Properties

Label 11.14.c.a.3.2
Level $11$
Weight $14$
Character 11.3
Analytic conductor $11.795$
Analytic rank $0$
Dimension $48$
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] = [11,14,Mod(3,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.3");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\), degree \(4\), 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: \(11.7954021847\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 3.2
Character \(\chi\) \(=\) 11.3
Dual form 11.14.c.a.4.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-101.017 + 73.3929i) q^{2} +(277.356 + 853.615i) q^{3} +(2286.38 - 7036.76i) q^{4} +(21001.8 + 15258.7i) q^{5} +(-90666.9 - 65873.3i) q^{6} +(183952. - 566147. i) q^{7} +(-30602.4 - 94184.4i) q^{8} +(638103. - 463609. i) q^{9} +O(q^{10})\) \(q+(-101.017 + 73.3929i) q^{2} +(277.356 + 853.615i) q^{3} +(2286.38 - 7036.76i) q^{4} +(21001.8 + 15258.7i) q^{5} +(-90666.9 - 65873.3i) q^{6} +(183952. - 566147. i) q^{7} +(-30602.4 - 94184.4i) q^{8} +(638103. - 463609. i) q^{9} -3.24141e6 q^{10} +(-849264. + 5.81390e6i) q^{11} +6.64082e6 q^{12} +(2.14624e7 - 1.55933e7i) q^{13} +(2.29689e7 + 7.06911e7i) q^{14} +(-7.20007e6 + 2.21595e7i) q^{15} +(5.90397e7 + 4.28948e7i) q^{16} +(-3.88257e7 - 2.82085e7i) q^{17} +(-3.04334e7 + 9.36644e7i) q^{18} +(4.38147e6 + 1.34848e7i) q^{19} +(1.55390e8 - 1.12897e8i) q^{20} +5.34292e8 q^{21} +(-3.40909e8 - 6.49631e8i) q^{22} -4.20704e8 q^{23} +(7.19094e7 - 5.22453e7i) q^{24} +(-1.68971e8 - 5.20038e8i) q^{25} +(-1.02362e9 + 3.15038e9i) q^{26} +(1.73041e9 + 1.25721e9i) q^{27} +(-3.56326e9 - 2.58886e9i) q^{28} +(3.80324e8 - 1.17052e9i) q^{29} +(-8.99025e8 - 2.76691e9i) q^{30} +(3.92163e9 - 2.84923e9i) q^{31} -8.30090e9 q^{32} +(-5.19838e9 + 8.87578e8i) q^{33} +5.99235e9 q^{34} +(1.25020e10 - 9.08323e9i) q^{35} +(-1.80336e9 - 5.55016e9i) q^{36} +(-4.23621e9 + 1.30377e10i) q^{37} +(-1.43229e9 - 1.04062e9i) q^{38} +(1.92634e10 + 1.39957e10i) q^{39} +(7.94426e8 - 2.44499e9i) q^{40} +(1.02766e10 + 3.16283e10i) q^{41} +(-5.39724e10 + 3.92132e10i) q^{42} +4.23230e10 q^{43} +(3.89693e10 + 1.92689e10i) q^{44} +2.04753e10 q^{45} +(4.24981e10 - 3.08767e10i) q^{46} +(-7.27521e9 - 2.23908e10i) q^{47} +(-2.02406e10 + 6.22943e10i) q^{48} +(-2.08299e11 - 1.51338e11i) q^{49} +(5.52360e10 + 4.01313e10i) q^{50} +(1.33107e10 - 4.09660e10i) q^{51} +(-6.06554e10 - 1.86678e11i) q^{52} +(2.08895e11 - 1.51771e11i) q^{53} -2.67071e11 q^{54} +(-1.06549e11 + 1.09144e11i) q^{55} -5.89516e10 q^{56} +(-1.02956e10 + 7.48017e9i) q^{57} +(4.74886e10 + 1.46155e11i) q^{58} +(-3.48464e10 + 1.07246e11i) q^{59} +(1.39469e11 + 1.01330e11i) q^{60} +(2.27933e11 + 1.65603e11i) q^{61} +(-1.87036e11 + 5.75639e11i) q^{62} +(-1.45090e11 - 4.46542e11i) q^{63} +(3.54876e11 - 2.57833e11i) q^{64} +6.88683e11 q^{65} +(4.59981e11 - 4.71185e11i) q^{66} -6.38926e11 q^{67} +(-2.87267e11 + 2.08712e11i) q^{68} +(-1.16685e11 - 3.59119e11i) q^{69} +(-5.96265e11 + 1.83511e12i) q^{70} +(9.28054e11 + 6.74271e11i) q^{71} +(-6.31921e10 - 4.59118e10i) q^{72} +(4.39118e11 - 1.35146e12i) q^{73} +(-5.28948e11 - 1.62793e12i) q^{74} +(3.97047e11 - 2.88472e11i) q^{75} +1.04907e11 q^{76} +(3.13530e12 + 1.55029e12i) q^{77} -2.97311e12 q^{78} +(-7.04000e11 + 5.11486e11i) q^{79} +(5.85419e11 + 1.80174e12i) q^{80} +(-2.04648e11 + 6.29842e11i) q^{81} +(-3.35940e12 - 2.44075e12i) q^{82} +(1.61641e12 + 1.17439e12i) q^{83} +(1.22160e12 - 3.75968e12i) q^{84} +(-3.84984e11 - 1.18486e12i) q^{85} +(-4.27533e12 + 3.10621e12i) q^{86} +1.10466e12 q^{87} +(5.73568e11 - 9.79317e10i) q^{88} -8.25985e11 q^{89} +(-2.06835e12 + 1.50275e12i) q^{90} +(-4.88007e12 - 1.50193e13i) q^{91} +(-9.61889e11 + 2.96039e12i) q^{92} +(3.51983e12 + 2.55731e12i) q^{93} +(2.37824e12 + 1.72789e12i) q^{94} +(-1.13741e11 + 3.50060e11i) q^{95} +(-2.30231e12 - 7.08577e12i) q^{96} +(-1.13002e12 + 8.21007e11i) q^{97} +3.21489e13 q^{98} +(2.15346e12 + 4.10359e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 59 q^{2} - 864 q^{3} - 44697 q^{4} - 52240 q^{5} - 130115 q^{6} + 390696 q^{7} + 876527 q^{8} - 3520244 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 59 q^{2} - 864 q^{3} - 44697 q^{4} - 52240 q^{5} - 130115 q^{6} + 390696 q^{7} + 876527 q^{8} - 3520244 q^{9} - 16293072 q^{10} - 82532 q^{11} + 62972038 q^{12} - 7063968 q^{13} + 2946296 q^{14} + 81100736 q^{15} + 60644511 q^{16} - 291410392 q^{17} + 126484674 q^{18} + 365166708 q^{19} - 788032074 q^{20} - 434553632 q^{21} - 733739679 q^{22} + 4188874272 q^{23} + 1308210897 q^{24} - 5079263484 q^{25} - 7197334352 q^{26} - 3672135540 q^{27} + 15293042118 q^{28} + 9462180848 q^{29} + 14934224730 q^{30} + 3808229976 q^{31} - 37924904892 q^{32} - 29220440404 q^{33} - 42631809486 q^{34} + 81447084648 q^{35} + 20776466352 q^{36} - 92150146992 q^{37} - 85759798456 q^{38} + 122431960136 q^{39} + 156222512604 q^{40} + 224837812784 q^{41} - 100995983242 q^{42} - 323982068136 q^{43} - 117395188832 q^{44} + 101655796640 q^{45} + 504337662372 q^{46} - 131674300816 q^{47} - 508856741764 q^{48} - 364186485732 q^{49} + 292932400779 q^{50} - 46205145276 q^{51} + 971895220146 q^{52} - 374673041144 q^{53} - 171438753484 q^{54} - 609291766368 q^{55} - 55316542488 q^{56} + 581441351340 q^{57} - 172510123284 q^{58} - 866818316348 q^{59} + 450475433796 q^{60} + 396717353376 q^{61} + 2190422590172 q^{62} - 814954660544 q^{63} + 687266758335 q^{64} - 1914281234704 q^{65} + 387191529606 q^{66} - 1385875174920 q^{67} - 1442260754434 q^{68} + 2415789828408 q^{69} + 6076465410072 q^{70} + 2500983206448 q^{71} - 6853058084009 q^{72} - 6144016960080 q^{73} - 9894533340936 q^{74} + 2088242191076 q^{75} + 7382638646262 q^{76} + 8181659595976 q^{77} + 485347989556 q^{78} - 9413148440424 q^{79} - 4271997351884 q^{80} + 19193312847832 q^{81} + 24451991571525 q^{82} - 4748400435188 q^{83} - 9210465158484 q^{84} - 9425037508176 q^{85} - 2302249550185 q^{86} - 22158779783712 q^{87} - 25622627417409 q^{88} - 12037611693640 q^{89} + 8065916202334 q^{90} + 23937874042464 q^{91} + 17043827782942 q^{92} + 18075650378312 q^{93} + 10662034186230 q^{94} + 17645734105464 q^{95} + 8702791487212 q^{96} - 18472776936684 q^{97} - 52286290693988 q^{98} - 51636755872396 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −101.017 + 73.3929i −1.11609 + 0.810885i −0.983611 0.180302i \(-0.942293\pi\)
−0.132476 + 0.991186i \(0.542293\pi\)
\(3\) 277.356 + 853.615i 0.219659 + 0.676042i 0.998790 + 0.0491804i \(0.0156609\pi\)
−0.779130 + 0.626862i \(0.784339\pi\)
\(4\) 2286.38 7036.76i 0.279099 0.858979i
\(5\) 21001.8 + 15258.7i 0.601106 + 0.436729i 0.846271 0.532752i \(-0.178842\pi\)
−0.245165 + 0.969481i \(0.578842\pi\)
\(6\) −90666.9 65873.3i −0.793351 0.576403i
\(7\) 183952. 566147.i 0.590974 1.81883i 0.0171479 0.999853i \(-0.494541\pi\)
0.573826 0.818977i \(-0.305459\pi\)
\(8\) −30602.4 94184.4i −0.0412734 0.127026i
\(9\) 638103. 463609.i 0.400234 0.290787i
\(10\) −3.24141e6 −1.02502
\(11\) −849264. + 5.81390e6i −0.144541 + 0.989499i
\(12\) 6.64082e6 0.642013
\(13\) 2.14624e7 1.55933e7i 1.23324 0.895999i 0.236108 0.971727i \(-0.424128\pi\)
0.997129 + 0.0757279i \(0.0241280\pi\)
\(14\) 2.29689e7 + 7.06911e7i 0.815283 + 2.50918i
\(15\) −7.20007e6 + 2.21595e7i −0.163209 + 0.502305i
\(16\) 5.90397e7 + 4.28948e7i 0.879760 + 0.639183i
\(17\) −3.88257e7 2.82085e7i −0.390123 0.283441i 0.375383 0.926870i \(-0.377511\pi\)
−0.765506 + 0.643429i \(0.777511\pi\)
\(18\) −3.04334e7 + 9.36644e7i −0.210901 + 0.649087i
\(19\) 4.38147e6 + 1.34848e7i 0.0213659 + 0.0657575i 0.961171 0.275954i \(-0.0889936\pi\)
−0.939805 + 0.341711i \(0.888994\pi\)
\(20\) 1.55390e8 1.12897e8i 0.542909 0.394447i
\(21\) 5.34292e8 1.35942
\(22\) −3.40909e8 6.49631e8i −0.641049 1.22157i
\(23\) −4.20704e8 −0.592578 −0.296289 0.955098i \(-0.595749\pi\)
−0.296289 + 0.955098i \(0.595749\pi\)
\(24\) 7.19094e7 5.22453e7i 0.0768091 0.0558051i
\(25\) −1.68971e8 5.20038e8i −0.138421 0.426016i
\(26\) −1.02362e9 + 3.15038e9i −0.649848 + 2.00003i
\(27\) 1.73041e9 + 1.25721e9i 0.859575 + 0.624518i
\(28\) −3.56326e9 2.58886e9i −1.39740 1.01527i
\(29\) 3.80324e8 1.17052e9i 0.118732 0.365419i −0.873975 0.485970i \(-0.838466\pi\)
0.992707 + 0.120551i \(0.0384663\pi\)
\(30\) −8.99025e8 2.76691e9i −0.225156 0.692959i
\(31\) 3.92163e9 2.84923e9i 0.793625 0.576602i −0.115412 0.993318i \(-0.536819\pi\)
0.909037 + 0.416716i \(0.136819\pi\)
\(32\) −8.30090e9 −1.36663
\(33\) −5.19838e9 + 8.87578e8i −0.700693 + 0.119637i
\(34\) 5.99235e9 0.665249
\(35\) 1.25020e10 9.08323e9i 1.14957 0.835214i
\(36\) −1.80336e9 5.55016e9i −0.138075 0.424951i
\(37\) −4.23621e9 + 1.30377e10i −0.271435 + 0.835392i 0.718705 + 0.695315i \(0.244735\pi\)
−0.990141 + 0.140077i \(0.955265\pi\)
\(38\) −1.43229e9 1.04062e9i −0.0771680 0.0560658i
\(39\) 1.92634e10 + 1.39957e10i 0.876625 + 0.636905i
\(40\) 7.94426e8 2.44499e9i 0.0306664 0.0943816i
\(41\) 1.02766e10 + 3.16283e10i 0.337875 + 1.03987i 0.965288 + 0.261186i \(0.0841137\pi\)
−0.627413 + 0.778686i \(0.715886\pi\)
\(42\) −5.39724e10 + 3.92132e10i −1.51723 + 1.10233i
\(43\) 4.23230e10 1.02101 0.510507 0.859873i \(-0.329458\pi\)
0.510507 + 0.859873i \(0.329458\pi\)
\(44\) 3.89693e10 + 1.92689e10i 0.809618 + 0.400326i
\(45\) 2.04753e10 0.367578
\(46\) 4.24981e10 3.08767e10i 0.661368 0.480512i
\(47\) −7.27521e9 2.23908e10i −0.0984486 0.302994i 0.889689 0.456568i \(-0.150921\pi\)
−0.988137 + 0.153574i \(0.950921\pi\)
\(48\) −2.02406e10 + 6.22943e10i −0.238867 + 0.735157i
\(49\) −2.08299e11 1.51338e11i −2.14988 1.56198i
\(50\) 5.52360e10 + 4.01313e10i 0.499939 + 0.363227i
\(51\) 1.33107e10 4.09660e10i 0.105924 0.326000i
\(52\) −6.06554e10 1.86678e11i −0.425449 1.30940i
\(53\) 2.08895e11 1.51771e11i 1.29460 0.940582i 0.294712 0.955586i \(-0.404776\pi\)
0.999887 + 0.0150044i \(0.00477624\pi\)
\(54\) −2.67071e11 −1.46577
\(55\) −1.06549e11 + 1.09144e11i −0.519027 + 0.531669i
\(56\) −5.89516e10 −0.255431
\(57\) −1.02956e10 + 7.48017e9i −0.0397616 + 0.0288885i
\(58\) 4.74886e10 + 1.46155e11i 0.163798 + 0.504117i
\(59\) −3.48464e10 + 1.07246e11i −0.107552 + 0.331012i −0.990321 0.138796i \(-0.955677\pi\)
0.882769 + 0.469808i \(0.155677\pi\)
\(60\) 1.39469e11 + 1.01330e11i 0.385918 + 0.280386i
\(61\) 2.27933e11 + 1.65603e11i 0.566452 + 0.411551i 0.833814 0.552045i \(-0.186152\pi\)
−0.267363 + 0.963596i \(0.586152\pi\)
\(62\) −1.87036e11 + 5.75639e11i −0.418196 + 1.28708i
\(63\) −1.45090e11 4.46542e11i −0.292365 0.899806i
\(64\) 3.54876e11 2.57833e11i 0.645516 0.468995i
\(65\) 6.88683e11 1.13261
\(66\) 4.59981e11 4.71185e11i 0.685022 0.701706i
\(67\) −6.38926e11 −0.862908 −0.431454 0.902135i \(-0.641999\pi\)
−0.431454 + 0.902135i \(0.641999\pi\)
\(68\) −2.87267e11 + 2.08712e11i −0.352353 + 0.255999i
\(69\) −1.16685e11 3.59119e11i −0.130165 0.400608i
\(70\) −5.96265e11 + 1.83511e12i −0.605762 + 1.86434i
\(71\) 9.28054e11 + 6.74271e11i 0.859794 + 0.624677i 0.927829 0.373006i \(-0.121673\pi\)
−0.0680352 + 0.997683i \(0.521673\pi\)
\(72\) −6.31921e10 4.59118e10i −0.0534567 0.0388385i
\(73\) 4.39118e11 1.35146e12i 0.339611 1.04522i −0.624794 0.780789i \(-0.714817\pi\)
0.964406 0.264427i \(-0.0851828\pi\)
\(74\) −5.28948e11 1.62793e12i −0.374461 1.15247i
\(75\) 3.97047e11 2.88472e11i 0.257599 0.187157i
\(76\) 1.04907e11 0.0624475
\(77\) 3.13530e12 + 1.55029e12i 1.71431 + 0.847663i
\(78\) −2.97311e12 −1.49485
\(79\) −7.04000e11 + 5.11486e11i −0.325834 + 0.236732i −0.738661 0.674077i \(-0.764541\pi\)
0.412827 + 0.910810i \(0.364541\pi\)
\(80\) 5.85419e11 + 1.80174e12i 0.249679 + 0.768433i
\(81\) −2.04648e11 + 6.29842e11i −0.0805109 + 0.247787i
\(82\) −3.35940e12 2.44075e12i −1.22032 0.886611i
\(83\) 1.61641e12 + 1.17439e12i 0.542680 + 0.394280i 0.825079 0.565017i \(-0.191130\pi\)
−0.282399 + 0.959297i \(0.591130\pi\)
\(84\) 1.22160e12 3.75968e12i 0.379413 1.16771i
\(85\) −3.84984e11 1.18486e12i −0.110718 0.340756i
\(86\) −4.27533e12 + 3.10621e12i −1.13954 + 0.827925i
\(87\) 1.10466e12 0.273119
\(88\) 5.73568e11 9.79317e10i 0.131658 0.0224795i
\(89\) −8.25985e11 −0.176172 −0.0880860 0.996113i \(-0.528075\pi\)
−0.0880860 + 0.996113i \(0.528075\pi\)
\(90\) −2.06835e12 + 1.50275e12i −0.410249 + 0.298064i
\(91\) −4.88007e12 1.50193e13i −0.900859 2.77256i
\(92\) −9.61889e11 + 2.96039e12i −0.165388 + 0.509012i
\(93\) 3.51983e12 + 2.55731e12i 0.564135 + 0.409868i
\(94\) 2.37824e12 + 1.72789e12i 0.355570 + 0.258337i
\(95\) −1.13741e11 + 3.50060e11i −0.0158750 + 0.0488583i
\(96\) −2.30231e12 7.08577e12i −0.300193 0.923898i
\(97\) −1.13002e12 + 8.21007e11i −0.137743 + 0.100076i −0.654523 0.756042i \(-0.727131\pi\)
0.516780 + 0.856118i \(0.327131\pi\)
\(98\) 3.21489e13 3.66603
\(99\) 2.15346e12 + 4.10359e12i 0.229883 + 0.438062i
\(100\) −4.04572e12 −0.404572
\(101\) −1.11858e13 + 8.12695e12i −1.04852 + 0.761796i −0.971931 0.235266i \(-0.924404\pi\)
−0.0765917 + 0.997063i \(0.524404\pi\)
\(102\) 1.66202e12 + 5.11516e12i 0.146128 + 0.449737i
\(103\) −6.94167e12 + 2.13643e13i −0.572825 + 1.76297i 0.0706437 + 0.997502i \(0.477495\pi\)
−0.643469 + 0.765472i \(0.722505\pi\)
\(104\) −2.12545e12 1.54423e12i −0.164715 0.119673i
\(105\) 1.12211e13 + 8.15260e12i 0.817155 + 0.593698i
\(106\) −9.96297e12 + 3.06629e13i −0.682182 + 2.09954i
\(107\) −4.67270e12 1.43811e13i −0.301005 0.926398i −0.981138 0.193309i \(-0.938078\pi\)
0.680133 0.733089i \(-0.261922\pi\)
\(108\) 1.28031e13 9.30199e12i 0.776355 0.564055i
\(109\) −9.86224e12 −0.563253 −0.281626 0.959524i \(-0.590874\pi\)
−0.281626 + 0.959524i \(0.590874\pi\)
\(110\) 2.75281e12 1.88452e13i 0.148158 1.01426i
\(111\) −1.23041e13 −0.624383
\(112\) 3.51453e13 2.55345e13i 1.68248 1.22239i
\(113\) −1.81801e12 5.59527e12i −0.0821461 0.252820i 0.901545 0.432685i \(-0.142434\pi\)
−0.983691 + 0.179865i \(0.942434\pi\)
\(114\) 4.91033e11 1.51124e12i 0.0209522 0.0644842i
\(115\) −8.83553e12 6.41939e12i −0.356202 0.258796i
\(116\) −7.36708e12 5.35250e12i −0.280749 0.203976i
\(117\) 6.46600e12 1.99003e13i 0.233039 0.717219i
\(118\) −4.35104e12 1.33911e13i −0.148375 0.456651i
\(119\) −2.31123e13 + 1.67921e13i −0.746084 + 0.542061i
\(120\) 2.30742e12 0.0705421
\(121\) −3.30802e13 9.87508e12i −0.958216 0.286046i
\(122\) −3.51791e13 −0.965930
\(123\) −2.41481e13 + 1.75446e13i −0.628780 + 0.456836i
\(124\) −1.10830e13 3.41099e13i −0.273789 0.842636i
\(125\) 1.41789e13 4.36380e13i 0.332450 1.02318i
\(126\) 4.74295e13 + 3.44596e13i 1.05594 + 0.767187i
\(127\) 5.44564e13 + 3.95649e13i 1.15166 + 0.836731i 0.988701 0.149901i \(-0.0478956\pi\)
0.162961 + 0.986633i \(0.447896\pi\)
\(128\) 4.08813e12 1.25820e13i 0.0821599 0.252862i
\(129\) 1.17386e13 + 3.61276e13i 0.224275 + 0.690249i
\(130\) −6.95684e13 + 5.05444e13i −1.26410 + 0.918420i
\(131\) 2.48576e12 0.0429730 0.0214865 0.999769i \(-0.493160\pi\)
0.0214865 + 0.999769i \(0.493160\pi\)
\(132\) −5.63981e12 + 3.86091e13i −0.0927970 + 0.635271i
\(133\) 8.44035e12 0.132228
\(134\) 6.45422e13 4.68926e13i 0.963080 0.699719i
\(135\) 1.71582e13 + 5.28075e13i 0.243951 + 0.750803i
\(136\) −1.46865e12 + 4.52003e12i −0.0199028 + 0.0612545i
\(137\) 1.16960e13 + 8.49765e12i 0.151131 + 0.109803i 0.660781 0.750579i \(-0.270225\pi\)
−0.509650 + 0.860382i \(0.670225\pi\)
\(138\) 3.81439e13 + 2.77132e13i 0.470122 + 0.341564i
\(139\) 1.97136e13 6.06721e13i 0.231830 0.713499i −0.765696 0.643202i \(-0.777605\pi\)
0.997526 0.0702964i \(-0.0223945\pi\)
\(140\) −3.53322e13 1.08741e14i −0.396586 1.22057i
\(141\) 1.70953e13 1.24205e13i 0.183211 0.133111i
\(142\) −1.43236e14 −1.46615
\(143\) 7.24309e13 + 1.38023e14i 0.708337 + 1.34979i
\(144\) 5.75598e13 0.537976
\(145\) 2.58481e13 1.87797e13i 0.230960 0.167802i
\(146\) 5.48297e13 + 1.68749e14i 0.468514 + 1.44194i
\(147\) 7.14115e13 2.19782e14i 0.583722 1.79651i
\(148\) 8.20576e13 + 5.96183e13i 0.641827 + 0.466314i
\(149\) −1.67151e14 1.21442e14i −1.25141 0.909200i −0.253104 0.967439i \(-0.581451\pi\)
−0.998303 + 0.0582391i \(0.981451\pi\)
\(150\) −1.89366e13 + 5.82809e13i −0.135740 + 0.417766i
\(151\) −2.89930e13 8.92312e13i −0.199041 0.612585i −0.999906 0.0137397i \(-0.995626\pi\)
0.800865 0.598845i \(-0.204374\pi\)
\(152\) 1.13597e12 8.25332e11i 0.00747110 0.00542807i
\(153\) −3.78525e13 −0.238562
\(154\) −4.30498e14 + 7.35037e13i −2.60068 + 0.444043i
\(155\) 1.25837e14 0.728872
\(156\) 1.42528e14 1.03553e14i 0.791754 0.575243i
\(157\) 5.18279e13 + 1.59510e14i 0.276195 + 0.850041i 0.988901 + 0.148578i \(0.0474696\pi\)
−0.712705 + 0.701463i \(0.752530\pi\)
\(158\) 3.35763e13 1.03337e14i 0.171697 0.528428i
\(159\) 1.87493e14 + 1.36221e14i 0.920244 + 0.668596i
\(160\) −1.74334e14 1.26661e14i −0.821488 0.596846i
\(161\) −7.73895e13 + 2.38180e14i −0.350198 + 1.07780i
\(162\) −2.55530e13 7.86442e13i −0.111070 0.341837i
\(163\) −1.64976e14 + 1.19862e14i −0.688973 + 0.500568i −0.876322 0.481725i \(-0.840010\pi\)
0.187350 + 0.982293i \(0.440010\pi\)
\(164\) 2.46057e14 0.987530
\(165\) −1.22719e14 6.06798e13i −0.473440 0.234098i
\(166\) −2.49476e14 −0.925394
\(167\) 1.55645e14 1.13083e14i 0.555236 0.403403i −0.274476 0.961594i \(-0.588504\pi\)
0.829712 + 0.558191i \(0.188504\pi\)
\(168\) −1.63506e13 5.03220e13i −0.0561078 0.172682i
\(169\) 1.23889e14 3.81290e14i 0.409042 1.25890i
\(170\) 1.25850e14 + 9.14354e13i 0.399885 + 0.290534i
\(171\) 9.04749e12 + 6.57338e12i 0.0276728 + 0.0201055i
\(172\) 9.67666e13 2.97817e14i 0.284964 0.877030i
\(173\) −1.25785e14 3.87126e14i −0.356721 1.09787i −0.955005 0.296590i \(-0.904150\pi\)
0.598284 0.801284i \(-0.295850\pi\)
\(174\) −1.11589e14 + 8.10740e13i −0.304825 + 0.221468i
\(175\) −3.25501e14 −0.856653
\(176\) −2.99527e14 + 3.06822e14i −0.759632 + 0.778133i
\(177\) −1.01212e14 −0.247403
\(178\) 8.34382e13 6.06214e13i 0.196623 0.142855i
\(179\) 5.72194e12 + 1.76103e13i 0.0130016 + 0.0400150i 0.957347 0.288941i \(-0.0933032\pi\)
−0.944345 + 0.328956i \(0.893303\pi\)
\(180\) 4.68144e13 1.44080e14i 0.102591 0.315742i
\(181\) 2.89752e14 + 2.10517e14i 0.612514 + 0.445017i 0.850299 0.526300i \(-0.176421\pi\)
−0.237785 + 0.971318i \(0.576421\pi\)
\(182\) 1.59528e15 + 1.15904e15i 3.25366 + 2.36393i
\(183\) −7.81425e13 + 2.40498e14i −0.153800 + 0.473346i
\(184\) 1.28745e13 + 3.96237e13i 0.0244577 + 0.0752730i
\(185\) −2.87906e14 + 2.09176e14i −0.528001 + 0.383615i
\(186\) −5.43250e14 −0.961979
\(187\) 1.96975e14 2.01772e14i 0.336853 0.345058i
\(188\) −1.74192e14 −0.287742
\(189\) 1.03008e15 7.48398e14i 1.64388 1.19435i
\(190\) −1.42021e13 4.37097e13i −0.0219006 0.0674030i
\(191\) −2.03706e14 + 6.26943e14i −0.303590 + 0.934353i 0.676610 + 0.736342i \(0.263448\pi\)
−0.980200 + 0.198012i \(0.936552\pi\)
\(192\) 3.18517e14 + 2.31416e14i 0.458854 + 0.333377i
\(193\) −4.06679e14 2.95469e14i −0.566407 0.411519i 0.267391 0.963588i \(-0.413838\pi\)
−0.833798 + 0.552069i \(0.813838\pi\)
\(194\) 5.38947e13 1.65871e14i 0.0725829 0.223387i
\(195\) 1.91010e14 + 5.87870e14i 0.248790 + 0.765695i
\(196\) −1.54118e15 + 1.11973e15i −1.94173 + 1.41075i
\(197\) 1.22834e15 1.49722 0.748612 0.663008i \(-0.230721\pi\)
0.748612 + 0.663008i \(0.230721\pi\)
\(198\) −5.18710e14 2.56483e14i −0.611787 0.302506i
\(199\) −2.14796e14 −0.245178 −0.122589 0.992458i \(-0.539120\pi\)
−0.122589 + 0.992458i \(0.539120\pi\)
\(200\) −4.38086e13 + 3.18288e13i −0.0484021 + 0.0351662i
\(201\) −1.77210e14 5.45397e14i −0.189546 0.583362i
\(202\) 5.33491e14 1.64192e15i 0.552514 1.70046i
\(203\) −5.92724e14 4.30639e14i −0.594468 0.431906i
\(204\) −2.57835e14 1.87328e14i −0.250464 0.181973i
\(205\) −2.66778e14 + 8.21058e14i −0.251044 + 0.772634i
\(206\) −8.66761e14 2.66762e15i −0.790246 2.43213i
\(207\) −2.68452e14 + 1.95042e14i −0.237170 + 0.172314i
\(208\) 1.93601e15 1.65766
\(209\) −8.21202e13 + 1.40213e13i −0.0681552 + 0.0116369i
\(210\) −1.73186e15 −1.39344
\(211\) −1.30077e15 + 9.45066e14i −1.01476 + 0.737270i −0.965203 0.261501i \(-0.915782\pi\)
−0.0495615 + 0.998771i \(0.515782\pi\)
\(212\) −5.90363e14 1.81695e15i −0.446618 1.37455i
\(213\) −3.18166e14 + 9.79214e14i −0.233446 + 0.718473i
\(214\) 1.52749e15 + 1.10979e15i 1.08715 + 0.789861i
\(215\) 8.88859e14 + 6.45794e14i 0.613738 + 0.445907i
\(216\) 6.54554e13 2.01451e14i 0.0438527 0.134965i
\(217\) −8.91690e14 2.74434e15i −0.579730 1.78423i
\(218\) 9.96250e14 7.23818e14i 0.628639 0.456733i
\(219\) 1.27542e15 0.781209
\(220\) 5.24407e14 + 9.99300e14i 0.311832 + 0.594222i
\(221\) −1.27316e15 −0.735077
\(222\) 1.24292e15 9.03035e14i 0.696866 0.506303i
\(223\) 4.97778e14 + 1.53200e15i 0.271053 + 0.834214i 0.990237 + 0.139395i \(0.0445157\pi\)
−0.719184 + 0.694819i \(0.755484\pi\)
\(224\) −1.52697e15 + 4.69953e15i −0.807641 + 2.48566i
\(225\) −3.48915e14 2.53502e14i −0.179281 0.130255i
\(226\) 5.94302e14 + 4.31786e14i 0.296690 + 0.215558i
\(227\) −1.52385e14 + 4.68994e14i −0.0739222 + 0.227509i −0.981190 0.193044i \(-0.938164\pi\)
0.907268 + 0.420553i \(0.138164\pi\)
\(228\) 2.90966e13 + 8.95500e13i 0.0137172 + 0.0422172i
\(229\) 1.98286e15 1.44063e15i 0.908577 0.660120i −0.0320773 0.999485i \(-0.510212\pi\)
0.940655 + 0.339365i \(0.110212\pi\)
\(230\) 1.36367e15 0.607406
\(231\) −4.53755e14 + 3.10632e15i −0.196491 + 1.34514i
\(232\) −1.21883e14 −0.0513183
\(233\) −2.85490e15 + 2.07421e15i −1.16890 + 0.849256i −0.990877 0.134770i \(-0.956970\pi\)
−0.178024 + 0.984026i \(0.556970\pi\)
\(234\) 8.07367e14 + 2.48482e15i 0.321490 + 0.989446i
\(235\) 1.88862e14 5.81257e14i 0.0731481 0.225127i
\(236\) 6.74993e14 + 4.90411e14i 0.254315 + 0.184770i
\(237\) −6.31871e14 4.59081e14i −0.231614 0.168277i
\(238\) 1.10231e15 3.39255e15i 0.393145 1.20998i
\(239\) −1.10714e15 3.40742e15i −0.384252 1.18261i −0.937022 0.349271i \(-0.886429\pi\)
0.552770 0.833334i \(-0.313571\pi\)
\(240\) −1.37562e15 + 9.99445e14i −0.464649 + 0.337587i
\(241\) 1.44516e13 0.00475121 0.00237561 0.999997i \(-0.499244\pi\)
0.00237561 + 0.999997i \(0.499244\pi\)
\(242\) 4.06641e15 1.43031e15i 1.30140 0.457751i
\(243\) 2.81570e15 0.877294
\(244\) 1.68645e15 1.22528e15i 0.511610 0.371706i
\(245\) −2.06543e15 6.35675e15i −0.610143 1.87783i
\(246\) 1.15171e15 3.54459e15i 0.331333 1.01974i
\(247\) 3.04310e14 + 2.21094e14i 0.0852679 + 0.0619507i
\(248\) −3.88364e14 2.82163e14i −0.105999 0.0770130i
\(249\) −5.54156e14 + 1.70552e15i −0.147345 + 0.453482i
\(250\) 1.77042e15 + 5.44880e15i 0.458634 + 1.41153i
\(251\) −4.32372e15 + 3.14137e15i −1.09139 + 0.792939i −0.979633 0.200797i \(-0.935647\pi\)
−0.111754 + 0.993736i \(0.535647\pi\)
\(252\) −3.47394e15 −0.854513
\(253\) 3.57289e14 2.44593e15i 0.0856516 0.586355i
\(254\) −8.40479e15 −1.96385
\(255\) 9.04636e14 6.57256e14i 0.206045 0.149701i
\(256\) 1.62089e15 + 4.98858e15i 0.359910 + 1.10769i
\(257\) −3.48024e14 + 1.07111e15i −0.0753431 + 0.231882i −0.981635 0.190771i \(-0.938901\pi\)
0.906291 + 0.422653i \(0.138901\pi\)
\(258\) −3.83730e15 2.78796e15i −0.810023 0.588516i
\(259\) 6.60200e15 + 4.79664e15i 1.35902 + 0.987389i
\(260\) 1.57459e15 4.84609e15i 0.316112 0.972892i
\(261\) −2.99976e14 9.23232e14i −0.0587386 0.180779i
\(262\) −2.51103e14 + 1.82437e14i −0.0479616 + 0.0348462i
\(263\) −7.75685e15 −1.44535 −0.722675 0.691188i \(-0.757088\pi\)
−0.722675 + 0.691188i \(0.757088\pi\)
\(264\) 2.42679e14 + 4.62444e14i 0.0441170 + 0.0840687i
\(265\) 6.70300e15 1.18897
\(266\) −8.52616e14 + 6.19462e14i −0.147578 + 0.107222i
\(267\) −2.29092e14 7.05073e14i −0.0386978 0.119100i
\(268\) −1.46083e15 + 4.49597e15i −0.240837 + 0.741220i
\(269\) −2.00873e15 1.45943e15i −0.323245 0.234852i 0.414314 0.910134i \(-0.364022\pi\)
−0.737559 + 0.675283i \(0.764022\pi\)
\(270\) −5.60896e15 4.07515e15i −0.881085 0.640146i
\(271\) −1.57963e15 + 4.86160e15i −0.242245 + 0.745553i 0.753832 + 0.657067i \(0.228203\pi\)
−0.996077 + 0.0884866i \(0.971797\pi\)
\(272\) −1.08226e15 3.33085e15i −0.162044 0.498720i
\(273\) 1.14672e16 8.33140e15i 1.67649 1.21804i
\(274\) −1.80516e15 −0.257713
\(275\) 3.16695e15 5.40729e14i 0.441549 0.0753907i
\(276\) −2.79382e15 −0.380443
\(277\) 6.93894e15 5.04144e15i 0.922943 0.670557i −0.0213119 0.999773i \(-0.506784\pi\)
0.944255 + 0.329216i \(0.106784\pi\)
\(278\) 2.46150e15 + 7.57573e15i 0.319823 + 0.984314i
\(279\) 1.18147e15 3.63620e15i 0.149967 0.461552i
\(280\) −1.23809e15 8.99524e14i −0.153541 0.111554i
\(281\) −2.22287e15 1.61501e15i −0.269354 0.195697i 0.444907 0.895577i \(-0.353237\pi\)
−0.714261 + 0.699880i \(0.753237\pi\)
\(282\) −8.15336e14 + 2.50935e15i −0.0965422 + 0.297126i
\(283\) 4.75763e15 + 1.46425e16i 0.550527 + 1.69435i 0.707472 + 0.706742i \(0.249836\pi\)
−0.156944 + 0.987607i \(0.550164\pi\)
\(284\) 6.86657e15 4.98885e15i 0.776552 0.564198i
\(285\) −3.30363e14 −0.0365174
\(286\) −1.74467e16 8.62672e15i −1.88509 0.932109i
\(287\) 1.97967e16 2.09103
\(288\) −5.29683e15 + 3.84837e15i −0.546971 + 0.397398i
\(289\) −2.34897e15 7.22938e15i −0.237160 0.729903i
\(290\) −1.23279e15 + 3.79413e15i −0.121703 + 0.374563i
\(291\) −1.01424e15 7.36890e14i −0.0979122 0.0711374i
\(292\) −8.50594e15 6.17993e15i −0.803034 0.583438i
\(293\) −3.39544e15 + 1.04501e16i −0.313514 + 0.964897i 0.662848 + 0.748754i \(0.269348\pi\)
−0.976362 + 0.216143i \(0.930652\pi\)
\(294\) 8.91669e15 + 2.74428e16i 0.805279 + 2.47839i
\(295\) −2.36827e15 + 1.72065e15i −0.209213 + 0.152002i
\(296\) 1.35759e15 0.117320
\(297\) −8.77890e15 + 8.99272e15i −0.742204 + 0.760281i
\(298\) 2.57980e16 2.13393
\(299\) −9.02931e15 + 6.56018e15i −0.730789 + 0.530949i
\(300\) −1.12210e15 3.45348e15i −0.0888680 0.273507i
\(301\) 7.78542e15 2.39611e16i 0.603393 1.85705i
\(302\) 9.47771e15 + 6.88596e15i 0.718883 + 0.522299i
\(303\) −1.00397e16 7.29430e15i −0.745324 0.541510i
\(304\) −3.19747e14 + 9.84079e14i −0.0232342 + 0.0715075i
\(305\) 2.26011e15 + 6.95591e15i 0.160761 + 0.494772i
\(306\) 3.82374e15 2.77811e15i 0.266255 0.193446i
\(307\) 1.19855e16 0.817065 0.408533 0.912744i \(-0.366041\pi\)
0.408533 + 0.912744i \(0.366041\pi\)
\(308\) 1.80775e16 1.85178e16i 1.20659 1.23597i
\(309\) −2.01622e16 −1.31767
\(310\) −1.27116e16 + 9.23551e15i −0.813484 + 0.591031i
\(311\) 7.34554e15 + 2.26073e16i 0.460343 + 1.41679i 0.864746 + 0.502209i \(0.167479\pi\)
−0.404403 + 0.914581i \(0.632521\pi\)
\(312\) 7.28671e14 2.24262e15i 0.0447225 0.137642i
\(313\) −2.65116e16 1.92618e16i −1.59367 1.15787i −0.898458 0.439060i \(-0.855312\pi\)
−0.695210 0.718807i \(-0.744688\pi\)
\(314\) −1.69424e16 1.23094e16i −0.997543 0.724758i
\(315\) 3.76649e15 1.15921e16i 0.217229 0.668563i
\(316\) 1.98959e15 + 6.12333e15i 0.112408 + 0.345956i
\(317\) −1.27753e16 + 9.28181e15i −0.707109 + 0.513745i −0.882240 0.470800i \(-0.843965\pi\)
0.175131 + 0.984545i \(0.443965\pi\)
\(318\) −2.89376e16 −1.56923
\(319\) 6.48228e15 + 3.20525e15i 0.344420 + 0.170303i
\(320\) 1.13872e16 0.592848
\(321\) 1.09799e16 7.97738e15i 0.560166 0.406984i
\(322\) −9.66312e15 2.97400e16i −0.483119 1.48689i
\(323\) 2.10272e14 6.47151e14i 0.0103030 0.0317095i
\(324\) 3.96414e15 + 2.88012e15i 0.190373 + 0.138314i
\(325\) −1.17357e16 8.52645e15i −0.552415 0.401353i
\(326\) 7.86831e15 2.42162e16i 0.363050 1.11735i
\(327\) −2.73535e15 8.41855e15i −0.123724 0.380783i
\(328\) 2.66440e15 1.93580e15i 0.118146 0.0858381i
\(329\) −1.40148e16 −0.609274
\(330\) 1.68501e16 2.87700e15i 0.718227 0.122631i
\(331\) 6.23709e15 0.260675 0.130338 0.991470i \(-0.458394\pi\)
0.130338 + 0.991470i \(0.458394\pi\)
\(332\) 1.19596e16 8.68918e15i 0.490140 0.356107i
\(333\) 3.34126e15 + 1.02833e16i 0.134284 + 0.413282i
\(334\) −7.42326e15 + 2.28465e16i −0.292579 + 0.900465i
\(335\) −1.34186e16 9.74917e15i −0.518699 0.376857i
\(336\) 3.15444e16 + 2.29184e16i 1.19596 + 0.868917i
\(337\) 2.16849e15 6.67392e15i 0.0806422 0.248191i −0.902605 0.430471i \(-0.858348\pi\)
0.983247 + 0.182280i \(0.0583476\pi\)
\(338\) 1.54692e16 + 4.76092e16i 0.564297 + 1.73673i
\(339\) 4.27197e15 3.10377e15i 0.152873 0.111068i
\(340\) −9.21779e15 −0.323604
\(341\) 1.32346e16 + 2.52197e16i 0.455836 + 0.868633i
\(342\) −1.39639e15 −0.0471885
\(343\) −7.73359e16 + 5.61878e16i −2.56430 + 1.86307i
\(344\) −1.29518e15 3.98617e15i −0.0421407 0.129696i
\(345\) 3.02909e15 9.32260e15i 0.0967139 0.297655i
\(346\) 4.11187e16 + 2.98745e16i 1.28838 + 0.936064i
\(347\) −8.79348e15 6.38883e15i −0.270408 0.196463i 0.444315 0.895871i \(-0.353447\pi\)
−0.714723 + 0.699408i \(0.753447\pi\)
\(348\) 2.52567e15 7.77320e15i 0.0762274 0.234604i
\(349\) 6.43605e15 + 1.98081e16i 0.190657 + 0.586783i 1.00000 0.000553766i \(-0.000176269\pi\)
−0.809342 + 0.587337i \(0.800176\pi\)
\(350\) 3.28810e16 2.38895e16i 0.956099 0.694647i
\(351\) 5.67429e16 1.61963
\(352\) 7.04966e15 4.82606e16i 0.197533 1.35228i
\(353\) 1.82463e16 0.501926 0.250963 0.967997i \(-0.419253\pi\)
0.250963 + 0.967997i \(0.419253\pi\)
\(354\) 1.02241e16 7.42823e15i 0.276123 0.200615i
\(355\) 9.20231e15 + 2.83218e16i 0.244013 + 0.750994i
\(356\) −1.88852e15 + 5.81225e15i −0.0491695 + 0.151328i
\(357\) −2.07443e16 1.50716e16i −0.530341 0.385315i
\(358\) −1.87048e15 1.35899e15i −0.0469585 0.0341173i
\(359\) −2.18149e16 + 6.71393e16i −0.537822 + 1.65525i 0.199649 + 0.979867i \(0.436020\pi\)
−0.737471 + 0.675379i \(0.763980\pi\)
\(360\) −6.26594e14 1.92846e15i −0.0151712 0.0466922i
\(361\) 3.38589e16 2.46000e16i 0.805149 0.584975i
\(362\) −4.47203e16 −1.04448
\(363\) −7.45493e14 3.09767e16i −0.0171021 0.710627i
\(364\) −1.16845e17 −2.63300
\(365\) 2.98438e16 2.16828e16i 0.660619 0.479968i
\(366\) −9.75714e15 3.00294e16i −0.212176 0.653009i
\(367\) −1.55048e16 + 4.77188e16i −0.331235 + 1.01944i 0.637312 + 0.770605i \(0.280046\pi\)
−0.968547 + 0.248830i \(0.919954\pi\)
\(368\) −2.48382e16 1.80460e16i −0.521326 0.378766i
\(369\) 2.12207e16 + 1.54177e16i 0.437611 + 0.317943i
\(370\) 1.37313e16 4.22606e16i 0.278227 0.856296i
\(371\) −4.74981e16 1.46184e17i −0.945684 2.91052i
\(372\) 2.60428e16 1.89212e16i 0.509517 0.370186i
\(373\) 5.67847e16 1.09175 0.545876 0.837866i \(-0.316197\pi\)
0.545876 + 0.837866i \(0.316197\pi\)
\(374\) −5.08909e15 + 3.48389e16i −0.0961556 + 0.658263i
\(375\) 4.11827e16 0.764736
\(376\) −1.88622e15 + 1.37042e15i −0.0344249 + 0.0250111i
\(377\) −1.00896e16 3.10527e16i −0.180991 0.557032i
\(378\) −4.91283e16 + 1.51201e17i −0.866233 + 2.66599i
\(379\) −5.35354e16 3.88957e16i −0.927868 0.674136i 0.0176018 0.999845i \(-0.494397\pi\)
−0.945470 + 0.325709i \(0.894397\pi\)
\(380\) 2.20323e15 + 1.60074e15i 0.0375376 + 0.0272727i
\(381\) −1.86694e16 + 5.74584e16i −0.312692 + 0.962368i
\(382\) −2.54354e16 7.82823e16i −0.418820 1.28900i
\(383\) 2.64201e16 1.91953e16i 0.427703 0.310744i −0.353027 0.935613i \(-0.614848\pi\)
0.780730 + 0.624869i \(0.214848\pi\)
\(384\) 1.18740e16 0.188993
\(385\) 4.21915e16 + 8.03994e16i 0.660283 + 1.25822i
\(386\) 6.27667e16 0.965854
\(387\) 2.70064e16 1.96213e16i 0.408645 0.296898i
\(388\) 3.19357e15 + 9.82880e15i 0.0475193 + 0.146250i
\(389\) 8.57051e15 2.63773e16i 0.125411 0.385974i −0.868565 0.495575i \(-0.834957\pi\)
0.993976 + 0.109601i \(0.0349573\pi\)
\(390\) −6.24407e16 4.53658e16i −0.898561 0.652843i
\(391\) 1.63341e16 + 1.18674e16i 0.231178 + 0.167961i
\(392\) −7.87926e15 + 2.42499e16i −0.109680 + 0.337559i
\(393\) 6.89441e14 + 2.12188e15i 0.00943943 + 0.0290516i
\(394\) −1.24082e17 + 9.01512e16i −1.67103 + 1.21408i
\(395\) −2.25899e16 −0.299249
\(396\) 3.37996e16 5.77098e15i 0.440446 0.0752023i
\(397\) −1.00332e17 −1.28618 −0.643089 0.765792i \(-0.722347\pi\)
−0.643089 + 0.765792i \(0.722347\pi\)
\(398\) 2.16980e16 1.57645e16i 0.273640 0.198811i
\(399\) 2.34098e15 + 7.20481e15i 0.0290452 + 0.0893920i
\(400\) 1.23310e16 3.79509e16i 0.150525 0.463267i
\(401\) 2.90695e16 + 2.11202e16i 0.349140 + 0.253665i 0.748508 0.663126i \(-0.230771\pi\)
−0.399368 + 0.916791i \(0.630771\pi\)
\(402\) 5.79294e16 + 4.20882e16i 0.684589 + 0.497383i
\(403\) 3.97385e16 1.22303e17i 0.462092 1.42217i
\(404\) 3.16124e16 + 9.72930e16i 0.361725 + 1.11328i
\(405\) −1.39085e16 + 1.01051e16i −0.156611 + 0.113785i
\(406\) 9.14809e16 1.01370
\(407\) −7.22023e16 3.57014e16i −0.787386 0.389333i
\(408\) −4.26570e15 −0.0457825
\(409\) −1.91382e16 + 1.39047e16i −0.202162 + 0.146879i −0.684260 0.729238i \(-0.739875\pi\)
0.482099 + 0.876117i \(0.339875\pi\)
\(410\) −3.33108e16 1.02520e17i −0.346330 1.06589i
\(411\) −4.00976e15 + 1.23408e16i −0.0410343 + 0.126290i
\(412\) 1.34464e17 + 9.76937e16i 1.35448 + 0.984089i
\(413\) 5.43070e16 + 3.94564e16i 0.538494 + 0.391239i
\(414\) 1.28034e16 3.94050e16i 0.124975 0.384635i
\(415\) 1.60278e16 + 4.93286e16i 0.154015 + 0.474008i
\(416\) −1.78157e17 + 1.29439e17i −1.68538 + 1.22450i
\(417\) 5.72583e16 0.533279
\(418\) 7.26644e15 7.44342e15i 0.0666310 0.0682538i
\(419\) 1.16487e17 1.05169 0.525844 0.850581i \(-0.323749\pi\)
0.525844 + 0.850581i \(0.323749\pi\)
\(420\) 8.30235e16 6.03201e16i 0.738041 0.536218i
\(421\) −1.36212e16 4.19216e16i −0.119229 0.366948i 0.873577 0.486686i \(-0.161794\pi\)
−0.992805 + 0.119738i \(0.961794\pi\)
\(422\) 6.20385e16 1.90935e17i 0.534725 1.64571i
\(423\) −1.50229e16 1.09148e16i −0.127509 0.0926408i
\(424\) −2.06872e16 1.50301e16i −0.172911 0.125627i
\(425\) −8.10912e15 + 2.49573e16i −0.0667491 + 0.205433i
\(426\) −3.97273e16 1.22268e17i −0.322053 0.991176i
\(427\) 1.35684e17 9.85805e16i 1.08330 0.787063i
\(428\) −1.11880e17 −0.879767
\(429\) −9.77294e16 + 1.00110e17i −0.756925 + 0.775361i
\(430\) −1.37186e17 −1.04656
\(431\) −1.14267e17 + 8.30202e16i −0.858658 + 0.623852i −0.927520 0.373774i \(-0.878063\pi\)
0.0688612 + 0.997626i \(0.478063\pi\)
\(432\) 4.82347e16 + 1.48451e17i 0.357039 + 1.09885i
\(433\) −4.09461e15 + 1.26019e16i −0.0298567 + 0.0918893i −0.964874 0.262712i \(-0.915383\pi\)
0.935018 + 0.354601i \(0.115383\pi\)
\(434\) 2.91491e17 + 2.11780e17i 2.09383 + 1.52126i
\(435\) 2.31998e16 + 1.68556e16i 0.164174 + 0.119279i
\(436\) −2.25488e16 + 6.93982e16i −0.157203 + 0.483822i
\(437\) −1.84330e15 5.67310e15i −0.0126610 0.0389664i
\(438\) −1.28839e17 + 9.36070e16i −0.871897 + 0.633471i
\(439\) −3.38328e16 −0.225589 −0.112795 0.993618i \(-0.535980\pi\)
−0.112795 + 0.993618i \(0.535980\pi\)
\(440\) 1.35403e16 + 6.69516e15i 0.0889580 + 0.0439864i
\(441\) −2.03078e17 −1.31466
\(442\) 1.28610e17 9.34408e16i 0.820410 0.596063i
\(443\) 4.45223e16 + 1.37026e17i 0.279868 + 0.861346i 0.987890 + 0.155155i \(0.0495877\pi\)
−0.708022 + 0.706190i \(0.750412\pi\)
\(444\) −2.81319e16 + 8.65811e16i −0.174265 + 0.536332i
\(445\) −1.73471e16 1.26034e16i −0.105898 0.0769394i
\(446\) −1.62722e17 1.18224e17i −0.978970 0.711263i
\(447\) 5.73046e16 1.76365e17i 0.339774 1.04572i
\(448\) −8.06910e16 2.48341e17i −0.471539 1.45125i
\(449\) 4.56590e16 3.31732e16i 0.262982 0.191067i −0.448479 0.893793i \(-0.648034\pi\)
0.711461 + 0.702726i \(0.248034\pi\)
\(450\) 5.38514e16 0.305714
\(451\) −1.92611e17 + 3.28867e16i −1.07779 + 0.184023i
\(452\) −4.35292e16 −0.240094
\(453\) 6.81277e16 4.94976e16i 0.370412 0.269120i
\(454\) −1.90274e16 5.85602e16i −0.101980 0.313862i
\(455\) 1.26685e17 3.89896e17i 0.669346 2.06003i
\(456\) 1.01958e15 + 7.40772e14i 0.00531070 + 0.00385845i
\(457\) 1.47115e16 + 1.06885e16i 0.0755443 + 0.0548862i 0.624916 0.780692i \(-0.285133\pi\)
−0.549372 + 0.835578i \(0.685133\pi\)
\(458\) −9.45698e16 + 2.91056e17i −0.478770 + 1.47350i
\(459\) −3.17201e16 9.76246e16i −0.158326 0.487278i
\(460\) −6.53730e16 + 4.74963e16i −0.321716 + 0.233740i
\(461\) 4.41073e16 0.214020 0.107010 0.994258i \(-0.465872\pi\)
0.107010 + 0.994258i \(0.465872\pi\)
\(462\) −1.82145e17 3.47093e17i −0.871455 1.66063i
\(463\) 2.19625e17 1.03611 0.518054 0.855348i \(-0.326657\pi\)
0.518054 + 0.855348i \(0.326657\pi\)
\(464\) 7.26634e16 5.27931e16i 0.338025 0.245590i
\(465\) 3.49016e16 + 1.07416e17i 0.160104 + 0.492748i
\(466\) 1.36160e17 4.19059e17i 0.615946 1.89569i
\(467\) 5.64449e16 + 4.10096e16i 0.251805 + 0.182947i 0.706527 0.707687i \(-0.250261\pi\)
−0.454721 + 0.890634i \(0.650261\pi\)
\(468\) −1.25250e17 9.09993e16i −0.551035 0.400350i
\(469\) −1.17532e17 + 3.61726e17i −0.509956 + 1.56948i
\(470\) 2.35819e16 + 7.25777e16i 0.100912 + 0.310575i
\(471\) −1.21785e17 + 8.84822e16i −0.513995 + 0.373439i
\(472\) 1.11673e16 0.0464863
\(473\) −3.59434e16 + 2.46062e17i −0.147578 + 1.01029i
\(474\) 9.75228e16 0.394954
\(475\) 6.27226e15 4.55707e15i 0.0250562 0.0182044i
\(476\) 6.53181e16 + 2.01028e17i 0.257388 + 0.792159i
\(477\) 6.29341e16 1.93691e17i 0.244634 0.752906i
\(478\) 3.61920e17 + 2.62950e17i 1.38781 + 1.00831i
\(479\) −3.23563e16 2.35082e16i −0.122399 0.0889282i 0.524901 0.851163i \(-0.324102\pi\)
−0.647301 + 0.762235i \(0.724102\pi\)
\(480\) 5.97670e16 1.83944e17i 0.223046 0.686464i
\(481\) 1.12382e17 + 3.45877e17i 0.413766 + 1.27344i
\(482\) −1.45985e15 + 1.06064e15i −0.00530276 + 0.00385268i
\(483\) −2.24779e17 −0.805562
\(484\) −1.45122e17 + 2.10199e17i −0.513145 + 0.743252i
\(485\) −3.62599e16 −0.126504
\(486\) −2.84432e17 + 2.06652e17i −0.979137 + 0.711384i
\(487\) −8.93093e15 2.74866e16i −0.0303360 0.0933647i 0.934742 0.355327i \(-0.115630\pi\)
−0.965078 + 0.261962i \(0.915630\pi\)
\(488\) 8.62192e15 2.65355e16i 0.0288985 0.0889404i
\(489\) −1.48073e17 1.07582e17i −0.489744 0.355820i
\(490\) 6.75184e17 + 4.90550e17i 2.20367 + 1.60106i
\(491\) −1.04827e16 + 3.22626e16i −0.0337633 + 0.103913i −0.966518 0.256599i \(-0.917398\pi\)
0.932755 + 0.360512i \(0.117398\pi\)
\(492\) 6.82454e16 + 2.10038e17i 0.216920 + 0.667612i
\(493\) −4.77850e16 + 3.47178e16i −0.149895 + 0.108905i
\(494\) −4.69671e16 −0.145401
\(495\) −1.73890e16 + 1.19042e17i −0.0531301 + 0.363718i
\(496\) 3.53749e17 1.06675
\(497\) 5.52455e17 4.01382e17i 1.64430 1.19465i
\(498\) −6.91938e16 2.12957e17i −0.203271 0.625605i
\(499\) −1.88707e17 + 5.80782e17i −0.547186 + 1.68407i 0.168548 + 0.985694i \(0.446092\pi\)
−0.715734 + 0.698373i \(0.753908\pi\)
\(500\) −2.74652e17 1.99546e17i −0.786100 0.571135i
\(501\) 1.39698e17 + 1.01497e17i 0.394680 + 0.286752i
\(502\) 2.06214e17 6.34661e17i 0.575101 1.76998i
\(503\) −1.76017e17 5.41724e17i −0.484577 1.49137i −0.832593 0.553885i \(-0.813145\pi\)
0.348017 0.937488i \(-0.386855\pi\)
\(504\) −3.76172e16 + 2.73305e16i −0.102232 + 0.0742760i
\(505\) −3.58928e17 −0.962972
\(506\) 1.43422e17 + 2.73302e17i 0.379872 + 0.723877i
\(507\) 3.59836e17 0.940920
\(508\) 4.02917e17 2.92736e17i 1.04016 0.755722i
\(509\) 8.34840e15 + 2.56937e16i 0.0212783 + 0.0654880i 0.961132 0.276090i \(-0.0890387\pi\)
−0.939854 + 0.341578i \(0.889039\pi\)
\(510\) −4.31453e16 + 1.32788e17i −0.108574 + 0.334158i
\(511\) −6.84351e17 4.97210e17i −1.70037 1.23539i
\(512\) −4.42186e17 3.21267e17i −1.08480 0.788154i
\(513\) −9.37153e15 + 2.88426e16i −0.0227011 + 0.0698669i
\(514\) −4.34554e16 1.33742e17i −0.103940 0.319895i
\(515\) −4.71778e17 + 3.42767e17i −1.11427 + 0.809565i
\(516\) 2.81060e17 0.655504
\(517\) 1.36356e17 2.32817e16i 0.314042 0.0536198i
\(518\) −1.01895e18 −2.31745
\(519\) 2.95569e17 2.14744e17i 0.663852 0.482317i
\(520\) −2.10753e16 6.48631e16i −0.0467468 0.143872i
\(521\) −1.49711e17 + 4.60762e17i −0.327950 + 1.00933i 0.642142 + 0.766586i \(0.278046\pi\)
−0.970091 + 0.242740i \(0.921954\pi\)
\(522\) 9.80613e16 + 7.12457e16i 0.212148 + 0.154135i
\(523\) −1.48579e17 1.07949e17i −0.317466 0.230652i 0.417628 0.908618i \(-0.362862\pi\)
−0.735093 + 0.677966i \(0.762862\pi\)
\(524\) 5.68339e15 1.74917e16i 0.0119937 0.0369129i
\(525\) −9.02797e16 2.77852e17i −0.188172 0.579134i
\(526\) 7.83571e17 5.69298e17i 1.61314 1.17201i
\(527\) −2.32633e17 −0.473044
\(528\) −3.44983e17 1.70581e17i −0.692911 0.342619i
\(529\) −3.27045e17 −0.648851
\(530\) −6.77115e17 + 4.91953e17i −1.32699 + 0.964118i
\(531\) 2.74847e16 + 8.45891e16i 0.0532079 + 0.163757i
\(532\) 1.92979e16 5.93927e16i 0.0369048 0.113581i
\(533\) 7.13752e17 + 5.18571e17i 1.34841 + 0.979674i
\(534\) 7.48894e16 + 5.44104e16i 0.139766 + 0.101546i
\(535\) 1.21302e17 3.73328e17i 0.223649 0.688321i
\(536\) 1.95526e16 + 6.01768e16i 0.0356151 + 0.109612i
\(537\) −1.34454e16 + 9.76866e15i −0.0241959 + 0.0175793i
\(538\) 3.10027e17 0.551207
\(539\) 1.05677e18 1.08251e18i 1.85632 1.90153i
\(540\) 4.10824e17 0.713011
\(541\) −5.39203e17 + 3.91754e17i −0.924635 + 0.671786i −0.944673 0.328013i \(-0.893621\pi\)
0.0200385 + 0.999799i \(0.493621\pi\)
\(542\) −1.97238e17 6.07036e17i −0.334191 1.02853i
\(543\) −9.93361e16 + 3.05725e17i −0.166306 + 0.511838i
\(544\) 3.22289e17 + 2.34156e17i 0.533153 + 0.387358i
\(545\) −2.07125e17 1.50485e17i −0.338575 0.245989i
\(546\) −5.46912e17 + 1.68322e18i −0.883415 + 2.71887i
\(547\) 2.12812e17 + 6.54968e17i 0.339687 + 1.04545i 0.964367 + 0.264567i \(0.0852292\pi\)
−0.624681 + 0.780880i \(0.714771\pi\)
\(548\) 8.65375e16 6.28732e16i 0.136499 0.0991726i
\(549\) 2.22219e17 0.346387
\(550\) −2.80229e17 + 2.87055e17i −0.431674 + 0.442188i
\(551\) 1.74506e16 0.0265659
\(552\) −3.02526e16 + 2.19798e16i −0.0455154 + 0.0330689i
\(553\) 1.60074e17 + 4.92657e17i 0.238016 + 0.732539i
\(554\) −3.30943e17 + 1.01854e18i −0.486340 + 1.49680i
\(555\) −2.58409e17 1.87745e17i −0.375321 0.272686i
\(556\) −3.81862e17 2.77439e17i −0.548177 0.398274i
\(557\) 2.49135e17 7.66758e17i 0.353489 1.08793i −0.603392 0.797445i \(-0.706185\pi\)
0.956881 0.290481i \(-0.0938154\pi\)
\(558\) 1.47523e17 + 4.54028e17i 0.206889 + 0.636738i
\(559\) 9.08354e17 6.59958e17i 1.25915 0.914828i
\(560\) 1.12774e18 1.54520
\(561\) 2.26868e17 + 1.12178e17i 0.307266 + 0.151932i
\(562\) 3.43077e17 0.459310
\(563\) 5.18301e15 3.76568e15i 0.00685927 0.00498355i −0.584350 0.811501i \(-0.698651\pi\)
0.591210 + 0.806518i \(0.298651\pi\)
\(564\) −4.83134e16 1.48693e17i −0.0632052 0.194526i
\(565\) 4.71949e16 1.45251e17i 0.0610352 0.187847i
\(566\) −1.55525e18 1.12996e18i −1.98836 1.44463i
\(567\) 3.18938e17 + 2.31722e17i 0.403103 + 0.292871i
\(568\) 3.51051e16 1.08043e17i 0.0438638 0.134999i
\(569\) −4.33661e17 1.33467e18i −0.535699 1.64871i −0.742134 0.670252i \(-0.766186\pi\)
0.206435 0.978460i \(-0.433814\pi\)
\(570\) 3.33722e16 2.42463e16i 0.0407566 0.0296114i
\(571\) −4.86920e17 −0.587926 −0.293963 0.955817i \(-0.594974\pi\)
−0.293963 + 0.955817i \(0.594974\pi\)
\(572\) 1.13684e18 1.94105e17i 1.35714 0.231720i
\(573\) −5.91667e17 −0.698349
\(574\) −1.99979e18 + 1.45293e18i −2.33377 + 1.69558i
\(575\) 7.10866e16 + 2.18782e17i 0.0820251 + 0.252447i
\(576\) 1.06914e17 3.29047e17i 0.121980 0.375416i
\(577\) 1.02127e18 + 7.41999e17i 1.15212 + 0.837067i 0.988762 0.149499i \(-0.0477660\pi\)
0.163363 + 0.986566i \(0.447766\pi\)
\(578\) 7.67870e17 + 5.57890e17i 0.856558 + 0.622326i
\(579\) 1.39422e17 4.29097e17i 0.153788 0.473309i
\(580\) −7.30498e16 2.24824e17i −0.0796777 0.245223i
\(581\) 9.62220e17 6.99094e17i 1.03784 0.754034i
\(582\) 1.56538e17 0.166963
\(583\) 7.04976e17 + 1.34339e18i 0.743582 + 1.41696i
\(584\) −1.40725e17 −0.146787
\(585\) 4.39450e17 3.19279e17i 0.453311 0.329350i
\(586\) −4.23967e17 1.30484e18i −0.432511 1.33113i
\(587\) −3.57382e17 + 1.09991e18i −0.360566 + 1.10971i 0.592146 + 0.805831i \(0.298281\pi\)
−0.952711 + 0.303877i \(0.901719\pi\)
\(588\) −1.38328e18 1.00501e18i −1.38025 1.00281i
\(589\) 5.56037e16 + 4.03984e16i 0.0548724 + 0.0398672i
\(590\) 1.12951e17 3.47629e17i 0.110244 0.339295i
\(591\) 3.40687e17 + 1.04853e18i 0.328879 + 1.01219i
\(592\) −8.09355e17 + 5.88031e17i −0.772766 + 0.561447i
\(593\) 4.96791e17 0.469157 0.234578 0.972097i \(-0.424629\pi\)
0.234578 + 0.972097i \(0.424629\pi\)
\(594\) 2.26813e17 1.55272e18i 0.211864 1.45038i
\(595\) −7.41624e17 −0.685209
\(596\) −1.23673e18 + 8.98538e17i −1.13025 + 0.821175i
\(597\) −5.95751e16 1.83353e17i −0.0538557 0.165751i
\(598\) 4.30640e17 1.32537e18i 0.385085 1.18517i
\(599\) 8.82561e16 + 6.41218e16i 0.0780675 + 0.0567194i 0.626134 0.779715i \(-0.284636\pi\)
−0.548067 + 0.836434i \(0.684636\pi\)
\(600\) −3.93201e16 2.85678e16i −0.0344058 0.0249973i
\(601\) −2.95913e16 + 9.10727e16i −0.0256142 + 0.0788323i −0.963046 0.269335i \(-0.913196\pi\)
0.937432 + 0.348168i \(0.113196\pi\)
\(602\) 9.72115e17 + 2.99186e18i 0.832416 + 2.56191i
\(603\) −4.07700e17 + 2.96212e17i −0.345365 + 0.250922i
\(604\) −6.94187e17 −0.581750
\(605\) −5.44063e17 7.12155e17i −0.451065 0.590425i
\(606\) 1.54953e18 1.27095
\(607\) −7.62306e17 + 5.53848e17i −0.618590 + 0.449432i −0.852429 0.522843i \(-0.824871\pi\)
0.233839 + 0.972275i \(0.424871\pi\)
\(608\) −3.63701e16 1.11936e17i −0.0291993 0.0898661i
\(609\) 2.03204e17 6.25399e17i 0.161406 0.496758i
\(610\) −7.38823e17 5.36786e17i −0.580626 0.421850i
\(611\) −5.05291e17 3.67115e17i −0.392892 0.285453i
\(612\) −8.65453e16 + 2.66359e17i −0.0665823 + 0.204919i
\(613\) −2.74463e17 8.44712e17i −0.208925 0.643006i −0.999529 0.0306785i \(-0.990233\pi\)
0.790604 0.612328i \(-0.209767\pi\)
\(614\) −1.21074e18 + 8.79651e17i −0.911916 + 0.662546i
\(615\) −7.74860e17 −0.577477
\(616\) 5.00655e16 3.42739e17i 0.0369202 0.252749i
\(617\) 2.50053e17 0.182464 0.0912322 0.995830i \(-0.470919\pi\)
0.0912322 + 0.995830i \(0.470919\pi\)
\(618\) 2.03671e18 1.47976e18i 1.47064 1.06848i
\(619\) −2.87874e17 8.85984e17i −0.205690 0.633048i −0.999684 0.0251232i \(-0.992002\pi\)
0.793995 0.607925i \(-0.207998\pi\)
\(620\) 2.87710e17 8.85482e17i 0.203427 0.626085i
\(621\) −7.27989e17 5.28915e17i −0.509365 0.370076i
\(622\) −2.40123e18 1.74460e18i −1.66264 1.20798i
\(623\) −1.51942e17 + 4.67629e17i −0.104113 + 0.320427i
\(624\) 5.36964e17 + 1.65260e18i 0.364120 + 1.12065i
\(625\) 4.23637e17 3.07790e17i 0.284298 0.206554i
\(626\) 4.09179e18 2.71757
\(627\) −3.47453e16 6.62101e16i −0.0228380 0.0435196i
\(628\) 1.24093e18 0.807254
\(629\) 5.32249e17 3.86701e17i 0.342677 0.248970i
\(630\) 4.70297e17 + 1.44743e18i 0.299681 + 0.922322i
\(631\) −4.22041e17 + 1.29891e18i −0.266173 + 0.819195i 0.725248 + 0.688488i \(0.241725\pi\)
−0.991421 + 0.130708i \(0.958275\pi\)
\(632\) 6.97180e16 + 5.06531e16i 0.0435195 + 0.0316188i
\(633\) −1.16750e18 8.48238e17i −0.721328 0.524075i
\(634\) 6.09301e17 1.87524e18i 0.372608 1.14677i
\(635\) 5.39973e17 + 1.66187e18i 0.326846 + 1.00593i
\(636\) 1.38724e18 1.00789e18i 0.831150 0.603865i
\(637\) −6.83048e18 −4.05084
\(638\) −8.90061e17 + 1.51970e17i −0.522499 + 0.0892121i
\(639\) 9.04792e17 0.525767
\(640\) 2.77842e17 2.01864e17i 0.159819 0.116115i
\(641\) 3.45960e17 + 1.06475e18i 0.196992 + 0.606279i 0.999948 + 0.0102400i \(0.00325955\pi\)
−0.802956 + 0.596039i \(0.796740\pi\)
\(642\) −5.23672e17 + 1.61170e18i −0.295176 + 0.908460i
\(643\) 2.14638e18 + 1.55944e18i 1.19767 + 0.870155i 0.994053 0.108897i \(-0.0347318\pi\)
0.203612 + 0.979052i \(0.434732\pi\)
\(644\) 1.49907e18 + 1.08914e18i 0.828066 + 0.601625i
\(645\) −3.04729e17 + 9.37858e17i −0.166638 + 0.512860i
\(646\) 2.62553e16 + 8.08055e16i 0.0142137 + 0.0437451i
\(647\) 1.80458e18 1.31111e18i 0.967161 0.702684i 0.0123585 0.999924i \(-0.496066\pi\)
0.954803 + 0.297240i \(0.0960661\pi\)
\(648\) 6.55840e16 0.0347985
\(649\) −5.93925e17 2.93674e17i −0.311990 0.154268i
\(650\) 1.81128e18 0.941994
\(651\) 2.09529e18 1.52232e18i 1.07887 0.783844i
\(652\) 4.66243e17 + 1.43495e18i 0.237686 + 0.731521i
\(653\) −6.95826e17 + 2.14153e18i −0.351208 + 1.08091i 0.606967 + 0.794727i \(0.292386\pi\)
−0.958175 + 0.286181i \(0.907614\pi\)
\(654\) 8.94178e17 + 6.49659e17i 0.446857 + 0.324661i
\(655\) 5.22054e16 + 3.79294e16i 0.0258313 + 0.0187676i
\(656\) −7.49959e17 + 2.30814e18i −0.367420 + 1.13080i
\(657\) −3.46349e17 1.06595e18i −0.168011 0.517086i
\(658\) 1.41573e18 1.02859e18i 0.680003 0.494051i
\(659\) −2.30387e18 −1.09573 −0.547865 0.836567i \(-0.684559\pi\)
−0.547865 + 0.836567i \(0.684559\pi\)
\(660\) −7.07570e17 + 7.24804e17i −0.333222 + 0.341338i
\(661\) 2.91607e18 1.35984 0.679921 0.733285i \(-0.262014\pi\)
0.679921 + 0.733285i \(0.262014\pi\)
\(662\) −6.30050e17 + 4.57758e17i −0.290936 + 0.211378i
\(663\) −3.53119e17 1.08679e18i −0.161467 0.496943i
\(664\) 6.11433e16 1.88180e17i 0.0276857 0.0852080i
\(665\) 1.77262e17 + 1.28789e17i 0.0794833 + 0.0577480i
\(666\) −1.09225e18 7.93564e17i −0.484996 0.352370i
\(667\) −1.60004e17 + 4.92441e17i −0.0703579 + 0.216539i
\(668\) −4.39871e17 1.35378e18i −0.191548 0.589525i
\(669\) −1.16968e18 + 8.49821e17i −0.504425 + 0.366486i
\(670\) 2.07102e18 0.884501
\(671\) −1.15637e18 + 1.18454e18i −0.489105 + 0.501017i
\(672\) −4.43511e18 −1.85782
\(673\) −8.58283e17 + 6.23579e17i −0.356068 + 0.258698i −0.751410 0.659835i \(-0.770626\pi\)
0.395342 + 0.918534i \(0.370626\pi\)
\(674\) 2.70765e17 + 8.33328e17i 0.111251 + 0.342394i
\(675\) 3.61412e17 1.11231e18i 0.147071 0.452639i
\(676\) −2.39979e18 1.74355e18i −0.967206 0.702717i
\(677\) 6.39516e16 + 4.64635e16i 0.0255285 + 0.0185475i 0.600476 0.799643i \(-0.294978\pi\)
−0.574948 + 0.818190i \(0.694978\pi\)
\(678\) −2.03745e17 + 6.27064e17i −0.0805554 + 0.247924i
\(679\) 2.56941e17 + 7.90783e17i 0.100619 + 0.309673i
\(680\) −9.98138e16 + 7.25190e16i −0.0387153 + 0.0281283i
\(681\) −4.42605e17 −0.170044
\(682\) −3.18787e18 1.57628e18i −1.21311 0.599840i
\(683\) −1.49854e18 −0.564851 −0.282426 0.959289i \(-0.591139\pi\)
−0.282426 + 0.959289i \(0.591139\pi\)
\(684\) 6.69413e16 4.86357e16i 0.0249936 0.0181589i
\(685\) 1.15974e17 + 3.56932e17i 0.0428916 + 0.132007i
\(686\) 3.68843e18 1.13518e19i 1.35125 4.15871i
\(687\) 1.77971e18 + 1.29303e18i 0.645847 + 0.469235i
\(688\) 2.49874e18 + 1.81544e18i 0.898247 + 0.652615i
\(689\) 2.11677e18 6.51475e18i 0.753788 2.31992i
\(690\) 3.78223e17 + 1.16405e18i 0.133423 + 0.410632i
\(691\) −2.12835e16 + 1.54633e16i −0.00743764 + 0.00540376i −0.591498 0.806307i \(-0.701463\pi\)
0.584060 + 0.811710i \(0.301463\pi\)
\(692\) −3.01170e18 −1.04261
\(693\) 2.71937e18 4.64309e17i 0.932615 0.159236i
\(694\) 1.35718e18 0.461107
\(695\) 1.33980e18 9.73420e17i 0.450960 0.327641i
\(696\) −3.38051e16 1.04041e17i −0.0112726 0.0346934i
\(697\) 4.93189e17 1.51788e18i 0.162930 0.501446i
\(698\) −2.10392e18 1.52859e18i −0.688604 0.500300i
\(699\) −2.56240e18 1.86169e18i −0.830893 0.603679i
\(700\) −7.44219e17 + 2.29047e18i −0.239091 + 0.735847i
\(701\) −8.68875e17 2.67412e18i −0.276561 0.851166i −0.988802 0.149232i \(-0.952320\pi\)
0.712242 0.701934i \(-0.247680\pi\)
\(702\) −5.73198e18 + 4.16452e18i −1.80765 + 1.31333i
\(703\) −1.94371e17 −0.0607327
\(704\) 1.19763e18 + 2.28218e18i 0.370767 + 0.706527i
\(705\) 5.48551e17 0.168263
\(706\) −1.84318e18 + 1.33915e18i −0.560193 + 0.407004i
\(707\) 2.54340e18 + 7.82778e18i 0.765929 + 2.35729i
\(708\) −2.31409e17 + 7.12203e17i −0.0690500 + 0.212514i
\(709\) −5.37217e17 3.90311e17i −0.158836 0.115401i 0.505528 0.862810i \(-0.331298\pi\)
−0.664364 + 0.747409i \(0.731298\pi\)
\(710\) −3.00820e18 2.18559e18i −0.881309 0.640308i
\(711\) −2.12095e17 + 6.52761e17i −0.0615712 + 0.189497i
\(712\) 2.52771e16 + 7.77948e16i 0.00727121 + 0.0223785i
\(713\) −1.64984e18 + 1.19868e18i −0.470284 + 0.341682i
\(714\) 3.20167e18 0.904352
\(715\) −5.84873e17 + 4.00393e18i −0.163709 + 1.12072i
\(716\) 1.37002e17 0.0380008
\(717\) 2.60156e18 1.89014e18i 0.715087 0.519541i
\(718\) −2.72388e18 8.38324e18i −0.741957 2.28351i
\(719\) −9.26425e17 + 2.85124e18i −0.250076 + 0.769655i 0.744684 + 0.667417i \(0.232600\pi\)
−0.994760 + 0.102238i \(0.967400\pi\)
\(720\) 1.20886e18 + 8.78287e17i 0.323381 + 0.234950i
\(721\) 1.08184e19 + 7.86001e18i 2.86803 + 2.08374i
\(722\) −1.61485e18 + 4.97001e18i −0.424269 + 1.30577i
\(723\) 4.00823e15 + 1.23361e16i 0.00104365 + 0.00321202i
\(724\) 2.14384e18 1.55759e18i 0.553213 0.401933i
\(725\) −6.72978e17 −0.172109
\(726\) 2.34878e18 + 3.07445e18i 0.595324 + 0.779254i
\(727\) −1.89263e18 −0.475437 −0.237719 0.971334i \(-0.576400\pi\)
−0.237719 + 0.971334i \(0.576400\pi\)
\(728\) −1.26524e18 + 9.19253e17i −0.315007 + 0.228866i
\(729\) 1.10723e18 + 3.40769e18i 0.273217 + 0.840875i
\(730\) −1.42336e18 + 4.38065e18i −0.348110 + 1.07137i
\(731\) −1.64322e18 1.19387e18i −0.398321 0.289397i
\(732\) 1.51366e18 + 1.09974e18i 0.363669 + 0.264221i
\(733\) 1.57870e18 4.85874e18i 0.375945 1.15704i −0.566894 0.823790i \(-0.691855\pi\)
0.942839 0.333248i \(-0.108145\pi\)
\(734\) −1.93598e18 5.95833e18i −0.456958 1.40637i
\(735\) 4.85336e18 3.52617e18i 1.13547 0.824965i
\(736\) 3.49222e18 0.809834
\(737\) 5.42617e17 3.71465e18i 0.124725 0.853846i
\(738\) −3.27520e18 −0.746227
\(739\) 2.32136e18 1.68656e18i 0.524267 0.380903i −0.293942 0.955823i \(-0.594967\pi\)
0.818209 + 0.574921i \(0.194967\pi\)
\(740\) 8.13658e17 + 2.50418e18i 0.182153 + 0.560609i
\(741\) −1.04327e17 + 3.21085e17i −0.0231514 + 0.0712527i
\(742\) 1.55270e19 + 1.12810e19i 3.41556 + 2.48155i
\(743\) −5.43529e18 3.94897e18i −1.18521 0.861106i −0.192461 0.981305i \(-0.561647\pi\)
−0.992750 + 0.120198i \(0.961647\pi\)
\(744\) 1.33143e17 4.09773e17i 0.0287803 0.0885766i
\(745\) −1.65742e18 5.10101e18i −0.355154 1.09305i
\(746\) −5.73620e18 + 4.16759e18i −1.21849 + 0.885285i
\(747\) 1.57589e18 0.331851
\(748\) −9.69464e17 1.84739e18i −0.202382 0.385655i
\(749\) −9.00138e18 −1.86285
\(750\) −4.16014e18 + 3.02252e18i −0.853511 + 0.620112i
\(751\) −2.63084e18 8.09689e18i −0.535100 1.64687i −0.743433 0.668810i \(-0.766804\pi\)
0.208334 0.978058i \(-0.433196\pi\)
\(752\) 5.30923e17 1.63401e18i 0.107057 0.329488i
\(753\) −3.88073e18 2.81952e18i −0.775794 0.563647i
\(754\) 3.29826e18 + 2.39633e18i 0.653690 + 0.474933i
\(755\) 7.52647e17 2.31641e18i 0.147889 0.455156i
\(756\) −2.91114e18 8.95955e18i −0.567115 1.74540i
\(757\) −3.22119e18 + 2.34033e18i −0.622147 + 0.452016i −0.853671 0.520813i \(-0.825629\pi\)
0.231524 + 0.972829i \(0.425629\pi\)
\(758\) 8.26264e18 1.58223
\(759\) 2.18698e18 3.73407e17i 0.415215 0.0708943i
\(760\) 3.64509e16 0.00686152
\(761\) 3.58812e18 2.60692e18i 0.669679 0.486550i −0.200239 0.979747i \(-0.564172\pi\)
0.869918 + 0.493197i \(0.164172\pi\)
\(762\) −2.33112e18 7.17445e18i −0.431378 1.32764i
\(763\) −1.81418e18 + 5.58348e18i −0.332868 + 1.02446i
\(764\) 3.94589e18 + 2.86686e18i 0.717858 + 0.521554i
\(765\) −7.94970e17 5.77580e17i −0.143401 0.104187i
\(766\) −1.26007e18 + 3.87809e18i −0.225376 + 0.693635i
\(767\) 9.24439e17 + 2.84513e18i 0.163949 + 0.504583i
\(768\) −3.80877e18 + 2.76723e18i −0.669786 + 0.486628i
\(769\) 7.60350e18 1.32584 0.662921 0.748689i \(-0.269316\pi\)
0.662921 + 0.748689i \(0.269316\pi\)
\(770\) −1.01628e19 5.02512e18i −1.75721 0.868874i
\(771\) −1.01084e18 −0.173312
\(772\) −3.00897e18 + 2.18614e18i −0.511570 + 0.371677i
\(773\) 1.76559e18 + 5.43393e18i 0.297662 + 0.916109i 0.982314 + 0.187239i \(0.0599540\pi\)
−0.684652 + 0.728870i \(0.740046\pi\)
\(774\) −1.28803e18 + 3.96416e18i −0.215333 + 0.662728i
\(775\) −2.14435e18 1.55796e18i −0.355496 0.258283i
\(776\) 1.11907e17 + 8.13054e16i 0.0183974 + 0.0133665i
\(777\) −2.26337e18 + 6.96595e18i −0.368994 + 1.13565i
\(778\) 1.07014e18 + 3.29356e18i 0.173011 + 0.532474i
\(779\) −3.81473e17 + 2.77157e17i −0.0611604 + 0.0444357i
\(780\) 4.57342e18 0.727153
\(781\) −4.70831e18 + 4.82298e18i −0.742392 + 0.760474i
\(782\) −2.52101e18 −0.394212
\(783\) 2.12971e18 1.54732e18i 0.330270 0.239955i
\(784\) −5.80629e18 1.78699e19i −0.892986 2.74833i
\(785\) −1.34543e18 + 4.14082e18i −0.205215 + 0.631588i
\(786\) −2.25376e17 1.63745e17i −0.0340927 0.0247698i
\(787\) 1.86549e18 + 1.35536e18i 0.279870 + 0.203338i 0.718861 0.695154i \(-0.244664\pi\)
−0.438991 + 0.898492i \(0.644664\pi\)
\(788\) 2.80844e18 8.64350e18i 0.417874 1.28608i
\(789\) −2.15141e18 6.62137e18i −0.317485 0.977118i
\(790\) 2.28195e18 1.65793e18i 0.333988 0.242656i
\(791\) −3.50217e18 −0.508382
\(792\) 3.20593e17 3.28402e17i 0.0461574 0.0472816i
\(793\) 7.47428e18 1.06732
\(794\) 1.01352e19 7.36365e18i 1.43549 1.04294i
\(795\) 1.85912e18 + 5.72178e18i 0.261169 + 0.803795i
\(796\) −4.91106e17 + 1.51147e18i −0.0684291 + 0.210603i
\(797\) −5.82474e18 4.23192e18i −0.805002 0.584869i 0.107375 0.994219i \(-0.465755\pi\)
−0.912377 + 0.409350i \(0.865755\pi\)
\(798\) −7.65260e17 5.55994e17i −0.104904 0.0762169i
\(799\) −3.49146e17 + 1.07456e18i −0.0474737 + 0.146109i
\(800\) 1.40261e18 + 4.31679e18i 0.189170 + 0.582205i
\(801\) −5.27063e17 + 3.82934e17i −0.0705101 + 0.0512286i
\(802\) −4.48658e18 −0.595363
\(803\) 7.48436e18 + 3.70074e18i 0.985153 + 0.487121i
\(804\) −4.24299e18 −0.553998
\(805\) −5.25964e18 + 3.82135e18i −0.681212 + 0.494930i
\(806\) 4.96189e18 + 1.52711e19i 0.637484 + 1.96197i
\(807\) 6.88656e17 2.11947e18i 0.0877656 0.270115i
\(808\) 1.10774e18 + 8.04823e17i 0.140044 + 0.101748i
\(809\) 7.90381e18 + 5.74245e18i 0.991222 + 0.720165i 0.960188 0.279353i \(-0.0901200\pi\)
0.0310340 + 0.999518i \(0.490120\pi\)
\(810\) 6.63348e17 2.04157e18i 0.0825256 0.253988i
\(811\) −4.87669e18 1.50089e19i −0.601852 1.85231i −0.517131 0.855906i \(-0.673000\pi\)
−0.0847213 0.996405i \(-0.527000\pi\)
\(812\) −4.38550e18 + 3.18625e18i −0.536914 + 0.390091i
\(813\) −4.58805e18 −0.557237
\(814\) 9.91386e18 1.69271e18i 1.19450 0.203950i
\(815\) −5.29373e18 −0.632758
\(816\) 2.54309e18 1.84766e18i 0.301561 0.219097i
\(817\) 1.85437e17 + 5.70717e17i 0.0218149 + 0.0671394i
\(818\) 9.12768e17 2.80921e18i 0.106528 0.327860i
\(819\) −1.00771e19 7.32142e18i −1.16678 0.847715i
\(820\) 5.16763e18 + 3.75450e18i 0.593610 + 0.431283i
\(821\) −4.05162e18 + 1.24696e19i −0.461741 + 1.42109i 0.401295 + 0.915949i \(0.368560\pi\)
−0.863036 + 0.505143i \(0.831440\pi\)
\(822\) −5.00673e17 1.54091e18i −0.0566092 0.174225i
\(823\) 2.79646e18 2.03175e18i 0.313696 0.227914i −0.419785 0.907624i \(-0.637894\pi\)
0.733481 + 0.679710i \(0.237894\pi\)
\(824\) 2.22461e18 0.247587
\(825\) 1.33995e18 + 2.55338e18i 0.147958 + 0.281946i
\(826\) −8.38173e18 −0.918256
\(827\) 9.21807e18 6.69732e18i 1.00197 0.727973i 0.0394592 0.999221i \(-0.487436\pi\)
0.962509 + 0.271248i \(0.0874365\pi\)
\(828\) 7.58678e17 + 2.33497e18i 0.0818202 + 0.251817i
\(829\) 1.96112e18 6.03571e18i 0.209846 0.645839i −0.789634 0.613578i \(-0.789729\pi\)
0.999480 0.0322602i \(-0.0102705\pi\)
\(830\) −5.23944e18 3.80668e18i −0.556260 0.404146i
\(831\) 6.22801e18 + 4.52491e18i 0.656058 + 0.476654i
\(832\) 3.59602e18 1.10674e19i 0.375855 1.15676i
\(833\) 3.81834e18 + 1.17516e19i 0.395988 + 1.21873i
\(834\) −5.78404e18 + 4.20235e18i −0.595185 + 0.432428i
\(835\) 4.99431e18 0.509933
\(836\) −8.90936e16 + 6.09918e17i −0.00902621 + 0.0617918i
\(837\) 1.03681e19 1.04228
\(838\) −1.17672e19 + 8.54934e18i −1.17378 + 0.852798i
\(839\) −3.56950e18 1.09858e19i −0.353309 1.08737i −0.956983 0.290143i \(-0.906297\pi\)
0.603674 0.797231i \(-0.293703\pi\)
\(840\) 4.24456e17 1.30634e18i 0.0416886 0.128304i
\(841\) 7.07556e18 + 5.14069e18i 0.689583 + 0.501011i
\(842\) 4.45271e18 + 3.23508e18i 0.430622 + 0.312865i
\(843\) 7.62070e17 2.34541e18i 0.0731334 0.225081i
\(844\) 3.67614e18 + 1.13140e19i 0.350079 + 1.07743i
\(845\) 8.41986e18 6.11739e18i 0.795676 0.578093i
\(846\) 2.31863e18 0.217432
\(847\) −1.16759e19 + 1.69117e19i −1.08655 + 1.57379i
\(848\) 1.88433e19 1.74014
\(849\) −1.11795e19 + 8.12237e18i −1.02452 + 0.744359i
\(850\) −1.01253e18 3.11625e18i −0.0920843 0.283406i
\(851\) 1.78219e18 5.48501e18i 0.160847 0.495035i
\(852\) 6.16304e18 + 4.47771e18i 0.551999 + 0.401050i
\(853\) −7.88030e18 5.72537e18i −0.700445 0.508903i 0.179632 0.983734i \(-0.442509\pi\)
−0.880077 + 0.474831i \(0.842509\pi\)
\(854\) −6.47128e18 + 1.99165e19i −0.570839 + 1.75686i
\(855\) 8.97121e16 + 2.76105e17i 0.00785365 + 0.0241710i
\(856\) −1.21148e18 + 8.80192e17i −0.105254 + 0.0764712i
\(857\) −1.89871e19 −1.63713 −0.818567 0.574411i \(-0.805231\pi\)
−0.818567 + 0.574411i \(0.805231\pi\)
\(858\) 2.52496e18 1.72854e19i 0.216066 1.47915i
\(859\) −2.14344e17 −0.0182036 −0.00910179 0.999959i \(-0.502897\pi\)
−0.00910179 + 0.999959i \(0.502897\pi\)
\(860\) 6.57656e18 4.77815e18i 0.554318 0.402736i
\(861\) 5.49073e18 + 1.68987e19i 0.459314 + 1.41362i
\(862\) 5.44983e18 1.67728e19i 0.452466 1.39255i
\(863\) 1.05785e19 + 7.68575e18i 0.871676 + 0.633310i 0.931036 0.364927i \(-0.118906\pi\)
−0.0593599 + 0.998237i \(0.518906\pi\)
\(864\) −1.43639e19 1.04360e19i −1.17472 0.853484i
\(865\) 3.26533e18 1.00496e19i 0.265047 0.815729i
\(866\) −5.11267e17 1.57352e18i −0.0411890 0.126767i
\(867\) 5.51960e18 4.01023e18i 0.441351 0.320660i
\(868\) −2.13500e19 −1.69441
\(869\) −2.37585e18 4.52737e18i −0.187150 0.356630i
\(870\) −3.58065e18 −0.279954
\(871\) −1.37129e19 + 9.96299e18i −1.06417 + 0.773164i
\(872\) 3.01808e17 + 9.28869e17i 0.0232473 + 0.0715480i
\(873\) −3.40442e17 + 1.04777e18i −0.0260286 + 0.0801078i
\(874\) 6.02569e17 + 4.37792e17i 0.0457280 + 0.0332234i
\(875\) −2.20973e19 1.60546e19i −1.66451 1.20934i
\(876\) 2.91610e18 8.97484e18i 0.218035 0.671042i
\(877\) 1.98229e18 + 6.10086e18i 0.147119 + 0.452786i 0.997277 0.0737409i \(-0.0234938\pi\)
−0.850158 + 0.526527i \(0.823494\pi\)
\(878\) 3.41767e18 2.48309e18i 0.251777 0.182927i
\(879\) −9.86211e18 −0.721177
\(880\) −1.09723e19 + 1.87342e18i −0.796453 + 0.135987i
\(881\) −8.42307e18 −0.606914 −0.303457 0.952845i \(-0.598141\pi\)
−0.303457 + 0.952845i \(0.598141\pi\)
\(882\) 2.05143e19 1.49045e19i 1.46727 1.06604i
\(883\) 1.67881e18 + 5.16685e18i 0.119195 + 0.366844i 0.992799 0.119793i \(-0.0382232\pi\)
−0.873604 + 0.486638i \(0.838223\pi\)
\(884\) −2.91093e18 + 8.95891e18i −0.205159 + 0.631416i
\(885\) −2.12563e18 1.54436e18i −0.148715 0.108048i
\(886\) −1.45542e19 1.05742e19i −1.01081 0.734396i
\(887\) 5.54586e18 1.70684e19i 0.382354 1.17676i −0.556028 0.831163i \(-0.687675\pi\)
0.938382 0.345600i \(-0.112325\pi\)
\(888\) 3.76535e17 + 1.15886e18i 0.0257704 + 0.0793132i
\(889\) 3.24170e19 2.35523e19i 2.20247 1.60019i
\(890\) 2.67735e18 0.180580
\(891\) −3.48804e18 1.72470e18i −0.233548 0.115481i
\(892\) 1.19184e19 0.792223
\(893\) 2.70059e17 1.96209e17i 0.0178207 0.0129475i
\(894\) 7.15525e18 + 2.20216e19i 0.468739 + 1.44263i
\(895\) −1.48539e17 + 4.57157e17i −0.00966033 + 0.0297314i
\(896\) −6.37123e18 4.62897e18i −0.411359 0.298870i
\(897\) −8.10420e18 5.88805e18i −0.519469 0.377416i
\(898\) −2.17764e18 + 6.70210e18i −0.138577 + 0.426496i
\(899\) −1.84358e18 5.67397e18i −0.116473 0.358467i
\(900\) −2.58158e18 + 1.87563e18i −0.161923 + 0.117644i
\(901\) −1.23918e19 −0.771653
\(902\) 1.70433e19 1.74584e19i 1.05369 1.07935i
\(903\) 2.26129e19 1.38799
\(904\) −4.71351e17 + 3.42457e17i −0.0287243 + 0.0208694i
\(905\) 2.87309e18 + 8.84248e18i 0.173834 + 0.535005i
\(906\) −3.24925e18 + 1.00002e19i −0.195187 + 0.600723i
\(907\) −1.29146e19 9.38303e18i −0.770255 0.559623i 0.131783 0.991279i \(-0.457930\pi\)
−0.902039 + 0.431655i \(0.857930\pi\)
\(908\) 2.95178e18 + 2.14460e18i 0.174794 + 0.126995i
\(909\) −3.36996e18 + 1.03717e19i −0.198134 + 0.609794i
\(910\) 1.58183e19 + 4.86837e19i 0.923402 + 2.84194i
\(911\) −6.59264e18 + 4.78983e18i −0.382111 + 0.277620i −0.762215 0.647324i \(-0.775888\pi\)
0.380104 + 0.924944i \(0.375888\pi\)
\(912\) −9.28708e17 −0.0534457
\(913\) −8.20055e18 + 8.40028e18i −0.468579 + 0.479992i
\(914\) −2.27057e18 −0.128820
\(915\) −5.31081e18 + 3.85853e18i −0.299174 + 0.217363i
\(916\) −5.60381e18 1.72468e19i −0.313446 0.964688i
\(917\) 4.57262e17 1.40731e18i 0.0253959 0.0781606i
\(918\) 1.03692e19 + 7.53367e18i 0.571832 + 0.415460i
\(919\) 1.21944e19 + 8.85973e18i 0.667742 + 0.485143i 0.869268 0.494340i \(-0.164590\pi\)
−0.201527 + 0.979483i \(0.564590\pi\)
\(920\) −3.34218e17 + 1.02862e18i −0.0181723 + 0.0559285i
\(921\) 3.32425e18 + 1.02310e19i 0.179476 + 0.552371i
\(922\) −4.45557e18 + 3.23716e18i −0.238865 + 0.173545i
\(923\) 3.04324e19 1.62004
\(924\) 2.08210e19 + 1.02952e19i 1.10061 + 0.544210i
\(925\) 7.49591e18 0.393462
\(926\) −2.21858e19 + 1.61189e19i −1.15639 + 0.840164i
\(927\) 5.47516e18 + 1.68508e19i 0.283386 + 0.872173i
\(928\) −3.15704e18 + 9.71636e18i −0.162262 + 0.499392i
\(929\) 2.23672e16 + 1.62507e16i 0.00114159 + 0.000829413i 0.588356 0.808602i \(-0.299775\pi\)
−0.587214 + 0.809431i \(0.699775\pi\)
\(930\) −1.14092e19 8.28928e18i −0.578251 0.420124i
\(931\) 1.12811e18 3.47196e18i 0.0567776 0.174744i
\(932\) 8.06830e18 + 2.48317e19i 0.403254 + 1.24109i
\(933\) −1.72606e19 + 1.25405e19i −0.856691 + 0.622422i
\(934\) −8.71169e18 −0.429386
\(935\) 7.21561e18 1.23200e18i 0.353181 0.0603026i
\(936\) −2.07217e18 −0.100724
\(937\) 3.08073e18 2.23828e18i 0.148712 0.108046i −0.510941 0.859616i \(-0.670703\pi\)
0.659653 + 0.751570i \(0.270703\pi\)
\(938\) −1.46754e19 4.51664e19i −0.703514 2.16519i
\(939\) 9.08900e18 2.79731e19i 0.432703 1.33172i
\(940\) −3.65835e18 2.65795e18i −0.172963 0.125665i
\(941\) 1.51238e19 + 1.09881e19i 0.710115 + 0.515928i 0.883211 0.468977i \(-0.155377\pi\)
−0.173096 + 0.984905i \(0.555377\pi\)
\(942\) 5.80838e18 1.78764e19i 0.270847 0.833581i
\(943\) −4.32342e18 1.33061e19i −0.200217 0.616206i
\(944\) −6.65763e18 + 4.83705e18i −0.306197 + 0.222465i
\(945\) 3.30531e19 1.50975
\(946\) −1.44283e19 2.74944e19i −0.654521 1.24724i
\(947\) 3.34746e19 1.50814 0.754068 0.656796i \(-0.228089\pi\)
0.754068 + 0.656796i \(0.228089\pi\)
\(948\) −4.67514e18 + 3.39669e18i −0.209190 + 0.151985i
\(949\) −1.16493e19 3.58530e19i −0.517692 1.59329i
\(950\) −2.99147e17 + 9.20679e17i −0.0132032 + 0.0406354i
\(951\) −1.14664e19 8.33083e18i −0.502637 0.365187i
\(952\) 2.28884e18 + 1.66294e18i 0.0996495 + 0.0723996i
\(953\) −1.17634e19 + 3.62040e19i −0.508662 + 1.56550i 0.285865 + 0.958270i \(0.407719\pi\)
−0.794527 + 0.607229i \(0.792281\pi\)
\(954\) 7.85817e18 + 2.41850e19i 0.337487 + 1.03868i
\(955\) −1.38445e19 + 1.00586e19i −0.590549 + 0.429059i
\(956\) −2.65086e19 −1.12308
\(957\) −9.38146e17 + 6.42237e18i −0.0394769 + 0.270251i
\(958\) 4.99387e18 0.208719
\(959\) 6.96244e18 5.05851e18i 0.289028 0.209991i
\(960\) 3.15832e18 + 9.72030e18i 0.130225 + 0.400790i
\(961\) −2.84386e17 + 8.75250e17i −0.0116468 + 0.0358451i
\(962\) −3.67374e19 2.66913e19i −1.49441 1.08575i
\(963\) −9.64887e18 7.01031e18i −0.389857 0.283248i
\(964\) 3.30418e16 1.01692e17i 0.00132606 0.00408119i
\(965\) −4.03250e18 1.24108e19i −0.160749 0.494733i
\(966\) 2.27064e19 1.64972e19i 0.899077 0.653218i
\(967\) −1.44676e19 −0.569016 −0.284508 0.958674i \(-0.591830\pi\)
−0.284508 + 0.958674i \(0.591830\pi\)
\(968\) 8.22547e16 + 3.41784e18i 0.00321345 + 0.133525i
\(969\) 6.10738e17 0.0237001
\(970\) 3.66285e18 2.66122e18i 0.141190 0.102580i
\(971\) −2.08604e18 6.42016e18i −0.0798725 0.245822i 0.903145 0.429337i \(-0.141253\pi\)
−0.983017 + 0.183514i \(0.941253\pi\)
\(972\) 6.43776e18 1.98134e19i 0.244852 0.753577i
\(973\) −3.07230e19 2.23216e19i −1.16073 0.843318i
\(974\) 2.91949e18 + 2.12114e18i 0.109566 + 0.0796041i
\(975\) 4.02335e18 1.23826e19i 0.149988 0.461617i
\(976\) 6.35357e18 + 1.95543e19i 0.235285 + 0.724132i
\(977\) 4.14117e19 3.00874e19i 1.52338 1.10680i 0.563602 0.826047i \(-0.309415\pi\)
0.959780 0.280755i \(-0.0905847\pi\)
\(978\) 2.28536e19 0.835126
\(979\) 7.01479e17 4.80219e18i 0.0254640 0.174322i
\(980\) −4.94533e19 −1.78330
\(981\) −6.29312e18 + 4.57222e18i −0.225433 + 0.163787i
\(982\) −1.30891e18 4.02842e18i −0.0465785 0.143354i
\(983\) −1.24066e19 + 3.81835e19i −0.438585 + 1.34983i 0.450783 + 0.892633i \(0.351145\pi\)
−0.889368 + 0.457192i \(0.848855\pi\)
\(984\) 2.39141e18 + 1.73746e18i 0.0839821 + 0.0610166i
\(985\) 2.57973e19 + 1.87428e19i 0.899991 + 0.653881i
\(986\) 2.27904e18 7.01416e18i 0.0789863 0.243095i
\(987\) −3.88709e18 1.19632e19i −0.133833 0.411895i
\(988\) 2.25155e18 1.63585e18i 0.0770126 0.0559529i
\(989\) −1.78055e19 −0.605031
\(990\) −6.98024e18 1.33014e19i −0.235636 0.449024i
\(991\) 1.40116e19 0.469905 0.234953 0.972007i \(-0.424506\pi\)
0.234953 + 0.972007i \(0.424506\pi\)
\(992\) −3.25530e19 + 2.36512e19i −1.08459 + 0.788001i
\(993\) 1.72990e18 + 5.32407e18i 0.0572598 + 0.176228i
\(994\) −2.63485e19 + 8.10925e19i −0.866453 + 2.66667i
\(995\) −4.51111e18 3.27751e18i −0.147378 0.107076i
\(996\) 1.07343e19 + 7.79892e18i 0.348408 + 0.253133i
\(997\) −1.29190e19 + 3.97606e19i −0.416591 + 1.28214i 0.494229 + 0.869332i \(0.335450\pi\)
−0.910820 + 0.412804i \(0.864550\pi\)
\(998\) −2.35627e19 7.25184e19i −0.754876 2.32327i
\(999\) −2.37216e19 + 1.72347e19i −0.755036 + 0.548566i
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 11.14.c.a.3.2 48
11.2 odd 10 121.14.a.i.1.4 24
11.4 even 5 inner 11.14.c.a.4.2 yes 48
11.9 even 5 121.14.a.h.1.21 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.14.c.a.3.2 48 1.1 even 1 trivial
11.14.c.a.4.2 yes 48 11.4 even 5 inner
121.14.a.h.1.21 24 11.9 even 5
121.14.a.i.1.4 24 11.2 odd 10