Properties

Label 17.10.b.a.16.8
Level $17$
Weight $10$
Character 17.16
Analytic conductor $8.756$
Analytic rank $0$
Dimension $12$
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] = [17,10,Mod(16,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.16");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.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: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{17}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 16.8
Root \(59.5904i\) of defining polynomial
Character \(\chi\) \(=\) 17.16
Dual form 17.10.b.a.16.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+11.8575 q^{2} +59.5904i q^{3} -371.399 q^{4} -633.821i q^{5} +706.595i q^{6} -10932.1i q^{7} -10474.9 q^{8} +16132.0 q^{9} +O(q^{10})\) \(q+11.8575 q^{2} +59.5904i q^{3} -371.399 q^{4} -633.821i q^{5} +706.595i q^{6} -10932.1i q^{7} -10474.9 q^{8} +16132.0 q^{9} -7515.55i q^{10} -26182.2i q^{11} -22131.8i q^{12} -132465. q^{13} -129628. i q^{14} +37769.6 q^{15} +65949.4 q^{16} +(97124.1 - 330386. i) q^{17} +191286. q^{18} -834785. q^{19} +235400. i q^{20} +651448. q^{21} -310456. i q^{22} +1.27202e6i q^{23} -624205. i q^{24} +1.55140e6 q^{25} -1.57071e6 q^{26} +2.13423e6i q^{27} +4.06017e6i q^{28} +6.34953e6i q^{29} +447855. q^{30} -8.52001e6i q^{31} +6.14516e6 q^{32} +1.56021e6 q^{33} +(1.15165e6 - 3.91756e6i) q^{34} -6.92899e6 q^{35} -5.99140e6 q^{36} -8.05093e6i q^{37} -9.89850e6 q^{38} -7.89366e6i q^{39} +6.63923e6i q^{40} -2.36819e7i q^{41} +7.72457e6 q^{42} +2.89782e6 q^{43} +9.72403e6i q^{44} -1.02248e7i q^{45} +1.50830e7i q^{46} +2.63358e7 q^{47} +3.92995e6i q^{48} -7.91572e7 q^{49} +1.83957e7 q^{50} +(1.96878e7 + 5.78766e6i) q^{51} +4.91975e7 q^{52} +2.45299e6 q^{53} +2.53067e7i q^{54} -1.65948e7 q^{55} +1.14513e8i q^{56} -4.97452e7i q^{57} +7.52898e7i q^{58} -8.84531e6 q^{59} -1.40276e7 q^{60} +6.18808e7i q^{61} -1.01026e8i q^{62} -1.76356e8i q^{63} +3.91004e7 q^{64} +8.39593e7i q^{65} +1.85002e7 q^{66} +1.46096e8 q^{67} +(-3.60718e7 + 1.22705e8i) q^{68} -7.58002e7 q^{69} -8.21608e7 q^{70} -2.08285e8i q^{71} -1.68981e8 q^{72} -7.44027e7i q^{73} -9.54641e7i q^{74} +9.24483e7i q^{75} +3.10038e8 q^{76} -2.86226e8 q^{77} -9.35993e7i q^{78} -1.47713e8i q^{79} -4.18001e7i q^{80} +1.90346e8 q^{81} -2.80809e8i q^{82} -5.69010e7 q^{83} -2.41947e8 q^{84} +(-2.09405e8 - 6.15593e7i) q^{85} +3.43609e7 q^{86} -3.78371e8 q^{87} +2.74256e8i q^{88} +1.03356e9 q^{89} -1.21241e8i q^{90} +1.44812e9i q^{91} -4.72427e8i q^{92} +5.07710e8 q^{93} +3.12277e8 q^{94} +5.29104e8i q^{95} +3.66193e8i q^{96} +1.03075e9i q^{97} -9.38609e8 q^{98} -4.22370e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.8575 0.524034 0.262017 0.965063i \(-0.415612\pi\)
0.262017 + 0.965063i \(0.415612\pi\)
\(3\) 59.5904i 0.424747i 0.977189 + 0.212374i \(0.0681194\pi\)
−0.977189 + 0.212374i \(0.931881\pi\)
\(4\) −371.399 −0.725388
\(5\) 633.821i 0.453525i −0.973950 0.226763i \(-0.927186\pi\)
0.973950 0.226763i \(-0.0728142\pi\)
\(6\) 706.595i 0.222582i
\(7\) 10932.1i 1.72093i −0.509512 0.860463i \(-0.670174\pi\)
0.509512 0.860463i \(-0.329826\pi\)
\(8\) −10474.9 −0.904162
\(9\) 16132.0 0.819590
\(10\) 7515.55i 0.237663i
\(11\) 26182.2i 0.539186i −0.962974 0.269593i \(-0.913111\pi\)
0.962974 0.269593i \(-0.0868891\pi\)
\(12\) 22131.8i 0.308107i
\(13\) −132465. −1.28634 −0.643172 0.765722i \(-0.722382\pi\)
−0.643172 + 0.765722i \(0.722382\pi\)
\(14\) 129628.i 0.901824i
\(15\) 37769.6 0.192634
\(16\) 65949.4 0.251577
\(17\) 97124.1 330386.i 0.282038 0.959403i
\(18\) 191286. 0.429493
\(19\) −834785. −1.46955 −0.734774 0.678312i \(-0.762712\pi\)
−0.734774 + 0.678312i \(0.762712\pi\)
\(20\) 235400.i 0.328982i
\(21\) 651448. 0.730959
\(22\) 310456.i 0.282552i
\(23\) 1.27202e6i 0.947805i 0.880577 + 0.473902i \(0.157155\pi\)
−0.880577 + 0.473902i \(0.842845\pi\)
\(24\) 624205.i 0.384040i
\(25\) 1.55140e6 0.794315
\(26\) −1.57071e6 −0.674088
\(27\) 2.13423e6i 0.772866i
\(28\) 4.06017e6i 1.24834i
\(29\) 6.34953e6i 1.66706i 0.552476 + 0.833529i \(0.313683\pi\)
−0.552476 + 0.833529i \(0.686317\pi\)
\(30\) 447855. 0.100947
\(31\) 8.52001e6i 1.65696i −0.560018 0.828480i \(-0.689206\pi\)
0.560018 0.828480i \(-0.310794\pi\)
\(32\) 6.14516e6 1.03600
\(33\) 1.56021e6 0.229018
\(34\) 1.15165e6 3.91756e6i 0.147797 0.502760i
\(35\) −6.92899e6 −0.780484
\(36\) −5.99140e6 −0.594521
\(37\) 8.05093e6i 0.706217i −0.935582 0.353109i \(-0.885125\pi\)
0.935582 0.353109i \(-0.114875\pi\)
\(38\) −9.89850e6 −0.770093
\(39\) 7.89366e6i 0.546371i
\(40\) 6.63923e6i 0.410060i
\(41\) 2.36819e7i 1.30885i −0.756127 0.654425i \(-0.772911\pi\)
0.756127 0.654425i \(-0.227089\pi\)
\(42\) 7.72457e6 0.383047
\(43\) 2.89782e6 0.129260 0.0646298 0.997909i \(-0.479413\pi\)
0.0646298 + 0.997909i \(0.479413\pi\)
\(44\) 9.72403e6i 0.391119i
\(45\) 1.02248e7i 0.371705i
\(46\) 1.50830e7i 0.496682i
\(47\) 2.63358e7 0.787238 0.393619 0.919274i \(-0.371223\pi\)
0.393619 + 0.919274i \(0.371223\pi\)
\(48\) 3.92995e6i 0.106857i
\(49\) −7.91572e7 −1.96159
\(50\) 1.83957e7 0.416248
\(51\) 1.96878e7 + 5.78766e6i 0.407504 + 0.119795i
\(52\) 4.91975e7 0.933099
\(53\) 2.45299e6 0.0427027 0.0213513 0.999772i \(-0.493203\pi\)
0.0213513 + 0.999772i \(0.493203\pi\)
\(54\) 2.53067e7i 0.405008i
\(55\) −1.65948e7 −0.244534
\(56\) 1.14513e8i 1.55600i
\(57\) 4.97452e7i 0.624186i
\(58\) 7.52898e7i 0.873595i
\(59\) −8.84531e6 −0.0950340 −0.0475170 0.998870i \(-0.515131\pi\)
−0.0475170 + 0.998870i \(0.515131\pi\)
\(60\) −1.40276e7 −0.139734
\(61\) 6.18808e7i 0.572231i 0.958195 + 0.286116i \(0.0923642\pi\)
−0.958195 + 0.286116i \(0.907636\pi\)
\(62\) 1.01026e8i 0.868304i
\(63\) 1.76356e8i 1.41045i
\(64\) 3.91004e7 0.291320
\(65\) 8.39593e7i 0.583389i
\(66\) 1.85002e7 0.120013
\(67\) 1.46096e8 0.885730 0.442865 0.896588i \(-0.353962\pi\)
0.442865 + 0.896588i \(0.353962\pi\)
\(68\) −3.60718e7 + 1.22705e8i −0.204587 + 0.695940i
\(69\) −7.58002e7 −0.402577
\(70\) −8.21608e7 −0.409000
\(71\) 2.08285e8i 0.972737i −0.873754 0.486369i \(-0.838321\pi\)
0.873754 0.486369i \(-0.161679\pi\)
\(72\) −1.68981e8 −0.741042
\(73\) 7.44027e7i 0.306645i −0.988176 0.153323i \(-0.951003\pi\)
0.988176 0.153323i \(-0.0489974\pi\)
\(74\) 9.54641e7i 0.370082i
\(75\) 9.24483e7i 0.337383i
\(76\) 3.10038e8 1.06599
\(77\) −2.86226e8 −0.927899
\(78\) 9.35993e7i 0.286317i
\(79\) 1.47713e8i 0.426676i −0.976978 0.213338i \(-0.931566\pi\)
0.976978 0.213338i \(-0.0684335\pi\)
\(80\) 4.18001e7i 0.114097i
\(81\) 1.90346e8 0.491317
\(82\) 2.80809e8i 0.685882i
\(83\) −5.69010e7 −0.131604 −0.0658019 0.997833i \(-0.520961\pi\)
−0.0658019 + 0.997833i \(0.520961\pi\)
\(84\) −2.41947e8 −0.530229
\(85\) −2.09405e8 6.15593e7i −0.435114 0.127911i
\(86\) 3.43609e7 0.0677364
\(87\) −3.78371e8 −0.708078
\(88\) 2.74256e8i 0.487511i
\(89\) 1.03356e9 1.74614 0.873071 0.487592i \(-0.162125\pi\)
0.873071 + 0.487592i \(0.162125\pi\)
\(90\) 1.21241e8i 0.194786i
\(91\) 1.44812e9i 2.21370i
\(92\) 4.72427e8i 0.687527i
\(93\) 5.07710e8 0.703789
\(94\) 3.12277e8 0.412539
\(95\) 5.29104e8i 0.666477i
\(96\) 3.66193e8i 0.440037i
\(97\) 1.03075e9i 1.18217i 0.806609 + 0.591086i \(0.201301\pi\)
−0.806609 + 0.591086i \(0.798699\pi\)
\(98\) −9.38609e8 −1.02794
\(99\) 4.22370e8i 0.441911i
\(100\) −5.76187e8 −0.576187
\(101\) −4.52386e8 −0.432576 −0.216288 0.976330i \(-0.569395\pi\)
−0.216288 + 0.976330i \(0.569395\pi\)
\(102\) 2.33449e8 + 6.86274e7i 0.213546 + 0.0627765i
\(103\) −2.13433e8 −0.186850 −0.0934250 0.995626i \(-0.529782\pi\)
−0.0934250 + 0.995626i \(0.529782\pi\)
\(104\) 1.38756e9 1.16306
\(105\) 4.12901e8i 0.331508i
\(106\) 2.90865e7 0.0223776
\(107\) 1.25133e9i 0.922881i −0.887171 0.461440i \(-0.847333\pi\)
0.887171 0.461440i \(-0.152667\pi\)
\(108\) 7.92650e8i 0.560628i
\(109\) 9.41035e8i 0.638538i 0.947664 + 0.319269i \(0.103437\pi\)
−0.947664 + 0.319269i \(0.896563\pi\)
\(110\) −1.96773e8 −0.128144
\(111\) 4.79758e8 0.299964
\(112\) 7.20965e8i 0.432946i
\(113\) 7.72792e7i 0.0445871i −0.999751 0.0222936i \(-0.992903\pi\)
0.999751 0.0222936i \(-0.00709685\pi\)
\(114\) 5.89855e8i 0.327095i
\(115\) 8.06233e8 0.429854
\(116\) 2.35821e9i 1.20926i
\(117\) −2.13693e9 −1.05427
\(118\) −1.04884e8 −0.0498010
\(119\) −3.61181e9 1.06177e9i −1.65106 0.485366i
\(120\) −3.95634e8 −0.174172
\(121\) 1.67244e9 0.709279
\(122\) 7.33754e8i 0.299869i
\(123\) 1.41122e9 0.555930
\(124\) 3.16432e9i 1.20194i
\(125\) 2.22124e9i 0.813767i
\(126\) 2.09115e9i 0.739126i
\(127\) 3.54892e9 1.21054 0.605271 0.796020i \(-0.293065\pi\)
0.605271 + 0.796020i \(0.293065\pi\)
\(128\) −2.68269e9 −0.883335
\(129\) 1.72682e8i 0.0549026i
\(130\) 9.95550e8i 0.305716i
\(131\) 2.85977e9i 0.848419i −0.905564 0.424209i \(-0.860552\pi\)
0.905564 0.424209i \(-0.139448\pi\)
\(132\) −5.79459e8 −0.166127
\(133\) 9.12596e9i 2.52898i
\(134\) 1.73234e9 0.464153
\(135\) 1.35272e9 0.350514
\(136\) −1.01737e9 + 3.46077e9i −0.255008 + 0.867456i
\(137\) −1.35821e8 −0.0329400 −0.0164700 0.999864i \(-0.505243\pi\)
−0.0164700 + 0.999864i \(0.505243\pi\)
\(138\) −8.98803e8 −0.210964
\(139\) 4.19737e8i 0.0953698i −0.998862 0.0476849i \(-0.984816\pi\)
0.998862 0.0476849i \(-0.0151843\pi\)
\(140\) 2.57342e9 0.566154
\(141\) 1.56936e9i 0.334377i
\(142\) 2.46975e9i 0.509747i
\(143\) 3.46823e9i 0.693578i
\(144\) 1.06389e9 0.206190
\(145\) 4.02447e9 0.756053
\(146\) 8.82233e8i 0.160692i
\(147\) 4.71701e9i 0.833179i
\(148\) 2.99011e9i 0.512282i
\(149\) −8.05680e9 −1.33913 −0.669567 0.742751i \(-0.733520\pi\)
−0.669567 + 0.742751i \(0.733520\pi\)
\(150\) 1.09621e9i 0.176800i
\(151\) −5.71660e9 −0.894832 −0.447416 0.894326i \(-0.647656\pi\)
−0.447416 + 0.894326i \(0.647656\pi\)
\(152\) 8.74432e9 1.32871
\(153\) 1.56681e9 5.32978e9i 0.231155 0.786317i
\(154\) −3.39394e9 −0.486251
\(155\) −5.40016e9 −0.751474
\(156\) 2.93170e9i 0.396331i
\(157\) −3.73112e9 −0.490107 −0.245053 0.969510i \(-0.578806\pi\)
−0.245053 + 0.969510i \(0.578806\pi\)
\(158\) 1.75152e9i 0.223593i
\(159\) 1.46175e8i 0.0181378i
\(160\) 3.89493e9i 0.469851i
\(161\) 1.39059e10 1.63110
\(162\) 2.25704e9 0.257467
\(163\) 3.76537e9i 0.417795i −0.977938 0.208898i \(-0.933012\pi\)
0.977938 0.208898i \(-0.0669876\pi\)
\(164\) 8.79544e9i 0.949425i
\(165\) 9.88891e8i 0.103865i
\(166\) −6.74705e8 −0.0689648
\(167\) 7.70007e9i 0.766074i −0.923733 0.383037i \(-0.874878\pi\)
0.923733 0.383037i \(-0.125122\pi\)
\(168\) −6.82387e9 −0.660905
\(169\) 6.94255e9 0.654680
\(170\) −2.48303e9 7.29942e8i −0.228014 0.0670298i
\(171\) −1.34667e10 −1.20443
\(172\) −1.07625e9 −0.0937634
\(173\) 5.96147e9i 0.505995i −0.967467 0.252997i \(-0.918584\pi\)
0.967467 0.252997i \(-0.0814164\pi\)
\(174\) −4.48655e9 −0.371057
\(175\) 1.69600e10i 1.36696i
\(176\) 1.72670e9i 0.135647i
\(177\) 5.27095e8i 0.0403654i
\(178\) 1.22554e10 0.915038
\(179\) 4.90200e9 0.356890 0.178445 0.983950i \(-0.442893\pi\)
0.178445 + 0.983950i \(0.442893\pi\)
\(180\) 3.79748e9i 0.269630i
\(181\) 6.71648e9i 0.465144i 0.972579 + 0.232572i \(0.0747142\pi\)
−0.972579 + 0.232572i \(0.925286\pi\)
\(182\) 1.71712e10i 1.16006i
\(183\) −3.68750e9 −0.243054
\(184\) 1.33243e10i 0.856969i
\(185\) −5.10285e9 −0.320287
\(186\) 6.02019e9 0.368810
\(187\) −8.65022e9 2.54292e9i −0.517297 0.152071i
\(188\) −9.78108e9 −0.571053
\(189\) 2.33316e10 1.33005
\(190\) 6.27387e9i 0.349257i
\(191\) −1.84682e10 −1.00409 −0.502046 0.864841i \(-0.667419\pi\)
−0.502046 + 0.864841i \(0.667419\pi\)
\(192\) 2.33001e9i 0.123738i
\(193\) 3.37714e10i 1.75203i 0.482287 + 0.876013i \(0.339806\pi\)
−0.482287 + 0.876013i \(0.660194\pi\)
\(194\) 1.22222e10i 0.619498i
\(195\) −5.00316e9 −0.247793
\(196\) 2.93989e10 1.42291
\(197\) 6.25236e9i 0.295765i 0.989005 + 0.147882i \(0.0472457\pi\)
−0.989005 + 0.147882i \(0.952754\pi\)
\(198\) 5.00827e9i 0.231576i
\(199\) 1.46173e10i 0.660735i −0.943852 0.330368i \(-0.892827\pi\)
0.943852 0.330368i \(-0.107173\pi\)
\(200\) −1.62508e10 −0.718189
\(201\) 8.70591e9i 0.376211i
\(202\) −5.36418e9 −0.226685
\(203\) 6.94137e10 2.86889
\(204\) −7.31203e9 2.14953e9i −0.295599 0.0868977i
\(205\) −1.50101e10 −0.593597
\(206\) −2.53078e9 −0.0979157
\(207\) 2.05202e10i 0.776811i
\(208\) −8.73600e9 −0.323614
\(209\) 2.18565e10i 0.792359i
\(210\) 4.89599e9i 0.173722i
\(211\) 2.69240e10i 0.935122i −0.883961 0.467561i \(-0.845133\pi\)
0.883961 0.467561i \(-0.154867\pi\)
\(212\) −9.11039e8 −0.0309760
\(213\) 1.24118e10 0.413167
\(214\) 1.48377e10i 0.483621i
\(215\) 1.83670e9i 0.0586225i
\(216\) 2.23559e10i 0.698796i
\(217\) −9.31416e10 −2.85151
\(218\) 1.11584e10i 0.334616i
\(219\) 4.43369e9 0.130247
\(220\) 6.16329e9 0.177382
\(221\) −1.28656e10 + 4.37646e10i −0.362797 + 1.23412i
\(222\) 5.68874e9 0.157191
\(223\) 1.09042e10 0.295273 0.147636 0.989042i \(-0.452834\pi\)
0.147636 + 0.989042i \(0.452834\pi\)
\(224\) 6.71795e10i 1.78287i
\(225\) 2.50271e10 0.651012
\(226\) 9.16341e8i 0.0233652i
\(227\) 5.73714e10i 1.43410i −0.697022 0.717050i \(-0.745492\pi\)
0.697022 0.717050i \(-0.254508\pi\)
\(228\) 1.84753e10i 0.452777i
\(229\) 4.85190e10 1.16587 0.582937 0.812517i \(-0.301903\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(230\) 9.55994e9 0.225258
\(231\) 1.70563e10i 0.394123i
\(232\) 6.65109e10i 1.50729i
\(233\) 1.92873e9i 0.0428717i 0.999770 + 0.0214358i \(0.00682376\pi\)
−0.999770 + 0.0214358i \(0.993176\pi\)
\(234\) −2.53387e10 −0.552475
\(235\) 1.66922e10i 0.357032i
\(236\) 3.28514e9 0.0689366
\(237\) 8.80230e9 0.181229
\(238\) −4.28272e10 1.25900e10i −0.865213 0.254348i
\(239\) −9.39248e10 −1.86204 −0.931021 0.364965i \(-0.881081\pi\)
−0.931021 + 0.364965i \(0.881081\pi\)
\(240\) 2.49088e9 0.0484622
\(241\) 4.52039e10i 0.863175i 0.902071 + 0.431588i \(0.142046\pi\)
−0.902071 + 0.431588i \(0.857954\pi\)
\(242\) 1.98310e10 0.371686
\(243\) 5.33508e10i 0.981551i
\(244\) 2.29825e10i 0.415090i
\(245\) 5.01715e10i 0.889630i
\(246\) 1.67335e10 0.291326
\(247\) 1.10580e11 1.89034
\(248\) 8.92465e10i 1.49816i
\(249\) 3.39075e9i 0.0558983i
\(250\) 2.63384e10i 0.426442i
\(251\) −4.87193e10 −0.774763 −0.387382 0.921919i \(-0.626620\pi\)
−0.387382 + 0.921919i \(0.626620\pi\)
\(252\) 6.54986e10i 1.02313i
\(253\) 3.33043e10 0.511043
\(254\) 4.20814e10 0.634365
\(255\) 3.66834e9 1.24785e10i 0.0543299 0.184813i
\(256\) −5.18295e10 −0.754218
\(257\) 8.25999e10 1.18108 0.590542 0.807007i \(-0.298914\pi\)
0.590542 + 0.807007i \(0.298914\pi\)
\(258\) 2.04758e9i 0.0287708i
\(259\) −8.80135e10 −1.21535
\(260\) 3.11824e10i 0.423184i
\(261\) 1.02431e11i 1.36630i
\(262\) 3.39098e10i 0.444600i
\(263\) 3.46665e10 0.446795 0.223398 0.974727i \(-0.428285\pi\)
0.223398 + 0.974727i \(0.428285\pi\)
\(264\) −1.63430e10 −0.207069
\(265\) 1.55476e9i 0.0193667i
\(266\) 1.08211e11i 1.32527i
\(267\) 6.15901e10i 0.741669i
\(268\) −5.42599e10 −0.642499
\(269\) 1.26130e11i 1.46871i −0.678768 0.734353i \(-0.737486\pi\)
0.678768 0.734353i \(-0.262514\pi\)
\(270\) 1.60399e10 0.183681
\(271\) 5.63928e10 0.635129 0.317564 0.948237i \(-0.397135\pi\)
0.317564 + 0.948237i \(0.397135\pi\)
\(272\) 6.40528e9 2.17887e10i 0.0709542 0.241364i
\(273\) −8.62942e10 −0.940264
\(274\) −1.61050e9 −0.0172617
\(275\) 4.06189e10i 0.428283i
\(276\) 2.81521e10 0.292025
\(277\) 4.76405e10i 0.486203i −0.970001 0.243102i \(-0.921835\pi\)
0.970001 0.243102i \(-0.0781648\pi\)
\(278\) 4.97705e9i 0.0499770i
\(279\) 1.37445e11i 1.35803i
\(280\) 7.25807e10 0.705684
\(281\) 1.14333e11 1.09394 0.546969 0.837153i \(-0.315782\pi\)
0.546969 + 0.837153i \(0.315782\pi\)
\(282\) 1.86087e10i 0.175225i
\(283\) 2.54590e10i 0.235941i −0.993017 0.117970i \(-0.962361\pi\)
0.993017 0.117970i \(-0.0376388\pi\)
\(284\) 7.73568e10i 0.705612i
\(285\) −3.15295e10 −0.283084
\(286\) 4.11246e10i 0.363459i
\(287\) −2.58893e11 −2.25243
\(288\) 9.91337e10 0.849093
\(289\) −9.97217e10 6.41769e10i −0.840910 0.541176i
\(290\) 4.77202e10 0.396197
\(291\) −6.14228e10 −0.502124
\(292\) 2.76331e10i 0.222437i
\(293\) 4.43928e10 0.351891 0.175946 0.984400i \(-0.443702\pi\)
0.175946 + 0.984400i \(0.443702\pi\)
\(294\) 5.59321e10i 0.436614i
\(295\) 5.60634e9i 0.0431003i
\(296\) 8.43329e10i 0.638535i
\(297\) 5.58787e10 0.416718
\(298\) −9.55337e10 −0.701752
\(299\) 1.68499e11i 1.21920i
\(300\) 3.43352e10i 0.244734i
\(301\) 3.16792e10i 0.222446i
\(302\) −6.77848e10 −0.468922
\(303\) 2.69578e10i 0.183735i
\(304\) −5.50536e10 −0.369704
\(305\) 3.92213e10 0.259521
\(306\) 1.85784e10 6.31980e10i 0.121133 0.412057i
\(307\) 1.77005e11 1.13727 0.568635 0.822590i \(-0.307472\pi\)
0.568635 + 0.822590i \(0.307472\pi\)
\(308\) 1.06304e11 0.673088
\(309\) 1.27185e10i 0.0793640i
\(310\) −6.40326e10 −0.393798
\(311\) 1.16929e11i 0.708764i −0.935101 0.354382i \(-0.884691\pi\)
0.935101 0.354382i \(-0.115309\pi\)
\(312\) 8.26855e10i 0.494008i
\(313\) 6.60894e10i 0.389208i 0.980882 + 0.194604i \(0.0623422\pi\)
−0.980882 + 0.194604i \(0.937658\pi\)
\(314\) −4.42419e10 −0.256833
\(315\) −1.11778e11 −0.639677
\(316\) 5.48606e10i 0.309506i
\(317\) 2.15865e11i 1.20065i 0.799757 + 0.600324i \(0.204962\pi\)
−0.799757 + 0.600324i \(0.795038\pi\)
\(318\) 1.73327e9i 0.00950484i
\(319\) 1.66245e11 0.898854
\(320\) 2.47826e10i 0.132121i
\(321\) 7.45674e10 0.391991
\(322\) 1.64889e11 0.854753
\(323\) −8.10778e10 + 2.75801e11i −0.414468 + 1.40989i
\(324\) −7.06945e10 −0.356396
\(325\) −2.05506e11 −1.02176
\(326\) 4.46480e10i 0.218939i
\(327\) −5.60767e10 −0.271217
\(328\) 2.48067e11i 1.18341i
\(329\) 2.87905e11i 1.35478i
\(330\) 1.17258e10i 0.0544289i
\(331\) 2.19673e11 1.00589 0.502946 0.864318i \(-0.332249\pi\)
0.502946 + 0.864318i \(0.332249\pi\)
\(332\) 2.11330e10 0.0954639
\(333\) 1.29877e11i 0.578808i
\(334\) 9.13039e10i 0.401449i
\(335\) 9.25987e10i 0.401701i
\(336\) 4.29626e10 0.183892
\(337\) 3.65398e11i 1.54323i 0.636088 + 0.771617i \(0.280552\pi\)
−0.636088 + 0.771617i \(0.719448\pi\)
\(338\) 8.23215e10 0.343074
\(339\) 4.60510e9 0.0189383
\(340\) 7.77730e10 + 2.28631e10i 0.315626 + 0.0927853i
\(341\) −2.23072e11 −0.893410
\(342\) −1.59682e11 −0.631160
\(343\) 4.24205e11i 1.65482i
\(344\) −3.03544e10 −0.116872
\(345\) 4.80438e10i 0.182579i
\(346\) 7.06883e10i 0.265158i
\(347\) 3.18226e11i 1.17829i 0.808026 + 0.589147i \(0.200536\pi\)
−0.808026 + 0.589147i \(0.799464\pi\)
\(348\) 1.40527e11 0.513632
\(349\) −1.05189e11 −0.379537 −0.189769 0.981829i \(-0.560774\pi\)
−0.189769 + 0.981829i \(0.560774\pi\)
\(350\) 2.01104e11i 0.716332i
\(351\) 2.82711e11i 0.994171i
\(352\) 1.60894e11i 0.558595i
\(353\) 2.74596e11 0.941258 0.470629 0.882331i \(-0.344027\pi\)
0.470629 + 0.882331i \(0.344027\pi\)
\(354\) 6.25005e9i 0.0211529i
\(355\) −1.32015e11 −0.441161
\(356\) −3.83862e11 −1.26663
\(357\) 6.32713e10 2.15229e11i 0.206158 0.701284i
\(358\) 5.81256e10 0.187022
\(359\) 3.36158e11 1.06812 0.534058 0.845448i \(-0.320666\pi\)
0.534058 + 0.845448i \(0.320666\pi\)
\(360\) 1.07104e11i 0.336081i
\(361\) 3.74179e11 1.15957
\(362\) 7.96408e10i 0.243751i
\(363\) 9.96614e10i 0.301264i
\(364\) 5.37832e11i 1.60579i
\(365\) −4.71580e10 −0.139071
\(366\) −4.37247e10 −0.127368
\(367\) 4.27664e11i 1.23057i 0.788306 + 0.615283i \(0.210958\pi\)
−0.788306 + 0.615283i \(0.789042\pi\)
\(368\) 8.38890e10i 0.238446i
\(369\) 3.82037e11i 1.07272i
\(370\) −6.05072e10 −0.167841
\(371\) 2.68164e10i 0.0734882i
\(372\) −1.88563e11 −0.510521
\(373\) −6.59774e11 −1.76484 −0.882420 0.470463i \(-0.844087\pi\)
−0.882420 + 0.470463i \(0.844087\pi\)
\(374\) −1.02570e11 3.01528e10i −0.271081 0.0796902i
\(375\) 1.32364e11 0.345645
\(376\) −2.75866e11 −0.711790
\(377\) 8.41093e11i 2.14441i
\(378\) 2.76655e11 0.696989
\(379\) 3.76630e11i 0.937645i −0.883292 0.468823i \(-0.844678\pi\)
0.883292 0.468823i \(-0.155322\pi\)
\(380\) 1.96509e11i 0.483455i
\(381\) 2.11482e11i 0.514174i
\(382\) −2.18987e11 −0.526178
\(383\) −2.37194e11 −0.563261 −0.281630 0.959523i \(-0.590875\pi\)
−0.281630 + 0.959523i \(0.590875\pi\)
\(384\) 1.59862e11i 0.375194i
\(385\) 1.81416e11i 0.420826i
\(386\) 4.00445e11i 0.918121i
\(387\) 4.67475e10 0.105940
\(388\) 3.82820e11i 0.857534i
\(389\) −3.64753e10 −0.0807656 −0.0403828 0.999184i \(-0.512858\pi\)
−0.0403828 + 0.999184i \(0.512858\pi\)
\(390\) −5.93252e10 −0.129852
\(391\) 4.20258e11 + 1.23544e11i 0.909327 + 0.267317i
\(392\) 8.29166e11 1.77359
\(393\) 1.70415e11 0.360363
\(394\) 7.41376e10i 0.154991i
\(395\) −9.36238e10 −0.193508
\(396\) 1.56868e11i 0.320557i
\(397\) 5.75210e11i 1.16217i 0.813844 + 0.581084i \(0.197371\pi\)
−0.813844 + 0.581084i \(0.802629\pi\)
\(398\) 1.73325e11i 0.346248i
\(399\) −5.43819e11 −1.07418
\(400\) 1.02314e11 0.199831
\(401\) 3.39949e11i 0.656545i 0.944583 + 0.328273i \(0.106466\pi\)
−0.944583 + 0.328273i \(0.893534\pi\)
\(402\) 1.03231e11i 0.197148i
\(403\) 1.12860e12i 2.13142i
\(404\) 1.68015e11 0.313786
\(405\) 1.20646e11i 0.222825i
\(406\) 8.23076e11 1.50339
\(407\) −2.10791e11 −0.380782
\(408\) −2.06229e11 6.06254e10i −0.368449 0.108314i
\(409\) −1.12478e11 −0.198752 −0.0993760 0.995050i \(-0.531685\pi\)
−0.0993760 + 0.995050i \(0.531685\pi\)
\(410\) −1.77983e11 −0.311065
\(411\) 8.09362e9i 0.0139912i
\(412\) 7.92686e10 0.135539
\(413\) 9.66978e10i 0.163547i
\(414\) 2.43319e11i 0.407075i
\(415\) 3.60650e10i 0.0596857i
\(416\) −8.14021e11 −1.33265
\(417\) 2.50123e10 0.0405081
\(418\) 2.59164e11i 0.415223i
\(419\) 2.86731e10i 0.0454477i −0.999742 0.0227239i \(-0.992766\pi\)
0.999742 0.0227239i \(-0.00723385\pi\)
\(420\) 1.53351e11i 0.240472i
\(421\) 7.41818e11 1.15087 0.575437 0.817846i \(-0.304832\pi\)
0.575437 + 0.817846i \(0.304832\pi\)
\(422\) 3.19252e11i 0.490036i
\(423\) 4.24849e11 0.645212
\(424\) −2.56949e10 −0.0386101
\(425\) 1.50678e11 5.12559e11i 0.224027 0.762068i
\(426\) 1.47173e11 0.216514
\(427\) 6.76487e11 0.984768
\(428\) 4.64743e11i 0.669447i
\(429\) −2.06673e11 −0.294595
\(430\) 2.17787e10i 0.0307202i
\(431\) 9.85196e10i 0.137523i 0.997633 + 0.0687614i \(0.0219047\pi\)
−0.997633 + 0.0687614i \(0.978095\pi\)
\(432\) 1.40751e11i 0.194435i
\(433\) −6.29756e11 −0.860948 −0.430474 0.902603i \(-0.641654\pi\)
−0.430474 + 0.902603i \(0.641654\pi\)
\(434\) −1.10443e12 −1.49429
\(435\) 2.39819e11i 0.321131i
\(436\) 3.49500e11i 0.463188i
\(437\) 1.06186e12i 1.39284i
\(438\) 5.25726e10 0.0682537
\(439\) 3.19248e10i 0.0410240i −0.999790 0.0205120i \(-0.993470\pi\)
0.999790 0.0205120i \(-0.00652962\pi\)
\(440\) 1.73829e11 0.221099
\(441\) −1.27696e12 −1.60770
\(442\) −1.52554e11 + 5.18941e11i −0.190118 + 0.646722i
\(443\) 9.76504e11 1.20464 0.602320 0.798255i \(-0.294243\pi\)
0.602320 + 0.798255i \(0.294243\pi\)
\(444\) −1.78182e11 −0.217590
\(445\) 6.55091e11i 0.791920i
\(446\) 1.29297e11 0.154733
\(447\) 4.80108e11i 0.568794i
\(448\) 4.27449e11i 0.501341i
\(449\) 3.18417e11i 0.369733i −0.982764 0.184867i \(-0.940815\pi\)
0.982764 0.184867i \(-0.0591853\pi\)
\(450\) 2.96760e11 0.341153
\(451\) −6.20044e11 −0.705713
\(452\) 2.87014e10i 0.0323430i
\(453\) 3.40654e11i 0.380077i
\(454\) 6.80284e11i 0.751517i
\(455\) 9.17851e11 1.00397
\(456\) 5.21077e11i 0.564365i
\(457\) 5.17641e11 0.555144 0.277572 0.960705i \(-0.410470\pi\)
0.277572 + 0.960705i \(0.410470\pi\)
\(458\) 5.75315e11 0.610958
\(459\) 7.05119e11 + 2.07285e11i 0.741490 + 0.217977i
\(460\) −2.99434e11 −0.311811
\(461\) −1.03511e12 −1.06741 −0.533704 0.845671i \(-0.679200\pi\)
−0.533704 + 0.845671i \(0.679200\pi\)
\(462\) 2.02246e11i 0.206534i
\(463\) −4.59441e11 −0.464638 −0.232319 0.972640i \(-0.574631\pi\)
−0.232319 + 0.972640i \(0.574631\pi\)
\(464\) 4.18748e11i 0.419393i
\(465\) 3.21797e11i 0.319186i
\(466\) 2.28700e10i 0.0224662i
\(467\) −1.31601e12 −1.28036 −0.640182 0.768223i \(-0.721141\pi\)
−0.640182 + 0.768223i \(0.721141\pi\)
\(468\) 7.93653e11 0.764758
\(469\) 1.59714e12i 1.52428i
\(470\) 1.97928e11i 0.187097i
\(471\) 2.22339e11i 0.208171i
\(472\) 9.26540e10 0.0859261
\(473\) 7.58711e10i 0.0696949i
\(474\) 1.04374e11 0.0949703
\(475\) −1.29508e12 −1.16728
\(476\) 1.34142e12 + 3.94340e11i 1.19766 + 0.352079i
\(477\) 3.95717e10 0.0349987
\(478\) −1.11372e12 −0.975773
\(479\) 2.08121e12i 1.80637i 0.429251 + 0.903185i \(0.358777\pi\)
−0.429251 + 0.903185i \(0.641223\pi\)
\(480\) 2.32100e11 0.199568
\(481\) 1.06647e12i 0.908438i
\(482\) 5.36006e11i 0.452333i
\(483\) 8.28655e11i 0.692806i
\(484\) −6.21143e11 −0.514503
\(485\) 6.53311e11 0.536145
\(486\) 6.32609e11i 0.514366i
\(487\) 7.18370e11i 0.578719i −0.957220 0.289360i \(-0.906558\pi\)
0.957220 0.289360i \(-0.0934424\pi\)
\(488\) 6.48197e11i 0.517390i
\(489\) 2.24380e11 0.177457
\(490\) 5.94910e11i 0.466196i
\(491\) 9.78925e11 0.760121 0.380060 0.924962i \(-0.375903\pi\)
0.380060 + 0.924962i \(0.375903\pi\)
\(492\) −5.24124e11 −0.403265
\(493\) 2.09780e12 + 6.16693e11i 1.59938 + 0.470173i
\(494\) 1.31121e12 0.990604
\(495\) −2.67707e11 −0.200418
\(496\) 5.61889e11i 0.416853i
\(497\) −2.27699e12 −1.67401
\(498\) 4.02059e10i 0.0292926i
\(499\) 1.70045e12i 1.22775i −0.789402 0.613876i \(-0.789609\pi\)
0.789402 0.613876i \(-0.210391\pi\)
\(500\) 8.24966e11i 0.590297i
\(501\) 4.58850e11 0.325388
\(502\) −5.77690e11 −0.406002
\(503\) 1.03194e11i 0.0718787i −0.999354 0.0359393i \(-0.988558\pi\)
0.999354 0.0359393i \(-0.0114423\pi\)
\(504\) 1.84732e12i 1.27528i
\(505\) 2.86731e11i 0.196184i
\(506\) 3.94906e11 0.267804
\(507\) 4.13709e11i 0.278073i
\(508\) −1.31807e12 −0.878113
\(509\) 7.49118e11 0.494675 0.247338 0.968929i \(-0.420444\pi\)
0.247338 + 0.968929i \(0.420444\pi\)
\(510\) 4.34975e10 1.47965e11i 0.0284707 0.0968484i
\(511\) −8.13378e11 −0.527714
\(512\) 7.58967e11 0.488099
\(513\) 1.78162e12i 1.13576i
\(514\) 9.79431e11 0.618928
\(515\) 1.35278e11i 0.0847412i
\(516\) 6.41339e10i 0.0398257i
\(517\) 6.89528e11i 0.424467i
\(518\) −1.04362e12 −0.636883
\(519\) 3.55246e11 0.214920
\(520\) 8.79468e11i 0.527479i
\(521\) 1.51334e12i 0.899843i 0.893068 + 0.449921i \(0.148548\pi\)
−0.893068 + 0.449921i \(0.851452\pi\)
\(522\) 1.21457e12i 0.715990i
\(523\) 1.87630e12 1.09659 0.548295 0.836285i \(-0.315277\pi\)
0.548295 + 0.836285i \(0.315277\pi\)
\(524\) 1.06212e12i 0.615433i
\(525\) 1.01065e12 0.580611
\(526\) 4.11059e11 0.234136
\(527\) −2.81489e12 8.27498e11i −1.58969 0.467325i
\(528\) 1.02895e11 0.0576156
\(529\) 1.83116e11 0.101666
\(530\) 1.84356e10i 0.0101488i
\(531\) −1.42692e11 −0.0778889
\(532\) 3.38937e12i 1.83450i
\(533\) 3.13703e12i 1.68363i
\(534\) 7.30307e11i 0.388660i
\(535\) −7.93121e11 −0.418550
\(536\) −1.53034e12 −0.800844
\(537\) 2.92112e11i 0.151588i
\(538\) 1.49560e12i 0.769652i
\(539\) 2.07251e12i 1.05766i
\(540\) −5.02398e11 −0.254259
\(541\) 2.51866e12i 1.26410i −0.774927 0.632050i \(-0.782214\pi\)
0.774927 0.632050i \(-0.217786\pi\)
\(542\) 6.68679e11 0.332829
\(543\) −4.00237e11 −0.197569
\(544\) 5.96844e11 2.03027e12i 0.292190 0.993939i
\(545\) 5.96448e11 0.289593
\(546\) −1.02324e12 −0.492730
\(547\) 2.33711e12i 1.11618i 0.829779 + 0.558091i \(0.188466\pi\)
−0.829779 + 0.558091i \(0.811534\pi\)
\(548\) 5.04437e10 0.0238943
\(549\) 9.98260e11i 0.468995i
\(550\) 4.81640e11i 0.224435i
\(551\) 5.30050e12i 2.44982i
\(552\) 7.94002e11 0.363995
\(553\) −1.61482e12 −0.734278
\(554\) 5.64899e11i 0.254787i
\(555\) 3.04081e11i 0.136041i
\(556\) 1.55890e11i 0.0691802i
\(557\) 7.35788e11 0.323895 0.161948 0.986799i \(-0.448222\pi\)
0.161948 + 0.986799i \(0.448222\pi\)
\(558\) 1.62975e12i 0.711653i
\(559\) −3.83860e11 −0.166272
\(560\) −4.56963e11 −0.196352
\(561\) 1.51534e11 5.15470e11i 0.0645916 0.219720i
\(562\) 1.35571e12 0.573261
\(563\) 2.80471e12 1.17652 0.588262 0.808670i \(-0.299812\pi\)
0.588262 + 0.808670i \(0.299812\pi\)
\(564\) 5.82858e11i 0.242553i
\(565\) −4.89812e10 −0.0202214
\(566\) 3.01881e11i 0.123641i
\(567\) 2.08089e12i 0.845521i
\(568\) 2.18177e12i 0.879512i
\(569\) −7.41576e11 −0.296586 −0.148293 0.988943i \(-0.547378\pi\)
−0.148293 + 0.988943i \(0.547378\pi\)
\(570\) −3.73862e11 −0.148346
\(571\) 2.37109e12i 0.933440i 0.884405 + 0.466720i \(0.154564\pi\)
−0.884405 + 0.466720i \(0.845436\pi\)
\(572\) 1.28810e12i 0.503114i
\(573\) 1.10052e12i 0.426485i
\(574\) −3.06984e12 −1.18035
\(575\) 1.97341e12i 0.752855i
\(576\) 6.30767e11 0.238763
\(577\) 1.64213e12 0.616759 0.308380 0.951263i \(-0.400213\pi\)
0.308380 + 0.951263i \(0.400213\pi\)
\(578\) −1.18245e12 7.60979e11i −0.440665 0.283594i
\(579\) −2.01245e12 −0.744168
\(580\) −1.49468e12 −0.548432
\(581\) 6.22047e11i 0.226481i
\(582\) −7.28323e11 −0.263130
\(583\) 6.42247e10i 0.0230247i
\(584\) 7.79364e11i 0.277257i
\(585\) 1.35443e12i 0.478140i
\(586\) 5.26389e11 0.184403
\(587\) 4.40209e12 1.53034 0.765168 0.643830i \(-0.222656\pi\)
0.765168 + 0.643830i \(0.222656\pi\)
\(588\) 1.75189e12i 0.604379i
\(589\) 7.11238e12i 2.43498i
\(590\) 6.64774e10i 0.0225860i
\(591\) −3.72581e11 −0.125625
\(592\) 5.30954e11i 0.177668i
\(593\) −3.23487e12 −1.07426 −0.537132 0.843498i \(-0.680492\pi\)
−0.537132 + 0.843498i \(0.680492\pi\)
\(594\) 6.62584e11 0.218374
\(595\) −6.72972e11 + 2.28924e12i −0.220126 + 0.748799i
\(596\) 2.99229e12 0.971393
\(597\) 8.71049e11 0.280645
\(598\) 1.99798e12i 0.638904i
\(599\) 4.90816e12 1.55775 0.778875 0.627179i \(-0.215791\pi\)
0.778875 + 0.627179i \(0.215791\pi\)
\(600\) 9.68389e11i 0.305049i
\(601\) 1.05961e12i 0.331292i −0.986185 0.165646i \(-0.947029\pi\)
0.986185 0.165646i \(-0.0529710\pi\)
\(602\) 3.75637e11i 0.116569i
\(603\) 2.35682e12 0.725936
\(604\) 2.12314e12 0.649101
\(605\) 1.06003e12i 0.321676i
\(606\) 3.19653e11i 0.0962836i
\(607\) 5.76988e11i 0.172511i 0.996273 + 0.0862556i \(0.0274902\pi\)
−0.996273 + 0.0862556i \(0.972510\pi\)
\(608\) −5.12989e12 −1.52245
\(609\) 4.13639e12i 1.21855i
\(610\) 4.65068e11 0.135998
\(611\) −3.48858e12 −1.01266
\(612\) −5.81910e11 + 1.97947e12i −0.167677 + 0.570385i
\(613\) −5.09644e12 −1.45779 −0.728895 0.684625i \(-0.759966\pi\)
−0.728895 + 0.684625i \(0.759966\pi\)
\(614\) 2.09884e12 0.595967
\(615\) 8.94458e11i 0.252128i
\(616\) 2.99820e12 0.838971
\(617\) 5.92498e12i 1.64590i 0.568113 + 0.822951i \(0.307674\pi\)
−0.568113 + 0.822951i \(0.692326\pi\)
\(618\) 1.50810e11i 0.0415894i
\(619\) 3.09980e12i 0.848644i 0.905511 + 0.424322i \(0.139487\pi\)
−0.905511 + 0.424322i \(0.860513\pi\)
\(620\) 2.00561e12 0.545110
\(621\) −2.71478e12 −0.732526
\(622\) 1.38649e12i 0.371417i
\(623\) 1.12990e13i 3.00498i
\(624\) 5.20582e11i 0.137454i
\(625\) 1.62220e12 0.425251
\(626\) 7.83657e11i 0.203958i
\(627\) −1.30244e12 −0.336552
\(628\) 1.38573e12 0.355518
\(629\) −2.65991e12 7.81939e11i −0.677547 0.199180i
\(630\) −1.32542e12 −0.335212
\(631\) −3.86695e11 −0.0971040 −0.0485520 0.998821i \(-0.515461\pi\)
−0.0485520 + 0.998821i \(0.515461\pi\)
\(632\) 1.54729e12i 0.385784i
\(633\) 1.60441e12 0.397191
\(634\) 2.55963e12i 0.629180i
\(635\) 2.24938e12i 0.549011i
\(636\) 5.42892e10i 0.0131570i
\(637\) 1.04856e13 2.52328
\(638\) 1.97125e12 0.471030
\(639\) 3.36005e12i 0.797245i
\(640\) 1.70034e12i 0.400615i
\(641\) 5.83791e12i 1.36583i −0.730499 0.682914i \(-0.760712\pi\)
0.730499 0.682914i \(-0.239288\pi\)
\(642\) 8.84185e11 0.205417
\(643\) 4.53130e12i 1.04538i −0.852523 0.522689i \(-0.824929\pi\)
0.852523 0.522689i \(-0.175071\pi\)
\(644\) −5.16462e12 −1.18318
\(645\) 1.09449e11 0.0248997
\(646\) −9.61383e11 + 3.27032e12i −0.217195 + 0.738830i
\(647\) −8.18289e12 −1.83585 −0.917925 0.396754i \(-0.870137\pi\)
−0.917925 + 0.396754i \(0.870137\pi\)
\(648\) −1.99387e12 −0.444231
\(649\) 2.31589e11i 0.0512410i
\(650\) −2.43680e12 −0.535438
\(651\) 5.55034e12i 1.21117i
\(652\) 1.39845e12i 0.303064i
\(653\) 2.43949e12i 0.525036i −0.964927 0.262518i \(-0.915447\pi\)
0.964927 0.262518i \(-0.0845529\pi\)
\(654\) −6.64931e11 −0.142127
\(655\) −1.81258e12 −0.384779
\(656\) 1.56181e12i 0.329276i
\(657\) 1.20026e12i 0.251323i
\(658\) 3.41385e12i 0.709950i
\(659\) −1.61269e12 −0.333094 −0.166547 0.986034i \(-0.553262\pi\)
−0.166547 + 0.986034i \(0.553262\pi\)
\(660\) 3.67273e11i 0.0753427i
\(661\) 7.30795e11 0.148898 0.0744491 0.997225i \(-0.476280\pi\)
0.0744491 + 0.997225i \(0.476280\pi\)
\(662\) 2.60478e12 0.527121
\(663\) −2.60795e12 7.66664e11i −0.524190 0.154097i
\(664\) 5.96034e11 0.118991
\(665\) 5.78422e12 1.14696
\(666\) 1.54003e12i 0.303315i
\(667\) −8.07674e12 −1.58005
\(668\) 2.85980e12i 0.555701i
\(669\) 6.49787e11i 0.125416i
\(670\) 1.09799e12i 0.210505i
\(671\) 1.62017e12 0.308539
\(672\) 4.00325e12 0.757271
\(673\) 4.80522e12i 0.902911i 0.892294 + 0.451456i \(0.149095\pi\)
−0.892294 + 0.451456i \(0.850905\pi\)
\(674\) 4.33272e12i 0.808707i
\(675\) 3.31103e12i 0.613899i
\(676\) −2.57846e12 −0.474897
\(677\) 2.48514e12i 0.454675i −0.973816 0.227337i \(-0.926998\pi\)
0.973816 0.227337i \(-0.0730020\pi\)
\(678\) 5.46051e10 0.00992429
\(679\) 1.12683e13 2.03443
\(680\) 2.19351e12 + 6.44830e11i 0.393413 + 0.115652i
\(681\) 3.41878e12 0.609130
\(682\) −2.64509e12 −0.468177
\(683\) 8.09671e11i 0.142369i −0.997463 0.0711845i \(-0.977322\pi\)
0.997463 0.0711845i \(-0.0226779\pi\)
\(684\) 5.00154e12 0.873677
\(685\) 8.60861e10i 0.0149391i
\(686\) 5.03002e12i 0.867184i
\(687\) 2.89126e12i 0.495202i
\(688\) 1.91109e11 0.0325187
\(689\) −3.24937e11 −0.0549303
\(690\) 5.69680e11i 0.0956776i
\(691\) 3.01668e12i 0.503359i −0.967811 0.251679i \(-0.919017\pi\)
0.967811 0.251679i \(-0.0809829\pi\)
\(692\) 2.21408e12i 0.367043i
\(693\) −4.61740e12 −0.760497
\(694\) 3.77338e12i 0.617465i
\(695\) −2.66038e11 −0.0432526
\(696\) 3.96341e12 0.640217
\(697\) −7.82417e12 2.30009e12i −1.25571 0.369145i
\(698\) −1.24728e12 −0.198890
\(699\) −1.14934e11 −0.0182096
\(700\) 6.29893e12i 0.991575i
\(701\) −4.71932e12 −0.738156 −0.369078 0.929398i \(-0.620326\pi\)
−0.369078 + 0.929398i \(0.620326\pi\)
\(702\) 3.35226e12i 0.520979i
\(703\) 6.72080e12i 1.03782i
\(704\) 1.02373e12i 0.157076i
\(705\) 9.94693e11 0.151648
\(706\) 3.25604e12 0.493251
\(707\) 4.94552e12i 0.744432i
\(708\) 1.95763e11i 0.0292806i
\(709\) 8.19568e12i 1.21808i 0.793138 + 0.609041i \(0.208446\pi\)
−0.793138 + 0.609041i \(0.791554\pi\)
\(710\) −1.56538e12 −0.231183
\(711\) 2.38291e12i 0.349699i
\(712\) −1.08264e13 −1.57880
\(713\) 1.08376e13 1.57048
\(714\) 7.50242e11 2.55209e12i 0.108034 0.367497i
\(715\) 2.19824e12 0.314555
\(716\) −1.82060e12 −0.258884
\(717\) 5.59701e12i 0.790897i
\(718\) 3.98601e12 0.559729
\(719\) 1.16808e13i 1.63001i −0.579452 0.815006i \(-0.696733\pi\)
0.579452 0.815006i \(-0.303267\pi\)
\(720\) 6.74319e11i 0.0935124i
\(721\) 2.33327e12i 0.321555i
\(722\) 4.43684e12 0.607654
\(723\) −2.69372e12 −0.366631
\(724\) 2.49449e12i 0.337410i
\(725\) 9.85064e12i 1.32417i
\(726\) 1.18174e12i 0.157873i
\(727\) −5.18587e12 −0.688520 −0.344260 0.938874i \(-0.611870\pi\)
−0.344260 + 0.938874i \(0.611870\pi\)
\(728\) 1.51690e13i 2.00155i
\(729\) 5.67392e11 0.0744063
\(730\) −5.59178e11 −0.0728781
\(731\) 2.81448e11 9.57397e11i 0.0364561 0.124012i
\(732\) 1.36953e12 0.176308
\(733\) 9.00169e10 0.0115175 0.00575873 0.999983i \(-0.498167\pi\)
0.00575873 + 0.999983i \(0.498167\pi\)
\(734\) 5.07104e12i 0.644859i
\(735\) −2.98974e12 −0.377868
\(736\) 7.81677e12i 0.981923i
\(737\) 3.82511e12i 0.477573i
\(738\) 4.53001e12i 0.562142i
\(739\) 1.27401e13 1.57135 0.785677 0.618638i \(-0.212315\pi\)
0.785677 + 0.618638i \(0.212315\pi\)
\(740\) 1.89519e12 0.232333
\(741\) 6.58951e12i 0.802918i
\(742\) 3.17976e11i 0.0385103i
\(743\) 7.98450e11i 0.0961165i 0.998845 + 0.0480583i \(0.0153033\pi\)
−0.998845 + 0.0480583i \(0.984697\pi\)
\(744\) −5.31823e12 −0.636340
\(745\) 5.10657e12i 0.607332i
\(746\) −7.82329e12 −0.924836
\(747\) −9.17926e11 −0.107861
\(748\) 3.21268e12 + 9.44438e11i 0.375241 + 0.110310i
\(749\) −1.36797e13 −1.58821
\(750\) 1.56952e12 0.181130
\(751\) 9.56992e12i 1.09781i −0.835883 0.548907i \(-0.815044\pi\)
0.835883 0.548907i \(-0.184956\pi\)
\(752\) 1.73683e12 0.198051
\(753\) 2.90320e12i 0.329078i
\(754\) 9.97328e12i 1.12374i
\(755\) 3.62330e12i 0.405829i
\(756\) −8.66533e12 −0.964799
\(757\) 1.18435e13 1.31084 0.655418 0.755267i \(-0.272493\pi\)
0.655418 + 0.755267i \(0.272493\pi\)
\(758\) 4.46590e12i 0.491358i
\(759\) 1.98461e12i 0.217064i
\(760\) 5.54233e12i 0.602603i
\(761\) 7.12456e12 0.770064 0.385032 0.922903i \(-0.374190\pi\)
0.385032 + 0.922903i \(0.374190\pi\)
\(762\) 2.50765e12i 0.269445i
\(763\) 1.02875e13 1.09888
\(764\) 6.85906e12 0.728357
\(765\) −3.37813e12 9.93074e11i −0.356615 0.104835i
\(766\) −2.81254e12 −0.295168
\(767\) 1.17170e12 0.122246
\(768\) 3.08854e12i 0.320352i
\(769\) −1.51364e13 −1.56082 −0.780411 0.625267i \(-0.784990\pi\)
−0.780411 + 0.625267i \(0.784990\pi\)
\(770\) 2.15115e12i 0.220527i
\(771\) 4.92216e12i 0.501662i
\(772\) 1.25426e13i 1.27090i
\(773\) −6.55361e12 −0.660196 −0.330098 0.943947i \(-0.607082\pi\)
−0.330098 + 0.943947i \(0.607082\pi\)
\(774\) 5.54310e11 0.0555161
\(775\) 1.32179e13i 1.31615i
\(776\) 1.07970e13i 1.06888i
\(777\) 5.24476e12i 0.516216i
\(778\) −4.32508e11 −0.0423239
\(779\) 1.97693e13i 1.92342i
\(780\) 1.85817e12 0.179746
\(781\) −5.45335e12 −0.524486
\(782\) 4.98322e12 + 1.46493e12i 0.476518 + 0.140083i
\(783\) −1.35514e13 −1.28841
\(784\) −5.22037e12 −0.493491
\(785\) 2.36486e12i 0.222276i
\(786\) 2.02070e12 0.188843
\(787\) 1.72441e13i 1.60234i 0.598439 + 0.801168i \(0.295788\pi\)
−0.598439 + 0.801168i \(0.704212\pi\)
\(788\) 2.32212e12i 0.214544i
\(789\) 2.06579e12i 0.189775i
\(790\) −1.11015e12 −0.101405
\(791\) −8.44824e11 −0.0767312
\(792\) 4.42430e12i 0.399559i
\(793\) 8.19706e12i 0.736086i
\(794\) 6.82057e12i 0.609015i
\(795\) 9.26487e10 0.00822597
\(796\) 5.42884e12i 0.479290i
\(797\) 1.92951e13 1.69389 0.846944 0.531682i \(-0.178440\pi\)
0.846944 + 0.531682i \(0.178440\pi\)
\(798\) −6.44835e12 −0.562906
\(799\) 2.55784e12 8.70097e12i 0.222031 0.755278i
\(800\) 9.53358e12 0.822908
\(801\) 1.66733e13 1.43112
\(802\) 4.03096e12i 0.344052i
\(803\) −1.94803e12 −0.165339
\(804\) 3.23337e12i 0.272899i
\(805\) 8.81382e12i 0.739746i
\(806\) 1.33825e13i 1.11694i
\(807\) 7.51616e12 0.623829
\(808\) 4.73871e12 0.391119
\(809\) 3.75180e12i 0.307944i −0.988075 0.153972i \(-0.950794\pi\)
0.988075 0.153972i \(-0.0492065\pi\)
\(810\) 1.43056e12i 0.116768i
\(811\) 4.21763e12i 0.342353i −0.985240 0.171177i \(-0.945243\pi\)
0.985240 0.171177i \(-0.0547569\pi\)
\(812\) −2.57802e13 −2.08106
\(813\) 3.36047e12i 0.269769i
\(814\) −2.49946e12 −0.199543
\(815\) −2.38657e12 −0.189481
\(816\) 1.29840e12 + 3.81693e11i 0.102519 + 0.0301376i
\(817\) −2.41905e12 −0.189953
\(818\) −1.33371e12 −0.104153
\(819\) 2.33611e13i 1.81433i
\(820\) 5.57474e12 0.430588
\(821\) 2.89064e12i 0.222050i −0.993818 0.111025i \(-0.964587\pi\)
0.993818 0.111025i \(-0.0354133\pi\)
\(822\) 9.59704e10i 0.00733186i
\(823\) 1.85820e11i 0.0141186i −0.999975 0.00705931i \(-0.997753\pi\)
0.999975 0.00705931i \(-0.00224707\pi\)
\(824\) 2.23569e12 0.168943
\(825\) 2.42050e12 0.181912
\(826\) 1.14660e12i 0.0857040i
\(827\) 2.19451e13i 1.63141i 0.578470 + 0.815704i \(0.303650\pi\)
−0.578470 + 0.815704i \(0.696350\pi\)
\(828\) 7.62119e12i 0.563490i
\(829\) 7.80531e12 0.573977 0.286989 0.957934i \(-0.407346\pi\)
0.286989 + 0.957934i \(0.407346\pi\)
\(830\) 4.27642e11i 0.0312773i
\(831\) 2.83892e12 0.206513
\(832\) −5.17944e12 −0.374738
\(833\) −7.68807e12 + 2.61524e13i −0.553242 + 1.88196i
\(834\) 2.96584e11 0.0212276
\(835\) −4.88047e12 −0.347434
\(836\) 8.11748e12i 0.574768i
\(837\) 1.81836e13 1.28061
\(838\) 3.39993e11i 0.0238161i
\(839\) 1.83657e13i 1.27962i −0.768535 0.639808i \(-0.779014\pi\)
0.768535 0.639808i \(-0.220986\pi\)
\(840\) 4.32511e12i 0.299737i
\(841\) −2.58094e13 −1.77908
\(842\) 8.79613e12 0.603097
\(843\) 6.81314e12i 0.464647i
\(844\) 9.99954e12i 0.678327i
\(845\) 4.40033e12i 0.296914i
\(846\) 5.03766e12 0.338113
\(847\) 1.82833e13i 1.22062i
\(848\) 1.61773e11 0.0107430
\(849\) 1.51711e12 0.100215
\(850\) 1.78667e12 6.07769e12i 0.117398 0.399350i
\(851\) 1.02409e13 0.669356
\(852\) −4.60972e12 −0.299707
\(853\) 1.15587e13i 0.747544i −0.927521 0.373772i \(-0.878064\pi\)
0.927521 0.373772i \(-0.121936\pi\)
\(854\) 8.02147e12 0.516052
\(855\) 8.53551e12i 0.546238i
\(856\) 1.31076e13i 0.834434i
\(857\) 3.67551e12i 0.232757i −0.993205 0.116379i \(-0.962871\pi\)
0.993205 0.116379i \(-0.0371286\pi\)
\(858\) −2.45063e12 −0.154378
\(859\) −2.36948e13 −1.48485 −0.742426 0.669928i \(-0.766325\pi\)
−0.742426 + 0.669928i \(0.766325\pi\)
\(860\) 6.82147e11i 0.0425241i
\(861\) 1.54275e13i 0.956715i
\(862\) 1.16820e12i 0.0720666i
\(863\) 8.18769e12 0.502473 0.251237 0.967926i \(-0.419163\pi\)
0.251237 + 0.967926i \(0.419163\pi\)
\(864\) 1.31152e13i 0.800686i
\(865\) −3.77850e12 −0.229481
\(866\) −7.46736e12 −0.451166
\(867\) 3.82432e12 5.94245e12i 0.229863 0.357174i
\(868\) 3.45927e13 2.06845
\(869\) −3.86746e12 −0.230058
\(870\) 2.84367e12i 0.168284i
\(871\) −1.93526e13 −1.13935
\(872\) 9.85728e12i 0.577342i
\(873\) 1.66281e13i 0.968896i
\(874\) 1.25911e13i 0.729898i
\(875\) −2.42828e13 −1.40043
\(876\) −1.64667e12 −0.0944794
\(877\) 1.34379e13i 0.767064i −0.923528 0.383532i \(-0.874708\pi\)
0.923528 0.383532i \(-0.125292\pi\)
\(878\) 3.78549e11i 0.0214979i
\(879\) 2.64538e12i 0.149465i
\(880\) −1.09442e12 −0.0615192
\(881\) 3.19613e13i 1.78745i −0.448618 0.893724i \(-0.648084\pi\)
0.448618 0.893724i \(-0.351916\pi\)
\(882\) −1.51416e13 −0.842489
\(883\) 9.21484e12 0.510111 0.255056 0.966926i \(-0.417906\pi\)
0.255056 + 0.966926i \(0.417906\pi\)
\(884\) 4.77826e12 1.62541e13i 0.263169 0.895218i
\(885\) −3.34084e11 −0.0183067
\(886\) 1.15789e13 0.631272
\(887\) 5.95887e12i 0.323227i −0.986854 0.161614i \(-0.948330\pi\)
0.986854 0.161614i \(-0.0516698\pi\)
\(888\) −5.02543e12 −0.271216
\(889\) 3.87972e13i 2.08325i
\(890\) 7.76776e12i 0.414993i
\(891\) 4.98368e12i 0.264911i
\(892\) −4.04982e12 −0.214187
\(893\) −2.19847e13 −1.15688
\(894\) 5.69289e12i 0.298067i
\(895\) 3.10699e12i 0.161859i
\(896\) 2.93274e13i 1.52016i
\(897\) 1.00409e13 0.517853
\(898\) 3.77565e12i 0.193753i
\(899\) 5.40981e13 2.76225
\(900\) −9.29504e12 −0.472237
\(901\) 2.38245e11 8.10434e11i 0.0120438 0.0409691i
\(902\) −7.35220e12 −0.369818
\(903\) 1.88778e12 0.0944834
\(904\) 8.09494e11i 0.0403140i
\(905\) 4.25704e12 0.210955
\(906\) 4.03932e12i 0.199173i
\(907\) 3.49523e13i 1.71491i 0.514555 + 0.857457i \(0.327957\pi\)
−0.514555 + 0.857457i \(0.672043\pi\)
\(908\) 2.13077e13i 1.04028i
\(909\) −7.29788e12 −0.354535
\(910\) 1.08834e13 0.526115
\(911\) 1.82282e12i 0.0876819i 0.999039 + 0.0438410i \(0.0139595\pi\)
−0.999039 + 0.0438410i \(0.986041\pi\)
\(912\) 3.28066e12i 0.157031i
\(913\) 1.48979e12i 0.0709589i
\(914\) 6.13795e12 0.290914
\(915\) 2.33721e12i 0.110231i
\(916\) −1.80199e13 −0.845712
\(917\) −3.12633e13 −1.46007
\(918\) 8.36097e12 + 2.45789e12i 0.388566 + 0.114227i
\(919\) −1.16854e13 −0.540411 −0.270206 0.962803i \(-0.587092\pi\)
−0.270206 + 0.962803i \(0.587092\pi\)
\(920\) −8.44524e12 −0.388657
\(921\) 1.05478e13i 0.483052i
\(922\) −1.22738e13 −0.559358
\(923\) 2.75905e13i 1.25127i
\(924\) 6.33470e12i 0.285892i
\(925\) 1.24902e13i 0.560959i
\(926\) −5.44783e12 −0.243486
\(927\) −3.44309e12 −0.153140
\(928\) 3.90189e13i 1.72707i
\(929\) 2.03224e13i 0.895166i 0.894242 + 0.447583i \(0.147715\pi\)
−0.894242 + 0.447583i \(0.852285\pi\)
\(930\) 3.81572e12i 0.167264i
\(931\) 6.60793e13 2.88265
\(932\) 7.16329e11i 0.0310986i
\(933\) 6.96787e12 0.301046
\(934\) −1.56046e13 −0.670954
\(935\) −1.61176e12 + 5.48269e12i −0.0689679 + 0.234607i
\(936\) 2.23842e13 0.953235
\(937\) −1.03126e13 −0.437061 −0.218530 0.975830i \(-0.570126\pi\)
−0.218530 + 0.975830i \(0.570126\pi\)
\(938\) 1.89381e13i 0.798773i
\(939\) −3.93829e12 −0.165315
\(940\) 6.19945e12i 0.258987i
\(941\) 9.97481e12i 0.414717i −0.978265 0.207358i \(-0.933513\pi\)
0.978265 0.207358i \(-0.0664866\pi\)
\(942\) 2.63639e12i 0.109089i
\(943\) 3.01239e13 1.24053
\(944\) −5.83343e11 −0.0239084
\(945\) 1.47881e13i 0.603209i
\(946\) 8.99644e11i 0.0365225i
\(947\) 7.55330e12i 0.305184i −0.988289 0.152592i \(-0.951238\pi\)
0.988289 0.152592i \(-0.0487620\pi\)
\(948\) −3.26916e12 −0.131462
\(949\) 9.85578e12i 0.394451i
\(950\) −1.53565e13 −0.611696
\(951\) −1.28635e13 −0.509972
\(952\) 3.78335e13 + 1.11220e13i 1.49283 + 0.438850i
\(953\) 5.11924e12 0.201042 0.100521 0.994935i \(-0.467949\pi\)
0.100521 + 0.994935i \(0.467949\pi\)
\(954\) 4.69222e11 0.0183405
\(955\) 1.17055e13i 0.455381i
\(956\) 3.48836e13 1.35070
\(957\) 9.90657e12i 0.381786i
\(958\) 2.46781e13i 0.946599i
\(959\) 1.48481e12i 0.0566874i
\(960\) 1.47681e12 0.0561181
\(961\) −4.61509e13 −1.74552
\(962\) 1.26457e13i 0.476052i
\(963\) 2.01865e13i 0.756384i
\(964\) 1.67887e13i 0.626137i
\(965\) 2.14050e13 0.794588
\(966\) 9.82581e12i 0.363054i
\(967\) −2.96090e13 −1.08894 −0.544471 0.838780i \(-0.683269\pi\)
−0.544471 + 0.838780i \(0.683269\pi\)
\(968\) −1.75187e13 −0.641303
\(969\) −1.64351e13 4.83146e12i −0.598846 0.176044i
\(970\) 7.74666e12 0.280958
\(971\) −2.36780e13 −0.854790 −0.427395 0.904065i \(-0.640569\pi\)
−0.427395 + 0.904065i \(0.640569\pi\)
\(972\) 1.98144e13i 0.712006i
\(973\) −4.58861e12 −0.164124
\(974\) 8.51810e12i 0.303269i
\(975\) 1.22462e13i 0.433990i
\(976\) 4.08100e12i 0.143960i
\(977\) 1.30708e13 0.458961 0.229480 0.973313i \(-0.426297\pi\)
0.229480 + 0.973313i \(0.426297\pi\)
\(978\) 2.66059e12 0.0929937
\(979\) 2.70608e13i 0.941496i
\(980\) 1.86336e13i 0.645328i
\(981\) 1.51808e13i 0.523339i
\(982\) 1.16076e13 0.398329
\(983\) 1.05637e13i 0.360850i −0.983589 0.180425i \(-0.942253\pi\)
0.983589 0.180425i \(-0.0577473\pi\)
\(984\) −1.47824e13 −0.502651
\(985\) 3.96288e12 0.134137
\(986\) 2.48747e13 + 7.31246e12i 0.838130 + 0.246387i
\(987\) 1.71564e13 0.575438
\(988\) −4.10693e13 −1.37123
\(989\) 3.68608e12i 0.122513i
\(990\) −3.17435e12 −0.105026
\(991\) 4.60965e13i 1.51823i 0.650958 + 0.759113i \(0.274367\pi\)
−0.650958 + 0.759113i \(0.725633\pi\)
\(992\) 5.23568e13i 1.71661i
\(993\) 1.30904e13i 0.427250i
\(994\) −2.69995e13 −0.877238
\(995\) −9.26473e12 −0.299660
\(996\) 1.25932e12i 0.0405480i
\(997\) 2.60737e13i 0.835748i −0.908505 0.417874i \(-0.862775\pi\)
0.908505 0.417874i \(-0.137225\pi\)
\(998\) 2.01631e13i 0.643384i
\(999\) 1.71825e13 0.545811
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 17.10.b.a.16.8 yes 12
3.2 odd 2 153.10.d.b.118.6 12
4.3 odd 2 272.10.b.c.33.5 12
17.4 even 4 289.10.a.c.1.6 12
17.13 even 4 289.10.a.c.1.5 12
17.16 even 2 inner 17.10.b.a.16.7 12
51.50 odd 2 153.10.d.b.118.5 12
68.67 odd 2 272.10.b.c.33.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.b.a.16.7 12 17.16 even 2 inner
17.10.b.a.16.8 yes 12 1.1 even 1 trivial
153.10.d.b.118.5 12 51.50 odd 2
153.10.d.b.118.6 12 3.2 odd 2
272.10.b.c.33.5 12 4.3 odd 2
272.10.b.c.33.8 12 68.67 odd 2
289.10.a.c.1.5 12 17.13 even 4
289.10.a.c.1.6 12 17.4 even 4