Properties

Label 6579.2.a.j.1.3
Level $6579$
Weight $2$
Character 6579.1
Self dual yes
Analytic conductor $52.534$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6579,2,Mod(1,6579)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6579, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6579.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6579 = 3^{2} \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6579.a (trivial)

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: yes
Analytic conductor: \(52.5335794898\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.2460365.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 7x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 731)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.30704\) of defining polynomial
Character \(\chi\) \(=\) 6579.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.291653 q^{2} -1.91494 q^{4} -3.99528 q^{5} -2.74049 q^{7} +1.14180 q^{8} +O(q^{10})\) \(q-0.291653 q^{2} -1.91494 q^{4} -3.99528 q^{5} -2.74049 q^{7} +1.14180 q^{8} +1.16523 q^{10} -3.05674 q^{11} -5.80993 q^{13} +0.799273 q^{14} +3.49687 q^{16} +1.00000 q^{17} -3.69042 q^{19} +7.65071 q^{20} +0.891508 q^{22} +2.72155 q^{23} +10.9622 q^{25} +1.69448 q^{26} +5.24788 q^{28} +10.1277 q^{29} +3.83106 q^{31} -3.30348 q^{32} -0.291653 q^{34} +10.9490 q^{35} -9.47073 q^{37} +1.07632 q^{38} -4.56182 q^{40} +10.0824 q^{41} -1.00000 q^{43} +5.85347 q^{44} -0.793748 q^{46} -7.25723 q^{47} +0.510306 q^{49} -3.19717 q^{50} +11.1257 q^{52} +0.0256123 q^{53} +12.2125 q^{55} -3.12911 q^{56} -2.95377 q^{58} +4.19905 q^{59} -6.73795 q^{61} -1.11734 q^{62} -6.03026 q^{64} +23.2123 q^{65} +11.5581 q^{67} -1.91494 q^{68} -3.19332 q^{70} +8.72587 q^{71} +3.33134 q^{73} +2.76217 q^{74} +7.06693 q^{76} +8.37698 q^{77} -6.10660 q^{79} -13.9709 q^{80} -2.94057 q^{82} +8.98937 q^{83} -3.99528 q^{85} +0.291653 q^{86} -3.49020 q^{88} +0.838307 q^{89} +15.9221 q^{91} -5.21160 q^{92} +2.11659 q^{94} +14.7442 q^{95} +17.2844 q^{97} -0.148832 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 5 q^{4} - 3 q^{5} - 7 q^{7} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + 5 q^{4} - 3 q^{5} - 7 q^{7} + 9 q^{8} - 4 q^{10} - 4 q^{11} - 10 q^{13} + 7 q^{14} - q^{16} + 6 q^{17} - 20 q^{19} - q^{20} + 2 q^{22} + 3 q^{23} - 7 q^{25} + 3 q^{26} - 11 q^{28} + 15 q^{29} + 12 q^{31} - q^{32} + q^{34} + 9 q^{35} - 14 q^{37} - 27 q^{38} - 7 q^{40} + 2 q^{41} - 6 q^{43} + 12 q^{44} + 14 q^{46} + 11 q^{47} + 3 q^{49} - 7 q^{50} - 5 q^{52} - 3 q^{53} + 6 q^{55} - 22 q^{56} - 21 q^{58} - 2 q^{59} - 20 q^{61} - 3 q^{62} - 39 q^{64} + 34 q^{65} - 2 q^{67} + 5 q^{68} - q^{70} - q^{71} + 13 q^{73} - 28 q^{74} - 29 q^{76} + 11 q^{77} - 26 q^{79} - 12 q^{80} - 9 q^{82} - 10 q^{83} - 3 q^{85} - q^{86} - 6 q^{88} + 15 q^{89} + 8 q^{91} + 9 q^{92} - 33 q^{94} + 21 q^{95} - 22 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.291653 −0.206230 −0.103115 0.994669i \(-0.532881\pi\)
−0.103115 + 0.994669i \(0.532881\pi\)
\(3\) 0 0
\(4\) −1.91494 −0.957469
\(5\) −3.99528 −1.78674 −0.893371 0.449320i \(-0.851666\pi\)
−0.893371 + 0.449320i \(0.851666\pi\)
\(6\) 0 0
\(7\) −2.74049 −1.03581 −0.517905 0.855438i \(-0.673288\pi\)
−0.517905 + 0.855438i \(0.673288\pi\)
\(8\) 1.14180 0.403688
\(9\) 0 0
\(10\) 1.16523 0.368479
\(11\) −3.05674 −0.921642 −0.460821 0.887493i \(-0.652445\pi\)
−0.460821 + 0.887493i \(0.652445\pi\)
\(12\) 0 0
\(13\) −5.80993 −1.61139 −0.805693 0.592333i \(-0.798207\pi\)
−0.805693 + 0.592333i \(0.798207\pi\)
\(14\) 0.799273 0.213615
\(15\) 0 0
\(16\) 3.49687 0.874217
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) −3.69042 −0.846641 −0.423320 0.905980i \(-0.639135\pi\)
−0.423320 + 0.905980i \(0.639135\pi\)
\(20\) 7.65071 1.71075
\(21\) 0 0
\(22\) 0.891508 0.190070
\(23\) 2.72155 0.567482 0.283741 0.958901i \(-0.408424\pi\)
0.283741 + 0.958901i \(0.408424\pi\)
\(24\) 0 0
\(25\) 10.9622 2.19245
\(26\) 1.69448 0.332316
\(27\) 0 0
\(28\) 5.24788 0.991756
\(29\) 10.1277 1.88067 0.940334 0.340254i \(-0.110513\pi\)
0.940334 + 0.340254i \(0.110513\pi\)
\(30\) 0 0
\(31\) 3.83106 0.688079 0.344039 0.938955i \(-0.388205\pi\)
0.344039 + 0.938955i \(0.388205\pi\)
\(32\) −3.30348 −0.583978
\(33\) 0 0
\(34\) −0.291653 −0.0500181
\(35\) 10.9490 1.85072
\(36\) 0 0
\(37\) −9.47073 −1.55698 −0.778489 0.627658i \(-0.784014\pi\)
−0.778489 + 0.627658i \(0.784014\pi\)
\(38\) 1.07632 0.174602
\(39\) 0 0
\(40\) −4.56182 −0.721287
\(41\) 10.0824 1.57461 0.787305 0.616564i \(-0.211476\pi\)
0.787305 + 0.616564i \(0.211476\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499
\(44\) 5.85347 0.882444
\(45\) 0 0
\(46\) −0.793748 −0.117032
\(47\) −7.25723 −1.05858 −0.529288 0.848442i \(-0.677541\pi\)
−0.529288 + 0.848442i \(0.677541\pi\)
\(48\) 0 0
\(49\) 0.510306 0.0729009
\(50\) −3.19717 −0.452148
\(51\) 0 0
\(52\) 11.1257 1.54285
\(53\) 0.0256123 0.00351813 0.00175906 0.999998i \(-0.499440\pi\)
0.00175906 + 0.999998i \(0.499440\pi\)
\(54\) 0 0
\(55\) 12.2125 1.64674
\(56\) −3.12911 −0.418144
\(57\) 0 0
\(58\) −2.95377 −0.387850
\(59\) 4.19905 0.546670 0.273335 0.961919i \(-0.411873\pi\)
0.273335 + 0.961919i \(0.411873\pi\)
\(60\) 0 0
\(61\) −6.73795 −0.862706 −0.431353 0.902183i \(-0.641964\pi\)
−0.431353 + 0.902183i \(0.641964\pi\)
\(62\) −1.11734 −0.141902
\(63\) 0 0
\(64\) −6.03026 −0.753783
\(65\) 23.2123 2.87913
\(66\) 0 0
\(67\) 11.5581 1.41205 0.706024 0.708188i \(-0.250487\pi\)
0.706024 + 0.708188i \(0.250487\pi\)
\(68\) −1.91494 −0.232220
\(69\) 0 0
\(70\) −3.19332 −0.381674
\(71\) 8.72587 1.03557 0.517785 0.855511i \(-0.326757\pi\)
0.517785 + 0.855511i \(0.326757\pi\)
\(72\) 0 0
\(73\) 3.33134 0.389904 0.194952 0.980813i \(-0.437545\pi\)
0.194952 + 0.980813i \(0.437545\pi\)
\(74\) 2.76217 0.321095
\(75\) 0 0
\(76\) 7.06693 0.810632
\(77\) 8.37698 0.954646
\(78\) 0 0
\(79\) −6.10660 −0.687046 −0.343523 0.939144i \(-0.611620\pi\)
−0.343523 + 0.939144i \(0.611620\pi\)
\(80\) −13.9709 −1.56200
\(81\) 0 0
\(82\) −2.94057 −0.324732
\(83\) 8.98937 0.986712 0.493356 0.869828i \(-0.335770\pi\)
0.493356 + 0.869828i \(0.335770\pi\)
\(84\) 0 0
\(85\) −3.99528 −0.433349
\(86\) 0.291653 0.0314497
\(87\) 0 0
\(88\) −3.49020 −0.372056
\(89\) 0.838307 0.0888604 0.0444302 0.999012i \(-0.485853\pi\)
0.0444302 + 0.999012i \(0.485853\pi\)
\(90\) 0 0
\(91\) 15.9221 1.66909
\(92\) −5.21160 −0.543347
\(93\) 0 0
\(94\) 2.11659 0.218310
\(95\) 14.7442 1.51273
\(96\) 0 0
\(97\) 17.2844 1.75497 0.877483 0.479607i \(-0.159221\pi\)
0.877483 + 0.479607i \(0.159221\pi\)
\(98\) −0.148832 −0.0150343
\(99\) 0 0
\(100\) −20.9920 −2.09920
\(101\) 5.66451 0.563640 0.281820 0.959467i \(-0.409062\pi\)
0.281820 + 0.959467i \(0.409062\pi\)
\(102\) 0 0
\(103\) 7.12119 0.701672 0.350836 0.936437i \(-0.385898\pi\)
0.350836 + 0.936437i \(0.385898\pi\)
\(104\) −6.63380 −0.650498
\(105\) 0 0
\(106\) −0.00746991 −0.000725542 0
\(107\) −19.2706 −1.86296 −0.931481 0.363790i \(-0.881483\pi\)
−0.931481 + 0.363790i \(0.881483\pi\)
\(108\) 0 0
\(109\) −3.88034 −0.371669 −0.185835 0.982581i \(-0.559499\pi\)
−0.185835 + 0.982581i \(0.559499\pi\)
\(110\) −3.56182 −0.339606
\(111\) 0 0
\(112\) −9.58314 −0.905522
\(113\) −16.4216 −1.54481 −0.772407 0.635128i \(-0.780947\pi\)
−0.772407 + 0.635128i \(0.780947\pi\)
\(114\) 0 0
\(115\) −10.8733 −1.01394
\(116\) −19.3939 −1.80068
\(117\) 0 0
\(118\) −1.22467 −0.112740
\(119\) −2.74049 −0.251221
\(120\) 0 0
\(121\) −1.65633 −0.150575
\(122\) 1.96514 0.177916
\(123\) 0 0
\(124\) −7.33624 −0.658814
\(125\) −23.8208 −2.13059
\(126\) 0 0
\(127\) −9.00730 −0.799268 −0.399634 0.916675i \(-0.630863\pi\)
−0.399634 + 0.916675i \(0.630863\pi\)
\(128\) 8.36570 0.739430
\(129\) 0 0
\(130\) −6.76993 −0.593762
\(131\) −17.6371 −1.54096 −0.770480 0.637464i \(-0.779983\pi\)
−0.770480 + 0.637464i \(0.779983\pi\)
\(132\) 0 0
\(133\) 10.1136 0.876958
\(134\) −3.37096 −0.291206
\(135\) 0 0
\(136\) 1.14180 0.0979088
\(137\) 14.7349 1.25889 0.629445 0.777045i \(-0.283282\pi\)
0.629445 + 0.777045i \(0.283282\pi\)
\(138\) 0 0
\(139\) 9.48346 0.804376 0.402188 0.915557i \(-0.368250\pi\)
0.402188 + 0.915557i \(0.368250\pi\)
\(140\) −20.9667 −1.77201
\(141\) 0 0
\(142\) −2.54493 −0.213565
\(143\) 17.7595 1.48512
\(144\) 0 0
\(145\) −40.4630 −3.36027
\(146\) −0.971595 −0.0804098
\(147\) 0 0
\(148\) 18.1359 1.49076
\(149\) −19.5571 −1.60218 −0.801091 0.598543i \(-0.795747\pi\)
−0.801091 + 0.598543i \(0.795747\pi\)
\(150\) 0 0
\(151\) 2.35499 0.191647 0.0958233 0.995398i \(-0.469452\pi\)
0.0958233 + 0.995398i \(0.469452\pi\)
\(152\) −4.21373 −0.341779
\(153\) 0 0
\(154\) −2.44317 −0.196876
\(155\) −15.3061 −1.22942
\(156\) 0 0
\(157\) 8.30078 0.662475 0.331237 0.943547i \(-0.392534\pi\)
0.331237 + 0.943547i \(0.392534\pi\)
\(158\) 1.78101 0.141689
\(159\) 0 0
\(160\) 13.1983 1.04342
\(161\) −7.45839 −0.587804
\(162\) 0 0
\(163\) 16.9278 1.32588 0.662942 0.748670i \(-0.269307\pi\)
0.662942 + 0.748670i \(0.269307\pi\)
\(164\) −19.3072 −1.50764
\(165\) 0 0
\(166\) −2.62178 −0.203489
\(167\) 3.65977 0.283202 0.141601 0.989924i \(-0.454775\pi\)
0.141601 + 0.989924i \(0.454775\pi\)
\(168\) 0 0
\(169\) 20.7553 1.59656
\(170\) 1.16523 0.0893694
\(171\) 0 0
\(172\) 1.91494 0.146013
\(173\) 8.91665 0.677920 0.338960 0.940801i \(-0.389925\pi\)
0.338960 + 0.940801i \(0.389925\pi\)
\(174\) 0 0
\(175\) −30.0419 −2.27096
\(176\) −10.6890 −0.805715
\(177\) 0 0
\(178\) −0.244495 −0.0183257
\(179\) 1.72001 0.128559 0.0642796 0.997932i \(-0.479525\pi\)
0.0642796 + 0.997932i \(0.479525\pi\)
\(180\) 0 0
\(181\) −18.1564 −1.34956 −0.674779 0.738020i \(-0.735761\pi\)
−0.674779 + 0.738020i \(0.735761\pi\)
\(182\) −4.64372 −0.344216
\(183\) 0 0
\(184\) 3.10748 0.229086
\(185\) 37.8382 2.78192
\(186\) 0 0
\(187\) −3.05674 −0.223531
\(188\) 13.8972 1.01355
\(189\) 0 0
\(190\) −4.30020 −0.311970
\(191\) 3.06795 0.221989 0.110994 0.993821i \(-0.464596\pi\)
0.110994 + 0.993821i \(0.464596\pi\)
\(192\) 0 0
\(193\) 11.9306 0.858785 0.429393 0.903118i \(-0.358728\pi\)
0.429393 + 0.903118i \(0.358728\pi\)
\(194\) −5.04105 −0.361926
\(195\) 0 0
\(196\) −0.977206 −0.0698004
\(197\) 1.46807 0.104596 0.0522980 0.998632i \(-0.483345\pi\)
0.0522980 + 0.998632i \(0.483345\pi\)
\(198\) 0 0
\(199\) −23.7362 −1.68261 −0.841306 0.540559i \(-0.818213\pi\)
−0.841306 + 0.540559i \(0.818213\pi\)
\(200\) 12.5167 0.885065
\(201\) 0 0
\(202\) −1.65207 −0.116239
\(203\) −27.7549 −1.94801
\(204\) 0 0
\(205\) −40.2821 −2.81342
\(206\) −2.07692 −0.144706
\(207\) 0 0
\(208\) −20.3166 −1.40870
\(209\) 11.2807 0.780300
\(210\) 0 0
\(211\) −16.7405 −1.15246 −0.576230 0.817287i \(-0.695477\pi\)
−0.576230 + 0.817287i \(0.695477\pi\)
\(212\) −0.0490461 −0.00336850
\(213\) 0 0
\(214\) 5.62034 0.384198
\(215\) 3.99528 0.272476
\(216\) 0 0
\(217\) −10.4990 −0.712718
\(218\) 1.13171 0.0766493
\(219\) 0 0
\(220\) −23.3862 −1.57670
\(221\) −5.80993 −0.390818
\(222\) 0 0
\(223\) 19.7499 1.32255 0.661275 0.750143i \(-0.270016\pi\)
0.661275 + 0.750143i \(0.270016\pi\)
\(224\) 9.05316 0.604890
\(225\) 0 0
\(226\) 4.78941 0.318587
\(227\) 18.2590 1.21189 0.605945 0.795506i \(-0.292795\pi\)
0.605945 + 0.795506i \(0.292795\pi\)
\(228\) 0 0
\(229\) −8.84328 −0.584381 −0.292190 0.956360i \(-0.594384\pi\)
−0.292190 + 0.956360i \(0.594384\pi\)
\(230\) 3.17124 0.209106
\(231\) 0 0
\(232\) 11.5638 0.759204
\(233\) −0.229827 −0.0150565 −0.00752823 0.999972i \(-0.502396\pi\)
−0.00752823 + 0.999972i \(0.502396\pi\)
\(234\) 0 0
\(235\) 28.9946 1.89140
\(236\) −8.04092 −0.523419
\(237\) 0 0
\(238\) 0.799273 0.0518092
\(239\) 11.0420 0.714244 0.357122 0.934058i \(-0.383758\pi\)
0.357122 + 0.934058i \(0.383758\pi\)
\(240\) 0 0
\(241\) −17.5678 −1.13164 −0.565821 0.824528i \(-0.691441\pi\)
−0.565821 + 0.824528i \(0.691441\pi\)
\(242\) 0.483073 0.0310531
\(243\) 0 0
\(244\) 12.9028 0.826015
\(245\) −2.03882 −0.130255
\(246\) 0 0
\(247\) 21.4411 1.36426
\(248\) 4.37432 0.277769
\(249\) 0 0
\(250\) 6.94740 0.439392
\(251\) 6.11065 0.385701 0.192851 0.981228i \(-0.438227\pi\)
0.192851 + 0.981228i \(0.438227\pi\)
\(252\) 0 0
\(253\) −8.31908 −0.523016
\(254\) 2.62700 0.164833
\(255\) 0 0
\(256\) 9.62065 0.601290
\(257\) 9.41028 0.586997 0.293499 0.955959i \(-0.405180\pi\)
0.293499 + 0.955959i \(0.405180\pi\)
\(258\) 0 0
\(259\) 25.9545 1.61273
\(260\) −44.4501 −2.75668
\(261\) 0 0
\(262\) 5.14391 0.317792
\(263\) 10.9976 0.678143 0.339072 0.940761i \(-0.389887\pi\)
0.339072 + 0.940761i \(0.389887\pi\)
\(264\) 0 0
\(265\) −0.102328 −0.00628598
\(266\) −2.94965 −0.180855
\(267\) 0 0
\(268\) −22.1331 −1.35199
\(269\) −22.1408 −1.34995 −0.674975 0.737841i \(-0.735845\pi\)
−0.674975 + 0.737841i \(0.735845\pi\)
\(270\) 0 0
\(271\) 10.4406 0.634221 0.317110 0.948389i \(-0.397287\pi\)
0.317110 + 0.948389i \(0.397287\pi\)
\(272\) 3.49687 0.212029
\(273\) 0 0
\(274\) −4.29749 −0.259621
\(275\) −33.5087 −2.02065
\(276\) 0 0
\(277\) 7.12840 0.428304 0.214152 0.976800i \(-0.431301\pi\)
0.214152 + 0.976800i \(0.431301\pi\)
\(278\) −2.76588 −0.165886
\(279\) 0 0
\(280\) 12.5016 0.747116
\(281\) −14.8324 −0.884827 −0.442414 0.896811i \(-0.645878\pi\)
−0.442414 + 0.896811i \(0.645878\pi\)
\(282\) 0 0
\(283\) −6.63105 −0.394175 −0.197088 0.980386i \(-0.563148\pi\)
−0.197088 + 0.980386i \(0.563148\pi\)
\(284\) −16.7095 −0.991527
\(285\) 0 0
\(286\) −5.17960 −0.306276
\(287\) −27.6308 −1.63100
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 11.8011 0.692987
\(291\) 0 0
\(292\) −6.37931 −0.373321
\(293\) 20.1059 1.17460 0.587301 0.809369i \(-0.300191\pi\)
0.587301 + 0.809369i \(0.300191\pi\)
\(294\) 0 0
\(295\) −16.7764 −0.976758
\(296\) −10.8137 −0.628534
\(297\) 0 0
\(298\) 5.70389 0.330418
\(299\) −15.8120 −0.914433
\(300\) 0 0
\(301\) 2.74049 0.157959
\(302\) −0.686840 −0.0395232
\(303\) 0 0
\(304\) −12.9049 −0.740147
\(305\) 26.9200 1.54143
\(306\) 0 0
\(307\) −8.05642 −0.459804 −0.229902 0.973214i \(-0.573841\pi\)
−0.229902 + 0.973214i \(0.573841\pi\)
\(308\) −16.0414 −0.914044
\(309\) 0 0
\(310\) 4.46408 0.253543
\(311\) 26.0287 1.47595 0.737975 0.674828i \(-0.235782\pi\)
0.737975 + 0.674828i \(0.235782\pi\)
\(312\) 0 0
\(313\) 15.0857 0.852692 0.426346 0.904560i \(-0.359801\pi\)
0.426346 + 0.904560i \(0.359801\pi\)
\(314\) −2.42095 −0.136622
\(315\) 0 0
\(316\) 11.6938 0.657826
\(317\) 15.4286 0.866559 0.433279 0.901260i \(-0.357356\pi\)
0.433279 + 0.901260i \(0.357356\pi\)
\(318\) 0 0
\(319\) −30.9578 −1.73330
\(320\) 24.0926 1.34682
\(321\) 0 0
\(322\) 2.17526 0.121223
\(323\) −3.69042 −0.205340
\(324\) 0 0
\(325\) −63.6899 −3.53288
\(326\) −4.93703 −0.273437
\(327\) 0 0
\(328\) 11.5121 0.635652
\(329\) 19.8884 1.09648
\(330\) 0 0
\(331\) 0.688160 0.0378247 0.0189123 0.999821i \(-0.493980\pi\)
0.0189123 + 0.999821i \(0.493980\pi\)
\(332\) −17.2141 −0.944746
\(333\) 0 0
\(334\) −1.06738 −0.0584046
\(335\) −46.1778 −2.52296
\(336\) 0 0
\(337\) −31.6565 −1.72444 −0.862221 0.506532i \(-0.830927\pi\)
−0.862221 + 0.506532i \(0.830927\pi\)
\(338\) −6.05335 −0.329259
\(339\) 0 0
\(340\) 7.65071 0.414918
\(341\) −11.7106 −0.634162
\(342\) 0 0
\(343\) 17.7850 0.960298
\(344\) −1.14180 −0.0615619
\(345\) 0 0
\(346\) −2.60057 −0.139807
\(347\) 14.0369 0.753543 0.376771 0.926306i \(-0.377034\pi\)
0.376771 + 0.926306i \(0.377034\pi\)
\(348\) 0 0
\(349\) −1.09785 −0.0587666 −0.0293833 0.999568i \(-0.509354\pi\)
−0.0293833 + 0.999568i \(0.509354\pi\)
\(350\) 8.76182 0.468339
\(351\) 0 0
\(352\) 10.0979 0.538219
\(353\) 4.70964 0.250669 0.125334 0.992115i \(-0.460000\pi\)
0.125334 + 0.992115i \(0.460000\pi\)
\(354\) 0 0
\(355\) −34.8623 −1.85030
\(356\) −1.60531 −0.0850811
\(357\) 0 0
\(358\) −0.501645 −0.0265128
\(359\) −12.9863 −0.685391 −0.342696 0.939446i \(-0.611340\pi\)
−0.342696 + 0.939446i \(0.611340\pi\)
\(360\) 0 0
\(361\) −5.38080 −0.283200
\(362\) 5.29538 0.278319
\(363\) 0 0
\(364\) −30.4898 −1.59810
\(365\) −13.3096 −0.696658
\(366\) 0 0
\(367\) −4.48210 −0.233964 −0.116982 0.993134i \(-0.537322\pi\)
−0.116982 + 0.993134i \(0.537322\pi\)
\(368\) 9.51690 0.496103
\(369\) 0 0
\(370\) −11.0356 −0.573714
\(371\) −0.0701905 −0.00364411
\(372\) 0 0
\(373\) −7.86900 −0.407441 −0.203721 0.979029i \(-0.565303\pi\)
−0.203721 + 0.979029i \(0.565303\pi\)
\(374\) 0.891508 0.0460988
\(375\) 0 0
\(376\) −8.28633 −0.427335
\(377\) −58.8413 −3.03048
\(378\) 0 0
\(379\) 17.3002 0.888654 0.444327 0.895865i \(-0.353443\pi\)
0.444327 + 0.895865i \(0.353443\pi\)
\(380\) −28.2343 −1.44839
\(381\) 0 0
\(382\) −0.894776 −0.0457807
\(383\) 5.67171 0.289811 0.144906 0.989445i \(-0.453712\pi\)
0.144906 + 0.989445i \(0.453712\pi\)
\(384\) 0 0
\(385\) −33.4684 −1.70571
\(386\) −3.47960 −0.177107
\(387\) 0 0
\(388\) −33.0986 −1.68033
\(389\) −17.1355 −0.868805 −0.434402 0.900719i \(-0.643040\pi\)
−0.434402 + 0.900719i \(0.643040\pi\)
\(390\) 0 0
\(391\) 2.72155 0.137635
\(392\) 0.582670 0.0294293
\(393\) 0 0
\(394\) −0.428168 −0.0215708
\(395\) 24.3976 1.22757
\(396\) 0 0
\(397\) 21.3267 1.07035 0.535177 0.844740i \(-0.320245\pi\)
0.535177 + 0.844740i \(0.320245\pi\)
\(398\) 6.92272 0.347005
\(399\) 0 0
\(400\) 38.3335 1.91667
\(401\) 32.6052 1.62823 0.814114 0.580705i \(-0.197223\pi\)
0.814114 + 0.580705i \(0.197223\pi\)
\(402\) 0 0
\(403\) −22.2582 −1.10876
\(404\) −10.8472 −0.539668
\(405\) 0 0
\(406\) 8.09480 0.401738
\(407\) 28.9496 1.43498
\(408\) 0 0
\(409\) −10.5782 −0.523056 −0.261528 0.965196i \(-0.584226\pi\)
−0.261528 + 0.965196i \(0.584226\pi\)
\(410\) 11.7484 0.580211
\(411\) 0 0
\(412\) −13.6366 −0.671829
\(413\) −11.5075 −0.566246
\(414\) 0 0
\(415\) −35.9150 −1.76300
\(416\) 19.1930 0.941014
\(417\) 0 0
\(418\) −3.29004 −0.160921
\(419\) 17.3706 0.848608 0.424304 0.905520i \(-0.360519\pi\)
0.424304 + 0.905520i \(0.360519\pi\)
\(420\) 0 0
\(421\) −4.46786 −0.217750 −0.108875 0.994055i \(-0.534725\pi\)
−0.108875 + 0.994055i \(0.534725\pi\)
\(422\) 4.88240 0.237672
\(423\) 0 0
\(424\) 0.0292443 0.00142023
\(425\) 10.9622 0.531746
\(426\) 0 0
\(427\) 18.4653 0.893599
\(428\) 36.9021 1.78373
\(429\) 0 0
\(430\) −1.16523 −0.0561926
\(431\) −10.0244 −0.482860 −0.241430 0.970418i \(-0.577616\pi\)
−0.241430 + 0.970418i \(0.577616\pi\)
\(432\) 0 0
\(433\) −9.06344 −0.435561 −0.217781 0.975998i \(-0.569882\pi\)
−0.217781 + 0.975998i \(0.569882\pi\)
\(434\) 3.06206 0.146984
\(435\) 0 0
\(436\) 7.43062 0.355862
\(437\) −10.0437 −0.480454
\(438\) 0 0
\(439\) 29.4502 1.40558 0.702791 0.711397i \(-0.251937\pi\)
0.702791 + 0.711397i \(0.251937\pi\)
\(440\) 13.9443 0.664769
\(441\) 0 0
\(442\) 1.69448 0.0805984
\(443\) −9.04833 −0.429899 −0.214950 0.976625i \(-0.568959\pi\)
−0.214950 + 0.976625i \(0.568959\pi\)
\(444\) 0 0
\(445\) −3.34927 −0.158771
\(446\) −5.76011 −0.272749
\(447\) 0 0
\(448\) 16.5259 0.780776
\(449\) −14.7810 −0.697557 −0.348779 0.937205i \(-0.613403\pi\)
−0.348779 + 0.937205i \(0.613403\pi\)
\(450\) 0 0
\(451\) −30.8194 −1.45123
\(452\) 31.4463 1.47911
\(453\) 0 0
\(454\) −5.32528 −0.249928
\(455\) −63.6131 −2.98223
\(456\) 0 0
\(457\) 3.87054 0.181056 0.0905281 0.995894i \(-0.471144\pi\)
0.0905281 + 0.995894i \(0.471144\pi\)
\(458\) 2.57917 0.120517
\(459\) 0 0
\(460\) 20.8218 0.970821
\(461\) −15.4345 −0.718854 −0.359427 0.933173i \(-0.617028\pi\)
−0.359427 + 0.933173i \(0.617028\pi\)
\(462\) 0 0
\(463\) −17.0689 −0.793260 −0.396630 0.917979i \(-0.629820\pi\)
−0.396630 + 0.917979i \(0.629820\pi\)
\(464\) 35.4152 1.64411
\(465\) 0 0
\(466\) 0.0670297 0.00310509
\(467\) 34.5188 1.59734 0.798670 0.601770i \(-0.205538\pi\)
0.798670 + 0.601770i \(0.205538\pi\)
\(468\) 0 0
\(469\) −31.6749 −1.46261
\(470\) −8.45637 −0.390063
\(471\) 0 0
\(472\) 4.79449 0.220684
\(473\) 3.05674 0.140549
\(474\) 0 0
\(475\) −40.4552 −1.85621
\(476\) 5.24788 0.240536
\(477\) 0 0
\(478\) −3.22042 −0.147298
\(479\) 6.40545 0.292673 0.146336 0.989235i \(-0.453252\pi\)
0.146336 + 0.989235i \(0.453252\pi\)
\(480\) 0 0
\(481\) 55.0243 2.50889
\(482\) 5.12371 0.233378
\(483\) 0 0
\(484\) 3.17177 0.144171
\(485\) −69.0560 −3.13567
\(486\) 0 0
\(487\) −28.4585 −1.28958 −0.644788 0.764361i \(-0.723054\pi\)
−0.644788 + 0.764361i \(0.723054\pi\)
\(488\) −7.69342 −0.348265
\(489\) 0 0
\(490\) 0.594627 0.0268625
\(491\) −25.9394 −1.17063 −0.585314 0.810807i \(-0.699029\pi\)
−0.585314 + 0.810807i \(0.699029\pi\)
\(492\) 0 0
\(493\) 10.1277 0.456129
\(494\) −6.25336 −0.281352
\(495\) 0 0
\(496\) 13.3967 0.601530
\(497\) −23.9132 −1.07265
\(498\) 0 0
\(499\) −36.4020 −1.62958 −0.814790 0.579757i \(-0.803148\pi\)
−0.814790 + 0.579757i \(0.803148\pi\)
\(500\) 45.6153 2.03998
\(501\) 0 0
\(502\) −1.78219 −0.0795430
\(503\) −38.9182 −1.73528 −0.867638 0.497197i \(-0.834363\pi\)
−0.867638 + 0.497197i \(0.834363\pi\)
\(504\) 0 0
\(505\) −22.6313 −1.00708
\(506\) 2.42628 0.107861
\(507\) 0 0
\(508\) 17.2484 0.765275
\(509\) 22.3222 0.989415 0.494708 0.869060i \(-0.335275\pi\)
0.494708 + 0.869060i \(0.335275\pi\)
\(510\) 0 0
\(511\) −9.12952 −0.403866
\(512\) −19.5373 −0.863434
\(513\) 0 0
\(514\) −2.74454 −0.121056
\(515\) −28.4511 −1.25371
\(516\) 0 0
\(517\) 22.1835 0.975629
\(518\) −7.56970 −0.332593
\(519\) 0 0
\(520\) 26.5039 1.16227
\(521\) 9.08470 0.398008 0.199004 0.979999i \(-0.436229\pi\)
0.199004 + 0.979999i \(0.436229\pi\)
\(522\) 0 0
\(523\) −10.0141 −0.437888 −0.218944 0.975737i \(-0.570261\pi\)
−0.218944 + 0.975737i \(0.570261\pi\)
\(524\) 33.7740 1.47542
\(525\) 0 0
\(526\) −3.20749 −0.139853
\(527\) 3.83106 0.166884
\(528\) 0 0
\(529\) −15.5932 −0.677964
\(530\) 0.0298444 0.00129636
\(531\) 0 0
\(532\) −19.3669 −0.839660
\(533\) −58.5782 −2.53730
\(534\) 0 0
\(535\) 76.9915 3.32863
\(536\) 13.1971 0.570027
\(537\) 0 0
\(538\) 6.45743 0.278400
\(539\) −1.55988 −0.0671886
\(540\) 0 0
\(541\) 17.4916 0.752024 0.376012 0.926615i \(-0.377295\pi\)
0.376012 + 0.926615i \(0.377295\pi\)
\(542\) −3.04503 −0.130795
\(543\) 0 0
\(544\) −3.30348 −0.141635
\(545\) 15.5030 0.664077
\(546\) 0 0
\(547\) 9.21314 0.393926 0.196963 0.980411i \(-0.436892\pi\)
0.196963 + 0.980411i \(0.436892\pi\)
\(548\) −28.2165 −1.20535
\(549\) 0 0
\(550\) 9.77292 0.416719
\(551\) −37.3755 −1.59225
\(552\) 0 0
\(553\) 16.7351 0.711649
\(554\) −2.07902 −0.0883290
\(555\) 0 0
\(556\) −18.1602 −0.770166
\(557\) 8.45542 0.358268 0.179134 0.983825i \(-0.442671\pi\)
0.179134 + 0.983825i \(0.442671\pi\)
\(558\) 0 0
\(559\) 5.80993 0.245734
\(560\) 38.2873 1.61793
\(561\) 0 0
\(562\) 4.32592 0.182478
\(563\) 29.1351 1.22790 0.613949 0.789346i \(-0.289580\pi\)
0.613949 + 0.789346i \(0.289580\pi\)
\(564\) 0 0
\(565\) 65.6088 2.76018
\(566\) 1.93397 0.0812907
\(567\) 0 0
\(568\) 9.96323 0.418048
\(569\) 13.0424 0.546767 0.273383 0.961905i \(-0.411857\pi\)
0.273383 + 0.961905i \(0.411857\pi\)
\(570\) 0 0
\(571\) 1.70766 0.0714633 0.0357317 0.999361i \(-0.488624\pi\)
0.0357317 + 0.999361i \(0.488624\pi\)
\(572\) −34.0083 −1.42196
\(573\) 0 0
\(574\) 8.05861 0.336360
\(575\) 29.8343 1.24417
\(576\) 0 0
\(577\) 34.3329 1.42930 0.714648 0.699484i \(-0.246587\pi\)
0.714648 + 0.699484i \(0.246587\pi\)
\(578\) −0.291653 −0.0121312
\(579\) 0 0
\(580\) 77.4841 3.21735
\(581\) −24.6353 −1.02205
\(582\) 0 0
\(583\) −0.0782903 −0.00324245
\(584\) 3.80374 0.157400
\(585\) 0 0
\(586\) −5.86396 −0.242238
\(587\) −9.88207 −0.407877 −0.203938 0.978984i \(-0.565374\pi\)
−0.203938 + 0.978984i \(0.565374\pi\)
\(588\) 0 0
\(589\) −14.1382 −0.582555
\(590\) 4.89288 0.201437
\(591\) 0 0
\(592\) −33.1179 −1.36114
\(593\) −10.8310 −0.444774 −0.222387 0.974958i \(-0.571385\pi\)
−0.222387 + 0.974958i \(0.571385\pi\)
\(594\) 0 0
\(595\) 10.9490 0.448866
\(596\) 37.4507 1.53404
\(597\) 0 0
\(598\) 4.61162 0.188583
\(599\) −14.7511 −0.602715 −0.301358 0.953511i \(-0.597440\pi\)
−0.301358 + 0.953511i \(0.597440\pi\)
\(600\) 0 0
\(601\) 11.1801 0.456047 0.228023 0.973656i \(-0.426774\pi\)
0.228023 + 0.973656i \(0.426774\pi\)
\(602\) −0.799273 −0.0325759
\(603\) 0 0
\(604\) −4.50966 −0.183496
\(605\) 6.61749 0.269039
\(606\) 0 0
\(607\) −44.3193 −1.79887 −0.899433 0.437059i \(-0.856020\pi\)
−0.899433 + 0.437059i \(0.856020\pi\)
\(608\) 12.1912 0.494419
\(609\) 0 0
\(610\) −7.85129 −0.317889
\(611\) 42.1640 1.70577
\(612\) 0 0
\(613\) −11.9423 −0.482344 −0.241172 0.970482i \(-0.577532\pi\)
−0.241172 + 0.970482i \(0.577532\pi\)
\(614\) 2.34968 0.0948253
\(615\) 0 0
\(616\) 9.56487 0.385379
\(617\) −20.8460 −0.839230 −0.419615 0.907702i \(-0.637835\pi\)
−0.419615 + 0.907702i \(0.637835\pi\)
\(618\) 0 0
\(619\) −44.3104 −1.78098 −0.890492 0.454999i \(-0.849640\pi\)
−0.890492 + 0.454999i \(0.849640\pi\)
\(620\) 29.3103 1.17713
\(621\) 0 0
\(622\) −7.59134 −0.304385
\(623\) −2.29738 −0.0920424
\(624\) 0 0
\(625\) 40.3594 1.61438
\(626\) −4.39978 −0.175851
\(627\) 0 0
\(628\) −15.8955 −0.634299
\(629\) −9.47073 −0.377623
\(630\) 0 0
\(631\) 11.4916 0.457473 0.228736 0.973488i \(-0.426541\pi\)
0.228736 + 0.973488i \(0.426541\pi\)
\(632\) −6.97254 −0.277353
\(633\) 0 0
\(634\) −4.49981 −0.178710
\(635\) 35.9866 1.42809
\(636\) 0 0
\(637\) −2.96485 −0.117472
\(638\) 9.02893 0.357459
\(639\) 0 0
\(640\) −33.4233 −1.32117
\(641\) 11.5475 0.456100 0.228050 0.973649i \(-0.426765\pi\)
0.228050 + 0.973649i \(0.426765\pi\)
\(642\) 0 0
\(643\) 26.3988 1.04107 0.520533 0.853842i \(-0.325733\pi\)
0.520533 + 0.853842i \(0.325733\pi\)
\(644\) 14.2824 0.562804
\(645\) 0 0
\(646\) 1.07632 0.0423473
\(647\) −33.2667 −1.30785 −0.653924 0.756561i \(-0.726878\pi\)
−0.653924 + 0.756561i \(0.726878\pi\)
\(648\) 0 0
\(649\) −12.8354 −0.503834
\(650\) 18.5753 0.728585
\(651\) 0 0
\(652\) −32.4156 −1.26949
\(653\) 11.1145 0.434945 0.217472 0.976067i \(-0.430219\pi\)
0.217472 + 0.976067i \(0.430219\pi\)
\(654\) 0 0
\(655\) 70.4651 2.75330
\(656\) 35.2569 1.37655
\(657\) 0 0
\(658\) −5.80051 −0.226127
\(659\) 32.1156 1.25104 0.625522 0.780206i \(-0.284886\pi\)
0.625522 + 0.780206i \(0.284886\pi\)
\(660\) 0 0
\(661\) −7.71808 −0.300199 −0.150099 0.988671i \(-0.547959\pi\)
−0.150099 + 0.988671i \(0.547959\pi\)
\(662\) −0.200704 −0.00780057
\(663\) 0 0
\(664\) 10.2641 0.398324
\(665\) −40.4065 −1.56690
\(666\) 0 0
\(667\) 27.5631 1.06725
\(668\) −7.00824 −0.271157
\(669\) 0 0
\(670\) 13.4679 0.520310
\(671\) 20.5962 0.795107
\(672\) 0 0
\(673\) 23.9188 0.922003 0.461002 0.887399i \(-0.347490\pi\)
0.461002 + 0.887399i \(0.347490\pi\)
\(674\) 9.23272 0.355631
\(675\) 0 0
\(676\) −39.7452 −1.52866
\(677\) −13.7725 −0.529321 −0.264661 0.964342i \(-0.585260\pi\)
−0.264661 + 0.964342i \(0.585260\pi\)
\(678\) 0 0
\(679\) −47.3678 −1.81781
\(680\) −4.56182 −0.174938
\(681\) 0 0
\(682\) 3.41542 0.130783
\(683\) −10.7891 −0.412835 −0.206418 0.978464i \(-0.566181\pi\)
−0.206418 + 0.978464i \(0.566181\pi\)
\(684\) 0 0
\(685\) −58.8701 −2.24931
\(686\) −5.18704 −0.198042
\(687\) 0 0
\(688\) −3.49687 −0.133317
\(689\) −0.148806 −0.00566906
\(690\) 0 0
\(691\) 4.14875 0.157826 0.0789130 0.996882i \(-0.474855\pi\)
0.0789130 + 0.996882i \(0.474855\pi\)
\(692\) −17.0748 −0.649088
\(693\) 0 0
\(694\) −4.09392 −0.155403
\(695\) −37.8890 −1.43721
\(696\) 0 0
\(697\) 10.0824 0.381899
\(698\) 0.320192 0.0121194
\(699\) 0 0
\(700\) 57.5285 2.17437
\(701\) −9.71741 −0.367021 −0.183511 0.983018i \(-0.558746\pi\)
−0.183511 + 0.983018i \(0.558746\pi\)
\(702\) 0 0
\(703\) 34.9510 1.31820
\(704\) 18.4330 0.694718
\(705\) 0 0
\(706\) −1.37358 −0.0516954
\(707\) −15.5236 −0.583824
\(708\) 0 0
\(709\) −35.0387 −1.31591 −0.657953 0.753059i \(-0.728578\pi\)
−0.657953 + 0.753059i \(0.728578\pi\)
\(710\) 10.1677 0.381586
\(711\) 0 0
\(712\) 0.957182 0.0358719
\(713\) 10.4264 0.390472
\(714\) 0 0
\(715\) −70.9540 −2.65353
\(716\) −3.29371 −0.123092
\(717\) 0 0
\(718\) 3.78750 0.141348
\(719\) −27.6154 −1.02988 −0.514940 0.857226i \(-0.672186\pi\)
−0.514940 + 0.857226i \(0.672186\pi\)
\(720\) 0 0
\(721\) −19.5156 −0.726798
\(722\) 1.56933 0.0584042
\(723\) 0 0
\(724\) 34.7685 1.29216
\(725\) 111.022 4.12326
\(726\) 0 0
\(727\) 14.5140 0.538293 0.269146 0.963099i \(-0.413258\pi\)
0.269146 + 0.963099i \(0.413258\pi\)
\(728\) 18.1799 0.673792
\(729\) 0 0
\(730\) 3.88179 0.143672
\(731\) −1.00000 −0.0369863
\(732\) 0 0
\(733\) −37.2894 −1.37732 −0.688659 0.725086i \(-0.741800\pi\)
−0.688659 + 0.725086i \(0.741800\pi\)
\(734\) 1.30722 0.0482503
\(735\) 0 0
\(736\) −8.99058 −0.331397
\(737\) −35.3301 −1.30140
\(738\) 0 0
\(739\) −19.9962 −0.735571 −0.367785 0.929911i \(-0.619884\pi\)
−0.367785 + 0.929911i \(0.619884\pi\)
\(740\) −72.4578 −2.66360
\(741\) 0 0
\(742\) 0.0204713 0.000751523 0
\(743\) 18.9825 0.696399 0.348199 0.937420i \(-0.386793\pi\)
0.348199 + 0.937420i \(0.386793\pi\)
\(744\) 0 0
\(745\) 78.1361 2.86269
\(746\) 2.29502 0.0840265
\(747\) 0 0
\(748\) 5.85347 0.214024
\(749\) 52.8110 1.92967
\(750\) 0 0
\(751\) −40.6916 −1.48486 −0.742429 0.669925i \(-0.766326\pi\)
−0.742429 + 0.669925i \(0.766326\pi\)
\(752\) −25.3776 −0.925425
\(753\) 0 0
\(754\) 17.1612 0.624975
\(755\) −9.40884 −0.342423
\(756\) 0 0
\(757\) −25.2060 −0.916128 −0.458064 0.888919i \(-0.651457\pi\)
−0.458064 + 0.888919i \(0.651457\pi\)
\(758\) −5.04567 −0.183267
\(759\) 0 0
\(760\) 16.8350 0.610671
\(761\) 26.2909 0.953043 0.476521 0.879163i \(-0.341897\pi\)
0.476521 + 0.879163i \(0.341897\pi\)
\(762\) 0 0
\(763\) 10.6341 0.384979
\(764\) −5.87493 −0.212547
\(765\) 0 0
\(766\) −1.65417 −0.0597677
\(767\) −24.3962 −0.880896
\(768\) 0 0
\(769\) 17.5206 0.631809 0.315905 0.948791i \(-0.397692\pi\)
0.315905 + 0.948791i \(0.397692\pi\)
\(770\) 9.76115 0.351767
\(771\) 0 0
\(772\) −22.8464 −0.822261
\(773\) 47.6695 1.71455 0.857277 0.514855i \(-0.172154\pi\)
0.857277 + 0.514855i \(0.172154\pi\)
\(774\) 0 0
\(775\) 41.9970 1.50858
\(776\) 19.7354 0.708460
\(777\) 0 0
\(778\) 4.99762 0.179173
\(779\) −37.2084 −1.33313
\(780\) 0 0
\(781\) −26.6727 −0.954426
\(782\) −0.793748 −0.0283844
\(783\) 0 0
\(784\) 1.78447 0.0637312
\(785\) −33.1639 −1.18367
\(786\) 0 0
\(787\) 41.4827 1.47870 0.739349 0.673322i \(-0.235133\pi\)
0.739349 + 0.673322i \(0.235133\pi\)
\(788\) −2.81127 −0.100147
\(789\) 0 0
\(790\) −7.11562 −0.253162
\(791\) 45.0033 1.60013
\(792\) 0 0
\(793\) 39.1471 1.39015
\(794\) −6.21999 −0.220739
\(795\) 0 0
\(796\) 45.4533 1.61105
\(797\) 29.7609 1.05419 0.527093 0.849808i \(-0.323282\pi\)
0.527093 + 0.849808i \(0.323282\pi\)
\(798\) 0 0
\(799\) −7.25723 −0.256742
\(800\) −36.2135 −1.28034
\(801\) 0 0
\(802\) −9.50941 −0.335789
\(803\) −10.1831 −0.359352
\(804\) 0 0
\(805\) 29.7983 1.05025
\(806\) 6.49167 0.228659
\(807\) 0 0
\(808\) 6.46776 0.227535
\(809\) 45.4805 1.59901 0.799504 0.600661i \(-0.205096\pi\)
0.799504 + 0.600661i \(0.205096\pi\)
\(810\) 0 0
\(811\) 20.1527 0.707659 0.353829 0.935310i \(-0.384879\pi\)
0.353829 + 0.935310i \(0.384879\pi\)
\(812\) 53.1489 1.86516
\(813\) 0 0
\(814\) −8.44323 −0.295935
\(815\) −67.6311 −2.36901
\(816\) 0 0
\(817\) 3.69042 0.129111
\(818\) 3.08515 0.107870
\(819\) 0 0
\(820\) 77.1377 2.69377
\(821\) −12.2357 −0.427029 −0.213515 0.976940i \(-0.568491\pi\)
−0.213515 + 0.976940i \(0.568491\pi\)
\(822\) 0 0
\(823\) 31.1224 1.08486 0.542430 0.840101i \(-0.317505\pi\)
0.542430 + 0.840101i \(0.317505\pi\)
\(824\) 8.13100 0.283257
\(825\) 0 0
\(826\) 3.35619 0.116777
\(827\) −45.4529 −1.58055 −0.790276 0.612750i \(-0.790063\pi\)
−0.790276 + 0.612750i \(0.790063\pi\)
\(828\) 0 0
\(829\) 0.205090 0.00712306 0.00356153 0.999994i \(-0.498866\pi\)
0.00356153 + 0.999994i \(0.498866\pi\)
\(830\) 10.4747 0.363583
\(831\) 0 0
\(832\) 35.0354 1.21464
\(833\) 0.510306 0.0176811
\(834\) 0 0
\(835\) −14.6218 −0.506008
\(836\) −21.6018 −0.747113
\(837\) 0 0
\(838\) −5.06618 −0.175008
\(839\) 15.1516 0.523093 0.261546 0.965191i \(-0.415768\pi\)
0.261546 + 0.965191i \(0.415768\pi\)
\(840\) 0 0
\(841\) 73.5704 2.53691
\(842\) 1.30307 0.0449066
\(843\) 0 0
\(844\) 32.0570 1.10345
\(845\) −82.9233 −2.85265
\(846\) 0 0
\(847\) 4.53916 0.155967
\(848\) 0.0895629 0.00307560
\(849\) 0 0
\(850\) −3.19717 −0.109662
\(851\) −25.7751 −0.883558
\(852\) 0 0
\(853\) 11.5839 0.396624 0.198312 0.980139i \(-0.436454\pi\)
0.198312 + 0.980139i \(0.436454\pi\)
\(854\) −5.38546 −0.184287
\(855\) 0 0
\(856\) −22.0033 −0.752056
\(857\) 13.1807 0.450246 0.225123 0.974330i \(-0.427722\pi\)
0.225123 + 0.974330i \(0.427722\pi\)
\(858\) 0 0
\(859\) 6.31531 0.215476 0.107738 0.994179i \(-0.465639\pi\)
0.107738 + 0.994179i \(0.465639\pi\)
\(860\) −7.65071 −0.260887
\(861\) 0 0
\(862\) 2.92366 0.0995801
\(863\) 54.1093 1.84190 0.920950 0.389680i \(-0.127414\pi\)
0.920950 + 0.389680i \(0.127414\pi\)
\(864\) 0 0
\(865\) −35.6245 −1.21127
\(866\) 2.64338 0.0898257
\(867\) 0 0
\(868\) 20.1049 0.682406
\(869\) 18.6663 0.633211
\(870\) 0 0
\(871\) −67.1518 −2.27535
\(872\) −4.43059 −0.150039
\(873\) 0 0
\(874\) 2.92926 0.0990838
\(875\) 65.2807 2.20689
\(876\) 0 0
\(877\) −10.1191 −0.341699 −0.170849 0.985297i \(-0.554651\pi\)
−0.170849 + 0.985297i \(0.554651\pi\)
\(878\) −8.58924 −0.289873
\(879\) 0 0
\(880\) 42.7056 1.43961
\(881\) −35.1813 −1.18529 −0.592643 0.805465i \(-0.701916\pi\)
−0.592643 + 0.805465i \(0.701916\pi\)
\(882\) 0 0
\(883\) 41.6661 1.40218 0.701088 0.713075i \(-0.252698\pi\)
0.701088 + 0.713075i \(0.252698\pi\)
\(884\) 11.1257 0.374197
\(885\) 0 0
\(886\) 2.63897 0.0886580
\(887\) −5.82622 −0.195625 −0.0978126 0.995205i \(-0.531185\pi\)
−0.0978126 + 0.995205i \(0.531185\pi\)
\(888\) 0 0
\(889\) 24.6844 0.827890
\(890\) 0.976824 0.0327432
\(891\) 0 0
\(892\) −37.8198 −1.26630
\(893\) 26.7822 0.896233
\(894\) 0 0
\(895\) −6.87190 −0.229702
\(896\) −22.9262 −0.765909
\(897\) 0 0
\(898\) 4.31091 0.143857
\(899\) 38.7998 1.29405
\(900\) 0 0
\(901\) 0.0256123 0.000853271 0
\(902\) 8.98856 0.299286
\(903\) 0 0
\(904\) −18.7502 −0.623623
\(905\) 72.5400 2.41131
\(906\) 0 0
\(907\) 10.9136 0.362381 0.181191 0.983448i \(-0.442005\pi\)
0.181191 + 0.983448i \(0.442005\pi\)
\(908\) −34.9648 −1.16035
\(909\) 0 0
\(910\) 18.5530 0.615025
\(911\) 13.1513 0.435723 0.217861 0.975980i \(-0.430092\pi\)
0.217861 + 0.975980i \(0.430092\pi\)
\(912\) 0 0
\(913\) −27.4782 −0.909395
\(914\) −1.12885 −0.0373392
\(915\) 0 0
\(916\) 16.9343 0.559526
\(917\) 48.3344 1.59614
\(918\) 0 0
\(919\) 48.1109 1.58703 0.793517 0.608548i \(-0.208248\pi\)
0.793517 + 0.608548i \(0.208248\pi\)
\(920\) −12.4152 −0.409318
\(921\) 0 0
\(922\) 4.50151 0.148249
\(923\) −50.6967 −1.66870
\(924\) 0 0
\(925\) −103.820 −3.41359
\(926\) 4.97820 0.163594
\(927\) 0 0
\(928\) −33.4567 −1.09827
\(929\) 25.2216 0.827495 0.413748 0.910392i \(-0.364220\pi\)
0.413748 + 0.910392i \(0.364220\pi\)
\(930\) 0 0
\(931\) −1.88325 −0.0617209
\(932\) 0.440104 0.0144161
\(933\) 0 0
\(934\) −10.0675 −0.329419
\(935\) 12.2125 0.399392
\(936\) 0 0
\(937\) 21.8619 0.714197 0.357098 0.934067i \(-0.383766\pi\)
0.357098 + 0.934067i \(0.383766\pi\)
\(938\) 9.23808 0.301634
\(939\) 0 0
\(940\) −55.5230 −1.81096
\(941\) −55.9850 −1.82506 −0.912530 0.409010i \(-0.865874\pi\)
−0.912530 + 0.409010i \(0.865874\pi\)
\(942\) 0 0
\(943\) 27.4398 0.893564
\(944\) 14.6835 0.477908
\(945\) 0 0
\(946\) −0.891508 −0.0289854
\(947\) −9.19797 −0.298894 −0.149447 0.988770i \(-0.547749\pi\)
−0.149447 + 0.988770i \(0.547749\pi\)
\(948\) 0 0
\(949\) −19.3549 −0.628286
\(950\) 11.7989 0.382807
\(951\) 0 0
\(952\) −3.12911 −0.101415
\(953\) −26.3104 −0.852276 −0.426138 0.904658i \(-0.640126\pi\)
−0.426138 + 0.904658i \(0.640126\pi\)
\(954\) 0 0
\(955\) −12.2573 −0.396637
\(956\) −21.1447 −0.683867
\(957\) 0 0
\(958\) −1.86817 −0.0603578
\(959\) −40.3810 −1.30397
\(960\) 0 0
\(961\) −16.3230 −0.526548
\(962\) −16.0480 −0.517408
\(963\) 0 0
\(964\) 33.6413 1.08351
\(965\) −47.6662 −1.53443
\(966\) 0 0
\(967\) −23.2676 −0.748237 −0.374118 0.927381i \(-0.622055\pi\)
−0.374118 + 0.927381i \(0.622055\pi\)
\(968\) −1.89120 −0.0607855
\(969\) 0 0
\(970\) 20.1404 0.646669
\(971\) 22.6891 0.728128 0.364064 0.931374i \(-0.381389\pi\)
0.364064 + 0.931374i \(0.381389\pi\)
\(972\) 0 0
\(973\) −25.9894 −0.833181
\(974\) 8.30000 0.265949
\(975\) 0 0
\(976\) −23.5617 −0.754192
\(977\) 33.2179 1.06273 0.531367 0.847142i \(-0.321679\pi\)
0.531367 + 0.847142i \(0.321679\pi\)
\(978\) 0 0
\(979\) −2.56249 −0.0818975
\(980\) 3.90421 0.124715
\(981\) 0 0
\(982\) 7.56530 0.241418
\(983\) −4.77329 −0.152244 −0.0761222 0.997098i \(-0.524254\pi\)
−0.0761222 + 0.997098i \(0.524254\pi\)
\(984\) 0 0
\(985\) −5.86536 −0.186886
\(986\) −2.95377 −0.0940674
\(987\) 0 0
\(988\) −41.0584 −1.30624
\(989\) −2.72155 −0.0865403
\(990\) 0 0
\(991\) −18.2124 −0.578537 −0.289268 0.957248i \(-0.593412\pi\)
−0.289268 + 0.957248i \(0.593412\pi\)
\(992\) −12.6558 −0.401823
\(993\) 0 0
\(994\) 6.97435 0.221213
\(995\) 94.8325 3.00639
\(996\) 0 0
\(997\) 19.0963 0.604785 0.302393 0.953183i \(-0.402215\pi\)
0.302393 + 0.953183i \(0.402215\pi\)
\(998\) 10.6168 0.336068
\(999\) 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 6579.2.a.j.1.3 6
3.2 odd 2 731.2.a.c.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.4 6 3.2 odd 2
6579.2.a.j.1.3 6 1.1 even 1 trivial