Properties

Label 3.15.b.a.2.3
Level $3$
Weight $15$
Character 3.2
Analytic conductor $3.730$
Analytic rank $0$
Dimension $4$
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] = [3,15,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 3.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: \(3.72986904456\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1929141760.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 364x^{2} + 3640 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{10}\cdot 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.3
Root \(3.20795i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.15.b.a.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+38.4954i q^{2} +(-824.672 - 2025.56i) q^{3} +14902.1 q^{4} -122931. i q^{5} +(77974.7 - 31746.1i) q^{6} -65585.1 q^{7} +1.20437e6i q^{8} +(-3.42280e6 + 3.34084e6i) q^{9} +O(q^{10})\) \(q+38.4954i q^{2} +(-824.672 - 2025.56i) q^{3} +14902.1 q^{4} -122931. i q^{5} +(77974.7 - 31746.1i) q^{6} -65585.1 q^{7} +1.20437e6i q^{8} +(-3.42280e6 + 3.34084e6i) q^{9} +4.73226e6 q^{10} -6.41681e6i q^{11} +(-1.22894e7 - 3.01851e7i) q^{12} +6.71391e7 q^{13} -2.52473e6i q^{14} +(-2.49003e8 + 1.01377e8i) q^{15} +1.97793e8 q^{16} +3.10586e8i q^{17} +(-1.28607e8 - 1.31762e8i) q^{18} +2.64721e8 q^{19} -1.83192e9i q^{20} +(5.40863e7 + 1.32847e8i) q^{21} +2.47018e8 q^{22} +3.74210e9i q^{23} +(2.43952e9 - 9.93212e8i) q^{24} -9.00839e9 q^{25} +2.58455e9i q^{26} +(9.58976e9 + 4.17798e9i) q^{27} -9.77357e8 q^{28} -2.30172e10i q^{29} +(-3.90256e9 - 9.58546e9i) q^{30} +1.42829e10 q^{31} +2.73465e10i q^{32} +(-1.29976e10 + 5.29177e9i) q^{33} -1.19561e10 q^{34} +8.06241e9i q^{35} +(-5.10069e10 + 4.97856e10i) q^{36} +7.16574e10 q^{37} +1.01905e10i q^{38} +(-5.53677e10 - 1.35994e11i) q^{39} +1.48054e11 q^{40} -9.96535e10i q^{41} +(-5.11398e9 + 2.08207e9i) q^{42} -2.62372e11 q^{43} -9.56240e10i q^{44} +(4.10692e11 + 4.20766e11i) q^{45} -1.44054e11 q^{46} +5.94893e11i q^{47} +(-1.63115e11 - 4.00642e11i) q^{48} -6.73922e11 q^{49} -3.46782e11i q^{50} +(6.29110e11 - 2.56132e11i) q^{51} +1.00051e12 q^{52} -7.14608e11i q^{53} +(-1.60833e11 + 3.69162e11i) q^{54} -7.88822e11 q^{55} -7.89889e10i q^{56} +(-2.18308e11 - 5.36208e11i) q^{57} +8.86056e11 q^{58} +2.54506e12i q^{59} +(-3.71067e12 + 1.51074e12i) q^{60} +2.14417e12 q^{61} +5.49826e11i q^{62} +(2.24485e11 - 2.19110e11i) q^{63} +2.18793e12 q^{64} -8.25344e12i q^{65} +(-2.03709e11 - 5.00349e11i) q^{66} -3.16198e12 q^{67} +4.62839e12i q^{68} +(7.57984e12 - 3.08601e12i) q^{69} -3.10366e11 q^{70} +4.44830e12i q^{71} +(-4.02362e12 - 4.12232e12i) q^{72} -1.16545e13 q^{73} +2.75848e12i q^{74} +(7.42897e12 + 1.82470e13i) q^{75} +3.94490e12 q^{76} +4.20848e11i q^{77} +(5.23515e12 - 2.13140e12i) q^{78} -1.15494e13 q^{79} -2.43148e13i q^{80} +(5.54323e11 - 2.28701e13i) q^{81} +3.83620e12 q^{82} +1.72455e13i q^{83} +(8.05999e11 + 1.97969e12i) q^{84} +3.81805e13 q^{85} -1.01001e13i q^{86} +(-4.66227e13 + 1.89817e13i) q^{87} +7.72822e12 q^{88} +9.51861e12i q^{89} +(-1.61976e13 + 1.58097e13i) q^{90} -4.40333e12 q^{91} +5.57652e13i q^{92} +(-1.17787e13 - 2.89308e13i) q^{93} -2.29007e13 q^{94} -3.25423e13i q^{95} +(5.53920e13 - 2.25519e13i) q^{96} +8.81078e13 q^{97} -2.59429e13i q^{98} +(2.14376e13 + 2.19635e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2196 q^{3} - 39296 q^{4} - 314496 q^{6} + 825608 q^{7} - 1624860 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2196 q^{3} - 39296 q^{4} - 314496 q^{6} + 825608 q^{7} - 1624860 q^{9} + 19918080 q^{10} - 157435776 q^{12} + 201696872 q^{13} - 449729280 q^{15} + 1113997312 q^{16} - 2066238720 q^{18} + 1314947240 q^{19} + 1947743784 q^{21} - 6769002240 q^{22} + 13425205248 q^{24} - 6882482780 q^{25} + 20862898164 q^{27} - 35011502848 q^{28} + 12293648640 q^{30} - 34970710072 q^{31} - 59537237760 q^{33} + 278847249408 q^{34} - 282390924672 q^{36} + 55576789928 q^{37} + 18888686856 q^{39} + 106207395840 q^{40} - 235283892480 q^{42} - 323678929048 q^{43} + 1007022481920 q^{45} - 273460142592 q^{46} + 1055038980096 q^{48} - 2246577120564 q^{49} + 2656416881664 q^{51} - 328297944832 q^{52} - 5027863591296 q^{54} - 832322050560 q^{55} + 1073653456968 q^{57} + 12943993870080 q^{58} - 9089286635520 q^{60} - 4171641626392 q^{61} + 2946514688712 q^{63} + 9874081841152 q^{64} - 14371860222720 q^{66} - 10964239937752 q^{67} + 15227331485184 q^{69} + 4380138846720 q^{70} + 24815696855040 q^{72} - 44644130922808 q^{73} + 36265563003060 q^{75} - 19249495285504 q^{76} - 5388124734720 q^{78} + 41215442578760 q^{79} - 17388818777916 q^{81} - 42500400284160 q^{82} - 61945380290304 q^{84} + 45292279818240 q^{85} - 41651639527680 q^{87} + 147397549178880 q^{88} - 5107487374080 q^{90} + 23445744391888 q^{91} - 145717264072728 q^{93} + 50952237493248 q^{94} + 81817830162432 q^{96} + 70529980615688 q^{97} - 86105375516160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 38.4954i 0.300745i 0.988629 + 0.150373i \(0.0480474\pi\)
−0.988629 + 0.150373i \(0.951953\pi\)
\(3\) −824.672 2025.56i −0.377079 0.926181i
\(4\) 14902.1 0.909552
\(5\) 122931.i 1.57351i −0.617265 0.786755i \(-0.711759\pi\)
0.617265 0.786755i \(-0.288241\pi\)
\(6\) 77974.7 31746.1i 0.278545 0.113405i
\(7\) −65585.1 −0.0796378 −0.0398189 0.999207i \(-0.512678\pi\)
−0.0398189 + 0.999207i \(0.512678\pi\)
\(8\) 1.20437e6i 0.574289i
\(9\) −3.42280e6 + 3.34084e6i −0.715622 + 0.698487i
\(10\) 4.73226e6 0.473226
\(11\) 6.41681e6i 0.329284i −0.986353 0.164642i \(-0.947353\pi\)
0.986353 0.164642i \(-0.0526469\pi\)
\(12\) −1.22894e7 3.01851e7i −0.342973 0.842410i
\(13\) 6.71391e7 1.06997 0.534985 0.844861i \(-0.320317\pi\)
0.534985 + 0.844861i \(0.320317\pi\)
\(14\) 2.52473e6i 0.0239507i
\(15\) −2.49003e8 + 1.01377e8i −1.45736 + 0.593338i
\(16\) 1.97793e8 0.736838
\(17\) 3.10586e8i 0.756902i 0.925621 + 0.378451i \(0.123543\pi\)
−0.925621 + 0.378451i \(0.876457\pi\)
\(18\) −1.28607e8 1.31762e8i −0.210067 0.215220i
\(19\) 2.64721e8 0.296151 0.148075 0.988976i \(-0.452692\pi\)
0.148075 + 0.988976i \(0.452692\pi\)
\(20\) 1.83192e9i 1.43119i
\(21\) 5.40863e7 + 1.32847e8i 0.0300298 + 0.0737590i
\(22\) 2.47018e8 0.0990306
\(23\) 3.74210e9i 1.09906i 0.835475 + 0.549529i \(0.185193\pi\)
−0.835475 + 0.549529i \(0.814807\pi\)
\(24\) 2.43952e9 9.93212e8i 0.531895 0.216552i
\(25\) −9.00839e9 −1.47594
\(26\) 2.58455e9i 0.321789i
\(27\) 9.58976e9 + 4.17798e9i 0.916772 + 0.399411i
\(28\) −9.77357e8 −0.0724347
\(29\) 2.30172e10i 1.33434i −0.744905 0.667170i \(-0.767505\pi\)
0.744905 0.667170i \(-0.232495\pi\)
\(30\) −3.90256e9 9.58546e9i −0.178444 0.438293i
\(31\) 1.42829e10 0.519140 0.259570 0.965724i \(-0.416419\pi\)
0.259570 + 0.965724i \(0.416419\pi\)
\(32\) 2.73465e10i 0.795889i
\(33\) −1.29976e10 + 5.29177e9i −0.304977 + 0.124166i
\(34\) −1.19561e10 −0.227635
\(35\) 8.06241e9i 0.125311i
\(36\) −5.10069e10 + 4.97856e10i −0.650896 + 0.635311i
\(37\) 7.16574e10 0.754830 0.377415 0.926044i \(-0.376813\pi\)
0.377415 + 0.926044i \(0.376813\pi\)
\(38\) 1.01905e10i 0.0890660i
\(39\) −5.53677e10 1.35994e11i −0.403464 0.990986i
\(40\) 1.48054e11 0.903650
\(41\) 9.96535e10i 0.511688i −0.966718 0.255844i \(-0.917647\pi\)
0.966718 0.255844i \(-0.0823534\pi\)
\(42\) −5.11398e9 + 2.08207e9i −0.0221827 + 0.00903131i
\(43\) −2.62372e11 −0.965248 −0.482624 0.875828i \(-0.660316\pi\)
−0.482624 + 0.875828i \(0.660316\pi\)
\(44\) 9.56240e10i 0.299501i
\(45\) 4.10692e11 + 4.20766e11i 1.09908 + 1.12604i
\(46\) −1.44054e11 −0.330537
\(47\) 5.94893e11i 1.17423i 0.809503 + 0.587116i \(0.199737\pi\)
−0.809503 + 0.587116i \(0.800263\pi\)
\(48\) −1.63115e11 4.00642e11i −0.277846 0.682445i
\(49\) −6.73922e11 −0.993658
\(50\) 3.46782e11i 0.443881i
\(51\) 6.29110e11 2.56132e11i 0.701028 0.285412i
\(52\) 1.00051e12 0.973194
\(53\) 7.14608e11i 0.608326i −0.952620 0.304163i \(-0.901623\pi\)
0.952620 0.304163i \(-0.0983768\pi\)
\(54\) −1.60833e11 + 3.69162e11i −0.120121 + 0.275715i
\(55\) −7.88822e11 −0.518132
\(56\) 7.89889e10i 0.0457351i
\(57\) −2.18308e11 5.36208e11i −0.111672 0.274289i
\(58\) 8.86056e11 0.401297
\(59\) 2.54506e12i 1.02266i 0.859383 + 0.511332i \(0.170848\pi\)
−0.859383 + 0.511332i \(0.829152\pi\)
\(60\) −3.71067e12 + 1.51074e12i −1.32554 + 0.539672i
\(61\) 2.14417e12 0.682260 0.341130 0.940016i \(-0.389190\pi\)
0.341130 + 0.940016i \(0.389190\pi\)
\(62\) 5.49826e11i 0.156129i
\(63\) 2.24485e11 2.19110e11i 0.0569906 0.0556260i
\(64\) 2.18793e12 0.497478
\(65\) 8.25344e12i 1.68361i
\(66\) −2.03709e11 5.00349e11i −0.0373424 0.0917203i
\(67\) −3.16198e12 −0.521717 −0.260859 0.965377i \(-0.584006\pi\)
−0.260859 + 0.965377i \(0.584006\pi\)
\(68\) 4.62839e12i 0.688442i
\(69\) 7.57984e12 3.08601e12i 1.01793 0.414432i
\(70\) −3.10366e11 −0.0376867
\(71\) 4.44830e12i 0.489087i 0.969638 + 0.244543i \(0.0786380\pi\)
−0.969638 + 0.244543i \(0.921362\pi\)
\(72\) −4.02362e12 4.12232e12i −0.401134 0.410974i
\(73\) −1.16545e13 −1.05495 −0.527475 0.849570i \(-0.676861\pi\)
−0.527475 + 0.849570i \(0.676861\pi\)
\(74\) 2.75848e12i 0.227012i
\(75\) 7.42897e12 + 1.82470e13i 0.556545 + 1.36698i
\(76\) 3.94490e12 0.269365
\(77\) 4.20848e11i 0.0262234i
\(78\) 5.23515e12 2.13140e12i 0.298035 0.121340i
\(79\) −1.15494e13 −0.601411 −0.300705 0.953717i \(-0.597222\pi\)
−0.300705 + 0.953717i \(0.597222\pi\)
\(80\) 2.43148e13i 1.15942i
\(81\) 5.54323e11 2.28701e13i 0.0242308 0.999706i
\(82\) 3.83620e12 0.153888
\(83\) 1.72455e13i 0.635519i 0.948171 + 0.317760i \(0.102930\pi\)
−0.948171 + 0.317760i \(0.897070\pi\)
\(84\) 8.05999e11 + 1.97969e12i 0.0273136 + 0.0670877i
\(85\) 3.81805e13 1.19099
\(86\) 1.01001e13i 0.290294i
\(87\) −4.66227e13 + 1.89817e13i −1.23584 + 0.503152i
\(88\) 7.72822e12 0.189104
\(89\) 9.51861e12i 0.215201i 0.994194 + 0.107600i \(0.0343167\pi\)
−0.994194 + 0.107600i \(0.965683\pi\)
\(90\) −1.61976e13 + 1.58097e13i −0.338651 + 0.330542i
\(91\) −4.40333e12 −0.0852101
\(92\) 5.57652e13i 0.999651i
\(93\) −1.17787e13 2.89308e13i −0.195757 0.480817i
\(94\) −2.29007e13 −0.353145
\(95\) 3.25423e13i 0.465997i
\(96\) 5.53920e13 2.25519e13i 0.737138 0.300113i
\(97\) 8.81078e13 1.09047 0.545233 0.838285i \(-0.316441\pi\)
0.545233 + 0.838285i \(0.316441\pi\)
\(98\) 2.59429e13i 0.298838i
\(99\) 2.14376e13 + 2.19635e13i 0.230001 + 0.235643i
\(100\) −1.34244e14 −1.34244
\(101\) 1.49993e14i 1.39901i −0.714627 0.699506i \(-0.753403\pi\)
0.714627 0.699506i \(-0.246597\pi\)
\(102\) 9.85990e12 + 2.42178e13i 0.0858363 + 0.210831i
\(103\) −1.66785e12 −0.0135611 −0.00678056 0.999977i \(-0.502158\pi\)
−0.00678056 + 0.999977i \(0.502158\pi\)
\(104\) 8.08604e13i 0.614472i
\(105\) 1.63309e13 6.64885e12i 0.116061 0.0472521i
\(106\) 2.75091e13 0.182951
\(107\) 2.47354e14i 1.54039i 0.637806 + 0.770197i \(0.279842\pi\)
−0.637806 + 0.770197i \(0.720158\pi\)
\(108\) 1.42908e14 + 6.22606e13i 0.833852 + 0.363285i
\(109\) −2.67988e14 −1.46599 −0.732994 0.680235i \(-0.761878\pi\)
−0.732994 + 0.680235i \(0.761878\pi\)
\(110\) 3.03660e13i 0.155826i
\(111\) −5.90939e13 1.45146e14i −0.284631 0.699109i
\(112\) −1.29723e13 −0.0586801
\(113\) 2.60088e13i 0.110553i −0.998471 0.0552765i \(-0.982396\pi\)
0.998471 0.0552765i \(-0.0176040\pi\)
\(114\) 2.06415e13 8.40386e12i 0.0824912 0.0335849i
\(115\) 4.60018e14 1.72938
\(116\) 3.43005e14i 1.21365i
\(117\) −2.29804e14 + 2.24301e14i −0.765695 + 0.747361i
\(118\) −9.79729e13 −0.307562
\(119\) 2.03698e13i 0.0602780i
\(120\) −1.22096e14 2.99892e14i −0.340748 0.836943i
\(121\) 3.38574e14 0.891572
\(122\) 8.25407e13i 0.205187i
\(123\) −2.01854e14 + 8.21815e13i −0.473916 + 0.192947i
\(124\) 2.12845e14 0.472185
\(125\) 3.57098e14i 0.748889i
\(126\) 8.43472e12 + 8.64163e12i 0.0167293 + 0.0171397i
\(127\) −7.59996e14 −1.42622 −0.713108 0.701054i \(-0.752713\pi\)
−0.713108 + 0.701054i \(0.752713\pi\)
\(128\) 5.32271e14i 0.945503i
\(129\) 2.16371e14 + 5.31451e14i 0.363975 + 0.893995i
\(130\) 3.17719e14 0.506338
\(131\) 1.01894e15i 1.53904i −0.638623 0.769520i \(-0.720496\pi\)
0.638623 0.769520i \(-0.279504\pi\)
\(132\) −1.93692e14 + 7.88585e13i −0.277392 + 0.112936i
\(133\) −1.73618e13 −0.0235848
\(134\) 1.21722e14i 0.156904i
\(135\) 5.13601e14 1.17887e15i 0.628477 1.44255i
\(136\) −3.74061e14 −0.434680
\(137\) 4.70567e14i 0.519491i 0.965677 + 0.259745i \(0.0836386\pi\)
−0.965677 + 0.259745i \(0.916361\pi\)
\(138\) 1.18797e14 + 2.91789e14i 0.124639 + 0.306137i
\(139\) 2.98471e14 0.297714 0.148857 0.988859i \(-0.452441\pi\)
0.148857 + 0.988859i \(0.452441\pi\)
\(140\) 1.20147e14i 0.113977i
\(141\) 1.20499e15 4.90592e14i 1.08755 0.442779i
\(142\) −1.71239e14 −0.147091
\(143\) 4.30819e14i 0.352324i
\(144\) −6.77007e14 + 6.60797e14i −0.527297 + 0.514672i
\(145\) −2.82952e15 −2.09960
\(146\) 4.48643e14i 0.317271i
\(147\) 5.55765e14 + 1.36507e15i 0.374688 + 0.920307i
\(148\) 1.06785e15 0.686557
\(149\) 1.70696e15i 1.04694i 0.852045 + 0.523468i \(0.175362\pi\)
−0.852045 + 0.523468i \(0.824638\pi\)
\(150\) −7.02426e14 + 2.85981e14i −0.411114 + 0.167378i
\(151\) 2.46501e15 1.37714 0.688572 0.725168i \(-0.258238\pi\)
0.688572 + 0.725168i \(0.258238\pi\)
\(152\) 3.18822e14i 0.170076i
\(153\) −1.03762e15 1.06307e15i −0.528686 0.541656i
\(154\) −1.62007e13 −0.00788658
\(155\) 1.75580e15i 0.816872i
\(156\) −8.25096e14 2.02660e15i −0.366971 0.901354i
\(157\) 2.11414e14 0.0899158 0.0449579 0.998989i \(-0.485685\pi\)
0.0449579 + 0.998989i \(0.485685\pi\)
\(158\) 4.44600e14i 0.180872i
\(159\) −1.44748e15 + 5.89317e14i −0.563420 + 0.229387i
\(160\) 3.36173e15 1.25234
\(161\) 2.45426e14i 0.0875266i
\(162\) 8.80393e14 + 2.13389e13i 0.300657 + 0.00728730i
\(163\) −1.94446e15 −0.636042 −0.318021 0.948084i \(-0.603018\pi\)
−0.318021 + 0.948084i \(0.603018\pi\)
\(164\) 1.48505e15i 0.465407i
\(165\) 6.50520e14 + 1.59780e15i 0.195377 + 0.479884i
\(166\) −6.63872e14 −0.191129
\(167\) 4.09979e15i 1.13174i 0.824495 + 0.565869i \(0.191459\pi\)
−0.824495 + 0.565869i \(0.808541\pi\)
\(168\) −1.59996e14 + 6.51399e13i −0.0423590 + 0.0172458i
\(169\) 5.70278e14 0.144837
\(170\) 1.46977e15i 0.358186i
\(171\) −9.06087e14 + 8.84391e14i −0.211932 + 0.206858i
\(172\) −3.90990e15 −0.877944
\(173\) 6.60096e14i 0.142326i 0.997465 + 0.0711630i \(0.0226711\pi\)
−0.997465 + 0.0711630i \(0.977329\pi\)
\(174\) −7.30706e14 1.79476e15i −0.151321 0.371673i
\(175\) 5.90817e14 0.117540
\(176\) 1.26920e15i 0.242629i
\(177\) 5.15516e15 2.09884e15i 0.947172 0.385626i
\(178\) −3.66423e14 −0.0647206
\(179\) 5.86552e15i 0.996174i −0.867127 0.498087i \(-0.834036\pi\)
0.867127 0.498087i \(-0.165964\pi\)
\(180\) 6.12017e15 + 6.27031e15i 0.999668 + 1.02419i
\(181\) −1.98346e15 −0.311655 −0.155828 0.987784i \(-0.549804\pi\)
−0.155828 + 0.987784i \(0.549804\pi\)
\(182\) 1.69508e14i 0.0256265i
\(183\) −1.76824e15 4.34314e15i −0.257266 0.631897i
\(184\) −4.50688e15 −0.631177
\(185\) 8.80889e15i 1.18773i
\(186\) 1.11370e15 4.53426e14i 0.144604 0.0588729i
\(187\) 1.99297e15 0.249236
\(188\) 8.86516e15i 1.06803i
\(189\) −6.28946e14 2.74013e14i −0.0730097 0.0318082i
\(190\) 1.25273e15 0.140146
\(191\) 1.70777e16i 1.84160i 0.390031 + 0.920802i \(0.372464\pi\)
−0.390031 + 0.920802i \(0.627536\pi\)
\(192\) −1.80433e15 4.43178e15i −0.187588 0.460754i
\(193\) 7.28710e15 0.730556 0.365278 0.930899i \(-0.380974\pi\)
0.365278 + 0.930899i \(0.380974\pi\)
\(194\) 3.39174e15i 0.327952i
\(195\) −1.67178e16 + 6.80638e15i −1.55933 + 0.634854i
\(196\) −1.00429e16 −0.903784
\(197\) 1.34309e16i 1.16639i −0.812333 0.583194i \(-0.801803\pi\)
0.812333 0.583194i \(-0.198197\pi\)
\(198\) −8.45492e14 + 8.25248e14i −0.0708685 + 0.0691716i
\(199\) 1.97699e16 1.59968 0.799839 0.600215i \(-0.204918\pi\)
0.799839 + 0.600215i \(0.204918\pi\)
\(200\) 1.08494e16i 0.847613i
\(201\) 2.60760e15 + 6.40477e15i 0.196729 + 0.483205i
\(202\) 5.77404e15 0.420746
\(203\) 1.50959e15i 0.106264i
\(204\) 9.37506e15 3.81690e15i 0.637622 0.259597i
\(205\) −1.22504e16 −0.805147
\(206\) 6.42044e13i 0.00407844i
\(207\) −1.25018e16 1.28085e16i −0.767678 0.786511i
\(208\) 1.32797e16 0.788394
\(209\) 1.69866e15i 0.0975177i
\(210\) 2.55950e14 + 6.28664e14i 0.0142109 + 0.0349047i
\(211\) −6.59808e15 −0.354356 −0.177178 0.984179i \(-0.556697\pi\)
−0.177178 + 0.984179i \(0.556697\pi\)
\(212\) 1.06492e16i 0.553305i
\(213\) 9.01029e15 3.66839e15i 0.452983 0.184424i
\(214\) −9.52198e15 −0.463266
\(215\) 3.22536e16i 1.51883i
\(216\) −5.03183e15 + 1.15496e16i −0.229377 + 0.526492i
\(217\) −9.36745e14 −0.0413431
\(218\) 1.03163e16i 0.440889i
\(219\) 9.61111e15 + 2.36068e16i 0.397800 + 0.977075i
\(220\) −1.17551e16 −0.471268
\(221\) 2.08525e16i 0.809863i
\(222\) 5.58746e15 2.27484e15i 0.210254 0.0856014i
\(223\) −1.37296e16 −0.500638 −0.250319 0.968163i \(-0.580535\pi\)
−0.250319 + 0.968163i \(0.580535\pi\)
\(224\) 1.79353e15i 0.0633829i
\(225\) 3.08339e16 3.00956e16i 1.05621 1.03092i
\(226\) 1.00122e15 0.0332483
\(227\) 4.03532e16i 1.29926i −0.760249 0.649632i \(-0.774923\pi\)
0.760249 0.649632i \(-0.225077\pi\)
\(228\) −3.25325e15 7.99062e15i −0.101572 0.249480i
\(229\) −4.63973e16 −1.40490 −0.702448 0.711735i \(-0.747910\pi\)
−0.702448 + 0.711735i \(0.747910\pi\)
\(230\) 1.77086e16i 0.520103i
\(231\) 8.52451e14 3.47061e14i 0.0242877 0.00988832i
\(232\) 2.77213e16 0.766297
\(233\) 1.99408e16i 0.534874i −0.963575 0.267437i \(-0.913823\pi\)
0.963575 0.267437i \(-0.0861768\pi\)
\(234\) −8.63456e15 8.84638e15i −0.224765 0.230279i
\(235\) 7.31305e16 1.84767
\(236\) 3.79267e16i 0.930167i
\(237\) 9.52451e15 + 2.33941e16i 0.226780 + 0.557015i
\(238\) 7.84145e14 0.0181283
\(239\) 7.55992e16i 1.69720i −0.529038 0.848598i \(-0.677447\pi\)
0.529038 0.848598i \(-0.322553\pi\)
\(240\) −4.92511e16 + 2.00518e16i −1.07383 + 0.437194i
\(241\) −4.79554e16 −1.01559 −0.507795 0.861478i \(-0.669539\pi\)
−0.507795 + 0.861478i \(0.669539\pi\)
\(242\) 1.30336e16i 0.268136i
\(243\) −4.67818e16 + 1.77375e16i −0.935046 + 0.354526i
\(244\) 3.19526e16 0.620552
\(245\) 8.28455e16i 1.56353i
\(246\) −3.16361e15 7.77044e15i −0.0580279 0.142528i
\(247\) 1.77731e16 0.316873
\(248\) 1.72019e16i 0.298136i
\(249\) 3.49317e16 1.42219e16i 0.588606 0.239641i
\(250\) −1.37466e16 −0.225225
\(251\) 5.85823e15i 0.0933362i −0.998910 0.0466681i \(-0.985140\pi\)
0.998910 0.0466681i \(-0.0148603\pi\)
\(252\) 3.34530e15 3.26520e15i 0.0518359 0.0505947i
\(253\) 2.40124e16 0.361902
\(254\) 2.92564e16i 0.428928i
\(255\) −3.14864e16 7.73368e16i −0.449099 1.10307i
\(256\) 1.53570e16 0.213122
\(257\) 1.74153e16i 0.235179i 0.993062 + 0.117590i \(0.0375168\pi\)
−0.993062 + 0.117590i \(0.962483\pi\)
\(258\) −2.04584e16 + 8.32930e15i −0.268865 + 0.109464i
\(259\) −4.69966e15 −0.0601130
\(260\) 1.22994e17i 1.53133i
\(261\) 7.68969e16 + 7.87833e16i 0.932020 + 0.954884i
\(262\) 3.92245e16 0.462859
\(263\) 1.15601e16i 0.132823i −0.997792 0.0664114i \(-0.978845\pi\)
0.997792 0.0664114i \(-0.0211550\pi\)
\(264\) −6.37325e15 1.56540e16i −0.0713073 0.175145i
\(265\) −8.78471e16 −0.957208
\(266\) 6.68348e14i 0.00709302i
\(267\) 1.92805e16 7.84973e15i 0.199315 0.0811477i
\(268\) −4.71201e16 −0.474529
\(269\) 1.20026e17i 1.17764i 0.808266 + 0.588818i \(0.200407\pi\)
−0.808266 + 0.588818i \(0.799593\pi\)
\(270\) 4.53812e16 + 1.97713e16i 0.433840 + 0.189011i
\(271\) −4.25215e16 −0.396117 −0.198058 0.980190i \(-0.563464\pi\)
−0.198058 + 0.980190i \(0.563464\pi\)
\(272\) 6.14319e16i 0.557714i
\(273\) 3.63130e15 + 8.91919e15i 0.0321310 + 0.0789200i
\(274\) −1.81147e16 −0.156234
\(275\) 5.78052e16i 0.486002i
\(276\) 1.12956e17 4.59880e16i 0.925858 0.376948i
\(277\) −1.58094e17 −1.26345 −0.631725 0.775193i \(-0.717653\pi\)
−0.631725 + 0.775193i \(0.717653\pi\)
\(278\) 1.14898e16i 0.0895360i
\(279\) −4.88875e16 + 4.77169e16i −0.371508 + 0.362612i
\(280\) −9.71014e15 −0.0719647
\(281\) 2.74660e17i 1.98541i −0.120551 0.992707i \(-0.538466\pi\)
0.120551 0.992707i \(-0.461534\pi\)
\(282\) 1.88855e16 + 4.63866e16i 0.133164 + 0.327076i
\(283\) 2.87031e17 1.97435 0.987173 0.159653i \(-0.0510375\pi\)
0.987173 + 0.159653i \(0.0510375\pi\)
\(284\) 6.62891e16i 0.444850i
\(285\) −6.59163e16 + 2.68367e16i −0.431597 + 0.175718i
\(286\) 1.65845e16 0.105960
\(287\) 6.53579e15i 0.0407497i
\(288\) −9.13605e16 9.36018e16i −0.555919 0.569556i
\(289\) 7.19141e16 0.427100
\(290\) 1.08923e17i 0.631444i
\(291\) −7.26600e16 1.78467e17i −0.411192 1.00997i
\(292\) −1.73676e17 −0.959533
\(293\) 3.75542e16i 0.202575i 0.994857 + 0.101287i \(0.0322961\pi\)
−0.994857 + 0.101287i \(0.967704\pi\)
\(294\) −5.25488e16 + 2.13944e16i −0.276778 + 0.112686i
\(295\) 3.12865e17 1.60917
\(296\) 8.63022e16i 0.433491i
\(297\) 2.68093e16 6.15357e16i 0.131520 0.301878i
\(298\) −6.57102e16 −0.314861
\(299\) 2.51241e17i 1.17596i
\(300\) 1.10707e17 + 2.71919e17i 0.506206 + 1.24334i
\(301\) 1.72077e16 0.0768702
\(302\) 9.48914e16i 0.414170i
\(303\) −3.03819e17 + 1.23695e17i −1.29574 + 0.527538i
\(304\) 5.23600e16 0.218215
\(305\) 2.63584e17i 1.07354i
\(306\) 4.09235e16 3.99436e16i 0.162900 0.159000i
\(307\) −3.96983e17 −1.54456 −0.772278 0.635285i \(-0.780883\pi\)
−0.772278 + 0.635285i \(0.780883\pi\)
\(308\) 6.27151e15i 0.0238516i
\(309\) 1.37543e15 + 3.37832e15i 0.00511362 + 0.0125601i
\(310\) 6.75903e16 0.245670
\(311\) 2.59474e17i 0.922086i −0.887378 0.461043i \(-0.847475\pi\)
0.887378 0.461043i \(-0.152525\pi\)
\(312\) 1.63787e17 6.66833e16i 0.569112 0.231705i
\(313\) 4.72356e17 1.60494 0.802470 0.596693i \(-0.203519\pi\)
0.802470 + 0.596693i \(0.203519\pi\)
\(314\) 8.13846e15i 0.0270417i
\(315\) −2.69353e16 2.75960e16i −0.0875281 0.0896753i
\(316\) −1.72111e17 −0.547015
\(317\) 3.04249e17i 0.945832i 0.881108 + 0.472916i \(0.156799\pi\)
−0.881108 + 0.472916i \(0.843201\pi\)
\(318\) −2.26860e16 5.57213e16i −0.0689871 0.169446i
\(319\) −1.47697e17 −0.439377
\(320\) 2.68963e17i 0.782786i
\(321\) 5.01029e17 2.03986e17i 1.42668 0.580851i
\(322\) 9.44778e15 0.0263232
\(323\) 8.22186e16i 0.224157i
\(324\) 8.26058e15 3.40812e17i 0.0220392 0.909285i
\(325\) −6.04815e17 −1.57921
\(326\) 7.48528e16i 0.191287i
\(327\) 2.21003e17 + 5.42826e17i 0.552794 + 1.35777i
\(328\) 1.20020e17 0.293857
\(329\) 3.90162e16i 0.0935133i
\(330\) −6.15081e16 + 2.50420e16i −0.144323 + 0.0587586i
\(331\) −2.80260e17 −0.643820 −0.321910 0.946770i \(-0.604325\pi\)
−0.321910 + 0.946770i \(0.604325\pi\)
\(332\) 2.56994e17i 0.578038i
\(333\) −2.45269e17 + 2.39396e17i −0.540173 + 0.527239i
\(334\) −1.57823e17 −0.340365
\(335\) 3.88704e17i 0.820928i
\(336\) 1.06979e16 + 2.62762e16i 0.0221271 + 0.0543484i
\(337\) 3.66345e17 0.742131 0.371065 0.928607i \(-0.378993\pi\)
0.371065 + 0.928607i \(0.378993\pi\)
\(338\) 2.19531e16i 0.0435590i
\(339\) −5.26823e16 + 2.14487e16i −0.102392 + 0.0416873i
\(340\) 5.68970e17 1.08327
\(341\) 9.16506e16i 0.170944i
\(342\) −3.40450e16 3.48802e16i −0.0622115 0.0637376i
\(343\) 8.86806e16 0.158771
\(344\) 3.15994e17i 0.554331i
\(345\) −3.79365e17 9.31794e17i −0.652113 1.60172i
\(346\) −2.54107e16 −0.0428039
\(347\) 1.96514e17i 0.324405i −0.986758 0.162202i \(-0.948140\pi\)
0.986758 0.162202i \(-0.0518598\pi\)
\(348\) −6.94776e17 + 2.82867e17i −1.12406 + 0.457643i
\(349\) 8.35267e16 0.132449 0.0662243 0.997805i \(-0.478905\pi\)
0.0662243 + 0.997805i \(0.478905\pi\)
\(350\) 2.27437e16i 0.0353497i
\(351\) 6.43848e17 + 2.80505e17i 0.980919 + 0.427358i
\(352\) 1.75478e17 0.262074
\(353\) 7.48154e17i 1.09539i −0.836678 0.547694i \(-0.815506\pi\)
0.836678 0.547694i \(-0.184494\pi\)
\(354\) 8.07956e16 + 1.98450e17i 0.115975 + 0.284858i
\(355\) 5.46832e17 0.769583
\(356\) 1.41847e17i 0.195736i
\(357\) −4.12603e16 + 1.67984e16i −0.0558283 + 0.0227296i
\(358\) 2.25796e17 0.299595
\(359\) 4.84462e16i 0.0630374i 0.999503 + 0.0315187i \(0.0100344\pi\)
−0.999503 + 0.0315187i \(0.989966\pi\)
\(360\) −5.06759e17 + 4.94625e17i −0.646672 + 0.631188i
\(361\) −7.28930e17 −0.912295
\(362\) 7.63543e16i 0.0937289i
\(363\) −2.79213e17 6.85802e17i −0.336193 0.825757i
\(364\) −6.56188e16 −0.0775030
\(365\) 1.43269e18i 1.65998i
\(366\) 1.67191e17 6.80690e16i 0.190040 0.0773716i
\(367\) −4.80054e17 −0.535338 −0.267669 0.963511i \(-0.586253\pi\)
−0.267669 + 0.963511i \(0.586253\pi\)
\(368\) 7.40163e17i 0.809827i
\(369\) 3.32927e17 + 3.41094e17i 0.357408 + 0.366176i
\(370\) 3.39102e17 0.357205
\(371\) 4.68677e16i 0.0484458i
\(372\) −1.75527e17 4.31130e17i −0.178051 0.437328i
\(373\) 6.20045e17 0.617250 0.308625 0.951184i \(-0.400131\pi\)
0.308625 + 0.951184i \(0.400131\pi\)
\(374\) 7.67203e16i 0.0749564i
\(375\) 7.23323e17 2.94489e17i 0.693607 0.282390i
\(376\) −7.16472e17 −0.674349
\(377\) 1.54535e18i 1.42770i
\(378\) 1.05482e16 2.42115e16i 0.00956616 0.0219573i
\(379\) −1.19985e18 −1.06820 −0.534100 0.845421i \(-0.679349\pi\)
−0.534100 + 0.845421i \(0.679349\pi\)
\(380\) 4.84948e17i 0.423848i
\(381\) 6.26748e17 + 1.53942e18i 0.537797 + 1.32093i
\(382\) −6.57413e17 −0.553854
\(383\) 1.56394e18i 1.29368i −0.762624 0.646842i \(-0.776089\pi\)
0.762624 0.646842i \(-0.223911\pi\)
\(384\) 1.07815e18 4.38949e17i 0.875707 0.356530i
\(385\) 5.17350e16 0.0412629
\(386\) 2.80520e17i 0.219711i
\(387\) 8.98048e17 8.76545e17i 0.690753 0.674214i
\(388\) 1.31299e18 0.991836
\(389\) 1.32813e18i 0.985359i 0.870211 + 0.492680i \(0.163983\pi\)
−0.870211 + 0.492680i \(0.836017\pi\)
\(390\) −2.62014e17 6.43559e17i −0.190929 0.468960i
\(391\) −1.16224e18 −0.831879
\(392\) 8.11652e17i 0.570647i
\(393\) −2.06392e18 + 8.40292e17i −1.42543 + 0.580340i
\(394\) 5.17030e17 0.350786
\(395\) 1.41978e18i 0.946326i
\(396\) 3.19465e17 + 3.27302e17i 0.209198 + 0.214330i
\(397\) 1.26662e18 0.814915 0.407457 0.913224i \(-0.366416\pi\)
0.407457 + 0.913224i \(0.366416\pi\)
\(398\) 7.61050e17i 0.481096i
\(399\) 1.43178e16 + 3.51672e16i 0.00889334 + 0.0218438i
\(400\) −1.78180e18 −1.08752
\(401\) 1.97233e18i 1.18296i 0.806320 + 0.591479i \(0.201456\pi\)
−0.806320 + 0.591479i \(0.798544\pi\)
\(402\) −2.46554e17 + 1.00380e17i −0.145322 + 0.0591653i
\(403\) 9.58940e17 0.555464
\(404\) 2.23521e18i 1.27247i
\(405\) −2.81143e18 6.81432e16i −1.57305 0.0381274i
\(406\) −5.81121e16 −0.0319584
\(407\) 4.59812e17i 0.248553i
\(408\) 3.08478e17 + 7.57682e17i 0.163909 + 0.402593i
\(409\) 1.78192e18 0.930731 0.465366 0.885119i \(-0.345923\pi\)
0.465366 + 0.885119i \(0.345923\pi\)
\(410\) 4.71586e17i 0.242144i
\(411\) 9.53161e17 3.88064e17i 0.481142 0.195889i
\(412\) −2.48544e16 −0.0123346
\(413\) 1.66918e17i 0.0814427i
\(414\) 4.93067e17 4.81261e17i 0.236539 0.230876i
\(415\) 2.12000e18 0.999996
\(416\) 1.83602e18i 0.851578i
\(417\) −2.46141e17 6.04571e17i −0.112262 0.275737i
\(418\) 6.53908e16 0.0293280
\(419\) 2.33841e18i 1.03139i −0.856773 0.515694i \(-0.827534\pi\)
0.856773 0.515694i \(-0.172466\pi\)
\(420\) 2.43365e17 9.90819e16i 0.105563 0.0429783i
\(421\) −2.14596e18 −0.915478 −0.457739 0.889087i \(-0.651341\pi\)
−0.457739 + 0.889087i \(0.651341\pi\)
\(422\) 2.53996e17i 0.106571i
\(423\) −1.98745e18 2.03620e18i −0.820186 0.840307i
\(424\) 8.60653e17 0.349355
\(425\) 2.79788e18i 1.11714i
\(426\) 1.41216e17 + 3.46855e17i 0.0554648 + 0.136232i
\(427\) −1.40626e17 −0.0543337
\(428\) 3.68609e18i 1.40107i
\(429\) −8.72648e17 + 3.55284e17i −0.326316 + 0.132854i
\(430\) −1.24161e18 −0.456781
\(431\) 1.47411e18i 0.533567i 0.963756 + 0.266784i \(0.0859609\pi\)
−0.963756 + 0.266784i \(0.914039\pi\)
\(432\) 1.89679e18 + 8.26376e17i 0.675512 + 0.294301i
\(433\) 4.14642e18 1.45297 0.726487 0.687181i \(-0.241152\pi\)
0.726487 + 0.687181i \(0.241152\pi\)
\(434\) 3.60604e16i 0.0124338i
\(435\) 2.33342e18 + 5.73135e18i 0.791715 + 1.94461i
\(436\) −3.99359e18 −1.33339
\(437\) 9.90613e17i 0.325487i
\(438\) −9.08752e17 + 3.69984e17i −0.293851 + 0.119636i
\(439\) −5.26499e18 −1.67551 −0.837753 0.546049i \(-0.816131\pi\)
−0.837753 + 0.546049i \(0.816131\pi\)
\(440\) 9.50034e17i 0.297557i
\(441\) 2.30670e18 2.25147e18i 0.711084 0.694057i
\(442\) −8.02724e17 −0.243562
\(443\) 2.03378e18i 0.607404i −0.952767 0.303702i \(-0.901777\pi\)
0.952767 0.303702i \(-0.0982228\pi\)
\(444\) −8.80624e17 2.16299e18i −0.258887 0.635876i
\(445\) 1.17013e18 0.338620
\(446\) 5.28526e17i 0.150565i
\(447\) 3.45755e18 1.40768e18i 0.969652 0.394778i
\(448\) −1.43496e17 −0.0396180
\(449\) 2.95114e18i 0.802168i 0.916041 + 0.401084i \(0.131367\pi\)
−0.916041 + 0.401084i \(0.868633\pi\)
\(450\) 1.15854e18 + 1.18696e18i 0.310045 + 0.317651i
\(451\) −6.39458e17 −0.168491
\(452\) 3.87586e17i 0.100554i
\(453\) −2.03282e18 4.99301e18i −0.519293 1.27548i
\(454\) 1.55341e18 0.390747
\(455\) 5.41303e17i 0.134079i
\(456\) 6.45793e17 2.62924e17i 0.157521 0.0641322i
\(457\) −2.32324e18 −0.558060 −0.279030 0.960282i \(-0.590013\pi\)
−0.279030 + 0.960282i \(0.590013\pi\)
\(458\) 1.78608e18i 0.422516i
\(459\) −1.29762e18 + 2.97845e18i −0.302315 + 0.693906i
\(460\) 6.85524e18 1.57296
\(461\) 3.05191e18i 0.689709i −0.938656 0.344854i \(-0.887928\pi\)
0.938656 0.344854i \(-0.112072\pi\)
\(462\) 1.33603e16 + 3.28154e16i 0.00297387 + 0.00730440i
\(463\) 9.23063e17 0.202379 0.101189 0.994867i \(-0.467735\pi\)
0.101189 + 0.994867i \(0.467735\pi\)
\(464\) 4.55265e18i 0.983192i
\(465\) −3.55648e18 + 1.44796e18i −0.756571 + 0.308025i
\(466\) 7.67630e17 0.160861
\(467\) 5.58017e18i 1.15194i 0.817472 + 0.575969i \(0.195375\pi\)
−0.817472 + 0.575969i \(0.804625\pi\)
\(468\) −3.42456e18 + 3.34256e18i −0.696439 + 0.679764i
\(469\) 2.07379e17 0.0415484
\(470\) 2.81519e18i 0.555677i
\(471\) −1.74347e17 4.28231e17i −0.0339054 0.0832783i
\(472\) −3.06519e18 −0.587305
\(473\) 1.68360e18i 0.317841i
\(474\) −9.00564e17 + 3.66650e17i −0.167520 + 0.0682029i
\(475\) −2.38471e18 −0.437100
\(476\) 3.03553e17i 0.0548260i
\(477\) 2.38739e18 + 2.44596e18i 0.424908 + 0.435332i
\(478\) 2.91022e18 0.510424
\(479\) 8.34404e18i 1.44221i 0.692827 + 0.721104i \(0.256365\pi\)
−0.692827 + 0.721104i \(0.743635\pi\)
\(480\) −2.77232e18 6.80937e18i −0.472232 1.15989i
\(481\) 4.81101e18 0.807646
\(482\) 1.84606e18i 0.305434i
\(483\) −4.97125e17 + 2.02396e17i −0.0810655 + 0.0330045i
\(484\) 5.04547e18 0.810931
\(485\) 1.08311e19i 1.71586i
\(486\) −6.82812e17 1.80088e18i −0.106622 0.281211i
\(487\) −6.93256e18 −1.06707 −0.533533 0.845779i \(-0.679136\pi\)
−0.533533 + 0.845779i \(0.679136\pi\)
\(488\) 2.58238e18i 0.391815i
\(489\) 1.60354e18 + 3.93862e18i 0.239838 + 0.589090i
\(490\) −3.18917e18 −0.470225
\(491\) 9.61225e18i 1.39719i −0.715518 0.698594i \(-0.753809\pi\)
0.715518 0.698594i \(-0.246191\pi\)
\(492\) −3.00805e18 + 1.22468e18i −0.431051 + 0.175495i
\(493\) 7.14882e18 1.00996
\(494\) 6.84183e17i 0.0952980i
\(495\) 2.69998e18 2.63533e18i 0.370787 0.361908i
\(496\) 2.82506e18 0.382522
\(497\) 2.91742e17i 0.0389498i
\(498\) 5.47477e17 + 1.34471e18i 0.0720710 + 0.177020i
\(499\) 9.37657e17 0.121714 0.0608569 0.998146i \(-0.480617\pi\)
0.0608569 + 0.998146i \(0.480617\pi\)
\(500\) 5.32151e18i 0.681153i
\(501\) 8.30435e18 3.38098e18i 1.04819 0.426755i
\(502\) 2.25515e17 0.0280704
\(503\) 2.44187e18i 0.299741i 0.988706 + 0.149870i \(0.0478857\pi\)
−0.988706 + 0.149870i \(0.952114\pi\)
\(504\) 2.63889e17 + 2.70363e17i 0.0319454 + 0.0327291i
\(505\) −1.84387e19 −2.20136
\(506\) 9.24366e17i 0.108840i
\(507\) −4.70292e17 1.15513e18i −0.0546150 0.134145i
\(508\) −1.13255e19 −1.29722
\(509\) 3.91889e18i 0.442730i 0.975191 + 0.221365i \(0.0710512\pi\)
−0.975191 + 0.221365i \(0.928949\pi\)
\(510\) 2.97711e18 1.21208e18i 0.331745 0.135064i
\(511\) 7.64359e17 0.0840139
\(512\) 9.31191e18i 1.00960i
\(513\) 2.53861e18 + 1.10600e18i 0.271503 + 0.118286i
\(514\) −6.70409e17 −0.0707291
\(515\) 2.05029e17i 0.0213386i
\(516\) 3.22439e18 + 7.91973e18i 0.331054 + 0.813135i
\(517\) 3.81732e18 0.386656
\(518\) 1.80915e17i 0.0180787i
\(519\) 1.33706e18 5.44363e17i 0.131820 0.0536682i
\(520\) 9.94020e18 0.966878
\(521\) 6.73712e18i 0.646562i −0.946303 0.323281i \(-0.895214\pi\)
0.946303 0.323281i \(-0.104786\pi\)
\(522\) −3.03279e18 + 2.96018e18i −0.287177 + 0.280301i
\(523\) −3.28728e18 −0.307132 −0.153566 0.988138i \(-0.549076\pi\)
−0.153566 + 0.988138i \(0.549076\pi\)
\(524\) 1.51844e19i 1.39984i
\(525\) −4.87230e17 1.19673e18i −0.0443220 0.108864i
\(526\) 4.45012e17 0.0399458
\(527\) 4.43607e18i 0.392938i
\(528\) −2.57084e18 + 1.04668e18i −0.224718 + 0.0914903i
\(529\) −2.41049e18 −0.207929
\(530\) 3.38171e18i 0.287876i
\(531\) −8.50263e18 8.71121e18i −0.714318 0.731842i
\(532\) −2.58727e17 −0.0214516
\(533\) 6.69064e18i 0.547491i
\(534\) 3.02179e17 + 7.42210e17i 0.0244048 + 0.0599430i
\(535\) 3.04073e19 2.42383
\(536\) 3.80820e18i 0.299616i
\(537\) −1.18809e19 + 4.83713e18i −0.922637 + 0.375637i
\(538\) −4.62047e18 −0.354169
\(539\) 4.32443e18i 0.327196i
\(540\) 7.65373e18 1.75677e19i 0.571633 1.31208i
\(541\) −7.23423e18 −0.533349 −0.266675 0.963787i \(-0.585925\pi\)
−0.266675 + 0.963787i \(0.585925\pi\)
\(542\) 1.63688e18i 0.119130i
\(543\) 1.63571e18 + 4.01762e18i 0.117519 + 0.288649i
\(544\) −8.49346e18 −0.602410
\(545\) 3.29439e19i 2.30675i
\(546\) −3.43348e17 + 1.39788e17i −0.0237348 + 0.00966324i
\(547\) 1.41948e19 0.968764 0.484382 0.874857i \(-0.339045\pi\)
0.484382 + 0.874857i \(0.339045\pi\)
\(548\) 7.01244e18i 0.472504i
\(549\) −7.33906e18 + 7.16333e18i −0.488241 + 0.476550i
\(550\) −2.22523e18 −0.146163
\(551\) 6.09314e18i 0.395166i
\(552\) 3.71670e18 + 9.12895e18i 0.238004 + 0.584584i
\(553\) 7.57472e17 0.0478950
\(554\) 6.08590e18i 0.379976i
\(555\) −1.78429e19 + 7.26445e18i −1.10006 + 0.447870i
\(556\) 4.44785e18 0.270786
\(557\) 7.43862e18i 0.447205i −0.974680 0.223602i \(-0.928218\pi\)
0.974680 0.223602i \(-0.0717817\pi\)
\(558\) −1.83688e18 1.88194e18i −0.109054 0.111729i
\(559\) −1.76154e19 −1.03279
\(560\) 1.59469e18i 0.0923338i
\(561\) −1.64355e18 4.03688e18i −0.0939816 0.230837i
\(562\) 1.05731e19 0.597104
\(563\) 2.60682e19i 1.45396i −0.686658 0.726981i \(-0.740923\pi\)
0.686658 0.726981i \(-0.259077\pi\)
\(564\) 1.79569e19 7.31085e18i 0.989185 0.402730i
\(565\) −3.19727e18 −0.173956
\(566\) 1.10494e19i 0.593775i
\(567\) −3.63554e16 + 1.49994e18i −0.00192969 + 0.0796144i
\(568\) −5.35741e18 −0.280877
\(569\) 3.01258e19i 1.56010i 0.625717 + 0.780051i \(0.284807\pi\)
−0.625717 + 0.780051i \(0.715193\pi\)
\(570\) −1.03309e18 2.53747e18i −0.0528463 0.129801i
\(571\) 1.99425e19 1.00769 0.503845 0.863794i \(-0.331918\pi\)
0.503845 + 0.863794i \(0.331918\pi\)
\(572\) 6.42011e18i 0.320457i
\(573\) 3.45919e19 1.40835e19i 1.70566 0.694431i
\(574\) −2.51598e17 −0.0122553
\(575\) 3.37103e19i 1.62214i
\(576\) −7.48884e18 + 7.30953e18i −0.356006 + 0.347482i
\(577\) −1.29010e19 −0.605886 −0.302943 0.953009i \(-0.597969\pi\)
−0.302943 + 0.953009i \(0.597969\pi\)
\(578\) 2.76836e18i 0.128448i
\(579\) −6.00947e18 1.47604e19i −0.275477 0.676627i
\(580\) −4.21657e19 −1.90969
\(581\) 1.13105e18i 0.0506113i
\(582\) 6.87017e18 2.79708e18i 0.303743 0.123664i
\(583\) −4.58550e18 −0.200312
\(584\) 1.40363e19i 0.605846i
\(585\) 2.75734e19 + 2.82499e19i 1.17598 + 1.20483i
\(586\) −1.44566e18 −0.0609234
\(587\) 8.63543e18i 0.359598i 0.983703 + 0.179799i \(0.0575447\pi\)
−0.983703 + 0.179799i \(0.942455\pi\)
\(588\) 8.28206e18 + 2.03424e19i 0.340798 + 0.837067i
\(589\) 3.78098e18 0.153744
\(590\) 1.20439e19i 0.483951i
\(591\) −2.72052e19 + 1.10761e19i −1.08029 + 0.439821i
\(592\) 1.41734e19 0.556187
\(593\) 2.44611e19i 0.948620i 0.880358 + 0.474310i \(0.157302\pi\)
−0.880358 + 0.474310i \(0.842698\pi\)
\(594\) 2.36884e18 + 1.03203e18i 0.0907885 + 0.0395539i
\(595\) −2.50407e18 −0.0948480
\(596\) 2.54373e19i 0.952243i
\(597\) −1.63037e19 4.00450e19i −0.603205 1.48159i
\(598\) −9.67163e18 −0.353664
\(599\) 4.76145e18i 0.172088i −0.996291 0.0860442i \(-0.972577\pi\)
0.996291 0.0860442i \(-0.0274226\pi\)
\(600\) −2.19762e19 + 8.94724e18i −0.785043 + 0.319617i
\(601\) −5.34152e18 −0.188601 −0.0943004 0.995544i \(-0.530061\pi\)
−0.0943004 + 0.995544i \(0.530061\pi\)
\(602\) 6.62419e17i 0.0231184i
\(603\) 1.08228e19 1.05637e19i 0.373353 0.364413i
\(604\) 3.67338e19 1.25258
\(605\) 4.16211e19i 1.40290i
\(606\) −4.76169e18 1.16957e19i −0.158655 0.389687i
\(607\) 2.37460e19 0.782115 0.391057 0.920366i \(-0.372109\pi\)
0.391057 + 0.920366i \(0.372109\pi\)
\(608\) 7.23920e18i 0.235703i
\(609\) 3.05775e18 1.24491e18i 0.0984196 0.0400699i
\(610\) 1.01468e19 0.322863
\(611\) 3.99406e19i 1.25639i
\(612\) −1.54627e19 1.58420e19i −0.480868 0.492664i
\(613\) −2.13066e19 −0.655074 −0.327537 0.944838i \(-0.606219\pi\)
−0.327537 + 0.944838i \(0.606219\pi\)
\(614\) 1.52820e19i 0.464518i
\(615\) 1.01026e19 + 2.48140e19i 0.303604 + 0.745712i
\(616\) −5.06857e17 −0.0150598
\(617\) 6.07266e19i 1.78395i −0.452085 0.891975i \(-0.649320\pi\)
0.452085 0.891975i \(-0.350680\pi\)
\(618\) −1.30050e17 + 5.29476e16i −0.00377738 + 0.00153790i
\(619\) 3.06934e19 0.881476 0.440738 0.897636i \(-0.354717\pi\)
0.440738 + 0.897636i \(0.354717\pi\)
\(620\) 2.61652e19i 0.742987i
\(621\) −1.56344e19 + 3.58859e19i −0.438976 + 1.00759i
\(622\) 9.98856e18 0.277313
\(623\) 6.24279e17i 0.0171381i
\(624\) −1.09514e19 2.68987e19i −0.297287 0.730196i
\(625\) −1.10846e19 −0.297551
\(626\) 1.81835e19i 0.482678i
\(627\) −3.44074e18 + 1.40084e18i −0.0903191 + 0.0367719i
\(628\) 3.15051e18 0.0817831
\(629\) 2.22558e19i 0.571332i
\(630\) 1.06232e18 1.03688e18i 0.0269694 0.0263237i
\(631\) 2.16168e18 0.0542734 0.0271367 0.999632i \(-0.491361\pi\)
0.0271367 + 0.999632i \(0.491361\pi\)
\(632\) 1.39098e19i 0.345384i
\(633\) 5.44125e18 + 1.33648e19i 0.133620 + 0.328198i
\(634\) −1.17122e19 −0.284454
\(635\) 9.34267e19i 2.24417i
\(636\) −2.15705e19 + 8.78207e18i −0.512460 + 0.208640i
\(637\) −4.52465e19 −1.06318
\(638\) 5.68566e18i 0.132141i
\(639\) −1.48611e19 1.52256e19i −0.341621 0.350001i
\(640\) 6.54324e19 1.48776
\(641\) 4.45341e17i 0.0100158i −0.999987 0.00500791i \(-0.998406\pi\)
0.999987 0.00500791i \(-0.00159407\pi\)
\(642\) 7.85251e18 + 1.92873e19i 0.174688 + 0.429069i
\(643\) −4.21110e19 −0.926656 −0.463328 0.886187i \(-0.653345\pi\)
−0.463328 + 0.886187i \(0.653345\pi\)
\(644\) 3.65737e18i 0.0796100i
\(645\) 6.53315e19 2.65986e19i 1.40671 0.572719i
\(646\) −3.16504e18 −0.0674142
\(647\) 1.01166e19i 0.213160i 0.994304 + 0.106580i \(0.0339900\pi\)
−0.994304 + 0.106580i \(0.966010\pi\)
\(648\) 2.75441e19 + 6.67611e17i 0.574120 + 0.0139155i
\(649\) 1.63311e19 0.336747
\(650\) 2.32826e19i 0.474939i
\(651\) 7.72508e17 + 1.89743e18i 0.0155896 + 0.0382912i
\(652\) −2.89766e19 −0.578514
\(653\) 6.72302e19i 1.32792i −0.747768 0.663960i \(-0.768874\pi\)
0.747768 0.663960i \(-0.231126\pi\)
\(654\) −2.08963e19 + 8.50758e18i −0.408343 + 0.166250i
\(655\) −1.25259e20 −2.42170
\(656\) 1.97108e19i 0.377031i
\(657\) 3.98909e19 3.89357e19i 0.754946 0.736870i
\(658\) 1.50194e18 0.0281237
\(659\) 2.11715e18i 0.0392241i −0.999808 0.0196121i \(-0.993757\pi\)
0.999808 0.0196121i \(-0.00624312\pi\)
\(660\) 9.69411e18 + 2.38107e19i 0.177705 + 0.436479i
\(661\) 8.18053e19 1.48379 0.741893 0.670518i \(-0.233928\pi\)
0.741893 + 0.670518i \(0.233928\pi\)
\(662\) 1.07887e19i 0.193626i
\(663\) 4.22379e19 1.71964e19i 0.750079 0.305382i
\(664\) −2.07700e19 −0.364972
\(665\) 2.13429e18i 0.0371109i
\(666\) −9.21566e18 9.44173e18i −0.158565 0.162455i
\(667\) 8.61327e19 1.46652
\(668\) 6.10954e19i 1.02937i
\(669\) 1.13224e19 + 2.78101e19i 0.188780 + 0.463681i
\(670\) −1.49633e19 −0.246890
\(671\) 1.37587e19i 0.224657i
\(672\) −3.63289e18 + 1.47907e18i −0.0587040 + 0.0239004i
\(673\) −5.70739e19 −0.912709 −0.456354 0.889798i \(-0.650845\pi\)
−0.456354 + 0.889798i \(0.650845\pi\)
\(674\) 1.41026e19i 0.223192i
\(675\) −8.63883e19 3.76369e19i −1.35310 0.589504i
\(676\) 8.49834e18 0.131737
\(677\) 5.97269e19i 0.916325i 0.888868 + 0.458163i \(0.151492\pi\)
−0.888868 + 0.458163i \(0.848508\pi\)
\(678\) −8.25677e17 2.02803e18i −0.0125373 0.0307940i
\(679\) −5.77856e18 −0.0868423
\(680\) 4.59835e19i 0.683974i
\(681\) −8.17378e19 + 3.32782e19i −1.20335 + 0.489925i
\(682\) 3.52813e18 0.0514107
\(683\) 6.68549e19i 0.964248i −0.876103 0.482124i \(-0.839866\pi\)
0.876103 0.482124i \(-0.160134\pi\)
\(684\) −1.35026e19 + 1.31793e19i −0.192763 + 0.188148i
\(685\) 5.78471e19 0.817424
\(686\) 3.41380e18i 0.0477495i
\(687\) 3.82626e19 + 9.39804e19i 0.529757 + 1.30119i
\(688\) −5.18955e19 −0.711231
\(689\) 4.79781e19i 0.650891i
\(690\) 3.58698e19 1.46038e19i 0.481709 0.196120i
\(691\) 7.46966e19 0.993012 0.496506 0.868033i \(-0.334616\pi\)
0.496506 + 0.868033i \(0.334616\pi\)
\(692\) 9.83682e18i 0.129453i
\(693\) −1.40599e18 1.44048e18i −0.0183167 0.0187661i
\(694\) 7.56489e18 0.0975632
\(695\) 3.66912e19i 0.468456i
\(696\) −2.28610e19 5.61510e19i −0.288955 0.709729i
\(697\) 3.09510e19 0.387298
\(698\) 3.21539e18i 0.0398333i
\(699\) −4.03913e19 + 1.64447e19i −0.495390 + 0.201690i
\(700\) 8.80441e18 0.106909
\(701\) 3.02354e18i 0.0363488i −0.999835 0.0181744i \(-0.994215\pi\)
0.999835 0.0181744i \(-0.00578541\pi\)
\(702\) −1.07982e19 + 2.47852e19i −0.128526 + 0.295007i
\(703\) 1.89692e19 0.223544
\(704\) 1.40395e19i 0.163811i
\(705\) −6.03087e19 1.48130e20i −0.696717 1.71127i
\(706\) 2.88005e19 0.329433
\(707\) 9.83731e18i 0.111414i
\(708\) 7.68227e19 3.12771e19i 0.861503 0.350747i
\(709\) 1.23202e19 0.136803 0.0684013 0.997658i \(-0.478210\pi\)
0.0684013 + 0.997658i \(0.478210\pi\)
\(710\) 2.10505e19i 0.231448i
\(711\) 3.95314e19 3.85849e19i 0.430383 0.420078i
\(712\) −1.14639e19 −0.123587
\(713\) 5.34480e19i 0.570565i
\(714\) −6.46663e17 1.58833e18i −0.00683582 0.0167901i
\(715\) −5.29608e19 −0.554386
\(716\) 8.74086e19i 0.906072i
\(717\) −1.53131e20 + 6.23446e19i −1.57191 + 0.639977i
\(718\) −1.86496e18 −0.0189582
\(719\) 8.17486e18i 0.0822958i 0.999153 + 0.0411479i \(0.0131015\pi\)
−0.999153 + 0.0411479i \(0.986899\pi\)
\(720\) 8.12320e19 + 8.32248e19i 0.809841 + 0.829708i
\(721\) 1.09386e17 0.00107998
\(722\) 2.80604e19i 0.274368i
\(723\) 3.95475e19 + 9.71365e19i 0.382958 + 0.940620i
\(724\) −2.95578e19 −0.283467
\(725\) 2.07348e20i 1.96940i
\(726\) 2.64002e19 1.07484e19i 0.248343 0.101109i
\(727\) −3.07501e19 −0.286487 −0.143244 0.989687i \(-0.545753\pi\)
−0.143244 + 0.989687i \(0.545753\pi\)
\(728\) 5.30324e18i 0.0489352i
\(729\) 7.45080e19 + 8.01316e19i 0.680942 + 0.732337i
\(730\) −5.51519e19 −0.499230
\(731\) 8.14892e19i 0.730598i
\(732\) −2.63505e19 6.47219e19i −0.233997 0.574743i
\(733\) −8.18832e19 −0.720223 −0.360112 0.932909i \(-0.617261\pi\)
−0.360112 + 0.932909i \(0.617261\pi\)
\(734\) 1.84799e19i 0.161000i
\(735\) 1.67808e20 6.83204e19i 1.44811 0.589575i
\(736\) −1.02334e20 −0.874729
\(737\) 2.02898e19i 0.171793i
\(738\) −1.31305e19 + 1.28161e19i −0.110126 + 0.107489i
\(739\) −8.38576e19 −0.696677 −0.348338 0.937369i \(-0.613254\pi\)
−0.348338 + 0.937369i \(0.613254\pi\)
\(740\) 1.31271e20i 1.08031i
\(741\) −1.46570e19 3.60005e19i −0.119486 0.293482i
\(742\) −1.80419e18 −0.0145698
\(743\) 9.95254e19i 0.796182i 0.917346 + 0.398091i \(0.130327\pi\)
−0.917346 + 0.398091i \(0.869673\pi\)
\(744\) 3.48434e19 1.41859e19i 0.276128 0.112421i
\(745\) 2.09838e20 1.64736
\(746\) 2.38689e19i 0.185635i
\(747\) −5.76145e19 5.90278e19i −0.443902 0.454792i
\(748\) 2.96995e19 0.226693
\(749\) 1.62227e19i 0.122674i
\(750\) 1.13365e19 + 2.78446e19i 0.0849276 + 0.208599i
\(751\) 5.86701e19 0.435449 0.217725 0.976010i \(-0.430137\pi\)
0.217725 + 0.976010i \(0.430137\pi\)
\(752\) 1.17666e20i 0.865218i
\(753\) −1.18662e19 + 4.83112e18i −0.0864462 + 0.0351952i
\(754\) 5.94890e19 0.429376
\(755\) 3.03024e20i 2.16695i
\(756\) −9.37262e18 4.08337e18i −0.0664061 0.0289312i
\(757\) −1.57745e20 −1.10735 −0.553676 0.832732i \(-0.686775\pi\)
−0.553676 + 0.832732i \(0.686775\pi\)
\(758\) 4.61887e19i 0.321256i
\(759\) −1.98023e19 4.86384e19i −0.136466 0.335187i
\(760\) 3.91930e19 0.267617
\(761\) 2.25035e20i 1.52250i −0.648459 0.761249i \(-0.724586\pi\)
0.648459 0.761249i \(-0.275414\pi\)
\(762\) −5.92605e19 + 2.41269e19i −0.397265 + 0.161740i
\(763\) 1.75761e19 0.116748
\(764\) 2.54494e20i 1.67503i
\(765\) −1.30684e20 + 1.27555e20i −0.852301 + 0.831893i
\(766\) 6.02044e19 0.389069
\(767\) 1.70873e20i 1.09422i
\(768\) −1.26645e19 3.11066e19i −0.0803638 0.197389i
\(769\) 1.08395e20 0.681591 0.340795 0.940137i \(-0.389304\pi\)
0.340795 + 0.940137i \(0.389304\pi\)
\(770\) 1.99156e18i 0.0124096i
\(771\) 3.52757e19 1.43619e19i 0.217819 0.0886813i
\(772\) 1.08593e20 0.664479
\(773\) 2.03020e20i 1.23107i 0.788109 + 0.615536i \(0.211060\pi\)
−0.788109 + 0.615536i \(0.788940\pi\)
\(774\) 3.37430e19 + 3.45707e19i 0.202767 + 0.207741i
\(775\) −1.28666e20 −0.766216
\(776\) 1.06114e20i 0.626242i
\(777\) 3.87568e18 + 9.51944e18i 0.0226674 + 0.0556755i
\(778\) −5.11270e19 −0.296342
\(779\) 2.63804e19i 0.151537i
\(780\) −2.49131e20 + 1.01429e20i −1.41829 + 0.577433i
\(781\) 2.85439e19 0.161048
\(782\) 4.47411e19i 0.250184i
\(783\) 9.61653e19 2.20729e20i 0.532950 1.22329i
\(784\) −1.33297e20 −0.732164
\(785\) 2.59892e19i 0.141483i
\(786\) −3.23474e19 7.94516e19i −0.174535 0.428691i
\(787\) 1.68006e20 0.898464 0.449232 0.893415i \(-0.351698\pi\)
0.449232 + 0.893415i \(0.351698\pi\)
\(788\) 2.00149e20i 1.06089i
\(789\) −2.34157e19 + 9.53332e18i −0.123018 + 0.0500847i
\(790\) −5.46549e19 −0.284603
\(791\) 1.70579e18i 0.00880420i
\(792\) −2.64522e19 + 2.58188e19i −0.135327 + 0.132087i
\(793\) 1.43958e20 0.729999
\(794\) 4.87590e19i 0.245082i
\(795\) 7.24451e19 + 1.77939e20i 0.360943 + 0.886548i
\(796\) 2.94613e20 1.45499
\(797\) 1.61596e20i 0.791084i −0.918448 0.395542i \(-0.870557\pi\)
0.918448 0.395542i \(-0.129443\pi\)
\(798\) −1.35378e18 + 5.51168e17i −0.00656942 + 0.00267463i
\(799\) −1.84766e20 −0.888778
\(800\) 2.46348e20i 1.17468i
\(801\) −3.18002e19 3.25803e19i −0.150315 0.154002i
\(802\) −7.59257e19 −0.355769
\(803\) 7.47845e19i 0.347378i
\(804\) 3.88587e19 + 9.54445e19i 0.178935 + 0.439500i
\(805\) −3.01704e19 −0.137724
\(806\) 3.69148e19i 0.167053i
\(807\) 2.43121e20 9.89825e19i 1.09070 0.444062i
\(808\) 1.80647e20 0.803437
\(809\) 1.11551e20i 0.491852i −0.969289 0.245926i \(-0.920908\pi\)
0.969289 0.245926i \(-0.0790921\pi\)
\(810\) 2.62320e18 1.08227e20i 0.0114666 0.473087i
\(811\) −4.47129e20 −1.93770 −0.968850 0.247647i \(-0.920343\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(812\) 2.24960e19i 0.0966526i
\(813\) 3.50663e19 + 8.61297e19i 0.149367 + 0.366876i
\(814\) 1.77007e19 0.0747513
\(815\) 2.39034e20i 1.00082i
\(816\) 1.24434e20 5.06612e19i 0.516544 0.210302i
\(817\) −6.94555e19 −0.285859
\(818\) 6.85956e19i 0.279913i
\(819\) 1.50717e19 1.47108e19i 0.0609782 0.0595182i
\(820\) −1.82557e20 −0.732323
\(821\) 2.52577e20i 1.00460i 0.864694 + 0.502299i \(0.167512\pi\)
−0.864694 + 0.502299i \(0.832488\pi\)
\(822\) 1.49387e19 + 3.66923e19i 0.0589128 + 0.144701i
\(823\) −4.42630e20 −1.73078 −0.865390 0.501099i \(-0.832929\pi\)
−0.865390 + 0.501099i \(0.832929\pi\)
\(824\) 2.00871e18i 0.00778800i
\(825\) 1.17088e20 4.76703e19i 0.450126 0.183261i
\(826\) 6.42557e18 0.0244935
\(827\) 2.72278e20i 1.02914i 0.857448 + 0.514570i \(0.172049\pi\)
−0.857448 + 0.514570i \(0.827951\pi\)
\(828\) −1.86303e20 1.90873e20i −0.698244 0.715373i
\(829\) 1.07852e20 0.400816 0.200408 0.979713i \(-0.435773\pi\)
0.200408 + 0.979713i \(0.435773\pi\)
\(830\) 8.16101e19i 0.300744i
\(831\) 1.30376e20 + 3.20229e20i 0.476421 + 1.17018i
\(832\) 1.46896e20 0.532286
\(833\) 2.09311e20i 0.752101i
\(834\) 2.32732e19 9.47529e18i 0.0829265 0.0337622i
\(835\) 5.03989e20 1.78080
\(836\) 2.53137e19i 0.0886975i
\(837\) 1.36969e20 + 5.96736e19i 0.475933 + 0.207350i
\(838\) 9.00179e19 0.310185
\(839\) 4.86182e20i 1.66137i −0.556746 0.830683i \(-0.687950\pi\)
0.556746 0.830683i \(-0.312050\pi\)
\(840\) 8.00768e18 + 1.96684e19i 0.0271364 + 0.0666523i
\(841\) −2.32233e20 −0.780464
\(842\) 8.26098e19i 0.275326i
\(843\) −5.56340e20 + 2.26505e20i −1.83885 + 0.748659i
\(844\) −9.83252e19 −0.322306
\(845\) 7.01045e19i 0.227902i
\(846\) 7.83843e19 7.65075e19i 0.252718 0.246667i
\(847\) −2.22054e19 −0.0710028
\(848\) 1.41345e20i 0.448238i
\(849\) −2.36706e20 5.81397e20i −0.744485 1.82860i
\(850\) 1.07706e20 0.335974
\(851\) 2.68149e20i 0.829602i
\(852\) 1.34272e20 5.46668e19i 0.412011 0.167744i
\(853\) 4.29971e20 1.30857 0.654284 0.756249i \(-0.272970\pi\)
0.654284 + 0.756249i \(0.272970\pi\)
\(854\) 5.41344e18i 0.0163406i
\(855\) 1.08719e20 + 1.11386e20i 0.325493 + 0.333478i
\(856\) −2.97906e20 −0.884631
\(857\) 4.88235e20i 1.43801i −0.695003 0.719007i \(-0.744597\pi\)
0.695003 0.719007i \(-0.255403\pi\)
\(858\) −1.36768e19 3.35930e19i −0.0399553 0.0981380i
\(859\) 4.60333e20 1.33389 0.666945 0.745107i \(-0.267601\pi\)
0.666945 + 0.745107i \(0.267601\pi\)
\(860\) 4.80646e20i 1.38145i
\(861\) 1.32386e19 5.38988e18i 0.0377416 0.0153659i
\(862\) −5.67465e19 −0.160468
\(863\) 2.76671e20i 0.776047i 0.921650 + 0.388023i \(0.126842\pi\)
−0.921650 + 0.388023i \(0.873158\pi\)
\(864\) −1.14253e20 + 2.62247e20i −0.317887 + 0.729649i
\(865\) 8.11459e19 0.223952
\(866\) 1.59618e20i 0.436975i
\(867\) −5.93056e19 1.45666e20i −0.161050 0.395572i
\(868\) −1.39595e19 −0.0376037
\(869\) 7.41106e19i 0.198035i
\(870\) −2.20631e20 + 8.98261e19i −0.584832 + 0.238105i
\(871\) −2.12292e20 −0.558222
\(872\) 3.22757e20i 0.841901i
\(873\) −3.01575e20 + 2.94354e20i −0.780362 + 0.761677i
\(874\) −3.81340e19 −0.0978887
\(875\) 2.34203e19i 0.0596398i
\(876\) 1.43226e20 + 3.51791e20i 0.361820 + 0.888701i
\(877\) −2.56763e20 −0.643480 −0.321740 0.946828i \(-0.604268\pi\)
−0.321740 + 0.946828i \(0.604268\pi\)
\(878\) 2.02678e20i 0.503901i
\(879\) 7.60682e19 3.09699e19i 0.187621 0.0763867i
\(880\) −1.56024e20 −0.381779
\(881\) 3.46483e20i 0.841106i 0.907268 + 0.420553i \(0.138164\pi\)
−0.907268 + 0.420553i \(0.861836\pi\)
\(882\) 8.66711e19 + 8.87973e19i 0.208735 + 0.213855i
\(883\) 8.21926e20 1.96385 0.981924 0.189278i \(-0.0606147\pi\)
0.981924 + 0.189278i \(0.0606147\pi\)
\(884\) 3.10746e20i 0.736612i
\(885\) −2.58011e20 6.33726e20i −0.606786 1.49039i
\(886\) 7.82912e19 0.182674
\(887\) 3.45271e20i 0.799271i −0.916674 0.399636i \(-0.869137\pi\)
0.916674 0.399636i \(-0.130863\pi\)
\(888\) 1.74810e20 7.11710e19i 0.401491 0.163460i
\(889\) 4.98445e19 0.113581
\(890\) 4.50445e19i 0.101838i
\(891\) −1.46753e20 3.55699e18i −0.329187 0.00797882i
\(892\) −2.04600e20 −0.455356
\(893\) 1.57481e20i 0.347750i
\(894\) 5.41894e19 + 1.33100e20i 0.118728 + 0.291618i
\(895\) −7.21051e20 −1.56749
\(896\) 3.49091e19i 0.0752978i
\(897\) 5.08904e20 2.07192e20i 1.08915 0.443430i
\(898\) −1.13605e20 −0.241248
\(899\) 3.28752e20i 0.692709i
\(900\) 4.59490e20 4.48488e20i 0.960680 0.937677i
\(901\) 2.21947e20 0.460443
\(902\) 2.46162e19i 0.0506728i
\(903\) −1.41907e19 3.48553e19i −0.0289862 0.0711958i
\(904\) 3.13242e19 0.0634894
\(905\) 2.43828e20i 0.490393i
\(906\) 1.92208e20 7.82543e19i 0.383596 0.156175i
\(907\) −3.86876e20 −0.766162 −0.383081 0.923715i \(-0.625137\pi\)
−0.383081 + 0.923715i \(0.625137\pi\)
\(908\) 6.01348e20i 1.18175i
\(909\) 5.01103e20 + 5.13396e20i 0.977192 + 1.00116i
\(910\) −2.08377e19 −0.0403236
\(911\) 1.87671e20i 0.360387i −0.983631 0.180193i \(-0.942328\pi\)
0.983631 0.180193i \(-0.0576724\pi\)
\(912\) −4.31799e19 1.06058e20i −0.0822844 0.202107i
\(913\) 1.10661e20 0.209266
\(914\) 8.94341e19i 0.167834i
\(915\) −5.33904e20 + 2.17370e20i −0.994296 + 0.404811i
\(916\) −6.91417e20 −1.27783
\(917\) 6.68274e19i 0.122566i
\(918\) −1.14656e20 4.99525e19i −0.208689 0.0909197i
\(919\) 4.07867e20 0.736733 0.368366 0.929681i \(-0.379917\pi\)
0.368366 + 0.929681i \(0.379917\pi\)
\(920\) 5.54033e20i 0.993164i
\(921\) 3.27381e20 + 8.04112e20i 0.582420 + 1.43054i
\(922\) 1.17485e20 0.207427
\(923\) 2.98655e20i 0.523308i
\(924\) 1.27033e19 5.17195e18i 0.0220909 0.00899394i
\(925\) −6.45518e20 −1.11408
\(926\) 3.55337e19i 0.0608644i
\(927\) 5.70871e18 5.57202e18i 0.00970464 0.00947227i
\(928\) 6.29441e20 1.06199
\(929\) 5.28931e20i 0.885705i 0.896594 + 0.442853i \(0.146033\pi\)
−0.896594 + 0.442853i \(0.853967\pi\)
\(930\) −5.57399e19 1.36908e20i −0.0926372 0.227535i
\(931\) −1.78401e20 −0.294273
\(932\) 2.97160e20i 0.486496i
\(933\) −5.25580e20 + 2.13981e20i −0.854018 + 0.347699i
\(934\) −2.14811e20 −0.346440
\(935\) 2.44997e20i 0.392175i
\(936\) −2.70142e20 2.76769e20i −0.429201 0.439730i
\(937\) 4.76361e19 0.0751207 0.0375603 0.999294i \(-0.488041\pi\)
0.0375603 + 0.999294i \(0.488041\pi\)
\(938\) 7.98313e18i 0.0124955i
\(939\) −3.89539e20 9.56784e20i −0.605190 1.48646i
\(940\) 1.08980e21 1.68055
\(941\) 4.29127e20i 0.656839i −0.944532 0.328419i \(-0.893484\pi\)
0.944532 0.328419i \(-0.106516\pi\)
\(942\) 1.64849e19 6.71156e18i 0.0250456 0.0101969i
\(943\) 3.72913e20 0.562375
\(944\) 5.03395e20i 0.753538i
\(945\) −3.36846e19 + 7.73166e19i −0.0500505 + 0.114882i
\(946\) −6.48107e19 −0.0955891
\(947\) 3.75227e20i 0.549343i 0.961538 + 0.274672i \(0.0885691\pi\)
−0.961538 + 0.274672i \(0.911431\pi\)
\(948\) 1.41935e20 + 3.48621e20i 0.206268 + 0.506635i
\(949\) −7.82469e20 −1.12877
\(950\) 9.18004e19i 0.131456i
\(951\) 6.16273e20 2.50906e20i 0.876011 0.356654i
\(952\) 2.45328e19 0.0346170
\(953\) 2.80481e20i 0.392874i −0.980516 0.196437i \(-0.937063\pi\)
0.980516 0.196437i \(-0.0629372\pi\)
\(954\) −9.41582e19 + 9.19036e19i −0.130924 + 0.127789i
\(955\) 2.09937e21 2.89778
\(956\) 1.12659e21i 1.54369i
\(957\) 1.21802e20 + 2.99169e20i 0.165680 + 0.406942i
\(958\) −3.21207e20 −0.433737
\(959\) 3.08622e19i 0.0413711i
\(960\) −5.44801e20 + 2.21807e20i −0.725002 + 0.295172i
\(961\) −5.52943e20 −0.730494
\(962\) 1.85202e20i 0.242896i
\(963\) −8.26370e20 8.46642e20i −1.07595 1.10234i
\(964\) −7.14637e20 −0.923732
\(965\) 8.95806e20i 1.14954i
\(966\) −7.79133e18 1.91370e19i −0.00992594 0.0243801i
\(967\) 5.81177e19 0.0735060 0.0367530 0.999324i \(-0.488299\pi\)
0.0367530 + 0.999324i \(0.488299\pi\)
\(968\) 4.07769e20i 0.512020i
\(969\) 1.66539e20 6.78034e19i 0.207610 0.0845250i
\(970\) 4.16949e20 0.516037
\(971\) 5.64465e20i 0.693589i 0.937941 + 0.346795i \(0.112730\pi\)
−0.937941 + 0.346795i \(0.887270\pi\)
\(972\) −6.97147e20 + 2.64326e20i −0.850473 + 0.322460i
\(973\) −1.95753e19 −0.0237093
\(974\) 2.66872e20i 0.320915i
\(975\) 4.98774e20 + 1.22509e21i 0.595486 + 1.46263i
\(976\) 4.24102e20 0.502715
\(977\) 1.62939e21i 1.91762i 0.284052 + 0.958809i \(0.408321\pi\)
−0.284052 + 0.958809i \(0.591679\pi\)
\(978\) −1.51619e20 + 6.17290e19i −0.177166 + 0.0721303i
\(979\) 6.10791e19 0.0708621
\(980\) 1.23457e21i 1.42211i
\(981\) 9.17270e20 8.95307e20i 1.04909 1.02397i
\(982\) 3.70028e20 0.420198
\(983\) 1.91394e20i 0.215801i −0.994162 0.107900i \(-0.965587\pi\)
0.994162 0.107900i \(-0.0344128\pi\)
\(984\) −9.89770e19 2.43107e20i −0.110807 0.272165i
\(985\) −1.65107e21 −1.83532
\(986\) 2.75197e20i 0.303742i
\(987\) −7.90295e19 + 3.21755e19i −0.0866102 + 0.0352619i
\(988\) 2.64857e20 0.288212
\(989\) 9.81825e20i 1.06086i
\(990\) 1.01448e20 + 1.03937e20i 0.108842 + 0.111512i
\(991\) −7.98378e20 −0.850536 −0.425268 0.905067i \(-0.639820\pi\)
−0.425268 + 0.905067i \(0.639820\pi\)
\(992\) 3.90588e20i 0.413178i
\(993\) 2.31122e20 + 5.67682e20i 0.242771 + 0.596294i
\(994\) 1.12307e19 0.0117140
\(995\) 2.43032e21i 2.51711i
\(996\) 5.20556e20 2.11936e20i 0.535368 0.217966i
\(997\) −5.86353e19 −0.0598816 −0.0299408 0.999552i \(-0.509532\pi\)
−0.0299408 + 0.999552i \(0.509532\pi\)
\(998\) 3.60955e19i 0.0366049i
\(999\) 6.87178e20 + 2.99383e20i 0.692007 + 0.301487i
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 3.15.b.a.2.3 yes 4
3.2 odd 2 inner 3.15.b.a.2.2 4
4.3 odd 2 48.15.e.b.17.4 4
5.2 odd 4 75.15.d.b.74.4 8
5.3 odd 4 75.15.d.b.74.5 8
5.4 even 2 75.15.c.d.26.2 4
12.11 even 2 48.15.e.b.17.3 4
15.2 even 4 75.15.d.b.74.6 8
15.8 even 4 75.15.d.b.74.3 8
15.14 odd 2 75.15.c.d.26.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.15.b.a.2.2 4 3.2 odd 2 inner
3.15.b.a.2.3 yes 4 1.1 even 1 trivial
48.15.e.b.17.3 4 12.11 even 2
48.15.e.b.17.4 4 4.3 odd 2
75.15.c.d.26.2 4 5.4 even 2
75.15.c.d.26.3 4 15.14 odd 2
75.15.d.b.74.3 8 15.8 even 4
75.15.d.b.74.4 8 5.2 odd 4
75.15.d.b.74.5 8 5.3 odd 4
75.15.d.b.74.6 8 15.2 even 4