Properties

Label 3.71.b.a.2.1
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 2.1
Character \(\chi\) \(=\) 3.2
Dual form 3.71.b.a.2.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.63817e10i q^{2} +(2.36972e16 - 4.40636e16i) q^{3} -3.22594e21 q^{4} +6.32737e23i q^{5} +(-2.92502e27 - 1.57306e27i) q^{6} -2.54650e29 q^{7} +1.35774e32i q^{8} +(-1.38004e33 - 2.08836e33i) q^{9} +O(q^{10})\) \(q-6.63817e10i q^{2} +(2.36972e16 - 4.40636e16i) q^{3} -3.22594e21 q^{4} +6.32737e23i q^{5} +(-2.92502e27 - 1.57306e27i) q^{6} -2.54650e29 q^{7} +1.35774e32i q^{8} +(-1.38004e33 - 2.08836e33i) q^{9} +4.20021e34 q^{10} -1.33911e36i q^{11} +(-7.64456e37 + 1.42146e38i) q^{12} -1.53510e39 q^{13} +1.69041e40i q^{14} +(2.78806e40 + 1.49941e40i) q^{15} +5.20436e42 q^{16} +7.59069e42i q^{17} +(-1.38629e44 + 9.16097e43i) q^{18} +8.19873e44 q^{19} -2.04117e45i q^{20} +(-6.03449e45 + 1.12208e46i) q^{21} -8.88922e46 q^{22} +6.91248e47i q^{23} +(5.98267e48 + 3.21745e48i) q^{24} +8.06997e48 q^{25} +1.01902e50i q^{26} +(-1.24724e50 + 1.13214e49i) q^{27} +8.21487e50 q^{28} -4.05488e50i q^{29} +(9.95332e50 - 1.85076e51i) q^{30} -1.63946e52 q^{31} -1.85181e53i q^{32} +(-5.90059e52 - 3.17330e52i) q^{33} +5.03883e53 q^{34} -1.61127e53i q^{35} +(4.45194e54 + 6.73693e54i) q^{36} +3.41760e54 q^{37} -5.44246e55i q^{38} +(-3.63775e55 + 6.76420e55i) q^{39} -8.59089e55 q^{40} -4.15548e56i q^{41} +(7.44856e56 + 4.00580e56i) q^{42} -8.83584e56 q^{43} +4.31988e57i q^{44} +(1.32138e57 - 8.73204e56i) q^{45} +4.58862e58 q^{46} -4.77253e57i q^{47} +(1.23329e59 - 2.29323e59i) q^{48} -7.86568e58 q^{49} -5.35699e59i q^{50} +(3.34473e59 + 1.79878e59i) q^{51} +4.95213e60 q^{52} -5.62909e59i q^{53} +(7.51531e59 + 8.27939e60i) q^{54} +8.47302e59 q^{55} -3.45748e61i q^{56} +(1.94287e61 - 3.61265e61i) q^{57} -2.69170e61 q^{58} +9.59463e61i q^{59} +(-8.99412e61 - 4.83699e61i) q^{60} -8.18161e61 q^{61} +1.08830e63i q^{62} +(3.51429e62 + 5.31803e62i) q^{63} -6.14843e63 q^{64} -9.71313e62i q^{65} +(-2.10649e63 + 3.91691e63i) q^{66} +2.40454e63 q^{67} -2.44871e64i q^{68} +(3.04588e64 + 1.63806e64i) q^{69} -1.06959e64 q^{70} +7.14405e64i q^{71} +(2.83545e65 - 1.87373e65i) q^{72} +1.52365e65 q^{73} -2.26866e65i q^{74} +(1.91236e65 - 3.55592e65i) q^{75} -2.64486e66 q^{76} +3.41004e65i q^{77} +(4.49019e66 + 2.41480e66i) q^{78} -2.33890e66 q^{79} +3.29299e66i q^{80} +(-2.45675e66 + 5.76407e66i) q^{81} -2.75848e67 q^{82} -2.67747e67i q^{83} +(1.94669e67 - 3.61976e67i) q^{84} -4.80291e66 q^{85} +5.86538e67i q^{86} +(-1.78672e67 - 9.60891e66i) q^{87} +1.81815e68 q^{88} +5.29244e67i q^{89} +(-5.79648e67 - 8.77158e67i) q^{90} +3.90914e68 q^{91} -2.22992e69i q^{92} +(-3.88506e68 + 7.22406e68i) q^{93} -3.16809e68 q^{94} +5.18764e68i q^{95} +(-8.15976e69 - 4.38828e69i) q^{96} +4.21837e69 q^{97} +5.22137e69i q^{98} +(-2.79654e69 + 1.84803e69i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.63817e10i 1.93196i −0.258614 0.965981i \(-0.583266\pi\)
0.258614 0.965981i \(-0.416734\pi\)
\(3\) 2.36972e16 4.40636e16i 0.473645 0.880716i
\(4\) −3.22594e21 −2.73248
\(5\) 6.32737e23i 0.217407i 0.994074 + 0.108703i \(0.0346699\pi\)
−0.994074 + 0.108703i \(0.965330\pi\)
\(6\) −2.92502e27 1.57306e27i −1.70151 0.915063i
\(7\) −2.54650e29 −0.672222 −0.336111 0.941822i \(-0.609112\pi\)
−0.336111 + 0.941822i \(0.609112\pi\)
\(8\) 1.35774e32i 3.34708i
\(9\) −1.38004e33 2.08836e33i −0.551322 0.834293i
\(10\) 4.20021e34 0.420021
\(11\) 1.33911e36i 0.476509i −0.971203 0.238255i \(-0.923425\pi\)
0.971203 0.238255i \(-0.0765753\pi\)
\(12\) −7.64456e37 + 1.42146e38i −1.29422 + 2.40654i
\(13\) −1.53510e39 −1.57804 −0.789022 0.614365i \(-0.789412\pi\)
−0.789022 + 0.614365i \(0.789412\pi\)
\(14\) 1.69041e40i 1.29871i
\(15\) 2.78806e40 + 1.49941e40i 0.191474 + 0.102973i
\(16\) 5.20436e42 3.73395
\(17\) 7.59069e42i 0.652483i 0.945287 + 0.326241i \(0.105782\pi\)
−0.945287 + 0.326241i \(0.894218\pi\)
\(18\) −1.38629e44 + 9.16097e43i −1.61182 + 1.06513i
\(19\) 8.19873e44 1.43671 0.718357 0.695674i \(-0.244894\pi\)
0.718357 + 0.695674i \(0.244894\pi\)
\(20\) 2.04117e45i 0.594058i
\(21\) −6.03449e45 + 1.12208e46i −0.318394 + 0.592037i
\(22\) −8.88922e46 −0.920597
\(23\) 6.91248e47i 1.51063i 0.655359 + 0.755317i \(0.272517\pi\)
−0.655359 + 0.755317i \(0.727483\pi\)
\(24\) 5.98267e48 + 3.21745e48i 2.94782 + 1.58532i
\(25\) 8.06997e48 0.952734
\(26\) 1.01902e50i 3.04872i
\(27\) −1.24724e50 + 1.13214e49i −0.995906 + 0.0903997i
\(28\) 8.21487e50 1.83683
\(29\) 4.05488e50i 0.265490i −0.991150 0.132745i \(-0.957621\pi\)
0.991150 0.132745i \(-0.0423791\pi\)
\(30\) 9.95332e50 1.85076e51i 0.198941 0.369920i
\(31\) −1.63946e52 −1.04002 −0.520011 0.854160i \(-0.674072\pi\)
−0.520011 + 0.854160i \(0.674072\pi\)
\(32\) 1.85181e53i 3.86677i
\(33\) −5.90059e52 3.17330e52i −0.419669 0.225696i
\(34\) 5.03883e53 1.26057
\(35\) 1.61127e53i 0.146146i
\(36\) 4.45194e54 + 6.73693e54i 1.50647 + 2.27968i
\(37\) 3.41760e54 0.443263 0.221631 0.975131i \(-0.428862\pi\)
0.221631 + 0.975131i \(0.428862\pi\)
\(38\) 5.44246e55i 2.77568i
\(39\) −3.63775e55 + 6.76420e55i −0.747432 + 1.38981i
\(40\) −8.59089e55 −0.727677
\(41\) 4.15548e56i 1.48315i −0.670868 0.741577i \(-0.734078\pi\)
0.670868 0.741577i \(-0.265922\pi\)
\(42\) 7.44856e56 + 4.00580e56i 1.14379 + 0.615126i
\(43\) −8.83584e56 −0.595459 −0.297730 0.954650i \(-0.596229\pi\)
−0.297730 + 0.954650i \(0.596229\pi\)
\(44\) 4.31988e57i 1.30205i
\(45\) 1.32138e57 8.73204e56i 0.181381 0.119861i
\(46\) 4.58862e58 2.91849
\(47\) 4.77253e57i 0.142996i −0.997441 0.0714979i \(-0.977222\pi\)
0.997441 0.0714979i \(-0.0227779\pi\)
\(48\) 1.23329e59 2.29323e59i 1.76856 3.28855i
\(49\) −7.86568e58 −0.548117
\(50\) 5.35699e59i 1.84065i
\(51\) 3.34473e59 + 1.79878e59i 0.574652 + 0.309045i
\(52\) 4.95213e60 4.31197
\(53\) 5.62909e59i 0.251642i −0.992053 0.125821i \(-0.959844\pi\)
0.992053 0.125821i \(-0.0401564\pi\)
\(54\) 7.51531e59 + 8.27939e60i 0.174649 + 1.92405i
\(55\) 8.47302e59 0.103596
\(56\) 3.45748e61i 2.24998i
\(57\) 1.94287e61 3.61265e61i 0.680492 1.26534i
\(58\) −2.69170e61 −0.512916
\(59\) 9.59463e61i 1.00510i 0.864549 + 0.502548i \(0.167604\pi\)
−0.864549 + 0.502548i \(0.832396\pi\)
\(60\) −8.99412e61 4.83699e61i −0.523197 0.281373i
\(61\) −8.18161e61 −0.266867 −0.133433 0.991058i \(-0.542600\pi\)
−0.133433 + 0.991058i \(0.542600\pi\)
\(62\) 1.08830e63i 2.00928i
\(63\) 3.51429e62 + 5.31803e62i 0.370611 + 0.560830i
\(64\) −6.14843e63 −3.73650
\(65\) 9.71313e62i 0.343077i
\(66\) −2.10649e63 + 3.91691e63i −0.436036 + 0.810785i
\(67\) 2.40454e63 0.294045 0.147022 0.989133i \(-0.453031\pi\)
0.147022 + 0.989133i \(0.453031\pi\)
\(68\) 2.44871e64i 1.78289i
\(69\) 3.04588e64 + 1.63806e64i 1.33044 + 0.715504i
\(70\) −1.06959e64 −0.282348
\(71\) 7.14405e64i 1.14789i 0.818892 + 0.573947i \(0.194589\pi\)
−0.818892 + 0.573947i \(0.805411\pi\)
\(72\) 2.83545e65 1.87373e65i 2.79244 1.84532i
\(73\) 1.52365e65 0.925947 0.462974 0.886372i \(-0.346782\pi\)
0.462974 + 0.886372i \(0.346782\pi\)
\(74\) 2.26866e65i 0.856366i
\(75\) 1.91236e65 3.55592e65i 0.451257 0.839088i
\(76\) −2.64486e66 −3.92579
\(77\) 3.41004e65i 0.320320i
\(78\) 4.49019e66 + 2.41480e66i 2.68506 + 1.44401i
\(79\) −2.33890e66 −0.895495 −0.447748 0.894160i \(-0.647774\pi\)
−0.447748 + 0.894160i \(0.647774\pi\)
\(80\) 3.29299e66i 0.811785i
\(81\) −2.45675e66 + 5.76407e66i −0.392089 + 0.919927i
\(82\) −2.75848e67 −2.86540
\(83\) 2.67747e67i 1.81966i −0.414976 0.909832i \(-0.636210\pi\)
0.414976 0.909832i \(-0.363790\pi\)
\(84\) 1.94669e67 3.61976e67i 0.870005 1.61773i
\(85\) −4.80291e66 −0.141854
\(86\) 5.86538e67i 1.15040i
\(87\) −1.78672e67 9.60891e66i −0.233821 0.125748i
\(88\) 1.81815e68 1.59491
\(89\) 5.29244e67i 0.312612i 0.987709 + 0.156306i \(0.0499586\pi\)
−0.987709 + 0.156306i \(0.950041\pi\)
\(90\) −5.79648e67 8.77158e67i −0.231567 0.350421i
\(91\) 3.90914e68 1.06080
\(92\) 2.22992e69i 4.12777i
\(93\) −3.88506e68 + 7.22406e68i −0.492601 + 0.915964i
\(94\) −3.16809e68 −0.276263
\(95\) 5.18764e68i 0.312351i
\(96\) −8.15976e69 4.38828e69i −3.40553 1.83147i
\(97\) 4.21837e69 1.22499 0.612497 0.790473i \(-0.290165\pi\)
0.612497 + 0.790473i \(0.290165\pi\)
\(98\) 5.22137e69i 1.05894i
\(99\) −2.79654e69 + 1.84803e69i −0.397548 + 0.262710i
\(100\) −2.60332e70 −2.60332
\(101\) 5.84441e69i 0.412565i 0.978492 + 0.206283i \(0.0661366\pi\)
−0.978492 + 0.206283i \(0.933863\pi\)
\(102\) 1.19406e70 2.22029e70i 0.597063 1.11021i
\(103\) 5.53027e69 0.196537 0.0982684 0.995160i \(-0.468670\pi\)
0.0982684 + 0.995160i \(0.468670\pi\)
\(104\) 2.08426e71i 5.28183i
\(105\) −7.09982e69 3.81825e69i −0.128713 0.0692211i
\(106\) −3.73668e70 −0.486162
\(107\) 3.46547e70i 0.324586i 0.986743 + 0.162293i \(0.0518890\pi\)
−0.986743 + 0.162293i \(0.948111\pi\)
\(108\) 4.02352e71 3.65220e70i 2.72129 0.247015i
\(109\) −1.46497e71 −0.717631 −0.358815 0.933409i \(-0.616819\pi\)
−0.358815 + 0.933409i \(0.616819\pi\)
\(110\) 5.62453e70i 0.200144i
\(111\) 8.09875e70 1.50592e71i 0.209949 0.390388i
\(112\) −1.32529e72 −2.51004
\(113\) 2.60988e71i 0.362139i 0.983470 + 0.181069i \(0.0579559\pi\)
−0.983470 + 0.181069i \(0.942044\pi\)
\(114\) −2.39814e72 1.28971e72i −2.44458 1.31468i
\(115\) −4.37378e71 −0.328422
\(116\) 1.30808e72i 0.725444i
\(117\) 2.11850e72 + 3.20585e72i 0.870010 + 1.31655i
\(118\) 6.36908e72 1.94181
\(119\) 1.93297e72i 0.438614i
\(120\) −2.03580e72 + 3.78545e72i −0.344660 + 0.640877i
\(121\) 6.10426e72 0.772939
\(122\) 5.43109e72i 0.515577i
\(123\) −1.83105e73 9.84731e72i −1.30624 0.702488i
\(124\) 5.28881e73 2.84183
\(125\) 1.04657e73i 0.424537i
\(126\) 3.53020e73 2.33284e73i 1.08350 0.716006i
\(127\) −2.34346e73 −0.545415 −0.272708 0.962097i \(-0.587919\pi\)
−0.272708 + 0.962097i \(0.587919\pi\)
\(128\) 1.89519e74i 3.35201i
\(129\) −2.09384e73 + 3.89339e73i −0.282036 + 0.524431i
\(130\) −6.44774e73 −0.662812
\(131\) 3.03202e73i 0.238362i −0.992873 0.119181i \(-0.961973\pi\)
0.992873 0.119181i \(-0.0380269\pi\)
\(132\) 1.90349e74 + 1.02369e74i 1.14674 + 0.616709i
\(133\) −2.08781e74 −0.965792
\(134\) 1.59617e74i 0.568083i
\(135\) −7.16344e72 7.89174e73i −0.0196535 0.216516i
\(136\) −1.03062e75 −2.18391
\(137\) 9.01556e74i 1.47833i 0.673522 + 0.739167i \(0.264781\pi\)
−0.673522 + 0.739167i \(0.735219\pi\)
\(138\) 1.08737e75 2.02191e75i 1.38233 2.57036i
\(139\) 6.69019e74 0.660572 0.330286 0.943881i \(-0.392855\pi\)
0.330286 + 0.943881i \(0.392855\pi\)
\(140\) 5.19785e74i 0.399339i
\(141\) −2.10295e74 1.13095e74i −0.125939 0.0677292i
\(142\) 4.74234e75 2.21769
\(143\) 2.05566e75i 0.751952i
\(144\) −7.18225e75 1.08686e76i −2.05861 3.11521i
\(145\) 2.56567e74 0.0577192
\(146\) 1.01143e76i 1.78889i
\(147\) −1.86394e75 + 3.46590e75i −0.259613 + 0.482735i
\(148\) −1.10250e76 −1.21120
\(149\) 3.80767e75i 0.330476i 0.986254 + 0.165238i \(0.0528392\pi\)
−0.986254 + 0.165238i \(0.947161\pi\)
\(150\) −2.36048e76 1.26945e76i −1.62109 0.871812i
\(151\) −6.40778e75 −0.348750 −0.174375 0.984679i \(-0.555790\pi\)
−0.174375 + 0.984679i \(0.555790\pi\)
\(152\) 1.11317e77i 4.80879i
\(153\) 1.58521e76 1.04755e76i 0.544362 0.359728i
\(154\) 2.26364e76 0.618846
\(155\) 1.03735e76i 0.226108i
\(156\) 1.17352e77 2.18209e77i 2.04234 3.79762i
\(157\) −6.98741e76 −0.972363 −0.486181 0.873858i \(-0.661611\pi\)
−0.486181 + 0.873858i \(0.661611\pi\)
\(158\) 1.55260e77i 1.73006i
\(159\) −2.48038e76 1.33393e76i −0.221625 0.119189i
\(160\) 1.17171e77 0.840661
\(161\) 1.76026e77i 1.01548i
\(162\) 3.82629e77 + 1.63083e77i 1.77726 + 0.757501i
\(163\) 4.49284e77 1.68250 0.841250 0.540646i \(-0.181820\pi\)
0.841250 + 0.540646i \(0.181820\pi\)
\(164\) 1.34053e78i 4.05268i
\(165\) 2.00787e76 3.73352e76i 0.0490678 0.0912389i
\(166\) −1.77735e78 −3.51552
\(167\) 2.65948e77i 0.426305i 0.977019 + 0.213152i \(0.0683731\pi\)
−0.977019 + 0.213152i \(0.931627\pi\)
\(168\) −1.52349e78 8.19325e77i −1.98159 1.06569i
\(169\) 1.41022e78 1.49022
\(170\) 3.18825e77i 0.274057i
\(171\) −1.13146e78 1.71219e78i −0.792092 1.19864i
\(172\) 2.85039e78 1.62708
\(173\) 5.17414e77i 0.241115i −0.992706 0.120558i \(-0.961532\pi\)
0.992706 0.120558i \(-0.0384682\pi\)
\(174\) −6.37856e77 + 1.18606e78i −0.242940 + 0.451733i
\(175\) −2.05502e78 −0.640449
\(176\) 6.96920e78i 1.77926i
\(177\) 4.22774e78 + 2.27366e78i 0.885205 + 0.476058i
\(178\) 3.51321e78 0.603954
\(179\) 6.60972e78i 0.933957i −0.884269 0.466978i \(-0.845343\pi\)
0.884269 0.466978i \(-0.154657\pi\)
\(180\) −4.26271e78 + 2.81690e78i −0.495619 + 0.327517i
\(181\) 1.35420e79 1.29698 0.648488 0.761225i \(-0.275402\pi\)
0.648488 + 0.761225i \(0.275402\pi\)
\(182\) 2.59495e79i 2.04942i
\(183\) −1.93881e78 + 3.60511e78i −0.126400 + 0.235034i
\(184\) −9.38532e79 −5.05621
\(185\) 2.16244e78i 0.0963682i
\(186\) 4.79546e79 + 2.57897e79i 1.76961 + 0.951685i
\(187\) 1.01647e79 0.310914
\(188\) 1.53959e79i 0.390733i
\(189\) 3.17610e79 2.88299e78i 0.669470 0.0607687i
\(190\) 3.44364e79 0.603451
\(191\) 2.69940e79i 0.393640i 0.980440 + 0.196820i \(0.0630614\pi\)
−0.980440 + 0.196820i \(0.936939\pi\)
\(192\) −1.45700e80 + 2.70922e80i −1.76977 + 3.29080i
\(193\) 9.29560e79 0.941394 0.470697 0.882295i \(-0.344002\pi\)
0.470697 + 0.882295i \(0.344002\pi\)
\(194\) 2.80023e80i 2.36664i
\(195\) −4.27995e79 2.30174e79i −0.302154 0.162497i
\(196\) 2.53742e80 1.49772
\(197\) 3.36879e80i 1.66401i −0.554768 0.832005i \(-0.687193\pi\)
0.554768 0.832005i \(-0.312807\pi\)
\(198\) 1.22675e80 + 1.85639e80i 0.507545 + 0.768048i
\(199\) 2.89620e80 1.00455 0.502275 0.864708i \(-0.332497\pi\)
0.502275 + 0.864708i \(0.332497\pi\)
\(200\) 1.09569e81i 3.18888i
\(201\) 5.69807e79 1.05952e80i 0.139273 0.258970i
\(202\) 3.87962e80 0.797060
\(203\) 1.03258e80i 0.178468i
\(204\) −1.07899e81 5.80275e80i −1.57022 0.844458i
\(205\) 2.62933e80 0.322448
\(206\) 3.67109e80i 0.379701i
\(207\) 1.44358e81 9.53952e80i 1.26031 0.832845i
\(208\) −7.98921e81 −5.89233
\(209\) 1.09790e81i 0.684608i
\(210\) −2.53462e80 + 4.71298e80i −0.133732 + 0.248668i
\(211\) 3.31637e81 1.48176 0.740878 0.671639i \(-0.234410\pi\)
0.740878 + 0.671639i \(0.234410\pi\)
\(212\) 1.81591e81i 0.687605i
\(213\) 3.14792e81 + 1.69294e81i 1.01097 + 0.543694i
\(214\) 2.30044e81 0.627089
\(215\) 5.59076e80i 0.129457i
\(216\) −1.53714e81 1.69342e82i −0.302575 3.33337i
\(217\) 4.17490e81 0.699126
\(218\) 9.72471e81i 1.38644i
\(219\) 3.61063e81 6.71377e81i 0.438570 0.815497i
\(220\) −2.73334e81 −0.283074
\(221\) 1.16525e82i 1.02965i
\(222\) −9.99654e81 5.37609e81i −0.754216 0.405613i
\(223\) 1.00171e82 0.645764 0.322882 0.946439i \(-0.395348\pi\)
0.322882 + 0.946439i \(0.395348\pi\)
\(224\) 4.71565e82i 2.59933i
\(225\) −1.11369e82 1.68530e82i −0.525263 0.794859i
\(226\) 1.73248e82 0.699638
\(227\) 1.32377e82i 0.458045i 0.973421 + 0.229022i \(0.0735529\pi\)
−0.973421 + 0.229022i \(0.926447\pi\)
\(228\) −6.26757e82 + 1.16542e83i −1.85943 + 3.45751i
\(229\) −2.29576e82 −0.584366 −0.292183 0.956362i \(-0.594382\pi\)
−0.292183 + 0.956362i \(0.594382\pi\)
\(230\) 2.90339e82i 0.634499i
\(231\) 1.50259e82 + 8.08083e81i 0.282111 + 0.151718i
\(232\) 5.50545e82 0.888614
\(233\) 1.67406e82i 0.232442i −0.993223 0.116221i \(-0.962922\pi\)
0.993223 0.116221i \(-0.0370780\pi\)
\(234\) 2.12809e83 1.40630e83i 2.54352 1.68083i
\(235\) 3.01975e81 0.0310883
\(236\) 3.09517e83i 2.74640i
\(237\) −5.54253e82 + 1.03060e83i −0.424146 + 0.788677i
\(238\) −1.28314e83 −0.847385
\(239\) 1.85976e83i 1.06055i 0.847826 + 0.530275i \(0.177911\pi\)
−0.847826 + 0.530275i \(0.822089\pi\)
\(240\) 1.45101e83 + 7.80346e82i 0.714952 + 0.384498i
\(241\) −6.16463e82 −0.262609 −0.131305 0.991342i \(-0.541917\pi\)
−0.131305 + 0.991342i \(0.541917\pi\)
\(242\) 4.05211e83i 1.49329i
\(243\) 1.95768e83 + 2.44845e83i 0.624484 + 0.781038i
\(244\) 2.63934e83 0.729207
\(245\) 4.97690e82i 0.119164i
\(246\) −6.53681e83 + 1.21548e84i −1.35718 + 2.52360i
\(247\) −1.25859e84 −2.26720
\(248\) 2.22596e84i 3.48103i
\(249\) −1.17979e84 6.34485e83i −1.60261 0.861874i
\(250\) 6.94728e83 0.820190
\(251\) 7.79373e83i 0.800138i 0.916485 + 0.400069i \(0.131014\pi\)
−0.916485 + 0.400069i \(0.868986\pi\)
\(252\) −1.13369e84 1.71556e84i −1.01269 1.53246i
\(253\) 9.25654e83 0.719831
\(254\) 1.55563e84i 1.05372i
\(255\) −1.13815e83 + 2.11633e83i −0.0671884 + 0.124933i
\(256\) 5.32184e84 2.73945
\(257\) 1.89034e84i 0.848945i 0.905441 + 0.424472i \(0.139540\pi\)
−0.905441 + 0.424472i \(0.860460\pi\)
\(258\) 2.58450e84 + 1.38993e84i 1.01318 + 0.544883i
\(259\) −8.70294e83 −0.297971
\(260\) 3.13340e84i 0.937450i
\(261\) −8.46806e83 + 5.59591e83i −0.221496 + 0.146370i
\(262\) −2.01271e84 −0.460506
\(263\) 7.44706e84i 1.49119i −0.666399 0.745596i \(-0.732165\pi\)
0.666399 0.745596i \(-0.267835\pi\)
\(264\) 4.30851e84 8.01144e84i 0.755422 1.40467i
\(265\) 3.56173e83 0.0547086
\(266\) 1.38592e85i 1.86587i
\(267\) 2.33204e84 + 1.25416e84i 0.275322 + 0.148067i
\(268\) −7.75688e84 −0.803470
\(269\) 1.38025e85i 1.25496i 0.778633 + 0.627479i \(0.215913\pi\)
−0.778633 + 0.627479i \(0.784087\pi\)
\(270\) −5.23867e84 + 4.75521e83i −0.418302 + 0.0379698i
\(271\) −1.67408e85 −1.17450 −0.587248 0.809407i \(-0.699789\pi\)
−0.587248 + 0.809407i \(0.699789\pi\)
\(272\) 3.95047e85i 2.43634i
\(273\) 9.26354e84 1.72251e85i 0.502440 0.934260i
\(274\) 5.98468e85 2.85609
\(275\) 1.08066e85i 0.453987i
\(276\) −9.82584e85 5.28428e85i −3.63540 1.95510i
\(277\) −1.46289e85 −0.476891 −0.238446 0.971156i \(-0.576638\pi\)
−0.238446 + 0.971156i \(0.576638\pi\)
\(278\) 4.44106e85i 1.27620i
\(279\) 2.26253e85 + 3.42380e85i 0.573386 + 0.867682i
\(280\) 2.18767e85 0.489161
\(281\) 3.86508e85i 0.762846i −0.924401 0.381423i \(-0.875434\pi\)
0.924401 0.381423i \(-0.124566\pi\)
\(282\) −7.50747e84 + 1.39597e85i −0.130850 + 0.243309i
\(283\) 9.93234e85 1.52942 0.764709 0.644375i \(-0.222883\pi\)
0.764709 + 0.644375i \(0.222883\pi\)
\(284\) 2.30463e86i 3.13659i
\(285\) 2.28586e85 + 1.22932e85i 0.275093 + 0.147944i
\(286\) 1.36458e86 1.45274
\(287\) 1.05820e86i 0.997010i
\(288\) −3.86726e86 + 2.55558e86i −3.22602 + 2.13183i
\(289\) 7.77209e85 0.574266
\(290\) 1.70313e85i 0.111511i
\(291\) 9.99635e85 1.85877e86i 0.580212 1.07887i
\(292\) −4.91521e86 −2.53013
\(293\) 4.64538e85i 0.212155i 0.994358 + 0.106078i \(0.0338292\pi\)
−0.994358 + 0.106078i \(0.966171\pi\)
\(294\) 2.30072e86 + 1.23732e86i 0.932626 + 0.501562i
\(295\) −6.07087e85 −0.218515
\(296\) 4.64020e86i 1.48363i
\(297\) 1.51605e85 + 1.67019e86i 0.0430763 + 0.474558i
\(298\) 2.52760e86 0.638467
\(299\) 1.06113e87i 2.38385i
\(300\) −6.16914e86 + 1.14712e87i −1.23305 + 2.29279i
\(301\) 2.25005e86 0.400281
\(302\) 4.25359e86i 0.673772i
\(303\) 2.57526e86 + 1.38496e86i 0.363353 + 0.195409i
\(304\) 4.26692e87 5.36462
\(305\) 5.17681e85i 0.0580186i
\(306\) −6.95381e86 1.05229e87i −0.694980 1.05169i
\(307\) −4.92341e86 −0.438958 −0.219479 0.975617i \(-0.570436\pi\)
−0.219479 + 0.975617i \(0.570436\pi\)
\(308\) 1.10006e87i 0.875267i
\(309\) 1.31052e86 2.43684e86i 0.0930886 0.173093i
\(310\) −6.88609e86 −0.436831
\(311\) 1.62337e87i 0.920033i 0.887910 + 0.460016i \(0.152156\pi\)
−0.887910 + 0.460016i \(0.847844\pi\)
\(312\) −9.18399e87 4.93910e87i −4.65180 2.50171i
\(313\) −1.00197e87 −0.453736 −0.226868 0.973926i \(-0.572849\pi\)
−0.226868 + 0.973926i \(0.572849\pi\)
\(314\) 4.63836e87i 1.87857i
\(315\) −3.36491e86 + 2.22362e86i −0.121928 + 0.0805733i
\(316\) 7.54514e87 2.44692
\(317\) 1.77919e87i 0.516593i 0.966066 + 0.258296i \(0.0831611\pi\)
−0.966066 + 0.258296i \(0.916839\pi\)
\(318\) −8.85488e86 + 1.64652e87i −0.230268 + 0.428171i
\(319\) −5.42991e86 −0.126508
\(320\) 3.89034e87i 0.812340i
\(321\) 1.52701e87 + 8.21219e86i 0.285869 + 0.153739i
\(322\) −1.16849e88 −1.96187
\(323\) 6.22340e87i 0.937432i
\(324\) 7.92531e87 1.85945e88i 1.07137 2.51368i
\(325\) −1.23882e88 −1.50346
\(326\) 2.98243e88i 3.25053i
\(327\) −3.47156e87 + 6.45518e87i −0.339902 + 0.632029i
\(328\) 5.64205e88 4.96423
\(329\) 1.21533e87i 0.0961250i
\(330\) −2.47837e87 1.33286e87i −0.176270 0.0947971i
\(331\) −1.46985e88 −0.940357 −0.470178 0.882571i \(-0.655810\pi\)
−0.470178 + 0.882571i \(0.655810\pi\)
\(332\) 8.63735e88i 4.97219i
\(333\) −4.71644e87 7.13720e87i −0.244380 0.369811i
\(334\) 1.76541e88 0.823604
\(335\) 1.52144e87i 0.0639272i
\(336\) −3.14057e88 + 5.83972e88i −1.18887 + 2.21064i
\(337\) −9.50112e87 −0.324137 −0.162068 0.986780i \(-0.551817\pi\)
−0.162068 + 0.986780i \(0.551817\pi\)
\(338\) 9.36125e88i 2.87905i
\(339\) 1.15001e88 + 6.18468e87i 0.318942 + 0.171525i
\(340\) 1.54939e88 0.387613
\(341\) 2.19542e88i 0.495580i
\(342\) −1.13658e89 + 7.51083e88i −2.31573 + 1.53029i
\(343\) 5.65732e88 1.04068
\(344\) 1.19967e89i 1.99305i
\(345\) −1.03646e88 + 1.92724e88i −0.155555 + 0.289246i
\(346\) −3.43468e88 −0.465825
\(347\) 7.07834e88i 0.867760i −0.900971 0.433880i \(-0.857144\pi\)
0.900971 0.433880i \(-0.142856\pi\)
\(348\) 5.76386e88 + 3.09977e88i 0.638910 + 0.343603i
\(349\) 1.31421e89 1.31758 0.658788 0.752328i \(-0.271069\pi\)
0.658788 + 0.752328i \(0.271069\pi\)
\(350\) 1.36416e89i 1.23732i
\(351\) 1.91464e89 1.73794e88i 1.57158 0.142655i
\(352\) −2.47978e89 −1.84255
\(353\) 5.79360e88i 0.389793i −0.980824 0.194897i \(-0.937563\pi\)
0.980824 0.194897i \(-0.0624371\pi\)
\(354\) 1.50929e89 2.80644e89i 0.919727 1.71018i
\(355\) −4.52030e88 −0.249560
\(356\) 1.70731e89i 0.854205i
\(357\) −8.51737e88 4.58060e88i −0.386294 0.207747i
\(358\) −4.38764e89 −1.80437
\(359\) 1.99472e89i 0.744004i 0.928232 + 0.372002i \(0.121329\pi\)
−0.928232 + 0.372002i \(0.878671\pi\)
\(360\) 1.18558e89 + 1.79409e89i 0.401184 + 0.607095i
\(361\) 3.46541e89 1.06415
\(362\) 8.98940e89i 2.50571i
\(363\) 1.44654e89 2.68976e89i 0.366098 0.680740i
\(364\) −1.26106e90 −2.89860
\(365\) 9.64072e88i 0.201307i
\(366\) 2.39313e89 + 1.28702e89i 0.454077 + 0.244200i
\(367\) 2.13853e89 0.368810 0.184405 0.982850i \(-0.440964\pi\)
0.184405 + 0.982850i \(0.440964\pi\)
\(368\) 3.59750e90i 5.64063i
\(369\) −8.67816e89 + 5.73475e89i −1.23738 + 0.817695i
\(370\) 1.43547e89 0.186180
\(371\) 1.43345e89i 0.169159i
\(372\) 1.25330e90 2.33044e90i 1.34602 2.50285i
\(373\) 1.92012e90 1.87724 0.938619 0.344957i \(-0.112106\pi\)
0.938619 + 0.344957i \(0.112106\pi\)
\(374\) 6.74753e89i 0.600674i
\(375\) 4.61154e89 + 2.48006e89i 0.373897 + 0.201080i
\(376\) 6.47983e89 0.478618
\(377\) 6.22464e89i 0.418954i
\(378\) −1.91378e89 2.10835e90i −0.117403 1.29339i
\(379\) −2.93102e90 −1.63925 −0.819626 0.572899i \(-0.805819\pi\)
−0.819626 + 0.572899i \(0.805819\pi\)
\(380\) 1.67350e90i 0.853492i
\(381\) −5.55333e89 + 1.03261e90i −0.258333 + 0.480356i
\(382\) 1.79191e90 0.760497
\(383\) 2.91177e90i 1.12772i 0.825871 + 0.563859i \(0.190684\pi\)
−0.825871 + 0.563859i \(0.809316\pi\)
\(384\) 8.35091e90 + 4.49107e90i 2.95217 + 1.58766i
\(385\) −2.15766e89 −0.0696397
\(386\) 6.17058e90i 1.81874i
\(387\) 1.21939e90 + 1.84525e90i 0.328290 + 0.496787i
\(388\) −1.36082e91 −3.34727
\(389\) 3.00943e90i 0.676469i 0.941062 + 0.338235i \(0.109830\pi\)
−0.941062 + 0.338235i \(0.890170\pi\)
\(390\) −1.52793e90 + 2.84111e90i −0.313937 + 0.583749i
\(391\) −5.24705e90 −0.985663
\(392\) 1.06795e91i 1.83459i
\(393\) −1.33602e90 7.18503e89i −0.209929 0.112899i
\(394\) −2.23626e91 −3.21480
\(395\) 1.47991e90i 0.194687i
\(396\) 9.02148e90 5.96162e90i 1.08629 0.717848i
\(397\) 6.05978e90 0.668020 0.334010 0.942570i \(-0.391598\pi\)
0.334010 + 0.942570i \(0.391598\pi\)
\(398\) 1.92255e91i 1.94075i
\(399\) −4.94752e90 + 9.19964e90i −0.457442 + 0.850588i
\(400\) 4.19991e91 3.55746
\(401\) 2.06431e91i 1.60222i 0.598520 + 0.801108i \(0.295756\pi\)
−0.598520 + 0.801108i \(0.704244\pi\)
\(402\) −7.03331e90 3.78248e90i −0.500320 0.269069i
\(403\) 2.51674e91 1.64120
\(404\) 1.88537e91i 1.12732i
\(405\) −3.64714e90 1.55447e90i −0.199998 0.0852427i
\(406\) 6.85441e90 0.344794
\(407\) 4.57653e90i 0.211219i
\(408\) −2.44227e91 + 4.54126e91i −1.03440 + 1.92340i
\(409\) −1.88971e91 −0.734650 −0.367325 0.930093i \(-0.619726\pi\)
−0.367325 + 0.930093i \(0.619726\pi\)
\(410\) 1.74539e91i 0.622956i
\(411\) 3.97258e91 + 2.13643e91i 1.30199 + 0.700205i
\(412\) −1.78403e91 −0.537032
\(413\) 2.44328e91i 0.675648i
\(414\) −6.33250e91 9.58271e91i −1.60903 2.43487i
\(415\) 1.69413e91 0.395607
\(416\) 2.84272e92i 6.10193i
\(417\) 1.58539e91 2.94794e91i 0.312876 0.581777i
\(418\) −7.28803e91 −1.32264
\(419\) 1.15475e92i 1.92751i 0.266789 + 0.963755i \(0.414037\pi\)
−0.266789 + 0.963755i \(0.585963\pi\)
\(420\) 2.29036e91 + 1.23174e91i 0.351705 + 0.189145i
\(421\) 4.31281e91 0.609379 0.304689 0.952452i \(-0.401447\pi\)
0.304689 + 0.952452i \(0.401447\pi\)
\(422\) 2.20146e92i 2.86270i
\(423\) −9.96678e90 + 6.58630e90i −0.119300 + 0.0788367i
\(424\) 7.64281e91 0.842264
\(425\) 6.12567e91i 0.621643i
\(426\) 1.12380e92 2.08964e92i 1.05040 1.95315i
\(427\) 2.08345e91 0.179394
\(428\) 1.11794e92i 0.886925i
\(429\) 9.05798e91 + 4.87134e91i 0.662256 + 0.356158i
\(430\) −3.71124e91 −0.250106
\(431\) 2.22171e92i 1.38033i −0.723652 0.690165i \(-0.757538\pi\)
0.723652 0.690165i \(-0.242462\pi\)
\(432\) −6.49109e92 + 5.89205e91i −3.71866 + 0.337548i
\(433\) 2.53676e92 1.34030 0.670151 0.742225i \(-0.266229\pi\)
0.670151 + 0.742225i \(0.266229\pi\)
\(434\) 2.77137e92i 1.35068i
\(435\) 6.07991e90 1.13053e91i 0.0273384 0.0508342i
\(436\) 4.72590e92 1.96091
\(437\) 5.66735e92i 2.17035i
\(438\) −4.45671e92 2.39680e92i −1.57551 0.847300i
\(439\) 2.94727e91 0.0961970 0.0480985 0.998843i \(-0.484684\pi\)
0.0480985 + 0.998843i \(0.484684\pi\)
\(440\) 1.15041e92i 0.346745i
\(441\) 1.08550e92 + 1.64264e92i 0.302189 + 0.457290i
\(442\) −7.73510e92 −1.98924
\(443\) 1.72364e92i 0.409558i 0.978808 + 0.204779i \(0.0656475\pi\)
−0.978808 + 0.204779i \(0.934352\pi\)
\(444\) −2.61261e92 + 4.85800e92i −0.573680 + 1.06673i
\(445\) −3.34872e91 −0.0679639
\(446\) 6.64955e92i 1.24759i
\(447\) 1.67780e92 + 9.02310e91i 0.291056 + 0.156528i
\(448\) 1.56570e93 2.51176
\(449\) 1.03310e93i 1.53292i −0.642290 0.766462i \(-0.722015\pi\)
0.642290 0.766462i \(-0.277985\pi\)
\(450\) −1.11873e93 + 7.39288e92i −1.53564 + 1.01479i
\(451\) −5.56463e92 −0.706737
\(452\) 8.41931e92i 0.989536i
\(453\) −1.51846e92 + 2.82350e92i −0.165184 + 0.307150i
\(454\) 8.78742e92 0.884925
\(455\) 2.47345e92i 0.230624i
\(456\) 4.90503e93 + 2.63790e93i 4.23518 + 2.27766i
\(457\) −2.36615e93 −1.89224 −0.946118 0.323822i \(-0.895032\pi\)
−0.946118 + 0.323822i \(0.895032\pi\)
\(458\) 1.52396e93i 1.12897i
\(459\) −8.59369e91 9.46741e92i −0.0589842 0.649811i
\(460\) 1.41095e93 0.897405
\(461\) 2.35999e93i 1.39116i 0.718449 + 0.695580i \(0.244853\pi\)
−0.718449 + 0.695580i \(0.755147\pi\)
\(462\) 5.36419e92 9.97442e92i 0.293113 0.545028i
\(463\) 8.48600e92 0.429901 0.214950 0.976625i \(-0.431041\pi\)
0.214950 + 0.976625i \(0.431041\pi\)
\(464\) 2.11031e93i 0.991325i
\(465\) −4.57093e92 2.45822e92i −0.199137 0.107095i
\(466\) −1.11127e93 −0.449068
\(467\) 6.86184e92i 0.257247i 0.991694 + 0.128623i \(0.0410558\pi\)
−0.991694 + 0.128623i \(0.958944\pi\)
\(468\) −6.83416e93 1.03419e94i −2.37728 3.59744i
\(469\) −6.12316e92 −0.197663
\(470\) 2.00456e92i 0.0600613i
\(471\) −1.65582e93 + 3.07890e93i −0.460554 + 0.856376i
\(472\) −1.30270e94 −3.36414
\(473\) 1.18321e93i 0.283742i
\(474\) 6.84132e93 + 3.67922e93i 1.52369 + 0.819435i
\(475\) 6.61635e93 1.36881
\(476\) 6.23565e93i 1.19850i
\(477\) −1.17556e93 + 7.76839e92i −0.209943 + 0.138735i
\(478\) 1.23454e94 2.04894
\(479\) 6.99075e93i 1.07840i −0.842177 0.539201i \(-0.818726\pi\)
0.842177 0.539201i \(-0.181274\pi\)
\(480\) 2.77662e93 5.16298e93i 0.398175 0.740384i
\(481\) −5.24636e93 −0.699488
\(482\) 4.09218e93i 0.507351i
\(483\) −7.75636e93 4.17133e93i −0.894352 0.480978i
\(484\) −1.96920e94 −2.11204
\(485\) 2.66912e93i 0.266322i
\(486\) 1.62532e94 1.29954e94i 1.50893 1.20648i
\(487\) 8.04645e93 0.695170 0.347585 0.937649i \(-0.387002\pi\)
0.347585 + 0.937649i \(0.387002\pi\)
\(488\) 1.11085e94i 0.893224i
\(489\) 1.06468e94 1.97971e94i 0.796907 1.48180i
\(490\) −3.30375e93 −0.230221
\(491\) 2.13489e94i 1.38524i −0.721305 0.692618i \(-0.756457\pi\)
0.721305 0.692618i \(-0.243543\pi\)
\(492\) 5.90687e94 + 3.17668e94i 3.56926 + 1.91953i
\(493\) 3.07793e93 0.173227
\(494\) 8.35471e94i 4.38014i
\(495\) −1.16931e93 1.76948e93i −0.0571149 0.0864296i
\(496\) −8.53236e94 −3.88339
\(497\) 1.81923e94i 0.771641i
\(498\) −4.21182e94 + 7.83164e94i −1.66511 + 3.09618i
\(499\) 1.02687e94 0.378440 0.189220 0.981935i \(-0.439404\pi\)
0.189220 + 0.981935i \(0.439404\pi\)
\(500\) 3.37616e94i 1.16004i
\(501\) 1.17186e94 + 6.30221e93i 0.375453 + 0.201917i
\(502\) 5.17361e94 1.54584
\(503\) 8.86184e93i 0.246970i −0.992346 0.123485i \(-0.960593\pi\)
0.992346 0.123485i \(-0.0394071\pi\)
\(504\) −7.22048e94 + 4.77147e94i −1.87714 + 1.24046i
\(505\) −3.69797e93 −0.0896944
\(506\) 6.14465e94i 1.39069i
\(507\) 3.34181e94 6.21392e94i 0.705835 1.31246i
\(508\) 7.55985e94 1.49033
\(509\) 2.07219e94i 0.381335i 0.981655 + 0.190668i \(0.0610653\pi\)
−0.981655 + 0.190668i \(0.938935\pi\)
\(510\) 1.40486e94 + 7.55525e93i 0.241366 + 0.129805i
\(511\) −3.87999e94 −0.622443
\(512\) 1.29528e95i 1.94050i
\(513\) −1.02258e95 + 9.28208e93i −1.43083 + 0.129879i
\(514\) 1.25484e95 1.64013
\(515\) 3.49921e93i 0.0427284i
\(516\) 6.75461e94 1.25598e95i 0.770657 1.43299i
\(517\) −6.39093e93 −0.0681389
\(518\) 5.77716e94i 0.575669i
\(519\) −2.27991e94 1.22612e94i −0.212354 0.114203i
\(520\) 1.31879e95 1.14831
\(521\) 2.19735e93i 0.0178887i −0.999960 0.00894437i \(-0.997153\pi\)
0.999960 0.00894437i \(-0.00284712\pi\)
\(522\) 3.71466e94 + 5.62124e94i 0.282782 + 0.427922i
\(523\) −1.60824e95 −1.14497 −0.572483 0.819916i \(-0.694020\pi\)
−0.572483 + 0.819916i \(0.694020\pi\)
\(524\) 9.78111e94i 0.651318i
\(525\) −4.86982e94 + 9.05517e94i −0.303345 + 0.564054i
\(526\) −4.94348e95 −2.88092
\(527\) 1.24447e95i 0.678596i
\(528\) −3.07088e95 1.65150e95i −1.56702 0.842737i
\(529\) −2.68437e95 −1.28202
\(530\) 2.36434e94i 0.105695i
\(531\) 2.00371e95 1.32410e95i 0.838545 0.554131i
\(532\) 6.73515e95 2.63900
\(533\) 6.37907e95i 2.34048i
\(534\) 8.32532e94 1.54805e95i 0.286060 0.531912i
\(535\) −2.19273e94 −0.0705673
\(536\) 3.26472e95i 0.984190i
\(537\) −2.91248e95 1.56632e95i −0.822551 0.442363i
\(538\) 9.16237e95 2.42453
\(539\) 1.05330e95i 0.261183i
\(540\) 2.31088e94 + 2.54583e95i 0.0537027 + 0.591626i
\(541\) 6.59796e94 0.143716 0.0718580 0.997415i \(-0.477107\pi\)
0.0718580 + 0.997415i \(0.477107\pi\)
\(542\) 1.11128e96i 2.26908i
\(543\) 3.20907e95 5.96708e95i 0.614306 1.14227i
\(544\) 1.40565e96 2.52300
\(545\) 9.26940e94i 0.156018i
\(546\) −1.14343e96 6.14930e95i −1.80496 0.970696i
\(547\) 1.26128e95 0.186748 0.0933742 0.995631i \(-0.470235\pi\)
0.0933742 + 0.995631i \(0.470235\pi\)
\(548\) 2.90836e96i 4.03951i
\(549\) 1.12910e95 + 1.70862e95i 0.147130 + 0.222645i
\(550\) −7.17358e95 −0.877085
\(551\) 3.32448e95i 0.381433i
\(552\) −2.22405e96 + 4.13551e96i −2.39485 + 4.45309i
\(553\) 5.95602e95 0.601972
\(554\) 9.71090e95i 0.921335i
\(555\) 9.52849e94 + 5.12437e94i 0.0848730 + 0.0456443i
\(556\) −2.15821e96 −1.80500
\(557\) 8.69547e94i 0.0682906i 0.999417 + 0.0341453i \(0.0108709\pi\)
−0.999417 + 0.0341453i \(0.989129\pi\)
\(558\) 2.27277e96 1.50191e96i 1.67633 1.10776i
\(559\) 1.35639e96 0.939661
\(560\) 8.38562e95i 0.545700i
\(561\) 2.40876e95 4.47895e95i 0.147263 0.273827i
\(562\) −2.56570e96 −1.47379
\(563\) 4.14614e95i 0.223795i 0.993720 + 0.111897i \(0.0356928\pi\)
−0.993720 + 0.111897i \(0.964307\pi\)
\(564\) 6.78398e95 + 3.64839e95i 0.344125 + 0.185068i
\(565\) −1.65137e95 −0.0787314
\(566\) 6.59326e96i 2.95478i
\(567\) 6.25611e95 1.46782e96i 0.263571 0.618396i
\(568\) −9.69973e96 −3.84209
\(569\) 3.82499e96i 1.42463i 0.701861 + 0.712314i \(0.252353\pi\)
−0.701861 + 0.712314i \(0.747647\pi\)
\(570\) 8.16045e95 1.51739e96i 0.285821 0.531469i
\(571\) 5.46607e96 1.80057 0.900287 0.435296i \(-0.143356\pi\)
0.900287 + 0.435296i \(0.143356\pi\)
\(572\) 6.63144e96i 2.05469i
\(573\) 1.18945e96 + 6.39681e95i 0.346685 + 0.186445i
\(574\) 7.02448e96 1.92618
\(575\) 5.57835e96i 1.43923i
\(576\) 8.48510e96 + 1.28402e97i 2.06001 + 3.11733i
\(577\) −1.64095e96 −0.374923 −0.187462 0.982272i \(-0.560026\pi\)
−0.187462 + 0.982272i \(0.560026\pi\)
\(578\) 5.15925e96i 1.10946i
\(579\) 2.20279e96 4.09597e96i 0.445886 0.829101i
\(580\) −8.27669e95 −0.157716
\(581\) 6.81819e96i 1.22322i
\(582\) −1.23388e97 6.63575e96i −2.08434 1.12095i
\(583\) −7.53795e95 −0.119910
\(584\) 2.06872e97i 3.09922i
\(585\) −2.02846e96 + 1.34045e96i −0.286227 + 0.189146i
\(586\) 3.08368e96 0.409876
\(587\) 5.92660e96i 0.742116i −0.928610 0.371058i \(-0.878995\pi\)
0.928610 0.371058i \(-0.121005\pi\)
\(588\) 6.01296e96 1.11808e97i 0.709385 1.31906i
\(589\) −1.34415e97 −1.49421
\(590\) 4.02995e96i 0.422162i
\(591\) −1.48441e97 7.98308e96i −1.46552 0.788149i
\(592\) 1.77864e97 1.65512
\(593\) 2.21183e97i 1.94016i 0.242786 + 0.970080i \(0.421939\pi\)
−0.242786 + 0.970080i \(0.578061\pi\)
\(594\) 1.10870e97 1.00638e96i 0.916828 0.0832217i
\(595\) 1.22306e96 0.0953575
\(596\) 1.22833e97i 0.903018i
\(597\) 6.86318e96 1.27617e97i 0.475799 0.884723i
\(598\) −7.04398e97 −4.60550
\(599\) 2.52028e97i 1.55421i 0.629371 + 0.777105i \(0.283313\pi\)
−0.629371 + 0.777105i \(0.716687\pi\)
\(600\) 4.82800e97 + 2.59647e97i 2.80849 + 1.51039i
\(601\) 1.48371e97 0.814220 0.407110 0.913379i \(-0.366537\pi\)
0.407110 + 0.913379i \(0.366537\pi\)
\(602\) 1.49362e97i 0.773328i
\(603\) −3.31837e96 5.02155e96i −0.162113 0.245319i
\(604\) 2.06711e97 0.952951
\(605\) 3.86239e96i 0.168042i
\(606\) 9.19359e96 1.70950e97i 0.377523 0.701983i
\(607\) 2.49382e97 0.966632 0.483316 0.875446i \(-0.339432\pi\)
0.483316 + 0.875446i \(0.339432\pi\)
\(608\) 1.51825e98i 5.55544i
\(609\) 4.54990e96 + 2.44691e96i 0.157180 + 0.0845305i
\(610\) −3.43645e96 −0.112090
\(611\) 7.32630e96i 0.225654i
\(612\) −5.11380e97 + 3.37933e97i −1.48745 + 0.982948i
\(613\) −6.24289e97 −1.71502 −0.857510 0.514467i \(-0.827990\pi\)
−0.857510 + 0.514467i \(0.827990\pi\)
\(614\) 3.26824e97i 0.848050i
\(615\) 6.23076e96 1.15857e97i 0.152726 0.283985i
\(616\) −4.62993e97 −1.07214
\(617\) 2.78657e97i 0.609662i 0.952406 + 0.304831i \(0.0985999\pi\)
−0.952406 + 0.304831i \(0.901400\pi\)
\(618\) −1.61761e97 8.69944e96i −0.334409 0.179844i
\(619\) 2.81197e97 0.549337 0.274668 0.961539i \(-0.411432\pi\)
0.274668 + 0.961539i \(0.411432\pi\)
\(620\) 3.34642e97i 0.617834i
\(621\) −7.82586e96 8.62151e97i −0.136561 1.50445i
\(622\) 1.07762e98 1.77747
\(623\) 1.34772e97i 0.210145i
\(624\) −1.89322e98 + 3.52033e98i −2.79087 + 5.18947i
\(625\) 6.17333e97 0.860437
\(626\) 6.65125e97i 0.876600i
\(627\) −4.83773e97 2.60171e97i −0.602945 0.324261i
\(628\) 2.25410e98 2.65696
\(629\) 2.59420e97i 0.289221i
\(630\) 1.47608e97 + 2.23369e97i 0.155664 + 0.235561i
\(631\) −1.71915e98 −1.71509 −0.857544 0.514410i \(-0.828011\pi\)
−0.857544 + 0.514410i \(0.828011\pi\)
\(632\) 3.17561e98i 2.99729i
\(633\) 7.85885e97 1.46131e98i 0.701826 1.30501i
\(634\) 1.18106e98 0.998038
\(635\) 1.48279e97i 0.118577i
\(636\) 8.00154e97 + 4.30319e97i 0.605584 + 0.325680i
\(637\) 1.20746e98 0.864953
\(638\) 3.60447e97i 0.244409i
\(639\) 1.49194e98 9.85910e97i 0.957680 0.632859i
\(640\) −1.19916e98 −0.728748
\(641\) 7.69412e97i 0.442719i 0.975192 + 0.221359i \(0.0710494\pi\)
−0.975192 + 0.221359i \(0.928951\pi\)
\(642\) 5.45139e97 1.01366e98i 0.297017 0.552287i
\(643\) −7.45449e97 −0.384622 −0.192311 0.981334i \(-0.561598\pi\)
−0.192311 + 0.981334i \(0.561598\pi\)
\(644\) 5.67851e98i 2.77478i
\(645\) −2.46349e97 1.32485e97i −0.114015 0.0613165i
\(646\) 4.13120e98 1.81108
\(647\) 1.69399e98i 0.703493i 0.936095 + 0.351747i \(0.114412\pi\)
−0.936095 + 0.351747i \(0.885588\pi\)
\(648\) −7.82608e98 3.33561e98i −3.07907 1.31235i
\(649\) 1.28482e98 0.478938
\(650\) 8.22350e98i 2.90462i
\(651\) 9.89333e97 1.83961e98i 0.331137 0.615731i
\(652\) −1.44936e99 −4.59739
\(653\) 5.57852e98i 1.67709i −0.544830 0.838547i \(-0.683406\pi\)
0.544830 0.838547i \(-0.316594\pi\)
\(654\) 4.28506e98 + 2.30448e98i 1.22106 + 0.656677i
\(655\) 1.91847e97 0.0518215
\(656\) 2.16266e99i 5.53802i
\(657\) −2.10271e98 3.18195e98i −0.510495 0.772511i
\(658\) 8.06754e97 0.185710
\(659\) 8.39543e98i 1.83254i 0.400561 + 0.916270i \(0.368815\pi\)
−0.400561 + 0.916270i \(0.631185\pi\)
\(660\) −6.47725e97 + 1.20441e98i −0.134077 + 0.249308i
\(661\) −8.60076e98 −1.68844 −0.844220 0.535997i \(-0.819936\pi\)
−0.844220 + 0.535997i \(0.819936\pi\)
\(662\) 9.75710e98i 1.81673i
\(663\) −5.13449e98 2.76130e98i −0.906826 0.487686i
\(664\) 3.63530e99 6.09056
\(665\) 1.32103e98i 0.209970i
\(666\) −4.73779e98 + 3.13085e98i −0.714460 + 0.472133i
\(667\) 2.80292e98 0.401058
\(668\) 8.57931e98i 1.16487i
\(669\) 2.37378e98 4.41391e98i 0.305863 0.568735i
\(670\) 1.00996e98 0.123505
\(671\) 1.09561e98i 0.127165i
\(672\) 2.07789e99 + 1.11748e99i 2.28927 + 1.23116i
\(673\) 3.13253e98 0.327619 0.163809 0.986492i \(-0.447622\pi\)
0.163809 + 0.986492i \(0.447622\pi\)
\(674\) 6.30701e98i 0.626220i
\(675\) −1.00652e99 + 9.13631e97i −0.948833 + 0.0861269i
\(676\) −4.54927e99 −4.07199
\(677\) 6.53853e98i 0.555746i 0.960618 + 0.277873i \(0.0896295\pi\)
−0.960618 + 0.277873i \(0.910370\pi\)
\(678\) 4.10549e98 7.63394e98i 0.331380 0.616183i
\(679\) −1.07421e99 −0.823469
\(680\) 6.52108e98i 0.474797i
\(681\) 5.83301e98 + 3.13696e98i 0.403407 + 0.216950i
\(682\) 1.45735e99 0.957441
\(683\) 2.94286e98i 0.183673i 0.995774 + 0.0918364i \(0.0292737\pi\)
−0.995774 + 0.0918364i \(0.970726\pi\)
\(684\) 3.65002e99 + 5.52343e99i 2.16437 + 3.27526i
\(685\) −5.70447e98 −0.321400
\(686\) 3.75543e99i 2.01055i
\(687\) −5.44030e98 + 1.01159e99i −0.276782 + 0.514660i
\(688\) −4.59850e99 −2.22341
\(689\) 8.64120e98i 0.397101i
\(690\) 1.27934e99 + 6.88021e98i 0.558813 + 0.300527i
\(691\) 7.70743e98 0.320021 0.160010 0.987115i \(-0.448847\pi\)
0.160010 + 0.987115i \(0.448847\pi\)
\(692\) 1.66914e99i 0.658841i
\(693\) 7.12141e98 4.70601e98i 0.267241 0.176599i
\(694\) −4.69872e99 −1.67648
\(695\) 4.23313e98i 0.143613i
\(696\) 1.30464e99 2.42590e99i 0.420887 0.782617i
\(697\) 3.15430e99 0.967733
\(698\) 8.72397e99i 2.54551i
\(699\) −7.37651e98 3.96705e98i −0.204715 0.110095i
\(700\) 6.62937e99 1.75001
\(701\) 2.68663e99i 0.674648i 0.941389 + 0.337324i \(0.109522\pi\)
−0.941389 + 0.337324i \(0.890478\pi\)
\(702\) −1.15367e99 1.27097e100i −0.275603 3.03624i
\(703\) 2.80200e99 0.636842
\(704\) 8.23340e99i 1.78048i
\(705\) 7.15596e97 1.33061e98i 0.0147248 0.0273799i
\(706\) −3.84589e99 −0.753065
\(707\) 1.48828e99i 0.277335i
\(708\) −1.36384e100 7.33467e99i −2.41880 1.30082i
\(709\) 4.51807e99 0.762667 0.381333 0.924438i \(-0.375465\pi\)
0.381333 + 0.924438i \(0.375465\pi\)
\(710\) 3.00065e99i 0.482140i
\(711\) 3.22778e99 + 4.88447e99i 0.493706 + 0.747105i
\(712\) −7.18573e99 −1.04634
\(713\) 1.13327e100i 1.57109i
\(714\) −3.04068e99 + 5.65397e99i −0.401359 + 0.746305i
\(715\) −1.30069e99 −0.163479
\(716\) 2.13225e100i 2.55201i
\(717\) 8.19479e99 + 4.40711e99i 0.934044 + 0.502324i
\(718\) 1.32413e100 1.43739
\(719\) 9.22457e99i 0.953751i 0.878971 + 0.476876i \(0.158231\pi\)
−0.878971 + 0.476876i \(0.841769\pi\)
\(720\) 6.87697e99 4.54447e99i 0.677267 0.447555i
\(721\) −1.40829e99 −0.132116
\(722\) 2.30040e100i 2.05590i
\(723\) −1.46084e99 + 2.71636e99i −0.124384 + 0.231284i
\(724\) −4.36856e100 −3.54396
\(725\) 3.27227e99i 0.252941i
\(726\) −1.78551e100 9.60236e99i −1.31516 0.707288i
\(727\) 2.22427e100 1.56129 0.780644 0.624976i \(-0.214891\pi\)
0.780644 + 0.624976i \(0.214891\pi\)
\(728\) 5.30757e100i 3.55057i
\(729\) 1.54279e100 2.82409e99i 0.983656 0.180059i
\(730\) 6.39967e99 0.388918
\(731\) 6.70702e99i 0.388527i
\(732\) 6.25448e99 1.16299e100i 0.345385 0.642225i
\(733\) −3.64397e100 −1.91839 −0.959193 0.282752i \(-0.908753\pi\)
−0.959193 + 0.282752i \(0.908753\pi\)
\(734\) 1.41959e100i 0.712527i
\(735\) −2.19300e99 1.17938e99i −0.104950 0.0564415i
\(736\) 1.28006e101 5.84127
\(737\) 3.21993e99i 0.140115i
\(738\) 3.80682e100 + 5.76071e100i 1.57976 + 2.39058i
\(739\) 5.10703e99 0.202122 0.101061 0.994880i \(-0.467776\pi\)
0.101061 + 0.994880i \(0.467776\pi\)
\(740\) 6.97590e99i 0.263324i
\(741\) −2.98249e100 + 5.54578e100i −1.07385 + 1.99676i
\(742\) 9.51548e99 0.326809
\(743\) 2.04411e100i 0.669723i −0.942267 0.334861i \(-0.891311\pi\)
0.942267 0.334861i \(-0.108689\pi\)
\(744\) −9.80837e100 5.27489e100i −3.06580 1.64877i
\(745\) −2.40925e99 −0.0718477
\(746\) 1.27461e101i 3.62675i
\(747\) −5.59153e100 + 3.69503e100i −1.51813 + 1.00322i
\(748\) −3.27908e100 −0.849565
\(749\) 8.82484e99i 0.218194i
\(750\) 1.64631e100 3.06122e100i 0.388479 0.722355i
\(751\) −2.05511e100 −0.462848 −0.231424 0.972853i \(-0.574338\pi\)
−0.231424 + 0.972853i \(0.574338\pi\)
\(752\) 2.48380e100i 0.533939i
\(753\) 3.43420e100 + 1.84689e100i 0.704695 + 0.378981i
\(754\) 4.13202e100 0.809404
\(755\) 4.05443e99i 0.0758206i
\(756\) −1.02459e101 + 9.30034e99i −1.82931 + 0.166049i
\(757\) −7.98590e100 −1.36134 −0.680672 0.732588i \(-0.738312\pi\)
−0.680672 + 0.732588i \(0.738312\pi\)
\(758\) 1.94566e101i 3.16697i
\(759\) 2.19354e100 4.07877e100i 0.340944 0.633967i
\(760\) −7.04344e100 −1.04546
\(761\) 9.06307e100i 1.28473i 0.766398 + 0.642366i \(0.222047\pi\)
−0.766398 + 0.642366i \(0.777953\pi\)
\(762\) 6.85465e100 + 3.68640e100i 0.928029 + 0.499089i
\(763\) 3.73055e100 0.482407
\(764\) 8.70809e100i 1.07561i
\(765\) 6.62822e99 + 1.00302e100i 0.0782072 + 0.118348i
\(766\) 1.93289e101 2.17871
\(767\) 1.47287e101i 1.58609i
\(768\) 1.26113e101 2.34499e101i 1.29752 2.41268i
\(769\) 4.51479e100 0.443829 0.221915 0.975066i \(-0.428769\pi\)
0.221915 + 0.975066i \(0.428769\pi\)
\(770\) 1.43229e100i 0.134541i
\(771\) 8.32950e100 + 4.47956e100i 0.747680 + 0.402098i
\(772\) −2.99870e101 −2.57234
\(773\) 1.64071e101i 1.34509i −0.740057 0.672544i \(-0.765202\pi\)
0.740057 0.672544i \(-0.234798\pi\)
\(774\) 1.22491e101 8.09449e100i 0.959774 0.634243i
\(775\) −1.32304e101 −0.990864
\(776\) 5.72744e101i 4.10015i
\(777\) −2.06235e100 + 3.83483e100i −0.141132 + 0.262428i
\(778\) 1.99771e101 1.30691
\(779\) 3.40697e101i 2.13087i
\(780\) 1.38069e101 + 7.42526e100i 0.825627 + 0.444018i
\(781\) 9.56664e100 0.546982
\(782\) 3.48308e101i 1.90426i
\(783\) 4.59067e99 + 5.05740e100i 0.0240002 + 0.264403i
\(784\) −4.09358e101 −2.04664
\(785\) 4.42119e100i 0.211398i
\(786\) −4.76955e100 + 8.86871e100i −0.218116 + 0.405575i
\(787\) 2.67770e101 1.17124 0.585621 0.810585i \(-0.300851\pi\)
0.585621 + 0.810585i \(0.300851\pi\)
\(788\) 1.08675e102i 4.54687i
\(789\) −3.28144e101 1.76474e101i −1.31332 0.706295i
\(790\) −9.82387e100 −0.376127
\(791\) 6.64607e100i 0.243438i
\(792\) −2.50913e101 3.79697e101i −0.879310 1.33062i
\(793\) 1.25596e101 0.421128
\(794\) 4.02259e101i 1.29059i
\(795\) 8.44029e99 1.56943e100i 0.0259124 0.0481827i
\(796\) −9.34297e101 −2.74491
\(797\) 1.59526e101i 0.448528i −0.974528 0.224264i \(-0.928002\pi\)
0.974528 0.224264i \(-0.0719977\pi\)
\(798\) 6.10688e101 + 3.28425e101i 1.64330 + 0.883761i
\(799\) 3.62268e100 0.0933023
\(800\) 1.49441e102i 3.68400i
\(801\) 1.10525e101 7.30380e100i 0.260810 0.172350i
\(802\) 1.37032e102 3.09542
\(803\) 2.04034e101i 0.441222i
\(804\) −1.83816e101 + 3.41796e101i −0.380559 + 0.707629i
\(805\) 1.11378e101 0.220773
\(806\) 1.67065e102i 3.17073i
\(807\) 6.08190e101 + 3.27081e101i 1.10526 + 0.594404i
\(808\) −7.93516e101 −1.38089
\(809\) 1.02101e102i 1.70150i 0.525569 + 0.850751i \(0.323853\pi\)
−0.525569 + 0.850751i \(0.676147\pi\)
\(810\) −1.03189e101 + 2.42103e101i −0.164686 + 0.386389i
\(811\) −5.68597e101 −0.869109 −0.434555 0.900645i \(-0.643094\pi\)
−0.434555 + 0.900645i \(0.643094\pi\)
\(812\) 3.33103e101i 0.487660i
\(813\) −3.96710e101 + 7.37661e101i −0.556294 + 1.03440i
\(814\) −3.03798e101 −0.408066
\(815\) 2.84279e101i 0.365787i
\(816\) 1.74072e102 + 9.36150e101i 2.14572 + 1.15396i
\(817\) −7.24427e101 −0.855505
\(818\) 1.25442e102i 1.41932i
\(819\) −5.39478e101 8.16370e101i −0.584840 0.885015i
\(820\) −8.48204e101 −0.881080
\(821\) 9.76445e101i 0.971935i −0.873977 0.485968i \(-0.838467\pi\)
0.873977 0.485968i \(-0.161533\pi\)
\(822\) 1.41820e102 2.63707e102i 1.35277 2.51540i
\(823\) 1.73425e101 0.158532 0.0792659 0.996854i \(-0.474742\pi\)
0.0792659 + 0.996854i \(0.474742\pi\)
\(824\) 7.50865e101i 0.657824i
\(825\) −4.76176e101 2.56085e101i −0.399833 0.215028i
\(826\) −1.62189e102 −1.30533
\(827\) 1.64045e102i 1.26553i 0.774345 + 0.632763i \(0.218079\pi\)
−0.774345 + 0.632763i \(0.781921\pi\)
\(828\) −4.65689e102 + 3.07739e102i −3.44377 + 2.27573i
\(829\) −9.95257e101 −0.705548 −0.352774 0.935709i \(-0.614762\pi\)
−0.352774 + 0.935709i \(0.614762\pi\)
\(830\) 1.12459e102i 0.764298i
\(831\) −3.46663e101 + 6.44601e101i −0.225877 + 0.420006i
\(832\) 9.43844e102 5.89636
\(833\) 5.97059e101i 0.357637i
\(834\) −1.95689e102 1.05241e102i −1.12397 0.604465i
\(835\) −1.68275e101 −0.0926815
\(836\) 3.54175e102i 1.87067i
\(837\) 2.04480e102 1.85610e101i 1.03576 0.0940176i
\(838\) 7.66542e102 3.72387
\(839\) 2.90931e102i 1.35557i 0.735262 + 0.677783i \(0.237059\pi\)
−0.735262 + 0.677783i \(0.762941\pi\)
\(840\) 5.18417e101 9.63968e101i 0.231688 0.430812i
\(841\) 2.16828e102 0.929515
\(842\) 2.86292e102i 1.17730i
\(843\) −1.70309e102 9.15914e101i −0.671851 0.361318i
\(844\) −1.06984e103 −4.04886
\(845\) 8.92295e101i 0.323984i
\(846\) 4.37210e101 + 6.61612e101i 0.152310 + 0.230484i
\(847\) −1.55445e102 −0.519587
\(848\) 2.92958e102i 0.939617i
\(849\) 2.35368e102 4.37655e102i 0.724401 1.34698i
\(850\) 4.06632e102 1.20099
\(851\) 2.36241e102i 0.669608i
\(852\) −1.01550e103 5.46131e102i −2.76245 1.48563i
\(853\) 2.75552e102 0.719428 0.359714 0.933063i \(-0.382874\pi\)
0.359714 + 0.933063i \(0.382874\pi\)
\(854\) 1.38303e102i 0.346582i
\(855\) 1.08337e102 7.15917e101i 0.260592 0.172206i
\(856\) −4.70520e102 −1.08642
\(857\) 6.19181e102i 1.37243i 0.727401 + 0.686213i \(0.240728\pi\)
−0.727401 + 0.686213i \(0.759272\pi\)
\(858\) 3.23368e102 6.01284e102i 0.688084 1.27945i
\(859\) 3.27450e102 0.668935 0.334468 0.942407i \(-0.391443\pi\)
0.334468 + 0.942407i \(0.391443\pi\)
\(860\) 1.80355e102i 0.353738i
\(861\) 4.66279e102 + 2.50762e102i 0.878082 + 0.472228i
\(862\) −1.47481e103 −2.66675
\(863\) 1.15167e102i 0.199964i 0.994989 + 0.0999820i \(0.0318785\pi\)
−0.994989 + 0.0999820i \(0.968121\pi\)
\(864\) 2.09651e102 + 2.30966e103i 0.349555 + 3.85094i
\(865\) 3.27387e101 0.0524200
\(866\) 1.68394e103i 2.58941i
\(867\) 1.84177e102 3.42466e102i 0.271998 0.505766i
\(868\) −1.34680e103 −1.91034
\(869\) 3.13204e102i 0.426712i
\(870\) −7.50462e101 4.03595e101i −0.0982098 0.0528167i
\(871\) −3.69120e102 −0.464015
\(872\) 1.98904e103i 2.40197i
\(873\) −5.82154e102 8.80950e102i −0.675366 1.02200i
\(874\) 3.76208e103 4.19303
\(875\) 2.66508e102i 0.285384i
\(876\) −1.16477e103 + 2.16582e103i −1.19838 + 2.22833i
\(877\) 5.90447e102 0.583707 0.291854 0.956463i \(-0.405728\pi\)
0.291854 + 0.956463i \(0.405728\pi\)
\(878\) 1.95645e102i 0.185849i
\(879\) 2.04692e102 + 1.10082e102i 0.186849 + 0.100486i
\(880\) 4.40967e102 0.386823
\(881\) 1.08160e103i 0.911824i −0.890025 0.455912i \(-0.849313\pi\)
0.890025 0.455912i \(-0.150687\pi\)
\(882\) 1.09041e103 7.20572e102i 0.883467 0.583817i
\(883\) −2.86872e102 −0.223390 −0.111695 0.993743i \(-0.535628\pi\)
−0.111695 + 0.993743i \(0.535628\pi\)
\(884\) 3.75901e103i 2.81348i
\(885\) −1.43862e102 + 2.67504e102i −0.103498 + 0.192449i
\(886\) 1.14418e103 0.791250
\(887\) 2.06382e103i 1.37197i 0.727614 + 0.685987i \(0.240629\pi\)
−0.727614 + 0.685987i \(0.759371\pi\)
\(888\) 2.04464e103 + 1.09960e103i 1.30666 + 0.702715i
\(889\) 5.96763e102 0.366640
\(890\) 2.22294e102i 0.131304i
\(891\) 7.71870e102 + 3.28984e102i 0.438354 + 0.186834i
\(892\) −3.23147e103 −1.76453
\(893\) 3.91287e102i 0.205444i
\(894\) 5.98969e102 1.11375e103i 0.302406 0.562308i
\(895\) 4.18221e102 0.203048
\(896\) 4.82612e103i 2.25329i
\(897\) −4.67573e103 2.51459e103i −2.09949 1.12910i
\(898\) −6.85790e103 −2.96155
\(899\) 6.64782e102i 0.276115i
\(900\) 3.59270e103 + 5.43669e103i 1.43527 + 2.17193i
\(901\) 4.27286e102 0.164192
\(902\) 3.69390e103i 1.36539i
\(903\) 5.33198e102 9.91453e102i 0.189591 0.352534i
\(904\) −3.54353e103 −1.21211
\(905\) 8.56851e102i 0.281971i
\(906\) 1.87428e103 + 1.00798e103i 0.593401 + 0.319128i
\(907\) −3.06332e103 −0.933120 −0.466560 0.884490i \(-0.654507\pi\)
−0.466560 + 0.884490i \(0.654507\pi\)
\(908\) 4.27040e103i 1.25160i
\(909\) 1.22053e103 8.06554e102i 0.344200 0.227456i
\(910\) 1.64192e103 0.445557
\(911\) 1.38756e103i 0.362334i −0.983452 0.181167i \(-0.942013\pi\)
0.983452 0.181167i \(-0.0579874\pi\)
\(912\) 1.01114e104 1.88016e104i 2.54092 4.72471i
\(913\) −3.58542e103 −0.867087
\(914\) 1.57069e104i 3.65573i
\(915\) −2.28109e102 1.22676e102i −0.0510979 0.0274802i
\(916\) 7.40598e103 1.59677
\(917\) 7.72105e102i 0.160232i
\(918\) −6.28463e103 + 5.70464e102i −1.25541 + 0.113955i
\(919\) −4.69756e103 −0.903295 −0.451648 0.892196i \(-0.649164\pi\)
−0.451648 + 0.892196i \(0.649164\pi\)
\(920\) 5.93843e103i 1.09925i
\(921\) −1.16671e103 + 2.16943e103i −0.207910 + 0.386597i
\(922\) 1.56660e104 2.68767
\(923\) 1.09668e104i 1.81143i
\(924\) −4.84725e103 2.60683e103i −0.770862 0.414565i
\(925\) 2.75800e103 0.422311
\(926\) 5.63315e103i 0.830552i
\(927\) −7.63202e102 1.15492e103i −0.108355 0.163969i
\(928\) −7.50888e103 −1.02659
\(929\) 6.06252e103i 0.798185i 0.916911 + 0.399092i \(0.130675\pi\)
−0.916911 + 0.399092i \(0.869325\pi\)
\(930\) −1.63181e103 + 3.03426e103i −0.206903 + 0.384724i
\(931\) −6.44886e103 −0.787488
\(932\) 5.40042e103i 0.635141i
\(933\) 7.15314e103 + 3.84692e103i 0.810287 + 0.435768i
\(934\) 4.55501e103 0.496991
\(935\) 6.43161e102i 0.0675948i
\(936\) −4.35269e104 + 2.87637e104i −4.40660 + 2.91199i
\(937\) 2.29002e103 0.223334 0.111667 0.993746i \(-0.464381\pi\)
0.111667 + 0.993746i \(0.464381\pi\)
\(938\) 4.06466e103i 0.381878i
\(939\) −2.37439e103 + 4.41504e103i −0.214909 + 0.399612i
\(940\) −9.74154e102 −0.0849479
\(941\) 1.32612e104i 1.11415i −0.830461 0.557077i \(-0.811923\pi\)
0.830461 0.557077i \(-0.188077\pi\)
\(942\) 2.04383e104 + 1.09916e104i 1.65449 + 0.889773i
\(943\) 2.87247e104 2.24050
\(944\) 4.99339e104i 3.75298i
\(945\) 1.82417e102 + 2.00964e103i 0.0132115 + 0.145547i
\(946\) 7.85437e103 0.548178
\(947\) 1.08526e104i 0.729936i −0.931020 0.364968i \(-0.881080\pi\)
0.931020 0.364968i \(-0.118920\pi\)
\(948\) 1.78799e104 3.32466e104i 1.15897 2.15504i
\(949\) −2.33896e104 −1.46119
\(950\) 4.39205e104i 2.64448i
\(951\) 7.83975e103 + 4.21618e103i 0.454972 + 0.244681i
\(952\) 2.62447e104 1.46807
\(953\) 5.46083e103i 0.294447i 0.989103 + 0.147224i \(0.0470337\pi\)
−0.989103 + 0.147224i \(0.952966\pi\)
\(954\) 5.15679e103 + 7.80356e103i 0.268032 + 0.405601i
\(955\) −1.70801e103 −0.0855799
\(956\) 5.99948e104i 2.89793i
\(957\) −1.28674e103 + 2.39261e103i −0.0599200 + 0.111418i
\(958\) −4.64058e104 −2.08343
\(959\) 2.29582e104i 0.993770i
\(960\) −1.71422e104 9.21899e103i −0.715441 0.384760i
\(961\) 2.02884e103 0.0816449
\(962\) 3.48262e104i 1.35138i
\(963\) 7.23717e103 4.78251e103i 0.270800 0.178952i
\(964\) 1.98867e104 0.717574
\(965\) 5.88167e103i 0.204665i
\(966\) −2.76900e104 + 5.14880e104i −0.929230 + 1.72785i
\(967\) 4.10955e104 1.33005 0.665025 0.746821i \(-0.268421\pi\)
0.665025 + 0.746821i \(0.268421\pi\)
\(968\) 8.28798e104i 2.58709i
\(969\) 2.74225e104 + 1.47477e104i 0.825611 + 0.444009i
\(970\) 1.77181e104 0.514524
\(971\) 4.10883e104i 1.15092i −0.817830 0.575460i \(-0.804823\pi\)
0.817830 0.575460i \(-0.195177\pi\)
\(972\) −6.31534e104 7.89855e104i −1.70639 2.13417i
\(973\) −1.70366e104 −0.444051
\(974\) 5.34137e104i 1.34304i
\(975\) −2.93565e104 + 5.45869e104i −0.712104 + 1.32412i
\(976\) −4.25801e104 −0.996467
\(977\) 2.84359e104i 0.642033i 0.947074 + 0.321016i \(0.104024\pi\)
−0.947074 + 0.321016i \(0.895976\pi\)
\(978\) −1.31416e105 7.06750e104i −2.86279 1.53959i
\(979\) 7.08714e103 0.148962
\(980\) 1.60552e104i 0.325614i
\(981\) 2.02172e104 + 3.05939e104i 0.395645 + 0.598714i
\(982\) −1.41718e105 −2.67622
\(983\) 8.43431e104i 1.53701i 0.639845 + 0.768504i \(0.278999\pi\)
−0.639845 + 0.768504i \(0.721001\pi\)
\(984\) 1.33701e105 2.48609e105i 2.35128 4.37208i
\(985\) 2.13156e104 0.361767
\(986\) 2.04318e104i 0.334669i
\(987\) 5.35516e103 + 2.87998e103i 0.0846589 + 0.0455291i
\(988\) 4.06012e105 6.19507
\(989\) 6.10776e104i 0.899521i
\(990\) −1.17461e104 + 7.76210e103i −0.166979 + 0.110344i
\(991\) −5.20468e104 −0.714194 −0.357097 0.934067i \(-0.616233\pi\)
−0.357097 + 0.934067i \(0.616233\pi\)
\(992\) 3.03598e105i 4.02152i
\(993\) −3.48312e104 + 6.47668e104i −0.445395 + 0.828187i
\(994\) −1.20764e105 −1.49078
\(995\) 1.83253e104i 0.218396i
\(996\) 3.80593e105 + 2.04681e105i 4.37909 + 2.35505i
\(997\) −1.08854e105 −1.20925 −0.604623 0.796512i \(-0.706676\pi\)
−0.604623 + 0.796512i \(0.706676\pi\)
\(998\) 6.81654e104i 0.731131i
\(999\) −4.26257e104 + 3.86919e103i −0.441448 + 0.0400708i
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.2.1 22
3.2 odd 2 inner 3.71.b.a.2.22 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.71.b.a.2.1 22 1.1 even 1 trivial
3.71.b.a.2.22 yes 22 3.2 odd 2 inner