Properties

Label 37.8.b.a.36.10
Level $37$
Weight $8$
Character 37.36
Analytic conductor $11.558$
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] = [37,8,Mod(36,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.36");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.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: \(11.5582459429\)
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: \( x^{20} + 1702 x^{18} + 1194509 x^{16} + 450999516 x^{14} + 100204783492 x^{12} + 13461378480848 x^{10} + \cdots + 13\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{19}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 36.10
Root \(-0.118026i\) of defining polynomial
Character \(\chi\) \(=\) 37.36
Dual form 37.8.b.a.36.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.118026i q^{2} -7.03331 q^{3} +127.986 q^{4} +225.549i q^{5} +0.830113i q^{6} +6.20125 q^{7} -30.2130i q^{8} -2137.53 q^{9} +O(q^{10})\) \(q-0.118026i q^{2} -7.03331 q^{3} +127.986 q^{4} +225.549i q^{5} +0.830113i q^{6} +6.20125 q^{7} -30.2130i q^{8} -2137.53 q^{9} +26.6207 q^{10} +5456.67 q^{11} -900.166 q^{12} +9336.83i q^{13} -0.731908i q^{14} -1586.36i q^{15} +16378.7 q^{16} +24263.8i q^{17} +252.284i q^{18} +36170.0i q^{19} +28867.2i q^{20} -43.6153 q^{21} -644.028i q^{22} -60783.9i q^{23} +212.497i q^{24} +27252.5 q^{25} +1101.99 q^{26} +30415.8 q^{27} +793.674 q^{28} +238742. i q^{29} -187.231 q^{30} -166706. i q^{31} -5800.37i q^{32} -38378.5 q^{33} +2863.75 q^{34} +1398.69i q^{35} -273574. q^{36} +(123926. - 282089. i) q^{37} +4269.00 q^{38} -65668.9i q^{39} +6814.52 q^{40} -415672. q^{41} +5.14774i q^{42} -900886. i q^{43} +698378. q^{44} -482119. i q^{45} -7174.07 q^{46} -585683. q^{47} -115196. q^{48} -823505. q^{49} -3216.51i q^{50} -170655. i q^{51} +1.19498e6i q^{52} +1.40140e6 q^{53} -3589.85i q^{54} +1.23075e6i q^{55} -187.358i q^{56} -254395. i q^{57} +28177.8 q^{58} +1.03209e6i q^{59} -203032. i q^{60} -944290. i q^{61} -19675.7 q^{62} -13255.4 q^{63} +2.09578e6 q^{64} -2.10592e6 q^{65} +4529.65i q^{66} +1.87144e6 q^{67} +3.10542e6i q^{68} +427512. i q^{69} +165.081 q^{70} +3.16808e6 q^{71} +64581.2i q^{72} -5.00057e6 q^{73} +(-33293.8 - 14626.5i) q^{74} -191676. q^{75} +4.62926e6i q^{76} +33838.2 q^{77} -7750.63 q^{78} -4.38910e6i q^{79} +3.69419e6i q^{80} +4.46086e6 q^{81} +49060.0i q^{82} +3.16473e6 q^{83} -5582.16 q^{84} -5.47267e6 q^{85} -106328. q^{86} -1.67915e6i q^{87} -164862. i q^{88} -9.98897e6i q^{89} -56902.5 q^{90} +57900.1i q^{91} -7.77949e6i q^{92} +1.17250e6i q^{93} +69125.8i q^{94} -8.15812e6 q^{95} +40795.8i q^{96} -3.91455e6i q^{97} +97194.9i q^{98} -1.16638e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 78 q^{3} - 844 q^{4} - 1746 q^{7} + 12362 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 78 q^{3} - 844 q^{4} - 1746 q^{7} + 12362 q^{9} - 882 q^{10} + 3498 q^{11} - 30374 q^{12} + 36116 q^{16} + 113482 q^{21} - 108112 q^{25} + 49278 q^{26} - 304110 q^{27} - 41192 q^{28} + 429776 q^{30} + 305646 q^{33} - 960356 q^{34} + 484758 q^{36} + 108732 q^{37} + 1049916 q^{38} - 496346 q^{40} - 1577742 q^{41} + 685266 q^{44} - 2906298 q^{46} - 1512786 q^{47} + 1522958 q^{48} + 3269246 q^{49} + 2999358 q^{53} + 405946 q^{58} + 3728310 q^{62} - 11995292 q^{63} - 11109700 q^{64} + 4251792 q^{65} + 3562224 q^{67} + 21605644 q^{70} - 15259086 q^{71} + 11088018 q^{73} - 2036544 q^{74} + 14882062 q^{75} - 2419122 q^{77} - 12178734 q^{78} - 17764972 q^{81} - 12873822 q^{83} + 9944396 q^{84} - 2698920 q^{85} + 15345336 q^{86} - 13219100 q^{90} + 48981192 q^{95} + 43111380 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.118026i 0.0104321i −0.999986 0.00521606i \(-0.998340\pi\)
0.999986 0.00521606i \(-0.00166033\pi\)
\(3\) −7.03331 −0.150396 −0.0751979 0.997169i \(-0.523959\pi\)
−0.0751979 + 0.997169i \(0.523959\pi\)
\(4\) 127.986 0.999891
\(5\) 225.549i 0.806949i 0.914991 + 0.403475i \(0.132198\pi\)
−0.914991 + 0.403475i \(0.867802\pi\)
\(6\) 0.830113i 0.00156895i
\(7\) 6.20125 0.00683339 0.00341669 0.999994i \(-0.498912\pi\)
0.00341669 + 0.999994i \(0.498912\pi\)
\(8\) 30.2130i 0.0208631i
\(9\) −2137.53 −0.977381
\(10\) 26.6207 0.00841819
\(11\) 5456.67 1.23610 0.618049 0.786139i \(-0.287923\pi\)
0.618049 + 0.786139i \(0.287923\pi\)
\(12\) −900.166 −0.150379
\(13\) 9336.83i 1.17869i 0.807883 + 0.589343i \(0.200613\pi\)
−0.807883 + 0.589343i \(0.799387\pi\)
\(14\) 0.731908i 7.12867e-5i
\(15\) 1586.36i 0.121362i
\(16\) 16378.7 0.999674
\(17\) 24263.8i 1.19781i 0.800821 + 0.598904i \(0.204397\pi\)
−0.800821 + 0.598904i \(0.795603\pi\)
\(18\) 252.284i 0.0101962i
\(19\) 36170.0i 1.20979i 0.796304 + 0.604897i \(0.206786\pi\)
−0.796304 + 0.604897i \(0.793214\pi\)
\(20\) 28867.2i 0.806862i
\(21\) −43.6153 −0.00102771
\(22\) 644.028i 0.0128951i
\(23\) 60783.9i 1.04170i −0.853650 0.520848i \(-0.825616\pi\)
0.853650 0.520848i \(-0.174384\pi\)
\(24\) 212.497i 0.00313772i
\(25\) 27252.5 0.348833
\(26\) 1101.99 0.0122962
\(27\) 30415.8 0.297390
\(28\) 793.674 0.00683265
\(29\) 238742.i 1.81776i 0.417057 + 0.908880i \(0.363061\pi\)
−0.417057 + 0.908880i \(0.636939\pi\)
\(30\) −187.231 −0.00126606
\(31\) 166706.i 1.00505i −0.864564 0.502523i \(-0.832405\pi\)
0.864564 0.502523i \(-0.167595\pi\)
\(32\) 5800.37i 0.0312918i
\(33\) −38378.5 −0.185904
\(34\) 2863.75 0.0124957
\(35\) 1398.69i 0.00551420i
\(36\) −273574. −0.977275
\(37\) 123926. 282089.i 0.402213 0.915546i
\(38\) 4269.00 0.0126207
\(39\) 65668.9i 0.177269i
\(40\) 6814.52 0.0168355
\(41\) −415672. −0.941905 −0.470952 0.882159i \(-0.656090\pi\)
−0.470952 + 0.882159i \(0.656090\pi\)
\(42\) 5.14774i 1.07212e-5i
\(43\) 900886.i 1.72795i −0.503538 0.863973i \(-0.667969\pi\)
0.503538 0.863973i \(-0.332031\pi\)
\(44\) 698378. 1.23596
\(45\) 482119.i 0.788697i
\(46\) −7174.07 −0.0108671
\(47\) −585683. −0.822849 −0.411425 0.911444i \(-0.634969\pi\)
−0.411425 + 0.911444i \(0.634969\pi\)
\(48\) −115196. −0.150347
\(49\) −823505. −0.999953
\(50\) 3216.51i 0.00363906i
\(51\) 170655.i 0.180145i
\(52\) 1.19498e6i 1.17856i
\(53\) 1.40140e6 1.29299 0.646496 0.762917i \(-0.276234\pi\)
0.646496 + 0.762917i \(0.276234\pi\)
\(54\) 3589.85i 0.00310240i
\(55\) 1.23075e6i 0.997469i
\(56\) 187.358i 0.000142566i
\(57\) 254395.i 0.181948i
\(58\) 28177.8 0.0189631
\(59\) 1.03209e6i 0.654240i 0.944983 + 0.327120i \(0.106078\pi\)
−0.944983 + 0.327120i \(0.893922\pi\)
\(60\) 203032.i 0.121349i
\(61\) 944290.i 0.532661i −0.963882 0.266330i \(-0.914189\pi\)
0.963882 0.266330i \(-0.0858112\pi\)
\(62\) −19675.7 −0.0104848
\(63\) −13255.4 −0.00667883
\(64\) 2.09578e6 0.999347
\(65\) −2.10592e6 −0.951140
\(66\) 4529.65i 0.00193937i
\(67\) 1.87144e6 0.760177 0.380089 0.924950i \(-0.375894\pi\)
0.380089 + 0.924950i \(0.375894\pi\)
\(68\) 3.10542e6i 1.19768i
\(69\) 427512.i 0.156667i
\(70\) 165.081 5.75248e−5
\(71\) 3.16808e6 1.05049 0.525244 0.850951i \(-0.323974\pi\)
0.525244 + 0.850951i \(0.323974\pi\)
\(72\) 64581.2i 0.0203912i
\(73\) −5.00057e6 −1.50449 −0.752246 0.658883i \(-0.771029\pi\)
−0.752246 + 0.658883i \(0.771029\pi\)
\(74\) −33293.8 14626.5i −0.00955108 0.00419593i
\(75\) −191676. −0.0524629
\(76\) 4.62926e6i 1.20966i
\(77\) 33838.2 0.00844675
\(78\) −7750.63 −0.00184929
\(79\) 4.38910e6i 1.00157i −0.865572 0.500784i \(-0.833045\pi\)
0.865572 0.500784i \(-0.166955\pi\)
\(80\) 3.69419e6i 0.806686i
\(81\) 4.46086e6 0.932655
\(82\) 49060.0i 0.00982606i
\(83\) 3.16473e6 0.607524 0.303762 0.952748i \(-0.401757\pi\)
0.303762 + 0.952748i \(0.401757\pi\)
\(84\) −5582.16 −0.00102760
\(85\) −5.47267e6 −0.966570
\(86\) −106328. −0.0180261
\(87\) 1.67915e6i 0.273383i
\(88\) 164862.i 0.0257888i
\(89\) 9.98897e6i 1.50195i −0.660331 0.750975i \(-0.729584\pi\)
0.660331 0.750975i \(-0.270416\pi\)
\(90\) −56902.5 −0.00822778
\(91\) 57900.1i 0.00805442i
\(92\) 7.77949e6i 1.04158i
\(93\) 1.17250e6i 0.151155i
\(94\) 69125.8i 0.00858406i
\(95\) −8.15812e6 −0.976242
\(96\) 40795.8i 0.00470615i
\(97\) 3.91455e6i 0.435493i −0.976005 0.217746i \(-0.930129\pi\)
0.976005 0.217746i \(-0.0698706\pi\)
\(98\) 97194.9i 0.0104316i
\(99\) −1.16638e7 −1.20814
\(100\) 3.48795e6 0.348795
\(101\) 3.54427e6 0.342296 0.171148 0.985245i \(-0.445252\pi\)
0.171148 + 0.985245i \(0.445252\pi\)
\(102\) −20141.7 −0.00187929
\(103\) 1.12121e7i 1.01102i −0.862822 0.505508i \(-0.831305\pi\)
0.862822 0.505508i \(-0.168695\pi\)
\(104\) 282094. 0.0245910
\(105\) 9837.41i 0.000829312i
\(106\) 165401.i 0.0134886i
\(107\) −3.13013e6 −0.247012 −0.123506 0.992344i \(-0.539414\pi\)
−0.123506 + 0.992344i \(0.539414\pi\)
\(108\) 3.89280e6 0.297357
\(109\) 1.32545e7i 0.980329i 0.871630 + 0.490164i \(0.163063\pi\)
−0.871630 + 0.490164i \(0.836937\pi\)
\(110\) 145260. 0.0104057
\(111\) −871609. + 1.98402e6i −0.0604911 + 0.137694i
\(112\) 101568. 0.00683116
\(113\) 6.10937e6i 0.398310i −0.979968 0.199155i \(-0.936180\pi\)
0.979968 0.199155i \(-0.0638198\pi\)
\(114\) −30025.2 −0.00189810
\(115\) 1.37098e7 0.840596
\(116\) 3.05557e7i 1.81756i
\(117\) 1.99578e7i 1.15202i
\(118\) 121814. 0.00682510
\(119\) 150466.i 0.00818508i
\(120\) −47928.6 −0.00253198
\(121\) 1.02881e7 0.527941
\(122\) −111451. −0.00555678
\(123\) 2.92355e6 0.141658
\(124\) 2.13361e7i 1.00494i
\(125\) 2.37678e7i 1.08844i
\(126\) 1564.48i 6.96743e-5i
\(127\) −2.86639e7 −1.24171 −0.620857 0.783924i \(-0.713215\pi\)
−0.620857 + 0.783924i \(0.713215\pi\)
\(128\) 989804.i 0.0417171i
\(129\) 6.33621e6i 0.259876i
\(130\) 248553.i 0.00992240i
\(131\) 4.10992e7i 1.59729i 0.601801 + 0.798646i \(0.294450\pi\)
−0.601801 + 0.798646i \(0.705550\pi\)
\(132\) −4.91191e6 −0.185884
\(133\) 224299.i 0.00826699i
\(134\) 220879.i 0.00793025i
\(135\) 6.86026e6i 0.239978i
\(136\) 733081. 0.0249900
\(137\) 3.56466e7 1.18439 0.592196 0.805794i \(-0.298261\pi\)
0.592196 + 0.805794i \(0.298261\pi\)
\(138\) 50457.5 0.00163436
\(139\) 5.45504e7 1.72285 0.861423 0.507888i \(-0.169574\pi\)
0.861423 + 0.507888i \(0.169574\pi\)
\(140\) 179013.i 0.00551360i
\(141\) 4.11929e6 0.123753
\(142\) 373915.i 0.0109588i
\(143\) 5.09480e7i 1.45697i
\(144\) −3.50099e7 −0.977062
\(145\) −5.38482e7 −1.46684
\(146\) 590197.i 0.0156950i
\(147\) 5.79197e6 0.150389
\(148\) 1.58608e7 3.61035e7i 0.402169 0.915447i
\(149\) 5.12903e7 1.27023 0.635116 0.772417i \(-0.280952\pi\)
0.635116 + 0.772417i \(0.280952\pi\)
\(150\) 22622.7i 0.000547299i
\(151\) −3.41108e7 −0.806254 −0.403127 0.915144i \(-0.632077\pi\)
−0.403127 + 0.915144i \(0.632077\pi\)
\(152\) 1.09280e6 0.0252400
\(153\) 5.18646e7i 1.17071i
\(154\) 3993.78i 8.81174e-5i
\(155\) 3.76005e7 0.811022
\(156\) 8.40470e6i 0.177250i
\(157\) −5.30635e7 −1.09433 −0.547164 0.837026i \(-0.684292\pi\)
−0.547164 + 0.837026i \(0.684292\pi\)
\(158\) −518027. −0.0104485
\(159\) −9.85647e6 −0.194461
\(160\) 1.30827e6 0.0252509
\(161\) 376936.i 0.00711831i
\(162\) 526497.i 0.00972956i
\(163\) 2.70879e7i 0.489913i −0.969534 0.244957i \(-0.921226\pi\)
0.969534 0.244957i \(-0.0787737\pi\)
\(164\) −5.32002e7 −0.941802
\(165\) 8.65623e6i 0.150015i
\(166\) 373520.i 0.00633776i
\(167\) 2.58701e7i 0.429824i 0.976633 + 0.214912i \(0.0689464\pi\)
−0.976633 + 0.214912i \(0.931054\pi\)
\(168\) 1317.75i 2.14413e-5i
\(169\) −2.44280e7 −0.389299
\(170\) 645917.i 0.0100834i
\(171\) 7.73146e7i 1.18243i
\(172\) 1.15301e8i 1.72776i
\(173\) −7.44012e7 −1.09249 −0.546246 0.837625i \(-0.683944\pi\)
−0.546246 + 0.837625i \(0.683944\pi\)
\(174\) −198183. −0.00285197
\(175\) 169000. 0.00238371
\(176\) 8.93729e7 1.23570
\(177\) 7.25904e6i 0.0983949i
\(178\) −1.17896e6 −0.0156685
\(179\) 1.02302e8i 1.33321i 0.745409 + 0.666607i \(0.232254\pi\)
−0.745409 + 0.666607i \(0.767746\pi\)
\(180\) 6.17045e7i 0.788611i
\(181\) 6.03017e7 0.755883 0.377941 0.925830i \(-0.376632\pi\)
0.377941 + 0.925830i \(0.376632\pi\)
\(182\) 6833.71 8.40246e−5
\(183\) 6.64148e6i 0.0801099i
\(184\) −1.83646e6 −0.0217330
\(185\) 6.36250e7 + 2.79514e7i 0.738799 + 0.324565i
\(186\) 138385. 0.00157686
\(187\) 1.32399e8i 1.48061i
\(188\) −7.49593e7 −0.822760
\(189\) 188616. 0.00203218
\(190\) 962869.i 0.0101843i
\(191\) 4.31250e7i 0.447829i −0.974609 0.223915i \(-0.928116\pi\)
0.974609 0.223915i \(-0.0718837\pi\)
\(192\) −1.47403e7 −0.150298
\(193\) 3.69409e7i 0.369877i −0.982750 0.184938i \(-0.940791\pi\)
0.982750 0.184938i \(-0.0592085\pi\)
\(194\) −462019. −0.00454311
\(195\) 1.48116e7 0.143047
\(196\) −1.05397e8 −0.999844
\(197\) 4.25981e7 0.396971 0.198485 0.980104i \(-0.436398\pi\)
0.198485 + 0.980104i \(0.436398\pi\)
\(198\) 1.37663e6i 0.0126035i
\(199\) 8.23772e7i 0.741006i −0.928831 0.370503i \(-0.879185\pi\)
0.928831 0.370503i \(-0.120815\pi\)
\(200\) 823381.i 0.00727773i
\(201\) −1.31624e7 −0.114327
\(202\) 418315.i 0.00357087i
\(203\) 1.48050e6i 0.0124215i
\(204\) 2.18414e7i 0.180126i
\(205\) 9.37544e7i 0.760070i
\(206\) −1.32332e6 −0.0105470
\(207\) 1.29927e8i 1.01813i
\(208\) 1.52925e8i 1.17830i
\(209\) 1.97368e8i 1.49542i
\(210\) −1161.07 −8.65148e−6
\(211\) −4.55502e7 −0.333812 −0.166906 0.985973i \(-0.553378\pi\)
−0.166906 + 0.985973i \(0.553378\pi\)
\(212\) 1.79359e8 1.29285
\(213\) −2.22821e7 −0.157989
\(214\) 369436.i 0.00257686i
\(215\) 2.03194e8 1.39437
\(216\) 918952.i 0.00620447i
\(217\) 1.03379e6i 0.00686788i
\(218\) 1.56438e6 0.0102269
\(219\) 3.51706e7 0.226269
\(220\) 1.57519e8i 0.997361i
\(221\) −2.26547e8 −1.41184
\(222\) 234166. + 102872.i 0.00143644 + 0.000631050i
\(223\) 2.06659e8 1.24792 0.623960 0.781456i \(-0.285523\pi\)
0.623960 + 0.781456i \(0.285523\pi\)
\(224\) 35969.5i 0.000213829i
\(225\) −5.82532e7 −0.340942
\(226\) −721064. −0.00415522
\(227\) 5.65625e7i 0.320951i 0.987040 + 0.160475i \(0.0513027\pi\)
−0.987040 + 0.160475i \(0.948697\pi\)
\(228\) 3.25590e7i 0.181928i
\(229\) 1.45433e8 0.800276 0.400138 0.916455i \(-0.368962\pi\)
0.400138 + 0.916455i \(0.368962\pi\)
\(230\) 1.61811e6i 0.00876919i
\(231\) −237995. −0.00127035
\(232\) 7.21312e6 0.0379241
\(233\) −1.53386e8 −0.794401 −0.397200 0.917732i \(-0.630018\pi\)
−0.397200 + 0.917732i \(0.630018\pi\)
\(234\) −2.35554e6 −0.0120181
\(235\) 1.32100e8i 0.663998i
\(236\) 1.32094e8i 0.654169i
\(237\) 3.08699e7i 0.150632i
\(238\) 17758.8 8.53877e−5
\(239\) 8.98230e7i 0.425594i 0.977096 + 0.212797i \(0.0682572\pi\)
−0.977096 + 0.212797i \(0.931743\pi\)
\(240\) 2.59824e7i 0.121322i
\(241\) 2.90622e7i 0.133742i −0.997762 0.0668711i \(-0.978698\pi\)
0.997762 0.0668711i \(-0.0213016\pi\)
\(242\) 1.21426e6i 0.00550754i
\(243\) −9.78940e7 −0.437657
\(244\) 1.20856e8i 0.532603i
\(245\) 1.85741e8i 0.806912i
\(246\) 345055.i 0.00147780i
\(247\) −3.37713e8 −1.42597
\(248\) −5.03670e6 −0.0209684
\(249\) −2.22585e7 −0.0913690
\(250\) 2.80522e6 0.0113547
\(251\) 1.97276e7i 0.0787437i 0.999225 + 0.0393718i \(0.0125357\pi\)
−0.999225 + 0.0393718i \(0.987464\pi\)
\(252\) −1.69650e6 −0.00667810
\(253\) 3.31677e8i 1.28764i
\(254\) 3.38308e6i 0.0129537i
\(255\) 3.84910e7 0.145368
\(256\) 2.68143e8 0.998912
\(257\) 4.16128e8i 1.52919i −0.644511 0.764595i \(-0.722939\pi\)
0.644511 0.764595i \(-0.277061\pi\)
\(258\) 747837. 0.00271105
\(259\) 768496. 1.74931e6i 0.00274848 0.00625628i
\(260\) −2.69528e8 −0.951036
\(261\) 5.10320e8i 1.77664i
\(262\) 4.85078e6 0.0166631
\(263\) 1.77175e8 0.600563 0.300281 0.953851i \(-0.402919\pi\)
0.300281 + 0.953851i \(0.402919\pi\)
\(264\) 1.15953e6i 0.00387853i
\(265\) 3.16084e8i 1.04338i
\(266\) 26473.1 8.62422e−5
\(267\) 7.02555e7i 0.225887i
\(268\) 2.39519e8 0.760094
\(269\) −2.79188e8 −0.874508 −0.437254 0.899338i \(-0.644049\pi\)
−0.437254 + 0.899338i \(0.644049\pi\)
\(270\) 809688. 0.00250348
\(271\) −3.00313e8 −0.916605 −0.458302 0.888796i \(-0.651542\pi\)
−0.458302 + 0.888796i \(0.651542\pi\)
\(272\) 3.97408e8i 1.19742i
\(273\) 407229.i 0.00121135i
\(274\) 4.20722e6i 0.0123557i
\(275\) 1.48708e8 0.431192
\(276\) 5.47156e7i 0.156650i
\(277\) 2.31585e7i 0.0654682i 0.999464 + 0.0327341i \(0.0104215\pi\)
−0.999464 + 0.0327341i \(0.989579\pi\)
\(278\) 6.43836e6i 0.0179729i
\(279\) 3.56340e8i 0.982314i
\(280\) 42258.5 0.000115043
\(281\) 3.91160e8i 1.05168i −0.850585 0.525838i \(-0.823752\pi\)
0.850585 0.525838i \(-0.176248\pi\)
\(282\) 486183.i 0.00129101i
\(283\) 2.84253e8i 0.745508i −0.927930 0.372754i \(-0.878413\pi\)
0.927930 0.372754i \(-0.121587\pi\)
\(284\) 4.05470e8 1.05037
\(285\) 5.73786e7 0.146823
\(286\) 6.01319e6 0.0151993
\(287\) −2.57768e6 −0.00643640
\(288\) 1.23985e7i 0.0305840i
\(289\) −1.78391e8 −0.434742
\(290\) 6.35548e6i 0.0153023i
\(291\) 2.75323e7i 0.0654963i
\(292\) −6.40004e8 −1.50433
\(293\) −2.97152e8 −0.690147 −0.345074 0.938576i \(-0.612146\pi\)
−0.345074 + 0.938576i \(0.612146\pi\)
\(294\) 683602.i 0.00156887i
\(295\) −2.32788e8 −0.527938
\(296\) −8.52275e6 3.74417e6i −0.0191011 0.00839140i
\(297\) 1.65969e8 0.367603
\(298\) 6.05358e6i 0.0132512i
\(299\) 5.67529e8 1.22783
\(300\) −2.45318e7 −0.0524572
\(301\) 5.58662e6i 0.0118077i
\(302\) 4.02595e6i 0.00841094i
\(303\) −2.49279e7 −0.0514798
\(304\) 5.92416e8i 1.20940i
\(305\) 2.12984e8 0.429830
\(306\) −6.12136e6 −0.0122130
\(307\) 9.19105e8 1.81293 0.906465 0.422281i \(-0.138771\pi\)
0.906465 + 0.422281i \(0.138771\pi\)
\(308\) 4.33082e6 0.00844583
\(309\) 7.88584e7i 0.152052i
\(310\) 4.43783e6i 0.00846067i
\(311\) 5.11798e8i 0.964800i 0.875951 + 0.482400i \(0.160235\pi\)
−0.875951 + 0.482400i \(0.839765\pi\)
\(312\) −1.98405e6 −0.00369839
\(313\) 6.11738e8i 1.12761i −0.825906 0.563807i \(-0.809336\pi\)
0.825906 0.563807i \(-0.190664\pi\)
\(314\) 6.26287e6i 0.0114161i
\(315\) 2.98974e6i 0.00538948i
\(316\) 5.61744e8i 1.00146i
\(317\) 2.59966e7 0.0458362 0.0229181 0.999737i \(-0.492704\pi\)
0.0229181 + 0.999737i \(0.492704\pi\)
\(318\) 1.16332e6i 0.00202863i
\(319\) 1.30274e9i 2.24693i
\(320\) 4.72702e8i 0.806423i
\(321\) 2.20152e7 0.0371496
\(322\) −44488.2 −7.42591e−5
\(323\) −8.77621e8 −1.44910
\(324\) 5.70928e8 0.932553
\(325\) 2.54452e8i 0.411164i
\(326\) −3.19708e6 −0.00511083
\(327\) 9.32233e7i 0.147437i
\(328\) 1.25587e7i 0.0196510i
\(329\) −3.63197e6 −0.00562285
\(330\) −1.02166e6 −0.00156498
\(331\) 2.55538e8i 0.387308i 0.981070 + 0.193654i \(0.0620340\pi\)
−0.981070 + 0.193654i \(0.937966\pi\)
\(332\) 4.05041e8 0.607458
\(333\) −2.64896e8 + 6.02975e8i −0.393115 + 0.894838i
\(334\) 3.05334e6 0.00448397
\(335\) 4.22102e8i 0.613424i
\(336\) −714360. −0.00102738
\(337\) 6.22166e8 0.885526 0.442763 0.896639i \(-0.353998\pi\)
0.442763 + 0.896639i \(0.353998\pi\)
\(338\) 2.88313e6i 0.00406121i
\(339\) 4.29691e7i 0.0599042i
\(340\) −7.00426e8 −0.966465
\(341\) 9.09662e8i 1.24234i
\(342\) −9.12512e6 −0.0123352
\(343\) −1.02138e7 −0.0136665
\(344\) −2.72185e7 −0.0360503
\(345\) −9.64250e7 −0.126422
\(346\) 8.78126e6i 0.0113970i
\(347\) 1.00916e9i 1.29660i −0.761383 0.648302i \(-0.775479\pi\)
0.761383 0.648302i \(-0.224521\pi\)
\(348\) 2.14908e8i 0.273354i
\(349\) 2.43348e8 0.306435 0.153218 0.988192i \(-0.451036\pi\)
0.153218 + 0.988192i \(0.451036\pi\)
\(350\) 19946.4i 2.48671e-5i
\(351\) 2.83987e8i 0.350529i
\(352\) 3.16507e7i 0.0386798i
\(353\) 6.70861e8i 0.811748i −0.913929 0.405874i \(-0.866967\pi\)
0.913929 0.405874i \(-0.133033\pi\)
\(354\) −856754. −0.00102647
\(355\) 7.14557e8i 0.847691i
\(356\) 1.27845e9i 1.50179i
\(357\) 1.05827e6i 0.00123100i
\(358\) 1.20743e7 0.0139082
\(359\) −9.91138e8 −1.13059 −0.565293 0.824890i \(-0.691237\pi\)
−0.565293 + 0.824890i \(0.691237\pi\)
\(360\) −1.45662e7 −0.0164547
\(361\) −4.14398e8 −0.463599
\(362\) 7.11716e6i 0.00788545i
\(363\) −7.23592e7 −0.0794000
\(364\) 7.41040e6i 0.00805354i
\(365\) 1.12788e9i 1.21405i
\(366\) 783867. 0.000835716
\(367\) 2.69313e8 0.284397 0.142199 0.989838i \(-0.454583\pi\)
0.142199 + 0.989838i \(0.454583\pi\)
\(368\) 9.95558e8i 1.04136i
\(369\) 8.88512e8 0.920600
\(370\) 3.29899e6 7.50940e6i 0.00338590 0.00770724i
\(371\) 8.69042e6 0.00883552
\(372\) 1.50063e8i 0.151138i
\(373\) 4.97436e8 0.496313 0.248157 0.968720i \(-0.420175\pi\)
0.248157 + 0.968720i \(0.420175\pi\)
\(374\) 1.56266e7 0.0154459
\(375\) 1.67167e8i 0.163697i
\(376\) 1.76952e7i 0.0171672i
\(377\) −2.22910e9 −2.14257
\(378\) 22261.6i 2.11999e-5i
\(379\) 4.95355e8 0.467390 0.233695 0.972310i \(-0.424918\pi\)
0.233695 + 0.972310i \(0.424918\pi\)
\(380\) −1.04413e9 −0.976136
\(381\) 2.01602e8 0.186749
\(382\) −5.08987e6 −0.00467180
\(383\) 2.85654e7i 0.0259803i 0.999916 + 0.0129901i \(0.00413501\pi\)
−0.999916 + 0.0129901i \(0.995865\pi\)
\(384\) 6.96160e6i 0.00627408i
\(385\) 7.63218e6i 0.00681610i
\(386\) −4.35998e6 −0.00385860
\(387\) 1.92567e9i 1.68886i
\(388\) 5.01008e8i 0.435446i
\(389\) 6.56407e7i 0.0565392i −0.999600 0.0282696i \(-0.991000\pi\)
0.999600 0.0282696i \(-0.00899970\pi\)
\(390\) 1.74815e6i 0.00149229i
\(391\) 1.47485e9 1.24775
\(392\) 2.48805e7i 0.0208621i
\(393\) 2.89064e8i 0.240226i
\(394\) 5.02768e6i 0.00414124i
\(395\) 9.89958e8 0.808215
\(396\) −1.49280e9 −1.20801
\(397\) −1.87721e9 −1.50573 −0.752864 0.658176i \(-0.771328\pi\)
−0.752864 + 0.658176i \(0.771328\pi\)
\(398\) −9.72265e6 −0.00773026
\(399\) 1.57757e6i 0.00124332i
\(400\) 4.46360e8 0.348719
\(401\) 1.98076e8i 0.153401i 0.997054 + 0.0767003i \(0.0244384\pi\)
−0.997054 + 0.0767003i \(0.975562\pi\)
\(402\) 1.55351e6i 0.00119268i
\(403\) 1.55651e9 1.18463
\(404\) 4.53617e8 0.342259
\(405\) 1.00614e9i 0.752605i
\(406\) 174738. 0.000129582
\(407\) 6.76223e8 1.53927e9i 0.497175 1.13171i
\(408\) −5.15599e6 −0.00375838
\(409\) 3.48048e8i 0.251540i −0.992059 0.125770i \(-0.959860\pi\)
0.992059 0.125770i \(-0.0401402\pi\)
\(410\) −1.10655e7 −0.00792913
\(411\) −2.50713e8 −0.178128
\(412\) 1.43500e9i 1.01091i
\(413\) 6.40027e6i 0.00447068i
\(414\) 1.53348e7 0.0106213
\(415\) 7.13803e8i 0.490241i
\(416\) 5.41571e7 0.0368832
\(417\) −3.83670e8 −0.259109
\(418\) 2.32945e7 0.0156004
\(419\) −2.10303e8 −0.139668 −0.0698339 0.997559i \(-0.522247\pi\)
−0.0698339 + 0.997559i \(0.522247\pi\)
\(420\) 1.25905e6i 0.000829222i
\(421\) 2.42616e9i 1.58465i 0.610102 + 0.792323i \(0.291128\pi\)
−0.610102 + 0.792323i \(0.708872\pi\)
\(422\) 5.37610e6i 0.00348236i
\(423\) 1.25192e9 0.804237
\(424\) 4.23404e7i 0.0269758i
\(425\) 6.61249e8i 0.417834i
\(426\) 2.62986e6i 0.00164816i
\(427\) 5.85578e6i 0.00363988i
\(428\) −4.00613e8 −0.246985
\(429\) 3.58333e8i 0.219122i
\(430\) 2.39822e7i 0.0145462i
\(431\) 5.19659e8i 0.312643i 0.987706 + 0.156321i \(0.0499635\pi\)
−0.987706 + 0.156321i \(0.950036\pi\)
\(432\) 4.98170e8 0.297293
\(433\) −2.71549e9 −1.60746 −0.803730 0.594995i \(-0.797154\pi\)
−0.803730 + 0.594995i \(0.797154\pi\)
\(434\) −122014. −7.16465e−5
\(435\) 3.78731e8 0.220607
\(436\) 1.69640e9i 0.980222i
\(437\) 2.19855e9 1.26024
\(438\) 4.15104e6i 0.00236047i
\(439\) 2.25261e9i 1.27075i 0.772205 + 0.635374i \(0.219154\pi\)
−0.772205 + 0.635374i \(0.780846\pi\)
\(440\) 3.71846e7 0.0208103
\(441\) 1.76027e9 0.977335
\(442\) 2.67384e7i 0.0147285i
\(443\) −1.57118e9 −0.858645 −0.429322 0.903151i \(-0.641248\pi\)
−0.429322 + 0.903151i \(0.641248\pi\)
\(444\) −1.11554e8 + 2.53927e8i −0.0604845 + 0.137679i
\(445\) 2.25300e9 1.21200
\(446\) 2.43911e7i 0.0130185i
\(447\) −3.60741e8 −0.191038
\(448\) 1.29965e7 0.00682893
\(449\) 2.88058e9i 1.50182i 0.660405 + 0.750909i \(0.270385\pi\)
−0.660405 + 0.750909i \(0.729615\pi\)
\(450\) 6.87539e6i 0.00355675i
\(451\) −2.26818e9 −1.16429
\(452\) 7.81914e8i 0.398267i
\(453\) 2.39912e8 0.121257
\(454\) 6.67584e6 0.00334819
\(455\) −1.30593e7 −0.00649951
\(456\) −7.68603e6 −0.00379599
\(457\) 1.17420e9i 0.575486i −0.957708 0.287743i \(-0.907095\pi\)
0.957708 0.287743i \(-0.0929049\pi\)
\(458\) 1.71649e7i 0.00834857i
\(459\) 7.38002e8i 0.356216i
\(460\) 1.75466e9 0.840504
\(461\) 3.28279e9i 1.56059i −0.625409 0.780297i \(-0.715068\pi\)
0.625409 0.780297i \(-0.284932\pi\)
\(462\) 28089.5i 1.32525e-5i
\(463\) 6.93602e8i 0.324771i −0.986727 0.162385i \(-0.948081\pi\)
0.986727 0.162385i \(-0.0519188\pi\)
\(464\) 3.91028e9i 1.81717i
\(465\) −2.64456e8 −0.121974
\(466\) 1.81035e7i 0.00828728i
\(467\) 8.58502e8i 0.390061i 0.980797 + 0.195030i \(0.0624805\pi\)
−0.980797 + 0.195030i \(0.937519\pi\)
\(468\) 2.55432e9i 1.15190i
\(469\) 1.16053e7 0.00519459
\(470\) −1.55913e7 −0.00692690
\(471\) 3.73212e8 0.164582
\(472\) 3.11826e7 0.0136495
\(473\) 4.91584e9i 2.13591i
\(474\) 3.64345e6 0.00157141
\(475\) 9.85725e8i 0.422015i
\(476\) 1.92575e7i 0.00818419i
\(477\) −2.99553e9 −1.26375
\(478\) 1.06014e7 0.00443984
\(479\) 1.00841e9i 0.419240i 0.977783 + 0.209620i \(0.0672227\pi\)
−0.977783 + 0.209620i \(0.932777\pi\)
\(480\) −9.20146e6 −0.00379763
\(481\) 2.63382e9 + 1.15708e9i 1.07914 + 0.474082i
\(482\) −3.43009e6 −0.00139521
\(483\) 2.65111e6i 0.00107056i
\(484\) 1.31673e9 0.527883
\(485\) 8.82924e8 0.351421
\(486\) 1.15540e7i 0.00456569i
\(487\) 4.51679e9i 1.77206i −0.463629 0.886030i \(-0.653453\pi\)
0.463629 0.886030i \(-0.346547\pi\)
\(488\) −2.85298e7 −0.0111130
\(489\) 1.90518e8i 0.0736809i
\(490\) −2.19222e7 −0.00841780
\(491\) −4.14586e9 −1.58063 −0.790313 0.612704i \(-0.790082\pi\)
−0.790313 + 0.612704i \(0.790082\pi\)
\(492\) 3.74174e8 0.141643
\(493\) −5.79279e9 −2.17733
\(494\) 3.98589e7i 0.0148758i
\(495\) 2.63076e9i 0.974908i
\(496\) 2.73043e9i 1.00472i
\(497\) 1.96460e7 0.00717840
\(498\) 2.62708e6i 0.000953172i
\(499\) 1.81428e9i 0.653661i −0.945083 0.326831i \(-0.894019\pi\)
0.945083 0.326831i \(-0.105981\pi\)
\(500\) 3.04195e9i 1.08832i
\(501\) 1.81952e8i 0.0646436i
\(502\) 2.32837e6 0.000821463
\(503\) 1.73846e9i 0.609085i −0.952499 0.304542i \(-0.901496\pi\)
0.952499 0.304542i \(-0.0985035\pi\)
\(504\) 400485.i 0.000139341i
\(505\) 7.99406e8i 0.276215i
\(506\) −3.91465e7 −0.0134328
\(507\) 1.71809e8 0.0585490
\(508\) −3.66858e9 −1.24158
\(509\) 4.32091e9 1.45232 0.726160 0.687525i \(-0.241303\pi\)
0.726160 + 0.687525i \(0.241303\pi\)
\(510\) 4.54294e6i 0.00151650i
\(511\) −3.10098e7 −0.0102808
\(512\) 1.58343e8i 0.0521379i
\(513\) 1.10014e9i 0.359780i
\(514\) −4.91139e7 −0.0159527
\(515\) 2.52889e9 0.815839
\(516\) 8.10947e8i 0.259847i
\(517\) −3.19588e9 −1.01712
\(518\) −206463. 90702.4i −6.52663e−5 2.86724e-5i
\(519\) 5.23287e8 0.164306
\(520\) 6.36260e7i 0.0198437i
\(521\) 3.09896e9 0.960030 0.480015 0.877260i \(-0.340631\pi\)
0.480015 + 0.877260i \(0.340631\pi\)
\(522\) −6.02309e7 −0.0185342
\(523\) 1.42280e9i 0.434898i −0.976072 0.217449i \(-0.930226\pi\)
0.976072 0.217449i \(-0.0697737\pi\)
\(524\) 5.26013e9i 1.59712i
\(525\) −1.18863e6 −0.000358500
\(526\) 2.09113e7i 0.00626514i
\(527\) 4.04492e9 1.20385
\(528\) −6.28587e8 −0.185843
\(529\) −2.89853e8 −0.0851300
\(530\) 3.73061e7 0.0108847
\(531\) 2.20613e9i 0.639442i
\(532\) 2.87072e7i 0.00826609i
\(533\) 3.88106e9i 1.11021i
\(534\) 8.29197e6 0.00235648
\(535\) 7.05998e8i 0.199326i
\(536\) 5.65419e7i 0.0158596i
\(537\) 7.19524e8i 0.200510i
\(538\) 3.29514e7i 0.00912297i
\(539\) −4.49359e9 −1.23604
\(540\) 8.78017e8i 0.239952i
\(541\) 3.02485e9i 0.821323i −0.911788 0.410661i \(-0.865298\pi\)
0.911788 0.410661i \(-0.134702\pi\)
\(542\) 3.54448e7i 0.00956213i
\(543\) −4.24121e8 −0.113682
\(544\) 1.40739e8 0.0374815
\(545\) −2.98955e9 −0.791076
\(546\) −48063.6 −1.26369e−5
\(547\) 2.82964e9i 0.739223i 0.929186 + 0.369611i \(0.120509\pi\)
−0.929186 + 0.369611i \(0.879491\pi\)
\(548\) 4.56226e9 1.18426
\(549\) 2.01845e9i 0.520613i
\(550\) 1.75514e7i 0.00449824i
\(551\) −8.63532e9 −2.19911
\(552\) 1.29164e7 0.00326855
\(553\) 2.72179e7i 0.00684411i
\(554\) 2.73330e6 0.000682972
\(555\) −4.47494e8 1.96591e8i −0.111112 0.0488133i
\(556\) 6.98170e9 1.72266
\(557\) 5.54519e9i 1.35964i 0.733380 + 0.679819i \(0.237942\pi\)
−0.733380 + 0.679819i \(0.762058\pi\)
\(558\) 4.20574e7 0.0102476
\(559\) 8.41142e9 2.03671
\(560\) 2.29086e7i 0.00551240i
\(561\) 9.31206e8i 0.222677i
\(562\) −4.61670e7 −0.0109712
\(563\) 1.10986e9i 0.262113i 0.991375 + 0.131057i \(0.0418370\pi\)
−0.991375 + 0.131057i \(0.958163\pi\)
\(564\) 5.27212e8 0.123740
\(565\) 1.37796e9 0.321416
\(566\) −3.35492e7 −0.00777723
\(567\) 2.76629e7 0.00637319
\(568\) 9.57170e7i 0.0219164i
\(569\) 6.13313e9i 1.39569i 0.716248 + 0.697845i \(0.245858\pi\)
−0.716248 + 0.697845i \(0.754142\pi\)
\(570\) 6.77216e6i 0.00153167i
\(571\) −5.69940e9 −1.28116 −0.640579 0.767892i \(-0.721306\pi\)
−0.640579 + 0.767892i \(0.721306\pi\)
\(572\) 6.52064e9i 1.45681i
\(573\) 3.03312e8i 0.0673516i
\(574\) 304234.i 6.71453e-5i
\(575\) 1.65652e9i 0.363377i
\(576\) −4.47980e9 −0.976743
\(577\) 5.45080e9i 1.18126i 0.806943 + 0.590629i \(0.201120\pi\)
−0.806943 + 0.590629i \(0.798880\pi\)
\(578\) 2.10548e7i 0.00453528i
\(579\) 2.59817e8i 0.0556279i
\(580\) −6.89182e9 −1.46668
\(581\) 1.96253e7 0.00415145
\(582\) 3.24952e6 0.000683265
\(583\) 7.64696e9 1.59827
\(584\) 1.51082e8i 0.0313883i
\(585\) 4.50146e9 0.929626
\(586\) 3.50716e7i 0.00719969i
\(587\) 3.59960e9i 0.734549i −0.930113 0.367274i \(-0.880291\pi\)
0.930113 0.367274i \(-0.119709\pi\)
\(588\) 7.41291e8 0.150372
\(589\) 6.02977e9 1.21590
\(590\) 2.74750e7i 0.00550751i
\(591\) −2.99606e8 −0.0597027
\(592\) 2.02974e9 4.62024e9i 0.402082 0.915247i
\(593\) 3.95945e9 0.779729 0.389865 0.920872i \(-0.372522\pi\)
0.389865 + 0.920872i \(0.372522\pi\)
\(594\) 1.95886e7i 0.00383488i
\(595\) −3.39374e7 −0.00660495
\(596\) 6.56444e9 1.27009
\(597\) 5.79385e8i 0.111444i
\(598\) 6.69831e7i 0.0128089i
\(599\) −6.41846e9 −1.22022 −0.610108 0.792318i \(-0.708874\pi\)
−0.610108 + 0.792318i \(0.708874\pi\)
\(600\) 5.79109e6i 0.00109454i
\(601\) 8.93587e8 0.167910 0.0839550 0.996470i \(-0.473245\pi\)
0.0839550 + 0.996470i \(0.473245\pi\)
\(602\) −659366. −0.000123180
\(603\) −4.00027e9 −0.742983
\(604\) −4.36570e9 −0.806167
\(605\) 2.32047e9i 0.426021i
\(606\) 2.94214e6i 0.000537043i
\(607\) 1.01241e10i 1.83737i 0.394987 + 0.918687i \(0.370749\pi\)
−0.394987 + 0.918687i \(0.629251\pi\)
\(608\) 2.09799e8 0.0378566
\(609\) 1.04128e7i 0.00186814i
\(610\) 2.51376e7i 0.00448404i
\(611\) 5.46843e9i 0.969880i
\(612\) 6.63794e9i 1.17059i
\(613\) −4.29861e9 −0.753730 −0.376865 0.926268i \(-0.622998\pi\)
−0.376865 + 0.926268i \(0.622998\pi\)
\(614\) 1.08478e8i 0.0189127i
\(615\) 6.59404e8i 0.114311i
\(616\) 1.02235e6i 0.000176225i
\(617\) −2.19805e9 −0.376738 −0.188369 0.982098i \(-0.560320\pi\)
−0.188369 + 0.982098i \(0.560320\pi\)
\(618\) 9.30734e6 0.00158623
\(619\) −3.19748e9 −0.541865 −0.270932 0.962598i \(-0.587332\pi\)
−0.270932 + 0.962598i \(0.587332\pi\)
\(620\) 4.81234e9 0.810934
\(621\) 1.84879e9i 0.309790i
\(622\) 6.04054e7 0.0100649
\(623\) 6.19441e7i 0.0102634i
\(624\) 1.07557e9i 0.177211i
\(625\) −3.23171e9 −0.529483
\(626\) −7.22010e7 −0.0117634
\(627\) 1.38815e9i 0.224905i
\(628\) −6.79139e9 −1.09421
\(629\) 6.84454e9 + 3.00691e9i 1.09665 + 0.481773i
\(630\) −352867. −5.62236e−5
\(631\) 1.01591e10i 1.60972i −0.593463 0.804861i \(-0.702240\pi\)
0.593463 0.804861i \(-0.297760\pi\)
\(632\) −1.32608e8 −0.0208958
\(633\) 3.20369e8 0.0502039
\(634\) 3.06827e6i 0.000478169i
\(635\) 6.46511e9i 1.00200i
\(636\) −1.26149e9 −0.194439
\(637\) 7.68893e9i 1.17863i
\(638\) 1.53757e8 0.0234402
\(639\) −6.77187e9 −1.02673
\(640\) 2.23249e8 0.0336636
\(641\) −5.17854e8 −0.0776612 −0.0388306 0.999246i \(-0.512363\pi\)
−0.0388306 + 0.999246i \(0.512363\pi\)
\(642\) 2.59836e6i 0.000387549i
\(643\) 9.35982e9i 1.38845i −0.719760 0.694223i \(-0.755748\pi\)
0.719760 0.694223i \(-0.244252\pi\)
\(644\) 4.82426e7i 0.00711754i
\(645\) −1.42913e9 −0.209707
\(646\) 1.03582e8i 0.0151172i
\(647\) 9.45516e9i 1.37247i 0.727378 + 0.686237i \(0.240739\pi\)
−0.727378 + 0.686237i \(0.759261\pi\)
\(648\) 1.34776e8i 0.0194581i
\(649\) 5.63179e9i 0.808705i
\(650\) 3.00320e7 0.00428931
\(651\) 7.27096e6i 0.00103290i
\(652\) 3.46688e9i 0.489860i
\(653\) 3.04622e9i 0.428120i 0.976820 + 0.214060i \(0.0686689\pi\)
−0.976820 + 0.214060i \(0.931331\pi\)
\(654\) −1.10028e7 −0.00153808
\(655\) −9.26990e9 −1.28893
\(656\) −6.80814e9 −0.941597
\(657\) 1.06889e10 1.47046
\(658\) 428666.i 5.86582e-5i
\(659\) 1.28087e10 1.74343 0.871717 0.490009i \(-0.163006\pi\)
0.871717 + 0.490009i \(0.163006\pi\)
\(660\) 1.10788e9i 0.149999i
\(661\) 2.58361e9i 0.347954i 0.984750 + 0.173977i \(0.0556619\pi\)
−0.984750 + 0.173977i \(0.944338\pi\)
\(662\) 3.01601e7 0.00404045
\(663\) 1.59337e9 0.212334
\(664\) 9.56160e7i 0.0126748i
\(665\) −5.05905e7 −0.00667104
\(666\) 7.11666e7 + 3.12645e7i 0.00933505 + 0.00410102i
\(667\) 1.45117e10 1.89355
\(668\) 3.31101e9i 0.429777i
\(669\) −1.45350e9 −0.187682
\(670\) 4.98190e7 0.00639931
\(671\) 5.15268e9i 0.658422i
\(672\) 252985.i 3.21590e-5i
\(673\) −6.95576e9 −0.879613 −0.439807 0.898092i \(-0.644953\pi\)
−0.439807 + 0.898092i \(0.644953\pi\)
\(674\) 7.34317e7i 0.00923791i
\(675\) 8.28908e8 0.103739
\(676\) −3.12644e9 −0.389257
\(677\) −8.39759e9 −1.04015 −0.520073 0.854122i \(-0.674095\pi\)
−0.520073 + 0.854122i \(0.674095\pi\)
\(678\) 5.07147e6 0.000624927
\(679\) 2.42751e7i 0.00297589i
\(680\) 1.65346e8i 0.0201656i
\(681\) 3.97822e8i 0.0482696i
\(682\) −1.07364e8 −0.0129602
\(683\) 8.58541e9i 1.03107i −0.856868 0.515535i \(-0.827593\pi\)
0.856868 0.515535i \(-0.172407\pi\)
\(684\) 9.89519e9i 1.18230i
\(685\) 8.04005e9i 0.955745i
\(686\) 1.20549e6i 0.000142570i
\(687\) −1.02288e9 −0.120358
\(688\) 1.47553e10i 1.72738i
\(689\) 1.30846e10i 1.52403i
\(690\) 1.13806e7i 0.00131885i
\(691\) −2.69314e9 −0.310517 −0.155258 0.987874i \(-0.549621\pi\)
−0.155258 + 0.987874i \(0.549621\pi\)
\(692\) −9.52231e9 −1.09237
\(693\) −7.23302e7 −0.00825569
\(694\) −1.19107e8 −0.0135263
\(695\) 1.23038e10i 1.39025i
\(696\) −5.07321e7 −0.00570362
\(697\) 1.00858e10i 1.12822i
\(698\) 2.87214e7i 0.00319677i
\(699\) 1.07881e9 0.119474
\(700\) 2.16296e7 0.00238345
\(701\) 4.84603e9i 0.531341i −0.964064 0.265670i \(-0.914407\pi\)
0.964064 0.265670i \(-0.0855933\pi\)
\(702\) 3.35178e7 0.00365676
\(703\) 1.02032e10 + 4.48240e9i 1.10762 + 0.486594i
\(704\) 1.14360e10 1.23529
\(705\) 9.29103e8i 0.0998624i
\(706\) −7.91790e7 −0.00846825
\(707\) 2.19789e7 0.00233904
\(708\) 9.29056e8i 0.0983842i
\(709\) 1.60424e10i 1.69047i 0.534398 + 0.845233i \(0.320538\pi\)
−0.534398 + 0.845233i \(0.679462\pi\)
\(710\) 8.43363e7 0.00884321
\(711\) 9.38184e9i 0.978914i
\(712\) −3.01796e8 −0.0313353
\(713\) −1.01331e10 −1.04695
\(714\) −124904. −1.28420e−5
\(715\) −1.14913e10 −1.17570
\(716\) 1.30933e10i 1.33307i
\(717\) 6.31753e8i 0.0640075i
\(718\) 1.16980e8i 0.0117944i
\(719\) 8.33955e9 0.836742 0.418371 0.908276i \(-0.362601\pi\)
0.418371 + 0.908276i \(0.362601\pi\)
\(720\) 7.89646e9i 0.788440i
\(721\) 6.95292e7i 0.00690866i
\(722\) 4.89097e7i 0.00483632i
\(723\) 2.04403e8i 0.0201142i
\(724\) 7.71777e9 0.755800
\(725\) 6.50634e9i 0.634094i
\(726\) 8.54026e6i 0.000828310i
\(727\) 4.49456e9i 0.433828i −0.976191 0.216914i \(-0.930401\pi\)
0.976191 0.216914i \(-0.0695991\pi\)
\(728\) 1.74933e6 0.000168040
\(729\) −9.06738e9 −0.866833
\(730\) −1.33118e8 −0.0126651
\(731\) 2.18589e10 2.06975
\(732\) 8.50018e8i 0.0801012i
\(733\) 1.73912e10 1.63104 0.815522 0.578727i \(-0.196450\pi\)
0.815522 + 0.578727i \(0.196450\pi\)
\(734\) 3.17859e7i 0.00296687i
\(735\) 1.30637e9i 0.121356i
\(736\) −3.52569e8 −0.0325965
\(737\) 1.02118e10 0.939654
\(738\) 1.04867e8i 0.00960380i
\(739\) −1.46686e10 −1.33701 −0.668503 0.743710i \(-0.733065\pi\)
−0.668503 + 0.743710i \(0.733065\pi\)
\(740\) 8.14311e9 + 3.57739e9i 0.738719 + 0.324530i
\(741\) 2.37524e9 0.214459
\(742\) 1.02569e6i 9.21732e-5i
\(743\) −8.50015e9 −0.760266 −0.380133 0.924932i \(-0.624122\pi\)
−0.380133 + 0.924932i \(0.624122\pi\)
\(744\) 3.54247e7 0.00315356
\(745\) 1.15685e10i 1.02501i
\(746\) 5.87103e7i 0.00517760i
\(747\) −6.76471e9 −0.593782
\(748\) 1.69453e10i 1.48045i
\(749\) −1.94107e7 −0.00168793
\(750\) −1.97300e7 −0.00170770
\(751\) 7.86967e9 0.677980 0.338990 0.940790i \(-0.389915\pi\)
0.338990 + 0.940790i \(0.389915\pi\)
\(752\) −9.59270e9 −0.822580
\(753\) 1.38750e8i 0.0118427i
\(754\) 2.63091e8i 0.0223515i
\(755\) 7.69366e9i 0.650607i
\(756\) 2.41402e7 0.00203196
\(757\) 1.50730e10i 1.26289i 0.775422 + 0.631444i \(0.217537\pi\)
−0.775422 + 0.631444i \(0.782463\pi\)
\(758\) 5.84647e7i 0.00487586i
\(759\) 2.33279e9i 0.193655i
\(760\) 2.46481e8i 0.0203674i
\(761\) −2.18794e9 −0.179966 −0.0899828 0.995943i \(-0.528681\pi\)
−0.0899828 + 0.995943i \(0.528681\pi\)
\(762\) 2.37943e7i 0.00194818i
\(763\) 8.21947e7i 0.00669897i
\(764\) 5.51940e9i 0.447780i
\(765\) 1.16980e10 0.944707
\(766\) 3.37145e6 0.000271029
\(767\) −9.63648e9 −0.771143
\(768\) −1.88594e9 −0.150232
\(769\) 1.90029e10i 1.50687i −0.657521 0.753436i \(-0.728395\pi\)
0.657521 0.753436i \(-0.271605\pi\)
\(770\) 900794. 7.11063e−5
\(771\) 2.92676e9i 0.229984i
\(772\) 4.72792e9i 0.369836i
\(773\) −1.35216e10 −1.05293 −0.526466 0.850196i \(-0.676483\pi\)
−0.526466 + 0.850196i \(0.676483\pi\)
\(774\) 2.27279e8 0.0176184
\(775\) 4.54317e9i 0.350593i
\(776\) −1.18270e8 −0.00908573
\(777\) −5.40507e6 + 1.23034e7i −0.000413359 + 0.000940919i
\(778\) −7.74731e6 −0.000589824
\(779\) 1.50349e10i 1.13951i
\(780\) 1.89567e9 0.143032
\(781\) 1.72871e10 1.29851
\(782\) 1.74070e8i 0.0130167i
\(783\) 7.26154e9i 0.540583i
\(784\) −1.34879e10 −0.999627
\(785\) 1.19684e10i 0.883067i
\(786\) −3.41170e7 −0.00250606
\(787\) −2.36053e10 −1.72623 −0.863113 0.505011i \(-0.831488\pi\)
−0.863113 + 0.505011i \(0.831488\pi\)
\(788\) 5.45196e9 0.396928
\(789\) −1.24613e9 −0.0903221
\(790\) 1.16841e8i 0.00843139i
\(791\) 3.78857e7i 0.00272181i
\(792\) 3.52398e8i 0.0252055i
\(793\) 8.81668e9 0.627840
\(794\) 2.21560e8i 0.0157079i
\(795\) 2.22312e9i 0.156920i
\(796\) 1.05431e10i 0.740925i
\(797\) 1.78368e10i 1.24799i −0.781426 0.623997i \(-0.785508\pi\)
0.781426 0.623997i \(-0.214492\pi\)
\(798\) −186194. −1.29705e−5
\(799\) 1.42109e10i 0.985615i
\(800\) 1.58075e8i 0.0109156i
\(801\) 2.13517e10i 1.46798i
\(802\) 2.33781e7 0.00160029
\(803\) −2.72865e10 −1.85970
\(804\) −1.68461e9 −0.114315
\(805\) 8.50176e7 0.00574412
\(806\) 1.83708e8i 0.0123582i
\(807\) 1.96362e9 0.131522
\(808\) 1.07083e8i 0.00714135i
\(809\) 9.57799e9i 0.635996i −0.948091 0.317998i \(-0.896989\pi\)
0.948091 0.317998i \(-0.103011\pi\)
\(810\) 1.18751e8 0.00785127
\(811\) 2.97576e9 0.195896 0.0979479 0.995192i \(-0.468772\pi\)
0.0979479 + 0.995192i \(0.468772\pi\)
\(812\) 1.89484e8i 0.0124201i
\(813\) 2.11220e9 0.137853
\(814\) −1.81673e8 7.98118e7i −0.0118061 0.00518659i
\(815\) 6.10966e9 0.395335
\(816\) 2.79509e9i 0.180086i
\(817\) 3.25851e10 2.09046
\(818\) −4.10787e7 −0.00262410
\(819\) 1.23763e8i 0.00787223i
\(820\) 1.19993e10i 0.759987i
\(821\) −2.20177e10 −1.38858 −0.694291 0.719695i \(-0.744282\pi\)
−0.694291 + 0.719695i \(0.744282\pi\)
\(822\) 2.95907e7i 0.00185825i
\(823\) 2.92011e10 1.82600 0.912998 0.407964i \(-0.133761\pi\)
0.912998 + 0.407964i \(0.133761\pi\)
\(824\) −3.38752e8 −0.0210929
\(825\) −1.04591e9 −0.0648494
\(826\) 755398. 4.66386e−5
\(827\) 2.73175e10i 1.67947i −0.543000 0.839733i \(-0.682712\pi\)
0.543000 0.839733i \(-0.317288\pi\)
\(828\) 1.66289e10i 1.01802i
\(829\) 1.46616e10i 0.893797i 0.894585 + 0.446899i \(0.147472\pi\)
−0.894585 + 0.446899i \(0.852528\pi\)
\(830\) 8.42472e7 0.00511425
\(831\) 1.62881e8i 0.00984614i
\(832\) 1.95680e10i 1.17792i
\(833\) 1.99813e10i 1.19775i
\(834\) 4.52830e7i 0.00270305i
\(835\) −5.83498e9 −0.346846
\(836\) 2.52603e10i 1.49526i
\(837\) 5.07051e9i 0.298891i
\(838\) 2.48212e7i 0.00145703i
\(839\) −1.93520e10 −1.13125 −0.565625 0.824662i \(-0.691365\pi\)
−0.565625 + 0.824662i \(0.691365\pi\)
\(840\) −297217. −1.73020e−5
\(841\) −3.97481e10 −2.30425
\(842\) 2.86350e8 0.0165312
\(843\) 2.75115e9i 0.158168i
\(844\) −5.82979e9 −0.333776
\(845\) 5.50971e9i 0.314145i
\(846\) 1.47759e8i 0.00838989i
\(847\) 6.37989e7 0.00360762
\(848\) 2.29530e10 1.29257
\(849\) 1.99924e9i 0.112121i
\(850\) 7.80445e7 0.00435889
\(851\) −1.71465e10 7.53269e9i −0.953721 0.418983i
\(852\) −2.85179e9 −0.157972
\(853\) 1.74995e10i 0.965395i 0.875787 + 0.482698i \(0.160343\pi\)
−0.875787 + 0.482698i \(0.839657\pi\)
\(854\) −691133. −3.79716e−5
\(855\) 1.74382e10 0.954160
\(856\) 9.45705e7i 0.00515344i
\(857\) 9.96612e8i 0.0540870i 0.999634 + 0.0270435i \(0.00860927\pi\)
−0.999634 + 0.0270435i \(0.991391\pi\)
\(858\) −4.22926e7 −0.00228591
\(859\) 1.88375e10i 1.01402i −0.861939 0.507012i \(-0.830750\pi\)
0.861939 0.507012i \(-0.169250\pi\)
\(860\) 2.60060e10 1.39421
\(861\) 1.81297e7 0.000968008
\(862\) 6.13333e7 0.00326152
\(863\) −6.43540e9 −0.340830 −0.170415 0.985372i \(-0.554511\pi\)
−0.170415 + 0.985372i \(0.554511\pi\)
\(864\) 1.76423e8i 0.00930586i
\(865\) 1.67811e10i 0.881586i
\(866\) 3.20498e8i 0.0167692i
\(867\) 1.25468e9 0.0653833
\(868\) 1.32310e8i 0.00686713i
\(869\) 2.39499e10i 1.23804i
\(870\) 4.47001e7i 0.00230139i
\(871\) 1.74734e10i 0.896010i
\(872\) 4.00459e8 0.0204527
\(873\) 8.36748e9i 0.425643i
\(874\) 2.59486e8i 0.0131469i
\(875\) 1.47390e8i 0.00743773i
\(876\) 4.50135e9 0.226244
\(877\) −1.06279e10 −0.532043 −0.266022 0.963967i \(-0.585709\pi\)
−0.266022 + 0.963967i \(0.585709\pi\)
\(878\) 2.65866e8 0.0132566
\(879\) 2.08996e9 0.103795
\(880\) 2.01580e10i 0.997144i
\(881\) 1.01389e10 0.499545 0.249772 0.968305i \(-0.419644\pi\)
0.249772 + 0.968305i \(0.419644\pi\)
\(882\) 2.07757e8i 0.0101957i
\(883\) 1.95154e10i 0.953925i 0.878924 + 0.476963i \(0.158262\pi\)
−0.878924 + 0.476963i \(0.841738\pi\)
\(884\) −2.89948e10 −1.41168
\(885\) 1.63727e9 0.0793997
\(886\) 1.85440e8i 0.00895748i
\(887\) 1.09529e9 0.0526983 0.0263492 0.999653i \(-0.491612\pi\)
0.0263492 + 0.999653i \(0.491612\pi\)
\(888\) 5.99432e7 + 2.63339e7i 0.00287273 + 0.00126203i
\(889\) −1.77752e8 −0.00848512
\(890\) 2.65913e8i 0.0126437i
\(891\) 2.43414e10 1.15285
\(892\) 2.64495e10 1.24778
\(893\) 2.11842e10i 0.995477i
\(894\) 4.25767e7i 0.00199293i
\(895\) −2.30742e10 −1.07584
\(896\) 6.13802e6i 0.000285069i
\(897\) −3.99161e9 −0.184661
\(898\) 3.39983e8 0.0156671
\(899\) 3.97999e10 1.82693
\(900\) −7.45560e9 −0.340905
\(901\) 3.40032e10i 1.54876i
\(902\) 2.67704e8i 0.0121460i
\(903\) 3.92925e7i 0.00177583i
\(904\) −1.84582e8 −0.00830999
\(905\) 1.36010e10i 0.609959i
\(906\) 2.83158e7i 0.00126497i
\(907\) 4.29573e10i 1.91166i 0.293912 + 0.955832i \(0.405043\pi\)
−0.293912 + 0.955832i \(0.594957\pi\)
\(908\) 7.23921e9i 0.320916i
\(909\) −7.57598e9 −0.334553
\(910\) 1.54134e6i 6.78036e-5i
\(911\) 1.95080e10i 0.854865i −0.904047 0.427432i \(-0.859418\pi\)
0.904047 0.427432i \(-0.140582\pi\)
\(912\) 4.16665e9i 0.181888i
\(913\) 1.72689e10 0.750960
\(914\) −1.38586e8 −0.00600353
\(915\) −1.49798e9 −0.0646447
\(916\) 1.86134e10 0.800189
\(917\) 2.54867e8i 0.0109149i
\(918\) 8.71033e7 0.00371608
\(919\) 2.58034e10i 1.09666i 0.836261 + 0.548331i \(0.184737\pi\)
−0.836261 + 0.548331i \(0.815263\pi\)
\(920\) 4.14213e8i 0.0175374i
\(921\) −6.46436e9 −0.272657
\(922\) −3.87454e8 −0.0162803
\(923\) 2.95798e10i 1.23820i
\(924\) −3.04600e7 −0.00127022
\(925\) 3.37730e9 7.68765e9i 0.140305 0.319372i
\(926\) −8.18630e7 −0.00338805
\(927\) 2.39663e10i 0.988148i
\(928\) 1.38479e9 0.0568810
\(929\) 5.62679e9 0.230253 0.115127 0.993351i \(-0.463273\pi\)
0.115127 + 0.993351i \(0.463273\pi\)
\(930\) 3.12127e7i 0.00127245i
\(931\) 2.97862e10i 1.20974i
\(932\) −1.96313e10 −0.794314
\(933\) 3.59964e9i 0.145102i
\(934\) 1.01325e8 0.00406916
\(935\) −2.98626e10 −1.19478
\(936\) −6.02984e8 −0.0240348
\(937\) −1.67508e10 −0.665192 −0.332596 0.943069i \(-0.607925\pi\)
−0.332596 + 0.943069i \(0.607925\pi\)
\(938\) 1.36972e6i 5.41905e-5i
\(939\) 4.30255e9i 0.169588i
\(940\) 1.69070e10i 0.663925i
\(941\) 2.95555e10 1.15631 0.578155 0.815927i \(-0.303773\pi\)
0.578155 + 0.815927i \(0.303773\pi\)
\(942\) 4.40487e7i 0.00171694i
\(943\) 2.52661e10i 0.981178i
\(944\) 1.69043e10i 0.654026i
\(945\) 4.25422e7i 0.00163987i
\(946\) −5.80196e8 −0.0222821
\(947\) 2.90619e10i 1.11199i −0.831187 0.555993i \(-0.812338\pi\)
0.831187 0.555993i \(-0.187662\pi\)
\(948\) 3.95092e9i 0.150615i
\(949\) 4.66895e10i 1.77332i
\(950\) 1.16341e8 0.00440251
\(951\) −1.82842e8 −0.00689357
\(952\) 4.54602e6 0.000170766
\(953\) −2.54602e10 −0.952878 −0.476439 0.879208i \(-0.658073\pi\)
−0.476439 + 0.879208i \(0.658073\pi\)
\(954\) 3.53551e8i 0.0131835i
\(955\) 9.72681e9 0.361375
\(956\) 1.14961e10i 0.425547i
\(957\) 9.16257e9i 0.337929i
\(958\) 1.19018e8 0.00437356
\(959\) 2.21053e8 0.00809342
\(960\) 3.32466e9i 0.121283i
\(961\) −2.78397e8 −0.0101189
\(962\) 1.36565e8 3.10859e8i 0.00494568 0.0112577i
\(963\) 6.69075e9 0.241425
\(964\) 3.71955e9i 0.133728i
\(965\) 8.33199e9 0.298472
\(966\) 312900. 1.11682e−5
\(967\) 1.24502e10i 0.442777i 0.975186 + 0.221389i \(0.0710589\pi\)
−0.975186 + 0.221389i \(0.928941\pi\)
\(968\) 3.10833e8i 0.0110145i
\(969\) 6.17258e9 0.217938
\(970\) 1.04208e8i 0.00366606i
\(971\) 1.50921e10 0.529032 0.264516 0.964381i \(-0.414788\pi\)
0.264516 + 0.964381i \(0.414788\pi\)
\(972\) −1.25291e10 −0.437609
\(973\) 3.38281e8 0.0117729
\(974\) −5.33098e8 −0.0184863
\(975\) 1.78964e9i 0.0618373i
\(976\) 1.54662e10i 0.532487i
\(977\) 1.37763e10i 0.472610i −0.971679 0.236305i \(-0.924064\pi\)
0.971679 0.236305i \(-0.0759365\pi\)
\(978\) 2.24860e7 0.000768647
\(979\) 5.45065e10i 1.85656i
\(980\) 2.37722e10i 0.806824i
\(981\) 2.83320e10i 0.958155i
\(982\) 4.89318e8i 0.0164893i
\(983\) 2.51612e10 0.844880 0.422440 0.906391i \(-0.361174\pi\)
0.422440 + 0.906391i \(0.361174\pi\)
\(984\) 8.83292e7i 0.00295543i
\(985\) 9.60797e9i 0.320335i
\(986\) 6.83699e8i 0.0227141i
\(987\) 2.55448e7 0.000845653
\(988\) −4.32226e10 −1.42581
\(989\) −5.47593e10 −1.79999
\(990\) −3.10498e8 −0.0101703
\(991\) 9.62789e9i 0.314248i −0.987579 0.157124i \(-0.949778\pi\)
0.987579 0.157124i \(-0.0502223\pi\)
\(992\) −9.66958e8 −0.0314497
\(993\) 1.79728e9i 0.0582495i
\(994\) 2.31874e6i 7.48859e-5i
\(995\) 1.85801e10 0.597954
\(996\) −2.84878e9 −0.0913591
\(997\) 1.20386e10i 0.384718i −0.981325 0.192359i \(-0.938386\pi\)
0.981325 0.192359i \(-0.0616139\pi\)
\(998\) −2.14132e8 −0.00681907
\(999\) 3.76930e9 8.57996e9i 0.119614 0.272274i
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 37.8.b.a.36.10 20
37.36 even 2 inner 37.8.b.a.36.11 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.8.b.a.36.10 20 1.1 even 1 trivial
37.8.b.a.36.11 yes 20 37.36 even 2 inner