Properties

Label 15.11.f.a.7.7
Level $15$
Weight $11$
Character 15.7
Analytic conductor $9.530$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 7.7
Root \(-15.9113 + 15.9113i\) of defining polynomial
Character \(\chi\) \(=\) 15.7
Dual form 15.11.f.a.13.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.6866 + 11.6866i) q^{2} +(99.2043 - 99.2043i) q^{3} -750.847i q^{4} +(2257.04 + 2161.34i) q^{5} +2318.72 q^{6} +(-21416.5 - 21416.5i) q^{7} +(20741.9 - 20741.9i) q^{8} -19683.0i q^{9} +O(q^{10})\) \(q+(11.6866 + 11.6866i) q^{2} +(99.2043 - 99.2043i) q^{3} -750.847i q^{4} +(2257.04 + 2161.34i) q^{5} +2318.72 q^{6} +(-21416.5 - 21416.5i) q^{7} +(20741.9 - 20741.9i) q^{8} -19683.0i q^{9} +(1118.39 + 51635.8i) q^{10} +144236. q^{11} +(-74487.3 - 74487.3i) q^{12} +(314136. - 314136. i) q^{13} -500571. i q^{14} +(438323. - 9493.74i) q^{15} -284063. q^{16} +(422713. + 422713. i) q^{17} +(230027. - 230027. i) q^{18} -1.72877e6i q^{19} +(1.62284e6 - 1.69469e6i) q^{20} -4.24921e6 q^{21} +(1.68562e6 + 1.68562e6i) q^{22} +(-4.18986e6 + 4.18986e6i) q^{23} -4.11538e6i q^{24} +(422834. + 9.75647e6i) q^{25} +7.34235e6 q^{26} +(-1.95264e6 - 1.95264e6i) q^{27} +(-1.60805e7 + 1.60805e7i) q^{28} +2.54576e7i q^{29} +(5.23345e6 + 5.01155e6i) q^{30} -7.20415e6 q^{31} +(-2.45594e7 - 2.45594e7i) q^{32} +(1.43088e7 - 1.43088e7i) q^{33} +9.88016e6i q^{34} +(-2.04953e6 - 9.46261e7i) q^{35} -1.47789e7 q^{36} +(8.48288e7 + 8.48288e7i) q^{37} +(2.02035e7 - 2.02035e7i) q^{38} -6.23273e7i q^{39} +(9.16457e7 - 1.98498e6i) q^{40} -4.68731e7 q^{41} +(-4.96588e7 - 4.96588e7i) q^{42} +(2.34944e7 - 2.34944e7i) q^{43} -1.08299e8i q^{44} +(4.25417e7 - 4.44253e7i) q^{45} -9.79304e7 q^{46} +(3.23645e7 + 3.23645e7i) q^{47} +(-2.81803e7 + 2.81803e7i) q^{48} +6.34855e8i q^{49} +(-1.09078e8 + 1.18961e8i) q^{50} +8.38700e7 q^{51} +(-2.35868e8 - 2.35868e8i) q^{52} +(4.66906e8 - 4.66906e8i) q^{53} -4.56394e7i q^{54} +(3.25546e8 + 3.11742e8i) q^{55} -8.88437e8 q^{56} +(-1.71502e8 - 1.71502e8i) q^{57} +(-2.97512e8 + 2.97512e8i) q^{58} +1.01716e9i q^{59} +(-7.12835e6 - 3.29113e8i) q^{60} +2.76359e7 q^{61} +(-8.41919e7 - 8.41919e7i) q^{62} +(-4.21540e8 + 4.21540e8i) q^{63} -2.83152e8i q^{64} +(1.38797e9 - 3.00624e7i) q^{65} +3.34442e8 q^{66} +(-1.06739e9 - 1.06739e9i) q^{67} +(3.17393e8 - 3.17393e8i) q^{68} +8.31305e8i q^{69} +(1.08190e9 - 1.12981e9i) q^{70} +1.17851e9 q^{71} +(-4.08263e8 - 4.08263e8i) q^{72} +(1.90205e9 - 1.90205e9i) q^{73} +1.98272e9i q^{74} +(1.00983e9 + 9.25937e8i) q^{75} -1.29805e9 q^{76} +(-3.08902e9 - 3.08902e9i) q^{77} +(7.28393e8 - 7.28393e8i) q^{78} -1.33930e9i q^{79} +(-6.41141e8 - 6.13957e8i) q^{80} -3.87420e8 q^{81} +(-5.47787e8 - 5.47787e8i) q^{82} +(-9.32585e8 + 9.32585e8i) q^{83} +3.19051e9i q^{84} +(4.04532e7 + 1.86771e9i) q^{85} +5.49139e8 q^{86} +(2.52550e9 + 2.52550e9i) q^{87} +(2.99172e9 - 2.99172e9i) q^{88} +7.88621e9i q^{89} +(1.01635e9 - 2.20133e7i) q^{90} -1.34554e10 q^{91} +(3.14595e9 + 3.14595e9i) q^{92} +(-7.14683e8 + 7.14683e8i) q^{93} +7.56461e8i q^{94} +(3.73647e9 - 3.90191e9i) q^{95} -4.87281e9 q^{96} +(2.17281e9 + 2.17281e9i) q^{97} +(-7.41929e9 + 7.41929e9i) q^{98} -2.83899e9i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.6866 + 11.6866i 0.365206 + 0.365206i 0.865725 0.500519i \(-0.166858\pi\)
−0.500519 + 0.865725i \(0.666858\pi\)
\(3\) 99.2043 99.2043i 0.408248 0.408248i
\(4\) 750.847i 0.733249i
\(5\) 2257.04 + 2161.34i 0.722253 + 0.691629i
\(6\) 2318.72 0.298189
\(7\) −21416.5 21416.5i −1.27426 1.27426i −0.943831 0.330427i \(-0.892807\pi\)
−0.330427 0.943831i \(-0.607193\pi\)
\(8\) 20741.9 20741.9i 0.632993 0.632993i
\(9\) 19683.0i 0.333333i
\(10\) 1118.39 + 51635.8i 0.0111839 + 0.516358i
\(11\) 144236. 0.895590 0.447795 0.894136i \(-0.352209\pi\)
0.447795 + 0.894136i \(0.352209\pi\)
\(12\) −74487.3 74487.3i −0.299348 0.299348i
\(13\) 314136. 314136.i 0.846059 0.846059i −0.143580 0.989639i \(-0.545861\pi\)
0.989639 + 0.143580i \(0.0458614\pi\)
\(14\) 500571.i 0.930734i
\(15\) 438323. 9493.74i 0.577215 0.0125020i
\(16\) −284063. −0.270903
\(17\) 422713. + 422713.i 0.297715 + 0.297715i 0.840118 0.542403i \(-0.182485\pi\)
−0.542403 + 0.840118i \(0.682485\pi\)
\(18\) 230027. 230027.i 0.121735 0.121735i
\(19\) 1.72877e6i 0.698185i −0.937088 0.349092i \(-0.886490\pi\)
0.937088 0.349092i \(-0.113510\pi\)
\(20\) 1.62284e6 1.69469e6i 0.507136 0.529591i
\(21\) −4.24921e6 −1.04043
\(22\) 1.68562e6 + 1.68562e6i 0.327075 + 0.327075i
\(23\) −4.18986e6 + 4.18986e6i −0.650969 + 0.650969i −0.953226 0.302257i \(-0.902260\pi\)
0.302257 + 0.953226i \(0.402260\pi\)
\(24\) 4.11538e6i 0.516837i
\(25\) 422834. + 9.75647e6i 0.0432982 + 0.999062i
\(26\) 7.34235e6 0.617972
\(27\) −1.95264e6 1.95264e6i −0.136083 0.136083i
\(28\) −1.60805e7 + 1.60805e7i −0.934349 + 0.934349i
\(29\) 2.54576e7i 1.24116i 0.784144 + 0.620579i \(0.213102\pi\)
−0.784144 + 0.620579i \(0.786898\pi\)
\(30\) 5.23345e6 + 5.01155e6i 0.215368 + 0.206237i
\(31\) −7.20415e6 −0.251637 −0.125818 0.992053i \(-0.540156\pi\)
−0.125818 + 0.992053i \(0.540156\pi\)
\(32\) −2.45594e7 2.45594e7i −0.731929 0.731929i
\(33\) 1.43088e7 1.43088e7i 0.365623 0.365623i
\(34\) 9.88016e6i 0.217455i
\(35\) −2.04953e6 9.46261e7i −0.0390224 1.80165i
\(36\) −1.47789e7 −0.244416
\(37\) 8.48288e7 + 8.48288e7i 1.22331 + 1.22331i 0.966450 + 0.256855i \(0.0826863\pi\)
0.256855 + 0.966450i \(0.417314\pi\)
\(38\) 2.02035e7 2.02035e7i 0.254981 0.254981i
\(39\) 6.23273e7i 0.690804i
\(40\) 9.16457e7 1.98498e6i 0.894977 0.0193845i
\(41\) −4.68731e7 −0.404580 −0.202290 0.979326i \(-0.564838\pi\)
−0.202290 + 0.979326i \(0.564838\pi\)
\(42\) −4.96588e7 4.96588e7i −0.379970 0.379970i
\(43\) 2.34944e7 2.34944e7i 0.159817 0.159817i −0.622669 0.782486i \(-0.713952\pi\)
0.782486 + 0.622669i \(0.213952\pi\)
\(44\) 1.08299e8i 0.656690i
\(45\) 4.25417e7 4.44253e7i 0.230543 0.240751i
\(46\) −9.79304e7 −0.475476
\(47\) 3.23645e7 + 3.23645e7i 0.141117 + 0.141117i 0.774136 0.633019i \(-0.218185\pi\)
−0.633019 + 0.774136i \(0.718185\pi\)
\(48\) −2.81803e7 + 2.81803e7i −0.110596 + 0.110596i
\(49\) 6.34855e8i 2.24747i
\(50\) −1.09078e8 + 1.18961e8i −0.349051 + 0.380676i
\(51\) 8.38700e7 0.243084
\(52\) −2.35868e8 2.35868e8i −0.620372 0.620372i
\(53\) 4.66906e8 4.66906e8i 1.11648 1.11648i 0.124225 0.992254i \(-0.460356\pi\)
0.992254 0.124225i \(-0.0396444\pi\)
\(54\) 4.56394e7i 0.0993965i
\(55\) 3.25546e8 + 3.11742e8i 0.646842 + 0.619416i
\(56\) −8.88437e8 −1.61319
\(57\) −1.71502e8 1.71502e8i −0.285033 0.285033i
\(58\) −2.97512e8 + 2.97512e8i −0.453278 + 0.453278i
\(59\) 1.01716e9i 1.42275i 0.702811 + 0.711376i \(0.251928\pi\)
−0.702811 + 0.711376i \(0.748072\pi\)
\(60\) −7.12835e6 3.29113e8i −0.00916712 0.423242i
\(61\) 2.76359e7 0.0327208 0.0163604 0.999866i \(-0.494792\pi\)
0.0163604 + 0.999866i \(0.494792\pi\)
\(62\) −8.41919e7 8.41919e7i −0.0918993 0.0918993i
\(63\) −4.21540e8 + 4.21540e8i −0.424753 + 0.424753i
\(64\) 2.83152e8i 0.263706i
\(65\) 1.38797e9 3.00624e7i 1.19623 0.0259094i
\(66\) 3.34442e8 0.267055
\(67\) −1.06739e9 1.06739e9i −0.790590 0.790590i 0.191000 0.981590i \(-0.438827\pi\)
−0.981590 + 0.191000i \(0.938827\pi\)
\(68\) 3.17393e8 3.17393e8i 0.218300 0.218300i
\(69\) 8.31305e8i 0.531514i
\(70\) 1.08190e9 1.12981e9i 0.643723 0.672225i
\(71\) 1.17851e9 0.653193 0.326597 0.945164i \(-0.394098\pi\)
0.326597 + 0.945164i \(0.394098\pi\)
\(72\) −4.08263e8 4.08263e8i −0.210998 0.210998i
\(73\) 1.90205e9 1.90205e9i 0.917501 0.917501i −0.0793462 0.996847i \(-0.525283\pi\)
0.996847 + 0.0793462i \(0.0252833\pi\)
\(74\) 1.98272e9i 0.893517i
\(75\) 1.00983e9 + 9.25937e8i 0.425542 + 0.390189i
\(76\) −1.29805e9 −0.511943
\(77\) −3.08902e9 3.08902e9i −1.14121 1.14121i
\(78\) 7.28393e8 7.28393e8i 0.252286 0.252286i
\(79\) 1.33930e9i 0.435255i −0.976032 0.217627i \(-0.930168\pi\)
0.976032 0.217627i \(-0.0698317\pi\)
\(80\) −6.41141e8 6.13957e8i −0.195661 0.187365i
\(81\) −3.87420e8 −0.111111
\(82\) −5.47787e8 5.47787e8i −0.147755 0.147755i
\(83\) −9.32585e8 + 9.32585e8i −0.236754 + 0.236754i −0.815505 0.578750i \(-0.803541\pi\)
0.578750 + 0.815505i \(0.303541\pi\)
\(84\) 3.19051e9i 0.762893i
\(85\) 4.04532e7 + 1.86771e9i 0.00911713 + 0.420934i
\(86\) 5.49139e8 0.116732
\(87\) 2.52550e9 + 2.52550e9i 0.506700 + 0.506700i
\(88\) 2.99172e9 2.99172e9i 0.566902 0.566902i
\(89\) 7.88621e9i 1.41227i 0.708076 + 0.706136i \(0.249563\pi\)
−0.708076 + 0.706136i \(0.750437\pi\)
\(90\) 1.01635e9 2.20133e7i 0.172119 0.00372798i
\(91\) −1.34554e10 −2.15620
\(92\) 3.14595e9 + 3.14595e9i 0.477323 + 0.477323i
\(93\) −7.14683e8 + 7.14683e8i −0.102730 + 0.102730i
\(94\) 7.56461e8i 0.103074i
\(95\) 3.73647e9 3.90191e9i 0.482885 0.504266i
\(96\) −4.87281e9 −0.597617
\(97\) 2.17281e9 + 2.17281e9i 0.253025 + 0.253025i 0.822210 0.569184i \(-0.192741\pi\)
−0.569184 + 0.822210i \(0.692741\pi\)
\(98\) −7.41929e9 + 7.41929e9i −0.820790 + 0.820790i
\(99\) 2.83899e9i 0.298530i
\(100\) 7.32562e9 3.17484e8i 0.732562 0.0317484i
\(101\) 1.31685e9 0.125294 0.0626469 0.998036i \(-0.480046\pi\)
0.0626469 + 0.998036i \(0.480046\pi\)
\(102\) 9.80154e8 + 9.80154e8i 0.0887756 + 0.0887756i
\(103\) 2.12255e9 2.12255e9i 0.183093 0.183093i −0.609609 0.792702i \(-0.708674\pi\)
0.792702 + 0.609609i \(0.208674\pi\)
\(104\) 1.30316e10i 1.07110i
\(105\) −9.59064e9 9.18400e9i −0.751452 0.719590i
\(106\) 1.09131e10 0.815490
\(107\) −7.88889e9 7.88889e9i −0.562467 0.562467i 0.367541 0.930007i \(-0.380200\pi\)
−0.930007 + 0.367541i \(0.880200\pi\)
\(108\) −1.46613e9 + 1.46613e9i −0.0997826 + 0.0997826i
\(109\) 6.94026e8i 0.0451069i −0.999746 0.0225535i \(-0.992820\pi\)
0.999746 0.0225535i \(-0.00717960\pi\)
\(110\) 1.61312e8 + 7.44772e9i 0.0100162 + 0.462445i
\(111\) 1.68308e10 0.998824
\(112\) 6.08362e9 + 6.08362e9i 0.345201 + 0.345201i
\(113\) 1.71240e10 1.71240e10i 0.929422 0.929422i −0.0682464 0.997668i \(-0.521740\pi\)
0.997668 + 0.0682464i \(0.0217404\pi\)
\(114\) 4.00855e9i 0.208191i
\(115\) −1.85124e10 + 4.00965e8i −0.920394 + 0.0199351i
\(116\) 1.91147e10 0.910077
\(117\) −6.18313e9 6.18313e9i −0.282020 0.282020i
\(118\) −1.18871e10 + 1.18871e10i −0.519598 + 0.519598i
\(119\) 1.81061e10i 0.758733i
\(120\) 8.89473e9 9.28857e9i 0.357459 0.373287i
\(121\) −5.13351e9 −0.197919
\(122\) 3.22969e8 + 3.22969e8i 0.0119498 + 0.0119498i
\(123\) −4.65002e9 + 4.65002e9i −0.165169 + 0.165169i
\(124\) 5.40921e9i 0.184512i
\(125\) −2.01327e10 + 2.29346e10i −0.659708 + 0.751522i
\(126\) −9.85274e9 −0.310245
\(127\) 3.71586e10 + 3.71586e10i 1.12471 + 1.12471i 0.991024 + 0.133685i \(0.0426811\pi\)
0.133685 + 0.991024i \(0.457319\pi\)
\(128\) −2.18398e10 + 2.18398e10i −0.635622 + 0.635622i
\(129\) 4.66149e9i 0.130490i
\(130\) 1.65720e10 + 1.58693e10i 0.446332 + 0.427407i
\(131\) −5.26963e9 −0.136592 −0.0682958 0.997665i \(-0.521756\pi\)
−0.0682958 + 0.997665i \(0.521756\pi\)
\(132\) −1.07437e10 1.07437e10i −0.268093 0.268093i
\(133\) −3.70242e10 + 3.70242e10i −0.889668 + 0.889668i
\(134\) 2.49484e10i 0.577456i
\(135\) −1.86865e8 8.62750e9i −0.00416735 0.192405i
\(136\) 1.75358e10 0.376904
\(137\) −1.07552e10 1.07552e10i −0.222851 0.222851i 0.586847 0.809698i \(-0.300369\pi\)
−0.809698 + 0.586847i \(0.800369\pi\)
\(138\) −9.71512e9 + 9.71512e9i −0.194112 + 0.194112i
\(139\) 6.42485e10i 1.23820i −0.785314 0.619098i \(-0.787498\pi\)
0.785314 0.619098i \(-0.212502\pi\)
\(140\) −7.10497e10 + 1.53888e9i −1.32106 + 0.0286132i
\(141\) 6.42140e9 0.115222
\(142\) 1.37728e10 + 1.37728e10i 0.238550 + 0.238550i
\(143\) 4.53096e10 4.53096e10i 0.757722 0.757722i
\(144\) 5.59121e9i 0.0903012i
\(145\) −5.50225e10 + 5.74587e10i −0.858420 + 0.896429i
\(146\) 4.44569e10 0.670154
\(147\) 6.29803e10 + 6.29803e10i 0.917526 + 0.917526i
\(148\) 6.36935e10 6.36935e10i 0.896987 0.896987i
\(149\) 1.12980e11i 1.53840i 0.639010 + 0.769198i \(0.279344\pi\)
−0.639010 + 0.769198i \(0.720656\pi\)
\(150\) 9.80434e8 + 2.26225e10i 0.0129111 + 0.297910i
\(151\) −8.95064e9 −0.114017 −0.0570085 0.998374i \(-0.518156\pi\)
−0.0570085 + 0.998374i \(0.518156\pi\)
\(152\) −3.58581e10 3.58581e10i −0.441946 0.441946i
\(153\) 8.32027e9 8.32027e9i 0.0992385 0.0992385i
\(154\) 7.22002e10i 0.833556i
\(155\) −1.62600e10 1.55706e10i −0.181745 0.174039i
\(156\) −4.67982e10 −0.506532
\(157\) −4.35079e10 4.35079e10i −0.456110 0.456110i 0.441266 0.897376i \(-0.354529\pi\)
−0.897376 + 0.441266i \(0.854529\pi\)
\(158\) 1.56519e10 1.56519e10i 0.158958 0.158958i
\(159\) 9.26383e10i 0.911601i
\(160\) −2.35031e9 1.08513e11i −0.0224143 1.03486i
\(161\) 1.79464e11 1.65901
\(162\) −4.52763e9 4.52763e9i −0.0405784 0.0405784i
\(163\) −1.65838e10 + 1.65838e10i −0.144127 + 0.144127i −0.775489 0.631361i \(-0.782496\pi\)
0.631361 + 0.775489i \(0.282496\pi\)
\(164\) 3.51946e10i 0.296658i
\(165\) 6.32217e10 1.36934e9i 0.516948 0.0111967i
\(166\) −2.17975e10 −0.172928
\(167\) 5.89827e10 + 5.89827e10i 0.454090 + 0.454090i 0.896710 0.442619i \(-0.145951\pi\)
−0.442619 + 0.896710i \(0.645951\pi\)
\(168\) −8.81368e10 + 8.81368e10i −0.658584 + 0.658584i
\(169\) 5.95040e10i 0.431631i
\(170\) −2.13544e10 + 2.22999e10i −0.150398 + 0.157057i
\(171\) −3.40275e10 −0.232728
\(172\) −1.76407e10 1.76407e10i −0.117185 0.117185i
\(173\) −1.10643e10 + 1.10643e10i −0.0713991 + 0.0713991i −0.741905 0.670505i \(-0.766077\pi\)
0.670505 + 0.741905i \(0.266077\pi\)
\(174\) 5.90290e10i 0.370100i
\(175\) 1.99893e11 2.18005e11i 1.21789 1.32824i
\(176\) −4.09720e10 −0.242618
\(177\) 1.00907e11 + 1.00907e11i 0.580836 + 0.580836i
\(178\) −9.21629e10 + 9.21629e10i −0.515770 + 0.515770i
\(179\) 6.51889e10i 0.354739i 0.984144 + 0.177369i \(0.0567587\pi\)
−0.984144 + 0.177369i \(0.943241\pi\)
\(180\) −3.33566e10 3.19423e10i −0.176530 0.169045i
\(181\) −3.30663e11 −1.70213 −0.851065 0.525060i \(-0.824043\pi\)
−0.851065 + 0.525060i \(0.824043\pi\)
\(182\) −1.57247e11 1.57247e11i −0.787456 0.787456i
\(183\) 2.74160e9 2.74160e9i 0.0133582 0.0133582i
\(184\) 1.73812e11i 0.824118i
\(185\) 8.11802e9 + 3.74806e11i 0.0374621 + 1.72961i
\(186\) −1.67044e10 −0.0750354
\(187\) 6.09703e10 + 6.09703e10i 0.266631 + 0.266631i
\(188\) 2.43008e10 2.43008e10i 0.103474 0.103474i
\(189\) 8.36372e10i 0.346809i
\(190\) 8.92667e10 1.93345e9i 0.360513 0.00780845i
\(191\) −2.55021e11 −1.00325 −0.501624 0.865085i \(-0.667264\pi\)
−0.501624 + 0.865085i \(0.667264\pi\)
\(192\) −2.80899e10 2.80899e10i −0.107657 0.107657i
\(193\) −5.64731e10 + 5.64731e10i −0.210889 + 0.210889i −0.804645 0.593756i \(-0.797645\pi\)
0.593756 + 0.804645i \(0.297645\pi\)
\(194\) 5.07856e10i 0.184813i
\(195\) 1.34710e11 1.40675e11i 0.477780 0.498935i
\(196\) 4.76679e11 1.64796
\(197\) −2.63535e11 2.63535e11i −0.888191 0.888191i 0.106158 0.994349i \(-0.466145\pi\)
−0.994349 + 0.106158i \(0.966145\pi\)
\(198\) 3.31781e10 3.31781e10i 0.109025 0.109025i
\(199\) 3.22945e11i 1.03482i 0.855739 + 0.517408i \(0.173103\pi\)
−0.855739 + 0.517408i \(0.826897\pi\)
\(200\) 2.11138e11 + 1.93597e11i 0.659807 + 0.604992i
\(201\) −2.11780e11 −0.645514
\(202\) 1.53895e10 + 1.53895e10i 0.0457581 + 0.0457581i
\(203\) 5.45211e11 5.45211e11i 1.58156 1.58156i
\(204\) 6.29735e10i 0.178241i
\(205\) −1.05795e11 1.01309e11i −0.292209 0.279820i
\(206\) 4.96108e10 0.133734
\(207\) 8.24691e10 + 8.24691e10i 0.216990 + 0.216990i
\(208\) −8.92343e10 + 8.92343e10i −0.229200 + 0.229200i
\(209\) 2.49351e11i 0.625287i
\(210\) −4.75229e9 2.19412e11i −0.0116361 0.537233i
\(211\) −3.92197e11 −0.937760 −0.468880 0.883262i \(-0.655342\pi\)
−0.468880 + 0.883262i \(0.655342\pi\)
\(212\) −3.50575e11 3.50575e11i −0.818657 0.818657i
\(213\) 1.16913e11 1.16913e11i 0.266665 0.266665i
\(214\) 1.84388e11i 0.410832i
\(215\) 1.03807e11 2.24839e9i 0.225962 0.00489417i
\(216\) −8.10029e10 −0.172279
\(217\) 1.54287e11 + 1.54287e11i 0.320650 + 0.320650i
\(218\) 8.11080e9 8.11080e9i 0.0164733 0.0164733i
\(219\) 3.77382e11i 0.749136i
\(220\) 2.34071e11 2.44435e11i 0.454186 0.474297i
\(221\) 2.65579e11 0.503770
\(222\) 1.96694e11 + 1.96694e11i 0.364777 + 0.364777i
\(223\) −9.57493e9 + 9.57493e9i −0.0173625 + 0.0173625i −0.715735 0.698372i \(-0.753908\pi\)
0.698372 + 0.715735i \(0.253908\pi\)
\(224\) 1.05195e12i 1.86533i
\(225\) 1.92037e11 8.32264e9i 0.333021 0.0144327i
\(226\) 4.00242e11 0.678861
\(227\) −6.38678e11 6.38678e11i −1.05963 1.05963i −0.998106 0.0615203i \(-0.980405\pi\)
−0.0615203 0.998106i \(-0.519595\pi\)
\(228\) −1.28772e11 + 1.28772e11i −0.209000 + 0.209000i
\(229\) 1.09189e12i 1.73381i 0.498471 + 0.866907i \(0.333895\pi\)
−0.498471 + 0.866907i \(0.666105\pi\)
\(230\) −2.21033e11 2.11661e11i −0.343414 0.328853i
\(231\) −6.12888e11 −0.931797
\(232\) 5.28038e11 + 5.28038e11i 0.785644 + 0.785644i
\(233\) −2.34856e10 + 2.34856e10i −0.0341996 + 0.0341996i −0.724000 0.689800i \(-0.757698\pi\)
0.689800 + 0.724000i \(0.257698\pi\)
\(234\) 1.44520e11i 0.205991i
\(235\) 3.09725e9 + 1.42999e11i 0.00432152 + 0.199523i
\(236\) 7.63732e11 1.04323
\(237\) −1.32865e11 1.32865e11i −0.177692 0.177692i
\(238\) 2.11598e11 2.11598e11i 0.277094 0.277094i
\(239\) 3.47769e11i 0.445966i −0.974822 0.222983i \(-0.928421\pi\)
0.974822 0.222983i \(-0.0715794\pi\)
\(240\) −1.24511e11 + 2.69682e9i −0.156370 + 0.00338685i
\(241\) −8.60967e11 −1.05901 −0.529506 0.848306i \(-0.677623\pi\)
−0.529506 + 0.848306i \(0.677623\pi\)
\(242\) −5.99932e10 5.99932e10i −0.0722812 0.0722812i
\(243\) −3.84338e10 + 3.84338e10i −0.0453609 + 0.0453609i
\(244\) 2.07503e10i 0.0239925i
\(245\) −1.37214e12 + 1.43289e12i −1.55442 + 1.62324i
\(246\) −1.08686e11 −0.120642
\(247\) −5.43070e11 5.43070e11i −0.590705 0.590705i
\(248\) −1.49428e11 + 1.49428e11i −0.159284 + 0.159284i
\(249\) 1.85033e11i 0.193309i
\(250\) −5.03310e11 + 3.27450e10i −0.515390 + 0.0335308i
\(251\) 1.89145e12 1.89857 0.949286 0.314414i \(-0.101808\pi\)
0.949286 + 0.314414i \(0.101808\pi\)
\(252\) 3.16512e11 + 3.16512e11i 0.311450 + 0.311450i
\(253\) −6.04327e11 + 6.04327e11i −0.583002 + 0.583002i
\(254\) 8.68514e11i 0.821501i
\(255\) 1.89298e11 + 1.81272e11i 0.175568 + 0.168124i
\(256\) −8.00413e11 −0.727972
\(257\) 5.56295e11 + 5.56295e11i 0.496181 + 0.496181i 0.910247 0.414066i \(-0.135892\pi\)
−0.414066 + 0.910247i \(0.635892\pi\)
\(258\) 5.44770e10 5.44770e10i 0.0476557 0.0476557i
\(259\) 3.63347e12i 3.11761i
\(260\) −2.25723e10 1.04215e12i −0.0189980 0.877133i
\(261\) 5.01081e11 0.413719
\(262\) −6.15841e10 6.15841e10i −0.0498841 0.0498841i
\(263\) 2.40805e11 2.40805e11i 0.191376 0.191376i −0.604914 0.796290i \(-0.706793\pi\)
0.796290 + 0.604914i \(0.206793\pi\)
\(264\) 5.93584e11i 0.462874i
\(265\) 2.06297e12 4.46824e10i 1.57857 0.0341906i
\(266\) −8.65374e11 −0.649824
\(267\) 7.82346e11 + 7.82346e11i 0.576558 + 0.576558i
\(268\) −8.01450e11 + 8.01450e11i −0.579699 + 0.579699i
\(269\) 1.50352e12i 1.06745i −0.845657 0.533727i \(-0.820791\pi\)
0.845657 0.533727i \(-0.179209\pi\)
\(270\) 9.86423e10 1.03010e11i 0.0687455 0.0717894i
\(271\) 1.24987e12 0.855101 0.427550 0.903991i \(-0.359377\pi\)
0.427550 + 0.903991i \(0.359377\pi\)
\(272\) −1.20077e11 1.20077e11i −0.0806521 0.0806521i
\(273\) −1.33483e12 + 1.33483e12i −0.880263 + 0.880263i
\(274\) 2.51382e11i 0.162773i
\(275\) 6.09877e10 + 1.40723e12i 0.0387774 + 0.894750i
\(276\) 6.24183e11 0.389732
\(277\) 1.80941e12 + 1.80941e12i 1.10953 + 1.10953i 0.993212 + 0.116315i \(0.0371083\pi\)
0.116315 + 0.993212i \(0.462892\pi\)
\(278\) 7.50846e11 7.50846e11i 0.452196 0.452196i
\(279\) 1.41799e11i 0.0838789i
\(280\) −2.00524e12 1.92022e12i −1.16513 1.11573i
\(281\) −2.89679e12 −1.65343 −0.826714 0.562622i \(-0.809793\pi\)
−0.826714 + 0.562622i \(0.809793\pi\)
\(282\) 7.50443e10 + 7.50443e10i 0.0420796 + 0.0420796i
\(283\) 1.86922e12 1.86922e12i 1.02974 1.02974i 0.0301957 0.999544i \(-0.490387\pi\)
0.999544 0.0301957i \(-0.00961304\pi\)
\(284\) 8.84881e11i 0.478953i
\(285\) −1.64125e10 7.57761e11i −0.00872874 0.403003i
\(286\) 1.05903e12 0.553449
\(287\) 1.00386e12 + 1.00386e12i 0.515540 + 0.515540i
\(288\) −4.83404e11 + 4.83404e11i −0.243976 + 0.243976i
\(289\) 1.65862e12i 0.822731i
\(290\) −1.31452e12 + 2.84716e10i −0.640882 + 0.0138810i
\(291\) 4.31105e11 0.206594
\(292\) −1.42815e12 1.42815e12i −0.672757 0.672757i
\(293\) 2.31503e11 2.31503e11i 0.107206 0.107206i −0.651469 0.758675i \(-0.725847\pi\)
0.758675 + 0.651469i \(0.225847\pi\)
\(294\) 1.47205e12i 0.670172i
\(295\) −2.19843e12 + 2.29577e12i −0.984017 + 1.02759i
\(296\) 3.51902e12 1.54869
\(297\) −2.81640e11 2.81640e11i −0.121874 0.121874i
\(298\) −1.32035e12 + 1.32035e12i −0.561832 + 0.561832i
\(299\) 2.63237e12i 1.10152i
\(300\) 6.95237e11 7.58229e11i 0.286106 0.312028i
\(301\) −1.00633e12 −0.407296
\(302\) −1.04603e11 1.04603e11i −0.0416397 0.0416397i
\(303\) 1.30637e11 1.30637e11i 0.0511510 0.0511510i
\(304\) 4.91081e11i 0.189141i
\(305\) 6.23752e10 + 5.97305e10i 0.0236327 + 0.0226306i
\(306\) 1.94471e11 0.0724850
\(307\) 7.98088e11 + 7.98088e11i 0.292657 + 0.292657i 0.838129 0.545472i \(-0.183650\pi\)
−0.545472 + 0.838129i \(0.683650\pi\)
\(308\) −2.31938e12 + 2.31938e12i −0.836793 + 0.836793i
\(309\) 4.21133e11i 0.149495i
\(310\) −8.05707e9 3.71992e11i −0.00281429 0.129935i
\(311\) 6.73547e11 0.231508 0.115754 0.993278i \(-0.463072\pi\)
0.115754 + 0.993278i \(0.463072\pi\)
\(312\) −1.29279e12 1.29279e12i −0.437274 0.437274i
\(313\) −2.59138e11 + 2.59138e11i −0.0862599 + 0.0862599i −0.748920 0.662660i \(-0.769427\pi\)
0.662660 + 0.748920i \(0.269427\pi\)
\(314\) 1.01692e12i 0.333148i
\(315\) −1.86253e12 + 4.03409e10i −0.600550 + 0.0130075i
\(316\) −1.00561e12 −0.319150
\(317\) −7.43982e11 7.43982e11i −0.232416 0.232416i 0.581284 0.813700i \(-0.302550\pi\)
−0.813700 + 0.581284i \(0.802550\pi\)
\(318\) 1.08263e12 1.08263e12i 0.332922 0.332922i
\(319\) 3.67189e12i 1.11157i
\(320\) 6.11988e11 6.39086e11i 0.182387 0.190462i
\(321\) −1.56522e12 −0.459252
\(322\) 2.09732e12 + 2.09732e12i 0.605879 + 0.605879i
\(323\) 7.30776e11 7.30776e11i 0.207860 0.207860i
\(324\) 2.90894e11i 0.0814721i
\(325\) 3.19768e12 + 2.93203e12i 0.881898 + 0.808633i
\(326\) −3.87617e11 −0.105272
\(327\) −6.88504e10 6.88504e10i −0.0184148 0.0184148i
\(328\) −9.72239e11 + 9.72239e11i −0.256097 + 0.256097i
\(329\) 1.38627e12i 0.359639i
\(330\) 7.54849e11 + 7.22844e11i 0.192882 + 0.184703i
\(331\) −2.55641e12 −0.643414 −0.321707 0.946839i \(-0.604257\pi\)
−0.321707 + 0.946839i \(0.604257\pi\)
\(332\) 7.00229e11 + 7.00229e11i 0.173600 + 0.173600i
\(333\) 1.66969e12 1.66969e12i 0.407768 0.407768i
\(334\) 1.37861e12i 0.331673i
\(335\) −1.02148e11 4.71616e12i −0.0242107 1.11780i
\(336\) 1.20704e12 0.281856
\(337\) −8.83879e11 8.83879e11i −0.203350 0.203350i 0.598084 0.801433i \(-0.295929\pi\)
−0.801433 + 0.598084i \(0.795929\pi\)
\(338\) 6.95399e11 6.95399e11i 0.157634 0.157634i
\(339\) 3.39755e12i 0.758870i
\(340\) 1.40236e12 3.03742e10i 0.308650 0.00668513i
\(341\) −1.03909e12 −0.225363
\(342\) −3.97665e11 3.97665e11i −0.0849937 0.0849937i
\(343\) 7.54672e12 7.54672e12i 1.58960 1.58960i
\(344\) 9.74638e11i 0.202326i
\(345\) −1.79673e12 + 1.87629e12i −0.367611 + 0.383888i
\(346\) −2.58607e11 −0.0521507
\(347\) −4.10042e12 4.10042e12i −0.815043 0.815043i 0.170342 0.985385i \(-0.445513\pi\)
−0.985385 + 0.170342i \(0.945513\pi\)
\(348\) 1.89626e12 1.89626e12i 0.371538 0.371538i
\(349\) 1.56174e11i 0.0301635i −0.999886 0.0150817i \(-0.995199\pi\)
0.999886 0.0150817i \(-0.00480084\pi\)
\(350\) 4.88380e12 2.11658e11i 0.929861 0.0402991i
\(351\) −1.22679e12 −0.230268
\(352\) −3.54235e12 3.54235e12i −0.655508 0.655508i
\(353\) −3.67864e12 + 3.67864e12i −0.671141 + 0.671141i −0.957979 0.286838i \(-0.907396\pi\)
0.286838 + 0.957979i \(0.407396\pi\)
\(354\) 2.35851e12i 0.424250i
\(355\) 2.65995e12 + 2.54716e12i 0.471771 + 0.451768i
\(356\) 5.92134e12 1.03555
\(357\) −1.79620e12 1.79620e12i −0.309751 0.309751i
\(358\) −7.61836e11 + 7.61836e11i −0.129553 + 0.129553i
\(359\) 2.88632e12i 0.484029i 0.970273 + 0.242015i \(0.0778082\pi\)
−0.970273 + 0.242015i \(0.922192\pi\)
\(360\) −3.90703e10 1.80386e12i −0.00646152 0.298326i
\(361\) 3.14241e12 0.512538
\(362\) −3.86432e12 3.86432e12i −0.621628 0.621628i
\(363\) −5.09266e11 + 5.09266e11i −0.0808001 + 0.0808001i
\(364\) 1.01029e13i 1.58103i
\(365\) 8.40396e12 1.82024e11i 1.29724 0.0280972i
\(366\) 6.40798e10 0.00975699
\(367\) −1.30889e12 1.30889e12i −0.196596 0.196596i 0.601943 0.798539i \(-0.294393\pi\)
−0.798539 + 0.601943i \(0.794393\pi\)
\(368\) 1.19018e12 1.19018e12i 0.176350 0.176350i
\(369\) 9.22604e11i 0.134860i
\(370\) −4.28533e12 + 4.47508e12i −0.617982 + 0.645345i
\(371\) −1.99990e13 −2.84537
\(372\) 5.36617e11 + 5.36617e11i 0.0753269 + 0.0753269i
\(373\) −3.21248e12 + 3.21248e12i −0.444934 + 0.444934i −0.893666 0.448732i \(-0.851876\pi\)
0.448732 + 0.893666i \(0.351876\pi\)
\(374\) 1.42507e12i 0.194750i
\(375\) 2.77963e11 + 4.27247e12i 0.0374827 + 0.576132i
\(376\) 1.34260e12 0.178652
\(377\) 7.99713e12 + 7.99713e12i 1.05009 + 1.05009i
\(378\) −9.77434e11 + 9.77434e11i −0.126657 + 0.126657i
\(379\) 2.67708e12i 0.342346i 0.985241 + 0.171173i \(0.0547557\pi\)
−0.985241 + 0.171173i \(0.945244\pi\)
\(380\) −2.92974e12 2.80552e12i −0.369752 0.354075i
\(381\) 7.37258e12 0.918321
\(382\) −2.98032e12 2.98032e12i −0.366393 0.366393i
\(383\) −5.35266e12 + 5.35266e12i −0.649495 + 0.649495i −0.952871 0.303376i \(-0.901886\pi\)
0.303376 + 0.952871i \(0.401886\pi\)
\(384\) 4.33320e12i 0.518983i
\(385\) −2.95615e11 1.36485e13i −0.0349481 1.61354i
\(386\) −1.31996e12 −0.154036
\(387\) −4.62440e11 4.62440e11i −0.0532722 0.0532722i
\(388\) 1.63145e12 1.63145e12i 0.185531 0.185531i
\(389\) 4.78950e12i 0.537703i −0.963182 0.268851i \(-0.913356\pi\)
0.963182 0.268851i \(-0.0866440\pi\)
\(390\) 3.21832e12 6.97064e10i 0.356702 0.00772591i
\(391\) −3.54222e12 −0.387607
\(392\) 1.31681e13 + 1.31681e13i 1.42263 + 1.42263i
\(393\) −5.22771e11 + 5.22771e11i −0.0557633 + 0.0557633i
\(394\) 6.15964e12i 0.648746i
\(395\) 2.89469e12 3.02286e12i 0.301035 0.314364i
\(396\) −2.13165e12 −0.218897
\(397\) −7.44312e12 7.44312e12i −0.754748 0.754748i 0.220613 0.975361i \(-0.429194\pi\)
−0.975361 + 0.220613i \(0.929194\pi\)
\(398\) −3.77413e12 + 3.77413e12i −0.377921 + 0.377921i
\(399\) 7.34593e12i 0.726411i
\(400\) −1.20111e11 2.77145e12i −0.0117296 0.270649i
\(401\) −8.09887e12 −0.781092 −0.390546 0.920583i \(-0.627714\pi\)
−0.390546 + 0.920583i \(0.627714\pi\)
\(402\) −2.47499e12 2.47499e12i −0.235745 0.235745i
\(403\) −2.26308e12 + 2.26308e12i −0.212900 + 0.212900i
\(404\) 9.88753e11i 0.0918716i
\(405\) −8.74424e11 8.37348e11i −0.0802503 0.0768477i
\(406\) 1.27433e13 1.15519
\(407\) 1.22353e13 + 1.22353e13i 1.09558 + 1.09558i
\(408\) 1.73962e12 1.73962e12i 0.153870 0.153870i
\(409\) 5.40623e12i 0.472366i −0.971709 0.236183i \(-0.924104\pi\)
0.971709 0.236183i \(-0.0758964\pi\)
\(410\) −5.24226e10 2.42033e12i −0.00452480 0.208908i
\(411\) −2.13392e12 −0.181957
\(412\) −1.59371e12 1.59371e12i −0.134253 0.134253i
\(413\) 2.17840e13 2.17840e13i 1.81295 1.81295i
\(414\) 1.92756e12i 0.158492i
\(415\) −4.12052e12 + 8.92474e10i −0.334743 + 0.00725028i
\(416\) −1.54300e13 −1.23851
\(417\) −6.37373e12 6.37373e12i −0.505491 0.505491i
\(418\) 2.91406e12 2.91406e12i 0.228359 0.228359i
\(419\) 1.12531e12i 0.0871371i 0.999050 + 0.0435686i \(0.0138727\pi\)
−0.999050 + 0.0435686i \(0.986127\pi\)
\(420\) −6.89578e12 + 7.20111e12i −0.527639 + 0.551001i
\(421\) 9.96777e12 0.753681 0.376841 0.926278i \(-0.377010\pi\)
0.376841 + 0.926278i \(0.377010\pi\)
\(422\) −4.58345e12 4.58345e12i −0.342476 0.342476i
\(423\) 6.37030e11 6.37030e11i 0.0470390 0.0470390i
\(424\) 1.93691e13i 1.41345i
\(425\) −3.94545e12 + 4.30293e12i −0.284546 + 0.310327i
\(426\) 2.73264e12 0.194775
\(427\) −5.91862e11 5.91862e11i −0.0416947 0.0416947i
\(428\) −5.92335e12 + 5.92335e12i −0.412428 + 0.412428i
\(429\) 8.98981e12i 0.618677i
\(430\) 1.23943e12 + 1.18688e12i 0.0843101 + 0.0807353i
\(431\) 2.30725e13 1.55134 0.775672 0.631137i \(-0.217411\pi\)
0.775672 + 0.631137i \(0.217411\pi\)
\(432\) 5.54672e11 + 5.54672e11i 0.0368653 + 0.0368653i
\(433\) 2.90034e12 2.90034e12i 0.190550 0.190550i −0.605384 0.795934i \(-0.706980\pi\)
0.795934 + 0.605384i \(0.206980\pi\)
\(434\) 3.60619e12i 0.234207i
\(435\) 2.41688e11 + 1.11586e13i 0.0155170 + 0.716414i
\(436\) −5.21108e11 −0.0330746
\(437\) 7.24333e12 + 7.24333e12i 0.454497 + 0.454497i
\(438\) 4.41031e12 4.41031e12i 0.273589 0.273589i
\(439\) 1.89524e13i 1.16236i 0.813775 + 0.581180i \(0.197409\pi\)
−0.813775 + 0.581180i \(0.802591\pi\)
\(440\) 1.32186e13 2.86305e11i 0.801533 0.0173606i
\(441\) 1.24958e13 0.749157
\(442\) 3.10371e12 + 3.10371e12i 0.183980 + 0.183980i
\(443\) −2.22224e13 + 2.22224e13i −1.30248 + 1.30248i −0.375771 + 0.926713i \(0.622622\pi\)
−0.926713 + 0.375771i \(0.877378\pi\)
\(444\) 1.26373e13i 0.732387i
\(445\) −1.70448e13 + 1.77995e13i −0.976769 + 1.02002i
\(446\) −2.23797e11 −0.0126817
\(447\) 1.12081e13 + 1.12081e13i 0.628048 + 0.628048i
\(448\) −6.06412e12 + 6.06412e12i −0.336030 + 0.336030i
\(449\) 3.18162e13i 1.74348i −0.489972 0.871738i \(-0.662993\pi\)
0.489972 0.871738i \(-0.337007\pi\)
\(450\) 2.34152e12 + 2.14699e12i 0.126892 + 0.116350i
\(451\) −6.76078e12 −0.362338
\(452\) −1.28575e13 1.28575e13i −0.681498 0.681498i
\(453\) −8.87943e11 + 8.87943e11i −0.0465472 + 0.0465472i
\(454\) 1.49279e13i 0.773964i
\(455\) −3.03693e13 2.90816e13i −1.55732 1.49129i
\(456\) −7.11456e12 −0.360847
\(457\) 3.99239e11 + 3.99239e11i 0.0200287 + 0.0200287i 0.717050 0.697022i \(-0.245492\pi\)
−0.697022 + 0.717050i \(0.745492\pi\)
\(458\) −1.27605e13 + 1.27605e13i −0.633199 + 0.633199i
\(459\) 1.65081e12i 0.0810279i
\(460\) 3.01063e11 + 1.39000e13i 0.0146174 + 0.674878i
\(461\) 2.83811e12 0.136309 0.0681546 0.997675i \(-0.478289\pi\)
0.0681546 + 0.997675i \(0.478289\pi\)
\(462\) −7.16257e12 7.16257e12i −0.340298 0.340298i
\(463\) −7.39172e12 + 7.39172e12i −0.347409 + 0.347409i −0.859143 0.511735i \(-0.829003\pi\)
0.511735 + 0.859143i \(0.329003\pi\)
\(464\) 7.23155e12i 0.336234i
\(465\) −3.15774e12 + 6.83943e10i −0.145248 + 0.00314598i
\(466\) −5.48932e11 −0.0249798
\(467\) 2.41845e13 + 2.41845e13i 1.08881 + 1.08881i 0.995651 + 0.0931594i \(0.0296966\pi\)
0.0931594 + 0.995651i \(0.470303\pi\)
\(468\) −4.64259e12 + 4.64259e12i −0.206791 + 0.206791i
\(469\) 4.57197e13i 2.01483i
\(470\) −1.63497e12 + 1.70736e12i −0.0712887 + 0.0744452i
\(471\) −8.63234e12 −0.372412
\(472\) 2.10978e13 + 2.10978e13i 0.900592 + 0.900592i
\(473\) 3.38873e12 3.38873e12i 0.143130 0.143130i
\(474\) 3.10547e12i 0.129788i
\(475\) 1.68667e13 7.30985e11i 0.697530 0.0302301i
\(476\) −1.35949e13 −0.556340
\(477\) −9.19012e12 9.19012e12i −0.372160 0.372160i
\(478\) 4.06423e12 4.06423e12i 0.162869 0.162869i
\(479\) 7.36494e12i 0.292073i 0.989279 + 0.146037i \(0.0466517\pi\)
−0.989279 + 0.146037i \(0.953348\pi\)
\(480\) −1.09981e13 1.05318e13i −0.431631 0.413329i
\(481\) 5.32955e13 2.06998
\(482\) −1.00618e13 1.00618e13i −0.386758 0.386758i
\(483\) 1.78036e13 1.78036e13i 0.677287 0.677287i
\(484\) 3.85448e12i 0.145124i
\(485\) 2.07936e11 + 9.60032e12i 0.00774856 + 0.357748i
\(486\) −8.98320e11 −0.0331322
\(487\) −2.49057e13 2.49057e13i −0.909187 0.909187i 0.0870194 0.996207i \(-0.472266\pi\)
−0.996207 + 0.0870194i \(0.972266\pi\)
\(488\) 5.73220e11 5.73220e11i 0.0207120 0.0207120i
\(489\) 3.29037e12i 0.117680i
\(490\) −3.27812e13 + 7.10018e11i −1.16050 + 0.0251356i
\(491\) 4.75289e13 1.66552 0.832760 0.553634i \(-0.186759\pi\)
0.832760 + 0.553634i \(0.186759\pi\)
\(492\) 3.49145e12 + 3.49145e12i 0.121110 + 0.121110i
\(493\) −1.07612e13 + 1.07612e13i −0.369512 + 0.369512i
\(494\) 1.26933e13i 0.431458i
\(495\) 6.13603e12 6.40771e12i 0.206472 0.215614i
\(496\) 2.04643e12 0.0681693
\(497\) −2.52395e13 2.52395e13i −0.832337 0.832337i
\(498\) −2.16240e12 + 2.16240e12i −0.0705977 + 0.0705977i
\(499\) 5.13275e13i 1.65900i −0.558504 0.829502i \(-0.688624\pi\)
0.558504 0.829502i \(-0.311376\pi\)
\(500\) 1.72204e13 + 1.51166e13i 0.551053 + 0.483731i
\(501\) 1.17027e13 0.370763
\(502\) 2.21046e13 + 2.21046e13i 0.693370 + 0.693370i
\(503\) 3.56079e12 3.56079e12i 0.110588 0.110588i −0.649648 0.760235i \(-0.725084\pi\)
0.760235 + 0.649648i \(0.225084\pi\)
\(504\) 1.74871e13i 0.537731i
\(505\) 2.97218e12 + 2.84616e12i 0.0904938 + 0.0866569i
\(506\) −1.41251e13 −0.425831
\(507\) −5.90306e12 5.90306e12i −0.176213 0.176213i
\(508\) 2.79004e13 2.79004e13i 0.824692 0.824692i
\(509\) 1.90323e13i 0.557062i −0.960427 0.278531i \(-0.910153\pi\)
0.960427 0.278531i \(-0.0898474\pi\)
\(510\) 9.37997e10 + 4.33070e12i 0.00271863 + 0.125518i
\(511\) −8.14702e13 −2.33827
\(512\) 1.30098e13 + 1.30098e13i 0.369762 + 0.369762i
\(513\) −3.37567e12 + 3.37567e12i −0.0950109 + 0.0950109i
\(514\) 1.30024e13i 0.362416i
\(515\) 9.37825e12 2.03126e11i 0.258872 0.00560698i
\(516\) −3.50007e12 −0.0956815
\(517\) 4.66811e12 + 4.66811e12i 0.126383 + 0.126383i
\(518\) 4.24628e13 4.24628e13i 1.13857 1.13857i
\(519\) 2.19525e12i 0.0582971i
\(520\) 2.81656e13 2.94127e13i 0.740803 0.773604i
\(521\) −3.57848e13 −0.932201 −0.466101 0.884732i \(-0.654342\pi\)
−0.466101 + 0.884732i \(0.654342\pi\)
\(522\) 5.85593e12 + 5.85593e12i 0.151093 + 0.151093i
\(523\) −1.06389e13 + 1.06389e13i −0.271886 + 0.271886i −0.829859 0.557973i \(-0.811579\pi\)
0.557973 + 0.829859i \(0.311579\pi\)
\(524\) 3.95669e12i 0.100156i
\(525\) −1.79671e12 4.14573e13i −0.0450487 1.03945i
\(526\) 5.62839e12 0.139783
\(527\) −3.04529e12 3.04529e12i −0.0749162 0.0749162i
\(528\) −4.06460e12 + 4.06460e12i −0.0990485 + 0.0990485i
\(529\) 6.31662e12i 0.152478i
\(530\) 2.46313e13 + 2.35869e13i 0.588990 + 0.564016i
\(531\) 2.00208e13 0.474251
\(532\) 2.77995e13 + 2.77995e13i 0.652348 + 0.652348i
\(533\) −1.47245e13 + 1.47245e13i −0.342299 + 0.342299i
\(534\) 1.82859e13i 0.421125i
\(535\) −7.54958e11 3.48561e13i −0.0172248 0.795262i
\(536\) −4.42796e13 −1.00088
\(537\) 6.46702e12 + 6.46702e12i 0.144821 + 0.144821i
\(538\) 1.75711e13 1.75711e13i 0.389841 0.389841i
\(539\) 9.15687e13i 2.01281i
\(540\) −6.47794e12 + 1.40307e11i −0.141081 + 0.00305571i
\(541\) −3.25694e13 −0.702788 −0.351394 0.936228i \(-0.614292\pi\)
−0.351394 + 0.936228i \(0.614292\pi\)
\(542\) 1.46067e13 + 1.46067e13i 0.312288 + 0.312288i
\(543\) −3.28032e13 + 3.28032e13i −0.694892 + 0.694892i
\(544\) 2.07632e13i 0.435813i
\(545\) 1.50003e12 1.56644e12i 0.0311973 0.0325786i
\(546\) −3.11992e13 −0.642955
\(547\) −3.15535e13 3.15535e13i −0.644334 0.644334i 0.307284 0.951618i \(-0.400580\pi\)
−0.951618 + 0.307284i \(0.900580\pi\)
\(548\) −8.07548e12 + 8.07548e12i −0.163405 + 0.163405i
\(549\) 5.43956e11i 0.0109069i
\(550\) −1.57330e13 + 1.71585e13i −0.312606 + 0.340930i
\(551\) 4.40104e13 0.866557
\(552\) 1.72429e13 + 1.72429e13i 0.336445 + 0.336445i
\(553\) −2.86831e13 + 2.86831e13i −0.554627 + 0.554627i
\(554\) 4.22917e13i 0.810412i
\(555\) 3.79877e13 + 3.63770e13i 0.721404 + 0.690816i
\(556\) −4.82408e13 −0.907906
\(557\) −4.73202e13 4.73202e13i −0.882614 0.882614i 0.111186 0.993800i \(-0.464535\pi\)
−0.993800 + 0.111186i \(0.964535\pi\)
\(558\) −1.65715e12 + 1.65715e12i −0.0306331 + 0.0306331i
\(559\) 1.47609e13i 0.270429i
\(560\) 5.82196e11 + 2.68798e13i 0.0105713 + 0.488074i
\(561\) 1.20970e13 0.217703
\(562\) −3.38536e13 3.38536e13i −0.603842 0.603842i
\(563\) −2.29376e13 + 2.29376e13i −0.405515 + 0.405515i −0.880171 0.474656i \(-0.842572\pi\)
0.474656 + 0.880171i \(0.342572\pi\)
\(564\) 4.82149e12i 0.0844862i
\(565\) 7.56604e13 1.63875e12i 1.31409 0.0284623i
\(566\) 4.36895e13 0.752134
\(567\) 8.29718e12 + 8.29718e12i 0.141584 + 0.141584i
\(568\) 2.44446e13 2.44446e13i 0.413467 0.413467i
\(569\) 5.10806e13i 0.856435i 0.903676 + 0.428218i \(0.140858\pi\)
−0.903676 + 0.428218i \(0.859142\pi\)
\(570\) 8.66383e12 9.04745e12i 0.143991 0.150367i
\(571\) 2.22964e13 0.367328 0.183664 0.982989i \(-0.441204\pi\)
0.183664 + 0.982989i \(0.441204\pi\)
\(572\) −3.40206e13 3.40206e13i −0.555599 0.555599i
\(573\) −2.52992e13 + 2.52992e13i −0.409575 + 0.409575i
\(574\) 2.34633e13i 0.376557i
\(575\) −4.26499e13 3.91066e13i −0.678545 0.622173i
\(576\) −5.57328e12 −0.0879020
\(577\) −2.57967e13 2.57967e13i −0.403353 0.403353i 0.476060 0.879413i \(-0.342065\pi\)
−0.879413 + 0.476060i \(0.842065\pi\)
\(578\) 1.93836e13 1.93836e13i 0.300466 0.300466i
\(579\) 1.12047e13i 0.172191i
\(580\) 4.31427e13 + 4.13135e13i 0.657306 + 0.629436i
\(581\) 3.99454e13 0.603373
\(582\) 5.03815e12 + 5.03815e12i 0.0754495 + 0.0754495i
\(583\) 6.73445e13 6.73445e13i 0.999907 0.999907i
\(584\) 7.89041e13i 1.16154i
\(585\) −5.91719e11 2.73194e13i −0.00863647 0.398742i
\(586\) 5.41096e12 0.0783044
\(587\) −7.23929e13 7.23929e13i −1.03874 1.03874i −0.999219 0.0395181i \(-0.987418\pi\)
−0.0395181 0.999219i \(-0.512582\pi\)
\(588\) 4.72886e13 4.72886e13i 0.672775 0.672775i
\(589\) 1.24543e13i 0.175689i
\(590\) −5.25219e13 + 1.13759e12i −0.734650 + 0.0159120i
\(591\) −5.22876e13 −0.725205
\(592\) −2.40967e13 2.40967e13i −0.331398 0.331398i
\(593\) 6.41987e13 6.41987e13i 0.875494 0.875494i −0.117571 0.993064i \(-0.537511\pi\)
0.993064 + 0.117571i \(0.0375107\pi\)
\(594\) 6.58283e12i 0.0890185i
\(595\) 3.91334e13 4.08661e13i 0.524762 0.547997i
\(596\) 8.48304e13 1.12803
\(597\) 3.20375e13 + 3.20375e13i 0.422462 + 0.422462i
\(598\) −3.07634e13 + 3.07634e13i −0.402281 + 0.402281i
\(599\) 8.75969e13i 1.13594i 0.823050 + 0.567969i \(0.192271\pi\)
−0.823050 + 0.567969i \(0.807729\pi\)
\(600\) 4.01515e13 1.74012e12i 0.516352 0.0223781i
\(601\) −2.02581e13 −0.258361 −0.129180 0.991621i \(-0.541235\pi\)
−0.129180 + 0.991621i \(0.541235\pi\)
\(602\) −1.17606e13 1.17606e13i −0.148747 0.148747i
\(603\) −2.10095e13 + 2.10095e13i −0.263530 + 0.263530i
\(604\) 6.72057e12i 0.0836029i
\(605\) −1.15865e13 1.10953e13i −0.142948 0.136887i
\(606\) 3.05341e12 0.0373613
\(607\) 8.06656e13 + 8.06656e13i 0.978915 + 0.978915i 0.999782 0.0208669i \(-0.00664263\pi\)
−0.0208669 + 0.999782i \(0.506643\pi\)
\(608\) −4.24577e13 + 4.24577e13i −0.511021 + 0.511021i
\(609\) 1.08175e14i 1.29133i
\(610\) 3.09078e10 + 1.42700e12i 0.000365947 + 0.0168956i
\(611\) 2.03337e13 0.238787
\(612\) −6.24725e12 6.24725e12i −0.0727665 0.0727665i
\(613\) −7.64703e13 + 7.64703e13i −0.883467 + 0.883467i −0.993885 0.110418i \(-0.964781\pi\)
0.110418 + 0.993885i \(0.464781\pi\)
\(614\) 1.86539e13i 0.213760i
\(615\) −2.05456e13 + 4.45002e11i −0.233530 + 0.00505808i
\(616\) −1.28144e14 −1.44476
\(617\) 6.75222e13 + 6.75222e13i 0.755128 + 0.755128i 0.975431 0.220303i \(-0.0707047\pi\)
−0.220303 + 0.975431i \(0.570705\pi\)
\(618\) 4.92161e12 4.92161e12i 0.0545965 0.0545965i
\(619\) 8.43752e13i 0.928456i −0.885716 0.464228i \(-0.846332\pi\)
0.885716 0.464228i \(-0.153668\pi\)
\(620\) −1.16912e13 + 1.22088e13i −0.127614 + 0.133265i
\(621\) 1.63626e13 0.177171
\(622\) 7.87147e12 + 7.87147e12i 0.0845481 + 0.0845481i
\(623\) 1.68895e14 1.68895e14i 1.79960 1.79960i
\(624\) 1.77049e13i 0.187141i
\(625\) −9.50099e13 + 8.25073e12i −0.996251 + 0.0865152i
\(626\) −6.05687e12 −0.0630052
\(627\) −2.47367e13 2.47367e13i −0.255272 0.255272i
\(628\) −3.26678e13 + 3.26678e13i −0.334442 + 0.334442i
\(629\) 7.17165e13i 0.728394i
\(630\) −2.22380e13 2.12951e13i −0.224075 0.214574i
\(631\) 1.38987e14 1.38940 0.694698 0.719301i \(-0.255538\pi\)
0.694698 + 0.719301i \(0.255538\pi\)
\(632\) −2.77797e13 2.77797e13i −0.275513 0.275513i
\(633\) −3.89076e13 + 3.89076e13i −0.382839 + 0.382839i
\(634\) 1.73892e13i 0.169760i
\(635\) 3.55603e12 + 1.64181e14i 0.0344427 + 1.59021i
\(636\) −6.95572e13 −0.668431
\(637\) 1.99431e14 + 1.99431e14i 1.90149 + 1.90149i
\(638\) −4.29118e13 + 4.29118e13i −0.405951 + 0.405951i
\(639\) 2.31966e13i 0.217731i
\(640\) −9.64965e13 + 2.09004e12i −0.898694 + 0.0194650i
\(641\) −1.18929e14 −1.09900 −0.549500 0.835494i \(-0.685182\pi\)
−0.549500 + 0.835494i \(0.685182\pi\)
\(642\) −1.82921e13 1.82921e13i −0.167722 0.167722i
\(643\) −3.02629e13 + 3.02629e13i −0.275331 + 0.275331i −0.831242 0.555911i \(-0.812370\pi\)
0.555911 + 0.831242i \(0.312370\pi\)
\(644\) 1.34750e14i 1.21647i
\(645\) 1.00751e13 1.05212e13i 0.0902506 0.0942466i
\(646\) 1.70806e13 0.151824
\(647\) −1.05612e14 1.05612e14i −0.931521 0.931521i 0.0662803 0.997801i \(-0.478887\pi\)
−0.997801 + 0.0662803i \(0.978887\pi\)
\(648\) −8.03584e12 + 8.03584e12i −0.0703326 + 0.0703326i
\(649\) 1.46711e14i 1.27420i
\(650\) 3.10460e12 + 7.16354e13i 0.0267571 + 0.617392i
\(651\) 3.06120e13 0.261810
\(652\) 1.24519e13 + 1.24519e13i 0.105681 + 0.105681i
\(653\) −6.91878e12 + 6.91878e12i −0.0582725 + 0.0582725i −0.735643 0.677370i \(-0.763120\pi\)
0.677370 + 0.735643i \(0.263120\pi\)
\(654\) 1.60925e12i 0.0134504i
\(655\) −1.18938e13 1.13895e13i −0.0986537 0.0944707i
\(656\) 1.33149e13 0.109602
\(657\) −3.74380e13 3.74380e13i −0.305834 0.305834i
\(658\) 1.62007e13 1.62007e13i 0.131342 0.131342i
\(659\) 1.02130e14i 0.821723i −0.911698 0.410862i \(-0.865228\pi\)
0.911698 0.410862i \(-0.134772\pi\)
\(660\) −1.02816e12 4.74699e13i −0.00820998 0.379052i
\(661\) 1.82173e14 1.44370 0.721850 0.692049i \(-0.243292\pi\)
0.721850 + 0.692049i \(0.243292\pi\)
\(662\) −2.98757e13 2.98757e13i −0.234979 0.234979i
\(663\) 2.63466e13 2.63466e13i 0.205663 0.205663i
\(664\) 3.86872e13i 0.299728i
\(665\) −1.63587e14 + 3.54318e12i −1.25789 + 0.0272449i
\(666\) 3.90259e13 0.297839
\(667\) −1.06664e14 1.06664e14i −0.807955 0.807955i
\(668\) 4.42870e13 4.42870e13i 0.332961 0.332961i
\(669\) 1.89975e12i 0.0141764i
\(670\) 5.39220e13 5.63096e13i 0.399386 0.417069i
\(671\) 3.98607e12 0.0293044
\(672\) 1.04358e14 + 1.04358e14i 0.761519 + 0.761519i
\(673\) −1.51317e14 + 1.51317e14i −1.09601 + 1.09601i −0.101133 + 0.994873i \(0.532247\pi\)
−0.994873 + 0.101133i \(0.967753\pi\)
\(674\) 2.06591e13i 0.148529i
\(675\) 1.82252e13 1.98765e13i 0.130063 0.141847i
\(676\) −4.46784e13 −0.316493
\(677\) 1.99536e14 + 1.99536e14i 1.40307 + 1.40307i 0.790134 + 0.612934i \(0.210011\pi\)
0.612934 + 0.790134i \(0.289989\pi\)
\(678\) 3.97058e13 3.97058e13i 0.277144 0.277144i
\(679\) 9.30680e13i 0.644840i
\(680\) 3.95789e13 + 3.79008e13i 0.272220 + 0.260677i
\(681\) −1.26719e14 −0.865181
\(682\) −1.21435e13 1.21435e13i −0.0823040 0.0823040i
\(683\) −1.46891e14 + 1.46891e14i −0.988304 + 0.988304i −0.999932 0.0116281i \(-0.996299\pi\)
0.0116281 + 0.999932i \(0.496299\pi\)
\(684\) 2.55494e13i 0.170648i
\(685\) −1.02926e12 4.75204e13i −0.00682450 0.315085i
\(686\) 1.76391e14 1.16106
\(687\) 1.08320e14 + 1.08320e14i 0.707826 + 0.707826i
\(688\) −6.67389e12 + 6.67389e12i −0.0432949 + 0.0432949i
\(689\) 2.93344e14i 1.88921i
\(690\) −4.29251e13 + 9.29726e11i −0.274452 + 0.00594442i
\(691\) 7.64083e13 0.485009 0.242505 0.970150i \(-0.422031\pi\)
0.242505 + 0.970150i \(0.422031\pi\)
\(692\) 8.30758e12 + 8.30758e12i 0.0523533 + 0.0523533i
\(693\) −6.08011e13 + 6.08011e13i −0.380404 + 0.380404i
\(694\) 9.58398e13i 0.595317i
\(695\) 1.38863e14 1.45012e14i 0.856372 0.894290i
\(696\) 1.04767e14 0.641475
\(697\) −1.98139e13 1.98139e13i −0.120450 0.120450i
\(698\) 1.82514e12 1.82514e12i 0.0110159 0.0110159i
\(699\) 4.65974e12i 0.0279239i
\(700\) −1.63688e14 1.50089e14i −0.973928 0.893017i
\(701\) −3.54204e13 −0.209249 −0.104625 0.994512i \(-0.533364\pi\)
−0.104625 + 0.994512i \(0.533364\pi\)
\(702\) −1.43370e13 1.43370e13i −0.0840953 0.0840953i
\(703\) 1.46650e14 1.46650e14i 0.854093 0.854093i
\(704\) 4.08406e13i 0.236172i
\(705\) 1.44934e13 + 1.38788e13i 0.0832191 + 0.0796906i
\(706\) −8.59816e13 −0.490210
\(707\) −2.82023e13 2.82023e13i −0.159657 0.159657i
\(708\) 7.57655e13 7.57655e13i 0.425898 0.425898i
\(709\) 2.21716e14i 1.23756i −0.785565 0.618780i \(-0.787627\pi\)
0.785565 0.618780i \(-0.212373\pi\)
\(710\) 1.31804e12 + 6.08534e13i 0.00730527 + 0.337282i
\(711\) −2.63615e13 −0.145085
\(712\) 1.63575e14 + 1.63575e14i 0.893958 + 0.893958i
\(713\) 3.01844e13 3.01844e13i 0.163808 0.163808i
\(714\) 4.19829e13i 0.226246i
\(715\) 2.00195e14 4.33607e12i 1.07133 0.0232042i
\(716\) 4.89469e13 0.260112
\(717\) −3.45002e13 3.45002e13i −0.182065 0.182065i
\(718\) −3.37312e13 + 3.37312e13i −0.176770 + 0.176770i
\(719\) 2.91623e14i 1.51767i 0.651284 + 0.758834i \(0.274231\pi\)
−0.651284 + 0.758834i \(0.725769\pi\)
\(720\) −1.20845e13 + 1.26196e13i −0.0624549 + 0.0652203i
\(721\) −9.09152e13 −0.466616
\(722\) 3.67240e13 + 3.67240e13i 0.187182 + 0.187182i
\(723\) −8.54116e13 + 8.54116e13i −0.432340 + 0.432340i
\(724\) 2.48277e14i 1.24809i
\(725\) −2.48376e14 + 1.07643e13i −1.23999 + 0.0537399i
\(726\) −1.19032e13 −0.0590173
\(727\) −2.17241e14 2.17241e14i −1.06972 1.06972i −0.997380 0.0723409i \(-0.976953\pi\)
−0.0723409 0.997380i \(-0.523047\pi\)
\(728\) −2.79090e14 + 2.79090e14i −1.36486 + 1.36486i
\(729\) 7.62560e12i 0.0370370i
\(730\) 1.00341e14 + 9.60864e13i 0.484020 + 0.463498i
\(731\) 1.98628e13 0.0951598
\(732\) −2.05852e12 2.05852e12i −0.00979489 0.00979489i
\(733\) 1.47497e14 1.47497e14i 0.697051 0.697051i −0.266723 0.963773i \(-0.585941\pi\)
0.963773 + 0.266723i \(0.0859408\pi\)
\(734\) 3.05930e13i 0.143596i
\(735\) 6.02715e12 + 2.78271e14i 0.0280980 + 1.29727i
\(736\) 2.05801e14 0.952926
\(737\) −1.53956e14 1.53956e14i −0.708044 0.708044i
\(738\) −1.07821e13 + 1.07821e13i −0.0492517 + 0.0492517i
\(739\) 2.87168e14i 1.30291i −0.758689 0.651453i \(-0.774160\pi\)
0.758689 0.651453i \(-0.225840\pi\)
\(740\) 2.81422e14 6.09539e12i 1.26823 0.0274690i
\(741\) −1.07750e14 −0.482309
\(742\) −2.33720e14 2.33720e14i −1.03914 1.03914i
\(743\) 1.11836e14 1.11836e14i 0.493899 0.493899i −0.415633 0.909532i \(-0.636440\pi\)
0.909532 + 0.415633i \(0.136440\pi\)
\(744\) 2.96478e13i 0.130055i
\(745\) −2.44187e14 + 2.54999e14i −1.06400 + 1.11111i
\(746\) −7.50858e13 −0.324985
\(747\) 1.83561e13 + 1.83561e13i 0.0789181 + 0.0789181i
\(748\) 4.57794e13 4.57794e13i 0.195507 0.195507i
\(749\) 3.37904e14i 1.43346i
\(750\) −4.66821e13 + 5.31790e13i −0.196718 + 0.224096i
\(751\) −3.88625e14 −1.62679 −0.813395 0.581712i \(-0.802383\pi\)
−0.813395 + 0.581712i \(0.802383\pi\)
\(752\) −9.19355e12 9.19355e12i −0.0382291 0.0382291i
\(753\) 1.87640e14 1.87640e14i 0.775089 0.775089i
\(754\) 1.86918e14i 0.767000i
\(755\) −2.02020e13 1.93454e13i −0.0823491 0.0788575i
\(756\) 6.27988e13 0.254298
\(757\) 1.45441e14 + 1.45441e14i 0.585071 + 0.585071i 0.936293 0.351221i \(-0.114233\pi\)
−0.351221 + 0.936293i \(0.614233\pi\)
\(758\) −3.12859e13 + 3.12859e13i −0.125027 + 0.125027i
\(759\) 1.19904e14i 0.476019i
\(760\) −3.43158e12 1.58435e14i −0.0135340 0.624859i
\(761\) −5.67180e13 −0.222227 −0.111114 0.993808i \(-0.535442\pi\)
−0.111114 + 0.993808i \(0.535442\pi\)
\(762\) 8.61603e13 + 8.61603e13i 0.335376 + 0.335376i
\(763\) −1.48636e13 + 1.48636e13i −0.0574779 + 0.0574779i
\(764\) 1.91482e14i 0.735631i
\(765\) 3.67621e13 7.96240e11i 0.140311 0.00303904i
\(766\) −1.25109e14 −0.474399
\(767\) 3.19526e14 + 3.19526e14i 1.20373 + 1.20373i
\(768\) −7.94045e13 + 7.94045e13i −0.297193 + 0.297193i
\(769\) 4.01367e14i 1.49248i 0.665674 + 0.746242i \(0.268144\pi\)
−0.665674 + 0.746242i \(0.731856\pi\)
\(770\) 1.56049e14 1.62959e14i 0.576511 0.602038i
\(771\) 1.10374e14 0.405130
\(772\) 4.24026e13 + 4.24026e13i 0.154635 + 0.154635i
\(773\) 3.05262e14 3.05262e14i 1.10605 1.10605i 0.112387 0.993665i \(-0.464150\pi\)
0.993665 0.112387i \(-0.0358496\pi\)
\(774\) 1.08087e13i 0.0389107i
\(775\) −3.04616e12 7.02870e13i −0.0108954 0.251401i
\(776\) 9.01367e13 0.320327
\(777\) −3.60456e14 3.60456e14i −1.27276 1.27276i
\(778\) 5.59729e13 5.59729e13i 0.196372 0.196372i
\(779\) 8.10331e13i 0.282472i
\(780\) −1.05625e14 1.01147e14i −0.365844 0.350332i
\(781\) 1.69983e14 0.584993
\(782\) −4.13965e13 4.13965e13i −0.141556 0.141556i
\(783\) 4.97094e13 4.97094e13i 0.168900 0.168900i
\(784\) 1.80339e14i 0.608848i
\(785\) −4.16366e12 1.92234e14i −0.0139678 0.644886i
\(786\) −1.22188e13 −0.0407302
\(787\) −1.73114e14 1.73114e14i −0.573403 0.573403i 0.359675 0.933078i \(-0.382888\pi\)
−0.933078 + 0.359675i \(0.882888\pi\)
\(788\) −1.97874e14 + 1.97874e14i −0.651266 + 0.651266i
\(789\) 4.77779e13i 0.156258i
\(790\) 6.91560e13 1.49787e12i 0.224747 0.00486786i
\(791\) −7.33471e14 −2.36865
\(792\) −5.88861e13 5.88861e13i −0.188967 0.188967i
\(793\) 8.68141e12 8.68141e12i 0.0276837 0.0276837i
\(794\) 1.73969e14i 0.551277i
\(795\) 2.00223e14 2.09088e14i 0.630490 0.658407i
\(796\) 2.42482e14 0.758778
\(797\) 1.54981e14 + 1.54981e14i 0.481932 + 0.481932i 0.905748 0.423816i \(-0.139310\pi\)
−0.423816 + 0.905748i \(0.639310\pi\)
\(798\) −8.58489e13 + 8.58489e13i −0.265290 + 0.265290i
\(799\) 2.73618e13i 0.0840255i
\(800\) 2.29229e14 2.49998e14i 0.699551 0.762933i
\(801\) 1.55224e14 0.470757
\(802\) −9.46481e13 9.46481e13i −0.285260 0.285260i
\(803\) 2.74343e14 2.74343e14i 0.821704 0.821704i
\(804\) 1.59015e14i 0.473322i
\(805\) 4.05058e14 + 3.87883e14i 1.19822 + 1.14742i
\(806\) −5.28954e13 −0.155504
\(807\) −1.49156e14 1.49156e14i −0.435786 0.435786i
\(808\) 2.73140e13 2.73140e13i 0.0793101 0.0793101i
\(809\) 5.41509e14i 1.56265i −0.624122 0.781327i \(-0.714543\pi\)
0.624122 0.781327i \(-0.285457\pi\)
\(810\) −4.33289e11 2.00048e13i −0.00124266 0.0573731i
\(811\) 7.42708e13 0.211696 0.105848 0.994382i \(-0.466244\pi\)
0.105848 + 0.994382i \(0.466244\pi\)
\(812\) −4.09370e14 4.09370e14i −1.15967 1.15967i
\(813\) 1.23992e14 1.23992e14i 0.349093 0.349093i
\(814\) 2.85979e14i 0.800224i
\(815\) −7.32736e13 + 1.58705e12i −0.203779 + 0.00441371i
\(816\) −2.38244e13 −0.0658522
\(817\) −4.06165e13 4.06165e13i −0.111582 0.111582i
\(818\) 6.31805e13 6.31805e13i 0.172511 0.172511i
\(819\) 2.64842e14i 0.718732i
\(820\) −7.60675e13 + 7.94356e13i −0.205177 + 0.214262i
\(821\) 5.08324e13 0.136278 0.0681389 0.997676i \(-0.478294\pi\)
0.0681389 + 0.997676i \(0.478294\pi\)
\(822\) −2.49382e13 2.49382e13i −0.0664517 0.0664517i
\(823\) −1.56162e14 + 1.56162e14i −0.413597 + 0.413597i −0.882990 0.469393i \(-0.844473\pi\)
0.469393 + 0.882990i \(0.344473\pi\)
\(824\) 8.80516e13i 0.231794i
\(825\) 1.45654e14 + 1.33553e14i 0.381111 + 0.349449i
\(826\) 5.09161e14 1.32420
\(827\) 3.83051e14 + 3.83051e14i 0.990215 + 0.990215i 0.999953 0.00973769i \(-0.00309965\pi\)
−0.00973769 + 0.999953i \(0.503100\pi\)
\(828\) 6.19217e13 6.19217e13i 0.159108 0.159108i
\(829\) 1.71588e14i 0.438242i 0.975698 + 0.219121i \(0.0703190\pi\)
−0.975698 + 0.219121i \(0.929681\pi\)
\(830\) −4.91978e13 4.71118e13i −0.124898 0.119602i
\(831\) 3.59003e14 0.905926
\(832\) −8.89482e13 8.89482e13i −0.223111 0.223111i
\(833\) −2.68362e14 + 2.68362e14i −0.669107 + 0.669107i
\(834\) 1.48974e14i 0.369217i
\(835\) 5.64457e12 + 2.60608e14i 0.0139059 + 0.642030i
\(836\) −1.87224e14 −0.458491
\(837\) 1.40671e13 + 1.40671e13i 0.0342434 + 0.0342434i
\(838\) −1.31511e13 + 1.31511e13i −0.0318230 + 0.0318230i
\(839\) 2.36405e14i 0.568653i 0.958728 + 0.284326i \(0.0917699\pi\)
−0.958728 + 0.284326i \(0.908230\pi\)
\(840\) −3.89422e14 + 8.43459e12i −0.931159 + 0.0201682i
\(841\) −2.27380e14 −0.540471
\(842\) 1.16489e14 + 1.16489e14i 0.275249 + 0.275249i
\(843\) −2.87374e14 + 2.87374e14i −0.675009 + 0.675009i
\(844\) 2.94480e14i 0.687612i
\(845\) 1.28608e14 1.34303e14i 0.298529 0.311747i
\(846\) 1.48894e13 0.0343579
\(847\) 1.09942e14 + 1.09942e14i 0.252200 + 0.252200i
\(848\) −1.32631e14 + 1.32631e14i −0.302458 + 0.302458i
\(849\) 3.70869e14i 0.840779i
\(850\) −9.63954e13 + 4.17767e12i −0.217251 + 0.00941541i
\(851\) −7.10842e14 −1.59267
\(852\) −8.77841e13 8.77841e13i −0.195532 0.195532i
\(853\) 1.64973e14 1.64973e14i 0.365314 0.365314i −0.500451 0.865765i \(-0.666832\pi\)
0.865765 + 0.500451i \(0.166832\pi\)
\(854\) 1.38337e13i 0.0304543i
\(855\) −7.68013e13 7.35450e13i −0.168089 0.160962i
\(856\) −3.27261e14 −0.712075
\(857\) −1.16143e13 1.16143e13i −0.0251239 0.0251239i 0.694433 0.719557i \(-0.255655\pi\)
−0.719557 + 0.694433i \(0.755655\pi\)
\(858\) 1.05060e14 1.05060e14i 0.225945 0.225945i
\(859\) 1.65139e14i 0.353089i 0.984293 + 0.176545i \(0.0564920\pi\)
−0.984293 + 0.176545i \(0.943508\pi\)
\(860\) −1.68820e12 7.79434e13i −0.00358865 0.165686i
\(861\) 1.99174e14 0.420937
\(862\) 2.69639e14 + 2.69639e14i 0.566560 + 0.566560i
\(863\) −3.69915e14 + 3.69915e14i −0.772766 + 0.772766i −0.978589 0.205823i \(-0.934013\pi\)
0.205823 + 0.978589i \(0.434013\pi\)
\(864\) 9.59115e13i 0.199206i
\(865\) −4.88862e13 + 1.05884e12i −0.100950 + 0.00218650i
\(866\) 6.77902e13 0.139180
\(867\) −1.64542e14 1.64542e14i −0.335879 0.335879i
\(868\) 1.15846e14 1.15846e14i 0.235117 0.235117i
\(869\) 1.93175e14i 0.389809i
\(870\) −1.27582e14 + 1.33231e14i −0.255972 + 0.267306i
\(871\) −6.70614e14 −1.33777
\(872\) −1.43954e13 1.43954e13i −0.0285524 0.0285524i
\(873\) 4.27675e13 4.27675e13i 0.0843418 0.0843418i
\(874\) 1.69300e14i 0.331970i
\(875\) 9.22350e14 6.00073e13i 1.79827 0.116994i
\(876\) −2.83356e14 −0.549304
\(877\) 2.06439e14 + 2.06439e14i 0.397918 + 0.397918i 0.877498 0.479580i \(-0.159211\pi\)
−0.479580 + 0.877498i \(0.659211\pi\)
\(878\) −2.21488e14 + 2.21488e14i −0.424501 + 0.424501i
\(879\) 4.59322e13i 0.0875331i
\(880\) −9.24754e13 8.85544e13i −0.175232 0.167802i
\(881\) 6.72129e14 1.26641 0.633203 0.773986i \(-0.281740\pi\)
0.633203 + 0.773986i \(0.281740\pi\)
\(882\) 1.46034e14 + 1.46034e14i 0.273597 + 0.273597i
\(883\) −2.04026e14 + 2.04026e14i −0.380086 + 0.380086i −0.871133 0.491047i \(-0.836614\pi\)
0.491047 + 0.871133i \(0.336614\pi\)
\(884\) 1.99409e14i 0.369389i
\(885\) 9.65666e12 + 4.45844e14i 0.0177873 + 0.821234i
\(886\) −5.19408e14 −0.951350
\(887\) 7.02000e14 + 7.02000e14i 1.27855 + 1.27855i 0.941478 + 0.337075i \(0.109438\pi\)
0.337075 + 0.941478i \(0.390562\pi\)
\(888\) 3.49102e14 3.49102e14i 0.632249 0.632249i
\(889\) 1.59161e15i 2.86634i
\(890\) −4.07211e14 + 8.81989e12i −0.729238 + 0.0157948i
\(891\) −5.58798e13 −0.0995100
\(892\) 7.18931e12 + 7.18931e12i 0.0127310 + 0.0127310i
\(893\) 5.59509e13 5.59509e13i 0.0985258 0.0985258i
\(894\) 2.61968e14i 0.458734i
\(895\) −1.40895e14 + 1.47134e14i −0.245348 + 0.256211i
\(896\) 9.35462e14 1.61989
\(897\) 2.61143e14 + 2.61143e14i 0.449692 + 0.449692i
\(898\) 3.71822e14 3.71822e14i 0.636728 0.636728i
\(899\) 1.83400e14i 0.312321i
\(900\) −6.24903e12 1.44190e14i −0.0105828 0.244187i
\(901\) 3.94735e14 0.664786
\(902\) −7.90105e13 7.90105e13i −0.132328 0.132328i
\(903\) −9.98327e13 + 9.98327e13i −0.166278 + 0.166278i
\(904\) 7.10369e14i 1.17664i
\(905\) −7.46320e14 7.14676e14i −1.22937 1.17724i
\(906\) −2.07540e13 −0.0339987
\(907\) −5.77421e14 5.77421e14i −0.940711 0.940711i 0.0576270 0.998338i \(-0.481647\pi\)
−0.998338 + 0.0576270i \(0.981647\pi\)
\(908\) −4.79550e14 + 4.79550e14i −0.776970 + 0.776970i
\(909\) 2.59196e13i 0.0417646i
\(910\) −1.50484e13 6.94778e14i −0.0241148 1.11337i
\(911\) −9.22325e13 −0.146991 −0.0734957 0.997296i \(-0.523416\pi\)
−0.0734957 + 0.997296i \(0.523416\pi\)
\(912\) 4.87173e13 + 4.87173e13i 0.0772163 + 0.0772163i
\(913\) −1.34512e14 + 1.34512e14i −0.212035 + 0.212035i
\(914\) 9.33149e12i 0.0146292i
\(915\) 1.21134e13 2.62368e11i 0.0188869 0.000409077i
\(916\) 8.19844e14 1.27132
\(917\) 1.12857e14 + 1.12857e14i 0.174053 + 0.174053i
\(918\) 1.92924e13 1.92924e13i 0.0295919 0.0295919i
\(919\) 1.90596e14i 0.290761i 0.989376 + 0.145381i \(0.0464407\pi\)
−0.989376 + 0.145381i \(0.953559\pi\)
\(920\) −3.75666e14 + 3.92300e14i −0.569984 + 0.595222i
\(921\) 1.58348e14 0.238953
\(922\) 3.31679e13 + 3.31679e13i 0.0497809 + 0.0497809i
\(923\) 3.70212e14 3.70212e14i 0.552640 0.552640i
\(924\) 4.60185e14i 0.683239i
\(925\) −7.91761e14 + 8.63498e14i −1.16919 + 1.27512i
\(926\) −1.72768e14 −0.253751
\(927\) −4.17782e13 4.17782e13i −0.0610311 0.0610311i
\(928\) 6.25224e14 6.25224e14i 0.908438 0.908438i
\(929\) 1.08880e14i 0.157351i 0.996900 + 0.0786753i \(0.0250690\pi\)
−0.996900 + 0.0786753i \(0.974931\pi\)
\(930\) −3.77025e13 3.61039e13i −0.0541946 0.0518967i
\(931\) 1.09752e15 1.56915
\(932\) 1.76341e13 + 1.76341e13i 0.0250768 + 0.0250768i
\(933\) 6.68188e13 6.68188e13i 0.0945127 0.0945127i
\(934\) 5.65268e14i 0.795280i
\(935\) 5.83479e12 + 2.69390e14i 0.00816521 + 0.376985i
\(936\) −2.56500e14 −0.357033
\(937\) 1.75741e14 + 1.75741e14i 0.243318 + 0.243318i 0.818221 0.574903i \(-0.194960\pi\)
−0.574903 + 0.818221i \(0.694960\pi\)
\(938\) −5.34307e14 + 5.34307e14i −0.735829 + 0.735829i
\(939\) 5.14151e13i 0.0704309i
\(940\) 1.07370e14 2.32556e12i 0.146300 0.00316875i
\(941\) 1.07510e15 1.45713 0.728566 0.684975i \(-0.240187\pi\)
0.728566 + 0.684975i \(0.240187\pi\)
\(942\) −1.00883e14 1.00883e14i −0.136007 0.136007i
\(943\) 1.96392e14 1.96392e14i 0.263369 0.263369i
\(944\) 2.88937e14i 0.385429i
\(945\) −1.80769e14 + 1.88773e14i −0.239863 + 0.250484i
\(946\) 7.92054e13 0.104544
\(947\) −7.06380e14 7.06380e14i −0.927445 0.927445i 0.0700948 0.997540i \(-0.477670\pi\)
−0.997540 + 0.0700948i \(0.977670\pi\)
\(948\) −9.97610e13 + 9.97610e13i −0.130292 + 0.130292i
\(949\) 1.19500e15i 1.55252i
\(950\) 2.05657e14 + 1.88572e14i 0.265782 + 0.243702i
\(951\) −1.47613e14 −0.189767
\(952\) −3.75554e14 3.75554e14i −0.480273 0.480273i
\(953\) 4.13424e14 4.13424e14i 0.525934 0.525934i −0.393423 0.919357i \(-0.628709\pi\)
0.919357 + 0.393423i \(0.128709\pi\)
\(954\) 2.14802e14i 0.271830i
\(955\) −5.75592e14 5.51187e14i −0.724599 0.693876i
\(956\) −2.61121e14 −0.327004
\(957\) 3.64267e14 + 3.64267e14i 0.453796 + 0.453796i
\(958\) −8.60710e13 + 8.60710e13i −0.106667 + 0.106667i
\(959\) 4.60675e14i 0.567939i
\(960\) −2.68817e12 1.24112e14i −0.00329686 0.152215i
\(961\) −7.67729e14 −0.936679
\(962\) 6.22843e14 + 6.22843e14i 0.755968 + 0.755968i
\(963\) −1.55277e14 + 1.55277e14i −0.187489 + 0.187489i
\(964\) 6.46454e14i 0.776520i
\(965\) −2.49520e14 + 5.40441e12i −0.298173 + 0.00645820i
\(966\) 4.16127e14 0.494698
\(967\) −1.66726e14 1.66726e14i −0.197183 0.197183i 0.601608 0.798791i \(-0.294527\pi\)
−0.798791 + 0.601608i \(0.794527\pi\)
\(968\) −1.06479e14 + 1.06479e14i −0.125281 + 0.125281i
\(969\) 1.44992e14i 0.169717i
\(970\) −1.09765e14 + 1.14625e14i −0.127822 + 0.133482i
\(971\) −1.34411e15 −1.55718 −0.778589 0.627534i \(-0.784064\pi\)
−0.778589 + 0.627534i \(0.784064\pi\)
\(972\) 2.88579e13 + 2.88579e13i 0.0332609 + 0.0332609i
\(973\) −1.37598e15 + 1.37598e15i −1.57778 + 1.57778i
\(974\) 5.82125e14i 0.664081i
\(975\) 6.08094e14 2.63541e13i 0.690156 0.0299106i
\(976\) −7.85032e12 −0.00886417
\(977\) −5.60729e13 5.60729e13i −0.0629912 0.0629912i 0.674909 0.737901i \(-0.264183\pi\)
−0.737901 + 0.674909i \(0.764183\pi\)
\(978\) −3.84533e13 + 3.84533e13i −0.0429773 + 0.0429773i
\(979\) 1.13747e15i 1.26482i
\(980\) 1.07588e15 + 1.03027e15i 1.19024 + 1.13977i
\(981\) −1.36605e13 −0.0150356
\(982\) 5.55450e14 + 5.55450e14i 0.608258 + 0.608258i
\(983\) 3.59073e14 3.59073e14i 0.391215 0.391215i −0.483905 0.875120i \(-0.660782\pi\)
0.875120 + 0.483905i \(0.160782\pi\)
\(984\) 1.92901e14i 0.209102i
\(985\) −2.52200e13 1.16440e15i −0.0271997 1.25580i
\(986\) −2.51525e14 −0.269896
\(987\) −1.37524e14 1.37524e14i −0.146822 0.146822i
\(988\) −4.07762e14 + 4.07762e14i −0.433134 + 0.433134i
\(989\) 1.96877e14i 0.208072i
\(990\) 1.46594e14 3.17511e12i 0.154148 0.00333874i
\(991\) 3.64343e14 0.381190 0.190595 0.981669i \(-0.438958\pi\)
0.190595 + 0.981669i \(0.438958\pi\)
\(992\) 1.76930e14 + 1.76930e14i 0.184180 + 0.184180i
\(993\) −2.53607e14 + 2.53607e14i −0.262673 + 0.262673i
\(994\) 5.89928e14i 0.607949i
\(995\) −6.97994e14 + 7.28900e14i −0.715709 + 0.747399i
\(996\) 1.38931e14 0.141744
\(997\) 3.19212e14 + 3.19212e14i 0.324043 + 0.324043i 0.850316 0.526273i \(-0.176411\pi\)
−0.526273 + 0.850316i \(0.676411\pi\)
\(998\) 5.99844e14 5.99844e14i 0.605878 0.605878i
\(999\) 3.31280e14i 0.332941i
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.7.7 20
3.2 odd 2 45.11.g.c.37.4 20
5.2 odd 4 75.11.f.d.43.4 20
5.3 odd 4 inner 15.11.f.a.13.7 yes 20
5.4 even 2 75.11.f.d.7.4 20
15.8 even 4 45.11.g.c.28.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.11.f.a.7.7 20 1.1 even 1 trivial
15.11.f.a.13.7 yes 20 5.3 odd 4 inner
45.11.g.c.28.4 20 15.8 even 4
45.11.g.c.37.4 20 3.2 odd 2
75.11.f.d.7.4 20 5.4 even 2
75.11.f.d.43.4 20 5.2 odd 4