Properties

Label 10.15.c.b.7.3
Level $10$
Weight $15$
Character 10.7
Analytic conductor $12.433$
Analytic rank $0$
Dimension $8$
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] = [10,15,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 10.c (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: \(12.4328968152\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 513401x^{6} + 81983771116x^{4} + 4511941511282436x^{2} + 65023716741123799296 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{4}\cdot 5^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.3
Root \(394.425i\) of defining polynomial
Character \(\chi\) \(=\) 10.7
Dual form 10.15.c.b.3.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(64.0000 + 64.0000i) q^{2} +(803.510 - 803.510i) q^{3} +8192.00i q^{4} +(-66844.3 - 40439.5i) q^{5} +102849. q^{6} +(-657264. - 657264. i) q^{7} +(-524288. + 524288. i) q^{8} +3.49171e6i q^{9} +O(q^{10})\) \(q+(64.0000 + 64.0000i) q^{2} +(803.510 - 803.510i) q^{3} +8192.00i q^{4} +(-66844.3 - 40439.5i) q^{5} +102849. q^{6} +(-657264. - 657264. i) q^{7} +(-524288. + 524288. i) q^{8} +3.49171e6i q^{9} +(-1.68991e6 - 6.86616e6i) q^{10} -3.22749e7 q^{11} +(6.58235e6 + 6.58235e6i) q^{12} +(6.03964e7 - 6.03964e7i) q^{13} -8.41298e7i q^{14} +(-8.62036e7 + 2.12165e7i) q^{15} -6.71089e7 q^{16} +(-4.71953e8 - 4.71953e8i) q^{17} +(-2.23470e8 + 2.23470e8i) q^{18} -1.04276e8i q^{19} +(3.31280e8 - 5.47589e8i) q^{20} -1.05624e9 q^{21} +(-2.06559e9 - 2.06559e9i) q^{22} +(1.62414e8 - 1.62414e8i) q^{23} +8.42541e8i q^{24} +(2.83281e9 + 5.40630e9i) q^{25} +7.73074e9 q^{26} +(6.64879e9 + 6.64879e9i) q^{27} +(5.38431e9 - 5.38431e9i) q^{28} +1.93503e10i q^{29} +(-6.87489e9 - 4.15917e9i) q^{30} +2.02592e10 q^{31} +(-4.29497e9 - 4.29497e9i) q^{32} +(-2.59332e10 + 2.59332e10i) q^{33} -6.04100e10i q^{34} +(1.73549e10 + 7.05138e10i) q^{35} -2.86041e10 q^{36} +(-5.96741e10 - 5.96741e10i) q^{37} +(6.67369e9 - 6.67369e9i) q^{38} -9.70582e10i q^{39} +(5.62476e10 - 1.38437e10i) q^{40} +5.92311e9 q^{41} +(-6.75991e10 - 6.75991e10i) q^{42} +(-2.19515e11 + 2.19515e11i) q^{43} -2.64396e11i q^{44} +(1.41203e11 - 2.33401e11i) q^{45} +2.07890e10 q^{46} +(8.05628e10 + 8.05628e10i) q^{47} +(-5.39226e10 + 5.39226e10i) q^{48} +1.85769e11i q^{49} +(-1.64703e11 + 5.27303e11i) q^{50} -7.58438e11 q^{51} +(4.94767e11 + 4.94767e11i) q^{52} +(8.11926e11 - 8.11926e11i) q^{53} +8.51045e11i q^{54} +(2.15739e12 + 1.30518e12i) q^{55} +6.89191e11 q^{56} +(-8.37871e10 - 8.37871e10i) q^{57} +(-1.23842e12 + 1.23842e12i) q^{58} -2.98543e12i q^{59} +(-1.73806e11 - 7.06180e11i) q^{60} -1.20995e12 q^{61} +(1.29659e12 + 1.29659e12i) q^{62} +(2.29498e12 - 2.29498e12i) q^{63} -5.49756e11i q^{64} +(-6.47955e12 + 1.59476e12i) q^{65} -3.31945e12 q^{66} +(-2.14532e12 - 2.14532e12i) q^{67} +(3.86624e12 - 3.86624e12i) q^{68} -2.61002e11i q^{69} +(-3.40217e12 + 5.62360e12i) q^{70} -1.46929e13 q^{71} +(-1.83066e12 - 1.83066e12i) q^{72} +(1.07590e13 - 1.07590e13i) q^{73} -7.63829e12i q^{74} +(6.62021e12 + 2.06783e12i) q^{75} +8.54232e11 q^{76} +(2.12131e13 + 2.12131e13i) q^{77} +(6.21172e12 - 6.21172e12i) q^{78} +1.48621e13i q^{79} +(4.48585e12 + 2.71385e12i) q^{80} -6.01602e12 q^{81} +(3.79079e11 + 3.79079e11i) q^{82} +(-4.77351e12 + 4.77351e12i) q^{83} -8.65269e12i q^{84} +(1.24618e13 + 5.06329e13i) q^{85} -2.80979e13 q^{86} +(1.55481e13 + 1.55481e13i) q^{87} +(1.69213e13 - 1.69213e13i) q^{88} -6.04797e13i q^{89} +(2.39747e13 - 5.90068e12i) q^{90} -7.93927e13 q^{91} +(1.33050e12 + 1.33050e12i) q^{92} +(1.62785e13 - 1.62785e13i) q^{93} +1.03120e13i q^{94} +(-4.21689e12 + 6.97029e12i) q^{95} -6.90210e12 q^{96} +(3.52779e12 + 3.52779e12i) q^{97} +(-1.18892e13 + 1.18892e13i) q^{98} -1.12695e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8} - 9034240 q^{10} + 8181256 q^{11} + 11501568 q^{12} - 10529136 q^{13} + 721621020 q^{15} - 536870912 q^{16} - 1669855424 q^{17} + 2079049728 q^{18} - 330137600 q^{20} + 192520776 q^{21} + 523600384 q^{22} - 4778918036 q^{23} + 15448124800 q^{25} - 1347729408 q^{26} - 20842498800 q^{27} - 10922196992 q^{28} + 48428597760 q^{30} + 35788345016 q^{31} - 34359738368 q^{32} - 130209466872 q^{33} - 30069746420 q^{35} + 266118365184 q^{36} - 31454650344 q^{37} - 100622935040 q^{38} + 31750881280 q^{40} + 94198718056 q^{41} + 12321329664 q^{42} - 942463128516 q^{43} + 2927734430100 q^{45} - 611701508608 q^{46} - 1797815170164 q^{47} - 94220845056 q^{48} + 712475699200 q^{50} - 1982287069224 q^{51} - 86254682112 q^{52} + 540438256184 q^{53} + 788235527880 q^{55} - 1398041214976 q^{56} + 6485834218080 q^{57} - 841739223040 q^{58} + 287341117440 q^{60} - 19913995236984 q^{61} + 2290454081024 q^{62} + 25848827893644 q^{63} - 7034160749880 q^{65} - 16666811759616 q^{66} + 13553624120956 q^{67} + 13679455633408 q^{68} - 16955995571200 q^{70} - 51541518798664 q^{71} + 17031575371776 q^{72} + 44383738947944 q^{73} - 19405526378100 q^{75} - 12879735685120 q^{76} + 74886492270632 q^{77} + 66217996893696 q^{78} + 6768600023040 q^{80} - 322723412222112 q^{81} + 6028717955584 q^{82} + 134272999400364 q^{83} + 145335752004880 q^{85} - 120635280450048 q^{86} + 68423417580480 q^{87} - 4289334345728 q^{88} + 112569467389440 q^{90} - 234891728536584 q^{91} - 39148896550912 q^{92} + 66751748435208 q^{93} + 26760204832400 q^{95} - 12060268167168 q^{96} + 167451300858216 q^{97} + 78801761769472 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 64.0000 + 64.0000i 0.500000 + 0.500000i
\(3\) 803.510 803.510i 0.367403 0.367403i −0.499126 0.866529i \(-0.666346\pi\)
0.866529 + 0.499126i \(0.166346\pi\)
\(4\) 8192.00i 0.500000i
\(5\) −66844.3 40439.5i −0.855607 0.517626i
\(6\) 102849. 0.367403
\(7\) −657264. 657264.i −0.798093 0.798093i 0.184701 0.982795i \(-0.440868\pi\)
−0.982795 + 0.184701i \(0.940868\pi\)
\(8\) −524288. + 524288.i −0.250000 + 0.250000i
\(9\) 3.49171e6i 0.730030i
\(10\) −1.68991e6 6.86616e6i −0.168991 0.686616i
\(11\) −3.22749e7 −1.65621 −0.828106 0.560572i \(-0.810581\pi\)
−0.828106 + 0.560572i \(0.810581\pi\)
\(12\) 6.58235e6 + 6.58235e6i 0.183701 + 0.183701i
\(13\) 6.03964e7 6.03964e7i 0.962515 0.962515i −0.0368076 0.999322i \(-0.511719\pi\)
0.999322 + 0.0368076i \(0.0117189\pi\)
\(14\) 8.41298e7i 0.798093i
\(15\) −8.62036e7 + 2.12165e7i −0.504529 + 0.124175i
\(16\) −6.71089e7 −0.250000
\(17\) −4.71953e8 4.71953e8i −1.15015 1.15015i −0.986521 0.163634i \(-0.947679\pi\)
−0.163634 0.986521i \(-0.552321\pi\)
\(18\) −2.23470e8 + 2.23470e8i −0.365015 + 0.365015i
\(19\) 1.04276e8i 0.116657i −0.998297 0.0583285i \(-0.981423\pi\)
0.998297 0.0583285i \(-0.0185771\pi\)
\(20\) 3.31280e8 5.47589e8i 0.258813 0.427804i
\(21\) −1.05624e9 −0.586443
\(22\) −2.06559e9 2.06559e9i −0.828106 0.828106i
\(23\) 1.62414e8 1.62414e8i 0.0477011 0.0477011i −0.682854 0.730555i \(-0.739261\pi\)
0.730555 + 0.682854i \(0.239261\pi\)
\(24\) 8.42541e8i 0.183701i
\(25\) 2.83281e9 + 5.40630e9i 0.464128 + 0.885768i
\(26\) 7.73074e9 0.962515
\(27\) 6.64879e9 + 6.64879e9i 0.635618 + 0.635618i
\(28\) 5.38431e9 5.38431e9i 0.399047 0.399047i
\(29\) 1.93503e10i 1.12176i 0.827896 + 0.560882i \(0.189538\pi\)
−0.827896 + 0.560882i \(0.810462\pi\)
\(30\) −6.87489e9 4.15917e9i −0.314352 0.190177i
\(31\) 2.02592e10 0.736360 0.368180 0.929754i \(-0.379981\pi\)
0.368180 + 0.929754i \(0.379981\pi\)
\(32\) −4.29497e9 4.29497e9i −0.125000 0.125000i
\(33\) −2.59332e10 + 2.59332e10i −0.608497 + 0.608497i
\(34\) 6.04100e10i 1.15015i
\(35\) 1.73549e10 + 7.05138e10i 0.269741 + 1.09597i
\(36\) −2.86041e10 −0.365015
\(37\) −5.96741e10 5.96741e10i −0.628599 0.628599i 0.319116 0.947716i \(-0.396614\pi\)
−0.947716 + 0.319116i \(0.896614\pi\)
\(38\) 6.67369e9 6.67369e9i 0.0583285 0.0583285i
\(39\) 9.70582e10i 0.707261i
\(40\) 5.62476e10 1.38437e10i 0.343308 0.0844954i
\(41\) 5.92311e9 0.0304133 0.0152066 0.999884i \(-0.495159\pi\)
0.0152066 + 0.999884i \(0.495159\pi\)
\(42\) −6.75991e10 6.75991e10i −0.293222 0.293222i
\(43\) −2.19515e11 + 2.19515e11i −0.807579 + 0.807579i −0.984267 0.176688i \(-0.943462\pi\)
0.176688 + 0.984267i \(0.443462\pi\)
\(44\) 2.64396e11i 0.828106i
\(45\) 1.41203e11 2.33401e11i 0.377882 0.624619i
\(46\) 2.07890e10 0.0477011
\(47\) 8.05628e10 + 8.05628e10i 0.159019 + 0.159019i 0.782132 0.623113i \(-0.214132\pi\)
−0.623113 + 0.782132i \(0.714132\pi\)
\(48\) −5.39226e10 + 5.39226e10i −0.0918507 + 0.0918507i
\(49\) 1.85769e11i 0.273906i
\(50\) −1.64703e11 + 5.27303e11i −0.210820 + 0.674948i
\(51\) −7.58438e11 −0.845140
\(52\) 4.94767e11 + 4.94767e11i 0.481257 + 0.481257i
\(53\) 8.11926e11 8.11926e11i 0.691171 0.691171i −0.271319 0.962490i \(-0.587460\pi\)
0.962490 + 0.271319i \(0.0874597\pi\)
\(54\) 8.51045e11i 0.635618i
\(55\) 2.15739e12 + 1.30518e12i 1.41707 + 0.857298i
\(56\) 6.89191e11 0.399047
\(57\) −8.37871e10 8.37871e10i −0.0428601 0.0428601i
\(58\) −1.23842e12 + 1.23842e12i −0.560882 + 0.560882i
\(59\) 2.98543e12i 1.19962i −0.800144 0.599808i \(-0.795244\pi\)
0.800144 0.599808i \(-0.204756\pi\)
\(60\) −1.73806e11 7.06180e11i −0.0620877 0.252265i
\(61\) −1.20995e12 −0.384997 −0.192499 0.981297i \(-0.561659\pi\)
−0.192499 + 0.981297i \(0.561659\pi\)
\(62\) 1.29659e12 + 1.29659e12i 0.368180 + 0.368180i
\(63\) 2.29498e12 2.29498e12i 0.582632 0.582632i
\(64\) 5.49756e11i 0.125000i
\(65\) −6.47955e12 + 1.59476e12i −1.32176 + 0.325312i
\(66\) −3.31945e12 −0.608497
\(67\) −2.14532e12 2.14532e12i −0.353971 0.353971i 0.507614 0.861585i \(-0.330528\pi\)
−0.861585 + 0.507614i \(0.830528\pi\)
\(68\) 3.86624e12 3.86624e12i 0.575077 0.575077i
\(69\) 2.61002e11i 0.0350510i
\(70\) −3.40217e12 + 5.62360e12i −0.413113 + 0.682854i
\(71\) −1.46929e13 −1.61547 −0.807737 0.589543i \(-0.799308\pi\)
−0.807737 + 0.589543i \(0.799308\pi\)
\(72\) −1.83066e12 1.83066e12i −0.182508 0.182508i
\(73\) 1.07590e13 1.07590e13i 0.973897 0.973897i −0.0257706 0.999668i \(-0.508204\pi\)
0.999668 + 0.0257706i \(0.00820395\pi\)
\(74\) 7.63829e12i 0.628599i
\(75\) 6.62021e12 + 2.06783e12i 0.495955 + 0.154912i
\(76\) 8.54232e11 0.0583285
\(77\) 2.12131e13 + 2.12131e13i 1.32181 + 1.32181i
\(78\) 6.21172e12 6.21172e12i 0.353631 0.353631i
\(79\) 1.48621e13i 0.773908i 0.922099 + 0.386954i \(0.126473\pi\)
−0.922099 + 0.386954i \(0.873527\pi\)
\(80\) 4.48585e12 + 2.71385e12i 0.213902 + 0.129406i
\(81\) −6.01602e12 −0.262975
\(82\) 3.79079e11 + 3.79079e11i 0.0152066 + 0.0152066i
\(83\) −4.77351e12 + 4.77351e12i −0.175910 + 0.175910i −0.789570 0.613660i \(-0.789697\pi\)
0.613660 + 0.789570i \(0.289697\pi\)
\(84\) 8.65269e12i 0.293222i
\(85\) 1.24618e13 + 5.06329e13i 0.388731 + 1.57943i
\(86\) −2.80979e13 −0.807579
\(87\) 1.55481e13 + 1.55481e13i 0.412139 + 0.412139i
\(88\) 1.69213e13 1.69213e13i 0.414053 0.414053i
\(89\) 6.04797e13i 1.36735i −0.729787 0.683675i \(-0.760381\pi\)
0.729787 0.683675i \(-0.239619\pi\)
\(90\) 2.39747e13 5.90068e12i 0.501251 0.123368i
\(91\) −7.93927e13 −1.53635
\(92\) 1.33050e12 + 1.33050e12i 0.0238506 + 0.0238506i
\(93\) 1.62785e13 1.62785e13i 0.270541 0.270541i
\(94\) 1.03120e13i 0.159019i
\(95\) −4.21689e12 + 6.97029e12i −0.0603847 + 0.0998126i
\(96\) −6.90210e12 −0.0918507
\(97\) 3.52779e12 + 3.52779e12i 0.0436617 + 0.0436617i 0.728601 0.684939i \(-0.240171\pi\)
−0.684939 + 0.728601i \(0.740171\pi\)
\(98\) −1.18892e13 + 1.18892e13i −0.136953 + 0.136953i
\(99\) 1.12695e14i 1.20909i
\(100\) −4.42884e13 + 2.32064e13i −0.442884 + 0.232064i
\(101\) −2.44883e13 −0.228406 −0.114203 0.993457i \(-0.536432\pi\)
−0.114203 + 0.993457i \(0.536432\pi\)
\(102\) −4.85400e13 4.85400e13i −0.422570 0.422570i
\(103\) 2.49581e13 2.49581e13i 0.202932 0.202932i −0.598323 0.801255i \(-0.704166\pi\)
0.801255 + 0.598323i \(0.204166\pi\)
\(104\) 6.33302e13i 0.481257i
\(105\) 7.06034e13 + 4.27137e13i 0.501765 + 0.303558i
\(106\) 1.03927e14 0.691171
\(107\) −4.22212e13 4.22212e13i −0.262932 0.262932i 0.563312 0.826244i \(-0.309527\pi\)
−0.826244 + 0.563312i \(0.809527\pi\)
\(108\) −5.44669e13 + 5.44669e13i −0.317809 + 0.317809i
\(109\) 2.61457e14i 1.43026i −0.698993 0.715128i \(-0.746368\pi\)
0.698993 0.715128i \(-0.253632\pi\)
\(110\) 5.45416e13 + 2.21605e14i 0.279885 + 1.13718i
\(111\) −9.58975e13 −0.461898
\(112\) 4.41082e13 + 4.41082e13i 0.199523 + 0.199523i
\(113\) −7.69947e13 + 7.69947e13i −0.327274 + 0.327274i −0.851549 0.524275i \(-0.824336\pi\)
0.524275 + 0.851549i \(0.324336\pi\)
\(114\) 1.07248e13i 0.0428601i
\(115\) −1.74244e13 + 4.28851e12i −0.0655047 + 0.0161221i
\(116\) −1.58518e14 −0.560882
\(117\) 2.10887e14 + 2.10887e14i 0.702665 + 0.702665i
\(118\) 1.91067e14 1.91067e14i 0.599808 0.599808i
\(119\) 6.20395e14i 1.83586i
\(120\) 3.40719e13 5.63191e13i 0.0950885 0.157176i
\(121\) 6.61918e14 1.74304
\(122\) −7.74367e13 7.74367e13i −0.192499 0.192499i
\(123\) 4.75928e12 4.75928e12i 0.0111739 0.0111739i
\(124\) 1.65963e14i 0.368180i
\(125\) 2.92708e13 4.75938e14i 0.0613854 0.998114i
\(126\) 2.93757e14 0.582632
\(127\) −3.49275e14 3.49275e14i −0.655454 0.655454i 0.298847 0.954301i \(-0.403398\pi\)
−0.954301 + 0.298847i \(0.903398\pi\)
\(128\) 3.51844e13 3.51844e13i 0.0625000 0.0625000i
\(129\) 3.52765e14i 0.593413i
\(130\) −5.16756e14 3.12627e14i −0.823535 0.498222i
\(131\) −1.18659e15 −1.79227 −0.896133 0.443786i \(-0.853635\pi\)
−0.896133 + 0.443786i \(0.853635\pi\)
\(132\) −2.12445e14 2.12445e14i −0.304248 0.304248i
\(133\) −6.85371e13 + 6.85371e13i −0.0931032 + 0.0931032i
\(134\) 2.74600e14i 0.353971i
\(135\) −1.75560e14 7.13307e14i −0.214827 0.872851i
\(136\) 4.94879e14 0.575077
\(137\) 8.96275e14 + 8.96275e14i 0.989457 + 0.989457i 0.999945 0.0104876i \(-0.00333838\pi\)
−0.0104876 + 0.999945i \(0.503338\pi\)
\(138\) 1.67042e13 1.67042e13i 0.0175255 0.0175255i
\(139\) 6.49657e14i 0.648008i −0.946056 0.324004i \(-0.894971\pi\)
0.946056 0.324004i \(-0.105029\pi\)
\(140\) −5.77649e14 + 1.42172e14i −0.547984 + 0.134870i
\(141\) 1.29466e14 0.116848
\(142\) −9.40348e14 9.40348e14i −0.807737 0.807737i
\(143\) −1.94929e15 + 1.94929e15i −1.59413 + 1.59413i
\(144\) 2.34325e14i 0.182508i
\(145\) 7.82516e14 1.29346e15i 0.580653 0.959789i
\(146\) 1.37716e15 0.973897
\(147\) 1.49267e14 + 1.49267e14i 0.100634 + 0.100634i
\(148\) 4.88850e14 4.88850e14i 0.314300 0.314300i
\(149\) 2.17503e15i 1.33402i 0.745050 + 0.667008i \(0.232425\pi\)
−0.745050 + 0.667008i \(0.767575\pi\)
\(150\) 2.91352e14 + 5.56034e14i 0.170522 + 0.325434i
\(151\) 2.45470e15 1.37139 0.685693 0.727891i \(-0.259499\pi\)
0.685693 + 0.727891i \(0.259499\pi\)
\(152\) 5.46709e13 + 5.46709e13i 0.0291643 + 0.0291643i
\(153\) 1.64792e15 1.64792e15i 0.839648 0.839648i
\(154\) 2.71528e15i 1.32181i
\(155\) −1.35421e15 8.19272e14i −0.630035 0.381159i
\(156\) 7.95100e14 0.353631
\(157\) 6.05092e14 + 6.05092e14i 0.257350 + 0.257350i 0.823975 0.566626i \(-0.191751\pi\)
−0.566626 + 0.823975i \(0.691751\pi\)
\(158\) −9.51172e14 + 9.51172e14i −0.386954 + 0.386954i
\(159\) 1.30478e15i 0.507876i
\(160\) 1.13408e14 + 4.60780e14i 0.0422477 + 0.171654i
\(161\) −2.13498e14 −0.0761399
\(162\) −3.85026e14 3.85026e14i −0.131487 0.131487i
\(163\) −2.75781e15 + 2.75781e15i −0.902091 + 0.902091i −0.995617 0.0935255i \(-0.970186\pi\)
0.0935255 + 0.995617i \(0.470186\pi\)
\(164\) 4.85221e13i 0.0152066i
\(165\) 2.78221e15 6.84761e14i 0.835608 0.205661i
\(166\) −6.11010e14 −0.175910
\(167\) −2.23202e15 2.23202e15i −0.616145 0.616145i 0.328395 0.944540i \(-0.393492\pi\)
−0.944540 + 0.328395i \(0.893492\pi\)
\(168\) 5.53772e14 5.53772e14i 0.146611 0.146611i
\(169\) 3.35807e15i 0.852870i
\(170\) −2.44295e15 + 4.03806e15i −0.595350 + 0.984081i
\(171\) 3.64103e14 0.0851632
\(172\) −1.79827e15 1.79827e15i −0.403789 0.403789i
\(173\) −2.01216e15 + 2.01216e15i −0.433851 + 0.433851i −0.889936 0.456085i \(-0.849251\pi\)
0.456085 + 0.889936i \(0.349251\pi\)
\(174\) 1.99016e15i 0.412139i
\(175\) 1.69146e15 5.41527e15i 0.336509 1.07734i
\(176\) 2.16593e15 0.414053
\(177\) −2.39882e15 2.39882e15i −0.440742 0.440742i
\(178\) 3.87070e15 3.87070e15i 0.683675 0.683675i
\(179\) 3.89718e15i 0.661879i −0.943652 0.330940i \(-0.892634\pi\)
0.943652 0.330940i \(-0.107366\pi\)
\(180\) 1.91202e15 + 1.15674e15i 0.312310 + 0.188941i
\(181\) −5.53039e15 −0.868973 −0.434486 0.900678i \(-0.643070\pi\)
−0.434486 + 0.900678i \(0.643070\pi\)
\(182\) −5.08114e15 5.08114e15i −0.768177 0.768177i
\(183\) −9.72205e14 + 9.72205e14i −0.141449 + 0.141449i
\(184\) 1.70303e14i 0.0238506i
\(185\) 1.57568e15 + 6.40207e15i 0.212455 + 0.863213i
\(186\) 2.08364e15 0.270541
\(187\) 1.52322e16 + 1.52322e16i 1.90490 + 1.90490i
\(188\) −6.59971e14 + 6.59971e14i −0.0795096 + 0.0795096i
\(189\) 8.74002e15i 1.01456i
\(190\) −7.15979e14 + 1.76218e14i −0.0800986 + 0.0197140i
\(191\) −1.55732e16 −1.67936 −0.839679 0.543082i \(-0.817257\pi\)
−0.839679 + 0.543082i \(0.817257\pi\)
\(192\) −4.41734e14 4.41734e14i −0.0459253 0.0459253i
\(193\) 2.69767e15 2.69767e15i 0.270450 0.270450i −0.558831 0.829281i \(-0.688750\pi\)
0.829281 + 0.558831i \(0.188750\pi\)
\(194\) 4.51557e14i 0.0436617i
\(195\) −3.92498e15 + 6.48779e15i −0.366096 + 0.605138i
\(196\) −1.52182e15 −0.136953
\(197\) 1.36065e16 + 1.36065e16i 1.18163 + 1.18163i 0.979322 + 0.202310i \(0.0648448\pi\)
0.202310 + 0.979322i \(0.435155\pi\)
\(198\) 7.21246e15 7.21246e15i 0.604543 0.604543i
\(199\) 1.18868e16i 0.961818i 0.876770 + 0.480909i \(0.159693\pi\)
−0.876770 + 0.480909i \(0.840307\pi\)
\(200\) −4.31967e15 1.34925e15i −0.337474 0.105410i
\(201\) −3.44756e15 −0.260100
\(202\) −1.56725e15 1.56725e15i −0.114203 0.114203i
\(203\) 1.27182e16 1.27182e16i 0.895272 0.895272i
\(204\) 6.21312e15i 0.422570i
\(205\) −3.95926e14 2.39528e14i −0.0260218 0.0157427i
\(206\) 3.19463e15 0.202932
\(207\) 5.67103e14 + 5.67103e14i 0.0348233 + 0.0348233i
\(208\) −4.05313e15 + 4.05313e15i −0.240629 + 0.240629i
\(209\) 3.36551e15i 0.193209i
\(210\) 1.78494e15 + 7.25229e15i 0.0991035 + 0.402662i
\(211\) 3.57939e15 0.192235 0.0961173 0.995370i \(-0.469358\pi\)
0.0961173 + 0.995370i \(0.469358\pi\)
\(212\) 6.65130e15 + 6.65130e15i 0.345585 + 0.345585i
\(213\) −1.18059e16 + 1.18059e16i −0.593530 + 0.593530i
\(214\) 5.40431e15i 0.262932i
\(215\) 2.35504e16 5.79625e15i 1.10899 0.272947i
\(216\) −6.97176e15 −0.317809
\(217\) −1.33156e16 1.33156e16i −0.587684 0.587684i
\(218\) 1.67332e16 1.67332e16i 0.715128 0.715128i
\(219\) 1.72900e16i 0.715625i
\(220\) −1.06920e16 + 1.76734e16i −0.428649 + 0.708533i
\(221\) −5.70085e16 −2.21408
\(222\) −6.13744e15 6.13744e15i −0.230949 0.230949i
\(223\) 1.59754e16 1.59754e16i 0.582530 0.582530i −0.353068 0.935598i \(-0.614862\pi\)
0.935598 + 0.353068i \(0.114862\pi\)
\(224\) 5.64586e15i 0.199523i
\(225\) −1.88773e16 + 9.89136e15i −0.646638 + 0.338827i
\(226\) −9.85532e15 −0.327274
\(227\) −1.72932e16 1.72932e16i −0.556793 0.556793i 0.371600 0.928393i \(-0.378809\pi\)
−0.928393 + 0.371600i \(0.878809\pi\)
\(228\) 6.86384e14 6.86384e14i 0.0214301 0.0214301i
\(229\) 2.08347e16i 0.630868i −0.948948 0.315434i \(-0.897850\pi\)
0.948948 0.315434i \(-0.102150\pi\)
\(230\) −1.38963e15 8.40696e14i −0.0408134 0.0246913i
\(231\) 3.40899e16 0.971274
\(232\) −1.01451e16 1.01451e16i −0.280441 0.280441i
\(233\) 1.59507e16 1.59507e16i 0.427847 0.427847i −0.460048 0.887894i \(-0.652168\pi\)
0.887894 + 0.460048i \(0.152168\pi\)
\(234\) 2.69935e16i 0.702665i
\(235\) −2.12725e15 8.64309e15i −0.0537456 0.218370i
\(236\) 2.44566e16 0.599808
\(237\) 1.19418e16 + 1.19418e16i 0.284336 + 0.284336i
\(238\) −3.97053e16 + 3.97053e16i −0.917931 + 0.917931i
\(239\) 1.56773e16i 0.351954i 0.984394 + 0.175977i \(0.0563085\pi\)
−0.984394 + 0.175977i \(0.943692\pi\)
\(240\) 5.78503e15 1.42382e15i 0.126132 0.0310439i
\(241\) 3.45641e16 0.731991 0.365996 0.930617i \(-0.380729\pi\)
0.365996 + 0.930617i \(0.380729\pi\)
\(242\) 4.23628e16 + 4.23628e16i 0.871519 + 0.871519i
\(243\) −3.66349e16 + 3.66349e16i −0.732236 + 0.732236i
\(244\) 9.91189e15i 0.192499i
\(245\) 7.51241e15 1.24176e16i 0.141780 0.234356i
\(246\) 6.09188e14 0.0111739
\(247\) −6.29792e15 6.29792e15i −0.112284 0.112284i
\(248\) −1.06217e16 + 1.06217e16i −0.184090 + 0.184090i
\(249\) 7.67113e15i 0.129260i
\(250\) 3.23334e16 2.85867e16i 0.529750 0.468364i
\(251\) 1.06204e17 1.69210 0.846051 0.533102i \(-0.178974\pi\)
0.846051 + 0.533102i \(0.178974\pi\)
\(252\) 1.88005e16 + 1.88005e16i 0.291316 + 0.291316i
\(253\) −5.24189e15 + 5.24189e15i −0.0790031 + 0.0790031i
\(254\) 4.47073e16i 0.655454i
\(255\) 5.06972e16 + 3.06708e16i 0.723108 + 0.437466i
\(256\) 4.50360e15 0.0625000
\(257\) −2.42209e16 2.42209e16i −0.327084 0.327084i 0.524393 0.851477i \(-0.324292\pi\)
−0.851477 + 0.524393i \(0.824292\pi\)
\(258\) −2.25769e16 + 2.25769e16i −0.296707 + 0.296707i
\(259\) 7.84433e16i 1.00336i
\(260\) −1.30642e16 5.30805e16i −0.162656 0.660878i
\(261\) −6.75656e16 −0.818922
\(262\) −7.59419e16 7.59419e16i −0.896133 0.896133i
\(263\) −5.11732e16 + 5.11732e16i −0.587966 + 0.587966i −0.937080 0.349114i \(-0.886483\pi\)
0.349114 + 0.937080i \(0.386483\pi\)
\(264\) 2.71929e16i 0.304248i
\(265\) −8.71065e16 + 2.14388e16i −0.949138 + 0.233603i
\(266\) −8.77275e15 −0.0931032
\(267\) −4.85960e16 4.85960e16i −0.502368 0.502368i
\(268\) 1.75744e16 1.75744e16i 0.176985 0.176985i
\(269\) 4.55495e16i 0.446908i −0.974715 0.223454i \(-0.928267\pi\)
0.974715 0.223454i \(-0.0717332\pi\)
\(270\) 3.44158e16 5.68875e16i 0.329012 0.543839i
\(271\) 8.13494e16 0.757825 0.378913 0.925432i \(-0.376298\pi\)
0.378913 + 0.925432i \(0.376298\pi\)
\(272\) 3.16722e16 + 3.16722e16i 0.287539 + 0.287539i
\(273\) −6.37928e16 + 6.37928e16i −0.564460 + 0.564460i
\(274\) 1.14723e17i 0.989457i
\(275\) −9.14286e16 1.74488e17i −0.768694 1.46702i
\(276\) 2.13813e15 0.0175255
\(277\) 1.76612e15 + 1.76612e15i 0.0141144 + 0.0141144i 0.714129 0.700014i \(-0.246823\pi\)
−0.700014 + 0.714129i \(0.746823\pi\)
\(278\) 4.15780e16 4.15780e16i 0.324004 0.324004i
\(279\) 7.07393e16i 0.537566i
\(280\) −4.60685e16 2.78706e16i −0.341427 0.206557i
\(281\) 1.55782e17 1.12609 0.563045 0.826426i \(-0.309630\pi\)
0.563045 + 0.826426i \(0.309630\pi\)
\(282\) 8.28583e15 + 8.28583e15i 0.0584241 + 0.0584241i
\(283\) 1.10583e17 1.10583e17i 0.760647 0.760647i −0.215792 0.976439i \(-0.569233\pi\)
0.976439 + 0.215792i \(0.0692333\pi\)
\(284\) 1.20365e17i 0.807737i
\(285\) 2.21238e15 + 8.98900e15i 0.0144859 + 0.0588569i
\(286\) −2.49509e17 −1.59413
\(287\) −3.89305e15 3.89305e15i −0.0242726 0.0242726i
\(288\) 1.49968e16 1.49968e16i 0.0912538 0.0912538i
\(289\) 2.77101e17i 1.64571i
\(290\) 1.32862e17 3.27002e16i 0.770221 0.189568i
\(291\) 5.66923e15 0.0320828
\(292\) 8.81380e16 + 8.81380e16i 0.486949 + 0.486949i
\(293\) 9.92848e16 9.92848e16i 0.535562 0.535562i −0.386660 0.922222i \(-0.626371\pi\)
0.922222 + 0.386660i \(0.126371\pi\)
\(294\) 1.91062e16i 0.100634i
\(295\) −1.20729e17 + 1.99559e17i −0.620952 + 1.02640i
\(296\) 6.25728e16 0.314300
\(297\) −2.14589e17 2.14589e17i −1.05272 1.05272i
\(298\) −1.39202e17 + 1.39202e17i −0.667008 + 0.667008i
\(299\) 1.96184e16i 0.0918261i
\(300\) −1.69396e16 + 5.42327e16i −0.0774560 + 0.247978i
\(301\) 2.88559e17 1.28905
\(302\) 1.57101e17 + 1.57101e17i 0.685693 + 0.685693i
\(303\) −1.96766e16 + 1.96766e16i −0.0839172 + 0.0839172i
\(304\) 6.99787e15i 0.0291643i
\(305\) 8.08781e16 + 4.89297e16i 0.329407 + 0.199284i
\(306\) 2.10934e17 0.839648
\(307\) 7.50777e16 + 7.50777e16i 0.292107 + 0.292107i 0.837912 0.545805i \(-0.183776\pi\)
−0.545805 + 0.837912i \(0.683776\pi\)
\(308\) −1.73778e17 + 1.73778e17i −0.660906 + 0.660906i
\(309\) 4.01081e16i 0.149115i
\(310\) −3.42362e16 1.39103e17i −0.124438 0.505597i
\(311\) −3.72883e17 −1.32510 −0.662552 0.749016i \(-0.730527\pi\)
−0.662552 + 0.749016i \(0.730527\pi\)
\(312\) 5.08864e16 + 5.08864e16i 0.176815 + 0.176815i
\(313\) 2.68205e17 2.68205e17i 0.911289 0.911289i −0.0850850 0.996374i \(-0.527116\pi\)
0.996374 + 0.0850850i \(0.0271162\pi\)
\(314\) 7.74518e16i 0.257350i
\(315\) −2.46214e17 + 6.05985e16i −0.800090 + 0.196919i
\(316\) −1.21750e17 −0.386954
\(317\) 1.52004e17 + 1.52004e17i 0.472542 + 0.472542i 0.902736 0.430194i \(-0.141555\pi\)
−0.430194 + 0.902736i \(0.641555\pi\)
\(318\) 8.35060e16 8.35060e16i 0.253938 0.253938i
\(319\) 6.24528e17i 1.85788i
\(320\) −2.22318e16 + 3.67481e16i −0.0647032 + 0.106951i
\(321\) −6.78503e16 −0.193204
\(322\) −1.36639e16 1.36639e16i −0.0380699 0.0380699i
\(323\) −4.92136e16 + 4.92136e16i −0.134174 + 0.134174i
\(324\) 4.92833e16i 0.131487i
\(325\) 4.97612e17 + 1.55430e17i 1.29929 + 0.405836i
\(326\) −3.52999e17 −0.902091
\(327\) −2.10083e17 2.10083e17i −0.525480 0.525480i
\(328\) −3.10542e15 + 3.10542e15i −0.00760331 + 0.00760331i
\(329\) 1.05902e17i 0.253824i
\(330\) 2.21886e17 + 1.34237e17i 0.520634 + 0.314973i
\(331\) −5.28017e17 −1.21297 −0.606487 0.795093i \(-0.707422\pi\)
−0.606487 + 0.795093i \(0.707422\pi\)
\(332\) −3.91046e16 3.91046e16i −0.0879552 0.0879552i
\(333\) 2.08365e17 2.08365e17i 0.458897 0.458897i
\(334\) 2.85699e17i 0.616145i
\(335\) 5.66467e16 + 2.30158e17i 0.119636 + 0.486085i
\(336\) 7.08828e16 0.146611
\(337\) 3.24151e16 + 3.24151e16i 0.0656656 + 0.0656656i 0.739177 0.673511i \(-0.235215\pi\)
−0.673511 + 0.739177i \(0.735215\pi\)
\(338\) 2.14916e17 2.14916e17i 0.426435 0.426435i
\(339\) 1.23732e17i 0.240483i
\(340\) −4.14785e17 + 1.02087e17i −0.789715 + 0.194366i
\(341\) −6.53863e17 −1.21957
\(342\) 2.33026e16 + 2.33026e16i 0.0425816 + 0.0425816i
\(343\) −3.23672e17 + 3.23672e17i −0.579491 + 0.579491i
\(344\) 2.30178e17i 0.403789i
\(345\) −1.05548e16 + 1.74465e16i −0.0181433 + 0.0299899i
\(346\) −2.57557e17 −0.433851
\(347\) −1.72047e17 1.72047e17i −0.284015 0.284015i 0.550693 0.834708i \(-0.314364\pi\)
−0.834708 + 0.550693i \(0.814364\pi\)
\(348\) −1.27370e17 + 1.27370e17i −0.206069 + 0.206069i
\(349\) 8.19436e16i 0.129938i 0.997887 + 0.0649691i \(0.0206949\pi\)
−0.997887 + 0.0649691i \(0.979305\pi\)
\(350\) 4.54831e17 2.38324e17i 0.706926 0.370417i
\(351\) 8.03125e17 1.22358
\(352\) 1.38620e17 + 1.38620e17i 0.207026 + 0.207026i
\(353\) −4.75391e17 + 4.75391e17i −0.696030 + 0.696030i −0.963552 0.267522i \(-0.913795\pi\)
0.267522 + 0.963552i \(0.413795\pi\)
\(354\) 3.07049e17i 0.440742i
\(355\) 9.82139e17 + 5.94175e17i 1.38221 + 0.836211i
\(356\) 4.95450e17 0.683675
\(357\) 4.98494e17 + 4.98494e17i 0.674500 + 0.674500i
\(358\) 2.49419e17 2.49419e17i 0.330940 0.330940i
\(359\) 6.51435e17i 0.847637i 0.905747 + 0.423818i \(0.139311\pi\)
−0.905747 + 0.423818i \(0.860689\pi\)
\(360\) 4.83383e16 + 1.96401e17i 0.0616842 + 0.250625i
\(361\) 7.88133e17 0.986391
\(362\) −3.53945e17 3.53945e17i −0.434486 0.434486i
\(363\) 5.31858e17 5.31858e17i 0.640397 0.640397i
\(364\) 6.50385e17i 0.768177i
\(365\) −1.15427e18 + 2.84090e17i −1.33739 + 0.329159i
\(366\) −1.24442e17 −0.141449
\(367\) 1.93211e17 + 1.93211e17i 0.215461 + 0.215461i 0.806583 0.591121i \(-0.201315\pi\)
−0.591121 + 0.806583i \(0.701315\pi\)
\(368\) −1.08994e16 + 1.08994e16i −0.0119253 + 0.0119253i
\(369\) 2.06818e16i 0.0222026i
\(370\) −3.08888e17 + 5.10576e17i −0.325379 + 0.537834i
\(371\) −1.06730e18 −1.10324
\(372\) 1.33353e17 + 1.33353e17i 0.135270 + 0.135270i
\(373\) 9.45700e17 9.45700e17i 0.941438 0.941438i −0.0569399 0.998378i \(-0.518134\pi\)
0.998378 + 0.0569399i \(0.0181343\pi\)
\(374\) 1.94973e18i 1.90490i
\(375\) −3.58901e17 4.05940e17i −0.344157 0.389263i
\(376\) −8.44763e16 −0.0795096
\(377\) 1.16869e18 + 1.16869e18i 1.07971 + 1.07971i
\(378\) 5.59361e17 5.59361e17i 0.507282 0.507282i
\(379\) 6.91007e17i 0.615188i −0.951518 0.307594i \(-0.900476\pi\)
0.951518 0.307594i \(-0.0995239\pi\)
\(380\) −5.71006e16 3.45447e16i −0.0499063 0.0301923i
\(381\) −5.61292e17 −0.481631
\(382\) −9.96683e17 9.96683e17i −0.839679 0.839679i
\(383\) −1.04056e18 + 1.04056e18i −0.860750 + 0.860750i −0.991425 0.130675i \(-0.958285\pi\)
0.130675 + 0.991425i \(0.458285\pi\)
\(384\) 5.65420e16i 0.0459253i
\(385\) −5.60129e17 2.27582e18i −0.446748 1.81515i
\(386\) 3.45302e17 0.270450
\(387\) −7.66483e17 7.66483e17i −0.589557 0.589557i
\(388\) −2.88997e16 + 2.88997e16i −0.0218308 + 0.0218308i
\(389\) 1.61552e18i 1.19858i −0.800533 0.599288i \(-0.795450\pi\)
0.800533 0.599288i \(-0.204550\pi\)
\(390\) −6.66417e17 + 1.64019e17i −0.485617 + 0.119521i
\(391\) −1.53304e17 −0.109727
\(392\) −9.73965e16 9.73965e16i −0.0684764 0.0684764i
\(393\) −9.53438e17 + 9.53438e17i −0.658483 + 0.658483i
\(394\) 1.74163e18i 1.18163i
\(395\) 6.01014e17 9.93445e17i 0.400595 0.662162i
\(396\) 9.23194e17 0.604543
\(397\) −1.39748e18 1.39748e18i −0.899111 0.899111i 0.0962469 0.995357i \(-0.469316\pi\)
−0.995357 + 0.0962469i \(0.969316\pi\)
\(398\) −7.60754e17 + 7.60754e17i −0.480909 + 0.480909i
\(399\) 1.10141e17i 0.0684127i
\(400\) −1.90107e17 3.62811e17i −0.116032 0.221442i
\(401\) 3.14384e17 0.188560 0.0942800 0.995546i \(-0.469945\pi\)
0.0942800 + 0.995546i \(0.469945\pi\)
\(402\) −2.20644e17 2.20644e17i −0.130050 0.130050i
\(403\) 1.22358e18 1.22358e18i 0.708758 0.708758i
\(404\) 2.00608e17i 0.114203i
\(405\) 4.02137e17 + 2.43285e17i 0.225003 + 0.136123i
\(406\) 1.62794e18 0.895272
\(407\) 1.92597e18 + 1.92597e18i 1.04109 + 1.04109i
\(408\) 3.97640e17 3.97640e17i 0.211285 0.211285i
\(409\) 2.53540e18i 1.32429i 0.749375 + 0.662145i \(0.230354\pi\)
−0.749375 + 0.662145i \(0.769646\pi\)
\(410\) −1.00095e16 4.06691e16i −0.00513956 0.0208822i
\(411\) 1.44033e18 0.727059
\(412\) 2.04456e17 + 2.04456e17i 0.101466 + 0.101466i
\(413\) −1.96221e18 + 1.96221e18i −0.957406 + 0.957406i
\(414\) 7.25892e16i 0.0348233i
\(415\) 5.12121e17 1.26044e17i 0.241566 0.0594545i
\(416\) −5.18801e17 −0.240629
\(417\) −5.22006e17 5.22006e17i −0.238080 0.238080i
\(418\) −2.15393e17 + 2.15393e17i −0.0966044 + 0.0966044i
\(419\) 1.62469e18i 0.716592i −0.933608 0.358296i \(-0.883358\pi\)
0.933608 0.358296i \(-0.116642\pi\)
\(420\) −3.49910e17 + 5.78383e17i −0.151779 + 0.250883i
\(421\) 1.08059e18 0.460984 0.230492 0.973074i \(-0.425966\pi\)
0.230492 + 0.973074i \(0.425966\pi\)
\(422\) 2.29081e17 + 2.29081e17i 0.0961173 + 0.0961173i
\(423\) −2.81302e17 + 2.81302e17i −0.116089 + 0.116089i
\(424\) 8.51366e17i 0.345585i
\(425\) 1.21457e18 3.88847e18i 0.484952 1.55259i
\(426\) −1.51116e18 −0.593530
\(427\) 7.95255e17 + 7.95255e17i 0.307264 + 0.307264i
\(428\) 3.45876e17 3.45876e17i 0.131466 0.131466i
\(429\) 3.13254e18i 1.17137i
\(430\) 1.87819e18 + 1.13627e18i 0.690970 + 0.418023i
\(431\) 1.22714e18 0.444174 0.222087 0.975027i \(-0.428713\pi\)
0.222087 + 0.975027i \(0.428713\pi\)
\(432\) −4.46193e17 4.46193e17i −0.158904 0.158904i
\(433\) −2.81886e18 + 2.81886e18i −0.987775 + 0.987775i −0.999926 0.0121513i \(-0.996132\pi\)
0.0121513 + 0.999926i \(0.496132\pi\)
\(434\) 1.70440e18i 0.587684i
\(435\) −4.10546e17 1.66806e18i −0.139295 0.565963i
\(436\) 2.14185e18 0.715128
\(437\) −1.69359e16 1.69359e16i −0.00556467 0.00556467i
\(438\) 1.10656e18 1.10656e18i 0.357813 0.357813i
\(439\) 2.69036e18i 0.856166i 0.903739 + 0.428083i \(0.140811\pi\)
−0.903739 + 0.428083i \(0.859189\pi\)
\(440\) −1.81539e18 + 4.46805e17i −0.568591 + 0.139942i
\(441\) −6.48652e17 −0.199959
\(442\) −3.64854e18 3.64854e18i −1.10704 1.10704i
\(443\) −5.80048e17 + 5.80048e17i −0.173236 + 0.173236i −0.788399 0.615164i \(-0.789090\pi\)
0.615164 + 0.788399i \(0.289090\pi\)
\(444\) 7.85592e17i 0.230949i
\(445\) −2.44577e18 + 4.04272e18i −0.707775 + 1.16991i
\(446\) 2.04485e18 0.582530
\(447\) 1.74766e18 + 1.74766e18i 0.490121 + 0.490121i
\(448\) −3.61335e17 + 3.61335e17i −0.0997617 + 0.0997617i
\(449\) 4.56796e18i 1.24165i −0.783951 0.620823i \(-0.786799\pi\)
0.783951 0.620823i \(-0.213201\pi\)
\(450\) −1.84119e18 5.75097e17i −0.492733 0.153905i
\(451\) −1.91168e17 −0.0503708
\(452\) −6.30741e17 6.30741e17i −0.163637 0.163637i
\(453\) 1.97238e18 1.97238e18i 0.503851 0.503851i
\(454\) 2.21353e18i 0.556793i
\(455\) 5.30695e18 + 3.21060e18i 1.31451 + 0.795256i
\(456\) 8.78572e16 0.0214301
\(457\) −2.61088e18 2.61088e18i −0.627154 0.627154i 0.320197 0.947351i \(-0.396251\pi\)
−0.947351 + 0.320197i \(0.896251\pi\)
\(458\) 1.33342e18 1.33342e18i 0.315434 0.315434i
\(459\) 6.27583e18i 1.46212i
\(460\) −3.51315e16 1.42741e17i −0.00806105 0.0327524i
\(461\) −5.14453e18 −1.16262 −0.581312 0.813681i \(-0.697460\pi\)
−0.581312 + 0.813681i \(0.697460\pi\)
\(462\) 2.18175e18 + 2.18175e18i 0.485637 + 0.485637i
\(463\) −3.16003e18 + 3.16003e18i −0.692825 + 0.692825i −0.962853 0.270027i \(-0.912967\pi\)
0.270027 + 0.962853i \(0.412967\pi\)
\(464\) 1.29858e18i 0.280441i
\(465\) −1.74642e18 + 4.29830e17i −0.371516 + 0.0914378i
\(466\) 2.04169e18 0.427847
\(467\) −3.72214e18 3.72214e18i −0.768377 0.768377i 0.209444 0.977821i \(-0.432835\pi\)
−0.977821 + 0.209444i \(0.932835\pi\)
\(468\) −1.72758e18 + 1.72758e18i −0.351333 + 0.351333i
\(469\) 2.82008e18i 0.565004i
\(470\) 4.17014e17 6.89301e17i 0.0823124 0.136058i
\(471\) 9.72395e17 0.189102
\(472\) 1.56522e18 + 1.56522e18i 0.299904 + 0.299904i
\(473\) 7.08482e18 7.08482e18i 1.33752 1.33752i
\(474\) 1.52855e18i 0.284336i
\(475\) 5.63750e17 2.95395e17i 0.103331 0.0541437i
\(476\) −5.08228e18 −0.917931
\(477\) 2.83501e18 + 2.83501e18i 0.504576 + 0.504576i
\(478\) −1.00335e18 + 1.00335e18i −0.175977 + 0.175977i
\(479\) 4.65636e18i 0.804819i 0.915460 + 0.402409i \(0.131827\pi\)
−0.915460 + 0.402409i \(0.868173\pi\)
\(480\) 4.61366e17 + 2.79117e17i 0.0785881 + 0.0475443i
\(481\) −7.20820e18 −1.21007
\(482\) 2.21210e18 + 2.21210e18i 0.365996 + 0.365996i
\(483\) −1.71548e17 + 1.71548e17i −0.0279740 + 0.0279740i
\(484\) 5.42243e18i 0.871519i
\(485\) −9.31507e16 3.78475e17i −0.0147569 0.0599577i
\(486\) −4.68926e18 −0.732236
\(487\) 6.02307e17 + 6.02307e17i 0.0927075 + 0.0927075i 0.751940 0.659232i \(-0.229119\pi\)
−0.659232 + 0.751940i \(0.729119\pi\)
\(488\) 6.34361e17 6.34361e17i 0.0962493 0.0962493i
\(489\) 4.43185e18i 0.662862i
\(490\) 1.27552e18 3.13933e17i 0.188068 0.0462875i
\(491\) 7.52825e18 1.09427 0.547134 0.837045i \(-0.315719\pi\)
0.547134 + 0.837045i \(0.315719\pi\)
\(492\) 3.89880e16 + 3.89880e16i 0.00558696 + 0.00558696i
\(493\) 9.13242e18 9.13242e18i 1.29020 1.29020i
\(494\) 8.06133e17i 0.112284i
\(495\) −4.55731e18 + 7.53300e18i −0.625853 + 1.03450i
\(496\) −1.35957e18 −0.184090
\(497\) 9.65714e18 + 9.65714e18i 1.28930 + 1.28930i
\(498\) −4.90952e17 + 4.90952e17i −0.0646300 + 0.0646300i
\(499\) 1.39305e19i 1.80827i −0.427250 0.904134i \(-0.640517\pi\)
0.427250 0.904134i \(-0.359483\pi\)
\(500\) 3.89888e18 + 2.39787e17i 0.499057 + 0.0306927i
\(501\) −3.58690e18 −0.452747
\(502\) 6.79708e18 + 6.79708e18i 0.846051 + 0.846051i
\(503\) 3.16546e18 3.16546e18i 0.388562 0.388562i −0.485612 0.874174i \(-0.661403\pi\)
0.874174 + 0.485612i \(0.161403\pi\)
\(504\) 2.40646e18i 0.291316i
\(505\) 1.63690e18 + 9.90293e17i 0.195426 + 0.118229i
\(506\) −6.70962e17 −0.0790031
\(507\) −2.69824e18 2.69824e18i −0.313347 0.313347i
\(508\) 2.86126e18 2.86126e18i 0.327727 0.327727i
\(509\) 5.30902e18i 0.599777i −0.953974 0.299889i \(-0.903050\pi\)
0.953974 0.299889i \(-0.0969496\pi\)
\(510\) 1.28169e18 + 5.20756e18i 0.142821 + 0.580287i
\(511\) −1.41430e19 −1.55452
\(512\) 2.88230e17 + 2.88230e17i 0.0312500 + 0.0312500i
\(513\) 6.93312e17 6.93312e17i 0.0741493 0.0741493i
\(514\) 3.10028e18i 0.327084i
\(515\) −2.67760e18 + 6.59013e17i −0.278673 + 0.0685872i
\(516\) −2.88985e18 −0.296707
\(517\) −2.60016e18 2.60016e18i −0.263370 0.263370i
\(518\) −5.02037e18 + 5.02037e18i −0.501681 + 0.501681i
\(519\) 3.23358e18i 0.318796i
\(520\) 2.56104e18 4.23326e18i 0.249111 0.411767i
\(521\) 6.72471e18 0.645371 0.322686 0.946506i \(-0.395414\pi\)
0.322686 + 0.946506i \(0.395414\pi\)
\(522\) −4.32420e18 4.32420e18i −0.409461 0.409461i
\(523\) −9.16785e18 + 9.16785e18i −0.856556 + 0.856556i −0.990931 0.134374i \(-0.957098\pi\)
0.134374 + 0.990931i \(0.457098\pi\)
\(524\) 9.72056e18i 0.896133i
\(525\) −2.99212e18 5.71033e18i −0.272184 0.519453i
\(526\) −6.55017e18 −0.587966
\(527\) −9.56139e18 9.56139e18i −0.846928 0.846928i
\(528\) 1.74035e18 1.74035e18i 0.152124 0.152124i
\(529\) 1.15401e19i 0.995449i
\(530\) −6.94690e18 4.20274e18i −0.591371 0.357768i
\(531\) 1.04243e19 0.875756
\(532\) −5.61456e17 5.61456e17i −0.0465516 0.0465516i
\(533\) 3.57735e17 3.57735e17i 0.0292732 0.0292732i
\(534\) 6.22029e18i 0.502368i
\(535\) 1.11484e18 + 4.52965e18i 0.0888663 + 0.361067i
\(536\) 2.24953e18 0.176985
\(537\) −3.13142e18 3.13142e18i −0.243176 0.243176i
\(538\) 2.91517e18 2.91517e18i 0.223454 0.223454i
\(539\) 5.99567e18i 0.453646i
\(540\) 5.84341e18 1.43819e18i 0.436426 0.107414i
\(541\) 1.02681e19 0.757021 0.378511 0.925597i \(-0.376436\pi\)
0.378511 + 0.925597i \(0.376436\pi\)
\(542\) 5.20636e18 + 5.20636e18i 0.378913 + 0.378913i
\(543\) −4.44373e18 + 4.44373e18i −0.319263 + 0.319263i
\(544\) 4.05405e18i 0.287539i
\(545\) −1.05732e19 + 1.74769e19i −0.740337 + 1.22374i
\(546\) −8.16548e18 −0.564460
\(547\) −1.37514e19 1.37514e19i −0.938504 0.938504i 0.0597118 0.998216i \(-0.480982\pi\)
−0.998216 + 0.0597118i \(0.980982\pi\)
\(548\) −7.34228e18 + 7.34228e18i −0.494729 + 0.494729i
\(549\) 4.22479e18i 0.281060i
\(550\) 5.31578e18 1.70186e19i 0.349163 1.11786i
\(551\) 2.01778e18 0.130862
\(552\) 1.36840e17 + 1.36840e17i 0.00876276 + 0.00876276i
\(553\) 9.76830e18 9.76830e18i 0.617651 0.617651i
\(554\) 2.26063e17i 0.0141144i
\(555\) 6.41020e18 + 3.87804e18i 0.395203 + 0.239090i
\(556\) 5.32199e18 0.324004
\(557\) 1.68618e19 + 1.68618e19i 1.01372 + 1.01372i 0.999905 + 0.0138151i \(0.00439763\pi\)
0.0138151 + 0.999905i \(0.495602\pi\)
\(558\) −4.52732e18 + 4.52732e18i −0.268783 + 0.268783i
\(559\) 2.65158e19i 1.55461i
\(560\) −1.16467e18 4.73210e18i −0.0674352 0.273992i
\(561\) 2.44785e19 1.39973
\(562\) 9.97005e18 + 9.97005e18i 0.563045 + 0.563045i
\(563\) 7.75422e17 7.75422e17i 0.0432493 0.0432493i −0.685151 0.728401i \(-0.740264\pi\)
0.728401 + 0.685151i \(0.240264\pi\)
\(564\) 1.06059e18i 0.0584241i
\(565\) 8.26029e18 2.03303e18i 0.449424 0.110613i
\(566\) 1.41546e19 0.760647
\(567\) 3.95412e18 + 3.95412e18i 0.209879 + 0.209879i
\(568\) 7.70333e18 7.70333e18i 0.403869 0.403869i
\(569\) 1.15213e19i 0.596644i 0.954465 + 0.298322i \(0.0964269\pi\)
−0.954465 + 0.298322i \(0.903573\pi\)
\(570\) −4.33704e17 + 7.16889e17i −0.0221855 + 0.0366714i
\(571\) −5.14309e18 −0.259879 −0.129939 0.991522i \(-0.541478\pi\)
−0.129939 + 0.991522i \(0.541478\pi\)
\(572\) −1.59686e19 1.59686e19i −0.797064 0.797064i
\(573\) −1.25132e19 + 1.25132e19i −0.617001 + 0.617001i
\(574\) 4.98310e17i 0.0242726i
\(575\) 1.33815e18 + 4.17971e17i 0.0643915 + 0.0201127i
\(576\) 1.91959e18 0.0912538
\(577\) −1.54960e19 1.54960e19i −0.727761 0.727761i 0.242412 0.970173i \(-0.422061\pi\)
−0.970173 + 0.242412i \(0.922061\pi\)
\(578\) −1.77345e19 + 1.77345e19i −0.822856 + 0.822856i
\(579\) 4.33521e18i 0.198728i
\(580\) 1.05960e19 + 6.41037e18i 0.479895 + 0.290327i
\(581\) 6.27492e18 0.280786
\(582\) 3.62831e17 + 3.62831e17i 0.0160414 + 0.0160414i
\(583\) −2.62048e19 + 2.62048e19i −1.14473 + 1.14473i
\(584\) 1.12817e19i 0.486949i
\(585\) −5.56843e18 2.26247e19i −0.237488 0.964923i
\(586\) 1.27085e19 0.535562
\(587\) −3.11856e19 3.11856e19i −1.29864 1.29864i −0.929294 0.369342i \(-0.879583\pi\)
−0.369342 0.929294i \(-0.620417\pi\)
\(588\) −1.22280e18 + 1.22280e18i −0.0503168 + 0.0503168i
\(589\) 2.11256e18i 0.0859016i
\(590\) −2.04984e19 + 5.04510e18i −0.823676 + 0.202724i
\(591\) 2.18659e19 0.868269
\(592\) 4.00466e18 + 4.00466e18i 0.157150 + 0.157150i
\(593\) 1.53125e19 1.53125e19i 0.593831 0.593831i −0.344833 0.938664i \(-0.612064\pi\)
0.938664 + 0.344833i \(0.112064\pi\)
\(594\) 2.74674e19i 1.05272i
\(595\) 2.50885e19 4.14699e19i 0.950289 1.57078i
\(596\) −1.78178e19 −0.667008
\(597\) 9.55115e18 + 9.55115e18i 0.353375 + 0.353375i
\(598\) 1.25558e18 1.25558e18i 0.0459130 0.0459130i
\(599\) 1.85841e19i 0.671667i 0.941921 + 0.335834i \(0.109018\pi\)
−0.941921 + 0.335834i \(0.890982\pi\)
\(600\) −4.55503e18 + 2.38676e18i −0.162717 + 0.0852609i
\(601\) −4.10179e19 −1.44828 −0.724139 0.689654i \(-0.757763\pi\)
−0.724139 + 0.689654i \(0.757763\pi\)
\(602\) 1.84677e19 + 1.84677e19i 0.644523 + 0.644523i
\(603\) 7.49083e18 7.49083e18i 0.258410 0.258410i
\(604\) 2.01089e19i 0.685693i
\(605\) −4.42455e19 2.67676e19i −1.49136 0.902241i
\(606\) −2.51860e18 −0.0839172
\(607\) 1.51335e19 + 1.51335e19i 0.498445 + 0.498445i 0.910954 0.412508i \(-0.135347\pi\)
−0.412508 + 0.910954i \(0.635347\pi\)
\(608\) −4.47864e17 + 4.47864e17i −0.0145821 + 0.0145821i
\(609\) 2.04385e19i 0.657851i
\(610\) 2.04470e18 + 8.30770e18i 0.0650610 + 0.264346i
\(611\) 9.73141e18 0.306117
\(612\) 1.34998e19 + 1.34998e19i 0.419824 + 0.419824i
\(613\) 3.41597e19 3.41597e19i 1.05024 1.05024i 0.0515757 0.998669i \(-0.483576\pi\)
0.998669 0.0515757i \(-0.0164243\pi\)
\(614\) 9.60995e18i 0.292107i
\(615\) −5.10594e17 + 1.25668e17i −0.0153444 + 0.00377658i
\(616\) −2.22436e19 −0.660906
\(617\) 6.90783e17 + 6.90783e17i 0.0202930 + 0.0202930i 0.717180 0.696888i \(-0.245432\pi\)
−0.696888 + 0.717180i \(0.745432\pi\)
\(618\) 2.56692e18 2.56692e18i 0.0745577 0.0745577i
\(619\) 3.74206e19i 1.07467i −0.843368 0.537336i \(-0.819431\pi\)
0.843368 0.537336i \(-0.180569\pi\)
\(620\) 6.71147e18 1.10937e19i 0.190579 0.315018i
\(621\) 2.15971e18 0.0606394
\(622\) −2.38645e19 2.38645e19i −0.662552 0.662552i
\(623\) −3.97511e19 + 3.97511e19i −1.09127 + 1.09127i
\(624\) 6.51346e18i 0.176815i
\(625\) −2.12033e19 + 3.06300e19i −0.569171 + 0.822219i
\(626\) 3.43302e19 0.911289
\(627\) 2.70422e18 + 2.70422e18i 0.0709854 + 0.0709854i
\(628\) −4.95691e18 + 4.95691e18i −0.128675 + 0.128675i
\(629\) 5.63267e19i 1.44597i
\(630\) −1.96360e19 1.18794e19i −0.498504 0.301585i
\(631\) 5.04599e19 1.26690 0.633448 0.773785i \(-0.281639\pi\)
0.633448 + 0.773785i \(0.281639\pi\)
\(632\) −7.79200e18 7.79200e18i −0.193477 0.193477i
\(633\) 2.87607e18 2.87607e18i 0.0706275 0.0706275i
\(634\) 1.94565e19i 0.472542i
\(635\) 9.22256e18 + 3.74716e19i 0.221531 + 0.900091i
\(636\) 1.06888e19 0.253938
\(637\) 1.12198e19 + 1.12198e19i 0.263638 + 0.263638i
\(638\) 3.99698e19 3.99698e19i 0.928939 0.928939i
\(639\) 5.13035e19i 1.17935i
\(640\) −3.77471e18 + 9.29037e17i −0.0858271 + 0.0211239i
\(641\) −7.11564e19 −1.60032 −0.800162 0.599784i \(-0.795253\pi\)
−0.800162 + 0.599784i \(0.795253\pi\)
\(642\) −4.34242e18 4.34242e18i −0.0966020 0.0966020i
\(643\) 2.55404e19 2.55404e19i 0.562020 0.562020i −0.367861 0.929881i \(-0.619910\pi\)
0.929881 + 0.367861i \(0.119910\pi\)
\(644\) 1.74897e18i 0.0380699i
\(645\) 1.42656e19 2.35803e19i 0.307166 0.507729i
\(646\) −6.29934e18 −0.134174
\(647\) 3.71373e19 + 3.71373e19i 0.782494 + 0.782494i 0.980251 0.197757i \(-0.0633658\pi\)
−0.197757 + 0.980251i \(0.563366\pi\)
\(648\) 3.15413e18 3.15413e18i 0.0657437 0.0657437i
\(649\) 9.63543e19i 1.98682i
\(650\) 2.18997e19 + 4.17947e19i 0.446730 + 0.852565i
\(651\) −2.13985e19 −0.431834
\(652\) −2.25919e19 2.25919e19i −0.451046 0.451046i
\(653\) −1.57979e19 + 1.57979e19i −0.312038 + 0.312038i −0.845699 0.533661i \(-0.820816\pi\)
0.533661 + 0.845699i \(0.320816\pi\)
\(654\) 2.68906e19i 0.525480i
\(655\) 7.93169e19 + 4.79852e19i 1.53348 + 0.927722i
\(656\) −3.97493e17 −0.00760331
\(657\) 3.75675e19 + 3.75675e19i 0.710975 + 0.710975i
\(658\) 6.77774e18 6.77774e18i 0.126912 0.126912i
\(659\) 1.01968e20i 1.88916i −0.328286 0.944579i \(-0.606471\pi\)
0.328286 0.944579i \(-0.393529\pi\)
\(660\) 5.60956e18 + 2.27919e19i 0.102830 + 0.417804i
\(661\) −9.17130e19 −1.66349 −0.831746 0.555157i \(-0.812658\pi\)
−0.831746 + 0.555157i \(0.812658\pi\)
\(662\) −3.37931e19 3.37931e19i −0.606487 0.606487i
\(663\) −4.58069e19 + 4.58069e19i −0.813460 + 0.813460i
\(664\) 5.00539e18i 0.0879552i
\(665\) 7.35293e18 1.80971e18i 0.127852 0.0314672i
\(666\) 2.66707e19 0.458897
\(667\) 3.14276e18 + 3.14276e18i 0.0535094 + 0.0535094i
\(668\) 1.82847e19 1.82847e19i 0.308073 0.308073i
\(669\) 2.56728e19i 0.428046i
\(670\) −1.11047e19 + 1.83555e19i −0.183224 + 0.302860i
\(671\) 3.90509e19 0.637637
\(672\) 4.53650e18 + 4.53650e18i 0.0733054 + 0.0733054i
\(673\) 7.14516e19 7.14516e19i 1.14263 1.14263i 0.154666 0.987967i \(-0.450570\pi\)
0.987967 0.154666i \(-0.0494301\pi\)
\(674\) 4.14913e18i 0.0656656i
\(675\) −1.71106e19 + 5.47801e19i −0.268002 + 0.858018i
\(676\) 2.75093e19 0.426435
\(677\) 4.33021e18 + 4.33021e18i 0.0664337 + 0.0664337i 0.739543 0.673109i \(-0.235042\pi\)
−0.673109 + 0.739543i \(0.735042\pi\)
\(678\) −7.91885e18 + 7.91885e18i −0.120241 + 0.120241i
\(679\) 4.63738e18i 0.0696922i
\(680\) −3.30798e19 2.00126e19i −0.492040 0.297675i
\(681\) −2.77905e19 −0.409135
\(682\) −4.18472e19 4.18472e19i −0.609784 0.609784i
\(683\) 1.29755e18 1.29755e18i 0.0187145 0.0187145i −0.697688 0.716402i \(-0.745788\pi\)
0.716402 + 0.697688i \(0.245788\pi\)
\(684\) 2.98273e18i 0.0425816i
\(685\) −2.36660e19 9.61558e19i −0.334418 1.35876i
\(686\) −4.14301e19 −0.579491
\(687\) −1.67409e19 1.67409e19i −0.231783 0.231783i
\(688\) 1.47314e19 1.47314e19i 0.201895 0.201895i
\(689\) 9.80748e19i 1.33052i
\(690\) −1.79209e18 + 4.41070e17i −0.0240666 + 0.00592331i
\(691\) −1.03076e20 −1.37028 −0.685140 0.728411i \(-0.740259\pi\)
−0.685140 + 0.728411i \(0.740259\pi\)
\(692\) −1.64836e19 1.64836e19i −0.216925 0.216925i
\(693\) −7.40701e19 + 7.40701e19i −0.964963 + 0.964963i
\(694\) 2.20220e19i 0.284015i
\(695\) −2.62718e19 + 4.34259e19i −0.335426 + 0.554440i
\(696\) −1.63034e19 −0.206069
\(697\) −2.79543e18 2.79543e18i −0.0349800 0.0349800i
\(698\) −5.24439e18 + 5.24439e18i −0.0649691 + 0.0649691i
\(699\) 2.56331e19i 0.314384i
\(700\) 4.43619e19 + 1.38565e19i 0.538671 + 0.168254i
\(701\) 8.07311e19 0.970542 0.485271 0.874364i \(-0.338721\pi\)
0.485271 + 0.874364i \(0.338721\pi\)
\(702\) 5.14000e19 + 5.14000e19i 0.611792 + 0.611792i
\(703\) −6.22260e18 + 6.22260e18i −0.0733305 + 0.0733305i
\(704\) 1.77433e19i 0.207026i
\(705\) −8.65407e18 5.23554e18i −0.0999762 0.0604836i
\(706\) −6.08500e19 −0.696030
\(707\) 1.60953e19 + 1.60953e19i 0.182290 + 0.182290i
\(708\) 1.96511e19 1.96511e19i 0.220371 0.220371i
\(709\) 4.52131e19i 0.502043i 0.967982 + 0.251022i \(0.0807665\pi\)
−0.967982 + 0.251022i \(0.919234\pi\)
\(710\) 2.48297e19 + 1.00884e20i 0.273000 + 1.10921i
\(711\) −5.18941e19 −0.564977
\(712\) 3.17088e19 + 3.17088e19i 0.341837 + 0.341837i
\(713\) 3.29038e18 3.29038e18i 0.0351252 0.0351252i
\(714\) 6.38072e19i 0.674500i
\(715\) 2.09127e20 5.14705e19i 2.18911 0.538786i
\(716\) 3.19257e19 0.330940
\(717\) 1.25969e19 + 1.25969e19i 0.129309 + 0.129309i
\(718\) −4.16918e19 + 4.16918e19i −0.423818 + 0.423818i
\(719\) 1.26641e20i 1.27489i −0.770497 0.637443i \(-0.779992\pi\)
0.770497 0.637443i \(-0.220008\pi\)
\(720\) −9.47598e18 + 1.56633e19i −0.0944706 + 0.156155i
\(721\) −3.28081e19 −0.323917
\(722\) 5.04405e19 + 5.04405e19i 0.493196 + 0.493196i
\(723\) 2.77726e19 2.77726e19i 0.268936 0.268936i
\(724\) 4.53050e19i 0.434486i
\(725\) −1.04613e20 + 5.48157e19i −0.993623 + 0.520641i
\(726\) 6.80778e19 0.640397
\(727\) −4.36485e18 4.36485e18i −0.0406657 0.0406657i 0.686482 0.727147i \(-0.259154\pi\)
−0.727147 + 0.686482i \(0.759154\pi\)
\(728\) 4.16247e19 4.16247e19i 0.384088 0.384088i
\(729\) 3.00985e19i 0.275076i
\(730\) −9.20551e19 5.56915e19i −0.833274 0.504114i
\(731\) 2.07201e20 1.85768
\(732\) −7.96430e18 7.96430e18i −0.0707245 0.0707245i
\(733\) 5.77817e18 5.77817e18i 0.0508233 0.0508233i −0.681238 0.732062i \(-0.738558\pi\)
0.732062 + 0.681238i \(0.238558\pi\)
\(734\) 2.47310e19i 0.215461i
\(735\) −3.94137e18 1.60140e19i −0.0340123 0.138193i
\(736\) −1.39513e18 −0.0119253
\(737\) 6.92398e19 + 6.92398e19i 0.586251 + 0.586251i
\(738\) −1.32364e18 + 1.32364e18i −0.0111013 + 0.0111013i
\(739\) 2.29620e20i 1.90765i 0.300368 + 0.953824i \(0.402891\pi\)
−0.300368 + 0.953824i \(0.597109\pi\)
\(740\) −5.24457e19 + 1.29080e19i −0.431607 + 0.106228i
\(741\) −1.01209e19 −0.0825070
\(742\) −6.83072e19 6.83072e19i −0.551619 0.551619i
\(743\) 2.69258e19 2.69258e19i 0.215401 0.215401i −0.591156 0.806557i \(-0.701328\pi\)
0.806557 + 0.591156i \(0.201328\pi\)
\(744\) 1.70692e19i 0.135270i
\(745\) 8.79571e19 1.45388e20i 0.690521 1.14139i
\(746\) 1.21050e20 0.941438
\(747\) −1.66677e19 1.66677e19i −0.128420 0.128420i
\(748\) −1.24782e20 + 1.24782e20i −0.952450 + 0.952450i
\(749\) 5.55009e19i 0.419689i
\(750\) 3.01048e18 4.89499e19i 0.0225532 0.366710i
\(751\) −1.12909e20 −0.838010 −0.419005 0.907984i \(-0.637621\pi\)
−0.419005 + 0.907984i \(0.637621\pi\)
\(752\) −5.40648e18 5.40648e18i −0.0397548 0.0397548i
\(753\) 8.53363e19 8.53363e19i 0.621683 0.621683i
\(754\) 1.49592e20i 1.07971i
\(755\) −1.64083e20 9.92668e19i −1.17337 0.709865i
\(756\) 7.15982e19 0.507282
\(757\) −6.51187e19 6.51187e19i −0.457124 0.457124i 0.440586 0.897710i \(-0.354771\pi\)
−0.897710 + 0.440586i \(0.854771\pi\)
\(758\) 4.42245e19 4.42245e19i 0.307594 0.307594i
\(759\) 8.42382e18i 0.0580519i
\(760\) −1.44357e18 5.86530e18i −0.00985699 0.0400493i
\(761\) −8.37664e19 −0.566731 −0.283366 0.959012i \(-0.591451\pi\)
−0.283366 + 0.959012i \(0.591451\pi\)
\(762\) −3.59227e19 3.59227e19i −0.240815 0.240815i
\(763\) −1.71846e20 + 1.71846e20i −1.14148 + 1.14148i
\(764\) 1.27575e20i 0.839679i
\(765\) −1.76796e20 + 4.35132e19i −1.15303 + 0.283786i
\(766\) −1.33192e20 −0.860750
\(767\) −1.80309e20 1.80309e20i −1.15465 1.15465i
\(768\) 3.61869e18 3.61869e18i 0.0229627 0.0229627i
\(769\) 1.62320e20i 1.02068i 0.859973 + 0.510339i \(0.170480\pi\)
−0.859973 + 0.510339i \(0.829520\pi\)
\(770\) 1.09805e20 1.81501e20i 0.684203 1.13095i
\(771\) −3.89235e19 −0.240343
\(772\) 2.20993e19 + 2.20993e19i 0.135225 + 0.135225i
\(773\) 2.22705e20 2.22705e20i 1.35044 1.35044i 0.465263 0.885172i \(-0.345960\pi\)
0.885172 0.465263i \(-0.154040\pi\)
\(774\) 9.81099e19i 0.589557i
\(775\) 5.73905e19 + 1.09527e20i 0.341765 + 0.652245i
\(776\) −3.69916e18 −0.0218308
\(777\) 6.30300e19 + 6.30300e19i 0.368638 + 0.368638i
\(778\) 1.03393e20 1.03393e20i 0.599288 0.599288i
\(779\) 6.17641e17i 0.00354792i
\(780\) −5.31479e19 3.21535e19i −0.302569 0.183048i
\(781\) 4.74213e20 2.67557
\(782\) −9.81143e18 9.81143e18i −0.0548637 0.0548637i
\(783\) −1.28656e20 + 1.28656e20i −0.713013 + 0.713013i
\(784\) 1.24667e19i 0.0684764i
\(785\) −1.59773e19 6.49166e19i −0.0869795 0.353401i
\(786\) −1.22040e20 −0.658483
\(787\) −1.43266e20 1.43266e20i −0.766161 0.766161i 0.211267 0.977428i \(-0.432241\pi\)
−0.977428 + 0.211267i \(0.932241\pi\)
\(788\) −1.11464e20 + 1.11464e20i −0.590816 + 0.590816i
\(789\) 8.22363e19i 0.432041i
\(790\) 1.02045e20 2.51155e19i 0.531378 0.130783i
\(791\) 1.01212e20 0.522391
\(792\) 5.90844e19 + 5.90844e19i 0.302271 + 0.302271i
\(793\) −7.30765e19 + 7.30765e19i −0.370566 + 0.370566i
\(794\) 1.78878e20i 0.899111i
\(795\) −5.27647e19 + 8.72172e19i −0.262890 + 0.434542i
\(796\) −9.73766e19 −0.480909
\(797\) 9.23139e19 + 9.23139e19i 0.451917 + 0.451917i 0.895990 0.444073i \(-0.146467\pi\)
−0.444073 + 0.895990i \(0.646467\pi\)
\(798\) −7.04899e18 + 7.04899e18i −0.0342064 + 0.0342064i
\(799\) 7.60437e19i 0.365794i
\(800\) 1.10531e19 3.53867e19i 0.0527051 0.168737i
\(801\) 2.11178e20 0.998207
\(802\) 2.01206e19 + 2.01206e19i 0.0942800 + 0.0942800i
\(803\) −3.47246e20 + 3.47246e20i −1.61298 + 1.61298i
\(804\) 2.82424e19i 0.130050i
\(805\) 1.42711e19 + 8.63374e18i 0.0651458 + 0.0394119i
\(806\) 1.56619e20 0.708758
\(807\) −3.65995e19 3.65995e19i −0.164195 0.164195i
\(808\) 1.28389e19 1.28389e19i 0.0571016 0.0571016i
\(809\) 1.28441e20i 0.566323i 0.959072 + 0.283162i \(0.0913833\pi\)
−0.959072 + 0.283162i \(0.908617\pi\)
\(810\) 1.01665e19 + 4.13070e19i 0.0444404 + 0.180563i
\(811\) 1.08142e20 0.468651 0.234325 0.972158i \(-0.424712\pi\)
0.234325 + 0.972158i \(0.424712\pi\)
\(812\) 1.04188e20 + 1.04188e20i 0.447636 + 0.447636i
\(813\) 6.53650e19 6.53650e19i 0.278427 0.278427i
\(814\) 2.46525e20i 1.04109i
\(815\) 2.95868e20 7.28194e19i 1.23878 0.304890i
\(816\) 5.08979e19 0.211285
\(817\) 2.28902e19 + 2.28902e19i 0.0942097 + 0.0942097i
\(818\) −1.62266e20 + 1.62266e20i −0.662145 + 0.662145i
\(819\) 2.77217e20i 1.12158i
\(820\) 1.96221e18 3.24343e18i 0.00787134 0.0130109i
\(821\) −2.31305e20 −0.919988 −0.459994 0.887922i \(-0.652148\pi\)
−0.459994 + 0.887922i \(0.652148\pi\)
\(822\) 9.21812e19 + 9.21812e19i 0.363529 + 0.363529i
\(823\) 1.62824e20 1.62824e20i 0.636678 0.636678i −0.313057 0.949734i \(-0.601353\pi\)
0.949734 + 0.313057i \(0.101353\pi\)
\(824\) 2.61704e19i 0.101466i
\(825\) −2.13666e20 6.67388e19i −0.821407 0.256567i
\(826\) −2.51163e20 −0.957406
\(827\) 4.31954e19 + 4.31954e19i 0.163267 + 0.163267i 0.784012 0.620745i \(-0.213170\pi\)
−0.620745 + 0.784012i \(0.713170\pi\)
\(828\) −4.64571e18 + 4.64571e18i −0.0174116 + 0.0174116i
\(829\) 5.78065e19i 0.214830i 0.994214 + 0.107415i \(0.0342574\pi\)
−0.994214 + 0.107415i \(0.965743\pi\)
\(830\) 4.08425e19 + 2.47089e19i 0.150510 + 0.0910557i
\(831\) 2.83819e18 0.0103713
\(832\) −3.32033e19 3.32033e19i −0.120314 0.120314i
\(833\) 8.76743e19 8.76743e19i 0.315034 0.315034i
\(834\) 6.68167e19i 0.238080i
\(835\) 5.89361e19 + 2.39460e20i 0.208246 + 0.846111i
\(836\) −2.75702e19 −0.0966044
\(837\) 1.34699e20 + 1.34699e20i 0.468044 + 0.468044i
\(838\) 1.03980e20 1.03980e20i 0.358296 0.358296i
\(839\) 7.42680e19i 0.253786i −0.991916 0.126893i \(-0.959499\pi\)
0.991916 0.126893i \(-0.0405005\pi\)
\(840\) −5.94108e19 + 1.46222e19i −0.201331 + 0.0495518i
\(841\) −7.68752e19 −0.258353
\(842\) 6.91577e19 + 6.91577e19i 0.230492 + 0.230492i
\(843\) 1.25172e20 1.25172e20i 0.413728 0.413728i
\(844\) 2.93223e19i 0.0961173i
\(845\) −1.35799e20 + 2.24468e20i −0.441467 + 0.729721i
\(846\) −3.60067e19 −0.116089
\(847\) −4.35055e20 4.35055e20i −1.39111 1.39111i
\(848\) −5.44874e19 + 5.44874e19i −0.172793 + 0.172793i
\(849\) 1.77709e20i 0.558928i
\(850\) 3.26595e20 1.71130e20i 1.01877 0.533819i
\(851\) −1.93838e19 −0.0599698
\(852\) −9.67141e19 9.67141e19i −0.296765 0.296765i
\(853\) 1.81274e20 1.81274e20i 0.551685 0.551685i −0.375242 0.926927i \(-0.622440\pi\)
0.926927 + 0.375242i \(0.122440\pi\)
\(854\) 1.01793e20i 0.307264i
\(855\) −2.43382e19 1.47242e19i −0.0728662 0.0440826i
\(856\) 4.42721e19 0.131466
\(857\) −2.03302e20 2.03302e20i −0.598793 0.598793i 0.341198 0.939991i \(-0.389167\pi\)
−0.939991 + 0.341198i \(0.889167\pi\)
\(858\) −2.00483e20 + 2.00483e20i −0.585687 + 0.585687i
\(859\) 7.68775e19i 0.222765i 0.993778 + 0.111383i \(0.0355279\pi\)
−0.993778 + 0.111383i \(0.964472\pi\)
\(860\) 4.74829e19 + 1.92925e20i 0.136473 + 0.554497i
\(861\) −6.25621e18 −0.0178357
\(862\) 7.85370e19 + 7.85370e19i 0.222087 + 0.222087i
\(863\) −4.01628e18 + 4.01628e18i −0.0112655 + 0.0112655i −0.712717 0.701452i \(-0.752536\pi\)
0.701452 + 0.712717i \(0.252536\pi\)
\(864\) 5.71127e19i 0.158904i
\(865\) 2.15872e20 5.31308e19i 0.595778 0.146634i
\(866\) −3.60814e20 −0.987775
\(867\) 2.22654e20 + 2.22654e20i 0.604639 + 0.604639i
\(868\) 1.09082e20 1.09082e20i 0.293842 0.293842i
\(869\) 4.79671e20i 1.28176i
\(870\) 8.04811e19 1.33031e20i 0.213334 0.352629i
\(871\) −2.59139e20 −0.681405
\(872\) 1.37079e20 + 1.37079e20i 0.357564 + 0.357564i
\(873\) −1.23180e19 + 1.23180e19i −0.0318744 + 0.0318744i
\(874\) 2.16780e18i 0.00556467i
\(875\) −3.32056e20 + 2.93578e20i −0.845579 + 0.747597i
\(876\) 1.41639e20 0.357813
\(877\) −2.82852e20 2.82852e20i −0.708862 0.708862i 0.257434 0.966296i \(-0.417123\pi\)
−0.966296 + 0.257434i \(0.917123\pi\)
\(878\) −1.72183e20 + 1.72183e20i −0.428083 + 0.428083i
\(879\) 1.59553e20i 0.393534i
\(880\) −1.44780e20 8.75891e19i −0.354267 0.214324i
\(881\) −5.52031e20 −1.34009 −0.670043 0.742323i \(-0.733724\pi\)
−0.670043 + 0.742323i \(0.733724\pi\)
\(882\) −4.15137e19 4.15137e19i −0.0999797 0.0999797i
\(883\) 4.89936e20 4.89936e20i 1.17062 1.17062i 0.188554 0.982063i \(-0.439620\pi\)
0.982063 0.188554i \(-0.0603799\pi\)
\(884\) 4.67014e20i 1.10704i
\(885\) 6.33404e19 + 2.57354e20i 0.148963 + 0.605242i
\(886\) −7.42461e19 −0.173236
\(887\) 3.77508e20 + 3.77508e20i 0.873899 + 0.873899i 0.992895 0.118996i \(-0.0379676\pi\)
−0.118996 + 0.992895i \(0.537968\pi\)
\(888\) 5.02779e19 5.02779e19i 0.115475 0.115475i
\(889\) 4.59132e20i 1.04623i
\(890\) −4.15264e20 + 1.02205e20i −0.938845 + 0.231070i
\(891\) 1.94166e20 0.435542
\(892\) 1.30871e20 + 1.30871e20i 0.291265 + 0.291265i
\(893\) 8.40080e18 8.40080e18i 0.0185507 0.0185507i
\(894\) 2.23700e20i 0.490121i
\(895\) −1.57600e20 + 2.60504e20i −0.342606 + 0.566309i
\(896\) −4.62508e19 −0.0997617
\(897\) −1.57636e19 1.57636e19i −0.0337371 0.0337371i
\(898\) 2.92349e20 2.92349e20i 0.620823 0.620823i
\(899\) 3.92021e20i 0.826022i
\(900\) −8.10300e19 1.54642e20i −0.169414 0.323319i
\(901\) −7.66382e20 −1.58991
\(902\) −1.22347e19 1.22347e19i −0.0251854 0.0251854i
\(903\) 2.31860e20 2.31860e20i 0.473599 0.473599i
\(904\) 8.07348e19i 0.163637i
\(905\) 3.69675e20 + 2.23646e20i 0.743499 + 0.449802i
\(906\) 2.52464e20 0.503851
\(907\) 2.78009e20 + 2.78009e20i 0.550565 + 0.550565i 0.926604 0.376039i \(-0.122714\pi\)
−0.376039 + 0.926604i \(0.622714\pi\)
\(908\) 1.41666e20 1.41666e20i 0.278396 0.278396i
\(909\) 8.55060e19i 0.166744i
\(910\) 1.34166e20 + 5.45124e20i 0.259630 + 1.05489i
\(911\) 8.47316e20 1.62711 0.813555 0.581488i \(-0.197529\pi\)
0.813555 + 0.581488i \(0.197529\pi\)
\(912\) 5.62286e18 + 5.62286e18i 0.0107150 + 0.0107150i
\(913\) 1.54065e20 1.54065e20i 0.291345 0.291345i
\(914\) 3.34193e20i 0.627154i
\(915\) 1.04302e20 2.56709e19i 0.194243 0.0478072i
\(916\) 1.70678e20 0.315434
\(917\) 7.79904e20 + 7.79904e20i 1.43039 + 1.43039i
\(918\) 4.01653e20 4.01653e20i 0.731059 0.731059i
\(919\) 4.04823e20i 0.731234i 0.930765 + 0.365617i \(0.119142\pi\)
−0.930765 + 0.365617i \(0.880858\pi\)
\(920\) 6.88698e18 1.13838e19i 0.0123457 0.0204067i
\(921\) 1.20651e20 0.214642
\(922\) −3.29250e20 3.29250e20i −0.581312 0.581312i
\(923\) −8.87400e20 + 8.87400e20i −1.55492 + 1.55492i
\(924\) 2.79264e20i 0.485637i
\(925\) 1.53571e20 4.91662e20i 0.265043 0.848544i
\(926\) −4.04483e20 −0.692825
\(927\) 8.71464e19 + 8.71464e19i 0.148146 + 0.148146i
\(928\) 8.31088e19 8.31088e19i 0.140220 0.140220i
\(929\) 8.05131e20i 1.34821i 0.738637 + 0.674104i \(0.235470\pi\)
−0.738637 + 0.674104i \(0.764530\pi\)
\(930\) −1.39280e20 8.42615e19i −0.231477 0.140039i
\(931\) 1.93713e19 0.0319530
\(932\) 1.30668e20 + 1.30668e20i 0.213923 + 0.213923i
\(933\) −2.99615e20 + 2.99615e20i −0.486847 + 0.486847i
\(934\) 4.76434e20i 0.768377i
\(935\) −4.02204e20 1.63417e21i −0.643821 2.61587i
\(936\) −2.21131e20 −0.351333
\(937\) −4.71181e20 4.71181e20i −0.743037 0.743037i 0.230124 0.973161i \(-0.426087\pi\)
−0.973161 + 0.230124i \(0.926087\pi\)
\(938\) −1.80485e20 + 1.80485e20i −0.282502 + 0.282502i
\(939\) 4.31010e20i 0.669620i
\(940\) 7.08042e19 1.74264e19i 0.109185 0.0268728i
\(941\) −6.14686e20 −0.940862 −0.470431 0.882437i \(-0.655902\pi\)
−0.470431 + 0.882437i \(0.655902\pi\)
\(942\) 6.22333e19 + 6.22333e19i 0.0945510 + 0.0945510i
\(943\) 9.61996e17 9.61996e17i 0.00145075 0.00145075i
\(944\) 2.00349e20i 0.299904i
\(945\) −3.53442e20 + 5.84221e20i −0.525165 + 0.868069i
\(946\) 9.06857e20 1.33752
\(947\) 5.85232e19 + 5.85232e19i 0.0856797 + 0.0856797i 0.748648 0.662968i \(-0.230703\pi\)
−0.662968 + 0.748648i \(0.730703\pi\)
\(948\) −9.78273e19 + 9.78273e19i −0.142168 + 0.142168i
\(949\) 1.29961e21i 1.87478i
\(950\) 5.49853e19 + 1.71747e19i 0.0787374 + 0.0245937i
\(951\) 2.44273e20 0.347226
\(952\) −3.25266e20 3.25266e20i −0.458965 0.458965i
\(953\) −2.15777e20 + 2.15777e20i −0.302242 + 0.302242i −0.841890 0.539649i \(-0.818557\pi\)
0.539649 + 0.841890i \(0.318557\pi\)
\(954\) 3.62882e20i 0.504576i
\(955\) 1.04098e21 + 6.29771e20i 1.43687 + 0.869279i
\(956\) −1.28429e20 −0.175977
\(957\) −5.01814e20 5.01814e20i −0.682589 0.682589i
\(958\) −2.98007e20 + 2.98007e20i −0.402409 + 0.402409i
\(959\) 1.17818e21i 1.57936i
\(960\) 1.16639e19 + 4.73909e19i 0.0155219 + 0.0630662i
\(961\) −3.46509e20 −0.457773
\(962\) −4.61325e20 4.61325e20i −0.605036 0.605036i
\(963\) 1.47424e20 1.47424e20i 0.191949 0.191949i
\(964\) 2.83149e20i 0.365996i
\(965\) −2.89416e20 + 7.12315e19i −0.371391 + 0.0914073i
\(966\) −2.19581e19 −0.0279740
\(967\) −3.29886e20 3.29886e20i −0.417232 0.417232i 0.467016 0.884249i \(-0.345329\pi\)
−0.884249 + 0.467016i \(0.845329\pi\)
\(968\) −3.47036e20 + 3.47036e20i −0.435759 + 0.435759i
\(969\) 7.90872e19i 0.0985915i
\(970\) 1.82607e19 3.01840e19i 0.0226004 0.0373573i
\(971\) −4.04627e20 −0.497188 −0.248594 0.968608i \(-0.579968\pi\)
−0.248594 + 0.968608i \(0.579968\pi\)
\(972\) −3.00113e20 3.00113e20i −0.366118 0.366118i
\(973\) −4.26996e20 + 4.26996e20i −0.517171 + 0.517171i
\(974\) 7.70953e19i 0.0927075i
\(975\) 5.24726e20 2.74947e20i 0.626470 0.328259i
\(976\) 8.11982e19 0.0962493
\(977\) −1.12448e20 1.12448e20i −0.132339 0.132339i 0.637834 0.770174i \(-0.279830\pi\)
−0.770174 + 0.637834i \(0.779830\pi\)
\(978\) −2.83638e20 + 2.83638e20i −0.331431 + 0.331431i
\(979\) 1.95198e21i 2.26462i
\(980\) 1.01725e20 + 6.15416e19i 0.117178 + 0.0708902i
\(981\) 9.12931e20 1.04413
\(982\) 4.81808e20 + 4.81808e20i 0.547134 + 0.547134i
\(983\) 9.61422e20 9.61422e20i 1.08403 1.08403i 0.0878954 0.996130i \(-0.471986\pi\)
0.996130 0.0878954i \(-0.0280141\pi\)
\(984\) 4.99047e18i 0.00558696i
\(985\) −3.59277e20 1.45975e21i −0.399370 1.62265i
\(986\) 1.16895e21 1.29020
\(987\) −8.50934e19 8.50934e19i −0.0932558 0.0932558i
\(988\) 5.15925e19 5.15925e19i 0.0561421 0.0561421i
\(989\) 7.13046e19i 0.0770448i
\(990\) −7.73780e20 + 1.90444e20i −0.830178 + 0.204324i
\(991\) −3.45922e20 −0.368521 −0.184261 0.982877i \(-0.558989\pi\)
−0.184261 + 0.982877i \(0.558989\pi\)
\(992\) −8.70126e19 8.70126e19i −0.0920451 0.0920451i
\(993\) −4.24267e20 + 4.24267e20i −0.445650 + 0.445650i
\(994\) 1.23611e21i 1.28930i
\(995\) 4.80696e20 7.94564e20i 0.497862 0.822939i
\(996\) −6.28419e19 −0.0646300
\(997\) 9.86724e20 + 9.86724e20i 1.00770 + 1.00770i 0.999970 + 0.00772627i \(0.00245937\pi\)
0.00772627 + 0.999970i \(0.497541\pi\)
\(998\) 8.91551e20 8.91551e20i 0.904134 0.904134i
\(999\) 7.93521e20i 0.799098i
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 10.15.c.b.7.3 yes 8
3.2 odd 2 90.15.g.b.37.3 8
4.3 odd 2 80.15.p.b.17.2 8
5.2 odd 4 50.15.c.e.43.2 8
5.3 odd 4 inner 10.15.c.b.3.3 8
5.4 even 2 50.15.c.e.7.2 8
15.8 even 4 90.15.g.b.73.3 8
20.3 even 4 80.15.p.b.33.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.15.c.b.3.3 8 5.3 odd 4 inner
10.15.c.b.7.3 yes 8 1.1 even 1 trivial
50.15.c.e.7.2 8 5.4 even 2
50.15.c.e.43.2 8 5.2 odd 4
80.15.p.b.17.2 8 4.3 odd 2
80.15.p.b.33.2 8 20.3 even 4
90.15.g.b.37.3 8 3.2 odd 2
90.15.g.b.73.3 8 15.8 even 4