Properties

Label 14.13.d.a.3.6
Level $14$
Weight $13$
Character 14.3
Analytic conductor $12.796$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,13,Mod(3,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.3");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 14.d (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: \(12.7959134419\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 527434 x^{14} - 31307480 x^{13} + 193554267483 x^{12} - 12267558721140 x^{11} + \cdots + 73\!\cdots\!36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{8}\cdot 7^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 3.6
Root \(65.8177 + 114.000i\) of defining polynomial
Character \(\chi\) \(=\) 14.3
Dual form 14.13.d.a.5.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(22.6274 + 39.1918i) q^{2} +(-444.082 - 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-12687.9 + 7325.35i) q^{5} -23205.9i q^{6} +(117217. - 10074.6i) q^{7} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +O(q^{10})\) \(q+(22.6274 + 39.1918i) q^{2} +(-444.082 - 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-12687.9 + 7325.35i) q^{5} -23205.9i q^{6} +(117217. - 10074.6i) q^{7} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +(-574187. - 331507. i) q^{10} +(1.34149e6 - 2.32353e6i) q^{11} +(909481. - 525089. i) q^{12} -1.34691e6i q^{13} +(3.04716e6 + 4.36598e6i) q^{14} +7.51261e6 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(6.20477e6 + 3.58233e6i) q^{17} +(6.07536e6 - 1.05228e7i) q^{18} +(6.33442e7 - 3.65718e7i) q^{19} -3.00046e7i q^{20} +(-5.46370e7 - 2.55794e7i) q^{21} +1.21418e8 q^{22} +(-1.14112e8 - 1.97648e8i) q^{23} +(4.11584e7 + 2.37628e7i) q^{24} +(-1.47489e7 + 2.55459e7i) q^{25} +(5.27880e7 - 3.04772e7i) q^{26} +4.10193e8i q^{27} +(-1.02162e8 + 2.18215e8i) q^{28} -5.69081e8 q^{29} +(1.69991e8 + 2.94433e8i) q^{30} +(2.67528e8 + 1.54457e8i) q^{31} +(9.49063e7 - 1.64382e8i) q^{32} +(-1.19146e9 + 6.87891e8i) q^{33} +3.24235e8i q^{34} +(-1.41343e9 + 9.86479e8i) q^{35} +5.49879e8 q^{36} +(-8.51831e8 - 1.47542e9i) q^{37} +(2.86663e9 + 1.65505e9i) q^{38} +(-3.45336e8 + 5.98140e8i) q^{39} +(1.17594e9 - 6.78927e8i) q^{40} -5.37658e9i q^{41} +(-2.33790e8 - 2.72012e9i) q^{42} -9.19904e9 q^{43} +(2.74737e9 + 4.75858e9i) q^{44} +(3.40664e9 + 1.96682e9i) q^{45} +(5.16414e9 - 8.94455e9i) q^{46} +(9.45381e9 - 5.45816e9i) q^{47} +2.15076e9i q^{48} +(1.36383e10 - 2.36182e9i) q^{49} -1.33492e9 q^{50} +(-1.83695e9 - 3.18170e9i) q^{51} +(2.38891e9 + 1.37924e9i) q^{52} +(7.92816e9 - 1.37320e10i) q^{53} +(-1.60762e10 + 9.28161e9i) q^{54} +3.93075e10i q^{55} +(-1.08639e10 + 9.33732e8i) q^{56} -3.75067e10 q^{57} +(-1.28768e10 - 2.23033e10i) q^{58} +(1.75457e10 + 1.01300e10i) q^{59} +(-7.69292e9 + 1.33245e10i) q^{60} +(2.38455e10 - 1.37672e10i) q^{61} +1.39799e10i q^{62} +(-1.80787e10 - 2.59032e10i) q^{63} +8.58993e9 q^{64} +(9.86660e9 + 1.70895e10i) q^{65} +(-5.39194e10 - 3.11304e10i) q^{66} +(-3.35056e10 + 5.80333e10i) q^{67} +(-1.27074e10 + 7.33661e9i) q^{68} +1.17030e11i q^{69} +(-7.06442e10 - 3.30735e10i) q^{70} +7.34393e10 q^{71} +(1.24423e10 + 2.15508e10i) q^{72} +(5.62093e10 + 3.24525e10i) q^{73} +(3.85495e10 - 6.67697e10i) q^{74} +(1.30995e10 - 7.56300e9i) q^{75} +1.49798e11i q^{76} +(1.33836e11 - 2.85871e11i) q^{77} -3.12563e10 q^{78} +(-3.16413e9 - 5.48043e9i) q^{79} +(5.32168e10 + 3.07247e10i) q^{80} +(3.38251e10 - 5.85869e10i) q^{81} +(2.10718e11 - 1.21658e11i) q^{82} -5.07191e11i q^{83} +(1.01316e11 - 7.07119e10i) q^{84} -1.04967e11 q^{85} +(-2.08151e11 - 3.60527e11i) q^{86} +(2.52719e11 + 1.45907e11i) q^{87} +(-1.24332e11 + 2.15349e11i) q^{88} +(-5.49695e11 + 3.17367e11i) q^{89} +1.78016e11i q^{90} +(-1.35696e10 - 1.57881e11i) q^{91} +4.67404e11 q^{92} +(-7.92030e10 - 1.37184e11i) q^{93} +(4.27831e11 + 2.47008e11i) q^{94} +(-5.35802e11 + 9.28037e11i) q^{95} +(-8.42924e10 + 4.86662e10i) q^{96} +3.89725e11i q^{97} +(4.01164e11 + 4.81068e11i) q^{98} -7.20367e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} - 2290176 q^{10} + 2072088 q^{11} - 11501568 q^{14} - 27163728 q^{15} - 33554432 q^{16} - 101561040 q^{17} - 4592640 q^{18} + 174931848 q^{19} - 323731368 q^{21} + 62776320 q^{22} + 25630560 q^{23} + 242221056 q^{24} + 521205808 q^{25} - 1434682368 q^{26} + 350863360 q^{28} + 532360944 q^{29} - 2151917568 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 1612540440 q^{35} - 9675767808 q^{36} + 5764524040 q^{37} - 149506560 q^{38} + 10526083272 q^{39} + 4690280448 q^{40} - 12685086720 q^{42} - 66929432000 q^{43} + 4243636224 q^{44} + 57253352184 q^{45} + 7203213312 q^{46} + 18116171640 q^{47} - 9977452064 q^{49} - 99248080896 q^{50} - 23299256376 q^{51} + 8269578240 q^{52} + 39134161800 q^{53} + 105152205312 q^{54} + 3623878656 q^{56} - 328243960080 q^{57} + 29637396480 q^{58} + 201845459088 q^{59} + 27815657472 q^{60} + 336780254328 q^{61} - 389095094520 q^{63} + 137438953472 q^{64} + 158322703896 q^{65} + 268884080640 q^{66} + 107767119920 q^{67} + 207997009920 q^{68} - 6077815296 q^{70} - 1150259029344 q^{71} - 9405726720 q^{72} - 738414283320 q^{73} + 4902778368 q^{74} + 1537028640000 q^{75} - 321203352960 q^{77} - 786088888320 q^{78} + 227632064768 q^{79} - 76101451776 q^{80} - 391984178400 q^{81} - 302578053120 q^{82} - 32685686784 q^{84} + 710209696080 q^{85} - 38105192448 q^{86} + 1957017683880 q^{87} - 64282951680 q^{88} - 2485007442792 q^{89} + 1803248333904 q^{91} - 104982773760 q^{92} - 458668768680 q^{93} - 2021298693120 q^{94} - 186503862960 q^{95} - 496068722688 q^{96} - 356371660800 q^{98} + 3921180354576 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.6274 + 39.1918i 0.353553 + 0.612372i
\(3\) −444.082 256.391i −0.609167 0.351702i 0.163473 0.986548i \(-0.447730\pi\)
−0.772639 + 0.634845i \(0.781064\pi\)
\(4\) −1024.00 + 1773.62i −0.250000 + 0.433013i
\(5\) −12687.9 + 7325.35i −0.812024 + 0.468822i −0.847658 0.530543i \(-0.821988\pi\)
0.0356345 + 0.999365i \(0.488655\pi\)
\(6\) 23205.9i 0.497382i
\(7\) 117217. 10074.6i 0.996327 0.0856326i
\(8\) −92681.9 −0.353553
\(9\) −134248. 232524.i −0.252611 0.437535i
\(10\) −574187. 331507.i −0.574187 0.331507i
\(11\) 1.34149e6 2.32353e6i 0.757235 1.31157i −0.187020 0.982356i \(-0.559883\pi\)
0.944255 0.329214i \(-0.106784\pi\)
\(12\) 909481. 525089.i 0.304583 0.175851i
\(13\) 1.34691e6i 0.279048i −0.990219 0.139524i \(-0.955443\pi\)
0.990219 0.139524i \(-0.0445573\pi\)
\(14\) 3.04716e6 + 4.36598e6i 0.404694 + 0.579847i
\(15\) 7.51261e6 0.659544
\(16\) −2.09715e6 3.63237e6i −0.125000 0.216506i
\(17\) 6.20477e6 + 3.58233e6i 0.257059 + 0.148413i 0.622992 0.782228i \(-0.285917\pi\)
−0.365933 + 0.930641i \(0.619250\pi\)
\(18\) 6.07536e6 1.05228e7i 0.178623 0.309384i
\(19\) 6.33442e7 3.65718e7i 1.34644 0.777365i 0.358692 0.933456i \(-0.383223\pi\)
0.987743 + 0.156091i \(0.0498894\pi\)
\(20\) 3.00046e7i 0.468822i
\(21\) −5.46370e7 2.55794e7i −0.637046 0.298246i
\(22\) 1.21418e8 1.07089
\(23\) −1.14112e8 1.97648e8i −0.770843 1.33514i −0.937102 0.349057i \(-0.886502\pi\)
0.166259 0.986082i \(-0.446831\pi\)
\(24\) 4.11584e7 + 2.37628e7i 0.215373 + 0.124346i
\(25\) −1.47489e7 + 2.55459e7i −0.0604117 + 0.104636i
\(26\) 5.27880e7 3.04772e7i 0.170881 0.0986585i
\(27\) 4.10193e8i 1.05878i
\(28\) −1.02162e8 + 2.18215e8i −0.212002 + 0.452830i
\(29\) −5.69081e8 −0.956723 −0.478362 0.878163i \(-0.658769\pi\)
−0.478362 + 0.878163i \(0.658769\pi\)
\(30\) 1.69991e8 + 2.94433e8i 0.233184 + 0.403886i
\(31\) 2.67528e8 + 1.54457e8i 0.301439 + 0.174036i 0.643089 0.765791i \(-0.277653\pi\)
−0.341650 + 0.939827i \(0.610986\pi\)
\(32\) 9.49063e7 1.64382e8i 0.0883883 0.153093i
\(33\) −1.19146e9 + 6.87891e8i −0.922565 + 0.532643i
\(34\) 3.24235e8i 0.209888i
\(35\) −1.41343e9 + 9.86479e8i −0.768895 + 0.536636i
\(36\) 5.49879e8 0.252611
\(37\) −8.51831e8 1.47542e9i −0.332004 0.575048i 0.650901 0.759163i \(-0.274391\pi\)
−0.982905 + 0.184115i \(0.941058\pi\)
\(38\) 2.86663e9 + 1.65505e9i 0.952073 + 0.549680i
\(39\) −3.45336e8 + 5.98140e8i −0.0981420 + 0.169987i
\(40\) 1.17594e9 6.78927e8i 0.287094 0.165754i
\(41\) 5.37658e9i 1.13189i −0.824444 0.565944i \(-0.808512\pi\)
0.824444 0.565944i \(-0.191488\pi\)
\(42\) −2.33790e8 2.72012e9i −0.0425921 0.495555i
\(43\) −9.19904e9 −1.45523 −0.727615 0.685985i \(-0.759371\pi\)
−0.727615 + 0.685985i \(0.759371\pi\)
\(44\) 2.74737e9 + 4.75858e9i 0.378618 + 0.655785i
\(45\) 3.40664e9 + 1.96682e9i 0.410252 + 0.236859i
\(46\) 5.16414e9 8.94455e9i 0.545068 0.944086i
\(47\) 9.45381e9 5.45816e9i 0.877041 0.506360i 0.00735915 0.999973i \(-0.497657\pi\)
0.869682 + 0.493613i \(0.164324\pi\)
\(48\) 2.15076e9i 0.175851i
\(49\) 1.36383e10 2.36182e9i 0.985334 0.170636i
\(50\) −1.33492e9 −0.0854350
\(51\) −1.83695e9 3.18170e9i −0.104394 0.180816i
\(52\) 2.38891e9 + 1.37924e9i 0.120831 + 0.0697621i
\(53\) 7.92816e9 1.37320e10i 0.357698 0.619552i −0.629877 0.776695i \(-0.716895\pi\)
0.987576 + 0.157143i \(0.0502282\pi\)
\(54\) −1.60762e10 + 9.28161e9i −0.648368 + 0.374335i
\(55\) 3.93075e10i 1.42003i
\(56\) −1.08639e10 + 9.33732e8i −0.352255 + 0.0302757i
\(57\) −3.75067e10 −1.09360
\(58\) −1.28768e10 2.23033e10i −0.338253 0.585871i
\(59\) 1.75457e10 + 1.01300e10i 0.415967 + 0.240159i 0.693350 0.720601i \(-0.256134\pi\)
−0.277383 + 0.960759i \(0.589467\pi\)
\(60\) −7.69292e9 + 1.33245e10i −0.164886 + 0.285591i
\(61\) 2.38455e10 1.37672e10i 0.462837 0.267219i −0.250399 0.968143i \(-0.580562\pi\)
0.713236 + 0.700924i \(0.247229\pi\)
\(62\) 1.39799e10i 0.246124i
\(63\) −1.80787e10 2.59032e10i −0.289150 0.414296i
\(64\) 8.58993e9 0.125000
\(65\) 9.86660e9 + 1.70895e10i 0.130824 + 0.226594i
\(66\) −5.39194e10 3.11304e10i −0.652352 0.376635i
\(67\) −3.35056e10 + 5.80333e10i −0.370398 + 0.641547i −0.989627 0.143663i \(-0.954112\pi\)
0.619229 + 0.785210i \(0.287445\pi\)
\(68\) −1.27074e10 + 7.33661e9i −0.128529 + 0.0742065i
\(69\) 1.17030e11i 1.08443i
\(70\) −7.06442e10 3.30735e10i −0.600466 0.281120i
\(71\) 7.34393e10 0.573295 0.286648 0.958036i \(-0.407459\pi\)
0.286648 + 0.958036i \(0.407459\pi\)
\(72\) 1.24423e10 + 2.15508e10i 0.0893114 + 0.154692i
\(73\) 5.62093e10 + 3.24525e10i 0.371425 + 0.214442i 0.674081 0.738658i \(-0.264540\pi\)
−0.302656 + 0.953100i \(0.597873\pi\)
\(74\) 3.85495e10 6.67697e10i 0.234762 0.406620i
\(75\) 1.30995e10 7.56300e9i 0.0736015 0.0424939i
\(76\) 1.49798e11i 0.777365i
\(77\) 1.33836e11 2.85871e11i 0.642140 1.37160i
\(78\) −3.12563e10 −0.138794
\(79\) −3.16413e9 5.48043e9i −0.0130164 0.0225451i 0.859444 0.511230i \(-0.170810\pi\)
−0.872460 + 0.488685i \(0.837477\pi\)
\(80\) 5.32168e10 + 3.07247e10i 0.203006 + 0.117206i
\(81\) 3.38251e10 5.85869e10i 0.119765 0.207439i
\(82\) 2.10718e11 1.21658e11i 0.693136 0.400183i
\(83\) 5.07191e11i 1.55133i −0.631147 0.775663i \(-0.717415\pi\)
0.631147 0.775663i \(-0.282585\pi\)
\(84\) 1.01316e11 7.07119e10i 0.288406 0.201288i
\(85\) −1.04967e11 −0.278317
\(86\) −2.08151e11 3.60527e11i −0.514502 0.891143i
\(87\) 2.52719e11 + 1.45907e11i 0.582804 + 0.336482i
\(88\) −1.24332e11 + 2.15349e11i −0.267723 + 0.463710i
\(89\) −5.49695e11 + 3.17367e11i −1.10607 + 0.638589i −0.937808 0.347154i \(-0.887148\pi\)
−0.168260 + 0.985743i \(0.553815\pi\)
\(90\) 1.78016e11i 0.334969i
\(91\) −1.35696e10 1.57881e11i −0.0238956 0.278023i
\(92\) 4.67404e11 0.770843
\(93\) −7.92030e10 1.37184e11i −0.122418 0.212033i
\(94\) 4.27831e11 + 2.47008e11i 0.620161 + 0.358050i
\(95\) −5.35802e11 + 9.28037e11i −0.728891 + 1.26248i
\(96\) −8.42924e10 + 4.86662e10i −0.107686 + 0.0621728i
\(97\) 3.89725e11i 0.467873i 0.972252 + 0.233937i \(0.0751609\pi\)
−0.972252 + 0.233937i \(0.924839\pi\)
\(98\) 4.01164e11 + 4.81068e11i 0.452861 + 0.543062i
\(99\) −7.20367e11 −0.765143
\(100\) −3.02058e10 5.23180e10i −0.0302058 0.0523180i
\(101\) 2.37129e9 + 1.36906e9i 0.00223386 + 0.00128972i 0.501117 0.865380i \(-0.332923\pi\)
−0.498883 + 0.866670i \(0.666256\pi\)
\(102\) 8.31310e10 1.43987e11i 0.0738180 0.127856i
\(103\) −1.83996e12 + 1.06230e12i −1.54094 + 0.889663i −0.542161 + 0.840274i \(0.682394\pi\)
−0.998780 + 0.0493885i \(0.984273\pi\)
\(104\) 1.24834e11i 0.0986585i
\(105\) 8.80605e11 7.56865e10i 0.657121 0.0564784i
\(106\) 7.17575e11 0.505862
\(107\) −9.41831e11 1.63130e12i −0.627582 1.08700i −0.988035 0.154227i \(-0.950711\pi\)
0.360453 0.932777i \(-0.382622\pi\)
\(108\) −7.27527e11 4.20038e11i −0.458465 0.264695i
\(109\) 1.30905e12 2.26734e12i 0.780544 1.35194i −0.151081 0.988521i \(-0.548276\pi\)
0.931625 0.363420i \(-0.118391\pi\)
\(110\) −1.54053e12 + 8.89426e11i −0.869590 + 0.502058i
\(111\) 8.73608e11i 0.467067i
\(112\) −2.82416e11 4.04647e11i −0.143081 0.205007i
\(113\) 2.59357e12 1.24574 0.622869 0.782326i \(-0.285967\pi\)
0.622869 + 0.782326i \(0.285967\pi\)
\(114\) −8.48681e11 1.46996e12i −0.386647 0.669693i
\(115\) 2.89569e12 + 1.67183e12i 1.25189 + 0.722776i
\(116\) 5.82739e11 1.00933e12i 0.239181 0.414273i
\(117\) −3.13189e11 + 1.80820e11i −0.122093 + 0.0704906i
\(118\) 9.16865e11i 0.339636i
\(119\) 7.63394e11 + 3.57399e11i 0.268823 + 0.125855i
\(120\) −6.96283e11 −0.233184
\(121\) −2.02997e12 3.51600e12i −0.646810 1.12031i
\(122\) 1.07913e12 + 6.23034e11i 0.327275 + 0.188952i
\(123\) −1.37851e12 + 2.38765e12i −0.398087 + 0.689508i
\(124\) −5.47897e11 + 3.16329e11i −0.150719 + 0.0870179i
\(125\) 4.00899e12i 1.05093i
\(126\) 6.06121e11 1.29466e12i 0.151473 0.323543i
\(127\) 6.80221e12 1.62117 0.810583 0.585623i \(-0.199150\pi\)
0.810583 + 0.585623i \(0.199150\pi\)
\(128\) 1.94368e11 + 3.36655e11i 0.0441942 + 0.0765466i
\(129\) 4.08513e12 + 2.35855e12i 0.886478 + 0.511808i
\(130\) −4.46511e11 + 7.73381e11i −0.0925066 + 0.160226i
\(131\) −7.06312e12 + 4.07789e12i −1.39755 + 0.806878i −0.994136 0.108137i \(-0.965511\pi\)
−0.403418 + 0.915016i \(0.632178\pi\)
\(132\) 2.81760e12i 0.532643i
\(133\) 7.05656e12 4.92500e12i 1.27492 0.889808i
\(134\) −3.03258e12 −0.523821
\(135\) −3.00481e12 5.20448e12i −0.496380 0.859755i
\(136\) −5.75070e11 3.32017e11i −0.0908840 0.0524719i
\(137\) −4.07097e12 + 7.05112e12i −0.615707 + 1.06644i 0.374553 + 0.927206i \(0.377796\pi\)
−0.990260 + 0.139230i \(0.955537\pi\)
\(138\) −4.58661e12 + 2.64808e12i −0.664075 + 0.383404i
\(139\) 1.24727e13i 1.72930i 0.502371 + 0.864652i \(0.332461\pi\)
−0.502371 + 0.864652i \(0.667539\pi\)
\(140\) −3.02284e11 3.51705e12i −0.0401465 0.467100i
\(141\) −5.59769e12 −0.712352
\(142\) 1.66174e12 + 2.87822e12i 0.202691 + 0.351070i
\(143\) −3.12959e12 1.80687e12i −0.365991 0.211305i
\(144\) −5.63076e11 + 9.75276e11i −0.0631527 + 0.109384i
\(145\) 7.22043e12 4.16872e12i 0.776882 0.448533i
\(146\) 2.93726e12i 0.303267i
\(147\) −6.66208e12 2.44789e12i −0.660246 0.242599i
\(148\) 3.48910e12 0.332004
\(149\) −2.91858e12 5.05512e12i −0.266719 0.461970i 0.701294 0.712872i \(-0.252606\pi\)
−0.968012 + 0.250902i \(0.919273\pi\)
\(150\) 5.92815e11 + 3.42262e11i 0.0520441 + 0.0300477i
\(151\) −4.06127e12 + 7.03433e12i −0.342610 + 0.593419i −0.984917 0.173029i \(-0.944644\pi\)
0.642306 + 0.766448i \(0.277978\pi\)
\(152\) −5.87086e12 + 3.38954e12i −0.476037 + 0.274840i
\(153\) 1.92368e12i 0.149963i
\(154\) 1.42322e13 1.22323e12i 1.06696 0.0917033i
\(155\) −4.52581e12 −0.326367
\(156\) −7.07249e11 1.22499e12i −0.0490710 0.0849934i
\(157\) 2.00528e13 + 1.15775e13i 1.33899 + 0.773065i 0.986657 0.162811i \(-0.0520562\pi\)
0.352330 + 0.935876i \(0.385390\pi\)
\(158\) 1.43192e11 2.48016e11i 0.00920400 0.0159418i
\(159\) −7.04151e12 + 4.06542e12i −0.435796 + 0.251607i
\(160\) 2.78088e12i 0.165754i
\(161\) −1.53671e13 2.20181e13i −0.882343 1.26423i
\(162\) 3.06150e12 0.169373
\(163\) −4.26181e12 7.38166e12i −0.227231 0.393576i 0.729755 0.683708i \(-0.239634\pi\)
−0.956987 + 0.290132i \(0.906301\pi\)
\(164\) 9.53601e12 + 5.50562e12i 0.490121 + 0.282972i
\(165\) 1.00781e13 1.74557e13i 0.499430 0.865037i
\(166\) 1.98778e13 1.14764e13i 0.949990 0.548477i
\(167\) 2.04015e13i 0.940509i 0.882531 + 0.470255i \(0.155838\pi\)
−0.882531 + 0.470255i \(0.844162\pi\)
\(168\) 5.06386e12 + 2.37075e12i 0.225230 + 0.105446i
\(169\) 2.14839e13 0.922132
\(170\) −2.37514e12 4.11385e12i −0.0983999 0.170434i
\(171\) −1.70076e13 9.81936e12i −0.680248 0.392741i
\(172\) 9.41982e12 1.63156e13i 0.363808 0.630133i
\(173\) −7.36291e12 + 4.25098e12i −0.274646 + 0.158567i −0.630997 0.775785i \(-0.717354\pi\)
0.356351 + 0.934352i \(0.384021\pi\)
\(174\) 1.32060e13i 0.475857i
\(175\) −1.47146e12 + 3.14300e12i −0.0512295 + 0.109425i
\(176\) −1.12532e13 −0.378618
\(177\) −5.19449e12 8.99713e12i −0.168929 0.292593i
\(178\) −2.48764e13 1.43624e13i −0.782108 0.451550i
\(179\) 9.88862e12 1.71276e13i 0.300620 0.520689i −0.675657 0.737216i \(-0.736140\pi\)
0.976276 + 0.216528i \(0.0694731\pi\)
\(180\) −6.97679e12 + 4.02805e12i −0.205126 + 0.118430i
\(181\) 2.46719e13i 0.701667i −0.936438 0.350833i \(-0.885898\pi\)
0.936438 0.350833i \(-0.114102\pi\)
\(182\) 5.88060e12 4.10425e12i 0.161805 0.112929i
\(183\) −1.41192e13 −0.375926
\(184\) 1.05762e13 + 1.83184e13i 0.272534 + 0.472043i
\(185\) 2.16159e13 + 1.24799e13i 0.539190 + 0.311302i
\(186\) 3.58432e12 6.20822e12i 0.0865623 0.149930i
\(187\) 1.66473e13 9.61130e12i 0.389308 0.224767i
\(188\) 2.23566e13i 0.506360i
\(189\) 4.13253e12 + 4.80815e13i 0.0906661 + 1.05489i
\(190\) −4.84953e13 −1.03081
\(191\) 2.07509e13 + 3.59417e13i 0.427403 + 0.740283i 0.996641 0.0818891i \(-0.0260953\pi\)
−0.569239 + 0.822172i \(0.692762\pi\)
\(192\) −3.81464e12 2.20238e12i −0.0761458 0.0439628i
\(193\) −2.98993e13 + 5.17871e13i −0.578519 + 1.00202i 0.417131 + 0.908846i \(0.363036\pi\)
−0.995650 + 0.0931772i \(0.970298\pi\)
\(194\) −1.52741e13 + 8.81848e12i −0.286513 + 0.165418i
\(195\) 1.01188e13i 0.184045i
\(196\) −9.77663e12 + 2.66077e13i −0.172446 + 0.469321i
\(197\) −5.28263e13 −0.903760 −0.451880 0.892079i \(-0.649246\pi\)
−0.451880 + 0.892079i \(0.649246\pi\)
\(198\) −1.63000e13 2.82325e13i −0.270519 0.468552i
\(199\) 6.62250e13 + 3.82350e13i 1.06636 + 0.615663i 0.927185 0.374605i \(-0.122222\pi\)
0.139175 + 0.990268i \(0.455555\pi\)
\(200\) 1.36696e12 2.36764e12i 0.0213588 0.0369944i
\(201\) 2.97585e13 1.71811e13i 0.451268 0.260539i
\(202\) 1.23913e11i 0.00182394i
\(203\) −6.67059e13 + 5.73326e12i −0.953209 + 0.0819267i
\(204\) 7.52416e12 0.104394
\(205\) 3.93853e13 + 6.82174e13i 0.530654 + 0.919119i
\(206\) −8.32673e13 4.80744e13i −1.08961 0.629087i
\(207\) −3.06387e13 + 5.30677e13i −0.389446 + 0.674541i
\(208\) −4.89249e12 + 2.82468e12i −0.0604157 + 0.0348810i
\(209\) 1.96243e14i 2.35459i
\(210\) 2.28921e13 + 3.27999e13i 0.266913 + 0.382435i
\(211\) 5.17345e13 0.586254 0.293127 0.956074i \(-0.405304\pi\)
0.293127 + 0.956074i \(0.405304\pi\)
\(212\) 1.62369e13 + 2.81231e13i 0.178849 + 0.309776i
\(213\) −3.26131e13 1.88292e13i −0.349232 0.201629i
\(214\) 4.26224e13 7.38242e13i 0.443768 0.768628i
\(215\) 1.16716e14 6.73862e13i 1.18168 0.682244i
\(216\) 3.80175e13i 0.374335i
\(217\) 3.29149e13 + 1.54098e13i 0.315235 + 0.147583i
\(218\) 1.18482e14 1.10386
\(219\) −1.66410e13 2.88231e13i −0.150840 0.261262i
\(220\) −6.97165e13 4.02508e13i −0.614893 0.355009i
\(221\) 4.82508e12 8.35729e12i 0.0414144 0.0717318i
\(222\) −3.42383e13 + 1.97675e13i −0.286019 + 0.165133i
\(223\) 6.07846e13i 0.494270i −0.968981 0.247135i \(-0.920511\pi\)
0.968981 0.247135i \(-0.0794891\pi\)
\(224\) 9.46853e12 2.02245e13i 0.0749539 0.160100i
\(225\) 7.92005e12 0.0610425
\(226\) 5.86857e13 + 1.01647e14i 0.440435 + 0.762856i
\(227\) −1.40116e14 8.08961e13i −1.02408 0.591251i −0.108795 0.994064i \(-0.534699\pi\)
−0.915282 + 0.402813i \(0.868033\pi\)
\(228\) 3.84069e13 6.65227e13i 0.273401 0.473545i
\(229\) 7.46197e13 4.30817e13i 0.517417 0.298731i −0.218460 0.975846i \(-0.570103\pi\)
0.735877 + 0.677115i \(0.236770\pi\)
\(230\) 1.51316e14i 1.02216i
\(231\) −1.32729e14 + 9.26359e13i −0.873564 + 0.609688i
\(232\) 5.27435e13 0.338253
\(233\) 7.78131e13 + 1.34776e14i 0.486314 + 0.842321i 0.999876 0.0157316i \(-0.00500772\pi\)
−0.513562 + 0.858052i \(0.671674\pi\)
\(234\) −1.41733e13 8.18298e12i −0.0863330 0.0498444i
\(235\) −7.99658e13 + 1.38505e14i −0.474785 + 0.822352i
\(236\) −3.59336e13 + 2.07463e13i −0.207983 + 0.120079i
\(237\) 3.24502e12i 0.0183116i
\(238\) 3.26654e12 + 3.80058e13i 0.0179732 + 0.209117i
\(239\) 2.13466e14 1.14536 0.572679 0.819780i \(-0.305904\pi\)
0.572679 + 0.819780i \(0.305904\pi\)
\(240\) −1.57551e13 2.72886e13i −0.0824429 0.142795i
\(241\) −9.99225e13 5.76903e13i −0.509989 0.294442i 0.222840 0.974855i \(-0.428467\pi\)
−0.732829 + 0.680413i \(0.761801\pi\)
\(242\) 9.18658e13 1.59116e14i 0.457364 0.792177i
\(243\) 1.58746e14 9.16518e13i 0.771017 0.445147i
\(244\) 5.63906e13i 0.267219i
\(245\) −1.55740e14 + 1.29872e14i −0.720117 + 0.600507i
\(246\) −1.24768e14 −0.562981
\(247\) −4.92590e13 8.53192e13i −0.216922 0.375720i
\(248\) −2.47950e13 1.43154e13i −0.106575 0.0615309i
\(249\) −1.30039e14 + 2.25235e14i −0.545605 + 0.945016i
\(250\) 1.57120e14 9.07132e13i 0.643563 0.371561i
\(251\) 3.21279e14i 1.28481i −0.766364 0.642406i \(-0.777936\pi\)
0.766364 0.642406i \(-0.222064\pi\)
\(252\) 6.44550e13 5.53980e12i 0.251683 0.0216317i
\(253\) −6.12322e14 −2.33484
\(254\) 1.53916e14 + 2.66591e14i 0.573169 + 0.992758i
\(255\) 4.66141e13 + 2.69126e13i 0.169541 + 0.0978848i
\(256\) −8.79609e12 + 1.52353e13i −0.0312500 + 0.0541266i
\(257\) −2.96288e14 + 1.71062e14i −1.02829 + 0.593683i −0.916494 0.400049i \(-0.868993\pi\)
−0.111795 + 0.993731i \(0.535660\pi\)
\(258\) 2.13472e14i 0.723806i
\(259\) −1.14713e14 1.64362e14i −0.380027 0.544505i
\(260\) −4.04136e13 −0.130824
\(261\) 7.63979e13 + 1.32325e14i 0.241679 + 0.418600i
\(262\) −3.19640e14 1.84544e14i −0.988220 0.570549i
\(263\) 5.15761e13 8.93325e13i 0.155853 0.269945i −0.777517 0.628863i \(-0.783521\pi\)
0.933369 + 0.358918i \(0.116854\pi\)
\(264\) 1.10427e14 6.37551e13i 0.326176 0.188318i
\(265\) 2.32306e14i 0.670788i
\(266\) 3.52692e14 + 1.65120e14i 0.995647 + 0.466132i
\(267\) 3.25480e14 0.898373
\(268\) −6.86194e13 1.18852e14i −0.185199 0.320774i
\(269\) 4.05993e14 + 2.34400e14i 1.07153 + 0.618650i 0.928600 0.371083i \(-0.121013\pi\)
0.142933 + 0.989732i \(0.454347\pi\)
\(270\) 1.35982e14 2.35528e14i 0.350993 0.607938i
\(271\) 3.78122e14 2.18309e14i 0.954589 0.551132i 0.0600855 0.998193i \(-0.480863\pi\)
0.894503 + 0.447061i \(0.147529\pi\)
\(272\) 3.00507e13i 0.0742065i
\(273\) −3.44532e13 + 7.35912e13i −0.0832251 + 0.177767i
\(274\) −3.68462e14 −0.870741
\(275\) 3.95711e13 + 6.85391e13i 0.0914917 + 0.158468i
\(276\) −2.07566e14 1.19838e14i −0.469572 0.271107i
\(277\) 9.87191e13 1.70986e14i 0.218536 0.378515i −0.735825 0.677172i \(-0.763205\pi\)
0.954361 + 0.298657i \(0.0965387\pi\)
\(278\) −4.88828e14 + 2.82225e14i −1.05898 + 0.611401i
\(279\) 8.29422e13i 0.175853i
\(280\) 1.31000e14 9.14287e13i 0.271845 0.189729i
\(281\) 8.30058e13 0.168605 0.0843025 0.996440i \(-0.473134\pi\)
0.0843025 + 0.996440i \(0.473134\pi\)
\(282\) −1.26661e14 2.19384e14i −0.251854 0.436225i
\(283\) 6.14491e14 + 3.54776e14i 1.19618 + 0.690615i 0.959701 0.281022i \(-0.0906733\pi\)
0.236479 + 0.971637i \(0.424007\pi\)
\(284\) −7.52019e13 + 1.30253e14i −0.143324 + 0.248244i
\(285\) 4.75881e14 2.74750e14i 0.888033 0.512706i
\(286\) 1.63539e14i 0.298831i
\(287\) −5.41669e13 6.30226e14i −0.0969264 1.12773i
\(288\) −5.09638e13 −0.0893114
\(289\) −2.65645e14 4.60111e14i −0.455947 0.789724i
\(290\) 3.26759e14 + 1.88655e14i 0.549339 + 0.317161i
\(291\) 9.99221e13 1.73070e14i 0.164552 0.285013i
\(292\) −1.15117e14 + 6.64626e13i −0.185712 + 0.107221i
\(293\) 1.90883e14i 0.301691i −0.988557 0.150845i \(-0.951800\pi\)
0.988557 0.150845i \(-0.0481996\pi\)
\(294\) −5.48082e13 3.16488e14i −0.0848714 0.490088i
\(295\) −2.96824e14 −0.450367
\(296\) 7.89494e13 + 1.36744e14i 0.117381 + 0.203310i
\(297\) 9.53094e14 + 5.50269e14i 1.38866 + 0.801745i
\(298\) 1.32080e14 2.28769e14i 0.188599 0.326662i
\(299\) −2.66215e14 + 1.53699e14i −0.372568 + 0.215102i
\(300\) 3.09780e13i 0.0424939i
\(301\) −1.07828e15 + 9.26766e13i −1.44989 + 0.124615i
\(302\) −3.67585e14 −0.484524
\(303\) −7.02031e11 1.21595e12i −0.000907195 0.00157131i
\(304\) −2.65685e14 1.53393e14i −0.336609 0.194341i
\(305\) −2.01699e14 + 3.49354e14i −0.250556 + 0.433976i
\(306\) 7.53924e13 4.35278e13i 0.0918331 0.0530199i
\(307\) 6.74575e14i 0.805750i 0.915255 + 0.402875i \(0.131989\pi\)
−0.915255 + 0.402875i \(0.868011\pi\)
\(308\) 3.69979e14 + 5.30107e14i 0.433383 + 0.620954i
\(309\) 1.08946e15 1.25159
\(310\) −1.02407e14 1.77375e14i −0.115388 0.199858i
\(311\) −5.62583e14 3.24807e14i −0.621762 0.358974i 0.155793 0.987790i \(-0.450207\pi\)
−0.777555 + 0.628815i \(0.783540\pi\)
\(312\) 3.20064e13 5.54368e13i 0.0346984 0.0600994i
\(313\) −1.00138e15 + 5.78145e14i −1.06496 + 0.614853i −0.926799 0.375558i \(-0.877451\pi\)
−0.138157 + 0.990410i \(0.544118\pi\)
\(314\) 1.04787e15i 1.09328i
\(315\) 4.19130e14 + 1.96224e14i 0.429028 + 0.200858i
\(316\) 1.29603e13 0.0130164
\(317\) −8.96159e14 1.55219e15i −0.883140 1.52964i −0.847831 0.530266i \(-0.822092\pi\)
−0.0353083 0.999376i \(-0.511241\pi\)
\(318\) −3.18662e14 1.83980e14i −0.308154 0.177913i
\(319\) −7.63416e14 + 1.32228e15i −0.724464 + 1.25481i
\(320\) −1.08988e14 + 6.29242e13i −0.101503 + 0.0586028i
\(321\) 9.65909e14i 0.882889i
\(322\) 5.15211e14 1.10048e15i 0.462222 0.987294i
\(323\) 5.24049e14 0.461484
\(324\) 6.92739e13 + 1.19986e14i 0.0598824 + 0.103719i
\(325\) 3.44081e13 + 1.98655e13i 0.0291985 + 0.0168578i
\(326\) 1.92867e14 3.34056e14i 0.160677 0.278300i
\(327\) −1.16265e15 + 6.71258e14i −0.950963 + 0.549038i
\(328\) 4.98312e14i 0.400183i
\(329\) 1.05316e15 7.35032e14i 0.830458 0.579603i
\(330\) 9.12164e14 0.706300
\(331\) −1.33115e14 2.30561e14i −0.101218 0.175315i 0.810969 0.585089i \(-0.198941\pi\)
−0.912187 + 0.409775i \(0.865607\pi\)
\(332\) 8.99565e14 + 5.19364e14i 0.671744 + 0.387832i
\(333\) −2.28713e14 + 3.96142e14i −0.167736 + 0.290527i
\(334\) −7.99572e14 + 4.61633e14i −0.575942 + 0.332520i
\(335\) 9.81759e14i 0.694602i
\(336\) 2.16681e13 + 2.52106e14i 0.0150586 + 0.175205i
\(337\) −2.34808e14 −0.160300 −0.0801498 0.996783i \(-0.525540\pi\)
−0.0801498 + 0.996783i \(0.525540\pi\)
\(338\) 4.86125e14 + 8.41994e14i 0.326023 + 0.564688i
\(339\) −1.15176e15 6.64968e14i −0.758862 0.438129i
\(340\) 1.07486e14 1.86172e14i 0.0695793 0.120515i
\(341\) 7.17771e14 4.14405e14i 0.456520 0.263572i
\(342\) 8.88747e14i 0.555420i
\(343\) 1.57484e15 4.14246e14i 0.967103 0.254386i
\(344\) 8.52585e14 0.514502
\(345\) −8.57282e14 1.48486e15i −0.508404 0.880582i
\(346\) −3.33207e14 1.92377e14i −0.194204 0.112124i
\(347\) −6.63393e14 + 1.14903e15i −0.380009 + 0.658195i −0.991063 0.133394i \(-0.957413\pi\)
0.611054 + 0.791589i \(0.290746\pi\)
\(348\) −5.17569e14 + 2.98818e14i −0.291402 + 0.168241i
\(349\) 2.62751e15i 1.45409i −0.686590 0.727045i \(-0.740893\pi\)
0.686590 0.727045i \(-0.259107\pi\)
\(350\) −1.56475e14 + 1.34488e13i −0.0851212 + 0.00731602i
\(351\) 5.52494e14 0.295451
\(352\) −2.54631e14 4.41034e14i −0.133862 0.231855i
\(353\) 2.19800e15 + 1.26902e15i 1.13601 + 0.655873i 0.945438 0.325801i \(-0.105634\pi\)
0.190567 + 0.981674i \(0.438967\pi\)
\(354\) 2.35076e14 4.07163e14i 0.119451 0.206895i
\(355\) −9.31789e14 + 5.37968e14i −0.465530 + 0.268774i
\(356\) 1.29993e15i 0.638589i
\(357\) −2.47376e14 3.54442e14i −0.119495 0.171213i
\(358\) 8.95016e14 0.425141
\(359\) −5.80208e14 1.00495e15i −0.271030 0.469437i 0.698096 0.716004i \(-0.254031\pi\)
−0.969126 + 0.246567i \(0.920698\pi\)
\(360\) −3.15733e14 1.82289e14i −0.145046 0.0837423i
\(361\) 1.56834e15 2.71644e15i 0.708592 1.22732i
\(362\) 9.66936e14 5.58261e14i 0.429681 0.248077i
\(363\) 2.08186e15i 0.909938i
\(364\) 2.93916e14 + 1.37603e14i 0.126362 + 0.0591587i
\(365\) −9.50902e14 −0.402141
\(366\) −3.19481e14 5.53357e14i −0.132910 0.230207i
\(367\) 1.55002e15 + 8.94904e14i 0.634367 + 0.366252i 0.782441 0.622724i \(-0.213974\pi\)
−0.148074 + 0.988976i \(0.547307\pi\)
\(368\) −4.78622e14 + 8.28998e14i −0.192711 + 0.333785i
\(369\) −1.25018e15 + 7.21794e14i −0.495240 + 0.285927i
\(370\) 1.12955e15i 0.440247i
\(371\) 7.90970e14 1.68949e15i 0.303331 0.647907i
\(372\) 3.24415e14 0.122418
\(373\) 2.39198e15 + 4.14303e15i 0.888187 + 1.53838i 0.842017 + 0.539451i \(0.181368\pi\)
0.0461697 + 0.998934i \(0.485298\pi\)
\(374\) 7.53369e14 + 4.34958e14i 0.275282 + 0.158934i
\(375\) −1.02787e15 + 1.78032e15i −0.369616 + 0.640194i
\(376\) −8.76197e14 + 5.05873e14i −0.310081 + 0.179025i
\(377\) 7.66503e14i 0.266972i
\(378\) −1.79090e15 + 1.24992e15i −0.613931 + 0.428482i
\(379\) −1.31568e15 −0.443931 −0.221965 0.975055i \(-0.571247\pi\)
−0.221965 + 0.975055i \(0.571247\pi\)
\(380\) −1.09732e15 1.90062e15i −0.364446 0.631239i
\(381\) −3.02074e15 1.74403e15i −0.987560 0.570168i
\(382\) −9.39080e14 + 1.62653e15i −0.302219 + 0.523459i
\(383\) −1.31260e15 + 7.57832e14i −0.415854 + 0.240093i −0.693302 0.720647i \(-0.743845\pi\)
0.277448 + 0.960741i \(0.410511\pi\)
\(384\) 1.99337e14i 0.0621728i
\(385\) 3.96006e14 + 4.60750e15i 0.121601 + 1.41482i
\(386\) −2.70618e15 −0.818149
\(387\) 1.23495e15 + 2.13900e15i 0.367607 + 0.636714i
\(388\) −6.91225e14 3.99079e14i −0.202595 0.116968i
\(389\) 1.38559e15 2.39991e15i 0.399886 0.692622i −0.593826 0.804594i \(-0.702383\pi\)
0.993711 + 0.111971i \(0.0357165\pi\)
\(390\) 3.96576e14 2.28963e14i 0.112704 0.0650696i
\(391\) 1.63515e15i 0.457612i
\(392\) −1.26402e15 + 2.18898e14i −0.348368 + 0.0603290i
\(393\) 4.18214e15 1.13512
\(394\) −1.19532e15 2.07036e15i −0.319527 0.553438i
\(395\) 8.02921e13 + 4.63567e13i 0.0211393 + 0.0122048i
\(396\) 7.37656e14 1.27766e15i 0.191286 0.331317i
\(397\) 3.04662e15 1.75897e15i 0.778172 0.449278i −0.0576103 0.998339i \(-0.518348\pi\)
0.835782 + 0.549062i \(0.185015\pi\)
\(398\) 3.46064e15i 0.870679i
\(399\) −4.39642e15 + 3.77865e14i −1.08959 + 0.0936482i
\(400\) 1.23723e14 0.0302058
\(401\) −2.45890e15 4.25894e15i −0.591391 1.02432i −0.994045 0.108967i \(-0.965246\pi\)
0.402655 0.915352i \(-0.368087\pi\)
\(402\) 1.34671e15 + 7.77526e14i 0.319094 + 0.184229i
\(403\) 2.08041e14 3.60337e14i 0.0485644 0.0841160i
\(404\) −4.85640e12 + 2.80384e12i −0.00111693 + 0.000644860i
\(405\) 9.91123e14i 0.224594i
\(406\) −1.73408e15 2.48460e15i −0.387180 0.554754i
\(407\) −4.57089e15 −1.00562
\(408\) 1.70252e14 + 2.94886e14i 0.0369090 + 0.0639282i
\(409\) 2.52087e15 + 1.45543e15i 0.538532 + 0.310921i 0.744484 0.667641i \(-0.232696\pi\)
−0.205952 + 0.978562i \(0.566029\pi\)
\(410\) −1.78238e15 + 3.08717e15i −0.375229 + 0.649915i
\(411\) 3.61569e15 2.08752e15i 0.750136 0.433091i
\(412\) 4.35120e15i 0.889663i
\(413\) 2.15871e15 + 1.01064e15i 0.435004 + 0.203656i
\(414\) −2.77310e15 −0.550760
\(415\) 3.71535e15 + 6.43518e15i 0.727296 + 1.25971i
\(416\) −2.21409e14 1.27830e14i −0.0427204 0.0246646i
\(417\) 3.19789e15 5.53890e15i 0.608201 1.05343i
\(418\) 7.69111e15 4.44046e15i 1.44189 0.832474i
\(419\) 1.87176e14i 0.0345912i −0.999850 0.0172956i \(-0.994494\pi\)
0.999850 0.0172956i \(-0.00550564\pi\)
\(420\) −7.67500e14 + 1.63936e15i −0.139824 + 0.298661i
\(421\) −2.95025e15 −0.529866 −0.264933 0.964267i \(-0.585350\pi\)
−0.264933 + 0.964267i \(0.585350\pi\)
\(422\) 1.17062e15 + 2.02757e15i 0.207272 + 0.359006i
\(423\) −2.53830e15 1.46549e15i −0.443100 0.255824i
\(424\) −7.34797e14 + 1.27271e15i −0.126466 + 0.219045i
\(425\) −1.83028e14 + 1.05671e14i −0.0310587 + 0.0179317i
\(426\) 1.70422e15i 0.285147i
\(427\) 2.65640e15 1.85399e15i 0.438254 0.305871i
\(428\) 3.85774e15 0.627582
\(429\) 9.26530e14 + 1.60480e15i 0.148633 + 0.257440i
\(430\) 5.28197e15 + 3.04955e15i 0.835575 + 0.482420i
\(431\) 9.33046e14 1.61608e15i 0.145559 0.252116i −0.784022 0.620733i \(-0.786835\pi\)
0.929581 + 0.368617i \(0.120169\pi\)
\(432\) 1.48997e15 8.60237e14i 0.229233 0.132348i
\(433\) 6.43623e15i 0.976572i 0.872684 + 0.488286i \(0.162378\pi\)
−0.872684 + 0.488286i \(0.837622\pi\)
\(434\) 1.40842e14 + 1.63868e15i 0.0210762 + 0.245220i
\(435\) −4.27529e15 −0.631001
\(436\) 2.68094e15 + 4.64352e15i 0.390272 + 0.675971i
\(437\) −1.44567e16 8.34659e15i −2.07578 1.19845i
\(438\) 7.53088e14 1.30439e15i 0.106660 0.184740i
\(439\) 3.66616e15 2.11666e15i 0.512181 0.295708i −0.221548 0.975149i \(-0.571111\pi\)
0.733730 + 0.679441i \(0.237778\pi\)
\(440\) 3.64309e15i 0.502058i
\(441\) −2.38009e15 2.85416e15i −0.323565 0.388013i
\(442\) 4.36717e14 0.0585688
\(443\) 3.53638e15 + 6.12518e15i 0.467882 + 0.810395i 0.999326 0.0366980i \(-0.0116840\pi\)
−0.531445 + 0.847093i \(0.678351\pi\)
\(444\) −1.54945e15 8.94575e14i −0.202246 0.116767i
\(445\) 4.64964e15 8.05342e15i 0.598769 1.03710i
\(446\) 2.38226e15 1.37540e15i 0.302677 0.174751i
\(447\) 2.99319e15i 0.375223i
\(448\) 1.00689e15 8.65401e13i 0.124541 0.0107041i
\(449\) −7.31324e15 −0.892549 −0.446274 0.894896i \(-0.647249\pi\)
−0.446274 + 0.894896i \(0.647249\pi\)
\(450\) 1.79210e14 + 3.10401e14i 0.0215818 + 0.0373808i
\(451\) −1.24926e16 7.21262e15i −1.48455 0.857105i
\(452\) −2.65581e15 + 4.60000e15i −0.311435 + 0.539421i
\(453\) 3.60708e15 2.08255e15i 0.417414 0.240994i
\(454\) 7.32188e15i 0.836156i
\(455\) 1.32870e15 + 1.90377e15i 0.149747 + 0.214559i
\(456\) 3.47620e15 0.386647
\(457\) 6.51453e15 + 1.12835e16i 0.715131 + 1.23864i 0.962909 + 0.269827i \(0.0869665\pi\)
−0.247777 + 0.968817i \(0.579700\pi\)
\(458\) 3.37690e15 + 1.94966e15i 0.365869 + 0.211235i
\(459\) −1.46945e15 + 2.54516e15i −0.157137 + 0.272169i
\(460\) −5.93037e15 + 3.42390e15i −0.625943 + 0.361388i
\(461\) 2.39251e15i 0.249257i −0.992203 0.124629i \(-0.960226\pi\)
0.992203 0.124629i \(-0.0397739\pi\)
\(462\) −6.63389e15 3.10579e15i −0.682208 0.319389i
\(463\) 7.43873e15 0.755115 0.377557 0.925986i \(-0.376764\pi\)
0.377557 + 0.925986i \(0.376764\pi\)
\(464\) 1.19345e15 + 2.06712e15i 0.119590 + 0.207137i
\(465\) 2.00983e15 + 1.16038e15i 0.198812 + 0.114784i
\(466\) −3.52142e15 + 6.09927e15i −0.343876 + 0.595611i
\(467\) −2.18404e15 + 1.26096e15i −0.210552 + 0.121562i −0.601568 0.798822i \(-0.705457\pi\)
0.391016 + 0.920384i \(0.372124\pi\)
\(468\) 7.40639e14i 0.0704906i
\(469\) −3.34275e15 + 7.14004e15i −0.314100 + 0.670909i
\(470\) −7.23768e15 −0.671448
\(471\) −5.93672e15 1.02827e16i −0.543777 0.941850i
\(472\) −1.62617e15 9.38869e14i −0.147067 0.0849089i
\(473\) −1.23404e16 + 2.13742e16i −1.10195 + 1.90864i
\(474\) −1.27178e14 + 7.34264e13i −0.0112135 + 0.00647414i
\(475\) 2.15758e15i 0.187848i
\(476\) −1.41561e15 + 9.87995e14i −0.121703 + 0.0849402i
\(477\) −4.25735e15 −0.361434
\(478\) 4.83018e15 + 8.36612e15i 0.404945 + 0.701385i
\(479\) 2.43833e15 + 1.40777e15i 0.201873 + 0.116552i 0.597529 0.801847i \(-0.296149\pi\)
−0.395656 + 0.918399i \(0.629483\pi\)
\(480\) 7.12994e14 1.23494e15i 0.0582960 0.100972i
\(481\) −1.98726e15 + 1.14734e15i −0.160466 + 0.0926452i
\(482\) 5.22153e15i 0.416404i
\(483\) 1.17903e15 + 1.37178e16i 0.0928625 + 1.08045i
\(484\) 8.31474e15 0.646810
\(485\) −2.85487e15 4.94479e15i −0.219349 0.379924i
\(486\) 7.18400e15 + 4.14769e15i 0.545191 + 0.314766i
\(487\) 1.11137e16 1.92494e16i 0.833074 1.44293i −0.0625147 0.998044i \(-0.519912\pi\)
0.895589 0.444883i \(-0.146755\pi\)
\(488\) −2.21005e15 + 1.27597e15i −0.163638 + 0.0944762i
\(489\) 4.37076e15i 0.319671i
\(490\) −8.61390e15 3.16506e15i −0.622334 0.228668i
\(491\) 2.73159e16 1.94952 0.974758 0.223265i \(-0.0716714\pi\)
0.974758 + 0.223265i \(0.0716714\pi\)
\(492\) −2.82318e15 4.88990e15i −0.199044 0.344754i
\(493\) −3.53102e15 2.03864e15i −0.245934 0.141990i
\(494\) 2.22921e15 3.86110e15i 0.153387 0.265674i
\(495\) 9.13992e15 5.27694e15i 0.621314 0.358716i
\(496\) 1.29568e15i 0.0870179i
\(497\) 8.60833e15 7.39871e14i 0.571190 0.0490928i
\(498\) −1.17698e16 −0.771603
\(499\) −9.95390e15 1.72407e16i −0.644748 1.11674i −0.984360 0.176171i \(-0.943629\pi\)
0.339612 0.940566i \(-0.389704\pi\)
\(500\) 7.11043e15 + 4.10521e15i 0.455068 + 0.262733i
\(501\) 5.23076e15 9.05994e15i 0.330779 0.572927i
\(502\) 1.25915e16 7.26971e15i 0.786784 0.454250i
\(503\) 6.87587e15i 0.424541i 0.977211 + 0.212271i \(0.0680858\pi\)
−0.977211 + 0.212271i \(0.931914\pi\)
\(504\) 1.67557e15 + 2.40076e15i 0.102230 + 0.146476i
\(505\) −4.01154e13 −0.00241860
\(506\) −1.38553e16 2.39980e16i −0.825490 1.42979i
\(507\) −9.54063e15 5.50828e15i −0.561732 0.324316i
\(508\) −6.96546e15 + 1.20645e16i −0.405292 + 0.701986i
\(509\) −6.71112e15 + 3.87467e15i −0.385912 + 0.222807i −0.680387 0.732853i \(-0.738188\pi\)
0.294475 + 0.955659i \(0.404855\pi\)
\(510\) 2.43585e15i 0.138430i
\(511\) 6.91562e15 + 3.23769e15i 0.388424 + 0.181849i
\(512\) −7.96131e14 −0.0441942
\(513\) 1.50015e16 + 2.59834e16i 0.823058 + 1.42558i
\(514\) −1.34085e16 7.74138e15i −0.727110 0.419797i
\(515\) 1.55635e16 2.69567e16i 0.834187 1.44485i
\(516\) −8.36635e15 + 4.83032e15i −0.443239 + 0.255904i
\(517\) 2.92882e16i 1.53373i
\(518\) 3.84597e15 8.21490e15i 0.199080 0.425230i
\(519\) 4.35965e15 0.223073
\(520\) −9.14455e14 1.58388e15i −0.0462533 0.0801130i
\(521\) 2.06740e16 + 1.19361e16i 1.03371 + 0.596811i 0.918044 0.396478i \(-0.129768\pi\)
0.115662 + 0.993289i \(0.463101\pi\)
\(522\) −3.45737e15 + 5.98835e15i −0.170893 + 0.295995i
\(523\) −1.80842e16 + 1.04409e16i −0.883670 + 0.510187i −0.871867 0.489743i \(-0.837090\pi\)
−0.0118030 + 0.999930i \(0.503757\pi\)
\(524\) 1.67031e16i 0.806878i
\(525\) 1.45929e15 1.01848e15i 0.0696923 0.0486405i
\(526\) 4.66814e15 0.220409
\(527\) 1.10663e15 + 1.91675e15i 0.0516583 + 0.0894748i
\(528\) 4.99736e15 + 2.88522e15i 0.230641 + 0.133161i
\(529\) −1.50860e16 + 2.61297e16i −0.688398 + 1.19234i
\(530\) −9.10450e15 + 5.25648e15i −0.410772 + 0.237159i
\(531\) 5.43973e15i 0.242667i
\(532\) 1.50915e15 + 1.75589e16i 0.0665678 + 0.774509i
\(533\) −7.24179e15 −0.315851
\(534\) 7.36477e15 + 1.27562e16i 0.317623 + 0.550139i
\(535\) 2.38997e16 + 1.37985e16i 1.01922 + 0.588449i
\(536\) 3.10536e15 5.37864e15i 0.130955 0.226821i
\(537\) −8.78273e15 + 5.07071e15i −0.366255 + 0.211457i
\(538\) 2.12155e16i 0.874903i
\(539\) 1.28079e16 3.48573e16i 0.522328 1.42155i
\(540\) 1.23077e16 0.496380
\(541\) −1.60100e16 2.77302e16i −0.638569 1.10603i −0.985747 0.168235i \(-0.946193\pi\)
0.347177 0.937799i \(-0.387140\pi\)
\(542\) 1.71119e16 + 9.87954e15i 0.674996 + 0.389709i
\(543\) −6.32565e15 + 1.09564e16i −0.246778 + 0.427432i
\(544\) 1.17774e15 6.79971e14i 0.0454420 0.0262359i
\(545\) 3.83570e16i 1.46375i
\(546\) −3.66376e15 + 3.14894e14i −0.138284 + 0.0118853i
\(547\) −3.33242e16 −1.24404 −0.622022 0.783000i \(-0.713688\pi\)
−0.622022 + 0.783000i \(0.713688\pi\)
\(548\) −8.33734e15 1.44407e16i −0.307854 0.533218i
\(549\) −6.40242e15 3.69644e15i −0.233835 0.135005i
\(550\) −1.79078e15 + 3.10173e15i −0.0646944 + 0.112054i
\(551\) −3.60480e16 + 2.08123e16i −1.28817 + 0.743723i
\(552\) 1.08465e16i 0.383404i
\(553\) −4.26102e14 6.10522e14i −0.0148992 0.0213477i
\(554\) 8.93503e15 0.309056
\(555\) −6.39948e15 1.10842e16i −0.218971 0.379269i
\(556\) −2.21218e16 1.27720e16i −0.748811 0.432326i
\(557\) −1.50168e15 + 2.60098e15i −0.0502857 + 0.0870975i −0.890073 0.455819i \(-0.849347\pi\)
0.839787 + 0.542916i \(0.182680\pi\)
\(558\) 3.25066e15 1.87677e15i 0.107688 0.0621735i
\(559\) 1.23903e16i 0.406080i
\(560\) 6.54744e15 + 3.06532e15i 0.212297 + 0.0993911i
\(561\) −9.85701e15 −0.316204
\(562\) 1.87821e15 + 3.25315e15i 0.0596109 + 0.103249i
\(563\) 2.59585e16 + 1.49872e16i 0.815135 + 0.470618i 0.848736 0.528817i \(-0.177364\pi\)
−0.0336009 + 0.999435i \(0.510698\pi\)
\(564\) 5.73204e15 9.92818e15i 0.178088 0.308457i
\(565\) −3.29068e16 + 1.89988e16i −1.01157 + 0.584030i
\(566\) 3.21107e16i 0.976677i
\(567\) 3.37464e15 7.20814e15i 0.101561 0.216933i
\(568\) −6.80650e15 −0.202691
\(569\) 1.35760e16 + 2.35144e16i 0.400037 + 0.692884i 0.993730 0.111808i \(-0.0356641\pi\)
−0.593693 + 0.804691i \(0.702331\pi\)
\(570\) 2.15359e16 + 1.24338e16i 0.627934 + 0.362538i
\(571\) −3.50961e15 + 6.07881e15i −0.101261 + 0.175389i −0.912204 0.409735i \(-0.865621\pi\)
0.810944 + 0.585124i \(0.198954\pi\)
\(572\) 6.40939e15 3.70046e15i 0.182996 0.105653i
\(573\) 2.12814e16i 0.601274i
\(574\) 2.34741e16 1.63833e16i 0.656322 0.458068i
\(575\) 6.73215e15 0.186272
\(576\) −1.15318e15 1.99736e15i −0.0315763 0.0546918i
\(577\) −4.43026e16 2.55781e16i −1.20053 0.693129i −0.239860 0.970807i \(-0.577102\pi\)
−0.960674 + 0.277679i \(0.910435\pi\)
\(578\) 1.20217e16 2.08222e16i 0.322403 0.558419i
\(579\) 2.65555e16 1.53318e16i 0.704828 0.406933i
\(580\) 1.70751e16i 0.448533i
\(581\) −5.10974e15 5.94514e16i −0.132844 1.54563i
\(582\) 9.04392e15 0.232712
\(583\) −2.12711e16 3.68426e16i −0.541724 0.938293i
\(584\) −5.20959e15 3.00776e15i −0.131319 0.0758168i
\(585\) 2.64914e15 4.58844e15i 0.0660951 0.114480i
\(586\) 7.48106e15 4.31919e15i 0.184747 0.106664i
\(587\) 2.97094e16i 0.726216i 0.931747 + 0.363108i \(0.118284\pi\)
−0.931747 + 0.363108i \(0.881716\pi\)
\(588\) 1.11636e16 9.30935e15i 0.270110 0.225245i
\(589\) 2.25951e16 0.541157
\(590\) −6.71635e15 1.16331e16i −0.159229 0.275792i
\(591\) 2.34592e16 + 1.35442e16i 0.550540 + 0.317855i
\(592\) −3.57284e15 + 6.18834e15i −0.0830010 + 0.143762i
\(593\) 4.00972e16 2.31501e16i 0.922116 0.532384i 0.0378064 0.999285i \(-0.487963\pi\)
0.884309 + 0.466901i \(0.154630\pi\)
\(594\) 4.98047e16i 1.13384i
\(595\) −1.23039e16 + 1.05750e15i −0.277295 + 0.0238330i
\(596\) 1.19545e16 0.266719
\(597\) −1.96063e16 3.39590e16i −0.433060 0.750083i
\(598\) −1.20475e16 6.95564e15i −0.263446 0.152100i
\(599\) −2.05859e16 + 3.56558e16i −0.445664 + 0.771914i −0.998098 0.0616433i \(-0.980366\pi\)
0.552434 + 0.833557i \(0.313699\pi\)
\(600\) −1.21409e15 + 7.00953e14i −0.0260221 + 0.0150239i
\(601\) 1.89158e15i 0.0401402i −0.999799 0.0200701i \(-0.993611\pi\)
0.999799 0.0200701i \(-0.00638893\pi\)
\(602\) −2.80309e16 4.01629e16i −0.588923 0.843812i
\(603\) 1.79922e16 0.374266
\(604\) −8.31749e15 1.44063e16i −0.171305 0.296709i
\(605\) 5.15119e16 + 2.97404e16i 1.05045 + 0.606478i
\(606\) 3.17703e13 5.50278e13i 0.000641484 0.00111108i
\(607\) 7.45528e15 4.30431e15i 0.149050 0.0860541i −0.423620 0.905840i \(-0.639241\pi\)
0.572670 + 0.819786i \(0.305908\pi\)
\(608\) 1.38836e16i 0.274840i
\(609\) 3.10929e16 + 1.45568e16i 0.609477 + 0.285339i
\(610\) −1.82557e16 −0.354340
\(611\) −7.35167e15 1.27335e16i −0.141299 0.244737i
\(612\) 3.41187e15 + 1.96985e15i 0.0649358 + 0.0374907i
\(613\) 7.75623e15 1.34342e16i 0.146180 0.253191i −0.783633 0.621225i \(-0.786635\pi\)
0.929813 + 0.368033i \(0.119969\pi\)
\(614\) −2.64378e16 + 1.52639e16i −0.493419 + 0.284876i
\(615\) 4.03922e16i 0.746529i
\(616\) −1.24042e16 + 2.64951e16i −0.227031 + 0.484932i
\(617\) 6.49218e16 1.17674 0.588368 0.808593i \(-0.299770\pi\)
0.588368 + 0.808593i \(0.299770\pi\)
\(618\) 2.46517e16 + 4.26980e16i 0.442503 + 0.766437i
\(619\) 3.01581e16 + 1.74118e16i 0.536117 + 0.309527i 0.743504 0.668732i \(-0.233163\pi\)
−0.207387 + 0.978259i \(0.566496\pi\)
\(620\) 4.63443e15 8.02707e15i 0.0815918 0.141321i
\(621\) 8.10741e16 4.68081e16i 1.41362 0.816153i
\(622\) 2.93982e16i 0.507666i
\(623\) −6.12362e16 + 4.27387e16i −1.04732 + 0.730959i
\(624\) 2.89689e15 0.0490710
\(625\) 2.57664e16 + 4.46288e16i 0.432289 + 0.748747i
\(626\) −4.53172e16 2.61639e16i −0.753038 0.434766i
\(627\) −5.03148e16 + 8.71479e16i −0.828115 + 1.43434i
\(628\) −4.10681e16 + 2.37107e16i −0.669494 + 0.386532i
\(629\) 1.22062e16i 0.197095i
\(630\) 1.79344e15 + 2.08665e16i 0.0286843 + 0.333739i
\(631\) −6.99817e16 −1.10869 −0.554343 0.832289i \(-0.687030\pi\)
−0.554343 + 0.832289i \(0.687030\pi\)
\(632\) 2.93257e14 + 5.07937e14i 0.00460200 + 0.00797090i
\(633\) −2.29744e16 1.32643e16i −0.357126 0.206187i
\(634\) 4.05555e16 7.02442e16i 0.624474 1.08162i
\(635\) −8.63055e16 + 4.98285e16i −1.31643 + 0.760039i
\(636\) 1.66520e16i 0.251607i
\(637\) −3.18117e15 1.83696e16i −0.0476157 0.274956i
\(638\) −6.90965e16 −1.02455
\(639\) −9.85906e15 1.70764e16i −0.144821 0.250837i
\(640\) −4.93223e15 2.84763e15i −0.0717734 0.0414384i
\(641\) −8.26267e15 + 1.43114e16i −0.119117 + 0.206316i −0.919418 0.393282i \(-0.871340\pi\)
0.800301 + 0.599598i \(0.204673\pi\)
\(642\) −3.78557e16 + 2.18560e16i −0.540657 + 0.312148i
\(643\) 2.58392e16i 0.365605i 0.983150 + 0.182803i \(0.0585170\pi\)
−0.983150 + 0.182803i \(0.941483\pi\)
\(644\) 5.47877e16 4.70891e15i 0.768011 0.0660093i
\(645\) −6.91088e16 −0.959788
\(646\) 1.18579e16 + 2.05384e16i 0.163159 + 0.282600i
\(647\) 8.66866e16 + 5.00485e16i 1.18175 + 0.682284i 0.956419 0.291998i \(-0.0943199\pi\)
0.225332 + 0.974282i \(0.427653\pi\)
\(648\) −3.13498e15 + 5.42994e15i −0.0423433 + 0.0733407i
\(649\) 4.70747e16 2.71786e16i 0.629969 0.363713i
\(650\) 1.79802e15i 0.0238405i
\(651\) −1.06660e16 1.52823e16i −0.140125 0.200772i
\(652\) 1.74564e16 0.227231
\(653\) −1.53565e16 2.65983e16i −0.198068 0.343064i 0.749834 0.661626i \(-0.230133\pi\)
−0.947902 + 0.318562i \(0.896800\pi\)
\(654\) −5.26156e16 3.03777e16i −0.672432 0.388229i
\(655\) 5.97440e16 1.03480e17i 0.756565 1.31041i
\(656\) −1.95298e16 + 1.12755e16i −0.245061 + 0.141486i
\(657\) 1.74267e16i 0.216682i
\(658\) 5.26375e16 + 2.46433e16i 0.648544 + 0.303629i
\(659\) 1.64417e16 0.200740 0.100370 0.994950i \(-0.467997\pi\)
0.100370 + 0.994950i \(0.467997\pi\)
\(660\) 2.06399e16 + 3.57494e16i 0.249715 + 0.432519i
\(661\) −6.43528e16 3.71541e16i −0.771540 0.445449i 0.0618837 0.998083i \(-0.480289\pi\)
−0.833424 + 0.552635i \(0.813623\pi\)
\(662\) 6.02408e15 1.04340e16i 0.0715719 0.123966i
\(663\) −4.28547e15 + 2.47422e15i −0.0504565 + 0.0291311i
\(664\) 4.70075e16i 0.548477i
\(665\) −5.34555e16 + 1.14180e17i −0.618105 + 1.32026i
\(666\) −2.07007e16 −0.237214
\(667\) 6.49392e16 + 1.12478e17i 0.737483 + 1.27736i
\(668\) −3.61845e16 2.08911e16i −0.407252 0.235127i
\(669\) −1.55846e16 + 2.69934e16i −0.173836 + 0.301093i
\(670\) 3.84770e16 2.22147e16i 0.425355 0.245579i
\(671\) 7.38743e16i 0.809391i
\(672\) −9.39020e15 + 6.55372e15i −0.101967 + 0.0711659i
\(673\) 1.00460e17 1.08119 0.540596 0.841283i \(-0.318199\pi\)
0.540596 + 0.841283i \(0.318199\pi\)
\(674\) −5.31309e15 9.20254e15i −0.0566745 0.0981631i
\(675\) −1.04788e16 6.04992e15i −0.110787 0.0639627i
\(676\) −2.19995e16 + 3.81043e16i −0.230533 + 0.399295i
\(677\) −2.84629e16 + 1.64330e16i −0.295629 + 0.170681i −0.640477 0.767977i \(-0.721264\pi\)
0.344849 + 0.938658i \(0.387930\pi\)
\(678\) 6.01860e16i 0.619608i
\(679\) 3.92632e15 + 4.56824e16i 0.0400652 + 0.466155i
\(680\) 9.72855e15 0.0983999
\(681\) 4.14821e16 + 7.18490e16i 0.415889 + 0.720341i
\(682\) 3.24826e16 + 1.87538e16i 0.322808 + 0.186373i
\(683\) −2.00945e16 + 3.48046e16i −0.197949 + 0.342857i −0.947863 0.318678i \(-0.896761\pi\)
0.749915 + 0.661535i \(0.230095\pi\)
\(684\) 3.48316e16 2.01101e16i 0.340124 0.196371i
\(685\) 1.19285e17i 1.15463i
\(686\) 5.18697e16 + 5.23477e16i 0.497701 + 0.502288i
\(687\) −4.41831e16 −0.420258
\(688\) 1.92918e16 + 3.34144e16i 0.181904 + 0.315067i
\(689\) −1.84958e16 1.06785e16i −0.172885 0.0998152i
\(690\) 3.87962e16 6.71969e16i 0.359496 0.622666i
\(691\) 1.38373e17 7.98899e16i 1.27111 0.733878i 0.295916 0.955214i \(-0.404375\pi\)
0.975198 + 0.221336i \(0.0710418\pi\)
\(692\) 1.74120e16i 0.158567i
\(693\) −8.44391e16 + 7.25740e15i −0.762332 + 0.0655212i
\(694\) −6.00435e16 −0.537414
\(695\) −9.13668e16 1.58252e17i −0.810736 1.40424i
\(696\) −2.34225e16 1.35230e16i −0.206052 0.118964i
\(697\) 1.92607e16 3.33605e16i 0.167987 0.290961i
\(698\) 1.02977e17 5.94537e16i 0.890444 0.514098i
\(699\) 7.98023e16i 0.684152i
\(700\) −4.06772e15 5.82824e15i −0.0345750 0.0495393i
\(701\) 1.35098e17 1.13852 0.569262 0.822156i \(-0.307229\pi\)
0.569262 + 0.822156i \(0.307229\pi\)
\(702\) 1.25015e16 + 2.16533e16i 0.104458 + 0.180926i
\(703\) −1.07917e17 6.23060e16i −0.894044 0.516176i
\(704\) 1.15233e16 1.99589e16i 0.0946544 0.163946i
\(705\) 7.10228e16 4.10050e16i 0.578447 0.333966i
\(706\) 1.14858e17i 0.927544i
\(707\) 2.91748e14 + 1.36588e14i 0.00233610 + 0.00109369i
\(708\) 2.12766e16 0.168929
\(709\) 3.51496e15 + 6.08809e15i 0.0276722 + 0.0479296i 0.879530 0.475844i \(-0.157857\pi\)
−0.851858 + 0.523773i \(0.824524\pi\)
\(710\) −4.21679e16 2.43457e16i −0.329179 0.190052i
\(711\) −8.49554e14 + 1.47147e15i −0.00657618 + 0.0113903i
\(712\) 5.09468e16 2.94141e16i 0.391054 0.225775i
\(713\) 7.05020e16i 0.536617i
\(714\) 8.29375e15 1.77152e16i 0.0625981 0.133708i
\(715\) 5.29437e16 0.396258
\(716\) 2.02519e16 + 3.50773e16i 0.150310 + 0.260344i
\(717\) −9.47964e16 5.47307e16i −0.697713 0.402825i
\(718\) 2.62572e16 4.54788e16i 0.191647 0.331942i
\(719\) −1.36454e17 + 7.87819e16i −0.987675 + 0.570234i −0.904578 0.426307i \(-0.859814\pi\)
−0.0830962 + 0.996542i \(0.526481\pi\)
\(720\) 1.64989e16i 0.118430i
\(721\) −2.04973e17 + 1.43057e17i −1.45910 + 1.01835i
\(722\) 1.41950e17 1.00210
\(723\) 2.95825e16 + 5.12385e16i 0.207112 + 0.358729i
\(724\) 4.37585e16 + 2.52640e16i 0.303831 + 0.175417i
\(725\) 8.39335e15 1.45377e16i 0.0577973 0.100108i
\(726\) −8.15920e16 + 4.71071e16i −0.557221 + 0.321712i
\(727\) 1.73285e17i 1.17370i 0.809697 + 0.586848i \(0.199631\pi\)
−0.809697 + 0.586848i \(0.800369\pi\)
\(728\) 1.25766e15 + 1.46327e16i 0.00844838 + 0.0982961i
\(729\) −1.29947e17 −0.865767
\(730\) −2.15165e16 3.72676e16i −0.142178 0.246260i
\(731\) −5.70780e16 3.29540e16i −0.374080 0.215975i
\(732\) 1.44580e16 2.50421e16i 0.0939816 0.162781i
\(733\) 1.32918e17 7.67401e16i 0.856957 0.494764i −0.00603505 0.999982i \(-0.501921\pi\)
0.862992 + 0.505217i \(0.168588\pi\)
\(734\) 8.09975e16i 0.517959i
\(735\) 1.02459e17 1.77435e16i 0.649871 0.112542i
\(736\) −4.33199e16 −0.272534
\(737\) 8.98946e16 + 1.55702e17i 0.560956 + 0.971604i
\(738\) −5.65768e16 3.26647e16i −0.350187 0.202181i
\(739\) −7.76288e16 + 1.34457e17i −0.476602 + 0.825499i −0.999641 0.0268099i \(-0.991465\pi\)
0.523038 + 0.852309i \(0.324798\pi\)
\(740\) −4.42693e16 + 2.55589e16i −0.269595 + 0.155651i
\(741\) 5.05183e16i 0.305168i
\(742\) 8.41119e16 7.22927e15i 0.504004 0.0433183i
\(743\) −1.55426e17 −0.923830 −0.461915 0.886924i \(-0.652838\pi\)
−0.461915 + 0.886924i \(0.652838\pi\)
\(744\) 7.34068e15 + 1.27144e16i 0.0432812 + 0.0749652i
\(745\) 7.40610e16 + 4.27592e16i 0.433164 + 0.250087i
\(746\) −1.08249e17 + 1.87492e17i −0.628043 + 1.08780i
\(747\) −1.17934e17 + 6.80893e16i −0.678759 + 0.391882i
\(748\) 3.93679e16i 0.224767i
\(749\) −1.26833e17 1.81727e17i −0.718360 1.02927i
\(750\) −9.30322e16 −0.522716
\(751\) 1.48252e17 + 2.56780e17i 0.826344 + 1.43127i 0.900888 + 0.434051i \(0.142916\pi\)
−0.0745445 + 0.997218i \(0.523750\pi\)
\(752\) −3.96522e16 2.28932e16i −0.219260 0.126590i
\(753\) −8.23731e16 + 1.42674e17i −0.451872 + 0.782665i
\(754\) −3.00407e16 + 1.73440e16i −0.163486 + 0.0943889i
\(755\) 1.19001e17i 0.642493i
\(756\) −8.95101e16 4.19060e16i −0.479448 0.224463i
\(757\) −2.70923e16 −0.143970 −0.0719848 0.997406i \(-0.522933\pi\)
−0.0719848 + 0.997406i \(0.522933\pi\)
\(758\) −2.97705e16 5.15639e16i −0.156953 0.271851i
\(759\) 2.71921e17 + 1.56994e17i 1.42230 + 0.821168i
\(760\) 4.96592e16 8.60122e16i 0.257702 0.446353i
\(761\) 2.95361e17 1.70527e17i 1.52071 0.877980i 0.521004 0.853554i \(-0.325558\pi\)
0.999702 0.0244255i \(-0.00777565\pi\)
\(762\) 1.57851e17i 0.806340i
\(763\) 1.30600e17 2.78959e17i 0.661907 1.41382i
\(764\) −8.49958e16 −0.427403
\(765\) 1.40916e16 + 2.44074e16i 0.0703059 + 0.121773i
\(766\) −5.94016e16 3.42955e16i −0.294053 0.169772i
\(767\) 1.36443e16 2.36325e16i 0.0670159 0.116075i
\(768\) 7.81238e15 4.51048e15i 0.0380729 0.0219814i
\(769\) 1.79123e17i 0.866153i 0.901357 + 0.433076i \(0.142572\pi\)
−0.901357 + 0.433076i \(0.857428\pi\)
\(770\) −1.71616e17 + 1.19776e17i −0.823403 + 0.574679i
\(771\) 1.75435e17 0.835199
\(772\) −6.12338e16 1.06060e17i −0.289259 0.501012i
\(773\) −5.21474e16 3.01073e16i −0.244431 0.141122i 0.372781 0.927919i \(-0.378404\pi\)
−0.617211 + 0.786797i \(0.711738\pi\)
\(774\) −5.58875e16 + 9.67999e16i −0.259937 + 0.450225i
\(775\) −7.89151e15 + 4.55617e15i −0.0364208 + 0.0210276i
\(776\) 3.61205e16i 0.165418i
\(777\) 8.80124e15 + 1.02402e17i 0.0399961 + 0.465351i
\(778\) 1.25409e17 0.565524
\(779\) −1.96631e17 3.40575e17i −0.879889 1.52401i
\(780\) 1.79470e16 + 1.03617e16i 0.0796936 + 0.0460111i
\(781\) 9.85180e16 1.70638e17i 0.434119 0.751917i
\(782\) 6.40846e16 3.69993e16i 0.280229 0.161790i
\(783\) 2.33433e17i 1.01296i
\(784\) −3.71806e16 4.45863e16i −0.160111 0.192002i
\(785\) −3.39236e17 −1.44972
\(786\) 9.46311e16 + 1.63906e17i 0.401327 + 0.695119i
\(787\) 1.49941e16 + 8.65682e15i 0.0631060 + 0.0364343i 0.531221 0.847233i \(-0.321733\pi\)
−0.468115 + 0.883668i \(0.655067\pi\)
\(788\) 5.40942e16 9.36938e16i 0.225940 0.391340i
\(789\) −4.58081e16 + 2.64473e16i −0.189880 + 0.109628i
\(790\) 4.19573e15i 0.0172602i
\(791\) 3.04010e17 2.61291e16i 1.24116 0.106676i
\(792\) 6.67650e16 0.270519
\(793\) −1.85433e16 3.21179e16i −0.0745670 0.129154i
\(794\) 1.37874e17 + 7.96018e16i 0.550250 + 0.317687i
\(795\) 5.95612e16 1.03163e17i 0.235918 0.408621i
\(796\) −1.35629e17 + 7.83054e16i −0.533180 + 0.307832i
\(797\) 1.59583e17i 0.622640i 0.950305 + 0.311320i \(0.100771\pi\)
−0.950305 + 0.311320i \(0.899229\pi\)
\(798\) −1.14289e17 1.63754e17i −0.442575 0.634124i
\(799\) 7.82117e16 0.300601
\(800\) 2.79953e15 + 4.84894e15i 0.0106794 + 0.0184972i
\(801\) 1.47591e17 + 8.52115e16i 0.558809 + 0.322629i
\(802\) 1.11277e17 1.92738e17i 0.418176 0.724303i
\(803\) 1.50808e17 8.70692e16i 0.562512 0.324766i
\(804\) 7.03736e16i 0.260539i
\(805\) 3.56266e17 + 1.66793e17i 1.30918 + 0.612919i
\(806\) 1.88297e16 0.0686804
\(807\) −1.20196e17 2.08186e17i −0.435161 0.753721i
\(808\) −2.19775e14 1.26887e14i −0.000789789 0.000455985i
\(809\) 9.64003e15 1.66970e16i 0.0343864 0.0595591i −0.848320 0.529484i \(-0.822386\pi\)
0.882706 + 0.469925i \(0.155719\pi\)
\(810\) −3.88439e16 + 2.24266e16i −0.137535 + 0.0794058i
\(811\) 3.01693e17i 1.06033i 0.847896 + 0.530163i \(0.177869\pi\)
−0.847896 + 0.530163i \(0.822131\pi\)
\(812\) 5.81382e16 1.24182e17i 0.202827 0.433233i
\(813\) −2.23890e17 −0.775338
\(814\) −1.03427e17 1.79141e17i −0.355540 0.615814i
\(815\) 1.08146e17 + 6.24384e16i 0.369034 + 0.213062i
\(816\) −7.70474e15 + 1.33450e16i −0.0260986 + 0.0452041i
\(817\) −5.82706e17 + 3.36426e17i −1.95937 + 1.13125i
\(818\) 1.31730e17i 0.439709i
\(819\) −3.48894e16 + 2.43504e16i −0.115609 + 0.0806868i
\(820\) −1.61322e17 −0.530654
\(821\) 8.00654e16 + 1.38677e17i 0.261448 + 0.452842i 0.966627 0.256188i \(-0.0824666\pi\)
−0.705179 + 0.709030i \(0.749133\pi\)
\(822\) 1.63627e17 + 9.44703e16i 0.530426 + 0.306242i
\(823\) 2.11116e17 3.65664e17i 0.679395 1.17675i −0.295769 0.955260i \(-0.595576\pi\)
0.975163 0.221486i \(-0.0710908\pi\)
\(824\) 1.70531e17 9.84563e16i 0.544805 0.314543i
\(825\) 4.05827e16i 0.128711i
\(826\) 9.23703e15 + 1.07472e17i 0.0290839 + 0.338388i
\(827\) 2.73276e17 0.854218 0.427109 0.904200i \(-0.359532\pi\)
0.427109 + 0.904200i \(0.359532\pi\)
\(828\) −6.27480e16 1.08683e17i −0.194723 0.337270i
\(829\) −3.32090e17 1.91732e17i −1.02312 0.590701i −0.108116 0.994138i \(-0.534482\pi\)
−0.915007 + 0.403438i \(0.867815\pi\)
\(830\) −1.68138e17 + 2.91223e17i −0.514276 + 0.890752i
\(831\) −8.76788e16 + 5.06214e16i −0.266249 + 0.153719i
\(832\) 1.15699e16i 0.0348810i
\(833\) 9.30833e16 + 3.42022e16i 0.278613 + 0.102373i
\(834\) 2.89440e17 0.860125
\(835\) −1.49448e17 2.58851e17i −0.440932 0.763716i
\(836\) 3.48060e17 + 2.00952e17i 1.01957 + 0.588648i
\(837\) −6.33574e16 + 1.09738e17i −0.184266 + 0.319157i
\(838\) 7.33577e15 4.23531e15i 0.0211827 0.0122298i
\(839\) 3.51637e17i 1.00814i 0.863662 + 0.504072i \(0.168165\pi\)
−0.863662 + 0.504072i \(0.831835\pi\)
\(840\) −8.16161e16 + 7.01477e15i −0.232327 + 0.0199681i
\(841\) −2.99612e16 −0.0846804
\(842\) −6.67565e16 1.15626e17i −0.187336 0.324475i
\(843\) −3.68614e16 2.12820e16i −0.102709 0.0592988i
\(844\) −5.29761e16 + 9.17574e16i −0.146563 + 0.253855i
\(845\) −2.72585e17 + 1.57377e17i −0.748793 + 0.432316i
\(846\) 1.32641e17i 0.361789i
\(847\) −2.73369e17 3.91684e17i −0.740369 1.06080i
\(848\) −6.65062e16 −0.178849
\(849\) −1.81923e17 3.15100e17i −0.485782 0.841399i
\(850\) −8.28289e15 4.78213e15i −0.0219618 0.0126797i
\(851\) −1.94409e17 + 3.36726e17i −0.511846 + 0.886543i
\(852\) 6.67916e16 3.85622e16i 0.174616 0.100815i
\(853\) 7.08810e13i 0.000184008i −1.00000 9.20038e-5i \(-0.999971\pi\)
1.00000 9.20038e-5i \(-2.92857e-5\pi\)
\(854\) 1.32769e17 + 6.21583e16i 0.342254 + 0.160233i
\(855\) 2.87721e17 0.736503
\(856\) 8.72907e16 + 1.51192e17i 0.221884 + 0.384314i
\(857\) −1.30185e14 7.51626e13i −0.000328607 0.000189722i 0.499836 0.866120i \(-0.333394\pi\)
−0.500164 + 0.865931i \(0.666727\pi\)
\(858\) −4.19299e16 + 7.26248e16i −0.105099 + 0.182038i
\(859\) −5.78263e17 + 3.33860e17i −1.43935 + 0.831009i −0.997804 0.0662290i \(-0.978903\pi\)
−0.441546 + 0.897239i \(0.645570\pi\)
\(860\) 2.76014e17i 0.682244i
\(861\) −1.37530e17 + 2.93760e17i −0.337581 + 0.721064i
\(862\) 8.44497e16 0.205852
\(863\) −2.04823e17 3.54764e17i −0.495808 0.858765i 0.504180 0.863599i \(-0.331795\pi\)
−0.999988 + 0.00483322i \(0.998462\pi\)
\(864\) 6.74286e16 + 3.89299e16i 0.162092 + 0.0935838i
\(865\) 6.22798e16 1.07872e17i 0.148679 0.257520i
\(866\) −2.52248e17 + 1.45635e17i −0.598025 + 0.345270i
\(867\) 2.72436e17i 0.641431i
\(868\) −6.10359e16 + 4.25989e16i −0.142714 + 0.0996047i
\(869\) −1.69786e16 −0.0394260
\(870\) −9.67387e16 1.67556e17i −0.223092 0.386407i
\(871\) 7.81659e16 + 4.51291e16i 0.179023 + 0.103359i
\(872\) −1.21325e17 + 2.10142e17i −0.275964 + 0.477984i
\(873\) 9.06205e16 5.23198e16i 0.204711 0.118190i
\(874\) 7.55447e17i 1.69487i
\(875\) −4.03890e16 4.69922e17i −0.0899942 1.04707i
\(876\) 6.81617e16 0.150840
\(877\) 3.89946e17 + 6.75407e17i 0.857052 + 1.48446i 0.874728 + 0.484614i \(0.161040\pi\)
−0.0176760 + 0.999844i \(0.505627\pi\)
\(878\) 1.65911e17 + 9.57889e16i 0.362167 + 0.209097i
\(879\) −4.89407e16 + 8.47679e16i −0.106105 + 0.183780i
\(880\) 1.42779e17 8.24337e16i 0.307446 0.177504i
\(881\) 5.86771e17i 1.25491i −0.778652 0.627456i \(-0.784096\pi\)
0.778652 0.627456i \(-0.215904\pi\)
\(882\) 5.80044e16 1.57862e17i 0.123211 0.335326i
\(883\) 1.02492e17 0.216235 0.108117 0.994138i \(-0.465518\pi\)
0.108117 + 0.994138i \(0.465518\pi\)
\(884\) 9.88177e15 + 1.71157e16i 0.0207072 + 0.0358659i
\(885\) 1.31814e17 + 7.61029e16i 0.274348 + 0.158395i
\(886\) −1.60038e17 + 2.77194e17i −0.330842 + 0.573036i
\(887\) −3.08202e17 + 1.77941e17i −0.632840 + 0.365370i −0.781851 0.623465i \(-0.785724\pi\)
0.149011 + 0.988836i \(0.452391\pi\)
\(888\) 8.09676e16i 0.165133i
\(889\) 7.97333e17 6.85295e16i 1.61521 0.138825i
\(890\) 4.20837e17 0.846787
\(891\) −9.07520e16 1.57187e17i −0.181380 0.314160i
\(892\) 1.07809e17 + 6.22434e16i 0.214025 + 0.123567i
\(893\) 3.99230e17 6.91486e17i 0.787252 1.36356i
\(894\) −1.17309e17 + 6.77281e16i −0.229776 + 0.132661i
\(895\) 2.89750e17i 0.563749i
\(896\) 2.61749e16 + 3.75035e16i 0.0505867 + 0.0724809i
\(897\) 1.57629e17 0.302608
\(898\) −1.65480e17 2.86619e17i −0.315564 0.546572i
\(899\) −1.52245e17 8.78988e16i −0.288393 0.166504i
\(900\) −8.11013e15 + 1.40472e16i −0.0152606 + 0.0264322i
\(901\) 9.83848e16 5.68025e16i 0.183899 0.106174i
\(902\) 6.52812e17i 1.21213i
\(903\) 5.02608e17 + 2.35306e17i 0.927049 + 0.434017i
\(904\) −2.40377e17 −0.440435
\(905\) 1.80730e17 + 3.13034e17i 0.328957 + 0.569770i
\(906\) 1.63238e17 + 9.42454e16i 0.295156 + 0.170408i
\(907\) −1.17389e17 + 2.03324e17i −0.210856 + 0.365213i −0.951983 0.306152i \(-0.900958\pi\)
0.741127 + 0.671365i \(0.234292\pi\)
\(908\) 2.86958e17 1.65675e17i 0.512039 0.295626i
\(909\) 7.35175e14i 0.00130319i
\(910\) −4.45472e16 + 9.51516e16i −0.0784462 + 0.167559i
\(911\) 2.85714e17 0.499829 0.249915 0.968268i \(-0.419597\pi\)
0.249915 + 0.968268i \(0.419597\pi\)
\(912\) 7.86573e16 + 1.36239e17i 0.136701 + 0.236772i
\(913\) −1.17847e18 6.80391e17i −2.03467 1.17472i
\(914\) −2.94814e17 + 5.10633e17i −0.505674 + 0.875854i
\(915\) 1.79142e17 1.03428e17i 0.305261 0.176243i
\(916\) 1.76463e17i 0.298731i
\(917\) −7.86833e17 + 5.49156e17i −1.32333 + 0.923591i
\(918\) −1.32999e17 −0.222225
\(919\) −2.02204e17 3.50228e17i −0.335658 0.581377i 0.647953 0.761680i \(-0.275625\pi\)
−0.983611 + 0.180304i \(0.942292\pi\)
\(920\) −2.68378e17 1.54948e17i −0.442608 0.255540i
\(921\) 1.72955e17 2.99567e17i 0.283384 0.490836i
\(922\) 9.37667e16 5.41362e16i 0.152638 0.0881257i
\(923\) 9.89164e16i 0.159977i
\(924\) −2.83862e16 3.30270e17i −0.0456116 0.530686i
\(925\) 5.02545e16 0.0802277
\(926\) 1.68319e17 + 2.91538e17i 0.266973 + 0.462411i
\(927\) 4.94022e17 + 2.85224e17i 0.778517 + 0.449477i
\(928\) −5.40094e16 + 9.35470e16i −0.0845632 + 0.146468i
\(929\) 1.04979e18 6.06094e17i 1.63308 0.942856i 0.649938 0.759987i \(-0.274795\pi\)
0.983137 0.182869i \(-0.0585384\pi\)
\(930\) 1.05025e17i 0.162329i
\(931\) 7.77531e17 6.48385e17i 1.19404 0.995714i
\(932\) −3.18722e17 −0.486314
\(933\) 1.66555e17 + 2.88482e17i 0.252504 + 0.437350i
\(934\) −9.88384e16 5.70644e16i −0.148883 0.0859575i
\(935\) −1.40812e17 + 2.43894e17i −0.210751 + 0.365032i
\(936\) 2.90270e16 1.67587e16i 0.0431665 0.0249222i
\(937\) 1.24564e17i 0.184058i 0.995756 + 0.0920292i \(0.0293353\pi\)
−0.995756 + 0.0920292i \(0.970665\pi\)
\(938\) −3.55469e17 + 3.05520e16i −0.521897 + 0.0448562i
\(939\) 5.92925e17 0.864981
\(940\) −1.63770e17 2.83658e17i −0.237393 0.411176i
\(941\) 6.82895e17 + 3.94269e17i 0.983594 + 0.567878i 0.903353 0.428897i \(-0.141098\pi\)
0.0802409 + 0.996775i \(0.474431\pi\)
\(942\) 2.68665e17 4.65342e17i 0.384509 0.665989i
\(943\) −1.06267e18 + 6.13535e17i −1.51123 + 0.872507i
\(944\) 8.49768e16i 0.120079i
\(945\) −4.04647e17 5.79780e17i −0.568179 0.814090i
\(946\) −1.11693e18 −1.55840
\(947\) 2.52162e17 + 4.36757e17i 0.349606 + 0.605536i 0.986180 0.165680i \(-0.0529820\pi\)
−0.636573 + 0.771216i \(0.719649\pi\)
\(948\) −5.75543e15 3.32290e15i −0.00792917 0.00457791i
\(949\) 4.37106e16 7.57090e16i 0.0598398 0.103646i
\(950\) −8.45596e16 + 4.88205e16i −0.115033 + 0.0664142i
\(951\) 9.19068e17i 1.24241i
\(952\) −7.07528e16 3.31244e16i −0.0950435 0.0444965i
\(953\) −1.53450e17 −0.204837 −0.102419 0.994741i \(-0.532658\pi\)
−0.102419 + 0.994741i \(0.532658\pi\)
\(954\) −9.63328e16 1.66853e17i −0.127786 0.221332i
\(955\) −5.26570e17 3.04015e17i −0.694122 0.400752i
\(956\) −2.18589e17 + 3.78607e17i −0.286339 + 0.495954i
\(957\) 6.78039e17 3.91466e17i 0.882639 0.509592i
\(958\) 1.27417e17i 0.164829i
\(959\) −4.06149e17 + 8.67523e17i −0.522124 + 1.11524i
\(960\) 6.45329e16 0.0824429
\(961\) −3.46117e17 5.99493e17i −0.439423 0.761103i
\(962\) −8.99329e16 5.19228e16i −0.113467 0.0655100i
\(963\) −2.52877e17 + 4.37997e17i −0.317068 + 0.549178i
\(964\) 2.04641e17 1.18150e17i 0.254995 0.147221i
\(965\) 8.76091e17i 1.08489i
\(966\) −5.10949e17 + 3.56608e17i −0.628804 + 0.438862i
\(967\) −7.09549e17 −0.867807 −0.433904 0.900959i \(-0.642864\pi\)
−0.433904 + 0.900959i \(0.642864\pi\)
\(968\) 1.88141e17 + 3.25870e17i 0.228682 + 0.396089i
\(969\) −2.32721e17 1.34361e17i −0.281121 0.162305i
\(970\) 1.29197e17 2.23775e17i 0.155103 0.268647i
\(971\) −1.82086e17 + 1.05128e17i −0.217251 + 0.125430i −0.604677 0.796471i \(-0.706698\pi\)
0.387426 + 0.921901i \(0.373364\pi\)
\(972\) 3.75406e17i 0.445147i
\(973\) 1.25657e17 + 1.46201e18i 0.148085 + 1.72295i
\(974\) 1.00589e18 1.17814
\(975\) −1.01867e16 1.76439e16i −0.0118578 0.0205384i
\(976\) −1.00015e17 5.77439e16i −0.115709 0.0668048i
\(977\) 3.67280e17 6.36148e17i 0.422309 0.731460i −0.573856 0.818956i \(-0.694553\pi\)
0.996165 + 0.0874959i \(0.0278865\pi\)
\(978\) −1.71298e17 + 9.88989e16i −0.195758 + 0.113021i
\(979\) 1.70297e18i 1.93425i
\(980\) −7.08656e16 4.09212e17i −0.0799980 0.461946i
\(981\) −7.02948e17 −0.788695
\(982\) 6.18089e17 + 1.07056e18i 0.689258 + 1.19383i
\(983\) −7.32090e17 4.22672e17i −0.811415 0.468471i 0.0360317 0.999351i \(-0.488528\pi\)
−0.847447 + 0.530880i \(0.821862\pi\)
\(984\) 1.27763e17 2.21291e17i 0.140745 0.243778i
\(985\) 6.70254e17 3.86971e17i 0.733875 0.423703i
\(986\) 1.84516e17i 0.200804i
\(987\) −6.56144e17 + 5.63945e16i −0.709735 + 0.0610005i
\(988\) 2.01765e17 0.216922
\(989\) 1.04972e18 + 1.81818e18i 1.12175 + 1.94294i
\(990\) 4.13626e17 + 2.38807e17i 0.439335 + 0.253650i
\(991\) 7.85878e17 1.36118e18i 0.829685 1.43706i −0.0686004 0.997644i \(-0.521853\pi\)
0.898285 0.439412i \(-0.144813\pi\)
\(992\) 5.07802e16 2.93179e16i 0.0532873 0.0307655i
\(993\) 1.36518e17i 0.142394i
\(994\) 2.23781e17 + 3.20635e17i 0.232009 + 0.332424i
\(995\) −1.12034e18 −1.15455
\(996\) −2.66321e17 4.61281e17i −0.272803 0.472508i
\(997\) −4.43092e17 2.55819e17i −0.451152 0.260473i 0.257165 0.966368i \(-0.417212\pi\)
−0.708316 + 0.705895i \(0.750545\pi\)
\(998\) 4.50462e17 7.80223e17i 0.455906 0.789652i
\(999\) 6.05205e17 3.49415e17i 0.608849 0.351519i
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 14.13.d.a.3.6 16
3.2 odd 2 126.13.n.a.73.4 16
4.3 odd 2 112.13.s.c.17.6 16
7.2 even 3 98.13.d.a.19.7 16
7.3 odd 6 98.13.b.c.97.3 16
7.4 even 3 98.13.b.c.97.6 16
7.5 odd 6 inner 14.13.d.a.5.6 yes 16
7.6 odd 2 98.13.d.a.31.7 16
21.5 even 6 126.13.n.a.19.4 16
28.19 even 6 112.13.s.c.33.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.13.d.a.3.6 16 1.1 even 1 trivial
14.13.d.a.5.6 yes 16 7.5 odd 6 inner
98.13.b.c.97.3 16 7.3 odd 6
98.13.b.c.97.6 16 7.4 even 3
98.13.d.a.19.7 16 7.2 even 3
98.13.d.a.31.7 16 7.6 odd 2
112.13.s.c.17.6 16 4.3 odd 2
112.13.s.c.33.6 16 28.19 even 6
126.13.n.a.19.4 16 21.5 even 6
126.13.n.a.73.4 16 3.2 odd 2