Properties

Label 3.71.b.a.2.3
Level $3$
Weight $71$
Character 3.2
Analytic conductor $93.095$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,71,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 71, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 71);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 71 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(93.0951693564\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.3
Character \(\chi\) \(=\) 3.2
Dual form 3.71.b.a.2.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.67567e10i q^{2} +(2.16075e15 + 4.99849e16i) q^{3} -2.04073e21 q^{4} +2.61507e24i q^{5} +(2.83697e27 - 1.22637e26i) q^{6} -2.08517e29 q^{7} +4.88185e31i q^{8} +(-2.49382e33 + 2.16009e32i) q^{9} +O(q^{10})\) \(q-5.67567e10i q^{2} +(2.16075e15 + 4.99849e16i) q^{3} -2.04073e21 q^{4} +2.61507e24i q^{5} +(2.83697e27 - 1.22637e26i) q^{6} -2.08517e29 q^{7} +4.88185e31i q^{8} +(-2.49382e33 + 2.16009e32i) q^{9} +1.48422e35 q^{10} +2.44874e36i q^{11} +(-4.40950e36 - 1.02006e38i) q^{12} +1.52613e39 q^{13} +1.18347e40i q^{14} +(-1.30714e41 + 5.65050e39i) q^{15} +3.61509e41 q^{16} +1.39013e43i q^{17} +(1.22600e43 + 1.41541e44i) q^{18} +6.05007e44 q^{19} -5.33664e45i q^{20} +(-4.50552e44 - 1.04227e46i) q^{21} +1.38982e47 q^{22} -5.18745e47i q^{23} +(-2.44019e48 + 1.05484e47i) q^{24} +1.63176e48 q^{25} -8.66181e49i q^{26} +(-1.61857e49 - 1.24186e50i) q^{27} +4.25526e50 q^{28} +1.74998e50i q^{29} +(3.20703e50 + 7.41887e51i) q^{30} +1.83290e52 q^{31} +3.71167e52i q^{32} +(-1.22400e53 + 5.29111e51i) q^{33} +7.88993e53 q^{34} -5.45285e53i q^{35} +(5.08920e54 - 4.40817e53i) q^{36} -5.50074e54 q^{37} -3.43382e55i q^{38} +(3.29758e54 + 7.62834e55i) q^{39} -1.27664e56 q^{40} +3.14908e56i q^{41} +(-5.91556e56 + 2.55718e55i) q^{42} -1.00222e57 q^{43} -4.99721e57i q^{44} +(-5.64879e56 - 6.52150e57i) q^{45} -2.94422e58 q^{46} +4.95679e58i q^{47} +(7.81130e56 + 1.80700e58i) q^{48} -1.00024e59 q^{49} -9.26134e58i q^{50} +(-6.94856e59 + 3.00373e58i) q^{51} -3.11442e60 q^{52} -2.19350e60i q^{53} +(-7.04841e60 + 9.18647e59i) q^{54} -6.40361e60 q^{55} -1.01795e61i q^{56} +(1.30727e60 + 3.02412e61i) q^{57} +9.93233e60 q^{58} +7.59389e61i q^{59} +(2.66751e62 - 1.15311e61i) q^{60} +2.47919e62 q^{61} -1.04029e63i q^{62} +(5.20002e62 - 4.50415e61i) q^{63} +2.53341e63 q^{64} +3.99093e63i q^{65} +(3.00306e62 + 6.94701e63i) q^{66} -1.18377e64 q^{67} -2.83688e64i q^{68} +(2.59294e64 - 1.12088e63i) q^{69} -3.09485e64 q^{70} +6.04004e64i q^{71} +(-1.05453e64 - 1.21744e65i) q^{72} -2.84733e65 q^{73} +3.12204e65i q^{74} +(3.52583e63 + 8.15634e64i) q^{75} -1.23465e66 q^{76} -5.10603e65i q^{77} +(4.32959e66 - 1.87160e65i) q^{78} -1.26491e66 q^{79} +9.45369e65i q^{80} +(6.17247e66 - 1.07738e66i) q^{81} +1.78731e67 q^{82} +7.76052e65i q^{83} +(9.19454e65 + 2.12698e67i) q^{84} -3.63529e67 q^{85} +5.68828e67i q^{86} +(-8.74727e66 + 3.78127e65i) q^{87} -1.19544e68 q^{88} -2.51424e68i q^{89} +(-3.70138e68 + 3.20606e67i) q^{90} -3.18224e68 q^{91} +1.05862e69i q^{92} +(3.96044e67 + 9.16173e68i) q^{93} +2.81331e69 q^{94} +1.58213e69i q^{95} +(-1.85527e69 + 8.01998e67i) q^{96} +5.38387e69 q^{97} +5.67705e69i q^{98} +(-5.28951e68 - 6.10671e69i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.67567e10i 1.65184i −0.563790 0.825918i \(-0.690657\pi\)
0.563790 0.825918i \(-0.309343\pi\)
\(3\) 2.16075e15 + 4.99849e16i 0.0431877 + 0.999067i
\(4\) −2.04073e21 −1.72856
\(5\) 2.61507e24i 0.898530i 0.893399 + 0.449265i \(0.148314\pi\)
−0.893399 + 0.449265i \(0.851686\pi\)
\(6\) 2.83697e27 1.22637e26i 1.65030 0.0713391i
\(7\) −2.08517e29 −0.550439 −0.275220 0.961381i \(-0.588751\pi\)
−0.275220 + 0.961381i \(0.588751\pi\)
\(8\) 4.88185e31i 1.20347i
\(9\) −2.49382e33 + 2.16009e32i −0.996270 + 0.0862948i
\(10\) 1.48422e35 1.48422
\(11\) 2.44874e36i 0.871361i 0.900101 + 0.435681i \(0.143492\pi\)
−0.900101 + 0.435681i \(0.856508\pi\)
\(12\) −4.40950e36 1.02006e38i −0.0746527 1.72695i
\(13\) 1.52613e39 1.56882 0.784412 0.620240i \(-0.212965\pi\)
0.784412 + 0.620240i \(0.212965\pi\)
\(14\) 1.18347e40i 0.909235i
\(15\) −1.30714e41 + 5.65050e39i −0.897691 + 0.0388054i
\(16\) 3.61509e41 0.259370
\(17\) 1.39013e43i 1.19493i 0.801894 + 0.597467i \(0.203826\pi\)
−0.801894 + 0.597467i \(0.796174\pi\)
\(18\) 1.22600e43 + 1.41541e44i 0.142545 + 1.64567i
\(19\) 6.05007e44 1.06019 0.530096 0.847938i \(-0.322156\pi\)
0.530096 + 0.847938i \(0.322156\pi\)
\(20\) 5.33664e45i 1.55317i
\(21\) −4.50552e44 1.04227e46i −0.0237722 0.549925i
\(22\) 1.38982e47 1.43935
\(23\) 5.18745e47i 1.13365i −0.823838 0.566826i \(-0.808171\pi\)
0.823838 0.566826i \(-0.191829\pi\)
\(24\) −2.44019e48 + 1.05484e47i −1.20235 + 0.0519751i
\(25\) 1.63176e48 0.192644
\(26\) 8.66181e49i 2.59144i
\(27\) −1.61857e49 1.24186e50i −0.129241 0.991613i
\(28\) 4.25526e50 0.951469
\(29\) 1.74998e50i 0.114579i 0.998358 + 0.0572894i \(0.0182458\pi\)
−0.998358 + 0.0572894i \(0.981754\pi\)
\(30\) 3.20703e50 + 7.41887e51i 0.0641003 + 1.48284i
\(31\) 1.83290e52 1.16273 0.581366 0.813642i \(-0.302519\pi\)
0.581366 + 0.813642i \(0.302519\pi\)
\(32\) 3.71167e52i 0.775032i
\(33\) −1.22400e53 + 5.29111e51i −0.870548 + 0.0376321i
\(34\) 7.88993e53 1.97384
\(35\) 5.45285e53i 0.494586i
\(36\) 5.08920e54 4.40817e53i 1.72212 0.149166i
\(37\) −5.50074e54 −0.713446 −0.356723 0.934210i \(-0.616106\pi\)
−0.356723 + 0.934210i \(0.616106\pi\)
\(38\) 3.43382e55i 1.75126i
\(39\) 3.29758e54 + 7.62834e55i 0.0677540 + 1.56736i
\(40\) −1.27664e56 −1.08135
\(41\) 3.14908e56i 1.12395i 0.827153 + 0.561977i \(0.189959\pi\)
−0.827153 + 0.561977i \(0.810041\pi\)
\(42\) −5.91556e56 + 2.55718e55i −0.908387 + 0.0392678i
\(43\) −1.00222e57 −0.675410 −0.337705 0.941252i \(-0.609651\pi\)
−0.337705 + 0.941252i \(0.609651\pi\)
\(44\) 4.99721e57i 1.50620i
\(45\) −5.64879e56 6.52150e57i −0.0775385 0.895178i
\(46\) −2.94422e58 −1.87261
\(47\) 4.95679e58i 1.48517i 0.669754 + 0.742583i \(0.266400\pi\)
−0.669754 + 0.742583i \(0.733600\pi\)
\(48\) 7.81130e56 + 1.80700e58i 0.0112016 + 0.259128i
\(49\) −1.00024e59 −0.697017
\(50\) 9.26134e58i 0.318217i
\(51\) −6.94856e59 + 3.00373e58i −1.19382 + 0.0516065i
\(52\) −3.11442e60 −2.71181
\(53\) 2.19350e60i 0.980578i −0.871560 0.490289i \(-0.836891\pi\)
0.871560 0.490289i \(-0.163109\pi\)
\(54\) −7.04841e60 + 9.18647e59i −1.63798 + 0.213485i
\(55\) −6.40361e60 −0.782944
\(56\) 1.01795e61i 0.662436i
\(57\) 1.30727e60 + 3.02412e61i 0.0457872 + 1.05920i
\(58\) 9.93233e60 0.189265
\(59\) 7.59389e61i 0.795507i 0.917492 + 0.397753i \(0.130210\pi\)
−0.917492 + 0.397753i \(0.869790\pi\)
\(60\) 2.66751e62 1.15311e61i 1.55172 0.0670777i
\(61\) 2.47919e62 0.808661 0.404330 0.914613i \(-0.367505\pi\)
0.404330 + 0.914613i \(0.367505\pi\)
\(62\) 1.04029e63i 1.92064i
\(63\) 5.20002e62 4.50415e61i 0.548386 0.0475001i
\(64\) 2.53341e63 1.53960
\(65\) 3.99093e63i 1.40964i
\(66\) 3.00306e62 + 6.94701e63i 0.0621621 + 1.43800i
\(67\) −1.18377e64 −1.44761 −0.723804 0.690006i \(-0.757608\pi\)
−0.723804 + 0.690006i \(0.757608\pi\)
\(68\) 2.83688e64i 2.06552i
\(69\) 2.59294e64 1.12088e63i 1.13259 0.0489598i
\(70\) −3.09485e64 −0.816975
\(71\) 6.04004e64i 0.970505i 0.874374 + 0.485253i \(0.161272\pi\)
−0.874374 + 0.485253i \(0.838728\pi\)
\(72\) −1.05453e64 1.21744e65i −0.103853 1.19898i
\(73\) −2.84733e65 −1.73037 −0.865183 0.501457i \(-0.832798\pi\)
−0.865183 + 0.501457i \(0.832798\pi\)
\(74\) 3.12204e65i 1.17850i
\(75\) 3.52583e63 + 8.15634e64i 0.00831988 + 0.192465i
\(76\) −1.23465e66 −1.83261
\(77\) 5.10603e65i 0.479631i
\(78\) 4.32959e66 1.87160e65i 2.58902 0.111918i
\(79\) −1.26491e66 −0.484296 −0.242148 0.970239i \(-0.577852\pi\)
−0.242148 + 0.970239i \(0.577852\pi\)
\(80\) 9.45369e65i 0.233052i
\(81\) 6.17247e66 1.07738e66i 0.985106 0.171946i
\(82\) 1.78731e67 1.85659
\(83\) 7.76052e65i 0.0527421i 0.999652 + 0.0263711i \(0.00839515\pi\)
−0.999652 + 0.0263711i \(0.991605\pi\)
\(84\) 9.19454e65 + 2.12698e67i 0.0410918 + 0.950581i
\(85\) −3.63529e67 −1.07368
\(86\) 5.68828e67i 1.11567i
\(87\) −8.74727e66 + 3.78127e65i −0.114472 + 0.00494840i
\(88\) −1.19544e68 −1.04866
\(89\) 2.51424e68i 1.48510i −0.669788 0.742552i \(-0.733615\pi\)
0.669788 0.742552i \(-0.266385\pi\)
\(90\) −3.70138e68 + 3.20606e67i −1.47869 + 0.128081i
\(91\) −3.18224e68 −0.863542
\(92\) 1.05862e69i 1.95959i
\(93\) 3.96044e67 + 9.16173e68i 0.0502157 + 1.16165i
\(94\) 2.81331e69 2.45325
\(95\) 1.58213e69i 0.952613i
\(96\) −1.85527e69 + 8.01998e67i −0.774309 + 0.0334719i
\(97\) 5.38387e69 1.56345 0.781725 0.623623i \(-0.214340\pi\)
0.781725 + 0.623623i \(0.214340\pi\)
\(98\) 5.67705e69i 1.15136i
\(99\) −5.28951e68 6.10671e69i −0.0751940 0.868111i
\(100\) −3.32998e69 −0.332998
\(101\) 1.86953e70i 1.31973i 0.751384 + 0.659865i \(0.229386\pi\)
−0.751384 + 0.659865i \(0.770614\pi\)
\(102\) 1.70481e69 + 3.94377e70i 0.0852454 + 1.97199i
\(103\) −1.60989e70 −0.572128 −0.286064 0.958210i \(-0.592347\pi\)
−0.286064 + 0.958210i \(0.592347\pi\)
\(104\) 7.45034e70i 1.88803i
\(105\) 2.72560e70 1.17822e69i 0.494124 0.0213600i
\(106\) −1.24496e71 −1.61975
\(107\) 1.16190e71i 1.08827i −0.838996 0.544137i \(-0.816857\pi\)
0.838996 0.544137i \(-0.183143\pi\)
\(108\) 3.30306e70 + 2.53431e71i 0.223401 + 1.71407i
\(109\) −1.47058e71 −0.720378 −0.360189 0.932879i \(-0.617288\pi\)
−0.360189 + 0.932879i \(0.617288\pi\)
\(110\) 3.63448e71i 1.29330i
\(111\) −1.18857e70 2.74954e71i −0.0308121 0.712780i
\(112\) −7.53806e70 −0.142767
\(113\) 1.03401e72i 1.43476i 0.696684 + 0.717378i \(0.254658\pi\)
−0.696684 + 0.717378i \(0.745342\pi\)
\(114\) 1.71639e72 7.41961e70i 1.74963 0.0756330i
\(115\) 1.35655e72 1.01862
\(116\) 3.57124e71i 0.198057i
\(117\) −3.80589e72 + 3.29659e71i −1.56297 + 0.135382i
\(118\) 4.31004e72 1.31405
\(119\) 2.89866e72i 0.657738i
\(120\) −2.75849e71 6.38125e72i −0.0467012 1.08034i
\(121\) 1.90115e72 0.240729
\(122\) 1.40711e73i 1.33578i
\(123\) −1.57406e73 + 6.80437e71i −1.12291 + 0.0485410i
\(124\) −3.74045e73 −2.00986
\(125\) 2.64176e73i 1.07163i
\(126\) −2.55641e72 2.95136e73i −0.0784623 0.905844i
\(127\) 6.94331e72 0.161598 0.0807990 0.996730i \(-0.474253\pi\)
0.0807990 + 0.996730i \(0.474253\pi\)
\(128\) 9.99685e73i 1.76813i
\(129\) −2.16555e72 5.00959e73i −0.0291694 0.674780i
\(130\) 2.26512e74 2.32849
\(131\) 1.85604e74i 1.45912i −0.683917 0.729560i \(-0.739725\pi\)
0.683917 0.729560i \(-0.260275\pi\)
\(132\) 2.49785e74 1.07977e73i 1.50480 0.0650495i
\(133\) −1.26154e74 −0.583571
\(134\) 6.71871e74i 2.39121i
\(135\) 3.24756e74 4.23267e73i 0.890994 0.116127i
\(136\) −6.78642e74 −1.43807
\(137\) 4.72325e74i 0.774499i 0.921975 + 0.387250i \(0.126575\pi\)
−0.921975 + 0.387250i \(0.873425\pi\)
\(138\) −6.36172e73 1.47167e75i −0.0808736 1.87086i
\(139\) −1.55543e75 −1.53579 −0.767896 0.640574i \(-0.778696\pi\)
−0.767896 + 0.640574i \(0.778696\pi\)
\(140\) 1.11278e75i 0.854923i
\(141\) −2.47764e75 + 1.07104e74i −1.48378 + 0.0641409i
\(142\) 3.42813e75 1.60312
\(143\) 3.73709e75i 1.36701i
\(144\) −9.01537e74 + 7.80893e73i −0.258402 + 0.0223823i
\(145\) −4.57632e74 −0.102952
\(146\) 1.61605e76i 2.85828i
\(147\) −2.16128e74 4.99971e75i −0.0301026 0.696367i
\(148\) 1.12255e76 1.23324
\(149\) 6.27147e75i 0.544314i −0.962253 0.272157i \(-0.912263\pi\)
0.962253 0.272157i \(-0.0877371\pi\)
\(150\) 4.62927e75 2.00114e74i 0.317920 0.0137431i
\(151\) 1.35242e76 0.736068 0.368034 0.929812i \(-0.380031\pi\)
0.368034 + 0.929812i \(0.380031\pi\)
\(152\) 2.95355e76i 1.27591i
\(153\) −3.00282e75 3.46674e76i −0.103117 1.19048i
\(154\) −2.89801e76 −0.792273
\(155\) 4.79315e76i 1.04475i
\(156\) −6.72947e75 1.55674e77i −0.117117 2.70928i
\(157\) −7.43206e76 −1.03424 −0.517120 0.855913i \(-0.672996\pi\)
−0.517120 + 0.855913i \(0.672996\pi\)
\(158\) 7.17920e76i 0.799978i
\(159\) 1.09642e77 4.73960e75i 0.979663 0.0423489i
\(160\) −9.70625e76 −0.696389
\(161\) 1.08167e77i 0.624006i
\(162\) −6.11483e76 3.50329e77i −0.284026 1.62723i
\(163\) −2.31545e76 −0.0867100 −0.0433550 0.999060i \(-0.513805\pi\)
−0.0433550 + 0.999060i \(0.513805\pi\)
\(164\) 6.42642e77i 1.94283i
\(165\) −1.38366e76 3.20084e77i −0.0338136 0.782214i
\(166\) 4.40461e76 0.0871214
\(167\) 3.77615e77i 0.605304i 0.953101 + 0.302652i \(0.0978719\pi\)
−0.953101 + 0.302652i \(0.902128\pi\)
\(168\) 5.08819e77 2.19953e76i 0.661818 0.0286091i
\(169\) 1.38276e78 1.46121
\(170\) 2.06327e78i 1.77355i
\(171\) −1.50878e78 + 1.30687e77i −1.05624 + 0.0914890i
\(172\) 2.04526e78 1.16749
\(173\) 8.86986e77i 0.413336i −0.978411 0.206668i \(-0.933738\pi\)
0.978411 0.206668i \(-0.0662620\pi\)
\(174\) 2.14613e76 + 4.96466e77i 0.00817394 + 0.189089i
\(175\) −3.40249e77 −0.106039
\(176\) 8.85241e77i 0.226005i
\(177\) −3.79580e78 + 1.64085e77i −0.794765 + 0.0343561i
\(178\) −1.42700e79 −2.45315
\(179\) 2.15731e78i 0.304829i −0.988317 0.152414i \(-0.951295\pi\)
0.988317 0.152414i \(-0.0487048\pi\)
\(180\) 1.15276e78 + 1.33086e79i 0.134030 + 1.54737i
\(181\) −1.27122e78 −0.121751 −0.0608754 0.998145i \(-0.519389\pi\)
−0.0608754 + 0.998145i \(0.519389\pi\)
\(182\) 1.80613e79i 1.42643i
\(183\) 5.35692e77 + 1.23922e79i 0.0349242 + 0.807906i
\(184\) 2.53243e79 1.36431
\(185\) 1.43848e79i 0.641052i
\(186\) 5.19989e79 2.24781e78i 1.91885 0.0829482i
\(187\) −3.40407e79 −1.04122
\(188\) 1.01155e80i 2.56721i
\(189\) 3.37499e78 + 2.58949e79i 0.0711393 + 0.545823i
\(190\) 8.97966e79 1.57356
\(191\) 1.66680e78i 0.0243062i 0.999926 + 0.0121531i \(0.00386855\pi\)
−0.999926 + 0.0121531i \(0.996131\pi\)
\(192\) 5.47407e78 + 1.26632e80i 0.0664917 + 1.53816i
\(193\) −1.63414e80 −1.65495 −0.827473 0.561505i \(-0.810222\pi\)
−0.827473 + 0.561505i \(0.810222\pi\)
\(194\) 3.05571e80i 2.58256i
\(195\) −1.99486e80 + 8.62340e78i −1.40832 + 0.0608789i
\(196\) 2.04123e80 1.20484
\(197\) 8.93355e79i 0.441272i −0.975356 0.220636i \(-0.929187\pi\)
0.975356 0.220636i \(-0.0708133\pi\)
\(198\) −3.46596e80 + 3.00215e79i −1.43398 + 0.124208i
\(199\) −3.93386e80 −1.36446 −0.682230 0.731138i \(-0.738990\pi\)
−0.682230 + 0.731138i \(0.738990\pi\)
\(200\) 7.96602e79i 0.231842i
\(201\) −2.55784e79 5.91708e80i −0.0625189 1.44626i
\(202\) 1.06108e81 2.17998
\(203\) 3.64901e79i 0.0630686i
\(204\) 1.41801e81 6.12979e79i 2.06359 0.0892051i
\(205\) −8.23505e80 −1.00991
\(206\) 9.13720e80i 0.945062i
\(207\) 1.12054e80 + 1.29365e81i 0.0978283 + 1.12942i
\(208\) 5.51710e80 0.406906
\(209\) 1.48150e81i 0.923810i
\(210\) −6.68720e79 1.54696e81i −0.0352833 0.816213i
\(211\) 6.66814e80 0.297933 0.148966 0.988842i \(-0.452405\pi\)
0.148966 + 0.988842i \(0.452405\pi\)
\(212\) 4.47634e81i 1.69499i
\(213\) −3.01911e81 + 1.30510e80i −0.969600 + 0.0419139i
\(214\) −6.59458e81 −1.79765
\(215\) 2.62088e81i 0.606876i
\(216\) 6.06259e81 7.90162e80i 1.19338 0.155537i
\(217\) −3.82190e81 −0.640013
\(218\) 8.34650e81i 1.18995i
\(219\) −6.15237e80 1.42323e82i −0.0747305 1.72875i
\(220\) 1.30680e82 1.35337
\(221\) 2.12152e82i 1.87464i
\(222\) −1.56055e82 + 6.74594e80i −1.17740 + 0.0508966i
\(223\) −1.34100e82 −0.864488 −0.432244 0.901757i \(-0.642278\pi\)
−0.432244 + 0.901757i \(0.642278\pi\)
\(224\) 7.73944e81i 0.426608i
\(225\) −4.06932e81 + 3.52476e80i −0.191926 + 0.0166242i
\(226\) 5.86868e82 2.36998
\(227\) 3.01073e82i 1.04176i −0.853631 0.520878i \(-0.825604\pi\)
0.853631 0.520878i \(-0.174396\pi\)
\(228\) −2.66778e81 6.17140e82i −0.0791462 1.83090i
\(229\) 1.52276e82 0.387604 0.193802 0.981041i \(-0.437918\pi\)
0.193802 + 0.981041i \(0.437918\pi\)
\(230\) 7.69934e82i 1.68259i
\(231\) 2.55224e82 1.10328e81i 0.479184 0.0207142i
\(232\) −8.54316e81 −0.137892
\(233\) 5.76506e82i 0.800473i 0.916412 + 0.400237i \(0.131072\pi\)
−0.916412 + 0.400237i \(0.868928\pi\)
\(234\) 1.87103e82 + 2.16010e83i 0.223628 + 2.58178i
\(235\) −1.29623e83 −1.33447
\(236\) 1.54971e83i 1.37508i
\(237\) −2.73315e81 6.32263e82i −0.0209156 0.483844i
\(238\) −1.64518e83 −1.08648
\(239\) 6.75327e81i 0.0385112i 0.999815 + 0.0192556i \(0.00612963\pi\)
−0.999815 + 0.0192556i \(0.993870\pi\)
\(240\) −4.72542e82 + 2.04271e81i −0.232834 + 0.0100650i
\(241\) 1.62791e83 0.693480 0.346740 0.937961i \(-0.387289\pi\)
0.346740 + 0.937961i \(0.387289\pi\)
\(242\) 1.07903e83i 0.397645i
\(243\) 6.71897e82 + 3.06202e83i 0.214330 + 0.976761i
\(244\) −5.05936e83 −1.39782
\(245\) 2.61570e83i 0.626290i
\(246\) 3.86193e82 + 8.93386e83i 0.0801818 + 1.85486i
\(247\) 9.23319e83 1.66325
\(248\) 8.94794e83i 1.39931i
\(249\) −3.87909e82 + 1.67685e81i −0.0526929 + 0.00227781i
\(250\) 1.49938e84 1.77015
\(251\) 3.34403e82i 0.0343313i 0.999853 + 0.0171657i \(0.00546427\pi\)
−0.999853 + 0.0171657i \(0.994536\pi\)
\(252\) −1.06118e84 + 9.19176e82i −0.947920 + 0.0821069i
\(253\) 1.27027e84 0.987820
\(254\) 3.94079e83i 0.266934i
\(255\) −7.85494e82 1.81709e84i −0.0463699 1.07268i
\(256\) −2.68295e84 −1.38106
\(257\) 1.99841e84i 0.897483i 0.893662 + 0.448742i \(0.148128\pi\)
−0.893662 + 0.448742i \(0.851872\pi\)
\(258\) −2.84328e84 + 1.22909e83i −1.11463 + 0.0481831i
\(259\) 1.14700e84 0.392708
\(260\) 8.14441e84i 2.43665i
\(261\) −3.78013e82 4.36414e83i −0.00988756 0.114151i
\(262\) −1.05342e85 −2.41023
\(263\) 3.03310e84i 0.607345i 0.952777 + 0.303672i \(0.0982128\pi\)
−0.952777 + 0.303672i \(0.901787\pi\)
\(264\) −2.58304e83 5.97538e84i −0.0452891 1.04768i
\(265\) 5.73615e84 0.881079
\(266\) 7.16008e84i 0.963963i
\(267\) 1.25674e85 5.43265e83i 1.48372 0.0641383i
\(268\) 2.41576e85 2.50228
\(269\) 2.16129e84i 0.196510i 0.995161 + 0.0982549i \(0.0313260\pi\)
−0.995161 + 0.0982549i \(0.968674\pi\)
\(270\) −2.40232e84 1.84320e85i −0.191823 1.47178i
\(271\) −1.24350e85 −0.872407 −0.436203 0.899848i \(-0.643677\pi\)
−0.436203 + 0.899848i \(0.643677\pi\)
\(272\) 5.02545e84i 0.309930i
\(273\) −6.87601e83 1.59064e85i −0.0372944 0.862737i
\(274\) 2.68076e85 1.27935
\(275\) 3.99576e84i 0.167863i
\(276\) −5.29148e85 + 2.28741e84i −1.95776 + 0.0846302i
\(277\) −5.47997e84 −0.178643 −0.0893215 0.996003i \(-0.528470\pi\)
−0.0893215 + 0.996003i \(0.528470\pi\)
\(278\) 8.82811e85i 2.53688i
\(279\) −4.57092e85 + 3.95924e84i −1.15839 + 0.100338i
\(280\) 2.66200e85 0.595219
\(281\) 8.73444e84i 0.172391i −0.996278 0.0861954i \(-0.972529\pi\)
0.996278 0.0861954i \(-0.0274709\pi\)
\(282\) 6.07885e84 + 1.40623e86i 0.105950 + 2.45096i
\(283\) −8.28406e85 −1.27561 −0.637805 0.770198i \(-0.720157\pi\)
−0.637805 + 0.770198i \(0.720157\pi\)
\(284\) 1.23261e86i 1.67758i
\(285\) −7.90827e85 + 3.41859e84i −0.951724 + 0.0411412i
\(286\) 2.12105e86 2.25808
\(287\) 6.56635e85i 0.618668i
\(288\) −8.01755e84 9.25622e85i −0.0668813 0.772141i
\(289\) −5.79072e85 −0.427866
\(290\) 2.59737e85i 0.170061i
\(291\) 1.16332e85 + 2.69112e86i 0.0675219 + 1.56199i
\(292\) 5.81063e86 2.99105
\(293\) 3.51835e85i 0.160684i 0.996767 + 0.0803419i \(0.0256012\pi\)
−0.996767 + 0.0803419i \(0.974399\pi\)
\(294\) −2.83767e86 + 1.22667e85i −1.15028 + 0.0497245i
\(295\) −1.98585e86 −0.714787
\(296\) 2.68538e86i 0.858610i
\(297\) 3.04100e86 3.96346e85i 0.864054 0.112616i
\(298\) −3.55948e86 −0.899119
\(299\) 7.91672e86i 1.77850i
\(300\) −7.19526e84 1.66449e86i −0.0143814 0.332688i
\(301\) 2.08980e86 0.371772
\(302\) 7.67588e86i 1.21586i
\(303\) −9.34483e86 + 4.03959e85i −1.31850 + 0.0569961i
\(304\) 2.18715e86 0.274982
\(305\) 6.48326e86i 0.726606i
\(306\) −1.96760e87 + 1.70430e86i −1.96647 + 0.170332i
\(307\) 1.56704e87 1.39713 0.698566 0.715546i \(-0.253822\pi\)
0.698566 + 0.715546i \(0.253822\pi\)
\(308\) 1.04200e87i 0.829074i
\(309\) −3.47857e85 8.04701e86i −0.0247089 0.571594i
\(310\) 2.72043e87 1.72575
\(311\) 2.62923e86i 0.149010i 0.997221 + 0.0745050i \(0.0237377\pi\)
−0.997221 + 0.0745050i \(0.976262\pi\)
\(312\) −3.72404e87 + 1.60983e86i −1.88627 + 0.0815398i
\(313\) 1.17384e87 0.531564 0.265782 0.964033i \(-0.414370\pi\)
0.265782 + 0.964033i \(0.414370\pi\)
\(314\) 4.21819e87i 1.70840i
\(315\) 1.17787e86 + 1.35984e87i 0.0426802 + 0.492741i
\(316\) 2.58134e87 0.837137
\(317\) 8.39797e86i 0.243837i −0.992540 0.121919i \(-0.961095\pi\)
0.992540 0.121919i \(-0.0389047\pi\)
\(318\) −2.69004e86 6.22290e87i −0.0699535 1.61824i
\(319\) −4.28525e86 −0.0998395
\(320\) 6.62504e87i 1.38337i
\(321\) 5.80776e87 2.51058e86i 1.08726 0.0470001i
\(322\) 6.13919e87 1.03076
\(323\) 8.41039e87i 1.26686i
\(324\) −1.25963e88 + 2.19863e87i −1.70282 + 0.297219i
\(325\) 2.49028e87 0.302225
\(326\) 1.31417e87i 0.143231i
\(327\) −3.17755e86 7.35066e87i −0.0311115 0.719705i
\(328\) −1.53733e88 −1.35264
\(329\) 1.03357e88i 0.817493i
\(330\) −1.81669e88 + 7.85319e86i −1.29209 + 0.0558545i
\(331\) −1.45913e88 −0.933503 −0.466751 0.884389i \(-0.654576\pi\)
−0.466751 + 0.884389i \(0.654576\pi\)
\(332\) 1.58371e87i 0.0911682i
\(333\) 1.37179e88 1.18821e87i 0.710785 0.0615667i
\(334\) 2.14322e88 0.999863
\(335\) 3.09565e88i 1.30072i
\(336\) −1.62879e86 3.76789e87i −0.00616580 0.142634i
\(337\) 4.65867e88 1.58934 0.794668 0.607045i \(-0.207645\pi\)
0.794668 + 0.607045i \(0.207645\pi\)
\(338\) 7.84810e88i 2.41368i
\(339\) −5.16847e88 + 2.23423e87i −1.43342 + 0.0619639i
\(340\) 7.41863e88 1.85593
\(341\) 4.48829e88i 1.01316i
\(342\) 7.41737e87 + 8.56331e88i 0.151125 + 1.74473i
\(343\) 5.07796e88 0.934104
\(344\) 4.89270e88i 0.812836i
\(345\) 2.93117e87 + 6.78070e88i 0.0439918 + 1.01767i
\(346\) −5.03424e88 −0.682764
\(347\) 1.55148e88i 0.190202i −0.995468 0.0951011i \(-0.969683\pi\)
0.995468 0.0951011i \(-0.0303174\pi\)
\(348\) 1.78508e88 7.71656e86i 0.197872 0.00855362i
\(349\) −1.82726e89 −1.83194 −0.915968 0.401252i \(-0.868575\pi\)
−0.915968 + 0.401252i \(0.868575\pi\)
\(350\) 1.93114e88i 0.175159i
\(351\) −2.47015e88 1.89525e89i −0.202756 1.55567i
\(352\) −9.08890e88 −0.675333
\(353\) 9.00675e88i 0.605973i −0.952995 0.302987i \(-0.902016\pi\)
0.952995 0.302987i \(-0.0979837\pi\)
\(354\) 9.31291e87 + 2.15437e89i 0.0567507 + 1.31282i
\(355\) −1.57951e89 −0.872028
\(356\) 5.13089e89i 2.56710i
\(357\) 1.44889e89 6.26327e87i 0.657124 0.0284062i
\(358\) −1.22442e89 −0.503527
\(359\) 1.92502e89i 0.718009i 0.933336 + 0.359004i \(0.116884\pi\)
−0.933336 + 0.359004i \(0.883116\pi\)
\(360\) 3.18370e89 2.75765e88i 1.07732 0.0933152i
\(361\) 4.03824e88 0.124005
\(362\) 7.21504e88i 0.201112i
\(363\) 4.10791e87 + 9.50288e88i 0.0103965 + 0.240505i
\(364\) 6.49408e89 1.49269
\(365\) 7.44596e89i 1.55478i
\(366\) 7.03341e89 3.04041e88i 1.33453 0.0576891i
\(367\) −8.49328e87 −0.0146475 −0.00732375 0.999973i \(-0.502331\pi\)
−0.00732375 + 0.999973i \(0.502331\pi\)
\(368\) 1.87531e89i 0.294035i
\(369\) −6.80231e88 7.85323e89i −0.0969915 1.11976i
\(370\) −8.16434e89 −1.05891
\(371\) 4.57381e89i 0.539748i
\(372\) −8.08217e88 1.86966e90i −0.0868011 2.00798i
\(373\) −6.27000e89 −0.612997 −0.306498 0.951871i \(-0.599157\pi\)
−0.306498 + 0.951871i \(0.599157\pi\)
\(374\) 1.93204e90i 1.71992i
\(375\) −1.32048e90 + 5.70819e88i −1.07063 + 0.0462811i
\(376\) −2.41983e90 −1.78735
\(377\) 2.67070e89i 0.179754i
\(378\) 1.46971e90 1.91553e89i 0.901610 0.117510i
\(379\) 7.01306e89 0.392225 0.196113 0.980581i \(-0.437168\pi\)
0.196113 + 0.980581i \(0.437168\pi\)
\(380\) 3.22870e90i 1.64665i
\(381\) 1.50027e88 + 3.47060e89i 0.00697905 + 0.161447i
\(382\) 9.46023e88 0.0401499
\(383\) 3.88315e90i 1.50393i −0.659205 0.751963i \(-0.729107\pi\)
0.659205 0.751963i \(-0.270893\pi\)
\(384\) 4.99691e90 2.16007e89i 1.76648 0.0763615i
\(385\) 1.33526e90 0.430963
\(386\) 9.27485e90i 2.73370i
\(387\) 2.49936e90 2.16489e89i 0.672891 0.0582844i
\(388\) −1.09870e91 −2.70252
\(389\) 4.45418e90i 1.00122i −0.865672 0.500612i \(-0.833108\pi\)
0.865672 0.500612i \(-0.166892\pi\)
\(390\) 4.89436e89 + 1.13222e91i 0.100562 + 2.32632i
\(391\) 7.21124e90 1.35464
\(392\) 4.88304e90i 0.838838i
\(393\) 9.27737e90 4.01043e89i 1.45776 0.0630161i
\(394\) −5.07039e90 −0.728909
\(395\) 3.30782e90i 0.435154i
\(396\) 1.07944e90 + 1.24621e91i 0.129978 + 1.50059i
\(397\) −1.05757e91 −1.16584 −0.582921 0.812529i \(-0.698090\pi\)
−0.582921 + 0.812529i \(0.698090\pi\)
\(398\) 2.23273e91i 2.25386i
\(399\) −2.72587e89 6.30579e90i −0.0252031 0.583026i
\(400\) 5.89897e89 0.0499662
\(401\) 8.84401e90i 0.686430i −0.939257 0.343215i \(-0.888484\pi\)
0.939257 0.343215i \(-0.111516\pi\)
\(402\) −3.35834e91 + 1.45174e90i −2.38898 + 0.103271i
\(403\) 2.79725e91 1.82412
\(404\) 3.81521e91i 2.28124i
\(405\) 2.81741e90 + 1.61414e91i 0.154498 + 0.885147i
\(406\) −2.07105e90 −0.104179
\(407\) 1.34699e91i 0.621669i
\(408\) −1.46637e90 3.39218e91i −0.0621068 1.43672i
\(409\) −2.98698e91 −1.16123 −0.580613 0.814180i \(-0.697187\pi\)
−0.580613 + 0.814180i \(0.697187\pi\)
\(410\) 4.67394e91i 1.66820i
\(411\) −2.36091e91 + 1.02057e90i −0.773776 + 0.0334488i
\(412\) 3.28535e91 0.988960
\(413\) 1.58345e91i 0.437878i
\(414\) 7.34236e91 6.35980e90i 1.86562 0.161596i
\(415\) −2.02943e90 −0.0473904
\(416\) 5.66449e91i 1.21589i
\(417\) −3.36089e90 7.77480e91i −0.0663274 1.53436i
\(418\) 8.40852e91 1.52598
\(419\) 6.14188e91i 1.02520i −0.858626 0.512602i \(-0.828682\pi\)
0.858626 0.512602i \(-0.171318\pi\)
\(420\) −5.56220e91 + 2.40443e90i −0.854126 + 0.0369222i
\(421\) −5.49596e91 −0.776552 −0.388276 0.921543i \(-0.626929\pi\)
−0.388276 + 0.921543i \(0.626929\pi\)
\(422\) 3.78461e91i 0.492137i
\(423\) −1.07071e91 1.23613e92i −0.128162 1.47963i
\(424\) 1.07083e92 1.18010
\(425\) 2.26836e91i 0.230197i
\(426\) 7.40732e90 + 1.71355e92i 0.0692349 + 1.60162i
\(427\) −5.16953e91 −0.445118
\(428\) 2.37113e92i 1.88115i
\(429\) −1.86798e92 + 8.07492e90i −1.36574 + 0.0590382i
\(430\) −1.48752e92 −1.00246
\(431\) 1.61558e92i 1.00375i 0.864940 + 0.501875i \(0.167356\pi\)
−0.864940 + 0.501875i \(0.832644\pi\)
\(432\) −5.85128e90 4.48945e91i −0.0335212 0.257195i
\(433\) 3.16030e91 0.166975 0.0834876 0.996509i \(-0.473394\pi\)
0.0834876 + 0.996509i \(0.473394\pi\)
\(434\) 2.16918e92i 1.05720i
\(435\) −9.88828e89 2.28747e91i −0.00444628 0.102856i
\(436\) 3.00105e92 1.24522
\(437\) 3.13844e92i 1.20189i
\(438\) −8.07781e92 + 3.49188e91i −2.85561 + 0.123443i
\(439\) −1.03963e91 −0.0339329 −0.0169664 0.999856i \(-0.505401\pi\)
−0.0169664 + 0.999856i \(0.505401\pi\)
\(440\) 3.12615e92i 0.942249i
\(441\) 2.49443e92 2.16062e91i 0.694417 0.0601490i
\(442\) 1.20411e93 3.09660
\(443\) 2.96785e91i 0.0705200i 0.999378 + 0.0352600i \(0.0112259\pi\)
−0.999378 + 0.0352600i \(0.988774\pi\)
\(444\) 2.42555e91 + 5.61106e92i 0.0532607 + 1.23209i
\(445\) 6.57491e92 1.33441
\(446\) 7.61108e92i 1.42799i
\(447\) 3.13479e92 1.35511e91i 0.543807 0.0235077i
\(448\) −5.28259e92 −0.847454
\(449\) 1.07715e93i 1.59829i −0.601140 0.799144i \(-0.705287\pi\)
0.601140 0.799144i \(-0.294713\pi\)
\(450\) 2.00054e91 + 2.30961e92i 0.0274605 + 0.317030i
\(451\) −7.71127e92 −0.979370
\(452\) 2.11013e93i 2.48007i
\(453\) 2.92224e91 + 6.76005e92i 0.0317891 + 0.735381i
\(454\) −1.70879e93 −1.72081
\(455\) 8.32176e92i 0.775918i
\(456\) −1.47633e93 + 6.38188e91i −1.27472 + 0.0551035i
\(457\) 6.34409e92 0.507344 0.253672 0.967290i \(-0.418362\pi\)
0.253672 + 0.967290i \(0.418362\pi\)
\(458\) 8.64266e92i 0.640259i
\(459\) 1.72635e93 2.25003e92i 1.18491 0.154434i
\(460\) −2.76835e93 −1.76075
\(461\) 8.34085e92i 0.491675i 0.969311 + 0.245837i \(0.0790629\pi\)
−0.969311 + 0.245837i \(0.920937\pi\)
\(462\) −6.26187e91 1.44857e93i −0.0342164 0.791533i
\(463\) 1.16626e93 0.590829 0.295415 0.955369i \(-0.404542\pi\)
0.295415 + 0.955369i \(0.404542\pi\)
\(464\) 6.32635e91i 0.0297183i
\(465\) −2.39585e93 + 1.03568e92i −1.04377 + 0.0451203i
\(466\) 3.27206e93 1.32225
\(467\) 4.59677e93i 1.72331i 0.507499 + 0.861653i \(0.330570\pi\)
−0.507499 + 0.861653i \(0.669430\pi\)
\(468\) 7.76679e93 6.72744e92i 2.70170 0.234016i
\(469\) 2.46837e93 0.796820
\(470\) 7.35698e93i 2.20432i
\(471\) −1.60588e92 3.71491e93i −0.0446665 1.03328i
\(472\) −3.70722e93 −0.957368
\(473\) 2.45418e93i 0.588527i
\(474\) −3.58851e93 + 1.55124e92i −0.799232 + 0.0345492i
\(475\) 9.87227e92 0.204240
\(476\) 5.91537e93i 1.13694i
\(477\) 4.73817e92 + 5.47019e93i 0.0846188 + 0.976920i
\(478\) 3.83293e92 0.0636143
\(479\) 1.82658e93i 0.281771i −0.990026 0.140885i \(-0.955005\pi\)
0.990026 0.140885i \(-0.0449949\pi\)
\(480\) −2.09728e92 4.85166e93i −0.0300755 0.695740i
\(481\) −8.39486e93 −1.11927
\(482\) 9.23948e93i 1.14552i
\(483\) −5.40671e93 + 2.33721e92i −0.623424 + 0.0269494i
\(484\) −3.87973e93 −0.416116
\(485\) 1.40792e94i 1.40481i
\(486\) 1.73790e94 3.81346e93i 1.61345 0.354038i
\(487\) −2.05417e94 −1.77469 −0.887346 0.461105i \(-0.847453\pi\)
−0.887346 + 0.461105i \(0.847453\pi\)
\(488\) 1.21031e94i 0.973198i
\(489\) −5.00310e91 1.15737e93i −0.00374481 0.0866291i
\(490\) −1.48459e94 −1.03453
\(491\) 3.14396e93i 0.203997i 0.994785 + 0.101999i \(0.0325238\pi\)
−0.994785 + 0.101999i \(0.967476\pi\)
\(492\) 3.21223e94 1.38859e93i 1.94101 0.0839063i
\(493\) −2.43271e93 −0.136914
\(494\) 5.24045e94i 2.74742i
\(495\) 1.59694e94 1.38324e93i 0.780023 0.0675640i
\(496\) 6.62610e93 0.301578
\(497\) 1.25945e94i 0.534204i
\(498\) 9.51726e91 + 2.20164e93i 0.00376257 + 0.0870401i
\(499\) 4.32031e94 1.59219 0.796097 0.605169i \(-0.206894\pi\)
0.796097 + 0.605169i \(0.206894\pi\)
\(500\) 5.39112e94i 1.85238i
\(501\) −1.88751e94 + 8.15932e92i −0.604739 + 0.0261417i
\(502\) 1.89796e93 0.0567097
\(503\) 4.87887e94i 1.35969i 0.733356 + 0.679845i \(0.237953\pi\)
−0.733356 + 0.679845i \(0.762047\pi\)
\(504\) 2.19886e93 + 2.53857e94i 0.0571648 + 0.659965i
\(505\) −4.88895e94 −1.18582
\(506\) 7.20963e94i 1.63172i
\(507\) 2.98780e93 + 6.91172e94i 0.0631064 + 1.45985i
\(508\) −1.41694e94 −0.279333
\(509\) 8.02521e94i 1.47684i 0.674340 + 0.738421i \(0.264428\pi\)
−0.674340 + 0.738421i \(0.735572\pi\)
\(510\) −1.03132e95 + 4.45820e93i −1.77189 + 0.0765956i
\(511\) 5.93716e94 0.952461
\(512\) 3.42535e94i 0.513164i
\(513\) −9.79247e93 7.51336e94i −0.137020 1.05130i
\(514\) 1.13423e95 1.48250
\(515\) 4.20997e94i 0.514074i
\(516\) 4.41930e93 + 1.02232e95i 0.0504212 + 1.16640i
\(517\) −1.21379e95 −1.29412
\(518\) 6.50997e94i 0.648690i
\(519\) 4.43359e94 1.91655e93i 0.412950 0.0178510i
\(520\) −1.94831e95 −1.69645
\(521\) 2.62710e94i 0.213873i −0.994266 0.106937i \(-0.965896\pi\)
0.994266 0.106937i \(-0.0341042\pi\)
\(522\) −2.47694e94 + 2.14548e93i −0.188559 + 0.0163326i
\(523\) 2.04777e95 1.45788 0.728941 0.684576i \(-0.240013\pi\)
0.728941 + 0.684576i \(0.240013\pi\)
\(524\) 3.78767e95i 2.52218i
\(525\) −7.35193e92 1.70073e94i −0.00457958 0.105940i
\(526\) 1.72149e95 1.00323
\(527\) 2.54797e95i 1.38939i
\(528\) −4.42486e94 + 1.91278e93i −0.225794 + 0.00976064i
\(529\) −5.97097e94 −0.285165
\(530\) 3.25565e95i 1.45540i
\(531\) −1.64035e94 1.89378e95i −0.0686482 0.792539i
\(532\) 2.57446e95 1.00874
\(533\) 4.80591e95i 1.76329i
\(534\) −3.08339e94 7.13284e95i −0.105946 2.45086i
\(535\) 3.03846e95 0.977847
\(536\) 5.77901e95i 1.74215i
\(537\) 1.07833e95 4.66140e93i 0.304544 0.0131649i
\(538\) 1.22668e95 0.324602
\(539\) 2.44934e95i 0.607354i
\(540\) −6.62738e95 + 8.63773e94i −1.54014 + 0.200733i
\(541\) −4.06029e95 −0.884408 −0.442204 0.896914i \(-0.645803\pi\)
−0.442204 + 0.896914i \(0.645803\pi\)
\(542\) 7.05767e95i 1.44107i
\(543\) −2.74679e93 6.35419e94i −0.00525814 0.121637i
\(544\) −5.15971e95 −0.926112
\(545\) 3.84565e95i 0.647281i
\(546\) −9.02792e95 + 3.90260e94i −1.42510 + 0.0616043i
\(547\) 7.77500e95 1.15118 0.575591 0.817738i \(-0.304772\pi\)
0.575591 + 0.817738i \(0.304772\pi\)
\(548\) 9.63887e95i 1.33877i
\(549\) −6.18266e95 + 5.35529e94i −0.805644 + 0.0697833i
\(550\) 2.26786e95 0.277282
\(551\) 1.05875e95i 0.121475i
\(552\) 5.47195e94 + 1.26583e96i 0.0589216 + 1.36304i
\(553\) 2.63754e95 0.266576
\(554\) 3.11025e95i 0.295089i
\(555\) 7.19023e95 3.10819e94i 0.640454 0.0276856i
\(556\) 3.17421e96 2.65472
\(557\) 1.00134e96i 0.786411i −0.919451 0.393206i \(-0.871366\pi\)
0.919451 0.393206i \(-0.128634\pi\)
\(558\) 2.24713e95 + 2.59430e96i 0.165742 + 1.91348i
\(559\) −1.52952e96 −1.05960
\(560\) 1.97125e95i 0.128281i
\(561\) −7.35534e94 1.70152e96i −0.0449679 1.04025i
\(562\) −4.95738e95 −0.284761
\(563\) 3.73226e95i 0.201455i 0.994914 + 0.100728i \(0.0321171\pi\)
−0.994914 + 0.100728i \(0.967883\pi\)
\(564\) 5.05620e96 2.18569e95i 2.56481 0.110872i
\(565\) −2.70400e96 −1.28917
\(566\) 4.70176e96i 2.10710i
\(567\) −1.28706e96 + 2.24651e95i −0.542241 + 0.0946457i
\(568\) −2.94866e96 −1.16797
\(569\) 9.68853e95i 0.360851i 0.983589 + 0.180426i \(0.0577476\pi\)
−0.983589 + 0.180426i \(0.942252\pi\)
\(570\) 1.94028e95 + 4.48847e96i 0.0679585 + 1.57209i
\(571\) 8.32759e95 0.274319 0.137159 0.990549i \(-0.456203\pi\)
0.137159 + 0.990549i \(0.456203\pi\)
\(572\) 7.62640e96i 2.36297i
\(573\) −8.33150e94 + 3.60155e93i −0.0242835 + 0.00104973i
\(574\) −3.72684e96 −1.02194
\(575\) 8.46468e95i 0.218392i
\(576\) −6.31787e96 + 5.47241e95i −1.53385 + 0.132859i
\(577\) −4.79842e96 −1.09634 −0.548169 0.836367i \(-0.684675\pi\)
−0.548169 + 0.836367i \(0.684675\pi\)
\(578\) 3.28662e96i 0.706765i
\(579\) −3.53097e95 8.16824e96i −0.0714734 1.65340i
\(580\) 9.33903e95 0.177960
\(581\) 1.61820e95i 0.0290313i
\(582\) 1.52739e97 6.60261e95i 2.58015 0.111535i
\(583\) 5.37131e96 0.854438
\(584\) 1.39002e97i 2.08244i
\(585\) −8.62079e95 9.95266e96i −0.121644 1.40438i
\(586\) 1.99690e96 0.265423
\(587\) 3.76796e96i 0.471816i 0.971775 + 0.235908i \(0.0758064\pi\)
−0.971775 + 0.235908i \(0.924194\pi\)
\(588\) 4.41058e95 + 1.02030e97i 0.0520342 + 1.20371i
\(589\) 1.10892e97 1.23272
\(590\) 1.12710e97i 1.18071i
\(591\) 4.46542e96 1.93032e95i 0.440860 0.0190575i
\(592\) −1.98857e96 −0.185046
\(593\) 1.96744e97i 1.72579i 0.505386 + 0.862894i \(0.331350\pi\)
−0.505386 + 0.862894i \(0.668650\pi\)
\(594\) −2.24953e96 1.72597e97i −0.186023 1.42728i
\(595\) 7.58017e96 0.590997
\(596\) 1.27984e97i 0.940882i
\(597\) −8.50007e95 1.96633e97i −0.0589279 1.36319i
\(598\) −4.49327e97 −2.93779
\(599\) 2.03648e97i 1.25586i −0.778269 0.627931i \(-0.783902\pi\)
0.778269 0.627931i \(-0.216098\pi\)
\(600\) −3.98180e96 + 1.72126e95i −0.231625 + 0.0100127i
\(601\) −8.18342e96 −0.449085 −0.224542 0.974464i \(-0.572089\pi\)
−0.224542 + 0.974464i \(0.572089\pi\)
\(602\) 1.18610e97i 0.614107i
\(603\) 2.95212e97 2.55706e96i 1.44221 0.124921i
\(604\) −2.75992e97 −1.27234
\(605\) 4.97163e96i 0.216302i
\(606\) 2.29274e96 + 5.30382e97i 0.0941482 + 2.17794i
\(607\) −3.58526e97 −1.38969 −0.694843 0.719162i \(-0.744526\pi\)
−0.694843 + 0.719162i \(0.744526\pi\)
\(608\) 2.24558e97i 0.821682i
\(609\) 1.82395e96 7.88459e94i 0.0630098 0.00272379i
\(610\) 3.67968e97 1.20023
\(611\) 7.56470e97i 2.32997i
\(612\) 6.12793e96 + 7.07467e97i 0.178244 + 2.05781i
\(613\) 3.98148e97 1.09377 0.546887 0.837207i \(-0.315813\pi\)
0.546887 + 0.837207i \(0.315813\pi\)
\(614\) 8.89401e97i 2.30783i
\(615\) −1.77939e96 4.11628e97i −0.0436155 1.00896i
\(616\) 2.49268e97 0.577221
\(617\) 8.90028e96i 0.194725i −0.995249 0.0973627i \(-0.968959\pi\)
0.995249 0.0973627i \(-0.0310407\pi\)
\(618\) −4.56722e97 + 1.97432e96i −0.944180 + 0.0408151i
\(619\) 9.61328e97 1.87801 0.939007 0.343897i \(-0.111747\pi\)
0.939007 + 0.343897i \(0.111747\pi\)
\(620\) 9.78152e97i 1.80592i
\(621\) −6.44210e97 + 8.39626e96i −1.12414 + 0.146514i
\(622\) 1.49226e97 0.246140
\(623\) 5.24261e97i 0.817459i
\(624\) 1.19211e96 + 2.75771e97i 0.0175733 + 0.406526i
\(625\) −5.52623e97 −0.770244
\(626\) 6.66230e97i 0.878057i
\(627\) −7.40527e97 + 3.20116e96i −0.922948 + 0.0398972i
\(628\) 1.51668e98 1.78775
\(629\) 7.64676e97i 0.852521i
\(630\) 7.71800e97 6.68518e96i 0.813927 0.0705007i
\(631\) −5.73538e97 −0.572182 −0.286091 0.958202i \(-0.592356\pi\)
−0.286091 + 0.958202i \(0.592356\pi\)
\(632\) 6.17510e97i 0.582835i
\(633\) 1.44082e96 + 3.33306e97i 0.0128670 + 0.297655i
\(634\) −4.76641e97 −0.402779
\(635\) 1.81572e97i 0.145201i
\(636\) −2.23749e98 + 9.67224e96i −1.69341 + 0.0732029i
\(637\) −1.52650e98 −1.09350
\(638\) 2.43217e97i 0.164919i
\(639\) −1.30471e97 1.50628e98i −0.0837496 0.966885i
\(640\) 2.61424e98 1.58872
\(641\) 2.69039e98i 1.54805i 0.633155 + 0.774025i \(0.281760\pi\)
−0.633155 + 0.774025i \(0.718240\pi\)
\(642\) −1.42492e97 3.29629e98i −0.0776364 1.79597i
\(643\) −2.68340e98 −1.38453 −0.692264 0.721644i \(-0.743387\pi\)
−0.692264 + 0.721644i \(0.743387\pi\)
\(644\) 2.20739e98i 1.07863i
\(645\) 1.31004e98 5.66305e96i 0.606310 0.0262096i
\(646\) 4.77346e98 2.09264
\(647\) 4.16208e98i 1.72847i 0.503092 + 0.864233i \(0.332196\pi\)
−0.503092 + 0.864233i \(0.667804\pi\)
\(648\) 5.25959e97 + 3.01331e98i 0.206932 + 1.18554i
\(649\) −1.85955e98 −0.693174
\(650\) 1.41340e98i 0.499227i
\(651\) −8.25817e96 1.91037e98i −0.0276407 0.639416i
\(652\) 4.72520e97 0.149884
\(653\) 5.73970e98i 1.72555i 0.505588 + 0.862775i \(0.331276\pi\)
−0.505588 + 0.862775i \(0.668724\pi\)
\(654\) −4.17199e98 + 1.80347e97i −1.18884 + 0.0513911i
\(655\) 4.85366e98 1.31106
\(656\) 1.13842e98i 0.291520i
\(657\) 7.10072e98 6.15050e97i 1.72391 0.149322i
\(658\) −5.86621e98 −1.35037
\(659\) 1.44836e98i 0.316145i −0.987428 0.158072i \(-0.949472\pi\)
0.987428 0.158072i \(-0.0505279\pi\)
\(660\) 2.82367e97 + 6.53204e98i 0.0584489 + 1.35211i
\(661\) 6.45779e98 1.26775 0.633874 0.773436i \(-0.281464\pi\)
0.633874 + 0.773436i \(0.281464\pi\)
\(662\) 8.28156e98i 1.54199i
\(663\) −1.06044e99 + 4.58408e97i −1.87289 + 0.0809615i
\(664\) −3.78857e97 −0.0634735
\(665\) 3.29901e98i 0.524355i
\(666\) −6.74390e97 7.78580e98i −0.101698 1.17410i
\(667\) 9.07795e97 0.129892
\(668\) 7.70611e98i 1.04631i
\(669\) −2.89757e97 6.70298e98i −0.0373353 0.863682i
\(670\) −1.75699e99 −2.14857
\(671\) 6.07090e98i 0.704636i
\(672\) 3.86855e98 1.67230e97i 0.426210 0.0184242i
\(673\) 1.84898e99 1.93377 0.966885 0.255211i \(-0.0821451\pi\)
0.966885 + 0.255211i \(0.0821451\pi\)
\(674\) 2.64411e99i 2.62532i
\(675\) −2.64112e97 2.02643e98i −0.0248976 0.191029i
\(676\) −2.82184e99 −2.52580
\(677\) 1.38220e99i 1.17481i 0.809293 + 0.587406i \(0.199851\pi\)
−0.809293 + 0.587406i \(0.800149\pi\)
\(678\) 1.26807e98 + 2.93345e99i 0.102354 + 2.36777i
\(679\) −1.12263e99 −0.860584
\(680\) 1.77469e99i 1.29214i
\(681\) 1.50491e99 6.50542e97i 1.04078 0.0449911i
\(682\) 2.54741e99 1.67357
\(683\) 3.87946e98i 0.242129i 0.992645 + 0.121064i \(0.0386307\pi\)
−0.992645 + 0.121064i \(0.961369\pi\)
\(684\) 3.07900e99 2.66697e98i 1.82577 0.158145i
\(685\) −1.23516e99 −0.695910
\(686\) 2.88208e99i 1.54299i
\(687\) 3.29029e97 + 7.61148e98i 0.0167398 + 0.387243i
\(688\) −3.62312e98 −0.175181
\(689\) 3.34757e99i 1.53836i
\(690\) 3.84850e99 1.66363e98i 1.68102 0.0726673i
\(691\) 3.02076e98 0.125425 0.0627126 0.998032i \(-0.480025\pi\)
0.0627126 + 0.998032i \(0.480025\pi\)
\(692\) 1.81010e99i 0.714478i
\(693\) 1.10295e98 + 1.27335e99i 0.0413897 + 0.477842i
\(694\) −8.80570e98 −0.314183
\(695\) 4.06755e99i 1.37996i
\(696\) −1.84596e97 4.27029e98i −0.00595524 0.137763i
\(697\) −4.37764e99 −1.34305
\(698\) 1.03709e100i 3.02606i
\(699\) −2.88166e99 + 1.24569e98i −0.799726 + 0.0345706i
\(700\) 6.94357e98 0.183295
\(701\) 5.56802e99i 1.39820i 0.715022 + 0.699102i \(0.246417\pi\)
−0.715022 + 0.699102i \(0.753583\pi\)
\(702\) −1.07568e100 + 1.40198e99i −2.56971 + 0.334920i
\(703\) −3.32799e99 −0.756389
\(704\) 6.20367e99i 1.34155i
\(705\) −2.80083e98 6.47920e99i −0.0576325 1.33322i
\(706\) −5.11193e99 −1.00097
\(707\) 3.89828e99i 0.726430i
\(708\) 7.74619e99 3.34853e98i 1.37380 0.0593868i
\(709\) 8.83625e99 1.49159 0.745795 0.666175i \(-0.232070\pi\)
0.745795 + 0.666175i \(0.232070\pi\)
\(710\) 8.96478e99i 1.44045i
\(711\) 3.15445e99 2.73232e98i 0.482490 0.0417923i
\(712\) 1.22742e100 1.78728
\(713\) 9.50807e99i 1.31813i
\(714\) −3.55482e98 8.22341e99i −0.0469224 1.08546i
\(715\) −9.77275e99 −1.22830
\(716\) 4.40248e99i 0.526916i
\(717\) −3.37561e98 + 1.45921e97i −0.0384753 + 0.00166321i
\(718\) 1.09258e100 1.18603
\(719\) 3.32168e99i 0.343436i 0.985146 + 0.171718i \(0.0549319\pi\)
−0.985146 + 0.171718i \(0.945068\pi\)
\(720\) −2.04209e98 2.35758e99i −0.0201112 0.232182i
\(721\) 3.35689e99 0.314922
\(722\) 2.29197e99i 0.204837i
\(723\) 3.51750e98 + 8.13709e99i 0.0299498 + 0.692833i
\(724\) 2.59422e99 0.210454
\(725\) 2.85556e98i 0.0220730i
\(726\) 5.39352e99 2.33151e98i 0.397274 0.0171734i
\(727\) 1.73653e100 1.21893 0.609464 0.792814i \(-0.291385\pi\)
0.609464 + 0.792814i \(0.291385\pi\)
\(728\) 1.55352e100i 1.03925i
\(729\) −1.51603e100 + 4.02009e99i −0.966594 + 0.256314i
\(730\) −4.22608e100 −2.56825
\(731\) 1.39322e100i 0.807071i
\(732\) −1.09320e99 2.52892e100i −0.0603687 1.39652i
\(733\) −2.82348e100 −1.48643 −0.743217 0.669051i \(-0.766701\pi\)
−0.743217 + 0.669051i \(0.766701\pi\)
\(734\) 4.82051e98i 0.0241953i
\(735\) 1.30746e100 5.65188e98i 0.625706 0.0270481i
\(736\) 1.92541e100 0.878616
\(737\) 2.89875e100i 1.26139i
\(738\) −4.45723e100 + 3.86076e99i −1.84966 + 0.160214i
\(739\) 2.00648e100 0.794109 0.397054 0.917795i \(-0.370032\pi\)
0.397054 + 0.917795i \(0.370032\pi\)
\(740\) 2.93555e100i 1.10810i
\(741\) 1.99506e99 + 4.61520e100i 0.0718322 + 1.66170i
\(742\) 2.59594e100 0.891576
\(743\) 6.05584e100i 1.98411i −0.125803 0.992055i \(-0.540151\pi\)
0.125803 0.992055i \(-0.459849\pi\)
\(744\) −4.47262e100 + 1.93343e99i −1.39801 + 0.0604331i
\(745\) 1.64003e100 0.489083
\(746\) 3.55864e100i 1.01257i
\(747\) −1.67635e98 1.93533e99i −0.00455138 0.0525454i
\(748\) 6.94678e100 1.79981
\(749\) 2.42276e100i 0.599028i
\(750\) 3.23978e99 + 7.49461e100i 0.0764488 + 1.76850i
\(751\) 5.41700e100 1.22000 0.610001 0.792401i \(-0.291169\pi\)
0.610001 + 0.792401i \(0.291169\pi\)
\(752\) 1.79192e100i 0.385207i
\(753\) −1.67151e99 + 7.22562e97i −0.0342993 + 0.00148269i
\(754\) 1.51580e100 0.296924
\(755\) 3.53666e100i 0.661379i
\(756\) −6.88744e99 5.28445e100i −0.122969 0.943489i
\(757\) −3.52653e100 −0.601162 −0.300581 0.953756i \(-0.597181\pi\)
−0.300581 + 0.953756i \(0.597181\pi\)
\(758\) 3.98038e100i 0.647892i
\(759\) 2.74473e99 + 6.34943e100i 0.0426617 + 0.986898i
\(760\) −7.72373e100 −1.14644
\(761\) 1.98121e100i 0.280845i −0.990092 0.140422i \(-0.955154\pi\)
0.990092 0.140422i \(-0.0448461\pi\)
\(762\) 1.96980e100 8.51506e98i 0.266685 0.0115283i
\(763\) 3.06640e100 0.396524
\(764\) 3.40150e99i 0.0420148i
\(765\) 9.06574e100 7.85256e99i 1.06968 0.0926533i
\(766\) −2.20394e101 −2.48424
\(767\) 1.15893e101i 1.24801i
\(768\) −5.79718e99 1.34107e101i −0.0596450 1.37978i
\(769\) −1.40777e101 −1.38391 −0.691957 0.721939i \(-0.743251\pi\)
−0.691957 + 0.721939i \(0.743251\pi\)
\(770\) 7.57849e100i 0.711880i
\(771\) −9.98905e100 + 4.31807e99i −0.896646 + 0.0387602i
\(772\) 3.33484e101 2.86068
\(773\) 8.99852e100i 0.737715i −0.929486 0.368858i \(-0.879749\pi\)
0.929486 0.368858i \(-0.120251\pi\)
\(774\) −1.22872e100 1.41855e101i −0.0962764 1.11151i
\(775\) 2.99086e100 0.223994
\(776\) 2.62833e101i 1.88156i
\(777\) 2.47837e99 + 5.73325e100i 0.0169602 + 0.392342i
\(778\) −2.52804e101 −1.65386
\(779\) 1.90521e101i 1.19161i
\(780\) 4.07097e101 1.75980e100i 2.43437 0.105233i
\(781\) −1.47905e101 −0.845661
\(782\) 4.09286e101i 2.23764i
\(783\) 2.17324e100 2.83247e99i 0.113618 0.0148083i
\(784\) −3.61597e100 −0.180785
\(785\) 1.94353e101i 0.929296i
\(786\) −2.27619e100 5.26553e101i −0.104092 2.40798i
\(787\) 1.19724e101 0.523679 0.261839 0.965111i \(-0.415671\pi\)
0.261839 + 0.965111i \(0.415671\pi\)
\(788\) 1.82310e101i 0.762767i
\(789\) −1.51609e101 + 6.55376e99i −0.606778 + 0.0262298i
\(790\) −1.87741e101 −0.718804
\(791\) 2.15608e101i 0.789746i
\(792\) 2.98120e101 2.58226e100i 1.04474 0.0904937i
\(793\) 3.78358e101 1.26865
\(794\) 6.00239e101i 1.92578i
\(795\) 1.23944e100 + 2.86720e101i 0.0380518 + 0.880256i
\(796\) 8.02793e101 2.35856
\(797\) 4.79264e101i 1.34751i 0.738953 + 0.673757i \(0.235321\pi\)
−0.738953 + 0.673757i \(0.764679\pi\)
\(798\) −3.57896e101 + 1.54711e100i −0.963064 + 0.0416314i
\(799\) −6.89059e101 −1.77468
\(800\) 6.05656e100i 0.149306i
\(801\) 5.43100e100 + 6.27006e101i 0.128157 + 1.47956i
\(802\) −5.01957e101 −1.13387
\(803\) 6.97237e101i 1.50777i
\(804\) 5.21985e100 + 1.20752e102i 0.108068 + 2.49995i
\(805\) −2.82863e101 −0.560688
\(806\) 1.58762e102i 3.01315i
\(807\) −1.08032e101 + 4.67001e99i −0.196326 + 0.00848681i
\(808\) −9.12678e101 −1.58825
\(809\) 6.49307e101i 1.08206i 0.841003 + 0.541031i \(0.181966\pi\)
−0.841003 + 0.541031i \(0.818034\pi\)
\(810\) 9.16133e101 1.59907e101i 1.46212 0.255206i
\(811\) 2.30173e101 0.351823 0.175912 0.984406i \(-0.443713\pi\)
0.175912 + 0.984406i \(0.443713\pi\)
\(812\) 7.44663e100i 0.109018i
\(813\) −2.68688e100 6.21560e101i −0.0376773 0.871593i
\(814\) −7.64506e101 −1.02690
\(815\) 6.05505e100i 0.0779115i
\(816\) −2.51196e101 + 1.08587e100i −0.309641 + 0.0133852i
\(817\) −6.06351e101 −0.716064
\(818\) 1.69531e102i 1.91815i
\(819\) 7.93592e101 6.87393e100i 0.860321 0.0745193i
\(820\) 1.68055e102 1.74569
\(821\) 7.15333e101i 0.712029i −0.934480 0.356015i \(-0.884135\pi\)
0.934480 0.356015i \(-0.115865\pi\)
\(822\) 5.79244e100 + 1.33997e102i 0.0552520 + 1.27815i
\(823\) 1.36477e102 1.24757 0.623784 0.781597i \(-0.285594\pi\)
0.623784 + 0.781597i \(0.285594\pi\)
\(824\) 7.85924e101i 0.688539i
\(825\) −1.99727e101 + 8.63383e99i −0.167706 + 0.00724962i
\(826\) −8.98715e101 −0.723303
\(827\) 1.81733e101i 0.140198i 0.997540 + 0.0700990i \(0.0223315\pi\)
−0.997540 + 0.0700990i \(0.977668\pi\)
\(828\) −2.28671e101 2.64000e102i −0.169102 1.95228i
\(829\) 2.01560e102 1.42888 0.714441 0.699696i \(-0.246681\pi\)
0.714441 + 0.699696i \(0.246681\pi\)
\(830\) 1.15184e101i 0.0782812i
\(831\) −1.18408e100 2.73915e101i −0.00771518 0.178476i
\(832\) 3.86632e102 2.41536
\(833\) 1.39047e102i 0.832889i
\(834\) −4.41272e102 + 1.90753e101i −2.53451 + 0.109562i
\(835\) −9.87489e101 −0.543883
\(836\) 3.02335e102i 1.59686i
\(837\) −2.96668e101 2.27621e102i −0.150273 1.15298i
\(838\) −3.48593e102 −1.69347
\(839\) 6.38125e101i 0.297329i 0.988888 + 0.148664i \(0.0474974\pi\)
−0.988888 + 0.148664i \(0.952503\pi\)
\(840\) 5.75191e100 + 1.33060e102i 0.0257061 + 0.594663i
\(841\) 2.30208e102 0.986872
\(842\) 3.11933e102i 1.28274i
\(843\) 4.36590e101 1.88729e100i 0.172230 0.00744516i
\(844\) −1.36079e102 −0.514996
\(845\) 3.61602e102i 1.31294i
\(846\) −7.01587e102 + 6.07701e101i −2.44410 + 0.211703i
\(847\) −3.96422e101 −0.132507
\(848\) 7.92970e101i 0.254332i
\(849\) −1.78998e101 4.14078e102i −0.0550907 1.27442i
\(850\) 1.28745e102 0.380248
\(851\) 2.85348e102i 0.808799i
\(852\) 6.16118e102 2.66336e101i 1.67602 0.0724509i
\(853\) −1.42229e102 −0.371341 −0.185671 0.982612i \(-0.559446\pi\)
−0.185671 + 0.982612i \(0.559446\pi\)
\(854\) 2.93405e102i 0.735263i
\(855\) −3.41755e101 3.94555e102i −0.0822056 0.949060i
\(856\) 5.67224e102 1.30970
\(857\) 5.12401e101i 0.113575i 0.998386 + 0.0567873i \(0.0180857\pi\)
−0.998386 + 0.0567873i \(0.981914\pi\)
\(858\) 4.58306e101 + 1.06020e103i 0.0975215 + 2.25598i
\(859\) −3.97003e102 −0.811023 −0.405512 0.914090i \(-0.632907\pi\)
−0.405512 + 0.914090i \(0.632907\pi\)
\(860\) 5.34849e102i 1.04902i
\(861\) 3.28218e102 1.41882e101i 0.618091 0.0267189i
\(862\) 9.16952e102 1.65803
\(863\) 3.08511e102i 0.535665i −0.963465 0.267833i \(-0.913693\pi\)
0.963465 0.267833i \(-0.0863074\pi\)
\(864\) 4.60939e102 6.00760e101i 0.768532 0.100166i
\(865\) 2.31953e102 0.371395
\(866\) 1.79368e102i 0.275816i
\(867\) −1.25123e101 2.89448e102i −0.0184786 0.427467i
\(868\) 7.79946e102 1.10630
\(869\) 3.09743e102i 0.421997i
\(870\) −1.29829e102 + 5.61226e100i −0.169902 + 0.00734453i
\(871\) −1.80659e103 −2.27104
\(872\) 7.17913e102i 0.866952i
\(873\) −1.34264e103 + 1.16297e102i −1.55762 + 0.134918i
\(874\) −1.78127e103 −1.98532
\(875\) 5.50851e102i 0.589865i
\(876\) 1.25553e102 + 2.90444e103i 0.129177 + 2.98826i
\(877\) 2.19361e102 0.216857 0.108429 0.994104i \(-0.465418\pi\)
0.108429 + 0.994104i \(0.465418\pi\)
\(878\) 5.90060e101i 0.0560516i
\(879\) −1.75864e102 + 7.60226e100i −0.160534 + 0.00693957i
\(880\) −2.31496e102 −0.203072
\(881\) 1.00108e103i 0.843941i 0.906610 + 0.421971i \(0.138661\pi\)
−0.906610 + 0.421971i \(0.861339\pi\)
\(882\) −1.22630e102 1.41575e103i −0.0993563 1.14706i
\(883\) 8.39073e102 0.653394 0.326697 0.945129i \(-0.394064\pi\)
0.326697 + 0.945129i \(0.394064\pi\)
\(884\) 4.32945e103i 3.24044i
\(885\) −4.29093e101 9.92626e102i −0.0308700 0.714120i
\(886\) 1.68446e102 0.116487
\(887\) 2.96647e101i 0.0197203i −0.999951 0.00986016i \(-0.996861\pi\)
0.999951 0.00986016i \(-0.00313864\pi\)
\(888\) 1.34228e103 5.80243e101i 0.857809 0.0370814i
\(889\) −1.44779e102 −0.0889499
\(890\) 3.73170e103i 2.20423i
\(891\) 2.63821e102 + 1.51148e103i 0.149827 + 0.858384i
\(892\) 2.73662e103 1.49432
\(893\) 2.99889e103i 1.57456i
\(894\) −7.69113e101 1.77920e103i −0.0388309 0.898280i
\(895\) 5.64150e102 0.273898
\(896\) 2.08451e103i 0.973248i
\(897\) 3.95716e103 1.71060e102i 1.77684 0.0768094i
\(898\) −6.11355e103 −2.64011
\(899\) 3.20755e102i 0.133224i
\(900\) 8.30437e102 7.19308e101i 0.331756 0.0287360i
\(901\) 3.04925e103 1.17173
\(902\) 4.37666e103i 1.61776i
\(903\) 4.51553e101 + 1.04458e103i 0.0160560 + 0.371425i
\(904\) −5.04787e103 −1.72668
\(905\) 3.32433e102i 0.109397i
\(906\) 3.83678e103 1.65856e102i 1.21473 0.0525104i
\(907\) −3.93503e101 −0.0119865 −0.00599326 0.999982i \(-0.501908\pi\)
−0.00599326 + 0.999982i \(0.501908\pi\)
\(908\) 6.14408e103i 1.80074i
\(909\) −4.03837e102 4.66227e103i −0.113886 1.31481i
\(910\) −4.72315e103 −1.28169
\(911\) 1.58636e103i 0.414245i −0.978315 0.207123i \(-0.933590\pi\)
0.978315 0.207123i \(-0.0664099\pi\)
\(912\) 4.72589e101 + 1.09325e103i 0.0118758 + 0.274725i
\(913\) −1.90035e102 −0.0459575
\(914\) 3.60070e103i 0.838050i
\(915\) −3.24065e103 + 1.40087e102i −0.725928 + 0.0313804i
\(916\) −3.10753e103 −0.669999
\(917\) 3.87014e103i 0.803157i
\(918\) −1.27704e103 9.79822e103i −0.255100 1.95728i
\(919\) 3.54574e103 0.681812 0.340906 0.940097i \(-0.389266\pi\)
0.340906 + 0.940097i \(0.389266\pi\)
\(920\) 6.62248e103i 1.22588i
\(921\) 3.38598e102 + 7.83284e103i 0.0603389 + 1.39583i
\(922\) 4.73399e103 0.812167
\(923\) 9.21790e103i 1.52255i
\(924\) −5.20843e103 + 2.25150e102i −0.828300 + 0.0358058i
\(925\) −8.97591e102 −0.137441
\(926\) 6.61933e103i 0.975954i
\(927\) 4.01477e103 3.47751e102i 0.569994 0.0493717i
\(928\) −6.49536e102 −0.0888022
\(929\) 9.90227e101i 0.0130372i 0.999979 + 0.00651861i \(0.00207495\pi\)
−0.999979 + 0.00651861i \(0.997925\pi\)
\(930\) 5.87817e102 + 1.35981e104i 0.0745314 + 1.72414i
\(931\) −6.05155e103 −0.738971
\(932\) 1.17649e104i 1.38367i
\(933\) −1.31422e103 + 5.68111e101i −0.148871 + 0.00643540i
\(934\) 2.60898e104 2.84662
\(935\) 8.90186e103i 0.935566i
\(936\) −1.60934e103 1.85798e104i −0.162927 1.88099i
\(937\) −7.91783e103 −0.772183 −0.386092 0.922460i \(-0.626175\pi\)
−0.386092 + 0.922460i \(0.626175\pi\)
\(938\) 1.40096e104i 1.31622i
\(939\) 2.53636e102 + 5.86740e103i 0.0229570 + 0.531068i
\(940\) 2.64526e104 2.30671
\(941\) 1.10499e104i 0.928370i −0.885738 0.464185i \(-0.846347\pi\)
0.885738 0.464185i \(-0.153653\pi\)
\(942\) −2.10846e104 + 9.11445e102i −1.70680 + 0.0737817i
\(943\) 1.63357e104 1.27417
\(944\) 2.74526e103i 0.206331i
\(945\) −6.77169e103 + 8.82582e102i −0.490438 + 0.0639207i
\(946\) −1.39291e104 −0.972150
\(947\) 4.56532e103i 0.307059i 0.988144 + 0.153530i \(0.0490640\pi\)
−0.988144 + 0.153530i \(0.950936\pi\)
\(948\) 5.57762e102 + 1.29028e104i 0.0361540 + 0.836356i
\(949\) −4.34540e104 −2.71464
\(950\) 5.60317e103i 0.337371i
\(951\) 4.19771e103 1.81459e102i 0.243610 0.0105308i
\(952\) 1.41508e104 0.791567
\(953\) 4.31607e103i 0.232722i 0.993207 + 0.116361i \(0.0371229\pi\)
−0.993207 + 0.116361i \(0.962877\pi\)
\(954\) 3.10470e104 2.68923e103i 1.61371 0.139777i
\(955\) −4.35880e102 −0.0218398
\(956\) 1.37816e103i 0.0665692i
\(957\) −9.25935e101 2.14198e103i −0.00431184 0.0997464i
\(958\) −1.03671e104 −0.465439
\(959\) 9.84876e103i 0.426314i
\(960\) −3.31152e104 + 1.43150e103i −1.38208 + 0.0597447i
\(961\) 8.74567e103 0.351945
\(962\) 4.76464e104i 1.84885i
\(963\) 2.50982e103 + 2.89758e104i 0.0939124 + 1.08421i
\(964\) −3.32212e104 −1.19872
\(965\) 4.27339e104i 1.48702i
\(966\) 1.32653e103 + 3.06867e104i 0.0445160 + 1.02979i
\(967\) 6.85055e103 0.221717 0.110858 0.993836i \(-0.464640\pi\)
0.110858 + 0.993836i \(0.464640\pi\)
\(968\) 9.28114e103i 0.289710i
\(969\) −4.20392e104 + 1.81727e103i −1.26568 + 0.0547127i
\(970\) 7.99087e104 2.32051
\(971\) 5.89247e104i 1.65053i −0.564744 0.825266i \(-0.691025\pi\)
0.564744 0.825266i \(-0.308975\pi\)
\(972\) −1.37116e104 6.24875e104i −0.370483 1.68839i
\(973\) 3.24333e104 0.845360
\(974\) 1.16588e105i 2.93150i
\(975\) 5.38087e102 + 1.24476e104i 0.0130524 + 0.301943i
\(976\) 8.96251e103 0.209742
\(977\) 4.70080e104i 1.06136i 0.847573 + 0.530680i \(0.178063\pi\)
−0.847573 + 0.530680i \(0.821937\pi\)
\(978\) −6.56887e103 + 2.83959e102i −0.143097 + 0.00618581i
\(979\) 6.15672e104 1.29406
\(980\) 5.33794e104i 1.08258i
\(981\) 3.66735e104 3.17658e103i 0.717690 0.0621649i
\(982\) 1.78441e104 0.336970
\(983\) 3.35312e104i 0.611049i −0.952184 0.305524i \(-0.901168\pi\)
0.952184 0.305524i \(-0.0988318\pi\)
\(984\) −3.32179e103 7.68434e104i −0.0584176 1.35138i
\(985\) 2.33618e104 0.396496
\(986\) 1.38072e104i 0.226160i
\(987\) 5.16630e104 2.23329e103i 0.816731 0.0353057i
\(988\) −1.88424e105 −2.87504
\(989\) 5.19897e104i 0.765680i
\(990\) −7.85081e103 9.06372e104i −0.111605 1.28847i
\(991\) −5.86446e104 −0.804730 −0.402365 0.915479i \(-0.631812\pi\)
−0.402365 + 0.915479i \(0.631812\pi\)
\(992\) 6.80311e104i 0.901154i
\(993\) −3.15282e103 7.29347e104i −0.0403159 0.932632i
\(994\) −7.14821e104 −0.882418
\(995\) 1.02873e105i 1.22601i
\(996\) 7.91616e103 3.42200e102i 0.0910831 0.00393735i
\(997\) −3.40988e104 −0.378799 −0.189399 0.981900i \(-0.560654\pi\)
−0.189399 + 0.981900i \(0.560654\pi\)
\(998\) 2.45207e105i 2.63004i
\(999\) 8.90335e103 + 6.83118e104i 0.0922064 + 0.707462i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3.71.b.a.2.3 22
3.2 odd 2 inner 3.71.b.a.2.20 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.71.b.a.2.3 22 1.1 even 1 trivial
3.71.b.a.2.20 yes 22 3.2 odd 2 inner