52} -5.59117e11i q^{53} +(-8.50627e12 + 5.78285e12i) q^{54} +1.68845e12 q^{55} +(8.89815e11 - 1.99346e11i) q^{56} -1.46870e13 q^{57} +(-2.30709e13 + 1.56844e13i) q^{58} -2.62540e13i q^{59} +(3.56898e12 - 9.02267e12i) q^{60} +3.59071e13i q^{61} +(-7.14490e12 - 1.05098e13i) q^{62} -2.31786e11 q^{63} +(3.18214e13 - 1.50114e13i) q^{64} +5.86554e12 q^{65} +(7.45192e12 + 1.09614e13i) q^{66} -1.80671e13i q^{67} +(3.27317e13 - 8.27484e13i) q^{68} +1.00897e14i q^{69} +(1.90166e12 - 1.29281e12i) q^{70} +1.14816e14 q^{71} +(-8.72710e12 + 1.95514e12i) q^{72} -5.99884e12 q^{73} +(-6.83955e13 + 4.64975e13i) q^{74} +8.48903e13i q^{75} +(-1.24887e14 - 4.93998e13i) q^{76} +3.14121e12i q^{77} +(2.58874e13 + 3.80791e13i) q^{78} +1.01573e14 q^{79} +(6.06954e13 - 6.47171e13i) q^{80} -1.81983e14 q^{81} +(-4.30447e13 - 6.33165e13i) q^{82} -1.34312e14i q^{83} +(1.67859e13 + 6.63979e12i) q^{84} -2.24401e14i q^{85} +(1.35745e14 - 9.22842e13i) q^{86} -5.52257e14 q^{87} +(2.64964e13 + 1.18271e14i) q^{88} +8.80035e13 q^{89} +(-1.86511e13 + 1.26796e13i) q^{90} +1.09123e13i q^{91} +(-3.39367e14 + 8.57947e14i) q^{92} -2.51576e14i q^{93} +(3.44489e14 + 5.06726e14i) q^{94} -3.38674e14 q^{95} +(6.88021e14 + 1.08407e14i) q^{96} +1.21693e15 q^{97} +(-4.80763e14 - 7.07178e14i) q^{98} -3.08082e13i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 101.772 + 149.701i 0.562216 + 0.826991i
\(3\) 3583.46i 0.946003i 0.881062 + 0.473002i \(0.156830\pi\)
−0.881062 + 0.473002i \(0.843170\pi\)
\(4\) −12052.9 + 30470.8i −0.367827 + 0.929894i
\(5\) 82632.2i 0.473014i 0.971630 + 0.236507i \(0.0760027\pi\)
−0.971630 + 0.236507i \(0.923997\pi\)
\(6\) −536448. + 364695.i −0.782336 + 0.531858i
\(7\) −153730. −0.0705543 −0.0352772 0.999378i \(-0.511231\pi\)
−0.0352772 + 0.999378i \(0.511231\pi\)
\(8\) −5.78817e6 + 1.29673e6i −0.975812 + 0.218612i
\(9\) 1.50775e6 0.105078
\(10\) −1.23701e7 + 8.40964e6i −0.391178 + 0.265936i
\(11\) 2.04333e7i 0.316150i −0.987427 0.158075i \(-0.949471\pi\)
0.987427 0.158075i \(-0.0505287\pi\)
\(12\) −1.09191e8 4.31912e7i −0.879683 0.347965i
\(13\) 7.09837e7i 0.313750i −0.987618 0.156875i \(-0.949858\pi\)
0.987618 0.156875i \(-0.0501420\pi\)
\(14\) −1.56454e7 2.30136e7i −0.0396668 0.0583478i
\(15\) −2.96109e8 −0.447473
\(16\) −7.83195e8 7.34525e8i −0.729407 0.684080i
\(17\) −2.71566e9 −1.60513 −0.802563 0.596567i \(-0.796531\pi\)
−0.802563 + 0.596567i \(0.796531\pi\)
\(18\) 1.53447e8 + 2.25712e8i 0.0590763 + 0.0868982i
\(19\) 4.09857e9i 1.05191i 0.850511 + 0.525957i \(0.176293\pi\)
−0.850511 + 0.525957i \(0.823707\pi\)
\(20\) −2.51787e9 9.95961e8i −0.439853 0.173987i
\(21\) 5.50885e8i 0.0667446i
\(22\) 3.05889e9 2.07953e9i 0.261453 0.177744i
\(23\) 2.81564e10 1.72432 0.862160 0.506636i \(-0.169111\pi\)
0.862160 + 0.506636i \(0.169111\pi\)
\(24\) −4.64677e9 2.07416e10i −0.206808 0.923121i
\(25\) 2.36895e10 0.776257
\(26\) 1.06264e10 7.22415e9i 0.259468 0.176395i
\(27\) 5.68216e10i 1.04541i
\(28\) 1.85290e9 4.68428e9i 0.0259518 0.0656081i
\(29\) 1.54113e11i 1.65903i 0.558484 + 0.829515i \(0.311383\pi\)
−0.558484 + 0.829515i \(0.688617\pi\)
\(30\) −3.01356e10 4.43279e10i −0.251577 0.370056i
\(31\) −7.02050e10 −0.458306 −0.229153 0.973390i \(-0.573596\pi\)
−0.229153 + 0.973390i \(0.573596\pi\)
\(32\) 3.02521e10 1.91999e11i 0.155643 0.987813i
\(33\) 7.32217e10 0.299079
\(34\) −2.76378e11 4.06538e11i −0.902427 1.32742i
\(35\) 1.27031e10i 0.0333732i
\(36\) −1.81728e10 + 4.59423e10i −0.0386504 + 0.0977111i
\(37\) 4.56880e11i 0.791205i 0.918422 + 0.395603i \(0.129464\pi\)
−0.918422 + 0.395603i \(0.870536\pi\)
\(38\) −6.13561e11 + 4.17119e11i −0.869923 + 0.591403i
\(39\) 2.54367e11 0.296808
\(40\) −1.07152e11 4.78289e11i −0.103407 0.461573i
\(41\) −4.22953e11 −0.339166 −0.169583 0.985516i \(-0.554242\pi\)
−0.169583 + 0.985516i \(0.554242\pi\)
\(42\) 8.24682e10 5.60646e10i 0.0551972 0.0375249i
\(43\) 9.06774e11i 0.508728i −0.967109 0.254364i \(-0.918134\pi\)
0.967109 0.254364i \(-0.0818661\pi\)
\(44\) 6.22618e11 + 2.46281e11i 0.293986 + 0.116288i
\(45\) 1.24589e11i 0.0497032i
\(46\) 2.86553e12 + 4.21505e12i 0.969440 + 1.42600i
\(47\) 3.38491e12 0.974571 0.487286 0.873243i \(-0.337987\pi\)
0.487286 + 0.873243i \(0.337987\pi\)
\(48\) 2.63214e12 2.80654e12i 0.647142 0.690022i
\(49\) −4.72393e12 −0.995022
\(50\) 2.41093e12 + 3.54635e12i 0.436424 + 0.641958i
\(51\) 9.73146e12i 1.51845i
\(52\) 2.16293e12 + 8.55563e11i 0.291754 + 0.115406i
\(53\) 5.59117e11i 0.0653783i −0.999466 0.0326892i \(-0.989593\pi\)
0.999466 0.0326892i \(-0.0104071\pi\)
\(54\) −8.50627e12 + 5.78285e12i −0.864542 + 0.587745i
\(55\) 1.68845e12 0.149543
\(56\) 8.89815e11 1.99346e11i 0.0688477 0.0154240i
\(57\) −1.46870e13 −0.995114
\(58\) −2.30709e13 + 1.56844e13i −1.37200 + 0.932733i
\(59\) 2.62540e13i 1.37343i −0.726929 0.686713i \(-0.759053\pi\)
0.726929 0.686713i \(-0.240947\pi\)
\(60\) 3.56898e12 9.02267e12i 0.164593 0.416103i
\(61\) 3.59071e13i 1.46287i 0.681910 + 0.731436i \(0.261150\pi\)
−0.681910 + 0.731436i \(0.738850\pi\)
\(62\) −7.14490e12 1.05098e13i −0.257667 0.379014i
\(63\) −2.31786e11 −0.00741368
\(64\) 3.18214e13 1.50114e13i 0.904417 0.426649i
\(65\) 5.86554e12 0.148408
\(66\) 7.45192e12 + 1.09614e13i 0.168147 + 0.247335i
\(67\) 1.80671e13i 0.364190i −0.983281 0.182095i \(-0.941712\pi\)
0.983281 0.182095i \(-0.0582879\pi\)
\(68\) 3.27317e13 8.27484e13i 0.590408 1.49260i
\(69\) 1.00897e14i 1.63121i
\(70\) 1.90166e12 1.29281e12i 0.0275993 0.0187629i
\(71\) 1.14816e14 1.49818 0.749091 0.662467i \(-0.230490\pi\)
0.749091 + 0.662467i \(0.230490\pi\)
\(72\) −8.72710e12 + 1.95514e12i −0.102536 + 0.0229713i
\(73\) −5.99884e12 −0.0635545 −0.0317772 0.999495i \(-0.510117\pi\)
−0.0317772 + 0.999495i \(0.510117\pi\)
\(74\) −6.83955e13 + 4.64975e13i −0.654319 + 0.444828i
\(75\) 8.48903e13i 0.734342i
\(76\) −1.24887e14 4.93998e13i −0.978169 0.386922i
\(77\) 3.14121e12i 0.0223057i
\(78\) 2.58874e13 + 3.80791e13i 0.166870 + 0.245458i
\(79\) 1.01573e14 0.595077 0.297538 0.954710i \(-0.403834\pi\)
0.297538 + 0.954710i \(0.403834\pi\)
\(80\) 6.06954e13 6.47171e13i 0.323580 0.345020i
\(81\) −1.81983e14 −0.883881
\(82\) −4.30447e13 6.33165e13i −0.190685 0.280487i
\(83\) 1.34312e14i 0.543286i −0.962398 0.271643i \(-0.912433\pi\)
0.962398 0.271643i \(-0.0875670\pi\)
\(84\) 1.67859e13 + 6.63979e12i 0.0620654 + 0.0245504i
\(85\) 2.24401e14i 0.759248i
\(86\) 1.35745e14 9.22842e13i 0.420713 0.286015i
\(87\) −5.52257e14 −1.56945
\(88\) 2.64964e13 + 1.18271e14i 0.0691142 + 0.308503i
\(89\) 8.80035e13 0.210899 0.105450 0.994425i \(-0.466372\pi\)
0.105450 + 0.994425i \(0.466372\pi\)
\(90\) −1.86511e13 + 1.26796e13i −0.0411041 + 0.0279439i
\(91\) 1.09123e13i 0.0221364i
\(92\) −3.39367e14 + 8.57947e14i −0.634251 + 1.60344i
\(93\) 2.51576e14i 0.433559i
\(94\) 3.44489e14 + 5.06726e14i 0.547920 + 0.805961i
\(95\) −3.38674e14 −0.497570
\(96\) 6.88021e14 + 1.08407e14i 0.934475 + 0.147239i
\(97\) 1.21693e15 1.52925 0.764624 0.644477i \(-0.222925\pi\)
0.764624 + 0.644477i \(0.222925\pi\)
\(98\) −4.80763e14 7.07178e14i −0.559417 0.822874i
\(99\) 3.08082e13i 0.0332203i
\(100\) −2.85528e14 + 7.21837e14i −0.285528 + 0.721837i
\(101\) 1.49284e15i 1.38549i −0.721183 0.692745i \(-0.756401\pi\)
0.721183 0.692745i \(-0.243599\pi\)
\(102\) 1.45681e15 9.90390e14i 1.25575 0.853699i
\(103\) 4.75271e14 0.380769 0.190385 0.981710i \(-0.439026\pi\)
0.190385 + 0.981710i \(0.439026\pi\)
\(104\) 9.20467e13 + 4.10865e14i 0.0685896 + 0.306161i
\(105\) 4.55208e13 0.0315712
\(106\) 8.37005e13 5.69024e13i 0.0540672 0.0367567i
\(107\) 2.70722e15i 1.62984i 0.579572 + 0.814921i \(0.303220\pi\)
−0.579572 + 0.814921i \(0.696780\pi\)
\(108\) −1.73140e15 6.84868e14i −0.972118 0.384529i
\(109\) 2.84661e14i 0.149152i 0.997215 + 0.0745760i \(0.0237603\pi\)
−0.997215 + 0.0745760i \(0.976240\pi\)
\(110\) 1.71836e14 + 2.52762e14i 0.0840756 + 0.123671i
\(111\) −1.63721e15 −0.748483
\(112\) 1.20401e14 + 1.12919e14i 0.0514628 + 0.0482648i
\(113\) −2.09888e15 −0.839267 −0.419633 0.907694i \(-0.637841\pi\)
−0.419633 + 0.907694i \(0.637841\pi\)
\(114\) −1.49473e15 2.19867e15i −0.559469 0.822950i
\(115\) 2.32662e15i 0.815628i
\(116\) −4.69594e15 1.85752e15i −1.54272 0.610236i
\(117\) 1.07026e14i 0.0329681i
\(118\) 3.93026e15 2.67192e15i 1.13581 0.772162i
\(119\) 4.17479e14 0.113249
\(120\) 1.71393e15 3.83973e14i 0.436650 0.0978231i
\(121\) 3.75973e15 0.900049
\(122\) −5.37534e15 + 3.65433e15i −1.20978 + 0.822450i
\(123\) 1.51563e15i 0.320853i
\(124\) 8.46176e14 2.13920e15i 0.168577 0.426176i
\(125\) 4.47925e15i 0.840195i
\(126\) −2.35894e13 3.46987e13i −0.00416809 0.00613104i
\(127\) 5.68754e15 0.947102 0.473551 0.880766i \(-0.342972\pi\)
0.473551 + 0.880766i \(0.342972\pi\)
\(128\) 5.48574e15 + 3.23596e15i 0.861312 + 0.508076i
\(129\) 3.24939e15 0.481258
\(130\) 5.96948e14 + 8.78079e14i 0.0834374 + 0.122732i
\(131\) 6.69503e15i 0.883523i −0.897133 0.441761i \(-0.854354\pi\)
0.897133 0.441761i \(-0.145646\pi\)
\(132\) −8.82537e14 + 2.23112e15i −0.110009 + 0.278111i
\(133\) 6.30073e14i 0.0742171i
\(134\) 2.70467e15 1.83873e15i 0.301182 0.204754i
\(135\) −4.69530e15 −0.494493
\(136\) 1.57187e16 3.52148e15i 1.56630 0.350900i
\(137\) −1.32688e16 −1.25149 −0.625743 0.780029i \(-0.715204\pi\)
−0.625743 + 0.780029i \(0.715204\pi\)
\(138\) −1.51044e16 + 1.02685e16i −1.34900 + 0.917094i
\(139\) 1.15579e16i 0.977841i −0.872328 0.488921i \(-0.837391\pi\)
0.872328 0.488921i \(-0.162609\pi\)
\(140\) 3.87072e14 + 1.53109e14i 0.0310336 + 0.0122756i
\(141\) 1.21297e16i 0.921948i
\(142\) 1.16850e16 + 1.71881e16i 0.842302 + 1.23898i
\(143\) −1.45043e15 −0.0991919
\(144\) −1.18086e15 1.10748e15i −0.0766444 0.0718815i
\(145\) −1.27347e16 −0.784745
\(146\) −6.10514e14 8.98035e14i −0.0357313 0.0525589i
\(147\) 1.69280e16i 0.941294i
\(148\) −1.39215e16 5.50675e15i −0.735737 0.291026i
\(149\) 2.44036e16i 1.22619i −0.790010 0.613094i \(-0.789925\pi\)
0.790010 0.613094i \(-0.210075\pi\)
\(150\) −1.27082e16 + 8.63945e15i −0.607294 + 0.412859i
\(151\) 2.34346e16 1.06545 0.532723 0.846290i \(-0.321169\pi\)
0.532723 + 0.846290i \(0.321169\pi\)
\(152\) −5.31474e15 2.37232e16i −0.229961 1.02647i
\(153\) −4.09454e15 −0.168663
\(154\) −4.70243e14 + 3.19687e14i −0.0184466 + 0.0125406i
\(155\) 5.80119e15i 0.216785i
\(156\) −3.06587e15 + 7.75076e15i −0.109174 + 0.276000i
\(157\) 3.64533e16i 1.23734i 0.785651 + 0.618670i \(0.212328\pi\)
−0.785651 + 0.618670i \(0.787672\pi\)
\(158\) 1.03372e16 + 1.52055e16i 0.334562 + 0.492123i
\(159\) 2.00357e15 0.0618481
\(160\) 1.58653e16 + 2.49979e15i 0.467250 + 0.0736215i
\(161\) −4.32848e15 −0.121658
\(162\) −1.85208e16 2.72431e16i −0.496932 0.730961i
\(163\) 6.21748e16i 1.59297i 0.604658 + 0.796485i \(0.293310\pi\)
−0.604658 + 0.796485i \(0.706690\pi\)
\(164\) 5.09782e15 1.28877e16i 0.124754 0.315389i
\(165\) 6.05047e15i 0.141468i
\(166\) 2.01066e16 1.36692e16i 0.449292 0.305444i
\(167\) −4.36211e15 −0.0931801 −0.0465901 0.998914i \(-0.514835\pi\)
−0.0465901 + 0.998914i \(0.514835\pi\)
\(168\) 7.14349e14 + 3.18861e15i 0.0145912 + 0.0651302i
\(169\) 4.61472e16 0.901561
\(170\) 3.35932e16 2.28378e16i 0.627891 0.426861i
\(171\) 6.17961e15i 0.110533i
\(172\) 2.76301e16 + 1.09293e16i 0.473063 + 0.187124i
\(173\) 2.78021e16i 0.455755i 0.973690 + 0.227877i \(0.0731785\pi\)
−0.973690 + 0.227877i \(0.926821\pi\)
\(174\) −5.62043e16 8.26736e16i −0.882369 1.29792i
\(175\) −3.64179e15 −0.0547683
\(176\) −1.50087e16 + 1.60032e16i −0.216272 + 0.230602i
\(177\) 9.40800e16 1.29927
\(178\) 8.95629e15 + 1.31742e16i 0.118571 + 0.174412i
\(179\) 1.09589e16i 0.139113i 0.997578 + 0.0695566i \(0.0221585\pi\)
−0.997578 + 0.0695566i \(0.977842\pi\)
\(180\) −3.79631e15 1.50166e15i −0.0462188 0.0182822i
\(181\) 1.18530e17i 1.38433i −0.721739 0.692165i \(-0.756657\pi\)
0.721739 0.692165i \(-0.243343\pi\)
\(182\) −1.63359e15 + 1.11057e15i −0.0183066 + 0.0124454i
\(183\) −1.28671e17 −1.38388
\(184\) −1.62974e17 + 3.65112e16i −1.68261 + 0.376958i
\(185\) −3.77530e16 −0.374251
\(186\) 3.76613e16 2.56034e16i 0.358549 0.243754i
\(187\) 5.54899e16i 0.507460i
\(188\) −4.07982e16 + 1.03141e17i −0.358473 + 0.906249i
\(189\) 8.73519e15i 0.0737580i
\(190\) −3.44675e16 5.06999e16i −0.279742 0.411486i
\(191\) −3.98558e16 −0.310986 −0.155493 0.987837i \(-0.549697\pi\)
−0.155493 + 0.987837i \(0.549697\pi\)
\(192\) 5.37926e16 + 1.14030e17i 0.403611 + 0.855582i
\(193\) −1.28332e17 −0.926094 −0.463047 0.886334i \(-0.653244\pi\)
−0.463047 + 0.886334i \(0.653244\pi\)
\(194\) 1.23849e17 + 1.82176e17i 0.859767 + 1.26467i
\(195\) 2.10189e16i 0.140395i
\(196\) 5.69372e16 1.43942e17i 0.365996 0.925265i
\(197\) 2.94561e17i 1.82255i −0.411802 0.911273i \(-0.635100\pi\)
0.411802 0.911273i \(-0.364900\pi\)
\(198\) 4.61203e15 3.13541e15i 0.0274728 0.0186770i
\(199\) 9.91123e16 0.568499 0.284249 0.958750i \(-0.408256\pi\)
0.284249 + 0.958750i \(0.408256\pi\)
\(200\) −1.37119e17 + 3.07189e16i −0.757481 + 0.169699i
\(201\) 6.47428e16 0.344525
\(202\) 2.23480e17 1.51929e17i 1.14579 0.778945i
\(203\) 2.36918e16i 0.117052i
\(204\) 2.96525e17 + 1.17293e17i 1.41200 + 0.558528i
\(205\) 3.49495e16i 0.160431i
\(206\) 4.83692e16 + 7.11487e16i 0.214075 + 0.314893i
\(207\) 4.24528e16 0.181188
\(208\) −5.21393e16 + 5.55941e16i −0.214630 + 0.228851i
\(209\) 8.37471e16 0.332562
\(210\) 4.63275e15 + 6.81453e15i 0.0177498 + 0.0261091i
\(211\) 8.69554e16i 0.321498i −0.986995 0.160749i \(-0.948609\pi\)
0.986995 0.160749i \(-0.0513909\pi\)
\(212\) 1.70367e16 + 6.73901e15i 0.0607949 + 0.0240479i
\(213\) 4.11438e17i 1.41729i
\(214\) −4.05274e17 + 2.75519e17i −1.34786 + 0.916323i
\(215\) 7.49288e16 0.240636
\(216\) −7.36823e16 3.28893e17i −0.228539 1.02012i
\(217\) 1.07926e16 0.0323354
\(218\) −4.26141e16 + 2.89705e16i −0.123347 + 0.0838556i
\(219\) 2.14966e16i 0.0601227i
\(220\) −2.03507e16 + 5.14483e16i −0.0550060 + 0.139059i
\(221\) 1.92768e17i 0.503608i
\(222\) −1.66622e17 2.45092e17i −0.420809 0.618988i
\(223\) −1.42111e17 −0.347010 −0.173505 0.984833i \(-0.555509\pi\)
−0.173505 + 0.984833i \(0.555509\pi\)
\(224\) −4.65065e15 + 2.95161e16i −0.0109813 + 0.0696945i
\(225\) 3.57178e16 0.0815673
\(226\) −2.13607e17 3.14206e17i −0.471849 0.694066i
\(227\) 4.43249e17i 0.947227i −0.880733 0.473613i \(-0.842949\pi\)
0.880733 0.473613i \(-0.157051\pi\)
\(228\) 1.77022e17 4.47526e17i 0.366029 0.925351i
\(229\) 6.08062e17i 1.21670i 0.793671 + 0.608348i \(0.208167\pi\)
−0.793671 + 0.608348i \(0.791833\pi\)
\(230\) −3.48299e17 + 2.36785e17i −0.674517 + 0.458559i
\(231\) −1.12564e16 −0.0211013
\(232\) −1.99843e17 8.92032e17i −0.362685 1.61890i
\(233\) −5.16263e17 −0.907197 −0.453599 0.891206i \(-0.649860\pi\)
−0.453599 + 0.891206i \(0.649860\pi\)
\(234\) 1.60219e16 1.08922e16i 0.0272643 0.0185352i
\(235\) 2.79703e17i 0.460986i
\(236\) 7.99980e17 + 3.16438e17i 1.27714 + 0.505183i
\(237\) 3.63981e17i 0.562945i
\(238\) 4.24877e16 + 6.24972e16i 0.0636701 + 0.0936555i
\(239\) 8.09435e17 1.17543 0.587716 0.809067i \(-0.300027\pi\)
0.587716 + 0.809067i \(0.300027\pi\)
\(240\) 2.31911e17 + 2.17499e17i 0.326390 + 0.306107i
\(241\) −5.07196e17 −0.691908 −0.345954 0.938251i \(-0.612445\pi\)
−0.345954 + 0.938251i \(0.612445\pi\)
\(242\) 3.82635e17 + 5.62836e17i 0.506022 + 0.744332i
\(243\) 1.63199e17i 0.209253i
\(244\) −1.09412e18 4.32786e17i −1.36032 0.538083i
\(245\) 3.90349e17i 0.470660i
\(246\) 2.26892e17 1.54249e17i 0.265342 0.180388i
\(247\) 2.90932e17 0.330038
\(248\) 4.06358e17 9.10369e16i 0.447220 0.100191i
\(249\) 4.81300e17 0.513950
\(250\) −6.70549e17 + 4.55862e17i −0.694834 + 0.472371i
\(251\) 9.30546e17i 0.935804i −0.883780 0.467902i \(-0.845010\pi\)
0.883780 0.467902i \(-0.154990\pi\)
\(252\) 2.79371e15 7.06271e15i 0.00272695 0.00689394i
\(253\) 5.75327e17i 0.545143i
\(254\) 5.78832e17 + 8.51432e17i 0.532476 + 0.783244i
\(255\) 8.04132e17 0.718251
\(256\) 7.38674e16 + 1.15055e18i 0.0640697 + 0.997945i
\(257\) 1.04519e17 0.0880433 0.0440217 0.999031i \(-0.485983\pi\)
0.0440217 + 0.999031i \(0.485983\pi\)
\(258\) 3.30696e17 + 4.86437e17i 0.270571 + 0.397996i
\(259\) 7.02362e16i 0.0558229i
\(260\) −7.06970e16 + 1.78728e17i −0.0545885 + 0.138004i
\(261\) 2.32364e17i 0.174327i
\(262\) 1.00225e18 6.81366e17i 0.730665 0.496730i
\(263\) −1.81980e18 −1.28930 −0.644652 0.764476i \(-0.722998\pi\)
−0.644652 + 0.764476i \(0.722998\pi\)
\(264\) −4.23819e17 + 9.49488e16i −0.291844 + 0.0653823i
\(265\) 4.62011e16 0.0309249
\(266\) 9.43228e16 6.41238e16i 0.0613768 0.0417260i
\(267\) 3.15357e17i 0.199511i
\(268\) 5.50520e17 + 2.17762e17i 0.338659 + 0.133959i
\(269\) 3.24756e18i 1.94274i −0.237572 0.971370i \(-0.576352\pi\)
0.237572 0.971370i \(-0.423648\pi\)
\(270\) −4.77850e17 7.02892e17i −0.278012 0.408941i
\(271\) −2.66200e18 −1.50639 −0.753197 0.657795i \(-0.771489\pi\)
−0.753197 + 0.657795i \(0.771489\pi\)
\(272\) 2.12689e18 + 1.99472e18i 1.17079 + 1.09803i
\(273\) −3.91039e16 −0.0209411
\(274\) −1.35039e18 1.98635e18i −0.703605 1.03497i
\(275\) 4.84054e17i 0.245413i
\(276\) −3.07441e18 1.21611e18i −1.51686 0.600004i
\(277\) 2.05102e18i 0.984851i 0.870354 + 0.492426i \(0.163890\pi\)
−0.870354 + 0.492426i \(0.836110\pi\)
\(278\) 1.73023e18 1.17627e18i 0.808665 0.549758i
\(279\) −1.05852e17 −0.0481577
\(280\) 1.64724e16 + 7.35274e16i 0.00729579 + 0.0325660i
\(281\) −1.26318e16 −0.00544713 −0.00272357 0.999996i \(-0.500867\pi\)
−0.00272357 + 0.999996i \(0.500867\pi\)
\(282\) −1.81583e18 + 1.23446e18i −0.762442 + 0.518334i
\(283\) 2.69764e18i 1.10302i 0.834167 + 0.551512i \(0.185949\pi\)
−0.834167 + 0.551512i \(0.814051\pi\)
\(284\) −1.38387e18 + 3.49853e18i −0.551071 + 1.39315i
\(285\) 1.21362e18i 0.470703i
\(286\) −1.47613e17 2.17131e17i −0.0557673 0.0820308i
\(287\) 6.50205e16 0.0239296
\(288\) 4.56125e16 2.89487e17i 0.0163546 0.103797i
\(289\) 4.51241e18 1.57643
\(290\) −1.29604e18 1.90640e18i −0.441196 0.648977i
\(291\) 4.36082e18i 1.44667i
\(292\) 7.23037e16 1.82789e17i 0.0233770 0.0590989i
\(293\) 2.63682e17i 0.0830947i −0.999137 0.0415474i \(-0.986771\pi\)
0.999137 0.0415474i \(-0.0132287\pi\)
\(294\) 2.53414e18 1.72279e18i 0.778441 0.529211i
\(295\) 2.16943e18 0.649650
\(296\) −5.92450e17 2.64450e18i −0.172967 0.772067i
\(297\) 1.16105e18 0.330505
\(298\) 3.65325e18 2.48360e18i 1.01405 0.689383i
\(299\) 1.99864e18i 0.541005i
\(300\) −2.58667e18 1.02318e18i −0.682861 0.270111i
\(301\) 1.39398e17i 0.0358930i
\(302\) 2.38499e18 + 3.50819e18i 0.599010 + 0.881113i
\(303\) 5.34953e18 1.31068
\(304\) 3.01050e18 3.20998e18i 0.719593 0.767274i
\(305\) −2.96708e18 −0.691960
\(306\) −4.16709e17 6.12958e17i −0.0948249 0.139483i
\(307\) 3.96417e18i 0.880268i 0.897932 + 0.440134i \(0.145069\pi\)
−0.897932 + 0.440134i \(0.854931\pi\)
\(308\) −9.57151e16 3.78608e16i −0.0207420 0.00820464i
\(309\) 1.70311e18i 0.360209i
\(310\) 8.68446e17 5.90399e17i 0.179279 0.121880i
\(311\) −7.87147e18 −1.58618 −0.793091 0.609104i \(-0.791529\pi\)
−0.793091 + 0.609104i \(0.791529\pi\)
\(312\) −1.47232e18 + 3.29845e17i −0.289629 + 0.0648860i
\(313\) 8.70513e16 0.0167183 0.00835916 0.999965i \(-0.497339\pi\)
0.00835916 + 0.999965i \(0.497339\pi\)
\(314\) −5.45710e18 + 3.70992e18i −1.02327 + 0.695652i
\(315\) 1.91530e16i 0.00350678i
\(316\) −1.22425e18 + 3.09499e18i −0.218885 + 0.553359i
\(317\) 1.70030e18i 0.296880i 0.988921 + 0.148440i \(0.0474252\pi\)
−0.988921 + 0.148440i \(0.952575\pi\)
\(318\) 2.03907e17 + 2.99937e17i 0.0347720 + 0.0511478i
\(319\) 3.14903e18 0.524502
\(320\) 1.24042e18 + 2.62947e18i 0.201811 + 0.427802i
\(321\) −9.70121e18 −1.54184
\(322\) −4.40518e17 6.47979e17i −0.0683982 0.100610i
\(323\) 1.11303e19i 1.68845i
\(324\) 2.19343e18 5.54517e18i 0.325115 0.821916i
\(325\) 1.68157e18i 0.243551i
\(326\) −9.30765e18 + 6.32765e18i −1.31737 + 0.895593i
\(327\) −1.02007e18 −0.141098
\(328\) 2.44812e18 5.48455e17i 0.330963 0.0741459i
\(329\) −5.20363e17 −0.0687602
\(330\) −9.05763e17 + 6.15768e17i −0.116993 + 0.0795358i
\(331\) 9.05755e18i 1.14367i −0.820368 0.571835i \(-0.806232\pi\)
0.820368 0.571835i \(-0.193768\pi\)
\(332\) 4.09259e18 + 1.61885e18i 0.505199 + 0.199835i
\(333\) 6.88860e17i 0.0831380i
\(334\) −4.43941e17 6.53014e17i −0.0523873 0.0770591i
\(335\) 1.49293e18 0.172267
\(336\) −4.04639e17 + 4.31450e17i −0.0456586 + 0.0486840i
\(337\) 1.06692e19 1.17736 0.588680 0.808366i \(-0.299648\pi\)
0.588680 + 0.808366i \(0.299648\pi\)
\(338\) 4.69649e18 + 6.90830e18i 0.506872 + 0.745582i
\(339\) 7.52126e18i 0.793949i
\(340\) 6.83768e18 + 2.70470e18i 0.706020 + 0.279271i
\(341\) 1.43452e18i 0.144893i
\(342\) −9.25096e17 + 6.28911e17i −0.0914094 + 0.0621432i
\(343\) 1.45605e18 0.140757
\(344\) 1.17584e18 + 5.24856e18i 0.111214 + 0.496423i
\(345\) −8.33735e18 −0.771587
\(346\) −4.16200e18 + 2.82947e18i −0.376905 + 0.256233i
\(347\) 2.62705e18i 0.232808i −0.993202 0.116404i \(-0.962863\pi\)
0.993202 0.116404i \(-0.0371368\pi\)
\(348\) 6.65633e18 1.68277e19i 0.577285 1.45942i
\(349\) 1.30852e19i 1.11068i 0.831622 + 0.555342i \(0.187413\pi\)
−0.831622 + 0.555342i \(0.812587\pi\)
\(350\) −3.70632e17 5.45180e17i −0.0307916 0.0452929i
\(351\) 4.03341e18 0.327996
\(352\) −3.92317e18 6.18148e17i −0.312297 0.0492065i
\(353\) −3.44105e18 −0.268152 −0.134076 0.990971i \(-0.542807\pi\)
−0.134076 + 0.990971i \(0.542807\pi\)
\(354\) 9.57471e18 + 1.40839e19i 0.730468 + 1.07448i
\(355\) 9.48750e18i 0.708662i
\(356\) −1.06070e18 + 2.68154e18i −0.0775743 + 0.196114i
\(357\) 1.49602e18i 0.107134i
\(358\) −1.64056e18 + 1.11531e18i −0.115045 + 0.0782117i
\(359\) 8.79527e17 0.0604005 0.0302003 0.999544i \(-0.490385\pi\)
0.0302003 + 0.999544i \(0.490385\pi\)
\(360\) −1.61558e17 7.21140e17i −0.0108657 0.0485010i
\(361\) −1.61714e18 −0.106523
\(362\) 1.77441e19 1.20631e19i 1.14483 0.778293i
\(363\) 1.34728e19i 0.851450i
\(364\) −3.32507e17 1.31526e17i −0.0205845 0.00814236i
\(365\) 4.95698e17i 0.0300622i
\(366\) −1.30951e19 1.92623e19i −0.778041 1.14446i
\(367\) 1.68813e19 0.982676 0.491338 0.870969i \(-0.336508\pi\)
0.491338 + 0.870969i \(0.336508\pi\)
\(368\) −2.20519e19 2.06816e19i −1.25773 1.17957i
\(369\) −6.37706e17 −0.0356388
\(370\) −3.84220e18 5.65167e18i −0.210410 0.309502i
\(371\) 8.59531e16i 0.00461272i
\(372\) 7.66573e18 + 3.03224e18i 0.403164 + 0.159474i
\(373\) 2.50203e19i 1.28966i −0.764325 0.644831i \(-0.776928\pi\)
0.764325 0.644831i \(-0.223072\pi\)
\(374\) −8.30691e18 + 5.64731e18i −0.419665 + 0.285302i
\(375\) −1.60512e19 −0.794828
\(376\) −1.95924e19 + 4.38932e18i −0.950998 + 0.213053i
\(377\) 1.09395e19 0.520521
\(378\) 1.30767e18 8.88998e17i 0.0609972 0.0414679i
\(379\) 2.47648e19i 1.13251i 0.824232 + 0.566253i \(0.191607\pi\)
−0.824232 + 0.566253i \(0.808393\pi\)
\(380\) 4.08202e18 1.03197e19i 0.183020 0.462688i
\(381\) 2.03811e19i 0.895961i
\(382\) −4.05620e18 5.96647e18i −0.174842 0.257183i
\(383\) 2.04166e19 0.862965 0.431483 0.902121i \(-0.357991\pi\)
0.431483 + 0.902121i \(0.357991\pi\)
\(384\) −1.15959e19 + 1.96579e19i −0.480641 + 0.814804i
\(385\) −2.59565e17 −0.0105509
\(386\) −1.30606e19 1.92115e19i −0.520665 0.765871i
\(387\) 1.36719e18i 0.0534559i
\(388\) −1.46676e19 + 3.70808e19i −0.562498 + 1.42204i
\(389\) 9.28297e18i 0.349193i −0.984640 0.174596i \(-0.944138\pi\)
0.984640 0.174596i \(-0.0558620\pi\)
\(390\) −3.14656e18 + 2.13914e18i −0.116105 + 0.0789321i
\(391\) −7.64633e19 −2.76775
\(392\) 2.73429e19 6.12566e18i 0.970954 0.217524i
\(393\) 2.39913e19 0.835815
\(394\) 4.40962e19 2.99781e19i 1.50723 1.02466i
\(395\) 8.39316e18i 0.281480i
\(396\) 9.38751e17 + 3.71330e17i 0.0308913 + 0.0122193i
\(397\) 2.03449e19i 0.656942i −0.944514 0.328471i \(-0.893467\pi\)
0.944514 0.328471i \(-0.106533\pi\)
\(398\) 1.00869e19 + 1.48372e19i 0.319619 + 0.470143i
\(399\) 2.25784e18 0.0702096
\(400\) −1.85535e19 1.74005e19i −0.566208 0.531022i
\(401\) 1.23695e19 0.370483 0.185242 0.982693i \(-0.440693\pi\)
0.185242 + 0.982693i \(0.440693\pi\)
\(402\) 6.58900e18 + 9.69208e18i 0.193698 + 0.284919i
\(403\) 4.98341e18i 0.143793i
\(404\) 4.54881e19 + 1.79931e19i 1.28836 + 0.509620i
\(405\) 1.50377e19i 0.418088i
\(406\) 3.54669e18 2.41116e18i 0.0968007 0.0658084i
\(407\) 9.33555e18 0.250139
\(408\) 1.26191e19 + 5.63273e19i 0.331953 + 1.48173i
\(409\) 1.53557e18 0.0396593 0.0198296 0.999803i \(-0.493688\pi\)
0.0198296 + 0.999803i \(0.493688\pi\)
\(410\) 5.23199e18 3.55688e18i 0.132675 0.0901966i
\(411\) 4.75480e19i 1.18391i
\(412\) −5.72841e18 + 1.44819e19i −0.140057 + 0.354075i
\(413\) 4.03603e18i 0.0969011i
\(414\) 4.32050e18 + 6.35523e18i 0.101867 + 0.149840i
\(415\) 1.10985e19 0.256982
\(416\) −1.36288e19 2.14740e18i −0.309926 0.0488330i
\(417\) 4.14173e19 0.925041
\(418\) 8.52311e18 + 1.25371e19i 0.186972 + 0.275026i
\(419\) 3.07067e19i 0.661649i 0.943692 + 0.330825i \(0.107327\pi\)
−0.943692 + 0.330825i \(0.892673\pi\)
\(420\) −5.48660e17 + 1.38706e18i −0.0116127 + 0.0293578i
\(421\) 7.88348e19i 1.63909i −0.573016 0.819544i \(-0.694227\pi\)
0.573016 0.819544i \(-0.305773\pi\)
\(422\) 1.30173e19 8.84962e18i 0.265876 0.180751i
\(423\) 5.10360e18 0.102406
\(424\) 7.25024e17 + 3.23626e18i 0.0142925 + 0.0637969i
\(425\) −6.43327e19 −1.24599
\(426\) −6.15928e19 + 4.18728e19i −1.17208 + 0.796821i
\(427\) 5.52000e18i 0.103212i
\(428\) −8.24911e19 3.26300e19i −1.51558 0.599499i
\(429\) 5.19755e18i 0.0938359i
\(430\) 7.62564e18 + 1.12169e19i 0.135289 + 0.199003i
\(431\) 5.48780e19 0.956794 0.478397 0.878144i \(-0.341218\pi\)
0.478397 + 0.878144i \(0.341218\pi\)
\(432\) 4.17369e19 4.45024e19i 0.715142 0.762528i
\(433\) −9.01703e19 −1.51846 −0.759232 0.650821i \(-0.774425\pi\)
−0.759232 + 0.650821i \(0.774425\pi\)
\(434\) 1.09839e18 + 1.61567e18i 0.0181795 + 0.0267411i
\(435\) 4.56342e19i 0.742372i
\(436\) −8.67384e18 3.43100e18i −0.138696 0.0548621i
\(437\) 1.15401e20i 1.81384i
\(438\) 3.21807e18 2.18775e18i 0.0497209 0.0338020i
\(439\) −9.88500e19 −1.50139 −0.750694 0.660650i \(-0.770281\pi\)
−0.750694 + 0.660650i \(0.770281\pi\)
\(440\) −9.77300e18 + 2.18946e18i −0.145926 + 0.0326920i
\(441\) −7.12250e18 −0.104555
\(442\) −2.88576e19 + 1.96184e19i −0.416479 + 0.283136i
\(443\) 5.95210e19i 0.844583i 0.906460 + 0.422292i \(0.138774\pi\)
−0.906460 + 0.422292i \(0.861226\pi\)
\(444\) 1.97332e19 4.98870e19i 0.275312 0.696010i
\(445\) 7.27192e18i 0.0997584i
\(446\) −1.44629e19 2.12742e19i −0.195095 0.286974i
\(447\) 8.74493e19 1.15998
\(448\) −4.89190e18 + 2.30770e18i −0.0638105 + 0.0301019i
\(449\) 1.87833e18 0.0240949 0.0120474 0.999927i \(-0.496165\pi\)
0.0120474 + 0.999927i \(0.496165\pi\)
\(450\) 3.63507e18 + 5.34700e18i 0.0458584 + 0.0674554i
\(451\) 8.64230e18i 0.107227i
\(452\) 2.52977e19 6.39546e19i 0.308705 0.780429i
\(453\) 8.39770e19i 1.00791i
\(454\) 6.63550e19 4.51103e19i 0.783348 0.532546i
\(455\) −9.01710e17 −0.0104708
\(456\) 8.50110e19 1.90451e19i 0.971044 0.217544i
\(457\) 1.02379e20 1.15038 0.575189 0.818020i \(-0.304928\pi\)
0.575189 + 0.818020i \(0.304928\pi\)
\(458\) −9.10277e19 + 6.18837e19i −1.00620 + 0.684045i
\(459\) 1.54308e20i 1.67801i
\(460\) −7.08940e19 2.80427e19i −0.758448 0.300010i
\(461\) 1.09488e20i 1.15242i 0.817302 + 0.576209i \(0.195469\pi\)
−0.817302 + 0.576209i \(0.804531\pi\)
\(462\) −1.14558e18 1.68509e18i −0.0118635 0.0174506i
\(463\) 1.60836e20 1.63880 0.819398 0.573225i \(-0.194308\pi\)
0.819398 + 0.573225i \(0.194308\pi\)
\(464\) 1.13200e20 1.20701e20i 1.13491 1.21011i
\(465\) 2.07883e19 0.205079
\(466\) −5.25411e19 7.72853e19i −0.510041 0.750244i
\(467\) 4.70891e18i 0.0449825i 0.999747 + 0.0224913i \(0.00715979\pi\)
−0.999747 + 0.0224913i \(0.992840\pi\)
\(468\) 3.26115e18 + 1.28997e18i 0.0306568 + 0.0121265i
\(469\) 2.77746e18i 0.0256952i
\(470\) −4.18719e19 + 2.84659e19i −0.381231 + 0.259174i
\(471\) −1.30629e20 −1.17053
\(472\) 3.40443e19 + 1.51962e20i 0.300248 + 1.34021i
\(473\) −1.85284e19 −0.160834
\(474\) −5.44884e19 + 3.70430e19i −0.465550 + 0.316496i
\(475\) 9.70930e19i 0.816556i
\(476\) −5.03185e18 + 1.27209e19i −0.0416558 + 0.105309i
\(477\) 8.43008e17i 0.00686980i
\(478\) 8.23778e19 + 1.21173e20i 0.660847 + 0.972072i
\(479\) 1.46825e20 1.15954 0.579768 0.814782i \(-0.303143\pi\)
0.579768 + 0.814782i \(0.303143\pi\)
\(480\) −8.95790e18 + 5.68527e19i −0.0696461 + 0.442020i
\(481\) 3.24310e19 0.248240
\(482\) −5.16184e19 7.59279e19i −0.389002 0.572201i
\(483\) 1.55109e19i 0.115089i
\(484\) −4.53158e19 + 1.14562e20i −0.331062 + 0.836951i
\(485\) 1.00558e20i 0.723356i
\(486\) −2.44311e19 + 1.66091e19i −0.173050 + 0.117645i
\(487\) −1.93413e20 −1.34902 −0.674511 0.738265i \(-0.735645\pi\)
−0.674511 + 0.738265i \(0.735645\pi\)
\(488\) −4.65618e19 2.07836e20i −0.319802 1.42749i
\(489\) −2.22801e20 −1.50695
\(490\) 5.84357e19 3.97265e19i 0.389231 0.264612i
\(491\) 1.70816e20i 1.12051i −0.828320 0.560255i \(-0.810703\pi\)
0.828320 0.560255i \(-0.189297\pi\)
\(492\) 4.61825e19 + 1.82678e19i 0.298359 + 0.118018i
\(493\) 4.18519e20i 2.66295i
\(494\) 2.96087e19 + 4.35528e19i 0.185553 + 0.272938i
\(495\) 2.54575e18 0.0157137
\(496\) 5.49842e19 + 5.15673e19i 0.334291 + 0.313518i
\(497\) −1.76507e19 −0.105703
\(498\) 4.89829e19 + 7.20513e19i 0.288951 + 0.425032i
\(499\) 6.57784e18i 0.0382234i 0.999817 + 0.0191117i \(0.00608381\pi\)
−0.999817 + 0.0191117i \(0.993916\pi\)
\(500\) −1.36486e20 5.39881e19i −0.781293 0.309046i
\(501\) 1.56314e19i 0.0881487i
\(502\) 1.39304e20 9.47035e19i 0.773901 0.526124i
\(503\) −1.05517e20 −0.577515 −0.288758 0.957402i \(-0.593242\pi\)
−0.288758 + 0.957402i \(0.593242\pi\)
\(504\) 1.34162e18 3.00564e17i 0.00723436 0.00162072i
\(505\) 1.23357e20 0.655357
\(506\) 8.61271e19 5.85521e19i 0.450828 0.306488i
\(507\) 1.65366e20i 0.852880i
\(508\) −6.85516e19 + 1.73304e20i −0.348369 + 0.880705i
\(509\) 1.27123e20i 0.636561i −0.947997 0.318281i \(-0.896895\pi\)
0.947997 0.318281i \(-0.103105\pi\)
\(510\) 8.18381e19 + 1.20380e20i 0.403812 + 0.593987i
\(511\) 9.22203e17 0.00448404
\(512\) −1.64722e20 + 1.28152e20i −0.789270 + 0.614046i
\(513\) −2.32887e20 −1.09968
\(514\) 1.06371e19 + 1.56466e19i 0.0494993 + 0.0728110i
\(515\) 3.92727e19i 0.180109i
\(516\) −3.91647e19 + 9.90113e19i −0.177020 + 0.447520i
\(517\) 6.91648e19i 0.308110i
\(518\) 1.05144e19 7.14807e18i 0.0461650 0.0313845i
\(519\) −9.96274e19 −0.431145
\(520\) −3.39507e19 + 7.60602e18i −0.144818 + 0.0324439i
\(521\) 2.72339e20 1.14506 0.572529 0.819885i \(-0.305963\pi\)
0.572529 + 0.819885i \(0.305963\pi\)
\(522\) −3.47852e19 + 2.36481e19i −0.144167 + 0.0980094i
\(523\) 2.30971e20i 0.943615i 0.881702 + 0.471807i \(0.156398\pi\)
−0.881702 + 0.471807i \(0.843602\pi\)
\(524\) 2.04003e20 + 8.06948e19i 0.821583 + 0.324983i
\(525\) 1.30502e19i 0.0518110i
\(526\) −1.85205e20 2.72426e20i −0.724867 1.06624i
\(527\) 1.90653e20 0.735638
\(528\) −5.73469e19 5.37832e19i −0.218150 0.204594i
\(529\) 5.26146e20 1.97328
\(530\) 4.70197e18 + 6.91636e18i 0.0173865 + 0.0255746i
\(531\) 3.95844e19i 0.144316i
\(532\) 1.91988e19 + 7.59424e18i 0.0690140 + 0.0272990i
\(533\) 3.00227e19i 0.106413i
\(534\) −4.72093e19 + 3.20945e19i −0.164994 + 0.112168i
\(535\) −2.23704e20 −0.770938
\(536\) 2.34282e19 + 1.04576e20i 0.0796165 + 0.355381i
\(537\) −3.92707e19 −0.131602
\(538\) 4.86163e20 3.30510e20i 1.60663 1.09224i
\(539\) 9.65253e19i 0.314576i
\(540\) 5.65921e19 1.43069e20i 0.181888 0.459826i
\(541\) 6.21640e19i 0.197042i 0.995135 + 0.0985211i \(0.0314112\pi\)
−0.995135 + 0.0985211i \(0.968589\pi\)
\(542\) −2.70917e20 3.98505e20i −0.846919 1.24577i
\(543\) 4.24748e20 1.30958
\(544\) −8.21544e19 + 5.21406e20i −0.249827 + 1.58556i
\(545\) −2.35222e19 −0.0705510
\(546\) −3.97968e18 5.85390e18i −0.0117734 0.0173181i
\(547\) 3.62211e20i 1.05696i 0.848947 + 0.528478i \(0.177237\pi\)
−0.848947 + 0.528478i \(0.822763\pi\)
\(548\) 1.59928e20 4.04309e20i 0.460330 1.16375i
\(549\) 5.41389e19i 0.153715i
\(550\) 7.24635e19 4.92631e19i 0.202955 0.137975i
\(551\) −6.31643e20 −1.74516
\(552\) −1.30836e20 5.84009e20i −0.356603 1.59176i
\(553\) −1.56148e19 −0.0419852
\(554\) −3.07040e20 + 2.08736e20i −0.814463 + 0.553699i
\(555\) 1.35286e20i 0.354043i
\(556\) 3.52178e20 + 1.39307e20i 0.909289 + 0.359676i
\(557\) 5.86660e20i 1.49442i 0.664588 + 0.747210i \(0.268607\pi\)
−0.664588 + 0.747210i \(0.731393\pi\)
\(558\) −1.07727e19 1.58461e19i −0.0270750 0.0398259i
\(559\) −6.43662e19 −0.159613
\(560\) −9.33071e18 + 9.94897e18i −0.0228299 + 0.0243427i
\(561\) −1.98846e20 −0.480059
\(562\) −1.28556e18 1.89100e18i −0.00306246 0.00450473i
\(563\) 3.68047e20i 0.865149i −0.901598 0.432574i \(-0.857605\pi\)
0.901598 0.432574i \(-0.142395\pi\)
\(564\) −3.69601e20 1.46198e20i −0.857314 0.339117i
\(565\) 1.73435e20i 0.396985i
\(566\) −4.03840e20 + 2.74544e20i −0.912191 + 0.620138i
\(567\) 2.79763e19 0.0623616
\(568\) −6.64574e20 + 1.48885e20i −1.46194 + 0.327521i
\(569\) −4.30541e20 −0.934700 −0.467350 0.884072i \(-0.654791\pi\)
−0.467350 + 0.884072i \(0.654791\pi\)
\(570\) 1.81681e20 1.23513e20i 0.389267 0.264637i
\(571\) 4.02443e20i 0.851009i 0.904956 + 0.425504i \(0.139903\pi\)
−0.904956 + 0.425504i \(0.860097\pi\)
\(572\) 1.74819e19 4.41957e19i 0.0364854 0.0922380i
\(573\) 1.42822e20i 0.294194i
\(574\) 6.61727e18 + 9.73366e18i 0.0134536 + 0.0197896i
\(575\) 6.67010e20 1.33852
\(576\) 4.79786e19 2.26334e19i 0.0950340 0.0448313i
\(577\) 1.05401e20 0.206076 0.103038 0.994677i \(-0.467144\pi\)
0.103038 + 0.994677i \(0.467144\pi\)
\(578\) 4.59236e20 + 6.75513e20i 0.886293 + 1.30369i
\(579\) 4.59872e20i 0.876088i
\(580\) 1.53491e20 3.88036e20i 0.288650 0.729730i
\(581\) 2.06478e19i 0.0383312i
\(582\) −6.52820e20 + 4.43809e20i −1.19639 + 0.813343i
\(583\) −1.14246e19 −0.0206693
\(584\) 3.47223e19 7.77888e18i 0.0620172 0.0138938i
\(585\) 8.84377e18 0.0155944
\(586\) 3.94735e19 2.68354e19i 0.0687186 0.0467172i
\(587\) 9.43833e20i 1.62222i −0.584895 0.811109i \(-0.698864\pi\)
0.584895 0.811109i \(-0.301136\pi\)
\(588\) 5.15809e20 + 2.04032e20i 0.875304 + 0.346233i
\(589\) 2.87740e20i 0.482098i
\(590\) 2.20787e20 + 3.24766e20i 0.365244 + 0.537255i
\(591\) 1.05555e21 1.72414
\(592\) 3.35590e20 3.57826e20i 0.541247 0.577111i
\(593\) −9.22953e20 −1.46984 −0.734919 0.678155i \(-0.762780\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(594\) 1.18162e20 + 1.73811e20i 0.185815 + 0.273325i
\(595\) 3.44972e19i 0.0535682i
\(596\) 7.43597e20 + 2.94135e20i 1.14023 + 0.451025i
\(597\) 3.55165e20i 0.537802i
\(598\) 2.99200e20 2.03406e20i 0.447406 0.304162i
\(599\) −1.14322e20 −0.168822 −0.0844109 0.996431i \(-0.526901\pi\)
−0.0844109 + 0.996431i \(0.526901\pi\)
\(600\) −1.10080e20 4.91359e20i −0.160536 0.716580i
\(601\) 3.40769e20 0.490797 0.245398 0.969422i \(-0.421081\pi\)
0.245398 + 0.969422i \(0.421081\pi\)
\(602\) −2.08681e19 + 1.41869e19i −0.0296831 + 0.0201796i
\(603\) 2.72407e19i 0.0382683i
\(604\) −2.82456e20 + 7.14072e20i −0.391899 + 0.990751i
\(605\) 3.10675e20i 0.425736i
\(606\) 5.44432e20 + 8.00832e20i 0.736884 + 1.08392i
\(607\) −1.00534e21 −1.34399 −0.671995 0.740556i \(-0.734562\pi\)
−0.671995 + 0.740556i \(0.734562\pi\)
\(608\) 7.86922e20 + 1.23990e20i 1.03909 + 0.163723i
\(609\) 8.48986e19 0.110731
\(610\) −3.01966e20 4.44176e20i −0.389031 0.572244i
\(611\) 2.40274e20i 0.305772i
\(612\) 4.93513e19 1.24764e20i 0.0620387 0.156839i
\(613\) 4.53810e20i 0.563534i −0.959483 0.281767i \(-0.909079\pi\)
0.959483 0.281767i \(-0.0909206\pi\)
\(614\) −5.93442e20 + 4.03442e20i −0.727973 + 0.494900i
\(615\) 1.25240e20 0.151768
\(616\) −4.07330e18 1.81818e19i −0.00487630 0.0217662i
\(617\) −2.74187e20 −0.324271 −0.162136 0.986768i \(-0.551838\pi\)
−0.162136 + 0.986768i \(0.551838\pi\)
\(618\) −2.54958e20 + 1.73329e20i −0.297890 + 0.202515i
\(619\) 8.27168e20i 0.954803i −0.878685 0.477402i \(-0.841579\pi\)
0.878685 0.477402i \(-0.158421\pi\)
\(620\) 1.76767e20 + 6.99214e19i 0.201587 + 0.0797393i
\(621\) 1.59989e21i 1.80262i
\(622\) −8.01095e20 1.17837e21i −0.891776 1.31176i
\(623\) −1.35288e19 −0.0148798
\(624\) −1.99219e20 1.86839e20i −0.216494 0.203041i
\(625\) 3.52816e20 0.378833
\(626\) 8.85938e18 + 1.30317e19i 0.00939931 + 0.0138259i
\(627\) 3.00104e20i 0.314605i
\(628\) −1.11076e21 4.39369e20i −1.15060 0.455127i
\(629\) 1.24073e21i 1.26998i
\(630\) 2.86723e18 1.94924e18i 0.00290007 0.00197157i
\(631\) −8.71825e20 −0.871383 −0.435691 0.900096i \(-0.643496\pi\)
−0.435691 + 0.900096i \(0.643496\pi\)
\(632\) −5.87919e20 + 1.31712e20i −0.580683 + 0.130091i
\(633\) 3.11601e20 0.304138
\(634\) −2.54537e20 + 1.73043e20i −0.245517 + 0.166911i
\(635\) 4.69974e20i 0.447993i
\(636\) −2.41489e19 + 6.10504e19i −0.0227494 + 0.0575122i
\(637\) 3.35322e20i 0.312188i
\(638\) 3.20483e20 + 4.71414e20i 0.294883 + 0.433758i
\(639\) 1.73114e20 0.157425
\(640\) −2.67395e20 + 4.53299e20i −0.240327 + 0.407413i
\(641\) 1.06761e21 0.948367 0.474184 0.880426i \(-0.342743\pi\)
0.474184 + 0.880426i \(0.342743\pi\)
\(642\) −9.87311e20 1.45228e21i −0.866844 1.27508i
\(643\) 1.92026e21i 1.66640i 0.552974 + 0.833199i \(0.313493\pi\)
−0.552974 + 0.833199i \(0.686507\pi\)
\(644\) 5.21709e19 1.31892e20i 0.0447491 0.113129i
\(645\) 2.68504e20i 0.227642i
\(646\) 1.66623e21 1.13276e21i 1.39634 0.949276i
\(647\) 4.75461e20 0.393852 0.196926 0.980418i \(-0.436904\pi\)
0.196926 + 0.980418i \(0.436904\pi\)
\(648\) 1.05335e21 2.35983e20i 0.862502 0.193227i
\(649\) −5.36455e20 −0.434208
\(650\) 2.51733e20 1.71136e20i 0.201414 0.136928i
\(651\) 3.86749e19i 0.0305894i
\(652\) −1.89452e21 7.49389e20i −1.48129 0.585937i
\(653\) 6.30709e20i 0.487507i −0.969837 0.243753i \(-0.921621\pi\)
0.969837 0.243753i \(-0.0783787\pi\)
\(654\) −1.03815e20 1.52706e20i −0.0793277 0.116687i
\(655\) 5.53225e20 0.417919
\(656\) 3.31254e20 + 3.10669e20i 0.247390 + 0.232017i
\(657\) −9.04475e18 −0.00667815
\(658\) −5.29584e19 7.78990e19i −0.0386581 0.0568641i
\(659\) 6.82905e20i 0.492855i −0.969161 0.246428i \(-0.920743\pi\)
0.969161 0.246428i \(-0.0792568\pi\)
\(660\) −1.84363e20 7.29260e19i −0.131551 0.0520359i
\(661\) 9.29821e20i 0.655977i −0.944682 0.327988i \(-0.893629\pi\)
0.944682 0.327988i \(-0.106371\pi\)
\(662\) 1.35593e21 9.21805e20i 0.945805 0.642990i
\(663\) −6.90775e20 −0.476415
\(664\) 1.74166e20 + 7.77419e20i 0.118769 + 0.530145i
\(665\) 5.20644e19 0.0351057
\(666\) −1.03123e20 + 7.01067e19i −0.0687543 + 0.0467415i
\(667\) 4.33926e21i 2.86070i
\(668\) 5.25763e19 1.32917e20i 0.0342741 0.0866477i
\(669\) 5.09250e20i 0.328273i
\(670\) 1.51938e20 + 2.23493e20i 0.0968514 + 0.142463i
\(671\) 7.33699e20 0.462487
\(672\) −1.05770e20 1.66654e19i −0.0659312 0.0103883i
\(673\) −2.08455e20 −0.128499 −0.0642494 0.997934i \(-0.520465\pi\)
−0.0642494 + 0.997934i \(0.520465\pi\)
\(674\) 1.08583e21 + 1.59720e21i 0.661930 + 0.973665i
\(675\) 1.34608e21i 0.811505i
\(676\) −5.56210e20 + 1.40614e21i −0.331618 + 0.838357i
\(677\) 1.08759e18i 0.000641285i −1.00000 0.000320642i \(-0.999898\pi\)
1.00000 0.000320642i \(-0.000102064\pi\)
\(678\) 1.12594e21 7.65453e20i 0.656588 0.446371i
\(679\) −1.87079e20 −0.107895
\(680\) 2.90988e20 + 1.29887e21i 0.165981 + 0.740883i
\(681\) 1.58836e21 0.896080
\(682\) −2.14749e20 + 1.45994e20i −0.119825 + 0.0814612i
\(683\) 3.05497e21i 1.68598i −0.537933 0.842988i \(-0.680794\pi\)
0.537933 0.842988i \(-0.319206\pi\)
\(684\) −1.88298e20 7.44825e19i −0.102784 0.0406568i
\(685\) 1.09643e21i 0.591971i
\(686\) 1.48185e20 + 2.17973e20i 0.0791361 + 0.116405i
\(687\) −2.17896e21 −1.15100
\(688\) −6.66048e20 + 7.10181e20i −0.348011 + 0.371070i
\(689\) −3.96882e19 −0.0205124
\(690\) −8.48509e20 1.24811e21i −0.433799 0.638095i
\(691\) 2.17146e21i 1.09816i −0.835768 0.549082i \(-0.814977\pi\)
0.835768 0.549082i \(-0.185023\pi\)
\(692\) −8.47150e20 3.35097e20i −0.423804 0.167639i
\(693\) 4.73615e18i 0.00234383i
\(694\) 3.93273e20 2.67360e20i 0.192530 0.130888i
\(695\) 9.55056e20 0.462533
\(696\) 3.19656e21 7.16129e20i 1.53149 0.343101i
\(697\) 1.14860e21 0.544405
\(698\) −1.95888e21 + 1.33171e21i −0.918525 + 0.624444i
\(699\) 1.85001e21i 0.858212i
\(700\) 4.38943e19 1.10968e20i 0.0201452 0.0509287i
\(701\) 2.23982e21i 1.01702i −0.861056 0.508509i \(-0.830197\pi\)
0.861056 0.508509i \(-0.169803\pi\)
\(702\) 4.10488e20 + 6.03807e20i 0.184405 + 0.271250i
\(703\) −1.87255e21 −0.832280
\(704\) −3.06731e20 6.50214e20i −0.134885 0.285931i
\(705\) −1.00230e21 −0.436095
\(706\) −3.50202e20 5.15130e20i −0.150759 0.221759i
\(707\) 2.29495e20i 0.0977523i
\(708\) −1.13394e21 + 2.86669e21i −0.477904 + 1.20818i
\(709\) 2.31658e20i 0.0966052i −0.998833 0.0483026i \(-0.984619\pi\)
0.998833 0.0483026i \(-0.0153812\pi\)
\(710\) −1.42029e21 + 9.65561e20i −0.586057 + 0.398421i
\(711\) 1.53146e20 0.0625293
\(712\) −5.09379e20 + 1.14117e20i −0.205798 + 0.0461052i
\(713\) −1.97672e21 −0.790266
\(714\) −2.23956e20 + 1.52253e20i −0.0885984 + 0.0602322i
\(715\) 1.19852e20i 0.0469192i
\(716\) −3.33926e20 1.32087e20i −0.129361 0.0511696i
\(717\) 2.90057e21i 1.11196i
\(718\) 8.95112e19 + 1.31666e20i 0.0339581 + 0.0499507i
\(719\) −3.78747e21 −1.42195 −0.710973 0.703220i \(-0.751745\pi\)
−0.710973 + 0.703220i \(0.751745\pi\)
\(720\) 9.15135e19 9.75772e19i 0.0340010 0.0362539i
\(721\) −7.30634e19 −0.0268649
\(722\) −1.64579e20 2.42087e20i −0.0598888 0.0880934i
\(723\) 1.81752e21i 0.654547i
\(724\) 3.61171e21 + 1.42864e21i 1.28728 + 0.509194i
\(725\) 3.65086e21i 1.28783i
\(726\) −2.01690e21 + 1.37116e21i −0.704141 + 0.478699i
\(727\) 4.78780e21 1.65435 0.827176 0.561943i \(-0.189946\pi\)
0.827176 + 0.561943i \(0.189946\pi\)
\(728\) −1.41503e19 6.31624e19i −0.00483929 0.0216010i
\(729\) −3.19608e21 −1.08183
\(730\) 7.42066e19 5.04481e19i 0.0248611 0.0169014i
\(731\) 2.46249e21i 0.816573i
\(732\) 1.55087e21 3.92072e21i 0.509029 1.28686i
\(733\) 8.55865e20i 0.278051i −0.990289 0.139026i \(-0.955603\pi\)
0.990289 0.139026i \(-0.0443971\pi\)
\(734\) 1.71804e21 + 2.52715e21i 0.552476 + 0.812664i
\(735\) 1.39880e21 0.445246
\(736\) 8.51788e20 5.40601e21i 0.268379 1.70331i
\(737\) −3.69171e20 −0.115139
\(738\) −6.49006e19 9.54655e19i −0.0200367 0.0294730i
\(739\) 2.01440e21i 0.615620i −0.951448 0.307810i \(-0.900404\pi\)
0.951448 0.307810i \(-0.0995961\pi\)
\(740\) 4.55035e20 1.15036e21i 0.137660 0.348014i
\(741\) 1.04254e21i 0.312217i
\(742\) −1.28673e19 + 8.74762e18i −0.00381468 + 0.00259335i
\(743\) 2.89435e21 0.849445 0.424722 0.905324i \(-0.360372\pi\)
0.424722 + 0.905324i \(0.360372\pi\)
\(744\) 3.26227e20 + 1.45617e21i 0.0947813 + 0.423072i
\(745\) 2.01653e21 0.580005
\(746\) 3.74557e21 2.54636e21i 1.06654 0.725068i
\(747\) 2.02509e20i 0.0570872i
\(748\) −1.69082e21 6.68816e20i −0.471884 0.186657i
\(749\) 4.16181e20i 0.114992i
\(750\) −1.63356e21 2.40288e21i −0.446865 0.657315i
\(751\) 5.60310e21 1.51750 0.758750 0.651382i \(-0.225811\pi\)
0.758750 + 0.651382i \(0.225811\pi\)
\(752\) −2.65105e21 2.48630e21i −0.710859 0.666685i
\(753\) 3.33457e21 0.885274
\(754\) 1.11334e21 + 1.63766e21i 0.292645 + 0.430466i
\(755\) 1.93646e21i 0.503971i
\(756\) 2.66168e20 + 1.05285e20i 0.0685871 + 0.0271301i
\(757\) 5.61932e21i 1.43372i 0.697216 + 0.716861i \(0.254422\pi\)
−0.697216 + 0.716861i \(0.745578\pi\)
\(758\) −3.70732e21 + 2.52036e21i −0.936571 + 0.636713i
\(759\) 2.06166e21 0.515707
\(760\) 1.96030e21 4.39168e20i 0.485535 0.108775i
\(761\) −1.48465e21 −0.364115 −0.182057 0.983288i \(-0.558276\pi\)
−0.182057 + 0.983288i \(0.558276\pi\)
\(762\) −3.05107e21 + 2.07422e21i −0.740952 + 0.503724i
\(763\) 4.37610e19i 0.0105233i
\(764\) 4.80380e20 1.21444e21i 0.114389 0.289185i
\(765\) 3.38341e20i 0.0797799i
\(766\) 2.07784e21 + 3.05640e21i 0.485173 + 0.713664i
\(767\) −1.86361e21 −0.430912
\(768\) −4.12296e21 + 2.64700e20i −0.944060 + 0.0606102i
\(769\) −3.53626e21 −0.801855 −0.400928 0.916110i \(-0.631312\pi\)
−0.400928 + 0.916110i \(0.631312\pi\)
\(770\) −2.64164e19 3.88572e19i −0.00593190 0.00872552i
\(771\) 3.74539e20i 0.0832893i
\(772\) 1.54678e21 3.91038e21i 0.340642 0.861170i
\(773\) 3.96702e21i 0.865204i 0.901585 + 0.432602i \(0.142405\pi\)
−0.901585 + 0.432602i \(0.857595\pi\)
\(774\) 2.04670e20 1.39141e20i 0.0442076 0.0300538i
\(775\) −1.66312e21 −0.355763
\(776\) −7.04380e21 + 1.57803e21i −1.49226 + 0.334312i
\(777\) 2.51688e20 0.0528087
\(778\) 1.38967e21 9.44746e20i 0.288779 0.196322i
\(779\) 1.73350e21i 0.356774i
\(780\) −6.40463e20 2.53340e20i −0.130552 0.0516409i
\(781\) 2.34607e21i 0.473650i
\(782\) −7.78181e21 1.14466e22i −1.55607 2.28890i
\(783\) −8.75695e21 −1.73436
\(784\) 3.69976e21 + 3.46984e21i 0.725776 + 0.680674i
\(785\) −3.01221e21 −0.585280
\(786\) 2.44164e21 + 3.59153e21i 0.469909 + 0.691211i
\(787\) 5.35959e19i 0.0102170i −0.999987 0.00510848i \(-0.998374\pi\)
0.999987 0.00510848i \(-0.00162609\pi\)
\(788\) 8.97551e21 + 3.55033e21i 1.69478 + 0.670381i
\(789\) 6.52117e21i 1.21969i
\(790\) −1.25647e21 + 8.54189e20i −0.232781 + 0.158252i
\(791\) 3.22662e20 0.0592139
\(792\) 3.99500e19 + 1.78323e20i 0.00726236 + 0.0324167i
\(793\) 2.54882e21 0.458976
\(794\) 3.04566e21 2.07054e21i 0.543285 0.369343i
\(795\) 1.65560e20i 0.0292550i
\(796\) −1.19459e21 + 3.02003e21i −0.209109 + 0.528644i
\(797\) 8.79737e20i 0.152551i 0.997087 + 0.0762755i \(0.0243029\pi\)
−0.997087 + 0.0762755i \(0.975697\pi\)
\(798\) 2.29785e20 + 3.38002e20i 0.0394729 + 0.0580627i
\(799\) −9.19229e21 −1.56431
\(800\) 7.16656e20 4.54837e21i 0.120819 0.766797i
\(801\) 1.32687e20 0.0221608
\(802\) 1.25887e21 + 1.85173e21i 0.208292 + 0.306386i
\(803\) 1.22576e20i 0.0200927i
\(804\) −7.80341e20 + 1.97276e21i −0.126726 + 0.320372i
\(805\) 3.57672e20i 0.0575461i
\(806\) −7.46023e20 + 5.07171e20i −0.118916 + 0.0808429i
\(807\) 1.16375e22 1.83784
\(808\) 1.93581e21 + 8.64082e21i 0.302885 + 1.35198i
\(809\) 4.57183e21 0.708723 0.354361 0.935109i \(-0.384698\pi\)
0.354361 + 0.935109i \(0.384698\pi\)
\(810\) 2.25116e21 1.53041e21i 0.345755 0.235056i
\(811\) 4.73117e21i 0.719967i −0.932959 0.359984i \(-0.882782\pi\)
0.932959 0.359984i \(-0.117218\pi\)
\(812\) 7.21908e20 + 2.85556e20i 0.108846 + 0.0430548i
\(813\) 9.53916e21i 1.42505i
\(814\) 9.50097e20 + 1.39754e21i 0.140632 + 0.206863i
\(815\) −5.13764e21 −0.753498
\(816\) −7.14800e21 + 7.62163e21i −1.03874 + 1.10757i
\(817\) 3.71648e21 0.535138
\(818\) 1.56278e20 + 2.29877e20i 0.0222971 + 0.0327978i
\(819\) 1.64531e19i 0.00232604i
\(820\) 1.06494e21 + 4.21244e20i 0.149183 + 0.0590106i
\(821\) 6.87046e21i 0.953701i −0.878984 0.476851i \(-0.841778\pi\)
0.878984 0.476851i \(-0.158222\pi\)
\(822\) 7.11800e21 4.83905e21i 0.979082 0.665613i
\(823\) 2.19064e21 0.298588 0.149294 0.988793i \(-0.452300\pi\)
0.149294 + 0.988793i \(0.452300\pi\)
\(824\) −2.75095e21 + 6.16298e20i −0.371559 + 0.0832409i
\(825\) 1.73459e21 0.232162
\(826\) −6.04199e20 + 4.10754e20i −0.0801363 + 0.0544794i
\(827\) 1.22814e22i 1.61420i 0.590416 + 0.807099i \(0.298964\pi\)
−0.590416 + 0.807099i \(0.701036\pi\)
\(828\) −5.11681e20 + 1.29357e21i −0.0666456 + 0.168485i
\(829\) 1.90989e21i 0.246518i 0.992375 + 0.123259i \(0.0393347\pi\)
−0.992375 + 0.123259i \(0.960665\pi\)
\(830\) 1.12951e21 + 1.66146e21i 0.144479 + 0.212522i
\(831\) −7.34972e21 −0.931673
\(832\) −1.06556e21 2.25880e21i −0.133861 0.283761i
\(833\) 1.28286e22 1.59714
\(834\) 4.21511e21 + 6.20022e21i 0.520073 + 0.765000i
\(835\) 3.60451e20i 0.0440755i
\(836\) −1.00940e21 + 2.55184e21i −0.122325 + 0.309248i
\(837\) 3.98916e21i 0.479116i
\(838\) −4.59683e21 + 3.12508e21i −0.547178 + 0.371990i
\(839\) 6.37998e21 0.752669 0.376335 0.926484i \(-0.377184\pi\)
0.376335 + 0.926484i \(0.377184\pi\)
\(840\) −2.63482e20 + 5.90282e19i −0.0308075 + 0.00690185i
\(841\) −1.51216e22 −1.75238
\(842\) 1.18017e22 8.02317e21i 1.35551 0.921521i
\(843\) 4.52655e19i 0.00515300i
\(844\) 2.64960e21 + 1.04807e21i 0.298959 + 0.118255i
\(845\) 3.81325e21i 0.426451i
\(846\) 5.19404e20 + 7.64016e20i 0.0575741 + 0.0846885i
\(847\) −5.77984e20 −0.0635024
\(848\) −4.10685e20 + 4.37898e20i −0.0447240 + 0.0476874i
\(849\) −9.66686e21 −1.04346
\(850\) −6.54726e21 9.63069e21i −0.700516 1.03042i
\(851\) 1.28641e22i 1.36429i
\(852\) −1.25368e22 4.95904e21i −1.31793 0.521315i
\(853\) 2.88561e20i 0.0300690i −0.999887 0.0150345i \(-0.995214\pi\)
0.999887 0.0150345i \(-0.00478582\pi\)
\(854\) 8.26351e20 5.61781e20i 0.0853553 0.0580274i
\(855\) −5.10635e20 −0.0522835
\(856\) −3.51053e21 1.56698e22i −0.356303 1.59042i
\(857\) 9.17156e21 0.922757 0.461378 0.887203i \(-0.347355\pi\)
0.461378 + 0.887203i \(0.347355\pi\)
\(858\) 7.78080e20 5.28965e20i 0.0776014 0.0527560i
\(859\) 1.00522e22i 0.993834i −0.867798 0.496917i \(-0.834465\pi\)
0.867798 0.496917i \(-0.165535\pi\)
\(860\) −9.03112e20 + 2.28314e21i −0.0885122 + 0.223766i
\(861\) 2.32998e20i 0.0226375i
\(862\) 5.58504e21 + 8.21530e21i 0.537925 + 0.791260i
\(863\) −1.87741e21 −0.179258 −0.0896288 0.995975i \(-0.528568\pi\)
−0.0896288 + 0.995975i \(0.528568\pi\)
\(864\) 1.09097e22 + 1.71897e21i 1.03267 + 0.162710i
\(865\) −2.29735e21 −0.215579
\(866\) −9.17681e21 1.34986e22i −0.853704 1.25575i
\(867\) 1.61700e22i 1.49131i
\(868\) −1.30083e20 + 3.28859e20i −0.0118938 + 0.0300685i
\(869\) 2.07546e21i 0.188133i
\(870\) 6.83150e21 4.64429e21i 0.613934 0.417373i
\(871\) −1.28247e21 −0.114265
\(872\) −3.69128e20 1.64766e21i −0.0326065 0.145544i
\(873\) 1.83483e21 0.160690
\(874\) −1.72757e22 + 1.17446e22i −1.50003 + 1.01977i
\(875\) 6.88596e20i 0.0592794i
\(876\) 6.55018e20 + 2.59097e20i 0.0559078 + 0.0221147i
\(877\) 1.36577e22i 1.15580i 0.816109 + 0.577898i \(0.196127\pi\)
−0.816109 + 0.577898i \(0.803873\pi\)
\(878\) −1.00602e22 1.47980e22i −0.844104 1.24163i
\(879\) 9.44893e20 0.0786079
\(880\) −1.32238e21 1.24021e21i −0.109078 0.102300i
\(881\) −3.72174e21 −0.304387 −0.152194 0.988351i \(-0.548634\pi\)
−0.152194 + 0.988351i \(0.548634\pi\)
\(882\) −7.24871e20 1.06625e21i −0.0587822 0.0864656i
\(883\) 2.07606e22i 1.66930i −0.550780 0.834651i \(-0.685670\pi\)
0.550780 0.834651i \(-0.314330\pi\)
\(884\) −5.87379e21 2.32342e21i −0.468302 0.185240i
\(885\) 7.77404e21i 0.614571i
\(886\) −8.91037e21 + 6.05757e21i −0.698462 + 0.474838i
\(887\) 1.13338e22 0.880944 0.440472 0.897766i \(-0.354811\pi\)
0.440472 + 0.897766i \(0.354811\pi\)
\(888\) 9.47644e21 2.12302e21i 0.730378 0.163628i
\(889\) −8.74346e20 −0.0668221
\(890\) −1.08862e21 + 7.40078e20i −0.0824992 + 0.0560857i
\(891\) 3.71851e21i 0.279439i
\(892\) 1.71286e21 4.33024e21i 0.127640 0.322683i
\(893\) 1.38733e22i 1.02517i
\(894\) 8.89989e21 + 1.30913e22i 0.652158 + 0.959291i
\(895\) −9.05557e20 −0.0658026
\(896\) −8.43324e20 4.97465e20i −0.0607693 0.0358469i
\(897\) 7.16205e21 0.511793
\(898\) 1.91162e20 + 2.81189e20i 0.0135465 + 0.0199262i
\(899\) 1.08195e22i 0.760343i
\(900\) −4.30505e20 + 1.08835e21i −0.0300026 + 0.0758490i
\(901\) 1.51837e21i 0.104940i
\(902\) −1.29376e21 + 8.79544e20i −0.0886760 + 0.0602849i
\(903\) −4.99528e20 −0.0339549
\(904\) 1.21487e22 2.72168e21i 0.818966 0.183474i
\(905\) 9.79442e21 0.654808
\(906\) −1.25715e22 + 8.54650e21i −0.833536 + 0.566666i
\(907\) 1.97341e21i 0.129766i −0.997893 0.0648832i \(-0.979333\pi\)
0.997893 0.0648832i \(-0.0206675\pi\)
\(908\) 1.35061e22 + 5.34246e21i 0.880821 + 0.348415i
\(909\) 2.25083e21i 0.145584i
\(910\) −9.17688e19 1.34987e20i −0.00588687 0.00865928i
\(911\) −1.04284e22 −0.663484 −0.331742 0.943370i \(-0.607636\pi\)
−0.331742 + 0.943370i \(0.607636\pi\)
\(912\) 1.15028e22 + 1.07880e22i 0.725843 + 0.680737i
\(913\) −2.74443e21 −0.171760
\(914\) 1.04193e22 + 1.53263e22i 0.646761 + 0.951352i
\(915\) 1.06324e22i 0.654596i
\(916\) −1.85281e22 7.32894e21i −1.13140 0.447533i
\(917\) 1.02923e21i 0.0623363i
\(918\) 2.31002e22 1.57043e22i 1.38770 0.943404i
\(919\) 2.97590e22 1.77318 0.886589 0.462559i \(-0.153069\pi\)
0.886589 + 0.462559i \(0.153069\pi\)
\(920\) −3.01700e21 1.34669e22i −0.178306 0.795900i
\(921\) −1.42054e22 −0.832736
\(922\) −1.63905e22 + 1.11428e22i −0.953039 + 0.647908i
\(923\) 8.15006e21i 0.470055i
\(924\) 1.35672e20 3.42991e20i 0.00776161 0.0196220i
\(925\) 1.08233e22i 0.614179i
\(926\) 1.63686e22 + 2.40773e22i 0.921357 + 1.35527i
\(927\) 7.16589e20 0.0400103
\(928\) 2.95896e22 + 4.66224e21i 1.63881 + 0.258217i
\(929\) −1.15495e22 −0.634521 −0.317261 0.948338i \(-0.602763\pi\)
−0.317261 + 0.948338i \(0.602763\pi\)
\(930\) 2.11567e21 + 3.11204e21i 0.115299 + 0.169599i
\(931\) 1.93613e22i 1.04668i
\(932\) 6.22249e21 1.57309e22i 0.333691 0.843598i
\(933\) 2.82071e22i 1.50053i
\(934\) −7.04930e20 + 4.79235e20i −0.0372001 + 0.0252899i
\(935\) −4.58525e21 −0.240036
\(936\) 1.38783e20 + 6.19482e20i 0.00720723 + 0.0321707i
\(937\) −2.26316e22 −1.16592 −0.582958 0.812502i \(-0.698105\pi\)
−0.582958 + 0.812502i \(0.698105\pi\)
\(938\) −4.15790e20 + 2.82668e20i −0.0212497 + 0.0144462i
\(939\) 3.11944e20i 0.0158156i
\(940\) −8.52277e21 3.37124e21i −0.428669 0.169563i
\(941\) 1.06350e22i 0.530656i −0.964158 0.265328i \(-0.914520\pi\)
0.964158 0.265328i \(-0.0854803\pi\)
\(942\) −1.32943e22 1.95553e22i −0.658089 0.968015i
\(943\) −1.19088e22 −0.584831
\(944\) −1.92842e22 + 2.05620e22i −0.939533 + 1.00179i
\(945\) 7.21808e20 0.0348886
\(946\) −1.88567e21 2.77372e21i −0.0904235 0.133008i
\(947\) 2.15212e22i 1.02386i 0.859026 + 0.511932i \(0.171070\pi\)
−0.859026 + 0.511932i \(0.828930\pi\)
\(948\) −1.10908e22 4.38704e21i −0.523479 0.207066i
\(949\) 4.25820e20i 0.0199402i
\(950\) −1.45349e22 + 9.88135e21i −0.675284 + 0.459081i
\(951\) −6.09295e21 −0.280850
\(952\) −2.41644e21 + 5.41358e20i −0.110509 + 0.0247575i
\(953\) −9.29601e21 −0.421794 −0.210897 0.977508i \(-0.567638\pi\)
−0.210897 + 0.977508i \(0.567638\pi\)
\(954\) 1.26199e20 8.57946e19i 0.00568126 0.00386231i
\(955\) 3.29337e21i 0.147101i
\(956\) −9.75607e21 + 2.46641e22i −0.432355 + 1.09303i
\(957\) 1.12844e22i 0.496181i
\(958\) 1.49427e22 + 2.19799e22i 0.651909 + 0.958925i
\(959\) 2.03981e21 0.0882977
\(960\) −9.42259e21 + 4.44500e21i −0.404702 + 0.190914i
\(961\) −1.85365e22 −0.789956
\(962\) 3.30057e21 + 4.85497e21i 0.139565 + 0.205293i
\(963\) 4.08181e21i 0.171260i
\(964\) 6.11321e21 1.54547e22i 0.254502 0.643401i
\(965\) 1.06044e22i 0.438056i
\(966\) 2.32201e21 1.57858e21i 0.0951776 0.0647049i
\(967\) 1.70383e22 0.692992 0.346496 0.938051i \(-0.387371\pi\)
0.346496 + 0.938051i \(0.387371\pi\)
\(968\) −2.17619e22 + 4.87535e21i −0.878279 + 0.196762i
\(969\) 3.98851e22 1.59728
\(970\) −1.50536e22 + 1.02339e22i −0.598209 + 0.406682i
\(971\) 1.90042e22i 0.749386i 0.927149 + 0.374693i \(0.122252\pi\)
−0.927149 + 0.374693i \(0.877748\pi\)
\(972\) −4.97281e21 1.96703e21i −0.194583 0.0769687i
\(973\) 1.77680e21i 0.0689909i
\(974\) −1.96840e22 2.89542e22i −0.758441 1.11563i
\(975\) 6.02583e21 0.230400
\(976\) 2.63747e22 2.81223e22i 1.00072 1.06703i
\(977\) 2.36787e22 0.891556 0.445778 0.895144i \(-0.352927\pi\)
0.445778 + 0.895144i \(0.352927\pi\)
\(978\) −2.26749e22 3.33536e22i −0.847234 1.24624i
\(979\) 1.79820e21i 0.0666757i
\(980\) 1.18942e22 + 4.70485e21i 0.437664 + 0.173121i
\(981\) 4.29197e20i 0.0156725i
\(982\) 2.55713e22 1.73842e22i 0.926652 0.629969i
\(983\) −4.28171e22 −1.53981 −0.769903 0.638161i \(-0.779695\pi\)
−0.769903 + 0.638161i \(0.779695\pi\)
\(984\) 1.96537e21 + 8.77273e21i 0.0701423 + 0.313092i
\(985\) 2.43402e22 0.862091
\(986\) 6.26529e22 4.25935e22i 2.20224 1.49715i
\(987\) 1.86470e21i 0.0650474i
\(988\) −3.50658e21 + 8.86491e21i −0.121397 + 0.306900i
\(989\) 2.55315e22i 0.877210i
\(990\) 2.59086e20 + 3.81102e20i 0.00883447 + 0.0129950i
\(991\) 1.02666e22 0.347435 0.173718 0.984795i \(-0.444422\pi\)
0.173718 + 0.984795i \(0.444422\pi\)
\(992\) −2.12384e21 + 1.34793e22i −0.0713321 + 0.452720i
\(993\) 3.24573e22 1.08192
\(994\) −1.79634e21 2.64233e21i −0.0594280 0.0874156i
\(995\) 8.18987e21i 0.268908i
\(996\) −5.80109e21 + 1.46656e22i −0.189045 + 0.477920i
\(997\) 5.17267e22i 1.67302i 0.547951 + 0.836511i \(0.315408\pi\)
−0.547951 + 0.836511i \(0.684592\pi\)
\(998\) −9.84711e20 + 6.69440e20i −0.0316104 + 0.0214898i
\(999\) −2.59607e22 −0.827131
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.5.10 yes 14
3.2 odd 2 72.16.d.b.37.5 14
4.3 odd 2 32.16.b.a.17.4 14
8.3 odd 2 32.16.b.a.17.11 14
8.5 even 2 inner 8.16.b.a.5.9 14
24.5 odd 2 72.16.d.b.37.6 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.16.b.a.5.9 14 8.5 even 2 inner
8.16.b.a.5.10 yes 14 1.1 even 1 trivial
32.16.b.a.17.4 14 4.3 odd 2
32.16.b.a.17.11 14 8.3 odd 2
72.16.d.b.37.5 14 3.2 odd 2
72.16.d.b.37.6 14 24.5 odd 2