Properties

Label 1386.2.k.r.793.2
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(793,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.793");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.2
Root \(1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.r.991.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(1.32288 + 2.29129i) q^{10} +(0.500000 + 0.866025i) q^{11} -4.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-2.64575 + 4.58258i) q^{19} -2.64575 q^{20} -1.00000 q^{22} +(-1.32288 + 2.29129i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(2.00000 - 3.46410i) q^{26} +2.64575 q^{28} -2.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +(3.50000 + 6.06218i) q^{35} +(-0.645751 + 1.11847i) q^{37} +(-2.64575 - 4.58258i) q^{38} +(1.32288 - 2.29129i) q^{40} -9.00000 q^{41} +9.29150 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.32288 - 2.29129i) q^{46} +(-1.96863 + 3.40976i) q^{47} +(-3.50000 - 6.06218i) q^{49} +2.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{53} +2.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +(1.00000 - 1.73205i) q^{58} +(3.29150 + 5.70105i) q^{59} +(-5.96863 + 10.3380i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.29150 + 9.16515i) q^{65} +(-3.79150 - 6.56708i) q^{67} +(-1.50000 + 2.59808i) q^{68} -7.00000 q^{70} +2.70850 q^{71} +(7.64575 + 13.2428i) q^{73} +(-0.645751 - 1.11847i) q^{74} +5.29150 q^{76} -2.64575 q^{77} +(-5.32288 + 9.21949i) q^{79} +(1.32288 + 2.29129i) q^{80} +(4.50000 - 7.79423i) q^{82} -15.5830 q^{83} -7.93725 q^{85} +(-4.64575 + 8.04668i) q^{86} +(0.500000 + 0.866025i) q^{88} +(1.35425 - 2.34563i) q^{89} +(5.29150 - 9.16515i) q^{91} +2.64575 q^{92} +(-1.96863 - 3.40976i) q^{94} +(7.00000 + 12.1244i) q^{95} -11.5830 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{11} - 16 q^{13} - 2 q^{16} - 6 q^{17} - 4 q^{22} - 4 q^{25} + 8 q^{26} - 8 q^{29} + 8 q^{31} - 2 q^{32} + 12 q^{34} + 14 q^{35} + 8 q^{37} - 36 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{47} - 14 q^{49} + 8 q^{50} + 8 q^{52} + 8 q^{53} + 4 q^{58} - 8 q^{59} - 8 q^{61} - 16 q^{62} + 4 q^{64} + 6 q^{67} - 6 q^{68} - 28 q^{70} + 32 q^{71} + 20 q^{73} + 8 q^{74} - 16 q^{79} + 18 q^{82} - 20 q^{83} - 8 q^{86} + 2 q^{88} + 16 q^{89} + 8 q^{94} + 28 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.32288 2.29129i 0.591608 1.02470i −0.402408 0.915460i \(-0.631827\pi\)
0.994016 0.109235i \(-0.0348400\pi\)
\(6\) 0 0
\(7\) −1.32288 + 2.29129i −0.500000 + 0.866025i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.32288 + 2.29129i 0.418330 + 0.724569i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −1.32288 2.29129i −0.353553 0.612372i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −2.64575 + 4.58258i −0.606977 + 1.05131i 0.384759 + 0.923017i \(0.374285\pi\)
−0.991736 + 0.128298i \(0.959049\pi\)
\(20\) −2.64575 −0.591608
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −1.32288 + 2.29129i −0.275839 + 0.477767i −0.970346 0.241719i \(-0.922289\pi\)
0.694508 + 0.719485i \(0.255622\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 2.00000 3.46410i 0.392232 0.679366i
\(27\) 0 0
\(28\) 2.64575 0.500000
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 3.50000 + 6.06218i 0.591608 + 1.02470i
\(36\) 0 0
\(37\) −0.645751 + 1.11847i −0.106161 + 0.183876i −0.914212 0.405236i \(-0.867189\pi\)
0.808051 + 0.589112i \(0.200523\pi\)
\(38\) −2.64575 4.58258i −0.429198 0.743392i
\(39\) 0 0
\(40\) 1.32288 2.29129i 0.209165 0.362284i
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) 9.29150 1.41694 0.708470 0.705740i \(-0.249386\pi\)
0.708470 + 0.705740i \(0.249386\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −1.32288 2.29129i −0.195047 0.337832i
\(47\) −1.96863 + 3.40976i −0.287154 + 0.497365i −0.973129 0.230260i \(-0.926042\pi\)
0.685975 + 0.727625i \(0.259376\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 2.00000 0.282843
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 0 0
\(55\) 2.64575 0.356753
\(56\) −1.32288 + 2.29129i −0.176777 + 0.306186i
\(57\) 0 0
\(58\) 1.00000 1.73205i 0.131306 0.227429i
\(59\) 3.29150 + 5.70105i 0.428517 + 0.742213i 0.996742 0.0806601i \(-0.0257028\pi\)
−0.568225 + 0.822874i \(0.692369\pi\)
\(60\) 0 0
\(61\) −5.96863 + 10.3380i −0.764204 + 1.32364i 0.176462 + 0.984307i \(0.443535\pi\)
−0.940666 + 0.339333i \(0.889799\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −5.29150 + 9.16515i −0.656330 + 1.13680i
\(66\) 0 0
\(67\) −3.79150 6.56708i −0.463206 0.802296i 0.535913 0.844273i \(-0.319968\pi\)
−0.999119 + 0.0419774i \(0.986634\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 0 0
\(70\) −7.00000 −0.836660
\(71\) 2.70850 0.321440 0.160720 0.987000i \(-0.448618\pi\)
0.160720 + 0.987000i \(0.448618\pi\)
\(72\) 0 0
\(73\) 7.64575 + 13.2428i 0.894868 + 1.54996i 0.833969 + 0.551812i \(0.186063\pi\)
0.0608990 + 0.998144i \(0.480603\pi\)
\(74\) −0.645751 1.11847i −0.0750671 0.130020i
\(75\) 0 0
\(76\) 5.29150 0.606977
\(77\) −2.64575 −0.301511
\(78\) 0 0
\(79\) −5.32288 + 9.21949i −0.598870 + 1.03727i 0.394118 + 0.919060i \(0.371050\pi\)
−0.992988 + 0.118214i \(0.962283\pi\)
\(80\) 1.32288 + 2.29129i 0.147902 + 0.256174i
\(81\) 0 0
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −15.5830 −1.71046 −0.855229 0.518251i \(-0.826583\pi\)
−0.855229 + 0.518251i \(0.826583\pi\)
\(84\) 0 0
\(85\) −7.93725 −0.860916
\(86\) −4.64575 + 8.04668i −0.500964 + 0.867696i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 1.35425 2.34563i 0.143550 0.248636i −0.785281 0.619140i \(-0.787482\pi\)
0.928831 + 0.370504i \(0.120815\pi\)
\(90\) 0 0
\(91\) 5.29150 9.16515i 0.554700 0.960769i
\(92\) 2.64575 0.275839
\(93\) 0 0
\(94\) −1.96863 3.40976i −0.203048 0.351690i
\(95\) 7.00000 + 12.1244i 0.718185 + 1.24393i
\(96\) 0 0
\(97\) −11.5830 −1.17608 −0.588038 0.808833i \(-0.700099\pi\)
−0.588038 + 0.808833i \(0.700099\pi\)
\(98\) 7.00000 0.707107
\(99\) 0 0
\(100\) −1.00000 + 1.73205i −0.100000 + 0.173205i
\(101\) 3.64575 + 6.31463i 0.362766 + 0.628329i 0.988415 0.151776i \(-0.0484992\pi\)
−0.625649 + 0.780105i \(0.715166\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i \(-0.690071\pi\)
0.997298 + 0.0734594i \(0.0234039\pi\)
\(108\) 0 0
\(109\) 1.96863 + 3.40976i 0.188560 + 0.326596i 0.944770 0.327733i \(-0.106285\pi\)
−0.756210 + 0.654329i \(0.772951\pi\)
\(110\) −1.32288 + 2.29129i −0.126131 + 0.218466i
\(111\) 0 0
\(112\) −1.32288 2.29129i −0.125000 0.216506i
\(113\) −12.5830 −1.18371 −0.591855 0.806045i \(-0.701604\pi\)
−0.591855 + 0.806045i \(0.701604\pi\)
\(114\) 0 0
\(115\) 3.50000 + 6.06218i 0.326377 + 0.565301i
\(116\) 1.00000 + 1.73205i 0.0928477 + 0.160817i
\(117\) 0 0
\(118\) −6.58301 −0.606015
\(119\) 7.93725 0.727607
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −5.96863 10.3380i −0.540374 0.935955i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 7.93725 0.709930
\(126\) 0 0
\(127\) 2.64575 0.234772 0.117386 0.993086i \(-0.462548\pi\)
0.117386 + 0.993086i \(0.462548\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −5.29150 9.16515i −0.464095 0.803837i
\(131\) −9.29150 + 16.0934i −0.811802 + 1.40608i 0.0997990 + 0.995008i \(0.468180\pi\)
−0.911601 + 0.411075i \(0.865153\pi\)
\(132\) 0 0
\(133\) −7.00000 12.1244i −0.606977 1.05131i
\(134\) 7.58301 0.655072
\(135\) 0 0
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) −6.64575 11.5108i −0.567785 0.983432i −0.996785 0.0801276i \(-0.974467\pi\)
0.429000 0.903305i \(-0.358866\pi\)
\(138\) 0 0
\(139\) −12.5830 −1.06728 −0.533638 0.845713i \(-0.679176\pi\)
−0.533638 + 0.845713i \(0.679176\pi\)
\(140\) 3.50000 6.06218i 0.295804 0.512348i
\(141\) 0 0
\(142\) −1.35425 + 2.34563i −0.113646 + 0.196841i
\(143\) −2.00000 3.46410i −0.167248 0.289683i
\(144\) 0 0
\(145\) −2.64575 + 4.58258i −0.219718 + 0.380562i
\(146\) −15.2915 −1.26553
\(147\) 0 0
\(148\) 1.29150 0.106161
\(149\) 9.93725 17.2118i 0.814092 1.41005i −0.0958868 0.995392i \(-0.530569\pi\)
0.909978 0.414656i \(-0.136098\pi\)
\(150\) 0 0
\(151\) −11.3229 19.6118i −0.921443 1.59599i −0.797185 0.603735i \(-0.793678\pi\)
−0.124258 0.992250i \(-0.539655\pi\)
\(152\) −2.64575 + 4.58258i −0.214599 + 0.371696i
\(153\) 0 0
\(154\) 1.32288 2.29129i 0.106600 0.184637i
\(155\) 10.5830 0.850047
\(156\) 0 0
\(157\) 0.354249 + 0.613577i 0.0282721 + 0.0489688i 0.879815 0.475316i \(-0.157666\pi\)
−0.851543 + 0.524285i \(0.824333\pi\)
\(158\) −5.32288 9.21949i −0.423465 0.733463i
\(159\) 0 0
\(160\) −2.64575 −0.209165
\(161\) −3.50000 6.06218i −0.275839 0.477767i
\(162\) 0 0
\(163\) 2.79150 4.83502i 0.218647 0.378708i −0.735747 0.677256i \(-0.763169\pi\)
0.954395 + 0.298548i \(0.0965022\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) 7.79150 13.4953i 0.604738 1.04744i
\(167\) −8.70850 −0.673884 −0.336942 0.941525i \(-0.609393\pi\)
−0.336942 + 0.941525i \(0.609393\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 3.96863 6.87386i 0.304380 0.527201i
\(171\) 0 0
\(172\) −4.64575 8.04668i −0.354235 0.613553i
\(173\) 2.00000 3.46410i 0.152057 0.263371i −0.779926 0.625871i \(-0.784744\pi\)
0.931984 + 0.362500i \(0.118077\pi\)
\(174\) 0 0
\(175\) 5.29150 0.400000
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 1.35425 + 2.34563i 0.101505 + 0.175812i
\(179\) 2.35425 + 4.07768i 0.175965 + 0.304780i 0.940495 0.339808i \(-0.110362\pi\)
−0.764530 + 0.644588i \(0.777029\pi\)
\(180\) 0 0
\(181\) −5.29150 −0.393314 −0.196657 0.980472i \(-0.563009\pi\)
−0.196657 + 0.980472i \(0.563009\pi\)
\(182\) 5.29150 + 9.16515i 0.392232 + 0.679366i
\(183\) 0 0
\(184\) −1.32288 + 2.29129i −0.0975237 + 0.168916i
\(185\) 1.70850 + 2.95920i 0.125611 + 0.217565i
\(186\) 0 0
\(187\) 1.50000 2.59808i 0.109691 0.189990i
\(188\) 3.93725 0.287154
\(189\) 0 0
\(190\) −14.0000 −1.01567
\(191\) 3.35425 5.80973i 0.242705 0.420377i −0.718779 0.695239i \(-0.755299\pi\)
0.961484 + 0.274861i \(0.0886320\pi\)
\(192\) 0 0
\(193\) 7.93725 + 13.7477i 0.571336 + 0.989583i 0.996429 + 0.0844334i \(0.0269080\pi\)
−0.425093 + 0.905150i \(0.639759\pi\)
\(194\) 5.79150 10.0312i 0.415806 0.720197i
\(195\) 0 0
\(196\) −3.50000 + 6.06218i −0.250000 + 0.433013i
\(197\) −21.8745 −1.55849 −0.779247 0.626717i \(-0.784398\pi\)
−0.779247 + 0.626717i \(0.784398\pi\)
\(198\) 0 0
\(199\) 9.58301 + 16.5983i 0.679321 + 1.17662i 0.975186 + 0.221389i \(0.0710590\pi\)
−0.295864 + 0.955230i \(0.595608\pi\)
\(200\) −1.00000 1.73205i −0.0707107 0.122474i
\(201\) 0 0
\(202\) −7.29150 −0.513028
\(203\) 2.64575 4.58258i 0.185695 0.321634i
\(204\) 0 0
\(205\) −11.9059 + 20.6216i −0.831543 + 1.44027i
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) −5.29150 −0.366021
\(210\) 0 0
\(211\) 21.2915 1.46577 0.732884 0.680354i \(-0.238174\pi\)
0.732884 + 0.680354i \(0.238174\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 0 0
\(214\) 4.50000 + 7.79423i 0.307614 + 0.532803i
\(215\) 12.2915 21.2895i 0.838274 1.45193i
\(216\) 0 0
\(217\) −10.5830 −0.718421
\(218\) −3.93725 −0.266664
\(219\) 0 0
\(220\) −1.32288 2.29129i −0.0891883 0.154479i
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) 28.4575 1.90566 0.952828 0.303511i \(-0.0981588\pi\)
0.952828 + 0.303511i \(0.0981588\pi\)
\(224\) 2.64575 0.176777
\(225\) 0 0
\(226\) 6.29150 10.8972i 0.418505 0.724871i
\(227\) 1.20850 + 2.09318i 0.0802108 + 0.138929i 0.903340 0.428924i \(-0.141107\pi\)
−0.823130 + 0.567854i \(0.807774\pi\)
\(228\) 0 0
\(229\) −3.35425 + 5.80973i −0.221655 + 0.383918i −0.955311 0.295604i \(-0.904479\pi\)
0.733656 + 0.679521i \(0.237813\pi\)
\(230\) −7.00000 −0.461566
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 10.0830 17.4643i 0.660560 1.14412i −0.319909 0.947448i \(-0.603652\pi\)
0.980469 0.196675i \(-0.0630143\pi\)
\(234\) 0 0
\(235\) 5.20850 + 9.02138i 0.339765 + 0.588490i
\(236\) 3.29150 5.70105i 0.214259 0.371107i
\(237\) 0 0
\(238\) −3.96863 + 6.87386i −0.257248 + 0.445566i
\(239\) −2.70850 −0.175198 −0.0875991 0.996156i \(-0.527919\pi\)
−0.0875991 + 0.996156i \(0.527919\pi\)
\(240\) 0 0
\(241\) 13.5830 + 23.5265i 0.874958 + 1.51547i 0.856807 + 0.515637i \(0.172445\pi\)
0.0181511 + 0.999835i \(0.494222\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) 11.9373 0.764204
\(245\) −18.5203 −1.18322
\(246\) 0 0
\(247\) 10.5830 18.3303i 0.673380 1.16633i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 0 0
\(250\) −3.96863 + 6.87386i −0.250998 + 0.434741i
\(251\) −23.2915 −1.47015 −0.735073 0.677988i \(-0.762852\pi\)
−0.735073 + 0.677988i \(0.762852\pi\)
\(252\) 0 0
\(253\) −2.64575 −0.166337
\(254\) −1.32288 + 2.29129i −0.0830046 + 0.143768i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.64575 8.04668i 0.289794 0.501938i −0.683966 0.729513i \(-0.739747\pi\)
0.973760 + 0.227576i \(0.0730799\pi\)
\(258\) 0 0
\(259\) −1.70850 2.95920i −0.106161 0.183876i
\(260\) 10.5830 0.656330
\(261\) 0 0
\(262\) −9.29150 16.0934i −0.574031 0.994251i
\(263\) 10.9373 + 18.9439i 0.674420 + 1.16813i 0.976638 + 0.214891i \(0.0689396\pi\)
−0.302218 + 0.953239i \(0.597727\pi\)
\(264\) 0 0
\(265\) 10.5830 0.650109
\(266\) 14.0000 0.858395
\(267\) 0 0
\(268\) −3.79150 + 6.56708i −0.231603 + 0.401148i
\(269\) −5.32288 9.21949i −0.324541 0.562122i 0.656878 0.753997i \(-0.271877\pi\)
−0.981419 + 0.191875i \(0.938543\pi\)
\(270\) 0 0
\(271\) −4.64575 + 8.04668i −0.282209 + 0.488801i −0.971929 0.235276i \(-0.924401\pi\)
0.689719 + 0.724077i \(0.257734\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 13.2915 0.802969
\(275\) 1.00000 1.73205i 0.0603023 0.104447i
\(276\) 0 0
\(277\) 8.58301 + 14.8662i 0.515703 + 0.893223i 0.999834 + 0.0182280i \(0.00580246\pi\)
−0.484131 + 0.874995i \(0.660864\pi\)
\(278\) 6.29150 10.8972i 0.377339 0.653571i
\(279\) 0 0
\(280\) 3.50000 + 6.06218i 0.209165 + 0.362284i
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) −15.2288 26.3770i −0.905256 1.56795i −0.820574 0.571541i \(-0.806346\pi\)
−0.0846819 0.996408i \(-0.526987\pi\)
\(284\) −1.35425 2.34563i −0.0803599 0.139187i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 11.9059 20.6216i 0.702782 1.21725i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −2.64575 4.58258i −0.155364 0.269098i
\(291\) 0 0
\(292\) 7.64575 13.2428i 0.447434 0.774978i
\(293\) 14.5830 0.851948 0.425974 0.904735i \(-0.359931\pi\)
0.425974 + 0.904735i \(0.359931\pi\)
\(294\) 0 0
\(295\) 17.4170 1.01406
\(296\) −0.645751 + 1.11847i −0.0375335 + 0.0650100i
\(297\) 0 0
\(298\) 9.93725 + 17.2118i 0.575650 + 0.997054i
\(299\) 5.29150 9.16515i 0.306015 0.530034i
\(300\) 0 0
\(301\) −12.2915 + 21.2895i −0.708470 + 1.22711i
\(302\) 22.6458 1.30312
\(303\) 0 0
\(304\) −2.64575 4.58258i −0.151744 0.262829i
\(305\) 15.7915 + 27.3517i 0.904219 + 1.56615i
\(306\) 0 0
\(307\) −11.4170 −0.651602 −0.325801 0.945438i \(-0.605634\pi\)
−0.325801 + 0.945438i \(0.605634\pi\)
\(308\) 1.32288 + 2.29129i 0.0753778 + 0.130558i
\(309\) 0 0
\(310\) −5.29150 + 9.16515i −0.300537 + 0.520546i
\(311\) 11.2601 + 19.5031i 0.638503 + 1.10592i 0.985761 + 0.168151i \(0.0537795\pi\)
−0.347258 + 0.937770i \(0.612887\pi\)
\(312\) 0 0
\(313\) 10.2915 17.8254i 0.581710 1.00755i −0.413567 0.910474i \(-0.635717\pi\)
0.995277 0.0970777i \(-0.0309495\pi\)
\(314\) −0.708497 −0.0399828
\(315\) 0 0
\(316\) 10.6458 0.598870
\(317\) 4.61438 7.99234i 0.259169 0.448894i −0.706850 0.707363i \(-0.749885\pi\)
0.966020 + 0.258469i \(0.0832179\pi\)
\(318\) 0 0
\(319\) −1.00000 1.73205i −0.0559893 0.0969762i
\(320\) 1.32288 2.29129i 0.0739510 0.128087i
\(321\) 0 0
\(322\) 7.00000 0.390095
\(323\) 15.8745 0.883281
\(324\) 0 0
\(325\) 4.00000 + 6.92820i 0.221880 + 0.384308i
\(326\) 2.79150 + 4.83502i 0.154607 + 0.267787i
\(327\) 0 0
\(328\) −9.00000 −0.496942
\(329\) −5.20850 9.02138i −0.287154 0.497365i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 7.79150 + 13.4953i 0.427614 + 0.740650i
\(333\) 0 0
\(334\) 4.35425 7.54178i 0.238254 0.412668i
\(335\) −20.0627 −1.09614
\(336\) 0 0
\(337\) 6.70850 0.365435 0.182718 0.983165i \(-0.441511\pi\)
0.182718 + 0.983165i \(0.441511\pi\)
\(338\) −1.50000 + 2.59808i −0.0815892 + 0.141317i
\(339\) 0 0
\(340\) 3.96863 + 6.87386i 0.215229 + 0.372788i
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) 9.29150 0.500964
\(345\) 0 0
\(346\) 2.00000 + 3.46410i 0.107521 + 0.186231i
\(347\) 14.7915 + 25.6196i 0.794049 + 1.37533i 0.923441 + 0.383740i \(0.125364\pi\)
−0.129392 + 0.991594i \(0.541302\pi\)
\(348\) 0 0
\(349\) −13.2288 −0.708119 −0.354060 0.935223i \(-0.615199\pi\)
−0.354060 + 0.935223i \(0.615199\pi\)
\(350\) −2.64575 + 4.58258i −0.141421 + 0.244949i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −11.6458 20.1710i −0.619841 1.07360i −0.989514 0.144434i \(-0.953864\pi\)
0.369674 0.929162i \(-0.379469\pi\)
\(354\) 0 0
\(355\) 3.58301 6.20595i 0.190166 0.329377i
\(356\) −2.70850 −0.143550
\(357\) 0 0
\(358\) −4.70850 −0.248852
\(359\) 10.2915 17.8254i 0.543165 0.940789i −0.455555 0.890208i \(-0.650559\pi\)
0.998720 0.0505814i \(-0.0161074\pi\)
\(360\) 0 0
\(361\) −4.50000 7.79423i −0.236842 0.410223i
\(362\) 2.64575 4.58258i 0.139058 0.240855i
\(363\) 0 0
\(364\) −10.5830 −0.554700
\(365\) 40.4575 2.11764
\(366\) 0 0
\(367\) −5.35425 9.27383i −0.279490 0.484090i 0.691768 0.722119i \(-0.256832\pi\)
−0.971258 + 0.238029i \(0.923499\pi\)
\(368\) −1.32288 2.29129i −0.0689597 0.119442i
\(369\) 0 0
\(370\) −3.41699 −0.177641
\(371\) −10.5830 −0.549442
\(372\) 0 0
\(373\) 7.90588 13.6934i 0.409351 0.709017i −0.585466 0.810697i \(-0.699088\pi\)
0.994817 + 0.101680i \(0.0324218\pi\)
\(374\) 1.50000 + 2.59808i 0.0775632 + 0.134343i
\(375\) 0 0
\(376\) −1.96863 + 3.40976i −0.101524 + 0.175845i
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −27.5830 −1.41684 −0.708422 0.705789i \(-0.750593\pi\)
−0.708422 + 0.705789i \(0.750593\pi\)
\(380\) 7.00000 12.1244i 0.359092 0.621966i
\(381\) 0 0
\(382\) 3.35425 + 5.80973i 0.171618 + 0.297252i
\(383\) 9.35425 16.2020i 0.477980 0.827885i −0.521702 0.853128i \(-0.674703\pi\)
0.999681 + 0.0252428i \(0.00803588\pi\)
\(384\) 0 0
\(385\) −3.50000 + 6.06218i −0.178377 + 0.308957i
\(386\) −15.8745 −0.807991
\(387\) 0 0
\(388\) 5.79150 + 10.0312i 0.294019 + 0.509256i
\(389\) 15.9686 + 27.6585i 0.809642 + 1.40234i 0.913112 + 0.407708i \(0.133672\pi\)
−0.103471 + 0.994632i \(0.532995\pi\)
\(390\) 0 0
\(391\) 7.93725 0.401404
\(392\) −3.50000 6.06218i −0.176777 0.306186i
\(393\) 0 0
\(394\) 10.9373 18.9439i 0.551011 0.954379i
\(395\) 14.0830 + 24.3925i 0.708593 + 1.22732i
\(396\) 0 0
\(397\) −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i \(-0.881443\pi\)
0.780870 + 0.624694i \(0.214776\pi\)
\(398\) −19.1660 −0.960705
\(399\) 0 0
\(400\) 2.00000 0.100000
\(401\) −17.9373 + 31.0682i −0.895744 + 1.55147i −0.0628623 + 0.998022i \(0.520023\pi\)
−0.832881 + 0.553451i \(0.813310\pi\)
\(402\) 0 0
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) 3.64575 6.31463i 0.181383 0.314164i
\(405\) 0 0
\(406\) 2.64575 + 4.58258i 0.131306 + 0.227429i
\(407\) −1.29150 −0.0640174
\(408\) 0 0
\(409\) −17.9373 31.0682i −0.886940 1.53623i −0.843474 0.537170i \(-0.819493\pi\)
−0.0434664 0.999055i \(-0.513840\pi\)
\(410\) −11.9059 20.6216i −0.587990 1.01843i
\(411\) 0 0
\(412\) −10.0000 −0.492665
\(413\) −17.4170 −0.857034
\(414\) 0 0
\(415\) −20.6144 + 35.7052i −1.01192 + 1.75270i
\(416\) 2.00000 + 3.46410i 0.0980581 + 0.169842i
\(417\) 0 0
\(418\) 2.64575 4.58258i 0.129408 0.224141i
\(419\) 9.87451 0.482401 0.241201 0.970475i \(-0.422459\pi\)
0.241201 + 0.970475i \(0.422459\pi\)
\(420\) 0 0
\(421\) 6.12549 0.298538 0.149269 0.988797i \(-0.452308\pi\)
0.149269 + 0.988797i \(0.452308\pi\)
\(422\) −10.6458 + 18.4390i −0.518227 + 0.897596i
\(423\) 0 0
\(424\) 2.00000 + 3.46410i 0.0971286 + 0.168232i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) −15.7915 27.3517i −0.764204 1.32364i
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 12.2915 + 21.2895i 0.592749 + 1.02667i
\(431\) −8.64575 14.9749i −0.416451 0.721315i 0.579128 0.815236i \(-0.303393\pi\)
−0.995580 + 0.0939217i \(0.970060\pi\)
\(432\) 0 0
\(433\) 1.58301 0.0760744 0.0380372 0.999276i \(-0.487889\pi\)
0.0380372 + 0.999276i \(0.487889\pi\)
\(434\) 5.29150 9.16515i 0.254000 0.439941i
\(435\) 0 0
\(436\) 1.96863 3.40976i 0.0942801 0.163298i
\(437\) −7.00000 12.1244i −0.334855 0.579987i
\(438\) 0 0
\(439\) 4.67712 8.10102i 0.223227 0.386640i −0.732559 0.680703i \(-0.761674\pi\)
0.955786 + 0.294063i \(0.0950076\pi\)
\(440\) 2.64575 0.126131
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −15.5830 + 26.9906i −0.740371 + 1.28236i 0.211956 + 0.977279i \(0.432017\pi\)
−0.952326 + 0.305081i \(0.901317\pi\)
\(444\) 0 0
\(445\) −3.58301 6.20595i −0.169851 0.294190i
\(446\) −14.2288 + 24.6449i −0.673751 + 1.16697i
\(447\) 0 0
\(448\) −1.32288 + 2.29129i −0.0625000 + 0.108253i
\(449\) −30.4575 −1.43738 −0.718689 0.695331i \(-0.755258\pi\)
−0.718689 + 0.695331i \(0.755258\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 6.29150 + 10.8972i 0.295927 + 0.512561i
\(453\) 0 0
\(454\) −2.41699 −0.113435
\(455\) −14.0000 24.2487i −0.656330 1.13680i
\(456\) 0 0
\(457\) 20.2915 35.1459i 0.949196 1.64406i 0.202074 0.979370i \(-0.435232\pi\)
0.747123 0.664686i \(-0.231435\pi\)
\(458\) −3.35425 5.80973i −0.156734 0.271471i
\(459\) 0 0
\(460\) 3.50000 6.06218i 0.163188 0.282650i
\(461\) 24.5830 1.14494 0.572472 0.819924i \(-0.305984\pi\)
0.572472 + 0.819924i \(0.305984\pi\)
\(462\) 0 0
\(463\) 39.0405 1.81437 0.907183 0.420735i \(-0.138228\pi\)
0.907183 + 0.420735i \(0.138228\pi\)
\(464\) 1.00000 1.73205i 0.0464238 0.0804084i
\(465\) 0 0
\(466\) 10.0830 + 17.4643i 0.467086 + 0.809017i
\(467\) 4.00000 6.92820i 0.185098 0.320599i −0.758512 0.651660i \(-0.774073\pi\)
0.943610 + 0.331061i \(0.107406\pi\)
\(468\) 0 0
\(469\) 20.0627 0.926412
\(470\) −10.4170 −0.480500
\(471\) 0 0
\(472\) 3.29150 + 5.70105i 0.151504 + 0.262412i
\(473\) 4.64575 + 8.04668i 0.213612 + 0.369987i
\(474\) 0 0
\(475\) 10.5830 0.485582
\(476\) −3.96863 6.87386i −0.181902 0.315063i
\(477\) 0 0
\(478\) 1.35425 2.34563i 0.0619419 0.107287i
\(479\) −16.9373 29.3362i −0.773883 1.34040i −0.935420 0.353538i \(-0.884979\pi\)
0.161537 0.986867i \(-0.448355\pi\)
\(480\) 0 0
\(481\) 2.58301 4.47390i 0.117775 0.203992i
\(482\) −27.1660 −1.23738
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −15.3229 + 26.5400i −0.695776 + 1.20512i
\(486\) 0 0
\(487\) −10.9373 18.9439i −0.495614 0.858429i 0.504373 0.863486i \(-0.331724\pi\)
−0.999987 + 0.00505681i \(0.998390\pi\)
\(488\) −5.96863 + 10.3380i −0.270187 + 0.467978i
\(489\) 0 0
\(490\) 9.26013 16.0390i 0.418330 0.724569i
\(491\) 1.00000 0.0451294 0.0225647 0.999745i \(-0.492817\pi\)
0.0225647 + 0.999745i \(0.492817\pi\)
\(492\) 0 0
\(493\) 3.00000 + 5.19615i 0.135113 + 0.234023i
\(494\) 10.5830 + 18.3303i 0.476152 + 0.824719i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −3.58301 + 6.20595i −0.160720 + 0.278375i
\(498\) 0 0
\(499\) 9.29150 16.0934i 0.415945 0.720437i −0.579582 0.814914i \(-0.696784\pi\)
0.995527 + 0.0944762i \(0.0301176\pi\)
\(500\) −3.96863 6.87386i −0.177482 0.307409i
\(501\) 0 0
\(502\) 11.6458 20.1710i 0.519775 0.900277i
\(503\) 1.29150 0.0575853 0.0287926 0.999585i \(-0.490834\pi\)
0.0287926 + 0.999585i \(0.490834\pi\)
\(504\) 0 0
\(505\) 19.2915 0.858461
\(506\) 1.32288 2.29129i 0.0588090 0.101860i
\(507\) 0 0
\(508\) −1.32288 2.29129i −0.0586931 0.101659i
\(509\) 12.5830 21.7944i 0.557732 0.966020i −0.439953 0.898021i \(-0.645005\pi\)
0.997685 0.0679994i \(-0.0216616\pi\)
\(510\) 0 0
\(511\) −40.4575 −1.78974
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 4.64575 + 8.04668i 0.204915 + 0.354924i
\(515\) −13.2288 22.9129i −0.582929 1.00966i
\(516\) 0 0
\(517\) −3.93725 −0.173160
\(518\) 3.41699 0.150134
\(519\) 0 0
\(520\) −5.29150 + 9.16515i −0.232048 + 0.401918i
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 0 0
\(523\) −1.35425 + 2.34563i −0.0592172 + 0.102567i −0.894114 0.447839i \(-0.852194\pi\)
0.834897 + 0.550406i \(0.185527\pi\)
\(524\) 18.5830 0.811802
\(525\) 0 0
\(526\) −21.8745 −0.953774
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 8.00000 + 13.8564i 0.347826 + 0.602452i
\(530\) −5.29150 + 9.16515i −0.229848 + 0.398109i
\(531\) 0 0
\(532\) −7.00000 + 12.1244i −0.303488 + 0.525657i
\(533\) 36.0000 1.55933
\(534\) 0 0
\(535\) −11.9059 20.6216i −0.514736 0.891549i
\(536\) −3.79150 6.56708i −0.163768 0.283654i
\(537\) 0 0
\(538\) 10.6458 0.458971
\(539\) 3.50000 6.06218i 0.150756 0.261116i
\(540\) 0 0
\(541\) −1.90588 + 3.30108i −0.0819402 + 0.141925i −0.904083 0.427356i \(-0.859445\pi\)
0.822143 + 0.569281i \(0.192778\pi\)
\(542\) −4.64575 8.04668i −0.199552 0.345634i
\(543\) 0 0
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) 10.4170 0.446215
\(546\) 0 0
\(547\) 14.7085 0.628890 0.314445 0.949276i \(-0.398182\pi\)
0.314445 + 0.949276i \(0.398182\pi\)
\(548\) −6.64575 + 11.5108i −0.283892 + 0.491716i
\(549\) 0 0
\(550\) 1.00000 + 1.73205i 0.0426401 + 0.0738549i
\(551\) 5.29150 9.16515i 0.225426 0.390449i
\(552\) 0 0
\(553\) −14.0830 24.3925i −0.598870 1.03727i
\(554\) −17.1660 −0.729314
\(555\) 0 0
\(556\) 6.29150 + 10.8972i 0.266819 + 0.462144i
\(557\) −9.64575 16.7069i −0.408704 0.707895i 0.586041 0.810281i \(-0.300686\pi\)
−0.994745 + 0.102386i \(0.967352\pi\)
\(558\) 0 0
\(559\) −37.1660 −1.57195
\(560\) −7.00000 −0.295804
\(561\) 0 0
\(562\) −1.50000 + 2.59808i −0.0632737 + 0.109593i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 0 0
\(565\) −16.6458 + 28.8313i −0.700292 + 1.21294i
\(566\) 30.4575 1.28022
\(567\) 0 0
\(568\) 2.70850 0.113646
\(569\) −7.58301 + 13.1342i −0.317896 + 0.550612i −0.980049 0.198757i \(-0.936310\pi\)
0.662153 + 0.749369i \(0.269643\pi\)
\(570\) 0 0
\(571\) 14.8745 + 25.7634i 0.622479 + 1.07816i 0.989023 + 0.147764i \(0.0472076\pi\)
−0.366544 + 0.930401i \(0.619459\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 11.9059 + 20.6216i 0.496942 + 0.860729i
\(575\) 5.29150 0.220671
\(576\) 0 0
\(577\) −11.3745 19.7012i −0.473527 0.820173i 0.526014 0.850476i \(-0.323686\pi\)
−0.999541 + 0.0303033i \(0.990353\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 0 0
\(580\) 5.29150 0.219718
\(581\) 20.6144 35.7052i 0.855229 1.48130i
\(582\) 0 0
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) 7.64575 + 13.2428i 0.316383 + 0.547992i
\(585\) 0 0
\(586\) −7.29150 + 12.6293i −0.301209 + 0.521710i
\(587\) −9.87451 −0.407565 −0.203782 0.979016i \(-0.565323\pi\)
−0.203782 + 0.979016i \(0.565323\pi\)
\(588\) 0 0
\(589\) −21.1660 −0.872130
\(590\) −8.70850 + 15.0836i −0.358523 + 0.620980i
\(591\) 0 0
\(592\) −0.645751 1.11847i −0.0265402 0.0459690i
\(593\) −12.8745 + 22.2993i −0.528693 + 0.915723i 0.470748 + 0.882268i \(0.343984\pi\)
−0.999440 + 0.0334546i \(0.989349\pi\)
\(594\) 0 0
\(595\) 10.5000 18.1865i 0.430458 0.745575i
\(596\) −19.8745 −0.814092
\(597\) 0 0
\(598\) 5.29150 + 9.16515i 0.216386 + 0.374791i
\(599\) 14.6771 + 25.4215i 0.599691 + 1.03870i 0.992866 + 0.119232i \(0.0380432\pi\)
−0.393175 + 0.919463i \(0.628623\pi\)
\(600\) 0 0
\(601\) −38.5830 −1.57383 −0.786917 0.617059i \(-0.788324\pi\)
−0.786917 + 0.617059i \(0.788324\pi\)
\(602\) −12.2915 21.2895i −0.500964 0.867696i
\(603\) 0 0
\(604\) −11.3229 + 19.6118i −0.460721 + 0.797993i
\(605\) 1.32288 + 2.29129i 0.0537825 + 0.0931541i
\(606\) 0 0
\(607\) 6.55163 11.3478i 0.265923 0.460591i −0.701882 0.712293i \(-0.747657\pi\)
0.967805 + 0.251702i \(0.0809901\pi\)
\(608\) 5.29150 0.214599
\(609\) 0 0
\(610\) −31.5830 −1.27876
\(611\) 7.87451 13.6390i 0.318568 0.551777i
\(612\) 0 0
\(613\) −3.90588 6.76518i −0.157757 0.273243i 0.776302 0.630361i \(-0.217093\pi\)
−0.934060 + 0.357117i \(0.883760\pi\)
\(614\) 5.70850 9.88741i 0.230376 0.399023i
\(615\) 0 0
\(616\) −2.64575 −0.106600
\(617\) 14.7085 0.592142 0.296071 0.955166i \(-0.404324\pi\)
0.296071 + 0.955166i \(0.404324\pi\)
\(618\) 0 0
\(619\) 20.5000 + 35.5070i 0.823965 + 1.42715i 0.902708 + 0.430254i \(0.141576\pi\)
−0.0787435 + 0.996895i \(0.525091\pi\)
\(620\) −5.29150 9.16515i −0.212512 0.368081i
\(621\) 0 0
\(622\) −22.5203 −0.902980
\(623\) 3.58301 + 6.20595i 0.143550 + 0.248636i
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) 10.2915 + 17.8254i 0.411331 + 0.712446i
\(627\) 0 0
\(628\) 0.354249 0.613577i 0.0141361 0.0244844i
\(629\) 3.87451 0.154487
\(630\) 0 0
\(631\) 41.8745 1.66700 0.833499 0.552521i \(-0.186334\pi\)
0.833499 + 0.552521i \(0.186334\pi\)
\(632\) −5.32288 + 9.21949i −0.211733 + 0.366732i
\(633\) 0 0
\(634\) 4.61438 + 7.99234i 0.183260 + 0.317416i
\(635\) 3.50000 6.06218i 0.138893 0.240570i
\(636\) 0 0
\(637\) 14.0000 + 24.2487i 0.554700 + 0.960769i
\(638\) 2.00000 0.0791808
\(639\) 0 0
\(640\) 1.32288 + 2.29129i 0.0522913 + 0.0905711i
\(641\) −13.2915 23.0216i −0.524983 0.909297i −0.999577 0.0290920i \(-0.990738\pi\)
0.474594 0.880205i \(-0.342595\pi\)
\(642\) 0 0
\(643\) −1.16601 −0.0459830 −0.0229915 0.999736i \(-0.507319\pi\)
−0.0229915 + 0.999736i \(0.507319\pi\)
\(644\) −3.50000 + 6.06218i −0.137919 + 0.238883i
\(645\) 0 0
\(646\) −7.93725 + 13.7477i −0.312287 + 0.540897i
\(647\) −13.1974 22.8585i −0.518843 0.898662i −0.999760 0.0218961i \(-0.993030\pi\)
0.480918 0.876766i \(-0.340304\pi\)
\(648\) 0 0
\(649\) −3.29150 + 5.70105i −0.129203 + 0.223786i
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) −5.58301 −0.218647
\(653\) −22.5516 + 39.0606i −0.882514 + 1.52856i −0.0339763 + 0.999423i \(0.510817\pi\)
−0.848537 + 0.529136i \(0.822516\pi\)
\(654\) 0 0
\(655\) 24.5830 + 42.5790i 0.960537 + 1.66370i
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 0 0
\(658\) 10.4170 0.406097
\(659\) 24.1660 0.941374 0.470687 0.882300i \(-0.344006\pi\)
0.470687 + 0.882300i \(0.344006\pi\)
\(660\) 0 0
\(661\) −10.3542 17.9341i −0.402734 0.697555i 0.591321 0.806436i \(-0.298607\pi\)
−0.994055 + 0.108881i \(0.965273\pi\)
\(662\) −6.50000 11.2583i −0.252630 0.437567i
\(663\) 0 0
\(664\) −15.5830 −0.604738
\(665\) −37.0405 −1.43637
\(666\) 0 0
\(667\) 2.64575 4.58258i 0.102444 0.177438i
\(668\) 4.35425 + 7.54178i 0.168471 + 0.291800i
\(669\) 0 0
\(670\) 10.0314 17.3748i 0.387546 0.671249i
\(671\) −11.9373 −0.460833
\(672\) 0 0
\(673\) −19.4170 −0.748470 −0.374235 0.927334i \(-0.622095\pi\)
−0.374235 + 0.927334i \(0.622095\pi\)
\(674\) −3.35425 + 5.80973i −0.129201 + 0.223782i
\(675\) 0 0
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) −4.06275 + 7.03688i −0.156144 + 0.270449i −0.933475 0.358642i \(-0.883240\pi\)
0.777331 + 0.629092i \(0.216573\pi\)
\(678\) 0 0
\(679\) 15.3229 26.5400i 0.588038 1.01851i
\(680\) −7.93725 −0.304380
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −8.58301 14.8662i −0.328420 0.568839i 0.653779 0.756686i \(-0.273183\pi\)
−0.982198 + 0.187846i \(0.939849\pi\)
\(684\) 0 0
\(685\) −35.1660 −1.34362
\(686\) −9.26013 + 16.0390i −0.353553 + 0.612372i
\(687\) 0 0
\(688\) −4.64575 + 8.04668i −0.177118 + 0.306777i
\(689\) −8.00000 13.8564i −0.304776 0.527887i
\(690\) 0 0
\(691\) −7.08301 + 12.2681i −0.269450 + 0.466701i −0.968720 0.248156i \(-0.920175\pi\)
0.699270 + 0.714858i \(0.253509\pi\)
\(692\) −4.00000 −0.152057
\(693\) 0 0
\(694\) −29.5830 −1.12296
\(695\) −16.6458 + 28.8313i −0.631409 + 1.09363i
\(696\) 0 0
\(697\) 13.5000 + 23.3827i 0.511349 + 0.885682i
\(698\) 6.61438 11.4564i 0.250358 0.433633i
\(699\) 0 0
\(700\) −2.64575 4.58258i −0.100000 0.173205i
\(701\) −42.4575 −1.60360 −0.801799 0.597594i \(-0.796124\pi\)
−0.801799 + 0.597594i \(0.796124\pi\)
\(702\) 0 0
\(703\) −3.41699 5.91841i −0.128874 0.223217i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 23.2915 0.876587
\(707\) −19.2915 −0.725532
\(708\) 0 0
\(709\) −7.87451 + 13.6390i −0.295733 + 0.512225i −0.975155 0.221523i \(-0.928897\pi\)
0.679422 + 0.733748i \(0.262231\pi\)
\(710\) 3.58301 + 6.20595i 0.134468 + 0.232905i
\(711\) 0 0
\(712\) 1.35425 2.34563i 0.0507526 0.0879061i
\(713\) −10.5830 −0.396337
\(714\) 0 0
\(715\) −10.5830 −0.395782
\(716\) 2.35425 4.07768i 0.0879824 0.152390i
\(717\) 0 0
\(718\) 10.2915 + 17.8254i 0.384075 + 0.665238i
\(719\) −14.0314 + 24.3031i −0.523282 + 0.906351i 0.476351 + 0.879255i \(0.341959\pi\)
−0.999633 + 0.0270956i \(0.991374\pi\)
\(720\) 0 0
\(721\) 13.2288 + 22.9129i 0.492665 + 0.853320i
\(722\) 9.00000 0.334945
\(723\) 0 0
\(724\) 2.64575 + 4.58258i 0.0983286 + 0.170310i
\(725\) 2.00000 + 3.46410i 0.0742781 + 0.128654i
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 5.29150 9.16515i 0.196116 0.339683i
\(729\) 0 0
\(730\) −20.2288 + 35.0372i −0.748700 + 1.29679i
\(731\) −13.9373 24.1400i −0.515488 0.892851i
\(732\) 0 0
\(733\) −5.96863 + 10.3380i −0.220456 + 0.381841i −0.954947 0.296778i \(-0.904088\pi\)
0.734490 + 0.678619i \(0.237421\pi\)
\(734\) 10.7085 0.395258
\(735\) 0 0
\(736\) 2.64575 0.0975237
\(737\) 3.79150 6.56708i 0.139662 0.241901i
\(738\) 0 0
\(739\) 12.2915 + 21.2895i 0.452150 + 0.783147i 0.998519 0.0543973i \(-0.0173238\pi\)
−0.546369 + 0.837544i \(0.683990\pi\)
\(740\) 1.70850 2.95920i 0.0628056 0.108783i
\(741\) 0 0
\(742\) 5.29150 9.16515i 0.194257 0.336463i
\(743\) 18.7085 0.686348 0.343174 0.939272i \(-0.388498\pi\)
0.343174 + 0.939272i \(0.388498\pi\)
\(744\) 0 0
\(745\) −26.2915 45.5382i −0.963246 1.66839i
\(746\) 7.90588 + 13.6934i 0.289455 + 0.501351i
\(747\) 0 0
\(748\) −3.00000 −0.109691
\(749\) 11.9059 + 20.6216i 0.435031 + 0.753497i
\(750\) 0 0
\(751\) 14.6458 25.3672i 0.534431 0.925662i −0.464760 0.885437i \(-0.653859\pi\)
0.999191 0.0402248i \(-0.0128074\pi\)
\(752\) −1.96863 3.40976i −0.0717884 0.124341i
\(753\) 0 0
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) −59.9150 −2.18053
\(756\) 0 0
\(757\) −32.5830 −1.18425 −0.592125 0.805846i \(-0.701711\pi\)
−0.592125 + 0.805846i \(0.701711\pi\)
\(758\) 13.7915 23.8876i 0.500930 0.867636i
\(759\) 0 0
\(760\) 7.00000 + 12.1244i 0.253917 + 0.439797i
\(761\) 23.7915 41.2081i 0.862441 1.49379i −0.00712426 0.999975i \(-0.502268\pi\)
0.869566 0.493818i \(-0.164399\pi\)
\(762\) 0 0
\(763\) −10.4170 −0.377121
\(764\) −6.70850 −0.242705
\(765\) 0 0
\(766\) 9.35425 + 16.2020i 0.337983 + 0.585403i
\(767\) −13.1660 22.8042i −0.475397 0.823412i
\(768\) 0 0
\(769\) −30.7085 −1.10738 −0.553688 0.832724i \(-0.686780\pi\)
−0.553688 + 0.832724i \(0.686780\pi\)
\(770\) −3.50000 6.06218i −0.126131 0.218466i
\(771\) 0 0
\(772\) 7.93725 13.7477i 0.285668 0.494792i
\(773\) −4.03137 6.98254i −0.144998 0.251145i 0.784374 0.620288i \(-0.212984\pi\)
−0.929372 + 0.369144i \(0.879651\pi\)
\(774\) 0 0
\(775\) 4.00000 6.92820i 0.143684 0.248868i
\(776\) −11.5830 −0.415806
\(777\) 0 0
\(778\) −31.9373 −1.14501
\(779\) 23.8118 41.2432i 0.853145 1.47769i
\(780\) 0 0
\(781\) 1.35425 + 2.34563i 0.0484588 + 0.0839332i
\(782\) −3.96863 + 6.87386i −0.141918 + 0.245809i
\(783\) 0 0
\(784\) 7.00000 0.250000
\(785\) 1.87451 0.0669041
\(786\) 0 0
\(787\) −4.64575 8.04668i −0.165603 0.286833i 0.771266 0.636513i \(-0.219624\pi\)
−0.936869 + 0.349680i \(0.886290\pi\)
\(788\) 10.9373 + 18.9439i 0.389624 + 0.674848i
\(789\) 0 0
\(790\) −28.1660 −1.00210
\(791\) 16.6458 28.8313i 0.591855 1.02512i
\(792\) 0 0
\(793\) 23.8745 41.3519i 0.847809 1.46845i
\(794\) −3.00000 5.19615i −0.106466 0.184405i
\(795\) 0 0
\(796\) 9.58301 16.5983i 0.339661 0.588309i
\(797\) −45.1033 −1.59764 −0.798820 0.601570i \(-0.794542\pi\)
−0.798820 + 0.601570i \(0.794542\pi\)
\(798\) 0 0
\(799\) 11.8118 0.417870
\(800\) −1.00000 + 1.73205i −0.0353553 + 0.0612372i
\(801\) 0 0
\(802\) −17.9373 31.0682i −0.633386 1.09706i
\(803\) −7.64575 + 13.2428i −0.269813 + 0.467329i
\(804\) 0 0
\(805\) −18.5203 −0.652753
\(806\) 16.0000 0.563576
\(807\) 0 0
\(808\) 3.64575 + 6.31463i 0.128257 + 0.222148i
\(809\) 22.6660 + 39.2587i 0.796894 + 1.38026i 0.921629 + 0.388072i \(0.126859\pi\)
−0.124735 + 0.992190i \(0.539808\pi\)
\(810\) 0 0
\(811\) 16.5830 0.582308 0.291154 0.956676i \(-0.405961\pi\)
0.291154 + 0.956676i \(0.405961\pi\)
\(812\) −5.29150 −0.185695
\(813\) 0 0
\(814\) 0.645751 1.11847i 0.0226336 0.0392025i
\(815\) −7.38562 12.7923i −0.258707 0.448094i
\(816\) 0 0
\(817\) −24.5830 + 42.5790i −0.860050 + 1.48965i
\(818\) 35.8745 1.25432
\(819\) 0 0
\(820\) 23.8118 0.831543
\(821\) −15.1660 + 26.2683i −0.529297 + 0.916770i 0.470119 + 0.882603i \(0.344211\pi\)
−0.999416 + 0.0341668i \(0.989122\pi\)
\(822\) 0 0
\(823\) 6.06275 + 10.5010i 0.211334 + 0.366041i 0.952132 0.305686i \(-0.0988859\pi\)
−0.740798 + 0.671728i \(0.765553\pi\)
\(824\) 5.00000 8.66025i 0.174183 0.301694i
\(825\) 0 0
\(826\) 8.70850 15.0836i 0.303007 0.524824i
\(827\) −35.3320 −1.22861 −0.614307 0.789067i \(-0.710565\pi\)
−0.614307 + 0.789067i \(0.710565\pi\)
\(828\) 0 0
\(829\) −9.93725 17.2118i −0.345135 0.597792i 0.640243 0.768172i \(-0.278834\pi\)
−0.985378 + 0.170381i \(0.945500\pi\)
\(830\) −20.6144 35.7052i −0.715536 1.23934i
\(831\) 0 0
\(832\) −4.00000 −0.138675
\(833\) −10.5000 + 18.1865i −0.363803 + 0.630126i
\(834\) 0 0
\(835\) −11.5203 + 19.9537i −0.398675 + 0.690525i
\(836\) 2.64575 + 4.58258i 0.0915052 + 0.158492i
\(837\) 0 0
\(838\) −4.93725 + 8.55157i −0.170555 + 0.295409i
\(839\) 37.1033 1.28095 0.640473 0.767980i \(-0.278738\pi\)
0.640473 + 0.767980i \(0.278738\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −3.06275 + 5.30483i −0.105549 + 0.182817i
\(843\) 0 0
\(844\) −10.6458 18.4390i −0.366442 0.634696i
\(845\) 3.96863 6.87386i 0.136525 0.236468i
\(846\) 0 0
\(847\) −1.32288 2.29129i −0.0454545 0.0787296i
\(848\) −4.00000 −0.137361
\(849\) 0 0
\(850\) −3.00000 5.19615i −0.102899 0.178227i
\(851\) −1.70850 2.95920i −0.0585665 0.101440i
\(852\) 0 0
\(853\) 14.5203 0.497164 0.248582 0.968611i \(-0.420035\pi\)
0.248582 + 0.968611i \(0.420035\pi\)
\(854\) 31.5830 1.08075
\(855\) 0 0
\(856\) 4.50000 7.79423i 0.153807 0.266401i
\(857\) 4.91699 + 8.51648i 0.167961 + 0.290918i 0.937703 0.347438i \(-0.112948\pi\)
−0.769742 + 0.638356i \(0.779615\pi\)
\(858\) 0 0
\(859\) −24.3745 + 42.2179i −0.831647 + 1.44046i 0.0650836 + 0.997880i \(0.479269\pi\)
−0.896731 + 0.442576i \(0.854065\pi\)
\(860\) −24.5830 −0.838274
\(861\) 0 0
\(862\) 17.2915 0.588951
\(863\) −16.5516 + 28.6683i −0.563424 + 0.975879i 0.433770 + 0.901024i \(0.357183\pi\)
−0.997194 + 0.0748557i \(0.976150\pi\)
\(864\) 0 0
\(865\) −5.29150 9.16515i −0.179916 0.311624i
\(866\) −0.791503 + 1.37092i −0.0268964 + 0.0465859i
\(867\) 0 0
\(868\) 5.29150 + 9.16515i 0.179605 + 0.311086i
\(869\) −10.6458 −0.361132
\(870\) 0 0
\(871\) 15.1660 + 26.2683i 0.513881 + 0.890067i
\(872\) 1.96863 + 3.40976i 0.0666661 + 0.115469i
\(873\) 0 0
\(874\) 14.0000 0.473557
\(875\) −10.5000 + 18.1865i −0.354965 + 0.614817i
\(876\) 0 0
\(877\) −5.38562 + 9.32817i −0.181860 + 0.314990i −0.942514 0.334167i \(-0.891545\pi\)
0.760654 + 0.649157i \(0.224878\pi\)
\(878\) 4.67712 + 8.10102i 0.157845 + 0.273396i
\(879\) 0 0
\(880\) −1.32288 + 2.29129i −0.0445941 + 0.0772393i
\(881\) −23.1660 −0.780483 −0.390241 0.920713i \(-0.627608\pi\)
−0.390241 + 0.920713i \(0.627608\pi\)
\(882\) 0 0
\(883\) −34.4170 −1.15822 −0.579112 0.815248i \(-0.696601\pi\)
−0.579112 + 0.815248i \(0.696601\pi\)
\(884\) 6.00000 10.3923i 0.201802 0.349531i
\(885\) 0 0
\(886\) −15.5830 26.9906i −0.523521 0.906765i
\(887\) −15.5203 + 26.8819i −0.521119 + 0.902605i 0.478579 + 0.878044i \(0.341152\pi\)
−0.999698 + 0.0245606i \(0.992181\pi\)
\(888\) 0 0
\(889\) −3.50000 + 6.06218i −0.117386 + 0.203319i
\(890\) 7.16601 0.240205
\(891\) 0 0
\(892\) −14.2288 24.6449i −0.476414 0.825173i
\(893\) −10.4170 18.0428i −0.348591 0.603778i
\(894\) 0 0
\(895\) 12.4575 0.416409
\(896\) −1.32288 2.29129i −0.0441942 0.0765466i
\(897\) 0 0
\(898\) 15.2288 26.3770i 0.508190 0.880211i
\(899\) −4.00000 6.92820i −0.133407 0.231069i
\(900\) 0 0
\(901\) 6.00000 10.3923i 0.199889 0.346218i
\(902\) 9.00000 0.299667
\(903\) 0 0
\(904\) −12.5830 −0.418505
\(905\) −7.00000 + 12.1244i −0.232688 + 0.403027i
\(906\) 0 0
\(907\) 7.91699 + 13.7126i 0.262879 + 0.455321i 0.967006 0.254754i \(-0.0819945\pi\)
−0.704126 + 0.710075i \(0.748661\pi\)
\(908\) 1.20850 2.09318i 0.0401054 0.0694646i
\(909\) 0 0
\(910\) 28.0000 0.928191
\(911\) 18.3948 0.609446 0.304723 0.952441i \(-0.401436\pi\)
0.304723 + 0.952441i \(0.401436\pi\)
\(912\) 0 0
\(913\) −7.79150 13.4953i −0.257861 0.446629i
\(914\) 20.2915 + 35.1459i 0.671183 + 1.16252i
\(915\) 0 0
\(916\) 6.70850 0.221655
\(917\) −24.5830 42.5790i −0.811802 1.40608i
\(918\) 0 0
\(919\) −4.67712 + 8.10102i −0.154284 + 0.267228i −0.932798 0.360399i \(-0.882640\pi\)
0.778514 + 0.627627i \(0.215974\pi\)
\(920\) 3.50000 + 6.06218i 0.115392 + 0.199864i
\(921\) 0 0
\(922\) −12.2915 + 21.2895i −0.404799 + 0.701133i
\(923\) −10.8340 −0.356605
\(924\) 0 0
\(925\) 2.58301 0.0849287
\(926\) −19.5203 + 33.8101i −0.641476 + 1.11107i
\(927\) 0 0
\(928\) 1.00000 + 1.73205i 0.0328266 + 0.0568574i
\(929\) −17.2288 + 29.8411i −0.565257 + 0.979054i 0.431769 + 0.901984i \(0.357890\pi\)
−0.997026 + 0.0770697i \(0.975444\pi\)
\(930\) 0 0
\(931\) 37.0405 1.21395
\(932\) −20.1660 −0.660560
\(933\) 0 0
\(934\) 4.00000 + 6.92820i 0.130884 + 0.226698i
\(935\) −3.96863 6.87386i −0.129788 0.224799i
\(936\) 0 0
\(937\) 50.0000 1.63343 0.816714 0.577042i \(-0.195793\pi\)
0.816714 + 0.577042i \(0.195793\pi\)
\(938\) −10.0314 + 17.3748i −0.327536 + 0.567309i
\(939\) 0 0
\(940\) 5.20850 9.02138i 0.169882 0.294245i
\(941\) 1.70850 + 2.95920i 0.0556954 + 0.0964673i 0.892529 0.450990i \(-0.148929\pi\)
−0.836833 + 0.547458i \(0.815596\pi\)
\(942\) 0 0
\(943\) 11.9059 20.6216i 0.387709 0.671531i
\(944\) −6.58301 −0.214259
\(945\) 0 0
\(946\) −9.29150 −0.302093
\(947\) −7.70850 + 13.3515i −0.250493 + 0.433866i −0.963662 0.267126i \(-0.913926\pi\)
0.713169 + 0.700992i \(0.247259\pi\)
\(948\) 0 0
\(949\) −30.5830 52.9713i −0.992766 1.71952i
\(950\) −5.29150 + 9.16515i −0.171679 + 0.297357i
\(951\) 0 0
\(952\) 7.93725 0.257248
\(953\) −26.7490 −0.866486 −0.433243 0.901277i \(-0.642631\pi\)
−0.433243 + 0.901277i \(0.642631\pi\)
\(954\) 0 0
\(955\) −8.87451 15.3711i −0.287172 0.497397i
\(956\) 1.35425 + 2.34563i 0.0437995 + 0.0758630i
\(957\) 0 0
\(958\) 33.8745 1.09444
\(959\) 35.1660 1.13557
\(960\) 0 0
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) 2.58301 + 4.47390i 0.0832794 + 0.144244i
\(963\) 0 0
\(964\) 13.5830 23.5265i 0.437479 0.757736i
\(965\) 42.0000 1.35203
\(966\) 0 0
\(967\) 40.0627 1.28833 0.644166 0.764886i \(-0.277205\pi\)
0.644166 + 0.764886i \(0.277205\pi\)
\(968\) −0.500000 + 0.866025i −0.0160706 + 0.0278351i
\(969\) 0 0
\(970\) −15.3229 26.5400i −0.491988 0.852148i
\(971\) 3.00000 5.19615i 0.0962746 0.166752i −0.813865 0.581054i \(-0.802641\pi\)
0.910140 + 0.414301i \(0.135974\pi\)
\(972\) 0 0
\(973\) 16.6458 28.8313i 0.533638 0.924289i
\(974\) 21.8745 0.700904
\(975\) 0 0
\(976\) −5.96863 10.3380i −0.191051 0.330910i
\(977\) 6.58301 + 11.4021i 0.210609 + 0.364785i 0.951905 0.306392i \(-0.0991220\pi\)
−0.741296 + 0.671178i \(0.765789\pi\)
\(978\) 0 0
\(979\) 2.70850 0.0865640
\(980\) 9.26013 + 16.0390i 0.295804 + 0.512348i
\(981\) 0 0
\(982\) −0.500000 + 0.866025i −0.0159556 + 0.0276360i
\(983\) 21.2601 + 36.8236i 0.678093 + 1.17449i 0.975555 + 0.219757i \(0.0705266\pi\)
−0.297462 + 0.954734i \(0.596140\pi\)
\(984\) 0 0
\(985\) −28.9373 + 50.1208i −0.922018 + 1.59698i
\(986\) −6.00000 −0.191079
\(987\) 0 0
\(988\) −21.1660 −0.673380
\(989\) −12.2915 + 21.2895i −0.390847 + 0.676967i
\(990\) 0 0
\(991\) 21.9373 + 37.9964i 0.696860 + 1.20700i 0.969550 + 0.244895i \(0.0787534\pi\)
−0.272690 + 0.962102i \(0.587913\pi\)
\(992\) 2.00000 3.46410i 0.0635001 0.109985i
\(993\) 0 0
\(994\) −3.58301 6.20595i −0.113646 0.196841i
\(995\) 50.7085 1.60757
\(996\) 0 0
\(997\) −3.41699 5.91841i −0.108217 0.187438i 0.806831 0.590783i \(-0.201181\pi\)
−0.915048 + 0.403345i \(0.867848\pi\)
\(998\) 9.29150 + 16.0934i 0.294117 + 0.509426i
\(999\) 0 0
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 1386.2.k.r.793.2 4
3.2 odd 2 462.2.i.e.331.1 yes 4
7.2 even 3 9702.2.a.db.1.1 2
7.4 even 3 inner 1386.2.k.r.991.2 4
7.5 odd 6 9702.2.a.dm.1.2 2
21.2 odd 6 3234.2.a.w.1.2 2
21.5 even 6 3234.2.a.ba.1.1 2
21.11 odd 6 462.2.i.e.67.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.e.67.1 4 21.11 odd 6
462.2.i.e.331.1 yes 4 3.2 odd 2
1386.2.k.r.793.2 4 1.1 even 1 trivial
1386.2.k.r.991.2 4 7.4 even 3 inner
3234.2.a.w.1.2 2 21.2 odd 6
3234.2.a.ba.1.1 2 21.5 even 6
9702.2.a.db.1.1 2 7.2 even 3
9702.2.a.dm.1.2 2 7.5 odd 6