Properties

Label 8.13.d.b.3.8
Level $8$
Weight $13$
Character 8.3
Analytic conductor $7.312$
Analytic rank $0$
Dimension $10$
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] = [8,13,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, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.3");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 13 \)
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: \(7.31195053821\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 5 x^{9} + 468 x^{8} + 1496 x^{7} + 710096 x^{6} + 29155008 x^{5} + 143571008 x^{4} + 28213427840 x^{3} + 1335549648384 x^{2} + \cdots + 824967906703360 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{45}\cdot 3^{3}\cdot 23 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.8
Root \(17.4695 - 29.8739i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.13.d.b.3.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(22.9390 + 59.7478i) q^{2} +271.191 q^{3} +(-3043.60 + 2741.11i) q^{4} +11036.2i q^{5} +(6220.87 + 16203.1i) q^{6} +58770.2i q^{7} +(-233593. - 118970. i) q^{8} -457896. q^{9} +O(q^{10})\) \(q+(22.9390 + 59.7478i) q^{2} +271.191 q^{3} +(-3043.60 + 2741.11i) q^{4} +11036.2i q^{5} +(6220.87 + 16203.1i) q^{6} +58770.2i q^{7} +(-233593. - 118970. i) q^{8} -457896. q^{9} +(-659388. + 253159. i) q^{10} -146799. q^{11} +(-825399. + 743367. i) q^{12} +4.26288e6i q^{13} +(-3.51139e6 + 1.34813e6i) q^{14} +2.99292e6i q^{15} +(1.74980e6 - 1.66857e7i) q^{16} +2.95267e7 q^{17} +(-1.05037e7 - 2.73583e7i) q^{18} +6.17776e7 q^{19} +(-3.02514e7 - 3.35897e7i) q^{20} +1.59380e7i q^{21} +(-3.36742e6 - 8.77090e6i) q^{22} +2.07436e8i q^{23} +(-6.33484e7 - 3.22636e7i) q^{24} +1.22343e8 q^{25} +(-2.54698e8 + 9.77863e7i) q^{26} -2.68300e8 q^{27} +(-1.61096e8 - 1.78873e8i) q^{28} -4.01062e8i q^{29} +(-1.78820e8 + 6.86547e7i) q^{30} +4.64456e8i q^{31} +(1.03707e9 - 2.78207e8i) q^{32} -3.98105e7 q^{33} +(6.77314e8 + 1.76416e9i) q^{34} -6.48599e8 q^{35} +(1.39365e9 - 1.25515e9i) q^{36} -4.99972e9i q^{37} +(1.41712e9 + 3.69107e9i) q^{38} +1.15606e9i q^{39} +(1.31298e9 - 2.57797e9i) q^{40} +7.68376e7 q^{41} +(-9.52260e8 + 3.65602e8i) q^{42} -7.15914e9 q^{43} +(4.46797e8 - 4.02392e8i) q^{44} -5.05343e9i q^{45} +(-1.23939e10 + 4.75839e9i) q^{46} +2.06601e10i q^{47} +(4.74532e8 - 4.52502e9i) q^{48} +1.03873e10 q^{49} +(2.80644e9 + 7.30974e9i) q^{50} +8.00739e9 q^{51} +(-1.16850e10 - 1.29745e10i) q^{52} -5.81907e9i q^{53} +(-6.15454e9 - 1.60303e10i) q^{54} -1.62010e9i q^{55} +(6.99190e9 - 1.37283e10i) q^{56} +1.67535e10 q^{57} +(2.39626e10 - 9.19998e9i) q^{58} +3.59188e10 q^{59} +(-8.20393e9 - 9.10925e9i) q^{60} +3.83534e10i q^{61} +(-2.77502e10 + 1.06542e10i) q^{62} -2.69107e10i q^{63} +(4.04117e10 + 5.55811e10i) q^{64} -4.70459e10 q^{65} +(-9.13215e8 - 2.37859e9i) q^{66} -8.74298e10 q^{67} +(-8.98675e10 + 8.09360e10i) q^{68} +5.62550e10i q^{69} +(-1.48782e10 - 3.87524e10i) q^{70} -1.98703e11i q^{71} +(1.06961e11 + 5.44759e10i) q^{72} -1.90567e11 q^{73} +(2.98722e11 - 1.14689e11i) q^{74} +3.31784e10 q^{75} +(-1.88026e11 + 1.69339e11i) q^{76} -8.62739e9i q^{77} +(-6.90718e10 + 2.65188e10i) q^{78} -4.39590e10i q^{79} +(1.84147e11 + 1.93112e10i) q^{80} +1.70584e11 q^{81} +(1.76258e9 + 4.59088e9i) q^{82} +3.26303e11 q^{83} +(-4.36878e10 - 4.85089e10i) q^{84} +3.25862e11i q^{85} +(-1.64224e11 - 4.27743e11i) q^{86} -1.08765e11i q^{87} +(3.42911e10 + 1.74646e10i) q^{88} +1.81425e11 q^{89} +(3.01931e11 - 1.15921e11i) q^{90} -2.50530e11 q^{91} +(-5.68607e11 - 6.31354e11i) q^{92} +1.25957e11i q^{93} +(-1.23439e12 + 4.73922e11i) q^{94} +6.81788e11i q^{95} +(2.81246e11 - 7.54474e10i) q^{96} +4.70836e10 q^{97} +(2.38276e11 + 6.20621e11i) q^{98} +6.72186e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 110 q^{2} - 660 q^{3} - 2444 q^{4} - 130788 q^{6} + 27160 q^{8} + 1692798 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 110 q^{2} - 660 q^{3} - 2444 q^{4} - 130788 q^{6} + 27160 q^{8} + 1692798 q^{9} + 1873200 q^{10} - 4591444 q^{11} - 5427720 q^{12} + 12728736 q^{14} - 38294000 q^{16} + 42876500 q^{17} + 8229270 q^{18} + 36062828 q^{19} + 17615520 q^{20} - 227004580 q^{22} + 169102992 q^{24} - 706946390 q^{25} + 151295184 q^{26} + 1382414040 q^{27} - 132075840 q^{28} + 456064800 q^{30} - 2651204000 q^{32} - 478018200 q^{33} + 4454663012 q^{34} - 2838470400 q^{35} - 4074739428 q^{36} + 1644178460 q^{38} + 8180322240 q^{40} - 12339248044 q^{41} + 14692585920 q^{42} + 25081495340 q^{43} - 27950589832 q^{44} - 16813594656 q^{46} + 13310114400 q^{48} - 39532486838 q^{49} + 24888425650 q^{50} + 36757299288 q^{51} - 36172521120 q^{52} - 74007907272 q^{54} + 154450364544 q^{56} + 80408630760 q^{57} + 193270394640 q^{58} - 109448026708 q^{59} - 347360715840 q^{60} - 299237961600 q^{62} + 276213192256 q^{64} + 96485235840 q^{65} + 486280823688 q^{66} - 49860896020 q^{67} - 296812951960 q^{68} - 799057954560 q^{70} + 1077572984520 q^{72} - 58835592940 q^{73} + 742739480496 q^{74} - 251792743380 q^{75} - 699737494024 q^{76} - 1795838526240 q^{78} + 1981932232320 q^{80} + 259515975474 q^{81} + 1654109754980 q^{82} - 146236977940 q^{83} - 3144240693120 q^{84} - 2261898070564 q^{86} + 2170357811600 q^{88} + 913341514388 q^{89} + 3983485096080 q^{90} + 361546645248 q^{91} - 2649411172800 q^{92} - 2517413216064 q^{94} + 2836588548672 q^{96} - 1474226441260 q^{97} + 2377890492370 q^{98} - 717160631484 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.9390 + 59.7478i 0.358422 + 0.933560i
\(3\) 271.191 0.372005 0.186002 0.982549i \(-0.440447\pi\)
0.186002 + 0.982549i \(0.440447\pi\)
\(4\) −3043.60 + 2741.11i −0.743067 + 0.669217i
\(5\) 11036.2i 0.706316i 0.935564 + 0.353158i \(0.114892\pi\)
−0.935564 + 0.353158i \(0.885108\pi\)
\(6\) 6220.87 + 16203.1i 0.133335 + 0.347289i
\(7\) 58770.2i 0.499539i 0.968305 + 0.249769i \(0.0803548\pi\)
−0.968305 + 0.249769i \(0.919645\pi\)
\(8\) −233593. 118970.i −0.891086 0.453835i
\(9\) −457896. −0.861613
\(10\) −659388. + 253159.i −0.659388 + 0.253159i
\(11\) −146799. −0.0828640 −0.0414320 0.999141i \(-0.513192\pi\)
−0.0414320 + 0.999141i \(0.513192\pi\)
\(12\) −825399. + 743367.i −0.276424 + 0.248952i
\(13\) 4.26288e6i 0.883167i 0.897220 + 0.441583i \(0.145583\pi\)
−0.897220 + 0.441583i \(0.854417\pi\)
\(14\) −3.51139e6 + 1.34813e6i −0.466349 + 0.179046i
\(15\) 2.99292e6i 0.262753i
\(16\) 1.74980e6 1.66857e7i 0.104296 0.994546i
\(17\) 2.95267e7 1.22327 0.611634 0.791141i \(-0.290513\pi\)
0.611634 + 0.791141i \(0.290513\pi\)
\(18\) −1.05037e7 2.73583e7i −0.308821 0.804367i
\(19\) 6.17776e7 1.31313 0.656567 0.754268i \(-0.272008\pi\)
0.656567 + 0.754268i \(0.272008\pi\)
\(20\) −3.02514e7 3.35897e7i −0.472679 0.524840i
\(21\) 1.59380e7i 0.185831i
\(22\) −3.36742e6 8.77090e6i −0.0297003 0.0773585i
\(23\) 2.07436e8i 1.40126i 0.713526 + 0.700629i \(0.247097\pi\)
−0.713526 + 0.700629i \(0.752903\pi\)
\(24\) −6.33484e7 3.22636e7i −0.331488 0.168829i
\(25\) 1.22343e8 0.501118
\(26\) −2.54698e8 + 9.77863e7i −0.824489 + 0.316547i
\(27\) −2.68300e8 −0.692529
\(28\) −1.61096e8 1.78873e8i −0.334300 0.371191i
\(29\) 4.01062e8i 0.674255i −0.941459 0.337127i \(-0.890545\pi\)
0.941459 0.337127i \(-0.109455\pi\)
\(30\) −1.78820e8 + 6.86547e7i −0.245295 + 0.0941765i
\(31\) 4.64456e8i 0.523329i 0.965159 + 0.261664i \(0.0842714\pi\)
−0.965159 + 0.261664i \(0.915729\pi\)
\(32\) 1.03707e9 2.78207e8i 0.965850 0.259101i
\(33\) −3.98105e7 −0.0308258
\(34\) 6.77314e8 + 1.76416e9i 0.438446 + 1.14199i
\(35\) −6.48599e8 −0.352832
\(36\) 1.39365e9 1.25515e9i 0.640236 0.576606i
\(37\) 4.99972e9i 1.94866i −0.225132 0.974328i \(-0.572281\pi\)
0.225132 0.974328i \(-0.427719\pi\)
\(38\) 1.41712e9 + 3.69107e9i 0.470657 + 1.22589i
\(39\) 1.15606e9i 0.328542i
\(40\) 1.31298e9 2.57797e9i 0.320551 0.629388i
\(41\) 7.68376e7 0.0161760 0.00808799 0.999967i \(-0.497425\pi\)
0.00808799 + 0.999967i \(0.497425\pi\)
\(42\) −9.52260e8 + 3.65602e8i −0.173484 + 0.0666059i
\(43\) −7.15914e9 −1.13253 −0.566266 0.824223i \(-0.691612\pi\)
−0.566266 + 0.824223i \(0.691612\pi\)
\(44\) 4.46797e8 4.02392e8i 0.0615735 0.0554540i
\(45\) 5.05343e9i 0.608571i
\(46\) −1.23939e10 + 4.75839e9i −1.30816 + 0.502242i
\(47\) 2.06601e10i 1.91666i 0.285666 + 0.958329i \(0.407785\pi\)
−0.285666 + 0.958329i \(0.592215\pi\)
\(48\) 4.74532e8 4.52502e9i 0.0387988 0.369976i
\(49\) 1.03873e10 0.750461
\(50\) 2.80644e9 + 7.30974e9i 0.179612 + 0.467823i
\(51\) 8.00739e9 0.455061
\(52\) −1.16850e10 1.29745e10i −0.591030 0.656252i
\(53\) 5.81907e9i 0.262542i −0.991347 0.131271i \(-0.958094\pi\)
0.991347 0.131271i \(-0.0419058\pi\)
\(54\) −6.15454e9 1.60303e10i −0.248218 0.646517i
\(55\) 1.62010e9i 0.0585282i
\(56\) 6.99190e9 1.37283e10i 0.226708 0.445132i
\(57\) 1.67535e10 0.488492
\(58\) 2.39626e10 9.19998e9i 0.629457 0.241668i
\(59\) 3.59188e10 0.851549 0.425775 0.904829i \(-0.360002\pi\)
0.425775 + 0.904829i \(0.360002\pi\)
\(60\) −8.20393e9 9.10925e9i −0.175839 0.195243i
\(61\) 3.83534e10i 0.744432i 0.928146 + 0.372216i \(0.121402\pi\)
−0.928146 + 0.372216i \(0.878598\pi\)
\(62\) −2.77502e10 + 1.06542e10i −0.488559 + 0.187573i
\(63\) 2.69107e10i 0.430409i
\(64\) 4.04117e10 + 5.55811e10i 0.588068 + 0.808811i
\(65\) −4.70459e10 −0.623795
\(66\) −9.13215e8 2.37859e9i −0.0110487 0.0287777i
\(67\) −8.74298e10 −0.966520 −0.483260 0.875477i \(-0.660547\pi\)
−0.483260 + 0.875477i \(0.660547\pi\)
\(68\) −8.98675e10 + 8.09360e10i −0.908969 + 0.818631i
\(69\) 5.62550e10i 0.521275i
\(70\) −1.48782e10 3.87524e10i −0.126463 0.329390i
\(71\) 1.98703e11i 1.55115i −0.631255 0.775576i \(-0.717460\pi\)
0.631255 0.775576i \(-0.282540\pi\)
\(72\) 1.06961e11 + 5.44759e10i 0.767771 + 0.391030i
\(73\) −1.90567e11 −1.25924 −0.629622 0.776902i \(-0.716790\pi\)
−0.629622 + 0.776902i \(0.716790\pi\)
\(74\) 2.98722e11 1.14689e11i 1.81919 0.698442i
\(75\) 3.31784e10 0.186418
\(76\) −1.88026e11 + 1.69339e11i −0.975746 + 0.878772i
\(77\) 8.62739e9i 0.0413938i
\(78\) −6.90718e10 + 2.65188e10i −0.306714 + 0.117757i
\(79\) 4.39590e10i 0.180836i −0.995904 0.0904181i \(-0.971180\pi\)
0.995904 0.0904181i \(-0.0288204\pi\)
\(80\) 1.84147e11 + 1.93112e10i 0.702464 + 0.0736663i
\(81\) 1.70584e11 0.603989
\(82\) 1.76258e9 + 4.59088e9i 0.00579783 + 0.0151012i
\(83\) 3.26303e11 0.998049 0.499025 0.866588i \(-0.333692\pi\)
0.499025 + 0.866588i \(0.333692\pi\)
\(84\) −4.36878e10 4.85089e10i −0.124361 0.138085i
\(85\) 3.25862e11i 0.864013i
\(86\) −1.64224e11 4.27743e11i −0.405925 1.05729i
\(87\) 1.08765e11i 0.250826i
\(88\) 3.42911e10 + 1.74646e10i 0.0738390 + 0.0376066i
\(89\) 1.81425e11 0.365054 0.182527 0.983201i \(-0.441572\pi\)
0.182527 + 0.983201i \(0.441572\pi\)
\(90\) 3.01931e11 1.15921e11i 0.568137 0.218125i
\(91\) −2.50530e11 −0.441176
\(92\) −5.68607e11 6.31354e11i −0.937746 1.04123i
\(93\) 1.25957e11i 0.194681i
\(94\) −1.23439e12 + 4.73922e11i −1.78931 + 0.686973i
\(95\) 6.81788e11i 0.927487i
\(96\) 2.81246e11 7.54474e10i 0.359301 0.0963867i
\(97\) 4.70836e10 0.0565249 0.0282624 0.999601i \(-0.491003\pi\)
0.0282624 + 0.999601i \(0.491003\pi\)
\(98\) 2.38276e11 + 6.20621e11i 0.268982 + 0.700600i
\(99\) 6.72186e10 0.0713967
\(100\) −3.72364e11 + 3.35357e11i −0.372364 + 0.335357i
\(101\) 8.79652e11i 0.828672i −0.910124 0.414336i \(-0.864014\pi\)
0.910124 0.414336i \(-0.135986\pi\)
\(102\) 1.83682e11 + 4.78424e11i 0.163104 + 0.424827i
\(103\) 1.45548e12i 1.21895i 0.792807 + 0.609473i \(0.208619\pi\)
−0.792807 + 0.609473i \(0.791381\pi\)
\(104\) 5.07155e11 9.95778e11i 0.400812 0.786978i
\(105\) −1.75895e11 −0.131255
\(106\) 3.47677e11 1.33484e11i 0.245098 0.0941008i
\(107\) −3.55167e11 −0.236663 −0.118331 0.992974i \(-0.537755\pi\)
−0.118331 + 0.992974i \(0.537755\pi\)
\(108\) 8.16598e11 7.35440e11i 0.514595 0.463452i
\(109\) 2.28440e12i 1.36211i −0.732231 0.681056i \(-0.761521\pi\)
0.732231 0.681056i \(-0.238479\pi\)
\(110\) 9.67973e10 3.71635e10i 0.0546395 0.0209778i
\(111\) 1.35588e12i 0.724909i
\(112\) 9.80624e11 + 1.02836e11i 0.496815 + 0.0521001i
\(113\) 1.95500e12 0.939021 0.469511 0.882927i \(-0.344430\pi\)
0.469511 + 0.882927i \(0.344430\pi\)
\(114\) 3.84310e11 + 1.00099e12i 0.175086 + 0.456036i
\(115\) −2.28931e12 −0.989731
\(116\) 1.09936e12 + 1.22067e12i 0.451223 + 0.501016i
\(117\) 1.95196e12i 0.760948i
\(118\) 8.23943e11 + 2.14607e12i 0.305214 + 0.794972i
\(119\) 1.73529e12i 0.611069i
\(120\) 3.56068e11 6.99124e11i 0.119246 0.234135i
\(121\) −3.11688e12 −0.993134
\(122\) −2.29153e12 + 8.79790e11i −0.694972 + 0.266821i
\(123\) 2.08377e10 0.00601754
\(124\) −1.27313e12 1.41362e12i −0.350221 0.388868i
\(125\) 4.04458e12i 1.06026i
\(126\) 1.60785e12 6.17305e11i 0.401812 0.154268i
\(127\) 1.24761e12i 0.297341i −0.988887 0.148671i \(-0.952501\pi\)
0.988887 0.148671i \(-0.0474994\pi\)
\(128\) −2.39384e12 + 3.68949e12i −0.544297 + 0.838893i
\(129\) −1.94150e12 −0.421307
\(130\) −1.07919e12 2.81089e12i −0.223582 0.582349i
\(131\) 3.97920e12 0.787350 0.393675 0.919250i \(-0.371204\pi\)
0.393675 + 0.919250i \(0.371204\pi\)
\(132\) 1.21167e11 1.09125e11i 0.0229056 0.0206292i
\(133\) 3.63068e12i 0.655962i
\(134\) −2.00555e12 5.22374e12i −0.346422 0.902304i
\(135\) 2.96101e12i 0.489144i
\(136\) −6.89722e12 3.51279e12i −1.09004 0.555161i
\(137\) 5.76362e12 0.871710 0.435855 0.900017i \(-0.356446\pi\)
0.435855 + 0.900017i \(0.356446\pi\)
\(138\) −3.36111e12 + 1.29044e12i −0.486641 + 0.186836i
\(139\) 4.37090e12 0.606013 0.303006 0.952989i \(-0.402010\pi\)
0.303006 + 0.952989i \(0.402010\pi\)
\(140\) 1.97408e12 1.77788e12i 0.262178 0.236121i
\(141\) 5.60283e12i 0.713006i
\(142\) 1.18721e13 4.55805e12i 1.44809 0.555967i
\(143\) 6.25785e11i 0.0731828i
\(144\) −8.01229e11 + 7.64033e12i −0.0898632 + 0.856913i
\(145\) 4.42620e12 0.476237
\(146\) −4.37142e12 1.13859e13i −0.451341 1.17558i
\(147\) 2.81696e12 0.279175
\(148\) 1.37048e13 + 1.52172e13i 1.30407 + 1.44798i
\(149\) 7.63175e12i 0.697440i 0.937227 + 0.348720i \(0.113384\pi\)
−0.937227 + 0.348720i \(0.886616\pi\)
\(150\) 7.61081e11 + 1.98234e12i 0.0668165 + 0.174033i
\(151\) 1.05853e13i 0.892978i −0.894789 0.446489i \(-0.852674\pi\)
0.894789 0.446489i \(-0.147326\pi\)
\(152\) −1.44308e13 7.34968e12i −1.17012 0.595946i
\(153\) −1.35202e13 −1.05398
\(154\) 5.15468e11 1.97904e11i 0.0386436 0.0148365i
\(155\) −5.12583e12 −0.369635
\(156\) −3.16888e12 3.51857e12i −0.219866 0.244129i
\(157\) 1.18606e13i 0.791971i −0.918257 0.395986i \(-0.870403\pi\)
0.918257 0.395986i \(-0.129597\pi\)
\(158\) 2.62646e12 1.00838e12i 0.168821 0.0648158i
\(159\) 1.57808e12i 0.0976668i
\(160\) 3.07035e12 + 1.14453e13i 0.183007 + 0.682195i
\(161\) −1.21911e13 −0.699983
\(162\) 3.91304e12 + 1.01920e13i 0.216483 + 0.563859i
\(163\) −4.52743e12 −0.241394 −0.120697 0.992689i \(-0.538513\pi\)
−0.120697 + 0.992689i \(0.538513\pi\)
\(164\) −2.33863e11 + 2.10621e11i −0.0120198 + 0.0108252i
\(165\) 4.39356e11i 0.0217728i
\(166\) 7.48507e12 + 1.94959e13i 0.357723 + 0.931738i
\(167\) 5.64186e12i 0.260090i 0.991508 + 0.130045i \(0.0415122\pi\)
−0.991508 + 0.130045i \(0.958488\pi\)
\(168\) 1.89614e12 3.72300e12i 0.0843365 0.165591i
\(169\) 5.12596e12 0.220016
\(170\) −1.94695e13 + 7.47496e12i −0.806607 + 0.309682i
\(171\) −2.82877e13 −1.13141
\(172\) 2.17896e13 1.96240e13i 0.841547 0.757910i
\(173\) 3.48709e12i 0.130073i −0.997883 0.0650364i \(-0.979284\pi\)
0.997883 0.0650364i \(-0.0207163\pi\)
\(174\) 6.49845e12 2.49496e12i 0.234161 0.0899016i
\(175\) 7.19014e12i 0.250328i
\(176\) −2.56869e11 + 2.44944e12i −0.00864243 + 0.0824121i
\(177\) 9.74087e12 0.316780
\(178\) 4.16171e12 + 1.08397e13i 0.130844 + 0.340800i
\(179\) 3.52407e13 1.07134 0.535668 0.844428i \(-0.320060\pi\)
0.535668 + 0.844428i \(0.320060\pi\)
\(180\) 1.38520e13 + 1.53806e13i 0.407266 + 0.452209i
\(181\) 4.56757e13i 1.29901i −0.760356 0.649507i \(-0.774975\pi\)
0.760356 0.649507i \(-0.225025\pi\)
\(182\) −5.74692e12 1.49686e13i −0.158127 0.411864i
\(183\) 1.04011e13i 0.276932i
\(184\) 2.46787e13 4.84557e13i 0.635939 1.24864i
\(185\) 5.51778e13 1.37637
\(186\) −7.52563e12 + 2.88932e12i −0.181746 + 0.0697780i
\(187\) −4.33448e12 −0.101365
\(188\) −5.66316e13 6.28810e13i −1.28266 1.42421i
\(189\) 1.57680e13i 0.345945i
\(190\) −4.07354e13 + 1.56396e13i −0.865865 + 0.332432i
\(191\) 9.20825e13i 1.89661i 0.317367 + 0.948303i \(0.397201\pi\)
−0.317367 + 0.948303i \(0.602799\pi\)
\(192\) 1.09593e13 + 1.50731e13i 0.218764 + 0.300882i
\(193\) −9.14371e12 −0.176921 −0.0884603 0.996080i \(-0.528195\pi\)
−0.0884603 + 0.996080i \(0.528195\pi\)
\(194\) 1.08005e12 + 2.81314e12i 0.0202598 + 0.0527693i
\(195\) −1.27584e13 −0.232055
\(196\) −3.16149e13 + 2.84729e13i −0.557643 + 0.502221i
\(197\) 5.41898e13i 0.927087i 0.886074 + 0.463544i \(0.153422\pi\)
−0.886074 + 0.463544i \(0.846578\pi\)
\(198\) 1.54193e12 + 4.01616e12i 0.0255902 + 0.0666531i
\(199\) 2.40613e13i 0.387436i 0.981057 + 0.193718i \(0.0620547\pi\)
−0.981057 + 0.193718i \(0.937945\pi\)
\(200\) −2.85785e13 1.45552e13i −0.446539 0.227425i
\(201\) −2.37102e13 −0.359550
\(202\) 5.25573e13 2.01784e13i 0.773615 0.297015i
\(203\) 2.35705e13 0.336816
\(204\) −2.43713e13 + 2.19492e13i −0.338141 + 0.304535i
\(205\) 8.47993e11i 0.0114253i
\(206\) −8.69620e13 + 3.33874e13i −1.13796 + 0.436897i
\(207\) 9.49844e13i 1.20734i
\(208\) 7.11292e13 + 7.45920e12i 0.878350 + 0.0921112i
\(209\) −9.06886e12 −0.108812
\(210\) −4.03485e12 1.05093e13i −0.0470448 0.122535i
\(211\) −3.69601e13 −0.418831 −0.209415 0.977827i \(-0.567156\pi\)
−0.209415 + 0.977827i \(0.567156\pi\)
\(212\) 1.59507e13 + 1.77109e13i 0.175697 + 0.195086i
\(213\) 5.38865e13i 0.577035i
\(214\) −8.14719e12 2.12205e13i −0.0848252 0.220939i
\(215\) 7.90096e13i 0.799925i
\(216\) 6.26729e13 + 3.19196e13i 0.617102 + 0.314293i
\(217\) −2.72962e13 −0.261423
\(218\) 1.36488e14 5.24019e13i 1.27161 0.488211i
\(219\) −5.16801e13 −0.468445
\(220\) 4.44087e12 + 4.93093e12i 0.0391681 + 0.0434903i
\(221\) 1.25869e14i 1.08035i
\(222\) 8.10109e13 3.11026e13i 0.676746 0.259824i
\(223\) 1.37554e14i 1.11852i −0.828993 0.559259i \(-0.811086\pi\)
0.828993 0.559259i \(-0.188914\pi\)
\(224\) 1.63503e13 + 6.09491e13i 0.129431 + 0.482480i
\(225\) −5.60205e13 −0.431770
\(226\) 4.48457e13 + 1.16807e14i 0.336566 + 0.876632i
\(227\) 2.35297e14 1.71973 0.859867 0.510518i \(-0.170546\pi\)
0.859867 + 0.510518i \(0.170546\pi\)
\(228\) −5.09911e13 + 4.59234e13i −0.362982 + 0.326907i
\(229\) 4.10302e13i 0.284506i 0.989830 + 0.142253i \(0.0454346\pi\)
−0.989830 + 0.142253i \(0.954565\pi\)
\(230\) −5.25145e13 1.36781e14i −0.354742 0.923973i
\(231\) 2.33968e12i 0.0153987i
\(232\) −4.77144e13 + 9.36853e13i −0.306000 + 0.600819i
\(233\) −1.76573e13 −0.110354 −0.0551770 0.998477i \(-0.517572\pi\)
−0.0551770 + 0.998477i \(0.517572\pi\)
\(234\) 1.16625e14 4.47760e13i 0.710390 0.272741i
\(235\) −2.28008e14 −1.35377
\(236\) −1.09323e14 + 9.84575e13i −0.632758 + 0.569871i
\(237\) 1.19213e13i 0.0672719i
\(238\) −1.03680e14 + 3.98059e13i −0.570470 + 0.219021i
\(239\) 8.88181e13i 0.476556i −0.971197 0.238278i \(-0.923417\pi\)
0.971197 0.238278i \(-0.0765830\pi\)
\(240\) 4.99390e13 + 5.23702e12i 0.261320 + 0.0274042i
\(241\) −1.16450e14 −0.594345 −0.297172 0.954824i \(-0.596044\pi\)
−0.297172 + 0.954824i \(0.596044\pi\)
\(242\) −7.14982e13 1.86227e14i −0.355961 0.927149i
\(243\) 1.88846e14 0.917215
\(244\) −1.05131e14 1.16733e14i −0.498187 0.553163i
\(245\) 1.14637e14i 0.530062i
\(246\) 4.77996e11 + 1.24501e12i 0.00215682 + 0.00561773i
\(247\) 2.63350e14i 1.15972i
\(248\) 5.52564e13 1.08494e14i 0.237505 0.466331i
\(249\) 8.84905e13 0.371279
\(250\) −2.41655e14 + 9.27788e13i −0.989819 + 0.380022i
\(251\) −2.12179e14 −0.848517 −0.424258 0.905541i \(-0.639465\pi\)
−0.424258 + 0.905541i \(0.639465\pi\)
\(252\) 7.37652e13 + 8.19054e13i 0.288037 + 0.319823i
\(253\) 3.04514e13i 0.116114i
\(254\) 7.45417e13 2.86189e13i 0.277586 0.106574i
\(255\) 8.83710e13i 0.321417i
\(256\) −2.75351e14 5.83935e13i −0.978244 0.207455i
\(257\) 3.91679e14 1.35935 0.679675 0.733513i \(-0.262121\pi\)
0.679675 + 0.733513i \(0.262121\pi\)
\(258\) −4.45361e13 1.16000e14i −0.151006 0.393315i
\(259\) 2.93835e14 0.973430
\(260\) 1.43189e14 1.28958e14i 0.463521 0.417454i
\(261\) 1.83645e14i 0.580946i
\(262\) 9.12790e13 + 2.37748e14i 0.282204 + 0.735038i
\(263\) 1.40060e14i 0.423234i −0.977353 0.211617i \(-0.932127\pi\)
0.977353 0.211617i \(-0.0678729\pi\)
\(264\) 9.29946e12 + 4.73626e12i 0.0274684 + 0.0139898i
\(265\) 6.42203e13 0.185437
\(266\) −2.16925e14 + 8.32843e13i −0.612379 + 0.235111i
\(267\) 4.92009e13 0.135802
\(268\) 2.66101e14 2.39655e14i 0.718189 0.646812i
\(269\) 4.24104e14i 1.11933i −0.828718 0.559666i \(-0.810929\pi\)
0.828718 0.559666i \(-0.189071\pi\)
\(270\) 1.76914e14 6.79226e13i 0.456645 0.175320i
\(271\) 5.78260e14i 1.45985i 0.683529 + 0.729923i \(0.260444\pi\)
−0.683529 + 0.729923i \(0.739556\pi\)
\(272\) 5.16659e13 4.92674e14i 0.127582 1.21660i
\(273\) −6.79417e13 −0.164120
\(274\) 1.32212e14 + 3.44364e14i 0.312440 + 0.813793i
\(275\) −1.79598e13 −0.0415247
\(276\) −1.54201e14 1.71218e14i −0.348846 0.387342i
\(277\) 8.12211e14i 1.79800i −0.437946 0.899001i \(-0.644294\pi\)
0.437946 0.899001i \(-0.355706\pi\)
\(278\) 1.00264e14 + 2.61151e14i 0.217208 + 0.565749i
\(279\) 2.12673e14i 0.450907i
\(280\) 1.51508e14 + 7.71639e13i 0.314404 + 0.160127i
\(281\) −5.48235e14 −1.11360 −0.556800 0.830647i \(-0.687971\pi\)
−0.556800 + 0.830647i \(0.687971\pi\)
\(282\) −3.34757e14 + 1.28524e14i −0.665633 + 0.255557i
\(283\) −8.25508e14 −1.60695 −0.803476 0.595338i \(-0.797018\pi\)
−0.803476 + 0.595338i \(0.797018\pi\)
\(284\) 5.44667e14 + 6.04772e14i 1.03806 + 1.15261i
\(285\) 1.84895e14i 0.345030i
\(286\) 3.73893e13 1.43549e13i 0.0683205 0.0262303i
\(287\) 4.51576e12i 0.00808053i
\(288\) −4.74872e14 + 1.27390e14i −0.832189 + 0.223244i
\(289\) 2.89203e14 0.496382
\(290\) 1.01533e14 + 2.64456e14i 0.170694 + 0.444595i
\(291\) 1.27687e13 0.0210275
\(292\) 5.80009e14 5.22365e14i 0.935702 0.842708i
\(293\) 1.43564e14i 0.226902i 0.993544 + 0.113451i \(0.0361905\pi\)
−0.993544 + 0.113451i \(0.963809\pi\)
\(294\) 6.46183e13 + 1.68307e14i 0.100063 + 0.260626i
\(295\) 3.96407e14i 0.601463i
\(296\) −5.94817e14 + 1.16790e15i −0.884368 + 1.73642i
\(297\) 3.93861e13 0.0573857
\(298\) −4.55980e14 + 1.75065e14i −0.651101 + 0.249978i
\(299\) −8.84276e14 −1.23754
\(300\) −1.00982e14 + 9.09459e13i −0.138521 + 0.124754i
\(301\) 4.20745e14i 0.565744i
\(302\) 6.32447e14 2.42816e14i 0.833648 0.320063i
\(303\) 2.38554e14i 0.308270i
\(304\) 1.08099e14 1.03080e15i 0.136955 1.30597i
\(305\) −4.23275e14 −0.525804
\(306\) −3.10139e14 8.07800e14i −0.377771 0.983955i
\(307\) 1.53573e15 1.83437 0.917183 0.398467i \(-0.130458\pi\)
0.917183 + 0.398467i \(0.130458\pi\)
\(308\) 2.36487e13 + 2.62584e13i 0.0277014 + 0.0307584i
\(309\) 3.94715e14i 0.453453i
\(310\) −1.17581e14 3.06257e14i −0.132486 0.345077i
\(311\) 7.26434e14i 0.802848i −0.915892 0.401424i \(-0.868515\pi\)
0.915892 0.401424i \(-0.131485\pi\)
\(312\) 1.37536e14 2.70046e14i 0.149104 0.292759i
\(313\) 8.78186e14 0.933943 0.466972 0.884272i \(-0.345345\pi\)
0.466972 + 0.884272i \(0.345345\pi\)
\(314\) 7.08646e14 2.72071e14i 0.739352 0.283860i
\(315\) 2.96991e14 0.304005
\(316\) 1.20497e14 + 1.33794e14i 0.121019 + 0.134373i
\(317\) 1.03708e15i 1.02202i 0.859576 + 0.511008i \(0.170728\pi\)
−0.859576 + 0.511008i \(0.829272\pi\)
\(318\) 9.42869e13 3.61997e13i 0.0911777 0.0350060i
\(319\) 5.88754e13i 0.0558715i
\(320\) −6.13403e14 + 4.45991e14i −0.571276 + 0.415362i
\(321\) −9.63183e13 −0.0880397
\(322\) −2.79652e14 7.28391e14i −0.250890 0.653476i
\(323\) 1.82409e15 1.60631
\(324\) −5.19190e14 + 4.67591e14i −0.448804 + 0.404200i
\(325\) 5.21534e14i 0.442571i
\(326\) −1.03855e14 2.70504e14i −0.0865210 0.225356i
\(327\) 6.19509e14i 0.506712i
\(328\) −1.79487e13 9.14137e12i −0.0144142 0.00734122i
\(329\) −1.21420e15 −0.957445
\(330\) 2.62506e13 1.00784e13i 0.0203262 0.00780384i
\(331\) −1.44918e15 −1.10193 −0.550964 0.834529i \(-0.685740\pi\)
−0.550964 + 0.834529i \(0.685740\pi\)
\(332\) −9.93135e14 + 8.94433e14i −0.741617 + 0.667912i
\(333\) 2.28935e15i 1.67899i
\(334\) −3.37089e14 + 1.29419e14i −0.242809 + 0.0932220i
\(335\) 9.64891e14i 0.682668i
\(336\) 2.65937e14 + 2.78884e13i 0.184817 + 0.0193815i
\(337\) 1.51299e15 1.03290 0.516449 0.856318i \(-0.327254\pi\)
0.516449 + 0.856318i \(0.327254\pi\)
\(338\) 1.17585e14 + 3.06265e14i 0.0788588 + 0.205398i
\(339\) 5.30178e14 0.349320
\(340\) −8.93225e14 9.91794e14i −0.578212 0.642019i
\(341\) 6.81816e13i 0.0433651i
\(342\) −6.48893e14 1.69013e15i −0.405524 1.05624i
\(343\) 1.42392e15i 0.874423i
\(344\) 1.67232e15 + 8.51724e14i 1.00918 + 0.513982i
\(345\) −6.20840e14 −0.368184
\(346\) 2.08346e14 7.99904e13i 0.121431 0.0466210i
\(347\) −2.67016e15 −1.52954 −0.764769 0.644305i \(-0.777147\pi\)
−0.764769 + 0.644305i \(0.777147\pi\)
\(348\) 2.98136e14 + 3.31036e14i 0.167857 + 0.186380i
\(349\) 2.60277e15i 1.44040i −0.693767 0.720199i \(-0.744050\pi\)
0.693767 0.720199i \(-0.255950\pi\)
\(350\) −4.29595e14 + 1.64935e14i −0.233696 + 0.0897231i
\(351\) 1.14373e15i 0.611618i
\(352\) −1.52241e14 + 4.08405e13i −0.0800342 + 0.0214701i
\(353\) −2.63038e15 −1.35947 −0.679737 0.733456i \(-0.737906\pi\)
−0.679737 + 0.733456i \(0.737906\pi\)
\(354\) 2.23446e14 + 5.81996e14i 0.113541 + 0.295733i
\(355\) 2.19292e15 1.09560
\(356\) −5.52185e14 + 4.97307e14i −0.271260 + 0.244300i
\(357\) 4.70596e14i 0.227321i
\(358\) 8.08387e14 + 2.10555e15i 0.383991 + 1.00016i
\(359\) 1.33956e15i 0.625742i −0.949796 0.312871i \(-0.898709\pi\)
0.949796 0.312871i \(-0.101291\pi\)
\(360\) −6.01206e14 + 1.18044e15i −0.276190 + 0.542289i
\(361\) 1.60315e15 0.724321
\(362\) 2.72902e15 1.04776e15i 1.21271 0.465596i
\(363\) −8.45271e14 −0.369450
\(364\) 7.62515e14 6.86732e14i 0.327823 0.295243i
\(365\) 2.10313e15i 0.889424i
\(366\) −6.21444e14 + 2.38592e14i −0.258533 + 0.0992587i
\(367\) 2.93675e15i 1.20191i 0.799285 + 0.600953i \(0.205212\pi\)
−0.799285 + 0.600953i \(0.794788\pi\)
\(368\) 3.46123e15 + 3.62973e14i 1.39362 + 0.146146i
\(369\) −3.51836e13 −0.0139374
\(370\) 1.26573e15 + 3.29675e15i 0.493321 + 1.28492i
\(371\) 3.41988e14 0.131150
\(372\) −3.45261e14 3.83362e14i −0.130284 0.144661i
\(373\) 2.60686e15i 0.967977i −0.875074 0.483989i \(-0.839188\pi\)
0.875074 0.483989i \(-0.160812\pi\)
\(374\) −9.94288e13 2.58976e14i −0.0363314 0.0946301i
\(375\) 1.09686e15i 0.394423i
\(376\) 2.45793e15 4.82605e15i 0.869846 1.70791i
\(377\) 1.70968e15 0.595479
\(378\) 9.42106e14 3.61704e14i 0.322960 0.123994i
\(379\) −4.34547e15 −1.46623 −0.733115 0.680105i \(-0.761934\pi\)
−0.733115 + 0.680105i \(0.761934\pi\)
\(380\) −1.86886e15 2.07509e15i −0.620691 0.689185i
\(381\) 3.38340e14i 0.110612i
\(382\) −5.50173e15 + 2.11228e15i −1.77059 + 0.679786i
\(383\) 2.23766e15i 0.708926i −0.935070 0.354463i \(-0.884664\pi\)
0.935070 0.354463i \(-0.115336\pi\)
\(384\) −6.49189e14 + 1.00056e15i −0.202481 + 0.312072i
\(385\) 9.52135e13 0.0292371
\(386\) −2.09748e14 5.46316e14i −0.0634123 0.165166i
\(387\) 3.27815e15 0.975804
\(388\) −1.43304e14 + 1.29062e14i −0.0420017 + 0.0378274i
\(389\) 9.97389e14i 0.287851i 0.989589 + 0.143925i \(0.0459725\pi\)
−0.989589 + 0.143925i \(0.954028\pi\)
\(390\) −2.92666e14 7.62289e14i −0.0831735 0.216637i
\(391\) 6.12491e15i 1.71411i
\(392\) −2.42641e15 1.23578e15i −0.668725 0.340585i
\(393\) 1.07912e15 0.292898
\(394\) −3.23772e15 + 1.24306e15i −0.865491 + 0.332289i
\(395\) 4.85140e14 0.127728
\(396\) −2.04587e14 + 1.84254e14i −0.0530525 + 0.0477799i
\(397\) 6.25341e14i 0.159725i 0.996806 + 0.0798627i \(0.0254482\pi\)
−0.996806 + 0.0798627i \(0.974552\pi\)
\(398\) −1.43761e15 + 5.51943e14i −0.361695 + 0.138866i
\(399\) 9.84610e14i 0.244021i
\(400\) 2.14077e14 2.04139e15i 0.0522648 0.498385i
\(401\) 1.75229e15 0.421445 0.210722 0.977546i \(-0.432418\pi\)
0.210722 + 0.977546i \(0.432418\pi\)
\(402\) −5.43889e14 1.41663e15i −0.128871 0.335661i
\(403\) −1.97992e15 −0.462187
\(404\) 2.41123e15 + 2.67731e15i 0.554562 + 0.615759i
\(405\) 1.88260e15i 0.426607i
\(406\) 5.40685e14 + 1.40829e15i 0.120723 + 0.314438i
\(407\) 7.33952e14i 0.161474i
\(408\) −1.87047e15 9.52639e14i −0.405499 0.206522i
\(409\) −2.66611e15 −0.569559 −0.284779 0.958593i \(-0.591920\pi\)
−0.284779 + 0.958593i \(0.591920\pi\)
\(410\) −5.06658e13 + 1.94521e13i −0.0106662 + 0.00409510i
\(411\) 1.56304e15 0.324280
\(412\) −3.98965e15 4.42991e15i −0.815739 0.905758i
\(413\) 2.11096e15i 0.425382i
\(414\) 5.67511e15 2.17885e15i 1.12713 0.432738i
\(415\) 3.60114e15i 0.704938i
\(416\) 1.18596e15 + 4.42092e15i 0.228829 + 0.853007i
\(417\) 1.18535e15 0.225440
\(418\) −2.08031e14 5.41845e14i −0.0390005 0.101582i
\(419\) 4.88044e15 0.901934 0.450967 0.892541i \(-0.351079\pi\)
0.450967 + 0.892541i \(0.351079\pi\)
\(420\) 5.35353e14 4.82147e14i 0.0975314 0.0878383i
\(421\) 7.51831e15i 1.35029i −0.737685 0.675146i \(-0.764081\pi\)
0.737685 0.675146i \(-0.235919\pi\)
\(422\) −8.47829e14 2.20829e15i −0.150118 0.391003i
\(423\) 9.46017e15i 1.65142i
\(424\) −6.92295e14 + 1.35929e15i −0.119151 + 0.233947i
\(425\) 3.61239e15 0.613001
\(426\) 3.21960e15 1.23610e15i 0.538697 0.206822i
\(427\) −2.25404e15 −0.371873
\(428\) 1.08099e15 9.73553e14i 0.175856 0.158379i
\(429\) 1.69707e14i 0.0272243i
\(430\) 4.72065e15 1.81240e15i 0.746778 0.286711i
\(431\) 4.80009e15i 0.748834i −0.927260 0.374417i \(-0.877843\pi\)
0.927260 0.374417i \(-0.122157\pi\)
\(432\) −4.69472e14 + 4.47677e15i −0.0722283 + 0.688752i
\(433\) −4.81144e15 −0.730042 −0.365021 0.930999i \(-0.618938\pi\)
−0.365021 + 0.930999i \(0.618938\pi\)
\(434\) −6.26149e14 1.63089e15i −0.0936999 0.244054i
\(435\) 1.20035e15 0.177162
\(436\) 6.26180e15 + 6.95280e15i 0.911549 + 1.01214i
\(437\) 1.28149e16i 1.84004i
\(438\) −1.18549e15 3.08777e15i −0.167901 0.437321i
\(439\) 7.01559e15i 0.980115i −0.871690 0.490057i \(-0.836976\pi\)
0.871690 0.490057i \(-0.163024\pi\)
\(440\) −1.92743e14 + 3.78443e14i −0.0265621 + 0.0521536i
\(441\) −4.75633e15 −0.646607
\(442\) −7.52038e15 + 2.88731e15i −1.00857 + 0.387221i
\(443\) −4.37539e15 −0.578888 −0.289444 0.957195i \(-0.593470\pi\)
−0.289444 + 0.957195i \(0.593470\pi\)
\(444\) 3.71662e15 + 4.12676e15i 0.485122 + 0.538656i
\(445\) 2.00224e15i 0.257843i
\(446\) 8.21853e15 3.15535e15i 1.04420 0.400902i
\(447\) 2.06967e15i 0.259451i
\(448\) −3.26651e15 + 2.37501e15i −0.404033 + 0.293763i
\(449\) −4.57989e15 −0.558956 −0.279478 0.960152i \(-0.590161\pi\)
−0.279478 + 0.960152i \(0.590161\pi\)
\(450\) −1.28506e15 3.34710e15i −0.154756 0.403083i
\(451\) −1.12797e13 −0.00134041
\(452\) −5.95023e15 + 5.35887e15i −0.697756 + 0.628409i
\(453\) 2.87064e15i 0.332192i
\(454\) 5.39749e15 + 1.40585e16i 0.616391 + 1.60547i
\(455\) 2.76490e15i 0.311610i
\(456\) −3.91351e15 1.99317e15i −0.435288 0.221695i
\(457\) −3.73761e15 −0.410295 −0.205148 0.978731i \(-0.565767\pi\)
−0.205148 + 0.978731i \(0.565767\pi\)
\(458\) −2.45147e15 + 9.41194e14i −0.265603 + 0.101973i
\(459\) −7.92200e15 −0.847147
\(460\) 6.96774e15 6.27525e15i 0.735436 0.662345i
\(461\) 5.99757e15i 0.624841i 0.949944 + 0.312421i \(0.101140\pi\)
−0.949944 + 0.312421i \(0.898860\pi\)
\(462\) 1.39790e14 5.36699e13i 0.0143756 0.00551923i
\(463\) 4.85727e15i 0.493067i −0.969134 0.246534i \(-0.920708\pi\)
0.969134 0.246534i \(-0.0792916\pi\)
\(464\) −6.69201e15 7.01781e14i −0.670577 0.0703224i
\(465\) −1.39008e15 −0.137506
\(466\) −4.05041e14 1.05498e15i −0.0395534 0.103022i
\(467\) 1.02535e16 0.988486 0.494243 0.869324i \(-0.335445\pi\)
0.494243 + 0.869324i \(0.335445\pi\)
\(468\) 5.35053e15 + 5.94097e15i 0.509239 + 0.565435i
\(469\) 5.13827e15i 0.482814i
\(470\) −5.23029e15 1.36230e16i −0.485220 1.26382i
\(471\) 3.21650e15i 0.294617i
\(472\) −8.39037e15 4.27326e15i −0.758804 0.386463i
\(473\) 1.05095e15 0.0938461
\(474\) 7.12272e14 2.73463e14i 0.0628024 0.0241118i
\(475\) 7.55807e15 0.658035
\(476\) −4.75663e15 5.28153e15i −0.408938 0.454065i
\(477\) 2.66453e15i 0.226209i
\(478\) 5.30669e15 2.03740e15i 0.444894 0.170808i
\(479\) 1.01603e16i 0.841190i 0.907248 + 0.420595i \(0.138179\pi\)
−0.907248 + 0.420595i \(0.861821\pi\)
\(480\) 8.32652e14 + 3.10388e15i 0.0680794 + 0.253780i
\(481\) 2.13132e16 1.72099
\(482\) −2.67126e15 6.95765e15i −0.213026 0.554856i
\(483\) −3.30612e15 −0.260397
\(484\) 9.48654e15 8.54372e15i 0.737965 0.664622i
\(485\) 5.19624e14i 0.0399244i
\(486\) 4.33196e15 + 1.12832e16i 0.328750 + 0.856275i
\(487\) 2.34412e16i 1.75714i 0.477617 + 0.878568i \(0.341501\pi\)
−0.477617 + 0.878568i \(0.658499\pi\)
\(488\) 4.56291e15 8.95908e15i 0.337849 0.663353i
\(489\) −1.22780e15 −0.0897997
\(490\) −6.84929e15 + 2.62965e15i −0.494845 + 0.189986i
\(491\) 2.04090e16 1.45657 0.728286 0.685273i \(-0.240317\pi\)
0.728286 + 0.685273i \(0.240317\pi\)
\(492\) −6.34216e13 + 5.71185e13i −0.00447143 + 0.00402704i
\(493\) 1.18420e16i 0.824794i
\(494\) −1.57346e16 + 6.04100e15i −1.08266 + 0.415668i
\(495\) 7.41836e14i 0.0504286i
\(496\) 7.74979e15 + 8.12708e14i 0.520475 + 0.0545814i
\(497\) 1.16778e16 0.774860
\(498\) 2.02989e15 + 5.28711e15i 0.133075 + 0.346611i
\(499\) −2.95094e16 −1.91143 −0.955714 0.294298i \(-0.904914\pi\)
−0.955714 + 0.294298i \(0.904914\pi\)
\(500\) −1.10867e16 1.23101e16i −0.709547 0.787846i
\(501\) 1.53002e15i 0.0967546i
\(502\) −4.86719e15 1.26772e16i −0.304127 0.792141i
\(503\) 1.23276e16i 0.761148i 0.924750 + 0.380574i \(0.124274\pi\)
−0.924750 + 0.380574i \(0.875726\pi\)
\(504\) −3.20156e15 + 6.28614e15i −0.195334 + 0.383531i
\(505\) 9.70801e15 0.585304
\(506\) 1.81940e15 6.98526e14i 0.108399 0.0416178i
\(507\) 1.39012e15 0.0818471
\(508\) 3.41983e15 + 3.79721e15i 0.198986 + 0.220944i
\(509\) 2.08634e16i 1.19972i −0.800106 0.599859i \(-0.795223\pi\)
0.800106 0.599859i \(-0.204777\pi\)
\(510\) −5.27997e15 + 2.02714e15i −0.300062 + 0.115203i
\(511\) 1.11997e16i 0.629041i
\(512\) −2.82741e15 1.77911e16i −0.156953 0.987606i
\(513\) −1.65749e16 −0.909383
\(514\) 8.98474e15 + 2.34020e16i 0.487222 + 1.26903i
\(515\) −1.60630e16 −0.860960
\(516\) 5.90915e15 5.32187e15i 0.313059 0.281946i
\(517\) 3.03287e15i 0.158822i
\(518\) 6.74028e15 + 1.75560e16i 0.348899 + 0.908755i
\(519\) 9.45669e14i 0.0483877i
\(520\) 1.09896e16 + 5.59705e15i 0.555855 + 0.283100i
\(521\) −1.72320e16 −0.861607 −0.430803 0.902446i \(-0.641770\pi\)
−0.430803 + 0.902446i \(0.641770\pi\)
\(522\) −1.09724e16 + 4.21264e15i −0.542348 + 0.208224i
\(523\) 1.15450e16 0.564137 0.282068 0.959394i \(-0.408980\pi\)
0.282068 + 0.959394i \(0.408980\pi\)
\(524\) −1.21111e16 + 1.09074e16i −0.585054 + 0.526908i
\(525\) 1.94991e15i 0.0931232i
\(526\) 8.36830e15 3.21285e15i 0.395114 0.151697i
\(527\) 1.37139e16i 0.640171i
\(528\) −6.96607e13 + 6.64267e14i −0.00321502 + 0.0306577i
\(529\) −2.11153e16 −0.963524
\(530\) 1.47315e15 + 3.83702e15i 0.0664649 + 0.173117i
\(531\) −1.64471e16 −0.733706
\(532\) −9.95211e15 1.10503e16i −0.438981 0.487423i
\(533\) 3.27549e14i 0.0142861i
\(534\) 1.12862e15 + 2.93965e15i 0.0486744 + 0.126779i
\(535\) 3.91969e15i 0.167159i
\(536\) 2.04230e16 + 1.04015e16i 0.861252 + 0.438640i
\(537\) 9.55697e15 0.398542
\(538\) 2.53393e16 9.72854e15i 1.04496 0.401194i
\(539\) −1.52485e15 −0.0621862
\(540\) 8.11645e15 + 9.01212e15i 0.327344 + 0.363467i
\(541\) 2.22285e15i 0.0886598i −0.999017 0.0443299i \(-0.985885\pi\)
0.999017 0.0443299i \(-0.0141153\pi\)
\(542\) −3.45497e16 + 1.32647e16i −1.36285 + 0.523242i
\(543\) 1.23869e16i 0.483239i
\(544\) 3.06214e16 8.21454e15i 1.18149 0.316949i
\(545\) 2.52110e16 0.962081
\(546\) −1.55852e15 4.05937e15i −0.0588241 0.153215i
\(547\) 1.84557e16 0.688981 0.344490 0.938790i \(-0.388052\pi\)
0.344490 + 0.938790i \(0.388052\pi\)
\(548\) −1.75422e16 + 1.57987e16i −0.647739 + 0.583363i
\(549\) 1.75619e16i 0.641412i
\(550\) −4.11981e14 1.07306e15i −0.0148834 0.0387657i
\(551\) 2.47767e16i 0.885387i
\(552\) 6.69266e15 1.31408e16i 0.236572 0.464500i
\(553\) 2.58348e15 0.0903348
\(554\) 4.85278e16 1.86313e16i 1.67854 0.644444i
\(555\) 1.49638e16 0.512015
\(556\) −1.33033e16 + 1.19811e16i −0.450308 + 0.405554i
\(557\) 2.98593e16i 0.999881i 0.866060 + 0.499940i \(0.166645\pi\)
−0.866060 + 0.499940i \(0.833355\pi\)
\(558\) 1.27067e16 4.87851e15i 0.420948 0.161615i
\(559\) 3.05186e16i 1.00021i
\(560\) −1.13492e15 + 1.08223e16i −0.0367992 + 0.350908i
\(561\) −1.17547e15 −0.0377082
\(562\) −1.25760e16 3.27559e16i −0.399139 1.03961i
\(563\) −2.83523e16 −0.890305 −0.445152 0.895455i \(-0.646850\pi\)
−0.445152 + 0.895455i \(0.646850\pi\)
\(564\) −1.53580e16 1.70528e16i −0.477156 0.529811i
\(565\) 2.15757e16i 0.663246i
\(566\) −1.89364e16 4.93223e16i −0.575967 1.50018i
\(567\) 1.00253e16i 0.301716i
\(568\) −2.36397e16 + 4.64156e16i −0.703966 + 1.38221i
\(569\) −1.48709e16 −0.438190 −0.219095 0.975704i \(-0.570310\pi\)
−0.219095 + 0.975704i \(0.570310\pi\)
\(570\) −1.10471e16 + 4.24132e15i −0.322106 + 0.123666i
\(571\) 3.35787e16 0.968830 0.484415 0.874838i \(-0.339033\pi\)
0.484415 + 0.874838i \(0.339033\pi\)
\(572\) 1.71535e15 + 1.90464e15i 0.0489752 + 0.0543797i
\(573\) 2.49720e16i 0.705546i
\(574\) −2.69807e14 + 1.03587e14i −0.00754365 + 0.00289624i
\(575\) 2.53785e16i 0.702196i
\(576\) −1.85044e16 2.54504e16i −0.506687 0.696882i
\(577\) −1.51145e16 −0.409581 −0.204790 0.978806i \(-0.565651\pi\)
−0.204790 + 0.978806i \(0.565651\pi\)
\(578\) 6.63404e15 + 1.72793e16i 0.177914 + 0.463402i
\(579\) −2.47969e15 −0.0658153
\(580\) −1.34716e16 + 1.21327e16i −0.353876 + 0.318706i
\(581\) 1.91769e16i 0.498564i
\(582\) 2.92901e14 + 7.62900e14i 0.00753673 + 0.0196304i
\(583\) 8.54232e14i 0.0217553i
\(584\) 4.45150e16 + 2.26717e16i 1.12209 + 0.571488i
\(585\) 2.15421e16 0.537469
\(586\) −8.57761e15 + 3.29321e15i −0.211827 + 0.0813268i
\(587\) 4.64906e16 1.13641 0.568207 0.822886i \(-0.307637\pi\)
0.568207 + 0.822886i \(0.307637\pi\)
\(588\) −8.57370e15 + 7.72161e15i −0.207446 + 0.186829i
\(589\) 2.86930e16i 0.687201i
\(590\) −2.36844e16 + 9.09318e15i −0.561501 + 0.215578i
\(591\) 1.46958e16i 0.344881i
\(592\) −8.34239e16 8.74853e15i −1.93803 0.203238i
\(593\) −9.55760e15 −0.219796 −0.109898 0.993943i \(-0.535052\pi\)
−0.109898 + 0.993943i \(0.535052\pi\)
\(594\) 9.03478e14 + 2.35323e15i 0.0205683 + 0.0535730i
\(595\) −1.91510e16 −0.431608
\(596\) −2.09195e16 2.32280e16i −0.466739 0.518244i
\(597\) 6.52521e15i 0.144128i
\(598\) −2.02844e16 5.28336e16i −0.443564 1.15532i
\(599\) 3.48480e16i 0.754427i −0.926126 0.377214i \(-0.876882\pi\)
0.926126 0.377214i \(-0.123118\pi\)
\(600\) −7.75025e15 3.94724e15i −0.166115 0.0846031i
\(601\) −2.82379e16 −0.599218 −0.299609 0.954062i \(-0.596856\pi\)
−0.299609 + 0.954062i \(0.596856\pi\)
\(602\) 2.51386e16 9.65148e15i 0.528155 0.202775i
\(603\) 4.00338e16 0.832765
\(604\) 2.90155e16 + 3.22174e16i 0.597596 + 0.663542i
\(605\) 3.43984e16i 0.701466i
\(606\) 1.42531e16 5.47220e15i 0.287788 0.110491i
\(607\) 4.04099e16i 0.807897i −0.914782 0.403948i \(-0.867638\pi\)
0.914782 0.403948i \(-0.132362\pi\)
\(608\) 6.40679e16 1.71870e16i 1.26829 0.340234i
\(609\) 6.39213e15 0.125297
\(610\) −9.70953e15 2.52898e16i −0.188460 0.490869i
\(611\) −8.80714e16 −1.69273
\(612\) 4.11500e16 3.70603e16i 0.783179 0.705343i
\(613\) 4.16832e16i 0.785595i 0.919625 + 0.392797i \(0.128493\pi\)
−0.919625 + 0.392797i \(0.871507\pi\)
\(614\) 3.52283e16 + 9.17568e16i 0.657478 + 1.71249i
\(615\) 2.29969e14i 0.00425028i
\(616\) −1.02640e15 + 2.01530e15i −0.0187859 + 0.0368854i
\(617\) 7.05658e16 1.27904 0.639519 0.768775i \(-0.279134\pi\)
0.639519 + 0.768775i \(0.279134\pi\)
\(618\) −2.35834e16 + 9.05438e15i −0.423326 + 0.162528i
\(619\) 7.32448e14 0.0130207 0.00651033 0.999979i \(-0.497928\pi\)
0.00651033 + 0.999979i \(0.497928\pi\)
\(620\) 1.56010e16 1.40505e16i 0.274664 0.247366i
\(621\) 5.56552e16i 0.970411i
\(622\) 4.34028e16 1.66637e16i 0.749507 0.287759i
\(623\) 1.06624e16i 0.182359i
\(624\) 1.92896e16 + 2.02287e15i 0.326750 + 0.0342658i
\(625\) −1.47678e16 −0.247763
\(626\) 2.01447e16 + 5.24697e16i 0.334746 + 0.871892i
\(627\) −2.45940e15 −0.0404784
\(628\) 3.25113e16 + 3.60990e16i 0.530001 + 0.588487i
\(629\) 1.47625e17i 2.38373i
\(630\) 6.81269e15 + 1.77446e16i 0.108962 + 0.283806i
\(631\) 1.39747e16i 0.221394i 0.993854 + 0.110697i \(0.0353083\pi\)
−0.993854 + 0.110697i \(0.964692\pi\)
\(632\) −5.22981e15 + 1.02685e16i −0.0820698 + 0.161141i
\(633\) −1.00233e16 −0.155807
\(634\) −6.19634e16 + 2.37897e16i −0.954113 + 0.366314i
\(635\) 1.37688e16 0.210017
\(636\) 4.32570e15 + 4.80305e15i 0.0653603 + 0.0725729i
\(637\) 4.42800e16i 0.662782i
\(638\) −3.51768e15 + 1.35055e15i −0.0521593 + 0.0200256i
\(639\) 9.09853e16i 1.33649i
\(640\) −4.07179e16 2.64189e16i −0.592523 0.384445i
\(641\) −7.70870e16 −1.11130 −0.555652 0.831415i \(-0.687531\pi\)
−0.555652 + 0.831415i \(0.687531\pi\)
\(642\) −2.20945e15 5.75480e15i −0.0315554 0.0821903i
\(643\) −5.78604e16 −0.818683 −0.409341 0.912381i \(-0.634242\pi\)
−0.409341 + 0.912381i \(0.634242\pi\)
\(644\) 3.71048e16 3.34172e16i 0.520134 0.468441i
\(645\) 2.14267e16i 0.297576i
\(646\) 4.18428e16 + 1.08985e17i 0.575739 + 1.49959i
\(647\) 2.38112e15i 0.0324605i 0.999868 + 0.0162303i \(0.00516648\pi\)
−0.999868 + 0.0162303i \(0.994834\pi\)
\(648\) −3.98473e16 2.02944e16i −0.538206 0.274111i
\(649\) −5.27283e15 −0.0705628
\(650\) −3.11605e16 + 1.19635e16i −0.413166 + 0.158627i
\(651\) −7.40250e15 −0.0972506
\(652\) 1.37797e16 1.24102e16i 0.179372 0.161545i
\(653\) 9.86680e16i 1.27262i −0.771435 0.636308i \(-0.780461\pi\)
0.771435 0.636308i \(-0.219539\pi\)
\(654\) 3.70143e16 1.42109e16i 0.473046 0.181617i
\(655\) 4.39152e16i 0.556118i
\(656\) 1.34451e14 1.28209e15i 0.00168710 0.0160878i
\(657\) 8.72598e16 1.08498
\(658\) −2.78525e16 7.25456e16i −0.343170 0.893832i
\(659\) −6.67559e16 −0.815037 −0.407518 0.913197i \(-0.633606\pi\)
−0.407518 + 0.913197i \(0.633606\pi\)
\(660\) 1.20433e15 + 1.33723e15i 0.0145707 + 0.0161786i
\(661\) 9.72864e16i 1.16639i 0.812333 + 0.583194i \(0.198197\pi\)
−0.812333 + 0.583194i \(0.801803\pi\)
\(662\) −3.32427e16 8.65851e16i −0.394956 1.02872i
\(663\) 3.41345e16i 0.401895i
\(664\) −7.62219e16 3.88202e16i −0.889348 0.452949i
\(665\) −4.00689e16 −0.463316
\(666\) −1.36784e17 + 5.25155e16i −1.56743 + 0.601786i
\(667\) 8.31950e16 0.944805
\(668\) −1.54650e16 1.71716e16i −0.174057 0.193264i
\(669\) 3.73034e16i 0.416094i
\(670\) 5.76501e16 2.21337e16i 0.637311 0.244684i
\(671\) 5.63023e15i 0.0616866i
\(672\) 4.43406e15 + 1.65289e16i 0.0481489 + 0.179485i
\(673\) 6.78970e16 0.730735 0.365368 0.930863i \(-0.380943\pi\)
0.365368 + 0.930863i \(0.380943\pi\)
\(674\) 3.47066e16 + 9.03980e16i 0.370214 + 0.964272i
\(675\) −3.28247e16 −0.347039
\(676\) −1.56014e16 + 1.40508e16i −0.163487 + 0.147239i
\(677\) 3.44804e16i 0.358130i 0.983837 + 0.179065i \(0.0573073\pi\)
−0.983837 + 0.179065i \(0.942693\pi\)
\(678\) 1.21618e16 + 3.16770e16i 0.125204 + 0.326111i
\(679\) 2.76712e15i 0.0282364i
\(680\) 3.87678e16 7.61190e16i 0.392119 0.769910i
\(681\) 6.38105e16 0.639749
\(682\) 4.07370e15 1.56402e15i 0.0404839 0.0155430i
\(683\) 5.65913e16 0.557475 0.278738 0.960367i \(-0.410084\pi\)
0.278738 + 0.960367i \(0.410084\pi\)
\(684\) 8.60965e16 7.75398e16i 0.840715 0.757161i
\(685\) 6.36084e16i 0.615702i
\(686\) −8.50763e16 + 3.26634e16i −0.816326 + 0.313413i
\(687\) 1.11270e16i 0.105837i
\(688\) −1.25271e16 + 1.19455e17i −0.118119 + 1.12636i
\(689\) 2.48060e16 0.231868
\(690\) −1.42415e16 3.70939e16i −0.131966 0.343722i
\(691\) 1.15097e17 1.05730 0.528648 0.848841i \(-0.322699\pi\)
0.528648 + 0.848841i \(0.322699\pi\)
\(692\) 9.55851e15 + 1.06133e16i 0.0870469 + 0.0966528i
\(693\) 3.95045e15i 0.0356654i
\(694\) −6.12509e16 1.59536e17i −0.548221 1.42791i
\(695\) 4.82380e16i 0.428036i
\(696\) −1.29397e16 + 2.54067e16i −0.113833 + 0.223507i
\(697\) 2.26876e15 0.0197875
\(698\) 1.55510e17 5.97050e16i 1.34470 0.516271i
\(699\) −4.78850e15 −0.0410522
\(700\) −1.97090e16 2.18839e16i −0.167524 0.186010i
\(701\) 1.29467e17i 1.09107i 0.838089 + 0.545533i \(0.183673\pi\)
−0.838089 + 0.545533i \(0.816327\pi\)
\(702\) 6.83353e16 2.62360e16i 0.570982 0.219218i
\(703\) 3.08870e17i 2.55885i
\(704\) −5.93239e15 8.15923e15i −0.0487297 0.0670214i
\(705\) −6.18339e16 −0.503607
\(706\) −6.03384e16 1.57160e17i −0.487266 1.26915i
\(707\) 5.16974e16 0.413954
\(708\) −2.96473e16 + 2.67008e16i −0.235389 + 0.211995i
\(709\) 1.13514e16i 0.0893657i 0.999001 + 0.0446829i \(0.0142277\pi\)
−0.999001 + 0.0446829i \(0.985772\pi\)
\(710\) 5.03035e16 + 1.31022e17i 0.392688 + 1.02281i
\(711\) 2.01287e16i 0.155811i
\(712\) −4.23796e16 2.15841e16i −0.325295 0.165674i
\(713\) −9.63452e16 −0.733319
\(714\) −2.81171e16 + 1.07950e16i −0.212217 + 0.0814768i
\(715\) 6.90628e15 0.0516901
\(716\) −1.07259e17 + 9.65987e16i −0.796075 + 0.716957i
\(717\) 2.40867e16i 0.177281i
\(718\) 8.00357e16 3.07282e16i 0.584167 0.224280i
\(719\) 3.34950e16i 0.242441i 0.992626 + 0.121221i \(0.0386809\pi\)
−0.992626 + 0.121221i \(0.961319\pi\)
\(720\) −8.43201e16 8.84251e15i −0.605252 0.0634718i
\(721\) −8.55392e16 −0.608911
\(722\) 3.67747e16 + 9.57848e16i 0.259613 + 0.676197i
\(723\) −3.15803e16 −0.221099
\(724\) 1.25202e17 + 1.39019e17i 0.869322 + 0.965254i
\(725\) 4.90673e16i 0.337881i
\(726\) −1.93897e16 5.05031e16i −0.132419 0.344904i
\(727\) 9.28323e16i 0.628771i −0.949295 0.314386i \(-0.898202\pi\)
0.949295 0.314386i \(-0.101798\pi\)
\(728\) 5.85221e16 + 2.98056e16i 0.393126 + 0.200221i
\(729\) −3.94419e16 −0.262780
\(730\) 1.25657e17 4.82437e16i 0.830330 0.318789i
\(731\) −2.11386e17 −1.38539
\(732\) −2.85106e16 3.16569e16i −0.185328 0.205779i
\(733\) 1.02514e17i 0.660939i 0.943817 + 0.330469i \(0.107207\pi\)
−0.943817 + 0.330469i \(0.892793\pi\)
\(734\) −1.75464e17 + 6.73662e16i −1.12205 + 0.430790i
\(735\) 3.10885e16i 0.197186i
\(736\) 5.77103e16 + 2.15127e17i 0.363067 + 1.35341i
\(737\) 1.28346e16 0.0800897
\(738\) −8.07078e14 2.10214e15i −0.00499548 0.0130114i
\(739\) 3.10260e16 0.190484 0.0952421 0.995454i \(-0.469637\pi\)
0.0952421 + 0.995454i \(0.469637\pi\)
\(740\) −1.67939e17 + 1.51249e17i −1.02273 + 0.921088i
\(741\) 7.14183e16i 0.431420i
\(742\) 7.84488e15 + 2.04330e16i 0.0470070 + 0.122436i
\(743\) 6.07618e16i 0.361158i −0.983560 0.180579i \(-0.942203\pi\)
0.983560 0.180579i \(-0.0577972\pi\)
\(744\) 1.49851e16 2.94225e16i 0.0883529 0.173477i
\(745\) −8.42254e16 −0.492613
\(746\) 1.55754e17 5.97989e16i 0.903664 0.346945i
\(747\) −1.49413e17 −0.859932
\(748\) 1.31924e16 1.18813e16i 0.0753208 0.0678351i
\(749\) 2.08733e16i 0.118222i
\(750\) −6.55348e16 + 2.51608e16i −0.368217 + 0.141370i
\(751\) 1.70978e17i 0.953018i −0.879170 0.476509i \(-0.841902\pi\)
0.879170 0.476509i \(-0.158098\pi\)
\(752\) 3.44728e17 + 3.61511e16i 1.90621 + 0.199901i
\(753\) −5.75412e16 −0.315652
\(754\) 3.92184e16 + 1.02150e17i 0.213433 + 0.555915i
\(755\) 1.16821e17 0.630724
\(756\) 4.32220e16 + 4.79916e16i 0.231512 + 0.257060i
\(757\) 1.08916e17i 0.578785i −0.957211 0.289393i \(-0.906547\pi\)
0.957211 0.289393i \(-0.0934533\pi\)
\(758\) −9.96810e16 2.59633e17i −0.525529 1.36881i
\(759\) 8.25816e15i 0.0431949i
\(760\) 8.11124e16 1.59261e17i 0.420926 0.826471i
\(761\) 1.35235e16 0.0696275 0.0348138 0.999394i \(-0.488916\pi\)
0.0348138 + 0.999394i \(0.488916\pi\)
\(762\) 2.02151e16 7.76119e15i 0.103263 0.0396459i
\(763\) 1.34255e17 0.680428
\(764\) −2.52409e17 2.80262e17i −1.26924 1.40930i
\(765\) 1.49211e17i 0.744444i
\(766\) 1.33695e17 5.13297e16i 0.661824 0.254095i
\(767\) 1.53117e17i 0.752060i
\(768\) −7.46729e16 1.58358e16i −0.363912 0.0771744i
\(769\) 3.05550e17 1.47749 0.738745 0.673986i \(-0.235419\pi\)
0.738745 + 0.673986i \(0.235419\pi\)
\(770\) 2.18411e15 + 5.68880e15i 0.0104792 + 0.0272946i
\(771\) 1.06220e17 0.505685
\(772\) 2.78298e16 2.50639e16i 0.131464 0.118398i
\(773\) 9.17640e16i 0.430126i 0.976600 + 0.215063i \(0.0689956\pi\)
−0.976600 + 0.215063i \(0.931004\pi\)
\(774\) 7.51975e16 + 1.95862e17i 0.349750 + 0.910971i
\(775\) 5.68231e16i 0.262250i
\(776\) −1.09984e16 5.60154e15i −0.0503685 0.0256529i
\(777\) 7.96855e16 0.362120
\(778\) −5.95918e16 + 2.28791e16i −0.268726 + 0.103172i
\(779\) 4.74684e15 0.0212412
\(780\) 3.88316e16 3.49724e16i 0.172432 0.155295i
\(781\) 2.91693e16i 0.128535i
\(782\) −3.65950e17 + 1.40500e17i −1.60023 + 0.614376i
\(783\) 1.07605e17i 0.466941i
\(784\) 1.81758e16 1.73320e17i 0.0782704 0.746368i
\(785\) 1.30896e17 0.559382
\(786\) 2.47541e16 + 6.44753e16i 0.104981 + 0.273438i
\(787\) −1.56040e16 −0.0656733 −0.0328366 0.999461i \(-0.510454\pi\)
−0.0328366 + 0.999461i \(0.510454\pi\)
\(788\) −1.48541e17 1.64932e17i −0.620423 0.688888i
\(789\) 3.79832e16i 0.157445i
\(790\) 1.11286e16 + 2.89861e16i 0.0457804 + 0.119241i
\(791\) 1.14896e17i 0.469078i
\(792\) −1.57018e16 7.99699e15i −0.0636206 0.0324023i
\(793\) −1.63496e17 −0.657458
\(794\) −3.73628e16 + 1.43447e16i −0.149113 + 0.0572492i
\(795\) 1.74160e16 0.0689836
\(796\) −6.59547e16 7.32330e16i −0.259279 0.287891i
\(797\) 4.85611e16i 0.189469i −0.995503 0.0947347i \(-0.969800\pi\)
0.995503 0.0947347i \(-0.0302003\pi\)
\(798\) −5.88283e16 + 2.25860e16i −0.227808 + 0.0874625i
\(799\) 6.10024e17i 2.34458i
\(800\) 1.26879e17 3.40368e16i 0.484005 0.129840i
\(801\) −8.30738e16 −0.314535
\(802\) 4.01959e16 + 1.04696e17i 0.151055 + 0.393444i
\(803\) 2.79749e16 0.104346
\(804\) 7.21644e16 6.49924e16i 0.267170 0.240617i
\(805\) 1.34543e17i 0.494409i
\(806\) −4.54175e16 1.18296e17i −0.165658 0.431479i
\(807\) 1.15013e17i 0.416397i
\(808\) −1.04652e17 + 2.05480e17i −0.376080 + 0.738418i
\(809\) 4.40284e17 1.57051 0.785257 0.619170i \(-0.212531\pi\)
0.785257 + 0.619170i \(0.212531\pi\)
\(810\) −1.12481e17 + 4.31850e16i −0.398263 + 0.152905i
\(811\) −3.50936e17 −1.23340 −0.616698 0.787200i \(-0.711530\pi\)
−0.616698 + 0.787200i \(0.711530\pi\)
\(812\) −7.17393e16 + 6.46095e16i −0.250277 + 0.225403i
\(813\) 1.56819e17i 0.543070i
\(814\) −4.38520e16 + 1.68362e16i −0.150745 + 0.0578757i
\(815\) 4.99656e16i 0.170500i
\(816\) 1.40114e16 1.33609e17i 0.0474613 0.452579i
\(817\) −4.42274e17 −1.48717
\(818\) −6.11580e16 1.59294e17i −0.204143 0.531717i
\(819\) 1.14717e17 0.380123
\(820\) −2.32445e15 2.58095e15i −0.00764604 0.00848979i
\(821\) 1.05121e17i 0.343267i −0.985161 0.171633i \(-0.945096\pi\)
0.985161 0.171633i \(-0.0549044\pi\)
\(822\) 3.58547e16 + 9.33885e16i 0.116229 + 0.302735i
\(823\) 6.15349e16i 0.198026i −0.995086 0.0990130i \(-0.968431\pi\)
0.995086 0.0990130i \(-0.0315686\pi\)
\(824\) 1.73159e17 3.39991e17i 0.553200 1.08619i
\(825\) −4.87055e15 −0.0154474
\(826\) −1.26125e17 + 4.84233e16i −0.397119 + 0.152466i
\(827\) −3.00278e17 −0.938622 −0.469311 0.883033i \(-0.655498\pi\)
−0.469311 + 0.883033i \(0.655498\pi\)
\(828\) 2.60363e17 + 2.89095e17i 0.807974 + 0.897135i
\(829\) 5.15625e17i 1.58857i −0.607544 0.794286i \(-0.707845\pi\)
0.607544 0.794286i \(-0.292155\pi\)
\(830\) −2.15160e17 + 8.26066e16i −0.658102 + 0.252666i
\(831\) 2.20265e17i 0.668865i
\(832\) −2.36935e17 + 1.72270e17i −0.714315 + 0.519362i
\(833\) 3.06704e17 0.918014
\(834\) 2.71908e16 + 7.08220e16i 0.0808026 + 0.210461i
\(835\) −6.22646e16 −0.183706
\(836\) 2.76020e16 2.48588e16i 0.0808543 0.0728186i
\(837\) 1.24614e17i 0.362420i
\(838\) 1.11953e17 + 2.91596e17i 0.323273 + 0.842009i
\(839\) 4.16410e17i 1.19385i 0.802297 + 0.596925i \(0.203611\pi\)
−0.802297 + 0.596925i \(0.796389\pi\)
\(840\) 4.10877e16 + 2.09262e16i 0.116960 + 0.0595682i
\(841\) 1.92964e17 0.545381
\(842\) 4.49202e17 1.72463e17i 1.26058 0.483975i
\(843\) −1.48677e17 −0.414264
\(844\) 1.12492e17 1.01312e17i 0.311219 0.280289i
\(845\) 5.65710e16i 0.155401i
\(846\) 5.65224e17 2.17007e17i 1.54170 0.591905i
\(847\) 1.83180e17i 0.496109i
\(848\) −9.70954e16 1.01822e16i −0.261110 0.0273822i
\(849\) −2.23871e17 −0.597793
\(850\) 8.28648e16 + 2.15832e17i 0.219713 + 0.572273i
\(851\) 1.03712e18 2.73057
\(852\) 1.47709e17 + 1.64009e17i 0.386162 + 0.428776i
\(853\) 5.70676e17i 1.48148i 0.671792 + 0.740740i \(0.265525\pi\)
−0.671792 + 0.740740i \(0.734475\pi\)
\(854\) −5.17055e16 1.34674e17i −0.133287 0.347165i
\(855\) 3.12188e17i 0.799135i
\(856\) 8.29645e16 + 4.22542e16i 0.210887 + 0.107406i
\(857\) −6.68524e17 −1.68746 −0.843728 0.536772i \(-0.819644\pi\)
−0.843728 + 0.536772i \(0.819644\pi\)
\(858\) 1.01396e16 3.89293e15i 0.0254155 0.00975781i
\(859\) −5.56346e17 −1.38480 −0.692399 0.721515i \(-0.743446\pi\)
−0.692399 + 0.721515i \(0.743446\pi\)
\(860\) 2.16574e17 + 2.40474e17i 0.535324 + 0.594398i
\(861\) 1.22464e15i 0.00300599i
\(862\) 2.86795e17 1.10109e17i 0.699081 0.268399i
\(863\) 4.97736e17i 1.20485i −0.798174 0.602427i \(-0.794201\pi\)
0.798174 0.602427i \(-0.205799\pi\)
\(864\) −2.78247e17 + 7.46429e16i −0.668879 + 0.179435i
\(865\) 3.84842e16 0.0918725
\(866\) −1.10370e17 2.87473e17i −0.261663 0.681537i
\(867\) 7.84295e16 0.184657
\(868\) 8.30788e16 7.48220e16i 0.194255 0.174949i
\(869\) 6.45313e15i 0.0149848i
\(870\) 2.75348e16 + 7.17181e16i 0.0634989 + 0.165392i
\(871\) 3.72703e17i 0.853598i
\(872\) −2.71775e17 + 5.33619e17i −0.618174 + 1.21376i
\(873\) −2.15594e16 −0.0487025
\(874\) −7.65663e17 + 2.93962e17i −1.71779 + 0.659511i
\(875\) −2.37701e17 −0.529643
\(876\) 1.57293e17 1.41661e17i 0.348086 0.313491i
\(877\) 1.21940e17i 0.268008i −0.990981 0.134004i \(-0.957216\pi\)
0.990981 0.134004i \(-0.0427836\pi\)
\(878\) 4.19166e17 1.60931e17i 0.914996 0.351295i
\(879\) 3.89332e16i 0.0844087i
\(880\) −2.70325e16 2.83485e15i −0.0582090 0.00610428i
\(881\) −1.61506e16 −0.0345410 −0.0172705 0.999851i \(-0.505498\pi\)
−0.0172705 + 0.999851i \(0.505498\pi\)
\(882\) −1.09106e17 2.84180e17i −0.231758 0.603646i
\(883\) 3.48909e17 0.736118 0.368059 0.929802i \(-0.380022\pi\)
0.368059 + 0.929802i \(0.380022\pi\)
\(884\) −3.45020e17 3.83094e17i −0.722988 0.802771i
\(885\) 1.07502e17i 0.223747i
\(886\) −1.00367e17 2.61420e17i −0.207486 0.540426i
\(887\) 1.79060e17i 0.367668i −0.982957 0.183834i \(-0.941149\pi\)
0.982957 0.183834i \(-0.0588509\pi\)
\(888\) −1.61309e17 + 3.16724e17i −0.328989 + 0.645957i
\(889\) 7.33221e16 0.148533
\(890\) −1.19629e17 + 4.59295e16i −0.240712 + 0.0924169i
\(891\) −2.50415e16 −0.0500489
\(892\) 3.77050e17 + 4.18659e17i 0.748532 + 0.831134i
\(893\) 1.27633e18i 2.51683i
\(894\) −1.23658e17 + 4.74761e16i −0.242213 + 0.0929930i
\(895\) 3.88923e17i 0.756702i
\(896\) −2.16832e17 1.40687e17i −0.419060 0.271897i
\(897\) −2.39808e17 −0.460372
\(898\) −1.05058e17 2.73639e17i −0.200342 0.521818i
\(899\) 1.86276e17 0.352857
\(900\) 1.70504e17 1.53559e17i 0.320834 0.288948i
\(901\) 1.71818e17i 0.321159i
\(902\) −2.58744e14 6.73934e14i −0.000480432 0.00125135i
\(903\) 1.14102e17i 0.210459i
\(904\) −4.56673e17 2.32586e17i −0.836749 0.426160i
\(905\) 5.04085e17 0.917514
\(906\) 1.71514e17 6.58497e16i 0.310121 0.119065i
\(907\) −2.91685e17 −0.523927 −0.261963 0.965078i \(-0.584370\pi\)
−0.261963 + 0.965078i \(0.584370\pi\)
\(908\) −7.16151e17 + 6.44976e17i −1.27788 + 1.15088i
\(909\) 4.02789e17i 0.713994i
\(910\) 1.65197e17 6.34241e16i 0.290906 0.111688i
\(911\) 3.15264e15i 0.00551523i 0.999996 + 0.00275761i \(0.000877777\pi\)
−0.999996 + 0.00275761i \(0.999122\pi\)
\(912\) 2.93154e16 2.79545e17i 0.0509480 0.485828i
\(913\) −4.79008e16 −0.0827024
\(914\) −8.57371e16 2.23314e17i −0.147059 0.383035i
\(915\) −1.14789e17 −0.195602
\(916\) −1.12469e17 1.24880e17i −0.190396 0.211407i
\(917\) 2.33858e17i 0.393312i
\(918\) −1.81723e17 4.73322e17i −0.303637 0.790863i
\(919\) 9.27348e17i 1.53939i 0.638409 + 0.769697i \(0.279593\pi\)
−0.638409 + 0.769697i \(0.720407\pi\)
\(920\) 5.34766e17 + 2.72359e17i 0.881935 + 0.449174i
\(921\) 4.16478e17 0.682393
\(922\) −3.58342e17 + 1.37578e17i −0.583327 + 0.223957i
\(923\) 8.47046e17 1.36993
\(924\) 6.41332e15 + 7.12104e15i 0.0103051 + 0.0114423i
\(925\) 6.11682e17i 0.976507i
\(926\) 2.90211e17 1.11421e17i 0.460308 0.176726i
\(927\) 6.66461e17i 1.05026i
\(928\) −1.11578e17 4.15931e17i −0.174700 0.651229i
\(929\) −9.18415e16 −0.142871 −0.0714356 0.997445i \(-0.522758\pi\)
−0.0714356 + 0.997445i \(0.522758\pi\)
\(930\) −3.18871e16 8.30542e16i −0.0492853 0.128370i
\(931\) 6.41705e17 0.985456
\(932\) 5.37417e16 4.84006e16i 0.0820005 0.0738509i
\(933\) 1.97003e17i 0.298663i
\(934\) 2.35205e17 + 6.12624e17i 0.354296 + 0.922811i
\(935\) 4.78361e16i 0.0715956i
\(936\) −2.32224e17 + 4.55963e17i −0.345344 + 0.678070i
\(937\) 1.41341e17 0.208848 0.104424 0.994533i \(-0.466700\pi\)
0.104424 + 0.994533i \(0.466700\pi\)
\(938\) 3.07000e17 1.17867e17i 0.450736 0.173051i
\(939\) 2.38157e17 0.347431
\(940\) 6.93967e17 6.24997e17i 1.00594 0.905964i
\(941\) 7.67731e17i 1.10579i −0.833252 0.552893i \(-0.813524\pi\)
0.833252 0.552893i \(-0.186476\pi\)
\(942\) 1.92179e17 7.37833e16i 0.275042 0.105597i
\(943\) 1.59389e16i 0.0226667i
\(944\) 6.28509e16 5.99331e17i 0.0888136 0.846905i
\(945\) 1.74019e17 0.244346
\(946\) 2.41078e16 + 6.27921e16i 0.0336366 + 0.0876110i
\(947\) −9.75819e17 −1.35291 −0.676456 0.736483i \(-0.736485\pi\)
−0.676456 + 0.736483i \(0.736485\pi\)
\(948\) 3.26777e16 + 3.62837e16i 0.0450195 + 0.0499876i
\(949\) 8.12362e17i 1.11212i
\(950\) 1.73375e17 + 4.51578e17i 0.235855 + 0.614315i
\(951\) 2.81248e17i 0.380195i
\(952\) 2.06448e17 4.05352e17i 0.277324 0.544515i
\(953\) −1.09905e18 −1.46710 −0.733552 0.679633i \(-0.762139\pi\)
−0.733552 + 0.679633i \(0.762139\pi\)
\(954\) −1.59200e17 + 6.11217e16i −0.211180 + 0.0810785i
\(955\) −1.01624e18 −1.33960
\(956\) 2.43461e17 + 2.70327e17i 0.318920 + 0.354113i
\(957\) 1.59665e16i 0.0207844i
\(958\) −6.07057e17 + 2.33068e17i −0.785301 + 0.301501i
\(959\) 3.38729e17i 0.435453i
\(960\) −1.66350e17 + 1.20949e17i −0.212517 + 0.154517i
\(961\) 5.71943e17 0.726127
\(962\) 4.88904e17 + 1.27342e18i 0.616841 + 1.60665i
\(963\) 1.62630e17 0.203912
\(964\) 3.54428e17 3.19204e17i 0.441638 0.397746i
\(965\) 1.00912e17i 0.124962i
\(966\) −7.58392e16 1.97533e17i −0.0933321 0.243096i
\(967\) 4.86043e17i 0.594451i 0.954807 + 0.297226i \(0.0960613\pi\)
−0.954807 + 0.297226i \(0.903939\pi\)
\(968\) 7.28080e17 + 3.70815e17i 0.884967 + 0.450718i
\(969\) 4.94677e17 0.597556
\(970\) −3.10464e16 + 1.19197e16i −0.0372718 + 0.0143098i
\(971\) −9.53000e17 −1.13704 −0.568522 0.822668i \(-0.692485\pi\)
−0.568522 + 0.822668i \(0.692485\pi\)
\(972\) −5.74773e17 + 5.17650e17i −0.681552 + 0.613816i
\(973\) 2.56879e17i 0.302727i
\(974\) −1.40056e18 + 5.37718e17i −1.64039 + 0.629797i
\(975\) 1.41436e17i 0.164638i
\(976\) 6.39954e17 + 6.71110e16i 0.740372 + 0.0776416i
\(977\) −3.17247e17 −0.364780 −0.182390 0.983226i \(-0.558383\pi\)
−0.182390 + 0.983226i \(0.558383\pi\)
\(978\) −2.81646e16 7.33584e16i −0.0321862 0.0838334i
\(979\) −2.66330e16 −0.0302498
\(980\) −3.14232e17 3.48908e17i −0.354727 0.393872i
\(981\) 1.04602e18i 1.17361i
\(982\) 4.68162e17 + 1.21939e18i 0.522068 + 1.35980i
\(983\) 1.23563e18i 1.36952i −0.728770 0.684759i \(-0.759907\pi\)
0.728770 0.684759i \(-0.240093\pi\)
\(984\) −4.86753e15 2.47906e15i −0.00536214 0.00273097i
\(985\) −5.98049e17 −0.654816
\(986\) 7.07536e17 2.71645e17i 0.769994 0.295624i
\(987\) −3.29280e17 −0.356174
\(988\) −7.21873e17 8.01533e17i −0.776102 0.861747i
\(989\) 1.48507e18i 1.58697i
\(990\) −4.43231e16 + 1.70170e16i −0.0470781 + 0.0180747i
\(991\) 5.61949e17i 0.593274i 0.954990 + 0.296637i \(0.0958651\pi\)
−0.954990 + 0.296637i \(0.904135\pi\)
\(992\) 1.29215e17 + 4.81675e17i 0.135595 + 0.505457i
\(993\) −3.93004e17 −0.409922
\(994\) 2.67878e17 + 6.97724e17i 0.277727 + 0.723378i
\(995\) −2.65545e17 −0.273652
\(996\) −2.69330e17 + 2.42562e17i −0.275885 + 0.248466i
\(997\) 1.39731e18i 1.42272i −0.702826 0.711361i \(-0.748079\pi\)
0.702826 0.711361i \(-0.251921\pi\)
\(998\) −6.76918e17 1.76312e18i −0.685098 1.78443i
\(999\) 1.34142e18i 1.34950i
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 8.13.d.b.3.8 yes 10
3.2 odd 2 72.13.b.b.19.3 10
4.3 odd 2 32.13.d.b.15.4 10
8.3 odd 2 inner 8.13.d.b.3.7 10
8.5 even 2 32.13.d.b.15.3 10
24.11 even 2 72.13.b.b.19.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.13.d.b.3.7 10 8.3 odd 2 inner
8.13.d.b.3.8 yes 10 1.1 even 1 trivial
32.13.d.b.15.3 10 8.5 even 2
32.13.d.b.15.4 10 4.3 odd 2
72.13.b.b.19.3 10 3.2 odd 2
72.13.b.b.19.4 10 24.11 even 2