Properties

Label 20.10.e.b.3.20
Level $20$
Weight $10$
Character 20.3
Analytic conductor $10.301$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,10,Mod(3,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 20.e (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: \(10.3007167233\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.20
Character \(\chi\) \(=\) 20.3
Dual form 20.10.e.b.7.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(20.3139 + 9.96719i) q^{2} +(-181.251 + 181.251i) q^{3} +(313.310 + 404.945i) q^{4} +(-997.734 - 978.597i) q^{5} +(-5488.49 + 1875.36i) q^{6} +(1096.38 + 1096.38i) q^{7} +(2328.39 + 11348.8i) q^{8} -46021.0i q^{9} +O(q^{10})\) \(q+(20.3139 + 9.96719i) q^{2} +(-181.251 + 181.251i) q^{3} +(313.310 + 404.945i) q^{4} +(-997.734 - 978.597i) q^{5} +(-5488.49 + 1875.36i) q^{6} +(1096.38 + 1096.38i) q^{7} +(2328.39 + 11348.8i) q^{8} -46021.0i q^{9} +(-10514.0 - 29823.7i) q^{10} -24135.6i q^{11} +(-130185. - 16609.0i) q^{12} +(-34010.0 - 34010.0i) q^{13} +(11344.0 + 33199.6i) q^{14} +(358212. - 3468.70i) q^{15} +(-65817.5 + 253747. i) q^{16} +(-348629. + 348629. i) q^{17} +(458701. - 934867. i) q^{18} -764214. q^{19} +(83677.9 - 710632. i) q^{20} -397441. q^{21} +(240565. - 490289. i) q^{22} +(-27449.8 + 27449.8i) q^{23} +(-2.47902e6 - 1.63497e6i) q^{24} +(37822.1 + 1.95276e6i) q^{25} +(-351892. - 1.02986e6i) q^{26} +(4.77380e6 + 4.77380e6i) q^{27} +(-100467. + 787482. i) q^{28} -5.01486e6i q^{29} +(7.31127e6 + 3.49991e6i) q^{30} +7.76401e6i q^{31} +(-3.86616e6 + 4.49858e6i) q^{32} +(4.37462e6 + 4.37462e6i) q^{33} +(-1.05569e7 + 3.60716e6i) q^{34} +(-20982.0 - 2.16681e6i) q^{35} +(1.86360e7 - 1.44189e7i) q^{36} +(3.31907e6 - 3.31907e6i) q^{37} +(-1.55242e7 - 7.61707e6i) q^{38} +1.23287e7 q^{39} +(8.78283e6 - 1.36017e7i) q^{40} -9.42386e6 q^{41} +(-8.07358e6 - 3.96137e6i) q^{42} +(-1.86665e7 + 1.86665e7i) q^{43} +(9.77362e6 - 7.56194e6i) q^{44} +(-4.50360e7 + 4.59168e7i) q^{45} +(-831210. + 284015. i) q^{46} +(1.31878e7 + 1.31878e7i) q^{47} +(-3.40625e7 - 5.79215e7i) q^{48} -3.79495e7i q^{49} +(-1.86952e7 + 4.00452e7i) q^{50} -1.26379e8i q^{51} +(3.11651e6 - 2.44279e7i) q^{52} +(1.97306e7 + 1.97306e7i) q^{53} +(4.93932e7 + 1.44556e8i) q^{54} +(-2.36191e7 + 2.40810e7i) q^{55} +(-9.88986e6 + 1.49955e7i) q^{56} +(1.38515e8 - 1.38515e8i) q^{57} +(4.99841e7 - 1.01871e8i) q^{58} -6.01499e7 q^{59} +(1.13636e8 + 1.43970e8i) q^{60} -4.79920e7 q^{61} +(-7.73853e7 + 1.57717e8i) q^{62} +(5.04566e7 - 5.04566e7i) q^{63} +(-1.23375e8 + 5.28490e7i) q^{64} +(650868. + 6.72151e7i) q^{65} +(4.52629e7 + 1.32468e8i) q^{66} +(-3.56673e7 - 3.56673e7i) q^{67} +(-2.50404e8 - 3.19466e7i) q^{68} -9.95061e6i q^{69} +(2.11708e7 - 4.42256e7i) q^{70} +2.39980e8i q^{71} +(5.22286e8 - 1.07155e8i) q^{72} +(2.27428e8 + 2.27428e8i) q^{73} +(1.00505e8 - 3.43415e7i) q^{74} +(-3.60795e8 - 3.47085e8i) q^{75} +(-2.39436e8 - 3.09465e8i) q^{76} +(2.64619e7 - 2.64619e7i) q^{77} +(2.50445e8 + 1.22883e8i) q^{78} -1.40201e8 q^{79} +(3.13984e8 - 1.88763e8i) q^{80} -8.24684e8 q^{81} +(-1.91435e8 - 9.39294e7i) q^{82} +(3.59910e8 - 3.59910e8i) q^{83} +(-1.24522e8 - 1.60942e8i) q^{84} +(6.89006e8 - 6.67189e6i) q^{85} +(-5.65242e8 + 1.93137e8i) q^{86} +(9.08950e8 + 9.08950e8i) q^{87} +(2.73912e8 - 5.61971e7i) q^{88} +2.91347e8i q^{89} +(-1.37252e9 + 4.83866e8i) q^{90} -7.45759e7i q^{91} +(-1.97160e7 - 2.51536e6i) q^{92} +(-1.40724e9 - 1.40724e9i) q^{93} +(1.36450e8 + 3.99341e8i) q^{94} +(7.62483e8 + 7.47858e8i) q^{95} +(-1.14628e8 - 1.51612e9i) q^{96} +(-1.13368e8 + 1.13368e8i) q^{97} +(3.78250e8 - 7.70903e8i) q^{98} -1.11075e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 30 q^{2} - 1440 q^{5} + 6152 q^{6} - 17100 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 30 q^{2} - 1440 q^{5} + 6152 q^{6} - 17100 q^{8} + 72790 q^{10} - 155360 q^{12} + 198960 q^{13} + 527288 q^{16} + 452880 q^{17} - 49230 q^{18} - 1562100 q^{20} - 634176 q^{21} + 3176920 q^{22} + 6148560 q^{25} - 20346636 q^{26} + 12731840 q^{28} + 15498680 q^{30} - 37481400 q^{32} - 2488000 q^{33} + 24617980 q^{36} + 23039440 q^{37} - 26115120 q^{38} - 48114900 q^{40} - 18757824 q^{41} + 82830200 q^{42} + 78566320 q^{45} - 92534488 q^{46} + 46448320 q^{48} - 28839030 q^{50} + 234908620 q^{52} - 171595440 q^{53} - 177356448 q^{56} + 62365440 q^{57} + 150783080 q^{58} + 166923520 q^{60} - 252113984 q^{61} - 292810200 q^{62} - 72509520 q^{65} + 614341200 q^{66} - 782859900 q^{68} - 203227600 q^{70} + 1252703940 q^{72} - 20961680 q^{73} - 1061841600 q^{76} - 277316160 q^{77} + 49362600 q^{78} + 586589520 q^{80} - 933107568 q^{81} - 349461720 q^{82} + 3229742960 q^{85} - 874588728 q^{86} + 865939360 q^{88} + 1476868470 q^{90} - 1106673600 q^{92} - 2554477120 q^{93} + 1870685312 q^{96} + 5873785520 q^{97} - 5176905450 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.3139 + 9.96719i 0.897757 + 0.440492i
\(3\) −181.251 + 181.251i −1.29192 + 1.29192i −0.358321 + 0.933599i \(0.616651\pi\)
−0.933599 + 0.358321i \(0.883349\pi\)
\(4\) 313.310 + 404.945i 0.611934 + 0.790909i
\(5\) −997.734 978.597i −0.713920 0.700227i
\(6\) −5488.49 + 1875.36i −1.72891 + 0.590749i
\(7\) 1096.38 + 1096.38i 0.172592 + 0.172592i 0.788117 0.615525i \(-0.211056\pi\)
−0.615525 + 0.788117i \(0.711056\pi\)
\(8\) 2328.39 + 11348.8i 0.200979 + 0.979596i
\(9\) 46021.0i 2.33811i
\(10\) −10514.0 29823.7i −0.332483 0.943109i
\(11\) 24135.6i 0.497041i −0.968627 0.248520i \(-0.920056\pi\)
0.968627 0.248520i \(-0.0799443\pi\)
\(12\) −130185. 16609.0i −1.81236 0.231221i
\(13\) −34010.0 34010.0i −0.330264 0.330264i 0.522422 0.852687i \(-0.325028\pi\)
−0.852687 + 0.522422i \(0.825028\pi\)
\(14\) 11344.0 + 33199.6i 0.0789202 + 0.230971i
\(15\) 358212. 3468.70i 1.82696 0.0176912i
\(16\) −65817.5 + 253747.i −0.251074 + 0.967968i
\(17\) −348629. + 348629.i −1.01238 + 1.01238i −0.0124561 + 0.999922i \(0.503965\pi\)
−0.999922 + 0.0124561i \(0.996035\pi\)
\(18\) 458701. 934867.i 1.02992 2.09905i
\(19\) −764214. −1.34531 −0.672657 0.739954i \(-0.734847\pi\)
−0.672657 + 0.739954i \(0.734847\pi\)
\(20\) 83677.9 710632.i 0.116943 0.993139i
\(21\) −397441. −0.445950
\(22\) 240565. 490289.i 0.218942 0.446221i
\(23\) −27449.8 + 27449.8i −0.0204533 + 0.0204533i −0.717259 0.696806i \(-0.754604\pi\)
0.696806 + 0.717259i \(0.254604\pi\)
\(24\) −2.47902e6 1.63497e6i −1.52521 1.00591i
\(25\) 37822.1 + 1.95276e6i 0.0193649 + 0.999812i
\(26\) −351892. 1.02986e6i −0.151018 0.441976i
\(27\) 4.77380e6 + 4.77380e6i 1.72873 + 1.72873i
\(28\) −100467. + 787482.i −0.0308896 + 0.242119i
\(29\) 5.01486e6i 1.31664i −0.752737 0.658321i \(-0.771267\pi\)
0.752737 0.658321i \(-0.228733\pi\)
\(30\) 7.31127e6 + 3.49991e6i 1.64796 + 0.788880i
\(31\) 7.76401e6i 1.50993i 0.655762 + 0.754967i \(0.272347\pi\)
−0.655762 + 0.754967i \(0.727653\pi\)
\(32\) −3.86616e6 + 4.49858e6i −0.651785 + 0.758404i
\(33\) 4.37462e6 + 4.37462e6i 0.642136 + 0.642136i
\(34\) −1.05569e7 + 3.60716e6i −1.35481 + 0.462925i
\(35\) −20982.0 2.16681e6i −0.00236342 0.244070i
\(36\) 1.86360e7 1.44189e7i 1.84923 1.43077i
\(37\) 3.31907e6 3.31907e6i 0.291144 0.291144i −0.546388 0.837532i \(-0.683998\pi\)
0.837532 + 0.546388i \(0.183998\pi\)
\(38\) −1.55242e7 7.61707e6i −1.20777 0.592600i
\(39\) 1.23287e7 0.853350
\(40\) 8.78283e6 1.36017e7i 0.542456 0.840084i
\(41\) −9.42386e6 −0.520837 −0.260418 0.965496i \(-0.583860\pi\)
−0.260418 + 0.965496i \(0.583860\pi\)
\(42\) −8.07358e6 3.96137e6i −0.400354 0.196437i
\(43\) −1.86665e7 + 1.86665e7i −0.832634 + 0.832634i −0.987876 0.155242i \(-0.950384\pi\)
0.155242 + 0.987876i \(0.450384\pi\)
\(44\) 9.77362e6 7.56194e6i 0.393114 0.304156i
\(45\) −4.50360e7 + 4.59168e7i −1.63721 + 1.66923i
\(46\) −831210. + 284015.i −0.0273716 + 0.00935258i
\(47\) 1.31878e7 + 1.31878e7i 0.394213 + 0.394213i 0.876186 0.481973i \(-0.160080\pi\)
−0.481973 + 0.876186i \(0.660080\pi\)
\(48\) −3.40625e7 5.79215e7i −0.926170 1.57490i
\(49\) 3.79495e7i 0.940424i
\(50\) −1.86952e7 + 4.00452e7i −0.423024 + 0.906118i
\(51\) 1.26379e8i 2.61582i
\(52\) 3.11651e6 2.44279e7i 0.0591091 0.463309i
\(53\) 1.97306e7 + 1.97306e7i 0.343478 + 0.343478i 0.857673 0.514195i \(-0.171909\pi\)
−0.514195 + 0.857673i \(0.671909\pi\)
\(54\) 4.93932e7 + 1.44556e8i 0.790488 + 2.31347i
\(55\) −2.36191e7 + 2.40810e7i −0.348041 + 0.354847i
\(56\) −9.88986e6 + 1.49955e7i −0.134383 + 0.203758i
\(57\) 1.38515e8 1.38515e8i 1.73804 1.73804i
\(58\) 4.99841e7 1.01871e8i 0.579970 1.18202i
\(59\) −6.01499e7 −0.646250 −0.323125 0.946356i \(-0.604733\pi\)
−0.323125 + 0.946356i \(0.604733\pi\)
\(60\) 1.13636e8 + 1.43970e8i 1.13197 + 1.43414i
\(61\) −4.79920e7 −0.443797 −0.221899 0.975070i \(-0.571225\pi\)
−0.221899 + 0.975070i \(0.571225\pi\)
\(62\) −7.73853e7 + 1.57717e8i −0.665114 + 1.35555i
\(63\) 5.04566e7 5.04566e7i 0.403539 0.403539i
\(64\) −1.23375e8 + 5.28490e7i −0.919215 + 0.393756i
\(65\) 650868. + 6.72151e7i 0.00452254 + 0.467043i
\(66\) 4.52629e7 + 1.32468e8i 0.293626 + 0.859338i
\(67\) −3.56673e7 3.56673e7i −0.216239 0.216239i 0.590673 0.806911i \(-0.298862\pi\)
−0.806911 + 0.590673i \(0.798862\pi\)
\(68\) −2.50404e8 3.19466e7i −1.42021 0.181190i
\(69\) 9.95061e6i 0.0528481i
\(70\) 2.11708e7 4.42256e7i 0.105389 0.220157i
\(71\) 2.39980e8i 1.12076i 0.828237 + 0.560379i \(0.189344\pi\)
−0.828237 + 0.560379i \(0.810656\pi\)
\(72\) 5.22286e8 1.07155e8i 2.29040 0.469911i
\(73\) 2.27428e8 + 2.27428e8i 0.937326 + 0.937326i 0.998149 0.0608227i \(-0.0193724\pi\)
−0.0608227 + 0.998149i \(0.519372\pi\)
\(74\) 1.00505e8 3.43415e7i 0.389623 0.133130i
\(75\) −3.60795e8 3.47085e8i −1.31669 1.26666i
\(76\) −2.39436e8 3.09465e8i −0.823244 1.06402i
\(77\) 2.64619e7 2.64619e7i 0.0857852 0.0857852i
\(78\) 2.50445e8 + 1.22883e8i 0.766101 + 0.375894i
\(79\) −1.40201e8 −0.404976 −0.202488 0.979285i \(-0.564903\pi\)
−0.202488 + 0.979285i \(0.564903\pi\)
\(80\) 3.13984e8 1.88763e8i 0.857044 0.515244i
\(81\) −8.24684e8 −2.12865
\(82\) −1.91435e8 9.39294e7i −0.467584 0.229424i
\(83\) 3.59910e8 3.59910e8i 0.832419 0.832419i −0.155428 0.987847i \(-0.549676\pi\)
0.987847 + 0.155428i \(0.0496756\pi\)
\(84\) −1.24522e8 1.60942e8i −0.272892 0.352706i
\(85\) 6.89006e8 6.67189e6i 1.43165 0.0138632i
\(86\) −5.65242e8 + 1.93137e8i −1.11427 + 0.380734i
\(87\) 9.08950e8 + 9.08950e8i 1.70100 + 1.70100i
\(88\) 2.73912e8 5.61971e7i 0.486899 0.0998947i
\(89\) 2.91347e8i 0.492215i 0.969242 + 0.246108i \(0.0791517\pi\)
−0.969242 + 0.246108i \(0.920848\pi\)
\(90\) −1.37252e9 + 4.83866e8i −2.20509 + 0.777382i
\(91\) 7.45759e7i 0.114002i
\(92\) −1.97160e7 2.51536e6i −0.0286928 0.00366063i
\(93\) −1.40724e9 1.40724e9i −1.95071 1.95071i
\(94\) 1.36450e8 + 3.99341e8i 0.180260 + 0.527555i
\(95\) 7.62483e8 + 7.47858e8i 0.960448 + 0.942025i
\(96\) −1.14628e8 1.51612e9i −0.137743 1.82185i
\(97\) −1.13368e8 + 1.13368e8i −0.130022 + 0.130022i −0.769123 0.639101i \(-0.779307\pi\)
0.639101 + 0.769123i \(0.279307\pi\)
\(98\) 3.78250e8 7.70903e8i 0.414249 0.844272i
\(99\) −1.11075e9 −1.16214
\(100\) −7.78911e8 + 6.27135e8i −0.778911 + 0.627135i
\(101\) 1.21402e9 1.16086 0.580431 0.814309i \(-0.302884\pi\)
0.580431 + 0.814309i \(0.302884\pi\)
\(102\) 1.25964e9 2.56725e9i 1.15225 2.34837i
\(103\) −6.91006e7 + 6.91006e7i −0.0604943 + 0.0604943i −0.736707 0.676212i \(-0.763620\pi\)
0.676212 + 0.736707i \(0.263620\pi\)
\(104\) 3.06786e8 4.65163e8i 0.257149 0.389902i
\(105\) 3.96541e8 + 3.88935e8i 0.318373 + 0.312266i
\(106\) 2.04147e8 + 5.97465e8i 0.157060 + 0.459659i
\(107\) −1.43181e8 1.43181e8i −0.105599 0.105599i 0.652333 0.757932i \(-0.273790\pi\)
−0.757932 + 0.652333i \(0.773790\pi\)
\(108\) −4.37448e8 + 3.42881e9i −0.309400 + 2.42514i
\(109\) 2.39868e9i 1.62762i 0.581133 + 0.813809i \(0.302610\pi\)
−0.581133 + 0.813809i \(0.697390\pi\)
\(110\) −7.19815e8 + 2.53763e8i −0.468764 + 0.165257i
\(111\) 1.20317e9i 0.752270i
\(112\) −3.50365e8 + 2.06042e8i −0.210397 + 0.123730i
\(113\) 9.12342e7 + 9.12342e7i 0.0526386 + 0.0526386i 0.732936 0.680297i \(-0.238149\pi\)
−0.680297 + 0.732936i \(0.738149\pi\)
\(114\) 4.19438e9 1.43317e9i 2.32593 0.794744i
\(115\) 5.42498e7 525321.i 0.0289240 0.000280082i
\(116\) 2.03074e9 1.57121e9i 1.04134 0.805698i
\(117\) −1.56518e9 + 1.56518e9i −0.772195 + 0.772195i
\(118\) −1.22188e9 5.99525e8i −0.580175 0.284668i
\(119\) −7.64460e8 −0.349457
\(120\) 8.73424e8 + 4.05722e9i 0.384511 + 1.78613i
\(121\) 1.77542e9 0.752951
\(122\) −9.74905e8 4.78345e8i −0.398422 0.195489i
\(123\) 1.70809e9 1.70809e9i 0.672879 0.672879i
\(124\) −3.14400e9 + 2.43254e9i −1.19422 + 0.923980i
\(125\) 1.87323e9 1.98535e9i 0.686270 0.727346i
\(126\) 1.52788e9 5.22061e8i 0.540036 0.184524i
\(127\) −1.18688e9 1.18688e9i −0.404848 0.404848i 0.475090 0.879937i \(-0.342416\pi\)
−0.879937 + 0.475090i \(0.842416\pi\)
\(128\) −3.03298e9 1.56131e8i −0.998678 0.0514095i
\(129\) 6.76665e9i 2.15139i
\(130\) −6.56724e8 + 1.37189e9i −0.201668 + 0.421283i
\(131\) 2.35144e8i 0.0697611i 0.999391 + 0.0348805i \(0.0111051\pi\)
−0.999391 + 0.0348805i \(0.988895\pi\)
\(132\) −4.00869e8 + 3.14209e9i −0.114926 + 0.900816i
\(133\) −8.37870e8 8.37870e8i −0.232191 0.232191i
\(134\) −3.69040e8 1.08004e9i −0.0988784 0.289381i
\(135\) −9.13588e7 9.43461e9i −0.0236727 2.44468i
\(136\) −4.76828e9 3.14479e9i −1.19519 0.788255i
\(137\) 9.71772e8 9.71772e8i 0.235679 0.235679i −0.579379 0.815058i \(-0.696705\pi\)
0.815058 + 0.579379i \(0.196705\pi\)
\(138\) 9.91797e7 2.02136e8i 0.0232791 0.0474447i
\(139\) −7.42286e9 −1.68657 −0.843286 0.537466i \(-0.819382\pi\)
−0.843286 + 0.537466i \(0.819382\pi\)
\(140\) 8.70867e8 6.87381e8i 0.191591 0.151224i
\(141\) −4.78060e9 −1.01858
\(142\) −2.39192e9 + 4.87492e9i −0.493684 + 1.00617i
\(143\) −8.20854e8 + 8.20854e8i −0.164155 + 0.164155i
\(144\) 1.16777e10 + 3.02899e9i 2.26322 + 0.587038i
\(145\) −4.90753e9 + 5.00350e9i −0.921948 + 0.939978i
\(146\) 2.35313e9 + 6.88676e9i 0.428606 + 1.25437i
\(147\) 6.87840e9 + 6.87840e9i 1.21495 + 1.21495i
\(148\) 2.38394e9 + 3.04143e8i 0.408430 + 0.0521075i
\(149\) 5.14844e9i 0.855731i −0.903842 0.427865i \(-0.859266\pi\)
0.903842 0.427865i \(-0.140734\pi\)
\(150\) −3.86970e9 1.06468e10i −0.624119 1.71715i
\(151\) 1.40337e9i 0.219672i 0.993950 + 0.109836i \(0.0350326\pi\)
−0.993950 + 0.109836i \(0.964967\pi\)
\(152\) −1.77939e9 8.67295e9i −0.270380 1.31786i
\(153\) 1.60443e10 + 1.60443e10i 2.36705 + 2.36705i
\(154\) 8.01295e8 2.73794e8i 0.114802 0.0392266i
\(155\) 7.59783e9 7.74641e9i 1.05730 1.07797i
\(156\) 3.86271e9 + 4.99246e9i 0.522194 + 0.674922i
\(157\) −6.62080e9 + 6.62080e9i −0.869686 + 0.869686i −0.992437 0.122752i \(-0.960828\pi\)
0.122752 + 0.992437i \(0.460828\pi\)
\(158\) −2.84803e9 1.39741e9i −0.363570 0.178389i
\(159\) −7.15240e9 −0.887492
\(160\) 8.25969e9 7.04980e8i 0.996377 0.0850427i
\(161\) −6.01909e7 −0.00706015
\(162\) −1.67526e10 8.21978e9i −1.91101 0.937654i
\(163\) −2.49844e9 + 2.49844e9i −0.277220 + 0.277220i −0.831998 0.554778i \(-0.812803\pi\)
0.554778 + 0.831998i \(0.312803\pi\)
\(164\) −2.95259e9 3.81615e9i −0.318718 0.411934i
\(165\) −8.37194e7 8.64569e9i −0.00879323 0.908075i
\(166\) 1.08985e10 3.72389e9i 1.11398 0.380636i
\(167\) −8.01922e8 8.01922e8i −0.0797825 0.0797825i 0.666089 0.745872i \(-0.267967\pi\)
−0.745872 + 0.666089i \(0.767967\pi\)
\(168\) −9.25397e8 4.51050e9i −0.0896265 0.436850i
\(169\) 8.29114e9i 0.781851i
\(170\) 1.40629e10 + 6.73192e9i 1.29138 + 0.618185i
\(171\) 3.51699e10i 3.14550i
\(172\) −1.34073e10 1.71051e9i −1.16806 0.149021i
\(173\) −1.61822e9 1.61822e9i −0.137350 0.137350i 0.635089 0.772439i \(-0.280963\pi\)
−0.772439 + 0.635089i \(0.780963\pi\)
\(174\) 9.40465e9 + 2.75240e10i 0.777806 + 2.27636i
\(175\) −2.09950e9 + 2.18244e9i −0.169217 + 0.175902i
\(176\) 6.12435e9 + 1.58855e9i 0.481119 + 0.124794i
\(177\) 1.09022e10 1.09022e10i 0.834903 0.834903i
\(178\) −2.90391e9 + 5.91839e9i −0.216817 + 0.441890i
\(179\) 1.91562e10 1.39467 0.697333 0.716747i \(-0.254370\pi\)
0.697333 + 0.716747i \(0.254370\pi\)
\(180\) −3.27040e10 3.85094e9i −2.32207 0.273427i
\(181\) −1.20403e10 −0.833843 −0.416922 0.908942i \(-0.636891\pi\)
−0.416922 + 0.908942i \(0.636891\pi\)
\(182\) 7.43313e8 1.51493e9i 0.0502169 0.102346i
\(183\) 8.69861e9 8.69861e9i 0.573350 0.573350i
\(184\) −3.75437e8 2.47610e8i −0.0241467 0.0159253i
\(185\) −6.55958e9 + 6.35188e7i −0.411721 + 0.00398685i
\(186\) −1.45603e10 4.26127e10i −0.891993 2.61054i
\(187\) 8.41438e9 + 8.41438e9i 0.503193 + 0.503193i
\(188\) −1.20846e9 + 9.47220e9i −0.0705543 + 0.553019i
\(189\) 1.04678e10i 0.596730i
\(190\) 8.03497e9 + 2.27917e10i 0.447294 + 1.26878i
\(191\) 1.57499e10i 0.856302i −0.903707 0.428151i \(-0.859165\pi\)
0.903707 0.428151i \(-0.140835\pi\)
\(192\) 1.27829e10 3.19408e10i 0.678850 1.69625i
\(193\) 9.45536e8 + 9.45536e8i 0.0490535 + 0.0490535i 0.731208 0.682155i \(-0.238957\pi\)
−0.682155 + 0.731208i \(0.738957\pi\)
\(194\) −3.43291e9 + 1.17299e9i −0.174002 + 0.0594547i
\(195\) −1.23008e10 1.20648e10i −0.609224 0.597539i
\(196\) 1.53675e10 1.18900e10i 0.743790 0.575477i
\(197\) −1.80154e10 + 1.80154e10i −0.852208 + 0.852208i −0.990405 0.138197i \(-0.955869\pi\)
0.138197 + 0.990405i \(0.455869\pi\)
\(198\) −2.25636e10 1.10710e10i −1.04332 0.511911i
\(199\) −2.43161e10 −1.09915 −0.549573 0.835446i \(-0.685210\pi\)
−0.549573 + 0.835446i \(0.685210\pi\)
\(200\) −2.20735e10 + 4.97602e9i −0.975520 + 0.219911i
\(201\) 1.29295e10 0.558726
\(202\) 2.46616e10 + 1.21004e10i 1.04217 + 0.511350i
\(203\) 5.49820e9 5.49820e9i 0.227242 0.227242i
\(204\) 5.11765e10 3.95958e10i 2.06888 1.60071i
\(205\) 9.40251e9 + 9.22216e9i 0.371836 + 0.364704i
\(206\) −2.09244e9 + 7.14965e8i −0.0809564 + 0.0276619i
\(207\) 1.26327e9 + 1.26327e9i 0.0478221 + 0.0478221i
\(208\) 1.08684e10 6.39149e9i 0.402606 0.236765i
\(209\) 1.84448e10i 0.668676i
\(210\) 4.17871e9 + 1.18532e10i 0.148271 + 0.420579i
\(211\) 2.79442e10i 0.970558i −0.874359 0.485279i \(-0.838718\pi\)
0.874359 0.485279i \(-0.161282\pi\)
\(212\) −1.80802e9 + 1.41716e10i −0.0614740 + 0.481846i
\(213\) −4.34966e10 4.34966e10i −1.44793 1.44793i
\(214\) −1.48146e9 4.33569e9i −0.0482866 0.141317i
\(215\) 3.68911e10 3.57230e8i 1.17747 0.0114019i
\(216\) −4.30619e10 + 6.52924e10i −1.34602 + 2.04090i
\(217\) −8.51231e9 + 8.51231e9i −0.260603 + 0.260603i
\(218\) −2.39081e10 + 4.87265e10i −0.716952 + 1.46120i
\(219\) −8.24431e10 −2.42190
\(220\) −1.71516e10 2.01962e9i −0.493630 0.0581256i
\(221\) 2.37137e10 0.668705
\(222\) −1.19922e10 + 2.44411e10i −0.331369 + 0.675355i
\(223\) −9.99812e9 + 9.99812e9i −0.270736 + 0.270736i −0.829397 0.558660i \(-0.811316\pi\)
0.558660 + 0.829397i \(0.311316\pi\)
\(224\) −9.17094e9 + 6.93379e8i −0.243387 + 0.0184015i
\(225\) 8.98680e10 1.74061e9i 2.33767 0.0452773i
\(226\) 9.43975e8 + 2.76267e9i 0.0240698 + 0.0704436i
\(227\) 6.76675e8 + 6.76675e8i 0.0169147 + 0.0169147i 0.715514 0.698599i \(-0.246193\pi\)
−0.698599 + 0.715514i \(0.746193\pi\)
\(228\) 9.94890e10 + 1.26928e10i 2.43819 + 0.311065i
\(229\) 5.99302e10i 1.44008i −0.693933 0.720040i \(-0.744124\pi\)
0.693933 0.720040i \(-0.255876\pi\)
\(230\) 1.10726e9 + 5.30047e8i 0.0260901 + 0.0124893i
\(231\) 9.59250e9i 0.221655i
\(232\) 5.69129e10 1.16765e10i 1.28978 0.264617i
\(233\) −1.34961e10 1.34961e10i −0.299990 0.299990i 0.541020 0.841010i \(-0.318038\pi\)
−0.841010 + 0.541020i \(0.818038\pi\)
\(234\) −4.73953e10 + 1.61944e10i −1.03339 + 0.353098i
\(235\) −2.52382e8 2.60634e10i −0.00539824 0.557476i
\(236\) −1.88456e10 2.43574e10i −0.395462 0.511125i
\(237\) 2.54116e10 2.54116e10i 0.523197 0.523197i
\(238\) −1.55292e10 7.61952e9i −0.313727 0.153933i
\(239\) 3.23573e10 0.641478 0.320739 0.947168i \(-0.396069\pi\)
0.320739 + 0.947168i \(0.396069\pi\)
\(240\) −2.26965e10 + 9.11236e10i −0.441578 + 1.77288i
\(241\) 3.28641e10 0.627545 0.313773 0.949498i \(-0.398407\pi\)
0.313773 + 0.949498i \(0.398407\pi\)
\(242\) 3.60657e10 + 1.76959e10i 0.675967 + 0.331669i
\(243\) 5.55122e10 5.55122e10i 1.02132 1.02132i
\(244\) −1.50364e10 1.94341e10i −0.271575 0.351003i
\(245\) −3.71373e10 + 3.78635e10i −0.658510 + 0.671388i
\(246\) 5.17227e10 1.76731e10i 0.900479 0.307684i
\(247\) 2.59909e10 + 2.59909e10i 0.444310 + 0.444310i
\(248\) −8.81125e10 + 1.80776e10i −1.47913 + 0.303465i
\(249\) 1.30468e11i 2.15084i
\(250\) 5.78409e10 2.16594e10i 0.936494 0.350684i
\(251\) 1.72860e10i 0.274893i −0.990509 0.137447i \(-0.956110\pi\)
0.990509 0.137447i \(-0.0438895\pi\)
\(252\) 3.62407e10 + 4.62360e9i 0.566102 + 0.0722234i
\(253\) 6.62518e8 + 6.62518e8i 0.0101661 + 0.0101661i
\(254\) −1.22804e10 3.59402e10i −0.185123 0.541787i
\(255\) −1.23674e11 + 1.26092e11i −1.83167 + 1.86749i
\(256\) −6.00556e10 3.34020e10i −0.873924 0.486063i
\(257\) 1.34525e10 1.34525e10i 0.192356 0.192356i −0.604358 0.796713i \(-0.706570\pi\)
0.796713 + 0.604358i \(0.206570\pi\)
\(258\) 6.74444e10 1.37457e11i 0.947671 1.93143i
\(259\) 7.27793e9 0.100498
\(260\) −2.70145e10 + 2.13227e10i −0.366621 + 0.289376i
\(261\) −2.30789e11 −3.07846
\(262\) −2.34373e9 + 4.77670e9i −0.0307292 + 0.0626285i
\(263\) 6.03390e9 6.03390e9i 0.0777673 0.0777673i −0.667153 0.744921i \(-0.732487\pi\)
0.744921 + 0.667153i \(0.232487\pi\)
\(264\) −3.94610e10 + 5.98327e10i −0.499978 + 0.758090i
\(265\) −3.77595e8 3.89942e10i −0.00470349 0.485729i
\(266\) −8.66921e9 2.53716e10i −0.106173 0.310729i
\(267\) −5.28070e10 5.28070e10i −0.635903 0.635903i
\(268\) 3.26838e9 2.56182e10i 0.0387013 0.303349i
\(269\) 1.62845e10i 0.189623i 0.995495 + 0.0948114i \(0.0302248\pi\)
−0.995495 + 0.0948114i \(0.969775\pi\)
\(270\) 9.21808e10 1.92565e11i 1.05561 2.20516i
\(271\) 1.82399e10i 0.205429i 0.994711 + 0.102714i \(0.0327527\pi\)
−0.994711 + 0.102714i \(0.967247\pi\)
\(272\) −6.55176e10 1.11409e11i −0.725768 1.23413i
\(273\) 1.35170e10 + 1.35170e10i 0.147281 + 0.147281i
\(274\) 2.94263e10 1.00547e10i 0.315398 0.107768i
\(275\) 4.71311e10 9.12861e8i 0.496947 0.00962515i
\(276\) 4.02946e9 3.11763e9i 0.0417980 0.0323395i
\(277\) 4.29789e10 4.29789e10i 0.438628 0.438628i −0.452922 0.891550i \(-0.649619\pi\)
0.891550 + 0.452922i \(0.149619\pi\)
\(278\) −1.50787e11 7.39851e10i −1.51413 0.742921i
\(279\) 3.57308e11 3.53040
\(280\) 2.45420e10 5.28330e9i 0.238615 0.0513682i
\(281\) 1.83347e11 1.75427 0.877134 0.480246i \(-0.159453\pi\)
0.877134 + 0.480246i \(0.159453\pi\)
\(282\) −9.71128e10 4.76492e10i −0.914440 0.448678i
\(283\) −1.33619e11 + 1.33619e11i −1.23831 + 1.23831i −0.277612 + 0.960693i \(0.589543\pi\)
−0.960693 + 0.277612i \(0.910457\pi\)
\(284\) −9.71786e10 + 7.51880e10i −0.886417 + 0.685829i
\(285\) −2.73751e11 + 2.65083e9i −2.45784 + 0.0238002i
\(286\) −2.48564e10 + 8.49315e9i −0.219680 + 0.0750622i
\(287\) −1.03321e10 1.03321e10i −0.0898922 0.0898922i
\(288\) 2.07029e11 + 1.77924e11i 1.77323 + 1.52395i
\(289\) 1.24496e11i 1.04982i
\(290\) −1.49562e11 + 5.27264e10i −1.24174 + 0.437761i
\(291\) 4.10962e10i 0.335957i
\(292\) −2.08404e10 + 1.63351e11i −0.167758 + 1.31492i
\(293\) 1.37563e11 + 1.37563e11i 1.09043 + 1.09043i 0.995482 + 0.0949453i \(0.0302676\pi\)
0.0949453 + 0.995482i \(0.469732\pi\)
\(294\) 7.11688e10 + 2.08285e11i 0.555555 + 1.62591i
\(295\) 6.00136e10 + 5.88625e10i 0.461371 + 0.452522i
\(296\) 4.53957e10 + 2.99395e10i 0.343718 + 0.226690i
\(297\) 1.15219e11 1.15219e11i 0.859250 0.859250i
\(298\) 5.13155e10 1.04585e11i 0.376942 0.768238i
\(299\) 1.86714e9 0.0135100
\(300\) 2.75095e10 2.54848e11i 0.196082 1.81650i
\(301\) −4.09312e10 −0.287412
\(302\) −1.39876e10 + 2.85079e10i −0.0967639 + 0.197212i
\(303\) −2.20043e11 + 2.20043e11i −1.49974 + 1.49974i
\(304\) 5.02986e10 1.93917e11i 0.337773 1.30222i
\(305\) 4.78832e10 + 4.69648e10i 0.316836 + 0.310759i
\(306\) 1.66005e11 + 4.85838e11i 1.08237 + 3.16771i
\(307\) 6.55913e10 + 6.55913e10i 0.421428 + 0.421428i 0.885695 0.464267i \(-0.153682\pi\)
−0.464267 + 0.885695i \(0.653682\pi\)
\(308\) 1.90064e10 + 2.42484e9i 0.120343 + 0.0153534i
\(309\) 2.50492e10i 0.156308i
\(310\) 2.31552e11 8.16310e10i 1.42403 0.502027i
\(311\) 3.02220e11i 1.83190i −0.401296 0.915948i \(-0.631440\pi\)
0.401296 0.915948i \(-0.368560\pi\)
\(312\) 2.87060e10 + 1.39917e11i 0.171505 + 0.835938i
\(313\) 1.00016e11 + 1.00016e11i 0.589008 + 0.589008i 0.937363 0.348354i \(-0.113259\pi\)
−0.348354 + 0.937363i \(0.613259\pi\)
\(314\) −2.00485e11 + 6.85036e10i −1.16386 + 0.397677i
\(315\) −9.97190e10 + 9.65615e8i −0.570664 + 0.00552595i
\(316\) −4.39265e10 5.67738e10i −0.247819 0.320299i
\(317\) −1.06789e11 + 1.06789e11i −0.593963 + 0.593963i −0.938699 0.344737i \(-0.887968\pi\)
0.344737 + 0.938699i \(0.387968\pi\)
\(318\) −1.45293e11 7.12893e10i −0.796752 0.390933i
\(319\) −1.21037e11 −0.654425
\(320\) 1.74813e11 + 6.80050e10i 0.931965 + 0.362548i
\(321\) 5.19036e10 0.272850
\(322\) −1.22271e9 5.99934e8i −0.00633830 0.00310994i
\(323\) 2.66427e11 2.66427e11i 1.36197 1.36197i
\(324\) −2.58382e11 3.33952e11i −1.30259 1.68357i
\(325\) 6.51270e10 6.76997e10i 0.323807 0.336598i
\(326\) −7.56556e10 + 2.58507e10i −0.370990 + 0.126763i
\(327\) −4.34763e11 4.34763e11i −2.10275 2.10275i
\(328\) −2.19424e10 1.06950e11i −0.104677 0.510209i
\(329\) 2.89177e10i 0.136076i
\(330\) 8.44726e10 1.76462e11i 0.392106 0.819104i
\(331\) 3.53429e11i 1.61837i 0.587557 + 0.809183i \(0.300090\pi\)
−0.587557 + 0.809183i \(0.699910\pi\)
\(332\) 2.58507e11 + 3.29804e10i 1.16775 + 0.148982i
\(333\) −1.52747e11 1.52747e11i −0.680728 0.680728i
\(334\) −8.29726e9 2.42831e10i −0.0364817 0.106769i
\(335\) 6.82584e8 + 7.04904e10i 0.00296111 + 0.305793i
\(336\) 2.61586e10 1.00849e11i 0.111966 0.431665i
\(337\) −2.43330e11 + 2.43330e11i −1.02769 + 1.02769i −0.0280829 + 0.999606i \(0.508940\pi\)
−0.999606 + 0.0280829i \(0.991060\pi\)
\(338\) 8.26393e10 1.68425e11i 0.344399 0.701912i
\(339\) −3.30726e10 −0.136010
\(340\) 2.18574e11 + 2.76919e11i 0.887041 + 1.12382i
\(341\) 1.87389e11 0.750499
\(342\) −3.50545e11 + 7.14439e11i −1.38556 + 2.82389i
\(343\) 8.58501e10 8.58501e10i 0.334902 0.334902i
\(344\) −2.55306e11 1.68380e11i −0.982987 0.648303i
\(345\) −9.73764e9 + 9.92807e9i −0.0370056 + 0.0377293i
\(346\) −1.67432e10 4.90014e10i −0.0628054 0.183809i
\(347\) 6.41385e10 + 6.41385e10i 0.237485 + 0.237485i 0.815808 0.578323i \(-0.196293\pi\)
−0.578323 + 0.815808i \(0.696293\pi\)
\(348\) −8.32918e10 + 6.52858e11i −0.304436 + 2.38623i
\(349\) 2.06015e11i 0.743335i −0.928366 0.371667i \(-0.878786\pi\)
0.928366 0.371667i \(-0.121214\pi\)
\(350\) −6.44018e10 + 2.34077e10i −0.229399 + 0.0833782i
\(351\) 3.24714e11i 1.14188i
\(352\) 1.08576e11 + 9.33121e10i 0.376957 + 0.323964i
\(353\) −1.87527e11 1.87527e11i −0.642803 0.642803i 0.308440 0.951244i \(-0.400193\pi\)
−0.951244 + 0.308440i \(0.900193\pi\)
\(354\) 3.30132e11 1.12802e11i 1.11731 0.381772i
\(355\) 2.34843e11 2.39436e11i 0.784784 0.800132i
\(356\) −1.17980e11 + 9.12819e10i −0.389298 + 0.301203i
\(357\) 1.38559e11 1.38559e11i 0.451470 0.451470i
\(358\) 3.89137e11 + 1.90933e11i 1.25207 + 0.614339i
\(359\) 5.56594e11 1.76854 0.884268 0.466980i \(-0.154658\pi\)
0.884268 + 0.466980i \(0.154658\pi\)
\(360\) −6.25964e11 4.04195e11i −1.96421 1.26832i
\(361\) 2.61336e11 0.809872
\(362\) −2.44586e11 1.20008e11i −0.748588 0.367301i
\(363\) −3.21797e11 + 3.21797e11i −0.972752 + 0.972752i
\(364\) 3.01992e10 2.33654e10i 0.0901652 0.0697617i
\(365\) −4.35241e9 4.49473e11i −0.0128355 1.32552i
\(366\) 2.63403e11 9.00021e10i 0.767285 0.262173i
\(367\) −4.15041e11 4.15041e11i −1.19425 1.19425i −0.975863 0.218383i \(-0.929922\pi\)
−0.218383 0.975863i \(-0.570078\pi\)
\(368\) −5.15862e9 8.77197e9i −0.0146629 0.0249334i
\(369\) 4.33696e11i 1.21777i
\(370\) −1.33884e11 6.40902e10i −0.371381 0.177780i
\(371\) 4.32646e10i 0.118563i
\(372\) 1.28952e11 1.01075e12i 0.349129 2.73655i
\(373\) −1.85481e11 1.85481e11i −0.496146 0.496146i 0.414090 0.910236i \(-0.364100\pi\)
−0.910236 + 0.414090i \(0.864100\pi\)
\(374\) 8.70612e10 + 2.54797e11i 0.230093 + 0.673397i
\(375\) 2.03219e10 + 6.99371e11i 0.0530669 + 1.82628i
\(376\) −1.18960e11 + 1.80372e11i −0.306941 + 0.465398i
\(377\) −1.70556e11 + 1.70556e11i −0.434840 + 0.434840i
\(378\) −1.04335e11 + 2.12642e11i −0.262855 + 0.535719i
\(379\) −3.38128e11 −0.841791 −0.420895 0.907109i \(-0.638284\pi\)
−0.420895 + 0.907109i \(0.638284\pi\)
\(380\) −6.39478e10 + 5.43075e11i −0.157326 + 1.33608i
\(381\) 4.30249e11 1.04606
\(382\) 1.56982e11 3.19941e11i 0.377194 0.768751i
\(383\) −2.23635e11 + 2.23635e11i −0.531063 + 0.531063i −0.920889 0.389826i \(-0.872535\pi\)
0.389826 + 0.920889i \(0.372535\pi\)
\(384\) 5.78031e11 5.21433e11i 1.35663 1.22379i
\(385\) −5.22974e10 + 5.06415e8i −0.121313 + 0.00117472i
\(386\) 9.78319e9 + 2.86319e10i 0.0224304 + 0.0656458i
\(387\) 8.59051e11 + 8.59051e11i 1.94679 + 1.94679i
\(388\) −8.14273e10 1.03885e10i −0.182401 0.0232707i
\(389\) 7.92082e11i 1.75387i 0.480611 + 0.876934i \(0.340415\pi\)
−0.480611 + 0.876934i \(0.659585\pi\)
\(390\) −1.29624e11 3.67688e11i −0.283724 0.804802i
\(391\) 1.91396e10i 0.0414130i
\(392\) 4.30683e11 8.83612e10i 0.921235 0.189005i
\(393\) −4.26202e10 4.26202e10i −0.0901257 0.0901257i
\(394\) −5.45526e11 + 1.86400e11i −1.14047 + 0.389685i
\(395\) 1.39884e11 + 1.37200e11i 0.289121 + 0.283575i
\(396\) −3.48008e11 4.49792e11i −0.711150 0.919144i
\(397\) −5.19606e11 + 5.19606e11i −1.04982 + 1.04982i −0.0511323 + 0.998692i \(0.516283\pi\)
−0.998692 + 0.0511323i \(0.983717\pi\)
\(398\) −4.93956e11 2.42363e11i −0.986766 0.484165i
\(399\) 3.03730e11 0.599943
\(400\) −4.97996e11 1.18928e11i −0.972648 0.232282i
\(401\) −6.48299e11 −1.25206 −0.626031 0.779798i \(-0.715322\pi\)
−0.626031 + 0.779798i \(0.715322\pi\)
\(402\) 2.62648e11 + 1.28871e11i 0.501600 + 0.246114i
\(403\) 2.64054e11 2.64054e11i 0.498678 0.498678i
\(404\) 3.80366e11 + 4.91613e11i 0.710371 + 0.918136i
\(405\) 8.22815e11 + 8.07033e11i 1.51969 + 1.49054i
\(406\) 1.66492e11 5.68884e10i 0.304106 0.103910i
\(407\) −8.01078e10 8.01078e10i −0.144711 0.144711i
\(408\) 1.43425e12 2.94259e11i 2.56245 0.525725i
\(409\) 4.02151e11i 0.710614i −0.934750 0.355307i \(-0.884376\pi\)
0.934750 0.355307i \(-0.115624\pi\)
\(410\) 9.90827e10 + 2.81055e11i 0.173169 + 0.491206i
\(411\) 3.52270e11i 0.608958i
\(412\) −4.96319e10 6.33205e9i −0.0848640 0.0108270i
\(413\) −6.59472e10 6.59472e10i −0.111538 0.111538i
\(414\) 1.30707e10 + 3.82531e10i 0.0218674 + 0.0639979i
\(415\) −7.11301e11 + 6.88779e9i −1.17716 + 0.0113989i
\(416\) 2.84485e11 2.15088e10i 0.465735 0.0352124i
\(417\) 1.34540e12 1.34540e12i 2.17891 2.17891i
\(418\) −1.83843e11 + 3.74686e11i −0.294546 + 0.600308i
\(419\) −6.71603e11 −1.06451 −0.532255 0.846584i \(-0.678655\pi\)
−0.532255 + 0.846584i \(0.678655\pi\)
\(420\) −3.32570e10 + 2.82434e11i −0.0521509 + 0.442890i
\(421\) −6.78707e11 −1.05296 −0.526481 0.850187i \(-0.676489\pi\)
−0.526481 + 0.850187i \(0.676489\pi\)
\(422\) 2.78526e11 5.67657e11i 0.427523 0.871325i
\(423\) 6.06915e11 6.06915e11i 0.921715 0.921715i
\(424\) −1.77979e11 + 2.69860e11i −0.267438 + 0.405502i
\(425\) −6.93974e11 6.67602e11i −1.03179 0.992584i
\(426\) −4.50047e11 1.31712e12i −0.662087 1.93769i
\(427\) −5.26175e10 5.26175e10i −0.0765958 0.0765958i
\(428\) 1.31204e10 1.02841e11i 0.0188995 0.148139i
\(429\) 2.97562e11i 0.424150i
\(430\) 7.52964e11 + 3.60444e11i 1.06210 + 0.508429i
\(431\) 7.68945e11i 1.07336i 0.843784 + 0.536682i \(0.180323\pi\)
−0.843784 + 0.536682i \(0.819677\pi\)
\(432\) −1.52554e12 + 8.97139e11i −2.10740 + 1.23932i
\(433\) 8.37526e11 + 8.37526e11i 1.14499 + 1.14499i 0.987524 + 0.157469i \(0.0503334\pi\)
0.157469 + 0.987524i \(0.449667\pi\)
\(434\) −2.57762e11 + 8.80745e10i −0.348751 + 0.119164i
\(435\) −1.73951e10 1.79639e12i −0.0232929 2.40546i
\(436\) −9.71333e11 + 7.51530e11i −1.28730 + 0.995994i
\(437\) 2.09775e10 2.09775e10i 0.0275161 0.0275161i
\(438\) −1.67474e12 8.21727e11i −2.17428 1.06683i
\(439\) 4.39195e11 0.564374 0.282187 0.959359i \(-0.408940\pi\)
0.282187 + 0.959359i \(0.408940\pi\)
\(440\) −3.28285e11 2.11979e11i −0.417556 0.269623i
\(441\) −1.74648e12 −2.19882
\(442\) 4.81719e11 + 2.36359e11i 0.600335 + 0.294559i
\(443\) 9.25287e11 9.25287e11i 1.14146 1.14146i 0.153274 0.988184i \(-0.451018\pi\)
0.988184 0.153274i \(-0.0489816\pi\)
\(444\) −4.87218e11 + 3.76966e11i −0.594977 + 0.460340i
\(445\) 2.85111e11 2.90687e11i 0.344662 0.351403i
\(446\) −3.02754e11 + 1.03448e11i −0.362312 + 0.123798i
\(447\) 9.33161e11 + 9.33161e11i 1.10554 + 1.10554i
\(448\) −1.93209e11 7.73233e10i −0.226608 0.0906900i
\(449\) 1.21765e12i 1.41389i −0.707271 0.706943i \(-0.750074\pi\)
0.707271 0.706943i \(-0.249926\pi\)
\(450\) 1.84292e12 + 8.60373e11i 2.11861 + 0.989078i
\(451\) 2.27451e11i 0.258877i
\(452\) −8.36026e9 + 6.55294e10i −0.00942099 + 0.0738437i
\(453\) −2.54362e11 2.54362e11i −0.283799 0.283799i
\(454\) 7.00137e9 + 2.04905e10i 0.00773449 + 0.0226360i
\(455\) −7.29798e10 + 7.44070e10i −0.0798272 + 0.0813883i
\(456\) 1.89450e12 + 1.24947e12i 2.05188 + 1.35327i
\(457\) −5.45551e11 + 5.45551e11i −0.585076 + 0.585076i −0.936294 0.351218i \(-0.885768\pi\)
0.351218 + 0.936294i \(0.385768\pi\)
\(458\) 5.97336e11 1.21742e12i 0.634343 1.29284i
\(459\) −3.32857e12 −3.50026
\(460\) 1.72098e10 + 2.18036e10i 0.0179211 + 0.0227049i
\(461\) 1.53544e12 1.58336 0.791679 0.610938i \(-0.209207\pi\)
0.791679 + 0.610938i \(0.209207\pi\)
\(462\) −9.56102e10 + 1.94861e11i −0.0976373 + 0.198992i
\(463\) −1.01535e12 + 1.01535e12i −1.02683 + 1.02683i −0.0272046 + 0.999630i \(0.508661\pi\)
−0.999630 + 0.0272046i \(0.991339\pi\)
\(464\) 1.27251e12 + 3.30065e11i 1.27447 + 0.330574i
\(465\) 2.69310e10 + 2.78116e12i 0.0267125 + 2.75860i
\(466\) −1.39641e11 4.08677e11i −0.137175 0.401462i
\(467\) −4.88692e11 4.88692e11i −0.475454 0.475454i 0.428220 0.903674i \(-0.359141\pi\)
−0.903674 + 0.428220i \(0.859141\pi\)
\(468\) −1.12420e12 1.43425e11i −1.08327 0.138204i
\(469\) 7.82099e10i 0.0746421i
\(470\) 2.54652e11 5.31966e11i 0.240717 0.502855i
\(471\) 2.40006e12i 2.24713i
\(472\) −1.40052e11 6.82632e11i −0.129883 0.633064i
\(473\) 4.50527e11 + 4.50527e11i 0.413853 + 0.413853i
\(474\) 7.69493e11 2.62927e11i 0.700167 0.239240i
\(475\) −2.89042e10 1.49233e12i −0.0260519 1.34506i
\(476\) −2.39513e11 3.09565e11i −0.213844 0.276388i
\(477\) 9.08023e11 9.08023e11i 0.803090 0.803090i
\(478\) 6.57303e11 + 3.22511e11i 0.575891 + 0.282566i
\(479\) 3.77631e11 0.327761 0.163881 0.986480i \(-0.447599\pi\)
0.163881 + 0.986480i \(0.447599\pi\)
\(480\) −1.36930e12 + 1.62486e12i −1.17737 + 1.39711i
\(481\) −2.25763e11 −0.192309
\(482\) 6.67599e11 + 3.27563e11i 0.563383 + 0.276429i
\(483\) 1.09097e10 1.09097e10i 0.00912115 0.00912115i
\(484\) 5.56257e11 + 7.18947e11i 0.460756 + 0.595515i
\(485\) 2.24053e11 2.16959e9i 0.183871 0.00178049i
\(486\) 1.68097e12 5.74369e11i 1.36677 0.467012i
\(487\) 1.08677e12 + 1.08677e12i 0.875504 + 0.875504i 0.993066 0.117562i \(-0.0375078\pi\)
−0.117562 + 0.993066i \(0.537508\pi\)
\(488\) −1.11744e11 5.44654e11i −0.0891939 0.434742i
\(489\) 9.05692e11i 0.716293i
\(490\) −1.13180e12 + 3.99002e11i −0.886923 + 0.312675i
\(491\) 5.95293e11i 0.462236i 0.972926 + 0.231118i \(0.0742384\pi\)
−0.972926 + 0.231118i \(0.925762\pi\)
\(492\) 1.22684e12 + 1.56521e11i 0.943943 + 0.120428i
\(493\) 1.74832e12 + 1.74832e12i 1.33294 + 1.33294i
\(494\) 2.68921e11 + 7.87035e11i 0.203167 + 0.594597i
\(495\) 1.10823e12 + 1.08697e12i 0.829673 + 0.813759i
\(496\) −1.97009e12 5.11007e11i −1.46157 0.379105i
\(497\) −2.63109e11 + 2.63109e11i −0.193434 + 0.193434i
\(498\) −1.30040e12 + 2.65032e12i −0.947426 + 1.93093i
\(499\) 5.61154e11 0.405163 0.202582 0.979265i \(-0.435067\pi\)
0.202582 + 0.979265i \(0.435067\pi\)
\(500\) 1.39086e12 + 1.36525e11i 0.995217 + 0.0976894i
\(501\) 2.90699e11 0.206145
\(502\) 1.72293e11 3.51147e11i 0.121088 0.246787i
\(503\) −1.46305e12 + 1.46305e12i −1.01907 + 1.01907i −0.0192528 + 0.999815i \(0.506129\pi\)
−0.999815 + 0.0192528i \(0.993871\pi\)
\(504\) 6.90107e11 + 4.55142e11i 0.476408 + 0.314202i
\(505\) −1.21127e12 1.18804e12i −0.828763 0.812867i
\(506\) 6.85489e9 + 2.00618e10i 0.00464861 + 0.0136048i
\(507\) 1.50278e12 + 1.50278e12i 1.01009 + 1.01009i
\(508\) 1.08760e11 8.52487e11i 0.0724576 0.567938i
\(509\) 2.68653e11i 0.177404i −0.996058 0.0887018i \(-0.971728\pi\)
0.996058 0.0887018i \(-0.0282718\pi\)
\(510\) −3.76909e12 + 1.32875e12i −2.46701 + 0.869716i
\(511\) 4.98695e11i 0.323550i
\(512\) −8.87041e11 1.27711e12i −0.570465 0.821322i
\(513\) −3.64821e12 3.64821e12i −2.32569 2.32569i
\(514\) 4.07357e11 1.39190e11i 0.257420 0.0879575i
\(515\) 1.36566e11 1.32242e9i 0.0855479 0.000828391i
\(516\) 2.74012e12 2.12006e12i 1.70156 1.31651i
\(517\) 3.18296e11 3.18296e11i 0.195940 0.195940i
\(518\) 1.47843e11 + 7.25405e10i 0.0902230 + 0.0442687i
\(519\) 5.86607e11 0.354891
\(520\) −7.61298e11 + 1.63889e11i −0.456604 + 0.0982960i
\(521\) 1.17766e12 0.700243 0.350122 0.936704i \(-0.386140\pi\)
0.350122 + 0.936704i \(0.386140\pi\)
\(522\) −4.68823e12 2.30032e12i −2.76370 1.35603i
\(523\) 1.70694e12 1.70694e12i 0.997610 0.997610i −0.00238710 0.999997i \(-0.500760\pi\)
0.999997 + 0.00238710i \(0.000759839\pi\)
\(524\) −9.52205e10 + 7.36730e10i −0.0551747 + 0.0426892i
\(525\) −1.50321e10 7.76107e11i −0.00863578 0.445866i
\(526\) 1.82713e11 6.24311e10i 0.104072 0.0355603i
\(527\) −2.70676e12 2.70676e12i −1.52863 1.52863i
\(528\) −1.39797e12 + 8.22120e11i −0.782791 + 0.460344i
\(529\) 1.79965e12i 0.999163i
\(530\) 3.80992e11 7.95889e11i 0.209737 0.438138i
\(531\) 2.76816e12i 1.51100i
\(532\) 7.67784e10 6.01805e11i 0.0415563 0.325727i
\(533\) 3.20506e11 + 3.20506e11i 0.172014 + 0.172014i
\(534\) −5.46379e11 1.59905e12i −0.290776 0.850996i
\(535\) 2.74014e9 + 2.82974e11i 0.00144604 + 0.149332i
\(536\) 3.21735e11 4.87830e11i 0.168367 0.255286i
\(537\) −3.47208e12 + 3.47208e12i −1.80180 + 1.80180i
\(538\) −1.62311e11 + 3.30803e11i −0.0835273 + 0.170235i
\(539\) −9.15936e11 −0.467429
\(540\) 3.79188e12 2.99296e12i 1.91903 1.51471i
\(541\) 1.07941e12 0.541751 0.270876 0.962614i \(-0.412687\pi\)
0.270876 + 0.962614i \(0.412687\pi\)
\(542\) −1.81801e11 + 3.70524e11i −0.0904896 + 0.184425i
\(543\) 2.18232e12 2.18232e12i 1.07726 1.07726i
\(544\) −2.20481e11 2.91619e12i −0.107939 1.42764i
\(545\) 2.34734e12 2.39324e12i 1.13970 1.16199i
\(546\) 1.39856e11 + 4.09309e11i 0.0673466 + 0.197099i
\(547\) 9.04234e10 + 9.04234e10i 0.0431855 + 0.0431855i 0.728370 0.685184i \(-0.240278\pi\)
−0.685184 + 0.728370i \(0.740278\pi\)
\(548\) 6.97980e11 + 8.90485e10i 0.330621 + 0.0421807i
\(549\) 2.20864e12i 1.03765i
\(550\) 9.66516e11 + 4.51221e11i 0.450378 + 0.210260i
\(551\) 3.83243e12i 1.77130i
\(552\) 1.12928e11 2.31689e10i 0.0517697 0.0106213i
\(553\) −1.53714e11 1.53714e11i −0.0698957 0.0698957i
\(554\) 1.30145e12 4.44690e11i 0.586993 0.200569i
\(555\) 1.17742e12 1.20044e12i 0.526760 0.537061i
\(556\) −2.32566e12 3.00585e12i −1.03207 1.33392i
\(557\) −2.74652e12 + 2.74652e12i −1.20902 + 1.20902i −0.237679 + 0.971344i \(0.576387\pi\)
−0.971344 + 0.237679i \(0.923613\pi\)
\(558\) 7.25832e12 + 3.56135e12i 3.16944 + 1.55511i
\(559\) 1.26969e12 0.549979
\(560\) 5.51203e11 + 1.37290e11i 0.236846 + 0.0589919i
\(561\) −3.05023e12 −1.30017
\(562\) 3.72450e12 + 1.82746e12i 1.57491 + 0.772740i
\(563\) −1.98502e12 + 1.98502e12i −0.832677 + 0.832677i −0.987882 0.155206i \(-0.950396\pi\)
0.155206 + 0.987882i \(0.450396\pi\)
\(564\) −1.49781e12 1.93588e12i −0.623306 0.805607i
\(565\) −1.74600e9 1.80309e11i −0.000720818 0.0744388i
\(566\) −4.04612e12 + 1.38251e12i −1.65716 + 0.566234i
\(567\) −9.04168e11 9.04168e11i −0.367388 0.367388i
\(568\) −2.72349e12 + 5.58765e11i −1.09789 + 0.225249i
\(569\) 9.22873e11i 0.369094i 0.982824 + 0.184547i \(0.0590818\pi\)
−0.982824 + 0.184547i \(0.940918\pi\)
\(570\) −5.58738e12 2.67468e12i −2.21703 1.06129i
\(571\) 5.78650e11i 0.227800i 0.993492 + 0.113900i \(0.0363343\pi\)
−0.993492 + 0.113900i \(0.963666\pi\)
\(572\) −5.89583e11 7.52191e10i −0.230283 0.0293796i
\(573\) 2.85468e12 + 2.85468e12i 1.10627 + 1.10627i
\(574\) −1.06904e11 3.12869e11i −0.0411045 0.120298i
\(575\) −5.46410e10 5.25646e10i −0.0208456 0.0200534i
\(576\) 2.43217e12 + 5.67784e12i 0.920645 + 2.14923i
\(577\) 1.82816e12 1.82816e12i 0.686630 0.686630i −0.274855 0.961486i \(-0.588630\pi\)
0.961486 + 0.274855i \(0.0886299\pi\)
\(578\) 1.24088e12 2.52900e12i 0.462437 0.942483i
\(579\) −3.42759e11 −0.126746
\(580\) −3.56372e12 4.19633e11i −1.30761 0.153973i
\(581\) 7.89197e11 0.287338
\(582\) 4.09614e11 8.34825e11i 0.147986 0.301608i
\(583\) 4.76211e11 4.76211e11i 0.170723 0.170723i
\(584\) −2.05150e12 + 3.11058e12i −0.729818 + 1.10658i
\(585\) 3.09331e12 2.99536e10i 1.09200 0.0105742i
\(586\) 1.42332e12 + 4.16556e12i 0.498614 + 1.45926i
\(587\) 2.29646e12 + 2.29646e12i 0.798338 + 0.798338i 0.982833 0.184496i \(-0.0590652\pi\)
−0.184496 + 0.982833i \(0.559065\pi\)
\(588\) −6.30303e11 + 4.94045e12i −0.217446 + 1.70439i
\(589\) 5.93336e12i 2.03134i
\(590\) 6.32417e11 + 1.79389e12i 0.214867 + 0.609485i
\(591\) 6.53062e12i 2.20197i
\(592\) 6.23751e11 + 1.06066e12i 0.208720 + 0.354917i
\(593\) −3.11210e12 3.11210e12i −1.03349 1.03349i −0.999419 0.0340736i \(-0.989152\pi\)
−0.0340736 0.999419i \(-0.510848\pi\)
\(594\) 3.48895e12 1.19214e12i 1.14989 0.392905i
\(595\) 7.62728e11 + 7.48098e11i 0.249484 + 0.244699i
\(596\) 2.08484e12 1.61306e12i 0.676805 0.523651i
\(597\) 4.40733e12 4.40733e12i 1.42001 1.42001i
\(598\) 3.79288e10 + 1.86101e10i 0.0121287 + 0.00595105i
\(599\) −6.02032e12 −1.91073 −0.955364 0.295432i \(-0.904536\pi\)
−0.955364 + 0.295432i \(0.904536\pi\)
\(600\) 3.09894e12 4.90276e12i 0.976186 1.54440i
\(601\) 4.37751e12 1.36865 0.684325 0.729177i \(-0.260097\pi\)
0.684325 + 0.729177i \(0.260097\pi\)
\(602\) −8.31472e11 4.07969e11i −0.258026 0.126603i
\(603\) −1.64145e12 + 1.64145e12i −0.505590 + 0.505590i
\(604\) −5.68287e11 + 4.39690e11i −0.173741 + 0.134425i
\(605\) −1.77140e12 1.73742e12i −0.537547 0.527236i
\(606\) −6.66315e12 + 2.27673e12i −2.00703 + 0.685779i
\(607\) −2.33910e12 2.33910e12i −0.699358 0.699358i 0.264914 0.964272i \(-0.414656\pi\)
−0.964272 + 0.264914i \(0.914656\pi\)
\(608\) 2.95457e12 3.43788e12i 0.876856 1.02029i
\(609\) 1.99311e12i 0.587156i
\(610\) 5.04589e11 + 1.43130e12i 0.147555 + 0.418549i
\(611\) 8.97034e11i 0.260389i
\(612\) −1.47022e12 + 1.15239e13i −0.423643 + 3.32060i
\(613\) 4.73820e11 + 4.73820e11i 0.135532 + 0.135532i 0.771618 0.636086i \(-0.219448\pi\)
−0.636086 + 0.771618i \(0.719448\pi\)
\(614\) 6.78655e11 + 1.98618e12i 0.192704 + 0.563975i
\(615\) −3.37574e12 + 3.26886e10i −0.951550 + 0.00921420i
\(616\) 3.61925e11 + 2.38698e11i 0.101276 + 0.0667938i
\(617\) −3.02429e12 + 3.02429e12i −0.840117 + 0.840117i −0.988874 0.148757i \(-0.952473\pi\)
0.148757 + 0.988874i \(0.452473\pi\)
\(618\) 2.49670e11 5.08846e11i 0.0688522 0.140326i
\(619\) 6.73202e12 1.84305 0.921526 0.388316i \(-0.126943\pi\)
0.921526 + 0.388316i \(0.126943\pi\)
\(620\) 5.51735e12 + 6.49675e11i 1.49957 + 0.176577i
\(621\) −2.62080e11 −0.0707166
\(622\) 3.01228e12 6.13926e12i 0.806935 1.64460i
\(623\) −3.19427e11 + 3.19427e11i −0.0849524 + 0.0849524i
\(624\) −8.11445e11 + 3.12838e12i −0.214254 + 0.826016i
\(625\) −3.81184e12 + 1.47715e11i −0.999250 + 0.0387226i
\(626\) 1.03484e12 + 3.02861e12i 0.269333 + 0.788240i
\(627\) −3.34314e12 3.34314e12i −0.863875 0.863875i
\(628\) −4.75543e12 6.06698e11i −1.22003 0.155652i
\(629\) 2.31424e12i 0.589497i
\(630\) −2.03531e12 9.74303e11i −0.514751 0.246412i
\(631\) 3.34050e12i 0.838842i −0.907792 0.419421i \(-0.862233\pi\)
0.907792 0.419421i \(-0.137767\pi\)
\(632\) −3.26443e11 1.59112e12i −0.0813917 0.396713i
\(633\) 5.06493e12 + 5.06493e12i 1.25388 + 1.25388i
\(634\) −3.23368e12 + 1.10491e12i −0.794870 + 0.271598i
\(635\) 2.27141e10 + 2.34568e12i 0.00554387 + 0.572515i
\(636\) −2.24092e12 2.89633e12i −0.543087 0.701925i
\(637\) −1.29066e12 + 1.29066e12i −0.310589 + 0.310589i
\(638\) −2.45873e12 1.20640e12i −0.587514 0.288269i
\(639\) 1.10441e13 2.62046
\(640\) 2.87332e12 + 3.12385e12i 0.676978 + 0.736003i
\(641\) −2.29892e12 −0.537852 −0.268926 0.963161i \(-0.586669\pi\)
−0.268926 + 0.963161i \(0.586669\pi\)
\(642\) 1.05436e12 + 5.17333e11i 0.244953 + 0.120188i
\(643\) −1.09154e12 + 1.09154e12i −0.251821 + 0.251821i −0.821717 0.569896i \(-0.806983\pi\)
0.569896 + 0.821717i \(0.306983\pi\)
\(644\) −1.88584e10 2.43740e10i −0.00432035 0.00558394i
\(645\) −6.62182e12 + 6.75131e12i −1.50646 + 1.53592i
\(646\) 8.06770e12 2.75665e12i 1.82265 0.622780i
\(647\) −3.57327e12 3.57327e12i −0.801672 0.801672i 0.181684 0.983357i \(-0.441845\pi\)
−0.983357 + 0.181684i \(0.941845\pi\)
\(648\) −1.92018e12 9.35921e12i −0.427814 2.08522i
\(649\) 1.45176e12i 0.321213i
\(650\) 1.99776e12 7.26112e11i 0.438969 0.159549i
\(651\) 3.08574e12i 0.673355i
\(652\) −1.79452e12 2.28945e11i −0.388897 0.0496155i
\(653\) −2.56777e12 2.56777e12i −0.552645 0.552645i 0.374558 0.927203i \(-0.377794\pi\)
−0.927203 + 0.374558i \(0.877794\pi\)
\(654\) −4.49837e12 1.31651e13i −0.961514 2.81400i
\(655\) 2.30111e11 2.34611e11i 0.0488486 0.0498039i
\(656\) 6.20254e11 2.39128e12i 0.130768 0.504153i
\(657\) 1.04665e13 1.04665e13i 2.19157 2.19157i
\(658\) −2.88228e11 + 5.87431e11i −0.0599404 + 0.122163i
\(659\) −6.71777e11 −0.138753 −0.0693763 0.997591i \(-0.522101\pi\)
−0.0693763 + 0.997591i \(0.522101\pi\)
\(660\) 3.47480e12 2.74268e12i 0.712824 0.562637i
\(661\) −4.23872e12 −0.863631 −0.431815 0.901962i \(-0.642127\pi\)
−0.431815 + 0.901962i \(0.642127\pi\)
\(662\) −3.52270e12 + 7.17954e12i −0.712877 + 1.45290i
\(663\) −4.29814e12 + 4.29814e12i −0.863913 + 0.863913i
\(664\) 4.92257e12 + 3.24655e12i 0.982733 + 0.648136i
\(665\) 1.60348e10 + 1.65591e12i 0.00317955 + 0.328352i
\(666\) −1.58043e12 4.62535e12i −0.311273 0.910983i
\(667\) 1.37657e11 + 1.37657e11i 0.0269297 + 0.0269297i
\(668\) 7.34842e10 5.75985e11i 0.0142791 0.111922i
\(669\) 3.62434e12i 0.699539i
\(670\) −6.88725e11 + 1.43874e12i −0.132041 + 0.275832i
\(671\) 1.15832e12i 0.220585i
\(672\) 1.53657e12 1.78792e12i 0.290663 0.338210i
\(673\) −1.63158e12 1.63158e12i −0.306577 0.306577i 0.537003 0.843580i \(-0.319556\pi\)
−0.843580 + 0.537003i \(0.819556\pi\)
\(674\) −7.36831e12 + 2.51767e12i −1.37530 + 0.469926i
\(675\) −9.14153e12 + 9.50264e12i −1.69493 + 1.76188i
\(676\) 3.35746e12 2.59770e12i 0.618373 0.478441i
\(677\) −2.09539e11 + 2.09539e11i −0.0383368 + 0.0383368i −0.726015 0.687678i \(-0.758630\pi\)
0.687678 + 0.726015i \(0.258630\pi\)
\(678\) −6.71834e11 3.29641e11i −0.122104 0.0599112i
\(679\) −2.48589e11 −0.0448816
\(680\) 1.67999e12 + 7.80388e12i 0.301312 + 1.39965i
\(681\) −2.45296e11 −0.0437048
\(682\) 3.80661e12 + 1.86774e12i 0.673765 + 0.330589i
\(683\) 6.47193e12 6.47193e12i 1.13800 1.13800i 0.149186 0.988809i \(-0.452335\pi\)
0.988809 0.149186i \(-0.0476655\pi\)
\(684\) −1.42419e13 + 1.10191e13i −2.48780 + 1.92484i
\(685\) −1.92054e12 + 1.85973e10i −0.333285 + 0.00322733i
\(686\) 2.59964e12 8.88267e11i 0.448182 0.153139i
\(687\) 1.08624e13 + 1.08624e13i 1.86047 + 1.86047i
\(688\) −3.50798e12 5.96514e12i −0.596911 1.01502i
\(689\) 1.34208e12i 0.226877i
\(690\) −2.96765e11 + 1.04621e11i −0.0498415 + 0.0175711i
\(691\) 4.71192e12i 0.786224i −0.919491 0.393112i \(-0.871398\pi\)
0.919491 0.393112i \(-0.128602\pi\)
\(692\) 1.48285e11 1.16229e12i 0.0245822 0.192681i
\(693\) −1.21780e12 1.21780e12i −0.200575 0.200575i
\(694\) 6.63623e11 + 1.94218e12i 0.108594 + 0.317814i
\(695\) 7.40604e12 + 7.26399e12i 1.20408 + 1.18098i
\(696\) −8.19914e12 + 1.24319e13i −1.32442 + 2.00815i
\(697\) 3.28543e12 3.28543e12i 0.527284 0.527284i
\(698\) 2.05339e12 4.18497e12i 0.327433 0.667334i
\(699\) 4.89238e12 0.775127
\(700\) −1.54156e12 1.66404e11i −0.242672 0.0261952i
\(701\) 4.93453e12 0.771818 0.385909 0.922537i \(-0.373888\pi\)
0.385909 + 0.922537i \(0.373888\pi\)
\(702\) 3.23649e12 6.59622e12i 0.502988 1.02513i
\(703\) −2.53648e12 + 2.53648e12i −0.391681 + 0.391681i
\(704\) 1.27555e12 + 2.97773e12i 0.195713 + 0.456887i
\(705\) 4.76977e12 + 4.67828e12i 0.727188 + 0.713240i
\(706\) −1.94029e12 5.67853e12i −0.293931 0.860230i
\(707\) 1.33103e12 + 1.33103e12i 0.200355 + 0.200355i
\(708\) 7.83059e12 + 9.99028e11i 1.17124 + 0.149427i
\(709\) 3.88215e12i 0.576984i 0.957482 + 0.288492i \(0.0931539\pi\)
−0.957482 + 0.288492i \(0.906846\pi\)
\(710\) 7.15709e12 2.52315e12i 1.05700 0.372632i
\(711\) 6.45220e12i 0.946880i
\(712\) −3.30645e12 + 6.78368e11i −0.482172 + 0.0989249i
\(713\) −2.13120e11 2.13120e11i −0.0308832 0.0308832i
\(714\) 4.19573e12 1.43364e12i 0.604179 0.206441i
\(715\) 1.62228e12 1.57091e10i 0.232139 0.00224789i
\(716\) 6.00183e12 + 7.75721e12i 0.853444 + 1.10305i
\(717\) −5.86480e12 + 5.86480e12i −0.828738 + 0.828738i
\(718\) 1.13066e13 + 5.54768e12i 1.58771 + 0.779026i
\(719\) −8.74554e12 −1.22041 −0.610206 0.792243i \(-0.708913\pi\)
−0.610206 + 0.792243i \(0.708913\pi\)
\(720\) −8.68708e12 1.44499e13i −1.20470 2.00386i
\(721\) −1.51521e11 −0.0208817
\(722\) 5.30875e12 + 2.60478e12i 0.727068 + 0.356742i
\(723\) −5.95666e12 + 5.95666e12i −0.810738 + 0.810738i
\(724\) −3.77235e12 4.87567e12i −0.510257 0.659494i
\(725\) 9.79281e12 1.89673e11i 1.31640 0.0254967i
\(726\) −9.74436e12 + 3.32954e12i −1.30178 + 0.444805i
\(727\) 4.43190e12 + 4.43190e12i 0.588417 + 0.588417i 0.937203 0.348785i \(-0.113406\pi\)
−0.348785 + 0.937203i \(0.613406\pi\)
\(728\) 8.46351e11 1.73642e11i 0.111676 0.0229120i
\(729\) 3.89106e12i 0.510262i
\(730\) 4.39156e12 9.17393e12i 0.572356 1.19565i
\(731\) 1.30153e13i 1.68588i
\(732\) 6.24782e12 + 7.97098e11i 0.804320 + 0.102615i
\(733\) −5.97687e11 5.97687e11i −0.0764726 0.0764726i 0.667836 0.744309i \(-0.267221\pi\)
−0.744309 + 0.667836i \(0.767221\pi\)
\(734\) −4.29431e12 1.25679e13i −0.546087 1.59820i
\(735\) −1.31636e11 1.35940e13i −0.0166372 1.71812i
\(736\) −1.73599e10 2.29610e11i −0.00218071 0.0288430i
\(737\) −8.60853e11 + 8.60853e11i −0.107479 + 0.107479i
\(738\) −4.32273e12 + 8.81006e12i −0.536419 + 1.09326i
\(739\) 2.05310e11 0.0253227 0.0126614 0.999920i \(-0.495970\pi\)
0.0126614 + 0.999920i \(0.495970\pi\)
\(740\) −2.08090e12 2.63637e12i −0.255099 0.323194i
\(741\) −9.42178e12 −1.14802
\(742\) −4.31226e11 + 8.78873e11i −0.0522261 + 0.106441i
\(743\) 2.84605e12 2.84605e12i 0.342605 0.342605i −0.514741 0.857346i \(-0.672112\pi\)
0.857346 + 0.514741i \(0.172112\pi\)
\(744\) 1.26939e13 1.92471e13i 1.51886 2.30296i
\(745\) −5.03824e12 + 5.13677e12i −0.599206 + 0.610924i
\(746\) −1.91912e12 5.61657e12i −0.226870 0.663967i
\(747\) −1.65634e13 1.65634e13i −1.94629 1.94629i
\(748\) −7.71053e11 + 6.04367e12i −0.0900589 + 0.705901i
\(749\) 3.13963e11i 0.0364510i
\(750\) −6.55795e12 + 1.44095e13i −0.756820 + 1.66293i
\(751\) 1.14586e13i 1.31448i 0.753683 + 0.657239i \(0.228276\pi\)
−0.753683 + 0.657239i \(0.771724\pi\)
\(752\) −4.21435e12 + 2.47837e12i −0.480563 + 0.282609i
\(753\) 3.13312e12 + 3.13312e12i 0.355140 + 0.355140i
\(754\) −5.16461e12 + 1.76469e12i −0.581924 + 0.198837i
\(755\) 1.37333e12 1.40019e12i 0.153820 0.156829i
\(756\) −4.23889e12 + 3.27967e12i −0.471959 + 0.365160i
\(757\) −5.37979e12 + 5.37979e12i −0.595435 + 0.595435i −0.939094 0.343660i \(-0.888333\pi\)
0.343660 + 0.939094i \(0.388333\pi\)
\(758\) −6.86869e12 3.37018e12i −0.755723 0.370802i
\(759\) −2.40164e11 −0.0262676
\(760\) −6.71196e12 + 1.03946e13i −0.729774 + 1.13018i
\(761\) 1.29032e12 0.139466 0.0697329 0.997566i \(-0.477785\pi\)
0.0697329 + 0.997566i \(0.477785\pi\)
\(762\) 8.74004e12 + 4.28837e12i 0.939109 + 0.460782i
\(763\) −2.62986e12 + 2.62986e12i −0.280914 + 0.280914i
\(764\) 6.37784e12 4.93459e12i 0.677257 0.524000i
\(765\) −3.07048e11 3.17088e13i −0.0324137 3.34736i
\(766\) −6.77192e12 + 2.31389e12i −0.710694 + 0.242836i
\(767\) 2.04570e12 + 2.04570e12i 0.213433 + 0.213433i
\(768\) 1.69393e13 4.83101e12i 1.75699 0.501086i
\(769\) 6.36131e12i 0.655961i 0.944684 + 0.327981i \(0.106368\pi\)
−0.944684 + 0.327981i \(0.893632\pi\)
\(770\) −1.06741e12 5.10971e11i −0.109427 0.0523827i
\(771\) 4.87658e12i 0.497016i
\(772\) −8.66443e10 + 6.79136e11i −0.00877935 + 0.0688143i
\(773\) −1.27078e13 1.27078e13i −1.28015 1.28015i −0.940580 0.339573i \(-0.889717\pi\)
−0.339573 0.940580i \(-0.610283\pi\)
\(774\) 8.88836e12 + 2.60130e13i 0.890199 + 2.60529i
\(775\) −1.51612e13 + 2.93651e11i −1.50965 + 0.0292398i
\(776\) −1.55056e12 1.02263e12i −0.153501 0.101238i
\(777\) −1.31913e12 + 1.31913e12i −0.129836 + 0.129836i
\(778\) −7.89483e12 + 1.60903e13i −0.772564 + 1.57455i
\(779\) 7.20185e12 0.700689
\(780\) 1.03164e12 8.76118e12i 0.0997936 0.847495i
\(781\) 5.79206e12 0.557062
\(782\) 1.90768e11 3.88799e11i 0.0182421 0.0371788i
\(783\) 2.39400e13 2.39400e13i 2.27612 2.27612i
\(784\) 9.62957e12 + 2.49774e12i 0.910300 + 0.236116i
\(785\) 1.30849e13 1.26706e11i 1.22986 0.0119092i
\(786\) −4.40979e11 1.29059e12i −0.0412113 0.120611i
\(787\) −1.08948e13 1.08948e13i −1.01235 1.01235i −0.999923 0.0124308i \(-0.996043\pi\)
−0.0124308 0.999923i \(-0.503957\pi\)
\(788\) −1.29397e13 1.65084e12i −1.19551 0.152524i
\(789\) 2.18730e12i 0.200938i
\(790\) 1.47408e12 + 4.18132e12i 0.134648 + 0.381937i
\(791\) 2.00055e11i 0.0181700i
\(792\) −2.58625e12 1.26057e13i −0.233565 1.13842i
\(793\) 1.63221e12 + 1.63221e12i 0.146570 + 0.146570i
\(794\) −1.57342e13 + 5.37622e12i −1.40493 + 0.480048i
\(795\) 7.13619e12 + 6.99931e12i 0.633599 + 0.621446i
\(796\) −7.61849e12 9.84670e12i −0.672605 0.869324i
\(797\) 2.58756e12 2.58756e12i 0.227158 0.227158i −0.584346 0.811504i \(-0.698649\pi\)
0.811504 + 0.584346i \(0.198649\pi\)
\(798\) 6.16995e12 + 3.02734e12i 0.538603 + 0.264270i
\(799\) −9.19528e12 −0.798186
\(800\) −8.93087e12 7.37952e12i −0.770883 0.636976i
\(801\) 1.34081e13 1.15085
\(802\) −1.31695e13 6.46172e12i −1.12405 0.551523i
\(803\) 5.48912e12 5.48912e12i 0.465889 0.465889i
\(804\) 4.05094e12 + 5.23573e12i 0.341903 + 0.441901i
\(805\) 6.00545e10 + 5.89026e10i 0.00504039 + 0.00494371i
\(806\) 7.99585e12 2.73209e12i 0.667355 0.228028i
\(807\) −2.95160e12 2.95160e12i −0.244977 0.244977i
\(808\) 2.82672e12 + 1.37778e13i 0.233309 + 1.13718i
\(809\) 4.44051e12i 0.364472i 0.983255 + 0.182236i \(0.0583335\pi\)
−0.983255 + 0.182236i \(0.941666\pi\)
\(810\) 8.67074e12 + 2.45951e13i 0.707740 + 2.00755i
\(811\) 6.27504e12i 0.509358i −0.967026 0.254679i \(-0.918030\pi\)
0.967026 0.254679i \(-0.0819697\pi\)
\(812\) 3.94911e12 + 5.03828e11i 0.318785 + 0.0406706i
\(813\) −3.30601e12 3.30601e12i −0.265397 0.265397i
\(814\) −8.28853e11 2.42575e12i −0.0661710 0.193659i
\(815\) 4.93775e12 4.78140e10i 0.392030 0.00379617i
\(816\) 3.20682e13 + 8.31793e12i 2.53203 + 0.656764i
\(817\) 1.42652e13 1.42652e13i 1.12016 1.12016i
\(818\) 4.00831e12 8.16925e12i 0.313020 0.637958i
\(819\) −3.43206e12 −0.266549
\(820\) −7.88568e11 + 6.69690e12i −0.0609084 + 0.517263i
\(821\) 6.38476e12 0.490456 0.245228 0.969465i \(-0.421137\pi\)
0.245228 + 0.969465i \(0.421137\pi\)
\(822\) −3.51114e12 + 7.15598e12i −0.268241 + 0.546696i
\(823\) −1.33274e13 + 1.33274e13i −1.01262 + 1.01262i −0.0127033 + 0.999919i \(0.504044\pi\)
−0.999919 + 0.0127033i \(0.995956\pi\)
\(824\) −9.45106e11 6.23319e11i −0.0714180 0.0471019i
\(825\) −8.37711e12 + 8.70803e12i −0.629581 + 0.654451i
\(826\) −6.82337e11 1.99695e12i −0.0510022 0.149265i
\(827\) 9.72206e12 + 9.72206e12i 0.722742 + 0.722742i 0.969163 0.246421i \(-0.0792545\pi\)
−0.246421 + 0.969163i \(0.579254\pi\)
\(828\) −1.15760e11 + 9.07349e11i −0.00855896 + 0.0670869i
\(829\) 6.28234e12i 0.461983i 0.972956 + 0.230992i \(0.0741970\pi\)
−0.972956 + 0.230992i \(0.925803\pi\)
\(830\) −1.45180e13 6.94975e12i −1.06183 0.508297i
\(831\) 1.55799e13i 1.13334i
\(832\) 5.99338e12 + 2.39859e12i 0.433628 + 0.173540i
\(833\) 1.32303e13 + 1.32303e13i 0.952065 + 0.952065i
\(834\) 4.07403e13 1.39205e13i 2.91593 0.996341i
\(835\) 1.53468e10 + 1.58486e12i 0.00109252 + 0.112824i
\(836\) −7.46914e12 + 5.77894e12i −0.528862 + 0.409186i
\(837\) −3.70638e13 + 3.70638e13i −2.61027 + 2.61027i
\(838\) −1.36429e13 6.69400e12i −0.955671 0.468908i
\(839\) −1.27012e13 −0.884942 −0.442471 0.896783i \(-0.645898\pi\)
−0.442471 + 0.896783i \(0.645898\pi\)
\(840\) −3.49066e12 + 5.40587e12i −0.241908 + 0.374635i
\(841\) −1.06417e13 −0.733548
\(842\) −1.37872e13 6.76480e12i −0.945304 0.463821i
\(843\) −3.32319e13 + 3.32319e13i −2.26637 + 2.26637i
\(844\) 1.13159e13 8.75522e12i 0.767623 0.593917i
\(845\) −8.11368e12 + 8.27235e12i −0.547473 + 0.558179i
\(846\) 1.83781e13 6.27959e12i 1.23348 0.421468i
\(847\) 1.94654e12 + 1.94654e12i 0.129953 + 0.129953i
\(848\) −6.30520e12 + 3.70796e12i −0.418714 + 0.246238i
\(849\) 4.84371e13i 3.19958i
\(850\) −7.44320e12 2.04786e13i −0.489074 1.34560i
\(851\) 1.82215e11i 0.0119097i
\(852\) 3.98582e12 3.12417e13i 0.259143 2.03122i
\(853\) 1.33812e13 + 1.33812e13i 0.865415 + 0.865415i 0.991961 0.126546i \(-0.0403892\pi\)
−0.126546 + 0.991961i \(0.540389\pi\)
\(854\) −5.44419e11 1.59332e12i −0.0350246 0.102504i
\(855\) 3.44172e13 3.50902e13i 2.20256 2.24563i
\(856\) 1.29156e12 1.95832e12i 0.0822210 0.124667i
\(857\) 1.94159e12 1.94159e12i 0.122954 0.122954i −0.642952 0.765906i \(-0.722291\pi\)
0.765906 + 0.642952i \(0.222291\pi\)
\(858\) 2.96585e12 6.04464e12i 0.186834 0.380783i
\(859\) 1.64722e13 1.03224 0.516122 0.856515i \(-0.327375\pi\)
0.516122 + 0.856515i \(0.327375\pi\)
\(860\) 1.17030e13 + 1.48270e13i 0.729550 + 0.924292i
\(861\) 3.74543e12 0.232267
\(862\) −7.66422e12 + 1.56203e13i −0.472808 + 0.963621i
\(863\) 4.23202e12 4.23202e12i 0.259716 0.259716i −0.565222 0.824939i \(-0.691210\pi\)
0.824939 + 0.565222i \(0.191210\pi\)
\(864\) −3.99316e13 + 3.01907e12i −2.43784 + 0.184315i
\(865\) 3.09687e10 + 3.19813e12i 0.00188083 + 0.194233i
\(866\) 8.66565e12 + 2.53612e13i 0.523565 + 1.53228i
\(867\) 2.25651e13 + 2.25651e13i 1.35628 + 1.35628i
\(868\) −6.11402e12 7.80027e11i −0.365585 0.0466413i
\(869\) 3.38385e12i 0.201290i
\(870\) 1.75516e13 3.66650e13i 1.03867 2.16978i
\(871\) 2.42609e12i 0.142832i
\(872\) −2.72222e13 + 5.58505e12i −1.59441 + 0.327117i
\(873\) 5.21732e12 + 5.21732e12i 0.304007 + 0.304007i
\(874\) 6.35222e11 2.17049e11i 0.0368234 0.0125822i
\(875\) 4.23047e12 1.22926e11i 0.243979 0.00708938i
\(876\) −2.58303e13 3.33850e13i −1.48204 1.91550i
\(877\) 1.07720e13 1.07720e13i 0.614889 0.614889i −0.329327 0.944216i \(-0.606822\pi\)
0.944216 + 0.329327i \(0.106822\pi\)
\(878\) 8.92177e12 + 4.37754e12i 0.506671 + 0.248602i
\(879\) −4.98669e13 −2.81749
\(880\) −4.55592e12 7.57821e12i −0.256097 0.425985i
\(881\) −2.80989e12 −0.157144 −0.0785720 0.996908i \(-0.525036\pi\)
−0.0785720 + 0.996908i \(0.525036\pi\)
\(882\) −3.54778e13 1.74075e13i −1.97400 0.968560i
\(883\) 2.03931e13 2.03931e13i 1.12891 1.12891i 0.138556 0.990355i \(-0.455754\pi\)
0.990355 0.138556i \(-0.0442460\pi\)
\(884\) 7.42976e12 + 9.60277e12i 0.409203 + 0.528885i
\(885\) −2.15464e13 + 2.08642e11i −1.18068 + 0.0114329i
\(886\) 2.80187e13 9.57369e12i 1.52755 0.521948i
\(887\) 1.62930e13 + 1.62930e13i 0.883783 + 0.883783i 0.993917 0.110133i \(-0.0351278\pi\)
−0.110133 + 0.993917i \(0.535128\pi\)
\(888\) −1.36546e13 + 2.80145e12i −0.736920 + 0.151190i
\(889\) 2.60256e12i 0.139747i
\(890\) 8.68905e12 3.06323e12i 0.464213 0.163653i
\(891\) 1.99043e13i 1.05803i
\(892\) −7.18121e12 9.16179e11i −0.379800 0.0484550i
\(893\) −1.00783e13 1.00783e13i −0.530341 0.530341i
\(894\) 9.65515e12 + 2.82571e13i 0.505522 + 1.47948i
\(895\) −1.91128e13 1.87462e13i −0.995681 0.976583i
\(896\) −3.15413e12 3.49649e12i −0.163491 0.181237i
\(897\) −3.38421e11 + 3.38421e11i −0.0174538 + 0.0174538i
\(898\) 1.21366e13 2.47353e13i 0.622805 1.26933i
\(899\) 3.89354e13 1.98804
\(900\) 2.88614e13 + 3.58463e13i 1.46631 + 1.82118i
\(901\) −1.37573e13 −0.695460
\(902\) −2.26705e12 + 4.62042e12i −0.114033 + 0.232408i
\(903\) 7.41883e12 7.41883e12i 0.371313 0.371313i
\(904\) −8.22974e11 + 1.24783e12i −0.0409853 + 0.0621438i
\(905\) 1.20130e13 + 1.17826e13i 0.595298 + 0.583879i
\(906\) −2.63182e12 7.70237e12i −0.129771 0.379794i
\(907\) 5.25120e12 + 5.25120e12i 0.257647 + 0.257647i 0.824097 0.566449i \(-0.191683\pi\)
−0.566449 + 0.824097i \(0.691683\pi\)
\(908\) −6.20072e10 + 4.86025e11i −0.00302730 + 0.0237286i
\(909\) 5.58706e13i 2.71422i
\(910\) −2.22413e12 + 7.84093e11i −0.107516 + 0.0379037i
\(911\) 1.60762e12i 0.0773306i 0.999252 + 0.0386653i \(0.0123106\pi\)
−0.999252 + 0.0386653i \(0.987689\pi\)
\(912\) 2.60310e13 + 4.42644e13i 1.24599 + 2.11874i
\(913\) −8.68665e12 8.68665e12i −0.413746 0.413746i
\(914\) −1.65199e13 + 5.64466e12i −0.782977 + 0.267535i
\(915\) −1.71913e13 + 1.66470e11i −0.810801 + 0.00785129i
\(916\) 2.42685e13 1.87768e13i 1.13897 0.881233i
\(917\) −2.57808e11 + 2.57808e11i −0.0120402 + 0.0120402i
\(918\) −6.76163e13 3.31765e13i −3.14238 1.54184i
\(919\) −1.16958e13 −0.540891 −0.270445 0.962735i \(-0.587171\pi\)
−0.270445 + 0.962735i \(0.587171\pi\)
\(920\) 1.32277e11 + 6.14450e11i 0.00608748 + 0.0282775i
\(921\) −2.37770e13 −1.08890
\(922\) 3.11908e13 + 1.53040e13i 1.42147 + 0.697456i
\(923\) 8.16171e12 8.16171e12i 0.370146 0.370146i
\(924\) −3.88444e12 + 3.00543e12i −0.175309 + 0.135638i
\(925\) 6.60687e12 + 6.35580e12i 0.296728 + 0.285452i
\(926\) −3.07459e13 + 1.05055e13i −1.37416 + 0.469535i
\(927\) 3.18008e12 + 3.18008e12i 0.141442 + 0.141442i
\(928\) 2.25598e13 + 1.93882e13i 0.998547 + 0.858168i
\(929\) 3.76597e13i 1.65884i 0.558622 + 0.829422i \(0.311330\pi\)
−0.558622 + 0.829422i \(0.688670\pi\)
\(930\) −2.71733e13 + 5.67647e13i −1.19116 + 2.48832i
\(931\) 2.90015e13i 1.26517i
\(932\) 1.23672e12 9.69366e12i 0.0536907 0.420839i
\(933\) 5.47777e13 + 5.47777e13i 2.36666 + 2.36666i
\(934\) −5.05636e12 1.47981e13i −0.217409 0.636276i
\(935\) −1.61030e11 1.66296e13i −0.00689058 0.711589i
\(936\) −2.14073e13 1.41186e13i −0.911634 0.601244i
\(937\) 7.38485e12 7.38485e12i 0.312978 0.312978i −0.533084 0.846062i \(-0.678967\pi\)
0.846062 + 0.533084i \(0.178967\pi\)
\(938\) 7.79533e11 1.58875e12i 0.0328792 0.0670105i
\(939\) −3.62562e13 −1.52190
\(940\) 1.04752e13 8.26814e12i 0.437609 0.345408i
\(941\) −1.15017e13 −0.478200 −0.239100 0.970995i \(-0.576852\pi\)
−0.239100 + 0.970995i \(0.576852\pi\)
\(942\) 2.39218e13 4.87546e13i 0.989841 2.01737i
\(943\) 2.58683e11 2.58683e11i 0.0106528 0.0106528i
\(944\) 3.95891e12 1.52628e13i 0.162256 0.625549i
\(945\) 1.02438e13 1.04441e13i 0.417847 0.426018i
\(946\) 4.66148e12 + 1.36425e13i 0.189240 + 0.553838i
\(947\) −3.28911e13 3.28911e13i −1.32894 1.32894i −0.906300 0.422636i \(-0.861105\pi\)
−0.422636 0.906300i \(-0.638895\pi\)
\(948\) 1.82521e13 + 2.32860e12i 0.733963 + 0.0936391i
\(949\) 1.54696e13i 0.619131i
\(950\) 1.42871e13 3.06031e13i 0.569101 1.21901i
\(951\) 3.87112e13i 1.53470i
\(952\) −1.77996e12 8.67574e12i −0.0702334 0.342326i
\(953\) −2.04121e13 2.04121e13i −0.801622 0.801622i 0.181727 0.983349i \(-0.441831\pi\)
−0.983349 + 0.181727i \(0.941831\pi\)
\(954\) 2.74959e13 9.39506e12i 1.07473 0.367225i
\(955\) −1.54128e13 + 1.57142e13i −0.599605 + 0.611331i
\(956\) 1.01379e13 + 1.31029e13i 0.392542 + 0.507350i
\(957\) 2.19381e13 2.19381e13i 0.845464 0.845464i
\(958\) 7.67116e12 + 3.76392e12i 0.294250 + 0.144376i
\(959\) 2.13087e12 0.0813528
\(960\) −4.40111e13 + 1.93591e13i −1.67241 + 0.735640i
\(961\) −3.38402e13 −1.27990
\(962\) −4.58613e12 2.25022e12i −0.172647 0.0847106i
\(963\) −6.58935e12 + 6.58935e12i −0.246902 + 0.246902i
\(964\) 1.02967e13 + 1.33082e13i 0.384016 + 0.496331i
\(965\) −1.80952e10 1.86869e12i −0.000671724 0.0693689i
\(966\) 3.30357e11 1.12879e11i 0.0122064 0.00417078i
\(967\) 4.58431e12 + 4.58431e12i 0.168599 + 0.168599i 0.786363 0.617764i \(-0.211961\pi\)
−0.617764 + 0.786363i \(0.711961\pi\)
\(968\) 4.13386e12 + 2.01490e13i 0.151327 + 0.737587i
\(969\) 9.65805e13i 3.51911i
\(970\) 4.57302e12 + 2.18911e12i 0.165856 + 0.0793951i
\(971\) 3.13384e13i 1.13133i −0.824634 0.565667i \(-0.808619\pi\)
0.824634 0.565667i \(-0.191381\pi\)
\(972\) 3.98719e13 + 5.08687e12i 1.43275 + 0.182790i
\(973\) −8.13829e12 8.13829e12i −0.291089 0.291089i
\(974\) 1.12445e13 + 3.29086e13i 0.400337 + 1.17164i
\(975\) 4.66298e11 + 2.40750e13i 0.0165251 + 0.853190i
\(976\) 3.15871e12 1.21778e13i 0.111426 0.429581i
\(977\) −1.55974e12 + 1.55974e12i −0.0547681 + 0.0547681i −0.733960 0.679192i \(-0.762330\pi\)
0.679192 + 0.733960i \(0.262330\pi\)
\(978\) 9.02720e12 1.83981e13i 0.315521 0.643057i
\(979\) 7.03184e12 0.244651
\(980\) −2.69681e13 3.17553e12i −0.933971 0.109976i
\(981\) 1.10390e14 3.80555
\(982\) −5.93340e12 + 1.20927e13i −0.203611 + 0.414975i
\(983\) 8.72591e12 8.72591e12i 0.298071 0.298071i −0.542187 0.840258i \(-0.682403\pi\)
0.840258 + 0.542187i \(0.182403\pi\)
\(984\) 2.33619e13 + 1.54077e13i 0.794383 + 0.523915i
\(985\) 3.56044e13 3.44770e11i 1.20515 0.0116699i
\(986\) 1.80894e13 + 5.29412e13i 0.609507 + 1.78381i
\(987\) −5.24137e12 5.24137e12i −0.175799 0.175799i
\(988\) −2.38168e12 + 1.86681e13i −0.0795203 + 0.623297i
\(989\) 1.02478e12i 0.0340603i
\(990\) 1.16784e13 + 3.31266e13i 0.386390 + 1.09602i
\(991\) 3.65275e13i 1.20306i 0.798849 + 0.601531i \(0.205442\pi\)
−0.798849 + 0.601531i \(0.794558\pi\)
\(992\) −3.49270e13 3.00169e13i −1.14514 0.984153i
\(993\) −6.40595e13 6.40595e13i −2.09080 2.09080i
\(994\) −7.96723e12 + 2.72232e12i −0.258862 + 0.0884504i
\(995\) 2.42610e13 + 2.37957e13i 0.784703 + 0.769652i
\(996\) −5.28325e13 + 4.08770e13i −1.70112 + 1.31617i
\(997\) −5.91654e12 + 5.91654e12i −0.189644 + 0.189644i −0.795542 0.605898i \(-0.792814\pi\)
0.605898 + 0.795542i \(0.292814\pi\)
\(998\) 1.13992e13 + 5.59313e12i 0.363738 + 0.178471i
\(999\) 3.16892e13 1.00662
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 20.10.e.b.3.20 yes 48
4.3 odd 2 inner 20.10.e.b.3.7 48
5.2 odd 4 inner 20.10.e.b.7.7 yes 48
5.3 odd 4 100.10.e.e.7.18 48
5.4 even 2 100.10.e.e.43.5 48
20.3 even 4 100.10.e.e.7.5 48
20.7 even 4 inner 20.10.e.b.7.20 yes 48
20.19 odd 2 100.10.e.e.43.18 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.10.e.b.3.7 48 4.3 odd 2 inner
20.10.e.b.3.20 yes 48 1.1 even 1 trivial
20.10.e.b.7.7 yes 48 5.2 odd 4 inner
20.10.e.b.7.20 yes 48 20.7 even 4 inner
100.10.e.e.7.5 48 20.3 even 4
100.10.e.e.7.18 48 5.3 odd 4
100.10.e.e.43.5 48 5.4 even 2
100.10.e.e.43.18 48 20.19 odd 2