Properties

Label 91.8.r.a.25.17
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 25.17
Character \(\chi\) \(=\) 91.25
Dual form 91.8.r.a.51.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.9207 + 6.30508i) q^{2} +(-7.65371 + 13.2566i) q^{3} +(15.5082 - 26.8609i) q^{4} +(37.8419 - 21.8480i) q^{5} -193.029i q^{6} +(-534.194 + 733.608i) q^{7} -1222.98i q^{8} +(976.341 + 1691.07i) q^{9} +O(q^{10})\) \(q+(-10.9207 + 6.30508i) q^{2} +(-7.65371 + 13.2566i) q^{3} +(15.5082 - 26.8609i) q^{4} +(37.8419 - 21.8480i) q^{5} -193.029i q^{6} +(-534.194 + 733.608i) q^{7} -1222.98i q^{8} +(976.341 + 1691.07i) q^{9} +(-275.507 + 477.192i) q^{10} +(2780.19 + 1605.14i) q^{11} +(237.390 + 411.171i) q^{12} +(-7921.40 - 3.49801i) q^{13} +(1208.33 - 11379.7i) q^{14} +668.873i q^{15} +(9696.04 + 16794.0i) q^{16} +(-11334.8 + 19632.5i) q^{17} +(-21324.7 - 12311.8i) q^{18} +(-8795.81 + 5078.26i) q^{19} -1355.29i q^{20} +(-5636.59 - 12696.4i) q^{21} -40482.3 q^{22} +(46168.0 + 79965.4i) q^{23} +(16212.6 + 9360.34i) q^{24} +(-38107.8 + 66004.7i) q^{25} +(86529.4 - 49906.9i) q^{26} -63367.9 q^{27} +(11421.0 + 25725.8i) q^{28} +14743.7 q^{29} +(-4217.30 - 7304.58i) q^{30} +(-205488. - 118639. i) q^{31} +(-76206.6 - 43997.9i) q^{32} +(-42557.6 + 24570.6i) q^{33} -285868. i q^{34} +(-4187.02 + 39432.1i) q^{35} +60565.0 q^{36} +(408067. - 235597. i) q^{37} +(64037.7 - 110917. i) q^{38} +(60674.4 - 104984. i) q^{39} +(-26719.7 - 46279.9i) q^{40} -280765. i q^{41} +(141608. + 103115. i) q^{42} -16564.7 q^{43} +(86231.3 - 49785.7i) q^{44} +(73893.2 + 42662.2i) q^{45} +(-1.00838e6 - 582187. i) q^{46} +(93465.3 - 53962.2i) q^{47} -296843. q^{48} +(-252817. - 783777. i) q^{49} -961092. i q^{50} +(-173507. - 300523. i) q^{51} +(-122940. + 212722. i) q^{52} +(661121. - 1.14510e6i) q^{53} +(692023. - 399540. i) q^{54} +140277. q^{55} +(897188. + 653309. i) q^{56} -155470. i q^{57} +(-161012. + 92960.2i) q^{58} +(-1.27861e6 - 738207. i) q^{59} +(17966.5 + 10373.0i) q^{60} +(-850620. - 1.47332e6i) q^{61} +2.99211e6 q^{62} +(-1.76214e6 - 187109. i) q^{63} -1.37254e6 q^{64} +(-299837. + 172934. i) q^{65} +(309840. - 536658. i) q^{66} +(856771. + 494657. i) q^{67} +(351565. + 608928. i) q^{68} -1.41343e6 q^{69} +(-202898. - 457027. i) q^{70} -3.08661e6i q^{71} +(2.06815e6 - 1.19405e6i) q^{72} +(2.70745e6 + 1.56314e6i) q^{73} +(-2.97092e6 + 5.14579e6i) q^{74} +(-583333. - 1.01036e6i) q^{75} +315018. i q^{76} +(-2.66271e6 + 1.18211e6i) q^{77} +(-675.219 + 1.52906e6i) q^{78} +(1.25107e6 + 2.16692e6i) q^{79} +(733832. + 423678. i) q^{80} +(-1.65026e6 + 2.85833e6i) q^{81} +(1.77025e6 + 3.06616e6i) q^{82} +4.71859e6i q^{83} +(-428450. - 45494.2i) q^{84} +990574. i q^{85} +(180899. - 104442. i) q^{86} +(-112844. + 195452. i) q^{87} +(1.96306e6 - 3.40012e6i) q^{88} +(-1.05933e7 + 6.11604e6i) q^{89} -1.07596e6 q^{90} +(4.23413e6 - 5.80933e6i) q^{91} +2.86392e6 q^{92} +(3.14549e6 - 1.81605e6i) q^{93} +(-680472. + 1.17861e6i) q^{94} +(-221900. + 384342. i) q^{95} +(1.16653e6 - 673494. i) q^{96} +3.81468e6i q^{97} +(7.70273e6 + 6.96538e6i) q^{98} +6.26868e6i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9207 + 6.30508i −0.965265 + 0.557296i −0.897789 0.440425i \(-0.854828\pi\)
−0.0674754 + 0.997721i \(0.521494\pi\)
\(3\) −7.65371 + 13.2566i −0.163662 + 0.283471i −0.936179 0.351523i \(-0.885664\pi\)
0.772517 + 0.634994i \(0.218997\pi\)
\(4\) 15.5082 26.8609i 0.121157 0.209851i
\(5\) 37.8419 21.8480i 0.135387 0.0781658i −0.430777 0.902459i \(-0.641760\pi\)
0.566164 + 0.824293i \(0.308427\pi\)
\(6\) 193.029i 0.364832i
\(7\) −534.194 + 733.608i −0.588648 + 0.808389i
\(8\) 1222.98i 0.844510i
\(9\) 976.341 + 1691.07i 0.446430 + 0.773239i
\(10\) −275.507 + 477.192i −0.0871230 + 0.150901i
\(11\) 2780.19 + 1605.14i 0.629797 + 0.363613i 0.780673 0.624939i \(-0.214876\pi\)
−0.150877 + 0.988553i \(0.548210\pi\)
\(12\) 237.390 + 411.171i 0.0396577 + 0.0686892i
\(13\) −7921.40 3.49801i −1.00000 0.000441591i
\(14\) 1208.33 11379.7i 0.117689 1.10836i
\(15\) 668.873i 0.0511711i
\(16\) 9696.04 + 16794.0i 0.591799 + 1.02503i
\(17\) −11334.8 + 19632.5i −0.559556 + 0.969180i 0.437977 + 0.898986i \(0.355695\pi\)
−0.997533 + 0.0701939i \(0.977638\pi\)
\(18\) −21324.7 12311.8i −0.861845 0.497587i
\(19\) −8795.81 + 5078.26i −0.294197 + 0.169855i −0.639833 0.768514i \(-0.720996\pi\)
0.345636 + 0.938369i \(0.387663\pi\)
\(20\) 1355.29i 0.0378815i
\(21\) −5636.59 12696.4i −0.132815 0.299167i
\(22\) −40482.3 −0.810561
\(23\) 46168.0 + 79965.4i 0.791214 + 1.37042i 0.925215 + 0.379442i \(0.123884\pi\)
−0.134001 + 0.990981i \(0.542783\pi\)
\(24\) 16212.6 + 9360.34i 0.239394 + 0.138214i
\(25\) −38107.8 + 66004.7i −0.487780 + 0.844860i
\(26\) 86529.4 49906.9i 0.965511 0.556870i
\(27\) −63367.9 −0.619578
\(28\) 11421.0 + 25725.8i 0.0983221 + 0.221471i
\(29\) 14743.7 0.112257 0.0561285 0.998424i \(-0.482124\pi\)
0.0561285 + 0.998424i \(0.482124\pi\)
\(30\) −4217.30 7304.58i −0.0285174 0.0493936i
\(31\) −205488. 118639.i −1.23886 0.715254i −0.269996 0.962862i \(-0.587022\pi\)
−0.968860 + 0.247608i \(0.920356\pi\)
\(32\) −76206.6 43997.9i −0.411119 0.237360i
\(33\) −42557.6 + 24570.6i −0.206148 + 0.119019i
\(34\) 285868.i 1.24735i
\(35\) −4187.02 + 39432.1i −0.0165070 + 0.155458i
\(36\) 60565.0 0.216353
\(37\) 408067. 235597.i 1.32442 0.764653i 0.339988 0.940430i \(-0.389577\pi\)
0.984430 + 0.175777i \(0.0562438\pi\)
\(38\) 64037.7 110917.i 0.189319 0.327909i
\(39\) 60674.4 104984.i 0.163787 0.283398i
\(40\) −26719.7 46279.9i −0.0660118 0.114336i
\(41\) 280765.i 0.636209i −0.948056 0.318104i \(-0.896954\pi\)
0.948056 0.318104i \(-0.103046\pi\)
\(42\) 141608. + 103115.i 0.294927 + 0.214758i
\(43\) −16564.7 −0.0317720 −0.0158860 0.999874i \(-0.505057\pi\)
−0.0158860 + 0.999874i \(0.505057\pi\)
\(44\) 86231.3 49785.7i 0.152609 0.0881089i
\(45\) 73893.2 + 42662.2i 0.120882 + 0.0697911i
\(46\) −1.00838e6 582187.i −1.52746 0.881881i
\(47\) 93465.3 53962.2i 0.131313 0.0758136i −0.432904 0.901440i \(-0.642511\pi\)
0.564218 + 0.825626i \(0.309178\pi\)
\(48\) −296843. −0.387420
\(49\) −252817. 783777.i −0.306987 0.951714i
\(50\) 961092.i 1.08735i
\(51\) −173507. 300523.i −0.183156 0.317236i
\(52\) −122940. + 212722.i −0.121250 + 0.209797i
\(53\) 661121. 1.14510e6i 0.609980 1.05652i −0.381263 0.924467i \(-0.624511\pi\)
0.991243 0.132050i \(-0.0421558\pi\)
\(54\) 692023. 399540.i 0.598057 0.345288i
\(55\) 140277. 0.113689
\(56\) 897188. + 653309.i 0.682693 + 0.497119i
\(57\) 155470.i 0.111195i
\(58\) −161012. + 92960.2i −0.108358 + 0.0625604i
\(59\) −1.27861e6 738207.i −0.810507 0.467946i 0.0366250 0.999329i \(-0.488339\pi\)
−0.847132 + 0.531383i \(0.821673\pi\)
\(60\) 17966.5 + 10373.0i 0.0107383 + 0.00619976i
\(61\) −850620. 1.47332e6i −0.479823 0.831078i 0.519909 0.854222i \(-0.325966\pi\)
−0.999732 + 0.0231437i \(0.992632\pi\)
\(62\) 2.99211e6 1.59443
\(63\) −1.76214e6 187109.i −0.887868 0.0942765i
\(64\) −1.37254e6 −0.654480
\(65\) −299837. + 172934.i −0.135422 + 0.0781060i
\(66\) 309840. 536658.i 0.132658 0.229770i
\(67\) 856771. + 494657.i 0.348019 + 0.200929i 0.663812 0.747899i \(-0.268937\pi\)
−0.315794 + 0.948828i \(0.602271\pi\)
\(68\) 351565. + 608928.i 0.135589 + 0.234847i
\(69\) −1.41343e6 −0.517967
\(70\) −202898. 457027.i −0.0707023 0.159257i
\(71\) 3.08661e6i 1.02348i −0.859141 0.511738i \(-0.829002\pi\)
0.859141 0.511738i \(-0.170998\pi\)
\(72\) 2.06815e6 1.19405e6i 0.653007 0.377014i
\(73\) 2.70745e6 + 1.56314e6i 0.814573 + 0.470294i 0.848541 0.529129i \(-0.177481\pi\)
−0.0339686 + 0.999423i \(0.510815\pi\)
\(74\) −2.97092e6 + 5.14579e6i −0.852276 + 1.47619i
\(75\) −583333. 1.01036e6i −0.159662 0.276543i
\(76\) 315018.i 0.0823166i
\(77\) −2.66271e6 + 1.18211e6i −0.664670 + 0.295081i
\(78\) −675.219 + 1.52906e6i −0.000161107 + 0.364832i
\(79\) 1.25107e6 + 2.16692e6i 0.285487 + 0.494478i 0.972727 0.231952i \(-0.0745113\pi\)
−0.687240 + 0.726430i \(0.741178\pi\)
\(80\) 733832. + 423678.i 0.160244 + 0.0925169i
\(81\) −1.65026e6 + 2.85833e6i −0.345028 + 0.597606i
\(82\) 1.77025e6 + 3.06616e6i 0.354556 + 0.614110i
\(83\) 4.71859e6i 0.905813i 0.891558 + 0.452907i \(0.149613\pi\)
−0.891558 + 0.452907i \(0.850387\pi\)
\(84\) −428450. 45494.2i −0.0788721 0.00837487i
\(85\) 990574.i 0.174953i
\(86\) 180899. 104442.i 0.0306684 0.0177064i
\(87\) −112844. + 195452.i −0.0183722 + 0.0318216i
\(88\) 1.96306e6 3.40012e6i 0.307075 0.531869i
\(89\) −1.05933e7 + 6.11604e6i −1.59282 + 0.919613i −0.599996 + 0.800003i \(0.704831\pi\)
−0.992821 + 0.119610i \(0.961836\pi\)
\(90\) −1.07596e6 −0.155577
\(91\) 4.23413e6 5.80933e6i 0.589005 0.808129i
\(92\) 2.86392e6 0.383446
\(93\) 3.14549e6 1.81605e6i 0.405507 0.234120i
\(94\) −680472. + 1.17861e6i −0.0845012 + 0.146360i
\(95\) −221900. + 384342.i −0.0265537 + 0.0459923i
\(96\) 1.16653e6 673494.i 0.134569 0.0776935i
\(97\) 3.81468e6i 0.424382i 0.977228 + 0.212191i \(0.0680598\pi\)
−0.977228 + 0.212191i \(0.931940\pi\)
\(98\) 7.70273e6 + 6.96538e6i 0.826710 + 0.747573i
\(99\) 6.26868e6i 0.649311i
\(100\) 1.18196e6 + 2.04722e6i 0.118196 + 0.204722i
\(101\) 4.43765e6 7.68624e6i 0.428577 0.742317i −0.568170 0.822911i \(-0.692349\pi\)
0.996747 + 0.0805944i \(0.0256818\pi\)
\(102\) 3.78965e6 + 2.18795e6i 0.353588 + 0.204144i
\(103\) −372515. 645215.i −0.0335903 0.0581800i 0.848742 0.528808i \(-0.177361\pi\)
−0.882332 + 0.470628i \(0.844027\pi\)
\(104\) −4278.00 + 9.68771e6i −0.000372927 + 0.844510i
\(105\) −490691. 357308.i −0.0413662 0.0301217i
\(106\) 1.66737e7i 1.35976i
\(107\) −2.03444e6 3.52375e6i −0.160547 0.278075i 0.774518 0.632552i \(-0.217992\pi\)
−0.935065 + 0.354477i \(0.884659\pi\)
\(108\) −982719. + 1.70212e6i −0.0750665 + 0.130019i
\(109\) −4.82330e6 2.78473e6i −0.356740 0.205964i 0.310910 0.950439i \(-0.399366\pi\)
−0.667650 + 0.744476i \(0.732700\pi\)
\(110\) −1.53193e6 + 884457.i −0.109740 + 0.0633582i
\(111\) 7.21277e6i 0.500578i
\(112\) −1.74998e7 1.85818e6i −1.17698 0.124975i
\(113\) −1.68688e7 −1.09979 −0.549896 0.835233i \(-0.685333\pi\)
−0.549896 + 0.835233i \(0.685333\pi\)
\(114\) 980252. + 1.69785e6i 0.0619685 + 0.107333i
\(115\) 3.49417e6 + 2.01736e6i 0.214241 + 0.123692i
\(116\) 228648. 396029.i 0.0136008 0.0235572i
\(117\) −7.72807e6 1.33991e7i −0.446088 0.773436i
\(118\) 1.86178e7 1.04314
\(119\) −8.34756e6 1.88029e7i −0.454093 1.02285i
\(120\) 818019. 0.0432145
\(121\) −4.59061e6 7.95116e6i −0.235571 0.408020i
\(122\) 1.85788e7 + 1.07265e7i 0.926313 + 0.534807i
\(123\) 3.72199e6 + 2.14889e6i 0.180347 + 0.104123i
\(124\) −6.37348e6 + 3.67973e6i −0.300193 + 0.173317i
\(125\) 6.74407e6i 0.308843i
\(126\) 2.04236e7 9.06707e6i 0.909568 0.403803i
\(127\) 2.83122e7 1.22648 0.613240 0.789897i \(-0.289866\pi\)
0.613240 + 0.789897i \(0.289866\pi\)
\(128\) 2.47436e7 1.42857e7i 1.04287 0.602099i
\(129\) 126782. 219592.i 0.00519987 0.00900644i
\(130\) 2.18407e6 3.77906e6i 0.0871896 0.150863i
\(131\) −1.44483e7 2.50252e7i −0.561523 0.972587i −0.997364 0.0725632i \(-0.976882\pi\)
0.435840 0.900024i \(-0.356451\pi\)
\(132\) 1.52418e6i 0.0576803i
\(133\) 973215. 9.16545e6i 0.0358697 0.337810i
\(134\) −1.24754e7 −0.447907
\(135\) −2.39796e6 + 1.38446e6i −0.0838829 + 0.0484298i
\(136\) 2.40102e7 + 1.38623e7i 0.818482 + 0.472551i
\(137\) −4.19556e7 2.42231e7i −1.39402 0.804836i −0.400259 0.916402i \(-0.631080\pi\)
−0.993757 + 0.111566i \(0.964413\pi\)
\(138\) 1.54357e7 8.91178e6i 0.499975 0.288661i
\(139\) 2.03246e7 0.641904 0.320952 0.947095i \(-0.395997\pi\)
0.320952 + 0.947095i \(0.395997\pi\)
\(140\) 994250. + 723987.i 0.0306230 + 0.0222989i
\(141\) 1.65204e6i 0.0496312i
\(142\) 1.94614e7 + 3.37081e7i 0.570379 + 0.987926i
\(143\) −2.20174e7 1.27247e7i −0.629636 0.363891i
\(144\) −1.89333e7 + 3.27934e7i −0.528393 + 0.915204i
\(145\) 557929. 322120.i 0.0151982 0.00877466i
\(146\) −3.94230e7 −1.04837
\(147\) 1.23252e7 + 2.64731e6i 0.320025 + 0.0687375i
\(148\) 1.46147e7i 0.370574i
\(149\) 3.04333e7 1.75706e7i 0.753696 0.435147i −0.0733316 0.997308i \(-0.523363\pi\)
0.827028 + 0.562161i \(0.190030\pi\)
\(150\) 1.27408e7 + 7.35592e6i 0.308232 + 0.177958i
\(151\) −3.13987e7 1.81281e7i −0.742152 0.428481i 0.0806995 0.996738i \(-0.474285\pi\)
−0.822851 + 0.568257i \(0.807618\pi\)
\(152\) 6.21062e6 + 1.07571e7i 0.143444 + 0.248452i
\(153\) −4.42667e7 −0.999210
\(154\) 2.16254e7 2.96981e7i 0.477135 0.655249i
\(155\) −1.03681e7 −0.223634
\(156\) −1.87902e6 3.25788e6i −0.0396274 0.0687067i
\(157\) −4.00545e7 + 6.93764e7i −0.826043 + 1.43075i 0.0750772 + 0.997178i \(0.476080\pi\)
−0.901120 + 0.433570i \(0.857254\pi\)
\(158\) −2.73252e7 1.57762e7i −0.551141 0.318202i
\(159\) 1.01201e7 + 1.75285e7i 0.199661 + 0.345823i
\(160\) −3.84507e6 −0.0742137
\(161\) −8.33259e7 8.84780e6i −1.57358 0.167088i
\(162\) 4.16201e7i 0.769131i
\(163\) 4.82308e7 2.78461e7i 0.872304 0.503625i 0.00419075 0.999991i \(-0.498666\pi\)
0.868113 + 0.496366i \(0.165333\pi\)
\(164\) −7.54161e6 4.35415e6i −0.133509 0.0770814i
\(165\) −1.07364e6 + 1.85960e6i −0.0186065 + 0.0322274i
\(166\) −2.97511e7 5.15304e7i −0.504806 0.874350i
\(167\) 4.06564e7i 0.675494i 0.941237 + 0.337747i \(0.109665\pi\)
−0.941237 + 0.337747i \(0.890335\pi\)
\(168\) −1.55275e7 + 6.89344e6i −0.252649 + 0.112164i
\(169\) 6.27485e7 + 55418.3i 1.00000 + 0.000883181i
\(170\) −6.24565e6 1.08178e7i −0.0975004 0.168876i
\(171\) −1.71754e7 9.91623e6i −0.262676 0.151656i
\(172\) −256889. + 444944.i −0.00384942 + 0.00666739i
\(173\) 4.56333e7 + 7.90392e7i 0.670071 + 1.16060i 0.977884 + 0.209149i \(0.0670695\pi\)
−0.307813 + 0.951447i \(0.599597\pi\)
\(174\) 2.84596e6i 0.0409550i
\(175\) −2.80646e7 6.32155e7i −0.395845 0.891642i
\(176\) 6.22542e7i 0.860744i
\(177\) 1.95722e7 1.13000e7i 0.265298 0.153170i
\(178\) 7.71243e7 1.33583e8i 1.02499 1.77534i
\(179\) −2.96489e7 + 5.13534e7i −0.386387 + 0.669242i −0.991961 0.126547i \(-0.959610\pi\)
0.605573 + 0.795789i \(0.292944\pi\)
\(180\) 2.29189e6 1.32323e6i 0.0292914 0.0169114i
\(181\) 3.53366e7 0.442945 0.221473 0.975167i \(-0.428914\pi\)
0.221473 + 0.975167i \(0.428914\pi\)
\(182\) −9.61144e6 + 9.01386e7i −0.118179 + 1.10831i
\(183\) 2.60416e7 0.314115
\(184\) 9.77961e7 5.64626e7i 1.15734 0.668188i
\(185\) 1.02947e7 1.78309e7i 0.119539 0.207048i
\(186\) −2.29007e7 + 3.96652e7i −0.260948 + 0.451975i
\(187\) −6.30260e7 + 3.63881e7i −0.704814 + 0.406924i
\(188\) 3.34742e6i 0.0367415i
\(189\) 3.38507e7 4.64871e7i 0.364713 0.500860i
\(190\) 5.59639e6i 0.0591930i
\(191\) −5.31069e7 9.19839e7i −0.551486 0.955202i −0.998168 0.0605086i \(-0.980728\pi\)
0.446682 0.894693i \(-0.352606\pi\)
\(192\) 1.05051e7 1.81953e7i 0.107113 0.185526i
\(193\) −1.14117e8 6.58853e7i −1.14261 0.659687i −0.195536 0.980697i \(-0.562645\pi\)
−0.947076 + 0.321009i \(0.895978\pi\)
\(194\) −2.40519e7 4.16590e7i −0.236506 0.409641i
\(195\) 2339.73 5.29841e6i 2.25967e−5 0.0511711i
\(196\) −2.49737e7 5.36404e6i −0.236912 0.0508857i
\(197\) 6.23098e7i 0.580664i −0.956926 0.290332i \(-0.906234\pi\)
0.956926 0.290332i \(-0.0937657\pi\)
\(198\) −3.95245e7 6.84585e7i −0.361858 0.626757i
\(199\) −5.68484e6 + 9.84644e6i −0.0511367 + 0.0885714i −0.890461 0.455060i \(-0.849618\pi\)
0.839324 + 0.543632i \(0.182951\pi\)
\(200\) 8.07225e7 + 4.66051e7i 0.713492 + 0.411935i
\(201\) −1.31149e7 + 7.57192e6i −0.113915 + 0.0657688i
\(202\) 1.11919e8i 0.955376i
\(203\) −7.87599e6 + 1.08161e7i −0.0660799 + 0.0907474i
\(204\) −1.07631e7 −0.0887629
\(205\) −6.13416e6 1.06247e7i −0.0497298 0.0861345i
\(206\) 8.13626e6 + 4.69747e6i 0.0648470 + 0.0374394i
\(207\) −9.01516e7 + 1.56147e8i −0.706443 + 1.22359i
\(208\) −7.67474e7 1.33066e8i −0.591346 1.02529i
\(209\) −3.26054e7 −0.247046
\(210\) 7.61155e6 + 808218.i 0.0567160 + 0.00602228i
\(211\) 2.31536e8 1.69679 0.848397 0.529360i \(-0.177568\pi\)
0.848397 + 0.529360i \(0.177568\pi\)
\(212\) −2.05055e7 3.55166e7i −0.147807 0.256010i
\(213\) 4.09180e7 + 2.36240e7i 0.290126 + 0.167504i
\(214\) 4.44351e7 + 2.56546e7i 0.309940 + 0.178944i
\(215\) −626841. + 361907.i −0.00430153 + 0.00248349i
\(216\) 7.74977e7i 0.523239i
\(217\) 1.96805e8 8.73716e7i 1.30745 0.580445i
\(218\) 7.02319e7 0.459131
\(219\) −4.14440e7 + 2.39277e7i −0.266629 + 0.153938i
\(220\) 2.17544e6 3.76796e6i 0.0137742 0.0238576i
\(221\) 8.98564e7 1.55477e8i 0.559984 0.968933i
\(222\) −4.54771e7 7.87687e7i −0.278970 0.483191i
\(223\) 1.97992e8i 1.19559i 0.801651 + 0.597793i \(0.203955\pi\)
−0.801651 + 0.597793i \(0.796045\pi\)
\(224\) 7.29863e7 3.24023e7i 0.433884 0.192623i
\(225\) −1.48825e8 −0.871038
\(226\) 1.84220e8 1.06359e8i 1.06159 0.612909i
\(227\) 3.91933e7 + 2.26282e7i 0.222393 + 0.128399i 0.607058 0.794658i \(-0.292350\pi\)
−0.384665 + 0.923056i \(0.625683\pi\)
\(228\) −4.17607e6 2.41106e6i −0.0233344 0.0134721i
\(229\) −1.70769e8 + 9.85936e7i −0.939691 + 0.542531i −0.889864 0.456227i \(-0.849201\pi\)
−0.0498277 + 0.998758i \(0.515867\pi\)
\(230\) −5.08785e7 −0.275732
\(231\) 4.70880e6 4.43460e7i 0.0251344 0.236708i
\(232\) 1.80313e7i 0.0948021i
\(233\) 1.22835e8 + 2.12756e8i 0.636173 + 1.10188i 0.986265 + 0.165169i \(0.0528169\pi\)
−0.350092 + 0.936715i \(0.613850\pi\)
\(234\) 1.68878e8 + 9.76015e7i 0.861626 + 0.497967i
\(235\) 2.35793e6 4.08406e6i 0.0118521 0.0205284i
\(236\) −3.96578e7 + 2.28965e7i −0.196398 + 0.113390i
\(237\) −3.83013e7 −0.186893
\(238\) 2.09715e8 + 1.52709e8i 1.00835 + 0.734252i
\(239\) 2.71669e8i 1.28720i 0.765360 + 0.643602i \(0.222561\pi\)
−0.765360 + 0.643602i \(0.777439\pi\)
\(240\) −1.12331e7 + 6.48542e6i −0.0524517 + 0.0302830i
\(241\) −1.75003e8 1.01038e8i −0.805353 0.464971i 0.0399863 0.999200i \(-0.487269\pi\)
−0.845340 + 0.534229i \(0.820602\pi\)
\(242\) 1.00265e8 + 5.78883e7i 0.454776 + 0.262565i
\(243\) −9.45540e7 1.63772e8i −0.422725 0.732181i
\(244\) −5.27662e7 −0.232537
\(245\) −2.66910e7 2.41360e7i −0.115954 0.104854i
\(246\) −5.41958e7 −0.232110
\(247\) 6.96928e7 4.01961e7i 0.294272 0.169725i
\(248\) −1.45093e8 + 2.51308e8i −0.604039 + 1.04623i
\(249\) −6.25525e7 3.61147e7i −0.256772 0.148247i
\(250\) −4.25219e7 7.36502e7i −0.172117 0.298115i
\(251\) −3.31117e8 −1.32167 −0.660836 0.750531i \(-0.729798\pi\)
−0.660836 + 0.750531i \(0.729798\pi\)
\(252\) −3.23535e7 + 4.44309e7i −0.127356 + 0.174898i
\(253\) 2.96426e8i 1.15078i
\(254\) −3.09190e8 + 1.78511e8i −1.18388 + 0.683512i
\(255\) −1.31317e7 7.58157e6i −0.0495940 0.0286331i
\(256\) −9.23027e7 + 1.59873e8i −0.343854 + 0.595573i
\(257\) 5.78582e7 + 1.00213e8i 0.212617 + 0.368264i 0.952533 0.304436i \(-0.0984679\pi\)
−0.739915 + 0.672700i \(0.765135\pi\)
\(258\) 3.19748e6i 0.0115915i
\(259\) −4.51506e7 + 4.25215e8i −0.161479 + 1.52076i
\(260\) −4740.82 + 1.07358e7i −1.67281e−5 + 0.0378815i
\(261\) 1.43949e7 + 2.49327e7i 0.0501148 + 0.0868015i
\(262\) 3.15572e8 + 1.82196e8i 1.08404 + 0.625869i
\(263\) −1.03811e8 + 1.79806e8i −0.351883 + 0.609480i −0.986579 0.163282i \(-0.947792\pi\)
0.634696 + 0.772762i \(0.281125\pi\)
\(264\) 3.00494e7 + 5.20471e7i 0.100513 + 0.174094i
\(265\) 5.77767e7i 0.190718i
\(266\) 4.71607e7 + 1.06230e8i 0.153637 + 0.346066i
\(267\) 1.87242e8i 0.602023i
\(268\) 2.65739e7 1.53424e7i 0.0843301 0.0486880i
\(269\) 2.00865e8 3.47908e8i 0.629174 1.08976i −0.358544 0.933513i \(-0.616727\pi\)
0.987718 0.156248i \(-0.0499399\pi\)
\(270\) 1.74583e7 3.02387e7i 0.0539795 0.0934952i
\(271\) 4.30155e8 2.48350e8i 1.31290 0.758005i 0.330327 0.943867i \(-0.392841\pi\)
0.982576 + 0.185862i \(0.0595077\pi\)
\(272\) −4.39612e8 −1.32458
\(273\) 4.46052e7 + 1.00593e8i 0.132683 + 0.299226i
\(274\) 6.10914e8 1.79413
\(275\) −2.11894e8 + 1.22337e8i −0.614405 + 0.354727i
\(276\) −2.19197e7 + 3.79659e7i −0.0627555 + 0.108696i
\(277\) −2.97408e8 + 5.15127e8i −0.840764 + 1.45625i 0.0484857 + 0.998824i \(0.484560\pi\)
−0.889250 + 0.457422i \(0.848773\pi\)
\(278\) −2.21959e8 + 1.28148e8i −0.619607 + 0.357731i
\(279\) 4.63327e8i 1.27724i
\(280\) 4.82247e7 + 5.12065e6i 0.131286 + 0.0139403i
\(281\) 2.49441e8i 0.670650i −0.942102 0.335325i \(-0.891154\pi\)
0.942102 0.335325i \(-0.108846\pi\)
\(282\) −1.04163e7 1.80415e7i −0.0276593 0.0479072i
\(283\) 3.44211e8 5.96190e8i 0.902759 1.56362i 0.0788618 0.996886i \(-0.474871\pi\)
0.823897 0.566739i \(-0.191795\pi\)
\(284\) −8.29092e7 4.78677e7i −0.214777 0.124002i
\(285\) −3.39671e6 5.88328e6i −0.00869164 0.0150544i
\(286\) 3.20676e8 + 141608.i 0.810561 + 0.000357936i
\(287\) 2.05971e8 + 1.49983e8i 0.514304 + 0.374503i
\(288\) 1.71828e8i 0.423858i
\(289\) −5.17875e7 8.96986e7i −0.126207 0.218596i
\(290\) −4.06199e6 + 7.03558e6i −0.00978016 + 0.0169397i
\(291\) −5.05697e7 2.91964e7i −0.120300 0.0694551i
\(292\) 8.39750e7 4.84830e7i 0.197383 0.113959i
\(293\) 7.73202e8i 1.79579i 0.440207 + 0.897896i \(0.354905\pi\)
−0.440207 + 0.897896i \(0.645095\pi\)
\(294\) −1.51292e8 + 4.88010e7i −0.347216 + 0.111999i
\(295\) −6.45134e7 −0.146310
\(296\) −2.88131e8 4.99057e8i −0.645757 1.11848i
\(297\) −1.76175e8 1.01715e8i −0.390208 0.225287i
\(298\) −2.21569e8 + 3.83768e8i −0.485011 + 0.840064i
\(299\) −3.65436e8 6.33599e8i −0.790609 1.37077i
\(300\) −3.61856e7 −0.0773770
\(301\) 8.84878e6 1.21520e7i 0.0187025 0.0256842i
\(302\) 4.57196e8 0.955164
\(303\) 6.79290e7 + 1.17657e8i 0.140283 + 0.242978i
\(304\) −1.70569e8 9.84780e7i −0.348211 0.201040i
\(305\) −6.43781e7 3.71687e7i −0.129924 0.0750115i
\(306\) 4.83424e8 2.79105e8i 0.964502 0.556856i
\(307\) 9.42625e8i 1.85932i −0.368416 0.929661i \(-0.620100\pi\)
0.368416 0.929661i \(-0.379900\pi\)
\(308\) −9.54109e6 + 8.98551e7i −0.0186067 + 0.175233i
\(309\) 1.14045e7 0.0219898
\(310\) 1.13227e8 6.53716e7i 0.215866 0.124630i
\(311\) −1.69737e8 + 2.93993e8i −0.319974 + 0.554212i −0.980482 0.196607i \(-0.937008\pi\)
0.660508 + 0.750819i \(0.270341\pi\)
\(312\) −1.28394e8 7.42037e7i −0.239333 0.138320i
\(313\) −1.76932e8 3.06455e8i −0.326138 0.564887i 0.655604 0.755105i \(-0.272414\pi\)
−0.981742 + 0.190218i \(0.939081\pi\)
\(314\) 1.01019e9i 1.84140i
\(315\) −7.07706e7 + 3.14187e7i −0.127575 + 0.0566371i
\(316\) 7.76071e7 0.138356
\(317\) −2.40722e8 + 1.38981e8i −0.424431 + 0.245046i −0.696972 0.717099i \(-0.745470\pi\)
0.272540 + 0.962144i \(0.412136\pi\)
\(318\) −2.21037e8 1.27616e8i −0.385451 0.222540i
\(319\) 4.09903e7 + 2.36658e7i 0.0706991 + 0.0408181i
\(320\) −5.19396e7 + 2.99874e7i −0.0886082 + 0.0511580i
\(321\) 6.22841e7 0.105102
\(322\) 9.65765e8 4.28752e8i 1.61204 0.715667i
\(323\) 2.30245e8i 0.380173i
\(324\) 5.11850e7 + 8.86549e7i 0.0836055 + 0.144809i
\(325\) 3.02098e8 5.22716e8i 0.488153 0.844645i
\(326\) −3.51144e8 + 6.08198e8i −0.561336 + 0.972263i
\(327\) 7.38322e7 4.26271e7i 0.116769 0.0674168i
\(328\) −3.43370e8 −0.537284
\(329\) −1.03415e7 + 9.73931e7i −0.0160102 + 0.150780i
\(330\) 2.70775e7i 0.0414773i
\(331\) −1.30233e8 + 7.51900e7i −0.197389 + 0.113963i −0.595437 0.803402i \(-0.703021\pi\)
0.398048 + 0.917365i \(0.369688\pi\)
\(332\) 1.26746e8 + 7.31766e7i 0.190086 + 0.109746i
\(333\) 7.96825e8 + 4.60047e8i 1.18252 + 0.682727i
\(334\) −2.56342e8 4.43998e8i −0.376450 0.652031i
\(335\) 4.32291e7 0.0628230
\(336\) 1.58572e8 2.17766e8i 0.228054 0.313186i
\(337\) −2.39652e8 −0.341095 −0.170548 0.985349i \(-0.554554\pi\)
−0.170548 + 0.985349i \(0.554554\pi\)
\(338\) −6.85608e8 + 3.95029e8i −0.965757 + 0.556443i
\(339\) 1.29109e8 2.23624e8i 0.179994 0.311759i
\(340\) 2.66077e7 + 1.53620e7i 0.0367140 + 0.0211968i
\(341\) −3.80864e8 6.59677e8i −0.520152 0.900929i
\(342\) 2.50091e8 0.338070
\(343\) 7.10038e8 + 2.33220e8i 0.950063 + 0.312059i
\(344\) 2.02584e7i 0.0268318i
\(345\) −5.34867e7 + 3.08806e7i −0.0701260 + 0.0404873i
\(346\) −9.96697e8 5.75444e8i −1.29359 0.746855i
\(347\) 5.27556e8 9.13754e8i 0.677822 1.17402i −0.297814 0.954624i \(-0.596257\pi\)
0.975635 0.219398i \(-0.0704093\pi\)
\(348\) 3.50000e6 + 6.06218e6i 0.00445186 + 0.00771084i
\(349\) 1.01767e9i 1.28150i −0.767751 0.640748i \(-0.778624\pi\)
0.767751 0.640748i \(-0.221376\pi\)
\(350\) 7.05064e8 + 5.13409e8i 0.879004 + 0.640067i
\(351\) 5.01962e8 + 221662.i 0.619578 + 0.000273600i
\(352\) −1.41246e8 2.44645e8i −0.172614 0.298977i
\(353\) −8.20766e8 4.73869e8i −0.993134 0.573386i −0.0869242 0.996215i \(-0.527704\pi\)
−0.906210 + 0.422829i \(0.861037\pi\)
\(354\) −1.42495e8 + 2.46809e8i −0.170722 + 0.295699i
\(355\) −6.74364e7 1.16803e8i −0.0800009 0.138566i
\(356\) 3.79394e8i 0.445672i
\(357\) 3.13152e8 + 3.32515e7i 0.364265 + 0.0386787i
\(358\) 7.47755e8i 0.861328i
\(359\) 2.81593e8 1.62578e8i 0.321212 0.185452i −0.330721 0.943729i \(-0.607292\pi\)
0.651933 + 0.758277i \(0.273959\pi\)
\(360\) 5.21751e7 9.03699e7i 0.0589392 0.102086i
\(361\) −3.95358e8 + 6.84781e8i −0.442299 + 0.766084i
\(362\) −3.85901e8 + 2.22800e8i −0.427559 + 0.246852i
\(363\) 1.40541e8 0.154216
\(364\) −9.03803e7 2.03824e8i −0.0982243 0.221514i
\(365\) 1.36606e8 0.147044
\(366\) −2.84393e8 + 1.64194e8i −0.303204 + 0.175055i
\(367\) −5.62213e8 + 9.73781e8i −0.593703 + 1.02832i 0.400025 + 0.916504i \(0.369001\pi\)
−0.993728 + 0.111820i \(0.964332\pi\)
\(368\) −8.95294e8 + 1.55070e9i −0.936480 + 1.62203i
\(369\) 4.74794e8 2.74123e8i 0.491941 0.284022i
\(370\) 2.59635e8i 0.266475i
\(371\) 4.86884e8 + 1.09671e9i 0.495013 + 1.11502i
\(372\) 1.12654e8i 0.113461i
\(373\) −3.32163e8 5.75323e8i −0.331413 0.574025i 0.651376 0.758755i \(-0.274192\pi\)
−0.982789 + 0.184731i \(0.940859\pi\)
\(374\) 4.58860e8 7.94769e8i 0.453555 0.785580i
\(375\) −8.94036e7 5.16172e7i −0.0875478 0.0505458i
\(376\) −6.59947e7 1.14306e8i −0.0640253 0.110895i
\(377\) −1.16791e8 51573.7i −0.112257 4.95716e-5i
\(378\) −7.65691e7 + 7.21105e8i −0.0729176 + 0.686716i
\(379\) 8.10185e8i 0.764446i 0.924070 + 0.382223i \(0.124841\pi\)
−0.924070 + 0.382223i \(0.875159\pi\)
\(380\) 6.88251e6 + 1.19209e7i 0.00643435 + 0.0111446i
\(381\) −2.16693e8 + 3.75324e8i −0.200728 + 0.347671i
\(382\) 1.15993e9 + 6.69687e8i 1.06466 + 0.614682i
\(383\) −5.29009e8 + 3.05423e8i −0.481135 + 0.277783i −0.720889 0.693050i \(-0.756266\pi\)
0.239754 + 0.970834i \(0.422933\pi\)
\(384\) 4.37356e8i 0.394163i
\(385\) −7.49350e7 + 1.02908e8i −0.0669225 + 0.0919046i
\(386\) 1.66165e9 1.47056
\(387\) −1.61728e7 2.80122e7i −0.0141840 0.0245674i
\(388\) 1.02466e8 + 5.91586e7i 0.0890569 + 0.0514170i
\(389\) −1.06305e9 + 1.84125e9i −0.915648 + 1.58595i −0.109699 + 0.993965i \(0.534989\pi\)
−0.805949 + 0.591985i \(0.798345\pi\)
\(390\) 3.33814e7 + 5.78772e7i 0.0284956 + 0.0494062i
\(391\) −2.09323e9 −1.77092
\(392\) −9.58544e8 + 3.09190e8i −0.803731 + 0.259253i
\(393\) 4.42333e8 0.367600
\(394\) 3.92869e8 + 6.80468e8i 0.323602 + 0.560494i
\(395\) 9.46856e7 + 5.46668e7i 0.0773026 + 0.0446307i
\(396\) 1.68382e8 + 9.72156e7i 0.136258 + 0.0786689i
\(397\) 6.29870e7 3.63656e7i 0.0505224 0.0291691i −0.474526 0.880241i \(-0.657381\pi\)
0.525048 + 0.851072i \(0.324047\pi\)
\(398\) 1.43374e8i 0.113993i
\(399\) 1.14054e8 + 8.30512e7i 0.0898888 + 0.0654547i
\(400\) −1.47798e9 −1.15467
\(401\) −1.13184e9 + 6.53467e8i −0.876555 + 0.506079i −0.869521 0.493896i \(-0.835572\pi\)
−0.00703393 + 0.999975i \(0.502239\pi\)
\(402\) 9.54831e7 1.65382e8i 0.0733053 0.126969i
\(403\) 1.62734e9 + 9.40502e8i 1.23854 + 0.715801i
\(404\) −1.37640e8 2.38399e8i −0.103851 0.179874i
\(405\) 1.44220e8i 0.107878i
\(406\) 1.78152e7 1.67778e8i 0.0132114 0.124421i
\(407\) 1.51267e9 1.11215
\(408\) −3.67534e8 + 2.12196e8i −0.267909 + 0.154677i
\(409\) 1.34528e9 + 7.76697e8i 0.972257 + 0.561333i 0.899923 0.436048i \(-0.143622\pi\)
0.0723332 + 0.997381i \(0.476956\pi\)
\(410\) 1.33979e8 + 7.73528e7i 0.0960048 + 0.0554284i
\(411\) 6.42232e8 3.70793e8i 0.456295 0.263442i
\(412\) −2.31081e7 −0.0162788
\(413\) 1.22458e9 5.43654e8i 0.855386 0.379749i
\(414\) 2.27365e9i 1.57479i
\(415\) 1.03092e8 + 1.78560e8i 0.0708036 + 0.122636i
\(416\) 6.03509e8 + 3.48791e8i 0.411014 + 0.237541i
\(417\) −1.55559e8 + 2.69435e8i −0.105055 + 0.181961i
\(418\) 3.56074e8 2.05580e8i 0.238465 0.137678i
\(419\) 8.16415e8 0.542203 0.271101 0.962551i \(-0.412612\pi\)
0.271101 + 0.962551i \(0.412612\pi\)
\(420\) −1.72073e7 + 7.63921e6i −0.0113329 + 0.00503125i
\(421\) 1.09838e9i 0.717408i 0.933451 + 0.358704i \(0.116781\pi\)
−0.933451 + 0.358704i \(0.883219\pi\)
\(422\) −2.52854e9 + 1.45985e9i −1.63786 + 0.945616i
\(423\) 1.82508e8 + 1.05371e8i 0.117244 + 0.0676909i
\(424\) −1.40043e9 8.08538e8i −0.892238 0.515134i
\(425\) −8.63892e8 1.49630e9i −0.545881 0.945494i
\(426\) −5.95806e8 −0.373398
\(427\) 1.53523e9 + 1.63016e8i 0.954281 + 0.101328i
\(428\) −1.26202e8 −0.0778058
\(429\) 3.37201e8 1.94485e8i 0.206200 0.118928i
\(430\) 4.56370e6 7.90457e6i 0.00276807 0.00479445i
\(431\) 8.68498e8 + 5.01427e8i 0.522514 + 0.301674i 0.737963 0.674841i \(-0.235788\pi\)
−0.215448 + 0.976515i \(0.569121\pi\)
\(432\) −6.14417e8 1.06420e9i −0.366666 0.635084i
\(433\) 3.01110e7 0.0178245 0.00891227 0.999960i \(-0.497163\pi\)
0.00891227 + 0.999960i \(0.497163\pi\)
\(434\) −1.59836e9 + 2.19503e9i −0.938559 + 1.28892i
\(435\) 9.86167e6i 0.00574431i
\(436\) −1.49601e8 + 8.63721e7i −0.0864433 + 0.0499081i
\(437\) −8.12171e8 4.68907e8i −0.465546 0.268783i
\(438\) 3.01733e8 5.22616e8i 0.171578 0.297183i
\(439\) 7.26446e8 + 1.25824e9i 0.409805 + 0.709804i 0.994868 0.101185i \(-0.0322633\pi\)
−0.585062 + 0.810988i \(0.698930\pi\)
\(440\) 1.71556e8i 0.0960111i
\(441\) 1.07859e9 1.19277e9i 0.598854 0.662247i
\(442\) −999971. + 2.26448e9i −0.000550820 + 1.24735i
\(443\) 8.55542e8 + 1.48184e9i 0.467550 + 0.809821i 0.999313 0.0370726i \(-0.0118033\pi\)
−0.531762 + 0.846894i \(0.678470\pi\)
\(444\) 1.93742e8 + 1.11857e8i 0.105047 + 0.0606488i
\(445\) −2.67247e8 + 4.62885e8i −0.143765 + 0.249008i
\(446\) −1.24836e9 2.16222e9i −0.666295 1.15406i
\(447\) 5.37923e8i 0.284868i
\(448\) 7.33204e8 1.00691e9i 0.385258 0.529075i
\(449\) 2.48167e9i 1.29385i 0.762555 + 0.646923i \(0.223945\pi\)
−0.762555 + 0.646923i \(0.776055\pi\)
\(450\) 1.62528e9 9.38354e8i 0.840782 0.485426i
\(451\) 4.50669e8 7.80581e8i 0.231334 0.400682i
\(452\) −2.61604e8 + 4.53112e8i −0.133248 + 0.230792i
\(453\) 4.80633e8 2.77494e8i 0.242924 0.140252i
\(454\) −5.70692e8 −0.286224
\(455\) 3.33050e7 3.12343e8i 0.0165756 0.155450i
\(456\) −1.90137e8 −0.0939052
\(457\) 2.18209e9 1.25983e9i 1.06946 0.617454i 0.141428 0.989949i \(-0.454831\pi\)
0.928035 + 0.372494i \(0.121497\pi\)
\(458\) 1.24328e9 2.15343e9i 0.604701 1.04737i
\(459\) 7.18264e8 1.24407e9i 0.346689 0.600483i
\(460\) 1.08376e8 6.25711e7i 0.0519137 0.0299724i
\(461\) 1.13365e9i 0.538924i 0.963011 + 0.269462i \(0.0868459\pi\)
−0.963011 + 0.269462i \(0.913154\pi\)
\(462\) 2.28182e8 + 5.13980e8i 0.107655 + 0.242493i
\(463\) 2.20815e9i 1.03394i −0.856004 0.516969i \(-0.827060\pi\)
0.856004 0.516969i \(-0.172940\pi\)
\(464\) 1.42955e8 + 2.47606e8i 0.0664336 + 0.115066i
\(465\) 7.93542e7 1.37446e8i 0.0366003 0.0633936i
\(466\) −2.68289e9 1.54897e9i −1.22815 0.709073i
\(467\) 6.36565e8 + 1.10256e9i 0.289224 + 0.500950i 0.973625 0.228156i \(-0.0732696\pi\)
−0.684401 + 0.729106i \(0.739936\pi\)
\(468\) −4.79759e8 211857.i −0.216353 9.55395e-5i
\(469\) −8.20565e8 + 3.64291e8i −0.367289 + 0.163058i
\(470\) 5.94679e7i 0.0264204i
\(471\) −6.13131e8 1.06197e9i −0.270383 0.468318i
\(472\) −9.02813e8 + 1.56372e9i −0.395185 + 0.684481i
\(473\) −4.60532e7 2.65888e7i −0.0200099 0.0115527i
\(474\) 4.18278e8 2.41493e8i 0.180402 0.104155i
\(475\) 7.74086e8i 0.331407i
\(476\) −6.34518e8 6.73750e7i −0.269662 0.0286335i
\(477\) 2.58192e9 1.08925
\(478\) −1.71290e9 2.96682e9i −0.717354 1.24249i
\(479\) −9.73135e8 5.61840e8i −0.404575 0.233581i 0.283881 0.958859i \(-0.408378\pi\)
−0.688456 + 0.725278i \(0.741711\pi\)
\(480\) 2.94290e7 5.09726e7i 0.0121460 0.0210374i
\(481\) −3.23328e9 + 1.86483e9i −1.32476 + 0.764068i
\(482\) 2.54822e9 1.03651
\(483\) 7.55044e8 1.03690e9i 0.304900 0.418719i
\(484\) −2.84767e8 −0.114165
\(485\) 8.33431e7 + 1.44354e8i 0.0331721 + 0.0574558i
\(486\) 2.06520e9 + 1.19234e9i 0.816083 + 0.471166i
\(487\) −1.24563e9 7.19164e8i −0.488694 0.282148i 0.235339 0.971913i \(-0.424380\pi\)
−0.724032 + 0.689766i \(0.757713\pi\)
\(488\) −1.80184e9 + 1.04029e9i −0.701853 + 0.405215i
\(489\) 8.52503e8i 0.329697i
\(490\) 4.43665e8 + 9.52938e7i 0.170361 + 0.0365914i
\(491\) −1.09759e9 −0.418462 −0.209231 0.977866i \(-0.567096\pi\)
−0.209231 + 0.977866i \(0.567096\pi\)
\(492\) 1.15443e8 6.66508e7i 0.0437007 0.0252306i
\(493\) −1.67117e8 + 2.89456e8i −0.0628141 + 0.108797i
\(494\) −5.07656e8 + 8.78390e8i −0.189463 + 0.327826i
\(495\) 1.36958e8 + 2.37218e8i 0.0507539 + 0.0879084i
\(496\) 4.60130e9i 1.69315i
\(497\) 2.26436e9 + 1.64885e9i 0.827368 + 0.602468i
\(498\) 9.10825e8 0.330470
\(499\) −1.00950e9 + 5.82836e8i −0.363710 + 0.209988i −0.670707 0.741723i \(-0.734009\pi\)
0.306997 + 0.951710i \(0.400676\pi\)
\(500\) 1.81152e8 + 1.04588e8i 0.0648109 + 0.0374186i
\(501\) −5.38967e8 3.11173e8i −0.191483 0.110553i
\(502\) 3.61604e9 2.08772e9i 1.27576 0.736562i
\(503\) −1.44654e9 −0.506807 −0.253403 0.967361i \(-0.581550\pi\)
−0.253403 + 0.967361i \(0.581550\pi\)
\(504\) −2.28831e8 + 2.15506e9i −0.0796174 + 0.749813i
\(505\) 3.87816e8i 0.134000i
\(506\) −1.86899e9 3.23718e9i −0.641327 1.11081i
\(507\) −4.80993e8 + 8.31408e8i −0.163912 + 0.283326i
\(508\) 4.39070e8 7.60491e8i 0.148597 0.257378i
\(509\) −8.70176e8 + 5.02397e8i −0.292479 + 0.168863i −0.639059 0.769157i \(-0.720676\pi\)
0.346580 + 0.938020i \(0.387343\pi\)
\(510\) 1.91210e8 0.0638284
\(511\) −2.59304e9 + 1.15118e9i −0.859677 + 0.381654i
\(512\) 1.32924e9i 0.437683i
\(513\) 5.57372e8 3.21799e8i 0.182278 0.105238i
\(514\) −1.26371e9 7.29601e8i −0.410464 0.236982i
\(515\) −2.81933e7 1.62774e7i −0.00909538 0.00525122i
\(516\) −3.93230e6 6.81095e6i −0.00126001 0.00218240i
\(517\) 3.46469e8 0.110267
\(518\) −2.18794e9 4.92834e9i −0.691642 1.55792i
\(519\) −1.39706e9 −0.438660
\(520\) 2.11495e8 + 3.66695e8i 0.0659613 + 0.114365i
\(521\) 4.91213e8 8.50805e8i 0.152173 0.263571i −0.779853 0.625963i \(-0.784706\pi\)
0.932026 + 0.362391i \(0.118040\pi\)
\(522\) −3.14405e8 1.81522e8i −0.0967482 0.0558576i
\(523\) 1.26338e9 + 2.18824e9i 0.386170 + 0.668867i 0.991931 0.126780i \(-0.0404643\pi\)
−0.605760 + 0.795647i \(0.707131\pi\)
\(524\) −8.96267e8 −0.272131
\(525\) 1.05282e9 + 1.11792e8i 0.317539 + 0.0337173i
\(526\) 2.61815e9i 0.784412i
\(527\) 4.65835e9 2.68950e9i 1.38642 0.800450i
\(528\) −8.25280e8 4.76475e8i −0.243996 0.140871i
\(529\) −2.56056e9 + 4.43503e9i −0.752040 + 1.30257i
\(530\) 3.64287e8 + 6.30964e8i 0.106287 + 0.184094i
\(531\) 2.88297e9i 0.835620i
\(532\) −2.31099e8 1.68281e8i −0.0665439 0.0484555i
\(533\) −982120. + 2.22405e9i −0.000280944 + 0.636209i
\(534\) 1.18057e9 + 2.04481e9i 0.335505 + 0.581111i
\(535\) −1.53974e8 8.88969e7i −0.0434720 0.0250985i
\(536\) 6.04955e8 1.04781e9i 0.169686 0.293905i
\(537\) −4.53848e8 7.86088e8i −0.126474 0.219059i
\(538\) 5.06587e9i 1.40254i
\(539\) 5.55196e8 2.58486e9i 0.152716 0.711011i
\(540\) 8.58818e7i 0.0234705i
\(541\) 2.58688e9 1.49354e9i 0.702404 0.405533i −0.105838 0.994383i \(-0.533753\pi\)
0.808242 + 0.588850i \(0.200419\pi\)
\(542\) −3.13174e9 + 5.42433e9i −0.844866 + 1.46335i
\(543\) −2.70456e8 + 4.68444e8i −0.0724932 + 0.125562i
\(544\) 1.72758e9 9.97418e8i 0.460089 0.265632i
\(545\) −2.43363e8 −0.0643973
\(546\) −1.12137e9 8.17310e8i −0.294832 0.214888i
\(547\) 1.08999e9 0.284751 0.142376 0.989813i \(-0.454526\pi\)
0.142376 + 0.989813i \(0.454526\pi\)
\(548\) −1.30131e9 + 7.51310e8i −0.337791 + 0.195024i
\(549\) 1.66099e9 2.87692e9i 0.428414 0.742035i
\(550\) 1.54269e9 2.67202e9i 0.395376 0.684811i
\(551\) −1.29683e8 + 7.48724e7i −0.0330257 + 0.0190674i
\(552\) 1.72859e9i 0.437428i
\(553\) −2.25798e9 2.39759e8i −0.567782 0.0602889i
\(554\) 7.50074e9i 1.87422i
\(555\) 1.57585e8 + 2.72945e8i 0.0391281 + 0.0677719i
\(556\) 3.15197e8 5.45937e8i 0.0777715 0.134704i
\(557\) −5.06486e9 2.92420e9i −1.24186 0.716990i −0.272390 0.962187i \(-0.587814\pi\)
−0.969473 + 0.245196i \(0.921148\pi\)
\(558\) 2.92132e9 + 5.05987e9i 0.711802 + 1.23288i
\(559\) 1.31216e8 + 57943.7i 0.0317720 + 1.40302e-5i
\(560\) −7.02822e8 + 3.12019e8i −0.169117 + 0.0750797i
\(561\) 1.11402e9i 0.266392i
\(562\) 1.57275e9 + 2.72408e9i 0.373751 + 0.647355i
\(563\) 4.95410e8 8.58075e8i 0.117000 0.202650i −0.801578 0.597891i \(-0.796006\pi\)
0.918577 + 0.395241i \(0.129339\pi\)
\(564\) 4.43754e7 + 2.56202e7i 0.0104151 + 0.00601319i
\(565\) −6.38348e8 + 3.68550e8i −0.148898 + 0.0859661i
\(566\) 8.68111e9i 2.01242i
\(567\) −1.21534e9 2.73755e9i −0.279999 0.630697i
\(568\) −3.77487e9 −0.864336
\(569\) 3.87928e9 + 6.71910e9i 0.882791 + 1.52904i 0.848225 + 0.529636i \(0.177671\pi\)
0.0345653 + 0.999402i \(0.488995\pi\)
\(570\) 7.41892e7 + 4.28331e7i 0.0167795 + 0.00968764i
\(571\) 2.42170e9 4.19451e9i 0.544370 0.942877i −0.454276 0.890861i \(-0.650102\pi\)
0.998646 0.0520161i \(-0.0165647\pi\)
\(572\) −6.83246e8 + 3.94070e8i −0.152648 + 0.0880415i
\(573\) 1.62586e9 0.361029
\(574\) −3.19501e9 3.39256e8i −0.705149 0.0748748i
\(575\) −7.03746e9 −1.54375
\(576\) −1.34007e9 2.32107e9i −0.292179 0.506069i
\(577\) 1.37973e9 + 7.96587e8i 0.299005 + 0.172631i 0.641996 0.766708i \(-0.278107\pi\)
−0.342991 + 0.939339i \(0.611440\pi\)
\(578\) 1.13111e9 + 6.53049e8i 0.243646 + 0.140669i
\(579\) 1.74683e9 1.00853e9i 0.374004 0.215931i
\(580\) 1.99820e7i 0.00425246i
\(581\) −3.46159e9 2.52064e9i −0.732250 0.533205i
\(582\) 7.36344e8 0.154828
\(583\) 3.67609e9 2.12239e9i 0.768327 0.443594i
\(584\) 1.91170e9 3.31115e9i 0.397168 0.687915i
\(585\) −5.85188e8 3.38203e8i −0.120851 0.0698444i
\(586\) −4.87510e9 8.44392e9i −1.00079 1.73342i
\(587\) 1.16683e9i 0.238108i −0.992888 0.119054i \(-0.962014\pi\)
0.992888 0.119054i \(-0.0379861\pi\)
\(588\) 2.62250e8 2.90012e8i 0.0531980 0.0588295i
\(589\) 2.40991e9 0.485957
\(590\) 7.04533e8 4.06762e8i 0.141228 0.0815378i
\(591\) 8.26017e8 + 4.76901e8i 0.164601 + 0.0950325i
\(592\) 7.91326e9 + 4.56872e9i 1.56758 + 0.905042i
\(593\) −8.38389e9 + 4.84044e9i −1.65103 + 0.953221i −0.674377 + 0.738387i \(0.735588\pi\)
−0.976651 + 0.214834i \(0.931079\pi\)
\(594\) 2.56528e9 0.502206
\(595\) −7.26693e8 5.29159e8i −0.141430 0.102986i
\(596\) 1.08995e9i 0.210885i
\(597\) −8.70203e7 1.50724e8i −0.0167383 0.0289915i
\(598\) 7.98572e9 + 4.61526e9i 1.52707 + 0.882555i
\(599\) 3.74133e9 6.48017e9i 0.711265 1.23195i −0.253117 0.967436i \(-0.581456\pi\)
0.964382 0.264512i \(-0.0852109\pi\)
\(600\) −1.23565e9 + 7.13404e8i −0.233543 + 0.134836i
\(601\) −5.10218e9 −0.958727 −0.479364 0.877616i \(-0.659132\pi\)
−0.479364 + 0.877616i \(0.659132\pi\)
\(602\) −2.00156e7 + 1.88501e8i −0.00373922 + 0.0352149i
\(603\) 1.93182e9i 0.358802i
\(604\) −9.73872e8 + 5.62265e8i −0.179834 + 0.103827i
\(605\) −3.47434e8 2.00591e8i −0.0637865 0.0368271i
\(606\) −1.48367e9 8.56596e8i −0.270821 0.156359i
\(607\) 2.57962e9 + 4.46803e9i 0.468161 + 0.810878i 0.999338 0.0363825i \(-0.0115835\pi\)
−0.531177 + 0.847261i \(0.678250\pi\)
\(608\) 8.93731e8 0.161267
\(609\) −8.31042e7 1.87192e8i −0.0149095 0.0335836i
\(610\) 9.37407e8 0.167214
\(611\) −7.40564e8 + 4.27129e8i −0.131346 + 0.0757556i
\(612\) −6.86494e8 + 1.18904e9i −0.121062 + 0.209685i
\(613\) −6.19438e9 3.57633e9i −1.08614 0.627084i −0.153595 0.988134i \(-0.549085\pi\)
−0.932546 + 0.361050i \(0.882418\pi\)
\(614\) 5.94333e9 + 1.02941e10i 1.03619 + 1.79474i
\(615\) 1.87796e8 0.0325555
\(616\) 1.44570e9 + 3.25644e9i 0.249199 + 0.561320i
\(617\) 9.95232e9i 1.70579i 0.522080 + 0.852896i \(0.325156\pi\)
−0.522080 + 0.852896i \(0.674844\pi\)
\(618\) −1.24545e8 + 7.19062e7i −0.0212260 + 0.0122548i
\(619\) −8.62071e9 4.97717e9i −1.46092 0.843461i −0.461864 0.886951i \(-0.652819\pi\)
−0.999054 + 0.0434897i \(0.986152\pi\)
\(620\) −1.60790e8 + 2.78496e8i −0.0270949 + 0.0469297i
\(621\) −2.92557e9 5.06724e9i −0.490219 0.849084i
\(622\) 4.28082e9i 0.713281i
\(623\) 1.17210e9 1.10385e10i 0.194203 1.82894i
\(624\) 2.35141e9 + 1.03836e6i 0.387420 + 0.000171081i
\(625\) −2.82983e9 4.90141e9i −0.463639 0.803047i
\(626\) 3.86445e9 + 2.23114e9i 0.629618 + 0.363510i
\(627\) 2.49552e8 4.32237e8i 0.0404320 0.0700302i
\(628\) 1.24234e9 + 2.15180e9i 0.200162 + 0.346692i
\(629\) 1.06818e10i 1.71147i
\(630\) 5.74769e8 7.89329e8i 0.0915801 0.125767i
\(631\) 7.78301e9i 1.23323i 0.787264 + 0.616616i \(0.211497\pi\)
−0.787264 + 0.616616i \(0.788503\pi\)
\(632\) 2.65010e9 1.53003e9i 0.417592 0.241097i
\(633\) −1.77211e9 + 3.06938e9i −0.277701 + 0.480992i
\(634\) 1.75257e9 3.03554e9i 0.273126 0.473068i
\(635\) 1.07139e9 6.18565e8i 0.166050 0.0958688i
\(636\) 6.27774e8 0.0967616
\(637\) 1.99992e9 + 6.20949e9i 0.306567 + 0.951849i
\(638\) −5.96859e8 −0.0909911
\(639\) 5.21969e9 3.01359e9i 0.791392 0.456910i
\(640\) 6.24230e8 1.08120e9i 0.0941271 0.163033i
\(641\) 6.07373e9 1.05200e10i 0.910862 1.57766i 0.0980120 0.995185i \(-0.468752\pi\)
0.812850 0.582473i \(-0.197915\pi\)
\(642\) −6.80187e8 + 3.92706e8i −0.101451 + 0.0585727i
\(643\) 5.36936e7i 0.00796497i −0.999992 0.00398248i \(-0.998732\pi\)
0.999992 0.00398248i \(-0.00126767\pi\)
\(644\) −1.52989e9 + 2.10100e9i −0.225715 + 0.309974i
\(645\) 1.10797e7i 0.00162581i
\(646\) 1.45171e9 + 2.51444e9i 0.211869 + 0.366968i
\(647\) −2.93127e9 + 5.07710e9i −0.425491 + 0.736972i −0.996466 0.0839953i \(-0.973232\pi\)
0.570975 + 0.820967i \(0.306565\pi\)
\(648\) 3.49569e9 + 2.01824e9i 0.504684 + 0.291380i
\(649\) −2.36986e9 4.10471e9i −0.340303 0.589422i
\(650\) −3.36191e6 + 7.61319e9i −0.000480164 + 1.08735i
\(651\) −3.48034e8 + 3.27768e9i −0.0494411 + 0.465622i
\(652\) 1.72736e9i 0.244072i
\(653\) −5.89937e8 1.02180e9i −0.0829104 0.143605i 0.821588 0.570081i \(-0.193088\pi\)
−0.904499 + 0.426476i \(0.859755\pi\)
\(654\) −5.37534e8 + 9.31037e8i −0.0751422 + 0.130150i
\(655\) −1.09350e9 6.31334e8i −0.152046 0.0877839i
\(656\) 4.71518e9 2.72231e9i 0.652131 0.376508i
\(657\) 6.10465e9i 0.839812i
\(658\) −5.01135e8 1.12881e9i −0.0685747 0.154465i
\(659\) −5.52309e9 −0.751767 −0.375884 0.926667i \(-0.622661\pi\)
−0.375884 + 0.926667i \(0.622661\pi\)
\(660\) 3.33003e7 + 5.76778e7i 0.00450863 + 0.00780917i
\(661\) −2.52374e9 1.45708e9i −0.339890 0.196236i 0.320333 0.947305i \(-0.396205\pi\)
−0.660224 + 0.751069i \(0.729538\pi\)
\(662\) 9.48159e8 1.64226e9i 0.127022 0.220008i
\(663\) 1.37337e9 + 2.38117e9i 0.183016 + 0.317317i
\(664\) 5.77074e9 0.764968
\(665\) −1.63418e8 3.68100e8i −0.0215489 0.0485390i
\(666\) −1.16025e10 −1.52192
\(667\) 6.80688e8 + 1.17899e9i 0.0888193 + 0.153840i
\(668\) 1.09207e9 + 6.30506e8i 0.141753 + 0.0818412i
\(669\) −2.62470e9 1.51537e9i −0.338914 0.195672i
\(670\) −4.72093e8 + 2.72563e8i −0.0606409 + 0.0350110i
\(671\) 5.46147e9i 0.697880i
\(672\) −1.29071e8 + 1.21555e9i −0.0164072 + 0.154518i
\(673\) 2.43818e9 0.308328 0.154164 0.988045i \(-0.450732\pi\)
0.154164 + 0.988045i \(0.450732\pi\)
\(674\) 2.61717e9 1.51102e9i 0.329247 0.190091i
\(675\) 2.41481e9 4.18258e9i 0.302218 0.523457i
\(676\) 9.74602e8 1.68462e9i 0.121343 0.209744i
\(677\) 3.75287e9 + 6.50017e9i 0.464840 + 0.805127i 0.999194 0.0401340i \(-0.0127785\pi\)
−0.534354 + 0.845261i \(0.679445\pi\)
\(678\) 3.25618e9i 0.401240i
\(679\) −2.79848e9 2.03778e9i −0.343066 0.249811i
\(680\) 1.21145e9 0.147749
\(681\) −5.99948e8 + 3.46380e8i −0.0727945 + 0.0420279i
\(682\) 8.31863e9 + 4.80276e9i 1.00417 + 0.579757i
\(683\) −1.98351e9 1.14518e9i −0.238211 0.137531i 0.376143 0.926561i \(-0.377250\pi\)
−0.614354 + 0.789031i \(0.710583\pi\)
\(684\) −5.32718e8 + 3.07565e8i −0.0636504 + 0.0367486i
\(685\) −2.11690e9 −0.251643
\(686\) −9.22461e9 + 1.92991e9i −1.09097 + 0.228246i
\(687\) 3.01843e9i 0.355167i
\(688\) −1.60612e8 2.78189e8i −0.0188027 0.0325672i
\(689\) −5.24101e9 + 9.06844e9i −0.610446 + 1.05625i
\(690\) 3.89409e8 6.74477e8i 0.0451268 0.0781619i
\(691\) 5.89032e9 3.40078e9i 0.679150 0.392107i −0.120385 0.992727i \(-0.538413\pi\)
0.799535 + 0.600620i \(0.205079\pi\)
\(692\) 2.83075e9 0.324736
\(693\) −4.59875e9 3.34869e9i −0.524896 0.382216i
\(694\) 1.33051e10i 1.51099i
\(695\) 7.69121e8 4.44052e8i 0.0869056 0.0501750i
\(696\) 2.39033e8 + 1.38006e8i 0.0268736 + 0.0155155i
\(697\) 5.51212e9 + 3.18242e9i 0.616601 + 0.355995i
\(698\) 6.41648e9 + 1.11137e10i 0.714172 + 1.23698i
\(699\) −3.76056e9 −0.416469
\(700\) −2.13326e9 2.26515e8i −0.235071 0.0249606i
\(701\) −6.23320e9 −0.683437 −0.341718 0.939802i \(-0.611009\pi\)
−0.341718 + 0.939802i \(0.611009\pi\)
\(702\) −5.48319e9 + 3.16249e9i −0.598209 + 0.345024i
\(703\) −2.39285e9 + 4.14454e9i −0.259760 + 0.449917i
\(704\) −3.81594e9 2.20313e9i −0.412189 0.237978i
\(705\) 3.60939e7 + 6.25164e7i 0.00387946 + 0.00671943i
\(706\) 1.19511e10 1.27818
\(707\) 3.26812e9 + 7.36144e9i 0.347800 + 0.783420i
\(708\) 7.00971e8i 0.0742307i
\(709\) −8.14030e9 + 4.69980e9i −0.857785 + 0.495243i −0.863270 0.504742i \(-0.831587\pi\)
0.00548479 + 0.999985i \(0.498254\pi\)
\(710\) 1.47291e9 + 8.50384e8i 0.154444 + 0.0891683i
\(711\) −2.44294e9 + 4.23130e9i −0.254900 + 0.441499i
\(712\) 7.47980e9 + 1.29554e10i 0.776622 + 1.34515i
\(713\) 2.19093e10i 2.26368i
\(714\) −3.62950e9 + 1.61132e9i −0.373167 + 0.165668i
\(715\) −1.11119e9 490690.i −0.113689 5.02038e-5i
\(716\) 9.19599e8 + 1.59279e9i 0.0936274 + 0.162167i
\(717\) −3.60141e9 2.07928e9i −0.364885 0.210666i
\(718\) −2.05013e9 + 3.55094e9i −0.206703 + 0.358020i
\(719\) −2.52038e9 4.36543e9i −0.252881 0.438002i 0.711437 0.702750i \(-0.248045\pi\)
−0.964318 + 0.264748i \(0.914711\pi\)
\(720\) 1.65462e9i 0.165209i
\(721\) 6.72329e8 + 7.13900e7i 0.0668050 + 0.00709355i
\(722\) 9.97107e9i 0.985965i
\(723\) 2.67885e9 1.54663e9i 0.263611 0.152196i
\(724\) 5.48006e8 9.49174e8i 0.0536661 0.0929524i
\(725\) −5.61850e8 + 9.73153e8i −0.0547567 + 0.0948415i
\(726\) −1.53481e9 + 8.86121e8i −0.148859 + 0.0859438i
\(727\) 1.94139e10 1.87388 0.936940 0.349492i \(-0.113646\pi\)
0.936940 + 0.349492i \(0.113646\pi\)
\(728\) −7.10469e9 5.17825e9i −0.682473 0.497420i
\(729\) −4.32348e9 −0.413321
\(730\) −1.49184e9 + 8.61315e8i −0.141936 + 0.0819468i
\(731\) 1.87759e8 3.25207e8i 0.0177782 0.0307928i
\(732\) 4.03857e8 6.99501e8i 0.0380574 0.0659173i
\(733\) −6.06070e9 + 3.49915e9i −0.568406 + 0.328169i −0.756513 0.653979i \(-0.773098\pi\)
0.188106 + 0.982149i \(0.439765\pi\)
\(734\) 1.41792e10i 1.32347i
\(735\) 5.24248e8 1.69103e8i 0.0487002 0.0157089i
\(736\) 8.12519e9i 0.751210i
\(737\) 1.58799e9 + 2.75048e9i 0.146121 + 0.253089i
\(738\) −3.45673e9 + 5.98723e9i −0.316569 + 0.548314i
\(739\) −1.17667e10 6.79349e9i −1.07250 0.619209i −0.143638 0.989630i \(-0.545880\pi\)
−0.928864 + 0.370421i \(0.879213\pi\)
\(740\) −3.19303e8 5.53048e8i −0.0289662 0.0501709i
\(741\) −543837. + 1.23154e9i −4.91026e−5 + 0.111195i
\(742\) −1.22319e10 8.90699e9i −1.09921 0.800418i
\(743\) 9.77797e8i 0.0874556i −0.999043 0.0437278i \(-0.986077\pi\)
0.999043 0.0437278i \(-0.0139234\pi\)
\(744\) −2.22100e9 3.84688e9i −0.197716 0.342455i
\(745\) 7.67767e8 1.32981e9i 0.0680272 0.117827i
\(746\) 7.25491e9 + 4.18863e9i 0.639803 + 0.369390i
\(747\) −7.97948e9 + 4.60695e9i −0.700410 + 0.404382i
\(748\) 2.25725e9i 0.197208i
\(749\) 3.67184e9 + 3.89887e8i 0.319299 + 0.0339041i
\(750\) 1.30180e9 0.112676
\(751\) 3.58506e9 + 6.20951e9i 0.308857 + 0.534955i 0.978113 0.208077i \(-0.0667203\pi\)
−0.669256 + 0.743032i \(0.733387\pi\)
\(752\) 1.81249e9 + 1.04644e9i 0.155422 + 0.0897329i
\(753\) 2.53427e9 4.38949e9i 0.216307 0.374655i
\(754\) 1.27576e9 7.35812e8i 0.108385 0.0625125i
\(755\) −1.58425e9 −0.133970
\(756\) −7.23725e8 1.63019e9i −0.0609182 0.137218i
\(757\) 6.04751e9 0.506689 0.253344 0.967376i \(-0.418469\pi\)
0.253344 + 0.967376i \(0.418469\pi\)
\(758\) −5.10828e9 8.84781e9i −0.426023 0.737893i
\(759\) −3.92960e9 2.26876e9i −0.326214 0.188340i
\(760\) 4.70042e8 + 2.71379e8i 0.0388409 + 0.0224248i
\(761\) −1.14870e10 + 6.63200e9i −0.944841 + 0.545504i −0.891475 0.453071i \(-0.850329\pi\)
−0.0533665 + 0.998575i \(0.516995\pi\)
\(762\) 5.46508e9i 0.447460i
\(763\) 4.61948e9 2.05082e9i 0.376493 0.167144i
\(764\) −3.29436e9 −0.267266
\(765\) −1.67513e9 + 9.67139e8i −0.135280 + 0.0781041i
\(766\) 3.85144e9 6.67089e9i 0.309615 0.536269i
\(767\) 1.01258e10 + 5.85210e9i 0.810300 + 0.468304i
\(768\) −1.41292e9 2.44724e9i −0.112552 0.194945i
\(769\) 5.10110e9i 0.404503i 0.979334 + 0.202252i \(0.0648259\pi\)
−0.979334 + 0.202252i \(0.935174\pi\)
\(770\) 1.69500e8 1.59630e9i 0.0133799 0.126008i
\(771\) −1.77132e9 −0.139189
\(772\) −3.53948e9 + 2.04352e9i −0.276872 + 0.159852i
\(773\) −1.65814e10 9.57329e9i −1.29120 0.745475i −0.312333 0.949973i \(-0.601111\pi\)
−0.978867 + 0.204498i \(0.934444\pi\)
\(774\) 3.53238e8 + 2.03942e8i 0.0273826 + 0.0158093i
\(775\) 1.56614e10 9.04212e9i 1.20858 0.697773i
\(776\) 4.66528e9 0.358394
\(777\) −5.29135e9 3.85302e9i −0.404662 0.294664i
\(778\) 2.68104e10i 2.04115i
\(779\) 1.42580e9 + 2.46956e9i 0.108063 + 0.187171i
\(780\) −1.42284e8 8.22314e7i −0.0107356 0.00620450i
\(781\) 4.95446e9 8.58138e9i 0.372150 0.644582i
\(782\) 2.28596e10 1.31980e10i 1.70940 0.986924i
\(783\) −9.34277e8 −0.0695520
\(784\) 1.07115e10 1.18453e10i 0.793857 0.877893i
\(785\) 3.50044e9i 0.258273i
\(786\) −4.83060e9 + 2.78895e9i −0.354831 + 0.204862i
\(787\) 1.44967e10 + 8.36965e9i 1.06012 + 0.612063i 0.925466 0.378830i \(-0.123673\pi\)
0.134657 + 0.990892i \(0.457007\pi\)
\(788\) −1.67370e9 9.66310e8i −0.121853 0.0703517i
\(789\) −1.58908e9 2.75237e9i −0.115180 0.199497i
\(790\) −1.37871e9 −0.0994900
\(791\) 9.01122e9 1.23751e10i 0.647390 0.889060i
\(792\) 7.66647e9 0.548349
\(793\) 6.73294e9 + 1.16737e10i 0.479456 + 0.831290i
\(794\) −4.58576e8 + 7.94277e8i −0.0325117 + 0.0563119i
\(795\) 7.65924e8 + 4.42206e8i 0.0540631 + 0.0312133i
\(796\) 1.76323e8 + 3.05400e8i 0.0123912 + 0.0214622i
\(797\) −6.05642e9 −0.423752 −0.211876 0.977297i \(-0.567957\pi\)
−0.211876 + 0.977297i \(0.567957\pi\)
\(798\) −1.76920e9 1.87859e8i −0.123244 0.0130864i
\(799\) 2.44661e9i 0.169688i
\(800\) 5.80814e9 3.35333e9i 0.401072 0.231559i
\(801\) −2.06853e10 1.19427e10i −1.42216 0.821085i
\(802\) 8.24033e9 1.42727e10i 0.564072 0.977001i
\(803\) 5.01815e9 + 8.69169e9i 0.342010 + 0.592379i
\(804\) 4.69706e8i 0.0318735i
\(805\) −3.34651e9 + 1.48569e9i −0.226103 + 0.100379i
\(806\) −2.37017e10 1.04664e7i −1.59443 0.000704086i
\(807\) 3.07472e9 + 5.32557e9i 0.205943 + 0.356705i
\(808\) −9.40012e9 5.42716e9i −0.626893 0.361937i
\(809\) 1.18225e10 2.04771e10i 0.785034 1.35972i −0.143944 0.989586i \(-0.545979\pi\)
0.928979 0.370134i \(-0.120688\pi\)
\(810\) −9.09316e8 1.57498e9i −0.0601198 0.104131i
\(811\) 2.73707e10i 1.80183i −0.433999 0.900913i \(-0.642898\pi\)
0.433999 0.900913i \(-0.357102\pi\)
\(812\) 1.68388e8 + 3.79294e8i 0.0110373 + 0.0248616i
\(813\) 7.60320e9i 0.496226i
\(814\) −1.65195e10 + 9.53752e9i −1.07352 + 0.619798i
\(815\) 1.21676e9 2.10749e9i 0.0787325 0.136369i
\(816\) 3.36466e9 5.82777e9i 0.216783 0.375480i
\(817\) 1.45700e8 8.41201e7i 0.00934723 0.00539663i
\(818\) −1.95886e10 −1.25131
\(819\) 1.39579e10 + 1.48833e9i 0.887826 + 0.0946686i
\(820\) −3.80518e8 −0.0241005
\(821\) −1.73274e10 + 1.00040e10i −1.09278 + 0.630916i −0.934315 0.356448i \(-0.883988\pi\)
−0.158464 + 0.987365i \(0.550654\pi\)
\(822\) −4.67576e9 + 8.09865e9i −0.293630 + 0.508582i
\(823\) −1.58918e8 + 2.75254e8i −0.00993742 + 0.0172121i −0.870951 0.491369i \(-0.836497\pi\)
0.861014 + 0.508581i \(0.169830\pi\)
\(824\) −7.89085e8 + 4.55578e8i −0.0491336 + 0.0283673i
\(825\) 3.74533e9i 0.232221i
\(826\) −9.94553e9 + 1.36582e10i −0.614041 + 0.843262i
\(827\) 1.40953e10i 0.866575i −0.901256 0.433287i \(-0.857354\pi\)
0.901256 0.433287i \(-0.142646\pi\)
\(828\) 2.79617e9 + 4.84311e9i 0.171182 + 0.296495i
\(829\) −7.81842e7 + 1.35419e8i −0.00476627 + 0.00825542i −0.868399 0.495867i \(-0.834850\pi\)
0.863632 + 0.504122i \(0.168184\pi\)
\(830\) −2.25167e9 1.30000e9i −0.136689 0.0789172i
\(831\) −4.55256e9 7.88526e9i −0.275202 0.476664i
\(832\) 1.08725e10 + 4.80118e6i 0.654480 + 0.000289012i
\(833\) 1.82531e10 + 3.92055e9i 1.09416 + 0.235012i
\(834\) 3.92324e9i 0.234187i
\(835\) 8.88262e8 + 1.53852e9i 0.0528006 + 0.0914532i
\(836\) −5.05649e8 + 8.75810e8i −0.0299314 + 0.0518428i
\(837\) 1.30213e10 + 7.51788e9i 0.767568 + 0.443156i
\(838\) −8.91584e9 + 5.14756e9i −0.523369 + 0.302167i
\(839\) 1.44174e10i 0.842790i −0.906877 0.421395i \(-0.861541\pi\)
0.906877 0.421395i \(-0.138459\pi\)
\(840\) −4.36981e8 + 6.00105e8i −0.0254381 + 0.0349341i
\(841\) −1.70325e10 −0.987398
\(842\) −6.92540e9 1.19951e10i −0.399809 0.692489i
\(843\) 3.30675e9 + 1.90915e9i 0.190110 + 0.109760i
\(844\) 3.59069e9 6.21926e9i 0.205579 0.356074i
\(845\) 2.37573e9 1.36883e9i 0.135456 0.0780462i
\(846\) −2.65749e9 −0.150895
\(847\) 8.28530e9 + 8.79759e8i 0.468508 + 0.0497475i
\(848\) 2.56410e10 1.44394
\(849\) 5.26898e9 + 9.12614e9i 0.295495 + 0.511812i
\(850\) 1.88686e10 + 1.08938e10i 1.05384 + 0.608435i
\(851\) 3.76793e10 + 2.17541e10i 2.09580 + 1.21001i
\(852\) 1.26913e9 7.32731e8i 0.0703018 0.0405888i
\(853\) 1.19888e10i 0.661383i 0.943739 + 0.330691i \(0.107282\pi\)
−0.943739 + 0.330691i \(0.892718\pi\)
\(854\) −1.77937e10 + 7.89952e9i −0.977604 + 0.434008i
\(855\) −8.66600e8 −0.0474173
\(856\) −4.30948e9 + 2.48808e9i −0.234837 + 0.135583i
\(857\) −4.87435e9 + 8.44262e9i −0.264535 + 0.458189i −0.967442 0.253094i \(-0.918552\pi\)
0.702906 + 0.711282i \(0.251885\pi\)
\(858\) −2.45624e9 + 4.25000e9i −0.132759 + 0.229712i
\(859\) 1.61064e10 + 2.78970e10i 0.867004 + 1.50170i 0.865043 + 0.501697i \(0.167291\pi\)
0.00196104 + 0.999998i \(0.499376\pi\)
\(860\) 2.24500e7i 0.00120357i
\(861\) −3.56471e9 + 1.58256e9i −0.190333 + 0.0844984i
\(862\) −1.26462e10 −0.672486
\(863\) 9.74681e9 5.62733e9i 0.516208 0.298033i −0.219174 0.975686i \(-0.570336\pi\)
0.735382 + 0.677653i \(0.237003\pi\)
\(864\) 4.82905e9 + 2.78805e9i 0.254720 + 0.147063i
\(865\) 3.45370e9 + 1.99399e9i 0.181438 + 0.104753i
\(866\) −3.28834e8 + 1.89853e8i −0.0172054 + 0.00993354i
\(867\) 1.58547e9 0.0826209
\(868\) 7.05196e8 6.64133e9i 0.0366008 0.344696i
\(869\) 8.03259e9i 0.415228i
\(870\) −6.21786e7 1.07697e8i −0.00320128 0.00554478i
\(871\) −6.78509e9 3.92137e9i −0.347930 0.201082i
\(872\) −3.40567e9 + 5.89880e9i −0.173938 + 0.301270i
\(873\) −6.45090e9 + 3.72443e9i −0.328148 + 0.189457i
\(874\) 1.18260e10 0.599166
\(875\) −4.94750e9 3.60264e9i −0.249665 0.181800i
\(876\) 1.48430e9i 0.0746031i
\(877\) −1.02177e10 + 5.89921e9i −0.511512 + 0.295322i −0.733455 0.679738i \(-0.762093\pi\)
0.221943 + 0.975060i \(0.428760\pi\)
\(878\) −1.58666e10 9.16061e9i −0.791141 0.456766i
\(879\) −1.02500e10 5.91786e9i −0.509055 0.293903i
\(880\) 1.36013e9 + 2.35581e9i 0.0672808 + 0.116534i
\(881\) 5.88203e9 0.289809 0.144904 0.989446i \(-0.453713\pi\)
0.144904 + 0.989446i \(0.453713\pi\)
\(882\) −4.25848e9 + 1.98265e10i −0.208985 + 0.972983i
\(883\) −2.44982e10 −1.19749 −0.598745 0.800939i \(-0.704334\pi\)
−0.598745 + 0.800939i \(0.704334\pi\)
\(884\) −2.78275e9 4.82479e9i −0.135485 0.234907i
\(885\) 4.93767e8 8.55229e8i 0.0239453 0.0414745i
\(886\) −1.86863e10 1.07885e10i −0.902620 0.521128i
\(887\) −9.40471e9 1.62894e10i −0.452494 0.783742i 0.546046 0.837755i \(-0.316132\pi\)
−0.998540 + 0.0540127i \(0.982799\pi\)
\(888\) 8.82108e9 0.422743
\(889\) −1.51242e10 + 2.07700e10i −0.721965 + 0.991474i
\(890\) 6.74005e9i 0.320478i
\(891\) −9.17608e9 + 5.29781e9i −0.434595 + 0.250914i
\(892\) 5.31825e9 + 3.07049e9i 0.250895 + 0.144854i
\(893\) −5.48068e8 + 9.49282e8i −0.0257546 + 0.0446083i
\(894\) −3.39165e9 5.87450e9i −0.158756 0.274973i
\(895\) 2.59108e9i 0.120809i
\(896\) −2.73777e9 + 2.57835e10i −0.127151 + 1.19747i
\(897\) 1.11963e10 + 4.94419e6i 0.517966 + 0.000228729i
\(898\) −1.56472e10 2.71017e10i −0.721055 1.24890i
\(899\) −3.02966e9 1.74917e9i −0.139070 0.0802923i
\(900\) −2.30800e9 + 3.99758e9i −0.105533 + 0.182788i
\(901\) 1.49874e10 + 2.59589e10i 0.682636 + 1.18236i
\(902\) 1.13660e10i 0.515686i
\(903\) 9.33686e7 + 2.10313e8i 0.00421982 + 0.00950515i
\(904\) 2.06302e10i 0.928785i
\(905\) 1.33720e9 7.72035e8i 0.0599691 0.0346232i
\(906\) −3.49924e9 + 6.06087e9i −0.156324 + 0.270761i
\(907\) −6.71557e9 + 1.16317e10i −0.298853 + 0.517629i −0.975874 0.218335i \(-0.929937\pi\)
0.677021 + 0.735964i \(0.263271\pi\)
\(908\) 1.21563e9 7.01844e8i 0.0538891 0.0311129i
\(909\) 1.73307e10 0.765317
\(910\) 1.60563e9 + 3.62100e9i 0.0706320 + 0.159288i
\(911\) 1.24391e10 0.545097 0.272548 0.962142i \(-0.412134\pi\)
0.272548 + 0.962142i \(0.412134\pi\)
\(912\) 2.61097e9 1.50744e9i 0.113978 0.0658051i
\(913\) −7.57402e9 + 1.31186e10i −0.329366 + 0.570478i
\(914\) −1.58867e10 + 2.75165e10i −0.688210 + 1.19201i
\(915\) 9.85462e8 5.68957e8i 0.0425271 0.0245531i
\(916\) 6.11602e9i 0.262927i
\(917\) 2.60769e10 + 2.76892e9i 1.11677 + 0.118582i
\(918\) 1.81149e10i 0.772833i
\(919\) −4.10470e9 7.10956e9i −0.174453 0.302161i 0.765519 0.643413i \(-0.222482\pi\)
−0.939972 + 0.341252i \(0.889149\pi\)
\(920\) 2.46719e9 4.27330e9i 0.104459 0.180928i
\(921\) 1.24960e10 + 7.21458e9i 0.527063 + 0.304300i
\(922\) −7.14779e9 1.23803e10i −0.300340 0.520204i
\(923\) −1.07970e7 + 2.44503e10i −0.000451958 + 1.02348i
\(924\) −1.11815e9 8.14208e8i −0.0466282 0.0339534i
\(925\) 3.59124e10i 1.49193i
\(926\) 1.39225e10 + 2.41146e10i 0.576209 + 0.998024i
\(927\) 7.27403e8 1.25990e9i 0.0299914 0.0519466i
\(928\) −1.12357e9 6.48692e8i −0.0461510 0.0266453i
\(929\) 2.49499e10 1.44048e10i 1.02097 0.589458i 0.106587 0.994303i \(-0.466008\pi\)
0.914385 + 0.404845i \(0.132675\pi\)
\(930\) 2.00134e9i 0.0815888i
\(931\) 6.20395e9 + 5.61008e9i 0.251968 + 0.227848i
\(932\) 7.61976e9 0.308308
\(933\) −2.59823e9 4.50027e9i −0.104735 0.181407i
\(934\) −1.39035e10 8.02719e9i −0.558355 0.322366i
\(935\) −1.59001e9 + 2.75399e9i −0.0636152 + 0.110185i
\(936\) −1.63868e10 + 9.45128e9i −0.653174 + 0.376726i
\(937\) −4.23519e10 −1.68184 −0.840919 0.541161i \(-0.817985\pi\)
−0.840919 + 0.541161i \(0.817985\pi\)
\(938\) 6.66428e9 9.15205e9i 0.263660 0.362083i
\(939\) 5.41674e9 0.213505
\(940\) −7.31344e7 1.26672e8i −0.00287193 0.00497433i
\(941\) 1.37164e9 + 7.91918e8i 0.0536633 + 0.0309825i 0.526592 0.850118i \(-0.323470\pi\)
−0.472928 + 0.881101i \(0.656803\pi\)
\(942\) 1.33917e10 + 7.73168e9i 0.521983 + 0.301367i
\(943\) 2.24515e10 1.29624e10i 0.871875 0.503377i
\(944\) 2.86307e10i 1.10772i
\(945\) 2.65323e8 2.49873e9i 0.0102274 0.0963182i
\(946\) 6.70579e8 0.0257532
\(947\) 2.03737e10 1.17628e10i 0.779551 0.450074i −0.0567199 0.998390i \(-0.518064\pi\)
0.836271 + 0.548316i \(0.184731\pi\)
\(948\) −5.93982e8 + 1.02881e9i −0.0226435 + 0.0392198i
\(949\) −2.14413e10 1.23918e10i −0.814365 0.470653i
\(950\) 4.88068e9 + 8.45358e9i 0.184692 + 0.319895i
\(951\) 4.25487e9i 0.160419i
\(952\) −2.29956e10 + 1.02089e10i −0.863803 + 0.383486i
\(953\) −1.03711e10 −0.388150 −0.194075 0.980987i \(-0.562171\pi\)
−0.194075 + 0.980987i \(0.562171\pi\)
\(954\) −2.81964e10 + 1.62792e10i −1.05142 + 0.607036i
\(955\) −4.01933e9 2.32056e9i −0.149328 0.0862147i
\(956\) 7.29728e9 + 4.21308e9i 0.270121 + 0.155954i
\(957\) −6.27456e8 + 3.62262e8i −0.0231415 + 0.0133608i
\(958\) 1.41698e10 0.520696
\(959\) 4.01826e10 1.78391e10i 1.47121 0.653143i
\(960\) 9.18058e8i 0.0334904i
\(961\) 1.43939e10 + 2.49310e10i 0.523176 + 0.906168i
\(962\) 2.35518e10 4.07514e10i 0.852928 1.47581i
\(963\) 3.97262e9 6.88077e9i 0.143346 0.248282i
\(964\) −5.42796e9 + 3.13383e9i −0.195149 + 0.112669i
\(965\) −5.75785e9 −0.206260
\(966\) −1.70788e9 + 1.60843e10i −0.0609590 + 0.574094i
\(967\) 4.81846e8i 0.0171363i −0.999963 0.00856813i \(-0.997273\pi\)
0.999963 0.00856813i \(-0.00272735\pi\)
\(968\) −9.72412e9 + 5.61422e9i −0.344577 + 0.198942i
\(969\) 3.05227e9 + 1.76223e9i 0.107768 + 0.0622198i
\(970\) −1.82033e9 1.05097e9i −0.0640398 0.0369734i
\(971\) −2.65049e10 4.59079e10i −0.929093 1.60924i −0.784843 0.619695i \(-0.787256\pi\)
−0.144250 0.989541i \(-0.546077\pi\)
\(972\) −5.86543e9 −0.204865
\(973\) −1.08573e10 + 1.49103e10i −0.377856 + 0.518908i
\(974\) 1.81375e10 0.628959
\(975\) 4.61727e9 + 8.00551e9i 0.159540 + 0.276613i
\(976\) 1.64953e10 2.85707e10i 0.567918 0.983662i
\(977\) 1.28809e10 + 7.43679e9i 0.441891 + 0.255126i 0.704399 0.709804i \(-0.251216\pi\)
−0.262508 + 0.964930i \(0.584550\pi\)
\(978\) −5.37510e9 9.30995e9i −0.183739 0.318245i
\(979\) −3.92685e10 −1.33753
\(980\) −1.06224e9 + 3.42640e8i −0.0360523 + 0.0116291i
\(981\) 1.08754e10i 0.367793i
\(982\) 1.19865e10 6.92041e9i 0.403927 0.233207i
\(983\) 3.85211e10 + 2.22402e10i 1.29349 + 0.746794i 0.979270 0.202558i \(-0.0649254\pi\)
0.314215 + 0.949352i \(0.398259\pi\)
\(984\) 2.62806e9 4.55193e9i 0.0879330 0.152304i
\(985\) −1.36135e9 2.35792e9i −0.0453881 0.0786144i
\(986\) 4.21476e9i 0.140024i
\(987\) −1.21195e9 8.82512e8i −0.0401213 0.0292153i
\(988\) 1.10194e6 2.49538e9i 3.63502e−5 0.0823166i
\(989\) −7.64762e8 1.32461e9i −0.0251385 0.0435411i
\(990\) −2.99136e9 1.72706e9i −0.0979820 0.0565699i
\(991\) 1.14584e10 1.98465e10i 0.373995 0.647779i −0.616181 0.787605i \(-0.711321\pi\)
0.990176 + 0.139826i \(0.0446542\pi\)
\(992\) 1.04397e10 + 1.80821e10i 0.339545 + 0.588109i
\(993\) 2.30193e9i 0.0746053i
\(994\) −3.51246e10 3.72964e9i −1.13438 0.120452i
\(995\) 4.96810e8i 0.0159886i
\(996\) −1.94015e9 + 1.12014e9i −0.0622196 + 0.0359225i
\(997\) 1.21137e10 2.09815e10i 0.387118 0.670508i −0.604943 0.796269i \(-0.706804\pi\)
0.992061 + 0.125761i \(0.0401374\pi\)
\(998\) 7.34966e9 1.27300e10i 0.234051 0.405388i
\(999\) −2.58583e10 + 1.49293e10i −0.820580 + 0.473762i
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.25.17 128
7.2 even 3 inner 91.8.r.a.51.48 yes 128
13.12 even 2 inner 91.8.r.a.25.48 yes 128
91.51 even 6 inner 91.8.r.a.51.17 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.r.a.25.17 128 1.1 even 1 trivial
91.8.r.a.25.48 yes 128 13.12 even 2 inner
91.8.r.a.51.17 yes 128 91.51 even 6 inner
91.8.r.a.51.48 yes 128 7.2 even 3 inner