Properties

Label 1014.2.i.e.361.1
Level $1014$
Weight $2$
Character 1014.361
Analytic conductor $8.097$
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] = [1014,2,Mod(361,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (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: \(8.09683076496\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.361
Dual form 1014.2.i.e.823.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.73205 + 1.00000i) q^{11} +1.00000 q^{12} +2.00000 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} -1.00000i q^{18} +(1.73205 + 1.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.00000 q^{25} -1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(4.50000 + 7.79423i) q^{29} +(-0.500000 + 0.866025i) q^{30} -4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +5.00000i q^{34} +(-1.00000 + 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{36} +(9.52628 - 5.50000i) q^{37} -2.00000 q^{38} +1.00000 q^{40} +(4.33013 - 2.50000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(5.00000 - 8.66025i) q^{43} +2.00000i q^{44} +(0.866025 + 0.500000i) q^{45} +(-5.19615 - 3.00000i) q^{46} -2.00000i q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-3.46410 + 2.00000i) q^{50} +5.00000 q^{51} -1.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{55} +(1.00000 - 1.73205i) q^{56} +2.00000i q^{57} +(-7.79423 - 4.50000i) q^{58} +(-6.92820 - 4.00000i) q^{59} -1.00000i q^{60} +(5.50000 - 9.52628i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(-3.00000 + 5.19615i) q^{69} -2.00000i q^{70} +(12.1244 + 7.00000i) q^{71} +(-0.866025 - 0.500000i) q^{72} +13.0000i q^{73} +(-5.50000 + 9.52628i) q^{74} +(2.00000 + 3.46410i) q^{75} +(1.73205 - 1.00000i) q^{76} +4.00000 q^{77} -4.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50000 + 4.33013i) q^{82} +6.00000i q^{83} +(-1.73205 - 1.00000i) q^{84} +(-4.33013 - 2.50000i) q^{85} +10.0000i q^{86} +(-4.50000 + 7.79423i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(-1.73205 + 1.00000i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(3.46410 - 2.00000i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.00000 - 1.73205i) q^{95} +1.00000i q^{96} +(1.73205 + 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} + 4 q^{12} + 8 q^{14} - 2 q^{16} + 10 q^{17} + 4 q^{22} + 12 q^{23} + 16 q^{25} - 4 q^{27} + 18 q^{29} - 2 q^{30} - 4 q^{35} + 2 q^{36} - 8 q^{38} + 4 q^{40} + 4 q^{42} + 20 q^{43} + 2 q^{48} - 6 q^{49} + 20 q^{51} - 4 q^{53} + 4 q^{55} + 4 q^{56} + 22 q^{61} + 8 q^{62} - 4 q^{64} + 8 q^{66} - 10 q^{68} - 12 q^{69} - 22 q^{74} + 8 q^{75} + 16 q^{77} - 16 q^{79} - 2 q^{81} - 10 q^{82} - 18 q^{87} - 4 q^{88} - 4 q^{90} + 24 q^{92} + 4 q^{94} + 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i −0.974679 0.223607i \(-0.928217\pi\)
0.974679 0.223607i \(-0.0717831\pi\)
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −1.73205 1.00000i −0.654654 0.377964i 0.135583 0.990766i \(-0.456709\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −1.73205 + 1.00000i −0.522233 + 0.301511i −0.737848 0.674967i \(-0.764158\pi\)
0.215615 + 0.976478i \(0.430824\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 2.00000 0.534522
\(15\) 0.866025 0.500000i 0.223607 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i \(-0.625971\pi\)
0.991838 0.127502i \(-0.0406959\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.73205 + 1.00000i 0.397360 + 0.229416i 0.685344 0.728219i \(-0.259652\pi\)
−0.287984 + 0.957635i \(0.592985\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 2.00000i 0.436436i
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.73205 + 1.00000i −0.327327 + 0.188982i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 5.00000i 0.857493i
\(35\) −1.00000 + 1.73205i −0.169031 + 0.292770i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 9.52628 5.50000i 1.56611 0.904194i 0.569495 0.821995i \(-0.307139\pi\)
0.996616 0.0821995i \(-0.0261945\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 4.33013 2.50000i 0.676252 0.390434i −0.122189 0.992507i \(-0.538991\pi\)
0.798441 + 0.602072i \(0.205658\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0.866025 + 0.500000i 0.129099 + 0.0745356i
\(46\) −5.19615 3.00000i −0.766131 0.442326i
\(47\) 2.00000i 0.291730i −0.989305 0.145865i \(-0.953403\pi\)
0.989305 0.145865i \(-0.0465965\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) −3.46410 + 2.00000i −0.489898 + 0.282843i
\(51\) 5.00000 0.700140
\(52\) 0 0
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 2.00000i 0.264906i
\(58\) −7.79423 4.50000i −1.02343 0.590879i
\(59\) −6.92820 4.00000i −0.901975 0.520756i −0.0241347 0.999709i \(-0.507683\pi\)
−0.877841 + 0.478953i \(0.841016\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i \(-0.584638\pi\)
0.966978 0.254858i \(-0.0820288\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 1.73205 1.00000i 0.218218 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 2.00000 0.246183
\(67\) 1.73205 1.00000i 0.211604 0.122169i −0.390453 0.920623i \(-0.627682\pi\)
0.602056 + 0.798454i \(0.294348\pi\)
\(68\) −2.50000 4.33013i −0.303170 0.525105i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 2.00000i 0.239046i
\(71\) 12.1244 + 7.00000i 1.43890 + 0.830747i 0.997773 0.0666994i \(-0.0212469\pi\)
0.441123 + 0.897447i \(0.354580\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 13.0000i 1.52153i 0.649025 + 0.760767i \(0.275177\pi\)
−0.649025 + 0.760767i \(0.724823\pi\)
\(74\) −5.50000 + 9.52628i −0.639362 + 1.10741i
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) 1.73205 1.00000i 0.198680 0.114708i
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −1.73205 1.00000i −0.188982 0.109109i
\(85\) −4.33013 2.50000i −0.469668 0.271163i
\(86\) 10.0000i 1.07833i
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) −1.73205 + 1.00000i −0.183597 + 0.106000i −0.588982 0.808146i \(-0.700471\pi\)
0.405385 + 0.914146i \(0.367138\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 3.46410 2.00000i 0.359211 0.207390i
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 1.00000i 0.102062i
\(97\) 1.73205 + 1.00000i 0.175863 + 0.101535i 0.585348 0.810782i \(-0.300958\pi\)
−0.409484 + 0.912317i \(0.634291\pi\)
\(98\) 2.59808 + 1.50000i 0.262445 + 0.151523i
\(99\) 2.00000i 0.201008i
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −2.50000 4.33013i −0.248759 0.430864i 0.714423 0.699715i \(-0.246689\pi\)
−0.963182 + 0.268851i \(0.913356\pi\)
\(102\) −4.33013 + 2.50000i −0.428746 + 0.247537i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 0.866025 0.500000i 0.0841158 0.0485643i
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) −1.73205 1.00000i −0.165145 0.0953463i
\(111\) 9.52628 + 5.50000i 0.904194 + 0.522037i
\(112\) 2.00000i 0.188982i
\(113\) 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i \(-0.788267\pi\)
0.927914 + 0.372794i \(0.121600\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 5.19615 3.00000i 0.484544 0.279751i
\(116\) 9.00000 0.835629
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) −8.66025 + 5.00000i −0.793884 + 0.458349i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 11.0000i 0.995893i
\(123\) 4.33013 + 2.50000i 0.390434 + 0.225417i
\(124\) −3.46410 2.00000i −0.311086 0.179605i
\(125\) 9.00000i 0.804984i
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −6.00000 10.3923i −0.532414 0.922168i −0.999284 0.0378419i \(-0.987952\pi\)
0.466870 0.884326i \(-0.345382\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −1.73205 + 1.00000i −0.150756 + 0.0870388i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) −1.00000 + 1.73205i −0.0863868 + 0.149626i
\(135\) 1.00000i 0.0860663i
\(136\) 4.33013 + 2.50000i 0.371305 + 0.214373i
\(137\) 14.7224 + 8.50000i 1.25782 + 0.726204i 0.972651 0.232273i \(-0.0746161\pi\)
0.285171 + 0.958477i \(0.407949\pi\)
\(138\) 6.00000i 0.510754i
\(139\) 6.00000 10.3923i 0.508913 0.881464i −0.491033 0.871141i \(-0.663381\pi\)
0.999947 0.0103230i \(-0.00328598\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 1.73205 1.00000i 0.145865 0.0842152i
\(142\) −14.0000 −1.17485
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 7.79423 4.50000i 0.647275 0.373705i
\(146\) −6.50000 11.2583i −0.537944 0.931746i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) 11.0000i 0.904194i
\(149\) −2.59808 1.50000i −0.212843 0.122885i 0.389789 0.920904i \(-0.372548\pi\)
−0.602632 + 0.798019i \(0.705881\pi\)
\(150\) −3.46410 2.00000i −0.282843 0.163299i
\(151\) 6.00000i 0.488273i 0.969741 + 0.244137i \(0.0785045\pi\)
−0.969741 + 0.244137i \(0.921495\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 2.50000 + 4.33013i 0.202113 + 0.350070i
\(154\) −3.46410 + 2.00000i −0.279145 + 0.161165i
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 3.46410 2.00000i 0.275589 0.159111i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 12.0000i 0.945732i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 17.3205 + 10.0000i 1.35665 + 0.783260i 0.989170 0.146772i \(-0.0468885\pi\)
0.367477 + 0.930033i \(0.380222\pi\)
\(164\) 5.00000i 0.390434i
\(165\) −1.00000 + 1.73205i −0.0778499 + 0.134840i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −20.7846 + 12.0000i −1.60836 + 0.928588i −0.618624 + 0.785687i \(0.712310\pi\)
−0.989737 + 0.142901i \(0.954357\pi\)
\(168\) 2.00000 0.154303
\(169\) 0 0
\(170\) 5.00000 0.383482
\(171\) −1.73205 + 1.00000i −0.132453 + 0.0764719i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 9.00000i 0.682288i
\(175\) −6.92820 4.00000i −0.523723 0.302372i
\(176\) 1.73205 + 1.00000i 0.130558 + 0.0753778i
\(177\) 8.00000i 0.601317i
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 11.0000 0.813143
\(184\) −5.19615 + 3.00000i −0.383065 + 0.221163i
\(185\) −5.50000 9.52628i −0.404368 0.700386i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 10.0000i 0.731272i
\(188\) −1.73205 1.00000i −0.126323 0.0729325i
\(189\) 1.73205 + 1.00000i 0.125988 + 0.0727393i
\(190\) 2.00000i 0.145095i
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 14.7224 8.50000i 1.05974 0.611843i 0.134382 0.990930i \(-0.457095\pi\)
0.925361 + 0.379086i \(0.123762\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 5.19615 3.00000i 0.370211 0.213741i −0.303340 0.952882i \(-0.598102\pi\)
0.673550 + 0.739141i \(0.264768\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 1.73205 + 1.00000i 0.122169 + 0.0705346i
\(202\) 4.33013 + 2.50000i 0.304667 + 0.175899i
\(203\) 18.0000i 1.26335i
\(204\) 2.50000 4.33013i 0.175035 0.303170i
\(205\) −2.50000 4.33013i −0.174608 0.302429i
\(206\) 8.66025 5.00000i 0.603388 0.348367i
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 1.73205 1.00000i 0.119523 0.0690066i
\(211\) −12.0000 20.7846i −0.826114 1.43087i −0.901065 0.433684i \(-0.857213\pi\)
0.0749508 0.997187i \(-0.476120\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 14.0000i 0.959264i
\(214\) −15.5885 9.00000i −1.06561 0.615227i
\(215\) −8.66025 5.00000i −0.590624 0.340997i
\(216\) 1.00000i 0.0680414i
\(217\) −4.00000 + 6.92820i −0.271538 + 0.470317i
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) −11.2583 + 6.50000i −0.760767 + 0.439229i
\(220\) 2.00000 0.134840
\(221\) 0 0
\(222\) −11.0000 −0.738272
\(223\) −13.8564 + 8.00000i −0.927894 + 0.535720i −0.886145 0.463409i \(-0.846626\pi\)
−0.0417488 + 0.999128i \(0.513293\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) −2.00000 + 3.46410i −0.133333 + 0.230940i
\(226\) 3.00000i 0.199557i
\(227\) −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i \(-0.487137\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(228\) 1.73205 + 1.00000i 0.114708 + 0.0662266i
\(229\) 10.0000i 0.660819i −0.943838 0.330409i \(-0.892813\pi\)
0.943838 0.330409i \(-0.107187\pi\)
\(230\) −3.00000 + 5.19615i −0.197814 + 0.342624i
\(231\) 2.00000 + 3.46410i 0.131590 + 0.227921i
\(232\) −7.79423 + 4.50000i −0.511716 + 0.295439i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −2.00000 −0.130466
\(236\) −6.92820 + 4.00000i −0.450988 + 0.260378i
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 5.00000 8.66025i 0.324102 0.561361i
\(239\) 6.00000i 0.388108i −0.980991 0.194054i \(-0.937836\pi\)
0.980991 0.194054i \(-0.0621637\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) 6.06218 + 3.50000i 0.390499 + 0.225455i 0.682376 0.731001i \(-0.260947\pi\)
−0.291877 + 0.956456i \(0.594280\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.50000 9.52628i −0.352101 0.609858i
\(245\) −2.59808 + 1.50000i −0.165985 + 0.0958315i
\(246\) −5.00000 −0.318788
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −5.19615 + 3.00000i −0.329293 + 0.190117i
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) 2.00000 3.46410i 0.126239 0.218652i −0.795978 0.605326i \(-0.793043\pi\)
0.922217 + 0.386674i \(0.126376\pi\)
\(252\) 2.00000i 0.125988i
\(253\) −10.3923 6.00000i −0.653359 0.377217i
\(254\) 10.3923 + 6.00000i 0.652071 + 0.376473i
\(255\) 5.00000i 0.313112i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) −8.66025 + 5.00000i −0.539164 + 0.311286i
\(259\) −22.0000 −1.36701
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) 6.92820 4.00000i 0.428026 0.247121i
\(263\) −7.00000 12.1244i −0.431638 0.747620i 0.565376 0.824833i \(-0.308731\pi\)
−0.997015 + 0.0772134i \(0.975398\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) 1.00000i 0.0614295i
\(266\) 3.46410 + 2.00000i 0.212398 + 0.122628i
\(267\) −1.73205 1.00000i −0.106000 0.0611990i
\(268\) 2.00000i 0.122169i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −6.92820 + 4.00000i −0.420858 + 0.242983i −0.695444 0.718580i \(-0.744792\pi\)
0.274586 + 0.961563i \(0.411459\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0 0
\(274\) −17.0000 −1.02701
\(275\) −6.92820 + 4.00000i −0.417786 + 0.241209i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −5.50000 + 9.52628i −0.330463 + 0.572379i −0.982603 0.185720i \(-0.940538\pi\)
0.652140 + 0.758099i \(0.273872\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 3.46410 + 2.00000i 0.207390 + 0.119737i
\(280\) −1.73205 1.00000i −0.103510 0.0597614i
\(281\) 25.0000i 1.49137i −0.666296 0.745687i \(-0.732121\pi\)
0.666296 0.745687i \(-0.267879\pi\)
\(282\) −1.00000 + 1.73205i −0.0595491 + 0.103142i
\(283\) 13.0000 + 22.5167i 0.772770 + 1.33848i 0.936039 + 0.351895i \(0.114463\pi\)
−0.163270 + 0.986581i \(0.552204\pi\)
\(284\) 12.1244 7.00000i 0.719448 0.415374i
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) 2.00000i 0.117242i
\(292\) 11.2583 + 6.50000i 0.658844 + 0.380384i
\(293\) −0.866025 0.500000i −0.0505937 0.0292103i 0.474490 0.880261i \(-0.342633\pi\)
−0.525084 + 0.851051i \(0.675966\pi\)
\(294\) 3.00000i 0.174964i
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) 5.50000 + 9.52628i 0.319681 + 0.553704i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 3.00000 0.173785
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) −17.3205 + 10.0000i −0.998337 + 0.576390i
\(302\) −3.00000 5.19615i −0.172631 0.299005i
\(303\) 2.50000 4.33013i 0.143621 0.248759i
\(304\) 2.00000i 0.114708i
\(305\) −9.52628 5.50000i −0.545473 0.314929i
\(306\) −4.33013 2.50000i −0.247537 0.142915i
\(307\) 14.0000i 0.799022i 0.916728 + 0.399511i \(0.130820\pi\)
−0.916728 + 0.399511i \(0.869180\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) −5.00000 8.66025i −0.284440 0.492665i
\(310\) 3.46410 2.00000i 0.196748 0.113592i
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 6.06218 3.50000i 0.342108 0.197516i
\(315\) −1.00000 1.73205i −0.0563436 0.0975900i
\(316\) −2.00000 + 3.46410i −0.112509 + 0.194871i
\(317\) 33.0000i 1.85346i −0.375722 0.926732i \(-0.622605\pi\)
0.375722 0.926732i \(-0.377395\pi\)
\(318\) 0.866025 + 0.500000i 0.0485643 + 0.0280386i
\(319\) −15.5885 9.00000i −0.872786 0.503903i
\(320\) 1.00000i 0.0559017i
\(321\) −9.00000 + 15.5885i −0.502331 + 0.870063i
\(322\) 6.00000 + 10.3923i 0.334367 + 0.579141i
\(323\) 8.66025 5.00000i 0.481869 0.278207i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) 1.73205 1.00000i 0.0957826 0.0553001i
\(328\) 2.50000 + 4.33013i 0.138039 + 0.239091i
\(329\) −2.00000 + 3.46410i −0.110264 + 0.190982i
\(330\) 2.00000i 0.110096i
\(331\) 24.2487 + 14.0000i 1.33283 + 0.769510i 0.985732 0.168320i \(-0.0538340\pi\)
0.347097 + 0.937829i \(0.387167\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) 11.0000i 0.602796i
\(334\) 12.0000 20.7846i 0.656611 1.13728i
\(335\) −1.00000 1.73205i −0.0546358 0.0946320i
\(336\) −1.73205 + 1.00000i −0.0944911 + 0.0545545i
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) 0 0
\(339\) 3.00000 0.162938
\(340\) −4.33013 + 2.50000i −0.234834 + 0.135582i
\(341\) 4.00000 + 6.92820i 0.216612 + 0.375183i
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) 20.0000i 1.07990i
\(344\) 8.66025 + 5.00000i 0.466930 + 0.269582i
\(345\) 5.19615 + 3.00000i 0.279751 + 0.161515i
\(346\) 22.0000i 1.18273i
\(347\) −3.00000 + 5.19615i −0.161048 + 0.278944i −0.935245 0.354001i \(-0.884821\pi\)
0.774197 + 0.632945i \(0.218154\pi\)
\(348\) 4.50000 + 7.79423i 0.241225 + 0.417815i
\(349\) −5.19615 + 3.00000i −0.278144 + 0.160586i −0.632583 0.774493i \(-0.718005\pi\)
0.354439 + 0.935079i \(0.384672\pi\)
\(350\) 8.00000 0.427618
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) 14.7224 8.50000i 0.783596 0.452409i −0.0541072 0.998535i \(-0.517231\pi\)
0.837703 + 0.546126i \(0.183898\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) 7.00000 12.1244i 0.371521 0.643494i
\(356\) 2.00000i 0.106000i
\(357\) −8.66025 5.00000i −0.458349 0.264628i
\(358\) 5.19615 + 3.00000i 0.274625 + 0.158555i
\(359\) 30.0000i 1.58334i 0.610949 + 0.791670i \(0.290788\pi\)
−0.610949 + 0.791670i \(0.709212\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) −7.50000 12.9904i −0.394737 0.683704i
\(362\) 4.33013 2.50000i 0.227586 0.131397i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 13.0000 0.680451
\(366\) −9.52628 + 5.50000i −0.497947 + 0.287490i
\(367\) 1.00000 + 1.73205i 0.0521996 + 0.0904123i 0.890945 0.454112i \(-0.150043\pi\)
−0.838745 + 0.544524i \(0.816710\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 5.00000i 0.260290i
\(370\) 9.52628 + 5.50000i 0.495248 + 0.285931i
\(371\) 1.73205 + 1.00000i 0.0899236 + 0.0519174i
\(372\) 4.00000i 0.207390i
\(373\) −4.50000 + 7.79423i −0.233001 + 0.403570i −0.958690 0.284453i \(-0.908188\pi\)
0.725689 + 0.688023i \(0.241521\pi\)
\(374\) −5.00000 8.66025i −0.258544 0.447811i
\(375\) 7.79423 4.50000i 0.402492 0.232379i
\(376\) 2.00000 0.103142
\(377\) 0 0
\(378\) −2.00000 −0.102869
\(379\) 10.3923 6.00000i 0.533817 0.308199i −0.208752 0.977969i \(-0.566940\pi\)
0.742569 + 0.669769i \(0.233607\pi\)
\(380\) −1.00000 1.73205i −0.0512989 0.0888523i
\(381\) 6.00000 10.3923i 0.307389 0.532414i
\(382\) 4.00000i 0.204658i
\(383\) −20.7846 12.0000i −1.06204 0.613171i −0.136047 0.990702i \(-0.543440\pi\)
−0.925997 + 0.377531i \(0.876773\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 4.00000i 0.203859i
\(386\) −8.50000 + 14.7224i −0.432639 + 0.749352i
\(387\) 5.00000 + 8.66025i 0.254164 + 0.440225i
\(388\) 1.73205 1.00000i 0.0879316 0.0507673i
\(389\) −19.0000 −0.963338 −0.481669 0.876353i \(-0.659969\pi\)
−0.481669 + 0.876353i \(0.659969\pi\)
\(390\) 0 0
\(391\) 30.0000 1.51717
\(392\) 2.59808 1.50000i 0.131223 0.0757614i
\(393\) −4.00000 6.92820i −0.201773 0.349482i
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 4.00000i 0.201262i
\(396\) −1.73205 1.00000i −0.0870388 0.0502519i
\(397\) −15.5885 9.00000i −0.782362 0.451697i 0.0549046 0.998492i \(-0.482515\pi\)
−0.837267 + 0.546795i \(0.815848\pi\)
\(398\) 10.0000i 0.501255i
\(399\) 2.00000 3.46410i 0.100125 0.173422i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 23.3827 13.5000i 1.16768 0.674158i 0.214544 0.976714i \(-0.431173\pi\)
0.953131 + 0.302556i \(0.0978401\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 0 0
\(404\) −5.00000 −0.248759
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) 9.00000 + 15.5885i 0.446663 + 0.773642i
\(407\) −11.0000 + 19.0526i −0.545250 + 0.944400i
\(408\) 5.00000i 0.247537i
\(409\) −19.9186 11.5000i −0.984911 0.568638i −0.0811615 0.996701i \(-0.525863\pi\)
−0.903749 + 0.428063i \(0.859196\pi\)
\(410\) 4.33013 + 2.50000i 0.213850 + 0.123466i
\(411\) 17.0000i 0.838548i
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) 8.00000 + 13.8564i 0.393654 + 0.681829i
\(414\) 5.19615 3.00000i 0.255377 0.147442i
\(415\) 6.00000 0.294528
\(416\) 0 0
\(417\) 12.0000 0.587643
\(418\) 3.46410 2.00000i 0.169435 0.0978232i
\(419\) 16.0000 + 27.7128i 0.781651 + 1.35386i 0.930979 + 0.365072i \(0.118956\pi\)
−0.149328 + 0.988788i \(0.547711\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) 23.0000i 1.12095i −0.828171 0.560476i \(-0.810618\pi\)
0.828171 0.560476i \(-0.189382\pi\)
\(422\) 20.7846 + 12.0000i 1.01178 + 0.584151i
\(423\) 1.73205 + 1.00000i 0.0842152 + 0.0486217i
\(424\) 1.00000i 0.0485643i
\(425\) 10.0000 17.3205i 0.485071 0.840168i
\(426\) −7.00000 12.1244i −0.339151 0.587427i
\(427\) −19.0526 + 11.0000i −0.922018 + 0.532327i
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) 10.0000 0.482243
\(431\) −1.73205 + 1.00000i −0.0834300 + 0.0481683i −0.541135 0.840936i \(-0.682005\pi\)
0.457705 + 0.889104i \(0.348672\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −10.5000 + 18.1865i −0.504598 + 0.873989i 0.495388 + 0.868672i \(0.335026\pi\)
−0.999986 + 0.00531724i \(0.998307\pi\)
\(434\) 8.00000i 0.384012i
\(435\) 7.79423 + 4.50000i 0.373705 + 0.215758i
\(436\) −1.73205 1.00000i −0.0829502 0.0478913i
\(437\) 12.0000i 0.574038i
\(438\) 6.50000 11.2583i 0.310582 0.537944i
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) −1.73205 + 1.00000i −0.0825723 + 0.0476731i
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) 20.0000 0.950229 0.475114 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) 9.52628 5.50000i 0.452097 0.261018i
\(445\) 1.00000 + 1.73205i 0.0474045 + 0.0821071i
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 3.00000i 0.141895i
\(448\) 1.73205 + 1.00000i 0.0818317 + 0.0472456i
\(449\) −25.9808 15.0000i −1.22611 0.707894i −0.259895 0.965637i \(-0.583688\pi\)
−0.966213 + 0.257743i \(0.917021\pi\)
\(450\) 4.00000i 0.188562i
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) −1.50000 2.59808i −0.0705541 0.122203i
\(453\) −5.19615 + 3.00000i −0.244137 + 0.140952i
\(454\) 14.0000 0.657053
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 2.59808 1.50000i 0.121533 0.0701670i −0.438001 0.898974i \(-0.644313\pi\)
0.559534 + 0.828807i \(0.310980\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) 6.00000i 0.279751i
\(461\) −2.59808 1.50000i −0.121004 0.0698620i 0.438276 0.898840i \(-0.355589\pi\)
−0.559281 + 0.828978i \(0.688923\pi\)
\(462\) −3.46410 2.00000i −0.161165 0.0930484i
\(463\) 14.0000i 0.650635i 0.945605 + 0.325318i \(0.105471\pi\)
−0.945605 + 0.325318i \(0.894529\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) −5.19615 + 3.00000i −0.240707 + 0.138972i
\(467\) 22.0000 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 1.73205 1.00000i 0.0798935 0.0461266i
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) 4.00000 6.92820i 0.184115 0.318896i
\(473\) 20.0000i 0.919601i
\(474\) 3.46410 + 2.00000i 0.159111 + 0.0918630i
\(475\) 6.92820 + 4.00000i 0.317888 + 0.183533i
\(476\) 10.0000i 0.458349i
\(477\) 0.500000 0.866025i 0.0228934 0.0396526i
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) −27.7128 + 16.0000i −1.26623 + 0.731059i −0.974273 0.225372i \(-0.927640\pi\)
−0.291958 + 0.956431i \(0.594307\pi\)
\(480\) 1.00000 0.0456435
\(481\) 0 0
\(482\) −7.00000 −0.318841
\(483\) 10.3923 6.00000i 0.472866 0.273009i
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 1.00000i 0.0453609i
\(487\) 22.5167 + 13.0000i 1.02033 + 0.589086i 0.914199 0.405266i \(-0.132821\pi\)
0.106129 + 0.994352i \(0.466154\pi\)
\(488\) 9.52628 + 5.50000i 0.431234 + 0.248973i
\(489\) 20.0000i 0.904431i
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) −15.0000 25.9808i −0.676941 1.17250i −0.975898 0.218229i \(-0.929972\pi\)
0.298957 0.954267i \(-0.403361\pi\)
\(492\) 4.33013 2.50000i 0.195217 0.112709i
\(493\) 45.0000 2.02670
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) −3.46410 + 2.00000i −0.155543 + 0.0898027i
\(497\) −14.0000 24.2487i −0.627986 1.08770i
\(498\) 3.00000 5.19615i 0.134433 0.232845i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −7.79423 4.50000i −0.348569 0.201246i
\(501\) −20.7846 12.0000i −0.928588 0.536120i
\(502\) 4.00000i 0.178529i
\(503\) 7.00000 12.1244i 0.312115 0.540598i −0.666705 0.745321i \(-0.732296\pi\)
0.978820 + 0.204723i \(0.0656294\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) −4.33013 + 2.50000i −0.192688 + 0.111249i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −12.0000 −0.532414
\(509\) 12.9904 7.50000i 0.575789 0.332432i −0.183669 0.982988i \(-0.558798\pi\)
0.759458 + 0.650556i \(0.225464\pi\)
\(510\) 2.50000 + 4.33013i 0.110702 + 0.191741i
\(511\) 13.0000 22.5167i 0.575086 0.996078i
\(512\) 1.00000i 0.0441942i
\(513\) −1.73205 1.00000i −0.0764719 0.0441511i
\(514\) 2.59808 + 1.50000i 0.114596 + 0.0661622i
\(515\) 10.0000i 0.440653i
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) 2.00000 + 3.46410i 0.0879599 + 0.152351i
\(518\) 19.0526 11.0000i 0.837121 0.483312i
\(519\) −22.0000 −0.965693
\(520\) 0 0
\(521\) 25.0000 1.09527 0.547635 0.836717i \(-0.315528\pi\)
0.547635 + 0.836717i \(0.315528\pi\)
\(522\) 7.79423 4.50000i 0.341144 0.196960i
\(523\) 19.0000 + 32.9090i 0.830812 + 1.43901i 0.897395 + 0.441228i \(0.145457\pi\)
−0.0665832 + 0.997781i \(0.521210\pi\)
\(524\) −4.00000 + 6.92820i −0.174741 + 0.302660i
\(525\) 8.00000i 0.349149i
\(526\) 12.1244 + 7.00000i 0.528647 + 0.305215i
\(527\) −17.3205 10.0000i −0.754493 0.435607i
\(528\) 2.00000i 0.0870388i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −0.500000 0.866025i −0.0217186 0.0376177i
\(531\) 6.92820 4.00000i 0.300658 0.173585i
\(532\) −4.00000 −0.173422
\(533\) 0 0
\(534\) 2.00000 0.0865485
\(535\) 15.5885 9.00000i 0.673948 0.389104i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) 3.00000 5.19615i 0.129460 0.224231i
\(538\) 14.0000i 0.603583i
\(539\) 5.19615 + 3.00000i 0.223814 + 0.129219i
\(540\) 0.866025 + 0.500000i 0.0372678 + 0.0215166i
\(541\) 7.00000i 0.300954i 0.988614 + 0.150477i \(0.0480809\pi\)
−0.988614 + 0.150477i \(0.951919\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) −2.50000 4.33013i −0.107285 0.185824i
\(544\) 4.33013 2.50000i 0.185653 0.107187i
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 14.7224 8.50000i 0.628911 0.363102i
\(549\) 5.50000 + 9.52628i 0.234734 + 0.406572i
\(550\) 4.00000 6.92820i 0.170561 0.295420i
\(551\) 18.0000i 0.766826i
\(552\) −5.19615 3.00000i −0.221163 0.127688i
\(553\) 6.92820 + 4.00000i 0.294617 + 0.170097i
\(554\) 11.0000i 0.467345i
\(555\) 5.50000 9.52628i 0.233462 0.404368i
\(556\) −6.00000 10.3923i −0.254457 0.440732i
\(557\) 7.79423 4.50000i 0.330252 0.190671i −0.325701 0.945473i \(-0.605600\pi\)
0.655953 + 0.754802i \(0.272267\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) 2.00000 0.0845154
\(561\) −8.66025 + 5.00000i −0.365636 + 0.211100i
\(562\) 12.5000 + 21.6506i 0.527281 + 0.913277i
\(563\) 20.0000 34.6410i 0.842900 1.45994i −0.0445334 0.999008i \(-0.514180\pi\)
0.887433 0.460937i \(-0.152487\pi\)
\(564\) 2.00000i 0.0842152i
\(565\) −2.59808 1.50000i −0.109302 0.0631055i
\(566\) −22.5167 13.0000i −0.946446 0.546431i
\(567\) 2.00000i 0.0839921i
\(568\) −7.00000 + 12.1244i −0.293713 + 0.508727i
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) −1.73205 + 1.00000i −0.0725476 + 0.0418854i
\(571\) 2.00000 0.0836974 0.0418487 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) 0 0
\(573\) −4.00000 −0.167102
\(574\) 8.66025 5.00000i 0.361472 0.208696i
\(575\) 12.0000 + 20.7846i 0.500435 + 0.866778i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 27.0000i 1.12402i 0.827129 + 0.562012i \(0.189973\pi\)
−0.827129 + 0.562012i \(0.810027\pi\)
\(578\) 6.92820 + 4.00000i 0.288175 + 0.166378i
\(579\) 14.7224 + 8.50000i 0.611843 + 0.353248i
\(580\) 9.00000i 0.373705i
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) −1.00000 1.73205i −0.0414513 0.0717958i
\(583\) 1.73205 1.00000i 0.0717342 0.0414158i
\(584\) −13.0000 −0.537944
\(585\) 0 0
\(586\) 1.00000 0.0413096
\(587\) −27.7128 + 16.0000i −1.14383 + 0.660391i −0.947376 0.320122i \(-0.896276\pi\)
−0.196454 + 0.980513i \(0.562943\pi\)
\(588\) −1.50000 2.59808i −0.0618590 0.107143i
\(589\) 4.00000 6.92820i 0.164817 0.285472i
\(590\) 8.00000i 0.329355i
\(591\) 5.19615 + 3.00000i 0.213741 + 0.123404i
\(592\) −9.52628 5.50000i −0.391528 0.226049i
\(593\) 39.0000i 1.60154i 0.598973 + 0.800769i \(0.295576\pi\)
−0.598973 + 0.800769i \(0.704424\pi\)
\(594\) −1.00000 + 1.73205i −0.0410305 + 0.0710669i
\(595\) 5.00000 + 8.66025i 0.204980 + 0.355036i
\(596\) −2.59808 + 1.50000i −0.106421 + 0.0614424i
\(597\) 10.0000 0.409273
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −3.46410 + 2.00000i −0.141421 + 0.0816497i
\(601\) −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i \(-0.238692\pi\)
−0.956124 + 0.292962i \(0.905359\pi\)
\(602\) 10.0000 17.3205i 0.407570 0.705931i
\(603\) 2.00000i 0.0814463i
\(604\) 5.19615 + 3.00000i 0.211428 + 0.122068i
\(605\) 6.06218 + 3.50000i 0.246463 + 0.142295i
\(606\) 5.00000i 0.203111i
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) 15.5885 9.00000i 0.631676 0.364698i
\(610\) 11.0000 0.445377
\(611\) 0 0
\(612\) 5.00000 0.202113
\(613\) 11.2583 6.50000i 0.454720 0.262533i −0.255102 0.966914i \(-0.582109\pi\)
0.709821 + 0.704382i \(0.248776\pi\)
\(614\) −7.00000 12.1244i −0.282497 0.489299i
\(615\) 2.50000 4.33013i 0.100810 0.174608i
\(616\) 4.00000i 0.161165i
\(617\) 12.9904 + 7.50000i 0.522973 + 0.301939i 0.738150 0.674636i \(-0.235700\pi\)
−0.215177 + 0.976575i \(0.569033\pi\)
\(618\) 8.66025 + 5.00000i 0.348367 + 0.201129i
\(619\) 32.0000i 1.28619i −0.765787 0.643094i \(-0.777650\pi\)
0.765787 0.643094i \(-0.222350\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 5.19615 3.00000i 0.208347 0.120289i
\(623\) 4.00000 0.160257
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) −5.19615 + 3.00000i −0.207680 + 0.119904i
\(627\) −2.00000 3.46410i −0.0798723 0.138343i
\(628\) −3.50000 + 6.06218i −0.139665 + 0.241907i
\(629\) 55.0000i 2.19299i
\(630\) 1.73205 + 1.00000i 0.0690066 + 0.0398410i
\(631\) 10.3923 + 6.00000i 0.413711 + 0.238856i 0.692383 0.721530i \(-0.256561\pi\)
−0.278672 + 0.960386i \(0.589894\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 12.0000 20.7846i 0.476957 0.826114i
\(634\) 16.5000 + 28.5788i 0.655299 + 1.13501i
\(635\) −10.3923 + 6.00000i −0.412406 + 0.238103i
\(636\) −1.00000 −0.0396526
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) −12.1244 + 7.00000i −0.479632 + 0.276916i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i \(-0.801851\pi\)
0.911165 + 0.412042i \(0.135184\pi\)
\(642\) 18.0000i 0.710403i
\(643\) −6.92820 4.00000i −0.273222 0.157745i 0.357129 0.934055i \(-0.383756\pi\)
−0.630351 + 0.776310i \(0.717089\pi\)
\(644\) −10.3923 6.00000i −0.409514 0.236433i
\(645\) 10.0000i 0.393750i
\(646\) −5.00000 + 8.66025i −0.196722 + 0.340733i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 17.3205 10.0000i 0.678323 0.391630i
\(653\) 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i \(-0.0250169\pi\)
−0.566450 + 0.824096i \(0.691684\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) 8.00000i 0.312586i
\(656\) −4.33013 2.50000i −0.169063 0.0976086i
\(657\) −11.2583 6.50000i −0.439229 0.253589i
\(658\) 4.00000i 0.155936i
\(659\) −12.0000 + 20.7846i −0.467454 + 0.809653i −0.999309 0.0371821i \(-0.988162\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(660\) 1.00000 + 1.73205i 0.0389249 + 0.0674200i
\(661\) −21.6506 + 12.5000i −0.842112 + 0.486194i −0.857982 0.513680i \(-0.828282\pi\)
0.0158695 + 0.999874i \(0.494948\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −3.46410 + 2.00000i −0.134332 + 0.0775567i
\(666\) −5.50000 9.52628i −0.213121 0.369136i
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) 24.0000i 0.928588i
\(669\) −13.8564 8.00000i −0.535720 0.309298i
\(670\) 1.73205 + 1.00000i 0.0669150 + 0.0386334i
\(671\) 22.0000i 0.849301i
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) 21.5000 + 37.2391i 0.828764 + 1.43546i 0.899008 + 0.437932i \(0.144289\pi\)
−0.0702442 + 0.997530i \(0.522378\pi\)
\(674\) −7.79423 + 4.50000i −0.300222 + 0.173334i
\(675\) −4.00000 −0.153960
\(676\) 0 0
\(677\) −46.0000 −1.76792 −0.883962 0.467559i \(-0.845134\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(678\) −2.59808 + 1.50000i −0.0997785 + 0.0576072i
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) 2.50000 4.33013i 0.0958706 0.166053i
\(681\) 14.0000i 0.536481i
\(682\) −6.92820 4.00000i −0.265295 0.153168i
\(683\) −34.6410 20.0000i −1.32550 0.765279i −0.340901 0.940099i \(-0.610732\pi\)
−0.984600 + 0.174820i \(0.944066\pi\)
\(684\) 2.00000i 0.0764719i
\(685\) 8.50000 14.7224i 0.324768 0.562515i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 8.66025 5.00000i 0.330409 0.190762i
\(688\) −10.0000 −0.381246
\(689\) 0 0
\(690\) −6.00000 −0.228416
\(691\) −1.73205 + 1.00000i −0.0658903 + 0.0380418i −0.532583 0.846378i \(-0.678779\pi\)
0.466693 + 0.884419i \(0.345445\pi\)
\(692\) 11.0000 + 19.0526i 0.418157 + 0.724270i
\(693\) −2.00000 + 3.46410i −0.0759737 + 0.131590i
\(694\) 6.00000i 0.227757i
\(695\) −10.3923 6.00000i −0.394203 0.227593i
\(696\) −7.79423 4.50000i −0.295439 0.170572i
\(697\) 25.0000i 0.946943i
\(698\) 3.00000 5.19615i 0.113552 0.196677i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) −6.92820 + 4.00000i −0.261861 + 0.151186i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 22.0000 0.829746
\(704\) 1.73205 1.00000i 0.0652791 0.0376889i
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) −8.50000 + 14.7224i −0.319902 + 0.554086i
\(707\) 10.0000i 0.376089i
\(708\) −6.92820 4.00000i −0.260378 0.150329i
\(709\) −12.9904 7.50000i −0.487864 0.281668i 0.235824 0.971796i \(-0.424221\pi\)
−0.723688 + 0.690127i \(0.757554\pi\)
\(710\) 14.0000i 0.525411i
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) −1.00000 1.73205i −0.0374766 0.0649113i
\(713\) 20.7846 12.0000i 0.778390 0.449404i
\(714\) 10.0000 0.374241
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 5.19615 3.00000i 0.194054 0.112037i
\(718\) −15.0000 25.9808i −0.559795 0.969593i
\(719\) 12.0000 20.7846i 0.447524 0.775135i −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 17.3205 + 10.0000i 0.645049 + 0.372419i
\(722\) 12.9904 + 7.50000i 0.483452 + 0.279121i
\(723\) 7.00000i 0.260333i
\(724\) −2.50000 + 4.33013i −0.0929118 + 0.160928i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 6.06218 3.50000i 0.224989 0.129897i
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −11.2583 + 6.50000i −0.416689 + 0.240576i
\(731\) −25.0000 43.3013i −0.924658 1.60156i
\(732\) 5.50000 9.52628i 0.203286 0.352101i
\(733\) 13.0000i 0.480166i 0.970752 + 0.240083i \(0.0771747\pi\)
−0.970752 + 0.240083i \(0.922825\pi\)
\(734\) −1.73205 1.00000i −0.0639312 0.0369107i
\(735\) −2.59808 1.50000i −0.0958315 0.0553283i
\(736\) 6.00000i 0.221163i
\(737\) −2.00000 + 3.46410i −0.0736709 + 0.127602i
\(738\) −2.50000 4.33013i −0.0920263 0.159394i
\(739\) −13.8564 + 8.00000i −0.509716 + 0.294285i −0.732717 0.680534i \(-0.761748\pi\)
0.223001 + 0.974818i \(0.428415\pi\)
\(740\) −11.0000 −0.404368
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) −10.3923 + 6.00000i −0.381257 + 0.220119i −0.678365 0.734725i \(-0.737311\pi\)
0.297108 + 0.954844i \(0.403978\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) −1.50000 + 2.59808i −0.0549557 + 0.0951861i
\(746\) 9.00000i 0.329513i
\(747\) −5.19615 3.00000i −0.190117 0.109764i
\(748\) 8.66025 + 5.00000i 0.316650 + 0.182818i
\(749\) 36.0000i 1.31541i
\(750\) −4.50000 + 7.79423i −0.164317 + 0.284605i
\(751\) 13.0000 + 22.5167i 0.474377 + 0.821645i 0.999570 0.0293387i \(-0.00934013\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(752\) −1.73205 + 1.00000i −0.0631614 + 0.0364662i
\(753\) 4.00000 0.145768
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 1.73205 1.00000i 0.0629941 0.0363696i
\(757\) 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i \(-0.0605917\pi\)
−0.654827 + 0.755779i \(0.727258\pi\)
\(758\) −6.00000 + 10.3923i −0.217930 + 0.377466i
\(759\) 12.0000i 0.435572i
\(760\) 1.73205 + 1.00000i 0.0628281 + 0.0362738i
\(761\) 29.4449 + 17.0000i 1.06738 + 0.616250i 0.927463 0.373914i \(-0.121985\pi\)
0.139912 + 0.990164i \(0.455318\pi\)
\(762\) 12.0000i 0.434714i
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) 4.33013 2.50000i 0.156556 0.0903877i
\(766\) 24.0000 0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −29.4449 + 17.0000i −1.06181 + 0.613036i −0.925932 0.377690i \(-0.876718\pi\)
−0.135877 + 0.990726i \(0.543385\pi\)
\(770\) 2.00000 + 3.46410i 0.0720750 + 0.124838i
\(771\) 1.50000 2.59808i 0.0540212 0.0935674i
\(772\) 17.0000i 0.611843i
\(773\) −15.5885 9.00000i −0.560678 0.323708i 0.192740 0.981250i \(-0.438263\pi\)
−0.753418 + 0.657542i \(0.771596\pi\)
\(774\) −8.66025 5.00000i −0.311286 0.179721i
\(775\) 16.0000i 0.574737i
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) −11.0000 19.0526i −0.394623 0.683507i
\(778\) 16.4545 9.50000i 0.589922 0.340592i
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) −25.9808 + 15.0000i −0.929070 + 0.536399i
\(783\) −4.50000 7.79423i −0.160817 0.278543i
\(784\) −1.50000 + 2.59808i −0.0535714 + 0.0927884i
\(785\) 7.00000i 0.249841i
\(786\) 6.92820 + 4.00000i 0.247121 + 0.142675i
\(787\) 3.46410 + 2.00000i 0.123482 + 0.0712923i 0.560469 0.828176i \(-0.310621\pi\)
−0.436987 + 0.899468i \(0.643954\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 7.00000 12.1244i 0.249207 0.431638i
\(790\) −2.00000 3.46410i −0.0711568 0.123247i
\(791\) −5.19615 + 3.00000i −0.184754 + 0.106668i
\(792\) 2.00000 0.0710669
\(793\) 0 0
\(794\) 18.0000 0.638796
\(795\) −0.866025 + 0.500000i −0.0307148 + 0.0177332i
\(796\) −5.00000 8.66025i −0.177220 0.306955i
\(797\) −1.00000 + 1.73205i −0.0354218 + 0.0613524i −0.883193 0.469010i \(-0.844611\pi\)
0.847771 + 0.530362i \(0.177944\pi\)
\(798\) 4.00000i 0.141598i
\(799\) −8.66025 5.00000i −0.306378 0.176887i
\(800\) 3.46410 + 2.00000i 0.122474 + 0.0707107i
\(801\) 2.00000i 0.0706665i
\(802\) −13.5000 + 23.3827i −0.476702 + 0.825671i
\(803\) −13.0000 22.5167i −0.458760 0.794596i
\(804\) 1.73205 1.00000i 0.0610847 0.0352673i
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) 14.0000 0.492823
\(808\) 4.33013 2.50000i 0.152333 0.0879497i
\(809\) −2.50000 4.33013i −0.0878953 0.152239i 0.818726 0.574184i \(-0.194681\pi\)
−0.906621 + 0.421945i \(0.861347\pi\)
\(810\) 0.500000 0.866025i 0.0175682 0.0304290i
\(811\) 36.0000i 1.26413i −0.774915 0.632065i \(-0.782207\pi\)
0.774915 0.632065i \(-0.217793\pi\)
\(812\) −15.5885 9.00000i −0.547048 0.315838i
\(813\) −6.92820 4.00000i −0.242983 0.140286i
\(814\) 22.0000i 0.771100i
\(815\) 10.0000 17.3205i 0.350285 0.606711i
\(816\) −2.50000 4.33013i −0.0875175 0.151585i
\(817\) 17.3205 10.0000i 0.605968 0.349856i
\(818\) 23.0000 0.804176
\(819\) 0 0
\(820\) −5.00000 −0.174608
\(821\) −25.9808 + 15.0000i −0.906735 + 0.523504i −0.879379 0.476122i \(-0.842042\pi\)
−0.0273557 + 0.999626i \(0.508709\pi\)
\(822\) −8.50000 14.7224i −0.296472 0.513504i
\(823\) −8.00000 + 13.8564i −0.278862 + 0.483004i −0.971102 0.238664i \(-0.923291\pi\)
0.692240 + 0.721668i \(0.256624\pi\)
\(824\) 10.0000i 0.348367i
\(825\) −6.92820 4.00000i −0.241209 0.139262i
\(826\) −13.8564 8.00000i −0.482126 0.278356i
\(827\) 8.00000i 0.278187i 0.990279 + 0.139094i \(0.0444189\pi\)
−0.990279 + 0.139094i \(0.955581\pi\)
\(828\) −3.00000 + 5.19615i −0.104257 + 0.180579i
\(829\) −17.5000 30.3109i −0.607800 1.05274i −0.991602 0.129325i \(-0.958719\pi\)
0.383802 0.923415i \(-0.374614\pi\)
\(830\) −5.19615 + 3.00000i −0.180361 + 0.104132i
\(831\) −11.0000 −0.381586
\(832\) 0 0
\(833\) −15.0000 −0.519719
\(834\) −10.3923 + 6.00000i −0.359856 + 0.207763i
\(835\) 12.0000 + 20.7846i 0.415277 + 0.719281i
\(836\) −2.00000 + 3.46410i −0.0691714 + 0.119808i
\(837\) 4.00000i 0.138260i
\(838\) −27.7128 16.0000i −0.957323 0.552711i
\(839\) 38.1051 + 22.0000i 1.31553 + 0.759524i 0.983007 0.183569i \(-0.0587651\pi\)
0.332528 + 0.943093i \(0.392098\pi\)
\(840\) 2.00000i 0.0690066i
\(841\) −26.0000 + 45.0333i −0.896552 + 1.55287i
\(842\) 11.5000 + 19.9186i 0.396316 + 0.686440i
\(843\) 21.6506 12.5000i 0.745687 0.430523i
\(844\) −24.0000 −0.826114
\(845\) 0 0
\(846\) −2.00000 −0.0687614
\(847\) 12.1244 7.00000i 0.416598 0.240523i
\(848\) 0.500000 + 0.866025i 0.0171701 + 0.0297394i
\(849\) −13.0000 + 22.5167i −0.446159 + 0.772770i
\(850\) 20.0000i 0.685994i
\(851\) 57.1577 + 33.0000i 1.95934 + 1.13123i
\(852\) 12.1244 + 7.00000i 0.415374 + 0.239816i
\(853\) 49.0000i 1.67773i −0.544341 0.838864i \(-0.683220\pi\)
0.544341 0.838864i \(-0.316780\pi\)
\(854\) 11.0000 19.0526i 0.376412 0.651965i
\(855\) 1.00000 + 1.73205i 0.0341993 + 0.0592349i
\(856\) −15.5885 + 9.00000i −0.532803 + 0.307614i
\(857\) −45.0000 −1.53717 −0.768585 0.639747i \(-0.779039\pi\)
−0.768585 + 0.639747i \(0.779039\pi\)
\(858\) 0 0
\(859\) −50.0000 −1.70598 −0.852989 0.521929i \(-0.825213\pi\)
−0.852989 + 0.521929i \(0.825213\pi\)
\(860\) −8.66025 + 5.00000i −0.295312 + 0.170499i
\(861\) −5.00000 8.66025i −0.170400 0.295141i
\(862\) 1.00000 1.73205i 0.0340601 0.0589939i
\(863\) 46.0000i 1.56586i 0.622111 + 0.782929i \(0.286275\pi\)
−0.622111 + 0.782929i \(0.713725\pi\)
\(864\) −0.866025 0.500000i −0.0294628 0.0170103i
\(865\) 19.0526 + 11.0000i 0.647806 + 0.374011i
\(866\) 21.0000i 0.713609i
\(867\) 4.00000 6.92820i 0.135847 0.235294i
\(868\) 4.00000 + 6.92820i 0.135769 + 0.235159i
\(869\) 6.92820 4.00000i 0.235023 0.135691i
\(870\) −9.00000 −0.305129
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) −1.73205 + 1.00000i −0.0586210 + 0.0338449i
\(874\) −6.00000 10.3923i −0.202953 0.351525i
\(875\) −9.00000 + 15.5885i −0.304256 + 0.526986i
\(876\) 13.0000i 0.439229i
\(877\) −32.0429 18.5000i −1.08201 0.624701i −0.150574 0.988599i \(-0.548112\pi\)
−0.931439 + 0.363898i \(0.881446\pi\)
\(878\) −8.66025 5.00000i −0.292269 0.168742i
\(879\) 1.00000i 0.0337292i
\(880\) 1.00000 1.73205i 0.0337100 0.0583874i
\(881\) 8.50000 + 14.7224i 0.286372 + 0.496011i 0.972941 0.231054i \(-0.0742173\pi\)
−0.686569 + 0.727065i \(0.740884\pi\)
\(882\) −2.59808 + 1.50000i −0.0874818 + 0.0505076i
\(883\) 8.00000 0.269221 0.134611 0.990899i \(-0.457022\pi\)
0.134611 + 0.990899i \(0.457022\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) −17.3205 + 10.0000i −0.581894 + 0.335957i
\(887\) −12.0000 20.7846i −0.402921 0.697879i 0.591156 0.806557i \(-0.298672\pi\)
−0.994077 + 0.108678i \(0.965338\pi\)
\(888\) −5.50000 + 9.52628i −0.184568 + 0.319681i
\(889\) 24.0000i 0.804934i
\(890\) −1.73205 1.00000i −0.0580585 0.0335201i
\(891\) 1.73205 + 1.00000i 0.0580259 + 0.0335013i
\(892\) 16.0000i 0.535720i
\(893\) 2.00000 3.46410i 0.0669274 0.115922i
\(894\) 1.50000 + 2.59808i 0.0501675 + 0.0868927i
\(895\) −5.19615 + 3.00000i −0.173688 + 0.100279i
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) 31.1769 18.0000i 1.03981 0.600334i
\(900\) 2.00000 + 3.46410i 0.0666667 + 0.115470i
\(901\) −2.50000 + 4.33013i −0.0832871 + 0.144257i
\(902\) 10.0000i 0.332964i
\(903\) −17.3205 10.0000i −0.576390 0.332779i
\(904\) 2.59808 + 1.50000i 0.0864107 + 0.0498893i
\(905\) 5.00000i 0.166206i
\(906\) 3.00000 5.19615i 0.0996683 0.172631i
\(907\) −22.0000 38.1051i −0.730498 1.26526i −0.956671 0.291172i \(-0.905955\pi\)
0.226173 0.974087i \(-0.427379\pi\)
\(908\) −12.1244 + 7.00000i −0.402361 + 0.232303i
\(909\) 5.00000 0.165840
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) 1.73205 1.00000i 0.0573539 0.0331133i
\(913\) −6.00000 10.3923i −0.198571 0.343935i
\(914\) −1.50000 + 2.59808i −0.0496156 + 0.0859367i
\(915\) 11.0000i 0.363649i
\(916\) −8.66025 5.00000i −0.286143 0.165205i
\(917\) 13.8564 + 8.00000i 0.457579 + 0.264183i
\(918\) 5.00000i 0.165025i
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 3.00000 + 5.19615i 0.0989071 + 0.171312i
\(921\) −12.1244 + 7.00000i −0.399511 + 0.230658i
\(922\) 3.00000 0.0987997
\(923\) 0 0
\(924\) 4.00000 0.131590
\(925\) 38.1051 22.0000i 1.25289 0.723356i
\(926\) −7.00000 12.1244i −0.230034 0.398431i
\(927\) 5.00000 8.66025i 0.164222 0.284440i
\(928\) 9.00000i 0.295439i
\(929\) 19.9186 + 11.5000i 0.653508 + 0.377303i 0.789799 0.613366i \(-0.210185\pi\)
−0.136291 + 0.990669i \(0.543518\pi\)
\(930\) 3.46410 + 2.00000i 0.113592 + 0.0655826i
\(931\) 6.00000i 0.196642i
\(932\) 3.00000 5.19615i 0.0982683 0.170206i
\(933\) −3.00000 5.19615i −0.0982156 0.170114i
\(934\) −19.0526 + 11.0000i −0.623419 + 0.359931i
\(935\) 10.0000 0.327035
\(936\) 0 0
\(937\) −1.00000 −0.0326686 −0.0163343 0.999867i \(-0.505200\pi\)
−0.0163343 + 0.999867i \(0.505200\pi\)
\(938\) 3.46410 2.00000i 0.113107 0.0653023i
\(939\) 3.00000 + 5.19615i 0.0979013 + 0.169570i
\(940\) −1.00000 + 1.73205i −0.0326164 + 0.0564933i
\(941\) 22.0000i 0.717180i −0.933495 0.358590i \(-0.883258\pi\)
0.933495 0.358590i \(-0.116742\pi\)
\(942\) 6.06218 + 3.50000i 0.197516 + 0.114036i
\(943\) 25.9808 + 15.0000i 0.846050 + 0.488467i
\(944\) 8.00000i 0.260378i
\(945\) 1.00000 1.73205i 0.0325300 0.0563436i
\(946\) −10.0000 17.3205i −0.325128 0.563138i
\(947\) −6.92820 + 4.00000i −0.225136 + 0.129983i −0.608326 0.793687i \(-0.708159\pi\)
0.383190 + 0.923670i \(0.374825\pi\)
\(948\) −4.00000 −0.129914
\(949\) 0 0
\(950\) −8.00000 −0.259554
\(951\) 28.5788 16.5000i 0.926732 0.535049i
\(952\) −5.00000 8.66025i −0.162051 0.280680i
\(953\) 27.0000 46.7654i 0.874616 1.51488i 0.0174443 0.999848i \(-0.494447\pi\)
0.857171 0.515031i \(-0.172220\pi\)
\(954\) 1.00000i 0.0323762i
\(955\) 3.46410 + 2.00000i 0.112096 + 0.0647185i
\(956\) −5.19615 3.00000i −0.168056 0.0970269i
\(957\) 18.0000i 0.581857i
\(958\) 16.0000 27.7128i 0.516937 0.895360i
\(959\) −17.0000 29.4449i −0.548959 0.950824i
\(960\) −0.866025 + 0.500000i −0.0279508 + 0.0161374i
\(961\) 15.0000 0.483871
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 6.06218 3.50000i 0.195250 0.112727i
\(965\) −8.50000 14.7224i −0.273625 0.473932i
\(966\) −6.00000 + 10.3923i −0.193047 + 0.334367i
\(967\) 50.0000i 1.60789i −0.594703 0.803946i \(-0.702730\pi\)
0.594703 0.803946i \(-0.297270\pi\)
\(968\) −6.06218 3.50000i −0.194846 0.112494i
\(969\) 8.66025 + 5.00000i 0.278207 + 0.160623i
\(970\) 2.00000i 0.0642161i
\(971\) −10.0000 + 17.3205i −0.320915 + 0.555842i −0.980677 0.195633i \(-0.937324\pi\)
0.659762 + 0.751475i \(0.270657\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) −20.7846 + 12.0000i −0.666324 + 0.384702i
\(974\) −26.0000 −0.833094
\(975\) 0 0
\(976\) −11.0000 −0.352101
\(977\) 18.1865 10.5000i 0.581839 0.335925i −0.180025 0.983662i \(-0.557618\pi\)
0.761864 + 0.647737i \(0.224285\pi\)
\(978\) −10.0000 17.3205i −0.319765 0.553849i
\(979\) 2.00000 3.46410i 0.0639203 0.110713i
\(980\) 3.00000i 0.0958315i
\(981\) 1.73205 + 1.00000i 0.0553001 + 0.0319275i
\(982\) 25.9808 + 15.0000i 0.829079 + 0.478669i
\(983\) 60.0000i 1.91370i −0.290578 0.956851i \(-0.593847\pi\)
0.290578 0.956851i \(-0.406153\pi\)
\(984\) −2.50000 + 4.33013i −0.0796971 + 0.138039i
\(985\) −3.00000 5.19615i −0.0955879 0.165563i
\(986\) −38.9711 + 22.5000i −1.24109 + 0.716546i
\(987\) −4.00000 −0.127321
\(988\) 0 0
\(989\) 60.0000 1.90789
\(990\) 1.73205 1.00000i 0.0550482 0.0317821i
\(991\) −9.00000 15.5885i −0.285894 0.495184i 0.686931 0.726722i \(-0.258957\pi\)
−0.972826 + 0.231539i \(0.925624\pi\)
\(992\) 2.00000 3.46410i 0.0635001 0.109985i
\(993\) 28.0000i 0.888553i
\(994\) 24.2487 + 14.0000i 0.769122 + 0.444053i
\(995\) −8.66025 5.00000i −0.274549 0.158511i
\(996\) 6.00000i 0.190117i
\(997\) 11.5000 19.9186i 0.364209 0.630828i −0.624440 0.781073i \(-0.714673\pi\)
0.988649 + 0.150245i \(0.0480062\pi\)
\(998\) 0 0
\(999\) −9.52628 + 5.50000i −0.301398 + 0.174012i
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 1014.2.i.e.361.1 4
13.2 odd 12 1014.2.a.a.1.1 1
13.3 even 3 1014.2.b.a.337.1 2
13.4 even 6 inner 1014.2.i.e.823.1 4
13.5 odd 4 78.2.e.b.55.1 2
13.6 odd 12 78.2.e.b.61.1 yes 2
13.7 odd 12 1014.2.e.d.529.1 2
13.8 odd 4 1014.2.e.d.991.1 2
13.9 even 3 inner 1014.2.i.e.823.2 4
13.10 even 6 1014.2.b.a.337.2 2
13.11 odd 12 1014.2.a.e.1.1 1
13.12 even 2 inner 1014.2.i.e.361.2 4
39.2 even 12 3042.2.a.m.1.1 1
39.5 even 4 234.2.h.b.55.1 2
39.11 even 12 3042.2.a.d.1.1 1
39.23 odd 6 3042.2.b.d.1351.1 2
39.29 odd 6 3042.2.b.d.1351.2 2
39.32 even 12 234.2.h.b.217.1 2
52.11 even 12 8112.2.a.bb.1.1 1
52.15 even 12 8112.2.a.x.1.1 1
52.19 even 12 624.2.q.b.529.1 2
52.31 even 4 624.2.q.b.289.1 2
65.18 even 4 1950.2.z.b.1849.2 4
65.19 odd 12 1950.2.i.b.451.1 2
65.32 even 12 1950.2.z.b.1699.2 4
65.44 odd 4 1950.2.i.b.601.1 2
65.57 even 4 1950.2.z.b.1849.1 4
65.58 even 12 1950.2.z.b.1699.1 4
156.71 odd 12 1872.2.t.i.1153.1 2
156.83 odd 4 1872.2.t.i.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.e.b.55.1 2 13.5 odd 4
78.2.e.b.61.1 yes 2 13.6 odd 12
234.2.h.b.55.1 2 39.5 even 4
234.2.h.b.217.1 2 39.32 even 12
624.2.q.b.289.1 2 52.31 even 4
624.2.q.b.529.1 2 52.19 even 12
1014.2.a.a.1.1 1 13.2 odd 12
1014.2.a.e.1.1 1 13.11 odd 12
1014.2.b.a.337.1 2 13.3 even 3
1014.2.b.a.337.2 2 13.10 even 6
1014.2.e.d.529.1 2 13.7 odd 12
1014.2.e.d.991.1 2 13.8 odd 4
1014.2.i.e.361.1 4 1.1 even 1 trivial
1014.2.i.e.361.2 4 13.12 even 2 inner
1014.2.i.e.823.1 4 13.4 even 6 inner
1014.2.i.e.823.2 4 13.9 even 3 inner
1872.2.t.i.289.1 2 156.83 odd 4
1872.2.t.i.1153.1 2 156.71 odd 12
1950.2.i.b.451.1 2 65.19 odd 12
1950.2.i.b.601.1 2 65.44 odd 4
1950.2.z.b.1699.1 4 65.58 even 12
1950.2.z.b.1699.2 4 65.32 even 12
1950.2.z.b.1849.1 4 65.57 even 4
1950.2.z.b.1849.2 4 65.18 even 4
3042.2.a.d.1.1 1 39.11 even 12
3042.2.a.m.1.1 1 39.2 even 12
3042.2.b.d.1351.1 2 39.23 odd 6
3042.2.b.d.1351.2 2 39.29 odd 6
8112.2.a.x.1.1 1 52.15 even 12
8112.2.a.bb.1.1 1 52.11 even 12