Properties

Label 1053.2.e.e.352.1
Level $1053$
Weight $2$
Character 1053.352
Analytic conductor $8.408$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1053,2,Mod(352,1053)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1053, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1053.352");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.e (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: \(8.40824733284\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1053.352
Dual form 1053.2.e.e.703.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20711 - 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(1.41421 - 2.44949i) q^{5} +(1.41421 + 2.44949i) q^{7} +4.41421 q^{8} +O(q^{10})\) \(q+(-1.20711 - 2.09077i) q^{2} +(-1.91421 + 3.31552i) q^{4} +(1.41421 - 2.44949i) q^{5} +(1.41421 + 2.44949i) q^{7} +4.41421 q^{8} -6.82843 q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(3.41421 - 5.91359i) q^{14} +(-1.50000 - 2.59808i) q^{16} +3.65685 q^{17} +2.82843 q^{19} +(5.41421 + 9.37769i) q^{20} +(-2.41421 + 4.18154i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{25} -2.41421 q^{26} -10.8284 q^{28} +(1.00000 + 1.73205i) q^{29} +(3.41421 - 5.91359i) q^{31} +(0.792893 - 1.37333i) q^{32} +(-4.41421 - 7.64564i) q^{34} +8.00000 q^{35} +3.65685 q^{37} +(-3.41421 - 5.91359i) q^{38} +(6.24264 - 10.8126i) q^{40} +(5.41421 - 9.37769i) q^{41} +(-4.82843 - 8.36308i) q^{43} +7.65685 q^{44} +9.65685 q^{46} +(-0.171573 - 0.297173i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-3.62132 + 6.27231i) q^{50} +(1.91421 + 3.31552i) q^{52} +2.00000 q^{53} -5.65685 q^{55} +(6.24264 + 10.8126i) q^{56} +(2.41421 - 4.18154i) q^{58} +(-1.82843 + 3.16693i) q^{59} +(4.65685 + 8.06591i) q^{61} -16.4853 q^{62} -9.82843 q^{64} +(-1.41421 - 2.44949i) q^{65} +(-0.585786 + 1.01461i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(-9.65685 - 16.7262i) q^{70} -2.00000 q^{71} +11.6569 q^{73} +(-4.41421 - 7.64564i) q^{74} +(-5.41421 + 9.37769i) q^{76} +(2.82843 - 4.89898i) q^{77} +(-5.65685 - 9.79796i) q^{79} -8.48528 q^{80} -26.1421 q^{82} +(-3.82843 - 6.63103i) q^{83} +(5.17157 - 8.95743i) q^{85} +(-11.6569 + 20.1903i) q^{86} +(-4.41421 - 7.64564i) q^{88} -9.17157 q^{89} +2.82843 q^{91} +(-7.65685 - 13.2621i) q^{92} +(-0.414214 + 0.717439i) q^{94} +(4.00000 - 6.92820i) q^{95} +(3.82843 + 6.63103i) q^{97} +2.41421 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8} - 16 q^{10} - 4 q^{11} + 2 q^{13} + 8 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 32 q^{28} + 4 q^{29} + 8 q^{31} + 6 q^{32} - 12 q^{34} + 32 q^{35} - 8 q^{37} - 8 q^{38} + 8 q^{40} + 16 q^{41} - 8 q^{43} + 8 q^{44} + 16 q^{46} - 12 q^{47} - 2 q^{49} - 6 q^{50} + 2 q^{52} + 8 q^{53} + 8 q^{56} + 4 q^{58} + 4 q^{59} - 4 q^{61} - 32 q^{62} - 28 q^{64} - 8 q^{67} - 28 q^{68} - 16 q^{70} - 8 q^{71} + 24 q^{73} - 12 q^{74} - 16 q^{76} - 48 q^{82} - 4 q^{83} + 32 q^{85} - 24 q^{86} - 12 q^{88} - 48 q^{89} - 8 q^{92} + 4 q^{94} + 16 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(730\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20711 2.09077i −0.853553 1.47840i −0.877981 0.478696i \(-0.841110\pi\)
0.0244272 0.999702i \(-0.492224\pi\)
\(3\) 0 0
\(4\) −1.91421 + 3.31552i −0.957107 + 1.65776i
\(5\) 1.41421 2.44949i 0.632456 1.09545i −0.354593 0.935021i \(-0.615380\pi\)
0.987048 0.160424i \(-0.0512862\pi\)
\(6\) 0 0
\(7\) 1.41421 + 2.44949i 0.534522 + 0.925820i 0.999186 + 0.0403329i \(0.0128419\pi\)
−0.464664 + 0.885487i \(0.653825\pi\)
\(8\) 4.41421 1.56066
\(9\) 0 0
\(10\) −6.82843 −2.15934
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) 3.41421 5.91359i 0.912487 1.58047i
\(15\) 0 0
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 3.65685 0.886917 0.443459 0.896295i \(-0.353751\pi\)
0.443459 + 0.896295i \(0.353751\pi\)
\(18\) 0 0
\(19\) 2.82843 0.648886 0.324443 0.945905i \(-0.394823\pi\)
0.324443 + 0.945905i \(0.394823\pi\)
\(20\) 5.41421 + 9.37769i 1.21065 + 2.09692i
\(21\) 0 0
\(22\) −2.41421 + 4.18154i −0.514712 + 0.891507i
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) −2.41421 −0.473466
\(27\) 0 0
\(28\) −10.8284 −2.04638
\(29\) 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i \(-0.107213\pi\)
−0.758115 + 0.652121i \(0.773880\pi\)
\(30\) 0 0
\(31\) 3.41421 5.91359i 0.613211 1.06211i −0.377485 0.926016i \(-0.623211\pi\)
0.990696 0.136097i \(-0.0434557\pi\)
\(32\) 0.792893 1.37333i 0.140165 0.242773i
\(33\) 0 0
\(34\) −4.41421 7.64564i −0.757031 1.31122i
\(35\) 8.00000 1.35225
\(36\) 0 0
\(37\) 3.65685 0.601183 0.300592 0.953753i \(-0.402816\pi\)
0.300592 + 0.953753i \(0.402816\pi\)
\(38\) −3.41421 5.91359i −0.553859 0.959311i
\(39\) 0 0
\(40\) 6.24264 10.8126i 0.987048 1.70962i
\(41\) 5.41421 9.37769i 0.845558 1.46455i −0.0395775 0.999217i \(-0.512601\pi\)
0.885136 0.465333i \(-0.154065\pi\)
\(42\) 0 0
\(43\) −4.82843 8.36308i −0.736328 1.27536i −0.954138 0.299367i \(-0.903225\pi\)
0.217810 0.975991i \(-0.430109\pi\)
\(44\) 7.65685 1.15431
\(45\) 0 0
\(46\) 9.65685 1.42383
\(47\) −0.171573 0.297173i −0.0250265 0.0433471i 0.853241 0.521517i \(-0.174634\pi\)
−0.878267 + 0.478170i \(0.841300\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −3.62132 + 6.27231i −0.512132 + 0.887039i
\(51\) 0 0
\(52\) 1.91421 + 3.31552i 0.265454 + 0.459779i
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) −5.65685 −0.762770
\(56\) 6.24264 + 10.8126i 0.834208 + 1.44489i
\(57\) 0 0
\(58\) 2.41421 4.18154i 0.317002 0.549063i
\(59\) −1.82843 + 3.16693i −0.238041 + 0.412299i −0.960152 0.279478i \(-0.909839\pi\)
0.722111 + 0.691777i \(0.243172\pi\)
\(60\) 0 0
\(61\) 4.65685 + 8.06591i 0.596249 + 1.03273i 0.993369 + 0.114967i \(0.0366763\pi\)
−0.397120 + 0.917767i \(0.629990\pi\)
\(62\) −16.4853 −2.09363
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) −1.41421 2.44949i −0.175412 0.303822i
\(66\) 0 0
\(67\) −0.585786 + 1.01461i −0.0715652 + 0.123955i −0.899587 0.436741i \(-0.856133\pi\)
0.828022 + 0.560695i \(0.189466\pi\)
\(68\) −7.00000 + 12.1244i −0.848875 + 1.47029i
\(69\) 0 0
\(70\) −9.65685 16.7262i −1.15421 1.99916i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 11.6569 1.36433 0.682166 0.731198i \(-0.261038\pi\)
0.682166 + 0.731198i \(0.261038\pi\)
\(74\) −4.41421 7.64564i −0.513142 0.888788i
\(75\) 0 0
\(76\) −5.41421 + 9.37769i −0.621053 + 1.07570i
\(77\) 2.82843 4.89898i 0.322329 0.558291i
\(78\) 0 0
\(79\) −5.65685 9.79796i −0.636446 1.10236i −0.986207 0.165518i \(-0.947071\pi\)
0.349761 0.936839i \(-0.386263\pi\)
\(80\) −8.48528 −0.948683
\(81\) 0 0
\(82\) −26.1421 −2.88692
\(83\) −3.82843 6.63103i −0.420224 0.727850i 0.575737 0.817635i \(-0.304715\pi\)
−0.995961 + 0.0897850i \(0.971382\pi\)
\(84\) 0 0
\(85\) 5.17157 8.95743i 0.560936 0.971569i
\(86\) −11.6569 + 20.1903i −1.25699 + 2.17717i
\(87\) 0 0
\(88\) −4.41421 7.64564i −0.470557 0.815028i
\(89\) −9.17157 −0.972185 −0.486092 0.873907i \(-0.661578\pi\)
−0.486092 + 0.873907i \(0.661578\pi\)
\(90\) 0 0
\(91\) 2.82843 0.296500
\(92\) −7.65685 13.2621i −0.798282 1.38267i
\(93\) 0 0
\(94\) −0.414214 + 0.717439i −0.0427229 + 0.0739982i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 3.82843 + 6.63103i 0.388718 + 0.673279i 0.992277 0.124039i \(-0.0395847\pi\)
−0.603559 + 0.797318i \(0.706251\pi\)
\(98\) 2.41421 0.243872
\(99\) 0 0
\(100\) 11.4853 1.14853
\(101\) −1.82843 3.16693i −0.181935 0.315121i 0.760604 0.649216i \(-0.224903\pi\)
−0.942540 + 0.334095i \(0.891569\pi\)
\(102\) 0 0
\(103\) −6.82843 + 11.8272i −0.672825 + 1.16537i 0.304275 + 0.952584i \(0.401586\pi\)
−0.977100 + 0.212783i \(0.931747\pi\)
\(104\) 2.20711 3.82282i 0.216425 0.374858i
\(105\) 0 0
\(106\) −2.41421 4.18154i −0.234489 0.406147i
\(107\) −11.3137 −1.09374 −0.546869 0.837218i \(-0.684180\pi\)
−0.546869 + 0.837218i \(0.684180\pi\)
\(108\) 0 0
\(109\) −17.3137 −1.65835 −0.829176 0.558987i \(-0.811190\pi\)
−0.829176 + 0.558987i \(0.811190\pi\)
\(110\) 6.82843 + 11.8272i 0.651065 + 1.12768i
\(111\) 0 0
\(112\) 4.24264 7.34847i 0.400892 0.694365i
\(113\) 8.65685 14.9941i 0.814368 1.41053i −0.0954122 0.995438i \(-0.530417\pi\)
0.909781 0.415090i \(-0.136250\pi\)
\(114\) 0 0
\(115\) 5.65685 + 9.79796i 0.527504 + 0.913664i
\(116\) −7.65685 −0.710921
\(117\) 0 0
\(118\) 8.82843 0.812723
\(119\) 5.17157 + 8.95743i 0.474077 + 0.821126i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 11.2426 19.4728i 1.01786 1.76299i
\(123\) 0 0
\(124\) 13.0711 + 22.6398i 1.17382 + 2.03311i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −5.65685 −0.501965 −0.250982 0.967992i \(-0.580754\pi\)
−0.250982 + 0.967992i \(0.580754\pi\)
\(128\) 10.2782 + 17.8023i 0.908471 + 1.57352i
\(129\) 0 0
\(130\) −3.41421 + 5.91359i −0.299446 + 0.518656i
\(131\) −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i \(-0.946976\pi\)
0.636676 + 0.771132i \(0.280309\pi\)
\(132\) 0 0
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) 2.82843 0.244339
\(135\) 0 0
\(136\) 16.1421 1.38418
\(137\) −2.58579 4.47871i −0.220919 0.382642i 0.734169 0.678967i \(-0.237572\pi\)
−0.955087 + 0.296325i \(0.904239\pi\)
\(138\) 0 0
\(139\) −7.65685 + 13.2621i −0.649446 + 1.12487i 0.333810 + 0.942641i \(0.391666\pi\)
−0.983255 + 0.182233i \(0.941668\pi\)
\(140\) −15.3137 + 26.5241i −1.29424 + 2.24170i
\(141\) 0 0
\(142\) 2.41421 + 4.18154i 0.202596 + 0.350907i
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) 5.65685 0.469776
\(146\) −14.0711 24.3718i −1.16453 2.01702i
\(147\) 0 0
\(148\) −7.00000 + 12.1244i −0.575396 + 0.996616i
\(149\) −7.41421 + 12.8418i −0.607396 + 1.05204i 0.384272 + 0.923220i \(0.374453\pi\)
−0.991668 + 0.128821i \(0.958881\pi\)
\(150\) 0 0
\(151\) 10.2426 + 17.7408i 0.833534 + 1.44372i 0.895218 + 0.445628i \(0.147020\pi\)
−0.0616840 + 0.998096i \(0.519647\pi\)
\(152\) 12.4853 1.01269
\(153\) 0 0
\(154\) −13.6569 −1.10050
\(155\) −9.65685 16.7262i −0.775657 1.34348i
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) −13.6569 + 23.6544i −1.08648 + 1.88184i
\(159\) 0 0
\(160\) −2.24264 3.88437i −0.177296 0.307086i
\(161\) −11.3137 −0.891645
\(162\) 0 0
\(163\) 13.1716 1.03168 0.515839 0.856686i \(-0.327480\pi\)
0.515839 + 0.856686i \(0.327480\pi\)
\(164\) 20.7279 + 35.9018i 1.61858 + 2.80346i
\(165\) 0 0
\(166\) −9.24264 + 16.0087i −0.717368 + 1.24252i
\(167\) 3.82843 6.63103i 0.296253 0.513125i −0.679023 0.734117i \(-0.737596\pi\)
0.975275 + 0.220993i \(0.0709296\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −24.9706 −1.91515
\(171\) 0 0
\(172\) 36.9706 2.81898
\(173\) −0.171573 0.297173i −0.0130444 0.0225936i 0.859429 0.511254i \(-0.170819\pi\)
−0.872474 + 0.488661i \(0.837486\pi\)
\(174\) 0 0
\(175\) 4.24264 7.34847i 0.320713 0.555492i
\(176\) −3.00000 + 5.19615i −0.226134 + 0.391675i
\(177\) 0 0
\(178\) 11.0711 + 19.1757i 0.829812 + 1.43728i
\(179\) 0.686292 0.0512958 0.0256479 0.999671i \(-0.491835\pi\)
0.0256479 + 0.999671i \(0.491835\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −3.41421 5.91359i −0.253078 0.438345i
\(183\) 0 0
\(184\) −8.82843 + 15.2913i −0.650840 + 1.12729i
\(185\) 5.17157 8.95743i 0.380222 0.658563i
\(186\) 0 0
\(187\) −3.65685 6.33386i −0.267416 0.463178i
\(188\) 1.31371 0.0958120
\(189\) 0 0
\(190\) −19.3137 −1.40116
\(191\) −9.65685 16.7262i −0.698745 1.21026i −0.968902 0.247446i \(-0.920409\pi\)
0.270156 0.962817i \(-0.412925\pi\)
\(192\) 0 0
\(193\) 8.65685 14.9941i 0.623134 1.07930i −0.365765 0.930707i \(-0.619192\pi\)
0.988899 0.148592i \(-0.0474742\pi\)
\(194\) 9.24264 16.0087i 0.663583 1.14936i
\(195\) 0 0
\(196\) −1.91421 3.31552i −0.136730 0.236823i
\(197\) 16.4853 1.17453 0.587264 0.809396i \(-0.300205\pi\)
0.587264 + 0.809396i \(0.300205\pi\)
\(198\) 0 0
\(199\) 10.3431 0.733206 0.366603 0.930377i \(-0.380521\pi\)
0.366603 + 0.930377i \(0.380521\pi\)
\(200\) −6.62132 11.4685i −0.468198 0.810943i
\(201\) 0 0
\(202\) −4.41421 + 7.64564i −0.310583 + 0.537946i
\(203\) −2.82843 + 4.89898i −0.198517 + 0.343841i
\(204\) 0 0
\(205\) −15.3137 26.5241i −1.06956 1.85252i
\(206\) 32.9706 2.29717
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) −2.82843 4.89898i −0.195646 0.338869i
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) −3.82843 + 6.63103i −0.262937 + 0.455421i
\(213\) 0 0
\(214\) 13.6569 + 23.6544i 0.933563 + 1.61698i
\(215\) −27.3137 −1.86278
\(216\) 0 0
\(217\) 19.3137 1.31110
\(218\) 20.8995 + 36.1990i 1.41549 + 2.45170i
\(219\) 0 0
\(220\) 10.8284 18.7554i 0.730052 1.26449i
\(221\) 1.82843 3.16693i 0.122993 0.213031i
\(222\) 0 0
\(223\) −2.24264 3.88437i −0.150178 0.260116i 0.781115 0.624388i \(-0.214651\pi\)
−0.931293 + 0.364271i \(0.881318\pi\)
\(224\) 4.48528 0.299685
\(225\) 0 0
\(226\) −41.7990 −2.78043
\(227\) 2.65685 + 4.60181i 0.176342 + 0.305433i 0.940625 0.339448i \(-0.110240\pi\)
−0.764283 + 0.644881i \(0.776907\pi\)
\(228\) 0 0
\(229\) −10.6569 + 18.4582i −0.704225 + 1.21975i 0.262746 + 0.964865i \(0.415372\pi\)
−0.966971 + 0.254888i \(0.917961\pi\)
\(230\) 13.6569 23.6544i 0.900506 1.55972i
\(231\) 0 0
\(232\) 4.41421 + 7.64564i 0.289807 + 0.501961i
\(233\) 26.9706 1.76690 0.883450 0.468525i \(-0.155214\pi\)
0.883450 + 0.468525i \(0.155214\pi\)
\(234\) 0 0
\(235\) −0.970563 −0.0633125
\(236\) −7.00000 12.1244i −0.455661 0.789228i
\(237\) 0 0
\(238\) 12.4853 21.6251i 0.809301 1.40175i
\(239\) 1.00000 1.73205i 0.0646846 0.112037i −0.831869 0.554971i \(-0.812729\pi\)
0.896554 + 0.442934i \(0.146063\pi\)
\(240\) 0 0
\(241\) −5.82843 10.0951i −0.375442 0.650285i 0.614951 0.788565i \(-0.289176\pi\)
−0.990393 + 0.138281i \(0.955842\pi\)
\(242\) −16.8995 −1.08634
\(243\) 0 0
\(244\) −35.6569 −2.28270
\(245\) 1.41421 + 2.44949i 0.0903508 + 0.156492i
\(246\) 0 0
\(247\) 1.41421 2.44949i 0.0899843 0.155857i
\(248\) 15.0711 26.1039i 0.957014 1.65760i
\(249\) 0 0
\(250\) −6.82843 11.8272i −0.431868 0.748017i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 6.82843 + 11.8272i 0.428454 + 0.742103i
\(255\) 0 0
\(256\) 14.9853 25.9553i 0.936580 1.62220i
\(257\) −7.82843 + 13.5592i −0.488324 + 0.845802i −0.999910 0.0134304i \(-0.995725\pi\)
0.511586 + 0.859232i \(0.329058\pi\)
\(258\) 0 0
\(259\) 5.17157 + 8.95743i 0.321346 + 0.556587i
\(260\) 10.8284 0.671551
\(261\) 0 0
\(262\) 19.3137 1.19320
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 2.82843 4.89898i 0.173749 0.300942i
\(266\) 9.65685 16.7262i 0.592100 1.02555i
\(267\) 0 0
\(268\) −2.24264 3.88437i −0.136991 0.237276i
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 11.7990 0.716738 0.358369 0.933580i \(-0.383333\pi\)
0.358369 + 0.933580i \(0.383333\pi\)
\(272\) −5.48528 9.50079i −0.332594 0.576070i
\(273\) 0 0
\(274\) −6.24264 + 10.8126i −0.377132 + 0.653211i
\(275\) −3.00000 + 5.19615i −0.180907 + 0.313340i
\(276\) 0 0
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 36.9706 2.21735
\(279\) 0 0
\(280\) 35.3137 2.11040
\(281\) 13.4142 + 23.2341i 0.800225 + 1.38603i 0.919468 + 0.393165i \(0.128620\pi\)
−0.119243 + 0.992865i \(0.538047\pi\)
\(282\) 0 0
\(283\) 2.48528 4.30463i 0.147735 0.255884i −0.782655 0.622455i \(-0.786135\pi\)
0.930390 + 0.366572i \(0.119469\pi\)
\(284\) 3.82843 6.63103i 0.227175 0.393479i
\(285\) 0 0
\(286\) 2.41421 + 4.18154i 0.142755 + 0.247260i
\(287\) 30.6274 1.80788
\(288\) 0 0
\(289\) −3.62742 −0.213377
\(290\) −6.82843 11.8272i −0.400979 0.694516i
\(291\) 0 0
\(292\) −22.3137 + 38.6485i −1.30581 + 2.26173i
\(293\) −13.0711 + 22.6398i −0.763620 + 1.32263i 0.177353 + 0.984147i \(0.443247\pi\)
−0.940973 + 0.338481i \(0.890087\pi\)
\(294\) 0 0
\(295\) 5.17157 + 8.95743i 0.301101 + 0.521522i
\(296\) 16.1421 0.938243
\(297\) 0 0
\(298\) 35.7990 2.07378
\(299\) 2.00000 + 3.46410i 0.115663 + 0.200334i
\(300\) 0 0
\(301\) 13.6569 23.6544i 0.787168 1.36341i
\(302\) 24.7279 42.8300i 1.42293 2.46459i
\(303\) 0 0
\(304\) −4.24264 7.34847i −0.243332 0.421464i
\(305\) 26.3431 1.50840
\(306\) 0 0
\(307\) −17.1716 −0.980033 −0.490017 0.871713i \(-0.663009\pi\)
−0.490017 + 0.871713i \(0.663009\pi\)
\(308\) 10.8284 + 18.7554i 0.617007 + 1.06869i
\(309\) 0 0
\(310\) −23.3137 + 40.3805i −1.32413 + 2.29346i
\(311\) 17.3137 29.9882i 0.981770 1.70048i 0.326279 0.945274i \(-0.394205\pi\)
0.655492 0.755203i \(-0.272461\pi\)
\(312\) 0 0
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) −24.1421 −1.36242
\(315\) 0 0
\(316\) 43.3137 2.43659
\(317\) −4.24264 7.34847i −0.238290 0.412731i 0.721933 0.691963i \(-0.243254\pi\)
−0.960224 + 0.279231i \(0.909920\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) −13.8995 + 24.0746i −0.777005 + 1.34581i
\(321\) 0 0
\(322\) 13.6569 + 23.6544i 0.761067 + 1.31821i
\(323\) 10.3431 0.575508
\(324\) 0 0
\(325\) −3.00000 −0.166410
\(326\) −15.8995 27.5387i −0.880592 1.52523i
\(327\) 0 0
\(328\) 23.8995 41.3951i 1.31963 2.28566i
\(329\) 0.485281 0.840532i 0.0267544 0.0463400i
\(330\) 0 0
\(331\) 1.07107 + 1.85514i 0.0588712 + 0.101968i 0.893959 0.448149i \(-0.147917\pi\)
−0.835088 + 0.550117i \(0.814583\pi\)
\(332\) 29.3137 1.60880
\(333\) 0 0
\(334\) −18.4853 −1.01147
\(335\) 1.65685 + 2.86976i 0.0905236 + 0.156792i
\(336\) 0 0
\(337\) 6.65685 11.5300i 0.362622 0.628080i −0.625770 0.780008i \(-0.715215\pi\)
0.988392 + 0.151928i \(0.0485483\pi\)
\(338\) −1.20711 + 2.09077i −0.0656580 + 0.113723i
\(339\) 0 0
\(340\) 19.7990 + 34.2929i 1.07375 + 1.85979i
\(341\) −13.6569 −0.739560
\(342\) 0 0
\(343\) 16.9706 0.916324
\(344\) −21.3137 36.9164i −1.14916 1.99040i
\(345\) 0 0
\(346\) −0.414214 + 0.717439i −0.0222683 + 0.0385698i
\(347\) −15.6569 + 27.1185i −0.840504 + 1.45580i 0.0489652 + 0.998800i \(0.484408\pi\)
−0.889469 + 0.456995i \(0.848926\pi\)
\(348\) 0 0
\(349\) 3.82843 + 6.63103i 0.204931 + 0.354951i 0.950111 0.311913i \(-0.100970\pi\)
−0.745180 + 0.666864i \(0.767636\pi\)
\(350\) −20.4853 −1.09498
\(351\) 0 0
\(352\) −3.17157 −0.169045
\(353\) 8.72792 + 15.1172i 0.464540 + 0.804608i 0.999181 0.0404722i \(-0.0128862\pi\)
−0.534640 + 0.845080i \(0.679553\pi\)
\(354\) 0 0
\(355\) −2.82843 + 4.89898i −0.150117 + 0.260011i
\(356\) 17.5563 30.4085i 0.930485 1.61165i
\(357\) 0 0
\(358\) −0.828427 1.43488i −0.0437837 0.0758357i
\(359\) −1.02944 −0.0543316 −0.0271658 0.999631i \(-0.508648\pi\)
−0.0271658 + 0.999631i \(0.508648\pi\)
\(360\) 0 0
\(361\) −11.0000 −0.578947
\(362\) −16.8995 29.2708i −0.888218 1.53844i
\(363\) 0 0
\(364\) −5.41421 + 9.37769i −0.283782 + 0.491525i
\(365\) 16.4853 28.5533i 0.862879 1.49455i
\(366\) 0 0
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) 12.0000 0.625543
\(369\) 0 0
\(370\) −24.9706 −1.29816
\(371\) 2.82843 + 4.89898i 0.146845 + 0.254342i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) −8.82843 + 15.2913i −0.456507 + 0.790693i
\(375\) 0 0
\(376\) −0.757359 1.31178i −0.0390578 0.0676501i
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) −16.4853 −0.846792 −0.423396 0.905945i \(-0.639162\pi\)
−0.423396 + 0.905945i \(0.639162\pi\)
\(380\) 15.3137 + 26.5241i 0.785577 + 1.36066i
\(381\) 0 0
\(382\) −23.3137 + 40.3805i −1.19283 + 2.06605i
\(383\) −1.48528 + 2.57258i −0.0758943 + 0.131453i −0.901475 0.432832i \(-0.857515\pi\)
0.825581 + 0.564284i \(0.190848\pi\)
\(384\) 0 0
\(385\) −8.00000 13.8564i −0.407718 0.706188i
\(386\) −41.7990 −2.12751
\(387\) 0 0
\(388\) −29.3137 −1.48818
\(389\) 3.48528 + 6.03668i 0.176711 + 0.306072i 0.940752 0.339095i \(-0.110121\pi\)
−0.764041 + 0.645167i \(0.776788\pi\)
\(390\) 0 0
\(391\) −7.31371 + 12.6677i −0.369870 + 0.640634i
\(392\) −2.20711 + 3.82282i −0.111476 + 0.193082i
\(393\) 0 0
\(394\) −19.8995 34.4669i −1.00252 1.73642i
\(395\) −32.0000 −1.61009
\(396\) 0 0
\(397\) −2.97056 −0.149088 −0.0745441 0.997218i \(-0.523750\pi\)
−0.0745441 + 0.997218i \(0.523750\pi\)
\(398\) −12.4853 21.6251i −0.625831 1.08397i
\(399\) 0 0
\(400\) −4.50000 + 7.79423i −0.225000 + 0.389711i
\(401\) −1.07107 + 1.85514i −0.0534866 + 0.0926415i −0.891529 0.452964i \(-0.850367\pi\)
0.838042 + 0.545605i \(0.183700\pi\)
\(402\) 0 0
\(403\) −3.41421 5.91359i −0.170074 0.294577i
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) 13.6569 0.677778
\(407\) −3.65685 6.33386i −0.181264 0.313958i
\(408\) 0 0
\(409\) 0.514719 0.891519i 0.0254512 0.0440828i −0.853019 0.521879i \(-0.825231\pi\)
0.878470 + 0.477797i \(0.158564\pi\)
\(410\) −36.9706 + 64.0349i −1.82585 + 3.16246i
\(411\) 0 0
\(412\) −26.1421 45.2795i −1.28793 2.23076i
\(413\) −10.3431 −0.508953
\(414\) 0 0
\(415\) −21.6569 −1.06309
\(416\) −0.792893 1.37333i −0.0388748 0.0673331i
\(417\) 0 0
\(418\) −6.82843 + 11.8272i −0.333989 + 0.578486i
\(419\) −15.3137 + 26.5241i −0.748124 + 1.29579i 0.200597 + 0.979674i \(0.435712\pi\)
−0.948721 + 0.316114i \(0.897622\pi\)
\(420\) 0 0
\(421\) −7.34315 12.7187i −0.357883 0.619872i 0.629724 0.776819i \(-0.283168\pi\)
−0.987607 + 0.156947i \(0.949835\pi\)
\(422\) −28.9706 −1.41026
\(423\) 0 0
\(424\) 8.82843 0.428746
\(425\) −5.48528 9.50079i −0.266075 0.460856i
\(426\) 0 0
\(427\) −13.1716 + 22.8138i −0.637417 + 1.10404i
\(428\) 21.6569 37.5108i 1.04682 1.81315i
\(429\) 0 0
\(430\) 32.9706 + 57.1067i 1.58998 + 2.75393i
\(431\) −19.6569 −0.946837 −0.473419 0.880838i \(-0.656980\pi\)
−0.473419 + 0.880838i \(0.656980\pi\)
\(432\) 0 0
\(433\) 1.31371 0.0631328 0.0315664 0.999502i \(-0.489950\pi\)
0.0315664 + 0.999502i \(0.489950\pi\)
\(434\) −23.3137 40.3805i −1.11909 1.93833i
\(435\) 0 0
\(436\) 33.1421 57.4039i 1.58722 2.74915i
\(437\) −5.65685 + 9.79796i −0.270604 + 0.468700i
\(438\) 0 0
\(439\) 8.48528 + 14.6969i 0.404980 + 0.701447i 0.994319 0.106439i \(-0.0339450\pi\)
−0.589339 + 0.807886i \(0.700612\pi\)
\(440\) −24.9706 −1.19042
\(441\) 0 0
\(442\) −8.82843 −0.419925
\(443\) 20.9706 + 36.3221i 0.996342 + 1.72571i 0.572182 + 0.820126i \(0.306097\pi\)
0.424159 + 0.905588i \(0.360570\pi\)
\(444\) 0 0
\(445\) −12.9706 + 22.4657i −0.614864 + 1.06498i
\(446\) −5.41421 + 9.37769i −0.256370 + 0.444047i
\(447\) 0 0
\(448\) −13.8995 24.0746i −0.656689 1.13742i
\(449\) −7.79899 −0.368057 −0.184029 0.982921i \(-0.558914\pi\)
−0.184029 + 0.982921i \(0.558914\pi\)
\(450\) 0 0
\(451\) −21.6569 −1.01978
\(452\) 33.1421 + 57.4039i 1.55887 + 2.70005i
\(453\) 0 0
\(454\) 6.41421 11.1097i 0.301034 0.521406i
\(455\) 4.00000 6.92820i 0.187523 0.324799i
\(456\) 0 0
\(457\) −1.82843 3.16693i −0.0855302 0.148143i 0.820087 0.572239i \(-0.193925\pi\)
−0.905617 + 0.424096i \(0.860592\pi\)
\(458\) 51.4558 2.40437
\(459\) 0 0
\(460\) −43.3137 −2.01951
\(461\) 5.41421 + 9.37769i 0.252165 + 0.436763i 0.964122 0.265461i \(-0.0855241\pi\)
−0.711957 + 0.702223i \(0.752191\pi\)
\(462\) 0 0
\(463\) 3.75736 6.50794i 0.174619 0.302449i −0.765410 0.643543i \(-0.777464\pi\)
0.940029 + 0.341093i \(0.110797\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −32.5563 56.3893i −1.50814 2.61218i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) −3.31371 −0.153013
\(470\) 1.17157 + 2.02922i 0.0540406 + 0.0936011i
\(471\) 0 0
\(472\) −8.07107 + 13.9795i −0.371501 + 0.643459i
\(473\) −9.65685 + 16.7262i −0.444023 + 0.769070i
\(474\) 0 0
\(475\) −4.24264 7.34847i −0.194666 0.337171i
\(476\) −39.5980 −1.81497
\(477\) 0 0
\(478\) −4.82843 −0.220847
\(479\) 1.34315 + 2.32640i 0.0613699 + 0.106296i 0.895078 0.445910i \(-0.147120\pi\)
−0.833708 + 0.552205i \(0.813786\pi\)
\(480\) 0 0
\(481\) 1.82843 3.16693i 0.0833691 0.144400i
\(482\) −14.0711 + 24.3718i −0.640920 + 1.11011i
\(483\) 0 0
\(484\) 13.3995 + 23.2086i 0.609068 + 1.05494i
\(485\) 21.6569 0.983387
\(486\) 0 0
\(487\) 31.7990 1.44095 0.720475 0.693481i \(-0.243924\pi\)
0.720475 + 0.693481i \(0.243924\pi\)
\(488\) 20.5563 + 35.6046i 0.930542 + 1.61175i
\(489\) 0 0
\(490\) 3.41421 5.91359i 0.154238 0.267149i
\(491\) −7.31371 + 12.6677i −0.330063 + 0.571686i −0.982524 0.186136i \(-0.940403\pi\)
0.652461 + 0.757822i \(0.273737\pi\)
\(492\) 0 0
\(493\) 3.65685 + 6.33386i 0.164696 + 0.285263i
\(494\) −6.82843 −0.307225
\(495\) 0 0
\(496\) −20.4853 −0.919816
\(497\) −2.82843 4.89898i −0.126872 0.219749i
\(498\) 0 0
\(499\) 1.07107 1.85514i 0.0479476 0.0830476i −0.841056 0.540949i \(-0.818065\pi\)
0.889003 + 0.457901i \(0.151399\pi\)
\(500\) −10.8284 + 18.7554i −0.484262 + 0.838766i
\(501\) 0 0
\(502\) 0 0
\(503\) −15.3137 −0.682805 −0.341402 0.939917i \(-0.610902\pi\)
−0.341402 + 0.939917i \(0.610902\pi\)
\(504\) 0 0
\(505\) −10.3431 −0.460264
\(506\) −9.65685 16.7262i −0.429300 0.743569i
\(507\) 0 0
\(508\) 10.8284 18.7554i 0.480434 0.832136i
\(509\) −13.8995 + 24.0746i −0.616084 + 1.06709i 0.374109 + 0.927385i \(0.377949\pi\)
−0.990193 + 0.139705i \(0.955385\pi\)
\(510\) 0 0
\(511\) 16.4853 + 28.5533i 0.729266 + 1.26313i
\(512\) −31.2426 −1.38074
\(513\) 0 0
\(514\) 37.7990 1.66724
\(515\) 19.3137 + 33.4523i 0.851064 + 1.47409i
\(516\) 0 0
\(517\) −0.343146 + 0.594346i −0.0150915 + 0.0261393i
\(518\) 12.4853 21.6251i 0.548572 0.950154i
\(519\) 0 0
\(520\) −6.24264 10.8126i −0.273758 0.474163i
\(521\) −2.68629 −0.117689 −0.0588443 0.998267i \(-0.518742\pi\)
−0.0588443 + 0.998267i \(0.518742\pi\)
\(522\) 0 0
\(523\) 7.31371 0.319806 0.159903 0.987133i \(-0.448882\pi\)
0.159903 + 0.987133i \(0.448882\pi\)
\(524\) −15.3137 26.5241i −0.668982 1.15871i
\(525\) 0 0
\(526\) 14.4853 25.0892i 0.631588 1.09394i
\(527\) 12.4853 21.6251i 0.543867 0.942006i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −13.6569 −0.593216
\(531\) 0 0
\(532\) −30.6274 −1.32787
\(533\) −5.41421 9.37769i −0.234516 0.406193i
\(534\) 0 0
\(535\) −16.0000 + 27.7128i −0.691740 + 1.19813i
\(536\) −2.58579 + 4.47871i −0.111689 + 0.193451i
\(537\) 0 0
\(538\) 21.7279 + 37.6339i 0.936757 + 1.62251i
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) −14.2426 24.6690i −0.611774 1.05962i
\(543\) 0 0
\(544\) 2.89949 5.02207i 0.124315 0.215320i
\(545\) −24.4853 + 42.4098i −1.04883 + 1.81663i
\(546\) 0 0
\(547\) −0.343146 0.594346i −0.0146719 0.0254124i 0.858596 0.512652i \(-0.171337\pi\)
−0.873268 + 0.487240i \(0.838004\pi\)
\(548\) 19.7990 0.845771
\(549\) 0 0
\(550\) 14.4853 0.617654
\(551\) 2.82843 + 4.89898i 0.120495 + 0.208704i
\(552\) 0 0
\(553\) 16.0000 27.7128i 0.680389 1.17847i
\(554\) 2.41421 4.18154i 0.102570 0.177657i
\(555\) 0 0
\(556\) −29.3137 50.7728i −1.24318 2.15325i
\(557\) −31.7990 −1.34737 −0.673683 0.739020i \(-0.735289\pi\)
−0.673683 + 0.739020i \(0.735289\pi\)
\(558\) 0 0
\(559\) −9.65685 −0.408441
\(560\) −12.0000 20.7846i −0.507093 0.878310i
\(561\) 0 0
\(562\) 32.3848 56.0921i 1.36607 2.36610i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 0 0
\(565\) −24.4853 42.4098i −1.03010 1.78419i
\(566\) −12.0000 −0.504398
\(567\) 0 0
\(568\) −8.82843 −0.370433
\(569\) −4.51472 7.81972i −0.189267 0.327820i 0.755739 0.654873i \(-0.227278\pi\)
−0.945006 + 0.327053i \(0.893944\pi\)
\(570\) 0 0
\(571\) −10.4853 + 18.1610i −0.438795 + 0.760016i −0.997597 0.0692856i \(-0.977928\pi\)
0.558801 + 0.829301i \(0.311261\pi\)
\(572\) 3.82843 6.63103i 0.160075 0.277257i
\(573\) 0 0
\(574\) −36.9706 64.0349i −1.54312 2.67276i
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 35.9411 1.49625 0.748124 0.663559i \(-0.230955\pi\)
0.748124 + 0.663559i \(0.230955\pi\)
\(578\) 4.37868 + 7.58410i 0.182129 + 0.315457i
\(579\) 0 0
\(580\) −10.8284 + 18.7554i −0.449626 + 0.778775i
\(581\) 10.8284 18.7554i 0.449239 0.778105i
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 51.4558 2.12926
\(585\) 0 0
\(586\) 63.1127 2.60716
\(587\) 11.4853 + 19.8931i 0.474048 + 0.821076i 0.999559 0.0297116i \(-0.00945887\pi\)
−0.525510 + 0.850787i \(0.676126\pi\)
\(588\) 0 0
\(589\) 9.65685 16.7262i 0.397904 0.689190i
\(590\) 12.4853 21.6251i 0.514011 0.890293i
\(591\) 0 0
\(592\) −5.48528 9.50079i −0.225444 0.390480i
\(593\) 3.51472 0.144332 0.0721661 0.997393i \(-0.477009\pi\)
0.0721661 + 0.997393i \(0.477009\pi\)
\(594\) 0 0
\(595\) 29.2548 1.19933
\(596\) −28.3848 49.1639i −1.16269 2.01383i
\(597\) 0 0
\(598\) 4.82843 8.36308i 0.197449 0.341992i
\(599\) −0.343146 + 0.594346i −0.0140206 + 0.0242843i −0.872951 0.487809i \(-0.837796\pi\)
0.858930 + 0.512093i \(0.171130\pi\)
\(600\) 0 0
\(601\) −22.3137 38.6485i −0.910195 1.57650i −0.813788 0.581162i \(-0.802598\pi\)
−0.0964075 0.995342i \(-0.530735\pi\)
\(602\) −65.9411 −2.68756
\(603\) 0 0
\(604\) −78.4264 −3.19113
\(605\) −9.89949 17.1464i −0.402472 0.697101i
\(606\) 0 0
\(607\) 12.9706 22.4657i 0.526459 0.911854i −0.473066 0.881027i \(-0.656853\pi\)
0.999525 0.0308265i \(-0.00981393\pi\)
\(608\) 2.24264 3.88437i 0.0909511 0.157532i
\(609\) 0 0
\(610\) −31.7990 55.0775i −1.28750 2.23002i
\(611\) −0.343146 −0.0138822
\(612\) 0 0
\(613\) −36.3431 −1.46789 −0.733943 0.679211i \(-0.762322\pi\)
−0.733943 + 0.679211i \(0.762322\pi\)
\(614\) 20.7279 + 35.9018i 0.836511 + 1.44888i
\(615\) 0 0
\(616\) 12.4853 21.6251i 0.503046 0.871302i
\(617\) −14.5858 + 25.2633i −0.587202 + 1.01706i 0.407395 + 0.913252i \(0.366437\pi\)
−0.994597 + 0.103811i \(0.966896\pi\)
\(618\) 0 0
\(619\) 7.89949 + 13.6823i 0.317508 + 0.549939i 0.979967 0.199158i \(-0.0638208\pi\)
−0.662460 + 0.749097i \(0.730487\pi\)
\(620\) 73.9411 2.96955
\(621\) 0 0
\(622\) −83.5980 −3.35197
\(623\) −12.9706 22.4657i −0.519655 0.900068i
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) −7.24264 + 12.5446i −0.289474 + 0.501384i
\(627\) 0 0
\(628\) 19.1421 + 33.1552i 0.763854 + 1.32303i
\(629\) 13.3726 0.533200
\(630\) 0 0
\(631\) −19.1127 −0.760865 −0.380432 0.924809i \(-0.624225\pi\)
−0.380432 + 0.924809i \(0.624225\pi\)
\(632\) −24.9706 43.2503i −0.993276 1.72040i
\(633\) 0 0
\(634\) −10.2426 + 17.7408i −0.406787 + 0.704576i
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) 0.500000 + 0.866025i 0.0198107 + 0.0343132i
\(638\) −9.65685 −0.382319
\(639\) 0 0
\(640\) 58.1421 2.29827
\(641\) −13.1421 22.7628i −0.519083 0.899078i −0.999754 0.0221773i \(-0.992940\pi\)
0.480671 0.876901i \(-0.340393\pi\)
\(642\) 0 0
\(643\) −8.58579 + 14.8710i −0.338590 + 0.586456i −0.984168 0.177239i \(-0.943283\pi\)
0.645577 + 0.763695i \(0.276617\pi\)
\(644\) 21.6569 37.5108i 0.853400 1.47813i
\(645\) 0 0
\(646\) −12.4853 21.6251i −0.491227 0.850830i
\(647\) 11.3137 0.444788 0.222394 0.974957i \(-0.428613\pi\)
0.222394 + 0.974957i \(0.428613\pi\)
\(648\) 0 0
\(649\) 7.31371 0.287088
\(650\) 3.62132 + 6.27231i 0.142040 + 0.246020i
\(651\) 0 0
\(652\) −25.2132 + 43.6705i −0.987425 + 1.71027i
\(653\) −1.34315 + 2.32640i −0.0525614 + 0.0910389i −0.891109 0.453789i \(-0.850072\pi\)
0.838548 + 0.544828i \(0.183405\pi\)
\(654\) 0 0
\(655\) 11.3137 + 19.5959i 0.442063 + 0.765676i
\(656\) −32.4853 −1.26834
\(657\) 0 0
\(658\) −2.34315 −0.0913453
\(659\) −12.3431 21.3790i −0.480821 0.832806i 0.518937 0.854812i \(-0.326328\pi\)
−0.999758 + 0.0220065i \(0.992995\pi\)
\(660\) 0 0
\(661\) 0.514719 0.891519i 0.0200202 0.0346761i −0.855842 0.517238i \(-0.826960\pi\)
0.875862 + 0.482562i \(0.160294\pi\)
\(662\) 2.58579 4.47871i 0.100499 0.174070i
\(663\) 0 0
\(664\) −16.8995 29.2708i −0.655828 1.13593i
\(665\) 22.6274 0.877454
\(666\) 0 0
\(667\) −8.00000 −0.309761
\(668\) 14.6569 + 25.3864i 0.567091 + 0.982230i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) 9.31371 16.1318i 0.359552 0.622762i
\(672\) 0 0
\(673\) 14.3137 + 24.7921i 0.551753 + 0.955664i 0.998148 + 0.0608282i \(0.0193742\pi\)
−0.446395 + 0.894836i \(0.647292\pi\)
\(674\) −32.1421 −1.23807
\(675\) 0 0
\(676\) 3.82843 0.147247
\(677\) 24.6569 + 42.7069i 0.947640 + 1.64136i 0.750377 + 0.661010i \(0.229872\pi\)
0.197263 + 0.980351i \(0.436795\pi\)
\(678\) 0 0
\(679\) −10.8284 + 18.7554i −0.415557 + 0.719766i
\(680\) 22.8284 39.5400i 0.875430 1.51629i
\(681\) 0 0
\(682\) 16.4853 + 28.5533i 0.631254 + 1.09336i
\(683\) 19.9411 0.763026 0.381513 0.924363i \(-0.375403\pi\)
0.381513 + 0.924363i \(0.375403\pi\)
\(684\) 0 0
\(685\) −14.6274 −0.558885
\(686\) −20.4853 35.4815i −0.782132 1.35469i
\(687\) 0 0
\(688\) −14.4853 + 25.0892i −0.552246 + 0.956518i
\(689\) 1.00000 1.73205i 0.0380970 0.0659859i
\(690\) 0 0
\(691\) 17.0711 + 29.5680i 0.649414 + 1.12482i 0.983263 + 0.182192i \(0.0583191\pi\)
−0.333849 + 0.942627i \(0.608348\pi\)
\(692\) 1.31371 0.0499397
\(693\) 0 0
\(694\) 75.5980 2.86966
\(695\) 21.6569 + 37.5108i 0.821491 + 1.42286i
\(696\) 0 0
\(697\) 19.7990 34.2929i 0.749940 1.29893i
\(698\) 9.24264 16.0087i 0.349839 0.605939i
\(699\) 0 0
\(700\) 16.2426 + 28.1331i 0.613914 + 1.06333i
\(701\) −38.9706 −1.47190 −0.735949 0.677037i \(-0.763264\pi\)
−0.735949 + 0.677037i \(0.763264\pi\)
\(702\) 0 0
\(703\) 10.3431 0.390099
\(704\) 9.82843 + 17.0233i 0.370423 + 0.641591i
\(705\) 0 0
\(706\) 21.0711 36.4962i 0.793020 1.37355i
\(707\) 5.17157 8.95743i 0.194497 0.336879i
\(708\) 0 0
\(709\) −20.3137 35.1844i −0.762897 1.32138i −0.941351 0.337429i \(-0.890443\pi\)
0.178454 0.983948i \(-0.442891\pi\)
\(710\) 13.6569 0.512533
\(711\) 0 0
\(712\) −40.4853 −1.51725
\(713\) 13.6569 + 23.6544i 0.511453 + 0.885863i
\(714\) 0 0
\(715\) −2.82843 + 4.89898i −0.105777 + 0.183211i
\(716\) −1.31371 + 2.27541i −0.0490956 + 0.0850361i
\(717\) 0 0
\(718\) 1.24264 + 2.15232i 0.0463749 + 0.0803237i
\(719\) −37.9411 −1.41497 −0.707483 0.706731i \(-0.750169\pi\)
−0.707483 + 0.706731i \(0.750169\pi\)
\(720\) 0 0
\(721\) −38.6274 −1.43856
\(722\) 13.2782 + 22.9985i 0.494162 + 0.855915i
\(723\) 0 0
\(724\) −26.7990 + 46.4172i −0.995977 + 1.72508i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) 10.8284 + 18.7554i 0.401604 + 0.695599i 0.993920 0.110107i \(-0.0351195\pi\)
−0.592316 + 0.805706i \(0.701786\pi\)
\(728\) 12.4853 0.462735
\(729\) 0 0
\(730\) −79.5980 −2.94605
\(731\) −17.6569 30.5826i −0.653062 1.13114i
\(732\) 0 0
\(733\) −4.31371 + 7.47156i −0.159330 + 0.275968i −0.934627 0.355628i \(-0.884267\pi\)
0.775297 + 0.631597i \(0.217600\pi\)
\(734\) 28.9706 50.1785i 1.06932 1.85212i
\(735\) 0 0
\(736\) 3.17157 + 5.49333i 0.116906 + 0.202487i
\(737\) 2.34315 0.0863109
\(738\) 0 0
\(739\) 10.1421 0.373084 0.186542 0.982447i \(-0.440272\pi\)
0.186542 + 0.982447i \(0.440272\pi\)
\(740\) 19.7990 + 34.2929i 0.727825 + 1.26063i
\(741\) 0 0
\(742\) 6.82843 11.8272i 0.250679 0.434190i
\(743\) 1.00000 1.73205i 0.0366864 0.0635428i −0.847099 0.531435i \(-0.821653\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(744\) 0 0
\(745\) 20.9706 + 36.3221i 0.768302 + 1.33074i
\(746\) 24.1421 0.883906
\(747\) 0 0
\(748\) 28.0000 1.02378
\(749\) −16.0000 27.7128i −0.584627 1.01260i
\(750\) 0 0
\(751\) −16.4853 + 28.5533i −0.601556 + 1.04193i 0.391029 + 0.920378i \(0.372119\pi\)
−0.992586 + 0.121548i \(0.961214\pi\)
\(752\) −0.514719 + 0.891519i −0.0187699 + 0.0325103i
\(753\) 0 0
\(754\) −2.41421 4.18154i −0.0879205 0.152283i
\(755\) 57.9411 2.10869
\(756\) 0 0
\(757\) −15.9411 −0.579390 −0.289695 0.957119i \(-0.593554\pi\)
−0.289695 + 0.957119i \(0.593554\pi\)
\(758\) 19.8995 + 34.4669i 0.722782 + 1.25190i
\(759\) 0 0
\(760\) 17.6569 30.5826i 0.640481 1.10935i
\(761\) 7.75736 13.4361i 0.281204 0.487060i −0.690478 0.723354i \(-0.742600\pi\)
0.971682 + 0.236294i \(0.0759329\pi\)
\(762\) 0 0
\(763\) −24.4853 42.4098i −0.886427 1.53534i
\(764\) 73.9411 2.67510
\(765\) 0 0
\(766\) 7.17157 0.259119
\(767\) 1.82843 + 3.16693i 0.0660207 + 0.114351i
\(768\) 0 0
\(769\) −21.0000 + 36.3731i −0.757279 + 1.31165i 0.186954 + 0.982369i \(0.440139\pi\)
−0.944233 + 0.329278i \(0.893195\pi\)
\(770\) −19.3137 + 33.4523i −0.696018 + 1.20554i
\(771\) 0 0
\(772\) 33.1421 + 57.4039i 1.19281 + 2.06601i
\(773\) −5.85786 −0.210693 −0.105346 0.994436i \(-0.533595\pi\)
−0.105346 + 0.994436i \(0.533595\pi\)
\(774\) 0 0
\(775\) −20.4853 −0.735853
\(776\) 16.8995 + 29.2708i 0.606657 + 1.05076i
\(777\) 0 0
\(778\) 8.41421 14.5738i 0.301664 0.522498i
\(779\) 15.3137 26.5241i 0.548671 0.950325i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 35.3137 1.26282
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −14.1421 24.4949i −0.504754 0.874260i
\(786\) 0 0
\(787\) −16.3848 + 28.3793i −0.584054 + 1.01161i 0.410938 + 0.911663i \(0.365201\pi\)
−0.994993 + 0.0999484i \(0.968132\pi\)
\(788\) −31.5563 + 54.6572i −1.12415 + 1.94708i
\(789\) 0 0
\(790\) 38.6274 + 66.9046i 1.37430 + 2.38036i
\(791\) 48.9706 1.74119
\(792\) 0 0
\(793\) 9.31371 0.330739
\(794\) 3.58579 + 6.21076i 0.127255 + 0.220412i
\(795\) 0 0
\(796\) −19.7990 + 34.2929i −0.701757 + 1.21548i
\(797\) 17.8284 30.8797i 0.631515 1.09382i −0.355727 0.934590i \(-0.615767\pi\)
0.987242 0.159227i \(-0.0509000\pi\)
\(798\) 0 0
\(799\) −0.627417 1.08672i −0.0221964 0.0384453i
\(800\) −4.75736 −0.168198
\(801\) 0 0
\(802\) 5.17157 0.182615
\(803\) −11.6569 20.1903i −0.411361 0.712499i
\(804\) 0 0
\(805\) −16.0000 + 27.7128i −0.563926 + 0.976748i
\(806\) −8.24264 + 14.2767i −0.290335 + 0.502874i
\(807\) 0 0
\(808\) −8.07107 13.9795i −0.283939 0.491797i
\(809\) −41.3137 −1.45251 −0.726256 0.687424i \(-0.758741\pi\)
−0.726256 + 0.687424i \(0.758741\pi\)
\(810\) 0 0
\(811\) −1.85786 −0.0652384 −0.0326192 0.999468i \(-0.510385\pi\)
−0.0326192 + 0.999468i \(0.510385\pi\)
\(812\) −10.8284 18.7554i −0.380003 0.658185i
\(813\) 0 0
\(814\) −8.82843 + 15.2913i −0.309436 + 0.535959i
\(815\) 18.6274 32.2636i 0.652490 1.13015i
\(816\) 0 0
\(817\) −13.6569 23.6544i −0.477793 0.827561i
\(818\) −2.48528 −0.0868958
\(819\) 0 0
\(820\) 117.255 4.09472
\(821\) 7.89949 + 13.6823i 0.275694 + 0.477516i 0.970310 0.241864i \(-0.0777589\pi\)
−0.694616 + 0.719381i \(0.744426\pi\)
\(822\) 0 0
\(823\) −24.4853 + 42.4098i −0.853503 + 1.47831i 0.0245234 + 0.999699i \(0.492193\pi\)
−0.878027 + 0.478612i \(0.841140\pi\)
\(824\) −30.1421 + 52.2077i −1.05005 + 1.81874i
\(825\) 0 0
\(826\) 12.4853 + 21.6251i 0.434418 + 0.752435i
\(827\) 26.0000 0.904109 0.452054 0.891990i \(-0.350691\pi\)
0.452054 + 0.891990i \(0.350691\pi\)
\(828\) 0 0
\(829\) 5.31371 0.184553 0.0922764 0.995733i \(-0.470586\pi\)
0.0922764 + 0.995733i \(0.470586\pi\)
\(830\) 26.1421 + 45.2795i 0.907407 + 1.57167i
\(831\) 0 0
\(832\) −4.91421 + 8.51167i −0.170370 + 0.295089i
\(833\) −1.82843 + 3.16693i −0.0633512 + 0.109728i
\(834\) 0 0
\(835\) −10.8284 18.7554i −0.374733 0.649057i
\(836\) 21.6569 0.749018
\(837\) 0 0
\(838\) 73.9411 2.55425
\(839\) −23.6274 40.9239i −0.815709 1.41285i −0.908818 0.417194i \(-0.863014\pi\)
0.0931087 0.995656i \(-0.470320\pi\)
\(840\) 0 0
\(841\) 12.5000 21.6506i 0.431034 0.746574i
\(842\) −17.7279 + 30.7057i −0.610945 + 1.05819i
\(843\) 0 0
\(844\) 22.9706 + 39.7862i 0.790679 + 1.36950i
\(845\) −2.82843 −0.0973009
\(846\) 0 0
\(847\) 19.7990 0.680301
\(848\) −3.00000 5.19615i −0.103020 0.178437i
\(849\) 0 0
\(850\) −13.2426 + 22.9369i −0.454219 + 0.786730i
\(851\) −7.31371 + 12.6677i −0.250711 + 0.434244i
\(852\) 0 0
\(853\) 3.82843 + 6.63103i 0.131083 + 0.227042i 0.924094 0.382165i \(-0.124821\pi\)
−0.793011 + 0.609207i \(0.791488\pi\)
\(854\) 63.5980 2.17628
\(855\) 0 0
\(856\) −49.9411 −1.70695
\(857\) 14.7990 + 25.6326i 0.505524 + 0.875593i 0.999980 + 0.00639020i \(0.00203408\pi\)
−0.494456 + 0.869203i \(0.664633\pi\)
\(858\) 0 0
\(859\) 11.6569 20.1903i 0.397727 0.688883i −0.595718 0.803193i \(-0.703133\pi\)
0.993445 + 0.114311i \(0.0364659\pi\)
\(860\) 52.2843 90.5590i 1.78288 3.08804i
\(861\) 0 0
\(862\) 23.7279 + 41.0980i 0.808176 + 1.39980i
\(863\) 39.6569 1.34994 0.674968 0.737847i \(-0.264158\pi\)
0.674968 + 0.737847i \(0.264158\pi\)
\(864\) 0 0
\(865\) −0.970563 −0.0330001
\(866\) −1.58579 2.74666i −0.0538872 0.0933354i
\(867\) 0 0
\(868\) −36.9706 + 64.0349i −1.25486 + 2.17349i
\(869\) −11.3137 + 19.5959i −0.383791 + 0.664746i
\(870\) 0 0
\(871\) 0.585786 + 1.01461i 0.0198486 + 0.0343788i
\(872\) −76.4264 −2.58812
\(873\) 0 0
\(874\) 27.3137 0.923900
\(875\) 8.00000 + 13.8564i 0.270449 + 0.468432i
\(876\) 0 0
\(877\) 7.14214 12.3705i 0.241173 0.417724i −0.719876 0.694103i \(-0.755801\pi\)
0.961049 + 0.276379i \(0.0891346\pi\)
\(878\) 20.4853 35.4815i 0.691345 1.19744i
\(879\) 0 0
\(880\) 8.48528 + 14.6969i 0.286039 + 0.495434i
\(881\) −53.5980 −1.80576 −0.902881 0.429891i \(-0.858552\pi\)
−0.902881 + 0.429891i \(0.858552\pi\)
\(882\) 0 0
\(883\) −51.5980 −1.73641 −0.868205 0.496205i \(-0.834726\pi\)
−0.868205 + 0.496205i \(0.834726\pi\)
\(884\) 7.00000 + 12.1244i 0.235435 + 0.407786i
\(885\) 0 0
\(886\) 50.6274 87.6893i 1.70086 2.94598i
\(887\) −4.00000 + 6.92820i −0.134307 + 0.232626i −0.925332 0.379157i \(-0.876214\pi\)
0.791026 + 0.611783i \(0.209547\pi\)
\(888\) 0 0
\(889\) −8.00000 13.8564i −0.268311 0.464729i
\(890\) 62.6274 2.09928
\(891\) 0 0
\(892\) 17.1716 0.574947
\(893\) −0.485281 0.840532i −0.0162393 0.0281273i
\(894\) 0 0
\(895\) 0.970563 1.68106i 0.0324423 0.0561918i
\(896\) −29.0711 + 50.3526i −0.971196 + 1.68216i
\(897\) 0 0
\(898\) 9.41421 + 16.3059i 0.314156 + 0.544135i
\(899\) 13.6569 0.455482
\(900\) 0 0
\(901\) 7.31371 0.243655
\(902\) 26.1421 + 45.2795i 0.870438 + 1.50764i
\(903\) 0 0
\(904\) 38.2132 66.1872i 1.27095 2.20135i
\(905\) 19.7990 34.2929i 0.658141 1.13993i
\(906\) 0 0
\(907\) −10.4853 18.1610i −0.348158 0.603027i 0.637764 0.770232i \(-0.279859\pi\)
−0.985922 + 0.167204i \(0.946526\pi\)
\(908\) −20.3431 −0.675111
\(909\) 0 0
\(910\) −19.3137 −0.640243
\(911\) −20.0000 34.6410i −0.662630 1.14771i −0.979922 0.199380i \(-0.936107\pi\)
0.317293 0.948328i \(-0.397226\pi\)
\(912\) 0 0
\(913\) −7.65685 + 13.2621i −0.253405 + 0.438910i
\(914\) −4.41421 + 7.64564i −0.146009 + 0.252895i
\(915\) 0 0
\(916\) −40.7990 70.6659i −1.34804 2.33487i
\(917\) −22.6274 −0.747223
\(918\) 0 0
\(919\) −19.3137 −0.637100 −0.318550 0.947906i \(-0.603196\pi\)
−0.318550 + 0.947906i \(0.603196\pi\)
\(920\) 24.9706 + 43.2503i 0.823255 + 1.42592i
\(921\) 0 0
\(922\) 13.0711 22.6398i 0.430473 0.745601i
\(923\) −1.00000 + 1.73205i −0.0329154 + 0.0570111i
\(924\) 0 0
\(925\) −5.48528 9.50079i −0.180355 0.312384i
\(926\) −18.1421 −0.596188
\(927\) 0 0
\(928\) 3.17157 0.104112
\(929\) −13.8995 24.0746i −0.456028 0.789863i 0.542719 0.839914i \(-0.317395\pi\)
−0.998747 + 0.0500513i \(0.984062\pi\)
\(930\) 0 0
\(931\) −1.41421 + 2.44949i −0.0463490 + 0.0802788i
\(932\) −51.6274 + 89.4213i −1.69111 + 2.92909i
\(933\) 0 0
\(934\) −9.65685 16.7262i −0.315982 0.547297i
\(935\) −20.6863 −0.676514
\(936\) 0 0
\(937\) 1.31371 0.0429170 0.0214585 0.999770i \(-0.493169\pi\)
0.0214585 + 0.999770i \(0.493169\pi\)
\(938\) 4.00000 + 6.92820i 0.130605 + 0.226214i
\(939\) 0 0
\(940\) 1.85786 3.21792i 0.0605969 0.104957i
\(941\) 2.92893 5.07306i 0.0954805 0.165377i −0.814329 0.580404i \(-0.802895\pi\)
0.909809 + 0.415027i \(0.136228\pi\)
\(942\) 0 0
\(943\) 21.6569 + 37.5108i 0.705244 + 1.22152i
\(944\) 10.9706 0.357061
\(945\) 0 0
\(946\) 46.6274 1.51599
\(947\) −27.4853 47.6059i −0.893152 1.54698i −0.836076 0.548614i \(-0.815156\pi\)
−0.0570760 0.998370i \(-0.518178\pi\)
\(948\) 0 0
\(949\) 5.82843 10.0951i 0.189199 0.327702i
\(950\) −10.2426 + 17.7408i −0.332315 + 0.575587i
\(951\) 0 0
\(952\) 22.8284 + 39.5400i 0.739874 + 1.28150i
\(953\) −51.6569 −1.67333 −0.836665 0.547715i \(-0.815498\pi\)
−0.836665 + 0.547715i \(0.815498\pi\)
\(954\) 0 0
\(955\) −54.6274 −1.76770
\(956\) 3.82843 + 6.63103i 0.123820 + 0.214463i
\(957\) 0 0
\(958\) 3.24264 5.61642i 0.104765 0.181458i
\(959\) 7.31371 12.6677i 0.236172 0.409062i
\(960\) 0 0
\(961\) −7.81371 13.5337i −0.252055 0.436572i
\(962\) −8.82843 −0.284640
\(963\) 0 0
\(964\) 44.6274 1.43735
\(965\) −24.4853 42.4098i −0.788209 1.36522i
\(966\) 0 0
\(967\) 5.07107 8.78335i 0.163075 0.282453i −0.772895 0.634534i \(-0.781192\pi\)
0.935970 + 0.352080i \(0.114526\pi\)
\(968\) 15.4497 26.7597i 0.496574 0.860091i
\(969\) 0 0
\(970\) −26.1421 45.2795i −0.839373 1.45384i
\(971\) −7.31371 −0.234708 −0.117354 0.993090i \(-0.537441\pi\)
−0.117354 + 0.993090i \(0.537441\pi\)
\(972\) 0 0
\(973\) −43.3137 −1.38857
\(974\) −38.3848 66.4844i −1.22993 2.13030i
\(975\) 0 0
\(976\) 13.9706 24.1977i 0.447187 0.774550i
\(977\) 6.92893 12.0013i 0.221676 0.383954i −0.733641 0.679537i \(-0.762181\pi\)
0.955317 + 0.295583i \(0.0955139\pi\)
\(978\) 0 0
\(979\) 9.17157 + 15.8856i 0.293125 + 0.507707i
\(980\) −10.8284 −0.345901
\(981\) 0 0
\(982\) 35.3137 1.12691
\(983\) 1.34315 + 2.32640i 0.0428397 + 0.0742005i 0.886650 0.462441i \(-0.153026\pi\)
−0.843811 + 0.536641i \(0.819693\pi\)
\(984\) 0 0
\(985\) 23.3137 40.3805i 0.742837 1.28663i
\(986\) 8.82843 15.2913i 0.281154 0.486974i
\(987\) 0 0
\(988\) 5.41421 + 9.37769i 0.172249 + 0.298344i
\(989\) 38.6274 1.22828
\(990\) 0 0
\(991\) 27.3137 0.867649 0.433824 0.900998i \(-0.357164\pi\)
0.433824 + 0.900998i \(0.357164\pi\)
\(992\) −5.41421 9.37769i −0.171901 0.297742i
\(993\) 0 0
\(994\) −6.82843 + 11.8272i −0.216585 + 0.375135i
\(995\) 14.6274 25.3354i 0.463720 0.803187i
\(996\) 0 0
\(997\) −25.6274 44.3880i −0.811628 1.40578i −0.911724 0.410804i \(-0.865248\pi\)
0.100095 0.994978i \(-0.468085\pi\)
\(998\) −5.17157 −0.163703
\(999\) 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 1053.2.e.e.352.1 4
3.2 odd 2 1053.2.e.m.352.2 4
9.2 odd 6 1053.2.e.m.703.2 4
9.4 even 3 117.2.a.c.1.2 2
9.5 odd 6 39.2.a.b.1.1 2
9.7 even 3 inner 1053.2.e.e.703.1 4
36.23 even 6 624.2.a.k.1.2 2
36.31 odd 6 1872.2.a.w.1.1 2
45.4 even 6 2925.2.a.v.1.1 2
45.13 odd 12 2925.2.c.u.2224.1 4
45.14 odd 6 975.2.a.l.1.2 2
45.22 odd 12 2925.2.c.u.2224.4 4
45.23 even 12 975.2.c.h.274.4 4
45.32 even 12 975.2.c.h.274.1 4
63.13 odd 6 5733.2.a.u.1.2 2
63.41 even 6 1911.2.a.h.1.1 2
72.5 odd 6 2496.2.a.bf.1.1 2
72.13 even 6 7488.2.a.cl.1.2 2
72.59 even 6 2496.2.a.bi.1.1 2
72.67 odd 6 7488.2.a.co.1.2 2
99.32 even 6 4719.2.a.p.1.2 2
117.5 even 12 507.2.b.e.337.4 4
117.23 odd 6 507.2.e.d.22.1 4
117.31 odd 12 1521.2.b.j.1351.1 4
117.32 even 12 507.2.j.f.361.4 8
117.41 even 12 507.2.j.f.316.1 8
117.50 even 12 507.2.j.f.316.4 8
117.59 even 12 507.2.j.f.361.1 8
117.68 odd 6 507.2.e.h.22.2 4
117.77 odd 6 507.2.a.h.1.2 2
117.86 even 12 507.2.b.e.337.1 4
117.95 odd 6 507.2.e.d.484.1 4
117.103 even 6 1521.2.a.f.1.1 2
117.112 odd 12 1521.2.b.j.1351.4 4
117.113 odd 6 507.2.e.h.484.2 4
468.311 even 6 8112.2.a.bm.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.a.b.1.1 2 9.5 odd 6
117.2.a.c.1.2 2 9.4 even 3
507.2.a.h.1.2 2 117.77 odd 6
507.2.b.e.337.1 4 117.86 even 12
507.2.b.e.337.4 4 117.5 even 12
507.2.e.d.22.1 4 117.23 odd 6
507.2.e.d.484.1 4 117.95 odd 6
507.2.e.h.22.2 4 117.68 odd 6
507.2.e.h.484.2 4 117.113 odd 6
507.2.j.f.316.1 8 117.41 even 12
507.2.j.f.316.4 8 117.50 even 12
507.2.j.f.361.1 8 117.59 even 12
507.2.j.f.361.4 8 117.32 even 12
624.2.a.k.1.2 2 36.23 even 6
975.2.a.l.1.2 2 45.14 odd 6
975.2.c.h.274.1 4 45.32 even 12
975.2.c.h.274.4 4 45.23 even 12
1053.2.e.e.352.1 4 1.1 even 1 trivial
1053.2.e.e.703.1 4 9.7 even 3 inner
1053.2.e.m.352.2 4 3.2 odd 2
1053.2.e.m.703.2 4 9.2 odd 6
1521.2.a.f.1.1 2 117.103 even 6
1521.2.b.j.1351.1 4 117.31 odd 12
1521.2.b.j.1351.4 4 117.112 odd 12
1872.2.a.w.1.1 2 36.31 odd 6
1911.2.a.h.1.1 2 63.41 even 6
2496.2.a.bf.1.1 2 72.5 odd 6
2496.2.a.bi.1.1 2 72.59 even 6
2925.2.a.v.1.1 2 45.4 even 6
2925.2.c.u.2224.1 4 45.13 odd 12
2925.2.c.u.2224.4 4 45.22 odd 12
4719.2.a.p.1.2 2 99.32 even 6
5733.2.a.u.1.2 2 63.13 odd 6
7488.2.a.cl.1.2 2 72.13 even 6
7488.2.a.co.1.2 2 72.67 odd 6
8112.2.a.bm.1.1 2 468.311 even 6