Properties

Label 23.13.b.c.22.12
Level $23$
Weight $13$
Character 23.22
Analytic conductor $21.022$
Analytic rank $0$
Dimension $20$
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] = [23,13,Mod(22,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, 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("23.22");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 23.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: \(21.0218577974\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + 3347471347 x^{18} + 50192028136 x^{17} + \cdots + 27\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: multiple of \( 2^{35}\cdot 3^{11}\cdot 67 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.12
Root \(-697.167 - 19533.2i\) of defining polynomial
Character \(\chi\) \(=\) 23.22
Dual form 23.13.b.c.22.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+20.5558 q^{2} +729.723 q^{3} -3673.46 q^{4} +19533.2i q^{5} +15000.0 q^{6} +5514.27i q^{7} -159707. q^{8} +1054.67 q^{9} +O(q^{10})\) \(q+20.5558 q^{2} +729.723 q^{3} -3673.46 q^{4} +19533.2i q^{5} +15000.0 q^{6} +5514.27i q^{7} -159707. q^{8} +1054.67 q^{9} +401520. i q^{10} -2.84785e6i q^{11} -2.68061e6 q^{12} -7.37127e6 q^{13} +113350. i q^{14} +1.42538e7i q^{15} +1.17636e7 q^{16} -2.30376e7i q^{17} +21679.6 q^{18} +5.27182e7i q^{19} -7.17545e7i q^{20} +4.02389e6i q^{21} -5.85399e7i q^{22} +(-1.45182e8 + 2.89269e7i) q^{23} -1.16542e8 q^{24} -1.37406e8 q^{25} -1.51522e8 q^{26} -3.87035e8 q^{27} -2.02564e7i q^{28} -2.08168e8 q^{29} +2.92999e8i q^{30} -9.37627e8 q^{31} +8.95971e8 q^{32} -2.07814e9i q^{33} -4.73555e8i q^{34} -1.07711e8 q^{35} -3.87430e6 q^{36} +4.16040e9i q^{37} +1.08366e9i q^{38} -5.37898e9 q^{39} -3.11960e9i q^{40} -2.43189e9 q^{41} +8.27141e7i q^{42} -1.05815e10i q^{43} +1.04615e10i q^{44} +2.06011e7i q^{45} +(-2.98433e9 + 5.94616e8i) q^{46} +9.05702e9 q^{47} +8.58416e9 q^{48} +1.38109e10 q^{49} -2.82449e9 q^{50} -1.68110e10i q^{51} +2.70781e10 q^{52} +3.52921e10i q^{53} -7.95581e9 q^{54} +5.56278e10 q^{55} -8.80668e8i q^{56} +3.84697e10i q^{57} -4.27905e9 q^{58} -1.98838e10 q^{59} -5.23609e10i q^{60} +9.34986e9i q^{61} -1.92737e10 q^{62} +5.81574e6i q^{63} -2.97663e10 q^{64} -1.43985e11i q^{65} -4.27179e10i q^{66} +1.05634e11i q^{67} +8.46276e10i q^{68} +(-1.05943e11 + 2.11086e10i) q^{69} -2.21409e9 q^{70} -2.74716e10 q^{71} -1.68439e8 q^{72} +4.00550e10 q^{73} +8.55202e10i q^{74} -1.00268e11 q^{75} -1.93658e11i q^{76} +1.57038e10 q^{77} -1.10569e11 q^{78} -1.55769e11i q^{79} +2.29781e11i q^{80} -2.82989e11 q^{81} -4.99893e10 q^{82} -2.09520e11i q^{83} -1.47816e10i q^{84} +4.49998e11 q^{85} -2.17511e11i q^{86} -1.51905e11 q^{87} +4.54823e11i q^{88} -1.16097e10i q^{89} +4.23473e8i q^{90} -4.06471e10i q^{91} +(5.33321e11 - 1.06262e11i) q^{92} -6.84208e11 q^{93} +1.86174e11 q^{94} -1.02976e12 q^{95} +6.53810e11 q^{96} +1.10100e12i q^{97} +2.83893e11 q^{98} -3.00355e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 88 q^{2} + 318 q^{3} + 36072 q^{4} + 264240 q^{6} - 767728 q^{8} + 1971426 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 88 q^{2} + 318 q^{3} + 36072 q^{4} + 264240 q^{6} - 767728 q^{8} + 1971426 q^{9} + 19833480 q^{12} + 8049118 q^{13} + 81743632 q^{16} + 36238080 q^{18} - 367189708 q^{23} + 530348736 q^{24} - 1824317212 q^{25} - 2465696728 q^{26} - 1765163178 q^{27} - 417897362 q^{29} - 1574125298 q^{31} + 1240884960 q^{32} + 4723363152 q^{35} + 3607269840 q^{36} + 1926187110 q^{39} - 132511250 q^{41} + 62599086544 q^{46} - 45052376402 q^{47} + 77275023312 q^{48} - 65534183260 q^{49} - 57446928200 q^{50} - 20407259400 q^{52} - 15082009344 q^{54} - 12572534832 q^{55} + 97529544392 q^{58} - 110336269112 q^{59} + 553127354432 q^{62} + 13799515808 q^{64} + 7914588558 q^{69} + 590935322064 q^{70} - 40523102210 q^{71} - 539385055680 q^{72} - 449748966242 q^{73} + 2570431278 q^{75} - 345974135760 q^{77} - 48894418992 q^{78} - 2694979782144 q^{81} - 1210586085208 q^{82} + 1051198266576 q^{85} - 2237359632618 q^{87} + 1936236755640 q^{92} - 116415989178 q^{93} + 3420883097024 q^{94} + 3777482201184 q^{95} + 3567911213376 q^{96} + 3590387133208 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.5558 0.321184 0.160592 0.987021i \(-0.448660\pi\)
0.160592 + 0.987021i \(0.448660\pi\)
\(3\) 729.723 1.00099 0.500496 0.865739i \(-0.333151\pi\)
0.500496 + 0.865739i \(0.333151\pi\)
\(4\) −3673.46 −0.896841
\(5\) 19533.2i 1.25013i 0.780574 + 0.625063i \(0.214927\pi\)
−0.780574 + 0.625063i \(0.785073\pi\)
\(6\) 15000.0 0.321503
\(7\) 5514.27i 0.0468705i 0.999725 + 0.0234352i \(0.00746035\pi\)
−0.999725 + 0.0234352i \(0.992540\pi\)
\(8\) −159707. −0.609235
\(9\) 1054.67 0.00198455
\(10\) 401520.i 0.401520i
\(11\) 2.84785e6i 1.60754i −0.594940 0.803770i \(-0.702824\pi\)
0.594940 0.803770i \(-0.297176\pi\)
\(12\) −2.68061e6 −0.897730
\(13\) −7.37127e6 −1.52715 −0.763576 0.645718i \(-0.776558\pi\)
−0.763576 + 0.645718i \(0.776558\pi\)
\(14\) 113350.i 0.0150540i
\(15\) 1.42538e7i 1.25137i
\(16\) 1.17636e7 0.701164
\(17\) 2.30376e7i 0.954428i −0.878787 0.477214i \(-0.841647\pi\)
0.878787 0.477214i \(-0.158353\pi\)
\(18\) 21679.6 0.000637406
\(19\) 5.27182e7i 1.12057i 0.828300 + 0.560284i \(0.189308\pi\)
−0.828300 + 0.560284i \(0.810692\pi\)
\(20\) 7.17545e7i 1.12116i
\(21\) 4.02389e6i 0.0469170i
\(22\) 5.85399e7i 0.516316i
\(23\) −1.45182e8 + 2.89269e7i −0.980723 + 0.195405i
\(24\) −1.16542e8 −0.609839
\(25\) −1.37406e8 −0.562815
\(26\) −1.51522e8 −0.490497
\(27\) −3.87035e8 −0.999005
\(28\) 2.02564e7i 0.0420354i
\(29\) −2.08168e8 −0.349965 −0.174983 0.984572i \(-0.555987\pi\)
−0.174983 + 0.984572i \(0.555987\pi\)
\(30\) 2.92999e8i 0.401919i
\(31\) −9.37627e8 −1.05648 −0.528239 0.849096i \(-0.677147\pi\)
−0.528239 + 0.849096i \(0.677147\pi\)
\(32\) 8.95971e8 0.834438
\(33\) 2.07814e9i 1.60913i
\(34\) 4.73555e8i 0.306547i
\(35\) −1.07711e8 −0.0585940
\(36\) −3.87430e6 −0.00177983
\(37\) 4.16040e9i 1.62153i 0.585374 + 0.810764i \(0.300948\pi\)
−0.585374 + 0.810764i \(0.699052\pi\)
\(38\) 1.08366e9i 0.359909i
\(39\) −5.37898e9 −1.52867
\(40\) 3.11960e9i 0.761620i
\(41\) −2.43189e9 −0.511965 −0.255982 0.966681i \(-0.582399\pi\)
−0.255982 + 0.966681i \(0.582399\pi\)
\(42\) 8.27141e7i 0.0150690i
\(43\) 1.05815e10i 1.67393i −0.547257 0.836965i \(-0.684328\pi\)
0.547257 0.836965i \(-0.315672\pi\)
\(44\) 1.04615e10i 1.44171i
\(45\) 2.06011e7i 0.00248094i
\(46\) −2.98433e9 + 5.94616e8i −0.314992 + 0.0627609i
\(47\) 9.05702e9 0.840230 0.420115 0.907471i \(-0.361990\pi\)
0.420115 + 0.907471i \(0.361990\pi\)
\(48\) 8.58416e9 0.701860
\(49\) 1.38109e10 0.997803
\(50\) −2.82449e9 −0.180767
\(51\) 1.68110e10i 0.955374i
\(52\) 2.70781e10 1.36961
\(53\) 3.52921e10i 1.59229i 0.605106 + 0.796145i \(0.293131\pi\)
−0.605106 + 0.796145i \(0.706869\pi\)
\(54\) −7.95581e9 −0.320864
\(55\) 5.56278e10 2.00963
\(56\) 8.80668e8i 0.0285551i
\(57\) 3.84697e10i 1.12168i
\(58\) −4.27905e9 −0.112403
\(59\) −1.98838e10 −0.471396 −0.235698 0.971826i \(-0.575738\pi\)
−0.235698 + 0.971826i \(0.575738\pi\)
\(60\) 5.23609e10i 1.12228i
\(61\) 9.34986e9i 0.181479i 0.995875 + 0.0907394i \(0.0289230\pi\)
−0.995875 + 0.0907394i \(0.971077\pi\)
\(62\) −1.92737e10 −0.339324
\(63\) 5.81574e6i 9.30169e-5i
\(64\) −2.97663e10 −0.433156
\(65\) 1.43985e11i 1.90913i
\(66\) 4.27179e10i 0.516828i
\(67\) 1.05634e11i 1.16777i 0.811838 + 0.583883i \(0.198467\pi\)
−0.811838 + 0.583883i \(0.801533\pi\)
\(68\) 8.46276e10i 0.855970i
\(69\) −1.05943e11 + 2.11086e10i −0.981695 + 0.195599i
\(70\) −2.21409e9 −0.0188195
\(71\) −2.74716e10 −0.214454 −0.107227 0.994235i \(-0.534197\pi\)
−0.107227 + 0.994235i \(0.534197\pi\)
\(72\) −1.68439e8 −0.00120906
\(73\) 4.00550e10 0.264679 0.132340 0.991204i \(-0.457751\pi\)
0.132340 + 0.991204i \(0.457751\pi\)
\(74\) 8.55202e10i 0.520809i
\(75\) −1.00268e11 −0.563373
\(76\) 1.93658e11i 1.00497i
\(77\) 1.57038e10 0.0753462
\(78\) −1.10569e11 −0.490983
\(79\) 1.55769e11i 0.640792i −0.947284 0.320396i \(-0.896184\pi\)
0.947284 0.320396i \(-0.103816\pi\)
\(80\) 2.29781e11i 0.876544i
\(81\) −2.82989e11 −1.00198
\(82\) −4.99893e10 −0.164435
\(83\) 2.09520e11i 0.640850i −0.947274 0.320425i \(-0.896174\pi\)
0.947274 0.320425i \(-0.103826\pi\)
\(84\) 1.47816e10i 0.0420771i
\(85\) 4.49998e11 1.19316
\(86\) 2.17511e11i 0.537639i
\(87\) −1.51905e11 −0.350312
\(88\) 4.54823e11i 0.979369i
\(89\) 1.16097e10i 0.0233604i −0.999932 0.0116802i \(-0.996282\pi\)
0.999932 0.0116802i \(-0.00371801\pi\)
\(90\) 4.23473e8i 0.000796838i
\(91\) 4.06471e10i 0.0715783i
\(92\) 5.33321e11 1.06262e11i 0.879552 0.175247i
\(93\) −6.84208e11 −1.05752
\(94\) 1.86174e11 0.269868
\(95\) −1.02976e12 −1.40085
\(96\) 6.53810e11 0.835265
\(97\) 1.10100e12i 1.32177i 0.750487 + 0.660885i \(0.229819\pi\)
−0.750487 + 0.660885i \(0.770181\pi\)
\(98\) 2.83893e11 0.320478
\(99\) 3.00355e9i 0.00319025i
\(100\) 5.04756e11 0.504756
\(101\) 6.11239e11 0.575815 0.287907 0.957658i \(-0.407040\pi\)
0.287907 + 0.957658i \(0.407040\pi\)
\(102\) 3.45564e11i 0.306851i
\(103\) 1.59048e12i 1.33200i −0.745953 0.665999i \(-0.768005\pi\)
0.745953 0.665999i \(-0.231995\pi\)
\(104\) 1.17725e12 0.930394
\(105\) −7.85995e10 −0.0586521
\(106\) 7.25457e11i 0.511418i
\(107\) 2.40207e12i 1.60060i −0.599599 0.800300i \(-0.704673\pi\)
0.599599 0.800300i \(-0.295327\pi\)
\(108\) 1.42176e12 0.895949
\(109\) 2.14754e12i 1.28051i 0.768163 + 0.640255i \(0.221171\pi\)
−0.768163 + 0.640255i \(0.778829\pi\)
\(110\) 1.14347e12 0.645460
\(111\) 3.03594e12i 1.62314i
\(112\) 6.48675e10i 0.0328639i
\(113\) 1.15629e12i 0.555387i 0.960670 + 0.277694i \(0.0895700\pi\)
−0.960670 + 0.277694i \(0.910430\pi\)
\(114\) 7.90773e11i 0.360266i
\(115\) −5.65036e11 2.83587e12i −0.244281 1.22603i
\(116\) 7.64695e11 0.313863
\(117\) −7.77427e9 −0.00303071
\(118\) −4.08726e11 −0.151405
\(119\) 1.27035e11 0.0447345
\(120\) 2.27644e12i 0.762376i
\(121\) −4.97185e12 −1.58418
\(122\) 1.92194e11i 0.0582881i
\(123\) −1.77460e12 −0.512473
\(124\) 3.44434e12 0.947492
\(125\) 2.08487e12i 0.546536i
\(126\) 1.19547e8i 2.98755e-5i
\(127\) −1.12667e12 −0.268519 −0.134259 0.990946i \(-0.542866\pi\)
−0.134259 + 0.990946i \(0.542866\pi\)
\(128\) −4.28176e12 −0.973561
\(129\) 7.72158e12i 1.67559i
\(130\) 2.95972e12i 0.613183i
\(131\) −7.85496e12 −1.55423 −0.777117 0.629356i \(-0.783319\pi\)
−0.777117 + 0.629356i \(0.783319\pi\)
\(132\) 7.63398e12i 1.44314i
\(133\) −2.90702e11 −0.0525216
\(134\) 2.17139e12i 0.375068i
\(135\) 7.56004e12i 1.24888i
\(136\) 3.67927e12i 0.581471i
\(137\) 2.84998e12i 0.431041i −0.976499 0.215521i \(-0.930855\pi\)
0.976499 0.215521i \(-0.0691449\pi\)
\(138\) −2.17774e12 + 4.33905e11i −0.315305 + 0.0628232i
\(139\) −6.37349e11 −0.0883667 −0.0441834 0.999023i \(-0.514069\pi\)
−0.0441834 + 0.999023i \(0.514069\pi\)
\(140\) 3.95673e11 0.0525495
\(141\) 6.60912e12 0.841063
\(142\) −5.64700e11 −0.0688792
\(143\) 2.09923e13i 2.45496i
\(144\) 1.24067e10 0.00139150
\(145\) 4.06618e12i 0.437501i
\(146\) 8.23362e11 0.0850108
\(147\) 1.00781e13 0.998793
\(148\) 1.52830e13i 1.45425i
\(149\) 4.29588e12i 0.392586i 0.980545 + 0.196293i \(0.0628903\pi\)
−0.980545 + 0.196293i \(0.937110\pi\)
\(150\) −2.06109e12 −0.180946
\(151\) −1.61951e13 −1.36623 −0.683113 0.730313i \(-0.739374\pi\)
−0.683113 + 0.730313i \(0.739374\pi\)
\(152\) 8.41947e12i 0.682690i
\(153\) 2.42971e10i 0.00189411i
\(154\) 3.22804e11 0.0242000
\(155\) 1.83149e13i 1.32073i
\(156\) 1.97595e13 1.37097
\(157\) 6.01997e11i 0.0401972i −0.999798 0.0200986i \(-0.993602\pi\)
0.999798 0.0200986i \(-0.00639802\pi\)
\(158\) 3.20194e12i 0.205812i
\(159\) 2.57535e13i 1.59387i
\(160\) 1.75012e13i 1.04315i
\(161\) −1.59511e11 8.00573e11i −0.00915872 0.0459669i
\(162\) −5.81706e12 −0.321820
\(163\) −6.23038e12 −0.332192 −0.166096 0.986110i \(-0.553116\pi\)
−0.166096 + 0.986110i \(0.553116\pi\)
\(164\) 8.93344e12 0.459151
\(165\) 4.05929e13 2.01162
\(166\) 4.30684e12i 0.205831i
\(167\) −2.87619e13 −1.32592 −0.662962 0.748653i \(-0.730701\pi\)
−0.662962 + 0.748653i \(0.730701\pi\)
\(168\) 6.42644e11i 0.0285835i
\(169\) 3.10375e13 1.33219
\(170\) 9.25006e12 0.383222
\(171\) 5.56004e10i 0.00222383i
\(172\) 3.88708e13i 1.50125i
\(173\) 2.64146e13 0.985297 0.492649 0.870228i \(-0.336029\pi\)
0.492649 + 0.870228i \(0.336029\pi\)
\(174\) −3.12252e12 −0.112515
\(175\) 7.57693e11i 0.0263794i
\(176\) 3.35010e13i 1.12715i
\(177\) −1.45096e13 −0.471864
\(178\) 2.38646e11i 0.00750299i
\(179\) 4.74549e13 1.44266 0.721328 0.692593i \(-0.243532\pi\)
0.721328 + 0.692593i \(0.243532\pi\)
\(180\) 7.56775e10i 0.00222501i
\(181\) 2.78991e13i 0.793449i −0.917938 0.396725i \(-0.870147\pi\)
0.917938 0.396725i \(-0.129853\pi\)
\(182\) 8.35533e11i 0.0229898i
\(183\) 6.82281e12i 0.181659i
\(184\) 2.31866e13 4.61984e12i 0.597490 0.119047i
\(185\) −8.12659e13 −2.02711
\(186\) −1.40644e13 −0.339660
\(187\) −6.56076e13 −1.53428
\(188\) −3.32706e13 −0.753553
\(189\) 2.13421e12i 0.0468239i
\(190\) −2.11674e13 −0.449931
\(191\) 2.72754e13i 0.561786i 0.959739 + 0.280893i \(0.0906306\pi\)
−0.959739 + 0.280893i \(0.909369\pi\)
\(192\) −2.17211e13 −0.433586
\(193\) 1.93538e13 0.374474 0.187237 0.982315i \(-0.440047\pi\)
0.187237 + 0.982315i \(0.440047\pi\)
\(194\) 2.26318e13i 0.424531i
\(195\) 1.05069e14i 1.91103i
\(196\) −5.07337e13 −0.894871
\(197\) −5.10053e13 −0.872606 −0.436303 0.899800i \(-0.643712\pi\)
−0.436303 + 0.899800i \(0.643712\pi\)
\(198\) 6.17404e10i 0.00102466i
\(199\) 3.35197e13i 0.539736i 0.962897 + 0.269868i \(0.0869801\pi\)
−0.962897 + 0.269868i \(0.913020\pi\)
\(200\) 2.19447e13 0.342887
\(201\) 7.70837e13i 1.16892i
\(202\) 1.25645e13 0.184942
\(203\) 1.14789e12i 0.0164030i
\(204\) 6.17547e13i 0.856819i
\(205\) 4.75026e13i 0.640021i
\(206\) 3.26935e13i 0.427816i
\(207\) −1.53120e11 + 3.05084e10i −0.00194630 + 0.000387791i
\(208\) −8.67126e13 −1.07078
\(209\) 1.50134e14 1.80136
\(210\) −1.61567e12 −0.0188381
\(211\) 5.06276e13 0.573710 0.286855 0.957974i \(-0.407390\pi\)
0.286855 + 0.957974i \(0.407390\pi\)
\(212\) 1.29644e14i 1.42803i
\(213\) −2.00467e13 −0.214667
\(214\) 4.93764e13i 0.514087i
\(215\) 2.06691e14 2.09262
\(216\) 6.18123e13 0.608629
\(217\) 5.17033e12i 0.0495176i
\(218\) 4.41444e13i 0.411279i
\(219\) 2.92291e13 0.264942
\(220\) −2.04346e14 −1.80232
\(221\) 1.69816e14i 1.45756i
\(222\) 6.24060e13i 0.521325i
\(223\) −1.88271e14 −1.53092 −0.765462 0.643481i \(-0.777489\pi\)
−0.765462 + 0.643481i \(0.777489\pi\)
\(224\) 4.94062e12i 0.0391105i
\(225\) −1.44918e11 −0.00111694
\(226\) 2.37684e13i 0.178381i
\(227\) 1.26516e14i 0.924678i 0.886703 + 0.462339i \(0.152990\pi\)
−0.886703 + 0.462339i \(0.847010\pi\)
\(228\) 1.41317e14i 1.00597i
\(229\) 1.27397e14i 0.883379i −0.897168 0.441689i \(-0.854379\pi\)
0.897168 0.441689i \(-0.145621\pi\)
\(230\) −1.16148e13 5.82936e13i −0.0784591 0.393780i
\(231\) 1.14594e13 0.0754209
\(232\) 3.32459e13 0.213211
\(233\) 1.50162e14 0.938478 0.469239 0.883071i \(-0.344528\pi\)
0.469239 + 0.883071i \(0.344528\pi\)
\(234\) −1.59806e11 −0.000973416
\(235\) 1.76913e14i 1.05039i
\(236\) 7.30422e13 0.422768
\(237\) 1.13668e14i 0.641428i
\(238\) 2.61131e12 0.0143680
\(239\) 2.59073e14 1.39007 0.695033 0.718978i \(-0.255390\pi\)
0.695033 + 0.718978i \(0.255390\pi\)
\(240\) 1.67676e14i 0.877413i
\(241\) 9.35922e13i 0.477680i −0.971059 0.238840i \(-0.923233\pi\)
0.971059 0.238840i \(-0.0767672\pi\)
\(242\) −1.02200e14 −0.508814
\(243\) −8.17202e11 −0.00396910
\(244\) 3.43463e13i 0.162758i
\(245\) 2.69771e14i 1.24738i
\(246\) −3.64784e13 −0.164598
\(247\) 3.88600e14i 1.71128i
\(248\) 1.49746e14 0.643643
\(249\) 1.52891e14i 0.641485i
\(250\) 4.28561e13i 0.175539i
\(251\) 1.84432e14i 0.737555i −0.929518 0.368778i \(-0.879776\pi\)
0.929518 0.368778i \(-0.120224\pi\)
\(252\) 2.13639e10i 8.34214e-5i
\(253\) 8.23797e13 + 4.13458e14i 0.314121 + 1.57655i
\(254\) −2.31596e13 −0.0862439
\(255\) 3.28374e14 1.19434
\(256\) 3.39077e13 0.120464
\(257\) 1.26033e14 0.437407 0.218703 0.975791i \(-0.429817\pi\)
0.218703 + 0.975791i \(0.429817\pi\)
\(258\) 1.58723e14i 0.538173i
\(259\) −2.29415e13 −0.0760018
\(260\) 5.28922e14i 1.71219i
\(261\) −2.19549e11 −0.000694525
\(262\) −1.61465e14 −0.499195
\(263\) 1.67551e14i 0.506306i −0.967426 0.253153i \(-0.918532\pi\)
0.967426 0.253153i \(-0.0814676\pi\)
\(264\) 3.31895e14i 0.980340i
\(265\) −6.89368e14 −1.99056
\(266\) −5.97560e12 −0.0168691
\(267\) 8.47186e12i 0.0233836i
\(268\) 3.88043e14i 1.04730i
\(269\) −4.35619e14 −1.14972 −0.574861 0.818251i \(-0.694944\pi\)
−0.574861 + 0.818251i \(0.694944\pi\)
\(270\) 1.55403e14i 0.401121i
\(271\) −3.58017e14 −0.903833 −0.451917 0.892060i \(-0.649260\pi\)
−0.451917 + 0.892060i \(0.649260\pi\)
\(272\) 2.71004e14i 0.669211i
\(273\) 2.96611e13i 0.0716493i
\(274\) 5.85836e13i 0.138444i
\(275\) 3.91312e14i 0.904748i
\(276\) 3.89176e14 7.75418e13i 0.880424 0.175421i
\(277\) −6.80322e14 −1.50604 −0.753019 0.657999i \(-0.771403\pi\)
−0.753019 + 0.657999i \(0.771403\pi\)
\(278\) −1.31012e13 −0.0283820
\(279\) −9.88890e11 −0.00209663
\(280\) 1.72023e13 0.0356975
\(281\) 8.41639e14i 1.70957i −0.518979 0.854787i \(-0.673688\pi\)
0.518979 0.854787i \(-0.326312\pi\)
\(282\) 1.35856e14 0.270136
\(283\) 2.82620e14i 0.550153i −0.961422 0.275077i \(-0.911297\pi\)
0.961422 0.275077i \(-0.0887032\pi\)
\(284\) 1.00916e14 0.192331
\(285\) −7.51436e14 −1.40224
\(286\) 4.31513e14i 0.788493i
\(287\) 1.34101e13i 0.0239960i
\(288\) 9.44955e11 0.00165599
\(289\) 5.18927e13 0.0890674
\(290\) 8.35835e13i 0.140518i
\(291\) 8.03423e14i 1.32308i
\(292\) −1.47141e14 −0.237375
\(293\) 3.31155e14i 0.523390i 0.965151 + 0.261695i \(0.0842814\pi\)
−0.965151 + 0.261695i \(0.915719\pi\)
\(294\) 2.07164e14 0.320796
\(295\) 3.88394e14i 0.589305i
\(296\) 6.64445e14i 0.987891i
\(297\) 1.10222e15i 1.60594i
\(298\) 8.83051e13i 0.126092i
\(299\) 1.07018e15 2.13228e14i 1.49771 0.298413i
\(300\) 3.68332e14 0.505256
\(301\) 5.83493e13 0.0784579
\(302\) −3.32903e14 −0.438810
\(303\) 4.46035e14 0.576386
\(304\) 6.20155e14i 0.785703i
\(305\) −1.82633e14 −0.226871
\(306\) 4.99445e11i 0.000608358i
\(307\) −3.73992e14 −0.446716 −0.223358 0.974736i \(-0.571702\pi\)
−0.223358 + 0.974736i \(0.571702\pi\)
\(308\) −5.76874e13 −0.0675735
\(309\) 1.16061e15i 1.33332i
\(310\) 3.76477e14i 0.424197i
\(311\) 7.83220e14 0.865609 0.432804 0.901488i \(-0.357524\pi\)
0.432804 + 0.901488i \(0.357524\pi\)
\(312\) 8.59063e14 0.931317
\(313\) 3.68279e14i 0.391661i 0.980638 + 0.195831i \(0.0627403\pi\)
−0.980638 + 0.195831i \(0.937260\pi\)
\(314\) 1.23745e13i 0.0129107i
\(315\) −1.13600e11 −0.000116283
\(316\) 5.72210e14i 0.574689i
\(317\) −4.24203e14 −0.418040 −0.209020 0.977911i \(-0.567027\pi\)
−0.209020 + 0.977911i \(0.567027\pi\)
\(318\) 5.29382e14i 0.511925i
\(319\) 5.92831e14i 0.562583i
\(320\) 5.81431e14i 0.541500i
\(321\) 1.75285e15i 1.60219i
\(322\) −3.27887e12 1.64564e13i −0.00294163 0.0147638i
\(323\) 1.21450e15 1.06950
\(324\) 1.03955e15 0.898617
\(325\) 1.01286e15 0.859504
\(326\) −1.28070e14 −0.106695
\(327\) 1.56711e15i 1.28178i
\(328\) 3.88390e14 0.311907
\(329\) 4.99428e13i 0.0393820i
\(330\) 8.34418e14 0.646100
\(331\) −8.59733e14 −0.653726 −0.326863 0.945072i \(-0.605992\pi\)
−0.326863 + 0.945072i \(0.605992\pi\)
\(332\) 7.69662e14i 0.574740i
\(333\) 4.38785e12i 0.00321801i
\(334\) −5.91223e14 −0.425865
\(335\) −2.06338e15 −1.45985
\(336\) 4.73353e13i 0.0328965i
\(337\) 2.81112e15i 1.91911i −0.281525 0.959554i \(-0.590840\pi\)
0.281525 0.959554i \(-0.409160\pi\)
\(338\) 6.38000e14 0.427879
\(339\) 8.43771e14i 0.555938i
\(340\) −1.65305e15 −1.07007
\(341\) 2.67023e15i 1.69833i
\(342\) 1.14291e12i 0.000714258i
\(343\) 1.52481e14i 0.0936380i
\(344\) 1.68995e15i 1.01982i
\(345\) −4.12320e14 2.06940e15i −0.244523 1.22724i
\(346\) 5.42973e14 0.316462
\(347\) −6.87742e13 −0.0393957 −0.0196979 0.999806i \(-0.506270\pi\)
−0.0196979 + 0.999806i \(0.506270\pi\)
\(348\) 5.58016e14 0.314175
\(349\) −2.44456e15 −1.35285 −0.676423 0.736514i \(-0.736471\pi\)
−0.676423 + 0.736514i \(0.736471\pi\)
\(350\) 1.55750e13i 0.00847265i
\(351\) 2.85294e15 1.52563
\(352\) 2.55159e15i 1.34139i
\(353\) −1.72335e15 −0.890686 −0.445343 0.895360i \(-0.646918\pi\)
−0.445343 + 0.895360i \(0.646918\pi\)
\(354\) −2.98257e14 −0.151555
\(355\) 5.36609e14i 0.268095i
\(356\) 4.26477e13i 0.0209506i
\(357\) 9.27006e13 0.0447789
\(358\) 9.75473e14 0.463358
\(359\) 2.86070e15i 1.33630i −0.744025 0.668151i \(-0.767086\pi\)
0.744025 0.668151i \(-0.232914\pi\)
\(360\) 3.29015e12i 0.00151148i
\(361\) −5.65889e14 −0.255675
\(362\) 5.73488e14i 0.254843i
\(363\) −3.62807e15 −1.58575
\(364\) 1.49316e14i 0.0641944i
\(365\) 7.82404e14i 0.330882i
\(366\) 1.40248e14i 0.0583459i
\(367\) 2.70015e15i 1.10508i 0.833488 + 0.552538i \(0.186340\pi\)
−0.833488 + 0.552538i \(0.813660\pi\)
\(368\) −1.70786e15 + 3.40284e14i −0.687648 + 0.137011i
\(369\) −2.56484e12 −0.00101602
\(370\) −1.67048e15 −0.651076
\(371\) −1.94610e14 −0.0746314
\(372\) 2.51341e15 0.948432
\(373\) 1.55815e15i 0.578569i 0.957243 + 0.289285i \(0.0934174\pi\)
−0.957243 + 0.289285i \(0.906583\pi\)
\(374\) −1.34862e15 −0.492786
\(375\) 1.52138e15i 0.547078i
\(376\) −1.44647e15 −0.511897
\(377\) 1.53446e15 0.534450
\(378\) 4.38704e13i 0.0150391i
\(379\) 1.15321e15i 0.389109i −0.980892 0.194555i \(-0.937674\pi\)
0.980892 0.194555i \(-0.0623261\pi\)
\(380\) 3.78276e15 1.25634
\(381\) −8.22158e14 −0.268785
\(382\) 5.60667e14i 0.180437i
\(383\) 2.36350e15i 0.748794i −0.927268 0.374397i \(-0.877850\pi\)
0.927268 0.374397i \(-0.122150\pi\)
\(384\) −3.12450e15 −0.974526
\(385\) 3.06746e14i 0.0941922i
\(386\) 3.97832e14 0.120275
\(387\) 1.11600e13i 0.00332200i
\(388\) 4.04447e15i 1.18542i
\(389\) 9.73213e14i 0.280873i 0.990090 + 0.140437i \(0.0448506\pi\)
−0.990090 + 0.140437i \(0.955149\pi\)
\(390\) 2.15977e15i 0.613791i
\(391\) 6.66406e14 + 3.34464e15i 0.186500 + 0.936029i
\(392\) −2.20570e15 −0.607897
\(393\) −5.73195e15 −1.55578
\(394\) −1.04845e15 −0.280267
\(395\) 3.04266e15 0.801071
\(396\) 1.10334e13i 0.00286114i
\(397\) 7.32666e15 1.87138 0.935692 0.352818i \(-0.114776\pi\)
0.935692 + 0.352818i \(0.114776\pi\)
\(398\) 6.89024e14i 0.173355i
\(399\) −2.12132e14 −0.0525737
\(400\) −1.61639e15 −0.394626
\(401\) 1.40000e15i 0.336715i 0.985726 + 0.168357i \(0.0538463\pi\)
−0.985726 + 0.168357i \(0.946154\pi\)
\(402\) 1.58451e15i 0.375440i
\(403\) 6.91150e15 1.61340
\(404\) −2.24536e15 −0.516414
\(405\) 5.52768e15i 1.25260i
\(406\) 2.35958e13i 0.00526840i
\(407\) 1.18482e16 2.60667
\(408\) 2.68485e15i 0.582047i
\(409\) 1.86884e15 0.399238 0.199619 0.979874i \(-0.436030\pi\)
0.199619 + 0.979874i \(0.436030\pi\)
\(410\) 9.76452e14i 0.205564i
\(411\) 2.07970e15i 0.431469i
\(412\) 5.84255e15i 1.19459i
\(413\) 1.09644e14i 0.0220946i
\(414\) −3.14749e12 + 6.27125e11i −0.000625119 + 0.000124552i
\(415\) 4.09259e15 0.801143
\(416\) −6.60444e15 −1.27431
\(417\) −4.65089e14 −0.0884544
\(418\) 3.08611e15 0.578568
\(419\) 3.82847e15i 0.707523i −0.935336 0.353762i \(-0.884902\pi\)
0.935336 0.353762i \(-0.115098\pi\)
\(420\) 2.88732e14 0.0526016
\(421\) 7.95700e15i 1.42908i 0.699594 + 0.714540i \(0.253364\pi\)
−0.699594 + 0.714540i \(0.746636\pi\)
\(422\) 1.04069e15 0.184266
\(423\) 9.55219e12 0.00166748
\(424\) 5.63641e15i 0.970079i
\(425\) 3.16550e15i 0.537166i
\(426\) −4.12075e14 −0.0689475
\(427\) −5.15576e13 −0.00850600
\(428\) 8.82391e15i 1.43548i
\(429\) 1.53186e16i 2.45739i
\(430\) 4.24870e15 0.672117
\(431\) 8.78299e15i 1.37018i −0.728457 0.685092i \(-0.759762\pi\)
0.728457 0.685092i \(-0.240238\pi\)
\(432\) −4.55292e15 −0.700467
\(433\) 6.57765e15i 0.998029i −0.866594 0.499014i \(-0.833695\pi\)
0.866594 0.499014i \(-0.166305\pi\)
\(434\) 1.06280e14i 0.0159043i
\(435\) 2.96719e15i 0.437935i
\(436\) 7.88891e15i 1.14841i
\(437\) −1.52497e15 7.65374e15i −0.218965 1.09897i
\(438\) 6.00826e14 0.0850951
\(439\) −4.74277e15 −0.662590 −0.331295 0.943527i \(-0.607485\pi\)
−0.331295 + 0.943527i \(0.607485\pi\)
\(440\) −8.88416e15 −1.22433
\(441\) 1.45660e13 0.00198019
\(442\) 3.49070e15i 0.468144i
\(443\) −7.59767e15 −1.00521 −0.502607 0.864515i \(-0.667626\pi\)
−0.502607 + 0.864515i \(0.667626\pi\)
\(444\) 1.11524e16i 1.45569i
\(445\) 2.26775e14 0.0292035
\(446\) −3.87005e15 −0.491708
\(447\) 3.13480e15i 0.392975i
\(448\) 1.64139e14i 0.0203022i
\(449\) 1.43574e16 1.75226 0.876129 0.482076i \(-0.160117\pi\)
0.876129 + 0.482076i \(0.160117\pi\)
\(450\) −2.97891e12 −0.000358742
\(451\) 6.92566e15i 0.823004i
\(452\) 4.24758e15i 0.498094i
\(453\) −1.18179e16 −1.36758
\(454\) 2.60064e15i 0.296992i
\(455\) 7.93969e14 0.0894819
\(456\) 6.14388e15i 0.683367i
\(457\) 9.08837e15i 0.997674i 0.866696 + 0.498837i \(0.166239\pi\)
−0.866696 + 0.498837i \(0.833761\pi\)
\(458\) 2.61875e15i 0.283727i
\(459\) 8.91635e15i 0.953478i
\(460\) 2.07564e15 + 1.04175e16i 0.219081 + 1.09955i
\(461\) 3.88514e15 0.404763 0.202381 0.979307i \(-0.435132\pi\)
0.202381 + 0.979307i \(0.435132\pi\)
\(462\) 2.35558e14 0.0242240
\(463\) 4.99994e15 0.507550 0.253775 0.967263i \(-0.418328\pi\)
0.253775 + 0.967263i \(0.418328\pi\)
\(464\) −2.44880e15 −0.245383
\(465\) 1.33648e16i 1.32204i
\(466\) 3.08669e15 0.301424
\(467\) 3.88089e15i 0.374136i 0.982347 + 0.187068i \(0.0598985\pi\)
−0.982347 + 0.187068i \(0.940101\pi\)
\(468\) 2.85585e13 0.00271807
\(469\) −5.82495e14 −0.0547337
\(470\) 3.63658e15i 0.337370i
\(471\) 4.39291e14i 0.0402371i
\(472\) 3.17558e15 0.287191
\(473\) −3.01346e16 −2.69091
\(474\) 2.33653e15i 0.206016i
\(475\) 7.24379e15i 0.630673i
\(476\) −4.66659e14 −0.0401197
\(477\) 3.72216e13i 0.00315998i
\(478\) 5.32545e15 0.446467
\(479\) 1.12520e16i 0.931569i 0.884898 + 0.465784i \(0.154228\pi\)
−0.884898 + 0.465784i \(0.845772\pi\)
\(480\) 1.27710e16i 1.04419i
\(481\) 3.06674e16i 2.47632i
\(482\) 1.92386e15i 0.153423i
\(483\) −1.16399e14 5.84197e14i −0.00916780 0.0460125i
\(484\) 1.82639e16 1.42076
\(485\) −2.15060e16 −1.65238
\(486\) −1.67982e13 −0.00127481
\(487\) 4.99647e15 0.374533 0.187266 0.982309i \(-0.440037\pi\)
0.187266 + 0.982309i \(0.440037\pi\)
\(488\) 1.49324e15i 0.110563i
\(489\) −4.54645e15 −0.332521
\(490\) 5.54535e15i 0.400638i
\(491\) 3.60546e15 0.257319 0.128660 0.991689i \(-0.458933\pi\)
0.128660 + 0.991689i \(0.458933\pi\)
\(492\) 6.51894e15 0.459606
\(493\) 4.79567e15i 0.334017i
\(494\) 7.98797e15i 0.549635i
\(495\) 5.86691e13 0.00398821
\(496\) −1.10299e16 −0.740764
\(497\) 1.51486e14i 0.0100516i
\(498\) 3.14280e15i 0.206035i
\(499\) −1.23847e16 −0.802202 −0.401101 0.916034i \(-0.631372\pi\)
−0.401101 + 0.916034i \(0.631372\pi\)
\(500\) 7.65869e15i 0.490156i
\(501\) −2.09882e16 −1.32724
\(502\) 3.79115e15i 0.236891i
\(503\) 5.45188e15i 0.336619i 0.985734 + 0.168309i \(0.0538308\pi\)
−0.985734 + 0.168309i \(0.946169\pi\)
\(504\) 9.28817e11i 5.66692e-5i
\(505\) 1.19395e16i 0.719841i
\(506\) 1.69338e15 + 8.49894e15i 0.100891 + 0.506363i
\(507\) 2.26488e16 1.33351
\(508\) 4.13878e15 0.240819
\(509\) −1.70661e16 −0.981358 −0.490679 0.871340i \(-0.663251\pi\)
−0.490679 + 0.871340i \(0.663251\pi\)
\(510\) 6.74998e15 0.383602
\(511\) 2.20874e14i 0.0124056i
\(512\) 1.82351e16 1.01225
\(513\) 2.04038e16i 1.11945i
\(514\) 2.59071e15 0.140488
\(515\) 3.10671e16 1.66517
\(516\) 2.83649e16i 1.50274i
\(517\) 2.57931e16i 1.35070i
\(518\) −4.71581e14 −0.0244106
\(519\) 1.92753e16 0.986275
\(520\) 2.29954e16i 1.16311i
\(521\) 3.27861e16i 1.63932i 0.572852 + 0.819659i \(0.305837\pi\)
−0.572852 + 0.819659i \(0.694163\pi\)
\(522\) −4.51299e12 −0.000223070
\(523\) 1.02947e16i 0.503041i 0.967852 + 0.251520i \(0.0809305\pi\)
−0.967852 + 0.251520i \(0.919069\pi\)
\(524\) 2.88549e16 1.39390
\(525\) 5.52906e14i 0.0264056i
\(526\) 3.44415e15i 0.162617i
\(527\) 2.16007e16i 1.00833i
\(528\) 2.44464e16i 1.12827i
\(529\) 2.02411e16 8.39935e15i 0.923634 0.383276i
\(530\) −1.41705e16 −0.639337
\(531\) −2.09708e13 −0.000935511
\(532\) 1.06788e15 0.0471035
\(533\) 1.79261e16 0.781848
\(534\) 1.74146e14i 0.00751043i
\(535\) 4.69202e16 2.00095
\(536\) 1.68705e16i 0.711443i
\(537\) 3.46289e16 1.44409
\(538\) −8.95448e15 −0.369272
\(539\) 3.93314e16i 1.60401i
\(540\) 2.77715e16i 1.12005i
\(541\) −4.53166e16 −1.80748 −0.903741 0.428079i \(-0.859191\pi\)
−0.903741 + 0.428079i \(0.859191\pi\)
\(542\) −7.35932e15 −0.290297
\(543\) 2.03586e16i 0.794236i
\(544\) 2.06410e16i 0.796411i
\(545\) −4.19484e16 −1.60080
\(546\) 6.09708e14i 0.0230126i
\(547\) −1.47231e16 −0.549637 −0.274818 0.961496i \(-0.588618\pi\)
−0.274818 + 0.961496i \(0.588618\pi\)
\(548\) 1.04693e16i 0.386575i
\(549\) 9.86104e12i 0.000360154i
\(550\) 8.04373e15i 0.290590i
\(551\) 1.09742e16i 0.392160i
\(552\) 1.69198e16 3.37120e15i 0.598083 0.119166i
\(553\) 8.58950e14 0.0300343
\(554\) −1.39845e16 −0.483715
\(555\) −5.93016e16 −2.02912
\(556\) 2.34128e15 0.0792509
\(557\) 1.48773e16i 0.498188i 0.968479 + 0.249094i \(0.0801328\pi\)
−0.968479 + 0.249094i \(0.919867\pi\)
\(558\) −2.03274e13 −0.000673405
\(559\) 7.79992e16i 2.55634i
\(560\) −1.26707e15 −0.0410840
\(561\) −4.78754e16 −1.53580
\(562\) 1.73005e16i 0.549088i
\(563\) 2.49578e16i 0.783709i 0.920027 + 0.391855i \(0.128166\pi\)
−0.920027 + 0.391855i \(0.871834\pi\)
\(564\) −2.42783e16 −0.754300
\(565\) −2.25861e16 −0.694304
\(566\) 5.80947e15i 0.176700i
\(567\) 1.56048e15i 0.0469633i
\(568\) 4.38742e15 0.130653
\(569\) 1.63399e16i 0.481478i −0.970590 0.240739i \(-0.922610\pi\)
0.970590 0.240739i \(-0.0773898\pi\)
\(570\) −1.54464e16 −0.450378
\(571\) 3.45158e16i 0.995868i −0.867215 0.497934i \(-0.834092\pi\)
0.867215 0.497934i \(-0.165908\pi\)
\(572\) 7.71144e16i 2.20171i
\(573\) 1.99035e16i 0.562343i
\(574\) 2.75654e14i 0.00770714i
\(575\) 1.99489e16 3.97474e15i 0.551966 0.109977i
\(576\) −3.13937e13 −0.000859621
\(577\) −1.46857e16 −0.397961 −0.198981 0.980003i \(-0.563763\pi\)
−0.198981 + 0.980003i \(0.563763\pi\)
\(578\) 1.06669e15 0.0286070
\(579\) 1.41229e16 0.374846
\(580\) 1.49370e16i 0.392369i
\(581\) 1.15535e15 0.0300369
\(582\) 1.65150e16i 0.424952i
\(583\) 1.00507e17 2.55967
\(584\) −6.39708e15 −0.161252
\(585\) 1.51857e14i 0.00378877i
\(586\) 6.80714e15i 0.168104i
\(587\) −4.11858e16 −1.00674 −0.503372 0.864070i \(-0.667907\pi\)
−0.503372 + 0.864070i \(0.667907\pi\)
\(588\) −3.70216e16 −0.895758
\(589\) 4.94300e16i 1.18386i
\(590\) 7.98373e15i 0.189275i
\(591\) −3.72198e16 −0.873472
\(592\) 4.89412e16i 1.13696i
\(593\) 6.12005e15 0.140743 0.0703715 0.997521i \(-0.477582\pi\)
0.0703715 + 0.997521i \(0.477582\pi\)
\(594\) 2.26570e16i 0.515802i
\(595\) 2.48141e15i 0.0559238i
\(596\) 1.57807e16i 0.352087i
\(597\) 2.44601e16i 0.540272i
\(598\) 2.19983e16 4.38307e15i 0.481041 0.0958454i
\(599\) 4.85506e16 1.05107 0.525537 0.850771i \(-0.323864\pi\)
0.525537 + 0.850771i \(0.323864\pi\)
\(600\) 1.60136e16 0.343227
\(601\) −5.47790e16 −1.16243 −0.581215 0.813750i \(-0.697423\pi\)
−0.581215 + 0.813750i \(0.697423\pi\)
\(602\) 1.19941e15 0.0251994
\(603\) 1.11409e14i 0.00231749i
\(604\) 5.94921e16 1.22529
\(605\) 9.71162e16i 1.98043i
\(606\) 9.16860e15 0.185126
\(607\) 1.51959e16 0.303804 0.151902 0.988396i \(-0.451460\pi\)
0.151902 + 0.988396i \(0.451460\pi\)
\(608\) 4.72339e16i 0.935045i
\(609\) 8.37643e14i 0.0164193i
\(610\) −3.75416e15 −0.0728675
\(611\) −6.67617e16 −1.28316
\(612\) 8.92544e13i 0.00169872i
\(613\) 2.14547e16i 0.404353i −0.979349 0.202176i \(-0.935199\pi\)
0.979349 0.202176i \(-0.0648014\pi\)
\(614\) −7.68769e15 −0.143478
\(615\) 3.46637e16i 0.640655i
\(616\) −2.50802e15 −0.0459035
\(617\) 7.31022e16i 1.32501i 0.749057 + 0.662506i \(0.230507\pi\)
−0.749057 + 0.662506i \(0.769493\pi\)
\(618\) 2.38572e16i 0.428241i
\(619\) 1.01544e17i 1.80514i 0.430539 + 0.902572i \(0.358323\pi\)
−0.430539 + 0.902572i \(0.641677\pi\)
\(620\) 6.72790e16i 1.18448i
\(621\) 5.61906e16 1.11957e16i 0.979747 0.195210i
\(622\) 1.60997e16 0.278020
\(623\) 6.40189e13 0.00109491
\(624\) −6.32761e16 −1.07185
\(625\) −7.42706e16 −1.24605
\(626\) 7.57026e15i 0.125795i
\(627\) 1.09556e17 1.80315
\(628\) 2.21141e15i 0.0360505i
\(629\) 9.58454e16 1.54763
\(630\) −2.33514e12 −3.73482e−5
\(631\) 9.47729e16i 1.50144i −0.660621 0.750720i \(-0.729707\pi\)
0.660621 0.750720i \(-0.270293\pi\)
\(632\) 2.48774e16i 0.390393i
\(633\) 3.69441e16 0.574279
\(634\) −8.71982e15 −0.134268
\(635\) 2.20075e16i 0.335682i
\(636\) 9.46043e16i 1.42945i
\(637\) −1.01804e17 −1.52380
\(638\) 1.21861e16i 0.180693i
\(639\) −2.89736e13 −0.000425595
\(640\) 8.36366e16i 1.21707i
\(641\) 1.20517e17i 1.73739i 0.495344 + 0.868697i \(0.335042\pi\)
−0.495344 + 0.868697i \(0.664958\pi\)
\(642\) 3.60311e16i 0.514597i
\(643\) 3.08086e16i 0.435920i 0.975958 + 0.217960i \(0.0699402\pi\)
−0.975958 + 0.217960i \(0.930060\pi\)
\(644\) 5.85957e14 + 2.94087e15i 0.00821392 + 0.0412250i
\(645\) 1.50827e17 2.09470
\(646\) 2.49650e16 0.343507
\(647\) 1.60873e16 0.219310 0.109655 0.993970i \(-0.465025\pi\)
0.109655 + 0.993970i \(0.465025\pi\)
\(648\) 4.51954e16 0.610442
\(649\) 5.66260e16i 0.757788i
\(650\) 2.08201e16 0.276059
\(651\) 3.77291e15i 0.0495667i
\(652\) 2.28871e16 0.297923
\(653\) 5.79193e16 0.747040 0.373520 0.927622i \(-0.378151\pi\)
0.373520 + 0.927622i \(0.378151\pi\)
\(654\) 3.22132e16i 0.411687i
\(655\) 1.53433e17i 1.94299i
\(656\) −2.86077e16 −0.358972
\(657\) 4.22449e13 0.000525270
\(658\) 1.02661e15i 0.0126489i
\(659\) 3.13243e15i 0.0382445i 0.999817 + 0.0191223i \(0.00608717\pi\)
−0.999817 + 0.0191223i \(0.993913\pi\)
\(660\) −1.49116e17 −1.80410
\(661\) 4.36627e16i 0.523482i 0.965138 + 0.261741i \(0.0842966\pi\)
−0.965138 + 0.261741i \(0.915703\pi\)
\(662\) −1.76725e16 −0.209966
\(663\) 1.23919e17i 1.45900i
\(664\) 3.34618e16i 0.390428i
\(665\) 5.67834e15i 0.0656586i
\(666\) 9.01957e13i 0.00103357i
\(667\) 3.02222e16 6.02165e15i 0.343219 0.0683849i
\(668\) 1.05656e17 1.18914
\(669\) −1.37385e17 −1.53244
\(670\) −4.24143e16 −0.468882
\(671\) 2.66270e16 0.291734
\(672\) 3.60528e15i 0.0391493i
\(673\) 1.97947e15 0.0213039 0.0106519 0.999943i \(-0.496609\pi\)
0.0106519 + 0.999943i \(0.496609\pi\)
\(674\) 5.77847e16i 0.616387i
\(675\) 5.31810e16 0.562255
\(676\) −1.14015e17 −1.19476
\(677\) 5.52494e16i 0.573846i 0.957954 + 0.286923i \(0.0926324\pi\)
−0.957954 + 0.286923i \(0.907368\pi\)
\(678\) 1.73444e16i 0.178558i
\(679\) −6.07119e15 −0.0619520
\(680\) −7.18679e16 −0.726912
\(681\) 9.23217e16i 0.925595i
\(682\) 5.48886e16i 0.545476i
\(683\) −8.11803e15 −0.0799699 −0.0399849 0.999200i \(-0.512731\pi\)
−0.0399849 + 0.999200i \(0.512731\pi\)
\(684\) 2.04246e14i 0.00199442i
\(685\) 5.56693e16 0.538856
\(686\) 3.13437e15i 0.0300750i
\(687\) 9.29647e16i 0.884255i
\(688\) 1.24477e17i 1.17370i
\(689\) 2.60148e17i 2.43167i
\(690\) −8.47555e15 4.25382e16i −0.0785369 0.394171i
\(691\) −1.04730e17 −0.962063 −0.481032 0.876703i \(-0.659738\pi\)
−0.481032 + 0.876703i \(0.659738\pi\)
\(692\) −9.70330e16 −0.883655
\(693\) 1.65624e13 0.000149528
\(694\) −1.41371e15 −0.0126533
\(695\) 1.24495e16i 0.110470i
\(696\) 2.42603e16 0.213423
\(697\) 5.60248e16i 0.488634i
\(698\) −5.02498e16 −0.434512
\(699\) 1.09577e17 0.939409
\(700\) 2.78336e15i 0.0236581i
\(701\) 4.92437e16i 0.414995i 0.978236 + 0.207498i \(0.0665319\pi\)
−0.978236 + 0.207498i \(0.933468\pi\)
\(702\) 5.86444e16 0.490009
\(703\) −2.19328e17 −1.81703
\(704\) 8.47700e16i 0.696316i
\(705\) 1.29097e17i 1.05144i
\(706\) −3.54248e16 −0.286074
\(707\) 3.37053e15i 0.0269887i
\(708\) 5.33006e16 0.423187
\(709\) 7.44193e16i 0.585879i −0.956131 0.292940i \(-0.905367\pi\)
0.956131 0.292940i \(-0.0946335\pi\)
\(710\) 1.10304e16i 0.0861077i
\(711\) 1.64285e14i 0.00127169i
\(712\) 1.85415e15i 0.0142320i
\(713\) 1.36127e17 2.71227e16i 1.03611 0.206441i
\(714\) 1.90553e15 0.0143823
\(715\) −4.10047e17 −3.06900
\(716\) −1.74324e17 −1.29383
\(717\) 1.89052e17 1.39144
\(718\) 5.88038e16i 0.429199i
\(719\) 2.09057e17 1.51318 0.756591 0.653889i \(-0.226864\pi\)
0.756591 + 0.653889i \(0.226864\pi\)
\(720\) 2.42343e14i 0.00173955i
\(721\) 8.77030e15 0.0624314
\(722\) −1.16323e16 −0.0821187
\(723\) 6.82964e16i 0.478154i
\(724\) 1.02486e17i 0.711598i
\(725\) 2.86035e16 0.196966
\(726\) −7.45778e16 −0.509319
\(727\) 9.98224e16i 0.676117i −0.941125 0.338058i \(-0.890230\pi\)
0.941125 0.338058i \(-0.109770\pi\)
\(728\) 6.49164e15i 0.0436080i
\(729\) 1.49796e17 0.998008
\(730\) 1.60829e16i 0.106274i
\(731\) −2.43772e17 −1.59764
\(732\) 2.50633e16i 0.162919i
\(733\) 7.93088e16i 0.511326i 0.966766 + 0.255663i \(0.0822937\pi\)
−0.966766 + 0.255663i \(0.917706\pi\)
\(734\) 5.55037e16i 0.354932i
\(735\) 1.96858e17i 1.24862i
\(736\) −1.30079e17 + 2.59177e16i −0.818352 + 0.163053i
\(737\) 3.00831e17 1.87723
\(738\) −5.27223e13 −0.000326330
\(739\) −2.14675e17 −1.31800 −0.658998 0.752144i \(-0.729020\pi\)
−0.658998 + 0.752144i \(0.729020\pi\)
\(740\) 2.98527e17 1.81800
\(741\) 2.83570e17i 1.71298i
\(742\) −4.00036e15 −0.0239704
\(743\) 2.85783e17i 1.69865i 0.527873 + 0.849323i \(0.322990\pi\)
−0.527873 + 0.849323i \(0.677010\pi\)
\(744\) 1.09273e17 0.644281
\(745\) −8.39123e16 −0.490781
\(746\) 3.20289e16i 0.185827i
\(747\) 2.20975e14i 0.00127180i
\(748\) 2.41007e17 1.37601
\(749\) 1.32457e16 0.0750209
\(750\) 3.12731e16i 0.175713i
\(751\) 6.85590e16i 0.382142i 0.981576 + 0.191071i \(0.0611961\pi\)
−0.981576 + 0.191071i \(0.938804\pi\)
\(752\) 1.06543e17 0.589139
\(753\) 1.34584e17i 0.738287i
\(754\) 3.15420e16 0.171657
\(755\) 3.16343e17i 1.70795i
\(756\) 7.83995e15i 0.0419936i
\(757\) 3.28827e17i 1.74740i −0.486467 0.873699i \(-0.661715\pi\)
0.486467 0.873699i \(-0.338285\pi\)
\(758\) 2.37050e16i 0.124976i
\(759\) 6.01144e16 + 3.01710e17i 0.314433 + 1.57811i
\(760\) 1.64459e17 0.853448
\(761\) −3.36910e17 −1.73462 −0.867312 0.497765i \(-0.834154\pi\)
−0.867312 + 0.497765i \(0.834154\pi\)
\(762\) −1.69001e16 −0.0863295
\(763\) −1.18421e16 −0.0600181
\(764\) 1.00195e17i 0.503833i
\(765\) 4.74600e14 0.00236788
\(766\) 4.85835e16i 0.240501i
\(767\) 1.46568e17 0.719894
\(768\) 2.47432e16 0.120584
\(769\) 2.17668e17i 1.05253i 0.850320 + 0.526267i \(0.176409\pi\)
−0.850320 + 0.526267i \(0.823591\pi\)
\(770\) 6.30541e15i 0.0302530i
\(771\) 9.19692e16 0.437841
\(772\) −7.10954e16 −0.335844
\(773\) 9.78596e16i 0.458698i 0.973344 + 0.229349i \(0.0736596\pi\)
−0.973344 + 0.229349i \(0.926340\pi\)
\(774\) 2.29403e14i 0.00106697i
\(775\) 1.28836e17 0.594601
\(776\) 1.75837e17i 0.805268i
\(777\) −1.67410e16 −0.0760771
\(778\) 2.00052e16i 0.0902120i
\(779\) 1.28205e17i 0.573692i
\(780\) 3.85966e17i 1.71389i
\(781\) 7.82352e16i 0.344743i
\(782\) 1.36985e16 + 6.87517e16i 0.0599008 + 0.300638i
\(783\) 8.05682e16 0.349617
\(784\) 1.62465e17 0.699624
\(785\) 1.17589e16 0.0502516
\(786\) −1.17825e17 −0.499690
\(787\) 4.32755e17i 1.82135i 0.413120 + 0.910676i \(0.364439\pi\)
−0.413120 + 0.910676i \(0.635561\pi\)
\(788\) 1.87366e17 0.782589
\(789\) 1.22266e17i 0.506808i
\(790\) 6.25443e16 0.257291
\(791\) −6.37609e15 −0.0260313
\(792\) 4.79689e14i 0.00194361i
\(793\) 6.89203e16i 0.277146i
\(794\) 1.50605e17 0.601059
\(795\) −5.03048e17 −1.99254
\(796\) 1.23133e17i 0.484058i
\(797\) 1.54274e17i 0.601924i 0.953636 + 0.300962i \(0.0973078\pi\)
−0.953636 + 0.300962i \(0.902692\pi\)
\(798\) −4.36054e15 −0.0168858
\(799\) 2.08652e17i 0.801939i
\(800\) −1.23112e17 −0.469634
\(801\) 1.22444e13i 4.63600e-5i
\(802\) 2.87781e16i 0.108147i
\(803\) 1.14071e17i 0.425482i
\(804\) 2.83164e17i 1.04834i
\(805\) 1.56378e16 3.11576e15i 0.0574645 0.0114496i
\(806\) 1.42071e17 0.518198
\(807\) −3.17881e17 −1.15086
\(808\) −9.76193e16 −0.350806
\(809\) −1.52845e17 −0.545204 −0.272602 0.962127i \(-0.587884\pi\)
−0.272602 + 0.962127i \(0.587884\pi\)
\(810\) 1.13626e17i 0.402316i
\(811\) 2.10280e17 0.739048 0.369524 0.929221i \(-0.379521\pi\)
0.369524 + 0.929221i \(0.379521\pi\)
\(812\) 4.21673e15i 0.0147109i
\(813\) −2.61253e17 −0.904730
\(814\) 2.43549e17 0.837220
\(815\) 1.21699e17i 0.415282i
\(816\) 1.97758e17i 0.669875i
\(817\) 5.57838e17 1.87575
\(818\) 3.84154e16 0.128229
\(819\) 4.28694e13i 0.000142051i
\(820\) 1.74499e17i 0.573997i
\(821\) −1.96166e17 −0.640568 −0.320284 0.947322i \(-0.603778\pi\)
−0.320284 + 0.947322i \(0.603778\pi\)
\(822\) 4.27498e16i 0.138581i
\(823\) −5.43712e17 −1.74973 −0.874863 0.484370i \(-0.839049\pi\)
−0.874863 + 0.484370i \(0.839049\pi\)
\(824\) 2.54010e17i 0.811500i
\(825\) 2.85550e17i 0.905645i
\(826\) 2.25382e15i 0.00709643i
\(827\) 1.48485e17i 0.464142i 0.972699 + 0.232071i \(0.0745501\pi\)
−0.972699 + 0.232071i \(0.925450\pi\)
\(828\) 5.62479e14 1.12072e14i 0.00174552 0.000347787i
\(829\) 1.60037e17 0.493053 0.246527 0.969136i \(-0.420711\pi\)
0.246527 + 0.969136i \(0.420711\pi\)
\(830\) 8.41264e16 0.257314
\(831\) −4.96447e17 −1.50753
\(832\) 2.19415e17 0.661495
\(833\) 3.18169e17i 0.952331i
\(834\) −9.56026e15 −0.0284101
\(835\) 5.61812e17i 1.65757i
\(836\) −5.51510e17 −1.61553
\(837\) 3.62895e17 1.05543
\(838\) 7.86971e16i 0.227245i
\(839\) 4.61878e17i 1.32420i 0.749413 + 0.662102i \(0.230336\pi\)
−0.749413 + 0.662102i \(0.769664\pi\)
\(840\) 1.25529e16 0.0357329
\(841\) −3.10481e17 −0.877524
\(842\) 1.63562e17i 0.458998i
\(843\) 6.14163e17i 1.71127i
\(844\) −1.85978e17 −0.514527
\(845\) 6.06263e17i 1.66541i
\(846\) 1.96353e14 0.000535568
\(847\) 2.74161e16i 0.0742514i
\(848\) 4.15162e17i 1.11646i
\(849\) 2.06234e17i 0.550699i
\(850\) 6.50693e16i 0.172529i
\(851\) −1.20347e17 6.04015e17i −0.316854 1.59027i
\(852\) 7.36407e16 0.192522
\(853\) −5.60063e17 −1.45393 −0.726963 0.686676i \(-0.759069\pi\)
−0.726963 + 0.686676i \(0.759069\pi\)
\(854\) −1.05981e15 −0.00273199
\(855\) −1.08605e15 −0.00278006
\(856\) 3.83628e17i 0.975142i
\(857\) 2.48605e17 0.627516 0.313758 0.949503i \(-0.398412\pi\)
0.313758 + 0.949503i \(0.398412\pi\)
\(858\) 3.14885e17i 0.789275i
\(859\) 6.30957e17 1.57051 0.785256 0.619172i \(-0.212531\pi\)
0.785256 + 0.619172i \(0.212531\pi\)
\(860\) −7.59271e17 −1.87675
\(861\) 9.78564e15i 0.0240198i
\(862\) 1.80541e17i 0.440081i
\(863\) −1.27577e17 −0.308820 −0.154410 0.988007i \(-0.549348\pi\)
−0.154410 + 0.988007i \(0.549348\pi\)
\(864\) −3.46772e17 −0.833608
\(865\) 5.15962e17i 1.23175i
\(866\) 1.35209e17i 0.320551i
\(867\) 3.78673e16 0.0891558
\(868\) 1.89930e16i 0.0444094i
\(869\) −4.43606e17 −1.03010
\(870\) 6.09928e16i 0.140658i
\(871\) 7.78658e17i 1.78335i
\(872\) 3.42978e17i 0.780131i
\(873\) 1.16119e15i 0.00262312i
\(874\) −3.13470e16 1.57328e17i −0.0703279 0.352971i
\(875\) −1.14965e16 −0.0256164
\(876\) −1.07372e17 −0.237611
\(877\) 8.76560e17 1.92657 0.963283 0.268487i \(-0.0865235\pi\)
0.963283 + 0.268487i \(0.0865235\pi\)
\(878\) −9.74913e16 −0.212813
\(879\) 2.41651e17i 0.523909i
\(880\) 6.54382e17 1.40908
\(881\) 3.28530e17i 0.702619i 0.936259 + 0.351309i \(0.114264\pi\)
−0.936259 + 0.351309i \(0.885736\pi\)
\(882\) 2.99414e14 0.000636006
\(883\) −1.91747e17 −0.404542 −0.202271 0.979330i \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(884\) 6.23813e17i 1.30720i
\(885\) 2.83420e17i 0.589889i
\(886\) −1.56176e17 −0.322858
\(887\) 8.25413e17 1.69484 0.847421 0.530921i \(-0.178154\pi\)
0.847421 + 0.530921i \(0.178154\pi\)
\(888\) 4.84861e17i 0.988871i
\(889\) 6.21276e15i 0.0125856i
\(890\) 4.66153e15 0.00937969
\(891\) 8.05911e17i 1.61072i
\(892\) 6.91605e17 1.37300
\(893\) 4.77469e17i 0.941536i
\(894\) 6.44383e16i 0.126217i
\(895\) 9.26947e17i 1.80350i
\(896\) 2.36108e16i 0.0456313i
\(897\) 7.80933e17 1.55598e17i 1.49920 0.298709i
\(898\) 2.95128e17 0.562797
\(899\) 1.95184e17 0.369730
\(900\) 5.32352e14 0.00100171
\(901\) 8.13044e17 1.51973
\(902\) 1.42362e17i 0.264336i
\(903\) 4.25788e16 0.0785357
\(904\) 1.84668e17i 0.338361i
\(905\) 5.44960e17 0.991912
\(906\) −2.42927e17 −0.439245
\(907\) 9.39102e17i 1.68682i 0.537270 + 0.843410i \(0.319456\pi\)
−0.537270 + 0.843410i \(0.680544\pi\)
\(908\) 4.64752e17i 0.829289i
\(909\) 6.44657e14 0.00114273
\(910\) 1.63207e16 0.0287402
\(911\) 1.05184e18i 1.84009i −0.391811 0.920046i \(-0.628151\pi\)
0.391811 0.920046i \(-0.371849\pi\)
\(912\) 4.52541e17i 0.786482i
\(913\) −5.96681e17 −1.03019
\(914\) 1.86818e17i 0.320437i
\(915\) −1.33271e17 −0.227096
\(916\) 4.67988e17i 0.792250i
\(917\) 4.33144e16i 0.0728477i
\(918\) 1.83282e17i 0.306242i
\(919\) 3.36581e16i 0.0558723i −0.999610 0.0279361i \(-0.991106\pi\)
0.999610 0.0279361i \(-0.00889350\pi\)
\(920\) 9.02404e16 + 4.52910e17i 0.148824 + 0.746938i
\(921\) −2.72910e17 −0.447159
\(922\) 7.98620e16 0.130003
\(923\) 2.02501e17 0.327504
\(924\) −4.20958e16 −0.0676405
\(925\) 5.71663e17i 0.912620i
\(926\) 1.02778e17 0.163017
\(927\) 1.67743e15i 0.00264342i
\(928\) −1.86512e17 −0.292024
\(929\) −8.45250e17 −1.31489 −0.657447 0.753501i \(-0.728364\pi\)
−0.657447 + 0.753501i \(0.728364\pi\)
\(930\) 2.74724e17i 0.424618i
\(931\) 7.28084e17i 1.11811i
\(932\) −5.51613e17 −0.841665
\(933\) 5.71534e17 0.866467
\(934\) 7.97746e16i 0.120167i
\(935\) 1.28153e18i 1.91804i
\(936\) 1.24161e15 0.00184642
\(937\) 9.46842e17i 1.39907i −0.714598 0.699536i \(-0.753390\pi\)
0.714598 0.699536i \(-0.246610\pi\)
\(938\) −1.19736e16 −0.0175796
\(939\) 2.68742e17i 0.392050i
\(940\) 6.49882e17i 0.942036i
\(941\) 3.16182e17i 0.455406i 0.973731 + 0.227703i \(0.0731216\pi\)
−0.973731 + 0.227703i \(0.926878\pi\)
\(942\) 9.02997e15i 0.0129235i
\(943\) 3.53067e17 7.03470e16i 0.502096 0.100040i
\(944\) −2.33904e17 −0.330526
\(945\) 4.16881e16 0.0585357
\(946\) −6.19440e17 −0.864276
\(947\) −2.66774e17 −0.369865 −0.184933 0.982751i \(-0.559207\pi\)
−0.184933 + 0.982751i \(0.559207\pi\)
\(948\) 4.17555e17i 0.575259i
\(949\) −2.95256e17 −0.404205
\(950\) 1.48902e17i 0.202562i
\(951\) −3.09551e17 −0.418455
\(952\) −2.02885e16 −0.0272538
\(953\) 1.03336e17i 0.137941i −0.997619 0.0689705i \(-0.978029\pi\)
0.997619 0.0689705i \(-0.0219714\pi\)
\(954\) 7.65119e14i 0.00101494i
\(955\) −5.32776e17 −0.702303
\(956\) −9.51696e17 −1.24667
\(957\) 4.32602e17i 0.563141i
\(958\) 2.31293e17i 0.299205i
\(959\) 1.57156e16 0.0202031
\(960\) 4.24284e17i 0.542037i
\(961\) 9.14823e16 0.116144
\(962\) 6.30392e17i 0.795354i
\(963\) 2.53340e15i 0.00317648i
\(964\) 3.43807e17i 0.428403i
\(965\) 3.78042e17i 0.468140i
\(966\) −2.39267e15 1.20086e16i −0.00294455 0.0147785i
\(967\) −1.21116e18 −1.48130 −0.740651 0.671890i \(-0.765483\pi\)
−0.740651 + 0.671890i \(0.765483\pi\)
\(968\) 7.94040e17 0.965140
\(969\) 8.86247e17 1.07056
\(970\) −4.42073e17 −0.530718
\(971\) 1.05891e18i 1.26340i 0.775211 + 0.631702i \(0.217643\pi\)
−0.775211 + 0.631702i \(0.782357\pi\)
\(972\) 3.00196e15 0.00355965
\(973\) 3.51451e15i 0.00414179i
\(974\) 1.02706e17 0.120294
\(975\) 7.39105e17 0.860356
\(976\) 1.09988e17i 0.127247i
\(977\) 4.62067e16i 0.0531298i 0.999647 + 0.0265649i \(0.00845686\pi\)
−0.999647 + 0.0265649i \(0.991543\pi\)
\(978\) −9.34558e16 −0.106801
\(979\) −3.30627e16 −0.0375528
\(980\) 9.90993e17i 1.11870i
\(981\) 2.26495e15i 0.00254124i
\(982\) 7.41130e16 0.0826467
\(983\) 5.45708e17i 0.604838i −0.953175 0.302419i \(-0.902206\pi\)
0.953175 0.302419i \(-0.0977942\pi\)
\(984\) 2.83417e17 0.312216
\(985\) 9.96299e17i 1.09087i
\(986\) 9.85788e16i 0.107281i
\(987\) 3.64444e16i 0.0394210i
\(988\) 1.42751e18i 1.53474i
\(989\) 3.06091e17 + 1.53625e18i 0.327094 + 1.64166i
\(990\) 1.20599e15 0.00128095
\(991\) 1.71753e18 1.81327 0.906637 0.421911i \(-0.138641\pi\)
0.906637 + 0.421911i \(0.138641\pi\)
\(992\) −8.40087e17 −0.881564
\(993\) −6.27367e17 −0.654374
\(994\) 3.11391e15i 0.00322840i
\(995\) −6.54748e17 −0.674739
\(996\) 5.61640e17i 0.575310i
\(997\) 1.31549e18 1.33942 0.669712 0.742621i \(-0.266418\pi\)
0.669712 + 0.742621i \(0.266418\pi\)
\(998\) −2.54578e17 −0.257654
\(999\) 1.61022e18i 1.61991i
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 23.13.b.c.22.12 yes 20
23.22 odd 2 inner 23.13.b.c.22.11 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.13.b.c.22.11 20 23.22 odd 2 inner
23.13.b.c.22.12 yes 20 1.1 even 1 trivial