Properties

Label 16.15.f.a.3.2
Level $16$
Weight $15$
Character 16.3
Analytic conductor $19.893$
Analytic rank $0$
Dimension $54$
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] = [16,15,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), 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: \(19.8926349043\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(27\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.2
Character \(\chi\) \(=\) 16.3
Dual form 16.15.f.a.11.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-123.321 - 34.2916i) q^{2} +(-39.1610 + 39.1610i) q^{3} +(14032.2 + 8457.74i) q^{4} +(-4748.26 + 4748.26i) q^{5} +(6172.27 - 3486.48i) q^{6} +903713. q^{7} +(-1.44043e6 - 1.52420e6i) q^{8} +4.77990e6i q^{9} +O(q^{10})\) \(q+(-123.321 - 34.2916i) q^{2} +(-39.1610 + 39.1610i) q^{3} +(14032.2 + 8457.74i) q^{4} +(-4748.26 + 4748.26i) q^{5} +(6172.27 - 3486.48i) q^{6} +903713. q^{7} +(-1.44043e6 - 1.52420e6i) q^{8} +4.77990e6i q^{9} +(748385. - 422735. i) q^{10} +(-2.30896e7 - 2.30896e7i) q^{11} +(-880728. + 218300. i) q^{12} +(-1.82293e7 - 1.82293e7i) q^{13} +(-1.11447e8 - 3.09897e7i) q^{14} -371893. i q^{15} +(1.25369e8 + 2.37361e8i) q^{16} +4.50577e8 q^{17} +(1.63910e8 - 5.89463e8i) q^{18} +(-9.06528e8 + 9.06528e8i) q^{19} +(-1.06788e8 + 2.64688e7i) q^{20} +(-3.53903e7 + 3.53903e7i) q^{21} +(2.05565e9 + 3.63921e9i) q^{22} +6.46520e9 q^{23} +(1.16098e8 + 3.28048e6i) q^{24} +6.05842e9i q^{25} +(1.62295e9 + 2.87317e9i) q^{26} +(-3.74492e8 - 3.74492e8i) q^{27} +(1.26811e10 + 7.64337e9i) q^{28} +(6.07266e9 + 6.07266e9i) q^{29} +(-1.27528e7 + 4.58622e7i) q^{30} +2.36384e10i q^{31} +(-7.32111e9 - 3.35707e10i) q^{32} +1.80842e9 q^{33} +(-5.55656e10 - 1.54510e10i) q^{34} +(-4.29106e9 + 4.29106e9i) q^{35} +(-4.04272e10 + 6.70724e10i) q^{36} +(2.37359e10 - 2.37359e10i) q^{37} +(1.42880e11 - 8.07078e10i) q^{38} +1.42776e9 q^{39} +(1.40769e10 + 3.97757e8i) q^{40} +1.62483e11i q^{41} +(5.57796e9 - 3.15078e9i) q^{42} +(1.13971e11 + 1.13971e11i) q^{43} +(-1.28711e11 - 5.19283e11i) q^{44} +(-2.26962e10 - 2.26962e10i) q^{45} +(-7.97296e11 - 2.21702e11i) q^{46} +8.90402e10i q^{47} +(-1.42049e10 - 4.38574e9i) q^{48} +1.38474e11 q^{49} +(2.07753e11 - 7.47131e11i) q^{50} +(-1.76450e10 + 1.76450e10i) q^{51} +(-1.01618e11 - 4.09976e11i) q^{52} +(-8.04400e11 + 8.04400e11i) q^{53} +(3.33408e10 + 5.90246e10i) q^{54} +2.19270e11 q^{55} +(-1.30174e12 - 1.37744e12i) q^{56} -7.10011e10i q^{57} +(-5.40646e11 - 9.57127e11i) q^{58} +(1.77186e12 + 1.77186e12i) q^{59} +(3.14537e9 - 5.21847e9i) q^{60} +(3.42607e12 + 3.42607e12i) q^{61} +(8.10596e11 - 2.91511e12i) q^{62} +4.31966e12i q^{63} +(-2.48345e11 + 4.39103e12i) q^{64} +1.73115e11 q^{65} +(-2.23016e11 - 6.20136e10i) q^{66} +(5.72229e11 - 5.72229e11i) q^{67} +(6.32257e12 + 3.81086e12i) q^{68} +(-2.53184e11 + 2.53184e11i) q^{69} +(6.76325e11 - 3.82031e11i) q^{70} +9.89607e12 q^{71} +(7.28554e12 - 6.88513e12i) q^{72} +1.28723e13i q^{73} +(-3.74108e12 + 2.11319e12i) q^{74} +(-2.37254e11 - 2.37254e11i) q^{75} +(-2.03877e13 + 5.05338e12i) q^{76} +(-2.08663e13 - 2.08663e13i) q^{77} +(-1.76072e11 - 4.89600e10i) q^{78} -1.87270e13i q^{79} +(-1.72233e12 - 5.31769e11i) q^{80} -2.28328e13 q^{81} +(5.57181e12 - 2.00376e13i) q^{82} +(7.23420e12 - 7.23420e12i) q^{83} +(-7.95925e11 + 1.97281e11i) q^{84} +(-2.13945e12 + 2.13945e12i) q^{85} +(-1.01468e13 - 1.79633e13i) q^{86} -4.75622e11 q^{87} +(-1.93419e12 + 6.84522e13i) q^{88} -6.10488e13i q^{89} +(2.02063e12 + 3.57721e12i) q^{90} +(-1.64741e13 - 1.64741e13i) q^{91} +(9.07209e13 + 5.46810e13i) q^{92} +(-9.25702e11 - 9.25702e11i) q^{93} +(3.05333e12 - 1.09805e13i) q^{94} -8.60885e12i q^{95} +(1.60136e12 + 1.02796e12i) q^{96} -6.70407e13 q^{97} +(-1.70768e13 - 4.74849e12i) q^{98} +(1.10366e14 - 1.10366e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 2 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 54 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 2 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8} + 16861596 q^{10} - 10455538 q^{11} - 87110828 q^{12} - 2 q^{13} + 66965260 q^{14} - 1059602728 q^{16} - 4 q^{17} + 438192046 q^{18} + 702532062 q^{19} + 1755464396 q^{20} - 9565940 q^{21} - 4795498204 q^{22} + 9748846012 q^{23} + 6975250608 q^{24} - 8671243576 q^{26} - 17865634112 q^{27} - 1297033864 q^{28} - 13109213938 q^{29} + 11736190852 q^{30} - 33545826552 q^{32} - 4 q^{33} - 50990884972 q^{34} + 125535560540 q^{35} + 60739632140 q^{36} + 115688878030 q^{37} - 763264561040 q^{38} + 207890167484 q^{39} + 1298710786600 q^{40} - 1441334806824 q^{42} + 834144712302 q^{43} - 1390640237388 q^{44} + 12216597186 q^{45} + 2618424802780 q^{46} - 4460553354264 q^{48} + 4069338437090 q^{49} - 14467226554 q^{50} - 109367594148 q^{51} + 700335676036 q^{52} - 1638253831762 q^{53} - 6106962841312 q^{54} + 7743608133372 q^{55} + 892124789080 q^{56} - 3111214006280 q^{58} - 2886464056530 q^{59} - 5948471456800 q^{60} + 6325590293982 q^{61} + 4387920975408 q^{62} - 11796533376704 q^{64} + 4831417084012 q^{65} + 3599619796132 q^{66} + 16035979669214 q^{67} - 11417990783952 q^{68} + 13777251815788 q^{69} + 6360571783424 q^{70} - 23491285382916 q^{71} - 17358886385420 q^{72} + 17391872660764 q^{74} + 38233839801842 q^{75} + 8965870021732 q^{76} - 9967029629748 q^{77} - 102277039258452 q^{78} + 184151019521512 q^{80} - 96590901476506 q^{81} - 60118295271632 q^{82} - 44676337597762 q^{83} - 30278459356760 q^{84} - 65266064531252 q^{85} + 200817997017700 q^{86} - 19584321079236 q^{87} - 98329880319368 q^{88} + 105728657951480 q^{90} + 12075497546300 q^{91} + 263822607742360 q^{92} - 149536300814816 q^{93} + 36585390208368 q^{94} - 124834847268944 q^{96} - 4 q^{97} + 73723998799370 q^{98} - 130415167656994 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −123.321 34.2916i −0.963446 0.267903i
\(3\) −39.1610 + 39.1610i −0.0179063 + 0.0179063i −0.716003 0.698097i \(-0.754030\pi\)
0.698097 + 0.716003i \(0.254030\pi\)
\(4\) 14032.2 + 8457.74i 0.856456 + 0.516220i
\(5\) −4748.26 + 4748.26i −0.0607777 + 0.0607777i −0.736842 0.676065i \(-0.763684\pi\)
0.676065 + 0.736842i \(0.263684\pi\)
\(6\) 6172.27 3486.48i 0.0220489 0.0124546i
\(7\) 903713. 1.09735 0.548674 0.836037i \(-0.315133\pi\)
0.548674 + 0.836037i \(0.315133\pi\)
\(8\) −1.44043e6 1.52420e6i −0.686853 0.726797i
\(9\) 4.77990e6i 0.999359i
\(10\) 748385. 422735.i 0.0748385 0.0422735i
\(11\) −2.30896e7 2.30896e7i −1.18486 1.18486i −0.978470 0.206390i \(-0.933828\pi\)
−0.206390 0.978470i \(-0.566172\pi\)
\(12\) −880728. + 218300.i −0.0245795 + 0.00609236i
\(13\) −1.82293e7 1.82293e7i −0.290514 0.290514i 0.546769 0.837283i \(-0.315857\pi\)
−0.837283 + 0.546769i \(0.815857\pi\)
\(14\) −1.11447e8 3.09897e7i −1.05724 0.293982i
\(15\) 371893.i 0.00217660i
\(16\) 1.25369e8 + 2.37361e8i 0.467034 + 0.884239i
\(17\) 4.50577e8 1.09806 0.549030 0.835802i \(-0.314997\pi\)
0.549030 + 0.835802i \(0.314997\pi\)
\(18\) 1.63910e8 5.89463e8i 0.267731 0.962828i
\(19\) −9.06528e8 + 9.06528e8i −1.01416 + 1.01416i −0.0142605 + 0.999898i \(0.504539\pi\)
−0.999898 + 0.0142605i \(0.995461\pi\)
\(20\) −1.06788e8 + 2.64688e7i −0.0834280 + 0.0206788i
\(21\) −3.53903e7 + 3.53903e7i −0.0196494 + 0.0196494i
\(22\) 2.05565e9 + 3.63921e9i 0.824121 + 1.45898i
\(23\) 6.46520e9 1.89883 0.949417 0.314017i \(-0.101675\pi\)
0.949417 + 0.314017i \(0.101675\pi\)
\(24\) 1.16098e8 + 3.28048e6i 0.0253132 + 0.000715251i
\(25\) 6.05842e9i 0.992612i
\(26\) 1.62295e9 + 2.87317e9i 0.202065 + 0.357724i
\(27\) −3.74492e8 3.74492e8i −0.0358010 0.0358010i
\(28\) 1.26811e10 + 7.64337e9i 0.939830 + 0.566472i
\(29\) 6.07266e9 + 6.07266e9i 0.352041 + 0.352041i 0.860868 0.508828i \(-0.169921\pi\)
−0.508828 + 0.860868i \(0.669921\pi\)
\(30\) −1.27528e7 + 4.58622e7i −0.000583118 + 0.00209704i
\(31\) 2.36384e10i 0.859183i 0.903023 + 0.429591i \(0.141342\pi\)
−0.903023 + 0.429591i \(0.858658\pi\)
\(32\) −7.32111e9 3.35707e10i −0.213072 0.977036i
\(33\) 1.80842e9 0.0424328
\(34\) −5.55656e10 1.54510e10i −1.05792 0.294174i
\(35\) −4.29106e9 + 4.29106e9i −0.0666942 + 0.0666942i
\(36\) −4.04272e10 + 6.70724e10i −0.515889 + 0.855907i
\(37\) 2.37359e10 2.37359e10i 0.250031 0.250031i −0.570952 0.820983i \(-0.693426\pi\)
0.820983 + 0.570952i \(0.193426\pi\)
\(38\) 1.42880e11 8.07078e10i 1.24878 0.705391i
\(39\) 1.42776e9 0.0104040
\(40\) 1.40769e10 + 3.97757e8i 0.0859183 + 0.00242771i
\(41\) 1.62483e11i 0.834300i 0.908838 + 0.417150i \(0.136971\pi\)
−0.908838 + 0.417150i \(0.863029\pi\)
\(42\) 5.57796e9 3.15078e9i 0.0241953 0.0136670i
\(43\) 1.13971e11 + 1.13971e11i 0.419290 + 0.419290i 0.884959 0.465669i \(-0.154186\pi\)
−0.465669 + 0.884959i \(0.654186\pi\)
\(44\) −1.28711e11 5.19283e11i −0.403133 1.62643i
\(45\) −2.26962e10 2.26962e10i −0.0607387 0.0607387i
\(46\) −7.97296e11 2.21702e11i −1.82942 0.508703i
\(47\) 8.90402e10i 0.175752i 0.996131 + 0.0878761i \(0.0280080\pi\)
−0.996131 + 0.0878761i \(0.971992\pi\)
\(48\) −1.42049e10 4.38574e9i −0.0241963 0.00747057i
\(49\) 1.38474e11 0.204172
\(50\) 2.07753e11 7.47131e11i 0.265924 0.956328i
\(51\) −1.76450e10 + 1.76450e10i −0.0196622 + 0.0196622i
\(52\) −1.01618e11 4.09976e11i −0.0988434 0.398781i
\(53\) −8.04400e11 + 8.04400e11i −0.684764 + 0.684764i −0.961070 0.276306i \(-0.910890\pi\)
0.276306 + 0.961070i \(0.410890\pi\)
\(54\) 3.33408e10 + 5.90246e10i 0.0249012 + 0.0440836i
\(55\) 2.19270e11 0.144026
\(56\) −1.30174e12 1.37744e12i −0.753716 0.797549i
\(57\) 7.10011e10i 0.0363196i
\(58\) −5.40646e11 9.57127e11i −0.244859 0.433485i
\(59\) 1.77186e12 + 1.77186e12i 0.711977 + 0.711977i 0.966949 0.254971i \(-0.0820660\pi\)
−0.254971 + 0.966949i \(0.582066\pi\)
\(60\) 3.14537e9 5.21847e9i 0.00112360 0.00186416i
\(61\) 3.42607e12 + 3.42607e12i 1.09015 + 1.09015i 0.995511 + 0.0946424i \(0.0301708\pi\)
0.0946424 + 0.995511i \(0.469829\pi\)
\(62\) 8.10596e11 2.91511e12i 0.230177 0.827776i
\(63\) 4.31966e12i 1.09664i
\(64\) −2.48345e11 + 4.39103e12i −0.0564670 + 0.998404i
\(65\) 1.73115e11 0.0353135
\(66\) −2.23016e11 6.20136e10i −0.0408817 0.0113679i
\(67\) 5.72229e11 5.72229e11i 0.0944161 0.0944161i −0.658321 0.752737i \(-0.728733\pi\)
0.752737 + 0.658321i \(0.228733\pi\)
\(68\) 6.32257e12 + 3.81086e12i 0.940441 + 0.566841i
\(69\) −2.53184e11 + 2.53184e11i −0.0340010 + 0.0340010i
\(70\) 6.76325e11 3.82031e11i 0.0821239 0.0463887i
\(71\) 9.89607e12 1.08806 0.544032 0.839065i \(-0.316897\pi\)
0.544032 + 0.839065i \(0.316897\pi\)
\(72\) 7.28554e12 6.88513e12i 0.726331 0.686412i
\(73\) 1.28723e13i 1.16519i 0.812763 + 0.582594i \(0.197962\pi\)
−0.812763 + 0.582594i \(0.802038\pi\)
\(74\) −3.74108e12 + 2.11319e12i −0.307875 + 0.173907i
\(75\) −2.37254e11 2.37254e11i −0.0177740 0.0177740i
\(76\) −2.03877e13 + 5.05338e12i −1.39211 + 0.345054i
\(77\) −2.08663e13 2.08663e13i −1.30020 1.30020i
\(78\) −1.76072e11 4.89600e10i −0.0100237 0.00278727i
\(79\) 1.87270e13i 0.975167i −0.873076 0.487583i \(-0.837878\pi\)
0.873076 0.487583i \(-0.162122\pi\)
\(80\) −1.72233e12 5.31769e11i −0.0821273 0.0253567i
\(81\) −2.28328e13 −0.998077
\(82\) 5.57181e12 2.00376e13i 0.223511 0.803803i
\(83\) 7.23420e12 7.23420e12i 0.266590 0.266590i −0.561135 0.827725i \(-0.689635\pi\)
0.827725 + 0.561135i \(0.189635\pi\)
\(84\) −7.95925e11 + 1.97281e11i −0.0269722 + 0.00668544i
\(85\) −2.13945e12 + 2.13945e12i −0.0667376 + 0.0667376i
\(86\) −1.01468e13 1.79633e13i −0.291634 0.516292i
\(87\) −4.75622e11 −0.0126075
\(88\) −1.93419e12 + 6.84522e13i −0.0473282 + 1.67498i
\(89\) 6.10488e13i 1.38022i −0.723707 0.690108i \(-0.757563\pi\)
0.723707 0.690108i \(-0.242437\pi\)
\(90\) 2.02063e12 + 3.57721e12i 0.0422464 + 0.0747905i
\(91\) −1.64741e13 1.64741e13i −0.318795 0.318795i
\(92\) 9.07209e13 + 5.46810e13i 1.62627 + 0.980216i
\(93\) −9.25702e11 9.25702e11i −0.0153848 0.0153848i
\(94\) 3.05333e12 1.09805e13i 0.0470845 0.169328i
\(95\) 8.60885e12i 0.123276i
\(96\) 1.60136e12 + 1.02796e12i 0.0213104 + 0.0136797i
\(97\) −6.70407e13 −0.829730 −0.414865 0.909883i \(-0.636171\pi\)
−0.414865 + 0.909883i \(0.636171\pi\)
\(98\) −1.70768e13 4.74849e12i −0.196708 0.0546982i
\(99\) 1.10366e14 1.10366e14i 1.18410 1.18410i
\(100\) −5.12406e13 + 8.50129e13i −0.512406 + 0.850129i
\(101\) −1.22072e14 + 1.22072e14i −1.13859 + 1.13859i −0.149882 + 0.988704i \(0.547889\pi\)
−0.988704 + 0.149882i \(0.952111\pi\)
\(102\) 2.78108e12 1.57093e12i 0.0242110 0.0136759i
\(103\) 8.98908e13 0.730895 0.365447 0.930832i \(-0.380916\pi\)
0.365447 + 0.930832i \(0.380916\pi\)
\(104\) −1.52705e12 + 5.40433e13i −0.0116043 + 0.410685i
\(105\) 3.36084e11i 0.00238849i
\(106\) 1.26784e14 7.16154e13i 0.843183 0.476283i
\(107\) 1.29842e14 + 1.29842e14i 0.808590 + 0.808590i 0.984420 0.175831i \(-0.0562611\pi\)
−0.175831 + 0.984420i \(0.556261\pi\)
\(108\) −2.08758e12 8.42228e12i −0.0121808 0.0491432i
\(109\) −1.39650e14 1.39650e14i −0.763932 0.763932i 0.213098 0.977031i \(-0.431645\pi\)
−0.977031 + 0.213098i \(0.931645\pi\)
\(110\) −2.70407e13 7.51912e12i −0.138761 0.0385850i
\(111\) 1.85904e12i 0.00895423i
\(112\) 1.13297e14 + 2.14506e14i 0.512499 + 0.970318i
\(113\) −9.17898e13 −0.390162 −0.195081 0.980787i \(-0.562497\pi\)
−0.195081 + 0.980787i \(0.562497\pi\)
\(114\) −2.43474e12 + 8.75593e12i −0.00973012 + 0.0349920i
\(115\) −3.06984e13 + 3.06984e13i −0.115407 + 0.115407i
\(116\) 3.38516e13 + 1.36574e14i 0.119777 + 0.483238i
\(117\) 8.71343e13 8.71343e13i 0.290327 0.290327i
\(118\) −1.57748e14 2.79268e14i −0.495211 0.876692i
\(119\) 4.07192e14 1.20495
\(120\) −5.66840e11 + 5.35687e11i −0.00158195 + 0.00149500i
\(121\) 6.86506e14i 1.80779i
\(122\) −3.05022e14 5.39992e14i −0.758249 1.34236i
\(123\) −6.36301e12 6.36301e12i −0.0149392 0.0149392i
\(124\) −1.99927e14 + 3.31698e14i −0.443527 + 0.735852i
\(125\) −5.77480e13 5.77480e13i −0.121106 0.121106i
\(126\) 1.48128e14 5.32705e14i 0.293794 1.05656i
\(127\) 3.37858e14i 0.634028i 0.948421 + 0.317014i \(0.102680\pi\)
−0.948421 + 0.317014i \(0.897320\pi\)
\(128\) 1.81201e14 5.32990e14i 0.321878 0.946781i
\(129\) −8.92643e12 −0.0150158
\(130\) −2.13487e13 5.93638e12i −0.0340227 0.00946059i
\(131\) 4.60482e14 4.60482e14i 0.695527 0.695527i −0.267915 0.963442i \(-0.586335\pi\)
0.963442 + 0.267915i \(0.0863348\pi\)
\(132\) 2.53761e13 + 1.52952e13i 0.0363418 + 0.0219047i
\(133\) −8.19241e14 + 8.19241e14i −1.11288 + 1.11288i
\(134\) −9.01904e13 + 5.09452e13i −0.116259 + 0.0656704i
\(135\) 3.55636e12 0.00435181
\(136\) −6.49026e14 6.86771e14i −0.754206 0.798067i
\(137\) 1.28399e15i 1.41748i −0.705469 0.708741i \(-0.749263\pi\)
0.705469 0.708741i \(-0.250737\pi\)
\(138\) 3.99049e13 2.25408e13i 0.0418671 0.0236492i
\(139\) 7.22475e13 + 7.22475e13i 0.0720641 + 0.0720641i 0.742220 0.670156i \(-0.233773\pi\)
−0.670156 + 0.742220i \(0.733773\pi\)
\(140\) −9.65056e13 + 2.39202e13i −0.0915496 + 0.0226918i
\(141\) −3.48690e12 3.48690e12i −0.00314707 0.00314707i
\(142\) −1.22039e15 3.39352e14i −1.04829 0.291495i
\(143\) 8.41814e14i 0.688436i
\(144\) −1.13456e15 + 5.99250e14i −0.883672 + 0.466735i
\(145\) −5.76690e13 −0.0427924
\(146\) 4.41411e14 1.58743e15i 0.312157 1.12260i
\(147\) −5.42278e12 + 5.42278e12i −0.00365595 + 0.00365595i
\(148\) 5.33818e14 1.32314e14i 0.343211 0.0850696i
\(149\) 1.23877e14 1.23877e14i 0.0759776 0.0759776i −0.668097 0.744074i \(-0.732891\pi\)
0.744074 + 0.668097i \(0.232891\pi\)
\(150\) 2.11226e13 + 3.73942e13i 0.0123626 + 0.0218860i
\(151\) 2.55415e14 0.142695 0.0713473 0.997452i \(-0.477270\pi\)
0.0713473 + 0.997452i \(0.477270\pi\)
\(152\) 2.68753e15 + 7.59389e13i 1.43366 + 0.0405097i
\(153\) 2.15371e15i 1.09736i
\(154\) 1.85772e15 + 3.28880e15i 0.904347 + 1.60100i
\(155\) −1.12241e14 1.12241e14i −0.0522191 0.0522191i
\(156\) 2.00345e13 + 1.20756e13i 0.00891060 + 0.00537077i
\(157\) −3.83432e14 3.83432e14i −0.163076 0.163076i 0.620852 0.783928i \(-0.286787\pi\)
−0.783928 + 0.620852i \(0.786787\pi\)
\(158\) −6.42178e14 + 2.30944e15i −0.261250 + 0.939521i
\(159\) 6.30022e13i 0.0245231i
\(160\) 1.94165e14 + 1.24640e14i 0.0723320 + 0.0464320i
\(161\) 5.84269e15 2.08368
\(162\) 2.81576e15 + 7.82972e14i 0.961593 + 0.267387i
\(163\) 9.41783e14 9.41783e14i 0.308062 0.308062i −0.536096 0.844157i \(-0.680101\pi\)
0.844157 + 0.536096i \(0.180101\pi\)
\(164\) −1.37424e15 + 2.28000e15i −0.430682 + 0.714541i
\(165\) −8.58684e12 + 8.58684e12i −0.00257897 + 0.00257897i
\(166\) −1.14020e15 + 6.44057e14i −0.328265 + 0.185425i
\(167\) −5.42408e15 −1.49731 −0.748654 0.662961i \(-0.769299\pi\)
−0.748654 + 0.662961i \(0.769299\pi\)
\(168\) 1.04919e14 + 2.96461e12i 0.0277774 + 0.000784879i
\(169\) 3.27276e15i 0.831204i
\(170\) 3.37205e14 1.90475e14i 0.0821772 0.0464189i
\(171\) −4.33311e15 4.33311e15i −1.01351 1.01351i
\(172\) 6.35323e14 + 2.56320e15i 0.142658 + 0.575550i
\(173\) −4.00646e15 4.00646e15i −0.863851 0.863851i 0.127932 0.991783i \(-0.459166\pi\)
−0.991783 + 0.127932i \(0.959166\pi\)
\(174\) 5.86543e13 + 1.63098e13i 0.0121466 + 0.00337757i
\(175\) 5.47508e15i 1.08924i
\(176\) 2.58586e15 8.37527e15i 0.494329 1.60107i
\(177\) −1.38776e14 −0.0254977
\(178\) −2.09346e15 + 7.52860e15i −0.369763 + 1.32976i
\(179\) 1.17263e15 1.17263e15i 0.199154 0.199154i −0.600483 0.799637i \(-0.705025\pi\)
0.799637 + 0.600483i \(0.205025\pi\)
\(180\) −1.26518e14 5.10436e14i −0.0206655 0.0833745i
\(181\) 3.60950e15 3.60950e15i 0.567148 0.567148i −0.364180 0.931329i \(-0.618651\pi\)
0.931329 + 0.364180i \(0.118651\pi\)
\(182\) 1.46668e15 + 2.59652e15i 0.221735 + 0.392547i
\(183\) −2.68337e14 −0.0390412
\(184\) −9.31270e15 9.85428e15i −1.30422 1.38007i
\(185\) 2.25408e14i 0.0303926i
\(186\) 8.24148e13 + 1.45902e14i 0.0107008 + 0.0189440i
\(187\) −1.04036e16 1.04036e16i −1.30105 1.30105i
\(188\) −7.53079e14 + 1.24943e15i −0.0907268 + 0.150524i
\(189\) −3.38433e14 3.38433e14i −0.0392862 0.0392862i
\(190\) −2.95211e14 + 1.06165e15i −0.0330261 + 0.118770i
\(191\) 1.11969e15i 0.120744i 0.998176 + 0.0603719i \(0.0192287\pi\)
−0.998176 + 0.0603719i \(0.980771\pi\)
\(192\) −1.62232e14 1.81682e14i −0.0168666 0.0188888i
\(193\) 1.53754e16 1.54143 0.770716 0.637178i \(-0.219899\pi\)
0.770716 + 0.637178i \(0.219899\pi\)
\(194\) 8.26754e15 + 2.29893e15i 0.799400 + 0.222287i
\(195\) −6.77935e12 + 6.77935e12i −0.000632333 + 0.000632333i
\(196\) 1.94309e15 + 1.17118e15i 0.174864 + 0.105397i
\(197\) −8.74344e15 + 8.74344e15i −0.759310 + 0.759310i −0.976197 0.216887i \(-0.930410\pi\)
0.216887 + 0.976197i \(0.430410\pi\)
\(198\) −1.73951e16 + 9.82582e15i −1.45804 + 0.823593i
\(199\) −8.24859e15 −0.667433 −0.333717 0.942673i \(-0.608303\pi\)
−0.333717 + 0.942673i \(0.608303\pi\)
\(200\) 9.23427e15 8.72676e15i 0.721427 0.681778i
\(201\) 4.48181e13i 0.00338128i
\(202\) 1.92401e16 1.08680e16i 1.40200 0.791935i
\(203\) 5.48794e15 + 5.48794e15i 0.386311 + 0.386311i
\(204\) −3.96836e14 + 9.83611e13i −0.0269898 + 0.00668979i
\(205\) −7.71513e14 7.71513e14i −0.0507068 0.0507068i
\(206\) −1.10854e16 3.08250e15i −0.704177 0.195809i
\(207\) 3.09030e16i 1.89762i
\(208\) 2.04155e15 6.61231e15i 0.121204 0.392564i
\(209\) 4.18627e16 2.40327
\(210\) −1.15249e13 + 4.14463e13i −0.000639883 + 0.00230118i
\(211\) 3.54377e14 3.54377e14i 0.0190322 0.0190322i −0.697527 0.716559i \(-0.745716\pi\)
0.716559 + 0.697527i \(0.245716\pi\)
\(212\) −1.80909e16 + 4.48408e15i −0.939959 + 0.232982i
\(213\) −3.87540e14 + 3.87540e14i −0.0194831 + 0.0194831i
\(214\) −1.15598e16 2.04647e16i −0.562409 0.995656i
\(215\) −1.08233e15 −0.0509670
\(216\) −3.13708e13 + 1.11023e15i −0.00143004 + 0.0506101i
\(217\) 2.13623e16i 0.942822i
\(218\) 1.24330e16 + 2.20106e16i 0.531348 + 0.940667i
\(219\) −5.04092e14 5.04092e14i −0.0208642 0.0208642i
\(220\) 3.07684e15 + 1.85453e15i 0.123352 + 0.0743491i
\(221\) −8.21370e15 8.21370e15i −0.319002 0.319002i
\(222\) 6.37494e13 2.29259e14i 0.00239886 0.00862692i
\(223\) 2.41605e16i 0.880991i 0.897755 + 0.440495i \(0.145197\pi\)
−0.897755 + 0.440495i \(0.854803\pi\)
\(224\) −6.61618e15 3.03383e16i −0.233814 1.07215i
\(225\) −2.89587e16 −0.991976
\(226\) 1.13196e16 + 3.14761e15i 0.375900 + 0.104526i
\(227\) 4.30535e16 4.30535e16i 1.38620 1.38620i 0.553067 0.833136i \(-0.313457\pi\)
0.833136 0.553067i \(-0.186543\pi\)
\(228\) 6.00509e14 9.96300e14i 0.0187489 0.0311061i
\(229\) −3.33270e16 + 3.33270e16i −1.00913 + 1.00913i −0.00917251 + 0.999958i \(0.502920\pi\)
−0.999958 + 0.00917251i \(0.997080\pi\)
\(230\) 4.83846e15 2.73307e15i 0.142106 0.0802704i
\(231\) 1.63429e15 0.0465636
\(232\) 5.08700e14 1.80032e16i 0.0140620 0.497662i
\(233\) 7.81007e15i 0.209490i −0.994499 0.104745i \(-0.966597\pi\)
0.994499 0.104745i \(-0.0334027\pi\)
\(234\) −1.37335e16 + 7.75753e15i −0.357494 + 0.201935i
\(235\) −4.22785e14 4.22785e14i −0.0106818 0.0106818i
\(236\) 9.87714e15 + 3.98491e16i 0.242241 + 0.977314i
\(237\) 7.33369e14 + 7.33369e14i 0.0174616 + 0.0174616i
\(238\) −5.02154e16 1.39633e16i −1.16091 0.322811i
\(239\) 2.40145e16i 0.539124i 0.962983 + 0.269562i \(0.0868788\pi\)
−0.962983 + 0.269562i \(0.913121\pi\)
\(240\) 8.82729e13 4.66237e13i 0.00192464 0.00101655i
\(241\) 7.06961e16 1.49719 0.748594 0.663029i \(-0.230729\pi\)
0.748594 + 0.663029i \(0.230729\pi\)
\(242\) 2.35414e16 8.46607e16i 0.484311 1.74170i
\(243\) 2.68534e15 2.68534e15i 0.0536729 0.0536729i
\(244\) 1.90984e16 + 7.70521e16i 0.370910 + 1.49643i
\(245\) −6.57510e14 + 6.57510e14i −0.0124091 + 0.0124091i
\(246\) 5.66496e14 + 1.00289e15i 0.0103909 + 0.0183954i
\(247\) 3.30508e16 0.589254
\(248\) 3.60297e16 3.40495e16i 0.624451 0.590132i
\(249\) 5.66597e14i 0.00954726i
\(250\) 5.14128e15 + 9.10181e15i 0.0842347 + 0.149124i
\(251\) −7.40218e16 7.40218e16i −1.17935 1.17935i −0.979909 0.199444i \(-0.936086\pi\)
−0.199444 0.979909i \(-0.563914\pi\)
\(252\) −3.65346e16 + 6.06142e16i −0.566109 + 0.939227i
\(253\) −1.49279e17 1.49279e17i −2.24985 2.24985i
\(254\) 1.15857e16 4.16651e16i 0.169858 0.610852i
\(255\) 1.67566e14i 0.00239004i
\(256\) −4.06230e16 + 5.95153e16i −0.563758 + 0.825940i
\(257\) −7.54711e16 −1.01917 −0.509587 0.860419i \(-0.670202\pi\)
−0.509587 + 0.860419i \(0.670202\pi\)
\(258\) 1.10082e15 + 3.06101e14i 0.0144670 + 0.00402279i
\(259\) 2.14504e16 2.14504e16i 0.274371 0.274371i
\(260\) 2.42918e15 + 1.46416e15i 0.0302445 + 0.0182295i
\(261\) −2.90267e16 + 2.90267e16i −0.351815 + 0.351815i
\(262\) −7.25779e16 + 4.09965e16i −0.856436 + 0.483769i
\(263\) 8.42605e16 0.968130 0.484065 0.875032i \(-0.339160\pi\)
0.484065 + 0.875032i \(0.339160\pi\)
\(264\) −2.60491e15 2.75640e15i −0.0291451 0.0308400i
\(265\) 7.63899e15i 0.0832367i
\(266\) 1.29123e17 7.29366e16i 1.37035 0.774059i
\(267\) 2.39073e15 + 2.39073e15i 0.0247145 + 0.0247145i
\(268\) 1.28694e16 3.18985e15i 0.129603 0.0321238i
\(269\) 4.03998e16 + 4.03998e16i 0.396381 + 0.396381i 0.876955 0.480573i \(-0.159571\pi\)
−0.480573 + 0.876955i \(0.659571\pi\)
\(270\) −4.38575e14 1.21953e14i −0.00419273 0.00116586i
\(271\) 4.38374e16i 0.408375i −0.978932 0.204188i \(-0.934545\pi\)
0.978932 0.204188i \(-0.0654553\pi\)
\(272\) 5.64882e16 + 1.06949e17i 0.512832 + 0.970948i
\(273\) 1.29028e15 0.0114168
\(274\) −4.40300e16 + 1.58343e17i −0.379747 + 1.36567i
\(275\) 1.39886e17 1.39886e17i 1.17611 1.17611i
\(276\) −5.69408e15 + 1.41136e15i −0.0466724 + 0.0115684i
\(277\) −1.05147e17 + 1.05147e17i −0.840311 + 0.840311i −0.988899 0.148588i \(-0.952527\pi\)
0.148588 + 0.988899i \(0.452527\pi\)
\(278\) −6.43216e15 1.13871e16i −0.0501237 0.0887361i
\(279\) −1.12989e17 −0.858632
\(280\) 1.27214e16 + 3.59458e14i 0.0942823 + 0.00266405i
\(281\) 2.35687e16i 0.170369i −0.996365 0.0851845i \(-0.972852\pi\)
0.996365 0.0851845i \(-0.0271480\pi\)
\(282\) 3.10437e14 + 5.49580e14i 0.00218892 + 0.00387514i
\(283\) 1.71729e17 + 1.71729e17i 1.18124 + 1.18124i 0.979424 + 0.201815i \(0.0646841\pi\)
0.201815 + 0.979424i \(0.435316\pi\)
\(284\) 1.38863e17 + 8.36984e16i 0.931879 + 0.561680i
\(285\) 3.37131e14 + 3.37131e14i 0.00220742 + 0.00220742i
\(286\) 2.88671e16 1.03813e17i 0.184434 0.663271i
\(287\) 1.46838e17i 0.915517i
\(288\) 1.60465e17 3.49942e16i 0.976410 0.212936i
\(289\) 3.46417e16 0.205738
\(290\) 7.11181e15 + 1.97756e15i 0.0412282 + 0.0114642i
\(291\) 2.62538e15 2.62538e15i 0.0148574 0.0148574i
\(292\) −1.08871e17 + 1.80626e17i −0.601493 + 0.997932i
\(293\) 1.00156e17 1.00156e17i 0.540261 0.540261i −0.383345 0.923605i \(-0.625228\pi\)
0.923605 + 0.383345i \(0.125228\pi\)
\(294\) 8.54699e14 4.82788e14i 0.00450175 0.00254287i
\(295\) −1.68265e16 −0.0865447
\(296\) −7.03683e16 1.98833e15i −0.353456 0.00998727i
\(297\) 1.72937e16i 0.0848384i
\(298\) −1.95245e16 + 1.10287e16i −0.0935549 + 0.0528457i
\(299\) −1.17856e17 1.17856e17i −0.551638 0.551638i
\(300\) −1.32256e15 5.33582e15i −0.00604735 0.0243979i
\(301\) 1.02997e17 + 1.02997e17i 0.460107 + 0.460107i
\(302\) −3.14980e16 8.75857e15i −0.137479 0.0382283i
\(303\) 9.56090e15i 0.0407756i
\(304\) −3.28825e17 1.01524e17i −1.37041 0.423112i
\(305\) −3.25357e16 −0.132514
\(306\) 7.38542e16 2.65598e17i 0.293985 1.05724i
\(307\) −1.88871e17 + 1.88871e17i −0.734846 + 0.734846i −0.971575 0.236730i \(-0.923924\pi\)
0.236730 + 0.971575i \(0.423924\pi\)
\(308\) −1.16318e17 4.69282e17i −0.442377 1.78476i
\(309\) −3.52021e15 + 3.52021e15i −0.0130876 + 0.0130876i
\(310\) 9.99276e15 + 1.76906e16i 0.0363207 + 0.0643000i
\(311\) 1.92728e17 0.684891 0.342446 0.939538i \(-0.388745\pi\)
0.342446 + 0.939538i \(0.388745\pi\)
\(312\) −2.05659e15 2.17619e15i −0.00714604 0.00756162i
\(313\) 9.92047e16i 0.337071i 0.985696 + 0.168536i \(0.0539038\pi\)
−0.985696 + 0.168536i \(0.946096\pi\)
\(314\) 3.41368e16 + 6.04337e16i 0.113427 + 0.200804i
\(315\) −2.05108e16 2.05108e16i −0.0666515 0.0666515i
\(316\) 1.58388e17 2.62781e17i 0.503400 0.835188i
\(317\) 2.94609e16 + 2.94609e16i 0.0915865 + 0.0915865i 0.751416 0.659829i \(-0.229371\pi\)
−0.659829 + 0.751416i \(0.729371\pi\)
\(318\) −2.16044e15 + 7.76950e15i −0.00656981 + 0.0236267i
\(319\) 2.80430e17i 0.834237i
\(320\) −1.96705e16 2.20289e16i −0.0572488 0.0641126i
\(321\) −1.01695e16 −0.0289576
\(322\) −7.20526e17 2.00355e17i −2.00751 0.558224i
\(323\) −4.08460e17 + 4.08460e17i −1.11361 + 1.11361i
\(324\) −3.20394e17 1.93114e17i −0.854809 0.515227i
\(325\) 1.10441e17 1.10441e17i 0.288367 0.288367i
\(326\) −1.48437e17 + 8.38465e16i −0.379331 + 0.214270i
\(327\) 1.09377e16 0.0273583
\(328\) 2.47658e17 2.34047e17i 0.606366 0.573041i
\(329\) 8.04667e16i 0.192861i
\(330\) 1.35340e15 7.64483e14i 0.00317561 0.00179378i
\(331\) −2.23918e16 2.23918e16i −0.0514390 0.0514390i 0.680919 0.732358i \(-0.261580\pi\)
−0.732358 + 0.680919i \(0.761580\pi\)
\(332\) 1.62697e17 4.03266e16i 0.365942 0.0907036i
\(333\) 1.13455e17 + 1.13455e17i 0.249870 + 0.249870i
\(334\) 6.68904e17 + 1.86000e17i 1.44257 + 0.401133i
\(335\) 5.43417e15i 0.0114768i
\(336\) −1.28371e16 3.96345e15i −0.0265517 0.00819782i
\(337\) 1.72423e17 0.349290 0.174645 0.984631i \(-0.444122\pi\)
0.174645 + 0.984631i \(0.444122\pi\)
\(338\) −1.12228e17 + 4.03600e17i −0.222682 + 0.800820i
\(339\) 3.59458e15 3.59458e15i 0.00698635 0.00698635i
\(340\) −4.81162e16 + 1.19262e16i −0.0916091 + 0.0227066i
\(341\) 5.45800e17 5.45800e17i 1.01801 1.01801i
\(342\) 3.85775e17 + 6.82954e17i 0.704939 + 1.24798i
\(343\) −4.87778e17 −0.873300
\(344\) 9.54722e15 3.37882e17i 0.0167482 0.592729i
\(345\) 2.40436e15i 0.00413301i
\(346\) 3.56694e17 + 6.31470e17i 0.600845 + 1.06370i
\(347\) 4.08856e17 + 4.08856e17i 0.674938 + 0.674938i 0.958850 0.283912i \(-0.0916324\pi\)
−0.283912 + 0.958850i \(0.591632\pi\)
\(348\) −6.67402e15 4.02269e15i −0.0107977 0.00650822i
\(349\) 8.60749e17 + 8.60749e17i 1.36489 + 1.36489i 0.867560 + 0.497333i \(0.165687\pi\)
0.497333 + 0.867560i \(0.334313\pi\)
\(350\) 1.87749e17 6.75192e17i 0.291811 1.04942i
\(351\) 1.36534e16i 0.0208014i
\(352\) −6.06092e17 + 9.44175e17i −0.905190 + 1.41011i
\(353\) −3.76118e17 −0.550683 −0.275341 0.961347i \(-0.588791\pi\)
−0.275341 + 0.961347i \(0.588791\pi\)
\(354\) 1.71140e16 + 4.75884e15i 0.0245657 + 0.00683091i
\(355\) −4.69891e16 + 4.69891e16i −0.0661300 + 0.0661300i
\(356\) 5.16335e17 8.56647e17i 0.712494 1.18209i
\(357\) −1.59460e16 + 1.59460e16i −0.0215762 + 0.0215762i
\(358\) −1.84821e17 + 1.04399e17i −0.245228 + 0.138520i
\(359\) −9.81985e17 −1.27774 −0.638872 0.769313i \(-0.720599\pi\)
−0.638872 + 0.769313i \(0.720599\pi\)
\(360\) −1.90124e15 + 6.72860e16i −0.00242616 + 0.0858632i
\(361\) 8.44579e17i 1.05704i
\(362\) −5.68902e17 + 3.21352e17i −0.698357 + 0.394476i
\(363\) −2.68843e16 2.68843e16i −0.0323707 0.0323707i
\(364\) −9.18336e16 3.70500e17i −0.108466 0.437602i
\(365\) −6.11210e16 6.11210e16i −0.0708174 0.0708174i
\(366\) 3.30916e16 + 9.20169e15i 0.0376140 + 0.0104592i
\(367\) 1.61520e18i 1.80121i −0.434639 0.900605i \(-0.643124\pi\)
0.434639 0.900605i \(-0.356876\pi\)
\(368\) 8.10533e17 + 1.53459e18i 0.886821 + 1.67902i
\(369\) −7.76655e17 −0.833765
\(370\) 7.72960e15 2.77976e16i 0.00814226 0.0292816i
\(371\) −7.26947e17 + 7.26947e17i −0.751424 + 0.751424i
\(372\) −5.16027e15 2.08190e16i −0.00523445 0.0211183i
\(373\) 8.93543e17 8.93543e17i 0.889516 0.889516i −0.104960 0.994476i \(-0.533472\pi\)
0.994476 + 0.104960i \(0.0334716\pi\)
\(374\) 9.26230e17 + 1.63974e18i 0.904935 + 1.60204i
\(375\) 4.52294e15 0.00433712
\(376\) 1.35715e17 1.28256e17i 0.127736 0.120716i
\(377\) 2.21401e17i 0.204545i
\(378\) 3.01305e16 + 5.33413e16i 0.0273252 + 0.0483750i
\(379\) −1.31979e17 1.31979e17i −0.117498 0.117498i 0.645913 0.763411i \(-0.276477\pi\)
−0.763411 + 0.645913i \(0.776477\pi\)
\(380\) 7.28115e16 1.20801e17i 0.0636377 0.105581i
\(381\) −1.32309e16 1.32309e16i −0.0113531 0.0113531i
\(382\) 3.83960e16 1.38082e17i 0.0323476 0.116330i
\(383\) 1.07068e18i 0.885665i −0.896604 0.442832i \(-0.853974\pi\)
0.896604 0.442832i \(-0.146026\pi\)
\(384\) 1.37764e16 + 2.79685e16i 0.0111897 + 0.0227169i
\(385\) 1.98157e17 0.158047
\(386\) −1.89611e18 5.27246e17i −1.48509 0.412954i
\(387\) −5.44770e17 + 5.44770e17i −0.419021 + 0.419021i
\(388\) −9.40728e17 5.67013e17i −0.710627 0.428323i
\(389\) −7.98073e17 + 7.98073e17i −0.592101 + 0.592101i −0.938198 0.346098i \(-0.887507\pi\)
0.346098 + 0.938198i \(0.387507\pi\)
\(390\) 1.06851e15 6.03562e14i 0.000778622 0.000439815i
\(391\) 2.91307e18 2.08504
\(392\) −1.99463e17 2.11063e17i −0.140236 0.148391i
\(393\) 3.60659e16i 0.0249086i
\(394\) 1.37808e18 7.78425e17i 0.934975 0.528133i
\(395\) 8.89207e16 + 8.89207e16i 0.0592684 + 0.0592684i
\(396\) 2.48212e18 6.15227e17i 1.62539 0.402874i
\(397\) −6.72115e17 6.72115e17i −0.432424 0.432424i 0.457028 0.889452i \(-0.348914\pi\)
−0.889452 + 0.457028i \(0.848914\pi\)
\(398\) 1.01722e18 + 2.82857e17i 0.643036 + 0.178807i
\(399\) 6.41646e16i 0.0398552i
\(400\) −1.43803e18 + 7.59536e17i −0.877706 + 0.463584i
\(401\) −3.13463e18 −1.88008 −0.940039 0.341067i \(-0.889212\pi\)
−0.940039 + 0.341067i \(0.889212\pi\)
\(402\) 1.53688e15 5.52701e15i 0.000905854 0.00325768i
\(403\) 4.30911e17 4.30911e17i 0.249604 0.249604i
\(404\) −2.74538e18 + 6.80481e17i −1.56291 + 0.387388i
\(405\) 1.08416e17 1.08416e17i 0.0606608 0.0606608i
\(406\) −4.88588e17 8.64968e17i −0.268696 0.475683i
\(407\) −1.09610e18 −0.592503
\(408\) 5.23111e16 + 1.47811e15i 0.0277954 + 0.000785389i
\(409\) 8.66344e16i 0.0452509i −0.999744 0.0226254i \(-0.992797\pi\)
0.999744 0.0226254i \(-0.00720252\pi\)
\(410\) 6.86874e16 + 1.21600e17i 0.0352688 + 0.0624378i
\(411\) 5.02823e16 + 5.02823e16i 0.0253818 + 0.0253818i
\(412\) 1.26136e18 + 7.60273e17i 0.625979 + 0.377302i
\(413\) 1.60126e18 + 1.60126e18i 0.781287 + 0.781287i
\(414\) 1.05971e18 3.81099e18i 0.508377 1.82825i
\(415\) 6.86997e16i 0.0324054i
\(416\) −4.78512e17 + 7.45430e17i −0.221942 + 0.345743i
\(417\) −5.65857e15 −0.00258080
\(418\) −5.16255e18 1.43554e18i −2.31542 0.643843i
\(419\) 5.71374e16 5.71374e16i 0.0252013 0.0252013i −0.694394 0.719595i \(-0.744327\pi\)
0.719595 + 0.694394i \(0.244327\pi\)
\(420\) 2.84252e15 4.71600e15i 0.00123298 0.00204564i
\(421\) 2.61552e18 2.61552e18i 1.11579 1.11579i 0.123438 0.992352i \(-0.460608\pi\)
0.992352 0.123438i \(-0.0393921\pi\)
\(422\) −5.58542e16 + 3.15500e16i −0.0234352 + 0.0132377i
\(423\) −4.25603e17 −0.175640
\(424\) 2.38475e18 + 6.73838e16i 0.968016 + 0.0273523i
\(425\) 2.72979e18i 1.08995i
\(426\) 6.10812e16 3.45025e16i 0.0239905 0.0135514i
\(427\) 3.09619e18 + 3.09619e18i 1.19628 + 1.19628i
\(428\) 7.23795e17 + 2.92013e18i 0.275112 + 1.10993i
\(429\) −3.29663e16 3.29663e16i −0.0123273 0.0123273i
\(430\) 1.33474e17 + 3.71146e16i 0.0491039 + 0.0136542i
\(431\) 7.06557e17i 0.255745i 0.991791 + 0.127872i \(0.0408148\pi\)
−0.991791 + 0.127872i \(0.959185\pi\)
\(432\) 4.19402e16 1.35839e17i 0.0149364 0.0483770i
\(433\) −1.66868e18 −0.584734 −0.292367 0.956306i \(-0.594443\pi\)
−0.292367 + 0.956306i \(0.594443\pi\)
\(434\) 7.32546e17 2.63442e18i 0.252585 0.908358i
\(435\) 2.25838e15 2.25838e15i 0.000766252 0.000766252i
\(436\) −7.78469e17 3.14071e18i −0.259918 1.04863i
\(437\) −5.86089e18 + 5.86089e18i −1.92572 + 1.92572i
\(438\) 4.48791e16 + 7.94512e16i 0.0145119 + 0.0256911i
\(439\) 4.57887e18 1.45716 0.728578 0.684962i \(-0.240181\pi\)
0.728578 + 0.684962i \(0.240181\pi\)
\(440\) −3.15845e17 3.34213e17i −0.0989247 0.104678i
\(441\) 6.61892e17i 0.204041i
\(442\) 7.31262e17 + 1.29458e18i 0.221880 + 0.392802i
\(443\) 1.35437e18 + 1.35437e18i 0.404493 + 0.404493i 0.879813 0.475320i \(-0.157668\pi\)
−0.475320 + 0.879813i \(0.657668\pi\)
\(444\) −1.57233e16 + 2.60864e16i −0.00462235 + 0.00766891i
\(445\) 2.89875e17 + 2.89875e17i 0.0838863 + 0.0838863i
\(446\) 8.28500e17 2.97950e18i 0.236020 0.848787i
\(447\) 9.70226e15i 0.00272095i
\(448\) −2.24432e17 + 3.96823e18i −0.0619640 + 1.09560i
\(449\) 2.92280e18 0.794466 0.397233 0.917718i \(-0.369971\pi\)
0.397233 + 0.917718i \(0.369971\pi\)
\(450\) 3.57121e18 + 9.93038e17i 0.955715 + 0.265753i
\(451\) 3.75167e18 3.75167e18i 0.988528 0.988528i
\(452\) −1.28801e18 7.76334e17i −0.334157 0.201409i
\(453\) −1.00023e16 + 1.00023e16i −0.00255513 + 0.00255513i
\(454\) −6.78577e18 + 3.83303e18i −1.70690 + 0.964165i
\(455\) 1.56446e17 0.0387512
\(456\) −1.08220e17 + 1.02272e17i −0.0263970 + 0.0249462i
\(457\) 2.51127e17i 0.0603227i −0.999545 0.0301613i \(-0.990398\pi\)
0.999545 0.0301613i \(-0.00960210\pi\)
\(458\) 5.25275e18 2.96708e18i 1.24259 0.701894i
\(459\) −1.68737e17 1.68737e17i −0.0393117 0.0393117i
\(460\) −6.90405e17 + 1.71126e17i −0.158416 + 0.0392656i
\(461\) −2.28492e18 2.28492e18i −0.516375 0.516375i 0.400098 0.916472i \(-0.368976\pi\)
−0.916472 + 0.400098i \(0.868976\pi\)
\(462\) −2.01543e17 5.60425e16i −0.0448615 0.0124745i
\(463\) 4.68005e18i 1.02609i 0.858363 + 0.513043i \(0.171482\pi\)
−0.858363 + 0.513043i \(0.828518\pi\)
\(464\) −6.80092e17 + 2.20273e18i −0.146873 + 0.475703i
\(465\) 8.79094e15 0.00187010
\(466\) −2.67820e17 + 9.63147e17i −0.0561230 + 0.201832i
\(467\) −2.23297e18 + 2.23297e18i −0.460961 + 0.460961i −0.898970 0.438010i \(-0.855684\pi\)
0.438010 + 0.898970i \(0.355684\pi\)
\(468\) 1.95964e18 4.85725e17i 0.398526 0.0987800i
\(469\) 5.17130e17 5.17130e17i 0.103607 0.103607i
\(470\) 3.76404e16 + 6.66363e16i 0.00742966 + 0.0131530i
\(471\) 3.00312e16 0.00584017
\(472\) 1.48427e17 5.25293e18i 0.0284393 1.00649i
\(473\) 5.26308e18i 0.993600i
\(474\) −6.52915e16 1.15588e17i −0.0121453 0.0215013i
\(475\) −5.49213e18 5.49213e18i −1.00667 1.00667i
\(476\) 5.71379e18 + 3.44393e18i 1.03199 + 0.622021i
\(477\) −3.84495e18 3.84495e18i −0.684325 0.684325i
\(478\) 8.23495e17 2.96149e18i 0.144433 0.519416i
\(479\) 4.94875e18i 0.855356i −0.903931 0.427678i \(-0.859332\pi\)
0.903931 0.427678i \(-0.140668\pi\)
\(480\) −1.24847e16 + 2.72267e15i −0.00212662 + 0.000463774i
\(481\) −8.65378e17 −0.145275
\(482\) −8.71832e18 2.42428e18i −1.44246 0.401101i
\(483\) −2.28805e17 + 2.28805e17i −0.0373110 + 0.0373110i
\(484\) −5.80629e18 + 9.63318e18i −0.933214 + 1.54829i
\(485\) 3.18327e17 3.18327e17i 0.0504290 0.0504290i
\(486\) −4.23243e17 + 2.39074e17i −0.0660900 + 0.0373318i
\(487\) −9.39631e18 −1.44629 −0.723144 0.690698i \(-0.757304\pi\)
−0.723144 + 0.690698i \(0.757304\pi\)
\(488\) 2.86999e17 1.01571e19i 0.0435453 1.54110i
\(489\) 7.37623e16i 0.0110325i
\(490\) 1.03632e17 5.85378e16i 0.0152799 0.00863106i
\(491\) −6.08846e18 6.08846e18i −0.884988 0.884988i 0.109049 0.994036i \(-0.465220\pi\)
−0.994036 + 0.109049i \(0.965220\pi\)
\(492\) −3.54702e16 1.43104e17i −0.00508286 0.0205067i
\(493\) 2.73620e18 + 2.73620e18i 0.386562 + 0.386562i
\(494\) −4.07585e18 1.13336e18i −0.567715 0.157863i
\(495\) 1.04809e18i 0.143934i
\(496\) −5.61083e18 + 2.96351e18i −0.759723 + 0.401268i
\(497\) 8.94320e18 1.19398
\(498\) 1.94295e16 6.98733e16i 0.00255774 0.00919827i
\(499\) 7.85027e18 7.85027e18i 1.01902 1.01902i 0.0191994 0.999816i \(-0.493888\pi\)
0.999816 0.0191994i \(-0.00611173\pi\)
\(500\) −3.21912e17 1.29875e18i −0.0412048 0.166240i
\(501\) 2.12412e17 2.12412e17i 0.0268112 0.0268112i
\(502\) 6.59013e18 + 1.16668e19i 0.820291 + 1.45219i
\(503\) −3.47585e17 −0.0426663 −0.0213331 0.999772i \(-0.506791\pi\)
−0.0213331 + 0.999772i \(0.506791\pi\)
\(504\) 6.58404e18 6.22219e18i 0.797037 0.753233i
\(505\) 1.15926e18i 0.138401i
\(506\) 1.32902e19 + 2.35282e19i 1.56487 + 2.77035i
\(507\) 1.28165e17 + 1.28165e17i 0.0148837 + 0.0148837i
\(508\) −2.85752e18 + 4.74089e18i −0.327298 + 0.543017i
\(509\) −9.20376e18 9.20376e18i −1.03978 1.03978i −0.999175 0.0406031i \(-0.987072\pi\)
−0.0406031 0.999175i \(-0.512928\pi\)
\(510\) −5.74611e15 + 2.06645e16i −0.000640299 + 0.00230268i
\(511\) 1.16329e19i 1.27862i
\(512\) 7.05055e18 5.94646e18i 0.764422 0.644717i
\(513\) 6.78974e17 0.0726159
\(514\) 9.30717e18 + 2.58802e18i 0.981920 + 0.273040i
\(515\) −4.26825e17 + 4.26825e17i −0.0444221 + 0.0444221i
\(516\) −1.25257e17 7.54974e16i −0.0128604 0.00775147i
\(517\) 2.05590e18 2.05590e18i 0.208242 0.208242i
\(518\) −3.38086e18 + 1.90972e18i −0.337846 + 0.190837i
\(519\) 3.13794e17 0.0309367
\(520\) −2.49361e17 2.63862e17i −0.0242552 0.0256657i
\(521\) 1.14285e19i 1.09679i 0.836219 + 0.548396i \(0.184761\pi\)
−0.836219 + 0.548396i \(0.815239\pi\)
\(522\) 4.57497e18 2.58423e18i 0.433207 0.244702i
\(523\) −2.97384e18 2.97384e18i −0.277847 0.277847i 0.554402 0.832249i \(-0.312947\pi\)
−0.832249 + 0.554402i \(0.812947\pi\)
\(524\) 1.03562e19 2.56693e18i 0.954733 0.236644i
\(525\) −2.14409e17 2.14409e17i −0.0195042 0.0195042i
\(526\) −1.03911e19 2.88942e18i −0.932741 0.259365i
\(527\) 1.06509e19i 0.943435i
\(528\) 2.26719e17 + 4.29249e17i 0.0198176 + 0.0375208i
\(529\) 3.02060e19 2.60557
\(530\) −2.61953e17 + 9.42049e17i −0.0222994 + 0.0801941i
\(531\) −8.46933e18 + 8.46933e18i −0.711521 + 0.711521i
\(532\) −1.84247e19 + 4.56681e18i −1.52763 + 0.378644i
\(533\) 2.96196e18 2.96196e18i 0.242376 0.242376i
\(534\) −2.12846e17 3.76809e17i −0.0171900 0.0304322i
\(535\) −1.23304e18 −0.0982884
\(536\) −1.69645e18 4.79350e16i −0.133471 0.00377137i
\(537\) 9.18427e16i 0.00713222i
\(538\) −3.59677e18 6.36751e18i −0.275700 0.488083i
\(539\) −3.19730e18 3.19730e18i −0.241915 0.241915i
\(540\) 4.99035e16 + 3.00788e16i 0.00372713 + 0.00224649i
\(541\) 5.03170e18 + 5.03170e18i 0.370966 + 0.370966i 0.867829 0.496863i \(-0.165515\pi\)
−0.496863 + 0.867829i \(0.665515\pi\)
\(542\) −1.50325e18 + 5.40607e18i −0.109405 + 0.393448i
\(543\) 2.82703e17i 0.0203110i
\(544\) −3.29872e18 1.51262e19i −0.233966 1.07285i
\(545\) 1.32619e18 0.0928601
\(546\) −1.59119e17 4.42457e16i −0.0109995 0.00305860i
\(547\) 1.31965e18 1.31965e18i 0.0900631 0.0900631i −0.660640 0.750703i \(-0.729715\pi\)
0.750703 + 0.660640i \(0.229715\pi\)
\(548\) 1.08597e19 1.80172e19i 0.731732 1.21401i
\(549\) −1.63763e19 + 1.63763e19i −1.08945 + 1.08945i
\(550\) −2.20479e19 + 1.24540e19i −1.44820 + 0.818033i
\(551\) −1.10101e19 −0.714050
\(552\) 7.50598e17 + 2.12089e16i 0.0480655 + 0.00135814i
\(553\) 1.69238e19i 1.07010i
\(554\) 1.65726e19 9.36122e18i 1.03472 0.584473i
\(555\) −8.82721e15 8.82721e15i −0.000544217 0.000544217i
\(556\) 4.02739e17 + 1.62484e18i 0.0245188 + 0.0989207i
\(557\) 8.76396e18 + 8.76396e18i 0.526883 + 0.526883i 0.919642 0.392759i \(-0.128479\pi\)
−0.392759 + 0.919642i \(0.628479\pi\)
\(558\) 1.39339e19 + 3.87457e18i 0.827245 + 0.230030i
\(559\) 4.15522e18i 0.243619i
\(560\) −1.55650e18 4.80567e17i −0.0901222 0.0278251i
\(561\) 8.14832e17 0.0465938
\(562\) −8.08206e17 + 2.90651e18i −0.0456424 + 0.164141i
\(563\) 1.32658e19 1.32658e19i 0.739901 0.739901i −0.232658 0.972559i \(-0.574742\pi\)
0.972559 + 0.232658i \(0.0747422\pi\)
\(564\) −1.94375e16 7.84201e16i −0.00107075 0.00431990i
\(565\) 4.35841e17 4.35841e17i 0.0237132 0.0237132i
\(566\) −1.52889e19 2.70666e19i −0.821603 1.45452i
\(567\) −2.06343e19 −1.09524
\(568\) −1.42546e19 1.50836e19i −0.747339 0.790801i
\(569\) 8.40244e18i 0.435130i 0.976046 + 0.217565i \(0.0698115\pi\)
−0.976046 + 0.217565i \(0.930189\pi\)
\(570\) −3.00146e16 5.31361e16i −0.00153536 0.00271810i
\(571\) 4.63828e18 + 4.63828e18i 0.234371 + 0.234371i 0.814514 0.580143i \(-0.197003\pi\)
−0.580143 + 0.814514i \(0.697003\pi\)
\(572\) −7.11984e18 + 1.18125e19i −0.355384 + 0.589615i
\(573\) −4.38482e16 4.38482e16i −0.00216207 0.00216207i
\(574\) 5.03532e18 1.81083e19i 0.245270 0.882051i
\(575\) 3.91689e19i 1.88481i
\(576\) −2.09887e19 1.18706e18i −0.997764 0.0564308i
\(577\) 8.68786e18 0.408021 0.204010 0.978969i \(-0.434602\pi\)
0.204010 + 0.978969i \(0.434602\pi\)
\(578\) −4.27205e18 1.18792e18i −0.198217 0.0551177i
\(579\) −6.02115e17 + 6.02115e17i −0.0276013 + 0.0276013i
\(580\) −8.09222e17 4.87750e17i −0.0366498 0.0220903i
\(581\) 6.53764e18 6.53764e18i 0.292542 0.292542i
\(582\) −4.13793e17 + 2.33737e17i −0.0182946 + 0.0103339i
\(583\) 3.71465e19 1.62270
\(584\) 1.96200e19 1.85417e19i 0.846855 0.800312i
\(585\) 8.27472e17i 0.0352909i
\(586\) −1.57858e19 + 8.91684e18i −0.665250 + 0.375775i
\(587\) −7.90753e18 7.90753e18i −0.329287 0.329287i 0.523028 0.852315i \(-0.324802\pi\)
−0.852315 + 0.523028i \(0.824802\pi\)
\(588\) −1.21958e17 + 3.02289e16i −0.00501844 + 0.00124389i
\(589\) −2.14288e19 2.14288e19i −0.871348 0.871348i
\(590\) 2.07507e18 + 5.77008e17i 0.0833811 + 0.0231856i
\(591\) 6.84804e17i 0.0271928i
\(592\) 8.60971e18 + 2.65824e18i 0.337860 + 0.104314i
\(593\) −2.64566e19 −1.02601 −0.513004 0.858386i \(-0.671467\pi\)
−0.513004 + 0.858386i \(0.671467\pi\)
\(594\) 5.93028e17 2.13268e18i 0.0227284 0.0817372i
\(595\) −1.93345e18 + 1.93345e18i −0.0732343 + 0.0732343i
\(596\) 2.78597e18 6.90542e17i 0.104293 0.0258503i
\(597\) 3.23023e17 3.23023e17i 0.0119512 0.0119512i
\(598\) 1.04927e19 + 1.85756e19i 0.383688 + 0.679258i
\(599\) 1.14496e19 0.413812 0.206906 0.978361i \(-0.433661\pi\)
0.206906 + 0.978361i \(0.433661\pi\)
\(600\) −1.98745e16 + 7.03372e17i −0.000709966 + 0.0251262i
\(601\) 3.33298e19i 1.17682i 0.808562 + 0.588411i \(0.200246\pi\)
−0.808562 + 0.588411i \(0.799754\pi\)
\(602\) −9.16977e18 1.62336e19i −0.320024 0.566552i
\(603\) 2.73520e18 + 2.73520e18i 0.0943555 + 0.0943555i
\(604\) 3.58403e18 + 2.16023e18i 0.122212 + 0.0736618i
\(605\) −3.25971e18 3.25971e18i −0.109873 0.109873i
\(606\) −3.27858e17 + 1.17906e18i −0.0109239 + 0.0392851i
\(607\) 4.55915e19i 1.50163i −0.660512 0.750816i \(-0.729661\pi\)
0.660512 0.750816i \(-0.270339\pi\)
\(608\) 3.70696e19 + 2.37960e19i 1.20696 + 0.774781i
\(609\) −4.29826e17 −0.0138348
\(610\) 4.01234e18 + 1.11570e18i 0.127670 + 0.0355009i
\(611\) 1.62314e18 1.62314e18i 0.0510584 0.0510584i
\(612\) −1.82156e19 + 3.02213e19i −0.566477 + 0.939838i
\(613\) −9.52743e18 + 9.52743e18i −0.292922 + 0.292922i −0.838234 0.545311i \(-0.816411\pi\)
0.545311 + 0.838234i \(0.316411\pi\)
\(614\) 2.97684e19 1.68151e19i 0.904851 0.511117i
\(615\) 6.04264e16 0.00181594
\(616\) −1.74795e18 + 6.18611e19i −0.0519355 + 1.83803i
\(617\) 1.04061e19i 0.305696i −0.988250 0.152848i \(-0.951155\pi\)
0.988250 0.152848i \(-0.0488446\pi\)
\(618\) 5.54830e17 3.13403e17i 0.0161154 0.00910298i
\(619\) 2.17179e19 + 2.17179e19i 0.623712 + 0.623712i 0.946479 0.322767i \(-0.104613\pi\)
−0.322767 + 0.946479i \(0.604613\pi\)
\(620\) −6.25680e17 2.52429e18i −0.0177669 0.0716799i
\(621\) −2.42116e18 2.42116e18i −0.0679803 0.0679803i
\(622\) −2.37674e19 6.60894e18i −0.659856 0.183484i
\(623\) 5.51706e19i 1.51458i
\(624\) 1.78996e17 + 3.38894e17i 0.00485904 + 0.00919965i
\(625\) −3.64293e19 −0.977891
\(626\) 3.40188e18 1.22340e19i 0.0903023 0.324750i
\(627\) −1.63938e18 + 1.63938e18i −0.0430336 + 0.0430336i
\(628\) −2.13742e18 8.62336e18i −0.0554845 0.223851i
\(629\) 1.06948e19 1.06948e19i 0.274549 0.274549i
\(630\) 1.82607e18 + 3.23277e18i 0.0463590 + 0.0820712i
\(631\) 1.58289e19 0.397415 0.198708 0.980059i \(-0.436326\pi\)
0.198708 + 0.980059i \(0.436326\pi\)
\(632\) −2.85438e19 + 2.69750e19i −0.708748 + 0.669796i
\(633\) 2.77555e16i 0.000681589i
\(634\) −2.62289e18 4.64341e18i −0.0637024 0.112775i
\(635\) −1.60424e18 1.60424e18i −0.0385348 0.0385348i
\(636\) 5.32856e17 8.84058e17i 0.0126593 0.0210030i
\(637\) −2.52429e18 2.52429e18i −0.0593147 0.0593147i
\(638\) −9.61638e18 + 3.45829e19i −0.223494 + 0.803743i
\(639\) 4.73022e19i 1.08737i
\(640\) 1.67038e18 + 3.39116e18i 0.0379801 + 0.0771062i
\(641\) −2.03416e19 −0.457487 −0.228744 0.973487i \(-0.573462\pi\)
−0.228744 + 0.973487i \(0.573462\pi\)
\(642\) 1.25411e18 + 3.48727e17i 0.0278991 + 0.00775783i
\(643\) −1.28578e19 + 1.28578e19i −0.282937 + 0.282937i −0.834279 0.551342i \(-0.814116\pi\)
0.551342 + 0.834279i \(0.314116\pi\)
\(644\) 8.19856e19 + 4.94159e19i 1.78458 + 1.07564i
\(645\) 4.23850e16 4.23850e16i 0.000912628 0.000912628i
\(646\) 6.43785e19 3.63650e19i 1.37124 0.774563i
\(647\) 2.40646e19 0.507047 0.253524 0.967329i \(-0.418410\pi\)
0.253524 + 0.967329i \(0.418410\pi\)
\(648\) 3.28891e19 + 3.48018e19i 0.685532 + 0.725399i
\(649\) 8.18231e19i 1.68719i
\(650\) −1.74069e19 + 9.83250e18i −0.355081 + 0.200572i
\(651\) −8.36569e17 8.36569e17i −0.0168824 0.0168824i
\(652\) 2.11806e19 5.24991e18i 0.422869 0.104814i
\(653\) 4.22608e19 + 4.22608e19i 0.834730 + 0.834730i 0.988160 0.153430i \(-0.0490319\pi\)
−0.153430 + 0.988160i \(0.549032\pi\)
\(654\) −1.34884e18 3.75069e17i −0.0263583 0.00732938i
\(655\) 4.37298e18i 0.0845450i
\(656\) −3.85673e19 + 2.03703e19i −0.737721 + 0.389647i
\(657\) −6.15283e19 −1.16444
\(658\) 2.75933e18 9.92325e18i 0.0516681 0.185811i
\(659\) 3.66181e19 3.66181e19i 0.678419 0.678419i −0.281223 0.959642i \(-0.590740\pi\)
0.959642 + 0.281223i \(0.0907401\pi\)
\(660\) −1.93117e17 + 4.78668e16i −0.00354009 + 0.000877459i
\(661\) −3.65811e18 + 3.65811e18i −0.0663508 + 0.0663508i −0.739504 0.673153i \(-0.764940\pi\)
0.673153 + 0.739504i \(0.264940\pi\)
\(662\) 1.99353e18 + 3.52923e18i 0.0357780 + 0.0633393i
\(663\) 6.43314e17 0.0114243
\(664\) −2.14468e19 6.06001e17i −0.376865 0.0106487i
\(665\) 7.77993e18i 0.135277i
\(666\) −1.01009e19 1.78820e19i −0.173796 0.307678i
\(667\) 3.92609e19 + 3.92609e19i 0.668467 + 0.668467i
\(668\) −7.61117e19 4.58755e19i −1.28238 0.772940i
\(669\) −9.46148e17 9.46148e17i −0.0157753 0.0157753i
\(670\) 1.86346e17 6.70148e17i 0.00307466 0.0110573i
\(671\) 1.58213e20i 2.58336i
\(672\) 1.44717e18 + 9.28981e17i 0.0233849 + 0.0150114i
\(673\) −6.53565e19 −1.04516 −0.522580 0.852590i \(-0.675031\pi\)
−0.522580 + 0.852590i \(0.675031\pi\)
\(674\) −2.12634e19 5.91266e18i −0.336522 0.0935758i
\(675\) 2.26883e18 2.26883e18i 0.0355365 0.0355365i
\(676\) 2.76802e19 4.59240e19i 0.429084 0.711889i
\(677\) −5.62255e19 + 5.62255e19i −0.862606 + 0.862606i −0.991640 0.129034i \(-0.958812\pi\)
0.129034 + 0.991640i \(0.458812\pi\)
\(678\) −5.66551e17 + 3.20024e17i −0.00860263 + 0.00485931i
\(679\) −6.05856e19 −0.910502
\(680\) 6.34271e18 + 1.79220e17i 0.0943436 + 0.00266578i
\(681\) 3.37203e18i 0.0496435i
\(682\) −8.60249e19 + 4.85923e19i −1.25353 + 0.708071i
\(683\) 1.46857e19 + 1.46857e19i 0.211811 + 0.211811i 0.805036 0.593225i \(-0.202146\pi\)
−0.593225 + 0.805036i \(0.702146\pi\)
\(684\) −2.41547e19 9.74514e19i −0.344833 1.39122i
\(685\) 6.09671e18 + 6.09671e18i 0.0861513 + 0.0861513i
\(686\) 6.01533e19 + 1.67267e19i 0.841378 + 0.233960i
\(687\) 2.61023e18i 0.0361395i
\(688\) −1.27639e19 + 4.13406e19i −0.174930 + 0.566576i
\(689\) 2.93273e19 0.397867
\(690\) −8.24493e16 + 2.96509e17i −0.00110724 + 0.00398193i
\(691\) −7.65422e19 + 7.65422e19i −1.01755 + 1.01755i −0.0177045 + 0.999843i \(0.505636\pi\)
−0.999843 + 0.0177045i \(0.994364\pi\)
\(692\) −2.23338e19 9.01051e19i −0.293914 1.18579i
\(693\) 9.97391e19 9.97391e19i 1.29937 1.29937i
\(694\) −3.64003e19 6.44409e19i −0.469449 0.831084i
\(695\) −6.86099e17 −0.00875978
\(696\) 6.85103e17 + 7.24945e17i 0.00865947 + 0.00916306i
\(697\) 7.32113e19i 0.916112i
\(698\) −7.66321e19 1.35665e20i −0.949342 1.68066i
\(699\) 3.05850e17 + 3.05850e17i 0.00375119 + 0.00375119i
\(700\) −4.63068e19 + 7.68272e19i −0.562287 + 0.932887i
\(701\) 3.43066e19 + 3.43066e19i 0.412432 + 0.412432i 0.882585 0.470153i \(-0.155801\pi\)
−0.470153 + 0.882585i \(0.655801\pi\)
\(702\) 4.68198e17 1.68376e18i 0.00557275 0.0200410i
\(703\) 4.30345e19i 0.507142i
\(704\) 1.07121e20 9.56528e19i 1.24987 1.11606i
\(705\) 3.31134e16 0.000382543
\(706\) 4.63833e19 + 1.28977e19i 0.530553 + 0.147529i
\(707\) −1.10318e20 + 1.10318e20i −1.24942 + 1.24942i
\(708\) −1.94733e18 1.17373e18i −0.0218377 0.0131624i
\(709\) 1.13634e20 1.13634e20i 1.26178 1.26178i 0.311551 0.950230i \(-0.399152\pi\)
0.950230 0.311551i \(-0.100848\pi\)
\(710\) 7.40607e18 4.18341e18i 0.0814290 0.0459962i
\(711\) 8.95133e19 0.974542
\(712\) −9.30507e19 + 8.79367e19i −1.00314 + 0.948004i
\(713\) 1.52827e20i 1.63145i
\(714\) 2.51330e18 1.41967e18i 0.0265679 0.0150072i
\(715\) −3.99715e18 3.99715e18i −0.0418415 0.0418415i
\(716\) 2.63724e19 6.53675e18i 0.273374 0.0677596i
\(717\) −9.40432e17 9.40432e17i −0.00965369 0.00965369i
\(718\) 1.21099e20 + 3.36738e19i 1.23104 + 0.342311i
\(719\) 4.25824e19i 0.428675i 0.976760 + 0.214337i \(0.0687592\pi\)
−0.976760 + 0.214337i \(0.931241\pi\)
\(720\) 2.54180e18 8.23259e18i 0.0253405 0.0820746i
\(721\) 8.12355e19 0.802045
\(722\) −2.89619e19 + 1.04154e20i −0.283183 + 1.01840i
\(723\) −2.76853e18 + 2.76853e18i −0.0268090 + 0.0268090i
\(724\) 8.11773e19 2.01209e19i 0.778511 0.192965i
\(725\) −3.67907e19 + 3.67907e19i −0.349440 + 0.349440i
\(726\) 2.39349e18 + 4.23730e18i 0.0225152 + 0.0398596i
\(727\) 1.94799e19 0.181488 0.0907438 0.995874i \(-0.471076\pi\)
0.0907438 + 0.995874i \(0.471076\pi\)
\(728\) −1.38002e18 + 4.88396e19i −0.0127340 + 0.450664i
\(729\) 1.08998e20i 0.996154i
\(730\) 5.44157e18 + 9.63343e18i 0.0492566 + 0.0872009i
\(731\) 5.13526e19 + 5.13526e19i 0.460406 + 0.460406i
\(732\) −3.76535e18 2.26952e18i −0.0334370 0.0201538i
\(733\) 1.06456e20 + 1.06456e20i 0.936358 + 0.936358i 0.998093 0.0617347i \(-0.0196633\pi\)
−0.0617347 + 0.998093i \(0.519663\pi\)
\(734\) −5.53878e19 + 1.99188e20i −0.482549 + 1.73537i
\(735\) 5.14975e16i 0.000444401i
\(736\) −4.73325e19 2.17041e20i −0.404589 1.85523i
\(737\) −2.64250e19 −0.223740
\(738\) 9.57779e19 + 2.66327e19i 0.803287 + 0.223368i
\(739\) 2.13499e19 2.13499e19i 0.177372 0.177372i −0.612837 0.790209i \(-0.709972\pi\)
0.790209 + 0.612837i \(0.209972\pi\)
\(740\) −1.90644e18 + 3.16297e18i −0.0156892 + 0.0260299i
\(741\) −1.29430e18 + 1.29430e18i −0.0105513 + 0.0105513i
\(742\) 1.14576e20 6.47197e19i 0.925265 0.522648i
\(743\) −1.64116e20 −1.31290 −0.656448 0.754371i \(-0.727942\pi\)
−0.656448 + 0.754371i \(0.727942\pi\)
\(744\) −7.75451e16 + 2.74437e18i −0.000614531 + 0.0217486i
\(745\) 1.17640e18i 0.00923548i
\(746\) −1.40834e20 + 7.95517e19i −1.09530 + 0.618697i
\(747\) 3.45788e19 + 3.45788e19i 0.266419 + 0.266419i
\(748\) −5.79943e19 2.33977e20i −0.442664 1.78592i
\(749\) 1.17340e20 + 1.17340e20i 0.887304 + 0.887304i
\(750\) −5.57774e17 1.55099e17i −0.00417858 0.00116193i
\(751\) 3.92175e19i 0.291072i −0.989353 0.145536i \(-0.953509\pi\)
0.989353 0.145536i \(-0.0464906\pi\)
\(752\) −2.11347e19 + 1.11628e19i −0.155407 + 0.0820824i
\(753\) 5.79754e18 0.0422356
\(754\) −7.59217e18 + 2.73034e19i −0.0547982 + 0.197068i
\(755\) −1.21278e18 + 1.21278e18i −0.00867265 + 0.00867265i
\(756\) −1.88657e18 7.61133e18i −0.0133666 0.0539272i
\(757\) −1.19161e20 + 1.19161e20i −0.836491 + 0.836491i −0.988395 0.151904i \(-0.951459\pi\)
0.151904 + 0.988395i \(0.451459\pi\)
\(758\) 1.17500e19 + 2.08015e19i 0.0817248 + 0.144681i
\(759\) 1.16918e19 0.0805729
\(760\) −1.31216e19 + 1.24005e19i −0.0895969 + 0.0846727i
\(761\) 2.18609e20i 1.47902i −0.673143 0.739512i \(-0.735056\pi\)
0.673143 0.739512i \(-0.264944\pi\)
\(762\) 1.17794e18 + 2.08535e18i 0.00789655 + 0.0139796i
\(763\) −1.26203e20 1.26203e20i −0.838299 0.838299i
\(764\) −9.47006e18 + 1.57117e19i −0.0623303 + 0.103412i
\(765\) −1.02264e19 1.02264e19i −0.0666948 0.0666948i
\(766\) −3.67154e19 + 1.32038e20i −0.237272 + 0.853290i
\(767\) 6.45997e19i 0.413678i
\(768\) −7.39840e17 3.92151e18i −0.00469471 0.0248843i
\(769\) 7.16620e18 0.0450614 0.0225307 0.999746i \(-0.492828\pi\)
0.0225307 + 0.999746i \(0.492828\pi\)
\(770\) −2.44370e19 6.79513e18i −0.152269 0.0423411i
\(771\) 2.95552e18 2.95552e18i 0.0182496 0.0182496i
\(772\) 2.15750e20 + 1.30041e20i 1.32017 + 0.795718i
\(773\) 2.00741e20 2.00741e20i 1.21725 1.21725i 0.248661 0.968591i \(-0.420010\pi\)
0.968591 0.248661i \(-0.0799904\pi\)
\(774\) 8.58626e19 4.85006e19i 0.515961 0.291447i
\(775\) −1.43211e20 −0.852835
\(776\) 9.65678e19 + 1.02184e20i 0.569902 + 0.603045i
\(777\) 1.68004e18i 0.00982590i
\(778\) 1.25786e20 7.10521e19i 0.729082 0.411832i
\(779\) −1.47296e20 1.47296e20i −0.846113 0.846113i
\(780\) −1.52467e17 + 3.77910e16i −0.000867988 + 0.000215143i
\(781\) −2.28496e20 2.28496e20i −1.28920 1.28920i
\(782\) −3.59243e20 9.98937e19i −2.00882 0.558587i
\(783\) 4.54832e18i 0.0252068i
\(784\) 1.73603e19 + 3.28683e19i 0.0953553 + 0.180537i
\(785\) 3.64127e18 0.0198228
\(786\) 1.23676e18 4.44769e18i 0.00667308 0.0239981i
\(787\) −1.47814e20 + 1.47814e20i −0.790482 + 0.790482i −0.981572 0.191090i \(-0.938798\pi\)
0.191090 + 0.981572i \(0.438798\pi\)
\(788\) −1.96639e20 + 4.87398e19i −1.04229 + 0.258345i
\(789\) −3.29972e18 + 3.29972e18i −0.0173356 + 0.0173356i
\(790\) −7.91656e18 1.40150e19i −0.0412237 0.0729800i
\(791\) −8.29516e19 −0.428144
\(792\) −3.27195e20 9.24524e18i −1.67390 0.0472979i
\(793\) 1.24910e20i 0.633409i
\(794\) 5.98381e19 + 1.05934e20i 0.300770 + 0.532465i
\(795\) 2.99151e17 + 2.99151e17i 0.00149046 + 0.00149046i
\(796\) −1.15746e20 6.97644e19i −0.571627 0.344542i
\(797\) −1.14410e20 1.14410e20i −0.560088 0.560088i 0.369245 0.929332i \(-0.379616\pi\)
−0.929332 + 0.369245i \(0.879616\pi\)
\(798\) −2.20030e18 + 7.91285e18i −0.0106773 + 0.0383983i
\(799\) 4.01194e19i 0.192987i
\(800\) 2.03386e20 4.43544e19i 0.969818 0.211498i
\(801\) 2.91807e20 1.37933
\(802\) 3.86566e20 + 1.07491e20i 1.81135 + 0.503678i
\(803\) 2.97216e20 2.97216e20i 1.38058 1.38058i
\(804\) −3.79060e17 + 6.28895e17i −0.00174548 + 0.00289592i
\(805\) −2.77426e19 + 2.77426e19i −0.126641 + 0.126641i
\(806\) −6.79170e19 + 3.83638e19i −0.307350 + 0.173611i
\(807\) −3.16419e18 −0.0141954
\(808\) 3.61899e20 + 1.02258e19i 1.60956 + 0.0454798i
\(809\) 3.71878e20i 1.63968i 0.572589 + 0.819842i \(0.305939\pi\)
−0.572589 + 0.819842i \(0.694061\pi\)
\(810\) −1.70877e19 + 9.65222e18i −0.0746946 + 0.0421922i
\(811\) 1.50522e20 + 1.50522e20i 0.652310 + 0.652310i 0.953549 0.301239i \(-0.0974001\pi\)
−0.301239 + 0.953549i \(0.597400\pi\)
\(812\) 3.05922e19 + 1.23423e20i 0.131437 + 0.530280i
\(813\) 1.71672e18 + 1.71672e18i 0.00731248 + 0.00731248i
\(814\) 1.35173e20 + 3.75871e19i 0.570844 + 0.158733i
\(815\) 8.94366e18i 0.0374466i
\(816\) −6.40038e18 1.97611e18i −0.0265690 0.00820315i
\(817\) −2.06636e20 −0.850454
\(818\) −2.97083e18 + 1.06838e19i −0.0121228 + 0.0435968i
\(819\) 7.87444e19 7.87444e19i 0.318590 0.318590i
\(820\) −4.30075e18 1.73513e19i −0.0172523 0.0696040i
\(821\) −2.35509e20 + 2.35509e20i −0.936712 + 0.936712i −0.998113 0.0614010i \(-0.980443\pi\)
0.0614010 + 0.998113i \(0.480443\pi\)
\(822\) −4.47661e18 7.92513e18i −0.0176541 0.0312539i
\(823\) 1.92599e20 0.753105 0.376553 0.926395i \(-0.377109\pi\)
0.376553 + 0.926395i \(0.377109\pi\)
\(824\) −1.29482e20 1.37012e20i −0.502017 0.531212i
\(825\) 1.09562e19i 0.0421193i
\(826\) −1.42559e20 2.52378e20i −0.543419 0.962036i
\(827\) −1.45188e20 1.45188e20i −0.548773 0.548773i 0.377313 0.926086i \(-0.376848\pi\)
−0.926086 + 0.377313i \(0.876848\pi\)
\(828\) −2.61370e20 + 4.33637e20i −0.979587 + 1.62523i
\(829\) −1.44466e20 1.44466e20i −0.536887 0.536887i 0.385726 0.922613i \(-0.373951\pi\)
−0.922613 + 0.385726i \(0.873951\pi\)
\(830\) 2.35582e18 8.47212e18i 0.00868151 0.0312209i
\(831\) 8.23535e18i 0.0300937i
\(832\) 8.45726e19 7.55183e19i 0.306455 0.273646i
\(833\) 6.23932e19 0.224193
\(834\) 6.97820e17 + 1.94041e17i 0.00248646 + 0.000691403i
\(835\) 2.57549e19 2.57549e19i 0.0910029 0.0910029i
\(836\) 5.87424e20 + 3.54064e20i 2.05830 + 1.24062i
\(837\) 8.85237e18 8.85237e18i 0.0307596 0.0307596i
\(838\) −9.00557e18 + 5.08691e18i −0.0310315 + 0.0175286i
\(839\) 3.63924e20 1.24359 0.621794 0.783181i \(-0.286404\pi\)
0.621794 + 0.783181i \(0.286404\pi\)
\(840\) −5.12261e17 + 4.84107e17i −0.00173595 + 0.00164054i
\(841\) 2.23804e20i 0.752135i
\(842\) −4.12238e20 + 2.32858e20i −1.37393 + 0.776081i
\(843\) 9.22972e17 + 9.22972e17i 0.00305067 + 0.00305067i
\(844\) 7.96990e18 1.97545e18i 0.0261250 0.00647543i
\(845\) 1.55399e19 + 1.55399e19i 0.0505186 + 0.0505186i
\(846\) 5.24858e19 + 1.45946e19i 0.169219 + 0.0470543i
\(847\) 6.20405e20i 1.98377i
\(848\) −2.91780e20 9.00868e19i −0.925304 0.285687i
\(849\) −1.34501e19 −0.0423031
\(850\) 9.36086e19 3.36640e20i 0.292000 1.05011i
\(851\) 1.53457e20 1.53457e20i 0.474767 0.474767i
\(852\) −8.71574e18 + 2.16032e18i −0.0267440 + 0.00662888i
\(853\) −6.48728e19 + 6.48728e19i −0.197433 + 0.197433i −0.798899 0.601466i \(-0.794584\pi\)
0.601466 + 0.798899i \(0.294584\pi\)
\(854\) −2.75652e20 4.87998e20i −0.832063 1.47303i
\(855\) 4.11495e19 0.123197
\(856\) 1.08767e19 3.84934e20i 0.0322984 1.14306i
\(857\) 4.85683e20i 1.43050i 0.698869 + 0.715249i \(0.253687\pi\)
−0.698869 + 0.715249i \(0.746313\pi\)
\(858\) 2.93497e18 + 5.19590e18i 0.00857418 + 0.0151792i
\(859\) 1.64146e18 + 1.64146e18i 0.00475638 + 0.00475638i 0.709481 0.704725i \(-0.248929\pi\)
−0.704725 + 0.709481i \(0.748929\pi\)
\(860\) −1.51874e19 9.15403e18i −0.0436510 0.0263102i
\(861\) −5.75034e18 5.75034e18i −0.0163935 0.0163935i
\(862\) 2.42290e19 8.71334e19i 0.0685147 0.246396i
\(863\) 3.79514e20i 1.06452i 0.846582 + 0.532258i \(0.178656\pi\)
−0.846582 + 0.532258i \(0.821344\pi\)
\(864\) −9.83025e18 + 1.53136e19i −0.0273507 + 0.0426071i
\(865\) 3.80474e19 0.105006
\(866\) 2.05784e20 + 5.72217e19i 0.563360 + 0.156652i
\(867\) −1.35660e18 + 1.35660e18i −0.00368399 + 0.00368399i
\(868\) −1.80677e20 + 2.99760e20i −0.486703 + 0.807486i
\(869\) −4.32399e20 + 4.32399e20i −1.15544 + 1.15544i
\(870\) −3.55949e17 + 2.01062e17i −0.000943523 + 0.000532961i
\(871\) −2.08627e19 −0.0548583
\(872\) −1.16983e19 + 4.14011e20i −0.0305146 + 1.07993i
\(873\) 3.20448e20i 0.829198i
\(874\) 9.23750e20 5.21792e20i 2.37123 1.33942i
\(875\) −5.21876e19 5.21876e19i −0.132896 0.132896i
\(876\) −2.81003e18 1.13370e19i −0.00709875 0.0286397i
\(877\) −1.79150e19 1.79150e19i −0.0448973 0.0448973i 0.684302 0.729199i \(-0.260107\pi\)
−0.729199 + 0.684302i \(0.760107\pi\)
\(878\) −5.64671e20 1.57016e20i −1.40389 0.390376i
\(879\) 7.84441e18i 0.0193481i
\(880\) 2.74896e19 + 5.20463e19i 0.0672651 + 0.127353i
\(881\) 5.86532e20 1.42384 0.711919 0.702262i \(-0.247826\pi\)
0.711919 + 0.702262i \(0.247826\pi\)
\(882\) 2.26973e19 8.16253e19i 0.0546631 0.196582i
\(883\) 4.46724e20 4.46724e20i 1.06737 1.06737i 0.0698075 0.997560i \(-0.477761\pi\)
0.997560 0.0698075i \(-0.0222385\pi\)
\(884\) −4.57868e19 1.84726e20i −0.108536 0.437886i
\(885\) 6.58943e17 6.58943e17i 0.00154969 0.00154969i
\(886\) −1.20579e20 2.13466e20i −0.281343 0.498072i
\(887\) 1.24414e20 0.288008 0.144004 0.989577i \(-0.454002\pi\)
0.144004 + 0.989577i \(0.454002\pi\)
\(888\) 2.83356e18 2.67783e18i 0.00650791 0.00615024i
\(889\) 3.05327e20i 0.695749i
\(890\) −2.58074e19 4.56880e19i −0.0583465 0.103293i
\(891\) 5.27199e20 + 5.27199e20i 1.18258 + 1.18258i
\(892\) −2.04343e20 + 3.39024e20i −0.454785 + 0.754530i
\(893\) −8.07174e19 8.07174e19i −0.178241 0.178241i
\(894\) 3.32706e17 1.19649e18i 0.000728949 0.00262149i
\(895\) 1.11359e19i 0.0242083i
\(896\) 1.63754e20 4.81670e20i 0.353212 1.03895i
\(897\) 9.23073e18 0.0197555
\(898\) −3.60443e20 1.00227e20i −0.765425 0.212840i
\(899\) −1.43548e20 + 1.43548e20i −0.302467 + 0.302467i
\(900\) −4.06353e20 2.44925e20i −0.849584 0.512077i
\(901\) −3.62444e20 + 3.62444e20i −0.751913 + 0.751913i
\(902\) −5.91311e20 + 3.34010e20i −1.21722 + 0.687564i
\(903\) −8.06693e18 −0.0164776
\(904\) 1.32217e20 + 1.39906e20i 0.267984 + 0.283569i
\(905\) 3.42776e19i 0.0689399i
\(906\) 1.57649e18 8.90500e17i 0.00314625 0.00177720i
\(907\) −3.93965e20 3.93965e20i −0.780202 0.780202i 0.199663 0.979865i \(-0.436015\pi\)
−0.979865 + 0.199663i \(0.936015\pi\)
\(908\) 9.68269e20 2.39999e20i 1.90281 0.471637i
\(909\) −5.83491e20 5.83491e20i −1.13786 1.13786i
\(910\) −1.92931e19 5.36478e18i −0.0373347 0.0103816i
\(911\) 7.40766e20i 1.42250i −0.702939 0.711250i \(-0.748129\pi\)
0.702939 0.711250i \(-0.251871\pi\)
\(912\) 1.68529e19 8.90131e18i 0.0321152 0.0169625i
\(913\) −3.34069e20 −0.631743
\(914\) −8.61154e18 + 3.09693e19i −0.0161606 + 0.0581176i
\(915\) 1.27413e18 1.27413e18i 0.00237283 0.00237283i
\(916\) −7.49521e20 + 1.85779e20i −1.38521 + 0.343343i
\(917\) 4.16144e20 4.16144e20i 0.763235 0.763235i
\(918\) 1.50226e19 + 2.65951e19i 0.0273430 + 0.0484064i
\(919\) −5.27167e20 −0.952225 −0.476112 0.879384i \(-0.657954\pi\)
−0.476112 + 0.879384i \(0.657954\pi\)
\(920\) 9.10097e19 + 2.57158e18i 0.163145 + 0.00460983i
\(921\) 1.47927e19i 0.0263167i
\(922\) 2.03426e20 + 3.60133e20i 0.359161 + 0.635837i
\(923\) −1.80398e20 1.80398e20i −0.316097 0.316097i
\(924\) 2.29327e19 + 1.38224e19i 0.0398796 + 0.0240370i
\(925\) 1.43802e20 + 1.43802e20i 0.248184 + 0.248184i
\(926\) 1.60486e20 5.77149e20i 0.274891 0.988578i
\(927\) 4.29669e20i 0.730426i
\(928\) 1.59405e20 2.48322e20i 0.268946 0.418967i
\(929\) −8.59765e19 −0.143969 −0.0719846 0.997406i \(-0.522933\pi\)
−0.0719846 + 0.997406i \(0.522933\pi\)
\(930\) −1.08411e18 3.01455e17i −0.00180174 0.000501005i
\(931\) −1.25531e20 + 1.25531e20i −0.207063 + 0.207063i
\(932\) 6.60556e19 1.09592e20i 0.108143 0.179419i
\(933\) −7.54741e18 + 7.54741e18i −0.0122638 + 0.0122638i
\(934\) 3.51944e20 1.98800e20i 0.567604 0.320618i
\(935\) 9.87981e19 0.158149
\(936\) −2.58322e20 7.29915e18i −0.410421 0.0115969i
\(937\) 4.43391e20i 0.699213i −0.936897 0.349607i \(-0.886315\pi\)
0.936897 0.349607i \(-0.113685\pi\)
\(938\) −8.15063e19 + 4.60399e19i −0.127577 + 0.0720633i
\(939\) −3.88495e18 3.88495e18i −0.00603569 0.00603569i
\(940\) −2.35679e18 9.50841e18i −0.00363434 0.0146627i
\(941\) 2.73762e20 + 2.73762e20i 0.419031 + 0.419031i 0.884870 0.465839i \(-0.154247\pi\)
−0.465839 + 0.884870i \(0.654247\pi\)
\(942\) −3.70348e18 1.02982e18i −0.00562669 0.00156460i
\(943\) 1.05049e21i 1.58420i
\(944\) −1.98435e20 + 6.42708e20i −0.297040 + 0.962076i
\(945\) 3.21393e18 0.00477545
\(946\) −1.80479e20 + 6.49048e20i −0.266188 + 0.957280i
\(947\) 8.32674e20 8.32674e20i 1.21906 1.21906i 0.251099 0.967961i \(-0.419208\pi\)
0.967961 0.251099i \(-0.0807919\pi\)
\(948\) 4.08812e18 + 1.64934e19i 0.00594107 + 0.0239691i
\(949\) 2.34653e20 2.34653e20i 0.338503 0.338503i
\(950\) 4.88962e20 + 8.65629e20i 0.700180 + 1.23956i
\(951\) −2.30744e18 −0.00327994
\(952\) −5.86534e20 6.20644e20i −0.827626 0.875757i
\(953\) 1.56854e20i 0.219707i −0.993948 0.109854i \(-0.964962\pi\)
0.993948 0.109854i \(-0.0350382\pi\)
\(954\) 3.42314e20 + 6.06013e20i 0.475978 + 0.842643i
\(955\) −5.31658e18 5.31658e18i −0.00733853 0.00733853i
\(956\) −2.03109e20 + 3.36976e20i −0.278306 + 0.461736i
\(957\) 1.09819e19 + 1.09819e19i 0.0149381 + 0.0149381i
\(958\) −1.69700e20 + 6.10285e20i −0.229152 + 0.824089i
\(959\) 1.16036e21i 1.55547i
\(960\) 1.63299e18 + 9.23576e16i 0.00217313 + 0.000122906i
\(961\) 1.98172e20 0.261805
\(962\) 1.06719e20 + 2.96751e19i 0.139964 + 0.0389195i
\(963\) −6.20631e20 + 6.20631e20i −0.808071 + 0.808071i
\(964\) 9.92021e20 + 5.97930e20i 1.28228 + 0.772878i
\(965\) −7.30062e19 + 7.30062e19i −0.0936847 + 0.0936847i
\(966\) 3.60626e19 2.03704e19i 0.0459428 0.0259514i
\(967\) −4.46936e20 −0.565275 −0.282638 0.959227i \(-0.591209\pi\)
−0.282638 + 0.959227i \(0.591209\pi\)
\(968\) 1.04638e21 9.88867e20i 1.31389 1.24168i
\(969\) 3.19914e19i 0.0398811i
\(970\) −5.01723e19 + 2.83405e19i −0.0620957 + 0.0350756i
\(971\) −8.69113e20 8.69113e20i −1.06793 1.06793i −0.997518 0.0704089i \(-0.977570\pi\)
−0.0704089 0.997518i \(-0.522430\pi\)
\(972\) 6.03930e19 1.49692e19i 0.0736754 0.0182615i
\(973\) 6.52910e19 + 6.52910e19i 0.0790794 + 0.0790794i
\(974\) 1.15876e21 + 3.22214e20i 1.39342 + 0.387464i
\(975\) 8.64995e18i 0.0103272i
\(976\) −3.83694e20 + 1.24274e21i −0.454817 + 1.47310i
\(977\) 9.65619e20 1.13643 0.568216 0.822879i \(-0.307634\pi\)
0.568216 + 0.822879i \(0.307634\pi\)
\(978\) 2.52943e18 9.09645e18i 0.00295563 0.0106292i
\(979\) −1.40959e21 + 1.40959e21i −1.63536 + 1.63536i
\(980\) −1.47873e19 + 3.66525e18i −0.0170337 + 0.00422202i
\(981\) 6.67513e20 6.67513e20i 0.763443 0.763443i
\(982\) 5.42053e20 + 9.59619e20i 0.615547 + 1.08973i
\(983\) 3.12335e20 0.352165 0.176082 0.984375i \(-0.443658\pi\)
0.176082 + 0.984375i \(0.443658\pi\)
\(984\) −5.33023e17 + 1.88640e19i −0.000596733 + 0.0211188i
\(985\) 8.30322e19i 0.0922981i
\(986\) −2.43602e20 4.31259e20i −0.268871 0.475993i
\(987\) −3.15116e18 3.15116e18i −0.00345343 0.00345343i
\(988\) 4.63774e20 + 2.79535e20i 0.504670 + 0.304185i
\(989\) 7.36845e20 + 7.36845e20i 0.796163 + 0.796163i
\(990\) 3.59407e19 1.29252e20i 0.0385602 0.138672i
\(991\) 7.77788e19i 0.0828601i −0.999141 0.0414300i \(-0.986809\pi\)
0.999141 0.0414300i \(-0.0131914\pi\)
\(992\) 7.93557e20 1.73059e20i 0.839453 0.183068i
\(993\) 1.75377e18 0.00184216
\(994\) −1.10289e21 3.06676e20i −1.15034 0.319872i
\(995\) 3.91664e19 3.91664e19i 0.0405651 0.0405651i
\(996\) −4.79213e18 + 7.95059e18i −0.00492848 + 0.00817681i
\(997\) 6.73482e20 6.73482e20i 0.687797 0.687797i −0.273948 0.961745i \(-0.588330\pi\)
0.961745 + 0.273948i \(0.0883296\pi\)
\(998\) −1.23730e21 + 6.98906e20i −1.25476 + 0.708769i
\(999\) −1.77778e19 −0.0179027
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 16.15.f.a.3.2 54
4.3 odd 2 64.15.f.a.47.14 54
16.5 even 4 64.15.f.a.15.14 54
16.11 odd 4 inner 16.15.f.a.11.2 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.15.f.a.3.2 54 1.1 even 1 trivial
16.15.f.a.11.2 yes 54 16.11 odd 4 inner
64.15.f.a.15.14 54 16.5 even 4
64.15.f.a.47.14 54 4.3 odd 2