Properties

Label 98.14.c.o.79.4
Level $98$
Weight $14$
Character 98.79
Analytic conductor $105.086$
Analytic rank $0$
Dimension $8$
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] = [98,14,Mod(67,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.67");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not 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: \(105.086310373\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + \cdots + 75\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{2}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.4
Root \(-35.6648 - 61.7733i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.14.c.o.67.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(32.0000 - 55.4256i) q^{2} +(746.854 + 1293.59i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(7178.20 - 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. + 551520. i) q^{9} +O(q^{10})\) \(q+(32.0000 - 55.4256i) q^{2} +(746.854 + 1293.59i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(7178.20 - 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. + 551520. i) q^{9} +(-459405. - 795712. i) q^{10} +(2.14272e6 + 3.71130e6i) q^{11} +(3.05911e6 - 5.29854e6i) q^{12} -5.50861e6 q^{13} +2.14443e7 q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +(-1.98554e7 - 3.43905e7i) q^{17} +(2.03789e7 + 3.52973e7i) q^{18} +(2.25114e7 - 3.89910e7i) q^{19} -5.88038e7 q^{20} +2.74268e8 q^{22} +(-3.77343e8 + 6.53577e8i) q^{23} +(-1.95783e8 - 3.39107e8i) q^{24} +(5.07299e8 + 8.78667e8i) q^{25} +(-1.76275e8 + 3.05318e8i) q^{26} +1.43020e9 q^{27} -2.46353e9 q^{29} +(6.86216e8 - 1.18856e9i) q^{30} +(3.06703e9 + 5.31225e9i) q^{31} +(5.36871e8 + 9.29888e8i) q^{32} +(-3.20060e9 + 5.54359e9i) q^{33} -2.54149e9 q^{34} +2.60850e9 q^{36} +(9.52417e9 - 1.64963e10i) q^{37} +(-1.44073e9 - 2.49542e9i) q^{38} +(-4.11413e9 - 7.12588e9i) q^{39} +(-1.88172e9 + 3.25924e9i) q^{40} +4.23093e10 q^{41} -7.42867e10 q^{43} +(8.77657e9 - 1.52015e10i) q^{44} +(4.57137e9 + 7.91784e9i) q^{45} +(2.41499e10 + 4.18289e10i) q^{46} +(4.03508e10 - 6.98897e10i) q^{47} -2.50603e10 q^{48} +6.49342e10 q^{50} +(2.96581e10 - 5.13694e10i) q^{51} +(1.12816e10 + 1.95404e10i) q^{52} +(1.10539e11 + 1.91459e11i) q^{53} +(4.57664e10 - 7.92697e10i) q^{54} +6.15234e10 q^{55} +6.72511e10 q^{57} +(-7.88329e10 + 1.36543e11i) q^{58} +(2.29890e11 + 3.98181e11i) q^{59} +(-4.39178e10 - 7.60679e10i) q^{60} +(3.23925e10 - 5.61055e10i) q^{61} +3.92580e11 q^{62} +6.87195e10 q^{64} +(-3.95419e10 + 6.84885e10i) q^{65} +(2.04838e11 + 3.54790e11i) q^{66} +(2.07214e11 + 3.58905e11i) q^{67} +(-8.13276e10 + 1.40864e11i) q^{68} -1.12728e12 q^{69} -6.38110e11 q^{71} +(8.34720e10 - 1.44578e11i) q^{72} +(2.92998e11 + 5.07488e11i) q^{73} +(-6.09547e11 - 1.05577e12i) q^{74} +(-7.57756e11 + 1.31247e12i) q^{75} -1.84414e11 q^{76} -5.26608e11 q^{78} +(-1.22943e12 + 2.12943e12i) q^{79} +(1.20430e11 + 2.08591e11i) q^{80} +(1.57581e12 + 2.72939e12i) q^{81} +(1.35390e12 - 2.34502e12i) q^{82} -3.32114e12 q^{83} -5.70103e11 q^{85} +(-2.37717e12 + 4.11739e12i) q^{86} +(-1.83990e12 - 3.18679e12i) q^{87} +(-5.61701e11 - 9.72894e11i) q^{88} +(-1.39203e12 + 2.41106e12i) q^{89} +5.85135e11 q^{90} +3.09119e12 q^{92} +(-4.58125e12 + 7.93495e12i) q^{93} +(-2.58245e12 - 4.47294e12i) q^{94} +(-3.23183e11 - 5.59770e11i) q^{95} +(-8.01928e11 + 1.38898e12i) q^{96} +7.80467e12 q^{97} -2.72914e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 256 q^{2} - 182 q^{3} - 16384 q^{4} - 1792 q^{5} - 23296 q^{6} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 256 q^{2} - 182 q^{3} - 16384 q^{4} - 1792 q^{5} - 23296 q^{6} - 2097152 q^{8} + 599840 q^{9} + 114688 q^{10} - 8726914 q^{11} - 745472 q^{12} - 1438416 q^{13} - 136873212 q^{15} - 67108864 q^{16} + 7943068 q^{17} - 38389760 q^{18} + 215706806 q^{19} + 14680064 q^{20} - 1117044992 q^{22} - 61927978 q^{23} + 47710208 q^{24} - 1327844792 q^{25} - 46029312 q^{26} + 3268643812 q^{27} - 6325846064 q^{29} - 4379942784 q^{30} - 6113775570 q^{31} + 4294967296 q^{32} - 25235960652 q^{33} + 1016712704 q^{34} - 4913889280 q^{36} - 3945652880 q^{37} - 13805235584 q^{38} - 23545599116 q^{39} + 469762048 q^{40} - 86378579952 q^{41} - 109074124256 q^{43} - 35745439744 q^{44} + 104964468168 q^{45} + 3963390592 q^{46} + 3141202722 q^{47} + 6106906624 q^{48} - 169964133376 q^{50} - 241278267462 q^{51} + 2945875968 q^{52} + 149625680376 q^{53} + 104596601984 q^{54} - 174912009748 q^{55} - 128207489960 q^{57} - 202427074048 q^{58} + 866297313938 q^{59} + 280316338176 q^{60} + 477908594184 q^{61} - 782563272960 q^{62} + 549755813888 q^{64} - 1099748343120 q^{65} + 1615101481728 q^{66} + 1895501016278 q^{67} + 32534806528 q^{68} - 3503301895632 q^{69} + 638832672128 q^{71} - 157244456960 q^{72} + 2966596192756 q^{73} + 252521784320 q^{74} + 1331079867376 q^{75} - 1767070154752 q^{76} - 3013836686848 q^{78} - 6505959677634 q^{79} - 30064771072 q^{80} + 2449216493684 q^{81} - 2764114558464 q^{82} + 3379817135968 q^{83} - 16684556982464 q^{85} - 3490371976192 q^{86} + 5273311164492 q^{87} + 2287708143616 q^{88} - 9586601667468 q^{89} + 13435451925504 q^{90} + 507313995776 q^{92} - 14195747226896 q^{93} - 201036974208 q^{94} + 14384410136978 q^{95} + 195421011968 q^{96} + 44560735311568 q^{97} + 24706419985464 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 32.0000 55.4256i 0.353553 0.612372i
\(3\) 746.854 + 1293.59i 0.591490 + 1.02449i 0.994032 + 0.109090i \(0.0347935\pi\)
−0.402542 + 0.915402i \(0.631873\pi\)
\(4\) −2048.00 3547.24i −0.250000 0.433013i
\(5\) 7178.20 12433.0i 0.205452 0.355853i −0.744825 0.667260i \(-0.767467\pi\)
0.950277 + 0.311407i \(0.100800\pi\)
\(6\) 95597.3 0.836494
\(7\) 0 0
\(8\) −262144. −0.353553
\(9\) −318420. + 551520.i −0.199721 + 0.345928i
\(10\) −459405. 795712.i −0.145276 0.251626i
\(11\) 2.14272e6 + 3.71130e6i 0.364681 + 0.631645i 0.988725 0.149744i \(-0.0478449\pi\)
−0.624044 + 0.781389i \(0.714512\pi\)
\(12\) 3.05911e6 5.29854e6i 0.295745 0.512246i
\(13\) −5.50861e6 −0.316527 −0.158263 0.987397i \(-0.550589\pi\)
−0.158263 + 0.987397i \(0.550589\pi\)
\(14\) 0 0
\(15\) 2.14443e7 0.486091
\(16\) −8.38861e6 + 1.45295e7i −0.125000 + 0.216506i
\(17\) −1.98554e7 3.43905e7i −0.199508 0.345558i 0.748861 0.662727i \(-0.230601\pi\)
−0.948369 + 0.317169i \(0.897268\pi\)
\(18\) 2.03789e7 + 3.52973e7i 0.141224 + 0.244608i
\(19\) 2.25114e7 3.89910e7i 0.109775 0.190137i −0.805904 0.592046i \(-0.798320\pi\)
0.915679 + 0.401910i \(0.131654\pi\)
\(20\) −5.88038e7 −0.205452
\(21\) 0 0
\(22\) 2.74268e8 0.515736
\(23\) −3.77343e8 + 6.53577e8i −0.531502 + 0.920589i 0.467822 + 0.883823i \(0.345039\pi\)
−0.999324 + 0.0367661i \(0.988294\pi\)
\(24\) −1.95783e8 3.39107e8i −0.209123 0.362212i
\(25\) 5.07299e8 + 8.78667e8i 0.415579 + 0.719804i
\(26\) −1.76275e8 + 3.05318e8i −0.111909 + 0.193832i
\(27\) 1.43020e9 0.710447
\(28\) 0 0
\(29\) −2.46353e9 −0.769078 −0.384539 0.923109i \(-0.625640\pi\)
−0.384539 + 0.923109i \(0.625640\pi\)
\(30\) 6.86216e8 1.18856e9i 0.171859 0.297669i
\(31\) 3.06703e9 + 5.31225e9i 0.620679 + 1.07505i 0.989360 + 0.145491i \(0.0464762\pi\)
−0.368681 + 0.929556i \(0.620190\pi\)
\(32\) 5.36871e8 + 9.29888e8i 0.0883883 + 0.153093i
\(33\) −3.20060e9 + 5.54359e9i −0.431410 + 0.747224i
\(34\) −2.54149e9 −0.282147
\(35\) 0 0
\(36\) 2.60850e9 0.199721
\(37\) 9.52417e9 1.64963e10i 0.610261 1.05700i −0.380935 0.924602i \(-0.624398\pi\)
0.991196 0.132401i \(-0.0422688\pi\)
\(38\) −1.44073e9 2.49542e9i −0.0776229 0.134447i
\(39\) −4.11413e9 7.12588e9i −0.187222 0.324279i
\(40\) −1.88172e9 + 3.25924e9i −0.0726382 + 0.125813i
\(41\) 4.23093e10 1.39104 0.695522 0.718505i \(-0.255173\pi\)
0.695522 + 0.718505i \(0.255173\pi\)
\(42\) 0 0
\(43\) −7.42867e10 −1.79212 −0.896058 0.443937i \(-0.853581\pi\)
−0.896058 + 0.443937i \(0.853581\pi\)
\(44\) 8.77657e9 1.52015e10i 0.182340 0.315823i
\(45\) 4.57137e9 + 7.91784e9i 0.0820663 + 0.142143i
\(46\) 2.41499e10 + 4.18289e10i 0.375829 + 0.650955i
\(47\) 4.03508e10 6.98897e10i 0.546030 0.945751i −0.452512 0.891758i \(-0.649472\pi\)
0.998541 0.0539926i \(-0.0171947\pi\)
\(48\) −2.50603e10 −0.295745
\(49\) 0 0
\(50\) 6.49342e10 0.587717
\(51\) 2.96581e10 5.13694e10i 0.236014 0.408788i
\(52\) 1.12816e10 + 1.95404e10i 0.0791316 + 0.137060i
\(53\) 1.10539e11 + 1.91459e11i 0.685049 + 1.18654i 0.973421 + 0.229021i \(0.0735526\pi\)
−0.288372 + 0.957518i \(0.593114\pi\)
\(54\) 4.57664e10 7.92697e10i 0.251181 0.435058i
\(55\) 6.15234e10 0.299697
\(56\) 0 0
\(57\) 6.72511e10 0.259724
\(58\) −7.88329e10 + 1.36543e11i −0.271910 + 0.470962i
\(59\) 2.29890e11 + 3.98181e11i 0.709548 + 1.22897i 0.965025 + 0.262158i \(0.0844342\pi\)
−0.255477 + 0.966815i \(0.582233\pi\)
\(60\) −4.39178e10 7.60679e10i −0.121523 0.210484i
\(61\) 3.23925e10 5.61055e10i 0.0805009 0.139432i −0.822964 0.568093i \(-0.807681\pi\)
0.903465 + 0.428661i \(0.141015\pi\)
\(62\) 3.92580e11 0.877772
\(63\) 0 0
\(64\) 6.87195e10 0.125000
\(65\) −3.95419e10 + 6.84885e10i −0.0650310 + 0.112637i
\(66\) 2.04838e11 + 3.54790e11i 0.305053 + 0.528367i
\(67\) 2.07214e11 + 3.58905e11i 0.279855 + 0.484722i 0.971348 0.237660i \(-0.0763804\pi\)
−0.691494 + 0.722382i \(0.743047\pi\)
\(68\) −8.13276e10 + 1.40864e11i −0.0997540 + 0.172779i
\(69\) −1.12728e12 −1.25751
\(70\) 0 0
\(71\) −6.38110e11 −0.591175 −0.295588 0.955316i \(-0.595515\pi\)
−0.295588 + 0.955316i \(0.595515\pi\)
\(72\) 8.34720e10 1.44578e11i 0.0706122 0.122304i
\(73\) 2.92998e11 + 5.07488e11i 0.226603 + 0.392488i 0.956799 0.290749i \(-0.0939046\pi\)
−0.730196 + 0.683238i \(0.760571\pi\)
\(74\) −6.09547e11 1.05577e12i −0.431520 0.747414i
\(75\) −7.57756e11 + 1.31247e12i −0.491622 + 0.851514i
\(76\) −1.84414e11 −0.109775
\(77\) 0 0
\(78\) −5.26608e11 −0.264772
\(79\) −1.22943e12 + 2.12943e12i −0.569019 + 0.985571i 0.427644 + 0.903947i \(0.359344\pi\)
−0.996663 + 0.0816233i \(0.973990\pi\)
\(80\) 1.20430e11 + 2.08591e11i 0.0513630 + 0.0889633i
\(81\) 1.57581e12 + 2.72939e12i 0.619944 + 1.07377i
\(82\) 1.35390e12 2.34502e12i 0.491808 0.851837i
\(83\) −3.32114e12 −1.11501 −0.557506 0.830173i \(-0.688242\pi\)
−0.557506 + 0.830173i \(0.688242\pi\)
\(84\) 0 0
\(85\) −5.70103e11 −0.163957
\(86\) −2.37717e12 + 4.11739e12i −0.633609 + 1.09744i
\(87\) −1.83990e12 3.18679e12i −0.454902 0.787913i
\(88\) −5.61701e11 9.72894e11i −0.128934 0.223320i
\(89\) −1.39203e12 + 2.41106e12i −0.296902 + 0.514249i −0.975426 0.220329i \(-0.929287\pi\)
0.678523 + 0.734579i \(0.262620\pi\)
\(90\) 5.85135e11 0.116059
\(91\) 0 0
\(92\) 3.09119e12 0.531502
\(93\) −4.58125e12 + 7.93495e12i −0.734251 + 1.27176i
\(94\) −2.58245e12 4.47294e12i −0.386101 0.668747i
\(95\) −3.23183e11 5.59770e11i −0.0451071 0.0781279i
\(96\) −8.01928e11 + 1.38898e12i −0.104562 + 0.181106i
\(97\) 7.80467e12 0.951345 0.475672 0.879622i \(-0.342205\pi\)
0.475672 + 0.879622i \(0.342205\pi\)
\(98\) 0 0
\(99\) −2.72914e12 −0.291338
\(100\) 2.07789e12 3.59902e12i 0.207789 0.359902i
\(101\) 6.58305e12 + 1.14022e13i 0.617076 + 1.06881i 0.990017 + 0.140951i \(0.0450160\pi\)
−0.372941 + 0.927855i \(0.621651\pi\)
\(102\) −1.89812e12 3.28764e12i −0.166887 0.289057i
\(103\) −8.84393e12 + 1.53181e13i −0.729799 + 1.26405i 0.227168 + 0.973855i \(0.427053\pi\)
−0.956968 + 0.290194i \(0.906280\pi\)
\(104\) 1.44405e12 0.111909
\(105\) 0 0
\(106\) 1.41490e13 0.968806
\(107\) 7.23079e12 1.25241e13i 0.465791 0.806774i −0.533446 0.845834i \(-0.679103\pi\)
0.999237 + 0.0390602i \(0.0124364\pi\)
\(108\) −2.92905e12 5.07326e12i −0.177612 0.307633i
\(109\) 7.96586e12 + 1.37973e13i 0.454947 + 0.787991i 0.998685 0.0512639i \(-0.0163250\pi\)
−0.543738 + 0.839255i \(0.682992\pi\)
\(110\) 1.96875e12 3.40997e12i 0.105959 0.183526i
\(111\) 2.84526e13 1.44385
\(112\) 0 0
\(113\) 4.86885e12 0.219997 0.109998 0.993932i \(-0.464915\pi\)
0.109998 + 0.993932i \(0.464915\pi\)
\(114\) 2.15203e12 3.72743e12i 0.0918264 0.159048i
\(115\) 5.41728e12 + 9.38301e12i 0.218396 + 0.378274i
\(116\) 5.04530e12 + 8.73872e12i 0.192269 + 0.333020i
\(117\) 1.75405e12 3.03811e12i 0.0632171 0.109495i
\(118\) 2.94259e13 1.00345
\(119\) 0 0
\(120\) −5.62148e12 −0.171859
\(121\) 8.07887e12 1.39930e13i 0.234016 0.405328i
\(122\) −2.07312e12 3.59075e12i −0.0569227 0.0985930i
\(123\) 3.15989e13 + 5.47309e13i 0.822789 + 1.42511i
\(124\) 1.25626e13 2.17590e13i 0.310339 0.537524i
\(125\) 3.20908e13 0.752430
\(126\) 0 0
\(127\) 1.02773e12 0.0217347 0.0108674 0.999941i \(-0.496541\pi\)
0.0108674 + 0.999941i \(0.496541\pi\)
\(128\) 2.19902e12 3.80882e12i 0.0441942 0.0765466i
\(129\) −5.54813e13 9.60965e13i −1.06002 1.83601i
\(130\) 2.53068e12 + 4.38327e12i 0.0459839 + 0.0796464i
\(131\) −3.08691e13 + 5.34668e13i −0.533654 + 0.924317i 0.465573 + 0.885010i \(0.345848\pi\)
−0.999227 + 0.0393070i \(0.987485\pi\)
\(132\) 2.62193e13 0.431410
\(133\) 0 0
\(134\) 2.65234e13 0.395774
\(135\) 1.02662e13 1.77817e13i 0.145963 0.252815i
\(136\) 5.20497e12 + 9.01527e12i 0.0705367 + 0.122173i
\(137\) 6.61761e13 + 1.14620e14i 0.855102 + 1.48108i 0.876551 + 0.481310i \(0.159839\pi\)
−0.0214489 + 0.999770i \(0.506828\pi\)
\(138\) −3.60730e13 + 6.24802e13i −0.444598 + 0.770067i
\(139\) 1.66284e14 1.95548 0.977742 0.209810i \(-0.0672845\pi\)
0.977742 + 0.209810i \(0.0672845\pi\)
\(140\) 0 0
\(141\) 1.20545e14 1.29188
\(142\) −2.04195e13 + 3.53676e13i −0.209012 + 0.362019i
\(143\) −1.18034e13 2.04441e13i −0.115431 0.199932i
\(144\) −5.34221e12 9.25298e12i −0.0499304 0.0864819i
\(145\) −1.76837e13 + 3.06290e13i −0.158009 + 0.273679i
\(146\) 3.75038e13 0.320465
\(147\) 0 0
\(148\) −7.80220e13 −0.610261
\(149\) −8.54482e13 + 1.48001e14i −0.639723 + 1.10803i 0.345770 + 0.938319i \(0.387618\pi\)
−0.985493 + 0.169714i \(0.945716\pi\)
\(150\) 4.84964e13 + 8.39982e13i 0.347629 + 0.602111i
\(151\) −1.34805e14 2.33490e14i −0.925458 1.60294i −0.790823 0.612045i \(-0.790347\pi\)
−0.134635 0.990895i \(-0.542986\pi\)
\(152\) −5.90124e12 + 1.02212e13i −0.0388115 + 0.0672234i
\(153\) 2.52894e13 0.159384
\(154\) 0 0
\(155\) 8.80630e13 0.510079
\(156\) −1.68515e13 + 2.91876e13i −0.0936112 + 0.162139i
\(157\) −2.65409e13 4.59702e13i −0.141439 0.244979i 0.786600 0.617463i \(-0.211839\pi\)
−0.928039 + 0.372484i \(0.878506\pi\)
\(158\) 7.86834e13 + 1.36284e14i 0.402358 + 0.696904i
\(159\) −1.65113e14 + 2.85984e14i −0.810400 + 1.40365i
\(160\) 1.54151e13 0.0726382
\(161\) 0 0
\(162\) 2.01704e14 0.876733
\(163\) −1.25923e14 + 2.18105e14i −0.525878 + 0.910847i 0.473668 + 0.880704i \(0.342930\pi\)
−0.999546 + 0.0301433i \(0.990404\pi\)
\(164\) −8.66495e13 1.50081e14i −0.347761 0.602340i
\(165\) 4.59490e13 + 7.95860e13i 0.177268 + 0.307037i
\(166\) −1.06277e14 + 1.84076e14i −0.394216 + 0.682803i
\(167\) 5.21452e12 0.0186019 0.00930095 0.999957i \(-0.497039\pi\)
0.00930095 + 0.999957i \(0.497039\pi\)
\(168\) 0 0
\(169\) −2.72530e14 −0.899811
\(170\) −1.82433e13 + 3.15983e13i −0.0579676 + 0.100403i
\(171\) 1.43362e13 + 2.48310e13i 0.0438490 + 0.0759487i
\(172\) 1.52139e14 + 2.63513e14i 0.448029 + 0.776009i
\(173\) 1.31565e14 2.27877e14i 0.373113 0.646251i −0.616929 0.787019i \(-0.711624\pi\)
0.990043 + 0.140767i \(0.0449569\pi\)
\(174\) −2.35507e14 −0.643329
\(175\) 0 0
\(176\) −7.18977e13 −0.182340
\(177\) −3.43388e14 + 5.94766e14i −0.839381 + 1.45385i
\(178\) 8.90899e13 + 1.54308e14i 0.209941 + 0.363629i
\(179\) 1.81035e14 + 3.13562e14i 0.411357 + 0.712490i 0.995038 0.0994921i \(-0.0317218\pi\)
−0.583682 + 0.811982i \(0.698388\pi\)
\(180\) 1.87243e13 3.24315e13i 0.0410332 0.0710715i
\(181\) 6.76438e14 1.42994 0.714969 0.699156i \(-0.246441\pi\)
0.714969 + 0.699156i \(0.246441\pi\)
\(182\) 0 0
\(183\) 9.67699e13 0.190462
\(184\) 9.89182e13 1.71331e14i 0.187914 0.325477i
\(185\) −1.36733e14 2.36828e14i −0.250759 0.434327i
\(186\) 2.93200e14 + 5.07837e14i 0.519194 + 0.899270i
\(187\) 8.50890e13 1.47378e14i 0.145513 0.252037i
\(188\) −3.30554e14 −0.546030
\(189\) 0 0
\(190\) −4.13674e13 −0.0637911
\(191\) 3.80180e14 6.58492e14i 0.566595 0.981372i −0.430304 0.902684i \(-0.641594\pi\)
0.996899 0.0786877i \(-0.0250730\pi\)
\(192\) 5.13234e13 + 8.88948e13i 0.0739363 + 0.128061i
\(193\) 3.21102e12 + 5.56164e12i 0.00447219 + 0.00774605i 0.868253 0.496122i \(-0.165243\pi\)
−0.863781 + 0.503868i \(0.831910\pi\)
\(194\) 2.49749e14 4.32578e14i 0.336351 0.582577i
\(195\) −1.18128e14 −0.153861
\(196\) 0 0
\(197\) 4.19711e14 0.511588 0.255794 0.966731i \(-0.417663\pi\)
0.255794 + 0.966731i \(0.417663\pi\)
\(198\) −8.73325e13 + 1.51264e14i −0.103004 + 0.178407i
\(199\) 7.53847e14 + 1.30570e15i 0.860475 + 1.49039i 0.871471 + 0.490447i \(0.163166\pi\)
−0.0109964 + 0.999940i \(0.503500\pi\)
\(200\) −1.32985e14 2.30337e14i −0.146929 0.254489i
\(201\) −3.09517e14 + 5.36099e14i −0.331062 + 0.573417i
\(202\) 8.42631e14 0.872677
\(203\) 0 0
\(204\) −2.42960e14 −0.236014
\(205\) 3.03705e14 5.26032e14i 0.285793 0.495008i
\(206\) 5.66012e14 + 9.80361e14i 0.516046 + 0.893818i
\(207\) −2.40307e14 4.16225e14i −0.212305 0.367723i
\(208\) 4.62096e13 8.00373e13i 0.0395658 0.0685300i
\(209\) 1.92943e14 0.160132
\(210\) 0 0
\(211\) −9.49543e14 −0.740762 −0.370381 0.928880i \(-0.620773\pi\)
−0.370381 + 0.928880i \(0.620773\pi\)
\(212\) 4.52767e14 7.84215e14i 0.342525 0.593270i
\(213\) −4.76575e14 8.25452e14i −0.349674 0.605654i
\(214\) −4.62771e14 8.01543e14i −0.329364 0.570476i
\(215\) −5.33245e14 + 9.23607e14i −0.368194 + 0.637730i
\(216\) −3.74918e14 −0.251181
\(217\) 0 0
\(218\) 1.01963e15 0.643392
\(219\) −4.37654e14 + 7.58038e14i −0.268067 + 0.464306i
\(220\) −1.26000e14 2.18238e14i −0.0749243 0.129773i
\(221\) 1.09376e14 + 1.89444e14i 0.0631496 + 0.109378i
\(222\) 9.10485e14 1.57701e15i 0.510479 0.884176i
\(223\) −6.07949e14 −0.331044 −0.165522 0.986206i \(-0.552931\pi\)
−0.165522 + 0.986206i \(0.552931\pi\)
\(224\) 0 0
\(225\) −6.46137e14 −0.332000
\(226\) 1.55803e14 2.69859e14i 0.0777806 0.134720i
\(227\) −1.39309e15 2.41290e15i −0.675788 1.17050i −0.976238 0.216702i \(-0.930470\pi\)
0.300450 0.953798i \(-0.402863\pi\)
\(228\) −1.37730e14 2.38556e14i −0.0649311 0.112464i
\(229\) 5.67556e14 9.83036e14i 0.260063 0.450442i −0.706196 0.708017i \(-0.749590\pi\)
0.966258 + 0.257575i \(0.0829235\pi\)
\(230\) 6.93412e14 0.308859
\(231\) 0 0
\(232\) 6.45799e14 0.271910
\(233\) 1.01995e15 1.76660e15i 0.417604 0.723312i −0.578094 0.815970i \(-0.696203\pi\)
0.995698 + 0.0926588i \(0.0295366\pi\)
\(234\) −1.12259e14 1.94439e14i −0.0447013 0.0774249i
\(235\) −5.79292e14 1.00336e15i −0.224366 0.388613i
\(236\) 9.41629e14 1.63095e15i 0.354774 0.614487i
\(237\) −3.67281e15 −1.34628
\(238\) 0 0
\(239\) −3.57648e15 −1.24128 −0.620639 0.784096i \(-0.713127\pi\)
−0.620639 + 0.784096i \(0.713127\pi\)
\(240\) −1.79888e14 + 3.11574e14i −0.0607614 + 0.105242i
\(241\) −9.08192e14 1.57304e15i −0.298584 0.517163i 0.677228 0.735773i \(-0.263181\pi\)
−0.975812 + 0.218610i \(0.929848\pi\)
\(242\) −5.17048e14 8.95553e14i −0.165474 0.286610i
\(243\) −1.21371e15 + 2.10220e15i −0.378158 + 0.654989i
\(244\) −2.65359e14 −0.0805009
\(245\) 0 0
\(246\) 4.04466e15 1.16360
\(247\) −1.24007e14 + 2.14786e14i −0.0347468 + 0.0601833i
\(248\) −8.04003e14 1.39257e15i −0.219443 0.380087i
\(249\) −2.48041e15 4.29619e15i −0.659519 1.14232i
\(250\) 1.02691e15 1.77866e15i 0.266024 0.460767i
\(251\) −5.30330e15 −1.33865 −0.669325 0.742970i \(-0.733417\pi\)
−0.669325 + 0.742970i \(0.733417\pi\)
\(252\) 0 0
\(253\) −3.23416e15 −0.775314
\(254\) 3.28873e13 5.69625e13i 0.00768439 0.0133098i
\(255\) −4.25784e14 7.37479e14i −0.0969791 0.167973i
\(256\) −1.40737e14 2.43764e14i −0.0312500 0.0541266i
\(257\) −1.07805e15 + 1.86724e15i −0.233385 + 0.404235i −0.958802 0.284074i \(-0.908314\pi\)
0.725417 + 0.688310i \(0.241647\pi\)
\(258\) −7.10161e15 −1.49909
\(259\) 0 0
\(260\) 3.23927e14 0.0650310
\(261\) 7.84437e14 1.35869e15i 0.153601 0.266045i
\(262\) 1.97562e15 + 3.42188e15i 0.377351 + 0.653591i
\(263\) −2.88067e15 4.98946e15i −0.536761 0.929697i −0.999076 0.0429812i \(-0.986314\pi\)
0.462315 0.886716i \(-0.347019\pi\)
\(264\) 8.39017e14 1.45322e15i 0.152526 0.264184i
\(265\) 3.17388e15 0.562979
\(266\) 0 0
\(267\) −4.15857e15 −0.702459
\(268\) 8.48748e14 1.47007e15i 0.139927 0.242361i
\(269\) 4.23859e15 + 7.34146e15i 0.682074 + 1.18139i 0.974347 + 0.225052i \(0.0722553\pi\)
−0.292272 + 0.956335i \(0.594411\pi\)
\(270\) −6.57040e14 1.13803e15i −0.103211 0.178767i
\(271\) −4.24299e14 + 7.34908e14i −0.0650687 + 0.112702i −0.896724 0.442589i \(-0.854060\pi\)
0.831656 + 0.555292i \(0.187393\pi\)
\(272\) 6.66236e14 0.0997540
\(273\) 0 0
\(274\) 8.47055e15 1.20930
\(275\) −2.17400e15 + 3.76547e15i −0.303107 + 0.524997i
\(276\) 2.30867e15 + 3.99873e15i 0.314378 + 0.544519i
\(277\) −3.47520e15 6.01923e15i −0.462234 0.800613i 0.536838 0.843685i \(-0.319619\pi\)
−0.999072 + 0.0430726i \(0.986285\pi\)
\(278\) 5.32109e15 9.21640e15i 0.691368 1.19748i
\(279\) −3.90642e15 −0.495851
\(280\) 0 0
\(281\) −1.13665e15 −0.137732 −0.0688661 0.997626i \(-0.521938\pi\)
−0.0688661 + 0.997626i \(0.521938\pi\)
\(282\) 3.85743e15 6.68126e15i 0.456750 0.791115i
\(283\) −5.46610e15 9.46756e15i −0.632508 1.09554i −0.987037 0.160491i \(-0.948692\pi\)
0.354530 0.935045i \(-0.384641\pi\)
\(284\) 1.30685e15 + 2.26353e15i 0.147794 + 0.255986i
\(285\) 4.82741e14 8.36133e14i 0.0533609 0.0924237i
\(286\) −1.51083e15 −0.163244
\(287\) 0 0
\(288\) −6.83803e14 −0.0706122
\(289\) 4.16382e15 7.21194e15i 0.420393 0.728142i
\(290\) 1.13176e15 + 1.96026e15i 0.111729 + 0.193520i
\(291\) 5.82895e15 + 1.00960e16i 0.562711 + 0.974644i
\(292\) 1.20012e15 2.07867e15i 0.113302 0.196244i
\(293\) 1.63957e15 0.151388 0.0756940 0.997131i \(-0.475883\pi\)
0.0756940 + 0.997131i \(0.475883\pi\)
\(294\) 0 0
\(295\) 6.60078e15 0.583112
\(296\) −2.49670e15 + 4.32442e15i −0.215760 + 0.373707i
\(297\) 3.06451e15 + 5.30789e15i 0.259086 + 0.448751i
\(298\) 5.46868e15 + 9.47204e15i 0.452352 + 0.783497i
\(299\) 2.07863e15 3.60030e15i 0.168235 0.291391i
\(300\) 6.20754e15 0.491622
\(301\) 0 0
\(302\) −1.72551e16 −1.30880
\(303\) −9.83316e15 + 1.70315e16i −0.729988 + 1.26438i
\(304\) 3.77679e14 + 6.54160e14i 0.0274438 + 0.0475341i
\(305\) −4.65040e14 8.05472e14i −0.0330781 0.0572930i
\(306\) 8.09262e14 1.40168e15i 0.0563508 0.0976024i
\(307\) −5.69931e15 −0.388528 −0.194264 0.980949i \(-0.562232\pi\)
−0.194264 + 0.980949i \(0.562232\pi\)
\(308\) 0 0
\(309\) −2.64205e16 −1.72668
\(310\) 2.81801e15 4.88094e15i 0.180340 0.312358i
\(311\) −4.65552e15 8.06360e15i −0.291760 0.505343i 0.682466 0.730917i \(-0.260907\pi\)
−0.974226 + 0.225574i \(0.927574\pi\)
\(312\) 1.07849e15 + 1.86801e15i 0.0661931 + 0.114650i
\(313\) −2.82191e15 + 4.88770e15i −0.169631 + 0.293810i −0.938290 0.345849i \(-0.887591\pi\)
0.768659 + 0.639659i \(0.220924\pi\)
\(314\) −3.39724e15 −0.200024
\(315\) 0 0
\(316\) 1.00715e16 0.569019
\(317\) 6.10586e15 1.05757e16i 0.337957 0.585359i −0.646091 0.763260i \(-0.723597\pi\)
0.984048 + 0.177901i \(0.0569308\pi\)
\(318\) 1.05672e16 + 1.83030e16i 0.573039 + 0.992533i
\(319\) −5.27864e15 9.14288e15i −0.280468 0.485784i
\(320\) 4.93282e14 8.54389e14i 0.0256815 0.0444817i
\(321\) 2.16014e16 1.10204
\(322\) 0 0
\(323\) −1.78789e15 −0.0876043
\(324\) 6.45454e15 1.11796e16i 0.309972 0.536887i
\(325\) −2.79451e15 4.84023e15i −0.131542 0.227837i
\(326\) 8.05906e15 + 1.39587e16i 0.371852 + 0.644066i
\(327\) −1.18987e16 + 2.06091e16i −0.538193 + 0.932178i
\(328\) −1.10911e16 −0.491808
\(329\) 0 0
\(330\) 5.88147e15 0.250695
\(331\) −6.64365e15 + 1.15071e16i −0.277667 + 0.480934i −0.970805 0.239872i \(-0.922895\pi\)
0.693137 + 0.720806i \(0.256228\pi\)
\(332\) 6.80170e15 + 1.17809e16i 0.278753 + 0.482815i
\(333\) 6.06538e15 + 1.05055e16i 0.243764 + 0.422212i
\(334\) 1.66865e14 2.89018e14i 0.00657676 0.0113913i
\(335\) 5.94968e15 0.229987
\(336\) 0 0
\(337\) 2.83215e16 1.05323 0.526614 0.850105i \(-0.323461\pi\)
0.526614 + 0.850105i \(0.323461\pi\)
\(338\) −8.72097e15 + 1.51052e16i −0.318131 + 0.551019i
\(339\) 3.63632e15 + 6.29829e15i 0.130126 + 0.225385i
\(340\) 1.16757e15 + 2.02229e15i 0.0409893 + 0.0709956i
\(341\) −1.31436e16 + 2.27653e16i −0.452699 + 0.784098i
\(342\) 1.83504e15 0.0620118
\(343\) 0 0
\(344\) 1.94738e16 0.633609
\(345\) −8.09184e15 + 1.40155e16i −0.258359 + 0.447490i
\(346\) −8.42016e15 1.45841e16i −0.263831 0.456969i
\(347\) −2.42080e16 4.19294e16i −0.744417 1.28937i −0.950467 0.310827i \(-0.899394\pi\)
0.206049 0.978542i \(-0.433939\pi\)
\(348\) −7.53621e15 + 1.30531e16i −0.227451 + 0.393957i
\(349\) 3.92608e16 1.16304 0.581519 0.813533i \(-0.302459\pi\)
0.581519 + 0.813533i \(0.302459\pi\)
\(350\) 0 0
\(351\) −7.87840e15 −0.224875
\(352\) −2.30073e15 + 3.98497e15i −0.0644670 + 0.111660i
\(353\) −1.09539e16 1.89728e16i −0.301325 0.521909i 0.675112 0.737716i \(-0.264095\pi\)
−0.976436 + 0.215806i \(0.930762\pi\)
\(354\) 2.19769e16 + 3.80650e16i 0.593532 + 1.02803i
\(355\) −4.58048e15 + 7.93362e15i −0.121458 + 0.210372i
\(356\) 1.14035e16 0.296902
\(357\) 0 0
\(358\) 2.31725e16 0.581746
\(359\) −2.51750e16 + 4.36043e16i −0.620662 + 1.07502i 0.368701 + 0.929548i \(0.379803\pi\)
−0.989363 + 0.145470i \(0.953531\pi\)
\(360\) −1.19836e15 2.07562e15i −0.0290148 0.0502552i
\(361\) 2.00130e16 + 3.46635e16i 0.475899 + 0.824281i
\(362\) 2.16460e16 3.74920e16i 0.505559 0.875655i
\(363\) 2.41350e16 0.553673
\(364\) 0 0
\(365\) 8.41279e15 0.186224
\(366\) 3.09664e15 5.36353e15i 0.0673385 0.116634i
\(367\) −4.30705e16 7.46002e16i −0.920132 1.59372i −0.799209 0.601053i \(-0.794748\pi\)
−0.120923 0.992662i \(-0.538585\pi\)
\(368\) −6.33076e15 1.09652e16i −0.132876 0.230147i
\(369\) −1.34722e16 + 2.33345e16i −0.277821 + 0.481201i
\(370\) −1.75018e16 −0.354626
\(371\) 0 0
\(372\) 3.75296e16 0.734251
\(373\) −1.65426e16 + 2.86526e16i −0.318051 + 0.550880i −0.980081 0.198597i \(-0.936362\pi\)
0.662030 + 0.749477i \(0.269695\pi\)
\(374\) −5.44569e15 9.43222e15i −0.102893 0.178217i
\(375\) 2.39672e16 + 4.15124e16i 0.445055 + 0.770858i
\(376\) −1.05777e16 + 1.83212e16i −0.193051 + 0.334373i
\(377\) 1.35706e16 0.243434
\(378\) 0 0
\(379\) 2.13699e16 0.370380 0.185190 0.982703i \(-0.440710\pi\)
0.185190 + 0.982703i \(0.440710\pi\)
\(380\) −1.32376e15 + 2.29282e15i −0.0225536 + 0.0390639i
\(381\) 7.67564e14 + 1.32946e15i 0.0128559 + 0.0222670i
\(382\) −2.43315e16 4.21435e16i −0.400643 0.693935i
\(383\) −1.11443e16 + 1.93025e16i −0.180410 + 0.312479i −0.942020 0.335556i \(-0.891076\pi\)
0.761610 + 0.648035i \(0.224409\pi\)
\(384\) 6.56940e15 0.104562
\(385\) 0 0
\(386\) 4.11010e14 0.00632463
\(387\) 2.36544e16 4.09706e16i 0.357924 0.619943i
\(388\) −1.59840e16 2.76850e16i −0.237836 0.411944i
\(389\) 1.09136e16 + 1.89028e16i 0.159696 + 0.276602i 0.934759 0.355282i \(-0.115615\pi\)
−0.775063 + 0.631884i \(0.782282\pi\)
\(390\) −3.78010e15 + 6.54732e15i −0.0543980 + 0.0942201i
\(391\) 2.99691e16 0.424156
\(392\) 0 0
\(393\) −9.22188e16 −1.26261
\(394\) 1.34308e16 2.32628e16i 0.180874 0.313282i
\(395\) 1.76502e16 + 3.05710e16i 0.233812 + 0.404975i
\(396\) 5.58928e15 + 9.68092e15i 0.0728345 + 0.126153i
\(397\) 1.31629e16 2.27988e16i 0.168738 0.292263i −0.769238 0.638962i \(-0.779364\pi\)
0.937977 + 0.346699i \(0.112697\pi\)
\(398\) 9.64924e16 1.21690
\(399\) 0 0
\(400\) −1.70221e16 −0.207789
\(401\) 8.00434e16 1.38639e17i 0.961362 1.66513i 0.242276 0.970207i \(-0.422106\pi\)
0.719086 0.694921i \(-0.244561\pi\)
\(402\) 1.98091e16 + 3.43103e16i 0.234097 + 0.405467i
\(403\) −1.68951e16 2.92631e16i −0.196461 0.340281i
\(404\) 2.69642e16 4.67033e16i 0.308538 0.534403i
\(405\) 4.52460e16 0.509475
\(406\) 0 0
\(407\) 8.16304e16 0.890202
\(408\) −7.77470e15 + 1.34662e16i −0.0834436 + 0.144528i
\(409\) 9.81791e15 + 1.70051e16i 0.103709 + 0.179630i 0.913210 0.407489i \(-0.133596\pi\)
−0.809501 + 0.587119i \(0.800262\pi\)
\(410\) −1.94371e16 3.36660e16i −0.202086 0.350023i
\(411\) −9.88478e16 + 1.71209e17i −1.01157 + 1.75209i
\(412\) 7.24495e16 0.729799
\(413\) 0 0
\(414\) −3.07593e16 −0.300244
\(415\) −2.38398e16 + 4.12917e16i −0.229081 + 0.396781i
\(416\) −2.95741e15 5.12239e15i −0.0279773 0.0484580i
\(417\) 1.24190e17 + 2.15103e17i 1.15665 + 2.00338i
\(418\) 6.17417e15 1.06940e16i 0.0566151 0.0980603i
\(419\) −1.22382e17 −1.10491 −0.552454 0.833544i \(-0.686308\pi\)
−0.552454 + 0.833544i \(0.686308\pi\)
\(420\) 0 0
\(421\) −2.43087e16 −0.212778 −0.106389 0.994325i \(-0.533929\pi\)
−0.106389 + 0.994325i \(0.533929\pi\)
\(422\) −3.03854e16 + 5.26290e16i −0.261899 + 0.453622i
\(423\) 2.56971e16 + 4.45086e16i 0.218108 + 0.377774i
\(424\) −2.89771e16 5.01898e16i −0.242201 0.419505i
\(425\) 2.01452e16 3.48925e16i 0.165823 0.287213i
\(426\) −6.10016e16 −0.494514
\(427\) 0 0
\(428\) −5.92347e16 −0.465791
\(429\) 1.76308e16 3.05375e16i 0.136553 0.236516i
\(430\) 3.41277e16 + 5.91108e16i 0.260352 + 0.450943i
\(431\) −6.14438e16 1.06424e17i −0.461717 0.799717i 0.537330 0.843372i \(-0.319433\pi\)
−0.999047 + 0.0436554i \(0.986100\pi\)
\(432\) −1.19974e16 + 2.07801e16i −0.0888059 + 0.153816i
\(433\) 1.41055e17 1.02853 0.514267 0.857630i \(-0.328064\pi\)
0.514267 + 0.857630i \(0.328064\pi\)
\(434\) 0 0
\(435\) −5.28285e16 −0.373842
\(436\) 3.26282e16 5.65136e16i 0.227473 0.393995i
\(437\) 1.69891e16 + 2.94259e16i 0.116692 + 0.202116i
\(438\) 2.80098e16 + 4.85145e16i 0.189552 + 0.328314i
\(439\) 7.34941e16 1.27296e17i 0.490042 0.848777i −0.509893 0.860238i \(-0.670315\pi\)
0.999934 + 0.0114609i \(0.00364820\pi\)
\(440\) −1.61280e16 −0.105959
\(441\) 0 0
\(442\) 1.40001e16 0.0893070
\(443\) −9.34433e16 + 1.61849e17i −0.587386 + 1.01738i 0.407187 + 0.913345i \(0.366510\pi\)
−0.994573 + 0.104038i \(0.966824\pi\)
\(444\) −5.82710e16 1.00928e17i −0.360964 0.625207i
\(445\) 1.99845e16 + 3.46142e16i 0.121998 + 0.211307i
\(446\) −1.94544e16 + 3.36959e16i −0.117042 + 0.202722i
\(447\) −2.55269e17 −1.51356
\(448\) 0 0
\(449\) 2.15477e17 1.24108 0.620540 0.784175i \(-0.286913\pi\)
0.620540 + 0.784175i \(0.286913\pi\)
\(450\) −2.06764e16 + 3.58125e16i −0.117380 + 0.203308i
\(451\) 9.06570e16 + 1.57022e17i 0.507287 + 0.878647i
\(452\) −9.97141e15 1.72710e16i −0.0549992 0.0952614i
\(453\) 2.01360e17 3.48765e17i 1.09480 1.89625i
\(454\) −1.78315e17 −0.955709
\(455\) 0 0
\(456\) −1.76295e16 −0.0918264
\(457\) 1.91954e16 3.32474e16i 0.0985694 0.170727i −0.812523 0.582929i \(-0.801907\pi\)
0.911093 + 0.412201i \(0.135240\pi\)
\(458\) −3.63236e16 6.29143e16i −0.183892 0.318510i
\(459\) −2.83971e16 4.91853e16i −0.141740 0.245501i
\(460\) 2.21892e16 3.84328e16i 0.109198 0.189137i
\(461\) −3.15284e17 −1.52984 −0.764921 0.644124i \(-0.777222\pi\)
−0.764921 + 0.644124i \(0.777222\pi\)
\(462\) 0 0
\(463\) −2.28642e17 −1.07865 −0.539323 0.842099i \(-0.681320\pi\)
−0.539323 + 0.842099i \(0.681320\pi\)
\(464\) 2.06656e16 3.57938e16i 0.0961347 0.166510i
\(465\) 6.57702e16 + 1.13917e17i 0.301707 + 0.522571i
\(466\) −6.52767e16 1.13063e17i −0.295291 0.511458i
\(467\) 1.06511e17 1.84482e17i 0.475153 0.822989i −0.524442 0.851446i \(-0.675726\pi\)
0.999595 + 0.0284570i \(0.00905938\pi\)
\(468\) −1.43692e16 −0.0632171
\(469\) 0 0
\(470\) −7.41494e16 −0.317301
\(471\) 3.96444e16 6.86661e16i 0.167319 0.289805i
\(472\) −6.02643e16 1.04381e17i −0.250863 0.434508i
\(473\) −1.59175e17 2.75700e17i −0.653550 1.13198i
\(474\) −1.17530e17 + 2.03568e17i −0.475981 + 0.824424i
\(475\) 4.56801e16 0.182481
\(476\) 0 0
\(477\) −1.40791e17 −0.547276
\(478\) −1.14447e17 + 1.98228e17i −0.438858 + 0.760124i
\(479\) 1.57833e16 + 2.73374e16i 0.0597058 + 0.103413i 0.894333 0.447401i \(-0.147650\pi\)
−0.834628 + 0.550815i \(0.814317\pi\)
\(480\) 1.15128e16 + 1.99408e16i 0.0429648 + 0.0744172i
\(481\) −5.24649e16 + 9.08719e16i −0.193164 + 0.334570i
\(482\) −1.16249e17 −0.422262
\(483\) 0 0
\(484\) −6.61821e16 −0.234016
\(485\) 5.60234e16 9.70354e16i 0.195456 0.338539i
\(486\) 7.76773e16 + 1.34541e17i 0.267398 + 0.463147i
\(487\) −2.71494e17 4.70241e17i −0.922193 1.59729i −0.796014 0.605278i \(-0.793062\pi\)
−0.126179 0.992008i \(-0.540271\pi\)
\(488\) −8.49150e15 + 1.47077e16i −0.0284614 + 0.0492965i
\(489\) −3.76184e17 −1.24421
\(490\) 0 0
\(491\) 2.87085e17 0.924658 0.462329 0.886708i \(-0.347014\pi\)
0.462329 + 0.886708i \(0.347014\pi\)
\(492\) 1.29429e17 2.24178e17i 0.411395 0.712556i
\(493\) 4.89143e16 + 8.47220e16i 0.153437 + 0.265761i
\(494\) 7.93643e15 + 1.37463e16i 0.0245697 + 0.0425560i
\(495\) −1.95903e16 + 3.39314e16i −0.0598560 + 0.103674i
\(496\) −1.02912e17 −0.310339
\(497\) 0 0
\(498\) −3.17492e17 −0.932701
\(499\) −2.64712e15 + 4.58495e15i −0.00767575 + 0.0132948i −0.869838 0.493338i \(-0.835777\pi\)
0.862162 + 0.506633i \(0.169110\pi\)
\(500\) −6.57221e16 1.13834e17i −0.188108 0.325812i
\(501\) 3.89449e15 + 6.74545e15i 0.0110028 + 0.0190575i
\(502\) −1.69706e17 + 2.93939e17i −0.473284 + 0.819753i
\(503\) −9.65557e16 −0.265819 −0.132909 0.991128i \(-0.542432\pi\)
−0.132909 + 0.991128i \(0.542432\pi\)
\(504\) 0 0
\(505\) 1.89018e17 0.507118
\(506\) −1.03493e17 + 1.79255e17i −0.274115 + 0.474781i
\(507\) −2.03540e17 3.52542e17i −0.532229 0.921848i
\(508\) −2.10479e15 3.64560e15i −0.00543369 0.00941142i
\(509\) 2.70435e17 4.68407e17i 0.689283 1.19387i −0.282787 0.959183i \(-0.591259\pi\)
0.972070 0.234691i \(-0.0754077\pi\)
\(510\) −5.45003e16 −0.137149
\(511\) 0 0
\(512\) −1.80144e16 −0.0441942
\(513\) 3.21958e16 5.57648e16i 0.0779896 0.135082i
\(514\) 6.89952e16 + 1.19503e17i 0.165028 + 0.285838i
\(515\) 1.26967e17 + 2.19913e17i 0.299877 + 0.519403i
\(516\) −2.27252e17 + 3.93611e17i −0.530010 + 0.918004i
\(517\) 3.45842e17 0.796506
\(518\) 0 0
\(519\) 3.93040e17 0.882772
\(520\) 1.03657e16 1.79539e16i 0.0229919 0.0398232i
\(521\) 6.51595e16 + 1.12860e17i 0.142736 + 0.247225i 0.928526 0.371268i \(-0.121077\pi\)
−0.785790 + 0.618493i \(0.787743\pi\)
\(522\) −5.02040e16 8.69559e16i −0.108613 0.188122i
\(523\) 4.34304e17 7.52237e17i 0.927969 1.60729i 0.141253 0.989974i \(-0.454887\pi\)
0.786716 0.617315i \(-0.211780\pi\)
\(524\) 2.52879e17 0.533654
\(525\) 0 0
\(526\) −3.68725e17 −0.759094
\(527\) 1.21794e17 2.10954e17i 0.247661 0.428961i
\(528\) −5.36971e16 9.30061e16i −0.107853 0.186806i
\(529\) −3.27570e16 5.67368e16i −0.0649894 0.112565i
\(530\) 1.01564e17 1.75914e17i 0.199043 0.344753i
\(531\) −2.92807e17 −0.566848
\(532\) 0 0
\(533\) −2.33065e17 −0.440302
\(534\) −1.33074e17 + 2.30491e17i −0.248357 + 0.430166i
\(535\) −1.03808e17 1.79801e17i −0.191396 0.331507i
\(536\) −5.43198e16 9.40847e16i −0.0989435 0.171375i
\(537\) −2.70414e17 + 4.68370e17i −0.486627 + 0.842862i
\(538\) 5.42540e17 0.964599
\(539\) 0 0
\(540\) −8.41011e16 −0.145963
\(541\) 2.99150e17 5.18143e17i 0.512988 0.888520i −0.486899 0.873458i \(-0.661872\pi\)
0.999887 0.0150622i \(-0.00479462\pi\)
\(542\) 2.71552e16 + 4.70341e16i 0.0460105 + 0.0796925i
\(543\) 5.05200e17 + 8.75033e17i 0.845794 + 1.46496i
\(544\) 2.13196e16 3.69265e16i 0.0352684 0.0610866i
\(545\) 2.28722e17 0.373879
\(546\) 0 0
\(547\) 6.94479e17 1.10851 0.554257 0.832345i \(-0.313002\pi\)
0.554257 + 0.832345i \(0.313002\pi\)
\(548\) 2.71057e17 4.69485e17i 0.427551 0.740540i
\(549\) 2.06289e16 + 3.57303e16i 0.0321555 + 0.0556950i
\(550\) 1.39136e17 + 2.40990e17i 0.214329 + 0.371229i
\(551\) −5.54576e16 + 9.60553e16i −0.0844258 + 0.146230i
\(552\) 2.95510e17 0.444598
\(553\) 0 0
\(554\) −4.44826e17 −0.653698
\(555\) 2.04239e17 3.53752e17i 0.296643 0.513800i
\(556\) −3.40550e17 5.89849e17i −0.488871 0.846750i
\(557\) −4.32451e17 7.49027e17i −0.613590 1.06277i −0.990630 0.136572i \(-0.956391\pi\)
0.377040 0.926197i \(-0.376942\pi\)
\(558\) −1.25005e17 + 2.16516e17i −0.175310 + 0.303646i
\(559\) 4.09216e17 0.567252
\(560\) 0 0
\(561\) 2.54196e17 0.344279
\(562\) −3.63728e16 + 6.29995e16i −0.0486957 + 0.0843434i
\(563\) 6.04730e16 + 1.04742e17i 0.0800307 + 0.138617i 0.903263 0.429088i \(-0.141165\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(564\) −2.46875e17 4.27601e17i −0.322971 0.559403i
\(565\) 3.49496e16 6.05344e16i 0.0451988 0.0782866i
\(566\) −6.99661e17 −0.894501
\(567\) 0 0
\(568\) 1.67277e17 0.209012
\(569\) 3.13843e17 5.43592e17i 0.387688 0.671496i −0.604450 0.796643i \(-0.706607\pi\)
0.992138 + 0.125147i \(0.0399404\pi\)
\(570\) −3.08954e16 5.35125e16i −0.0377318 0.0653535i
\(571\) 6.18567e17 + 1.07139e18i 0.746882 + 1.29364i 0.949310 + 0.314340i \(0.101783\pi\)
−0.202428 + 0.979297i \(0.564883\pi\)
\(572\) −4.83467e16 + 8.37390e16i −0.0577155 + 0.0999662i
\(573\) 1.13576e18 1.34054
\(574\) 0 0
\(575\) −7.65702e17 −0.883525
\(576\) −2.18817e16 + 3.79002e16i −0.0249652 + 0.0432410i
\(577\) 4.22370e17 + 7.31566e17i 0.476486 + 0.825298i 0.999637 0.0269418i \(-0.00857688\pi\)
−0.523151 + 0.852240i \(0.675244\pi\)
\(578\) −2.66484e17 4.61564e17i −0.297263 0.514874i
\(579\) −4.79632e15 + 8.30747e15i −0.00529051 + 0.00916343i
\(580\) 1.44865e17 0.158009
\(581\) 0 0
\(582\) 7.46105e17 0.795794
\(583\) −4.73707e17 + 8.20485e17i −0.499648 + 0.865416i
\(584\) −7.68077e16 1.33035e17i −0.0801164 0.138766i
\(585\) −2.51819e16 4.36163e16i −0.0259762 0.0449920i
\(586\) 5.24663e16 9.08744e16i 0.0535237 0.0927058i
\(587\) 9.19950e17 0.928146 0.464073 0.885797i \(-0.346387\pi\)
0.464073 + 0.885797i \(0.346387\pi\)
\(588\) 0 0
\(589\) 2.76173e17 0.272541
\(590\) 2.11225e17 3.65852e17i 0.206161 0.357082i
\(591\) 3.13463e17 + 5.42934e17i 0.302599 + 0.524117i
\(592\) 1.59789e17 + 2.76763e17i 0.152565 + 0.264251i
\(593\) −3.65725e16 + 6.33454e16i −0.0345381 + 0.0598218i −0.882778 0.469791i \(-0.844329\pi\)
0.848240 + 0.529613i \(0.177663\pi\)
\(594\) 3.92258e17 0.366403
\(595\) 0 0
\(596\) 6.99991e17 0.639723
\(597\) −1.12603e18 + 1.95034e18i −1.01792 + 1.76310i
\(598\) −1.33033e17 2.30419e17i −0.118960 0.206044i
\(599\) 1.99308e17 + 3.45212e17i 0.176299 + 0.305360i 0.940610 0.339489i \(-0.110254\pi\)
−0.764311 + 0.644848i \(0.776921\pi\)
\(600\) 1.98641e17 3.44057e17i 0.173815 0.301056i
\(601\) −2.02331e18 −1.75137 −0.875686 0.482882i \(-0.839590\pi\)
−0.875686 + 0.482882i \(0.839590\pi\)
\(602\) 0 0
\(603\) −2.63924e17 −0.223572
\(604\) −5.52162e17 + 9.56373e17i −0.462729 + 0.801470i
\(605\) −1.15983e17 2.00889e17i −0.0961582 0.166551i
\(606\) 6.29322e17 + 1.09002e18i 0.516180 + 0.894049i
\(607\) −9.11136e17 + 1.57813e18i −0.739361 + 1.28061i 0.213422 + 0.976960i \(0.431539\pi\)
−0.952783 + 0.303651i \(0.901794\pi\)
\(608\) 4.83430e16 0.0388115
\(609\) 0 0
\(610\) −5.95251e16 −0.0467795
\(611\) −2.22277e17 + 3.84995e17i −0.172833 + 0.299355i
\(612\) −5.17928e16 8.97077e16i −0.0398460 0.0690153i
\(613\) 8.93380e17 + 1.54738e18i 0.680054 + 1.17789i 0.974964 + 0.222363i \(0.0713769\pi\)
−0.294910 + 0.955525i \(0.595290\pi\)
\(614\) −1.82378e17 + 3.15888e17i −0.137366 + 0.237924i
\(615\) 9.07292e17 0.676175
\(616\) 0 0
\(617\) 8.80000e17 0.642139 0.321070 0.947056i \(-0.395958\pi\)
0.321070 + 0.947056i \(0.395958\pi\)
\(618\) −8.45456e17 + 1.46437e18i −0.610472 + 1.05737i
\(619\) −4.84990e16 8.40027e16i −0.0346532 0.0600211i 0.848179 0.529710i \(-0.177699\pi\)
−0.882832 + 0.469689i \(0.844366\pi\)
\(620\) −1.80353e17 3.12380e17i −0.127520 0.220871i
\(621\) −5.39675e17 + 9.34745e17i −0.377604 + 0.654030i
\(622\) −5.95906e17 −0.412611
\(623\) 0 0
\(624\) 1.38047e17 0.0936112
\(625\) −3.88906e17 + 6.73606e17i −0.260991 + 0.452049i
\(626\) 1.80602e17 + 3.12813e17i 0.119947 + 0.207755i
\(627\) 1.44100e17 + 2.49589e17i 0.0947164 + 0.164054i
\(628\) −1.08712e17 + 1.88294e17i −0.0707193 + 0.122489i
\(629\) −7.56424e17 −0.487008
\(630\) 0 0
\(631\) −8.85605e15 −0.00558533 −0.00279267 0.999996i \(-0.500889\pi\)
−0.00279267 + 0.999996i \(0.500889\pi\)
\(632\) 3.22287e17 5.58218e17i 0.201179 0.348452i
\(633\) −7.09170e17 1.22832e18i −0.438153 0.758904i
\(634\) −3.90775e17 6.76842e17i −0.238972 0.413911i
\(635\) 7.37724e15 1.27778e16i 0.00446545 0.00773438i
\(636\) 1.35260e18 0.810400
\(637\) 0 0
\(638\) −6.75666e17 −0.396641
\(639\) 2.03187e17 3.51931e17i 0.118070 0.204504i
\(640\) −3.15700e16 5.46809e16i −0.0181596 0.0314533i
\(641\) −3.07694e17 5.32941e17i −0.175203 0.303460i 0.765029 0.643996i \(-0.222725\pi\)
−0.940232 + 0.340536i \(0.889392\pi\)
\(642\) 6.91244e17 1.19727e18i 0.389631 0.674861i
\(643\) 9.48803e17 0.529425 0.264713 0.964327i \(-0.414723\pi\)
0.264713 + 0.964327i \(0.414723\pi\)
\(644\) 0 0
\(645\) −1.59302e18 −0.871132
\(646\) −5.72126e16 + 9.90951e16i −0.0309728 + 0.0536464i
\(647\) 9.09981e16 + 1.57613e17i 0.0487702 + 0.0844725i 0.889380 0.457169i \(-0.151136\pi\)
−0.840610 + 0.541641i \(0.817803\pi\)
\(648\) −4.13090e17 7.15494e17i −0.219183 0.379637i
\(649\) −9.85178e17 + 1.70638e18i −0.517517 + 0.896365i
\(650\) −3.57697e17 −0.186028
\(651\) 0 0
\(652\) 1.03156e18 0.525878
\(653\) −1.38478e18 + 2.39851e18i −0.698947 + 1.21061i 0.269884 + 0.962893i \(0.413015\pi\)
−0.968832 + 0.247720i \(0.920319\pi\)
\(654\) 7.61515e17 + 1.31898e18i 0.380560 + 0.659149i
\(655\) 4.43169e17 + 7.67590e17i 0.219281 + 0.379805i
\(656\) −3.54916e17 + 6.14733e17i −0.173881 + 0.301170i
\(657\) −3.73186e17 −0.181030
\(658\) 0 0
\(659\) −1.98995e18 −0.946427 −0.473213 0.880948i \(-0.656906\pi\)
−0.473213 + 0.880948i \(0.656906\pi\)
\(660\) 1.88207e17 3.25984e17i 0.0886340 0.153519i
\(661\) −5.81844e17 1.00778e18i −0.271330 0.469957i 0.697873 0.716222i \(-0.254130\pi\)
−0.969203 + 0.246265i \(0.920797\pi\)
\(662\) 4.25194e17 + 7.36457e17i 0.196340 + 0.340072i
\(663\) −1.63375e17 + 2.82974e17i −0.0747047 + 0.129392i
\(664\) 8.70617e17 0.394216
\(665\) 0 0
\(666\) 7.76368e17 0.344735
\(667\) 9.29594e17 1.61010e18i 0.408767 0.708005i
\(668\) −1.06793e16 1.84972e16i −0.00465047 0.00805486i
\(669\) −4.54049e17 7.86436e17i −0.195809 0.339151i
\(670\) 1.90390e17 3.29765e17i 0.0813126 0.140837i
\(671\) 2.77632e17 0.117428
\(672\) 0 0
\(673\) 1.44542e18 0.599650 0.299825 0.953994i \(-0.403072\pi\)
0.299825 + 0.953994i \(0.403072\pi\)
\(674\) 9.06289e17 1.56974e18i 0.372372 0.644967i
\(675\) 7.25538e17 + 1.25667e18i 0.295247 + 0.511383i
\(676\) 5.58142e17 + 9.66731e17i 0.224953 + 0.389630i
\(677\) 1.90818e18 3.30507e18i 0.761716 1.31933i −0.180249 0.983621i \(-0.557690\pi\)
0.941965 0.335710i \(-0.108976\pi\)
\(678\) 4.65449e17 0.184026
\(679\) 0 0
\(680\) 1.49449e17 0.0579676
\(681\) 2.08087e18 3.60417e18i 0.799444 1.38468i
\(682\) 8.41188e17 + 1.45698e18i 0.320107 + 0.554441i
\(683\) −1.14349e17 1.98058e17i −0.0431019 0.0746547i 0.843670 0.536863i \(-0.180391\pi\)
−0.886772 + 0.462208i \(0.847057\pi\)
\(684\) 5.87211e16 1.01708e17i 0.0219245 0.0379743i
\(685\) 1.90010e18 0.702729
\(686\) 0 0
\(687\) 1.69553e18 0.615298
\(688\) 6.23162e17 1.07935e18i 0.224015 0.388005i
\(689\) −6.08915e17 1.05467e18i −0.216836 0.375571i
\(690\) 5.17878e17 + 8.96990e17i 0.182687 + 0.316423i
\(691\) −1.65297e18 + 2.86303e18i −0.577642 + 1.00051i 0.418107 + 0.908398i \(0.362694\pi\)
−0.995749 + 0.0921074i \(0.970640\pi\)
\(692\) −1.07778e18 −0.373113
\(693\) 0 0
\(694\) −3.09862e18 −1.05276
\(695\) 1.19362e18 2.06741e18i 0.401758 0.695866i
\(696\) 4.82317e17 + 8.35398e17i 0.160832 + 0.278569i
\(697\) −8.40068e17 1.45504e18i −0.277524 0.480686i
\(698\) 1.25634e18 2.17605e18i 0.411196 0.712212i
\(699\) 3.04701e18 0.988035
\(700\) 0 0
\(701\) −1.97078e18 −0.627293 −0.313647 0.949540i \(-0.601551\pi\)
−0.313647 + 0.949540i \(0.601551\pi\)
\(702\) −2.52109e17 + 4.36666e17i −0.0795055 + 0.137708i
\(703\) −4.28805e17 7.42713e17i −0.133983 0.232066i
\(704\) 1.47246e17 + 2.55038e17i 0.0455851 + 0.0789557i
\(705\) 8.65293e17 1.49873e18i 0.265420 0.459721i
\(706\) −1.40210e18 −0.426137
\(707\) 0 0
\(708\) 2.81304e18 0.839381
\(709\) −1.90872e18 + 3.30601e18i −0.564342 + 0.977470i 0.432768 + 0.901505i \(0.357537\pi\)
−0.997111 + 0.0759644i \(0.975796\pi\)
\(710\) 2.93151e17 + 5.07752e17i 0.0858839 + 0.148755i
\(711\) −7.82950e17 1.35611e18i −0.227291 0.393679i
\(712\) 3.64912e17 6.32046e17i 0.104971 0.181815i
\(713\) −4.62929e18 −1.31957
\(714\) 0 0
\(715\) −3.38908e17 −0.0948622
\(716\) 7.41520e17 1.28435e18i 0.205678 0.356245i
\(717\) −2.67111e18 4.62649e18i −0.734204 1.27168i
\(718\) 1.61120e18 + 2.79068e18i 0.438874 + 0.760152i
\(719\) 1.80548e18 3.12718e18i 0.487365 0.844141i −0.512529 0.858670i \(-0.671291\pi\)
0.999894 + 0.0145287i \(0.00462480\pi\)
\(720\) −1.53390e17 −0.0410332
\(721\) 0 0
\(722\) 2.56166e18 0.673022
\(723\) 1.35657e18 2.34966e18i 0.353219 0.611794i
\(724\) −1.38534e18 2.39949e18i −0.357484 0.619181i
\(725\) −1.24974e18 2.16462e18i −0.319613 0.553585i
\(726\) 7.72319e17 1.33769e18i 0.195753 0.339054i
\(727\) 3.60755e18 0.906230 0.453115 0.891452i \(-0.350313\pi\)
0.453115 + 0.891452i \(0.350313\pi\)
\(728\) 0 0
\(729\) 1.39886e18 0.345181
\(730\) 2.69209e17 4.66284e17i 0.0658403 0.114039i
\(731\) 1.47499e18 + 2.55476e18i 0.357541 + 0.619280i
\(732\) −1.98185e17 3.43266e17i −0.0476155 0.0824724i
\(733\) −5.46187e17 + 9.46024e17i −0.130067 + 0.225282i −0.923702 0.383112i \(-0.874852\pi\)
0.793635 + 0.608394i \(0.208186\pi\)
\(734\) −5.51302e18 −1.30126
\(735\) 0 0
\(736\) −8.10337e17 −0.187914
\(737\) −8.88001e17 + 1.53806e18i −0.204115 + 0.353538i
\(738\) 8.62218e17 + 1.49341e18i 0.196449 + 0.340260i
\(739\) −2.64348e18 4.57864e18i −0.597018 1.03407i −0.993259 0.115919i \(-0.963019\pi\)
0.396241 0.918147i \(-0.370315\pi\)
\(740\) −5.60057e17 + 9.70047e17i −0.125379 + 0.217163i
\(741\) −3.70460e17 −0.0822096
\(742\) 0 0
\(743\) −1.06272e18 −0.231736 −0.115868 0.993265i \(-0.536965\pi\)
−0.115868 + 0.993265i \(0.536965\pi\)
\(744\) 1.20095e18 2.08010e18i 0.259597 0.449635i
\(745\) 1.22673e18 + 2.12475e18i 0.262865 + 0.455295i
\(746\) 1.05873e18 + 1.83377e18i 0.224896 + 0.389531i
\(747\) 1.05752e18 1.83168e18i 0.222692 0.385714i
\(748\) −6.97049e17 −0.145513
\(749\) 0 0
\(750\) 3.06780e18 0.629403
\(751\) −4.48188e17 + 7.76285e17i −0.0911593 + 0.157892i −0.907999 0.418972i \(-0.862391\pi\)
0.816840 + 0.576864i \(0.195724\pi\)
\(752\) 6.76974e17 + 1.17255e18i 0.136507 + 0.236438i
\(753\) −3.96079e18 6.86029e18i −0.791799 1.37144i
\(754\) 4.34259e17 7.52159e17i 0.0860668 0.149072i
\(755\) −3.87063e18 −0.760549
\(756\) 0 0
\(757\) −6.71607e18 −1.29716 −0.648578 0.761148i \(-0.724636\pi\)
−0.648578 + 0.761148i \(0.724636\pi\)
\(758\) 6.83837e17 1.18444e18i 0.130949 0.226811i
\(759\) −2.41544e18 4.18367e18i −0.458591 0.794303i
\(760\) 8.47205e16 + 1.46740e17i 0.0159478 + 0.0276224i
\(761\) −3.56938e18 + 6.18234e18i −0.666181 + 1.15386i 0.312783 + 0.949825i \(0.398739\pi\)
−0.978964 + 0.204034i \(0.934595\pi\)
\(762\) 9.82481e16 0.0181810
\(763\) 0 0
\(764\) −3.11444e18 −0.566595
\(765\) 1.81533e17 3.14424e17i 0.0327458 0.0567173i
\(766\) 7.13234e17 + 1.23536e18i 0.127569 + 0.220956i
\(767\) −1.26637e18 2.19342e18i −0.224591 0.389003i
\(768\) 2.10221e17 3.64113e17i 0.0369681 0.0640307i
\(769\) −9.57731e18 −1.67002 −0.835011 0.550233i \(-0.814539\pi\)
−0.835011 + 0.550233i \(0.814539\pi\)
\(770\) 0 0
\(771\) −3.22059e18 −0.552181
\(772\) 1.31523e16 2.27805e16i 0.00223609 0.00387303i
\(773\) 1.07825e18 + 1.86758e18i 0.181783 + 0.314857i 0.942488 0.334241i \(-0.108480\pi\)
−0.760705 + 0.649098i \(0.775147\pi\)
\(774\) −1.51388e18 2.62212e18i −0.253090 0.438366i
\(775\) −3.11180e18 + 5.38979e18i −0.515882 + 0.893534i
\(776\) −2.04595e18 −0.336351
\(777\) 0 0
\(778\) 1.39694e18 0.225844
\(779\) 9.52444e17 1.64968e18i 0.152702 0.264488i
\(780\) 2.41926e17 + 4.19029e17i 0.0384652 + 0.0666237i
\(781\) −1.36729e18 2.36822e18i −0.215590 0.373413i
\(782\) 9.59012e17 1.66106e18i 0.149962 0.259741i
\(783\) −3.52333e18 −0.546389
\(784\) 0 0
\(785\) −7.62063e17 −0.116235
\(786\) −2.95100e18 + 5.11128e18i −0.446398 + 0.773185i
\(787\) −1.41242e18 2.44639e18i −0.211899 0.367020i 0.740410 0.672156i \(-0.234631\pi\)
−0.952309 + 0.305136i \(0.901298\pi\)
\(788\) −8.59569e17 1.48882e18i −0.127897 0.221524i
\(789\) 4.30288e18 7.45280e18i 0.634977 1.09981i
\(790\) 2.25922e18 0.330661
\(791\) 0 0
\(792\) 7.15428e17 0.103004
\(793\) −1.78438e17 + 3.09063e17i −0.0254807 + 0.0441338i
\(794\) −8.42427e17 1.45913e18i −0.119316 0.206661i
\(795\) 2.37042e18 + 4.10569e18i 0.332996 + 0.576767i
\(796\) 3.08776e18 5.34815e18i 0.430237 0.745193i
\(797\) −8.37611e18 −1.15761 −0.578806 0.815465i \(-0.696481\pi\)
−0.578806 + 0.815465i \(0.696481\pi\)
\(798\) 0 0
\(799\) −3.20472e18 −0.435749
\(800\) −5.44708e17 + 9.43461e17i −0.0734647 + 0.127245i
\(801\) −8.86501e17 1.53546e18i −0.118595 0.205413i
\(802\) −5.12278e18 8.87291e18i −0.679786 1.17742i
\(803\) −1.25562e18 + 2.17481e18i −0.165276 + 0.286266i
\(804\) 2.53556e18 0.331062
\(805\) 0 0
\(806\) −2.16257e18 −0.277838
\(807\) −6.33122e18 + 1.09660e19i −0.806881 + 1.39756i
\(808\) −1.72571e18 2.98901e18i −0.218169 0.377880i
\(809\) 1.08897e18 + 1.88615e18i 0.136569 + 0.236544i 0.926196 0.377043i \(-0.123059\pi\)
−0.789627 + 0.613587i \(0.789726\pi\)
\(810\) 1.44787e18 2.50779e18i 0.180127 0.311988i
\(811\) 1.05998e19 1.30817 0.654084 0.756422i \(-0.273054\pi\)
0.654084 + 0.756422i \(0.273054\pi\)
\(812\) 0 0
\(813\) −1.26756e18 −0.153950
\(814\) 2.61217e18 4.52442e18i 0.314734 0.545135i
\(815\) 1.80780e18 + 3.13120e18i 0.216085 + 0.374271i
\(816\) 4.97581e17 + 8.61836e17i 0.0590035 + 0.102197i
\(817\) −1.67230e18 + 2.89651e18i −0.196730 + 0.340747i
\(818\) 1.25669e18 0.146667
\(819\) 0 0
\(820\) −2.48795e18 −0.285793
\(821\) −5.15388e16 + 8.92679e16i −0.00587360 + 0.0101734i −0.868947 0.494905i \(-0.835203\pi\)
0.863074 + 0.505078i \(0.168536\pi\)
\(822\) 6.32626e18 + 1.09574e19i 0.715287 + 1.23891i
\(823\) 5.26006e18 + 9.11070e18i 0.590054 + 1.02200i 0.994224 + 0.107320i \(0.0342271\pi\)
−0.404170 + 0.914684i \(0.632440\pi\)
\(824\) 2.31838e18 4.01556e18i 0.258023 0.446909i
\(825\) −6.49463e18 −0.717140
\(826\) 0 0
\(827\) 1.20216e19 1.30670 0.653350 0.757056i \(-0.273363\pi\)
0.653350 + 0.757056i \(0.273363\pi\)
\(828\) −9.84299e17 + 1.70486e18i −0.106152 + 0.183861i
\(829\) 1.57256e18 + 2.72375e18i 0.168268 + 0.291449i 0.937811 0.347146i \(-0.112849\pi\)
−0.769543 + 0.638595i \(0.779516\pi\)
\(830\) 1.52575e18 + 2.64267e18i 0.161985 + 0.280566i
\(831\) 5.19094e18 8.99097e18i 0.546814 0.947109i
\(832\) −3.78549e17 −0.0395658
\(833\) 0 0
\(834\) 1.58963e19 1.63575
\(835\) 3.74308e16 6.48321e16i 0.00382180 0.00661955i
\(836\) −3.95147e17 6.84414e17i −0.0400330 0.0693391i
\(837\) 4.38646e18 + 7.59757e18i 0.440960 + 0.763765i
\(838\) −3.91622e18 + 6.78309e18i −0.390644 + 0.676615i
\(839\) −5.05894e18 −0.500734 −0.250367 0.968151i \(-0.580551\pi\)
−0.250367 + 0.968151i \(0.580551\pi\)
\(840\) 0 0
\(841\) −4.19166e18 −0.408519
\(842\) −7.77878e17 + 1.34732e18i −0.0752286 + 0.130300i
\(843\) −8.48911e17 1.47036e18i −0.0814672 0.141105i
\(844\) 1.94466e18 + 3.36826e18i 0.185190 + 0.320759i
\(845\) −1.95628e18 + 3.38837e18i −0.184868 + 0.320201i
\(846\) 3.28922e18 0.308451
\(847\) 0 0
\(848\) −3.70907e18 −0.342525
\(849\) 8.16476e18 1.41418e19i 0.748244 1.29600i
\(850\) −1.28929e18 2.23312e18i −0.117254 0.203090i
\(851\) 7.18775e18 + 1.24495e19i 0.648710 + 1.12360i
\(852\) −1.95205e18 + 3.38105e18i −0.174837 + 0.302827i
\(853\) 1.27122e19 1.12993 0.564967 0.825114i \(-0.308889\pi\)
0.564967 + 0.825114i \(0.308889\pi\)
\(854\) 0 0
\(855\) 4.11633e17 0.0360355
\(856\) −1.89551e18 + 3.28312e18i −0.164682 + 0.285238i
\(857\) 9.91400e18 + 1.71715e19i 0.854818 + 1.48059i 0.876814 + 0.480830i \(0.159664\pi\)
−0.0219964 + 0.999758i \(0.507002\pi\)
\(858\) −1.12837e18 1.95440e18i −0.0965573 0.167242i
\(859\) −3.16105e18 + 5.47510e18i −0.268458 + 0.464982i −0.968464 0.249155i \(-0.919847\pi\)
0.700006 + 0.714137i \(0.253181\pi\)
\(860\) 4.36834e18 0.368194
\(861\) 0 0
\(862\) −7.86480e18 −0.652966
\(863\) 3.01615e18 5.22413e18i 0.248532 0.430471i −0.714586 0.699547i \(-0.753385\pi\)
0.963119 + 0.269076i \(0.0867184\pi\)
\(864\) 7.67832e17 + 1.32992e18i 0.0627953 + 0.108765i
\(865\) −1.88880e18 3.27150e18i −0.153314 0.265547i
\(866\) 4.51377e18 7.81808e18i 0.363641 0.629845i
\(867\) 1.24391e19 0.994634
\(868\) 0 0
\(869\) −1.05373e19 −0.830041
\(870\) −1.69051e18 + 2.92805e18i −0.132173 + 0.228931i
\(871\) −1.14146e18 1.97707e18i −0.0885814 0.153427i
\(872\) −2.08820e18 3.61687e18i −0.160848 0.278597i
\(873\) −2.48517e18 + 4.30443e18i −0.190004 + 0.329097i
\(874\) 2.17460e18 0.165027
\(875\) 0 0
\(876\) 3.58526e18 0.268067
\(877\) 1.59022e18 2.75435e18i 0.118021 0.204419i −0.800962 0.598715i \(-0.795678\pi\)
0.918984 + 0.394296i \(0.129012\pi\)
\(878\) −4.70362e18 8.14691e18i −0.346512 0.600176i
\(879\) 1.22452e18 + 2.12093e18i 0.0895445 + 0.155096i
\(880\) −5.16096e17 + 8.93904e17i −0.0374622 + 0.0648864i
\(881\) 2.33099e19 1.67956 0.839782 0.542924i \(-0.182683\pi\)
0.839782 + 0.542924i \(0.182683\pi\)
\(882\) 0 0
\(883\) −1.95630e18 −0.138896 −0.0694482 0.997586i \(-0.522124\pi\)
−0.0694482 + 0.997586i \(0.522124\pi\)
\(884\) 4.48002e17 7.75962e17i 0.0315748 0.0546891i
\(885\) 4.92982e18 + 8.53870e18i 0.344905 + 0.597393i
\(886\) 5.98037e18 + 1.03583e19i 0.415345 + 0.719399i
\(887\) −5.03283e18 + 8.71712e18i −0.346983 + 0.600993i −0.985712 0.168439i \(-0.946127\pi\)
0.638729 + 0.769432i \(0.279461\pi\)
\(888\) −7.45869e18 −0.510479
\(889\) 0 0
\(890\) 2.55802e18 0.172532
\(891\) −6.75305e18 + 1.16966e19i −0.452163 + 0.783170i
\(892\) 1.24508e18 + 2.15654e18i 0.0827609 + 0.143346i
\(893\) −1.81671e18 3.14663e18i −0.119881 0.207640i
\(894\) −8.16862e18 + 1.41485e19i −0.535124 + 0.926862i
\(895\) 5.19803e18 0.338056
\(896\) 0 0
\(897\) 6.20974e18 0.398036
\(898\) 6.89527e18 1.19430e19i 0.438788 0.760003i
\(899\) −7.55571e18 1.30869e19i −0.477350 0.826795i
\(900\) 1.32329e18 + 2.29200e18i 0.0830000 + 0.143760i
\(901\) 4.38958e18 7.60298e18i 0.273345 0.473448i
\(902\) 1.16041e19 0.717412
\(903\) 0 0
\(904\) −1.27634e18 −0.0777806
\(905\) 4.85560e18 8.41015e18i 0.293784 0.508848i
\(906\) −1.28870e19 2.23210e19i −0.774140 1.34085i
\(907\) 6.24089e18 + 1.08095e19i 0.372220 + 0.644703i 0.989907 0.141721i \(-0.0452635\pi\)
−0.617687 + 0.786424i \(0.711930\pi\)
\(908\) −5.70609e18 + 9.88324e18i −0.337894 + 0.585250i
\(909\) −8.38471e18 −0.492973
\(910\) 0 0
\(911\) 2.22935e19 1.29214 0.646068 0.763280i \(-0.276412\pi\)
0.646068 + 0.763280i \(0.276412\pi\)
\(912\) −5.64143e17 + 9.77124e17i −0.0324655 + 0.0562320i
\(913\) −7.11627e18 1.23257e19i −0.406623 0.704292i
\(914\) −1.22851e18 2.12784e18i −0.0696991 0.120722i
\(915\) 6.94633e17 1.20314e18i 0.0391308 0.0677765i
\(916\) −4.64942e18 −0.260063
\(917\) 0 0
\(918\) −3.63483e18 −0.200451
\(919\) −1.24631e19 + 2.15867e19i −0.682455 + 1.18205i 0.291774 + 0.956487i \(0.405754\pi\)
−0.974229 + 0.225560i \(0.927579\pi\)
\(920\) −1.42011e18 2.45970e18i −0.0772148 0.133740i
\(921\) −4.25655e18 7.37256e18i −0.229811 0.398044i
\(922\) −1.00891e19 + 1.74748e19i −0.540881 + 0.936833i
\(923\) 3.51510e18 0.187123
\(924\) 0 0
\(925\) 1.93264e19 1.01445
\(926\) −7.31653e18 + 1.26726e19i −0.381359 + 0.660533i
\(927\) −5.63218e18 9.75522e18i −0.291513 0.504916i
\(928\) −1.32260e18 2.29080e18i −0.0679775 0.117741i
\(929\) 1.55121e19 2.68677e19i 0.791713 1.37129i −0.133193 0.991090i \(-0.542523\pi\)
0.924906 0.380197i \(-0.124144\pi\)
\(930\) 8.41858e18 0.426678
\(931\) 0 0
\(932\) −8.35542e18 −0.417604
\(933\) 6.95399e18 1.20447e19i 0.345146 0.597811i
\(934\) −6.81668e18 1.18068e19i −0.335984 0.581941i
\(935\) −1.22157e18 2.11582e18i −0.0597920 0.103563i
\(936\) −4.59815e17 + 7.96422e17i −0.0223506 + 0.0387124i
\(937\) −4.17037e17 −0.0201311 −0.0100655 0.999949i \(-0.503204\pi\)
−0.0100655 + 0.999949i \(0.503204\pi\)
\(938\) 0 0
\(939\) −8.43023e18 −0.401340
\(940\) −2.37278e18 + 4.10978e18i −0.112183 + 0.194306i
\(941\) −9.59391e17 1.66171e18i −0.0450467 0.0780232i 0.842623 0.538504i \(-0.181010\pi\)
−0.887670 + 0.460481i \(0.847677\pi\)
\(942\) −2.53724e18 4.39463e18i −0.118312 0.204923i
\(943\) −1.59651e19 + 2.76524e19i −0.739343 + 1.28058i
\(944\) −7.71382e18 −0.354774
\(945\) 0 0
\(946\) −2.03745e19 −0.924259
\(947\) −1.75162e19 + 3.03389e19i −0.789158 + 1.36686i 0.137325 + 0.990526i \(0.456150\pi\)
−0.926483 + 0.376336i \(0.877184\pi\)
\(948\) 7.52192e18 + 1.30284e19i 0.336569 + 0.582955i
\(949\) −1.61401e18 2.79555e18i −0.0717260 0.124233i
\(950\) 1.46176e18 2.53185e18i 0.0645169 0.111747i
\(951\) 1.82407e19 0.799593
\(952\) 0 0
\(953\) 3.82110e19 1.65228 0.826142 0.563462i \(-0.190531\pi\)
0.826142 + 0.563462i \(0.190531\pi\)
\(954\) −4.50532e18 + 7.80345e18i −0.193491 + 0.335137i
\(955\) −5.45802e18 9.45357e18i −0.232816 0.403250i
\(956\) 7.32462e18 + 1.26866e19i 0.310320 + 0.537489i
\(957\) 7.88475e18 1.36568e19i 0.331788 0.574673i
\(958\) 2.02026e18 0.0844368
\(959\) 0 0
\(960\) 1.47364e18 0.0607614
\(961\) −6.60457e18 + 1.14394e19i −0.270484 + 0.468493i
\(962\) 3.35775e18 + 5.81580e18i 0.136587 + 0.236576i
\(963\) 4.60487e18 + 7.97586e18i 0.186057 + 0.322260i
\(964\) −3.71996e18 + 6.44315e18i −0.149292 + 0.258582i
\(965\) 9.21972e16 0.00367528
\(966\) 0 0
\(967\) 3.71357e19 1.46056 0.730281 0.683147i \(-0.239389\pi\)
0.730281 + 0.683147i \(0.239389\pi\)
\(968\) −2.11783e18 + 3.66819e18i −0.0827372 + 0.143305i
\(969\) −1.33530e18 2.31280e18i −0.0518171 0.0897498i
\(970\) −3.58550e18 6.21027e18i −0.138208 0.239383i
\(971\) −5.96924e18 + 1.03390e19i −0.228557 + 0.395872i −0.957381 0.288829i \(-0.906734\pi\)
0.728824 + 0.684701i \(0.240067\pi\)
\(972\) 9.94270e18 0.378158
\(973\) 0 0
\(974\) −3.47512e19 −1.30418
\(975\) 4.17418e18 7.22989e18i 0.155611 0.269527i
\(976\) 5.43456e17 + 9.41293e17i 0.0201252 + 0.0348579i
\(977\) 4.03279e18 + 6.98499e18i 0.148351 + 0.256952i 0.930618 0.365992i \(-0.119270\pi\)
−0.782267 + 0.622943i \(0.785937\pi\)
\(978\) −1.20379e19 + 2.08502e19i −0.439893 + 0.761918i
\(979\) −1.19309e19 −0.433098
\(980\) 0 0
\(981\) −1.01460e19 −0.363450
\(982\) 9.18673e18 1.59119e19i 0.326916 0.566235i
\(983\) 1.32814e19 + 2.30040e19i 0.469511 + 0.813216i 0.999392 0.0348552i \(-0.0110970\pi\)
−0.529882 + 0.848072i \(0.677764\pi\)
\(984\) −8.28346e18 1.43474e19i −0.290900 0.503853i
\(985\) 3.01277e18 5.21827e18i 0.105107 0.182050i
\(986\) 6.26103e18 0.216993
\(987\) 0 0
\(988\) 1.01586e18 0.0347468
\(989\) 2.80316e19 4.85521e19i 0.952514 1.64980i
\(990\) 1.25378e18 + 2.17161e18i 0.0423246 + 0.0733083i
\(991\) −1.86864e19 3.23658e19i −0.626682 1.08544i −0.988213 0.153085i \(-0.951079\pi\)
0.361531 0.932360i \(-0.382254\pi\)
\(992\) −3.29320e18 + 5.70399e18i −0.109722 + 0.190043i
\(993\) −1.98473e19 −0.656950
\(994\) 0 0
\(995\) 2.16450e19 0.707145
\(996\) −1.01597e19 + 1.75972e19i −0.329759 + 0.571160i
\(997\) 7.48500e17 + 1.29644e18i 0.0241364 + 0.0418055i 0.877841 0.478952i \(-0.158983\pi\)
−0.853705 + 0.520757i \(0.825650\pi\)
\(998\) 1.69416e17 + 2.93437e17i 0.00542757 + 0.00940083i
\(999\) 1.36214e19 2.35930e19i 0.433558 0.750945i
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 98.14.c.o.79.4 8
7.2 even 3 98.14.a.j.1.1 4
7.3 odd 6 14.14.c.b.11.1 yes 8
7.4 even 3 inner 98.14.c.o.67.4 8
7.5 odd 6 98.14.a.h.1.4 4
7.6 odd 2 14.14.c.b.9.1 8
21.17 even 6 126.14.g.b.109.2 8
21.20 even 2 126.14.g.b.37.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.14.c.b.9.1 8 7.6 odd 2
14.14.c.b.11.1 yes 8 7.3 odd 6
98.14.a.h.1.4 4 7.5 odd 6
98.14.a.j.1.1 4 7.2 even 3
98.14.c.o.67.4 8 7.4 even 3 inner
98.14.c.o.79.4 8 1.1 even 1 trivial
126.14.g.b.37.2 8 21.20 even 2
126.14.g.b.109.2 8 21.17 even 6