Properties

Label 8.17.d.b.3.14
Level $8$
Weight $17$
Character 8.3
Analytic conductor $12.986$
Analytic rank $0$
Dimension $14$
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] = [8,17,Mod(3,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.3");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 8.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: \(12.9859635085\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} - 652293490688 x^{8} + 465478371454976 x^{7} + \cdots + 27\!\cdots\!20 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{91}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.14
Root \(-137.581 - 24.7690i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.17.d.b.3.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(251.161 + 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 + 24884.1i) q^{4} -699404. i q^{5} +(1.55255e6 + 306219. i) q^{6} -4.65744e6i q^{7} +(1.39947e7 + 9.25331e6i) q^{8} -4.83590e6 q^{9} +O(q^{10})\) \(q+(251.161 + 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 + 24884.1i) q^{4} -699404. i q^{5} +(1.55255e6 + 306219. i) q^{6} -4.65744e6i q^{7} +(1.39947e7 + 9.25331e6i) q^{8} -4.83590e6 q^{9} +(3.46471e7 - 1.75663e8i) q^{10} -2.50802e7 q^{11} +(3.74771e8 + 1.53821e8i) q^{12} +9.99771e8i q^{13} +(2.30721e8 - 1.16977e9i) q^{14} -4.32336e9i q^{15} +(3.05653e9 + 3.01734e9i) q^{16} +1.78097e9 q^{17} +(-1.21459e9 - 2.39561e8i) q^{18} +2.70321e10 q^{19} +(1.74040e10 - 4.24035e10i) q^{20} -2.87899e10i q^{21} +(-6.29917e9 - 1.24242e9i) q^{22} +7.64077e10i q^{23} +(8.65080e10 + 5.71992e10i) q^{24} -3.36579e11 q^{25} +(-4.95267e10 + 2.51104e11i) q^{26} -2.95986e11 q^{27} +(1.15896e11 - 2.82371e11i) q^{28} +7.60372e11i q^{29} +(2.14171e11 - 1.08586e12i) q^{30} -2.35983e11i q^{31} +(6.18210e11 + 9.09254e11i) q^{32} -1.55033e11 q^{33} +(4.47310e11 + 8.82257e10i) q^{34} -3.25744e12 q^{35} +(-2.93191e11 - 1.20337e11i) q^{36} -2.42830e12i q^{37} +(6.78943e12 + 1.33912e12i) q^{38} +6.18007e12i q^{39} +(6.47180e12 - 9.78795e12i) q^{40} +1.88090e12 q^{41} +(1.42620e12 - 7.23092e12i) q^{42} -9.47032e12 q^{43} +(-1.52056e12 - 6.24097e11i) q^{44} +3.38225e12i q^{45} +(-3.78509e12 + 1.91907e13i) q^{46} -1.60529e13i q^{47} +(1.88939e13 + 1.86517e13i) q^{48} +1.15412e13 q^{49} +(-8.45355e13 - 1.66734e13i) q^{50} +1.10090e13 q^{51} +(-2.48784e13 + 6.06141e13i) q^{52} +1.92778e13i q^{53} +(-7.43402e13 - 1.46626e13i) q^{54} +1.75412e13i q^{55} +(4.30967e13 - 6.51795e13i) q^{56} +1.67099e14 q^{57} +(-3.76673e13 + 1.90976e14i) q^{58} -3.49569e13 q^{59} +(1.07583e14 - 2.62117e14i) q^{60} -3.45553e14i q^{61} +(1.16901e13 - 5.92698e13i) q^{62} +2.25229e13i q^{63} +(1.10228e14 + 2.58994e14i) q^{64} +6.99244e14 q^{65} +(-3.89382e13 - 7.68002e12i) q^{66} -6.70291e14 q^{67} +(1.07977e14 + 4.43178e13i) q^{68} +4.72314e14i q^{69} +(-8.18142e14 - 1.61367e14i) q^{70} +2.20461e14i q^{71} +(-6.76769e13 - 4.47481e13i) q^{72} +1.81005e14 q^{73} +(1.20293e14 - 6.09895e14i) q^{74} -2.08056e15 q^{75} +(1.63890e15 + 6.72670e14i) q^{76} +1.16809e14i q^{77} +(-3.06149e14 + 1.55220e15i) q^{78} +1.45789e14i q^{79} +(2.11034e15 - 2.13775e15i) q^{80} -1.62146e15 q^{81} +(4.72409e14 + 9.31760e13i) q^{82} -3.18974e14 q^{83} +(7.16411e14 - 1.74548e15i) q^{84} -1.24562e15i q^{85} +(-2.37858e15 - 4.69141e14i) q^{86} +4.70023e15i q^{87} +(-3.50989e14 - 2.32075e14i) q^{88} +2.96458e15 q^{89} +(-1.67550e14 + 8.49491e14i) q^{90} +4.65638e15 q^{91} +(-1.90134e15 + 4.63244e15i) q^{92} -1.45873e15i q^{93} +(7.95231e14 - 4.03188e15i) q^{94} -1.89064e16i q^{95} +(3.82146e15 + 5.62054e15i) q^{96} +7.93720e15 q^{97} +(2.89869e15 + 5.71726e14i) q^{98} +1.21285e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 251.161 + 49.5380i 0.981099 + 0.193508i
\(3\) 6181.49 0.942157 0.471078 0.882091i \(-0.343865\pi\)
0.471078 + 0.882091i \(0.343865\pi\)
\(4\) 60628.0 + 24884.1i 0.925109 + 0.379701i
\(5\) 699404.i 1.79048i −0.445589 0.895238i \(-0.647006\pi\)
0.445589 0.895238i \(-0.352994\pi\)
\(6\) 1.55255e6 + 306219.i 0.924349 + 0.182315i
\(7\) 4.65744e6i 0.807911i −0.914779 0.403955i \(-0.867635\pi\)
0.914779 0.403955i \(-0.132365\pi\)
\(8\) 1.39947e7 + 9.25331e6i 0.834148 + 0.551540i
\(9\) −4.83590e6 −0.112341
\(10\) 3.46471e7 1.75663e8i 0.346471 1.75663i
\(11\) −2.50802e7 −0.117001 −0.0585004 0.998287i \(-0.518632\pi\)
−0.0585004 + 0.998287i \(0.518632\pi\)
\(12\) 3.74771e8 + 1.53821e8i 0.871598 + 0.357738i
\(13\) 9.99771e8i 1.22561i 0.790233 + 0.612807i \(0.209960\pi\)
−0.790233 + 0.612807i \(0.790040\pi\)
\(14\) 2.30721e8 1.16977e9i 0.156337 0.792640i
\(15\) 4.32336e9i 1.68691i
\(16\) 3.05653e9 + 3.01734e9i 0.711655 + 0.702530i
\(17\) 1.78097e9 0.255308 0.127654 0.991819i \(-0.459255\pi\)
0.127654 + 0.991819i \(0.459255\pi\)
\(18\) −1.21459e9 2.39561e8i −0.110217 0.0217388i
\(19\) 2.70321e10 1.59166 0.795832 0.605517i \(-0.207034\pi\)
0.795832 + 0.605517i \(0.207034\pi\)
\(20\) 1.74040e10 4.24035e10i 0.679845 1.65639i
\(21\) 2.87899e10i 0.761178i
\(22\) −6.29917e9 1.24242e9i −0.114789 0.0226406i
\(23\) 7.64077e10i 0.975696i 0.872929 + 0.487848i \(0.162218\pi\)
−0.872929 + 0.487848i \(0.837782\pi\)
\(24\) 8.65080e10 + 5.71992e10i 0.785899 + 0.519637i
\(25\) −3.36579e11 −2.20580
\(26\) −4.95267e10 + 2.51104e11i −0.237166 + 1.20245i
\(27\) −2.95986e11 −1.04800
\(28\) 1.15896e11 2.82371e11i 0.306764 0.747406i
\(29\) 7.60372e11i 1.51999i 0.649926 + 0.759997i \(0.274800\pi\)
−0.649926 + 0.759997i \(0.725200\pi\)
\(30\) 2.14171e11 1.08586e12i 0.326430 1.65502i
\(31\) 2.35983e11i 0.276686i −0.990384 0.138343i \(-0.955822\pi\)
0.990384 0.138343i \(-0.0441777\pi\)
\(32\) 6.18210e11 + 9.09254e11i 0.562258 + 0.826962i
\(33\) −1.55033e11 −0.110233
\(34\) 4.47310e11 + 8.82257e10i 0.250483 + 0.0494042i
\(35\) −3.25744e12 −1.44654
\(36\) −2.93191e11 1.20337e11i −0.103928 0.0426559i
\(37\) 2.42830e12i 0.691336i −0.938357 0.345668i \(-0.887652\pi\)
0.938357 0.345668i \(-0.112348\pi\)
\(38\) 6.78943e12 + 1.33912e12i 1.56158 + 0.308000i
\(39\) 6.18007e12i 1.15472i
\(40\) 6.47180e12 9.78795e12i 0.987519 1.49352i
\(41\) 1.88090e12 0.235556 0.117778 0.993040i \(-0.462423\pi\)
0.117778 + 0.993040i \(0.462423\pi\)
\(42\) 1.42620e12 7.23092e12i 0.147294 0.746791i
\(43\) −9.47032e12 −0.810246 −0.405123 0.914262i \(-0.632771\pi\)
−0.405123 + 0.914262i \(0.632771\pi\)
\(44\) −1.52056e12 6.24097e11i −0.108239 0.0444253i
\(45\) 3.38225e12i 0.201143i
\(46\) −3.78509e12 + 1.91907e13i −0.188805 + 0.957254i
\(47\) 1.60529e13i 0.674174i −0.941474 0.337087i \(-0.890558\pi\)
0.941474 0.337087i \(-0.109442\pi\)
\(48\) 1.88939e13 + 1.86517e13i 0.670490 + 0.661893i
\(49\) 1.15412e13 0.347281
\(50\) −8.45355e13 1.66734e13i −2.16411 0.426840i
\(51\) 1.10090e13 0.240540
\(52\) −2.48784e13 + 6.06141e13i −0.465367 + 1.13383i
\(53\) 1.92778e13i 0.309635i 0.987943 + 0.154817i \(0.0494789\pi\)
−0.987943 + 0.154817i \(0.950521\pi\)
\(54\) −7.43402e13 1.46626e13i −1.02819 0.202796i
\(55\) 1.75412e13i 0.209487i
\(56\) 4.30967e13 6.51795e13i 0.445595 0.673917i
\(57\) 1.67099e14 1.49960
\(58\) −3.76673e13 + 1.90976e14i −0.294131 + 1.49126i
\(59\) −3.49569e13 −0.238076 −0.119038 0.992890i \(-0.537981\pi\)
−0.119038 + 0.992890i \(0.537981\pi\)
\(60\) 1.07583e14 2.62117e14i 0.640521 1.56057i
\(61\) 3.45553e14i 1.80250i −0.433297 0.901251i \(-0.642650\pi\)
0.433297 0.901251i \(-0.357350\pi\)
\(62\) 1.16901e13 5.92698e13i 0.0535410 0.271456i
\(63\) 2.25229e13i 0.0907613i
\(64\) 1.10228e14 + 2.58994e14i 0.391607 + 0.920132i
\(65\) 6.99244e14 2.19443
\(66\) −3.89382e13 7.68002e12i −0.108150 0.0213310i
\(67\) −6.70291e14 −1.65069 −0.825344 0.564630i \(-0.809019\pi\)
−0.825344 + 0.564630i \(0.809019\pi\)
\(68\) 1.07977e14 + 4.43178e13i 0.236188 + 0.0969408i
\(69\) 4.72314e14i 0.919259i
\(70\) −8.18142e14 1.61367e14i −1.41920 0.279918i
\(71\) 2.20461e14i 0.341401i 0.985323 + 0.170700i \(0.0546030\pi\)
−0.985323 + 0.170700i \(0.945397\pi\)
\(72\) −6.76769e13 4.47481e13i −0.0937089 0.0619604i
\(73\) 1.81005e14 0.224444 0.112222 0.993683i \(-0.464203\pi\)
0.112222 + 0.993683i \(0.464203\pi\)
\(74\) 1.20293e14 6.09895e14i 0.133779 0.678268i
\(75\) −2.08056e15 −2.07821
\(76\) 1.63890e15 + 6.72670e14i 1.47246 + 0.604356i
\(77\) 1.16809e14i 0.0945262i
\(78\) −3.06149e14 + 1.55220e15i −0.223448 + 1.13289i
\(79\) 1.45789e14i 0.0960965i 0.998845 + 0.0480482i \(0.0153001\pi\)
−0.998845 + 0.0480482i \(0.984700\pi\)
\(80\) 2.11034e15 2.13775e15i 1.25786 1.27420i
\(81\) −1.62146e15 −0.875039
\(82\) 4.72409e14 + 9.31760e13i 0.231104 + 0.0455820i
\(83\) −3.18974e14 −0.141622 −0.0708110 0.997490i \(-0.522559\pi\)
−0.0708110 + 0.997490i \(0.522559\pi\)
\(84\) 7.16411e14 1.74548e15i 0.289020 0.704173i
\(85\) 1.24562e15i 0.457123i
\(86\) −2.37858e15 4.69141e14i −0.794932 0.156789i
\(87\) 4.70023e15i 1.43207i
\(88\) −3.50989e14 2.32075e14i −0.0975961 0.0645307i
\(89\) 2.96458e15 0.753083 0.376541 0.926400i \(-0.377113\pi\)
0.376541 + 0.926400i \(0.377113\pi\)
\(90\) −1.67550e14 + 8.49491e14i −0.0389229 + 0.197342i
\(91\) 4.65638e15 0.990186
\(92\) −1.90134e15 + 4.63244e15i −0.370473 + 0.902625i
\(93\) 1.45873e15i 0.260682i
\(94\) 7.95231e14 4.03188e15i 0.130458 0.661431i
\(95\) 1.89064e16i 2.84984i
\(96\) 3.82146e15 + 5.62054e15i 0.529735 + 0.779127i
\(97\) 7.93720e15 1.01273 0.506365 0.862319i \(-0.330989\pi\)
0.506365 + 0.862319i \(0.330989\pi\)
\(98\) 2.89869e15 + 5.71726e14i 0.340717 + 0.0672016i
\(99\) 1.21285e14 0.0131440
\(100\) −2.04061e16 8.37545e15i −2.04061 0.837545i
\(101\) 1.00307e16i 0.926321i 0.886274 + 0.463160i \(0.153285\pi\)
−0.886274 + 0.463160i \(0.846715\pi\)
\(102\) 2.76504e15 + 5.45366e14i 0.235994 + 0.0465465i
\(103\) 2.46355e16i 1.94475i 0.233429 + 0.972374i \(0.425005\pi\)
−0.233429 + 0.972374i \(0.574995\pi\)
\(104\) −9.25119e15 + 1.39915e16i −0.675975 + 1.02234i
\(105\) −2.01358e16 −1.36287
\(106\) −9.54983e14 + 4.84183e15i −0.0599168 + 0.303782i
\(107\) 1.00547e16 0.585194 0.292597 0.956236i \(-0.405481\pi\)
0.292597 + 0.956236i \(0.405481\pi\)
\(108\) −1.79450e16 7.36534e15i −0.969514 0.397926i
\(109\) 1.73713e16i 0.871806i −0.899994 0.435903i \(-0.856429\pi\)
0.899994 0.435903i \(-0.143571\pi\)
\(110\) −8.68956e14 + 4.40567e15i −0.0405374 + 0.205528i
\(111\) 1.50105e16i 0.651346i
\(112\) 1.40531e16 1.42356e16i 0.567581 0.574953i
\(113\) −2.11437e16 −0.795342 −0.397671 0.917528i \(-0.630181\pi\)
−0.397671 + 0.917528i \(0.630181\pi\)
\(114\) 4.19688e16 + 8.27775e15i 1.47125 + 0.290184i
\(115\) 5.34399e16 1.74696
\(116\) −1.89211e16 + 4.60998e16i −0.577143 + 1.40616i
\(117\) 4.83479e15i 0.137686i
\(118\) −8.77981e15 1.73169e15i −0.233576 0.0460697i
\(119\) 8.29476e15i 0.206266i
\(120\) 4.00054e16 6.05041e16i 0.930397 1.40713i
\(121\) −4.53207e16 −0.986311
\(122\) 1.71180e16 8.67895e16i 0.348798 1.76843i
\(123\) 1.16267e16 0.221931
\(124\) 5.87222e15 1.43072e16i 0.105058 0.255965i
\(125\) 1.28684e17i 2.15896i
\(126\) −1.11574e15 + 5.65689e15i −0.0175630 + 0.0890458i
\(127\) 6.32709e16i 0.934920i −0.884014 0.467460i \(-0.845169\pi\)
0.884014 0.467460i \(-0.154831\pi\)
\(128\) 1.48548e16 + 7.05098e16i 0.206152 + 0.978520i
\(129\) −5.85407e16 −0.763379
\(130\) 1.75623e17 + 3.46392e16i 2.15295 + 0.424640i
\(131\) −1.18988e17 −1.37194 −0.685968 0.727632i \(-0.740621\pi\)
−0.685968 + 0.727632i \(0.740621\pi\)
\(132\) −9.39933e15 3.85785e15i −0.101978 0.0418556i
\(133\) 1.25901e17i 1.28592i
\(134\) −1.68351e17 3.32049e16i −1.61949 0.319421i
\(135\) 2.07014e17i 1.87642i
\(136\) 2.49241e16 + 1.64799e16i 0.212965 + 0.140813i
\(137\) 1.01693e16 0.0819460 0.0409730 0.999160i \(-0.486954\pi\)
0.0409730 + 0.999160i \(0.486954\pi\)
\(138\) −2.33975e16 + 1.18627e17i −0.177884 + 0.901883i
\(139\) −4.95907e16 −0.355862 −0.177931 0.984043i \(-0.556940\pi\)
−0.177931 + 0.984043i \(0.556940\pi\)
\(140\) −1.97492e17 8.10583e16i −1.33821 0.549254i
\(141\) 9.92311e16i 0.635177i
\(142\) −1.09212e16 + 5.53712e16i −0.0660637 + 0.334948i
\(143\) 2.50744e16i 0.143398i
\(144\) −1.47811e16 1.45916e16i −0.0799478 0.0789227i
\(145\) 5.31807e17 2.72151
\(146\) 4.54615e16 + 8.96665e15i 0.220202 + 0.0434317i
\(147\) 7.13415e16 0.327193
\(148\) 6.04260e16 1.47223e17i 0.262501 0.639561i
\(149\) 1.18135e17i 0.486284i 0.969991 + 0.243142i \(0.0781781\pi\)
−0.969991 + 0.243142i \(0.921822\pi\)
\(150\) −5.22556e17 1.03067e17i −2.03893 0.402150i
\(151\) 3.38113e17i 1.25097i −0.780237 0.625484i \(-0.784902\pi\)
0.780237 0.625484i \(-0.215098\pi\)
\(152\) 3.78306e17 + 2.50137e17i 1.32768 + 0.877867i
\(153\) −8.61259e15 −0.0286815
\(154\) −5.78651e15 + 2.93380e16i −0.0182916 + 0.0927396i
\(155\) −1.65048e17 −0.495400
\(156\) −1.53785e17 + 3.74685e17i −0.438448 + 1.06824i
\(157\) 1.51106e17i 0.409341i −0.978831 0.204670i \(-0.934388\pi\)
0.978831 0.204670i \(-0.0656122\pi\)
\(158\) −7.22209e15 + 3.66165e16i −0.0185954 + 0.0942801i
\(159\) 1.19165e17i 0.291725i
\(160\) 6.35936e17 4.32378e17i 1.48065 1.00671i
\(161\) 3.55865e17 0.788275
\(162\) −4.07249e17 8.03242e16i −0.858499 0.169327i
\(163\) −1.53662e16 −0.0308365 −0.0154183 0.999881i \(-0.504908\pi\)
−0.0154183 + 0.999881i \(0.504908\pi\)
\(164\) 1.14035e17 + 4.68044e16i 0.217915 + 0.0894408i
\(165\) 1.08431e17i 0.197370i
\(166\) −8.01140e16 1.58014e16i −0.138945 0.0274050i
\(167\) 4.82750e16i 0.0797976i 0.999204 + 0.0398988i \(0.0127036\pi\)
−0.999204 + 0.0398988i \(0.987296\pi\)
\(168\) 2.66402e17 4.02906e17i 0.419820 0.634936i
\(169\) −3.34125e17 −0.502130
\(170\) 6.17055e16 3.12851e17i 0.0884570 0.448483i
\(171\) −1.30725e17 −0.178809
\(172\) −5.74166e17 2.35660e17i −0.749567 0.307651i
\(173\) 5.34968e17i 0.666744i −0.942795 0.333372i \(-0.891814\pi\)
0.942795 0.333372i \(-0.108186\pi\)
\(174\) −2.32840e17 + 1.18052e18i −0.277117 + 1.40500i
\(175\) 1.56760e18i 1.78209i
\(176\) −7.66584e16 7.56755e16i −0.0832642 0.0821966i
\(177\) −2.16086e17 −0.224305
\(178\) 7.44587e17 + 1.46859e17i 0.738849 + 0.145728i
\(179\) −1.66428e18 −1.57907 −0.789536 0.613704i \(-0.789679\pi\)
−0.789536 + 0.613704i \(0.789679\pi\)
\(180\) −8.41642e16 + 2.05059e17i −0.0763743 + 0.186080i
\(181\) 8.37583e17i 0.727108i 0.931573 + 0.363554i \(0.118437\pi\)
−0.931573 + 0.363554i \(0.881563\pi\)
\(182\) 1.16950e18 + 2.30668e17i 0.971471 + 0.191609i
\(183\) 2.13603e18i 1.69824i
\(184\) −7.07024e17 + 1.06930e18i −0.538135 + 0.813875i
\(185\) −1.69837e18 −1.23782
\(186\) 7.22625e16 3.66376e17i 0.0504440 0.255754i
\(187\) −4.46670e16 −0.0298713
\(188\) 3.99463e17 9.73257e17i 0.255984 0.623684i
\(189\) 1.37854e18i 0.846690i
\(190\) 9.36586e17 4.74856e18i 0.551466 2.79597i
\(191\) 1.41104e18i 0.796659i 0.917242 + 0.398329i \(0.130410\pi\)
−0.917242 + 0.398329i \(0.869590\pi\)
\(192\) 6.81371e17 + 1.60097e18i 0.368955 + 0.866909i
\(193\) 2.23870e18 1.16289 0.581444 0.813586i \(-0.302488\pi\)
0.581444 + 0.813586i \(0.302488\pi\)
\(194\) 1.99352e18 + 3.93193e17i 0.993588 + 0.195971i
\(195\) 4.32237e18 2.06750
\(196\) 6.99717e17 + 2.87191e17i 0.321273 + 0.131863i
\(197\) 1.68645e18i 0.743436i −0.928346 0.371718i \(-0.878769\pi\)
0.928346 0.371718i \(-0.121231\pi\)
\(198\) 3.04622e16 + 6.00824e15i 0.0128955 + 0.00254346i
\(199\) 2.99452e18i 1.21759i −0.793326 0.608797i \(-0.791652\pi\)
0.793326 0.608797i \(-0.208348\pi\)
\(200\) −4.71031e18 3.11447e18i −1.83997 1.21659i
\(201\) −4.14340e18 −1.55521
\(202\) −4.96903e17 + 2.51933e18i −0.179250 + 0.908812i
\(203\) 3.54139e18 1.22802
\(204\) 6.67456e17 + 2.73950e17i 0.222526 + 0.0913334i
\(205\) 1.31551e18i 0.421757i
\(206\) −1.22039e18 + 6.18748e18i −0.376324 + 1.90799i
\(207\) 3.69500e17i 0.109610i
\(208\) −3.01665e18 + 3.05583e18i −0.861030 + 0.872214i
\(209\) −6.77971e17 −0.186226
\(210\) −5.05734e18 9.97489e17i −1.33711 0.263726i
\(211\) 2.76684e18 0.704246 0.352123 0.935954i \(-0.385460\pi\)
0.352123 + 0.935954i \(0.385460\pi\)
\(212\) −4.79709e17 + 1.16877e18i −0.117569 + 0.286446i
\(213\) 1.36278e18i 0.321653i
\(214\) 2.52536e18 + 4.98091e17i 0.574133 + 0.113240i
\(215\) 6.62359e18i 1.45073i
\(216\) −4.14223e18 2.73885e18i −0.874187 0.578014i
\(217\) −1.09908e18 −0.223538
\(218\) 8.60539e17 4.36299e18i 0.168701 0.855327i
\(219\) 1.11888e18 0.211462
\(220\) −4.36496e17 + 1.06349e18i −0.0795425 + 0.193799i
\(221\) 1.78056e18i 0.312909i
\(222\) 7.43592e17 3.77006e18i 0.126041 0.639035i
\(223\) 8.31324e18i 1.35935i −0.733513 0.679675i \(-0.762121\pi\)
0.733513 0.679675i \(-0.237879\pi\)
\(224\) 4.23480e18 2.87928e18i 0.668111 0.454254i
\(225\) 1.62766e18 0.247802
\(226\) −5.31048e18 1.04742e18i −0.780309 0.153905i
\(227\) −9.98439e18 −1.41617 −0.708083 0.706129i \(-0.750440\pi\)
−0.708083 + 0.706129i \(0.750440\pi\)
\(228\) 1.01309e19 + 4.15810e18i 1.38729 + 0.569398i
\(229\) 5.03614e16i 0.00665907i −0.999994 0.00332954i \(-0.998940\pi\)
0.999994 0.00332954i \(-0.00105983\pi\)
\(230\) 1.34220e19 + 2.64731e18i 1.71394 + 0.338051i
\(231\) 7.22057e17i 0.0890585i
\(232\) −7.03595e18 + 1.06412e19i −0.838338 + 1.26790i
\(233\) 6.71996e18 0.773605 0.386803 0.922162i \(-0.373579\pi\)
0.386803 + 0.922162i \(0.373579\pi\)
\(234\) 2.39506e17 1.21431e18i 0.0266434 0.135084i
\(235\) −1.12275e19 −1.20709
\(236\) −2.11936e18 8.69869e17i −0.220247 0.0903978i
\(237\) 9.01192e17i 0.0905379i
\(238\) 4.10906e17 2.08332e18i 0.0399142 0.202368i
\(239\) 1.61742e18i 0.151929i −0.997111 0.0759643i \(-0.975796\pi\)
0.997111 0.0759643i \(-0.0242035\pi\)
\(240\) 1.30451e19 1.32145e19i 1.18510 1.20050i
\(241\) 9.87362e18 0.867641 0.433821 0.900999i \(-0.357165\pi\)
0.433821 + 0.900999i \(0.357165\pi\)
\(242\) −1.13828e19 2.24510e18i −0.967668 0.190859i
\(243\) 2.71816e18 0.223576
\(244\) 8.59876e18 2.09502e19i 0.684411 1.66751i
\(245\) 8.07193e18i 0.621797i
\(246\) 2.92019e18 + 5.75966e17i 0.217736 + 0.0429454i
\(247\) 2.70259e19i 1.95077i
\(248\) 2.18362e18 3.30251e18i 0.152603 0.230797i
\(249\) −1.97174e18 −0.133430
\(250\) −6.37475e18 + 3.23204e19i −0.417776 + 2.11815i
\(251\) −1.58923e19 −1.00878 −0.504390 0.863476i \(-0.668283\pi\)
−0.504390 + 0.863476i \(0.668283\pi\)
\(252\) −5.60463e17 + 1.36552e18i −0.0344621 + 0.0839641i
\(253\) 1.91632e18i 0.114157i
\(254\) 3.13432e18 1.58912e19i 0.180914 0.917248i
\(255\) 7.69977e18i 0.430682i
\(256\) 2.38044e17 + 1.84452e19i 0.0129044 + 0.999917i
\(257\) −1.59897e19 −0.840187 −0.420093 0.907481i \(-0.638003\pi\)
−0.420093 + 0.907481i \(0.638003\pi\)
\(258\) −1.47032e19 2.89999e18i −0.748950 0.147720i
\(259\) −1.13097e19 −0.558537
\(260\) 4.23938e19 + 1.74000e19i 2.03009 + 0.833228i
\(261\) 3.67708e18i 0.170757i
\(262\) −2.98853e19 5.89445e18i −1.34600 0.265481i
\(263\) 1.53959e19i 0.672602i −0.941755 0.336301i \(-0.890824\pi\)
0.941755 0.336301i \(-0.109176\pi\)
\(264\) −2.16964e18 1.43457e18i −0.0919508 0.0607980i
\(265\) 1.34830e19 0.554394
\(266\) 6.23687e18 3.16214e19i 0.248836 1.26162i
\(267\) 1.83255e19 0.709522
\(268\) −4.06384e19 1.66796e19i −1.52707 0.626768i
\(269\) 3.47917e19i 1.26899i 0.772927 + 0.634494i \(0.218792\pi\)
−0.772927 + 0.634494i \(0.781208\pi\)
\(270\) −1.02551e19 + 5.19939e19i −0.363102 + 1.84095i
\(271\) 1.10793e19i 0.380854i −0.981701 0.190427i \(-0.939013\pi\)
0.981701 0.190427i \(-0.0609873\pi\)
\(272\) 5.44359e18 + 5.37379e18i 0.181691 + 0.179362i
\(273\) 2.87833e19 0.932911
\(274\) 2.55414e18 + 5.03769e17i 0.0803971 + 0.0158572i
\(275\) 8.44145e18 0.258081
\(276\) −1.17531e19 + 2.86354e19i −0.349043 + 0.850415i
\(277\) 1.03237e19i 0.297850i 0.988848 + 0.148925i \(0.0475813\pi\)
−0.988848 + 0.148925i \(0.952419\pi\)
\(278\) −1.24553e19 2.45663e18i −0.349136 0.0688622i
\(279\) 1.14119e18i 0.0310831i
\(280\) −4.55868e19 3.01421e19i −1.20663 0.797827i
\(281\) 3.43188e19 0.882840 0.441420 0.897301i \(-0.354475\pi\)
0.441420 + 0.897301i \(0.354475\pi\)
\(282\) 4.91571e18 2.49230e19i 0.122912 0.623172i
\(283\) 3.83778e19 0.932800 0.466400 0.884574i \(-0.345551\pi\)
0.466400 + 0.884574i \(0.345551\pi\)
\(284\) −5.48596e18 + 1.33661e19i −0.129630 + 0.315833i
\(285\) 1.16870e20i 2.68499i
\(286\) 1.24214e18 6.29773e18i 0.0277486 0.140687i
\(287\) 8.76017e18i 0.190308i
\(288\) −2.98960e18 4.39706e18i −0.0631645 0.0929015i
\(289\) −4.54893e19 −0.934818
\(290\) 1.33569e20 + 2.63447e19i 2.67007 + 0.526634i
\(291\) 4.90637e19 0.954150
\(292\) 1.09740e19 + 4.50415e18i 0.207635 + 0.0852217i
\(293\) 2.69218e19i 0.495636i 0.968807 + 0.247818i \(0.0797136\pi\)
−0.968807 + 0.247818i \(0.920286\pi\)
\(294\) 1.79182e19 + 3.53412e18i 0.321008 + 0.0633144i
\(295\) 2.44490e19i 0.426270i
\(296\) 2.24698e19 3.39833e19i 0.381299 0.576676i
\(297\) 7.42338e18 0.122617
\(298\) −5.85219e18 + 2.96710e19i −0.0940998 + 0.477092i
\(299\) −7.63902e19 −1.19583
\(300\) −1.26140e20 5.17728e19i −1.92257 0.789099i
\(301\) 4.41075e19i 0.654607i
\(302\) 1.67494e19 8.49208e19i 0.242072 1.22732i
\(303\) 6.20048e19i 0.872739i
\(304\) 8.26246e19 + 8.15652e19i 1.13272 + 1.11819i
\(305\) −2.41681e20 −3.22734
\(306\) −2.16315e18 4.26651e17i −0.0281394 0.00555011i
\(307\) 3.17040e19 0.401797 0.200899 0.979612i \(-0.435614\pi\)
0.200899 + 0.979612i \(0.435614\pi\)
\(308\) −2.90670e18 + 7.08192e18i −0.0358917 + 0.0874471i
\(309\) 1.52284e20i 1.83226i
\(310\) −4.14536e19 8.17614e18i −0.486036 0.0958638i
\(311\) 1.11218e20i 1.27084i −0.772165 0.635422i \(-0.780826\pi\)
0.772165 0.635422i \(-0.219174\pi\)
\(312\) −5.71861e19 + 8.64882e19i −0.636875 + 0.963208i
\(313\) −2.59112e19 −0.281277 −0.140638 0.990061i \(-0.544915\pi\)
−0.140638 + 0.990061i \(0.544915\pi\)
\(314\) 7.48550e18 3.79520e19i 0.0792107 0.401603i
\(315\) 1.57526e19 0.162506
\(316\) −3.62782e18 + 8.83888e18i −0.0364879 + 0.0888997i
\(317\) 9.95998e19i 0.976752i 0.872633 + 0.488376i \(0.162411\pi\)
−0.872633 + 0.488376i \(0.837589\pi\)
\(318\) −5.90322e18 + 2.99297e19i −0.0564510 + 0.286211i
\(319\) 1.90703e19i 0.177841i
\(320\) 1.81142e20 7.70937e19i 1.64747 0.701163i
\(321\) 6.21532e19 0.551345
\(322\) 8.93794e19 + 1.76288e19i 0.773376 + 0.152538i
\(323\) 4.81434e19 0.406365
\(324\) −9.83061e19 4.03486e19i −0.809507 0.332253i
\(325\) 3.36502e20i 2.70346i
\(326\) −3.85939e18 7.61211e17i −0.0302537 0.00596711i
\(327\) 1.07380e20i 0.821377i
\(328\) 2.63226e19 + 1.74045e19i 0.196489 + 0.129919i
\(329\) −7.47657e19 −0.544672
\(330\) −5.37144e18 + 2.72336e19i −0.0381926 + 0.193639i
\(331\) 1.21654e20 0.844311 0.422155 0.906524i \(-0.361274\pi\)
0.422155 + 0.906524i \(0.361274\pi\)
\(332\) −1.93388e19 7.93738e18i −0.131016 0.0537740i
\(333\) 1.17430e19i 0.0776652i
\(334\) −2.39145e18 + 1.21248e19i −0.0154415 + 0.0782894i
\(335\) 4.68805e20i 2.95552i
\(336\) 8.68691e19 8.79974e19i 0.534750 0.541696i
\(337\) 2.30463e20 1.38536 0.692680 0.721245i \(-0.256430\pi\)
0.692680 + 0.721245i \(0.256430\pi\)
\(338\) −8.39194e19 1.65519e19i −0.492639 0.0971661i
\(339\) −1.30700e20 −0.749337
\(340\) 3.09960e19 7.55193e19i 0.173570 0.422889i
\(341\) 5.91850e18i 0.0323725i
\(342\) −3.28330e19 6.47585e18i −0.175429 0.0346009i
\(343\) 2.08533e20i 1.08848i
\(344\) −1.32534e20 8.76318e19i −0.675866 0.446883i
\(345\) 3.30338e20 1.64591
\(346\) 2.65013e19 1.34363e20i 0.129020 0.654142i
\(347\) −3.36488e20 −1.60079 −0.800393 0.599476i \(-0.795376\pi\)
−0.800393 + 0.599476i \(0.795376\pi\)
\(348\) −1.16961e20 + 2.84965e20i −0.543759 + 1.32482i
\(349\) 5.21190e19i 0.236806i 0.992966 + 0.118403i \(0.0377775\pi\)
−0.992966 + 0.118403i \(0.962223\pi\)
\(350\) −7.76556e19 + 3.93719e20i −0.344849 + 1.74841i
\(351\) 2.95918e20i 1.28444i
\(352\) −1.55048e19 2.28042e19i −0.0657847 0.0967552i
\(353\) −7.64010e18 −0.0316885 −0.0158442 0.999874i \(-0.505044\pi\)
−0.0158442 + 0.999874i \(0.505044\pi\)
\(354\) −5.42723e19 1.07045e19i −0.220066 0.0434049i
\(355\) 1.54191e20 0.611269
\(356\) 1.79736e20 + 7.37708e19i 0.696684 + 0.285946i
\(357\) 5.12740e19i 0.194335i
\(358\) −4.18003e20 8.24452e19i −1.54923 0.305563i
\(359\) 1.32120e20i 0.478865i 0.970913 + 0.239432i \(0.0769613\pi\)
−0.970913 + 0.239432i \(0.923039\pi\)
\(360\) −3.12970e19 + 4.73336e19i −0.110939 + 0.167783i
\(361\) 4.42295e20 1.53340
\(362\) −4.14922e19 + 2.10368e20i −0.140701 + 0.713365i
\(363\) −2.80150e20 −0.929259
\(364\) 2.82307e20 + 1.15870e20i 0.916031 + 0.375975i
\(365\) 1.26596e20i 0.401862i
\(366\) 1.05815e20 5.36488e20i 0.328623 1.66614i
\(367\) 2.21954e20i 0.674425i −0.941429 0.337213i \(-0.890516\pi\)
0.941429 0.337213i \(-0.109484\pi\)
\(368\) −2.30548e20 + 2.33543e20i −0.685455 + 0.694359i
\(369\) −9.09584e18 −0.0264625
\(370\) −4.26564e20 8.41337e19i −1.21442 0.239528i
\(371\) 8.97851e19 0.250157
\(372\) 3.62991e19 8.84397e19i 0.0989811 0.241159i
\(373\) 5.49011e20i 1.46525i 0.680635 + 0.732623i \(0.261704\pi\)
−0.680635 + 0.732623i \(0.738296\pi\)
\(374\) −1.12186e19 2.21272e18i −0.0293067 0.00578033i
\(375\) 7.95459e20i 2.03408i
\(376\) 1.48543e20 2.24656e20i 0.371834 0.562361i
\(377\) −7.60198e20 −1.86293
\(378\) −6.82901e19 + 3.46235e20i −0.163841 + 0.830686i
\(379\) −1.81621e20 −0.426631 −0.213316 0.976983i \(-0.568426\pi\)
−0.213316 + 0.976983i \(0.568426\pi\)
\(380\) 4.70468e20 1.14626e21i 1.08209 2.63641i
\(381\) 3.91108e20i 0.880841i
\(382\) −6.99002e19 + 3.54399e20i −0.154160 + 0.781601i
\(383\) 1.94155e20i 0.419333i −0.977773 0.209666i \(-0.932762\pi\)
0.977773 0.209666i \(-0.0672378\pi\)
\(384\) 9.18251e19 + 4.35856e20i 0.194228 + 0.921919i
\(385\) 8.16971e19 0.169247
\(386\) 5.62275e20 + 1.10901e20i 1.14091 + 0.225028i
\(387\) 4.57976e19 0.0910237
\(388\) 4.81216e20 + 1.97510e20i 0.936886 + 0.384534i
\(389\) 6.76602e20i 1.29044i −0.763998 0.645218i \(-0.776766\pi\)
0.763998 0.645218i \(-0.223234\pi\)
\(390\) 1.08561e21 + 2.14122e20i 2.02842 + 0.400077i
\(391\) 1.36080e20i 0.249103i
\(392\) 1.61515e20 + 1.06794e20i 0.289684 + 0.191539i
\(393\) −7.35525e20 −1.29258
\(394\) 8.35435e19 4.23571e20i 0.143861 0.729384i
\(395\) 1.01965e20 0.172058
\(396\) 7.35328e18 + 3.01807e18i 0.0121596 + 0.00499078i
\(397\) 5.08193e20i 0.823578i 0.911279 + 0.411789i \(0.135096\pi\)
−0.911279 + 0.411789i \(0.864904\pi\)
\(398\) 1.48343e20 7.52108e20i 0.235614 1.19458i
\(399\) 7.78254e20i 1.21154i
\(400\) −1.02876e21 1.01557e21i −1.56977 1.54964i
\(401\) 6.93111e20 1.03669 0.518344 0.855172i \(-0.326549\pi\)
0.518344 + 0.855172i \(0.326549\pi\)
\(402\) −1.04066e21 2.05256e20i −1.52581 0.300945i
\(403\) 2.35929e20 0.339110
\(404\) −2.49605e20 + 6.08143e20i −0.351725 + 0.856948i
\(405\) 1.13406e21i 1.56674i
\(406\) 8.89460e20 + 1.75433e20i 1.20481 + 0.237632i
\(407\) 6.09022e19i 0.0808869i
\(408\) 1.54068e20 + 1.01870e20i 0.200646 + 0.132668i
\(409\) −1.79393e20 −0.229097 −0.114548 0.993418i \(-0.536542\pi\)
−0.114548 + 0.993418i \(0.536542\pi\)
\(410\) 6.51677e19 3.30405e20i 0.0816134 0.413786i
\(411\) 6.28616e19 0.0772060
\(412\) −6.13031e20 + 1.49360e21i −0.738422 + 1.79910i
\(413\) 1.62810e20i 0.192344i
\(414\) 1.83043e19 9.28042e19i 0.0212105 0.107539i
\(415\) 2.23092e20i 0.253571i
\(416\) −9.09046e20 + 6.18068e20i −1.01354 + 0.689112i
\(417\) −3.06545e20 −0.335278
\(418\) −1.70280e20 3.35853e19i −0.182706 0.0360362i
\(419\) 1.13823e21 1.19817 0.599086 0.800685i \(-0.295531\pi\)
0.599086 + 0.800685i \(0.295531\pi\)
\(420\) −1.22079e21 5.01061e20i −1.26080 0.517483i
\(421\) 1.54426e21i 1.56482i −0.622765 0.782409i \(-0.713991\pi\)
0.622765 0.782409i \(-0.286009\pi\)
\(422\) 6.94923e20 + 1.37064e20i 0.690935 + 0.136277i
\(423\) 7.76305e19i 0.0757372i
\(424\) −1.78383e20 + 2.69786e20i −0.170776 + 0.258281i
\(425\) −5.99436e20 −0.563160
\(426\) −6.75092e19 + 3.42276e20i −0.0622424 + 0.315573i
\(427\) −1.60939e21 −1.45626
\(428\) 6.09598e20 + 2.50203e20i 0.541369 + 0.222199i
\(429\) 1.54997e20i 0.135103i
\(430\) −3.28119e20 + 1.66359e21i −0.280727 + 1.42331i
\(431\) 7.13757e20i 0.599421i −0.954030 0.299710i \(-0.903110\pi\)
0.954030 0.299710i \(-0.0968901\pi\)
\(432\) −9.04691e20 8.93091e20i −0.745813 0.736251i
\(433\) −5.31329e20 −0.429992 −0.214996 0.976615i \(-0.568974\pi\)
−0.214996 + 0.976615i \(0.568974\pi\)
\(434\) −2.76046e20 5.44462e19i −0.219312 0.0432563i
\(435\) 3.28736e21 2.56409
\(436\) 4.32268e20 1.05318e21i 0.331025 0.806515i
\(437\) 2.06546e21i 1.55298i
\(438\) 2.81020e20 + 5.54272e19i 0.207465 + 0.0409195i
\(439\) 6.79982e20i 0.492926i 0.969152 + 0.246463i \(0.0792683\pi\)
−0.969152 + 0.246463i \(0.920732\pi\)
\(440\) −1.62314e20 + 2.45483e20i −0.115541 + 0.174743i
\(441\) −5.58119e19 −0.0390138
\(442\) −8.82055e19 + 4.47208e20i −0.0605505 + 0.306995i
\(443\) 9.44712e20 0.636898 0.318449 0.947940i \(-0.396838\pi\)
0.318449 + 0.947940i \(0.396838\pi\)
\(444\) 3.73523e20 9.10057e20i 0.247317 0.602567i
\(445\) 2.07344e21i 1.34838i
\(446\) 4.11821e20 2.08796e21i 0.263045 1.33366i
\(447\) 7.30253e20i 0.458155i
\(448\) 1.20625e21 5.13379e20i 0.743385 0.316384i
\(449\) 1.93362e21 1.17058 0.585288 0.810825i \(-0.300981\pi\)
0.585288 + 0.810825i \(0.300981\pi\)
\(450\) 4.08806e20 + 8.06312e19i 0.243118 + 0.0479516i
\(451\) −4.71732e19 −0.0275603
\(452\) −1.28190e21 5.26142e20i −0.735778 0.301992i
\(453\) 2.09004e21i 1.17861i
\(454\) −2.50769e21 4.94607e20i −1.38940 0.274040i
\(455\) 3.25669e21i 1.77290i
\(456\) 2.33850e21 + 1.54622e21i 1.25089 + 0.827088i
\(457\) −7.52884e19 −0.0395729 −0.0197865 0.999804i \(-0.506299\pi\)
−0.0197865 + 0.999804i \(0.506299\pi\)
\(458\) 2.49480e18 1.26488e19i 0.00128858 0.00653321i
\(459\) −5.27142e20 −0.267563
\(460\) 3.23995e21 + 1.32980e21i 1.61613 + 0.663322i
\(461\) 2.80291e21i 1.37405i 0.726636 + 0.687023i \(0.241083\pi\)
−0.726636 + 0.687023i \(0.758917\pi\)
\(462\) −3.57693e19 + 1.81353e20i −0.0172335 + 0.0873752i
\(463\) 1.79913e21i 0.851950i 0.904735 + 0.425975i \(0.140069\pi\)
−0.904735 + 0.425975i \(0.859931\pi\)
\(464\) −2.29430e21 + 2.32410e21i −1.06784 + 1.08171i
\(465\) −1.02024e21 −0.466744
\(466\) 1.68779e21 + 3.32894e20i 0.758983 + 0.149699i
\(467\) −2.66105e21 −1.17630 −0.588150 0.808752i \(-0.700143\pi\)
−0.588150 + 0.808752i \(0.700143\pi\)
\(468\) 1.20309e20 2.93124e20i 0.0522797 0.127375i
\(469\) 3.12184e21i 1.33361i
\(470\) −2.81991e21 5.56188e20i −1.18428 0.233582i
\(471\) 9.34061e20i 0.385663i
\(472\) −4.89210e20 3.23467e20i −0.198591 0.131309i
\(473\) 2.37517e20 0.0947995
\(474\) −4.46433e19 + 2.26344e20i −0.0175198 + 0.0888266i
\(475\) −9.09844e21 −3.51090
\(476\) 2.06407e20 5.02895e20i 0.0783195 0.190819i
\(477\) 9.32254e19i 0.0347846i
\(478\) 8.01238e19 4.06233e20i 0.0293994 0.149057i
\(479\) 3.29728e21i 1.18979i 0.803802 + 0.594897i \(0.202807\pi\)
−0.803802 + 0.594897i \(0.797193\pi\)
\(480\) 3.93103e21 2.67274e21i 1.39501 0.948478i
\(481\) 2.42775e21 0.847310
\(482\) 2.47987e21 + 4.89120e20i 0.851242 + 0.167896i
\(483\) 2.19977e21 0.742679
\(484\) −2.74770e21 1.12776e21i −0.912445 0.374503i
\(485\) 5.55131e21i 1.81327i
\(486\) 6.82696e20 + 1.34652e20i 0.219350 + 0.0432637i
\(487\) 3.78361e21i 1.19585i 0.801554 + 0.597923i \(0.204007\pi\)
−0.801554 + 0.597923i \(0.795993\pi\)
\(488\) 3.19751e21 4.83590e21i 0.994152 1.50355i
\(489\) −9.49859e19 −0.0290528
\(490\) 3.99868e20 2.02736e21i 0.120323 0.610045i
\(491\) −1.52093e21 −0.450254 −0.225127 0.974329i \(-0.572280\pi\)
−0.225127 + 0.974329i \(0.572280\pi\)
\(492\) 7.04906e20 + 2.89321e20i 0.205310 + 0.0842673i
\(493\) 1.35420e21i 0.388067i
\(494\) −1.33881e21 + 6.78787e21i −0.377489 + 1.91389i
\(495\) 8.48275e19i 0.0235340i
\(496\) 7.12042e20 7.21290e20i 0.194380 0.196905i
\(497\) 1.02678e21 0.275821
\(498\) −4.95224e20 9.76759e19i −0.130908 0.0258198i
\(499\) −2.42572e20 −0.0631010 −0.0315505 0.999502i \(-0.510044\pi\)
−0.0315505 + 0.999502i \(0.510044\pi\)
\(500\) −3.20218e21 + 7.80185e21i −0.819759 + 1.99727i
\(501\) 2.98411e20i 0.0751819i
\(502\) −3.99152e21 7.87272e20i −0.989712 0.195207i
\(503\) 4.58027e21i 1.11776i −0.829250 0.558878i \(-0.811232\pi\)
0.829250 0.558878i \(-0.188768\pi\)
\(504\) −2.08412e20 + 3.15202e20i −0.0500585 + 0.0757084i
\(505\) 7.01554e21 1.65855
\(506\) 9.49307e19 4.81305e20i 0.0220903 0.112000i
\(507\) −2.06539e21 −0.473085
\(508\) 1.57444e21 3.83599e21i 0.354990 0.864903i
\(509\) 4.31209e21i 0.957074i −0.878067 0.478537i \(-0.841167\pi\)
0.878067 0.478537i \(-0.158833\pi\)
\(510\) 3.81432e20 1.93388e21i 0.0833403 0.422541i
\(511\) 8.43022e20i 0.181331i
\(512\) −8.53952e20 + 4.64451e21i −0.180831 + 0.983514i
\(513\) −8.00113e21 −1.66806
\(514\) −4.01600e21 7.92099e20i −0.824306 0.162583i
\(515\) 1.72302e22 3.48202
\(516\) −3.54920e21 1.45673e21i −0.706209 0.289856i
\(517\) 4.02611e20i 0.0788789i
\(518\) −2.84055e21 5.60259e20i −0.547980 0.108081i
\(519\) 3.30690e21i 0.628177i
\(520\) 9.78571e21 + 6.47032e21i 1.83048 + 1.21032i
\(521\) 6.59580e21 1.21497 0.607485 0.794331i \(-0.292178\pi\)
0.607485 + 0.794331i \(0.292178\pi\)
\(522\) 1.82155e20 9.23541e20i 0.0330429 0.167530i
\(523\) −1.51693e20 −0.0270990 −0.0135495 0.999908i \(-0.504313\pi\)
−0.0135495 + 0.999908i \(0.504313\pi\)
\(524\) −7.21402e21 2.96091e21i −1.26919 0.520925i
\(525\) 9.69008e21i 1.67901i
\(526\) 7.62681e20 3.86684e21i 0.130154 0.659889i
\(527\) 4.20279e20i 0.0706403i
\(528\) −4.73863e20 4.67787e20i −0.0784479 0.0774420i
\(529\) 2.94471e20 0.0480173
\(530\) 3.38640e21 + 6.67919e20i 0.543915 + 0.107280i
\(531\) 1.69048e20 0.0267457
\(532\) 3.13292e21 7.63310e21i 0.488266 1.18962i
\(533\) 1.88047e21i 0.288701i
\(534\) 4.60266e21 + 9.07810e20i 0.696111 + 0.137298i
\(535\) 7.03232e21i 1.04778i
\(536\) −9.38052e21 6.20241e21i −1.37692 0.910421i
\(537\) −1.02877e22 −1.48773
\(538\) −1.72351e21 + 8.73834e21i −0.245559 + 1.24500i
\(539\) −2.89454e20 −0.0406321
\(540\) −5.15135e21 + 1.25508e22i −0.712477 + 1.73589i
\(541\) 9.66048e21i 1.31650i −0.752800 0.658250i \(-0.771297\pi\)
0.752800 0.658250i \(-0.228703\pi\)
\(542\) 5.48848e20 2.78270e21i 0.0736983 0.373655i
\(543\) 5.17751e21i 0.685050i
\(544\) 1.10101e21 + 1.61935e21i 0.143549 + 0.211130i
\(545\) −1.21495e22 −1.56095
\(546\) 7.22926e21 + 1.42587e21i 0.915278 + 0.180526i
\(547\) 1.48555e21 0.185348 0.0926740 0.995697i \(-0.470459\pi\)
0.0926740 + 0.995697i \(0.470459\pi\)
\(548\) 6.16546e20 + 2.53054e20i 0.0758090 + 0.0311150i
\(549\) 1.67106e21i 0.202494i
\(550\) 2.12017e21 + 4.18173e20i 0.253203 + 0.0499407i
\(551\) 2.05545e22i 2.41932i
\(552\) −4.37046e21 + 6.60988e21i −0.507008 + 0.766798i
\(553\) 6.79003e20 0.0776373
\(554\) −5.11417e20 + 2.59292e21i −0.0576364 + 0.292220i
\(555\) −1.04984e22 −1.16622
\(556\) −3.00659e21 1.23402e21i −0.329212 0.135121i
\(557\) 9.75638e21i 1.05305i −0.850161 0.526523i \(-0.823495\pi\)
0.850161 0.526523i \(-0.176505\pi\)
\(558\) −5.65324e19 + 2.86623e20i −0.00601483 + 0.0304956i
\(559\) 9.46815e21i 0.993049i
\(560\) −9.95646e21 9.82880e21i −1.02944 1.01624i
\(561\) −2.76109e20 −0.0281434
\(562\) 8.61956e21 + 1.70009e21i 0.866153 + 0.170837i
\(563\) 1.86765e22 1.85025 0.925123 0.379668i \(-0.123962\pi\)
0.925123 + 0.379668i \(0.123962\pi\)
\(564\) 2.46927e21 6.01618e21i 0.241177 0.587608i
\(565\) 1.47880e22i 1.42404i
\(566\) 9.63901e21 + 1.90116e21i 0.915168 + 0.180504i
\(567\) 7.55188e21i 0.706953i
\(568\) −2.03999e21 + 3.08528e21i −0.188296 + 0.284779i
\(569\) −1.04130e21 −0.0947711 −0.0473856 0.998877i \(-0.515089\pi\)
−0.0473856 + 0.998877i \(0.515089\pi\)
\(570\) 5.78950e21 2.93531e22i 0.519567 2.63424i
\(571\) −1.77834e22 −1.57371 −0.786856 0.617137i \(-0.788293\pi\)
−0.786856 + 0.617137i \(0.788293\pi\)
\(572\) 6.23954e20 1.52021e21i 0.0544483 0.132659i
\(573\) 8.72233e21i 0.750577i
\(574\) 4.33962e20 2.20022e21i 0.0368262 0.186711i
\(575\) 2.57172e22i 2.15219i
\(576\) −5.33050e20 1.25247e21i −0.0439935 0.103368i
\(577\) 8.34008e21 0.678834 0.339417 0.940636i \(-0.389770\pi\)
0.339417 + 0.940636i \(0.389770\pi\)
\(578\) −1.14252e22 2.25345e21i −0.917148 0.180895i
\(579\) 1.38385e22 1.09562
\(580\) 3.22424e22 + 1.32335e22i 2.51770 + 1.03336i
\(581\) 1.48560e21i 0.114418i
\(582\) 1.23229e22 + 2.43052e21i 0.936115 + 0.184636i
\(583\) 4.83490e20i 0.0362275i
\(584\) 2.53311e21 + 1.67490e21i 0.187220 + 0.123790i
\(585\) −3.38148e21 −0.246524
\(586\) −1.33365e21 + 6.76171e21i −0.0959096 + 0.486268i
\(587\) −9.67063e21 −0.686041 −0.343020 0.939328i \(-0.611450\pi\)
−0.343020 + 0.939328i \(0.611450\pi\)
\(588\) 4.32529e21 + 1.77527e21i 0.302689 + 0.124235i
\(589\) 6.37913e21i 0.440392i
\(590\) −1.21115e21 + 6.14064e21i −0.0824866 + 0.418213i
\(591\) 1.04248e22i 0.700434i
\(592\) 7.32702e21 7.42218e21i 0.485684 0.491992i
\(593\) −2.33346e22 −1.52603 −0.763016 0.646379i \(-0.776282\pi\)
−0.763016 + 0.646379i \(0.776282\pi\)
\(594\) 1.86447e21 + 3.67740e20i 0.120299 + 0.0237273i
\(595\) −5.80139e21 −0.369315
\(596\) −2.93969e21 + 7.16231e21i −0.184642 + 0.449866i
\(597\) 1.85106e22i 1.14716i
\(598\) −1.91863e22 3.78422e21i −1.17322 0.231402i
\(599\) 2.00138e22i 1.20758i 0.797144 + 0.603789i \(0.206343\pi\)
−0.797144 + 0.603789i \(0.793657\pi\)
\(600\) −2.91168e22 1.92520e22i −1.73354 1.14622i
\(601\) 1.72003e22 1.01051 0.505255 0.862970i \(-0.331398\pi\)
0.505255 + 0.862970i \(0.331398\pi\)
\(602\) −2.18500e21 + 1.10781e22i −0.126672 + 0.642234i
\(603\) 3.24146e21 0.185440
\(604\) 8.41362e21 2.04991e22i 0.474993 1.15728i
\(605\) 3.16975e22i 1.76597i
\(606\) −3.07160e21 + 1.55732e22i −0.168882 + 0.856243i
\(607\) 3.46685e22i 1.88116i 0.339570 + 0.940581i \(0.389718\pi\)
−0.339570 + 0.940581i \(0.610282\pi\)
\(608\) 1.67115e22 + 2.45791e22i 0.894927 + 1.31625i
\(609\) 2.18911e22 1.15699
\(610\) −6.07009e22 1.19724e22i −3.16633 0.624515i
\(611\) 1.60493e22 0.826277
\(612\) −5.22164e20 2.14316e20i −0.0265336 0.0108904i
\(613\) 2.69106e22i 1.34971i −0.737952 0.674853i \(-0.764207\pi\)
0.737952 0.674853i \(-0.235793\pi\)
\(614\) 7.96282e21 + 1.57055e21i 0.394203 + 0.0777510i
\(615\) 8.13180e21i 0.397361i
\(616\) −1.08087e21 + 1.63471e21i −0.0521350 + 0.0788489i
\(617\) −1.76570e21 −0.0840689 −0.0420345 0.999116i \(-0.513384\pi\)
−0.0420345 + 0.999116i \(0.513384\pi\)
\(618\) −7.54385e21 + 3.82478e22i −0.354556 + 1.79763i
\(619\) −1.74733e22 −0.810682 −0.405341 0.914166i \(-0.632847\pi\)
−0.405341 + 0.914166i \(0.632847\pi\)
\(620\) −1.00065e22 4.10706e21i −0.458299 0.188104i
\(621\) 2.26156e22i 1.02253i
\(622\) 5.50953e21 2.79337e22i 0.245918 1.24682i
\(623\) 1.38074e22i 0.608424i
\(624\) −1.86474e22 + 1.88896e22i −0.811225 + 0.821762i
\(625\) 3.86443e22 1.65976
\(626\) −6.50790e21 1.28359e21i −0.275960 0.0544293i
\(627\) −4.19087e21 −0.175454
\(628\) 3.76014e21 9.16125e21i 0.155427 0.378685i
\(629\) 4.32473e21i 0.176504i
\(630\) 3.95645e21 + 7.80355e20i 0.159434 + 0.0314462i
\(631\) 1.69094e22i 0.672810i −0.941717 0.336405i \(-0.890789\pi\)
0.941717 0.336405i \(-0.109211\pi\)
\(632\) −1.34903e21 + 2.04027e21i −0.0530010 + 0.0801587i
\(633\) 1.71032e22 0.663510
\(634\) −4.93398e21 + 2.50156e22i −0.189009 + 0.958290i
\(635\) −4.42520e22 −1.67395
\(636\) −2.96532e21 + 7.22475e21i −0.110768 + 0.269877i
\(637\) 1.15385e22i 0.425632i
\(638\) 9.44703e20 4.78971e21i 0.0344136 0.174479i
\(639\) 1.06613e21i 0.0383532i
\(640\) 4.93149e22 1.03895e22i 1.75202 0.369111i
\(641\) 1.67907e22 0.589119 0.294560 0.955633i \(-0.404827\pi\)
0.294560 + 0.955633i \(0.404827\pi\)
\(642\) 1.56105e22 + 3.07895e21i 0.540924 + 0.106690i
\(643\) 1.76394e22 0.603665 0.301833 0.953361i \(-0.402402\pi\)
0.301833 + 0.953361i \(0.402402\pi\)
\(644\) 2.15753e22 + 8.85536e21i 0.729241 + 0.299309i
\(645\) 4.09436e22i 1.36681i
\(646\) 1.20918e22 + 2.38493e21i 0.398684 + 0.0786349i
\(647\) 5.24930e22i 1.70949i −0.519046 0.854747i \(-0.673713\pi\)
0.519046 0.854747i \(-0.326287\pi\)
\(648\) −2.26919e22 1.50039e22i −0.729912 0.482619i
\(649\) 8.76724e20 0.0278551
\(650\) 1.66696e22 8.45162e22i 0.523141 2.65236i
\(651\) −6.79394e21 −0.210607
\(652\) −9.31620e20 3.82373e20i −0.0285271 0.0117086i
\(653\) 1.05339e22i 0.318628i 0.987228 + 0.159314i \(0.0509283\pi\)
−0.987228 + 0.159314i \(0.949072\pi\)
\(654\) 5.31941e21 2.69698e22i 0.158943 0.805852i
\(655\) 8.32209e22i 2.45642i
\(656\) 5.74902e21 + 5.67531e21i 0.167635 + 0.165485i
\(657\) −8.75324e20 −0.0252142
\(658\) −1.87782e22 3.70374e21i −0.534377 0.105398i
\(659\) −2.04422e21 −0.0574704 −0.0287352 0.999587i \(-0.509148\pi\)
−0.0287352 + 0.999587i \(0.509148\pi\)
\(660\) −2.69820e21 + 6.57393e21i −0.0749415 + 0.182589i
\(661\) 2.82087e22i 0.774055i −0.922068 0.387028i \(-0.873502\pi\)
0.922068 0.387028i \(-0.126498\pi\)
\(662\) 3.05548e22 + 6.02650e21i 0.828352 + 0.163381i
\(663\) 1.10065e22i 0.294810i
\(664\) −4.46395e21 2.95157e21i −0.118134 0.0781102i
\(665\) −8.80555e22 −2.30241
\(666\) −5.81727e20 + 2.94939e21i −0.0150288 + 0.0761972i
\(667\) −5.80983e22 −1.48305
\(668\) −1.20128e21 + 2.92681e21i −0.0302992 + 0.0738215i
\(669\) 5.13882e22i 1.28072i
\(670\) −2.32237e22 + 1.17746e23i −0.571916 + 2.89965i
\(671\) 8.66653e21i 0.210894i
\(672\) 2.61774e22 1.77982e22i 0.629465 0.427979i
\(673\) −4.51475e21 −0.107279 −0.0536393 0.998560i \(-0.517082\pi\)
−0.0536393 + 0.998560i \(0.517082\pi\)
\(674\) 5.78835e22 + 1.14167e22i 1.35917 + 0.268078i
\(675\) 9.96226e22 2.31168
\(676\) −2.02573e22 8.31440e21i −0.464525 0.190659i
\(677\) 4.53332e22i 1.02732i 0.857993 + 0.513662i \(0.171711\pi\)
−0.857993 + 0.513662i \(0.828289\pi\)
\(678\) −3.28267e22 6.47461e21i −0.735173 0.145003i
\(679\) 3.69671e22i 0.818195i
\(680\) 1.15261e22 1.74320e22i 0.252122 0.381309i
\(681\) −6.17184e22 −1.33425
\(682\) −2.93191e20 + 1.48650e21i −0.00626434 + 0.0317606i
\(683\) 7.32299e22 1.54640 0.773202 0.634160i \(-0.218654\pi\)
0.773202 + 0.634160i \(0.218654\pi\)
\(684\) −7.92558e21 3.25297e21i −0.165418 0.0678939i
\(685\) 7.11248e21i 0.146722i
\(686\) 1.03303e22 5.23754e22i 0.210630 1.06791i
\(687\) 3.11308e20i 0.00627389i
\(688\) −2.89464e22 2.85752e22i −0.576616 0.569222i
\(689\) −1.92734e22 −0.379493
\(690\) 8.29682e22 + 1.63643e22i 1.61480 + 0.318497i
\(691\) −8.01612e22 −1.54220 −0.771099 0.636715i \(-0.780293\pi\)
−0.771099 + 0.636715i \(0.780293\pi\)
\(692\) 1.33122e22 3.24340e22i 0.253163 0.616811i
\(693\) 5.64879e20i 0.0106192i
\(694\) −8.45127e22 1.66689e22i −1.57053 0.309765i
\(695\) 3.46840e22i 0.637163i
\(696\) −4.34927e22 + 6.57783e22i −0.789845 + 1.19456i
\(697\) 3.34982e21 0.0601394
\(698\) −2.58187e21 + 1.30903e22i −0.0458239 + 0.232330i
\(699\) 4.15394e22 0.728857
\(700\) −3.90082e22 + 9.50402e22i −0.676661 + 1.64863i
\(701\) 8.15142e22i 1.39794i 0.715150 + 0.698971i \(0.246358\pi\)
−0.715150 + 0.698971i \(0.753642\pi\)
\(702\) 1.46592e22 7.43232e22i 0.248550 1.26016i
\(703\) 6.56422e22i 1.10037i
\(704\) −2.76453e21 6.49562e21i −0.0458184 0.107656i
\(705\) −6.94027e22 −1.13727
\(706\) −1.91890e21 3.78476e20i −0.0310895 0.00613198i
\(707\) 4.67175e22 0.748384
\(708\) −1.31008e22 5.37709e21i −0.207507 0.0851689i
\(709\) 7.65528e22i 1.19892i 0.800403 + 0.599462i \(0.204619\pi\)
−0.800403 + 0.599462i \(0.795381\pi\)
\(710\) 3.87269e22 + 7.63833e21i 0.599716 + 0.118286i
\(711\) 7.05020e20i 0.0107956i
\(712\) 4.14883e22 + 2.74321e22i 0.628183 + 0.415355i
\(713\) 1.80309e22 0.269962
\(714\) 2.54001e21 1.28780e22i 0.0376054 0.190662i
\(715\) −1.75372e22 −0.256750
\(716\) −1.00902e23 4.14141e22i −1.46081 0.599575i
\(717\) 9.99807e21i 0.143141i
\(718\) −6.54496e21 + 3.31834e22i −0.0926641 + 0.469813i
\(719\) 1.14958e21i 0.0160956i 0.999968 + 0.00804779i \(0.00256172\pi\)
−0.999968 + 0.00804779i \(0.997438\pi\)
\(720\) −1.02054e22 + 1.03380e22i −0.141309 + 0.143145i
\(721\) 1.14738e23 1.57118
\(722\) 1.11087e23 + 2.19104e22i 1.50441 + 0.296725i
\(723\) 6.10337e22 0.817454
\(724\) −2.08425e22 + 5.07809e22i −0.276084 + 0.672655i
\(725\) 2.55925e23i 3.35281i
\(726\) −7.03627e22 1.38781e22i −0.911695 0.179819i
\(727\) 6.79227e22i 0.870442i −0.900324 0.435221i \(-0.856670\pi\)
0.900324 0.435221i \(-0.143330\pi\)
\(728\) 6.51645e22 + 4.30869e22i 0.825962 + 0.546127i
\(729\) 8.66010e22 1.08568
\(730\) 6.27131e21 3.17960e22i 0.0777635 0.394266i
\(731\) −1.68663e22 −0.206863
\(732\) 5.31532e22 1.29503e23i 0.644823 1.57106i
\(733\) 5.54834e22i 0.665781i −0.942966 0.332890i \(-0.891976\pi\)
0.942966 0.332890i \(-0.108024\pi\)
\(734\) 1.09952e22 5.57462e22i 0.130507 0.661678i
\(735\) 4.98966e22i 0.585831i
\(736\) −6.94740e22 + 4.72360e22i −0.806863 + 0.548593i
\(737\) 1.68110e22 0.193132
\(738\) −2.28452e21 4.50590e20i −0.0259624 0.00512071i
\(739\) 1.07018e23 1.20310 0.601548 0.798836i \(-0.294551\pi\)
0.601548 + 0.798836i \(0.294551\pi\)
\(740\) −1.02968e23 4.22622e22i −1.14512 0.470001i
\(741\) 1.67061e23i 1.83793i
\(742\) 2.25505e22 + 4.44778e21i 0.245429 + 0.0484074i
\(743\) 1.43921e23i 1.54958i 0.632217 + 0.774791i \(0.282145\pi\)
−0.632217 + 0.774791i \(0.717855\pi\)
\(744\) 1.34981e22 2.04144e22i 0.143776 0.217447i
\(745\) 8.26244e22 0.870679
\(746\) −2.71969e22 + 1.37890e23i −0.283537 + 1.43755i
\(747\) 1.54253e21 0.0159099
\(748\) −2.70807e21 1.11150e21i −0.0276342 0.0113422i
\(749\) 4.68293e22i 0.472785i
\(750\) −3.94055e22 + 1.99788e23i −0.393610 + 1.99563i
\(751\) 8.40625e22i 0.830774i 0.909645 + 0.415387i \(0.136354\pi\)
−0.909645 + 0.415387i \(0.863646\pi\)
\(752\) 4.84372e22 4.90663e22i 0.473627 0.479779i
\(753\) −9.82379e22 −0.950428
\(754\) −1.90932e23 3.76587e22i −1.82771 0.360491i
\(755\) −2.36478e23 −2.23983
\(756\) −3.43036e22 + 8.35779e22i −0.321489 + 0.783281i
\(757\) 3.71747e22i 0.344731i 0.985033 + 0.172366i \(0.0551410\pi\)
−0.985033 + 0.172366i \(0.944859\pi\)
\(758\) −4.56162e22 8.99715e21i −0.418567 0.0825565i
\(759\) 1.18457e22i 0.107554i
\(760\) 1.74947e23 2.64589e23i 1.57180 2.37719i
\(761\) −1.53461e23 −1.36434 −0.682168 0.731195i \(-0.738963\pi\)
−0.682168 + 0.731195i \(0.738963\pi\)
\(762\) 1.93747e22 9.82313e22i 0.170450 0.864192i
\(763\) −8.09057e22 −0.704341
\(764\) −3.51124e22 + 8.55485e22i −0.302492 + 0.736997i
\(765\) 6.02369e21i 0.0513536i
\(766\) 9.61807e21 4.87643e22i 0.0811442 0.411407i
\(767\) 3.49489e22i 0.291790i
\(768\) 1.47147e21 + 1.14019e23i 0.0121580 + 0.942078i
\(769\) 9.31513e22 0.761690 0.380845 0.924639i \(-0.375633\pi\)
0.380845 + 0.924639i \(0.375633\pi\)
\(770\) 2.05191e22 + 4.04711e21i 0.166048 + 0.0327506i
\(771\) −9.88403e22 −0.791587
\(772\) 1.35728e23 + 5.57080e22i 1.07580 + 0.441550i
\(773\) 1.15903e23i 0.909196i 0.890697 + 0.454598i \(0.150217\pi\)
−0.890697 + 0.454598i \(0.849783\pi\)
\(774\) 1.15026e22 + 2.26872e21i 0.0893033 + 0.0176138i
\(775\) 7.94269e22i 0.610315i
\(776\) 1.11079e23 + 7.34454e22i 0.844767 + 0.558561i
\(777\) −6.99107e22 −0.526230
\(778\) 3.35175e22 1.69936e23i 0.249710 1.26605i
\(779\) 5.08447e22 0.374926
\(780\) 2.62057e23 + 1.07558e23i 1.91266 + 0.785031i
\(781\) 5.52919e21i 0.0399442i
\(782\) −6.74112e21 + 3.41780e22i −0.0482035 + 0.244395i
\(783\) 2.25059e23i 1.59295i
\(784\) 3.52759e22 + 3.48236e22i 0.247144 + 0.243975i
\(785\) −1.05684e23 −0.732914
\(786\) −1.84735e23 3.64365e22i −1.26815 0.250124i
\(787\) −2.21417e23 −1.50457 −0.752285 0.658838i \(-0.771048\pi\)
−0.752285 + 0.658838i \(0.771048\pi\)
\(788\) 4.19658e22 1.02246e23i 0.282283 0.687760i
\(789\) 9.51694e22i 0.633696i
\(790\) 2.56097e22 + 5.05116e21i 0.168806 + 0.0332947i
\(791\) 9.84757e22i 0.642565i
\(792\) 1.69735e21 + 1.12229e21i 0.0109640 + 0.00724943i
\(793\) 3.45474e23 2.20917
\(794\) −2.51749e22 + 1.27638e23i −0.159369 + 0.808011i
\(795\) 8.33448e22 0.522326
\(796\) 7.45159e22 1.81552e23i 0.462322 1.12641i
\(797\) 1.86468e23i 1.14535i 0.819783 + 0.572674i \(0.194094\pi\)
−0.819783 + 0.572674i \(0.805906\pi\)
\(798\) 3.85532e22 1.95467e23i 0.234443 1.18864i
\(799\) 2.85898e22i 0.172122i
\(800\) −2.08076e23 3.06036e23i −1.24023 1.82411i
\(801\) −1.43364e22 −0.0846019
\(802\) 1.74083e23 + 3.43354e22i 1.01709 + 0.200607i
\(803\) −4.53964e21 −0.0262602
\(804\) −2.51206e23 1.03105e23i −1.43874 0.590514i
\(805\) 2.48893e23i 1.41139i
\(806\) 5.92562e22 + 1.16875e22i 0.332701 + 0.0656206i
\(807\) 2.15065e23i 1.19559i
\(808\) −9.28174e22 + 1.40377e23i −0.510903 + 0.772689i
\(809\) 3.28894e23 1.79254 0.896268 0.443514i \(-0.146268\pi\)
0.896268 + 0.443514i \(0.146268\pi\)
\(810\) −5.61791e22 + 2.84832e23i −0.303176 + 1.53712i
\(811\) 1.57001e23 0.838951 0.419476 0.907767i \(-0.362214\pi\)
0.419476 + 0.907767i \(0.362214\pi\)
\(812\) 2.14707e23 + 8.81242e22i 1.13605 + 0.466280i
\(813\) 6.84867e22i 0.358824i
\(814\) −3.01698e21 + 1.52963e22i −0.0156523 + 0.0793580i
\(815\) 1.07472e22i 0.0552120i
\(816\) 3.36495e22 + 3.32180e22i 0.171182 + 0.168987i
\(817\) −2.56003e23 −1.28964
\(818\) −4.50566e22 8.88678e21i −0.224767 0.0443320i
\(819\) −2.25178e22 −0.111238
\(820\) 3.27352e22 7.97566e22i 0.160142 0.390172i
\(821\) 1.32878e23i 0.643735i −0.946785 0.321868i \(-0.895689\pi\)
0.946785 0.321868i \(-0.104311\pi\)
\(822\) 1.57884e22 + 3.11404e21i 0.0757467 + 0.0149400i
\(823\) 1.08398e23i 0.515018i −0.966276 0.257509i \(-0.917098\pi\)
0.966276 0.257509i \(-0.0829017\pi\)
\(824\) −2.27960e23 + 3.44766e23i −1.07261 + 1.62221i
\(825\) 5.21808e22 0.243153
\(826\) −8.06527e21 + 4.08915e22i −0.0372202 + 0.188709i
\(827\) −9.67193e22 −0.442048 −0.221024 0.975268i \(-0.570940\pi\)
−0.221024 + 0.975268i \(0.570940\pi\)
\(828\) 9.19467e21 2.24020e22i 0.0416192 0.101402i
\(829\) 1.48169e22i 0.0664234i −0.999448 0.0332117i \(-0.989426\pi\)
0.999448 0.0332117i \(-0.0105736\pi\)
\(830\) −1.10515e22 + 5.60321e22i −0.0490680 + 0.248778i
\(831\) 6.38160e22i 0.280622i
\(832\) −2.58935e23 + 1.10202e23i −1.12773 + 0.479959i
\(833\) 2.05544e22 0.0886636
\(834\) −7.69921e22 1.51856e22i −0.328941 0.0648790i
\(835\) 3.37637e22 0.142876
\(836\) −4.11040e22 1.68707e22i −0.172280 0.0707102i
\(837\) 6.98477e22i 0.289967i
\(838\) 2.85880e23 + 5.63858e22i 1.17552 + 0.231856i
\(839\) 3.62220e23i 1.47529i −0.675191 0.737643i \(-0.735939\pi\)
0.675191 0.737643i \(-0.264061\pi\)
\(840\) −2.81794e23 1.86323e23i −1.13684 0.751678i
\(841\) −3.27919e23 −1.31038
\(842\) 7.64997e22 3.87859e23i 0.302805 1.53524i
\(843\) 2.12142e23 0.831774
\(844\) 1.67748e23 + 6.88503e22i 0.651505 + 0.267403i
\(845\) 2.33689e23i 0.899051i
\(846\) −3.84566e21 + 1.94978e22i −0.0146558 + 0.0743057i
\(847\) 2.11079e23i 0.796851i
\(848\) −5.81676e22 + 5.89231e22i −0.217528 + 0.220353i
\(849\) 2.37232e23 0.878843
\(850\) −1.50555e23 2.96949e22i −0.552515 0.108976i
\(851\) 1.85541e23 0.674533
\(852\) −3.39114e22 + 8.26223e22i −0.122132 + 0.297564i
\(853\) 3.18100e23i 1.13494i 0.823395 + 0.567469i \(0.192077\pi\)
−0.823395 + 0.567469i \(0.807923\pi\)
\(854\) −4.04217e23 7.97262e22i −1.42874 0.281798i
\(855\) 9.14295e22i 0.320153i
\(856\) 1.40713e23 + 9.30395e22i 0.488139 + 0.322758i
\(857\) −3.38794e23 −1.16436 −0.582182 0.813059i \(-0.697801\pi\)
−0.582182 + 0.813059i \(0.697801\pi\)
\(858\) 7.67826e21 3.89293e22i 0.0261436 0.132550i
\(859\) 5.84793e23 1.97268 0.986341 0.164717i \(-0.0526711\pi\)
0.986341 + 0.164717i \(0.0526711\pi\)
\(860\) −1.64822e23 + 4.01575e23i −0.550842 + 1.34208i
\(861\) 5.41509e22i 0.179300i
\(862\) 3.53581e22 1.79268e23i 0.115993 0.588091i
\(863\) 1.38504e23i 0.450170i −0.974339 0.225085i \(-0.927734\pi\)
0.974339 0.225085i \(-0.0722659\pi\)
\(864\) −1.82981e23 2.69126e23i −0.589246 0.866655i
\(865\) −3.74159e23 −1.19379
\(866\) −1.33449e23 2.63210e22i −0.421864 0.0832068i
\(867\) −2.81192e23 −0.880745
\(868\) −6.66349e22 2.73495e22i −0.206797 0.0848774i
\(869\) 3.65641e21i 0.0112434i
\(870\) 8.25658e23 + 1.62849e23i 2.51563 + 0.496172i
\(871\) 6.70138e23i 2.02311i
\(872\) 1.60742e23 2.43106e23i 0.480836 0.727215i
\(873\) −3.83835e22 −0.113771
\(874\) −1.02319e23 + 5.18765e23i −0.300514 + 1.52363i
\(875\) 5.99338e23 1.74425
\(876\) 6.78356e22 + 2.78424e22i 0.195625 + 0.0802922i
\(877\) 3.04222e23i 0.869348i −0.900588 0.434674i \(-0.856864\pi\)
0.900588 0.434674i \(-0.143136\pi\)
\(878\) −3.36850e22 + 1.70785e23i −0.0953851 + 0.483609i
\(879\) 1.66417e23i 0.466967i
\(880\) −5.29277e22 + 5.36152e22i −0.147171 + 0.149083i
\(881\) 1.55764e23 0.429201 0.214601 0.976702i \(-0.431155\pi\)
0.214601 + 0.976702i \(0.431155\pi\)
\(882\) −1.40178e22 2.76481e21i −0.0382764 0.00754948i
\(883\) −5.02093e23 −1.35862 −0.679310 0.733851i \(-0.737721\pi\)
−0.679310 + 0.733851i \(0.737721\pi\)
\(884\) −4.43076e22 + 1.07952e23i −0.118812 + 0.289475i
\(885\) 1.51131e23i 0.401613i
\(886\) 2.37275e23 + 4.67992e22i 0.624860 + 0.123245i
\(887\) 6.65140e22i 0.173590i 0.996226 + 0.0867948i \(0.0276625\pi\)
−0.996226 + 0.0867948i \(0.972338\pi\)
\(888\) 1.38897e23 2.10068e23i 0.359244 0.543320i
\(889\) −2.94681e23 −0.755331
\(890\) 1.02714e23 5.20767e23i 0.260922 1.32289i
\(891\) 4.06666e22 0.102380
\(892\) 2.06867e23 5.04015e23i 0.516146 1.25755i
\(893\) 4.33945e23i 1.07306i
\(894\) −3.61753e22 + 1.83411e23i −0.0886567 + 0.449496i
\(895\) 1.16400e24i 2.82729i
\(896\) 3.28395e23 6.91856e22i 0.790557 0.166553i
\(897\) −4.72205e23 −1.12666
\(898\) 4.85650e23 + 9.57876e22i 1.14845 + 0.226516i
\(899\) 1.79435e23 0.420561
\(900\) 9.86818e22 + 4.05029e22i 0.229244 + 0.0940905i
\(901\) 3.43331e22i 0.0790523i
\(902\) −1.18481e22 2.33687e21i −0.0270393 0.00533313i
\(903\) 2.72650e23i 0.616742i
\(904\) −2.95900e23 1.95649e23i −0.663433 0.438663i
\(905\) 5.85809e23 1.30187
\(906\) 1.03537e23 5.24937e23i 0.228070 1.15633i
\(907\) −1.68108e23 −0.367054 −0.183527 0.983015i \(-0.558751\pi\)
−0.183527 + 0.983015i \(0.558751\pi\)
\(908\) −6.05333e23 2.48452e23i −1.31011 0.537720i
\(909\) 4.85076e22i 0.104064i
\(910\) 1.61330e23 8.17955e23i 0.343071 1.73939i
\(911\) 5.30378e23i 1.11799i −0.829171 0.558996i \(-0.811187\pi\)
0.829171 0.558996i \(-0.188813\pi\)
\(912\) 5.10743e23 + 5.04194e23i 1.06720 + 1.05351i
\(913\) 7.99993e21 0.0165699
\(914\) −1.89095e22 3.72964e21i −0.0388250 0.00765768i
\(915\) −1.49395e24 −3.04066
\(916\) 1.25320e21 3.05331e21i 0.00252846 0.00616037i
\(917\) 5.54181e23i 1.10840i
\(918\) −1.32398e23 2.61136e22i −0.262506 0.0517756i
\(919\) 6.79014e23i 1.33461i −0.744784 0.667305i \(-0.767448\pi\)
0.744784 0.667305i \(-0.232552\pi\)
\(920\) 7.47875e23 + 4.94496e23i 1.45722 + 0.963518i
\(921\) 1.95978e23 0.378556
\(922\) −1.38851e23 + 7.03982e23i −0.265889 + 1.34807i
\(923\) −2.20410e23 −0.418425
\(924\) −1.79677e22 + 4.37768e22i −0.0338156 + 0.0823889i
\(925\) 8.17315e23i 1.52495i
\(926\) −8.91253e22 + 4.51871e23i −0.164859 + 0.835847i
\(927\) 1.19135e23i 0.218474i
\(928\) −6.91371e23 + 4.70069e23i −1.25698 + 0.854629i
\(929\) 9.06740e23 1.63440 0.817198 0.576357i \(-0.195526\pi\)
0.817198 + 0.576357i \(0.195526\pi\)
\(930\) −2.56245e23 5.05407e22i −0.457922 0.0903187i
\(931\) 3.11982e23 0.552754
\(932\) 4.07418e23 + 1.67220e23i 0.715670 + 0.293739i
\(933\) 6.87494e23i 1.19733i
\(934\) −6.68352e23 1.31823e23i −1.15407 0.227623i
\(935\) 3.12403e22i 0.0534838i
\(936\) 4.47378e22 6.76614e22i 0.0759396 0.114851i
\(937\) −9.57272e23 −1.61108 −0.805542 0.592538i \(-0.798126\pi\)
−0.805542 + 0.592538i \(0.798126\pi\)
\(938\) −1.54650e23 + 7.84086e23i −0.258064 + 1.30840i
\(939\) −1.60170e23 −0.265007
\(940\) −6.80700e23 2.79386e23i −1.11669 0.458334i
\(941\) 2.45725e23i 0.399698i −0.979827 0.199849i \(-0.935955\pi\)
0.979827 0.199849i \(-0.0640451\pi\)
\(942\) 4.62715e22 2.34600e23i 0.0746288 0.378373i
\(943\) 1.43715e23i 0.229831i
\(944\) −1.06847e23 1.05477e23i −0.169428 0.167256i
\(945\) 9.64155e23 1.51598
\(946\) 5.96552e22 + 1.17661e22i 0.0930077 + 0.0183445i
\(947\) −4.17834e23 −0.645958 −0.322979 0.946406i \(-0.604684\pi\)
−0.322979 + 0.946406i \(0.604684\pi\)
\(948\) −2.24253e22 + 5.46374e22i −0.0343773 + 0.0837575i
\(949\) 1.80964e23i 0.275082i
\(950\) −2.28518e24 4.50719e23i −3.44454 0.679387i
\(951\) 6.15675e23i 0.920253i
\(952\) 7.67540e22 1.16083e23i 0.113764 0.172057i
\(953\) 5.39088e23 0.792348 0.396174 0.918175i \(-0.370338\pi\)
0.396174 + 0.918175i \(0.370338\pi\)
\(954\) 4.61820e21 2.34146e22i 0.00673110 0.0341271i
\(955\) 9.86888e23 1.42640
\(956\) 4.02480e22 9.80609e22i 0.0576874 0.140551i
\(957\) 1.17883e23i 0.167554i
\(958\) −1.63341e23 + 8.28149e23i −0.230235 + 1.16730i
\(959\) 4.73631e22i 0.0662051i
\(960\) 1.11973e24 4.76554e23i 1.55218 0.660605i
\(961\) 6.71735e23 0.923445
\(962\) 6.09756e23 + 1.20266e23i 0.831295 + 0.163961i
\(963\) −4.86237e22 −0.0657412
\(964\) 5.98618e23 + 2.45696e23i 0.802663 + 0.329444i
\(965\) 1.56576e24i 2.08212i
\(966\) 5.52498e23 + 1.08972e23i 0.728641 + 0.143714i
\(967\) 7.48210e23i 0.978614i 0.872111 + 0.489307i \(0.162750\pi\)
−0.872111 + 0.489307i \(0.837250\pi\)
\(968\) −6.34249e23 4.19366e23i −0.822730 0.543990i
\(969\) 2.97598e23 0.382860
\(970\) 2.75001e23 1.39428e24i 0.350882 1.77899i
\(971\) 1.41552e24 1.79128 0.895640 0.444781i \(-0.146718\pi\)
0.895640 + 0.444781i \(0.146718\pi\)
\(972\) 1.64796e23 + 6.76389e22i 0.206832 + 0.0848919i
\(973\) 2.30966e23i 0.287505i
\(974\) −1.87433e23 + 9.50297e23i −0.231406 + 1.17324i
\(975\) 2.08008e24i 2.54708i
\(976\) 1.04265e24 1.05619e24i 1.26631 1.28276i
\(977\) −3.64742e23 −0.439369 −0.219685 0.975571i \(-0.570503\pi\)
−0.219685 + 0.975571i \(0.570503\pi\)
\(978\) −2.38568e22 4.70542e21i −0.0285037 0.00562195i
\(979\) −7.43521e22 −0.0881113
\(980\) 2.00863e23 4.89385e23i 0.236097 0.575231i
\(981\) 8.40058e22i 0.0979393i
\(982\) −3.81999e23 7.53439e22i −0.441743 0.0871277i
\(983\) 1.32002e24i 1.51410i 0.653359 + 0.757049i \(0.273359\pi\)
−0.653359 + 0.757049i \(0.726641\pi\)
\(984\) 1.62713e23 + 1.07586e23i 0.185123 + 0.122404i
\(985\) −1.17951e24 −1.33110
\(986\) −6.70843e22 + 3.40122e23i −0.0750941 + 0.380732i
\(987\) −4.62163e23 −0.513166
\(988\) −6.72516e23 + 1.63853e24i −0.740708 + 1.80467i
\(989\) 7.23606e23i 0.790554i
\(990\) 4.20219e21 2.13054e22i 0.00455401 0.0230891i
\(991\) 7.48922e23i 0.805095i −0.915399 0.402548i \(-0.868125\pi\)
0.915399 0.402548i \(-0.131875\pi\)
\(992\) 2.14569e23 1.45887e23i 0.228809 0.155569i
\(993\) 7.52003e23 0.795473
\(994\) 2.57888e23 + 5.08648e22i 0.270608 + 0.0533736i
\(995\) −2.09438e24 −2.18007
\(996\) −1.19542e23 4.90648e22i −0.123437 0.0506635i
\(997\) 4.07882e23i 0.417805i 0.977937 + 0.208902i \(0.0669891\pi\)
−0.977937 + 0.208902i \(0.933011\pi\)
\(998\) −6.09247e22 1.20165e22i −0.0619083 0.0122105i
\(999\) 7.18743e23i 0.724519i
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 8.17.d.b.3.14 yes 14
3.2 odd 2 72.17.b.b.19.1 14
4.3 odd 2 32.17.d.b.15.3 14
8.3 odd 2 inner 8.17.d.b.3.13 14
8.5 even 2 32.17.d.b.15.4 14
24.11 even 2 72.17.b.b.19.2 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.17.d.b.3.13 14 8.3 odd 2 inner
8.17.d.b.3.14 yes 14 1.1 even 1 trivial
32.17.d.b.15.3 14 4.3 odd 2
32.17.d.b.15.4 14 8.5 even 2
72.17.b.b.19.1 14 3.2 odd 2
72.17.b.b.19.2 14 24.11 even 2