Properties

Label 8.13.d.b.3.2
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 3.2
Root \(-25.4137 - 6.09761i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.13.d.b.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-62.8274 + 12.1952i) q^{2} +24.0930 q^{3} +(3798.55 - 1532.39i) q^{4} +25133.2i q^{5} +(-1513.70 + 293.819i) q^{6} -190438. i q^{7} +(-219965. + 142600. i) q^{8} -530861. q^{9} +O(q^{10})\) \(q+(-62.8274 + 12.1952i) q^{2} +24.0930 q^{3} +(3798.55 - 1532.39i) q^{4} +25133.2i q^{5} +(-1513.70 + 293.819i) q^{6} -190438. i q^{7} +(-219965. + 142600. i) q^{8} -530861. q^{9} +(-306505. - 1.57906e6i) q^{10} -1.60494e6 q^{11} +(91518.6 - 36919.8i) q^{12} -3.13062e6i q^{13} +(2.32243e6 + 1.19647e7i) q^{14} +605535. i q^{15} +(1.20808e7 - 1.16417e7i) q^{16} -1.87119e7 q^{17} +(3.33526e7 - 6.47396e6i) q^{18} -2.37206e7 q^{19} +(3.85138e7 + 9.54700e7i) q^{20} -4.58823e6i q^{21} +(1.00834e8 - 1.95726e7i) q^{22} -9.22388e7i q^{23} +(-5.29963e6 + 3.43566e6i) q^{24} -3.87539e8 q^{25} +(3.81786e7 + 1.96689e8i) q^{26} -2.55940e7 q^{27} +(-2.91825e8 - 7.23389e8i) q^{28} -4.84649e8i q^{29} +(-7.38463e6 - 3.80442e7i) q^{30} +6.86189e8i q^{31} +(-6.17032e8 + 8.78745e8i) q^{32} -3.86678e7 q^{33} +(1.17562e9 - 2.28195e8i) q^{34} +4.78633e9 q^{35} +(-2.01650e9 + 8.13483e8i) q^{36} +2.95206e9i q^{37} +(1.49030e9 - 2.89278e8i) q^{38} -7.54260e7i q^{39} +(-3.58400e9 - 5.52844e9i) q^{40} -4.28864e9 q^{41} +(5.59544e7 + 2.88266e8i) q^{42} +5.06490e9 q^{43} +(-6.09645e9 + 2.45939e9i) q^{44} -1.33422e10i q^{45} +(1.12487e9 + 5.79512e9i) q^{46} +8.78567e9i q^{47} +(2.91063e8 - 2.80484e8i) q^{48} -2.24254e10 q^{49} +(2.43481e10 - 4.72612e9i) q^{50} -4.50825e8 q^{51} +(-4.79732e9 - 1.18918e10i) q^{52} +1.91993e10i q^{53} +(1.60801e9 - 3.12125e8i) q^{54} -4.03373e10i q^{55} +(2.71565e10 + 4.18898e10i) q^{56} -5.71501e8 q^{57} +(5.91040e9 + 3.04492e10i) q^{58} -3.49769e9 q^{59} +(9.27914e8 + 2.30016e9i) q^{60} -2.44704e10i q^{61} +(-8.36822e9 - 4.31115e10i) q^{62} +1.01096e11i q^{63} +(2.80500e10 - 6.27341e10i) q^{64} +7.86826e10 q^{65} +(2.42940e9 - 4.71562e8i) q^{66} -8.26763e10 q^{67} +(-7.10780e10 + 2.86738e10i) q^{68} -2.22231e9i q^{69} +(-3.00712e11 + 5.83703e10i) q^{70} -1.93928e11i q^{71} +(1.16771e11 - 7.57007e10i) q^{72} +1.67338e11 q^{73} +(-3.60010e10 - 1.85470e11i) q^{74} -9.33698e9 q^{75} +(-9.01041e10 + 3.63492e10i) q^{76} +3.05641e11i q^{77} +(9.19837e8 + 4.73882e9i) q^{78} +1.86669e11i q^{79} +(2.92594e11 + 3.03630e11i) q^{80} +2.81504e11 q^{81} +(2.69444e11 - 5.23009e10i) q^{82} -1.03167e11 q^{83} +(-7.03093e9 - 1.74286e10i) q^{84} -4.70290e11i q^{85} +(-3.18214e11 + 6.17675e10i) q^{86} -1.16767e10i q^{87} +(3.53031e11 - 2.28864e11i) q^{88} -4.34582e11 q^{89} +(1.62712e11 + 8.38258e11i) q^{90} -5.96189e11 q^{91} +(-1.41346e11 - 3.50374e11i) q^{92} +1.65324e10i q^{93} +(-1.07143e11 - 5.51980e11i) q^{94} -5.96176e11i q^{95} +(-1.48661e10 + 2.11716e10i) q^{96} -1.22566e12 q^{97} +(1.40893e12 - 2.73482e11i) q^{98} +8.51999e11 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −62.8274 + 12.1952i −0.981677 + 0.190550i
\(3\) 24.0930 0.0330494 0.0165247 0.999863i \(-0.494740\pi\)
0.0165247 + 0.999863i \(0.494740\pi\)
\(4\) 3798.55 1532.39i 0.927381 0.374118i
\(5\) 25133.2i 1.60853i 0.594273 + 0.804264i \(0.297440\pi\)
−0.594273 + 0.804264i \(0.702560\pi\)
\(6\) −1513.70 + 293.819i −0.0324438 + 0.00629757i
\(7\) 190438.i 1.61870i −0.587329 0.809348i \(-0.699820\pi\)
0.587329 0.809348i \(-0.300180\pi\)
\(8\) −219965. + 142600.i −0.839101 + 0.543976i
\(9\) −530861. −0.998908
\(10\) −306505. 1.57906e6i −0.306505 1.57906i
\(11\) −1.60494e6 −0.905946 −0.452973 0.891524i \(-0.649637\pi\)
−0.452973 + 0.891524i \(0.649637\pi\)
\(12\) 91518.6 36919.8i 0.0306494 0.0123644i
\(13\) 3.13062e6i 0.648590i −0.945956 0.324295i \(-0.894873\pi\)
0.945956 0.324295i \(-0.105127\pi\)
\(14\) 2.32243e6 + 1.19647e7i 0.308443 + 1.58904i
\(15\) 605535.i 0.0531609i
\(16\) 1.20808e7 1.16417e7i 0.720072 0.693900i
\(17\) −1.87119e7 −0.775218 −0.387609 0.921824i \(-0.626699\pi\)
−0.387609 + 0.921824i \(0.626699\pi\)
\(18\) 3.33526e7 6.47396e6i 0.980605 0.190342i
\(19\) −2.37206e7 −0.504202 −0.252101 0.967701i \(-0.581122\pi\)
−0.252101 + 0.967701i \(0.581122\pi\)
\(20\) 3.85138e7 + 9.54700e7i 0.601779 + 1.49172i
\(21\) 4.58823e6i 0.0534969i
\(22\) 1.00834e8 1.95726e7i 0.889347 0.172628i
\(23\) 9.22388e7i 0.623084i −0.950232 0.311542i \(-0.899154\pi\)
0.950232 0.311542i \(-0.100846\pi\)
\(24\) −5.29963e6 + 3.43566e6i −0.0277318 + 0.0179781i
\(25\) −3.87539e8 −1.58736
\(26\) 3.81786e7 + 1.96689e8i 0.123589 + 0.636706i
\(27\) −2.55940e7 −0.0660627
\(28\) −2.91825e8 7.23389e8i −0.605583 1.50115i
\(29\) 4.84649e8i 0.814779i −0.913255 0.407389i \(-0.866439\pi\)
0.913255 0.407389i \(-0.133561\pi\)
\(30\) −7.38463e6 3.80442e7i −0.0101298 0.0521868i
\(31\) 6.86189e8i 0.773168i 0.922254 + 0.386584i \(0.126345\pi\)
−0.922254 + 0.386584i \(0.873655\pi\)
\(32\) −6.17032e8 + 8.78745e8i −0.574656 + 0.818395i
\(33\) −3.86678e7 −0.0299410
\(34\) 1.17562e9 2.28195e8i 0.761014 0.147718i
\(35\) 4.78633e9 2.60372
\(36\) −2.01650e9 + 8.13483e8i −0.926368 + 0.373709i
\(37\) 2.95206e9i 1.15057i 0.817952 + 0.575287i \(0.195110\pi\)
−0.817952 + 0.575287i \(0.804890\pi\)
\(38\) 1.49030e9 2.89278e8i 0.494964 0.0960758i
\(39\) 7.54260e7i 0.0214355i
\(40\) −3.58400e9 5.52844e9i −0.875000 1.34972i
\(41\) −4.28864e9 −0.902852 −0.451426 0.892308i \(-0.649085\pi\)
−0.451426 + 0.892308i \(0.649085\pi\)
\(42\) 5.59544e7 + 2.88266e8i 0.0101939 + 0.0525167i
\(43\) 5.06490e9 0.801235 0.400617 0.916245i \(-0.368796\pi\)
0.400617 + 0.916245i \(0.368796\pi\)
\(44\) −6.09645e9 + 2.45939e9i −0.840157 + 0.338930i
\(45\) 1.33422e10i 1.60677i
\(46\) 1.12487e9 + 5.79512e9i 0.118729 + 0.611668i
\(47\) 8.78567e9i 0.815056i 0.913193 + 0.407528i \(0.133609\pi\)
−0.913193 + 0.407528i \(0.866391\pi\)
\(48\) 2.91063e8 2.80484e8i 0.0237979 0.0229330i
\(49\) −2.24254e10 −1.62018
\(50\) 2.43481e10 4.72612e9i 1.55828 0.302472i
\(51\) −4.50825e8 −0.0256205
\(52\) −4.79732e9 1.18918e10i −0.242649 0.601490i
\(53\) 1.91993e10i 0.866222i 0.901341 + 0.433111i \(0.142584\pi\)
−0.901341 + 0.433111i \(0.857416\pi\)
\(54\) 1.60801e9 3.12125e8i 0.0648522 0.0125883i
\(55\) 4.03373e10i 1.45724i
\(56\) 2.71565e10 + 4.18898e10i 0.880532 + 1.35825i
\(57\) −5.71501e8 −0.0166636
\(58\) 5.91040e9 + 3.04492e10i 0.155256 + 0.799850i
\(59\) −3.49769e9 −0.0829219 −0.0414609 0.999140i \(-0.513201\pi\)
−0.0414609 + 0.999140i \(0.513201\pi\)
\(60\) 9.27914e8 + 2.30016e9i 0.0198884 + 0.0493004i
\(61\) 2.44704e10i 0.474965i −0.971392 0.237482i \(-0.923678\pi\)
0.971392 0.237482i \(-0.0763222\pi\)
\(62\) −8.36822e9 4.31115e10i −0.147327 0.759001i
\(63\) 1.01096e11i 1.61693i
\(64\) 2.80500e10 6.27341e10i 0.408181 0.912901i
\(65\) 7.86826e10 1.04327
\(66\) 2.42940e9 4.71562e8i 0.0293924 0.00570526i
\(67\) −8.26763e10 −0.913971 −0.456985 0.889474i \(-0.651071\pi\)
−0.456985 + 0.889474i \(0.651071\pi\)
\(68\) −7.10780e10 + 2.86738e10i −0.718922 + 0.290023i
\(69\) 2.22231e9i 0.0205926i
\(70\) −3.00712e11 + 5.83703e10i −2.55601 + 0.496139i
\(71\) 1.93928e11i 1.51388i −0.653486 0.756939i \(-0.726694\pi\)
0.653486 0.756939i \(-0.273306\pi\)
\(72\) 1.16771e11 7.57007e10i 0.838184 0.543381i
\(73\) 1.67338e11 1.10575 0.552874 0.833265i \(-0.313531\pi\)
0.552874 + 0.833265i \(0.313531\pi\)
\(74\) −3.60010e10 1.85470e11i −0.219242 1.12949i
\(75\) −9.33698e9 −0.0524613
\(76\) −9.01041e10 + 3.63492e10i −0.467587 + 0.188631i
\(77\) 3.05641e11i 1.46645i
\(78\) 9.19837e8 + 4.73882e9i 0.00408454 + 0.0210427i
\(79\) 1.86669e11i 0.767910i 0.923352 + 0.383955i \(0.125438\pi\)
−0.923352 + 0.383955i \(0.874562\pi\)
\(80\) 2.92594e11 + 3.03630e11i 1.11616 + 1.15826i
\(81\) 2.81504e11 0.996724
\(82\) 2.69444e11 5.23009e10i 0.886310 0.172039i
\(83\) −1.03167e11 −0.315553 −0.157777 0.987475i \(-0.550433\pi\)
−0.157777 + 0.987475i \(0.550433\pi\)
\(84\) −7.03093e9 1.74286e10i −0.0200142 0.0496121i
\(85\) 4.70290e11i 1.24696i
\(86\) −3.18214e11 + 6.17675e10i −0.786554 + 0.152675i
\(87\) 1.16767e10i 0.0269279i
\(88\) 3.53031e11 2.28864e11i 0.760180 0.492813i
\(89\) −4.34582e11 −0.874444 −0.437222 0.899354i \(-0.644038\pi\)
−0.437222 + 0.899354i \(0.644038\pi\)
\(90\) 1.62712e11 + 8.38258e11i 0.306170 + 1.57733i
\(91\) −5.96189e11 −1.04987
\(92\) −1.41346e11 3.50374e11i −0.233107 0.577837i
\(93\) 1.65324e10i 0.0255527i
\(94\) −1.07143e11 5.51980e11i −0.155309 0.800123i
\(95\) 5.96176e11i 0.811023i
\(96\) −1.48661e10 + 2.11716e10i −0.0189920 + 0.0270475i
\(97\) −1.22566e12 −1.47143 −0.735713 0.677293i \(-0.763153\pi\)
−0.735713 + 0.677293i \(0.763153\pi\)
\(98\) 1.40893e12 2.73482e11i 1.59049 0.308726i
\(99\) 8.51999e11 0.904956
\(100\) −1.47209e12 + 5.93860e11i −1.47209 + 0.593860i
\(101\) 1.80880e11i 0.170397i 0.996364 + 0.0851983i \(0.0271524\pi\)
−0.996364 + 0.0851983i \(0.972848\pi\)
\(102\) 2.83242e10 5.49791e9i 0.0251510 0.00488199i
\(103\) 8.06974e11i 0.675828i 0.941177 + 0.337914i \(0.109721\pi\)
−0.941177 + 0.337914i \(0.890279\pi\)
\(104\) 4.46426e11 + 6.88628e11i 0.352817 + 0.544232i
\(105\) 1.15317e11 0.0860513
\(106\) −2.34139e11 1.20624e12i −0.165059 0.850350i
\(107\) 1.97329e12 1.31488 0.657442 0.753505i \(-0.271638\pi\)
0.657442 + 0.753505i \(0.271638\pi\)
\(108\) −9.72203e10 + 3.92199e10i −0.0612653 + 0.0247152i
\(109\) 5.54844e11i 0.330835i −0.986224 0.165418i \(-0.947103\pi\)
0.986224 0.165418i \(-0.0528972\pi\)
\(110\) 4.91922e11 + 2.53429e12i 0.277677 + 1.43054i
\(111\) 7.11240e10i 0.0380258i
\(112\) −2.21702e12 2.30064e12i −1.12321 1.16558i
\(113\) 3.67045e11 0.176298 0.0881491 0.996107i \(-0.471905\pi\)
0.0881491 + 0.996107i \(0.471905\pi\)
\(114\) 3.59059e10 6.96958e9i 0.0163582 0.00317525i
\(115\) 2.31826e12 1.00225
\(116\) −7.42670e11 1.84097e12i −0.304823 0.755611i
\(117\) 1.66192e12i 0.647881i
\(118\) 2.19751e11 4.26551e10i 0.0814025 0.0158008i
\(119\) 3.56345e12i 1.25484i
\(120\) −8.63493e10 1.33197e11i −0.0289182 0.0446073i
\(121\) −5.62601e11 −0.179262
\(122\) 2.98421e11 + 1.53741e12i 0.0905047 + 0.466262i
\(123\) −1.03326e11 −0.0298387
\(124\) 1.05151e12 + 2.60653e12i 0.289256 + 0.717021i
\(125\) 3.60407e12i 0.944786i
\(126\) −1.23289e12 6.35160e12i −0.308106 1.58730i
\(127\) 6.92557e12i 1.65057i −0.564718 0.825284i \(-0.691015\pi\)
0.564718 0.825284i \(-0.308985\pi\)
\(128\) −9.97251e11 + 4.28349e12i −0.226749 + 0.973953i
\(129\) 1.22029e11 0.0264803
\(130\) −4.94342e12 + 9.59551e11i −1.02416 + 0.198796i
\(131\) −9.09784e12 −1.80016 −0.900079 0.435727i \(-0.856491\pi\)
−0.900079 + 0.435727i \(0.856491\pi\)
\(132\) −1.46882e11 + 5.92540e10i −0.0277667 + 0.0112014i
\(133\) 4.51731e12i 0.816150i
\(134\) 5.19433e12 1.00826e12i 0.897224 0.174157i
\(135\) 6.43261e11i 0.106264i
\(136\) 4.11596e12 2.66831e12i 0.650486 0.421699i
\(137\) −1.11865e12 −0.169189 −0.0845943 0.996415i \(-0.526959\pi\)
−0.0845943 + 0.996415i \(0.526959\pi\)
\(138\) 2.71016e10 + 1.39622e11i 0.00392392 + 0.0202152i
\(139\) −3.44169e12 −0.477181 −0.238590 0.971120i \(-0.576685\pi\)
−0.238590 + 0.971120i \(0.576685\pi\)
\(140\) 1.81811e13 7.33450e12i 2.41464 0.974097i
\(141\) 2.11673e11i 0.0269371i
\(142\) 2.36499e12 + 1.21840e13i 0.288470 + 1.48614i
\(143\) 5.02445e12i 0.587587i
\(144\) −6.41322e12 + 6.18012e12i −0.719285 + 0.693142i
\(145\) 1.21808e13 1.31059
\(146\) −1.05134e13 + 2.04072e12i −1.08549 + 0.210701i
\(147\) −5.40295e11 −0.0535460
\(148\) 4.52369e12 + 1.12136e13i 0.430450 + 1.06702i
\(149\) 1.15080e13i 1.05167i −0.850586 0.525837i \(-0.823752\pi\)
0.850586 0.525837i \(-0.176248\pi\)
\(150\) 5.86618e11 1.13867e11i 0.0515001 0.00999651i
\(151\) 1.45861e12i 0.123049i −0.998106 0.0615246i \(-0.980404\pi\)
0.998106 0.0615246i \(-0.0195963\pi\)
\(152\) 5.21771e12 3.38256e12i 0.423076 0.274274i
\(153\) 9.93339e12 0.774371
\(154\) −3.72736e12 1.92026e13i −0.279433 1.43958i
\(155\) −1.72462e13 −1.24366
\(156\) −1.15582e11 2.86510e11i −0.00801940 0.0198789i
\(157\) 2.09908e13i 1.40162i 0.713348 + 0.700810i \(0.247178\pi\)
−0.713348 + 0.700810i \(0.752822\pi\)
\(158\) −2.27647e12 1.17279e13i −0.146325 0.753840i
\(159\) 4.62568e11i 0.0286281i
\(160\) −2.20857e13 1.55080e13i −1.31641 0.924349i
\(161\) −1.75658e13 −1.00858
\(162\) −1.76862e13 + 3.43301e12i −0.978462 + 0.189926i
\(163\) 3.15997e13 1.68483 0.842417 0.538826i \(-0.181132\pi\)
0.842417 + 0.538826i \(0.181132\pi\)
\(164\) −1.62906e13 + 6.57186e12i −0.837288 + 0.337773i
\(165\) 9.71847e11i 0.0481609i
\(166\) 6.48171e12 1.25814e12i 0.309771 0.0601287i
\(167\) 3.19093e13i 1.47102i −0.677515 0.735509i \(-0.736943\pi\)
0.677515 0.735509i \(-0.263057\pi\)
\(168\) 6.54281e11 + 1.00925e12i 0.0291010 + 0.0448893i
\(169\) 1.34973e13 0.579331
\(170\) 5.73529e12 + 2.95471e13i 0.237608 + 1.22411i
\(171\) 1.25923e13 0.503651
\(172\) 1.92393e13 7.76138e12i 0.743050 0.299756i
\(173\) 6.15011e12i 0.229407i −0.993400 0.114703i \(-0.963408\pi\)
0.993400 0.114703i \(-0.0365918\pi\)
\(174\) 1.42399e11 + 7.33614e11i 0.00513113 + 0.0264346i
\(175\) 7.38022e13i 2.56946i
\(176\) −1.93889e13 + 1.86842e13i −0.652346 + 0.628635i
\(177\) −8.42698e10 −0.00274052
\(178\) 2.73036e13 5.29982e12i 0.858422 0.166625i
\(179\) 1.73833e12 0.0528462 0.0264231 0.999651i \(-0.491588\pi\)
0.0264231 + 0.999651i \(0.491588\pi\)
\(180\) −2.04455e13 5.06812e13i −0.601121 1.49009i
\(181\) 3.18525e13i 0.905884i −0.891540 0.452942i \(-0.850374\pi\)
0.891540 0.452942i \(-0.149626\pi\)
\(182\) 3.74570e13 7.27065e12i 1.03063 0.200053i
\(183\) 5.89565e11i 0.0156973i
\(184\) 1.31533e13 + 2.02893e13i 0.338943 + 0.522831i
\(185\) −7.41948e13 −1.85073
\(186\) −2.01616e11 1.03868e12i −0.00486908 0.0250845i
\(187\) 3.00314e13 0.702305
\(188\) 1.34630e13 + 3.33728e13i 0.304927 + 0.755868i
\(189\) 4.87408e12i 0.106935i
\(190\) 7.27050e12 + 3.74562e13i 0.154541 + 0.796163i
\(191\) 8.30187e13i 1.70992i −0.518694 0.854960i \(-0.673582\pi\)
0.518694 0.854960i \(-0.326418\pi\)
\(192\) 6.75808e11 1.51145e12i 0.0134901 0.0301708i
\(193\) −4.06576e13 −0.786680 −0.393340 0.919393i \(-0.628680\pi\)
−0.393340 + 0.919393i \(0.628680\pi\)
\(194\) 7.70048e13 1.49471e13i 1.44447 0.280381i
\(195\) 1.89570e12 0.0344796
\(196\) −8.51840e13 + 3.43643e13i −1.50252 + 0.606138i
\(197\) 6.98237e13i 1.19455i 0.802035 + 0.597277i \(0.203751\pi\)
−0.802035 + 0.597277i \(0.796249\pi\)
\(198\) −5.35288e13 + 1.03903e13i −0.888375 + 0.172440i
\(199\) 6.00170e12i 0.0966398i −0.998832 0.0483199i \(-0.984613\pi\)
0.998832 0.0483199i \(-0.0153867\pi\)
\(200\) 8.52452e13 5.52631e13i 1.33196 0.863485i
\(201\) −1.99192e12 −0.0302062
\(202\) −2.20586e12 1.13642e13i −0.0324691 0.167275i
\(203\) −9.22957e13 −1.31888
\(204\) −1.71248e12 + 6.90838e11i −0.0237599 + 0.00958507i
\(205\) 1.07788e14i 1.45226i
\(206\) −9.84122e12 5.07000e13i −0.128779 0.663445i
\(207\) 4.89660e13i 0.622404i
\(208\) −3.64457e13 3.78204e13i −0.450056 0.467031i
\(209\) 3.80701e13 0.456780
\(210\) −7.24506e12 + 1.40632e12i −0.0844746 + 0.0163971i
\(211\) 5.39452e13 0.611305 0.305653 0.952143i \(-0.401125\pi\)
0.305653 + 0.952143i \(0.401125\pi\)
\(212\) 2.94207e13 + 7.29294e13i 0.324069 + 0.803318i
\(213\) 4.67231e12i 0.0500327i
\(214\) −1.23976e14 + 2.40647e13i −1.29079 + 0.250551i
\(215\) 1.27297e14i 1.28881i
\(216\) 5.62980e12 3.64971e12i 0.0554333 0.0359365i
\(217\) 1.30677e14 1.25152
\(218\) 6.76644e12 + 3.48594e13i 0.0630408 + 0.324774i
\(219\) 4.03167e12 0.0365443
\(220\) −6.18123e13 1.53223e14i −0.545179 1.35142i
\(221\) 5.85797e13i 0.502798i
\(222\) −8.67372e11 4.46853e12i −0.00724582 0.0373290i
\(223\) 1.68020e14i 1.36626i −0.730299 0.683128i \(-0.760619\pi\)
0.730299 0.683128i \(-0.239381\pi\)
\(224\) 1.67347e14 + 1.17506e14i 1.32473 + 0.930193i
\(225\) 2.05729e14 1.58563
\(226\) −2.30604e13 + 4.47619e12i −0.173068 + 0.0335937i
\(227\) 2.18840e13 0.159946 0.0799728 0.996797i \(-0.474517\pi\)
0.0799728 + 0.996797i \(0.474517\pi\)
\(228\) −2.17088e12 + 8.75761e11i −0.0154535 + 0.00623414i
\(229\) 2.42819e14i 1.68372i 0.539699 + 0.841858i \(0.318538\pi\)
−0.539699 + 0.841858i \(0.681462\pi\)
\(230\) −1.45650e14 + 2.82717e13i −0.983885 + 0.190979i
\(231\) 7.36382e12i 0.0484653i
\(232\) 6.91110e13 + 1.06606e14i 0.443220 + 0.683682i
\(233\) 6.71846e13 0.419889 0.209944 0.977713i \(-0.432672\pi\)
0.209944 + 0.977713i \(0.432672\pi\)
\(234\) −2.02675e13 1.04414e14i −0.123454 0.636011i
\(235\) −2.20812e14 −1.31104
\(236\) −1.32862e13 + 5.35981e12i −0.0769002 + 0.0310225i
\(237\) 4.49743e12i 0.0253790i
\(238\) −4.34571e13 2.23882e14i −0.239110 1.23185i
\(239\) 6.19250e13i 0.332260i −0.986104 0.166130i \(-0.946873\pi\)
0.986104 0.166130i \(-0.0531272\pi\)
\(240\) 7.04946e12 + 7.31535e12i 0.0368883 + 0.0382796i
\(241\) −2.92732e14 −1.49406 −0.747030 0.664791i \(-0.768521\pi\)
−0.747030 + 0.664791i \(0.768521\pi\)
\(242\) 3.53467e13 6.86103e12i 0.175977 0.0341584i
\(243\) 2.03840e13 0.0990038
\(244\) −3.74981e13 9.29520e13i −0.177693 0.440474i
\(245\) 5.63622e14i 2.60610i
\(246\) 6.49172e12 1.26009e12i 0.0292920 0.00568578i
\(247\) 7.42602e13i 0.327020i
\(248\) −9.78505e13 1.50938e14i −0.420584 0.648766i
\(249\) −2.48560e12 −0.0104288
\(250\) 4.39524e13 + 2.26434e14i 0.180029 + 0.927475i
\(251\) −4.22767e14 −1.69067 −0.845335 0.534236i \(-0.820599\pi\)
−0.845335 + 0.534236i \(0.820599\pi\)
\(252\) 1.54918e14 + 3.84019e14i 0.604922 + 1.49951i
\(253\) 1.48038e14i 0.564481i
\(254\) 8.44588e13 + 4.35115e14i 0.314516 + 1.62033i
\(255\) 1.13307e13i 0.0412112i
\(256\) 1.04165e13 2.81282e14i 0.0370069 0.999315i
\(257\) 5.23143e13 0.181561 0.0907803 0.995871i \(-0.471064\pi\)
0.0907803 + 0.995871i \(0.471064\pi\)
\(258\) −7.66673e12 + 1.48816e12i −0.0259951 + 0.00504583i
\(259\) 5.62184e14 1.86243
\(260\) 2.98880e14 1.20572e14i 0.967513 0.390307i
\(261\) 2.57281e14i 0.813889i
\(262\) 5.71593e14 1.10950e14i 1.76717 0.343020i
\(263\) 1.22242e13i 0.0369391i 0.999829 + 0.0184695i \(0.00587937\pi\)
−0.999829 + 0.0184695i \(0.994121\pi\)
\(264\) 8.50557e12 5.51403e12i 0.0251235 0.0162872i
\(265\) −4.82539e14 −1.39334
\(266\) −5.50896e13 2.83811e14i −0.155518 0.801196i
\(267\) −1.04704e13 −0.0288998
\(268\) −3.14050e14 + 1.26692e14i −0.847599 + 0.341933i
\(269\) 1.96941e14i 0.519783i 0.965638 + 0.259892i \(0.0836869\pi\)
−0.965638 + 0.259892i \(0.916313\pi\)
\(270\) 7.84471e12 + 4.04144e13i 0.0202486 + 0.104317i
\(271\) 8.50754e13i 0.214777i 0.994217 + 0.107389i \(0.0342489\pi\)
−0.994217 + 0.107389i \(0.965751\pi\)
\(272\) −2.26054e14 + 2.17838e14i −0.558212 + 0.537923i
\(273\) −1.43640e13 −0.0346976
\(274\) 7.02819e13 1.36422e13i 0.166089 0.0322389i
\(275\) 6.21977e14 1.43806
\(276\) −3.40544e12 8.44157e12i −0.00770404 0.0190972i
\(277\) 5.61149e14i 1.24222i −0.783722 0.621112i \(-0.786681\pi\)
0.783722 0.621112i \(-0.213319\pi\)
\(278\) 2.16232e14 4.19721e13i 0.468438 0.0909269i
\(279\) 3.64271e14i 0.772323i
\(280\) −1.05283e15 + 6.82530e14i −2.18478 + 1.41636i
\(281\) 1.07441e14 0.218239 0.109119 0.994029i \(-0.465197\pi\)
0.109119 + 0.994029i \(0.465197\pi\)
\(282\) −2.58140e12 1.32989e13i −0.00513287 0.0264436i
\(283\) 2.56049e14 0.498430 0.249215 0.968448i \(-0.419827\pi\)
0.249215 + 0.968448i \(0.419827\pi\)
\(284\) −2.97173e14 7.36646e14i −0.566368 1.40394i
\(285\) 1.43637e13i 0.0268038i
\(286\) −6.12743e13 3.15673e14i −0.111965 0.576821i
\(287\) 8.16721e14i 1.46144i
\(288\) 3.27558e14 4.66491e14i 0.574028 0.817501i
\(289\) −2.32488e14 −0.399038
\(290\) −7.65288e14 + 1.48548e14i −1.28658 + 0.249734i
\(291\) −2.95298e13 −0.0486297
\(292\) 6.35641e14 2.56426e14i 1.02545 0.413680i
\(293\) 8.02439e14i 1.26825i 0.773229 + 0.634127i \(0.218640\pi\)
−0.773229 + 0.634127i \(0.781360\pi\)
\(294\) 3.39453e13 6.58901e12i 0.0525649 0.0102032i
\(295\) 8.79083e13i 0.133382i
\(296\) −4.20963e14 6.49350e14i −0.625884 0.965448i
\(297\) 4.10769e13 0.0598492
\(298\) 1.40342e14 + 7.23015e14i 0.200397 + 1.03240i
\(299\) −2.88765e14 −0.404126
\(300\) −3.54670e13 + 1.43079e13i −0.0486516 + 0.0196267i
\(301\) 9.64549e14i 1.29696i
\(302\) 1.77881e13 + 9.16409e13i 0.0234471 + 0.120795i
\(303\) 4.35793e12i 0.00563151i
\(304\) −2.86564e14 + 2.76148e14i −0.363062 + 0.349866i
\(305\) 6.15020e14 0.763994
\(306\) −6.24089e14 + 1.21140e14i −0.760182 + 0.147557i
\(307\) 9.10083e14 1.08705 0.543527 0.839392i \(-0.317089\pi\)
0.543527 + 0.839392i \(0.317089\pi\)
\(308\) 4.68361e14 + 1.16100e15i 0.548626 + 1.35996i
\(309\) 1.94424e13i 0.0223357i
\(310\) 1.08353e15 2.10321e14i 1.22087 0.236980i
\(311\) 1.09063e15i 1.20535i −0.797986 0.602676i \(-0.794101\pi\)
0.797986 0.602676i \(-0.205899\pi\)
\(312\) 1.07557e13 + 1.65911e13i 0.0116604 + 0.0179865i
\(313\) −1.36097e14 −0.144738 −0.0723688 0.997378i \(-0.523056\pi\)
−0.0723688 + 0.997378i \(0.523056\pi\)
\(314\) −2.55987e14 1.31879e15i −0.267079 1.37594i
\(315\) −2.54087e15 −2.60087
\(316\) 2.86050e14 + 7.09073e14i 0.287289 + 0.712145i
\(317\) 6.95183e14i 0.685083i 0.939503 + 0.342542i \(0.111288\pi\)
−0.939503 + 0.342542i \(0.888712\pi\)
\(318\) −5.64111e12 2.90619e13i −0.00545509 0.0281036i
\(319\) 7.77833e14i 0.738146i
\(320\) 1.57671e15 + 7.04987e14i 1.46843 + 0.656570i
\(321\) 4.75424e13 0.0434561
\(322\) 1.10361e15 2.14219e14i 0.990105 0.192186i
\(323\) 4.43857e14 0.390866
\(324\) 1.06931e15 4.31373e14i 0.924343 0.372892i
\(325\) 1.21324e15i 1.02955i
\(326\) −1.98532e15 + 3.85365e14i −1.65396 + 0.321045i
\(327\) 1.33679e13i 0.0109339i
\(328\) 9.43353e14 6.11560e14i 0.757584 0.491130i
\(329\) 1.67313e15 1.31933
\(330\) 1.18519e13 + 6.10586e13i 0.00917706 + 0.0472784i
\(331\) −1.71367e15 −1.30304 −0.651522 0.758630i \(-0.725869\pi\)
−0.651522 + 0.758630i \(0.725869\pi\)
\(332\) −3.91886e14 + 1.58092e14i −0.292638 + 0.118054i
\(333\) 1.56713e15i 1.14932i
\(334\) 3.89140e14 + 2.00477e15i 0.280303 + 1.44407i
\(335\) 2.07792e15i 1.47015i
\(336\) −5.34148e13 5.54294e13i −0.0371215 0.0385216i
\(337\) −1.43398e15 −0.978959 −0.489480 0.872015i \(-0.662813\pi\)
−0.489480 + 0.872015i \(0.662813\pi\)
\(338\) −8.48000e14 + 1.64603e14i −0.568716 + 0.110392i
\(339\) 8.84321e12 0.00582655
\(340\) −7.20666e14 1.78642e15i −0.466509 1.15641i
\(341\) 1.10129e15i 0.700448i
\(342\) −7.91144e14 + 1.53566e14i −0.494423 + 0.0959709i
\(343\) 1.63474e15i 1.00388i
\(344\) −1.11410e15 + 7.22254e14i −0.672317 + 0.435852i
\(345\) 5.58539e13 0.0331237
\(346\) 7.50019e13 + 3.86395e14i 0.0437135 + 0.225204i
\(347\) −2.28118e15 −1.30672 −0.653360 0.757047i \(-0.726641\pi\)
−0.653360 + 0.757047i \(0.726641\pi\)
\(348\) −1.78932e13 4.43544e13i −0.0100742 0.0249725i
\(349\) 4.21458e14i 0.233239i 0.993177 + 0.116620i \(0.0372058\pi\)
−0.993177 + 0.116620i \(0.962794\pi\)
\(350\) −9.00034e14 4.63680e15i −0.489610 2.52238i
\(351\) 8.01252e13i 0.0428476i
\(352\) 9.90298e14 1.41033e15i 0.520607 0.741422i
\(353\) 2.36861e15 1.22418 0.612091 0.790787i \(-0.290329\pi\)
0.612091 + 0.790787i \(0.290329\pi\)
\(354\) 5.29445e12 1.02769e12i 0.00269030 0.000522206i
\(355\) 4.87404e15 2.43511
\(356\) −1.65078e15 + 6.65948e14i −0.810943 + 0.327145i
\(357\) 8.58543e13i 0.0414718i
\(358\) −1.09215e14 + 2.11993e13i −0.0518780 + 0.0100699i
\(359\) 2.67033e15i 1.24738i 0.781673 + 0.623689i \(0.214367\pi\)
−0.781673 + 0.623689i \(0.785633\pi\)
\(360\) 1.90260e15 + 2.93483e15i 0.874044 + 1.34824i
\(361\) −1.65065e15 −0.745780
\(362\) 3.88449e14 + 2.00121e15i 0.172616 + 0.889286i
\(363\) −1.35547e13 −0.00592450
\(364\) −2.26466e15 + 9.13592e14i −0.973630 + 0.392775i
\(365\) 4.20574e15i 1.77863i
\(366\) 7.18987e12 + 3.70408e13i 0.00299112 + 0.0154097i
\(367\) 3.55243e15i 1.45388i −0.686700 0.726941i \(-0.740941\pi\)
0.686700 0.726941i \(-0.259059\pi\)
\(368\) −1.07382e15 1.11432e15i −0.432358 0.448665i
\(369\) 2.27667e15 0.901866
\(370\) 4.66146e15 9.04822e14i 1.81682 0.352657i
\(371\) 3.65627e15 1.40215
\(372\) 2.53340e13 + 6.27991e13i 0.00955973 + 0.0236971i
\(373\) 1.18076e15i 0.438439i −0.975676 0.219220i \(-0.929649\pi\)
0.975676 0.219220i \(-0.0703511\pi\)
\(374\) −1.88679e15 + 3.66239e14i −0.689437 + 0.133824i
\(375\) 8.68329e13i 0.0312246i
\(376\) −1.25284e15 1.93254e15i −0.443371 0.683915i
\(377\) −1.51725e15 −0.528457
\(378\) −5.94404e13 3.06226e14i −0.0203766 0.104976i
\(379\) 2.57544e15 0.868991 0.434496 0.900674i \(-0.356927\pi\)
0.434496 + 0.900674i \(0.356927\pi\)
\(380\) −9.13572e14 2.26461e15i −0.303418 0.752127i
\(381\) 1.66858e14i 0.0545503i
\(382\) 1.01243e15 + 5.21584e15i 0.325826 + 1.67859i
\(383\) 2.65161e15i 0.840074i 0.907507 + 0.420037i \(0.137983\pi\)
−0.907507 + 0.420037i \(0.862017\pi\)
\(384\) −2.40268e13 + 1.03202e14i −0.00749390 + 0.0321886i
\(385\) −7.68176e15 −2.35883
\(386\) 2.55441e15 4.95828e14i 0.772266 0.149902i
\(387\) −2.68875e15 −0.800360
\(388\) −4.65572e15 + 1.87818e15i −1.36457 + 0.550487i
\(389\) 6.46338e15i 1.86536i −0.360709 0.932678i \(-0.617465\pi\)
0.360709 0.932678i \(-0.382535\pi\)
\(390\) −1.19102e14 + 2.31185e13i −0.0338478 + 0.00657009i
\(391\) 1.72596e15i 0.483026i
\(392\) 4.93280e15 3.19786e15i 1.35949 0.881338i
\(393\) −2.19194e14 −0.0594941
\(394\) −8.51515e14 4.38684e15i −0.227622 1.17267i
\(395\) −4.69161e15 −1.23520
\(396\) 3.23636e15 1.30559e15i 0.839240 0.338560i
\(397\) 3.33297e15i 0.851312i −0.904885 0.425656i \(-0.860043\pi\)
0.904885 0.425656i \(-0.139957\pi\)
\(398\) 7.31920e13 + 3.77071e14i 0.0184147 + 0.0948691i
\(399\) 1.08836e14i 0.0269733i
\(400\) −4.68178e15 + 4.51162e15i −1.14301 + 1.10147i
\(401\) 4.76253e14 0.114544 0.0572719 0.998359i \(-0.481760\pi\)
0.0572719 + 0.998359i \(0.481760\pi\)
\(402\) 1.25147e14 2.42919e13i 0.0296527 0.00575579i
\(403\) 2.14820e15 0.501469
\(404\) 2.77177e14 + 6.87081e14i 0.0637484 + 0.158023i
\(405\) 7.07512e15i 1.60326i
\(406\) 5.79870e15 1.12557e15i 1.29471 0.251313i
\(407\) 4.73787e15i 1.04236i
\(408\) 9.91659e13 6.42876e13i 0.0214982 0.0139369i
\(409\) −3.11273e15 −0.664969 −0.332484 0.943109i \(-0.607887\pi\)
−0.332484 + 0.943109i \(0.607887\pi\)
\(410\) 1.31449e15 + 6.77200e15i 0.276729 + 1.42565i
\(411\) −2.69517e13 −0.00559158
\(412\) 1.23660e15 + 3.06533e15i 0.252839 + 0.626750i
\(413\) 6.66093e14i 0.134225i
\(414\) −5.97150e14 3.07640e15i −0.118599 0.611000i
\(415\) 2.59292e15i 0.507576i
\(416\) 2.75102e15 + 1.93169e15i 0.530803 + 0.372716i
\(417\) −8.29206e13 −0.0157705
\(418\) −2.39185e15 + 4.64274e14i −0.448410 + 0.0870395i
\(419\) 2.81541e15 0.520305 0.260152 0.965568i \(-0.416227\pi\)
0.260152 + 0.965568i \(0.416227\pi\)
\(420\) 4.38038e14 1.76710e14i 0.0798024 0.0321933i
\(421\) 2.35273e15i 0.422551i 0.977427 + 0.211275i \(0.0677617\pi\)
−0.977427 + 0.211275i \(0.932238\pi\)
\(422\) −3.38924e15 + 6.57873e14i −0.600105 + 0.116484i
\(423\) 4.66397e15i 0.814166i
\(424\) −2.73781e15 4.22317e15i −0.471203 0.726847i
\(425\) 7.25158e15 1.23055
\(426\) 5.69798e13 + 2.93549e14i 0.00953375 + 0.0491160i
\(427\) −4.66009e15 −0.768824
\(428\) 7.49563e15 3.02384e15i 1.21940 0.491921i
\(429\) 1.21054e14i 0.0194194i
\(430\) −1.55242e15 7.99775e15i −0.245583 1.26519i
\(431\) 1.20497e16i 1.87981i 0.341434 + 0.939906i \(0.389087\pi\)
−0.341434 + 0.939906i \(0.610913\pi\)
\(432\) −3.09196e14 + 2.97958e14i −0.0475699 + 0.0458409i
\(433\) 5.48809e15 0.832710 0.416355 0.909202i \(-0.363307\pi\)
0.416355 + 0.909202i \(0.363307\pi\)
\(434\) −8.21006e15 + 1.59363e15i −1.22859 + 0.238478i
\(435\) 2.93472e14 0.0433143
\(436\) −8.50235e14 2.10760e15i −0.123771 0.306811i
\(437\) 2.18796e15i 0.314160i
\(438\) −2.53299e14 + 4.91670e13i −0.0358747 + 0.00696353i
\(439\) 5.61937e15i 0.785056i 0.919740 + 0.392528i \(0.128399\pi\)
−0.919740 + 0.392528i \(0.871601\pi\)
\(440\) 5.75210e15 + 8.87281e15i 0.792703 + 1.22277i
\(441\) 1.19047e16 1.61841
\(442\) −7.14392e14 3.68041e15i −0.0958083 0.493586i
\(443\) −8.80399e15 −1.16482 −0.582408 0.812897i \(-0.697889\pi\)
−0.582408 + 0.812897i \(0.697889\pi\)
\(444\) 1.08989e14 + 2.70168e14i 0.0142261 + 0.0352644i
\(445\) 1.09225e16i 1.40657i
\(446\) 2.04904e15 + 1.05563e16i 0.260340 + 1.34122i
\(447\) 2.77261e14i 0.0347572i
\(448\) −1.19470e16 5.34179e15i −1.47771 0.660721i
\(449\) 5.50713e15 0.672121 0.336061 0.941840i \(-0.390905\pi\)
0.336061 + 0.941840i \(0.390905\pi\)
\(450\) −1.29254e16 + 2.50891e15i −1.55657 + 0.302142i
\(451\) 6.88301e15 0.817936
\(452\) 1.39424e15 5.62454e14i 0.163496 0.0659563i
\(453\) 3.51424e13i 0.00406670i
\(454\) −1.37492e15 + 2.66881e14i −0.157015 + 0.0304777i
\(455\) 1.49842e16i 1.68875i
\(456\) 1.25710e14 8.14960e13i 0.0139824 0.00906458i
\(457\) −1.11057e16 −1.21912 −0.609561 0.792739i \(-0.708654\pi\)
−0.609561 + 0.792739i \(0.708654\pi\)
\(458\) −2.96122e15 1.52556e16i −0.320833 1.65287i
\(459\) 4.78912e14 0.0512130
\(460\) 8.80604e15 3.55247e15i 0.929466 0.374959i
\(461\) 1.21877e16i 1.26975i 0.772616 + 0.634874i \(0.218948\pi\)
−0.772616 + 0.634874i \(0.781052\pi\)
\(462\) −8.98034e13 4.62649e14i −0.00923508 0.0475773i
\(463\) 1.17797e14i 0.0119578i −0.999982 0.00597888i \(-0.998097\pi\)
0.999982 0.00597888i \(-0.00190315\pi\)
\(464\) −5.64214e15 5.85495e15i −0.565375 0.586699i
\(465\) −4.15512e14 −0.0411023
\(466\) −4.22103e15 + 8.19331e14i −0.412195 + 0.0800099i
\(467\) −1.73578e16 −1.67337 −0.836687 0.547681i \(-0.815511\pi\)
−0.836687 + 0.547681i \(0.815511\pi\)
\(468\) 2.54671e15 + 6.31290e15i 0.242384 + 0.600833i
\(469\) 1.57447e16i 1.47944i
\(470\) 1.38731e16 2.69285e15i 1.28702 0.249819i
\(471\) 5.05731e14i 0.0463227i
\(472\) 7.69370e14 4.98770e14i 0.0695798 0.0451075i
\(473\) −8.12885e15 −0.725876
\(474\) −5.48471e13 2.82561e14i −0.00483597 0.0249140i
\(475\) 9.19267e15 0.800350
\(476\) 5.46058e15 + 1.35360e16i 0.469459 + 1.16372i
\(477\) 1.01921e16i 0.865276i
\(478\) 7.55189e14 + 3.89058e15i 0.0633123 + 0.326173i
\(479\) 9.01540e15i 0.746400i −0.927751 0.373200i \(-0.878260\pi\)
0.927751 0.373200i \(-0.121740\pi\)
\(480\) −5.32111e14 3.73635e14i −0.0435066 0.0305492i
\(481\) 9.24177e15 0.746251
\(482\) 1.83916e16 3.56993e15i 1.46668 0.284693i
\(483\) −4.23213e14 −0.0333331
\(484\) −2.13707e15 + 8.62121e14i −0.166244 + 0.0670650i
\(485\) 3.08047e16i 2.36683i
\(486\) −1.28067e15 + 2.48587e14i −0.0971898 + 0.0188652i
\(487\) 1.44952e16i 1.08655i 0.839554 + 0.543276i \(0.182816\pi\)
−0.839554 + 0.543276i \(0.817184\pi\)
\(488\) 3.48947e15 + 5.38263e15i 0.258369 + 0.398544i
\(489\) 7.61331e14 0.0556827
\(490\) 6.87350e15 + 3.54109e16i 0.496594 + 2.55835i
\(491\) 8.18112e15 0.583880 0.291940 0.956437i \(-0.405699\pi\)
0.291940 + 0.956437i \(0.405699\pi\)
\(492\) −3.92491e14 + 1.58336e14i −0.0276719 + 0.0111632i
\(493\) 9.06870e15i 0.631631i
\(494\) −9.05620e14 4.66558e15i −0.0623138 0.321028i
\(495\) 2.14135e16i 1.45565i
\(496\) 7.98841e15 + 8.28971e15i 0.536501 + 0.556736i
\(497\) −3.69313e16 −2.45051
\(498\) 1.56164e14 3.03125e13i 0.0102378 0.00198722i
\(499\) 1.38967e16 0.900135 0.450067 0.892995i \(-0.351400\pi\)
0.450067 + 0.892995i \(0.351400\pi\)
\(500\) −5.52283e15 1.36903e16i −0.353461 0.876176i
\(501\) 7.68790e14i 0.0486162i
\(502\) 2.65614e16 5.15574e15i 1.65969 0.322158i
\(503\) 1.70388e15i 0.105203i −0.998616 0.0526017i \(-0.983249\pi\)
0.998616 0.0526017i \(-0.0167514\pi\)
\(504\) −1.44163e16 2.22376e16i −0.879570 1.35677i
\(505\) −4.54609e15 −0.274088
\(506\) −1.80535e15 9.30082e15i −0.107562 0.554138i
\(507\) 3.25191e14 0.0191465
\(508\) −1.06127e16 2.63072e16i −0.617507 1.53071i
\(509\) 1.60688e16i 0.924012i 0.886877 + 0.462006i \(0.152870\pi\)
−0.886877 + 0.462006i \(0.847130\pi\)
\(510\) 1.38180e14 + 7.11878e14i 0.00785281 + 0.0404561i
\(511\) 3.18675e16i 1.78987i
\(512\) 2.77585e15 + 1.77992e16i 0.154091 + 0.988057i
\(513\) 6.07107e14 0.0333089
\(514\) −3.28677e15 + 6.37984e14i −0.178234 + 0.0345964i
\(515\) −2.02819e16 −1.08709
\(516\) 4.63532e14 1.86995e14i 0.0245574 0.00990676i
\(517\) 1.41005e16i 0.738397i
\(518\) −3.53206e16 + 6.85596e15i −1.82831 + 0.354887i
\(519\) 1.48175e14i 0.00758176i
\(520\) −1.73074e16 + 1.12201e16i −0.875413 + 0.567516i
\(521\) −2.05693e15 −0.102847 −0.0514236 0.998677i \(-0.516376\pi\)
−0.0514236 + 0.998677i \(0.516376\pi\)
\(522\) −3.13760e15 1.61643e16i −0.155087 0.798976i
\(523\) 3.83630e16 1.87458 0.937288 0.348557i \(-0.113328\pi\)
0.937288 + 0.348557i \(0.113328\pi\)
\(524\) −3.45586e16 + 1.39414e16i −1.66943 + 0.673471i
\(525\) 1.77812e15i 0.0849189i
\(526\) −1.49077e14 7.68015e14i −0.00703875 0.0362623i
\(527\) 1.28399e16i 0.599373i
\(528\) −4.67138e14 + 4.50159e14i −0.0215596 + 0.0207760i
\(529\) 1.34066e16 0.611766
\(530\) 3.03167e16 5.88467e15i 1.36781 0.265502i
\(531\) 1.85679e15 0.0828313
\(532\) 6.92226e15 + 1.71592e16i 0.305336 + 0.756882i
\(533\) 1.34261e16i 0.585581i
\(534\) 6.57827e14 1.27689e14i 0.0283703 0.00550687i
\(535\) 4.95951e16i 2.11503i
\(536\) 1.81859e16 1.17896e16i 0.766914 0.497178i
\(537\) 4.18816e13 0.00174654
\(538\) −2.40174e15 1.23733e16i −0.0990448 0.510260i
\(539\) 3.59913e16 1.46780
\(540\) −9.85724e14 2.44346e15i −0.0397551 0.0985469i
\(541\) 3.00552e15i 0.119877i −0.998202 0.0599386i \(-0.980910\pi\)
0.998202 0.0599386i \(-0.0190905\pi\)
\(542\) −1.03751e15 5.34506e15i −0.0409258 0.210842i
\(543\) 7.67423e14i 0.0299389i
\(544\) 1.15458e16 1.64430e16i 0.445483 0.634434i
\(545\) 1.39450e16 0.532158
\(546\) 9.02451e14 1.75172e14i 0.0340618 0.00661163i
\(547\) −4.32641e16 −1.61512 −0.807559 0.589787i \(-0.799212\pi\)
−0.807559 + 0.589787i \(0.799212\pi\)
\(548\) −4.24926e15 + 1.71421e15i −0.156902 + 0.0632965i
\(549\) 1.29904e16i 0.474446i
\(550\) −3.90771e16 + 7.58514e15i −1.41171 + 0.274023i
\(551\) 1.14962e16i 0.410813i
\(552\) 3.16901e14 + 4.88831e14i 0.0112018 + 0.0172792i
\(553\) 3.55489e16 1.24301
\(554\) 6.84334e15 + 3.52555e16i 0.236706 + 1.21946i
\(555\) −1.78758e15 −0.0611655
\(556\) −1.30734e16 + 5.27400e15i −0.442528 + 0.178522i
\(557\) 2.58426e16i 0.865377i −0.901544 0.432688i \(-0.857565\pi\)
0.901544 0.432688i \(-0.142435\pi\)
\(558\) 4.44236e15 + 2.28862e16i 0.147166 + 0.758172i
\(559\) 1.58563e16i 0.519673i
\(560\) 5.78227e16 5.57210e16i 1.87486 1.80672i
\(561\) 7.23547e14 0.0232108
\(562\) −6.75024e15 + 1.31027e15i −0.214240 + 0.0415855i
\(563\) −2.30517e16 −0.723858 −0.361929 0.932206i \(-0.617882\pi\)
−0.361929 + 0.932206i \(0.617882\pi\)
\(564\) 3.24365e14 + 8.04052e14i 0.0100777 + 0.0249810i
\(565\) 9.22502e15i 0.283581i
\(566\) −1.60869e16 + 3.12257e15i −0.489297 + 0.0949759i
\(567\) 5.36092e16i 1.61339i
\(568\) 2.76541e16 + 4.26575e16i 0.823512 + 1.27030i
\(569\) 2.64650e15 0.0779828 0.0389914 0.999240i \(-0.487585\pi\)
0.0389914 + 0.999240i \(0.487585\pi\)
\(570\) 1.75168e14 + 9.02432e14i 0.00510747 + 0.0263127i
\(571\) −5.11842e16 −1.47679 −0.738396 0.674368i \(-0.764416\pi\)
−0.738396 + 0.674368i \(0.764416\pi\)
\(572\) 7.69940e15 + 1.90856e16i 0.219827 + 0.544917i
\(573\) 2.00017e15i 0.0565118i
\(574\) −9.96009e15 5.13124e16i −0.278479 1.43467i
\(575\) 3.57462e16i 0.989059i
\(576\) −1.48906e16 + 3.33030e16i −0.407735 + 0.911904i
\(577\) −1.35781e16 −0.367945 −0.183972 0.982931i \(-0.558896\pi\)
−0.183972 + 0.982931i \(0.558896\pi\)
\(578\) 1.46066e16 2.83524e15i 0.391726 0.0760367i
\(579\) −9.79564e14 −0.0259993
\(580\) 4.62695e16 1.86657e16i 1.21542 0.490317i
\(581\) 1.96469e16i 0.510785i
\(582\) 1.85528e15 3.60122e14i 0.0477387 0.00926641i
\(583\) 3.08136e16i 0.784750i
\(584\) −3.68085e16 + 2.38623e16i −0.927835 + 0.601500i
\(585\) −4.17695e16 −1.04213
\(586\) −9.78591e15 5.04151e16i −0.241666 1.24502i
\(587\) −2.85301e15 −0.0697387 −0.0348694 0.999392i \(-0.511102\pi\)
−0.0348694 + 0.999392i \(0.511102\pi\)
\(588\) −2.05234e15 + 8.27940e14i −0.0496575 + 0.0200325i
\(589\) 1.62768e16i 0.389833i
\(590\) 1.07206e15 + 5.52304e15i 0.0254160 + 0.130938i
\(591\) 1.68226e15i 0.0394793i
\(592\) 3.43670e16 + 3.56632e16i 0.798383 + 0.828496i
\(593\) 4.45903e16 1.02544 0.512722 0.858555i \(-0.328637\pi\)
0.512722 + 0.858555i \(0.328637\pi\)
\(594\) −2.58075e15 + 5.00941e14i −0.0587526 + 0.0114043i
\(595\) −8.95611e16 −2.01845
\(596\) −1.76346e16 4.37136e16i −0.393450 0.975302i
\(597\) 1.44599e14i 0.00319389i
\(598\) 1.81423e16 3.52155e15i 0.396722 0.0770063i
\(599\) 1.40027e16i 0.303146i −0.988446 0.151573i \(-0.951566\pi\)
0.988446 0.151573i \(-0.0484338\pi\)
\(600\) 2.05381e15 1.33145e15i 0.0440203 0.0285377i
\(601\) 1.60858e14 0.00341347 0.00170673 0.999999i \(-0.499457\pi\)
0.00170673 + 0.999999i \(0.499457\pi\)
\(602\) 1.17629e16 + 6.06001e16i 0.247135 + 1.27319i
\(603\) 4.38896e16 0.912972
\(604\) −2.23516e15 5.54063e15i −0.0460349 0.114114i
\(605\) 1.41400e16i 0.288348i
\(606\) −5.31459e13 2.73797e14i −0.00107308 0.00552832i
\(607\) 1.11179e16i 0.222274i 0.993805 + 0.111137i \(0.0354493\pi\)
−0.993805 + 0.111137i \(0.964551\pi\)
\(608\) 1.46364e16 2.08444e16i 0.289742 0.412637i
\(609\) −2.22368e15 −0.0435882
\(610\) −3.86401e16 + 7.50030e15i −0.749996 + 0.145579i
\(611\) 2.75046e16 0.528637
\(612\) 3.77325e16 1.52218e16i 0.718137 0.289706i
\(613\) 2.67476e16i 0.504106i 0.967713 + 0.252053i \(0.0811057\pi\)
−0.967713 + 0.252053i \(0.918894\pi\)
\(614\) −5.71781e16 + 1.10987e16i −1.06714 + 0.207138i
\(615\) 2.59693e15i 0.0479964i
\(616\) −4.35845e16 6.72305e16i −0.797714 1.23050i
\(617\) 3.68437e16 0.667808 0.333904 0.942607i \(-0.391634\pi\)
0.333904 + 0.942607i \(0.391634\pi\)
\(618\) −2.37105e14 1.22152e15i −0.00425607 0.0219264i
\(619\) 8.60978e16 1.53055 0.765276 0.643702i \(-0.222603\pi\)
0.765276 + 0.643702i \(0.222603\pi\)
\(620\) −6.55105e16 + 2.64278e16i −1.15335 + 0.465276i
\(621\) 2.36076e15i 0.0411626i
\(622\) 1.33004e16 + 6.85212e16i 0.229680 + 1.18327i
\(623\) 8.27610e16i 1.41546i
\(624\) −8.78087e14 9.11207e14i −0.0148741 0.0154351i
\(625\) −4.03208e15 −0.0676471
\(626\) 8.55059e15 1.65973e15i 0.142086 0.0275798i
\(627\) 9.17224e14 0.0150963
\(628\) 3.21660e16 + 7.97345e16i 0.524371 + 1.29984i
\(629\) 5.52385e16i 0.891945i
\(630\) 1.59636e17 3.09865e16i 2.55322 0.495597i
\(631\) 1.95166e16i 0.309192i −0.987978 0.154596i \(-0.950592\pi\)
0.987978 0.154596i \(-0.0494076\pi\)
\(632\) −2.66190e16 4.10608e16i −0.417724 0.644354i
\(633\) 1.29970e15 0.0202033
\(634\) −8.47790e15 4.36765e16i −0.130543 0.672531i
\(635\) 1.74062e17 2.65498
\(636\) 7.08832e14 + 1.75709e15i 0.0107103 + 0.0265492i
\(637\) 7.02053e16i 1.05083i
\(638\) −9.48584e15 4.88692e16i −0.140654 0.724621i
\(639\) 1.02949e17i 1.51222i
\(640\) −1.07658e17 2.50641e16i −1.56663 0.364731i
\(641\) −6.95403e16 −1.00251 −0.501254 0.865300i \(-0.667128\pi\)
−0.501254 + 0.865300i \(0.667128\pi\)
\(642\) −2.98696e15 + 5.79790e14i −0.0426599 + 0.00828057i
\(643\) −1.06417e17 −1.50573 −0.752863 0.658177i \(-0.771328\pi\)
−0.752863 + 0.658177i \(0.771328\pi\)
\(644\) −6.67246e16 + 2.69176e16i −0.935343 + 0.377329i
\(645\) 3.06697e15i 0.0425943i
\(646\) −2.78864e16 + 5.41293e15i −0.383705 + 0.0744797i
\(647\) 2.80616e16i 0.382549i −0.981537 0.191274i \(-0.938738\pi\)
0.981537 0.191274i \(-0.0612620\pi\)
\(648\) −6.19212e16 + 4.01425e16i −0.836352 + 0.542194i
\(649\) 5.61358e15 0.0751227
\(650\) −1.47957e16 7.62245e16i −0.196180 1.01068i
\(651\) 3.14839e15 0.0413621
\(652\) 1.20033e17 4.84229e16i 1.56248 0.630326i
\(653\) 3.61637e16i 0.466437i 0.972424 + 0.233219i \(0.0749258\pi\)
−0.972424 + 0.233219i \(0.925074\pi\)
\(654\) 1.63024e14 + 8.39867e14i 0.00208346 + 0.0107336i
\(655\) 2.28658e17i 2.89560i
\(656\) −5.18102e16 + 4.99271e16i −0.650119 + 0.626489i
\(657\) −8.88329e16 −1.10454
\(658\) −1.05118e17 + 2.04041e16i −1.29516 + 0.251399i
\(659\) 5.19401e16 0.634147 0.317074 0.948401i \(-0.397300\pi\)
0.317074 + 0.948401i \(0.397300\pi\)
\(660\) −1.48924e15 3.69161e15i −0.0180178 0.0446635i
\(661\) 1.42475e17i 1.70817i −0.520135 0.854084i \(-0.674118\pi\)
0.520135 0.854084i \(-0.325882\pi\)
\(662\) 1.07665e17 2.08986e16i 1.27917 0.248295i
\(663\) 1.41136e15i 0.0166172i
\(664\) 2.26932e16 1.47116e16i 0.264781 0.171653i
\(665\) −1.13535e17 −1.31280
\(666\) 1.91115e16 + 9.84587e16i 0.219003 + 1.12826i
\(667\) −4.47035e16 −0.507676
\(668\) −4.88973e16 1.21209e17i −0.550334 1.36419i
\(669\) 4.04811e15i 0.0451539i
\(670\) 2.53407e16 + 1.30550e17i 0.280137 + 1.44321i
\(671\) 3.92734e16i 0.430293i
\(672\) 4.03188e15 + 2.83108e15i 0.0437817 + 0.0307423i
\(673\) 4.48938e16 0.483165 0.241583 0.970380i \(-0.422333\pi\)
0.241583 + 0.970380i \(0.422333\pi\)
\(674\) 9.00934e16 1.74877e16i 0.961022 0.186541i
\(675\) 9.91869e15 0.104865
\(676\) 5.12702e16 2.06831e16i 0.537261 0.216738i
\(677\) 1.04649e17i 1.08693i 0.839431 + 0.543466i \(0.182888\pi\)
−0.839431 + 0.543466i \(0.817112\pi\)
\(678\) −5.55595e14 + 1.07845e14i −0.00571979 + 0.00111025i
\(679\) 2.33412e17i 2.38179i
\(680\) 6.70633e16 + 1.03447e17i 0.678315 + 1.04632i
\(681\) 5.27252e14 0.00528611
\(682\) 1.34305e16 + 6.91912e16i 0.133471 + 0.687614i
\(683\) −3.83475e16 −0.377757 −0.188879 0.982000i \(-0.560485\pi\)
−0.188879 + 0.982000i \(0.560485\pi\)
\(684\) 4.78327e16 1.92963e16i 0.467077 0.188425i
\(685\) 2.81153e16i 0.272145i
\(686\) −1.99360e16 1.02706e17i −0.191290 0.985490i
\(687\) 5.85023e15i 0.0556458i
\(688\) 6.11880e16 5.89640e16i 0.576947 0.555977i
\(689\) 6.01055e16 0.561823
\(690\) −3.50915e15 + 6.81150e14i −0.0325168 + 0.00631173i
\(691\) −1.07827e17 −0.990510 −0.495255 0.868748i \(-0.664925\pi\)
−0.495255 + 0.868748i \(0.664925\pi\)
\(692\) −9.42435e15 2.33615e16i −0.0858252 0.212748i
\(693\) 1.62253e17i 1.46485i
\(694\) 1.43320e17 2.78195e16i 1.28278 0.248996i
\(695\) 8.65008e16i 0.767558i
\(696\) 1.66509e15 + 2.56846e15i 0.0146481 + 0.0225953i
\(697\) 8.02485e16 0.699907
\(698\) −5.13977e15 2.64791e16i −0.0444438 0.228966i
\(699\) 1.61868e15 0.0138771
\(700\) 1.13094e17 + 2.80342e17i 0.961279 + 2.38286i
\(701\) 1.68907e16i 0.142344i 0.997464 + 0.0711719i \(0.0226739\pi\)
−0.997464 + 0.0711719i \(0.977326\pi\)
\(702\) −9.77144e14 5.03405e15i −0.00816462 0.0420625i
\(703\) 7.00247e16i 0.580122i
\(704\) −4.50185e16 + 1.00684e17i −0.369790 + 0.827039i
\(705\) −5.32003e15 −0.0433291
\(706\) −1.48814e17 + 2.88857e16i −1.20175 + 0.233268i
\(707\) 3.44463e16 0.275821
\(708\) −3.20104e14 + 1.29134e14i −0.00254150 + 0.00102528i
\(709\) 1.88733e17i 1.48584i 0.669382 + 0.742919i \(0.266559\pi\)
−0.669382 + 0.742919i \(0.733441\pi\)
\(710\) −3.06223e17 + 5.94400e16i −2.39050 + 0.464011i
\(711\) 9.90954e16i 0.767071i
\(712\) 9.55930e16 6.19714e16i 0.733747 0.475676i
\(713\) 6.32933e16 0.481749
\(714\) −1.04701e15 5.39400e15i −0.00790246 0.0407119i
\(715\) −1.26281e17 −0.945150
\(716\) 6.60314e15 2.66379e15i 0.0490086 0.0197707i
\(717\) 1.49196e15i 0.0109810i
\(718\) −3.25652e16 1.67770e17i −0.237688 1.22452i
\(719\) 1.50283e17i 1.08777i −0.839160 0.543884i \(-0.816953\pi\)
0.839160 0.543884i \(-0.183047\pi\)
\(720\) −1.55326e17 1.61185e17i −1.11494 1.15699i
\(721\) 1.53679e17 1.09396
\(722\) 1.03706e17 2.01300e16i 0.732116 0.142109i
\(723\) −7.05279e15 −0.0493778
\(724\) −4.88104e16 1.20994e17i −0.338907 0.840100i
\(725\) 1.87821e17i 1.29335i
\(726\) 8.51608e14 1.65303e14i 0.00581594 0.00112891i
\(727\) 1.88422e17i 1.27622i 0.769947 + 0.638108i \(0.220283\pi\)
−0.769947 + 0.638108i \(0.779717\pi\)
\(728\) 1.31141e17 8.50165e16i 0.880947 0.571104i
\(729\) −1.49112e17 −0.993452
\(730\) −5.12899e16 2.64235e17i −0.338918 1.74604i
\(731\) −9.47737e16 −0.621131
\(732\) −9.03441e14 2.23949e15i −0.00587264 0.0145574i
\(733\) 4.73850e16i 0.305504i −0.988265 0.152752i \(-0.951186\pi\)
0.988265 0.152752i \(-0.0488136\pi\)
\(734\) 4.33227e16 + 2.23190e17i 0.277038 + 1.42724i
\(735\) 1.35794e16i 0.0861301i
\(736\) 8.10545e16 + 5.69143e16i 0.509929 + 0.358059i
\(737\) 1.32690e17 0.828008
\(738\) −1.43037e17 + 2.77645e16i −0.885342 + 0.171851i
\(739\) 9.08599e16 0.557835 0.278917 0.960315i \(-0.410024\pi\)
0.278917 + 0.960315i \(0.410024\pi\)
\(740\) −2.81833e17 + 1.13695e17i −1.71633 + 0.692391i
\(741\) 1.78915e15i 0.0108078i
\(742\) −2.29714e17 + 4.45890e16i −1.37646 + 0.267180i
\(743\) 8.47788e16i 0.503912i 0.967739 + 0.251956i \(0.0810737\pi\)
−0.967739 + 0.251956i \(0.918926\pi\)
\(744\) −2.35751e15 3.63655e15i −0.0139001 0.0214413i
\(745\) 2.89232e17 1.69165
\(746\) 1.43996e16 + 7.41841e16i 0.0835447 + 0.430406i
\(747\) 5.47673e16 0.315209
\(748\) 1.14076e17 4.60197e16i 0.651305 0.262745i
\(749\) 3.75789e17i 2.12840i
\(750\) 1.05895e15 + 5.45548e15i 0.00594985 + 0.0306525i
\(751\) 1.48426e17i 0.827315i 0.910433 + 0.413657i \(0.135749\pi\)
−0.910433 + 0.413657i \(0.864251\pi\)
\(752\) 1.02280e17 + 1.06138e17i 0.565567 + 0.586899i
\(753\) −1.01857e16 −0.0558756
\(754\) 9.53250e16 1.85032e16i 0.518775 0.100698i
\(755\) 3.66597e16 0.197928
\(756\) 7.46897e15 + 1.85145e16i 0.0400065 + 0.0991699i
\(757\) 9.42029e16i 0.500598i −0.968169 0.250299i \(-0.919471\pi\)
0.968169 0.250299i \(-0.0805289\pi\)
\(758\) −1.61808e17 + 3.14080e16i −0.853069 + 0.165586i
\(759\) 3.56667e15i 0.0186557i
\(760\) 8.50147e16 + 1.31138e17i 0.441177 + 0.680530i
\(761\) −6.48622e16 −0.333952 −0.166976 0.985961i \(-0.553400\pi\)
−0.166976 + 0.985961i \(0.553400\pi\)
\(762\) 2.03487e15 + 1.04832e16i 0.0103946 + 0.0535508i
\(763\) −1.05663e17 −0.535522
\(764\) −1.27217e17 3.15351e17i −0.639711 1.58575i
\(765\) 2.49658e17i 1.24560i
\(766\) −3.23370e16 1.66594e17i −0.160076 0.824682i
\(767\) 1.09499e16i 0.0537823i
\(768\) 2.50966e14 6.77693e15i 0.00122306 0.0330268i
\(769\) −1.78979e17 −0.865454 −0.432727 0.901525i \(-0.642449\pi\)
−0.432727 + 0.901525i \(0.642449\pi\)
\(770\) 4.82625e17 9.36807e16i 2.31561 0.449475i
\(771\) 1.26041e15 0.00600047
\(772\) −1.54440e17 + 6.23032e16i −0.729552 + 0.294311i
\(773\) 1.22731e17i 0.575278i 0.957739 + 0.287639i \(0.0928703\pi\)
−0.957739 + 0.287639i \(0.907130\pi\)
\(774\) 1.68927e17 3.27899e16i 0.785695 0.152509i
\(775\) 2.65925e17i 1.22730i
\(776\) 2.69602e17 1.74779e17i 1.23468 0.800420i
\(777\) 1.35447e16 0.0615522
\(778\) 7.88223e16 + 4.06077e17i 0.355444 + 1.83118i
\(779\) 1.01729e17 0.455220
\(780\) 7.20092e15 2.90495e15i 0.0319757 0.0128994i
\(781\) 3.11243e17i 1.37149i
\(782\) −2.10485e16 1.08438e17i −0.0920407 0.474176i
\(783\) 1.24041e16i 0.0538265i
\(784\) −2.70916e17 + 2.61070e17i −1.16665 + 1.12424i
\(785\) −5.27566e17 −2.25454
\(786\) 1.37714e16 2.67312e15i 0.0584040 0.0113366i
\(787\) 3.54881e17 1.49360 0.746800 0.665049i \(-0.231589\pi\)
0.746800 + 0.665049i \(0.231589\pi\)
\(788\) 1.06997e17 + 2.65229e17i 0.446904 + 1.10781i
\(789\) 2.94518e14i 0.00122081i
\(790\) 2.94761e17 5.72151e16i 1.21257 0.235369i
\(791\) 6.98993e16i 0.285374i
\(792\) −1.87410e17 + 1.21495e17i −0.759350 + 0.492274i
\(793\) −7.66074e16 −0.308057
\(794\) 4.06463e16 + 2.09402e17i 0.162218 + 0.835713i
\(795\) −1.16258e16 −0.0460491
\(796\) −9.19692e15 2.27978e16i −0.0361547 0.0896219i
\(797\) 3.68183e17i 1.43653i −0.695771 0.718264i \(-0.744937\pi\)
0.695771 0.718264i \(-0.255063\pi\)
\(798\) −1.32727e15 6.83785e15i −0.00513976 0.0264790i
\(799\) 1.64396e17i 0.631846i
\(800\) 2.39124e17 3.40548e17i 0.912186 1.29909i
\(801\) 2.30703e17 0.873489
\(802\) −2.99217e16 + 5.80801e15i −0.112445 + 0.0218264i
\(803\) −2.68567e17 −1.00175
\(804\) −7.56642e15 + 3.05239e15i −0.0280126 + 0.0113007i
\(805\) 4.41485e17i 1.62234i
\(806\) −1.34966e17 + 2.61977e16i −0.492280 + 0.0955550i
\(807\) 4.74490e15i 0.0171785i
\(808\) −2.57934e16 3.97872e16i −0.0926916 0.142980i
\(809\) −5.30501e17 −1.89232 −0.946161 0.323696i \(-0.895075\pi\)
−0.946161 + 0.323696i \(0.895075\pi\)
\(810\) −8.62826e16 4.44511e17i −0.305501 1.57388i
\(811\) −1.81588e17 −0.638208 −0.319104 0.947720i \(-0.603382\pi\)
−0.319104 + 0.947720i \(0.603382\pi\)
\(812\) −3.50590e17 + 1.41433e17i −1.22310 + 0.493416i
\(813\) 2.04972e15i 0.00709825i
\(814\) 5.77794e16 + 2.97668e17i 0.198622 + 1.02326i
\(815\) 7.94202e17i 2.71010i
\(816\) −5.44633e15 + 5.24837e15i −0.0184486 + 0.0177780i
\(817\) −1.20143e17 −0.403984
\(818\) 1.95564e17 3.79604e16i 0.652785 0.126710i
\(819\) 3.16493e17 1.04872
\(820\) −1.65172e17 4.09437e17i −0.543317 1.34680i
\(821\) 1.83914e17i 0.600559i −0.953851 0.300280i \(-0.902920\pi\)
0.953851 0.300280i \(-0.0970800\pi\)
\(822\) 1.69330e15 3.28681e14i 0.00548913 0.00106548i
\(823\) 1.97259e17i 0.634800i −0.948292 0.317400i \(-0.897190\pi\)
0.948292 0.317400i \(-0.102810\pi\)
\(824\) −1.15074e17 1.77506e17i −0.367634 0.567088i
\(825\) 1.49853e16 0.0475271
\(826\) −8.12315e15 4.18489e16i −0.0255767 0.131766i
\(827\) −3.28518e17 −1.02690 −0.513448 0.858121i \(-0.671632\pi\)
−0.513448 + 0.858121i \(0.671632\pi\)
\(828\) 7.50348e16 + 1.86000e17i 0.232852 + 0.577206i
\(829\) 3.57199e17i 1.10048i 0.835006 + 0.550241i \(0.185464\pi\)
−0.835006 + 0.550241i \(0.814536\pi\)
\(830\) 3.16213e16 + 1.62906e17i 0.0967187 + 0.498276i
\(831\) 1.35198e16i 0.0410547i
\(832\) −1.96397e17 8.78138e16i −0.592098 0.264742i
\(833\) 4.19621e17 1.25599
\(834\) 5.20969e15 1.01124e15i 0.0154816 0.00300508i
\(835\) 8.01983e17 2.36617
\(836\) 1.44611e17 5.83382e16i 0.423609 0.170889i
\(837\) 1.75624e16i 0.0510775i
\(838\) −1.76885e17 + 3.43346e16i −0.510772 + 0.0991442i
\(839\) 3.98851e17i 1.14351i −0.820426 0.571753i \(-0.806263\pi\)
0.820426 0.571753i \(-0.193737\pi\)
\(840\) −2.53657e16 + 1.64442e16i −0.0722057 + 0.0468098i
\(841\) 1.18930e17 0.336135
\(842\) −2.86920e16 1.47816e17i −0.0805171 0.414809i
\(843\) 2.58858e15 0.00721266
\(844\) 2.04914e17 8.26649e16i 0.566913 0.228700i
\(845\) 3.39231e17i 0.931870i
\(846\) 5.68781e16 + 2.93025e17i 0.155140 + 0.799249i
\(847\) 1.07141e17i 0.290171i
\(848\) 2.23512e17 + 2.31942e17i 0.601071 + 0.623742i
\(849\) 6.16898e15 0.0164728
\(850\) −4.55598e17 + 8.84346e16i −1.20800 + 0.234482i
\(851\) 2.72294e17 0.716905
\(852\) −7.15978e15 1.77480e16i −0.0187181 0.0463994i
\(853\) 5.41457e17i 1.40563i 0.711375 + 0.702813i \(0.248073\pi\)
−0.711375 + 0.702813i \(0.751927\pi\)
\(854\) 2.92781e17 5.68308e16i 0.754737 0.146500i
\(855\) 3.16486e17i 0.810137i
\(856\) −4.34055e17 + 2.81391e17i −1.10332 + 0.715265i
\(857\) 5.21930e17 1.31743 0.658714 0.752393i \(-0.271101\pi\)
0.658714 + 0.752393i \(0.271101\pi\)
\(858\) −1.47628e15 7.60551e15i −0.00370037 0.0190636i
\(859\) −2.55344e17 −0.635575 −0.317787 0.948162i \(-0.602940\pi\)
−0.317787 + 0.948162i \(0.602940\pi\)
\(860\) 1.95069e17 + 4.83545e17i 0.482166 + 1.19522i
\(861\) 1.96773e16i 0.0482999i
\(862\) −1.46949e17 7.57054e17i −0.358198 1.84537i
\(863\) 5.24738e17i 1.27022i −0.772423 0.635108i \(-0.780956\pi\)
0.772423 0.635108i \(-0.219044\pi\)
\(864\) 1.57923e16 2.24906e16i 0.0379633 0.0540654i
\(865\) 1.54572e17 0.369007
\(866\) −3.44802e17 + 6.69284e16i −0.817453 + 0.158673i
\(867\) −5.60134e15 −0.0131880
\(868\) 4.96382e17 2.00247e17i 1.16064 0.468217i
\(869\) 2.99593e17i 0.695685i
\(870\) −1.84381e16 + 3.57896e15i −0.0425207 + 0.00825356i
\(871\) 2.58828e17i 0.592792i
\(872\) 7.91207e16 + 1.22046e17i 0.179966 + 0.277604i
\(873\) 6.50653e17 1.46982
\(874\) −2.66827e16 1.37464e17i −0.0598633 0.308404i
\(875\) −6.86352e17 −1.52932
\(876\) 1.53145e16 6.17807e15i 0.0338905 0.0136719i
\(877\) 3.45631e17i 0.759653i −0.925058 0.379827i \(-0.875984\pi\)
0.925058 0.379827i \(-0.124016\pi\)
\(878\) −6.85295e16 3.53050e17i −0.149593 0.770672i
\(879\) 1.93332e16i 0.0419150i
\(880\) −4.69595e17 4.87307e17i −1.01118 1.04932i
\(881\) 5.86814e16 0.125500 0.0627502 0.998029i \(-0.480013\pi\)
0.0627502 + 0.998029i \(0.480013\pi\)
\(882\) −7.47944e17 + 1.45181e17i −1.58876 + 0.308388i
\(883\) −5.84143e17 −1.23241 −0.616205 0.787586i \(-0.711331\pi\)
−0.616205 + 0.787586i \(0.711331\pi\)
\(884\) 8.97668e16 + 2.22518e17i 0.188106 + 0.466286i
\(885\) 2.11797e15i 0.00440820i
\(886\) 5.53132e17 1.07367e17i 1.14347 0.221956i
\(887\) 1.24494e17i 0.255627i 0.991798 + 0.127813i \(0.0407958\pi\)
−0.991798 + 0.127813i \(0.959204\pi\)
\(888\) −1.01423e16 1.56448e16i −0.0206851 0.0319075i
\(889\) −1.31889e18 −2.67177
\(890\) 1.33202e17 + 6.86229e17i 0.268022 + 1.38079i
\(891\) −4.51797e17 −0.902978
\(892\) −2.57472e17 6.38233e17i −0.511141 1.26704i
\(893\) 2.08402e17i 0.410953i
\(894\) 3.38126e15 + 1.74196e16i 0.00662299 + 0.0341203i
\(895\) 4.36899e16i 0.0850046i
\(896\) 8.15740e17 + 1.89915e17i 1.57654 + 0.367037i
\(897\) −6.95721e15 −0.0133561
\(898\) −3.45999e17 + 6.71607e16i −0.659806 + 0.128073i
\(899\) 3.32561e17 0.629961
\(900\) 7.81474e17 3.15257e17i 1.47048 0.593211i
\(901\) 3.59254e17i 0.671510i
\(902\) −4.32441e17 + 8.39398e16i −0.802949 + 0.155858i
\(903\) 2.32389e16i 0.0428636i
\(904\) −8.07371e16 + 5.23405e16i −0.147932 + 0.0959020i
\(905\) 8.00557e17 1.45714
\(906\) 4.28569e14 + 2.20790e15i 0.000774911 + 0.00399219i
\(907\) −3.14671e17 −0.565213 −0.282607 0.959236i \(-0.591199\pi\)
−0.282607 + 0.959236i \(0.591199\pi\)
\(908\) 8.31277e16 3.35348e16i 0.148331 0.0598385i
\(909\) 9.60218e16i 0.170211i
\(910\) 1.82735e17 + 9.41415e17i 0.321791 + 1.65780i
\(911\) 1.09959e18i 1.92362i −0.273716 0.961811i \(-0.588253\pi\)
0.273716 0.961811i \(-0.411747\pi\)
\(912\) −6.90419e15 + 6.65325e15i −0.0119990 + 0.0115628i
\(913\) 1.65577e17 0.285874
\(914\) 6.97740e17 1.35436e17i 1.19679 0.232304i
\(915\) 1.48177e16 0.0252495
\(916\) 3.72092e17 + 9.22359e17i 0.629908 + 1.56145i
\(917\) 1.73258e18i 2.91391i
\(918\) −3.00888e16 + 5.84044e15i −0.0502746 + 0.00975864i
\(919\) 3.89660e17i 0.646834i 0.946257 + 0.323417i \(0.104832\pi\)
−0.946257 + 0.323417i \(0.895168\pi\)
\(920\) −5.09937e17 + 3.30584e17i −0.840988 + 0.545199i
\(921\) 2.19266e16 0.0359264
\(922\) −1.48632e17 7.65723e17i −0.241951 1.24648i
\(923\) −6.07115e17 −0.981885
\(924\) 1.12842e16 + 2.79719e16i 0.0181317 + 0.0449459i
\(925\) 1.14404e18i 1.82638i
\(926\) 1.43656e15 + 7.40090e15i 0.00227855 + 0.0117387i
\(927\) 4.28390e17i 0.675090i
\(928\) 4.25883e17 + 2.99044e17i 0.666811 + 0.468217i
\(929\) −9.01757e17 −1.40280 −0.701399 0.712769i \(-0.747441\pi\)
−0.701399 + 0.712769i \(0.747441\pi\)
\(930\) 2.61055e16 5.06726e15i 0.0403492 0.00783204i
\(931\) 5.31944e17 0.816898
\(932\) 2.55204e17 1.02953e17i 0.389397 0.157088i
\(933\) 2.62765e16i 0.0398361i
\(934\) 1.09054e18 2.11682e17i 1.64271 0.318862i
\(935\) 7.54786e17i 1.12968i
\(936\) −2.36990e17 3.65565e17i −0.352432 0.543638i
\(937\) 2.84937e17 0.421028 0.210514 0.977591i \(-0.432486\pi\)
0.210514 + 0.977591i \(0.432486\pi\)
\(938\) −1.92010e17 9.89199e17i −0.281908 1.45233i
\(939\) −3.27898e15 −0.00478349
\(940\) −8.38768e17 + 3.38370e17i −1.21583 + 0.490484i
\(941\) 7.97698e17i 1.14895i 0.818522 + 0.574475i \(0.194794\pi\)
−0.818522 + 0.574475i \(0.805206\pi\)
\(942\) −6.16749e15 3.17737e16i −0.00882680 0.0454739i
\(943\) 3.95580e17i 0.562553i
\(944\) −4.22549e16 + 4.07191e16i −0.0597097 + 0.0575395i
\(945\) −1.22501e17 −0.172009
\(946\) 5.10714e17 9.91330e16i 0.712576 0.138316i
\(947\) 8.11827e17 1.12555 0.562773 0.826611i \(-0.309734\pi\)
0.562773 + 0.826611i \(0.309734\pi\)
\(948\) 6.89179e15 + 1.70837e16i 0.00949472 + 0.0235360i
\(949\) 5.23870e17i 0.717177i
\(950\) −5.77551e17 + 1.12107e17i −0.785686 + 0.152507i
\(951\) 1.67490e16i 0.0226416i
\(952\) −5.08148e17 7.83836e17i −0.682604 1.05294i
\(953\) −5.02264e17 −0.670463 −0.335231 0.942136i \(-0.608814\pi\)
−0.335231 + 0.942136i \(0.608814\pi\)
\(954\) 1.24295e17 + 6.40344e17i 0.164878 + 0.849421i
\(955\) 2.08653e18 2.75045
\(956\) −9.48930e16 2.35225e17i −0.124305 0.308132i
\(957\) 1.87403e16i 0.0243953i
\(958\) 1.09945e17 + 5.66414e17i 0.142227 + 0.732724i
\(959\) 2.13034e17i 0.273865i
\(960\) 3.79877e16 + 1.69853e16i 0.0485306 + 0.0216992i
\(961\) 3.16807e17 0.402212
\(962\) −5.80636e17 + 1.12705e17i −0.732578 + 0.142198i
\(963\) −1.04754e18 −1.31345
\(964\) −1.11196e18 + 4.48578e17i −1.38556 + 0.558954i
\(965\) 1.02186e18i 1.26540i
\(966\) 2.65893e16 5.16117e15i 0.0327224 0.00635163i
\(967\) 5.04696e17i 0.617264i −0.951182 0.308632i \(-0.900129\pi\)
0.951182 0.308632i \(-0.0998711\pi\)
\(968\) 1.23753e17 8.02268e16i 0.150419 0.0975141i
\(969\) 1.06939e16 0.0129179
\(970\) 3.75670e17 + 1.93538e18i 0.451000 + 2.32346i
\(971\) 3.85943e16 0.0460477 0.0230238 0.999735i \(-0.492671\pi\)
0.0230238 + 0.999735i \(0.492671\pi\)
\(972\) 7.74297e16 3.12362e16i 0.0918143 0.0370391i
\(973\) 6.55429e17i 0.772411i
\(974\) −1.76772e17 9.10695e17i −0.207043 1.06664i
\(975\) 2.92305e16i 0.0340259i
\(976\) −2.84877e17 2.95622e17i −0.329578 0.342009i
\(977\) 6.44700e17 0.741294 0.370647 0.928774i \(-0.379136\pi\)
0.370647 + 0.928774i \(0.379136\pi\)
\(978\) −4.78324e16 + 9.28460e15i −0.0546625 + 0.0106104i
\(979\) 6.97478e17 0.792199
\(980\) −8.63687e17 2.14095e18i −0.974990 2.41685i
\(981\) 2.94545e17i 0.330474i
\(982\) −5.13998e17 + 9.97705e16i −0.573182 + 0.111258i
\(983\) 5.46969e16i 0.0606236i 0.999540 + 0.0303118i \(0.00965003\pi\)
−0.999540 + 0.0303118i \(0.990350\pi\)
\(984\) 2.27282e16 1.47343e16i 0.0250377 0.0162315i
\(985\) −1.75490e18 −1.92147
\(986\) −1.10595e17 5.69762e17i −0.120357 0.620058i
\(987\) 4.03106e16 0.0436030
\(988\) 1.13795e17 + 2.82082e17i 0.122344 + 0.303272i
\(989\) 4.67180e17i 0.499237i
\(990\) −2.61142e17 1.34535e18i −0.277374 1.42898i
\(991\) 1.53333e18i 1.61880i 0.587259 + 0.809399i \(0.300207\pi\)
−0.587259 + 0.809399i \(0.699793\pi\)
\(992\) −6.02986e17 4.23400e17i −0.632757 0.444305i
\(993\) −4.12875e16 −0.0430648
\(994\) 2.32030e18 4.50385e17i 2.40561 0.466945i
\(995\) 1.50842e17 0.155448
\(996\) −9.44170e15 + 3.80891e15i −0.00967151 + 0.00390161i
\(997\) 4.69347e17i 0.477885i 0.971034 + 0.238942i \(0.0768007\pi\)
−0.971034 + 0.238942i \(0.923199\pi\)
\(998\) −8.73091e17 + 1.69473e17i −0.883642 + 0.171521i
\(999\) 7.55551e16i 0.0760100i
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.3.2 yes 10
3.2 odd 2 72.13.b.b.19.9 10
4.3 odd 2 32.13.d.b.15.6 10
8.3 odd 2 inner 8.13.d.b.3.1 10
8.5 even 2 32.13.d.b.15.5 10
24.11 even 2 72.13.b.b.19.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.13.d.b.3.1 10 8.3 odd 2 inner
8.13.d.b.3.2 yes 10 1.1 even 1 trivial
32.13.d.b.15.5 10 8.5 even 2
32.13.d.b.15.6 10 4.3 odd 2
72.13.b.b.19.9 10 3.2 odd 2
72.13.b.b.19.10 10 24.11 even 2