Properties

Label 23.15.b.b.22.12
Level $23$
Weight $15$
Character 23.22
Analytic conductor $28.596$
Analytic rank $0$
Dimension $24$
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] = [23,15,Mod(22,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.22");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.5956626749\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.12
Character \(\chi\) \(=\) 23.22
Dual form 23.15.b.b.22.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-54.1371 q^{2} -3497.25 q^{3} -13453.2 q^{4} -104018. i q^{5} +189331. q^{6} -363656. i q^{7} +1.61530e6 q^{8} +7.44782e6 q^{9} +O(q^{10})\) \(q-54.1371 q^{2} -3497.25 q^{3} -13453.2 q^{4} -104018. i q^{5} +189331. q^{6} -363656. i q^{7} +1.61530e6 q^{8} +7.44782e6 q^{9} +5.63123e6i q^{10} +1.70377e7i q^{11} +4.70492e7 q^{12} +4.63838e7 q^{13} +1.96873e7i q^{14} +3.63778e8i q^{15} +1.32969e8 q^{16} -7.43123e8i q^{17} -4.03203e8 q^{18} -1.19078e9i q^{19} +1.39937e9i q^{20} +1.27180e9i q^{21} -9.22370e8i q^{22} +(3.02387e9 - 1.56494e9i) q^{23} -5.64910e9 q^{24} -4.71624e9 q^{25} -2.51108e9 q^{26} -9.31965e9 q^{27} +4.89233e9i q^{28} +1.91522e10 q^{29} -1.96939e10i q^{30} +1.15243e10 q^{31} -3.36636e10 q^{32} -5.95851e10i q^{33} +4.02305e10i q^{34} -3.78268e10 q^{35} -1.00197e11 q^{36} -4.82300e10i q^{37} +6.44654e10i q^{38} -1.62216e11 q^{39} -1.68020e11i q^{40} -2.83740e11 q^{41} -6.88514e10i q^{42} +2.89161e11i q^{43} -2.29211e11i q^{44} -7.74707e11i q^{45} +(-1.63704e11 + 8.47212e10i) q^{46} +1.70535e11 q^{47} -4.65028e11 q^{48} +5.45977e11 q^{49} +2.55324e11 q^{50} +2.59889e12i q^{51} -6.24010e11 q^{52} -2.00801e12i q^{53} +5.04538e11 q^{54} +1.77223e12 q^{55} -5.87412e11i q^{56} +4.16446e12i q^{57} -1.03684e12 q^{58} +1.84293e12 q^{59} -4.89397e12i q^{60} +2.15010e12i q^{61} -6.23891e11 q^{62} -2.70844e12i q^{63} -3.56122e11 q^{64} -4.82476e12i q^{65} +3.22576e12i q^{66} -3.48837e12i q^{67} +9.99737e12i q^{68} +(-1.05752e13 + 5.47299e12i) q^{69} +2.04783e12 q^{70} +5.84451e12 q^{71} +1.20304e13 q^{72} +1.12981e13 q^{73} +2.61103e12i q^{74} +1.64939e13 q^{75} +1.60198e13i q^{76} +6.19585e12 q^{77} +8.78190e12 q^{78} +1.67367e13i q^{79} -1.38312e13i q^{80} -3.02950e12 q^{81} +1.53608e13 q^{82} -2.84328e13i q^{83} -1.71097e13i q^{84} -7.72982e13 q^{85} -1.56543e13i q^{86} -6.69800e13 q^{87} +2.75209e13i q^{88} -7.66878e13i q^{89} +4.19404e13i q^{90} -1.68678e13i q^{91} +(-4.06807e13 + 2.10534e13i) q^{92} -4.03034e13 q^{93} -9.23228e12 q^{94} -1.23863e14 q^{95} +1.17730e14 q^{96} -1.08940e14i q^{97} -2.95576e13 q^{98} +1.26893e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9} - 61408584 q^{12} - 75796032 q^{13} + 61604880 q^{16} + 2078422368 q^{18} + 11061310696 q^{23} - 31030771920 q^{24} - 46421538840 q^{25} - 2664699128 q^{26} + 53616275568 q^{27} + 34752122960 q^{29} - 66504561216 q^{31} - 119385530304 q^{32} + 268767587760 q^{35} - 826304812272 q^{36} - 531040317600 q^{39} - 586388906608 q^{41} - 219014904864 q^{46} + 552854704544 q^{47} + 1314198459696 q^{48} - 2682585958584 q^{49} + 1292374320920 q^{50} - 614830645416 q^{52} - 756511540560 q^{54} - 4886166096240 q^{55} - 4069251029352 q^{58} + 17167207160144 q^{59} + 7479493046896 q^{62} + 18607147469856 q^{64} - 1866422538000 q^{69} + 10676769015360 q^{70} + 15000981757712 q^{71} + 5949703969824 q^{72} + 17535136179168 q^{73} - 79533751619520 q^{75} + 53823905395344 q^{77} + 6433358950512 q^{78} + 149774494087944 q^{81} - 27510435600840 q^{82} - 170228194057680 q^{85} - 286575506293872 q^{87} + 133024510658856 q^{92} + 66347882278032 q^{93} - 205878296932464 q^{94} - 211992774994560 q^{95} + 494703018436320 q^{96} - 537018388090408 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −54.1371 −0.422946 −0.211473 0.977384i \(-0.567826\pi\)
−0.211473 + 0.977384i \(0.567826\pi\)
\(3\) −3497.25 −1.59911 −0.799555 0.600593i \(-0.794931\pi\)
−0.799555 + 0.600593i \(0.794931\pi\)
\(4\) −13453.2 −0.821117
\(5\) 104018.i 1.33143i −0.746206 0.665716i \(-0.768126\pi\)
0.746206 0.665716i \(-0.231874\pi\)
\(6\) 189331. 0.676337
\(7\) 363656.i 0.441575i −0.975322 0.220787i \(-0.929137\pi\)
0.975322 0.220787i \(-0.0708627\pi\)
\(8\) 1.61530e6 0.770234
\(9\) 7.44782e6 1.55715
\(10\) 5.63123e6i 0.563123i
\(11\) 1.70377e7i 0.874302i 0.899388 + 0.437151i \(0.144012\pi\)
−0.899388 + 0.437151i \(0.855988\pi\)
\(12\) 4.70492e7 1.31306
\(13\) 4.63838e7 0.739202 0.369601 0.929191i \(-0.379494\pi\)
0.369601 + 0.929191i \(0.379494\pi\)
\(14\) 1.96873e7i 0.186762i
\(15\) 3.63778e8i 2.12911i
\(16\) 1.32969e8 0.495350
\(17\) 7.43123e8i 1.81100i −0.424347 0.905500i \(-0.639496\pi\)
0.424347 0.905500i \(-0.360504\pi\)
\(18\) −4.03203e8 −0.658591
\(19\) 1.19078e9i 1.33216i −0.745880 0.666080i \(-0.767971\pi\)
0.745880 0.666080i \(-0.232029\pi\)
\(20\) 1.39937e9i 1.09326i
\(21\) 1.27180e9i 0.706127i
\(22\) 9.22370e8i 0.369782i
\(23\) 3.02387e9 1.56494e9i 0.888114 0.459624i
\(24\) −5.64910e9 −1.23169
\(25\) −4.71624e9 −0.772709
\(26\) −2.51108e9 −0.312642
\(27\) −9.31965e9 −0.890950
\(28\) 4.89233e9i 0.362585i
\(29\) 1.91522e10 1.11028 0.555139 0.831758i \(-0.312665\pi\)
0.555139 + 0.831758i \(0.312665\pi\)
\(30\) 1.96939e10i 0.900496i
\(31\) 1.15243e10 0.418873 0.209436 0.977822i \(-0.432837\pi\)
0.209436 + 0.977822i \(0.432837\pi\)
\(32\) −3.36636e10 −0.979740
\(33\) 5.95851e10i 1.39811i
\(34\) 4.02305e10i 0.765955i
\(35\) −3.78268e10 −0.587927
\(36\) −1.00197e11 −1.27860
\(37\) 4.82300e10i 0.508049i −0.967198 0.254024i \(-0.918246\pi\)
0.967198 0.254024i \(-0.0817543\pi\)
\(38\) 6.44654e10i 0.563432i
\(39\) −1.62216e11 −1.18207
\(40\) 1.68020e11i 1.02551i
\(41\) −2.83740e11 −1.45691 −0.728456 0.685093i \(-0.759762\pi\)
−0.728456 + 0.685093i \(0.759762\pi\)
\(42\) 6.88514e10i 0.298653i
\(43\) 2.89161e11i 1.06380i 0.846807 + 0.531900i \(0.178522\pi\)
−0.846807 + 0.531900i \(0.821478\pi\)
\(44\) 2.29211e11i 0.717904i
\(45\) 7.74707e11i 2.07324i
\(46\) −1.63704e11 + 8.47212e10i −0.375624 + 0.194396i
\(47\) 1.70535e11 0.336612 0.168306 0.985735i \(-0.446170\pi\)
0.168306 + 0.985735i \(0.446170\pi\)
\(48\) −4.65028e11 −0.792119
\(49\) 5.45977e11 0.805012
\(50\) 2.55324e11 0.326814
\(51\) 2.59889e12i 2.89599i
\(52\) −6.24010e11 −0.606971
\(53\) 2.00801e12i 1.70937i −0.519151 0.854683i \(-0.673752\pi\)
0.519151 0.854683i \(-0.326248\pi\)
\(54\) 5.04538e11 0.376823
\(55\) 1.77223e12 1.16407
\(56\) 5.87412e11i 0.340116i
\(57\) 4.16446e12i 2.13027i
\(58\) −1.03684e12 −0.469587
\(59\) 1.84293e12 0.740532 0.370266 0.928926i \(-0.379267\pi\)
0.370266 + 0.928926i \(0.379267\pi\)
\(60\) 4.89397e12i 1.74824i
\(61\) 2.15010e12i 0.684149i 0.939673 + 0.342075i \(0.111130\pi\)
−0.939673 + 0.342075i \(0.888870\pi\)
\(62\) −6.23891e11 −0.177161
\(63\) 2.70844e12i 0.687600i
\(64\) −3.56122e11 −0.0809728
\(65\) 4.82476e12i 0.984197i
\(66\) 3.22576e12i 0.591323i
\(67\) 3.48837e12i 0.575571i −0.957695 0.287786i \(-0.907081\pi\)
0.957695 0.287786i \(-0.0929191\pi\)
\(68\) 9.99737e12i 1.48704i
\(69\) −1.05752e13 + 5.47299e12i −1.42019 + 0.734989i
\(70\) 2.04783e12 0.248661
\(71\) 5.84451e12 0.642599 0.321299 0.946978i \(-0.395880\pi\)
0.321299 + 0.946978i \(0.395880\pi\)
\(72\) 1.20304e13 1.19937
\(73\) 1.12981e13 1.02270 0.511348 0.859374i \(-0.329146\pi\)
0.511348 + 0.859374i \(0.329146\pi\)
\(74\) 2.61103e12i 0.214877i
\(75\) 1.64939e13 1.23565
\(76\) 1.60198e13i 1.09386i
\(77\) 6.19585e12 0.386070
\(78\) 8.78190e12 0.499950
\(79\) 1.67367e13i 0.871528i 0.900061 + 0.435764i \(0.143522\pi\)
−0.900061 + 0.435764i \(0.856478\pi\)
\(80\) 1.38312e13i 0.659524i
\(81\) −3.02950e12 −0.132427
\(82\) 1.53608e13 0.616195
\(83\) 2.84328e13i 1.04779i −0.851784 0.523894i \(-0.824479\pi\)
0.851784 0.523894i \(-0.175521\pi\)
\(84\) 1.71097e13i 0.579813i
\(85\) −7.72982e13 −2.41122
\(86\) 1.56543e13i 0.449930i
\(87\) −6.69800e13 −1.77546
\(88\) 2.75209e13i 0.673417i
\(89\) 7.66878e13i 1.73379i −0.498492 0.866894i \(-0.666113\pi\)
0.498492 0.866894i \(-0.333887\pi\)
\(90\) 4.19404e13i 0.876869i
\(91\) 1.68678e13i 0.326413i
\(92\) −4.06807e13 + 2.10534e13i −0.729245 + 0.377405i
\(93\) −4.03034e13 −0.669824
\(94\) −9.23228e12 −0.142369
\(95\) −1.23863e14 −1.77368
\(96\) 1.17730e14 1.56671
\(97\) 1.08940e14i 1.34829i −0.738597 0.674147i \(-0.764511\pi\)
0.738597 0.674147i \(-0.235489\pi\)
\(98\) −2.95576e13 −0.340476
\(99\) 1.26893e14i 1.36142i
\(100\) 6.34485e13 0.634485
\(101\) −1.92236e13 −0.179302 −0.0896509 0.995973i \(-0.528575\pi\)
−0.0896509 + 0.995973i \(0.528575\pi\)
\(102\) 1.40696e14i 1.22485i
\(103\) 4.69048e13i 0.381379i −0.981650 0.190689i \(-0.938928\pi\)
0.981650 0.190689i \(-0.0610723\pi\)
\(104\) 7.49237e13 0.569358
\(105\) 1.32290e14 0.940160
\(106\) 1.08708e14i 0.722969i
\(107\) 8.43182e13i 0.525091i 0.964920 + 0.262546i \(0.0845620\pi\)
−0.964920 + 0.262546i \(0.915438\pi\)
\(108\) 1.25379e14 0.731574
\(109\) 3.64514e13i 0.199402i 0.995017 + 0.0997008i \(0.0317885\pi\)
−0.995017 + 0.0997008i \(0.968211\pi\)
\(110\) −9.59431e13 −0.492340
\(111\) 1.68673e14i 0.812426i
\(112\) 4.83551e13i 0.218734i
\(113\) 2.47998e14i 1.05414i 0.849821 + 0.527072i \(0.176710\pi\)
−0.849821 + 0.527072i \(0.823290\pi\)
\(114\) 2.25452e14i 0.900990i
\(115\) −1.62782e14 3.14537e14i −0.611958 1.18246i
\(116\) −2.57657e14 −0.911668
\(117\) 3.45458e14 1.15105
\(118\) −9.97706e13 −0.313205
\(119\) −2.70241e14 −0.799692
\(120\) 5.87609e14i 1.63991i
\(121\) 8.94675e13 0.235596
\(122\) 1.16400e14i 0.289358i
\(123\) 9.92310e14 2.32976
\(124\) −1.55038e14 −0.343944
\(125\) 1.44301e14i 0.302622i
\(126\) 1.46627e14i 0.290817i
\(127\) 3.36880e14 0.632192 0.316096 0.948727i \(-0.397628\pi\)
0.316096 + 0.948727i \(0.397628\pi\)
\(128\) 5.70824e14 1.01399
\(129\) 1.01127e15i 1.70113i
\(130\) 2.61198e14i 0.416262i
\(131\) 6.45474e13 0.0974944 0.0487472 0.998811i \(-0.484477\pi\)
0.0487472 + 0.998811i \(0.484477\pi\)
\(132\) 8.01609e14i 1.14801i
\(133\) −4.33035e14 −0.588249
\(134\) 1.88850e14i 0.243435i
\(135\) 9.69412e14i 1.18624i
\(136\) 1.20036e15i 1.39489i
\(137\) 1.27294e15i 1.40528i 0.711544 + 0.702641i \(0.247996\pi\)
−0.711544 + 0.702641i \(0.752004\pi\)
\(138\) 5.72513e14 2.96292e14i 0.600664 0.310861i
\(139\) −4.66027e14 −0.464845 −0.232422 0.972615i \(-0.574665\pi\)
−0.232422 + 0.972615i \(0.574665\pi\)
\(140\) 5.08891e14 0.482757
\(141\) −5.96405e14 −0.538279
\(142\) −3.16405e14 −0.271784
\(143\) 7.90273e14i 0.646286i
\(144\) 9.90332e14 0.771335
\(145\) 1.99217e15i 1.47826i
\(146\) −6.11647e14 −0.432545
\(147\) −1.90942e15 −1.28730
\(148\) 6.48847e14i 0.417167i
\(149\) 3.72395e14i 0.228402i −0.993458 0.114201i \(-0.963569\pi\)
0.993458 0.114201i \(-0.0364308\pi\)
\(150\) −8.92931e14 −0.522612
\(151\) −3.57307e15 −1.99619 −0.998097 0.0616603i \(-0.980360\pi\)
−0.998097 + 0.0616603i \(0.980360\pi\)
\(152\) 1.92347e15i 1.02608i
\(153\) 5.53464e15i 2.82000i
\(154\) −3.35425e14 −0.163287
\(155\) 1.19873e15i 0.557700i
\(156\) 2.18232e15 0.970614
\(157\) 9.97719e14i 0.424337i 0.977233 + 0.212168i \(0.0680525\pi\)
−0.977233 + 0.212168i \(0.931947\pi\)
\(158\) 9.06078e14i 0.368609i
\(159\) 7.02252e15i 2.73346i
\(160\) 3.50162e15i 1.30446i
\(161\) −5.69099e14 1.09965e15i −0.202958 0.392169i
\(162\) 1.64008e14 0.0560094
\(163\) −6.93882e14 −0.226972 −0.113486 0.993540i \(-0.536202\pi\)
−0.113486 + 0.993540i \(0.536202\pi\)
\(164\) 3.81720e15 1.19629
\(165\) −6.19792e15 −1.86148
\(166\) 1.53927e15i 0.443157i
\(167\) 5.06681e15 1.39868 0.699341 0.714788i \(-0.253477\pi\)
0.699341 + 0.714788i \(0.253477\pi\)
\(168\) 2.05433e15i 0.543883i
\(169\) −1.78592e15 −0.453580
\(170\) 4.18470e15 1.01982
\(171\) 8.86872e15i 2.07438i
\(172\) 3.89013e15i 0.873504i
\(173\) −5.99671e15 −1.29297 −0.646487 0.762925i \(-0.723763\pi\)
−0.646487 + 0.762925i \(0.723763\pi\)
\(174\) 3.62610e15 0.750922
\(175\) 1.71509e15i 0.341209i
\(176\) 2.26549e15i 0.433085i
\(177\) −6.44518e15 −1.18419
\(178\) 4.15165e15i 0.733299i
\(179\) 6.80266e15 1.15533 0.577667 0.816273i \(-0.303963\pi\)
0.577667 + 0.816273i \(0.303963\pi\)
\(180\) 1.04223e16i 1.70237i
\(181\) 7.23728e15i 1.13717i −0.822625 0.568585i \(-0.807491\pi\)
0.822625 0.568585i \(-0.192509\pi\)
\(182\) 9.13171e14i 0.138055i
\(183\) 7.51946e15i 1.09403i
\(184\) 4.88445e15 2.52784e15i 0.684055 0.354018i
\(185\) −5.01679e15 −0.676432
\(186\) 2.18191e15 0.283299
\(187\) 1.26611e16 1.58336
\(188\) −2.29424e15 −0.276398
\(189\) 3.38914e15i 0.393421i
\(190\) 6.70556e15 0.750171
\(191\) 5.10982e15i 0.551026i 0.961297 + 0.275513i \(0.0888477\pi\)
−0.961297 + 0.275513i \(0.911152\pi\)
\(192\) 1.24545e15 0.129484
\(193\) −1.05662e16 −1.05930 −0.529649 0.848217i \(-0.677676\pi\)
−0.529649 + 0.848217i \(0.677676\pi\)
\(194\) 5.89769e15i 0.570256i
\(195\) 1.68734e16i 1.57384i
\(196\) −7.34513e15 −0.661009
\(197\) 9.62662e15 0.836007 0.418004 0.908445i \(-0.362730\pi\)
0.418004 + 0.908445i \(0.362730\pi\)
\(198\) 6.86964e15i 0.575808i
\(199\) 8.89744e15i 0.719936i −0.932965 0.359968i \(-0.882788\pi\)
0.932965 0.359968i \(-0.117212\pi\)
\(200\) −7.61814e15 −0.595167
\(201\) 1.21997e16i 0.920402i
\(202\) 1.04071e15 0.0758350
\(203\) 6.96480e15i 0.490271i
\(204\) 3.49633e16i 2.37794i
\(205\) 2.95141e16i 1.93978i
\(206\) 2.53929e15i 0.161303i
\(207\) 2.25212e16 1.16554e16i 1.38293 0.715705i
\(208\) 6.16763e15 0.366164
\(209\) 2.02881e16 1.16471
\(210\) −7.16179e15 −0.397637
\(211\) 1.84823e16 0.992610 0.496305 0.868148i \(-0.334690\pi\)
0.496305 + 0.868148i \(0.334690\pi\)
\(212\) 2.70141e16i 1.40359i
\(213\) −2.04397e16 −1.02759
\(214\) 4.56474e15i 0.222085i
\(215\) 3.00779e16 1.41638
\(216\) −1.50540e16 −0.686239
\(217\) 4.19088e15i 0.184964i
\(218\) 1.97337e15i 0.0843360i
\(219\) −3.95124e16 −1.63540
\(220\) −2.38421e16 −0.955840
\(221\) 3.44689e16i 1.33869i
\(222\) 9.13144e15i 0.343612i
\(223\) −3.22061e16 −1.17437 −0.587185 0.809453i \(-0.699764\pi\)
−0.587185 + 0.809453i \(0.699764\pi\)
\(224\) 1.22420e16i 0.432629i
\(225\) −3.51257e16 −1.20323
\(226\) 1.34259e16i 0.445846i
\(227\) 4.70834e16i 1.51596i 0.652280 + 0.757978i \(0.273813\pi\)
−0.652280 + 0.757978i \(0.726187\pi\)
\(228\) 5.60253e16i 1.74920i
\(229\) 2.22913e15i 0.0674975i 0.999430 + 0.0337488i \(0.0107446\pi\)
−0.999430 + 0.0337488i \(0.989255\pi\)
\(230\) 8.81254e15 + 1.70281e16i 0.258825 + 0.500118i
\(231\) −2.16685e16 −0.617368
\(232\) 3.09364e16 0.855174
\(233\) −4.84546e16 −1.29970 −0.649850 0.760062i \(-0.725169\pi\)
−0.649850 + 0.760062i \(0.725169\pi\)
\(234\) −1.87021e16 −0.486832
\(235\) 1.77388e16i 0.448176i
\(236\) −2.47932e16 −0.608063
\(237\) 5.85326e16i 1.39367i
\(238\) 1.46301e16 0.338226
\(239\) −2.85573e15 −0.0641108 −0.0320554 0.999486i \(-0.510205\pi\)
−0.0320554 + 0.999486i \(0.510205\pi\)
\(240\) 4.83713e16i 1.05465i
\(241\) 1.91486e15i 0.0405526i −0.999794 0.0202763i \(-0.993545\pi\)
0.999794 0.0202763i \(-0.00645459\pi\)
\(242\) −4.84351e15 −0.0996443
\(243\) 5.51705e16 1.10271
\(244\) 2.89257e16i 0.561766i
\(245\) 5.67915e16i 1.07182i
\(246\) −5.37207e16 −0.985363
\(247\) 5.52330e16i 0.984736i
\(248\) 1.86152e16 0.322630
\(249\) 9.94367e16i 1.67553i
\(250\) 7.81205e15i 0.127993i
\(251\) 4.33087e16i 0.690015i 0.938600 + 0.345008i \(0.112124\pi\)
−0.938600 + 0.345008i \(0.887876\pi\)
\(252\) 3.64372e16i 0.564600i
\(253\) 2.66629e16 + 5.15197e16i 0.401850 + 0.776480i
\(254\) −1.82377e16 −0.267383
\(255\) 2.70332e17 3.85581
\(256\) −2.50680e16 −0.347889
\(257\) 1.08722e17 1.46820 0.734101 0.679041i \(-0.237604\pi\)
0.734101 + 0.679041i \(0.237604\pi\)
\(258\) 5.47471e16i 0.719488i
\(259\) −1.75391e16 −0.224342
\(260\) 6.49083e16i 0.808141i
\(261\) 1.42642e17 1.72887
\(262\) −3.49441e15 −0.0412349
\(263\) 6.64568e16i 0.763570i −0.924251 0.381785i \(-0.875309\pi\)
0.924251 0.381785i \(-0.124691\pi\)
\(264\) 9.62476e16i 1.07687i
\(265\) −2.08869e17 −2.27590
\(266\) 2.34432e16 0.248797
\(267\) 2.68197e17i 2.77252i
\(268\) 4.69297e16i 0.472611i
\(269\) −9.83762e16 −0.965215 −0.482607 0.875837i \(-0.660310\pi\)
−0.482607 + 0.875837i \(0.660310\pi\)
\(270\) 5.24811e16i 0.501714i
\(271\) −6.73653e16 −0.627554 −0.313777 0.949497i \(-0.601594\pi\)
−0.313777 + 0.949497i \(0.601594\pi\)
\(272\) 9.88126e16i 0.897078i
\(273\) 5.89908e16i 0.521971i
\(274\) 6.89132e16i 0.594358i
\(275\) 8.03538e16i 0.675581i
\(276\) 1.42271e17 7.36291e16i 1.16614 0.603512i
\(277\) −8.87282e16 −0.709093 −0.354547 0.935038i \(-0.615365\pi\)
−0.354547 + 0.935038i \(0.615365\pi\)
\(278\) 2.52293e16 0.196604
\(279\) 8.58308e16 0.652249
\(280\) −6.11015e16 −0.452841
\(281\) 2.50651e17i 1.81187i −0.423422 0.905933i \(-0.639171\pi\)
0.423422 0.905933i \(-0.360829\pi\)
\(282\) 3.22876e16 0.227663
\(283\) 2.29216e16i 0.157667i −0.996888 0.0788334i \(-0.974880\pi\)
0.996888 0.0788334i \(-0.0251195\pi\)
\(284\) −7.86273e16 −0.527649
\(285\) 4.33179e17 2.83631
\(286\) 4.27830e16i 0.273344i
\(287\) 1.03184e17i 0.643336i
\(288\) −2.50720e17 −1.52561
\(289\) −3.83854e17 −2.27972
\(290\) 1.07850e17i 0.625223i
\(291\) 3.80990e17i 2.15607i
\(292\) −1.51996e17 −0.839752
\(293\) 2.28366e17i 1.23185i 0.787805 + 0.615924i \(0.211217\pi\)
−0.787805 + 0.615924i \(0.788783\pi\)
\(294\) 1.03370e17 0.544459
\(295\) 1.91698e17i 0.985967i
\(296\) 7.79058e16i 0.391316i
\(297\) 1.58785e17i 0.778959i
\(298\) 2.01604e16i 0.0966017i
\(299\) 1.40259e17 7.25879e16i 0.656496 0.339755i
\(300\) −2.21895e17 −1.01461
\(301\) 1.05155e17 0.469748
\(302\) 1.93435e17 0.844282
\(303\) 6.72298e16 0.286723
\(304\) 1.58337e17i 0.659885i
\(305\) 2.23650e17 0.910898
\(306\) 2.99629e17i 1.19271i
\(307\) 1.77181e17 0.689362 0.344681 0.938720i \(-0.387987\pi\)
0.344681 + 0.938720i \(0.387987\pi\)
\(308\) −8.33539e16 −0.317008
\(309\) 1.64038e17i 0.609867i
\(310\) 6.48960e16i 0.235877i
\(311\) −3.98607e17 −1.41652 −0.708259 0.705952i \(-0.750519\pi\)
−0.708259 + 0.705952i \(0.750519\pi\)
\(312\) −2.62027e17 −0.910467
\(313\) 4.75005e17i 1.61394i −0.590591 0.806971i \(-0.701105\pi\)
0.590591 0.806971i \(-0.298895\pi\)
\(314\) 5.40136e16i 0.179471i
\(315\) −2.81727e17 −0.915492
\(316\) 2.25162e17i 0.715626i
\(317\) 5.59180e17 1.73835 0.869174 0.494507i \(-0.164651\pi\)
0.869174 + 0.494507i \(0.164651\pi\)
\(318\) 3.80179e17i 1.15611i
\(319\) 3.26308e17i 0.970719i
\(320\) 3.70432e16i 0.107810i
\(321\) 2.94882e17i 0.839679i
\(322\) 3.08094e16 + 5.95318e16i 0.0858404 + 0.165866i
\(323\) −8.84897e17 −2.41254
\(324\) 4.07564e16 0.108738
\(325\) −2.18757e17 −0.571188
\(326\) 3.75648e16 0.0959969
\(327\) 1.27480e17i 0.318865i
\(328\) −4.58324e17 −1.12216
\(329\) 6.20162e16i 0.148639i
\(330\) 3.35537e17 0.787306
\(331\) −3.39881e17 −0.780784 −0.390392 0.920649i \(-0.627661\pi\)
−0.390392 + 0.920649i \(0.627661\pi\)
\(332\) 3.82512e17i 0.860356i
\(333\) 3.59208e17i 0.791109i
\(334\) −2.74302e17 −0.591567
\(335\) −3.62854e17 −0.766334
\(336\) 1.69110e17i 0.349780i
\(337\) 7.58375e17i 1.53630i 0.640273 + 0.768148i \(0.278821\pi\)
−0.640273 + 0.768148i \(0.721179\pi\)
\(338\) 9.66842e16 0.191840
\(339\) 8.67313e17i 1.68569i
\(340\) 1.03991e18 1.97989
\(341\) 1.96347e17i 0.366221i
\(342\) 4.80126e17i 0.877350i
\(343\) 4.45188e17i 0.797048i
\(344\) 4.67081e17i 0.819375i
\(345\) 5.69290e17 + 1.10002e18i 0.978588 + 1.89089i
\(346\) 3.24644e17 0.546858
\(347\) 1.07300e18 1.77131 0.885655 0.464343i \(-0.153710\pi\)
0.885655 + 0.464343i \(0.153710\pi\)
\(348\) 9.01093e17 1.45786
\(349\) −1.14112e17 −0.180947 −0.0904737 0.995899i \(-0.528838\pi\)
−0.0904737 + 0.995899i \(0.528838\pi\)
\(350\) 9.28499e16i 0.144313i
\(351\) −4.32281e17 −0.658592
\(352\) 5.73550e17i 0.856589i
\(353\) 5.45475e17 0.798642 0.399321 0.916811i \(-0.369246\pi\)
0.399321 + 0.916811i \(0.369246\pi\)
\(354\) 3.48923e17 0.500849
\(355\) 6.07935e17i 0.855576i
\(356\) 1.03169e18i 1.42364i
\(357\) 9.45102e17 1.27880
\(358\) −3.68276e17 −0.488644
\(359\) 4.94984e17i 0.644066i 0.946728 + 0.322033i \(0.104366\pi\)
−0.946728 + 0.322033i \(0.895634\pi\)
\(360\) 1.25138e18i 1.59688i
\(361\) −6.18952e17 −0.774652
\(362\) 3.91805e17i 0.480961i
\(363\) −3.12890e17 −0.376744
\(364\) 2.26925e17i 0.268023i
\(365\) 1.17521e18i 1.36165i
\(366\) 4.07082e17i 0.462715i
\(367\) 2.94484e17i 0.328397i 0.986427 + 0.164198i \(0.0525037\pi\)
−0.986427 + 0.164198i \(0.947496\pi\)
\(368\) 4.02083e17 2.08089e17i 0.439927 0.227675i
\(369\) −2.11324e18 −2.26863
\(370\) 2.71594e17 0.286094
\(371\) −7.30225e17 −0.754813
\(372\) 5.42208e17 0.550004
\(373\) 1.93366e18i 1.92495i 0.271379 + 0.962473i \(0.412520\pi\)
−0.271379 + 0.962473i \(0.587480\pi\)
\(374\) −6.85434e17 −0.669676
\(375\) 5.04658e17i 0.483926i
\(376\) 2.75465e17 0.259270
\(377\) 8.88351e17 0.820720
\(378\) 1.83478e17i 0.166396i
\(379\) 1.54669e18i 1.37698i −0.725244 0.688492i \(-0.758273\pi\)
0.725244 0.688492i \(-0.241727\pi\)
\(380\) 1.66635e18 1.45640
\(381\) −1.17816e18 −1.01095
\(382\) 2.76631e17i 0.233054i
\(383\) 4.10276e17i 0.339379i −0.985498 0.169690i \(-0.945724\pi\)
0.985498 0.169690i \(-0.0542765\pi\)
\(384\) −1.99632e18 −1.62148
\(385\) 6.44481e17i 0.514026i
\(386\) 5.72023e17 0.448025
\(387\) 2.15362e18i 1.65650i
\(388\) 1.46559e18i 1.10711i
\(389\) 7.29254e17i 0.541043i −0.962714 0.270522i \(-0.912804\pi\)
0.962714 0.270522i \(-0.0871961\pi\)
\(390\) 9.13476e17i 0.665649i
\(391\) −1.16294e18 2.24711e18i −0.832379 1.60837i
\(392\) 8.81916e17 0.620047
\(393\) −2.25739e17 −0.155904
\(394\) −5.21157e17 −0.353586
\(395\) 1.74092e18 1.16038
\(396\) 1.70712e18i 1.11789i
\(397\) −6.73100e17 −0.433058 −0.216529 0.976276i \(-0.569474\pi\)
−0.216529 + 0.976276i \(0.569474\pi\)
\(398\) 4.81681e17i 0.304494i
\(399\) 1.51443e18 0.940675
\(400\) −6.27116e17 −0.382761
\(401\) 1.76399e18i 1.05800i 0.848622 + 0.529000i \(0.177433\pi\)
−0.848622 + 0.529000i \(0.822567\pi\)
\(402\) 6.60457e17i 0.389280i
\(403\) 5.34541e17 0.309632
\(404\) 2.58618e17 0.147228
\(405\) 3.15123e17i 0.176317i
\(406\) 3.77054e17i 0.207358i
\(407\) 8.21727e17 0.444188
\(408\) 4.19798e18i 2.23059i
\(409\) −3.07282e18 −1.60500 −0.802499 0.596654i \(-0.796496\pi\)
−0.802499 + 0.596654i \(0.796496\pi\)
\(410\) 1.59780e18i 0.820421i
\(411\) 4.45179e18i 2.24720i
\(412\) 6.31018e17i 0.313157i
\(413\) 6.70191e17i 0.327000i
\(414\) −1.21923e18 + 6.30988e17i −0.584904 + 0.302704i
\(415\) −2.95753e18 −1.39506
\(416\) −1.56145e18 −0.724226
\(417\) 1.62982e18 0.743338
\(418\) −1.09834e18 −0.492610
\(419\) 2.33105e17i 0.102814i 0.998678 + 0.0514071i \(0.0163706\pi\)
−0.998678 + 0.0514071i \(0.983629\pi\)
\(420\) −1.77972e18 −0.771981
\(421\) 1.17297e18i 0.500394i −0.968195 0.250197i \(-0.919505\pi\)
0.968195 0.250197i \(-0.0804954\pi\)
\(422\) −1.00058e18 −0.419820
\(423\) 1.27012e18 0.524156
\(424\) 3.24353e18i 1.31661i
\(425\) 3.50475e18i 1.39938i
\(426\) 1.10655e18 0.434613
\(427\) 7.81898e17 0.302103
\(428\) 1.13435e18i 0.431161i
\(429\) 2.76378e18i 1.03348i
\(430\) −1.62833e18 −0.599051
\(431\) 3.91693e18i 1.41777i 0.705325 + 0.708884i \(0.250801\pi\)
−0.705325 + 0.708884i \(0.749199\pi\)
\(432\) −1.23923e18 −0.441332
\(433\) 2.71222e18i 0.950408i −0.879876 0.475204i \(-0.842374\pi\)
0.879876 0.475204i \(-0.157626\pi\)
\(434\) 2.26882e17i 0.0782297i
\(435\) 6.96713e18i 2.36390i
\(436\) 4.90387e17i 0.163732i
\(437\) −1.86350e18 3.60077e18i −0.612293 1.18311i
\(438\) 2.13909e18 0.691686
\(439\) 1.52974e18 0.486818 0.243409 0.969924i \(-0.421734\pi\)
0.243409 + 0.969924i \(0.421734\pi\)
\(440\) 2.86267e18 0.896608
\(441\) 4.06634e18 1.25353
\(442\) 1.86605e18i 0.566195i
\(443\) 4.44473e18 1.32745 0.663727 0.747975i \(-0.268974\pi\)
0.663727 + 0.747975i \(0.268974\pi\)
\(444\) 2.26918e18i 0.667096i
\(445\) −7.97692e18 −2.30842
\(446\) 1.74355e18 0.496695
\(447\) 1.30236e18i 0.365240i
\(448\) 1.29506e17i 0.0357556i
\(449\) −2.67135e18 −0.726118 −0.363059 0.931766i \(-0.618268\pi\)
−0.363059 + 0.931766i \(0.618268\pi\)
\(450\) 1.90160e18 0.508900
\(451\) 4.83427e18i 1.27378i
\(452\) 3.33637e18i 0.865575i
\(453\) 1.24959e19 3.19213
\(454\) 2.54896e18i 0.641168i
\(455\) −1.75455e18 −0.434597
\(456\) 6.72685e18i 1.64081i
\(457\) 6.73286e18i 1.61728i 0.588302 + 0.808641i \(0.299797\pi\)
−0.588302 + 0.808641i \(0.700203\pi\)
\(458\) 1.20679e17i 0.0285478i
\(459\) 6.92564e18i 1.61351i
\(460\) 2.18993e18 + 4.23153e18i 0.502489 + 0.970940i
\(461\) 1.59506e18 0.360471 0.180235 0.983624i \(-0.442314\pi\)
0.180235 + 0.983624i \(0.442314\pi\)
\(462\) 1.17307e18 0.261113
\(463\) 2.18155e18 0.478298 0.239149 0.970983i \(-0.423132\pi\)
0.239149 + 0.970983i \(0.423132\pi\)
\(464\) 2.54665e18 0.549976
\(465\) 4.19228e18i 0.891825i
\(466\) 2.62319e18 0.549703
\(467\) 1.58011e18i 0.326189i −0.986610 0.163095i \(-0.947852\pi\)
0.986610 0.163095i \(-0.0521476\pi\)
\(468\) −4.64751e18 −0.945147
\(469\) −1.26857e18 −0.254158
\(470\) 9.60324e17i 0.189554i
\(471\) 3.48928e18i 0.678561i
\(472\) 2.97687e18 0.570382
\(473\) −4.92663e18 −0.930083
\(474\) 3.16878e18i 0.589446i
\(475\) 5.61601e18i 1.02937i
\(476\) 3.63560e18 0.656640
\(477\) 1.49553e19i 2.66174i
\(478\) 1.54601e17 0.0271154
\(479\) 1.91799e18i 0.331511i 0.986167 + 0.165755i \(0.0530062\pi\)
−0.986167 + 0.165755i \(0.946994\pi\)
\(480\) 1.22461e19i 2.08597i
\(481\) 2.23709e18i 0.375551i
\(482\) 1.03665e17i 0.0171515i
\(483\) 1.99029e18 + 3.84575e18i 0.324553 + 0.627121i
\(484\) −1.20362e18 −0.193452
\(485\) −1.13317e19 −1.79516
\(486\) −2.98677e18 −0.466389
\(487\) −5.60381e18 −0.862543 −0.431271 0.902222i \(-0.641935\pi\)
−0.431271 + 0.902222i \(0.641935\pi\)
\(488\) 3.47306e18i 0.526955i
\(489\) 2.42668e18 0.362953
\(490\) 3.07453e18i 0.453321i
\(491\) −7.91090e18 −1.14989 −0.574944 0.818193i \(-0.694976\pi\)
−0.574944 + 0.818193i \(0.694976\pi\)
\(492\) −1.33497e19 −1.91301
\(493\) 1.42324e19i 2.01071i
\(494\) 2.99015e18i 0.416490i
\(495\) 1.31992e19 1.81264
\(496\) 1.53238e18 0.207489
\(497\) 2.12539e18i 0.283755i
\(498\) 5.38321e18i 0.708657i
\(499\) 1.50726e19 1.95652 0.978261 0.207376i \(-0.0664923\pi\)
0.978261 + 0.207376i \(0.0664923\pi\)
\(500\) 1.94131e18i 0.248488i
\(501\) −1.77199e19 −2.23665
\(502\) 2.34460e18i 0.291839i
\(503\) 5.74019e18i 0.704613i 0.935885 + 0.352306i \(0.114602\pi\)
−0.935885 + 0.352306i \(0.885398\pi\)
\(504\) 4.37494e18i 0.529613i
\(505\) 1.99960e18i 0.238728i
\(506\) −1.44345e18 2.78913e18i −0.169961 0.328409i
\(507\) 6.24580e18 0.725325
\(508\) −4.53211e18 −0.519104
\(509\) 5.37325e18 0.607033 0.303516 0.952826i \(-0.401839\pi\)
0.303516 + 0.952826i \(0.401839\pi\)
\(510\) −1.46350e19 −1.63080
\(511\) 4.10863e18i 0.451597i
\(512\) −7.99527e18 −0.866849
\(513\) 1.10977e19i 1.18689i
\(514\) −5.88589e18 −0.620970
\(515\) −4.87894e18 −0.507780
\(516\) 1.36048e19i 1.39683i
\(517\) 2.90553e18i 0.294300i
\(518\) 9.49517e17 0.0948843
\(519\) 2.09720e19 2.06761
\(520\) 7.79342e18i 0.758062i
\(521\) 2.80563e18i 0.269257i 0.990896 + 0.134628i \(0.0429841\pi\)
−0.990896 + 0.134628i \(0.957016\pi\)
\(522\) −7.72221e18 −0.731220
\(523\) 1.31581e19i 1.22936i 0.788775 + 0.614682i \(0.210716\pi\)
−0.788775 + 0.614682i \(0.789284\pi\)
\(524\) −8.68368e17 −0.0800543
\(525\) 5.99811e18i 0.545631i
\(526\) 3.59777e18i 0.322949i
\(527\) 8.56396e18i 0.758579i
\(528\) 7.92299e18i 0.692551i
\(529\) 6.69477e18 9.46435e18i 0.577492 0.816397i
\(530\) 1.13076e19 0.962584
\(531\) 1.37258e19 1.15312
\(532\) 5.82569e18 0.483021
\(533\) −1.31609e19 −1.07695
\(534\) 1.45194e19i 1.17263i
\(535\) 8.77061e18 0.699123
\(536\) 5.63476e18i 0.443324i
\(537\) −2.37906e19 −1.84751
\(538\) 5.32580e18 0.408234
\(539\) 9.30219e18i 0.703823i
\(540\) 1.30417e19i 0.974040i
\(541\) 7.93256e18 0.584834 0.292417 0.956291i \(-0.405541\pi\)
0.292417 + 0.956291i \(0.405541\pi\)
\(542\) 3.64696e18 0.265421
\(543\) 2.53106e19i 1.81846i
\(544\) 2.50162e19i 1.77431i
\(545\) 3.79160e18 0.265489
\(546\) 3.19359e18i 0.220765i
\(547\) −3.44897e18 −0.235385 −0.117692 0.993050i \(-0.537550\pi\)
−0.117692 + 0.993050i \(0.537550\pi\)
\(548\) 1.71251e19i 1.15390i
\(549\) 1.60136e19i 1.06533i
\(550\) 4.35012e18i 0.285734i
\(551\) 2.28060e19i 1.47907i
\(552\) −1.70822e19 + 8.84050e18i −1.09388 + 0.566114i
\(553\) 6.08641e18 0.384845
\(554\) 4.80348e18 0.299908
\(555\) 1.75450e19 1.08169
\(556\) 6.26955e18 0.381692
\(557\) 2.53328e19i 1.52299i −0.648173 0.761493i \(-0.724466\pi\)
0.648173 0.761493i \(-0.275534\pi\)
\(558\) −4.64663e18 −0.275866
\(559\) 1.34124e19i 0.786364i
\(560\) −5.02981e18 −0.291229
\(561\) −4.42790e19 −2.53197
\(562\) 1.35695e19i 0.766321i
\(563\) 3.60984e17i 0.0201340i −0.999949 0.0100670i \(-0.996796\pi\)
0.999949 0.0100670i \(-0.00320448\pi\)
\(564\) 8.02355e18 0.441990
\(565\) 2.57963e19 1.40352
\(566\) 1.24091e18i 0.0666845i
\(567\) 1.10170e18i 0.0584764i
\(568\) 9.44062e18 0.494951
\(569\) 2.25204e19i 1.16625i 0.812383 + 0.583124i \(0.198170\pi\)
−0.812383 + 0.583124i \(0.801830\pi\)
\(570\) −2.34511e19 −1.19961
\(571\) 1.93126e19i 0.975862i 0.872882 + 0.487931i \(0.162248\pi\)
−0.872882 + 0.487931i \(0.837752\pi\)
\(572\) 1.06317e19i 0.530676i
\(573\) 1.78703e19i 0.881151i
\(574\) 5.58606e18i 0.272096i
\(575\) −1.42613e19 + 7.38063e18i −0.686254 + 0.355156i
\(576\) −2.65233e18 −0.126087
\(577\) −1.40650e19 −0.660553 −0.330277 0.943884i \(-0.607142\pi\)
−0.330277 + 0.943884i \(0.607142\pi\)
\(578\) 2.07807e19 0.964197
\(579\) 3.69527e19 1.69393
\(580\) 2.68010e19i 1.21382i
\(581\) −1.03398e19 −0.462677
\(582\) 2.06257e19i 0.911901i
\(583\) 3.42118e19 1.49450
\(584\) 1.82498e19 0.787714
\(585\) 3.59339e19i 1.53255i
\(586\) 1.23630e19i 0.521005i
\(587\) 2.38786e19 0.994358 0.497179 0.867648i \(-0.334369\pi\)
0.497179 + 0.867648i \(0.334369\pi\)
\(588\) 2.56878e19 1.05703
\(589\) 1.37229e19i 0.558006i
\(590\) 1.03779e19i 0.417011i
\(591\) −3.36667e19 −1.33687
\(592\) 6.41312e18i 0.251662i
\(593\) 3.48176e18 0.135025 0.0675127 0.997718i \(-0.478494\pi\)
0.0675127 + 0.997718i \(0.478494\pi\)
\(594\) 8.59616e18i 0.329457i
\(595\) 2.81100e19i 1.06473i
\(596\) 5.00990e18i 0.187545i
\(597\) 3.11166e19i 1.15126i
\(598\) −7.59320e18 + 3.92969e18i −0.277662 + 0.143698i
\(599\) −4.69083e19 −1.69536 −0.847679 0.530509i \(-0.822001\pi\)
−0.847679 + 0.530509i \(0.822001\pi\)
\(600\) 2.66426e19 0.951737
\(601\) 4.46391e18 0.157614 0.0788068 0.996890i \(-0.474889\pi\)
0.0788068 + 0.996890i \(0.474889\pi\)
\(602\) −5.69278e18 −0.198678
\(603\) 2.59808e19i 0.896253i
\(604\) 4.80691e19 1.63911
\(605\) 9.30623e18i 0.313680i
\(606\) −3.63962e18 −0.121268
\(607\) −1.82390e19 −0.600732 −0.300366 0.953824i \(-0.597109\pi\)
−0.300366 + 0.953824i \(0.597109\pi\)
\(608\) 4.00860e19i 1.30517i
\(609\) 2.43577e19i 0.783997i
\(610\) −1.21077e19 −0.385260
\(611\) 7.91008e18 0.248824
\(612\) 7.44585e19i 2.31555i
\(613\) 2.82394e18i 0.0868226i 0.999057 + 0.0434113i \(0.0138226\pi\)
−0.999057 + 0.0434113i \(0.986177\pi\)
\(614\) −9.59203e18 −0.291563
\(615\) 1.03218e20i 3.10192i
\(616\) 1.00081e19 0.297364
\(617\) 4.24441e19i 1.24687i −0.781875 0.623435i \(-0.785736\pi\)
0.781875 0.623435i \(-0.214264\pi\)
\(618\) 8.88053e18i 0.257941i
\(619\) 3.21398e19i 0.923013i −0.887137 0.461507i \(-0.847309\pi\)
0.887137 0.461507i \(-0.152691\pi\)
\(620\) 1.61268e19i 0.457937i
\(621\) −2.81814e19 + 1.45847e19i −0.791264 + 0.409502i
\(622\) 2.15794e19 0.599111
\(623\) −2.78880e19 −0.765598
\(624\) −2.15698e19 −0.585536
\(625\) −4.37956e19 −1.17563
\(626\) 2.57154e19i 0.682610i
\(627\) −7.09528e19 −1.86250
\(628\) 1.34225e19i 0.348430i
\(629\) −3.58408e19 −0.920076
\(630\) 1.52519e19 0.387204
\(631\) 2.19634e19i 0.551434i −0.961239 0.275717i \(-0.911085\pi\)
0.961239 0.275717i \(-0.0889152\pi\)
\(632\) 2.70348e19i 0.671280i
\(633\) −6.46373e19 −1.58729
\(634\) −3.02723e19 −0.735227
\(635\) 3.50416e19i 0.841721i
\(636\) 9.44753e19i 2.24449i
\(637\) 2.53245e19 0.595066
\(638\) 1.76654e19i 0.410561i
\(639\) 4.35289e19 1.00062
\(640\) 5.93760e19i 1.35005i
\(641\) 1.83694e19i 0.413132i −0.978433 0.206566i \(-0.933771\pi\)
0.978433 0.206566i \(-0.0662288\pi\)
\(642\) 1.59640e19i 0.355139i
\(643\) 1.12644e19i 0.247873i 0.992290 + 0.123937i \(0.0395519\pi\)
−0.992290 + 0.123937i \(0.960448\pi\)
\(644\) 7.65620e18 + 1.47938e19i 0.166653 + 0.322016i
\(645\) −1.05190e20 −2.26494
\(646\) 4.79057e19 1.02037
\(647\) −5.58592e18 −0.117697 −0.0588484 0.998267i \(-0.518743\pi\)
−0.0588484 + 0.998267i \(0.518743\pi\)
\(648\) −4.89355e18 −0.102000
\(649\) 3.13992e19i 0.647448i
\(650\) 1.18429e19 0.241582
\(651\) 1.46566e19i 0.295777i
\(652\) 9.33492e18 0.186371
\(653\) 6.34906e19 1.25406 0.627028 0.778996i \(-0.284271\pi\)
0.627028 + 0.778996i \(0.284271\pi\)
\(654\) 6.90138e18i 0.134863i
\(655\) 6.71410e18i 0.129807i
\(656\) −3.77287e19 −0.721681
\(657\) 8.41463e19 1.59249
\(658\) 3.35737e18i 0.0628664i
\(659\) 4.28614e19i 0.794087i 0.917800 + 0.397044i \(0.129964\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(660\) 8.33818e19 1.52849
\(661\) 1.01826e20i 1.84692i 0.383700 + 0.923458i \(0.374650\pi\)
−0.383700 + 0.923458i \(0.625350\pi\)
\(662\) 1.84002e19 0.330229
\(663\) 1.20546e20i 2.14072i
\(664\) 4.59274e19i 0.807041i
\(665\) 4.50434e19i 0.783213i
\(666\) 1.94465e19i 0.334596i
\(667\) 5.79137e19 2.99720e19i 0.986053 0.510310i
\(668\) −6.81647e19 −1.14848
\(669\) 1.12633e20 1.87795
\(670\) 1.96438e19 0.324118
\(671\) −3.66328e19 −0.598153
\(672\) 4.28133e19i 0.691821i
\(673\) −9.87680e19 −1.57947 −0.789734 0.613449i \(-0.789781\pi\)
−0.789734 + 0.613449i \(0.789781\pi\)
\(674\) 4.10562e19i 0.649770i
\(675\) 4.39537e19 0.688445
\(676\) 2.40262e19 0.372442
\(677\) 8.03279e18i 0.123238i −0.998100 0.0616192i \(-0.980374\pi\)
0.998100 0.0616192i \(-0.0196264\pi\)
\(678\) 4.69538e19i 0.712956i
\(679\) −3.96166e19 −0.595373
\(680\) −1.24860e20 −1.85720
\(681\) 1.64663e20i 2.42418i
\(682\) 1.06297e19i 0.154892i
\(683\) 5.80621e19 0.837428 0.418714 0.908118i \(-0.362481\pi\)
0.418714 + 0.908118i \(0.362481\pi\)
\(684\) 1.19312e20i 1.70331i
\(685\) 1.32409e20 1.87104
\(686\) 2.41012e19i 0.337108i
\(687\) 7.79585e18i 0.107936i
\(688\) 3.84495e19i 0.526953i
\(689\) 9.31392e19i 1.26357i
\(690\) −3.08197e19 5.95517e19i −0.413890 0.799743i
\(691\) −2.22123e19 −0.295289 −0.147644 0.989040i \(-0.547169\pi\)
−0.147644 + 0.989040i \(0.547169\pi\)
\(692\) 8.06748e19 1.06168
\(693\) 4.61456e19 0.601170
\(694\) −5.80893e19 −0.749168
\(695\) 4.84753e19i 0.618909i
\(696\) −1.08193e20 −1.36752
\(697\) 2.10854e20i 2.63847i
\(698\) 6.17768e18 0.0765310
\(699\) 1.69458e20 2.07837
\(700\) 2.30734e19i 0.280173i
\(701\) 1.23169e20i 1.48073i −0.672206 0.740364i \(-0.734653\pi\)
0.672206 0.740364i \(-0.265347\pi\)
\(702\) 2.34024e19 0.278549
\(703\) −5.74314e19 −0.676802
\(704\) 6.06750e18i 0.0707947i
\(705\) 6.20369e19i 0.716682i
\(706\) −2.95304e19 −0.337782
\(707\) 6.99077e18i 0.0791752i
\(708\) 8.67081e19 0.972360
\(709\) 1.16029e20i 1.28837i −0.764868 0.644187i \(-0.777196\pi\)
0.764868 0.644187i \(-0.222804\pi\)
\(710\) 3.29118e19i 0.361862i
\(711\) 1.24652e20i 1.35710i
\(712\) 1.23874e20i 1.33542i
\(713\) 3.48480e19 1.80348e19i 0.372007 0.192524i
\(714\) −5.11650e19 −0.540861
\(715\) 8.22026e19 0.860485
\(716\) −9.15174e19 −0.948664
\(717\) 9.98720e18 0.102520
\(718\) 2.67970e19i 0.272405i
\(719\) −1.06708e20 −1.07422 −0.537110 0.843513i \(-0.680484\pi\)
−0.537110 + 0.843513i \(0.680484\pi\)
\(720\) 1.03012e20i 1.02698i
\(721\) −1.70572e19 −0.168407
\(722\) 3.35083e19 0.327636
\(723\) 6.69676e18i 0.0648481i
\(724\) 9.73644e19i 0.933749i
\(725\) −9.03263e19 −0.857922
\(726\) 1.69390e19 0.159342
\(727\) 1.19170e20i 1.11027i 0.831761 + 0.555133i \(0.187333\pi\)
−0.831761 + 0.555133i \(0.812667\pi\)
\(728\) 2.72464e19i 0.251414i
\(729\) −1.78455e20 −1.63094
\(730\) 6.36223e19i 0.575903i
\(731\) 2.14882e20 1.92654
\(732\) 1.01161e20i 0.898326i
\(733\) 1.34342e20i 1.18163i −0.806805 0.590817i \(-0.798805\pi\)
0.806805 0.590817i \(-0.201195\pi\)
\(734\) 1.59425e19i 0.138894i
\(735\) 1.98614e20i 1.71395i
\(736\) −1.01794e20 + 5.26815e19i −0.870120 + 0.450312i
\(737\) 5.94337e19 0.503223
\(738\) 1.14405e20 0.959509
\(739\) 1.35112e20 1.12249 0.561246 0.827649i \(-0.310322\pi\)
0.561246 + 0.827649i \(0.310322\pi\)
\(740\) 6.74918e19 0.555430
\(741\) 1.93164e20i 1.57470i
\(742\) 3.95322e19 0.319245
\(743\) 2.12605e20i 1.70079i −0.526142 0.850397i \(-0.676362\pi\)
0.526142 0.850397i \(-0.323638\pi\)
\(744\) −6.51019e19 −0.515921
\(745\) −3.87358e19 −0.304102
\(746\) 1.04683e20i 0.814147i
\(747\) 2.11762e20i 1.63157i
\(748\) −1.70332e20 −1.30012
\(749\) 3.06628e19 0.231867
\(750\) 2.73207e19i 0.204674i
\(751\) 1.82216e20i 1.35240i −0.736717 0.676201i \(-0.763625\pi\)
0.736717 0.676201i \(-0.236375\pi\)
\(752\) 2.26760e19 0.166741
\(753\) 1.51461e20i 1.10341i
\(754\) −4.80927e19 −0.347120
\(755\) 3.71664e20i 2.65780i
\(756\) 4.55948e19i 0.323045i
\(757\) 9.81424e19i 0.688946i −0.938796 0.344473i \(-0.888058\pi\)
0.938796 0.344473i \(-0.111942\pi\)
\(758\) 8.37333e19i 0.582390i
\(759\) −9.32470e19 1.80178e20i −0.642603 1.24168i
\(760\) −2.00075e20 −1.36615
\(761\) −1.75838e19 −0.118965 −0.0594827 0.998229i \(-0.518945\pi\)
−0.0594827 + 0.998229i \(0.518945\pi\)
\(762\) 6.37819e19 0.427575
\(763\) 1.32558e19 0.0880507
\(764\) 6.87433e19i 0.452457i
\(765\) −5.75703e20 −3.75464
\(766\) 2.22112e19i 0.143539i
\(767\) 8.54819e19 0.547403
\(768\) 8.76692e19 0.556312
\(769\) 7.00513e19i 0.440486i −0.975445 0.220243i \(-0.929315\pi\)
0.975445 0.220243i \(-0.0706850\pi\)
\(770\) 3.48903e19i 0.217405i
\(771\) −3.80228e20 −2.34782
\(772\) 1.42149e20 0.869807
\(773\) 1.64802e20i 0.999325i −0.866220 0.499662i \(-0.833457\pi\)
0.866220 0.499662i \(-0.166543\pi\)
\(774\) 1.16590e20i 0.700610i
\(775\) −5.43514e19 −0.323667
\(776\) 1.75970e20i 1.03850i
\(777\) 6.13388e19 0.358747
\(778\) 3.94797e19i 0.228832i
\(779\) 3.37872e20i 1.94084i
\(780\) 2.27001e20i 1.29231i
\(781\) 9.95769e19i 0.561825i
\(782\) 6.29583e19 + 1.21652e20i 0.352051 + 0.680255i
\(783\) −1.78491e20 −0.989202
\(784\) 7.25983e19 0.398762
\(785\) 1.03781e20 0.564975
\(786\) 1.22208e19 0.0659391
\(787\) 7.47706e19i 0.399860i 0.979810 + 0.199930i \(0.0640714\pi\)
−0.979810 + 0.199930i \(0.935929\pi\)
\(788\) −1.29509e20 −0.686460
\(789\) 2.32416e20i 1.22103i
\(790\) −9.42485e19 −0.490778
\(791\) 9.01861e19 0.465483
\(792\) 2.04971e20i 1.04861i
\(793\) 9.97301e19i 0.505724i
\(794\) 3.64397e19 0.183160
\(795\) 7.30469e20 3.63942
\(796\) 1.19699e20i 0.591151i
\(797\) 2.69481e20i 1.31923i 0.751605 + 0.659614i \(0.229280\pi\)
−0.751605 + 0.659614i \(0.770720\pi\)
\(798\) −8.19869e19 −0.397854
\(799\) 1.26729e20i 0.609604i
\(800\) 1.58766e20 0.757054
\(801\) 5.71157e20i 2.69978i
\(802\) 9.54973e19i 0.447477i
\(803\) 1.92494e20i 0.894144i
\(804\) 1.64125e20i 0.755758i
\(805\) −1.14383e20 + 5.91966e19i −0.522146 + 0.270225i
\(806\) −2.89385e19 −0.130957
\(807\) 3.44046e20 1.54348
\(808\) −3.10518e19 −0.138104
\(809\) 6.11606e19 0.269670 0.134835 0.990868i \(-0.456950\pi\)
0.134835 + 0.990868i \(0.456950\pi\)
\(810\) 1.70598e19i 0.0745727i
\(811\) −3.22032e17 −0.00139557 −0.000697786 1.00000i \(-0.500222\pi\)
−0.000697786 1.00000i \(0.500222\pi\)
\(812\) 9.36987e19i 0.402570i
\(813\) 2.35593e20 1.00353
\(814\) −4.44859e19 −0.187867
\(815\) 7.21763e19i 0.302198i
\(816\) 3.45573e20i 1.43453i
\(817\) 3.44327e20 1.41715
\(818\) 1.66354e20 0.678827
\(819\) 1.25628e20i 0.508275i
\(820\) 3.97058e20i 1.59278i
\(821\) 1.31502e20 0.523033 0.261517 0.965199i \(-0.415777\pi\)
0.261517 + 0.965199i \(0.415777\pi\)
\(822\) 2.41007e20i 0.950444i
\(823\) 7.77131e19 0.303875 0.151938 0.988390i \(-0.451449\pi\)
0.151938 + 0.988390i \(0.451449\pi\)
\(824\) 7.57652e19i 0.293751i
\(825\) 2.81018e20i 1.08033i
\(826\) 3.62822e19i 0.138303i
\(827\) 2.75747e20i 1.04225i 0.853481 + 0.521125i \(0.174487\pi\)
−0.853481 + 0.521125i \(0.825513\pi\)
\(828\) −3.02982e20 + 1.56802e20i −1.13555 + 0.587677i
\(829\) −4.59792e20 −1.70876 −0.854378 0.519652i \(-0.826062\pi\)
−0.854378 + 0.519652i \(0.826062\pi\)
\(830\) 1.60112e20 0.590033
\(831\) 3.10305e20 1.13392
\(832\) −1.65183e19 −0.0598553
\(833\) 4.05728e20i 1.45788i
\(834\) −8.82334e19 −0.314392
\(835\) 5.27040e20i 1.86225i
\(836\) −2.72940e20 −0.956364
\(837\) −1.07402e20 −0.373195
\(838\) 1.26196e19i 0.0434848i
\(839\) 2.54217e20i 0.868702i −0.900744 0.434351i \(-0.856978\pi\)
0.900744 0.434351i \(-0.143022\pi\)
\(840\) 2.13688e20 0.724143
\(841\) 6.92470e19 0.232718
\(842\) 6.35011e19i 0.211640i
\(843\) 8.76592e20i 2.89737i
\(844\) −2.48646e20 −0.815049
\(845\) 1.85768e20i 0.603911i
\(846\) −6.87603e19 −0.221690
\(847\) 3.25354e19i 0.104033i
\(848\) 2.67004e20i 0.846734i
\(849\) 8.01627e19i 0.252127i
\(850\) 1.89737e20i 0.591860i
\(851\) −7.54770e19 1.45841e20i −0.233511 0.451205i
\(852\) 2.74980e20 0.843768
\(853\) −1.16392e20 −0.354224 −0.177112 0.984191i \(-0.556676\pi\)
−0.177112 + 0.984191i \(0.556676\pi\)
\(854\) −4.23297e19 −0.127773
\(855\) −9.22507e20 −2.76189
\(856\) 1.36199e20i 0.404443i
\(857\) 1.42230e20 0.418914 0.209457 0.977818i \(-0.432830\pi\)
0.209457 + 0.977818i \(0.432830\pi\)
\(858\) 1.49623e20i 0.437107i
\(859\) −2.67639e20 −0.775527 −0.387764 0.921759i \(-0.626752\pi\)
−0.387764 + 0.921759i \(0.626752\pi\)
\(860\) −4.04644e20 −1.16301
\(861\) 3.60859e20i 1.02876i
\(862\) 2.12051e20i 0.599639i
\(863\) −3.07709e20 −0.863106 −0.431553 0.902087i \(-0.642034\pi\)
−0.431553 + 0.902087i \(0.642034\pi\)
\(864\) 3.13733e20 0.872899
\(865\) 6.23766e20i 1.72151i
\(866\) 1.46832e20i 0.401971i
\(867\) 1.34244e21 3.64552
\(868\) 5.63806e19i 0.151877i
\(869\) −2.85155e20 −0.761978
\(870\) 3.77180e20i 0.999801i
\(871\) 1.61804e20i 0.425464i
\(872\) 5.88798e19i 0.153586i
\(873\) 8.11364e20i 2.09950i
\(874\) 1.00884e20 + 1.94935e20i 0.258967 + 0.500391i
\(875\) −5.24760e19 −0.133630
\(876\) 5.31567e20 1.34286
\(877\) −1.79409e19 −0.0449622 −0.0224811 0.999747i \(-0.507157\pi\)
−0.0224811 + 0.999747i \(0.507157\pi\)
\(878\) −8.28158e19 −0.205898
\(879\) 7.98652e20i 1.96986i
\(880\) 2.35652e20 0.576623
\(881\) 4.03729e20i 0.980073i 0.871702 + 0.490037i \(0.163017\pi\)
−0.871702 + 0.490037i \(0.836983\pi\)
\(882\) −2.20140e20 −0.530174
\(883\) −3.53907e19 −0.0845598 −0.0422799 0.999106i \(-0.513462\pi\)
−0.0422799 + 0.999106i \(0.513462\pi\)
\(884\) 4.63716e20i 1.09922i
\(885\) 6.70415e20i 1.57667i
\(886\) −2.40625e20 −0.561441
\(887\) 3.83746e20 0.888339 0.444169 0.895943i \(-0.353499\pi\)
0.444169 + 0.895943i \(0.353499\pi\)
\(888\) 2.72456e20i 0.625758i
\(889\) 1.22508e20i 0.279160i
\(890\) 4.31847e20 0.976337
\(891\) 5.16157e19i 0.115781i
\(892\) 4.33275e20 0.964294
\(893\) 2.03070e20i 0.448421i
\(894\) 7.05060e19i 0.154477i
\(895\) 7.07600e20i 1.53825i
\(896\) 2.07584e20i 0.447751i
\(897\) −4.90521e20 + 2.53858e20i −1.04981 + 0.543306i
\(898\) 1.44619e20 0.307108
\(899\) 2.20715e20 0.465065
\(900\) 4.72553e20 0.987990
\(901\) −1.49220e21 −3.09566
\(902\) 2.61713e20i 0.538740i
\(903\) −3.67754e20 −0.751178
\(904\) 4.00591e20i 0.811937i
\(905\) −7.52808e20 −1.51406
\(906\) −6.76493e20 −1.35010
\(907\) 4.78981e20i 0.948565i 0.880373 + 0.474283i \(0.157293\pi\)
−0.880373 + 0.474283i \(0.842707\pi\)
\(908\) 6.33421e20i 1.24478i
\(909\) −1.43174e20 −0.279200
\(910\) 9.49863e19 0.183811
\(911\) 7.46334e19i 0.143319i 0.997429 + 0.0716596i \(0.0228295\pi\)
−0.997429 + 0.0716596i \(0.977170\pi\)
\(912\) 5.53746e20i 1.05523i
\(913\) 4.84429e20 0.916083
\(914\) 3.64497e20i 0.684023i
\(915\) −7.82160e20 −1.45663
\(916\) 2.99889e19i 0.0554233i
\(917\) 2.34731e19i 0.0430511i
\(918\) 3.74934e20i 0.682427i
\(919\) 4.69237e20i 0.847585i 0.905759 + 0.423793i \(0.139301\pi\)
−0.905759 + 0.423793i \(0.860699\pi\)
\(920\) −2.62941e20 5.08071e20i −0.471350 0.910772i
\(921\) −6.19645e20 −1.10237
\(922\) −8.63518e19 −0.152460
\(923\) 2.71091e20 0.475010
\(924\) 2.91510e20 0.506932
\(925\) 2.27464e20i 0.392574i
\(926\) −1.18103e20 −0.202294
\(927\) 3.49338e20i 0.593865i
\(928\) −6.44731e20 −1.08778
\(929\) 4.93994e20 0.827202 0.413601 0.910458i \(-0.364271\pi\)
0.413601 + 0.910458i \(0.364271\pi\)
\(930\) 2.26958e20i 0.377193i
\(931\) 6.50139e20i 1.07240i
\(932\) 6.51868e20 1.06721
\(933\) 1.39403e21 2.26517
\(934\) 8.55426e19i 0.137960i
\(935\) 1.31698e21i 2.10814i
\(936\) 5.58018e20 0.886578
\(937\) 9.88783e20i 1.55928i −0.626229 0.779639i \(-0.715402\pi\)
0.626229 0.779639i \(-0.284598\pi\)
\(938\) 6.86765e19 0.107495
\(939\) 1.66121e21i 2.58087i
\(940\) 2.38643e20i 0.368004i
\(941\) 3.99115e18i 0.00610901i 0.999995 + 0.00305450i \(0.000972280\pi\)
−0.999995 + 0.00305450i \(0.999028\pi\)
\(942\) 1.88899e20i 0.286995i
\(943\) −8.57993e20 + 4.44035e20i −1.29390 + 0.669631i
\(944\) 2.45053e20 0.366822
\(945\) 3.52532e20 0.523813
\(946\) 2.66713e20 0.393375
\(947\) −7.76261e20 −1.13647 −0.568235 0.822866i \(-0.692374\pi\)
−0.568235 + 0.822866i \(0.692374\pi\)
\(948\) 7.87450e20i 1.14436i
\(949\) 5.24050e20 0.755978
\(950\) 3.04034e20i 0.435369i
\(951\) −1.95559e21 −2.77981
\(952\) −4.36520e20 −0.615950
\(953\) 4.14059e20i 0.579979i −0.957030 0.289989i \(-0.906348\pi\)
0.957030 0.289989i \(-0.0936518\pi\)
\(954\) 8.09636e20i 1.12577i
\(955\) 5.31513e20 0.733653
\(956\) 3.84186e19 0.0526425
\(957\) 1.14118e21i 1.55229i
\(958\) 1.03834e20i 0.140211i
\(959\) 4.62912e20 0.620537
\(960\) 1.29549e20i 0.172400i
\(961\) −6.24135e20 −0.824546
\(962\) 1.21110e20i 0.158838i
\(963\) 6.27986e20i 0.817648i
\(964\) 2.57610e19i 0.0332984i
\(965\) 1.09908e21i 1.41038i
\(966\) −1.07748e20 2.08198e20i −0.137268 0.265238i
\(967\) −2.33192e20 −0.294936 −0.147468 0.989067i \(-0.547112\pi\)
−0.147468 + 0.989067i \(0.547112\pi\)
\(968\) 1.44517e20 0.181464
\(969\) 3.09471e21 3.85792
\(970\) 6.13466e20 0.759256
\(971\) 9.46454e20i 1.16296i −0.813560 0.581480i \(-0.802474\pi\)
0.813560 0.581480i \(-0.197526\pi\)
\(972\) −7.42219e20 −0.905458
\(973\) 1.69474e20i 0.205264i
\(974\) 3.03374e20 0.364809
\(975\) 7.65050e20 0.913393
\(976\) 2.85898e20i 0.338893i
\(977\) 4.23888e20i 0.498872i 0.968391 + 0.249436i \(0.0802452\pi\)
−0.968391 + 0.249436i \(0.919755\pi\)
\(978\) −1.31373e20 −0.153510
\(979\) 1.30658e21 1.51586
\(980\) 7.64026e20i 0.880087i
\(981\) 2.71483e20i 0.310499i
\(982\) 4.28273e20 0.486340
\(983\) 1.64800e21i 1.85816i 0.369879 + 0.929080i \(0.379399\pi\)
−0.369879 + 0.929080i \(0.620601\pi\)
\(984\) 1.60288e21 1.79446
\(985\) 1.00134e21i 1.11309i
\(986\) 7.70501e20i 0.850423i
\(987\) 2.16886e20i 0.237691i
\(988\) 7.43059e20i 0.808583i
\(989\) 4.52519e20 + 8.74385e20i 0.488948 + 0.944776i
\(990\) −7.14567e20 −0.766649
\(991\) −1.64342e21 −1.75078 −0.875392 0.483414i \(-0.839397\pi\)
−0.875392 + 0.483414i \(0.839397\pi\)
\(992\) −3.87949e20 −0.410386
\(993\) 1.18865e21 1.24856
\(994\) 1.15062e20i 0.120013i
\(995\) −9.25495e20 −0.958545
\(996\) 1.33774e21i 1.37580i
\(997\) 8.30679e20 0.848335 0.424167 0.905584i \(-0.360567\pi\)
0.424167 + 0.905584i \(0.360567\pi\)
\(998\) −8.15987e20 −0.827503
\(999\) 4.49487e20i 0.452646i
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 23.15.b.b.22.12 yes 24
23.22 odd 2 inner 23.15.b.b.22.11 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.15.b.b.22.11 24 23.22 odd 2 inner
23.15.b.b.22.12 yes 24 1.1 even 1 trivial