Properties

Label 91.8.r.a.25.4
Level $91$
Weight $8$
Character 91.25
Analytic conductor $28.427$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,8,Mod(25,91)]
 
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([4, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.25");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.r (of order \(6\), 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: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.4
Character \(\chi\) \(=\) 91.25
Dual form 91.8.r.a.51.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-17.5746 + 10.1467i) q^{2} +(-9.13036 + 15.8143i) q^{3} +(141.910 - 245.795i) q^{4} +(-149.843 + 86.5119i) q^{5} -370.571i q^{6} +(-905.314 - 62.8521i) q^{7} +3162.10i q^{8} +(926.773 + 1605.22i) q^{9} +O(q^{10})\) \(q+(-17.5746 + 10.1467i) q^{2} +(-9.13036 + 15.8143i) q^{3} +(141.910 - 245.795i) q^{4} +(-149.843 + 86.5119i) q^{5} -370.571i q^{6} +(-905.314 - 62.8521i) q^{7} +3162.10i q^{8} +(926.773 + 1605.22i) q^{9} +(1755.62 - 3040.82i) q^{10} +(738.586 + 426.423i) q^{11} +(2591.38 + 4488.40i) q^{12} +(1924.10 + 7684.16i) q^{13} +(16548.2 - 8081.32i) q^{14} -3159.54i q^{15} +(-13920.4 - 24110.8i) q^{16} +(-10574.8 + 18316.1i) q^{17} +(-32575.2 - 18807.3i) q^{18} +(-45892.1 + 26495.8i) q^{19} +49107.6i q^{20} +(9259.80 - 13743.0i) q^{21} -17307.1 q^{22} +(-29550.3 - 51182.7i) q^{23} +(-50006.3 - 28871.2i) q^{24} +(-24093.9 + 41731.8i) q^{25} +(-111784. - 115523. i) q^{26} -73783.3 q^{27} +(-143922. + 213602. i) q^{28} -9939.75 q^{29} +(32058.8 + 55527.5i) q^{30} +(239567. + 138314. i) q^{31} +(138765. + 80116.1i) q^{32} +(-13487.1 + 7786.79i) q^{33} -429197. i q^{34} +(141092. - 68902.5i) q^{35} +526073. q^{36} +(-448585. + 258991. i) q^{37} +(537688. - 931304. i) q^{38} +(-139087. - 39731.1i) q^{39} +(-273560. - 473819. i) q^{40} -104730. i q^{41} +(-23291.2 + 335483. i) q^{42} +319415. q^{43} +(209625. - 121027. i) q^{44} +(-277741. - 160354. i) q^{45} +(1.03867e6 + 599675. i) q^{46} +(1.02917e6 - 594194. i) q^{47} +508392. q^{48} +(815642. + 113802. i) q^{49} -977891. i q^{50} +(-193104. - 334466. i) q^{51} +(2.16178e6 + 617525. i) q^{52} +(-897631. + 1.55474e6i) q^{53} +(1.29671e6 - 748655. i) q^{54} -147563. q^{55} +(198745. - 2.86270e6i) q^{56} -967665. i q^{57} +(174687. - 100855. i) q^{58} +(327222. + 188922. i) q^{59} +(-776600. - 448370. i) q^{60} +(-442226. - 765957. i) q^{61} -5.61370e6 q^{62} +(-738129. - 1.51147e6i) q^{63} +311966. q^{64} +(-953084. - 984961. i) q^{65} +(158020. - 273699. i) q^{66} +(-2.24534e6 - 1.29635e6i) q^{67} +(3.00134e6 + 5.19847e6i) q^{68} +1.07922e6 q^{69} +(-1.78050e6 + 2.64255e6i) q^{70} -5.15129e6i q^{71} +(-5.07587e6 + 2.93055e6i) q^{72} +(1.82473e6 + 1.05351e6i) q^{73} +(5.25578e6 - 9.10329e6i) q^{74} +(-439972. - 762053. i) q^{75} +1.50401e7i q^{76} +(-641850. - 432468. i) q^{77} +(2.84753e6 - 713015. i) q^{78} +(2.89244e6 + 5.00986e6i) q^{79} +(4.17174e6 + 2.40856e6i) q^{80} +(-1.35318e6 + 2.34378e6i) q^{81} +(1.06266e6 + 1.84059e6i) q^{82} +103458. i q^{83} +(-2.06390e6 - 4.22628e6i) q^{84} -3.65939e6i q^{85} +(-5.61357e6 + 3.24100e6i) q^{86} +(90753.5 - 157190. i) q^{87} +(-1.34839e6 + 2.33549e6i) q^{88} +(3.07050e6 - 1.77276e6i) q^{89} +6.50823e6 q^{90} +(-1.25894e6 - 7.07751e6i) q^{91} -1.67739e7 q^{92} +(-4.37466e6 + 2.52571e6i) q^{93} +(-1.20582e7 + 2.08854e7i) q^{94} +(4.58441e6 - 7.94042e6i) q^{95} +(-2.53395e6 + 1.46298e6i) q^{96} -1.22083e7i q^{97} +(-1.54893e7 + 6.27604e6i) q^{98} +1.58079e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9} - 4514 q^{10} + 2090 q^{12} + 11132 q^{13} + 18748 q^{14} - 230074 q^{16} - 28972 q^{17} + 179920 q^{22} + 20508 q^{23} + 920040 q^{25} + 144684 q^{26} - 357584 q^{27} + 44600 q^{29} + 46580 q^{30} - 1216824 q^{35} - 4529248 q^{36} - 129032 q^{38} + 104546 q^{39} + 2082020 q^{40} + 2426496 q^{42} - 1434416 q^{43} - 3783940 q^{48} - 34428 q^{49} - 756008 q^{51} - 2348612 q^{52} + 1103824 q^{53} - 4216216 q^{55} + 8135574 q^{56} + 531568 q^{61} + 26627120 q^{62} - 27402496 q^{64} - 7495542 q^{65} + 2808402 q^{66} + 531760 q^{68} + 24238760 q^{69} - 7462590 q^{74} - 1547944 q^{75} - 1811116 q^{77} - 31233508 q^{78} + 2961020 q^{79} - 34639872 q^{81} - 10292872 q^{82} + 43455484 q^{87} + 21936790 q^{88} - 58442348 q^{90} + 16479848 q^{91} + 24834900 q^{92} + 26036992 q^{94} + 89048 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.5746 + 10.1467i −1.55339 + 0.896848i −0.555523 + 0.831501i \(0.687482\pi\)
−0.997863 + 0.0653463i \(0.979185\pi\)
\(3\) −9.13036 + 15.8143i −0.195238 + 0.338162i −0.946978 0.321297i \(-0.895881\pi\)
0.751741 + 0.659459i \(0.229214\pi\)
\(4\) 141.910 245.795i 1.10867 1.92027i
\(5\) −149.843 + 86.5119i −0.536095 + 0.309514i −0.743495 0.668742i \(-0.766833\pi\)
0.207400 + 0.978256i \(0.433500\pi\)
\(6\) 370.571i 0.700394i
\(7\) −905.314 62.8521i −0.997599 0.0692590i
\(8\) 3162.10i 2.18354i
\(9\) 926.773 + 1605.22i 0.423764 + 0.733982i
\(10\) 1755.62 3040.82i 0.555175 0.961591i
\(11\) 738.586 + 426.423i 0.167312 + 0.0965976i 0.581318 0.813677i \(-0.302537\pi\)
−0.414006 + 0.910274i \(0.635871\pi\)
\(12\) 2591.38 + 4488.40i 0.432909 + 0.749820i
\(13\) 1924.10 + 7684.16i 0.242899 + 0.970052i
\(14\) 16548.2 8081.32i 1.61177 0.787108i
\(15\) 3159.54i 0.241716i
\(16\) −13920.4 24110.8i −0.849632 1.47161i
\(17\) −10574.8 + 18316.1i −0.522037 + 0.904195i 0.477634 + 0.878559i \(0.341494\pi\)
−0.999671 + 0.0256361i \(0.991839\pi\)
\(18\) −32575.2 18807.3i −1.31654 0.760104i
\(19\) −45892.1 + 26495.8i −1.53497 + 0.886216i −0.535849 + 0.844314i \(0.680008\pi\)
−0.999122 + 0.0419018i \(0.986658\pi\)
\(20\) 49107.6i 1.37260i
\(21\) 9259.80 13743.0i 0.218190 0.323828i
\(22\) −17307.1 −0.346533
\(23\) −29550.3 51182.7i −0.506425 0.877154i −0.999972 0.00743470i \(-0.997633\pi\)
0.493548 0.869719i \(-0.335700\pi\)
\(24\) −50006.3 28871.2i −0.738390 0.426309i
\(25\) −24093.9 + 41731.8i −0.308402 + 0.534167i
\(26\) −111784. 115523.i −1.24730 1.28902i
\(27\) −73783.3 −0.721415
\(28\) −143922. + 213602.i −1.23901 + 1.83888i
\(29\) −9939.75 −0.0756802 −0.0378401 0.999284i \(-0.512048\pi\)
−0.0378401 + 0.999284i \(0.512048\pi\)
\(30\) 32058.8 + 55527.5i 0.216782 + 0.375477i
\(31\) 239567. + 138314.i 1.44431 + 0.833873i 0.998133 0.0610722i \(-0.0194520\pi\)
0.446177 + 0.894945i \(0.352785\pi\)
\(32\) 138765. + 80116.1i 0.748610 + 0.432210i
\(33\) −13487.1 + 7786.79i −0.0653312 + 0.0377190i
\(34\) 429197.i 1.87275i
\(35\) 141092. 68902.5i 0.556244 0.271642i
\(36\) 526073. 1.87926
\(37\) −448585. + 258991.i −1.45592 + 0.840578i −0.998807 0.0488291i \(-0.984451\pi\)
−0.457116 + 0.889407i \(0.651118\pi\)
\(38\) 537688. 931304.i 1.58960 2.75327i
\(39\) −139087. 39731.1i −0.375457 0.107252i
\(40\) −273560. 473819.i −0.675837 1.17058i
\(41\) 104730.i 0.237317i −0.992935 0.118659i \(-0.962141\pi\)
0.992935 0.118659i \(-0.0378594\pi\)
\(42\) −23291.2 + 335483.i −0.0485086 + 0.698712i
\(43\) 319415. 0.612654 0.306327 0.951926i \(-0.400900\pi\)
0.306327 + 0.951926i \(0.400900\pi\)
\(44\) 209625. 121027.i 0.370988 0.214190i
\(45\) −277741. 160354.i −0.454356 0.262322i
\(46\) 1.03867e6 + 599675.i 1.57335 + 0.908372i
\(47\) 1.02917e6 594194.i 1.44593 0.834807i 0.447692 0.894188i \(-0.352246\pi\)
0.998235 + 0.0593812i \(0.0189127\pi\)
\(48\) 508392. 0.663521
\(49\) 815642. + 113802.i 0.990406 + 0.138185i
\(50\) 977891.i 1.10636i
\(51\) −193104. 334466.i −0.203843 0.353066i
\(52\) 2.16178e6 + 617525.i 2.13206 + 0.609036i
\(53\) −897631. + 1.55474e6i −0.828194 + 1.43447i 0.0712588 + 0.997458i \(0.477298\pi\)
−0.899453 + 0.437017i \(0.856035\pi\)
\(54\) 1.29671e6 748655.i 1.12064 0.646999i
\(55\) −147563. −0.119593
\(56\) 198745. 2.86270e6i 0.151230 2.17830i
\(57\) 967665.i 0.692091i
\(58\) 174687. 100855.i 0.117561 0.0678736i
\(59\) 327222. + 188922.i 0.207425 + 0.119757i 0.600114 0.799914i \(-0.295122\pi\)
−0.392689 + 0.919671i \(0.628455\pi\)
\(60\) −776600. 448370.i −0.464160 0.267983i
\(61\) −442226. 765957.i −0.249453 0.432066i 0.713921 0.700226i \(-0.246918\pi\)
−0.963374 + 0.268160i \(0.913584\pi\)
\(62\) −5.61370e6 −2.99143
\(63\) −738129. 1.51147e6i −0.371912 0.761569i
\(64\) 311966. 0.148757
\(65\) −953084. 984961.i −0.430462 0.444859i
\(66\) 158020. 273699.i 0.0676563 0.117184i
\(67\) −2.24534e6 1.29635e6i −0.912053 0.526574i −0.0309617 0.999521i \(-0.509857\pi\)
−0.881091 + 0.472947i \(0.843190\pi\)
\(68\) 3.00134e6 + 5.19847e6i 1.15753 + 2.00491i
\(69\) 1.07922e6 0.395493
\(70\) −1.78050e6 + 2.64255e6i −0.620440 + 0.920831i
\(71\) 5.15129e6i 1.70809i −0.520195 0.854047i \(-0.674141\pi\)
0.520195 0.854047i \(-0.325859\pi\)
\(72\) −5.07587e6 + 2.93055e6i −1.60268 + 0.925307i
\(73\) 1.82473e6 + 1.05351e6i 0.548996 + 0.316963i 0.748717 0.662890i \(-0.230670\pi\)
−0.199721 + 0.979853i \(0.564004\pi\)
\(74\) 5.25578e6 9.10329e6i 1.50774 2.61148i
\(75\) −439972. 762053.i −0.120423 0.208579i
\(76\) 1.50401e7i 3.93009i
\(77\) −641850. 432468.i −0.160220 0.107953i
\(78\) 2.84753e6 713015.i 0.679418 0.170125i
\(79\) 2.89244e6 + 5.00986e6i 0.660040 + 1.14322i 0.980605 + 0.195996i \(0.0627940\pi\)
−0.320565 + 0.947227i \(0.603873\pi\)
\(80\) 4.17174e6 + 2.40856e6i 0.910966 + 0.525947i
\(81\) −1.35318e6 + 2.34378e6i −0.282917 + 0.490027i
\(82\) 1.06266e6 + 1.84059e6i 0.212837 + 0.368645i
\(83\) 103458.i 0.0198606i 0.999951 + 0.00993030i \(0.00316096\pi\)
−0.999951 + 0.00993030i \(0.996839\pi\)
\(84\) −2.06390e6 4.22628e6i −0.379937 0.778002i
\(85\) 3.65939e6i 0.646312i
\(86\) −5.61357e6 + 3.24100e6i −0.951688 + 0.549457i
\(87\) 90753.5 157190.i 0.0147756 0.0255922i
\(88\) −1.34839e6 + 2.33549e6i −0.210925 + 0.365332i
\(89\) 3.07050e6 1.77276e6i 0.461684 0.266553i −0.251068 0.967969i \(-0.580782\pi\)
0.712752 + 0.701416i \(0.247448\pi\)
\(90\) 6.50823e6 0.941053
\(91\) −1.25894e6 7.07751e6i −0.175130 0.984545i
\(92\) −1.67739e7 −2.24583
\(93\) −4.37466e6 + 2.52571e6i −0.563968 + 0.325607i
\(94\) −1.20582e7 + 2.08854e7i −1.49739 + 2.59355i
\(95\) 4.58441e6 7.94042e6i 0.548593 0.950191i
\(96\) −2.53395e6 + 1.46298e6i −0.292314 + 0.168767i
\(97\) 1.22083e7i 1.35817i −0.734059 0.679085i \(-0.762377\pi\)
0.734059 0.679085i \(-0.237623\pi\)
\(98\) −1.54893e7 + 6.27604e6i −1.66241 + 0.673588i
\(99\) 1.58079e6i 0.163738i
\(100\) 6.83832e6 + 1.18443e7i 0.683832 + 1.18443i
\(101\) 2.15768e6 3.73722e6i 0.208383 0.360930i −0.742822 0.669489i \(-0.766513\pi\)
0.951205 + 0.308558i \(0.0998466\pi\)
\(102\) 6.78742e6 + 3.91872e6i 0.633293 + 0.365632i
\(103\) 115057. + 199284.i 0.0103748 + 0.0179697i 0.871166 0.490988i \(-0.163364\pi\)
−0.860791 + 0.508958i \(0.830031\pi\)
\(104\) −2.42981e7 + 6.08419e6i −2.11815 + 0.530379i
\(105\) −198584. + 2.86038e6i −0.0167410 + 0.241135i
\(106\) 3.64319e7i 2.97106i
\(107\) −462182. 800523.i −0.0364729 0.0631729i 0.847213 0.531254i \(-0.178279\pi\)
−0.883686 + 0.468081i \(0.844946\pi\)
\(108\) −1.04706e7 + 1.81356e7i −0.799811 + 1.38531i
\(109\) 409672. + 236524.i 0.0303001 + 0.0174938i 0.515074 0.857146i \(-0.327765\pi\)
−0.484773 + 0.874640i \(0.661098\pi\)
\(110\) 2.59335e6 1.49727e6i 0.185775 0.107257i
\(111\) 9.45871e6i 0.656450i
\(112\) 1.10869e7 + 2.27027e7i 0.745670 + 1.52692i
\(113\) −1.52647e7 −0.995208 −0.497604 0.867404i \(-0.665787\pi\)
−0.497604 + 0.867404i \(0.665787\pi\)
\(114\) 9.81858e6 + 1.70063e7i 0.620700 + 1.07508i
\(115\) 8.85582e6 + 5.11291e6i 0.542983 + 0.313492i
\(116\) −1.41055e6 + 2.44314e6i −0.0839045 + 0.145327i
\(117\) −1.05516e7 + 1.02101e7i −0.609068 + 0.589357i
\(118\) −7.66771e6 −0.429614
\(119\) 1.07247e7 1.59172e7i 0.583407 0.865868i
\(120\) 9.99080e6 0.527796
\(121\) −9.37991e6 1.62465e7i −0.481338 0.833702i
\(122\) 1.55438e7 + 8.97423e6i 0.774995 + 0.447443i
\(123\) 1.65623e6 + 956226.i 0.0802515 + 0.0463332i
\(124\) 6.79938e7 3.92562e7i 3.20253 1.84898i
\(125\) 2.18551e7i 1.00085i
\(126\) 2.83087e7 + 1.90739e7i 1.26073 + 0.849461i
\(127\) 8.81278e6 0.381769 0.190884 0.981613i \(-0.438864\pi\)
0.190884 + 0.981613i \(0.438864\pi\)
\(128\) −2.32446e7 + 1.34203e7i −0.979687 + 0.565623i
\(129\) −2.91637e6 + 5.05131e6i −0.119613 + 0.207176i
\(130\) 2.67441e7 + 7.63962e6i 1.06764 + 0.304979i
\(131\) −3.39639e6 5.88271e6i −0.131998 0.228627i 0.792449 0.609939i \(-0.208806\pi\)
−0.924447 + 0.381311i \(0.875473\pi\)
\(132\) 4.42009e6i 0.167272i
\(133\) 4.32120e7 2.11026e7i 1.59266 0.777777i
\(134\) 5.26144e7 1.88903
\(135\) 1.10559e7 6.38314e6i 0.386747 0.223288i
\(136\) −5.79175e7 3.34387e7i −1.97435 1.13989i
\(137\) −3.58454e7 2.06954e7i −1.19100 0.687624i −0.232466 0.972605i \(-0.574679\pi\)
−0.958533 + 0.284981i \(0.908013\pi\)
\(138\) −1.89668e7 + 1.09505e7i −0.614353 + 0.354697i
\(139\) −1.30491e7 −0.412124 −0.206062 0.978539i \(-0.566065\pi\)
−0.206062 + 0.978539i \(0.566065\pi\)
\(140\) 3.08651e6 4.44578e7i 0.0950649 1.36930i
\(141\) 2.17008e7i 0.651943i
\(142\) 5.22685e7 + 9.05317e7i 1.53190 + 2.65333i
\(143\) −1.85559e6 + 6.49590e6i −0.0530648 + 0.185765i
\(144\) 2.58020e7 4.46904e7i 0.720088 1.24723i
\(145\) 1.48940e6 859907.i 0.0405718 0.0234241i
\(146\) −4.27584e7 −1.13707
\(147\) −9.24680e6 + 1.18597e7i −0.240094 + 0.307938i
\(148\) 1.47013e8i 3.72770i
\(149\) 3.75556e7 2.16827e7i 0.930084 0.536984i 0.0432460 0.999064i \(-0.486230\pi\)
0.886838 + 0.462080i \(0.152897\pi\)
\(150\) 1.54646e7 + 8.92850e6i 0.374127 + 0.216003i
\(151\) 1.85148e7 + 1.06895e7i 0.437622 + 0.252661i 0.702588 0.711597i \(-0.252028\pi\)
−0.264966 + 0.964258i \(0.585361\pi\)
\(152\) −8.37825e7 1.45116e8i −1.93509 3.35167i
\(153\) −3.92018e7 −0.884883
\(154\) 1.56683e7 + 1.08779e6i 0.345701 + 0.0240006i
\(155\) −4.78632e7 −1.03238
\(156\) −2.95035e7 + 2.85487e7i −0.622211 + 0.602074i
\(157\) 1.63772e7 2.83661e7i 0.337746 0.584994i −0.646262 0.763115i \(-0.723669\pi\)
0.984008 + 0.178122i \(0.0570021\pi\)
\(158\) −1.01667e8 5.86974e7i −2.05059 1.18391i
\(159\) −1.63914e7 2.83907e7i −0.323390 0.560127i
\(160\) −2.77240e7 −0.535101
\(161\) 2.35354e7 + 4.81937e7i 0.444458 + 0.910122i
\(162\) 5.49213e7i 1.01493i
\(163\) −3.34359e7 + 1.93042e7i −0.604723 + 0.349137i −0.770897 0.636959i \(-0.780192\pi\)
0.166174 + 0.986096i \(0.446859\pi\)
\(164\) −2.57422e7 1.48623e7i −0.455714 0.263107i
\(165\) 1.34730e6 2.33359e6i 0.0233491 0.0404419i
\(166\) −1.04976e6 1.81823e6i −0.0178119 0.0308512i
\(167\) 6.34365e7i 1.05398i 0.849872 + 0.526989i \(0.176679\pi\)
−0.849872 + 0.526989i \(0.823321\pi\)
\(168\) 4.34568e7 + 2.92805e7i 0.707091 + 0.476426i
\(169\) −5.53442e7 + 2.95701e7i −0.882001 + 0.471248i
\(170\) 3.71306e7 + 6.43121e7i 0.579644 + 1.00397i
\(171\) −8.50631e7 4.91112e7i −1.30093 0.751093i
\(172\) 4.53281e7 7.85106e7i 0.679232 1.17646i
\(173\) −1.36878e7 2.37080e7i −0.200989 0.348123i 0.747858 0.663858i \(-0.231082\pi\)
−0.948847 + 0.315735i \(0.897749\pi\)
\(174\) 3.68339e6i 0.0530060i
\(175\) 2.44354e7 3.62660e7i 0.344657 0.511525i
\(176\) 2.37439e7i 0.328289i
\(177\) −5.97531e6 + 3.44985e6i −0.0809943 + 0.0467621i
\(178\) −3.59752e7 + 6.23108e7i −0.478115 + 0.828120i
\(179\) 4.57167e7 7.91836e7i 0.595784 1.03193i −0.397651 0.917537i \(-0.630175\pi\)
0.993436 0.114392i \(-0.0364921\pi\)
\(180\) −7.88284e7 + 4.55116e7i −1.00746 + 0.581659i
\(181\) −4.99849e7 −0.626562 −0.313281 0.949661i \(-0.601428\pi\)
−0.313281 + 0.949661i \(0.601428\pi\)
\(182\) 9.39386e7 + 1.11610e8i 1.15503 + 1.37231i
\(183\) 1.61507e7 0.194811
\(184\) 1.61845e8 9.34412e7i 1.91530 1.10580i
\(185\) 4.48115e7 7.76159e7i 0.520342 0.901259i
\(186\) 5.12551e7 8.87765e7i 0.584039 1.01159i
\(187\) −1.56208e7 + 9.01868e6i −0.174686 + 0.100855i
\(188\) 3.37288e8i 3.70210i
\(189\) 6.67970e7 + 4.63743e6i 0.719682 + 0.0499645i
\(190\) 1.86066e8i 1.96802i
\(191\) 3.27303e7 + 5.66906e7i 0.339886 + 0.588700i 0.984411 0.175883i \(-0.0562781\pi\)
−0.644525 + 0.764583i \(0.722945\pi\)
\(192\) −2.84836e6 + 4.93351e6i −0.0290430 + 0.0503039i
\(193\) 1.60416e8 + 9.26160e7i 1.60619 + 0.927332i 0.990213 + 0.139565i \(0.0445705\pi\)
0.615974 + 0.787767i \(0.288763\pi\)
\(194\) 1.23874e8 + 2.14556e8i 1.21807 + 2.10976i
\(195\) 2.42784e7 6.07926e6i 0.234477 0.0587124i
\(196\) 1.43720e8 1.84331e8i 1.36339 1.74865i
\(197\) 6.60901e7i 0.615892i 0.951404 + 0.307946i \(0.0996417\pi\)
−0.951404 + 0.307946i \(0.900358\pi\)
\(198\) −1.60397e7 2.77817e7i −0.146848 0.254349i
\(199\) −6.79995e7 + 1.17779e8i −0.611674 + 1.05945i 0.379284 + 0.925280i \(0.376170\pi\)
−0.990958 + 0.134170i \(0.957163\pi\)
\(200\) −1.31960e8 7.61873e7i −1.16638 0.673407i
\(201\) 4.10015e7 2.36722e7i 0.356134 0.205614i
\(202\) 8.75732e7i 0.747552i
\(203\) 8.99859e6 + 624734.i 0.0754985 + 0.00524154i
\(204\) −1.09613e8 −0.903978
\(205\) 9.06042e6 + 1.56931e7i 0.0734531 + 0.127224i
\(206\) −4.04414e6 2.33488e6i −0.0322322 0.0186093i
\(207\) 5.47729e7 9.48694e7i 0.429210 0.743413i
\(208\) 1.58487e8 1.53358e8i 1.22116 1.18164i
\(209\) −4.51937e7 −0.342425
\(210\) −2.55333e7 5.22848e7i −0.190256 0.389590i
\(211\) −1.02772e8 −0.753161 −0.376581 0.926384i \(-0.622900\pi\)
−0.376581 + 0.926384i \(0.622900\pi\)
\(212\) 2.54765e8 + 4.41267e8i 1.83639 + 3.18072i
\(213\) 8.14639e7 + 4.70332e7i 0.577612 + 0.333485i
\(214\) 1.62453e7 + 9.37922e6i 0.113313 + 0.0654212i
\(215\) −4.78621e7 + 2.76332e7i −0.328441 + 0.189625i
\(216\) 2.33311e8i 1.57524i
\(217\) −2.08190e8 1.40275e8i −1.38309 0.931902i
\(218\) −9.59974e6 −0.0627569
\(219\) −3.33209e7 + 1.92378e7i −0.214369 + 0.123766i
\(220\) −2.09406e7 + 3.62702e7i −0.132590 + 0.229652i
\(221\) −1.61091e8 4.60166e7i −1.00392 0.286775i
\(222\) 9.59744e7 + 1.66233e8i 0.588735 + 1.01972i
\(223\) 3.60815e7i 0.217880i 0.994048 + 0.108940i \(0.0347456\pi\)
−0.994048 + 0.108940i \(0.965254\pi\)
\(224\) −1.20591e8 8.12519e7i −0.716878 0.483020i
\(225\) −8.93182e7 −0.522759
\(226\) 2.68270e8 1.54886e8i 1.54594 0.892550i
\(227\) −8.34479e7 4.81787e7i −0.473505 0.273378i 0.244201 0.969725i \(-0.421474\pi\)
−0.717706 + 0.696346i \(0.754808\pi\)
\(228\) −2.37847e8 1.37321e8i −1.32900 0.767301i
\(229\) −5.59782e7 + 3.23190e7i −0.308031 + 0.177842i −0.646045 0.763299i \(-0.723578\pi\)
0.338014 + 0.941141i \(0.390245\pi\)
\(230\) −2.07516e8 −1.12462
\(231\) 1.26995e7 6.20180e6i 0.0677867 0.0331036i
\(232\) 3.14305e7i 0.165251i
\(233\) 1.06506e8 + 1.84474e8i 0.551607 + 0.955412i 0.998159 + 0.0606538i \(0.0193185\pi\)
−0.446552 + 0.894758i \(0.647348\pi\)
\(234\) 8.18407e7 2.86501e8i 0.417555 1.46174i
\(235\) −1.02810e8 + 1.78072e8i −0.516769 + 0.895071i
\(236\) 9.28721e7 5.36197e7i 0.459932 0.265542i
\(237\) −1.05636e8 −0.515459
\(238\) −2.69759e7 + 3.88557e8i −0.129705 + 1.86825i
\(239\) 1.12585e8i 0.533445i 0.963773 + 0.266722i \(0.0859407\pi\)
−0.963773 + 0.266722i \(0.914059\pi\)
\(240\) −7.61790e7 + 4.39820e7i −0.355710 + 0.205369i
\(241\) 2.57986e8 + 1.48948e8i 1.18723 + 0.685450i 0.957677 0.287845i \(-0.0929388\pi\)
0.229558 + 0.973295i \(0.426272\pi\)
\(242\) 3.29695e8 + 1.90350e8i 1.49541 + 0.863373i
\(243\) −1.05392e8 1.82545e8i −0.471179 0.816107i
\(244\) −2.51025e8 −1.10625
\(245\) −1.32064e8 + 5.35104e7i −0.573722 + 0.232465i
\(246\) −3.88101e7 −0.166215
\(247\) −2.91899e8 3.01662e8i −1.23252 1.27374i
\(248\) −4.37363e8 + 7.57535e8i −1.82079 + 3.15371i
\(249\) −1.63612e6 944613.i −0.00671609 0.00387754i
\(250\) 2.21757e8 + 3.84094e8i 0.897608 + 1.55470i
\(251\) 3.80819e8 1.52006 0.760030 0.649888i \(-0.225184\pi\)
0.760030 + 0.649888i \(0.225184\pi\)
\(252\) −4.76261e8 3.30648e7i −1.87475 0.130156i
\(253\) 5.04038e7i 0.195678i
\(254\) −1.54881e8 + 8.94204e7i −0.593034 + 0.342388i
\(255\) 5.78705e7 + 3.34116e7i 0.218558 + 0.126185i
\(256\) 2.52377e8 4.37129e8i 0.940176 1.62843i
\(257\) −1.77040e8 3.06642e8i −0.650588 1.12685i −0.982981 0.183710i \(-0.941189\pi\)
0.332393 0.943141i \(-0.392144\pi\)
\(258\) 1.18366e8i 0.429099i
\(259\) 4.22388e8 2.06273e8i 1.51064 0.737723i
\(260\) −3.77351e8 + 9.44877e7i −1.33149 + 0.333402i
\(261\) −9.21189e6 1.59555e7i −0.0320706 0.0555479i
\(262\) 1.19380e8 + 6.89240e7i 0.410088 + 0.236764i
\(263\) −1.93890e8 + 3.35827e8i −0.657219 + 1.13834i 0.324114 + 0.946018i \(0.394934\pi\)
−0.981333 + 0.192318i \(0.938399\pi\)
\(264\) −2.46227e7 4.26477e7i −0.0823609 0.142653i
\(265\) 3.10623e8i 1.02535i
\(266\) −5.45311e8 + 8.09327e8i −1.77647 + 2.63656i
\(267\) 6.47436e7i 0.208165i
\(268\) −6.37271e8 + 3.67929e8i −2.02233 + 1.16759i
\(269\) 2.11562e8 3.66437e8i 0.662683 1.14780i −0.317225 0.948350i \(-0.602751\pi\)
0.979908 0.199450i \(-0.0639155\pi\)
\(270\) −1.29535e8 + 2.24361e8i −0.400511 + 0.693705i
\(271\) 1.04273e8 6.02019e7i 0.318257 0.183746i −0.332358 0.943153i \(-0.607844\pi\)
0.650616 + 0.759407i \(0.274511\pi\)
\(272\) 5.88821e8 1.77416
\(273\) 1.23420e8 + 4.47110e7i 0.367127 + 0.132998i
\(274\) 8.39956e8 2.46677
\(275\) −3.55908e7 + 2.05484e7i −0.103198 + 0.0595817i
\(276\) 1.53152e8 2.65267e8i 0.438471 0.759455i
\(277\) −3.90848e7 + 6.76969e7i −0.110492 + 0.191377i −0.915969 0.401250i \(-0.868576\pi\)
0.805477 + 0.592627i \(0.201909\pi\)
\(278\) 2.29332e8 1.32405e8i 0.640188 0.369613i
\(279\) 5.12742e8i 1.41346i
\(280\) 2.17877e8 + 4.46149e8i 0.593141 + 1.21458i
\(281\) 6.41592e8i 1.72499i −0.506065 0.862495i \(-0.668900\pi\)
0.506065 0.862495i \(-0.331100\pi\)
\(282\) −2.20191e8 3.81382e8i −0.584693 1.01272i
\(283\) −2.06444e8 + 3.57571e8i −0.541438 + 0.937798i 0.457384 + 0.889269i \(0.348787\pi\)
−0.998822 + 0.0485288i \(0.984547\pi\)
\(284\) −1.26616e9 7.31019e8i −3.28001 1.89372i
\(285\) 8.37146e7 + 1.44998e8i 0.214212 + 0.371026i
\(286\) −3.33005e7 1.32991e8i −0.0841724 0.336155i
\(287\) −6.58252e6 + 9.48138e7i −0.0164364 + 0.236747i
\(288\) 2.96998e8i 0.732621i
\(289\) −1.84840e7 3.20152e7i −0.0450456 0.0780213i
\(290\) −1.74504e7 + 3.02250e7i −0.0420157 + 0.0727734i
\(291\) 1.93065e8 + 1.11466e8i 0.459281 + 0.265166i
\(292\) 5.17895e8 2.99007e8i 1.21731 0.702815i
\(293\) 4.92525e7i 0.114391i −0.998363 0.0571955i \(-0.981784\pi\)
0.998363 0.0571955i \(-0.0182158\pi\)
\(294\) 4.21716e7 3.02254e8i 0.0967842 0.693674i
\(295\) −6.53759e7 −0.148266
\(296\) −8.18955e8 1.41847e9i −1.83544 3.17907i
\(297\) −5.44953e7 3.14629e7i −0.120701 0.0696869i
\(298\) −4.40015e8 + 7.62128e8i −0.963186 + 1.66829i
\(299\) 3.36438e8 3.25550e8i 0.727874 0.704318i
\(300\) −2.49745e8 −0.534039
\(301\) −2.89171e8 2.00759e7i −0.611183 0.0424318i
\(302\) −4.33852e8 −0.906394
\(303\) 3.94008e7 + 6.82443e7i 0.0813685 + 0.140934i
\(304\) 1.27767e9 + 7.37663e8i 2.60832 + 1.50591i
\(305\) 1.32529e8 + 7.65156e7i 0.267461 + 0.154419i
\(306\) 6.88954e8 3.97768e8i 1.37456 0.793605i
\(307\) 3.57762e7i 0.0705684i 0.999377 + 0.0352842i \(0.0112336\pi\)
−0.999377 + 0.0352842i \(0.988766\pi\)
\(308\) −1.97383e8 + 9.63922e7i −0.384931 + 0.187981i
\(309\) −4.20203e6 −0.00810223
\(310\) 8.41174e8 4.85652e8i 1.60369 0.925890i
\(311\) 2.66066e8 4.60839e8i 0.501566 0.868737i −0.498433 0.866928i \(-0.666091\pi\)
0.999998 0.00180869i \(-0.000575724\pi\)
\(312\) 1.25634e8 4.39808e8i 0.234188 0.819826i
\(313\) 2.54509e8 + 4.40822e8i 0.469135 + 0.812565i 0.999377 0.0352807i \(-0.0112325\pi\)
−0.530243 + 0.847846i \(0.677899\pi\)
\(314\) 6.64696e8i 1.21163i
\(315\) 2.41364e8 + 1.62627e8i 0.435097 + 0.293161i
\(316\) 1.64187e9 2.92707
\(317\) −9.90107e7 + 5.71638e7i −0.174572 + 0.100789i −0.584740 0.811221i \(-0.698803\pi\)
0.410168 + 0.912010i \(0.365470\pi\)
\(318\) 5.76143e8 + 3.32636e8i 1.00470 + 0.580062i
\(319\) −7.34136e6 4.23854e6i −0.0126622 0.00731053i
\(320\) −4.67460e7 + 2.69888e7i −0.0797479 + 0.0460425i
\(321\) 1.68796e7 0.0284835
\(322\) −9.02629e8 6.08176e8i −1.50665 1.01516i
\(323\) 1.12075e9i 1.85055i
\(324\) 3.84060e8 + 6.65212e8i 0.627324 + 1.08656i
\(325\) −3.67033e8 1.04845e8i −0.593080 0.169417i
\(326\) 3.91747e8 6.78526e8i 0.626245 1.08469i
\(327\) −7.48091e6 + 4.31911e6i −0.0118314 + 0.00683088i
\(328\) 3.31168e8 0.518192
\(329\) −9.69072e8 + 4.73246e8i −1.50027 + 0.732658i
\(330\) 5.46825e7i 0.0837625i
\(331\) 7.03062e8 4.05913e8i 1.06560 0.615227i 0.138627 0.990345i \(-0.455731\pi\)
0.926977 + 0.375118i \(0.122398\pi\)
\(332\) 2.54296e7 + 1.46818e7i 0.0381378 + 0.0220189i
\(333\) −8.31473e8 4.80051e8i −1.23394 0.712414i
\(334\) −6.43670e8 1.11487e9i −0.945258 1.63723i
\(335\) 4.48598e8 0.651929
\(336\) −4.60254e8 3.19535e7i −0.661927 0.0459548i
\(337\) 4.85364e7 0.0690816 0.0345408 0.999403i \(-0.489003\pi\)
0.0345408 + 0.999403i \(0.489003\pi\)
\(338\) 6.72611e8 1.08124e9i 0.947449 1.52305i
\(339\) 1.39372e8 2.41400e8i 0.194302 0.336541i
\(340\) −8.99460e8 5.19304e8i −1.24110 0.716548i
\(341\) 1.17960e8 + 2.04313e8i 0.161100 + 0.279034i
\(342\) 1.99326e9 2.69447
\(343\) −7.31259e8 1.54291e8i −0.978458 0.206448i
\(344\) 1.01002e9i 1.33776i
\(345\) −1.61714e8 + 9.33655e7i −0.212022 + 0.122411i
\(346\) 4.81114e8 + 2.77771e8i 0.624427 + 0.360513i
\(347\) 8.46507e7 1.46619e8i 0.108762 0.188381i −0.806507 0.591225i \(-0.798645\pi\)
0.915269 + 0.402843i \(0.131978\pi\)
\(348\) −2.57576e7 4.46136e7i −0.0327626 0.0567466i
\(349\) 3.36989e8i 0.424353i −0.977231 0.212176i \(-0.931945\pi\)
0.977231 0.212176i \(-0.0680552\pi\)
\(350\) −6.14624e7 + 8.85298e8i −0.0766252 + 1.10370i
\(351\) −1.41966e8 5.66963e8i −0.175231 0.699809i
\(352\) 6.83267e7 + 1.18345e8i 0.0835009 + 0.144628i
\(353\) 7.30842e8 + 4.21952e8i 0.884325 + 0.510565i 0.872082 0.489360i \(-0.162770\pi\)
0.0122428 + 0.999925i \(0.496103\pi\)
\(354\) 7.00090e7 1.21259e8i 0.0838769 0.145279i
\(355\) 4.45648e8 + 7.71885e8i 0.528680 + 0.915701i
\(356\) 1.00629e9i 1.18208i
\(357\) 1.53798e8 + 3.14933e8i 0.178900 + 0.366336i
\(358\) 1.85549e9i 2.13731i
\(359\) −6.92388e8 + 3.99750e8i −0.789803 + 0.455993i −0.839893 0.542752i \(-0.817382\pi\)
0.0500903 + 0.998745i \(0.484049\pi\)
\(360\) 5.07055e8 8.78246e8i 0.572792 0.992104i
\(361\) 9.57119e8 1.65778e9i 1.07076 1.85460i
\(362\) 8.78462e8 5.07180e8i 0.973292 0.561930i
\(363\) 3.42568e8 0.375901
\(364\) −1.91827e9 6.94926e8i −2.08476 0.755238i
\(365\) −3.64564e8 −0.392418
\(366\) −2.83842e8 + 1.63876e8i −0.302616 + 0.174716i
\(367\) 3.36493e8 5.82823e8i 0.355340 0.615468i −0.631836 0.775102i \(-0.717698\pi\)
0.987176 + 0.159635i \(0.0510316\pi\)
\(368\) −8.22703e8 + 1.42496e9i −0.860549 + 1.49052i
\(369\) 1.68115e8 9.70613e7i 0.174186 0.100567i
\(370\) 1.81875e9i 1.86667i
\(371\) 9.10356e8 1.35111e9i 0.925556 1.37367i
\(372\) 1.43369e9i 1.44396i
\(373\) 1.58753e8 + 2.74969e8i 0.158395 + 0.274348i 0.934290 0.356514i \(-0.116035\pi\)
−0.775895 + 0.630862i \(0.782701\pi\)
\(374\) 1.83019e8 3.16999e8i 0.180903 0.313333i
\(375\) 3.45622e8 + 1.99545e8i 0.338448 + 0.195403i
\(376\) 1.87890e9 + 3.25436e9i 1.82283 + 3.15724i
\(377\) −1.91250e7 7.63787e7i −0.0183826 0.0734137i
\(378\) −1.22098e9 + 5.96267e8i −1.16275 + 0.567831i
\(379\) 1.49581e9i 1.41137i 0.708528 + 0.705683i \(0.249360\pi\)
−0.708528 + 0.705683i \(0.750640\pi\)
\(380\) −1.30114e9 2.25365e9i −1.21642 2.10690i
\(381\) −8.04639e7 + 1.39368e8i −0.0745356 + 0.129099i
\(382\) −1.15044e9 6.64208e8i −1.05595 0.609652i
\(383\) −1.09130e9 + 6.30061e8i −0.992539 + 0.573043i −0.906032 0.423208i \(-0.860904\pi\)
−0.0865069 + 0.996251i \(0.527570\pi\)
\(384\) 4.90128e8i 0.441723i
\(385\) 1.33590e8 + 9.27462e6i 0.119306 + 0.00828292i
\(386\) −3.75898e9 −3.32670
\(387\) 2.96025e8 + 5.12730e8i 0.259621 + 0.449677i
\(388\) −3.00074e9 1.73248e9i −2.60806 1.50576i
\(389\) −6.37992e8 + 1.10503e9i −0.549530 + 0.951814i 0.448776 + 0.893644i \(0.351860\pi\)
−0.998307 + 0.0581702i \(0.981473\pi\)
\(390\) −3.64998e8 + 3.53186e8i −0.311577 + 0.301493i
\(391\) 1.24996e9 1.05749
\(392\) −3.59853e8 + 2.57915e9i −0.301734 + 2.16259i
\(393\) 1.24041e8 0.103084
\(394\) −6.70595e8 1.16150e9i −0.552361 0.956718i
\(395\) −8.66825e8 5.00462e8i −0.707688 0.408584i
\(396\) 3.88550e8 + 2.24330e8i 0.314423 + 0.181532i
\(397\) −7.34336e8 + 4.23969e8i −0.589018 + 0.340069i −0.764709 0.644376i \(-0.777117\pi\)
0.175691 + 0.984445i \(0.443784\pi\)
\(398\) 2.75988e9i 2.19431i
\(399\) −6.08198e7 + 8.76040e8i −0.0479335 + 0.690429i
\(400\) 1.34158e9 1.04811
\(401\) −9.78504e8 + 5.64940e8i −0.757805 + 0.437519i −0.828507 0.559979i \(-0.810809\pi\)
0.0707021 + 0.997497i \(0.477476\pi\)
\(402\) −4.80389e8 + 8.32058e8i −0.368809 + 0.638796i
\(403\) −6.01877e8 + 2.10700e9i −0.458079 + 1.60360i
\(404\) −6.12393e8 1.06070e9i −0.462057 0.800306i
\(405\) 4.68266e8i 0.350268i
\(406\) −1.64485e8 + 8.03263e7i −0.121979 + 0.0595685i
\(407\) −4.41758e8 −0.324791
\(408\) 1.05761e9 6.10614e8i 0.770934 0.445099i
\(409\) −2.15919e9 1.24661e9i −1.56048 0.900946i −0.997208 0.0746782i \(-0.976207\pi\)
−0.563277 0.826268i \(-0.690460\pi\)
\(410\) −3.18466e8 1.83866e8i −0.228202 0.131752i
\(411\) 6.54563e8 3.77912e8i 0.465056 0.268500i
\(412\) 6.53107e7 0.0460091
\(413\) −2.84364e8 1.91600e8i −0.198632 0.133835i
\(414\) 2.22305e9i 1.53974i
\(415\) −8.95038e6 1.55025e7i −0.00614714 0.0106472i
\(416\) −3.48628e8 + 1.22045e9i −0.237430 + 0.831174i
\(417\) 1.19143e8 2.06361e8i 0.0804622 0.139365i
\(418\) 7.94258e8 4.58565e8i 0.531918 0.307103i
\(419\) 8.08083e8 0.536669 0.268335 0.963326i \(-0.413527\pi\)
0.268335 + 0.963326i \(0.413527\pi\)
\(420\) 6.74885e8 + 4.54726e8i 0.444485 + 0.299487i
\(421\) 1.47819e8i 0.0965476i 0.998834 + 0.0482738i \(0.0153720\pi\)
−0.998834 + 0.0482738i \(0.984628\pi\)
\(422\) 1.80618e9 1.04280e9i 1.16995 0.675471i
\(423\) 1.90762e9 + 1.10137e9i 1.22547 + 0.707523i
\(424\) −4.91626e9 2.83840e9i −3.13223 1.80840i
\(425\) −5.09576e8 8.82612e8i −0.321994 0.557710i
\(426\) −1.90892e9 −1.19634
\(427\) 3.52211e8 + 7.21226e8i 0.218930 + 0.448305i
\(428\) −2.62353e8 −0.161746
\(429\) −8.57855e7 8.86547e7i −0.0524582 0.0542127i
\(430\) 5.60770e8 9.71282e8i 0.340130 0.589122i
\(431\) 1.06956e7 + 6.17509e6i 0.00643478 + 0.00371512i 0.503214 0.864162i \(-0.332151\pi\)
−0.496779 + 0.867877i \(0.665484\pi\)
\(432\) 1.02709e9 + 1.77897e9i 0.612937 + 1.06164i
\(433\) −5.75010e8 −0.340383 −0.170191 0.985411i \(-0.554439\pi\)
−0.170191 + 0.985411i \(0.554439\pi\)
\(434\) 5.08216e9 + 3.52833e8i 2.98424 + 0.207183i
\(435\) 3.14051e7i 0.0182931i
\(436\) 1.16273e8 6.71303e7i 0.0671856 0.0387896i
\(437\) 2.71225e9 + 1.56592e9i 1.55469 + 0.897603i
\(438\) 3.90400e8 6.76193e8i 0.221999 0.384513i
\(439\) 9.08796e8 + 1.57408e9i 0.512673 + 0.887976i 0.999892 + 0.0146958i \(0.00467799\pi\)
−0.487219 + 0.873280i \(0.661989\pi\)
\(440\) 4.66609e8i 0.261137i
\(441\) 5.73239e8 + 1.41475e9i 0.318273 + 0.785498i
\(442\) 3.29802e9 8.25815e8i 1.81667 0.454889i
\(443\) 9.37454e8 + 1.62372e9i 0.512315 + 0.887355i 0.999898 + 0.0142786i \(0.00454518\pi\)
−0.487583 + 0.873076i \(0.662121\pi\)
\(444\) −2.32491e9 1.34228e9i −1.26056 0.727787i
\(445\) −3.06729e8 + 5.31270e8i −0.165004 + 0.285796i
\(446\) −3.66107e8 6.34115e8i −0.195405 0.338451i
\(447\) 7.91884e8i 0.419358i
\(448\) −2.82427e8 1.96077e7i −0.148400 0.0103028i
\(449\) 1.56806e9i 0.817523i 0.912641 + 0.408761i \(0.134039\pi\)
−0.912641 + 0.408761i \(0.865961\pi\)
\(450\) 1.56973e9 9.06282e8i 0.812046 0.468835i
\(451\) 4.46594e7 7.73524e7i 0.0229243 0.0397060i
\(452\) −2.16621e9 + 3.75199e9i −1.10336 + 1.91107i
\(453\) −3.38093e8 + 1.95198e8i −0.170881 + 0.0986579i
\(454\) 1.95541e9 0.980715
\(455\) 8.00933e8 + 9.51602e8i 0.398618 + 0.473604i
\(456\) 3.05986e9 1.51121
\(457\) 1.59271e9 9.19550e8i 0.780601 0.450680i −0.0560419 0.998428i \(-0.517848\pi\)
0.836643 + 0.547748i \(0.184515\pi\)
\(458\) 6.55862e8 1.13599e9i 0.318994 0.552514i
\(459\) 7.80245e8 1.35142e9i 0.376605 0.652299i
\(460\) 2.51346e9 1.45115e9i 1.20398 0.695118i
\(461\) 1.86137e9i 0.884868i 0.896801 + 0.442434i \(0.145885\pi\)
−0.896801 + 0.442434i \(0.854115\pi\)
\(462\) −1.60260e8 + 2.37851e8i −0.0756099 + 0.112217i
\(463\) 1.90461e9i 0.891810i 0.895080 + 0.445905i \(0.147118\pi\)
−0.895080 + 0.445905i \(0.852882\pi\)
\(464\) 1.38365e8 + 2.39655e8i 0.0643003 + 0.111371i
\(465\) 4.37008e8 7.56921e8i 0.201560 0.349112i
\(466\) −3.74360e9 2.16137e9i −1.71372 0.989415i
\(467\) −1.28402e9 2.22399e9i −0.583395 1.01047i −0.995073 0.0991410i \(-0.968391\pi\)
0.411678 0.911329i \(-0.364943\pi\)
\(468\) 1.01221e9 + 4.04243e9i 0.456470 + 1.82298i
\(469\) 1.95126e9 + 1.31472e9i 0.873393 + 0.588477i
\(470\) 4.17271e9i 1.85385i
\(471\) 2.99059e8 + 5.17986e8i 0.131882 + 0.228426i
\(472\) −5.97390e8 + 1.03471e9i −0.261494 + 0.452920i
\(473\) 2.35915e8 + 1.36206e8i 0.102504 + 0.0591809i
\(474\) 1.85651e9 1.07186e9i 0.800706 0.462288i
\(475\) 2.55355e9i 1.09324i
\(476\) −2.39042e9 4.89489e9i −1.01590 2.08026i
\(477\) −3.32760e9 −1.40384
\(478\) −1.14237e9 1.97864e9i −0.478419 0.828645i
\(479\) −2.31667e8 1.33753e8i −0.0963140 0.0556069i 0.451069 0.892489i \(-0.351043\pi\)
−0.547383 + 0.836882i \(0.684376\pi\)
\(480\) 2.53130e8 4.38434e8i 0.104472 0.180951i
\(481\) −2.85325e9 2.94868e9i −1.16905 1.20815i
\(482\) −6.04532e9 −2.45898
\(483\) −9.77034e8 6.78313e7i −0.394543 0.0273915i
\(484\) −5.32441e9 −2.13458
\(485\) 1.05616e9 + 1.82933e9i 0.420374 + 0.728108i
\(486\) 3.70444e9 + 2.13876e9i 1.46385 + 0.845152i
\(487\) 1.25567e8 + 7.24959e7i 0.0492632 + 0.0284421i 0.524429 0.851454i \(-0.324279\pi\)
−0.475166 + 0.879896i \(0.657612\pi\)
\(488\) 2.42204e9 1.39836e9i 0.943433 0.544692i
\(489\) 7.05019e8i 0.272659i
\(490\) 1.77800e9 2.28043e9i 0.682726 0.875648i
\(491\) −6.31303e8 −0.240687 −0.120343 0.992732i \(-0.538400\pi\)
−0.120343 + 0.992732i \(0.538400\pi\)
\(492\) 4.70072e8 2.71396e8i 0.177945 0.102737i
\(493\) 1.05111e8 1.82058e8i 0.0395079 0.0684297i
\(494\) 8.19085e9 + 2.33977e9i 3.05693 + 0.873230i
\(495\) −1.36757e8 2.36870e8i −0.0506794 0.0877793i
\(496\) 7.70152e9i 2.83394i
\(497\) −3.23769e8 + 4.66354e9i −0.118301 + 1.70399i
\(498\) 3.83387e7 0.0139102
\(499\) −3.04852e9 + 1.76007e9i −1.09834 + 0.634128i −0.935785 0.352571i \(-0.885308\pi\)
−0.162557 + 0.986699i \(0.551974\pi\)
\(500\) −5.37188e9 3.10146e9i −1.92190 1.10961i
\(501\) −1.00320e9 5.79199e8i −0.356415 0.205776i
\(502\) −6.69273e9 + 3.86405e9i −2.36124 + 1.36326i
\(503\) 1.59663e9 0.559392 0.279696 0.960089i \(-0.409766\pi\)
0.279696 + 0.960089i \(0.409766\pi\)
\(504\) 4.77944e9 2.33404e9i 1.66292 0.812085i
\(505\) 7.46661e8i 0.257990i
\(506\) 5.11430e8 + 8.85823e8i 0.175493 + 0.303963i
\(507\) 3.76833e7 1.14521e9i 0.0128416 0.390264i
\(508\) 1.25062e9 2.16614e9i 0.423256 0.733100i
\(509\) 1.62976e9 9.40941e8i 0.547786 0.316264i −0.200443 0.979705i \(-0.564238\pi\)
0.748228 + 0.663441i \(0.230905\pi\)
\(510\) −1.35606e9 −0.452673
\(511\) −1.58574e9 1.06844e9i −0.525725 0.354225i
\(512\) 6.80754e9i 2.24153i
\(513\) 3.38607e9 1.95495e9i 1.10735 0.639329i
\(514\) 6.22280e9 + 3.59274e9i 2.02123 + 1.16696i
\(515\) −3.44809e7 1.99075e7i −0.0111238 0.00642232i
\(516\) 8.27724e8 + 1.43366e9i 0.265223 + 0.459380i
\(517\) 1.01351e9 0.322561
\(518\) −5.33029e9 + 7.91099e9i −1.68499 + 2.50079i
\(519\) 4.99898e8 0.156963
\(520\) 3.11455e9 3.01375e9i 0.971368 0.939930i
\(521\) −2.07817e9 + 3.59949e9i −0.643796 + 1.11509i 0.340782 + 0.940142i \(0.389308\pi\)
−0.984578 + 0.174946i \(0.944025\pi\)
\(522\) 3.23790e8 + 1.86940e8i 0.0996360 + 0.0575249i
\(523\) −1.93719e9 3.35531e9i −0.592129 1.02560i −0.993945 0.109877i \(-0.964954\pi\)
0.401816 0.915720i \(-0.368379\pi\)
\(524\) −1.92792e9 −0.585370
\(525\) 3.50416e8 + 7.17550e8i 0.105688 + 0.216419i
\(526\) 7.86935e9i 2.35770i
\(527\) −5.06674e9 + 2.92529e9i −1.50797 + 0.870625i
\(528\) 3.75491e8 + 2.16790e8i 0.111015 + 0.0640945i
\(529\) −4.40319e7 + 7.62655e7i −0.0129322 + 0.0223992i
\(530\) 3.15179e9 + 5.45906e9i 0.919585 + 1.59277i
\(531\) 7.00350e8i 0.202995i
\(532\) 9.45299e8 1.36160e10i 0.272194 3.92065i
\(533\) 8.04765e8 2.01511e8i 0.230210 0.0576440i
\(534\) −6.56933e8 1.13784e9i −0.186692 0.323361i
\(535\) 1.38510e8 + 7.99685e7i 0.0391058 + 0.0225778i
\(536\) 4.09918e9 7.09999e9i 1.14980 1.99150i
\(537\) 8.34820e8 + 1.44595e9i 0.232639 + 0.402943i
\(538\) 8.58662e9i 2.37730i
\(539\) 5.53894e8 + 4.31861e8i 0.152358 + 0.118791i
\(540\) 3.62332e9i 0.990213i
\(541\) −5.35097e9 + 3.08938e9i −1.45292 + 0.838844i −0.998646 0.0520183i \(-0.983435\pi\)
−0.454274 + 0.890862i \(0.650101\pi\)
\(542\) −1.22170e9 + 2.11604e9i −0.329584 + 0.570857i
\(543\) 4.56380e8 7.90474e8i 0.122328 0.211879i
\(544\) −2.93483e9 + 1.69443e9i −0.781605 + 0.451260i
\(545\) −8.18487e7 −0.0216583
\(546\) −2.62272e9 + 4.66529e8i −0.689569 + 0.122660i
\(547\) 4.91377e8 0.128369 0.0641844 0.997938i \(-0.479555\pi\)
0.0641844 + 0.997938i \(0.479555\pi\)
\(548\) −1.01736e10 + 5.87375e9i −2.64085 + 1.52470i
\(549\) 8.19685e8 1.41974e9i 0.211419 0.366188i
\(550\) 4.16995e8 7.22256e8i 0.106871 0.185107i
\(551\) 4.56156e8 2.63362e8i 0.116167 0.0670690i
\(552\) 3.41261e9i 0.863575i
\(553\) −2.30369e9 4.71729e9i −0.579276 1.18619i
\(554\) 1.58632e9i 0.396376i
\(555\) 8.18291e8 + 1.41732e9i 0.203181 + 0.351919i
\(556\) −1.85179e9 + 3.20740e9i −0.456910 + 0.791392i
\(557\) 4.24340e9 + 2.44993e9i 1.04045 + 0.600704i 0.919961 0.392011i \(-0.128220\pi\)
0.120489 + 0.992715i \(0.461554\pi\)
\(558\) −5.20263e9 9.01121e9i −1.26766 2.19565i
\(559\) 6.14585e8 + 2.45444e9i 0.148813 + 0.594306i
\(560\) −3.62535e9 2.44270e9i −0.872352 0.587776i
\(561\) 3.29375e8i 0.0787628i
\(562\) 6.51002e9 + 1.12757e10i 1.54705 + 2.67958i
\(563\) 3.06283e9 5.30497e9i 0.723341 1.25286i −0.236313 0.971677i \(-0.575939\pi\)
0.959653 0.281186i \(-0.0907277\pi\)
\(564\) 5.33396e9 + 3.07956e9i 1.25191 + 0.722790i
\(565\) 2.28731e9 1.32058e9i 0.533526 0.308031i
\(566\) 8.37886e9i 1.94235i
\(567\) 1.37237e9 2.03681e9i 0.316177 0.469256i
\(568\) 1.62889e10 3.72969
\(569\) 2.93236e8 + 5.07899e8i 0.0667304 + 0.115581i 0.897460 0.441095i \(-0.145410\pi\)
−0.830730 + 0.556676i \(0.812077\pi\)
\(570\) −2.94249e9 1.69885e9i −0.665508 0.384231i
\(571\) 2.88991e9 5.00547e9i 0.649618 1.12517i −0.333596 0.942716i \(-0.608262\pi\)
0.983214 0.182456i \(-0.0584046\pi\)
\(572\) 1.33333e9 + 1.37793e9i 0.297888 + 0.307851i
\(573\) −1.19536e9 −0.265434
\(574\) −8.46360e8 1.73310e9i −0.186794 0.382501i
\(575\) 2.84793e9 0.624729
\(576\) 2.89122e8 + 5.00774e8i 0.0630379 + 0.109185i
\(577\) 4.10491e9 + 2.36997e9i 0.889587 + 0.513603i 0.873807 0.486272i \(-0.161644\pi\)
0.0157798 + 0.999875i \(0.494977\pi\)
\(578\) 6.49695e8 + 3.75101e8i 0.139946 + 0.0807981i
\(579\) −2.92931e9 + 1.69124e9i −0.627176 + 0.362100i
\(580\) 4.88117e8i 0.103879i
\(581\) 6.50257e6 9.36623e7i 0.00137553 0.0198129i
\(582\) −4.52405e9 −0.951254
\(583\) −1.32596e9 + 7.65541e8i −0.277134 + 0.160003i
\(584\) −3.33131e9 + 5.76999e9i −0.692101 + 1.19875i
\(585\) 6.97785e8 2.44274e9i 0.144104 0.504466i
\(586\) 4.99749e8 + 8.65591e8i 0.102591 + 0.177693i
\(587\) 4.32226e9i 0.882017i −0.897503 0.441009i \(-0.854621\pi\)
0.897503 0.441009i \(-0.145379\pi\)
\(588\) 1.60285e9 + 3.95583e9i 0.325141 + 0.802448i
\(589\) −1.46589e10 −2.95596
\(590\) 1.14895e9 6.63348e8i 0.230314 0.132972i
\(591\) −1.04517e9 6.03427e8i −0.208271 0.120245i
\(592\) 1.24889e10 + 7.21049e9i 2.47400 + 1.42836i
\(593\) 5.47623e9 3.16170e9i 1.07843 0.622629i 0.147955 0.988994i \(-0.452731\pi\)
0.930471 + 0.366365i \(0.119398\pi\)
\(594\) 1.27697e9 0.249994
\(595\) −2.30000e8 + 3.31289e9i −0.0447630 + 0.644760i
\(596\) 1.23080e10i 2.38136i
\(597\) −1.24172e9 2.15072e9i −0.238844 0.413689i
\(598\) −2.60951e9 + 9.13513e9i −0.499004 + 1.74687i
\(599\) 2.71201e9 4.69734e9i 0.515581 0.893013i −0.484255 0.874927i \(-0.660909\pi\)
0.999836 0.0180862i \(-0.00575732\pi\)
\(600\) 2.40969e9 1.39124e9i 0.455441 0.262949i
\(601\) −9.87533e9 −1.85563 −0.927814 0.373044i \(-0.878314\pi\)
−0.927814 + 0.373044i \(0.878314\pi\)
\(602\) 5.28575e9 2.58129e9i 0.987458 0.482225i
\(603\) 4.80568e9i 0.892573i
\(604\) 5.25486e9 3.03389e9i 0.970357 0.560236i
\(605\) 2.81103e9 + 1.62295e9i 0.516085 + 0.297962i
\(606\) −1.38490e9 7.99575e8i −0.252793 0.145950i
\(607\) −9.79466e7 1.69648e8i −0.0177758 0.0307886i 0.857001 0.515315i \(-0.172325\pi\)
−0.874776 + 0.484527i \(0.838992\pi\)
\(608\) −8.49096e9 −1.53213
\(609\) −9.20401e7 + 1.36602e8i −0.0165126 + 0.0245074i
\(610\) −3.10551e9 −0.553961
\(611\) 6.54612e9 + 6.76506e9i 1.16102 + 1.19985i
\(612\) −5.56312e9 + 9.63561e9i −0.981044 + 1.69922i
\(613\) −2.88935e9 1.66817e9i −0.506627 0.292501i 0.224819 0.974401i \(-0.427821\pi\)
−0.731446 + 0.681899i \(0.761154\pi\)
\(614\) −3.63009e8 6.28751e8i −0.0632891 0.109620i
\(615\) −3.30900e8 −0.0573632
\(616\) 1.36751e9 2.02960e9i 0.235721 0.349847i
\(617\) 5.29674e9i 0.907842i −0.891042 0.453921i \(-0.850025\pi\)
0.891042 0.453921i \(-0.149975\pi\)
\(618\) 7.38488e7 4.26367e7i 0.0125859 0.00726647i
\(619\) 3.42229e9 + 1.97586e9i 0.579962 + 0.334841i 0.761118 0.648613i \(-0.224651\pi\)
−0.181157 + 0.983454i \(0.557984\pi\)
\(620\) −6.79226e9 + 1.17645e10i −1.14457 + 1.98246i
\(621\) 2.18032e9 + 3.77643e9i 0.365342 + 0.632791i
\(622\) 1.07987e10i 1.79931i
\(623\) −2.89119e9 + 1.41191e9i −0.479036 + 0.233937i
\(624\) 9.78195e8 + 3.90657e9i 0.161168 + 0.643649i
\(625\) 8.39428e6 + 1.45393e7i 0.00137532 + 0.00238212i
\(626\) −8.94576e9 5.16483e9i −1.45749 0.841485i
\(627\) 4.12635e8 7.14704e8i 0.0668543 0.115795i
\(628\) −4.64817e9 8.05087e9i −0.748899 1.29713i
\(629\) 1.09551e10i 1.75525i
\(630\) −5.89199e9 4.09056e8i −0.938793 0.0651764i
\(631\) 8.79406e9i 1.39343i −0.717346 0.696717i \(-0.754643\pi\)
0.717346 0.696717i \(-0.245357\pi\)
\(632\) −1.58417e10 + 9.14621e9i −2.49627 + 1.44122i
\(633\) 9.38349e8 1.62527e9i 0.147045 0.254690i
\(634\) 1.16005e9 2.00926e9i 0.180785 0.313129i
\(635\) −1.32053e9 + 7.62411e8i −0.204664 + 0.118163i
\(636\) −9.30440e9 −1.43413
\(637\) 6.94903e8 + 6.48649e9i 0.106521 + 0.994310i
\(638\) 1.72028e8 0.0262257
\(639\) 8.26895e9 4.77408e9i 1.25371 0.723830i
\(640\) 2.32203e9 4.02187e9i 0.350137 0.606455i
\(641\) 9.40626e8 1.62921e9i 0.141063 0.244329i −0.786834 0.617165i \(-0.788281\pi\)
0.927897 + 0.372836i \(0.121615\pi\)
\(642\) −2.96651e8 + 1.71271e8i −0.0442459 + 0.0255454i
\(643\) 5.88015e9i 0.872268i 0.899882 + 0.436134i \(0.143653\pi\)
−0.899882 + 0.436134i \(0.856347\pi\)
\(644\) 1.51857e10 + 1.05428e9i 2.24044 + 0.155544i
\(645\) 1.00920e9i 0.148088i
\(646\) 1.13719e10 + 1.96967e10i 1.65966 + 2.87462i
\(647\) 4.53383e9 7.85283e9i 0.658113 1.13989i −0.322990 0.946402i \(-0.604688\pi\)
0.981104 0.193483i \(-0.0619785\pi\)
\(648\) −7.41129e9 4.27891e9i −1.06999 0.617761i
\(649\) 1.61121e8 + 2.79070e8i 0.0231364 + 0.0400735i
\(650\) 7.51427e9 1.88156e9i 1.07322 0.268733i
\(651\) 4.11919e9 2.01160e9i 0.585164 0.285765i
\(652\) 1.09578e10i 1.54831i
\(653\) −3.21571e9 5.56977e9i −0.451940 0.782782i 0.546567 0.837415i \(-0.315934\pi\)
−0.998507 + 0.0546330i \(0.982601\pi\)
\(654\) 8.76491e7 1.51813e8i 0.0122525 0.0212220i
\(655\) 1.01785e9 + 5.87656e8i 0.141527 + 0.0817106i
\(656\) −2.52513e9 + 1.45788e9i −0.349237 + 0.201632i
\(657\) 3.90545e9i 0.537270i
\(658\) 1.22291e10 1.81499e10i 1.67342 2.48362i
\(659\) −4.65728e9 −0.633919 −0.316959 0.948439i \(-0.602662\pi\)
−0.316959 + 0.948439i \(0.602662\pi\)
\(660\) −3.82391e8 6.62320e8i −0.0517730 0.0896735i
\(661\) −9.45268e9 5.45751e9i −1.27306 0.735003i −0.297500 0.954722i \(-0.596153\pi\)
−0.975563 + 0.219718i \(0.929486\pi\)
\(662\) −8.23734e9 + 1.42675e10i −1.10353 + 1.91137i
\(663\) 2.19854e9 2.12738e9i 0.292979 0.283497i
\(664\) −3.27146e8 −0.0433664
\(665\) −4.64940e9 + 6.90043e9i −0.613085 + 0.909915i
\(666\) 1.94837e10 2.55571
\(667\) 2.93723e8 + 5.08743e8i 0.0383264 + 0.0663832i
\(668\) 1.55924e10 + 9.00227e9i 2.02393 + 1.16852i
\(669\) −5.70601e8 3.29437e8i −0.0736786 0.0425384i
\(670\) −7.88390e9 + 4.55177e9i −1.01270 + 0.584681i
\(671\) 7.54300e8i 0.0963863i
\(672\) 2.38597e9 1.16519e9i 0.303301 0.148117i
\(673\) −1.30461e9 −0.164979 −0.0824894 0.996592i \(-0.526287\pi\)
−0.0824894 + 0.996592i \(0.526287\pi\)
\(674\) −8.53005e8 + 4.92482e8i −0.107310 + 0.0619557i
\(675\) 1.77773e9 3.07911e9i 0.222485 0.385356i
\(676\) −5.85697e8 + 1.77996e10i −0.0729222 + 2.21614i
\(677\) −2.86272e9 4.95838e9i −0.354584 0.614157i 0.632463 0.774591i \(-0.282044\pi\)
−0.987047 + 0.160434i \(0.948711\pi\)
\(678\) 5.65666e9i 0.697037i
\(679\) −7.67317e8 + 1.10523e10i −0.0940656 + 1.35491i
\(680\) 1.15714e10 1.41125
\(681\) 1.52382e9 8.79777e8i 0.184892 0.106748i
\(682\) −4.14620e9 2.39381e9i −0.500501 0.288965i
\(683\) 5.74648e9 + 3.31773e9i 0.690128 + 0.398445i 0.803660 0.595089i \(-0.202883\pi\)
−0.113532 + 0.993534i \(0.536217\pi\)
\(684\) −2.41426e10 + 1.39387e10i −2.88461 + 1.66543i
\(685\) 7.16158e9 0.851318
\(686\) 1.44171e10 4.70825e9i 1.70507 0.556834i
\(687\) 1.18034e9i 0.138886i
\(688\) −4.44637e9 7.70134e9i −0.520530 0.901585i
\(689\) −1.36740e10 3.90607e9i −1.59268 0.454960i
\(690\) 1.89470e9 3.28171e9i 0.219568 0.380302i
\(691\) −6.60554e8 + 3.81371e8i −0.0761614 + 0.0439718i −0.537597 0.843202i \(-0.680668\pi\)
0.461436 + 0.887174i \(0.347335\pi\)
\(692\) −7.76974e9 −0.891323
\(693\) 9.93559e7 1.43111e9i 0.0113404 0.163345i
\(694\) 3.43569e9i 0.390172i
\(695\) 1.95531e9 1.12890e9i 0.220938 0.127558i
\(696\) 4.97050e8 + 2.86972e8i 0.0558815 + 0.0322632i
\(697\) 1.91825e9 + 1.10750e9i 0.214581 + 0.123888i
\(698\) 3.41932e9 + 5.92244e9i 0.380580 + 0.659184i
\(699\) −3.88977e9 −0.430778
\(700\) −5.44638e9 1.11526e10i −0.600157 1.22895i
\(701\) −1.58319e10 −1.73588 −0.867941 0.496668i \(-0.834557\pi\)
−0.867941 + 0.496668i \(0.834557\pi\)
\(702\) 8.24778e9 + 8.52364e9i 0.899823 + 0.929919i
\(703\) 1.37243e10 2.37712e10i 1.48987 2.58052i
\(704\) 2.30414e8 + 1.33030e8i 0.0248888 + 0.0143696i
\(705\) −1.87738e9 3.25172e9i −0.201786 0.349503i
\(706\) −1.71256e10 −1.83160
\(707\) −2.18827e9 + 3.24774e9i −0.232880 + 0.345631i
\(708\) 1.95827e9i 0.207375i
\(709\) −8.42791e9 + 4.86585e9i −0.888092 + 0.512740i −0.873318 0.487151i \(-0.838036\pi\)
−0.0147741 + 0.999891i \(0.504703\pi\)
\(710\) −1.56641e10 9.04369e9i −1.64249 0.948291i
\(711\) −5.36128e9 + 9.28601e9i −0.559403 + 0.968914i
\(712\) 5.60564e9 + 9.70925e9i 0.582030 + 1.00811i
\(713\) 1.63489e10i 1.68918i
\(714\) −5.89845e9 3.97427e9i −0.606449 0.408615i
\(715\) −2.83925e8 1.13390e9i −0.0290491 0.116012i
\(716\) −1.29753e10 2.24739e10i −1.32106 2.28814i
\(717\) −1.78045e9 1.02795e9i −0.180391 0.104149i
\(718\) 8.11227e9 1.40509e10i 0.817912 1.41667i
\(719\) −3.18588e9 5.51811e9i −0.319653 0.553655i 0.660763 0.750595i \(-0.270233\pi\)
−0.980416 + 0.196940i \(0.936900\pi\)
\(720\) 8.92874e9i 0.891510i
\(721\) −9.16369e7 1.87646e8i −0.00910535 0.0186451i
\(722\) 3.88463e10i 3.84122i
\(723\) −4.71101e9 + 2.71990e9i −0.463586 + 0.267651i
\(724\) −7.09335e9 + 1.22860e10i −0.694651 + 1.20317i
\(725\) 2.39487e8 4.14804e8i 0.0233399 0.0404259i
\(726\) −6.02048e9 + 3.47593e9i −0.583919 + 0.337126i
\(727\) 1.47537e10 1.42407 0.712036 0.702143i \(-0.247773\pi\)
0.712036 + 0.702143i \(0.247773\pi\)
\(728\) 2.23798e10 3.98091e9i 2.14979 0.382404i
\(729\) −2.06975e9 −0.197866
\(730\) 6.40705e9 3.69911e9i 0.609577 0.351939i
\(731\) −3.37775e9 + 5.85044e9i −0.319828 + 0.553959i
\(732\) 2.29195e9 3.96977e9i 0.215981 0.374090i
\(733\) 1.91401e9 1.10506e9i 0.179507 0.103638i −0.407554 0.913181i \(-0.633618\pi\)
0.587061 + 0.809543i \(0.300285\pi\)
\(734\) 1.36571e10i 1.27474i
\(735\) 3.59561e8 2.57706e9i 0.0334016 0.239397i
\(736\) 9.46983e9i 0.875528i
\(737\) −1.10558e9 1.91493e9i −0.101732 0.176204i
\(738\) −1.96970e9 + 3.41162e9i −0.180386 + 0.312437i
\(739\) −5.67896e9 3.27875e9i −0.517622 0.298849i 0.218339 0.975873i \(-0.429936\pi\)
−0.735961 + 0.677024i \(0.763269\pi\)
\(740\) −1.27184e10 2.20289e10i −1.15378 1.99840i
\(741\) 7.43570e9 1.86188e9i 0.671364 0.168108i
\(742\) −2.28982e9 + 3.29823e10i −0.205773 + 2.96392i
\(743\) 5.91773e8i 0.0529291i −0.999650 0.0264645i \(-0.991575\pi\)
0.999650 0.0264645i \(-0.00842491\pi\)
\(744\) −7.98656e9 1.38331e10i −0.710976 1.23145i
\(745\) −3.75163e9 + 6.49801e9i −0.332409 + 0.575749i
\(746\) −5.58004e9 3.22164e9i −0.492097 0.284113i
\(747\) −1.66073e8 + 9.58824e7i −0.0145773 + 0.00841622i
\(748\) 5.11936e9i 0.447260i
\(749\) 3.68105e8 + 7.53773e8i 0.0320100 + 0.0655472i
\(750\) −8.09888e9 −0.700988
\(751\) 4.77215e9 + 8.26560e9i 0.411125 + 0.712089i 0.995013 0.0997448i \(-0.0318026\pi\)
−0.583888 + 0.811834i \(0.698469\pi\)
\(752\) −2.86530e10 1.65428e10i −2.45701 1.41856i
\(753\) −3.47702e9 + 6.02237e9i −0.296773 + 0.514026i
\(754\) 1.11110e9 + 1.14827e9i 0.0943962 + 0.0975534i
\(755\) −3.69908e9 −0.312809
\(756\) 1.06190e10 1.57603e10i 0.893836 1.32659i
\(757\) −2.26020e10 −1.89370 −0.946852 0.321669i \(-0.895756\pi\)
−0.946852 + 0.321669i \(0.895756\pi\)
\(758\) −1.51775e10 2.62882e10i −1.26578 2.19239i
\(759\) 7.97098e8 + 4.60205e8i 0.0661707 + 0.0382036i
\(760\) 2.51084e10 + 1.44964e10i 2.07478 + 1.19788i
\(761\) 1.51400e10 8.74108e9i 1.24532 0.718983i 0.275144 0.961403i \(-0.411275\pi\)
0.970171 + 0.242420i \(0.0779412\pi\)
\(762\) 3.26576e9i 0.267388i
\(763\) −3.56016e8 2.39877e8i −0.0290157 0.0195503i
\(764\) 1.85790e10 1.50729
\(765\) 5.87412e9 3.39142e9i 0.474381 0.273884i
\(766\) 1.27861e10 2.21461e10i 1.02786 1.78031i
\(767\) −8.22099e8 + 2.87793e9i −0.0657870 + 0.230301i
\(768\) 4.60858e9 + 7.98229e9i 0.367116 + 0.635863i
\(769\) 1.66266e10i 1.31844i 0.751948 + 0.659222i \(0.229114\pi\)
−0.751948 + 0.659222i \(0.770886\pi\)
\(770\) −2.44190e9 + 1.19250e9i −0.192757 + 0.0941329i
\(771\) 6.46576e9 0.508077
\(772\) 4.55291e10 2.62862e10i 3.56146 2.05621i
\(773\) 2.49832e9 + 1.44240e9i 0.194545 + 0.112320i 0.594108 0.804385i \(-0.297505\pi\)
−0.399564 + 0.916705i \(0.630838\pi\)
\(774\) −1.04050e10 6.00734e9i −0.806583 0.465681i
\(775\) −1.15442e10 + 6.66503e9i −0.890855 + 0.514335i
\(776\) 3.86039e10 2.96562
\(777\) −5.94500e8 + 8.56310e9i −0.0454651 + 0.654874i
\(778\) 2.58940e10i 1.97138i
\(779\) 2.77491e9 + 4.80629e9i 0.210314 + 0.364275i
\(780\) 1.95110e9 6.83023e9i 0.147214 0.515352i
\(781\) 2.19663e9 3.80467e9i 0.164998 0.285785i
\(782\) −2.19674e10 + 1.26829e10i −1.64269 + 0.948408i
\(783\) 7.33388e8 0.0545968
\(784\) −8.61019e9 2.12499e10i −0.638126 1.57489i
\(785\) 5.66729e9i 0.418149i
\(786\) −2.17996e9 + 1.25860e9i −0.160129 + 0.0924506i
\(787\) 1.33151e10 + 7.68748e9i 0.973717 + 0.562176i 0.900368 0.435130i \(-0.143298\pi\)
0.0733499 + 0.997306i \(0.476631\pi\)
\(788\) 1.62446e10 + 9.37884e9i 1.18268 + 0.682822i
\(789\) −3.54057e9 6.13245e9i −0.256628 0.444492i
\(790\) 2.03121e10 1.46575
\(791\) 1.38193e10 + 9.59418e8i 0.992818 + 0.0689271i
\(792\) −4.99862e9 −0.357530
\(793\) 5.03486e9 4.87191e9i 0.358534 0.346931i
\(794\) 8.60375e9 1.49021e10i 0.609981 1.05652i
\(795\) 4.91227e9 + 2.83610e9i 0.346735 + 0.200187i
\(796\) 1.92996e10 + 3.34279e10i 1.35629 + 2.34916i
\(797\) 6.44976e9 0.451273 0.225637 0.974212i \(-0.427554\pi\)
0.225637 + 0.974212i \(0.427554\pi\)
\(798\) −7.82001e9 1.60131e10i −0.544750 1.11549i
\(799\) 2.51340e10i 1.74320i
\(800\) −6.68678e9 + 3.86062e9i −0.461745 + 0.266589i
\(801\) 5.69132e9 + 3.28589e9i 0.391290 + 0.225912i
\(802\) 1.14645e10 1.98571e10i 0.784776 1.35927i
\(803\) 8.98481e8 + 1.55621e9i 0.0612357 + 0.106063i
\(804\) 1.34373e10i 0.911834i
\(805\) −7.69594e9 5.18540e9i −0.519967 0.350345i
\(806\) −1.08013e10 4.31366e10i −0.726613 2.90184i
\(807\) 3.86328e9 + 6.69140e9i 0.258761 + 0.448188i
\(808\) 1.18175e10 + 6.82282e9i 0.788106 + 0.455013i
\(809\) 6.06198e9 1.04997e10i 0.402527 0.697196i −0.591504 0.806302i \(-0.701465\pi\)
0.994030 + 0.109106i \(0.0347988\pi\)
\(810\) 4.75134e9 + 8.22957e9i 0.314137 + 0.544101i
\(811\) 2.00162e9i 0.131768i 0.997827 + 0.0658838i \(0.0209867\pi\)
−0.997827 + 0.0658838i \(0.979013\pi\)
\(812\) 1.43055e9 2.12315e9i 0.0937682 0.139167i
\(813\) 2.19866e9i 0.143497i
\(814\) 7.76370e9 4.48237e9i 0.504526 0.291288i
\(815\) 3.34009e9 5.78521e9i 0.216126 0.374341i
\(816\) −5.37615e9 + 9.31177e9i −0.346382 + 0.599952i
\(817\) −1.46586e10 + 8.46315e9i −0.940406 + 0.542944i
\(818\) 5.05958e10 3.23205
\(819\) 1.01942e10 8.58013e9i 0.648424 0.545758i
\(820\) 5.14306e9 0.325741
\(821\) −1.04237e10 + 6.01810e9i −0.657384 + 0.379541i −0.791279 0.611455i \(-0.790585\pi\)
0.133896 + 0.990995i \(0.457251\pi\)
\(822\) −7.66910e9 + 1.32833e10i −0.481607 + 0.834168i
\(823\) −3.25714e9 + 5.64154e9i −0.203675 + 0.352775i −0.949710 0.313132i \(-0.898622\pi\)
0.746035 + 0.665907i \(0.231955\pi\)
\(824\) −6.30156e8 + 3.63821e8i −0.0392376 + 0.0226539i
\(825\) 7.50456e8i 0.0465304i
\(826\) 6.94168e9 + 4.81931e8i 0.428583 + 0.0297547i
\(827\) 2.35663e10i 1.44884i −0.689357 0.724421i \(-0.742107\pi\)
0.689357 0.724421i \(-0.257893\pi\)
\(828\) −1.55456e10 2.69258e10i −0.951705 1.64840i
\(829\) 7.18719e9 1.24486e10i 0.438146 0.758890i −0.559401 0.828897i \(-0.688969\pi\)
0.997547 + 0.0700068i \(0.0223021\pi\)
\(830\) 3.14598e8 + 1.81633e8i 0.0190978 + 0.0110261i
\(831\) −7.13718e8 1.23620e9i −0.0431442 0.0747280i
\(832\) 6.00253e8 + 2.39720e9i 0.0361329 + 0.144302i
\(833\) −1.07097e10 + 1.37360e10i −0.641976 + 0.823382i
\(834\) 4.83561e9i 0.288649i
\(835\) −5.48802e9 9.50552e9i −0.326222 0.565032i
\(836\) −6.41343e9 + 1.11084e10i −0.379637 + 0.657550i
\(837\) −1.76760e10 1.02053e10i −1.04195 0.601568i
\(838\) −1.42017e10 + 8.19935e9i −0.833654 + 0.481311i
\(839\) 2.40444e9i 0.140555i 0.997527 + 0.0702776i \(0.0223885\pi\)
−0.997527 + 0.0702776i \(0.977611\pi\)
\(840\) −9.04481e9 6.27942e8i −0.526528 0.0365546i
\(841\) −1.71511e10 −0.994273
\(842\) −1.49987e9 2.59784e9i −0.0865885 0.149976i
\(843\) 1.01463e10 + 5.85797e9i 0.583326 + 0.336783i
\(844\) −1.45844e10 + 2.52610e10i −0.835008 + 1.44628i
\(845\) 5.73478e9 9.21881e9i 0.326978 0.525626i
\(846\) −4.47008e10 −2.53816
\(847\) 7.47064e9 + 1.52977e10i 0.422441 + 0.865037i
\(848\) 4.99814e10 2.81464
\(849\) −3.76981e9 6.52950e9i −0.211418 0.366187i
\(850\) 1.79112e10 + 1.03410e10i 1.00036 + 0.577559i
\(851\) 2.65117e10 + 1.53065e10i 1.47463 + 0.851379i
\(852\) 2.31211e10 1.33489e10i 1.28076 0.739449i
\(853\) 2.36258e9i 0.130336i 0.997874 + 0.0651682i \(0.0207584\pi\)
−0.997874 + 0.0651682i \(0.979242\pi\)
\(854\) −1.35080e10 9.10146e9i −0.742144 0.500044i
\(855\) 1.69948e10 0.929897
\(856\) 2.53134e9 1.46147e9i 0.137941 0.0796400i
\(857\) −1.77583e8 + 3.07582e8i −0.00963757 + 0.0166928i −0.870804 0.491630i \(-0.836401\pi\)
0.861166 + 0.508323i \(0.169734\pi\)
\(858\) 2.40719e9 + 6.87629e8i 0.130108 + 0.0371663i
\(859\) 1.14810e10 + 1.98858e10i 0.618024 + 1.07045i 0.989846 + 0.142145i \(0.0453999\pi\)
−0.371822 + 0.928304i \(0.621267\pi\)
\(860\) 1.56857e10i 0.840928i
\(861\) −1.43931e9 9.69782e8i −0.0768498 0.0517801i
\(862\) −2.50626e8 −0.0133276
\(863\) −3.00582e10 + 1.73541e10i −1.59194 + 0.919105i −0.598962 + 0.800777i \(0.704420\pi\)
−0.992975 + 0.118328i \(0.962247\pi\)
\(864\) −1.02386e10 5.91123e9i −0.540058 0.311803i
\(865\) 4.10204e9 + 2.36832e9i 0.215498 + 0.124418i
\(866\) 1.01055e10 5.83443e9i 0.528746 0.305271i
\(867\) 6.75061e8 0.0351784
\(868\) −6.40230e10 + 3.12656e10i −3.32290 + 1.62274i
\(869\) 4.93362e9i 0.255033i
\(870\) −3.18657e8 5.51930e8i −0.0164061 0.0284162i
\(871\) 5.64109e9 1.97478e10i 0.289268 1.01264i
\(872\) −7.47915e8 + 1.29543e9i −0.0381983 + 0.0661614i
\(873\) 1.95970e10 1.13143e10i 0.996872 0.575545i
\(874\) −6.35555e10 −3.22005
\(875\) −1.37364e9 + 1.97857e10i −0.0693178 + 0.998445i
\(876\) 1.09202e10i 0.548864i
\(877\) −2.62039e10 + 1.51288e10i −1.31180 + 0.757368i −0.982394 0.186820i \(-0.940182\pi\)
−0.329406 + 0.944188i \(0.606848\pi\)
\(878\) −3.19433e10 1.84425e10i −1.59276 0.919579i
\(879\) 7.78892e8 + 4.49693e8i 0.0386826 + 0.0223334i
\(880\) 2.05413e9 + 3.55785e9i 0.101610 + 0.175994i
\(881\) −1.14740e10 −0.565328 −0.282664 0.959219i \(-0.591218\pi\)
−0.282664 + 0.959219i \(0.591218\pi\)
\(882\) −2.44294e10 1.90472e10i −1.19887 0.934739i
\(883\) −1.01168e10 −0.494517 −0.247259 0.968950i \(-0.579530\pi\)
−0.247259 + 0.968950i \(0.579530\pi\)
\(884\) −3.41711e10 + 3.30652e10i −1.66370 + 1.60986i
\(885\) 5.96906e8 1.03387e9i 0.0289471 0.0501378i
\(886\) −3.29507e10 1.90241e10i −1.59164 0.918936i
\(887\) 1.83836e10 + 3.18413e10i 0.884498 + 1.53200i 0.846288 + 0.532726i \(0.178833\pi\)
0.0382108 + 0.999270i \(0.487834\pi\)
\(888\) 2.99094e10 1.43338
\(889\) −7.97833e9 5.53902e8i −0.380852 0.0264409i
\(890\) 1.24491e10i 0.591934i
\(891\) −1.99889e9 + 1.15406e9i −0.0946708 + 0.0546582i
\(892\) 8.86865e9 + 5.12032e9i 0.418389 + 0.241557i
\(893\) −3.14873e10 + 5.45376e10i −1.47964 + 2.56281i
\(894\) −8.03499e9 1.39170e10i −0.376101 0.651425i
\(895\) 1.58202e10i 0.737616i
\(896\) 2.18872e10 1.06886e10i 1.01651 0.496412i
\(897\) 2.07653e9 + 8.29291e9i 0.0960647 + 0.383649i
\(898\) −1.59106e10 2.75579e10i −0.733193 1.26993i
\(899\) −2.38123e9 1.37481e9i −0.109306 0.0631077i
\(900\) −1.26751e10 + 2.19540e10i −0.579567 + 1.00384i
\(901\) −1.89846e10 3.28822e10i −0.864697 1.49770i
\(902\) 1.81258e9i 0.0822382i
\(903\) 2.95772e9 4.38972e9i 0.133675 0.198394i
\(904\) 4.82686e10i 2.17308i
\(905\) 7.48989e9 4.32429e9i 0.335896 0.193930i
\(906\) 3.96122e9 6.86104e9i 0.176962 0.306508i
\(907\) 1.13165e10 1.96007e10i 0.503601 0.872262i −0.496390 0.868099i \(-0.665342\pi\)
0.999991 0.00416290i \(-0.00132510\pi\)
\(908\) −2.36842e10 + 1.36741e10i −1.04992 + 0.606173i
\(909\) 7.99873e9 0.353222
\(910\) −2.37316e10 8.59717e9i −1.04396 0.378191i
\(911\) 9.05506e9 0.396805 0.198403 0.980121i \(-0.436425\pi\)
0.198403 + 0.980121i \(0.436425\pi\)
\(912\) −2.33312e10 + 1.34703e10i −1.01848 + 0.588022i
\(913\) −4.41170e7 + 7.64129e7i −0.00191849 + 0.00332291i
\(914\) −1.86607e10 + 3.23214e10i −0.808383 + 1.40016i
\(915\) −2.42007e9 + 1.39723e9i −0.104437 + 0.0602968i
\(916\) 1.83456e10i 0.788673i
\(917\) 2.70505e9 + 5.53917e9i 0.115847 + 0.237220i
\(918\) 3.16675e10i 1.35103i
\(919\) −3.46490e9 6.00139e9i −0.147261 0.255063i 0.782953 0.622080i \(-0.213712\pi\)
−0.930214 + 0.367017i \(0.880379\pi\)
\(920\) −1.61676e10 + 2.80030e10i −0.684522 + 1.18563i
\(921\) −5.65774e8 3.26650e8i −0.0238635 0.0137776i
\(922\) −1.88867e10 3.27127e10i −0.793592 1.37454i
\(923\) 3.95834e10 9.91158e9i 1.65694 0.414894i
\(924\) 2.77812e8 4.00157e9i 0.0115851 0.166870i
\(925\) 2.49603e10i 1.03694i
\(926\) −1.93255e10 3.34727e10i −0.799818 1.38533i
\(927\) −2.13263e8 + 3.69382e8i −0.00879297 + 0.0152299i
\(928\) −1.37929e9 7.96334e8i −0.0566550 0.0327098i
\(929\) 6.53590e8 3.77350e8i 0.0267455 0.0154415i −0.486568 0.873643i \(-0.661751\pi\)
0.513313 + 0.858201i \(0.328418\pi\)
\(930\) 1.77367e10i 0.723074i
\(931\) −4.04468e10 + 1.63885e10i −1.64271 + 0.665603i
\(932\) 6.04572e10 2.44620
\(933\) 4.85856e9 + 8.41526e9i 0.195849 + 0.339220i
\(934\) 4.51322e10 + 2.60571e10i 1.81248 + 1.04643i
\(935\) 1.56045e9 2.70277e9i 0.0624322 0.108136i
\(936\) −3.22853e10 3.33651e10i −1.28688 1.32993i
\(937\) 3.19315e10 1.26803 0.634017 0.773319i \(-0.281405\pi\)
0.634017 + 0.773319i \(0.281405\pi\)
\(938\) −4.76325e10 3.30692e9i −1.88449 0.130832i
\(939\) −9.29503e9 −0.366371
\(940\) 2.91794e10 + 5.05403e10i 1.14585 + 1.98468i
\(941\) 5.93574e9 + 3.42700e9i 0.232226 + 0.134076i 0.611599 0.791168i \(-0.290527\pi\)
−0.379372 + 0.925244i \(0.623860\pi\)
\(942\) −1.05117e10 6.06892e9i −0.409726 0.236555i
\(943\) −5.36038e9 + 3.09482e9i −0.208164 + 0.120183i
\(944\) 1.05194e10i 0.406997i
\(945\) −1.04103e10 + 5.08385e9i −0.401283 + 0.195966i
\(946\) −5.52814e9 −0.212305
\(947\) −8.82873e9 + 5.09727e9i −0.337811 + 0.195035i −0.659303 0.751877i \(-0.729149\pi\)
0.321493 + 0.946912i \(0.395815\pi\)
\(948\) −1.49908e10 + 2.59649e10i −0.571474 + 0.989822i
\(949\) −4.58438e9 + 1.60486e10i −0.174120 + 0.609544i
\(950\) 2.59100e10 + 4.48774e10i 0.980471 + 1.69823i
\(951\) 2.08771e9i 0.0787114i
\(952\) 5.03318e10 + 3.39127e10i 1.89066 + 1.27389i
\(953\) 2.32097e10 0.868650 0.434325 0.900756i \(-0.356987\pi\)
0.434325 + 0.900756i \(0.356987\pi\)
\(954\) 5.84811e10 3.37641e10i 2.18070 1.25903i
\(955\) −9.80882e9 5.66313e9i −0.364422 0.210399i
\(956\) 2.76729e10 + 1.59770e10i 1.02436 + 0.591415i
\(957\) 1.34059e8 7.73988e7i 0.00494428 0.00285458i
\(958\) 5.42858e9 0.199484
\(959\) 3.11506e10 + 2.09887e10i 1.14052 + 0.768460i
\(960\) 9.85670e8i 0.0359569i
\(961\) 2.45051e10 + 4.24442e10i 0.890688 + 1.54272i
\(962\) 8.00638e10 + 2.28707e10i 2.89950 + 0.828261i
\(963\) 8.56676e8 1.48381e9i 0.0309118 0.0535408i
\(964\) 7.32215e10 4.22745e10i 2.63251 1.51988i
\(965\) −3.20495e10 −1.14809
\(966\) 1.78592e10 8.72153e9i 0.637444 0.311296i
\(967\) 5.40693e9i 0.192290i −0.995367 0.0961452i \(-0.969349\pi\)
0.995367 0.0961452i \(-0.0306513\pi\)
\(968\) 5.13731e10 2.96603e10i 1.82042 1.05102i
\(969\) 1.77239e10 + 1.02329e10i 0.625785 + 0.361297i
\(970\) −3.71232e10 2.14331e10i −1.30600 0.754022i
\(971\) −2.05300e10 3.55589e10i −0.719649 1.24647i −0.961139 0.276066i \(-0.910969\pi\)
0.241489 0.970403i \(-0.422364\pi\)
\(972\) −5.98248e10 −2.08953
\(973\) 1.18135e10 + 8.20162e8i 0.411135 + 0.0285433i
\(974\) −2.94237e9 −0.102033
\(975\) 5.00919e9 4.84708e9i 0.173082 0.167480i
\(976\) −1.23119e10 + 2.13248e10i −0.423887 + 0.734194i
\(977\) 1.05008e10 + 6.06266e9i 0.360241 + 0.207985i 0.669186 0.743095i \(-0.266643\pi\)
−0.308945 + 0.951080i \(0.599976\pi\)
\(978\) 7.15359e9 + 1.23904e10i 0.244533 + 0.423544i
\(979\) 3.02378e9 0.102994
\(980\) −5.58853e9 + 4.00542e10i −0.189673 + 1.35943i
\(981\) 8.76817e8i 0.0296529i
\(982\) 1.10949e10 6.40562e9i 0.373880 0.215860i
\(983\) −3.06019e10 1.76680e10i −1.02757 0.593268i −0.111283 0.993789i \(-0.535496\pi\)
−0.916288 + 0.400521i \(0.868829\pi\)
\(984\) −3.02369e9 + 5.23718e9i −0.101171 + 0.175232i
\(985\) −5.71758e9 9.90314e9i −0.190628 0.330177i
\(986\) 4.26611e9i 0.141730i
\(987\) 1.36394e9 1.96461e10i 0.0451529 0.650377i
\(988\) −1.15570e11 + 2.89385e10i −3.81239 + 0.954613i
\(989\) −9.43881e9 1.63485e10i −0.310263 0.537392i
\(990\) 4.80689e9 + 2.77526e9i 0.157449 + 0.0909034i
\(991\) 2.79888e10 4.84780e10i 0.913537 1.58229i 0.104507 0.994524i \(-0.466673\pi\)
0.809029 0.587768i \(-0.199993\pi\)
\(992\) 2.21623e10 + 3.83863e10i 0.720817 + 1.24849i
\(993\) 1.48245e10i 0.480462i
\(994\) −4.16293e10 8.52447e10i −1.34446 2.75306i
\(995\) 2.35311e10i 0.757288i
\(996\) −4.64362e8 + 2.68100e8i −0.0148919 + 0.00859783i
\(997\) −1.76645e10 + 3.05959e10i −0.564507 + 0.977755i 0.432588 + 0.901592i \(0.357600\pi\)
−0.997095 + 0.0761635i \(0.975733\pi\)
\(998\) 3.57176e10 6.18648e10i 1.13743 1.97009i
\(999\) 3.30981e10 1.91092e10i 1.05032 0.606405i
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.r.a.25.4 128
7.2 even 3 inner 91.8.r.a.51.61 yes 128
13.12 even 2 inner 91.8.r.a.25.61 yes 128
91.51 even 6 inner 91.8.r.a.51.4 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.r.a.25.4 128 1.1 even 1 trivial
91.8.r.a.25.61 yes 128 13.12 even 2 inner
91.8.r.a.51.4 yes 128 91.51 even 6 inner
91.8.r.a.51.61 yes 128 7.2 even 3 inner