Properties

Label 83.13.b.c.82.19
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 82.19
Character \(\chi\) \(=\) 83.82
Dual form 83.13.b.c.82.62

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-82.5668i q^{2} -867.031 q^{3} -2721.28 q^{4} +8790.22i q^{5} +71588.0i q^{6} -11496.7 q^{7} -113506. i q^{8} +220301. q^{9} +O(q^{10})\) \(q-82.5668i q^{2} -867.031 q^{3} -2721.28 q^{4} +8790.22i q^{5} +71588.0i q^{6} -11496.7 q^{7} -113506. i q^{8} +220301. q^{9} +725781. q^{10} +1.21224e6 q^{11} +2.35944e6 q^{12} -5.08347e6i q^{13} +949247. i q^{14} -7.62139e6i q^{15} -2.05182e7 q^{16} -4.29631e7 q^{17} -1.81896e7i q^{18} -1.94044e7i q^{19} -2.39207e7i q^{20} +9.96800e6 q^{21} -1.00091e8i q^{22} -7.29795e7 q^{23} +9.84131e7i q^{24} +1.66873e8 q^{25} -4.19726e8 q^{26} +2.69768e8 q^{27} +3.12858e7 q^{28} -9.12773e8 q^{29} -6.29274e8 q^{30} +1.07602e8 q^{31} +1.22920e9i q^{32} -1.05105e9 q^{33} +3.54733e9i q^{34} -1.01059e8i q^{35} -5.99502e8 q^{36} +1.17230e9 q^{37} -1.60216e9 q^{38} +4.40753e9i q^{39} +9.97743e8 q^{40} -4.70768e9 q^{41} -8.23026e8i q^{42} -5.03554e9i q^{43} -3.29885e9 q^{44} +1.93650e9i q^{45} +6.02569e9i q^{46} +2.94237e9i q^{47} +1.77899e10 q^{48} -1.37091e10 q^{49} -1.37781e10i q^{50} +3.72503e10 q^{51} +1.38336e10i q^{52} +2.41304e10i q^{53} -2.22739e10i q^{54} +1.06559e10i q^{55} +1.30495e9i q^{56} +1.68242e10i q^{57} +7.53648e10i q^{58} +4.28123e9 q^{59} +2.07400e10i q^{60} +3.04317e10 q^{61} -8.88434e9i q^{62} -2.53274e9 q^{63} +1.74489e10 q^{64} +4.46849e10 q^{65} +8.67819e10i q^{66} -6.61861e9i q^{67} +1.16915e11 q^{68} +6.32754e10 q^{69} -8.34410e9 q^{70} +1.41623e11i q^{71} -2.50055e10i q^{72} -7.21726e10i q^{73} -9.67927e10i q^{74} -1.44684e11 q^{75} +5.28050e10i q^{76} -1.39368e10 q^{77} +3.63916e11 q^{78} -3.88746e11i q^{79} -1.80360e11i q^{80} -3.50974e11 q^{81} +3.88698e11i q^{82} +(3.26193e11 + 2.20944e10i) q^{83} -2.71258e10 q^{84} -3.77655e11i q^{85} -4.15768e11 q^{86} +7.91402e11 q^{87} -1.37597e11i q^{88} -8.48384e11i q^{89} +1.59890e11 q^{90} +5.84432e10i q^{91} +1.98598e11 q^{92} -9.32941e10 q^{93} +2.42942e11 q^{94} +1.70569e11 q^{95} -1.06576e12i q^{96} +1.52273e12i q^{97} +1.13192e12i q^{98} +2.67058e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 82.5668i 1.29011i −0.764137 0.645053i \(-0.776835\pi\)
0.764137 0.645053i \(-0.223165\pi\)
\(3\) −867.031 −1.18934 −0.594671 0.803969i \(-0.702718\pi\)
−0.594671 + 0.803969i \(0.702718\pi\)
\(4\) −2721.28 −0.664376
\(5\) 8790.22i 0.562574i 0.959624 + 0.281287i \(0.0907613\pi\)
−0.959624 + 0.281287i \(0.909239\pi\)
\(6\) 71588.0i 1.53438i
\(7\) −11496.7 −0.0977204 −0.0488602 0.998806i \(-0.515559\pi\)
−0.0488602 + 0.998806i \(0.515559\pi\)
\(8\) 113506.i 0.432991i
\(9\) 220301. 0.414535
\(10\) 725781. 0.725781
\(11\) 1.21224e6 0.684279 0.342139 0.939649i \(-0.388848\pi\)
0.342139 + 0.939649i \(0.388848\pi\)
\(12\) 2.35944e6 0.790171
\(13\) 5.08347e6i 1.05318i −0.850121 0.526588i \(-0.823471\pi\)
0.850121 0.526588i \(-0.176529\pi\)
\(14\) 949247.i 0.126070i
\(15\) 7.62139e6i 0.669094i
\(16\) −2.05182e7 −1.22298
\(17\) −4.29631e7 −1.77993 −0.889963 0.456033i \(-0.849270\pi\)
−0.889963 + 0.456033i \(0.849270\pi\)
\(18\) 1.81896e7i 0.534795i
\(19\) 1.94044e7i 0.412458i −0.978504 0.206229i \(-0.933881\pi\)
0.978504 0.206229i \(-0.0661191\pi\)
\(20\) 2.39207e7i 0.373761i
\(21\) 9.96800e6 0.116223
\(22\) 1.00091e8i 0.882793i
\(23\) −7.29795e7 −0.492985 −0.246493 0.969145i \(-0.579278\pi\)
−0.246493 + 0.969145i \(0.579278\pi\)
\(24\) 9.84131e7i 0.514974i
\(25\) 1.66873e8 0.683510
\(26\) −4.19726e8 −1.35871
\(27\) 2.69768e8 0.696318
\(28\) 3.12858e7 0.0649231
\(29\) −9.12773e8 −1.53453 −0.767264 0.641332i \(-0.778382\pi\)
−0.767264 + 0.641332i \(0.778382\pi\)
\(30\) −6.29274e8 −0.863202
\(31\) 1.07602e8 0.121241 0.0606205 0.998161i \(-0.480692\pi\)
0.0606205 + 0.998161i \(0.480692\pi\)
\(32\) 1.22920e9i 1.14478i
\(33\) −1.05105e9 −0.813842
\(34\) 3.54733e9i 2.29629i
\(35\) 1.01059e8i 0.0549750i
\(36\) −5.99502e8 −0.275407
\(37\) 1.17230e9 0.456906 0.228453 0.973555i \(-0.426633\pi\)
0.228453 + 0.973555i \(0.426633\pi\)
\(38\) −1.60216e9 −0.532114
\(39\) 4.40753e9i 1.25259i
\(40\) 9.97743e8 0.243590
\(41\) −4.70768e9 −0.991068 −0.495534 0.868588i \(-0.665028\pi\)
−0.495534 + 0.868588i \(0.665028\pi\)
\(42\) 8.23026e8i 0.149940i
\(43\) 5.03554e9i 0.796590i −0.917257 0.398295i \(-0.869602\pi\)
0.917257 0.398295i \(-0.130398\pi\)
\(44\) −3.29885e9 −0.454618
\(45\) 1.93650e9i 0.233207i
\(46\) 6.02569e9i 0.636003i
\(47\) 2.94237e9i 0.272967i 0.990642 + 0.136483i \(0.0435800\pi\)
−0.990642 + 0.136483i \(0.956420\pi\)
\(48\) 1.77899e10 1.45454
\(49\) −1.37091e10 −0.990451
\(50\) 1.37781e10i 0.881801i
\(51\) 3.72503e10 2.11694
\(52\) 1.38336e10i 0.699704i
\(53\) 2.41304e10i 1.08870i 0.838857 + 0.544352i \(0.183224\pi\)
−0.838857 + 0.544352i \(0.816776\pi\)
\(54\) 2.22739e10i 0.898325i
\(55\) 1.06559e10i 0.384958i
\(56\) 1.30495e9i 0.0423121i
\(57\) 1.68242e10i 0.490553i
\(58\) 7.53648e10i 1.97970i
\(59\) 4.28123e9 0.101498 0.0507489 0.998711i \(-0.483839\pi\)
0.0507489 + 0.998711i \(0.483839\pi\)
\(60\) 2.07400e10i 0.444530i
\(61\) 3.04317e10 0.590673 0.295336 0.955393i \(-0.404568\pi\)
0.295336 + 0.955393i \(0.404568\pi\)
\(62\) 8.88434e9i 0.156414i
\(63\) −2.53274e9 −0.0405086
\(64\) 1.74489e10 0.253914
\(65\) 4.46849e10 0.592489
\(66\) 8.67819e10i 1.04994i
\(67\) 6.61861e9i 0.0731675i −0.999331 0.0365837i \(-0.988352\pi\)
0.999331 0.0365837i \(-0.0116476\pi\)
\(68\) 1.16915e11 1.18254
\(69\) 6.32754e10 0.586328
\(70\) −8.34410e9 −0.0709236
\(71\) 1.41623e11i 1.10556i 0.833327 + 0.552781i \(0.186433\pi\)
−0.833327 + 0.552781i \(0.813567\pi\)
\(72\) 2.50055e10i 0.179490i
\(73\) 7.21726e10i 0.476909i −0.971154 0.238454i \(-0.923359\pi\)
0.971154 0.238454i \(-0.0766408\pi\)
\(74\) 9.67927e10i 0.589457i
\(75\) −1.44684e11 −0.812928
\(76\) 5.28050e10i 0.274027i
\(77\) −1.39368e10 −0.0668680
\(78\) 3.63916e11 1.61597
\(79\) 3.88746e11i 1.59920i −0.600532 0.799601i \(-0.705045\pi\)
0.600532 0.799601i \(-0.294955\pi\)
\(80\) 1.80360e11i 0.688017i
\(81\) −3.50974e11 −1.24270
\(82\) 3.88698e11i 1.27858i
\(83\) 3.26193e11 + 2.20944e10i 0.997714 + 0.0675793i
\(84\) −2.71258e10 −0.0772158
\(85\) 3.77655e11i 1.00134i
\(86\) −4.15768e11 −1.02769
\(87\) 7.91402e11 1.82508
\(88\) 1.37597e11i 0.296286i
\(89\) 8.48384e11i 1.70707i −0.521032 0.853537i \(-0.674453\pi\)
0.521032 0.853537i \(-0.325547\pi\)
\(90\) 1.59890e11 0.300862
\(91\) 5.84432e10i 0.102917i
\(92\) 1.98598e11 0.327527
\(93\) −9.32941e10 −0.144197
\(94\) 2.42942e11 0.352156
\(95\) 1.70569e11 0.232038
\(96\) 1.06576e12i 1.36154i
\(97\) 1.52273e12i 1.82807i 0.405632 + 0.914036i \(0.367051\pi\)
−0.405632 + 0.914036i \(0.632949\pi\)
\(98\) 1.13192e12i 1.27779i
\(99\) 2.67058e11 0.283658
\(100\) −4.54108e11 −0.454108
\(101\) 2.81582e11i 0.265263i −0.991165 0.132631i \(-0.957657\pi\)
0.991165 0.132631i \(-0.0423426\pi\)
\(102\) 3.07564e12i 2.73108i
\(103\) 6.31888e11i 0.529196i −0.964359 0.264598i \(-0.914761\pi\)
0.964359 0.264598i \(-0.0852393\pi\)
\(104\) −5.77005e11 −0.456015
\(105\) 8.76210e10i 0.0653841i
\(106\) 1.99237e12 1.40454
\(107\) 9.99424e11i 0.665959i 0.942934 + 0.332979i \(0.108054\pi\)
−0.942934 + 0.332979i \(0.891946\pi\)
\(108\) −7.34115e11 −0.462617
\(109\) 3.00150e12 1.78969 0.894847 0.446373i \(-0.147285\pi\)
0.894847 + 0.446373i \(0.147285\pi\)
\(110\) 8.79822e11 0.496637
\(111\) −1.01642e12 −0.543417
\(112\) 2.35892e11 0.119510
\(113\) 1.11606e12 0.536064 0.268032 0.963410i \(-0.413627\pi\)
0.268032 + 0.963410i \(0.413627\pi\)
\(114\) 1.38912e12 0.632866
\(115\) 6.41506e11i 0.277341i
\(116\) 2.48391e12 1.01950
\(117\) 1.11990e12i 0.436578i
\(118\) 3.53488e11i 0.130943i
\(119\) 4.93934e11 0.173935
\(120\) −8.65074e11 −0.289711
\(121\) −1.66890e12 −0.531763
\(122\) 2.51265e12i 0.762031i
\(123\) 4.08170e12 1.17872
\(124\) −2.92815e11 −0.0805496
\(125\) 3.61290e12i 0.947100i
\(126\) 2.09120e11i 0.0522604i
\(127\) −5.28863e10 −0.0126044 −0.00630219 0.999980i \(-0.502006\pi\)
−0.00630219 + 0.999980i \(0.502006\pi\)
\(128\) 3.59412e12i 0.817208i
\(129\) 4.36596e12i 0.947418i
\(130\) 3.68949e12i 0.764375i
\(131\) 9.92149e12 1.96313 0.981565 0.191127i \(-0.0612142\pi\)
0.981565 + 0.191127i \(0.0612142\pi\)
\(132\) 2.86021e12 0.540697
\(133\) 2.23087e11i 0.0403055i
\(134\) −5.46478e11 −0.0943939
\(135\) 2.37132e12i 0.391731i
\(136\) 4.87656e12i 0.770691i
\(137\) 9.50330e12i 1.43731i 0.695366 + 0.718656i \(0.255242\pi\)
−0.695366 + 0.718656i \(0.744758\pi\)
\(138\) 5.22445e12i 0.756426i
\(139\) 1.24806e13i 1.73040i 0.501426 + 0.865200i \(0.332809\pi\)
−0.501426 + 0.865200i \(0.667191\pi\)
\(140\) 2.75009e11i 0.0365241i
\(141\) 2.55112e12i 0.324651i
\(142\) 1.16933e13 1.42629
\(143\) 6.16240e12i 0.720665i
\(144\) −4.52018e12 −0.506969
\(145\) 8.02348e12i 0.863286i
\(146\) −5.95907e12 −0.615263
\(147\) 1.18862e13 1.17799
\(148\) −3.19015e12 −0.303557
\(149\) 6.08559e12i 0.556141i 0.960561 + 0.278070i \(0.0896949\pi\)
−0.960561 + 0.278070i \(0.910305\pi\)
\(150\) 1.19461e13i 1.04876i
\(151\) −4.86349e12 −0.410286 −0.205143 0.978732i \(-0.565766\pi\)
−0.205143 + 0.978732i \(0.565766\pi\)
\(152\) −2.20252e12 −0.178590
\(153\) −9.46481e12 −0.737842
\(154\) 1.15072e12i 0.0862669i
\(155\) 9.45844e11i 0.0682071i
\(156\) 1.19941e13i 0.832188i
\(157\) 6.07643e12i 0.405743i 0.979205 + 0.202871i \(0.0650273\pi\)
−0.979205 + 0.202871i \(0.934973\pi\)
\(158\) −3.20975e13 −2.06314
\(159\) 2.09218e13i 1.29484i
\(160\) −1.08050e13 −0.644027
\(161\) 8.39024e11 0.0481747
\(162\) 2.89788e13i 1.60321i
\(163\) 2.37540e13i 1.26652i 0.773940 + 0.633259i \(0.218283\pi\)
−0.773940 + 0.633259i \(0.781717\pi\)
\(164\) 1.28109e13 0.658442
\(165\) 9.23897e12i 0.457847i
\(166\) 1.82427e12 2.69327e13i 0.0871846 1.28716i
\(167\) −2.95286e12 −0.136127 −0.0680634 0.997681i \(-0.521682\pi\)
−0.0680634 + 0.997681i \(0.521682\pi\)
\(168\) 1.13143e12i 0.0503235i
\(169\) −2.54363e12 −0.109178
\(170\) −3.11818e13 −1.29184
\(171\) 4.27482e12i 0.170978i
\(172\) 1.37031e13i 0.529235i
\(173\) 3.60914e13 1.34625 0.673126 0.739528i \(-0.264951\pi\)
0.673126 + 0.739528i \(0.264951\pi\)
\(174\) 6.53436e13i 2.35455i
\(175\) −1.91849e12 −0.0667929
\(176\) −2.48730e13 −0.836860
\(177\) −3.71196e12 −0.120716
\(178\) −7.00484e13 −2.20231
\(179\) 3.40909e13i 1.03638i −0.855265 0.518191i \(-0.826606\pi\)
0.855265 0.518191i \(-0.173394\pi\)
\(180\) 5.26976e12i 0.154937i
\(181\) 1.72907e13i 0.491745i 0.969302 + 0.245872i \(0.0790744\pi\)
−0.969302 + 0.245872i \(0.920926\pi\)
\(182\) 4.82547e12 0.132774
\(183\) −2.63852e13 −0.702512
\(184\) 8.28361e12i 0.213458i
\(185\) 1.03047e13i 0.257044i
\(186\) 7.70300e12i 0.186030i
\(187\) −5.20816e13 −1.21797
\(188\) 8.00702e12i 0.181353i
\(189\) −3.10144e12 −0.0680445
\(190\) 1.40834e13i 0.299354i
\(191\) −6.13783e12 −0.126420 −0.0632098 0.998000i \(-0.520134\pi\)
−0.0632098 + 0.998000i \(0.520134\pi\)
\(192\) −1.51287e13 −0.301991
\(193\) 4.47415e13 0.865699 0.432850 0.901466i \(-0.357508\pi\)
0.432850 + 0.901466i \(0.357508\pi\)
\(194\) 1.25727e14 2.35841
\(195\) −3.87432e13 −0.704673
\(196\) 3.73064e13 0.658032
\(197\) 3.39180e13 0.580273 0.290137 0.956985i \(-0.406299\pi\)
0.290137 + 0.956985i \(0.406299\pi\)
\(198\) 2.20502e13i 0.365949i
\(199\) −3.94240e13 −0.634807 −0.317404 0.948291i \(-0.602811\pi\)
−0.317404 + 0.948291i \(0.602811\pi\)
\(200\) 1.89410e13i 0.295954i
\(201\) 5.73854e12i 0.0870212i
\(202\) −2.32493e13 −0.342217
\(203\) 1.04939e13 0.149955
\(204\) −1.01369e14 −1.40644
\(205\) 4.13815e13i 0.557550i
\(206\) −5.21730e13 −0.682720
\(207\) −1.60775e13 −0.204360
\(208\) 1.04304e14i 1.28801i
\(209\) 2.35229e13i 0.282236i
\(210\) 7.23459e12 0.0843525
\(211\) 8.21807e13i 0.931269i 0.884977 + 0.465635i \(0.154174\pi\)
−0.884977 + 0.465635i \(0.845826\pi\)
\(212\) 6.56657e13i 0.723309i
\(213\) 1.22791e14i 1.31489i
\(214\) 8.25193e13 0.859158
\(215\) 4.42635e13 0.448141
\(216\) 3.06202e13i 0.301499i
\(217\) −1.23707e12 −0.0118477
\(218\) 2.47824e14i 2.30890i
\(219\) 6.25759e13i 0.567208i
\(220\) 2.89977e13i 0.255757i
\(221\) 2.18402e14i 1.87457i
\(222\) 8.39223e13i 0.701067i
\(223\) 1.32645e14i 1.07860i 0.842114 + 0.539300i \(0.181311\pi\)
−0.842114 + 0.539300i \(0.818689\pi\)
\(224\) 1.41318e13i 0.111869i
\(225\) 3.67622e13 0.283339
\(226\) 9.21495e13i 0.691580i
\(227\) −9.70001e13 −0.708953 −0.354476 0.935065i \(-0.615341\pi\)
−0.354476 + 0.935065i \(0.615341\pi\)
\(228\) 4.57835e13i 0.325912i
\(229\) −1.90648e14 −1.32196 −0.660981 0.750402i \(-0.729860\pi\)
−0.660981 + 0.750402i \(0.729860\pi\)
\(230\) −5.29671e13 −0.357799
\(231\) 1.20836e13 0.0795290
\(232\) 1.03605e14i 0.664436i
\(233\) 1.31626e14i 0.822634i 0.911492 + 0.411317i \(0.134931\pi\)
−0.911492 + 0.411317i \(0.865069\pi\)
\(234\) −9.24662e13 −0.563233
\(235\) −2.58641e13 −0.153564
\(236\) −1.16504e13 −0.0674327
\(237\) 3.37055e14i 1.90200i
\(238\) 4.07826e13i 0.224395i
\(239\) 1.87659e14i 1.00689i 0.864028 + 0.503444i \(0.167934\pi\)
−0.864028 + 0.503444i \(0.832066\pi\)
\(240\) 1.56377e14i 0.818288i
\(241\) 5.69759e13 0.290796 0.145398 0.989373i \(-0.453554\pi\)
0.145398 + 0.989373i \(0.453554\pi\)
\(242\) 1.37796e14i 0.686031i
\(243\) 1.60940e14 0.781673
\(244\) −8.28132e13 −0.392429
\(245\) 1.20506e14i 0.557202i
\(246\) 3.37013e14i 1.52067i
\(247\) −9.86419e13 −0.434390
\(248\) 1.22134e13i 0.0524962i
\(249\) −2.82819e14 1.91565e13i −1.18662 0.0803750i
\(250\) 2.98306e14 1.22186
\(251\) 2.68129e14i 1.07226i 0.844134 + 0.536131i \(0.180115\pi\)
−0.844134 + 0.536131i \(0.819885\pi\)
\(252\) 6.89230e12 0.0269129
\(253\) −8.84688e13 −0.337339
\(254\) 4.36666e12i 0.0162610i
\(255\) 3.27439e14i 1.19094i
\(256\) 3.68226e14 1.30820
\(257\) 6.17317e13i 0.214245i 0.994246 + 0.107122i \(0.0341636\pi\)
−0.994246 + 0.107122i \(0.965836\pi\)
\(258\) 3.60484e14 1.22227
\(259\) −1.34775e13 −0.0446490
\(260\) −1.21600e14 −0.393636
\(261\) −2.01085e14 −0.636116
\(262\) 8.19186e14i 2.53265i
\(263\) 5.77976e13i 0.174653i −0.996180 0.0873264i \(-0.972168\pi\)
0.996180 0.0873264i \(-0.0278323\pi\)
\(264\) 1.19300e14i 0.352386i
\(265\) −2.12112e14 −0.612477
\(266\) 1.84196e13 0.0519985
\(267\) 7.35575e14i 2.03030i
\(268\) 1.80111e13i 0.0486107i
\(269\) 4.34618e14i 1.14708i −0.819177 0.573541i \(-0.805569\pi\)
0.819177 0.573541i \(-0.194431\pi\)
\(270\) 1.95792e14 0.505374
\(271\) 3.23008e14i 0.815451i −0.913105 0.407725i \(-0.866322\pi\)
0.913105 0.407725i \(-0.133678\pi\)
\(272\) 8.81525e14 2.17681
\(273\) 5.06721e13i 0.122403i
\(274\) 7.84658e14 1.85429
\(275\) 2.02290e14 0.467711
\(276\) −1.72190e14 −0.389542
\(277\) −2.30679e14 −0.510657 −0.255329 0.966854i \(-0.582184\pi\)
−0.255329 + 0.966854i \(0.582184\pi\)
\(278\) 1.03048e15 2.23240
\(279\) 2.37048e13 0.0502587
\(280\) −1.14708e13 −0.0238037
\(281\) 6.76321e14i 1.37377i −0.726765 0.686886i \(-0.758977\pi\)
0.726765 0.686886i \(-0.241023\pi\)
\(282\) −2.10638e14 −0.418835
\(283\) 3.66389e14i 0.713220i −0.934253 0.356610i \(-0.883933\pi\)
0.934253 0.356610i \(-0.116067\pi\)
\(284\) 3.85396e14i 0.734509i
\(285\) −1.47889e14 −0.275973
\(286\) −5.08810e14 −0.929735
\(287\) 5.41228e13 0.0968476
\(288\) 2.70795e14i 0.474554i
\(289\) 1.26320e15 2.16813
\(290\) −6.62473e14 −1.11373
\(291\) 1.32026e15i 2.17420i
\(292\) 1.96402e14i 0.316847i
\(293\) 8.91901e14 1.40965 0.704824 0.709382i \(-0.251026\pi\)
0.704824 + 0.709382i \(0.251026\pi\)
\(294\) 9.81408e14i 1.51973i
\(295\) 3.76330e13i 0.0571000i
\(296\) 1.33062e14i 0.197836i
\(297\) 3.27024e14 0.476476
\(298\) 5.02468e14 0.717481
\(299\) 3.70989e14i 0.519200i
\(300\) 3.93725e14 0.540090
\(301\) 5.78921e13i 0.0778431i
\(302\) 4.01563e14i 0.529312i
\(303\) 2.44140e14i 0.315488i
\(304\) 3.98144e14i 0.504428i
\(305\) 2.67501e14i 0.332297i
\(306\) 7.81480e14i 0.951895i
\(307\) 1.27235e15i 1.51977i −0.650058 0.759884i \(-0.725256\pi\)
0.650058 0.759884i \(-0.274744\pi\)
\(308\) 3.79260e13 0.0444255
\(309\) 5.47866e14i 0.629395i
\(310\) 7.80954e13 0.0879944
\(311\) 5.35532e14i 0.591866i 0.955209 + 0.295933i \(0.0956305\pi\)
−0.955209 + 0.295933i \(0.904370\pi\)
\(312\) 5.00281e14 0.542358
\(313\) −1.02530e15 −1.09039 −0.545197 0.838308i \(-0.683545\pi\)
−0.545197 + 0.838308i \(0.683545\pi\)
\(314\) 5.01712e14 0.523452
\(315\) 2.22633e13i 0.0227891i
\(316\) 1.05789e15i 1.06247i
\(317\) −1.37443e15 −1.35446 −0.677232 0.735769i \(-0.736821\pi\)
−0.677232 + 0.735769i \(0.736821\pi\)
\(318\) −1.72745e15 −1.67048
\(319\) −1.10650e15 −1.05004
\(320\) 1.53379e14i 0.142846i
\(321\) 8.66532e14i 0.792053i
\(322\) 6.92756e13i 0.0621505i
\(323\) 8.33674e14i 0.734144i
\(324\) 9.55100e14 0.825617
\(325\) 8.48293e14i 0.719856i
\(326\) 1.96129e15 1.63394
\(327\) −2.60239e15 −2.12856
\(328\) 5.34349e14i 0.429124i
\(329\) 3.38276e13i 0.0266744i
\(330\) −7.62833e14 −0.590671
\(331\) 1.08760e15i 0.826993i −0.910506 0.413496i \(-0.864307\pi\)
0.910506 0.413496i \(-0.135693\pi\)
\(332\) −8.87664e14 6.01252e13i −0.662857 0.0448981i
\(333\) 2.58258e14 0.189404
\(334\) 2.43808e14i 0.175618i
\(335\) 5.81791e13 0.0411621
\(336\) −2.04526e14 −0.142139
\(337\) 1.50998e15i 1.03084i −0.856938 0.515419i \(-0.827636\pi\)
0.856938 0.515419i \(-0.172364\pi\)
\(338\) 2.10019e14i 0.140851i
\(339\) −9.67658e14 −0.637564
\(340\) 1.02771e15i 0.665267i
\(341\) 1.30439e14 0.0829626
\(342\) −3.52958e14 −0.220580
\(343\) 3.16739e14 0.194508
\(344\) −5.71563e14 −0.344916
\(345\) 5.56205e14i 0.329853i
\(346\) 2.97995e15i 1.73681i
\(347\) 1.63823e15i 0.938422i 0.883086 + 0.469211i \(0.155462\pi\)
−0.883086 + 0.469211i \(0.844538\pi\)
\(348\) −2.15363e15 −1.21254
\(349\) 2.37222e15 1.31281 0.656405 0.754409i \(-0.272076\pi\)
0.656405 + 0.754409i \(0.272076\pi\)
\(350\) 1.58403e14i 0.0861700i
\(351\) 1.37136e15i 0.733345i
\(352\) 1.49009e15i 0.783352i
\(353\) −8.55675e14 −0.442243 −0.221121 0.975246i \(-0.570972\pi\)
−0.221121 + 0.975246i \(0.570972\pi\)
\(354\) 3.06485e14i 0.155736i
\(355\) −1.24490e15 −0.621961
\(356\) 2.30869e15i 1.13414i
\(357\) −4.28256e14 −0.206868
\(358\) −2.81478e15 −1.33704
\(359\) −3.30003e15 −1.54153 −0.770763 0.637122i \(-0.780125\pi\)
−0.770763 + 0.637122i \(0.780125\pi\)
\(360\) 2.19804e14 0.100977
\(361\) 1.83678e15 0.829879
\(362\) 1.42763e15 0.634404
\(363\) 1.44699e15 0.632448
\(364\) 1.59041e14i 0.0683754i
\(365\) 6.34414e14 0.268297
\(366\) 2.17854e15i 0.906316i
\(367\) 4.29828e15i 1.75913i 0.475779 + 0.879565i \(0.342166\pi\)
−0.475779 + 0.879565i \(0.657834\pi\)
\(368\) 1.49741e15 0.602911
\(369\) −1.03711e15 −0.410833
\(370\) 8.50830e14 0.331614
\(371\) 2.77420e14i 0.106389i
\(372\) 2.53880e14 0.0958010
\(373\) 3.19315e14 0.118568 0.0592839 0.998241i \(-0.481118\pi\)
0.0592839 + 0.998241i \(0.481118\pi\)
\(374\) 4.30022e15i 1.57131i
\(375\) 3.13249e15i 1.12643i
\(376\) 3.33976e14 0.118192
\(377\) 4.64006e15i 1.61613i
\(378\) 2.56076e14i 0.0877847i
\(379\) 2.52108e15i 0.850651i 0.905041 + 0.425325i \(0.139840\pi\)
−0.905041 + 0.425325i \(0.860160\pi\)
\(380\) −4.64168e14 −0.154161
\(381\) 4.58541e13 0.0149909
\(382\) 5.06781e14i 0.163095i
\(383\) 5.80400e14 0.183880 0.0919401 0.995765i \(-0.470693\pi\)
0.0919401 + 0.995765i \(0.470693\pi\)
\(384\) 3.11621e15i 0.971940i
\(385\) 1.22508e14i 0.0376182i
\(386\) 3.69417e15i 1.11684i
\(387\) 1.10933e15i 0.330215i
\(388\) 4.14379e15i 1.21453i
\(389\) 1.62500e15i 0.468982i 0.972118 + 0.234491i \(0.0753423\pi\)
−0.972118 + 0.234491i \(0.924658\pi\)
\(390\) 3.19890e15i 0.909103i
\(391\) 3.13542e15 0.877477
\(392\) 1.55607e15i 0.428856i
\(393\) −8.60224e15 −2.33483
\(394\) 2.80050e15i 0.748615i
\(395\) 3.41716e15 0.899670
\(396\) −7.26741e14 −0.188455
\(397\) 4.82490e15 1.23238 0.616191 0.787597i \(-0.288675\pi\)
0.616191 + 0.787597i \(0.288675\pi\)
\(398\) 3.25511e15i 0.818969i
\(399\) 1.93423e14i 0.0479371i
\(400\) −3.42393e15 −0.835920
\(401\) −2.47784e15 −0.595947 −0.297973 0.954574i \(-0.596311\pi\)
−0.297973 + 0.954574i \(0.596311\pi\)
\(402\) 4.73813e14 0.112267
\(403\) 5.46991e14i 0.127688i
\(404\) 7.66264e14i 0.176234i
\(405\) 3.08514e15i 0.699109i
\(406\) 8.66447e14i 0.193458i
\(407\) 1.42111e15 0.312651
\(408\) 4.22813e15i 0.916616i
\(409\) −3.09892e15 −0.662019 −0.331009 0.943627i \(-0.607389\pi\)
−0.331009 + 0.943627i \(0.607389\pi\)
\(410\) −3.41674e15 −0.719299
\(411\) 8.23966e15i 1.70946i
\(412\) 1.71955e15i 0.351585i
\(413\) −4.92201e13 −0.00991841
\(414\) 1.32747e15i 0.263646i
\(415\) −1.94215e14 + 2.86731e15i −0.0380184 + 0.561288i
\(416\) 6.24862e15 1.20566
\(417\) 1.08211e16i 2.05804i
\(418\) −1.94221e15 −0.364115
\(419\) −3.66816e15 −0.677897 −0.338949 0.940805i \(-0.610071\pi\)
−0.338949 + 0.940805i \(0.610071\pi\)
\(420\) 2.38442e14i 0.0434396i
\(421\) 7.75594e15i 1.39297i −0.717571 0.696485i \(-0.754746\pi\)
0.717571 0.696485i \(-0.245254\pi\)
\(422\) 6.78540e15 1.20144
\(423\) 6.48207e14i 0.113154i
\(424\) 2.73895e15 0.471399
\(425\) −7.16936e15 −1.21660
\(426\) −1.01385e16 −1.69635
\(427\) −3.49864e14 −0.0577208
\(428\) 2.71972e15i 0.442447i
\(429\) 5.34299e15i 0.857118i
\(430\) 3.65470e15i 0.578150i
\(431\) −8.42234e15 −1.31392 −0.656960 0.753925i \(-0.728158\pi\)
−0.656960 + 0.753925i \(0.728158\pi\)
\(432\) −5.53515e15 −0.851583
\(433\) 8.73975e15i 1.32609i −0.748582 0.663043i \(-0.769265\pi\)
0.748582 0.663043i \(-0.230735\pi\)
\(434\) 1.02141e14i 0.0152848i
\(435\) 6.95660e15i 1.02674i
\(436\) −8.16792e15 −1.18903
\(437\) 1.41613e15i 0.203335i
\(438\) 5.16669e15 0.731759
\(439\) 8.46221e15i 1.18222i −0.806592 0.591108i \(-0.798691\pi\)
0.806592 0.591108i \(-0.201309\pi\)
\(440\) 1.20951e15 0.166683
\(441\) −3.02013e15 −0.410577
\(442\) 1.80327e16 2.41840
\(443\) −3.92705e15 −0.519570 −0.259785 0.965666i \(-0.583652\pi\)
−0.259785 + 0.965666i \(0.583652\pi\)
\(444\) 2.76596e15 0.361034
\(445\) 7.45749e15 0.960356
\(446\) 1.09521e16 1.39151
\(447\) 5.27639e15i 0.661442i
\(448\) −2.00605e14 −0.0248126
\(449\) 4.53577e15i 0.553570i 0.960932 + 0.276785i \(0.0892690\pi\)
−0.960932 + 0.276785i \(0.910731\pi\)
\(450\) 3.03534e15i 0.365538i
\(451\) −5.70684e15 −0.678167
\(452\) −3.03711e15 −0.356148
\(453\) 4.21679e15 0.487970
\(454\) 8.00900e15i 0.914625i
\(455\) −5.13729e14 −0.0578983
\(456\) 1.90965e15 0.212405
\(457\) 9.26229e15i 1.01677i 0.861131 + 0.508383i \(0.169757\pi\)
−0.861131 + 0.508383i \(0.830243\pi\)
\(458\) 1.57412e16i 1.70547i
\(459\) −1.15901e16 −1.23939
\(460\) 1.74572e15i 0.184259i
\(461\) 3.53752e15i 0.368548i 0.982875 + 0.184274i \(0.0589934\pi\)
−0.982875 + 0.184274i \(0.941007\pi\)
\(462\) 9.97707e14i 0.102601i
\(463\) −2.91140e15 −0.295540 −0.147770 0.989022i \(-0.547209\pi\)
−0.147770 + 0.989022i \(0.547209\pi\)
\(464\) 1.87285e16 1.87670
\(465\) 8.20076e14i 0.0811215i
\(466\) 1.08680e16 1.06129
\(467\) 1.95529e16i 1.88499i 0.334217 + 0.942496i \(0.391528\pi\)
−0.334217 + 0.942496i \(0.608472\pi\)
\(468\) 3.04755e15i 0.290052i
\(469\) 7.60923e13i 0.00714996i
\(470\) 2.13551e15i 0.198114i
\(471\) 5.26845e15i 0.482567i
\(472\) 4.85945e14i 0.0439476i
\(473\) 6.10429e15i 0.545090i
\(474\) 2.78295e16 2.45378
\(475\) 3.23807e15i 0.281919i
\(476\) −1.34414e15 −0.115558
\(477\) 5.31596e15i 0.451306i
\(478\) 1.54944e16 1.29899
\(479\) 3.05099e15 0.252597 0.126298 0.991992i \(-0.459690\pi\)
0.126298 + 0.991992i \(0.459690\pi\)
\(480\) 9.36824e15 0.765968
\(481\) 5.95933e15i 0.481202i
\(482\) 4.70432e15i 0.375158i
\(483\) −7.27460e14 −0.0572962
\(484\) 4.54155e15 0.353290
\(485\) −1.33852e16 −1.02843
\(486\) 1.32883e16i 1.00844i
\(487\) 1.53515e16i 1.15074i 0.817894 + 0.575369i \(0.195142\pi\)
−0.817894 + 0.575369i \(0.804858\pi\)
\(488\) 3.45418e15i 0.255756i
\(489\) 2.05955e16i 1.50632i
\(490\) −9.94982e15 −0.718850
\(491\) 6.82025e15i 0.486756i −0.969932 0.243378i \(-0.921744\pi\)
0.969932 0.243378i \(-0.0782556\pi\)
\(492\) −1.11075e16 −0.783113
\(493\) 3.92155e16 2.73134
\(494\) 8.14455e15i 0.560410i
\(495\) 2.34750e15i 0.159579i
\(496\) −2.20780e15 −0.148275
\(497\) 1.62820e15i 0.108036i
\(498\) −1.58169e15 + 2.33515e16i −0.103692 + 1.53087i
\(499\) −1.70492e16 −1.10434 −0.552168 0.833733i \(-0.686199\pi\)
−0.552168 + 0.833733i \(0.686199\pi\)
\(500\) 9.83172e15i 0.629230i
\(501\) 2.56022e15 0.161901
\(502\) 2.21386e16 1.38333
\(503\) 2.11569e16i 1.30631i 0.757226 + 0.653153i \(0.226554\pi\)
−0.757226 + 0.653153i \(0.773446\pi\)
\(504\) 2.87481e14i 0.0175398i
\(505\) 2.47517e15 0.149230
\(506\) 7.30459e15i 0.435204i
\(507\) 2.20540e15 0.129850
\(508\) 1.43919e14 0.00837404
\(509\) −5.23984e15 −0.301308 −0.150654 0.988587i \(-0.548138\pi\)
−0.150654 + 0.988587i \(0.548138\pi\)
\(510\) 2.70356e16 1.53644
\(511\) 8.29748e14i 0.0466037i
\(512\) 1.56817e16i 0.870510i
\(513\) 5.23469e15i 0.287202i
\(514\) 5.09700e15 0.276398
\(515\) 5.55444e15 0.297712
\(516\) 1.18810e16i 0.629442i
\(517\) 3.56686e15i 0.186785i
\(518\) 1.11280e15i 0.0576020i
\(519\) −3.12923e16 −1.60116
\(520\) 5.07200e15i 0.256542i
\(521\) 3.31130e15 0.165566 0.0827832 0.996568i \(-0.473619\pi\)
0.0827832 + 0.996568i \(0.473619\pi\)
\(522\) 1.66029e16i 0.820658i
\(523\) −3.70738e15 −0.181158 −0.0905788 0.995889i \(-0.528872\pi\)
−0.0905788 + 0.995889i \(0.528872\pi\)
\(524\) −2.69992e16 −1.30426
\(525\) 1.66339e15 0.0794396
\(526\) −4.77217e15 −0.225321
\(527\) −4.62290e15 −0.215800
\(528\) 2.15657e16 0.995313
\(529\) −1.65886e16 −0.756966
\(530\) 1.75134e16i 0.790160i
\(531\) 9.43160e14 0.0420744
\(532\) 6.07084e14i 0.0267780i
\(533\) 2.39314e16i 1.04377i
\(534\) 6.07341e16 2.61930
\(535\) −8.78517e15 −0.374651
\(536\) −7.51252e14 −0.0316808
\(537\) 2.95578e16i 1.23261i
\(538\) −3.58851e16 −1.47986
\(539\) −1.66188e16 −0.677744
\(540\) 6.45303e15i 0.260256i
\(541\) 1.22352e16i 0.488009i 0.969774 + 0.244004i \(0.0784611\pi\)
−0.969774 + 0.244004i \(0.921539\pi\)
\(542\) −2.66698e16 −1.05202
\(543\) 1.49915e16i 0.584853i
\(544\) 5.28104e16i 2.03763i
\(545\) 2.63838e16i 1.00684i
\(546\) −4.18383e15 −0.157913
\(547\) −4.07221e16 −1.52022 −0.760109 0.649795i \(-0.774855\pi\)
−0.760109 + 0.649795i \(0.774855\pi\)
\(548\) 2.58612e16i 0.954916i
\(549\) 6.70413e15 0.244855
\(550\) 1.67024e16i 0.603398i
\(551\) 1.77118e16i 0.632928i
\(552\) 7.18214e15i 0.253875i
\(553\) 4.46930e15i 0.156275i
\(554\) 1.90464e16i 0.658802i
\(555\) 8.93452e15i 0.305713i
\(556\) 3.39633e16i 1.14964i
\(557\) −4.14237e15 −0.138713 −0.0693566 0.997592i \(-0.522095\pi\)
−0.0693566 + 0.997592i \(0.522095\pi\)
\(558\) 1.95723e15i 0.0648391i
\(559\) −2.55980e16 −0.838949
\(560\) 2.07354e15i 0.0672334i
\(561\) 4.51564e16 1.44858
\(562\) −5.58417e16 −1.77231
\(563\) 3.88681e16 1.22051 0.610257 0.792204i \(-0.291066\pi\)
0.610257 + 0.792204i \(0.291066\pi\)
\(564\) 6.94233e15i 0.215690i
\(565\) 9.81041e15i 0.301576i
\(566\) −3.02516e16 −0.920130
\(567\) 4.03505e15 0.121437
\(568\) 1.60750e16 0.478698
\(569\) 4.28307e16i 1.26206i 0.775757 + 0.631032i \(0.217368\pi\)
−0.775757 + 0.631032i \(0.782632\pi\)
\(570\) 1.22107e16i 0.356034i
\(571\) 3.54697e16i 1.02339i −0.859168 0.511694i \(-0.829018\pi\)
0.859168 0.511694i \(-0.170982\pi\)
\(572\) 1.67696e16i 0.478793i
\(573\) 5.32168e15 0.150356
\(574\) 4.46875e15i 0.124944i
\(575\) −1.21783e16 −0.336960
\(576\) 3.84401e15 0.105257
\(577\) 3.39986e16i 0.921312i −0.887579 0.460656i \(-0.847614\pi\)
0.887579 0.460656i \(-0.152386\pi\)
\(578\) 1.04299e17i 2.79713i
\(579\) −3.87923e16 −1.02961
\(580\) 2.18342e16i 0.573546i
\(581\) −3.75015e15 2.54013e14i −0.0974970 0.00660388i
\(582\) −1.09009e17 −2.80496
\(583\) 2.92519e16i 0.744977i
\(584\) −8.19202e15 −0.206497
\(585\) 9.84413e15 0.245608
\(586\) 7.36414e16i 1.81860i
\(587\) 3.24372e16i 0.792894i −0.918058 0.396447i \(-0.870243\pi\)
0.918058 0.396447i \(-0.129757\pi\)
\(588\) −3.23458e16 −0.782625
\(589\) 2.08795e15i 0.0500068i
\(590\) 3.10724e15 0.0736652
\(591\) −2.94079e16 −0.690144
\(592\) −2.40534e16 −0.558787
\(593\) 3.20871e16 0.737909 0.368955 0.929447i \(-0.379716\pi\)
0.368955 + 0.929447i \(0.379716\pi\)
\(594\) 2.70013e16i 0.614704i
\(595\) 4.34179e15i 0.0978514i
\(596\) 1.65606e16i 0.369487i
\(597\) 3.41818e16 0.755003
\(598\) 3.06314e16 0.669823
\(599\) 3.72205e16i 0.805789i 0.915246 + 0.402894i \(0.131996\pi\)
−0.915246 + 0.402894i \(0.868004\pi\)
\(600\) 1.64225e16i 0.351990i
\(601\) 4.23168e16i 0.897980i −0.893537 0.448990i \(-0.851784\pi\)
0.893537 0.448990i \(-0.148216\pi\)
\(602\) 4.77997e15 0.100426
\(603\) 1.45809e15i 0.0303305i
\(604\) 1.32349e16 0.272584
\(605\) 1.46700e16i 0.299156i
\(606\) 2.01579e16 0.407013
\(607\) −8.65379e16 −1.73011 −0.865056 0.501675i \(-0.832718\pi\)
−0.865056 + 0.501675i \(0.832718\pi\)
\(608\) 2.38520e16 0.472175
\(609\) −9.09852e15 −0.178347
\(610\) 2.20867e16 0.428699
\(611\) 1.49575e16 0.287482
\(612\) 2.57564e16 0.490205
\(613\) 3.85088e16i 0.725768i 0.931834 + 0.362884i \(0.118208\pi\)
−0.931834 + 0.362884i \(0.881792\pi\)
\(614\) −1.05054e17 −1.96066
\(615\) 3.58791e16i 0.663117i
\(616\) 1.58191e15i 0.0289532i
\(617\) 1.03870e17 1.88270 0.941348 0.337436i \(-0.109560\pi\)
0.941348 + 0.337436i \(0.109560\pi\)
\(618\) 4.52356e16 0.811987
\(619\) 3.32620e16 0.591295 0.295648 0.955297i \(-0.404465\pi\)
0.295648 + 0.955297i \(0.404465\pi\)
\(620\) 2.57391e15i 0.0453151i
\(621\) −1.96875e16 −0.343274
\(622\) 4.42172e16 0.763570
\(623\) 9.75363e15i 0.166816i
\(624\) 9.04346e16i 1.53189i
\(625\) 8.98219e15 0.150696
\(626\) 8.46555e16i 1.40673i
\(627\) 2.03950e16i 0.335675i
\(628\) 1.65357e16i 0.269566i
\(629\) −5.03654e16 −0.813258
\(630\) −1.83821e15 −0.0294004
\(631\) 5.99569e16i 0.949867i −0.880022 0.474934i \(-0.842472\pi\)
0.880022 0.474934i \(-0.157528\pi\)
\(632\) −4.41250e16 −0.692440
\(633\) 7.12532e16i 1.10760i
\(634\) 1.13483e17i 1.74740i
\(635\) 4.64883e14i 0.00709090i
\(636\) 5.69342e16i 0.860262i
\(637\) 6.96899e16i 1.04312i
\(638\) 9.13603e16i 1.35467i
\(639\) 3.11997e16i 0.458294i
\(640\) −3.15931e16 −0.459740
\(641\) 6.84764e16i 0.987172i 0.869697 + 0.493586i \(0.164314\pi\)
−0.869697 + 0.493586i \(0.835686\pi\)
\(642\) −7.15468e16 −1.02183
\(643\) 5.37067e16i 0.759911i −0.925005 0.379956i \(-0.875939\pi\)
0.925005 0.379956i \(-0.124061\pi\)
\(644\) −2.28322e15 −0.0320061
\(645\) −3.83778e16 −0.532993
\(646\) 6.88338e16 0.947124
\(647\) 2.97579e16i 0.405674i −0.979213 0.202837i \(-0.934984\pi\)
0.979213 0.202837i \(-0.0650161\pi\)
\(648\) 3.98376e16i 0.538076i
\(649\) 5.18989e15 0.0694528
\(650\) −7.00408e16 −0.928691
\(651\) 1.07257e15 0.0140910
\(652\) 6.46414e16i 0.841444i
\(653\) 7.89588e16i 1.01841i 0.860646 + 0.509204i \(0.170060\pi\)
−0.860646 + 0.509204i \(0.829940\pi\)
\(654\) 2.14871e17i 2.74607i
\(655\) 8.72121e16i 1.10441i
\(656\) 9.65931e16 1.21206
\(657\) 1.58997e16i 0.197696i
\(658\) −2.79303e15 −0.0344129
\(659\) 8.92868e16 1.09012 0.545061 0.838397i \(-0.316507\pi\)
0.545061 + 0.838397i \(0.316507\pi\)
\(660\) 2.51419e16i 0.304182i
\(661\) 8.72098e16i 1.04558i 0.852462 + 0.522789i \(0.175109\pi\)
−0.852462 + 0.522789i \(0.824891\pi\)
\(662\) −8.97998e16 −1.06691
\(663\) 1.89361e17i 2.22951i
\(664\) 2.50785e15 3.70248e16i 0.0292612 0.432001i
\(665\) −1.96099e15 −0.0226749
\(666\) 2.13235e16i 0.244351i
\(667\) 6.66137e16 0.756499
\(668\) 8.03556e15 0.0904394
\(669\) 1.15007e17i 1.28283i
\(670\) 4.80366e15i 0.0531036i
\(671\) 3.68905e16 0.404185
\(672\) 1.22527e16i 0.133050i
\(673\) 7.04351e16 0.758052 0.379026 0.925386i \(-0.376259\pi\)
0.379026 + 0.925386i \(0.376259\pi\)
\(674\) −1.24674e17 −1.32989
\(675\) 4.50168e16 0.475940
\(676\) 6.92194e15 0.0725350
\(677\) 8.04172e16i 0.835251i −0.908619 0.417625i \(-0.862862\pi\)
0.908619 0.417625i \(-0.137138\pi\)
\(678\) 7.98964e16i 0.822525i
\(679\) 1.75064e16i 0.178640i
\(680\) −4.28661e16 −0.433571
\(681\) 8.41021e16 0.843187
\(682\) 1.07700e16i 0.107031i
\(683\) 6.95506e16i 0.685136i 0.939493 + 0.342568i \(0.111297\pi\)
−0.939493 + 0.342568i \(0.888703\pi\)
\(684\) 1.16330e16i 0.113594i
\(685\) −8.35362e16 −0.808595
\(686\) 2.61521e16i 0.250936i
\(687\) 1.65298e17 1.57227
\(688\) 1.03320e17i 0.974214i
\(689\) 1.22666e17 1.14660
\(690\) 4.59241e16 0.425546
\(691\) −1.81056e16 −0.166320 −0.0831601 0.996536i \(-0.526501\pi\)
−0.0831601 + 0.996536i \(0.526501\pi\)
\(692\) −9.82148e16 −0.894418
\(693\) −3.07029e15 −0.0277192
\(694\) 1.35264e17 1.21067
\(695\) −1.09707e17 −0.973479
\(696\) 8.98288e16i 0.790242i
\(697\) 2.02256e17 1.76403
\(698\) 1.95866e17i 1.69366i
\(699\) 1.14124e17i 0.978394i
\(700\) 5.22075e15 0.0443756
\(701\) −1.01202e17 −0.852869 −0.426435 0.904518i \(-0.640231\pi\)
−0.426435 + 0.904518i \(0.640231\pi\)
\(702\) −1.13229e17 −0.946093
\(703\) 2.27477e16i 0.188454i
\(704\) 2.11522e16 0.173748
\(705\) 2.24249e16 0.182640
\(706\) 7.06504e16i 0.570540i
\(707\) 3.23726e15i 0.0259216i
\(708\) 1.01013e16 0.0802006
\(709\) 3.20927e16i 0.252655i −0.991989 0.126328i \(-0.959681\pi\)
0.991989 0.126328i \(-0.0403191\pi\)
\(710\) 1.02787e17i 0.802396i
\(711\) 8.56411e16i 0.662926i
\(712\) −9.62967e16 −0.739148
\(713\) −7.85272e15 −0.0597700
\(714\) 3.53597e16i 0.266882i
\(715\) 5.41689e16 0.405428
\(716\) 9.27709e16i 0.688547i
\(717\) 1.62706e17i 1.19753i
\(718\) 2.72473e17i 1.98873i
\(719\) 1.65694e17i 1.19931i −0.800257 0.599657i \(-0.795304\pi\)
0.800257 0.599657i \(-0.204696\pi\)
\(720\) 3.97334e16i 0.285208i
\(721\) 7.26463e15i 0.0517133i
\(722\) 1.51657e17i 1.07063i
\(723\) −4.93998e16 −0.345856
\(724\) 4.70528e16i 0.326704i
\(725\) −1.52317e17 −1.04887
\(726\) 1.19473e17i 0.815925i
\(727\) −2.61537e16 −0.177144 −0.0885721 0.996070i \(-0.528230\pi\)
−0.0885721 + 0.996070i \(0.528230\pi\)
\(728\) 6.63366e15 0.0445620
\(729\) 4.69825e16 0.313019
\(730\) 5.23815e16i 0.346131i
\(731\) 2.16342e17i 1.41787i
\(732\) 7.18016e16 0.466732
\(733\) 1.30814e17 0.843393 0.421696 0.906737i \(-0.361435\pi\)
0.421696 + 0.906737i \(0.361435\pi\)
\(734\) 3.54895e17 2.26947
\(735\) 1.04483e17i 0.662704i
\(736\) 8.97066e16i 0.564362i
\(737\) 8.02336e15i 0.0500669i
\(738\) 8.56306e16i 0.530018i
\(739\) −1.47989e17 −0.908581 −0.454291 0.890854i \(-0.650107\pi\)
−0.454291 + 0.890854i \(0.650107\pi\)
\(740\) 2.80421e16i 0.170774i
\(741\) 8.55256e16 0.516639
\(742\) −2.29057e16 −0.137253
\(743\) 1.13182e17i 0.672738i 0.941730 + 0.336369i \(0.109199\pi\)
−0.941730 + 0.336369i \(0.890801\pi\)
\(744\) 1.05894e16i 0.0624360i
\(745\) −5.34937e16 −0.312871
\(746\) 2.63649e16i 0.152965i
\(747\) 7.18607e16 + 4.86742e15i 0.413588 + 0.0280140i
\(748\) 1.41729e17 0.809187
\(749\) 1.14901e16i 0.0650778i
\(750\) −2.58640e17 −1.45321
\(751\) −2.65556e15 −0.0148019 −0.00740093 0.999973i \(-0.502356\pi\)
−0.00740093 + 0.999973i \(0.502356\pi\)
\(752\) 6.03721e16i 0.333833i
\(753\) 2.32476e17i 1.27529i
\(754\) 3.83115e17 2.08498
\(755\) 4.27512e16i 0.230816i
\(756\) 8.43991e15 0.0452071
\(757\) 1.40938e17 0.748948 0.374474 0.927237i \(-0.377823\pi\)
0.374474 + 0.927237i \(0.377823\pi\)
\(758\) 2.08158e17 1.09743
\(759\) 7.67051e16 0.401212
\(760\) 1.93606e16i 0.100470i
\(761\) 2.44400e16i 0.125833i 0.998019 + 0.0629163i \(0.0200401\pi\)
−0.998019 + 0.0629163i \(0.979960\pi\)
\(762\) 3.78603e15i 0.0193399i
\(763\) −3.45073e16 −0.174890
\(764\) 1.67028e16 0.0839902
\(765\) 8.31978e16i 0.415091i
\(766\) 4.79218e16i 0.237225i
\(767\) 2.17635e16i 0.106895i
\(768\) −3.19263e17 −1.55590
\(769\) 1.25665e17i 0.607653i −0.952727 0.303827i \(-0.901736\pi\)
0.952727 0.303827i \(-0.0982644\pi\)
\(770\) −1.01151e16 −0.0485315
\(771\) 5.35233e16i 0.254810i
\(772\) −1.21754e17 −0.575150
\(773\) −6.69139e16 −0.313646 −0.156823 0.987627i \(-0.550125\pi\)
−0.156823 + 0.987627i \(0.550125\pi\)
\(774\) −9.15942e16 −0.426012
\(775\) 1.79558e16 0.0828694
\(776\) 1.72839e17 0.791539
\(777\) 1.16854e16 0.0531030
\(778\) 1.34171e17 0.605037
\(779\) 9.13498e16i 0.408774i
\(780\) 1.05431e17 0.468168
\(781\) 1.71681e17i 0.756512i
\(782\) 2.58882e17i 1.13204i
\(783\) −2.46237e17 −1.06852
\(784\) 2.81286e17 1.21130
\(785\) −5.34132e16 −0.228261
\(786\) 7.10260e17i 3.01219i
\(787\) −2.30222e17 −0.968946 −0.484473 0.874806i \(-0.660989\pi\)
−0.484473 + 0.874806i \(0.660989\pi\)
\(788\) −9.23005e16 −0.385520
\(789\) 5.01123e16i 0.207722i
\(790\) 2.82144e17i 1.16067i
\(791\) −1.28310e16 −0.0523844
\(792\) 3.03127e16i 0.122821i
\(793\) 1.54699e17i 0.622082i
\(794\) 3.98377e17i 1.58991i
\(795\) 1.83907e17 0.728445
\(796\) 1.07284e17 0.421751
\(797\) 4.85656e17i 1.89487i −0.319954 0.947433i \(-0.603667\pi\)
0.319954 0.947433i \(-0.396333\pi\)
\(798\) −1.59704e16 −0.0618440
\(799\) 1.26413e17i 0.485861i
\(800\) 2.05120e17i 0.782472i
\(801\) 1.86900e17i 0.707643i
\(802\) 2.04588e17i 0.768835i
\(803\) 8.74907e16i 0.326339i
\(804\) 1.56162e16i 0.0578148i
\(805\) 7.37521e15i 0.0271019i
\(806\) −4.51633e16 −0.164731
\(807\) 3.76827e17i 1.36427i
\(808\) −3.19612e16 −0.114856
\(809\) 4.20012e17i 1.49820i 0.662455 + 0.749101i \(0.269514\pi\)
−0.662455 + 0.749101i \(0.730486\pi\)
\(810\) −2.54730e17 −0.901925
\(811\) 4.38197e17 1.54008 0.770041 0.637994i \(-0.220236\pi\)
0.770041 + 0.637994i \(0.220236\pi\)
\(812\) −2.85568e16 −0.0996263
\(813\) 2.80058e17i 0.969850i
\(814\) 1.17336e17i 0.403353i
\(815\) −2.08803e17 −0.712510
\(816\) −7.64309e17 −2.58898
\(817\) −9.77117e16 −0.328560
\(818\) 2.55868e17i 0.854075i
\(819\) 1.28751e16i 0.0426626i
\(820\) 1.12611e17i 0.370423i
\(821\) 6.94386e16i 0.226747i −0.993552 0.113374i \(-0.963834\pi\)
0.993552 0.113374i \(-0.0361657\pi\)
\(822\) −6.80322e17 −2.20538
\(823\) 3.60013e16i 0.115856i −0.998321 0.0579281i \(-0.981551\pi\)
0.998321 0.0579281i \(-0.0184494\pi\)
\(824\) −7.17230e16 −0.229137
\(825\) −1.75392e17 −0.556269
\(826\) 4.06395e15i 0.0127958i
\(827\) 1.79611e17i 0.561435i −0.959790 0.280718i \(-0.909428\pi\)
0.959790 0.280718i \(-0.0905724\pi\)
\(828\) 4.37513e16 0.135772
\(829\) 3.57922e17i 1.10271i 0.834271 + 0.551355i \(0.185889\pi\)
−0.834271 + 0.551355i \(0.814111\pi\)
\(830\) 2.36745e17 + 1.60357e16i 0.724122 + 0.0490478i
\(831\) 2.00006e17 0.607346
\(832\) 8.87009e16i 0.267416i
\(833\) 5.88986e17 1.76293
\(834\) −8.93461e17 −2.65509
\(835\) 2.59563e16i 0.0765814i
\(836\) 6.40124e16i 0.187511i
\(837\) 2.90275e16 0.0844222
\(838\) 3.02868e17i 0.874560i
\(839\) −2.38812e16 −0.0684676 −0.0342338 0.999414i \(-0.510899\pi\)
−0.0342338 + 0.999414i \(0.510899\pi\)
\(840\) 9.94550e15 0.0283107
\(841\) 4.79339e17 1.35477
\(842\) −6.40383e17 −1.79708
\(843\) 5.86391e17i 1.63389i
\(844\) 2.23637e17i 0.618713i
\(845\) 2.23591e16i 0.0614205i
\(846\) 5.35204e16 0.145981
\(847\) 1.91868e16 0.0519641
\(848\) 4.95113e17i 1.33146i
\(849\) 3.17670e17i 0.848263i
\(850\) 5.91951e17i 1.56954i
\(851\) −8.55535e16 −0.225248
\(852\) 3.34150e17i 0.873582i
\(853\) 4.46852e17 1.16003 0.580016 0.814605i \(-0.303046\pi\)
0.580016 + 0.814605i \(0.303046\pi\)
\(854\) 2.88872e16i 0.0744660i
\(855\) 3.75766e16 0.0961880
\(856\) 1.13441e17 0.288354
\(857\) −1.68717e17 −0.425866 −0.212933 0.977067i \(-0.568302\pi\)
−0.212933 + 0.977067i \(0.568302\pi\)
\(858\) 4.41154e17 1.10577
\(859\) 2.66618e17 0.663638 0.331819 0.943343i \(-0.392338\pi\)
0.331819 + 0.943343i \(0.392338\pi\)
\(860\) −1.20454e17 −0.297734
\(861\) −4.69261e16 −0.115185
\(862\) 6.95406e17i 1.69510i
\(863\) −2.47135e17 −0.598232 −0.299116 0.954217i \(-0.596692\pi\)
−0.299116 + 0.954217i \(0.596692\pi\)
\(864\) 3.31599e17i 0.797134i
\(865\) 3.17251e17i 0.757367i
\(866\) −7.21613e17 −1.71079
\(867\) −1.09524e18 −2.57865
\(868\) 3.36641e15 0.00787134
\(869\) 4.71254e17i 1.09430i
\(870\) 5.74385e17 1.32461
\(871\) −3.36455e16 −0.0770582
\(872\) 3.40688e17i 0.774921i
\(873\) 3.35460e17i 0.757801i
\(874\) 1.16925e17 0.262324
\(875\) 4.15365e16i 0.0925510i
\(876\) 1.70287e17i 0.376839i
\(877\) 1.99061e17i 0.437512i 0.975780 + 0.218756i \(0.0701998\pi\)
−0.975780 + 0.218756i \(0.929800\pi\)
\(878\) −6.98698e17 −1.52518
\(879\) −7.73305e17 −1.67655
\(880\) 2.18639e17i 0.470796i
\(881\) −7.66604e17 −1.63951 −0.819757 0.572711i \(-0.805892\pi\)
−0.819757 + 0.572711i \(0.805892\pi\)
\(882\) 2.49363e17i 0.529688i
\(883\) 7.74010e16i 0.163299i 0.996661 + 0.0816493i \(0.0260187\pi\)
−0.996661 + 0.0816493i \(0.973981\pi\)
\(884\) 5.94333e17i 1.24542i
\(885\) 3.26289e16i 0.0679115i
\(886\) 3.24244e17i 0.670301i
\(887\) 9.06963e17i 1.86229i −0.364646 0.931146i \(-0.618810\pi\)
0.364646 0.931146i \(-0.381190\pi\)
\(888\) 1.15369e17i 0.235295i
\(889\) 6.08019e14 0.00123170
\(890\) 6.15741e17i 1.23896i
\(891\) −4.25465e17 −0.850350
\(892\) 3.60964e17i 0.716596i
\(893\) 5.70950e16 0.112587
\(894\) −4.35655e17 −0.853331
\(895\) 2.99666e17 0.583042
\(896\) 4.13206e16i 0.0798579i
\(897\) 3.21659e17i 0.617506i
\(898\) 3.74504e17 0.714165
\(899\) −9.82160e16 −0.186048
\(900\) −1.00040e17 −0.188244
\(901\) 1.03672e18i 1.93781i
\(902\) 4.71196e17i 0.874908i
\(903\) 5.01942e16i 0.0925821i
\(904\) 1.26679e17i 0.232111i
\(905\) −1.51989e17 −0.276643
\(906\) 3.48167e17i 0.629533i
\(907\) 7.91790e17 1.42222 0.711109 0.703082i \(-0.248193\pi\)
0.711109 + 0.703082i \(0.248193\pi\)
\(908\) 2.63965e17 0.471011
\(909\) 6.20328e16i 0.109961i
\(910\) 4.24170e16i 0.0746950i
\(911\) 5.82123e17 1.01837 0.509184 0.860658i \(-0.329947\pi\)
0.509184 + 0.860658i \(0.329947\pi\)
\(912\) 3.45203e17i 0.599937i
\(913\) 3.95425e17 + 2.67838e16i 0.682714 + 0.0462431i
\(914\) 7.64758e17 1.31174
\(915\) 2.31932e17i 0.395215i
\(916\) 5.18807e17 0.878280
\(917\) −1.14065e17 −0.191838
\(918\) 9.56954e17i 1.59895i
\(919\) 2.87542e16i 0.0477319i −0.999715 0.0238659i \(-0.992403\pi\)
0.999715 0.0238659i \(-0.00759749\pi\)
\(920\) −7.28148e16 −0.120086
\(921\) 1.10317e18i 1.80753i
\(922\) 2.92082e17 0.475466
\(923\) 7.19936e17 1.16435
\(924\) −3.28830e16 −0.0528371
\(925\) 1.95624e17 0.312300
\(926\) 2.40385e17i 0.381278i
\(927\) 1.39206e17i 0.219371i
\(928\) 1.12198e18i 1.75670i
\(929\) −1.17405e17 −0.182639 −0.0913196 0.995822i \(-0.529108\pi\)
−0.0913196 + 0.995822i \(0.529108\pi\)
\(930\) −6.77111e16 −0.104655
\(931\) 2.66018e17i 0.408519i
\(932\) 3.58192e17i 0.546538i
\(933\) 4.64323e17i 0.703931i
\(934\) 1.61442e18 2.43184
\(935\) 4.57809e17i 0.685196i
\(936\) −1.27115e17 −0.189034
\(937\) 2.25774e17i 0.333608i −0.985990 0.166804i \(-0.946655\pi\)
0.985990 0.166804i \(-0.0533446\pi\)
\(938\) 6.28270e15 0.00922421
\(939\) 8.88964e17 1.29685
\(940\) 7.03835e16 0.102024
\(941\) −8.96450e17 −1.29119 −0.645593 0.763682i \(-0.723390\pi\)
−0.645593 + 0.763682i \(0.723390\pi\)
\(942\) −4.35000e17 −0.622563
\(943\) 3.43564e17 0.488582
\(944\) −8.78432e16 −0.124130
\(945\) 2.72624e16i 0.0382801i
\(946\) −5.04012e17 −0.703224
\(947\) 1.08483e18i 1.50405i 0.659136 + 0.752023i \(0.270922\pi\)
−0.659136 + 0.752023i \(0.729078\pi\)
\(948\) 9.17221e17i 1.26364i
\(949\) −3.66888e17 −0.502269
\(950\) −2.67357e17 −0.363706
\(951\) 1.19167e18 1.61092
\(952\) 5.60645e16i 0.0753123i
\(953\) 8.98711e16 0.119967 0.0599836 0.998199i \(-0.480895\pi\)
0.0599836 + 0.998199i \(0.480895\pi\)
\(954\) 4.38922e17 0.582233
\(955\) 5.39529e16i 0.0711204i
\(956\) 5.10672e17i 0.668952i
\(957\) 9.59370e17 1.24886
\(958\) 2.51911e17i 0.325877i
\(959\) 1.09257e17i 0.140455i
\(960\) 1.32985e17i 0.169893i
\(961\) −7.76085e17 −0.985301
\(962\) −4.92043e17 −0.620802
\(963\) 2.20174e17i 0.276064i
\(964\) −1.55048e17 −0.193198
\(965\) 3.93288e17i 0.487020i
\(966\) 6.00640e16i 0.0739183i
\(967\) 1.55492e18i 1.90174i 0.309598 + 0.950868i \(0.399806\pi\)
−0.309598 + 0.950868i \(0.600194\pi\)
\(968\) 1.89430e17i 0.230248i
\(969\) 7.22821e17i 0.873148i
\(970\) 1.10517e18i 1.32678i
\(971\) 7.37837e17i 0.880330i −0.897917 0.440165i \(-0.854920\pi\)
0.897917 0.440165i \(-0.145080\pi\)
\(972\) −4.37962e17 −0.519325
\(973\) 1.43486e17i 0.169096i
\(974\) 1.26752e18 1.48458
\(975\) 7.35496e17i 0.856155i
\(976\) −6.24403e17 −0.722381
\(977\) −1.08800e18 −1.25101 −0.625504 0.780221i \(-0.715106\pi\)
−0.625504 + 0.780221i \(0.715106\pi\)
\(978\) −1.70050e18 −1.94332
\(979\) 1.02845e18i 1.16811i
\(980\) 3.27932e17i 0.370192i
\(981\) 6.61233e17 0.741891
\(982\) −5.63127e17 −0.627967
\(983\) 9.43822e17 1.04609 0.523045 0.852305i \(-0.324796\pi\)
0.523045 + 0.852305i \(0.324796\pi\)
\(984\) 4.63297e17i 0.510375i
\(985\) 2.98147e17i 0.326447i
\(986\) 3.23790e18i 3.52373i
\(987\) 2.93295e16i 0.0317250i
\(988\) 2.68433e17 0.288598
\(989\) 3.67491e17i 0.392707i
\(990\) 1.93826e17 0.205873
\(991\) 8.75161e17 0.923945 0.461972 0.886894i \(-0.347142\pi\)
0.461972 + 0.886894i \(0.347142\pi\)
\(992\) 1.32264e17i 0.138795i
\(993\) 9.42983e17i 0.983577i
\(994\) −1.34435e17 −0.139378
\(995\) 3.46545e17i 0.357126i
\(996\) 7.69632e17 + 5.21304e16i 0.788364 + 0.0533992i
\(997\) −7.41865e17 −0.755360 −0.377680 0.925936i \(-0.623278\pi\)
−0.377680 + 0.925936i \(0.623278\pi\)
\(998\) 1.40770e18i 1.42471i
\(999\) 3.16248e17 0.318152
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.82.19 80
83.82 odd 2 inner 83.13.b.c.82.62 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
83.13.b.c.82.19 80 1.1 even 1 trivial
83.13.b.c.82.62 yes 80 83.82 odd 2 inner