Properties

Label 12.17.d.a.7.9
Level $12$
Weight $17$
Character 12.7
Analytic conductor $19.479$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 7.9
Root \(-66.3279 + 114.883i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.17.d.a.7.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.3734 - 255.747i) q^{2} +3788.00i q^{3} +(-65277.3 - 5817.42i) q^{4} +86591.3 q^{5} +(968769. + 43082.3i) q^{6} -1.07917e7i q^{7} +(-2.23021e6 + 1.66283e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})\) \(q+(11.3734 - 255.747i) q^{2} +3788.00i q^{3} +(-65277.3 - 5817.42i) q^{4} +86591.3 q^{5} +(968769. + 43082.3i) q^{6} -1.07917e7i q^{7} +(-2.23021e6 + 1.66283e7i) q^{8} -1.43489e7 q^{9} +(984836. - 2.21455e7i) q^{10} +3.08747e8i q^{11} +(2.20364e7 - 2.47270e8i) q^{12} -9.27660e8 q^{13} +(-2.75994e9 - 1.22738e8i) q^{14} +3.28007e8i q^{15} +(4.22728e9 + 7.59491e8i) q^{16} +1.04989e9 q^{17} +(-1.63196e8 + 3.66969e9i) q^{18} +2.14400e10i q^{19} +(-5.65245e9 - 5.03738e8i) q^{20} +4.08789e10 q^{21} +(7.89612e10 + 3.51149e9i) q^{22} +8.03506e10i q^{23} +(-6.29880e10 - 8.44803e9i) q^{24} -1.45090e11 q^{25} +(-1.05506e10 + 2.37247e11i) q^{26} -5.43536e10i q^{27} +(-6.27798e10 + 7.04452e11i) q^{28} +6.46948e10 q^{29} +(8.38870e10 + 3.73055e9i) q^{30} +1.00444e12i q^{31} +(2.42316e11 - 1.07248e12i) q^{32} -1.16953e12 q^{33} +(1.19408e10 - 2.68506e11i) q^{34} -9.34466e11i q^{35} +(9.36658e11 + 8.34736e10i) q^{36} +1.20118e12 q^{37} +(5.48323e12 + 2.43846e11i) q^{38} -3.51397e12i q^{39} +(-1.93117e11 + 1.43987e12i) q^{40} -1.21222e13 q^{41} +(4.64931e11 - 1.04547e13i) q^{42} +2.28614e12i q^{43} +(1.79611e12 - 2.01542e13i) q^{44} -1.24249e12 q^{45} +(2.05494e13 + 9.13858e11i) q^{46} -2.13186e13i q^{47} +(-2.87695e12 + 1.60129e13i) q^{48} -8.32276e13 q^{49} +(-1.65016e12 + 3.71063e13i) q^{50} +3.97697e12i q^{51} +(6.05551e13 + 5.39659e12i) q^{52} +1.37605e13 q^{53} +(-1.39008e13 - 6.18184e11i) q^{54} +2.67348e13i q^{55} +(1.79448e14 + 2.40678e13i) q^{56} -8.12148e13 q^{57} +(7.35799e11 - 1.65455e13i) q^{58} +1.78862e14i q^{59} +(1.90816e12 - 2.14114e13i) q^{60} -5.51686e13 q^{61} +(2.56884e14 + 1.14239e13i) q^{62} +1.54849e14i q^{63} +(-2.71527e14 - 7.41694e13i) q^{64} -8.03273e13 q^{65} +(-1.33015e13 + 2.99104e14i) q^{66} -2.57456e14i q^{67} +(-6.85338e13 - 6.10763e12i) q^{68} -3.04368e14 q^{69} +(-2.38987e14 - 1.06280e13i) q^{70} -4.05525e14i q^{71} +(3.20011e13 - 2.38598e14i) q^{72} -2.94670e14 q^{73} +(1.36615e13 - 3.07199e14i) q^{74} -5.49600e14i q^{75} +(1.24726e14 - 1.39955e15i) q^{76} +3.33190e15 q^{77} +(-8.98689e14 - 3.99657e13i) q^{78} -1.81169e14i q^{79} +(3.66046e14 + 6.57653e13i) q^{80} +2.05891e14 q^{81} +(-1.37870e14 + 3.10022e15i) q^{82} -1.39106e15i q^{83} +(-2.66846e15 - 2.37809e14i) q^{84} +9.09111e13 q^{85} +(5.84673e14 + 2.60011e13i) q^{86} +2.45064e14i q^{87} +(-5.13394e15 - 6.88571e14i) q^{88} +3.78150e15 q^{89} +(-1.41313e13 + 3.17764e14i) q^{90} +1.00110e16i q^{91} +(4.67433e14 - 5.24507e15i) q^{92} -3.80483e15 q^{93} +(-5.45219e15 - 2.42465e14i) q^{94} +1.85652e15i q^{95} +(4.06254e15 + 9.17892e14i) q^{96} +8.34786e15 q^{97} +(-9.46579e14 + 2.12852e16i) q^{98} -4.43018e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.3734 255.747i 0.0444273 0.999013i
\(3\) 3788.00i 0.577350i
\(4\) −65277.3 5817.42i −0.996052 0.0887668i
\(5\) 86591.3 0.221674 0.110837 0.993839i \(-0.464647\pi\)
0.110837 + 0.993839i \(0.464647\pi\)
\(6\) 968769. + 43082.3i 0.576780 + 0.0256501i
\(7\) 1.07917e7i 1.87200i −0.352005 0.935998i \(-0.614500\pi\)
0.352005 0.935998i \(-0.385500\pi\)
\(8\) −2.23021e6 + 1.66283e7i −0.132931 + 0.991125i
\(9\) −1.43489e7 −0.333333
\(10\) 984836. 2.21455e7i 0.00984836 0.221455i
\(11\) 3.08747e8i 1.44033i 0.693804 + 0.720163i \(0.255933\pi\)
−0.693804 + 0.720163i \(0.744067\pi\)
\(12\) 2.20364e7 2.47270e8i 0.0512495 0.575071i
\(13\) −9.27660e8 −1.13721 −0.568607 0.822609i \(-0.692517\pi\)
−0.568607 + 0.822609i \(0.692517\pi\)
\(14\) −2.75994e9 1.22738e8i −1.87015 0.0831677i
\(15\) 3.28007e8i 0.127983i
\(16\) 4.22728e9 + 7.59491e8i 0.984241 + 0.176833i
\(17\) 1.04989e9 0.150505 0.0752525 0.997165i \(-0.476024\pi\)
0.0752525 + 0.997165i \(0.476024\pi\)
\(18\) −1.63196e8 + 3.66969e9i −0.0148091 + 0.333004i
\(19\) 2.14400e10i 1.26240i 0.775620 + 0.631200i \(0.217437\pi\)
−0.775620 + 0.631200i \(0.782563\pi\)
\(20\) −5.65245e9 5.03738e8i −0.220799 0.0196773i
\(21\) 4.08789e10 1.08080
\(22\) 7.89612e10 + 3.51149e9i 1.43890 + 0.0639898i
\(23\) 8.03506e10i 1.02605i 0.858375 + 0.513023i \(0.171474\pi\)
−0.858375 + 0.513023i \(0.828526\pi\)
\(24\) −6.29880e10 8.44803e9i −0.572226 0.0767478i
\(25\) −1.45090e11 −0.950861
\(26\) −1.05506e10 + 2.37247e11i −0.0505233 + 1.13609i
\(27\) 5.43536e10i 0.192450i
\(28\) −6.27798e10 + 7.04452e11i −0.166171 + 1.86461i
\(29\) 6.46948e10 0.129326 0.0646630 0.997907i \(-0.479403\pi\)
0.0646630 + 0.997907i \(0.479403\pi\)
\(30\) 8.38870e10 + 3.73055e9i 0.127857 + 0.00568595i
\(31\) 1.00444e12i 1.17769i 0.808245 + 0.588846i \(0.200418\pi\)
−0.808245 + 0.588846i \(0.799582\pi\)
\(32\) 2.42316e11 1.07248e12i 0.220385 0.975413i
\(33\) −1.16953e12 −0.831573
\(34\) 1.19408e10 2.68506e11i 0.00668653 0.150356i
\(35\) 9.34466e11i 0.414972i
\(36\) 9.36658e11 + 8.34736e10i 0.332017 + 0.0295889i
\(37\) 1.20118e12 0.341975 0.170988 0.985273i \(-0.445304\pi\)
0.170988 + 0.985273i \(0.445304\pi\)
\(38\) 5.48323e12 + 2.43846e11i 1.26115 + 0.0560849i
\(39\) 3.51397e12i 0.656571i
\(40\) −1.93117e11 + 1.43987e12i −0.0294673 + 0.219706i
\(41\) −1.21222e13 −1.51814 −0.759068 0.651011i \(-0.774345\pi\)
−0.759068 + 0.651011i \(0.774345\pi\)
\(42\) 4.64931e11 1.04547e13i 0.0480169 1.07973i
\(43\) 2.28614e12i 0.195594i 0.995206 + 0.0977968i \(0.0311795\pi\)
−0.995206 + 0.0977968i \(0.968820\pi\)
\(44\) 1.79611e12 2.01542e13i 0.127853 1.43464i
\(45\) −1.24249e12 −0.0738912
\(46\) 2.05494e13 + 9.13858e11i 1.02503 + 0.0455844i
\(47\) 2.13186e13i 0.895317i −0.894205 0.447658i \(-0.852258\pi\)
0.894205 0.447658i \(-0.147742\pi\)
\(48\) −2.87695e12 + 1.60129e13i −0.102094 + 0.568252i
\(49\) −8.32276e13 −2.50437
\(50\) −1.65016e12 + 3.71063e13i −0.0422441 + 0.949922i
\(51\) 3.97697e12i 0.0868942i
\(52\) 6.05551e13 + 5.39659e12i 1.13272 + 0.100947i
\(53\) 1.37605e13 0.221018 0.110509 0.993875i \(-0.464752\pi\)
0.110509 + 0.993875i \(0.464752\pi\)
\(54\) −1.39008e13 6.18184e11i −0.192260 0.00855003i
\(55\) 2.67348e13i 0.319283i
\(56\) 1.79448e14 + 2.40678e13i 1.85538 + 0.248846i
\(57\) −8.12148e13 −0.728847
\(58\) 7.35799e11 1.65455e13i 0.00574560 0.129198i
\(59\) 1.78862e14i 1.21815i 0.793112 + 0.609076i \(0.208460\pi\)
−0.793112 + 0.609076i \(0.791540\pi\)
\(60\) 1.90816e12 2.14114e13i 0.0113607 0.127478i
\(61\) −5.51686e13 −0.287775 −0.143888 0.989594i \(-0.545960\pi\)
−0.143888 + 0.989594i \(0.545960\pi\)
\(62\) 2.56884e14 + 1.14239e13i 1.17653 + 0.0523216i
\(63\) 1.54849e14i 0.623999i
\(64\) −2.71527e14 7.41694e13i −0.964659 0.263503i
\(65\) −8.03273e13 −0.252090
\(66\) −1.33015e13 + 2.99104e14i −0.0369445 + 0.830752i
\(67\) 2.57456e14i 0.634021i −0.948422 0.317011i \(-0.897321\pi\)
0.948422 0.317011i \(-0.102679\pi\)
\(68\) −6.85338e13 6.10763e12i −0.149911 0.0133599i
\(69\) −3.04368e14 −0.592387
\(70\) −2.38987e14 1.06280e13i −0.414563 0.0184361i
\(71\) 4.05525e14i 0.627987i −0.949425 0.313993i \(-0.898333\pi\)
0.949425 0.313993i \(-0.101667\pi\)
\(72\) 3.20011e13 2.38598e14i 0.0443103 0.330375i
\(73\) −2.94670e14 −0.365387 −0.182693 0.983170i \(-0.558482\pi\)
−0.182693 + 0.983170i \(0.558482\pi\)
\(74\) 1.36615e13 3.07199e14i 0.0151930 0.341638i
\(75\) 5.49600e14i 0.548980i
\(76\) 1.24726e14 1.39955e15i 0.112059 1.25742i
\(77\) 3.33190e15 2.69629
\(78\) −8.98689e14 3.99657e13i −0.655922 0.0291696i
\(79\) 1.81169e14i 0.119417i −0.998216 0.0597085i \(-0.980983\pi\)
0.998216 0.0597085i \(-0.0190171\pi\)
\(80\) 3.66046e14 + 6.57653e13i 0.218180 + 0.0391992i
\(81\) 2.05891e14 0.111111
\(82\) −1.37870e14 + 3.10022e15i −0.0674466 + 1.51664i
\(83\) 1.39106e15i 0.617620i −0.951124 0.308810i \(-0.900069\pi\)
0.951124 0.308810i \(-0.0999308\pi\)
\(84\) −2.66846e15 2.37809e14i −1.07653 0.0959389i
\(85\) 9.09111e13 0.0333630
\(86\) 5.84673e14 + 2.60011e13i 0.195400 + 0.00868969i
\(87\) 2.45064e14i 0.0746664i
\(88\) −5.13394e15 6.88571e14i −1.42754 0.191464i
\(89\) 3.78150e15 0.960604 0.480302 0.877103i \(-0.340527\pi\)
0.480302 + 0.877103i \(0.340527\pi\)
\(90\) −1.41313e13 + 3.17764e14i −0.00328279 + 0.0738183i
\(91\) 1.00110e16i 2.12886i
\(92\) 4.67433e14 5.24507e15i 0.0910787 1.02199i
\(93\) −3.80483e15 −0.679941
\(94\) −5.45219e15 2.42465e14i −0.894433 0.0397765i
\(95\) 1.85652e15i 0.279841i
\(96\) 4.06254e15 + 9.17892e14i 0.563155 + 0.127239i
\(97\) 8.34786e15 1.06513 0.532564 0.846390i \(-0.321229\pi\)
0.532564 + 0.846390i \(0.321229\pi\)
\(98\) −9.46579e14 + 2.12852e16i −0.111262 + 2.50190i
\(99\) 4.43018e15i 0.480109i
\(100\) 9.47107e15 + 8.44048e14i 0.947107 + 0.0844048i
\(101\) −2.02699e15 −0.187189 −0.0935947 0.995610i \(-0.529836\pi\)
−0.0935947 + 0.995610i \(0.529836\pi\)
\(102\) 1.01710e15 + 4.52315e13i 0.0868084 + 0.00386047i
\(103\) 1.04678e16i 0.826342i −0.910654 0.413171i \(-0.864421\pi\)
0.910654 0.413171i \(-0.135579\pi\)
\(104\) 2.06888e15 1.54254e16i 0.151171 1.12712i
\(105\) 3.53975e15 0.239584
\(106\) 1.56504e14 3.51922e15i 0.00981923 0.220800i
\(107\) 8.34371e15i 0.485612i −0.970075 0.242806i \(-0.921932\pi\)
0.970075 0.242806i \(-0.0780678\pi\)
\(108\) −3.16198e14 + 3.54806e15i −0.0170832 + 0.191690i
\(109\) −2.25395e16 −1.13118 −0.565591 0.824686i \(-0.691352\pi\)
−0.565591 + 0.824686i \(0.691352\pi\)
\(110\) 6.83735e15 + 3.04065e14i 0.318967 + 0.0141849i
\(111\) 4.55007e15i 0.197439i
\(112\) 8.19619e15 4.56195e16i 0.331030 1.84250i
\(113\) −3.96494e16 −1.49145 −0.745726 0.666253i \(-0.767897\pi\)
−0.745726 + 0.666253i \(0.767897\pi\)
\(114\) −9.23686e14 + 2.07705e16i −0.0323807 + 0.728127i
\(115\) 6.95766e15i 0.227447i
\(116\) −4.22310e15 3.76357e14i −0.128815 0.0114798i
\(117\) 1.33109e16 0.379071
\(118\) 4.57434e16 + 2.03426e15i 1.21695 + 0.0541191i
\(119\) 1.13301e16i 0.281745i
\(120\) −5.45421e15 7.31526e14i −0.126848 0.0170130i
\(121\) −4.93749e16 −1.07454
\(122\) −6.27453e14 + 1.41092e16i −0.0127851 + 0.287491i
\(123\) 4.59188e16i 0.876496i
\(124\) 5.84327e15 6.55673e16i 0.104540 1.17304i
\(125\) −2.57763e16 −0.432455
\(126\) 3.96022e16 + 1.76116e15i 0.623383 + 0.0277226i
\(127\) 9.50930e16i 1.40514i 0.711616 + 0.702569i \(0.247964\pi\)
−0.711616 + 0.702569i \(0.752036\pi\)
\(128\) −2.20568e16 + 6.85988e16i −0.306100 + 0.952000i
\(129\) −8.65988e15 −0.112926
\(130\) −9.13593e14 + 2.05435e16i −0.0111997 + 0.251841i
\(131\) 1.40724e16i 0.162254i 0.996704 + 0.0811272i \(0.0258520\pi\)
−0.996704 + 0.0811272i \(0.974148\pi\)
\(132\) 7.63439e16 + 6.80366e15i 0.828290 + 0.0738161i
\(133\) 2.31374e17 2.36321
\(134\) −6.58436e16 2.92814e15i −0.633395 0.0281678i
\(135\) 4.70655e15i 0.0426611i
\(136\) −2.34147e15 + 1.74579e16i −0.0200068 + 0.149169i
\(137\) −1.77783e17 −1.43260 −0.716300 0.697793i \(-0.754166\pi\)
−0.716300 + 0.697793i \(0.754166\pi\)
\(138\) −3.46169e15 + 7.78412e16i −0.0263181 + 0.591802i
\(139\) 2.20734e17i 1.58398i 0.610532 + 0.791992i \(0.290956\pi\)
−0.610532 + 0.791992i \(0.709044\pi\)
\(140\) −5.43618e15 + 6.09994e16i −0.0368358 + 0.413334i
\(141\) 8.07549e16 0.516911
\(142\) −1.03712e17 4.61219e15i −0.627367 0.0278997i
\(143\) 2.86412e17i 1.63796i
\(144\) −6.06569e16 1.08979e16i −0.328080 0.0589442i
\(145\) 5.60201e15 0.0286682
\(146\) −3.35139e15 + 7.53610e16i −0.0162331 + 0.365026i
\(147\) 3.15266e17i 1.44590i
\(148\) −7.84098e16 6.98777e15i −0.340625 0.0303560i
\(149\) 3.42196e17 1.40859 0.704296 0.709906i \(-0.251263\pi\)
0.704296 + 0.709906i \(0.251263\pi\)
\(150\) −1.40559e17 6.25080e15i −0.548438 0.0243897i
\(151\) 3.61914e17i 1.33903i 0.742799 + 0.669514i \(0.233498\pi\)
−0.742799 + 0.669514i \(0.766502\pi\)
\(152\) −3.56512e17 4.78158e16i −1.25120 0.167812i
\(153\) −1.50647e16 −0.0501684
\(154\) 3.78950e16 8.52124e17i 0.119789 2.69362i
\(155\) 8.69761e16i 0.261064i
\(156\) −2.04422e16 + 2.29383e17i −0.0582817 + 0.653979i
\(157\) −1.92467e17 −0.521386 −0.260693 0.965422i \(-0.583951\pi\)
−0.260693 + 0.965422i \(0.583951\pi\)
\(158\) −4.63334e16 2.06050e15i −0.119299 0.00530537i
\(159\) 5.21248e16i 0.127605i
\(160\) 2.09825e16 9.28673e16i 0.0488536 0.216223i
\(161\) 8.67119e17 1.92075
\(162\) 2.34168e15 5.26561e16i 0.00493636 0.111001i
\(163\) 3.03025e17i 0.608103i −0.952656 0.304051i \(-0.901661\pi\)
0.952656 0.304051i \(-0.0983395\pi\)
\(164\) 7.91305e17 + 7.05199e16i 1.51214 + 0.134760i
\(165\) −1.01271e17 −0.184338
\(166\) −3.55760e17 1.58211e16i −0.617011 0.0274392i
\(167\) 9.25468e17i 1.52978i −0.644159 0.764891i \(-0.722793\pi\)
0.644159 0.764891i \(-0.277207\pi\)
\(168\) −9.11685e16 + 6.79747e17i −0.143672 + 1.07121i
\(169\) 1.95137e17 0.293255
\(170\) 1.03397e15 2.32503e16i 0.00148223 0.0333301i
\(171\) 3.07641e17i 0.420800i
\(172\) 1.32994e16 1.49233e17i 0.0173622 0.194821i
\(173\) −1.28458e18 −1.60100 −0.800502 0.599330i \(-0.795434\pi\)
−0.800502 + 0.599330i \(0.795434\pi\)
\(174\) 6.26744e16 + 2.78720e15i 0.0745926 + 0.00331722i
\(175\) 1.56576e18i 1.78001i
\(176\) −2.34490e17 + 1.30516e18i −0.254697 + 1.41763i
\(177\) −6.77527e17 −0.703300
\(178\) 4.30084e16 9.67108e17i 0.0426770 0.959655i
\(179\) 1.51930e18i 1.44152i 0.693187 + 0.720758i \(0.256206\pi\)
−0.693187 + 0.720758i \(0.743794\pi\)
\(180\) 8.11064e16 + 7.22809e15i 0.0735996 + 0.00655909i
\(181\) −5.20028e17 −0.451438 −0.225719 0.974192i \(-0.572473\pi\)
−0.225719 + 0.974192i \(0.572473\pi\)
\(182\) 2.56029e18 + 1.13859e17i 2.12676 + 0.0945794i
\(183\) 2.08978e17i 0.166147i
\(184\) −1.33610e18 1.79199e17i −1.01694 0.136393i
\(185\) 1.04012e17 0.0758069
\(186\) −4.32737e16 + 9.73074e17i −0.0302079 + 0.679270i
\(187\) 3.24149e17i 0.216777i
\(188\) −1.24020e17 + 1.39162e18i −0.0794744 + 0.891783i
\(189\) −5.86567e17 −0.360266
\(190\) 4.74800e17 + 2.11149e16i 0.279565 + 0.0124326i
\(191\) 2.42860e18i 1.37116i −0.727996 0.685582i \(-0.759548\pi\)
0.727996 0.685582i \(-0.240452\pi\)
\(192\) 2.80953e17 1.02854e18i 0.152133 0.556946i
\(193\) −2.42269e18 −1.25846 −0.629230 0.777219i \(-0.716630\pi\)
−0.629230 + 0.777219i \(0.716630\pi\)
\(194\) 9.49434e16 2.13494e18i 0.0473207 1.06408i
\(195\) 3.04279e17i 0.145544i
\(196\) 5.43287e18 + 4.84170e17i 2.49448 + 0.222305i
\(197\) 3.03655e18 1.33860 0.669300 0.742992i \(-0.266594\pi\)
0.669300 + 0.742992i \(0.266594\pi\)
\(198\) −1.13301e18 5.03861e16i −0.479635 0.0213299i
\(199\) 2.93148e18i 1.19196i 0.802998 + 0.595981i \(0.203237\pi\)
−0.802998 + 0.595981i \(0.796763\pi\)
\(200\) 3.23581e17 2.41260e18i 0.126399 0.942422i
\(201\) 9.75241e17 0.366052
\(202\) −2.30538e16 + 5.18398e17i −0.00831632 + 0.187005i
\(203\) 6.98166e17i 0.242098i
\(204\) 2.31357e16 2.59606e17i 0.00771331 0.0865511i
\(205\) −1.04968e18 −0.336531
\(206\) −2.67712e18 1.19055e17i −0.825526 0.0367121i
\(207\) 1.15294e18i 0.342015i
\(208\) −3.92148e18 7.04549e17i −1.11929 0.201097i
\(209\) −6.61955e18 −1.81827
\(210\) 4.02590e16 9.05282e17i 0.0106441 0.239348i
\(211\) 4.81806e18i 1.22634i −0.789950 0.613172i \(-0.789893\pi\)
0.789950 0.613172i \(-0.210107\pi\)
\(212\) −8.98250e17 8.00508e16i −0.220146 0.0196191i
\(213\) 1.53613e18 0.362568
\(214\) −2.13388e18 9.48962e16i −0.485132 0.0215744i
\(215\) 1.97960e17i 0.0433580i
\(216\) 9.03809e17 + 1.21220e17i 0.190742 + 0.0255826i
\(217\) 1.08396e19 2.20464
\(218\) −2.56350e17 + 5.76442e18i −0.0502553 + 1.13006i
\(219\) 1.11621e18i 0.210956i
\(220\) 1.55528e17 1.74517e18i 0.0283417 0.318022i
\(221\) −9.73938e17 −0.171156
\(222\) 1.16367e18 + 5.17496e16i 0.197245 + 0.00877169i
\(223\) 4.28116e18i 0.700039i −0.936742 0.350020i \(-0.886175\pi\)
0.936742 0.350020i \(-0.113825\pi\)
\(224\) −1.15738e19 2.61500e18i −1.82597 0.412560i
\(225\) 2.08188e18 0.316954
\(226\) −4.50948e17 + 1.01402e19i −0.0662611 + 1.48998i
\(227\) 7.61610e18i 1.08025i 0.841583 + 0.540127i \(0.181624\pi\)
−0.841583 + 0.540127i \(0.818376\pi\)
\(228\) 5.30148e18 + 4.72460e17i 0.725970 + 0.0646974i
\(229\) 5.72737e18 0.757307 0.378653 0.925539i \(-0.376387\pi\)
0.378653 + 0.925539i \(0.376387\pi\)
\(230\) 1.77940e18 + 7.91321e16i 0.227223 + 0.0101049i
\(231\) 1.26212e19i 1.55670i
\(232\) −1.44283e17 + 1.07577e18i −0.0171914 + 0.128178i
\(233\) 9.31720e18 1.07260 0.536300 0.844027i \(-0.319822\pi\)
0.536300 + 0.844027i \(0.319822\pi\)
\(234\) 1.51390e17 3.40423e18i 0.0168411 0.378697i
\(235\) 1.84601e18i 0.198468i
\(236\) 1.04051e18 1.16756e19i 0.108131 1.21334i
\(237\) 6.86266e17 0.0689454
\(238\) −2.89763e18 1.28861e17i −0.281467 0.0125172i
\(239\) 1.10615e19i 1.03903i 0.854460 + 0.519517i \(0.173888\pi\)
−0.854460 + 0.519517i \(0.826112\pi\)
\(240\) −2.49119e17 + 1.38658e18i −0.0226317 + 0.125966i
\(241\) −3.38785e18 −0.297707 −0.148853 0.988859i \(-0.547558\pi\)
−0.148853 + 0.988859i \(0.547558\pi\)
\(242\) −5.61559e17 + 1.26275e19i −0.0477389 + 1.07348i
\(243\) 7.79915e17i 0.0641500i
\(244\) 3.60126e18 + 3.20939e17i 0.286639 + 0.0255449i
\(245\) −7.20679e18 −0.555153
\(246\) −1.17436e19 5.22252e17i −0.875631 0.0389403i
\(247\) 1.98891e19i 1.43562i
\(248\) −1.67022e19 2.24012e18i −1.16724 0.156552i
\(249\) 5.26934e18 0.356583
\(250\) −2.93164e17 + 6.59222e18i −0.0192128 + 0.432028i
\(251\) 8.87067e18i 0.563076i −0.959550 0.281538i \(-0.909156\pi\)
0.959550 0.281538i \(-0.0908445\pi\)
\(252\) 9.00821e17 1.01081e19i 0.0553904 0.621536i
\(253\) −2.48080e19 −1.47784
\(254\) 2.43198e19 + 1.08153e18i 1.40375 + 0.0624264i
\(255\) 3.44371e17i 0.0192622i
\(256\) 1.72931e19 + 6.42116e18i 0.937460 + 0.348092i
\(257\) −2.60354e18 −0.136804 −0.0684021 0.997658i \(-0.521790\pi\)
−0.0684021 + 0.997658i \(0.521790\pi\)
\(258\) −9.84920e16 + 2.21474e18i −0.00501699 + 0.112815i
\(259\) 1.29628e19i 0.640176i
\(260\) 5.24355e18 + 4.67298e17i 0.251095 + 0.0223773i
\(261\) −9.28300e17 −0.0431086
\(262\) 3.59897e18 + 1.60050e17i 0.162094 + 0.00720852i
\(263\) 1.18064e19i 0.515788i 0.966173 + 0.257894i \(0.0830285\pi\)
−0.966173 + 0.257894i \(0.916971\pi\)
\(264\) 2.60830e18 1.94473e19i 0.110542 0.824193i
\(265\) 1.19154e18 0.0489939
\(266\) 2.63151e18 5.91733e19i 0.104991 2.36087i
\(267\) 1.43243e19i 0.554605i
\(268\) −1.49773e18 + 1.68060e19i −0.0562800 + 0.631519i
\(269\) −1.50417e19 −0.548628 −0.274314 0.961640i \(-0.588451\pi\)
−0.274314 + 0.961640i \(0.588451\pi\)
\(270\) −1.20369e18 5.35293e16i −0.0426190 0.00189532i
\(271\) 1.48927e19i 0.511941i −0.966685 0.255970i \(-0.917605\pi\)
0.966685 0.255970i \(-0.0823950\pi\)
\(272\) 4.43817e18 + 7.97380e17i 0.148133 + 0.0266142i
\(273\) −3.79217e19 −1.22910
\(274\) −2.02199e18 + 4.54674e19i −0.0636465 + 1.43118i
\(275\) 4.47960e19i 1.36955i
\(276\) 1.98683e19 + 1.77063e18i 0.590049 + 0.0525843i
\(277\) 5.25867e18 0.151718 0.0758592 0.997119i \(-0.475830\pi\)
0.0758592 + 0.997119i \(0.475830\pi\)
\(278\) 5.64521e19 + 2.51049e18i 1.58242 + 0.0703720i
\(279\) 1.44127e19i 0.392564i
\(280\) 1.55386e19 + 2.08406e18i 0.411290 + 0.0551627i
\(281\) 2.72271e19 0.700409 0.350204 0.936673i \(-0.386112\pi\)
0.350204 + 0.936673i \(0.386112\pi\)
\(282\) 9.18456e17 2.06529e19i 0.0229650 0.516401i
\(283\) 2.29628e19i 0.558128i 0.960273 + 0.279064i \(0.0900241\pi\)
−0.960273 + 0.279064i \(0.909976\pi\)
\(284\) −2.35911e18 + 2.64716e19i −0.0557444 + 0.625508i
\(285\) −7.03249e18 −0.161566
\(286\) −7.32491e19 3.25747e18i −1.63634 0.0727700i
\(287\) 1.30819e20i 2.84195i
\(288\) −3.47697e18 + 1.53889e19i −0.0734618 + 0.325138i
\(289\) −4.75589e19 −0.977348
\(290\) 6.37138e16 1.43270e18i 0.00127365 0.0286399i
\(291\) 3.16217e19i 0.614951i
\(292\) 1.92353e19 + 1.71422e18i 0.363945 + 0.0324342i
\(293\) 4.58027e19 0.843239 0.421619 0.906773i \(-0.361462\pi\)
0.421619 + 0.906773i \(0.361462\pi\)
\(294\) −8.06283e19 3.58564e18i −1.44447 0.0642373i
\(295\) 1.54879e19i 0.270032i
\(296\) −2.67889e18 + 1.99736e19i −0.0454591 + 0.338940i
\(297\) 1.67815e19 0.277191
\(298\) 3.89193e18 8.75158e19i 0.0625799 1.40720i
\(299\) 7.45380e19i 1.16683i
\(300\) −3.19725e18 + 3.58764e19i −0.0487312 + 0.546813i
\(301\) 2.46713e19 0.366150
\(302\) 9.25585e19 + 4.11619e18i 1.33771 + 0.0594894i
\(303\) 7.67824e18i 0.108074i
\(304\) −1.62835e19 + 9.06331e19i −0.223234 + 1.24251i
\(305\) −4.77712e18 −0.0637922
\(306\) −1.71337e17 + 3.85276e18i −0.00222884 + 0.0501188i
\(307\) 7.08212e19i 0.897545i −0.893646 0.448773i \(-0.851861\pi\)
0.893646 0.448773i \(-0.148139\pi\)
\(308\) −2.17497e20 1.93831e19i −2.68564 0.239341i
\(309\) 3.96522e19 0.477089
\(310\) 2.22439e19 + 9.89212e17i 0.260806 + 0.0115983i
\(311\) 6.64720e19i 0.759549i −0.925079 0.379774i \(-0.876002\pi\)
0.925079 0.379774i \(-0.123998\pi\)
\(312\) 5.84315e19 + 7.83690e18i 0.650744 + 0.0872786i
\(313\) 2.79684e19 0.303608 0.151804 0.988411i \(-0.451492\pi\)
0.151804 + 0.988411i \(0.451492\pi\)
\(314\) −2.18900e18 + 4.92229e19i −0.0231638 + 0.520871i
\(315\) 1.34086e19i 0.138324i
\(316\) −1.05393e18 + 1.18262e19i −0.0106003 + 0.118946i
\(317\) 1.53397e20 1.50433 0.752165 0.658975i \(-0.229010\pi\)
0.752165 + 0.658975i \(0.229010\pi\)
\(318\) 1.33308e19 + 5.92835e17i 0.127479 + 0.00566914i
\(319\) 1.99743e19i 0.186272i
\(320\) −2.35119e19 6.42242e18i −0.213840 0.0584116i
\(321\) 3.16060e19 0.280368
\(322\) 9.86207e18 2.21763e20i 0.0853338 1.91886i
\(323\) 2.25096e19i 0.189998i
\(324\) −1.34400e19 1.19776e18i −0.110672 0.00986298i
\(325\) 1.34594e20 1.08133
\(326\) −7.74977e19 3.44641e18i −0.607502 0.0270163i
\(327\) 8.53795e19i 0.653088i
\(328\) 2.70351e19 2.01572e20i 0.201807 1.50466i
\(329\) −2.30064e20 −1.67603
\(330\) −1.15180e18 + 2.58998e19i −0.00818963 + 0.184156i
\(331\) 2.20271e19i 0.152874i 0.997074 + 0.0764371i \(0.0243544\pi\)
−0.997074 + 0.0764371i \(0.975646\pi\)
\(332\) −8.09239e18 + 9.08047e19i −0.0548242 + 0.615182i
\(333\) −1.72356e19 −0.113992
\(334\) −2.36686e20 1.05257e19i −1.52827 0.0679641i
\(335\) 2.22934e19i 0.140546i
\(336\) 1.72806e20 + 3.10471e19i 1.06377 + 0.191120i
\(337\) 1.11783e20 0.671948 0.335974 0.941871i \(-0.390935\pi\)
0.335974 + 0.941871i \(0.390935\pi\)
\(338\) 2.21936e18 4.99057e19i 0.0130285 0.292965i
\(339\) 1.50192e20i 0.861090i
\(340\) −5.93443e18 5.28868e17i −0.0332313 0.00296153i
\(341\) −3.10119e20 −1.69626
\(342\) −7.86784e19 3.49892e18i −0.420384 0.0186950i
\(343\) 5.39527e20i 2.81618i
\(344\) −3.80146e19 5.09857e18i −0.193858 0.0260005i
\(345\) −2.63556e19 −0.131317
\(346\) −1.46100e19 + 3.28528e20i −0.0711282 + 1.59942i
\(347\) 2.52380e20i 1.20066i −0.799754 0.600328i \(-0.795037\pi\)
0.799754 0.600328i \(-0.204963\pi\)
\(348\) 1.42564e18 1.59971e19i 0.00662789 0.0743716i
\(349\) −1.31132e20 −0.595805 −0.297903 0.954596i \(-0.596287\pi\)
−0.297903 + 0.954596i \(0.596287\pi\)
\(350\) 4.00440e20 + 1.78080e19i 1.77825 + 0.0790809i
\(351\) 5.04217e19i 0.218857i
\(352\) 3.31124e20 + 7.48143e19i 1.40491 + 0.317427i
\(353\) 1.27633e20 0.529379 0.264690 0.964334i \(-0.414731\pi\)
0.264690 + 0.964334i \(0.414731\pi\)
\(354\) −7.70578e18 + 1.73276e20i −0.0312457 + 0.702606i
\(355\) 3.51149e19i 0.139208i
\(356\) −2.46846e20 2.19986e19i −0.956811 0.0852697i
\(357\) 4.29182e19 0.162666
\(358\) 3.88557e20 + 1.72796e19i 1.44009 + 0.0640426i
\(359\) 2.34814e20i 0.851075i 0.904941 + 0.425537i \(0.139915\pi\)
−0.904941 + 0.425537i \(0.860085\pi\)
\(360\) 2.77102e18 2.06605e19i 0.00982244 0.0732355i
\(361\) −1.71234e20 −0.593653
\(362\) −5.91448e18 + 1.32996e20i −0.0200562 + 0.450992i
\(363\) 1.87032e20i 0.620387i
\(364\) 5.82383e19 6.53492e20i 0.188972 2.12046i
\(365\) −2.55159e19 −0.0809967
\(366\) −5.34456e19 2.37679e18i −0.165983 0.00738145i
\(367\) 3.65051e20i 1.10924i 0.832104 + 0.554619i \(0.187136\pi\)
−0.832104 + 0.554619i \(0.812864\pi\)
\(368\) −6.10255e19 + 3.39665e20i −0.181438 + 1.00988i
\(369\) 1.73940e20 0.506045
\(370\) 1.18297e18 2.66007e19i 0.00336789 0.0757321i
\(371\) 1.48499e20i 0.413745i
\(372\) 2.48369e20 + 2.21343e19i 0.677257 + 0.0603562i
\(373\) −4.99356e20 −1.33272 −0.666362 0.745629i \(-0.732149\pi\)
−0.666362 + 0.745629i \(0.732149\pi\)
\(374\) 8.29003e19 + 3.68667e18i 0.216562 + 0.00963079i
\(375\) 9.76405e19i 0.249678i
\(376\) 3.54493e20 + 4.75451e19i 0.887371 + 0.119015i
\(377\) −6.00148e19 −0.147071
\(378\) −6.67125e18 + 1.50013e20i −0.0160056 + 0.359910i
\(379\) 2.81240e20i 0.660639i −0.943869 0.330319i \(-0.892844\pi\)
0.943869 0.330319i \(-0.107156\pi\)
\(380\) 1.08002e19 1.21189e20i 0.0248406 0.278736i
\(381\) −3.60212e20 −0.811256
\(382\) −6.21108e20 2.76214e19i −1.36981 0.0609170i
\(383\) 2.75719e20i 0.595492i −0.954645 0.297746i \(-0.903765\pi\)
0.954645 0.297746i \(-0.0962348\pi\)
\(384\) −2.59852e20 8.35510e19i −0.549637 0.176727i
\(385\) 2.88514e20 0.597696
\(386\) −2.75542e19 + 6.19597e20i −0.0559099 + 1.25722i
\(387\) 3.28036e19i 0.0651979i
\(388\) −5.44926e20 4.85630e19i −1.06092 0.0945479i
\(389\) −2.91955e20 −0.556826 −0.278413 0.960461i \(-0.589808\pi\)
−0.278413 + 0.960461i \(0.589808\pi\)
\(390\) −7.78186e19 3.46068e18i −0.145401 0.00646614i
\(391\) 8.43590e19i 0.154425i
\(392\) 1.85615e20 1.38394e21i 0.332909 2.48215i
\(393\) −5.33060e19 −0.0936776
\(394\) 3.45358e19 7.76589e20i 0.0594703 1.33728i
\(395\) 1.56876e19i 0.0264716i
\(396\) −2.57722e19 + 2.89190e20i −0.0426177 + 0.478214i
\(397\) 6.92196e20 1.12177 0.560886 0.827893i \(-0.310460\pi\)
0.560886 + 0.827893i \(0.310460\pi\)
\(398\) 7.49719e20 + 3.33409e19i 1.19079 + 0.0529556i
\(399\) 8.76445e20i 1.36440i
\(400\) −6.13336e20 1.10194e20i −0.935876 0.168143i
\(401\) 1.00851e21 1.50844 0.754219 0.656623i \(-0.228016\pi\)
0.754219 + 0.656623i \(0.228016\pi\)
\(402\) 1.10918e19 2.49415e20i 0.0162627 0.365691i
\(403\) 9.31782e20i 1.33929i
\(404\) 1.32317e20 + 1.17919e19i 0.186451 + 0.0166162i
\(405\) 1.78284e19 0.0246304
\(406\) −1.78554e20 7.94051e18i −0.241859 0.0107557i
\(407\) 3.70861e20i 0.492556i
\(408\) −6.61303e19 8.86948e18i −0.0861230 0.0115509i
\(409\) −1.90540e20 −0.243333 −0.121666 0.992571i \(-0.538824\pi\)
−0.121666 + 0.992571i \(0.538824\pi\)
\(410\) −1.19384e19 + 2.68452e20i −0.0149511 + 0.336199i
\(411\) 6.73440e20i 0.827112i
\(412\) −6.08959e19 + 6.83313e20i −0.0733517 + 0.823080i
\(413\) 1.93022e21 2.28038
\(414\) −2.94862e20 1.31129e19i −0.341677 0.0151948i
\(415\) 1.20454e20i 0.136910i
\(416\) −2.24787e20 + 9.94895e20i −0.250625 + 1.10925i
\(417\) −8.36139e20 −0.914513
\(418\) −7.52866e19 + 1.69293e21i −0.0807807 + 1.81647i
\(419\) 6.02298e19i 0.0634015i −0.999497 0.0317007i \(-0.989908\pi\)
0.999497 0.0317007i \(-0.0100923\pi\)
\(420\) −2.31066e20 2.05922e19i −0.238639 0.0212671i
\(421\) 3.25175e20 0.329504 0.164752 0.986335i \(-0.447318\pi\)
0.164752 + 0.986335i \(0.447318\pi\)
\(422\) −1.23220e21 5.47976e19i −1.22513 0.0544831i
\(423\) 3.05899e20i 0.298439i
\(424\) −3.06889e19 + 2.28814e20i −0.0293802 + 0.219057i
\(425\) −1.52328e20 −0.143109
\(426\) 1.74709e19 3.92860e20i 0.0161079 0.362210i
\(427\) 5.95362e20i 0.538714i
\(428\) −4.85389e19 + 5.44655e20i −0.0431062 + 0.483695i
\(429\) 1.08493e21 0.945676
\(430\) 5.06276e19 + 2.25147e18i 0.0433151 + 0.00192628i
\(431\) 1.23048e21i 1.03337i 0.856174 + 0.516687i \(0.172835\pi\)
−0.856174 + 0.516687i \(0.827165\pi\)
\(432\) 4.12811e19 2.29768e20i 0.0340315 0.189417i
\(433\) −1.61953e21 −1.31065 −0.655324 0.755348i \(-0.727468\pi\)
−0.655324 + 0.755348i \(0.727468\pi\)
\(434\) 1.23283e20 2.77221e21i 0.0979459 2.20246i
\(435\) 2.12204e19i 0.0165516i
\(436\) 1.47132e21 + 1.31122e20i 1.12672 + 0.100411i
\(437\) −1.72272e21 −1.29528
\(438\) −2.85467e20 1.26951e19i −0.210748 0.00937221i
\(439\) 7.38096e20i 0.535053i 0.963551 + 0.267526i \(0.0862063\pi\)
−0.963551 + 0.267526i \(0.913794\pi\)
\(440\) −4.44555e20 5.96243e19i −0.316449 0.0424426i
\(441\) 1.19422e21 0.834790
\(442\) −1.10770e19 + 2.49082e20i −0.00760401 + 0.170987i
\(443\) 5.24293e20i 0.353463i −0.984259 0.176732i \(-0.943448\pi\)
0.984259 0.176732i \(-0.0565525\pi\)
\(444\) 2.64696e19 2.97016e20i 0.0175261 0.196660i
\(445\) 3.27445e20 0.212941
\(446\) −1.09489e21 4.86912e19i −0.699348 0.0311008i
\(447\) 1.29624e21i 0.813251i
\(448\) −8.00413e20 + 2.93024e21i −0.493276 + 1.80584i
\(449\) −3.38302e20 −0.204802 −0.102401 0.994743i \(-0.532652\pi\)
−0.102401 + 0.994743i \(0.532652\pi\)
\(450\) 2.36780e19 5.32435e20i 0.0140814 0.316641i
\(451\) 3.74269e21i 2.18661i
\(452\) 2.58821e21 + 2.30657e20i 1.48556 + 0.132391i
\(453\) −1.37093e21 −0.773089
\(454\) 1.94780e21 + 8.66208e19i 1.07919 + 0.0479927i
\(455\) 8.66867e20i 0.471912i
\(456\) 1.81126e20 1.35047e21i 0.0968863 0.722378i
\(457\) 2.94882e21 1.54995 0.774976 0.631991i \(-0.217762\pi\)
0.774976 + 0.631991i \(0.217762\pi\)
\(458\) 6.51396e19 1.46476e21i 0.0336451 0.756559i
\(459\) 5.70651e19i 0.0289647i
\(460\) 4.04756e19 4.54177e20i 0.0201898 0.226549i
\(461\) −3.14872e21 −1.54357 −0.771785 0.635883i \(-0.780636\pi\)
−0.771785 + 0.635883i \(0.780636\pi\)
\(462\) 3.22784e21 + 1.43546e20i 1.55516 + 0.0691600i
\(463\) 7.56882e20i 0.358410i −0.983812 0.179205i \(-0.942647\pi\)
0.983812 0.179205i \(-0.0573526\pi\)
\(464\) 2.73483e20 + 4.91351e19i 0.127288 + 0.0228691i
\(465\) −3.29465e20 −0.150725
\(466\) 1.05968e20 2.38285e21i 0.0476527 1.07154i
\(467\) 3.65068e20i 0.161376i −0.996739 0.0806880i \(-0.974288\pi\)
0.996739 0.0806880i \(-0.0257117\pi\)
\(468\) −8.68900e20 7.74351e19i −0.377575 0.0336489i
\(469\) −2.77838e21 −1.18689
\(470\) −4.72112e20 2.09954e19i −0.198272 0.00881740i
\(471\) 7.29065e20i 0.301022i
\(472\) −2.97417e21 3.98900e20i −1.20734 0.161930i
\(473\) −7.05838e20 −0.281719
\(474\) 7.80516e18 1.75511e20i 0.00306306 0.0688774i
\(475\) 3.11073e21i 1.20037i
\(476\) −6.59117e19 + 7.39595e20i −0.0250096 + 0.280633i
\(477\) −1.97449e20 −0.0736727
\(478\) 2.82894e21 + 1.25806e20i 1.03801 + 0.0461614i
\(479\) 1.16860e21i 0.421678i 0.977521 + 0.210839i \(0.0676196\pi\)
−0.977521 + 0.210839i \(0.932380\pi\)
\(480\) 3.51781e20 + 7.94815e19i 0.124837 + 0.0282057i
\(481\) −1.11429e21 −0.388899
\(482\) −3.85313e19 + 8.66434e20i −0.0132263 + 0.297413i
\(483\) 3.28464e21i 1.10895i
\(484\) 3.22306e21 + 2.87234e20i 1.07030 + 0.0953836i
\(485\) 7.22852e20 0.236111
\(486\) 1.99461e20 + 8.87026e18i 0.0640867 + 0.00285001i
\(487\) 1.89144e21i 0.597808i 0.954283 + 0.298904i \(0.0966210\pi\)
−0.954283 + 0.298904i \(0.903379\pi\)
\(488\) 1.23038e20 9.17361e20i 0.0382542 0.285221i
\(489\) 1.14786e21 0.351088
\(490\) −8.19655e19 + 1.84312e21i −0.0246639 + 0.554605i
\(491\) 1.22609e21i 0.362969i −0.983394 0.181484i \(-0.941910\pi\)
0.983394 0.181484i \(-0.0580902\pi\)
\(492\) −2.67129e20 + 2.99746e21i −0.0778037 + 0.873036i
\(493\) 6.79223e19 0.0194642
\(494\) −5.08658e21 2.26206e20i −1.43420 0.0637806i
\(495\) 3.83615e20i 0.106428i
\(496\) −7.62866e20 + 4.24607e21i −0.208255 + 1.15913i
\(497\) −4.37630e21 −1.17559
\(498\) 5.99301e19 1.34762e21i 0.0158420 0.356231i
\(499\) 2.70150e21i 0.702750i −0.936235 0.351375i \(-0.885714\pi\)
0.936235 0.351375i \(-0.114286\pi\)
\(500\) 1.68261e21 + 1.49952e20i 0.430747 + 0.0383876i
\(501\) 3.50567e21 0.883221
\(502\) −2.26865e21 1.00889e20i −0.562520 0.0250159i
\(503\) 5.65754e21i 1.38065i 0.723499 + 0.690325i \(0.242532\pi\)
−0.723499 + 0.690325i \(0.757468\pi\)
\(504\) −2.57488e21 3.45346e20i −0.618461 0.0829488i
\(505\) −1.75520e20 −0.0414950
\(506\) −2.82151e20 + 6.34458e21i −0.0656564 + 1.47638i
\(507\) 7.39177e20i 0.169311i
\(508\) 5.53196e20 6.20741e21i 0.124730 1.39959i
\(509\) 7.61503e21 1.69017 0.845083 0.534635i \(-0.179551\pi\)
0.845083 + 0.534635i \(0.179551\pi\)
\(510\) 8.80719e19 + 3.91666e18i 0.0192431 + 0.000855765i
\(511\) 3.17999e21i 0.684003i
\(512\) 1.83888e21 4.34963e21i 0.389397 0.921070i
\(513\) 1.16534e21 0.242949
\(514\) −2.96110e19 + 6.65848e20i −0.00607783 + 0.136669i
\(515\) 9.06425e20i 0.183178i
\(516\) 5.65293e20 + 5.03781e19i 0.112480 + 0.0100241i
\(517\) 6.58207e21 1.28955
\(518\) −3.31519e21 1.47430e20i −0.639544 0.0284413i
\(519\) 4.86598e21i 0.924340i
\(520\) 1.79147e20 1.33571e21i 0.0335106 0.249853i
\(521\) 2.49450e21 0.459495 0.229748 0.973250i \(-0.426210\pi\)
0.229748 + 0.973250i \(0.426210\pi\)
\(522\) −1.05579e19 + 2.37410e20i −0.00191520 + 0.0430661i
\(523\) 9.64800e21i 1.72355i 0.507291 + 0.861775i \(0.330647\pi\)
−0.507291 + 0.861775i \(0.669353\pi\)
\(524\) 8.18648e19 9.18605e20i 0.0144028 0.161614i
\(525\) −5.93111e21 −1.02769
\(526\) 3.01945e21 + 1.34279e20i 0.515279 + 0.0229150i
\(527\) 1.05455e21i 0.177249i
\(528\) −4.94394e21 8.88248e20i −0.818468 0.147049i
\(529\) −3.23608e20 −0.0527684
\(530\) 1.35519e19 3.04734e20i 0.00217667 0.0489456i
\(531\) 2.56647e21i 0.406051i
\(532\) −1.51035e22 1.34600e21i −2.35388 0.209774i
\(533\) 1.12453e22 1.72644
\(534\) 3.66340e21 + 1.62916e20i 0.554057 + 0.0246396i
\(535\) 7.22493e20i 0.107647i
\(536\) 4.28106e21 + 5.74181e20i 0.628395 + 0.0842811i
\(537\) −5.75510e21 −0.832259
\(538\) −1.71075e20 + 3.84687e21i −0.0243740 + 0.548086i
\(539\) 2.56963e22i 3.60711i
\(540\) −2.73800e19 + 3.07231e20i −0.00378689 + 0.0424927i
\(541\) −1.85308e20 −0.0252532 −0.0126266 0.999920i \(-0.504019\pi\)
−0.0126266 + 0.999920i \(0.504019\pi\)
\(542\) −3.80877e21 1.69381e20i −0.511435 0.0227441i
\(543\) 1.96986e21i 0.260638i
\(544\) 2.54405e20 1.12598e21i 0.0331691 0.146805i
\(545\) −1.95173e21 −0.250753
\(546\) −4.31298e20 + 9.69837e21i −0.0546054 + 1.22788i
\(547\) 3.32896e21i 0.415346i 0.978198 + 0.207673i \(0.0665890\pi\)
−0.978198 + 0.207673i \(0.933411\pi\)
\(548\) 1.16052e22 + 1.03424e21i 1.42694 + 0.127167i
\(549\) 7.91609e20 0.0959250
\(550\) −1.14565e22 5.09482e20i −1.36820 0.0608454i
\(551\) 1.38706e21i 0.163261i
\(552\) 6.78804e20 5.06112e21i 0.0787466 0.587130i
\(553\) −1.95511e21 −0.223548
\(554\) 5.98089e19 1.34489e21i 0.00674043 0.151569i
\(555\) 3.93996e20i 0.0437671i
\(556\) 1.28410e21 1.44089e22i 0.140605 1.57773i
\(557\) −1.43792e22 −1.55201 −0.776003 0.630730i \(-0.782756\pi\)
−0.776003 + 0.630730i \(0.782756\pi\)
\(558\) −3.68600e21 1.63921e20i −0.392177 0.0174405i
\(559\) 2.12076e21i 0.222432i
\(560\) 7.09719e20 3.95025e21i 0.0733807 0.408433i
\(561\) −1.22788e21 −0.125156
\(562\) 3.09665e20 6.96327e21i 0.0311172 0.699717i
\(563\) 1.86531e22i 1.84793i 0.382483 + 0.923963i \(0.375069\pi\)
−0.382483 + 0.923963i \(0.624931\pi\)
\(564\) −5.27146e21 4.69785e20i −0.514871 0.0458846i
\(565\) −3.43329e21 −0.330616
\(566\) 5.87268e21 + 2.61165e20i 0.557577 + 0.0247961i
\(567\) 2.22191e21i 0.208000i
\(568\) 6.74320e21 + 9.04406e20i 0.622414 + 0.0834789i
\(569\) 1.93429e22 1.76045 0.880224 0.474558i \(-0.157392\pi\)
0.880224 + 0.474558i \(0.157392\pi\)
\(570\) −7.99832e19 + 1.79854e21i −0.00717794 + 0.161407i
\(571\) 1.79385e22i 1.58744i 0.608281 + 0.793721i \(0.291859\pi\)
−0.608281 + 0.793721i \(0.708141\pi\)
\(572\) −1.66618e21 + 1.86962e22i −0.145396 + 1.63149i
\(573\) 9.19953e21 0.791642
\(574\) 3.34566e22 + 1.48785e21i 2.83914 + 0.126260i
\(575\) 1.16581e22i 0.975626i
\(576\) 3.89612e21 + 1.06425e21i 0.321553 + 0.0878342i
\(577\) −9.13899e21 −0.743861 −0.371930 0.928261i \(-0.621304\pi\)
−0.371930 + 0.928261i \(0.621304\pi\)
\(578\) −5.40906e20 + 1.21631e22i −0.0434209 + 0.976383i
\(579\) 9.17714e21i 0.726572i
\(580\) −3.65684e20 3.25892e19i −0.0285550 0.00254478i
\(581\) −1.50119e22 −1.15618
\(582\) 8.08715e21 + 3.59645e20i 0.614344 + 0.0273206i
\(583\) 4.24852e21i 0.318339i
\(584\) 6.57177e20 4.89987e21i 0.0485712 0.362144i
\(585\) 1.15261e21 0.0840301
\(586\) 5.20932e20 1.17139e22i 0.0374628 0.842406i
\(587\) 6.18065e21i 0.438459i 0.975673 + 0.219230i \(0.0703544\pi\)
−0.975673 + 0.219230i \(0.929646\pi\)
\(588\) −1.83403e21 + 2.05797e22i −0.128348 + 1.44019i
\(589\) −2.15353e22 −1.48672
\(590\) 3.96098e21 + 1.76149e20i 0.269766 + 0.0119968i
\(591\) 1.15024e22i 0.772841i
\(592\) 5.07773e21 + 9.12286e20i 0.336586 + 0.0604724i
\(593\) −1.54453e22 −1.01009 −0.505045 0.863093i \(-0.668524\pi\)
−0.505045 + 0.863093i \(0.668524\pi\)
\(594\) 1.90862e20 4.29182e21i 0.0123148 0.276917i
\(595\) 9.81084e20i 0.0624555i
\(596\) −2.23377e22 1.99070e21i −1.40303 0.125036i
\(597\) −1.11044e22 −0.688180
\(598\) −1.90629e22 8.47749e20i −1.16568 0.0518392i
\(599\) 2.88339e21i 0.173976i −0.996209 0.0869880i \(-0.972276\pi\)
0.996209 0.0869880i \(-0.0277242\pi\)
\(600\) 9.13892e21 + 1.22572e21i 0.544108 + 0.0729764i
\(601\) 3.09120e22 1.81607 0.908033 0.418899i \(-0.137584\pi\)
0.908033 + 0.418899i \(0.137584\pi\)
\(602\) 2.80596e20 6.30961e21i 0.0162671 0.365789i
\(603\) 3.69421e21i 0.211340i
\(604\) 2.10541e21 2.36248e22i 0.118861 1.33374i
\(605\) −4.27544e21 −0.238198
\(606\) −1.96369e21 8.73276e19i −0.107967 0.00480143i
\(607\) 5.21560e21i 0.283005i −0.989938 0.141503i \(-0.954807\pi\)
0.989938 0.141503i \(-0.0451934\pi\)
\(608\) 2.29940e22 + 5.19527e21i 1.23136 + 0.278214i
\(609\) 2.64465e21 0.139775
\(610\) −5.43320e19 + 1.22174e21i −0.00283411 + 0.0637292i
\(611\) 1.97765e22i 1.01817i
\(612\) 9.83385e20 + 8.76379e19i 0.0499703 + 0.00445328i
\(613\) −1.12100e22 −0.562239 −0.281119 0.959673i \(-0.590706\pi\)
−0.281119 + 0.959673i \(0.590706\pi\)
\(614\) −1.81123e22 8.05476e20i −0.896659 0.0398755i
\(615\) 3.97617e21i 0.194296i
\(616\) −7.43084e21 + 5.54039e22i −0.358420 + 2.67236i
\(617\) −7.59471e21 −0.361601 −0.180801 0.983520i \(-0.557869\pi\)
−0.180801 + 0.983520i \(0.557869\pi\)
\(618\) 4.50979e20 1.01409e22i 0.0211957 0.476617i
\(619\) 1.37221e22i 0.636642i −0.947983 0.318321i \(-0.896881\pi\)
0.947983 0.318321i \(-0.103119\pi\)
\(620\) 5.05976e20 5.67756e21i 0.0231738 0.260033i
\(621\) 4.36734e21 0.197462
\(622\) −1.70000e22 7.56011e20i −0.758799 0.0337447i
\(623\) 4.08088e22i 1.79825i
\(624\) 2.66883e21 1.48546e22i 0.116103 0.646224i
\(625\) 1.99069e22 0.854997
\(626\) 3.18096e20 7.15285e21i 0.0134885 0.303308i
\(627\) 2.50748e22i 1.04978i
\(628\) 1.25637e22 + 1.11966e21i 0.519328 + 0.0462818i
\(629\) 1.26110e21 0.0514690
\(630\) 3.42920e21 + 1.52501e20i 0.138188 + 0.00614536i
\(631\) 1.18843e22i 0.472865i −0.971648 0.236433i \(-0.924022\pi\)
0.971648 0.236433i \(-0.0759782\pi\)
\(632\) 3.01253e21 + 4.04044e20i 0.118357 + 0.0158742i
\(633\) 1.82508e22 0.708030
\(634\) 1.74464e21 3.92309e22i 0.0668333 1.50284i
\(635\) 8.23423e21i 0.311482i
\(636\) 3.03232e20 3.40257e21i 0.0113271 0.127101i
\(637\) 7.72069e22 2.84800
\(638\) 5.10838e21 + 2.27176e20i 0.186088 + 0.00827554i
\(639\) 5.81884e21i 0.209329i
\(640\) −1.90993e21 + 5.94006e21i −0.0678542 + 0.211033i
\(641\) −1.01345e22 −0.355582 −0.177791 0.984068i \(-0.556895\pi\)
−0.177791 + 0.984068i \(0.556895\pi\)
\(642\) 3.59466e20 8.08313e21i 0.0124560 0.280091i
\(643\) 1.20343e22i 0.411845i 0.978568 + 0.205922i \(0.0660194\pi\)
−0.978568 + 0.205922i \(0.933981\pi\)
\(644\) −5.66031e22 5.04439e21i −1.91317 0.170499i
\(645\) −7.49870e20 −0.0250327
\(646\) 5.75677e21 + 2.56010e20i 0.189810 + 0.00844107i
\(647\) 2.59972e21i 0.0846628i −0.999104 0.0423314i \(-0.986521\pi\)
0.999104 0.0423314i \(-0.0134785\pi\)
\(648\) −4.59181e20 + 3.42362e21i −0.0147701 + 0.110125i
\(649\) −5.52230e22 −1.75454
\(650\) 1.53079e21 3.44221e22i 0.0480406 1.08026i
\(651\) 4.10605e22i 1.27285i
\(652\) −1.76282e21 + 1.97806e22i −0.0539793 + 0.605702i
\(653\) 4.59610e22 1.39022 0.695111 0.718903i \(-0.255355\pi\)
0.695111 + 0.718903i \(0.255355\pi\)
\(654\) −2.18356e22 9.71054e20i −0.652443 0.0290149i
\(655\) 1.21854e21i 0.0359675i
\(656\) −5.12440e22 9.20670e21i −1.49421 0.268456i
\(657\) 4.22819e21 0.121796
\(658\) −2.61661e21 + 5.88383e22i −0.0744614 + 1.67438i
\(659\) 4.92808e22i 1.38546i 0.721196 + 0.692731i \(0.243593\pi\)
−0.721196 + 0.692731i \(0.756407\pi\)
\(660\) 6.61071e21 + 5.89137e20i 0.183610 + 0.0163631i
\(661\) −5.05160e22 −1.38617 −0.693086 0.720855i \(-0.743749\pi\)
−0.693086 + 0.720855i \(0.743749\pi\)
\(662\) 5.63338e21 + 2.50523e20i 0.152723 + 0.00679178i
\(663\) 3.68927e21i 0.0988172i
\(664\) 2.31310e22 + 3.10236e21i 0.612139 + 0.0821009i
\(665\) 2.00350e22 0.523861
\(666\) −1.96027e20 + 4.40797e21i −0.00506434 + 0.113879i
\(667\) 5.19827e21i 0.132694i
\(668\) −5.38384e21 + 6.04121e22i −0.135794 + 1.52374i
\(669\) 1.62170e22 0.404168
\(670\) −5.70148e21 2.53551e20i −0.140407 0.00624407i
\(671\) 1.70331e22i 0.414490i
\(672\) 9.90561e21 4.38417e22i 0.238192 1.05422i
\(673\) 3.85828e22 0.916797 0.458398 0.888747i \(-0.348423\pi\)
0.458398 + 0.888747i \(0.348423\pi\)
\(674\) 1.27135e21 2.85881e22i 0.0298528 0.671284i
\(675\) 7.88615e21i 0.182993i
\(676\) −1.27380e22 1.13519e21i −0.292097 0.0260313i
\(677\) 1.69357e21 0.0383790 0.0191895 0.999816i \(-0.493891\pi\)
0.0191895 + 0.999816i \(0.493891\pi\)
\(678\) −3.84111e22 1.70819e21i −0.860240 0.0382559i
\(679\) 9.00875e22i 1.99391i
\(680\) −2.02751e20 + 1.51170e21i −0.00443498 + 0.0330669i
\(681\) −2.88498e22 −0.623685
\(682\) −3.52710e21 + 7.93120e22i −0.0753603 + 1.69459i
\(683\) 5.11935e22i 1.08106i 0.841326 + 0.540529i \(0.181776\pi\)
−0.841326 + 0.540529i \(0.818224\pi\)
\(684\) −1.78968e21 + 2.00820e22i −0.0373530 + 0.419139i
\(685\) −1.53944e22 −0.317570
\(686\) 1.37982e23 + 6.13624e21i 2.81340 + 0.125115i
\(687\) 2.16953e22i 0.437231i
\(688\) −1.73630e21 + 9.66415e21i −0.0345873 + 0.192511i
\(689\) −1.27651e22 −0.251345
\(690\) −2.99752e20 + 6.74037e21i −0.00583404 + 0.131187i
\(691\) 5.80131e22i 1.11610i −0.829809 0.558048i \(-0.811551\pi\)
0.829809 0.558048i \(-0.188449\pi\)
\(692\) 8.38539e22 + 7.47294e21i 1.59468 + 0.142116i
\(693\) −4.78091e22 −0.898762
\(694\) −6.45454e22 2.87041e21i −1.19947 0.0533418i
\(695\) 1.91136e22i 0.351127i
\(696\) −4.07500e21 5.46544e20i −0.0740037 0.00992547i
\(697\) −1.27269e22 −0.228487
\(698\) −1.49141e21 + 3.35366e22i −0.0264700 + 0.595217i
\(699\) 3.52935e22i 0.619266i
\(700\) 9.10871e21 1.02209e23i 0.158006 1.77298i
\(701\) 4.57259e22 0.784184 0.392092 0.919926i \(-0.371752\pi\)
0.392092 + 0.919926i \(0.371752\pi\)
\(702\) 1.28952e22 + 5.73465e20i 0.218641 + 0.00972321i
\(703\) 2.57534e22i 0.431709i
\(704\) 2.28996e22 8.38332e22i 0.379530 1.38942i
\(705\) 6.99268e21 0.114586
\(706\) 1.45162e21 3.26419e22i 0.0235189 0.528856i
\(707\) 2.18747e22i 0.350418i
\(708\) 4.42272e22 + 3.94146e21i 0.700524 + 0.0624297i
\(709\) 1.97438e21 0.0309215 0.0154607 0.999880i \(-0.495078\pi\)
0.0154607 + 0.999880i \(0.495078\pi\)
\(710\) −8.98054e21 3.99375e20i −0.139071 0.00618464i
\(711\) 2.59957e21i 0.0398057i
\(712\) −8.43355e21 + 6.28800e22i −0.127694 + 0.952078i
\(713\) −8.07076e22 −1.20837
\(714\) 4.88125e20 1.09762e22i 0.00722678 0.162505i
\(715\) 2.48008e22i 0.363093i
\(716\) 8.83840e21 9.91758e22i 0.127959 1.43582i
\(717\) −4.19008e22 −0.599886
\(718\) 6.00529e22 + 2.67062e21i 0.850234 + 0.0378109i
\(719\) 1.09202e23i 1.52897i −0.644642 0.764485i \(-0.722993\pi\)
0.644642 0.764485i \(-0.277007\pi\)
\(720\) −5.25236e21 9.43660e20i −0.0727268 0.0130664i
\(721\) −1.12966e23 −1.54691
\(722\) −1.94751e21 + 4.37926e22i −0.0263744 + 0.593067i
\(723\) 1.28332e22i 0.171881i
\(724\) 3.39460e22 + 3.02522e21i 0.449656 + 0.0400727i
\(725\) −9.38656e21 −0.122971
\(726\) −4.78329e22 2.12718e21i −0.619774 0.0275621i
\(727\) 6.91664e22i 0.886380i −0.896428 0.443190i \(-0.853847\pi\)
0.896428 0.443190i \(-0.146153\pi\)
\(728\) −1.66466e23 2.23267e22i −2.10997 0.282992i
\(729\) −2.95431e21 −0.0370370
\(730\) −2.90201e20 + 6.52561e21i −0.00359846 + 0.0809167i
\(731\) 2.40019e21i 0.0294378i
\(732\) −1.21571e21 + 1.36415e22i −0.0147483 + 0.165491i
\(733\) −2.16381e22 −0.259649 −0.129825 0.991537i \(-0.541441\pi\)
−0.129825 + 0.991537i \(0.541441\pi\)
\(734\) 9.33608e22 + 4.15186e21i 1.10814 + 0.0492804i
\(735\) 2.72993e22i 0.320518i
\(736\) 8.61742e22 + 1.94702e22i 1.00082 + 0.226125i
\(737\) 7.94886e22 0.913198
\(738\) 1.97829e21 4.44848e22i 0.0224822 0.505546i
\(739\) 6.07196e22i 0.682612i 0.939952 + 0.341306i \(0.110869\pi\)
−0.939952 + 0.341306i \(0.889131\pi\)
\(740\) −6.78961e21 6.05080e20i −0.0755077 0.00672914i
\(741\) 7.53397e22 0.828854
\(742\) −3.79783e22 1.68894e21i −0.413337 0.0183816i
\(743\) 8.98422e22i 0.967319i 0.875256 + 0.483660i \(0.160693\pi\)
−0.875256 + 0.483660i \(0.839307\pi\)
\(744\) 8.48557e21 6.32679e22i 0.0903853 0.673907i
\(745\) 2.96312e22 0.312248
\(746\) −5.67937e21 + 1.27709e23i −0.0592092 + 1.33141i
\(747\) 1.99602e22i 0.205873i
\(748\) 1.88571e21 2.11596e22i 0.0192426 0.215921i
\(749\) −9.00428e22 −0.909064
\(750\) −2.49713e22 1.11050e21i −0.249431 0.0110925i
\(751\) 8.45223e22i 0.835318i 0.908604 + 0.417659i \(0.137149\pi\)
−0.908604 + 0.417659i \(0.862851\pi\)
\(752\) 1.61913e22 9.01200e22i 0.158321 0.881208i
\(753\) 3.36021e22 0.325092
\(754\) −6.82571e20 + 1.53486e22i −0.00653397 + 0.146926i
\(755\) 3.13386e22i 0.296828i
\(756\) 3.82895e22 + 3.41231e21i 0.358844 + 0.0319796i
\(757\) 5.06405e21 0.0469603 0.0234802 0.999724i \(-0.492525\pi\)
0.0234802 + 0.999724i \(0.492525\pi\)
\(758\) −7.19265e22 3.19865e21i −0.659986 0.0293504i
\(759\) 9.39726e22i 0.853231i
\(760\) −3.08708e22 4.14044e21i −0.277357 0.0371995i
\(761\) 2.94175e22 0.261534 0.130767 0.991413i \(-0.458256\pi\)
0.130767 + 0.991413i \(0.458256\pi\)
\(762\) −4.09683e21 + 9.21232e22i −0.0360419 + 0.810455i
\(763\) 2.43239e23i 2.11757i
\(764\) −1.41282e22 + 1.58532e23i −0.121714 + 1.36575i
\(765\) −1.30447e21 −0.0111210
\(766\) −7.05143e22 3.13585e21i −0.594904 0.0264561i
\(767\) 1.65923e23i 1.38530i
\(768\) −2.43233e22 + 6.55061e22i −0.200971 + 0.541243i
\(769\) 1.97968e23 1.61877 0.809384 0.587280i \(-0.199801\pi\)
0.809384 + 0.587280i \(0.199801\pi\)
\(770\) 3.28137e21 7.37865e22i 0.0265540 0.597106i
\(771\) 9.86220e21i 0.0789839i
\(772\) 1.58147e23 + 1.40938e22i 1.25349 + 0.111709i
\(773\) 6.25457e22 0.490638 0.245319 0.969442i \(-0.421107\pi\)
0.245319 + 0.969442i \(0.421107\pi\)
\(774\) −8.38942e21 3.73087e20i −0.0651335 0.00289656i
\(775\) 1.45735e23i 1.11982i
\(776\) −1.86175e22 + 1.38811e23i −0.141588 + 1.05567i
\(777\) 4.91029e22 0.369606
\(778\) −3.32052e21 + 7.46668e22i −0.0247383 + 0.556276i
\(779\) 2.59901e23i 1.91649i
\(780\) −1.77012e21 + 1.98625e22i −0.0129195 + 0.144970i
\(781\) 1.25204e23 0.904506
\(782\) 2.15746e22 + 9.59447e20i 0.154273 + 0.00686068i
\(783\) 3.51640e21i 0.0248888i
\(784\) −3.51827e23 6.32106e22i −2.46490 0.442855i
\(785\) −1.66660e22 −0.115578
\(786\) −6.06269e20 + 1.36329e22i −0.00416184 + 0.0935851i
\(787\) 2.18866e23i 1.48724i 0.668603 + 0.743619i \(0.266893\pi\)
−0.668603 + 0.743619i \(0.733107\pi\)
\(788\) −1.98218e23 1.76649e22i −1.33332 0.118823i
\(789\) −4.47226e22 −0.297790
\(790\) −4.01207e21 1.78421e20i −0.0264455 0.00117606i
\(791\) 4.27884e23i 2.79199i
\(792\) 7.36665e22 + 9.88024e21i 0.475848 + 0.0638214i
\(793\) 5.11777e22 0.327262
\(794\) 7.87260e21 1.77027e23i 0.0498373 1.12067i
\(795\) 4.51356e21i 0.0282867i
\(796\) 1.70537e22 1.91359e23i 0.105807 1.18726i
\(797\) −4.97106e22 −0.305339 −0.152669 0.988277i \(-0.548787\pi\)
−0.152669 + 0.988277i \(0.548787\pi\)
\(798\) 2.24148e23 + 9.96813e21i 1.36305 + 0.0606165i
\(799\) 2.23822e22i 0.134750i
\(800\) −3.51576e22 + 1.55606e23i −0.209556 + 0.927482i
\(801\) −5.42604e22 −0.320201
\(802\) 1.14702e22 2.57925e23i 0.0670157 1.50695i
\(803\) 9.09784e22i 0.526277i
\(804\) −6.36611e22 5.67338e21i −0.364607 0.0324933i
\(805\) 7.50849e22 0.425780
\(806\) −2.38301e23 1.05975e22i −1.33797 0.0595009i
\(807\) 5.69778e22i 0.316751i
\(808\) 4.52063e21 3.37055e22i 0.0248833 0.185528i
\(809\) −2.58507e23 −1.40891 −0.704455 0.709748i \(-0.748809\pi\)
−0.704455 + 0.709748i \(0.748809\pi\)
\(810\) 2.02769e20 4.55956e21i 0.00109426 0.0246061i
\(811\) 9.75187e22i 0.521100i −0.965460 0.260550i \(-0.916096\pi\)
0.965460 0.260550i \(-0.0839039\pi\)
\(812\) −4.06153e21 + 4.55744e22i −0.0214902 + 0.241142i
\(813\) 5.64136e22 0.295569
\(814\) 9.48466e22 + 4.21794e21i 0.492070 + 0.0218829i
\(815\) 2.62393e22i 0.134800i
\(816\) −3.02047e21 + 1.68118e22i −0.0153657 + 0.0855248i
\(817\) −4.90149e22 −0.246917
\(818\) −2.16709e21 + 4.87302e22i −0.0108106 + 0.243092i
\(819\) 1.43647e23i 0.709620i
\(820\) 6.85201e22 + 6.10641e21i 0.335202 + 0.0298728i
\(821\) 1.80543e23 0.874653 0.437327 0.899303i \(-0.355925\pi\)
0.437327 + 0.899303i \(0.355925\pi\)
\(822\) −1.72230e23 7.65928e21i −0.826295 0.0367463i
\(823\) 5.84547e22i 0.277729i −0.990311 0.138864i \(-0.955655\pi\)
0.990311 0.138864i \(-0.0443452\pi\)
\(824\) 1.74063e23 + 2.33455e22i 0.819008 + 0.109846i
\(825\) 1.69687e23 0.790710
\(826\) 2.19531e22 4.93648e23i 0.101311 2.27812i
\(827\) 2.70285e23i 1.23532i −0.786446 0.617658i \(-0.788081\pi\)
0.786446 0.617658i \(-0.211919\pi\)
\(828\) −6.70715e21 + 7.52610e22i −0.0303596 + 0.340665i
\(829\) −3.13380e23 −1.40487 −0.702433 0.711749i \(-0.747903\pi\)
−0.702433 + 0.711749i \(0.747903\pi\)
\(830\) −3.08057e22 1.36997e21i −0.136775 0.00608255i
\(831\) 1.99198e22i 0.0875946i
\(832\) 2.51885e23 + 6.88040e22i 1.09702 + 0.299659i
\(833\) −8.73796e22 −0.376921
\(834\) −9.50972e21 + 2.13840e23i −0.0406293 + 0.913610i
\(835\) 8.01375e22i 0.339113i
\(836\) 4.32106e23 + 3.85087e22i 1.81109 + 0.161402i
\(837\) 5.45951e22 0.226647
\(838\) −1.54036e22 6.85016e20i −0.0633389 0.00281675i
\(839\) 1.22175e23i 0.497608i −0.968554 0.248804i \(-0.919963\pi\)
0.968554 0.248804i \(-0.0800375\pi\)
\(840\) −7.89440e21 + 5.88602e22i −0.0318482 + 0.237458i
\(841\) −2.46061e23 −0.983275
\(842\) 3.69834e21 8.31627e22i 0.0146390 0.329179i
\(843\) 1.03136e23i 0.404381i
\(844\) −2.80287e22 + 3.14510e23i −0.108859 + 1.22150i
\(845\) 1.68971e22 0.0650069
\(846\) 7.82329e22 + 3.47911e21i 0.298144 + 0.0132588i
\(847\) 5.32838e23i 2.01154i
\(848\) 5.81696e22 + 1.04510e22i 0.217535 + 0.0390833i
\(849\) −8.69830e22 −0.322235
\(850\) −1.73248e21 + 3.89574e22i −0.00635796 + 0.142968i
\(851\) 9.65156e22i 0.350882i
\(852\) −1.00274e23 8.93629e21i −0.361137 0.0321840i
\(853\) 1.08159e23 0.385896 0.192948 0.981209i \(-0.438195\pi\)
0.192948 + 0.981209i \(0.438195\pi\)
\(854\) 1.52262e23 + 6.77128e21i 0.538182 + 0.0239336i
\(855\) 2.66391e22i 0.0932803i
\(856\) 1.38742e23 + 1.86083e22i 0.481302 + 0.0645529i
\(857\) 2.22560e23 0.764894 0.382447 0.923977i \(-0.375081\pi\)
0.382447 + 0.923977i \(0.375081\pi\)
\(858\) 1.23393e22 2.77467e23i 0.0420138 0.944743i
\(859\) 6.15550e22i 0.207643i 0.994596 + 0.103822i \(0.0331071\pi\)
−0.994596 + 0.103822i \(0.966893\pi\)
\(860\) 1.15161e21 1.29223e22i 0.00384875 0.0431868i
\(861\) −4.95542e23 −1.64080
\(862\) 3.14693e23 + 1.39947e22i 1.03235 + 0.0459100i
\(863\) 3.86238e22i 0.125536i 0.998028 + 0.0627681i \(0.0199928\pi\)
−0.998028 + 0.0627681i \(0.980007\pi\)
\(864\) −5.82930e22 1.31708e22i −0.187718 0.0424132i
\(865\) −1.11233e23 −0.354900
\(866\) −1.84195e22 + 4.14190e23i −0.0582285 + 1.30935i
\(867\) 1.80153e23i 0.564272i
\(868\) −7.07582e23 6.30587e22i −2.19593 0.195698i
\(869\) 5.59352e22 0.171999
\(870\) 5.42705e21 + 2.41347e20i 0.0165352 + 0.000735341i
\(871\) 2.38831e23i 0.721018i
\(872\) 5.02679e22 3.74794e23i 0.150369 1.12114i
\(873\) −1.19783e23 −0.355042
\(874\) −1.95931e22 + 4.40581e23i −0.0575457 + 1.29400i
\(875\) 2.78170e23i 0.809554i
\(876\) −6.49345e21 + 7.28631e22i −0.0187259 + 0.210123i
\(877\) −6.96394e23 −1.99002 −0.995011 0.0997617i \(-0.968192\pi\)
−0.995011 + 0.0997617i \(0.968192\pi\)
\(878\) 1.88766e23 + 8.39465e21i 0.534525 + 0.0237709i
\(879\) 1.73501e23i 0.486844i
\(880\) −2.03048e22 + 1.13016e23i −0.0564596 + 0.314251i
\(881\) −3.36202e23 −0.926388 −0.463194 0.886257i \(-0.653297\pi\)
−0.463194 + 0.886257i \(0.653297\pi\)
\(882\) 1.35824e22 3.05420e23i 0.0370874 0.833966i
\(883\) 4.48123e23i 1.21258i −0.795242 0.606292i \(-0.792656\pi\)
0.795242 0.606292i \(-0.207344\pi\)
\(884\) 6.35761e22 + 5.66581e21i 0.170481 + 0.0151930i
\(885\) −5.86680e22 −0.155903
\(886\) −1.34086e23 5.96298e21i −0.353114 0.0157034i
\(887\) 6.64749e21i 0.0173488i 0.999962 + 0.00867439i \(0.00276118\pi\)
−0.999962 + 0.00867439i \(0.997239\pi\)
\(888\) −7.56600e22 1.01476e22i −0.195687 0.0262458i
\(889\) 1.02621e24 2.63041
\(890\) 3.72416e21 8.37432e22i 0.00946037 0.212730i
\(891\) 6.35682e22i 0.160036i
\(892\) −2.49053e22 + 2.79462e23i −0.0621402 + 0.697276i
\(893\) 4.57073e23 1.13025
\(894\) 3.31509e23 + 1.47426e22i 0.812448 + 0.0361305i
\(895\) 1.31558e23i 0.319546i
\(896\) 7.40297e23 + 2.38030e23i 1.78214 + 0.573017i
\(897\) 2.82350e23 0.673671
\(898\) −3.84764e21 + 8.65198e22i −0.00909878 + 0.204600i
\(899\) 6.49823e22i 0.152306i
\(900\) −1.35900e23 1.21112e22i −0.315702 0.0281349i
\(901\) 1.44470e22 0.0332644
\(902\) −9.57183e23 4.25670e22i −2.18445 0.0971452i
\(903\) 9.34547e22i 0.211397i
\(904\) 8.84266e22 6.59303e23i 0.198260 1.47822i
\(905\) −4.50299e22 −0.100072
\(906\) −1.55921e22 + 3.50611e23i −0.0343462 + 0.772325i
\(907\) 4.63696e23i 1.01245i −0.862400 0.506227i \(-0.831040\pi\)
0.862400 0.506227i \(-0.168960\pi\)
\(908\) 4.43061e22 4.97159e23i 0.0958907 1.07599i
\(909\) 2.90851e22 0.0623965
\(910\) 2.21699e23 + 9.85921e21i 0.471446 + 0.0209658i
\(911\) 5.45620e23i 1.15012i −0.818111 0.575060i \(-0.804979\pi\)
0.818111 0.575060i \(-0.195021\pi\)
\(912\) −3.43318e23 6.16819e22i −0.717361 0.128884i
\(913\) 4.29486e23 0.889575
\(914\) 3.35380e22 7.54152e23i 0.0688601 1.54842i
\(915\) 1.80957e22i 0.0368304i
\(916\) −3.73867e23 3.33185e22i −0.754317 0.0672237i
\(917\) 1.51864e23 0.303740
\(918\) −1.45942e22 6.49023e20i −0.0289361 0.00128682i
\(919\) 3.81492e23i 0.749827i 0.927060 + 0.374913i \(0.122328\pi\)
−0.927060 + 0.374913i \(0.877672\pi\)
\(920\) −1.15694e23 1.55171e22i −0.225429 0.0302348i
\(921\) 2.68270e23 0.518198
\(922\) −3.58116e22 + 8.05276e23i −0.0685766 + 1.54205i
\(923\) 3.76189e23i 0.714155i
\(924\) 7.34229e22 8.23879e23i 0.138183 1.55056i
\(925\) −1.74279e23 −0.325171
\(926\) −1.93571e23 8.60831e21i −0.358056 0.0159232i
\(927\) 1.50202e23i 0.275447i
\(928\) 1.56766e22 6.93838e22i 0.0285015 0.126146i
\(929\) 2.87790e23 0.518740 0.259370 0.965778i \(-0.416485\pi\)
0.259370 + 0.965778i \(0.416485\pi\)
\(930\) −3.74713e21 + 8.42597e22i −0.00669630 + 0.150576i
\(931\) 1.78440e24i 3.16152i
\(932\) −6.08201e23 5.42020e22i −1.06837 0.0952113i
\(933\) 2.51796e23 0.438526
\(934\) −9.33651e22 4.15206e21i −0.161217 0.00716949i
\(935\) 2.80685e22i 0.0480537i
\(936\) −2.96862e22 + 2.21338e23i −0.0503903 + 0.375707i
\(937\) −9.03324e23 −1.52029 −0.760146 0.649753i \(-0.774872\pi\)
−0.760146 + 0.649753i \(0.774872\pi\)
\(938\) −3.15996e22 + 7.10563e23i −0.0527301 + 1.18571i
\(939\) 1.05944e23i 0.175288i
\(940\) −1.07390e22 + 1.20503e23i −0.0176174 + 0.197685i
\(941\) 3.62505e23 0.589653 0.294826 0.955551i \(-0.404738\pi\)
0.294826 + 0.955551i \(0.404738\pi\)
\(942\) −1.86456e23 8.29193e21i −0.300725 0.0133736i
\(943\) 9.74026e23i 1.55768i
\(944\) −1.35844e23 + 7.56099e23i −0.215409 + 1.19895i
\(945\) −5.07916e22 −0.0798615
\(946\) −8.02776e21 + 1.80516e23i −0.0125160 + 0.281441i
\(947\) 2.76095e23i 0.426834i 0.976961 + 0.213417i \(0.0684593\pi\)
−0.976961 + 0.213417i \(0.931541\pi\)
\(948\) −4.47976e22 3.99229e21i −0.0686733 0.00612006i
\(949\) 2.73354e23 0.415523
\(950\) −7.95561e23 3.53795e22i −1.19918 0.0533290i
\(951\) 5.81068e23i 0.868525i
\(952\) 1.88400e23 + 2.52684e22i 0.279245 + 0.0374526i
\(953\) −2.33311e23 −0.342919 −0.171459 0.985191i \(-0.554848\pi\)
−0.171459 + 0.985191i \(0.554848\pi\)
\(954\) −2.24566e21 + 5.04969e22i −0.00327308 + 0.0736000i
\(955\) 2.10296e23i 0.303951i
\(956\) 6.43492e22 7.22063e23i 0.0922316 1.03493i
\(957\) −7.56626e22 −0.107544
\(958\) 2.98866e23 + 1.32909e22i 0.421262 + 0.0187340i
\(959\) 1.91857e24i 2.68182i
\(960\) 2.43281e22 8.90630e22i 0.0337240 0.123460i
\(961\) −2.81483e23 −0.386960
\(962\) −1.26732e22 + 2.84976e23i −0.0172777 + 0.388515i
\(963\) 1.19723e23i 0.161871i
\(964\) 2.21150e23 + 1.97086e22i 0.296531 + 0.0264264i
\(965\) −2.09784e23 −0.278968
\(966\) 8.40038e23 + 3.73575e22i 1.10785 + 0.0492675i
\(967\) 1.41945e24i 1.85656i 0.371879 + 0.928281i \(0.378714\pi\)
−0.371879 + 0.928281i \(0.621286\pi\)
\(968\) 1.10116e23 8.21022e23i 0.142840 1.06501i
\(969\) −8.52663e22 −0.109695
\(970\) 8.22127e21 1.84867e23i 0.0104898 0.235878i
\(971\) 1.02803e24i 1.30092i −0.759539 0.650462i \(-0.774575\pi\)
0.759539 0.650462i \(-0.225425\pi\)
\(972\) 4.53709e21 5.09107e22i 0.00569439 0.0638968i
\(973\) 2.38209e24 2.96521
\(974\) 4.83731e23 + 2.15121e22i 0.597218 + 0.0265590i
\(975\) 5.09842e23i 0.624307i
\(976\) −2.33213e23 4.19000e22i −0.283240 0.0508880i
\(977\) −1.25942e24 −1.51710 −0.758549 0.651615i \(-0.774092\pi\)
−0.758549 + 0.651615i \(0.774092\pi\)
\(978\) 1.30550e22 2.93561e23i 0.0155979 0.350742i
\(979\) 1.16753e24i 1.38358i
\(980\) 4.70439e23 + 4.19249e22i 0.552962 + 0.0492792i
\(981\) 3.23417e23 0.377061
\(982\) −3.13568e23 1.39448e22i −0.362610 0.0161257i
\(983\) 5.44196e23i 0.624205i −0.950048 0.312103i \(-0.898967\pi\)
0.950048 0.312103i \(-0.101033\pi\)
\(984\) 7.63553e23 + 1.02409e23i 0.868718 + 0.116514i
\(985\) 2.62939e23 0.296732
\(986\) 7.72505e20 1.73709e22i 0.000864741 0.0194450i
\(987\) 8.71482e23i 0.967656i
\(988\) −1.15703e23 + 1.29830e24i −0.127435 + 1.42995i
\(989\) −1.83692e23 −0.200688
\(990\) −9.81085e22 4.36300e21i −0.106322 0.00472828i
\(991\) 1.42399e24i 1.53080i −0.643553 0.765401i \(-0.722541\pi\)
0.643553 0.765401i \(-0.277459\pi\)
\(992\) 1.07724e24 + 2.43393e23i 1.14874 + 0.259546i
\(993\) −8.34387e22 −0.0882620
\(994\) −4.97733e22 + 1.11923e24i −0.0522282 + 1.17443i
\(995\) 2.53841e23i 0.264227i
\(996\) −3.43968e23 3.06539e22i −0.355176 0.0316528i
\(997\) −1.83119e24 −1.87574 −0.937869 0.346989i \(-0.887204\pi\)
−0.937869 + 0.346989i \(0.887204\pi\)
\(998\) −6.90902e23 3.07252e22i −0.702056 0.0312213i
\(999\) 6.52885e22i 0.0658132i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 12.17.d.a.7.9 16
3.2 odd 2 36.17.d.d.19.8 16
4.3 odd 2 inner 12.17.d.a.7.10 yes 16
12.11 even 2 36.17.d.d.19.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.17.d.a.7.9 16 1.1 even 1 trivial
12.17.d.a.7.10 yes 16 4.3 odd 2 inner
36.17.d.d.19.7 16 12.11 even 2
36.17.d.d.19.8 16 3.2 odd 2