Properties

Label 5.35.c.a.2.11
Level $5$
Weight $35$
Character 5.2
Analytic conductor $36.613$
Analytic rank $0$
Dimension $32$
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] = [5,35,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 35, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.2");
 
S:= CuspForms(chi, 35);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 35 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), 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: \(36.6128270213\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.11
Character \(\chi\) \(=\) 5.2
Dual form 5.35.c.a.3.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(67956.3 + 67956.3i) q^{2} +(-7.73822e7 + 7.73822e7i) q^{3} -7.94376e9i q^{4} +(-6.92309e11 + 3.20600e11i) q^{5} -1.05172e13 q^{6} +(-2.59708e14 - 2.59708e14i) q^{7} +(1.70731e15 - 1.70731e15i) q^{8} +4.70118e15i q^{9} +O(q^{10})\) \(q+(67956.3 + 67956.3i) q^{2} +(-7.73822e7 + 7.73822e7i) q^{3} -7.94376e9i q^{4} +(-6.92309e11 + 3.20600e11i) q^{5} -1.05172e13 q^{6} +(-2.59708e14 - 2.59708e14i) q^{7} +(1.70731e15 - 1.70731e15i) q^{8} +4.70118e15i q^{9} +(-6.88336e16 - 2.52599e16i) q^{10} -8.17717e16 q^{11} +(6.14706e17 + 6.14706e17i) q^{12} +(1.39558e18 - 1.39558e18i) q^{13} -3.52975e19i q^{14} +(2.87636e19 - 7.83812e19i) q^{15} +9.55718e19 q^{16} +(3.22164e20 + 3.22164e20i) q^{17} +(-3.19474e20 + 3.19474e20i) q^{18} +2.60332e21i q^{19} +(2.54677e21 + 5.49954e21i) q^{20} +4.01935e22 q^{21} +(-5.55690e21 - 5.55690e21i) q^{22} +(5.14001e22 - 5.14001e22i) q^{23} +2.64230e23i q^{24} +(3.76507e23 - 4.43909e23i) q^{25} +1.89677e23 q^{26} +(-1.65430e24 - 1.65430e24i) q^{27} +(-2.06306e24 + 2.06306e24i) q^{28} +1.01031e25i q^{29} +(7.28116e24 - 3.37182e24i) q^{30} -9.26973e24 q^{31} +(-2.28366e25 - 2.28366e25i) q^{32} +(6.32767e24 - 6.32767e24i) q^{33} +4.37861e25i q^{34} +(2.63061e26 + 9.65356e25i) q^{35} +3.73450e25 q^{36} +(4.80955e26 + 4.80955e26i) q^{37} +(-1.76912e26 + 1.76912e26i) q^{38} +2.15986e26i q^{39} +(-6.34621e26 + 1.72935e27i) q^{40} +2.99041e27 q^{41} +(2.73140e27 + 2.73140e27i) q^{42} +(-3.50684e27 + 3.50684e27i) q^{43} +6.49575e26i q^{44} +(-1.50720e27 - 3.25467e27i) q^{45} +6.98591e27 q^{46} +(3.01254e28 + 3.01254e28i) q^{47} +(-7.39555e27 + 7.39555e27i) q^{48} +8.07793e28i q^{49} +(5.57524e28 - 4.58039e27i) q^{50} -4.98594e28 q^{51} +(-1.10861e28 - 1.10861e28i) q^{52} +(1.96696e29 - 1.96696e29i) q^{53} -2.24841e29i q^{54} +(5.66113e28 - 2.62160e28i) q^{55} -8.86802e29 q^{56} +(-2.01451e29 - 2.01451e29i) q^{57} +(-6.86567e29 + 6.86567e29i) q^{58} -1.74853e30i q^{59} +(-6.22641e29 - 2.28491e29i) q^{60} +2.76233e29 q^{61} +(-6.29936e29 - 6.29936e29i) q^{62} +(1.22093e30 - 1.22093e30i) q^{63} -4.74569e30i q^{64} +(-5.18749e29 + 1.41360e30i) q^{65} +8.60010e29 q^{66} +(6.56107e30 + 6.56107e30i) q^{67} +(2.55919e30 - 2.55919e30i) q^{68} +7.95490e30i q^{69} +(1.13164e31 + 2.44368e31i) q^{70} -4.26783e31 q^{71} +(8.02636e30 + 8.02636e30i) q^{72} +(4.46612e31 - 4.46612e31i) q^{73} +6.53678e31i q^{74} +(5.21572e30 + 6.34856e31i) q^{75} +2.06802e31 q^{76} +(2.12367e31 + 2.12367e31i) q^{77} +(-1.46776e31 + 1.46776e31i) q^{78} -2.33726e32i q^{79} +(-6.61652e31 + 3.06404e31i) q^{80} +1.77625e32 q^{81} +(2.03217e32 + 2.03217e32i) q^{82} +(-1.29241e32 + 1.29241e32i) q^{83} -3.19288e32i q^{84} +(-3.26323e32 - 1.19751e32i) q^{85} -4.76623e32 q^{86} +(-7.81798e32 - 7.81798e32i) q^{87} +(-1.39609e32 + 1.39609e32i) q^{88} -1.79750e33i q^{89} +(1.18751e32 - 3.23599e32i) q^{90} -7.24885e32 q^{91} +(-4.08310e32 - 4.08310e32i) q^{92} +(7.17312e32 - 7.17312e32i) q^{93} +4.09442e33i q^{94} +(-8.34626e32 - 1.80230e33i) q^{95} +3.53430e33 q^{96} +(8.38959e33 + 8.38959e33i) q^{97} +(-5.48946e33 + 5.48946e33i) q^{98} -3.84423e32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 131070 q^{2} - 78988260 q^{3} - 730721770860 q^{5} - 44043049959816 q^{6} + 5337954235100 q^{7} - 45\!\cdots\!20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 131070 q^{2} - 78988260 q^{3} - 730721770860 q^{5} - 44043049959816 q^{6} + 5337954235100 q^{7} - 45\!\cdots\!20 q^{8}+ \cdots + 25\!\cdots\!70 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 67956.3 + 67956.3i 0.518465 + 0.518465i 0.917107 0.398642i \(-0.130518\pi\)
−0.398642 + 0.917107i \(0.630518\pi\)
\(3\) −7.73822e7 + 7.73822e7i −0.599211 + 0.599211i −0.940103 0.340892i \(-0.889271\pi\)
0.340892 + 0.940103i \(0.389271\pi\)
\(4\) 7.94376e9i 0.462388i
\(5\) −6.92309e11 + 3.20600e11i −0.907423 + 0.420217i
\(6\) −1.05172e13 −0.621340
\(7\) −2.59708e14 2.59708e14i −1.11640 1.11640i −0.992266 0.124130i \(-0.960386\pi\)
−0.124130 0.992266i \(-0.539614\pi\)
\(8\) 1.70731e15 1.70731e15i 0.758197 0.758197i
\(9\) 4.70118e15i 0.281893i
\(10\) −6.88336e16 2.52599e16i −0.688336 0.252599i
\(11\) −8.17717e16 −0.161781 −0.0808904 0.996723i \(-0.525776\pi\)
−0.0808904 + 0.996723i \(0.525776\pi\)
\(12\) 6.14706e17 + 6.14706e17i 0.277068 + 0.277068i
\(13\) 1.39558e18 1.39558e18i 0.161331 0.161331i −0.621825 0.783156i \(-0.713609\pi\)
0.783156 + 0.621825i \(0.213609\pi\)
\(14\) 3.52975e19i 1.15762i
\(15\) 2.87636e19 7.83812e19i 0.291939 0.795537i
\(16\) 9.55718e19 0.323810
\(17\) 3.22164e20 + 3.22164e20i 0.389444 + 0.389444i 0.874489 0.485045i \(-0.161197\pi\)
−0.485045 + 0.874489i \(0.661197\pi\)
\(18\) −3.19474e20 + 3.19474e20i −0.146152 + 0.146152i
\(19\) 2.60332e21i 0.475025i 0.971385 + 0.237512i \(0.0763320\pi\)
−0.971385 + 0.237512i \(0.923668\pi\)
\(20\) 2.54677e21 + 5.49954e21i 0.194303 + 0.419582i
\(21\) 4.01935e22 1.33791
\(22\) −5.55690e21 5.55690e21i −0.0838777 0.0838777i
\(23\) 5.14001e22 5.14001e22i 0.364410 0.364410i −0.501023 0.865434i \(-0.667043\pi\)
0.865434 + 0.501023i \(0.167043\pi\)
\(24\) 2.64230e23i 0.908640i
\(25\) 3.76507e23 4.43909e23i 0.646835 0.762630i
\(26\) 1.89677e23 0.167289
\(27\) −1.65430e24 1.65430e24i −0.768124 0.768124i
\(28\) −2.06306e24 + 2.06306e24i −0.516208 + 0.516208i
\(29\) 1.01031e25i 1.39215i 0.717967 + 0.696077i \(0.245073\pi\)
−0.717967 + 0.696077i \(0.754927\pi\)
\(30\) 7.28116e24 3.37182e24i 0.563818 0.261098i
\(31\) −9.26973e24 −0.411072 −0.205536 0.978650i \(-0.565894\pi\)
−0.205536 + 0.978650i \(0.565894\pi\)
\(32\) −2.28366e25 2.28366e25i −0.590313 0.590313i
\(33\) 6.32767e24 6.32767e24i 0.0969408 0.0969408i
\(34\) 4.37861e25i 0.403826i
\(35\) 2.63061e26 + 9.65356e25i 1.48217 + 0.543915i
\(36\) 3.73450e25 0.130344
\(37\) 4.80955e26 + 4.80955e26i 1.05360 + 1.05360i 0.998480 + 0.0551194i \(0.0175539\pi\)
0.0551194 + 0.998480i \(0.482446\pi\)
\(38\) −1.76912e26 + 1.76912e26i −0.246284 + 0.246284i
\(39\) 2.15986e26i 0.193342i
\(40\) −6.34621e26 + 1.72935e27i −0.369398 + 1.00661i
\(41\) 2.99041e27 1.14395 0.571973 0.820273i \(-0.306178\pi\)
0.571973 + 0.820273i \(0.306178\pi\)
\(42\) 2.73140e27 + 2.73140e27i 0.693661 + 0.693661i
\(43\) −3.50684e27 + 3.50684e27i −0.596969 + 0.596969i −0.939505 0.342536i \(-0.888714\pi\)
0.342536 + 0.939505i \(0.388714\pi\)
\(44\) 6.49575e26i 0.0748055i
\(45\) −1.50720e27 3.25467e27i −0.118456 0.255796i
\(46\) 6.98591e27 0.377868
\(47\) 3.01254e28 + 3.01254e28i 1.13050 + 1.13050i 0.990094 + 0.140403i \(0.0448399\pi\)
0.140403 + 0.990094i \(0.455160\pi\)
\(48\) −7.39555e27 + 7.39555e27i −0.194030 + 0.194030i
\(49\) 8.07793e28i 1.49268i
\(50\) 5.57524e28 4.58039e27i 0.730758 0.0600361i
\(51\) −4.98594e28 −0.466718
\(52\) −1.10861e28 1.10861e28i −0.0745974 0.0745974i
\(53\) 1.96696e29 1.96696e29i 0.957426 0.957426i −0.0417044 0.999130i \(-0.513279\pi\)
0.999130 + 0.0417044i \(0.0132788\pi\)
\(54\) 2.24841e29i 0.796491i
\(55\) 5.66113e28 2.62160e28i 0.146804 0.0679832i
\(56\) −8.86802e29 −1.69290
\(57\) −2.01451e29 2.01451e29i −0.284640 0.284640i
\(58\) −6.86567e29 + 6.86567e29i −0.721784 + 0.721784i
\(59\) 1.74853e30i 1.37464i −0.726354 0.687321i \(-0.758786\pi\)
0.726354 0.687321i \(-0.241214\pi\)
\(60\) −6.22641e29 2.28491e29i −0.367846 0.134989i
\(61\) 2.76233e29 0.123216 0.0616081 0.998100i \(-0.480377\pi\)
0.0616081 + 0.998100i \(0.480377\pi\)
\(62\) −6.29936e29 6.29936e29i −0.213127 0.213127i
\(63\) 1.22093e30 1.22093e30i 0.314704 0.314704i
\(64\) 4.74569e30i 0.935923i
\(65\) −5.18749e29 + 1.41360e30i −0.0786013 + 0.214189i
\(66\) 8.60010e29 0.100521
\(67\) 6.56107e30 + 6.56107e30i 0.593886 + 0.593886i 0.938679 0.344793i \(-0.112051\pi\)
−0.344793 + 0.938679i \(0.612051\pi\)
\(68\) 2.55919e30 2.55919e30i 0.180074 0.180074i
\(69\) 7.95490e30i 0.436717i
\(70\) 1.13164e31 + 2.44368e31i 0.486454 + 1.05046i
\(71\) −4.26783e31 −1.44150 −0.720751 0.693194i \(-0.756203\pi\)
−0.720751 + 0.693194i \(0.756203\pi\)
\(72\) 8.02636e30 + 8.02636e30i 0.213730 + 0.213730i
\(73\) 4.46612e31 4.46612e31i 0.940680 0.940680i −0.0576567 0.998336i \(-0.518363\pi\)
0.998336 + 0.0576567i \(0.0183629\pi\)
\(74\) 6.53678e31i 1.09251i
\(75\) 5.21572e30 + 6.34856e31i 0.0693861 + 0.844567i
\(76\) 2.06802e31 0.219646
\(77\) 2.12367e31 + 2.12367e31i 0.180612 + 0.180612i
\(78\) −1.46776e31 + 1.46776e31i −0.100241 + 0.100241i
\(79\) 2.33726e32i 1.28542i −0.766108 0.642712i \(-0.777809\pi\)
0.766108 0.642712i \(-0.222191\pi\)
\(80\) −6.61652e31 + 3.06404e31i −0.293833 + 0.136071i
\(81\) 1.77625e32 0.638644
\(82\) 2.03217e32 + 2.03217e32i 0.593096 + 0.593096i
\(83\) −1.29241e32 + 1.29241e32i −0.306953 + 0.306953i −0.843727 0.536773i \(-0.819643\pi\)
0.536773 + 0.843727i \(0.319643\pi\)
\(84\) 3.19288e32i 0.618635i
\(85\) −3.26323e32 1.19751e32i −0.517041 0.189739i
\(86\) −4.76623e32 −0.619015
\(87\) −7.81798e32 7.81798e32i −0.834194 0.834194i
\(88\) −1.39609e32 + 1.39609e32i −0.122662 + 0.122662i
\(89\) 1.79750e33i 1.30328i −0.758527 0.651641i \(-0.774081\pi\)
0.758527 0.651641i \(-0.225919\pi\)
\(90\) 1.18751e32 3.23599e32i 0.0712059 0.194037i
\(91\) −7.24885e32 −0.360218
\(92\) −4.08310e32 4.08310e32i −0.168499 0.168499i
\(93\) 7.17312e32 7.17312e32i 0.246319 0.246319i
\(94\) 4.09442e33i 1.17225i
\(95\) −8.34626e32 1.80230e33i −0.199614 0.431049i
\(96\) 3.53430e33 0.707444
\(97\) 8.38959e33 + 8.38959e33i 1.40806 + 1.40806i 0.769924 + 0.638136i \(0.220294\pi\)
0.638136 + 0.769924i \(0.279706\pi\)
\(98\) −5.48946e33 + 5.48946e33i −0.773903 + 0.773903i
\(99\) 3.84423e32i 0.0456049i
\(100\) −3.52631e33 2.99088e33i −0.352631 0.299088i
\(101\) 2.15841e34 1.82252 0.911258 0.411837i \(-0.135113\pi\)
0.911258 + 0.411837i \(0.135113\pi\)
\(102\) −3.38826e33 3.38826e33i −0.241977 0.241977i
\(103\) −6.33700e33 + 6.33700e33i −0.383399 + 0.383399i −0.872325 0.488926i \(-0.837389\pi\)
0.488926 + 0.872325i \(0.337389\pi\)
\(104\) 4.76537e33i 0.244641i
\(105\) −2.78263e34 + 1.28861e34i −1.21405 + 0.562214i
\(106\) 2.67334e34 0.992784
\(107\) 1.25797e34 + 1.25797e34i 0.398243 + 0.398243i 0.877613 0.479370i \(-0.159135\pi\)
−0.479370 + 0.877613i \(0.659135\pi\)
\(108\) −1.31414e34 + 1.31414e34i −0.355171 + 0.355171i
\(109\) 4.98129e34i 1.15104i −0.817787 0.575521i \(-0.804799\pi\)
0.817787 0.575521i \(-0.195201\pi\)
\(110\) 5.62863e33 + 2.06555e33i 0.111360 + 0.0408657i
\(111\) −7.44347e34 −1.26266
\(112\) −2.48207e34 2.48207e34i −0.361500 0.361500i
\(113\) 2.32442e34 2.32442e34i 0.291059 0.291059i −0.546440 0.837498i \(-0.684017\pi\)
0.837498 + 0.546440i \(0.184017\pi\)
\(114\) 2.73797e34i 0.295152i
\(115\) −1.91059e34 + 5.20636e34i −0.177543 + 0.483806i
\(116\) 8.02564e34 0.643715
\(117\) 6.56086e33 + 6.56086e33i 0.0454780 + 0.0454780i
\(118\) 1.18824e35 1.18824e35i 0.712704 0.712704i
\(119\) 1.67337e35i 0.869547i
\(120\) −8.47124e34 1.82929e35i −0.381826 0.824521i
\(121\) −2.48790e35 −0.973827
\(122\) 1.87717e34 + 1.87717e34i 0.0638833 + 0.0638833i
\(123\) −2.31405e35 + 2.31405e35i −0.685465 + 0.685465i
\(124\) 7.36365e34i 0.190075i
\(125\) −1.18342e35 + 4.28031e35i −0.266482 + 0.963840i
\(126\) 1.65940e35 0.326326
\(127\) 7.98848e35 + 7.98848e35i 1.37341 + 1.37341i 0.855332 + 0.518080i \(0.173353\pi\)
0.518080 + 0.855332i \(0.326647\pi\)
\(128\) −6.98307e34 + 6.98307e34i −0.105070 + 0.105070i
\(129\) 5.42733e35i 0.715421i
\(130\) −1.31315e35 + 6.08104e34i −0.151802 + 0.0702977i
\(131\) 2.04340e34 0.0207368 0.0103684 0.999946i \(-0.496700\pi\)
0.0103684 + 0.999946i \(0.496700\pi\)
\(132\) −5.02655e34 5.02655e34i −0.0448243 0.0448243i
\(133\) 6.76102e35 6.76102e35i 0.530316 0.530316i
\(134\) 8.91732e35i 0.615818i
\(135\) 1.67566e36 + 6.14919e35i 1.01979 + 0.374235i
\(136\) 1.10006e36 0.590550
\(137\) −9.31467e35 9.31467e35i −0.441487 0.441487i 0.451025 0.892512i \(-0.351059\pi\)
−0.892512 + 0.451025i \(0.851059\pi\)
\(138\) −5.40585e35 + 5.40585e35i −0.226423 + 0.226423i
\(139\) 3.44082e36i 1.27471i 0.770572 + 0.637353i \(0.219971\pi\)
−0.770572 + 0.637353i \(0.780029\pi\)
\(140\) 7.66856e35 2.08969e36i 0.251500 0.685339i
\(141\) −4.66234e36 −1.35481
\(142\) −2.90026e36 2.90026e36i −0.747369 0.747369i
\(143\) −1.14119e35 + 1.14119e35i −0.0261002 + 0.0261002i
\(144\) 4.49300e35i 0.0912796i
\(145\) −3.23905e36 6.99445e36i −0.585008 1.26327i
\(146\) 6.07002e36 0.975419
\(147\) −6.25088e36 6.25088e36i −0.894430 0.894430i
\(148\) 3.82059e36 3.82059e36i 0.487171 0.487171i
\(149\) 9.17060e35i 0.104287i 0.998640 + 0.0521436i \(0.0166054\pi\)
−0.998640 + 0.0521436i \(0.983395\pi\)
\(150\) −3.95981e36 + 4.66869e36i −0.401904 + 0.473853i
\(151\) −4.13188e36 −0.374576 −0.187288 0.982305i \(-0.559970\pi\)
−0.187288 + 0.982305i \(0.559970\pi\)
\(152\) 4.44467e36 + 4.44467e36i 0.360162 + 0.360162i
\(153\) −1.51455e36 + 1.51455e36i −0.109781 + 0.109781i
\(154\) 2.88634e36i 0.187282i
\(155\) 6.41752e36 2.97188e36i 0.373017 0.172740i
\(156\) 1.71574e36 0.0893991
\(157\) 1.51944e37 + 1.51944e37i 0.710214 + 0.710214i 0.966580 0.256366i \(-0.0825253\pi\)
−0.256366 + 0.966580i \(0.582525\pi\)
\(158\) 1.58831e37 1.58831e37i 0.666447 0.666447i
\(159\) 3.04415e37i 1.14740i
\(160\) 2.31314e37 + 8.48857e36i 0.783724 + 0.287604i
\(161\) −2.66980e37 −0.813652
\(162\) 1.20707e37 + 1.20707e37i 0.331114 + 0.331114i
\(163\) −3.02315e37 + 3.02315e37i −0.746914 + 0.746914i −0.973898 0.226984i \(-0.927113\pi\)
0.226984 + 0.973898i \(0.427113\pi\)
\(164\) 2.37551e37i 0.528946i
\(165\) −2.35205e36 + 6.40936e36i −0.0472302 + 0.128703i
\(166\) −1.75654e37 −0.318289
\(167\) −2.14424e37 2.14424e37i −0.350828 0.350828i 0.509590 0.860418i \(-0.329797\pi\)
−0.860418 + 0.509590i \(0.829797\pi\)
\(168\) 6.86227e37 6.86227e37i 1.01440 1.01440i
\(169\) 7.09344e37i 0.947945i
\(170\) −1.40378e37 3.03135e37i −0.169695 0.366441i
\(171\) −1.22387e37 −0.133906
\(172\) 2.78575e37 + 2.78575e37i 0.276031 + 0.276031i
\(173\) −1.65984e34 + 1.65984e34i −0.000149033 + 0.000149033i −0.707181 0.707032i \(-0.750034\pi\)
0.707032 + 0.707181i \(0.250034\pi\)
\(174\) 1.06256e38i 0.865001i
\(175\) −2.13069e38 + 1.75048e37i −1.57352 + 0.129274i
\(176\) −7.81506e36 −0.0523862
\(177\) 1.35305e38 + 1.35305e38i 0.823701 + 0.823701i
\(178\) 1.22151e38 1.22151e38i 0.675707 0.675707i
\(179\) 1.55792e38i 0.783508i −0.920070 0.391754i \(-0.871868\pi\)
0.920070 0.391754i \(-0.128132\pi\)
\(180\) −2.58543e37 + 1.19728e37i −0.118277 + 0.0547727i
\(181\) −5.58045e37 −0.232345 −0.116172 0.993229i \(-0.537063\pi\)
−0.116172 + 0.993229i \(0.537063\pi\)
\(182\) −4.92605e37 4.92605e37i −0.186761 0.186761i
\(183\) −2.13755e37 + 2.13755e37i −0.0738325 + 0.0738325i
\(184\) 1.75512e38i 0.552589i
\(185\) −4.87164e38 1.78775e38i −1.39880 0.513320i
\(186\) 9.74916e37 0.255416
\(187\) −2.63438e37 2.63438e37i −0.0630046 0.0630046i
\(188\) 2.39309e38 2.39309e38i 0.522728 0.522728i
\(189\) 8.59271e38i 1.71506i
\(190\) 6.57597e37 1.79196e38i 0.119991 0.326976i
\(191\) 1.97226e38 0.329152 0.164576 0.986364i \(-0.447374\pi\)
0.164576 + 0.986364i \(0.447374\pi\)
\(192\) 3.67232e38 + 3.67232e38i 0.560815 + 0.560815i
\(193\) −3.25332e38 + 3.25332e38i −0.454834 + 0.454834i −0.896955 0.442121i \(-0.854226\pi\)
0.442121 + 0.896955i \(0.354226\pi\)
\(194\) 1.14025e39i 1.46006i
\(195\) −6.92452e37 1.49529e38i −0.0812458 0.175443i
\(196\) 6.41692e38 0.690197
\(197\) 3.17547e38 + 3.17547e38i 0.313243 + 0.313243i 0.846165 0.532921i \(-0.178906\pi\)
−0.532921 + 0.846165i \(0.678906\pi\)
\(198\) 2.61240e37 2.61240e37i 0.0236445 0.0236445i
\(199\) 9.44538e36i 0.00784725i −0.999992 0.00392362i \(-0.998751\pi\)
0.999992 0.00392362i \(-0.00124893\pi\)
\(200\) −1.15076e38 1.40070e39i −0.0877960 1.06865i
\(201\) −1.01542e39 −0.711726
\(202\) 1.46678e39 + 1.46678e39i 0.944911 + 0.944911i
\(203\) 2.62385e39 2.62385e39i 1.55420 1.55420i
\(204\) 3.96071e38i 0.215805i
\(205\) −2.07029e39 + 9.58727e38i −1.03804 + 0.480706i
\(206\) −8.61278e38 −0.397558
\(207\) 2.41641e38 + 2.41641e38i 0.102725 + 0.102725i
\(208\) 1.33378e38 1.33378e38i 0.0522405 0.0522405i
\(209\) 2.12878e38i 0.0768499i
\(210\) −2.76666e39 1.01529e39i −0.920933 0.337956i
\(211\) −5.32019e39 −1.63352 −0.816762 0.576975i \(-0.804233\pi\)
−0.816762 + 0.576975i \(0.804233\pi\)
\(212\) −1.56250e39 1.56250e39i −0.442702 0.442702i
\(213\) 3.30254e39 3.30254e39i 0.863764 0.863764i
\(214\) 1.70975e39i 0.412950i
\(215\) 1.30352e39 3.55211e39i 0.290847 0.792560i
\(216\) −5.64881e39 −1.16478
\(217\) 2.40742e39 + 2.40742e39i 0.458919 + 0.458919i
\(218\) 3.38510e39 3.38510e39i 0.596775 0.596775i
\(219\) 6.91196e39i 1.12733i
\(220\) −2.08254e38 4.49706e38i −0.0314346 0.0678803i
\(221\) 8.99209e38 0.125659
\(222\) −5.05831e39 5.05831e39i −0.654643 0.654643i
\(223\) 1.12852e40 1.12852e40i 1.35309 1.35309i 0.470912 0.882180i \(-0.343925\pi\)
0.882180 0.470912i \(-0.156075\pi\)
\(224\) 1.18617e40i 1.31805i
\(225\) 2.08690e39 + 1.77003e39i 0.214980 + 0.182338i
\(226\) 3.15917e39 0.301807
\(227\) 5.35193e39 + 5.35193e39i 0.474319 + 0.474319i 0.903309 0.428990i \(-0.141130\pi\)
−0.428990 + 0.903309i \(0.641130\pi\)
\(228\) −1.60028e39 + 1.60028e39i −0.131614 + 0.131614i
\(229\) 7.90446e39i 0.603489i 0.953389 + 0.301744i \(0.0975689\pi\)
−0.953389 + 0.301744i \(0.902431\pi\)
\(230\) −4.83641e39 + 2.23969e39i −0.342886 + 0.158787i
\(231\) −3.28669e39 −0.216449
\(232\) 1.72491e40 + 1.72491e40i 1.05553 + 1.05553i
\(233\) −3.09113e39 + 3.09113e39i −0.175819 + 0.175819i −0.789531 0.613711i \(-0.789676\pi\)
0.613711 + 0.789531i \(0.289676\pi\)
\(234\) 8.91704e38i 0.0471575i
\(235\) −3.05143e40 1.11979e40i −1.50089 0.550785i
\(236\) −1.38899e40 −0.635618
\(237\) 1.80862e40 + 1.80862e40i 0.770240 + 0.770240i
\(238\) 1.13716e40 1.13716e40i 0.450830 0.450830i
\(239\) 2.93007e39i 0.108172i 0.998536 + 0.0540859i \(0.0172245\pi\)
−0.998536 + 0.0540859i \(0.982776\pi\)
\(240\) 2.74899e39 7.49102e39i 0.0945327 0.257603i
\(241\) 2.60118e40 0.833454 0.416727 0.909032i \(-0.363177\pi\)
0.416727 + 0.909032i \(0.363177\pi\)
\(242\) −1.69068e40 1.69068e40i −0.504895 0.504895i
\(243\) 1.38441e40 1.38441e40i 0.385442 0.385442i
\(244\) 2.19433e39i 0.0569736i
\(245\) −2.58979e40 5.59243e40i −0.627250 1.35449i
\(246\) −3.14508e40 −0.710779
\(247\) 3.63314e39 + 3.63314e39i 0.0766361 + 0.0766361i
\(248\) −1.58263e40 + 1.58263e40i −0.311674 + 0.311674i
\(249\) 2.00019e40i 0.367859i
\(250\) −3.71295e40 + 2.10453e40i −0.637879 + 0.361556i
\(251\) 8.73238e40 1.40178 0.700889 0.713270i \(-0.252787\pi\)
0.700889 + 0.713270i \(0.252787\pi\)
\(252\) −9.69880e39 9.69880e39i −0.145515 0.145515i
\(253\) −4.20307e39 + 4.20307e39i −0.0589546 + 0.0589546i
\(254\) 1.08573e41i 1.42413i
\(255\) 3.45181e40 1.59850e40i 0.423511 0.196123i
\(256\) −9.10213e40 −1.04487
\(257\) −6.78066e39 6.78066e39i −0.0728465 0.0728465i 0.669745 0.742591i \(-0.266403\pi\)
−0.742591 + 0.669745i \(0.766403\pi\)
\(258\) 3.68821e40 3.68821e40i 0.370921 0.370921i
\(259\) 2.49816e41i 2.35247i
\(260\) 1.12293e40 + 4.12082e39i 0.0990386 + 0.0363443i
\(261\) −4.74963e40 −0.392438
\(262\) 1.38862e39 + 1.38862e39i 0.0107513 + 0.0107513i
\(263\) −7.96532e40 + 7.96532e40i −0.578037 + 0.578037i −0.934362 0.356325i \(-0.884030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(264\) 2.16066e40i 0.147001i
\(265\) −7.31135e40 + 1.99235e41i −0.466463 + 1.27112i
\(266\) 9.18908e40 0.549900
\(267\) 1.39094e41 + 1.39094e41i 0.780941 + 0.780941i
\(268\) 5.21196e40 5.21196e40i 0.274606 0.274606i
\(269\) 1.79805e41i 0.889228i 0.895722 + 0.444614i \(0.146659\pi\)
−0.895722 + 0.444614i \(0.853341\pi\)
\(270\) 7.20840e40 + 1.55659e41i 0.334699 + 0.722755i
\(271\) 1.01536e41 0.442733 0.221366 0.975191i \(-0.428948\pi\)
0.221366 + 0.975191i \(0.428948\pi\)
\(272\) 3.07897e40 + 3.07897e40i 0.126106 + 0.126106i
\(273\) 5.60932e40 5.60932e40i 0.215847 0.215847i
\(274\) 1.26598e41i 0.457791i
\(275\) −3.07876e40 + 3.62992e40i −0.104645 + 0.123379i
\(276\) 6.31918e40 0.201933
\(277\) −4.75876e40 4.75876e40i −0.143001 0.143001i 0.631982 0.774983i \(-0.282242\pi\)
−0.774983 + 0.631982i \(0.782242\pi\)
\(278\) −2.33825e41 + 2.33825e41i −0.660891 + 0.660891i
\(279\) 4.35786e40i 0.115878i
\(280\) 6.13941e41 2.84309e41i 1.53617 0.711385i
\(281\) −1.19477e41 −0.281370 −0.140685 0.990054i \(-0.544930\pi\)
−0.140685 + 0.990054i \(0.544930\pi\)
\(282\) −3.16835e41 3.16835e41i −0.702423 0.702423i
\(283\) −1.19388e41 + 1.19388e41i −0.249225 + 0.249225i −0.820652 0.571428i \(-0.806390\pi\)
0.571428 + 0.820652i \(0.306390\pi\)
\(284\) 3.39026e41i 0.666533i
\(285\) 2.04051e41 + 7.48809e40i 0.377900 + 0.138678i
\(286\) −1.55102e40 −0.0270641
\(287\) −7.76633e41 7.76633e41i −1.27710 1.27710i
\(288\) 1.07359e41 1.07359e41i 0.166405 0.166405i
\(289\) 4.76748e41i 0.696667i
\(290\) 2.55203e41 6.95430e41i 0.351657 0.958269i
\(291\) −1.29841e42 −1.68745
\(292\) −3.54778e41 3.54778e41i −0.434959 0.434959i
\(293\) −9.44709e41 + 9.44709e41i −1.09282 + 1.09282i −0.0975934 + 0.995226i \(0.531114\pi\)
−0.995226 + 0.0975934i \(0.968886\pi\)
\(294\) 8.49573e41i 0.927462i
\(295\) 5.60581e41 + 1.21053e42i 0.577649 + 1.24738i
\(296\) 1.64228e42 1.59767
\(297\) 1.35275e41 + 1.35275e41i 0.124268 + 0.124268i
\(298\) −6.23200e40 + 6.23200e40i −0.0540693 + 0.0540693i
\(299\) 1.43466e41i 0.117581i
\(300\) 5.04315e41 4.14324e40i 0.390517 0.0320833i
\(301\) 1.82151e42 1.33291
\(302\) −2.80787e41 2.80787e41i −0.194205 0.194205i
\(303\) −1.67023e42 + 1.67023e42i −1.09207 + 1.09207i
\(304\) 2.48804e41i 0.153818i
\(305\) −1.91238e41 + 8.85603e40i −0.111809 + 0.0517776i
\(306\) −2.05846e41 −0.113836
\(307\) 6.13445e41 + 6.13445e41i 0.320939 + 0.320939i 0.849127 0.528188i \(-0.177128\pi\)
−0.528188 + 0.849127i \(0.677128\pi\)
\(308\) 1.68700e41 1.68700e41i 0.0835126 0.0835126i
\(309\) 9.80742e41i 0.459474i
\(310\) 6.38068e41 + 2.34153e41i 0.282956 + 0.103837i
\(311\) 2.97928e42 1.25079 0.625395 0.780308i \(-0.284938\pi\)
0.625395 + 0.780308i \(0.284938\pi\)
\(312\) 3.68754e41 + 3.68754e41i 0.146592 + 0.146592i
\(313\) 8.83692e41 8.83692e41i 0.332696 0.332696i −0.520914 0.853609i \(-0.674409\pi\)
0.853609 + 0.520914i \(0.174409\pi\)
\(314\) 2.06511e42i 0.736442i
\(315\) −4.53831e41 + 1.23669e42i −0.153326 + 0.417814i
\(316\) −1.85666e42 −0.594364
\(317\) −1.41949e42 1.41949e42i −0.430652 0.430652i 0.458198 0.888850i \(-0.348495\pi\)
−0.888850 + 0.458198i \(0.848495\pi\)
\(318\) −2.06869e42 + 2.06869e42i −0.594887 + 0.594887i
\(319\) 8.26145e41i 0.225224i
\(320\) 1.52147e42 + 3.28549e42i 0.393291 + 0.849279i
\(321\) −1.94690e42 −0.477263
\(322\) −1.81430e42 1.81430e42i −0.421850 0.421850i
\(323\) −8.38695e41 + 8.38695e41i −0.184995 + 0.184995i
\(324\) 1.41101e42i 0.295301i
\(325\) −9.40648e40 1.14496e42i −0.0186814 0.227390i
\(326\) −4.10884e42 −0.774498
\(327\) 3.85463e42 + 3.85463e42i 0.689717 + 0.689717i
\(328\) 5.10555e42 5.10555e42i 0.867336 0.867336i
\(329\) 1.56476e43i 2.52417i
\(330\) −5.95392e41 + 2.75719e41i −0.0912150 + 0.0422406i
\(331\) 1.64418e42 0.239262 0.119631 0.992818i \(-0.461829\pi\)
0.119631 + 0.992818i \(0.461829\pi\)
\(332\) 1.02666e42 + 1.02666e42i 0.141931 + 0.141931i
\(333\) −2.26106e42 + 2.26106e42i −0.297002 + 0.297002i
\(334\) 2.91430e42i 0.363784i
\(335\) −6.64577e42 2.43881e42i −0.788467 0.289345i
\(336\) 3.84136e42 0.433229
\(337\) 5.88430e41 + 5.88430e41i 0.0630938 + 0.0630938i 0.737950 0.674856i \(-0.235794\pi\)
−0.674856 + 0.737950i \(0.735794\pi\)
\(338\) −4.82044e42 + 4.82044e42i −0.491476 + 0.491476i
\(339\) 3.59737e42i 0.348811i
\(340\) −9.51273e41 + 2.59223e42i −0.0877331 + 0.239074i
\(341\) 7.58001e41 0.0665036
\(342\) −8.31694e41 8.31694e41i −0.0694256 0.0694256i
\(343\) 6.92442e42 6.92442e42i 0.550026 0.550026i
\(344\) 1.19745e43i 0.905240i
\(345\) −2.55034e42 5.50725e42i −0.183516 0.396287i
\(346\) −2.25593e39 −0.000154537
\(347\) 3.62955e42 + 3.62955e42i 0.236729 + 0.236729i 0.815494 0.578765i \(-0.196465\pi\)
−0.578765 + 0.815494i \(0.696465\pi\)
\(348\) −6.21041e42 + 6.21041e42i −0.385721 + 0.385721i
\(349\) 2.41730e43i 1.42988i 0.699187 + 0.714939i \(0.253545\pi\)
−0.699187 + 0.714939i \(0.746455\pi\)
\(350\) −1.56689e43 1.32898e43i −0.882840 0.748792i
\(351\) −4.61742e42 −0.247844
\(352\) 1.86739e42 + 1.86739e42i 0.0955014 + 0.0955014i
\(353\) 1.84650e43 1.84650e43i 0.899870 0.899870i −0.0955541 0.995424i \(-0.530462\pi\)
0.995424 + 0.0955541i \(0.0304623\pi\)
\(354\) 1.83897e43i 0.854120i
\(355\) 2.95466e43 1.36827e43i 1.30805 0.605745i
\(356\) −1.42789e43 −0.602622
\(357\) 1.29489e43 + 1.29489e43i 0.521042 + 0.521042i
\(358\) 1.05870e43 1.05870e43i 0.406222 0.406222i
\(359\) 3.14832e43i 1.15205i 0.817431 + 0.576027i \(0.195398\pi\)
−0.817431 + 0.576027i \(0.804602\pi\)
\(360\) −8.12998e42 2.98347e42i −0.283757 0.104131i
\(361\) 2.32574e43 0.774351
\(362\) −3.79226e42 3.79226e42i −0.120463 0.120463i
\(363\) 1.92519e43 1.92519e43i 0.583528 0.583528i
\(364\) 5.75832e42i 0.166561i
\(365\) −1.66010e43 + 4.52378e43i −0.458305 + 1.24888i
\(366\) −2.90520e42 −0.0765591
\(367\) −1.46395e43 1.46395e43i −0.368300 0.368300i 0.498557 0.866857i \(-0.333863\pi\)
−0.866857 + 0.498557i \(0.833863\pi\)
\(368\) 4.91240e42 4.91240e42i 0.118000 0.118000i
\(369\) 1.40585e43i 0.322470i
\(370\) −2.09570e43 4.52548e43i −0.459091 0.991368i
\(371\) −1.02167e44 −2.13773
\(372\) −5.69815e42 5.69815e42i −0.113895 0.113895i
\(373\) 4.34650e43 4.34650e43i 0.830022 0.830022i −0.157498 0.987519i \(-0.550343\pi\)
0.987519 + 0.157498i \(0.0503427\pi\)
\(374\) 3.58046e42i 0.0653313i
\(375\) −2.39644e43 4.22795e43i −0.417864 0.737222i
\(376\) 1.02867e44 1.71428
\(377\) 1.40996e43 + 1.40996e43i 0.224597 + 0.224597i
\(378\) −5.83929e43 + 5.83929e43i −0.889199 + 0.889199i
\(379\) 9.45767e43i 1.37695i −0.725261 0.688474i \(-0.758281\pi\)
0.725261 0.688474i \(-0.241719\pi\)
\(380\) −1.43171e43 + 6.63007e42i −0.199312 + 0.0922989i
\(381\) −1.23633e44 −1.64593
\(382\) 1.34027e43 + 1.34027e43i 0.170654 + 0.170654i
\(383\) 4.75065e43 4.75065e43i 0.578594 0.578594i −0.355922 0.934516i \(-0.615833\pi\)
0.934516 + 0.355922i \(0.115833\pi\)
\(384\) 1.08073e43i 0.125918i
\(385\) −2.15109e43 7.89388e42i −0.239787 0.0879950i
\(386\) −4.42167e43 −0.471631
\(387\) −1.64863e43 1.64863e43i −0.168281 0.168281i
\(388\) 6.66449e43 6.66449e43i 0.651070 0.651070i
\(389\) 1.20858e44i 1.13014i 0.825042 + 0.565072i \(0.191152\pi\)
−0.825042 + 0.565072i \(0.808848\pi\)
\(390\) 5.45579e42 1.48671e43i 0.0488381 0.133084i
\(391\) 3.31185e43 0.283835
\(392\) 1.37915e44 + 1.37915e44i 1.13175 + 1.13175i
\(393\) −1.58123e42 + 1.58123e42i −0.0124257 + 0.0124257i
\(394\) 4.31586e43i 0.324811i
\(395\) 7.49326e43 + 1.61811e44i 0.540158 + 1.16642i
\(396\) −3.05377e42 −0.0210871
\(397\) 8.26372e43 + 8.26372e43i 0.546685 + 0.546685i 0.925480 0.378796i \(-0.123662\pi\)
−0.378796 + 0.925480i \(0.623662\pi\)
\(398\) 6.41873e41 6.41873e41i 0.00406852 0.00406852i
\(399\) 1.04637e44i 0.635542i
\(400\) 3.59835e43 4.24252e43i 0.209451 0.246947i
\(401\) −3.35129e43 −0.186964 −0.0934819 0.995621i \(-0.529800\pi\)
−0.0934819 + 0.995621i \(0.529800\pi\)
\(402\) −6.90041e43 6.90041e43i −0.369005 0.369005i
\(403\) −1.29366e43 + 1.29366e43i −0.0663186 + 0.0663186i
\(404\) 1.71459e44i 0.842709i
\(405\) −1.22971e44 + 5.69466e43i −0.579520 + 0.268369i
\(406\) 3.56614e44 1.61159
\(407\) −3.93285e43 3.93285e43i −0.170452 0.170452i
\(408\) −8.51254e43 + 8.51254e43i −0.353864 + 0.353864i
\(409\) 3.95351e44i 1.57647i −0.615372 0.788236i \(-0.710994\pi\)
0.615372 0.788236i \(-0.289006\pi\)
\(410\) −2.05841e44 7.55376e43i −0.787418 0.288960i
\(411\) 1.44158e44 0.529088
\(412\) 5.03396e43 + 5.03396e43i 0.177279 + 0.177279i
\(413\) −4.54108e44 + 4.54108e44i −1.53465 + 1.53465i
\(414\) 3.28420e43i 0.106518i
\(415\) 4.80399e43 1.30909e44i 0.149549 0.407524i
\(416\) −6.37406e43 −0.190471
\(417\) −2.66258e44 2.66258e44i −0.763817 0.763817i
\(418\) 1.44664e43 1.44664e43i 0.0398440 0.0398440i
\(419\) 2.10092e44i 0.555611i 0.960637 + 0.277805i \(0.0896071\pi\)
−0.960637 + 0.277805i \(0.910393\pi\)
\(420\) 1.02364e44 + 2.21046e44i 0.259961 + 0.561364i
\(421\) 3.76106e44 0.917306 0.458653 0.888615i \(-0.348332\pi\)
0.458653 + 0.888615i \(0.348332\pi\)
\(422\) −3.61540e44 3.61540e44i −0.846925 0.846925i
\(423\) −1.41625e44 + 1.41625e44i −0.318679 + 0.318679i
\(424\) 6.71640e44i 1.45183i
\(425\) 2.64308e44 2.17145e43i 0.548907 0.0450959i
\(426\) 4.48857e44 0.895663
\(427\) −7.17397e43 7.17397e43i −0.137558 0.137558i
\(428\) 9.99305e43 9.99305e43i 0.184143 0.184143i
\(429\) 1.76615e43i 0.0312791i
\(430\) 3.29970e44 1.52806e44i 0.561709 0.260121i
\(431\) −1.11882e45 −1.83082 −0.915411 0.402520i \(-0.868134\pi\)
−0.915411 + 0.402520i \(0.868134\pi\)
\(432\) −1.58105e44 1.58105e44i −0.248726 0.248726i
\(433\) 2.89363e44 2.89363e44i 0.437672 0.437672i −0.453556 0.891228i \(-0.649845\pi\)
0.891228 + 0.453556i \(0.149845\pi\)
\(434\) 3.27199e44i 0.475867i
\(435\) 7.91890e44 + 2.90601e44i 1.10751 + 0.406424i
\(436\) −3.95702e44 −0.532228
\(437\) 1.33811e44 + 1.33811e44i 0.173104 + 0.173104i
\(438\) −4.69711e44 + 4.69711e44i −0.584482 + 0.584482i
\(439\) 1.29055e44i 0.154483i 0.997012 + 0.0772413i \(0.0246112\pi\)
−0.997012 + 0.0772413i \(0.975389\pi\)
\(440\) 5.18940e43 1.41412e44i 0.0597616 0.162851i
\(441\) −3.79758e44 −0.420776
\(442\) 6.11069e43 + 6.11069e43i 0.0651496 + 0.0651496i
\(443\) 1.58949e44 1.58949e44i 0.163077 0.163077i −0.620851 0.783928i \(-0.713213\pi\)
0.783928 + 0.620851i \(0.213213\pi\)
\(444\) 5.91292e44i 0.583837i
\(445\) 5.76279e44 + 1.24443e45i 0.547662 + 1.18263i
\(446\) 1.53380e45 1.40306
\(447\) −7.09641e43 7.09641e43i −0.0624900 0.0624900i
\(448\) −1.23249e45 + 1.23249e45i −1.04486 + 1.04486i
\(449\) 1.53129e45i 1.24988i −0.780672 0.624941i \(-0.785123\pi\)
0.780672 0.624941i \(-0.214877\pi\)
\(450\) 2.15332e43 + 2.62102e44i 0.0169237 + 0.205996i
\(451\) −2.44531e44 −0.185069
\(452\) −1.84646e44 1.84646e44i −0.134582 0.134582i
\(453\) 3.19734e44 3.19734e44i 0.224450 0.224450i
\(454\) 7.27394e44i 0.491836i
\(455\) 5.01845e44 2.32399e44i 0.326870 0.151370i
\(456\) −6.87876e44 −0.431626
\(457\) 8.16319e44 + 8.16319e44i 0.493497 + 0.493497i 0.909406 0.415909i \(-0.136537\pi\)
−0.415909 + 0.909406i \(0.636537\pi\)
\(458\) −5.37158e44 + 5.37158e44i −0.312888 + 0.312888i
\(459\) 1.06591e45i 0.598282i
\(460\) 4.13581e44 + 1.51772e44i 0.223706 + 0.0820936i
\(461\) 1.96054e45 1.02202 0.511011 0.859574i \(-0.329271\pi\)
0.511011 + 0.859574i \(0.329271\pi\)
\(462\) −2.23351e44 2.23351e44i −0.112221 0.112221i
\(463\) 1.13717e45 1.13717e45i 0.550741 0.550741i −0.375914 0.926655i \(-0.622671\pi\)
0.926655 + 0.375914i \(0.122671\pi\)
\(464\) 9.65568e44i 0.450793i
\(465\) −2.66631e44 + 7.26572e44i −0.120008 + 0.327023i
\(466\) −4.20124e44 −0.182313
\(467\) −1.08103e45 1.08103e45i −0.452326 0.452326i 0.443800 0.896126i \(-0.353630\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(468\) 5.21179e43 5.21179e43i 0.0210285 0.0210285i
\(469\) 3.40792e45i 1.32602i
\(470\) −1.31267e45 2.83461e45i −0.492599 1.06372i
\(471\) −2.35155e45 −0.851135
\(472\) −2.98529e45 2.98529e45i −1.04225 1.04225i
\(473\) 2.86760e44 2.86760e44i 0.0965782 0.0965782i
\(474\) 2.45814e45i 0.798685i
\(475\) 1.15564e45 + 9.80169e44i 0.362268 + 0.307262i
\(476\) −1.32928e45 −0.402068
\(477\) 9.24701e44 + 9.24701e44i 0.269891 + 0.269891i
\(478\) −1.99117e44 + 1.99117e44i −0.0560833 + 0.0560833i
\(479\) 2.62021e45i 0.712250i 0.934438 + 0.356125i \(0.115902\pi\)
−0.934438 + 0.356125i \(0.884098\pi\)
\(480\) −2.44683e45 + 1.13310e45i −0.641951 + 0.297280i
\(481\) 1.34242e45 0.339956
\(482\) 1.76767e45 + 1.76767e45i 0.432117 + 0.432117i
\(483\) 2.06595e45 2.06595e45i 0.487549 0.487549i
\(484\) 1.97633e45i 0.450286i
\(485\) −8.49789e45 3.11848e45i −1.86940 0.686015i
\(486\) 1.88159e45 0.399676
\(487\) 1.15951e45 + 1.15951e45i 0.237838 + 0.237838i 0.815954 0.578116i \(-0.196212\pi\)
−0.578116 + 0.815954i \(0.696212\pi\)
\(488\) 4.71614e44 4.71614e44i 0.0934221 0.0934221i
\(489\) 4.67876e45i 0.895118i
\(490\) 2.04048e45 5.56033e45i 0.377050 1.02746i
\(491\) 5.34078e45 0.953278 0.476639 0.879099i \(-0.341855\pi\)
0.476639 + 0.879099i \(0.341855\pi\)
\(492\) 1.83822e45 + 1.83822e45i 0.316950 + 0.316950i
\(493\) −3.25484e45 + 3.25484e45i −0.542166 + 0.542166i
\(494\) 4.93789e44i 0.0794663i
\(495\) 1.23246e44 + 2.66140e44i 0.0191640 + 0.0413829i
\(496\) −8.85924e44 −0.133109
\(497\) 1.10839e46 + 1.10839e46i 1.60929 + 1.60929i
\(498\) 1.35925e45 1.35925e45i 0.190722 0.190722i
\(499\) 9.42765e45i 1.27848i 0.769007 + 0.639240i \(0.220751\pi\)
−0.769007 + 0.639240i \(0.779249\pi\)
\(500\) 3.40018e45 + 9.40080e44i 0.445668 + 0.123218i
\(501\) 3.31852e45 0.420440
\(502\) 5.93420e45 + 5.93420e45i 0.726773 + 0.726773i
\(503\) 1.78441e44 1.78441e44i 0.0211271 0.0211271i −0.696464 0.717591i \(-0.745245\pi\)
0.717591 + 0.696464i \(0.245245\pi\)
\(504\) 4.16902e45i 0.477215i
\(505\) −1.49429e46 + 6.91988e45i −1.65379 + 0.765853i
\(506\) −5.71250e44 −0.0611318
\(507\) −5.48906e45 5.48906e45i −0.568019 0.568019i
\(508\) 6.34586e45 6.34586e45i 0.635049 0.635049i
\(509\) 4.99224e45i 0.483162i 0.970381 + 0.241581i \(0.0776659\pi\)
−0.970381 + 0.241581i \(0.922334\pi\)
\(510\) 3.43200e45 + 1.25945e45i 0.321258 + 0.117893i
\(511\) −2.31977e46 −2.10034
\(512\) −4.98578e45 4.98578e45i −0.436661 0.436661i
\(513\) 4.30668e45 4.30668e45i 0.364878 0.364878i
\(514\) 9.21576e44i 0.0755368i
\(515\) 2.35552e45 6.41881e45i 0.186794 0.509016i
\(516\) −4.31134e45 −0.330802
\(517\) −2.46341e45 2.46341e45i −0.182893 0.182893i
\(518\) 1.69765e46 1.69765e46i 1.21967 1.21967i
\(519\) 2.56884e42i 0.000178604i
\(520\) 1.52778e45 + 3.29911e45i 0.102802 + 0.221993i
\(521\) −1.29314e46 −0.842177 −0.421088 0.907020i \(-0.638352\pi\)
−0.421088 + 0.907020i \(0.638352\pi\)
\(522\) −3.22767e45 3.22767e45i −0.203466 0.203466i
\(523\) 6.06529e44 6.06529e44i 0.0370103 0.0370103i −0.688359 0.725370i \(-0.741669\pi\)
0.725370 + 0.688359i \(0.241669\pi\)
\(524\) 1.62323e44i 0.00958845i
\(525\) 1.51331e46 1.78423e46i 0.865408 1.02033i
\(526\) −1.08259e46 −0.599384
\(527\) −2.98637e45 2.98637e45i −0.160089 0.160089i
\(528\) 6.04747e44 6.04747e44i 0.0313904 0.0313904i
\(529\) 1.46112e46i 0.734410i
\(530\) −1.85078e46 + 8.57074e45i −0.900875 + 0.417185i
\(531\) 8.22017e45 0.387502
\(532\) −5.37080e45 5.37080e45i −0.245212 0.245212i
\(533\) 4.17335e45 4.17335e45i 0.184554 0.184554i
\(534\) 1.89047e46i 0.809781i
\(535\) −1.27421e46 4.67600e45i −0.528723 0.194026i
\(536\) 2.24035e46 0.900565
\(537\) 1.20555e46 + 1.20555e46i 0.469486 + 0.469486i
\(538\) −1.22189e46 + 1.22189e46i −0.461033 + 0.461033i
\(539\) 6.60546e45i 0.241487i
\(540\) 4.88477e45 1.33110e46i 0.173042 0.471540i
\(541\) 2.24150e46 0.769458 0.384729 0.923029i \(-0.374295\pi\)
0.384729 + 0.923029i \(0.374295\pi\)
\(542\) 6.90000e45 + 6.90000e45i 0.229541 + 0.229541i
\(543\) 4.31827e45 4.31827e45i 0.139224 0.139224i
\(544\) 1.47143e46i 0.459787i
\(545\) 1.59700e46 + 3.44859e46i 0.483688 + 1.04448i
\(546\) 7.62377e45 0.223818
\(547\) −2.35640e46 2.35640e46i −0.670602 0.670602i 0.287253 0.957855i \(-0.407258\pi\)
−0.957855 + 0.287253i \(0.907258\pi\)
\(548\) −7.39935e45 + 7.39935e45i −0.204138 + 0.204138i
\(549\) 1.29862e45i 0.0347338i
\(550\) −4.55897e45 + 3.74546e44i −0.118223 + 0.00971269i
\(551\) −2.63015e46 −0.661308
\(552\) 1.35815e46 + 1.35815e46i 0.331118 + 0.331118i
\(553\) −6.07004e46 + 6.07004e46i −1.43504 + 1.43504i
\(554\) 6.46776e45i 0.148282i
\(555\) 5.15319e46 2.38638e46i 1.14576 0.530590i
\(556\) 2.73330e46 0.589408
\(557\) 5.56372e45 + 5.56372e45i 0.116366 + 0.116366i 0.762892 0.646526i \(-0.223779\pi\)
−0.646526 + 0.762892i \(0.723779\pi\)
\(558\) 2.96144e45 2.96144e45i 0.0600789 0.0600789i
\(559\) 9.78813e45i 0.192619i
\(560\) 2.51412e46 + 9.22608e45i 0.479942 + 0.176125i
\(561\) 4.07709e45 0.0755060
\(562\) −8.11922e45 8.11922e45i −0.145880 0.145880i
\(563\) 2.94138e46 2.94138e46i 0.512754 0.512754i −0.402615 0.915369i \(-0.631899\pi\)
0.915369 + 0.402615i \(0.131899\pi\)
\(564\) 3.70365e46i 0.626449i
\(565\) −8.64006e45 + 2.35442e46i −0.141805 + 0.386421i
\(566\) −1.62263e46 −0.258429
\(567\) −4.61306e46 4.61306e46i −0.712979 0.712979i
\(568\) −7.28650e46 + 7.28650e46i −1.09294 + 1.09294i
\(569\) 6.94152e46i 1.01052i −0.862966 0.505261i \(-0.831396\pi\)
0.862966 0.505261i \(-0.168604\pi\)
\(570\) 8.77793e45 + 1.89552e46i 0.124028 + 0.267828i
\(571\) 6.43763e46 0.882901 0.441450 0.897286i \(-0.354464\pi\)
0.441450 + 0.897286i \(0.354464\pi\)
\(572\) 9.06533e44 + 9.06533e44i 0.0120684 + 0.0120684i
\(573\) −1.52617e46 + 1.52617e46i −0.197231 + 0.197231i
\(574\) 1.05554e47i 1.32426i
\(575\) −3.46447e45 4.21695e46i −0.0421972 0.513623i
\(576\) 2.23104e46 0.263830
\(577\) 5.14827e46 + 5.14827e46i 0.591116 + 0.591116i 0.937933 0.346817i \(-0.112738\pi\)
−0.346817 + 0.937933i \(0.612738\pi\)
\(578\) 3.23980e46 3.23980e46i 0.361198 0.361198i
\(579\) 5.03498e46i 0.545083i
\(580\) −5.55622e46 + 2.57302e46i −0.584122 + 0.270500i
\(581\) 6.71297e46 0.685363
\(582\) −8.82350e46 8.82350e46i −0.874884 0.874884i
\(583\) −1.60841e46 + 1.60841e46i −0.154893 + 0.154893i
\(584\) 1.52501e47i 1.42644i
\(585\) −6.64556e45 2.43873e45i −0.0603785 0.0221572i
\(586\) −1.28398e47 −1.13318
\(587\) −3.00344e46 3.00344e46i −0.257496 0.257496i 0.566539 0.824035i \(-0.308282\pi\)
−0.824035 + 0.566539i \(0.808282\pi\)
\(588\) −4.96555e46 + 4.96555e46i −0.413574 + 0.413574i
\(589\) 2.41321e46i 0.195269i
\(590\) −4.41678e46 + 1.20358e47i −0.347234 + 0.946215i
\(591\) −4.91449e46 −0.375398
\(592\) 4.59657e46 + 4.59657e46i 0.341166 + 0.341166i
\(593\) −3.43717e46 + 3.43717e46i −0.247897 + 0.247897i −0.820107 0.572210i \(-0.806086\pi\)
0.572210 + 0.820107i \(0.306086\pi\)
\(594\) 1.83856e46i 0.128857i
\(595\) 5.36482e46 + 1.15849e47i 0.365399 + 0.789047i
\(596\) 7.28490e45 0.0482211
\(597\) 7.30904e44 + 7.30904e44i 0.00470215 + 0.00470215i
\(598\) 9.74939e45 9.74939e45i 0.0609617 0.0609617i
\(599\) 3.14444e46i 0.191112i −0.995424 0.0955558i \(-0.969537\pi\)
0.995424 0.0955558i \(-0.0304628\pi\)
\(600\) 1.17294e47 + 9.94847e46i 0.692956 + 0.587740i
\(601\) 2.76387e47 1.58728 0.793638 0.608391i \(-0.208185\pi\)
0.793638 + 0.608391i \(0.208185\pi\)
\(602\) 1.23783e47 + 1.23783e47i 0.691066 + 0.691066i
\(603\) −3.08448e46 + 3.08448e46i −0.167412 + 0.167412i
\(604\) 3.28227e46i 0.173199i
\(605\) 1.72240e47 7.97622e46i 0.883673 0.409219i
\(606\) −2.27005e47 −1.13240
\(607\) −1.32824e47 1.32824e47i −0.644272 0.644272i 0.307330 0.951603i \(-0.400564\pi\)
−0.951603 + 0.307330i \(0.900564\pi\)
\(608\) 5.94510e46 5.94510e46i 0.280413 0.280413i
\(609\) 4.06078e47i 1.86258i
\(610\) −1.90141e46 6.97762e45i −0.0848141 0.0311243i
\(611\) 8.40848e46 0.364768
\(612\) 1.20312e46 + 1.20312e46i 0.0507616 + 0.0507616i
\(613\) 1.22216e47 1.22216e47i 0.501532 0.501532i −0.410382 0.911914i \(-0.634605\pi\)
0.911914 + 0.410382i \(0.134605\pi\)
\(614\) 8.33748e46i 0.332792i
\(615\) 8.60151e46 2.34392e47i 0.333962 0.910051i
\(616\) 7.25153e46 0.273878
\(617\) −8.48498e46 8.48498e46i −0.311747 0.311747i 0.533839 0.845586i \(-0.320749\pi\)
−0.845586 + 0.533839i \(0.820749\pi\)
\(618\) 6.66476e46 6.66476e46i 0.238221 0.238221i
\(619\) 2.29897e45i 0.00799451i 0.999992 + 0.00399726i \(0.00127237\pi\)
−0.999992 + 0.00399726i \(0.998728\pi\)
\(620\) −2.36079e46 5.09792e46i −0.0798727 0.172478i
\(621\) −1.70063e47 −0.559824
\(622\) 2.02461e47 + 2.02461e47i 0.648491 + 0.648491i
\(623\) −4.66825e47 + 4.66825e47i −1.45498 + 1.45498i
\(624\) 2.06421e46i 0.0626061i
\(625\) −5.52977e46 3.34270e47i −0.163210 0.986591i
\(626\) 1.20105e47 0.344982
\(627\) 1.64729e46 + 1.64729e46i 0.0460493 + 0.0460493i
\(628\) 1.20701e47 1.20701e47i 0.328394 0.328394i
\(629\) 3.09893e47i 0.820635i
\(630\) −1.14882e47 + 5.32005e46i −0.296116 + 0.137128i
\(631\) −5.04387e47 −1.26551 −0.632754 0.774353i \(-0.718075\pi\)
−0.632754 + 0.774353i \(0.718075\pi\)
\(632\) −3.99042e47 3.99042e47i −0.974605 0.974605i
\(633\) 4.11688e47 4.11688e47i 0.978825 0.978825i
\(634\) 1.92927e47i 0.446556i
\(635\) −8.09161e47 2.96939e47i −1.82340 0.669135i
\(636\) 2.41820e47 0.530544
\(637\) 1.12734e47 + 1.12734e47i 0.240815 + 0.240815i
\(638\) 5.61417e46 5.61417e46i 0.116771 0.116771i
\(639\) 2.00638e47i 0.406349i
\(640\) 2.59567e46 7.07321e46i 0.0511905 0.139495i
\(641\) −1.85685e47 −0.356608 −0.178304 0.983975i \(-0.557061\pi\)
−0.178304 + 0.983975i \(0.557061\pi\)
\(642\) −1.32304e47 1.32304e47i −0.247444 0.247444i
\(643\) 5.80223e47 5.80223e47i 1.05684 1.05684i 0.0585541 0.998284i \(-0.481351\pi\)
0.998284 0.0585541i \(-0.0186490\pi\)
\(644\) 2.12083e47i 0.376223i
\(645\) 1.74001e47 + 3.75739e47i 0.300632 + 0.649189i
\(646\) −1.13989e47 −0.191827
\(647\) 4.69490e47 + 4.69490e47i 0.769580 + 0.769580i 0.978032 0.208453i \(-0.0668427\pi\)
−0.208453 + 0.978032i \(0.566843\pi\)
\(648\) 3.03260e47 3.03260e47i 0.484218 0.484218i
\(649\) 1.42981e47i 0.222391i
\(650\) 7.14146e46 8.41992e46i 0.108208 0.127580i
\(651\) −3.72583e47 −0.549979
\(652\) 2.40152e47 + 2.40152e47i 0.345364 + 0.345364i
\(653\) −8.67113e47 + 8.67113e47i −1.21493 + 1.21493i −0.245547 + 0.969385i \(0.578968\pi\)
−0.969385 + 0.245547i \(0.921032\pi\)
\(654\) 5.23893e47i 0.715189i
\(655\) −1.41467e46 + 6.55116e45i −0.0188171 + 0.00871397i
\(656\) 2.85799e47 0.370421
\(657\) 2.09960e47 + 2.09960e47i 0.265171 + 0.265171i
\(658\) 1.06335e48 1.06335e48i 1.30869 1.30869i
\(659\) 3.34007e47i 0.400593i −0.979735 0.200296i \(-0.935810\pi\)
0.979735 0.200296i \(-0.0641905\pi\)
\(660\) 5.09144e46 + 1.86841e46i 0.0595105 + 0.0218386i
\(661\) 1.20808e47 0.137617 0.0688084 0.997630i \(-0.478080\pi\)
0.0688084 + 0.997630i \(0.478080\pi\)
\(662\) 1.11732e47 + 1.11732e47i 0.124049 + 0.124049i
\(663\) −6.95828e46 + 6.95828e46i −0.0752960 + 0.0752960i
\(664\) 4.41308e47i 0.465462i
\(665\) −2.51313e47 + 6.84831e47i −0.258373 + 0.704069i
\(666\) −3.07306e47 −0.307970
\(667\) 5.19299e47 + 5.19299e47i 0.507315 + 0.507315i
\(668\) −1.70334e47 + 1.70334e47i −0.162219 + 0.162219i
\(669\) 1.74655e48i 1.62158i
\(670\) −2.85890e47 6.17354e47i −0.258778 0.558808i
\(671\) −2.25880e46 −0.0199340
\(672\) −9.17884e47 9.17884e47i −0.789788 0.789788i
\(673\) 4.39107e46 4.39107e46i 0.0368396 0.0368396i −0.688447 0.725287i \(-0.741707\pi\)
0.725287 + 0.688447i \(0.241707\pi\)
\(674\) 7.99750e46i 0.0654238i
\(675\) −1.35722e48 + 1.11503e47i −1.08264 + 0.0889455i
\(676\) 5.63486e47 0.438318
\(677\) 1.83676e48 + 1.83676e48i 1.39330 + 1.39330i 0.817807 + 0.575493i \(0.195190\pi\)
0.575493 + 0.817807i \(0.304810\pi\)
\(678\) −2.44464e47 + 2.44464e47i −0.180846 + 0.180846i
\(679\) 4.35768e48i 3.14390i
\(680\) −7.61585e47 + 3.52681e47i −0.535879 + 0.248160i
\(681\) −8.28287e47 −0.568434
\(682\) 5.15109e46 + 5.15109e46i 0.0344798 + 0.0344798i
\(683\) 9.42364e47 9.42364e47i 0.615272 0.615272i −0.329043 0.944315i \(-0.606726\pi\)
0.944315 + 0.329043i \(0.106726\pi\)
\(684\) 9.72211e46i 0.0619165i
\(685\) 9.43492e47 + 3.46234e47i 0.586136 + 0.215095i
\(686\) 9.41116e47 0.570339
\(687\) −6.11665e47 6.11665e47i −0.361617 0.361617i
\(688\) −3.35155e47 + 3.35155e47i −0.193304 + 0.193304i
\(689\) 5.49009e47i 0.308925i
\(690\) 2.00940e47 5.47564e47i 0.110314 0.300608i
\(691\) 5.66789e47 0.303595 0.151797 0.988412i \(-0.451494\pi\)
0.151797 + 0.988412i \(0.451494\pi\)
\(692\) 1.31854e44 + 1.31854e44i 6.89110e−5 + 6.89110e-5i
\(693\) −9.98377e46 + 9.98377e46i −0.0509131 + 0.0509131i
\(694\) 4.93301e47i 0.245472i
\(695\) −1.10313e48 2.38211e48i −0.535654 1.15670i
\(696\) −2.66954e48 −1.26497
\(697\) 9.63402e47 + 9.63402e47i 0.445502 + 0.445502i
\(698\) −1.64271e48 + 1.64271e48i −0.741342 + 0.741342i
\(699\) 4.78397e47i 0.210706i
\(700\) 1.39054e47 + 1.69257e48i 0.0597747 + 0.727577i
\(701\) 5.58939e47 0.234508 0.117254 0.993102i \(-0.462591\pi\)
0.117254 + 0.993102i \(0.462591\pi\)
\(702\) −3.13783e47 3.13783e47i −0.128499 0.128499i
\(703\) −1.25208e48 + 1.25208e48i −0.500486 + 0.500486i
\(704\) 3.88063e47i 0.151414i
\(705\) 3.22778e48 1.49475e48i 1.22939 0.569316i
\(706\) 2.50963e48 0.933103
\(707\) −5.60557e48 5.60557e48i −2.03465 2.03465i
\(708\) 1.07483e48 1.07483e48i 0.380869 0.380869i
\(709\) 2.87907e48i 0.996016i 0.867172 + 0.498008i \(0.165935\pi\)
−0.867172 + 0.498008i \(0.834065\pi\)
\(710\) 2.93770e48 + 1.07805e48i 0.992237 + 0.364123i
\(711\) 1.09879e48 0.362352
\(712\) −3.06888e48 3.06888e48i −0.988145 0.988145i
\(713\) −4.76465e47 + 4.76465e47i −0.149799 + 0.149799i
\(714\) 1.75992e48i 0.540284i
\(715\) 4.24189e46 1.15592e47i 0.0127162 0.0346517i
\(716\) −1.23757e48 −0.362285
\(717\) −2.26735e47 2.26735e47i −0.0648177 0.0648177i
\(718\) −2.13948e48 + 2.13948e48i −0.597300 + 0.597300i
\(719\) 3.82883e48i 1.04394i −0.852964 0.521969i \(-0.825198\pi\)
0.852964 0.521969i \(-0.174802\pi\)
\(720\) −1.44046e47 3.11054e47i −0.0383573 0.0828293i
\(721\) 3.29154e48 0.856050
\(722\) 1.58048e48 + 1.58048e48i 0.401474 + 0.401474i
\(723\) −2.01285e48 + 2.01285e48i −0.499414 + 0.499414i
\(724\) 4.43297e47i 0.107433i
\(725\) 4.48485e48 + 3.80388e48i 1.06170 + 0.900494i
\(726\) 2.61658e48 0.605077
\(727\) 6.09193e48 + 6.09193e48i 1.37616 + 1.37616i 0.851004 + 0.525160i \(0.175994\pi\)
0.525160 + 0.851004i \(0.324006\pi\)
\(728\) −1.23760e48 + 1.23760e48i −0.273116 + 0.273116i
\(729\) 5.10486e48i 1.10057i
\(730\) −4.20233e48 + 1.94605e48i −0.885118 + 0.409888i
\(731\) −2.25955e48 −0.464972
\(732\) 1.69802e47 + 1.69802e47i 0.0341392 + 0.0341392i
\(733\) 2.81523e48 2.81523e48i 0.553026 0.553026i −0.374287 0.927313i \(-0.622112\pi\)
0.927313 + 0.374287i \(0.122112\pi\)
\(734\) 1.98968e48i 0.381901i
\(735\) 6.33158e48 + 2.32351e48i 1.18748 + 0.435772i
\(736\) −2.34761e48 −0.430232
\(737\) −5.36510e47 5.36510e47i −0.0960794 0.0960794i
\(738\) −9.55360e47 + 9.55360e47i −0.167189 + 0.167189i
\(739\) 7.58569e48i 1.29730i −0.761088 0.648649i \(-0.775334\pi\)
0.761088 0.648649i \(-0.224666\pi\)
\(740\) −1.42015e48 + 3.86992e48i −0.237353 + 0.646789i
\(741\) −5.62280e47 −0.0918424
\(742\) −6.94287e48 6.94287e48i −1.10834 1.10834i
\(743\) 3.35478e48 3.35478e48i 0.523425 0.523425i −0.395179 0.918604i \(-0.629317\pi\)
0.918604 + 0.395179i \(0.129317\pi\)
\(744\) 2.44934e48i 0.373517i
\(745\) −2.94010e47 6.34889e47i −0.0438233 0.0946327i
\(746\) 5.90744e48 0.860674
\(747\) −6.07584e47 6.07584e47i −0.0865279 0.0865279i
\(748\) −2.09269e47 + 2.09269e47i −0.0291325 + 0.0291325i
\(749\) 6.53412e48i 0.889193i
\(750\) 1.24463e48 4.50169e48i 0.165576 0.598872i
\(751\) −1.49177e49 −1.94010 −0.970048 0.242913i \(-0.921897\pi\)
−0.970048 + 0.242913i \(0.921897\pi\)
\(752\) 2.87914e48 + 2.87914e48i 0.366066 + 0.366066i
\(753\) −6.75730e48 + 6.75730e48i −0.839960 + 0.839960i
\(754\) 1.91632e48i 0.232892i
\(755\) 2.86054e48 1.32468e48i 0.339899 0.157403i
\(756\) 6.82585e48 0.793023
\(757\) 7.60388e47 + 7.60388e47i 0.0863785 + 0.0863785i 0.748976 0.662597i \(-0.230546\pi\)
−0.662597 + 0.748976i \(0.730546\pi\)
\(758\) 6.42708e48 6.42708e48i 0.713899 0.713899i
\(759\) 6.50485e47i 0.0706525i
\(760\) −4.50205e48 1.65212e48i −0.478166 0.175473i
\(761\) −1.43211e49 −1.48744 −0.743718 0.668494i \(-0.766939\pi\)
−0.743718 + 0.668494i \(0.766939\pi\)
\(762\) −8.40165e48 8.40165e48i −0.853356 0.853356i
\(763\) −1.29368e49 + 1.29368e49i −1.28502 + 1.28502i
\(764\) 1.56671e48i 0.152196i
\(765\) 5.62971e47 1.53410e48i 0.0534862 0.145750i
\(766\) 6.45673e48 0.599962
\(767\) −2.44022e48 2.44022e48i −0.221772 0.221772i
\(768\) 7.04342e48 7.04342e48i 0.626099 0.626099i
\(769\) 1.10209e48i 0.0958225i 0.998852 + 0.0479112i \(0.0152565\pi\)
−0.998852 + 0.0479112i \(0.984744\pi\)
\(770\) −9.25362e47 1.99824e48i −0.0786990 0.169944i
\(771\) 1.04940e48 0.0873008
\(772\) 2.58436e48 + 2.58436e48i 0.210310 + 0.210310i
\(773\) 3.85327e47 3.85327e47i 0.0306746 0.0306746i −0.691603 0.722278i \(-0.743095\pi\)
0.722278 + 0.691603i \(0.243095\pi\)
\(774\) 2.24069e48i 0.174496i
\(775\) −3.49012e48 + 4.11492e48i −0.265896 + 0.313496i
\(776\) 2.86472e49 2.13517
\(777\) 1.93313e49 + 1.93313e49i 1.40962 + 1.40962i
\(778\) −8.21309e48 + 8.21309e48i −0.585940 + 0.585940i
\(779\) 7.78500e48i 0.543403i
\(780\) −1.18782e48 + 5.50067e47i −0.0811229 + 0.0375671i
\(781\) 3.48988e48 0.233208
\(782\) 2.25061e48 + 2.25061e48i 0.147158 + 0.147158i
\(783\) 1.67136e49 1.67136e49i 1.06935 1.06935i
\(784\) 7.72022e48i 0.483344i
\(785\) −1.53905e49 5.64788e48i −0.942909 0.346020i
\(786\) −2.14909e47 −0.0128846
\(787\) 9.94569e47 + 9.94569e47i 0.0583532 + 0.0583532i 0.735681 0.677328i \(-0.236862\pi\)
−0.677328 + 0.735681i \(0.736862\pi\)
\(788\) 2.52252e48 2.52252e48i 0.144840 0.144840i
\(789\) 1.23275e49i 0.692732i
\(790\) −5.90390e48 + 1.60882e49i −0.324697 + 0.884803i
\(791\) −1.20734e49 −0.649873
\(792\) −6.56329e47 6.56329e47i −0.0345775 0.0345775i
\(793\) 3.85504e47 3.85504e47i 0.0198786 0.0198786i
\(794\) 1.12314e49i 0.566874i
\(795\) −9.75955e48 2.10749e49i −0.482157 1.04118i
\(796\) −7.50319e46 −0.00362847
\(797\) 2.49194e49 + 2.49194e49i 1.17963 + 1.17963i 0.979838 + 0.199794i \(0.0640274\pi\)
0.199794 + 0.979838i \(0.435973\pi\)
\(798\) −7.11071e48 + 7.11071e48i −0.329506 + 0.329506i
\(799\) 1.94106e49i 0.880530i
\(800\) −1.87355e49 + 1.53924e48i −0.832026 + 0.0683558i
\(801\) 8.45036e48 0.367386
\(802\) −2.27741e48 2.27741e48i −0.0969342 0.0969342i
\(803\) −3.65202e48 + 3.65202e48i −0.152184 + 0.152184i
\(804\) 8.06625e48i 0.329093i
\(805\) 1.84833e49 8.55939e48i 0.738327 0.341911i
\(806\) −1.75825e48 −0.0687678
\(807\) −1.39137e49 1.39137e49i −0.532835 0.532835i
\(808\) 3.68508e49 3.68508e49i 1.38183 1.38183i
\(809\) 2.87976e49i 1.05738i 0.848815 + 0.528690i \(0.177316\pi\)
−0.848815 + 0.528690i \(0.822684\pi\)
\(810\) −1.22266e49 4.48679e48i −0.439601 0.161321i
\(811\) −5.08727e49 −1.79114 −0.895572 0.444917i \(-0.853233\pi\)
−0.895572 + 0.444917i \(0.853233\pi\)
\(812\) −2.08432e49 2.08432e49i −0.718641 0.718641i
\(813\) −7.85707e48 + 7.85707e48i −0.265290 + 0.265290i
\(814\) 5.34524e48i 0.176747i
\(815\) 1.12373e49 3.06218e49i 0.363901 0.991634i
\(816\) −4.76515e48 −0.151128
\(817\) −9.12942e48 9.12942e48i −0.283575 0.283575i
\(818\) 2.68666e49 2.68666e49i 0.817346 0.817346i
\(819\) 3.40781e48i 0.101543i
\(820\) 7.61590e48 + 1.64459e49i 0.222273 + 0.479978i
\(821\) 2.26744e49 0.648190 0.324095 0.946024i \(-0.394940\pi\)
0.324095 + 0.946024i \(0.394940\pi\)
\(822\) 9.79643e48 + 9.79643e48i 0.274313 + 0.274313i
\(823\) 2.80478e49 2.80478e49i 0.769310 0.769310i −0.208675 0.977985i \(-0.566915\pi\)
0.977985 + 0.208675i \(0.0669150\pi\)
\(824\) 2.16384e49i 0.581384i
\(825\) −4.26498e47 5.19132e48i −0.0112253 0.136635i
\(826\) −6.17189e49 −1.59132
\(827\) 1.06712e48 + 1.06712e48i 0.0269539 + 0.0269539i 0.720455 0.693501i \(-0.243933\pi\)
−0.693501 + 0.720455i \(0.743933\pi\)
\(828\) 1.91954e48 1.91954e48i 0.0474986 0.0474986i
\(829\) 3.21095e49i 0.778407i −0.921152 0.389203i \(-0.872750\pi\)
0.921152 0.389203i \(-0.127250\pi\)
\(830\) 1.21607e49 5.63149e48i 0.288823 0.133751i
\(831\) 7.36487e48 0.171375
\(832\) −6.62299e48 6.62299e48i −0.150993 0.150993i
\(833\) −2.60242e49 + 2.60242e49i −0.581315 + 0.581315i
\(834\) 3.61878e49i 0.792025i
\(835\) 2.17193e49 + 7.97034e48i 0.465773 + 0.170925i
\(836\) −1.69105e48 −0.0355345
\(837\) 1.53349e49 + 1.53349e49i 0.315754 + 0.315754i
\(838\) −1.42771e49 + 1.42771e49i −0.288065 + 0.288065i
\(839\) 1.26696e49i 0.250501i 0.992125 + 0.125250i \(0.0399734\pi\)
−0.992125 + 0.125250i \(0.960027\pi\)
\(840\) −2.55077e49 + 6.95086e49i −0.494223 + 1.34676i
\(841\) −4.94058e49 −0.938094
\(842\) 2.55587e49 + 2.55587e49i 0.475591 + 0.475591i
\(843\) 9.24540e48 9.24540e48i 0.168600 0.168600i
\(844\) 4.22623e49i 0.755322i
\(845\) −2.27416e49 4.91085e49i −0.398343 0.860187i
\(846\) −1.92486e49 −0.330448
\(847\) 6.46127e49 + 6.46127e49i 1.08718 + 1.08718i
\(848\) 1.87986e49 1.87986e49i 0.310024 0.310024i
\(849\) 1.84770e49i 0.298676i
\(850\) 1.94370e49 + 1.64858e49i 0.307970 + 0.261209i
\(851\) 4.94423e49 0.767885
\(852\) −2.62346e49 2.62346e49i −0.399394 0.399394i
\(853\) −1.42058e49 + 1.42058e49i −0.211998 + 0.211998i −0.805116 0.593117i \(-0.797897\pi\)
0.593117 + 0.805116i \(0.297897\pi\)
\(854\) 9.75033e48i 0.142638i
\(855\) 8.47294e48 3.92372e48i 0.121510 0.0562697i
\(856\) 4.29550e49 0.603893
\(857\) −2.55442e49 2.55442e49i −0.352061 0.352061i 0.508815 0.860876i \(-0.330084\pi\)
−0.860876 + 0.508815i \(0.830084\pi\)
\(858\) 1.20021e48 1.20021e48i 0.0162171 0.0162171i
\(859\) 1.28561e49i 0.170304i 0.996368 + 0.0851520i \(0.0271376\pi\)
−0.996368 + 0.0851520i \(0.972862\pi\)
\(860\) −2.82171e49 1.03549e49i −0.366470 0.134484i
\(861\) 1.20195e50 1.53050
\(862\) −7.60307e49 7.60307e49i −0.949217 0.949217i
\(863\) −7.57613e49 + 7.57613e49i −0.927393 + 0.927393i −0.997537 0.0701438i \(-0.977654\pi\)
0.0701438 + 0.997537i \(0.477654\pi\)
\(864\) 7.55575e49i 0.906867i
\(865\) 6.16976e45 1.68127e46i 7.26097e−5 0.000197862i
\(866\) 3.93280e49 0.453835
\(867\) 3.68918e49 + 3.68918e49i 0.417450 + 0.417450i
\(868\) 1.91240e49 1.91240e49i 0.212199 0.212199i
\(869\) 1.91122e49i 0.207957i
\(870\) 3.40658e49 + 7.35621e49i 0.363489 + 0.784922i
\(871\) 1.83130e49 0.191624
\(872\) −8.50460e49 8.50460e49i −0.872717 0.872717i
\(873\) −3.94409e49 + 3.94409e49i −0.396922 + 0.396922i
\(874\) 1.81866e49i 0.179497i
\(875\) 1.41897e50 8.04286e49i 1.37353 0.778527i
\(876\) 5.49070e49 0.521264
\(877\) 6.44344e49 + 6.44344e49i 0.599963 + 0.599963i 0.940303 0.340340i \(-0.110542\pi\)
−0.340340 + 0.940303i \(0.610542\pi\)
\(878\) −8.77012e48 + 8.77012e48i −0.0800938 + 0.0800938i
\(879\) 1.46207e50i 1.30966i
\(880\) 5.41044e48 2.50551e48i 0.0475365 0.0220136i
\(881\) −1.19713e50 −1.03170 −0.515848 0.856680i \(-0.672523\pi\)
−0.515848 + 0.856680i \(0.672523\pi\)
\(882\) −2.58069e49 2.58069e49i −0.218158 0.218158i
\(883\) −2.74430e49 + 2.74430e49i −0.227562 + 0.227562i −0.811674 0.584111i \(-0.801443\pi\)
0.584111 + 0.811674i \(0.301443\pi\)
\(884\) 7.14310e48i 0.0581030i
\(885\) −1.37052e50 5.02942e49i −1.09358 0.401312i
\(886\) 2.16031e49 0.169100
\(887\) −6.34355e49 6.34355e49i −0.487114 0.487114i 0.420280 0.907394i \(-0.361932\pi\)
−0.907394 + 0.420280i \(0.861932\pi\)
\(888\) −1.27083e50 + 1.27083e50i −0.957342 + 0.957342i
\(889\) 4.14934e50i 3.06654i
\(890\) −4.54047e49 + 1.23728e50i −0.329208 + 0.897096i
\(891\) −1.45247e49 −0.103320
\(892\) −8.96471e49 8.96471e49i −0.625653 0.625653i
\(893\) −7.84261e49 + 7.84261e49i −0.537014 + 0.537014i
\(894\) 9.64491e48i 0.0647978i
\(895\) 4.99470e49 + 1.07856e50i 0.329244 + 0.710973i
\(896\) 3.62711e49 0.234598
\(897\) 1.11017e49 + 1.11017e49i 0.0704559 + 0.0704559i
\(898\) 1.04061e50 1.04061e50i 0.648021 0.648021i
\(899\) 9.36527e49i 0.572276i
\(900\) 1.40607e49 1.65778e49i 0.0843109 0.0994041i
\(901\) 1.26736e50 0.745727
\(902\) −1.66174e49 1.66174e49i −0.0959516 0.0959516i
\(903\) −1.40952e50 + 1.40952e50i −0.798693 + 0.798693i
\(904\) 7.93699e49i 0.441360i
\(905\) 3.86339e49 1.78909e49i 0.210835 0.0976354i
\(906\) 4.34559e49 0.232739
\(907\) 2.10353e50 + 2.10353e50i 1.10567 + 1.10567i 0.993713 + 0.111956i \(0.0357114\pi\)
0.111956 + 0.993713i \(0.464289\pi\)
\(908\) 4.25144e49 4.25144e49i 0.219319 0.219319i
\(909\) 1.01471e50i 0.513754i
\(910\) 4.98964e49 + 1.83106e49i 0.247951 + 0.0909909i
\(911\) −1.88897e50 −0.921325 −0.460662 0.887575i \(-0.652388\pi\)
−0.460662 + 0.887575i \(0.652388\pi\)
\(912\) −1.92530e49 1.92530e49i −0.0921692 0.0921692i
\(913\) 1.05682e49 1.05682e49i 0.0496592 0.0496592i
\(914\) 1.10948e50i 0.511722i
\(915\) 7.94545e48 2.16514e49i 0.0359716 0.0980230i
\(916\) 6.27912e49 0.279046
\(917\) −5.30688e48 5.30688e48i −0.0231505 0.0231505i
\(918\) 7.24355e49 7.24355e49i 0.310188 0.310188i
\(919\) 3.19012e50i 1.34105i 0.741889 + 0.670523i \(0.233930\pi\)
−0.741889 + 0.670523i \(0.766070\pi\)
\(920\) 5.62691e49 + 1.21508e50i 0.232208 + 0.501433i
\(921\) −9.49394e49 −0.384621
\(922\) 1.33231e50 + 1.33231e50i 0.529883 + 0.529883i
\(923\) −5.95610e49 + 5.95610e49i −0.232559 + 0.232559i
\(924\) 2.61087e49i 0.100083i
\(925\) 3.94584e50 3.24174e49i 1.48501 0.122002i
\(926\) 1.54555e50 0.571080
\(927\) −2.97914e49 2.97914e49i −0.108077 0.108077i
\(928\) 2.30720e50 2.30720e50i 0.821807 0.821807i
\(929\) 2.61825e50i 0.915681i 0.889034 + 0.457841i \(0.151377\pi\)
−0.889034 + 0.457841i \(0.848623\pi\)
\(930\) −6.74943e49 + 3.12559e49i −0.231770 + 0.107330i
\(931\) −2.10294e50 −0.709060
\(932\) 2.45552e49 + 2.45552e49i 0.0812968 + 0.0812968i
\(933\) −2.30543e50 + 2.30543e50i −0.749487 + 0.749487i
\(934\) 1.46926e50i 0.469030i
\(935\) 2.66839e49 + 9.79224e48i 0.0836474 + 0.0306962i
\(936\) 2.24028e49 0.0689626
\(937\) −3.42945e50 3.42945e50i −1.03670 1.03670i −0.999301 0.0373952i \(-0.988094\pi\)
−0.0373952 0.999301i \(-0.511906\pi\)
\(938\) 2.31590e50 2.31590e50i 0.687497 0.687497i
\(939\) 1.36764e50i 0.398710i
\(940\) −8.89533e49 + 2.42399e50i −0.254676 + 0.693995i
\(941\) −4.56648e50 −1.28398 −0.641989 0.766714i \(-0.721891\pi\)
−0.641989 + 0.766714i \(0.721891\pi\)
\(942\) −1.59802e50 1.59802e50i −0.441284 0.441284i
\(943\) 1.53707e50 1.53707e50i 0.416865 0.416865i
\(944\) 1.67110e50i 0.445123i
\(945\) −2.75483e50 5.94881e50i −0.720699 1.55629i
\(946\) 3.89743e49 0.100145
\(947\) 2.44821e50 + 2.44821e50i 0.617874 + 0.617874i 0.944986 0.327112i \(-0.106075\pi\)
−0.327112 + 0.944986i \(0.606075\pi\)
\(948\) 1.43673e50 1.43673e50i 0.356149 0.356149i
\(949\) 1.24656e50i 0.303521i
\(950\) 1.19242e49 + 1.45141e50i 0.0285186 + 0.347128i
\(951\) 2.19687e50 0.516102
\(952\) −2.85695e50 2.85695e50i −0.659288 0.659288i
\(953\) 4.71306e49 4.71306e49i 0.106837 0.106837i −0.651667 0.758505i \(-0.725930\pi\)
0.758505 + 0.651667i \(0.225930\pi\)
\(954\) 1.25678e50i 0.279859i
\(955\) −1.36541e50 + 6.32306e49i −0.298680 + 0.138315i
\(956\) 2.32758e49 0.0500173
\(957\) 6.39289e49 + 6.39289e49i 0.134957 + 0.134957i
\(958\) −1.78060e50 + 1.78060e50i −0.369277 + 0.369277i
\(959\) 4.83819e50i 0.985749i
\(960\) −3.71973e50 1.36503e50i −0.744561 0.273233i
\(961\) −4.22580e50 −0.831020
\(962\) 9.12260e49 + 9.12260e49i 0.176255 + 0.176255i
\(963\) −5.91396e49 + 5.91396e49i −0.112262 + 0.112262i
\(964\) 2.06632e50i 0.385379i
\(965\) 1.20929e50 3.29532e50i 0.221598 0.603856i
\(966\) 2.80788e50 0.505555
\(967\) 5.66212e50 + 5.66212e50i 1.00168 + 1.00168i 0.999999 + 0.00168064i \(0.000534965\pi\)
0.00168064 + 0.999999i \(0.499465\pi\)
\(968\) −4.24761e50 + 4.24761e50i −0.738353 + 0.738353i
\(969\) 1.29800e50i 0.221703i
\(970\) −3.65565e50 7.89405e50i −0.613543 1.32489i
\(971\) 6.69164e50 1.10358 0.551792 0.833981i \(-0.313944\pi\)
0.551792 + 0.833981i \(0.313944\pi\)
\(972\) −1.09974e50 1.09974e50i −0.178224 0.178224i
\(973\) 8.93607e50 8.93607e50i 1.42308 1.42308i
\(974\) 1.57591e50i 0.246621i
\(975\) 9.58781e49 + 8.13202e49i 0.147449 + 0.125061i
\(976\) 2.64000e49 0.0398986
\(977\) −6.93643e50 6.93643e50i −1.03022 1.03022i −0.999529 0.0306880i \(-0.990230\pi\)
−0.0306880 0.999529i \(-0.509770\pi\)
\(978\) 3.17951e50 3.17951e50i 0.464088 0.464088i
\(979\) 1.46984e50i 0.210846i
\(980\) −4.44249e50 + 2.05727e50i −0.626301 + 0.290033i
\(981\) 2.34179e50 0.324471
\(982\) 3.62939e50 + 3.62939e50i 0.494241 + 0.494241i
\(983\) 1.01850e50 1.01850e50i 0.136318 0.136318i −0.635655 0.771973i \(-0.719270\pi\)
0.771973 + 0.635655i \(0.219270\pi\)
\(984\) 7.90158e50i 1.03943i
\(985\) −3.21646e50 1.18035e50i −0.415875 0.152614i
\(986\) −4.42374e50 −0.562188
\(987\) 1.21085e51 + 1.21085e51i 1.51251 + 1.51251i
\(988\) 2.88608e49 2.88608e49i 0.0354356 0.0354356i
\(989\) 3.60503e50i 0.435083i
\(990\) −9.71050e48 + 2.64612e49i −0.0115198 + 0.0313915i
\(991\) −1.37291e51 −1.60100 −0.800498 0.599335i \(-0.795432\pi\)
−0.800498 + 0.599335i \(0.795432\pi\)
\(992\) 2.11689e50 + 2.11689e50i 0.242661 + 0.242661i
\(993\) −1.27230e50 + 1.27230e50i −0.143368 + 0.143368i
\(994\) 1.50644e51i 1.66872i
\(995\) 3.02819e48 + 6.53912e48i 0.00329755 + 0.00712077i
\(996\) −1.58890e50 −0.170094
\(997\) 4.57054e49 + 4.57054e49i 0.0481005 + 0.0481005i 0.730748 0.682647i \(-0.239172\pi\)
−0.682647 + 0.730748i \(0.739172\pi\)
\(998\) −6.40668e50 + 6.40668e50i −0.662848 + 0.662848i
\(999\) 1.59129e51i 1.61859i
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 5.35.c.a.2.11 32
5.2 odd 4 25.35.c.b.18.6 32
5.3 odd 4 inner 5.35.c.a.3.11 yes 32
5.4 even 2 25.35.c.b.7.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.35.c.a.2.11 32 1.1 even 1 trivial
5.35.c.a.3.11 yes 32 5.3 odd 4 inner
25.35.c.b.7.6 32 5.4 even 2
25.35.c.b.18.6 32 5.2 odd 4