Properties

Label 12.21.d.a.7.16
Level $12$
Weight $21$
Character 12.7
Analytic conductor $30.422$
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] = [12,21,Mod(7,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 21, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 21);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\), degree \(1\), 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: \(30.4216518123\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{174}\cdot 3^{82}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.16
Root \(-144.957 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.21.d.a.7.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(734.722 + 713.274i) q^{2} +34092.0i q^{3} +(31057.2 + 1.04812e6i) q^{4} +6.80556e6 q^{5} +(-2.43169e7 + 2.50481e7i) q^{6} +4.46066e7i q^{7} +(-7.24775e8 + 7.92226e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\) \(q+(734.722 + 713.274i) q^{2} +34092.0i q^{3} +(31057.2 + 1.04812e6i) q^{4} +6.80556e6 q^{5} +(-2.43169e7 + 2.50481e7i) q^{6} +4.46066e7i q^{7} +(-7.24775e8 + 7.92226e8i) q^{8} -1.16226e9 q^{9} +(5.00020e9 + 4.85423e9i) q^{10} +3.23666e10i q^{11} +(-3.57323e10 + 1.05880e9i) q^{12} +7.05819e10 q^{13} +(-3.18167e10 + 3.27735e10i) q^{14} +2.32015e11i q^{15} +(-1.09758e12 + 6.51032e10i) q^{16} -1.15701e12 q^{17} +(-8.53939e11 - 8.29011e11i) q^{18} +4.69812e12i q^{19} +(2.11362e11 + 7.13302e12i) q^{20} -1.52073e12 q^{21} +(-2.30862e13 + 2.37805e13i) q^{22} -3.62713e13i q^{23} +(-2.70085e13 - 2.47090e13i) q^{24} -4.90518e13 q^{25} +(5.18581e13 + 5.03442e13i) q^{26} -3.96238e13i q^{27} +(-4.67529e13 + 1.38536e12i) q^{28} +3.47780e14 q^{29} +(-1.65490e14 + 1.70466e14i) q^{30} -3.23494e14i q^{31} +(-8.52855e14 - 7.35044e14i) q^{32} -1.10344e15 q^{33} +(-8.50083e14 - 8.25267e14i) q^{34} +3.03573e14i q^{35} +(-3.60966e13 - 1.21818e15i) q^{36} -6.74908e15 q^{37} +(-3.35105e15 + 3.45181e15i) q^{38} +2.40627e15i q^{39} +(-4.93250e15 + 5.39154e15i) q^{40} -2.06196e16 q^{41} +(-1.11731e15 - 1.08470e15i) q^{42} +2.47203e16i q^{43} +(-3.39240e16 + 1.00522e15i) q^{44} -7.90984e15 q^{45} +(2.58714e16 - 2.66493e16i) q^{46} -4.97745e16i q^{47} +(-2.21949e15 - 3.74187e16i) q^{48} +7.78025e16 q^{49} +(-3.60394e16 - 3.49873e16i) q^{50} -3.94448e16i q^{51} +(2.19208e15 + 7.39780e16i) q^{52} +2.42735e17 q^{53} +(2.82626e16 - 2.91125e16i) q^{54} +2.20273e17i q^{55} +(-3.53386e16 - 3.23298e16i) q^{56} -1.60168e17 q^{57} +(2.55521e17 + 2.48062e17i) q^{58} +2.94263e17i q^{59} +(-2.43179e17 + 7.20574e15i) q^{60} +1.13045e18 q^{61} +(2.30740e17 - 2.37678e17i) q^{62} -5.18446e16i q^{63} +(-1.02324e17 - 1.14837e18i) q^{64} +4.80349e17 q^{65} +(-8.10722e17 - 7.87055e17i) q^{66} +2.38409e18i q^{67} +(-3.59336e16 - 1.21268e18i) q^{68} +1.23656e18 q^{69} +(-2.16531e17 + 2.23042e17i) q^{70} +3.37689e18i q^{71} +(8.42378e17 - 9.20774e17i) q^{72} +3.65986e18 q^{73} +(-4.95870e18 - 4.81394e18i) q^{74} -1.67227e18i q^{75} +(-4.92418e18 + 1.45911e17i) q^{76} -1.44377e18 q^{77} +(-1.71633e18 + 1.76794e18i) q^{78} -1.94374e18i q^{79} +(-7.46967e18 + 4.43064e17i) q^{80} +1.35085e18 q^{81} +(-1.51497e19 - 1.47074e19i) q^{82} +2.58303e19i q^{83} +(-4.72296e16 - 1.59390e18i) q^{84} -7.87412e18 q^{85} +(-1.76323e19 + 1.81625e19i) q^{86} +1.18565e19i q^{87} +(-2.56417e19 - 2.34585e19i) q^{88} +4.32814e19 q^{89} +(-5.81154e18 - 5.64188e18i) q^{90} +3.14842e18i q^{91} +(3.80165e19 - 1.12649e18i) q^{92} +1.10286e19 q^{93} +(3.55028e19 - 3.65704e19i) q^{94} +3.19734e19i q^{95} +(2.50591e19 - 2.90755e19i) q^{96} +2.46901e19 q^{97} +(5.71632e19 + 5.54945e19i) q^{98} -3.76185e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 734.722 + 713.274i 0.717502 + 0.696556i
\(3\) 34092.0i 0.577350i
\(4\) 31057.2 + 1.04812e6i 0.0296185 + 0.999561i
\(5\) 6.80556e6 0.696889 0.348445 0.937329i \(-0.386710\pi\)
0.348445 + 0.937329i \(0.386710\pi\)
\(6\) −2.43169e7 + 2.50481e7i −0.402157 + 0.414250i
\(7\) 4.46066e7i 0.157913i 0.996878 + 0.0789567i \(0.0251589\pi\)
−0.996878 + 0.0789567i \(0.974841\pi\)
\(8\) −7.24775e8 + 7.92226e8i −0.674999 + 0.737818i
\(9\) −1.16226e9 −0.333333
\(10\) 5.00020e9 + 4.85423e9i 0.500020 + 0.485423i
\(11\) 3.23666e10i 1.24787i 0.781475 + 0.623936i \(0.214468\pi\)
−0.781475 + 0.623936i \(0.785532\pi\)
\(12\) −3.57323e10 + 1.05880e9i −0.577097 + 0.0171002i
\(13\) 7.05819e10 0.511988 0.255994 0.966678i \(-0.417597\pi\)
0.255994 + 0.966678i \(0.417597\pi\)
\(14\) −3.18167e10 + 3.27735e10i −0.109996 + 0.113303i
\(15\) 2.32015e11i 0.402349i
\(16\) −1.09758e12 + 6.51032e10i −0.998245 + 0.0592110i
\(17\) −1.15701e12 −0.573917 −0.286958 0.957943i \(-0.592644\pi\)
−0.286958 + 0.957943i \(0.592644\pi\)
\(18\) −8.53939e11 8.29011e11i −0.239167 0.232185i
\(19\) 4.69812e12i 0.766282i 0.923690 + 0.383141i \(0.125158\pi\)
−0.923690 + 0.383141i \(0.874842\pi\)
\(20\) 2.11362e11 + 7.13302e12i 0.0206408 + 0.696584i
\(21\) −1.52073e12 −0.0911714
\(22\) −2.30862e13 + 2.37805e13i −0.869214 + 0.895351i
\(23\) 3.62713e13i 0.875558i −0.899083 0.437779i \(-0.855765\pi\)
0.899083 0.437779i \(-0.144235\pi\)
\(24\) −2.70085e13 2.47090e13i −0.425980 0.389711i
\(25\) −4.90518e13 −0.514345
\(26\) 5.18581e13 + 5.03442e13i 0.367352 + 0.356628i
\(27\) 3.96238e13i 0.192450i
\(28\) −4.67529e13 + 1.38536e12i −0.157844 + 0.00467716i
\(29\) 3.47780e14 0.826655 0.413327 0.910583i \(-0.364367\pi\)
0.413327 + 0.910583i \(0.364367\pi\)
\(30\) −1.65490e14 + 1.70466e14i −0.280259 + 0.288686i
\(31\) 3.23494e14i 0.394684i −0.980335 0.197342i \(-0.936769\pi\)
0.980335 0.197342i \(-0.0632310\pi\)
\(32\) −8.52855e14 7.35044e14i −0.757487 0.652850i
\(33\) −1.10344e15 −0.720460
\(34\) −8.50083e14 8.25267e14i −0.411786 0.399765i
\(35\) 3.03573e14i 0.110048i
\(36\) −3.60966e13 1.21818e15i −0.00987283 0.333187i
\(37\) −6.74908e15 −1.40355 −0.701774 0.712400i \(-0.747608\pi\)
−0.701774 + 0.712400i \(0.747608\pi\)
\(38\) −3.35105e15 + 3.45181e15i −0.533758 + 0.549809i
\(39\) 2.40627e15i 0.295596i
\(40\) −4.93250e15 + 5.39154e15i −0.470400 + 0.514178i
\(41\) −2.06196e16 −1.53618 −0.768089 0.640343i \(-0.778792\pi\)
−0.768089 + 0.640343i \(0.778792\pi\)
\(42\) −1.11731e15 1.08470e15i −0.0654157 0.0635060i
\(43\) 2.47203e16i 1.14385i 0.820306 + 0.571925i \(0.193803\pi\)
−0.820306 + 0.571925i \(0.806197\pi\)
\(44\) −3.39240e16 + 1.00522e15i −1.24733 + 0.0369601i
\(45\) −7.90984e15 −0.232296
\(46\) 2.58714e16 2.66493e16i 0.609875 0.628215i
\(47\) 4.97745e16i 0.946299i −0.880982 0.473149i \(-0.843117\pi\)
0.880982 0.473149i \(-0.156883\pi\)
\(48\) −2.21949e15 3.74187e16i −0.0341855 0.576337i
\(49\) 7.78025e16 0.975063
\(50\) −3.60394e16 3.49873e16i −0.369044 0.358270i
\(51\) 3.94448e16i 0.331351i
\(52\) 2.19208e15 + 7.39780e16i 0.0151643 + 0.511763i
\(53\) 2.42735e17 1.38795 0.693974 0.720000i \(-0.255858\pi\)
0.693974 + 0.720000i \(0.255858\pi\)
\(54\) 2.82626e16 2.91125e16i 0.134052 0.138083i
\(55\) 2.20273e17i 0.869629i
\(56\) −3.53386e16 3.23298e16i −0.116511 0.106591i
\(57\) −1.60168e17 −0.442413
\(58\) 2.55521e17 + 2.48062e17i 0.593126 + 0.575812i
\(59\) 2.94263e17i 0.575726i 0.957672 + 0.287863i \(0.0929447\pi\)
−0.957672 + 0.287863i \(0.907055\pi\)
\(60\) −2.43179e17 + 7.20574e15i −0.402173 + 0.0119170i
\(61\) 1.13045e18 1.58472 0.792360 0.610053i \(-0.208852\pi\)
0.792360 + 0.610053i \(0.208852\pi\)
\(62\) 2.30740e17 2.37678e17i 0.274920 0.283187i
\(63\) 5.18446e16i 0.0526378i
\(64\) −1.02324e17 1.14837e18i −0.0887515 0.996054i
\(65\) 4.80349e17 0.356799
\(66\) −8.10722e17 7.87055e17i −0.516931 0.501841i
\(67\) 2.38409e18i 1.30790i 0.756537 + 0.653951i \(0.226890\pi\)
−0.756537 + 0.653951i \(0.773110\pi\)
\(68\) −3.59336e16 1.21268e18i −0.0169985 0.573665i
\(69\) 1.23656e18 0.505504
\(70\) −2.16531e17 + 2.23042e17i −0.0766548 + 0.0789598i
\(71\) 3.37689e18i 1.03737i 0.854966 + 0.518685i \(0.173578\pi\)
−0.854966 + 0.518685i \(0.826422\pi\)
\(72\) 8.42378e17 9.20774e17i 0.225000 0.245939i
\(73\) 3.65986e18 0.851601 0.425801 0.904817i \(-0.359993\pi\)
0.425801 + 0.904817i \(0.359993\pi\)
\(74\) −4.95870e18 4.81394e18i −1.00705 0.977650i
\(75\) 1.67227e18i 0.296957i
\(76\) −4.92418e18 + 1.45911e17i −0.765945 + 0.0226961i
\(77\) −1.44377e18 −0.197056
\(78\) −1.71633e18 + 1.76794e18i −0.205900 + 0.212091i
\(79\) 1.94374e18i 0.205290i −0.994718 0.102645i \(-0.967269\pi\)
0.994718 0.102645i \(-0.0327306\pi\)
\(80\) −7.46967e18 + 4.43064e17i −0.695667 + 0.0412635i
\(81\) 1.35085e18 0.111111
\(82\) −1.51497e19 1.47074e19i −1.10221 1.07003i
\(83\) 2.58303e19i 1.66475i 0.554213 + 0.832375i \(0.313019\pi\)
−0.554213 + 0.832375i \(0.686981\pi\)
\(84\) −4.72296e16 1.59390e18i −0.00270036 0.0911314i
\(85\) −7.87412e18 −0.399956
\(86\) −1.76323e19 + 1.81625e19i −0.796755 + 0.820714i
\(87\) 1.18565e19i 0.477269i
\(88\) −2.56417e19 2.34585e19i −0.920703 0.842313i
\(89\) 4.32814e19 1.38804 0.694020 0.719956i \(-0.255838\pi\)
0.694020 + 0.719956i \(0.255838\pi\)
\(90\) −5.81154e18 5.64188e18i −0.166673 0.161808i
\(91\) 3.14842e18i 0.0808498i
\(92\) 3.80165e19 1.12649e18i 0.875174 0.0259327i
\(93\) 1.10286e19 0.227871
\(94\) 3.55028e19 3.65704e19i 0.659150 0.678971i
\(95\) 3.19734e19i 0.534014i
\(96\) 2.50591e19 2.90755e19i 0.376923 0.437335i
\(97\) 2.46901e19 0.334815 0.167408 0.985888i \(-0.446460\pi\)
0.167408 + 0.985888i \(0.446460\pi\)
\(98\) 5.71632e19 + 5.54945e19i 0.699610 + 0.679187i
\(99\) 3.76185e19i 0.415958i
\(100\) −1.52341e18 5.14119e19i −0.0152341 0.514119i
\(101\) 5.44781e19 0.493183 0.246592 0.969119i \(-0.420689\pi\)
0.246592 + 0.969119i \(0.420689\pi\)
\(102\) 2.81350e19 2.89810e19i 0.230805 0.237745i
\(103\) 1.28800e20i 0.958393i −0.877708 0.479196i \(-0.840928\pi\)
0.877708 0.479196i \(-0.159072\pi\)
\(104\) −5.11560e19 + 5.59168e19i −0.345592 + 0.377754i
\(105\) −1.03494e19 −0.0635364
\(106\) 1.78343e20 + 1.73136e20i 0.995856 + 0.966784i
\(107\) 1.89241e20i 0.962004i 0.876719 + 0.481002i \(0.159727\pi\)
−0.876719 + 0.481002i \(0.840273\pi\)
\(108\) 4.15303e19 1.23060e18i 0.192366 0.00570008i
\(109\) −1.36179e18 −0.00575235 −0.00287618 0.999996i \(-0.500916\pi\)
−0.00287618 + 0.999996i \(0.500916\pi\)
\(110\) −1.57115e20 + 1.61839e20i −0.605746 + 0.623961i
\(111\) 2.30089e20i 0.810339i
\(112\) −2.90403e18 4.89595e19i −0.00935021 0.157636i
\(113\) −5.55681e20 −1.63697 −0.818485 0.574528i \(-0.805186\pi\)
−0.818485 + 0.574528i \(0.805186\pi\)
\(114\) −1.17679e20 1.14244e20i −0.317432 0.308165i
\(115\) 2.46847e20i 0.610167i
\(116\) 1.08011e19 + 3.64513e20i 0.0244843 + 0.826292i
\(117\) −8.20346e19 −0.170663
\(118\) −2.09890e20 + 2.16202e20i −0.401025 + 0.413084i
\(119\) 5.16104e19i 0.0906292i
\(120\) −1.83808e20 1.68159e20i −0.296861 0.271586i
\(121\) −3.74847e20 −0.557186
\(122\) 8.30566e20 + 8.06320e20i 1.13704 + 1.10385i
\(123\) 7.02962e20i 0.886913i
\(124\) 3.39060e20 1.00468e19i 0.394511 0.0116899i
\(125\) −9.82854e20 −1.05533
\(126\) 3.69794e19 3.80914e19i 0.0366652 0.0377677i
\(127\) 1.22633e21i 1.12349i −0.827309 0.561747i \(-0.810129\pi\)
0.827309 0.561747i \(-0.189871\pi\)
\(128\) 7.43924e20 9.16719e20i 0.630128 0.776491i
\(129\) −8.42762e20 −0.660402
\(130\) 3.52923e20 + 3.42621e20i 0.256004 + 0.248531i
\(131\) 1.17661e21i 0.790535i 0.918566 + 0.395267i \(0.129348\pi\)
−0.918566 + 0.395267i \(0.870652\pi\)
\(132\) −3.42698e19 1.15653e21i −0.0213389 0.720144i
\(133\) −2.09567e20 −0.121006
\(134\) −1.70051e21 + 1.75165e21i −0.911028 + 0.938423i
\(135\) 2.69662e20i 0.134116i
\(136\) 8.38574e20 9.16616e20i 0.387393 0.423446i
\(137\) 1.78135e21 0.764792 0.382396 0.923999i \(-0.375099\pi\)
0.382396 + 0.923999i \(0.375099\pi\)
\(138\) 9.08528e20 + 8.82006e20i 0.362700 + 0.352112i
\(139\) 1.12261e21i 0.416947i 0.978028 + 0.208474i \(0.0668495\pi\)
−0.978028 + 0.208474i \(0.933150\pi\)
\(140\) −3.18180e20 + 9.42814e18i −0.110000 + 0.00325946i
\(141\) 1.69691e21 0.546346
\(142\) −2.40865e21 + 2.48108e21i −0.722586 + 0.744315i
\(143\) 2.28450e21i 0.638896i
\(144\) 1.27568e21 7.56669e19i 0.332748 0.0197370i
\(145\) 2.36684e21 0.576087
\(146\) 2.68898e21 + 2.61048e21i 0.611026 + 0.593188i
\(147\) 2.65244e21i 0.562953i
\(148\) −2.09608e20 7.07382e21i −0.0415710 1.40293i
\(149\) 4.00639e21 0.742831 0.371416 0.928467i \(-0.378872\pi\)
0.371416 + 0.928467i \(0.378872\pi\)
\(150\) 1.19279e21 1.22865e21i 0.206847 0.213067i
\(151\) 7.29464e21i 1.18368i −0.806055 0.591840i \(-0.798402\pi\)
0.806055 0.591840i \(-0.201598\pi\)
\(152\) −3.72198e21 3.40508e21i −0.565377 0.517240i
\(153\) 1.34475e21 0.191306
\(154\) −1.06077e21 1.02980e21i −0.141388 0.137261i
\(155\) 2.20156e21i 0.275051i
\(156\) −2.52205e21 + 7.47322e19i −0.295467 + 0.00875512i
\(157\) 8.81074e21 0.968313 0.484156 0.874981i \(-0.339127\pi\)
0.484156 + 0.874981i \(0.339127\pi\)
\(158\) 1.38642e21 1.42811e21i 0.142996 0.147296i
\(159\) 8.27530e21i 0.801332i
\(160\) −5.80415e21 5.00239e21i −0.527885 0.454964i
\(161\) 1.61794e21 0.138262
\(162\) 9.92501e20 + 9.63527e20i 0.0797225 + 0.0773952i
\(163\) 1.97253e22i 1.48987i 0.667140 + 0.744933i \(0.267518\pi\)
−0.667140 + 0.744933i \(0.732482\pi\)
\(164\) −6.40387e20 2.16117e22i −0.0454993 1.53550i
\(165\) −7.50953e21 −0.502081
\(166\) −1.84241e22 + 1.89781e22i −1.15959 + 1.19446i
\(167\) 1.68957e22i 1.00141i 0.865619 + 0.500704i \(0.166925\pi\)
−0.865619 + 0.500704i \(0.833075\pi\)
\(168\) 1.10219e21 1.20476e21i 0.0615406 0.0672679i
\(169\) −1.40232e22 −0.737868
\(170\) −5.78529e21 5.61640e21i −0.286970 0.278592i
\(171\) 5.46045e21i 0.255427i
\(172\) −2.59097e22 + 7.67743e20i −1.14335 + 0.0338791i
\(173\) −1.66335e22 −0.692664 −0.346332 0.938112i \(-0.612573\pi\)
−0.346332 + 0.938112i \(0.612573\pi\)
\(174\) −8.45692e21 + 8.71122e21i −0.332445 + 0.342442i
\(175\) 2.18803e21i 0.0812220i
\(176\) −2.10717e21 3.55250e22i −0.0738878 1.24568i
\(177\) −1.00320e22 −0.332395
\(178\) 3.17998e22 + 3.08715e22i 0.995921 + 0.966847i
\(179\) 4.84099e22i 1.43352i −0.697320 0.716759i \(-0.745625\pi\)
0.697320 0.716759i \(-0.254375\pi\)
\(180\) −2.45658e20 8.29043e21i −0.00688027 0.232195i
\(181\) 6.45669e22 1.71090 0.855449 0.517887i \(-0.173281\pi\)
0.855449 + 0.517887i \(0.173281\pi\)
\(182\) −2.24569e21 + 2.31321e21i −0.0563164 + 0.0580099i
\(183\) 3.85392e22i 0.914939i
\(184\) 2.87351e22 + 2.62885e22i 0.646003 + 0.591001i
\(185\) −4.59313e22 −0.978118
\(186\) 8.10292e21 + 7.86638e21i 0.163498 + 0.158725i
\(187\) 3.74486e22i 0.716175i
\(188\) 5.21694e22 1.54586e21i 0.945884 0.0280279i
\(189\) 1.76748e21 0.0303905
\(190\) −2.28058e22 + 2.34915e22i −0.371971 + 0.383156i
\(191\) 6.09764e22i 0.943688i −0.881682 0.471844i \(-0.843589\pi\)
0.881682 0.471844i \(-0.156411\pi\)
\(192\) 3.91502e22 3.48841e21i 0.575072 0.0512407i
\(193\) 6.71512e22 0.936441 0.468221 0.883612i \(-0.344895\pi\)
0.468221 + 0.883612i \(0.344895\pi\)
\(194\) 1.81403e22 + 1.76108e22i 0.240230 + 0.233218i
\(195\) 1.63760e22i 0.205998i
\(196\) 2.41633e21 + 8.15461e22i 0.0288799 + 0.974636i
\(197\) 4.80894e22 0.546245 0.273122 0.961979i \(-0.411944\pi\)
0.273122 + 0.961979i \(0.411944\pi\)
\(198\) 2.68323e22 2.76391e22i 0.289738 0.298450i
\(199\) 5.44705e22i 0.559282i −0.960105 0.279641i \(-0.909785\pi\)
0.960105 0.279641i \(-0.0902155\pi\)
\(200\) 3.55515e22 3.88601e22i 0.347183 0.379493i
\(201\) −8.12784e22 −0.755118
\(202\) 4.00263e22 + 3.88578e22i 0.353860 + 0.343530i
\(203\) 1.55133e22i 0.130540i
\(204\) 4.13427e22 1.22505e21i 0.331206 0.00981411i
\(205\) −1.40328e23 −1.07055
\(206\) 9.18696e22 9.46322e22i 0.667574 0.687649i
\(207\) 4.21567e22i 0.291853i
\(208\) −7.74694e22 + 4.59510e21i −0.511090 + 0.0303153i
\(209\) −1.52062e23 −0.956222
\(210\) −7.60394e21 7.38196e21i −0.0455875 0.0442567i
\(211\) 2.08170e23i 1.19013i −0.803679 0.595063i \(-0.797127\pi\)
0.803679 0.595063i \(-0.202873\pi\)
\(212\) 7.53867e21 + 2.54414e23i 0.0411089 + 1.38734i
\(213\) −1.15125e23 −0.598926
\(214\) −1.34981e23 + 1.39039e23i −0.670090 + 0.690240i
\(215\) 1.68235e23i 0.797136i
\(216\) 3.13910e22 + 2.87183e22i 0.141993 + 0.129904i
\(217\) 1.44300e22 0.0623259
\(218\) −1.00054e21 9.71330e20i −0.00412732 0.00400684i
\(219\) 1.24772e23i 0.491672i
\(220\) −2.30872e23 + 6.84107e21i −0.869248 + 0.0257571i
\(221\) −8.16641e22 −0.293838
\(222\) 1.64117e23 1.69052e23i 0.564447 0.581420i
\(223\) 4.56842e23i 1.50216i −0.660209 0.751082i \(-0.729532\pi\)
0.660209 0.751082i \(-0.270468\pi\)
\(224\) 3.27878e22 3.80430e22i 0.103094 0.119617i
\(225\) 5.70110e22 0.171448
\(226\) −4.08271e23 3.96352e23i −1.17453 1.14024i
\(227\) 4.29781e23i 1.18301i 0.806301 + 0.591505i \(0.201466\pi\)
−0.806301 + 0.591505i \(0.798534\pi\)
\(228\) −4.97438e21 1.67875e23i −0.0131036 0.442219i
\(229\) 7.90228e23 1.99250 0.996248 0.0865428i \(-0.0275819\pi\)
0.996248 + 0.0865428i \(0.0275819\pi\)
\(230\) 1.76069e23 1.81364e23i 0.425016 0.437796i
\(231\) 4.92208e22i 0.113770i
\(232\) −2.52062e23 + 2.75520e23i −0.557991 + 0.609921i
\(233\) −3.95801e23 −0.839302 −0.419651 0.907686i \(-0.637847\pi\)
−0.419651 + 0.907686i \(0.637847\pi\)
\(234\) −6.02726e22 5.85131e22i −0.122451 0.118876i
\(235\) 3.38743e23i 0.659466i
\(236\) −3.08422e23 + 9.13900e21i −0.575473 + 0.0170521i
\(237\) 6.62660e22 0.118524
\(238\) 3.68124e22 3.79193e22i 0.0631283 0.0650266i
\(239\) 9.99178e23i 1.64310i 0.570137 + 0.821550i \(0.306890\pi\)
−0.570137 + 0.821550i \(0.693110\pi\)
\(240\) −1.51049e22 2.54655e23i −0.0238235 0.401643i
\(241\) 7.12027e23 1.07727 0.538637 0.842538i \(-0.318939\pi\)
0.538637 + 0.842538i \(0.318939\pi\)
\(242\) −2.75408e23 2.67368e23i −0.399782 0.388111i
\(243\) 4.60532e22i 0.0641500i
\(244\) 3.51086e22 + 1.18484e24i 0.0469370 + 1.58403i
\(245\) 5.29490e23 0.679511
\(246\) 5.01404e23 5.16482e23i 0.617785 0.636362i
\(247\) 3.31602e23i 0.392327i
\(248\) 2.56281e23 + 2.34461e23i 0.291205 + 0.266412i
\(249\) −8.80607e23 −0.961144
\(250\) −7.22124e23 7.01044e23i −0.757202 0.735098i
\(251\) 1.17581e24i 1.18468i 0.805689 + 0.592339i \(0.201795\pi\)
−0.805689 + 0.592339i \(0.798205\pi\)
\(252\) 5.43391e22 1.61015e21i 0.0526147 0.00155905i
\(253\) 1.17398e24 1.09258
\(254\) 8.74710e23 9.01013e23i 0.782577 0.806109i
\(255\) 2.68444e23i 0.230915i
\(256\) 1.20045e24 1.42912e23i 0.992988 0.118214i
\(257\) 4.64222e23 0.369313 0.184656 0.982803i \(-0.440883\pi\)
0.184656 + 0.982803i \(0.440883\pi\)
\(258\) −6.19196e23 6.01120e23i −0.473839 0.460007i
\(259\) 3.01054e23i 0.221639i
\(260\) 1.49183e22 + 5.03462e23i 0.0105678 + 0.356642i
\(261\) −4.04211e23 −0.275552
\(262\) −8.39247e23 + 8.64484e23i −0.550652 + 0.567210i
\(263\) 1.09646e24i 0.692522i −0.938138 0.346261i \(-0.887451\pi\)
0.938138 0.346261i \(-0.112549\pi\)
\(264\) 7.99746e23 8.74175e23i 0.486310 0.531568i
\(265\) 1.65195e24 0.967247
\(266\) −1.53974e23 1.49479e23i −0.0868222 0.0842876i
\(267\) 1.47555e24i 0.801385i
\(268\) −2.49881e24 + 7.40433e22i −1.30733 + 0.0387381i
\(269\) −1.35487e24 −0.682929 −0.341464 0.939895i \(-0.610923\pi\)
−0.341464 + 0.939895i \(0.610923\pi\)
\(270\) 1.92343e23 1.98127e23i 0.0934197 0.0962288i
\(271\) 1.97275e24i 0.923378i −0.887042 0.461689i \(-0.847244\pi\)
0.887042 0.461689i \(-0.152756\pi\)
\(272\) 1.26992e24 7.53252e22i 0.572910 0.0339822i
\(273\) −1.07336e23 −0.0466786
\(274\) 1.30880e24 + 1.27059e24i 0.548740 + 0.532720i
\(275\) 1.58764e24i 0.641837i
\(276\) 3.84041e22 + 1.29606e24i 0.0149723 + 0.505282i
\(277\) −3.29424e24 −1.23867 −0.619337 0.785125i \(-0.712599\pi\)
−0.619337 + 0.785125i \(0.712599\pi\)
\(278\) −8.00728e23 + 8.24806e23i −0.290427 + 0.299160i
\(279\) 3.75985e23i 0.131561i
\(280\) −2.40499e23 2.20022e23i −0.0811956 0.0742825i
\(281\) −3.12153e24 −1.01696 −0.508481 0.861073i \(-0.669793\pi\)
−0.508481 + 0.861073i \(0.669793\pi\)
\(282\) 1.24676e24 + 1.21036e24i 0.392004 + 0.380561i
\(283\) 2.96270e24i 0.899133i −0.893247 0.449567i \(-0.851578\pi\)
0.893247 0.449567i \(-0.148422\pi\)
\(284\) −3.53937e24 + 1.04877e23i −1.03691 + 0.0307253i
\(285\) −1.09003e24 −0.308313
\(286\) −1.62947e24 + 1.67847e24i −0.445027 + 0.458409i
\(287\) 9.19771e23i 0.242583i
\(288\) 9.91240e23 + 8.54313e23i 0.252496 + 0.217617i
\(289\) −2.72555e24 −0.670620
\(290\) 1.73897e24 + 1.68820e24i 0.413344 + 0.401277i
\(291\) 8.41733e23i 0.193306i
\(292\) 1.13665e23 + 3.83596e24i 0.0252231 + 0.851228i
\(293\) −3.37322e24 −0.723383 −0.361692 0.932298i \(-0.617801\pi\)
−0.361692 + 0.932298i \(0.617801\pi\)
\(294\) −1.89192e24 + 1.94881e24i −0.392129 + 0.403920i
\(295\) 2.00263e24i 0.401217i
\(296\) 4.89157e24 5.34680e24i 0.947394 1.03556i
\(297\) 1.28249e24 0.240153
\(298\) 2.94358e24 + 2.85765e24i 0.532983 + 0.517424i
\(299\) 2.56010e24i 0.448275i
\(300\) 1.75273e24 5.19361e22i 0.296827 0.00879542i
\(301\) −1.10269e24 −0.180629
\(302\) 5.20308e24 5.35954e24i 0.824500 0.849293i
\(303\) 1.85727e24i 0.284740i
\(304\) −3.05863e23 5.15658e24i −0.0453723 0.764937i
\(305\) 7.69334e24 1.10438
\(306\) 9.88018e23 + 9.59176e23i 0.137262 + 0.133255i
\(307\) 1.98725e24i 0.267220i −0.991034 0.133610i \(-0.957343\pi\)
0.991034 0.133610i \(-0.0426570\pi\)
\(308\) −4.48394e22 1.51323e24i −0.00583650 0.196969i
\(309\) 4.39104e24 0.553328
\(310\) 1.57031e24 1.61753e24i 0.191589 0.197350i
\(311\) 6.19352e24i 0.731701i −0.930674 0.365851i \(-0.880778\pi\)
0.930674 0.365851i \(-0.119222\pi\)
\(312\) −1.90631e24 1.74401e24i −0.218096 0.199527i
\(313\) 7.98735e24 0.885033 0.442516 0.896760i \(-0.354086\pi\)
0.442516 + 0.896760i \(0.354086\pi\)
\(314\) 6.47344e24 + 6.28447e24i 0.694767 + 0.674484i
\(315\) 3.52831e23i 0.0366827i
\(316\) 2.03727e24 6.03672e22i 0.205200 0.00608038i
\(317\) 5.13715e24 0.501337 0.250668 0.968073i \(-0.419350\pi\)
0.250668 + 0.968073i \(0.419350\pi\)
\(318\) −5.90256e24 + 6.08005e24i −0.558173 + 0.574958i
\(319\) 1.12564e25i 1.03156i
\(320\) −6.96369e23 7.81532e24i −0.0618500 0.694139i
\(321\) −6.45159e24 −0.555414
\(322\) 1.18874e24 + 1.15404e24i 0.0992036 + 0.0963075i
\(323\) 5.43579e24i 0.439782i
\(324\) 4.19537e22 + 1.41585e24i 0.00329094 + 0.111062i
\(325\) −3.46217e24 −0.263338
\(326\) −1.40695e25 + 1.44926e25i −1.03777 + 1.06898i
\(327\) 4.64261e22i 0.00332112i
\(328\) 1.49446e25 1.63354e25i 1.03692 1.13342i
\(329\) 2.22027e24 0.149433
\(330\) −5.51742e24 5.35635e24i −0.360244 0.349728i
\(331\) 2.60799e25i 1.65206i 0.563624 + 0.826032i \(0.309407\pi\)
−0.563624 + 0.826032i \(0.690593\pi\)
\(332\) −2.70732e25 + 8.02219e23i −1.66402 + 0.0493074i
\(333\) 7.84420e24 0.467849
\(334\) −1.20512e25 + 1.24136e25i −0.697537 + 0.718512i
\(335\) 1.62251e25i 0.911463i
\(336\) 1.66912e24 9.90042e22i 0.0910114 0.00539835i
\(337\) −1.20056e24 −0.0635454 −0.0317727 0.999495i \(-0.510115\pi\)
−0.0317727 + 0.999495i \(0.510115\pi\)
\(338\) −1.03031e25 1.00024e25i −0.529422 0.513967i
\(339\) 1.89442e25i 0.945105i
\(340\) −2.44548e23 8.25299e24i −0.0118461 0.399781i
\(341\) 1.04704e25 0.492516
\(342\) 3.89479e24 4.01191e24i 0.177919 0.183270i
\(343\) 7.02977e24i 0.311889i
\(344\) −1.95841e25 1.79166e25i −0.843953 0.772097i
\(345\) 8.41548e24 0.352280
\(346\) −1.22210e25 1.18642e25i −0.496988 0.482479i
\(347\) 9.80143e24i 0.387253i −0.981075 0.193627i \(-0.937975\pi\)
0.981075 0.193627i \(-0.0620250\pi\)
\(348\) −1.24270e25 + 3.68230e23i −0.477060 + 0.0141360i
\(349\) −3.29545e25 −1.22931 −0.614653 0.788797i \(-0.710704\pi\)
−0.614653 + 0.788797i \(0.710704\pi\)
\(350\) 1.56067e24 1.60760e24i 0.0565757 0.0582770i
\(351\) 2.79672e24i 0.0985321i
\(352\) 2.37909e25 2.76040e25i 0.814674 0.945247i
\(353\) −8.82040e24 −0.293590 −0.146795 0.989167i \(-0.546896\pi\)
−0.146795 + 0.989167i \(0.546896\pi\)
\(354\) −7.37073e24 7.15556e24i −0.238494 0.231532i
\(355\) 2.29816e25i 0.722932i
\(356\) 1.34420e24 + 4.53640e25i 0.0411116 + 1.38743i
\(357\) 1.75950e24 0.0523248
\(358\) 3.45295e25 3.55678e25i 0.998527 1.02855i
\(359\) 3.05618e25i 0.859478i 0.902953 + 0.429739i \(0.141394\pi\)
−0.902953 + 0.429739i \(0.858606\pi\)
\(360\) 5.73286e24 6.26638e24i 0.156800 0.171393i
\(361\) 1.55176e25 0.412813
\(362\) 4.74387e25 + 4.60539e25i 1.22757 + 1.19174i
\(363\) 1.27793e25i 0.321692i
\(364\) −3.29991e24 + 9.77812e22i −0.0808143 + 0.00239465i
\(365\) 2.49074e25 0.593472
\(366\) −2.74890e25 + 2.83156e25i −0.637306 + 0.656471i
\(367\) 4.75297e25i 1.07227i −0.844132 0.536135i \(-0.819884\pi\)
0.844132 0.536135i \(-0.180116\pi\)
\(368\) 2.36138e24 + 3.98108e25i 0.0518426 + 0.874022i
\(369\) 2.39654e25 0.512059
\(370\) −3.37467e25 3.27616e25i −0.701802 0.681314i
\(371\) 1.08276e25i 0.219176i
\(372\) 3.42516e23 + 1.15592e25i 0.00674919 + 0.227771i
\(373\) −1.01643e26 −1.94979 −0.974893 0.222673i \(-0.928522\pi\)
−0.974893 + 0.222673i \(0.928522\pi\)
\(374\) 2.67111e25 2.75143e25i 0.498856 0.513857i
\(375\) 3.35074e25i 0.609296i
\(376\) 3.94327e25 + 3.60753e25i 0.698197 + 0.638751i
\(377\) 2.45469e25 0.423237
\(378\) 1.29861e24 + 1.26070e24i 0.0218052 + 0.0211687i
\(379\) 3.14986e25i 0.515109i −0.966264 0.257555i \(-0.917083\pi\)
0.966264 0.257555i \(-0.0829167\pi\)
\(380\) −3.35118e25 + 9.93004e23i −0.533779 + 0.0158167i
\(381\) 4.18081e25 0.648650
\(382\) 4.34929e25 4.48007e25i 0.657332 0.677098i
\(383\) 1.38501e25i 0.203922i −0.994788 0.101961i \(-0.967488\pi\)
0.994788 0.101961i \(-0.0325117\pi\)
\(384\) 3.12527e25 + 2.53618e25i 0.448307 + 0.363805i
\(385\) −9.82563e24 −0.137326
\(386\) 4.93375e25 + 4.78972e25i 0.671899 + 0.652284i
\(387\) 2.87314e25i 0.381283i
\(388\) 7.66805e23 + 2.58781e25i 0.00991671 + 0.334668i
\(389\) 2.02805e25 0.255613 0.127807 0.991799i \(-0.459206\pi\)
0.127807 + 0.991799i \(0.459206\pi\)
\(390\) −1.16806e25 + 1.20318e25i −0.143489 + 0.147804i
\(391\) 4.19664e25i 0.502497i
\(392\) −5.63893e25 + 6.16372e25i −0.658167 + 0.719420i
\(393\) −4.01131e25 −0.456415
\(394\) 3.53324e25 + 3.43009e25i 0.391932 + 0.380490i
\(395\) 1.32283e25i 0.143064i
\(396\) 3.94285e25 1.16832e24i 0.415775 0.0123200i
\(397\) 6.26890e25 0.644594 0.322297 0.946639i \(-0.395545\pi\)
0.322297 + 0.946639i \(0.395545\pi\)
\(398\) 3.88524e25 4.00207e25i 0.389571 0.401286i
\(399\) 7.14457e24i 0.0698629i
\(400\) 5.38384e25 3.19342e24i 0.513443 0.0304549i
\(401\) −1.44421e26 −1.34334 −0.671672 0.740849i \(-0.734423\pi\)
−0.671672 + 0.740849i \(0.734423\pi\)
\(402\) −5.97171e25 5.79738e25i −0.541799 0.525982i
\(403\) 2.28328e25i 0.202074i
\(404\) 1.69194e24 + 5.70994e25i 0.0146073 + 0.492967i
\(405\) 9.19330e24 0.0774322
\(406\) −1.10652e25 + 1.13980e25i −0.0909284 + 0.0936626i
\(407\) 2.18445e26i 1.75145i
\(408\) 3.12492e25 + 2.85886e25i 0.244477 + 0.223662i
\(409\) −1.74636e26 −1.33322 −0.666609 0.745408i \(-0.732255\pi\)
−0.666609 + 0.745408i \(0.732255\pi\)
\(410\) −1.03102e26 1.00092e26i −0.768119 0.745696i
\(411\) 6.07296e25i 0.441553i
\(412\) 1.34997e26 4.00017e24i 0.957972 0.0283861i
\(413\) −1.31261e25 −0.0909148
\(414\) −3.00693e25 + 3.09735e25i −0.203292 + 0.209405i
\(415\) 1.75790e26i 1.16015i
\(416\) −6.01961e25 5.18808e25i −0.387824 0.334251i
\(417\) −3.82720e25 −0.240725
\(418\) −1.11724e26 1.08462e26i −0.686091 0.666062i
\(419\) 5.60940e25i 0.336338i −0.985758 0.168169i \(-0.946215\pi\)
0.985758 0.168169i \(-0.0537855\pi\)
\(420\) −3.21424e23 1.08474e25i −0.00188185 0.0635085i
\(421\) 3.18608e25 0.182153 0.0910763 0.995844i \(-0.470969\pi\)
0.0910763 + 0.995844i \(0.470969\pi\)
\(422\) 1.48482e26 1.52947e26i 0.828989 0.853917i
\(423\) 5.78510e25i 0.315433i
\(424\) −1.75928e26 + 1.92301e26i −0.936865 + 1.02405i
\(425\) 5.67535e25 0.295191
\(426\) −8.45847e25 8.21155e25i −0.429730 0.417185i
\(427\) 5.04255e25i 0.250249i
\(428\) −1.98346e26 + 5.87730e24i −0.961582 + 0.0284931i
\(429\) −7.78829e25 −0.368867
\(430\) −1.19998e26 + 1.23606e26i −0.555250 + 0.571947i
\(431\) 2.27471e26i 1.02838i 0.857677 + 0.514189i \(0.171907\pi\)
−0.857677 + 0.514189i \(0.828093\pi\)
\(432\) 2.57963e24 + 4.34904e25i 0.0113952 + 0.192112i
\(433\) 2.82108e26 1.21769 0.608845 0.793289i \(-0.291633\pi\)
0.608845 + 0.793289i \(0.291633\pi\)
\(434\) 1.06020e25 + 1.02925e25i 0.0447190 + 0.0434135i
\(435\) 8.06900e25i 0.332604i
\(436\) −4.22935e22 1.42731e24i −0.000170376 0.00574983i
\(437\) 1.70407e26 0.670924
\(438\) −8.89965e25 + 9.16727e25i −0.342477 + 0.352776i
\(439\) 2.29649e26i 0.863814i 0.901918 + 0.431907i \(0.142159\pi\)
−0.901918 + 0.431907i \(0.857841\pi\)
\(440\) −1.74506e26 1.59648e26i −0.641628 0.586999i
\(441\) −9.04269e25 −0.325021
\(442\) −6.00004e25 5.82489e25i −0.210830 0.204675i
\(443\) 5.36533e25i 0.184314i −0.995744 0.0921571i \(-0.970624\pi\)
0.995744 0.0921571i \(-0.0293762\pi\)
\(444\) 2.41160e26 7.14594e24i 0.809983 0.0240010i
\(445\) 2.94555e26 0.967310
\(446\) 3.25853e26 3.35652e26i 1.04634 1.07781i
\(447\) 1.36586e26i 0.428874i
\(448\) 5.12250e25 4.56431e24i 0.157290 0.0140151i
\(449\) 2.39589e26 0.719454 0.359727 0.933058i \(-0.382870\pi\)
0.359727 + 0.933058i \(0.382870\pi\)
\(450\) 4.18872e25 + 4.06644e25i 0.123015 + 0.119423i
\(451\) 6.67386e26i 1.91695i
\(452\) −1.72579e25 5.82418e26i −0.0484846 1.63625i
\(453\) 2.48689e26 0.683398
\(454\) −3.06551e26 + 3.15770e26i −0.824034 + 0.848813i
\(455\) 2.14268e25i 0.0563434i
\(456\) 1.16086e26 1.26889e26i 0.298628 0.326420i
\(457\) 5.24638e26 1.32038 0.660188 0.751100i \(-0.270476\pi\)
0.660188 + 0.751100i \(0.270476\pi\)
\(458\) 5.80598e26 + 5.63649e26i 1.42962 + 1.38789i
\(459\) 4.58452e25i 0.110450i
\(460\) 2.58724e26 7.66637e24i 0.609899 0.0180722i
\(461\) −2.71648e26 −0.626610 −0.313305 0.949653i \(-0.601436\pi\)
−0.313305 + 0.949653i \(0.601436\pi\)
\(462\) 3.51079e25 3.61636e25i 0.0792474 0.0816304i
\(463\) 1.40917e26i 0.311282i 0.987814 + 0.155641i \(0.0497442\pi\)
−0.987814 + 0.155641i \(0.950256\pi\)
\(464\) −3.81717e26 + 2.26415e25i −0.825204 + 0.0489470i
\(465\) 7.50555e25 0.158801
\(466\) −2.90804e26 2.82315e26i −0.602201 0.584621i
\(467\) 1.67552e26i 0.339610i 0.985478 + 0.169805i \(0.0543137\pi\)
−0.985478 + 0.169805i \(0.945686\pi\)
\(468\) −2.54777e24 8.59818e25i −0.00505477 0.170588i
\(469\) −1.06346e26 −0.206535
\(470\) 2.41617e26 2.48882e26i 0.459355 0.473168i
\(471\) 3.00375e26i 0.559056i
\(472\) −2.33123e26 2.13275e26i −0.424781 0.388615i
\(473\) −8.00111e26 −1.42738
\(474\) 4.86871e25 + 4.72658e25i 0.0850414 + 0.0825588i
\(475\) 2.30451e26i 0.394133i
\(476\) 5.40937e25 1.60288e24i 0.0905894 0.00268430i
\(477\) −2.82121e26 −0.462650
\(478\) −7.12687e26 + 7.34118e26i −1.14451 + 1.17893i
\(479\) 1.04506e27i 1.64356i 0.569802 + 0.821782i \(0.307020\pi\)
−0.569802 + 0.821782i \(0.692980\pi\)
\(480\) 1.70541e26 1.97875e26i 0.262674 0.304774i
\(481\) −4.76363e26 −0.718600
\(482\) 5.23142e26 + 5.07870e26i 0.772946 + 0.750382i
\(483\) 5.51588e25i 0.0798258i
\(484\) −1.16417e25 3.92883e26i −0.0165030 0.556942i
\(485\) 1.68030e26 0.233329
\(486\) −3.28485e25 + 3.38363e25i −0.0446841 + 0.0460278i
\(487\) 1.19020e27i 1.58610i −0.609155 0.793051i \(-0.708491\pi\)
0.609155 0.793051i \(-0.291509\pi\)
\(488\) −8.19321e26 + 8.95572e26i −1.06969 + 1.16924i
\(489\) −6.72473e26 −0.860174
\(490\) 3.89028e26 + 3.77671e26i 0.487551 + 0.473318i
\(491\) 8.00412e26i 0.982875i −0.870913 0.491438i \(-0.836472\pi\)
0.870913 0.491438i \(-0.163528\pi\)
\(492\) 7.36786e26 2.18321e25i 0.886524 0.0262690i
\(493\) −4.02385e26 −0.474431
\(494\) −2.36523e26 + 2.43636e26i −0.273278 + 0.281495i
\(495\) 2.56015e26i 0.289876i
\(496\) 2.10605e25 + 3.55062e26i 0.0233696 + 0.393992i
\(497\) −1.50632e26 −0.163815
\(498\) −6.47001e26 6.28114e26i −0.689623 0.669491i
\(499\) 1.31447e27i 1.37324i −0.727017 0.686620i \(-0.759094\pi\)
0.727017 0.686620i \(-0.240906\pi\)
\(500\) −3.05247e25 1.03014e27i −0.0312573 1.05487i
\(501\) −5.76007e26 −0.578163
\(502\) −8.38676e26 + 8.63895e26i −0.825195 + 0.850009i
\(503\) 6.91567e26i 0.667044i 0.942742 + 0.333522i \(0.108237\pi\)
−0.942742 + 0.333522i \(0.891763\pi\)
\(504\) 4.10726e25 + 3.75757e25i 0.0388371 + 0.0355305i
\(505\) 3.70754e26 0.343694
\(506\) 8.62548e26 + 8.37368e26i 0.783932 + 0.761047i
\(507\) 4.78077e26i 0.426008i
\(508\) 1.28534e27 3.80865e25i 1.12300 0.0332762i
\(509\) −1.04999e27 −0.899509 −0.449755 0.893152i \(-0.648489\pi\)
−0.449755 + 0.893152i \(0.648489\pi\)
\(510\) 1.91474e26 1.97232e26i 0.160845 0.165682i
\(511\) 1.63254e26i 0.134479i
\(512\) 9.83932e26 + 7.51248e26i 0.794814 + 0.606853i
\(513\) 1.86157e26 0.147471
\(514\) 3.41074e26 + 3.31117e26i 0.264983 + 0.257247i
\(515\) 8.76556e26i 0.667894i
\(516\) −2.61739e25 8.83313e26i −0.0195601 0.660112i
\(517\) 1.61103e27 1.18086
\(518\) 2.14734e26 2.21191e26i 0.154384 0.159027i
\(519\) 5.67068e26i 0.399910i
\(520\) −3.48145e26 + 3.80545e26i −0.240839 + 0.263253i
\(521\) 1.08094e27 0.733541 0.366771 0.930311i \(-0.380463\pi\)
0.366771 + 0.930311i \(0.380463\pi\)
\(522\) −2.96983e26 2.88313e26i −0.197709 0.191937i
\(523\) 1.08490e27i 0.708556i 0.935140 + 0.354278i \(0.115273\pi\)
−0.935140 + 0.354278i \(0.884727\pi\)
\(524\) −1.23323e27 + 3.65424e25i −0.790188 + 0.0234144i
\(525\) 7.45944e25 0.0468935
\(526\) 7.82073e26 8.05590e26i 0.482381 0.496886i
\(527\) 3.74287e26i 0.226516i
\(528\) 1.21112e27 7.18375e25i 0.719196 0.0426591i
\(529\) 4.00548e26 0.233398
\(530\) 1.21372e27 + 1.17829e27i 0.694002 + 0.673742i
\(531\) 3.42011e26i 0.191909i
\(532\) −6.50859e24 2.19651e26i −0.00358402 0.120953i
\(533\) −1.45537e27 −0.786505
\(534\) −1.05247e27 + 1.08412e27i −0.558210 + 0.574995i
\(535\) 1.28789e27i 0.670411i
\(536\) −1.88874e27 1.72793e27i −0.964994 0.882833i
\(537\) 1.65039e27 0.827643
\(538\) −9.95454e26 9.66394e26i −0.490003 0.475698i
\(539\) 2.51820e27i 1.21675i
\(540\) 2.82637e26 8.37495e24i 0.134058 0.00397233i
\(541\) 4.24156e26 0.197494 0.0987469 0.995113i \(-0.468517\pi\)
0.0987469 + 0.995113i \(0.468517\pi\)
\(542\) 1.40711e27 1.44942e27i 0.643185 0.662525i
\(543\) 2.20121e27i 0.987788i
\(544\) 9.86763e26 + 8.50455e26i 0.434734 + 0.374682i
\(545\) −9.26775e24 −0.00400875
\(546\) −7.88620e25 7.65598e25i −0.0334920 0.0325143i
\(547\) 1.75220e27i 0.730654i −0.930879 0.365327i \(-0.880957\pi\)
0.930879 0.365327i \(-0.119043\pi\)
\(548\) 5.53237e25 + 1.86706e27i 0.0226520 + 0.764456i
\(549\) −1.31388e27 −0.528240
\(550\) 1.13242e27 1.16647e27i 0.447076 0.460519i
\(551\) 1.63391e27i 0.633450i
\(552\) −8.96228e26 + 9.79635e26i −0.341215 + 0.372970i
\(553\) 8.67038e25 0.0324180
\(554\) −2.42035e27 2.34969e27i −0.888751 0.862806i
\(555\) 1.56589e27i 0.564717i
\(556\) −1.17663e27 + 3.48652e25i −0.416764 + 0.0123493i
\(557\) 3.78069e27 1.31528 0.657642 0.753331i \(-0.271554\pi\)
0.657642 + 0.753331i \(0.271554\pi\)
\(558\) −2.68180e26 + 2.76244e26i −0.0916399 + 0.0943956i
\(559\) 1.74480e27i 0.585637i
\(560\) −1.97636e25 3.33197e26i −0.00651606 0.109855i
\(561\) 1.27669e27 0.413484
\(562\) −2.29346e27 2.22651e27i −0.729673 0.708372i
\(563\) 5.51625e27i 1.72409i −0.506831 0.862045i \(-0.669183\pi\)
0.506831 0.862045i \(-0.330817\pi\)
\(564\) 5.27013e25 + 1.77856e27i 0.0161819 + 0.546106i
\(565\) −3.78172e27 −1.14079
\(566\) 2.11322e27 2.17676e27i 0.626297 0.645130i
\(567\) 6.02570e25i 0.0175459i
\(568\) −2.67526e27 2.44749e27i −0.765390 0.700224i
\(569\) 4.63358e27 1.30255 0.651275 0.758842i \(-0.274235\pi\)
0.651275 + 0.758842i \(0.274235\pi\)
\(570\) −8.00873e26 7.77493e26i −0.221215 0.214757i
\(571\) 2.14483e27i 0.582145i 0.956701 + 0.291073i \(0.0940121\pi\)
−0.956701 + 0.291073i \(0.905988\pi\)
\(572\) −2.39442e27 + 7.09501e25i −0.638615 + 0.0189231i
\(573\) 2.07881e27 0.544838
\(574\) 6.56048e26 6.75776e26i 0.168973 0.174054i
\(575\) 1.77917e27i 0.450339i
\(576\) 1.18927e26 + 1.33471e27i 0.0295838 + 0.332018i
\(577\) −4.73352e27 −1.15725 −0.578623 0.815595i \(-0.696410\pi\)
−0.578623 + 0.815595i \(0.696410\pi\)
\(578\) −2.00252e27 1.94407e27i −0.481171 0.467124i
\(579\) 2.28932e27i 0.540655i
\(580\) 7.35074e25 + 2.48072e27i 0.0170628 + 0.575834i
\(581\) −1.15220e27 −0.262886
\(582\) −6.00386e26 + 6.18440e26i −0.134648 + 0.138697i
\(583\) 7.85650e27i 1.73198i
\(584\) −2.65258e27 + 2.89944e27i −0.574830 + 0.628327i
\(585\) −5.58292e26 −0.118933
\(586\) −2.47838e27 2.40603e27i −0.519029 0.503877i
\(587\) 8.80412e27i 1.81261i −0.422622 0.906306i \(-0.638890\pi\)
0.422622 0.906306i \(-0.361110\pi\)
\(588\) −2.78006e27 + 8.23774e25i −0.562706 + 0.0166738i
\(589\) 1.51982e27 0.302439
\(590\) −1.42842e27 + 1.47137e27i −0.279470 + 0.287874i
\(591\) 1.63946e27i 0.315375i
\(592\) 7.40767e27 4.39386e26i 1.40109 0.0831055i
\(593\) −3.10069e27 −0.576648 −0.288324 0.957533i \(-0.593098\pi\)
−0.288324 + 0.957533i \(0.593098\pi\)
\(594\) 9.42271e26 + 9.14764e26i 0.172310 + 0.167280i
\(595\) 3.51238e26i 0.0631585i
\(596\) 1.24427e26 + 4.19916e27i 0.0220015 + 0.742506i
\(597\) 1.85701e27 0.322902
\(598\) 1.82605e27 1.88096e27i 0.312249 0.321638i
\(599\) 1.85197e27i 0.311434i −0.987802 0.155717i \(-0.950231\pi\)
0.987802 0.155717i \(-0.0497689\pi\)
\(600\) 1.32482e27 + 1.21202e27i 0.219100 + 0.200446i
\(601\) −5.45089e27 −0.886590 −0.443295 0.896376i \(-0.646191\pi\)
−0.443295 + 0.896376i \(0.646191\pi\)
\(602\) −8.10170e26 7.86519e26i −0.129602 0.125818i
\(603\) 2.77094e27i 0.435967i
\(604\) 7.64563e27 2.26551e26i 1.18316 0.0350588i
\(605\) −2.55104e27 −0.388297
\(606\) −1.32474e27 + 1.36457e27i −0.198337 + 0.204301i
\(607\) 3.53803e27i 0.521045i 0.965468 + 0.260522i \(0.0838948\pi\)
−0.965468 + 0.260522i \(0.916105\pi\)
\(608\) 3.45333e27 4.00682e27i 0.500267 0.580448i
\(609\) −5.28878e26 −0.0753672
\(610\) 5.65247e27 + 5.48746e27i 0.792391 + 0.769259i
\(611\) 3.51318e27i 0.484494i
\(612\) 4.17642e25 + 1.40946e27i 0.00566618 + 0.191222i
\(613\) 5.25248e26 0.0701067 0.0350534 0.999385i \(-0.488840\pi\)
0.0350534 + 0.999385i \(0.488840\pi\)
\(614\) 1.41745e27 1.46008e27i 0.186134 0.191731i
\(615\) 4.78405e27i 0.618080i
\(616\) 1.04641e27 1.14379e27i 0.133013 0.145391i
\(617\) 3.18164e27 0.397924 0.198962 0.980007i \(-0.436243\pi\)
0.198962 + 0.980007i \(0.436243\pi\)
\(618\) 3.22620e27 + 3.13201e27i 0.397014 + 0.385424i
\(619\) 7.66961e27i 0.928681i −0.885657 0.464340i \(-0.846291\pi\)
0.885657 0.464340i \(-0.153709\pi\)
\(620\) 2.30749e27 6.83744e25i 0.274931 0.00814660i
\(621\) −1.43721e27 −0.168501
\(622\) 4.41768e27 4.55052e27i 0.509671 0.524997i
\(623\) 1.93064e27i 0.219190i
\(624\) −1.56656e26 2.64108e27i −0.0175026 0.295078i
\(625\) −2.01093e27 −0.221104
\(626\) 5.86848e27 + 5.69717e27i 0.635013 + 0.616475i
\(627\) 5.18410e27i 0.552075i
\(628\) 2.73637e26 + 9.23467e27i 0.0286800 + 0.967888i
\(629\) 7.80877e27 0.805520
\(630\) 2.51665e26 2.59233e26i 0.0255516 0.0263199i
\(631\) 1.65860e28i 1.65748i 0.559632 + 0.828741i \(0.310943\pi\)
−0.559632 + 0.828741i \(0.689057\pi\)
\(632\) 1.53988e27 + 1.40878e27i 0.151467 + 0.138571i
\(633\) 7.09691e27 0.687119
\(634\) 3.77438e27 + 3.66419e27i 0.359710 + 0.349209i
\(635\) 8.34588e27i 0.782951i
\(636\) −8.67348e27 + 2.57008e26i −0.800981 + 0.0237343i
\(637\) 5.49145e27 0.499221
\(638\) −8.02893e27 + 8.27036e27i −0.718539 + 0.740146i
\(639\) 3.92483e27i 0.345790i
\(640\) 5.06282e27 6.23879e27i 0.439130 0.541128i
\(641\) −6.63028e27 −0.566176 −0.283088 0.959094i \(-0.591359\pi\)
−0.283088 + 0.959094i \(0.591359\pi\)
\(642\) −4.74013e27 4.60175e27i −0.398510 0.386877i
\(643\) 2.19500e28i 1.81687i −0.418022 0.908437i \(-0.637277\pi\)
0.418022 0.908437i \(-0.362723\pi\)
\(644\) 5.02488e25 + 1.69579e27i 0.00409512 + 0.138202i
\(645\) −5.73547e27 −0.460227
\(646\) 3.87720e27 3.99379e27i 0.306333 0.315544i
\(647\) 8.47014e27i 0.658943i 0.944166 + 0.329471i \(0.106871\pi\)
−0.944166 + 0.329471i \(0.893129\pi\)
\(648\) −9.79064e26 + 1.07018e27i −0.0749999 + 0.0819798i
\(649\) −9.52429e27 −0.718432
\(650\) −2.54373e27 2.46947e27i −0.188946 0.183430i
\(651\) 4.91947e26i 0.0359839i
\(652\) −2.06744e28 + 6.12612e26i −1.48921 + 0.0441275i
\(653\) −1.27267e28 −0.902783 −0.451391 0.892326i \(-0.649072\pi\)
−0.451391 + 0.892326i \(0.649072\pi\)
\(654\) 3.31145e25 3.41103e25i 0.00231335 0.00238291i
\(655\) 8.00752e27i 0.550915i
\(656\) 2.26317e28 1.34240e27i 1.53348 0.0909586i
\(657\) −4.25372e27 −0.283867
\(658\) 1.63128e27 + 1.58366e27i 0.107219 + 0.104089i
\(659\) 7.25771e27i 0.469835i 0.972015 + 0.234917i \(0.0754820\pi\)
−0.972015 + 0.234917i \(0.924518\pi\)
\(660\) −2.33225e26 7.87086e27i −0.0148709 0.501860i
\(661\) −1.61821e28 −1.01630 −0.508148 0.861270i \(-0.669670\pi\)
−0.508148 + 0.861270i \(0.669670\pi\)
\(662\) −1.86021e28 + 1.91615e28i −1.15076 + 1.18536i
\(663\) 2.78409e27i 0.169648i
\(664\) −2.04635e28 1.87212e28i −1.22828 1.12371i
\(665\) −1.42622e27 −0.0843279
\(666\) 5.76330e27 + 5.59506e27i 0.335683 + 0.325883i
\(667\) 1.26144e28i 0.723784i
\(668\) −1.77086e28 + 5.24733e26i −1.00097 + 0.0296602i
\(669\) 1.55746e28 0.867275
\(670\) −1.15729e28 + 1.19209e28i −0.634886 + 0.653977i
\(671\) 3.65888e28i 1.97753i
\(672\) 1.29696e27 + 1.11780e27i 0.0690611 + 0.0595213i
\(673\) 1.29113e28 0.677362 0.338681 0.940901i \(-0.390019\pi\)
0.338681 + 0.940901i \(0.390019\pi\)
\(674\) −8.82077e26 8.56327e26i −0.0455940 0.0442630i
\(675\) 1.94362e27i 0.0989858i
\(676\) −4.35521e26 1.46979e28i −0.0218545 0.737545i
\(677\) 8.50196e27 0.420371 0.210185 0.977662i \(-0.432593\pi\)
0.210185 + 0.977662i \(0.432593\pi\)
\(678\) 1.35124e28 1.39187e28i 0.658319 0.678115i
\(679\) 1.10134e27i 0.0528718i
\(680\) 5.70697e27 6.23808e27i 0.269970 0.295095i
\(681\) −1.46521e28 −0.683011
\(682\) 7.69284e27 + 7.46827e27i 0.353381 + 0.343065i
\(683\) 2.84927e27i 0.128981i 0.997918 + 0.0644906i \(0.0205423\pi\)
−0.997918 + 0.0644906i \(0.979458\pi\)
\(684\) 5.72318e27 1.69586e26i 0.255315 0.00756537i
\(685\) 1.21231e28 0.532975
\(686\) −5.01415e27 + 5.16493e27i −0.217248 + 0.223781i
\(687\) 2.69404e28i 1.15037i
\(688\) −1.60937e27 2.71325e28i −0.0677284 1.14184i
\(689\) 1.71327e28 0.710613
\(690\) 6.18304e27 + 6.00254e27i 0.252762 + 0.245383i
\(691\) 7.52148e26i 0.0303056i 0.999885 + 0.0151528i \(0.00482347\pi\)
−0.999885 + 0.0151528i \(0.995177\pi\)
\(692\) −5.16590e26 1.74338e28i −0.0205157 0.692360i
\(693\) 1.67803e27 0.0656853
\(694\) 6.99111e27 7.20133e27i 0.269744 0.277855i
\(695\) 7.63999e27i 0.290566i
\(696\) −9.39302e27 8.59329e27i −0.352138 0.322157i
\(697\) 2.38571e28 0.881638
\(698\) −2.42124e28 2.35056e28i −0.882030 0.856281i
\(699\) 1.34936e28i 0.484571i
\(700\) 2.29331e27 6.79543e25i 0.0811864 0.00240567i
\(701\) 2.49892e28 0.872111 0.436055 0.899920i \(-0.356375\pi\)
0.436055 + 0.899920i \(0.356375\pi\)
\(702\) 1.99483e27 2.05481e27i 0.0686332 0.0706970i
\(703\) 3.17080e28i 1.07551i
\(704\) 3.71689e28 3.31186e27i 1.24295 0.110751i
\(705\) 1.15484e28 0.380743
\(706\) −6.48054e27 6.29136e27i −0.210651 0.204502i
\(707\) 2.43009e27i 0.0778803i
\(708\) −3.11566e26 1.05147e28i −0.00984505 0.332250i
\(709\) 4.53449e28 1.41275 0.706376 0.707837i \(-0.250329\pi\)
0.706376 + 0.707837i \(0.250329\pi\)
\(710\) −1.63922e28 + 1.68851e28i −0.503563 + 0.518705i
\(711\) 2.25914e27i 0.0684300i
\(712\) −3.13693e28 + 3.42887e28i −0.936926 + 1.02412i
\(713\) −1.17336e28 −0.345569
\(714\) 1.29274e27 + 1.25501e27i 0.0375431 + 0.0364472i
\(715\) 1.55473e28i 0.445240i
\(716\) 5.07391e28 1.50348e27i 1.43289 0.0424587i
\(717\) −3.40639e28 −0.948644
\(718\) −2.17989e28 + 2.24544e28i −0.598675 + 0.616677i
\(719\) 2.03741e28i 0.551811i −0.961185 0.275905i \(-0.911022\pi\)
0.961185 0.275905i \(-0.0889777\pi\)
\(720\) 8.68170e27 5.14956e26i 0.231889 0.0137545i
\(721\) 5.74533e27 0.151343
\(722\) 1.14011e28 + 1.10683e28i 0.296194 + 0.287547i
\(723\) 2.42744e28i 0.621964i
\(724\) 2.00527e27 + 6.76736e28i 0.0506742 + 1.71015i
\(725\) −1.70592e28 −0.425186
\(726\) 9.11511e27 9.38921e27i 0.224076 0.230814i
\(727\) 3.71664e28i 0.901169i 0.892734 + 0.450585i \(0.148784\pi\)
−0.892734 + 0.450585i \(0.851216\pi\)
\(728\) −2.49426e27 2.28190e27i −0.0596524 0.0545736i
\(729\) −1.57004e27 −0.0370370
\(730\) 1.83000e28 + 1.77658e28i 0.425817 + 0.413387i
\(731\) 2.86017e28i 0.656474i
\(732\) −4.03936e28 + 1.19692e27i −0.914537 + 0.0270991i
\(733\) −6.98760e27 −0.156059 −0.0780294 0.996951i \(-0.524863\pi\)
−0.0780294 + 0.996951i \(0.524863\pi\)
\(734\) 3.39017e28 3.49211e28i 0.746897 0.769356i
\(735\) 1.80513e28i 0.392316i
\(736\) −2.66610e28 + 3.09342e28i −0.571608 + 0.663224i
\(737\) −7.71650e28 −1.63210
\(738\) 1.76079e28 + 1.70939e28i 0.367404 + 0.356678i
\(739\) 4.71283e28i 0.970148i −0.874473 0.485074i \(-0.838793\pi\)
0.874473 0.485074i \(-0.161207\pi\)
\(740\) −1.42650e27 4.81413e28i −0.0289704 0.977689i
\(741\) −1.13050e28 −0.226510
\(742\) −7.72303e27 + 7.95527e27i −0.152668 + 0.157259i
\(743\) 8.89929e27i 0.173567i 0.996227 + 0.0867835i \(0.0276588\pi\)
−0.996227 + 0.0867835i \(0.972341\pi\)
\(744\) −7.99322e27 + 8.73711e27i −0.153813 + 0.168127i
\(745\) 2.72657e28 0.517671
\(746\) −7.46790e28 7.24989e28i −1.39898 1.35814i
\(747\) 3.00216e28i 0.554917i
\(748\) 3.92504e28 1.16305e27i 0.715861 0.0212120i
\(749\) −8.44140e27 −0.151913
\(750\) 2.39000e28 2.46186e28i 0.424409 0.437171i
\(751\) 6.86746e28i 1.20336i −0.798736 0.601682i \(-0.794497\pi\)
0.798736 0.601682i \(-0.205503\pi\)
\(752\) 3.24048e27 + 5.46316e28i 0.0560313 + 0.944639i
\(753\) −4.00857e28 −0.683975
\(754\) 1.80352e28 + 1.75087e28i 0.303674 + 0.294809i
\(755\) 4.96441e28i 0.824895i
\(756\) 5.48931e25 + 1.85253e27i 0.000900119 + 0.0303771i
\(757\) −5.91786e28 −0.957648 −0.478824 0.877911i \(-0.658937\pi\)
−0.478824 + 0.877911i \(0.658937\pi\)
\(758\) 2.24671e28 2.31427e28i 0.358803 0.369592i
\(759\) 4.00232e28i 0.630804i
\(760\) −2.53301e28 2.31735e28i −0.394005 0.360459i
\(761\) −1.70853e26 −0.00262287 −0.00131143 0.999999i \(-0.500417\pi\)
−0.00131143 + 0.999999i \(0.500417\pi\)
\(762\) 3.07173e28 + 2.98206e28i 0.465407 + 0.451821i
\(763\) 6.07449e25i 0.000908374i
\(764\) 6.39104e28 1.89376e27i 0.943274 0.0279506i
\(765\) 9.15179e27 0.133319
\(766\) 9.87890e27 1.01760e28i 0.142043 0.146315i
\(767\) 2.07696e28i 0.294765i
\(768\) 4.87216e27 + 4.09257e28i 0.0682510 + 0.573302i
\(769\) 5.09126e28 0.703982 0.351991 0.936003i \(-0.385505\pi\)
0.351991 + 0.936003i \(0.385505\pi\)
\(770\) −7.21911e27 7.00837e27i −0.0985318 0.0956554i
\(771\) 1.58262e28i 0.213223i
\(772\) 2.08553e27 + 7.03822e28i 0.0277360 + 0.936031i
\(773\) −1.48178e29 −1.94532 −0.972658 0.232243i \(-0.925394\pi\)
−0.972658 + 0.232243i \(0.925394\pi\)
\(774\) 2.04934e28 2.11096e28i 0.265585 0.273571i
\(775\) 1.58680e28i 0.203004i
\(776\) −1.78947e28 + 1.95601e28i −0.226000 + 0.247033i
\(777\) 1.02635e28 0.127963
\(778\) 1.49006e28 + 1.44656e28i 0.183403 + 0.178049i
\(779\) 9.68734e28i 1.17714i
\(780\) −1.71640e28 + 5.08595e26i −0.205908 + 0.00610135i
\(781\) −1.09298e29 −1.29450
\(782\) −2.99335e28 + 3.08336e28i −0.350018 + 0.360543i
\(783\) 1.37803e28i 0.159090i
\(784\) −8.53947e28 + 5.06519e27i −0.973353 + 0.0577345i
\(785\) 5.99620e28 0.674807
\(786\) −2.94719e28 2.86116e28i −0.327479 0.317919i
\(787\) 3.62601e27i 0.0397815i −0.999802 0.0198908i \(-0.993668\pi\)
0.999802 0.0198908i \(-0.00633184\pi\)
\(788\) 1.49352e27 + 5.04033e28i 0.0161789 + 0.546005i
\(789\) 3.73803e28 0.399828
\(790\) 9.43537e27 9.71909e27i 0.0996524 0.102649i
\(791\) 2.47870e28i 0.258500i
\(792\) 2.98023e28 + 2.72649e28i 0.306901 + 0.280771i
\(793\) 7.97892e28 0.811358
\(794\) 4.60590e28 + 4.47144e28i 0.462497 + 0.448996i
\(795\) 5.63181e28i 0.558440i
\(796\) 5.70914e28 1.69170e27i 0.559037 0.0165651i
\(797\) 1.79945e29 1.74003 0.870015 0.493026i \(-0.164109\pi\)
0.870015 + 0.493026i \(0.164109\pi\)
\(798\) 5.09603e27 5.24927e27i 0.0486635 0.0501268i
\(799\) 5.75897e28i 0.543097i
\(800\) 4.18340e28 + 3.60552e28i 0.389610 + 0.335790i
\(801\) −5.03044e28 −0.462680
\(802\) −1.06109e29 1.03012e29i −0.963852 0.935714i
\(803\) 1.18457e29i 1.06269i
\(804\) −2.52428e27 8.51892e28i −0.0223654 0.754786i
\(805\) 1.10110e28 0.0963536
\(806\) 1.62861e28 1.67758e28i 0.140756 0.144988i
\(807\) 4.61902e28i 0.394289i
\(808\) −3.94844e28 + 4.31590e28i −0.332898 + 0.363880i
\(809\) 1.65606e29 1.37909 0.689543 0.724245i \(-0.257811\pi\)
0.689543 + 0.724245i \(0.257811\pi\)
\(810\) 6.75452e27 + 6.55734e27i 0.0555577 + 0.0539359i
\(811\) 9.73666e28i 0.791045i −0.918456 0.395523i \(-0.870564\pi\)
0.918456 0.395523i \(-0.129436\pi\)
\(812\) −1.62597e28 + 4.81800e26i −0.130483 + 0.00386639i
\(813\) 6.72549e28 0.533112
\(814\) 1.55811e29 1.60496e29i 1.21998 1.25667i
\(815\) 1.34242e29i 1.03827i
\(816\) 2.56798e27 + 4.32939e28i 0.0196196 + 0.330770i
\(817\) −1.16139e29 −0.876510
\(818\) −1.28309e29 1.24563e29i −0.956586 0.928661i
\(819\) 3.65929e27i 0.0269499i
\(820\) −4.35820e27 1.47080e29i −0.0317080 1.07008i
\(821\) 7.58552e28 0.545197 0.272599 0.962128i \(-0.412117\pi\)
0.272599 + 0.962128i \(0.412117\pi\)
\(822\) −4.33169e28 + 4.46194e28i −0.307566 + 0.316815i
\(823\) 7.89044e28i 0.553481i 0.960945 + 0.276740i \(0.0892542\pi\)
−0.960945 + 0.276740i \(0.910746\pi\)
\(824\) 1.02039e29 + 9.33510e28i 0.707119 + 0.646914i
\(825\) 5.41257e28 0.370565
\(826\) −9.64403e27 9.36249e27i −0.0652316 0.0633273i
\(827\) 7.12169e28i 0.475914i 0.971276 + 0.237957i \(0.0764777\pi\)
−0.971276 + 0.237957i \(0.923522\pi\)
\(828\) −4.41852e28 + 1.30927e27i −0.291725 + 0.00864423i
\(829\) 1.95023e29 1.27216 0.636079 0.771624i \(-0.280555\pi\)
0.636079 + 0.771624i \(0.280555\pi\)
\(830\) −1.25386e29 + 1.29157e29i −0.808108 + 0.832408i
\(831\) 1.12307e29i 0.715149i
\(832\) −7.22219e27 8.10543e28i −0.0454397 0.509968i
\(833\) −9.00185e28 −0.559605
\(834\) −2.81193e28 2.72984e28i −0.172720 0.167678i
\(835\) 1.14985e29i 0.697870i
\(836\) −4.72263e27 1.59379e29i −0.0283218 0.955802i
\(837\) −1.28181e28 −0.0759570
\(838\) 4.00104e28 4.12135e28i 0.234279 0.241323i
\(839\) 2.01853e28i 0.116793i 0.998293 + 0.0583963i \(0.0185987\pi\)
−0.998293 + 0.0583963i \(0.981401\pi\)
\(840\) 7.50099e27 8.19907e27i 0.0428870 0.0468783i
\(841\) −5.60439e28 −0.316642
\(842\) 2.34088e28 + 2.27254e28i 0.130695 + 0.126880i
\(843\) 1.06419e29i 0.587144i
\(844\) 2.18186e29 6.46517e27i 1.18960 0.0352497i
\(845\) −9.54355e28 −0.514213
\(846\) −4.12636e28 + 4.25044e28i −0.219717 + 0.226324i
\(847\) 1.67207e28i 0.0879872i
\(848\) −2.66421e29 + 1.58028e28i −1.38551 + 0.0821818i
\(849\) 1.01004e29 0.519115
\(850\) 4.16981e28 + 4.04808e28i 0.211800 + 0.205617i
\(851\) 2.44798e29i 1.22889i
\(852\) −3.57546e27 1.20664e29i −0.0177393 0.598663i
\(853\) −2.38026e29 −1.16717 −0.583586 0.812051i \(-0.698351\pi\)
−0.583586 + 0.812051i \(0.698351\pi\)
\(854\) −3.59672e28 + 3.70488e28i −0.174312 + 0.179554i
\(855\) 3.71614e28i 0.178005i
\(856\) −1.49922e29 1.37157e29i −0.709784 0.649352i
\(857\) −2.28117e29 −1.06745 −0.533727 0.845657i \(-0.679209\pi\)
−0.533727 + 0.845657i \(0.679209\pi\)
\(858\) −5.72223e28 5.55518e28i −0.264663 0.256936i
\(859\) 3.10756e29i 1.42065i 0.703872 + 0.710327i \(0.251453\pi\)
−0.703872 + 0.710327i \(0.748547\pi\)
\(860\) −1.76330e29 + 5.22492e27i −0.796787 + 0.0236100i
\(861\) 3.13568e28 0.140055
\(862\) −1.62249e29 + 1.67128e29i −0.716324 + 0.737864i
\(863\) 3.18530e29i 1.39009i −0.718968 0.695043i \(-0.755385\pi\)
0.718968 0.695043i \(-0.244615\pi\)
\(864\) −2.91252e28 + 3.37933e28i −0.125641 + 0.145778i
\(865\) −1.13200e29 −0.482710
\(866\) 2.07271e29 + 2.01220e29i 0.873695 + 0.848190i
\(867\) 9.29195e28i 0.387182i
\(868\) 4.48156e26 + 1.51243e28i 0.00184600 + 0.0622986i
\(869\) 6.29123e28 0.256176
\(870\) −5.75541e28 + 5.92848e28i −0.231677 + 0.238644i
\(871\) 1.68274e29i 0.669630i
\(872\) 9.86992e26 1.07885e27i 0.00388283 0.00424419i
\(873\) −2.86963e28 −0.111605
\(874\) 1.25202e29 + 1.21547e29i 0.481389 + 0.467336i
\(875\) 4.38418e28i 0.166651i
\(876\) −1.30775e29 + 3.87507e27i −0.491456 + 0.0145626i
\(877\) 7.71724e28 0.286725 0.143363 0.989670i \(-0.454208\pi\)
0.143363 + 0.989670i \(0.454208\pi\)
\(878\) −1.63803e29 + 1.68728e29i −0.601695 + 0.619788i
\(879\) 1.15000e29i 0.417646i
\(880\) −1.43405e28 2.41768e29i −0.0514916 0.868104i
\(881\) 4.67747e28 0.166055 0.0830275 0.996547i \(-0.473541\pi\)
0.0830275 + 0.996547i \(0.473541\pi\)
\(882\) −6.64386e28 6.44991e28i −0.233203 0.226396i
\(883\) 1.45636e29i 0.505430i −0.967541 0.252715i \(-0.918676\pi\)
0.967541 0.252715i \(-0.0813235\pi\)
\(884\) −2.53626e27 8.55935e28i −0.00870305 0.293710i
\(885\) −6.82734e28 −0.231643
\(886\) 3.82695e28 3.94202e28i 0.128385 0.132246i
\(887\) 2.59212e29i 0.859841i −0.902867 0.429921i \(-0.858542\pi\)
0.902867 0.429921i \(-0.141458\pi\)
\(888\) 1.82283e29 + 1.66763e29i 0.597883 + 0.546978i
\(889\) 5.47025e28 0.177415
\(890\) 2.16416e29 + 2.10098e29i 0.694047 + 0.673786i
\(891\) 4.37225e28i 0.138653i
\(892\) 4.78823e29 1.41882e28i 1.50151 0.0444918i
\(893\) 2.33847e29 0.725131
\(894\) −9.74229e28 + 1.00352e29i −0.298735 + 0.307718i
\(895\) 3.29456e29i 0.999004i
\(896\) 4.08918e28 + 3.31840e28i 0.122618 + 0.0995057i
\(897\) 8.72787e28 0.258812
\(898\) 1.76031e29 + 1.70892e29i 0.516210 + 0.501140i
\(899\) 1.12505e29i 0.326267i
\(900\) 1.77060e27 + 5.97541e28i 0.00507804 + 0.171373i
\(901\) −2.80847e29 −0.796567
\(902\) 4.76029e29 4.90343e29i 1.33527 1.37542i
\(903\) 3.75928e28i 0.104286i
\(904\) 4.02743e29 4.40225e29i 1.10495 1.20779i
\(905\) 4.39414e29 1.19231
\(906\) 1.82717e29 + 1.77383e29i 0.490340 + 0.476026i
\(907\) 4.96477e29i 1.31773i 0.752262 + 0.658864i \(0.228963\pi\)
−0.752262 + 0.658864i \(0.771037\pi\)
\(908\) −4.50460e29 + 1.33478e28i −1.18249 + 0.0350390i
\(909\) −6.33178e28 −0.164394
\(910\) −1.52832e28 + 1.57427e28i −0.0392463 + 0.0404265i
\(911\) 4.77893e29i 1.21380i −0.794778 0.606900i \(-0.792413\pi\)
0.794778 0.606900i \(-0.207587\pi\)
\(912\) 1.75798e29 1.04275e28i 0.441637 0.0261957i
\(913\) −8.36040e29 −2.07740
\(914\) 3.85463e29 + 3.74211e29i 0.947373 + 0.919717i
\(915\) 2.62281e29i 0.637611i
\(916\) 2.45423e28 + 8.28250e29i 0.0590147 + 1.99162i
\(917\) −5.24848e28 −0.124836
\(918\) −3.27002e28 + 3.36835e28i −0.0769349 + 0.0792483i
\(919\) 7.74788e29i 1.80313i −0.432640 0.901567i \(-0.642418\pi\)
0.432640 0.901567i \(-0.357582\pi\)
\(920\) 1.95558e29 + 1.78908e29i 0.450192 + 0.411862i
\(921\) 6.77493e28 0.154280
\(922\) −1.99586e29 1.93759e29i −0.449594 0.436469i
\(923\) 2.38347e29i 0.531121i
\(924\) 5.15891e28 1.52866e27i 0.113720 0.00336970i
\(925\) 3.31054e29 0.721908
\(926\) −1.00512e29 + 1.03535e29i −0.216825 + 0.223345i
\(927\) 1.49699e29i 0.319464i
\(928\) −2.96605e29 2.55633e29i −0.626180 0.539682i
\(929\) −2.23342e29 −0.466458 −0.233229 0.972422i \(-0.574929\pi\)
−0.233229 + 0.972422i \(0.574929\pi\)
\(930\) 5.51449e28 + 5.35351e28i 0.113940 + 0.110614i
\(931\) 3.65526e29i 0.747173i
\(932\) −1.22925e28 4.14846e29i −0.0248588 0.838933i
\(933\) 2.11149e29 0.422448
\(934\) −1.19510e29 + 1.23104e29i −0.236557 + 0.243671i
\(935\) 2.54858e29i 0.499095i
\(936\) 5.94566e28 6.49900e28i 0.115197 0.125918i
\(937\) 1.49570e29 0.286714 0.143357 0.989671i \(-0.454210\pi\)
0.143357 + 0.989671i \(0.454210\pi\)
\(938\) −7.81351e28 7.58541e28i −0.148190 0.143864i
\(939\) 2.72304e29i 0.510974i
\(940\) 3.55042e29 1.05204e28i 0.659176 0.0195324i
\(941\) −5.48715e29 −1.00798 −0.503989 0.863710i \(-0.668135\pi\)
−0.503989 + 0.863710i \(0.668135\pi\)
\(942\) −2.14250e29 + 2.20692e29i −0.389414 + 0.401124i
\(943\) 7.47900e29i 1.34501i
\(944\) −1.91575e28 3.22978e29i −0.0340893 0.574716i
\(945\) 1.20287e28 0.0211788
\(946\) −5.87859e29 5.70698e29i −1.02415 0.994249i
\(947\) 2.71697e29i 0.468366i −0.972193 0.234183i \(-0.924758\pi\)
0.972193 0.234183i \(-0.0752415\pi\)
\(948\) 2.05804e27 + 6.94544e28i 0.00351051 + 0.118472i
\(949\) 2.58320e29 0.436010
\(950\) 1.64375e29 1.69318e29i 0.274536 0.282791i
\(951\) 1.75135e29i 0.289447i
\(952\) 4.08872e28 + 3.74060e28i 0.0668679 + 0.0611746i
\(953\) −5.38208e29 −0.871006 −0.435503 0.900187i \(-0.643429\pi\)
−0.435503 + 0.900187i \(0.643429\pi\)
\(954\) −2.07281e29 2.01230e29i −0.331952 0.322261i
\(955\) 4.14979e29i 0.657646i
\(956\) −1.04725e30 + 3.10317e28i −1.64238 + 0.0486661i
\(957\) −3.83754e29 −0.595571
\(958\) −7.45415e29 + 7.67829e29i −1.14483 + 1.17926i
\(959\) 7.94600e28i 0.120771i
\(960\) 2.66439e29 2.37406e28i 0.400762 0.0357091i
\(961\) 5.67142e29 0.844224
\(962\) −3.49994e29 3.39777e29i −0.515597 0.500545i
\(963\) 2.19947e29i 0.320668i
\(964\) 2.21136e28 + 7.46287e29i 0.0319072 + 1.07680i
\(965\) 4.57002e29 0.652596
\(966\) −3.93433e28 + 4.05264e28i −0.0556032 + 0.0572752i
\(967\) 9.17171e29i 1.28288i −0.767174 0.641439i \(-0.778338\pi\)
0.767174 0.641439i \(-0.221662\pi\)
\(968\) 2.71680e29 2.96964e29i 0.376100 0.411102i
\(969\) 1.85317e29 0.253908
\(970\) 1.23455e29 + 1.19851e29i 0.167414 + 0.162527i
\(971\) 9.27236e29i 1.24451i 0.782815 + 0.622254i \(0.213783\pi\)
−0.782815 + 0.622254i \(0.786217\pi\)
\(972\) −4.82691e28 + 1.43028e27i −0.0641219 + 0.00190003i
\(973\) −5.00759e28 −0.0658416
\(974\) 8.48940e29 8.74468e29i 1.10481 1.13803i
\(975\) 1.18032e29i 0.152039i
\(976\) −1.24076e30 + 7.35958e28i −1.58194 + 0.0938329i
\(977\) 1.46598e29 0.185005 0.0925024 0.995712i \(-0.470513\pi\)
0.0925024 + 0.995712i \(0.470513\pi\)
\(978\) −4.94081e29 4.79657e29i −0.617177 0.599160i
\(979\) 1.40087e30i 1.73210i
\(980\) 1.64445e28 + 5.54967e29i 0.0201261 + 0.679213i
\(981\) 1.58276e27 0.00191745
\(982\) 5.70913e29 5.88080e29i 0.684628 0.705215i
\(983\) 3.74401e29i 0.444429i 0.974998 + 0.222214i \(0.0713285\pi\)
−0.974998 + 0.222214i \(0.928672\pi\)
\(984\) 5.56905e29 + 5.09490e29i 0.654380 + 0.598666i
\(985\) 3.27276e29 0.380672
\(986\) −2.95641e29 2.87011e29i −0.340405 0.330468i
\(987\) 7.56935e28i 0.0862754i
\(988\) −3.47558e29 + 1.02987e28i −0.392155 + 0.0116201i
\(989\) 8.96637e29 1.00151
\(990\) 1.82609e29 1.88100e29i 0.201915 0.207987i
\(991\) 9.45710e29i 1.03519i −0.855625 0.517597i \(-0.826827\pi\)
0.855625 0.517597i \(-0.173173\pi\)
\(992\) −2.37783e29 + 2.75894e29i −0.257670 + 0.298968i
\(993\) −8.89116e29 −0.953819
\(994\) −1.10672e29 1.07442e29i −0.117537 0.114106i
\(995\) 3.70703e29i 0.389758i
\(996\) −2.73492e28 9.22978e29i −0.0284676 0.960722i
\(997\) 1.11720e30 1.15128 0.575638 0.817704i \(-0.304754\pi\)
0.575638 + 0.817704i \(0.304754\pi\)
\(998\) 9.37579e29 9.65772e29i 0.956538 0.985302i
\(999\) 2.67424e29i 0.270113i
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 12.21.d.a.7.16 yes 20
3.2 odd 2 36.21.d.c.19.5 20
4.3 odd 2 inner 12.21.d.a.7.15 20
12.11 even 2 36.21.d.c.19.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.21.d.a.7.15 20 4.3 odd 2 inner
12.21.d.a.7.16 yes 20 1.1 even 1 trivial
36.21.d.c.19.5 20 3.2 odd 2
36.21.d.c.19.6 20 12.11 even 2