Properties

Label 1150.2.e.d.1057.3
Level $1150$
Weight $2$
Character 1150.1057
Analytic conductor $9.183$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1150,2,Mod(643,1150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1150, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1150.643");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.18279623245\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 40 x^{14} - 116 x^{13} + 800 x^{12} - 2584 x^{11} + 9564 x^{10} - 27124 x^{9} + 33538 x^{8} + 44880 x^{7} - 233952 x^{6} + 263772 x^{5} + 797544 x^{4} + \cdots + 2313441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.3
Root \(-2.02927 + 4.89908i\) of defining polynomial
Character \(\chi\) \(=\) 1150.1057
Dual form 1150.2.e.d.643.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.93185 - 1.93185i) q^{3} +1.00000i q^{4} -2.73205 q^{6} +(-3.35143 + 3.35143i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.46410i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.93185 - 1.93185i) q^{3} +1.00000i q^{4} -2.73205 q^{6} +(-3.35143 + 3.35143i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.46410i q^{9} +4.73963i q^{11} +(1.93185 + 1.93185i) q^{12} +(-1.74238 + 1.74238i) q^{13} +4.73963 q^{14} -1.00000 q^{16} +(-3.15660 + 3.15660i) q^{18} +4.73963 q^{19} +12.9489i q^{21} +(3.35143 - 3.35143i) q^{22} +(-2.83379 - 3.86906i) q^{23} -2.73205i q^{24} +2.46410 q^{26} +(-2.82843 - 2.82843i) q^{27} +(-3.35143 - 3.35143i) q^{28} +9.19615i q^{29} +6.92820 q^{31} +(0.707107 + 0.707107i) q^{32} +(9.15626 + 9.15626i) q^{33} +4.46410 q^{36} +(2.45341 - 2.45341i) q^{37} +(-3.35143 - 3.35143i) q^{38} +6.73205i q^{39} -0.464102 q^{41} +(9.15626 - 9.15626i) q^{42} +(5.80484 + 5.80484i) q^{43} -4.73963 q^{44} +(-0.732051 + 4.73963i) q^{46} +(5.41662 + 5.41662i) q^{47} +(-1.93185 + 1.93185i) q^{48} -15.4641i q^{49} +(-1.74238 - 1.74238i) q^{52} +(-2.45341 - 2.45341i) q^{53} +4.00000i q^{54} +4.73963i q^{56} +(9.15626 - 9.15626i) q^{57} +(6.50266 - 6.50266i) q^{58} +4.73205i q^{59} +12.9489i q^{61} +(-4.89898 - 4.89898i) q^{62} +(14.9611 + 14.9611i) q^{63} -1.00000i q^{64} -12.9489i q^{66} +(-6.70285 + 6.70285i) q^{67} +(-12.9489 - 2.00000i) q^{69} -9.46410 q^{71} +(-3.15660 - 3.15660i) q^{72} +(-4.70951 + 4.70951i) q^{73} -3.46965 q^{74} +4.73963i q^{76} +(-15.8845 - 15.8845i) q^{77} +(4.76028 - 4.76028i) q^{78} -1.26998 q^{79} +2.46410 q^{81} +(0.328169 + 0.328169i) q^{82} +(-5.80484 - 5.80484i) q^{83} -12.9489 q^{84} -8.20928i q^{86} +(17.7656 + 17.7656i) q^{87} +(3.35143 + 3.35143i) q^{88} -11.6789i q^{91} +(3.86906 - 2.83379i) q^{92} +(13.3843 - 13.3843i) q^{93} -7.66025i q^{94} +2.73205 q^{96} +(9.15626 - 9.15626i) q^{97} +(-10.9348 + 10.9348i) q^{98} +21.1582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{6} - 16 q^{16} - 16 q^{26} + 16 q^{36} + 48 q^{41} + 16 q^{46} - 96 q^{71} - 16 q^{81} + 16 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 1.93185 1.93185i 1.11536 1.11536i 0.122941 0.992414i \(-0.460767\pi\)
0.992414 0.122941i \(-0.0392326\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) −2.73205 −1.11536
\(7\) −3.35143 + 3.35143i −1.26672 + 1.26672i −0.318947 + 0.947772i \(0.603329\pi\)
−0.947772 + 0.318947i \(0.896671\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 4.46410i 1.48803i
\(10\) 0 0
\(11\) 4.73963i 1.42905i 0.699609 + 0.714526i \(0.253358\pi\)
−0.699609 + 0.714526i \(0.746642\pi\)
\(12\) 1.93185 + 1.93185i 0.557678 + 0.557678i
\(13\) −1.74238 + 1.74238i −0.483250 + 0.483250i −0.906168 0.422918i \(-0.861006\pi\)
0.422918 + 0.906168i \(0.361006\pi\)
\(14\) 4.73963 1.26672
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) −3.15660 + 3.15660i −0.744017 + 0.744017i
\(19\) 4.73963 1.08735 0.543673 0.839297i \(-0.317033\pi\)
0.543673 + 0.839297i \(0.317033\pi\)
\(20\) 0 0
\(21\) 12.9489i 2.82568i
\(22\) 3.35143 3.35143i 0.714526 0.714526i
\(23\) −2.83379 3.86906i −0.590885 0.806755i
\(24\) 2.73205i 0.557678i
\(25\) 0 0
\(26\) 2.46410 0.483250
\(27\) −2.82843 2.82843i −0.544331 0.544331i
\(28\) −3.35143 3.35143i −0.633360 0.633360i
\(29\) 9.19615i 1.70768i 0.520533 + 0.853841i \(0.325733\pi\)
−0.520533 + 0.853841i \(0.674267\pi\)
\(30\) 0 0
\(31\) 6.92820 1.24434 0.622171 0.782881i \(-0.286251\pi\)
0.622171 + 0.782881i \(0.286251\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 9.15626 + 9.15626i 1.59390 + 1.59390i
\(34\) 0 0
\(35\) 0 0
\(36\) 4.46410 0.744017
\(37\) 2.45341 2.45341i 0.403339 0.403339i −0.476069 0.879408i \(-0.657939\pi\)
0.879408 + 0.476069i \(0.157939\pi\)
\(38\) −3.35143 3.35143i −0.543673 0.543673i
\(39\) 6.73205i 1.07799i
\(40\) 0 0
\(41\) −0.464102 −0.0724805 −0.0362402 0.999343i \(-0.511538\pi\)
−0.0362402 + 0.999343i \(0.511538\pi\)
\(42\) 9.15626 9.15626i 1.41284 1.41284i
\(43\) 5.80484 + 5.80484i 0.885230 + 0.885230i 0.994060 0.108831i \(-0.0347106\pi\)
−0.108831 + 0.994060i \(0.534711\pi\)
\(44\) −4.73963 −0.714526
\(45\) 0 0
\(46\) −0.732051 + 4.73963i −0.107935 + 0.698820i
\(47\) 5.41662 + 5.41662i 0.790095 + 0.790095i 0.981509 0.191414i \(-0.0613074\pi\)
−0.191414 + 0.981509i \(0.561307\pi\)
\(48\) −1.93185 + 1.93185i −0.278839 + 0.278839i
\(49\) 15.4641i 2.20916i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.74238 1.74238i −0.241625 0.241625i
\(53\) −2.45341 2.45341i −0.337002 0.337002i 0.518236 0.855238i \(-0.326589\pi\)
−0.855238 + 0.518236i \(0.826589\pi\)
\(54\) 4.00000i 0.544331i
\(55\) 0 0
\(56\) 4.73963i 0.633360i
\(57\) 9.15626 9.15626i 1.21278 1.21278i
\(58\) 6.50266 6.50266i 0.853841 0.853841i
\(59\) 4.73205i 0.616061i 0.951377 + 0.308030i \(0.0996698\pi\)
−0.951377 + 0.308030i \(0.900330\pi\)
\(60\) 0 0
\(61\) 12.9489i 1.65794i 0.559294 + 0.828969i \(0.311072\pi\)
−0.559294 + 0.828969i \(0.688928\pi\)
\(62\) −4.89898 4.89898i −0.622171 0.622171i
\(63\) 14.9611 + 14.9611i 1.88492 + 1.88492i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 12.9489i 1.59390i
\(67\) −6.70285 + 6.70285i −0.818884 + 0.818884i −0.985946 0.167063i \(-0.946572\pi\)
0.167063 + 0.985946i \(0.446572\pi\)
\(68\) 0 0
\(69\) −12.9489 2.00000i −1.55887 0.240772i
\(70\) 0 0
\(71\) −9.46410 −1.12318 −0.561591 0.827415i \(-0.689811\pi\)
−0.561591 + 0.827415i \(0.689811\pi\)
\(72\) −3.15660 3.15660i −0.372008 0.372008i
\(73\) −4.70951 + 4.70951i −0.551207 + 0.551207i −0.926789 0.375582i \(-0.877443\pi\)
0.375582 + 0.926789i \(0.377443\pi\)
\(74\) −3.46965 −0.403339
\(75\) 0 0
\(76\) 4.73963i 0.543673i
\(77\) −15.8845 15.8845i −1.81021 1.81021i
\(78\) 4.76028 4.76028i 0.538995 0.538995i
\(79\) −1.26998 −0.142884 −0.0714420 0.997445i \(-0.522760\pi\)
−0.0714420 + 0.997445i \(0.522760\pi\)
\(80\) 0 0
\(81\) 2.46410 0.273789
\(82\) 0.328169 + 0.328169i 0.0362402 + 0.0362402i
\(83\) −5.80484 5.80484i −0.637164 0.637164i 0.312691 0.949855i \(-0.398770\pi\)
−0.949855 + 0.312691i \(0.898770\pi\)
\(84\) −12.9489 −1.41284
\(85\) 0 0
\(86\) 8.20928i 0.885230i
\(87\) 17.7656 + 17.7656i 1.90467 + 1.90467i
\(88\) 3.35143 + 3.35143i 0.357263 + 0.357263i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 11.6789i 1.22428i
\(92\) 3.86906 2.83379i 0.403378 0.295443i
\(93\) 13.3843 13.3843i 1.38788 1.38788i
\(94\) 7.66025i 0.790095i
\(95\) 0 0
\(96\) 2.73205 0.278839
\(97\) 9.15626 9.15626i 0.929678 0.929678i −0.0680071 0.997685i \(-0.521664\pi\)
0.997685 + 0.0680071i \(0.0216641\pi\)
\(98\) −10.9348 + 10.9348i −1.10458 + 1.10458i
\(99\) 21.1582 2.12648
\(100\) 0 0
\(101\) −16.9282 −1.68442 −0.842210 0.539150i \(-0.818745\pi\)
−0.842210 + 0.539150i \(0.818745\pi\)
\(102\) 0 0
\(103\) −8.25825 8.25825i −0.813710 0.813710i 0.171478 0.985188i \(-0.445146\pi\)
−0.985188 + 0.171478i \(0.945146\pi\)
\(104\) 2.46410i 0.241625i
\(105\) 0 0
\(106\) 3.46965i 0.337002i
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 2.82843 2.82843i 0.272166 0.272166i
\(109\) −6.00961 −0.575616 −0.287808 0.957688i \(-0.592927\pi\)
−0.287808 + 0.957688i \(0.592927\pi\)
\(110\) 0 0
\(111\) 9.47926i 0.899732i
\(112\) 3.35143 3.35143i 0.316680 0.316680i
\(113\) −4.24944 4.24944i −0.399753 0.399753i 0.478393 0.878146i \(-0.341220\pi\)
−0.878146 + 0.478393i \(0.841220\pi\)
\(114\) −12.9489 −1.21278
\(115\) 0 0
\(116\) −9.19615 −0.853841
\(117\) 7.77817 + 7.77817i 0.719092 + 0.719092i
\(118\) 3.34607 3.34607i 0.308030 0.308030i
\(119\) 0 0
\(120\) 0 0
\(121\) −11.4641 −1.04219
\(122\) 9.15626 9.15626i 0.828969 0.828969i
\(123\) −0.896575 + 0.896575i −0.0808415 + 0.0808415i
\(124\) 6.92820i 0.622171i
\(125\) 0 0
\(126\) 21.1582i 1.88492i
\(127\) 1.55291 + 1.55291i 0.137799 + 0.137799i 0.772641 0.634843i \(-0.218935\pi\)
−0.634843 + 0.772641i \(0.718935\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 22.4282 1.97469
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) −9.15626 + 9.15626i −0.796950 + 0.796950i
\(133\) −15.8845 + 15.8845i −1.37736 + 1.37736i
\(134\) 9.47926 0.818884
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(138\) 7.74205 + 10.5705i 0.659047 + 0.899819i
\(139\) 6.53590i 0.554368i −0.960817 0.277184i \(-0.910599\pi\)
0.960817 0.277184i \(-0.0894011\pi\)
\(140\) 0 0
\(141\) 20.9282 1.76247
\(142\) 6.69213 + 6.69213i 0.561591 + 0.561591i
\(143\) −8.25825 8.25825i −0.690590 0.690590i
\(144\) 4.46410i 0.372008i
\(145\) 0 0
\(146\) 6.66025 0.551207
\(147\) −29.8744 29.8744i −2.46399 2.46399i
\(148\) 2.45341 + 2.45341i 0.201669 + 0.201669i
\(149\) 18.9585 1.55314 0.776571 0.630029i \(-0.216957\pi\)
0.776571 + 0.630029i \(0.216957\pi\)
\(150\) 0 0
\(151\) 15.3205 1.24677 0.623383 0.781917i \(-0.285758\pi\)
0.623383 + 0.781917i \(0.285758\pi\)
\(152\) 3.35143 3.35143i 0.271836 0.271836i
\(153\) 0 0
\(154\) 22.4641i 1.81021i
\(155\) 0 0
\(156\) −6.73205 −0.538995
\(157\) −15.8591 + 15.8591i −1.26570 + 1.26570i −0.317405 + 0.948290i \(0.602811\pi\)
−0.948290 + 0.317405i \(0.897189\pi\)
\(158\) 0.898012 + 0.898012i 0.0714420 + 0.0714420i
\(159\) −9.47926 −0.751754
\(160\) 0 0
\(161\) 22.4641 + 3.46965i 1.77042 + 0.273447i
\(162\) −1.74238 1.74238i −0.136895 0.136895i
\(163\) 7.86611 7.86611i 0.616121 0.616121i −0.328413 0.944534i \(-0.606514\pi\)
0.944534 + 0.328413i \(0.106514\pi\)
\(164\) 0.464102i 0.0362402i
\(165\) 0 0
\(166\) 8.20928i 0.637164i
\(167\) 3.58630 + 3.58630i 0.277516 + 0.277516i 0.832117 0.554600i \(-0.187129\pi\)
−0.554600 + 0.832117i \(0.687129\pi\)
\(168\) 9.15626 + 9.15626i 0.706421 + 0.706421i
\(169\) 6.92820i 0.532939i
\(170\) 0 0
\(171\) 21.1582i 1.61801i
\(172\) −5.80484 + 5.80484i −0.442615 + 0.442615i
\(173\) −0.429705 + 0.429705i −0.0326699 + 0.0326699i −0.723253 0.690583i \(-0.757354\pi\)
0.690583 + 0.723253i \(0.257354\pi\)
\(174\) 25.1244i 1.90467i
\(175\) 0 0
\(176\) 4.73963i 0.357263i
\(177\) 9.14162 + 9.14162i 0.687126 + 0.687126i
\(178\) 0 0
\(179\) 22.1962i 1.65902i −0.558493 0.829509i \(-0.688620\pi\)
0.558493 0.829509i \(-0.311380\pi\)
\(180\) 0 0
\(181\) 25.8978i 1.92497i 0.271335 + 0.962485i \(0.412535\pi\)
−0.271335 + 0.962485i \(0.587465\pi\)
\(182\) −8.25825 + 8.25825i −0.612142 + 0.612142i
\(183\) 25.0154 + 25.0154i 1.84919 + 1.84919i
\(184\) −4.73963 0.732051i −0.349410 0.0539675i
\(185\) 0 0
\(186\) −18.9282 −1.38788
\(187\) 0 0
\(188\) −5.41662 + 5.41662i −0.395047 + 0.395047i
\(189\) 18.9585 1.37903
\(190\) 0 0
\(191\) 17.6885i 1.27990i −0.768417 0.639949i \(-0.778955\pi\)
0.768417 0.639949i \(-0.221045\pi\)
\(192\) −1.93185 1.93185i −0.139419 0.139419i
\(193\) 7.07107 7.07107i 0.508987 0.508987i −0.405229 0.914215i \(-0.632808\pi\)
0.914215 + 0.405229i \(0.132808\pi\)
\(194\) −12.9489 −0.929678
\(195\) 0 0
\(196\) 15.4641 1.10458
\(197\) 4.94975 + 4.94975i 0.352655 + 0.352655i 0.861096 0.508442i \(-0.169778\pi\)
−0.508442 + 0.861096i \(0.669778\pi\)
\(198\) −14.9611 14.9611i −1.06324 1.06324i
\(199\) 17.6885 1.25391 0.626954 0.779056i \(-0.284301\pi\)
0.626954 + 0.779056i \(0.284301\pi\)
\(200\) 0 0
\(201\) 25.8978i 1.82669i
\(202\) 11.9700 + 11.9700i 0.842210 + 0.842210i
\(203\) −30.8202 30.8202i −2.16316 2.16316i
\(204\) 0 0
\(205\) 0 0
\(206\) 11.6789i 0.813710i
\(207\) −17.2719 + 12.6503i −1.20048 + 0.879258i
\(208\) 1.74238 1.74238i 0.120813 0.120813i
\(209\) 22.4641i 1.55387i
\(210\) 0 0
\(211\) −22.2487 −1.53166 −0.765832 0.643040i \(-0.777673\pi\)
−0.765832 + 0.643040i \(0.777673\pi\)
\(212\) 2.45341 2.45341i 0.168501 0.168501i
\(213\) −18.2832 + 18.2832i −1.25275 + 1.25275i
\(214\) 0 0
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) −23.2194 + 23.2194i −1.57623 + 1.57623i
\(218\) 4.24944 + 4.24944i 0.287808 + 0.287808i
\(219\) 18.1962i 1.22958i
\(220\) 0 0
\(221\) 0 0
\(222\) −6.70285 + 6.70285i −0.449866 + 0.449866i
\(223\) −3.34607 + 3.34607i −0.224069 + 0.224069i −0.810209 0.586140i \(-0.800647\pi\)
0.586140 + 0.810209i \(0.300647\pi\)
\(224\) −4.73963 −0.316680
\(225\) 0 0
\(226\) 6.00961i 0.399753i
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 9.15626 + 9.15626i 0.606388 + 0.606388i
\(229\) 6.93930 0.458562 0.229281 0.973360i \(-0.426363\pi\)
0.229281 + 0.973360i \(0.426363\pi\)
\(230\) 0 0
\(231\) −61.3731 −4.03805
\(232\) 6.50266 + 6.50266i 0.426921 + 0.426921i
\(233\) 4.43211 4.43211i 0.290357 0.290357i −0.546864 0.837221i \(-0.684179\pi\)
0.837221 + 0.546864i \(0.184179\pi\)
\(234\) 11.0000i 0.719092i
\(235\) 0 0
\(236\) −4.73205 −0.308030
\(237\) −2.45341 + 2.45341i −0.159366 + 0.159366i
\(238\) 0 0
\(239\) 23.5167i 1.52117i −0.649241 0.760583i \(-0.724913\pi\)
0.649241 0.760583i \(-0.275087\pi\)
\(240\) 0 0
\(241\) 15.4889i 0.997726i −0.866681 0.498863i \(-0.833751\pi\)
0.866681 0.498863i \(-0.166249\pi\)
\(242\) 8.10634 + 8.10634i 0.521096 + 0.521096i
\(243\) 13.2456 13.2456i 0.849703 0.849703i
\(244\) −12.9489 −0.828969
\(245\) 0 0
\(246\) 1.26795 0.0808415
\(247\) −8.25825 + 8.25825i −0.525460 + 0.525460i
\(248\) 4.89898 4.89898i 0.311086 0.311086i
\(249\) −22.4282 −1.42133
\(250\) 0 0
\(251\) 9.47926i 0.598326i −0.954202 0.299163i \(-0.903293\pi\)
0.954202 0.299163i \(-0.0967074\pi\)
\(252\) −14.9611 + 14.9611i −0.942461 + 0.942461i
\(253\) 18.3379 13.4311i 1.15290 0.844406i
\(254\) 2.19615i 0.137799i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −0.656339 0.656339i −0.0409413 0.0409413i 0.686340 0.727281i \(-0.259216\pi\)
−0.727281 + 0.686340i \(0.759216\pi\)
\(258\) −15.8591 15.8591i −0.987345 0.987345i
\(259\) 16.4449i 1.02183i
\(260\) 0 0
\(261\) 41.0526 2.54109
\(262\) −5.65685 5.65685i −0.349482 0.349482i
\(263\) 6.70285 + 6.70285i 0.413315 + 0.413315i 0.882892 0.469576i \(-0.155593\pi\)
−0.469576 + 0.882892i \(0.655593\pi\)
\(264\) 12.9489 0.796950
\(265\) 0 0
\(266\) 22.4641 1.37736
\(267\) 0 0
\(268\) −6.70285 6.70285i −0.409442 0.409442i
\(269\) 15.5885i 0.950445i −0.879866 0.475223i \(-0.842368\pi\)
0.879866 0.475223i \(-0.157632\pi\)
\(270\) 0 0
\(271\) 4.19615 0.254898 0.127449 0.991845i \(-0.459321\pi\)
0.127449 + 0.991845i \(0.459321\pi\)
\(272\) 0 0
\(273\) −22.5620 22.5620i −1.36551 1.36551i
\(274\) 0 0
\(275\) 0 0
\(276\) 2.00000 12.9489i 0.120386 0.779433i
\(277\) 2.77766 + 2.77766i 0.166893 + 0.166893i 0.785612 0.618719i \(-0.212348\pi\)
−0.618719 + 0.785612i \(0.712348\pi\)
\(278\) −4.62158 + 4.62158i −0.277184 + 0.277184i
\(279\) 30.9282i 1.85162i
\(280\) 0 0
\(281\) 22.4282i 1.33795i −0.743284 0.668976i \(-0.766733\pi\)
0.743284 0.668976i \(-0.233267\pi\)
\(282\) −14.7985 14.7985i −0.881236 0.881236i
\(283\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(284\) 9.46410i 0.561591i
\(285\) 0 0
\(286\) 11.6789i 0.690590i
\(287\) 1.55540 1.55540i 0.0918125 0.0918125i
\(288\) 3.15660 3.15660i 0.186004 0.186004i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 35.3771i 2.07384i
\(292\) −4.70951 4.70951i −0.275603 0.275603i
\(293\) −18.3125 18.3125i −1.06983 1.06983i −0.997371 0.0724578i \(-0.976916\pi\)
−0.0724578 0.997371i \(-0.523084\pi\)
\(294\) 42.2487i 2.46399i
\(295\) 0 0
\(296\) 3.46965i 0.201669i
\(297\) 13.4057 13.4057i 0.777878 0.777878i
\(298\) −13.4057 13.4057i −0.776571 0.776571i
\(299\) 11.6789 + 1.80385i 0.675410 + 0.104319i
\(300\) 0 0
\(301\) −38.9090 −2.24268
\(302\) −10.8332 10.8332i −0.623383 0.623383i
\(303\) −32.7028 + 32.7028i −1.87873 + 1.87873i
\(304\) −4.73963 −0.271836
\(305\) 0 0
\(306\) 0 0
\(307\) −3.10583 3.10583i −0.177259 0.177259i 0.612901 0.790160i \(-0.290003\pi\)
−0.790160 + 0.612901i \(0.790003\pi\)
\(308\) 15.8845 15.8845i 0.905104 0.905104i
\(309\) −31.9074 −1.81515
\(310\) 0 0
\(311\) −3.80385 −0.215696 −0.107848 0.994167i \(-0.534396\pi\)
−0.107848 + 0.994167i \(0.534396\pi\)
\(312\) 4.76028 + 4.76028i 0.269498 + 0.269498i
\(313\) −9.15626 9.15626i −0.517543 0.517543i 0.399284 0.916827i \(-0.369259\pi\)
−0.916827 + 0.399284i \(0.869259\pi\)
\(314\) 22.4282 1.26570
\(315\) 0 0
\(316\) 1.26998i 0.0714420i
\(317\) 17.9551 + 17.9551i 1.00846 + 1.00846i 0.999964 + 0.00849332i \(0.00270354\pi\)
0.00849332 + 0.999964i \(0.497296\pi\)
\(318\) 6.70285 + 6.70285i 0.375877 + 0.375877i
\(319\) −43.5864 −2.44037
\(320\) 0 0
\(321\) 0 0
\(322\) −13.4311 18.3379i −0.748486 1.02193i
\(323\) 0 0
\(324\) 2.46410i 0.136895i
\(325\) 0 0
\(326\) −11.1244 −0.616121
\(327\) −11.6097 + 11.6097i −0.642017 + 0.642017i
\(328\) −0.328169 + 0.328169i −0.0181201 + 0.0181201i
\(329\) −36.3068 −2.00166
\(330\) 0 0
\(331\) 33.8564 1.86092 0.930458 0.366398i \(-0.119409\pi\)
0.930458 + 0.366398i \(0.119409\pi\)
\(332\) 5.80484 5.80484i 0.318582 0.318582i
\(333\) −10.9523 10.9523i −0.600182 0.600182i
\(334\) 5.07180i 0.277516i
\(335\) 0 0
\(336\) 12.9489i 0.706421i
\(337\) 9.15626 9.15626i 0.498773 0.498773i −0.412283 0.911056i \(-0.635268\pi\)
0.911056 + 0.412283i \(0.135268\pi\)
\(338\) 4.89898 4.89898i 0.266469 0.266469i
\(339\) −16.4186 −0.891734
\(340\) 0 0
\(341\) 32.8371i 1.77823i
\(342\) −14.9611 + 14.9611i −0.809004 + 0.809004i
\(343\) 28.3668 + 28.3668i 1.53166 + 1.53166i
\(344\) 8.20928 0.442615
\(345\) 0 0
\(346\) 0.607695 0.0326699
\(347\) 21.8695 + 21.8695i 1.17402 + 1.17402i 0.981243 + 0.192776i \(0.0617490\pi\)
0.192776 + 0.981243i \(0.438251\pi\)
\(348\) −17.7656 + 17.7656i −0.952336 + 0.952336i
\(349\) 12.6603i 0.677688i 0.940843 + 0.338844i \(0.110036\pi\)
−0.940843 + 0.338844i \(0.889964\pi\)
\(350\) 0 0
\(351\) 9.85641 0.526096
\(352\) −3.35143 + 3.35143i −0.178632 + 0.178632i
\(353\) 4.98691 4.98691i 0.265427 0.265427i −0.561828 0.827254i \(-0.689902\pi\)
0.827254 + 0.561828i \(0.189902\pi\)
\(354\) 12.9282i 0.687126i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −15.6950 + 15.6950i −0.829509 + 0.829509i
\(359\) −24.6278 −1.29981 −0.649904 0.760016i \(-0.725191\pi\)
−0.649904 + 0.760016i \(0.725191\pi\)
\(360\) 0 0
\(361\) 3.46410 0.182321
\(362\) 18.3125 18.3125i 0.962485 0.962485i
\(363\) −22.1469 + 22.1469i −1.16241 + 1.16241i
\(364\) 11.6789 0.612142
\(365\) 0 0
\(366\) 35.3771i 1.84919i
\(367\) −3.35143 + 3.35143i −0.174943 + 0.174943i −0.789147 0.614204i \(-0.789477\pi\)
0.614204 + 0.789147i \(0.289477\pi\)
\(368\) 2.83379 + 3.86906i 0.147721 + 0.201689i
\(369\) 2.07180i 0.107853i
\(370\) 0 0
\(371\) 16.4449 0.853775
\(372\) 13.3843 + 13.3843i 0.693942 + 0.693942i
\(373\) 13.4057 + 13.4057i 0.694121 + 0.694121i 0.963136 0.269015i \(-0.0866982\pi\)
−0.269015 + 0.963136i \(0.586698\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 7.66025 0.395047
\(377\) −16.0232 16.0232i −0.825238 0.825238i
\(378\) −13.4057 13.4057i −0.689515 0.689515i
\(379\) 9.47926 0.486917 0.243458 0.969911i \(-0.421718\pi\)
0.243458 + 0.969911i \(0.421718\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) −12.5077 + 12.5077i −0.639949 + 0.639949i
\(383\) 5.14745 + 5.14745i 0.263022 + 0.263022i 0.826281 0.563258i \(-0.190452\pi\)
−0.563258 + 0.826281i \(0.690452\pi\)
\(384\) 2.73205i 0.139419i
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 25.9134 25.9134i 1.31725 1.31725i
\(388\) 9.15626 + 9.15626i 0.464839 + 0.464839i
\(389\) −19.8882 −1.00837 −0.504186 0.863595i \(-0.668207\pi\)
−0.504186 + 0.863595i \(0.668207\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −10.9348 10.9348i −0.552289 0.552289i
\(393\) 15.4548 15.4548i 0.779592 0.779592i
\(394\) 7.00000i 0.352655i
\(395\) 0 0
\(396\) 21.1582i 1.06324i
\(397\) 16.4901 + 16.4901i 0.827614 + 0.827614i 0.987186 0.159572i \(-0.0510115\pi\)
−0.159572 + 0.987186i \(0.551012\pi\)
\(398\) −12.5077 12.5077i −0.626954 0.626954i
\(399\) 61.3731i 3.07250i
\(400\) 0 0
\(401\) 22.4282i 1.12001i 0.828489 + 0.560005i \(0.189201\pi\)
−0.828489 + 0.560005i \(0.810799\pi\)
\(402\) 18.3125 18.3125i 0.913346 0.913346i
\(403\) −12.0716 + 12.0716i −0.601328 + 0.601328i
\(404\) 16.9282i 0.842210i
\(405\) 0 0
\(406\) 43.5864i 2.16316i
\(407\) 11.6283 + 11.6283i 0.576392 + 0.576392i
\(408\) 0 0
\(409\) 3.53590i 0.174839i 0.996172 + 0.0874195i \(0.0278620\pi\)
−0.996172 + 0.0874195i \(0.972138\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.25825 8.25825i 0.406855 0.406855i
\(413\) −15.8591 15.8591i −0.780376 0.780376i
\(414\) 21.1582 + 3.26795i 1.03987 + 0.160611i
\(415\) 0 0
\(416\) −2.46410 −0.120813
\(417\) −12.6264 12.6264i −0.618317 0.618317i
\(418\) 15.8845 15.8845i 0.776937 0.776937i
\(419\) 18.6182 0.909560 0.454780 0.890604i \(-0.349718\pi\)
0.454780 + 0.890604i \(0.349718\pi\)
\(420\) 0 0
\(421\) 18.9585i 0.923982i −0.886885 0.461991i \(-0.847135\pi\)
0.886885 0.461991i \(-0.152865\pi\)
\(422\) 15.7322 + 15.7322i 0.765832 + 0.765832i
\(423\) 24.1803 24.1803i 1.17569 1.17569i
\(424\) −3.46965 −0.168501
\(425\) 0 0
\(426\) 25.8564 1.25275
\(427\) −43.3973 43.3973i −2.10014 2.10014i
\(428\) 0 0
\(429\) −31.9074 −1.54051
\(430\) 0 0
\(431\) 32.8371i 1.58171i −0.612004 0.790854i \(-0.709637\pi\)
0.612004 0.790854i \(-0.290363\pi\)
\(432\) 2.82843 + 2.82843i 0.136083 + 0.136083i
\(433\) 27.4688 + 27.4688i 1.32007 + 1.32007i 0.913719 + 0.406347i \(0.133198\pi\)
0.406347 + 0.913719i \(0.366802\pi\)
\(434\) 32.8371 1.57623
\(435\) 0 0
\(436\) 6.00961i 0.287808i
\(437\) −13.4311 18.3379i −0.642497 0.877222i
\(438\) 12.8666 12.8666i 0.614791 0.614791i
\(439\) 13.8564i 0.661330i −0.943748 0.330665i \(-0.892727\pi\)
0.943748 0.330665i \(-0.107273\pi\)
\(440\) 0 0
\(441\) −69.0333 −3.28730
\(442\) 0 0
\(443\) −27.5264 + 27.5264i −1.30782 + 1.30782i −0.384832 + 0.922987i \(0.625741\pi\)
−0.922987 + 0.384832i \(0.874259\pi\)
\(444\) 9.47926 0.449866
\(445\) 0 0
\(446\) 4.73205 0.224069
\(447\) 36.6251 36.6251i 1.73231 1.73231i
\(448\) 3.35143 + 3.35143i 0.158340 + 0.158340i
\(449\) 18.5359i 0.874763i 0.899276 + 0.437382i \(0.144094\pi\)
−0.899276 + 0.437382i \(0.855906\pi\)
\(450\) 0 0
\(451\) 2.19967i 0.103578i
\(452\) 4.24944 4.24944i 0.199877 0.199877i
\(453\) 29.5969 29.5969i 1.39059 1.39059i
\(454\) 0 0
\(455\) 0 0
\(456\) 12.9489i 0.606388i
\(457\) −4.24944 + 4.24944i −0.198780 + 0.198780i −0.799477 0.600697i \(-0.794890\pi\)
0.600697 + 0.799477i \(0.294890\pi\)
\(458\) −4.90683 4.90683i −0.229281 0.229281i
\(459\) 0 0
\(460\) 0 0
\(461\) −8.51666 −0.396660 −0.198330 0.980135i \(-0.563552\pi\)
−0.198330 + 0.980135i \(0.563552\pi\)
\(462\) 43.3973 + 43.3973i 2.01903 + 2.01903i
\(463\) 9.52056 9.52056i 0.442458 0.442458i −0.450379 0.892837i \(-0.648711\pi\)
0.892837 + 0.450379i \(0.148711\pi\)
\(464\) 9.19615i 0.426921i
\(465\) 0 0
\(466\) −6.26795 −0.290357
\(467\) 19.2105 19.2105i 0.888958 0.888958i −0.105465 0.994423i \(-0.533633\pi\)
0.994423 + 0.105465i \(0.0336332\pi\)
\(468\) −7.77817 + 7.77817i −0.359546 + 0.359546i
\(469\) 44.9282i 2.07459i
\(470\) 0 0
\(471\) 61.2749i 2.82340i
\(472\) 3.34607 + 3.34607i 0.154015 + 0.154015i
\(473\) −27.5128 + 27.5128i −1.26504 + 1.26504i
\(474\) 3.46965 0.159366
\(475\) 0 0
\(476\) 0 0
\(477\) −10.9523 + 10.9523i −0.501471 + 0.501471i
\(478\) −16.6288 + 16.6288i −0.760583 + 0.760583i
\(479\) 20.2285 0.924264 0.462132 0.886811i \(-0.347085\pi\)
0.462132 + 0.886811i \(0.347085\pi\)
\(480\) 0 0
\(481\) 8.54957i 0.389827i
\(482\) −10.9523 + 10.9523i −0.498863 + 0.498863i
\(483\) 50.1002 36.6945i 2.27964 1.66966i
\(484\) 11.4641i 0.521096i
\(485\) 0 0
\(486\) −18.7321 −0.849703
\(487\) −0.0371647 0.0371647i −0.00168410 0.00168410i 0.706264 0.707948i \(-0.250379\pi\)
−0.707948 + 0.706264i \(0.750379\pi\)
\(488\) 9.15626 + 9.15626i 0.414485 + 0.414485i
\(489\) 30.3923i 1.37439i
\(490\) 0 0
\(491\) 17.1244 0.772811 0.386406 0.922329i \(-0.373716\pi\)
0.386406 + 0.922329i \(0.373716\pi\)
\(492\) −0.896575 0.896575i −0.0404207 0.0404207i
\(493\) 0 0
\(494\) 11.6789 0.525460
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) 31.7182 31.7182i 1.42276 1.42276i
\(498\) 15.8591 + 15.8591i 0.710664 + 0.710664i
\(499\) 32.4449i 1.45243i −0.687467 0.726216i \(-0.741277\pi\)
0.687467 0.726216i \(-0.258723\pi\)
\(500\) 0 0
\(501\) 13.8564 0.619059
\(502\) −6.70285 + 6.70285i −0.299163 + 0.299163i
\(503\) 3.35143 + 3.35143i 0.149433 + 0.149433i 0.777865 0.628432i \(-0.216303\pi\)
−0.628432 + 0.777865i \(0.716303\pi\)
\(504\) 21.1582 0.942461
\(505\) 0 0
\(506\) −22.4641 3.46965i −0.998651 0.154245i
\(507\) 13.3843 + 13.3843i 0.594416 + 0.594416i
\(508\) −1.55291 + 1.55291i −0.0688994 + 0.0688994i
\(509\) 6.92820i 0.307087i 0.988142 + 0.153544i \(0.0490686\pi\)
−0.988142 + 0.153544i \(0.950931\pi\)
\(510\) 0 0
\(511\) 31.5671i 1.39645i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −13.4057 13.4057i −0.591876 0.591876i
\(514\) 0.928203i 0.0409413i
\(515\) 0 0
\(516\) 22.4282i 0.987345i
\(517\) −25.6728 + 25.6728i −1.12909 + 1.12909i
\(518\) 11.6283 11.6283i 0.510917 0.510917i
\(519\) 1.66025i 0.0728771i
\(520\) 0 0
\(521\) 36.3068i 1.59063i −0.606197 0.795314i \(-0.707306\pi\)
0.606197 0.795314i \(-0.292694\pi\)
\(522\) −29.0285 29.0285i −1.27054 1.27054i
\(523\) −0.898012 0.898012i −0.0392673 0.0392673i 0.687200 0.726468i \(-0.258839\pi\)
−0.726468 + 0.687200i \(0.758839\pi\)
\(524\) 8.00000i 0.349482i
\(525\) 0 0
\(526\) 9.47926i 0.413315i
\(527\) 0 0
\(528\) −9.15626 9.15626i −0.398475 0.398475i
\(529\) −6.93930 + 21.9282i −0.301709 + 0.953400i
\(530\) 0 0
\(531\) 21.1244 0.916719
\(532\) −15.8845 15.8845i −0.688681 0.688681i
\(533\) 0.808643 0.808643i 0.0350262 0.0350262i
\(534\) 0 0
\(535\) 0 0
\(536\) 9.47926i 0.409442i
\(537\) −42.8797 42.8797i −1.85039 1.85039i
\(538\) −11.0227 + 11.0227i −0.475223 + 0.475223i
\(539\) 73.2941 3.15700
\(540\) 0 0
\(541\) −9.87564 −0.424587 −0.212294 0.977206i \(-0.568093\pi\)
−0.212294 + 0.977206i \(0.568093\pi\)
\(542\) −2.96713 2.96713i −0.127449 0.127449i
\(543\) 50.0308 + 50.0308i 2.14703 + 2.14703i
\(544\) 0 0
\(545\) 0 0
\(546\) 31.9074i 1.36551i
\(547\) −12.7651 12.7651i −0.545796 0.545796i 0.379426 0.925222i \(-0.376121\pi\)
−0.925222 + 0.379426i \(0.876121\pi\)
\(548\) 0 0
\(549\) 57.8053 2.46707
\(550\) 0 0
\(551\) 43.5864i 1.85684i
\(552\) −10.5705 + 7.74205i −0.449909 + 0.329524i
\(553\) 4.25624 4.25624i 0.180994 0.180994i
\(554\) 3.92820i 0.166893i
\(555\) 0 0
\(556\) 6.53590 0.277184
\(557\) −10.9523 + 10.9523i −0.464063 + 0.464063i −0.899985 0.435921i \(-0.856423\pi\)
0.435921 + 0.899985i \(0.356423\pi\)
\(558\) −21.8695 + 21.8695i −0.925812 + 0.925812i
\(559\) −20.2285 −0.855575
\(560\) 0 0
\(561\) 0 0
\(562\) −15.8591 + 15.8591i −0.668976 + 0.668976i
\(563\) 4.00882 + 4.00882i 0.168951 + 0.168951i 0.786518 0.617567i \(-0.211882\pi\)
−0.617567 + 0.786518i \(0.711882\pi\)
\(564\) 20.9282i 0.881236i
\(565\) 0 0
\(566\) 0 0
\(567\) −8.25825 + 8.25825i −0.346814 + 0.346814i
\(568\) −6.69213 + 6.69213i −0.280796 + 0.280796i
\(569\) 12.0192 0.503872 0.251936 0.967744i \(-0.418933\pi\)
0.251936 + 0.967744i \(0.418933\pi\)
\(570\) 0 0
\(571\) 23.3579i 0.977496i −0.872425 0.488748i \(-0.837454\pi\)
0.872425 0.488748i \(-0.162546\pi\)
\(572\) 8.25825 8.25825i 0.345295 0.345295i
\(573\) −34.1716 34.1716i −1.42754 1.42754i
\(574\) −2.19967 −0.0918125
\(575\) 0 0
\(576\) −4.46410 −0.186004
\(577\) 29.0285 + 29.0285i 1.20847 + 1.20847i 0.971521 + 0.236953i \(0.0761487\pi\)
0.236953 + 0.971521i \(0.423851\pi\)
\(578\) 12.0208 12.0208i 0.500000 0.500000i
\(579\) 27.3205i 1.13540i
\(580\) 0 0
\(581\) 38.9090 1.61422
\(582\) −25.0154 + 25.0154i −1.03692 + 1.03692i
\(583\) 11.6283 11.6283i 0.481594 0.481594i
\(584\) 6.66025i 0.275603i
\(585\) 0 0
\(586\) 25.8978i 1.06983i
\(587\) 5.03768 + 5.03768i 0.207927 + 0.207927i 0.803386 0.595459i \(-0.203030\pi\)
−0.595459 + 0.803386i \(0.703030\pi\)
\(588\) 29.8744 29.8744i 1.23200 1.23200i
\(589\) 32.8371 1.35303
\(590\) 0 0
\(591\) 19.1244 0.786671
\(592\) −2.45341 + 2.45341i −0.100835 + 0.100835i
\(593\) −8.39735 + 8.39735i −0.344838 + 0.344838i −0.858182 0.513345i \(-0.828406\pi\)
0.513345 + 0.858182i \(0.328406\pi\)
\(594\) −18.9585 −0.777878
\(595\) 0 0
\(596\) 18.9585i 0.776571i
\(597\) 34.1716 34.1716i 1.39855 1.39855i
\(598\) −6.98274 9.53377i −0.285545 0.389865i
\(599\) 3.21539i 0.131377i 0.997840 + 0.0656886i \(0.0209244\pi\)
−0.997840 + 0.0656886i \(0.979076\pi\)
\(600\) 0 0
\(601\) 25.1769 1.02699 0.513494 0.858093i \(-0.328351\pi\)
0.513494 + 0.858093i \(0.328351\pi\)
\(602\) 27.5128 + 27.5128i 1.12134 + 1.12134i
\(603\) 29.9222 + 29.9222i 1.21853 + 1.21853i
\(604\) 15.3205i 0.623383i
\(605\) 0 0
\(606\) 46.2487 1.87873
\(607\) 8.52245 + 8.52245i 0.345915 + 0.345915i 0.858586 0.512670i \(-0.171344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(608\) 3.35143 + 3.35143i 0.135918 + 0.135918i
\(609\) −119.080 −4.82537
\(610\) 0 0
\(611\) −18.8756 −0.763627
\(612\) 0 0
\(613\) 25.6728 + 25.6728i 1.03691 + 1.03691i 0.999292 + 0.0376213i \(0.0119781\pi\)
0.0376213 + 0.999292i \(0.488022\pi\)
\(614\) 4.39230i 0.177259i
\(615\) 0 0
\(616\) −22.4641 −0.905104
\(617\) −13.4057 + 13.4057i −0.539693 + 0.539693i −0.923439 0.383746i \(-0.874634\pi\)
0.383746 + 0.923439i \(0.374634\pi\)
\(618\) 22.5620 + 22.5620i 0.907575 + 0.907575i
\(619\) 42.3164 1.70084 0.850420 0.526105i \(-0.176348\pi\)
0.850420 + 0.526105i \(0.176348\pi\)
\(620\) 0 0
\(621\) −2.92820 + 18.9585i −0.117505 + 0.760779i
\(622\) 2.68973 + 2.68973i 0.107848 + 0.107848i
\(623\) 0 0
\(624\) 6.73205i 0.269498i
\(625\) 0 0
\(626\) 12.9489i 0.517543i
\(627\) 43.3973 + 43.3973i 1.73312 + 1.73312i
\(628\) −15.8591 15.8591i −0.632848 0.632848i
\(629\) 0 0
\(630\) 0 0
\(631\) 27.1678i 1.08153i −0.841173 0.540767i \(-0.818134\pi\)
0.841173 0.540767i \(-0.181866\pi\)
\(632\) −0.898012 + 0.898012i −0.0357210 + 0.0357210i
\(633\) −42.9812 + 42.9812i −1.70835 + 1.70835i
\(634\) 25.3923i 1.00846i
\(635\) 0 0
\(636\) 9.47926i 0.375877i
\(637\) 26.9444 + 26.9444i 1.06758 + 1.06758i
\(638\) 30.8202 + 30.8202i 1.22018 + 1.22018i
\(639\) 42.2487i 1.67133i
\(640\) 0 0
\(641\) 12.0192i 0.474731i −0.971420 0.237365i \(-0.923716\pi\)
0.971420 0.237365i \(-0.0762839\pi\)
\(642\) 0 0
\(643\) 14.3037 + 14.3037i 0.564083 + 0.564083i 0.930465 0.366381i \(-0.119403\pi\)
−0.366381 + 0.930465i \(0.619403\pi\)
\(644\) −3.46965 + 22.4641i −0.136723 + 0.885210i
\(645\) 0 0
\(646\) 0 0
\(647\) −34.2557 34.2557i −1.34673 1.34673i −0.889188 0.457542i \(-0.848730\pi\)
−0.457542 0.889188i \(-0.651270\pi\)
\(648\) 1.74238 1.74238i 0.0684473 0.0684473i
\(649\) −22.4282 −0.880383
\(650\) 0 0
\(651\) 89.7127i 3.51612i
\(652\) 7.86611 + 7.86611i 0.308061 + 0.308061i
\(653\) 20.7835 20.7835i 0.813321 0.813321i −0.171809 0.985130i \(-0.554961\pi\)
0.985130 + 0.171809i \(0.0549612\pi\)
\(654\) 16.4186 0.642017
\(655\) 0 0
\(656\) 0.464102 0.0181201
\(657\) 21.0237 + 21.0237i 0.820214 + 0.820214i
\(658\) 25.6728 + 25.6728i 1.00083 + 1.00083i
\(659\) 21.1582 0.824206 0.412103 0.911137i \(-0.364794\pi\)
0.412103 + 0.911137i \(0.364794\pi\)
\(660\) 0 0
\(661\) 24.9681i 0.971148i −0.874196 0.485574i \(-0.838611\pi\)
0.874196 0.485574i \(-0.161389\pi\)
\(662\) −23.9401 23.9401i −0.930458 0.930458i
\(663\) 0 0
\(664\) −8.20928 −0.318582
\(665\) 0 0
\(666\) 15.4889i 0.600182i
\(667\) 35.5805 26.0599i 1.37768 1.00904i
\(668\) −3.58630 + 3.58630i −0.138758 + 0.138758i
\(669\) 12.9282i 0.499833i
\(670\) 0 0
\(671\) −61.3731 −2.36928
\(672\) −9.15626 + 9.15626i −0.353211 + 0.353211i
\(673\) −11.4016 + 11.4016i −0.439501 + 0.439501i −0.891844 0.452343i \(-0.850588\pi\)
0.452343 + 0.891844i \(0.350588\pi\)
\(674\) −12.9489 −0.498773
\(675\) 0 0
\(676\) −6.92820 −0.266469
\(677\) −6.04546 + 6.04546i −0.232346 + 0.232346i −0.813671 0.581325i \(-0.802534\pi\)
0.581325 + 0.813671i \(0.302534\pi\)
\(678\) 11.6097 + 11.6097i 0.445867 + 0.445867i
\(679\) 61.3731i 2.35528i
\(680\) 0 0
\(681\) 0 0
\(682\) 23.2194 23.2194i 0.889115 0.889115i
\(683\) 14.1421 14.1421i 0.541134 0.541134i −0.382727 0.923861i \(-0.625015\pi\)
0.923861 + 0.382727i \(0.125015\pi\)
\(684\) 21.1582 0.809004
\(685\) 0 0
\(686\) 40.1167i 1.53166i
\(687\) 13.4057 13.4057i 0.511459 0.511459i
\(688\) −5.80484 5.80484i −0.221307 0.221307i
\(689\) 8.54957 0.325713
\(690\) 0 0
\(691\) −42.2487 −1.60722 −0.803608 0.595158i \(-0.797089\pi\)
−0.803608 + 0.595158i \(0.797089\pi\)
\(692\) −0.429705 0.429705i −0.0163349 0.0163349i
\(693\) −70.9101 + 70.9101i −2.69365 + 2.69365i
\(694\) 30.9282i 1.17402i
\(695\) 0 0
\(696\) 25.1244 0.952336
\(697\) 0 0
\(698\) 8.95215 8.95215i 0.338844 0.338844i
\(699\) 17.1244i 0.647703i
\(700\) 0 0
\(701\) 12.0192i 0.453960i 0.973899 + 0.226980i \(0.0728852\pi\)
−0.973899 + 0.226980i \(0.927115\pi\)
\(702\) −6.96953 6.96953i −0.263048 0.263048i
\(703\) 11.6283 11.6283i 0.438569 0.438569i
\(704\) 4.73963 0.178632
\(705\) 0 0
\(706\) −7.05256 −0.265427
\(707\) 56.7336 56.7336i 2.13369 2.13369i
\(708\) −9.14162 + 9.14162i −0.343563 + 0.343563i
\(709\) 6.93930 0.260611 0.130305 0.991474i \(-0.458404\pi\)
0.130305 + 0.991474i \(0.458404\pi\)
\(710\) 0 0
\(711\) 5.66932i 0.212616i
\(712\) 0 0
\(713\) −19.6331 26.8057i −0.735264 1.00388i
\(714\) 0 0
\(715\) 0 0
\(716\) 22.1962 0.829509
\(717\) −45.4307 45.4307i −1.69664 1.69664i
\(718\) 17.4145 + 17.4145i 0.649904 + 0.649904i
\(719\) 4.48334i 0.167200i −0.996499 0.0836002i \(-0.973358\pi\)
0.996499 0.0836002i \(-0.0266419\pi\)
\(720\) 0 0
\(721\) 55.3538 2.06148
\(722\) −2.44949 2.44949i −0.0911606 0.0911606i
\(723\) −29.9222 29.9222i −1.11282 1.11282i
\(724\) −25.8978 −0.962485
\(725\) 0 0
\(726\) 31.3205 1.16241
\(727\) −4.90683 + 4.90683i −0.181984 + 0.181984i −0.792220 0.610236i \(-0.791075\pi\)
0.610236 + 0.792220i \(0.291075\pi\)
\(728\) −8.25825 8.25825i −0.306071 0.306071i
\(729\) 43.7846i 1.62165i
\(730\) 0 0
\(731\) 0 0
\(732\) −25.0154 + 25.0154i −0.924595 + 0.924595i
\(733\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(734\) 4.73963 0.174943
\(735\) 0 0
\(736\) 0.732051 4.73963i 0.0269838 0.174705i
\(737\) −31.7690 31.7690i −1.17023 1.17023i
\(738\) 1.46498 1.46498i 0.0539267 0.0539267i
\(739\) 12.0000i 0.441427i 0.975339 + 0.220714i \(0.0708386\pi\)
−0.975339 + 0.220714i \(0.929161\pi\)
\(740\) 0 0
\(741\) 31.9074i 1.17215i
\(742\) −11.6283 11.6283i −0.426887 0.426887i
\(743\) 13.1651 + 13.1651i 0.482980 + 0.482980i 0.906082 0.423102i \(-0.139059\pi\)
−0.423102 + 0.906082i \(0.639059\pi\)
\(744\) 18.9282i 0.693942i
\(745\) 0 0
\(746\) 18.9585i 0.694121i
\(747\) −25.9134 + 25.9134i −0.948121 + 0.948121i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 46.1263i 1.68317i 0.540122 + 0.841587i \(0.318378\pi\)
−0.540122 + 0.841587i \(0.681622\pi\)
\(752\) −5.41662 5.41662i −0.197524 0.197524i
\(753\) −18.3125 18.3125i −0.667346 0.667346i
\(754\) 22.6603i 0.825238i
\(755\) 0 0
\(756\) 18.9585i 0.689515i
\(757\) 20.7659 20.7659i 0.754751 0.754751i −0.220611 0.975362i \(-0.570805\pi\)
0.975362 + 0.220611i \(0.0708051\pi\)
\(758\) −6.70285 6.70285i −0.243458 0.243458i
\(759\) 9.47926 61.3731i 0.344075 2.22770i
\(760\) 0 0
\(761\) −6.71281 −0.243339 −0.121670 0.992571i \(-0.538825\pi\)
−0.121670 + 0.992571i \(0.538825\pi\)
\(762\) −4.24264 4.24264i −0.153695 0.153695i
\(763\) 20.1408 20.1408i 0.729145 0.729145i
\(764\) 17.6885 0.639949
\(765\) 0 0
\(766\) 7.27959i 0.263022i
\(767\) −8.24504 8.24504i −0.297711 0.297711i
\(768\) 1.93185 1.93185i 0.0697097 0.0697097i
\(769\) −3.46965 −0.125119 −0.0625594 0.998041i \(-0.519926\pi\)
−0.0625594 + 0.998041i \(0.519926\pi\)
\(770\) 0 0
\(771\) −2.53590 −0.0913281
\(772\) 7.07107 + 7.07107i 0.254493 + 0.254493i
\(773\) −10.9523 10.9523i −0.393926 0.393926i 0.482158 0.876084i \(-0.339853\pi\)
−0.876084 + 0.482158i \(0.839853\pi\)
\(774\) −36.6471 −1.31725
\(775\) 0 0
\(776\) 12.9489i 0.464839i
\(777\) 31.7690 + 31.7690i 1.13971 + 1.13971i
\(778\) 14.0631 + 14.0631i 0.504186 + 0.504186i
\(779\) −2.19967 −0.0788114
\(780\) 0 0
\(781\) 44.8563i 1.60509i
\(782\) 0 0
\(783\) 26.0106 26.0106i 0.929545 0.929545i
\(784\) 15.4641i 0.552289i
\(785\) 0 0
\(786\) −21.8564 −0.779592
\(787\) 32.6162 32.6162i 1.16264 1.16264i 0.178749 0.983895i \(-0.442795\pi\)
0.983895 0.178749i \(-0.0572049\pi\)
\(788\) −4.94975 + 4.94975i −0.176327 + 0.176327i
\(789\) 25.8978 0.921987
\(790\) 0 0
\(791\) 28.4833 1.01275
\(792\) 14.9611 14.9611i 0.531620 0.531620i
\(793\) −22.5620 22.5620i −0.801199 0.801199i
\(794\) 23.3205i 0.827614i
\(795\) 0 0
\(796\) 17.6885i 0.626954i
\(797\) −20.7659 + 20.7659i −0.735567 + 0.735567i −0.971717 0.236149i \(-0.924115\pi\)
0.236149 + 0.971717i \(0.424115\pi\)
\(798\) 43.3973 43.3973i 1.53625 1.53625i
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 15.8591 15.8591i 0.560005 0.560005i
\(803\) −22.3213 22.3213i −0.787703 0.787703i
\(804\) −25.8978 −0.913346
\(805\) 0 0
\(806\) 17.0718 0.601328
\(807\) −30.1146 30.1146i −1.06008 1.06008i
\(808\) −11.9700 + 11.9700i −0.421105 + 0.421105i
\(809\) 18.8564i 0.662956i −0.943463 0.331478i \(-0.892453\pi\)
0.943463 0.331478i \(-0.107547\pi\)
\(810\) 0 0
\(811\) 8.78461 0.308469 0.154235 0.988034i \(-0.450709\pi\)
0.154235 + 0.988034i \(0.450709\pi\)
\(812\) 30.8202 30.8202i 1.08158 1.08158i
\(813\) 8.10634 8.10634i 0.284302 0.284302i
\(814\) 16.4449i 0.576392i
\(815\) 0 0
\(816\) 0 0
\(817\) 27.5128 + 27.5128i 0.962551 + 0.962551i
\(818\) 2.50026 2.50026i 0.0874195 0.0874195i
\(819\) −52.1359 −1.82178
\(820\) 0 0
\(821\) −40.9090 −1.42773 −0.713866 0.700282i \(-0.753058\pi\)
−0.713866 + 0.700282i \(0.753058\pi\)
\(822\) 0 0
\(823\) 35.0507 35.0507i 1.22179 1.22179i 0.254797 0.966995i \(-0.417991\pi\)
0.966995 0.254797i \(-0.0820087\pi\)
\(824\) −11.6789 −0.406855
\(825\) 0 0
\(826\) 22.4282i 0.780376i
\(827\) 5.80484 5.80484i 0.201854 0.201854i −0.598940 0.800794i \(-0.704411\pi\)
0.800794 + 0.598940i \(0.204411\pi\)
\(828\) −12.6503 17.2719i −0.439629 0.600240i
\(829\) 21.8756i 0.759773i 0.925033 + 0.379886i \(0.124037\pi\)
−0.925033 + 0.379886i \(0.875963\pi\)
\(830\) 0 0
\(831\) 10.7321 0.372291
\(832\) 1.74238 + 1.74238i 0.0604063 + 0.0604063i
\(833\) 0 0
\(834\) 17.8564i 0.618317i
\(835\) 0 0
\(836\) −22.4641 −0.776937
\(837\) −19.5959 19.5959i −0.677334 0.677334i
\(838\) −13.1651 13.1651i −0.454780 0.454780i
\(839\) 22.0879 0.762558 0.381279 0.924460i \(-0.375484\pi\)
0.381279 + 0.924460i \(0.375484\pi\)
\(840\) 0 0
\(841\) −55.5692 −1.91618
\(842\) −13.4057 + 13.4057i −0.461991 + 0.461991i
\(843\) −43.3279 43.3279i −1.49229 1.49229i
\(844\) 22.2487i 0.765832i
\(845\) 0 0
\(846\) −34.1962 −1.17569
\(847\) 38.4211 38.4211i 1.32016 1.32016i
\(848\) 2.45341 + 2.45341i 0.0842506 + 0.0842506i
\(849\) 0 0
\(850\) 0 0
\(851\) −16.4449 2.53996i −0.563723 0.0870687i
\(852\) −18.2832 18.2832i −0.626373 0.626373i
\(853\) −9.67286 + 9.67286i −0.331192 + 0.331192i −0.853039 0.521847i \(-0.825243\pi\)
0.521847 + 0.853039i \(0.325243\pi\)
\(854\) 61.3731i 2.10014i
\(855\) 0 0
\(856\) 0 0
\(857\) −1.41421 1.41421i −0.0483086 0.0483086i 0.682540 0.730848i \(-0.260875\pi\)
−0.730848 + 0.682540i \(0.760875\pi\)
\(858\) 22.5620 + 22.5620i 0.770253 + 0.770253i
\(859\) 0.732051i 0.0249773i −0.999922 0.0124886i \(-0.996025\pi\)
0.999922 0.0124886i \(-0.00397536\pi\)
\(860\) 0 0
\(861\) 6.00961i 0.204807i
\(862\) −23.2194 + 23.2194i −0.790854 + 0.790854i
\(863\) 4.10394 4.10394i 0.139700 0.139700i −0.633798 0.773498i \(-0.718505\pi\)
0.773498 + 0.633798i \(0.218505\pi\)
\(864\) 4.00000i 0.136083i
\(865\) 0 0
\(866\) 38.8467i 1.32007i
\(867\) 32.8415 + 32.8415i 1.11536 + 1.11536i
\(868\) −23.2194 23.2194i −0.788116 0.788116i
\(869\) 6.01924i 0.204189i
\(870\) 0 0
\(871\) 23.3579i 0.791451i
\(872\) −4.24944 + 4.24944i −0.143904 + 0.143904i
\(873\) −40.8745 40.8745i −1.38339 1.38339i
\(874\) −3.46965 + 22.4641i −0.117363 + 0.759860i
\(875\) 0 0
\(876\) −18.1962 −0.614791
\(877\) 15.9353 + 15.9353i 0.538096 + 0.538096i 0.922969 0.384873i \(-0.125755\pi\)
−0.384873 + 0.922969i \(0.625755\pi\)
\(878\) −9.79796 + 9.79796i −0.330665 + 0.330665i
\(879\) −70.7542 −2.38648
\(880\) 0 0
\(881\) 22.4282i 0.755624i 0.925882 + 0.377812i \(0.123324\pi\)
−0.925882 + 0.377812i \(0.876676\pi\)
\(882\) 48.8139 + 48.8139i 1.64365 + 1.64365i
\(883\) −33.2576 + 33.2576i −1.11921 + 1.11921i −0.127349 + 0.991858i \(0.540647\pi\)
−0.991858 + 0.127349i \(0.959353\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 38.9282 1.30782
\(887\) −15.6579 15.6579i −0.525740 0.525740i 0.393559 0.919299i \(-0.371244\pi\)
−0.919299 + 0.393559i \(0.871244\pi\)
\(888\) −6.70285 6.70285i −0.224933 0.224933i
\(889\) −10.4090 −0.349105
\(890\) 0 0
\(891\) 11.6789i 0.391259i
\(892\) −3.34607 3.34607i −0.112035 0.112035i
\(893\) 25.6728 + 25.6728i 0.859106 + 0.859106i
\(894\) −51.7957 −1.73231
\(895\) 0 0
\(896\) 4.73963i 0.158340i
\(897\) 26.0467 19.0772i 0.869675 0.636969i
\(898\) 13.1069 13.1069i 0.437382 0.437382i
\(899\) 63.7128i 2.12494i
\(900\) 0 0
\(901\) 0 0
\(902\) −1.55540 + 1.55540i −0.0517892 + 0.0517892i
\(903\) −75.1663 + 75.1663i −2.50138 + 2.50138i
\(904\) −6.00961 −0.199877
\(905\) 0 0
\(906\) −41.8564 −1.39059
\(907\) 0.898012 0.898012i 0.0298180 0.0298180i −0.692041 0.721859i \(-0.743288\pi\)
0.721859 + 0.692041i \(0.243288\pi\)
\(908\) 0 0
\(909\) 75.5692i 2.50647i
\(910\) 0 0
\(911\) 36.6471i 1.21417i −0.794636 0.607086i \(-0.792338\pi\)
0.794636 0.607086i \(-0.207662\pi\)
\(912\) −9.15626 + 9.15626i −0.303194 + 0.303194i
\(913\) 27.5128 27.5128i 0.910541 0.910541i
\(914\) 6.00961 0.198780
\(915\) 0 0
\(916\) 6.93930i 0.229281i
\(917\) −26.8114 + 26.8114i −0.885390 + 0.885390i
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 6.02219 + 6.02219i 0.198330 + 0.198330i
\(923\) 16.4901 16.4901i 0.542778 0.542778i
\(924\) 61.3731i 2.01903i
\(925\) 0 0
\(926\) −13.4641 −0.442458
\(927\) −36.8657 + 36.8657i −1.21083 + 1.21083i
\(928\) −6.50266 + 6.50266i −0.213460 + 0.213460i
\(929\) 34.3205i 1.12602i −0.826450 0.563010i \(-0.809643\pi\)
0.826450 0.563010i \(-0.190357\pi\)
\(930\) 0 0
\(931\) 73.2941i 2.40212i
\(932\) 4.43211 + 4.43211i 0.145179 + 0.145179i
\(933\) −7.34847 + 7.34847i −0.240578 + 0.240578i
\(934\) −27.1678 −0.888958
\(935\) 0 0
\(936\) 11.0000 0.359546
\(937\) −17.6551 + 17.6551i −0.576768 + 0.576768i −0.934011 0.357243i \(-0.883717\pi\)
0.357243 + 0.934011i \(0.383717\pi\)
\(938\) −31.7690 + 31.7690i −1.03730 + 1.03730i
\(939\) −35.3771 −1.15449
\(940\) 0 0
\(941\) 43.9267i 1.43197i −0.698117 0.715984i \(-0.745978\pi\)
0.698117 0.715984i \(-0.254022\pi\)
\(942\) 43.3279 43.3279i 1.41170 1.41170i
\(943\) 1.31517 + 1.79564i 0.0428277 + 0.0584740i
\(944\) 4.73205i 0.154015i
\(945\) 0 0
\(946\) 38.9090 1.26504
\(947\) −2.82843 2.82843i −0.0919115 0.0919115i 0.659656 0.751568i \(-0.270702\pi\)
−0.751568 + 0.659656i \(0.770702\pi\)
\(948\) −2.45341 2.45341i −0.0796832 0.0796832i
\(949\) 16.4115i 0.532741i
\(950\) 0 0
\(951\) 69.3731 2.24958
\(952\) 0 0
\(953\) −9.15626 9.15626i −0.296600 0.296600i 0.543080 0.839681i \(-0.317258\pi\)
−0.839681 + 0.543080i \(0.817258\pi\)
\(954\) 15.4889 0.501471
\(955\) 0 0
\(956\) 23.5167 0.760583
\(957\) −84.2024 + 84.2024i −2.72188 + 2.72188i
\(958\) −14.3037 14.3037i −0.462132 0.462132i
\(959\) 0 0
\(960\) 0 0
\(961\) 17.0000 0.548387
\(962\) 6.04546 6.04546i 0.194913 0.194913i
\(963\) 0 0
\(964\) 15.4889 0.498863
\(965\) 0 0
\(966\) −61.3731 9.47926i −1.97465 0.304990i
\(967\) −18.5606 18.5606i −0.596870 0.596870i 0.342608 0.939478i \(-0.388690\pi\)
−0.939478 + 0.342608i \(0.888690\pi\)
\(968\) −8.10634 + 8.10634i −0.260548 + 0.260548i
\(969\) 0 0
\(970\) 0 0
\(971\) 9.13897i 0.293284i 0.989190 + 0.146642i \(0.0468465\pi\)
−0.989190 + 0.146642i \(0.953154\pi\)
\(972\) 13.2456 + 13.2456i 0.424852 + 0.424852i
\(973\) 21.9046 + 21.9046i 0.702228 + 0.702228i
\(974\) 0.0525589i 0.00168410i
\(975\) 0 0
\(976\) 12.9489i 0.414485i
\(977\) 31.0608 31.0608i 0.993724 0.993724i −0.00625617 0.999980i \(-0.501991\pi\)
0.999980 + 0.00625617i \(0.00199141\pi\)
\(978\) −21.4906 + 21.4906i −0.687194 + 0.687194i
\(979\) 0 0
\(980\) 0 0
\(981\) 26.8275i 0.856537i
\(982\) −12.1087 12.1087i −0.386406 0.386406i
\(983\) −24.7748 24.7748i −0.790192 0.790192i 0.191333 0.981525i \(-0.438719\pi\)
−0.981525 + 0.191333i \(0.938719\pi\)
\(984\) 1.26795i 0.0404207i
\(985\) 0 0
\(986\) 0 0
\(987\) −70.1393 + 70.1393i −2.23256 + 2.23256i
\(988\) −8.25825 8.25825i −0.262730 0.262730i
\(989\) 6.00961 38.9090i 0.191095 1.23723i
\(990\) 0 0
\(991\) 24.1962 0.768616 0.384308 0.923205i \(-0.374440\pi\)
0.384308 + 0.923205i \(0.374440\pi\)
\(992\) 4.89898 + 4.89898i 0.155543 + 0.155543i
\(993\) 65.4056 65.4056i 2.07558 2.07558i
\(994\) −44.8563 −1.42276
\(995\) 0 0
\(996\) 22.4282i 0.710664i
\(997\) −24.4441 24.4441i −0.774153 0.774153i 0.204676 0.978830i \(-0.434386\pi\)
−0.978830 + 0.204676i \(0.934386\pi\)
\(998\) −22.9420 + 22.9420i −0.726216 + 0.726216i
\(999\) −13.8786 −0.439100
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 1150.2.e.d.1057.3 yes 16
5.2 odd 4 inner 1150.2.e.d.643.5 yes 16
5.3 odd 4 inner 1150.2.e.d.643.4 yes 16
5.4 even 2 inner 1150.2.e.d.1057.6 yes 16
23.22 odd 2 inner 1150.2.e.d.1057.4 yes 16
115.22 even 4 inner 1150.2.e.d.643.6 yes 16
115.68 even 4 inner 1150.2.e.d.643.3 16
115.114 odd 2 inner 1150.2.e.d.1057.5 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.2.e.d.643.3 16 115.68 even 4 inner
1150.2.e.d.643.4 yes 16 5.3 odd 4 inner
1150.2.e.d.643.5 yes 16 5.2 odd 4 inner
1150.2.e.d.643.6 yes 16 115.22 even 4 inner
1150.2.e.d.1057.3 yes 16 1.1 even 1 trivial
1150.2.e.d.1057.4 yes 16 23.22 odd 2 inner
1150.2.e.d.1057.5 yes 16 115.114 odd 2 inner
1150.2.e.d.1057.6 yes 16 5.4 even 2 inner