Properties

Label 100.9.j.b.91.18
Level $100$
Weight $9$
Character 100.91
Analytic conductor $40.738$
Analytic rank $0$
Dimension $464$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(40.7378610061\)
Analytic rank: \(0\)
Dimension: \(464\)
Relative dimension: \(116\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 91.18
Character \(\chi\) \(=\) 100.91
Dual form 100.9.j.b.11.18

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-14.2154 + 7.34320i) q^{2} +(23.9209 - 7.77239i) q^{3} +(148.155 - 208.773i) q^{4} +(443.111 + 440.770i) q^{5} +(-282.972 + 286.144i) q^{6} +2979.31i q^{7} +(-573.020 + 4055.72i) q^{8} +(-4796.16 + 3484.61i) q^{9} +(-9535.65 - 3011.87i) q^{10} +(-1572.76 + 2164.72i) q^{11} +(1921.34 - 6145.56i) q^{12} +(-7228.32 + 5251.68i) q^{13} +(-21877.7 - 42352.1i) q^{14} +(14025.5 + 7099.60i) q^{15} +(-21636.2 - 61861.5i) q^{16} +(-5405.02 + 16634.9i) q^{17} +(42591.1 - 84754.3i) q^{18} +(-72375.6 - 23516.2i) q^{19} +(157670. - 27207.3i) q^{20} +(23156.4 + 71267.9i) q^{21} +(6461.44 - 42321.4i) q^{22} +(55583.6 - 76504.3i) q^{23} +(17815.4 + 101470. i) q^{24} +(2069.22 + 390620. i) q^{25} +(64189.3 - 127734. i) q^{26} +(-184642. + 254139. i) q^{27} +(621999. + 441400. i) q^{28} +(105628. + 325091. i) q^{29} +(-251511. + 2068.11i) q^{30} +(-1.08360e6 - 352082. i) q^{31} +(761829. + 720506. i) q^{32} +(-20796.9 + 64006.1i) q^{33} +(-45319.1 - 276162. i) q^{34} +(-1.31319e6 + 1.32016e6i) q^{35} +(16918.4 + 1.51757e6i) q^{36} +(1.80740e6 - 1.31315e6i) q^{37} +(1.20153e6 - 197175. i) q^{38} +(-132090. + 181807. i) q^{39} +(-2.04155e6 + 1.54456e6i) q^{40} +(2.33729e6 - 1.69814e6i) q^{41} +(-852511. - 843060. i) q^{42} -210225. i q^{43} +(218922. + 649063. i) q^{44} +(-3.66114e6 - 569932. i) q^{45} +(-228357. + 1.49570e6i) q^{46} +(-534618. + 173708. i) q^{47} +(-998371. - 1.31162e6i) q^{48} -3.11150e6 q^{49} +(-2.89781e6 - 5.53762e6i) q^{50} +439933. i q^{51} +(25497.8 + 2.28714e6i) q^{52} +(-2.11588e6 - 6.51200e6i) q^{53} +(758576. - 4.96855e6i) q^{54} +(-1.65105e6 + 265985. i) q^{55} +(-1.20833e7 - 1.70721e6i) q^{56} -1.91407e6 q^{57} +(-3.88876e6 - 3.84565e6i) q^{58} +(-5.55230e6 - 7.64209e6i) q^{59} +(3.56014e6 - 1.87630e6i) q^{60} +(-1.62764e6 - 1.18255e6i) q^{61} +(1.79892e7 - 2.95208e6i) q^{62} +(-1.03817e7 - 1.42893e7i) q^{63} +(-1.61205e7 - 4.64802e6i) q^{64} +(-5.51773e6 - 858948. i) q^{65} +(-174374. - 1.06259e6i) q^{66} +(1.60727e7 + 5.22233e6i) q^{67} +(2.67214e6 + 3.59297e6i) q^{68} +(734992. - 2.26207e6i) q^{69} +(8.97329e6 - 2.84097e7i) q^{70} +(-3.07619e7 + 9.99514e6i) q^{71} +(-1.13843e7 - 2.14486e7i) q^{72} +(-2.43171e7 - 1.76674e7i) q^{73} +(-1.60502e7 + 3.19391e7i) q^{74} +(3.08554e6 + 9.32791e6i) q^{75} +(-1.56324e7 + 1.16260e7i) q^{76} +(-6.44936e6 - 4.68574e6i) q^{77} +(542673. - 3.55442e6i) q^{78} +(-5.19131e7 + 1.68676e7i) q^{79} +(1.76794e7 - 3.69481e7i) q^{80} +(9.57799e6 - 2.94780e7i) q^{81} +(-2.07558e7 + 4.13030e7i) q^{82} +(-8.13518e7 - 2.64328e7i) q^{83} +(1.83095e7 + 5.72428e6i) q^{84} +(-9.72719e6 + 4.98875e6i) q^{85} +(1.54372e6 + 2.98842e6i) q^{86} +(5.05347e6 + 6.95550e6i) q^{87} +(-7.87826e6 - 7.61909e6i) q^{88} +(8.23488e7 + 5.98299e7i) q^{89} +(5.62297e7 - 1.87827e7i) q^{90} +(-1.56464e7 - 2.15354e7i) q^{91} +(-7.73704e6 - 2.29388e7i) q^{92} -2.86572e7 q^{93} +(6.32424e6 - 6.39513e6i) q^{94} +(-2.17051e7 - 4.23213e7i) q^{95} +(2.38237e7 + 1.13140e7i) q^{96} +(2.82622e7 + 8.69821e7i) q^{97} +(4.42311e7 - 2.28483e7i) q^{98} -1.58628e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.2154 + 7.34320i −0.888462 + 0.458950i
\(3\) 23.9209 7.77239i 0.295320 0.0959554i −0.157610 0.987501i \(-0.550379\pi\)
0.452930 + 0.891546i \(0.350379\pi\)
\(4\) 148.155 208.773i 0.578730 0.815519i
\(5\) 443.111 + 440.770i 0.708977 + 0.705231i
\(6\) −282.972 + 286.144i −0.218342 + 0.220790i
\(7\) 2979.31i 1.24086i 0.784261 + 0.620431i \(0.213042\pi\)
−0.784261 + 0.620431i \(0.786958\pi\)
\(8\) −573.020 + 4055.72i −0.139897 + 0.990166i
\(9\) −4796.16 + 3484.61i −0.731010 + 0.531110i
\(10\) −9535.65 3011.87i −0.953565 0.301187i
\(11\) −1572.76 + 2164.72i −0.107422 + 0.147853i −0.859343 0.511400i \(-0.829127\pi\)
0.751922 + 0.659253i \(0.229127\pi\)
\(12\) 1921.34 6145.56i 0.0926573 0.296372i
\(13\) −7228.32 + 5251.68i −0.253084 + 0.183876i −0.707092 0.707121i \(-0.749993\pi\)
0.454009 + 0.890997i \(0.349993\pi\)
\(14\) −21877.7 42352.1i −0.569494 1.10246i
\(15\) 14025.5 + 7099.60i 0.277046 + 0.140239i
\(16\) −21636.2 61861.5i −0.330143 0.943931i
\(17\) −5405.02 + 16634.9i −0.0647144 + 0.199171i −0.978186 0.207733i \(-0.933391\pi\)
0.913471 + 0.406904i \(0.133391\pi\)
\(18\) 42591.1 84754.3i 0.405722 0.807368i
\(19\) −72375.6 23516.2i −0.555364 0.180449i 0.0178702 0.999840i \(-0.494311\pi\)
−0.573234 + 0.819392i \(0.694311\pi\)
\(20\) 157670. 27207.3i 0.985436 0.170046i
\(21\) 23156.4 + 71267.9i 0.119067 + 0.366452i
\(22\) 6461.44 42321.4i 0.0275828 0.180663i
\(23\) 55583.6 76504.3i 0.198626 0.273385i −0.698073 0.716027i \(-0.745959\pi\)
0.896698 + 0.442642i \(0.145959\pi\)
\(24\) 17815.4 + 101470.i 0.0536972 + 0.305840i
\(25\) 2069.22 + 390620.i 0.00529719 + 0.999986i
\(26\) 64189.3 127734.i 0.140465 0.279520i
\(27\) −184642. + 254139.i −0.347437 + 0.478206i
\(28\) 621999. + 441400.i 1.01195 + 0.718125i
\(29\) 105628. + 325091.i 0.149344 + 0.459635i 0.997544 0.0700418i \(-0.0223133\pi\)
−0.848200 + 0.529677i \(0.822313\pi\)
\(30\) −251511. + 2068.11i −0.310508 + 0.00255322i
\(31\) −1.08360e6 352082.i −1.17333 0.381238i −0.343446 0.939172i \(-0.611594\pi\)
−0.829885 + 0.557934i \(0.811594\pi\)
\(32\) 761829. + 720506.i 0.726536 + 0.687128i
\(33\) −20796.9 + 64006.1i −0.0175365 + 0.0539717i
\(34\) −45319.1 276162.i −0.0339130 0.206656i
\(35\) −1.31319e6 + 1.32016e6i −0.875095 + 0.879743i
\(36\) 16918.4 + 1.51757e6i 0.0100728 + 0.903522i
\(37\) 1.80740e6 1.31315e6i 0.964379 0.700663i 0.0102157 0.999948i \(-0.496748\pi\)
0.954164 + 0.299285i \(0.0967482\pi\)
\(38\) 1.20153e6 197175.i 0.576237 0.0945623i
\(39\) −132090. + 181807.i −0.0570968 + 0.0785871i
\(40\) −2.04155e6 + 1.54456e6i −0.797480 + 0.603345i
\(41\) 2.33729e6 1.69814e6i 0.827138 0.600951i −0.0916101 0.995795i \(-0.529201\pi\)
0.918748 + 0.394844i \(0.129201\pi\)
\(42\) −852511. 843060.i −0.273970 0.270933i
\(43\) 210225.i 0.0614907i −0.999527 0.0307454i \(-0.990212\pi\)
0.999527 0.0307454i \(-0.00978809\pi\)
\(44\) 218922. + 649063.i 0.0584089 + 0.173171i
\(45\) −3.66114e6 569932.i −0.892825 0.138987i
\(46\) −228357. + 1.49570e6i −0.0510015 + 0.334051i
\(47\) −534618. + 173708.i −0.109560 + 0.0355982i −0.363284 0.931678i \(-0.618345\pi\)
0.253724 + 0.967277i \(0.418345\pi\)
\(48\) −998371. 1.31162e6i −0.188073 0.247083i
\(49\) −3.11150e6 −0.539740
\(50\) −2.89781e6 5.53762e6i −0.463650 0.886019i
\(51\) 439933.i 0.0650288i
\(52\) 25497.8 + 2.28714e6i 0.00348729 + 0.312809i
\(53\) −2.11588e6 6.51200e6i −0.268156 0.825299i −0.990950 0.134235i \(-0.957142\pi\)
0.722794 0.691064i \(-0.242858\pi\)
\(54\) 758576. 4.96855e6i 0.0892122 0.584325i
\(55\) −1.65105e6 + 265985.i −0.180430 + 0.0290674i
\(56\) −1.20833e7 1.70721e6i −1.22866 0.173594i
\(57\) −1.91407e6 −0.181325
\(58\) −3.88876e6 3.84565e6i −0.343636 0.339827i
\(59\) −5.55230e6 7.64209e6i −0.458211 0.630673i 0.515926 0.856633i \(-0.327448\pi\)
−0.974136 + 0.225960i \(0.927448\pi\)
\(60\) 3.56014e6 1.87630e6i 0.274703 0.144776i
\(61\) −1.62764e6 1.18255e6i −0.117554 0.0854082i 0.527455 0.849583i \(-0.323146\pi\)
−0.645009 + 0.764175i \(0.723146\pi\)
\(62\) 1.79892e7 2.95208e6i 1.21743 0.199784i
\(63\) −1.03817e7 1.42893e7i −0.659035 0.907084i
\(64\) −1.61205e7 4.64802e6i −0.960857 0.277043i
\(65\) −5.51773e6 858948.i −0.309106 0.0481186i
\(66\) −174374. 1.06259e6i −0.00918981 0.0560001i
\(67\) 1.60727e7 + 5.22233e6i 0.797607 + 0.259158i 0.679340 0.733824i \(-0.262266\pi\)
0.118267 + 0.992982i \(0.462266\pi\)
\(68\) 2.67214e6 + 3.59297e6i 0.124975 + 0.168042i
\(69\) 734992. 2.26207e6i 0.0324255 0.0997953i
\(70\) 8.97329e6 2.84097e7i 0.373731 1.18324i
\(71\) −3.07619e7 + 9.99514e6i −1.21054 + 0.393329i −0.843629 0.536927i \(-0.819585\pi\)
−0.366912 + 0.930256i \(0.619585\pi\)
\(72\) −1.13843e7 2.14486e7i −0.423621 0.798123i
\(73\) −2.43171e7 1.76674e7i −0.856288 0.622130i 0.0705845 0.997506i \(-0.477514\pi\)
−0.926873 + 0.375376i \(0.877514\pi\)
\(74\) −1.60502e7 + 3.19391e7i −0.535246 + 1.06511i
\(75\) 3.08554e6 + 9.32791e6i 0.0975184 + 0.294808i
\(76\) −1.56324e7 + 1.16260e7i −0.468565 + 0.348479i
\(77\) −6.44936e6 4.68574e6i −0.183465 0.133295i
\(78\) 542673. 3.55442e6i 0.0146609 0.0960262i
\(79\) −5.19131e7 + 1.68676e7i −1.33281 + 0.433057i −0.886876 0.462008i \(-0.847129\pi\)
−0.445936 + 0.895065i \(0.647129\pi\)
\(80\) 1.76794e7 3.69481e7i 0.431626 0.902053i
\(81\) 9.57799e6 2.94780e7i 0.222502 0.684792i
\(82\) −2.07558e7 + 4.13030e7i −0.459075 + 0.913537i
\(83\) −8.13518e7 2.64328e7i −1.71417 0.556969i −0.723155 0.690686i \(-0.757309\pi\)
−0.991020 + 0.133717i \(0.957309\pi\)
\(84\) 1.83095e7 + 5.72428e6i 0.367757 + 0.114975i
\(85\) −9.72719e6 + 4.98875e6i −0.186342 + 0.0955687i
\(86\) 1.54372e6 + 2.98842e6i 0.0282212 + 0.0546322i
\(87\) 5.05347e6 + 6.95550e6i 0.0882089 + 0.121409i
\(88\) −7.87826e6 7.61909e6i −0.131371 0.127049i
\(89\) 8.23488e7 + 5.98299e7i 1.31249 + 0.953583i 0.999993 + 0.00366510i \(0.00116664\pi\)
0.312501 + 0.949918i \(0.398833\pi\)
\(90\) 5.62297e7 1.87827e7i 0.857029 0.286278i
\(91\) −1.56464e7 2.15354e7i −0.228165 0.314042i
\(92\) −7.73704e6 2.29388e7i −0.108000 0.320199i
\(93\) −2.86572e7 −0.383090
\(94\) 6.32424e6 6.39513e6i 0.0810022 0.0819102i
\(95\) −2.17051e7 4.23213e7i −0.266482 0.519594i
\(96\) 2.38237e7 + 1.13140e7i 0.280495 + 0.133208i
\(97\) 2.82622e7 + 8.69821e7i 0.319241 + 0.982523i 0.973973 + 0.226662i \(0.0727814\pi\)
−0.654732 + 0.755861i \(0.727219\pi\)
\(98\) 4.42311e7 2.28483e7i 0.479539 0.247714i
\(99\) 1.58628e7i 0.165135i
\(100\) 8.18573e7 + 5.74402e7i 0.818573 + 0.574402i
\(101\) 9.68254e7 0.930473 0.465236 0.885186i \(-0.345969\pi\)
0.465236 + 0.885186i \(0.345969\pi\)
\(102\) −3.23052e6 6.25382e6i −0.0298450 0.0577756i
\(103\) 3.12222e6 1.01447e6i 0.0277405 0.00901344i −0.295114 0.955462i \(-0.595358\pi\)
0.322854 + 0.946449i \(0.395358\pi\)
\(104\) −1.71574e7 3.23254e7i −0.146662 0.276319i
\(105\) −2.11519e7 + 4.17862e7i −0.174017 + 0.343776i
\(106\) 7.78970e7 + 7.70334e7i 0.617017 + 0.610177i
\(107\) 9.48926e7i 0.723931i −0.932191 0.361966i \(-0.882106\pi\)
0.932191 0.361966i \(-0.117894\pi\)
\(108\) 2.57015e7 + 7.62002e7i 0.188914 + 0.560094i
\(109\) −1.27808e8 + 9.28580e7i −0.905425 + 0.657830i −0.939854 0.341578i \(-0.889039\pi\)
0.0344288 + 0.999407i \(0.489039\pi\)
\(110\) 2.15171e7 1.59050e7i 0.146965 0.108634i
\(111\) 3.30284e7 4.54597e7i 0.217568 0.299457i
\(112\) 1.84305e8 6.44611e7i 1.17129 0.409662i
\(113\) −1.30711e8 + 9.49672e7i −0.801676 + 0.582452i −0.911405 0.411510i \(-0.865002\pi\)
0.109730 + 0.993961i \(0.465002\pi\)
\(114\) 2.72093e7 1.40554e7i 0.161101 0.0832192i
\(115\) 5.83505e7 9.40030e6i 0.333621 0.0537465i
\(116\) 8.35196e7 + 2.61115e7i 0.461271 + 0.144211i
\(117\) 1.63681e7 5.03758e7i 0.0873483 0.268831i
\(118\) 1.35046e8 + 6.78637e7i 0.696550 + 0.350033i
\(119\) −4.95606e7 1.61032e7i −0.247143 0.0803017i
\(120\) −3.68309e7 + 5.28151e7i −0.177618 + 0.254703i
\(121\) 6.40281e7 + 1.97058e8i 0.298696 + 0.919291i
\(122\) 3.18212e7 + 4.85833e6i 0.143641 + 0.0219304i
\(123\) 4.27117e7 5.87876e7i 0.186606 0.256841i
\(124\) −2.34045e8 + 1.74063e8i −0.989949 + 0.736240i
\(125\) −1.71256e8 + 1.74000e8i −0.701466 + 0.712703i
\(126\) 2.52509e8 + 1.26892e8i 1.00183 + 0.503446i
\(127\) −1.09892e8 + 1.51253e8i −0.422425 + 0.581418i −0.966194 0.257817i \(-0.916997\pi\)
0.543769 + 0.839235i \(0.316997\pi\)
\(128\) 2.63291e8 5.23027e7i 0.980834 0.194843i
\(129\) −1.63395e6 5.02877e6i −0.00590036 0.0181595i
\(130\) 8.47441e7 2.83075e7i 0.296713 0.0991124i
\(131\) −1.99289e8 6.47530e7i −0.676704 0.219874i −0.0495521 0.998772i \(-0.515779\pi\)
−0.627152 + 0.778897i \(0.715779\pi\)
\(132\) 1.02816e7 + 1.38246e7i 0.0338661 + 0.0455364i
\(133\) 7.00622e7 2.15629e8i 0.223912 0.689130i
\(134\) −2.66828e8 + 4.37874e7i −0.827584 + 0.135809i
\(135\) −1.93834e8 + 3.12267e7i −0.583571 + 0.0940137i
\(136\) −6.43694e7 3.14534e7i −0.188159 0.0919415i
\(137\) 1.45244e8 1.05526e8i 0.412304 0.299556i −0.362230 0.932089i \(-0.617985\pi\)
0.774534 + 0.632533i \(0.217985\pi\)
\(138\) 6.16264e6 + 3.75534e7i 0.0169922 + 0.103546i
\(139\) 2.35524e8 3.24171e8i 0.630923 0.868392i −0.367167 0.930155i \(-0.619672\pi\)
0.998091 + 0.0617633i \(0.0196724\pi\)
\(140\) 8.10591e7 + 4.69747e8i 0.211003 + 1.22279i
\(141\) −1.14384e7 + 8.31052e6i −0.0289395 + 0.0210258i
\(142\) 3.63896e8 3.67975e8i 0.895002 0.905035i
\(143\) 2.39069e7i 0.0571714i
\(144\) 3.19334e8 + 2.21303e8i 0.742669 + 0.514681i
\(145\) −9.64852e7 + 1.90609e8i −0.218267 + 0.431193i
\(146\) 4.75412e8 + 7.25838e7i 1.04631 + 0.159745i
\(147\) −7.44299e7 + 2.41837e7i −0.159396 + 0.0517910i
\(148\) −6.37558e6 5.71887e8i −0.0132884 1.19196i
\(149\) −8.58273e8 −1.74133 −0.870663 0.491879i \(-0.836310\pi\)
−0.870663 + 0.491879i \(0.836310\pi\)
\(150\) −1.12359e8 1.09942e8i −0.221943 0.217170i
\(151\) 5.85568e7i 0.112634i 0.998413 + 0.0563170i \(0.0179358\pi\)
−0.998413 + 0.0563170i \(0.982064\pi\)
\(152\) 1.36848e8 2.80060e8i 0.256368 0.524658i
\(153\) −3.20430e7 9.86181e7i −0.0584746 0.179966i
\(154\) 1.26089e8 + 1.92507e7i 0.224178 + 0.0342265i
\(155\) −3.24966e8 6.33627e8i −0.563004 1.09776i
\(156\) 1.83865e7 + 5.45124e7i 0.0310456 + 0.0920443i
\(157\) 5.04632e8 0.830571 0.415285 0.909691i \(-0.363682\pi\)
0.415285 + 0.909691i \(0.363682\pi\)
\(158\) 6.14104e8 6.20988e8i 0.985402 0.996449i
\(159\) −1.01228e8 1.39328e8i −0.158384 0.217997i
\(160\) 1.99973e7 + 6.55055e8i 0.0305135 + 0.999534i
\(161\) 2.27930e8 + 1.65601e8i 0.339233 + 0.246467i
\(162\) 8.03081e7 + 4.89375e8i 0.116600 + 0.710529i
\(163\) 1.99928e8 + 2.75178e8i 0.283220 + 0.389819i 0.926797 0.375563i \(-0.122550\pi\)
−0.643577 + 0.765381i \(0.722550\pi\)
\(164\) −8.24476e6 7.39552e8i −0.0113973 1.02234i
\(165\) −3.74273e7 + 1.91952e7i −0.0504955 + 0.0258974i
\(166\) 1.35055e9 2.21630e8i 1.77860 0.291874i
\(167\) −1.02615e9 3.33417e8i −1.31931 0.428669i −0.437050 0.899437i \(-0.643977\pi\)
−0.882257 + 0.470768i \(0.843977\pi\)
\(168\) −3.02312e8 + 5.30777e7i −0.379506 + 0.0666309i
\(169\) −2.27406e8 + 6.99884e8i −0.278776 + 0.857985i
\(170\) 1.01643e8 1.42346e8i 0.121697 0.170431i
\(171\) 4.29070e8 1.39413e8i 0.501815 0.163050i
\(172\) −4.38892e7 3.11458e7i −0.0501469 0.0355865i
\(173\) −3.06541e8 2.22715e8i −0.342219 0.248637i 0.403378 0.915033i \(-0.367836\pi\)
−0.745598 + 0.666396i \(0.767836\pi\)
\(174\) −1.22913e8 6.17666e7i −0.134091 0.0673840i
\(175\) −1.16378e9 + 6.16484e6i −1.24085 + 0.00657309i
\(176\) 1.67941e8 + 5.04568e7i 0.175028 + 0.0525859i
\(177\) −1.92214e8 1.39651e8i −0.195835 0.142283i
\(178\) −1.60996e9 2.45802e8i −1.60375 0.244853i
\(179\) −2.28414e6 + 742164.i −0.00222491 + 0.000722915i −0.310129 0.950694i \(-0.600372\pi\)
0.307904 + 0.951417i \(0.400372\pi\)
\(180\) −6.61402e8 + 6.79909e8i −0.630051 + 0.647680i
\(181\) −5.59385e8 + 1.72161e9i −0.521190 + 1.60406i 0.250539 + 0.968107i \(0.419392\pi\)
−0.771729 + 0.635952i \(0.780608\pi\)
\(182\) 3.80559e8 + 1.91240e8i 0.346845 + 0.174298i
\(183\) −4.81259e7 1.56370e7i −0.0429116 0.0139428i
\(184\) 2.78429e8 + 2.69270e8i 0.242909 + 0.234918i
\(185\) 1.37968e9 + 2.14775e8i 1.17785 + 0.183357i
\(186\) 4.07373e8 2.10435e8i 0.340361 0.175819i
\(187\) −2.75091e7 3.78630e7i −0.0224963 0.0309634i
\(188\) −4.29408e7 + 1.37349e8i −0.0343747 + 0.109950i
\(189\) −7.57158e8 5.50107e8i −0.593389 0.431122i
\(190\) 6.19320e8 + 4.42228e8i 0.475227 + 0.339338i
\(191\) 9.39990e8 + 1.29378e9i 0.706301 + 0.972139i 0.999869 + 0.0162013i \(0.00515725\pi\)
−0.293568 + 0.955938i \(0.594843\pi\)
\(192\) −4.21744e8 + 1.41099e7i −0.310345 + 0.0103829i
\(193\) 1.02147e9 0.736203 0.368102 0.929786i \(-0.380008\pi\)
0.368102 + 0.929786i \(0.380008\pi\)
\(194\) −1.04048e9 1.02895e9i −0.734563 0.726419i
\(195\) −1.38665e8 + 2.23391e7i −0.0959024 + 0.0154499i
\(196\) −4.60983e8 + 6.49596e8i −0.312364 + 0.440169i
\(197\) −6.67059e8 2.05300e9i −0.442894 1.36309i −0.884777 0.466014i \(-0.845690\pi\)
0.441884 0.897072i \(-0.354310\pi\)
\(198\) 1.16484e8 + 2.25496e8i 0.0757886 + 0.146716i
\(199\) 1.17695e9i 0.750492i 0.926925 + 0.375246i \(0.122442\pi\)
−0.926925 + 0.375246i \(0.877558\pi\)
\(200\) −1.58543e9 2.15441e8i −0.990893 0.134650i
\(201\) 4.25064e8 0.260417
\(202\) −1.37641e9 + 7.11008e8i −0.826690 + 0.427040i
\(203\) −9.68547e8 + 3.14700e8i −0.570344 + 0.185316i
\(204\) 9.18461e7 + 6.51782e7i 0.0530322 + 0.0376341i
\(205\) 1.78417e9 + 2.77743e8i 1.01023 + 0.157263i
\(206\) −3.69341e7 + 3.73482e7i −0.0205097 + 0.0207396i
\(207\) 5.60614e8i 0.305339i
\(208\) 4.81270e8 + 3.33528e8i 0.257120 + 0.178188i
\(209\) 1.64735e8 1.19687e8i 0.0863379 0.0627282i
\(210\) −6.16153e6 7.49330e8i −0.00316819 0.385297i
\(211\) 1.32474e9 1.82335e9i 0.668345 0.919898i −0.331376 0.943499i \(-0.607513\pi\)
0.999721 + 0.0236005i \(0.00751297\pi\)
\(212\) −1.67301e9 5.23047e8i −0.828237 0.258939i
\(213\) −6.58167e8 + 4.78186e8i −0.319755 + 0.232316i
\(214\) 6.96815e8 + 1.34894e9i 0.332248 + 0.643185i
\(215\) 9.26606e7 9.31527e7i 0.0433652 0.0435955i
\(216\) −9.24911e8 8.94484e8i −0.424898 0.410920i
\(217\) 1.04896e9 3.22837e9i 0.473065 1.45594i
\(218\) 1.13497e9 2.25853e9i 0.502525 1.00000i
\(219\) −7.19005e8 2.33619e8i −0.312576 0.101562i
\(220\) −1.89080e8 + 3.84101e8i −0.0807153 + 0.163966i
\(221\) −4.82922e7 1.48628e8i −0.0202445 0.0623062i
\(222\) −1.35692e8 + 8.88762e8i −0.0558655 + 0.365910i
\(223\) 2.06285e9 2.83927e9i 0.834157 1.14812i −0.152978 0.988230i \(-0.548886\pi\)
0.987135 0.159889i \(-0.0511136\pi\)
\(224\) −2.14661e9 + 2.26972e9i −0.852631 + 0.901532i
\(225\) −1.37108e9 1.86626e9i −0.534975 0.728187i
\(226\) 1.16075e9 2.30983e9i 0.444943 0.885415i
\(227\) −4.56586e8 + 6.28437e8i −0.171957 + 0.236678i −0.886294 0.463124i \(-0.846728\pi\)
0.714337 + 0.699802i \(0.246728\pi\)
\(228\) −2.83579e8 + 3.99606e8i −0.104938 + 0.147874i
\(229\) 4.81681e8 + 1.48246e9i 0.175153 + 0.539066i 0.999640 0.0268148i \(-0.00853643\pi\)
−0.824487 + 0.565880i \(0.808536\pi\)
\(230\) −7.60447e8 + 5.62108e8i −0.271742 + 0.200867i
\(231\) −1.90694e8 6.19603e7i −0.0669714 0.0217603i
\(232\) −1.37901e9 + 2.42116e8i −0.476008 + 0.0835740i
\(233\) 2.00742e8 6.17821e8i 0.0681106 0.209623i −0.911208 0.411946i \(-0.864849\pi\)
0.979319 + 0.202323i \(0.0648492\pi\)
\(234\) 1.37241e8 + 8.36306e8i 0.0457740 + 0.278934i
\(235\) −3.13460e8 1.58672e8i −0.102781 0.0520269i
\(236\) −2.41806e9 + 2.69573e7i −0.779506 + 0.00869018i
\(237\) −1.11071e9 + 8.06978e8i −0.352052 + 0.255781i
\(238\) 8.22773e8 1.35020e8i 0.256432 0.0420813i
\(239\) −2.45716e9 + 3.38199e9i −0.753081 + 1.03653i 0.244677 + 0.969605i \(0.421318\pi\)
−0.997758 + 0.0669226i \(0.978682\pi\)
\(240\) 1.35733e8 1.02124e9i 0.0409111 0.307811i
\(241\) 1.03476e9 7.51799e8i 0.306742 0.222861i −0.423756 0.905777i \(-0.639288\pi\)
0.730497 + 0.682916i \(0.239288\pi\)
\(242\) −2.35722e9 2.33109e9i −0.687289 0.679669i
\(243\) 2.84061e9i 0.814679i
\(244\) −4.88027e8 + 1.64606e8i −0.137684 + 0.0464395i
\(245\) −1.37874e9 1.37145e9i −0.382664 0.380642i
\(246\) −1.75475e8 + 1.14933e9i −0.0479152 + 0.313837i
\(247\) 6.46654e8 2.10111e8i 0.173734 0.0564495i
\(248\) 2.04887e9 4.19301e9i 0.541635 1.10846i
\(249\) −2.15146e9 −0.559675
\(250\) 1.15676e9 3.73104e9i 0.296131 0.955147i
\(251\) 5.34789e9i 1.34737i 0.739018 + 0.673686i \(0.235290\pi\)
−0.739018 + 0.673686i \(0.764710\pi\)
\(252\) −4.52132e9 + 5.04050e7i −1.12115 + 0.0124989i
\(253\) 7.81905e7 + 2.40646e8i 0.0190841 + 0.0587348i
\(254\) 4.51473e8 2.95707e9i 0.108467 0.710439i
\(255\) −1.93909e8 + 1.94939e8i −0.0458604 + 0.0461039i
\(256\) −3.35871e9 + 2.67690e9i −0.782011 + 0.623264i
\(257\) 1.11535e9 0.255670 0.127835 0.991795i \(-0.459197\pi\)
0.127835 + 0.991795i \(0.459197\pi\)
\(258\) 6.01544e7 + 5.94875e7i 0.0135765 + 0.0134260i
\(259\) 3.91230e9 + 5.38481e9i 0.869426 + 1.19666i
\(260\) −9.96804e8 + 1.02469e9i −0.218130 + 0.224234i
\(261\) −1.63943e9 1.19111e9i −0.353289 0.256680i
\(262\) 3.30847e9 5.42931e8i 0.702137 0.115223i
\(263\) 2.32880e9 + 3.20531e9i 0.486753 + 0.669958i 0.979785 0.200053i \(-0.0641115\pi\)
−0.493032 + 0.870011i \(0.664111\pi\)
\(264\) −2.47674e8 1.21023e8i −0.0509876 0.0249145i
\(265\) 1.93273e9 3.81815e9i 0.391910 0.774230i
\(266\) 5.87447e8 + 3.57974e9i 0.117339 + 0.715031i
\(267\) 2.43488e9 + 7.91141e8i 0.479107 + 0.155671i
\(268\) 3.47153e9 2.58183e9i 0.672948 0.500481i
\(269\) 2.62041e8 8.06479e8i 0.0500449 0.154023i −0.922911 0.385013i \(-0.874197\pi\)
0.972956 + 0.230991i \(0.0741968\pi\)
\(270\) 2.52612e9 1.86726e9i 0.475333 0.351358i
\(271\) 5.60697e9 1.82181e9i 1.03956 0.337775i 0.260999 0.965339i \(-0.415948\pi\)
0.778565 + 0.627564i \(0.215948\pi\)
\(272\) 1.14601e9 2.55552e7i 0.209368 0.00466879i
\(273\) −5.41658e8 3.93538e8i −0.0975157 0.0708493i
\(274\) −1.28981e9 + 2.56665e9i −0.228835 + 0.455371i
\(275\) −8.48835e8 6.09871e8i −0.148420 0.106637i
\(276\) −3.63367e8 4.88583e8i −0.0626194 0.0841981i
\(277\) 5.75953e8 + 4.18455e8i 0.0978292 + 0.0710770i 0.635624 0.771998i \(-0.280743\pi\)
−0.537795 + 0.843075i \(0.680743\pi\)
\(278\) −9.67617e8 + 6.33773e9i −0.162003 + 1.06110i
\(279\) 6.42397e9 2.08727e9i 1.06020 0.344479i
\(280\) −4.60173e9 6.08241e9i −0.748668 0.989564i
\(281\) −2.20741e9 + 6.79372e9i −0.354045 + 1.08964i 0.602516 + 0.798107i \(0.294165\pi\)
−0.956561 + 0.291532i \(0.905835\pi\)
\(282\) 1.01576e8 2.02132e8i 0.0160619 0.0319624i
\(283\) −3.20196e8 1.04038e8i −0.0499194 0.0162198i 0.283951 0.958839i \(-0.408355\pi\)
−0.333870 + 0.942619i \(0.608355\pi\)
\(284\) −2.47081e9 + 7.90308e9i −0.379810 + 1.21485i
\(285\) −8.48145e8 8.43664e8i −0.128555 0.127876i
\(286\) 1.75553e8 + 3.39846e8i 0.0262388 + 0.0507946i
\(287\) 5.05930e9 + 6.96353e9i 0.745698 + 1.02636i
\(288\) −6.16454e9 8.00982e8i −0.896046 0.116427i
\(289\) 5.39600e9 + 3.92042e9i 0.773536 + 0.562007i
\(290\) −2.81060e7 3.41809e9i −0.00397381 0.483272i
\(291\) 1.35212e9 + 1.86103e9i 0.188557 + 0.259526i
\(292\) −7.29117e9 + 2.45924e9i −1.00292 + 0.338274i
\(293\) 5.10197e9 0.692257 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(294\) 8.80465e8 8.90335e8i 0.117848 0.119169i
\(295\) 9.08116e8 5.83358e9i 0.119909 0.770277i
\(296\) 4.29011e9 + 8.08278e9i 0.558858 + 1.05292i
\(297\) −2.59740e8 7.99397e8i −0.0333820 0.102739i
\(298\) 1.22007e10 6.30247e9i 1.54710 0.799182i
\(299\) 8.44905e8i 0.105712i
\(300\) 2.40455e9 + 7.37797e8i 0.296858 + 0.0910861i
\(301\) 6.26324e8 0.0763015
\(302\) −4.29994e8 8.32408e8i −0.0516934 0.100071i
\(303\) 2.31615e9 7.52564e8i 0.274787 0.0892839i
\(304\) 1.11186e8 + 4.98606e9i 0.0130184 + 0.583799i
\(305\) −1.99993e8 1.24141e9i −0.0231108 0.143455i
\(306\) 1.17968e9 + 1.16660e9i 0.134548 + 0.133056i
\(307\) 3.79168e9i 0.426853i 0.976959 + 0.213426i \(0.0684624\pi\)
−0.976959 + 0.213426i \(0.931538\pi\)
\(308\) −1.93376e9 + 6.52237e8i −0.214882 + 0.0724774i
\(309\) 6.68016e7 4.85342e7i 0.00732745 0.00532370i
\(310\) 9.27237e9 + 6.62097e9i 1.00402 + 0.716927i
\(311\) 9.16918e9 1.26203e10i 0.980142 1.34905i 0.0433897 0.999058i \(-0.486184\pi\)
0.936753 0.349992i \(-0.113816\pi\)
\(312\) −6.61666e8 6.39899e8i −0.0698265 0.0675295i
\(313\) 1.02960e10 7.48047e9i 1.07273 0.779384i 0.0963294 0.995350i \(-0.469290\pi\)
0.976401 + 0.215965i \(0.0692898\pi\)
\(314\) −7.17355e9 + 3.70562e9i −0.737931 + 0.381190i
\(315\) 1.69800e9 1.09077e10i 0.172463 1.10787i
\(316\) −4.16969e9 + 1.33371e10i −0.418172 + 1.33756i
\(317\) −1.85012e9 + 5.69408e9i −0.183216 + 0.563880i −0.999913 0.0131863i \(-0.995803\pi\)
0.816697 + 0.577066i \(0.195803\pi\)
\(318\) 2.46210e9 + 1.23727e9i 0.240767 + 0.120991i
\(319\) −8.69858e8 2.82634e8i −0.0840012 0.0272936i
\(320\) −5.09447e9 9.16502e9i −0.485846 0.874044i
\(321\) −7.37542e8 2.26992e9i −0.0694651 0.213792i
\(322\) −4.45616e9 6.80347e8i −0.414512 0.0632859i
\(323\) 7.82382e8 1.07686e9i 0.0718801 0.0989345i
\(324\) −4.73519e9 6.36694e9i −0.429692 0.577764i
\(325\) −2.06637e9 2.81266e9i −0.185214 0.252106i
\(326\) −4.86274e9 2.44365e9i −0.430537 0.216355i
\(327\) −2.33556e9 + 3.21463e9i −0.204268 + 0.281151i
\(328\) 5.54788e9 + 1.04525e10i 0.479327 + 0.903076i
\(329\) −5.17530e8 1.59279e9i −0.0441725 0.135949i
\(330\) 3.91089e8 5.47703e8i 0.0329777 0.0461838i
\(331\) 4.78995e9 + 1.55635e9i 0.399043 + 0.129657i 0.501662 0.865064i \(-0.332722\pi\)
−0.102619 + 0.994721i \(0.532722\pi\)
\(332\) −1.75711e10 + 1.30679e10i −1.44626 + 1.07561i
\(333\) −4.09275e9 + 1.25962e10i −0.332842 + 1.02438i
\(334\) 1.70355e10 2.79558e9i 1.36889 0.224640i
\(335\) 4.82013e9 + 9.39842e9i 0.382719 + 0.746235i
\(336\) 3.90772e9 2.97446e9i 0.306596 0.233373i
\(337\) −9.27479e9 + 6.73853e9i −0.719092 + 0.522451i −0.886094 0.463506i \(-0.846591\pi\)
0.167002 + 0.985957i \(0.446591\pi\)
\(338\) −1.90672e9 1.16190e10i −0.146090 0.890231i
\(339\) −2.38861e9 + 3.28764e9i −0.180862 + 0.248935i
\(340\) −3.99616e8 + 2.76988e9i −0.0299038 + 0.207274i
\(341\) 2.46639e9 1.79194e9i 0.182408 0.132527i
\(342\) −5.07566e9 + 5.13256e9i −0.371012 + 0.375171i
\(343\) 7.90502e9i 0.571119i
\(344\) 8.52612e8 + 1.20463e8i 0.0608860 + 0.00860239i
\(345\) 1.32274e9 6.78386e8i 0.0933677 0.0478851i
\(346\) 5.99304e9 + 9.14992e8i 0.418161 + 0.0638429i
\(347\) −1.63695e10 + 5.31878e9i −1.12906 + 0.366855i −0.813220 0.581957i \(-0.802287\pi\)
−0.315843 + 0.948812i \(0.602287\pi\)
\(348\) 2.20082e9 2.45354e7i 0.150061 0.00167292i
\(349\) 9.89300e9 0.666847 0.333423 0.942777i \(-0.391796\pi\)
0.333423 + 0.942777i \(0.391796\pi\)
\(350\) 1.64983e10 8.63348e9i 1.09943 0.575326i
\(351\) 2.80668e9i 0.184912i
\(352\) −2.75786e9 + 5.15961e8i −0.179640 + 0.0336083i
\(353\) 4.48663e9 + 1.38084e10i 0.288949 + 0.889295i 0.985187 + 0.171484i \(0.0548560\pi\)
−0.696238 + 0.717811i \(0.745144\pi\)
\(354\) 3.75788e9 + 5.73737e8i 0.239293 + 0.0365342i
\(355\) −1.80365e10 9.12995e9i −1.13563 0.574851i
\(356\) 2.46912e10 8.32810e9i 1.53724 0.518497i
\(357\) −1.31070e9 −0.0806918
\(358\) 2.70202e7 2.73231e7i 0.00164496 0.00166340i
\(359\) 4.99405e9 + 6.87372e9i 0.300660 + 0.413823i 0.932440 0.361325i \(-0.117675\pi\)
−0.631780 + 0.775148i \(0.717675\pi\)
\(360\) 4.40939e9 1.45220e10i 0.262524 0.864601i
\(361\) −9.05478e9 6.57868e9i −0.533150 0.387356i
\(362\) −4.69024e9 2.85810e10i −0.273125 1.66435i
\(363\) 3.06323e9 + 4.21617e9i 0.176422 + 0.242824i
\(364\) −6.81410e9 + 7.59658e7i −0.388153 + 0.00432725i
\(365\) −2.98791e9 1.85468e10i −0.168343 1.04496i
\(366\) 7.98954e8 1.31111e8i 0.0445244 0.00730659i
\(367\) −1.95260e10 6.34438e9i −1.07634 0.349724i −0.283386 0.959006i \(-0.591458\pi\)
−0.792953 + 0.609282i \(0.791458\pi\)
\(368\) −5.93529e9 1.78322e9i −0.323631 0.0972329i
\(369\) −5.29266e9 + 1.62891e10i −0.285475 + 0.878603i
\(370\) −2.11898e10 + 7.07813e9i −1.13063 + 0.377669i
\(371\) 1.94013e10 6.30386e9i 1.02408 0.332745i
\(372\) −4.24570e9 + 5.98284e9i −0.221706 + 0.312418i
\(373\) 2.84965e10 + 2.07039e10i 1.47216 + 1.06959i 0.979980 + 0.199098i \(0.0638011\pi\)
0.492183 + 0.870492i \(0.336199\pi\)
\(374\) 6.69089e8 + 3.36233e8i 0.0341977 + 0.0171852i
\(375\) −2.74422e9 + 5.49331e9i −0.138769 + 0.277785i
\(376\) −3.98164e8 2.26780e9i −0.0199210 0.113463i
\(377\) −2.47079e9 1.79514e9i −0.122312 0.0888652i
\(378\) 1.48028e10 + 2.26003e9i 0.725067 + 0.110700i
\(379\) −1.81242e10 + 5.88891e9i −0.878420 + 0.285416i −0.713301 0.700858i \(-0.752801\pi\)
−0.165119 + 0.986274i \(0.552801\pi\)
\(380\) −1.20513e10 1.73866e9i −0.577960 0.0833834i
\(381\) −1.45311e9 + 4.47223e9i −0.0689604 + 0.212238i
\(382\) −2.28628e10 1.14891e10i −1.07368 0.539553i
\(383\) −3.62521e10 1.17790e10i −1.68476 0.547412i −0.698935 0.715185i \(-0.746342\pi\)
−0.985826 + 0.167773i \(0.946342\pi\)
\(384\) 5.89165e9 3.29753e9i 0.270964 0.151657i
\(385\) −7.92451e8 4.91898e9i −0.0360686 0.223889i
\(386\) −1.45206e10 + 7.50088e9i −0.654089 + 0.337880i
\(387\) 7.32551e8 + 1.00827e9i 0.0326583 + 0.0449503i
\(388\) 2.23467e10 + 6.98644e9i 0.986021 + 0.308269i
\(389\) −2.69563e10 1.95849e10i −1.17723 0.855308i −0.185374 0.982668i \(-0.559350\pi\)
−0.991857 + 0.127360i \(0.959350\pi\)
\(390\) 1.80714e9 1.33581e9i 0.0781149 0.0577411i
\(391\) 9.72213e8 + 1.33814e9i 0.0415963 + 0.0572523i
\(392\) 1.78295e9 1.26194e10i 0.0755083 0.534433i
\(393\) −5.27047e9 −0.220943
\(394\) 2.45581e10 + 2.42858e10i 1.01908 + 1.00778i
\(395\) −3.04380e10 1.54075e10i −1.25034 0.632914i
\(396\) −3.31172e9 2.35015e9i −0.134671 0.0955685i
\(397\) −1.40201e10 4.31493e10i −0.564401 1.73705i −0.669724 0.742610i \(-0.733588\pi\)
0.105323 0.994438i \(-0.466412\pi\)
\(398\) −8.64258e9 1.67308e10i −0.344438 0.666783i
\(399\) 5.70261e9i 0.225000i
\(400\) 2.41195e10 8.57954e9i 0.942169 0.335138i
\(401\) −4.35465e10 −1.68413 −0.842065 0.539376i \(-0.818660\pi\)
−0.842065 + 0.539376i \(0.818660\pi\)
\(402\) −6.04245e9 + 3.12133e9i −0.231371 + 0.119518i
\(403\) 9.68160e9 3.14574e9i 0.367051 0.119262i
\(404\) 1.43452e10 2.02145e10i 0.538493 0.758818i
\(405\) 1.72371e10 8.84034e9i 0.640686 0.328586i
\(406\) 1.14574e10 1.15858e10i 0.421678 0.426405i
\(407\) 5.97779e9i 0.217853i
\(408\) −1.78425e9 2.52090e8i −0.0643893 0.00909737i
\(409\) −1.31774e10 + 9.57392e9i −0.470908 + 0.342134i −0.797795 0.602929i \(-0.794000\pi\)
0.326887 + 0.945063i \(0.394000\pi\)
\(410\) −2.74022e10 + 9.15329e9i −0.969729 + 0.323923i
\(411\) 2.65419e9 3.65318e9i 0.0930176 0.128028i
\(412\) 2.50778e8 8.02133e8i 0.00870364 0.0278393i
\(413\) 2.27682e10 1.65420e10i 0.782578 0.568577i
\(414\) −4.11670e9 7.96935e9i −0.140135 0.271282i
\(415\) −2.43971e10 4.75701e10i −0.822518 1.60377i
\(416\) −9.29061e9 1.20717e9i −0.310221 0.0403082i
\(417\) 3.11438e9 9.58507e9i 0.102998 0.316994i
\(418\) −1.46289e9 + 2.91108e9i −0.0479189 + 0.0953564i
\(419\) −3.54437e10 1.15164e10i −1.14996 0.373645i −0.328833 0.944388i \(-0.606655\pi\)
−0.821129 + 0.570743i \(0.806655\pi\)
\(420\) 5.59007e9 + 1.06068e10i 0.179647 + 0.340868i
\(421\) 6.25257e8 + 1.92434e9i 0.0199035 + 0.0612568i 0.960515 0.278228i \(-0.0897472\pi\)
−0.940611 + 0.339485i \(0.889747\pi\)
\(422\) −5.44250e9 + 3.56474e10i −0.171612 + 1.12403i
\(423\) 1.95881e9 2.69607e9i 0.0611830 0.0842111i
\(424\) 2.76233e10 4.84990e9i 0.854697 0.150062i
\(425\) −6.50911e9 2.07688e9i −0.199511 0.0636585i
\(426\) 5.84469e9 1.16307e10i 0.177469 0.353156i
\(427\) 3.52318e9 4.84924e9i 0.105980 0.145869i
\(428\) −1.98110e10 1.40588e10i −0.590380 0.418961i
\(429\) −1.85814e8 5.71875e8i −0.00548591 0.0168839i
\(430\) −6.33168e8 + 2.00463e9i −0.0185202 + 0.0586354i
\(431\) 1.35314e10 + 4.39662e9i 0.392134 + 0.127412i 0.498446 0.866921i \(-0.333904\pi\)
−0.106312 + 0.994333i \(0.533904\pi\)
\(432\) 1.97163e10 + 5.92365e9i 0.566098 + 0.170080i
\(433\) −4.55944e9 + 1.40325e10i −0.129706 + 0.399194i −0.994729 0.102538i \(-0.967304\pi\)
0.865023 + 0.501732i \(0.167304\pi\)
\(434\) 8.79516e9 + 5.35953e10i 0.247905 + 1.51066i
\(435\) −8.26528e8 + 5.30947e9i −0.0230834 + 0.148284i
\(436\) 4.50840e8 + 4.04402e10i 0.0124760 + 1.11910i
\(437\) −5.82199e9 + 4.22992e9i −0.159641 + 0.115986i
\(438\) 1.19365e10 1.95881e9i 0.324324 0.0532226i
\(439\) −3.59392e10 + 4.94660e10i −0.967632 + 1.33183i −0.0243973 + 0.999702i \(0.507767\pi\)
−0.943234 + 0.332128i \(0.892233\pi\)
\(440\) −1.32677e8 6.84860e9i −0.00353984 0.182722i
\(441\) 1.49232e10 1.08424e10i 0.394556 0.286662i
\(442\) 1.77790e9 + 1.75819e9i 0.0465819 + 0.0460655i
\(443\) 4.13606e10i 1.07392i −0.843608 0.536960i \(-0.819573\pi\)
0.843608 0.536960i \(-0.180427\pi\)
\(444\) −4.59744e9 1.36305e10i −0.118300 0.350736i
\(445\) 1.01184e10 + 6.28081e10i 0.258032 + 1.60168i
\(446\) −8.47490e9 + 5.55092e10i −0.214188 + 1.40290i
\(447\) −2.05307e10 + 6.67083e9i −0.514249 + 0.167090i
\(448\) 1.38479e10 4.80280e10i 0.343773 1.19229i
\(449\) −3.57981e10 −0.880794 −0.440397 0.897803i \(-0.645162\pi\)
−0.440397 + 0.897803i \(0.645162\pi\)
\(450\) 3.31948e10 + 1.64615e10i 0.809506 + 0.401440i
\(451\) 7.73035e9i 0.186850i
\(452\) 4.61081e8 + 4.13588e10i 0.0110465 + 0.990864i
\(453\) 4.55126e8 + 1.40073e9i 0.0108078 + 0.0332631i
\(454\) 1.87582e9 1.22863e10i 0.0441537 0.289199i
\(455\) 2.55907e9 1.64390e10i 0.0597086 0.383558i
\(456\) 1.09680e9 7.76293e9i 0.0253669 0.179542i
\(457\) 2.73470e10 0.626966 0.313483 0.949594i \(-0.398504\pi\)
0.313483 + 0.949594i \(0.398504\pi\)
\(458\) −1.77333e10 1.75367e10i −0.403021 0.398553i
\(459\) −3.22958e9 4.44514e9i −0.0727604 0.100146i
\(460\) 6.68238e9 1.35747e10i 0.149245 0.303179i
\(461\) 6.71775e10 + 4.88073e10i 1.48737 + 1.08064i 0.975086 + 0.221826i \(0.0712016\pi\)
0.512287 + 0.858814i \(0.328798\pi\)
\(462\) 3.16578e9 5.19515e8i 0.0694885 0.0114033i
\(463\) 3.09475e10 + 4.25956e10i 0.673445 + 0.926917i 0.999832 0.0183191i \(-0.00583148\pi\)
−0.326388 + 0.945236i \(0.605831\pi\)
\(464\) 1.78252e10 1.35681e10i 0.384559 0.292716i
\(465\) −1.26983e10 1.26312e10i −0.271602 0.270167i
\(466\) 1.68315e9 + 1.02567e10i 0.0356927 + 0.217501i
\(467\) 6.65587e10 + 2.16262e10i 1.39939 + 0.454688i 0.908992 0.416813i \(-0.136853\pi\)
0.490394 + 0.871501i \(0.336853\pi\)
\(468\) −8.09209e9 1.08806e10i −0.168685 0.226815i
\(469\) −1.55589e10 + 4.78855e10i −0.321580 + 0.989721i
\(470\) 5.62112e9 4.62209e7i 0.115194 0.000947211i
\(471\) 1.20713e10 3.92220e9i 0.245284 0.0796977i
\(472\) 3.41758e10 1.81395e10i 0.688573 0.365475i
\(473\) 4.55076e8 + 3.30632e8i 0.00909159 + 0.00660543i
\(474\) 9.86338e9 1.96277e10i 0.195395 0.388826i
\(475\) 9.03614e9 2.83200e10i 0.177504 0.556312i
\(476\) −1.07046e10 + 7.96114e9i −0.208517 + 0.155077i
\(477\) 3.28399e10 + 2.38596e10i 0.634349 + 0.460882i
\(478\) 1.00949e10 6.61197e10i 0.193370 1.26654i
\(479\) −4.06306e10 + 1.32017e10i −0.771812 + 0.250777i −0.668341 0.743855i \(-0.732995\pi\)
−0.103472 + 0.994632i \(0.532995\pi\)
\(480\) 5.56969e9 + 1.55141e10i 0.104922 + 0.292255i
\(481\) −6.16821e9 + 1.89838e10i −0.115234 + 0.354652i
\(482\) −9.18895e9 + 1.82856e10i −0.170246 + 0.338782i
\(483\) 6.73942e9 + 2.18977e9i 0.123832 + 0.0402355i
\(484\) 5.06265e10 + 1.58278e10i 0.922564 + 0.288429i
\(485\) −2.58158e10 + 5.09998e10i −0.466572 + 0.921726i
\(486\) 2.08592e10 + 4.03804e10i 0.373897 + 0.723811i
\(487\) 4.42546e10 + 6.09113e10i 0.786761 + 1.08288i 0.994504 + 0.104700i \(0.0333882\pi\)
−0.207743 + 0.978183i \(0.566612\pi\)
\(488\) 5.72876e9 5.92362e9i 0.101014 0.104450i
\(489\) 6.92126e9 + 5.02859e9i 0.121046 + 0.0879449i
\(490\) 2.96701e10 + 9.37141e9i 0.514678 + 0.162563i
\(491\) −2.76936e10 3.81169e10i −0.476489 0.655831i 0.501336 0.865252i \(-0.332842\pi\)
−0.977825 + 0.209422i \(0.932842\pi\)
\(492\) −5.94531e9 1.76267e10i −0.101464 0.300823i
\(493\) −5.97879e9 −0.101210
\(494\) −7.64955e9 + 7.73531e9i −0.128448 + 0.129888i
\(495\) 6.99183e9 7.02897e9i 0.116458 0.117077i
\(496\) 1.66466e9 + 7.46506e10i 0.0275042 + 1.23341i
\(497\) −2.97786e10 9.16492e10i −0.488067 1.50212i
\(498\) 3.05838e10 1.57986e10i 0.497250 0.256863i
\(499\) 5.50740e10i 0.888268i −0.895960 0.444134i \(-0.853511\pi\)
0.895960 0.444134i \(-0.146489\pi\)
\(500\) 1.09540e10 + 6.15326e10i 0.175263 + 0.984522i
\(501\) −2.71380e10 −0.430751
\(502\) −3.92706e10 7.60224e10i −0.618376 1.19709i
\(503\) −8.02755e10 + 2.60831e10i −1.25404 + 0.407462i −0.859367 0.511360i \(-0.829142\pi\)
−0.394672 + 0.918822i \(0.629142\pi\)
\(504\) 6.39022e10 3.39174e10i 0.990361 0.525655i
\(505\) 4.29044e10 + 4.26777e10i 0.659684 + 0.656199i
\(506\) −2.87862e9 2.84670e9i −0.0439118 0.0434250i
\(507\) 1.85094e10i 0.280130i
\(508\) 1.52965e10 + 4.53512e10i 0.229687 + 0.680979i
\(509\) 2.55058e10 1.85310e10i 0.379986 0.276076i −0.381354 0.924429i \(-0.624542\pi\)
0.761340 + 0.648353i \(0.224542\pi\)
\(510\) 1.32502e9 4.19505e9i 0.0195858 0.0620092i
\(511\) 5.26367e10 7.24481e10i 0.771978 1.06254i
\(512\) 2.80884e10 6.27169e10i 0.408740 0.912651i
\(513\) 1.93400e10 1.40513e10i 0.279246 0.202884i
\(514\) −1.58552e10 + 8.19025e9i −0.227153 + 0.117340i
\(515\) 1.83064e9 + 9.26657e8i 0.0260239 + 0.0131732i
\(516\) −1.29195e9 4.03913e8i −0.0182241 0.00569756i
\(517\) 4.64797e8 1.43050e9i 0.00650580 0.0200228i
\(518\) −9.51566e10 4.78185e10i −1.32166 0.664166i
\(519\) −9.06378e9 2.94500e9i −0.124922 0.0405897i
\(520\) 6.64542e9 2.18862e10i 0.0908885 0.299334i
\(521\) −1.90322e10 5.85750e10i −0.258308 0.794989i −0.993160 0.116762i \(-0.962749\pi\)
0.734852 0.678227i \(-0.237251\pi\)
\(522\) 3.20517e10 + 4.89351e9i 0.431687 + 0.0659081i
\(523\) −1.51439e10 + 2.08438e10i −0.202410 + 0.278594i −0.898140 0.439710i \(-0.855081\pi\)
0.695730 + 0.718304i \(0.255081\pi\)
\(524\) −4.30443e10 + 3.20127e10i −0.570941 + 0.424617i
\(525\) −2.77907e10 + 9.19279e9i −0.365816 + 0.121007i
\(526\) −5.66420e10 2.84640e10i −0.739939 0.371837i
\(527\) 1.17137e10 1.61225e10i 0.151863 0.209021i
\(528\) 4.40948e9 9.83287e7i 0.0567351 0.00126516i
\(529\) 2.14361e10 + 6.59734e10i 0.273730 + 0.842454i
\(530\) 5.63001e8 + 6.84690e10i 0.00713519 + 0.867741i
\(531\) 5.32595e10 + 1.73050e10i 0.669913 + 0.217668i
\(532\) −3.46375e10 4.65736e10i −0.432414 0.581425i
\(533\) −7.97660e9 + 2.45495e10i −0.0988346 + 0.304182i
\(534\) −4.04223e10 + 6.63344e9i −0.497114 + 0.0815781i
\(535\) 4.18258e10 4.20479e10i 0.510539 0.513251i
\(536\) −3.03903e10 + 6.21938e10i −0.368193 + 0.753508i
\(537\) −4.88705e7 + 3.55065e7i −0.000587692 + 0.000426983i
\(538\) 2.19712e9 + 1.33886e10i 0.0262256 + 0.159811i
\(539\) 4.89363e9 6.73551e9i 0.0579797 0.0798023i
\(540\) −2.21981e10 + 4.50936e10i −0.261060 + 0.530322i
\(541\) 5.26721e10 3.82685e10i 0.614881 0.446737i −0.236249 0.971693i \(-0.575918\pi\)
0.851130 + 0.524955i \(0.175918\pi\)
\(542\) −6.63273e10 + 6.70709e10i −0.768591 + 0.777207i
\(543\) 4.55303e10i 0.523722i
\(544\) −1.61033e10 + 8.77862e9i −0.183873 + 0.100238i
\(545\) −9.75621e10 1.51875e10i −1.10585 0.172148i
\(546\) 1.05897e10 + 1.61679e9i 0.119155 + 0.0181921i
\(547\) 9.48039e10 3.08036e10i 1.05895 0.344075i 0.272777 0.962077i \(-0.412058\pi\)
0.786176 + 0.618003i \(0.212058\pi\)
\(548\) −5.12347e8 4.59573e10i −0.00568122 0.509603i
\(549\) 1.19271e10 0.131295
\(550\) 1.65449e10 + 2.43639e9i 0.180806 + 0.0266254i
\(551\) 2.60126e10i 0.282214i
\(552\) 8.75317e9 + 4.27713e9i 0.0942777 + 0.0460677i
\(553\) −5.02538e10 1.54665e11i −0.537364 1.65384i
\(554\) −1.12602e10 1.71916e9i −0.119538 0.0182506i
\(555\) 3.46725e10 5.58576e9i 0.365438 0.0588723i
\(556\) −3.27841e10 9.71987e10i −0.343056 1.01709i
\(557\) 3.65008e10 0.379211 0.189606 0.981860i \(-0.439279\pi\)
0.189606 + 0.981860i \(0.439279\pi\)
\(558\) −7.59920e10 + 7.68439e10i −0.783846 + 0.792634i
\(559\) 1.10403e9 + 1.51957e9i 0.0113067 + 0.0155623i
\(560\) 1.10080e11 + 5.26724e10i 1.11932 + 0.535589i
\(561\) −9.52330e8 6.91908e8i −0.00961471 0.00698549i
\(562\) −1.85084e10 1.12785e11i −0.185534 1.13059i
\(563\) 1.08423e11 + 1.49232e11i 1.07917 + 1.48535i 0.860435 + 0.509561i \(0.170192\pi\)
0.218732 + 0.975785i \(0.429808\pi\)
\(564\) 4.03489e7 + 3.61928e9i 0.000398763 + 0.0357689i
\(565\) −9.97781e10 1.55325e10i −0.979133 0.152422i
\(566\) 5.31568e9 8.72320e8i 0.0517956 0.00849983i
\(567\) 8.78242e10 + 2.85358e10i 0.849732 + 0.276095i
\(568\) −2.29103e10 1.30489e11i −0.220109 1.25366i
\(569\) 1.13831e10 3.50335e10i 0.108595 0.334221i −0.881962 0.471320i \(-0.843778\pi\)
0.990557 + 0.137099i \(0.0437778\pi\)
\(570\) 1.82519e10 + 5.76492e9i 0.172905 + 0.0546127i
\(571\) −3.14761e10 + 1.02272e10i −0.296099 + 0.0962084i −0.453299 0.891358i \(-0.649753\pi\)
0.157200 + 0.987567i \(0.449753\pi\)
\(572\) −4.99111e9 3.54192e9i −0.0466244 0.0330868i
\(573\) 3.25412e10 + 2.36426e10i 0.301867 + 0.219319i
\(574\) −1.23055e11 6.18379e10i −1.13357 0.569649i
\(575\) 2.99991e10 + 2.15537e10i 0.274433 + 0.197175i
\(576\) 9.35131e10 3.38811e10i 0.849537 0.307799i
\(577\) 1.33842e11 + 9.72418e10i 1.20750 + 0.877303i 0.995002 0.0998578i \(-0.0318388\pi\)
0.212502 + 0.977161i \(0.431839\pi\)
\(578\) −1.05495e11 1.61065e10i −0.945190 0.144308i
\(579\) 2.44346e10 7.93929e9i 0.217416 0.0706427i
\(580\) 2.54993e10 + 4.83832e10i 0.225328 + 0.427545i
\(581\) 7.87516e10 2.42372e11i 0.691122 2.12705i
\(582\) −3.28868e10 1.65264e10i −0.286635 0.144041i
\(583\) 1.74244e10 + 5.66153e9i 0.150829 + 0.0490072i
\(584\) 8.55882e10 8.84995e10i 0.735804 0.760833i
\(585\) 2.94570e10 1.51075e10i 0.251516 0.128994i
\(586\) −7.25265e10 + 3.74647e10i −0.615044 + 0.317711i
\(587\) 1.27053e11 + 1.74873e11i 1.07012 + 1.47289i 0.869958 + 0.493125i \(0.164146\pi\)
0.200158 + 0.979764i \(0.435854\pi\)
\(588\) −5.97825e9 + 1.91219e10i −0.0500109 + 0.159964i
\(589\) 7.01462e10 + 5.09642e10i 0.582832 + 0.423452i
\(590\) 2.99279e10 + 8.95951e10i 0.246984 + 0.739395i
\(591\) −3.19134e10 4.39250e10i −0.261591 0.360049i
\(592\) −1.20339e11 8.33968e10i −0.979760 0.678989i
\(593\) −1.07772e10 −0.0871537 −0.0435768 0.999050i \(-0.513875\pi\)
−0.0435768 + 0.999050i \(0.513875\pi\)
\(594\) 9.56243e9 + 9.45642e9i 0.0768109 + 0.0759593i
\(595\) −1.48630e10 2.89803e10i −0.118588 0.231225i
\(596\) −1.27157e11 + 1.79184e11i −1.00776 + 1.42009i
\(597\) 9.14771e9 + 2.81538e10i 0.0720137 + 0.221635i
\(598\) −6.20430e9 1.20107e10i −0.0485164 0.0939209i
\(599\) 5.81919e10i 0.452018i 0.974125 + 0.226009i \(0.0725678\pi\)
−0.974125 + 0.226009i \(0.927432\pi\)
\(600\) −3.95994e10 + 7.16902e9i −0.305551 + 0.0553165i
\(601\) −1.58431e11 −1.21434 −0.607172 0.794570i \(-0.707696\pi\)
−0.607172 + 0.794570i \(0.707696\pi\)
\(602\) −8.90345e9 + 4.59922e9i −0.0677910 + 0.0350186i
\(603\) −9.52849e10 + 3.09599e10i −0.720700 + 0.234170i
\(604\) 1.22251e10 + 8.67548e9i 0.0918552 + 0.0651847i
\(605\) −5.84858e10 + 1.15540e11i −0.436545 + 0.862406i
\(606\) −2.73988e10 + 2.77060e10i −0.203161 + 0.205439i
\(607\) 1.13850e11i 0.838648i −0.907837 0.419324i \(-0.862267\pi\)
0.907837 0.419324i \(-0.137733\pi\)
\(608\) −3.81942e10 7.00624e10i −0.279501 0.512708i
\(609\) −2.07226e10 + 1.50558e10i −0.150652 + 0.109455i
\(610\) 1.19589e10 + 1.61786e10i 0.0863719 + 0.116848i
\(611\) 2.95213e9 4.06326e9i 0.0211822 0.0291548i
\(612\) −2.53361e10 7.92106e9i −0.180607 0.0564648i
\(613\) 3.67488e10 2.66996e10i 0.260256 0.189087i −0.450004 0.893027i \(-0.648577\pi\)
0.710260 + 0.703939i \(0.248577\pi\)
\(614\) −2.78431e10 5.39002e10i −0.195904 0.379243i
\(615\) 4.48378e10 7.22339e9i 0.313432 0.0504941i
\(616\) 2.26997e10 2.34718e10i 0.157651 0.163013i
\(617\) 4.42547e10 1.36202e11i 0.305364 0.939815i −0.674177 0.738570i \(-0.735501\pi\)
0.979541 0.201245i \(-0.0644986\pi\)
\(618\) −5.93215e8 + 1.18047e9i −0.00406685 + 0.00809284i
\(619\) −2.37811e11 7.72694e10i −1.61983 0.526314i −0.647927 0.761703i \(-0.724364\pi\)
−0.971901 + 0.235389i \(0.924364\pi\)
\(620\) −1.80430e11 2.60309e10i −1.22107 0.176166i
\(621\) 9.17959e9 + 2.82519e10i 0.0617244 + 0.189968i
\(622\) −3.76702e10 + 2.46734e11i −0.251673 + 1.64842i
\(623\) −1.78252e11 + 2.45343e11i −1.18327 + 1.62862i
\(624\) 1.41048e10 + 4.23768e9i 0.0930309 + 0.0279505i
\(625\) −1.52579e11 + 1.61655e9i −0.999944 + 0.0105942i
\(626\) −9.14309e10 + 1.81943e11i −0.595382 + 1.18478i
\(627\) 3.01037e9 4.14342e9i 0.0194782 0.0268095i
\(628\) 7.47638e10 1.05354e11i 0.480676 0.677346i
\(629\) 1.20752e10 + 3.71636e10i 0.0771421 + 0.237419i
\(630\) 5.59594e10 + 1.67526e11i 0.355231 + 1.06346i
\(631\) 1.70625e11 + 5.54394e10i 1.07628 + 0.349704i 0.792930 0.609313i \(-0.208555\pi\)
0.283349 + 0.959017i \(0.408555\pi\)
\(632\) −3.86630e10 2.20211e11i −0.242341 1.38029i
\(633\) 1.75173e10 5.39126e10i 0.109107 0.335796i
\(634\) −1.55126e10 9.45294e10i −0.0960124 0.585073i
\(635\) −1.15362e11 + 1.85848e10i −0.709524 + 0.114305i
\(636\) −4.40853e10 + 4.91476e8i −0.269442 + 0.00300382i
\(637\) 2.24909e10 1.63406e10i 0.136599 0.0992453i
\(638\) 1.44408e10 2.36978e9i 0.0871583 0.0143030i
\(639\) 1.12710e11 1.55132e11i 0.676017 0.930458i
\(640\) 1.39720e11 + 9.28747e10i 0.832798 + 0.553576i
\(641\) 1.31921e11 9.58461e10i 0.781415 0.567731i −0.123989 0.992284i \(-0.539569\pi\)
0.905403 + 0.424553i \(0.139569\pi\)
\(642\) 2.71529e10 + 2.68519e10i 0.159837 + 0.158065i
\(643\) 3.04362e11i 1.78052i 0.455454 + 0.890259i \(0.349477\pi\)
−0.455454 + 0.890259i \(0.650523\pi\)
\(644\) 6.83419e10 2.30510e10i 0.397323 0.134013i
\(645\) 1.49251e9 2.94850e9i 0.00862340 0.0170358i
\(646\) −3.21430e9 + 2.10531e10i −0.0184568 + 0.120889i
\(647\) 5.08883e10 1.65346e10i 0.290403 0.0943575i −0.160193 0.987086i \(-0.551212\pi\)
0.450596 + 0.892728i \(0.351212\pi\)
\(648\) 1.14066e11 + 5.57372e10i 0.646930 + 0.316115i
\(649\) 2.52754e10 0.142469
\(650\) 5.00281e10 + 2.48093e10i 0.280260 + 0.138983i
\(651\) 8.53786e10i 0.475363i
\(652\) 8.70700e10 9.70683e8i 0.481812 0.00537140i
\(653\) 1.76184e10 + 5.42240e10i 0.0968980 + 0.298221i 0.987744 0.156085i \(-0.0498873\pi\)
−0.890846 + 0.454306i \(0.849887\pi\)
\(654\) 9.59531e9 6.28477e10i 0.0524503 0.343541i
\(655\) −5.97660e10 1.16533e11i −0.324705 0.633119i
\(656\) −1.55620e11 1.07847e11i −0.840330 0.582362i
\(657\) 1.78193e11 0.956375
\(658\) 1.90531e10 + 1.88419e10i 0.101639 + 0.100513i
\(659\) −1.83069e11 2.51973e11i −0.970672 1.33602i −0.941707 0.336435i \(-0.890779\pi\)
−0.0289657 0.999580i \(-0.509221\pi\)
\(660\) −1.53760e9 + 1.06577e10i −0.00810341 + 0.0561676i
\(661\) −8.86777e10 6.44281e10i −0.464525 0.337497i 0.330779 0.943708i \(-0.392689\pi\)
−0.795304 + 0.606211i \(0.792689\pi\)
\(662\) −7.95197e10 + 1.30494e10i −0.414040 + 0.0679454i
\(663\) −2.31039e9 3.17998e9i −0.0119572 0.0164577i
\(664\) 1.53820e11 3.14794e11i 0.791300 1.61940i
\(665\) 1.26088e11 6.46664e10i 0.644745 0.330668i
\(666\) −3.43163e10 2.09114e11i −0.174423 1.06288i
\(667\) 3.07421e10 + 9.98870e9i 0.155321 + 0.0504668i
\(668\) −2.21638e11 + 1.64835e11i −1.11311 + 0.827837i
\(669\) 2.72774e10 8.39512e10i 0.136175 0.419105i
\(670\) −1.37534e11 9.82070e10i −0.682515 0.487353i
\(671\) 5.11976e9 1.66351e9i 0.0252557 0.00820608i
\(672\) −3.37078e10 + 7.09783e10i −0.165293 + 0.348055i
\(673\) −1.10494e10 8.02786e9i −0.0538615 0.0391327i 0.560529 0.828135i \(-0.310598\pi\)
−0.614390 + 0.789002i \(0.710598\pi\)
\(674\) 8.23624e10 1.63897e11i 0.399107 0.794205i
\(675\) −9.96535e10 7.15991e10i −0.480040 0.344899i
\(676\) 1.12426e11 + 1.51168e11i 0.538367 + 0.723889i
\(677\) −1.41619e11 1.02893e11i −0.674168 0.489812i 0.197250 0.980353i \(-0.436799\pi\)
−0.871418 + 0.490541i \(0.836799\pi\)
\(678\) 9.81326e9 6.42752e10i 0.0464402 0.304176i
\(679\) −2.59147e11 + 8.42019e10i −1.21918 + 0.396135i
\(680\) −1.46591e10 4.23094e10i −0.0685601 0.197880i
\(681\) −6.03752e9 + 1.85816e10i −0.0280718 + 0.0863960i
\(682\) −2.19022e10 + 4.35843e10i −0.101239 + 0.201462i
\(683\) 1.16477e11 + 3.78457e10i 0.535251 + 0.173914i 0.564156 0.825669i \(-0.309202\pi\)
−0.0289043 + 0.999582i \(0.509202\pi\)
\(684\) 3.44631e10 1.10233e11i 0.157445 0.503601i
\(685\) 1.10872e11 + 1.72595e10i 0.503570 + 0.0783910i
\(686\) −5.80481e10 1.12373e11i −0.262115 0.507418i
\(687\) 2.30445e10 + 3.17181e10i 0.103452 + 0.142390i
\(688\) −1.30048e10 + 4.54847e9i −0.0580430 + 0.0203007i
\(689\) 4.94932e10 + 3.59589e10i 0.219619 + 0.159562i
\(690\) −1.38217e10 + 1.93566e10i −0.0609768 + 0.0853952i
\(691\) 1.47645e11 + 2.03216e11i 0.647601 + 0.891346i 0.998992 0.0448828i \(-0.0142914\pi\)
−0.351392 + 0.936229i \(0.614291\pi\)
\(692\) −9.19125e10 + 3.10011e10i −0.400821 + 0.135193i
\(693\) 4.72602e10 0.204910
\(694\) 1.93642e11 1.95813e11i 0.834761 0.844119i
\(695\) 2.47248e11 3.98319e10i 1.05973 0.170723i
\(696\) −3.11053e10 + 1.65098e10i −0.132555 + 0.0703566i
\(697\) 1.56154e10 + 4.80592e10i 0.0661640 + 0.203632i
\(698\) −1.40633e11 + 7.26462e10i −0.592468 + 0.306049i
\(699\) 1.63391e10i 0.0684415i
\(700\) −1.71132e11 + 2.43878e11i −0.712754 + 1.01574i
\(701\) −2.98200e11 −1.23491 −0.617455 0.786606i \(-0.711836\pi\)
−0.617455 + 0.786606i \(0.711836\pi\)
\(702\) 2.06100e10 + 3.98980e10i 0.0848651 + 0.164287i
\(703\) −1.61692e11 + 5.25370e10i −0.662015 + 0.215102i
\(704\) 3.54153e10 2.75861e10i 0.144178 0.112305i
\(705\) −8.73152e9 1.35924e9i −0.0353454 0.00550224i
\(706\) −1.65177e11 1.63346e11i −0.664862 0.657492i
\(707\) 2.88473e11i 1.15459i
\(708\) −5.76328e10 + 1.94390e10i −0.229370 + 0.0773642i
\(709\) −5.31939e10 + 3.86477e10i −0.210512 + 0.152946i −0.688045 0.725668i \(-0.741531\pi\)
0.477533 + 0.878614i \(0.341531\pi\)
\(710\) 3.23439e11 2.65955e9i 1.27280 0.0104658i
\(711\) 1.90207e11 2.61797e11i 0.744299 1.02444i
\(712\) −2.89841e11 + 2.99700e11i −1.12782 + 1.16618i
\(713\) −8.71659e10 + 6.33298e10i −0.337279 + 0.245047i
\(714\) 1.86321e10 9.62471e9i 0.0716916 0.0370335i
\(715\) 1.05374e10 1.05934e10i 0.0403191 0.0405332i
\(716\) −1.83464e8 + 5.86823e8i −0.000698068 + 0.00223283i
\(717\) −3.24914e10 + 9.99984e10i −0.122940 + 0.378370i
\(718\) −1.21468e11 6.10404e10i −0.457049 0.229678i
\(719\) −2.15612e11 7.00564e10i −0.806782 0.262139i −0.123548 0.992339i \(-0.539427\pi\)
−0.683234 + 0.730199i \(0.739427\pi\)
\(720\) 4.39565e10 + 2.38815e11i 0.163566 + 0.888651i
\(721\) 3.02242e9 + 9.30206e9i 0.0111844 + 0.0344222i
\(722\) 1.77026e11 + 2.70275e10i 0.651460 + 0.0994621i
\(723\) 1.89092e10 2.60263e10i 0.0692023 0.0952488i
\(724\) 2.76550e11 + 3.71849e11i 1.00651 + 1.35336i
\(725\) −1.26768e11 + 4.19332e10i −0.458837 + 0.151777i
\(726\) −7.45051e10 3.74406e10i −0.268188 0.134771i
\(727\) 1.59372e11 2.19356e11i 0.570524 0.785259i −0.422093 0.906553i \(-0.638704\pi\)
0.992617 + 0.121294i \(0.0387043\pi\)
\(728\) 9.63073e10 5.11172e10i 0.342873 0.181987i
\(729\) 4.07629e10 + 1.25455e11i 0.144329 + 0.444200i
\(730\) 1.78667e11 + 2.41710e11i 0.629149 + 0.851144i
\(731\) 3.49707e9 + 1.13627e9i 0.0122471 + 0.00397934i
\(732\) −1.03947e10 + 7.73067e9i −0.0362048 + 0.0269261i
\(733\) −1.40103e11 + 4.31193e11i −0.485324 + 1.49367i 0.346187 + 0.938165i \(0.387476\pi\)
−0.831511 + 0.555508i \(0.812524\pi\)
\(734\) 3.24158e11 5.31954e10i 1.11679 0.183269i
\(735\) −4.36402e10 2.20904e10i −0.149533 0.0756926i
\(736\) 9.74670e10 1.82348e10i 0.332159 0.0621428i
\(737\) −3.65833e10 + 2.65793e10i −0.123997 + 0.0900894i
\(738\) −4.43771e10 2.70422e11i −0.149601 0.911624i
\(739\) −8.21413e10 + 1.13058e11i −0.275413 + 0.379073i −0.924208 0.381890i \(-0.875273\pi\)
0.648795 + 0.760963i \(0.275273\pi\)
\(740\) 2.49245e11 2.56219e11i 0.831190 0.854447i
\(741\) 1.38355e10 1.00521e10i 0.0458904 0.0333414i
\(742\) −2.29507e11 + 2.32079e11i −0.757146 + 0.765634i
\(743\) 3.20508e11i 1.05168i 0.850584 + 0.525840i \(0.176249\pi\)
−0.850584 + 0.525840i \(0.823751\pi\)
\(744\) 1.64211e10 1.16225e11i 0.0535934 0.379323i
\(745\) −3.80310e11 3.78301e11i −1.23456 1.22804i
\(746\) −5.57122e11 8.50589e10i −1.79885 0.274640i
\(747\) 4.82284e11 1.56704e11i 1.54889 0.503265i
\(748\) −1.19804e10 + 1.33561e8i −0.0382705 + 0.000426652i
\(749\) 2.82715e11 0.898299
\(750\) −1.32827e9 9.82409e10i −0.00419800 0.310490i
\(751\) 3.58573e11i 1.12724i −0.826033 0.563621i \(-0.809408\pi\)
0.826033 0.563621i \(-0.190592\pi\)
\(752\) 2.23130e10 + 2.93139e10i 0.0697727 + 0.0916646i
\(753\) 4.15659e10 + 1.27927e11i 0.129288 + 0.397906i
\(754\) 4.83053e10 + 7.37504e9i 0.149455 + 0.0228181i
\(755\) −2.58101e10 + 2.59472e10i −0.0794331 + 0.0798550i
\(756\) −2.27024e11 + 7.65729e10i −0.695000 + 0.234416i
\(757\) 6.53419e10 0.198979 0.0994897 0.995039i \(-0.468279\pi\)
0.0994897 + 0.995039i \(0.468279\pi\)
\(758\) 2.14399e11 2.16803e11i 0.649452 0.656732i
\(759\) 3.74078e9 + 5.14874e9i 0.0112718 + 0.0155144i
\(760\) 1.84081e11 6.37790e10i 0.551764 0.191172i
\(761\) −4.52282e11 3.28602e11i −1.34856 0.979786i −0.999082 0.0428416i \(-0.986359\pi\)
−0.349478 0.936945i \(-0.613641\pi\)
\(762\) −1.21838e10 7.42450e10i −0.0361380 0.220215i
\(763\) −2.76653e11 3.80780e11i −0.816276 1.12351i
\(764\) 4.09371e11 4.56380e9i 1.20156 0.0133953i
\(765\) 2.92693e10 5.78223e10i 0.0854607 0.168830i
\(766\) 6.01834e11 9.87629e10i 1.74808 0.286866i
\(767\) 8.02677e10 + 2.60805e10i 0.231931 + 0.0753590i
\(768\) −5.95377e10 + 9.01392e10i −0.171138 + 0.259101i
\(769\) −7.79853e10 + 2.40014e11i −0.223001 + 0.686328i 0.775487 + 0.631364i \(0.217504\pi\)
−0.998488 + 0.0549640i \(0.982496\pi\)
\(770\) 4.73861e10 + 6.41062e10i 0.134799 + 0.182363i
\(771\) 2.66803e10 8.66895e9i 0.0755045 0.0245329i
\(772\) 1.51336e11 2.13256e11i 0.426063 0.600388i
\(773\) 4.86746e11 + 3.53642e11i 1.36328 + 0.990479i 0.998229 + 0.0594910i \(0.0189478\pi\)
0.365049 + 0.930988i \(0.381052\pi\)
\(774\) −1.78174e10 8.95369e9i −0.0496457 0.0249481i
\(775\) 1.35288e11 4.24002e11i 0.375018 1.17533i
\(776\) −3.68970e11 + 6.47811e10i −1.01752 + 0.178649i
\(777\) 1.35439e11 + 9.84020e10i 0.371585 + 0.269973i
\(778\) 5.27010e11 + 8.04616e10i 1.43847 + 0.219619i
\(779\) −2.09097e11 + 6.79397e10i −0.567803 + 0.184491i
\(780\) −1.58802e10 + 3.22592e10i −0.0429019 + 0.0871516i
\(781\) 2.67444e10 8.23107e10i 0.0718833 0.221234i
\(782\) −2.36466e10 1.18830e10i −0.0632327 0.0317759i
\(783\) −1.02122e11 3.31813e10i −0.271688 0.0882768i
\(784\) 6.73211e10 + 1.92482e11i 0.178191 + 0.509478i
\(785\) 2.23608e11 + 2.22427e11i 0.588856 + 0.585744i
\(786\) 7.49218e10 3.87021e10i 0.196299 0.101402i
\(787\) −1.28274e10 1.76554e10i −0.0334380 0.0460234i 0.791971 0.610559i \(-0.209055\pi\)
−0.825409 + 0.564536i \(0.809055\pi\)
\(788\) −5.27438e11 1.64898e11i −1.36794 0.427671i
\(789\) 8.06200e10 + 5.85738e10i 0.208034 + 0.151146i
\(790\) 5.45829e11 4.48820e9i 1.40135 0.0115229i
\(791\) −2.82937e11 3.89429e11i −0.722742 0.994770i
\(792\) 6.43350e10 + 9.08969e9i 0.163511 + 0.0231019i
\(793\) 1.79755e10 0.0454556
\(794\) 5.16155e11 + 5.10432e11i 1.29867 + 1.28427i
\(795\) 1.65565e10 1.06356e11i 0.0414475 0.266252i
\(796\) 2.45715e11 + 1.74371e11i 0.612040 + 0.434332i
\(797\) 3.44524e10 + 1.06034e11i 0.0853859 + 0.262791i 0.984629 0.174658i \(-0.0558821\pi\)
−0.899243 + 0.437449i \(0.855882\pi\)
\(798\) 4.18754e10 + 8.10648e10i 0.103264 + 0.199904i
\(799\) 9.83223e9i 0.0241249i
\(800\) −2.79867e11 + 2.99076e11i −0.683270 + 0.730166i
\(801\) −6.03442e11 −1.46590
\(802\) 6.19031e11 3.19770e11i 1.49629 0.772931i
\(803\) 7.64898e10 2.48530e10i 0.183968 0.0597747i
\(804\) 6.29752e10 8.87417e10i 0.150711 0.212375i
\(805\) 2.80064e10 + 1.73844e11i 0.0666920 + 0.413977i
\(806\) −1.14528e11 + 1.15812e11i −0.271376 + 0.274418i
\(807\) 2.13284e10i 0.0502881i
\(808\) −5.54829e10 + 3.92697e11i −0.130171 + 0.921322i
\(809\) 2.16456e11 1.57264e11i 0.505330 0.367144i −0.305719 0.952122i \(-0.598897\pi\)
0.811049 + 0.584978i \(0.198897\pi\)
\(810\) −1.80116e11 + 2.52245e11i −0.418420 + 0.585979i
\(811\) −2.76061e11 + 3.79965e11i −0.638147 + 0.878334i −0.998515 0.0544760i \(-0.982651\pi\)
0.360368 + 0.932810i \(0.382651\pi\)
\(812\) −7.77942e10 + 2.48831e11i −0.178946 + 0.572374i
\(813\) 1.19964e11 8.71591e10i 0.274593 0.199503i
\(814\) −4.38961e10 8.49766e10i −0.0999834 0.193554i
\(815\) −3.26996e10 + 2.10056e11i −0.0741160 + 0.476108i
\(816\) 2.72149e10 9.51850e9i 0.0613827 0.0214688i
\(817\) −4.94369e9 + 1.52151e10i −0.0110959 + 0.0341497i
\(818\) 1.17018e11 2.32861e11i 0.261361 0.520096i
\(819\) 1.50085e11 + 4.87656e10i 0.333582 + 0.108387i
\(820\) 3.22319e11 3.31338e11i 0.712903 0.732850i
\(821\) 2.35145e11 + 7.23703e11i 0.517564 + 1.59290i 0.778568 + 0.627560i \(0.215946\pi\)
−0.261005 + 0.965338i \(0.584054\pi\)
\(822\) −1.09044e10 + 7.14217e10i −0.0238843 + 0.156438i
\(823\) −4.57837e11 + 6.30158e11i −0.997955 + 1.37357i −0.0713839 + 0.997449i \(0.522742\pi\)
−0.926571 + 0.376119i \(0.877258\pi\)
\(824\) 2.32531e9 + 1.32442e10i 0.00504397 + 0.0287287i
\(825\) −2.50451e10 7.99122e9i −0.0540638 0.0172503i
\(826\) −2.02187e11 + 4.02343e11i −0.434343 + 0.864323i
\(827\) −3.06625e10 + 4.22033e10i −0.0655519 + 0.0902244i −0.840534 0.541759i \(-0.817759\pi\)
0.774982 + 0.631983i \(0.217759\pi\)
\(828\) 1.17041e11 + 8.30577e10i 0.249010 + 0.176709i
\(829\) 1.78666e11 + 5.49878e11i 0.378290 + 1.16426i 0.941232 + 0.337760i \(0.109669\pi\)
−0.562943 + 0.826496i \(0.690331\pi\)
\(830\) 6.96131e11 + 4.97075e11i 1.46683 + 1.04739i
\(831\) 1.70297e10 + 5.53330e9i 0.0357112 + 0.0116033i
\(832\) 1.40934e11 5.10625e10i 0.294119 0.106563i
\(833\) 1.68177e10 5.17595e10i 0.0349290 0.107500i
\(834\) 2.61130e10 + 1.59125e11i 0.0539749 + 0.328908i
\(835\) −3.07739e11 6.00037e11i −0.633048 1.23433i
\(836\) −5.81100e8 5.21245e10i −0.00118967 0.106713i
\(837\) 2.89555e11 2.10374e11i 0.589970 0.428638i
\(838\) 5.88414e11 9.65606e10i 1.19318 0.195805i
\(839\) −3.03165e11 + 4.17270e11i −0.611830 + 0.842111i −0.996726 0.0808483i \(-0.974237\pi\)
0.384897 + 0.922960i \(0.374237\pi\)
\(840\) −1.57353e11 1.09731e11i −0.316051 0.220399i
\(841\) 3.10181e11 2.25360e11i 0.620057 0.450497i
\(842\) −2.30191e10 2.27639e10i −0.0457973 0.0452896i
\(843\) 1.79669e11i 0.355765i
\(844\) −1.84399e11 5.46708e11i −0.363403 1.07742i
\(845\) −4.09254e11 + 2.09892e11i −0.802724 + 0.411690i
\(846\) −8.04747e9 + 5.27096e10i −0.0157101 + 0.102898i
\(847\) −5.87098e11 + 1.90760e11i −1.14071 + 0.370641i
\(848\) −3.57062e11 + 2.71787e11i −0.690495 + 0.525587i
\(849\) −8.46801e9 −0.0162986
\(850\) 1.07781e11 1.82740e10i 0.206474 0.0350072i
\(851\) 2.11264e11i 0.402816i
\(852\) 2.32167e9 + 2.08253e11i 0.00440598 + 0.395215i
\(853\) −1.11735e11 3.43886e11i −0.211054 0.649558i −0.999410 0.0343386i \(-0.989068\pi\)
0.788356 0.615219i \(-0.210932\pi\)
\(854\) −1.44745e10 + 9.48053e10i −0.0272127 + 0.178238i
\(855\) 2.51575e11 + 1.27345e11i 0.470763 + 0.238297i
\(856\) 3.84858e11 + 5.43754e10i 0.716812 + 0.101276i
\(857\) −1.03972e12 −1.92749 −0.963746 0.266821i \(-0.914027\pi\)
−0.963746 + 0.266821i \(0.914027\pi\)
\(858\) 6.84081e9 + 6.76497e9i 0.0126229 + 0.0124829i
\(859\) −2.63350e11 3.62471e11i −0.483684 0.665733i 0.495524 0.868594i \(-0.334976\pi\)
−0.979208 + 0.202861i \(0.934976\pi\)
\(860\) −5.71965e9 3.31461e10i −0.0104562 0.0605952i
\(861\) 1.75146e11 + 1.27251e11i 0.318705 + 0.231553i
\(862\) −2.24640e11 + 3.68641e10i −0.406871 + 0.0667690i
\(863\) −7.02512e10 9.66925e10i −0.126652 0.174321i 0.740982 0.671525i \(-0.234360\pi\)
−0.867634 + 0.497204i \(0.834360\pi\)
\(864\) −3.23774e11 + 6.05740e10i −0.581015 + 0.108701i
\(865\) −3.76656e10 2.33801e11i −0.0672791 0.417621i
\(866\) −3.82293e10 2.32959e11i −0.0679711 0.414197i
\(867\) 1.59548e11 + 5.18404e10i 0.282368 + 0.0917471i
\(868\) −5.18587e11 6.97293e11i −0.913573 1.22839i
\(869\) 4.51333e10 1.38906e11i 0.0791439 0.243580i
\(870\) −2.72391e10 8.15456e10i −0.0475461 0.142339i
\(871\) −1.43604e11 + 4.66599e10i −0.249514 + 0.0810721i
\(872\) −3.03370e11 5.71563e11i −0.524694 0.988550i
\(873\) −4.38649e11 3.18697e11i −0.755197 0.548683i
\(874\) 5.17007e10 1.02882e11i 0.0886035 0.176317i
\(875\) −5.18399e11 5.10226e11i −0.884367 0.870423i
\(876\) −1.55297e11 + 1.15497e11i −0.263723 + 0.196135i
\(877\) 4.92028e11 + 3.57479e11i 0.831747 + 0.604299i 0.920053 0.391794i \(-0.128145\pi\)
−0.0883061 + 0.996093i \(0.528145\pi\)
\(878\) 1.47651e11 9.67088e11i 0.248461 1.62738i
\(879\) 1.22044e11 3.96545e10i 0.204437 0.0664257i
\(880\) 5.21767e10 + 9.63813e10i 0.0870053 + 0.160717i
\(881\) 1.81024e11 5.57134e11i 0.300491 0.924817i −0.680830 0.732441i \(-0.738381\pi\)
0.981321 0.192376i \(-0.0616192\pi\)
\(882\) −1.32522e11 + 2.63713e11i −0.218985 + 0.435769i
\(883\) 3.78994e11 + 1.23143e11i 0.623432 + 0.202565i 0.603664 0.797239i \(-0.293707\pi\)
0.0197686 + 0.999805i \(0.493707\pi\)
\(884\) −3.81842e10 1.19379e10i −0.0625281 0.0195487i
\(885\) −2.36178e10 1.46603e11i −0.0385005 0.238984i
\(886\) 3.03719e11 + 5.87957e11i 0.492876 + 0.954138i
\(887\) 2.34632e11 + 3.22943e11i 0.379046 + 0.521712i 0.955332 0.295536i \(-0.0954983\pi\)
−0.576285 + 0.817249i \(0.695498\pi\)
\(888\) 1.65446e11 + 1.60003e11i 0.266075 + 0.257322i
\(889\) −4.50629e11 3.27401e11i −0.721460 0.524171i
\(890\) −6.05050e11 8.18541e11i −0.964342 1.30461i
\(891\) 4.87477e10 + 6.70955e10i 0.0773470 + 0.106459i
\(892\) −2.87141e11 8.51318e11i −0.453561 1.34472i
\(893\) 4.27782e10 0.0672693
\(894\) 2.42867e11 2.45589e11i 0.380205 0.384467i
\(895\) −1.33925e9 6.77921e8i −0.00208723 0.00105654i
\(896\) 1.55826e11 + 7.84425e11i 0.241773 + 1.21708i
\(897\) 6.56693e9 + 2.02109e10i 0.0101436 + 0.0312188i
\(898\) 5.08884e11 2.62872e11i 0.782552 0.404240i
\(899\) 3.89457e11i 0.596240i
\(900\) −5.92758e11 + 9.74882e9i −0.903456 + 0.0148587i
\(901\) 1.19763e11 0.181729
\(902\) −5.67655e10 1.09890e11i −0.0857548 0.166009i
\(903\) 1.49823e10 4.86803e9i 0.0225334 0.00732154i
\(904\) −3.10260e11 5.84546e11i −0.464571 0.875276i
\(905\) −1.00670e12 + 5.16304e11i −1.50074 + 0.769681i
\(906\) −1.67557e10 1.65699e10i −0.0248685 0.0245928i
\(907\) 7.43208e11i 1.09820i 0.835757 + 0.549100i \(0.185029\pi\)
−0.835757 + 0.549100i \(0.814971\pi\)
\(908\) 6.35551e10 + 1.88429e11i 0.0934990 + 0.277207i
\(909\) −4.64390e11 + 3.37399e11i −0.680185 + 0.494183i
\(910\) 8.43368e10 + 2.52479e11i 0.122985 + 0.368180i
\(911\) 4.99846e11 6.87979e11i 0.725709 0.998853i −0.273606 0.961842i \(-0.588216\pi\)
0.999315 0.0370108i \(-0.0117836\pi\)
\(912\) 4.14133e10 + 1.18407e11i 0.0598632 + 0.171158i
\(913\) 1.85166e11 1.34531e11i 0.266489 0.193615i
\(914\) −3.88748e11 + 2.00814e11i −0.557036 + 0.287746i
\(915\) −1.44328e10 2.81414e10i −0.0205904 0.0401477i
\(916\) 3.80861e11 + 1.19072e11i 0.540985 + 0.169133i
\(917\) 1.92919e11 5.93745e11i 0.272834 0.839697i
\(918\) 7.85513e10 + 3.94739e10i 0.110607 + 0.0555827i
\(919\) −2.54991e11 8.28514e10i −0.357488 0.116155i 0.124766 0.992186i \(-0.460182\pi\)
−0.482255 + 0.876031i \(0.660182\pi\)
\(920\) 4.68899e9 + 2.42040e11i 0.00654527 + 0.337859i
\(921\) 2.94704e10 + 9.07006e10i 0.0409588 + 0.126058i
\(922\) −1.31336e12 2.00518e11i −1.81743 0.277478i
\(923\) 1.69865e11 2.33800e11i 0.234044 0.322134i
\(924\) −4.11879e10 + 3.06321e10i −0.0565044 + 0.0420231i
\(925\) 5.16684e11 + 7.03289e11i 0.705761 + 0.960654i
\(926\) −7.52719e11 3.78260e11i −1.02374 0.514453i
\(927\) −1.14396e10 + 1.57453e10i −0.0154915 + 0.0213222i
\(928\) −1.53759e11 + 3.23770e11i −0.207324 + 0.436560i
\(929\) −2.72545e11 8.38809e11i −0.365912 1.12616i −0.949408 0.314044i \(-0.898316\pi\)
0.583497 0.812115i \(-0.301684\pi\)
\(930\) 2.73265e11 + 8.63115e10i 0.365302 + 0.115382i
\(931\) 2.25196e11 + 7.31707e10i 0.299752 + 0.0973954i
\(932\) −9.92433e10 1.33443e11i −0.131534 0.176861i
\(933\) 1.21246e11 3.73156e11i 0.160007 0.492452i
\(934\) −1.10496e12 + 1.81328e11i −1.45198 + 0.238275i
\(935\) 4.49930e9 2.89027e10i 0.00588706 0.0378174i
\(936\) 1.94931e11 + 9.52507e10i 0.253967 + 0.124098i
\(937\) 5.08403e11 3.69376e11i 0.659553 0.479193i −0.206959 0.978350i \(-0.566357\pi\)
0.866512 + 0.499156i \(0.166357\pi\)
\(938\) −1.30456e11 7.94964e11i −0.168521 1.02692i
\(939\) 1.88149e11 2.58964e11i 0.242013 0.333102i
\(940\) −7.95670e10 + 4.19340e10i −0.101911 + 0.0537100i
\(941\) 1.52284e11 1.10641e11i 0.194221 0.141110i −0.486425 0.873722i \(-0.661699\pi\)
0.680646 + 0.732613i \(0.261699\pi\)
\(942\) −1.42797e11 + 1.44397e11i −0.181349 + 0.183382i
\(943\) 2.73202e11i 0.345491i
\(944\) −3.52620e11 + 5.08820e11i −0.444037 + 0.640731i
\(945\) −9.30341e10 5.77491e11i −0.116658 0.724132i
\(946\) −8.89699e9 1.35835e9i −0.0111091 0.00169609i
\(947\) 7.07205e11 2.29785e11i 0.879317 0.285707i 0.165643 0.986186i \(-0.447030\pi\)
0.713674 + 0.700478i \(0.247030\pi\)
\(948\) 3.91801e9 + 3.51444e11i 0.00485101 + 0.435134i
\(949\) 2.68555e11 0.331107
\(950\) 7.95068e10 + 4.68934e11i 0.0976134 + 0.575728i
\(951\) 1.50588e11i 0.184106i
\(952\) 9.37094e10 1.91777e11i 0.114087 0.233479i
\(953\) −3.79555e11 1.16815e12i −0.460154 1.41621i −0.864976 0.501813i \(-0.832667\pi\)
0.404823 0.914395i \(-0.367333\pi\)
\(954\) −6.42038e11 9.80236e10i −0.775117 0.118341i
\(955\) −1.53742e11 + 9.87609e11i −0.184832 + 1.18733i
\(956\) 3.42028e11 + 1.01405e12i 0.409477 + 1.21402i
\(957\) −2.30046e10 −0.0274262
\(958\) 4.80638e11 4.86026e11i 0.570632 0.577029i
\(959\) 3.14395e11 + 4.32728e11i 0.371708 + 0.511612i
\(960\) −1.93099e11 1.79640e11i −0.227350 0.211503i
\(961\) 3.60215e11 + 2.61712e11i 0.422346 + 0.306853i
\(962\) −5.17183e10 3.15157e11i −0.0603870 0.367982i
\(963\) 3.30664e11 + 4.55120e11i 0.384487 + 0.529201i
\(964\) −3.65010e9 3.27413e11i −0.00422666 0.379130i
\(965\) 4.52626e11 + 4.50234e11i 0.521951 + 0.519194i
\(966\) −1.11883e11 + 1.83604e10i −0.128486 + 0.0210850i
\(967\) −1.39747e12 4.54064e11i −1.59821 0.519291i −0.631550 0.775335i \(-0.717581\pi\)
−0.966665 + 0.256044i \(0.917581\pi\)
\(968\) −8.35902e11 + 1.46762e11i −0.952038 + 0.167152i
\(969\) 1.03456e10 3.18404e10i 0.0117344 0.0361147i
\(970\) −7.52011e9 9.14553e11i −0.00849449 1.03305i
\(971\) 7.12341e11 2.31454e11i 0.801330 0.260368i 0.120408 0.992724i \(-0.461580\pi\)
0.680921 + 0.732357i \(0.261580\pi\)
\(972\) −5.93042e11 4.20850e11i −0.664386 0.471479i
\(973\) 9.65808e11 + 7.01700e11i 1.07755 + 0.782889i
\(974\) −1.07638e12 5.40907e11i −1.19600 0.601017i
\(975\) −7.12905e10 5.12208e10i −0.0788884 0.0566797i
\(976\) −3.79382e10 + 1.26274e11i −0.0418097 + 0.139160i
\(977\) −1.28096e12 9.30672e11i −1.40591 1.02145i −0.993901 0.110273i \(-0.964827\pi\)
−0.412008 0.911180i \(-0.635173\pi\)
\(978\) −1.35314e11 2.06592e10i −0.147907 0.0225818i
\(979\) −2.59030e11 + 8.41638e10i −0.281980 + 0.0916209i
\(980\) −4.90589e11 + 8.46555e10i −0.531880 + 0.0917806i
\(981\) 2.89414e11 8.90724e11i 0.312495 0.961760i
\(982\) 6.73575e11 + 3.38488e11i 0.724336 + 0.363996i
\(983\) 2.41989e11 + 7.86271e10i 0.259168 + 0.0842089i 0.435719 0.900083i \(-0.356494\pi\)
−0.176551 + 0.984292i \(0.556494\pi\)
\(984\) 2.13951e11 + 2.06913e11i 0.228210 + 0.220703i
\(985\) 6.09318e11 1.20372e12i 0.647290 1.27874i
\(986\) 8.49908e10 4.39034e10i 0.0899217 0.0464505i
\(987\) −2.47596e10 3.40787e10i −0.0260901 0.0359099i
\(988\) 5.19395e10 1.66133e11i 0.0545093 0.174352i
\(989\) −1.60831e10 1.16850e10i −0.0168106 0.0122136i
\(990\) −4.77766e10 + 1.51262e11i −0.0497364 + 0.157467i
\(991\) 7.51916e11 + 1.03492e12i 0.779605 + 1.07303i 0.995325 + 0.0965788i \(0.0307900\pi\)
−0.215721 + 0.976455i \(0.569210\pi\)
\(992\) −5.71838e11 1.04896e12i −0.590508 1.08321i
\(993\) 1.26677e11 0.130287
\(994\) 1.09631e12 + 1.08416e12i 1.12302 + 1.11057i
\(995\) −5.18764e11 + 5.21519e11i −0.529270 + 0.532081i
\(996\) −3.18749e11 + 4.49166e11i −0.323901 + 0.456425i
\(997\) 3.60361e11 + 1.10908e12i 0.364718 + 1.12249i 0.950157 + 0.311771i \(0.100922\pi\)
−0.585439 + 0.810716i \(0.699078\pi\)
\(998\) 4.04419e11 + 7.82898e11i 0.407671 + 0.789193i
\(999\) 7.01795e11i 0.704609i
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 100.9.j.b.91.18 yes 464
4.3 odd 2 inner 100.9.j.b.91.62 yes 464
25.11 even 5 inner 100.9.j.b.11.62 yes 464
100.11 odd 10 inner 100.9.j.b.11.18 464
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
100.9.j.b.11.18 464 100.11 odd 10 inner
100.9.j.b.11.62 yes 464 25.11 even 5 inner
100.9.j.b.91.18 yes 464 1.1 even 1 trivial
100.9.j.b.91.62 yes 464 4.3 odd 2 inner