Properties

Label 3.41.b.a.2.6
Level $3$
Weight $41$
Character 3.2
Analytic conductor $30.403$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,41,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 41, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 41);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 41 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.4026855589\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.6
Root \(-18015.5i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.41.b.a.2.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-108093. i q^{2} +(-2.05308e9 - 2.81825e9i) q^{3} +1.08783e12 q^{4} -1.13503e14i q^{5} +(-3.04633e14 + 2.21924e14i) q^{6} -1.19157e17 q^{7} -2.36436e17i q^{8} +(-3.72735e18 + 1.15722e19i) q^{9} +O(q^{10})\) \(q-108093. i q^{2} +(-2.05308e9 - 2.81825e9i) q^{3} +1.08783e12 q^{4} -1.13503e14i q^{5} +(-3.04633e14 + 2.21924e14i) q^{6} -1.19157e17 q^{7} -2.36436e17i q^{8} +(-3.72735e18 + 1.15722e19i) q^{9} -1.22689e19 q^{10} -1.08238e21i q^{11} +(-2.23340e21 - 3.06577e21i) q^{12} +9.34761e21 q^{13} +1.28800e22i q^{14} +(-3.19879e23 + 2.33031e23i) q^{15} +1.17052e24 q^{16} -1.14562e24i q^{17} +(1.25087e24 + 4.02901e23i) q^{18} -4.02644e25 q^{19} -1.23472e26i q^{20} +(2.44639e26 + 3.35813e26i) q^{21} -1.16998e26 q^{22} +1.54324e26i q^{23} +(-6.66335e26 + 4.85423e26i) q^{24} -3.78798e27 q^{25} -1.01041e27i q^{26} +(4.02659e28 - 1.32541e28i) q^{27} -1.29622e29 q^{28} +3.32449e29i q^{29} +(2.51890e28 + 3.45767e28i) q^{30} -2.50582e29 q^{31} -3.86489e29i q^{32} +(-3.05042e30 + 2.22223e30i) q^{33} -1.23834e29 q^{34} +1.35246e31i q^{35} +(-4.05472e30 + 1.25886e31i) q^{36} -2.26165e31 q^{37} +4.35230e30i q^{38} +(-1.91914e31 - 2.63439e31i) q^{39} -2.68362e31 q^{40} +2.34363e32i q^{41} +(3.62990e31 - 2.64437e31i) q^{42} +8.11516e31 q^{43} -1.17745e33i q^{44} +(1.31348e33 + 4.23066e32i) q^{45} +1.66813e31 q^{46} -2.91765e33i q^{47} +(-2.40318e33 - 3.29882e33i) q^{48} +7.83153e33 q^{49} +4.09454e32i q^{50} +(-3.22865e33 + 2.35206e33i) q^{51} +1.01686e34 q^{52} +1.51489e34i q^{53} +(-1.43267e33 - 4.35246e33i) q^{54} -1.22854e35 q^{55} +2.81729e34i q^{56} +(8.26662e34 + 1.13475e35i) q^{57} +3.59354e34 q^{58} +7.34418e34i q^{59} +(-3.47974e35 + 2.53498e35i) q^{60} -1.65923e35 q^{61} +2.70861e34i q^{62} +(4.44140e35 - 1.37891e36i) q^{63} +1.24523e36 q^{64} -1.06098e36i q^{65} +(2.40207e35 + 3.29729e35i) q^{66} +8.14731e35 q^{67} -1.24624e36i q^{68} +(4.34922e35 - 3.16840e35i) q^{69} +1.46192e36 q^{70} -3.89618e36i q^{71} +(2.73608e36 + 8.81281e35i) q^{72} -1.48310e37 q^{73} +2.44468e36i q^{74} +(7.77704e36 + 1.06755e37i) q^{75} -4.38007e37 q^{76} +1.28973e38i q^{77} +(-2.84759e36 + 2.07446e36i) q^{78} +5.20652e37 q^{79} -1.32858e38i q^{80} +(-1.20022e38 - 8.62673e37i) q^{81} +2.53330e37 q^{82} -2.17493e38i q^{83} +(2.66125e38 + 3.65307e38i) q^{84} -1.30032e38 q^{85} -8.77192e36i q^{86} +(9.36922e38 - 6.82545e38i) q^{87} -2.55914e38 q^{88} -3.50974e38i q^{89} +(4.57304e37 - 1.41978e38i) q^{90} -1.11383e39 q^{91} +1.67878e38i q^{92} +(5.14465e38 + 7.06201e38i) q^{93} -3.15378e38 q^{94} +4.57013e39i q^{95} +(-1.08922e39 + 7.93495e38i) q^{96} -7.87477e39 q^{97} -8.46533e38i q^{98} +(1.25256e40 + 4.03443e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 108093.i 0.103085i −0.998671 0.0515427i \(-0.983586\pi\)
0.998671 0.0515427i \(-0.0164138\pi\)
\(3\) −2.05308e9 2.81825e9i −0.588819 0.808265i
\(4\) 1.08783e12 0.989373
\(5\) 1.13503e14i 1.19016i −0.803665 0.595082i \(-0.797119\pi\)
0.803665 0.595082i \(-0.202881\pi\)
\(6\) −3.04633e14 + 2.21924e14i −0.0833204 + 0.0606987i
\(7\) −1.19157e17 −1.49334 −0.746669 0.665196i \(-0.768348\pi\)
−0.746669 + 0.665196i \(0.768348\pi\)
\(8\) 2.36436e17i 0.205076i
\(9\) −3.72735e18 + 1.15722e19i −0.306585 + 0.951843i
\(10\) −1.22689e19 −0.122689
\(11\) 1.08238e21i 1.60889i −0.594024 0.804447i \(-0.702462\pi\)
0.594024 0.804447i \(-0.297538\pi\)
\(12\) −2.23340e21 3.06577e21i −0.582562 0.799676i
\(13\) 9.34761e21 0.491851 0.245925 0.969289i \(-0.420908\pi\)
0.245925 + 0.969289i \(0.420908\pi\)
\(14\) 1.28800e22i 0.153941i
\(15\) −3.19879e23 + 2.33031e23i −0.961969 + 0.700792i
\(16\) 1.17052e24 0.968233
\(17\) 1.14562e24i 0.281879i −0.990018 0.140940i \(-0.954988\pi\)
0.990018 0.140940i \(-0.0450124\pi\)
\(18\) 1.25087e24 + 4.02901e23i 0.0981212 + 0.0316044i
\(19\) −4.02644e25 −1.07115 −0.535574 0.844489i \(-0.679905\pi\)
−0.535574 + 0.844489i \(0.679905\pi\)
\(20\) 1.23472e26i 1.17752i
\(21\) 2.44639e26 + 3.35813e26i 0.879305 + 1.20701i
\(22\) −1.16998e26 −0.165854
\(23\) 1.54324e26i 0.0899241i 0.998989 + 0.0449620i \(0.0143167\pi\)
−0.998989 + 0.0449620i \(0.985683\pi\)
\(24\) −6.66335e26 + 4.85423e26i −0.165755 + 0.120752i
\(25\) −3.78798e27 −0.416493
\(26\) 1.01041e27i 0.0507027i
\(27\) 4.02659e28 1.32541e28i 0.949865 0.312662i
\(28\) −1.29622e29 −1.47747
\(29\) 3.32449e29i 1.87830i 0.343509 + 0.939149i \(0.388384\pi\)
−0.343509 + 0.939149i \(0.611616\pi\)
\(30\) 2.51890e28 + 3.45767e28i 0.0722414 + 0.0991650i
\(31\) −2.50582e29 −0.373006 −0.186503 0.982454i \(-0.559715\pi\)
−0.186503 + 0.982454i \(0.559715\pi\)
\(32\) 3.86489e29i 0.304886i
\(33\) −3.05042e30 + 2.22223e30i −1.30041 + 0.947347i
\(34\) −1.23834e29 −0.0290577
\(35\) 1.35246e31i 1.77732i
\(36\) −4.05472e30 + 1.25886e31i −0.303327 + 0.941728i
\(37\) −2.26165e31 −0.978117 −0.489059 0.872251i \(-0.662660\pi\)
−0.489059 + 0.872251i \(0.662660\pi\)
\(38\) 4.35230e30i 0.110420i
\(39\) −1.91914e31 2.63439e31i −0.289611 0.397546i
\(40\) −2.68362e31 −0.244074
\(41\) 2.34363e32i 1.30080i 0.759590 + 0.650402i \(0.225400\pi\)
−0.759590 + 0.650402i \(0.774600\pi\)
\(42\) 3.62990e31 2.64437e31i 0.124425 0.0906436i
\(43\) 8.11516e31 0.173751 0.0868756 0.996219i \(-0.472312\pi\)
0.0868756 + 0.996219i \(0.472312\pi\)
\(44\) 1.17745e33i 1.59180i
\(45\) 1.31348e33 + 4.23066e32i 1.13285 + 0.364886i
\(46\) 1.66813e31 0.00926987
\(47\) 2.91765e33i 1.05457i −0.849688 0.527286i \(-0.823209\pi\)
0.849688 0.527286i \(-0.176791\pi\)
\(48\) −2.40318e33 3.29882e33i −0.570114 0.782589i
\(49\) 7.83153e33 1.23006
\(50\) 4.09454e32i 0.0429344i
\(51\) −3.22865e33 + 2.35206e33i −0.227833 + 0.165976i
\(52\) 1.01686e34 0.486624
\(53\) 1.51489e34i 0.495294i 0.968850 + 0.247647i \(0.0796573\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(54\) −1.43267e33 4.35246e33i −0.0322309 0.0979173i
\(55\) −1.22854e35 −1.91485
\(56\) 2.81729e34i 0.306247i
\(57\) 8.26662e34 + 1.13475e35i 0.630712 + 0.865771i
\(58\) 3.59354e34 0.193625
\(59\) 7.34418e34i 0.281127i 0.990072 + 0.140564i \(0.0448915\pi\)
−0.990072 + 0.140564i \(0.955109\pi\)
\(60\) −3.47974e35 + 2.53498e35i −0.951746 + 0.693345i
\(61\) −1.65923e35 −0.326070 −0.163035 0.986620i \(-0.552128\pi\)
−0.163035 + 0.986620i \(0.552128\pi\)
\(62\) 2.70861e34i 0.0384515i
\(63\) 4.44140e35 1.37891e36i 0.457834 1.42142i
\(64\) 1.24523e36 0.936804
\(65\) 1.06098e36i 0.585384i
\(66\) 2.40207e35 + 3.29729e35i 0.0976578 + 0.134054i
\(67\) 8.14731e35 0.245199 0.122599 0.992456i \(-0.460877\pi\)
0.122599 + 0.992456i \(0.460877\pi\)
\(68\) 1.24624e36i 0.278884i
\(69\) 4.34922e35 3.16840e35i 0.0726825 0.0529490i
\(70\) 1.46192e36 0.183216
\(71\) 3.89618e36i 0.367682i −0.982956 0.183841i \(-0.941147\pi\)
0.982956 0.183841i \(-0.0588532\pi\)
\(72\) 2.73608e36 + 8.81281e35i 0.195200 + 0.0628730i
\(73\) −1.48310e37 −0.802995 −0.401498 0.915860i \(-0.631510\pi\)
−0.401498 + 0.915860i \(0.631510\pi\)
\(74\) 2.44468e36i 0.100830i
\(75\) 7.77704e36 + 1.06755e37i 0.245239 + 0.336636i
\(76\) −4.38007e37 −1.05976
\(77\) 1.28973e38i 2.40262i
\(78\) −2.84759e36 + 2.07446e36i −0.0409812 + 0.0298547i
\(79\) 5.20652e37 0.580772 0.290386 0.956910i \(-0.406216\pi\)
0.290386 + 0.956910i \(0.406216\pi\)
\(80\) 1.32858e38i 1.15236i
\(81\) −1.20022e38 8.62673e37i −0.812012 0.583641i
\(82\) 2.53330e37 0.134094
\(83\) 2.17493e38i 0.903405i −0.892169 0.451703i \(-0.850817\pi\)
0.892169 0.451703i \(-0.149183\pi\)
\(84\) 2.66125e38 + 3.65307e38i 0.869961 + 1.19419i
\(85\) −1.30032e38 −0.335483
\(86\) 8.77192e36i 0.0179112i
\(87\) 9.36922e38 6.82545e38i 1.51816 1.10598i
\(88\) −2.55914e38 −0.329945
\(89\) 3.50974e38i 0.360973i −0.983577 0.180487i \(-0.942233\pi\)
0.983577 0.180487i \(-0.0577673\pi\)
\(90\) 4.57304e37 1.41978e38i 0.0376145 0.116780i
\(91\) −1.11383e39 −0.734499
\(92\) 1.67878e38i 0.0889685i
\(93\) 5.14465e38 + 7.06201e38i 0.219633 + 0.301487i
\(94\) −3.15378e38 −0.108711
\(95\) 4.57013e39i 1.27484i
\(96\) −1.08922e39 + 7.93495e38i −0.246429 + 0.179523i
\(97\) −7.87477e39 −1.44812 −0.724058 0.689740i \(-0.757725\pi\)
−0.724058 + 0.689740i \(0.757725\pi\)
\(98\) 8.46533e38i 0.126801i
\(99\) 1.25256e40 + 4.03443e39i 1.53142 + 0.493263i
\(100\) −4.12067e39 −0.412067
\(101\) 4.39351e39i 0.360068i −0.983660 0.180034i \(-0.942379\pi\)
0.983660 0.180034i \(-0.0576207\pi\)
\(102\) 2.54241e38 + 3.48994e38i 0.0171097 + 0.0234863i
\(103\) −1.79465e40 −0.993654 −0.496827 0.867850i \(-0.665502\pi\)
−0.496827 + 0.867850i \(0.665502\pi\)
\(104\) 2.21011e39i 0.100867i
\(105\) 3.81158e40 2.77672e40i 1.43654 1.04652i
\(106\) 1.63749e39 0.0510576
\(107\) 7.12764e39i 0.184192i −0.995750 0.0920959i \(-0.970643\pi\)
0.995750 0.0920959i \(-0.0293566\pi\)
\(108\) 4.38023e40 1.44182e40i 0.939771 0.309339i
\(109\) −2.25766e40 −0.402836 −0.201418 0.979505i \(-0.564555\pi\)
−0.201418 + 0.979505i \(0.564555\pi\)
\(110\) 1.32796e40i 0.197393i
\(111\) 4.64336e40 + 6.37388e40i 0.575934 + 0.790578i
\(112\) −1.39476e41 −1.44590
\(113\) 1.88589e41i 1.63662i −0.574780 0.818308i \(-0.694912\pi\)
0.574780 0.818308i \(-0.305088\pi\)
\(114\) 1.22658e40 8.93563e39i 0.0892484 0.0650172i
\(115\) 1.75162e40 0.107025
\(116\) 3.61647e41i 1.85834i
\(117\) −3.48418e40 + 1.08172e41i −0.150794 + 0.468165i
\(118\) 7.93855e39 0.0289802
\(119\) 1.36509e41i 0.420941i
\(120\) 5.50970e40 + 7.56310e40i 0.143715 + 0.197276i
\(121\) −7.18962e41 −1.58854
\(122\) 1.79351e40i 0.0336131i
\(123\) 6.60493e41 4.81167e41i 1.05139 0.765938i
\(124\) −2.72590e41 −0.369042
\(125\) 6.02357e41i 0.694470i
\(126\) −1.49050e41 4.80084e40i −0.146528 0.0471961i
\(127\) 2.05337e42 1.72342 0.861712 0.507398i \(-0.169392\pi\)
0.861712 + 0.507398i \(0.169392\pi\)
\(128\) 5.59550e41i 0.401457i
\(129\) −1.66611e41 2.28705e41i −0.102308 0.140437i
\(130\) −1.14685e41 −0.0603446
\(131\) 6.40342e41i 0.289059i −0.989500 0.144529i \(-0.953833\pi\)
0.989500 0.144529i \(-0.0461668\pi\)
\(132\) −3.31833e42 + 2.41740e42i −1.28659 + 0.937280i
\(133\) 4.79777e42 1.59958
\(134\) 8.80667e40i 0.0252764i
\(135\) −1.50438e42 4.57030e42i −0.372119 1.13050i
\(136\) −2.70867e41 −0.0578066
\(137\) 1.12866e42i 0.208042i 0.994575 + 0.104021i \(0.0331710\pi\)
−0.994575 + 0.104021i \(0.966829\pi\)
\(138\) −3.42481e40 4.70120e40i −0.00545827 0.00749251i
\(139\) −5.82513e42 −0.803544 −0.401772 0.915740i \(-0.631605\pi\)
−0.401772 + 0.915740i \(0.631605\pi\)
\(140\) 1.47125e43i 1.75843i
\(141\) −8.22267e42 + 5.99019e42i −0.852374 + 0.620952i
\(142\) −4.21150e41 −0.0379027
\(143\) 1.01177e43i 0.791336i
\(144\) −4.36295e42 + 1.35455e43i −0.296846 + 0.921606i
\(145\) 3.77339e43 2.23549
\(146\) 1.60313e42i 0.0827771i
\(147\) −1.60788e43 2.20712e43i −0.724280 0.994212i
\(148\) −2.46028e43 −0.967723
\(149\) 4.17735e43i 1.43607i −0.696007 0.718035i \(-0.745042\pi\)
0.696007 0.718035i \(-0.254958\pi\)
\(150\) 1.15394e42 8.40643e41i 0.0347023 0.0252806i
\(151\) 4.60012e43 1.21124 0.605620 0.795754i \(-0.292925\pi\)
0.605620 + 0.795754i \(0.292925\pi\)
\(152\) 9.51995e42i 0.219666i
\(153\) 1.32574e43 + 4.27014e42i 0.268305 + 0.0864199i
\(154\) 1.39411e43 0.247675
\(155\) 2.84418e43i 0.443938i
\(156\) −2.08770e43 2.86576e43i −0.286533 0.393321i
\(157\) 1.47730e41 0.00178434 0.000892168 1.00000i \(-0.499716\pi\)
0.000892168 1.00000i \(0.499716\pi\)
\(158\) 5.62788e42i 0.0598692i
\(159\) 4.26933e43 3.11019e43i 0.400329 0.291638i
\(160\) −4.38677e43 −0.362865
\(161\) 1.83887e43i 0.134287i
\(162\) −9.32489e42 + 1.29736e43i −0.0601650 + 0.0837066i
\(163\) −3.33578e44 −1.90303 −0.951514 0.307605i \(-0.900473\pi\)
−0.951514 + 0.307605i \(0.900473\pi\)
\(164\) 2.54947e44i 1.28698i
\(165\) 2.52229e44 + 3.46232e44i 1.12750 + 1.54771i
\(166\) −2.35094e43 −0.0931280
\(167\) 2.38931e44i 0.839348i −0.907675 0.419674i \(-0.862144\pi\)
0.907675 0.419674i \(-0.137856\pi\)
\(168\) 7.93983e43 5.78414e43i 0.247529 0.180324i
\(169\) −2.73811e44 −0.758083
\(170\) 1.40555e43i 0.0345834i
\(171\) 1.50080e44 4.65947e44i 0.328397 1.01956i
\(172\) 8.82790e43 0.171905
\(173\) 5.45959e44i 0.946756i 0.880860 + 0.473378i \(0.156965\pi\)
−0.880860 + 0.473378i \(0.843035\pi\)
\(174\) −7.37783e43 1.01275e44i −0.114010 0.156501i
\(175\) 4.51363e44 0.621964
\(176\) 1.26695e45i 1.55778i
\(177\) 2.06977e44 1.50782e44i 0.227226 0.165533i
\(178\) −3.79379e43 −0.0372111
\(179\) 4.75963e44i 0.417362i −0.977984 0.208681i \(-0.933083\pi\)
0.977984 0.208681i \(-0.0669170\pi\)
\(180\) 1.42884e45 + 4.60223e44i 1.12081 + 0.361009i
\(181\) −1.39046e45 −0.976305 −0.488153 0.872758i \(-0.662329\pi\)
−0.488153 + 0.872758i \(0.662329\pi\)
\(182\) 1.20397e44i 0.0757162i
\(183\) 3.40655e44 + 4.67613e44i 0.191996 + 0.263551i
\(184\) 3.64877e43 0.0184412
\(185\) 2.56704e45i 1.16412i
\(186\) 7.63354e43 5.56101e43i 0.0310790 0.0226410i
\(187\) −1.24000e45 −0.453514
\(188\) 3.17390e45i 1.04337i
\(189\) −4.79795e45 + 1.57931e45i −1.41847 + 0.466909i
\(190\) 4.93999e44 0.131418
\(191\) 5.74210e45i 1.37532i 0.726033 + 0.687660i \(0.241362\pi\)
−0.726033 + 0.687660i \(0.758638\pi\)
\(192\) −2.55655e45 3.50935e45i −0.551608 0.757186i
\(193\) 5.42847e45 1.05568 0.527839 0.849344i \(-0.323002\pi\)
0.527839 + 0.849344i \(0.323002\pi\)
\(194\) 8.51207e44i 0.149280i
\(195\) −2.99011e45 + 2.17828e45i −0.473145 + 0.344685i
\(196\) 8.51935e45 1.21699
\(197\) 9.09772e44i 0.117384i 0.998276 + 0.0586919i \(0.0186930\pi\)
−0.998276 + 0.0586919i \(0.981307\pi\)
\(198\) 4.36093e44 1.35392e45i 0.0508482 0.157867i
\(199\) −4.16830e45 −0.439438 −0.219719 0.975563i \(-0.570514\pi\)
−0.219719 + 0.975563i \(0.570514\pi\)
\(200\) 8.95615e44i 0.0854125i
\(201\) −1.67271e45 2.29611e45i −0.144378 0.198186i
\(202\) −4.74908e44 −0.0371178
\(203\) 3.96135e46i 2.80493i
\(204\) −3.51221e45 + 2.55864e45i −0.225412 + 0.164212i
\(205\) 2.66009e46 1.54817
\(206\) 1.93989e45i 0.102431i
\(207\) −1.78586e45 5.75219e44i −0.0855937 0.0275694i
\(208\) 1.09416e46 0.476226
\(209\) 4.35815e46i 1.72336i
\(210\) −3.00144e45 4.12005e45i −0.107881 0.148087i
\(211\) −4.23119e46 −1.38297 −0.691486 0.722390i \(-0.743044\pi\)
−0.691486 + 0.722390i \(0.743044\pi\)
\(212\) 1.64794e46i 0.490031i
\(213\) −1.09804e46 + 7.99920e45i −0.297185 + 0.216498i
\(214\) −7.70448e44 −0.0189875
\(215\) 9.21095e45i 0.206793i
\(216\) −3.13374e45 9.52030e45i −0.0641192 0.194794i
\(217\) 2.98585e46 0.557023
\(218\) 2.44037e45i 0.0415266i
\(219\) 3.04493e46 + 4.17974e46i 0.472819 + 0.649033i
\(220\) −1.33644e47 −1.89450
\(221\) 1.07088e46i 0.138643i
\(222\) 6.88972e45 5.01914e45i 0.0814971 0.0593704i
\(223\) 7.95251e46 0.859818 0.429909 0.902872i \(-0.358546\pi\)
0.429909 + 0.902872i \(0.358546\pi\)
\(224\) 4.60528e46i 0.455298i
\(225\) 1.41191e46 4.38352e46i 0.127690 0.396436i
\(226\) −2.03851e46 −0.168711
\(227\) 1.10749e47i 0.839118i −0.907728 0.419559i \(-0.862185\pi\)
0.907728 0.419559i \(-0.137815\pi\)
\(228\) 8.99266e46 + 1.23441e47i 0.624009 + 0.856570i
\(229\) −1.39153e47 −0.884672 −0.442336 0.896849i \(-0.645850\pi\)
−0.442336 + 0.896849i \(0.645850\pi\)
\(230\) 1.89338e45i 0.0110327i
\(231\) 3.63479e47 2.64793e47i 1.94196 1.41471i
\(232\) 7.86028e46 0.385193
\(233\) 2.19142e47i 0.985386i −0.870203 0.492693i \(-0.836013\pi\)
0.870203 0.492693i \(-0.163987\pi\)
\(234\) 1.16927e46 + 3.76616e45i 0.0482610 + 0.0155447i
\(235\) −3.31162e47 −1.25512
\(236\) 7.98921e46i 0.278140i
\(237\) −1.06894e47 1.46733e47i −0.341970 0.469418i
\(238\) 1.47556e46 0.0433929
\(239\) 6.15537e47i 1.66455i 0.554365 + 0.832273i \(0.312961\pi\)
−0.554365 + 0.832273i \(0.687039\pi\)
\(240\) −3.74426e47 + 2.72768e47i −0.931410 + 0.678530i
\(241\) 5.24429e47 1.20046 0.600228 0.799829i \(-0.295077\pi\)
0.600228 + 0.799829i \(0.295077\pi\)
\(242\) 7.77147e46i 0.163756i
\(243\) 3.29368e45 + 5.15367e47i 0.00639082 + 0.999980i
\(244\) −1.80496e47 −0.322605
\(245\) 8.88902e47i 1.46397i
\(246\) −5.20108e46 7.13946e46i −0.0789571 0.108384i
\(247\) −3.76376e47 −0.526845
\(248\) 5.92465e46i 0.0764943i
\(249\) −6.12947e47 + 4.46531e47i −0.730191 + 0.531942i
\(250\) −6.51105e46 −0.0715898
\(251\) 1.18485e48i 1.20278i 0.798954 + 0.601392i \(0.205387\pi\)
−0.798954 + 0.601392i \(0.794613\pi\)
\(252\) 4.83147e47 1.50001e48i 0.452969 1.40632i
\(253\) 1.67038e47 0.144678
\(254\) 2.21955e47i 0.177660i
\(255\) 2.66966e47 + 3.66461e47i 0.197539 + 0.271159i
\(256\) 1.30866e48 0.895419
\(257\) 4.52221e47i 0.286212i −0.989707 0.143106i \(-0.954291\pi\)
0.989707 0.143106i \(-0.0457090\pi\)
\(258\) −2.47214e46 + 1.80095e46i −0.0144770 + 0.0105465i
\(259\) 2.69491e48 1.46066
\(260\) 1.15416e48i 0.579163i
\(261\) −3.84716e48 1.23915e48i −1.78785 0.575858i
\(262\) −6.92165e46 −0.0297978
\(263\) 1.78553e48i 0.712280i −0.934433 0.356140i \(-0.884093\pi\)
0.934433 0.356140i \(-0.115907\pi\)
\(264\) 5.25414e47 + 7.21230e47i 0.194278 + 0.266683i
\(265\) 1.71944e48 0.589482
\(266\) 5.18606e47i 0.164894i
\(267\) −9.89132e47 + 7.20580e47i −0.291762 + 0.212548i
\(268\) 8.86287e47 0.242593
\(269\) 5.13521e48i 1.30471i 0.757915 + 0.652353i \(0.226218\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(270\) −4.94017e47 + 1.62613e47i −0.116538 + 0.0383601i
\(271\) −5.29935e48 −1.16101 −0.580506 0.814256i \(-0.697145\pi\)
−0.580506 + 0.814256i \(0.697145\pi\)
\(272\) 1.34098e48i 0.272925i
\(273\) 2.28679e48 + 3.13905e48i 0.432487 + 0.593670i
\(274\) 1.22000e47 0.0214462
\(275\) 4.10005e48i 0.670093i
\(276\) 4.73120e47 3.44667e47i 0.0719101 0.0523863i
\(277\) −5.34662e48 −0.755934 −0.377967 0.925819i \(-0.623377\pi\)
−0.377967 + 0.925819i \(0.623377\pi\)
\(278\) 6.29655e47i 0.0828337i
\(279\) 9.34007e47 2.89978e48i 0.114358 0.355043i
\(280\) 3.19771e48 0.364484
\(281\) 6.38334e48i 0.677520i 0.940873 + 0.338760i \(0.110007\pi\)
−0.940873 + 0.338760i \(0.889993\pi\)
\(282\) 6.47497e47 + 8.88812e47i 0.0640112 + 0.0878674i
\(283\) −1.29528e49 −1.19298 −0.596492 0.802619i \(-0.703439\pi\)
−0.596492 + 0.802619i \(0.703439\pi\)
\(284\) 4.23838e48i 0.363775i
\(285\) 1.28797e49 9.38286e48i 1.03041 0.750651i
\(286\) −1.09365e48 −0.0815753
\(287\) 2.79259e49i 1.94254i
\(288\) 4.47253e48 + 1.44058e48i 0.290204 + 0.0934735i
\(289\) 1.52055e49 0.920544
\(290\) 4.07877e48i 0.230446i
\(291\) 1.61676e49 + 2.21930e49i 0.852678 + 1.17046i
\(292\) −1.61336e49 −0.794462
\(293\) 1.44357e49i 0.663875i 0.943301 + 0.331937i \(0.107702\pi\)
−0.943301 + 0.331937i \(0.892298\pi\)
\(294\) −2.38574e48 + 1.73800e48i −0.102489 + 0.0746628i
\(295\) 8.33587e48 0.334588
\(296\) 5.34735e48i 0.200588i
\(297\) −1.43460e49 4.35831e49i −0.503039 1.52823i
\(298\) −4.51542e48 −0.148038
\(299\) 1.44256e48i 0.0442292i
\(300\) 8.46008e48 + 1.16131e49i 0.242633 + 0.333059i
\(301\) −9.66976e48 −0.259469
\(302\) 4.97241e48i 0.124861i
\(303\) −1.23820e49 + 9.02025e48i −0.291030 + 0.212015i
\(304\) −4.71304e49 −1.03712
\(305\) 1.88328e49i 0.388077i
\(306\) 4.61573e47 1.43303e48i 0.00890864 0.0276584i
\(307\) 2.03168e49 0.367357 0.183678 0.982986i \(-0.441200\pi\)
0.183678 + 0.982986i \(0.441200\pi\)
\(308\) 1.40301e50i 2.37709i
\(309\) 3.68457e49 + 5.05776e49i 0.585082 + 0.803136i
\(310\) 3.07436e48 0.0457636
\(311\) 1.26635e50i 1.76745i −0.468009 0.883724i \(-0.655029\pi\)
0.468009 0.883724i \(-0.344971\pi\)
\(312\) −6.22864e48 + 4.53754e48i −0.0815269 + 0.0593921i
\(313\) −3.21332e49 −0.394518 −0.197259 0.980351i \(-0.563204\pi\)
−0.197259 + 0.980351i \(0.563204\pi\)
\(314\) 1.59686e46i 0.000183939i
\(315\) −1.56510e50 5.04112e49i −1.69173 0.544899i
\(316\) 5.66380e49 0.574600
\(317\) 6.96883e49i 0.663705i −0.943331 0.331852i \(-0.892326\pi\)
0.943331 0.331852i \(-0.107674\pi\)
\(318\) −3.36190e48 4.61484e48i −0.0300637 0.0412681i
\(319\) 3.59837e50 3.02198
\(320\) 1.41337e50i 1.11495i
\(321\) −2.00874e49 + 1.46336e49i −0.148876 + 0.108456i
\(322\) −1.98769e48 −0.0138430
\(323\) 4.61278e49i 0.301934i
\(324\) −1.30564e50 9.38440e49i −0.803383 0.577439i
\(325\) −3.54085e49 −0.204852
\(326\) 3.60574e49i 0.196175i
\(327\) 4.63517e49 + 6.36264e49i 0.237198 + 0.325598i
\(328\) 5.54119e49 0.266763
\(329\) 3.47658e50i 1.57483i
\(330\) 3.74253e49 2.72642e49i 0.159546 0.116229i
\(331\) −2.72248e50 −1.09246 −0.546230 0.837636i \(-0.683937\pi\)
−0.546230 + 0.837636i \(0.683937\pi\)
\(332\) 2.36594e50i 0.893805i
\(333\) 8.42997e49 2.61722e50i 0.299876 0.931014i
\(334\) −2.58267e49 −0.0865246
\(335\) 9.24744e49i 0.291827i
\(336\) 2.86355e50 + 3.93077e50i 0.851372 + 1.16867i
\(337\) −5.28872e49 −0.148167 −0.0740837 0.997252i \(-0.523603\pi\)
−0.0740837 + 0.997252i \(0.523603\pi\)
\(338\) 2.95970e49i 0.0781473i
\(339\) −5.31489e50 + 3.87189e50i −1.32282 + 0.963671i
\(340\) −1.41452e50 −0.331918
\(341\) 2.71226e50i 0.600127i
\(342\) −5.03656e49 1.62226e49i −0.105102 0.0338530i
\(343\) −1.74532e50 −0.343552
\(344\) 1.91872e49i 0.0356321i
\(345\) −3.59622e49 4.93650e49i −0.0630180 0.0865042i
\(346\) 5.90143e49 0.0975968
\(347\) 4.99538e50i 0.779793i 0.920859 + 0.389896i \(0.127489\pi\)
−0.920859 + 0.389896i \(0.872511\pi\)
\(348\) 1.01921e51 7.42491e50i 1.50203 1.09422i
\(349\) 1.76342e50 0.245384 0.122692 0.992445i \(-0.460847\pi\)
0.122692 + 0.992445i \(0.460847\pi\)
\(350\) 4.87892e49i 0.0641155i
\(351\) 3.76389e50 1.23894e50i 0.467192 0.153783i
\(352\) −4.18330e50 −0.490530
\(353\) 1.29915e51i 1.43935i −0.694311 0.719675i \(-0.744291\pi\)
0.694311 0.719675i \(-0.255709\pi\)
\(354\) −1.62985e49 2.23728e49i −0.0170641 0.0234237i
\(355\) −4.42229e50 −0.437602
\(356\) 3.81800e50i 0.357137i
\(357\) 3.84715e50 2.80264e50i 0.340232 0.247858i
\(358\) −5.14482e49 −0.0430239
\(359\) 1.20829e50i 0.0955613i −0.998858 0.0477806i \(-0.984785\pi\)
0.998858 0.0477806i \(-0.0152148\pi\)
\(360\) 1.00028e50 3.10554e50i 0.0748293 0.232320i
\(361\) 2.08215e50 0.147356
\(362\) 1.50298e50i 0.100643i
\(363\) 1.47609e51 + 2.02621e51i 0.935363 + 1.28396i
\(364\) −1.21166e51 −0.726694
\(365\) 1.68336e51i 0.955697i
\(366\) 5.05457e49 3.68224e49i 0.0271683 0.0197920i
\(367\) 1.03875e51 0.528677 0.264339 0.964430i \(-0.414846\pi\)
0.264339 + 0.964430i \(0.414846\pi\)
\(368\) 1.80639e50i 0.0870675i
\(369\) −2.71209e51 8.73554e50i −1.23816 0.398807i
\(370\) 2.77479e50 0.120004
\(371\) 1.80509e51i 0.739641i
\(372\) 5.59650e50 + 7.68225e50i 0.217299 + 0.298284i
\(373\) −3.34287e51 −1.23011 −0.615053 0.788486i \(-0.710865\pi\)
−0.615053 + 0.788486i \(0.710865\pi\)
\(374\) 1.34036e50i 0.0467507i
\(375\) −1.69759e51 + 1.23669e51i −0.561316 + 0.408917i
\(376\) −6.89838e50 −0.216267
\(377\) 3.10760e51i 0.923843i
\(378\) 1.70713e50 + 5.18625e50i 0.0481316 + 0.146224i
\(379\) 5.71675e51 1.52885 0.764425 0.644713i \(-0.223023\pi\)
0.764425 + 0.644713i \(0.223023\pi\)
\(380\) 4.97151e51i 1.26129i
\(381\) −4.21574e51 5.78689e51i −1.01478 1.39298i
\(382\) 6.20681e50 0.141776
\(383\) 5.35561e51i 1.16100i −0.814259 0.580502i \(-0.802857\pi\)
0.814259 0.580502i \(-0.197143\pi\)
\(384\) −1.57695e51 + 1.14880e51i −0.324484 + 0.236386i
\(385\) 1.46389e52 2.85952
\(386\) 5.86780e50i 0.108825i
\(387\) −3.02481e50 + 9.39102e50i −0.0532695 + 0.165384i
\(388\) −8.56639e51 −1.43273
\(389\) 6.15052e51i 0.977056i −0.872548 0.488528i \(-0.837534\pi\)
0.872548 0.488528i \(-0.162466\pi\)
\(390\) 2.35457e50 + 3.23209e50i 0.0355320 + 0.0487744i
\(391\) 1.76797e50 0.0253478
\(392\) 1.85166e51i 0.252254i
\(393\) −1.80464e51 + 1.31468e51i −0.233636 + 0.170203i
\(394\) 9.83400e49 0.0121006
\(395\) 5.90956e51i 0.691215i
\(396\) 1.36256e52 + 4.38876e51i 1.51514 + 0.488021i
\(397\) 3.02413e51 0.319735 0.159868 0.987138i \(-0.448893\pi\)
0.159868 + 0.987138i \(0.448893\pi\)
\(398\) 4.50564e50i 0.0452997i
\(399\) −9.85024e51 1.35213e52i −0.941865 1.29289i
\(400\) −4.43391e51 −0.403262
\(401\) 1.73505e52i 1.50116i 0.660782 + 0.750578i \(0.270225\pi\)
−0.660782 + 0.750578i \(0.729775\pi\)
\(402\) −2.48194e50 + 1.80808e50i −0.0204301 + 0.0148832i
\(403\) −2.34234e51 −0.183463
\(404\) 4.77938e51i 0.356241i
\(405\) −9.79160e51 + 1.36229e52i −0.694629 + 0.966428i
\(406\) −4.28194e51 −0.289148
\(407\) 2.44797e52i 1.57369i
\(408\) 5.56112e50 + 7.63369e50i 0.0340376 + 0.0467230i
\(409\) 1.71171e52 0.997619 0.498809 0.866712i \(-0.333771\pi\)
0.498809 + 0.866712i \(0.333771\pi\)
\(410\) 2.87537e51i 0.159594i
\(411\) 3.18084e51 2.31724e51i 0.168153 0.122499i
\(412\) −1.95227e52 −0.983095
\(413\) 8.75109e51i 0.419818i
\(414\) −6.21772e49 + 1.93039e50i −0.00284200 + 0.00882346i
\(415\) −2.46861e52 −1.07520
\(416\) 3.61275e51i 0.149959i
\(417\) 1.19595e52 + 1.64166e52i 0.473142 + 0.649476i
\(418\) 4.71086e51 0.177654
\(419\) 3.31810e52i 1.19291i −0.802645 0.596457i \(-0.796575\pi\)
0.802645 0.596457i \(-0.203425\pi\)
\(420\) 4.14634e52 3.02060e52i 1.42128 1.03540i
\(421\) −3.09470e52 −1.01152 −0.505762 0.862673i \(-0.668789\pi\)
−0.505762 + 0.862673i \(0.668789\pi\)
\(422\) 4.57362e51i 0.142564i
\(423\) 3.37637e52 + 1.08751e52i 1.00379 + 0.323316i
\(424\) 3.58174e51 0.101573
\(425\) 4.33960e51i 0.117401i
\(426\) 8.64657e50 + 1.18690e51i 0.0223178 + 0.0306354i
\(427\) 1.97709e52 0.486932
\(428\) 7.75364e51i 0.182234i
\(429\) −2.85142e52 + 2.07725e52i −0.639609 + 0.465954i
\(430\) −9.95639e50 −0.0213173
\(431\) 9.81535e50i 0.0200614i 0.999950 + 0.0100307i \(0.00319292\pi\)
−0.999950 + 0.0100307i \(0.996807\pi\)
\(432\) 4.71321e52 1.55142e52i 0.919690 0.302729i
\(433\) 5.74733e51 0.107080 0.0535399 0.998566i \(-0.482950\pi\)
0.0535399 + 0.998566i \(0.482950\pi\)
\(434\) 3.22749e51i 0.0574210i
\(435\) −7.74709e52 1.06343e53i −1.31630 1.80686i
\(436\) −2.45594e52 −0.398555
\(437\) 6.21375e51i 0.0963219i
\(438\) 4.51800e51 3.29135e51i 0.0669059 0.0487407i
\(439\) 6.68531e52 0.945869 0.472935 0.881098i \(-0.343195\pi\)
0.472935 + 0.881098i \(0.343195\pi\)
\(440\) 2.90471e52i 0.392689i
\(441\) −2.91909e52 + 9.06280e52i −0.377117 + 1.17082i
\(442\) −1.15755e51 −0.0142920
\(443\) 1.09893e53i 1.29687i 0.761269 + 0.648436i \(0.224577\pi\)
−0.761269 + 0.648436i \(0.775423\pi\)
\(444\) 5.05117e52 + 6.93369e52i 0.569814 + 0.782177i
\(445\) −3.98366e52 −0.429618
\(446\) 8.59610e51i 0.0886348i
\(447\) −1.17728e53 + 8.57646e52i −1.16073 + 0.845585i
\(448\) −1.48377e53 −1.39896
\(449\) 7.85528e51i 0.0708329i 0.999373 + 0.0354164i \(0.0112758\pi\)
−0.999373 + 0.0354164i \(0.988724\pi\)
\(450\) −4.73828e51 1.52618e51i −0.0408668 0.0131630i
\(451\) 2.53671e53 2.09286
\(452\) 2.05152e53i 1.61922i
\(453\) −9.44443e52 1.29643e53i −0.713201 0.979003i
\(454\) −1.19712e52 −0.0865009
\(455\) 1.26423e53i 0.874175i
\(456\) 2.68296e52 1.95453e52i 0.177548 0.129344i
\(457\) 6.95029e52 0.440229 0.220115 0.975474i \(-0.429357\pi\)
0.220115 + 0.975474i \(0.429357\pi\)
\(458\) 1.50414e52i 0.0911969i
\(459\) −1.51842e52 4.61295e52i −0.0881329 0.267747i
\(460\) 1.90546e52 0.105887
\(461\) 2.62065e53i 1.39441i −0.716871 0.697206i \(-0.754426\pi\)
0.716871 0.697206i \(-0.245574\pi\)
\(462\) −2.86223e52 3.92895e52i −0.145836 0.200187i
\(463\) 2.26385e53 1.10466 0.552329 0.833626i \(-0.313739\pi\)
0.552329 + 0.833626i \(0.313739\pi\)
\(464\) 3.89138e53i 1.81863i
\(465\) 8.01559e52 5.83934e52i 0.358820 0.261399i
\(466\) −2.36877e52 −0.101579
\(467\) 3.37419e53i 1.38622i −0.720833 0.693109i \(-0.756241\pi\)
0.720833 0.693109i \(-0.243759\pi\)
\(468\) −3.79019e52 + 1.17673e53i −0.149192 + 0.463190i
\(469\) −9.70807e52 −0.366164
\(470\) 3.57963e52i 0.129384i
\(471\) −3.03303e50 4.16340e50i −0.00105065 0.00144222i
\(472\) 1.73643e52 0.0576524
\(473\) 8.78372e52i 0.279547i
\(474\) −1.58608e52 + 1.15545e52i −0.0483902 + 0.0352521i
\(475\) 1.52521e53 0.446125
\(476\) 1.48498e53i 0.416468i
\(477\) −1.75306e53 5.64652e52i −0.471442 0.151850i
\(478\) 6.65352e52 0.171591
\(479\) 1.29204e53i 0.319569i −0.987152 0.159784i \(-0.948920\pi\)
0.987152 0.159784i \(-0.0510799\pi\)
\(480\) 9.00641e52 + 1.23630e53i 0.213662 + 0.293291i
\(481\) −2.11410e53 −0.481088
\(482\) 5.66871e52i 0.123750i
\(483\) −5.18239e52 + 3.77536e52i −0.108539 + 0.0790707i
\(484\) −7.82107e53 −1.57166
\(485\) 8.93810e53i 1.72350i
\(486\) 5.57076e52 3.56024e50i 0.103083 0.000658800i
\(487\) −5.88712e53 −1.04550 −0.522749 0.852487i \(-0.675094\pi\)
−0.522749 + 0.852487i \(0.675094\pi\)
\(488\) 3.92303e52i 0.0668690i
\(489\) 6.84864e53 + 9.40105e53i 1.12054 + 1.53815i
\(490\) −9.60841e52 −0.150914
\(491\) 2.12361e53i 0.320217i −0.987099 0.160108i \(-0.948816\pi\)
0.987099 0.160108i \(-0.0511844\pi\)
\(492\) 7.18502e53 5.23427e53i 1.04022 0.757799i
\(493\) 3.80861e53 0.529454
\(494\) 4.06836e52i 0.0543100i
\(495\) 4.57920e53 1.42169e54i 0.587064 1.82264i
\(496\) −2.93311e53 −0.361156
\(497\) 4.64257e53i 0.549073i
\(498\) 4.82668e52 + 6.62553e52i 0.0548355 + 0.0752721i
\(499\) −2.91330e53 −0.317961 −0.158980 0.987282i \(-0.550821\pi\)
−0.158980 + 0.987282i \(0.550821\pi\)
\(500\) 6.55260e53i 0.687090i
\(501\) −6.73365e53 + 4.90544e53i −0.678416 + 0.494224i
\(502\) 1.28074e53 0.123990
\(503\) 1.95537e54i 1.81915i −0.415535 0.909577i \(-0.636406\pi\)
0.415535 0.909577i \(-0.363594\pi\)
\(504\) −3.26023e53 1.05011e53i −0.291499 0.0938907i
\(505\) −4.98676e53 −0.428540
\(506\) 1.80556e52i 0.0149142i
\(507\) 5.62157e53 + 7.71666e53i 0.446373 + 0.612732i
\(508\) 2.23371e54 1.70511
\(509\) 3.00436e53i 0.220494i 0.993904 + 0.110247i \(0.0351642\pi\)
−0.993904 + 0.110247i \(0.964836\pi\)
\(510\) 3.96119e52 2.88571e52i 0.0279526 0.0203634i
\(511\) 1.76721e54 1.19914
\(512\) 7.56688e53i 0.493762i
\(513\) −1.62128e54 + 5.33668e53i −1.01744 + 0.334906i
\(514\) −4.88819e52 −0.0295043
\(515\) 2.03698e54i 1.18261i
\(516\) −1.81244e53 2.48792e53i −0.101221 0.138945i
\(517\) −3.15802e54 −1.69670
\(518\) 2.91301e53i 0.150573i
\(519\) 1.53865e54 1.12090e54i 0.765229 0.557468i
\(520\) −2.50854e53 −0.120048
\(521\) 2.81714e54i 1.29734i 0.761069 + 0.648671i \(0.224675\pi\)
−0.761069 + 0.648671i \(0.775325\pi\)
\(522\) −1.33944e53 + 4.15851e53i −0.0593626 + 0.184301i
\(523\) −1.35385e54 −0.577481 −0.288741 0.957407i \(-0.593237\pi\)
−0.288741 + 0.957407i \(0.593237\pi\)
\(524\) 6.96582e53i 0.285987i
\(525\) −9.26687e53 1.27205e54i −0.366224 0.502712i
\(526\) −1.93003e53 −0.0734258
\(527\) 2.87072e53i 0.105143i
\(528\) −3.57059e54 + 2.60116e54i −1.25910 + 0.917253i
\(529\) 2.92138e54 0.991914
\(530\) 1.85860e53i 0.0607670i
\(531\) −8.49883e53 2.73744e53i −0.267589 0.0861894i
\(532\) 5.21915e54 1.58259
\(533\) 2.19073e54i 0.639802i
\(534\) 7.78896e52 + 1.06918e53i 0.0219106 + 0.0300764i
\(535\) −8.09008e53 −0.219219
\(536\) 1.92632e53i 0.0502843i
\(537\) −1.34138e54 + 9.77192e53i −0.337339 + 0.245750i
\(538\) 5.55080e53 0.134496
\(539\) 8.47672e54i 1.97903i
\(540\) −1.63650e54 4.97169e54i −0.368164 1.11848i
\(541\) 1.57638e54 0.341756 0.170878 0.985292i \(-0.445340\pi\)
0.170878 + 0.985292i \(0.445340\pi\)
\(542\) 5.72822e53i 0.119683i
\(543\) 2.85472e54 + 3.91865e54i 0.574867 + 0.789113i
\(544\) −4.42771e53 −0.0859412
\(545\) 2.56251e54i 0.479442i
\(546\) 3.39309e53 2.47186e53i 0.0611988 0.0445831i
\(547\) 4.38693e54 0.762806 0.381403 0.924409i \(-0.375441\pi\)
0.381403 + 0.924409i \(0.375441\pi\)
\(548\) 1.22779e54i 0.205832i
\(549\) 6.18455e53 1.92010e54i 0.0999681 0.310368i
\(550\) 4.43186e53 0.0690768
\(551\) 1.33858e55i 2.01193i
\(552\) −7.49123e52 1.02831e53i −0.0108585 0.0149054i
\(553\) −6.20392e54 −0.867289
\(554\) 5.77932e53i 0.0779258i
\(555\) 7.23455e54 5.27035e54i 0.940918 0.685456i
\(556\) −6.33673e54 −0.795005
\(557\) 1.43649e55i 1.73859i 0.494293 + 0.869295i \(0.335427\pi\)
−0.494293 + 0.869295i \(0.664573\pi\)
\(558\) −3.13446e53 1.00960e53i −0.0365998 0.0117886i
\(559\) 7.58573e53 0.0854597
\(560\) 1.58309e55i 1.72086i
\(561\) 2.54583e54 + 3.49464e54i 0.267038 + 0.366560i
\(562\) 6.89995e53 0.0698424
\(563\) 5.10238e54i 0.498431i −0.968448 0.249215i \(-0.919827\pi\)
0.968448 0.249215i \(-0.0801727\pi\)
\(564\) −8.94484e54 + 6.51629e54i −0.843317 + 0.614354i
\(565\) −2.14054e55 −1.94784
\(566\) 1.40011e54i 0.122979i
\(567\) 1.43015e55 + 1.02793e55i 1.21261 + 0.871573i
\(568\) −9.21198e53 −0.0754026
\(569\) 1.08403e55i 0.856634i −0.903628 0.428317i \(-0.859107\pi\)
0.903628 0.428317i \(-0.140893\pi\)
\(570\) −1.01422e54 1.39221e54i −0.0773812 0.106220i
\(571\) 1.56093e53 0.0114990 0.00574951 0.999983i \(-0.498170\pi\)
0.00574951 + 0.999983i \(0.498170\pi\)
\(572\) 1.10063e55i 0.782927i
\(573\) 1.61827e55 1.17890e55i 1.11162 0.809814i
\(574\) −3.01860e54 −0.200248
\(575\) 5.84575e53i 0.0374527i
\(576\) −4.64140e54 + 1.44100e55i −0.287210 + 0.891690i
\(577\) −2.64011e55 −1.57800 −0.788999 0.614395i \(-0.789400\pi\)
−0.788999 + 0.614395i \(0.789400\pi\)
\(578\) 1.64361e54i 0.0948947i
\(579\) −1.11451e55 1.52988e55i −0.621603 0.853268i
\(580\) 4.10480e55 2.21173
\(581\) 2.59157e55i 1.34909i
\(582\) 2.39891e54 1.74760e54i 0.120658 0.0878987i
\(583\) 1.63969e55 0.796876
\(584\) 3.50658e54i 0.164675i
\(585\) 1.22779e55 + 3.95465e54i 0.557193 + 0.179470i
\(586\) 1.56040e54 0.0684359
\(587\) 1.90360e55i 0.806889i −0.915004 0.403445i \(-0.867813\pi\)
0.915004 0.403445i \(-0.132187\pi\)
\(588\) −1.74910e55 2.40096e55i −0.716584 0.983647i
\(589\) 1.00895e55 0.399544
\(590\) 9.01049e53i 0.0344912i
\(591\) 2.56396e54 1.86784e54i 0.0948772 0.0691178i
\(592\) −2.64731e55 −0.947045
\(593\) 1.61772e55i 0.559511i −0.960071 0.279755i \(-0.909747\pi\)
0.960071 0.279755i \(-0.0902534\pi\)
\(594\) −4.71103e54 + 1.55070e54i −0.157539 + 0.0518561i
\(595\) 1.54942e55 0.500989
\(596\) 4.54424e55i 1.42081i
\(597\) 8.55788e54 + 1.17473e55i 0.258749 + 0.355182i
\(598\) 1.55930e53 0.00455939
\(599\) 3.38952e55i 0.958521i 0.877673 + 0.479261i \(0.159095\pi\)
−0.877673 + 0.479261i \(0.840905\pi\)
\(600\) 2.52406e54 1.83877e54i 0.0690359 0.0502925i
\(601\) −3.44925e55 −0.912506 −0.456253 0.889850i \(-0.650809\pi\)
−0.456253 + 0.889850i \(0.650809\pi\)
\(602\) 1.04523e54i 0.0267475i
\(603\) −3.03679e54 + 9.42822e54i −0.0751742 + 0.233391i
\(604\) 5.00414e55 1.19837
\(605\) 8.16043e55i 1.89063i
\(606\) 9.75025e53 + 1.33841e54i 0.0218556 + 0.0300010i
\(607\) −1.09354e55 −0.237170 −0.118585 0.992944i \(-0.537836\pi\)
−0.118585 + 0.992944i \(0.537836\pi\)
\(608\) 1.55618e55i 0.326578i
\(609\) −1.11641e56 + 8.13299e55i −2.26713 + 1.65160i
\(610\) 2.03569e54 0.0400051
\(611\) 2.72731e55i 0.518693i
\(612\) 1.44217e55 + 4.64518e54i 0.265454 + 0.0855016i
\(613\) 1.75716e55 0.313042 0.156521 0.987675i \(-0.449972\pi\)
0.156521 + 0.987675i \(0.449972\pi\)
\(614\) 2.19610e54i 0.0378691i
\(615\) −5.46139e55 7.49679e55i −0.911593 1.25133i
\(616\) 3.04939e55 0.492719
\(617\) 8.39830e55i 1.31368i −0.754032 0.656838i \(-0.771894\pi\)
0.754032 0.656838i \(-0.228106\pi\)
\(618\) 5.46709e54 3.98276e54i 0.0827916 0.0603135i
\(619\) 1.05937e56 1.55323 0.776617 0.629974i \(-0.216934\pi\)
0.776617 + 0.629974i \(0.216934\pi\)
\(620\) 3.09397e55i 0.439221i
\(621\) 2.04542e54 + 6.21398e54i 0.0281158 + 0.0854157i
\(622\) −1.36884e55 −0.182198
\(623\) 4.18210e55i 0.539055i
\(624\) −2.24640e55 3.08361e55i −0.280411 0.384917i
\(625\) −1.02821e56 −1.24303
\(626\) 3.47337e54i 0.0406691i
\(627\) 1.22823e56 8.94765e55i 1.39293 1.01475i
\(628\) 1.60705e53 0.00176537
\(629\) 2.59100e55i 0.275711i
\(630\) −5.44909e54 + 1.69176e55i −0.0561711 + 0.174393i
\(631\) −2.26793e55 −0.226487 −0.113243 0.993567i \(-0.536124\pi\)
−0.113243 + 0.993567i \(0.536124\pi\)
\(632\) 1.23101e55i 0.119102i
\(633\) 8.68699e55 + 1.19245e56i 0.814320 + 1.11781i
\(634\) −7.53282e54 −0.0684183
\(635\) 2.33063e56i 2.05116i
\(636\) 4.64429e55 3.38335e55i 0.396075 0.288539i
\(637\) 7.32061e55 0.605004
\(638\) 3.88959e55i 0.311523i
\(639\) 4.50874e55 + 1.45225e55i 0.349976 + 0.112726i
\(640\) −6.35106e55 −0.477800
\(641\) 1.60220e56i 1.16830i 0.811645 + 0.584151i \(0.198573\pi\)
−0.811645 + 0.584151i \(0.801427\pi\)
\(642\) 1.58179e54 + 2.17131e54i 0.0111802 + 0.0153469i
\(643\) −1.34900e56 −0.924256 −0.462128 0.886813i \(-0.652914\pi\)
−0.462128 + 0.886813i \(0.652914\pi\)
\(644\) 2.00038e55i 0.132860i
\(645\) −2.59587e55 + 1.89109e55i −0.167143 + 0.121763i
\(646\) 4.98609e54 0.0311250
\(647\) 3.06483e55i 0.185490i 0.995690 + 0.0927452i \(0.0295642\pi\)
−0.995690 + 0.0927452i \(0.970436\pi\)
\(648\) −2.03967e55 + 2.83776e55i −0.119691 + 0.166524i
\(649\) 7.94923e55 0.452304
\(650\) 3.82741e54i 0.0211173i
\(651\) −6.13020e55 8.41486e55i −0.327986 0.450223i
\(652\) −3.62875e56 −1.88281
\(653\) 1.79299e56i 0.902222i 0.892468 + 0.451111i \(0.148972\pi\)
−0.892468 + 0.451111i \(0.851028\pi\)
\(654\) 6.87757e54 5.01029e54i 0.0335645 0.0244516i
\(655\) −7.26808e55 −0.344028
\(656\) 2.74327e56i 1.25948i
\(657\) 5.52804e55 1.71627e56i 0.246186 0.764326i
\(658\) 3.75794e55 0.162342
\(659\) 6.55167e55i 0.274564i 0.990532 + 0.137282i \(0.0438367\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(660\) 2.74382e56 + 3.76641e56i 1.11552 + 1.53126i
\(661\) 1.73011e56 0.682409 0.341205 0.939989i \(-0.389165\pi\)
0.341205 + 0.939989i \(0.389165\pi\)
\(662\) 2.94281e55i 0.112617i
\(663\) −3.01801e55 + 2.19861e55i −0.112060 + 0.0816354i
\(664\) −5.14231e55 −0.185266
\(665\) 5.44562e56i 1.90377i
\(666\) −2.82904e55 9.11221e54i −0.0959741 0.0309128i
\(667\) −5.13047e55 −0.168904
\(668\) 2.59915e56i 0.830429i
\(669\) −1.63272e56 2.24121e56i −0.506277 0.694961i
\(670\) −9.99583e54 −0.0300831
\(671\) 1.79593e56i 0.524612i
\(672\) 1.29788e56 9.45503e55i 0.368002 0.268088i
\(673\) 2.41957e56 0.665943 0.332971 0.942937i \(-0.391949\pi\)
0.332971 + 0.942937i \(0.391949\pi\)
\(674\) 5.71674e54i 0.0152739i
\(675\) −1.52526e56 + 5.02062e55i −0.395612 + 0.130221i
\(676\) −2.97859e56 −0.750027
\(677\) 3.89497e56i 0.952206i −0.879389 0.476103i \(-0.842049\pi\)
0.879389 0.476103i \(-0.157951\pi\)
\(678\) 4.18524e55 + 5.74503e55i 0.0993405 + 0.136364i
\(679\) 9.38332e56 2.16252
\(680\) 3.07442e55i 0.0687994i
\(681\) −3.12118e56 + 2.27377e56i −0.678230 + 0.494088i
\(682\) 2.93176e55 0.0618644
\(683\) 2.39575e55i 0.0490938i −0.999699 0.0245469i \(-0.992186\pi\)
0.999699 0.0245469i \(-0.00781431\pi\)
\(684\) 1.63261e56 5.06870e56i 0.324908 1.00873i
\(685\) 1.28106e56 0.247605
\(686\) 1.88657e55i 0.0354152i
\(687\) 2.85693e56 + 3.92167e56i 0.520912 + 0.715050i
\(688\) 9.49897e55 0.168232
\(689\) 1.41606e56i 0.243611i
\(690\) −5.33601e54 + 3.88727e54i −0.00891732 + 0.00649625i
\(691\) −6.14613e56 −0.997794 −0.498897 0.866661i \(-0.666261\pi\)
−0.498897 + 0.866661i \(0.666261\pi\)
\(692\) 5.93909e56i 0.936695i
\(693\) −1.49250e57 4.80729e56i −2.28692 0.736607i
\(694\) 5.39966e55 0.0803853
\(695\) 6.61169e56i 0.956349i
\(696\) −1.61378e56 2.21522e56i −0.226809 0.311338i
\(697\) 2.68492e56 0.366670
\(698\) 1.90613e55i 0.0252956i
\(699\) −6.17595e56 + 4.49916e56i −0.796453 + 0.580214i
\(700\) 4.91005e56 0.615355
\(701\) 2.87457e56i 0.350117i 0.984558 + 0.175058i \(0.0560114\pi\)
−0.984558 + 0.175058i \(0.943989\pi\)
\(702\) −1.33921e55 4.06851e55i −0.0158528 0.0481607i
\(703\) 9.10639e56 1.04771
\(704\) 1.34781e57i 1.50722i
\(705\) 6.79904e56 + 9.33297e56i 0.739036 + 1.01447i
\(706\) −1.40429e56 −0.148376
\(707\) 5.23517e56i 0.537703i
\(708\) 2.25155e56 1.64025e56i 0.224811 0.163774i
\(709\) −1.38335e57 −1.34279 −0.671395 0.741100i \(-0.734305\pi\)
−0.671395 + 0.741100i \(0.734305\pi\)
\(710\) 4.78018e55i 0.0451105i
\(711\) −1.94066e56 + 6.02509e56i −0.178056 + 0.552804i
\(712\) −8.29830e55 −0.0740268
\(713\) 3.86707e55i 0.0335422i
\(714\) −3.02946e55 4.15850e55i −0.0255506 0.0350730i
\(715\) −1.14839e57 −0.941820
\(716\) 5.17766e56i 0.412926i
\(717\) 1.73473e57 1.26375e57i 1.34539 0.980116i
\(718\) −1.30608e55 −0.00985098
\(719\) 1.40918e56i 0.103369i −0.998663 0.0516844i \(-0.983541\pi\)
0.998663 0.0516844i \(-0.0164590\pi\)
\(720\) 1.53746e57 + 4.95208e56i 1.09686 + 0.353295i
\(721\) 2.13845e57 1.48386
\(722\) 2.25066e55i 0.0151903i
\(723\) −1.07670e57 1.47797e57i −0.706851 0.970286i
\(724\) −1.51258e57 −0.965930
\(725\) 1.25931e57i 0.782298i
\(726\) 2.19019e56 1.59555e56i 0.132358 0.0964224i
\(727\) −1.00482e57 −0.590742 −0.295371 0.955383i \(-0.595443\pi\)
−0.295371 + 0.955383i \(0.595443\pi\)
\(728\) 2.63350e56i 0.150628i
\(729\) 1.44567e57 1.06737e57i 0.804486 0.593972i
\(730\) 1.81960e56 0.0985185
\(731\) 9.29692e55i 0.0489769i
\(732\) 3.70573e56 + 5.08682e56i 0.189956 + 0.260750i
\(733\) 1.26612e57 0.631532 0.315766 0.948837i \(-0.397739\pi\)
0.315766 + 0.948837i \(0.397739\pi\)
\(734\) 1.12282e56i 0.0544990i
\(735\) −2.50514e57 + 1.82499e57i −1.18328 + 0.862013i
\(736\) 5.96445e55 0.0274166
\(737\) 8.81851e56i 0.394499i
\(738\) −9.44251e55 + 2.93158e56i −0.0411112 + 0.127637i
\(739\) 4.06472e55 0.0172243 0.00861215 0.999963i \(-0.497259\pi\)
0.00861215 + 0.999963i \(0.497259\pi\)
\(740\) 2.79250e57i 1.15175i
\(741\) 7.72731e56 + 1.06072e57i 0.310216 + 0.425830i
\(742\) −1.95118e56 −0.0762463
\(743\) 2.79186e57i 1.06198i 0.847378 + 0.530991i \(0.178180\pi\)
−0.847378 + 0.530991i \(0.821820\pi\)
\(744\) 1.66971e56 1.21638e56i 0.0618277 0.0450413i
\(745\) −4.74142e57 −1.70916
\(746\) 3.61341e56i 0.126806i
\(747\) 2.51687e57 + 8.10672e56i 0.859900 + 0.276970i
\(748\) −1.34891e57 −0.448695
\(749\) 8.49307e56i 0.275060i
\(750\) 1.33677e56 + 1.83497e56i 0.0421534 + 0.0578635i
\(751\) −3.61104e57 −1.10875 −0.554374 0.832268i \(-0.687042\pi\)
−0.554374 + 0.832268i \(0.687042\pi\)
\(752\) 3.41518e57i 1.02107i
\(753\) 3.33919e57 2.43259e57i 0.972168 0.708222i
\(754\) 3.35910e56 0.0952348
\(755\) 5.22127e57i 1.44158i
\(756\) −5.21934e57 + 1.71802e57i −1.40339 + 0.461948i
\(757\) 4.20138e57 1.10021 0.550104 0.835096i \(-0.314588\pi\)
0.550104 + 0.835096i \(0.314588\pi\)
\(758\) 6.17940e56i 0.157602i
\(759\) −3.42942e56 4.70753e56i −0.0851894 0.116938i
\(760\) 1.08054e57 0.261439
\(761\) 5.80497e57i 1.36807i 0.729451 + 0.684033i \(0.239776\pi\)
−0.729451 + 0.684033i \(0.760224\pi\)
\(762\) −6.25522e56 + 4.55691e56i −0.143596 + 0.104610i
\(763\) 2.69015e57 0.601570
\(764\) 6.24642e57i 1.36070i
\(765\) 4.84674e56 1.50475e57i 0.102854 0.319327i
\(766\) −5.78904e56 −0.119683
\(767\) 6.86505e56i 0.138273i
\(768\) −2.68678e57 3.68812e57i −0.527240 0.723736i
\(769\) 7.43323e57 1.42119 0.710593 0.703603i \(-0.248427\pi\)
0.710593 + 0.703603i \(0.248427\pi\)
\(770\) 1.58236e57i 0.294775i
\(771\) −1.27447e57 + 9.28447e56i −0.231335 + 0.168527i
\(772\) 5.90524e57 1.04446
\(773\) 1.13457e58i 1.95543i −0.209927 0.977717i \(-0.567323\pi\)
0.209927 0.977717i \(-0.432677\pi\)
\(774\) 1.01510e56 + 3.26961e55i 0.0170487 + 0.00549131i
\(775\) 9.49198e56 0.155354
\(776\) 1.86188e57i 0.296973i
\(777\) −5.53287e57 7.59492e57i −0.860063 1.18060i
\(778\) −6.64828e56 −0.100720
\(779\) 9.43648e57i 1.39335i
\(780\) −3.25272e57 + 2.36960e57i −0.468117 + 0.341022i
\(781\) −4.21717e57 −0.591562
\(782\) 1.91105e55i 0.00261299i
\(783\) 4.40630e57 + 1.33863e58i 0.587272 + 1.78413i
\(784\) 9.16698e57 1.19098
\(785\) 1.67678e55i 0.00212365i
\(786\) 1.42107e56 + 1.95069e56i 0.0175455 + 0.0240845i
\(787\) −5.94377e57 −0.715430 −0.357715 0.933831i \(-0.616444\pi\)
−0.357715 + 0.933831i \(0.616444\pi\)
\(788\) 9.89675e56i 0.116136i
\(789\) −5.03205e57 + 3.66583e57i −0.575711 + 0.419404i
\(790\) −6.38781e56 −0.0712542
\(791\) 2.24716e58i 2.44402i
\(792\) 9.53884e56 2.96149e57i 0.101156 0.314056i
\(793\) −1.55099e57 −0.160378
\(794\) 3.26888e56i 0.0329601i
\(795\) −3.53016e57 4.84581e57i −0.347098 0.476457i
\(796\) −4.53439e57 −0.434768
\(797\) 4.16698e57i 0.389632i −0.980840 0.194816i \(-0.937589\pi\)
0.980840 0.194816i \(-0.0624110\pi\)
\(798\) −1.46156e57 + 1.06474e57i −0.133278 + 0.0970926i
\(799\) −3.34253e57 −0.297262
\(800\) 1.46401e57i 0.126983i
\(801\) 4.06154e57 + 1.30821e57i 0.343590 + 0.110669i
\(802\) 1.87547e57 0.154747
\(803\) 1.60528e58i 1.29193i
\(804\) −1.81962e57 2.49777e57i −0.142843 0.196079i
\(805\) −2.08717e57 −0.159824
\(806\) 2.53190e56i 0.0189124i
\(807\) 1.44723e58 1.05430e58i 1.05455 0.768235i
\(808\) −1.03878e57 −0.0738411
\(809\) 1.41711e58i 0.982728i −0.870954 0.491364i \(-0.836499\pi\)
0.870954 0.491364i \(-0.163501\pi\)
\(810\) 1.47254e57 + 1.05840e57i 0.0996247 + 0.0716062i
\(811\) −1.58235e58 −1.04444 −0.522221 0.852810i \(-0.674896\pi\)
−0.522221 + 0.852810i \(0.674896\pi\)
\(812\) 4.30927e58i 2.77513i
\(813\) 1.08800e58 + 1.49349e58i 0.683626 + 0.938405i
\(814\) 2.64609e57 0.162224
\(815\) 3.78621e58i 2.26492i
\(816\) −3.77920e57 + 2.75314e57i −0.220596 + 0.160703i
\(817\) −3.26752e57 −0.186113
\(818\) 1.85024e57i 0.102840i
\(819\) 4.15164e57 1.28895e58i 0.225186 0.699128i
\(820\) 2.89372e58 1.53172
\(821\) 8.62420e57i 0.445508i −0.974875 0.222754i \(-0.928495\pi\)
0.974875 0.222754i \(-0.0715047\pi\)
\(822\) −2.50477e56 3.43827e56i −0.0126279 0.0173342i
\(823\) −3.14799e58 −1.54895 −0.774474 0.632606i \(-0.781985\pi\)
−0.774474 + 0.632606i \(0.781985\pi\)
\(824\) 4.24320e57i 0.203774i
\(825\) 1.15549e58 8.41774e57i 0.541613 0.394563i
\(826\) −9.45932e56 −0.0432772
\(827\) 3.29187e58i 1.47005i −0.678040 0.735025i \(-0.737170\pi\)
0.678040 0.735025i \(-0.262830\pi\)
\(828\) −1.94271e57 6.25740e56i −0.0846841 0.0272764i
\(829\) 3.25021e58 1.38300 0.691499 0.722378i \(-0.256951\pi\)
0.691499 + 0.722378i \(0.256951\pi\)
\(830\) 2.66839e57i 0.110838i
\(831\) 1.09771e58 + 1.50681e58i 0.445108 + 0.610995i
\(832\) 1.16399e58 0.460768
\(833\) 8.97198e57i 0.346728i
\(834\) 1.77452e57 1.29274e57i 0.0669516 0.0487740i
\(835\) −2.71193e58 −0.998963
\(836\) 4.74092e58i 1.70505i
\(837\) −1.00899e58 + 3.32123e57i −0.354305 + 0.116625i
\(838\) −3.58663e57 −0.122972
\(839\) 8.79650e57i 0.294490i −0.989100 0.147245i \(-0.952959\pi\)
0.989100 0.147245i \(-0.0470406\pi\)
\(840\) −6.56518e57 9.01194e57i −0.214615 0.294600i
\(841\) −7.91950e58 −2.52801
\(842\) 3.34515e57i 0.104273i
\(843\) 1.79898e58 1.31055e58i 0.547615 0.398936i
\(844\) −4.60280e58 −1.36828
\(845\) 3.10784e58i 0.902244i
\(846\) 1.17553e57 3.64961e57i 0.0333292 0.103476i
\(847\) 8.56692e58 2.37223
\(848\) 1.77321e58i 0.479560i
\(849\) 2.65932e58 + 3.65042e58i 0.702452 + 0.964248i
\(850\) 4.69080e56 0.0121023
\(851\) 3.49026e57i 0.0879563i
\(852\) −1.19448e58 + 8.70174e57i −0.294027 + 0.214198i
\(853\) 5.31286e57 0.127746 0.0638731 0.997958i \(-0.479655\pi\)
0.0638731 + 0.997958i \(0.479655\pi\)
\(854\) 2.13709e57i 0.0501957i
\(855\) −5.28864e58 1.70345e58i −1.21345 0.390847i
\(856\) −1.68523e57 −0.0377732
\(857\) 1.38461e58i 0.303187i 0.988443 + 0.151593i \(0.0484404\pi\)
−0.988443 + 0.151593i \(0.951560\pi\)
\(858\) 2.24536e57 + 3.08218e57i 0.0480331 + 0.0659344i
\(859\) 5.63532e58 1.17776 0.588878 0.808222i \(-0.299570\pi\)
0.588878 + 0.808222i \(0.299570\pi\)
\(860\) 1.00199e58i 0.204595i
\(861\) −7.87022e58 + 5.73343e58i −1.57009 + 1.14380i
\(862\) 1.06097e56 0.00206804
\(863\) 9.71213e58i 1.84969i −0.380347 0.924844i \(-0.624196\pi\)
0.380347 0.924844i \(-0.375804\pi\)
\(864\) −5.12256e57 1.55623e58i −0.0953262 0.289601i
\(865\) 6.19680e58 1.12680
\(866\) 6.21246e56i 0.0110384i
\(867\) −3.12182e58 4.28529e58i −0.542034 0.744044i
\(868\) 3.24809e58 0.551104
\(869\) 5.63545e58i 0.934401i
\(870\) −1.14950e58 + 8.37406e57i −0.186262 + 0.135691i
\(871\) 7.61578e57 0.120601
\(872\) 5.33792e57i 0.0826119i
\(873\) 2.93521e58 9.11283e58i 0.443970 1.37838i
\(874\) −6.71663e56 −0.00992939
\(875\) 7.17749e58i 1.03708i
\(876\) 3.31236e58 + 4.54683e58i 0.467794 + 0.642136i
\(877\) 1.00937e59 1.39335 0.696676 0.717386i \(-0.254662\pi\)
0.696676 + 0.717386i \(0.254662\pi\)
\(878\) 7.22635e57i 0.0975054i
\(879\) 4.06834e58 2.96378e58i 0.536587 0.390902i
\(880\) −1.43803e59 −1.85402
\(881\) 1.09043e59i 1.37430i 0.726516 + 0.687150i \(0.241138\pi\)
−0.726516 + 0.687150i \(0.758862\pi\)
\(882\) 9.79625e57 + 3.15533e57i 0.120695 + 0.0388752i
\(883\) 1.03905e59 1.25147 0.625736 0.780035i \(-0.284799\pi\)
0.625736 + 0.780035i \(0.284799\pi\)
\(884\) 1.16494e58i 0.137169i
\(885\) −1.71142e58 2.34925e58i −0.197012 0.270436i
\(886\) 1.18787e58 0.133689
\(887\) 1.39065e59i 1.53019i −0.643916 0.765096i \(-0.722692\pi\)
0.643916 0.765096i \(-0.277308\pi\)
\(888\) 1.50702e58 1.09786e58i 0.162128 0.118110i
\(889\) −2.44673e59 −2.57365
\(890\) 4.30606e57i 0.0442874i
\(891\) −9.33744e58 + 1.29910e59i −0.939017 + 1.30644i
\(892\) 8.65096e58 0.850682
\(893\) 1.17478e59i 1.12960i
\(894\) 9.27055e57 + 1.27256e58i 0.0871676 + 0.119654i
\(895\) −5.40232e58 −0.496729
\(896\) 6.66741e58i 0.599511i
\(897\) 4.06548e57 2.96169e57i 0.0357489 0.0260430i
\(898\) 8.49101e56 0.00730184
\(899\) 8.33056e58i 0.700616i
\(900\) 1.53592e58 4.76852e58i 0.126333 0.392223i
\(901\) 1.73549e58 0.139613
\(902\) 2.74200e58i 0.215743i
\(903\) 1.98528e58 + 2.72518e58i 0.152780 + 0.209720i
\(904\) −4.45892e58 −0.335630
\(905\) 1.57821e59i 1.16196i
\(906\) −1.40135e58 + 1.02088e58i −0.100921 + 0.0735207i
\(907\) 6.22392e58 0.438448 0.219224 0.975675i \(-0.429647\pi\)
0.219224 + 0.975675i \(0.429647\pi\)
\(908\) 1.20476e59i 0.830201i
\(909\) 5.08425e58 + 1.63762e58i 0.342728 + 0.110391i
\(910\) 1.36654e58 0.0901148
\(911\) 2.53157e58i 0.163313i −0.996661 0.0816567i \(-0.973979\pi\)
0.996661 0.0816567i \(-0.0260211\pi\)
\(912\) 9.67626e58 + 1.32825e59i 0.610676 + 0.838268i
\(913\) −2.35410e59 −1.45348
\(914\) 7.51278e57i 0.0453813i
\(915\) 5.30754e58 3.86653e58i 0.313669 0.228507i
\(916\) −1.51374e59 −0.875271
\(917\) 7.63011e58i 0.431662i
\(918\) −4.98628e57 + 1.64130e57i −0.0276009 + 0.00908522i
\(919\) 1.77477e59 0.961241 0.480621 0.876929i \(-0.340411\pi\)
0.480621 + 0.876929i \(0.340411\pi\)
\(920\) 4.14146e57i 0.0219481i
\(921\) −4.17121e58 5.72577e58i −0.216306 0.296921i
\(922\) −2.83274e58 −0.143744
\(923\) 3.64200e58i 0.180845i
\(924\) 3.95402e59 2.88049e59i 1.92132 1.39968i
\(925\) 8.56708e58 0.407379
\(926\) 2.44706e58i 0.113874i
\(927\) 6.68929e58 2.07680e59i 0.304639 0.945803i
\(928\) 1.28488e59 0.572668
\(929\) 2.44892e59i 1.06822i −0.845415 0.534110i \(-0.820647\pi\)
0.845415 0.534110i \(-0.179353\pi\)
\(930\) −6.31191e57 8.66429e57i −0.0269465 0.0369891i
\(931\) −3.15332e59 −1.31757
\(932\) 2.38388e59i 0.974915i
\(933\) −3.56889e59 + 2.59993e59i −1.42857 + 1.04071i
\(934\) −3.64726e58 −0.142899
\(935\) 1.40744e59i 0.539757i
\(936\) 2.55758e58 + 8.23787e57i 0.0960092 + 0.0309242i
\(937\) 4.70534e59 1.72902 0.864509 0.502617i \(-0.167630\pi\)
0.864509 + 0.502617i \(0.167630\pi\)
\(938\) 1.04937e58i 0.0377462i
\(939\) 6.59722e58 + 9.05593e58i 0.232300 + 0.318876i
\(940\) −3.60248e59 −1.24178
\(941\) 4.64871e59i 1.56870i 0.620319 + 0.784350i \(0.287003\pi\)
−0.620319 + 0.784350i \(0.712997\pi\)
\(942\) −4.50035e55 + 3.27849e55i −0.000148672 + 0.000108307i
\(943\) −3.61678e58 −0.116974
\(944\) 8.59653e58i 0.272197i
\(945\) 1.79257e59 + 5.44582e59i 0.555699 + 1.68821i
\(946\) −9.49458e57 −0.0288173
\(947\) 3.33540e59i 0.991171i −0.868559 0.495586i \(-0.834954\pi\)
0.868559 0.495586i \(-0.165046\pi\)
\(948\) −1.16283e59 1.59620e59i −0.338336 0.464429i
\(949\) −1.38634e59 −0.394954
\(950\) 1.64864e58i 0.0459890i
\(951\) −1.96399e59 + 1.43076e59i −0.536449 + 0.390802i
\(952\) 3.22756e58 0.0863247
\(953\) 9.58504e58i 0.251036i 0.992091 + 0.125518i \(0.0400593\pi\)
−0.992091 + 0.125518i \(0.959941\pi\)
\(954\) −6.10350e57 + 1.89493e58i −0.0156535 + 0.0485989i
\(955\) 6.51746e59 1.63686
\(956\) 6.69598e59i 1.64686i
\(957\) −7.38776e59 1.01411e60i −1.77940 2.44256i
\(958\) −1.39660e58 −0.0329429
\(959\) 1.34488e59i 0.310678i
\(960\) −3.98322e59 + 2.90176e59i −0.901176 + 0.656504i
\(961\) −3.88511e59 −0.860867
\(962\) 2.28519e58i 0.0495932i
\(963\) 8.24824e58 + 2.65672e58i 0.175322 + 0.0564704i
\(964\) 5.70489e59 1.18770
\(965\) 6.16148e59i 1.25643i
\(966\) 4.08090e57 + 5.60180e57i 0.00815104 + 0.0111888i
\(967\) 1.45692e59 0.285040 0.142520 0.989792i \(-0.454480\pi\)
0.142520 + 0.989792i \(0.454480\pi\)
\(968\) 1.69988e59i 0.325771i
\(969\) 1.30000e59 9.47043e58i 0.244043 0.177785i
\(970\) 9.66145e58 0.177667
\(971\) 6.17773e59i 1.11287i 0.830891 + 0.556435i \(0.187831\pi\)
−0.830891 + 0.556435i \(0.812169\pi\)
\(972\) 3.58296e57 + 5.60630e59i 0.00632290 + 0.989353i
\(973\) 6.94103e59 1.19996
\(974\) 6.36356e58i 0.107776i
\(975\) 7.26967e58 + 9.97900e58i 0.120621 + 0.165575i
\(976\) −1.94217e59 −0.315712
\(977\) 5.80301e59i 0.924192i −0.886830 0.462096i \(-0.847098\pi\)
0.886830 0.462096i \(-0.152902\pi\)
\(978\) 1.01619e59 7.40290e58i 0.158561 0.115511i
\(979\) −3.79889e59 −0.580768
\(980\) 9.66972e59i 1.44841i
\(981\) 8.41510e58 2.61261e59i 0.123503 0.383437i
\(982\) −2.29547e58 −0.0330097
\(983\) 4.95264e59i 0.697857i −0.937149 0.348929i \(-0.886546\pi\)
0.937149 0.348929i \(-0.113454\pi\)
\(984\) −1.13765e59 1.56164e59i −0.157075 0.215615i
\(985\) 1.03262e59 0.139706
\(986\) 4.11684e58i 0.0545790i
\(987\) 9.79786e59 7.13772e59i 1.27288 0.927291i
\(988\) −4.09432e59 −0.521246
\(989\) 1.25236e58i 0.0156244i
\(990\) −1.53674e59 4.94979e58i −0.187887 0.0605178i
\(991\) 4.47741e59 0.536481 0.268240 0.963352i \(-0.413558\pi\)
0.268240 + 0.963352i \(0.413558\pi\)
\(992\) 9.68472e58i 0.113724i
\(993\) 5.58949e59 + 7.67263e59i 0.643261 + 0.882997i
\(994\) 5.01829e58 0.0566015
\(995\) 4.73115e59i 0.523004i
\(996\) −6.66781e59 + 4.85748e59i −0.722431 + 0.526289i
\(997\) −9.25444e59 −0.982758 −0.491379 0.870946i \(-0.663507\pi\)
−0.491379 + 0.870946i \(0.663507\pi\)
\(998\) 3.14907e58i 0.0327771i
\(999\) −9.10673e59 + 2.99761e59i −0.929079 + 0.305820i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3.41.b.a.2.6 12
3.2 odd 2 inner 3.41.b.a.2.7 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.41.b.a.2.6 12 1.1 even 1 trivial
3.41.b.a.2.7 yes 12 3.2 odd 2 inner