Properties

Label 91.8.h.a.16.11
Level $91$
Weight $8$
Character 91.16
Analytic conductor $28.427$
Analytic rank $0$
Dimension $126$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,8,Mod(16,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.16");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.h (of order \(3\), degree \(2\), 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: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(63\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.11
Character \(\chi\) \(=\) 91.16
Dual form 91.8.h.a.74.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-15.9608 q^{2} +(38.5973 - 66.8525i) q^{3} +126.746 q^{4} +(172.468 - 298.723i) q^{5} +(-616.042 + 1067.02i) q^{6} +(-37.4390 + 906.720i) q^{7} +20.0123 q^{8} +(-1886.00 - 3266.65i) q^{9} +O(q^{10})\) \(q-15.9608 q^{2} +(38.5973 - 66.8525i) q^{3} +126.746 q^{4} +(172.468 - 298.723i) q^{5} +(-616.042 + 1067.02i) q^{6} +(-37.4390 + 906.720i) q^{7} +20.0123 q^{8} +(-1886.00 - 3266.65i) q^{9} +(-2752.72 + 4767.84i) q^{10} +(2796.09 - 4842.97i) q^{11} +(4892.06 - 8473.29i) q^{12} +(7296.61 - 3083.49i) q^{13} +(597.555 - 14472.0i) q^{14} +(-13313.6 - 23059.8i) q^{15} -16542.9 q^{16} +23853.3 q^{17} +(30102.0 + 52138.2i) q^{18} +(-13878.5 - 24038.2i) q^{19} +(21859.6 - 37861.9i) q^{20} +(59171.4 + 37499.8i) q^{21} +(-44627.7 + 77297.5i) q^{22} +106500. q^{23} +(772.421 - 1337.87i) q^{24} +(-20427.6 - 35381.7i) q^{25} +(-116460. + 49214.9i) q^{26} -122354. q^{27} +(-4745.25 + 114923. i) q^{28} +(-32226.1 - 55817.3i) q^{29} +(212495. + 368052. i) q^{30} +(81663.5 + 141445. i) q^{31} +261476. q^{32} +(-215843. - 373851. i) q^{33} -380717. q^{34} +(264401. + 167564. i) q^{35} +(-239043. - 414035. i) q^{36} +103945. q^{37} +(221511. + 383668. i) q^{38} +(75490.4 - 606811. i) q^{39} +(3451.48 - 5978.13i) q^{40} +(-280077. - 485108. i) q^{41} +(-944421. - 598526. i) q^{42} +(190998. - 330818. i) q^{43} +(354393. - 613827. i) q^{44} -1.30110e6 q^{45} -1.69983e6 q^{46} +(-272477. + 471944. i) q^{47} +(-638512. + 1.10593e6i) q^{48} +(-820740. - 67893.4i) q^{49} +(326041. + 564719. i) q^{50} +(920671. - 1.59465e6i) q^{51} +(924818. - 390821. i) q^{52} +(619396. + 1.07283e6i) q^{53} +1.95286e6 q^{54} +(-964469. - 1.67051e6i) q^{55} +(-749.241 + 18145.6i) q^{56} -2.14268e6 q^{57} +(514354. + 890887. i) q^{58} -1.12035e6 q^{59} +(-1.68744e6 - 2.92274e6i) q^{60} +(-814508. - 1.41077e6i) q^{61} +(-1.30341e6 - 2.25758e6i) q^{62} +(3.03255e6 - 1.58777e6i) q^{63} -2.05587e6 q^{64} +(337320. - 2.71147e6i) q^{65} +(3.44502e6 + 5.96695e6i) q^{66} +(-565220. + 978989. i) q^{67} +3.02331e6 q^{68} +(4.11062e6 - 7.11981e6i) q^{69} +(-4.22004e6 - 2.67445e6i) q^{70} +(-1.19456e6 + 2.06903e6i) q^{71} +(-37743.3 - 65373.2i) q^{72} +(3.14855e6 + 5.45345e6i) q^{73} -1.65905e6 q^{74} -3.15380e6 q^{75} +(-1.75904e6 - 3.04675e6i) q^{76} +(4.28653e6 + 2.71659e6i) q^{77} +(-1.20488e6 + 9.68517e6i) q^{78} +(-4.01256e6 + 6.94995e6i) q^{79} +(-2.85312e6 + 4.94174e6i) q^{80} +(-597829. + 1.03547e6i) q^{81} +(4.47025e6 + 7.74269e6i) q^{82} -2.41352e6 q^{83} +(7.49975e6 + 4.75296e6i) q^{84} +(4.11392e6 - 7.12551e6i) q^{85} +(-3.04848e6 + 5.28011e6i) q^{86} -4.97536e6 q^{87} +(55956.2 - 96919.0i) q^{88} -9.90260e6 q^{89} +2.07665e7 q^{90} +(2.52269e6 + 6.73143e6i) q^{91} +1.34985e7 q^{92} +1.26080e7 q^{93} +(4.34894e6 - 7.53259e6i) q^{94} -9.57434e6 q^{95} +(1.00923e7 - 1.74803e7i) q^{96} +(-4.44499e6 + 7.69894e6i) q^{97} +(1.30996e7 + 1.08363e6i) q^{98} -2.10937e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.9608 −1.41075 −0.705373 0.708836i \(-0.749220\pi\)
−0.705373 + 0.708836i \(0.749220\pi\)
\(3\) 38.5973 66.8525i 0.825339 1.42953i −0.0763210 0.997083i \(-0.524317\pi\)
0.901660 0.432446i \(-0.142349\pi\)
\(4\) 126.746 0.990204
\(5\) 172.468 298.723i 0.617039 1.06874i −0.372984 0.927838i \(-0.621666\pi\)
0.990023 0.140905i \(-0.0450012\pi\)
\(6\) −616.042 + 1067.02i −1.16434 + 2.01670i
\(7\) −37.4390 + 906.720i −0.0412554 + 0.999149i
\(8\) 20.0123 0.0138192
\(9\) −1886.00 3266.65i −0.862369 1.49367i
\(10\) −2752.72 + 4767.84i −0.870485 + 1.50772i
\(11\) 2796.09 4842.97i 0.633398 1.09708i −0.353454 0.935452i \(-0.614993\pi\)
0.986852 0.161625i \(-0.0516736\pi\)
\(12\) 4892.06 8473.29i 0.817254 1.41553i
\(13\) 7296.61 3083.49i 0.921127 0.389261i
\(14\) 597.555 14472.0i 0.0582009 1.40954i
\(15\) −13313.6 23059.8i −1.01853 1.76415i
\(16\) −16542.9 −1.00970
\(17\) 23853.3 1.17754 0.588771 0.808300i \(-0.299612\pi\)
0.588771 + 0.808300i \(0.299612\pi\)
\(18\) 30102.0 + 52138.2i 1.21658 + 2.10718i
\(19\) −13878.5 24038.2i −0.464199 0.804015i 0.534966 0.844873i \(-0.320324\pi\)
−0.999165 + 0.0408579i \(0.986991\pi\)
\(20\) 21859.6 37861.9i 0.610994 1.05827i
\(21\) 59171.4 + 37499.8i 1.39426 + 0.883612i
\(22\) −44627.7 + 77297.5i −0.893563 + 1.54770i
\(23\) 106500. 1.82517 0.912585 0.408887i \(-0.134083\pi\)
0.912585 + 0.408887i \(0.134083\pi\)
\(24\) 772.421 1337.87i 0.0114055 0.0197549i
\(25\) −20427.6 35381.7i −0.261474 0.452886i
\(26\) −116460. + 49214.9i −1.29948 + 0.549149i
\(27\) −122354. −1.19631
\(28\) −4745.25 + 114923.i −0.0408513 + 0.989361i
\(29\) −32226.1 55817.3i −0.245366 0.424987i 0.716868 0.697209i \(-0.245575\pi\)
−0.962235 + 0.272222i \(0.912242\pi\)
\(30\) 212495. + 368052.i 1.43689 + 2.48877i
\(31\) 81663.5 + 141445.i 0.492336 + 0.852752i 0.999961 0.00882662i \(-0.00280964\pi\)
−0.507625 + 0.861578i \(0.669476\pi\)
\(32\) 261476. 1.41061
\(33\) −215843. 373851.i −1.04554 1.81092i
\(34\) −380717. −1.66121
\(35\) 264401. + 167564.i 1.04238 + 0.660605i
\(36\) −239043. 414035.i −0.853921 1.47904i
\(37\) 103945. 0.337364 0.168682 0.985671i \(-0.446049\pi\)
0.168682 + 0.985671i \(0.446049\pi\)
\(38\) 221511. + 383668.i 0.654866 + 1.13426i
\(39\) 75490.4 606811.i 0.203782 1.63805i
\(40\) 3451.48 5978.13i 0.00852698 0.0147692i
\(41\) −280077. 485108.i −0.634650 1.09925i −0.986589 0.163223i \(-0.947811\pi\)
0.351939 0.936023i \(-0.385522\pi\)
\(42\) −944421. 598526.i −1.96695 1.24655i
\(43\) 190998. 330818.i 0.366344 0.634527i −0.622647 0.782503i \(-0.713943\pi\)
0.988991 + 0.147976i \(0.0472760\pi\)
\(44\) 354393. 613827.i 0.627193 1.08633i
\(45\) −1.30110e6 −2.12846
\(46\) −1.69983e6 −2.57485
\(47\) −272477. + 471944.i −0.382814 + 0.663052i −0.991463 0.130387i \(-0.958378\pi\)
0.608650 + 0.793439i \(0.291711\pi\)
\(48\) −638512. + 1.10593e6i −0.833345 + 1.44340i
\(49\) −820740. 67893.4i −0.996596 0.0824406i
\(50\) 326041. + 564719.i 0.368873 + 0.638907i
\(51\) 920671. 1.59465e6i 0.971872 1.68333i
\(52\) 924818. 390821.i 0.912104 0.385448i
\(53\) 619396. + 1.07283e6i 0.571482 + 0.989836i 0.996414 + 0.0846110i \(0.0269648\pi\)
−0.424932 + 0.905225i \(0.639702\pi\)
\(54\) 1.95286e6 1.68769
\(55\) −964469. 1.67051e6i −0.781662 1.35388i
\(56\) −749.241 + 18145.6i −0.000570116 + 0.0138074i
\(57\) −2.14268e6 −1.53248
\(58\) 514354. + 890887.i 0.346150 + 0.599549i
\(59\) −1.12035e6 −0.710187 −0.355094 0.934831i \(-0.615551\pi\)
−0.355094 + 0.934831i \(0.615551\pi\)
\(60\) −1.68744e6 2.92274e6i −1.00856 1.74687i
\(61\) −814508. 1.41077e6i −0.459453 0.795795i 0.539479 0.841999i \(-0.318621\pi\)
−0.998932 + 0.0462034i \(0.985288\pi\)
\(62\) −1.30341e6 2.25758e6i −0.694562 1.20302i
\(63\) 3.03255e6 1.58777e6i 1.52797 0.800013i
\(64\) −2.05587e6 −0.980314
\(65\) 337320. 2.71147e6i 0.152351 1.22464i
\(66\) 3.44502e6 + 5.96695e6i 1.47499 + 2.55475i
\(67\) −565220. + 978989.i −0.229591 + 0.397664i −0.957687 0.287812i \(-0.907072\pi\)
0.728096 + 0.685475i \(0.240406\pi\)
\(68\) 3.02331e6 1.16601
\(69\) 4.11062e6 7.11981e6i 1.50638 2.60913i
\(70\) −4.22004e6 2.67445e6i −1.47053 0.931946i
\(71\) −1.19456e6 + 2.06903e6i −0.396098 + 0.686062i −0.993241 0.116073i \(-0.962969\pi\)
0.597143 + 0.802135i \(0.296303\pi\)
\(72\) −37743.3 65373.2i −0.0119172 0.0206413i
\(73\) 3.14855e6 + 5.45345e6i 0.947284 + 1.64074i 0.751112 + 0.660175i \(0.229518\pi\)
0.196172 + 0.980569i \(0.437149\pi\)
\(74\) −1.65905e6 −0.475935
\(75\) −3.15380e6 −0.863218
\(76\) −1.75904e6 3.04675e6i −0.459651 0.796140i
\(77\) 4.28653e6 + 2.71659e6i 1.07001 + 0.678119i
\(78\) −1.20488e6 + 9.68517e6i −0.287484 + 2.31087i
\(79\) −4.01256e6 + 6.94995e6i −0.915644 + 1.58594i −0.109687 + 0.993966i \(0.534985\pi\)
−0.805956 + 0.591975i \(0.798348\pi\)
\(80\) −2.85312e6 + 4.94174e6i −0.623024 + 1.07911i
\(81\) −597829. + 1.03547e6i −0.124991 + 0.216491i
\(82\) 4.47025e6 + 7.74269e6i 0.895330 + 1.55076i
\(83\) −2.41352e6 −0.463316 −0.231658 0.972797i \(-0.574415\pi\)
−0.231658 + 0.972797i \(0.574415\pi\)
\(84\) 7.49975e6 + 4.75296e6i 1.38060 + 0.874957i
\(85\) 4.11392e6 7.12551e6i 0.726589 1.25849i
\(86\) −3.04848e6 + 5.28011e6i −0.516819 + 0.895156i
\(87\) −4.97536e6 −0.810042
\(88\) 55956.2 96919.0i 0.00875304 0.0151607i
\(89\) −9.90260e6 −1.48896 −0.744482 0.667643i \(-0.767303\pi\)
−0.744482 + 0.667643i \(0.767303\pi\)
\(90\) 2.07665e7 3.00272
\(91\) 2.52269e6 + 6.73143e6i 0.350929 + 0.936402i
\(92\) 1.34985e7 1.80729
\(93\) 1.26080e7 1.62538
\(94\) 4.34894e6 7.53259e6i 0.540053 0.935399i
\(95\) −9.57434e6 −1.14571
\(96\) 1.00923e7 1.74803e7i 1.16423 2.01651i
\(97\) −4.44499e6 + 7.69894e6i −0.494503 + 0.856505i −0.999980 0.00633523i \(-0.997983\pi\)
0.505476 + 0.862840i \(0.331317\pi\)
\(98\) 1.30996e7 + 1.08363e6i 1.40594 + 0.116303i
\(99\) −2.10937e7 −2.18489
\(100\) −2.58912e6 4.48449e6i −0.258912 0.448449i
\(101\) 215804. 373784.i 0.0208418 0.0360991i −0.855416 0.517941i \(-0.826699\pi\)
0.876258 + 0.481842i \(0.160032\pi\)
\(102\) −1.46946e7 + 2.54518e7i −1.37106 + 2.37475i
\(103\) 4.22984e6 7.32629e6i 0.381411 0.660623i −0.609853 0.792514i \(-0.708772\pi\)
0.991264 + 0.131891i \(0.0421049\pi\)
\(104\) 146022. 61707.9i 0.0127292 0.00537928i
\(105\) 2.14072e7 1.12083e7i 1.80467 0.944884i
\(106\) −9.88604e6 1.71231e7i −0.806216 1.39641i
\(107\) −1.25112e7 −0.987317 −0.493659 0.869656i \(-0.664341\pi\)
−0.493659 + 0.869656i \(0.664341\pi\)
\(108\) −1.55078e7 −1.18459
\(109\) −3.23843e6 5.60912e6i −0.239520 0.414860i 0.721057 0.692876i \(-0.243657\pi\)
−0.960577 + 0.278016i \(0.910323\pi\)
\(110\) 1.53937e7 + 2.66626e7i 1.10273 + 1.90998i
\(111\) 4.01200e6 6.94899e6i 0.278439 0.482271i
\(112\) 619350. 1.49998e7i 0.0416556 1.00884i
\(113\) 1.66254e6 2.87960e6i 0.108392 0.187740i −0.806727 0.590924i \(-0.798763\pi\)
0.915119 + 0.403184i \(0.132097\pi\)
\(114\) 3.41989e7 2.16195
\(115\) 1.83678e7 3.18140e7i 1.12620 1.95064i
\(116\) −4.08454e6 7.07463e6i −0.242963 0.420824i
\(117\) −2.38341e7 1.80200e7i −1.37578 1.04017i
\(118\) 1.78817e7 1.00189
\(119\) −893042. + 2.16282e7i −0.0485800 + 1.17654i
\(120\) −266435. 461479.i −0.0140753 0.0243791i
\(121\) −5.89264e6 1.02063e7i −0.302385 0.523747i
\(122\) 1.30002e7 + 2.25170e7i 0.648171 + 1.12267i
\(123\) −4.32409e7 −2.09520
\(124\) 1.03505e7 + 1.79276e7i 0.487514 + 0.844398i
\(125\) 1.28556e7 0.588720
\(126\) −4.84018e7 + 2.53421e7i −2.15558 + 1.12861i
\(127\) 1.83011e6 + 3.16984e6i 0.0792801 + 0.137317i 0.902940 0.429768i \(-0.141405\pi\)
−0.823659 + 0.567085i \(0.808071\pi\)
\(128\) −655732. −0.0276371
\(129\) −1.47440e7 2.55374e7i −0.604716 1.04740i
\(130\) −5.38389e6 + 4.32771e7i −0.214929 + 1.72765i
\(131\) 7.66904e6 1.32832e7i 0.298052 0.516241i −0.677638 0.735395i \(-0.736997\pi\)
0.975690 + 0.219154i \(0.0703299\pi\)
\(132\) −2.73573e7 4.73841e7i −1.03529 1.79318i
\(133\) 2.23155e7 1.16839e7i 0.822482 0.430633i
\(134\) 9.02134e6 1.56254e7i 0.323895 0.561003i
\(135\) −2.11020e7 + 3.65498e7i −0.738169 + 1.27855i
\(136\) 477359. 0.0162727
\(137\) −2.75106e7 −0.914069 −0.457034 0.889449i \(-0.651088\pi\)
−0.457034 + 0.889449i \(0.651088\pi\)
\(138\) −6.56087e7 + 1.13638e8i −2.12513 + 3.68082i
\(139\) 8.87362e6 1.53696e7i 0.280252 0.485411i −0.691195 0.722669i \(-0.742915\pi\)
0.971447 + 0.237258i \(0.0762486\pi\)
\(140\) 3.35118e7 + 2.12381e7i 1.03217 + 0.654134i
\(141\) 2.10337e7 + 3.64315e7i 0.631902 + 1.09449i
\(142\) 1.90660e7 3.30233e7i 0.558793 0.967859i
\(143\) 5.46872e6 4.39590e7i 0.156390 1.25710i
\(144\) 3.12000e7 + 5.40399e7i 0.870734 + 1.50815i
\(145\) −2.22318e7 −0.605602
\(146\) −5.02532e7 8.70412e7i −1.33638 2.31467i
\(147\) −3.62172e7 + 5.22480e7i −0.940381 + 1.35662i
\(148\) 1.31747e7 0.334059
\(149\) 3.88628e7 + 6.73123e7i 0.962458 + 1.66703i 0.716294 + 0.697798i \(0.245837\pi\)
0.246164 + 0.969228i \(0.420830\pi\)
\(150\) 5.03371e7 1.21778
\(151\) 1.02396e7 + 1.77355e7i 0.242026 + 0.419202i 0.961291 0.275534i \(-0.0888547\pi\)
−0.719265 + 0.694736i \(0.755521\pi\)
\(152\) −277740. 481060.i −0.00641485 0.0111108i
\(153\) −4.49873e7 7.79203e7i −1.01548 1.75886i
\(154\) −6.84164e7 4.33588e7i −1.50952 0.956653i
\(155\) 5.63372e7 1.21516
\(156\) 9.56811e6 7.69110e7i 0.201786 1.62201i
\(157\) −1.49462e7 2.58875e7i −0.308234 0.533877i 0.669742 0.742594i \(-0.266405\pi\)
−0.977976 + 0.208717i \(0.933071\pi\)
\(158\) 6.40435e7 1.10927e8i 1.29174 2.23736i
\(159\) 9.56280e7 1.88667
\(160\) 4.50962e7 7.81088e7i 0.870401 1.50758i
\(161\) −3.98726e6 + 9.65659e7i −0.0752982 + 1.82362i
\(162\) 9.54182e6 1.65269e7i 0.176331 0.305414i
\(163\) 2.69908e6 + 4.67495e6i 0.0488157 + 0.0845513i 0.889401 0.457128i \(-0.151122\pi\)
−0.840585 + 0.541680i \(0.817789\pi\)
\(164\) −3.54987e7 6.14855e7i −0.628433 1.08848i
\(165\) −1.48904e8 −2.58054
\(166\) 3.85216e7 0.653622
\(167\) 4.55690e7 + 7.89278e7i 0.757115 + 1.31136i 0.944316 + 0.329040i \(0.106725\pi\)
−0.187201 + 0.982322i \(0.559942\pi\)
\(168\) 1.18416e6 + 750459.i 0.0192676 + 0.0122108i
\(169\) 4.37326e7 4.49981e7i 0.696951 0.717119i
\(170\) −6.56613e7 + 1.13729e8i −1.02503 + 1.77541i
\(171\) −5.23496e7 + 9.06721e7i −0.800621 + 1.38672i
\(172\) 2.42083e7 4.19299e7i 0.362756 0.628311i
\(173\) 6.24306e6 + 1.08133e7i 0.0916719 + 0.158780i 0.908215 0.418504i \(-0.137446\pi\)
−0.816543 + 0.577285i \(0.804112\pi\)
\(174\) 7.94106e7 1.14276
\(175\) 3.28461e7 1.71975e7i 0.463287 0.242567i
\(176\) −4.62555e7 + 8.01168e7i −0.639542 + 1.10772i
\(177\) −4.32426e7 + 7.48984e7i −0.586145 + 1.01523i
\(178\) 1.58053e8 2.10055
\(179\) −1.24987e7 + 2.16484e7i −0.162885 + 0.282125i −0.935902 0.352260i \(-0.885413\pi\)
0.773017 + 0.634385i \(0.218747\pi\)
\(180\) −1.64909e8 −2.10761
\(181\) −2.01268e7 −0.252290 −0.126145 0.992012i \(-0.540260\pi\)
−0.126145 + 0.992012i \(0.540260\pi\)
\(182\) −4.02640e7 1.07439e8i −0.495071 1.32103i
\(183\) −1.25751e8 −1.51682
\(184\) 2.13132e6 0.0252224
\(185\) 1.79272e7 3.10508e7i 0.208167 0.360555i
\(186\) −2.01233e8 −2.29300
\(187\) 6.66958e7 1.15521e8i 0.745853 1.29186i
\(188\) −3.45354e7 + 5.98171e7i −0.379064 + 0.656557i
\(189\) 4.58079e6 1.10940e8i 0.0493542 1.19529i
\(190\) 1.52814e8 1.61631
\(191\) 9.32969e6 + 1.61595e7i 0.0968837 + 0.167807i 0.910393 0.413744i \(-0.135779\pi\)
−0.813510 + 0.581552i \(0.802446\pi\)
\(192\) −7.93509e7 + 1.37440e8i −0.809091 + 1.40139i
\(193\) 2.06832e7 3.58243e7i 0.207094 0.358697i −0.743704 0.668509i \(-0.766933\pi\)
0.950798 + 0.309812i \(0.100266\pi\)
\(194\) 7.09454e7 1.22881e8i 0.697619 1.20831i
\(195\) −1.68249e8 1.27206e8i −1.62491 1.22853i
\(196\) −1.04026e8 8.60522e6i −0.986834 0.0816330i
\(197\) −8.48822e6 1.47020e7i −0.0791015 0.137008i 0.823761 0.566937i \(-0.191872\pi\)
−0.902863 + 0.429929i \(0.858538\pi\)
\(198\) 3.36672e8 3.08232
\(199\) 1.47367e8 1.32560 0.662802 0.748795i \(-0.269367\pi\)
0.662802 + 0.748795i \(0.269367\pi\)
\(200\) −408804. 708070.i −0.00361335 0.00625851i
\(201\) 4.36319e7 + 7.55726e7i 0.378981 + 0.656415i
\(202\) −3.44440e6 + 5.96588e6i −0.0294025 + 0.0509266i
\(203\) 5.18172e7 2.71303e7i 0.434748 0.227625i
\(204\) 1.16692e8 2.02116e8i 0.962352 1.66684i
\(205\) −1.93217e8 −1.56641
\(206\) −6.75115e7 + 1.16933e8i −0.538074 + 0.931972i
\(207\) −2.00860e8 3.47899e8i −1.57397 2.72620i
\(208\) −1.20707e8 + 5.10100e7i −0.930062 + 0.393037i
\(209\) −1.55222e8 −1.17609
\(210\) −3.41675e8 + 1.78894e8i −2.54593 + 1.33299i
\(211\) 460478. + 797571.i 0.00337458 + 0.00584495i 0.867708 0.497075i \(-0.165593\pi\)
−0.864333 + 0.502920i \(0.832259\pi\)
\(212\) 7.85061e7 + 1.35976e8i 0.565884 + 0.980140i
\(213\) 9.22133e7 + 1.59718e8i 0.653830 + 1.13247i
\(214\) 1.99689e8 1.39285
\(215\) −6.58819e7 1.14111e8i −0.452097 0.783055i
\(216\) −2.44858e6 −0.0165320
\(217\) −1.31309e8 + 6.87504e7i −0.872337 + 0.456737i
\(218\) 5.16878e7 + 8.95258e7i 0.337901 + 0.585262i
\(219\) 4.86102e8 3.12732
\(220\) −1.22243e8 2.11731e8i −0.774005 1.34062i
\(221\) 1.74048e8 7.35514e7i 1.08467 0.458372i
\(222\) −6.40347e7 + 1.10911e8i −0.392807 + 0.680362i
\(223\) −5.13732e7 8.89810e7i −0.310220 0.537317i 0.668190 0.743991i \(-0.267069\pi\)
−0.978410 + 0.206674i \(0.933736\pi\)
\(224\) −9.78940e6 + 2.37086e8i −0.0581953 + 1.40941i
\(225\) −7.70530e7 + 1.33460e8i −0.450973 + 0.781109i
\(226\) −2.65354e7 + 4.59607e7i −0.152914 + 0.264854i
\(227\) 2.28079e8 1.29418 0.647090 0.762413i \(-0.275986\pi\)
0.647090 + 0.762413i \(0.275986\pi\)
\(228\) −2.71577e8 −1.51747
\(229\) 7.22321e7 1.25110e8i 0.397471 0.688440i −0.595942 0.803028i \(-0.703221\pi\)
0.993413 + 0.114587i \(0.0365545\pi\)
\(230\) −2.93165e8 + 5.07777e8i −1.58878 + 2.75185i
\(231\) 3.47059e8 1.81712e8i 1.85251 0.969935i
\(232\) −644920. 1.11703e6i −0.00339077 0.00587298i
\(233\) 8.06305e7 1.39656e8i 0.417593 0.723293i −0.578103 0.815964i \(-0.696207\pi\)
0.995697 + 0.0926705i \(0.0295403\pi\)
\(234\) 3.80411e8 + 2.87613e8i 1.94087 + 1.46742i
\(235\) 9.39869e7 + 1.62790e8i 0.472422 + 0.818258i
\(236\) −1.42000e8 −0.703231
\(237\) 3.09748e8 + 5.36499e8i 1.51143 + 2.61788i
\(238\) 1.42536e7 3.45203e8i 0.0685341 1.65980i
\(239\) −3.14727e8 −1.49122 −0.745610 0.666383i \(-0.767842\pi\)
−0.745610 + 0.666383i \(0.767842\pi\)
\(240\) 2.20245e8 + 3.81476e8i 1.02841 + 1.78126i
\(241\) −2.59675e8 −1.19501 −0.597504 0.801866i \(-0.703841\pi\)
−0.597504 + 0.801866i \(0.703841\pi\)
\(242\) 9.40510e7 + 1.62901e8i 0.426589 + 0.738874i
\(243\) −8.76444e7 1.51805e8i −0.391834 0.678676i
\(244\) −1.03236e8 1.78810e8i −0.454952 0.788000i
\(245\) −1.61832e8 + 2.33464e8i −0.703046 + 1.01424i
\(246\) 6.90157e8 2.95580
\(247\) −1.75387e8 1.32603e8i −0.740558 0.559906i
\(248\) 1.63428e6 + 2.83065e6i 0.00680369 + 0.0117843i
\(249\) −9.31553e7 + 1.61350e8i −0.382393 + 0.662324i
\(250\) −2.05186e8 −0.830534
\(251\) 1.35065e8 2.33940e8i 0.539120 0.933784i −0.459831 0.888006i \(-0.652090\pi\)
0.998952 0.0457776i \(-0.0145766\pi\)
\(252\) 3.84364e8 2.01244e8i 1.51300 0.792176i
\(253\) 2.97784e8 5.15777e8i 1.15606 2.00235i
\(254\) −2.92100e7 5.05931e7i −0.111844 0.193720i
\(255\) −3.17572e8 5.50051e8i −1.19937 2.07736i
\(256\) 2.73617e8 1.01930
\(257\) 1.11406e8 0.409396 0.204698 0.978825i \(-0.434379\pi\)
0.204698 + 0.978825i \(0.434379\pi\)
\(258\) 2.35326e8 + 4.07596e8i 0.853101 + 1.47761i
\(259\) −3.89160e6 + 9.42492e7i −0.0139181 + 0.337077i
\(260\) 4.27540e7 3.43668e8i 0.150859 1.21264i
\(261\) −1.21557e8 + 2.10543e8i −0.423193 + 0.732991i
\(262\) −1.22404e8 + 2.12010e8i −0.420475 + 0.728285i
\(263\) 4.48394e7 7.76640e7i 0.151990 0.263254i −0.779969 0.625818i \(-0.784765\pi\)
0.931959 + 0.362564i \(0.118099\pi\)
\(264\) −4.31952e6 7.48162e6i −0.0144485 0.0250255i
\(265\) 4.27303e8 1.41051
\(266\) −3.56173e8 + 1.86484e8i −1.16031 + 0.607514i
\(267\) −3.82213e8 + 6.62013e8i −1.22890 + 2.12852i
\(268\) −7.16394e7 + 1.24083e8i −0.227342 + 0.393768i
\(269\) 4.58480e8 1.43611 0.718055 0.695986i \(-0.245033\pi\)
0.718055 + 0.695986i \(0.245033\pi\)
\(270\) 3.36804e8 5.83362e8i 1.04137 1.80370i
\(271\) −4.95004e8 −1.51083 −0.755416 0.655246i \(-0.772565\pi\)
−0.755416 + 0.655246i \(0.772565\pi\)
\(272\) −3.94603e8 −1.18896
\(273\) 5.47382e8 + 9.11670e7i 1.62825 + 0.271187i
\(274\) 4.39091e8 1.28952
\(275\) −2.28470e8 −0.662467
\(276\) 5.21006e8 9.02408e8i 1.49163 2.58358i
\(277\) −6.47705e8 −1.83104 −0.915520 0.402272i \(-0.868221\pi\)
−0.915520 + 0.402272i \(0.868221\pi\)
\(278\) −1.41630e8 + 2.45310e8i −0.395364 + 0.684791i
\(279\) 3.08035e8 5.33532e8i 0.849151 1.47077i
\(280\) 5.29127e6 + 3.35334e6i 0.0144048 + 0.00912902i
\(281\) −5.00662e8 −1.34608 −0.673042 0.739604i \(-0.735013\pi\)
−0.673042 + 0.739604i \(0.735013\pi\)
\(282\) −3.35715e8 5.81475e8i −0.891453 1.54404i
\(283\) −6.12867e7 + 1.06152e8i −0.160736 + 0.278403i −0.935133 0.354297i \(-0.884720\pi\)
0.774397 + 0.632700i \(0.218054\pi\)
\(284\) −1.51405e8 + 2.62242e8i −0.392218 + 0.679341i
\(285\) −3.69543e8 + 6.40068e8i −0.945602 + 1.63783i
\(286\) −8.72850e7 + 7.01619e8i −0.220627 + 1.77346i
\(287\) 4.50343e8 2.35790e8i 1.12449 0.588760i
\(288\) −4.93144e8 8.54151e8i −1.21647 2.10698i
\(289\) 1.58640e8 0.386607
\(290\) 3.54837e8 0.854351
\(291\) 3.43129e8 + 5.94317e8i 0.816266 + 1.41381i
\(292\) 3.99066e8 + 6.91203e8i 0.938005 + 1.62467i
\(293\) −4.72477e7 + 8.18354e7i −0.109735 + 0.190066i −0.915663 0.401947i \(-0.868333\pi\)
0.805928 + 0.592013i \(0.201667\pi\)
\(294\) 5.78054e8 8.33918e8i 1.32664 1.91385i
\(295\) −1.93225e8 + 3.34675e8i −0.438213 + 0.759007i
\(296\) 2.08019e6 0.00466209
\(297\) −3.42111e8 + 5.92554e8i −0.757739 + 1.31244i
\(298\) −6.20280e8 1.07436e9i −1.35778 2.35175i
\(299\) 7.77092e8 3.28393e8i 1.68121 0.710468i
\(300\) −3.99733e8 −0.854762
\(301\) 2.92809e8 + 1.85567e8i 0.618873 + 0.392210i
\(302\) −1.63431e8 2.83071e8i −0.341437 0.591387i
\(303\) −1.66589e7 2.88541e7i −0.0344031 0.0595879i
\(304\) 2.29590e8 + 3.97662e8i 0.468701 + 0.811814i
\(305\) −5.61905e8 −1.13400
\(306\) 7.18032e8 + 1.24367e9i 1.43258 + 2.48130i
\(307\) −5.99765e8 −1.18303 −0.591516 0.806293i \(-0.701470\pi\)
−0.591516 + 0.806293i \(0.701470\pi\)
\(308\) 5.43302e8 + 3.44317e8i 1.05953 + 0.671476i
\(309\) −3.26520e8 5.65550e8i −0.629587 1.09048i
\(310\) −8.99185e8 −1.71429
\(311\) 3.48452e8 + 6.03537e8i 0.656874 + 1.13774i 0.981420 + 0.191870i \(0.0614550\pi\)
−0.324546 + 0.945870i \(0.605212\pi\)
\(312\) 1.51074e6 1.21437e7i 0.00281610 0.0226365i
\(313\) 4.41726e7 7.65091e7i 0.0814231 0.141029i −0.822438 0.568854i \(-0.807387\pi\)
0.903861 + 0.427825i \(0.140720\pi\)
\(314\) 2.38552e8 + 4.13184e8i 0.434840 + 0.753165i
\(315\) 4.87117e7 1.17973e9i 0.0878105 2.12665i
\(316\) −5.08576e8 + 8.80880e8i −0.906674 + 1.57041i
\(317\) −3.77512e8 + 6.53870e8i −0.665615 + 1.15288i 0.313503 + 0.949587i \(0.398497\pi\)
−0.979118 + 0.203292i \(0.934836\pi\)
\(318\) −1.52630e9 −2.66161
\(319\) −3.60428e8 −0.621658
\(320\) −3.54570e8 + 6.14134e8i −0.604892 + 1.04770i
\(321\) −4.82900e8 + 8.36407e8i −0.814872 + 1.41140i
\(322\) 6.36398e7 1.54127e9i 0.106227 2.57266i
\(323\) −3.31047e8 5.73390e8i −0.546614 0.946763i
\(324\) −7.57726e7 + 1.31242e8i −0.123767 + 0.214371i
\(325\) −2.58152e8 1.95178e8i −0.417141 0.315384i
\(326\) −4.30794e7 7.46158e7i −0.0688665 0.119280i
\(327\) −4.99978e8 −0.790740
\(328\) −5.60499e6 9.70813e6i −0.00877035 0.0151907i
\(329\) −4.17720e8 2.64729e8i −0.646695 0.409842i
\(330\) 2.37662e9 3.64049
\(331\) 1.72551e8 + 2.98868e8i 0.261529 + 0.452982i 0.966648 0.256107i \(-0.0824399\pi\)
−0.705119 + 0.709089i \(0.749107\pi\)
\(332\) −3.05904e8 −0.458778
\(333\) −1.96041e8 3.39553e8i −0.290932 0.503909i
\(334\) −7.27316e8 1.25975e9i −1.06810 1.85000i
\(335\) 1.94964e8 + 3.37688e8i 0.283333 + 0.490748i
\(336\) −9.78868e8 6.20357e8i −1.40779 0.892183i
\(337\) 8.15446e8 1.16062 0.580311 0.814395i \(-0.302931\pi\)
0.580311 + 0.814395i \(0.302931\pi\)
\(338\) −6.98007e8 + 7.18205e8i −0.983221 + 1.01167i
\(339\) −1.28339e8 2.22290e8i −0.178920 0.309899i
\(340\) 5.21423e8 9.03131e8i 0.719472 1.24616i
\(341\) 9.13353e8 1.24738
\(342\) 8.35540e8 1.44720e9i 1.12947 1.95630i
\(343\) 9.22879e7 7.41639e8i 0.123485 0.992346i
\(344\) 3.82231e6 6.62044e6i 0.00506258 0.00876864i
\(345\) −1.41790e9 2.45587e9i −1.85899 3.21987i
\(346\) −9.96441e7 1.72589e8i −0.129326 0.223999i
\(347\) 1.88432e8 0.242104 0.121052 0.992646i \(-0.461373\pi\)
0.121052 + 0.992646i \(0.461373\pi\)
\(348\) −6.30608e8 −0.802107
\(349\) −2.03516e8 3.52499e8i −0.256277 0.443884i 0.708965 0.705244i \(-0.249162\pi\)
−0.965241 + 0.261360i \(0.915829\pi\)
\(350\) −5.24249e8 + 2.74485e8i −0.653581 + 0.342200i
\(351\) −8.92766e8 + 3.77276e8i −1.10195 + 0.465677i
\(352\) 7.31110e8 1.26632e9i 0.893478 1.54755i
\(353\) −1.77906e8 + 3.08143e8i −0.215268 + 0.372855i −0.953355 0.301850i \(-0.902396\pi\)
0.738087 + 0.674705i \(0.235729\pi\)
\(354\) 6.90185e8 1.19544e9i 0.826902 1.43224i
\(355\) 4.12045e8 + 7.13682e8i 0.488815 + 0.846653i
\(356\) −1.25512e9 −1.47438
\(357\) 1.41143e9 + 8.94493e8i 1.64180 + 1.04049i
\(358\) 1.99489e8 3.45526e8i 0.229789 0.398006i
\(359\) 6.06338e8 1.05021e9i 0.691646 1.19797i −0.279652 0.960101i \(-0.590219\pi\)
0.971298 0.237865i \(-0.0764475\pi\)
\(360\) −2.60380e7 −0.0294136
\(361\) 6.17124e7 1.06889e8i 0.0690395 0.119580i
\(362\) 3.21240e8 0.355917
\(363\) −9.09759e8 −0.998282
\(364\) 3.19741e8 + 8.53183e8i 0.347491 + 0.927230i
\(365\) 2.17209e9 2.33804
\(366\) 2.00709e9 2.13984
\(367\) 3.35630e8 5.81328e8i 0.354429 0.613889i −0.632591 0.774486i \(-0.718009\pi\)
0.987020 + 0.160597i \(0.0513420\pi\)
\(368\) −1.76183e9 −1.84287
\(369\) −1.05645e9 + 1.82983e9i −1.09460 + 1.89591i
\(370\) −2.86132e8 + 4.95594e8i −0.293670 + 0.508652i
\(371\) −9.95942e8 + 5.21453e8i −1.01257 + 0.530160i
\(372\) 1.59801e9 1.60946
\(373\) 4.36831e8 + 7.56614e8i 0.435846 + 0.754907i 0.997364 0.0725570i \(-0.0231159\pi\)
−0.561518 + 0.827464i \(0.689783\pi\)
\(374\) −1.06452e9 + 1.84380e9i −1.05221 + 1.82248i
\(375\) 4.96193e8 8.59431e8i 0.485894 0.841592i
\(376\) −5.45290e6 + 9.44469e6i −0.00529017 + 0.00916285i
\(377\) −4.07254e8 3.07908e8i −0.391445 0.295956i
\(378\) −7.31130e7 + 1.77069e9i −0.0696263 + 1.68625i
\(379\) 1.49474e8 + 2.58896e8i 0.141035 + 0.244280i 0.927887 0.372862i \(-0.121624\pi\)
−0.786851 + 0.617142i \(0.788290\pi\)
\(380\) −1.21351e9 −1.13449
\(381\) 2.82549e8 0.261732
\(382\) −1.48909e8 2.57918e8i −0.136678 0.236734i
\(383\) 7.28454e8 + 1.26172e9i 0.662531 + 1.14754i 0.979948 + 0.199252i \(0.0638512\pi\)
−0.317417 + 0.948286i \(0.602815\pi\)
\(384\) −2.53095e7 + 4.38373e7i −0.0228099 + 0.0395080i
\(385\) 1.55079e9 8.11961e8i 1.38497 0.725142i
\(386\) −3.30120e8 + 5.71784e8i −0.292157 + 0.506030i
\(387\) −1.44089e9 −1.26370
\(388\) −5.63385e8 + 9.75811e8i −0.489660 + 0.848115i
\(389\) 1.10500e9 + 1.91392e9i 0.951788 + 1.64855i 0.741552 + 0.670895i \(0.234090\pi\)
0.210236 + 0.977651i \(0.432577\pi\)
\(390\) 2.68538e9 + 2.03030e9i 2.29234 + 1.73315i
\(391\) 2.54038e9 2.14922
\(392\) −1.64249e7 1.35870e6i −0.0137721 0.00113926i
\(393\) −5.92009e8 1.02539e9i −0.491987 0.852147i
\(394\) 1.35479e8 + 2.34656e8i 0.111592 + 0.193283i
\(395\) 1.38407e9 + 2.39728e9i 1.12998 + 1.95717i
\(396\) −2.67355e9 −2.16349
\(397\) −3.75836e8 6.50967e8i −0.301461 0.522146i 0.675006 0.737812i \(-0.264141\pi\)
−0.976467 + 0.215666i \(0.930808\pi\)
\(398\) −2.35209e9 −1.87009
\(399\) 8.02199e7 1.94281e9i 0.0632233 1.53118i
\(400\) 3.37933e8 + 5.85316e8i 0.264010 + 0.457278i
\(401\) 3.50693e8 0.271595 0.135798 0.990737i \(-0.456640\pi\)
0.135798 + 0.990737i \(0.456640\pi\)
\(402\) −6.96398e8 1.20620e9i −0.534646 0.926035i
\(403\) 1.03201e9 + 7.80263e8i 0.785448 + 0.593845i
\(404\) 2.73524e7 4.73757e7i 0.0206376 0.0357454i
\(405\) 2.06212e8 + 3.57170e8i 0.154249 + 0.267167i
\(406\) −8.27042e8 + 4.33021e8i −0.613319 + 0.321120i
\(407\) 2.90640e8 5.03403e8i 0.213685 0.370114i
\(408\) 1.84248e7 3.19126e7i 0.0134305 0.0232623i
\(409\) −4.59744e8 −0.332265 −0.166132 0.986103i \(-0.553128\pi\)
−0.166132 + 0.986103i \(0.553128\pi\)
\(410\) 3.08389e9 2.20981
\(411\) −1.06184e9 + 1.83915e9i −0.754416 + 1.30669i
\(412\) 5.36116e8 9.28580e8i 0.377675 0.654152i
\(413\) 4.19449e7 1.01585e9i 0.0292991 0.709583i
\(414\) 3.20587e9 + 5.55274e9i 2.22047 + 3.84597i
\(415\) −4.16254e8 + 7.20973e8i −0.285884 + 0.495166i
\(416\) 1.90789e9 8.06260e8i 1.29935 0.549096i
\(417\) −6.84995e8 1.18645e9i −0.462606 0.801257i
\(418\) 2.47746e9 1.65916
\(419\) 2.42823e7 + 4.20582e7i 0.0161265 + 0.0279319i 0.873976 0.485969i \(-0.161533\pi\)
−0.857850 + 0.513901i \(0.828200\pi\)
\(420\) 2.71328e9 1.42061e9i 1.78699 0.935629i
\(421\) −1.36380e9 −0.890768 −0.445384 0.895340i \(-0.646933\pi\)
−0.445384 + 0.895340i \(0.646933\pi\)
\(422\) −7.34958e6 1.27298e7i −0.00476068 0.00824574i
\(423\) 2.05557e9 1.32051
\(424\) 1.23956e7 + 2.14697e7i 0.00789742 + 0.0136787i
\(425\) −4.87266e8 8.43969e8i −0.307896 0.533292i
\(426\) −1.47179e9 2.54922e9i −0.922388 1.59762i
\(427\) 1.30967e9 6.85713e8i 0.814073 0.426231i
\(428\) −1.58575e9 −0.977646
\(429\) −2.72769e9 2.06229e9i −1.66799 1.26110i
\(430\) 1.05153e9 + 1.82130e9i 0.637794 + 1.10469i
\(431\) 5.70351e8 9.87876e8i 0.343140 0.594336i −0.641874 0.766810i \(-0.721843\pi\)
0.985014 + 0.172474i \(0.0551761\pi\)
\(432\) 2.02408e9 1.20791
\(433\) −1.29346e9 + 2.24034e9i −0.765678 + 1.32619i 0.174210 + 0.984709i \(0.444263\pi\)
−0.939888 + 0.341484i \(0.889070\pi\)
\(434\) 2.09579e9 1.09731e9i 1.23065 0.644339i
\(435\) −8.58089e8 + 1.48625e9i −0.499827 + 0.865726i
\(436\) −4.10458e8 7.10934e8i −0.237173 0.410796i
\(437\) −1.47806e9 2.56008e9i −0.847241 1.46746i
\(438\) −7.75856e9 −4.41186
\(439\) −1.24983e9 −0.705056 −0.352528 0.935801i \(-0.614678\pi\)
−0.352528 + 0.935801i \(0.614678\pi\)
\(440\) −1.93013e7 3.34308e7i −0.0108019 0.0187095i
\(441\) 1.32613e9 + 2.80912e9i 0.736295 + 1.55968i
\(442\) −2.77794e9 + 1.17394e9i −1.53019 + 0.646646i
\(443\) −9.50197e8 + 1.64579e9i −0.519279 + 0.899418i 0.480470 + 0.877011i \(0.340466\pi\)
−0.999749 + 0.0224065i \(0.992867\pi\)
\(444\) 5.08506e8 8.80758e8i 0.275712 0.477547i
\(445\) −1.70788e9 + 2.95813e9i −0.918748 + 1.59132i
\(446\) 8.19956e8 + 1.42021e9i 0.437642 + 0.758017i
\(447\) 5.99999e9 3.17742
\(448\) 7.69696e7 1.86410e9i 0.0404432 0.979479i
\(449\) 1.38296e8 2.39537e8i 0.0721023 0.124885i −0.827720 0.561141i \(-0.810363\pi\)
0.899822 + 0.436256i \(0.143696\pi\)
\(450\) 1.22983e9 2.13012e9i 0.636209 1.10195i
\(451\) −3.13248e9 −1.60794
\(452\) 2.10720e8 3.64978e8i 0.107330 0.185901i
\(453\) 1.58088e9 0.799015
\(454\) −3.64032e9 −1.82576
\(455\) 2.44591e9 + 4.07369e8i 1.21731 + 0.202744i
\(456\) −4.28801e7 −0.0211777
\(457\) 5.26391e8 0.257989 0.128995 0.991645i \(-0.458825\pi\)
0.128995 + 0.991645i \(0.458825\pi\)
\(458\) −1.15288e9 + 1.99685e9i −0.560731 + 0.971215i
\(459\) −2.91853e9 −1.40870
\(460\) 2.32805e9 4.03231e9i 1.11517 1.93153i
\(461\) −3.98922e8 + 6.90954e8i −0.189642 + 0.328470i −0.945131 0.326692i \(-0.894066\pi\)
0.755489 + 0.655162i \(0.227399\pi\)
\(462\) −5.53933e9 + 2.90027e9i −2.61343 + 1.36833i
\(463\) 3.16121e9 1.48020 0.740099 0.672498i \(-0.234779\pi\)
0.740099 + 0.672498i \(0.234779\pi\)
\(464\) 5.33114e8 + 9.23381e8i 0.247746 + 0.429109i
\(465\) 2.17446e9 3.76628e9i 1.00292 1.73711i
\(466\) −1.28692e9 + 2.22902e9i −0.589118 + 1.02038i
\(467\) 7.35412e8 1.27377e9i 0.334135 0.578739i −0.649183 0.760632i \(-0.724889\pi\)
0.983318 + 0.181893i \(0.0582226\pi\)
\(468\) −3.02088e9 2.28397e9i −1.36230 1.02998i
\(469\) −8.66508e8 5.49148e8i −0.387853 0.245802i
\(470\) −1.50010e9 2.59825e9i −0.666467 1.15435i
\(471\) −2.30752e9 −1.01759
\(472\) −2.24209e7 −0.00981421
\(473\) −1.06809e9 1.84999e9i −0.464083 0.803815i
\(474\) −4.94381e9 8.56293e9i −2.13225 3.69316i
\(475\) −5.67008e8 + 9.82087e8i −0.242751 + 0.420458i
\(476\) −1.13190e8 + 2.74130e9i −0.0481041 + 1.16502i
\(477\) 2.33636e9 4.04670e9i 0.985657 1.70721i
\(478\) 5.02329e9 2.10373
\(479\) 9.88354e8 1.71188e9i 0.410902 0.711703i −0.584087 0.811691i \(-0.698547\pi\)
0.994989 + 0.0999883i \(0.0318806\pi\)
\(480\) −3.48118e9 6.02958e9i −1.43675 2.48853i
\(481\) 7.58448e8 3.20514e8i 0.310755 0.131323i
\(482\) 4.14461e9 1.68585
\(483\) 6.30177e9 + 3.99374e9i 2.54477 + 1.61274i
\(484\) −7.46869e8 1.29361e9i −0.299423 0.518616i
\(485\) 1.53323e9 + 2.65564e9i 0.610256 + 1.05699i
\(486\) 1.39887e9 + 2.42292e9i 0.552778 + 0.957440i
\(487\) 3.53270e9 1.38598 0.692988 0.720949i \(-0.256294\pi\)
0.692988 + 0.720949i \(0.256294\pi\)
\(488\) −1.63002e7 2.82328e7i −0.00634926 0.0109972i
\(489\) 4.16709e8 0.161158
\(490\) 2.58297e9 3.72627e9i 0.991819 1.43083i
\(491\) −4.64669e8 8.04831e8i −0.177157 0.306845i 0.763749 0.645514i \(-0.223357\pi\)
−0.940906 + 0.338669i \(0.890023\pi\)
\(492\) −5.48061e9 −2.07468
\(493\) −7.68698e8 1.33142e9i −0.288929 0.500440i
\(494\) 2.79932e9 + 2.11645e9i 1.04474 + 0.789885i
\(495\) −3.63798e9 + 6.30116e9i −1.34816 + 2.33508i
\(496\) −1.35095e9 2.33992e9i −0.497112 0.861023i
\(497\) −1.83131e9 1.16059e9i −0.669136 0.424064i
\(498\) 1.48683e9 2.57527e9i 0.539460 0.934371i
\(499\) −1.64050e9 + 2.84143e9i −0.591051 + 1.02373i 0.403041 + 0.915182i \(0.367953\pi\)
−0.994091 + 0.108548i \(0.965380\pi\)
\(500\) 1.62940e9 0.582953
\(501\) 7.03536e9 2.49951
\(502\) −2.15575e9 + 3.73386e9i −0.760562 + 1.31733i
\(503\) 3.14180e8 5.44176e8i 0.110076 0.190656i −0.805725 0.592290i \(-0.798224\pi\)
0.915801 + 0.401633i \(0.131557\pi\)
\(504\) 6.06883e7 3.17751e7i 0.0211153 0.0110555i
\(505\) −7.44385e7 1.28931e8i −0.0257204 0.0445490i
\(506\) −4.75287e9 + 8.23220e9i −1.63091 + 2.82481i
\(507\) −1.32027e9 4.66044e9i −0.449921 1.58818i
\(508\) 2.31959e8 + 4.01766e8i 0.0785035 + 0.135972i
\(509\) −2.60015e9 −0.873950 −0.436975 0.899474i \(-0.643950\pi\)
−0.436975 + 0.899474i \(0.643950\pi\)
\(510\) 5.06869e9 + 8.77923e9i 1.69200 + 2.93063i
\(511\) −5.06263e9 + 2.65068e9i −1.67843 + 0.878788i
\(512\) −4.28320e9 −1.41034
\(513\) 1.69808e9 + 2.94116e9i 0.555325 + 0.961851i
\(514\) −1.77813e9 −0.577554
\(515\) −1.45902e9 2.52710e9i −0.470691 0.815261i
\(516\) −1.86875e9 3.23676e9i −0.598793 1.03714i
\(517\) 1.52374e9 + 2.63919e9i 0.484946 + 0.839952i
\(518\) 6.21130e7 1.50429e9i 0.0196349 0.475529i
\(519\) 9.63861e8 0.302642
\(520\) 6.75056e6 5.42627e7i 0.00210537 0.0169235i
\(521\) −2.29143e9 3.96887e9i −0.709863 1.22952i −0.964908 0.262589i \(-0.915424\pi\)
0.255045 0.966929i \(-0.417910\pi\)
\(522\) 1.94014e9 3.36043e9i 0.597017 1.03406i
\(523\) −1.71128e8 −0.0523076 −0.0261538 0.999658i \(-0.508326\pi\)
−0.0261538 + 0.999658i \(0.508326\pi\)
\(524\) 9.72022e8 1.68359e9i 0.295132 0.511184i
\(525\) 1.18075e8 2.85962e9i 0.0356124 0.862483i
\(526\) −7.15671e8 + 1.23958e9i −0.214419 + 0.371384i
\(527\) 1.94794e9 + 3.37393e9i 0.579747 + 1.00415i
\(528\) 3.57067e9 + 6.18458e9i 1.05568 + 1.82849i
\(529\) 7.93749e9 2.33125
\(530\) −6.82008e9 −1.98987
\(531\) 2.11299e9 + 3.65980e9i 0.612443 + 1.06078i
\(532\) 2.82841e9 1.48089e9i 0.814425 0.426415i
\(533\) −3.53944e9 2.67603e9i −1.01249 0.765501i
\(534\) 6.10042e9 1.05662e10i 1.73367 3.00280i
\(535\) −2.15778e9 + 3.73739e9i −0.609213 + 1.05519i
\(536\) −1.13114e7 + 1.95918e7i −0.00317277 + 0.00549539i
\(537\) 9.64834e8 + 1.67114e9i 0.268870 + 0.465697i
\(538\) −7.31770e9 −2.02599
\(539\) −2.62367e9 + 3.78498e9i −0.721685 + 1.04112i
\(540\) −2.67460e9 + 4.63254e9i −0.730938 + 1.26602i
\(541\) −4.37282e8 + 7.57394e8i −0.118733 + 0.205651i −0.919266 0.393637i \(-0.871217\pi\)
0.800533 + 0.599289i \(0.204550\pi\)
\(542\) 7.90064e9 2.13140
\(543\) −7.76841e8 + 1.34553e9i −0.208225 + 0.360656i
\(544\) 6.23706e9 1.66105
\(545\) −2.23409e9 −0.591172
\(546\) −8.73663e9 1.45510e9i −2.29705 0.382576i
\(547\) −2.11108e9 −0.551505 −0.275752 0.961229i \(-0.588927\pi\)
−0.275752 + 0.961229i \(0.588927\pi\)
\(548\) −3.48687e9 −0.905115
\(549\) −3.07232e9 + 5.32142e9i −0.792435 + 1.37254i
\(550\) 3.64655e9 0.934573
\(551\) −8.94498e8 + 1.54932e9i −0.227797 + 0.394557i
\(552\) 8.22631e7 1.42484e8i 0.0208170 0.0360561i
\(553\) −6.15144e9 3.89847e9i −1.54682 0.980293i
\(554\) 1.03379e10 2.58313
\(555\) −1.38388e9 2.39695e9i −0.343616 0.595160i
\(556\) 1.12470e9 1.94803e9i 0.277507 0.480656i
\(557\) −2.52361e9 + 4.37103e9i −0.618770 + 1.07174i 0.370940 + 0.928657i \(0.379036\pi\)
−0.989710 + 0.143085i \(0.954298\pi\)
\(558\) −4.91647e9 + 8.51558e9i −1.19794 + 2.07489i
\(559\) 3.73563e8 3.00279e9i 0.0904529 0.727083i
\(560\) −4.37396e9 2.77199e9i −1.05249 0.667013i
\(561\) −5.14856e9 8.91756e9i −1.23116 2.13244i
\(562\) 7.99095e9 1.89898
\(563\) 4.70672e9 1.11157 0.555787 0.831325i \(-0.312417\pi\)
0.555787 + 0.831325i \(0.312417\pi\)
\(564\) 2.66595e9 + 4.61755e9i 0.625712 + 1.08376i
\(565\) −5.73468e8 9.93276e8i −0.133764 0.231686i
\(566\) 9.78183e8 1.69426e9i 0.226758 0.392756i
\(567\) −9.16500e8 5.80831e8i −0.211150 0.133816i
\(568\) −2.39059e7 + 4.14062e7i −0.00547375 + 0.00948082i
\(569\) 5.43300e9 1.23637 0.618183 0.786034i \(-0.287869\pi\)
0.618183 + 0.786034i \(0.287869\pi\)
\(570\) 5.89820e9 1.02160e10i 1.33400 2.31056i
\(571\) 1.62839e9 + 2.82045e9i 0.366042 + 0.634004i 0.988943 0.148297i \(-0.0473792\pi\)
−0.622900 + 0.782301i \(0.714046\pi\)
\(572\) 6.93139e8 5.57163e9i 0.154858 1.24479i
\(573\) 1.44040e9 0.319847
\(574\) −7.18782e9 + 3.76338e9i −1.58637 + 0.830590i
\(575\) −2.17555e9 3.76816e9i −0.477234 0.826593i
\(576\) 3.87737e9 + 6.71580e9i 0.845392 + 1.46426i
\(577\) 1.12551e9 + 1.94943e9i 0.243912 + 0.422467i 0.961825 0.273665i \(-0.0882360\pi\)
−0.717913 + 0.696132i \(0.754903\pi\)
\(578\) −2.53201e9 −0.545404
\(579\) −1.59663e9 2.76544e9i −0.341845 0.592093i
\(580\) −2.81780e9 −0.599670
\(581\) 9.03598e7 2.18839e9i 0.0191143 0.462922i
\(582\) −5.47660e9 9.48575e9i −1.15154 1.99453i
\(583\) 6.92754e9 1.44790
\(584\) 6.30098e7 + 1.09136e8i 0.0130907 + 0.0226738i
\(585\) −9.49359e9 + 4.01192e9i −1.96058 + 0.828527i
\(586\) 7.54109e8 1.30616e9i 0.154808 0.268135i
\(587\) 1.66060e9 + 2.87625e9i 0.338869 + 0.586939i 0.984220 0.176947i \(-0.0566222\pi\)
−0.645351 + 0.763886i \(0.723289\pi\)
\(588\) −4.59039e9 + 6.62223e9i −0.931169 + 1.34333i
\(589\) 2.26673e9 3.92609e9i 0.457084 0.791692i
\(590\) 3.08401e9 5.34167e9i 0.618207 1.07077i
\(591\) −1.31049e9 −0.261142
\(592\) −1.71956e9 −0.340636
\(593\) 2.74879e9 4.76105e9i 0.541315 0.937586i −0.457514 0.889203i \(-0.651260\pi\)
0.998829 0.0483830i \(-0.0154068\pi\)
\(594\) 5.46036e9 9.45762e9i 1.06898 1.85152i
\(595\) 6.30682e9 + 3.99694e9i 1.22744 + 0.777890i
\(596\) 4.92571e9 + 8.53158e9i 0.953030 + 1.65070i
\(597\) 5.68796e9 9.85183e9i 1.09407 1.89499i
\(598\) −1.24030e10 + 5.24140e9i −2.37177 + 1.00229i
\(599\) 9.04427e8 + 1.56651e9i 0.171941 + 0.297811i 0.939098 0.343648i \(-0.111663\pi\)
−0.767157 + 0.641459i \(0.778329\pi\)
\(600\) −6.31149e7 −0.0119290
\(601\) −2.44861e9 4.24112e9i −0.460107 0.796929i 0.538859 0.842396i \(-0.318856\pi\)
−0.998966 + 0.0454674i \(0.985522\pi\)
\(602\) −4.67345e9 2.96180e9i −0.873072 0.553309i
\(603\) 4.26402e9 0.791969
\(604\) 1.29783e9 + 2.24790e9i 0.239655 + 0.415095i
\(605\) −4.06515e9 −0.746334
\(606\) 2.65889e8 + 4.60534e8i 0.0485340 + 0.0840634i
\(607\) −2.63883e9 4.57059e9i −0.478907 0.829491i 0.520801 0.853678i \(-0.325633\pi\)
−0.999707 + 0.0241875i \(0.992300\pi\)
\(608\) −3.62889e9 6.28542e9i −0.654803 1.13415i
\(609\) 1.86273e8 4.51126e9i 0.0334186 0.809352i
\(610\) 8.96843e9 1.59979
\(611\) −5.32923e8 + 4.28377e9i −0.0945193 + 0.759770i
\(612\) −5.70196e9 9.87609e9i −1.00553 1.74163i
\(613\) 1.91005e9 3.30830e9i 0.334913 0.580086i −0.648555 0.761168i \(-0.724626\pi\)
0.983468 + 0.181081i \(0.0579597\pi\)
\(614\) 9.57270e9 1.66896
\(615\) −7.45765e9 + 1.29170e10i −1.29282 + 2.23923i
\(616\) 8.57835e7 + 5.43652e7i 0.0147867 + 0.00937105i
\(617\) −4.12723e9 + 7.14857e9i −0.707392 + 1.22524i 0.258429 + 0.966030i \(0.416795\pi\)
−0.965821 + 0.259209i \(0.916538\pi\)
\(618\) 5.21152e9 + 9.02661e9i 0.888187 + 1.53839i
\(619\) 3.06800e9 + 5.31392e9i 0.519921 + 0.900530i 0.999732 + 0.0231577i \(0.00737200\pi\)
−0.479811 + 0.877372i \(0.659295\pi\)
\(620\) 7.14053e9 1.20326
\(621\) −1.30307e10 −2.18347
\(622\) −5.56157e9 9.63292e9i −0.926683 1.60506i
\(623\) 3.70743e8 8.97889e9i 0.0614278 1.48770i
\(624\) −1.24883e9 + 1.00384e10i −0.205758 + 1.65394i
\(625\) 3.81309e9 6.60447e9i 0.624737 1.08208i
\(626\) −7.05028e8 + 1.22114e9i −0.114867 + 0.198956i
\(627\) −5.99113e9 + 1.03769e10i −0.970672 + 1.68125i
\(628\) −1.89437e9 3.28114e9i −0.305215 0.528647i
\(629\) 2.47943e9 0.397260
\(630\) −7.77476e8 + 1.88294e10i −0.123878 + 3.00016i
\(631\) −4.25202e9 + 7.36472e9i −0.673740 + 1.16695i 0.303095 + 0.952960i \(0.401980\pi\)
−0.976835 + 0.213992i \(0.931353\pi\)
\(632\) −8.03006e7 + 1.39085e8i −0.0126535 + 0.0219164i
\(633\) 7.10928e7 0.0111407
\(634\) 6.02538e9 1.04363e10i 0.939014 1.62642i
\(635\) 1.26254e9 0.195676
\(636\) 1.21205e10 1.86819
\(637\) −6.19797e9 + 2.03535e9i −0.950083 + 0.311998i
\(638\) 5.75271e9 0.877002
\(639\) 9.01174e9 1.36633
\(640\) −1.13093e8 + 1.95882e8i −0.0170531 + 0.0295369i
\(641\) −6.67238e9 −1.00064 −0.500320 0.865841i \(-0.666784\pi\)
−0.500320 + 0.865841i \(0.666784\pi\)
\(642\) 7.70745e9 1.33497e10i 1.14958 1.99113i
\(643\) −9.35767e8 + 1.62080e9i −0.138813 + 0.240431i −0.927047 0.374944i \(-0.877662\pi\)
0.788235 + 0.615375i \(0.210995\pi\)
\(644\) −5.05370e8 + 1.22394e10i −0.0745606 + 1.80575i
\(645\) −1.01715e10 −1.49253
\(646\) 5.28376e9 + 9.15174e9i 0.771133 + 1.33564i
\(647\) −3.03661e9 + 5.25957e9i −0.440783 + 0.763458i −0.997748 0.0670779i \(-0.978632\pi\)
0.556965 + 0.830536i \(0.311966\pi\)
\(648\) −1.19640e7 + 2.07222e7i −0.00172728 + 0.00299173i
\(649\) −3.13261e9 + 5.42583e9i −0.449831 + 0.779130i
\(650\) 4.12030e9 + 3.11519e9i 0.588481 + 0.444926i
\(651\) −4.72029e8 + 1.14319e10i −0.0670556 + 1.62399i
\(652\) 3.42098e8 + 5.92532e8i 0.0483375 + 0.0837230i
\(653\) −6.77417e8 −0.0952050 −0.0476025 0.998866i \(-0.515158\pi\)
−0.0476025 + 0.998866i \(0.515158\pi\)
\(654\) 7.98003e9 1.11553
\(655\) −2.64532e9 4.58183e9i −0.367819 0.637081i
\(656\) 4.63329e9 + 8.02510e9i 0.640806 + 1.10991i
\(657\) 1.18763e10 2.05704e10i 1.63382 2.82985i
\(658\) 6.66713e9 + 4.22529e9i 0.912322 + 0.578183i
\(659\) 1.69604e9 2.93763e9i 0.230854 0.399850i −0.727206 0.686419i \(-0.759181\pi\)
0.958060 + 0.286569i \(0.0925148\pi\)
\(660\) −1.88730e10 −2.55527
\(661\) 1.08559e9 1.88029e9i 0.146204 0.253233i −0.783617 0.621244i \(-0.786628\pi\)
0.929822 + 0.368011i \(0.119961\pi\)
\(662\) −2.75405e9 4.77016e9i −0.368951 0.639042i
\(663\) 1.80069e9 1.44744e10i 0.239962 1.92887i
\(664\) −4.83002e7 −0.00640266
\(665\) 3.58454e8 8.68125e9i 0.0472669 1.14474i
\(666\) 3.12896e9 + 5.41952e9i 0.410431 + 0.710888i
\(667\) −3.43209e9 5.94456e9i −0.447835 0.775674i
\(668\) 5.77570e9 + 1.00038e10i 0.749699 + 1.29852i
\(669\) −7.93147e9 −1.02415
\(670\) −3.11178e9 5.38976e9i −0.399712 0.692321i
\(671\) −9.10974e9 −1.16407
\(672\) 1.54719e10 + 9.80531e9i 1.96676 + 1.24643i
\(673\) 9.35218e8 + 1.61984e9i 0.118266 + 0.204843i 0.919081 0.394070i \(-0.128933\pi\)
−0.800815 + 0.598912i \(0.795600\pi\)
\(674\) −1.30151e10 −1.63734
\(675\) 2.49939e9 + 4.32907e9i 0.312803 + 0.541791i
\(676\) 5.54295e9 5.70334e9i 0.690124 0.710094i
\(677\) 9.03636e8 1.56514e9i 0.111927 0.193863i −0.804620 0.593790i \(-0.797631\pi\)
0.916547 + 0.399927i \(0.130965\pi\)
\(678\) 2.04839e9 + 3.54791e9i 0.252411 + 0.437189i
\(679\) −6.81437e9 4.31860e9i −0.835375 0.529418i
\(680\) 8.23290e7 1.42598e8i 0.0100409 0.0173913i
\(681\) 8.80323e9 1.52476e10i 1.06814 1.85007i
\(682\) −1.45778e10 −1.75974
\(683\) 1.10961e10 1.33260 0.666298 0.745686i \(-0.267878\pi\)
0.666298 + 0.745686i \(0.267878\pi\)
\(684\) −6.63511e9 + 1.14923e10i −0.792778 + 1.37313i
\(685\) −4.74469e9 + 8.21805e9i −0.564016 + 0.976904i
\(686\) −1.47299e9 + 1.18371e10i −0.174207 + 1.39995i
\(687\) −5.57592e9 9.65778e9i −0.656097 1.13639i
\(688\) −3.15966e9 + 5.47270e9i −0.369898 + 0.640681i
\(689\) 7.82754e9 + 5.91809e9i 0.911713 + 0.689309i
\(690\) 2.26307e10 + 3.91976e10i 2.62257 + 4.54242i
\(691\) 5.72174e9 0.659713 0.329856 0.944031i \(-0.393000\pi\)
0.329856 + 0.944031i \(0.393000\pi\)
\(692\) 7.91284e8 + 1.37054e9i 0.0907739 + 0.157225i
\(693\) 7.89727e8 1.91261e10i 0.0901385 2.18303i
\(694\) −3.00753e9 −0.341548
\(695\) −3.06082e9 5.30150e9i −0.345853 0.599035i
\(696\) −9.95686e7 −0.0111941
\(697\) −6.68075e9 1.15714e10i −0.747327 1.29441i
\(698\) 3.24827e9 + 5.62616e9i 0.361541 + 0.626208i
\(699\) −6.22424e9 1.07807e10i −0.689312 1.19392i
\(700\) 4.16311e9 2.17972e9i 0.458749 0.240191i
\(701\) 1.16156e9 0.127359 0.0636794 0.997970i \(-0.479716\pi\)
0.0636794 + 0.997970i \(0.479716\pi\)
\(702\) 1.42492e10 6.02162e9i 1.55458 0.656952i
\(703\) −1.44260e9 2.49866e9i −0.156604 0.271246i
\(704\) −5.74839e9 + 9.95650e9i −0.620928 + 1.07548i
\(705\) 1.45106e10 1.55963
\(706\) 2.83952e9 4.91819e9i 0.303689 0.526004i
\(707\) 3.30838e8 + 2.09668e8i 0.0352085 + 0.0223133i
\(708\) −5.48083e9 + 9.49308e9i −0.580404 + 1.00529i
\(709\) −3.18933e8 5.52408e8i −0.0336076 0.0582101i 0.848732 0.528823i \(-0.177366\pi\)
−0.882340 + 0.470613i \(0.844033\pi\)
\(710\) −6.57655e9 1.13909e10i −0.689594 1.19441i
\(711\) 3.02707e10 3.15849
\(712\) −1.98174e8 −0.0205763
\(713\) 8.69718e9 + 1.50640e10i 0.898598 + 1.55642i
\(714\) −2.25275e10 1.42768e10i −2.31617 1.46787i
\(715\) −1.21884e10 9.21513e9i −1.24702 0.942823i
\(716\) −1.58417e9 + 2.74386e9i −0.161289 + 0.279361i
\(717\) −1.21476e10 + 2.10403e10i −1.23076 + 2.13174i
\(718\) −9.67761e9 + 1.67621e10i −0.975737 + 1.69003i
\(719\) −5.34442e9 9.25682e9i −0.536228 0.928775i −0.999103 0.0423510i \(-0.986515\pi\)
0.462874 0.886424i \(-0.346818\pi\)
\(720\) 2.15239e10 2.14911
\(721\) 6.48454e9 + 4.10957e9i 0.644326 + 0.408341i
\(722\) −9.84978e8 + 1.70603e9i −0.0973971 + 0.168697i
\(723\) −1.00227e10 + 1.73599e10i −0.986286 + 1.70830i
\(724\) −2.55100e9 −0.249819
\(725\) −1.31661e9 + 2.28043e9i −0.128314 + 0.222246i
\(726\) 1.45205e10 1.40832
\(727\) 1.77003e10 1.70848 0.854242 0.519876i \(-0.174022\pi\)
0.854242 + 0.519876i \(0.174022\pi\)
\(728\) 5.04848e7 + 1.34712e8i 0.00484955 + 0.0129403i
\(729\) −1.61462e10 −1.54357
\(730\) −3.46682e10 −3.29839
\(731\) 4.55593e9 7.89110e9i 0.431386 0.747182i
\(732\) −1.59385e10 −1.50196
\(733\) −1.78785e9 + 3.09664e9i −0.167674 + 0.290420i −0.937602 0.347711i \(-0.886959\pi\)
0.769927 + 0.638131i \(0.220292\pi\)
\(734\) −5.35691e9 + 9.27843e9i −0.500009 + 0.866041i
\(735\) 9.36136e9 + 1.98300e10i 0.869628 + 1.84211i
\(736\) 2.78473e10 2.57460
\(737\) 3.16081e9 + 5.47468e9i 0.290845 + 0.503759i
\(738\) 1.68618e10 2.92055e10i 1.54421 2.67465i
\(739\) 4.55069e7 7.88202e7i 0.00414784 0.00718426i −0.863944 0.503588i \(-0.832013\pi\)
0.868092 + 0.496404i \(0.165346\pi\)
\(740\) 2.27220e9 3.93557e9i 0.206127 0.357023i
\(741\) −1.56343e10 + 6.60695e9i −1.41161 + 0.596537i
\(742\) 1.58960e10 8.32279e9i 1.42848 0.747921i
\(743\) 6.38396e9 + 1.10573e10i 0.570991 + 0.988986i 0.996464 + 0.0840150i \(0.0267744\pi\)
−0.425473 + 0.904971i \(0.639892\pi\)
\(744\) 2.52314e8 0.0224614
\(745\) 2.68103e10 2.37550
\(746\) −6.97217e9 1.20761e10i −0.614868 1.06498i
\(747\) 4.55190e9 + 7.88413e9i 0.399550 + 0.692040i
\(748\) 8.45344e9 1.46418e10i 0.738547 1.27920i
\(749\) 4.68408e8 1.13442e10i 0.0407322 0.986477i
\(750\) −7.91962e9 + 1.37172e10i −0.685472 + 1.18727i
\(751\) −1.27845e10 −1.10140 −0.550698 0.834705i \(-0.685638\pi\)
−0.550698 + 0.834705i \(0.685638\pi\)
\(752\) 4.50756e9 7.80733e9i 0.386527 0.669484i
\(753\) −1.04263e10 1.80589e10i −0.889914 1.54138i
\(754\) 6.50009e9 + 4.91445e9i 0.552229 + 0.417518i
\(755\) 7.06397e9 0.597358
\(756\) 5.80598e8 1.40613e10i 0.0488708 1.18358i
\(757\) 6.07636e9 + 1.05246e10i 0.509106 + 0.881797i 0.999944 + 0.0105465i \(0.00335713\pi\)
−0.490839 + 0.871251i \(0.663310\pi\)
\(758\) −2.38572e9 4.13218e9i −0.198965 0.344618i
\(759\) −2.29873e10 3.98152e10i −1.90828 3.30524i
\(760\) −1.91605e8 −0.0158328
\(761\) −8.78448e9 1.52152e10i −0.722553 1.25150i −0.959973 0.280092i \(-0.909635\pi\)
0.237420 0.971407i \(-0.423698\pi\)
\(762\) −4.50970e9 −0.369237
\(763\) 5.20714e9 2.72635e9i 0.424389 0.222201i
\(764\) 1.18250e9 + 2.04815e9i 0.0959346 + 0.166164i
\(765\) −3.10354e10 −2.50635
\(766\) −1.16267e10 2.01380e10i −0.934663 1.61888i
\(767\) −8.17479e9 + 3.45460e9i −0.654173 + 0.276449i
\(768\) 1.05609e10 1.82920e10i 0.841270 1.45712i
\(769\) −5.26257e9 9.11504e9i −0.417307 0.722797i 0.578360 0.815781i \(-0.303693\pi\)
−0.995668 + 0.0929841i \(0.970359\pi\)
\(770\) −2.47519e10 + 1.29595e10i −1.95385 + 1.02299i
\(771\) 4.29998e9 7.44778e9i 0.337891 0.585244i
\(772\) 2.62151e9 4.54060e9i 0.205065 0.355183i
\(773\) −1.11360e10 −0.867166 −0.433583 0.901114i \(-0.642751\pi\)
−0.433583 + 0.901114i \(0.642751\pi\)
\(774\) 2.29977e10 1.78275
\(775\) 3.33638e9 5.77878e9i 0.257466 0.445944i
\(776\) −8.89545e7 + 1.54074e8i −0.00683364 + 0.0118362i
\(777\) 6.15059e9 + 3.89793e9i 0.470374 + 0.298099i
\(778\) −1.76367e10 3.05477e10i −1.34273 2.32568i
\(779\) −7.77408e9 + 1.34651e10i −0.589207 + 1.02054i
\(780\) −2.13249e10 1.61229e10i −1.60900 1.21650i
\(781\) 6.68017e9 + 1.15704e10i 0.501775 + 0.869100i
\(782\) −4.05464e10 −3.03200
\(783\) 3.94298e9 + 6.82944e9i 0.293534 + 0.508416i
\(784\) 1.35774e10 + 1.12315e9i 1.00626 + 0.0832402i
\(785\) −1.03109e10 −0.760769
\(786\) 9.44891e9 + 1.63660e10i 0.694069 + 1.20216i
\(787\) −2.79527e9 −0.204415 −0.102207 0.994763i \(-0.532591\pi\)
−0.102207 + 0.994763i \(0.532591\pi\)
\(788\) −1.07585e9 1.86343e9i −0.0783267 0.135666i
\(789\) −3.46135e9 5.99524e9i −0.250886 0.434547i
\(790\) −2.20909e10 3.82625e10i −1.59411 2.76108i
\(791\) 2.54875e9 + 1.61527e9i 0.183109 + 0.116045i
\(792\) −4.22134e8 −0.0301934
\(793\) −1.02932e10 7.78231e9i −0.732987 0.554182i
\(794\) 5.99863e9 + 1.03899e10i 0.425285 + 0.736616i
\(795\) 1.64927e10 2.85662e10i 1.16415 2.01636i
\(796\) 1.86782e10 1.31262
\(797\) −7.85901e9 + 1.36122e10i −0.549875 + 0.952411i 0.448408 + 0.893829i \(0.351991\pi\)
−0.998283 + 0.0585822i \(0.981342\pi\)
\(798\) −1.28037e9 + 3.10088e10i −0.0891920 + 2.16011i
\(799\) −6.49947e9 + 1.12574e10i −0.450779 + 0.780773i
\(800\) −5.34134e9 9.25147e9i −0.368838 0.638845i
\(801\) 1.86763e10 + 3.23483e10i 1.28404 + 2.22402i
\(802\) −5.59733e9 −0.383152
\(803\) 3.52145e10 2.40003
\(804\) 5.53017e9 + 9.57854e9i 0.375269 + 0.649985i
\(805\) 2.81588e10 + 1.78456e10i 1.90251 + 1.20572i
\(806\) −1.64717e10 1.24536e10i −1.10807 0.837765i
\(807\) 1.76961e10 3.06505e10i 1.18528 2.05296i
\(808\) 4.31875e6 7.48029e6i 0.000288017 0.000498860i
\(809\) −1.16743e10 + 2.02204e10i −0.775194 + 1.34268i 0.159492 + 0.987199i \(0.449014\pi\)
−0.934685 + 0.355476i \(0.884319\pi\)
\(810\) −3.29131e9 5.70071e9i −0.217606 0.376905i
\(811\) −3.49086e9 −0.229805 −0.114903 0.993377i \(-0.536656\pi\)
−0.114903 + 0.993377i \(0.536656\pi\)
\(812\) 6.56763e9 3.43867e9i 0.430489 0.225395i
\(813\) −1.91058e10 + 3.30922e10i −1.24695 + 2.15978i
\(814\) −4.63884e9 + 8.03470e9i −0.301456 + 0.522137i
\(815\) 1.86202e9 0.120485
\(816\) −1.52306e10 + 2.63802e10i −0.981299 + 1.69966i
\(817\) −1.06030e10 −0.680226
\(818\) 7.33786e9 0.468741
\(819\) 1.72314e10 2.09362e10i 1.09604 1.33169i
\(820\) −2.44895e10 −1.55107
\(821\) −1.88951e10 −1.19165 −0.595825 0.803114i \(-0.703175\pi\)
−0.595825 + 0.803114i \(0.703175\pi\)
\(822\) 1.69477e10 2.93543e10i 1.06429 1.84340i
\(823\) 1.40579e10 0.879065 0.439533 0.898227i \(-0.355144\pi\)
0.439533 + 0.898227i \(0.355144\pi\)
\(824\) 8.46489e7 1.46616e8i 0.00527079 0.00912928i
\(825\) −8.81831e9 + 1.52738e10i −0.546760 + 0.947016i
\(826\) −6.69473e8 + 1.62137e10i −0.0413336 + 1.00104i
\(827\) −1.66878e10 −1.02596 −0.512980 0.858400i \(-0.671459\pi\)
−0.512980 + 0.858400i \(0.671459\pi\)
\(828\) −2.54582e10 4.40949e10i −1.55855 2.69949i
\(829\) −1.40177e10 + 2.42794e10i −0.854549 + 1.48012i 0.0225147 + 0.999747i \(0.492833\pi\)
−0.877063 + 0.480375i \(0.840501\pi\)
\(830\) 6.64374e9 1.15073e10i 0.403310 0.698553i
\(831\) −2.49996e10 + 4.33007e10i −1.51123 + 2.61753i
\(832\) −1.50009e10 + 6.33925e9i −0.902994 + 0.381598i
\(833\) −1.95773e10 1.61948e9i −1.17353 0.0970773i
\(834\) 1.09330e10 + 1.89366e10i 0.652619 + 1.13037i
\(835\) 3.14367e10 1.86868
\(836\) −1.96737e10 −1.16457
\(837\) −9.99181e9 1.73063e10i −0.588986 1.02015i
\(838\) −3.87564e8 6.71281e8i −0.0227504 0.0394049i
\(839\) 9.50579e9 1.64645e10i 0.555676 0.962458i −0.442175 0.896929i \(-0.645793\pi\)
0.997851 0.0655296i \(-0.0208737\pi\)
\(840\) 4.28408e8 2.24305e8i 0.0249390 0.0130575i
\(841\) 6.54789e9 1.13413e10i 0.379591 0.657470i
\(842\) 2.17674e10 1.25665
\(843\) −1.93242e10 + 3.34705e10i −1.11098 + 1.92427i
\(844\) 5.83638e7 + 1.01089e8i 0.00334153 + 0.00578769i
\(845\) −5.89949e9 2.08246e10i −0.336369 1.18735i
\(846\) −3.28084e10 −1.86290
\(847\) 9.47491e9 4.96086e9i 0.535776 0.280521i
\(848\) −1.02466e10 1.77477e10i −0.577026 0.999438i
\(849\) 4.73100e9 + 8.19433e9i 0.265324 + 0.459554i
\(850\) 7.77714e9 + 1.34704e10i 0.434364 + 0.752340i
\(851\) 1.10702e10 0.615746
\(852\) 1.16877e10 + 2.02437e10i 0.647425 + 1.12137i
\(853\) 2.71878e10 1.49987 0.749934 0.661513i \(-0.230085\pi\)
0.749934 + 0.661513i \(0.230085\pi\)
\(854\) −2.09033e10 + 1.09445e10i −1.14845 + 0.601303i
\(855\) 1.80572e10 + 3.12760e10i 0.988028 + 1.71131i
\(856\) −2.50379e8 −0.0136439
\(857\) 1.08861e10 + 1.88552e10i 0.590797 + 1.02329i 0.994125 + 0.108235i \(0.0345198\pi\)
−0.403329 + 0.915055i \(0.632147\pi\)
\(858\) 4.35360e10 + 3.29158e10i 2.35311 + 1.77909i
\(859\) −3.96241e9 + 6.86310e9i −0.213297 + 0.369440i −0.952744 0.303774i \(-0.901753\pi\)
0.739448 + 0.673214i \(0.235087\pi\)
\(860\) −8.35028e9 1.44631e10i −0.447668 0.775385i
\(861\) 1.61889e9 3.92074e10i 0.0864385 2.09342i
\(862\) −9.10323e9 + 1.57673e10i −0.484084 + 0.838457i
\(863\) 5.49290e9 9.51398e9i 0.290914 0.503877i −0.683112 0.730313i \(-0.739374\pi\)
0.974026 + 0.226436i \(0.0727074\pi\)
\(864\) −3.19925e10 −1.68753
\(865\) 4.30690e9 0.226261
\(866\) 2.06446e10 3.57576e10i 1.08018 1.87092i
\(867\) 6.12306e9 1.06055e10i 0.319082 0.552666i
\(868\) −1.66429e10 + 8.71384e9i −0.863792 + 0.452263i
\(869\) 2.24389e10 + 3.88654e10i 1.15993 + 2.00906i
\(870\) 1.36958e10 2.37218e10i 0.705129 1.22132i
\(871\) −1.10548e9 + 8.88616e9i −0.0566876 + 0.455670i
\(872\) −6.48084e7 1.12251e8i −0.00330997 0.00573303i
\(873\) 3.35330e10 1.70578
\(874\) 2.35910e10 + 4.08608e10i 1.19524 + 2.07022i
\(875\) −4.81302e8 + 1.16565e10i −0.0242879 + 0.588219i
\(876\) 6.16115e10 3.09669
\(877\) −1.48189e10 2.56671e10i −0.741854 1.28493i −0.951650 0.307183i \(-0.900614\pi\)
0.209797 0.977745i \(-0.432720\pi\)
\(878\) 1.99482e10 0.994655
\(879\) 3.64726e9 + 6.31725e9i 0.181137 + 0.313738i
\(880\) 1.59551e10 + 2.76351e10i 0.789244 + 1.36701i
\(881\) −9.35252e9 1.61990e10i −0.460800 0.798130i 0.538201 0.842817i \(-0.319104\pi\)
−0.999001 + 0.0446871i \(0.985771\pi\)
\(882\) −2.11661e10 4.48356e10i −1.03872 2.20031i
\(883\) −3.89354e10 −1.90319 −0.951595 0.307355i \(-0.900556\pi\)
−0.951595 + 0.307355i \(0.900556\pi\)
\(884\) 2.20599e10 9.32236e9i 1.07404 0.453882i
\(885\) 1.49159e10 + 2.58351e10i 0.723349 + 1.25288i
\(886\) 1.51659e10 2.62681e10i 0.732571 1.26885i
\(887\) 3.41575e10 1.64344 0.821719 0.569892i \(-0.193015\pi\)
0.821719 + 0.569892i \(0.193015\pi\)
\(888\) 8.02895e7 1.39066e8i 0.00384781 0.00666460i
\(889\) −2.94268e9 + 1.54072e9i −0.140471 + 0.0735475i
\(890\) 2.72590e10 4.72140e10i 1.29612 2.24495i
\(891\) 3.34317e9 + 5.79054e9i 0.158338 + 0.274250i
\(892\) −6.51136e9 1.12780e10i −0.307181 0.532053i
\(893\) 1.51262e10 0.710806
\(894\) −9.57645e10 −4.48253
\(895\) 4.31125e9 + 7.46731e9i 0.201012 + 0.348164i
\(896\) 2.45500e7 5.94566e8i 0.00114018 0.0276135i
\(897\) 8.03975e9 6.46256e10i 0.371936 2.98972i
\(898\) −2.20732e9 + 3.82319e9i −0.101718 + 0.176181i
\(899\) 5.26340e9 9.11647e9i 0.241606 0.418473i
\(900\) −9.76618e9 + 1.69155e10i −0.446556 + 0.773457i
\(901\) 1.47746e10 + 2.55904e10i 0.672945 + 1.16557i
\(902\) 4.99968e10 2.26840
\(903\) 2.37072e10 1.24126e10i 1.07146 0.560990i
\(904\) 3.32713e7 5.76275e7i 0.00149789 0.00259442i
\(905\) −3.47123e9 + 6.01234e9i −0.155673 + 0.269633i
\(906\) −2.52320e10 −1.12721
\(907\) 9.43699e9 1.63453e10i 0.419960 0.727392i −0.575975 0.817467i \(-0.695377\pi\)
0.995935 + 0.0900752i \(0.0287107\pi\)
\(908\) 2.89081e10 1.28150
\(909\) −1.62803e9 −0.0718933
\(910\) −3.90386e10 6.50193e9i −1.71731 0.286021i
\(911\) −2.87337e9 −0.125915 −0.0629575 0.998016i \(-0.520053\pi\)
−0.0629575 + 0.998016i \(0.520053\pi\)
\(912\) 3.54462e10 1.54735
\(913\) −6.74842e9 + 1.16886e10i −0.293464 + 0.508294i
\(914\) −8.40161e9 −0.363958
\(915\) −2.16880e10 + 3.75647e10i −0.935935 + 1.62109i
\(916\) 9.15513e9 1.58572e10i 0.393578 0.681697i
\(917\) 1.17570e10 + 7.45098e9i 0.503505 + 0.319096i
\(918\) 4.65820e10 1.98732
\(919\) −8.17807e9 1.41648e10i −0.347573 0.602015i 0.638244 0.769834i \(-0.279661\pi\)
−0.985818 + 0.167819i \(0.946328\pi\)
\(920\) 3.67583e8 6.36673e8i 0.0155632 0.0269562i
\(921\) −2.31493e10 + 4.00957e10i −0.976402 + 1.69118i
\(922\) 6.36711e9 1.10282e10i 0.267537 0.463388i
\(923\) −2.33637e9 + 1.87803e10i −0.0977992 + 0.786136i
\(924\) 4.39884e10 2.30314e10i 1.83437 0.960434i
\(925\) −2.12335e9 3.67776e9i −0.0882117 0.152787i
\(926\) −5.04553e10 −2.08818
\(927\) −3.19099e10 −1.31567
\(928\) −8.42636e9 1.45949e10i −0.346116 0.599491i
\(929\) −3.85127e9 6.67059e9i −0.157597 0.272967i 0.776404 0.630235i \(-0.217041\pi\)
−0.934002 + 0.357268i \(0.883708\pi\)
\(930\) −3.47061e10 + 6.01127e10i −1.41487 + 2.45062i
\(931\) 9.75857e9 + 2.06714e10i 0.396335 + 0.839547i
\(932\) 1.02196e10 1.77009e10i 0.413503 0.716208i
\(933\) 5.37973e10 2.16858
\(934\) −1.17377e10 + 2.03304e10i −0.471379 + 0.816453i
\(935\) −2.30057e10 3.98471e10i −0.920440 1.59425i
\(936\) −4.76976e8 3.60622e8i −0.0190121 0.0143743i
\(937\) −4.14679e10 −1.64674 −0.823368 0.567508i \(-0.807908\pi\)
−0.823368 + 0.567508i \(0.807908\pi\)
\(938\) 1.38301e10 + 8.76483e9i 0.547163 + 0.346764i
\(939\) −3.40988e9 5.90609e9i −0.134403 0.232793i
\(940\) 1.19125e10 + 2.06330e10i 0.467794 + 0.810243i
\(941\) −4.03031e9 6.98071e9i −0.157680 0.273109i 0.776352 0.630300i \(-0.217068\pi\)
−0.934031 + 0.357191i \(0.883735\pi\)
\(942\) 3.68298e10 1.43556
\(943\) −2.98283e10 5.16641e10i −1.15834 2.00631i
\(944\) 1.85339e10 0.717076
\(945\) −3.23504e10 2.05020e10i −1.24700 0.790287i
\(946\) 1.70476e10 + 2.95273e10i 0.654703 + 1.13398i
\(947\) 3.89519e10 1.49040 0.745202 0.666839i \(-0.232353\pi\)
0.745202 + 0.666839i \(0.232353\pi\)
\(948\) 3.92593e10 + 6.79991e10i 1.49663 + 2.59223i
\(949\) 3.97894e10 + 3.00832e10i 1.51125 + 1.14259i
\(950\) 9.04989e9 1.56749e10i 0.342461 0.593159i
\(951\) 2.91419e10 + 5.04752e10i 1.09872 + 1.90303i
\(952\) −1.78719e7 + 4.32831e8i −0.000671336 + 0.0162588i
\(953\) 2.14025e10 3.70702e10i 0.801013 1.38740i −0.117937 0.993021i \(-0.537628\pi\)
0.918950 0.394374i \(-0.129039\pi\)
\(954\) −3.72901e10 + 6.45884e10i −1.39051 + 2.40844i
\(955\) 6.43628e9 0.239124
\(956\) −3.98905e10 −1.47661
\(957\) −1.39116e10 + 2.40955e10i −0.513079 + 0.888678i
\(958\) −1.57749e10 + 2.73229e10i −0.579678 + 1.00403i
\(959\) 1.02997e9 2.49445e10i 0.0377103 0.913290i
\(960\) 2.73709e10 + 4.74078e10i 0.998481 + 1.72942i
\(961\) 4.18457e8 7.24789e8i 0.0152096 0.0263439i
\(962\) −1.21054e10 + 5.11566e9i −0.438396 + 0.185263i
\(963\) 2.35962e10 + 4.08698e10i 0.851432 + 1.47472i
\(964\) −3.29128e10 −1.18330
\(965\) −7.13436e9 1.23571e10i −0.255570 0.442660i
\(966\) −1.00581e11 6.37432e10i −3.59002 2.27517i
\(967\) 1.53637e10 0.546389 0.273195 0.961959i \(-0.411920\pi\)
0.273195 + 0.961959i \(0.411920\pi\)
\(968\) −1.17925e8 2.04253e8i −0.00417872 0.00723776i
\(969\) −5.11100e10 −1.80457
\(970\) −2.44716e10 4.23860e10i −0.860916 1.49115i
\(971\) 1.71834e10 + 2.97625e10i 0.602339 + 1.04328i 0.992466 + 0.122521i \(0.0390978\pi\)
−0.390127 + 0.920761i \(0.627569\pi\)
\(972\) −1.11086e10 1.92406e10i −0.387996 0.672028i
\(973\) 1.36037e10 + 8.62131e9i 0.473436 + 0.300039i
\(974\) −5.63847e10 −1.95526
\(975\) −2.30121e10 + 9.72473e9i −0.795133 + 0.336017i
\(976\) 1.34743e10 + 2.33382e10i 0.463909 + 0.803514i
\(977\) 1.31225e10 2.27289e10i 0.450180 0.779735i −0.548217 0.836336i \(-0.684693\pi\)
0.998397 + 0.0566014i \(0.0180264\pi\)
\(978\) −6.65100e9 −0.227353
\(979\) −2.76885e10 + 4.79580e10i −0.943106 + 1.63351i
\(980\) −2.05116e10 + 2.95907e10i −0.696159 + 1.00430i
\(981\) −1.22153e10 + 2.11576e10i −0.413109 + 0.715525i
\(982\) 7.41648e9 + 1.28457e10i 0.249924 + 0.432881i
\(983\) −1.38865e10 2.40522e10i −0.466291 0.807640i 0.532968 0.846136i \(-0.321077\pi\)
−0.999259 + 0.0384959i \(0.987743\pi\)
\(984\) −8.65350e8 −0.0289540
\(985\) −5.85577e9 −0.195235
\(986\) 1.22690e10 + 2.12506e10i 0.407606 + 0.705994i
\(987\) −3.38207e10 + 1.77078e10i −1.11962 + 0.586210i
\(988\) −2.22297e10 1.68070e10i −0.733304 0.554421i
\(989\) 2.03413e10 3.52322e10i 0.668640 1.15812i
\(990\) 5.80649e10 1.00571e11i 1.90191 3.29421i
\(991\) 9.76838e9 1.69193e10i 0.318834 0.552237i −0.661411 0.750024i \(-0.730042\pi\)
0.980245 + 0.197787i \(0.0633754\pi\)
\(992\) 2.13531e10 + 3.69846e10i 0.694495 + 1.20290i
\(993\) 2.66400e10 0.863401
\(994\) 2.92291e10 + 1.85239e10i 0.943981 + 0.598247i
\(995\) 2.54160e10 4.40218e10i 0.817949 1.41673i
\(996\) −1.18071e10 + 2.04505e10i −0.378647 + 0.655836i
\(997\) −5.25066e9 −0.167796 −0.0838978 0.996474i \(-0.526737\pi\)
−0.0838978 + 0.996474i \(0.526737\pi\)
\(998\) 2.61837e10 4.53514e10i 0.833822 1.44422i
\(999\) −1.27181e10 −0.403591
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 91.8.h.a.16.11 yes 126
7.4 even 3 91.8.g.a.81.53 yes 126
13.9 even 3 91.8.g.a.9.53 126
91.74 even 3 inner 91.8.h.a.74.11 yes 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.g.a.9.53 126 13.9 even 3
91.8.g.a.81.53 yes 126 7.4 even 3
91.8.h.a.16.11 yes 126 1.1 even 1 trivial
91.8.h.a.74.11 yes 126 91.74 even 3 inner