Properties

Label 637.2.r.a.324.2
Level $637$
Weight $2$
Character 637.324
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(116,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.116");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.r (of order \(6\), degree \(2\), not 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 324.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 637.324
Dual form 637.2.r.a.116.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 + 1.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} -4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.73205 + 1.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} -4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.73205 + 1.00000i) q^{11} +(2.00000 - 3.46410i) q^{12} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.73205 + 1.00000i) q^{18} +(2.59808 + 1.50000i) q^{19} -2.00000i q^{20} -4.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(6.46410 - 3.19615i) q^{26} -4.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{30} +(-2.59808 + 1.50000i) q^{31} +(6.92820 - 4.00000i) q^{32} +(3.46410 + 2.00000i) q^{33} -12.0000i q^{34} -2.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(3.00000 + 5.19615i) q^{38} +(-7.19615 - 0.464102i) q^{39} +10.0000i q^{41} +1.00000 q^{43} +(-3.46410 - 2.00000i) q^{44} +(0.866025 - 0.500000i) q^{45} +(5.19615 - 3.00000i) q^{46} +(9.52628 + 5.50000i) q^{47} -8.00000 q^{48} -8.00000i q^{50} +(-6.00000 + 10.3923i) q^{51} +(7.19615 + 0.464102i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-6.92820 - 4.00000i) q^{54} +2.00000 q^{55} -6.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(6.92820 - 4.00000i) q^{59} +(-3.46410 + 2.00000i) q^{60} +(-4.00000 + 6.92820i) q^{61} -6.00000 q^{62} +8.00000 q^{64} +(-3.23205 + 1.59808i) q^{65} +(4.00000 + 6.92820i) q^{66} +(10.3923 - 6.00000i) q^{67} +(6.00000 - 10.3923i) q^{68} -6.00000 q^{69} +14.0000i q^{71} +(7.79423 - 4.50000i) q^{73} +(-6.00000 - 10.3923i) q^{74} +(-4.00000 + 6.92820i) q^{75} +6.00000i q^{76} +(-12.0000 - 8.00000i) q^{78} +(4.50000 - 7.79423i) q^{79} +(-3.46410 + 2.00000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-10.0000 + 17.3205i) q^{82} +11.0000i q^{83} +6.00000i q^{85} +(1.73205 + 1.00000i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(-4.33013 - 2.50000i) q^{89} +2.00000 q^{90} +6.00000 q^{92} +(5.19615 + 3.00000i) q^{93} +(11.0000 + 19.0526i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(-13.8564 - 8.00000i) q^{96} -9.00000i q^{97} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{4} - 2 q^{9} - 4 q^{10} + 8 q^{12} + 8 q^{13} + 8 q^{16} - 12 q^{17} - 16 q^{22} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 16 q^{27} + 12 q^{29} - 8 q^{30} - 8 q^{36} + 12 q^{38} - 8 q^{39} + 4 q^{43} - 32 q^{48} - 24 q^{51} + 8 q^{52} + 18 q^{53} + 8 q^{55} - 16 q^{61} - 24 q^{62} + 32 q^{64} - 6 q^{65} + 16 q^{66} + 24 q^{68} - 24 q^{69} - 24 q^{74} - 16 q^{75} - 48 q^{78} + 18 q^{79} + 22 q^{81} - 40 q^{82} - 12 q^{87} + 8 q^{90} + 24 q^{92} + 44 q^{94} - 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 + 1.00000i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −0.866025 0.500000i −0.387298 0.223607i 0.293691 0.955901i \(-0.405116\pi\)
−0.680989 + 0.732294i \(0.738450\pi\)
\(6\) 4.00000i 1.63299i
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) −1.73205 + 1.00000i −0.522233 + 0.301511i −0.737848 0.674967i \(-0.764158\pi\)
0.215615 + 0.976478i \(0.430824\pi\)
\(12\) 2.00000 3.46410i 0.577350 1.00000i
\(13\) 2.00000 3.00000i 0.554700 0.832050i
\(14\) 0 0
\(15\) 2.00000i 0.516398i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −1.73205 + 1.00000i −0.408248 + 0.235702i
\(19\) 2.59808 + 1.50000i 0.596040 + 0.344124i 0.767482 0.641071i \(-0.221509\pi\)
−0.171442 + 0.985194i \(0.554843\pi\)
\(20\) 2.00000i 0.447214i
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 6.46410 3.19615i 1.26771 0.626817i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −2.00000 + 3.46410i −0.365148 + 0.632456i
\(31\) −2.59808 + 1.50000i −0.466628 + 0.269408i −0.714827 0.699301i \(-0.753495\pi\)
0.248199 + 0.968709i \(0.420161\pi\)
\(32\) 6.92820 4.00000i 1.22474 0.707107i
\(33\) 3.46410 + 2.00000i 0.603023 + 0.348155i
\(34\) 12.0000i 2.05798i
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −5.19615 3.00000i −0.854242 0.493197i 0.00783774 0.999969i \(-0.497505\pi\)
−0.862080 + 0.506772i \(0.830838\pi\)
\(38\) 3.00000 + 5.19615i 0.486664 + 0.842927i
\(39\) −7.19615 0.464102i −1.15231 0.0743157i
\(40\) 0 0
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −3.46410 2.00000i −0.522233 0.301511i
\(45\) 0.866025 0.500000i 0.129099 0.0745356i
\(46\) 5.19615 3.00000i 0.766131 0.442326i
\(47\) 9.52628 + 5.50000i 1.38955 + 0.802257i 0.993264 0.115870i \(-0.0369655\pi\)
0.396286 + 0.918127i \(0.370299\pi\)
\(48\) −8.00000 −1.15470
\(49\) 0 0
\(50\) 8.00000i 1.13137i
\(51\) −6.00000 + 10.3923i −0.840168 + 1.45521i
\(52\) 7.19615 + 0.464102i 0.997927 + 0.0643593i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) −6.92820 4.00000i −0.942809 0.544331i
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 5.19615 + 3.00000i 0.682288 + 0.393919i
\(59\) 6.92820 4.00000i 0.901975 0.520756i 0.0241347 0.999709i \(-0.492317\pi\)
0.877841 + 0.478953i \(0.158984\pi\)
\(60\) −3.46410 + 2.00000i −0.447214 + 0.258199i
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) −3.23205 + 1.59808i −0.400887 + 0.198217i
\(66\) 4.00000 + 6.92820i 0.492366 + 0.852803i
\(67\) 10.3923 6.00000i 1.26962 0.733017i 0.294706 0.955588i \(-0.404778\pi\)
0.974916 + 0.222571i \(0.0714450\pi\)
\(68\) 6.00000 10.3923i 0.727607 1.26025i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 14.0000i 1.66149i 0.556650 + 0.830747i \(0.312086\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(72\) 0 0
\(73\) 7.79423 4.50000i 0.912245 0.526685i 0.0310925 0.999517i \(-0.490101\pi\)
0.881153 + 0.472831i \(0.156768\pi\)
\(74\) −6.00000 10.3923i −0.697486 1.20808i
\(75\) −4.00000 + 6.92820i −0.461880 + 0.800000i
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) −12.0000 8.00000i −1.35873 0.905822i
\(79\) 4.50000 7.79423i 0.506290 0.876919i −0.493684 0.869641i \(-0.664350\pi\)
0.999974 0.00727784i \(-0.00231663\pi\)
\(80\) −3.46410 + 2.00000i −0.387298 + 0.223607i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −10.0000 + 17.3205i −1.10432 + 1.91273i
\(83\) 11.0000i 1.20741i 0.797209 + 0.603703i \(0.206309\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(84\) 0 0
\(85\) 6.00000i 0.650791i
\(86\) 1.73205 + 1.00000i 0.186772 + 0.107833i
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) −4.33013 2.50000i −0.458993 0.264999i 0.252628 0.967563i \(-0.418705\pi\)
−0.711621 + 0.702564i \(0.752038\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 5.19615 + 3.00000i 0.538816 + 0.311086i
\(94\) 11.0000 + 19.0526i 1.13456 + 1.96512i
\(95\) −1.50000 2.59808i −0.153897 0.266557i
\(96\) −13.8564 8.00000i −1.41421 0.816497i
\(97\) 9.00000i 0.913812i −0.889515 0.456906i \(-0.848958\pi\)
0.889515 0.456906i \(-0.151042\pi\)
\(98\) 0 0
\(99\) 2.00000i 0.201008i
\(100\) 4.00000 6.92820i 0.400000 0.692820i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) −20.7846 + 12.0000i −2.05798 + 1.18818i
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000i 1.74831i
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) −4.00000 6.92820i −0.384900 0.666667i
\(109\) −15.5885 + 9.00000i −1.49310 + 0.862044i −0.999969 0.00790932i \(-0.997482\pi\)
−0.493135 + 0.869953i \(0.664149\pi\)
\(110\) 3.46410 + 2.00000i 0.330289 + 0.190693i
\(111\) 12.0000i 1.13899i
\(112\) 0 0
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) −2.59808 + 1.50000i −0.242272 + 0.139876i
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 1.59808 + 3.23205i 0.147742 + 0.298803i
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) −13.8564 + 8.00000i −1.25450 + 0.724286i
\(123\) 17.3205 10.0000i 1.56174 0.901670i
\(124\) −5.19615 3.00000i −0.466628 0.269408i
\(125\) 9.00000i 0.804984i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) −7.19615 0.464102i −0.631144 0.0407044i
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 8.00000i 0.696311i
\(133\) 0 0
\(134\) 24.0000 2.07328
\(135\) 3.46410 + 2.00000i 0.298142 + 0.172133i
\(136\) 0 0
\(137\) 1.73205 1.00000i 0.147979 0.0854358i −0.424182 0.905577i \(-0.639438\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(138\) −10.3923 6.00000i −0.884652 0.510754i
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) 0 0
\(141\) 22.0000i 1.85273i
\(142\) −14.0000 + 24.2487i −1.17485 + 2.03491i
\(143\) −0.464102 + 7.19615i −0.0388101 + 0.601772i
\(144\) 2.00000 + 3.46410i 0.166667 + 0.288675i
\(145\) −2.59808 1.50000i −0.215758 0.124568i
\(146\) 18.0000 1.48969
\(147\) 0 0
\(148\) 12.0000i 0.986394i
\(149\) 8.66025 + 5.00000i 0.709476 + 0.409616i 0.810867 0.585231i \(-0.198996\pi\)
−0.101391 + 0.994847i \(0.532329\pi\)
\(150\) −13.8564 + 8.00000i −1.13137 + 0.653197i
\(151\) 5.19615 3.00000i 0.422857 0.244137i −0.273442 0.961888i \(-0.588162\pi\)
0.696299 + 0.717752i \(0.254829\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) −6.39230 12.9282i −0.511794 1.03508i
\(157\) −9.00000 15.5885i −0.718278 1.24409i −0.961681 0.274169i \(-0.911597\pi\)
0.243403 0.969925i \(-0.421736\pi\)
\(158\) 15.5885 9.00000i 1.24015 0.716002i
\(159\) 9.00000 15.5885i 0.713746 1.23625i
\(160\) −8.00000 −0.632456
\(161\) 0 0
\(162\) 22.0000i 1.72848i
\(163\) 10.3923 + 6.00000i 0.813988 + 0.469956i 0.848339 0.529454i \(-0.177603\pi\)
−0.0343508 + 0.999410i \(0.510936\pi\)
\(164\) −17.3205 + 10.0000i −1.35250 + 0.780869i
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) −11.0000 + 19.0526i −0.853766 + 1.47877i
\(167\) 1.00000i 0.0773823i −0.999251 0.0386912i \(-0.987681\pi\)
0.999251 0.0386912i \(-0.0123189\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) −6.00000 + 10.3923i −0.460179 + 0.797053i
\(171\) −2.59808 + 1.50000i −0.198680 + 0.114708i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) 8.00000i 0.603023i
\(177\) −13.8564 8.00000i −1.04151 0.601317i
\(178\) −5.00000 8.66025i −0.374766 0.649113i
\(179\) −4.50000 7.79423i −0.336346 0.582568i 0.647397 0.762153i \(-0.275858\pi\)
−0.983742 + 0.179585i \(0.942524\pi\)
\(180\) 1.73205 + 1.00000i 0.129099 + 0.0745356i
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 16.0000 1.18275
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) 10.3923 + 6.00000i 0.759961 + 0.438763i
\(188\) 22.0000i 1.60451i
\(189\) 0 0
\(190\) 6.00000i 0.435286i
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −8.00000 13.8564i −0.577350 1.00000i
\(193\) −10.3923 + 6.00000i −0.748054 + 0.431889i −0.824991 0.565147i \(-0.808820\pi\)
0.0769360 + 0.997036i \(0.475486\pi\)
\(194\) 9.00000 15.5885i 0.646162 1.11919i
\(195\) 6.00000 + 4.00000i 0.429669 + 0.286446i
\(196\) 0 0
\(197\) 4.00000i 0.284988i 0.989796 + 0.142494i \(0.0455122\pi\)
−0.989796 + 0.142494i \(0.954488\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) 1.00000 + 1.73205i 0.0708881 + 0.122782i 0.899291 0.437351i \(-0.144083\pi\)
−0.828403 + 0.560133i \(0.810750\pi\)
\(200\) 0 0
\(201\) −20.7846 12.0000i −1.46603 0.846415i
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) −24.0000 −1.68034
\(205\) 5.00000 8.66025i 0.349215 0.604858i
\(206\) 0 0
\(207\) 1.50000 + 2.59808i 0.104257 + 0.180579i
\(208\) −6.39230 12.9282i −0.443227 0.896410i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) −9.00000 + 15.5885i −0.618123 + 1.07062i
\(213\) 24.2487 14.0000i 1.66149 0.959264i
\(214\) 20.7846 12.0000i 1.42081 0.820303i
\(215\) −0.866025 0.500000i −0.0590624 0.0340997i
\(216\) 0 0
\(217\) 0 0
\(218\) −36.0000 −2.43823
\(219\) −15.5885 9.00000i −1.05337 0.608164i
\(220\) 2.00000 + 3.46410i 0.134840 + 0.233550i
\(221\) −21.5885 1.39230i −1.45220 0.0936566i
\(222\) −12.0000 + 20.7846i −0.805387 + 1.39497i
\(223\) 21.0000i 1.40626i −0.711059 0.703132i \(-0.751784\pi\)
0.711059 0.703132i \(-0.248216\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) −25.9808 15.0000i −1.72821 0.997785i
\(227\) −17.3205 + 10.0000i −1.14960 + 0.663723i −0.948790 0.315906i \(-0.897691\pi\)
−0.200812 + 0.979630i \(0.564358\pi\)
\(228\) 10.3923 6.00000i 0.688247 0.397360i
\(229\) −5.19615 3.00000i −0.343371 0.198246i 0.318390 0.947960i \(-0.396858\pi\)
−0.661762 + 0.749714i \(0.730191\pi\)
\(230\) −6.00000 −0.395628
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) −0.464102 + 7.19615i −0.0303393 + 0.470427i
\(235\) −5.50000 9.52628i −0.358780 0.621426i
\(236\) 13.8564 + 8.00000i 0.901975 + 0.520756i
\(237\) −18.0000 −1.16923
\(238\) 0 0
\(239\) 8.00000i 0.517477i −0.965947 0.258738i \(-0.916693\pi\)
0.965947 0.258738i \(-0.0833068\pi\)
\(240\) 6.92820 + 4.00000i 0.447214 + 0.258199i
\(241\) 18.1865 10.5000i 1.17150 0.676364i 0.217465 0.976068i \(-0.430221\pi\)
0.954032 + 0.299704i \(0.0968878\pi\)
\(242\) −12.1244 + 7.00000i −0.779383 + 0.449977i
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) −16.0000 −1.02430
\(245\) 0 0
\(246\) 40.0000 2.55031
\(247\) 9.69615 4.79423i 0.616951 0.305049i
\(248\) 0 0
\(249\) 19.0526 11.0000i 1.20741 0.697097i
\(250\) −9.00000 + 15.5885i −0.569210 + 0.985901i
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) 6.00000i 0.377217i
\(254\) 0 0
\(255\) 10.3923 6.00000i 0.650791 0.375735i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) −6.00000 4.00000i −0.372104 0.248069i
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 20.7846 12.0000i 1.28408 0.741362i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 9.00000i 0.552866i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 20.7846 + 12.0000i 1.26962 + 0.733017i
\(269\) 12.0000 + 20.7846i 0.731653 + 1.26726i 0.956176 + 0.292791i \(0.0945841\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(270\) 4.00000 + 6.92820i 0.243432 + 0.421637i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −24.0000 −1.45521
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 6.92820 + 4.00000i 0.417786 + 0.241209i
\(276\) −6.00000 10.3923i −0.361158 0.625543i
\(277\) 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) 31.1769 + 18.0000i 1.86987 + 1.07957i
\(279\) 3.00000i 0.179605i
\(280\) 0 0
\(281\) 2.00000i 0.119310i 0.998219 + 0.0596550i \(0.0190001\pi\)
−0.998219 + 0.0596550i \(0.981000\pi\)
\(282\) 22.0000 38.1051i 1.31008 2.26913i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −24.2487 + 14.0000i −1.43890 + 0.830747i
\(285\) −3.00000 + 5.19615i −0.177705 + 0.307794i
\(286\) −8.00000 + 12.0000i −0.473050 + 0.709575i
\(287\) 0 0
\(288\) 8.00000i 0.471405i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) −15.5885 + 9.00000i −0.913812 + 0.527589i
\(292\) 15.5885 + 9.00000i 0.912245 + 0.526685i
\(293\) 1.00000i 0.0584206i −0.999573 0.0292103i \(-0.990701\pi\)
0.999573 0.0292103i \(-0.00929925\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 6.92820 4.00000i 0.402015 0.232104i
\(298\) 10.0000 + 17.3205i 0.579284 + 1.00335i
\(299\) −4.79423 9.69615i −0.277257 0.560743i
\(300\) −16.0000 −0.923760
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) −6.00000 + 10.3923i −0.344691 + 0.597022i
\(304\) 10.3923 6.00000i 0.596040 0.344124i
\(305\) 6.92820 4.00000i 0.396708 0.229039i
\(306\) 10.3923 + 6.00000i 0.594089 + 0.342997i
\(307\) 33.0000i 1.88341i 0.336440 + 0.941705i \(0.390777\pi\)
−0.336440 + 0.941705i \(0.609223\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 5.19615 + 3.00000i 0.295122 + 0.170389i
\(311\) 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i \(0.157077\pi\)
−0.0301210 + 0.999546i \(0.509589\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 36.0000i 2.03160i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) 17.3205 + 10.0000i 0.972817 + 0.561656i 0.900094 0.435696i \(-0.143498\pi\)
0.0727229 + 0.997352i \(0.476831\pi\)
\(318\) 31.1769 18.0000i 1.74831 1.00939i
\(319\) −5.19615 + 3.00000i −0.290929 + 0.167968i
\(320\) −6.92820 4.00000i −0.387298 0.223607i
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 18.0000i 1.00155i
\(324\) −11.0000 + 19.0526i −0.611111 + 1.05848i
\(325\) −14.3923 0.928203i −0.798341 0.0514875i
\(326\) 12.0000 + 20.7846i 0.664619 + 1.15115i
\(327\) 31.1769 + 18.0000i 1.72409 + 0.995402i
\(328\) 0 0
\(329\) 0 0
\(330\) 8.00000i 0.440386i
\(331\) 10.3923 + 6.00000i 0.571213 + 0.329790i 0.757634 0.652680i \(-0.226355\pi\)
−0.186421 + 0.982470i \(0.559689\pi\)
\(332\) −19.0526 + 11.0000i −1.04565 + 0.603703i
\(333\) 5.19615 3.00000i 0.284747 0.164399i
\(334\) 1.00000 1.73205i 0.0547176 0.0947736i
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 27.0000 1.47078 0.735392 0.677642i \(-0.236998\pi\)
0.735392 + 0.677642i \(0.236998\pi\)
\(338\) 3.33975 25.7846i 0.181658 1.40250i
\(339\) 15.0000 + 25.9808i 0.814688 + 1.41108i
\(340\) −10.3923 + 6.00000i −0.563602 + 0.325396i
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) 0 0
\(345\) 5.19615 + 3.00000i 0.279751 + 0.161515i
\(346\) −10.3923 + 6.00000i −0.558694 + 0.322562i
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 6.00000 10.3923i 0.321634 0.557086i
\(349\) 27.0000i 1.44528i −0.691226 0.722638i \(-0.742929\pi\)
0.691226 0.722638i \(-0.257071\pi\)
\(350\) 0 0
\(351\) −8.00000 + 12.0000i −0.427008 + 0.640513i
\(352\) −8.00000 + 13.8564i −0.426401 + 0.738549i
\(353\) 1.73205 1.00000i 0.0921878 0.0532246i −0.453197 0.891410i \(-0.649717\pi\)
0.545385 + 0.838186i \(0.316383\pi\)
\(354\) −16.0000 27.7128i −0.850390 1.47292i
\(355\) 7.00000 12.1244i 0.371521 0.643494i
\(356\) 10.0000i 0.529999i
\(357\) 0 0
\(358\) 18.0000i 0.951330i
\(359\) −19.0526 11.0000i −1.00556 0.580558i −0.0956683 0.995413i \(-0.530499\pi\)
−0.909887 + 0.414855i \(0.863832\pi\)
\(360\) 0 0
\(361\) −5.00000 8.66025i −0.263158 0.455803i
\(362\) 31.1769 + 18.0000i 1.63862 + 0.946059i
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) −9.00000 −0.471082
\(366\) 27.7128 + 16.0000i 1.44857 + 0.836333i
\(367\) −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) −6.00000 10.3923i −0.312772 0.541736i
\(369\) −8.66025 5.00000i −0.450835 0.260290i
\(370\) 12.0000i 0.623850i
\(371\) 0 0
\(372\) 12.0000i 0.622171i
\(373\) 9.00000 15.5885i 0.466002 0.807140i −0.533244 0.845962i \(-0.679027\pi\)
0.999246 + 0.0388219i \(0.0123605\pi\)
\(374\) 12.0000 + 20.7846i 0.620505 + 1.07475i
\(375\) 15.5885 9.00000i 0.804984 0.464758i
\(376\) 0 0
\(377\) 6.00000 9.00000i 0.309016 0.463524i
\(378\) 0 0
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) 0 0
\(382\) 0 0
\(383\) 6.92820 + 4.00000i 0.354015 + 0.204390i 0.666452 0.745548i \(-0.267812\pi\)
−0.312437 + 0.949938i \(0.601145\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.0000 −1.22157
\(387\) −0.500000 + 0.866025i −0.0254164 + 0.0440225i
\(388\) 15.5885 9.00000i 0.791384 0.456906i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) 6.39230 + 12.9282i 0.323687 + 0.654645i
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) −7.79423 + 4.50000i −0.392170 + 0.226420i
\(396\) 3.46410 2.00000i 0.174078 0.100504i
\(397\) −18.1865 10.5000i −0.912756 0.526980i −0.0314391 0.999506i \(-0.510009\pi\)
−0.881317 + 0.472526i \(0.843342\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) −24.2487 14.0000i −1.21092 0.699127i −0.247962 0.968770i \(-0.579761\pi\)
−0.962960 + 0.269643i \(0.913094\pi\)
\(402\) −24.0000 41.5692i −1.19701 2.07328i
\(403\) −0.696152 + 10.7942i −0.0346778 + 0.537699i
\(404\) 6.00000 10.3923i 0.298511 0.517036i
\(405\) 11.0000i 0.546594i
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) −7.79423 + 4.50000i −0.385400 + 0.222511i −0.680165 0.733059i \(-0.738092\pi\)
0.294765 + 0.955570i \(0.404759\pi\)
\(410\) 17.3205 10.0000i 0.855399 0.493865i
\(411\) −3.46410 2.00000i −0.170872 0.0986527i
\(412\) 0 0
\(413\) 0 0
\(414\) 6.00000i 0.294884i
\(415\) 5.50000 9.52628i 0.269984 0.467627i
\(416\) 1.85641 28.7846i 0.0910178 1.41128i
\(417\) −18.0000 31.1769i −0.881464 1.52674i
\(418\) −10.3923 6.00000i −0.508304 0.293470i
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 30.0000i 1.46211i 0.682318 + 0.731055i \(0.260972\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −15.5885 9.00000i −0.758834 0.438113i
\(423\) −9.52628 + 5.50000i −0.463184 + 0.267419i
\(424\) 0 0
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 56.0000 2.71321
\(427\) 0 0
\(428\) 24.0000 1.16008
\(429\) 12.9282 6.39230i 0.624180 0.308623i
\(430\) −1.00000 1.73205i −0.0482243 0.0835269i
\(431\) −3.46410 + 2.00000i −0.166860 + 0.0963366i −0.581104 0.813829i \(-0.697379\pi\)
0.414244 + 0.910166i \(0.364046\pi\)
\(432\) −8.00000 + 13.8564i −0.384900 + 0.666667i
\(433\) 20.0000 0.961139 0.480569 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) 0 0
\(435\) 6.00000i 0.287678i
\(436\) −31.1769 18.0000i −1.49310 0.862044i
\(437\) 7.79423 4.50000i 0.372849 0.215264i
\(438\) −18.0000 31.1769i −0.860073 1.48969i
\(439\) 18.0000 31.1769i 0.859093 1.48799i −0.0137020 0.999906i \(-0.504362\pi\)
0.872795 0.488087i \(-0.162305\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −36.0000 24.0000i −1.71235 1.14156i
\(443\) −13.5000 + 23.3827i −0.641404 + 1.11094i 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) −20.7846 + 12.0000i −0.986394 + 0.569495i
\(445\) 2.50000 + 4.33013i 0.118511 + 0.205268i
\(446\) 21.0000 36.3731i 0.994379 1.72231i
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) 4.00000i 0.188772i 0.995536 + 0.0943858i \(0.0300887\pi\)
−0.995536 + 0.0943858i \(0.969911\pi\)
\(450\) 6.92820 + 4.00000i 0.326599 + 0.188562i
\(451\) −10.0000 17.3205i −0.470882 0.815591i
\(452\) −15.0000 25.9808i −0.705541 1.22203i
\(453\) −10.3923 6.00000i −0.488273 0.281905i
\(454\) −40.0000 −1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) −36.3731 21.0000i −1.70146 0.982339i −0.944286 0.329125i \(-0.893246\pi\)
−0.757174 0.653213i \(-0.773421\pi\)
\(458\) −6.00000 10.3923i −0.280362 0.485601i
\(459\) 12.0000 + 20.7846i 0.560112 + 0.970143i
\(460\) −5.19615 3.00000i −0.242272 0.139876i
\(461\) 2.00000i 0.0931493i 0.998915 + 0.0465746i \(0.0148305\pi\)
−0.998915 + 0.0465746i \(0.985169\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) 6.00000 10.3923i 0.278543 0.482451i
\(465\) −3.00000 5.19615i −0.139122 0.240966i
\(466\) 5.19615 3.00000i 0.240707 0.138972i
\(467\) −21.0000 + 36.3731i −0.971764 + 1.68314i −0.281539 + 0.959550i \(0.590845\pi\)
−0.690225 + 0.723595i \(0.742488\pi\)
\(468\) −4.00000 + 6.00000i −0.184900 + 0.277350i
\(469\) 0 0
\(470\) 22.0000i 1.01478i
\(471\) −18.0000 + 31.1769i −0.829396 + 1.43656i
\(472\) 0 0
\(473\) −1.73205 + 1.00000i −0.0796398 + 0.0459800i
\(474\) −31.1769 18.0000i −1.43200 0.826767i
\(475\) 12.0000i 0.550598i
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) 8.00000 13.8564i 0.365911 0.633777i
\(479\) −25.1147 + 14.5000i −1.14752 + 0.662522i −0.948282 0.317429i \(-0.897181\pi\)
−0.199240 + 0.979951i \(0.563847\pi\)
\(480\) 8.00000 + 13.8564i 0.365148 + 0.632456i
\(481\) −19.3923 + 9.58846i −0.884213 + 0.437196i
\(482\) 42.0000 1.91305
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) −4.50000 + 7.79423i −0.204334 + 0.353918i
\(486\) 17.3205 10.0000i 0.785674 0.453609i
\(487\) −10.3923 + 6.00000i −0.470920 + 0.271886i −0.716625 0.697459i \(-0.754314\pi\)
0.245705 + 0.969345i \(0.420981\pi\)
\(488\) 0 0
\(489\) 24.0000i 1.08532i
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 34.6410 + 20.0000i 1.56174 + 0.901670i
\(493\) −9.00000 15.5885i −0.405340 0.702069i
\(494\) 21.5885 + 1.39230i 0.971311 + 0.0626428i
\(495\) −1.00000 + 1.73205i −0.0449467 + 0.0778499i
\(496\) 12.0000i 0.538816i
\(497\) 0 0
\(498\) 44.0000 1.97169
\(499\) 5.19615 + 3.00000i 0.232612 + 0.134298i 0.611776 0.791031i \(-0.290455\pi\)
−0.379165 + 0.925329i \(0.623789\pi\)
\(500\) −15.5885 + 9.00000i −0.697137 + 0.402492i
\(501\) −1.73205 + 1.00000i −0.0773823 + 0.0446767i
\(502\) 10.3923 + 6.00000i 0.463831 + 0.267793i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 6.00000i 0.266996i
\(506\) −6.00000 + 10.3923i −0.266733 + 0.461994i
\(507\) −15.7846 + 20.6603i −0.701019 + 0.917554i
\(508\) 0 0
\(509\) −32.0429 18.5000i −1.42028 0.819998i −0.423956 0.905683i \(-0.639359\pi\)
−0.996322 + 0.0856847i \(0.972692\pi\)
\(510\) 24.0000 1.06274
\(511\) 0 0
\(512\) 32.0000i 1.41421i
\(513\) −10.3923 6.00000i −0.458831 0.264906i
\(514\) 10.3923 6.00000i 0.458385 0.264649i
\(515\) 0 0
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) −22.0000 −0.967559
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) −12.0000 20.7846i −0.525730 0.910590i −0.999551 0.0299693i \(-0.990459\pi\)
0.473821 0.880621i \(-0.342874\pi\)
\(522\) −5.19615 + 3.00000i −0.227429 + 0.131306i
\(523\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 18.0000i 0.784837i
\(527\) 15.5885 + 9.00000i 0.679044 + 0.392046i
\(528\) 13.8564 8.00000i 0.603023 0.348155i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 9.00000 15.5885i 0.390935 0.677119i
\(531\) 8.00000i 0.347170i
\(532\) 0 0
\(533\) 30.0000 + 20.0000i 1.29944 + 0.866296i
\(534\) −10.0000 + 17.3205i −0.432742 + 0.749532i
\(535\) −10.3923 + 6.00000i −0.449299 + 0.259403i
\(536\) 0 0
\(537\) −9.00000 + 15.5885i −0.388379 + 0.672692i
\(538\) 48.0000i 2.06943i
\(539\) 0 0
\(540\) 8.00000i 0.344265i
\(541\) 15.5885 + 9.00000i 0.670200 + 0.386940i 0.796152 0.605096i \(-0.206865\pi\)
−0.125952 + 0.992036i \(0.540199\pi\)
\(542\) 0 0
\(543\) −18.0000 31.1769i −0.772454 1.33793i
\(544\) −41.5692 24.0000i −1.78227 1.02899i
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 3.46410 + 2.00000i 0.147979 + 0.0854358i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) 8.00000 + 13.8564i 0.341121 + 0.590839i
\(551\) 7.79423 + 4.50000i 0.332045 + 0.191706i
\(552\) 0 0
\(553\) 0 0
\(554\) 34.0000i 1.44452i
\(555\) 6.00000 10.3923i 0.254686 0.441129i
\(556\) 18.0000 + 31.1769i 0.763370 + 1.32220i
\(557\) 27.7128 16.0000i 1.17423 0.677942i 0.219557 0.975600i \(-0.429539\pi\)
0.954673 + 0.297658i \(0.0962055\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) 2.00000 3.00000i 0.0845910 0.126886i
\(560\) 0 0
\(561\) 24.0000i 1.01328i
\(562\) −2.00000 + 3.46410i −0.0843649 + 0.146124i
\(563\) 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i \(0.107454\pi\)
−0.184950 + 0.982748i \(0.559212\pi\)
\(564\) 38.1051 22.0000i 1.60451 0.926367i
\(565\) 12.9904 + 7.50000i 0.546509 + 0.315527i
\(566\) 8.00000i 0.336265i
\(567\) 0 0
\(568\) 0 0
\(569\) 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i \(-0.731525\pi\)
0.979313 + 0.202350i \(0.0648579\pi\)
\(570\) −10.3923 + 6.00000i −0.435286 + 0.251312i
\(571\) −4.50000 7.79423i −0.188319 0.326178i 0.756371 0.654143i \(-0.226971\pi\)
−0.944690 + 0.327965i \(0.893637\pi\)
\(572\) −12.9282 + 6.39230i −0.540555 + 0.267276i
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) −4.00000 + 6.92820i −0.166667 + 0.288675i
\(577\) −36.3731 + 21.0000i −1.51423 + 0.874241i −0.514370 + 0.857569i \(0.671974\pi\)
−0.999861 + 0.0166728i \(0.994693\pi\)
\(578\) −32.9090 + 19.0000i −1.36883 + 0.790296i
\(579\) 20.7846 + 12.0000i 0.863779 + 0.498703i
\(580\) 6.00000i 0.249136i
\(581\) 0 0
\(582\) −36.0000 −1.49225
\(583\) −15.5885 9.00000i −0.645608 0.372742i
\(584\) 0 0
\(585\) 0.232051 3.59808i 0.00959412 0.148762i
\(586\) 1.00000 1.73205i 0.0413096 0.0715504i
\(587\) 43.0000i 1.77480i 0.461000 + 0.887400i \(0.347491\pi\)
−0.461000 + 0.887400i \(0.652509\pi\)
\(588\) 0 0
\(589\) −9.00000 −0.370839
\(590\) −13.8564 8.00000i −0.570459 0.329355i
\(591\) 6.92820 4.00000i 0.284988 0.164538i
\(592\) −20.7846 + 12.0000i −0.854242 + 0.493197i
\(593\) 11.2583 + 6.50000i 0.462324 + 0.266923i 0.713021 0.701143i \(-0.247326\pi\)
−0.250697 + 0.968066i \(0.580660\pi\)
\(594\) 16.0000 0.656488
\(595\) 0 0
\(596\) 20.0000i 0.819232i
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 1.39230 21.5885i 0.0569356 0.882818i
\(599\) 10.5000 + 18.1865i 0.429018 + 0.743082i 0.996786 0.0801071i \(-0.0255262\pi\)
−0.567768 + 0.823189i \(0.692193\pi\)
\(600\) 0 0
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 10.3923 + 6.00000i 0.422857 + 0.244137i
\(605\) 6.06218 3.50000i 0.246463 0.142295i
\(606\) −20.7846 + 12.0000i −0.844317 + 0.487467i
\(607\) 9.00000 15.5885i 0.365299 0.632716i −0.623525 0.781803i \(-0.714300\pi\)
0.988824 + 0.149087i \(0.0476335\pi\)
\(608\) 24.0000 0.973329
\(609\) 0 0
\(610\) 16.0000 0.647821
\(611\) 35.5526 17.5788i 1.43830 0.711164i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) −20.7846 + 12.0000i −0.839482 + 0.484675i −0.857088 0.515170i \(-0.827729\pi\)
0.0176058 + 0.999845i \(0.494396\pi\)
\(614\) −33.0000 + 57.1577i −1.33177 + 2.30670i
\(615\) −20.0000 −0.806478
\(616\) 0 0
\(617\) 8.00000i 0.322068i −0.986949 0.161034i \(-0.948517\pi\)
0.986949 0.161034i \(-0.0514829\pi\)
\(618\) 0 0
\(619\) −31.1769 + 18.0000i −1.25311 + 0.723481i −0.971725 0.236115i \(-0.924126\pi\)
−0.281381 + 0.959596i \(0.590792\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) −6.00000 + 10.3923i −0.240772 + 0.417029i
\(622\) 60.0000i 2.40578i
\(623\) 0 0
\(624\) −16.0000 + 24.0000i −0.640513 + 0.960769i
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 17.3205 10.0000i 0.692267 0.399680i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) 18.0000 31.1769i 0.718278 1.24409i
\(629\) 36.0000i 1.43541i
\(630\) 0 0
\(631\) 12.0000i 0.477712i −0.971055 0.238856i \(-0.923228\pi\)
0.971055 0.238856i \(-0.0767725\pi\)
\(632\) 0 0
\(633\) 9.00000 + 15.5885i 0.357718 + 0.619586i
\(634\) 20.0000 + 34.6410i 0.794301 + 1.37577i
\(635\) 0 0
\(636\) 36.0000 1.42749
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) −12.1244 7.00000i −0.479632 0.276916i
\(640\) 0 0
\(641\) −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) −41.5692 24.0000i −1.64061 0.947204i
\(643\) 12.0000i 0.473234i −0.971603 0.236617i \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) 0 0
\(645\) 2.00000i 0.0787499i
\(646\) 18.0000 31.1769i 0.708201 1.22664i
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) −8.00000 + 13.8564i −0.314027 + 0.543912i
\(650\) −24.0000 16.0000i −0.941357 0.627572i
\(651\) 0 0
\(652\) 24.0000i 0.939913i
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 36.0000 + 62.3538i 1.40771 + 2.43823i
\(655\) −10.3923 + 6.00000i −0.406061 + 0.234439i
\(656\) 34.6410 + 20.0000i 1.35250 + 0.780869i
\(657\) 9.00000i 0.351123i
\(658\) 0 0
\(659\) −39.0000 −1.51922 −0.759612 0.650376i \(-0.774611\pi\)
−0.759612 + 0.650376i \(0.774611\pi\)
\(660\) 4.00000 6.92820i 0.155700 0.269680i
\(661\) −2.59808 + 1.50000i −0.101053 + 0.0583432i −0.549675 0.835379i \(-0.685248\pi\)
0.448622 + 0.893722i \(0.351915\pi\)
\(662\) 12.0000 + 20.7846i 0.466393 + 0.807817i
\(663\) 19.1769 + 38.7846i 0.744770 + 1.50627i
\(664\) 0 0
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) 4.50000 7.79423i 0.174241 0.301794i
\(668\) 1.73205 1.00000i 0.0670151 0.0386912i
\(669\) −36.3731 + 21.0000i −1.40626 + 0.811907i
\(670\) −20.7846 12.0000i −0.802980 0.463600i
\(671\) 16.0000i 0.617673i
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 46.7654 + 27.0000i 1.80133 + 1.04000i
\(675\) 8.00000 + 13.8564i 0.307920 + 0.533333i
\(676\) 15.7846 20.6603i 0.607100 0.794625i
\(677\) −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) 60.0000i 2.30429i
\(679\) 0 0
\(680\) 0 0
\(681\) 34.6410 + 20.0000i 1.32745 + 0.766402i
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) −34.6410 + 20.0000i −1.32550 + 0.765279i −0.984600 0.174820i \(-0.944066\pi\)
−0.340901 + 0.940099i \(0.610732\pi\)
\(684\) −5.19615 3.00000i −0.198680 0.114708i
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 12.0000i 0.457829i
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 32.3827 + 2.08846i 1.23368 + 0.0795639i
\(690\) 6.00000 + 10.3923i 0.228416 + 0.395628i
\(691\) −12.9904 7.50000i −0.494177 0.285313i 0.232128 0.972685i \(-0.425431\pi\)
−0.726306 + 0.687372i \(0.758764\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 48.0000i 1.82206i
\(695\) −15.5885 9.00000i −0.591304 0.341389i
\(696\) 0 0
\(697\) 51.9615 30.0000i 1.96818 1.13633i
\(698\) 27.0000 46.7654i 1.02197 1.77010i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) −25.8564 + 12.7846i −0.975887 + 0.482524i
\(703\) −9.00000 15.5885i −0.339441 0.587930i
\(704\) −13.8564 + 8.00000i −0.522233 + 0.301511i
\(705\) −11.0000 + 19.0526i −0.414284 + 0.717561i
\(706\) 4.00000 0.150542
\(707\) 0 0
\(708\) 32.0000i 1.20263i
\(709\) 25.9808 + 15.0000i 0.975728 + 0.563337i 0.900978 0.433865i \(-0.142851\pi\)
0.0747503 + 0.997202i \(0.476184\pi\)
\(710\) 24.2487 14.0000i 0.910038 0.525411i
\(711\) 4.50000 + 7.79423i 0.168763 + 0.292306i
\(712\) 0 0
\(713\) 9.00000i 0.337053i
\(714\) 0 0
\(715\) 4.00000 6.00000i 0.149592 0.224387i
\(716\) 9.00000 15.5885i 0.336346 0.582568i
\(717\) −13.8564 + 8.00000i −0.517477 + 0.298765i
\(718\) −22.0000 38.1051i −0.821033 1.42207i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 4.00000i 0.149071i
\(721\) 0 0
\(722\) 20.0000i 0.744323i
\(723\) −36.3731 21.0000i −1.35273 0.780998i
\(724\) 18.0000 + 31.1769i 0.668965 + 1.15868i
\(725\) −6.00000 10.3923i −0.222834 0.385961i
\(726\) 24.2487 + 14.0000i 0.899954 + 0.519589i
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −15.5885 9.00000i −0.576955 0.333105i
\(731\) −3.00000 5.19615i −0.110959 0.192187i
\(732\) 16.0000 + 27.7128i 0.591377 + 1.02430i
\(733\) −12.9904 7.50000i −0.479811 0.277019i 0.240527 0.970642i \(-0.422680\pi\)
−0.720338 + 0.693624i \(0.756013\pi\)
\(734\) 36.0000i 1.32878i
\(735\) 0 0
\(736\) 24.0000i 0.884652i
\(737\) −12.0000 + 20.7846i −0.442026 + 0.765611i
\(738\) −10.0000 17.3205i −0.368105 0.637577i
\(739\) 25.9808 15.0000i 0.955718 0.551784i 0.0608653 0.998146i \(-0.480614\pi\)
0.894852 + 0.446362i \(0.147281\pi\)
\(740\) −6.00000 + 10.3923i −0.220564 + 0.382029i
\(741\) −18.0000 12.0000i −0.661247 0.440831i
\(742\) 0 0
\(743\) 44.0000i 1.61420i −0.590412 0.807102i \(-0.701035\pi\)
0.590412 0.807102i \(-0.298965\pi\)
\(744\) 0 0
\(745\) −5.00000 8.66025i −0.183186 0.317287i
\(746\) 31.1769 18.0000i 1.14147 0.659027i
\(747\) −9.52628 5.50000i −0.348548 0.201234i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) 36.0000 1.31453
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 38.1051 22.0000i 1.38955 0.802257i
\(753\) −6.00000 10.3923i −0.218652 0.378717i
\(754\) 19.3923 9.58846i 0.706226 0.349191i
\(755\) −6.00000 −0.218362
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) −18.0000 + 31.1769i −0.653789 + 1.13240i
\(759\) 10.3923 6.00000i 0.377217 0.217786i
\(760\) 0 0
\(761\) −16.4545 9.50000i −0.596475 0.344375i 0.171179 0.985240i \(-0.445242\pi\)
−0.767653 + 0.640865i \(0.778576\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −5.19615 3.00000i −0.187867 0.108465i
\(766\) 8.00000 + 13.8564i 0.289052 + 0.500652i
\(767\) 1.85641 28.7846i 0.0670310 1.03935i
\(768\) −16.0000 + 27.7128i −0.577350 + 1.00000i
\(769\) 9.00000i 0.324548i 0.986746 + 0.162274i \(0.0518829\pi\)
−0.986746 + 0.162274i \(0.948117\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −20.7846 12.0000i −0.748054 0.431889i
\(773\) 12.1244 7.00000i 0.436083 0.251773i −0.265852 0.964014i \(-0.585653\pi\)
0.701935 + 0.712241i \(0.252320\pi\)
\(774\) −1.73205 + 1.00000i −0.0622573 + 0.0359443i
\(775\) 10.3923 + 6.00000i 0.373303 + 0.215526i
\(776\) 0 0
\(777\) 0 0
\(778\) 60.0000i 2.15110i
\(779\) −15.0000 + 25.9808i −0.537431 + 0.930857i
\(780\) −0.928203 + 14.3923i −0.0332350 + 0.515327i
\(781\) −14.0000 24.2487i −0.500959 0.867687i
\(782\) −31.1769 18.0000i −1.11488 0.643679i
\(783\) −12.0000 −0.428845
\(784\) 0 0
\(785\) 18.0000i 0.642448i
\(786\) −41.5692 24.0000i −1.48272 0.856052i
\(787\) −18.1865 + 10.5000i −0.648280 + 0.374285i −0.787797 0.615935i \(-0.788778\pi\)
0.139517 + 0.990220i \(0.455445\pi\)
\(788\) −6.92820 + 4.00000i −0.246807 + 0.142494i
\(789\) −9.00000 + 15.5885i −0.320408 + 0.554964i
\(790\) −18.0000 −0.640411
\(791\) 0 0
\(792\) 0 0
\(793\) 12.7846 + 25.8564i 0.453995 + 0.918188i
\(794\) −21.0000 36.3731i −0.745262 1.29083i
\(795\) −15.5885 + 9.00000i −0.552866 + 0.319197i
\(796\) −2.00000 + 3.46410i −0.0708881 + 0.122782i
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 66.0000i 2.33491i
\(800\) −27.7128 16.0000i −0.979796 0.565685i
\(801\) 4.33013 2.50000i 0.152998 0.0883332i
\(802\) −28.0000 48.4974i −0.988714 1.71250i
\(803\) −9.00000 + 15.5885i −0.317603 + 0.550105i
\(804\) 48.0000i 1.69283i
\(805\) 0 0
\(806\) −12.0000 + 18.0000i −0.422682 + 0.634023i
\(807\) 24.0000 41.5692i 0.844840 1.46331i
\(808\) 0 0
\(809\) 7.50000 + 12.9904i 0.263686 + 0.456717i 0.967219 0.253946i \(-0.0817284\pi\)
−0.703533 + 0.710663i \(0.748395\pi\)
\(810\) 11.0000 19.0526i 0.386501 0.669439i
\(811\) 12.0000i 0.421377i 0.977553 + 0.210688i \(0.0675706\pi\)
−0.977553 + 0.210688i \(0.932429\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 20.7846 + 12.0000i 0.728500 + 0.420600i
\(815\) −6.00000 10.3923i −0.210171 0.364027i
\(816\) 24.0000 + 41.5692i 0.840168 + 1.45521i
\(817\) 2.59808 + 1.50000i 0.0908952 + 0.0524784i
\(818\) −18.0000 −0.629355
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) 13.8564 + 8.00000i 0.483592 + 0.279202i 0.721912 0.691985i \(-0.243263\pi\)
−0.238320 + 0.971187i \(0.576597\pi\)
\(822\) −4.00000 6.92820i −0.139516 0.241649i
\(823\) 20.0000 + 34.6410i 0.697156 + 1.20751i 0.969448 + 0.245295i \(0.0788849\pi\)
−0.272292 + 0.962215i \(0.587782\pi\)
\(824\) 0 0
\(825\) 16.0000i 0.557048i
\(826\) 0 0
\(827\) 4.00000i 0.139094i −0.997579 0.0695468i \(-0.977845\pi\)
0.997579 0.0695468i \(-0.0221553\pi\)
\(828\) −3.00000 + 5.19615i −0.104257 + 0.180579i
\(829\) 1.00000 + 1.73205i 0.0347314 + 0.0601566i 0.882869 0.469620i \(-0.155609\pi\)
−0.848137 + 0.529777i \(0.822276\pi\)
\(830\) 19.0526 11.0000i 0.661324 0.381816i
\(831\) 17.0000 29.4449i 0.589723 1.02143i
\(832\) 16.0000 24.0000i 0.554700 0.832050i
\(833\) 0 0
\(834\) 72.0000i 2.49316i
\(835\) −0.500000 + 0.866025i −0.0173032 + 0.0299700i
\(836\) −6.00000 10.3923i −0.207514 0.359425i
\(837\) 10.3923 6.00000i 0.359211 0.207390i
\(838\) −10.3923 6.00000i −0.358996 0.207267i
\(839\) 16.0000i 0.552381i −0.961103 0.276191i \(-0.910928\pi\)
0.961103 0.276191i \(-0.0890721\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −30.0000 + 51.9615i −1.03387 + 1.79071i
\(843\) 3.46410 2.00000i 0.119310 0.0688837i
\(844\) −9.00000 15.5885i −0.309793 0.536577i
\(845\) −1.66987 + 12.8923i −0.0574454 + 0.443509i
\(846\) −22.0000 −0.756376
\(847\) 0 0
\(848\) 36.0000 1.23625
\(849\) 4.00000 6.92820i 0.137280 0.237775i
\(850\) −41.5692 + 24.0000i −1.42581 + 0.823193i
\(851\) −15.5885 + 9.00000i −0.534365 + 0.308516i
\(852\) 48.4974 + 28.0000i 1.66149 + 0.959264i
\(853\) 45.0000i 1.54077i −0.637579 0.770385i \(-0.720064\pi\)
0.637579 0.770385i \(-0.279936\pi\)
\(854\) 0 0
\(855\) 3.00000 0.102598
\(856\) 0 0
\(857\) −18.0000 31.1769i −0.614868 1.06498i −0.990408 0.138177i \(-0.955876\pi\)
0.375539 0.926806i \(-0.377458\pi\)
\(858\) 28.7846 + 1.85641i 0.982690 + 0.0633767i
\(859\) 2.00000 3.46410i 0.0682391 0.118194i −0.829887 0.557931i \(-0.811595\pi\)
0.898126 + 0.439738i \(0.144929\pi\)
\(860\) 2.00000i 0.0681994i
\(861\) 0 0
\(862\) −8.00000 −0.272481
\(863\) 27.7128 + 16.0000i 0.943355 + 0.544646i 0.891010 0.453983i \(-0.149997\pi\)
0.0523446 + 0.998629i \(0.483331\pi\)
\(864\) −27.7128 + 16.0000i −0.942809 + 0.544331i
\(865\) 5.19615 3.00000i 0.176674 0.102003i
\(866\) 34.6410 + 20.0000i 1.17715 + 0.679628i
\(867\) 38.0000 1.29055
\(868\) 0 0
\(869\) 18.0000i 0.610608i
\(870\) −6.00000 + 10.3923i −0.203419 + 0.352332i
\(871\) 2.78461 43.1769i 0.0943529 1.46299i
\(872\) 0 0
\(873\) 7.79423 + 4.50000i 0.263795 + 0.152302i
\(874\) 18.0000 0.608859
\(875\) 0 0
\(876\) 36.0000i 1.21633i
\(877\) 15.5885 + 9.00000i 0.526385 + 0.303908i 0.739543 0.673109i \(-0.235042\pi\)
−0.213158 + 0.977018i \(0.568375\pi\)
\(878\) 62.3538 36.0000i 2.10434 1.21494i
\(879\) −1.73205 + 1.00000i −0.0584206 + 0.0337292i
\(880\) 4.00000 6.92820i 0.134840 0.233550i
\(881\) −12.0000 −0.404290 −0.202145 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 0 0
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) −19.1769 38.7846i −0.644989 1.30447i
\(885\) 8.00000 + 13.8564i 0.268917 + 0.465778i
\(886\) −46.7654 + 27.0000i −1.57111 + 0.907083i
\(887\) 18.0000 31.1769i 0.604381 1.04682i −0.387768 0.921757i \(-0.626754\pi\)
0.992149 0.125061i \(-0.0399128\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 10.0000i 0.335201i
\(891\) −19.0526 11.0000i −0.638285 0.368514i
\(892\) 36.3731 21.0000i 1.21786 0.703132i
\(893\) 16.5000 + 28.5788i 0.552151 + 0.956354i
\(894\) 20.0000 34.6410i 0.668900 1.15857i
\(895\) 9.00000i 0.300837i
\(896\) 0 0
\(897\) −12.0000 + 18.0000i −0.400668 + 0.601003i
\(898\) −4.00000 + 6.92820i −0.133482 + 0.231197i
\(899\) −7.79423 + 4.50000i −0.259952 + 0.150083i
\(900\) 4.00000 + 6.92820i 0.133333 + 0.230940i
\(901\) 27.0000 46.7654i 0.899500 1.55798i
\(902\) 40.0000i 1.33185i
\(903\) 0 0
\(904\) 0 0
\(905\) −15.5885 9.00000i −0.518178 0.299170i
\(906\) −12.0000 20.7846i −0.398673 0.690522i
\(907\) −4.50000 7.79423i −0.149420 0.258803i 0.781593 0.623788i \(-0.214407\pi\)
−0.931013 + 0.364985i \(0.881074\pi\)
\(908\) −34.6410 20.0000i −1.14960 0.663723i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −27.0000 −0.894550 −0.447275 0.894397i \(-0.647605\pi\)
−0.447275 + 0.894397i \(0.647605\pi\)
\(912\) −20.7846 12.0000i −0.688247 0.397360i
\(913\) −11.0000 19.0526i −0.364047 0.630548i
\(914\) −42.0000 72.7461i −1.38924 2.40623i
\(915\) −13.8564 8.00000i −0.458079 0.264472i
\(916\) 12.0000i 0.396491i
\(917\) 0 0
\(918\) 48.0000i 1.58424i
\(919\) −18.0000 + 31.1769i −0.593765 + 1.02843i 0.399955 + 0.916535i \(0.369026\pi\)
−0.993720 + 0.111897i \(0.964307\pi\)
\(920\) 0 0
\(921\) 57.1577 33.0000i 1.88341 1.08739i
\(922\) −2.00000 + 3.46410i −0.0658665 + 0.114084i
\(923\) 42.0000 + 28.0000i 1.38245 + 0.921631i
\(924\) 0 0
\(925\) 24.0000i 0.789115i
\(926\) 30.0000 51.9615i 0.985861 1.70756i
\(927\) 0 0
\(928\) 20.7846 12.0000i 0.682288 0.393919i
\(929\) 6.06218 + 3.50000i 0.198894 + 0.114831i 0.596139 0.802881i \(-0.296701\pi\)
−0.397246 + 0.917712i \(0.630034\pi\)
\(930\) 12.0000i 0.393496i
\(931\) 0 0
\(932\) 6.00000 0.196537
\(933\) 30.0000 51.9615i 0.982156 1.70114i
\(934\) −72.7461 + 42.0000i −2.38033 + 1.37428i
\(935\) −6.00000 10.3923i −0.196221 0.339865i
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) −20.0000 −0.652675
\(940\) 11.0000 19.0526i 0.358780 0.621426i
\(941\) −0.866025 + 0.500000i −0.0282316 + 0.0162995i −0.514049 0.857761i \(-0.671855\pi\)
0.485818 + 0.874060i \(0.338522\pi\)
\(942\) −62.3538 + 36.0000i −2.03160 + 1.17294i
\(943\) 25.9808 + 15.0000i 0.846050 + 0.488467i
\(944\) 32.0000i 1.04151i
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) 13.8564 + 8.00000i 0.450273 + 0.259965i 0.707945 0.706267i \(-0.249622\pi\)
−0.257673 + 0.966232i \(0.582956\pi\)
\(948\) −18.0000 31.1769i −0.584613 1.01258i
\(949\) 2.08846 32.3827i 0.0677942 1.05119i
\(950\) 12.0000 20.7846i 0.389331 0.674342i
\(951\) 40.0000i 1.29709i
\(952\) 0 0
\(953\) 3.00000 0.0971795 0.0485898 0.998819i \(-0.484527\pi\)
0.0485898 + 0.998819i \(0.484527\pi\)
\(954\) −15.5885 9.00000i −0.504695 0.291386i
\(955\) 0 0
\(956\) 13.8564 8.00000i 0.448148 0.258738i
\(957\) 10.3923 + 6.00000i 0.335936 + 0.193952i
\(958\) −58.0000 −1.87389
\(959\) 0 0
\(960\) 16.0000i 0.516398i
\(961\) −11.0000 + 19.0526i −0.354839 + 0.614599i
\(962\) −43.1769 2.78461i −1.39208 0.0897794i
\(963\) 6.00000 + 10.3923i 0.193347 + 0.334887i
\(964\) 36.3731 + 21.0000i 1.17150 + 0.676364i
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) 54.0000i 1.73652i 0.496107 + 0.868261i \(0.334762\pi\)
−0.496107 + 0.868261i \(0.665238\pi\)
\(968\) 0 0
\(969\) −31.1769 + 18.0000i −1.00155 + 0.578243i
\(970\) −15.5885 + 9.00000i −0.500515 + 0.288973i
\(971\) −6.00000 + 10.3923i −0.192549 + 0.333505i −0.946094 0.323891i \(-0.895009\pi\)
0.753545 + 0.657396i \(0.228342\pi\)
\(972\) 20.0000 0.641500
\(973\) 0 0
\(974\) −24.0000 −0.769010
\(975\) 12.7846 + 25.8564i 0.409435 + 0.828068i
\(976\) 16.0000 + 27.7128i 0.512148 + 0.887066i
\(977\) 8.66025 5.00000i 0.277066 0.159964i −0.355028 0.934856i \(-0.615529\pi\)
0.632094 + 0.774891i \(0.282195\pi\)
\(978\) 24.0000 41.5692i 0.767435 1.32924i
\(979\) 10.0000 0.319601
\(980\) 0 0
\(981\) 18.0000i 0.574696i
\(982\) 20.7846 + 12.0000i 0.663264 + 0.382935i
\(983\) −25.1147 + 14.5000i −0.801036 + 0.462478i −0.843833 0.536606i \(-0.819706\pi\)
0.0427975 + 0.999084i \(0.486373\pi\)
\(984\) 0 0
\(985\) 2.00000 3.46410i 0.0637253 0.110375i
\(986\) 36.0000i 1.14647i
\(987\) 0 0
\(988\) 18.0000 + 12.0000i 0.572656 + 0.381771i
\(989\) 1.50000 2.59808i 0.0476972 0.0826140i
\(990\) −3.46410 + 2.00000i −0.110096 + 0.0635642i
\(991\) 28.0000 + 48.4974i 0.889449 + 1.54057i 0.840528 + 0.541769i \(0.182245\pi\)
0.0489218 + 0.998803i \(0.484422\pi\)
\(992\) −12.0000 + 20.7846i −0.381000 + 0.659912i
\(993\) 24.0000i 0.761617i
\(994\) 0 0
\(995\) 2.00000i 0.0634043i
\(996\) 38.1051 + 22.0000i 1.20741 + 0.697097i
\(997\) 18.0000 + 31.1769i 0.570066 + 0.987383i 0.996559 + 0.0828918i \(0.0264156\pi\)
−0.426493 + 0.904491i \(0.640251\pi\)
\(998\) 6.00000 + 10.3923i 0.189927 + 0.328963i
\(999\) 20.7846 + 12.0000i 0.657596 + 0.379663i
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 637.2.r.a.324.2 4
7.2 even 3 637.2.c.c.246.1 yes 2
7.3 odd 6 637.2.r.c.116.1 4
7.4 even 3 inner 637.2.r.a.116.1 4
7.5 odd 6 637.2.c.a.246.1 2
7.6 odd 2 637.2.r.c.324.2 4
13.12 even 2 inner 637.2.r.a.324.1 4
91.5 even 12 8281.2.a.a.1.1 1
91.12 odd 6 637.2.c.a.246.2 yes 2
91.25 even 6 inner 637.2.r.a.116.2 4
91.38 odd 6 637.2.r.c.116.2 4
91.44 odd 12 8281.2.a.b.1.1 1
91.47 even 12 8281.2.a.k.1.1 1
91.51 even 6 637.2.c.c.246.2 yes 2
91.86 odd 12 8281.2.a.m.1.1 1
91.90 odd 2 637.2.r.c.324.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.c.a.246.1 2 7.5 odd 6
637.2.c.a.246.2 yes 2 91.12 odd 6
637.2.c.c.246.1 yes 2 7.2 even 3
637.2.c.c.246.2 yes 2 91.51 even 6
637.2.r.a.116.1 4 7.4 even 3 inner
637.2.r.a.116.2 4 91.25 even 6 inner
637.2.r.a.324.1 4 13.12 even 2 inner
637.2.r.a.324.2 4 1.1 even 1 trivial
637.2.r.c.116.1 4 7.3 odd 6
637.2.r.c.116.2 4 91.38 odd 6
637.2.r.c.324.1 4 91.90 odd 2
637.2.r.c.324.2 4 7.6 odd 2
8281.2.a.a.1.1 1 91.5 even 12
8281.2.a.b.1.1 1 91.44 odd 12
8281.2.a.k.1.1 1 91.47 even 12
8281.2.a.m.1.1 1 91.86 odd 12