Properties

Label 1134.2.f.m.379.1
Level $1134$
Weight $2$
Character 1134.379
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(379,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.m.757.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{17} +2.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(1.00000 + 1.73205i) q^{23} +(2.00000 - 3.46410i) q^{25} -3.00000 q^{26} -1.00000 q^{28} +(3.50000 - 6.06218i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{34} +1.00000 q^{35} -7.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.50000 + 2.59808i) q^{52} +6.00000 q^{53} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.50000 - 6.06218i) q^{58} +(5.00000 + 8.66025i) q^{59} +(4.50000 - 7.79423i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(0.500000 - 0.866025i) q^{70} +4.00000 q^{71} -11.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +6.00000 q^{82} +(-5.00000 + 8.66025i) q^{83} +(0.500000 + 0.866025i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{88} -15.0000 q^{89} -3.00000 q^{91} +(1.00000 - 1.73205i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 2 q^{11} - 3 q^{13} - q^{14} - q^{16} + 2 q^{17} + 4 q^{19} + q^{20} - 2 q^{22} + 2 q^{23} + 4 q^{25} - 6 q^{26} - 2 q^{28} + 7 q^{29} - 6 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 3.50000 6.06218i 0.649934 1.12572i −0.333205 0.942855i \(-0.608130\pi\)
0.983138 0.182864i \(-0.0585367\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0.500000 0.866025i 0.0857493 0.148522i
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 2.00000 0.294884
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) −1.50000 + 2.59808i −0.208013 + 0.360288i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −3.50000 6.06218i −0.459573 0.796003i
\(59\) 5.00000 + 8.66025i 0.650945 + 1.12747i 0.982894 + 0.184172i \(0.0589603\pi\)
−0.331949 + 0.943297i \(0.607706\pi\)
\(60\) 0 0
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50000 2.59808i 0.186052 0.322252i
\(66\) 0 0
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) −0.500000 0.866025i −0.0606339 0.105021i
\(69\) 0 0
\(70\) 0.500000 0.866025i 0.0597614 0.103510i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −1.00000 1.73205i −0.113961 0.197386i
\(78\) 0 0
\(79\) 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −5.00000 + 8.66025i −0.548821 + 0.950586i 0.449534 + 0.893263i \(0.351590\pi\)
−0.998356 + 0.0573233i \(0.981743\pi\)
\(84\) 0 0
\(85\) 0.500000 + 0.866025i 0.0542326 + 0.0939336i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) −1.00000 + 1.73205i −0.106600 + 0.184637i
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 1.00000 1.73205i 0.104257 0.180579i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) 1.50000 + 2.59808i 0.147087 + 0.254762i
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −11.0000 −1.05361 −0.526804 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) 1.00000 1.73205i 0.0953463 0.165145i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) 0 0
\(115\) −1.00000 + 1.73205i −0.0932505 + 0.161515i
\(116\) −7.00000 −0.649934
\(117\) 0 0
\(118\) 10.0000 0.920575
\(119\) 0.500000 0.866025i 0.0458349 0.0793884i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −4.50000 7.79423i −0.407411 0.705656i
\(123\) 0 0
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) 8.00000 + 13.8564i 0.698963 + 1.21064i 0.968826 + 0.247741i \(0.0796882\pi\)
−0.269863 + 0.962899i \(0.586978\pi\)
\(132\) 0 0
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) −1.00000 −0.0857493
\(137\) −5.50000 + 9.52628i −0.469897 + 0.813885i −0.999408 0.0344182i \(-0.989042\pi\)
0.529511 + 0.848303i \(0.322376\pi\)
\(138\) 0 0
\(139\) 1.00000 + 1.73205i 0.0848189 + 0.146911i 0.905314 0.424743i \(-0.139635\pi\)
−0.820495 + 0.571654i \(0.806302\pi\)
\(140\) −0.500000 0.866025i −0.0422577 0.0731925i
\(141\) 0 0
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) −6.00000 −0.501745
\(144\) 0 0
\(145\) 7.00000 0.581318
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) −10.5000 18.1865i −0.860194 1.48990i −0.871742 0.489966i \(-0.837009\pi\)
0.0115483 0.999933i \(-0.496324\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −3.00000 5.19615i −0.238667 0.413384i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 2.00000 0.157622
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) 5.00000 + 8.66025i 0.388075 + 0.672166i
\(167\) 11.0000 + 19.0526i 0.851206 + 1.47433i 0.880121 + 0.474749i \(0.157461\pi\)
−0.0289155 + 0.999582i \(0.509205\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 1.00000 0.0766965
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 6.50000 11.2583i 0.494186 0.855955i −0.505792 0.862656i \(-0.668800\pi\)
0.999978 + 0.00670064i \(0.00213290\pi\)
\(174\) 0 0
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −7.50000 + 12.9904i −0.562149 + 0.973670i
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) −1.50000 + 2.59808i −0.111187 + 0.192582i
\(183\) 0 0
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 0 0
\(187\) 1.00000 1.73205i 0.0731272 0.126660i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 2.00000 0.145095
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) 1.00000 + 1.73205i 0.0703598 + 0.121867i
\(203\) −3.50000 6.06218i −0.245652 0.425481i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) 3.00000 0.208013
\(209\) 2.00000 3.46410i 0.138343 0.239617i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) −5.50000 + 9.52628i −0.372507 + 0.645201i
\(219\) 0 0
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) −1.50000 2.59808i −0.100901 0.174766i
\(222\) 0 0
\(223\) −10.0000 + 17.3205i −0.669650 + 1.15987i 0.308353 + 0.951272i \(0.400222\pi\)
−0.978002 + 0.208595i \(0.933111\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 1.00000 0.0665190
\(227\) −12.0000 + 20.7846i −0.796468 + 1.37952i 0.125435 + 0.992102i \(0.459967\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(228\) 0 0
\(229\) 14.5000 + 25.1147i 0.958187 + 1.65963i 0.726900 + 0.686743i \(0.240960\pi\)
0.231287 + 0.972886i \(0.425707\pi\)
\(230\) 1.00000 + 1.73205i 0.0659380 + 0.114208i
\(231\) 0 0
\(232\) −3.50000 + 6.06218i −0.229786 + 0.398001i
\(233\) 19.0000 1.24473 0.622366 0.782727i \(-0.286172\pi\)
0.622366 + 0.782727i \(0.286172\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 5.00000 8.66025i 0.325472 0.563735i
\(237\) 0 0
\(238\) −0.500000 0.866025i −0.0324102 0.0561361i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 0 0
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −9.00000 −0.576166
\(245\) 0.500000 0.866025i 0.0319438 0.0553283i
\(246\) 0 0
\(247\) −3.00000 5.19615i −0.190885 0.330623i
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 0 0
\(250\) 4.50000 7.79423i 0.284605 0.492950i
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 6.00000 10.3923i 0.376473 0.652071i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.50000 7.79423i −0.280702 0.486191i 0.690856 0.722993i \(-0.257234\pi\)
−0.971558 + 0.236802i \(0.923901\pi\)
\(258\) 0 0
\(259\) −3.50000 + 6.06218i −0.217479 + 0.376685i
\(260\) −3.00000 −0.186052
\(261\) 0 0
\(262\) 16.0000 0.988483
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) 3.00000 + 5.19615i 0.184289 + 0.319197i
\(266\) −1.00000 1.73205i −0.0613139 0.106199i
\(267\) 0 0
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) −1.00000 −0.0609711 −0.0304855 0.999535i \(-0.509705\pi\)
−0.0304855 + 0.999535i \(0.509705\pi\)
\(270\) 0 0
\(271\) 30.0000 1.82237 0.911185 0.411997i \(-0.135169\pi\)
0.911185 + 0.411997i \(0.135169\pi\)
\(272\) −0.500000 + 0.866025i −0.0303170 + 0.0525105i
\(273\) 0 0
\(274\) 5.50000 + 9.52628i 0.332267 + 0.575504i
\(275\) −4.00000 6.92820i −0.241209 0.417786i
\(276\) 0 0
\(277\) −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 2.00000 0.119952
\(279\) 0 0
\(280\) −1.00000 −0.0597614
\(281\) 14.5000 25.1147i 0.864997 1.49822i −0.00205220 0.999998i \(-0.500653\pi\)
0.867050 0.498222i \(-0.166013\pi\)
\(282\) 0 0
\(283\) −8.00000 13.8564i −0.475551 0.823678i 0.524057 0.851683i \(-0.324418\pi\)
−0.999608 + 0.0280052i \(0.991084\pi\)
\(284\) −2.00000 3.46410i −0.118678 0.205557i
\(285\) 0 0
\(286\) −3.00000 + 5.19615i −0.177394 + 0.307255i
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 3.50000 6.06218i 0.205527 0.355983i
\(291\) 0 0
\(292\) 5.50000 + 9.52628i 0.321863 + 0.557483i
\(293\) −7.50000 12.9904i −0.438155 0.758906i 0.559393 0.828903i \(-0.311034\pi\)
−0.997547 + 0.0699967i \(0.977701\pi\)
\(294\) 0 0
\(295\) −5.00000 + 8.66025i −0.291111 + 0.504219i
\(296\) 7.00000 0.406867
\(297\) 0 0
\(298\) −21.0000 −1.21650
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 9.00000 0.515339
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −1.00000 + 1.73205i −0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) −7.00000 12.1244i −0.396934 0.687509i 0.596412 0.802678i \(-0.296592\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) 0 0
\(319\) −7.00000 12.1244i −0.391925 0.678834i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 1.00000 1.73205i 0.0557278 0.0965234i
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) −12.0000 −0.665640
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 10.0000 0.548821
\(333\) 0 0
\(334\) 22.0000 1.20379
\(335\) 5.00000 8.66025i 0.273179 0.473160i
\(336\) 0 0
\(337\) 9.00000 + 15.5885i 0.490261 + 0.849157i 0.999937 0.0112091i \(-0.00356804\pi\)
−0.509676 + 0.860366i \(0.670235\pi\)
\(338\) −2.00000 3.46410i −0.108786 0.188422i
\(339\) 0 0
\(340\) 0.500000 0.866025i 0.0271163 0.0469668i
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −2.00000 + 3.46410i −0.107833 + 0.186772i
\(345\) 0 0
\(346\) −6.50000 11.2583i −0.349442 0.605252i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −5.00000 + 8.66025i −0.267644 + 0.463573i −0.968253 0.249973i \(-0.919578\pi\)
0.700609 + 0.713545i \(0.252912\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 2.00000 0.106600
\(353\) −15.0000 + 25.9808i −0.798369 + 1.38282i 0.122308 + 0.992492i \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) 0 0
\(355\) 2.00000 + 3.46410i 0.106149 + 0.183855i
\(356\) 7.50000 + 12.9904i 0.397499 + 0.688489i
\(357\) 0 0
\(358\) 9.00000 15.5885i 0.475665 0.823876i
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 9.00000 15.5885i 0.473029 0.819311i
\(363\) 0 0
\(364\) 1.50000 + 2.59808i 0.0786214 + 0.136176i
\(365\) −5.50000 9.52628i −0.287883 0.498628i
\(366\) 0 0
\(367\) 5.00000 8.66025i 0.260998 0.452062i −0.705509 0.708700i \(-0.749282\pi\)
0.966507 + 0.256639i \(0.0826151\pi\)
\(368\) −2.00000 −0.104257
\(369\) 0 0
\(370\) −7.00000 −0.363913
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) −1.00000 1.73205i −0.0517088 0.0895622i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −21.0000 −1.08156
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 1.00000 1.73205i 0.0512989 0.0888523i
\(381\) 0 0
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) 16.0000 + 27.7128i 0.817562 + 1.41606i 0.907474 + 0.420109i \(0.138008\pi\)
−0.0899119 + 0.995950i \(0.528659\pi\)
\(384\) 0 0
\(385\) 1.00000 1.73205i 0.0509647 0.0882735i
\(386\) −11.0000 −0.559885
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) 17.0000 29.4449i 0.861934 1.49291i −0.00812520 0.999967i \(-0.502586\pi\)
0.870059 0.492947i \(-0.164080\pi\)
\(390\) 0 0
\(391\) 1.00000 + 1.73205i 0.0505722 + 0.0875936i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) 0.500000 0.866025i 0.0251896 0.0436297i
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) 39.0000 1.95735 0.978677 0.205406i \(-0.0658513\pi\)
0.978677 + 0.205406i \(0.0658513\pi\)
\(398\) −5.00000 + 8.66025i −0.250627 + 0.434099i
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) −9.00000 + 15.5885i −0.448322 + 0.776516i
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) −7.00000 −0.347404
\(407\) −7.00000 + 12.1244i −0.346977 + 0.600982i
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 3.00000 + 5.19615i 0.148159 + 0.256620i
\(411\) 0 0
\(412\) 8.00000 13.8564i 0.394132 0.682656i
\(413\) 10.0000 0.492068
\(414\) 0 0
\(415\) −10.0000 −0.490881
\(416\) 1.50000 2.59808i 0.0735436 0.127381i
\(417\) 0 0
\(418\) −2.00000 3.46410i −0.0978232 0.169435i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) −4.50000 + 7.79423i −0.219317 + 0.379867i −0.954599 0.297893i \(-0.903716\pi\)
0.735283 + 0.677761i \(0.237049\pi\)
\(422\) 22.0000 1.07094
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) −4.50000 7.79423i −0.217770 0.377189i
\(428\) 0 0
\(429\) 0 0
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) −3.00000 + 5.19615i −0.144005 + 0.249423i
\(435\) 0 0
\(436\) 5.50000 + 9.52628i 0.263402 + 0.456226i
\(437\) 2.00000 + 3.46410i 0.0956730 + 0.165710i
\(438\) 0 0
\(439\) 6.00000 10.3923i 0.286364 0.495998i −0.686575 0.727059i \(-0.740887\pi\)
0.972939 + 0.231062i \(0.0742199\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) −3.00000 −0.142695
\(443\) −11.0000 + 19.0526i −0.522626 + 0.905214i 0.477028 + 0.878888i \(0.341714\pi\)
−0.999653 + 0.0263261i \(0.991619\pi\)
\(444\) 0 0
\(445\) −7.50000 12.9904i −0.355534 0.615803i
\(446\) 10.0000 + 17.3205i 0.473514 + 0.820150i
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) 0.500000 0.866025i 0.0235180 0.0407344i
\(453\) 0 0
\(454\) 12.0000 + 20.7846i 0.563188 + 0.975470i
\(455\) −1.50000 2.59808i −0.0703211 0.121800i
\(456\) 0 0
\(457\) 20.5000 35.5070i 0.958950 1.66095i 0.233890 0.972263i \(-0.424854\pi\)
0.725059 0.688686i \(-0.241812\pi\)
\(458\) 29.0000 1.35508
\(459\) 0 0
\(460\) 2.00000 0.0932505
\(461\) 11.0000 19.0526i 0.512321 0.887366i −0.487577 0.873080i \(-0.662119\pi\)
0.999898 0.0142861i \(-0.00454755\pi\)
\(462\) 0 0
\(463\) −17.0000 29.4449i −0.790057 1.36842i −0.925931 0.377693i \(-0.876718\pi\)
0.135874 0.990726i \(-0.456616\pi\)
\(464\) 3.50000 + 6.06218i 0.162483 + 0.281430i
\(465\) 0 0
\(466\) 9.50000 16.4545i 0.440079 0.762239i
\(467\) −34.0000 −1.57333 −0.786666 0.617379i \(-0.788195\pi\)
−0.786666 + 0.617379i \(0.788195\pi\)
\(468\) 0 0
\(469\) −10.0000 −0.461757
\(470\) 3.00000 5.19615i 0.138380 0.239681i
\(471\) 0 0
\(472\) −5.00000 8.66025i −0.230144 0.398621i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) 4.00000 6.92820i 0.183533 0.317888i
\(476\) −1.00000 −0.0458349
\(477\) 0 0
\(478\) −6.00000 −0.274434
\(479\) −11.0000 + 19.0526i −0.502603 + 0.870534i 0.497393 + 0.867526i \(0.334291\pi\)
−0.999995 + 0.00300810i \(0.999042\pi\)
\(480\) 0 0
\(481\) 10.5000 + 18.1865i 0.478759 + 0.829235i
\(482\) −3.50000 6.06218i −0.159421 0.276125i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) −10.0000 −0.453143 −0.226572 0.973995i \(-0.572752\pi\)
−0.226572 + 0.973995i \(0.572752\pi\)
\(488\) −4.50000 + 7.79423i −0.203705 + 0.352828i
\(489\) 0 0
\(490\) −0.500000 0.866025i −0.0225877 0.0391230i
\(491\) 18.0000 + 31.1769i 0.812329 + 1.40699i 0.911230 + 0.411897i \(0.135134\pi\)
−0.0989017 + 0.995097i \(0.531533\pi\)
\(492\) 0 0
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 2.00000 3.46410i 0.0897123 0.155386i
\(498\) 0 0
\(499\) −11.0000 19.0526i −0.492428 0.852910i 0.507534 0.861632i \(-0.330557\pi\)
−0.999962 + 0.00872186i \(0.997224\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) 0 0
\(502\) 3.00000 5.19615i 0.133897 0.231916i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) 2.00000 3.46410i 0.0889108 0.153998i
\(507\) 0 0
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) −5.50000 + 9.52628i −0.243306 + 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −9.00000 −0.396973
\(515\) −8.00000 + 13.8564i −0.352522 + 0.610586i
\(516\) 0 0
\(517\) −6.00000 10.3923i −0.263880 0.457053i
\(518\) 3.50000 + 6.06218i 0.153781 + 0.266357i
\(519\) 0 0
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 8.00000 13.8564i 0.349482 0.605320i
\(525\) 0 0
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −3.00000 5.19615i −0.130682 0.226348i
\(528\) 0 0
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 6.00000 0.260623
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 0 0
\(535\) 0 0
\(536\) 5.00000 + 8.66025i 0.215967 + 0.374066i
\(537\) 0 0
\(538\) −0.500000 + 0.866025i −0.0215565 + 0.0373370i
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −3.00000 −0.128980 −0.0644900 0.997918i \(-0.520542\pi\)
−0.0644900 + 0.997918i \(0.520542\pi\)
\(542\) 15.0000 25.9808i 0.644305 1.11597i
\(543\) 0 0
\(544\) 0.500000 + 0.866025i 0.0214373 + 0.0371305i
\(545\) −5.50000 9.52628i −0.235594 0.408061i
\(546\) 0 0
\(547\) 3.00000 5.19615i 0.128271 0.222171i −0.794736 0.606955i \(-0.792391\pi\)
0.923007 + 0.384784i \(0.125724\pi\)
\(548\) 11.0000 0.469897
\(549\) 0 0
\(550\) −8.00000 −0.341121
\(551\) 7.00000 12.1244i 0.298210 0.516515i
\(552\) 0 0
\(553\) −3.00000 5.19615i −0.127573 0.220963i
\(554\) 7.00000 + 12.1244i 0.297402 + 0.515115i
\(555\) 0 0
\(556\) 1.00000 1.73205i 0.0424094 0.0734553i
\(557\) 17.0000 0.720313 0.360157 0.932892i \(-0.382723\pi\)
0.360157 + 0.932892i \(0.382723\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) −0.500000 + 0.866025i −0.0211289 + 0.0365963i
\(561\) 0 0
\(562\) −14.5000 25.1147i −0.611646 1.05940i
\(563\) 4.00000 + 6.92820i 0.168580 + 0.291989i 0.937921 0.346850i \(-0.112749\pi\)
−0.769341 + 0.638838i \(0.779415\pi\)
\(564\) 0 0
\(565\) −0.500000 + 0.866025i −0.0210352 + 0.0364340i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −13.5000 + 23.3827i −0.565949 + 0.980253i 0.431011 + 0.902347i \(0.358157\pi\)
−0.996961 + 0.0779066i \(0.975176\pi\)
\(570\) 0 0
\(571\) −9.00000 15.5885i −0.376638 0.652357i 0.613933 0.789359i \(-0.289587\pi\)
−0.990571 + 0.137002i \(0.956253\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) −35.0000 −1.45707 −0.728535 0.685009i \(-0.759798\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) 0 0
\(580\) −3.50000 6.06218i −0.145330 0.251718i
\(581\) 5.00000 + 8.66025i 0.207435 + 0.359288i
\(582\) 0 0
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 11.0000 0.455183
\(585\) 0 0
\(586\) −15.0000 −0.619644
\(587\) 1.00000 1.73205i 0.0412744 0.0714894i −0.844650 0.535319i \(-0.820192\pi\)
0.885925 + 0.463829i \(0.153525\pi\)
\(588\) 0 0
\(589\) −6.00000 10.3923i −0.247226 0.428207i
\(590\) 5.00000 + 8.66025i 0.205847 + 0.356537i
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −39.0000 −1.60154 −0.800769 0.598973i \(-0.795576\pi\)
−0.800769 + 0.598973i \(0.795576\pi\)
\(594\) 0 0
\(595\) 1.00000 0.0409960
\(596\) −10.5000 + 18.1865i −0.430097 + 0.744949i
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) 0 0
\(607\) 3.00000 + 5.19615i 0.121766 + 0.210905i 0.920464 0.390827i \(-0.127811\pi\)
−0.798698 + 0.601732i \(0.794478\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) 0 0
\(610\) 4.50000 7.79423i 0.182200 0.315579i
\(611\) −18.0000 −0.728202
\(612\) 0 0
\(613\) −18.0000 −0.727013 −0.363507 0.931592i \(-0.618421\pi\)
−0.363507 + 0.931592i \(0.618421\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 0 0
\(616\) 1.00000 + 1.73205i 0.0402911 + 0.0697863i
\(617\) −3.50000 6.06218i −0.140905 0.244054i 0.786933 0.617039i \(-0.211668\pi\)
−0.927838 + 0.372985i \(0.878334\pi\)
\(618\) 0 0
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) −6.00000 −0.240966
\(621\) 0 0
\(622\) −14.0000 −0.561349
\(623\) −7.50000 + 12.9904i −0.300481 + 0.520449i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) 0 0
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −7.00000 −0.279108
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −3.00000 + 5.19615i −0.119334 + 0.206692i
\(633\) 0 0
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 0 0
\(637\) −1.50000 + 2.59808i −0.0594322 + 0.102940i
\(638\) −14.0000 −0.554265
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i \(-0.724350\pi\)
0.983625 + 0.180229i \(0.0576838\pi\)
\(642\) 0 0
\(643\) −13.0000 22.5167i −0.512670 0.887970i −0.999892 0.0146923i \(-0.995323\pi\)
0.487222 0.873278i \(-0.338010\pi\)
\(644\) −1.00000 1.73205i −0.0394055 0.0682524i
\(645\) 0 0
\(646\) 1.00000 1.73205i 0.0393445 0.0681466i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) −6.00000 + 10.3923i −0.235339 + 0.407620i
\(651\) 0 0
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 16.0000 27.7128i 0.623272 1.07954i −0.365601 0.930772i \(-0.619136\pi\)
0.988872 0.148766i \(-0.0475302\pi\)
\(660\) 0 0
\(661\) −3.50000 6.06218i −0.136134 0.235791i 0.789896 0.613241i \(-0.210135\pi\)
−0.926030 + 0.377450i \(0.876801\pi\)
\(662\) 10.0000 + 17.3205i 0.388661 + 0.673181i
\(663\) 0 0
\(664\) 5.00000 8.66025i 0.194038 0.336083i
\(665\) 2.00000 0.0775567
\(666\) 0 0
\(667\) 14.0000 0.542082
\(668\) 11.0000 19.0526i 0.425603 0.737166i
\(669\) 0 0
\(670\) −5.00000 8.66025i −0.193167 0.334575i
\(671\) −9.00000 15.5885i −0.347441 0.601786i
\(672\) 0 0
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) 18.0000 0.693334
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) 0 0
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) −0.500000 0.866025i −0.0191741 0.0332106i
\(681\) 0 0
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −11.0000 −0.420288
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −9.00000 15.5885i −0.342873 0.593873i
\(690\) 0 0
\(691\) 2.00000 3.46410i 0.0760836 0.131781i −0.825473 0.564441i \(-0.809092\pi\)
0.901557 + 0.432660i \(0.142425\pi\)
\(692\) −13.0000 −0.494186
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −1.00000 + 1.73205i −0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 0 0
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) 5.00000 0.188847 0.0944237 0.995532i \(-0.469899\pi\)
0.0944237 + 0.995532i \(0.469899\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) 1.00000 1.73205i 0.0376889 0.0652791i
\(705\) 0 0
\(706\) 15.0000 + 25.9808i 0.564532 + 0.977799i
\(707\) 1.00000 + 1.73205i 0.0376089 + 0.0651405i
\(708\) 0 0
\(709\) −2.50000 + 4.33013i −0.0938895 + 0.162621i −0.909145 0.416481i \(-0.863263\pi\)
0.815255 + 0.579102i \(0.196597\pi\)
\(710\) 4.00000 0.150117
\(711\) 0 0
\(712\) 15.0000 0.562149
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) −3.00000 5.19615i −0.112194 0.194325i
\(716\) −9.00000 15.5885i −0.336346 0.582568i
\(717\) 0 0
\(718\) −8.00000 + 13.8564i −0.298557 + 0.517116i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) 0 0
\(724\) −9.00000 15.5885i −0.334482 0.579340i
\(725\) −14.0000 24.2487i −0.519947 0.900575i
\(726\) 0 0
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) 3.00000 0.111187
\(729\) 0 0
\(730\) −11.0000 −0.407128
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 0 0
\(733\) −21.0000 36.3731i −0.775653 1.34347i −0.934427 0.356155i \(-0.884088\pi\)
0.158774 0.987315i \(-0.449246\pi\)
\(734\) −5.00000 8.66025i −0.184553 0.319656i
\(735\) 0 0
\(736\) −1.00000 + 1.73205i −0.0368605 + 0.0638442i
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) −6.00000 −0.220714 −0.110357 0.993892i \(-0.535199\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(740\) −3.50000 + 6.06218i −0.128663 + 0.222850i
\(741\) 0 0
\(742\) −3.00000 5.19615i −0.110133 0.190757i
\(743\) 12.0000 + 20.7846i 0.440237 + 0.762513i 0.997707 0.0676840i \(-0.0215610\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(744\) 0 0
\(745\) 10.5000 18.1865i 0.384690 0.666303i
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) −2.00000 −0.0731272
\(749\) 0 0
\(750\) 0 0
\(751\) −6.00000 10.3923i −0.218943 0.379221i 0.735542 0.677479i \(-0.236928\pi\)
−0.954485 + 0.298259i \(0.903594\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −10.5000 + 18.1865i −0.382387 + 0.662314i
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 5.00000 8.66025i 0.181608 0.314555i
\(759\) 0 0
\(760\) −1.00000 1.73205i −0.0362738 0.0628281i
\(761\) 5.50000 + 9.52628i 0.199375 + 0.345327i 0.948326 0.317298i \(-0.102776\pi\)
−0.748951 + 0.662625i \(0.769442\pi\)
\(762\) 0 0
\(763\) −5.50000 + 9.52628i −0.199113 + 0.344874i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 32.0000 1.15621
\(767\) 15.0000 25.9808i 0.541619 0.938111i
\(768\) 0 0
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) −1.00000 1.73205i −0.0360375 0.0624188i
\(771\) 0 0
\(772\) −5.50000 + 9.52628i −0.197949 + 0.342858i
\(773\) 35.0000 1.25886 0.629431 0.777056i \(-0.283288\pi\)
0.629431 + 0.777056i \(0.283288\pi\)
\(774\) 0 0
\(775\) −24.0000 −0.862105
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) −17.0000 29.4449i −0.609480 1.05565i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 4.00000 6.92820i 0.143131 0.247911i
\(782\) 2.00000 0.0715199
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −6.50000 + 11.2583i −0.231995 + 0.401827i
\(786\) 0 0
\(787\) 12.0000 + 20.7846i 0.427754 + 0.740891i 0.996673 0.0815020i \(-0.0259717\pi\)
−0.568919 + 0.822393i \(0.692638\pi\)
\(788\) −0.500000 0.866025i −0.0178118 0.0308509i
\(789\) 0 0
\(790\) 3.00000 5.19615i 0.106735 0.184871i
\(791\) 1.00000 0.0355559
\(792\) 0 0
\(793\) −27.0000 −0.958798
\(794\) 19.5000 33.7750i 0.692029 1.19863i
\(795\) 0 0
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) −1.50000 2.59808i −0.0531327 0.0920286i 0.838236 0.545308i \(-0.183587\pi\)
−0.891368 + 0.453279i \(0.850254\pi\)
\(798\) 0 0
\(799\) 3.00000 5.19615i 0.106132 0.183827i
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) −3.00000 −0.105934
\(803\) −11.0000 + 19.0526i −0.388182 + 0.672350i
\(804\) 0 0
\(805\) 1.00000 + 1.73205i 0.0352454 + 0.0610468i
\(806\) 9.00000 + 15.5885i 0.317011 + 0.549080i
\(807\) 0 0
\(808\) 1.00000 1.73205i 0.0351799 0.0609333i
\(809\) −1.00000 −0.0351581 −0.0175791 0.999845i \(-0.505596\pi\)
−0.0175791 + 0.999845i \(0.505596\pi\)
\(810\) 0 0
\(811\) 34.0000 1.19390 0.596951 0.802278i \(-0.296379\pi\)
0.596951 + 0.802278i \(0.296379\pi\)
\(812\) −3.50000 + 6.06218i −0.122826 + 0.212741i
\(813\) 0 0
\(814\) 7.00000 + 12.1244i 0.245350 + 0.424958i
\(815\) −8.00000 13.8564i −0.280228 0.485369i
\(816\) 0 0
\(817\) 4.00000 6.92820i 0.139942 0.242387i
\(818\) 7.00000 0.244749
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 5.50000 9.52628i 0.191951 0.332469i −0.753946 0.656937i \(-0.771852\pi\)
0.945897 + 0.324468i \(0.105185\pi\)
\(822\) 0 0
\(823\) −8.00000 13.8564i −0.278862 0.483004i 0.692240 0.721668i \(-0.256624\pi\)
−0.971102 + 0.238664i \(0.923291\pi\)
\(824\) −8.00000 13.8564i −0.278693 0.482711i
\(825\) 0 0
\(826\) 5.00000 8.66025i 0.173972 0.301329i
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 0 0
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) −5.00000 + 8.66025i −0.173553 + 0.300602i
\(831\) 0 0
\(832\) −1.50000 2.59808i −0.0520031 0.0900721i
\(833\) −0.500000 0.866025i −0.0173240 0.0300060i
\(834\) 0 0
\(835\) −11.0000 + 19.0526i −0.380671 + 0.659341i
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) 12.0000 0.414533
\(839\) 16.0000 27.7128i 0.552381 0.956753i −0.445721 0.895172i \(-0.647053\pi\)
0.998102 0.0615805i \(-0.0196141\pi\)
\(840\) 0 0
\(841\) −10.0000 17.3205i −0.344828 0.597259i
\(842\) 4.50000 + 7.79423i 0.155080 + 0.268607i
\(843\) 0 0
\(844\) 11.0000 19.0526i 0.378636 0.655816i
\(845\) 4.00000 0.137604
\(846\) 0 0
\(847\) 7.00000 0.240523
\(848\) −3.00000 + 5.19615i −0.103020 + 0.178437i
\(849\) 0 0
\(850\) −2.00000 3.46410i −0.0685994 0.118818i
\(851\) −7.00000 12.1244i −0.239957 0.415618i
\(852\) 0 0
\(853\) 5.00000 8.66025i 0.171197 0.296521i −0.767642 0.640879i \(-0.778570\pi\)
0.938839 + 0.344358i \(0.111903\pi\)
\(854\) −9.00000 −0.307974
\(855\) 0 0
\(856\) 0 0
\(857\) 1.50000 2.59808i 0.0512390 0.0887486i −0.839268 0.543718i \(-0.817016\pi\)
0.890507 + 0.454969i \(0.150350\pi\)
\(858\) 0 0
\(859\) 26.0000 + 45.0333i 0.887109 + 1.53652i 0.843278 + 0.537478i \(0.180623\pi\)
0.0438309 + 0.999039i \(0.486044\pi\)
\(860\) −2.00000 3.46410i −0.0681994 0.118125i
\(861\) 0 0
\(862\) −6.00000 + 10.3923i −0.204361 + 0.353963i
\(863\) 14.0000 0.476566 0.238283 0.971196i \(-0.423415\pi\)
0.238283 + 0.971196i \(0.423415\pi\)
\(864\) 0 0
\(865\) 13.0000 0.442013
\(866\) 2.50000 4.33013i 0.0849535 0.147144i
\(867\) 0 0
\(868\) 3.00000 + 5.19615i 0.101827 + 0.176369i
\(869\) −6.00000 10.3923i −0.203536 0.352535i
\(870\) 0 0
\(871\) −15.0000 + 25.9808i −0.508256 + 0.880325i
\(872\) 11.0000 0.372507
\(873\) 0 0
\(874\) 4.00000 0.135302
\(875\) 4.50000 7.79423i 0.152128 0.263493i
\(876\) 0 0
\(877\) 11.5000 + 19.9186i 0.388327 + 0.672603i 0.992225 0.124459i \(-0.0397196\pi\)
−0.603897 + 0.797062i \(0.706386\pi\)
\(878\) −6.00000 10.3923i −0.202490 0.350723i
\(879\) 0 0
\(880\) −1.00000 + 1.73205i −0.0337100 + 0.0583874i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) −10.0000 −0.336527 −0.168263 0.985742i \(-0.553816\pi\)
−0.168263 + 0.985742i \(0.553816\pi\)
\(884\) −1.50000 + 2.59808i −0.0504505 + 0.0873828i
\(885\) 0 0
\(886\) 11.0000 + 19.0526i 0.369552 + 0.640083i
\(887\) 21.0000 + 36.3731i 0.705111 + 1.22129i 0.966651 + 0.256096i \(0.0824362\pi\)
−0.261540 + 0.965193i \(0.584230\pi\)
\(888\) 0 0
\(889\) 6.00000 10.3923i 0.201234 0.348547i
\(890\) −15.0000 −0.502801
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) 6.00000 10.3923i 0.200782 0.347765i
\(894\) 0 0
\(895\) 9.00000 + 15.5885i 0.300837 + 0.521065i
\(896\) −0.500000 0.866025i −0.0167038 0.0289319i
\(897\) 0 0
\(898\) −17.0000 + 29.4449i −0.567297 + 0.982588i
\(899\) −42.0000 −1.40078
\(900\) 0 0
\(901\) 6.00000 0.199889
\(902\) 6.00000 10.3923i 0.199778 0.346026i
\(903\) 0 0
\(904\) −0.500000 0.866025i −0.0166298 0.0288036i
\(905\) 9.00000 + 15.5885i 0.299170 + 0.518178i
\(906\) 0 0
\(907\) 6.00000 10.3923i 0.199227 0.345071i −0.749051 0.662512i \(-0.769490\pi\)
0.948278 + 0.317441i \(0.102824\pi\)
\(908\) 24.0000 0.796468
\(909\) 0 0
\(910\) −3.00000 −0.0994490
\(911\) 6.00000 10.3923i 0.198789 0.344312i −0.749347 0.662177i \(-0.769633\pi\)
0.948136 + 0.317865i \(0.102966\pi\)
\(912\) 0 0
\(913\) 10.0000 + 17.3205i 0.330952 + 0.573225i
\(914\) −20.5000 35.5070i −0.678080 1.17447i
\(915\) 0 0
\(916\) 14.5000 25.1147i 0.479093 0.829814i
\(917\) 16.0000 0.528367
\(918\) 0 0
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 1.00000 1.73205i 0.0329690 0.0571040i
\(921\) 0 0
\(922\) −11.0000 19.0526i −0.362266 0.627463i
\(923\) −6.00000 10.3923i −0.197492 0.342067i
\(924\) 0 0
\(925\) −14.0000 + 24.2487i −0.460317 + 0.797293i
\(926\) −34.0000 −1.11731
\(927\) 0 0
\(928\) 7.00000 0.229786
\(929\) −16.5000 + 28.5788i −0.541347 + 0.937641i 0.457480 + 0.889220i \(0.348752\pi\)
−0.998827 + 0.0484211i \(0.984581\pi\)
\(930\) 0 0
\(931\) −1.00000 1.73205i −0.0327737 0.0567657i
\(932\) −9.50000 16.4545i −0.311183 0.538985i
\(933\) 0 0
\(934\) −17.0000 + 29.4449i −0.556257 + 0.963465i
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) −43.0000 −1.40475 −0.702374 0.711808i \(-0.747877\pi\)
−0.702374 + 0.711808i \(0.747877\pi\)
\(938\) −5.00000 + 8.66025i −0.163256 + 0.282767i
\(939\) 0 0
\(940\) −3.00000 5.19615i −0.0978492 0.169480i
\(941\) 12.5000 + 21.6506i 0.407488 + 0.705791i 0.994608 0.103710i \(-0.0330714\pi\)
−0.587119 + 0.809500i \(0.699738\pi\)
\(942\) 0 0
\(943\) −6.00000 + 10.3923i −0.195387 + 0.338420i
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) 2.00000 3.46410i 0.0649913 0.112568i −0.831699 0.555227i \(-0.812631\pi\)
0.896690 + 0.442659i \(0.145965\pi\)
\(948\) 0 0
\(949\) 16.5000 + 28.5788i 0.535613 + 0.927708i
\(950\) −4.00000 6.92820i −0.129777 0.224781i
\(951\) 0 0
\(952\) −0.500000 + 0.866025i −0.0162051 + 0.0280680i
\(953\) 19.0000 0.615470 0.307735 0.951472i \(-0.400429\pi\)
0.307735 + 0.951472i \(0.400429\pi\)
\(954\) 0 0
\(955\) −18.0000 −0.582466
\(956\) −3.00000 + 5.19615i −0.0970269 + 0.168056i
\(957\) 0 0
\(958\) 11.0000 + 19.0526i 0.355394 + 0.615560i
\(959\) 5.50000 + 9.52628i 0.177604 + 0.307620i
\(960\) 0 0
\(961\) −2.50000 + 4.33013i −0.0806452 + 0.139682i
\(962\) 21.0000 0.677067
\(963\) 0 0
\(964\) −7.00000 −0.225455
\(965\) 5.50000 9.52628i 0.177051 0.306662i
\(966\) 0 0
\(967\) 11.0000 + 19.0526i 0.353736 + 0.612689i 0.986901 0.161328i \(-0.0515777\pi\)
−0.633165 + 0.774017i \(0.718244\pi\)
\(968\) −3.50000 6.06218i −0.112494 0.194846i
\(969\) 0 0
\(970\) 1.00000 1.73205i 0.0321081 0.0556128i
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 0 0
\(973\) 2.00000 0.0641171
\(974\) −5.00000 + 8.66025i −0.160210 + 0.277492i
\(975\) 0 0
\(976\) 4.50000 + 7.79423i 0.144041 + 0.249487i
\(977\) 9.00000 + 15.5885i 0.287936 + 0.498719i 0.973317 0.229465i \(-0.0736978\pi\)
−0.685381 + 0.728184i \(0.740364\pi\)
\(978\) 0 0
\(979\) −15.0000 + 25.9808i −0.479402 + 0.830349i
\(980\) −1.00000 −0.0319438
\(981\) 0 0
\(982\) 36.0000 1.14881
\(983\) −30.0000 + 51.9615i −0.956851 + 1.65732i −0.226778 + 0.973946i \(0.572819\pi\)
−0.730073 + 0.683369i \(0.760514\pi\)
\(984\) 0 0
\(985\) 0.500000 + 0.866025i 0.0159313 + 0.0275939i
\(986\) −3.50000 6.06218i −0.111463 0.193059i
\(987\) 0 0
\(988\) −3.00000 + 5.19615i −0.0954427 + 0.165312i
\(989\) 8.00000 0.254385
\(990\) 0 0
\(991\) 62.0000 1.96949 0.984747 0.173990i \(-0.0556660\pi\)
0.984747 + 0.173990i \(0.0556660\pi\)
\(992\) 3.00000 5.19615i 0.0952501 0.164978i
\(993\) 0 0
\(994\) −2.00000 3.46410i −0.0634361 0.109875i
\(995\) −5.00000 8.66025i −0.158511 0.274549i
\(996\) 0 0
\(997\) −11.5000 + 19.9186i −0.364209 + 0.630828i −0.988649 0.150245i \(-0.951994\pi\)
0.624440 + 0.781073i \(0.285327\pi\)
\(998\) −22.0000 −0.696398
\(999\) 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 1134.2.f.m.379.1 2
3.2 odd 2 1134.2.f.d.379.1 2
9.2 odd 6 1134.2.a.g.1.1 yes 1
9.4 even 3 inner 1134.2.f.m.757.1 2
9.5 odd 6 1134.2.f.d.757.1 2
9.7 even 3 1134.2.a.b.1.1 1
36.7 odd 6 9072.2.a.k.1.1 1
36.11 even 6 9072.2.a.p.1.1 1
63.20 even 6 7938.2.a.w.1.1 1
63.34 odd 6 7938.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.a.b.1.1 1 9.7 even 3
1134.2.a.g.1.1 yes 1 9.2 odd 6
1134.2.f.d.379.1 2 3.2 odd 2
1134.2.f.d.757.1 2 9.5 odd 6
1134.2.f.m.379.1 2 1.1 even 1 trivial
1134.2.f.m.757.1 2 9.4 even 3 inner
7938.2.a.j.1.1 1 63.34 odd 6
7938.2.a.w.1.1 1 63.20 even 6
9072.2.a.k.1.1 1 36.7 odd 6
9072.2.a.p.1.1 1 36.11 even 6