Properties

Label 14.15.d.a.5.10
Level $14$
Weight $15$
Character 14.5
Analytic conductor $17.406$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,15,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, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.3");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 15 \)
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: \(17.4060555413\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} + 5366534 x^{18} + 786490608 x^{17} + 19826027932115 x^{16} + \cdots + 13\!\cdots\!24 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{76}\cdot 3^{12}\cdot 7^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.10
Root \(811.055 - 1404.79i\) of defining polynomial
Character \(\chi\) \(=\) 14.5
Dual form 14.15.d.a.3.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(45.2548 - 78.3837i) q^{2} +(3382.61 - 1952.95i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(38553.6 + 22259.0i) q^{5} -353522. i q^{6} +(725749. - 389245. i) q^{7} -741455. q^{8} +(5.23657e6 - 9.07000e6i) q^{9} +O(q^{10})\) \(q+(45.2548 - 78.3837i) q^{2} +(3382.61 - 1952.95i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(38553.6 + 22259.0i) q^{5} -353522. i q^{6} +(725749. - 389245. i) q^{7} -741455. q^{8} +(5.23657e6 - 9.07000e6i) q^{9} +(3.48948e6 - 2.01465e6i) q^{10} +(2.67149e6 + 4.62715e6i) q^{11} +(-2.77104e7 - 1.59986e7i) q^{12} +7.96385e7i q^{13} +(2.33322e6 - 7.45021e7i) q^{14} +1.73883e8 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(1.07709e8 - 6.21860e7i) q^{17} +(-4.73960e8 - 8.20922e8i) q^{18} +(-1.05852e9 - 6.11137e8i) q^{19} -3.64691e8i q^{20} +(1.69475e9 - 2.73402e9i) q^{21} +4.83591e8 q^{22} +(-1.96995e9 + 3.41205e9i) q^{23} +(-2.50806e9 + 1.44803e9i) q^{24} +(-2.06084e9 - 3.56947e9i) q^{25} +(6.24236e9 + 3.60403e9i) q^{26} -2.22252e10i q^{27} +(-5.73416e9 - 3.55447e9i) q^{28} -9.13120e9 q^{29} +(7.86903e9 - 1.36296e10i) q^{30} +(2.41487e10 - 1.39423e10i) q^{31} +(3.03700e9 + 5.26024e9i) q^{32} +(1.80732e10 + 1.04346e10i) q^{33} -1.12569e10i q^{34} +(3.66444e10 + 1.14762e9i) q^{35} -8.57959e10 q^{36} +(-8.71230e10 + 1.50902e11i) q^{37} +(-9.58063e10 + 5.53138e10i) q^{38} +(1.55530e11 + 2.69386e11i) q^{39} +(-2.85858e10 - 1.65040e10i) q^{40} +1.93428e11i q^{41} +(-1.37607e11 - 2.56568e11i) q^{42} +2.74771e11 q^{43} +(2.18848e10 - 3.79056e10i) q^{44} +(4.03777e11 - 2.33121e11i) q^{45} +(1.78299e11 + 3.08824e11i) q^{46} +(-6.24524e11 - 3.60569e11i) q^{47} +2.62121e11i q^{48} +(3.75200e11 - 5.64988e11i) q^{49} -3.73051e11 q^{50} +(2.42893e11 - 4.20702e11i) q^{51} +(5.64994e11 - 3.26199e11i) q^{52} +(8.95694e11 + 1.55139e12i) q^{53} +(-1.74210e12 - 1.00580e12i) q^{54} +2.37858e11i q^{55} +(-5.38110e11 + 2.88607e11i) q^{56} -4.77409e12 q^{57} +(-4.13231e11 + 7.15737e11i) q^{58} +(3.83391e12 - 2.21351e12i) q^{59} +(-7.12224e11 - 1.23361e12i) q^{60} +(3.55754e12 + 2.05395e12i) q^{61} -2.52382e12i q^{62} +(2.69984e11 - 8.62085e12i) q^{63} +5.49756e11 q^{64} +(-1.77267e12 + 3.07035e12i) q^{65} +(1.63580e12 - 9.44431e11i) q^{66} +(-4.21267e11 - 7.29656e11i) q^{67} +(-8.82354e11 - 5.09427e11i) q^{68} +1.53889e13i q^{69} +(1.74829e12 - 2.82039e12i) q^{70} +6.19751e12 q^{71} +(-3.88268e12 + 6.72500e12i) q^{72} +(-8.71841e12 + 5.03358e12i) q^{73} +(7.88548e12 + 1.36580e13i) q^{74} +(-1.39420e13 - 8.04943e12i) q^{75} +1.00129e13i q^{76} +(3.73993e12 + 2.31829e12i) q^{77} +2.81540e13 q^{78} +(-1.88187e12 + 3.25949e12i) q^{79} +(-2.58729e12 + 1.49377e12i) q^{80} +(-1.83585e13 - 3.17979e13i) q^{81} +(1.51616e13 + 8.75354e12i) q^{82} +7.24696e12i q^{83} +(-2.63381e13 - 8.24847e11i) q^{84} +5.53678e12 q^{85} +(1.24347e13 - 2.15375e13i) q^{86} +(-3.08873e13 + 1.78328e13i) q^{87} +(-1.98079e12 - 3.43083e12i) q^{88} +(-1.74616e13 - 1.00814e13i) q^{89} -4.21994e13i q^{90} +(3.09988e13 + 5.77975e13i) q^{91} +3.22756e13 q^{92} +(5.44571e13 - 9.43225e13i) q^{93} +(-5.65255e13 + 3.26350e13i) q^{94} +(-2.72065e13 - 4.71231e13i) q^{95} +(2.05460e13 + 1.18622e13i) q^{96} +4.36526e12i q^{97} +(-2.73062e13 - 5.49780e13i) q^{98} +5.59577e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 45.2548 78.3837i 0.353553 0.612372i
\(3\) 3382.61 1952.95i 1.54669 0.892983i 0.548300 0.836282i \(-0.315275\pi\)
0.998391 0.0567009i \(-0.0180581\pi\)
\(4\) −4096.00 7094.48i −0.250000 0.433013i
\(5\) 38553.6 + 22259.0i 0.493487 + 0.284915i 0.726020 0.687674i \(-0.241368\pi\)
−0.232533 + 0.972588i \(0.574701\pi\)
\(6\) 353522.i 1.26287i
\(7\) 725749. 389245.i 0.881252 0.472646i
\(8\) −741455. −0.353553
\(9\) 5.23657e6 9.07000e6i 1.09484 1.89631i
\(10\) 3.48948e6 2.01465e6i 0.348948 0.201465i
\(11\) 2.67149e6 + 4.62715e6i 0.137090 + 0.237446i 0.926394 0.376556i \(-0.122892\pi\)
−0.789304 + 0.614002i \(0.789559\pi\)
\(12\) −2.77104e7 1.59986e7i −0.773346 0.446491i
\(13\) 7.96385e7i 1.26917i 0.772854 + 0.634584i \(0.218829\pi\)
−0.772854 + 0.634584i \(0.781171\pi\)
\(14\) 2.33322e6 7.45021e7i 0.0221340 0.706760i
\(15\) 1.73883e8 1.01770
\(16\) −3.35544e7 + 5.81180e7i −0.125000 + 0.216506i
\(17\) 1.07709e8 6.21860e7i 0.262489 0.151548i −0.362981 0.931797i \(-0.618241\pi\)
0.625469 + 0.780249i \(0.284908\pi\)
\(18\) −4.73960e8 8.20922e8i −0.774166 1.34089i
\(19\) −1.05852e9 6.11137e8i −1.18420 0.683696i −0.227215 0.973845i \(-0.572962\pi\)
−0.956982 + 0.290148i \(0.906295\pi\)
\(20\) 3.64691e8i 0.284915i
\(21\) 1.69475e9 2.73402e9i 0.940960 1.51798i
\(22\) 4.83591e8 0.193874
\(23\) −1.96995e9 + 3.41205e9i −0.578575 + 1.00212i 0.417068 + 0.908875i \(0.363058\pi\)
−0.995643 + 0.0932466i \(0.970275\pi\)
\(24\) −2.50806e9 + 1.44803e9i −0.546838 + 0.315717i
\(25\) −2.06084e9 3.56947e9i −0.337647 0.584822i
\(26\) 6.24236e9 + 3.60403e9i 0.777204 + 0.448719i
\(27\) 2.22252e10i 2.12471i
\(28\) −5.73416e9 3.55447e9i −0.424975 0.263432i
\(29\) −9.13120e9 −0.529349 −0.264674 0.964338i \(-0.585264\pi\)
−0.264674 + 0.964338i \(0.585264\pi\)
\(30\) 7.86903e9 1.36296e10i 0.359810 0.623208i
\(31\) 2.41487e10 1.39423e10i 0.877732 0.506759i 0.00782184 0.999969i \(-0.497510\pi\)
0.869910 + 0.493211i \(0.164177\pi\)
\(32\) 3.03700e9 + 5.26024e9i 0.0883883 + 0.153093i
\(33\) 1.80732e10 + 1.04346e10i 0.424071 + 0.244837i
\(34\) 1.12569e10i 0.214321i
\(35\) 3.66444e10 + 1.14762e9i 0.569550 + 0.0178369i
\(36\) −8.57959e10 −1.09484
\(37\) −8.71230e10 + 1.50902e11i −0.917743 + 1.58958i −0.114907 + 0.993376i \(0.536657\pi\)
−0.802835 + 0.596201i \(0.796676\pi\)
\(38\) −9.58063e10 + 5.53138e10i −0.837354 + 0.483446i
\(39\) 1.55530e11 + 2.69386e11i 1.13335 + 1.96301i
\(40\) −2.85858e10 1.65040e10i −0.174474 0.100733i
\(41\) 1.93428e11i 0.993189i 0.867983 + 0.496595i \(0.165416\pi\)
−0.867983 + 0.496595i \(0.834584\pi\)
\(42\) −1.37607e11 2.56568e11i −0.596890 1.11291i
\(43\) 2.74771e11 1.01086 0.505430 0.862867i \(-0.331334\pi\)
0.505430 + 0.862867i \(0.331334\pi\)
\(44\) 2.18848e10 3.79056e10i 0.0685448 0.118723i
\(45\) 4.03777e11 2.33121e11i 1.08057 0.623869i
\(46\) 1.78299e11 + 3.08824e11i 0.409115 + 0.708607i
\(47\) −6.24524e11 3.60569e11i −1.23272 0.711711i −0.265123 0.964215i \(-0.585413\pi\)
−0.967596 + 0.252504i \(0.918746\pi\)
\(48\) 2.62121e11i 0.446491i
\(49\) 3.75200e11 5.64988e11i 0.553211 0.833041i
\(50\) −3.73051e11 −0.477505
\(51\) 2.42893e11 4.20702e11i 0.270659 0.468796i
\(52\) 5.64994e11 3.26199e11i 0.549566 0.317292i
\(53\) 8.95694e11 + 1.55139e12i 0.762480 + 1.32065i 0.941569 + 0.336821i \(0.109352\pi\)
−0.179089 + 0.983833i \(0.557315\pi\)
\(54\) −1.74210e12 1.00580e12i −1.30112 0.751199i
\(55\) 2.37858e11i 0.156235i
\(56\) −5.38110e11 + 2.88607e11i −0.311570 + 0.167106i
\(57\) −4.77409e12 −2.44212
\(58\) −4.13231e11 + 7.15737e11i −0.187153 + 0.324159i
\(59\) 3.83391e12 2.21351e12i 1.54056 0.889441i 0.541753 0.840538i \(-0.317761\pi\)
0.998804 0.0489034i \(-0.0155726\pi\)
\(60\) −7.12224e11 1.23361e12i −0.254424 0.440675i
\(61\) 3.55754e12 + 2.05395e12i 1.13199 + 0.653553i 0.944434 0.328702i \(-0.106611\pi\)
0.187553 + 0.982254i \(0.439944\pi\)
\(62\) 2.52382e12i 0.716665i
\(63\) 2.69984e11 8.62085e12i 0.0685416 2.18860i
\(64\) 5.49756e11 0.125000
\(65\) −1.77267e12 + 3.07035e12i −0.361605 + 0.626318i
\(66\) 1.63580e12 9.44431e11i 0.299863 0.173126i
\(67\) −4.21267e11 7.29656e11i −0.0695078 0.120391i 0.829177 0.558986i \(-0.188810\pi\)
−0.898685 + 0.438595i \(0.855476\pi\)
\(68\) −8.82354e11 5.09427e11i −0.131244 0.0757740i
\(69\) 1.53889e13i 2.06663i
\(70\) 1.74829e12 2.82039e12i 0.212289 0.342470i
\(71\) 6.19751e12 0.681410 0.340705 0.940170i \(-0.389334\pi\)
0.340705 + 0.940170i \(0.389334\pi\)
\(72\) −3.88268e12 + 6.72500e12i −0.387083 + 0.670447i
\(73\) −8.71841e12 + 5.03358e12i −0.789182 + 0.455635i −0.839675 0.543090i \(-0.817254\pi\)
0.0504924 + 0.998724i \(0.483921\pi\)
\(74\) 7.88548e12 + 1.36580e13i 0.648942 + 1.12400i
\(75\) −1.39420e13 8.04943e12i −1.04447 0.603026i
\(76\) 1.00129e13i 0.683696i
\(77\) 3.73993e12 + 2.31829e12i 0.233039 + 0.144455i
\(78\) 2.81540e13 1.60279
\(79\) −1.88187e12 + 3.25949e12i −0.0979939 + 0.169730i −0.910854 0.412728i \(-0.864576\pi\)
0.812860 + 0.582459i \(0.197909\pi\)
\(80\) −2.58729e12 + 1.49377e12i −0.123372 + 0.0712286i
\(81\) −1.83585e13 3.17979e13i −0.802495 1.38996i
\(82\) 1.51616e13 + 8.75354e12i 0.608202 + 0.351145i
\(83\) 7.24696e12i 0.267060i 0.991045 + 0.133530i \(0.0426313\pi\)
−0.991045 + 0.133530i \(0.957369\pi\)
\(84\) −2.63381e13 8.24847e11i −0.892545 0.0279523i
\(85\) 5.53678e12 0.172713
\(86\) 1.24347e13 2.15375e13i 0.357393 0.619023i
\(87\) −3.08873e13 + 1.78328e13i −0.818739 + 0.472699i
\(88\) −1.98079e12 3.43083e12i −0.0484685 0.0839499i
\(89\) −1.74616e13 1.00814e13i −0.394778 0.227925i 0.289450 0.957193i \(-0.406528\pi\)
−0.684228 + 0.729268i \(0.739861\pi\)
\(90\) 4.21994e13i 0.882285i
\(91\) 3.09988e13 + 5.77975e13i 0.599868 + 1.11846i
\(92\) 3.22756e13 0.578575
\(93\) 5.44571e13 9.43225e13i 0.905053 1.56760i
\(94\) −5.65255e13 + 3.26350e13i −0.871664 + 0.503256i
\(95\) −2.72065e13 4.71231e13i −0.389590 0.674790i
\(96\) 2.05460e13 + 1.18622e13i 0.273419 + 0.157859i
\(97\) 4.36526e12i 0.0540266i 0.999635 + 0.0270133i \(0.00859964\pi\)
−0.999635 + 0.0270133i \(0.991400\pi\)
\(98\) −2.73062e13 5.49780e13i −0.314542 0.633296i
\(99\) 5.59577e13 0.600362
\(100\) −1.68824e13 + 2.92411e13i −0.168824 + 0.292411i
\(101\) −6.26219e13 + 3.61548e13i −0.584085 + 0.337222i −0.762755 0.646687i \(-0.776154\pi\)
0.178670 + 0.983909i \(0.442821\pi\)
\(102\) −2.19841e13 3.80776e13i −0.191385 0.331489i
\(103\) −5.63391e13 3.25274e13i −0.458088 0.264477i 0.253152 0.967427i \(-0.418533\pi\)
−0.711240 + 0.702949i \(0.751866\pi\)
\(104\) 5.90484e13i 0.448719i
\(105\) 1.26195e14 6.76829e13i 0.896846 0.481010i
\(106\) 1.62138e14 1.07831
\(107\) 9.17359e13 1.58891e14i 0.571285 0.989494i −0.425150 0.905123i \(-0.639779\pi\)
0.996434 0.0843712i \(-0.0268881\pi\)
\(108\) −1.57677e14 + 9.10346e13i −0.920027 + 0.531178i
\(109\) −6.68227e13 1.15740e14i −0.365543 0.633140i 0.623320 0.781967i \(-0.285783\pi\)
−0.988863 + 0.148827i \(0.952450\pi\)
\(110\) 1.86442e13 + 1.07642e13i 0.0956742 + 0.0552375i
\(111\) 6.80589e14i 3.27811i
\(112\) −1.72998e12 + 5.52400e13i −0.00782556 + 0.249877i
\(113\) −3.46999e14 −1.47496 −0.737478 0.675371i \(-0.763983\pi\)
−0.737478 + 0.675371i \(0.763983\pi\)
\(114\) −2.16050e14 + 3.74210e14i −0.863418 + 1.49548i
\(115\) −1.51897e14 + 8.76980e13i −0.571038 + 0.329689i
\(116\) 3.74014e13 + 6.47811e13i 0.132337 + 0.229215i
\(117\) 7.22321e14 + 4.17032e14i 2.40674 + 1.38953i
\(118\) 4.00688e14i 1.25786i
\(119\) 5.39643e13 8.70567e13i 0.159690 0.257616i
\(120\) −1.28926e14 −0.359810
\(121\) 1.75601e14 3.04150e14i 0.462413 0.800923i
\(122\) 3.21992e14 1.85902e14i 0.800436 0.462132i
\(123\) 3.77755e14 + 6.54292e14i 0.886901 + 1.53616i
\(124\) −1.97826e14 1.14215e14i −0.438866 0.253379i
\(125\) 4.55204e14i 0.954632i
\(126\) −6.63516e14 4.11297e14i −1.31600 0.815759i
\(127\) −3.65726e14 −0.686325 −0.343162 0.939276i \(-0.611498\pi\)
−0.343162 + 0.939276i \(0.611498\pi\)
\(128\) 2.48791e13 4.30919e13i 0.0441942 0.0765466i
\(129\) 9.29443e14 5.36614e14i 1.56349 0.902681i
\(130\) 1.60444e14 + 2.77897e14i 0.255693 + 0.442874i
\(131\) −4.12238e14 2.38006e14i −0.622657 0.359491i 0.155246 0.987876i \(-0.450383\pi\)
−0.777903 + 0.628385i \(0.783716\pi\)
\(132\) 1.70960e14i 0.244837i
\(133\) −1.00610e15 3.15087e13i −1.36672 0.0428025i
\(134\) −7.62574e13 −0.0982989
\(135\) 4.94711e14 8.56864e14i 0.605361 1.04852i
\(136\) −7.98616e13 + 4.61081e13i −0.0928038 + 0.0535803i
\(137\) 2.49725e14 + 4.32537e14i 0.275688 + 0.477506i 0.970309 0.241871i \(-0.0777609\pi\)
−0.694620 + 0.719377i \(0.744428\pi\)
\(138\) 1.20624e15 + 6.96421e14i 1.26555 + 0.730665i
\(139\) 8.98704e14i 0.896423i 0.893928 + 0.448212i \(0.147939\pi\)
−0.893928 + 0.448212i \(0.852061\pi\)
\(140\) −1.41954e14 2.64674e14i −0.134664 0.251082i
\(141\) −2.81670e15 −2.54218
\(142\) 2.80467e14 4.85783e14i 0.240915 0.417277i
\(143\) −3.68499e14 + 2.12753e14i −0.301359 + 0.173990i
\(144\) 3.51420e14 + 6.08677e14i 0.273709 + 0.474078i
\(145\) −3.52041e14 2.03251e14i −0.261226 0.150819i
\(146\) 9.11175e14i 0.644365i
\(147\) 1.65763e14 2.64388e15i 0.111755 1.78247i
\(148\) 1.42742e15 0.917743
\(149\) 3.71458e14 6.43383e14i 0.227827 0.394608i −0.729337 0.684155i \(-0.760171\pi\)
0.957164 + 0.289547i \(0.0935046\pi\)
\(150\) −1.26189e15 + 7.28551e14i −0.738554 + 0.426404i
\(151\) −6.40987e14 1.11022e15i −0.358105 0.620256i 0.629539 0.776969i \(-0.283244\pi\)
−0.987644 + 0.156712i \(0.949910\pi\)
\(152\) 7.84845e14 + 4.53131e14i 0.418677 + 0.241723i
\(153\) 1.30256e15i 0.663680i
\(154\) 3.50966e14 1.88235e14i 0.170852 0.0916339i
\(155\) 1.24136e15 0.577532
\(156\) 1.27410e15 2.20681e15i 0.566673 0.981506i
\(157\) −1.78177e15 + 1.02870e15i −0.757798 + 0.437515i −0.828504 0.559982i \(-0.810808\pi\)
0.0707068 + 0.997497i \(0.477475\pi\)
\(158\) 1.70327e14 + 2.95015e14i 0.0692921 + 0.120018i
\(159\) 6.05957e15 + 3.49850e15i 2.35864 + 1.36176i
\(160\) 2.70402e14i 0.100733i
\(161\) −1.01566e14 + 3.24308e15i −0.0362214 + 1.15658i
\(162\) −3.32325e15 −1.13490
\(163\) −1.05994e15 + 1.83587e15i −0.346711 + 0.600521i −0.985663 0.168726i \(-0.946035\pi\)
0.638952 + 0.769246i \(0.279368\pi\)
\(164\) 1.37227e15 7.92280e14i 0.430064 0.248297i
\(165\) 4.64526e14 + 8.04582e14i 0.139515 + 0.241648i
\(166\) 5.68043e14 + 3.27960e14i 0.163540 + 0.0944200i
\(167\) 1.07353e15i 0.296345i 0.988962 + 0.148173i \(0.0473391\pi\)
−0.988962 + 0.148173i \(0.952661\pi\)
\(168\) −1.25658e15 + 2.02715e15i −0.332680 + 0.536687i
\(169\) −2.40491e15 −0.610790
\(170\) 2.50566e14 4.33993e14i 0.0610632 0.105765i
\(171\) −1.10860e16 + 6.40052e15i −2.59300 + 1.49707i
\(172\) −1.12546e15 1.94936e15i −0.252715 0.437716i
\(173\) 5.18857e15 + 2.99562e15i 1.11873 + 0.645899i 0.941076 0.338195i \(-0.109816\pi\)
0.177653 + 0.984093i \(0.443150\pi\)
\(174\) 3.22808e15i 0.668498i
\(175\) −2.88505e15 1.78837e15i −0.573967 0.355788i
\(176\) −3.58561e14 −0.0685448
\(177\) 8.64576e15 1.49749e16i 1.58851 2.75138i
\(178\) −1.58044e15 + 9.12468e14i −0.279150 + 0.161168i
\(179\) 9.34762e14 + 1.61906e15i 0.158756 + 0.274973i 0.934420 0.356172i \(-0.115918\pi\)
−0.775664 + 0.631146i \(0.782585\pi\)
\(180\) −3.30774e15 1.90973e15i −0.540287 0.311935i
\(181\) 6.49718e15i 1.02088i −0.859913 0.510441i \(-0.829482\pi\)
0.859913 0.510441i \(-0.170518\pi\)
\(182\) 5.93323e15 + 1.85814e14i 0.896998 + 0.0280918i
\(183\) 1.60451e16 2.33445
\(184\) 1.46063e15 2.52988e15i 0.204557 0.354304i
\(185\) −6.71782e15 + 3.87854e15i −0.905787 + 0.522957i
\(186\) −4.92890e15 8.53710e15i −0.639969 1.10846i
\(187\) 5.75488e14 + 3.32258e14i 0.0719689 + 0.0415513i
\(188\) 5.90756e15i 0.711711i
\(189\) −8.65106e15 1.61299e16i −1.00424 1.87241i
\(190\) −4.92491e15 −0.550964
\(191\) −3.46574e14 + 6.00284e14i −0.0373734 + 0.0647327i −0.884107 0.467284i \(-0.845232\pi\)
0.846734 + 0.532017i \(0.178566\pi\)
\(192\) 1.85961e15 1.07365e15i 0.193336 0.111623i
\(193\) −4.38683e15 7.59821e15i −0.439794 0.761746i 0.557879 0.829922i \(-0.311615\pi\)
−0.997673 + 0.0681763i \(0.978282\pi\)
\(194\) 3.42165e14 + 1.97549e14i 0.0330844 + 0.0191013i
\(195\) 1.38478e16i 1.29163i
\(196\) −5.54512e15 3.47660e14i −0.499020 0.0312869i
\(197\) 1.82865e16 1.58806 0.794032 0.607876i \(-0.207978\pi\)
0.794032 + 0.607876i \(0.207978\pi\)
\(198\) 2.53236e15 4.38617e15i 0.212260 0.367645i
\(199\) −1.02883e15 + 5.93997e14i −0.0832479 + 0.0480632i −0.541046 0.840993i \(-0.681972\pi\)
0.457798 + 0.889056i \(0.348638\pi\)
\(200\) 1.52802e15 + 2.64660e15i 0.119376 + 0.206766i
\(201\) −2.84997e15 1.64543e15i −0.215014 0.124139i
\(202\) 6.54471e15i 0.476904i
\(203\) −6.62696e15 + 3.55427e15i −0.466490 + 0.250195i
\(204\) −3.97955e15 −0.270659
\(205\) −4.30550e15 + 7.45735e15i −0.282974 + 0.490125i
\(206\) −5.09923e15 + 2.94404e15i −0.323917 + 0.187014i
\(207\) 2.06315e16 + 3.57349e16i 1.26689 + 2.19432i
\(208\) −4.62843e15 2.67222e15i −0.274783 0.158646i
\(209\) 6.53058e15i 0.374911i
\(210\) 4.05708e14 1.29546e16i 0.0225257 0.719266i
\(211\) −2.72476e16 −1.46336 −0.731680 0.681648i \(-0.761264\pi\)
−0.731680 + 0.681648i \(0.761264\pi\)
\(212\) 7.33752e15 1.27090e16i 0.381240 0.660327i
\(213\) 2.09638e16 1.21034e16i 1.05393 0.608487i
\(214\) −8.30298e15 1.43812e16i −0.403959 0.699678i
\(215\) 1.05934e16 + 6.11611e15i 0.498846 + 0.288009i
\(216\) 1.64790e16i 0.751199i
\(217\) 1.20989e16 1.95183e16i 0.533985 0.861439i
\(218\) −1.20962e16 −0.516956
\(219\) −1.96607e16 + 3.40533e16i −0.813747 + 1.40945i
\(220\) 1.68748e15 9.74267e14i 0.0676519 0.0390588i
\(221\) 4.95240e15 + 8.57780e15i 0.192340 + 0.333142i
\(222\) 5.33470e16 + 3.07999e16i 2.00743 + 1.15899i
\(223\) 8.06396e15i 0.294045i −0.989133 0.147023i \(-0.953031\pi\)
0.989133 0.147023i \(-0.0469690\pi\)
\(224\) 4.25162e15 + 2.63548e15i 0.150251 + 0.0931372i
\(225\) −4.31668e16 −1.47867
\(226\) −1.57034e16 + 2.71991e16i −0.521476 + 0.903223i
\(227\) 6.15886e14 3.55582e14i 0.0198299 0.0114488i −0.490052 0.871693i \(-0.663022\pi\)
0.509882 + 0.860244i \(0.329689\pi\)
\(228\) 1.95547e16 + 3.38697e16i 0.610529 + 1.05747i
\(229\) −4.57486e16 2.64130e16i −1.38525 0.799776i −0.392478 0.919762i \(-0.628382\pi\)
−0.992776 + 0.119985i \(0.961715\pi\)
\(230\) 1.58750e16i 0.466251i
\(231\) 1.71782e16 + 5.37981e14i 0.489435 + 0.0153279i
\(232\) 6.77038e15 0.187153
\(233\) 1.61306e16 2.79389e16i 0.432671 0.749408i −0.564431 0.825480i \(-0.690904\pi\)
0.997102 + 0.0760717i \(0.0242378\pi\)
\(234\) 6.53770e16 3.77454e16i 1.70182 0.982547i
\(235\) −1.60518e16 2.78025e16i −0.405554 0.702439i
\(236\) −3.14074e16 1.81331e16i −0.770278 0.444720i
\(237\) 1.47008e16i 0.350027i
\(238\) −4.38167e15 8.16966e15i −0.101298 0.188871i
\(239\) 2.47318e16 0.555227 0.277613 0.960693i \(-0.410457\pi\)
0.277613 + 0.960693i \(0.410457\pi\)
\(240\) −5.83454e15 + 1.01057e16i −0.127212 + 0.220337i
\(241\) −5.48108e16 + 3.16450e16i −1.16077 + 0.670172i −0.951489 0.307683i \(-0.900446\pi\)
−0.209283 + 0.977855i \(0.567113\pi\)
\(242\) −1.58936e16 2.75285e16i −0.326975 0.566338i
\(243\) −3.21387e16 1.85553e16i −0.642370 0.370872i
\(244\) 3.36519e16i 0.653553i
\(245\) 2.70414e16 1.34308e16i 0.510348 0.253477i
\(246\) 6.83810e16 1.25427
\(247\) 4.86700e16 8.42989e16i 0.867726 1.50295i
\(248\) −1.79052e16 + 1.03376e16i −0.310325 + 0.179166i
\(249\) 1.41530e16 + 2.45137e16i 0.238480 + 0.413060i
\(250\) −3.56806e16 2.06002e16i −0.584590 0.337513i
\(251\) 9.04032e16i 1.44035i −0.693793 0.720175i \(-0.744062\pi\)
0.693793 0.720175i \(-0.255938\pi\)
\(252\) −6.22663e16 + 3.33956e16i −0.964826 + 0.517470i
\(253\) −2.10508e16 −0.317267
\(254\) −1.65509e16 + 2.86669e16i −0.242652 + 0.420286i
\(255\) 1.87288e16 1.08131e16i 0.267133 0.154230i
\(256\) −2.25180e15 3.90023e15i −0.0312500 0.0541266i
\(257\) 1.39819e16 + 8.07248e15i 0.188815 + 0.109012i 0.591428 0.806358i \(-0.298565\pi\)
−0.402613 + 0.915370i \(0.631898\pi\)
\(258\) 9.71376e16i 1.27658i
\(259\) −4.49184e15 + 1.43429e17i −0.0574548 + 1.83459i
\(260\) 2.90434e16 0.361605
\(261\) −4.78161e16 + 8.28200e16i −0.579550 + 1.00381i
\(262\) −3.73115e16 + 2.15418e16i −0.440285 + 0.254199i
\(263\) 6.07368e15 + 1.05199e16i 0.0697849 + 0.120871i 0.898807 0.438346i \(-0.144435\pi\)
−0.829022 + 0.559217i \(0.811102\pi\)
\(264\) −1.34005e16 7.73678e15i −0.149932 0.0865631i
\(265\) 7.97488e16i 0.868967i
\(266\) −4.80007e16 + 7.74360e16i −0.509421 + 0.821810i
\(267\) −7.87543e16 −0.814133
\(268\) −3.45102e15 + 5.97734e15i −0.0347539 + 0.0601955i
\(269\) 8.14901e16 4.70483e16i 0.799538 0.461613i −0.0437718 0.999042i \(-0.513937\pi\)
0.843309 + 0.537428i \(0.180604\pi\)
\(270\) −4.47761e16 7.75545e16i −0.428055 0.741413i
\(271\) 1.13271e17 + 6.53972e16i 1.05520 + 0.609220i 0.924101 0.382149i \(-0.124816\pi\)
0.131100 + 0.991369i \(0.458149\pi\)
\(272\) 8.34646e15i 0.0757740i
\(273\) 2.17733e17 + 1.34967e17i 1.92657 + 1.19424i
\(274\) 4.52051e16 0.389882
\(275\) 1.10110e16 1.90716e16i 0.0925759 0.160346i
\(276\) 1.09176e17 6.30328e16i 0.894878 0.516658i
\(277\) −5.90475e16 1.02273e17i −0.471893 0.817342i 0.527590 0.849499i \(-0.323096\pi\)
−0.999483 + 0.0321569i \(0.989762\pi\)
\(278\) 7.04437e16 + 4.06707e16i 0.548945 + 0.316933i
\(279\) 2.92038e17i 2.21927i
\(280\) −2.71702e16 8.50905e14i −0.201366 0.00630631i
\(281\) 7.38675e16 0.533961 0.266980 0.963702i \(-0.413974\pi\)
0.266980 + 0.963702i \(0.413974\pi\)
\(282\) −1.27469e17 + 2.20783e17i −0.898797 + 1.55676i
\(283\) −1.24777e17 + 7.20402e16i −0.858283 + 0.495530i −0.863437 0.504457i \(-0.831693\pi\)
0.00515374 + 0.999987i \(0.498360\pi\)
\(284\) −2.53850e16 4.39681e16i −0.170352 0.295059i
\(285\) −1.84058e17 1.06266e17i −1.20515 0.695794i
\(286\) 3.85125e16i 0.246059i
\(287\) 7.52908e16 + 1.40380e17i 0.469427 + 0.875250i
\(288\) 6.36138e16 0.387083
\(289\) −7.64547e16 + 1.32423e17i −0.454066 + 0.786466i
\(290\) −3.18631e16 + 1.83962e16i −0.184715 + 0.106645i
\(291\) 8.52514e15 + 1.47660e16i 0.0482448 + 0.0835624i
\(292\) 7.14212e16 + 4.12351e16i 0.394591 + 0.227817i
\(293\) 1.95449e17i 1.05429i 0.849775 + 0.527146i \(0.176738\pi\)
−0.849775 + 0.527146i \(0.823262\pi\)
\(294\) −1.99736e17 1.32642e17i −1.05202 0.698632i
\(295\) 1.97082e17 1.01366
\(296\) 6.45978e16 1.11887e17i 0.324471 0.562000i
\(297\) 1.02840e17 5.93745e16i 0.504505 0.291276i
\(298\) −3.36205e16 5.82324e16i −0.161098 0.279030i
\(299\) −2.71731e17 1.56884e17i −1.27186 0.734310i
\(300\) 1.31882e17i 0.603026i
\(301\) 1.99415e17 1.06953e17i 0.890823 0.477780i
\(302\) −1.16031e17 −0.506437
\(303\) −1.41217e17 + 2.44595e17i −0.602267 + 1.04316i
\(304\) 7.10361e16 4.10127e16i 0.296049 0.170924i
\(305\) 9.14375e16 + 1.58374e17i 0.372414 + 0.645039i
\(306\) −1.02100e17 5.89473e16i −0.406420 0.234646i
\(307\) 5.43740e16i 0.211555i 0.994390 + 0.105777i \(0.0337331\pi\)
−0.994390 + 0.105777i \(0.966267\pi\)
\(308\) 1.12833e15 3.60285e16i 0.00429121 0.137022i
\(309\) −2.54098e17 −0.944695
\(310\) 5.61775e16 9.73023e16i 0.204188 0.353664i
\(311\) 1.24757e17 7.20284e16i 0.443345 0.255965i −0.261671 0.965157i \(-0.584273\pi\)
0.705015 + 0.709192i \(0.250940\pi\)
\(312\) −1.15319e17 1.99738e17i −0.400698 0.694030i
\(313\) −2.82041e17 1.62837e17i −0.958302 0.553276i −0.0626520 0.998035i \(-0.519956\pi\)
−0.895650 + 0.444760i \(0.853289\pi\)
\(314\) 1.86215e17i 0.618739i
\(315\) 2.02300e17 3.26355e17i 0.657388 1.06052i
\(316\) 3.08325e16 0.0979939
\(317\) 1.48518e17 2.57241e17i 0.461705 0.799696i −0.537341 0.843365i \(-0.680571\pi\)
0.999046 + 0.0436690i \(0.0139047\pi\)
\(318\) 5.48450e17 3.16648e17i 1.66781 0.962912i
\(319\) −2.43939e16 4.22515e16i −0.0725682 0.125692i
\(320\) 2.11951e16 + 1.22370e16i 0.0616858 + 0.0356143i
\(321\) 7.16623e17i 2.04059i
\(322\) 2.49609e17 + 1.54726e17i 0.695454 + 0.431095i
\(323\) −1.52017e17 −0.414451
\(324\) −1.50393e17 + 2.60488e17i −0.401248 + 0.694981i
\(325\) 2.84267e17 1.64122e17i 0.742238 0.428532i
\(326\) 9.59347e16 + 1.66164e17i 0.245162 + 0.424632i
\(327\) −4.52071e17 2.61003e17i −1.13077 0.652848i
\(328\) 1.43418e17i 0.351145i
\(329\) −5.93597e17 1.85900e16i −1.42272 0.0445563i
\(330\) 8.40882e16 0.197305
\(331\) 1.88604e16 3.26672e16i 0.0433267 0.0750440i −0.843549 0.537052i \(-0.819538\pi\)
0.886876 + 0.462008i \(0.152871\pi\)
\(332\) 5.14134e16 2.96835e16i 0.115640 0.0667650i
\(333\) 9.12451e17 + 1.58041e18i 2.00956 + 3.48065i
\(334\) 8.41470e16 + 4.85823e16i 0.181474 + 0.104774i
\(335\) 3.75078e16i 0.0792152i
\(336\) 1.02029e17 + 1.90234e17i 0.211033 + 0.393471i
\(337\) −2.49681e17 −0.505796 −0.252898 0.967493i \(-0.581384\pi\)
−0.252898 + 0.967493i \(0.581384\pi\)
\(338\) −1.08834e17 + 1.88506e17i −0.215947 + 0.374031i
\(339\) −1.17376e18 + 6.77673e17i −2.28130 + 1.31711i
\(340\) −2.26786e16 3.92806e16i −0.0431782 0.0747869i
\(341\) 1.29026e17 + 7.44932e16i 0.240656 + 0.138943i
\(342\) 1.15862e18i 2.11718i
\(343\) 5.23827e16 5.56084e17i 0.0937840 0.995593i
\(344\) −2.03730e17 −0.357393
\(345\) −3.42540e17 + 5.93297e17i −0.588813 + 1.01985i
\(346\) 4.69616e17 2.71133e17i 0.791061 0.456719i
\(347\) −3.25398e17 5.63605e17i −0.537166 0.930398i −0.999055 0.0434606i \(-0.986162\pi\)
0.461890 0.886937i \(-0.347172\pi\)
\(348\) 2.53029e17 + 1.46086e17i 0.409369 + 0.236350i
\(349\) 6.27518e17i 0.995057i 0.867448 + 0.497528i \(0.165759\pi\)
−0.867448 + 0.497528i \(0.834241\pi\)
\(350\) −2.70742e17 + 1.45208e17i −0.420803 + 0.225691i
\(351\) 1.76998e18 2.69662
\(352\) −1.62266e16 + 2.81053e16i −0.0242342 + 0.0419750i
\(353\) −3.86571e17 + 2.23187e17i −0.565987 + 0.326773i −0.755545 0.655097i \(-0.772628\pi\)
0.189558 + 0.981870i \(0.439295\pi\)
\(354\) −7.82524e17 1.35537e18i −1.12325 1.94552i
\(355\) 2.38936e17 + 1.37950e17i 0.336267 + 0.194144i
\(356\) 1.65174e17i 0.227925i
\(357\) 1.25229e16 3.99869e17i 0.0169445 0.541053i
\(358\) 1.69210e17 0.224515
\(359\) 2.55847e17 4.43140e17i 0.332904 0.576607i −0.650176 0.759784i \(-0.725305\pi\)
0.983080 + 0.183177i \(0.0586382\pi\)
\(360\) −2.99383e17 + 1.72849e17i −0.382040 + 0.220571i
\(361\) 3.47473e17 + 6.01841e17i 0.434882 + 0.753237i
\(362\) −5.09273e17 2.94029e17i −0.625159 0.360936i
\(363\) 1.37176e18i 1.65171i
\(364\) 2.83072e17 4.56659e17i 0.334339 0.539365i
\(365\) −4.48169e17 −0.519268
\(366\) 7.26117e17 1.25767e18i 0.825351 1.42955i
\(367\) −6.76573e17 + 3.90620e17i −0.754488 + 0.435604i −0.827313 0.561741i \(-0.810132\pi\)
0.0728252 + 0.997345i \(0.476798\pi\)
\(368\) −1.32201e17 2.28979e17i −0.144644 0.250531i
\(369\) 1.75439e18 + 1.01290e18i 1.88340 + 1.08738i
\(370\) 7.02090e17i 0.739572i
\(371\) 1.25392e18 + 7.77274e17i 1.29614 + 0.803446i
\(372\) −8.92226e17 −0.905053
\(373\) −1.82687e17 + 3.16422e17i −0.181863 + 0.314996i −0.942515 0.334164i \(-0.891546\pi\)
0.760652 + 0.649160i \(0.224879\pi\)
\(374\) 5.20872e16 3.00726e16i 0.0508897 0.0293812i
\(375\) −8.88992e17 1.53978e18i −0.852470 1.47652i
\(376\) 4.63057e17 + 2.67346e17i 0.435832 + 0.251628i
\(377\) 7.27195e17i 0.671833i
\(378\) −1.65583e18 5.18565e16i −1.50166 0.0470284i
\(379\) 8.66799e17 0.771692 0.385846 0.922563i \(-0.373910\pi\)
0.385846 + 0.922563i \(0.373910\pi\)
\(380\) −2.22876e17 + 3.86032e17i −0.194795 + 0.337395i
\(381\) −1.23711e18 + 7.14245e17i −1.06153 + 0.612876i
\(382\) 3.13683e16 + 5.43315e16i 0.0264270 + 0.0457729i
\(383\) 3.55044e17 + 2.04985e17i 0.293691 + 0.169562i 0.639605 0.768704i \(-0.279098\pi\)
−0.345914 + 0.938266i \(0.612431\pi\)
\(384\) 1.94351e17i 0.157859i
\(385\) 9.25850e16 + 1.72625e17i 0.0738441 + 0.137683i
\(386\) −7.94101e17 −0.621963
\(387\) 1.43886e18 2.49217e18i 1.10673 1.91691i
\(388\) 3.09692e16 1.78801e16i 0.0233942 0.0135066i
\(389\) −2.78940e17 4.83138e17i −0.206949 0.358446i 0.743803 0.668399i \(-0.233020\pi\)
−0.950752 + 0.309953i \(0.899687\pi\)
\(390\) 1.08544e18 + 6.26678e17i 0.790957 + 0.456659i
\(391\) 4.90013e17i 0.350728i
\(392\) −2.78194e17 + 4.18913e17i −0.195590 + 0.294525i
\(393\) −1.85925e18 −1.28408
\(394\) 8.27554e17 1.43337e18i 0.561465 0.972486i
\(395\) −1.45106e17 + 8.37767e16i −0.0967173 + 0.0558398i
\(396\) −2.29203e17 3.96991e17i −0.150091 0.259965i
\(397\) −6.39071e17 3.68968e17i −0.411165 0.237386i 0.280125 0.959963i \(-0.409624\pi\)
−0.691290 + 0.722577i \(0.742957\pi\)
\(398\) 1.07525e17i 0.0679716i
\(399\) −3.46479e18 + 1.85829e18i −2.15212 + 1.15426i
\(400\) 2.76601e17 0.168824
\(401\) 1.10884e18 1.92057e18i 0.665055 1.15191i −0.314215 0.949352i \(-0.601741\pi\)
0.979270 0.202558i \(-0.0649254\pi\)
\(402\) −2.57949e17 + 1.48927e17i −0.152038 + 0.0877792i
\(403\) 1.11034e18 + 1.92316e18i 0.643162 + 1.11399i
\(404\) 5.12998e17 + 2.96180e17i 0.292043 + 0.168611i
\(405\) 1.63457e18i 0.914570i
\(406\) −2.13051e16 + 6.80293e17i −0.0117166 + 0.374123i
\(407\) −9.30993e17 −0.503252
\(408\) −1.80094e17 + 3.11932e17i −0.0956925 + 0.165744i
\(409\) 2.21511e18 1.27889e18i 1.15699 0.667991i 0.206412 0.978465i \(-0.433821\pi\)
0.950582 + 0.310474i \(0.100488\pi\)
\(410\) 3.89689e17 + 6.74962e17i 0.200093 + 0.346571i
\(411\) 1.68945e18 + 9.75403e17i 0.852809 + 0.492370i
\(412\) 5.32929e17i 0.264477i
\(413\) 1.92086e18 3.09878e18i 0.937228 1.51196i
\(414\) 3.73471e18 1.79165
\(415\) −1.61310e17 + 2.79397e17i −0.0760893 + 0.131791i
\(416\) −4.18917e17 + 2.41862e17i −0.194301 + 0.112180i
\(417\) 1.75513e18 + 3.03997e18i 0.800490 + 1.38649i
\(418\) −5.11891e17 2.95540e17i −0.229585 0.132551i
\(419\) 3.54851e18i 1.56512i 0.622574 + 0.782561i \(0.286087\pi\)
−0.622574 + 0.782561i \(0.713913\pi\)
\(420\) −9.97071e17 6.18060e17i −0.432495 0.268093i
\(421\) −2.35456e18 −1.00446 −0.502232 0.864733i \(-0.667488\pi\)
−0.502232 + 0.864733i \(0.667488\pi\)
\(422\) −1.23309e18 + 2.13577e18i −0.517376 + 0.896122i
\(423\) −6.54072e18 + 3.77629e18i −2.69925 + 1.55841i
\(424\) −6.64117e17 1.15028e18i −0.269577 0.466922i
\(425\) −4.43942e17 2.56310e17i −0.177257 0.102340i
\(426\) 2.19096e18i 0.860531i
\(427\) 3.38137e18 + 1.05896e17i 1.30647 + 0.0409153i
\(428\) −1.50300e18 −0.571285
\(429\) −8.30994e17 + 1.43932e18i −0.310740 + 0.538217i
\(430\) 9.58806e17 5.53567e17i 0.352738 0.203653i
\(431\) 3.39210e17 + 5.87529e17i 0.122780 + 0.212661i 0.920863 0.389886i \(-0.127486\pi\)
−0.798083 + 0.602548i \(0.794152\pi\)
\(432\) 1.29169e18 + 7.45755e17i 0.460014 + 0.265589i
\(433\) 3.54821e18i 1.24335i 0.783275 + 0.621675i \(0.213548\pi\)
−0.783275 + 0.621675i \(0.786452\pi\)
\(434\) −9.82383e17 1.83166e18i −0.338729 0.631562i
\(435\) −1.58776e18 −0.538716
\(436\) −5.47412e17 + 9.48145e17i −0.182772 + 0.316570i
\(437\) 4.17046e18 2.40782e18i 1.37029 0.791140i
\(438\) 1.77948e18 + 3.08215e18i 0.575406 + 0.996633i
\(439\) 2.53109e18 + 1.46133e18i 0.805484 + 0.465046i 0.845385 0.534157i \(-0.179371\pi\)
−0.0399014 + 0.999204i \(0.512704\pi\)
\(440\) 1.76361e17i 0.0552375i
\(441\) −3.15968e18 6.36166e18i −0.974031 1.96110i
\(442\) 8.96479e17 0.272010
\(443\) 2.85984e18 4.95338e18i 0.854113 1.47937i −0.0233533 0.999727i \(-0.507434\pi\)
0.877466 0.479639i \(-0.159232\pi\)
\(444\) 4.82842e18 2.78769e18i 1.41946 0.819528i
\(445\) −4.48805e17 7.77352e17i −0.129878 0.224956i
\(446\) −6.32083e17 3.64933e17i −0.180065 0.103961i
\(447\) 2.90176e18i 0.813782i
\(448\) 3.98985e17 2.13990e17i 0.110157 0.0590808i
\(449\) −6.27750e18 −1.70633 −0.853163 0.521644i \(-0.825319\pi\)
−0.853163 + 0.521644i \(0.825319\pi\)
\(450\) −1.95351e18 + 3.38357e18i −0.522790 + 0.905499i
\(451\) −8.95020e17 + 5.16740e17i −0.235829 + 0.136156i
\(452\) 1.42131e18 + 2.46178e18i 0.368739 + 0.638675i
\(453\) −4.33642e18 2.50364e18i −1.10776 0.639563i
\(454\) 6.43672e16i 0.0161910i
\(455\) −9.13943e16 + 2.91831e18i −0.0226381 + 0.722855i
\(456\) 3.53977e18 0.863418
\(457\) 7.70753e17 1.33498e18i 0.185141 0.320673i −0.758483 0.651692i \(-0.774059\pi\)
0.943624 + 0.331020i \(0.107393\pi\)
\(458\) −4.14069e18 + 2.39063e18i −0.979522 + 0.565527i
\(459\) −1.38210e18 2.39386e18i −0.321996 0.557713i
\(460\) 1.24434e18 + 7.18422e17i 0.285519 + 0.164845i
\(461\) 2.82419e18i 0.638245i −0.947713 0.319123i \(-0.896612\pi\)
0.947713 0.319123i \(-0.103388\pi\)
\(462\) 8.19567e17 1.32215e18i 0.182428 0.294297i
\(463\) −5.56867e18 −1.22091 −0.610457 0.792050i \(-0.709014\pi\)
−0.610457 + 0.792050i \(0.709014\pi\)
\(464\) 3.06392e17 5.30687e17i 0.0661686 0.114607i
\(465\) 4.19904e18 2.42432e18i 0.893263 0.515726i
\(466\) −1.45997e18 2.52874e18i −0.305945 0.529912i
\(467\) 1.39975e18 + 8.08148e17i 0.288957 + 0.166830i 0.637471 0.770474i \(-0.279980\pi\)
−0.348514 + 0.937303i \(0.613314\pi\)
\(468\) 6.83265e18i 1.38953i
\(469\) −5.89749e17 3.65571e17i −0.118156 0.0732423i
\(470\) −2.90568e18 −0.573539
\(471\) −4.01802e18 + 6.95941e18i −0.781386 + 1.35340i
\(472\) −2.84267e18 + 1.64122e18i −0.544669 + 0.314465i
\(473\) 7.34047e17 + 1.27141e18i 0.138579 + 0.240025i
\(474\) 1.15230e18 + 6.65281e17i 0.214347 + 0.123753i
\(475\) 5.03781e18i 0.923393i
\(476\) −8.38660e17 2.62648e16i −0.151474 0.00474379i
\(477\) 1.87614e19 3.33916
\(478\) 1.11923e18 1.93857e18i 0.196302 0.340005i
\(479\) 7.34016e18 4.23784e18i 1.26869 0.732481i 0.293953 0.955820i \(-0.405029\pi\)
0.974741 + 0.223339i \(0.0716957\pi\)
\(480\) 5.28082e17 + 9.14665e17i 0.0899524 + 0.155802i
\(481\) −1.20176e19 6.93835e18i −2.01744 1.16477i
\(482\) 5.72836e18i 0.947767i
\(483\) 5.99003e18 + 1.11685e19i 0.976786 + 1.82122i
\(484\) −2.87705e18 −0.462413
\(485\) −9.71660e16 + 1.68296e17i −0.0153930 + 0.0266614i
\(486\) −2.90887e18 + 1.67943e18i −0.454224 + 0.262246i
\(487\) −6.25813e18 1.08394e19i −0.963257 1.66841i −0.714227 0.699914i \(-0.753222\pi\)
−0.249030 0.968496i \(-0.580112\pi\)
\(488\) −2.63776e18 1.52291e18i −0.400218 0.231066i
\(489\) 8.28004e18i 1.23843i
\(490\) 1.70999e17 2.72741e18i 0.0252129 0.402140i
\(491\) 1.12919e19 1.64134 0.820669 0.571405i \(-0.193601\pi\)
0.820669 + 0.571405i \(0.193601\pi\)
\(492\) 3.09457e18 5.35996e18i 0.443450 0.768078i
\(493\) −9.83515e17 + 5.67832e17i −0.138948 + 0.0802217i
\(494\) −4.40511e18 7.62987e18i −0.613575 1.06274i
\(495\) 2.15737e18 + 1.24556e18i 0.296271 + 0.171052i
\(496\) 1.87130e18i 0.253379i
\(497\) 4.49783e18 2.41235e18i 0.600494 0.322066i
\(498\) 2.56196e18 0.337262
\(499\) 1.65033e18 2.85846e18i 0.214224 0.371047i −0.738808 0.673916i \(-0.764611\pi\)
0.953032 + 0.302869i \(0.0979444\pi\)
\(500\) −3.22944e18 + 1.86452e18i −0.413368 + 0.238658i
\(501\) 2.09655e18 + 3.63133e18i 0.264631 + 0.458355i
\(502\) −7.08614e18 4.09118e18i −0.882030 0.509241i
\(503\) 7.11585e18i 0.873475i 0.899589 + 0.436738i \(0.143866\pi\)
−0.899589 + 0.436738i \(0.856134\pi\)
\(504\) −2.00181e17 + 6.39197e18i −0.0242331 + 0.773786i
\(505\) −3.21907e18 −0.384318
\(506\) −9.52650e17 + 1.65004e18i −0.112171 + 0.194285i
\(507\) −8.13488e18 + 4.69667e18i −0.944703 + 0.545425i
\(508\) 1.49801e18 + 2.59463e18i 0.171581 + 0.297187i
\(509\) 7.75832e18 + 4.47927e18i 0.876483 + 0.506038i 0.869497 0.493938i \(-0.164443\pi\)
0.00698572 + 0.999976i \(0.497776\pi\)
\(510\) 1.95737e18i 0.218114i
\(511\) −4.36808e18 + 7.04671e18i −0.480114 + 0.774533i
\(512\) −4.07619e17 −0.0441942
\(513\) −1.35827e19 + 2.35259e19i −1.45266 + 2.51608i
\(514\) 1.26550e18 7.30638e17i 0.133512 0.0770833i
\(515\) −1.44805e18 2.50810e18i −0.150707 0.261032i
\(516\) −7.61400e18 4.39595e18i −0.781745 0.451341i
\(517\) 3.85303e18i 0.390273i
\(518\) 1.10392e19 + 6.84293e18i 1.10314 + 0.683808i
\(519\) 2.34012e19 2.30710
\(520\) 1.31435e18 2.27653e18i 0.127847 0.221437i
\(521\) −3.55444e18 + 2.05216e18i −0.341120 + 0.196946i −0.660767 0.750591i \(-0.729769\pi\)
0.319647 + 0.947537i \(0.396436\pi\)
\(522\) 4.32782e18 + 7.49601e18i 0.409804 + 0.709801i
\(523\) −6.77270e18 3.91022e18i −0.632776 0.365333i 0.149050 0.988830i \(-0.452378\pi\)
−0.781826 + 0.623496i \(0.785712\pi\)
\(524\) 3.89948e18i 0.359491i
\(525\) −1.32516e19 4.15008e17i −1.20546 0.0377521i
\(526\) 1.09945e18 0.0986907
\(527\) 1.73403e18 3.00342e18i 0.153596 0.266037i
\(528\) −1.21287e18 + 7.00253e17i −0.106018 + 0.0612093i
\(529\) −1.96498e18 3.40344e18i −0.169499 0.293581i
\(530\) 6.25101e18 + 3.60902e18i 0.532131 + 0.307226i
\(531\) 4.63647e19i 3.89517i
\(532\) 3.89746e18 + 7.26683e18i 0.323147 + 0.602509i
\(533\) −1.54043e19 −1.26052
\(534\) −3.56401e18 + 6.17305e18i −0.287840 + 0.498553i
\(535\) 7.07350e18 4.08389e18i 0.563843 0.325535i
\(536\) 3.12350e17 + 5.41007e17i 0.0245747 + 0.0425647i
\(537\) 6.32388e18 + 3.65109e18i 0.491093 + 0.283533i
\(538\) 8.51666e18i 0.652820i
\(539\) 3.61663e18 + 2.26751e17i 0.273642 + 0.0171564i
\(540\) −8.10534e18 −0.605361
\(541\) 1.89449e18 3.28135e18i 0.139673 0.241920i −0.787700 0.616059i \(-0.788728\pi\)
0.927373 + 0.374139i \(0.122062\pi\)
\(542\) 1.02521e19 5.91908e18i 0.746139 0.430784i
\(543\) −1.26887e19 2.19775e19i −0.911629 1.57899i
\(544\) 6.54226e17 + 3.77718e17i 0.0464019 + 0.0267901i
\(545\) 5.94962e18i 0.416594i
\(546\) 2.04327e19 1.09588e19i 1.41246 0.757554i
\(547\) −1.39588e19 −0.952658 −0.476329 0.879267i \(-0.658033\pi\)
−0.476329 + 0.879267i \(0.658033\pi\)
\(548\) 2.04575e18 3.54334e18i 0.137844 0.238753i
\(549\) 3.72586e19 2.15113e19i 2.47868 1.43107i
\(550\) −9.96602e17 1.72617e18i −0.0654610 0.113382i
\(551\) 9.66556e18 + 5.58041e18i 0.626853 + 0.361914i
\(552\) 1.14102e19i 0.730665i
\(553\) −9.70242e16 + 3.09808e18i −0.00613486 + 0.195892i
\(554\) −1.06887e19 −0.667357
\(555\) −1.51492e19 + 2.62392e19i −0.933982 + 1.61770i
\(556\) 6.37584e18 3.68109e18i 0.388163 0.224106i
\(557\) 6.88069e17 + 1.19177e18i 0.0413662 + 0.0716484i 0.885967 0.463748i \(-0.153496\pi\)
−0.844601 + 0.535396i \(0.820162\pi\)
\(558\) −2.28910e19 1.32161e19i −1.35902 0.784630i
\(559\) 2.18823e19i 1.28295i
\(560\) −1.29628e18 + 2.09119e18i −0.0750555 + 0.121082i
\(561\) 2.59554e18 0.148418
\(562\) 3.34286e18 5.79001e18i 0.188784 0.326983i
\(563\) −2.93601e19 + 1.69510e19i −1.63756 + 0.945448i −0.655895 + 0.754852i \(0.727709\pi\)
−0.981669 + 0.190596i \(0.938958\pi\)
\(564\) 1.15372e19 + 1.99830e19i 0.635545 + 1.10080i
\(565\) −1.33781e19 7.72383e18i −0.727871 0.420237i
\(566\) 1.30407e19i 0.700785i
\(567\) −2.57008e19 1.59313e19i −1.36416 0.845611i
\(568\) −4.59517e18 −0.240915
\(569\) −1.85744e18 + 3.21718e18i −0.0961897 + 0.166605i −0.910105 0.414379i \(-0.863999\pi\)
0.813915 + 0.580984i \(0.197332\pi\)
\(570\) −1.66591e19 + 9.61811e18i −0.852171 + 0.492001i
\(571\) 1.48754e19 + 2.57649e19i 0.751650 + 1.30190i 0.947022 + 0.321167i \(0.104075\pi\)
−0.195372 + 0.980729i \(0.562591\pi\)
\(572\) 3.01875e18 + 1.74287e18i 0.150680 + 0.0869949i
\(573\) 2.70737e18i 0.133495i
\(574\) 1.44108e19 + 4.51311e17i 0.701947 + 0.0219833i
\(575\) 1.62390e19 0.781418
\(576\) 2.87883e18 4.98628e18i 0.136854 0.237039i
\(577\) 2.05080e19 1.18403e19i 0.963146 0.556073i 0.0660064 0.997819i \(-0.478974\pi\)
0.897140 + 0.441746i \(0.145641\pi\)
\(578\) 6.91989e18 + 1.19856e19i 0.321073 + 0.556116i
\(579\) −2.96779e19 1.71345e19i −1.36045 0.785457i
\(580\) 3.33006e18i 0.150819i
\(581\) 2.82084e18 + 5.25947e18i 0.126225 + 0.235347i
\(582\) 1.54321e18 0.0682285
\(583\) −4.78567e18 + 8.28903e18i −0.209056 + 0.362096i
\(584\) 6.46431e18 3.73217e18i 0.279018 0.161091i
\(585\) 1.85654e19 + 3.21562e19i 0.791796 + 1.37143i
\(586\) 1.53200e19 + 8.84503e18i 0.645620 + 0.372749i
\(587\) 2.85495e19i 1.18886i 0.804146 + 0.594432i \(0.202623\pi\)
−0.804146 + 0.594432i \(0.797377\pi\)
\(588\) −1.94359e19 + 9.65335e18i −0.799769 + 0.397225i
\(589\) −3.40825e19 −1.38588
\(590\) 8.91889e18 1.54480e19i 0.358382 0.620737i
\(591\) 6.18563e19 3.57127e19i 2.45624 1.41811i
\(592\) −5.84673e18 1.01268e19i −0.229436 0.397394i
\(593\) 5.03486e18 + 2.90688e18i 0.195256 + 0.112731i 0.594441 0.804139i \(-0.297373\pi\)
−0.399185 + 0.916871i \(0.630707\pi\)
\(594\) 1.07479e19i 0.411926i
\(595\) 4.01831e18 2.15516e18i 0.152204 0.0816321i
\(596\) −6.08596e18 −0.227827
\(597\) −2.32010e18 + 4.01852e18i −0.0858392 + 0.148678i
\(598\) −2.45942e19 + 1.41995e19i −0.899342 + 0.519236i
\(599\) −1.58214e19 2.74036e19i −0.571819 0.990419i −0.996379 0.0850197i \(-0.972905\pi\)
0.424560 0.905400i \(-0.360429\pi\)
\(600\) 1.03374e19 + 5.96829e18i 0.369277 + 0.213202i
\(601\) 1.11746e19i 0.394556i −0.980348 0.197278i \(-0.936790\pi\)
0.980348 0.197278i \(-0.0632102\pi\)
\(602\) 6.41102e17 2.04710e19i 0.0223744 0.714436i
\(603\) −8.82397e18 −0.304399
\(604\) −5.25097e18 + 9.09494e18i −0.179053 + 0.310128i
\(605\) 1.35401e19 7.81740e18i 0.456389 0.263496i
\(606\) 1.27815e19 + 2.21382e19i 0.425867 + 0.737623i
\(607\) 1.72270e19 + 9.94600e18i 0.567398 + 0.327588i 0.756110 0.654445i \(-0.227098\pi\)
−0.188711 + 0.982033i \(0.560431\pi\)
\(608\) 7.42409e18i 0.241723i
\(609\) −1.54751e19 + 2.49649e19i −0.498096 + 0.803541i
\(610\) 1.65520e19 0.526672
\(611\) 2.87152e19 4.97361e19i 0.903281 1.56453i
\(612\) −9.24101e18 + 5.33530e18i −0.287382 + 0.165920i
\(613\) −7.93642e18 1.37463e19i −0.244006 0.422631i 0.717845 0.696203i \(-0.245128\pi\)
−0.961852 + 0.273571i \(0.911795\pi\)
\(614\) 4.26203e18 + 2.46069e18i 0.129550 + 0.0747958i
\(615\) 3.36338e19i 1.01076i
\(616\) −2.77299e18 1.71891e18i −0.0823916 0.0510726i
\(617\) −1.84386e19 −0.541666 −0.270833 0.962626i \(-0.587299\pi\)
−0.270833 + 0.962626i \(0.587299\pi\)
\(618\) −1.14992e19 + 1.99171e19i −0.334000 + 0.578505i
\(619\) −2.03486e19 + 1.17482e19i −0.584385 + 0.337395i −0.762874 0.646547i \(-0.776212\pi\)
0.178489 + 0.983942i \(0.442879\pi\)
\(620\) −5.08461e18 8.80680e18i −0.144383 0.250079i
\(621\) 7.58336e19 + 4.37826e19i 2.12922 + 1.22931i
\(622\) 1.30385e19i 0.361990i
\(623\) −1.65969e19 5.19774e17i −0.455627 0.0142691i
\(624\) −2.08749e19 −0.566673
\(625\) −2.44598e18 + 4.23657e18i −0.0656588 + 0.113724i
\(626\) −2.55275e19 + 1.47383e19i −0.677622 + 0.391225i
\(627\) −1.27539e19 2.20904e19i −0.334789 0.579871i
\(628\) 1.45962e19 + 8.42714e18i 0.378899 + 0.218757i
\(629\) 2.16713e19i 0.556328i
\(630\) −1.64259e19 3.06262e19i −0.417009 0.777515i
\(631\) 4.50708e19 1.13159 0.565796 0.824545i \(-0.308569\pi\)
0.565796 + 0.824545i \(0.308569\pi\)
\(632\) 1.39532e18 2.41676e18i 0.0346461 0.0600088i
\(633\) −9.21682e19 + 5.32133e19i −2.26337 + 1.30676i
\(634\) −1.34423e19 2.32828e19i −0.326474 0.565470i
\(635\) −1.41001e19 8.14067e18i −0.338692 0.195544i
\(636\) 5.73193e19i 1.36176i
\(637\) 4.49948e19 + 2.98804e19i 1.05727 + 0.702118i
\(638\) −4.41577e18 −0.102627
\(639\) 3.24536e19 5.62114e19i 0.746032 1.29217i
\(640\) 1.91836e18 1.10757e18i 0.0436185 0.0251831i
\(641\) −3.71351e19 6.43200e19i −0.835178 1.44657i −0.893886 0.448295i \(-0.852031\pi\)
0.0587079 0.998275i \(-0.481302\pi\)
\(642\) −5.61716e19 3.24307e19i −1.24960 0.721457i
\(643\) 1.53471e19i 0.337715i −0.985641 0.168857i \(-0.945992\pi\)
0.985641 0.168857i \(-0.0540077\pi\)
\(644\) 2.34240e19 1.25631e19i 0.509871 0.273462i
\(645\) 4.77779e19 1.02875
\(646\) −6.87948e18 + 1.19156e19i −0.146531 + 0.253798i
\(647\) −1.41075e19 + 8.14499e18i −0.297250 + 0.171617i −0.641207 0.767368i \(-0.721566\pi\)
0.343957 + 0.938985i \(0.388233\pi\)
\(648\) 1.36120e19 + 2.35767e19i 0.283725 + 0.491426i
\(649\) 2.04845e19 + 1.18267e19i 0.422389 + 0.243866i
\(650\) 2.97092e19i 0.606035i
\(651\) 2.80767e18 8.96516e19i 0.0566604 1.80922i
\(652\) 1.73660e19 0.346711
\(653\) 2.70795e19 4.69030e19i 0.534869 0.926421i −0.464300 0.885678i \(-0.653694\pi\)
0.999170 0.0407430i \(-0.0129725\pi\)
\(654\) −4.09168e19 + 2.36233e19i −0.799572 + 0.461633i
\(655\) −1.05955e19 1.83520e19i −0.204848 0.354808i
\(656\) −1.12416e19 6.49036e18i −0.215032 0.124149i
\(657\) 1.05435e20i 1.99538i
\(658\) −2.83203e19 + 4.56871e19i −0.530294 + 0.855484i
\(659\) −1.49061e19 −0.276163 −0.138081 0.990421i \(-0.544094\pi\)
−0.138081 + 0.990421i \(0.544094\pi\)
\(660\) 3.80540e18 6.59114e18i 0.0697577 0.120824i
\(661\) −1.30899e18 + 7.55746e17i −0.0237425 + 0.0137077i −0.511824 0.859090i \(-0.671030\pi\)
0.488082 + 0.872798i \(0.337697\pi\)
\(662\) −1.70705e18 2.95670e18i −0.0306366 0.0530641i
\(663\) 3.35041e19 + 1.93436e19i 0.594981 + 0.343512i
\(664\) 5.37329e18i 0.0944200i
\(665\) −3.80875e19 2.36095e19i −0.662264 0.410522i
\(666\) 1.65171e20 2.84194
\(667\) 1.79880e19 3.11561e19i 0.306268 0.530472i
\(668\) 7.61612e18 4.39717e18i 0.128321 0.0740863i
\(669\) −1.57485e19 2.72773e19i −0.262577 0.454798i
\(670\) −2.94000e18 1.69741e18i −0.0485092 0.0280068i
\(671\) 2.19484e19i 0.358381i
\(672\) 1.95286e19 + 6.11587e17i 0.315562 + 0.00988265i
\(673\) 4.17784e19 0.668107 0.334054 0.942554i \(-0.391583\pi\)
0.334054 + 0.942554i \(0.391583\pi\)
\(674\) −1.12993e19 + 1.95709e19i −0.178826 + 0.309736i
\(675\) −7.93324e19 + 4.58026e19i −1.24258 + 0.717403i
\(676\) 9.85051e18 + 1.70616e19i 0.152697 + 0.264480i
\(677\) −4.84118e19 2.79506e19i −0.742730 0.428815i 0.0803311 0.996768i \(-0.474402\pi\)
−0.823061 + 0.567953i \(0.807736\pi\)
\(678\) 1.22672e20i 1.86268i
\(679\) 1.69915e18 + 3.16808e18i 0.0255355 + 0.0476110i
\(680\) −4.10527e18 −0.0610632
\(681\) 1.38887e18 2.40559e18i 0.0204471 0.0354154i
\(682\) 1.16781e19 6.74235e18i 0.170169 0.0982473i
\(683\) 6.33178e19 + 1.09670e20i 0.913232 + 1.58176i 0.809469 + 0.587163i \(0.199755\pi\)
0.103763 + 0.994602i \(0.466912\pi\)
\(684\) 9.08167e19 + 5.24330e19i 1.29650 + 0.748535i
\(685\) 2.22345e19i 0.314190i
\(686\) −4.12173e19 2.92714e19i −0.576516 0.409426i
\(687\) −2.06333e20 −2.85675
\(688\) −9.21978e18 + 1.59691e19i −0.126358 + 0.218858i
\(689\) −1.23550e20 + 7.13317e19i −1.67613 + 0.967716i
\(690\) 3.10032e19 + 5.36991e19i 0.416354 + 0.721146i
\(691\) 6.65969e19 + 3.84497e19i 0.885335 + 0.511148i 0.872414 0.488768i \(-0.162554\pi\)
0.0129211 + 0.999917i \(0.495887\pi\)
\(692\) 4.90803e19i 0.645899i
\(693\) 4.06113e19 2.17812e19i 0.529071 0.283759i
\(694\) −5.89033e19 −0.759667
\(695\) −2.00042e19 + 3.46483e19i −0.255404 + 0.442373i
\(696\) 2.29016e19 1.32222e19i 0.289468 0.167124i
\(697\) 1.20285e19 + 2.08340e19i 0.150516 + 0.260701i
\(698\) 4.91871e19 + 2.83982e19i 0.609345 + 0.351806i
\(699\) 1.26009e20i 1.54547i
\(700\) −8.70412e17 + 2.77931e19i −0.0105691 + 0.337482i
\(701\) 1.80979e19 0.217571 0.108786 0.994065i \(-0.465304\pi\)
0.108786 + 0.994065i \(0.465304\pi\)
\(702\) 8.01003e19 1.38738e20i 0.953399 1.65133i
\(703\) 1.84443e20 1.06488e20i 2.17358 1.25491i
\(704\) 1.46867e18 + 2.54381e18i 0.0171362 + 0.0296808i
\(705\) −1.08594e20 6.26967e19i −1.25453 0.724305i
\(706\) 4.04012e19i 0.462127i
\(707\) −3.13747e19 + 5.06145e19i −0.355340 + 0.573243i
\(708\) −1.41652e20 −1.58851
\(709\) 7.13792e19 1.23632e20i 0.792589 1.37280i −0.131770 0.991280i \(-0.542066\pi\)
0.924359 0.381524i \(-0.124601\pi\)
\(710\) 2.16261e19 1.24858e19i 0.237776 0.137280i
\(711\) 1.97090e19 + 3.41370e19i 0.214574 + 0.371654i
\(712\) 1.29470e19 + 7.47494e18i 0.139575 + 0.0805838i
\(713\) 1.09862e20i 1.17279i
\(714\) −3.07765e19 1.90776e19i −0.325335 0.201668i
\(715\) −1.89427e19 −0.198289
\(716\) 7.65757e18 1.32633e19i 0.0793780 0.137487i
\(717\) 8.36581e19 4.83000e19i 0.858764 0.495808i
\(718\) −2.31566e19 4.01084e19i −0.235399 0.407722i
\(719\) 9.32773e18 + 5.38537e18i 0.0939018 + 0.0542142i 0.546216 0.837645i \(-0.316068\pi\)
−0.452314 + 0.891859i \(0.649401\pi\)
\(720\) 3.12890e19i 0.311935i
\(721\) −5.35492e19 1.67703e18i −0.528696 0.0165575i
\(722\) 6.28994e19 0.615015
\(723\) −1.23603e20 + 2.14086e20i −1.19690 + 2.07310i
\(724\) −4.60941e19 + 2.66125e19i −0.442055 + 0.255220i
\(725\) 1.88179e19 + 3.25936e19i 0.178733 + 0.309575i
\(726\) −1.07524e20 6.20789e19i −1.01146 0.583966i
\(727\) 3.78756e19i 0.352873i 0.984312 + 0.176436i \(0.0564570\pi\)
−0.984312 + 0.176436i \(0.943543\pi\)
\(728\) −2.29843e19 4.28543e19i −0.212085 0.395435i
\(729\) 3.06658e19 0.280260
\(730\) −2.02818e19 + 3.51291e19i −0.183589 + 0.317985i
\(731\) 2.95954e19 1.70869e19i 0.265340 0.153194i
\(732\) −6.57206e19 1.13831e20i −0.583611 1.01084i
\(733\) −4.43918e19 2.56296e19i −0.390459 0.225432i 0.291900 0.956449i \(-0.405713\pi\)
−0.682359 + 0.731017i \(0.739046\pi\)
\(734\) 7.07097e19i 0.616037i
\(735\) 6.52408e19 9.82416e19i 0.563000 0.847782i
\(736\) −2.39309e19 −0.204557
\(737\) 2.25082e18 3.89853e18i 0.0190576 0.0330087i
\(738\) 1.58789e20 9.16770e19i 1.33176 0.768893i
\(739\) 8.81253e19 + 1.52637e20i 0.732132 + 1.26809i 0.955970 + 0.293464i \(0.0948079\pi\)
−0.223838 + 0.974626i \(0.571859\pi\)
\(740\) 5.50324e19 + 3.17730e19i 0.452894 + 0.261478i
\(741\) 3.80201e20i 3.09946i
\(742\) 1.17671e20 6.31113e19i 0.950263 0.509659i
\(743\) −6.26592e19 −0.501260 −0.250630 0.968083i \(-0.580638\pi\)
−0.250630 + 0.968083i \(0.580638\pi\)
\(744\) −4.03775e19 + 6.99359e19i −0.319985 + 0.554230i
\(745\) 2.86421e19 1.65365e19i 0.224859 0.129823i
\(746\) 1.65349e19 + 2.86393e19i 0.128597 + 0.222736i
\(747\) 6.57299e19 + 3.79492e19i 0.506429 + 0.292387i
\(748\) 5.44372e18i 0.0415513i
\(749\) 4.72967e18 1.51023e20i 0.0357650 1.14201i
\(750\) −1.60925e20 −1.20557
\(751\) −1.21616e20 + 2.10644e20i −0.902629 + 1.56340i −0.0785611 + 0.996909i \(0.525033\pi\)
−0.824068 + 0.566491i \(0.808301\pi\)
\(752\) 4.19111e19 2.41974e19i 0.308180 0.177928i
\(753\) −1.76553e20 3.05799e20i −1.28621 2.22778i
\(754\) −5.70002e19 3.29091e19i −0.411412 0.237529i
\(755\) 5.70708e19i 0.408118i
\(756\) −7.89989e19 + 1.27443e20i −0.559717 + 0.902949i
\(757\) 2.19935e20 1.54391 0.771956 0.635676i \(-0.219279\pi\)
0.771956 + 0.635676i \(0.219279\pi\)
\(758\) 3.92268e19 6.79429e19i 0.272834 0.472563i
\(759\) −7.12067e19 + 4.11112e19i −0.490714 + 0.283314i
\(760\) 2.01724e19 + 3.49397e19i 0.137741 + 0.238574i
\(761\) 8.60729e19 + 4.96942e19i 0.582336 + 0.336212i 0.762061 0.647505i \(-0.224188\pi\)
−0.179725 + 0.983717i \(0.557521\pi\)
\(762\) 1.29292e20i 0.866737i
\(763\) −9.35479e19 5.79881e19i −0.621387 0.385183i
\(764\) 5.67827e18 0.0373734
\(765\) 2.89937e19 5.02186e19i 0.189092 0.327517i
\(766\) 3.21349e19 1.85531e19i 0.207671 0.119899i
\(767\) 1.76280e20 + 3.05327e20i 1.12885 + 1.95523i
\(768\) −1.52339e19 8.79532e18i −0.0966682 0.0558114i
\(769\) 2.45034e20i 1.54078i −0.637570 0.770392i \(-0.720060\pi\)
0.637570 0.770392i \(-0.279940\pi\)
\(770\) 1.77209e19 + 5.54977e17i 0.110421 + 0.00345812i
\(771\) 6.30607e19 0.389384
\(772\) −3.59369e19 + 6.22445e19i −0.219897 + 0.380873i
\(773\) −1.27651e20 + 7.36995e19i −0.774050 + 0.446898i −0.834317 0.551284i \(-0.814138\pi\)
0.0602677 + 0.998182i \(0.480805\pi\)
\(774\) −1.30230e20 2.25566e20i −0.782574 1.35546i
\(775\) −9.95330e19 5.74654e19i −0.592728 0.342211i
\(776\) 3.23664e18i 0.0191013i
\(777\) 2.64916e20 + 4.93937e20i 1.54939 + 2.88884i
\(778\) −5.04935e19 −0.292670
\(779\) 1.18211e20 2.04747e20i 0.679040 1.17613i
\(780\) 9.82426e19 5.67204e19i 0.559291 0.322907i
\(781\) 1.65566e19 + 2.86768e19i 0.0934142 + 0.161798i
\(782\) 3.84090e19 + 2.21754e19i 0.214776 + 0.124001i
\(783\) 2.02943e20i 1.12471i
\(784\) 2.02463e19 + 4.07637e19i 0.111207 + 0.223904i
\(785\) −9.15914e19 −0.498617
\(786\) −8.41403e19 + 1.45735e20i −0.453990 + 0.786333i
\(787\) 7.71007e19 4.45141e19i 0.412321 0.238053i −0.279466 0.960156i \(-0.590157\pi\)
0.691786 + 0.722102i \(0.256824\pi\)
\(788\) −7.49017e19 1.29733e20i −0.397016 0.687652i
\(789\) 4.10898e19 + 2.37232e19i 0.215871 + 0.124633i
\(790\) 1.51652e19i 0.0789694i
\(791\) −2.51834e20 + 1.35068e20i −1.29981 + 0.697133i
\(792\) −4.14901e19 −0.212260
\(793\) −1.63573e20 + 2.83317e20i −0.829469 + 1.43668i
\(794\) −5.78421e19 + 3.33952e19i −0.290737 + 0.167857i
\(795\) 1.55746e20 + 2.69759e20i 0.775972 + 1.34402i
\(796\) 8.42820e18 + 4.86602e18i 0.0416239 + 0.0240316i
\(797\) 1.70408e20i 0.834225i −0.908855 0.417112i \(-0.863042\pi\)
0.908855 0.417112i \(-0.136958\pi\)
\(798\) −1.11390e19 + 3.55679e20i −0.0540538 + 1.72599i
\(799\) −8.96894e19 −0.431433
\(800\) 1.25175e19 2.16810e19i 0.0596882 0.103383i
\(801\) −1.82877e20 + 1.05584e20i −0.864435 + 0.499082i
\(802\) −1.00361e20 1.73830e20i −0.470265 0.814523i
\(803\) −4.65823e19 2.68943e19i −0.216377 0.124926i
\(804\) 2.69587e19i 0.124139i
\(805\) −7.61034e19 + 1.22772e20i −0.347402 + 0.560439i
\(806\) 2.00993e20 0.909569
\(807\) 1.83766e20 3.18293e20i 0.824425 1.42795i
\(808\) 4.64313e19 2.68071e19i 0.206505 0.119226i
\(809\) 1.08746e20 + 1.88354e20i 0.479484 + 0.830490i 0.999723 0.0235305i \(-0.00749069\pi\)
−0.520240 + 0.854020i \(0.674157\pi\)
\(810\) −1.28123e20 7.39720e19i −0.560058 0.323349i
\(811\) 1.24772e20i 0.540717i −0.962760 0.270359i \(-0.912858\pi\)
0.962760 0.270359i \(-0.0871423\pi\)
\(812\) 5.23597e19 + 3.24565e19i 0.224960 + 0.139447i
\(813\) 5.10871e20 2.17609
\(814\) −4.21319e19 + 7.29746e19i −0.177926 + 0.308178i
\(815\) −8.17289e19 + 4.71862e19i −0.342194 + 0.197566i
\(816\) 1.63002e19 + 2.82328e19i 0.0676648 + 0.117199i
\(817\) −2.90850e20 1.67923e20i −1.19706 0.691122i
\(818\) 2.31504e20i 0.944682i
\(819\) 6.86551e20 + 2.15011e19i 2.77770 + 0.0869909i
\(820\) 7.05413e19 0.282974
\(821\) −3.87923e19 + 6.71902e19i −0.154292 + 0.267242i −0.932801 0.360392i \(-0.882643\pi\)
0.778509 + 0.627633i \(0.215976\pi\)
\(822\) 1.52911e20 8.82834e19i 0.603027 0.348158i
\(823\) −1.96370e20 3.40123e20i −0.767850 1.32996i −0.938727 0.344663i \(-0.887993\pi\)
0.170877 0.985292i \(-0.445340\pi\)
\(824\) 4.17729e19 + 2.41176e19i 0.161959 + 0.0935069i
\(825\) 8.60159e19i 0.330675i
\(826\) −1.55966e20 2.90799e20i −0.594523 1.10849i
\(827\) 1.72427e20 0.651727 0.325864 0.945417i \(-0.394345\pi\)
0.325864 + 0.945417i \(0.394345\pi\)
\(828\) 1.69013e20 2.92740e20i 0.633445 1.09716i
\(829\) −2.25989e20 + 1.30475e20i −0.839859 + 0.484893i −0.857216 0.514957i \(-0.827808\pi\)
0.0173575 + 0.999849i \(0.494475\pi\)
\(830\) 1.46001e19 + 2.52881e19i 0.0538033 + 0.0931900i
\(831\) −3.99470e20 2.30634e20i −1.45974 0.842784i
\(832\) 4.37817e19i 0.158646i
\(833\) 5.27822e18 8.41866e19i 0.0189659 0.302502i
\(834\) 3.17712e20 1.13206
\(835\) −2.38956e19 + 4.13884e19i −0.0844331 + 0.146242i
\(836\) −4.63311e19 + 2.67493e19i −0.162341 + 0.0937277i
\(837\) −3.09870e20 5.36710e20i −1.07672 1.86493i
\(838\) 2.78145e20 + 1.60587e20i 0.958437 + 0.553354i
\(839\) 2.35212e19i 0.0803758i −0.999192 0.0401879i \(-0.987204\pi\)
0.999192 0.0401879i \(-0.0127957\pi\)
\(840\) −9.35681e19 + 5.01839e19i −0.317083 + 0.170063i
\(841\) −2.14179e20 −0.719790
\(842\) −1.06555e20 + 1.84559e20i −0.355132 + 0.615106i
\(843\) 2.49865e20 1.44260e20i 0.825872 0.476818i
\(844\) 1.11606e20 + 1.93308e20i 0.365840 + 0.633654i
\(845\) −9.27180e19 5.35308e19i −0.301417 0.174023i
\(846\) 6.83581e20i 2.20393i
\(847\) 9.05355e18 2.89089e20i 0.0289491 0.924373i
\(848\) −1.20218e20 −0.381240
\(849\) −2.81382e20 + 4.87369e20i −0.884999 + 1.53286i
\(850\) −4.01811e19 + 2.31985e19i −0.125340 + 0.0723650i
\(851\) −3.43256e20 5.94537e20i −1.06197 1.83938i
\(852\) −1.71735e20 9.91514e19i −0.526965 0.304244i
\(853\) 2.15554e19i 0.0656013i 0.999462 + 0.0328007i \(0.0104426\pi\)
−0.999462 + 0.0328007i \(0.989557\pi\)
\(854\) 1.61324e20 2.60252e20i 0.486961 0.785578i
\(855\) −5.69875e20 −1.70615
\(856\) −6.80180e19 + 1.17811e20i −0.201980 + 0.349839i
\(857\) 7.17916e19 4.14489e19i 0.211450 0.122081i −0.390535 0.920588i \(-0.627710\pi\)
0.601985 + 0.798507i \(0.294377\pi\)
\(858\) 7.52130e19 + 1.30273e20i 0.219726 + 0.380577i
\(859\) −3.05644e20 1.76464e20i −0.885654 0.511332i −0.0131354 0.999914i \(-0.504181\pi\)
−0.872518 + 0.488581i \(0.837515\pi\)
\(860\) 1.00206e20i 0.288009i
\(861\) 5.28835e20 + 3.27812e20i 1.50764 + 0.934551i
\(862\) 6.14035e19 0.173637
\(863\) −1.25873e20 + 2.18018e20i −0.353067 + 0.611530i −0.986785 0.162034i \(-0.948195\pi\)
0.633718 + 0.773564i \(0.281528\pi\)
\(864\) 1.16910e20 6.74981e19i 0.325279 0.187800i
\(865\) 1.33359e20 + 2.30984e20i 0.368052 + 0.637484i
\(866\) 2.78121e20 + 1.60573e20i 0.761394 + 0.439591i
\(867\) 5.97250e20i 1.62189i
\(868\) −1.88030e20 5.88863e18i −0.506510 0.0158627i
\(869\) −2.01095e19 −0.0537358
\(870\) −7.18537e19 + 1.24454e20i −0.190465 + 0.329895i
\(871\) 5.81087e19 3.35490e19i 0.152797 0.0882172i
\(872\) 4.95461e19 + 8.58163e19i 0.129239 + 0.223849i
\(873\) 3.95929e19 + 2.28589e19i 0.102451 + 0.0591502i
\(874\) 4.35861e20i 1.11884i
\(875\) −1.77186e20 3.30364e20i −0.451203 0.841271i
\(876\) 3.22120e20 0.813747
\(877\) 1.90881e20 3.30616e20i 0.478372 0.828565i −0.521320 0.853361i \(-0.674560\pi\)
0.999693 + 0.0247962i \(0.00789370\pi\)
\(878\) 2.29089e20 1.32264e20i 0.569563 0.328837i
\(879\) 3.81704e20 + 6.61130e20i 0.941465 + 1.63067i
\(880\) −1.38238e19 7.98120e18i −0.0338259 0.0195294i
\(881\) 2.65263e20i 0.643941i −0.946750 0.321970i \(-0.895655\pi\)
0.946750 0.321970i \(-0.104345\pi\)
\(882\) −6.41641e20 4.02287e19i −1.54530 0.0968850i
\(883\) 3.08288e20 0.736601 0.368300 0.929707i \(-0.379940\pi\)
0.368300 + 0.929707i \(0.379940\pi\)
\(884\) 4.05700e19 7.02693e19i 0.0961699 0.166571i
\(885\) 6.66651e20 3.84891e20i 1.56782 0.905180i
\(886\) −2.58843e20 4.48329e20i −0.603949 1.04607i
\(887\) 3.38946e20 + 1.95690e20i 0.784630 + 0.453006i 0.838069 0.545565i \(-0.183685\pi\)
−0.0534389 + 0.998571i \(0.517018\pi\)
\(888\) 5.04626e20i 1.15899i
\(889\) −2.65425e20 + 1.42357e20i −0.604825 + 0.324389i
\(890\) −8.12423e19 −0.183676
\(891\) 9.80891e19 1.69895e20i 0.220027 0.381099i
\(892\) −5.72096e19 + 3.30300e19i −0.127325 + 0.0735114i
\(893\) 4.40714e20 + 7.63339e20i 0.973188 + 1.68561i
\(894\) −2.27450e20 1.31319e20i −0.498338 0.287716i
\(895\) 8.32273e19i 0.180928i
\(896\) 1.28270e18 4.09579e19i 0.00276675 0.0883450i
\(897\) −1.22555e21 −2.62290
\(898\) −2.84087e20 + 4.92053e20i −0.603277 + 1.04491i
\(899\) −2.20507e20 + 1.27310e20i −0.464626 + 0.268252i
\(900\) 1.76811e20 + 3.06246e20i 0.369668 + 0.640284i
\(901\) 1.92949e20 + 1.11399e20i 0.400285 + 0.231105i
\(902\) 9.35400e19i 0.192554i
\(903\) 4.65668e20 7.51228e20i 0.951180 1.53447i
\(904\) 2.57284e20 0.521476
\(905\) 1.44621e20 2.50490e20i 0.290864 0.503791i
\(906\) −3.92488e20 + 2.26603e20i −0.783302 + 0.452240i
\(907\) 7.93635e19 + 1.37462e20i 0.157170 + 0.272226i 0.933847 0.357673i \(-0.116430\pi\)
−0.776677 + 0.629899i \(0.783096\pi\)
\(908\) −5.04534e18 2.91293e18i −0.00991493 0.00572439i
\(909\) 7.57307e20i 1.47681i
\(910\) 2.24612e20 + 1.39231e20i 0.434653 + 0.269431i
\(911\) 3.49365e20 0.670889 0.335445 0.942060i \(-0.391113\pi\)
0.335445 + 0.942060i \(0.391113\pi\)
\(912\) 1.60192e20 2.77460e20i 0.305265 0.528734i
\(913\) −3.35328e19 + 1.93602e19i −0.0634124 + 0.0366112i
\(914\) −6.97606e19 1.20829e20i −0.130914 0.226750i
\(915\) 6.18595e20 + 3.57146e20i 1.15202 + 0.665118i
\(916\) 4.32750e20i 0.799776i
\(917\) −3.91824e20 1.22710e19i −0.718630 0.0225057i
\(918\) −2.50186e20 −0.455371
\(919\) −6.03407e19 + 1.04513e20i −0.108994 + 0.188783i −0.915363 0.402630i \(-0.868096\pi\)
0.806369 + 0.591413i \(0.201430\pi\)
\(920\) 1.12625e20 6.50241e19i 0.201893 0.116563i
\(921\) 1.06190e20 + 1.83926e20i 0.188915 + 0.327210i
\(922\) −2.21370e20 1.27808e20i −0.390844 0.225654i
\(923\) 4.93560e20i 0.864824i
\(924\) −6.65454e19 1.24074e20i −0.115721 0.215763i
\(925\) 7.18185e20 1.23949
\(926\) −2.52009e20 + 4.36493e20i −0.431658 + 0.747654i
\(927\) −5.90047e20 + 3.40664e20i −1.00306 + 0.579119i
\(928\) −2.77315e19 4.80323e19i −0.0467883 0.0810396i
\(929\) 3.15644e20 + 1.82237e20i 0.528552 + 0.305159i 0.740426 0.672137i \(-0.234624\pi\)
−0.211875 + 0.977297i \(0.567957\pi\)
\(930\) 4.38848e20i 0.729346i
\(931\) −7.42442e20 + 3.68752e20i −1.22466 + 0.608257i
\(932\) −2.64283e20 −0.432671
\(933\) 2.81336e20 4.87288e20i 0.457145 0.791798i
\(934\) 1.26691e20 7.31452e19i 0.204324 0.117966i
\(935\) 1.47914e19 + 2.56195e19i 0.0236771 + 0.0410100i
\(936\) −5.35568e20 3.09211e20i −0.850911 0.491274i
\(937\) 4.84631e20i 0.764248i 0.924111 + 0.382124i \(0.124807\pi\)
−0.924111 + 0.382124i \(0.875193\pi\)
\(938\) −5.53438e19 + 2.96828e19i −0.0866261 + 0.0464606i
\(939\) −1.27205e21 −1.97626
\(940\) −1.31496e20 + 2.27758e20i −0.202777 + 0.351220i
\(941\) 2.38054e20 1.37440e20i 0.364374 0.210372i −0.306624 0.951831i \(-0.599199\pi\)
0.670998 + 0.741459i \(0.265866\pi\)
\(942\) 3.63670e20 + 6.29894e20i 0.552523 + 0.956998i
\(943\) −6.59986e20 3.81043e20i −0.995297 0.574635i
\(944\) 2.97092e20i 0.444720i
\(945\) 2.55060e19 8.14431e20i 0.0378983 1.21013i
\(946\) 1.32877e20 0.195980
\(947\) 5.24233e20 9.07998e20i 0.767493 1.32934i −0.171426 0.985197i \(-0.554837\pi\)
0.938918 0.344140i \(-0.111829\pi\)
\(948\) 1.04294e20 6.02144e19i 0.151566 0.0875068i
\(949\) −4.00866e20 6.94321e20i −0.578277 1.00161i
\(950\) 3.94882e20 + 2.27985e20i 0.565461 + 0.326469i
\(951\) 1.16019e21i 1.64918i
\(952\) −4.00121e19 + 6.45486e19i −0.0564590 + 0.0910811i
\(953\) 9.35175e20 1.30991 0.654957 0.755666i \(-0.272687\pi\)
0.654957 + 0.755666i \(0.272687\pi\)
\(954\) 8.49046e20 1.47059e21i 1.18057 2.04481i
\(955\) −2.67234e19 + 1.54288e19i −0.0368866 + 0.0212965i
\(956\) −1.01301e20 1.75459e20i −0.138807 0.240420i
\(957\) −1.65030e20 9.52803e19i −0.224481 0.129604i
\(958\) 7.67131e20i 1.03588i
\(959\) 3.49600e20 + 2.16709e20i 0.468642 + 0.290500i
\(960\) 9.55930e19 0.127212
\(961\) 1.03009e19 1.78418e19i 0.0136086 0.0235708i
\(962\) −1.08771e21 + 6.27987e20i −1.42655 + 0.823617i
\(963\) −9.60762e20 1.66409e21i −1.25093 2.16667i
\(964\) 4.49010e20 + 2.59236e20i 0.580386 + 0.335086i
\(965\) 3.90585e20i 0.501215i
\(966\) 1.14650e21 + 3.59057e19i 1.46061 + 0.0457429i
\(967\) 9.32261e20 1.17910 0.589552 0.807730i \(-0.299304\pi\)
0.589552 + 0.807730i \(0.299304\pi\)
\(968\) −1.30200e20 + 2.25514e20i −0.163488 + 0.283169i
\(969\) −5.14213e20 + 2.96881e20i −0.641028 + 0.370098i
\(970\) 8.79446e18 + 1.52325e19i 0.0108845 + 0.0188525i
\(971\) 8.85544e20 + 5.11269e20i 1.08812 + 0.628225i 0.933074 0.359683i \(-0.117115\pi\)
0.155042 + 0.987908i \(0.450449\pi\)
\(972\) 3.04010e20i 0.370872i
\(973\) 3.49816e20 + 6.52233e20i 0.423691 + 0.789975i
\(974\) −1.13284e21 −1.36225
\(975\) 6.41044e20 1.11032e21i 0.765342 1.32561i
\(976\) −2.38743e20 + 1.37838e20i −0.282997 + 0.163388i
\(977\) 4.47836e20 + 7.75675e20i 0.527056 + 0.912888i 0.999503 + 0.0315289i \(0.0100376\pi\)
−0.472447 + 0.881359i \(0.656629\pi\)
\(978\) 6.49020e20 + 3.74712e20i 0.758378 + 0.437850i
\(979\) 1.07730e20i 0.124985i
\(980\) −2.06046e20 1.36832e20i −0.237346 0.157618i
\(981\) −1.39969e21 −1.60084
\(982\) 5.11014e20 8.85103e20i 0.580300 1.00511i
\(983\) −9.46057e20 + 5.46206e20i −1.06670 + 0.615860i −0.927278 0.374373i \(-0.877858\pi\)
−0.139423 + 0.990233i \(0.544525\pi\)
\(984\) −2.80089e20 4.85128e20i −0.313567 0.543113i
\(985\) 7.05013e20 + 4.07039e20i 0.783688 + 0.452463i
\(986\) 1.02789e20i 0.113451i
\(987\) −2.04422e21 + 1.09638e21i −2.24030 + 1.20155i
\(988\) −7.97409e20 −0.867726
\(989\) −5.41284e20 + 9.37532e20i −0.584859 + 1.01301i
\(990\) 1.95263e20 1.12735e20i 0.209495 0.120952i
\(991\) 2.42367e20 + 4.19791e20i 0.258200 + 0.447216i 0.965760 0.259437i \(-0.0835372\pi\)
−0.707559 + 0.706654i \(0.750204\pi\)
\(992\) 1.46679e20 + 8.46853e19i 0.155163 + 0.0895831i
\(993\) 1.47334e20i 0.154760i
\(994\) 1.44602e19 4.61727e20i 0.0150823 0.481593i
\(995\) −5.28870e19 −0.0547756
\(996\) 1.15941e20 2.00816e20i 0.119240 0.206530i
\(997\) 5.07994e19 2.93291e19i 0.0518791 0.0299524i −0.473836 0.880613i \(-0.657131\pi\)
0.525715 + 0.850661i \(0.323798\pi\)
\(998\) −1.49371e20 2.58718e20i −0.151479 0.262370i
\(999\) 3.35382e21 + 1.93633e21i 3.37739 + 1.94994i
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 14.15.d.a.5.10 yes 20
3.2 odd 2 126.15.n.b.19.2 20
7.2 even 3 98.15.b.c.97.10 20
7.3 odd 6 inner 14.15.d.a.3.10 20
7.4 even 3 98.15.d.b.31.6 20
7.5 odd 6 98.15.b.c.97.1 20
7.6 odd 2 98.15.d.b.19.6 20
21.17 even 6 126.15.n.b.73.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.15.d.a.3.10 20 7.3 odd 6 inner
14.15.d.a.5.10 yes 20 1.1 even 1 trivial
98.15.b.c.97.1 20 7.5 odd 6
98.15.b.c.97.10 20 7.2 even 3
98.15.d.b.19.6 20 7.6 odd 2
98.15.d.b.31.6 20 7.4 even 3
126.15.n.b.19.2 20 3.2 odd 2
126.15.n.b.73.2 20 21.17 even 6