Properties

Label 38.9.b.a.37.5
Level $38$
Weight $9$
Character 38.37
Analytic conductor $15.480$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,9,Mod(37,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.37");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 38.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: \(15.4803871823\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 46118 x^{10} + 738386961 x^{8} + 5214446299656 x^{6} + \cdots + 92\!\cdots\!64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{21} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.5
Root \(63.2768i\) of defining polynomial
Character \(\chi\) \(=\) 38.37
Dual form 38.9.b.a.37.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-11.3137i q^{2} +76.0047i q^{3} -128.000 q^{4} +1155.75 q^{5} +859.895 q^{6} -2869.50 q^{7} +1448.15i q^{8} +784.279 q^{9} +O(q^{10})\) \(q-11.3137i q^{2} +76.0047i q^{3} -128.000 q^{4} +1155.75 q^{5} +859.895 q^{6} -2869.50 q^{7} +1448.15i q^{8} +784.279 q^{9} -13075.8i q^{10} -4907.91 q^{11} -9728.61i q^{12} +41678.7i q^{13} +32464.7i q^{14} +87842.2i q^{15} +16384.0 q^{16} +51317.5 q^{17} -8873.11i q^{18} +(94212.1 + 90042.5i) q^{19} -147936. q^{20} -218095. i q^{21} +55526.7i q^{22} -88541.5 q^{23} -110067. q^{24} +945126. q^{25} +471541. q^{26} +558276. i q^{27} +367296. q^{28} +180690. i q^{29} +993821. q^{30} +888002. i q^{31} -185364. i q^{32} -373025. i q^{33} -580591. i q^{34} -3.31641e6 q^{35} -100388. q^{36} +2.53247e6i q^{37} +(1.01871e6 - 1.06589e6i) q^{38} -3.16778e6 q^{39} +1.67370e6i q^{40} -3.37210e6i q^{41} -2.46747e6 q^{42} +3.46074e6 q^{43} +628213. q^{44} +906428. q^{45} +1.00173e6i q^{46} -5.32862e6 q^{47} +1.24526e6i q^{48} +2.46922e6 q^{49} -1.06929e7i q^{50} +3.90037e6i q^{51} -5.33487e6i q^{52} -7.74166e6i q^{53} +6.31617e6 q^{54} -5.67230e6 q^{55} -4.15548e6i q^{56} +(-6.84366e6 + 7.16056e6i) q^{57} +2.04428e6 q^{58} -1.04388e7i q^{59} -1.12438e7i q^{60} -1.38848e7 q^{61} +1.00466e7 q^{62} -2.25049e6 q^{63} -2.09715e6 q^{64} +4.81700e7i q^{65} -4.22029e6 q^{66} -1.81780e7i q^{67} -6.56864e6 q^{68} -6.72957e6i q^{69} +3.75209e7i q^{70} -1.83448e7i q^{71} +1.13576e6i q^{72} +4.49830e7 q^{73} +2.86516e7 q^{74} +7.18340e7i q^{75} +(-1.20591e7 - 1.15254e7i) q^{76} +1.40832e7 q^{77} +3.58393e7i q^{78} -5.30791e7i q^{79} +1.89358e7 q^{80} -3.72860e7 q^{81} -3.81510e7 q^{82} +1.92972e7 q^{83} +2.79162e7i q^{84} +5.93100e7 q^{85} -3.91539e7i q^{86} -1.37333e7 q^{87} -7.10741e6i q^{88} +2.43432e7i q^{89} -1.02551e7i q^{90} -1.19597e8i q^{91} +1.13333e7 q^{92} -6.74923e7 q^{93} +6.02865e7i q^{94} +(1.08885e8 + 1.04066e8i) q^{95} +1.40885e7 q^{96} +7.02129e7i q^{97} -2.79360e7i q^{98} -3.84917e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 1536 q^{4} + 558 q^{5} + 1792 q^{6} - 5422 q^{7} - 15592 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 1536 q^{4} + 558 q^{5} + 1792 q^{6} - 5422 q^{7} - 15592 q^{9} - 12546 q^{11} + 196608 q^{16} + 270810 q^{17} + 41512 q^{19} - 71424 q^{20} - 823956 q^{23} - 229376 q^{24} + 865538 q^{25} - 431616 q^{26} + 694016 q^{28} + 71168 q^{30} - 1194378 q^{35} + 1995776 q^{36} + 998784 q^{38} + 5786100 q^{39} - 8383744 q^{42} + 7586646 q^{43} + 1605888 q^{44} + 2226046 q^{45} - 20260530 q^{47} - 19498842 q^{49} + 16933888 q^{54} - 14858554 q^{55} + 14430564 q^{57} - 5506560 q^{58} - 41363266 q^{61} + 32266752 q^{62} + 84235798 q^{63} - 25165824 q^{64} + 14371328 q^{66} - 34663680 q^{68} + 87906498 q^{73} - 2149632 q^{74} - 5313536 q^{76} - 78817962 q^{77} + 9142272 q^{80} - 100904812 q^{81} - 49609728 q^{82} - 55944960 q^{83} + 25440254 q^{85} + 119189604 q^{87} + 105466368 q^{92} + 105500856 q^{93} + 81396774 q^{95} + 29360128 q^{96} - 85554938 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.3137i 0.707107i
\(3\) 76.0047i 0.938330i 0.883110 + 0.469165i \(0.155445\pi\)
−0.883110 + 0.469165i \(0.844555\pi\)
\(4\) −128.000 −0.500000
\(5\) 1155.75 1.84919 0.924597 0.380946i \(-0.124401\pi\)
0.924597 + 0.380946i \(0.124401\pi\)
\(6\) 859.895 0.663500
\(7\) −2869.50 −1.19513 −0.597563 0.801822i \(-0.703864\pi\)
−0.597563 + 0.801822i \(0.703864\pi\)
\(8\) 1448.15i 0.353553i
\(9\) 784.279 0.119537
\(10\) 13075.8i 1.30758i
\(11\) −4907.91 −0.335217 −0.167608 0.985854i \(-0.553604\pi\)
−0.167608 + 0.985854i \(0.553604\pi\)
\(12\) 9728.61i 0.469165i
\(13\) 41678.7i 1.45929i 0.683828 + 0.729644i \(0.260314\pi\)
−0.683828 + 0.729644i \(0.739686\pi\)
\(14\) 32464.7i 0.845082i
\(15\) 87842.2i 1.73516i
\(16\) 16384.0 0.250000
\(17\) 51317.5 0.614426 0.307213 0.951641i \(-0.400604\pi\)
0.307213 + 0.951641i \(0.400604\pi\)
\(18\) 8873.11i 0.0845251i
\(19\) 94212.1 + 90042.5i 0.722923 + 0.690929i
\(20\) −147936. −0.924597
\(21\) 218095.i 1.12142i
\(22\) 55526.7i 0.237034i
\(23\) −88541.5 −0.316399 −0.158200 0.987407i \(-0.550569\pi\)
−0.158200 + 0.987407i \(0.550569\pi\)
\(24\) −110067. −0.331750
\(25\) 945126. 2.41952
\(26\) 471541. 1.03187
\(27\) 558276.i 1.05049i
\(28\) 367296. 0.597563
\(29\) 180690.i 0.255471i 0.991808 + 0.127736i \(0.0407709\pi\)
−0.991808 + 0.127736i \(0.959229\pi\)
\(30\) 993821. 1.22694
\(31\) 888002.i 0.961539i 0.876847 + 0.480770i \(0.159643\pi\)
−0.876847 + 0.480770i \(0.840357\pi\)
\(32\) 185364.i 0.176777i
\(33\) 373025.i 0.314544i
\(34\) 580591.i 0.434465i
\(35\) −3.31641e6 −2.21002
\(36\) −100388. −0.0597683
\(37\) 2.53247e6i 1.35125i 0.737243 + 0.675627i \(0.236127\pi\)
−0.737243 + 0.675627i \(0.763873\pi\)
\(38\) 1.01871e6 1.06589e6i 0.488560 0.511184i
\(39\) −3.16778e6 −1.36929
\(40\) 1.67370e6i 0.653789i
\(41\) 3.37210e6i 1.19334i −0.802485 0.596672i \(-0.796489\pi\)
0.802485 0.596672i \(-0.203511\pi\)
\(42\) −2.46747e6 −0.792966
\(43\) 3.46074e6 1.01227 0.506134 0.862455i \(-0.331074\pi\)
0.506134 + 0.862455i \(0.331074\pi\)
\(44\) 628213. 0.167608
\(45\) 906428. 0.221046
\(46\) 1.00173e6i 0.223728i
\(47\) −5.32862e6 −1.09200 −0.546001 0.837785i \(-0.683850\pi\)
−0.546001 + 0.837785i \(0.683850\pi\)
\(48\) 1.24526e6i 0.234583i
\(49\) 2.46922e6 0.428327
\(50\) 1.06929e7i 1.71086i
\(51\) 3.90037e6i 0.576535i
\(52\) 5.33487e6i 0.729644i
\(53\) 7.74166e6i 0.981139i −0.871402 0.490569i \(-0.836789\pi\)
0.871402 0.490569i \(-0.163211\pi\)
\(54\) 6.31617e6 0.742812
\(55\) −5.67230e6 −0.619881
\(56\) 4.15548e6i 0.422541i
\(57\) −6.84366e6 + 7.16056e6i −0.648319 + 0.678341i
\(58\) 2.04428e6 0.180646
\(59\) 1.04388e7i 0.861473i −0.902478 0.430737i \(-0.858254\pi\)
0.902478 0.430737i \(-0.141746\pi\)
\(60\) 1.12438e7i 0.867578i
\(61\) −1.38848e7 −1.00281 −0.501406 0.865212i \(-0.667184\pi\)
−0.501406 + 0.865212i \(0.667184\pi\)
\(62\) 1.00466e7 0.679911
\(63\) −2.25049e6 −0.142861
\(64\) −2.09715e6 −0.125000
\(65\) 4.81700e7i 2.69851i
\(66\) −4.22029e6 −0.222416
\(67\) 1.81780e7i 0.902082i −0.892503 0.451041i \(-0.851053\pi\)
0.892503 0.451041i \(-0.148947\pi\)
\(68\) −6.56864e6 −0.307213
\(69\) 6.72957e6i 0.296887i
\(70\) 3.75209e7i 1.56272i
\(71\) 1.83448e7i 0.721904i −0.932584 0.360952i \(-0.882452\pi\)
0.932584 0.360952i \(-0.117548\pi\)
\(72\) 1.13576e6i 0.0422626i
\(73\) 4.49830e7 1.58401 0.792004 0.610516i \(-0.209038\pi\)
0.792004 + 0.610516i \(0.209038\pi\)
\(74\) 2.86516e7 0.955481
\(75\) 7.18340e7i 2.27031i
\(76\) −1.20591e7 1.15254e7i −0.361462 0.345464i
\(77\) 1.40832e7 0.400627
\(78\) 3.58393e7i 0.968236i
\(79\) 5.30791e7i 1.36275i −0.731935 0.681374i \(-0.761383\pi\)
0.731935 0.681374i \(-0.238617\pi\)
\(80\) 1.89358e7 0.462299
\(81\) −3.72860e7 −0.866174
\(82\) −3.81510e7 −0.843822
\(83\) 1.92972e7 0.406613 0.203307 0.979115i \(-0.434831\pi\)
0.203307 + 0.979115i \(0.434831\pi\)
\(84\) 2.79162e7i 0.560712i
\(85\) 5.93100e7 1.13619
\(86\) 3.91539e7i 0.715782i
\(87\) −1.37333e7 −0.239717
\(88\) 7.10741e6i 0.118517i
\(89\) 2.43432e7i 0.387987i 0.981003 + 0.193993i \(0.0621440\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(90\) 1.02551e7i 0.156303i
\(91\) 1.19597e8i 1.74403i
\(92\) 1.13333e7 0.158200
\(93\) −6.74923e7 −0.902241
\(94\) 6.02865e7i 0.772162i
\(95\) 1.08885e8 + 1.04066e8i 1.33683 + 1.27766i
\(96\) 1.40885e7 0.165875
\(97\) 7.02129e7i 0.793103i 0.918012 + 0.396552i \(0.129793\pi\)
−0.918012 + 0.396552i \(0.870207\pi\)
\(98\) 2.79360e7i 0.302873i
\(99\) −3.84917e6 −0.0400707
\(100\) −1.20976e8 −1.20976
\(101\) 1.09928e8 1.05638 0.528192 0.849125i \(-0.322870\pi\)
0.528192 + 0.849125i \(0.322870\pi\)
\(102\) 4.41277e7 0.407671
\(103\) 1.98935e8i 1.76751i 0.467946 + 0.883757i \(0.344994\pi\)
−0.467946 + 0.883757i \(0.655006\pi\)
\(104\) −6.03572e7 −0.515936
\(105\) 2.52063e8i 2.07373i
\(106\) −8.75869e7 −0.693770
\(107\) 1.82276e8i 1.39057i −0.718732 0.695287i \(-0.755277\pi\)
0.718732 0.695287i \(-0.244723\pi\)
\(108\) 7.14593e7i 0.525247i
\(109\) 1.88301e8i 1.33397i −0.745070 0.666987i \(-0.767584\pi\)
0.745070 0.666987i \(-0.232416\pi\)
\(110\) 6.41748e7i 0.438322i
\(111\) −1.92480e8 −1.26792
\(112\) −4.70139e7 −0.298782
\(113\) 1.54544e8i 0.947847i −0.880566 0.473923i \(-0.842837\pi\)
0.880566 0.473923i \(-0.157163\pi\)
\(114\) 8.10125e7 + 7.74271e7i 0.479659 + 0.458431i
\(115\) −1.02332e8 −0.585084
\(116\) 2.31283e7i 0.127736i
\(117\) 3.26877e7i 0.174438i
\(118\) −1.18101e8 −0.609153
\(119\) −1.47255e8 −0.734317
\(120\) −1.27209e8 −0.613470
\(121\) −1.90271e8 −0.887630
\(122\) 1.57088e8i 0.709096i
\(123\) 2.56296e8 1.11975
\(124\) 1.13664e8i 0.480770i
\(125\) 6.40862e8 2.62497
\(126\) 2.54614e7i 0.101018i
\(127\) 4.44809e6i 0.0170985i −0.999963 0.00854926i \(-0.997279\pi\)
0.999963 0.00854926i \(-0.00272135\pi\)
\(128\) 2.37266e7i 0.0883883i
\(129\) 2.63033e8i 0.949842i
\(130\) 5.44982e8 1.90813
\(131\) −4.41022e8 −1.49753 −0.748764 0.662837i \(-0.769352\pi\)
−0.748764 + 0.662837i \(0.769352\pi\)
\(132\) 4.77471e7i 0.157272i
\(133\) −2.70341e8 2.58377e8i −0.863984 0.825747i
\(134\) −2.05660e8 −0.637868
\(135\) 6.45226e8i 1.94257i
\(136\) 7.43157e7i 0.217232i
\(137\) −5.19418e8 −1.47447 −0.737233 0.675639i \(-0.763868\pi\)
−0.737233 + 0.675639i \(0.763868\pi\)
\(138\) −7.61364e7 −0.209931
\(139\) 2.29949e8 0.615987 0.307994 0.951388i \(-0.400342\pi\)
0.307994 + 0.951388i \(0.400342\pi\)
\(140\) 4.24501e8 1.10501
\(141\) 4.05000e8i 1.02466i
\(142\) −2.07548e8 −0.510463
\(143\) 2.04555e8i 0.489178i
\(144\) 1.28496e7 0.0298841
\(145\) 2.08832e8i 0.472417i
\(146\) 5.08925e8i 1.12006i
\(147\) 1.87672e8i 0.401912i
\(148\) 3.24156e8i 0.675627i
\(149\) 9.23988e8 1.87465 0.937327 0.348451i \(-0.113292\pi\)
0.937327 + 0.348451i \(0.113292\pi\)
\(150\) 8.12709e8 1.60535
\(151\) 5.06741e8i 0.974717i 0.873202 + 0.487358i \(0.162039\pi\)
−0.873202 + 0.487358i \(0.837961\pi\)
\(152\) −1.30395e8 + 1.36434e8i −0.244280 + 0.255592i
\(153\) 4.02472e7 0.0734464
\(154\) 1.59334e8i 0.283286i
\(155\) 1.02631e9i 1.77807i
\(156\) 4.05476e8 0.684647
\(157\) 5.44968e7 0.0896958 0.0448479 0.998994i \(-0.485720\pi\)
0.0448479 + 0.998994i \(0.485720\pi\)
\(158\) −6.00522e8 −0.963608
\(159\) 5.88403e8 0.920632
\(160\) 2.14234e8i 0.326895i
\(161\) 2.54070e8 0.378137
\(162\) 4.21843e8i 0.612478i
\(163\) 1.07938e8 0.152905 0.0764527 0.997073i \(-0.475641\pi\)
0.0764527 + 0.997073i \(0.475641\pi\)
\(164\) 4.31629e8i 0.596672i
\(165\) 4.31122e8i 0.581653i
\(166\) 2.18323e8i 0.287519i
\(167\) 5.79071e8i 0.744502i 0.928132 + 0.372251i \(0.121414\pi\)
−0.928132 + 0.372251i \(0.878586\pi\)
\(168\) 3.15836e8 0.396483
\(169\) −9.21383e8 −1.12952
\(170\) 6.71016e8i 0.803410i
\(171\) 7.38886e7 + 7.06185e7i 0.0864157 + 0.0825912i
\(172\) −4.42975e8 −0.506134
\(173\) 1.19382e9i 1.33277i −0.745608 0.666385i \(-0.767841\pi\)
0.745608 0.666385i \(-0.232159\pi\)
\(174\) 1.55375e8i 0.169505i
\(175\) −2.71204e9 −2.89163
\(176\) −8.04112e7 −0.0838042
\(177\) 7.93397e8 0.808346
\(178\) 2.75411e8 0.274348
\(179\) 1.06451e9i 1.03690i −0.855108 0.518450i \(-0.826509\pi\)
0.855108 0.518450i \(-0.173491\pi\)
\(180\) −1.16023e8 −0.110523
\(181\) 1.76596e9i 1.64539i 0.568486 + 0.822693i \(0.307529\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(182\) −1.35309e9 −1.23322
\(183\) 1.05531e9i 0.940969i
\(184\) 1.28222e8i 0.111864i
\(185\) 2.92689e9i 2.49873i
\(186\) 7.63589e8i 0.637981i
\(187\) −2.51862e8 −0.205966
\(188\) 6.82063e8 0.546001
\(189\) 1.60197e9i 1.25547i
\(190\) 1.17738e9 1.23190e9i 0.903443 0.945278i
\(191\) −2.47773e8 −0.186175 −0.0930874 0.995658i \(-0.529674\pi\)
−0.0930874 + 0.995658i \(0.529674\pi\)
\(192\) 1.59393e8i 0.117291i
\(193\) 1.04978e9i 0.756607i −0.925682 0.378304i \(-0.876508\pi\)
0.925682 0.378304i \(-0.123492\pi\)
\(194\) 7.94368e8 0.560809
\(195\) −3.66115e9 −2.53209
\(196\) −3.16060e8 −0.214163
\(197\) −4.22634e8 −0.280608 −0.140304 0.990108i \(-0.544808\pi\)
−0.140304 + 0.990108i \(0.544808\pi\)
\(198\) 4.35484e7i 0.0283342i
\(199\) 1.95755e9 1.24825 0.624124 0.781325i \(-0.285456\pi\)
0.624124 + 0.781325i \(0.285456\pi\)
\(200\) 1.36869e9i 0.855430i
\(201\) 1.38161e9 0.846450
\(202\) 1.24369e9i 0.746976i
\(203\) 5.18490e8i 0.305321i
\(204\) 4.99248e8i 0.288267i
\(205\) 3.89730e9i 2.20673i
\(206\) 2.25070e9 1.24982
\(207\) −6.94413e7 −0.0378213
\(208\) 6.82864e8i 0.364822i
\(209\) −4.62384e8 4.41921e8i −0.242336 0.231611i
\(210\) −2.85177e9 −1.46635
\(211\) 2.40016e9i 1.21091i −0.795881 0.605453i \(-0.792992\pi\)
0.795881 0.605453i \(-0.207008\pi\)
\(212\) 9.90932e8i 0.490569i
\(213\) 1.39429e9 0.677384
\(214\) −2.06222e9 −0.983284
\(215\) 3.99974e9 1.87188
\(216\) −8.08470e8 −0.371406
\(217\) 2.54812e9i 1.14916i
\(218\) −2.13039e9 −0.943262
\(219\) 3.41892e9i 1.48632i
\(220\) 7.26055e8 0.309941
\(221\) 2.13885e9i 0.896624i
\(222\) 2.17766e9i 0.896557i
\(223\) 1.31765e8i 0.0532819i −0.999645 0.0266409i \(-0.991519\pi\)
0.999645 0.0266409i \(-0.00848107\pi\)
\(224\) 5.31901e8i 0.211270i
\(225\) 7.41243e8 0.289221
\(226\) −1.74846e9 −0.670229
\(227\) 2.48274e9i 0.935035i 0.883984 + 0.467517i \(0.154851\pi\)
−0.883984 + 0.467517i \(0.845149\pi\)
\(228\) 8.75988e8 9.16552e8i 0.324160 0.339170i
\(229\) 3.34493e9 1.21631 0.608156 0.793818i \(-0.291910\pi\)
0.608156 + 0.793818i \(0.291910\pi\)
\(230\) 1.15775e9i 0.413717i
\(231\) 1.07039e9i 0.375920i
\(232\) −2.61667e8 −0.0903228
\(233\) 1.23387e9 0.418644 0.209322 0.977847i \(-0.432874\pi\)
0.209322 + 0.977847i \(0.432874\pi\)
\(234\) 3.69820e8 0.123346
\(235\) −6.15854e9 −2.01932
\(236\) 1.33616e9i 0.430737i
\(237\) 4.03427e9 1.27871
\(238\) 1.66601e9i 0.519240i
\(239\) 1.00656e9 0.308496 0.154248 0.988032i \(-0.450705\pi\)
0.154248 + 0.988032i \(0.450705\pi\)
\(240\) 1.43921e9i 0.433789i
\(241\) 2.78434e9i 0.825380i 0.910871 + 0.412690i \(0.135411\pi\)
−0.910871 + 0.412690i \(0.864589\pi\)
\(242\) 2.15267e9i 0.627649i
\(243\) 8.28939e8i 0.237737i
\(244\) 1.77725e9 0.501406
\(245\) 2.85379e9 0.792060
\(246\) 2.89966e9i 0.791783i
\(247\) −3.75285e9 + 3.92664e9i −1.00826 + 1.05495i
\(248\) −1.28596e9 −0.339955
\(249\) 1.46668e9i 0.381537i
\(250\) 7.25053e9i 1.85614i
\(251\) −3.39707e9 −0.855873 −0.427936 0.903809i \(-0.640759\pi\)
−0.427936 + 0.903809i \(0.640759\pi\)
\(252\) 2.88062e8 0.0714306
\(253\) 4.34554e8 0.106062
\(254\) −5.03244e7 −0.0120905
\(255\) 4.50784e9i 1.06612i
\(256\) 2.68435e8 0.0625000
\(257\) 1.08377e9i 0.248430i −0.992255 0.124215i \(-0.960359\pi\)
0.992255 0.124215i \(-0.0396412\pi\)
\(258\) 2.97588e9 0.671640
\(259\) 7.26691e9i 1.61492i
\(260\) 6.16576e9i 1.34925i
\(261\) 1.41712e8i 0.0305382i
\(262\) 4.98959e9i 1.05891i
\(263\) 3.42971e9 0.716860 0.358430 0.933557i \(-0.383312\pi\)
0.358430 + 0.933557i \(0.383312\pi\)
\(264\) 5.40197e8 0.111208
\(265\) 8.94740e9i 1.81432i
\(266\) −2.92320e9 + 3.05856e9i −0.583891 + 0.610929i
\(267\) −1.85020e9 −0.364060
\(268\) 2.32678e9i 0.451041i
\(269\) 3.38539e9i 0.646547i −0.946306 0.323273i \(-0.895217\pi\)
0.946306 0.323273i \(-0.104783\pi\)
\(270\) 7.29990e9 1.37360
\(271\) 2.23995e9 0.415299 0.207650 0.978203i \(-0.433419\pi\)
0.207650 + 0.978203i \(0.433419\pi\)
\(272\) 8.40786e8 0.153607
\(273\) 9.08994e9 1.63648
\(274\) 5.87654e9i 1.04260i
\(275\) −4.63859e9 −0.811065
\(276\) 8.61386e8i 0.148444i
\(277\) −7.70540e9 −1.30881 −0.654404 0.756145i \(-0.727081\pi\)
−0.654404 + 0.756145i \(0.727081\pi\)
\(278\) 2.60157e9i 0.435569i
\(279\) 6.96441e8i 0.114939i
\(280\) 4.80268e9i 0.781361i
\(281\) 9.53553e9i 1.52939i −0.644390 0.764697i \(-0.722888\pi\)
0.644390 0.764697i \(-0.277112\pi\)
\(282\) −4.58206e9 −0.724543
\(283\) 9.62545e9 1.50064 0.750318 0.661077i \(-0.229900\pi\)
0.750318 + 0.661077i \(0.229900\pi\)
\(284\) 2.34813e9i 0.360952i
\(285\) −7.90953e9 + 8.27580e9i −1.19887 + 1.25438i
\(286\) −2.31428e9 −0.345901
\(287\) 9.67625e9i 1.42620i
\(288\) 1.45377e8i 0.0211313i
\(289\) −4.34227e9 −0.622481
\(290\) 2.36266e9 0.334049
\(291\) −5.33651e9 −0.744193
\(292\) −5.75783e9 −0.792004
\(293\) 1.32147e9i 0.179303i 0.995973 + 0.0896515i \(0.0285753\pi\)
−0.995973 + 0.0896515i \(0.971425\pi\)
\(294\) 2.12327e9 0.284195
\(295\) 1.20646e10i 1.59303i
\(296\) −3.66741e9 −0.477741
\(297\) 2.73997e9i 0.352144i
\(298\) 1.04537e10i 1.32558i
\(299\) 3.69029e9i 0.461717i
\(300\) 9.19476e9i 1.13516i
\(301\) −9.93060e9 −1.20979
\(302\) 5.73312e9 0.689229
\(303\) 8.35503e9i 0.991237i
\(304\) 1.54357e9 + 1.47526e9i 0.180731 + 0.172732i
\(305\) −1.60473e10 −1.85440
\(306\) 4.55346e8i 0.0519344i
\(307\) 6.27589e9i 0.706516i 0.935526 + 0.353258i \(0.114926\pi\)
−0.935526 + 0.353258i \(0.885074\pi\)
\(308\) −1.80265e9 −0.200313
\(309\) −1.51200e10 −1.65851
\(310\) 1.16113e10 1.25729
\(311\) −6.55650e7 −0.00700859 −0.00350429 0.999994i \(-0.501115\pi\)
−0.00350429 + 0.999994i \(0.501115\pi\)
\(312\) 4.58743e9i 0.484118i
\(313\) 4.03513e9 0.420417 0.210208 0.977657i \(-0.432586\pi\)
0.210208 + 0.977657i \(0.432586\pi\)
\(314\) 6.16561e8i 0.0634245i
\(315\) −2.60099e9 −0.264178
\(316\) 6.79413e9i 0.681374i
\(317\) 9.49658e8i 0.0940438i 0.998894 + 0.0470219i \(0.0149731\pi\)
−0.998894 + 0.0470219i \(0.985027\pi\)
\(318\) 6.65702e9i 0.650985i
\(319\) 8.86811e8i 0.0856384i
\(320\) −2.42378e9 −0.231149
\(321\) 1.38538e10 1.30482
\(322\) 2.87447e9i 0.267383i
\(323\) 4.83473e9 + 4.62075e9i 0.444183 + 0.424525i
\(324\) 4.77260e9 0.433087
\(325\) 3.93916e10i 3.53078i
\(326\) 1.22118e9i 0.108120i
\(327\) 1.43118e10 1.25171
\(328\) 4.88333e9 0.421911
\(329\) 1.52905e10 1.30508
\(330\) −4.87759e9 −0.411291
\(331\) 6.32042e9i 0.526543i −0.964722 0.263272i \(-0.915198\pi\)
0.964722 0.263272i \(-0.0848015\pi\)
\(332\) −2.47004e9 −0.203307
\(333\) 1.98616e9i 0.161524i
\(334\) 6.55144e9 0.526443
\(335\) 2.10091e10i 1.66812i
\(336\) 3.57328e9i 0.280356i
\(337\) 6.66861e9i 0.517030i 0.966007 + 0.258515i \(0.0832332\pi\)
−0.966007 + 0.258515i \(0.916767\pi\)
\(338\) 1.04243e10i 0.798691i
\(339\) 1.17461e10 0.889393
\(340\) −7.59168e9 −0.568097
\(341\) 4.35823e9i 0.322324i
\(342\) 7.98957e8 8.35954e8i 0.0584008 0.0611051i
\(343\) 9.45667e9 0.683222
\(344\) 5.01169e9i 0.357891i
\(345\) 7.77768e9i 0.549002i
\(346\) −1.35066e10 −0.942411
\(347\) 2.52011e10 1.73821 0.869103 0.494632i \(-0.164697\pi\)
0.869103 + 0.494632i \(0.164697\pi\)
\(348\) 1.75786e9 0.119858
\(349\) −2.93228e10 −1.97653 −0.988267 0.152736i \(-0.951192\pi\)
−0.988267 + 0.152736i \(0.951192\pi\)
\(350\) 3.06832e10i 2.04469i
\(351\) −2.32682e10 −1.53297
\(352\) 9.09749e8i 0.0592585i
\(353\) −4.05561e9 −0.261191 −0.130595 0.991436i \(-0.541689\pi\)
−0.130595 + 0.991436i \(0.541689\pi\)
\(354\) 8.97626e9i 0.571587i
\(355\) 2.12019e10i 1.33494i
\(356\) 3.11592e9i 0.193993i
\(357\) 1.11921e10i 0.689032i
\(358\) −1.20435e10 −0.733199
\(359\) −9.40026e9 −0.565929 −0.282965 0.959130i \(-0.591318\pi\)
−0.282965 + 0.959130i \(0.591318\pi\)
\(360\) 1.31265e9i 0.0781517i
\(361\) 7.68260e8 + 1.69662e10i 0.0452355 + 0.998976i
\(362\) 1.99796e10 1.16346
\(363\) 1.44615e10i 0.832890i
\(364\) 1.53084e10i 0.872016i
\(365\) 5.19890e10 2.92914
\(366\) −1.19395e10 −0.665366
\(367\) −2.66414e9 −0.146856 −0.0734281 0.997301i \(-0.523394\pi\)
−0.0734281 + 0.997301i \(0.523394\pi\)
\(368\) −1.45066e9 −0.0790998
\(369\) 2.64467e9i 0.142648i
\(370\) 3.31140e10 1.76687
\(371\) 2.22147e10i 1.17258i
\(372\) 8.63902e9 0.451121
\(373\) 1.71702e10i 0.887035i −0.896266 0.443517i \(-0.853730\pi\)
0.896266 0.443517i \(-0.146270\pi\)
\(374\) 2.84949e9i 0.145640i
\(375\) 4.87086e10i 2.46309i
\(376\) 7.71667e9i 0.386081i
\(377\) −7.53093e9 −0.372806
\(378\) −1.81242e10 −0.887754
\(379\) 9.05015e9i 0.438631i 0.975654 + 0.219315i \(0.0703823\pi\)
−0.975654 + 0.219315i \(0.929618\pi\)
\(380\) −1.39373e10 1.33205e10i −0.668413 0.638831i
\(381\) 3.38076e8 0.0160441
\(382\) 2.80323e9i 0.131645i
\(383\) 9.57995e9i 0.445213i 0.974908 + 0.222607i \(0.0714566\pi\)
−0.974908 + 0.222607i \(0.928543\pi\)
\(384\) −1.80333e9 −0.0829375
\(385\) 1.62767e10 0.740837
\(386\) −1.18769e10 −0.535002
\(387\) 2.71419e9 0.121003
\(388\) 8.98725e9i 0.396552i
\(389\) −2.19375e10 −0.958053 −0.479026 0.877800i \(-0.659010\pi\)
−0.479026 + 0.877800i \(0.659010\pi\)
\(390\) 4.14212e10i 1.79046i
\(391\) −4.54373e9 −0.194404
\(392\) 3.57581e9i 0.151436i
\(393\) 3.35197e10i 1.40517i
\(394\) 4.78156e9i 0.198420i
\(395\) 6.13460e10i 2.51999i
\(396\) 4.92694e8 0.0200353
\(397\) 5.05069e9 0.203324 0.101662 0.994819i \(-0.467584\pi\)
0.101662 + 0.994819i \(0.467584\pi\)
\(398\) 2.21472e10i 0.882644i
\(399\) 1.96379e10 2.05472e10i 0.774823 0.810703i
\(400\) 1.54849e10 0.604880
\(401\) 2.54035e10i 0.982464i −0.871029 0.491232i \(-0.836547\pi\)
0.871029 0.491232i \(-0.163453\pi\)
\(402\) 1.56311e10i 0.598531i
\(403\) −3.70108e10 −1.40316
\(404\) −1.40707e10 −0.528192
\(405\) −4.30931e10 −1.60173
\(406\) −5.86604e9 −0.215894
\(407\) 1.24291e10i 0.452963i
\(408\) −5.64834e9 −0.203836
\(409\) 4.77621e10i 1.70683i 0.521231 + 0.853415i \(0.325473\pi\)
−0.521231 + 0.853415i \(0.674527\pi\)
\(410\) −4.40929e10 −1.56039
\(411\) 3.94782e10i 1.38354i
\(412\) 2.54637e10i 0.883757i
\(413\) 2.99541e10i 1.02957i
\(414\) 7.85638e8i 0.0267437i
\(415\) 2.23026e10 0.751907
\(416\) 7.72572e9 0.257968
\(417\) 1.74772e10i 0.578000i
\(418\) −4.99976e9 + 5.23128e9i −0.163774 + 0.171357i
\(419\) −3.91913e10 −1.27155 −0.635775 0.771874i \(-0.719320\pi\)
−0.635775 + 0.771874i \(0.719320\pi\)
\(420\) 3.22641e10i 1.03686i
\(421\) 1.27758e10i 0.406685i 0.979108 + 0.203342i \(0.0651805\pi\)
−0.979108 + 0.203342i \(0.934820\pi\)
\(422\) −2.71547e10 −0.856240
\(423\) −4.17913e9 −0.130534
\(424\) 1.12111e10 0.346885
\(425\) 4.85015e10 1.48662
\(426\) 1.57746e10i 0.478983i
\(427\) 3.98424e10 1.19849
\(428\) 2.33313e10i 0.695287i
\(429\) 1.55472e10 0.459010
\(430\) 4.52519e10i 1.32362i
\(431\) 3.52399e10i 1.02123i −0.859808 0.510617i \(-0.829417\pi\)
0.859808 0.510617i \(-0.170583\pi\)
\(432\) 9.14679e9i 0.262624i
\(433\) 8.20445e9i 0.233398i 0.993167 + 0.116699i \(0.0372313\pi\)
−0.993167 + 0.116699i \(0.962769\pi\)
\(434\) −2.88287e10 −0.812580
\(435\) −1.58722e10 −0.443283
\(436\) 2.41026e10i 0.666987i
\(437\) −8.34168e9 7.97250e9i −0.228732 0.218609i
\(438\) 3.86807e10 1.05099
\(439\) 6.65038e7i 0.00179056i −1.00000 0.000895279i \(-0.999715\pi\)
1.00000 0.000895279i \(-0.000284976\pi\)
\(440\) 8.21437e9i 0.219161i
\(441\) 1.93656e9 0.0512007
\(442\) 2.41983e10 0.634009
\(443\) 8.14225e9 0.211412 0.105706 0.994397i \(-0.466290\pi\)
0.105706 + 0.994397i \(0.466290\pi\)
\(444\) 2.46374e10 0.633961
\(445\) 2.81345e10i 0.717463i
\(446\) −1.49075e9 −0.0376760
\(447\) 7.02275e10i 1.75904i
\(448\) 6.01777e9 0.149391
\(449\) 9.39424e9i 0.231141i −0.993299 0.115570i \(-0.963130\pi\)
0.993299 0.115570i \(-0.0368695\pi\)
\(450\) 8.38620e9i 0.204510i
\(451\) 1.65500e10i 0.400029i
\(452\) 1.97816e10i 0.473923i
\(453\) −3.85147e10 −0.914606
\(454\) 2.80890e10 0.661169
\(455\) 1.38224e11i 3.22506i
\(456\) −1.03696e10 9.91067e9i −0.239830 0.229215i
\(457\) −3.13612e10 −0.718998 −0.359499 0.933145i \(-0.617052\pi\)
−0.359499 + 0.933145i \(0.617052\pi\)
\(458\) 3.78435e10i 0.860062i
\(459\) 2.86493e10i 0.645451i
\(460\) 1.30984e10 0.292542
\(461\) 2.63379e9 0.0583146 0.0291573 0.999575i \(-0.490718\pi\)
0.0291573 + 0.999575i \(0.490718\pi\)
\(462\) 1.21101e10 0.265816
\(463\) 8.85572e10 1.92708 0.963540 0.267563i \(-0.0862182\pi\)
0.963540 + 0.267563i \(0.0862182\pi\)
\(464\) 2.96043e9i 0.0638679i
\(465\) −7.80041e10 −1.66842
\(466\) 1.39596e10i 0.296026i
\(467\) 3.29979e10 0.693775 0.346887 0.937907i \(-0.387239\pi\)
0.346887 + 0.937907i \(0.387239\pi\)
\(468\) 4.18403e9i 0.0872191i
\(469\) 5.21616e10i 1.07810i
\(470\) 6.96759e10i 1.42788i
\(471\) 4.14201e9i 0.0841643i
\(472\) 1.51170e10 0.304577
\(473\) −1.69850e10 −0.339330
\(474\) 4.56425e10i 0.904183i
\(475\) 8.90422e10 + 8.51015e10i 1.74913 + 1.67172i
\(476\) 1.88487e10 0.367158
\(477\) 6.07162e9i 0.117282i
\(478\) 1.13880e10i 0.218140i
\(479\) −4.27389e10 −0.811860 −0.405930 0.913904i \(-0.633052\pi\)
−0.405930 + 0.913904i \(0.633052\pi\)
\(480\) 1.62828e10 0.306735
\(481\) −1.05550e11 −1.97187
\(482\) 3.15012e10 0.583632
\(483\) 1.93105e10i 0.354817i
\(484\) 2.43547e10 0.443815
\(485\) 8.11483e10i 1.46660i
\(486\) 9.37837e9 0.168106
\(487\) 2.99875e10i 0.533119i −0.963818 0.266559i \(-0.914113\pi\)
0.963818 0.266559i \(-0.0858869\pi\)
\(488\) 2.01073e10i 0.354548i
\(489\) 8.20378e9i 0.143476i
\(490\) 3.22870e10i 0.560071i
\(491\) 1.26087e10 0.216942 0.108471 0.994100i \(-0.465405\pi\)
0.108471 + 0.994100i \(0.465405\pi\)
\(492\) −3.28059e10 −0.559875
\(493\) 9.27256e9i 0.156968i
\(494\) 4.44248e10 + 4.24587e10i 0.745964 + 0.712950i
\(495\) −4.44867e9 −0.0740985
\(496\) 1.45490e10i 0.240385i
\(497\) 5.26403e10i 0.862766i
\(498\) 1.65936e10 0.269788
\(499\) 3.70124e10 0.596960 0.298480 0.954416i \(-0.403520\pi\)
0.298480 + 0.954416i \(0.403520\pi\)
\(500\) −8.20304e10 −1.31249
\(501\) −4.40121e10 −0.698589
\(502\) 3.84334e10i 0.605193i
\(503\) −2.48541e10 −0.388264 −0.194132 0.980975i \(-0.562189\pi\)
−0.194132 + 0.980975i \(0.562189\pi\)
\(504\) 3.25905e9i 0.0505091i
\(505\) 1.27049e11 1.95346
\(506\) 4.91642e9i 0.0749974i
\(507\) 7.00295e10i 1.05986i
\(508\) 5.69355e8i 0.00854926i
\(509\) 4.24098e10i 0.631822i −0.948789 0.315911i \(-0.897690\pi\)
0.948789 0.315911i \(-0.102310\pi\)
\(510\) 5.10004e10 0.753864
\(511\) −1.29079e11 −1.89309
\(512\) 3.03700e9i 0.0441942i
\(513\) −5.02686e10 + 5.25963e10i −0.725817 + 0.759427i
\(514\) −1.22614e10 −0.175666
\(515\) 2.29919e11i 3.26848i
\(516\) 3.36682e10i 0.474921i
\(517\) 2.61524e10 0.366057
\(518\) −8.22157e10 −1.14192
\(519\) 9.07362e10 1.25058
\(520\) −6.97576e10 −0.954066
\(521\) 6.28514e10i 0.853030i −0.904481 0.426515i \(-0.859741\pi\)
0.904481 0.426515i \(-0.140259\pi\)
\(522\) 1.60328e9 0.0215938
\(523\) 2.26507e10i 0.302743i −0.988477 0.151372i \(-0.951631\pi\)
0.988477 0.151372i \(-0.0483690\pi\)
\(524\) 5.64508e10 0.748764
\(525\) 2.06128e11i 2.71331i
\(526\) 3.88027e10i 0.506896i
\(527\) 4.55700e10i 0.590795i
\(528\) 6.11163e9i 0.0786360i
\(529\) −7.04714e10 −0.899891
\(530\) −1.01228e11 −1.28292
\(531\) 8.18692e9i 0.102978i
\(532\) 3.46037e10 + 3.30722e10i 0.431992 + 0.412873i
\(533\) 1.40545e11 1.74143
\(534\) 2.09326e10i 0.257429i
\(535\) 2.10665e11i 2.57144i
\(536\) 2.63245e10 0.318934
\(537\) 8.09076e10 0.972954
\(538\) −3.83013e10 −0.457178
\(539\) −1.21187e10 −0.143582
\(540\) 8.25889e10i 0.971285i
\(541\) 6.24255e10 0.728740 0.364370 0.931254i \(-0.381284\pi\)
0.364370 + 0.931254i \(0.381284\pi\)
\(542\) 2.53421e10i 0.293661i
\(543\) −1.34222e11 −1.54392
\(544\) 9.51240e9i 0.108616i
\(545\) 2.17629e11i 2.46678i
\(546\) 1.02841e11i 1.15716i
\(547\) 5.38177e10i 0.601141i −0.953760 0.300570i \(-0.902823\pi\)
0.953760 0.300570i \(-0.0971770\pi\)
\(548\) 6.64855e10 0.737233
\(549\) −1.08895e10 −0.119873
\(550\) 5.24797e10i 0.573509i
\(551\) −1.62698e10 + 1.70232e10i −0.176513 + 0.184686i
\(552\) 9.74546e9 0.104965
\(553\) 1.52310e11i 1.62866i
\(554\) 8.71767e10i 0.925467i
\(555\) −2.22458e11 −2.34464
\(556\) −2.94334e10 −0.307994
\(557\) 3.66646e10 0.380913 0.190457 0.981696i \(-0.439003\pi\)
0.190457 + 0.981696i \(0.439003\pi\)
\(558\) 7.87934e9 0.0812742
\(559\) 1.44239e11i 1.47719i
\(560\) −5.43361e10 −0.552505
\(561\) 1.91427e10i 0.193264i
\(562\) −1.07882e11 −1.08145
\(563\) 1.94465e11i 1.93557i 0.251780 + 0.967784i \(0.418984\pi\)
−0.251780 + 0.967784i \(0.581016\pi\)
\(564\) 5.18401e10i 0.512329i
\(565\) 1.78614e11i 1.75275i
\(566\) 1.08900e11i 1.06111i
\(567\) 1.06992e11 1.03519
\(568\) 2.65661e10 0.255231
\(569\) 1.32228e11i 1.26146i −0.776003 0.630730i \(-0.782756\pi\)
0.776003 0.630730i \(-0.217244\pi\)
\(570\) 9.36300e10 + 8.94862e10i 0.886983 + 0.847728i
\(571\) 3.62336e10 0.340853 0.170426 0.985370i \(-0.445485\pi\)
0.170426 + 0.985370i \(0.445485\pi\)
\(572\) 2.61831e10i 0.244589i
\(573\) 1.88319e10i 0.174693i
\(574\) 1.09474e11 1.00847
\(575\) −8.36829e10 −0.765535
\(576\) −1.64475e9 −0.0149421
\(577\) 9.54873e10 0.861475 0.430737 0.902477i \(-0.358254\pi\)
0.430737 + 0.902477i \(0.358254\pi\)
\(578\) 4.91272e10i 0.440160i
\(579\) 7.97885e10 0.709947
\(580\) 2.67305e10i 0.236208i
\(581\) −5.53732e10 −0.485954
\(582\) 6.03757e10i 0.526224i
\(583\) 3.79954e10i 0.328894i
\(584\) 6.51424e10i 0.560031i
\(585\) 3.77788e10i 0.322570i
\(586\) 1.49507e10 0.126786
\(587\) −1.95703e10 −0.164833 −0.0824167 0.996598i \(-0.526264\pi\)
−0.0824167 + 0.996598i \(0.526264\pi\)
\(588\) 2.40221e10i 0.200956i
\(589\) −7.99579e10 + 8.36605e10i −0.664355 + 0.695119i
\(590\) −1.36495e11 −1.12644
\(591\) 3.21222e10i 0.263303i
\(592\) 4.14920e10i 0.337814i
\(593\) 7.21741e10 0.583664 0.291832 0.956470i \(-0.405735\pi\)
0.291832 + 0.956470i \(0.405735\pi\)
\(594\) −3.09992e10 −0.249003
\(595\) −1.70190e11 −1.35789
\(596\) −1.18270e11 −0.937327
\(597\) 1.48783e11i 1.17127i
\(598\) −4.17509e10 −0.326484
\(599\) 2.60479e10i 0.202332i −0.994870 0.101166i \(-0.967743\pi\)
0.994870 0.101166i \(-0.0322573\pi\)
\(600\) −1.04027e11 −0.802676
\(601\) 2.01515e11i 1.54458i −0.635270 0.772290i \(-0.719111\pi\)
0.635270 0.772290i \(-0.280889\pi\)
\(602\) 1.12352e11i 0.855450i
\(603\) 1.42566e10i 0.107832i
\(604\) 6.48629e10i 0.487358i
\(605\) −2.19905e11 −1.64140
\(606\) 9.45263e10 0.700910
\(607\) 1.85499e11i 1.36643i 0.730219 + 0.683213i \(0.239418\pi\)
−0.730219 + 0.683213i \(0.760582\pi\)
\(608\) 1.66906e10 1.74635e10i 0.122140 0.127796i
\(609\) 3.94077e10 0.286492
\(610\) 1.81554e11i 1.31126i
\(611\) 2.22090e11i 1.59354i
\(612\) −5.15165e9 −0.0367232
\(613\) 1.64157e10 0.116257 0.0581283 0.998309i \(-0.481487\pi\)
0.0581283 + 0.998309i \(0.481487\pi\)
\(614\) 7.10036e10 0.499582
\(615\) 2.96213e11 2.07064
\(616\) 2.03947e10i 0.141643i
\(617\) 2.57869e11 1.77934 0.889669 0.456606i \(-0.150935\pi\)
0.889669 + 0.456606i \(0.150935\pi\)
\(618\) 1.71064e11i 1.17274i
\(619\) 1.58897e11 1.08231 0.541155 0.840923i \(-0.317987\pi\)
0.541155 + 0.840923i \(0.317987\pi\)
\(620\) 1.31367e11i 0.889037i
\(621\) 4.94306e10i 0.332376i
\(622\) 7.41783e8i 0.00495582i
\(623\) 6.98527e10i 0.463693i
\(624\) −5.19009e10 −0.342323
\(625\) 3.71485e11 2.43456
\(626\) 4.56522e10i 0.297279i
\(627\) 3.35881e10 3.51434e10i 0.217328 0.227391i
\(628\) −6.97559e9 −0.0448479
\(629\) 1.29960e11i 0.830246i
\(630\) 2.94269e10i 0.186802i
\(631\) −2.87396e11 −1.81285 −0.906427 0.422363i \(-0.861201\pi\)
−0.906427 + 0.422363i \(0.861201\pi\)
\(632\) 7.68668e10 0.481804
\(633\) 1.82424e11 1.13623
\(634\) 1.07442e10 0.0664990
\(635\) 5.14086e9i 0.0316185i
\(636\) −7.53155e10 −0.460316
\(637\) 1.02914e11i 0.625052i
\(638\) −1.00331e10 −0.0605555
\(639\) 1.43874e10i 0.0862939i
\(640\) 2.74219e10i 0.163447i
\(641\) 2.16808e11i 1.28423i 0.766608 + 0.642116i \(0.221943\pi\)
−0.766608 + 0.642116i \(0.778057\pi\)
\(642\) 1.56738e11i 0.922645i
\(643\) 1.00531e11 0.588107 0.294054 0.955789i \(-0.404996\pi\)
0.294054 + 0.955789i \(0.404996\pi\)
\(644\) −3.25209e10 −0.189069
\(645\) 3.04000e11i 1.75644i
\(646\) 5.22779e10 5.46987e10i 0.300184 0.314085i
\(647\) 1.18417e11 0.675766 0.337883 0.941188i \(-0.390289\pi\)
0.337883 + 0.941188i \(0.390289\pi\)
\(648\) 5.39959e10i 0.306239i
\(649\) 5.12326e10i 0.288780i
\(650\) 4.45665e11 2.49664
\(651\) 1.93669e11 1.07829
\(652\) −1.38160e10 −0.0764527
\(653\) −1.42936e11 −0.786119 −0.393059 0.919513i \(-0.628583\pi\)
−0.393059 + 0.919513i \(0.628583\pi\)
\(654\) 1.61919e11i 0.885091i
\(655\) −5.09709e11 −2.76922
\(656\) 5.52486e10i 0.298336i
\(657\) 3.52793e10 0.189347
\(658\) 1.72992e11i 0.922831i
\(659\) 1.65523e11i 0.877641i −0.898575 0.438821i \(-0.855396\pi\)
0.898575 0.438821i \(-0.144604\pi\)
\(660\) 5.51836e10i 0.290827i
\(661\) 1.29844e11i 0.680165i −0.940396 0.340083i \(-0.889545\pi\)
0.940396 0.340083i \(-0.110455\pi\)
\(662\) −7.15074e10 −0.372322
\(663\) −1.62562e11 −0.841329
\(664\) 2.79453e10i 0.143759i
\(665\) −3.12446e11 2.98618e11i −1.59768 1.52697i
\(666\) 2.24709e10 0.114215
\(667\) 1.59986e10i 0.0808310i
\(668\) 7.41211e10i 0.372251i
\(669\) 1.00147e10 0.0499960
\(670\) −2.37691e11 −1.17954
\(671\) 6.81453e10 0.336160
\(672\) −4.04270e10 −0.198241
\(673\) 4.76706e10i 0.232376i −0.993227 0.116188i \(-0.962933\pi\)
0.993227 0.116188i \(-0.0370674\pi\)
\(674\) 7.54468e10 0.365596
\(675\) 5.27641e11i 2.54170i
\(676\) 1.17937e11 0.564760
\(677\) 2.95654e11i 1.40744i 0.710480 + 0.703718i \(0.248478\pi\)
−0.710480 + 0.703718i \(0.751522\pi\)
\(678\) 1.32892e11i 0.628896i
\(679\) 2.01476e11i 0.947858i
\(680\) 8.58901e10i 0.401705i
\(681\) −1.88700e11 −0.877371
\(682\) −4.93078e10 −0.227918
\(683\) 1.73886e11i 0.799064i −0.916719 0.399532i \(-0.869173\pi\)
0.916719 0.399532i \(-0.130827\pi\)
\(684\) −9.45774e9 9.03916e9i −0.0432079 0.0412956i
\(685\) −6.00315e11 −2.72657
\(686\) 1.06990e11i 0.483111i
\(687\) 2.54230e11i 1.14130i
\(688\) 5.67008e10 0.253067
\(689\) 3.22662e11 1.43176
\(690\) −8.79944e10 −0.388203
\(691\) −3.55302e11 −1.55842 −0.779211 0.626761i \(-0.784380\pi\)
−0.779211 + 0.626761i \(0.784380\pi\)
\(692\) 1.52809e11i 0.666385i
\(693\) 1.10452e10 0.0478895
\(694\) 2.85118e11i 1.22910i
\(695\) 2.65763e11 1.13908
\(696\) 1.98880e10i 0.0847526i
\(697\) 1.73048e11i 0.733222i
\(698\) 3.31750e11i 1.39762i
\(699\) 9.37799e10i 0.392827i
\(700\) 3.47141e11 1.44582
\(701\) 3.34079e11 1.38350 0.691748 0.722139i \(-0.256841\pi\)
0.691748 + 0.722139i \(0.256841\pi\)
\(702\) 2.63250e11i 1.08398i
\(703\) −2.28030e11 + 2.38589e11i −0.933620 + 0.976853i
\(704\) 1.02926e10 0.0419021
\(705\) 4.68078e11i 1.89479i
\(706\) 4.58840e10i 0.184690i
\(707\) −3.15437e11 −1.26251
\(708\) −1.01555e11 −0.404173
\(709\) 3.05528e11 1.20911 0.604556 0.796563i \(-0.293351\pi\)
0.604556 + 0.796563i \(0.293351\pi\)
\(710\) −2.39872e11 −0.943945
\(711\) 4.16289e10i 0.162898i
\(712\) −3.52527e10 −0.137174
\(713\) 7.86250e10i 0.304230i
\(714\) −1.26624e11 −0.487219
\(715\) 2.36414e11i 0.904585i
\(716\) 1.36257e11i 0.518450i
\(717\) 7.65036e10i 0.289471i
\(718\) 1.06352e11i 0.400172i
\(719\) 9.46989e10 0.354347 0.177174 0.984180i \(-0.443305\pi\)
0.177174 + 0.984180i \(0.443305\pi\)
\(720\) 1.48509e10 0.0552616
\(721\) 5.70844e11i 2.11240i
\(722\) 1.91950e11 8.69187e9i 0.706383 0.0319863i
\(723\) −2.11623e11 −0.774479
\(724\) 2.26044e11i 0.822693i
\(725\) 1.70775e11i 0.618119i
\(726\) −1.63613e11 −0.588942
\(727\) −2.03292e11 −0.727752 −0.363876 0.931447i \(-0.618547\pi\)
−0.363876 + 0.931447i \(0.618547\pi\)
\(728\) 1.73195e11 0.616609
\(729\) −3.07637e11 −1.08925
\(730\) 5.88188e11i 2.07121i
\(731\) 1.77597e11 0.621964
\(732\) 1.35080e11i 0.470485i
\(733\) −2.58631e11 −0.895912 −0.447956 0.894056i \(-0.647848\pi\)
−0.447956 + 0.894056i \(0.647848\pi\)
\(734\) 3.01413e10i 0.103843i
\(735\) 2.16902e11i 0.743214i
\(736\) 1.64124e10i 0.0559320i
\(737\) 8.92158e10i 0.302393i
\(738\) −2.99210e10 −0.100868
\(739\) −7.22594e10 −0.242280 −0.121140 0.992635i \(-0.538655\pi\)
−0.121140 + 0.992635i \(0.538655\pi\)
\(740\) 3.74642e11i 1.24937i
\(741\) −2.98443e11 2.85235e11i −0.989894 0.946084i
\(742\) 2.51330e11 0.829143
\(743\) 4.17980e11i 1.37151i −0.727830 0.685757i \(-0.759471\pi\)
0.727830 0.685757i \(-0.240529\pi\)
\(744\) 9.77394e10i 0.318990i
\(745\) 1.06790e12 3.46660
\(746\) −1.94259e11 −0.627228
\(747\) 1.51344e10 0.0486051
\(748\) 3.22383e10 0.102983
\(749\) 5.23040e11i 1.66191i
\(750\) 5.51075e11 1.74167
\(751\) 1.85959e11i 0.584599i −0.956327 0.292299i \(-0.905580\pi\)
0.956327 0.292299i \(-0.0944204\pi\)
\(752\) −8.73041e10 −0.273000
\(753\) 2.58193e11i 0.803091i
\(754\) 8.52027e10i 0.263614i
\(755\) 5.85665e11i 1.80244i
\(756\) 2.05052e11i 0.627737i
\(757\) −4.78405e11 −1.45684 −0.728421 0.685130i \(-0.759746\pi\)
−0.728421 + 0.685130i \(0.759746\pi\)
\(758\) 1.02391e11 0.310159
\(759\) 3.30282e10i 0.0995216i
\(760\) −1.50704e11 + 1.57683e11i −0.451722 + 0.472639i
\(761\) 2.99794e10 0.0893891 0.0446946 0.999001i \(-0.485769\pi\)
0.0446946 + 0.999001i \(0.485769\pi\)
\(762\) 3.82489e9i 0.0113449i
\(763\) 5.40330e11i 1.59427i
\(764\) 3.17150e10 0.0930874
\(765\) 4.65156e10 0.135817
\(766\) 1.08385e11 0.314813
\(767\) 4.35075e11 1.25714
\(768\) 2.04024e10i 0.0586456i
\(769\) −1.36083e11 −0.389134 −0.194567 0.980889i \(-0.562330\pi\)
−0.194567 + 0.980889i \(0.562330\pi\)
\(770\) 1.84149e11i 0.523851i
\(771\) 8.23714e10 0.233109
\(772\) 1.34372e11i 0.378304i
\(773\) 3.83430e11i 1.07391i 0.843611 + 0.536955i \(0.180425\pi\)
−0.843611 + 0.536955i \(0.819575\pi\)
\(774\) 3.07076e10i 0.0855621i
\(775\) 8.39273e11i 2.32647i
\(776\) −1.01679e11 −0.280404
\(777\) 5.52320e11 1.51533
\(778\) 2.48195e11i 0.677446i
\(779\) 3.03633e11 3.17693e11i 0.824515 0.862696i
\(780\) 4.68627e11 1.26604
\(781\) 9.00346e10i 0.241994i
\(782\) 5.14064e10i 0.137464i
\(783\) −1.00875e11 −0.268371
\(784\) 4.04557e10 0.107082
\(785\) 6.29845e10 0.165865
\(786\) −3.79232e11 −0.993609
\(787\) 6.40375e11i 1.66930i −0.550778 0.834652i \(-0.685669\pi\)
0.550778 0.834652i \(-0.314331\pi\)
\(788\) 5.40972e10 0.140304
\(789\) 2.60674e11i 0.672651i
\(790\) −6.94051e11 −1.78190
\(791\) 4.43464e11i 1.13280i
\(792\) 5.57420e9i 0.0141671i
\(793\) 5.78700e11i 1.46339i
\(794\) 5.71420e10i 0.143772i
\(795\) 6.80044e11 1.70243
\(796\) −2.50567e11 −0.624124
\(797\) 2.74440e11i 0.680165i −0.940396 0.340083i \(-0.889545\pi\)
0.940396 0.340083i \(-0.110455\pi\)
\(798\) −2.32465e11 2.22177e11i −0.573253 0.547883i
\(799\) −2.73451e11 −0.670954
\(800\) 1.75192e11i 0.427715i
\(801\) 1.90918e10i 0.0463786i
\(802\) −2.87408e11 −0.694707
\(803\) −2.20773e11 −0.530986
\(804\) −1.76846e11 −0.423225
\(805\) 2.93640e11 0.699249
\(806\) 4.18729e11i 0.992185i
\(807\) 2.57306e11 0.606674
\(808\) 1.59192e11i 0.373488i
\(809\) −3.21744e11 −0.751133 −0.375567 0.926795i \(-0.622552\pi\)
−0.375567 + 0.926795i \(0.622552\pi\)
\(810\) 4.87543e11i 1.13259i
\(811\) 5.63846e11i 1.30340i −0.758478 0.651699i \(-0.774056\pi\)
0.758478 0.651699i \(-0.225944\pi\)
\(812\) 6.63667e10i 0.152660i
\(813\) 1.70247e11i 0.389688i
\(814\) −1.40620e11 −0.320293
\(815\) 1.24749e11 0.282752
\(816\) 6.39037e10i 0.144134i
\(817\) 3.26044e11 + 3.11614e11i 0.731792 + 0.699405i
\(818\) 5.40367e11 1.20691
\(819\) 9.37974e10i 0.208476i
\(820\) 4.98854e11i 1.10336i
\(821\) −6.95776e11 −1.53143 −0.765714 0.643181i \(-0.777614\pi\)
−0.765714 + 0.643181i \(0.777614\pi\)
\(822\) −4.46645e11 −0.978307
\(823\) 6.32636e11 1.37897 0.689485 0.724300i \(-0.257837\pi\)
0.689485 + 0.724300i \(0.257837\pi\)
\(824\) −2.88089e11 −0.624911
\(825\) 3.52555e11i 0.761046i
\(826\) 3.38892e11 0.728015
\(827\) 7.69772e11i 1.64566i −0.568287 0.822830i \(-0.692394\pi\)
0.568287 0.822830i \(-0.307606\pi\)
\(828\) 8.88848e9 0.0189106
\(829\) 4.60248e11i 0.974482i 0.873268 + 0.487241i \(0.161997\pi\)
−0.873268 + 0.487241i \(0.838003\pi\)
\(830\) 2.52326e11i 0.531678i
\(831\) 5.85647e11i 1.22809i
\(832\) 8.74066e10i 0.182411i
\(833\) 1.26714e11 0.263175
\(834\) 1.97732e11 0.408707
\(835\) 6.69260e11i 1.37673i
\(836\) 5.91852e10 + 5.65658e10i 0.121168 + 0.115805i
\(837\) −4.95750e11 −1.01009
\(838\) 4.43399e11i 0.899122i
\(839\) 5.13894e11i 1.03711i −0.855044 0.518556i \(-0.826470\pi\)
0.855044 0.518556i \(-0.173530\pi\)
\(840\) 3.65026e11 0.733174
\(841\) 4.67597e11 0.934734
\(842\) 1.44541e11 0.287570
\(843\) 7.24746e11 1.43508
\(844\) 3.07220e11i 0.605453i
\(845\) −1.06489e12 −2.08870
\(846\) 4.72814e10i 0.0923016i
\(847\) 5.45983e11 1.06083
\(848\) 1.26839e11i 0.245285i
\(849\) 7.31580e11i 1.40809i
\(850\) 5.48732e11i 1.05120i
\(851\) 2.24229e11i 0.427536i
\(852\) −1.78469e11 −0.338692
\(853\) −7.41234e10 −0.140010 −0.0700050 0.997547i \(-0.522302\pi\)
−0.0700050 + 0.997547i \(0.522302\pi\)
\(854\) 4.50765e11i 0.847459i
\(855\) 8.53965e10 + 8.16171e10i 0.159800 + 0.152727i
\(856\) 2.63964e11 0.491642
\(857\) 8.78805e11i 1.62918i 0.580037 + 0.814590i \(0.303038\pi\)
−0.580037 + 0.814590i \(0.696962\pi\)
\(858\) 1.75896e11i 0.324569i
\(859\) −4.07221e11 −0.747923 −0.373962 0.927444i \(-0.622001\pi\)
−0.373962 + 0.927444i \(0.622001\pi\)
\(860\) −5.11967e11 −0.935941
\(861\) −7.35441e11 −1.33824
\(862\) −3.98694e11 −0.722122
\(863\) 1.98526e11i 0.357911i 0.983857 + 0.178955i \(0.0572717\pi\)
−0.983857 + 0.178955i \(0.942728\pi\)
\(864\) 1.03484e11 0.185703
\(865\) 1.37976e12i 2.46455i
\(866\) 9.28227e10 0.165038
\(867\) 3.30033e11i 0.584092i
\(868\) 3.26159e11i 0.574580i
\(869\) 2.60508e11i 0.456816i
\(870\) 1.79574e11i 0.313448i
\(871\) 7.57634e11 1.31640
\(872\) 2.72689e11 0.471631
\(873\) 5.50665e10i 0.0948048i
\(874\) −9.01985e10 + 9.43753e10i −0.154580 + 0.161738i
\(875\) −1.83895e12 −3.13717
\(876\) 4.37622e11i 0.743161i
\(877\) 9.45892e11i 1.59898i −0.600679 0.799490i \(-0.705103\pi\)
0.600679 0.799490i \(-0.294897\pi\)
\(878\) −7.52405e8 −0.00126612
\(879\) −1.00438e11 −0.168245
\(880\) −9.29350e10 −0.154970
\(881\) −8.71114e11 −1.44601 −0.723005 0.690843i \(-0.757240\pi\)
−0.723005 + 0.690843i \(0.757240\pi\)
\(882\) 2.19096e10i 0.0362044i
\(883\) −7.40621e11 −1.21830 −0.609148 0.793056i \(-0.708489\pi\)
−0.609148 + 0.793056i \(0.708489\pi\)
\(884\) 2.73772e11i 0.448312i
\(885\) 9.16966e11 1.49479
\(886\) 9.21191e10i 0.149491i
\(887\) 1.27828e11i 0.206506i 0.994655 + 0.103253i \(0.0329251\pi\)
−0.994655 + 0.103253i \(0.967075\pi\)
\(888\) 2.78740e11i 0.448278i
\(889\) 1.27638e10i 0.0204349i
\(890\) 3.18306e11 0.507323
\(891\) 1.82996e11 0.290356
\(892\) 1.68659e10i 0.0266409i
\(893\) −5.02020e11 4.79802e11i −0.789433 0.754495i
\(894\) 7.94533e11 1.24383
\(895\) 1.23030e12i 1.91743i
\(896\) 6.80833e10i 0.105635i
\(897\) 2.80480e11 0.433243
\(898\) −1.06284e11 −0.163441
\(899\) −1.60453e11 −0.245646
\(900\) −9.48790e10 −0.144611
\(901\) 3.97282e11i 0.602837i
\(902\) 1.87242e11 0.282863
\(903\) 7.54773e11i 1.13518i
\(904\) 2.23804e11 0.335114
\(905\) 2.04101e12i 3.04264i
\(906\) 4.35745e11i 0.646724i
\(907\) 4.56362e9i 0.00674343i −0.999994 0.00337171i \(-0.998927\pi\)
0.999994 0.00337171i \(-0.00107325\pi\)
\(908\) 3.17791e11i 0.467517i
\(909\) 8.62140e10 0.126276
\(910\) −1.56382e12 −2.28046
\(911\) 7.74104e11i 1.12390i 0.827173 + 0.561948i \(0.189948\pi\)
−0.827173 + 0.561948i \(0.810052\pi\)
\(912\) −1.12126e11 + 1.17319e11i −0.162080 + 0.169585i
\(913\) −9.47088e10 −0.136304
\(914\) 3.54811e11i 0.508408i
\(915\) 1.21967e12i 1.74004i
\(916\) −4.28151e11 −0.608156
\(917\) 1.26551e12 1.78973
\(918\) 3.24130e11 0.456403
\(919\) 1.28875e12 1.80678 0.903391 0.428818i \(-0.141070\pi\)
0.903391 + 0.428818i \(0.141070\pi\)
\(920\) 1.48192e11i 0.206858i
\(921\) −4.76998e11 −0.662945
\(922\) 2.97979e10i 0.0412346i
\(923\) 7.64587e11 1.05346
\(924\) 1.37010e11i 0.187960i
\(925\) 2.39350e12i 3.26939i
\(926\) 1.00191e12i 1.36265i
\(927\) 1.56021e11i 0.211283i
\(928\) 3.34934e10 0.0451614
\(929\) −7.44599e11 −0.999677 −0.499838 0.866119i \(-0.666607\pi\)
−0.499838 + 0.866119i \(0.666607\pi\)
\(930\) 8.82515e11i 1.17975i
\(931\) 2.32630e11 + 2.22335e11i 0.309647 + 0.295943i
\(932\) −1.57935e11 −0.209322
\(933\) 4.98325e9i 0.00657637i
\(934\) 3.73328e11i 0.490573i
\(935\) −2.91088e11 −0.380871
\(936\) −4.73369e10 −0.0616732
\(937\) 5.69314e11 0.738573 0.369287 0.929316i \(-0.379602\pi\)
0.369287 + 0.929316i \(0.379602\pi\)
\(938\) 5.90141e11 0.762333
\(939\) 3.06689e11i 0.394490i
\(940\) 7.88293e11 1.00966
\(941\) 1.43384e11i 0.182869i 0.995811 + 0.0914347i \(0.0291453\pi\)
−0.995811 + 0.0914347i \(0.970855\pi\)
\(942\) 4.68615e10 0.0595131
\(943\) 2.98571e11i 0.377573i
\(944\) 1.71029e11i 0.215368i
\(945\) 1.85147e12i 2.32162i
\(946\) 1.92164e11i 0.239942i
\(947\) −6.81778e11 −0.847702 −0.423851 0.905732i \(-0.639322\pi\)
−0.423851 + 0.905732i \(0.639322\pi\)
\(948\) −5.16386e11 −0.639354
\(949\) 1.87483e12i 2.31152i
\(950\) 9.62813e11 1.00740e12i 1.18208 1.23682i
\(951\) −7.21785e10 −0.0882442
\(952\) 2.13249e11i 0.259620i
\(953\) 1.16217e12i 1.40896i 0.709725 + 0.704479i \(0.248819\pi\)
−0.709725 + 0.704479i \(0.751181\pi\)
\(954\) −6.86926e10 −0.0829309
\(955\) −2.86363e11 −0.344274
\(956\) −1.28840e11 −0.154248
\(957\) 6.74018e10 0.0803571
\(958\) 4.83535e11i 0.574072i
\(959\) 1.49047e12 1.76217
\(960\) 1.84219e11i 0.216894i
\(961\) 6.43439e10 0.0754421
\(962\) 1.19416e12i 1.39432i
\(963\) 1.42955e11i 0.166224i
\(964\) 3.56396e11i 0.412690i
\(965\) 1.21328e12i 1.39911i
\(966\) 2.18473e11 0.250894
\(967\) −1.33496e11 −0.152673 −0.0763364 0.997082i \(-0.524322\pi\)
−0.0763364 + 0.997082i \(0.524322\pi\)
\(968\) 2.75542e11i 0.313824i
\(969\) −3.51199e11 + 3.67462e11i −0.398344 + 0.416790i
\(970\) 9.18088e11 1.03704
\(971\) 7.76210e11i 0.873177i 0.899661 + 0.436589i \(0.143813\pi\)
−0.899661 + 0.436589i \(0.856187\pi\)
\(972\) 1.06104e11i 0.118869i
\(973\) −6.59838e11 −0.736183
\(974\) −3.39270e11 −0.376972
\(975\) −2.99395e12 −3.31303
\(976\) −2.27488e11 −0.250703
\(977\) 5.28023e10i 0.0579528i −0.999580 0.0289764i \(-0.990775\pi\)
0.999580 0.0289764i \(-0.00922477\pi\)
\(978\) 9.28152e10 0.101453
\(979\) 1.19474e11i 0.130060i
\(980\) −3.65285e11 −0.396030
\(981\) 1.47681e11i 0.159459i
\(982\) 1.42651e11i 0.153401i
\(983\) 3.57496e11i 0.382875i 0.981505 + 0.191438i \(0.0613150\pi\)
−0.981505 + 0.191438i \(0.938685\pi\)
\(984\) 3.71156e11i 0.395892i
\(985\) −4.88458e11 −0.518898
\(986\) 1.04907e11 0.110993
\(987\) 1.16215e12i 1.22460i
\(988\) 4.80365e11 5.02609e11i 0.504132 0.527476i
\(989\) −3.06420e11 −0.320281
\(990\) 5.03309e10i 0.0523955i
\(991\) 1.23547e12i 1.28097i 0.767972 + 0.640484i \(0.221266\pi\)
−0.767972 + 0.640484i \(0.778734\pi\)
\(992\) 1.64603e11 0.169978
\(993\) 4.80382e11 0.494071
\(994\) 5.95557e11 0.610068
\(995\) 2.26243e12 2.30825
\(996\) 1.87735e11i 0.190769i
\(997\) −5.40410e11 −0.546944 −0.273472 0.961880i \(-0.588172\pi\)
−0.273472 + 0.961880i \(0.588172\pi\)
\(998\) 4.18748e11i 0.422115i
\(999\) −1.41382e12 −1.41949
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 38.9.b.a.37.5 12
3.2 odd 2 342.9.d.a.37.7 12
4.3 odd 2 304.9.e.e.113.3 12
19.18 odd 2 inner 38.9.b.a.37.8 yes 12
57.56 even 2 342.9.d.a.37.1 12
76.75 even 2 304.9.e.e.113.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.9.b.a.37.5 12 1.1 even 1 trivial
38.9.b.a.37.8 yes 12 19.18 odd 2 inner
304.9.e.e.113.3 12 4.3 odd 2
304.9.e.e.113.10 12 76.75 even 2
342.9.d.a.37.1 12 57.56 even 2
342.9.d.a.37.7 12 3.2 odd 2