Properties

Label 126.9.n.d.19.5
Level $126$
Weight $9$
Character 126.19
Analytic conductor $51.330$
Analytic rank $0$
Dimension $20$
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] = [126,9,Mod(19,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\), 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: \(51.3297048677\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} - 1891249463672 x^{14} + 11806020599312 x^{13} + \cdots + 42\!\cdots\!32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{18}\cdot 7^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.5
Root \(70.5683 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 126.19
Dual form 126.9.n.d.73.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(814.617 + 470.320i) q^{5} +(14.7985 - 2400.95i) q^{7} +1448.15 q^{8} +O(q^{10})\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(814.617 + 470.320i) q^{5} +(14.7985 - 2400.95i) q^{7} +1448.15 q^{8} +(-9216.34 + 5321.06i) q^{10} +(522.290 + 904.633i) q^{11} -47076.6i q^{13} +(23440.7 + 13726.8i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(55462.6 - 32021.4i) q^{17} +(-203421. - 117445. i) q^{19} -120402. i q^{20} -11818.1 q^{22} +(-135729. + 235089. i) q^{23} +(247089. + 427970. i) q^{25} +(461254. + 266305. i) q^{26} +(-267096. + 152021. i) q^{28} -1.26478e6 q^{29} +(143445. - 82818.0i) q^{31} +(-92681.9 - 160530. i) q^{32} +724561. i q^{34} +(1.14127e6 - 1.94890e6i) q^{35} +(-1.35572e6 + 2.34818e6i) q^{37} +(2.30144e6 - 1.32874e6i) q^{38} +(1.17969e6 + 681096. i) q^{40} +1.48329e6i q^{41} -928927. q^{43} +(66853.1 - 115793. i) q^{44} +(-1.53560e6 - 2.65973e6i) q^{46} +(-8.09682e6 - 4.67470e6i) q^{47} +(-5.76436e6 - 71061.3i) q^{49} -5.59098e6 q^{50} +(-5.21850e6 + 3.01290e6i) q^{52} +(-462964. - 801877. i) q^{53} +982573. i q^{55} +(21430.6 - 3.47695e6i) q^{56} +(7.15469e6 - 1.23923e7i) q^{58} +(1.14511e7 - 6.61132e6i) q^{59} +(-1.21666e7 - 7.02438e6i) q^{61} +1.87396e6i q^{62} +2.09715e6 q^{64} +(2.21410e7 - 3.83494e7i) q^{65} +(8.70876e6 + 1.50840e7i) q^{67} +(-7.09922e6 - 4.09874e6i) q^{68} +(1.26392e7 + 2.22068e7i) q^{70} -5.33768e6 q^{71} +(2.95255e7 - 1.70466e7i) q^{73} +(-1.53382e7 - 2.65666e7i) q^{74} +3.00659e7i q^{76} +(2.17971e6 - 1.24061e6i) q^{77} +(1.61504e7 - 2.79734e7i) q^{79} +(-1.33467e7 + 7.70572e6i) q^{80} +(-1.45332e7 - 8.39075e6i) q^{82} -6.53156e7i q^{83} +6.02411e7 q^{85} +(5.25480e6 - 9.10159e6i) q^{86} +(756357. + 1.31005e6i) q^{88} +(-2.58655e7 - 1.49334e7i) q^{89} +(-1.13029e8 - 696665. i) q^{91} +3.47466e7 q^{92} +(9.16051e7 - 5.28882e7i) q^{94} +(-1.10473e8 - 1.91345e8i) q^{95} -5.40321e7i q^{97} +(3.33044e7 - 5.60770e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65685 + 9.79796i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −64.0000 110.851i −0.250000 0.433013i
\(5\) 814.617 + 470.320i 1.30339 + 0.752511i 0.980984 0.194091i \(-0.0621756\pi\)
0.322404 + 0.946602i \(0.395509\pi\)
\(6\) 0 0
\(7\) 14.7985 2400.95i 0.00616349 0.999981i
\(8\) 1448.15 0.353553
\(9\) 0 0
\(10\) −9216.34 + 5321.06i −0.921634 + 0.532106i
\(11\) 522.290 + 904.633i 0.0356731 + 0.0617876i 0.883311 0.468788i \(-0.155309\pi\)
−0.847638 + 0.530576i \(0.821976\pi\)
\(12\) 0 0
\(13\) 47076.6i 1.64828i −0.566385 0.824141i \(-0.691658\pi\)
0.566385 0.824141i \(-0.308342\pi\)
\(14\) 23440.7 + 13726.8i 0.610182 + 0.357321i
\(15\) 0 0
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) 55462.6 32021.4i 0.664056 0.383393i −0.129765 0.991545i \(-0.541422\pi\)
0.793821 + 0.608152i \(0.208089\pi\)
\(18\) 0 0
\(19\) −203421. 117445.i −1.56092 0.901197i −0.997164 0.0752548i \(-0.976023\pi\)
−0.563755 0.825942i \(-0.690644\pi\)
\(20\) 120402.i 0.752511i
\(21\) 0 0
\(22\) −11818.1 −0.0504494
\(23\) −135729. + 235089.i −0.485022 + 0.840082i −0.999852 0.0172101i \(-0.994522\pi\)
0.514830 + 0.857292i \(0.327855\pi\)
\(24\) 0 0
\(25\) 247089. + 427970.i 0.632547 + 1.09560i
\(26\) 461254. + 266305.i 1.00936 + 0.582756i
\(27\) 0 0
\(28\) −267096. + 152021.i −0.434545 + 0.247326i
\(29\) −1.26478e6 −1.78823 −0.894116 0.447836i \(-0.852195\pi\)
−0.894116 + 0.447836i \(0.852195\pi\)
\(30\) 0 0
\(31\) 143445. 82818.0i 0.155324 0.0896764i −0.420323 0.907374i \(-0.638083\pi\)
0.575647 + 0.817698i \(0.304750\pi\)
\(32\) −92681.9 160530.i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 724561.i 0.542200i
\(35\) 1.14127e6 1.94890e6i 0.760530 1.29873i
\(36\) 0 0
\(37\) −1.35572e6 + 2.34818e6i −0.723375 + 1.25292i 0.236265 + 0.971689i \(0.424077\pi\)
−0.959639 + 0.281233i \(0.909257\pi\)
\(38\) 2.30144e6 1.32874e6i 1.10374 0.637243i
\(39\) 0 0
\(40\) 1.17969e6 + 681096.i 0.460817 + 0.266053i
\(41\) 1.48329e6i 0.524917i 0.964943 + 0.262458i \(0.0845332\pi\)
−0.964943 + 0.262458i \(0.915467\pi\)
\(42\) 0 0
\(43\) −928927. −0.271711 −0.135856 0.990729i \(-0.543378\pi\)
−0.135856 + 0.990729i \(0.543378\pi\)
\(44\) 66853.1 115793.i 0.0178366 0.0308938i
\(45\) 0 0
\(46\) −1.53560e6 2.65973e6i −0.342962 0.594028i
\(47\) −8.09682e6 4.67470e6i −1.65929 0.957993i −0.973042 0.230628i \(-0.925922\pi\)
−0.686251 0.727365i \(-0.740745\pi\)
\(48\) 0 0
\(49\) −5.76436e6 71061.3i −0.999924 0.0123268i
\(50\) −5.59098e6 −0.894556
\(51\) 0 0
\(52\) −5.21850e6 + 3.01290e6i −0.713727 + 0.412070i
\(53\) −462964. 801877.i −0.0586737 0.101626i 0.835197 0.549952i \(-0.185354\pi\)
−0.893870 + 0.448326i \(0.852020\pi\)
\(54\) 0 0
\(55\) 982573.i 0.107378i
\(56\) 21430.6 3.47695e6i 0.00217912 0.353547i
\(57\) 0 0
\(58\) 7.15469e6 1.23923e7i 0.632235 1.09506i
\(59\) 1.14511e7 6.61132e6i 0.945019 0.545607i 0.0534889 0.998568i \(-0.482966\pi\)
0.891530 + 0.452961i \(0.149632\pi\)
\(60\) 0 0
\(61\) −1.21666e7 7.02438e6i −0.878717 0.507328i −0.00848188 0.999964i \(-0.502700\pi\)
−0.870235 + 0.492636i \(0.836033\pi\)
\(62\) 1.87396e6i 0.126822i
\(63\) 0 0
\(64\) 2.09715e6 0.125000
\(65\) 2.21410e7 3.83494e7i 1.24035 2.14835i
\(66\) 0 0
\(67\) 8.70876e6 + 1.50840e7i 0.432172 + 0.748544i 0.997060 0.0766234i \(-0.0244139\pi\)
−0.564888 + 0.825168i \(0.691081\pi\)
\(68\) −7.09922e6 4.09874e6i −0.332028 0.191697i
\(69\) 0 0
\(70\) 1.26392e7 + 2.22068e7i 0.526415 + 0.924897i
\(71\) −5.33768e6 −0.210048 −0.105024 0.994470i \(-0.533492\pi\)
−0.105024 + 0.994470i \(0.533492\pi\)
\(72\) 0 0
\(73\) 2.95255e7 1.70466e7i 1.03970 0.600268i 0.119948 0.992780i \(-0.461727\pi\)
0.919747 + 0.392512i \(0.128394\pi\)
\(74\) −1.53382e7 2.65666e7i −0.511503 0.885950i
\(75\) 0 0
\(76\) 3.00659e7i 0.901197i
\(77\) 2.17971e6 1.24061e6i 0.0620063 0.0352916i
\(78\) 0 0
\(79\) 1.61504e7 2.79734e7i 0.414644 0.718185i −0.580747 0.814084i \(-0.697239\pi\)
0.995391 + 0.0958993i \(0.0305727\pi\)
\(80\) −1.33467e7 + 7.70572e6i −0.325847 + 0.188128i
\(81\) 0 0
\(82\) −1.45332e7 8.39075e6i −0.321444 0.185586i
\(83\) 6.53156e7i 1.37627i −0.725582 0.688136i \(-0.758429\pi\)
0.725582 0.688136i \(-0.241571\pi\)
\(84\) 0 0
\(85\) 6.02411e7 1.15403
\(86\) 5.25480e6 9.10159e6i 0.0960645 0.166389i
\(87\) 0 0
\(88\) 756357. + 1.31005e6i 0.0126123 + 0.0218452i
\(89\) −2.58655e7 1.49334e7i −0.412250 0.238012i 0.279506 0.960144i \(-0.409829\pi\)
−0.691756 + 0.722131i \(0.743163\pi\)
\(90\) 0 0
\(91\) −1.13029e8 696665.i −1.64825 0.0101592i
\(92\) 3.47466e7 0.485022
\(93\) 0 0
\(94\) 9.16051e7 5.28882e7i 1.17330 0.677403i
\(95\) −1.10473e8 1.91345e8i −1.35632 2.34922i
\(96\) 0 0
\(97\) 5.40321e7i 0.610330i −0.952299 0.305165i \(-0.901288\pi\)
0.952299 0.305165i \(-0.0987116\pi\)
\(98\) 3.33044e7 5.60770e7i 0.361075 0.607968i
\(99\) 0 0
\(100\) 3.16273e7 5.47801e7i 0.316273 0.547801i
\(101\) −8.47958e7 + 4.89569e7i −0.814871 + 0.470466i −0.848644 0.528964i \(-0.822581\pi\)
0.0337737 + 0.999430i \(0.489247\pi\)
\(102\) 0 0
\(103\) −1.64140e8 9.47665e7i −1.45837 0.841988i −0.459435 0.888211i \(-0.651948\pi\)
−0.998931 + 0.0462234i \(0.985281\pi\)
\(104\) 6.81742e7i 0.582756i
\(105\) 0 0
\(106\) 1.04757e7 0.0829772
\(107\) −3.06326e7 + 5.30573e7i −0.233695 + 0.404772i −0.958893 0.283769i \(-0.908415\pi\)
0.725198 + 0.688541i \(0.241748\pi\)
\(108\) 0 0
\(109\) 6.66765e7 + 1.15487e8i 0.472353 + 0.818139i 0.999499 0.0316350i \(-0.0100714\pi\)
−0.527146 + 0.849774i \(0.676738\pi\)
\(110\) −9.62721e6 5.55827e6i −0.0657551 0.0379637i
\(111\) 0 0
\(112\) 3.39458e7 + 1.98786e7i 0.215732 + 0.126332i
\(113\) 2.67016e8 1.63766 0.818831 0.574035i \(-0.194623\pi\)
0.818831 + 0.574035i \(0.194623\pi\)
\(114\) 0 0
\(115\) −2.21134e8 + 1.27672e8i −1.26434 + 0.729968i
\(116\) 8.09460e7 + 1.40203e8i 0.447058 + 0.774327i
\(117\) 0 0
\(118\) 1.49597e8i 0.771605i
\(119\) −7.60611e7 1.33637e8i −0.379293 0.666407i
\(120\) 0 0
\(121\) 1.06634e8 1.84695e8i 0.497455 0.861617i
\(122\) 1.37649e8 7.94717e7i 0.621347 0.358735i
\(123\) 0 0
\(124\) −1.83610e7 1.06007e7i −0.0776620 0.0448382i
\(125\) 9.74051e7i 0.398971i
\(126\) 0 0
\(127\) 1.08576e8 0.417368 0.208684 0.977983i \(-0.433082\pi\)
0.208684 + 0.977983i \(0.433082\pi\)
\(128\) −1.18633e7 + 2.05478e7i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.50497e8 + 4.33874e8i 0.877060 + 1.51911i
\(131\) −1.17441e8 6.78047e7i −0.398782 0.230237i 0.287176 0.957878i \(-0.407283\pi\)
−0.685958 + 0.727641i \(0.740617\pi\)
\(132\) 0 0
\(133\) −2.84990e8 + 4.86665e8i −0.910801 + 1.55533i
\(134\) −1.97057e8 −0.611184
\(135\) 0 0
\(136\) 8.03185e7 4.63719e7i 0.234779 0.135550i
\(137\) 2.77423e8 + 4.80510e8i 0.787516 + 1.36402i 0.927484 + 0.373862i \(0.121967\pi\)
−0.139968 + 0.990156i \(0.544700\pi\)
\(138\) 0 0
\(139\) 7.11909e7i 0.190706i 0.995444 + 0.0953532i \(0.0303980\pi\)
−0.995444 + 0.0953532i \(0.969602\pi\)
\(140\) −2.89079e8 1.78177e6i −0.752497 0.00463810i
\(141\) 0 0
\(142\) 3.01945e7 5.22984e7i 0.0742633 0.128628i
\(143\) 4.25870e7 2.45876e7i 0.101843 0.0587993i
\(144\) 0 0
\(145\) −1.03031e9 5.94852e8i −2.33076 1.34566i
\(146\) 3.85720e8i 0.848908i
\(147\) 0 0
\(148\) 3.47065e8 0.723375
\(149\) −1.42326e8 + 2.46517e8i −0.288762 + 0.500151i −0.973515 0.228625i \(-0.926577\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(150\) 0 0
\(151\) −2.56501e8 4.44273e8i −0.493380 0.854559i 0.506591 0.862187i \(-0.330905\pi\)
−0.999971 + 0.00762721i \(0.997572\pi\)
\(152\) −2.94584e8 1.70078e8i −0.551868 0.318621i
\(153\) 0 0
\(154\) −174890. + 2.83747e7i −0.000310945 + 0.0504484i
\(155\) 1.55804e8 0.269930
\(156\) 0 0
\(157\) 4.41830e8 2.55091e8i 0.727204 0.419851i −0.0901944 0.995924i \(-0.528749\pi\)
0.817398 + 0.576073i \(0.195415\pi\)
\(158\) 1.82721e8 + 3.16482e8i 0.293198 + 0.507833i
\(159\) 0 0
\(160\) 1.74360e8i 0.266053i
\(161\) 5.62430e8 + 3.29358e8i 0.837077 + 0.490190i
\(162\) 0 0
\(163\) −9.54375e7 + 1.65303e8i −0.135197 + 0.234169i −0.925673 0.378325i \(-0.876500\pi\)
0.790475 + 0.612494i \(0.209834\pi\)
\(164\) 1.64424e8 9.49305e7i 0.227296 0.131229i
\(165\) 0 0
\(166\) 6.39959e8 + 3.69481e8i 0.842791 + 0.486586i
\(167\) 1.37420e9i 1.76678i 0.468636 + 0.883391i \(0.344746\pi\)
−0.468636 + 0.883391i \(0.655254\pi\)
\(168\) 0 0
\(169\) −1.40047e9 −1.71683
\(170\) −3.40775e8 + 5.90240e8i −0.408011 + 0.706696i
\(171\) 0 0
\(172\) 5.94513e7 + 1.02973e8i 0.0679278 + 0.117654i
\(173\) 1.02182e9 + 5.89945e8i 1.14074 + 0.658608i 0.946615 0.322368i \(-0.104479\pi\)
0.194129 + 0.980976i \(0.437812\pi\)
\(174\) 0 0
\(175\) 1.03119e9 5.86915e8i 1.09948 0.625782i
\(176\) −1.71144e7 −0.0178366
\(177\) 0 0
\(178\) 2.92634e8 1.68952e8i 0.291504 0.168300i
\(179\) −7.26254e8 1.25791e9i −0.707419 1.22529i −0.965811 0.259245i \(-0.916526\pi\)
0.258393 0.966040i \(-0.416807\pi\)
\(180\) 0 0
\(181\) 3.51470e8i 0.327471i −0.986504 0.163736i \(-0.947646\pi\)
0.986504 0.163736i \(-0.0523544\pi\)
\(182\) 6.46213e8 1.10351e9i 0.588966 1.00575i
\(183\) 0 0
\(184\) −1.96556e8 + 3.40446e8i −0.171481 + 0.297014i
\(185\) −2.20879e9 + 1.27524e9i −1.88568 + 1.08870i
\(186\) 0 0
\(187\) 5.79352e7 + 3.34489e7i 0.0473779 + 0.0273536i
\(188\) 1.19672e9i 0.957993i
\(189\) 0 0
\(190\) 2.49972e9 1.91813
\(191\) 1.43167e8 2.47972e8i 0.107574 0.186324i −0.807213 0.590261i \(-0.799025\pi\)
0.914787 + 0.403936i \(0.132358\pi\)
\(192\) 0 0
\(193\) 1.60498e8 + 2.77991e8i 0.115676 + 0.200356i 0.918050 0.396466i \(-0.129763\pi\)
−0.802374 + 0.596821i \(0.796430\pi\)
\(194\) 5.29404e8 + 3.05652e8i 0.373749 + 0.215784i
\(195\) 0 0
\(196\) 3.61042e8 + 6.43535e8i 0.244643 + 0.436061i
\(197\) 9.97043e8 0.661986 0.330993 0.943633i \(-0.392616\pi\)
0.330993 + 0.943633i \(0.392616\pi\)
\(198\) 0 0
\(199\) 9.03419e7 5.21589e7i 0.0576072 0.0332595i −0.470920 0.882176i \(-0.656078\pi\)
0.528527 + 0.848917i \(0.322745\pi\)
\(200\) 3.57822e8 + 6.19767e8i 0.223639 + 0.387354i
\(201\) 0 0
\(202\) 1.10777e9i 0.665339i
\(203\) −1.87169e7 + 3.03668e9i −0.0110218 + 1.78820i
\(204\) 0 0
\(205\) −6.97620e8 + 1.20831e9i −0.395006 + 0.684170i
\(206\) 1.85704e9 1.07216e9i 1.03122 0.595375i
\(207\) 0 0
\(208\) 6.67968e8 + 3.85651e8i 0.356863 + 0.206035i
\(209\) 2.45361e8i 0.128594i
\(210\) 0 0
\(211\) −5.58407e8 −0.281722 −0.140861 0.990029i \(-0.544987\pi\)
−0.140861 + 0.990029i \(0.544987\pi\)
\(212\) −5.92594e7 + 1.02640e8i −0.0293369 + 0.0508129i
\(213\) 0 0
\(214\) −3.46569e8 6.00275e8i −0.165247 0.286217i
\(215\) −7.56720e8 4.36893e8i −0.354145 0.204466i
\(216\) 0 0
\(217\) −1.96719e8 3.45630e8i −0.0887173 0.155874i
\(218\) −1.50872e9 −0.668008
\(219\) 0 0
\(220\) 1.08919e8 6.28847e7i 0.0464959 0.0268444i
\(221\) −1.50746e9 2.61099e9i −0.631940 1.09455i
\(222\) 0 0
\(223\) 1.47205e9i 0.595254i −0.954682 0.297627i \(-0.903805\pi\)
0.954682 0.297627i \(-0.0961951\pi\)
\(224\) −3.86796e8 + 2.20149e8i −0.153635 + 0.0874431i
\(225\) 0 0
\(226\) −1.51047e9 + 2.61621e9i −0.579001 + 1.00286i
\(227\) 1.03779e9 5.99169e8i 0.390847 0.225656i −0.291680 0.956516i \(-0.594214\pi\)
0.682527 + 0.730860i \(0.260881\pi\)
\(228\) 0 0
\(229\) 3.13100e7 + 1.80768e7i 0.0113852 + 0.00657326i 0.505682 0.862720i \(-0.331241\pi\)
−0.494297 + 0.869293i \(0.664574\pi\)
\(230\) 2.88889e9i 1.03233i
\(231\) 0 0
\(232\) −1.83160e9 −0.632235
\(233\) 1.64329e9 2.84627e9i 0.557560 0.965722i −0.440140 0.897929i \(-0.645071\pi\)
0.997699 0.0677924i \(-0.0215955\pi\)
\(234\) 0 0
\(235\) −4.39721e9 7.61619e9i −1.44180 2.49727i
\(236\) −1.46575e9 8.46249e8i −0.472510 0.272803i
\(237\) 0 0
\(238\) 1.73964e9 + 1.07225e7i 0.542189 + 0.00334184i
\(239\) 3.73479e9 1.14465 0.572327 0.820025i \(-0.306041\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(240\) 0 0
\(241\) 1.92362e9 1.11060e9i 0.570231 0.329223i −0.187011 0.982358i \(-0.559880\pi\)
0.757241 + 0.653135i \(0.226547\pi\)
\(242\) 1.20642e9 + 2.08959e9i 0.351754 + 0.609255i
\(243\) 0 0
\(244\) 1.79824e9i 0.507328i
\(245\) −4.66233e9 2.76898e9i −1.29401 0.768521i
\(246\) 0 0
\(247\) −5.52890e9 + 9.57634e9i −1.48543 + 2.57283i
\(248\) 2.07731e8 1.19933e8i 0.0549153 0.0317054i
\(249\) 0 0
\(250\) −9.54371e8 5.51007e8i −0.244319 0.141058i
\(251\) 3.49708e9i 0.881069i −0.897736 0.440535i \(-0.854789\pi\)
0.897736 0.440535i \(-0.145211\pi\)
\(252\) 0 0
\(253\) −2.83559e8 −0.0692089
\(254\) −6.14198e8 + 1.06382e9i −0.147562 + 0.255584i
\(255\) 0 0
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) −7.77094e8 4.48656e8i −0.178132 0.102844i 0.408283 0.912855i \(-0.366128\pi\)
−0.586415 + 0.810011i \(0.699461\pi\)
\(258\) 0 0
\(259\) 5.61780e9 + 3.28977e9i 1.24844 + 0.731084i
\(260\) −5.66810e9 −1.24035
\(261\) 0 0
\(262\) 1.32870e9 7.67123e8i 0.281981 0.162802i
\(263\) −1.47398e9 2.55300e9i −0.308083 0.533615i 0.669860 0.742487i \(-0.266354\pi\)
−0.977943 + 0.208872i \(0.933021\pi\)
\(264\) 0 0
\(265\) 8.70964e8i 0.176611i
\(266\) −3.15618e9 5.54532e9i −0.630428 1.10764i
\(267\) 0 0
\(268\) 1.11472e9 1.93075e9i 0.216086 0.374272i
\(269\) 3.58685e9 2.07087e9i 0.685021 0.395497i −0.116723 0.993164i \(-0.537239\pi\)
0.801744 + 0.597668i \(0.203906\pi\)
\(270\) 0 0
\(271\) 1.98614e9 + 1.14670e9i 0.368241 + 0.212604i 0.672690 0.739925i \(-0.265139\pi\)
−0.304449 + 0.952529i \(0.598472\pi\)
\(272\) 1.04928e9i 0.191697i
\(273\) 0 0
\(274\) −6.27736e9 −1.11372
\(275\) −2.58104e8 + 4.47049e8i −0.0451298 + 0.0781671i
\(276\) 0 0
\(277\) 4.31629e9 + 7.47604e9i 0.733149 + 1.26985i 0.955531 + 0.294891i \(0.0952833\pi\)
−0.222382 + 0.974960i \(0.571383\pi\)
\(278\) −6.97525e8 4.02716e8i −0.116783 0.0674249i
\(279\) 0 0
\(280\) 1.65274e9 2.82231e9i 0.268888 0.459169i
\(281\) −1.42076e9 −0.227874 −0.113937 0.993488i \(-0.536346\pi\)
−0.113937 + 0.993488i \(0.536346\pi\)
\(282\) 0 0
\(283\) −2.50006e9 + 1.44341e9i −0.389766 + 0.225032i −0.682059 0.731297i \(-0.738915\pi\)
0.292293 + 0.956329i \(0.405582\pi\)
\(284\) 3.41612e8 + 5.91689e8i 0.0525121 + 0.0909536i
\(285\) 0 0
\(286\) 5.56354e8i 0.0831548i
\(287\) 3.56131e9 + 2.19505e7i 0.524907 + 0.00323532i
\(288\) 0 0
\(289\) −1.43714e9 + 2.48920e9i −0.206020 + 0.356836i
\(290\) 1.16567e10 6.72998e9i 1.64810 0.951528i
\(291\) 0 0
\(292\) −3.77927e9 2.18196e9i −0.519848 0.300134i
\(293\) 9.77296e9i 1.32604i −0.748603 0.663019i \(-0.769275\pi\)
0.748603 0.663019i \(-0.230725\pi\)
\(294\) 0 0
\(295\) 1.24377e10 1.64230
\(296\) −1.96329e9 + 3.40052e9i −0.255752 + 0.442975i
\(297\) 0 0
\(298\) −1.61024e9 2.78902e9i −0.204186 0.353660i
\(299\) 1.10672e10 + 6.38965e9i 1.38469 + 0.799452i
\(300\) 0 0
\(301\) −1.37468e7 + 2.23031e9i −0.00167469 + 0.271706i
\(302\) 5.80396e9 0.697745
\(303\) 0 0
\(304\) 3.33284e9 1.92422e9i 0.390230 0.225299i
\(305\) −6.60740e9 1.14444e10i −0.763539 1.32249i
\(306\) 0 0
\(307\) 1.57927e10i 1.77788i −0.458024 0.888940i \(-0.651443\pi\)
0.458024 0.888940i \(-0.348557\pi\)
\(308\) −2.77024e8 1.62225e8i −0.0307833 0.0180266i
\(309\) 0 0
\(310\) −8.81359e8 + 1.52656e9i −0.0954346 + 0.165298i
\(311\) −4.52636e9 + 2.61329e9i −0.483846 + 0.279349i −0.722018 0.691874i \(-0.756785\pi\)
0.238172 + 0.971223i \(0.423452\pi\)
\(312\) 0 0
\(313\) −8.51493e9 4.91610e9i −0.887164 0.512204i −0.0141503 0.999900i \(-0.504504\pi\)
−0.873014 + 0.487695i \(0.837838\pi\)
\(314\) 5.77204e9i 0.593760i
\(315\) 0 0
\(316\) −4.13451e9 −0.414644
\(317\) −1.96496e9 + 3.40341e9i −0.194588 + 0.337036i −0.946765 0.321924i \(-0.895670\pi\)
0.752177 + 0.658961i \(0.229004\pi\)
\(318\) 0 0
\(319\) −6.60583e8 1.14416e9i −0.0637918 0.110491i
\(320\) 1.70838e9 + 9.86332e8i 0.162923 + 0.0940639i
\(321\) 0 0
\(322\) −6.40862e9 + 3.64754e9i −0.596130 + 0.339294i
\(323\) −1.50430e10 −1.38205
\(324\) 0 0
\(325\) 2.01474e10 1.16321e10i 1.80586 1.04262i
\(326\) −1.07975e9 1.87018e9i −0.0955990 0.165582i
\(327\) 0 0
\(328\) 2.14803e9i 0.185586i
\(329\) −1.13436e10 + 1.93709e10i −0.968202 + 1.65336i
\(330\) 0 0
\(331\) 6.65125e9 1.15203e10i 0.554104 0.959736i −0.443869 0.896092i \(-0.646394\pi\)
0.997973 0.0636440i \(-0.0202722\pi\)
\(332\) −7.24031e9 + 4.18020e9i −0.595943 + 0.344068i
\(333\) 0 0
\(334\) −1.34643e10 7.77363e9i −1.08193 0.624652i
\(335\) 1.63836e10i 1.30086i
\(336\) 0 0
\(337\) 1.53635e10 1.19116 0.595580 0.803296i \(-0.296922\pi\)
0.595580 + 0.803296i \(0.296922\pi\)
\(338\) 7.92227e9 1.37218e10i 0.606992 1.05134i
\(339\) 0 0
\(340\) −3.85543e9 6.67780e9i −0.288508 0.499710i
\(341\) 1.49840e8 + 8.65100e7i 0.0110818 + 0.00639807i
\(342\) 0 0
\(343\) −2.55919e8 + 1.38389e10i −0.0184895 + 0.999829i
\(344\) −1.34523e9 −0.0960645
\(345\) 0 0
\(346\) −1.15605e10 + 6.67447e9i −0.806627 + 0.465706i
\(347\) −1.41386e9 2.44888e9i −0.0975191 0.168908i 0.813138 0.582071i \(-0.197757\pi\)
−0.910657 + 0.413163i \(0.864424\pi\)
\(348\) 0 0
\(349\) 1.88443e10i 1.27022i 0.772423 + 0.635109i \(0.219045\pi\)
−0.772423 + 0.635109i \(0.780955\pi\)
\(350\) −8.27383e7 + 1.34237e10i −0.00551359 + 0.894539i
\(351\) 0 0
\(352\) 9.68136e7 1.67686e8i 0.00630617 0.0109226i
\(353\) 1.19955e10 6.92562e9i 0.772539 0.446026i −0.0612403 0.998123i \(-0.519506\pi\)
0.833780 + 0.552097i \(0.186172\pi\)
\(354\) 0 0
\(355\) −4.34817e9 2.51042e9i −0.273775 0.158064i
\(356\) 3.82296e9i 0.238012i
\(357\) 0 0
\(358\) 1.64333e10 1.00044
\(359\) 2.92238e9 5.06172e9i 0.175938 0.304733i −0.764548 0.644567i \(-0.777038\pi\)
0.940485 + 0.339834i \(0.110371\pi\)
\(360\) 0 0
\(361\) 1.90948e10 + 3.30732e10i 1.12431 + 1.94737i
\(362\) 3.44368e9 + 1.98821e9i 0.200534 + 0.115779i
\(363\) 0 0
\(364\) 7.15661e9 + 1.25740e10i 0.407664 + 0.716253i
\(365\) 3.20693e10 1.80683
\(366\) 0 0
\(367\) 4.52947e9 2.61509e9i 0.249680 0.144153i −0.369938 0.929057i \(-0.620621\pi\)
0.619618 + 0.784904i \(0.287288\pi\)
\(368\) −2.22378e9 3.85170e9i −0.121255 0.210020i
\(369\) 0 0
\(370\) 2.88555e10i 1.53965i
\(371\) −1.93212e9 + 1.09969e9i −0.101986 + 0.0580463i
\(372\) 0 0
\(373\) −6.35811e9 + 1.10126e10i −0.328468 + 0.568922i −0.982208 0.187796i \(-0.939865\pi\)
0.653740 + 0.756719i \(0.273199\pi\)
\(374\) −6.55461e8 + 3.78431e8i −0.0335012 + 0.0193419i
\(375\) 0 0
\(376\) −1.17254e10 6.76969e9i −0.586649 0.338702i
\(377\) 5.95416e10i 2.94751i
\(378\) 0 0
\(379\) −1.59283e10 −0.771991 −0.385995 0.922501i \(-0.626142\pi\)
−0.385995 + 0.922501i \(0.626142\pi\)
\(380\) −1.41406e10 + 2.44922e10i −0.678161 + 1.17461i
\(381\) 0 0
\(382\) 1.61975e9 + 2.80549e9i 0.0760666 + 0.131751i
\(383\) 3.16640e9 + 1.82812e9i 0.147154 + 0.0849593i 0.571769 0.820415i \(-0.306257\pi\)
−0.424615 + 0.905374i \(0.639591\pi\)
\(384\) 0 0
\(385\) 2.35911e9 + 1.45407e7i 0.107376 + 0.000661822i
\(386\) −3.63167e9 −0.163590
\(387\) 0 0
\(388\) −5.98952e9 + 3.45805e9i −0.264281 + 0.152583i
\(389\) 5.63251e9 + 9.75580e9i 0.245982 + 0.426054i 0.962407 0.271610i \(-0.0875561\pi\)
−0.716425 + 0.697664i \(0.754223\pi\)
\(390\) 0 0
\(391\) 1.73849e10i 0.743816i
\(392\) −8.34769e9 1.02908e8i −0.353527 0.00435817i
\(393\) 0 0
\(394\) −5.64013e9 + 9.76898e9i −0.234047 + 0.405382i
\(395\) 2.63128e10 1.51917e10i 1.08088 0.624049i
\(396\) 0 0
\(397\) −2.73124e10 1.57688e10i −1.09951 0.634800i −0.163415 0.986557i \(-0.552251\pi\)
−0.936091 + 0.351757i \(0.885584\pi\)
\(398\) 1.18022e9i 0.0470361i
\(399\) 0 0
\(400\) −8.09660e9 −0.316273
\(401\) −1.90026e10 + 3.29135e10i −0.734914 + 1.27291i 0.219848 + 0.975534i \(0.429444\pi\)
−0.954761 + 0.297373i \(0.903889\pi\)
\(402\) 0 0
\(403\) −3.89879e9 6.75290e9i −0.147812 0.256018i
\(404\) 1.08539e10 + 6.26648e9i 0.407435 + 0.235233i
\(405\) 0 0
\(406\) −2.96474e10 1.73615e10i −1.09115 0.638973i
\(407\) −2.83232e9 −0.103220
\(408\) 0 0
\(409\) 9.88374e9 5.70638e9i 0.353206 0.203924i −0.312890 0.949789i \(-0.601297\pi\)
0.666096 + 0.745866i \(0.267964\pi\)
\(410\) −7.89267e9 1.36705e10i −0.279311 0.483781i
\(411\) 0 0
\(412\) 2.42602e10i 0.841988i
\(413\) −1.57040e10 2.75915e10i −0.539772 0.948364i
\(414\) 0 0
\(415\) 3.07192e10 5.32072e10i 1.03566 1.79382i
\(416\) −7.55719e9 + 4.36315e9i −0.252341 + 0.145689i
\(417\) 0 0
\(418\) 2.40404e9 + 1.38797e9i 0.0787474 + 0.0454648i
\(419\) 7.05049e9i 0.228751i 0.993438 + 0.114376i \(0.0364867\pi\)
−0.993438 + 0.114376i \(0.963513\pi\)
\(420\) 0 0
\(421\) −3.15471e10 −1.00422 −0.502112 0.864803i \(-0.667444\pi\)
−0.502112 + 0.864803i \(0.667444\pi\)
\(422\) 3.15883e9 5.47125e9i 0.0996038 0.172519i
\(423\) 0 0
\(424\) −6.70444e8 1.16124e9i −0.0207443 0.0359302i
\(425\) 2.74084e10 + 1.58242e10i 0.840093 + 0.485028i
\(426\) 0 0
\(427\) −1.70453e10 + 2.91074e10i −0.512734 + 0.875573i
\(428\) 7.84196e9 0.233695
\(429\) 0 0
\(430\) 8.56131e9 4.94287e9i 0.250419 0.144579i
\(431\) −1.60391e10 2.77805e10i −0.464805 0.805066i 0.534387 0.845240i \(-0.320542\pi\)
−0.999193 + 0.0401733i \(0.987209\pi\)
\(432\) 0 0
\(433\) 2.28833e10i 0.650979i 0.945546 + 0.325489i \(0.105529\pi\)
−0.945546 + 0.325489i \(0.894471\pi\)
\(434\) 4.49929e9 + 2.77319e7i 0.126819 + 0.000781664i
\(435\) 0 0
\(436\) 8.53459e9 1.47823e10i 0.236177 0.409070i
\(437\) 5.52201e10 3.18813e10i 1.51416 0.874200i
\(438\) 0 0
\(439\) −2.93893e9 1.69679e9i −0.0791282 0.0456847i 0.459914 0.887964i \(-0.347880\pi\)
−0.539042 + 0.842279i \(0.681214\pi\)
\(440\) 1.42292e9i 0.0379637i
\(441\) 0 0
\(442\) 3.41098e10 0.893698
\(443\) −2.58531e10 + 4.47789e10i −0.671271 + 1.16268i 0.306273 + 0.951944i \(0.400918\pi\)
−0.977544 + 0.210732i \(0.932415\pi\)
\(444\) 0 0
\(445\) −1.40470e10 2.43301e10i −0.358214 0.620445i
\(446\) 1.44231e10 + 8.32715e9i 0.364517 + 0.210454i
\(447\) 0 0
\(448\) 3.10348e7 5.03517e9i 0.000770437 0.124998i
\(449\) −5.01205e10 −1.23319 −0.616595 0.787281i \(-0.711488\pi\)
−0.616595 + 0.787281i \(0.711488\pi\)
\(450\) 0 0
\(451\) −1.34183e9 + 7.74707e8i −0.0324334 + 0.0187254i
\(452\) −1.70890e10 2.95991e10i −0.409415 0.709128i
\(453\) 0 0
\(454\) 1.35576e10i 0.319125i
\(455\) −9.17475e10 5.37271e10i −2.14066 1.25357i
\(456\) 0 0
\(457\) −3.95560e10 + 6.85130e10i −0.906875 + 1.57075i −0.0884942 + 0.996077i \(0.528205\pi\)
−0.818381 + 0.574677i \(0.805128\pi\)
\(458\) −3.54232e8 + 2.04516e8i −0.00805056 + 0.00464799i
\(459\) 0 0
\(460\) 2.83052e10 + 1.63420e10i 0.632171 + 0.364984i
\(461\) 1.40115e10i 0.310228i −0.987897 0.155114i \(-0.950426\pi\)
0.987897 0.155114i \(-0.0495745\pi\)
\(462\) 0 0
\(463\) 6.61893e10 1.44034 0.720168 0.693800i \(-0.244065\pi\)
0.720168 + 0.693800i \(0.244065\pi\)
\(464\) 1.03611e10 1.79459e10i 0.223529 0.387163i
\(465\) 0 0
\(466\) 1.85917e10 + 3.22018e10i 0.394254 + 0.682868i
\(467\) −3.14542e10 1.81601e10i −0.661319 0.381813i 0.131460 0.991321i \(-0.458033\pi\)
−0.792780 + 0.609509i \(0.791367\pi\)
\(468\) 0 0
\(469\) 3.63449e10 2.06861e10i 0.751194 0.427550i
\(470\) 9.94974e10 2.03902
\(471\) 0 0
\(472\) 1.65830e10 9.57421e9i 0.334115 0.192901i
\(473\) −4.85169e8 8.40338e8i −0.00969279 0.0167884i
\(474\) 0 0
\(475\) 1.16077e11i 2.28020i
\(476\) −9.94593e9 + 1.69842e10i −0.193739 + 0.330840i
\(477\) 0 0
\(478\) −2.11272e10 + 3.65933e10i −0.404697 + 0.700955i
\(479\) 6.34734e10 3.66464e10i 1.20573 0.696128i 0.243906 0.969799i \(-0.421571\pi\)
0.961823 + 0.273671i \(0.0882378\pi\)
\(480\) 0 0
\(481\) 1.10544e11 + 6.38227e10i 2.06517 + 1.19233i
\(482\) 2.51300e10i 0.465591i
\(483\) 0 0
\(484\) −2.72983e10 −0.497455
\(485\) 2.54124e10 4.40155e10i 0.459280 0.795497i
\(486\) 0 0
\(487\) −3.96063e10 6.86001e10i −0.704123 1.21958i −0.967007 0.254749i \(-0.918007\pi\)
0.262884 0.964827i \(-0.415326\pi\)
\(488\) −1.76191e10 1.01724e10i −0.310673 0.179367i
\(489\) 0 0
\(490\) 5.35045e10 3.00176e10i 0.928124 0.520705i
\(491\) 5.63231e10 0.969082 0.484541 0.874769i \(-0.338987\pi\)
0.484541 + 0.874769i \(0.338987\pi\)
\(492\) 0 0
\(493\) −7.01481e10 + 4.05001e10i −1.18749 + 0.685595i
\(494\) −6.25524e10 1.08344e11i −1.05036 1.81927i
\(495\) 0 0
\(496\) 2.71378e9i 0.0448382i
\(497\) −7.89900e7 + 1.28155e10i −0.00129463 + 0.210044i
\(498\) 0 0
\(499\) 1.34346e10 2.32693e10i 0.216681 0.375303i −0.737110 0.675773i \(-0.763810\pi\)
0.953791 + 0.300470i \(0.0971434\pi\)
\(500\) 1.07975e10 6.23393e9i 0.172760 0.0997428i
\(501\) 0 0
\(502\) 3.42642e10 + 1.97824e10i 0.539543 + 0.311505i
\(503\) 4.60200e10i 0.718910i 0.933162 + 0.359455i \(0.117037\pi\)
−0.933162 + 0.359455i \(0.882963\pi\)
\(504\) 0 0
\(505\) −9.21015e10 −1.41612
\(506\) 1.60405e9 2.77830e9i 0.0244690 0.0423816i
\(507\) 0 0
\(508\) −6.94886e9 1.20358e10i −0.104342 0.180725i
\(509\) −9.09077e10 5.24856e10i −1.35435 0.781932i −0.365492 0.930815i \(-0.619099\pi\)
−0.988855 + 0.148882i \(0.952432\pi\)
\(510\) 0 0
\(511\) −4.04911e10 7.11417e10i −0.593849 1.04338i
\(512\) 3.03700e9 0.0441942
\(513\) 0 0
\(514\) 8.79182e9 5.07596e9i 0.125958 0.0727220i
\(515\) −8.91411e10 1.54397e11i −1.26721 2.19487i
\(516\) 0 0
\(517\) 9.76620e9i 0.136698i
\(518\) −6.40122e10 + 3.64333e10i −0.889086 + 0.506033i
\(519\) 0 0
\(520\) 3.20636e10 5.55359e10i 0.438530 0.759557i
\(521\) 4.56369e10 2.63485e10i 0.619391 0.357606i −0.157241 0.987560i \(-0.550260\pi\)
0.776632 + 0.629955i \(0.216927\pi\)
\(522\) 0 0
\(523\) −3.74118e10 2.15997e10i −0.500037 0.288697i 0.228692 0.973499i \(-0.426555\pi\)
−0.728729 + 0.684802i \(0.759889\pi\)
\(524\) 1.73580e10i 0.230237i
\(525\) 0 0
\(526\) 3.33523e10 0.435695
\(527\) 5.30389e9 9.18661e9i 0.0687626 0.119100i
\(528\) 0 0
\(529\) 2.31081e9 + 4.00245e9i 0.0295082 + 0.0511096i
\(530\) 8.53367e9 + 4.92692e9i 0.108151 + 0.0624413i
\(531\) 0 0
\(532\) 7.21868e10 + 4.44932e8i 0.901180 + 0.00555452i
\(533\) 6.98282e10 0.865211
\(534\) 0 0
\(535\) −4.99078e10 + 2.88143e10i −0.609190 + 0.351716i
\(536\) 1.26116e10 + 2.18440e10i 0.152796 + 0.264650i
\(537\) 0 0
\(538\) 4.68584e10i 0.559317i
\(539\) −2.94638e9 5.25175e9i −0.0349088 0.0622227i
\(540\) 0 0
\(541\) −1.65828e10 + 2.87222e10i −0.193583 + 0.335296i −0.946435 0.322894i \(-0.895344\pi\)
0.752852 + 0.658190i \(0.228678\pi\)
\(542\) −2.24706e10 + 1.29734e10i −0.260386 + 0.150334i
\(543\) 0 0
\(544\) −1.02808e10 5.93560e9i −0.117390 0.0677750i
\(545\) 1.25437e11i 1.42180i
\(546\) 0 0
\(547\) −1.44828e11 −1.61772 −0.808860 0.588001i \(-0.799915\pi\)
−0.808860 + 0.588001i \(0.799915\pi\)
\(548\) 3.55101e10 6.15053e10i 0.393758 0.682009i
\(549\) 0 0
\(550\) −2.92011e9 5.05778e9i −0.0319116 0.0552725i
\(551\) 2.57283e11 + 1.48542e11i 2.79128 + 1.61155i
\(552\) 0 0
\(553\) −6.69238e10 3.91904e10i −0.715616 0.419063i
\(554\) −9.76666e10 −1.03683
\(555\) 0 0
\(556\) 7.89160e9 4.55622e9i 0.0825783 0.0476766i
\(557\) −9.10260e10 1.57662e11i −0.945682 1.63797i −0.754381 0.656437i \(-0.772063\pi\)
−0.191301 0.981531i \(-0.561271\pi\)
\(558\) 0 0
\(559\) 4.37307e10i 0.447857i
\(560\) 1.83036e10 + 3.21588e10i 0.186116 + 0.327000i
\(561\) 0 0
\(562\) 8.03703e9 1.39205e10i 0.0805657 0.139544i
\(563\) 1.36642e11 7.88902e10i 1.36003 0.785216i 0.370407 0.928870i \(-0.379218\pi\)
0.989628 + 0.143653i \(0.0458850\pi\)
\(564\) 0 0
\(565\) 2.17516e11 + 1.25583e11i 2.13451 + 1.23236i
\(566\) 3.26606e10i 0.318243i
\(567\) 0 0
\(568\) −7.72979e9 −0.0742633
\(569\) 7.37347e9 1.27712e10i 0.0703433 0.121838i −0.828708 0.559680i \(-0.810924\pi\)
0.899052 + 0.437842i \(0.144257\pi\)
\(570\) 0 0
\(571\) 2.95716e9 + 5.12196e9i 0.0278183 + 0.0481828i 0.879599 0.475715i \(-0.157811\pi\)
−0.851781 + 0.523898i \(0.824477\pi\)
\(572\) −5.45114e9 3.14722e9i −0.0509217 0.0293997i
\(573\) 0 0
\(574\) −2.03609e10 + 3.47694e10i −0.187564 + 0.320295i
\(575\) −1.34148e11 −1.22720
\(576\) 0 0
\(577\) −6.08835e10 + 3.51511e10i −0.549283 + 0.317129i −0.748833 0.662759i \(-0.769385\pi\)
0.199549 + 0.979888i \(0.436052\pi\)
\(578\) −1.62594e10 2.81621e10i −0.145678 0.252321i
\(579\) 0 0
\(580\) 1.52282e11i 1.34566i
\(581\) −1.56820e11 9.66576e8i −1.37625 0.00848264i
\(582\) 0 0
\(583\) 4.83603e8 8.37625e8i 0.00418615 0.00725062i
\(584\) 4.27575e10 2.46861e10i 0.367588 0.212227i
\(585\) 0 0
\(586\) 9.57551e10 + 5.52842e10i 0.812029 + 0.468825i
\(587\) 1.35170e11i 1.13849i 0.822168 + 0.569245i \(0.192764\pi\)
−0.822168 + 0.569245i \(0.807236\pi\)
\(588\) 0 0
\(589\) −3.89062e10 −0.323264
\(590\) −7.03584e10 + 1.21864e11i −0.580641 + 1.00570i
\(591\) 0 0
\(592\) −2.22121e10 3.84725e10i −0.180844 0.313231i
\(593\) −5.35885e10 3.09393e10i −0.433364 0.250203i 0.267415 0.963582i \(-0.413831\pi\)
−0.700779 + 0.713379i \(0.747164\pi\)
\(594\) 0 0
\(595\) 8.91481e8 1.44636e11i 0.00711286 1.15401i
\(596\) 3.64356e10 0.288762
\(597\) 0 0
\(598\) −1.25211e11 + 7.22907e10i −0.979125 + 0.565298i
\(599\) 5.68987e9 + 9.85515e9i 0.0441972 + 0.0765519i 0.887278 0.461235i \(-0.152594\pi\)
−0.843081 + 0.537787i \(0.819260\pi\)
\(600\) 0 0
\(601\) 4.63889e10i 0.355563i −0.984070 0.177781i \(-0.943108\pi\)
0.984070 0.177781i \(-0.0568920\pi\)
\(602\) −2.17747e10 1.27512e10i −0.165793 0.0970882i
\(603\) 0 0
\(604\) −3.28322e10 + 5.68670e10i −0.246690 + 0.427280i
\(605\) 1.73732e11 1.00304e11i 1.29675 0.748681i
\(606\) 0 0
\(607\) −1.52237e11 8.78940e10i −1.12141 0.647447i −0.179650 0.983731i \(-0.557497\pi\)
−0.941761 + 0.336284i \(0.890830\pi\)
\(608\) 4.35401e10i 0.318621i
\(609\) 0 0
\(610\) 1.49508e11 1.07981
\(611\) −2.20069e11 + 3.81171e11i −1.57904 + 2.73498i
\(612\) 0 0
\(613\) 1.02160e11 + 1.76947e11i 0.723504 + 1.25315i 0.959587 + 0.281412i \(0.0908029\pi\)
−0.236083 + 0.971733i \(0.575864\pi\)
\(614\) 1.54736e11 + 8.93369e10i 1.08872 + 0.628575i
\(615\) 0 0
\(616\) 3.15656e9 1.79659e9i 0.0219225 0.0124775i
\(617\) −1.15941e11 −0.800009 −0.400005 0.916513i \(-0.630991\pi\)
−0.400005 + 0.916513i \(0.630991\pi\)
\(618\) 0 0
\(619\) 3.73665e10 2.15736e10i 0.254519 0.146947i −0.367313 0.930097i \(-0.619722\pi\)
0.621832 + 0.783151i \(0.286389\pi\)
\(620\) −9.97144e9 1.72710e10i −0.0674825 0.116883i
\(621\) 0 0
\(622\) 5.91321e10i 0.395059i
\(623\) −3.62373e10 + 6.18808e10i −0.240549 + 0.410775i
\(624\) 0 0
\(625\) 5.07074e10 8.78278e10i 0.332316 0.575588i
\(626\) 9.63355e10 5.56193e10i 0.627320 0.362183i
\(627\) 0 0
\(628\) −5.65542e10 3.26516e10i −0.363602 0.209926i
\(629\) 1.73648e11i 1.10935i
\(630\) 0 0
\(631\) −1.09578e11 −0.691204 −0.345602 0.938381i \(-0.612325\pi\)
−0.345602 + 0.938381i \(0.612325\pi\)
\(632\) 2.33883e10 4.05098e10i 0.146599 0.253917i
\(633\) 0 0
\(634\) −2.22310e10 3.85052e10i −0.137595 0.238321i
\(635\) 8.84479e10 + 5.10654e10i 0.543992 + 0.314074i
\(636\) 0 0
\(637\) −3.34532e9 + 2.71366e11i −0.0203180 + 1.64816i
\(638\) 1.49473e10 0.0902152
\(639\) 0 0
\(640\) −1.93281e10 + 1.11591e10i −0.115204 + 0.0665132i
\(641\) 1.02428e11 + 1.77410e11i 0.606718 + 1.05087i 0.991778 + 0.127974i \(0.0408474\pi\)
−0.385060 + 0.922892i \(0.625819\pi\)
\(642\) 0 0
\(643\) 1.78587e11i 1.04474i −0.852720 0.522369i \(-0.825049\pi\)
0.852720 0.522369i \(-0.174951\pi\)
\(644\) 5.14199e8 8.34250e10i 0.00298943 0.485012i
\(645\) 0 0
\(646\) 8.50960e10 1.47391e11i 0.488629 0.846330i
\(647\) 1.20405e10 6.95156e9i 0.0687109 0.0396703i −0.465251 0.885179i \(-0.654036\pi\)
0.533962 + 0.845509i \(0.320703\pi\)
\(648\) 0 0
\(649\) 1.19616e10 + 6.90605e9i 0.0674235 + 0.0389270i
\(650\) 2.63204e11i 1.47448i
\(651\) 0 0
\(652\) 2.44320e10 0.135197
\(653\) 1.33723e11 2.31615e11i 0.735452 1.27384i −0.219073 0.975708i \(-0.570303\pi\)
0.954525 0.298131i \(-0.0963633\pi\)
\(654\) 0 0
\(655\) −6.37798e10 1.10470e11i −0.346512 0.600176i
\(656\) −2.10463e10 1.21511e10i −0.113648 0.0656146i
\(657\) 0 0
\(658\) −1.25627e11 2.20722e11i −0.670159 1.17745i
\(659\) 2.98246e11 1.58137 0.790684 0.612225i \(-0.209725\pi\)
0.790684 + 0.612225i \(0.209725\pi\)
\(660\) 0 0
\(661\) −6.89538e10 + 3.98105e10i −0.361204 + 0.208541i −0.669609 0.742714i \(-0.733538\pi\)
0.308405 + 0.951255i \(0.400205\pi\)
\(662\) 7.52503e10 + 1.30337e11i 0.391810 + 0.678636i
\(663\) 0 0
\(664\) 9.45870e10i 0.486586i
\(665\) −4.61046e11 + 2.62410e11i −2.35753 + 1.34182i
\(666\) 0 0
\(667\) 1.71667e11 2.97337e11i 0.867331 1.50226i
\(668\) 1.52331e11 8.79486e10i 0.765039 0.441696i
\(669\) 0 0
\(670\) −1.60526e11 9.26796e10i −0.796610 0.459923i
\(671\) 1.46750e10i 0.0723918i
\(672\) 0 0
\(673\) 2.67506e11 1.30398 0.651992 0.758226i \(-0.273933\pi\)
0.651992 + 0.758226i \(0.273933\pi\)
\(674\) −8.69089e10 + 1.50531e11i −0.421138 + 0.729433i
\(675\) 0 0
\(676\) 8.96303e10 + 1.55244e11i 0.429208 + 0.743410i
\(677\) 2.29678e11 + 1.32605e11i 1.09336 + 0.631254i 0.934470 0.356041i \(-0.115874\pi\)
0.158894 + 0.987296i \(0.449207\pi\)
\(678\) 0 0
\(679\) −1.29729e11 7.99597e8i −0.610319 0.00376177i
\(680\) 8.72384e10 0.408011
\(681\) 0 0
\(682\) −1.69524e9 + 9.78749e8i −0.00783600 + 0.00452412i
\(683\) −1.38922e11 2.40619e11i −0.638391 1.10573i −0.985786 0.168007i \(-0.946267\pi\)
0.347394 0.937719i \(-0.387067\pi\)
\(684\) 0 0
\(685\) 5.21909e11i 2.37046i
\(686\) −1.34145e11 8.07922e10i −0.605731 0.364815i
\(687\) 0 0
\(688\) 7.60977e9 1.31805e10i 0.0339639 0.0588272i
\(689\) −3.77496e10 + 2.17948e10i −0.167508 + 0.0967108i
\(690\) 0 0
\(691\) 2.28031e11 + 1.31654e11i 1.00019 + 0.577459i 0.908304 0.418311i \(-0.137378\pi\)
0.0918837 + 0.995770i \(0.470711\pi\)
\(692\) 1.51026e11i 0.658608i
\(693\) 0 0
\(694\) 3.19921e10 0.137913
\(695\) −3.34825e10 + 5.79933e10i −0.143509 + 0.248564i
\(696\) 0 0
\(697\) 4.74969e10 + 8.22671e10i 0.201249 + 0.348574i
\(698\) −1.84636e11 1.06599e11i −0.777846 0.449090i
\(699\) 0 0
\(700\) −1.31057e11 7.67464e10i −0.545842 0.319644i
\(701\) 3.04779e11 1.26216 0.631078 0.775719i \(-0.282613\pi\)
0.631078 + 0.775719i \(0.282613\pi\)
\(702\) 0 0
\(703\) 5.51563e11 3.18445e11i 2.25826 1.30381i
\(704\) 1.09532e9 + 1.89715e9i 0.00445914 + 0.00772345i
\(705\) 0 0
\(706\) 1.56709e11i 0.630776i
\(707\) 1.16288e11 + 2.04315e11i 0.465434 + 0.817755i
\(708\) 0 0
\(709\) 1.59806e11 2.76793e11i 0.632425 1.09539i −0.354629 0.935007i \(-0.615393\pi\)
0.987054 0.160386i \(-0.0512737\pi\)
\(710\) 4.91939e10 2.84021e10i 0.193588 0.111768i
\(711\) 0 0
\(712\) −3.74572e10 2.16259e10i −0.145752 0.0841501i
\(713\) 4.49632e10i 0.173980i
\(714\) 0 0
\(715\) 4.62562e10 0.176989
\(716\) −9.29606e10 + 1.61012e11i −0.353709 + 0.612643i
\(717\) 0 0
\(718\) 3.30630e10 + 5.72668e10i 0.124407 + 0.215479i
\(719\) 3.85186e10 + 2.22387e10i 0.144130 + 0.0832136i 0.570331 0.821415i \(-0.306815\pi\)
−0.426201 + 0.904629i \(0.640148\pi\)
\(720\) 0 0
\(721\) −2.29959e11 + 3.92691e11i −0.850961 + 1.45315i
\(722\) −4.32067e11 −1.59002
\(723\) 0 0
\(724\) −3.89608e10 + 2.24940e10i −0.141799 + 0.0818679i
\(725\) −3.12513e11 5.41289e11i −1.13114 1.95919i
\(726\) 0 0
\(727\) 4.83129e10i 0.172952i −0.996254 0.0864760i \(-0.972439\pi\)
0.996254 0.0864760i \(-0.0275606\pi\)
\(728\) −1.63683e11 1.00888e9i −0.582745 0.00359181i
\(729\) 0 0
\(730\) −1.81412e11 + 3.14214e11i −0.638813 + 1.10646i
\(731\) −5.15207e10 + 2.97455e10i −0.180432 + 0.104172i
\(732\) 0 0
\(733\) −7.14347e10 4.12428e10i −0.247453 0.142867i 0.371144 0.928575i \(-0.378966\pi\)
−0.618598 + 0.785708i \(0.712299\pi\)
\(734\) 5.91728e10i 0.203863i
\(735\) 0 0
\(736\) 5.03185e10 0.171481
\(737\) −9.09699e9 + 1.57564e10i −0.0308339 + 0.0534058i
\(738\) 0 0
\(739\) 2.42038e11 + 4.19222e11i 0.811532 + 1.40561i 0.911792 + 0.410653i \(0.134699\pi\)
−0.100260 + 0.994961i \(0.531968\pi\)
\(740\) 2.82725e11 + 1.63231e11i 0.942838 + 0.544348i
\(741\) 0 0
\(742\) 1.55025e8 2.51516e10i 0.000511429 0.0829756i
\(743\) −1.64425e11 −0.539527 −0.269763 0.962927i \(-0.586945\pi\)
−0.269763 + 0.962927i \(0.586945\pi\)
\(744\) 0 0
\(745\) −2.31883e11 + 1.33878e11i −0.752738 + 0.434594i
\(746\) −7.19338e10 1.24593e11i −0.232262 0.402289i
\(747\) 0 0
\(748\) 8.56291e9i 0.0273536i
\(749\) 1.26935e11 + 7.43327e10i 0.403323 + 0.236185i
\(750\) 0 0
\(751\) 2.10159e11 3.64006e11i 0.660675 1.14432i −0.319763 0.947498i \(-0.603603\pi\)
0.980438 0.196826i \(-0.0630633\pi\)
\(752\) 1.32658e11 7.65903e10i 0.414823 0.239498i
\(753\) 0 0
\(754\) −5.83386e11 3.36818e11i −1.80497 1.04210i
\(755\) 4.82550e11i 1.48510i
\(756\) 0 0
\(757\) −2.03317e11 −0.619143 −0.309572 0.950876i \(-0.600186\pi\)
−0.309572 + 0.950876i \(0.600186\pi\)
\(758\) 9.01040e10 1.56065e11i 0.272940 0.472746i
\(759\) 0 0
\(760\) −1.59982e11 2.77098e11i −0.479532 0.830574i
\(761\) 1.16599e11 + 6.73185e10i 0.347661 + 0.200722i 0.663655 0.748039i \(-0.269004\pi\)
−0.315993 + 0.948761i \(0.602338\pi\)
\(762\) 0 0
\(763\) 2.78266e11 1.58378e11i 0.821035 0.467301i
\(764\) −3.66507e10 −0.107574
\(765\) 0 0
\(766\) −3.58238e10 + 2.06829e10i −0.104053 + 0.0600753i
\(767\) −3.11238e11 5.39080e11i −0.899314 1.55766i
\(768\) 0 0
\(769\) 2.56622e11i 0.733817i −0.930257 0.366909i \(-0.880416\pi\)
0.930257 0.366909i \(-0.119584\pi\)
\(770\) −1.34876e10 + 2.30322e10i −0.0383683 + 0.0655199i
\(771\) 0 0
\(772\) 2.05438e10 3.55829e10i 0.0578378 0.100178i
\(773\) 1.03389e11 5.96919e10i 0.289573 0.167185i −0.348176 0.937429i \(-0.613199\pi\)
0.637749 + 0.770244i \(0.279866\pi\)
\(774\) 0 0
\(775\) 7.08872e10 + 4.09268e10i 0.196499 + 0.113449i
\(776\) 7.82468e10i 0.215784i
\(777\) 0 0
\(778\) −1.27449e11 −0.347872
\(779\) 1.74205e11 3.01731e11i 0.473053 0.819352i
\(780\) 0 0
\(781\) −2.78782e9 4.82864e9i −0.00749308 0.0129784i
\(782\) −1.70337e11 9.83439e10i −0.455492 0.262979i
\(783\) 0 0
\(784\) 4.82299e10 8.12082e10i 0.127659 0.214949i
\(785\) 4.79896e11 1.26377
\(786\) 0 0
\(787\) −2.33037e11 + 1.34544e11i −0.607472 + 0.350724i −0.771975 0.635652i \(-0.780731\pi\)
0.164503 + 0.986377i \(0.447398\pi\)
\(788\) −6.38107e10 1.10523e11i −0.165497 0.286648i
\(789\) 0 0
\(790\) 3.43750e11i 0.882539i
\(791\) 3.95145e9 6.41094e11i 0.0100937 1.63763i
\(792\) 0 0
\(793\) −3.30684e11 + 5.72761e11i −0.836219 + 1.44837i
\(794\) 3.09004e11 1.78404e11i 0.777468 0.448872i
\(795\) 0 0
\(796\) −1.15638e10 6.67634e9i −0.0288036 0.0166298i
\(797\) 6.65272e11i 1.64879i 0.566013 + 0.824396i \(0.308485\pi\)
−0.566013 + 0.824396i \(0.691515\pi\)
\(798\) 0 0
\(799\) −5.98761e11 −1.46915
\(800\) 4.58013e10 7.93301e10i 0.111820 0.193677i
\(801\) 0 0
\(802\) −2.14990e11 3.72374e11i −0.519662 0.900082i
\(803\) 3.08418e10 + 1.78065e10i 0.0741783 + 0.0428269i
\(804\) 0 0
\(805\) 3.03262e11 + 5.32823e11i 0.722162 + 1.26882i
\(806\) 8.82195e10 0.209038
\(807\) 0 0
\(808\) −1.22797e11 + 7.08971e10i −0.288100 + 0.166335i
\(809\) −5.08703e10 8.81100e10i −0.118760 0.205699i 0.800516 0.599311i \(-0.204559\pi\)
−0.919277 + 0.393612i \(0.871225\pi\)
\(810\) 0 0
\(811\) 6.79465e11i 1.57067i −0.619074 0.785333i \(-0.712492\pi\)
0.619074 0.785333i \(-0.287508\pi\)
\(812\) 3.37818e11 1.92273e11i 0.777068 0.442277i
\(813\) 0 0
\(814\) 1.60220e10 2.77509e10i 0.0364938 0.0632092i
\(815\) −1.55490e11 + 8.97722e10i −0.352429 + 0.203475i
\(816\) 0 0
\(817\) 1.88963e11 + 1.09098e11i 0.424119 + 0.244865i
\(818\) 1.29121e11i 0.288391i
\(819\) 0 0
\(820\) 1.78591e11 0.395006
\(821\) 8.29553e10 1.43683e11i 0.182588 0.316251i −0.760173 0.649720i \(-0.774886\pi\)
0.942761 + 0.333469i \(0.108219\pi\)
\(822\) 0 0
\(823\) −2.01168e11 3.48433e11i −0.438489 0.759485i 0.559084 0.829111i \(-0.311153\pi\)
−0.997573 + 0.0696256i \(0.977820\pi\)
\(824\) −2.37701e11 1.37237e11i −0.515610 0.297688i
\(825\) 0 0
\(826\) 3.59176e11 + 2.21382e9i 0.771590 + 0.00475578i
\(827\) −7.25185e11 −1.55034 −0.775170 0.631753i \(-0.782336\pi\)
−0.775170 + 0.631753i \(0.782336\pi\)
\(828\) 0 0
\(829\) 4.13337e11 2.38640e11i 0.875158 0.505273i 0.00609923 0.999981i \(-0.498059\pi\)
0.869059 + 0.494709i \(0.164725\pi\)
\(830\) 3.47548e11 + 6.01971e11i 0.732322 + 1.26842i
\(831\) 0 0
\(832\) 9.87267e10i 0.206035i
\(833\) −3.21982e11 + 1.80642e11i −0.668732 + 0.375178i
\(834\) 0 0
\(835\) −6.46312e11 + 1.11944e12i −1.32952 + 2.30280i
\(836\) −2.71986e10 + 1.57031e10i −0.0556828 + 0.0321485i
\(837\) 0 0
\(838\) −6.90804e10 3.98836e10i −0.140081 0.0808758i
\(839\) 4.84023e11i 0.976828i 0.872612 + 0.488414i \(0.162424\pi\)
−0.872612 + 0.488414i \(0.837576\pi\)
\(840\) 0 0
\(841\) 1.09943e12 2.19777
\(842\) 1.78457e11 3.09097e11i 0.355047 0.614959i
\(843\) 0 0
\(844\) 3.57380e10 + 6.19001e10i 0.0704305 + 0.121989i
\(845\) −1.14085e12 6.58670e11i −2.23770 1.29194i
\(846\) 0 0
\(847\) −4.41867e11 2.58756e11i −0.858535 0.502756i
\(848\) 1.51704e10 0.0293369
\(849\) 0 0
\(850\) −3.10090e11 + 1.79031e11i −0.594035 + 0.342967i
\(851\) −3.68021e11 6.37431e11i −0.701705 1.21539i
\(852\) 0 0
\(853\) 5.15896e10i 0.0974464i 0.998812 + 0.0487232i \(0.0155152\pi\)
−0.998812 + 0.0487232i \(0.984485\pi\)
\(854\) −1.88771e11 3.31665e11i −0.354898 0.623546i
\(855\) 0 0
\(856\) −4.43608e10 + 7.68352e10i −0.0826236 + 0.143108i
\(857\) 7.06025e11 4.07624e11i 1.30887 0.755677i 0.326963 0.945037i \(-0.393975\pi\)
0.981908 + 0.189360i \(0.0606414\pi\)
\(858\) 0 0
\(859\) 4.78407e11 + 2.76208e11i 0.878667 + 0.507299i 0.870219 0.492666i \(-0.163977\pi\)
0.00844851 + 0.999964i \(0.497311\pi\)
\(860\) 1.11844e11i 0.204466i
\(861\) 0 0
\(862\) 3.62923e11 0.657334
\(863\) −1.19370e11 + 2.06755e11i −0.215205 + 0.372746i −0.953336 0.301912i \(-0.902375\pi\)
0.738131 + 0.674657i \(0.235709\pi\)
\(864\) 0 0
\(865\) 5.54926e11 + 9.61159e11i 0.991221 + 1.71684i
\(866\) −2.24209e11 1.29447e11i −0.398641 0.230156i
\(867\) 0 0
\(868\) −2.57235e10 + 4.39269e10i −0.0453160 + 0.0773842i
\(869\) 3.37408e10 0.0591666
\(870\) 0 0
\(871\) 7.10103e11 4.09978e11i 1.23381 0.712342i
\(872\) 9.65579e10 + 1.67243e11i 0.167002 + 0.289256i
\(873\) 0 0
\(874\) 7.21392e11i 1.23631i
\(875\) 2.33865e11 + 1.44145e9i 0.398964 + 0.00245906i
\(876\) 0 0
\(877\) 3.70803e10 6.42249e10i 0.0626822 0.108569i −0.832981 0.553301i \(-0.813368\pi\)
0.895664 + 0.444732i \(0.146701\pi\)
\(878\) 3.32502e10 1.91970e10i 0.0559521 0.0323039i
\(879\) 0 0
\(880\) −1.39417e10 8.04924e9i −0.0232479 0.0134222i
\(881\) 1.01123e12i 1.67860i −0.543669 0.839300i \(-0.682965\pi\)
0.543669 0.839300i \(-0.317035\pi\)
\(882\) 0 0
\(883\) −9.12397e11 −1.50086 −0.750432 0.660948i \(-0.770154\pi\)
−0.750432 + 0.660948i \(0.770154\pi\)
\(884\) −1.92954e11 + 3.34207e11i −0.315970 + 0.547276i
\(885\) 0 0
\(886\) −2.92495e11 5.06615e11i −0.474660 0.822136i
\(887\) 8.38886e11 + 4.84331e11i 1.35522 + 0.782434i 0.988974 0.148086i \(-0.0473113\pi\)
0.366241 + 0.930520i \(0.380645\pi\)
\(888\) 0 0
\(889\) 1.60677e9 2.60686e11i 0.00257244 0.417360i
\(890\) 3.17847e11 0.506591
\(891\) 0 0
\(892\) −1.63178e11 + 9.42110e10i −0.257752 + 0.148813i
\(893\) 1.09804e12 + 1.90186e12i 1.72668 + 2.99070i
\(894\) 0 0
\(895\) 1.36629e12i 2.12936i
\(896\) 4.91588e10 + 2.87873e10i 0.0762727 + 0.0446651i
\(897\) 0 0
\(898\) 2.83524e11 4.91078e11i 0.435998 0.755171i
\(899\) −1.81427e11 + 1.04747e11i −0.277755 + 0.160362i
\(900\) 0 0
\(901\) −5.13544e10 2.96495e10i −0.0779253 0.0449902i
\(902\) 1.75296e10i 0.0264817i
\(903\) 0 0
\(904\) 3.86681e11 0.579001
\(905\) 1.65303e11 2.86313e11i 0.246426 0.426822i
\(906\) 0 0
\(907\) −5.82503e11 1.00893e12i −0.860735 1.49084i −0.871221 0.490891i \(-0.836671\pi\)
0.0104860 0.999945i \(-0.496662\pi\)
\(908\) −1.32837e11 7.66936e10i −0.195423 0.112828i
\(909\) 0 0
\(910\) 1.04542e12 5.95012e11i 1.52449 0.867681i
\(911\) 3.53799e11 0.513669 0.256835 0.966455i \(-0.417320\pi\)
0.256835 + 0.966455i \(0.417320\pi\)
\(912\) 0 0
\(913\) 5.90866e10 3.41137e10i 0.0850366 0.0490959i
\(914\) −4.47525e11 7.75136e11i −0.641257 1.11069i
\(915\) 0 0
\(916\) 4.62767e9i 0.00657326i
\(917\) −1.64534e11 + 2.80968e11i −0.232690 + 0.397355i
\(918\) 0 0
\(919\) −2.37089e11 + 4.10651e11i −0.332392 + 0.575719i −0.982980 0.183711i \(-0.941189\pi\)
0.650589 + 0.759430i \(0.274522\pi\)
\(920\) −3.20237e11 + 1.84889e11i −0.447013 + 0.258083i
\(921\) 0 0
\(922\) 1.37284e11 + 7.92610e10i 0.189975 + 0.109682i
\(923\) 2.51280e11i 0.346219i
\(924\) 0 0
\(925\) −1.33993e12 −1.83027
\(926\) −3.74423e11 + 6.48520e11i −0.509235 + 0.882022i
\(927\) 0 0
\(928\) 1.17222e11 + 2.03035e11i 0.158059 + 0.273766i
\(929\) −3.72827e11 2.15252e11i −0.500546 0.288990i 0.228393 0.973569i \(-0.426653\pi\)
−0.728939 + 0.684579i \(0.759986\pi\)
\(930\) 0 0
\(931\) 1.16424e12 + 6.91450e11i 1.54969 + 0.920370i
\(932\) −4.20683e11 −0.557560
\(933\) 0 0
\(934\) 3.55864e11 2.05458e11i 0.467623 0.269983i
\(935\) 3.14633e10 + 5.44961e10i 0.0411678 + 0.0713048i
\(936\) 0 0
\(937\) 1.06322e12i 1.37932i −0.724134 0.689659i \(-0.757760\pi\)
0.724134 0.689659i \(-0.242240\pi\)
\(938\) −2.91615e9 + 4.73124e11i −0.00376703 + 0.611172i
\(939\) 0 0
\(940\) −5.62842e11 + 9.74872e11i −0.720901 + 1.24864i
\(941\) −1.26165e12 + 7.28416e11i −1.60910 + 0.929012i −0.619523 + 0.784979i \(0.712674\pi\)
−0.989573 + 0.144033i \(0.953993\pi\)
\(942\) 0 0
\(943\) −3.48706e11 2.01325e11i −0.440973 0.254596i
\(944\) 2.16640e11i 0.272803i
\(945\) 0 0
\(946\) 1.09781e10 0.0137077
\(947\) −6.32117e11 + 1.09486e12i −0.785954 + 1.36131i 0.142473 + 0.989799i \(0.454495\pi\)
−0.928427 + 0.371514i \(0.878839\pi\)
\(948\) 0 0
\(949\) −8.02494e11 1.38996e12i −0.989411 1.71371i
\(950\) 1.13732e12 + 6.56632e11i 1.39633 + 0.806171i
\(951\) 0 0
\(952\) −1.10148e11 1.93527e11i −0.134100 0.235610i
\(953\) 7.86324e11 0.953300 0.476650 0.879093i \(-0.341851\pi\)
0.476650 + 0.879093i \(0.341851\pi\)
\(954\) 0 0
\(955\) 2.33253e11 1.34668e11i 0.280423 0.161902i
\(956\) −2.39027e11 4.14006e11i −0.286164 0.495650i
\(957\) 0 0
\(958\) 8.29213e11i 0.984474i
\(959\) 1.15779e12 6.58968e11i 1.36885 0.779094i
\(960\) 0 0
\(961\) −4.12728e11 + 7.14866e11i −0.483916 + 0.838168i
\(962\) −1.25066e12 + 7.22071e11i −1.46029 + 0.843102i
\(963\) 0 0
\(964\) −2.46223e11 1.42157e11i −0.285115 0.164611i
\(965\) 3.01942e11i 0.348189i
\(966\) 0 0
\(967\) 2.31465e11 0.264715 0.132358 0.991202i \(-0.457745\pi\)
0.132358 + 0.991202i \(0.457745\pi\)
\(968\) 1.54422e11 2.67467e11i 0.175877 0.304628i
\(969\) 0 0
\(970\) 2.87508e11 + 4.97978e11i 0.324760 + 0.562501i
\(971\) 1.04667e12 + 6.04295e11i 1.17742 + 0.679786i 0.955417 0.295260i \(-0.0954061\pi\)
0.222006 + 0.975045i \(0.428739\pi\)
\(972\) 0 0
\(973\) 1.70926e11 + 1.05352e9i 0.190703 + 0.00117542i
\(974\) 8.96188e11 0.995780
\(975\) 0 0
\(976\) 1.99337e11 1.15087e11i 0.219679 0.126832i
\(977\) 5.07309e11 + 8.78684e11i 0.556793 + 0.964394i 0.997762 + 0.0668716i \(0.0213018\pi\)
−0.440968 + 0.897523i \(0.645365\pi\)
\(978\) 0 0
\(979\) 3.11983e10i 0.0339626i
\(980\) −8.55591e9 + 6.94040e11i −0.00927602 + 0.752454i
\(981\) 0 0
\(982\) −3.18612e11 + 5.51851e11i −0.342622 + 0.593439i
\(983\) −2.92626e11 + 1.68948e11i −0.313400 + 0.180942i −0.648447 0.761260i \(-0.724581\pi\)
0.335047 + 0.942201i \(0.391248\pi\)
\(984\) 0 0
\(985\) 8.12208e11 + 4.68929e11i 0.862825 + 0.498152i
\(986\) 9.16412e11i 0.969578i
\(987\) 0 0
\(988\) 1.41540e12 1.48543
\(989\) 1.26082e11 2.18381e11i 0.131786 0.228260i
\(990\) 0 0
\(991\) 5.53859e11 + 9.59312e11i 0.574255 + 0.994639i 0.996122 + 0.0879813i \(0.0280416\pi\)
−0.421867 + 0.906658i \(0.638625\pi\)
\(992\) −2.65895e10 1.53515e10i −0.0274577 0.0158527i
\(993\) 0 0
\(994\) −1.25119e11 7.32695e10i −0.128168 0.0750547i
\(995\) 9.81254e10 0.100113
\(996\) 0 0
\(997\) −4.16099e11 + 2.40235e11i −0.421130 + 0.243139i −0.695561 0.718468i \(-0.744844\pi\)
0.274431 + 0.961607i \(0.411511\pi\)
\(998\) 1.51995e11 + 2.63263e11i 0.153217 + 0.265379i
\(999\) 0 0
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 126.9.n.d.19.5 20
3.2 odd 2 inner 126.9.n.d.19.6 yes 20
7.3 odd 6 inner 126.9.n.d.73.5 yes 20
21.17 even 6 inner 126.9.n.d.73.6 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.9.n.d.19.5 20 1.1 even 1 trivial
126.9.n.d.19.6 yes 20 3.2 odd 2 inner
126.9.n.d.73.5 yes 20 7.3 odd 6 inner
126.9.n.d.73.6 yes 20 21.17 even 6 inner