Properties

Label 83.13.b.c.82.11
Level $83$
Weight $13$
Character 83.82
Analytic conductor $75.861$
Analytic rank $0$
Dimension $80$
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] = [83,13,Mod(82,83)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(83, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("83.82");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 83.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: \(75.8614868339\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 82.11
Character \(\chi\) \(=\) 83.82
Dual form 83.13.b.c.82.70

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-102.696i q^{2} -81.5431 q^{3} -6450.37 q^{4} +18424.7i q^{5} +8374.11i q^{6} +214939. q^{7} +241783. i q^{8} -524792. q^{9} +O(q^{10})\) \(q-102.696i q^{2} -81.5431 q^{3} -6450.37 q^{4} +18424.7i q^{5} +8374.11i q^{6} +214939. q^{7} +241783. i q^{8} -524792. q^{9} +1.89213e6 q^{10} -2.57610e6 q^{11} +525983. q^{12} -4.43368e6i q^{13} -2.20732e7i q^{14} -1.50240e6i q^{15} -1.59065e6 q^{16} -6.28598e6 q^{17} +5.38938e7i q^{18} -1.47181e7i q^{19} -1.18846e8i q^{20} -1.75268e7 q^{21} +2.64554e8i q^{22} -9.92752e7 q^{23} -1.97158e7i q^{24} -9.53277e7 q^{25} -4.55319e8 q^{26} +8.61285e7 q^{27} -1.38643e9 q^{28} +1.12330e9 q^{29} -1.54290e8 q^{30} -9.73251e8 q^{31} +1.15370e9i q^{32} +2.10063e8 q^{33} +6.45543e8i q^{34} +3.96017e9i q^{35} +3.38510e9 q^{36} +3.95456e9 q^{37} -1.51148e9 q^{38} +3.61536e8i q^{39} -4.45478e9 q^{40} +3.30591e9 q^{41} +1.79992e9i q^{42} -6.34747e9i q^{43} +1.66168e10 q^{44} -9.66911e9i q^{45} +1.01951e10i q^{46} +1.24063e10i q^{47} +1.29706e8 q^{48} +3.23573e10 q^{49} +9.78973e9i q^{50} +5.12579e8 q^{51} +2.85989e10i q^{52} +3.84521e10i q^{53} -8.84501e9i q^{54} -4.74638e10i q^{55} +5.19686e10i q^{56} +1.20016e9i q^{57} -1.15358e11i q^{58} -1.08532e10 q^{59} +9.69107e9i q^{60} -5.41860e10 q^{61} +9.99485e10i q^{62} -1.12798e11 q^{63} +1.11964e11 q^{64} +8.16890e10 q^{65} -2.15725e10i q^{66} +1.57078e11i q^{67} +4.05469e10 q^{68} +8.09521e9 q^{69} +4.06692e11 q^{70} +1.65315e11i q^{71} -1.26886e11i q^{72} +2.06517e11i q^{73} -4.06115e11i q^{74} +7.77332e9 q^{75} +9.49373e10i q^{76} -5.53703e11 q^{77} +3.71281e10 q^{78} +1.81447e11i q^{79} -2.93072e10i q^{80} +2.71873e11 q^{81} -3.39502e11i q^{82} +(2.84580e11 + 1.60948e11i) q^{83} +1.13054e11 q^{84} -1.15817e11i q^{85} -6.51857e11 q^{86} -9.15974e10 q^{87} -6.22858e11i q^{88} -3.14521e11i q^{89} -9.92975e11 q^{90} -9.52969e11i q^{91} +6.40362e11 q^{92} +7.93619e10 q^{93} +1.27407e12 q^{94} +2.71176e11 q^{95} -9.40761e10i q^{96} -1.21462e12i q^{97} -3.32295e12i q^{98} +1.35192e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9} + 1177482 q^{10} + 510406 q^{11} - 9260402 q^{12} + 203791850 q^{16} + 5571718 q^{17} + 46565862 q^{21} + 804389464 q^{23} - 4263713272 q^{25} + 18061794 q^{26} - 2326165338 q^{27} - 204811652 q^{28} + 1486960270 q^{29} - 2621683648 q^{30} - 665743010 q^{31} + 135224502 q^{33} - 54936709824 q^{36} - 280627202 q^{37} + 6646145310 q^{38} - 7119722058 q^{40} + 51318109072 q^{41} - 11512674650 q^{44} + 85368259738 q^{48} + 148785395094 q^{49} - 100143389562 q^{51} - 63584241050 q^{59} - 29216180978 q^{61} - 332932206620 q^{63} - 323596534090 q^{64} + 362112989184 q^{65} - 86115426752 q^{68} + 272383417100 q^{69} + 105630718656 q^{70} + 785418808326 q^{75} - 663355117738 q^{77} + 1483841884620 q^{78} + 2430778545148 q^{81} + 837315119192 q^{83} - 3013574788354 q^{84} + 452180651958 q^{86} - 682263689498 q^{87} - 499714512022 q^{90} + 997428187414 q^{92} - 1487992716298 q^{93} + 3169817690580 q^{94} + 1542762610848 q^{95} + 2021347267420 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 102.696i 1.60462i −0.596909 0.802309i \(-0.703605\pi\)
0.596909 0.802309i \(-0.296395\pi\)
\(3\) −81.5431 −0.111856 −0.0559281 0.998435i \(-0.517812\pi\)
−0.0559281 + 0.998435i \(0.517812\pi\)
\(4\) −6450.37 −1.57480
\(5\) 18424.7i 1.17918i 0.807703 + 0.589589i \(0.200710\pi\)
−0.807703 + 0.589589i \(0.799290\pi\)
\(6\) 8374.11i 0.179486i
\(7\) 214939. 1.82695 0.913474 0.406897i \(-0.133389\pi\)
0.913474 + 0.406897i \(0.133389\pi\)
\(8\) 241783.i 0.922330i
\(9\) −524792. −0.987488
\(10\) 1.89213e6 1.89213
\(11\) −2.57610e6 −1.45414 −0.727070 0.686563i \(-0.759119\pi\)
−0.727070 + 0.686563i \(0.759119\pi\)
\(12\) 525983. 0.176151
\(13\) 4.43368e6i 0.918552i −0.888294 0.459276i \(-0.848109\pi\)
0.888294 0.459276i \(-0.151891\pi\)
\(14\) 2.20732e7i 2.93155i
\(15\) 1.50240e6i 0.131898i
\(16\) −1.59065e6 −0.0948101
\(17\) −6.28598e6 −0.260423 −0.130212 0.991486i \(-0.541566\pi\)
−0.130212 + 0.991486i \(0.541566\pi\)
\(18\) 5.38938e7i 1.58454i
\(19\) 1.47181e7i 0.312846i −0.987690 0.156423i \(-0.950004\pi\)
0.987690 0.156423i \(-0.0499963\pi\)
\(20\) 1.18846e8i 1.85697i
\(21\) −1.75268e7 −0.204355
\(22\) 2.64554e8i 2.33334i
\(23\) −9.92752e7 −0.670616 −0.335308 0.942109i \(-0.608840\pi\)
−0.335308 + 0.942109i \(0.608840\pi\)
\(24\) 1.97158e7i 0.103168i
\(25\) −9.53277e7 −0.390462
\(26\) −4.55319e8 −1.47393
\(27\) 8.61285e7 0.222313
\(28\) −1.38643e9 −2.87707
\(29\) 1.12330e9 1.88846 0.944231 0.329285i \(-0.106808\pi\)
0.944231 + 0.329285i \(0.106808\pi\)
\(30\) −1.54290e8 −0.211646
\(31\) −9.73251e8 −1.09662 −0.548308 0.836276i \(-0.684728\pi\)
−0.548308 + 0.836276i \(0.684728\pi\)
\(32\) 1.15370e9i 1.07446i
\(33\) 2.10063e8 0.162655
\(34\) 6.45543e8i 0.417880i
\(35\) 3.96017e9i 2.15430i
\(36\) 3.38510e9 1.55509
\(37\) 3.95456e9 1.54130 0.770651 0.637258i \(-0.219931\pi\)
0.770651 + 0.637258i \(0.219931\pi\)
\(38\) −1.51148e9 −0.501998
\(39\) 3.61536e8i 0.102746i
\(40\) −4.45478e9 −1.08759
\(41\) 3.30591e9 0.695966 0.347983 0.937501i \(-0.386867\pi\)
0.347983 + 0.937501i \(0.386867\pi\)
\(42\) 1.79992e9i 0.327912i
\(43\) 6.34747e9i 1.00413i −0.864830 0.502065i \(-0.832574\pi\)
0.864830 0.502065i \(-0.167426\pi\)
\(44\) 1.66168e10 2.28998
\(45\) 9.66911e9i 1.16443i
\(46\) 1.01951e10i 1.07608i
\(47\) 1.24063e10i 1.15094i 0.817822 + 0.575471i \(0.195181\pi\)
−0.817822 + 0.575471i \(0.804819\pi\)
\(48\) 1.29706e8 0.0106051
\(49\) 3.23573e10 2.33774
\(50\) 9.78973e9i 0.626543i
\(51\) 5.12579e8 0.0291299
\(52\) 2.85989e10i 1.44653i
\(53\) 3.84521e10i 1.73486i 0.497560 + 0.867430i \(0.334230\pi\)
−0.497560 + 0.867430i \(0.665770\pi\)
\(54\) 8.84501e9i 0.356727i
\(55\) 4.74638e10i 1.71469i
\(56\) 5.19686e10i 1.68505i
\(57\) 1.20016e9i 0.0349937i
\(58\) 1.15358e11i 3.03026i
\(59\) −1.08532e10 −0.257303 −0.128652 0.991690i \(-0.541065\pi\)
−0.128652 + 0.991690i \(0.541065\pi\)
\(60\) 9.69107e9i 0.207713i
\(61\) −5.41860e10 −1.05174 −0.525870 0.850565i \(-0.676260\pi\)
−0.525870 + 0.850565i \(0.676260\pi\)
\(62\) 9.99485e10i 1.75965i
\(63\) −1.12798e11 −1.80409
\(64\) 1.11964e11 1.62929
\(65\) 8.16890e10 1.08314
\(66\) 2.15725e10i 0.260998i
\(67\) 1.57078e11i 1.73647i 0.496157 + 0.868233i \(0.334744\pi\)
−0.496157 + 0.868233i \(0.665256\pi\)
\(68\) 4.05469e10 0.410114
\(69\) 8.09521e9 0.0750125
\(70\) 4.06692e11 3.45683
\(71\) 1.65315e11i 1.29051i 0.763967 + 0.645256i \(0.223249\pi\)
−0.763967 + 0.645256i \(0.776751\pi\)
\(72\) 1.26886e11i 0.910790i
\(73\) 2.06517e11i 1.36464i 0.731052 + 0.682321i \(0.239029\pi\)
−0.731052 + 0.682321i \(0.760971\pi\)
\(74\) 4.06115e11i 2.47320i
\(75\) 7.77332e9 0.0436756
\(76\) 9.49373e10i 0.492669i
\(77\) −5.53703e11 −2.65664
\(78\) 3.71281e10 0.164868
\(79\) 1.81447e11i 0.746428i 0.927745 + 0.373214i \(0.121744\pi\)
−0.927745 + 0.373214i \(0.878256\pi\)
\(80\) 2.93072e10i 0.111798i
\(81\) 2.71873e11 0.962621
\(82\) 3.39502e11i 1.11676i
\(83\) 2.84580e11 + 1.60948e11i 0.870434 + 0.492285i
\(84\) 1.13054e11 0.321818
\(85\) 1.15817e11i 0.307086i
\(86\) −6.51857e11 −1.61125
\(87\) −9.15974e10 −0.211236
\(88\) 6.22858e11i 1.34120i
\(89\) 3.14521e11i 0.632863i −0.948615 0.316432i \(-0.897515\pi\)
0.948615 0.316432i \(-0.102485\pi\)
\(90\) −9.92975e11 −1.86846
\(91\) 9.52969e11i 1.67815i
\(92\) 6.40362e11 1.05608
\(93\) 7.93619e10 0.122663
\(94\) 1.27407e12 1.84682
\(95\) 2.71176e11 0.368901
\(96\) 9.40761e10i 0.120185i
\(97\) 1.21462e12i 1.45818i −0.684418 0.729089i \(-0.739944\pi\)
0.684418 0.729089i \(-0.260056\pi\)
\(98\) 3.32295e12i 3.75118i
\(99\) 1.35192e12 1.43595
\(100\) 6.14899e11 0.614899
\(101\) 1.51863e12i 1.43062i 0.698809 + 0.715308i \(0.253714\pi\)
−0.698809 + 0.715308i \(0.746286\pi\)
\(102\) 5.26395e10i 0.0467424i
\(103\) 4.09363e11i 0.342835i −0.985198 0.171417i \(-0.945165\pi\)
0.985198 0.171417i \(-0.0548347\pi\)
\(104\) 1.07199e12 0.847209
\(105\) 3.22925e11i 0.240971i
\(106\) 3.94885e12 2.78379
\(107\) 8.14800e11i 0.542936i −0.962447 0.271468i \(-0.912491\pi\)
0.962447 0.271468i \(-0.0875091\pi\)
\(108\) −5.55561e11 −0.350098
\(109\) 1.69615e11 0.101136 0.0505679 0.998721i \(-0.483897\pi\)
0.0505679 + 0.998721i \(0.483897\pi\)
\(110\) −4.87432e12 −2.75142
\(111\) −3.22467e11 −0.172404
\(112\) −3.41892e11 −0.173213
\(113\) 2.14626e12 1.03089 0.515445 0.856923i \(-0.327627\pi\)
0.515445 + 0.856923i \(0.327627\pi\)
\(114\) 1.23251e11 0.0561516
\(115\) 1.82911e12i 0.790776i
\(116\) −7.24571e12 −2.97394
\(117\) 2.32676e12i 0.907060i
\(118\) 1.11457e12i 0.412873i
\(119\) −1.35110e12 −0.475780
\(120\) 3.63256e11 0.121654
\(121\) 3.49785e12 1.11452
\(122\) 5.56466e12i 1.68764i
\(123\) −2.69574e11 −0.0778480
\(124\) 6.27783e12 1.72695
\(125\) 2.74183e12i 0.718754i
\(126\) 1.15839e13i 2.89487i
\(127\) 5.61719e12 1.33874 0.669370 0.742929i \(-0.266564\pi\)
0.669370 + 0.742929i \(0.266564\pi\)
\(128\) 6.77268e12i 1.53993i
\(129\) 5.17593e11i 0.112318i
\(130\) 8.38910e12i 1.73802i
\(131\) −2.88968e12 −0.571772 −0.285886 0.958264i \(-0.592288\pi\)
−0.285886 + 0.958264i \(0.592288\pi\)
\(132\) −1.35498e12 −0.256148
\(133\) 3.16349e12i 0.571553i
\(134\) 1.61312e13 2.78636
\(135\) 1.58689e12i 0.262146i
\(136\) 1.51985e12i 0.240196i
\(137\) 7.34209e12i 1.11044i −0.831702 0.555222i \(-0.812633\pi\)
0.831702 0.555222i \(-0.187367\pi\)
\(138\) 8.31341e11i 0.120366i
\(139\) 9.72175e12i 1.34789i 0.738780 + 0.673947i \(0.235402\pi\)
−0.738780 + 0.673947i \(0.764598\pi\)
\(140\) 2.55446e13i 3.39258i
\(141\) 1.01165e12i 0.128740i
\(142\) 1.69771e13 2.07078
\(143\) 1.14216e13i 1.33570i
\(144\) 8.34759e11 0.0936238
\(145\) 2.06964e13i 2.22683i
\(146\) 2.12084e13 2.18973
\(147\) −2.63852e12 −0.261491
\(148\) −2.55084e13 −2.42724
\(149\) 1.04941e13i 0.959016i 0.877538 + 0.479508i \(0.159185\pi\)
−0.877538 + 0.479508i \(0.840815\pi\)
\(150\) 7.98285e11i 0.0700826i
\(151\) −5.02885e12 −0.424236 −0.212118 0.977244i \(-0.568036\pi\)
−0.212118 + 0.977244i \(0.568036\pi\)
\(152\) 3.55859e12 0.288547
\(153\) 3.29883e12 0.257165
\(154\) 5.68628e13i 4.26289i
\(155\) 1.79318e13i 1.29311i
\(156\) 2.33204e12i 0.161804i
\(157\) 1.60128e13i 1.06922i −0.845098 0.534611i \(-0.820458\pi\)
0.845098 0.534611i \(-0.179542\pi\)
\(158\) 1.86338e13 1.19773
\(159\) 3.13550e12i 0.194055i
\(160\) −2.12565e13 −1.26699
\(161\) −2.13381e13 −1.22518
\(162\) 2.79201e13i 1.54464i
\(163\) 1.20510e13i 0.642535i −0.946989 0.321267i \(-0.895891\pi\)
0.946989 0.321267i \(-0.104109\pi\)
\(164\) −2.13243e13 −1.09600
\(165\) 3.87034e12i 0.191799i
\(166\) 1.65286e13 2.92251e13i 0.789929 1.39671i
\(167\) −7.21540e12 −0.332630 −0.166315 0.986073i \(-0.553187\pi\)
−0.166315 + 0.986073i \(0.553187\pi\)
\(168\) 4.23768e12i 0.188483i
\(169\) 3.64059e12 0.156262
\(170\) −1.18939e13 −0.492755
\(171\) 7.72394e12i 0.308932i
\(172\) 4.09435e13i 1.58130i
\(173\) 5.99192e12 0.223506 0.111753 0.993736i \(-0.464353\pi\)
0.111753 + 0.993736i \(0.464353\pi\)
\(174\) 9.40665e12i 0.338953i
\(175\) −2.04896e13 −0.713355
\(176\) 4.09767e12 0.137867
\(177\) 8.85002e11 0.0287809
\(178\) −3.22999e13 −1.01550
\(179\) 1.99120e13i 0.605336i 0.953096 + 0.302668i \(0.0978774\pi\)
−0.953096 + 0.302668i \(0.902123\pi\)
\(180\) 6.23694e13i 1.83373i
\(181\) 3.03193e13i 0.862279i −0.902285 0.431140i \(-0.858112\pi\)
0.902285 0.431140i \(-0.141888\pi\)
\(182\) −9.78656e13 −2.69279
\(183\) 4.41850e12 0.117643
\(184\) 2.40031e13i 0.618529i
\(185\) 7.28614e13i 1.81747i
\(186\) 8.15012e12i 0.196828i
\(187\) 1.61933e13 0.378692
\(188\) 8.00250e13i 1.81250i
\(189\) 1.85123e13 0.406154
\(190\) 2.78486e13i 0.591945i
\(191\) 3.21566e13 0.662324 0.331162 0.943574i \(-0.392559\pi\)
0.331162 + 0.943574i \(0.392559\pi\)
\(192\) −9.12991e12 −0.182247
\(193\) −9.98454e13 −1.93190 −0.965949 0.258734i \(-0.916695\pi\)
−0.965949 + 0.258734i \(0.916695\pi\)
\(194\) −1.24736e14 −2.33982
\(195\) −6.66118e12 −0.121156
\(196\) −2.08717e14 −3.68147
\(197\) 3.28214e13 0.561512 0.280756 0.959779i \(-0.409415\pi\)
0.280756 + 0.959779i \(0.409415\pi\)
\(198\) 1.38836e14i 2.30415i
\(199\) −3.57560e12 −0.0575745 −0.0287873 0.999586i \(-0.509165\pi\)
−0.0287873 + 0.999586i \(0.509165\pi\)
\(200\) 2.30487e13i 0.360135i
\(201\) 1.28086e13i 0.194234i
\(202\) 1.55956e14 2.29559
\(203\) 2.41441e14 3.45012
\(204\) −3.30632e12 −0.0458738
\(205\) 6.09103e13i 0.820668i
\(206\) −4.20397e13 −0.550119
\(207\) 5.20988e13 0.662225
\(208\) 7.05242e12i 0.0870880i
\(209\) 3.79153e13i 0.454922i
\(210\) −3.31629e13 −0.386667
\(211\) 5.10791e13i 0.578827i 0.957204 + 0.289413i \(0.0934602\pi\)
−0.957204 + 0.289413i \(0.906540\pi\)
\(212\) 2.48030e14i 2.73205i
\(213\) 1.34803e13i 0.144352i
\(214\) −8.36764e13 −0.871205
\(215\) 1.16950e14 1.18405
\(216\) 2.08244e13i 0.205046i
\(217\) −2.09189e14 −2.00346
\(218\) 1.74187e13i 0.162284i
\(219\) 1.68400e13i 0.152644i
\(220\) 3.06159e14i 2.70029i
\(221\) 2.78700e13i 0.239212i
\(222\) 3.31159e13i 0.276642i
\(223\) 1.09046e14i 0.886709i 0.896346 + 0.443354i \(0.146212\pi\)
−0.896346 + 0.443354i \(0.853788\pi\)
\(224\) 2.47974e14i 1.96299i
\(225\) 5.00272e13 0.385577
\(226\) 2.20411e14i 1.65418i
\(227\) 7.92511e13 0.579229 0.289614 0.957143i \(-0.406473\pi\)
0.289614 + 0.957143i \(0.406473\pi\)
\(228\) 7.74148e12i 0.0551080i
\(229\) 1.49134e14 1.03410 0.517051 0.855954i \(-0.327030\pi\)
0.517051 + 0.855954i \(0.327030\pi\)
\(230\) −1.87842e14 −1.26889
\(231\) 4.51507e13 0.297161
\(232\) 2.71595e14i 1.74178i
\(233\) 7.16947e13i 0.448076i 0.974580 + 0.224038i \(0.0719239\pi\)
−0.974580 + 0.224038i \(0.928076\pi\)
\(234\) 2.38948e14 1.45548
\(235\) −2.28581e14 −1.35717
\(236\) 7.00070e13 0.405200
\(237\) 1.47958e13i 0.0834925i
\(238\) 1.38752e14i 0.763445i
\(239\) 2.17256e14i 1.16569i 0.812582 + 0.582847i \(0.198061\pi\)
−0.812582 + 0.582847i \(0.801939\pi\)
\(240\) 2.38980e12i 0.0125053i
\(241\) −1.99050e14 −1.01592 −0.507961 0.861380i \(-0.669601\pi\)
−0.507961 + 0.861380i \(0.669601\pi\)
\(242\) 3.59214e14i 1.78839i
\(243\) −6.79416e13 −0.329988
\(244\) 3.49520e14 1.65628
\(245\) 5.96173e14i 2.75661i
\(246\) 2.76841e13i 0.124916i
\(247\) −6.52554e13 −0.287365
\(248\) 2.35316e14i 1.01144i
\(249\) −2.32055e13 1.31242e13i −0.0973634 0.0550650i
\(250\) 2.81574e14 1.15333
\(251\) 1.42409e14i 0.569502i −0.958601 0.284751i \(-0.908089\pi\)
0.958601 0.284751i \(-0.0919109\pi\)
\(252\) 7.27589e14 2.84108
\(253\) 2.55743e14 0.975169
\(254\) 5.76860e14i 2.14817i
\(255\) 9.44409e12i 0.0343494i
\(256\) −2.36919e14 −0.841704
\(257\) 1.30773e14i 0.453858i 0.973911 + 0.226929i \(0.0728685\pi\)
−0.973911 + 0.226929i \(0.927132\pi\)
\(258\) 5.31544e13 0.180228
\(259\) 8.49987e14 2.81588
\(260\) −5.26924e14 −1.70572
\(261\) −5.89499e14 −1.86483
\(262\) 2.96758e14i 0.917475i
\(263\) 1.51194e13i 0.0456878i 0.999739 + 0.0228439i \(0.00727207\pi\)
−0.999739 + 0.0228439i \(0.992728\pi\)
\(264\) 5.07898e13i 0.150021i
\(265\) −7.08466e14 −2.04571
\(266\) −3.24876e14 −0.917125
\(267\) 2.56470e13i 0.0707896i
\(268\) 1.01321e15i 2.73458i
\(269\) 7.32663e14i 1.93371i −0.255331 0.966854i \(-0.582184\pi\)
0.255331 0.966854i \(-0.417816\pi\)
\(270\) 1.62966e14 0.420645
\(271\) 7.84010e14i 1.97927i 0.143595 + 0.989637i \(0.454134\pi\)
−0.143595 + 0.989637i \(0.545866\pi\)
\(272\) 9.99879e12 0.0246907
\(273\) 7.77080e13i 0.187711i
\(274\) −7.54000e14 −1.78184
\(275\) 2.45574e14 0.567787
\(276\) −5.22171e13 −0.118129
\(277\) −2.68014e14 −0.593305 −0.296653 0.954985i \(-0.595870\pi\)
−0.296653 + 0.954985i \(0.595870\pi\)
\(278\) 9.98380e14 2.16285
\(279\) 5.10754e14 1.08290
\(280\) −9.57504e14 −1.98698
\(281\) 4.90304e14i 0.995928i 0.867198 + 0.497964i \(0.165919\pi\)
−0.867198 + 0.497964i \(0.834081\pi\)
\(282\) −1.03891e14 −0.206578
\(283\) 3.93873e14i 0.766721i −0.923599 0.383360i \(-0.874767\pi\)
0.923599 0.383360i \(-0.125233\pi\)
\(284\) 1.06634e15i 2.03229i
\(285\) −2.21126e13 −0.0412639
\(286\) 1.17295e15 2.14329
\(287\) 7.10568e14 1.27149
\(288\) 6.05451e14i 1.06102i
\(289\) −5.43109e14 −0.932180
\(290\) 2.12543e15 3.57322
\(291\) 9.90441e13i 0.163106i
\(292\) 1.33211e15i 2.14904i
\(293\) −1.83625e14 −0.290219 −0.145109 0.989416i \(-0.546353\pi\)
−0.145109 + 0.989416i \(0.546353\pi\)
\(294\) 2.70964e14i 0.419592i
\(295\) 1.99966e14i 0.303406i
\(296\) 9.56146e14i 1.42159i
\(297\) −2.21876e14 −0.323274
\(298\) 1.07769e15 1.53885
\(299\) 4.40154e14i 0.615996i
\(300\) −5.01408e13 −0.0687802
\(301\) 1.36432e15i 1.83449i
\(302\) 5.16440e14i 0.680736i
\(303\) 1.23834e14i 0.160023i
\(304\) 2.34113e13i 0.0296609i
\(305\) 9.98359e14i 1.24019i
\(306\) 3.38775e14i 0.412651i
\(307\) 1.51936e14i 0.181481i −0.995875 0.0907406i \(-0.971077\pi\)
0.995875 0.0907406i \(-0.0289234\pi\)
\(308\) 3.57159e15 4.18367
\(309\) 3.33807e13i 0.0383482i
\(310\) −1.84152e15 −2.07494
\(311\) 3.30490e14i 0.365255i −0.983182 0.182627i \(-0.941540\pi\)
0.983182 0.182627i \(-0.0584602\pi\)
\(312\) −8.74134e13 −0.0947655
\(313\) −3.22547e14 −0.343026 −0.171513 0.985182i \(-0.554866\pi\)
−0.171513 + 0.985182i \(0.554866\pi\)
\(314\) −1.64444e15 −1.71569
\(315\) 2.07827e15i 2.12734i
\(316\) 1.17040e15i 1.17547i
\(317\) 3.09162e14 0.304670 0.152335 0.988329i \(-0.451321\pi\)
0.152335 + 0.988329i \(0.451321\pi\)
\(318\) −3.22002e14 −0.311384
\(319\) −2.89373e15 −2.74609
\(320\) 2.06290e15i 1.92123i
\(321\) 6.64414e13i 0.0607307i
\(322\) 2.19132e15i 1.96595i
\(323\) 9.25178e13i 0.0814724i
\(324\) −1.75368e15 −1.51593
\(325\) 4.22652e14i 0.358660i
\(326\) −1.23758e15 −1.03102
\(327\) −1.38309e13 −0.0113127
\(328\) 7.99314e14i 0.641910i
\(329\) 2.66659e15i 2.10271i
\(330\) 3.97467e14 0.307764
\(331\) 1.85040e15i 1.40701i 0.710690 + 0.703505i \(0.248383\pi\)
−0.710690 + 0.703505i \(0.751617\pi\)
\(332\) −1.83565e15 1.03817e15i −1.37076 0.775249i
\(333\) −2.07532e15 −1.52202
\(334\) 7.40989e14i 0.533744i
\(335\) −2.89411e15 −2.04760
\(336\) 2.78789e13 0.0193749
\(337\) 8.56215e14i 0.584525i −0.956338 0.292263i \(-0.905592\pi\)
0.956338 0.292263i \(-0.0944081\pi\)
\(338\) 3.73873e14i 0.250740i
\(339\) −1.75013e14 −0.115311
\(340\) 7.47064e14i 0.483598i
\(341\) 2.50719e15 1.59463
\(342\) 7.93214e14 0.495717
\(343\) 3.97982e15 2.44398
\(344\) 1.53471e15 0.926140
\(345\) 1.49151e14i 0.0884531i
\(346\) 6.15343e14i 0.358642i
\(347\) 3.98226e14i 0.228114i −0.993474 0.114057i \(-0.963615\pi\)
0.993474 0.114057i \(-0.0363847\pi\)
\(348\) 5.90837e14 0.332654
\(349\) −8.29039e14 −0.458799 −0.229399 0.973332i \(-0.573676\pi\)
−0.229399 + 0.973332i \(0.573676\pi\)
\(350\) 2.10419e15i 1.14466i
\(351\) 3.81866e14i 0.204206i
\(352\) 2.97204e15i 1.56242i
\(353\) 2.39223e15 1.23639 0.618193 0.786026i \(-0.287865\pi\)
0.618193 + 0.786026i \(0.287865\pi\)
\(354\) 9.08858e13i 0.0461824i
\(355\) −3.04587e15 −1.52174
\(356\) 2.02878e15i 0.996631i
\(357\) 1.10173e14 0.0532189
\(358\) 2.04487e15 0.971333
\(359\) 2.33002e15 1.08841 0.544205 0.838952i \(-0.316831\pi\)
0.544205 + 0.838952i \(0.316831\pi\)
\(360\) 2.33783e15 1.07398
\(361\) 1.99669e15 0.902127
\(362\) −3.11366e15 −1.38363
\(363\) −2.85226e14 −0.124666
\(364\) 6.14700e15i 2.64274i
\(365\) −3.80501e15 −1.60916
\(366\) 4.53760e14i 0.188773i
\(367\) 1.84378e15i 0.754591i −0.926093 0.377296i \(-0.876854\pi\)
0.926093 0.377296i \(-0.123146\pi\)
\(368\) 1.57912e14 0.0635811
\(369\) −1.73491e15 −0.687258
\(370\) 7.48254e15 2.91634
\(371\) 8.26483e15i 3.16950i
\(372\) −5.11914e14 −0.193170
\(373\) 1.69100e15 0.627901 0.313951 0.949439i \(-0.398347\pi\)
0.313951 + 0.949439i \(0.398347\pi\)
\(374\) 1.66298e15i 0.607656i
\(375\) 2.23577e14i 0.0803970i
\(376\) −2.99963e15 −1.06155
\(377\) 4.98035e15i 1.73465i
\(378\) 1.90114e15i 0.651722i
\(379\) 2.01260e15i 0.679081i 0.940591 + 0.339541i \(0.110272\pi\)
−0.940591 + 0.339541i \(0.889728\pi\)
\(380\) −1.74919e15 −0.580945
\(381\) −4.58043e14 −0.149746
\(382\) 3.30234e15i 1.06278i
\(383\) −3.40783e15 −1.07965 −0.539827 0.841776i \(-0.681510\pi\)
−0.539827 + 0.841776i \(0.681510\pi\)
\(384\) 5.52266e14i 0.172251i
\(385\) 1.02018e16i 3.13265i
\(386\) 1.02537e16i 3.09996i
\(387\) 3.33110e15i 0.991567i
\(388\) 7.83476e15i 2.29634i
\(389\) 1.05007e15i 0.303053i 0.988453 + 0.151527i \(0.0484189\pi\)
−0.988453 + 0.151527i \(0.951581\pi\)
\(390\) 6.84073e14i 0.194408i
\(391\) 6.24042e14 0.174644
\(392\) 7.82347e15i 2.15617i
\(393\) 2.35634e14 0.0639562
\(394\) 3.37061e15i 0.901012i
\(395\) −3.34310e15 −0.880172
\(396\) −8.72035e15 −2.26133
\(397\) −9.40540e14 −0.240234 −0.120117 0.992760i \(-0.538327\pi\)
−0.120117 + 0.992760i \(0.538327\pi\)
\(398\) 3.67198e14i 0.0923851i
\(399\) 2.57961e14i 0.0639317i
\(400\) 1.51633e14 0.0370198
\(401\) 1.03495e15 0.248917 0.124458 0.992225i \(-0.460281\pi\)
0.124458 + 0.992225i \(0.460281\pi\)
\(402\) −1.31539e15 −0.311672
\(403\) 4.31508e15i 1.00730i
\(404\) 9.79572e15i 2.25293i
\(405\) 5.00916e15i 1.13510i
\(406\) 2.47949e16i 5.53612i
\(407\) −1.01873e16 −2.24127
\(408\) 1.23933e14i 0.0268674i
\(409\) 2.26576e15 0.484031 0.242016 0.970272i \(-0.422191\pi\)
0.242016 + 0.970272i \(0.422191\pi\)
\(410\) 6.25521e15 1.31686
\(411\) 5.98697e14i 0.124210i
\(412\) 2.64054e15i 0.539896i
\(413\) −2.33277e15 −0.470079
\(414\) 5.35031e15i 1.06262i
\(415\) −2.96541e15 + 5.24329e15i −0.580491 + 1.02640i
\(416\) 5.11512e15 0.986952
\(417\) 7.92742e14i 0.150770i
\(418\) 3.89373e15 0.729976
\(419\) 2.70313e15 0.499555 0.249777 0.968303i \(-0.419643\pi\)
0.249777 + 0.968303i \(0.419643\pi\)
\(420\) 2.08299e15i 0.379481i
\(421\) 6.43430e15i 1.15560i −0.816177 0.577802i \(-0.803911\pi\)
0.816177 0.577802i \(-0.196089\pi\)
\(422\) 5.24560e15 0.928796
\(423\) 6.51070e15i 1.13654i
\(424\) −9.29707e15 −1.60011
\(425\) 5.99229e14 0.101685
\(426\) −1.38437e15 −0.231629
\(427\) −1.16467e16 −1.92147
\(428\) 5.25577e15i 0.855014i
\(429\) 9.31352e14i 0.149407i
\(430\) 1.20102e16i 1.89995i
\(431\) −6.83958e15 −1.06700 −0.533502 0.845799i \(-0.679124\pi\)
−0.533502 + 0.845799i \(0.679124\pi\)
\(432\) −1.37000e14 −0.0210775
\(433\) 9.06436e15i 1.37534i −0.726024 0.687670i \(-0.758634\pi\)
0.726024 0.687670i \(-0.241366\pi\)
\(434\) 2.14828e16i 3.21479i
\(435\) 1.68765e15i 0.249085i
\(436\) −1.09408e15 −0.159268
\(437\) 1.46114e15i 0.209799i
\(438\) −1.72940e15 −0.244935
\(439\) 4.13303e15i 0.577406i −0.957419 0.288703i \(-0.906776\pi\)
0.957419 0.288703i \(-0.0932240\pi\)
\(440\) 1.14759e16 1.58151
\(441\) −1.69809e16 −2.30849
\(442\) 2.86213e15 0.383844
\(443\) −3.22185e15 −0.426268 −0.213134 0.977023i \(-0.568367\pi\)
−0.213134 + 0.977023i \(0.568367\pi\)
\(444\) 2.08003e15 0.271501
\(445\) 5.79495e15 0.746259
\(446\) 1.11985e16 1.42283
\(447\) 8.55718e14i 0.107272i
\(448\) 2.40654e16 2.97664
\(449\) 6.09869e15i 0.744318i 0.928169 + 0.372159i \(0.121382\pi\)
−0.928169 + 0.372159i \(0.878618\pi\)
\(450\) 5.13757e15i 0.618704i
\(451\) −8.51635e15 −1.01203
\(452\) −1.38442e16 −1.62344
\(453\) 4.10068e14 0.0474533
\(454\) 8.13873e15i 0.929441i
\(455\) 1.75581e16 1.97884
\(456\) −2.90179e14 −0.0322758
\(457\) 9.68950e15i 1.06366i −0.846850 0.531832i \(-0.821504\pi\)
0.846850 0.531832i \(-0.178496\pi\)
\(458\) 1.53154e16i 1.65934i
\(459\) −5.41402e14 −0.0578954
\(460\) 1.17985e16i 1.24531i
\(461\) 7.26262e15i 0.756637i −0.925675 0.378319i \(-0.876502\pi\)
0.925675 0.378319i \(-0.123498\pi\)
\(462\) 4.63677e15i 0.476830i
\(463\) 8.03002e15 0.815137 0.407568 0.913175i \(-0.366377\pi\)
0.407568 + 0.913175i \(0.366377\pi\)
\(464\) −1.78678e15 −0.179045
\(465\) 1.46222e15i 0.144642i
\(466\) 7.36272e15 0.718990
\(467\) 1.15742e15i 0.111581i −0.998442 0.0557906i \(-0.982232\pi\)
0.998442 0.0557906i \(-0.0177679\pi\)
\(468\) 1.50084e16i 1.42844i
\(469\) 3.37621e16i 3.17243i
\(470\) 2.34743e16i 2.17773i
\(471\) 1.30573e15i 0.119599i
\(472\) 2.62412e15i 0.237318i
\(473\) 1.63517e16i 1.46015i
\(474\) −1.51946e15 −0.133974
\(475\) 1.40304e15i 0.122155i
\(476\) 8.71510e15 0.749257
\(477\) 2.01793e16i 1.71315i
\(478\) 2.23112e16 1.87049
\(479\) 1.55276e16 1.28555 0.642777 0.766053i \(-0.277782\pi\)
0.642777 + 0.766053i \(0.277782\pi\)
\(480\) 1.73332e15 0.141720
\(481\) 1.75332e16i 1.41577i
\(482\) 2.04416e16i 1.63017i
\(483\) 1.73997e15 0.137044
\(484\) −2.25625e16 −1.75515
\(485\) 2.23790e16 1.71945
\(486\) 6.97729e15i 0.529504i
\(487\) 5.25307e15i 0.393767i −0.980427 0.196883i \(-0.936918\pi\)
0.980427 0.196883i \(-0.0630820\pi\)
\(488\) 1.31013e16i 0.970051i
\(489\) 9.82674e14i 0.0718715i
\(490\) 6.12243e16 4.42331
\(491\) 4.61810e15i 0.329591i −0.986328 0.164795i \(-0.947304\pi\)
0.986328 0.164795i \(-0.0526963\pi\)
\(492\) 1.73885e15 0.122595
\(493\) −7.06105e15 −0.491799
\(494\) 6.70143e15i 0.461112i
\(495\) 2.49086e16i 1.69324i
\(496\) 1.54810e15 0.103970
\(497\) 3.55326e16i 2.35770i
\(498\) −1.34779e15 + 2.38311e15i −0.0883583 + 0.156231i
\(499\) −1.90552e16 −1.23427 −0.617134 0.786858i \(-0.711706\pi\)
−0.617134 + 0.786858i \(0.711706\pi\)
\(500\) 1.76858e16i 1.13189i
\(501\) 5.88366e14 0.0372067
\(502\) −1.46248e16 −0.913833
\(503\) 1.16281e16i 0.717963i −0.933345 0.358982i \(-0.883124\pi\)
0.933345 0.358982i \(-0.116876\pi\)
\(504\) 2.72727e16i 1.66397i
\(505\) −2.79802e16 −1.68695
\(506\) 2.62636e16i 1.56477i
\(507\) −2.96865e14 −0.0174788
\(508\) −3.62329e16 −2.10825
\(509\) −4.52400e15 −0.260145 −0.130072 0.991504i \(-0.541521\pi\)
−0.130072 + 0.991504i \(0.541521\pi\)
\(510\) 9.69866e14 0.0551177
\(511\) 4.43885e16i 2.49313i
\(512\) 3.41042e15i 0.189316i
\(513\) 1.26765e15i 0.0695496i
\(514\) 1.34298e16 0.728268
\(515\) 7.54237e15 0.404264
\(516\) 3.33866e15i 0.176878i
\(517\) 3.19597e16i 1.67363i
\(518\) 8.72899e16i 4.51841i
\(519\) −4.88600e14 −0.0250005
\(520\) 1.97510e16i 0.999010i
\(521\) 1.72950e16 0.864759 0.432379 0.901692i \(-0.357674\pi\)
0.432379 + 0.901692i \(0.357674\pi\)
\(522\) 6.05389e16i 2.99234i
\(523\) 2.75403e16 1.34573 0.672865 0.739765i \(-0.265063\pi\)
0.672865 + 0.739765i \(0.265063\pi\)
\(524\) 1.86395e16 0.900425
\(525\) 1.67079e15 0.0797931
\(526\) 1.55270e15 0.0733115
\(527\) 6.11784e15 0.285584
\(528\) −3.34137e14 −0.0154213
\(529\) −1.20591e16 −0.550275
\(530\) 7.27563e16i 3.28258i
\(531\) 5.69566e15 0.254084
\(532\) 2.04057e16i 0.900081i
\(533\) 1.46573e16i 0.639281i
\(534\) 2.63384e15 0.113590
\(535\) 1.50124e16 0.640219
\(536\) −3.79788e16 −1.60159
\(537\) 1.62369e15i 0.0677106i
\(538\) −7.52413e16 −3.10286
\(539\) −8.33557e16 −3.39940
\(540\) 1.02360e16i 0.412828i
\(541\) 3.79875e16i 1.51515i 0.652746 + 0.757577i \(0.273617\pi\)
−0.652746 + 0.757577i \(0.726383\pi\)
\(542\) 8.05143e16 3.17598
\(543\) 2.47233e15i 0.0964512i
\(544\) 7.25212e15i 0.279816i
\(545\) 3.12510e15i 0.119257i
\(546\) 7.98027e15 0.301205
\(547\) −1.06702e16 −0.398334 −0.199167 0.979966i \(-0.563824\pi\)
−0.199167 + 0.979966i \(0.563824\pi\)
\(548\) 4.73592e16i 1.74872i
\(549\) 2.84364e16 1.03858
\(550\) 2.52193e16i 0.911081i
\(551\) 1.65329e16i 0.590797i
\(552\) 1.95729e15i 0.0691863i
\(553\) 3.90000e16i 1.36369i
\(554\) 2.75238e16i 0.952028i
\(555\) 5.94134e15i 0.203295i
\(556\) 6.27089e16i 2.12266i
\(557\) −3.66460e16 −1.22714 −0.613572 0.789639i \(-0.710268\pi\)
−0.613572 + 0.789639i \(0.710268\pi\)
\(558\) 5.24522e16i 1.73763i
\(559\) −2.81426e16 −0.922346
\(560\) 6.29924e15i 0.204249i
\(561\) −1.32045e15 −0.0423590
\(562\) 5.03521e16 1.59808
\(563\) −2.52291e16 −0.792229 −0.396114 0.918201i \(-0.629642\pi\)
−0.396114 + 0.918201i \(0.629642\pi\)
\(564\) 6.52549e15i 0.202739i
\(565\) 3.95442e16i 1.21560i
\(566\) −4.04490e16 −1.23029
\(567\) 5.84359e16 1.75866
\(568\) −3.99704e16 −1.19028
\(569\) 3.56960e16i 1.05183i −0.850537 0.525915i \(-0.823723\pi\)
0.850537 0.525915i \(-0.176277\pi\)
\(570\) 2.27086e15i 0.0662127i
\(571\) 5.20726e14i 0.0150242i 0.999972 + 0.00751212i \(0.00239120\pi\)
−0.999972 + 0.00751212i \(0.997609\pi\)
\(572\) 7.36735e16i 2.10346i
\(573\) −2.62215e15 −0.0740850
\(574\) 7.29721e16i 2.04026i
\(575\) 9.46367e15 0.261850
\(576\) −5.87579e16 −1.60891
\(577\) 7.04619e16i 1.90941i 0.297550 + 0.954706i \(0.403830\pi\)
−0.297550 + 0.954706i \(0.596170\pi\)
\(578\) 5.57748e16i 1.49579i
\(579\) 8.14170e15 0.216095
\(580\) 1.33500e17i 3.50681i
\(581\) 6.11673e16 + 3.45939e16i 1.59024 + 0.899379i
\(582\) 1.01714e16 0.261723
\(583\) 9.90563e16i 2.52273i
\(584\) −4.99324e16 −1.25865
\(585\) −4.28697e16 −1.06959
\(586\) 1.88574e16i 0.465690i
\(587\) 4.25316e16i 1.03964i 0.854276 + 0.519820i \(0.174001\pi\)
−0.854276 + 0.519820i \(0.825999\pi\)
\(588\) 1.70194e16 0.411795
\(589\) 1.43244e16i 0.343072i
\(590\) −2.05356e16 −0.486851
\(591\) −2.67636e15 −0.0628086
\(592\) −6.29031e15 −0.146131
\(593\) 3.18595e16 0.732675 0.366338 0.930482i \(-0.380612\pi\)
0.366338 + 0.930482i \(0.380612\pi\)
\(594\) 2.27856e16i 0.518731i
\(595\) 2.48936e16i 0.561030i
\(596\) 6.76906e16i 1.51026i
\(597\) 2.91565e14 0.00644006
\(598\) 4.52018e16 0.988437
\(599\) 6.64467e16i 1.43851i 0.694747 + 0.719254i \(0.255516\pi\)
−0.694747 + 0.719254i \(0.744484\pi\)
\(600\) 1.87946e15i 0.0402833i
\(601\) 2.19119e16i 0.464979i 0.972599 + 0.232490i \(0.0746872\pi\)
−0.972599 + 0.232490i \(0.925313\pi\)
\(602\) −1.40109e17 −2.94366
\(603\) 8.24331e16i 1.71474i
\(604\) 3.24380e16 0.668085
\(605\) 6.44468e16i 1.31422i
\(606\) −1.27172e16 −0.256776
\(607\) 9.29933e16 1.85917 0.929586 0.368605i \(-0.120164\pi\)
0.929586 + 0.368605i \(0.120164\pi\)
\(608\) 1.69802e16 0.336142
\(609\) −1.96878e16 −0.385917
\(610\) −1.02527e17 −1.99003
\(611\) 5.50054e16 1.05720
\(612\) −2.12787e16 −0.404983
\(613\) 7.15582e16i 1.34864i 0.738438 + 0.674321i \(0.235564\pi\)
−0.738438 + 0.674321i \(0.764436\pi\)
\(614\) −1.56032e16 −0.291208
\(615\) 4.96681e15i 0.0917967i
\(616\) 1.33876e17i 2.45030i
\(617\) 2.30947e16 0.418602 0.209301 0.977851i \(-0.432881\pi\)
0.209301 + 0.977851i \(0.432881\pi\)
\(618\) 3.42805e15 0.0615342
\(619\) −5.23539e16 −0.930691 −0.465345 0.885129i \(-0.654070\pi\)
−0.465345 + 0.885129i \(0.654070\pi\)
\(620\) 1.15667e17i 2.03638i
\(621\) −8.55042e15 −0.149086
\(622\) −3.39398e16 −0.586094
\(623\) 6.76028e16i 1.15621i
\(624\) 5.75077e14i 0.00974133i
\(625\) −7.37906e16 −1.23800
\(626\) 3.31241e16i 0.550425i
\(627\) 3.09173e15i 0.0508858i
\(628\) 1.03288e17i 1.68381i
\(629\) −2.48583e16 −0.401391
\(630\) −2.13429e17 −3.41357
\(631\) 5.54192e16i 0.877979i 0.898492 + 0.438990i \(0.144663\pi\)
−0.898492 + 0.438990i \(0.855337\pi\)
\(632\) −4.38709e16 −0.688453
\(633\) 4.16515e15i 0.0647453i
\(634\) 3.17495e16i 0.488880i
\(635\) 1.03495e17i 1.57861i
\(636\) 2.02251e16i 0.305597i
\(637\) 1.43462e17i 2.14734i
\(638\) 2.97173e17i 4.40642i
\(639\) 8.67559e16i 1.27436i
\(640\) 1.24784e17 1.81585
\(641\) 7.13287e16i 1.02829i 0.857703 + 0.514146i \(0.171891\pi\)
−0.857703 + 0.514146i \(0.828109\pi\)
\(642\) 6.82323e15 0.0974496
\(643\) 7.81020e16i 1.10509i 0.833484 + 0.552544i \(0.186343\pi\)
−0.833484 + 0.552544i \(0.813657\pi\)
\(644\) 1.37638e17 1.92941
\(645\) −9.53647e15 −0.132443
\(646\) 9.50117e15 0.130732
\(647\) 6.30278e15i 0.0859224i 0.999077 + 0.0429612i \(0.0136792\pi\)
−0.999077 + 0.0429612i \(0.986321\pi\)
\(648\) 6.57343e16i 0.887855i
\(649\) 2.79589e16 0.374155
\(650\) 4.34045e16 0.575512
\(651\) 1.70579e16 0.224099
\(652\) 7.77333e16i 1.01186i
\(653\) 9.55730e16i 1.23270i −0.787474 0.616348i \(-0.788611\pi\)
0.787474 0.616348i \(-0.211389\pi\)
\(654\) 1.42037e15i 0.0181525i
\(655\) 5.32415e16i 0.674221i
\(656\) −5.25854e15 −0.0659845
\(657\) 1.08378e17i 1.34757i
\(658\) 2.73846e17 3.37405
\(659\) −3.13363e16 −0.382592 −0.191296 0.981532i \(-0.561269\pi\)
−0.191296 + 0.981532i \(0.561269\pi\)
\(660\) 2.49651e16i 0.302044i
\(661\) 9.47187e15i 0.113560i 0.998387 + 0.0567802i \(0.0180834\pi\)
−0.998387 + 0.0567802i \(0.981917\pi\)
\(662\) 1.90028e17 2.25771
\(663\) 2.27261e15i 0.0267574i
\(664\) −3.89145e16 + 6.88067e16i −0.454049 + 0.802828i
\(665\) 5.82863e16 0.673964
\(666\) 2.13126e17i 2.44225i
\(667\) −1.11516e17 −1.26643
\(668\) 4.65420e16 0.523825
\(669\) 8.89196e15i 0.0991838i
\(670\) 2.97212e17i 3.28562i
\(671\) 1.39588e17 1.52938
\(672\) 2.02206e16i 0.219573i
\(673\) −1.51920e17 −1.63503 −0.817515 0.575908i \(-0.804649\pi\)
−0.817515 + 0.575908i \(0.804649\pi\)
\(674\) −8.79294e16 −0.937939
\(675\) −8.21043e15 −0.0868047
\(676\) −2.34832e16 −0.246080
\(677\) 4.73122e16i 0.491407i −0.969345 0.245703i \(-0.920981\pi\)
0.969345 0.245703i \(-0.0790189\pi\)
\(678\) 1.79730e16i 0.185031i
\(679\) 2.61069e17i 2.66402i
\(680\) 2.80027e16 0.283234
\(681\) −6.46238e15 −0.0647903
\(682\) 2.57477e17i 2.55878i
\(683\) 5.54012e16i 0.545751i −0.962049 0.272876i \(-0.912025\pi\)
0.962049 0.272876i \(-0.0879748\pi\)
\(684\) 4.98223e16i 0.486505i
\(685\) 1.35276e17 1.30941
\(686\) 4.08709e17i 3.92166i
\(687\) −1.21608e16 −0.115671
\(688\) 1.00966e16i 0.0952016i
\(689\) 1.70484e17 1.59356
\(690\) 1.53172e16 0.141933
\(691\) 1.00223e17 0.920656 0.460328 0.887749i \(-0.347732\pi\)
0.460328 + 0.887749i \(0.347732\pi\)
\(692\) −3.86501e16 −0.351977
\(693\) 2.90579e17 2.62340
\(694\) −4.08960e16 −0.366036
\(695\) −1.79120e17 −1.58941
\(696\) 2.21467e16i 0.194829i
\(697\) −2.07809e16 −0.181246
\(698\) 8.51386e16i 0.736197i
\(699\) 5.84621e15i 0.0501200i
\(700\) 1.32166e17 1.12339
\(701\) 1.50777e17 1.27066 0.635328 0.772242i \(-0.280865\pi\)
0.635328 + 0.772242i \(0.280865\pi\)
\(702\) −3.92159e16 −0.327672
\(703\) 5.82036e16i 0.482190i
\(704\) −2.88431e17 −2.36922
\(705\) 1.86392e16 0.151807
\(706\) 2.45671e17i 1.98393i
\(707\) 3.26412e17i 2.61366i
\(708\) −5.70859e15 −0.0453241
\(709\) 1.30643e17i 1.02851i 0.857636 + 0.514257i \(0.171932\pi\)
−0.857636 + 0.514257i \(0.828068\pi\)
\(710\) 3.12797e17i 2.44182i
\(711\) 9.52220e16i 0.737089i
\(712\) 7.60460e16 0.583709
\(713\) 9.66197e16 0.735408
\(714\) 1.13143e16i 0.0853960i
\(715\) −2.10439e17 −1.57503
\(716\) 1.28440e17i 0.953282i
\(717\) 1.77158e16i 0.130390i
\(718\) 2.39282e17i 1.74648i
\(719\) 1.18102e17i 0.854838i 0.904054 + 0.427419i \(0.140577\pi\)
−0.904054 + 0.427419i \(0.859423\pi\)
\(720\) 1.53802e16i 0.110399i
\(721\) 8.79879e16i 0.626342i
\(722\) 2.05051e17i 1.44757i
\(723\) 1.62312e16 0.113637
\(724\) 1.95571e17i 1.35792i
\(725\) −1.07082e17 −0.737373
\(726\) 2.92914e16i 0.200042i
\(727\) −5.12825e16 −0.347346 −0.173673 0.984803i \(-0.555564\pi\)
−0.173673 + 0.984803i \(0.555564\pi\)
\(728\) 2.30412e17 1.54781
\(729\) −1.38944e17 −0.925710
\(730\) 3.90757e17i 2.58208i
\(731\) 3.99001e16i 0.261499i
\(732\) −2.85009e16 −0.185265
\(733\) −2.20545e17 −1.42192 −0.710958 0.703235i \(-0.751738\pi\)
−0.710958 + 0.703235i \(0.751738\pi\)
\(734\) −1.89348e17 −1.21083
\(735\) 4.86138e16i 0.308344i
\(736\) 1.14533e17i 0.720552i
\(737\) 4.04648e17i 2.52506i
\(738\) 1.78168e17i 1.10279i
\(739\) −1.92698e15 −0.0118307 −0.00591534 0.999983i \(-0.501883\pi\)
−0.00591534 + 0.999983i \(0.501883\pi\)
\(740\) 4.69983e17i 2.86215i
\(741\) 5.32112e15 0.0321436
\(742\) 8.48761e17 5.08583
\(743\) 5.93516e16i 0.352776i −0.984321 0.176388i \(-0.943559\pi\)
0.984321 0.176388i \(-0.0564414\pi\)
\(744\) 1.91884e16i 0.113136i
\(745\) −1.93350e17 −1.13085
\(746\) 1.73658e17i 1.00754i
\(747\) −1.49345e17 8.44640e16i −0.859544 0.486125i
\(748\) −1.04453e17 −0.596363
\(749\) 1.75132e17i 0.991916i
\(750\) −2.29604e16 −0.129006
\(751\) 1.41646e17 0.789522 0.394761 0.918784i \(-0.370827\pi\)
0.394761 + 0.918784i \(0.370827\pi\)
\(752\) 1.97340e16i 0.109121i
\(753\) 1.16125e16i 0.0637023i
\(754\) −5.11460e17 −2.78345
\(755\) 9.26549e16i 0.500250i
\(756\) −1.19411e17 −0.639610
\(757\) 1.17817e17 0.626086 0.313043 0.949739i \(-0.398652\pi\)
0.313043 + 0.949739i \(0.398652\pi\)
\(758\) 2.06685e17 1.08967
\(759\) −2.08540e16 −0.109079
\(760\) 6.55659e16i 0.340249i
\(761\) 1.12418e17i 0.578800i 0.957208 + 0.289400i \(0.0934558\pi\)
−0.957208 + 0.289400i \(0.906544\pi\)
\(762\) 4.70389e16i 0.240286i
\(763\) 3.64568e16 0.184770
\(764\) −2.07422e17 −1.04303
\(765\) 6.07799e16i 0.303243i
\(766\) 3.49968e17i 1.73243i
\(767\) 4.81195e16i 0.236346i
\(768\) 1.93191e16 0.0941498
\(769\) 3.08796e16i 0.149318i 0.997209 + 0.0746592i \(0.0237869\pi\)
−0.997209 + 0.0746592i \(0.976213\pi\)
\(770\) −1.04768e18 −5.02671
\(771\) 1.06636e16i 0.0507668i
\(772\) 6.44040e17 3.04235
\(773\) −1.25105e17 −0.586405 −0.293203 0.956050i \(-0.594721\pi\)
−0.293203 + 0.956050i \(0.594721\pi\)
\(774\) 3.42089e17 1.59109
\(775\) 9.27778e16 0.428187
\(776\) 2.93675e17 1.34492
\(777\) −6.93106e16 −0.314973
\(778\) 1.07837e17 0.486284
\(779\) 4.86567e16i 0.217730i
\(780\) 4.29671e16 0.190795
\(781\) 4.25867e17i 1.87658i
\(782\) 6.40863e16i 0.280237i
\(783\) 9.67482e16 0.419829
\(784\) −5.14692e16 −0.221641
\(785\) 2.95030e17 1.26080
\(786\) 2.41985e16i 0.102625i
\(787\) −3.31873e17 −1.39677 −0.698383 0.715725i \(-0.746097\pi\)
−0.698383 + 0.715725i \(0.746097\pi\)
\(788\) −2.11710e17 −0.884268
\(789\) 1.23288e15i 0.00511046i
\(790\) 3.43322e17i 1.41234i
\(791\) 4.61315e17 1.88338
\(792\) 3.26871e17i 1.32442i
\(793\) 2.40243e17i 0.966078i
\(794\) 9.65892e16i 0.385483i
\(795\) 5.77705e16 0.228825
\(796\) 2.30639e16 0.0906682
\(797\) 8.04085e16i 0.313727i −0.987620 0.156863i \(-0.949862\pi\)
0.987620 0.156863i \(-0.0501383\pi\)
\(798\) 2.64914e16 0.102586
\(799\) 7.79856e16i 0.299732i
\(800\) 1.09979e17i 0.419538i
\(801\) 1.65058e17i 0.624945i
\(802\) 1.06285e17i 0.399416i
\(803\) 5.32008e17i 1.98438i
\(804\) 8.26203e16i 0.305880i
\(805\) 3.93147e17i 1.44471i
\(806\) 4.43140e17 1.61633
\(807\) 5.97437e16i 0.216297i
\(808\) −3.67179e17 −1.31950
\(809\) 7.72796e16i 0.275660i 0.990456 + 0.137830i \(0.0440128\pi\)
−0.990456 + 0.137830i \(0.955987\pi\)
\(810\) 5.14419e17 1.82141
\(811\) −1.03923e17 −0.365248 −0.182624 0.983183i \(-0.558459\pi\)
−0.182624 + 0.983183i \(0.558459\pi\)
\(812\) −1.55738e18 −5.43324
\(813\) 6.39306e16i 0.221394i
\(814\) 1.04619e18i 3.59638i
\(815\) 2.22035e17 0.757663
\(816\) −8.15333e14 −0.00276181
\(817\) −9.34228e16 −0.314138
\(818\) 2.32683e17i 0.776685i
\(819\) 5.00110e17i 1.65715i
\(820\) 3.92894e17i 1.29239i
\(821\) 4.67469e17i 1.52649i 0.646110 + 0.763244i \(0.276395\pi\)
−0.646110 + 0.763244i \(0.723605\pi\)
\(822\) 6.14835e16 0.199309
\(823\) 1.31783e17i 0.424092i 0.977260 + 0.212046i \(0.0680127\pi\)
−0.977260 + 0.212046i \(0.931987\pi\)
\(824\) 9.89771e16 0.316207
\(825\) −2.00248e16 −0.0635105
\(826\) 2.39565e17i 0.754298i
\(827\) 3.87435e17i 1.21106i 0.795822 + 0.605530i \(0.207039\pi\)
−0.795822 + 0.605530i \(0.792961\pi\)
\(828\) −3.36057e17 −1.04287
\(829\) 1.94458e17i 0.599099i −0.954081 0.299549i \(-0.903164\pi\)
0.954081 0.299549i \(-0.0968363\pi\)
\(830\) 5.38463e17 + 3.04534e17i 1.64698 + 0.931467i
\(831\) 2.18547e16 0.0663648
\(832\) 4.96413e17i 1.49659i
\(833\) −2.03398e17 −0.608802
\(834\) −8.14110e16 −0.241928
\(835\) 1.32941e17i 0.392230i
\(836\) 2.44568e17i 0.716410i
\(837\) −8.38247e16 −0.243792
\(838\) 2.77600e17i 0.801595i
\(839\) 6.41957e16 0.184049 0.0920247 0.995757i \(-0.470666\pi\)
0.0920247 + 0.995757i \(0.470666\pi\)
\(840\) 7.80779e16 0.222255
\(841\) 9.07990e17 2.56629
\(842\) −6.60774e17 −1.85430
\(843\) 3.99809e16i 0.111401i
\(844\) 3.29479e17i 0.911535i
\(845\) 6.70767e16i 0.184260i
\(846\) −6.68620e17 −1.82372
\(847\) 7.51824e17 2.03618
\(848\) 6.11637e16i 0.164482i
\(849\) 3.21176e16i 0.0857624i
\(850\) 6.15381e16i 0.163166i
\(851\) −3.92589e17 −1.03362
\(852\) 8.69529e16i 0.227325i
\(853\) 3.91663e17 1.01676 0.508380 0.861133i \(-0.330245\pi\)
0.508380 + 0.861133i \(0.330245\pi\)
\(854\) 1.19606e18i 3.08323i
\(855\) −1.42311e17 −0.364286
\(856\) 1.97005e17 0.500766
\(857\) −4.25240e17 −1.07337 −0.536685 0.843783i \(-0.680323\pi\)
−0.536685 + 0.843783i \(0.680323\pi\)
\(858\) −9.56457e16 −0.239741
\(859\) 2.19889e17 0.547325 0.273663 0.961826i \(-0.411765\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(860\) −7.54371e17 −1.86464
\(861\) −5.79419e16 −0.142224
\(862\) 7.02394e17i 1.71213i
\(863\) 8.05630e16 0.195016 0.0975082 0.995235i \(-0.468913\pi\)
0.0975082 + 0.995235i \(0.468913\pi\)
\(864\) 9.93662e16i 0.238867i
\(865\) 1.10399e17i 0.263554i
\(866\) −9.30870e17 −2.20689
\(867\) 4.42868e16 0.104270
\(868\) 1.34935e18 3.15505
\(869\) 4.67426e17i 1.08541i
\(870\) −1.73314e17 −0.399686
\(871\) 6.96432e17 1.59503
\(872\) 4.10101e16i 0.0932807i
\(873\) 6.37424e17i 1.43993i
\(874\) 1.50053e17 0.336648
\(875\) 5.89325e17i 1.31313i
\(876\) 1.08625e17i 0.240383i
\(877\) 1.48669e17i 0.326754i −0.986564 0.163377i \(-0.947761\pi\)
0.986564 0.163377i \(-0.0522388\pi\)
\(878\) −4.24444e17 −0.926516
\(879\) 1.49733e16 0.0324627
\(880\) 7.54982e16i 0.162570i
\(881\) −7.44384e17 −1.59199 −0.795997 0.605301i \(-0.793053\pi\)
−0.795997 + 0.605301i \(0.793053\pi\)
\(882\) 1.74386e18i 3.70425i
\(883\) 2.88314e16i 0.0608278i 0.999537 + 0.0304139i \(0.00968253\pi\)
−0.999537 + 0.0304139i \(0.990317\pi\)
\(884\) 1.79772e17i 0.376711i
\(885\) 1.63059e16i 0.0339378i
\(886\) 3.30870e17i 0.683998i
\(887\) 1.49033e17i 0.306013i −0.988225 0.153006i \(-0.951105\pi\)
0.988225 0.153006i \(-0.0488955\pi\)
\(888\) 7.79671e16i 0.159013i
\(889\) 1.20735e18 2.44581
\(890\) 5.95115e17i 1.19746i
\(891\) −7.00371e17 −1.39979
\(892\) 7.03388e17i 1.39639i
\(893\) 1.82597e17 0.360068
\(894\) −8.78784e16 −0.172130
\(895\) −3.66872e17 −0.713800
\(896\) 1.45571e18i 2.81337i
\(897\) 3.58915e16i 0.0689029i
\(898\) 6.26308e17 1.19435
\(899\) −1.09325e18 −2.07092
\(900\) −3.22694e17 −0.607206
\(901\) 2.41709e17i 0.451798i
\(902\) 8.74591e17i 1.62392i
\(903\) 1.11251e17i 0.205199i
\(904\) 5.18930e17i 0.950821i
\(905\) 5.58623e17 1.01678
\(906\) 4.21122e16i 0.0761445i
\(907\) 8.92521e15 0.0160315 0.00801576 0.999968i \(-0.497448\pi\)
0.00801576 + 0.999968i \(0.497448\pi\)
\(908\) −5.11199e17 −0.912168
\(909\) 7.96964e17i 1.41272i
\(910\) 1.80314e18i 3.17528i
\(911\) −1.45200e17 −0.254013 −0.127006 0.991902i \(-0.540537\pi\)
−0.127006 + 0.991902i \(0.540537\pi\)
\(912\) 1.90903e15i 0.00331776i
\(913\) −7.33106e17 4.14617e17i −1.26573 0.715851i
\(914\) −9.95068e17 −1.70677
\(915\) 8.14093e16i 0.138723i
\(916\) −9.61970e17 −1.62850
\(917\) −6.21105e17 −1.04460
\(918\) 5.55996e16i 0.0929000i
\(919\) 6.56309e17i 1.08947i 0.838608 + 0.544735i \(0.183370\pi\)
−0.838608 + 0.544735i \(0.816630\pi\)
\(920\) 4.42249e17 0.729356
\(921\) 1.23894e16i 0.0202998i
\(922\) −7.45838e17 −1.21411
\(923\) 7.32953e17 1.18540
\(924\) −2.91239e17 −0.467969
\(925\) −3.76979e17 −0.601820
\(926\) 8.24647e17i 1.30798i
\(927\) 2.14830e17i 0.338545i
\(928\) 1.29595e18i 2.02908i
\(929\) 5.41171e17 0.841860 0.420930 0.907093i \(-0.361704\pi\)
0.420930 + 0.907093i \(0.361704\pi\)
\(930\) 1.50163e17 0.232095
\(931\) 4.76239e17i 0.731353i
\(932\) 4.62457e17i 0.705629i
\(933\) 2.69492e16i 0.0408560i
\(934\) −1.18862e17 −0.179045
\(935\) 2.98356e17i 0.446546i
\(936\) −5.62571e17 −0.836609
\(937\) 4.20352e17i 0.621120i −0.950554 0.310560i \(-0.899483\pi\)
0.950554 0.310560i \(-0.100517\pi\)
\(938\) 3.46722e18 5.09054
\(939\) 2.63015e16 0.0383695
\(940\) 1.47443e18 2.13726
\(941\) −5.20024e17 −0.749006 −0.374503 0.927226i \(-0.622187\pi\)
−0.374503 + 0.927226i \(0.622187\pi\)
\(942\) 1.34093e17 0.191911
\(943\) −3.28195e17 −0.466725
\(944\) 1.72636e16 0.0243949
\(945\) 3.41084e17i 0.478928i
\(946\) 1.67925e18 2.34298
\(947\) 8.76164e17i 1.21475i −0.794417 0.607373i \(-0.792223\pi\)
0.794417 0.607373i \(-0.207777\pi\)
\(948\) 9.54382e16i 0.131484i
\(949\) 9.15630e17 1.25350
\(950\) 1.44086e17 0.196011
\(951\) −2.52100e16 −0.0340793
\(952\) 3.26674e17i 0.438826i
\(953\) −4.66013e17 −0.622072 −0.311036 0.950398i \(-0.600676\pi\)
−0.311036 + 0.950398i \(0.600676\pi\)
\(954\) −2.07233e18 −2.74896
\(955\) 5.92475e17i 0.780998i
\(956\) 1.40138e18i 1.83573i
\(957\) 2.35964e17 0.307167
\(958\) 1.59461e18i 2.06282i
\(959\) 1.57810e18i 2.02872i
\(960\) 1.68216e17i 0.214901i
\(961\) 1.59555e17 0.202568
\(962\) −1.80058e18 −2.27176
\(963\) 4.27601e17i 0.536143i
\(964\) 1.28395e18 1.59987
\(965\) 1.83962e18i 2.27805i
\(966\) 1.78687e17i 0.219903i
\(967\) 1.04397e18i 1.27682i −0.769697 0.638409i \(-0.779593\pi\)
0.769697 0.638409i \(-0.220407\pi\)
\(968\) 8.45723e17i 1.02796i
\(969\) 7.54419e15i 0.00911318i
\(970\) 2.29822e18i 2.75907i
\(971\) 1.35130e18i 1.61227i 0.591733 + 0.806134i \(0.298444\pi\)
−0.591733 + 0.806134i \(0.701556\pi\)
\(972\) 4.38248e17 0.519664
\(973\) 2.08958e18i 2.46253i
\(974\) −5.39466e17 −0.631845
\(975\) 3.44644e16i 0.0401183i
\(976\) 8.61909e16 0.0997155
\(977\) 6.44626e17 0.741209 0.370604 0.928791i \(-0.379151\pi\)
0.370604 + 0.928791i \(0.379151\pi\)
\(978\) 1.00916e17 0.115326
\(979\) 8.10237e17i 0.920272i
\(980\) 3.84554e18i 4.34111i
\(981\) −8.90125e16 −0.0998704
\(982\) −4.74259e17 −0.528867
\(983\) −5.46795e17 −0.606043 −0.303022 0.952984i \(-0.597995\pi\)
−0.303022 + 0.952984i \(0.597995\pi\)
\(984\) 6.51785e16i 0.0718016i
\(985\) 6.04723e17i 0.662123i
\(986\) 7.25138e17i 0.789150i
\(987\) 2.17442e17i 0.235201i
\(988\) 4.20921e17 0.452542
\(989\) 6.30146e17i 0.673385i
\(990\) 2.55800e18 2.71700
\(991\) 1.26745e17 0.133810 0.0669049 0.997759i \(-0.478688\pi\)
0.0669049 + 0.997759i \(0.478688\pi\)
\(992\) 1.12284e18i 1.17828i
\(993\) 1.50887e17i 0.157383i
\(994\) 3.64903e18 3.78320
\(995\) 6.58792e16i 0.0678906i
\(996\) 1.49684e17 + 8.46558e16i 0.153328 + 0.0867163i
\(997\) 1.49108e17 0.151820 0.0759102 0.997115i \(-0.475814\pi\)
0.0759102 + 0.997115i \(0.475814\pi\)
\(998\) 1.95688e18i 1.98053i
\(999\) 3.40600e17 0.342651
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 83.13.b.c.82.11 80
83.82 odd 2 inner 83.13.b.c.82.70 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
83.13.b.c.82.11 80 1.1 even 1 trivial
83.13.b.c.82.70 yes 80 83.82 odd 2 inner