Properties

Label 5.20.b.a.4.2
Level $5$
Weight $20$
Character 5.4
Analytic conductor $11.441$
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] = [5,20,Mod(4,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 20, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.4");
 
S:= CuspForms(chi, 20);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 5.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.4408348278\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 726881x^{6} + 160513523376x^{4} + 10607307647230976x^{2} + 32429098232548950016 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{8}\cdot 5^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.2
Root \(-490.322i\) of defining polynomial
Character \(\chi\) \(=\) 5.4
Dual form 5.20.b.a.4.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-980.644i q^{2} -42067.9i q^{3} -437374. q^{4} +(-2.12371e6 - 3.81619e6i) q^{5} -4.12537e7 q^{6} -4.16374e7i q^{7} -8.52313e7i q^{8} -6.07450e8 q^{9} +O(q^{10})\) \(q-980.644i q^{2} -42067.9i q^{3} -437374. q^{4} +(-2.12371e6 - 3.81619e6i) q^{5} -4.12537e7 q^{6} -4.16374e7i q^{7} -8.52313e7i q^{8} -6.07450e8 q^{9} +(-3.74233e9 + 2.08261e9i) q^{10} +1.14407e10 q^{11} +1.83994e10i q^{12} +4.17570e10i q^{13} -4.08315e10 q^{14} +(-1.60539e11 + 8.93403e10i) q^{15} -3.12892e11 q^{16} -7.42315e9i q^{17} +5.95692e11i q^{18} +2.13723e12 q^{19} +(9.28858e11 + 1.66910e12i) q^{20} -1.75160e12 q^{21} -1.12193e13i q^{22} -9.51745e12i q^{23} -3.58551e12 q^{24} +(-1.00532e13 + 1.62090e13i) q^{25} +4.09487e13 q^{26} -2.33398e13i q^{27} +1.82111e13i q^{28} -5.19464e13 q^{29} +(8.76110e13 + 1.57432e14i) q^{30} -2.16926e14 q^{31} +2.62150e14i q^{32} -4.81287e14i q^{33} -7.27947e12 q^{34} +(-1.58896e14 + 8.84260e13i) q^{35} +2.65683e14 q^{36} +7.79624e14i q^{37} -2.09586e15i q^{38} +1.75663e15 q^{39} +(-3.25259e14 + 1.81007e14i) q^{40} +1.01438e15 q^{41} +1.71770e15i q^{42} -3.59622e15i q^{43} -5.00387e15 q^{44} +(1.29005e15 + 2.31815e15i) q^{45} -9.33323e15 q^{46} -5.35264e14i q^{47} +1.31627e16i q^{48} +9.66522e15 q^{49} +(1.58953e16 + 9.85858e15i) q^{50} -3.12277e14 q^{51} -1.82634e16i q^{52} +1.44320e16i q^{53} -2.28880e16 q^{54} +(-2.42968e16 - 4.36599e16i) q^{55} -3.54881e15 q^{56} -8.99087e16i q^{57} +5.09409e16i q^{58} +1.09094e17 q^{59} +(7.02158e16 - 3.90751e16i) q^{60} -1.12610e17 q^{61} +2.12727e17i q^{62} +2.52927e16i q^{63} +9.30300e16 q^{64} +(1.59353e17 - 8.86799e16i) q^{65} -4.71971e17 q^{66} +5.23746e16i q^{67} +3.24670e15i q^{68} -4.00380e17 q^{69} +(8.67144e16 + 1.55821e17i) q^{70} +2.62839e17 q^{71} +5.17738e16i q^{72} -4.11875e17i q^{73} +7.64534e17 q^{74} +(6.81879e17 + 4.22916e17i) q^{75} -9.34768e17 q^{76} -4.76361e17i q^{77} -1.72263e18i q^{78} +6.87674e17 q^{79} +(6.64492e17 + 1.19406e18i) q^{80} -1.68787e18 q^{81} -9.94743e17i q^{82} +1.74169e18i q^{83} +7.66105e17 q^{84} +(-2.83282e16 + 1.57646e16i) q^{85} -3.52662e18 q^{86} +2.18528e18i q^{87} -9.75106e17i q^{88} -4.41598e17 q^{89} +(2.27328e18 - 1.26508e18i) q^{90} +1.73865e18 q^{91} +4.16269e18i q^{92} +9.12562e18i q^{93} -5.24904e17 q^{94} +(-4.53886e18 - 8.15607e18i) q^{95} +1.10281e19 q^{96} -8.34283e18i q^{97} -9.47814e18i q^{98} -6.94966e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9} - 610691000 q^{10} - 3379575264 q^{11} + 177250591032 q^{14} - 242324628000 q^{15} - 312730276832 q^{16} + 4547188380640 q^{19} - 4180429431000 q^{20} - 2983154334624 q^{21} - 6176642779680 q^{24} + 17715709625000 q^{25} + 15909228128496 q^{26} - 188222300345040 q^{29} + 148501482939000 q^{30} + 72115006686976 q^{31} + 378440221985792 q^{34} - 299115755916000 q^{35} - 964020253238712 q^{36} + 30\!\cdots\!28 q^{39}+ \cdots - 16\!\cdots\!72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 980.644i 1.35434i −0.735829 0.677168i \(-0.763207\pi\)
0.735829 0.677168i \(-0.236793\pi\)
\(3\) 42067.9i 1.23396i −0.786981 0.616978i \(-0.788357\pi\)
0.786981 0.616978i \(-0.211643\pi\)
\(4\) −437374. −0.834225
\(5\) −2.12371e6 3.81619e6i −0.486274 0.873806i
\(6\) −4.12537e7 −1.67119
\(7\) 4.16374e7i 0.389989i −0.980804 0.194995i \(-0.937531\pi\)
0.980804 0.194995i \(-0.0624689\pi\)
\(8\) 8.52313e7i 0.224514i
\(9\) −6.07450e8 −0.522645
\(10\) −3.74233e9 + 2.08261e9i −1.18343 + 0.658578i
\(11\) 1.14407e10 1.46293 0.731463 0.681881i \(-0.238838\pi\)
0.731463 + 0.681881i \(0.238838\pi\)
\(12\) 1.83994e10i 1.02940i
\(13\) 4.17570e10i 1.09211i 0.837749 + 0.546056i \(0.183871\pi\)
−0.837749 + 0.546056i \(0.816129\pi\)
\(14\) −4.08315e10 −0.528176
\(15\) −1.60539e11 + 8.93403e10i −1.07824 + 0.600040i
\(16\) −3.12892e11 −1.13829
\(17\) 7.42315e9i 0.0151818i −0.999971 0.00759090i \(-0.997584\pi\)
0.999971 0.00759090i \(-0.00241628\pi\)
\(18\) 5.95692e11i 0.707837i
\(19\) 2.13723e12 1.51947 0.759733 0.650235i \(-0.225329\pi\)
0.759733 + 0.650235i \(0.225329\pi\)
\(20\) 9.28858e11 + 1.66910e12i 0.405662 + 0.728952i
\(21\) −1.75160e12 −0.481229
\(22\) 1.12193e13i 1.98129i
\(23\) 9.51745e12i 1.10181i −0.834568 0.550904i \(-0.814283\pi\)
0.834568 0.550904i \(-0.185717\pi\)
\(24\) −3.58551e12 −0.277041
\(25\) −1.00532e13 + 1.62090e13i −0.527076 + 0.849818i
\(26\) 4.09487e13 1.47909
\(27\) 2.33398e13i 0.589035i
\(28\) 1.82111e13i 0.325339i
\(29\) −5.19464e13 −0.664928 −0.332464 0.943116i \(-0.607880\pi\)
−0.332464 + 0.943116i \(0.607880\pi\)
\(30\) 8.76110e13 + 1.57432e14i 0.812656 + 1.46030i
\(31\) −2.16926e14 −1.47358 −0.736792 0.676119i \(-0.763660\pi\)
−0.736792 + 0.676119i \(0.763660\pi\)
\(32\) 2.62150e14i 1.31712i
\(33\) 4.81287e14i 1.80518i
\(34\) −7.27947e12 −0.0205613
\(35\) −1.58896e14 + 8.84260e13i −0.340775 + 0.189642i
\(36\) 2.65683e14 0.436004
\(37\) 7.79624e14i 0.986209i 0.869970 + 0.493105i \(0.164138\pi\)
−0.869970 + 0.493105i \(0.835862\pi\)
\(38\) 2.09586e15i 2.05787i
\(39\) 1.75663e15 1.34762
\(40\) −3.25259e14 + 1.81007e14i −0.196182 + 0.109175i
\(41\) 1.01438e15 0.483897 0.241948 0.970289i \(-0.422214\pi\)
0.241948 + 0.970289i \(0.422214\pi\)
\(42\) 1.71770e15i 0.651746i
\(43\) 3.59622e15i 1.09118i −0.838052 0.545590i \(-0.816306\pi\)
0.838052 0.545590i \(-0.183694\pi\)
\(44\) −5.00387e15 −1.22041
\(45\) 1.29005e15 + 2.31815e15i 0.254149 + 0.456691i
\(46\) −9.33323e15 −1.49222
\(47\) 5.35264e14i 0.0697652i −0.999391 0.0348826i \(-0.988894\pi\)
0.999391 0.0348826i \(-0.0111057\pi\)
\(48\) 1.31627e16i 1.40460i
\(49\) 9.66522e15 0.847908
\(50\) 1.58953e16 + 9.85858e15i 1.15094 + 0.713837i
\(51\) −3.12277e14 −0.0187337
\(52\) 1.82634e16i 0.911068i
\(53\) 1.44320e16i 0.600767i 0.953819 + 0.300383i \(0.0971146\pi\)
−0.953819 + 0.300383i \(0.902885\pi\)
\(54\) −2.28880e16 −0.797751
\(55\) −2.42968e16 4.36599e16i −0.711383 1.27831i
\(56\) −3.54881e15 −0.0875582
\(57\) 8.99087e16i 1.87495i
\(58\) 5.09409e16i 0.900536i
\(59\) 1.09094e17 1.63949 0.819745 0.572729i \(-0.194115\pi\)
0.819745 + 0.572729i \(0.194115\pi\)
\(60\) 7.02158e16 3.90751e16i 0.899493 0.500569i
\(61\) −1.12610e17 −1.23294 −0.616472 0.787377i \(-0.711439\pi\)
−0.616472 + 0.787377i \(0.711439\pi\)
\(62\) 2.12727e17i 1.99573i
\(63\) 2.52927e16i 0.203826i
\(64\) 9.30300e16 0.645525
\(65\) 1.59353e17 8.86799e16i 0.954295 0.531066i
\(66\) −4.71971e17 −2.44483
\(67\) 5.23746e16i 0.235185i 0.993062 + 0.117593i \(0.0375177\pi\)
−0.993062 + 0.117593i \(0.962482\pi\)
\(68\) 3.24670e15i 0.0126650i
\(69\) −4.00380e17 −1.35958
\(70\) 8.67144e16 + 1.55821e17i 0.256838 + 0.461524i
\(71\) 2.62839e17 0.680354 0.340177 0.940361i \(-0.389513\pi\)
0.340177 + 0.940361i \(0.389513\pi\)
\(72\) 5.17738e16i 0.117341i
\(73\) 4.11875e17i 0.818838i −0.912346 0.409419i \(-0.865731\pi\)
0.912346 0.409419i \(-0.134269\pi\)
\(74\) 7.64534e17 1.33566
\(75\) 6.81879e17 + 4.22916e17i 1.04864 + 0.650387i
\(76\) −9.34768e17 −1.26758
\(77\) 4.76361e17i 0.570525i
\(78\) 1.72263e18i 1.82513i
\(79\) 6.87674e17 0.645543 0.322771 0.946477i \(-0.395386\pi\)
0.322771 + 0.946477i \(0.395386\pi\)
\(80\) 6.64492e17 + 1.19406e18i 0.553522 + 0.994648i
\(81\) −1.68787e18 −1.24949
\(82\) 9.94743e17i 0.655359i
\(83\) 1.74169e18i 1.02266i 0.859386 + 0.511328i \(0.170846\pi\)
−0.859386 + 0.511328i \(0.829154\pi\)
\(84\) 7.66105e17 0.401453
\(85\) −2.83282e16 + 1.57646e16i −0.0132660 + 0.00738251i
\(86\) −3.52662e18 −1.47782
\(87\) 2.18528e18i 0.820491i
\(88\) 9.75106e17i 0.328448i
\(89\) −4.41598e17 −0.133605 −0.0668023 0.997766i \(-0.521280\pi\)
−0.0668023 + 0.997766i \(0.521280\pi\)
\(90\) 2.27328e18 1.26508e18i 0.618512 0.344203i
\(91\) 1.73865e18 0.425912
\(92\) 4.16269e18i 0.919157i
\(93\) 9.12562e18i 1.81834i
\(94\) −5.24904e17 −0.0944854
\(95\) −4.53886e18 8.15607e18i −0.738877 1.32772i
\(96\) 1.10281e19 1.62526
\(97\) 8.34283e18i 1.11425i −0.830429 0.557124i \(-0.811905\pi\)
0.830429 0.557124i \(-0.188095\pi\)
\(98\) 9.47814e18i 1.14835i
\(99\) −6.94966e18 −0.764591
\(100\) 4.39700e18 7.08940e18i 0.439700 0.708940i
\(101\) −1.28630e19 −1.17028 −0.585141 0.810932i \(-0.698961\pi\)
−0.585141 + 0.810932i \(0.698961\pi\)
\(102\) 3.06232e17i 0.0253717i
\(103\) 1.19999e19i 0.906200i 0.891460 + 0.453100i \(0.149682\pi\)
−0.891460 + 0.453100i \(0.850318\pi\)
\(104\) 3.55900e18 0.245195
\(105\) 3.71990e18 + 6.68445e18i 0.234009 + 0.420501i
\(106\) 1.41527e19 0.813640
\(107\) 1.09925e19i 0.578031i −0.957324 0.289015i \(-0.906672\pi\)
0.957324 0.289015i \(-0.0933279\pi\)
\(108\) 1.02082e19i 0.491388i
\(109\) 2.91204e19 1.28424 0.642119 0.766605i \(-0.278055\pi\)
0.642119 + 0.766605i \(0.278055\pi\)
\(110\) −4.28148e19 + 2.38265e19i −1.73127 + 0.963451i
\(111\) 3.27972e19 1.21694
\(112\) 1.30280e19i 0.443922i
\(113\) 7.96559e18i 0.249444i 0.992192 + 0.124722i \(0.0398039\pi\)
−0.992192 + 0.124722i \(0.960196\pi\)
\(114\) −8.81684e19 −2.53932
\(115\) −3.63204e19 + 2.02123e19i −0.962768 + 0.535781i
\(116\) 2.27200e19 0.554700
\(117\) 2.53653e19i 0.570787i
\(118\) 1.06983e20i 2.22042i
\(119\) −3.09081e17 −0.00592074
\(120\) 7.61459e18 + 1.36830e19i 0.134718 + 0.242080i
\(121\) 6.97306e19 1.14015
\(122\) 1.10430e20i 1.66982i
\(123\) 4.26728e19i 0.597107i
\(124\) 9.48778e19 1.22930
\(125\) 8.32067e19 + 3.94155e18i 0.998880 + 0.0473175i
\(126\) 2.48031e19 0.276049
\(127\) 1.17395e20i 1.21204i −0.795450 0.606019i \(-0.792766\pi\)
0.795450 0.606019i \(-0.207234\pi\)
\(128\) 4.62126e19i 0.442859i
\(129\) −1.51286e20 −1.34647
\(130\) −8.69634e19 1.56268e20i −0.719241 1.29244i
\(131\) −7.72292e19 −0.593888 −0.296944 0.954895i \(-0.595967\pi\)
−0.296944 + 0.954895i \(0.595967\pi\)
\(132\) 2.10503e20i 1.50593i
\(133\) 8.89886e19i 0.592575i
\(134\) 5.13608e19 0.318520
\(135\) −8.90691e19 + 4.95670e19i −0.514702 + 0.286432i
\(136\) −6.32685e17 −0.00340853
\(137\) 5.30215e19i 0.266444i −0.991086 0.133222i \(-0.957468\pi\)
0.991086 0.133222i \(-0.0425324\pi\)
\(138\) 3.92630e20i 1.84133i
\(139\) 2.98946e19 0.130904 0.0654519 0.997856i \(-0.479151\pi\)
0.0654519 + 0.997856i \(0.479151\pi\)
\(140\) 6.94972e19 3.86753e19i 0.284283 0.158204i
\(141\) −2.25175e19 −0.0860871
\(142\) 2.57751e20i 0.921428i
\(143\) 4.77729e20i 1.59768i
\(144\) 1.90066e20 0.594923
\(145\) 1.10319e20 + 1.98238e20i 0.323337 + 0.581018i
\(146\) −4.03903e20 −1.10898
\(147\) 4.06596e20i 1.04628i
\(148\) 3.40988e20i 0.822721i
\(149\) 3.32734e20 0.753057 0.376529 0.926405i \(-0.377118\pi\)
0.376529 + 0.926405i \(0.377118\pi\)
\(150\) 4.14730e20 6.68681e20i 0.880843 1.42021i
\(151\) −2.93056e20 −0.584345 −0.292172 0.956366i \(-0.594378\pi\)
−0.292172 + 0.956366i \(0.594378\pi\)
\(152\) 1.82159e20i 0.341142i
\(153\) 4.50919e18i 0.00793469i
\(154\) −4.67141e20 −0.772683
\(155\) 4.60688e20 + 8.27830e20i 0.716565 + 1.28763i
\(156\) −7.68305e20 −1.12422
\(157\) 8.15273e18i 0.0112268i 0.999984 + 0.00561340i \(0.00178681\pi\)
−0.999984 + 0.00561340i \(0.998213\pi\)
\(158\) 6.74363e20i 0.874282i
\(159\) 6.07125e20 0.741319
\(160\) 1.00041e21 5.56731e20i 1.15091 0.640480i
\(161\) −3.96282e20 −0.429693
\(162\) 1.65520e21i 1.69223i
\(163\) 5.95063e20i 0.573827i −0.957957 0.286913i \(-0.907371\pi\)
0.957957 0.286913i \(-0.0926292\pi\)
\(164\) −4.43663e20 −0.403679
\(165\) −1.83668e21 + 1.02212e21i −1.57738 + 0.877814i
\(166\) 1.70798e21 1.38502
\(167\) 1.29434e21i 0.991382i 0.868499 + 0.495691i \(0.165085\pi\)
−0.868499 + 0.495691i \(0.834915\pi\)
\(168\) 1.49291e20i 0.108043i
\(169\) −2.81726e20 −0.192709
\(170\) 1.54595e19 + 2.77798e19i 0.00999840 + 0.0179666i
\(171\) −1.29826e21 −0.794142
\(172\) 1.57290e21i 0.910290i
\(173\) 2.62946e21i 1.44022i −0.693859 0.720111i \(-0.744091\pi\)
0.693859 0.720111i \(-0.255909\pi\)
\(174\) 2.14298e21 1.11122
\(175\) 6.74901e20 + 4.18588e20i 0.331420 + 0.205554i
\(176\) −3.57970e21 −1.66524
\(177\) 4.58938e21i 2.02306i
\(178\) 4.33050e20i 0.180946i
\(179\) −8.09069e20 −0.320539 −0.160270 0.987073i \(-0.551236\pi\)
−0.160270 + 0.987073i \(0.551236\pi\)
\(180\) −5.64235e20 1.01390e21i −0.212017 0.380983i
\(181\) 3.10735e21 1.10776 0.553878 0.832598i \(-0.313147\pi\)
0.553878 + 0.832598i \(0.313147\pi\)
\(182\) 1.70500e21i 0.576828i
\(183\) 4.73727e21i 1.52140i
\(184\) −8.11185e20 −0.247372
\(185\) 2.97520e21 1.65570e21i 0.861756 0.479568i
\(186\) 8.94898e21 2.46264
\(187\) 8.49261e19i 0.0222099i
\(188\) 2.34111e20i 0.0581999i
\(189\) −9.71808e20 −0.229717
\(190\) −7.99820e21 + 4.45100e21i −1.79818 + 1.00069i
\(191\) 3.37556e21 0.721986 0.360993 0.932569i \(-0.382438\pi\)
0.360993 + 0.932569i \(0.382438\pi\)
\(192\) 3.91358e21i 0.796549i
\(193\) 3.16222e21i 0.612629i 0.951930 + 0.306314i \(0.0990959\pi\)
−0.951930 + 0.306314i \(0.900904\pi\)
\(194\) −8.18135e21 −1.50907
\(195\) −3.73058e21 6.70364e21i −0.655311 1.17756i
\(196\) −4.22732e21 −0.707347
\(197\) 1.08962e21i 0.173718i −0.996221 0.0868588i \(-0.972317\pi\)
0.996221 0.0868588i \(-0.0276829\pi\)
\(198\) 6.81514e21i 1.03551i
\(199\) −1.26294e21 −0.182927 −0.0914635 0.995808i \(-0.529154\pi\)
−0.0914635 + 0.995808i \(0.529154\pi\)
\(200\) 1.38151e21 + 8.56844e20i 0.190796 + 0.118336i
\(201\) 2.20329e21 0.290208
\(202\) 1.26141e22i 1.58495i
\(203\) 2.16292e21i 0.259315i
\(204\) 1.36582e20 0.0156281
\(205\) −2.15425e21 3.87106e21i −0.235306 0.422832i
\(206\) 1.17676e22 1.22730
\(207\) 5.78138e21i 0.575855i
\(208\) 1.30654e22i 1.24314i
\(209\) 2.44514e22 2.22287
\(210\) 6.55506e21 3.64790e21i 0.569500 0.316927i
\(211\) −1.13686e22 −0.944110 −0.472055 0.881569i \(-0.656488\pi\)
−0.472055 + 0.881569i \(0.656488\pi\)
\(212\) 6.31219e21i 0.501175i
\(213\) 1.10571e22i 0.839527i
\(214\) −1.07797e22 −0.782848
\(215\) −1.37239e22 + 7.63735e21i −0.953480 + 0.530612i
\(216\) −1.98928e21 −0.132247
\(217\) 9.03223e21i 0.574682i
\(218\) 2.85568e22i 1.73929i
\(219\) −1.73267e22 −1.01041
\(220\) 1.06268e22 + 1.90957e22i 0.593453 + 1.06640i
\(221\) 3.09968e20 0.0165802
\(222\) 3.21624e22i 1.64814i
\(223\) 1.73802e21i 0.0853414i 0.999089 + 0.0426707i \(0.0135866\pi\)
−0.999089 + 0.0426707i \(0.986413\pi\)
\(224\) 1.09152e22 0.513661
\(225\) 6.10680e21 9.84616e21i 0.275473 0.444153i
\(226\) 7.81141e21 0.337831
\(227\) 3.40756e22i 1.41318i 0.707623 + 0.706590i \(0.249768\pi\)
−0.707623 + 0.706590i \(0.750232\pi\)
\(228\) 3.93238e22i 1.56413i
\(229\) 6.46428e21 0.246651 0.123326 0.992366i \(-0.460644\pi\)
0.123326 + 0.992366i \(0.460644\pi\)
\(230\) 1.98211e22 + 3.56174e22i 0.725627 + 1.30391i
\(231\) −2.00395e22 −0.704002
\(232\) 4.42746e21i 0.149286i
\(233\) 3.38945e21i 0.109711i −0.998494 0.0548553i \(-0.982530\pi\)
0.998494 0.0548553i \(-0.0174698\pi\)
\(234\) −2.48743e22 −0.773037
\(235\) −2.04267e21 + 1.13675e21i −0.0609612 + 0.0339250i
\(236\) −4.77151e22 −1.36770
\(237\) 2.89290e22i 0.796571i
\(238\) 3.03098e20i 0.00801867i
\(239\) 2.86059e22 0.727238 0.363619 0.931548i \(-0.381541\pi\)
0.363619 + 0.931548i \(0.381541\pi\)
\(240\) 5.02314e22 2.79538e22i 1.22735 0.683022i
\(241\) −5.82109e22 −1.36723 −0.683616 0.729842i \(-0.739594\pi\)
−0.683616 + 0.729842i \(0.739594\pi\)
\(242\) 6.83809e22i 1.54415i
\(243\) 4.38784e22i 0.952776i
\(244\) 4.92527e22 1.02855
\(245\) −2.05262e22 3.68843e22i −0.412316 0.740908i
\(246\) −4.18468e22 −0.808683
\(247\) 8.92441e22i 1.65943i
\(248\) 1.84889e22i 0.330841i
\(249\) 7.32694e22 1.26191
\(250\) 3.86526e21 8.15962e22i 0.0640838 1.35282i
\(251\) 6.40096e22 1.02175 0.510875 0.859655i \(-0.329321\pi\)
0.510875 + 0.859655i \(0.329321\pi\)
\(252\) 1.10624e22i 0.170037i
\(253\) 1.08886e23i 1.61186i
\(254\) −1.15123e23 −1.64151
\(255\) 6.63186e20 + 1.19171e21i 0.00910969 + 0.0163696i
\(256\) 9.40926e22 1.24531
\(257\) 2.55646e22i 0.326043i −0.986623 0.163021i \(-0.947876\pi\)
0.986623 0.163021i \(-0.0521239\pi\)
\(258\) 1.48357e23i 1.82357i
\(259\) 3.24616e22 0.384611
\(260\) −6.96968e22 + 3.87863e22i −0.796097 + 0.443028i
\(261\) 3.15549e22 0.347521
\(262\) 7.57344e22i 0.804323i
\(263\) 1.34746e22i 0.138018i −0.997616 0.0690092i \(-0.978016\pi\)
0.997616 0.0690092i \(-0.0219838\pi\)
\(264\) −4.10207e22 −0.405290
\(265\) 5.50753e22 3.06494e22i 0.524954 0.292137i
\(266\) −8.72661e22 −0.802546
\(267\) 1.85771e22i 0.164862i
\(268\) 2.29073e22i 0.196197i
\(269\) −9.65349e22 −0.798064 −0.399032 0.916937i \(-0.630654\pi\)
−0.399032 + 0.916937i \(0.630654\pi\)
\(270\) 4.86076e22 + 8.73450e22i 0.387925 + 0.697080i
\(271\) −1.68889e23 −1.30135 −0.650674 0.759358i \(-0.725513\pi\)
−0.650674 + 0.759358i \(0.725513\pi\)
\(272\) 2.32264e21i 0.0172813i
\(273\) 7.31416e22i 0.525556i
\(274\) −5.19952e22 −0.360855
\(275\) −1.15015e23 + 1.85442e23i −0.771072 + 1.24322i
\(276\) 1.75116e23 1.13420
\(277\) 1.67203e23i 1.04637i −0.852218 0.523187i \(-0.824743\pi\)
0.852218 0.523187i \(-0.175257\pi\)
\(278\) 2.93159e22i 0.177288i
\(279\) 1.31772e23 0.770161
\(280\) 7.53666e21 + 1.35429e22i 0.0425772 + 0.0765089i
\(281\) 3.43594e23 1.87644 0.938222 0.346035i \(-0.112472\pi\)
0.938222 + 0.346035i \(0.112472\pi\)
\(282\) 2.20816e22i 0.116591i
\(283\) 2.60310e23i 1.32898i −0.747296 0.664492i \(-0.768648\pi\)
0.747296 0.664492i \(-0.231352\pi\)
\(284\) −1.14959e23 −0.567569
\(285\) −3.43109e23 + 1.90940e23i −1.63835 + 0.911741i
\(286\) 4.68482e23 2.16379
\(287\) 4.22361e22i 0.188715i
\(288\) 1.59243e23i 0.688385i
\(289\) 2.39017e23 0.999770
\(290\) 1.94400e23 1.08184e23i 0.786894 0.437907i
\(291\) −3.50966e23 −1.37493
\(292\) 1.80144e23i 0.683096i
\(293\) 3.60152e23i 1.32203i 0.750371 + 0.661017i \(0.229875\pi\)
−0.750371 + 0.661017i \(0.770125\pi\)
\(294\) −3.98726e23 −1.41702
\(295\) −2.31685e23 4.16326e23i −0.797241 1.43260i
\(296\) 6.64484e22 0.221418
\(297\) 2.67023e23i 0.861714i
\(298\) 3.26294e23i 1.01989i
\(299\) 3.97420e23 1.20330
\(300\) −2.98237e23 1.84973e23i −0.874800 0.542570i
\(301\) −1.49738e23 −0.425548
\(302\) 2.87383e23i 0.791399i
\(303\) 5.41121e23i 1.44407i
\(304\) −6.68720e23 −1.72960
\(305\) 2.39151e23 + 4.29741e23i 0.599548 + 1.07735i
\(306\) 4.42191e21 0.0107462
\(307\) 7.14964e23i 1.68449i 0.539092 + 0.842247i \(0.318767\pi\)
−0.539092 + 0.842247i \(0.681233\pi\)
\(308\) 2.08348e23i 0.475947i
\(309\) 5.04811e23 1.11821
\(310\) 8.11807e23 4.51771e23i 1.74388 0.970470i
\(311\) 3.19170e22 0.0664965 0.0332482 0.999447i \(-0.489415\pi\)
0.0332482 + 0.999447i \(0.489415\pi\)
\(312\) 1.49720e23i 0.302560i
\(313\) 8.15443e23i 1.59854i 0.600975 + 0.799268i \(0.294779\pi\)
−0.600975 + 0.799268i \(0.705221\pi\)
\(314\) 7.99492e21 0.0152049
\(315\) 9.65217e22 5.37144e22i 0.178104 0.0991152i
\(316\) −3.00771e23 −0.538528
\(317\) 1.03020e24i 1.79003i −0.446039 0.895014i \(-0.647166\pi\)
0.446039 0.895014i \(-0.352834\pi\)
\(318\) 5.95373e23i 1.00400i
\(319\) −5.94304e23 −0.972740
\(320\) −1.97569e23 3.55020e23i −0.313902 0.564064i
\(321\) −4.62432e23 −0.713264
\(322\) 3.88612e23i 0.581949i
\(323\) 1.58649e22i 0.0230682i
\(324\) 7.38232e23 1.04235
\(325\) −6.76839e23 4.19790e23i −0.928097 0.575626i
\(326\) −5.83545e23 −0.777154
\(327\) 1.22504e24i 1.58469i
\(328\) 8.64567e22i 0.108642i
\(329\) −2.22870e22 −0.0272076
\(330\) 1.00233e24 + 1.80113e24i 1.18885 + 2.13630i
\(331\) 6.75312e23 0.778285 0.389143 0.921178i \(-0.372771\pi\)
0.389143 + 0.921178i \(0.372771\pi\)
\(332\) 7.61772e23i 0.853126i
\(333\) 4.73583e23i 0.515437i
\(334\) 1.26928e24 1.34266
\(335\) 1.99871e23 1.11229e23i 0.205506 0.114364i
\(336\) 5.48061e23 0.547780
\(337\) 1.16149e24i 1.12858i 0.825578 + 0.564288i \(0.190849\pi\)
−0.825578 + 0.564288i \(0.809151\pi\)
\(338\) 2.76273e23i 0.260993i
\(339\) 3.35096e23 0.307803
\(340\) 1.23900e22 6.89505e21i 0.0110668 0.00615868i
\(341\) −2.48178e24 −2.15574
\(342\) 1.27313e24i 1.07553i
\(343\) 8.77056e23i 0.720664i
\(344\) −3.06511e23 −0.244986
\(345\) 8.50292e23 + 1.52793e24i 0.661129 + 1.18801i
\(346\) −2.57857e24 −1.95054
\(347\) 3.58478e23i 0.263835i −0.991261 0.131918i \(-0.957887\pi\)
0.991261 0.131918i \(-0.0421134\pi\)
\(348\) 9.55785e23i 0.684475i
\(349\) 6.18204e23 0.430814 0.215407 0.976524i \(-0.430892\pi\)
0.215407 + 0.976524i \(0.430892\pi\)
\(350\) 4.10486e23 6.61838e23i 0.278389 0.448854i
\(351\) 9.74599e23 0.643292
\(352\) 2.99918e24i 1.92684i
\(353\) 5.21273e23i 0.325991i −0.986627 0.162995i \(-0.947884\pi\)
0.986627 0.162995i \(-0.0521155\pi\)
\(354\) −4.50055e24 −2.73990
\(355\) −5.58194e23 1.00304e24i −0.330838 0.594498i
\(356\) 1.93144e23 0.111456
\(357\) 1.30024e22i 0.00730592i
\(358\) 7.93408e23i 0.434118i
\(359\) 3.25395e24 1.73386 0.866930 0.498430i \(-0.166090\pi\)
0.866930 + 0.498430i \(0.166090\pi\)
\(360\) 1.97579e23 1.09953e23i 0.102534 0.0570600i
\(361\) 2.58931e24 1.30878
\(362\) 3.04721e24i 1.50027i
\(363\) 2.93342e24i 1.40690i
\(364\) −7.60442e23 −0.355307
\(365\) −1.57179e24 + 8.74704e23i −0.715506 + 0.398180i
\(366\) 4.64557e24 2.06048
\(367\) 3.66499e24i 1.58396i 0.610546 + 0.791981i \(0.290950\pi\)
−0.610546 + 0.791981i \(0.709050\pi\)
\(368\) 2.97793e24i 1.25418i
\(369\) −6.16184e23 −0.252906
\(370\) −1.62365e24 2.91761e24i −0.649496 1.16711i
\(371\) 6.00912e23 0.234293
\(372\) 3.99131e24i 1.51690i
\(373\) 2.72449e24i 1.00937i 0.863303 + 0.504685i \(0.168392\pi\)
−0.863303 + 0.504685i \(0.831608\pi\)
\(374\) −8.32822e22 −0.0300796
\(375\) 1.65813e23 3.50034e24i 0.0583877 1.23257i
\(376\) −4.56213e22 −0.0156633
\(377\) 2.16913e24i 0.726176i
\(378\) 9.52997e23i 0.311114i
\(379\) 1.76456e23 0.0561777 0.0280889 0.999605i \(-0.491058\pi\)
0.0280889 + 0.999605i \(0.491058\pi\)
\(380\) 1.98518e24 + 3.56725e24i 0.616390 + 1.10762i
\(381\) −4.93859e24 −1.49560
\(382\) 3.31022e24i 0.977811i
\(383\) 1.90659e23i 0.0549375i 0.999623 + 0.0274687i \(0.00874467\pi\)
−0.999623 + 0.0274687i \(0.991255\pi\)
\(384\) 1.94407e24 0.546468
\(385\) −1.81789e24 + 1.01166e24i −0.498529 + 0.277431i
\(386\) 3.10101e24 0.829705
\(387\) 2.18453e24i 0.570300i
\(388\) 3.64894e24i 0.929535i
\(389\) −2.68719e24 −0.668000 −0.334000 0.942573i \(-0.608399\pi\)
−0.334000 + 0.942573i \(0.608399\pi\)
\(390\) −6.57388e24 + 3.65837e24i −1.59481 + 0.887511i
\(391\) −7.06495e22 −0.0167274
\(392\) 8.23779e23i 0.190368i
\(393\) 3.24887e24i 0.732831i
\(394\) −1.06852e24 −0.235272
\(395\) −1.46042e24 2.62430e24i −0.313911 0.564079i
\(396\) 3.03960e24 0.637841
\(397\) 3.03148e24i 0.621077i 0.950561 + 0.310538i \(0.100509\pi\)
−0.950561 + 0.310538i \(0.899491\pi\)
\(398\) 1.23849e24i 0.247745i
\(399\) −3.74357e24 −0.731211
\(400\) 3.14555e24 5.07166e24i 0.599967 0.967343i
\(401\) 8.40661e24 1.56585 0.782923 0.622118i \(-0.213728\pi\)
0.782923 + 0.622118i \(0.213728\pi\)
\(402\) 2.16064e24i 0.393039i
\(403\) 9.05816e24i 1.60932i
\(404\) 5.62596e24 0.976279
\(405\) 3.58456e24 + 6.44124e24i 0.607593 + 1.09181i
\(406\) 2.12105e24 0.351199
\(407\) 8.91945e24i 1.44275i
\(408\) 2.66157e22i 0.00420598i
\(409\) −8.70689e24 −1.34429 −0.672143 0.740421i \(-0.734626\pi\)
−0.672143 + 0.740421i \(0.734626\pi\)
\(410\) −3.79613e24 + 2.11255e24i −0.572657 + 0.318684i
\(411\) −2.23050e24 −0.328780
\(412\) 5.24845e24i 0.755975i
\(413\) 4.54241e24i 0.639383i
\(414\) 5.66947e24 0.779901
\(415\) 6.64664e24 3.69886e24i 0.893604 0.497291i
\(416\) −1.09466e25 −1.43844
\(417\) 1.25760e24i 0.161529i
\(418\) 2.39781e25i 3.01051i
\(419\) −4.91947e24 −0.603789 −0.301895 0.953341i \(-0.597619\pi\)
−0.301895 + 0.953341i \(0.597619\pi\)
\(420\) −1.62699e24 2.92361e24i −0.195216 0.350793i
\(421\) 4.45443e24 0.522531 0.261266 0.965267i \(-0.415860\pi\)
0.261266 + 0.965267i \(0.415860\pi\)
\(422\) 1.11485e25i 1.27864i
\(423\) 3.25146e23i 0.0364624i
\(424\) 1.23006e24 0.134881
\(425\) 1.20322e23 + 7.46262e22i 0.0129018 + 0.00800196i
\(426\) −1.08431e25 −1.13700
\(427\) 4.68879e24i 0.480835i
\(428\) 4.80784e24i 0.482208i
\(429\) 2.00971e25 1.97146
\(430\) 7.48952e24 + 1.34582e25i 0.718627 + 1.29133i
\(431\) −8.48482e24 −0.796359 −0.398179 0.917308i \(-0.630358\pi\)
−0.398179 + 0.917308i \(0.630358\pi\)
\(432\) 7.30282e24i 0.670494i
\(433\) 1.61543e25i 1.45095i 0.688247 + 0.725476i \(0.258380\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(434\) 8.85740e24 0.778312
\(435\) 8.33945e24 4.64091e24i 0.716951 0.398983i
\(436\) −1.27365e25 −1.07134
\(437\) 2.03409e25i 1.67416i
\(438\) 1.69914e25i 1.36843i
\(439\) −2.83535e23 −0.0223457 −0.0111729 0.999938i \(-0.503557\pi\)
−0.0111729 + 0.999938i \(0.503557\pi\)
\(440\) −3.72119e24 + 2.07085e24i −0.287000 + 0.159716i
\(441\) −5.87114e24 −0.443155
\(442\) 3.03969e23i 0.0224552i
\(443\) 2.95742e23i 0.0213834i 0.999943 + 0.0106917i \(0.00340334\pi\)
−0.999943 + 0.0106917i \(0.996597\pi\)
\(444\) −1.43447e25 −1.01520
\(445\) 9.37827e23 + 1.68522e24i 0.0649685 + 0.116745i
\(446\) 1.70438e24 0.115581
\(447\) 1.39974e25i 0.929239i
\(448\) 3.87353e24i 0.251748i
\(449\) −3.12295e25 −1.98712 −0.993560 0.113303i \(-0.963857\pi\)
−0.993560 + 0.113303i \(0.963857\pi\)
\(450\) −9.65558e24 5.98859e24i −0.601533 0.373083i
\(451\) 1.16052e25 0.707905
\(452\) 3.48395e24i 0.208092i
\(453\) 1.23283e25i 0.721055i
\(454\) 3.34160e25 1.91392
\(455\) −3.69240e24 6.63504e24i −0.207110 0.372165i
\(456\) −7.66303e24 −0.420954
\(457\) 2.81853e25i 1.51641i −0.652013 0.758207i \(-0.726075\pi\)
0.652013 0.758207i \(-0.273925\pi\)
\(458\) 6.33916e24i 0.334048i
\(459\) −1.73255e23 −0.00894261
\(460\) 1.58856e25 8.84036e24i 0.803165 0.446962i
\(461\) 9.39614e24 0.465362 0.232681 0.972553i \(-0.425250\pi\)
0.232681 + 0.972553i \(0.425250\pi\)
\(462\) 1.96517e25i 0.953456i
\(463\) 2.13716e25i 1.01582i 0.861409 + 0.507911i \(0.169582\pi\)
−0.861409 + 0.507911i \(0.830418\pi\)
\(464\) 1.62536e25 0.756883
\(465\) 3.48251e25 1.93802e25i 1.58887 0.884210i
\(466\) −3.32385e24 −0.148585
\(467\) 2.08363e25i 0.912663i 0.889810 + 0.456332i \(0.150837\pi\)
−0.889810 + 0.456332i \(0.849163\pi\)
\(468\) 1.10941e25i 0.476165i
\(469\) 2.18074e24 0.0917196
\(470\) 1.11474e24 + 2.00313e24i 0.0459458 + 0.0825620i
\(471\) 3.42969e23 0.0138534
\(472\) 9.29826e24i 0.368089i
\(473\) 4.11433e25i 1.59632i
\(474\) −2.83691e25 −1.07882
\(475\) −2.14859e25 + 3.46423e25i −0.800874 + 1.29127i
\(476\) 1.35184e23 0.00493923
\(477\) 8.76672e24i 0.313988i
\(478\) 2.80522e25i 0.984924i
\(479\) 7.09286e24 0.244137 0.122069 0.992522i \(-0.461047\pi\)
0.122069 + 0.992522i \(0.461047\pi\)
\(480\) −2.34205e25 4.20853e25i −0.790323 1.42017i
\(481\) −3.25548e25 −1.07705
\(482\) 5.70842e25i 1.85169i
\(483\) 1.66708e25i 0.530222i
\(484\) −3.04984e25 −0.951144
\(485\) −3.18379e25 + 1.77178e25i −0.973638 + 0.541830i
\(486\) 4.30291e25 1.29038
\(487\) 2.13989e25i 0.629313i 0.949206 + 0.314657i \(0.101889\pi\)
−0.949206 + 0.314657i \(0.898111\pi\)
\(488\) 9.59789e24i 0.276814i
\(489\) −2.50331e25 −0.708077
\(490\) −3.61704e25 + 2.01289e25i −1.00344 + 0.558414i
\(491\) 4.33772e25 1.18029 0.590143 0.807299i \(-0.299071\pi\)
0.590143 + 0.807299i \(0.299071\pi\)
\(492\) 1.86640e25i 0.498122i
\(493\) 3.85606e23i 0.0100948i
\(494\) 8.75167e25 2.24742
\(495\) 1.47591e25 + 2.65212e25i 0.371800 + 0.668104i
\(496\) 6.78743e25 1.67737
\(497\) 1.09439e25i 0.265331i
\(498\) 7.18512e25i 1.70905i
\(499\) −7.92853e25 −1.85028 −0.925140 0.379627i \(-0.876052\pi\)
−0.925140 + 0.379627i \(0.876052\pi\)
\(500\) −3.63925e25 1.72393e24i −0.833291 0.0394735i
\(501\) 5.44501e25 1.22332
\(502\) 6.27706e25i 1.38379i
\(503\) 1.33196e25i 0.288136i −0.989568 0.144068i \(-0.953982\pi\)
0.989568 0.144068i \(-0.0460183\pi\)
\(504\) 2.15573e24 0.0457618
\(505\) 2.73174e25 + 4.90878e25i 0.569077 + 1.02260i
\(506\) −1.06779e26 −2.18301
\(507\) 1.18516e25i 0.237795i
\(508\) 5.13458e25i 1.01111i
\(509\) 6.86620e25 1.32708 0.663541 0.748140i \(-0.269053\pi\)
0.663541 + 0.748140i \(0.269053\pi\)
\(510\) 1.16864e24 6.50349e23i 0.0221699 0.0123376i
\(511\) −1.71494e25 −0.319338
\(512\) 6.80426e25i 1.24370i
\(513\) 4.98824e25i 0.895018i
\(514\) −2.50698e25 −0.441571
\(515\) 4.57939e25 2.54844e25i 0.791843 0.440661i
\(516\) 6.61685e25 1.12326
\(517\) 6.12380e24i 0.102061i
\(518\) 3.18332e25i 0.520892i
\(519\) −1.10616e26 −1.77717
\(520\) −7.55830e24 1.35818e25i −0.119232 0.214253i
\(521\) 2.67103e25 0.413734 0.206867 0.978369i \(-0.433673\pi\)
0.206867 + 0.978369i \(0.433673\pi\)
\(522\) 3.09441e25i 0.470661i
\(523\) 5.66730e25i 0.846467i 0.906021 + 0.423233i \(0.139105\pi\)
−0.906021 + 0.423233i \(0.860895\pi\)
\(524\) 3.37781e25 0.495436
\(525\) 1.76091e25 2.83917e25i 0.253644 0.408957i
\(526\) −1.32138e25 −0.186923
\(527\) 1.61027e24i 0.0223717i
\(528\) 1.50591e26i 2.05483i
\(529\) −1.59664e25 −0.213983
\(530\) −3.00562e25 5.40093e25i −0.395652 0.710964i
\(531\) −6.62694e25 −0.856871
\(532\) 3.89213e25i 0.494342i
\(533\) 4.23573e25i 0.528470i
\(534\) 1.82175e25 0.223279
\(535\) −4.19495e25 + 2.33449e25i −0.505087 + 0.281081i
\(536\) 4.46395e24 0.0528025
\(537\) 3.40358e25i 0.395531i
\(538\) 9.46664e25i 1.08085i
\(539\) 1.10577e26 1.24043
\(540\) 3.89565e25 2.16793e25i 0.429378 0.238949i
\(541\) −6.52211e24 −0.0706341 −0.0353171 0.999376i \(-0.511244\pi\)
−0.0353171 + 0.999376i \(0.511244\pi\)
\(542\) 1.65620e26i 1.76246i
\(543\) 1.30720e26i 1.36692i
\(544\) 1.94598e24 0.0199962
\(545\) −6.18434e25 1.11129e26i −0.624492 1.12218i
\(546\) −7.17258e25 −0.711779
\(547\) 8.52380e25i 0.831292i −0.909526 0.415646i \(-0.863556\pi\)
0.909526 0.415646i \(-0.136444\pi\)
\(548\) 2.31902e25i 0.222275i
\(549\) 6.84049e25 0.644392
\(550\) 1.81853e26 + 1.12789e26i 1.68374 + 1.04429i
\(551\) −1.11021e26 −1.01034
\(552\) 3.41249e25i 0.305246i
\(553\) 2.86330e25i 0.251755i
\(554\) −1.63967e26 −1.41714
\(555\) −6.96518e25 1.25160e26i −0.591765 1.06337i
\(556\) −1.30751e25 −0.109203
\(557\) 9.71730e25i 0.797850i 0.916984 + 0.398925i \(0.130617\pi\)
−0.916984 + 0.398925i \(0.869383\pi\)
\(558\) 1.29221e26i 1.04306i
\(559\) 1.50167e26 1.19169
\(560\) 4.97174e25 2.76677e25i 0.387902 0.215868i
\(561\) −3.57266e24 −0.0274060
\(562\) 3.36943e26i 2.54133i
\(563\) 6.87630e25i 0.509947i 0.966948 + 0.254973i \(0.0820667\pi\)
−0.966948 + 0.254973i \(0.917933\pi\)
\(564\) 9.84856e24 0.0718160
\(565\) 3.03982e25 1.69166e25i 0.217966 0.121298i
\(566\) −2.55271e26 −1.79989
\(567\) 7.02786e25i 0.487286i
\(568\) 2.24021e25i 0.152749i
\(569\) 9.27451e25 0.621905 0.310953 0.950425i \(-0.399352\pi\)
0.310953 + 0.950425i \(0.399352\pi\)
\(570\) 1.87244e26 + 3.36468e26i 1.23480 + 2.21887i
\(571\) 6.52681e25 0.423310 0.211655 0.977344i \(-0.432115\pi\)
0.211655 + 0.977344i \(0.432115\pi\)
\(572\) 2.08947e26i 1.33282i
\(573\) 1.42003e26i 0.890898i
\(574\) −4.14185e25 −0.255583
\(575\) 1.54268e26 + 9.56805e25i 0.936337 + 0.580736i
\(576\) −5.65111e25 −0.337381
\(577\) 1.80949e26i 1.06264i 0.847172 + 0.531319i \(0.178303\pi\)
−0.847172 + 0.531319i \(0.821697\pi\)
\(578\) 2.34391e26i 1.35402i
\(579\) 1.33028e26 0.755957
\(580\) −4.82508e25 8.67040e25i −0.269736 0.484700i
\(581\) 7.25196e25 0.398825
\(582\) 3.44173e26i 1.86212i
\(583\) 1.65112e26i 0.878877i
\(584\) −3.51046e25 −0.183841
\(585\) −9.67988e25 + 5.38686e25i −0.498757 + 0.277559i
\(586\) 3.53180e26 1.79048
\(587\) 1.28037e26i 0.638663i −0.947643 0.319332i \(-0.896542\pi\)
0.947643 0.319332i \(-0.103458\pi\)
\(588\) 1.77835e26i 0.872834i
\(589\) −4.63619e26 −2.23906
\(590\) −4.08267e26 + 2.27201e26i −1.94022 + 1.07973i
\(591\) −4.58379e25 −0.214360
\(592\) 2.43938e26i 1.12260i
\(593\) 2.74621e25i 0.124370i 0.998065 + 0.0621849i \(0.0198068\pi\)
−0.998065 + 0.0621849i \(0.980193\pi\)
\(594\) −2.61855e26 −1.16705
\(595\) 6.56399e23 + 1.17951e24i 0.00287910 + 0.00517358i
\(596\) −1.45529e26 −0.628219
\(597\) 5.31292e25i 0.225724i
\(598\) 3.89728e26i 1.62967i
\(599\) 2.61932e26 1.07804 0.539019 0.842294i \(-0.318795\pi\)
0.539019 + 0.842294i \(0.318795\pi\)
\(600\) 3.60457e25 5.81175e25i 0.146021 0.235434i
\(601\) −2.34392e26 −0.934621 −0.467310 0.884093i \(-0.654777\pi\)
−0.467310 + 0.884093i \(0.654777\pi\)
\(602\) 1.46839e26i 0.576335i
\(603\) 3.18149e25i 0.122918i
\(604\) 1.28175e26 0.487475
\(605\) −1.48088e26 2.66106e26i −0.554426 0.996272i
\(606\) 5.30647e26 1.95576
\(607\) 8.78652e24i 0.0318804i −0.999873 0.0159402i \(-0.994926\pi\)
0.999873 0.0159402i \(-0.00507414\pi\)
\(608\) 5.60273e26i 2.00132i
\(609\) 9.09894e25 0.319983
\(610\) 4.21423e26 2.34522e26i 1.45910 0.811990i
\(611\) 2.23510e25 0.0761914
\(612\) 1.97221e24i 0.00661932i
\(613\) 2.55308e26i 0.843703i 0.906665 + 0.421852i \(0.138620\pi\)
−0.906665 + 0.421852i \(0.861380\pi\)
\(614\) 7.01125e26 2.28137
\(615\) −1.62847e26 + 9.06247e25i −0.521756 + 0.290358i
\(616\) −4.06009e25 −0.128091
\(617\) 4.69474e26i 1.45849i 0.684254 + 0.729244i \(0.260128\pi\)
−0.684254 + 0.729244i \(0.739872\pi\)
\(618\) 4.95040e26i 1.51443i
\(619\) −1.55379e26 −0.468093 −0.234046 0.972225i \(-0.575197\pi\)
−0.234046 + 0.972225i \(0.575197\pi\)
\(620\) −2.01493e26 3.62072e26i −0.597777 1.07417i
\(621\) −2.22135e26 −0.649004
\(622\) 3.12992e25i 0.0900585i
\(623\) 1.83870e25i 0.0521044i
\(624\) −5.49635e26 −1.53398
\(625\) −1.61666e26 3.25904e26i −0.444383 0.895837i
\(626\) 7.99659e26 2.16495
\(627\) 1.02862e27i 2.74292i
\(628\) 3.56579e24i 0.00936569i
\(629\) 5.78727e24 0.0149724
\(630\) −5.26747e25 9.46534e25i −0.134235 0.241213i
\(631\) 4.79202e26 1.20293 0.601464 0.798900i \(-0.294584\pi\)
0.601464 + 0.798900i \(0.294584\pi\)
\(632\) 5.86113e25i 0.144934i
\(633\) 4.78252e26i 1.16499i
\(634\) −1.01026e27 −2.42430
\(635\) −4.48004e26 + 2.49314e26i −1.05909 + 0.589382i
\(636\) −2.65541e26 −0.618427
\(637\) 4.03590e26i 0.926011i
\(638\) 5.82800e26i 1.31742i
\(639\) −1.59661e26 −0.355584
\(640\) 1.76356e26 9.81423e25i 0.386973 0.215351i
\(641\) 1.42467e26 0.308010 0.154005 0.988070i \(-0.450783\pi\)
0.154005 + 0.988070i \(0.450783\pi\)
\(642\) 4.53481e26i 0.965999i
\(643\) 3.85589e26i 0.809320i −0.914467 0.404660i \(-0.867390\pi\)
0.914467 0.404660i \(-0.132610\pi\)
\(644\) 1.73324e26 0.358461
\(645\) 3.21288e26 + 5.77336e26i 0.654752 + 1.17655i
\(646\) −1.55579e25 −0.0312422
\(647\) 6.19721e26i 1.22633i −0.789957 0.613163i \(-0.789897\pi\)
0.789957 0.613163i \(-0.210103\pi\)
\(648\) 1.43860e26i 0.280528i
\(649\) 1.24812e27 2.39845
\(650\) −4.11664e26 + 6.63738e26i −0.779590 + 1.25696i
\(651\) 3.79967e26 0.709131
\(652\) 2.60265e26i 0.478701i
\(653\) 3.56634e26i 0.646469i −0.946319 0.323235i \(-0.895230\pi\)
0.946319 0.323235i \(-0.104770\pi\)
\(654\) −1.20132e27 −2.14621
\(655\) 1.64013e26 + 2.94722e26i 0.288792 + 0.518943i
\(656\) −3.17390e26 −0.550817
\(657\) 2.50193e26i 0.427962i
\(658\) 2.18556e25i 0.0368483i
\(659\) 6.41633e26 1.06629 0.533145 0.846024i \(-0.321010\pi\)
0.533145 + 0.846024i \(0.321010\pi\)
\(660\) 8.03318e26 4.47047e26i 1.31589 0.732295i
\(661\) −7.50359e26 −1.21159 −0.605794 0.795621i \(-0.707144\pi\)
−0.605794 + 0.795621i \(0.707144\pi\)
\(662\) 6.62241e26i 1.05406i
\(663\) 1.30397e25i 0.0204593i
\(664\) 1.48447e26 0.229601
\(665\) −3.39598e26 + 1.88986e26i −0.517796 + 0.288154i
\(666\) −4.64416e26 −0.698075
\(667\) 4.94397e26i 0.732623i
\(668\) 5.66110e26i 0.827036i
\(669\) 7.31151e25 0.105307
\(670\) −1.09076e26 1.96003e26i −0.154888 0.278325i
\(671\) −1.28834e27 −1.80370
\(672\) 4.59181e26i 0.633835i
\(673\) 8.83509e26i 1.20245i −0.799079 0.601226i \(-0.794679\pi\)
0.799079 0.601226i \(-0.205321\pi\)
\(674\) 1.13901e27 1.52847
\(675\) 3.78314e26 + 2.34639e26i 0.500573 + 0.310466i
\(676\) 1.23220e26 0.160763
\(677\) 1.08791e27i 1.39959i −0.714346 0.699793i \(-0.753275\pi\)
0.714346 0.699793i \(-0.246725\pi\)
\(678\) 3.28610e26i 0.416868i
\(679\) −3.47374e26 −0.434545
\(680\) 1.34364e24 + 2.41445e24i 0.00165748 + 0.00297840i
\(681\) 1.43349e27 1.74380
\(682\) 2.43375e27i 2.91960i
\(683\) 1.43692e27i 1.69995i −0.526825 0.849974i \(-0.676618\pi\)
0.526825 0.849974i \(-0.323382\pi\)
\(684\) 5.67825e26 0.662493
\(685\) −2.02340e26 + 1.12602e26i −0.232821 + 0.129565i
\(686\) −8.60079e26 −0.976021
\(687\) 2.71939e26i 0.304356i
\(688\) 1.12523e27i 1.24208i
\(689\) −6.02637e26 −0.656105
\(690\) 1.49835e27 8.33833e26i 1.60897 0.895391i
\(691\) −2.88640e26 −0.305714 −0.152857 0.988248i \(-0.548847\pi\)
−0.152857 + 0.988248i \(0.548847\pi\)
\(692\) 1.15006e27i 1.20147i
\(693\) 2.89366e26i 0.298182i
\(694\) −3.51539e26 −0.357321
\(695\) −6.34875e25 1.14084e26i −0.0636551 0.114385i
\(696\) 1.86254e26 0.184212
\(697\) 7.52987e24i 0.00734643i
\(698\) 6.06238e26i 0.583467i
\(699\) −1.42587e26 −0.135378
\(700\) −2.95184e26 1.83080e26i −0.276479 0.171478i
\(701\) −7.83699e26 −0.724149 −0.362075 0.932149i \(-0.617931\pi\)
−0.362075 + 0.932149i \(0.617931\pi\)
\(702\) 9.55734e26i 0.871233i
\(703\) 1.66623e27i 1.49851i
\(704\) 1.06433e27 0.944356
\(705\) 4.78206e25 + 8.59310e25i 0.0418619 + 0.0752234i
\(706\) −5.11183e26 −0.441501
\(707\) 5.35584e26i 0.456397i
\(708\) 2.00728e27i 1.68768i
\(709\) −1.61337e27 −1.33843 −0.669215 0.743068i \(-0.733370\pi\)
−0.669215 + 0.743068i \(0.733370\pi\)
\(710\) −9.83628e26 + 5.47390e26i −0.805150 + 0.448066i
\(711\) −4.17727e26 −0.337390
\(712\) 3.76379e25i 0.0299962i
\(713\) 2.06458e27i 1.62361i
\(714\) 1.27507e25 0.00989468
\(715\) 1.82311e27 1.01456e27i 1.39606 0.776910i
\(716\) 3.53866e26 0.267402
\(717\) 1.20339e27i 0.897378i
\(718\) 3.19097e27i 2.34823i
\(719\) 8.92361e26 0.648061 0.324031 0.946047i \(-0.394962\pi\)
0.324031 + 0.946047i \(0.394962\pi\)
\(720\) −4.03646e26 7.25329e26i −0.289296 0.519848i
\(721\) 4.99645e26 0.353408
\(722\) 2.53919e27i 1.77253i
\(723\) 2.44881e27i 1.68710i
\(724\) −1.35908e27 −0.924119
\(725\) 5.22226e26 8.42000e26i 0.350467 0.565068i
\(726\) −2.87664e27 −1.90541
\(727\) 1.51778e27i 0.992274i 0.868244 + 0.496137i \(0.165249\pi\)
−0.868244 + 0.496137i \(0.834751\pi\)
\(728\) 1.48188e26i 0.0956234i
\(729\) −1.15875e26 −0.0738040
\(730\) 8.57773e26 + 1.54137e27i 0.539269 + 0.969036i
\(731\) −2.66953e25 −0.0165661
\(732\) 2.07196e27i 1.26919i
\(733\) 1.49384e27i 0.903267i −0.892204 0.451633i \(-0.850842\pi\)
0.892204 0.451633i \(-0.149158\pi\)
\(734\) 3.59405e27 2.14522
\(735\) −1.55165e27 + 8.63493e26i −0.914247 + 0.508779i
\(736\) 2.49500e27 1.45121
\(737\) 5.99202e26i 0.344058i
\(738\) 6.04257e26i 0.342520i
\(739\) −4.93504e26 −0.276165 −0.138083 0.990421i \(-0.544094\pi\)
−0.138083 + 0.990421i \(0.544094\pi\)
\(740\) −1.30128e27 + 7.24160e26i −0.718899 + 0.400068i
\(741\) 3.75432e27 2.04766
\(742\) 5.89280e26i 0.317311i
\(743\) 1.02399e26i 0.0544378i 0.999629 + 0.0272189i \(0.00866512\pi\)
−0.999629 + 0.0272189i \(0.991335\pi\)
\(744\) 7.77788e26 0.408243
\(745\) −7.06632e26 1.26978e27i −0.366192 0.658026i
\(746\) 2.67175e27 1.36703
\(747\) 1.05799e27i 0.534486i
\(748\) 3.71445e25i 0.0185280i
\(749\) −4.57700e26 −0.225426
\(750\) −3.43258e27 1.62603e26i −1.66932 0.0790765i
\(751\) 5.99732e26 0.287990 0.143995 0.989578i \(-0.454005\pi\)
0.143995 + 0.989578i \(0.454005\pi\)
\(752\) 1.67480e26i 0.0794132i
\(753\) 2.69275e27i 1.26079i
\(754\) −2.12714e27 −0.983486
\(755\) 6.22366e26 + 1.11836e27i 0.284152 + 0.510604i
\(756\) 4.25044e26 0.191636
\(757\) 1.93512e27i 0.861583i 0.902451 + 0.430792i \(0.141766\pi\)
−0.902451 + 0.430792i \(0.858234\pi\)
\(758\) 1.73041e26i 0.0760835i
\(759\) −4.58062e27 −1.98897
\(760\) −6.95152e26 + 3.86853e26i −0.298092 + 0.165889i
\(761\) −2.57157e27 −1.08904 −0.544520 0.838748i \(-0.683288\pi\)
−0.544520 + 0.838748i \(0.683288\pi\)
\(762\) 4.84299e27i 2.02554i
\(763\) 1.21250e27i 0.500839i
\(764\) −1.47638e27 −0.602299
\(765\) 1.72079e25 9.57623e24i 0.00693339 0.00385843i
\(766\) 1.86968e26 0.0744038
\(767\) 4.55546e27i 1.79051i
\(768\) 3.95828e27i 1.53665i
\(769\) 1.16936e27 0.448380 0.224190 0.974545i \(-0.428026\pi\)
0.224190 + 0.974545i \(0.428026\pi\)
\(770\) 9.92074e26 + 1.78270e27i 0.375735 + 0.675175i
\(771\) −1.07545e27 −0.402322
\(772\) 1.38307e27i 0.511071i
\(773\) 4.80957e26i 0.175550i 0.996140 + 0.0877750i \(0.0279757\pi\)
−0.996140 + 0.0877750i \(0.972024\pi\)
\(774\) 2.14224e27 0.772377
\(775\) 2.18079e27 3.51615e27i 0.776690 1.25228i
\(776\) −7.11071e26 −0.250165
\(777\) 1.36559e27i 0.474592i
\(778\) 2.63517e27i 0.904697i
\(779\) 2.16795e27 0.735265
\(780\) 1.63166e27 + 2.93200e27i 0.546677 + 0.982348i
\(781\) 3.00706e27 0.995308
\(782\) 6.92820e25i 0.0226546i
\(783\) 1.21242e27i 0.391666i
\(784\) −3.02417e27 −0.965169
\(785\) 3.11124e25 1.73141e25i 0.00981006 0.00545930i
\(786\) 3.18599e27 0.992499
\(787\) 3.62998e26i 0.111723i 0.998439 + 0.0558616i \(0.0177906\pi\)
−0.998439 + 0.0558616i \(0.982209\pi\)
\(788\) 4.76570e26i 0.144920i
\(789\) −5.66850e26 −0.170308
\(790\) −2.57350e27 + 1.43215e27i −0.763953 + 0.425140i
\(791\) 3.31667e26 0.0972804
\(792\) 5.92328e26i 0.171662i
\(793\) 4.70225e27i 1.34651i
\(794\) 2.97280e27 0.841146
\(795\) −1.28936e27 2.31691e27i −0.360484 0.647770i
\(796\) 5.52377e26 0.152602
\(797\) 5.25128e27i 1.43355i −0.697307 0.716773i \(-0.745619\pi\)
0.697307 0.716773i \(-0.254381\pi\)
\(798\) 3.67111e27i 0.990306i
\(799\) −3.97335e24 −0.00105916
\(800\) −4.24918e27 2.63543e27i −1.11931 0.694220i
\(801\) 2.68249e26 0.0698278
\(802\) 8.24389e27i 2.12068i
\(803\) 4.71214e27i 1.19790i
\(804\) −9.63663e26 −0.242099
\(805\) 8.41590e26 + 1.51229e27i 0.208949 + 0.375469i
\(806\) −8.88283e27 −2.17956
\(807\) 4.06103e27i 0.984775i
\(808\) 1.09633e27i 0.262745i
\(809\) −2.41547e27 −0.572126 −0.286063 0.958211i \(-0.592347\pi\)
−0.286063 + 0.958211i \(0.592347\pi\)
\(810\) 6.31657e27 3.51517e27i 1.47868 0.822885i
\(811\) −9.47666e26 −0.219259 −0.109629 0.993973i \(-0.534966\pi\)
−0.109629 + 0.993973i \(0.534966\pi\)
\(812\) 9.46004e26i 0.216327i
\(813\) 7.10481e27i 1.60580i
\(814\) 8.74681e27 1.95397
\(815\) −2.27088e27 + 1.26374e27i −0.501414 + 0.279037i
\(816\) 9.77087e25 0.0213244
\(817\) 7.68594e27i 1.65801i
\(818\) 8.53836e27i 1.82062i
\(819\) −1.05615e27 −0.222601
\(820\) 9.42212e26 + 1.69310e27i 0.196299 + 0.352737i
\(821\) 5.43634e27 1.11956 0.559780 0.828642i \(-0.310886\pi\)
0.559780 + 0.828642i \(0.310886\pi\)
\(822\) 2.18733e27i 0.445279i
\(823\) 6.66652e27i 1.34153i 0.741670 + 0.670765i \(0.234034\pi\)
−0.741670 + 0.670765i \(0.765966\pi\)
\(824\) 1.02277e27 0.203455
\(825\) 7.80118e27 + 4.83846e27i 1.53408 + 0.951469i
\(826\) −4.45449e27 −0.865939
\(827\) 4.87544e27i 0.936939i 0.883480 + 0.468469i \(0.155194\pi\)
−0.883480 + 0.468469i \(0.844806\pi\)
\(828\) 2.52863e27i 0.480393i
\(829\) 2.36253e27 0.443720 0.221860 0.975079i \(-0.428787\pi\)
0.221860 + 0.975079i \(0.428787\pi\)
\(830\) −3.62726e27 6.51798e27i −0.673499 1.21024i
\(831\) −7.03390e27 −1.29118
\(832\) 3.88465e27i 0.704986i
\(833\) 7.17464e25i 0.0128728i
\(834\) −1.23326e27 −0.218765
\(835\) 4.93944e27 2.74880e27i 0.866276 0.482083i
\(836\) −1.06944e28 −1.85437
\(837\) 5.06300e27i 0.867992i
\(838\) 4.82425e27i 0.817734i
\(839\) −5.58105e27 −0.935356 −0.467678 0.883899i \(-0.654909\pi\)
−0.467678 + 0.883899i \(0.654909\pi\)
\(840\) 5.69724e26 3.17052e26i 0.0944085 0.0525384i
\(841\) −3.40483e27 −0.557871
\(842\) 4.36821e27i 0.707683i
\(843\) 1.44543e28i 2.31545i
\(844\) 4.97232e27 0.787600
\(845\) 5.98305e26 + 1.07512e27i 0.0937095 + 0.168391i
\(846\) 3.18853e26 0.0493823
\(847\) 2.90340e27i 0.444647i
\(848\) 4.51565e27i 0.683849i
\(849\) −1.09507e28 −1.63991
\(850\) 7.31817e25 1.17993e26i 0.0108373 0.0174733i
\(851\) 7.42004e27 1.08661
\(852\) 4.83609e27i 0.700354i
\(853\) 3.15672e27i 0.452085i 0.974117 + 0.226042i \(0.0725788\pi\)
−0.974117 + 0.226042i \(0.927421\pi\)
\(854\) 4.59803e27 0.651211
\(855\) 2.75713e27 + 4.95440e27i 0.386170 + 0.693926i
\(856\) −9.36906e26 −0.129776
\(857\) 8.00001e27i 1.09590i 0.836510 + 0.547952i \(0.184592\pi\)
−0.836510 + 0.547952i \(0.815408\pi\)
\(858\) 1.97081e28i 2.67002i
\(859\) 2.39064e27 0.320316 0.160158 0.987091i \(-0.448800\pi\)
0.160158 + 0.987091i \(0.448800\pi\)
\(860\) 6.00248e27 3.34038e27i 0.795417 0.442650i
\(861\) −1.77678e27 −0.232865
\(862\) 8.32059e27i 1.07854i
\(863\) 4.56844e27i 0.585687i 0.956160 + 0.292843i \(0.0946015\pi\)
−0.956160 + 0.292843i \(0.905399\pi\)
\(864\) 6.11851e27 0.775828
\(865\) −1.00345e28 + 5.58423e27i −1.25847 + 0.700342i
\(866\) 1.58416e28 1.96508
\(867\) 1.00550e28i 1.23367i
\(868\) 3.95047e27i 0.479414i
\(869\) 7.86747e27 0.944381
\(870\) −4.55108e27 8.17803e27i −0.540358 0.970992i
\(871\) −2.18700e27 −0.256849
\(872\) 2.48197e27i 0.288330i
\(873\) 5.06786e27i 0.582357i
\(874\) −1.99472e28 −2.26738
\(875\) 1.64116e26 3.46451e27i 0.0184533 0.389552i
\(876\) 7.57827e27 0.842909
\(877\) 1.23776e28i 1.36189i −0.732335 0.680945i \(-0.761569\pi\)
0.732335 0.680945i \(-0.238431\pi\)
\(878\) 2.78047e26i 0.0302636i
\(879\) 1.51508e28 1.63133
\(880\) 7.60226e27 + 1.36608e28i 0.809762 + 1.45510i
\(881\) −6.55182e26 −0.0690384 −0.0345192 0.999404i \(-0.510990\pi\)
−0.0345192 + 0.999404i \(0.510990\pi\)
\(882\) 5.75750e27i 0.600181i
\(883\) 8.50704e27i 0.877308i −0.898656 0.438654i \(-0.855455\pi\)
0.898656 0.438654i \(-0.144545\pi\)
\(884\) −1.35572e26 −0.0138317
\(885\) −1.75140e28 + 9.74653e27i −1.76776 + 0.983759i
\(886\) 2.90017e26 0.0289603
\(887\) 1.88564e28i 1.86288i 0.363894 + 0.931440i \(0.381447\pi\)
−0.363894 + 0.931440i \(0.618553\pi\)
\(888\) 2.79535e27i 0.273220i
\(889\) −4.88804e27 −0.472681
\(890\) 1.65260e27 9.19674e26i 0.158111 0.0879891i
\(891\) −1.93104e28 −1.82791
\(892\) 7.60167e26i 0.0711939i
\(893\) 1.14398e27i 0.106006i
\(894\) −1.37265e28 −1.25850
\(895\) 1.71823e27 + 3.08756e27i 0.155870 + 0.280089i
\(896\) 1.92417e27 0.172710
\(897\) 1.67186e28i 1.48482i
\(898\) 3.06250e28i 2.69123i
\(899\) 1.12685e28 0.979827
\(900\) −2.67096e27 + 4.30646e27i −0.229807 + 0.370524i
\(901\) 1.07131e26 0.00912072
\(902\) 1.13806e28i 0.958741i
\(903\) 6.29915e27i 0.525108i
\(904\) 6.78918e26 0.0560038
\(905\) −6.59913e27 1.18583e28i −0.538673 0.967965i
\(906\) 1.20896e28 0.976551
\(907\) 1.92154e28i 1.53596i −0.640474 0.767980i \(-0.721262\pi\)
0.640474 0.767980i \(-0.278738\pi\)
\(908\) 1.49038e28i 1.17891i
\(909\) 7.81365e27 0.611642
\(910\) −6.50661e27 + 3.62093e27i −0.504036 + 0.280496i
\(911\) 1.12959e28 0.865959 0.432979 0.901404i \(-0.357462\pi\)
0.432979 + 0.901404i \(0.357462\pi\)
\(912\) 2.81317e28i 2.13425i
\(913\) 1.99262e28i 1.49607i
\(914\) −2.76397e28 −2.05374
\(915\) 1.80783e28 1.00606e28i 1.32941 0.739815i
\(916\) −2.82731e27 −0.205763
\(917\) 3.21563e27i 0.231610i
\(918\) 1.69901e26i 0.0121113i
\(919\) −1.54023e28 −1.08664 −0.543321 0.839525i \(-0.682833\pi\)
−0.543321 + 0.839525i \(0.682833\pi\)
\(920\) 1.72272e27 + 3.09564e27i 0.120291 + 0.216155i
\(921\) 3.00770e28 2.07859
\(922\) 9.21426e27i 0.630256i
\(923\) 1.09754e28i 0.743023i
\(924\) 8.76478e27 0.587297
\(925\) −1.26369e28 7.83770e27i −0.838099 0.519807i
\(926\) 2.09579e28 1.37576
\(927\) 7.28934e27i 0.473621i
\(928\) 1.36177e28i 0.875788i
\(929\) −1.68314e28 −1.07145 −0.535724 0.844393i \(-0.679961\pi\)
−0.535724 + 0.844393i \(0.679961\pi\)
\(930\) −1.90051e28 3.41510e28i −1.19752 2.15187i
\(931\) 2.06568e28 1.28837
\(932\) 1.48246e27i 0.0915234i
\(933\) 1.34268e27i 0.0820536i
\(934\) 2.04330e28 1.23605
\(935\) −3.24094e26 + 1.80359e26i −0.0194071 + 0.0108001i
\(936\) −2.16192e27 −0.128150
\(937\) 2.26174e28i 1.32714i 0.748115 + 0.663569i \(0.230959\pi\)
−0.748115 + 0.663569i \(0.769041\pi\)
\(938\) 2.13853e27i 0.124219i
\(939\) 3.43040e28 1.97252
\(940\) 8.93412e26 4.97184e26i 0.0508554 0.0283011i
\(941\) −1.47239e28 −0.829701 −0.414850 0.909890i \(-0.636166\pi\)
−0.414850 + 0.909890i \(0.636166\pi\)
\(942\) 3.36330e26i 0.0187621i
\(943\) 9.65429e27i 0.533162i
\(944\) −3.41348e28 −1.86622
\(945\) 2.06384e27 + 3.70861e27i 0.111705 + 0.200728i
\(946\) −4.03470e28 −2.16195
\(947\) 3.07941e28i 1.63359i −0.576927 0.816796i \(-0.695748\pi\)
0.576927 0.816796i \(-0.304252\pi\)
\(948\) 1.26528e28i 0.664520i
\(949\) 1.71987e28 0.894263
\(950\) 3.39718e28 + 2.10700e28i 1.74881 + 1.08465i
\(951\) −4.33385e28 −2.20881
\(952\) 2.63434e25i 0.00132929i
\(953\) 9.87591e27i 0.493395i −0.969093 0.246697i \(-0.920655\pi\)
0.969093 0.246697i \(-0.0793454\pi\)
\(954\) −8.59703e27 −0.425245
\(955\) −7.16872e27 1.28818e28i −0.351083 0.630876i
\(956\) −1.25115e28 −0.606680
\(957\) 2.50011e28i 1.20032i
\(958\) 6.95557e27i 0.330644i
\(959\) −2.20768e27 −0.103910
\(960\) −1.49350e28 + 8.31133e27i −0.696030 + 0.387341i
\(961\) 2.53861e28 1.17145
\(962\) 3.19246e28i 1.45869i
\(963\) 6.67740e27i 0.302105i
\(964\) 2.54600e28 1.14058
\(965\) 1.20676e28 6.71565e27i 0.535319 0.297905i
\(966\) 1.63481e28 0.718099
\(967\) 1.51028e28i 0.656910i 0.944520 + 0.328455i \(0.106528\pi\)
−0.944520 + 0.328455i \(0.893472\pi\)
\(968\) 5.94323e27i 0.255980i
\(969\) −6.67406e26 −0.0284652
\(970\) 1.73748e28 + 3.12216e28i 0.733820 + 1.31863i
\(971\) −3.73488e28 −1.56205 −0.781023 0.624502i \(-0.785302\pi\)
−0.781023 + 0.624502i \(0.785302\pi\)
\(972\) 1.91913e28i 0.794830i
\(973\) 1.24473e27i 0.0510510i
\(974\) 2.09847e28 0.852302
\(975\) −1.76597e28 + 2.84732e28i −0.710296 + 1.14523i
\(976\) 3.52347e28 1.40345
\(977\) 2.10264e28i 0.829403i 0.909958 + 0.414701i \(0.136114\pi\)
−0.909958 + 0.414701i \(0.863886\pi\)
\(978\) 2.45485e28i 0.958973i
\(979\) −5.05219e27 −0.195454
\(980\) 8.97762e27 + 1.61323e28i 0.343964 + 0.618084i
\(981\) −1.76892e28 −0.671201
\(982\) 4.25376e28i 1.59850i
\(983\) 4.82839e28i 1.79698i −0.438990 0.898492i \(-0.644664\pi\)
0.438990 0.898492i \(-0.355336\pi\)
\(984\) −3.63705e27 −0.134059
\(985\) −4.15818e27 + 2.31403e27i −0.151796 + 0.0844744i
\(986\) 3.78142e26 0.0136718
\(987\) 9.37569e26i 0.0335730i
\(988\) 3.90331e28i 1.38434i
\(989\) −3.42269e28 −1.20227
\(990\) 2.60079e28 1.44734e28i 0.904838 0.503543i
\(991\) −3.64175e28 −1.25490 −0.627452 0.778655i \(-0.715902\pi\)
−0.627452 + 0.778655i \(0.715902\pi\)
\(992\) 5.68670e28i 1.94088i
\(993\) 2.84090e28i 0.960369i
\(994\) −1.07321e28 −0.359347
\(995\) 2.68212e27 + 4.81961e27i 0.0889526 + 0.159843i
\(996\) −3.20462e28 −1.05272
\(997\) 2.05615e28i 0.669037i 0.942389 + 0.334519i \(0.108574\pi\)
−0.942389 + 0.334519i \(0.891426\pi\)
\(998\) 7.77506e28i 2.50590i
\(999\) 1.81963e28 0.580911
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 5.20.b.a.4.2 8
3.2 odd 2 45.20.b.b.19.7 8
4.3 odd 2 80.20.c.a.49.8 8
5.2 odd 4 25.20.a.f.1.7 8
5.3 odd 4 25.20.a.f.1.2 8
5.4 even 2 inner 5.20.b.a.4.7 yes 8
15.14 odd 2 45.20.b.b.19.2 8
20.19 odd 2 80.20.c.a.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.20.b.a.4.2 8 1.1 even 1 trivial
5.20.b.a.4.7 yes 8 5.4 even 2 inner
25.20.a.f.1.2 8 5.3 odd 4
25.20.a.f.1.7 8 5.2 odd 4
45.20.b.b.19.2 8 15.14 odd 2
45.20.b.b.19.7 8 3.2 odd 2
80.20.c.a.49.1 8 20.19 odd 2
80.20.c.a.49.8 8 4.3 odd 2