Properties

Label 15.11.f.a.7.4
Level $15$
Weight $11$
Character 15.7
Analytic conductor $9.530$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,11,Mod(7,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.7");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.53035879011\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} + 8 x^{18} - 49316 x^{17} + 18276332 x^{16} - 230627572 x^{15} + 1992333560 x^{14} - 394917674060 x^{13} + 80687382741790 x^{12} + \cdots + 14\!\cdots\!04 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{34}\cdot 5^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.4
Root \(17.5986 - 17.5986i\) of defining polynomial
Character \(\chi\) \(=\) 15.7
Dual form 15.11.f.a.13.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-19.3738 - 19.3738i) q^{2} +(-99.2043 + 99.2043i) q^{3} -273.309i q^{4} +(-2998.53 + 880.025i) q^{5} +3843.94 q^{6} +(3127.99 + 3127.99i) q^{7} +(-25133.9 + 25133.9i) q^{8} -19683.0i q^{9} +O(q^{10})\) \(q+(-19.3738 - 19.3738i) q^{2} +(-99.2043 + 99.2043i) q^{3} -273.309i q^{4} +(-2998.53 + 880.025i) q^{5} +3843.94 q^{6} +(3127.99 + 3127.99i) q^{7} +(-25133.9 + 25133.9i) q^{8} -19683.0i q^{9} +(75142.5 + 41043.6i) q^{10} +230381. q^{11} +(27113.5 + 27113.5i) q^{12} +(287704. - 287704. i) q^{13} -121202. i q^{14} +(210165. - 384769. i) q^{15} +694009. q^{16} +(1.39122e6 + 1.39122e6i) q^{17} +(-381335. + 381335. i) q^{18} +323424. i q^{19} +(240519. + 819526. i) q^{20} -620621. q^{21} +(-4.46336e6 - 4.46336e6i) q^{22} +(-7.28021e6 + 7.28021e6i) q^{23} -4.98677e6i q^{24} +(8.21674e6 - 5.27756e6i) q^{25} -1.11479e7 q^{26} +(1.95264e6 + 1.95264e6i) q^{27} +(854910. - 854910. i) q^{28} -5.58509e6i q^{29} +(-1.15262e7 + 3.38276e6i) q^{30} -3.90283e6 q^{31} +(1.22914e7 + 1.22914e7i) q^{32} +(-2.28548e7 + 2.28548e7i) q^{33} -5.39066e7i q^{34} +(-1.21321e7 - 6.62667e6i) q^{35} -5.37955e6 q^{36} +(8.90358e7 + 8.90358e7i) q^{37} +(6.26596e6 - 6.26596e6i) q^{38} +5.70830e7i q^{39} +(5.32462e7 - 9.74830e7i) q^{40} -3.06972e7 q^{41} +(1.20238e7 + 1.20238e7i) q^{42} +(5.99364e7 - 5.99364e7i) q^{43} -6.29653e7i q^{44} +(1.73215e7 + 5.90201e7i) q^{45} +2.82091e8 q^{46} +(1.25579e8 + 1.25579e8i) q^{47} +(-6.88487e7 + 6.88487e7i) q^{48} -2.62907e8i q^{49} +(-2.61436e8 - 5.69431e7i) q^{50} -2.76030e8 q^{51} +(-7.86322e7 - 7.86322e7i) q^{52} +(-2.38773e8 + 2.38773e8i) q^{53} -7.56602e7i q^{54} +(-6.90804e8 + 2.02741e8i) q^{55} -1.57237e8 q^{56} +(-3.20851e7 - 3.20851e7i) q^{57} +(-1.08205e8 + 1.08205e8i) q^{58} +1.52981e8i q^{59} +(-1.05161e8 - 5.74400e7i) q^{60} +9.12337e8 q^{61} +(7.56127e7 + 7.56127e7i) q^{62} +(6.15683e7 - 6.15683e7i) q^{63} -1.18693e9i q^{64} +(-6.09503e8 + 1.11588e9i) q^{65} +8.85570e8 q^{66} +(1.02130e8 + 1.02130e8i) q^{67} +(3.80234e8 - 3.80234e8i) q^{68} -1.44446e9i q^{69} +(1.06661e8 + 3.63429e8i) q^{70} +3.21746e9 q^{71} +(4.94710e8 + 4.94710e8i) q^{72} +(-1.64457e9 + 1.64457e9i) q^{73} -3.44993e9i q^{74} +(-2.91579e8 + 1.33869e9i) q^{75} +8.83948e7 q^{76} +(7.20630e8 + 7.20630e8i) q^{77} +(1.10592e9 - 1.10592e9i) q^{78} +4.86313e9i q^{79} +(-2.08101e9 + 6.10745e8i) q^{80} -3.87420e8 q^{81} +(5.94723e8 + 5.94723e8i) q^{82} +(2.32096e9 - 2.32096e9i) q^{83} +1.69622e8i q^{84} +(-5.39593e9 - 2.94731e9i) q^{85} -2.32239e9 q^{86} +(5.54065e8 + 5.54065e8i) q^{87} +(-5.79036e9 + 5.79036e9i) q^{88} -7.27765e9i q^{89} +(8.07860e8 - 1.47903e9i) q^{90} +1.79987e9 q^{91} +(1.98975e9 + 1.98975e9i) q^{92} +(3.87177e8 - 3.87177e8i) q^{93} -4.86589e9i q^{94} +(-2.84621e8 - 9.69797e8i) q^{95} -2.43873e9 q^{96} +(9.72979e8 + 9.72979e8i) q^{97} +(-5.09351e9 + 5.09351e9i) q^{98} -4.53459e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 64 q^{2} + 10676 q^{5} - 4860 q^{6} + 10604 q^{7} - 39948 q^{8} + 153704 q^{10} + 32080 q^{11} - 620136 q^{12} - 69352 q^{13} + 662904 q^{15} - 3111700 q^{16} + 347360 q^{17} - 1259712 q^{18} + 24132564 q^{20} + 1448280 q^{21} - 27255980 q^{22} - 30995704 q^{23} + 36824936 q^{25} + 80977840 q^{26} - 104897636 q^{28} - 6436584 q^{30} - 8846480 q^{31} - 81249676 q^{32} + 86048244 q^{33} + 91578920 q^{35} + 177540660 q^{36} - 27635896 q^{37} + 44187744 q^{38} - 887009352 q^{40} + 149264920 q^{41} + 442105452 q^{42} + 675552392 q^{43} - 183996684 q^{45} - 1916100680 q^{46} - 257112832 q^{47} + 1182772368 q^{48} + 909704384 q^{50} - 711183240 q^{51} + 1397512520 q^{52} - 152646064 q^{53} - 1181518004 q^{55} + 1735516800 q^{56} + 342507528 q^{57} - 1947576252 q^{58} - 1084331124 q^{60} + 2582791000 q^{61} - 969372632 q^{62} + 208718532 q^{63} + 7250334488 q^{65} - 1968290280 q^{66} - 6731030200 q^{67} - 12869460704 q^{68} + 7421027700 q^{70} + 7511442640 q^{71} + 786296484 q^{72} + 1660222316 q^{73} + 72454824 q^{75} + 9998646360 q^{76} - 13264676792 q^{77} - 5574993480 q^{78} - 15692039116 q^{80} - 7748409780 q^{81} + 27089146528 q^{82} + 30753878864 q^{83} - 2653017808 q^{85} - 46532117120 q^{86} + 3048661476 q^{87} + 5813201532 q^{88} + 8161910244 q^{90} + 14175275920 q^{91} + 30045377384 q^{92} - 6062778072 q^{93} - 58265269776 q^{95} - 18513718020 q^{96} - 32149992820 q^{97} + 54432471592 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −19.3738 19.3738i −0.605432 0.605432i 0.336317 0.941749i \(-0.390819\pi\)
−0.941749 + 0.336317i \(0.890819\pi\)
\(3\) −99.2043 + 99.2043i −0.408248 + 0.408248i
\(4\) 273.309i 0.266904i
\(5\) −2998.53 + 880.025i −0.959530 + 0.281608i
\(6\) 3843.94 0.494333
\(7\) 3127.99 + 3127.99i 0.186113 + 0.186113i 0.794013 0.607901i \(-0.207988\pi\)
−0.607901 + 0.794013i \(0.707988\pi\)
\(8\) −25133.9 + 25133.9i −0.767024 + 0.767024i
\(9\) 19683.0i 0.333333i
\(10\) 75142.5 + 41043.6i 0.751425 + 0.410436i
\(11\) 230381. 1.43048 0.715242 0.698877i \(-0.246316\pi\)
0.715242 + 0.698877i \(0.246316\pi\)
\(12\) 27113.5 + 27113.5i 0.108963 + 0.108963i
\(13\) 287704. 287704.i 0.774871 0.774871i −0.204083 0.978954i \(-0.565421\pi\)
0.978954 + 0.204083i \(0.0654212\pi\)
\(14\) 121202.i 0.225357i
\(15\) 210165. 384769.i 0.276760 0.506692i
\(16\) 694009. 0.661859
\(17\) 1.39122e6 + 1.39122e6i 0.979832 + 0.979832i 0.999801 0.0199685i \(-0.00635660\pi\)
−0.0199685 + 0.999801i \(0.506357\pi\)
\(18\) −381335. + 381335.i −0.201811 + 0.201811i
\(19\) 323424.i 0.130618i 0.997865 + 0.0653092i \(0.0208034\pi\)
−0.997865 + 0.0653092i \(0.979197\pi\)
\(20\) 240519. + 819526.i 0.0751622 + 0.256102i
\(21\) −620621. −0.151960
\(22\) −4.46336e6 4.46336e6i −0.866061 0.866061i
\(23\) −7.28021e6 + 7.28021e6i −1.13111 + 1.13111i −0.141116 + 0.989993i \(0.545069\pi\)
−0.989993 + 0.141116i \(0.954931\pi\)
\(24\) 4.98677e6i 0.626273i
\(25\) 8.21674e6 5.27756e6i 0.841394 0.540422i
\(26\) −1.11479e7 −0.938264
\(27\) 1.95264e6 + 1.95264e6i 0.136083 + 0.136083i
\(28\) 854910. 854910.i 0.0496741 0.0496741i
\(29\) 5.58509e6i 0.272295i −0.990689 0.136148i \(-0.956528\pi\)
0.990689 0.136148i \(-0.0434721\pi\)
\(30\) −1.15262e7 + 3.38276e6i −0.474327 + 0.139208i
\(31\) −3.90283e6 −0.136324 −0.0681618 0.997674i \(-0.521713\pi\)
−0.0681618 + 0.997674i \(0.521713\pi\)
\(32\) 1.22914e7 + 1.22914e7i 0.366314 + 0.366314i
\(33\) −2.28548e7 + 2.28548e7i −0.583993 + 0.583993i
\(34\) 5.39066e7i 1.18644i
\(35\) −1.21321e7 6.62667e6i −0.230991 0.126170i
\(36\) −5.37955e6 −0.0889679
\(37\) 8.90358e7 + 8.90358e7i 1.28397 + 1.28397i 0.938387 + 0.345586i \(0.112320\pi\)
0.345586 + 0.938387i \(0.387680\pi\)
\(38\) 6.26596e6 6.26596e6i 0.0790806 0.0790806i
\(39\) 5.70830e7i 0.632679i
\(40\) 5.32462e7 9.74830e7i 0.519982 0.951983i
\(41\) −3.06972e7 −0.264960 −0.132480 0.991186i \(-0.542294\pi\)
−0.132480 + 0.991186i \(0.542294\pi\)
\(42\) 1.20238e7 + 1.20238e7i 0.0920016 + 0.0920016i
\(43\) 5.99364e7 5.99364e7i 0.407707 0.407707i −0.473231 0.880938i \(-0.656913\pi\)
0.880938 + 0.473231i \(0.156913\pi\)
\(44\) 6.29653e7i 0.381802i
\(45\) 1.73215e7 + 5.90201e7i 0.0938693 + 0.319843i
\(46\) 2.82091e8 1.36962
\(47\) 1.25579e8 + 1.25579e8i 0.547555 + 0.547555i 0.925733 0.378178i \(-0.123449\pi\)
−0.378178 + 0.925733i \(0.623449\pi\)
\(48\) −6.88487e7 + 6.88487e7i −0.270203 + 0.270203i
\(49\) 2.62907e8i 0.930724i
\(50\) −2.61436e8 5.69431e7i −0.836596 0.182218i
\(51\) −2.76030e8 −0.800030
\(52\) −7.86322e7 7.86322e7i −0.206816 0.206816i
\(53\) −2.38773e8 + 2.38773e8i −0.570960 + 0.570960i −0.932397 0.361437i \(-0.882286\pi\)
0.361437 + 0.932397i \(0.382286\pi\)
\(54\) 7.56602e7i 0.164778i
\(55\) −6.90804e8 + 2.02741e8i −1.37259 + 0.402836i
\(56\) −1.57237e8 −0.285506
\(57\) −3.20851e7 3.20851e7i −0.0533247 0.0533247i
\(58\) −1.08205e8 + 1.08205e8i −0.164856 + 0.164856i
\(59\) 1.52981e8i 0.213982i 0.994260 + 0.106991i \(0.0341215\pi\)
−0.994260 + 0.106991i \(0.965878\pi\)
\(60\) −1.05161e8 5.74400e7i −0.135238 0.0738684i
\(61\) 9.12337e8 1.08021 0.540103 0.841599i \(-0.318385\pi\)
0.540103 + 0.841599i \(0.318385\pi\)
\(62\) 7.56127e7 + 7.56127e7i 0.0825347 + 0.0825347i
\(63\) 6.15683e7 6.15683e7i 0.0620375 0.0620375i
\(64\) 1.18693e9i 1.10541i
\(65\) −6.09503e8 + 1.11588e9i −0.525302 + 0.961721i
\(66\) 8.85570e8 0.707136
\(67\) 1.02130e8 + 1.02130e8i 0.0756445 + 0.0756445i 0.743917 0.668272i \(-0.232966\pi\)
−0.668272 + 0.743917i \(0.732966\pi\)
\(68\) 3.80234e8 3.80234e8i 0.261521 0.261521i
\(69\) 1.44446e9i 0.923547i
\(70\) 1.06661e8 + 3.63429e8i 0.0634623 + 0.216237i
\(71\) 3.21746e9 1.78329 0.891643 0.452740i \(-0.149553\pi\)
0.891643 + 0.452740i \(0.149553\pi\)
\(72\) 4.94710e8 + 4.94710e8i 0.255675 + 0.255675i
\(73\) −1.64457e9 + 1.64457e9i −0.793299 + 0.793299i −0.982029 0.188730i \(-0.939563\pi\)
0.188730 + 0.982029i \(0.439563\pi\)
\(74\) 3.44993e9i 1.55472i
\(75\) −2.91579e8 + 1.33869e9i −0.122871 + 0.564124i
\(76\) 8.83948e7 0.0348625
\(77\) 7.20630e8 + 7.20630e8i 0.266231 + 0.266231i
\(78\) 1.10592e9 1.10592e9i 0.383045 0.383045i
\(79\) 4.86313e9i 1.58045i 0.612817 + 0.790225i \(0.290036\pi\)
−0.612817 + 0.790225i \(0.709964\pi\)
\(80\) −2.08101e9 + 6.10745e8i −0.635073 + 0.186385i
\(81\) −3.87420e8 −0.111111
\(82\) 5.94723e8 + 5.94723e8i 0.160415 + 0.160415i
\(83\) 2.32096e9 2.32096e9i 0.589220 0.589220i −0.348200 0.937420i \(-0.613207\pi\)
0.937420 + 0.348200i \(0.113207\pi\)
\(84\) 1.69622e8i 0.0405588i
\(85\) −5.39593e9 2.94731e9i −1.21611 0.664249i
\(86\) −2.32239e9 −0.493678
\(87\) 5.54065e8 + 5.54065e8i 0.111164 + 0.111164i
\(88\) −5.79036e9 + 5.79036e9i −1.09722 + 1.09722i
\(89\) 7.27765e9i 1.30329i −0.758524 0.651646i \(-0.774079\pi\)
0.758524 0.651646i \(-0.225921\pi\)
\(90\) 8.07860e8 1.47903e9i 0.136812 0.250475i
\(91\) 1.79987e9 0.288426
\(92\) 1.98975e9 + 1.98975e9i 0.301897 + 0.301897i
\(93\) 3.87177e8 3.87177e8i 0.0556538 0.0556538i
\(94\) 4.86589e9i 0.663015i
\(95\) −2.84621e8 9.69797e8i −0.0367832 0.125332i
\(96\) −2.43873e9 −0.299094
\(97\) 9.72979e8 + 9.72979e8i 0.113304 + 0.113304i 0.761486 0.648182i \(-0.224470\pi\)
−0.648182 + 0.761486i \(0.724470\pi\)
\(98\) −5.09351e9 + 5.09351e9i −0.563490 + 0.563490i
\(99\) 4.53459e9i 0.476828i
\(100\) −1.44241e9 2.24571e9i −0.144241 0.224571i
\(101\) −5.83910e9 −0.555571 −0.277785 0.960643i \(-0.589600\pi\)
−0.277785 + 0.960643i \(0.589600\pi\)
\(102\) 5.34777e9 + 5.34777e9i 0.484364 + 0.484364i
\(103\) 2.62735e9 2.62735e9i 0.226637 0.226637i −0.584649 0.811286i \(-0.698768\pi\)
0.811286 + 0.584649i \(0.198768\pi\)
\(104\) 1.44622e10i 1.18869i
\(105\) 1.86095e9 5.46162e8i 0.145810 0.0427932i
\(106\) 9.25188e9 0.691355
\(107\) 9.66716e8 + 9.66716e8i 0.0689255 + 0.0689255i 0.740729 0.671804i \(-0.234480\pi\)
−0.671804 + 0.740729i \(0.734480\pi\)
\(108\) 5.33674e8 5.33674e8i 0.0363210 0.0363210i
\(109\) 1.71835e9i 0.111681i 0.998440 + 0.0558403i \(0.0177838\pi\)
−0.998440 + 0.0558403i \(0.982216\pi\)
\(110\) 1.73114e10 + 9.45566e9i 1.07490 + 0.587122i
\(111\) −1.76655e10 −1.04836
\(112\) 2.17086e9 + 2.17086e9i 0.123180 + 0.123180i
\(113\) 1.05676e10 1.05676e10i 0.573566 0.573566i −0.359557 0.933123i \(-0.617072\pi\)
0.933123 + 0.359557i \(0.117072\pi\)
\(114\) 1.24322e9i 0.0645690i
\(115\) 1.54232e10 2.82367e10i 0.766804 1.40386i
\(116\) −1.52646e9 −0.0726766
\(117\) −5.66288e9 5.66288e9i −0.258290 0.258290i
\(118\) 2.96382e9 2.96382e9i 0.129551 0.129551i
\(119\) 8.70346e9i 0.364718i
\(120\) 4.38848e9 + 1.49530e10i 0.176363 + 0.600927i
\(121\) 2.71380e10 1.04629
\(122\) −1.76755e10 1.76755e10i −0.653991 0.653991i
\(123\) 3.04530e9 3.04530e9i 0.108169 0.108169i
\(124\) 1.06668e9i 0.0363852i
\(125\) −1.99938e10 + 2.30559e10i −0.655155 + 0.755494i
\(126\) −2.38563e9 −0.0751190
\(127\) −1.38358e10 1.38358e10i −0.418779 0.418779i 0.466003 0.884783i \(-0.345693\pi\)
−0.884783 + 0.466003i \(0.845693\pi\)
\(128\) −1.04089e10 + 1.04089e10i −0.302940 + 0.302940i
\(129\) 1.18919e10i 0.332891i
\(130\) 3.34272e10 9.81039e9i 0.900292 0.264222i
\(131\) −2.03264e10 −0.526871 −0.263436 0.964677i \(-0.584856\pi\)
−0.263436 + 0.964677i \(0.584856\pi\)
\(132\) 6.24643e9 + 6.24643e9i 0.155870 + 0.155870i
\(133\) −1.01167e9 + 1.01167e9i −0.0243097 + 0.0243097i
\(134\) 3.95728e9i 0.0915952i
\(135\) −7.57342e9 4.13668e9i −0.168897 0.0922535i
\(136\) −6.99335e10 −1.50311
\(137\) −5.02310e10 5.02310e10i −1.04080 1.04080i −0.999131 0.0416734i \(-0.986731\pi\)
−0.0416734 0.999131i \(-0.513269\pi\)
\(138\) −2.79847e10 + 2.79847e10i −0.559145 + 0.559145i
\(139\) 9.64298e10i 1.85839i 0.369589 + 0.929195i \(0.379499\pi\)
−0.369589 + 0.929195i \(0.620501\pi\)
\(140\) −1.81113e9 + 3.31582e9i −0.0336752 + 0.0616524i
\(141\) −2.49160e10 −0.447077
\(142\) −6.23344e10 6.23344e10i −1.07966 1.07966i
\(143\) 6.62816e10 6.62816e10i 1.10844 1.10844i
\(144\) 1.36602e10i 0.220620i
\(145\) 4.91501e9 + 1.67470e10i 0.0766805 + 0.261275i
\(146\) 6.37231e10 0.960578
\(147\) 2.60815e10 + 2.60815e10i 0.379967 + 0.379967i
\(148\) 2.43343e10 2.43343e10i 0.342697 0.342697i
\(149\) 1.12032e11i 1.52550i 0.646694 + 0.762750i \(0.276151\pi\)
−0.646694 + 0.762750i \(0.723849\pi\)
\(150\) 3.15846e10 2.02866e10i 0.415929 0.267149i
\(151\) 6.20370e10 0.790253 0.395127 0.918627i \(-0.370701\pi\)
0.395127 + 0.918627i \(0.370701\pi\)
\(152\) −8.12889e9 8.12889e9i −0.100188 0.100188i
\(153\) 2.73834e10 2.73834e10i 0.326611 0.326611i
\(154\) 2.79227e10i 0.322370i
\(155\) 1.17027e10 3.43458e9i 0.130806 0.0383898i
\(156\) 1.56013e10 0.168864
\(157\) 1.11725e11 + 1.11725e11i 1.17125 + 1.17125i 0.981911 + 0.189344i \(0.0606360\pi\)
0.189344 + 0.981911i \(0.439364\pi\)
\(158\) 9.42176e10 9.42176e10i 0.956856 0.956856i
\(159\) 4.73746e10i 0.466187i
\(160\) −4.76730e10 2.60395e10i −0.454646 0.248332i
\(161\) −4.55449e10 −0.421027
\(162\) 7.50582e9 + 7.50582e9i 0.0672702 + 0.0672702i
\(163\) −7.98259e10 + 7.98259e10i −0.693754 + 0.693754i −0.963056 0.269302i \(-0.913207\pi\)
0.269302 + 0.963056i \(0.413207\pi\)
\(164\) 8.38984e9i 0.0707188i
\(165\) 4.84180e10 8.86435e10i 0.395901 0.724815i
\(166\) −8.99318e10 −0.713465
\(167\) −1.41288e10 1.41288e10i −0.108773 0.108773i 0.650626 0.759399i \(-0.274507\pi\)
−0.759399 + 0.650626i \(0.774507\pi\)
\(168\) 1.55986e10 1.55986e10i 0.116557 0.116557i
\(169\) 2.76888e10i 0.200850i
\(170\) 4.74391e10 + 1.61640e11i 0.334112 + 1.13843i
\(171\) 6.36596e9 0.0435395
\(172\) −1.63812e10 1.63812e10i −0.108818 0.108818i
\(173\) −1.21959e11 + 1.21959e11i −0.787018 + 0.787018i −0.981004 0.193986i \(-0.937858\pi\)
0.193986 + 0.981004i \(0.437858\pi\)
\(174\) 2.14687e10i 0.134605i
\(175\) 4.22101e10 + 9.19373e9i 0.257173 + 0.0560146i
\(176\) 1.59887e11 0.946779
\(177\) −1.51763e10 1.51763e10i −0.0873576 0.0873576i
\(178\) −1.40996e11 + 1.40996e11i −0.789054 + 0.789054i
\(179\) 9.05533e10i 0.492764i −0.969173 0.246382i \(-0.920758\pi\)
0.969173 0.246382i \(-0.0792418\pi\)
\(180\) 1.61307e10 4.73413e9i 0.0853673 0.0250541i
\(181\) −3.62000e11 −1.86344 −0.931722 0.363174i \(-0.881693\pi\)
−0.931722 + 0.363174i \(0.881693\pi\)
\(182\) −3.48704e10 3.48704e10i −0.174623 0.174623i
\(183\) −9.05078e10 + 9.05078e10i −0.440992 + 0.440992i
\(184\) 3.65959e11i 1.73518i
\(185\) −3.45330e11 1.88623e11i −1.59359 0.870433i
\(186\) −1.50022e10 −0.0673893
\(187\) 3.20511e11 + 3.20511e11i 1.40163 + 1.40163i
\(188\) 3.43219e10 3.43219e10i 0.146144 0.146144i
\(189\) 1.22157e10i 0.0506534i
\(190\) −1.32745e10 + 2.43029e10i −0.0536105 + 0.0981499i
\(191\) 4.77485e11 1.87842 0.939210 0.343344i \(-0.111560\pi\)
0.939210 + 0.343344i \(0.111560\pi\)
\(192\) 1.17749e11 + 1.17749e11i 0.451284 + 0.451284i
\(193\) 2.48930e10 2.48930e10i 0.0929587 0.0929587i −0.659098 0.752057i \(-0.729062\pi\)
0.752057 + 0.659098i \(0.229062\pi\)
\(194\) 3.77007e10i 0.137196i
\(195\) −5.02344e10 1.71165e11i −0.178168 0.607075i
\(196\) −7.18548e10 −0.248414
\(197\) −3.26049e11 3.26049e11i −1.09888 1.09888i −0.994541 0.104342i \(-0.966726\pi\)
−0.104342 0.994541i \(-0.533274\pi\)
\(198\) −8.78523e10 + 8.78523e10i −0.288687 + 0.288687i
\(199\) 1.34833e11i 0.432047i −0.976388 0.216024i \(-0.930691\pi\)
0.976388 0.216024i \(-0.0693088\pi\)
\(200\) −7.38729e10 + 3.39164e11i −0.230853 + 1.05989i
\(201\) −2.02634e10 −0.0617635
\(202\) 1.13126e11 + 1.13126e11i 0.336360 + 0.336360i
\(203\) 1.74701e10 1.74701e10i 0.0506776 0.0506776i
\(204\) 7.54417e10i 0.213531i
\(205\) 9.20466e10 2.70143e10i 0.254237 0.0746148i
\(206\) −1.01803e11 −0.274427
\(207\) 1.43296e11 + 1.43296e11i 0.377036 + 0.377036i
\(208\) 1.99669e11 1.99669e11i 0.512855 0.512855i
\(209\) 7.45108e10i 0.186848i
\(210\) −4.66350e10 2.54725e10i −0.114187 0.0623699i
\(211\) 6.66286e11 1.59312 0.796560 0.604560i \(-0.206651\pi\)
0.796560 + 0.604560i \(0.206651\pi\)
\(212\) 6.52588e10 + 6.52588e10i 0.152391 + 0.152391i
\(213\) −3.19186e11 + 3.19186e11i −0.728023 + 0.728023i
\(214\) 3.74580e10i 0.0834595i
\(215\) −1.26975e11 + 2.32466e11i −0.276393 + 0.506020i
\(216\) −9.81547e10 −0.208758
\(217\) −1.22080e10 1.22080e10i −0.0253715 0.0253715i
\(218\) 3.32909e10 3.32909e10i 0.0676151 0.0676151i
\(219\) 3.26296e11i 0.647726i
\(220\) 5.54110e10 + 1.88803e11i 0.107518 + 0.366350i
\(221\) 8.00520e11 1.51849
\(222\) 3.42248e11 + 3.42248e11i 0.634711 + 0.634711i
\(223\) 4.60329e11 4.60329e11i 0.834726 0.834726i −0.153433 0.988159i \(-0.549033\pi\)
0.988159 + 0.153433i \(0.0490328\pi\)
\(224\) 7.68951e10i 0.136351i
\(225\) −1.03878e11 1.61730e11i −0.180141 0.280465i
\(226\) −4.09469e11 −0.694510
\(227\) −2.28848e11 2.28848e11i −0.379680 0.379680i 0.491307 0.870986i \(-0.336519\pi\)
−0.870986 + 0.491307i \(0.836519\pi\)
\(228\) −8.76915e9 + 8.76915e9i −0.0142326 + 0.0142326i
\(229\) 5.54642e11i 0.880716i −0.897822 0.440358i \(-0.854852\pi\)
0.897822 0.440358i \(-0.145148\pi\)
\(230\) −8.45858e11 + 2.48247e11i −1.31419 + 0.385696i
\(231\) −1.42979e11 −0.217377
\(232\) 1.40375e11 + 1.40375e11i 0.208857 + 0.208857i
\(233\) 1.45797e11 1.45797e11i 0.212309 0.212309i −0.592939 0.805248i \(-0.702032\pi\)
0.805248 + 0.592939i \(0.202032\pi\)
\(234\) 2.19423e11i 0.312755i
\(235\) −4.87065e11 2.66040e11i −0.679591 0.371199i
\(236\) 4.18110e10 0.0571125
\(237\) −4.82444e11 4.82444e11i −0.645216 0.645216i
\(238\) 1.68619e11 1.68619e11i 0.220812 0.220812i
\(239\) 9.95227e11i 1.27624i 0.769937 + 0.638120i \(0.220288\pi\)
−0.769937 + 0.638120i \(0.779712\pi\)
\(240\) 1.45856e11 2.67034e11i 0.183176 0.335359i
\(241\) −5.91275e11 −0.727285 −0.363642 0.931539i \(-0.618467\pi\)
−0.363642 + 0.931539i \(0.618467\pi\)
\(242\) −5.25766e11 5.25766e11i −0.633455 0.633455i
\(243\) 3.84338e10 3.84338e10i 0.0453609 0.0453609i
\(244\) 2.49350e11i 0.288311i
\(245\) 2.31364e11 + 7.88333e11i 0.262099 + 0.893057i
\(246\) −1.17998e11 −0.130978
\(247\) 9.30505e10 + 9.30505e10i 0.101212 + 0.101212i
\(248\) 9.80931e10 9.80931e10i 0.104563 0.104563i
\(249\) 4.60499e11i 0.481096i
\(250\) 8.34036e11 5.93247e10i 0.854053 0.0607485i
\(251\) −2.15028e11 −0.215837 −0.107919 0.994160i \(-0.534419\pi\)
−0.107919 + 0.994160i \(0.534419\pi\)
\(252\) −1.68272e10 1.68272e10i −0.0165580 0.0165580i
\(253\) −1.67722e12 + 1.67722e12i −1.61803 + 1.61803i
\(254\) 5.36104e11i 0.507085i
\(255\) 8.27685e11 2.42914e11i 0.767652 0.225295i
\(256\) −8.12094e11 −0.738595
\(257\) −1.29066e12 1.29066e12i −1.15119 1.15119i −0.986314 0.164875i \(-0.947278\pi\)
−0.164875 0.986314i \(-0.552722\pi\)
\(258\) 2.30392e11 2.30392e11i 0.201543 0.201543i
\(259\) 5.57007e11i 0.477927i
\(260\) 3.04979e11 + 1.66583e11i 0.256687 + 0.140205i
\(261\) −1.09931e11 −0.0907651
\(262\) 3.93801e11 + 3.93801e11i 0.318985 + 0.318985i
\(263\) 8.67165e11 8.67165e11i 0.689164 0.689164i −0.272883 0.962047i \(-0.587977\pi\)
0.962047 + 0.272883i \(0.0879772\pi\)
\(264\) 1.14886e12i 0.895873i
\(265\) 5.05841e11 9.26093e11i 0.387066 0.708639i
\(266\) 3.91998e10 0.0294358
\(267\) 7.21975e11 + 7.21975e11i 0.532066 + 0.532066i
\(268\) 2.79130e10 2.79130e10i 0.0201898 0.0201898i
\(269\) 6.98198e11i 0.495698i −0.968799 0.247849i \(-0.920276\pi\)
0.968799 0.247849i \(-0.0797237\pi\)
\(270\) 6.65828e10 + 2.26869e11i 0.0464027 + 0.158109i
\(271\) 1.42090e12 0.972116 0.486058 0.873927i \(-0.338434\pi\)
0.486058 + 0.873927i \(0.338434\pi\)
\(272\) 9.65521e11 + 9.65521e11i 0.648510 + 0.648510i
\(273\) −1.78555e11 + 1.78555e11i −0.117750 + 0.117750i
\(274\) 1.94634e12i 1.26027i
\(275\) 1.89298e12 1.21585e12i 1.20360 0.773066i
\(276\) −3.94783e11 −0.246498
\(277\) −8.78959e11 8.78959e11i −0.538976 0.538976i 0.384252 0.923228i \(-0.374459\pi\)
−0.923228 + 0.384252i \(0.874459\pi\)
\(278\) 1.86821e12 1.86821e12i 1.12513 1.12513i
\(279\) 7.68193e10i 0.0454412i
\(280\) 4.71480e11 1.38373e11i 0.273951 0.0804007i
\(281\) 1.50905e12 0.861335 0.430668 0.902511i \(-0.358278\pi\)
0.430668 + 0.902511i \(0.358278\pi\)
\(282\) 4.82717e11 + 4.82717e11i 0.270675 + 0.270675i
\(283\) −1.51591e12 + 1.51591e12i −0.835104 + 0.835104i −0.988210 0.153106i \(-0.951073\pi\)
0.153106 + 0.988210i \(0.451073\pi\)
\(284\) 8.79361e11i 0.475965i
\(285\) 1.24444e11 + 6.79724e10i 0.0661833 + 0.0361500i
\(286\) −2.56826e12 −1.34217
\(287\) −9.60208e10 9.60208e10i −0.0493124 0.0493124i
\(288\) 2.41933e11 2.41933e11i 0.122105 0.122105i
\(289\) 1.85500e12i 0.920142i
\(290\) 2.29232e11 4.19677e11i 0.111760 0.204609i
\(291\) −1.93048e11 −0.0925123
\(292\) 4.49475e11 + 4.49475e11i 0.211734 + 0.211734i
\(293\) −1.62088e12 + 1.62088e12i −0.750606 + 0.750606i −0.974592 0.223986i \(-0.928093\pi\)
0.223986 + 0.974592i \(0.428093\pi\)
\(294\) 1.01060e12i 0.460088i
\(295\) −1.34627e11 4.58717e11i −0.0602589 0.205322i
\(296\) −4.47562e12 −1.96968
\(297\) 4.49851e11 + 4.49851e11i 0.194664 + 0.194664i
\(298\) 2.17050e12 2.17050e12i 0.923587 0.923587i
\(299\) 4.18909e12i 1.75293i
\(300\) 3.65877e11 + 7.96913e10i 0.150567 + 0.0327948i
\(301\) 3.74961e11 0.151759
\(302\) −1.20189e12 1.20189e12i −0.478445 0.478445i
\(303\) 5.79264e11 5.79264e11i 0.226811 0.226811i
\(304\) 2.24459e11i 0.0864510i
\(305\) −2.73567e12 + 8.02879e11i −1.03649 + 0.304194i
\(306\) −1.06104e12 −0.395481
\(307\) −2.69296e12 2.69296e12i −0.987503 0.987503i 0.0124200 0.999923i \(-0.496046\pi\)
−0.999923 + 0.0124200i \(0.996046\pi\)
\(308\) 1.96955e11 1.96955e11i 0.0710581 0.0710581i
\(309\) 5.21288e11i 0.185048i
\(310\) −2.93268e11 1.60186e11i −0.102437 0.0559520i
\(311\) −3.25599e11 −0.111913 −0.0559566 0.998433i \(-0.517821\pi\)
−0.0559566 + 0.998433i \(0.517821\pi\)
\(312\) −1.43472e12 1.43472e12i −0.485280 0.485280i
\(313\) −6.24856e11 + 6.24856e11i −0.207997 + 0.207997i −0.803416 0.595418i \(-0.796986\pi\)
0.595418 + 0.803416i \(0.296986\pi\)
\(314\) 4.32907e12i 1.41823i
\(315\) −1.30433e11 + 2.38796e11i −0.0420566 + 0.0769971i
\(316\) 1.32914e12 0.421828
\(317\) 2.66764e12 + 2.66764e12i 0.833356 + 0.833356i 0.987974 0.154619i \(-0.0494149\pi\)
−0.154619 + 0.987974i \(0.549415\pi\)
\(318\) −9.17827e11 + 9.17827e11i −0.282244 + 0.282244i
\(319\) 1.28670e12i 0.389514i
\(320\) 1.04453e12 + 3.55905e12i 0.311294 + 1.06068i
\(321\) −1.91805e11 −0.0562775
\(322\) 8.82379e11 + 8.82379e11i 0.254904 + 0.254904i
\(323\) −4.49955e11 + 4.49955e11i −0.127984 + 0.127984i
\(324\) 1.05886e11i 0.0296560i
\(325\) 8.45614e11 3.88237e12i 0.233214 1.07073i
\(326\) 3.09307e12 0.840042
\(327\) −1.70467e11 1.70467e11i −0.0455934 0.0455934i
\(328\) 7.71540e11 7.71540e11i 0.203231 0.203231i
\(329\) 7.85620e11i 0.203814i
\(330\) −2.65541e12 + 7.79323e11i −0.678518 + 0.199135i
\(331\) 6.37656e12 1.60489 0.802447 0.596723i \(-0.203531\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(332\) −6.34340e11 6.34340e11i −0.157265 0.157265i
\(333\) 1.75249e12 1.75249e12i 0.427991 0.427991i
\(334\) 5.47456e11i 0.131709i
\(335\) −3.96115e11 2.16362e11i −0.0938852 0.0512810i
\(336\) −4.30717e11 −0.100576
\(337\) 4.60234e10 + 4.60234e10i 0.0105884 + 0.0105884i 0.712381 0.701793i \(-0.247617\pi\)
−0.701793 + 0.712381i \(0.747617\pi\)
\(338\) −5.36439e11 + 5.36439e11i −0.121601 + 0.121601i
\(339\) 2.09670e12i 0.468314i
\(340\) −8.05527e11 + 1.47476e12i −0.177291 + 0.324583i
\(341\) −8.99137e11 −0.195009
\(342\) −1.23333e11 1.23333e11i −0.0263602 0.0263602i
\(343\) 1.70595e12 1.70595e12i 0.359332 0.359332i
\(344\) 3.01286e12i 0.625442i
\(345\) 1.27116e12 + 4.33125e12i 0.260078 + 0.886171i
\(346\) 4.72564e12 0.952972
\(347\) −8.26438e11 8.26438e11i −0.164272 0.164272i 0.620184 0.784456i \(-0.287058\pi\)
−0.784456 + 0.620184i \(0.787058\pi\)
\(348\) 1.51431e11 1.51431e11i 0.0296701 0.0296701i
\(349\) 8.53882e12i 1.64919i −0.565723 0.824595i \(-0.691403\pi\)
0.565723 0.824595i \(-0.308597\pi\)
\(350\) −6.39653e11 9.95889e11i −0.121788 0.189614i
\(351\) 1.12356e12 0.210893
\(352\) 2.83172e12 + 2.83172e12i 0.524006 + 0.524006i
\(353\) −1.40537e12 + 1.40537e12i −0.256399 + 0.256399i −0.823588 0.567189i \(-0.808031\pi\)
0.567189 + 0.823588i \(0.308031\pi\)
\(354\) 5.88048e11i 0.105778i
\(355\) −9.64764e12 + 2.83144e12i −1.71111 + 0.502187i
\(356\) −1.98905e12 −0.347853
\(357\) −8.63421e11 8.63421e11i −0.148896 0.148896i
\(358\) −1.75437e12 + 1.75437e12i −0.298335 + 0.298335i
\(359\) 8.59688e12i 1.44168i −0.693102 0.720840i \(-0.743756\pi\)
0.693102 0.720840i \(-0.256244\pi\)
\(360\) −1.91876e12 1.04804e12i −0.317328 0.173327i
\(361\) 6.02646e12 0.982939
\(362\) 7.01333e12 + 7.01333e12i 1.12819 + 1.12819i
\(363\) −2.69220e12 + 2.69220e12i −0.427144 + 0.427144i
\(364\) 4.91922e11i 0.0769821i
\(365\) 3.48402e12 6.37854e12i 0.537795 0.984593i
\(366\) 3.50697e12 0.533981
\(367\) 4.00237e11 + 4.00237e11i 0.0601156 + 0.0601156i 0.736525 0.676410i \(-0.236465\pi\)
−0.676410 + 0.736525i \(0.736465\pi\)
\(368\) −5.05253e12 + 5.05253e12i −0.748635 + 0.748635i
\(369\) 6.04214e11i 0.0883199i
\(370\) 3.03602e12 + 1.03447e13i 0.437821 + 1.49180i
\(371\) −1.49376e12 −0.212526
\(372\) −1.05819e11 1.05819e11i −0.0148542 0.0148542i
\(373\) 2.97007e11 2.97007e11i 0.0411361 0.0411361i −0.686240 0.727376i \(-0.740740\pi\)
0.727376 + 0.686240i \(0.240740\pi\)
\(374\) 1.24190e13i 1.69719i
\(375\) −3.03774e11 4.27071e12i −0.0409632 0.575895i
\(376\) −6.31257e12 −0.839976
\(377\) −1.60685e12 1.60685e12i −0.210994 0.210994i
\(378\) 2.36665e11 2.36665e11i 0.0306672 0.0306672i
\(379\) 1.15290e12i 0.147433i 0.997279 + 0.0737165i \(0.0234860\pi\)
−0.997279 + 0.0737165i \(0.976514\pi\)
\(380\) −2.65055e11 + 7.77896e10i −0.0334516 + 0.00981757i
\(381\) 2.74514e12 0.341932
\(382\) −9.25071e12 9.25071e12i −1.13726 1.13726i
\(383\) −1.27369e12 + 1.27369e12i −0.154550 + 0.154550i −0.780147 0.625597i \(-0.784856\pi\)
0.625597 + 0.780147i \(0.284856\pi\)
\(384\) 2.06522e12i 0.247350i
\(385\) −2.79500e12 1.52666e12i −0.330429 0.180484i
\(386\) −9.64544e11 −0.112560
\(387\) −1.17973e12 1.17973e12i −0.135902 0.135902i
\(388\) 2.65924e11 2.65924e11i 0.0302412 0.0302412i
\(389\) 3.23506e12i 0.363191i 0.983373 + 0.181595i \(0.0581261\pi\)
−0.983373 + 0.181595i \(0.941874\pi\)
\(390\) −2.34289e12 + 4.28936e12i −0.259674 + 0.475411i
\(391\) −2.02568e13 −2.21659
\(392\) 6.60785e12 + 6.60785e12i 0.713888 + 0.713888i
\(393\) 2.01647e12 2.01647e12i 0.215094 0.215094i
\(394\) 1.26336e13i 1.33060i
\(395\) −4.27968e12 1.45823e13i −0.445067 1.51649i
\(396\) −1.23935e12 −0.127267
\(397\) 8.49815e12 + 8.49815e12i 0.861731 + 0.861731i 0.991539 0.129808i \(-0.0414362\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(398\) −2.61223e12 + 2.61223e12i −0.261575 + 0.261575i
\(399\) 2.00724e11i 0.0198488i
\(400\) 5.70249e12 3.66268e12i 0.556884 0.357683i
\(401\) −2.58787e12 −0.249586 −0.124793 0.992183i \(-0.539827\pi\)
−0.124793 + 0.992183i \(0.539827\pi\)
\(402\) 3.92579e11 + 3.92579e11i 0.0373936 + 0.0373936i
\(403\) −1.12286e12 + 1.12286e12i −0.105633 + 0.105633i
\(404\) 1.59588e12i 0.148284i
\(405\) 1.16169e12 3.40940e11i 0.106614 0.0312898i
\(406\) −6.76926e11 −0.0613636
\(407\) 2.05121e13 + 2.05121e13i 1.83670 + 1.83670i
\(408\) 6.93771e12 6.93771e12i 0.613642 0.613642i
\(409\) 4.14544e12i 0.362205i −0.983464 0.181102i \(-0.942033\pi\)
0.983464 0.181102i \(-0.0579666\pi\)
\(410\) −2.30667e12 1.25992e12i −0.199097 0.108749i
\(411\) 9.96627e12 0.849814
\(412\) −7.18078e11 7.18078e11i −0.0604903 0.0604903i
\(413\) −4.78523e11 + 4.78523e11i −0.0398247 + 0.0398247i
\(414\) 5.55240e12i 0.456540i
\(415\) −4.91697e12 + 9.00197e12i −0.399445 + 0.731303i
\(416\) 7.07260e12 0.567692
\(417\) −9.56625e12 9.56625e12i −0.758685 0.758685i
\(418\) 1.44356e12 1.44356e12i 0.113124 0.113124i
\(419\) 6.01062e12i 0.465424i 0.972546 + 0.232712i \(0.0747600\pi\)
−0.972546 + 0.232712i \(0.925240\pi\)
\(420\) −1.49271e11 5.08615e11i −0.0114217 0.0389173i
\(421\) 6.72155e12 0.508228 0.254114 0.967174i \(-0.418216\pi\)
0.254114 + 0.967174i \(0.418216\pi\)
\(422\) −1.29085e13 1.29085e13i −0.964526 0.964526i
\(423\) 2.47177e12 2.47177e12i 0.182518 0.182518i
\(424\) 1.20026e13i 0.875880i
\(425\) 1.87736e13 + 4.08905e12i 1.35395 + 0.294902i
\(426\) 1.23677e13 0.881537
\(427\) 2.85379e12 + 2.85379e12i 0.201040 + 0.201040i
\(428\) 2.64213e11 2.64213e11i 0.0183965 0.0183965i
\(429\) 1.31508e13i 0.905038i
\(430\) 6.96377e12 2.04376e12i 0.473698 0.139024i
\(431\) −6.69149e12 −0.449921 −0.224961 0.974368i \(-0.572225\pi\)
−0.224961 + 0.974368i \(0.572225\pi\)
\(432\) 1.35515e12 + 1.35515e12i 0.0900676 + 0.0900676i
\(433\) 8.76838e12 8.76838e12i 0.576076 0.576076i −0.357744 0.933820i \(-0.616454\pi\)
0.933820 + 0.357744i \(0.116454\pi\)
\(434\) 4.73032e11i 0.0307215i
\(435\) −2.14897e12 1.17379e12i −0.137970 0.0753605i
\(436\) 4.69640e11 0.0298080
\(437\) −2.35460e12 2.35460e12i −0.147744 0.147744i
\(438\) −6.32161e12 + 6.32161e12i −0.392154 + 0.392154i
\(439\) 1.28383e13i 0.787378i 0.919244 + 0.393689i \(0.128801\pi\)
−0.919244 + 0.393689i \(0.871199\pi\)
\(440\) 1.22669e13 2.24582e13i 0.743827 1.36180i
\(441\) −5.17479e12 −0.310241
\(442\) −1.55091e13 1.55091e13i −0.919341 0.919341i
\(443\) 3.12846e12 3.12846e12i 0.183363 0.183363i −0.609457 0.792819i \(-0.708612\pi\)
0.792819 + 0.609457i \(0.208612\pi\)
\(444\) 4.82814e12i 0.279811i
\(445\) 6.40452e12 + 2.18223e13i 0.367017 + 1.25055i
\(446\) −1.78367e13 −1.01074
\(447\) −1.11141e13 1.11141e13i −0.622783 0.622783i
\(448\) 3.71271e12 3.71271e12i 0.205732 0.205732i
\(449\) 1.72912e13i 0.947532i 0.880651 + 0.473766i \(0.157106\pi\)
−0.880651 + 0.473766i \(0.842894\pi\)
\(450\) −1.12081e12 + 5.14585e12i −0.0607393 + 0.278865i
\(451\) −7.07206e12 −0.379021
\(452\) −2.88822e12 2.88822e12i −0.153087 0.153087i
\(453\) −6.15434e12 + 6.15434e12i −0.322620 + 0.322620i
\(454\) 8.86731e12i 0.459740i
\(455\) −5.39697e12 + 1.58393e12i −0.276754 + 0.0812232i
\(456\) 1.61284e12 0.0818028
\(457\) −7.97734e12 7.97734e12i −0.400200 0.400200i 0.478104 0.878303i \(-0.341324\pi\)
−0.878303 + 0.478104i \(0.841324\pi\)
\(458\) −1.07455e13 + 1.07455e13i −0.533214 + 0.533214i
\(459\) 5.43311e12i 0.266677i
\(460\) −7.71735e12 4.21529e12i −0.374696 0.204663i
\(461\) −1.02581e13 −0.492677 −0.246339 0.969184i \(-0.579228\pi\)
−0.246339 + 0.969184i \(0.579228\pi\)
\(462\) 2.77006e12 + 2.77006e12i 0.131607 + 0.131607i
\(463\) 2.71629e12 2.71629e12i 0.127665 0.127665i −0.640387 0.768052i \(-0.721226\pi\)
0.768052 + 0.640387i \(0.221226\pi\)
\(464\) 3.87610e12i 0.180221i
\(465\) −8.20237e11 + 1.50169e12i −0.0377289 + 0.0690741i
\(466\) −5.64929e12 −0.257078
\(467\) −2.20310e13 2.20310e13i −0.991859 0.991859i 0.00810801 0.999967i \(-0.497419\pi\)
−0.999967 + 0.00810801i \(0.997419\pi\)
\(468\) −1.54772e12 + 1.54772e12i −0.0689386 + 0.0689386i
\(469\) 6.38921e11i 0.0281568i
\(470\) 4.28210e12 + 1.45905e13i 0.186710 + 0.636182i
\(471\) −2.21672e13 −0.956325
\(472\) −3.84499e12 3.84499e12i −0.164129 0.164129i
\(473\) 1.38082e13 1.38082e13i 0.583218 0.583218i
\(474\) 1.86936e13i 0.781269i
\(475\) 1.70689e12 + 2.65749e12i 0.0705891 + 0.109902i
\(476\) 2.37874e12 0.0973446
\(477\) 4.69976e12 + 4.69976e12i 0.190320 + 0.190320i
\(478\) 1.92814e13 1.92814e13i 0.772677 0.772677i
\(479\) 3.71794e12i 0.147443i −0.997279 0.0737217i \(-0.976512\pi\)
0.997279 0.0737217i \(-0.0234877\pi\)
\(480\) 7.31260e12 2.14614e12i 0.286989 0.0842272i
\(481\) 5.12319e13 1.98983
\(482\) 1.14553e13 + 1.14553e13i 0.440322 + 0.440322i
\(483\) 4.51825e12 4.51825e12i 0.171884 0.171884i
\(484\) 7.41706e12i 0.279258i
\(485\) −3.77375e12 2.06126e12i −0.140626 0.0768112i
\(486\) −1.48922e12 −0.0549259
\(487\) −7.76585e12 7.76585e12i −0.283494 0.283494i 0.551007 0.834501i \(-0.314244\pi\)
−0.834501 + 0.551007i \(0.814244\pi\)
\(488\) −2.29305e13 + 2.29305e13i −0.828544 + 0.828544i
\(489\) 1.58381e13i 0.566448i
\(490\) 1.07906e13 1.97554e13i 0.382002 0.699369i
\(491\) −2.81134e13 −0.985159 −0.492580 0.870267i \(-0.663946\pi\)
−0.492580 + 0.870267i \(0.663946\pi\)
\(492\) −8.32309e11 8.32309e11i −0.0288708 0.0288708i
\(493\) 7.77009e12 7.77009e12i 0.266804 0.266804i
\(494\) 3.60549e12i 0.122555i
\(495\) 3.99055e12 + 1.35971e13i 0.134279 + 0.457531i
\(496\) −2.70860e12 −0.0902269
\(497\) 1.00642e13 + 1.00642e13i 0.331892 + 0.331892i
\(498\) 8.92162e12 8.92162e12i 0.291271 0.291271i
\(499\) 3.18691e12i 0.103007i −0.998673 0.0515035i \(-0.983599\pi\)
0.998673 0.0515035i \(-0.0164013\pi\)
\(500\) 6.30138e12 + 5.46448e12i 0.201644 + 0.174863i
\(501\) 2.80327e12 0.0888129
\(502\) 4.16592e12 + 4.16592e12i 0.130675 + 0.130675i
\(503\) 1.22457e13 1.22457e13i 0.380315 0.380315i −0.490900 0.871216i \(-0.663332\pi\)
0.871216 + 0.490900i \(0.163332\pi\)
\(504\) 3.09490e12i 0.0951686i
\(505\) 1.75087e13 5.13855e12i 0.533086 0.156453i
\(506\) 6.49884e13 1.95922
\(507\) 2.74685e12 + 2.74685e12i 0.0819966 + 0.0819966i
\(508\) −3.78145e12 + 3.78145e12i −0.111774 + 0.111774i
\(509\) 1.15777e13i 0.338870i 0.985541 + 0.169435i \(0.0541943\pi\)
−0.985541 + 0.169435i \(0.945806\pi\)
\(510\) −2.07416e13 1.13293e13i −0.601162 0.328361i
\(511\) −1.02884e13 −0.295286
\(512\) 2.63921e13 + 2.63921e13i 0.750110 + 0.750110i
\(513\) −6.31531e11 + 6.31531e11i −0.0177749 + 0.0177749i
\(514\) 5.00101e13i 1.39393i
\(515\) −5.56604e12 + 1.01903e13i −0.153642 + 0.281288i
\(516\) 3.25017e12 0.0888499
\(517\) 2.89310e13 + 2.89310e13i 0.783269 + 0.783269i
\(518\) 1.07914e13 1.07914e13i 0.289352 0.289352i
\(519\) 2.41978e13i 0.642598i
\(520\) −1.27271e13 4.33654e13i −0.334744 1.14058i
\(521\) −2.03576e13 −0.530319 −0.265160 0.964205i \(-0.585425\pi\)
−0.265160 + 0.964205i \(0.585425\pi\)
\(522\) 2.12979e12 + 2.12979e12i 0.0549521 + 0.0549521i
\(523\) −4.62281e13 + 4.62281e13i −1.18140 + 1.18140i −0.202021 + 0.979381i \(0.564751\pi\)
−0.979381 + 0.202021i \(0.935249\pi\)
\(524\) 5.55540e12i 0.140624i
\(525\) −5.09948e12 + 3.27537e12i −0.127858 + 0.0821227i
\(526\) −3.36006e13 −0.834485
\(527\) −5.42970e12 5.42970e12i −0.133574 0.133574i
\(528\) −1.58614e13 + 1.58614e13i −0.386521 + 0.386521i
\(529\) 6.45764e13i 1.55882i
\(530\) −2.77421e13 + 8.14189e12i −0.663375 + 0.194691i
\(531\) 3.01112e12 0.0713272
\(532\) 2.76499e11 + 2.76499e11i 0.00648836 + 0.00648836i
\(533\) −8.83172e12 + 8.83172e12i −0.205310 + 0.205310i
\(534\) 2.79748e13i 0.644260i
\(535\) −3.74946e12 2.04799e12i −0.0855461 0.0467261i
\(536\) −5.13382e12 −0.116042
\(537\) 8.98328e12 + 8.98328e12i 0.201170 + 0.201170i
\(538\) −1.35268e13 + 1.35268e13i −0.300112 + 0.300112i
\(539\) 6.05687e13i 1.33139i
\(540\) −1.13059e12 + 2.06989e12i −0.0246228 + 0.0450793i
\(541\) −2.10515e13 −0.454251 −0.227126 0.973865i \(-0.572933\pi\)
−0.227126 + 0.973865i \(0.572933\pi\)
\(542\) −2.75283e13 2.75283e13i −0.588550 0.588550i
\(543\) 3.59120e13 3.59120e13i 0.760747 0.760747i
\(544\) 3.42002e13i 0.717852i
\(545\) −1.51219e12 5.15251e12i −0.0314501 0.107161i
\(546\) 6.91860e12 0.142579
\(547\) 4.15569e13 + 4.15569e13i 0.848606 + 0.848606i 0.989959 0.141353i \(-0.0451453\pi\)
−0.141353 + 0.989959i \(0.545145\pi\)
\(548\) −1.37286e13 + 1.37286e13i −0.277795 + 0.277795i
\(549\) 1.79575e13i 0.360068i
\(550\) −6.02299e13 1.31186e13i −1.19674 0.260660i
\(551\) 1.80635e12 0.0355668
\(552\) 3.63048e13 + 3.63048e13i 0.708383 + 0.708383i
\(553\) −1.52119e13 + 1.52119e13i −0.294142 + 0.294142i
\(554\) 3.40576e13i 0.652627i
\(555\) 5.29704e13 1.55460e13i 1.00593 0.295226i
\(556\) 2.63552e13 0.496011
\(557\) −5.59600e12 5.59600e12i −0.104376 0.104376i 0.652990 0.757366i \(-0.273514\pi\)
−0.757366 + 0.652990i \(0.773514\pi\)
\(558\) 1.48828e12 1.48828e12i 0.0275116 0.0275116i
\(559\) 3.44879e13i 0.631840i
\(560\) −8.41979e12 4.59897e12i −0.152884 0.0835066i
\(561\) −6.35921e13 −1.14443
\(562\) −2.92361e13 2.92361e13i −0.521480 0.521480i
\(563\) 4.89913e13 4.89913e13i 0.866118 0.866118i −0.125922 0.992040i \(-0.540189\pi\)
0.992040 + 0.125922i \(0.0401888\pi\)
\(564\) 6.80976e12i 0.119326i
\(565\) −2.23875e13 + 4.09869e13i −0.388833 + 0.711874i
\(566\) 5.87379e13 1.01120
\(567\) −1.21185e12 1.21185e12i −0.0206792 0.0206792i
\(568\) −8.08670e13 + 8.08670e13i −1.36782 + 1.36782i
\(569\) 7.04691e13i 1.18151i −0.806851 0.590755i \(-0.798830\pi\)
0.806851 0.590755i \(-0.201170\pi\)
\(570\) −1.09407e12 3.72784e12i −0.0181832 0.0619559i
\(571\) 6.55472e13 1.07988 0.539938 0.841705i \(-0.318448\pi\)
0.539938 + 0.841705i \(0.318448\pi\)
\(572\) −1.81154e13 1.81154e13i −0.295847 0.295847i
\(573\) −4.73686e13 + 4.73686e13i −0.766862 + 0.766862i
\(574\) 3.72058e12i 0.0597106i
\(575\) −2.13978e13 + 9.82413e13i −0.340432 + 1.56299i
\(576\) −2.33623e13 −0.368472
\(577\) −3.36364e13 3.36364e13i −0.525933 0.525933i 0.393424 0.919357i \(-0.371290\pi\)
−0.919357 + 0.393424i \(0.871290\pi\)
\(578\) 3.59385e13 3.59385e13i 0.557083 0.557083i
\(579\) 4.93898e12i 0.0759004i
\(580\) 4.57713e12 1.34332e12i 0.0697353 0.0204663i
\(581\) 1.45199e13 0.219322
\(582\) 3.74007e12 + 3.74007e12i 0.0560099 + 0.0560099i
\(583\) −5.50087e13 + 5.50087e13i −0.816749 + 0.816749i
\(584\) 8.26686e13i 1.21696i
\(585\) 2.19638e13 + 1.19968e13i 0.320574 + 0.175101i
\(586\) 6.28052e13 0.908882
\(587\) 1.69574e13 + 1.69574e13i 0.243315 + 0.243315i 0.818220 0.574905i \(-0.194961\pi\)
−0.574905 + 0.818220i \(0.694961\pi\)
\(588\) 7.12831e12 7.12831e12i 0.101414 0.101414i
\(589\) 1.26227e12i 0.0178064i
\(590\) −6.27887e12 + 1.14953e13i −0.0878257 + 0.160791i
\(591\) 6.46909e13 0.897235
\(592\) 6.17916e13 + 6.17916e13i 0.849809 + 0.849809i
\(593\) 2.05210e13 2.05210e13i 0.279850 0.279850i −0.553199 0.833049i \(-0.686593\pi\)
0.833049 + 0.553199i \(0.186593\pi\)
\(594\) 1.74307e13i 0.235712i
\(595\) −7.65926e12 2.60976e13i −0.102708 0.349958i
\(596\) 3.06195e13 0.407161
\(597\) 1.33760e13 + 1.33760e13i 0.176383 + 0.176383i
\(598\) 8.11588e13 8.11588e13i 1.06128 1.06128i
\(599\) 7.92364e13i 1.02752i 0.857934 + 0.513760i \(0.171748\pi\)
−0.857934 + 0.513760i \(0.828252\pi\)
\(600\) −2.63180e13 4.09750e13i −0.338452 0.526942i
\(601\) −3.80901e13 −0.485781 −0.242890 0.970054i \(-0.578096\pi\)
−0.242890 + 0.970054i \(0.578096\pi\)
\(602\) −7.26443e12 7.26443e12i −0.0918796 0.0918796i
\(603\) 2.01022e12 2.01022e12i 0.0252148 0.0252148i
\(604\) 1.69553e13i 0.210921i
\(605\) −8.13740e13 + 2.38821e13i −1.00394 + 0.294642i
\(606\) −2.24451e13 −0.274637
\(607\) 2.93515e13 + 2.93515e13i 0.356194 + 0.356194i 0.862408 0.506214i \(-0.168955\pi\)
−0.506214 + 0.862408i \(0.668955\pi\)
\(608\) −3.97535e12 + 3.97535e12i −0.0478473 + 0.0478473i
\(609\) 3.46622e12i 0.0413780i
\(610\) 6.85553e13 + 3.74456e13i 0.811693 + 0.443355i
\(611\) 7.22592e13 0.848569
\(612\) −7.48414e12 7.48414e12i −0.0871736 0.0871736i
\(613\) 1.13080e14 1.13080e14i 1.30642 1.30642i 0.382443 0.923979i \(-0.375083\pi\)
0.923979 0.382443i \(-0.124917\pi\)
\(614\) 1.04346e14i 1.19573i
\(615\) −6.45148e12 + 1.18114e13i −0.0733304 + 0.134253i
\(616\) −3.62244e13 −0.408412
\(617\) −7.40831e13 7.40831e13i −0.828502 0.828502i 0.158808 0.987310i \(-0.449235\pi\)
−0.987310 + 0.158808i \(0.949235\pi\)
\(618\) 1.00993e13 1.00993e13i 0.112034 0.112034i
\(619\) 8.58743e12i 0.0944953i −0.998883 0.0472476i \(-0.984955\pi\)
0.998883 0.0472476i \(-0.0150450\pi\)
\(620\) −9.38704e11 3.19847e12i −0.0102464 0.0349127i
\(621\) −2.84312e13 −0.307849
\(622\) 6.30810e12 + 6.30810e12i 0.0677559 + 0.0677559i
\(623\) 2.27645e13 2.27645e13i 0.242559 0.242559i
\(624\) 3.96161e13i 0.418744i
\(625\) 3.96621e13 8.67287e13i 0.415888 0.909416i
\(626\) 2.42117e13 0.251857
\(627\) −7.39179e12 7.39179e12i −0.0762802 0.0762802i
\(628\) 3.05354e13 3.05354e13i 0.312612 0.312612i
\(629\) 2.47737e14i 2.51616i
\(630\) 7.15338e12 2.09941e12i 0.0720789 0.0211541i
\(631\) −9.17553e13 −0.917243 −0.458621 0.888632i \(-0.651657\pi\)
−0.458621 + 0.888632i \(0.651657\pi\)
\(632\) −1.22229e14 1.22229e14i −1.21224 1.21224i
\(633\) −6.60985e13 + 6.60985e13i −0.650388 + 0.650388i
\(634\) 1.03365e14i 1.00908i
\(635\) 5.36629e13 + 2.93112e13i 0.519763 + 0.283900i
\(636\) −1.29479e13 −0.124427
\(637\) −7.56393e13 7.56393e13i −0.721191 0.721191i
\(638\) −2.49283e13 + 2.49283e13i −0.235824 + 0.235824i
\(639\) 6.33292e13i 0.594428i
\(640\) 2.20514e13 4.03717e13i 0.205370 0.375990i
\(641\) −1.50268e14 −1.38860 −0.694298 0.719688i \(-0.744285\pi\)
−0.694298 + 0.719688i \(0.744285\pi\)
\(642\) 3.71600e12 + 3.71600e12i 0.0340722 + 0.0340722i
\(643\) −8.46613e13 + 8.46613e13i −0.770248 + 0.770248i −0.978150 0.207902i \(-0.933336\pi\)
0.207902 + 0.978150i \(0.433336\pi\)
\(644\) 1.24478e13i 0.112374i
\(645\) −1.04652e13 3.56582e13i −0.0937448 0.319419i
\(646\) 1.74347e13 0.154971
\(647\) 6.78537e13 + 6.78537e13i 0.598483 + 0.598483i 0.939909 0.341425i \(-0.110910\pi\)
−0.341425 + 0.939909i \(0.610910\pi\)
\(648\) 9.73737e12 9.73737e12i 0.0852249 0.0852249i
\(649\) 3.52438e13i 0.306097i
\(650\) −9.15991e13 + 5.88335e13i −0.789449 + 0.507058i
\(651\) 2.42218e12 0.0207158
\(652\) 2.18172e13 + 2.18172e13i 0.185165 + 0.185165i
\(653\) −4.85301e13 + 4.85301e13i −0.408738 + 0.408738i −0.881298 0.472560i \(-0.843330\pi\)
0.472560 + 0.881298i \(0.343330\pi\)
\(654\) 6.60521e12i 0.0552075i
\(655\) 6.09494e13 1.78878e13i 0.505549 0.148371i
\(656\) −2.13042e13 −0.175366
\(657\) 3.23700e13 + 3.23700e13i 0.264433 + 0.264433i
\(658\) 1.52205e13 1.52205e13i 0.123395 0.123395i
\(659\) 1.36281e14i 1.09650i −0.836316 0.548248i \(-0.815295\pi\)
0.836316 0.548248i \(-0.184705\pi\)
\(660\) −2.42271e13 1.32331e13i −0.193456 0.105668i
\(661\) −1.44495e14 −1.14510 −0.572551 0.819869i \(-0.694046\pi\)
−0.572551 + 0.819869i \(0.694046\pi\)
\(662\) −1.23538e14 1.23538e14i −0.971655 0.971655i
\(663\) −7.94151e13 + 7.94151e13i −0.619920 + 0.619920i
\(664\) 1.16669e14i 0.903892i
\(665\) 2.14323e12 3.92381e12i 0.0164801 0.0301717i
\(666\) −6.79049e13 −0.518239
\(667\) 4.06606e13 + 4.06606e13i 0.307996 + 0.307996i
\(668\) −3.86152e12 + 3.86152e12i −0.0290319 + 0.0290319i
\(669\) 9.13333e13i 0.681551i
\(670\) 3.48250e12 + 1.18660e13i 0.0257939 + 0.0878883i
\(671\) 2.10185e14 1.54522
\(672\) −7.62833e12 7.62833e12i −0.0556651 0.0556651i
\(673\) 1.27146e14 1.27146e14i 0.920932 0.920932i −0.0761637 0.997095i \(-0.524267\pi\)
0.997095 + 0.0761637i \(0.0242672\pi\)
\(674\) 1.78330e12i 0.0128211i
\(675\) 2.63495e13 + 5.73915e12i 0.188041 + 0.0409571i
\(676\) −7.56762e12 −0.0536075
\(677\) 7.64265e13 + 7.64265e13i 0.537404 + 0.537404i 0.922766 0.385362i \(-0.125923\pi\)
−0.385362 + 0.922766i \(0.625923\pi\)
\(678\) 4.06211e13 4.06211e13i 0.283533 0.283533i
\(679\) 6.08695e12i 0.0421746i
\(680\) 2.09698e14 6.15432e13i 1.44228 0.423288i
\(681\) 4.54054e13 0.310007
\(682\) 1.74197e13 + 1.74197e13i 0.118065 + 0.118065i
\(683\) 1.74091e14 1.74091e14i 1.17132 1.17132i 0.189420 0.981896i \(-0.439339\pi\)
0.981896 0.189420i \(-0.0606606\pi\)
\(684\) 1.73988e12i 0.0116208i
\(685\) 1.94824e14 + 1.06415e14i 1.29178 + 0.705584i
\(686\) −6.61016e13 −0.435102
\(687\) 5.50229e13 + 5.50229e13i 0.359551 + 0.359551i
\(688\) 4.15964e13 4.15964e13i 0.269844 0.269844i
\(689\) 1.37392e14i 0.884840i
\(690\) 5.92856e13 1.08540e14i 0.379057 0.693976i
\(691\) −1.59952e14 −1.01531 −0.507656 0.861560i \(-0.669488\pi\)
−0.507656 + 0.861560i \(0.669488\pi\)
\(692\) 3.33326e13 + 3.33326e13i 0.210058 + 0.210058i
\(693\) 1.41842e13 1.41842e13i 0.0887437 0.0887437i
\(694\) 3.20225e13i 0.198911i
\(695\) −8.48606e13 2.89147e14i −0.523338 1.78318i
\(696\) −2.78516e13 −0.170531
\(697\) −4.27067e13 4.27067e13i −0.259616 0.259616i
\(698\) −1.65430e14 + 1.65430e14i −0.998473 + 0.998473i
\(699\) 2.89274e13i 0.173350i
\(700\) 2.51273e12 1.15364e13i 0.0149505 0.0686405i
\(701\) −5.32572e13 −0.314622 −0.157311 0.987549i \(-0.550282\pi\)
−0.157311 + 0.987549i \(0.550282\pi\)
\(702\) −2.17678e13 2.17678e13i −0.127682 0.127682i
\(703\) −2.87963e13 + 2.87963e13i −0.167711 + 0.167711i
\(704\) 2.73446e14i 1.58128i
\(705\) 7.47112e13 2.19267e13i 0.428983 0.125900i
\(706\) 5.44547e13 0.310464
\(707\) −1.82647e13 1.82647e13i −0.103399 0.103399i
\(708\) −4.14784e12 + 4.14784e12i −0.0233161 + 0.0233161i
\(709\) 1.45905e14i 0.814403i −0.913338 0.407201i \(-0.866505\pi\)
0.913338 0.407201i \(-0.133495\pi\)
\(710\) 2.41768e14 + 1.32056e14i 1.34000 + 0.731924i
\(711\) 9.57211e13 0.526817
\(712\) 1.82916e14 + 1.82916e14i 0.999656 + 0.999656i
\(713\) 2.84134e13 2.84134e13i 0.154197 0.154197i
\(714\) 3.34556e13i 0.180292i
\(715\) −1.40418e14 + 2.57077e14i −0.751436 + 1.37573i
\(716\) −2.47491e13 −0.131521
\(717\) −9.87308e13 9.87308e13i −0.521023 0.521023i
\(718\) −1.66555e14 + 1.66555e14i −0.872839 + 0.872839i
\(719\) 2.00526e14i 1.04358i 0.853073 + 0.521791i \(0.174736\pi\)
−0.853073 + 0.521791i \(0.825264\pi\)
\(720\) 1.20213e13 + 4.09605e13i 0.0621282 + 0.211691i
\(721\) 1.64366e13 0.0843600
\(722\) −1.16756e14 1.16756e14i −0.595103 0.595103i
\(723\) 5.86571e13 5.86571e13i 0.296913 0.296913i
\(724\) 9.89381e13i 0.497360i
\(725\) −2.94756e13 4.58912e13i −0.147154 0.229108i
\(726\) 1.04317e14 0.517214
\(727\) −1.43344e14 1.43344e14i −0.705841 0.705841i 0.259817 0.965658i \(-0.416338\pi\)
−0.965658 + 0.259817i \(0.916338\pi\)
\(728\) −4.52378e13 + 4.52378e13i −0.221230 + 0.221230i
\(729\) 7.62560e12i 0.0370370i
\(730\) −1.91076e14 + 5.60779e13i −0.921703 + 0.270506i
\(731\) 1.66769e14 0.798969
\(732\) 2.47366e13 + 2.47366e13i 0.117702 + 0.117702i
\(733\) −1.53239e14 + 1.53239e14i −0.724183 + 0.724183i −0.969454 0.245271i \(-0.921123\pi\)
0.245271 + 0.969454i \(0.421123\pi\)
\(734\) 1.55083e13i 0.0727918i
\(735\) −1.01158e14 5.52537e13i −0.471591 0.257588i
\(736\) −1.78969e14 −0.828682
\(737\) 2.35287e13 + 2.35287e13i 0.108208 + 0.108208i
\(738\) 1.17059e13 1.17059e13i 0.0534717 0.0534717i
\(739\) 1.18250e14i 0.536510i −0.963348 0.268255i \(-0.913553\pi\)
0.963348 0.268255i \(-0.0864470\pi\)
\(740\) −5.15524e13 + 9.43819e13i −0.232322 + 0.425334i
\(741\) −1.84620e13 −0.0826396
\(742\) 2.89398e13 + 2.89398e13i 0.128670 + 0.128670i
\(743\) 7.93545e13 7.93545e13i 0.350451 0.350451i −0.509826 0.860277i \(-0.670290\pi\)
0.860277 + 0.509826i \(0.170290\pi\)
\(744\) 1.94625e13i 0.0853757i
\(745\) −9.85912e13 3.35932e14i −0.429593 1.46376i
\(746\) −1.15083e13 −0.0498102
\(747\) −4.56835e13 4.56835e13i −0.196407 0.196407i
\(748\) 8.75986e13 8.75986e13i 0.374101 0.374101i
\(749\) 6.04777e12i 0.0256558i
\(750\) −7.68547e13 + 8.86252e13i −0.323865 + 0.373466i
\(751\) −3.34618e13 −0.140072 −0.0700358 0.997544i \(-0.522311\pi\)
−0.0700358 + 0.997544i \(0.522311\pi\)
\(752\) 8.71530e13 + 8.71530e13i 0.362404 + 0.362404i
\(753\) 2.13317e13 2.13317e13i 0.0881152 0.0881152i
\(754\) 6.22618e13i 0.255485i
\(755\) −1.86020e14 + 5.45941e13i −0.758271 + 0.222542i
\(756\) 3.33866e12 0.0135196
\(757\) −8.70456e13 8.70456e13i −0.350161 0.350161i 0.510009 0.860169i \(-0.329642\pi\)
−0.860169 + 0.510009i \(0.829642\pi\)
\(758\) 2.23360e13 2.23360e13i 0.0892607 0.0892607i
\(759\) 3.32775e14i 1.32112i
\(760\) 3.15284e13 + 1.72211e13i 0.124346 + 0.0679193i
\(761\) −1.71905e14 −0.673542 −0.336771 0.941587i \(-0.609335\pi\)
−0.336771 + 0.941587i \(0.609335\pi\)
\(762\) −5.31839e13 5.31839e13i −0.207017 0.207017i
\(763\) −5.37497e12 + 5.37497e12i −0.0207852 + 0.0207852i
\(764\) 1.30501e14i 0.501357i
\(765\) −5.80119e13 + 1.06208e14i −0.221416 + 0.405369i
\(766\) 4.93525e13 0.187139
\(767\) 4.40132e13 + 4.40132e13i 0.165808 + 0.165808i
\(768\) 8.05633e13 8.05633e13i 0.301530 0.301530i
\(769\) 1.68570e14i 0.626828i 0.949617 + 0.313414i \(0.101473\pi\)
−0.949617 + 0.313414i \(0.898527\pi\)
\(770\) 2.45727e13 + 8.37272e13i 0.0907819 + 0.309323i
\(771\) 2.56078e14 0.939942
\(772\) −6.80348e12 6.80348e12i −0.0248110 0.0248110i
\(773\) −6.52829e12 + 6.52829e12i −0.0236538 + 0.0236538i −0.718835 0.695181i \(-0.755324\pi\)
0.695181 + 0.718835i \(0.255324\pi\)
\(774\) 4.57117e13i 0.164559i
\(775\) −3.20685e13 + 2.05974e13i −0.114702 + 0.0736723i
\(776\) −4.89094e13 −0.173814
\(777\) −5.52575e13 5.52575e13i −0.195113 0.195113i
\(778\) 6.26755e13 6.26755e13i 0.219887 0.219887i
\(779\) 9.92823e12i 0.0346086i
\(780\) −4.67810e13 + 1.37295e13i −0.162030 + 0.0475536i
\(781\) 7.41240e14 2.55096
\(782\) 3.92451e14 + 3.92451e14i 1.34200 + 1.34200i
\(783\) 1.09057e13 1.09057e13i 0.0370547 0.0370547i
\(784\) 1.82460e14i 0.616008i
\(785\) −4.33331e14 2.36690e14i −1.45369 0.794019i
\(786\) −7.81335e13 −0.260450
\(787\) −1.24436e14 1.24436e14i −0.412167 0.412167i 0.470326 0.882493i \(-0.344136\pi\)
−0.882493 + 0.470326i \(0.844136\pi\)
\(788\) −8.91122e13 + 8.91122e13i −0.293296 + 0.293296i
\(789\) 1.72053e14i 0.562700i
\(790\) −1.99600e14 + 3.65428e14i −0.648673 + 1.18759i
\(791\) 6.61106e13 0.213496
\(792\) 1.13972e14 + 1.13972e14i 0.365739 + 0.365739i
\(793\) 2.62483e14 2.62483e14i 0.837019 0.837019i
\(794\) 3.29283e14i 1.04344i
\(795\) 4.16908e13 + 1.42054e14i 0.131282 + 0.447320i
\(796\) −3.68512e13 −0.115315
\(797\) 1.74781e14 + 1.74781e14i 0.543503 + 0.543503i 0.924554 0.381051i \(-0.124438\pi\)
−0.381051 + 0.924554i \(0.624438\pi\)
\(798\) −3.88879e12 + 3.88879e12i −0.0120171 + 0.0120171i
\(799\) 3.49416e14i 1.07302i
\(800\) 1.65864e14 + 3.61267e13i 0.506178 + 0.110250i
\(801\) −1.43246e14 −0.434430
\(802\) 5.01369e13 + 5.01369e13i 0.151107 + 0.151107i
\(803\) −3.78877e14 + 3.78877e14i −1.13480 + 1.13480i
\(804\) 5.53817e12i 0.0164849i
\(805\) 1.36568e14 4.00806e13i 0.403988 0.118565i
\(806\) 4.35082e13 0.127907
\(807\) 6.92643e13 + 6.92643e13i 0.202368 + 0.202368i
\(808\) 1.46759e14 1.46759e14i 0.426136 0.426136i
\(809\) 2.76524e14i 0.797977i −0.916956 0.398988i \(-0.869361\pi\)
0.916956 0.398988i \(-0.130639\pi\)
\(810\) −2.91117e13 1.59011e13i −0.0834916 0.0456040i
\(811\) 4.11773e14 1.17369 0.586845 0.809700i \(-0.300370\pi\)
0.586845 + 0.809700i \(0.300370\pi\)
\(812\) −4.77475e12 4.77475e12i −0.0135260 0.0135260i
\(813\) −1.40960e14 + 1.40960e14i −0.396865 + 0.396865i
\(814\) 7.94798e14i 2.22400i
\(815\) 1.69111e14 3.09609e14i 0.470311 0.861044i
\(816\) −1.91568e14 −0.529507
\(817\) 1.93849e13 + 1.93849e13i 0.0532540 + 0.0532540i
\(818\) −8.03131e13 + 8.03131e13i −0.219291 + 0.219291i
\(819\) 3.54269e13i 0.0961421i
\(820\) −7.38327e12 2.51572e13i −0.0199150 0.0678567i
\(821\) −1.22882e14 −0.329438 −0.164719 0.986341i \(-0.552672\pi\)
−0.164719 + 0.986341i \(0.552672\pi\)
\(822\) −1.93085e14 1.93085e14i −0.514504 0.514504i
\(823\) −2.83711e14 + 2.83711e14i −0.751409 + 0.751409i −0.974742 0.223333i \(-0.928306\pi\)
0.223333 + 0.974742i \(0.428306\pi\)
\(824\) 1.32071e14i 0.347672i
\(825\) −6.71743e13 + 3.08409e14i −0.175765 + 0.806971i
\(826\) 1.85416e13 0.0482223
\(827\) 2.76194e14 + 2.76194e14i 0.713980 + 0.713980i 0.967365 0.253385i \(-0.0815440\pi\)
−0.253385 + 0.967365i \(0.581544\pi\)
\(828\) 3.91642e13 3.91642e13i 0.100632 0.100632i
\(829\) 5.06104e14i 1.29261i 0.763080 + 0.646304i \(0.223686\pi\)
−0.763080 + 0.646304i \(0.776314\pi\)
\(830\) 2.69663e14 7.91422e13i 0.684591 0.200917i
\(831\) 1.74393e14 0.440072
\(832\) −3.41485e14 3.41485e14i −0.856554 0.856554i
\(833\) 3.65761e14 3.65761e14i 0.911953 0.911953i
\(834\) 3.70670e14i 0.918665i
\(835\) 5.47991e13 + 2.99318e13i 0.135002 + 0.0737396i
\(836\) 2.03645e13 0.0498703
\(837\) −7.62081e12 7.62081e12i −0.0185513 0.0185513i
\(838\) 1.16449e14 1.16449e14i 0.281783 0.281783i
\(839\) 6.76549e14i 1.62738i −0.581298 0.813691i \(-0.697455\pi\)
0.581298 0.813691i \(-0.302545\pi\)
\(840\) −3.30457e13 + 6.05000e13i −0.0790167 + 0.144664i
\(841\) 3.89514e14 0.925855
\(842\) −1.30222e14 1.30222e14i −0.307698 0.307698i
\(843\) −1.49704e14 + 1.49704e14i −0.351639 + 0.351639i
\(844\) 1.82102e14i 0.425209i
\(845\) 2.43669e13 + 8.30258e13i 0.0565609 + 0.192721i
\(846\) −9.57753e13 −0.221005
\(847\) 8.48874e13 + 8.48874e13i 0.194727 + 0.194727i
\(848\) −1.65710e14 + 1.65710e14i −0.377895 + 0.377895i
\(849\) 3.00769e14i 0.681860i
\(850\) −2.84495e14 4.42936e14i −0.641181 0.998267i
\(851\) −1.29640e15 −2.90463
\(852\) 8.72364e13 + 8.72364e13i 0.194312 + 0.194312i
\(853\) −2.87513e14 + 2.87513e14i −0.636668 + 0.636668i −0.949732 0.313064i \(-0.898645\pi\)
0.313064 + 0.949732i \(0.398645\pi\)
\(854\) 1.10578e14i 0.243432i
\(855\) −1.90885e13 + 5.60220e12i −0.0417774 + 0.0122611i
\(856\) −4.85946e13 −0.105735
\(857\) 1.42114e14 + 1.42114e14i 0.307421 + 0.307421i 0.843908 0.536488i \(-0.180249\pi\)
−0.536488 + 0.843908i \(0.680249\pi\)
\(858\) 2.54782e14 2.54782e14i 0.547939 0.547939i
\(859\) 7.62838e12i 0.0163105i 0.999967 + 0.00815523i \(0.00259592\pi\)
−0.999967 + 0.00815523i \(0.997404\pi\)
\(860\) 6.35353e13 + 3.47036e13i 0.135059 + 0.0737704i
\(861\) 1.90514e13 0.0402634
\(862\) 1.29640e14 + 1.29640e14i 0.272397 + 0.272397i
\(863\) −5.51158e14 + 5.51158e14i −1.15139 + 1.15139i −0.165114 + 0.986274i \(0.552799\pi\)
−0.986274 + 0.165114i \(0.947201\pi\)
\(864\) 4.80015e13i 0.0996980i
\(865\) 2.58372e14 4.73026e14i 0.533537 0.976798i
\(866\) −3.39754e14 −0.697550
\(867\) −1.84024e14 1.84024e14i −0.375646 0.375646i
\(868\) −3.33657e12 + 3.33657e12i −0.00677175 + 0.00677175i
\(869\) 1.12037e15i 2.26081i
\(870\) 1.88930e13 + 6.43746e13i 0.0379057 + 0.129157i
\(871\) 5.87662e13 0.117229
\(872\) −4.31886e13 4.31886e13i −0.0856618 0.0856618i
\(873\) 1.91512e13 1.91512e13i 0.0377680 0.0377680i
\(874\) 9.12351e13i 0.178898i
\(875\) −1.34659e14 + 9.57824e12i −0.262540 + 0.0186743i
\(876\) −8.91798e13 −0.172880
\(877\) 2.02513e14 + 2.02513e14i 0.390351 + 0.390351i 0.874813 0.484461i \(-0.160984\pi\)
−0.484461 + 0.874813i \(0.660984\pi\)
\(878\) 2.48726e14 2.48726e14i 0.476704 0.476704i
\(879\) 3.21596e14i 0.612867i
\(880\) −4.79424e14 + 1.40704e14i −0.908462 + 0.266620i
\(881\) 4.41083e14 0.831076 0.415538 0.909576i \(-0.363593\pi\)
0.415538 + 0.909576i \(0.363593\pi\)
\(882\) 1.00256e14 + 1.00256e14i 0.187830 + 0.187830i
\(883\) −5.16406e14 + 5.16406e14i −0.962028 + 0.962028i −0.999305 0.0372771i \(-0.988132\pi\)
0.0372771 + 0.999305i \(0.488132\pi\)
\(884\) 2.18790e14i 0.405290i
\(885\) 5.88623e13 + 3.21512e13i 0.108423 + 0.0592216i
\(886\) −1.21220e14 −0.222028
\(887\) 7.68826e13 + 7.68826e13i 0.140026 + 0.140026i 0.773645 0.633619i \(-0.218431\pi\)
−0.633619 + 0.773645i \(0.718431\pi\)
\(888\) 4.44001e14 4.44001e14i 0.804117 0.804117i
\(889\) 8.65565e13i 0.155880i
\(890\) 2.98701e14 5.46861e14i 0.534917 0.979325i
\(891\) −8.92543e13 −0.158943
\(892\) −1.25812e14 1.25812e14i −0.222792 0.222792i
\(893\) −4.06153e13 + 4.06153e13i −0.0715207 + 0.0715207i
\(894\) 4.30645e14i 0.754105i
\(895\) 7.96892e13 + 2.71527e14i 0.138766 + 0.472822i
\(896\) −6.51182e13 −0.112762
\(897\) −4.15576e14 4.15576e14i −0.715630 0.715630i
\(898\) 3.34997e14 3.34997e14i 0.573667 0.573667i
\(899\) 2.17976e13i 0.0371202i
\(900\) −4.42023e13 + 2.83909e13i −0.0748570 + 0.0480802i
\(901\) −6.64371e14 −1.11889
\(902\) 1.37013e14 + 1.37013e14i 0.229471 + 0.229471i
\(903\) −3.71978e13 + 3.71978e13i −0.0619553 + 0.0619553i
\(904\) 5.31208e14i 0.879878i
\(905\) 1.08547e15 3.18569e14i 1.78803 0.524760i
\(906\) 2.38466e14 0.390648
\(907\) −4.66630e14 4.66630e14i −0.760215 0.760215i 0.216146 0.976361i \(-0.430651\pi\)
−0.976361 + 0.216146i \(0.930651\pi\)
\(908\) −6.25462e13 + 6.25462e13i −0.101338 + 0.101338i
\(909\) 1.14931e14i 0.185190i
\(910\) 1.35247e14 + 7.38732e13i 0.216731 + 0.118380i
\(911\) 6.14213e14 0.978874 0.489437 0.872039i \(-0.337202\pi\)
0.489437 + 0.872039i \(0.337202\pi\)
\(912\) −2.22673e13 2.22673e13i −0.0352935 0.0352935i
\(913\) 5.34705e14 5.34705e14i 0.842870 0.842870i
\(914\) 3.09103e14i 0.484588i
\(915\) 1.91741e14 3.51039e14i 0.298958 0.547332i
\(916\) −1.51589e14 −0.235066
\(917\) −6.35809e13 6.35809e13i −0.0980574 0.0980574i
\(918\) 1.05260e14 1.05260e14i 0.161455 0.161455i
\(919\) 5.29233e14i 0.807364i 0.914899 + 0.403682i \(0.132270\pi\)
−0.914899 + 0.403682i \(0.867730\pi\)
\(920\) 3.22053e14 + 1.09734e15i 0.488640 + 1.66495i
\(921\) 5.34307e14 0.806293
\(922\) 1.98739e14 + 1.98739e14i 0.298283 + 0.298283i
\(923\) 9.25675e14 9.25675e14i 1.38182 1.38182i
\(924\) 3.90776e13i 0.0580187i
\(925\) 1.20148e15 + 2.61692e14i 1.77421 + 0.386440i
\(926\) −1.05250e14 −0.154585
\(927\) −5.17140e13 5.17140e13i −0.0755457 0.0755457i
\(928\) 6.86488e13 6.86488e13i 0.0997454 0.0997454i
\(929\) 4.26804e14i 0.616808i −0.951256 0.308404i \(-0.900205\pi\)
0.951256 0.308404i \(-0.0997948\pi\)
\(930\) 4.49846e13 1.32023e13i 0.0646620 0.0189773i
\(931\) 8.50303e13 0.121570
\(932\) −3.98477e13 3.98477e13i −0.0566661 0.0566661i
\(933\) 3.23009e13 3.23009e13i 0.0456884 0.0456884i
\(934\) 8.53650e14i 1.20101i
\(935\) −1.24312e15 6.79004e14i −1.73962 0.950198i
\(936\) 2.84660e14 0.396230
\(937\) −7.69391e14 7.69391e14i −1.06524 1.06524i −0.997717 0.0675269i \(-0.978489\pi\)
−0.0675269 0.997717i \(-0.521511\pi\)
\(938\) 1.23783e13 1.23783e13i 0.0170470 0.0170470i
\(939\) 1.23977e14i 0.169829i
\(940\) −7.27111e13 + 1.33119e14i −0.0990744 + 0.181385i
\(941\) −4.47671e14 −0.606751 −0.303376 0.952871i \(-0.598114\pi\)
−0.303376 + 0.952871i \(0.598114\pi\)
\(942\) 4.29463e14 + 4.29463e14i 0.578990 + 0.578990i
\(943\) 2.23482e14 2.23482e14i 0.299699 0.299699i
\(944\) 1.06170e14i 0.141626i
\(945\) −1.07501e13 3.66291e13i −0.0142644 0.0486035i
\(946\) −5.35035e14 −0.706198
\(947\) 4.56644e14 + 4.56644e14i 0.599553 + 0.599553i 0.940194 0.340640i \(-0.110644\pi\)
−0.340640 + 0.940194i \(0.610644\pi\)
\(948\) −1.31856e14 + 1.31856e14i −0.172211 + 0.172211i
\(949\) 9.46297e14i 1.22941i
\(950\) 1.84168e13 8.45548e13i 0.0238010 0.109275i
\(951\) −5.29282e14 −0.680432
\(952\) −2.18752e14 2.18752e14i −0.279748 0.279748i
\(953\) 1.31748e14 1.31748e14i 0.167602 0.167602i −0.618323 0.785924i \(-0.712188\pi\)
0.785924 + 0.618323i \(0.212188\pi\)
\(954\) 1.82105e14i 0.230452i
\(955\) −1.43175e15 + 4.20198e14i −1.80240 + 0.528978i
\(956\) 2.72005e14 0.340633
\(957\) 1.27646e14 + 1.27646e14i 0.159018 + 0.159018i
\(958\) −7.20308e13 + 7.20308e13i −0.0892670 + 0.0892670i
\(959\) 3.14245e14i 0.387414i
\(960\) −4.56694e14 2.49451e14i −0.560105 0.305935i
\(961\) −8.04396e14 −0.981416
\(962\) −9.92559e14 9.92559e14i −1.20471 1.20471i
\(963\) 1.90279e13 1.90279e13i 0.0229752 0.0229752i
\(964\) 1.61601e14i 0.194115i
\(965\) −5.27359e13 + 9.65487e13i −0.0630187 + 0.115374i
\(966\) −1.75072e14 −0.208128
\(967\) −8.05270e13 8.05270e13i −0.0952378 0.0952378i 0.657883 0.753120i \(-0.271452\pi\)
−0.753120 + 0.657883i \(0.771452\pi\)
\(968\) −6.82081e14 + 6.82081e14i −0.802527 + 0.802527i
\(969\) 8.92749e13i 0.104499i
\(970\) 3.31775e13 + 1.13047e14i 0.0386354 + 0.131643i
\(971\) 6.04346e14 0.700148 0.350074 0.936722i \(-0.386156\pi\)
0.350074 + 0.936722i \(0.386156\pi\)
\(972\) −1.05043e13 1.05043e13i −0.0121070 0.0121070i
\(973\) −3.01632e14 + 3.01632e14i −0.345870 + 0.345870i
\(974\) 3.00908e14i 0.343273i
\(975\) 3.01259e14 + 4.69036e14i 0.341914 + 0.532333i
\(976\) 6.33170e14 0.714943
\(977\) −1.18795e15 1.18795e15i −1.33452 1.33452i −0.901280 0.433237i \(-0.857371\pi\)
−0.433237 0.901280i \(-0.642629\pi\)
\(978\) −3.06845e14 + 3.06845e14i −0.342946 + 0.342946i
\(979\) 1.67663e15i 1.86434i
\(980\) 2.15459e14 6.32340e13i 0.238360 0.0699553i
\(981\) 3.38222e13 0.0372269
\(982\) 5.44665e14 + 5.44665e14i 0.596447 + 0.596447i
\(983\) −3.11566e13 + 3.11566e13i −0.0339455 + 0.0339455i −0.723876 0.689930i \(-0.757641\pi\)
0.689930 + 0.723876i \(0.257641\pi\)
\(984\) 1.53080e14i 0.165937i
\(985\) 1.26460e15 + 6.90736e14i 1.36387 + 0.744957i
\(986\) −3.01073e14 −0.323063
\(987\) −7.79370e13 7.79370e13i −0.0832066 0.0832066i
\(988\) 2.54316e13 2.54316e13i 0.0270140 0.0270140i
\(989\) 8.72698e14i 0.922322i
\(990\) 1.86116e14 3.40740e14i 0.195707 0.358300i
\(991\) 2.03999e14 0.213432 0.106716 0.994290i \(-0.465966\pi\)
0.106716 + 0.994290i \(0.465966\pi\)
\(992\) −4.79714e13 4.79714e13i −0.0499372 0.0499372i
\(993\) −6.32582e14 + 6.32582e14i −0.655195 + 0.655195i
\(994\) 3.89963e14i 0.401876i
\(995\) 1.18656e14 + 4.04301e14i 0.121668 + 0.414562i
\(996\) 1.25859e14 0.128406
\(997\) 3.47182e14 + 3.47182e14i 0.352437 + 0.352437i 0.861016 0.508579i \(-0.169829\pi\)
−0.508579 + 0.861016i \(0.669829\pi\)
\(998\) −6.17426e13 + 6.17426e13i −0.0623637 + 0.0623637i
\(999\) 3.47709e14i 0.349453i
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 15.11.f.a.7.4 20
3.2 odd 2 45.11.g.c.37.7 20
5.2 odd 4 75.11.f.d.43.7 20
5.3 odd 4 inner 15.11.f.a.13.4 yes 20
5.4 even 2 75.11.f.d.7.7 20
15.8 even 4 45.11.g.c.28.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.11.f.a.7.4 20 1.1 even 1 trivial
15.11.f.a.13.4 yes 20 5.3 odd 4 inner
45.11.g.c.28.7 20 15.8 even 4
45.11.g.c.37.7 20 3.2 odd 2
75.11.f.d.7.7 20 5.4 even 2
75.11.f.d.43.7 20 5.2 odd 4