Properties

Label 6579.2.a.j.1.2
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 1.2
Root \(0.668929\) 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)
 
\(f(q)\) \(=\) \(q-1.55253 q^{2} +0.410361 q^{4} +1.37639 q^{5} -3.35157 q^{7} +2.46797 q^{8} +O(q^{10})\) \(q-1.55253 q^{2} +0.410361 q^{4} +1.37639 q^{5} -3.35157 q^{7} +2.46797 q^{8} -2.13690 q^{10} -2.05761 q^{11} -1.60557 q^{13} +5.20343 q^{14} -4.65233 q^{16} +1.00000 q^{17} +4.43647 q^{19} +0.564818 q^{20} +3.19450 q^{22} +2.95501 q^{23} -3.10554 q^{25} +2.49271 q^{26} -1.37535 q^{28} +3.13539 q^{29} -4.72687 q^{31} +2.28696 q^{32} -1.55253 q^{34} -4.61308 q^{35} +6.73408 q^{37} -6.88777 q^{38} +3.39690 q^{40} -9.28079 q^{41} -1.00000 q^{43} -0.844362 q^{44} -4.58775 q^{46} +8.52365 q^{47} +4.23304 q^{49} +4.82146 q^{50} -0.658865 q^{52} -9.33387 q^{53} -2.83208 q^{55} -8.27157 q^{56} -4.86779 q^{58} +9.83672 q^{59} +2.75383 q^{61} +7.33862 q^{62} +5.75407 q^{64} -2.20990 q^{65} +8.84901 q^{67} +0.410361 q^{68} +7.16197 q^{70} +1.37235 q^{71} -0.237911 q^{73} -10.4549 q^{74} +1.82055 q^{76} +6.89622 q^{77} -7.25698 q^{79} -6.40343 q^{80} +14.4087 q^{82} +2.15336 q^{83} +1.37639 q^{85} +1.55253 q^{86} -5.07811 q^{88} +13.4194 q^{89} +5.38120 q^{91} +1.21262 q^{92} -13.2332 q^{94} +6.10633 q^{95} -12.3738 q^{97} -6.57194 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 5 q^{4} - 3 q^{5} - 7 q^{7} + 9 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55253 −1.09781 −0.548904 0.835886i \(-0.684955\pi\)
−0.548904 + 0.835886i \(0.684955\pi\)
\(3\) 0 0
\(4\) 0.410361 0.205180
\(5\) 1.37639 0.615542 0.307771 0.951460i \(-0.400417\pi\)
0.307771 + 0.951460i \(0.400417\pi\)
\(6\) 0 0
\(7\) −3.35157 −1.26678 −0.633388 0.773835i \(-0.718336\pi\)
−0.633388 + 0.773835i \(0.718336\pi\)
\(8\) 2.46797 0.872559
\(9\) 0 0
\(10\) −2.13690 −0.675746
\(11\) −2.05761 −0.620392 −0.310196 0.950673i \(-0.600395\pi\)
−0.310196 + 0.950673i \(0.600395\pi\)
\(12\) 0 0
\(13\) −1.60557 −0.445306 −0.222653 0.974898i \(-0.571472\pi\)
−0.222653 + 0.974898i \(0.571472\pi\)
\(14\) 5.20343 1.39068
\(15\) 0 0
\(16\) −4.65233 −1.16308
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) 4.43647 1.01780 0.508898 0.860827i \(-0.330053\pi\)
0.508898 + 0.860827i \(0.330053\pi\)
\(20\) 0.564818 0.126297
\(21\) 0 0
\(22\) 3.19450 0.681071
\(23\) 2.95501 0.616162 0.308081 0.951360i \(-0.400313\pi\)
0.308081 + 0.951360i \(0.400313\pi\)
\(24\) 0 0
\(25\) −3.10554 −0.621108
\(26\) 2.49271 0.488860
\(27\) 0 0
\(28\) −1.37535 −0.259918
\(29\) 3.13539 0.582226 0.291113 0.956689i \(-0.405974\pi\)
0.291113 + 0.956689i \(0.405974\pi\)
\(30\) 0 0
\(31\) −4.72687 −0.848970 −0.424485 0.905435i \(-0.639545\pi\)
−0.424485 + 0.905435i \(0.639545\pi\)
\(32\) 2.28696 0.404281
\(33\) 0 0
\(34\) −1.55253 −0.266257
\(35\) −4.61308 −0.779753
\(36\) 0 0
\(37\) 6.73408 1.10708 0.553538 0.832824i \(-0.313277\pi\)
0.553538 + 0.832824i \(0.313277\pi\)
\(38\) −6.88777 −1.11734
\(39\) 0 0
\(40\) 3.39690 0.537096
\(41\) −9.28079 −1.44942 −0.724708 0.689056i \(-0.758025\pi\)
−0.724708 + 0.689056i \(0.758025\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499
\(44\) −0.844362 −0.127292
\(45\) 0 0
\(46\) −4.58775 −0.676427
\(47\) 8.52365 1.24330 0.621651 0.783295i \(-0.286462\pi\)
0.621651 + 0.783295i \(0.286462\pi\)
\(48\) 0 0
\(49\) 4.23304 0.604720
\(50\) 4.82146 0.681857
\(51\) 0 0
\(52\) −0.658865 −0.0913681
\(53\) −9.33387 −1.28211 −0.641053 0.767497i \(-0.721502\pi\)
−0.641053 + 0.767497i \(0.721502\pi\)
\(54\) 0 0
\(55\) −2.83208 −0.381877
\(56\) −8.27157 −1.10534
\(57\) 0 0
\(58\) −4.86779 −0.639172
\(59\) 9.83672 1.28063 0.640316 0.768111i \(-0.278803\pi\)
0.640316 + 0.768111i \(0.278803\pi\)
\(60\) 0 0
\(61\) 2.75383 0.352591 0.176296 0.984337i \(-0.443589\pi\)
0.176296 + 0.984337i \(0.443589\pi\)
\(62\) 7.33862 0.932006
\(63\) 0 0
\(64\) 5.75407 0.719259
\(65\) −2.20990 −0.274104
\(66\) 0 0
\(67\) 8.84901 1.08108 0.540539 0.841319i \(-0.318220\pi\)
0.540539 + 0.841319i \(0.318220\pi\)
\(68\) 0.410361 0.0497636
\(69\) 0 0
\(70\) 7.16197 0.856019
\(71\) 1.37235 0.162868 0.0814342 0.996679i \(-0.474050\pi\)
0.0814342 + 0.996679i \(0.474050\pi\)
\(72\) 0 0
\(73\) −0.237911 −0.0278454 −0.0139227 0.999903i \(-0.504432\pi\)
−0.0139227 + 0.999903i \(0.504432\pi\)
\(74\) −10.4549 −1.21536
\(75\) 0 0
\(76\) 1.82055 0.208832
\(77\) 6.89622 0.785897
\(78\) 0 0
\(79\) −7.25698 −0.816474 −0.408237 0.912876i \(-0.633856\pi\)
−0.408237 + 0.912876i \(0.633856\pi\)
\(80\) −6.40343 −0.715925
\(81\) 0 0
\(82\) 14.4087 1.59118
\(83\) 2.15336 0.236362 0.118181 0.992992i \(-0.462294\pi\)
0.118181 + 0.992992i \(0.462294\pi\)
\(84\) 0 0
\(85\) 1.37639 0.149291
\(86\) 1.55253 0.167414
\(87\) 0 0
\(88\) −5.07811 −0.541328
\(89\) 13.4194 1.42246 0.711229 0.702961i \(-0.248139\pi\)
0.711229 + 0.702961i \(0.248139\pi\)
\(90\) 0 0
\(91\) 5.38120 0.564103
\(92\) 1.21262 0.126424
\(93\) 0 0
\(94\) −13.2332 −1.36491
\(95\) 6.10633 0.626496
\(96\) 0 0
\(97\) −12.3738 −1.25636 −0.628182 0.778066i \(-0.716201\pi\)
−0.628182 + 0.778066i \(0.716201\pi\)
\(98\) −6.57194 −0.663866
\(99\) 0 0
\(100\) −1.27439 −0.127439
\(101\) 16.9693 1.68850 0.844252 0.535946i \(-0.180045\pi\)
0.844252 + 0.535946i \(0.180045\pi\)
\(102\) 0 0
\(103\) 1.00189 0.0987190 0.0493595 0.998781i \(-0.484282\pi\)
0.0493595 + 0.998781i \(0.484282\pi\)
\(104\) −3.96250 −0.388555
\(105\) 0 0
\(106\) 14.4911 1.40750
\(107\) −17.2371 −1.66637 −0.833185 0.552994i \(-0.813485\pi\)
−0.833185 + 0.552994i \(0.813485\pi\)
\(108\) 0 0
\(109\) −9.48121 −0.908135 −0.454068 0.890967i \(-0.650028\pi\)
−0.454068 + 0.890967i \(0.650028\pi\)
\(110\) 4.39690 0.419228
\(111\) 0 0
\(112\) 15.5926 1.47336
\(113\) 5.69643 0.535875 0.267937 0.963436i \(-0.413658\pi\)
0.267937 + 0.963436i \(0.413658\pi\)
\(114\) 0 0
\(115\) 4.06725 0.379273
\(116\) 1.28664 0.119462
\(117\) 0 0
\(118\) −15.2718 −1.40589
\(119\) −3.35157 −0.307238
\(120\) 0 0
\(121\) −6.76625 −0.615114
\(122\) −4.27541 −0.387077
\(123\) 0 0
\(124\) −1.93972 −0.174192
\(125\) −11.1564 −0.997860
\(126\) 0 0
\(127\) −9.03729 −0.801930 −0.400965 0.916093i \(-0.631325\pi\)
−0.400965 + 0.916093i \(0.631325\pi\)
\(128\) −13.5073 −1.19389
\(129\) 0 0
\(130\) 3.43095 0.300914
\(131\) −13.2079 −1.15398 −0.576990 0.816751i \(-0.695773\pi\)
−0.576990 + 0.816751i \(0.695773\pi\)
\(132\) 0 0
\(133\) −14.8691 −1.28932
\(134\) −13.7384 −1.18682
\(135\) 0 0
\(136\) 2.46797 0.211627
\(137\) −0.498421 −0.0425830 −0.0212915 0.999773i \(-0.506778\pi\)
−0.0212915 + 0.999773i \(0.506778\pi\)
\(138\) 0 0
\(139\) 13.0119 1.10366 0.551829 0.833957i \(-0.313930\pi\)
0.551829 + 0.833957i \(0.313930\pi\)
\(140\) −1.89303 −0.159990
\(141\) 0 0
\(142\) −2.13062 −0.178798
\(143\) 3.30364 0.276264
\(144\) 0 0
\(145\) 4.31552 0.358385
\(146\) 0.369365 0.0305689
\(147\) 0 0
\(148\) 2.76341 0.227151
\(149\) 18.6715 1.52963 0.764813 0.644253i \(-0.222832\pi\)
0.764813 + 0.644253i \(0.222832\pi\)
\(150\) 0 0
\(151\) −14.9169 −1.21392 −0.606960 0.794733i \(-0.707611\pi\)
−0.606960 + 0.794733i \(0.707611\pi\)
\(152\) 10.9491 0.888086
\(153\) 0 0
\(154\) −10.7066 −0.862764
\(155\) −6.50603 −0.522577
\(156\) 0 0
\(157\) 19.2406 1.53556 0.767782 0.640711i \(-0.221360\pi\)
0.767782 + 0.640711i \(0.221360\pi\)
\(158\) 11.2667 0.896331
\(159\) 0 0
\(160\) 3.14775 0.248852
\(161\) −9.90393 −0.780539
\(162\) 0 0
\(163\) 6.92729 0.542587 0.271294 0.962497i \(-0.412549\pi\)
0.271294 + 0.962497i \(0.412549\pi\)
\(164\) −3.80848 −0.297392
\(165\) 0 0
\(166\) −3.34316 −0.259480
\(167\) −11.3060 −0.874881 −0.437441 0.899247i \(-0.644115\pi\)
−0.437441 + 0.899247i \(0.644115\pi\)
\(168\) 0 0
\(169\) −10.4221 −0.801703
\(170\) −2.13690 −0.163893
\(171\) 0 0
\(172\) −0.410361 −0.0312897
\(173\) −18.8950 −1.43656 −0.718281 0.695754i \(-0.755071\pi\)
−0.718281 + 0.695754i \(0.755071\pi\)
\(174\) 0 0
\(175\) 10.4084 0.786805
\(176\) 9.57266 0.721566
\(177\) 0 0
\(178\) −20.8341 −1.56158
\(179\) 16.1432 1.20660 0.603300 0.797515i \(-0.293852\pi\)
0.603300 + 0.797515i \(0.293852\pi\)
\(180\) 0 0
\(181\) −17.6672 −1.31319 −0.656596 0.754242i \(-0.728004\pi\)
−0.656596 + 0.754242i \(0.728004\pi\)
\(182\) −8.35449 −0.619276
\(183\) 0 0
\(184\) 7.29287 0.537637
\(185\) 9.26875 0.681452
\(186\) 0 0
\(187\) −2.05761 −0.150467
\(188\) 3.49777 0.255101
\(189\) 0 0
\(190\) −9.48028 −0.687772
\(191\) 5.21087 0.377045 0.188523 0.982069i \(-0.439630\pi\)
0.188523 + 0.982069i \(0.439630\pi\)
\(192\) 0 0
\(193\) −10.0275 −0.721797 −0.360898 0.932605i \(-0.617530\pi\)
−0.360898 + 0.932605i \(0.617530\pi\)
\(194\) 19.2107 1.37925
\(195\) 0 0
\(196\) 1.73707 0.124077
\(197\) 8.23341 0.586606 0.293303 0.956020i \(-0.405246\pi\)
0.293303 + 0.956020i \(0.405246\pi\)
\(198\) 0 0
\(199\) −0.596092 −0.0422559 −0.0211279 0.999777i \(-0.506726\pi\)
−0.0211279 + 0.999777i \(0.506726\pi\)
\(200\) −7.66438 −0.541953
\(201\) 0 0
\(202\) −26.3454 −1.85365
\(203\) −10.5085 −0.737550
\(204\) 0 0
\(205\) −12.7740 −0.892176
\(206\) −1.55547 −0.108374
\(207\) 0 0
\(208\) 7.46965 0.517927
\(209\) −9.12851 −0.631432
\(210\) 0 0
\(211\) −2.11726 −0.145758 −0.0728790 0.997341i \(-0.523219\pi\)
−0.0728790 + 0.997341i \(0.523219\pi\)
\(212\) −3.83026 −0.263063
\(213\) 0 0
\(214\) 26.7611 1.82935
\(215\) −1.37639 −0.0938693
\(216\) 0 0
\(217\) 15.8424 1.07545
\(218\) 14.7199 0.996958
\(219\) 0 0
\(220\) −1.16217 −0.0783538
\(221\) −1.60557 −0.108003
\(222\) 0 0
\(223\) −21.3509 −1.42976 −0.714881 0.699247i \(-0.753519\pi\)
−0.714881 + 0.699247i \(0.753519\pi\)
\(224\) −7.66490 −0.512133
\(225\) 0 0
\(226\) −8.84389 −0.588287
\(227\) −17.2277 −1.14344 −0.571720 0.820449i \(-0.693724\pi\)
−0.571720 + 0.820449i \(0.693724\pi\)
\(228\) 0 0
\(229\) −0.830329 −0.0548697 −0.0274348 0.999624i \(-0.508734\pi\)
−0.0274348 + 0.999624i \(0.508734\pi\)
\(230\) −6.31455 −0.416369
\(231\) 0 0
\(232\) 7.73803 0.508027
\(233\) 17.7159 1.16061 0.580303 0.814401i \(-0.302934\pi\)
0.580303 + 0.814401i \(0.302934\pi\)
\(234\) 0 0
\(235\) 11.7319 0.765304
\(236\) 4.03661 0.262761
\(237\) 0 0
\(238\) 5.20343 0.337288
\(239\) 20.7223 1.34041 0.670207 0.742174i \(-0.266205\pi\)
0.670207 + 0.742174i \(0.266205\pi\)
\(240\) 0 0
\(241\) 8.01971 0.516595 0.258297 0.966065i \(-0.416839\pi\)
0.258297 + 0.966065i \(0.416839\pi\)
\(242\) 10.5048 0.675276
\(243\) 0 0
\(244\) 1.13006 0.0723449
\(245\) 5.82633 0.372230
\(246\) 0 0
\(247\) −7.12308 −0.453231
\(248\) −11.6658 −0.740776
\(249\) 0 0
\(250\) 17.3207 1.09546
\(251\) −12.0601 −0.761228 −0.380614 0.924734i \(-0.624287\pi\)
−0.380614 + 0.924734i \(0.624287\pi\)
\(252\) 0 0
\(253\) −6.08025 −0.382262
\(254\) 14.0307 0.880365
\(255\) 0 0
\(256\) 9.46240 0.591400
\(257\) 0.113536 0.00708217 0.00354108 0.999994i \(-0.498873\pi\)
0.00354108 + 0.999994i \(0.498873\pi\)
\(258\) 0 0
\(259\) −22.5698 −1.40242
\(260\) −0.906857 −0.0562409
\(261\) 0 0
\(262\) 20.5057 1.26685
\(263\) 1.04330 0.0643325 0.0321663 0.999483i \(-0.489759\pi\)
0.0321663 + 0.999483i \(0.489759\pi\)
\(264\) 0 0
\(265\) −12.8471 −0.789190
\(266\) 23.0849 1.41542
\(267\) 0 0
\(268\) 3.63129 0.221816
\(269\) 3.25815 0.198653 0.0993265 0.995055i \(-0.468331\pi\)
0.0993265 + 0.995055i \(0.468331\pi\)
\(270\) 0 0
\(271\) 2.16125 0.131286 0.0656432 0.997843i \(-0.479090\pi\)
0.0656432 + 0.997843i \(0.479090\pi\)
\(272\) −4.65233 −0.282089
\(273\) 0 0
\(274\) 0.773816 0.0467479
\(275\) 6.38998 0.385330
\(276\) 0 0
\(277\) −2.06077 −0.123820 −0.0619098 0.998082i \(-0.519719\pi\)
−0.0619098 + 0.998082i \(0.519719\pi\)
\(278\) −20.2015 −1.21160
\(279\) 0 0
\(280\) −11.3849 −0.680380
\(281\) −19.6254 −1.17075 −0.585375 0.810763i \(-0.699053\pi\)
−0.585375 + 0.810763i \(0.699053\pi\)
\(282\) 0 0
\(283\) 29.8412 1.77388 0.886939 0.461888i \(-0.152828\pi\)
0.886939 + 0.461888i \(0.152828\pi\)
\(284\) 0.563160 0.0334174
\(285\) 0 0
\(286\) −5.12901 −0.303285
\(287\) 31.1053 1.83608
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) −6.70000 −0.393437
\(291\) 0 0
\(292\) −0.0976295 −0.00571334
\(293\) −9.76035 −0.570206 −0.285103 0.958497i \(-0.592028\pi\)
−0.285103 + 0.958497i \(0.592028\pi\)
\(294\) 0 0
\(295\) 13.5392 0.788283
\(296\) 16.6195 0.965989
\(297\) 0 0
\(298\) −28.9881 −1.67923
\(299\) −4.74448 −0.274381
\(300\) 0 0
\(301\) 3.35157 0.193181
\(302\) 23.1590 1.33265
\(303\) 0 0
\(304\) −20.6399 −1.18378
\(305\) 3.79035 0.217035
\(306\) 0 0
\(307\) 5.45230 0.311179 0.155590 0.987822i \(-0.450272\pi\)
0.155590 + 0.987822i \(0.450272\pi\)
\(308\) 2.82994 0.161251
\(309\) 0 0
\(310\) 10.1008 0.573689
\(311\) −6.91146 −0.391913 −0.195956 0.980613i \(-0.562781\pi\)
−0.195956 + 0.980613i \(0.562781\pi\)
\(312\) 0 0
\(313\) −30.2823 −1.71166 −0.855830 0.517258i \(-0.826953\pi\)
−0.855830 + 0.517258i \(0.826953\pi\)
\(314\) −29.8716 −1.68575
\(315\) 0 0
\(316\) −2.97798 −0.167525
\(317\) 1.05835 0.0594431 0.0297215 0.999558i \(-0.490538\pi\)
0.0297215 + 0.999558i \(0.490538\pi\)
\(318\) 0 0
\(319\) −6.45139 −0.361209
\(320\) 7.91987 0.442734
\(321\) 0 0
\(322\) 15.3762 0.856881
\(323\) 4.43647 0.246852
\(324\) 0 0
\(325\) 4.98617 0.276583
\(326\) −10.7549 −0.595656
\(327\) 0 0
\(328\) −22.9047 −1.26470
\(329\) −28.5676 −1.57498
\(330\) 0 0
\(331\) 6.60561 0.363077 0.181539 0.983384i \(-0.441892\pi\)
0.181539 + 0.983384i \(0.441892\pi\)
\(332\) 0.883654 0.0484968
\(333\) 0 0
\(334\) 17.5529 0.960451
\(335\) 12.1797 0.665449
\(336\) 0 0
\(337\) −7.79916 −0.424847 −0.212424 0.977178i \(-0.568136\pi\)
−0.212424 + 0.977178i \(0.568136\pi\)
\(338\) 16.1807 0.880115
\(339\) 0 0
\(340\) 0.564818 0.0306316
\(341\) 9.72604 0.526694
\(342\) 0 0
\(343\) 9.27367 0.500731
\(344\) −2.46797 −0.133064
\(345\) 0 0
\(346\) 29.3351 1.57707
\(347\) 9.84344 0.528424 0.264212 0.964465i \(-0.414888\pi\)
0.264212 + 0.964465i \(0.414888\pi\)
\(348\) 0 0
\(349\) −30.2937 −1.62158 −0.810791 0.585335i \(-0.800963\pi\)
−0.810791 + 0.585335i \(0.800963\pi\)
\(350\) −16.1595 −0.863760
\(351\) 0 0
\(352\) −4.70566 −0.250812
\(353\) 3.33858 0.177695 0.0888473 0.996045i \(-0.471682\pi\)
0.0888473 + 0.996045i \(0.471682\pi\)
\(354\) 0 0
\(355\) 1.88890 0.100252
\(356\) 5.50681 0.291861
\(357\) 0 0
\(358\) −25.0629 −1.32461
\(359\) −32.9629 −1.73972 −0.869858 0.493301i \(-0.835790\pi\)
−0.869858 + 0.493301i \(0.835790\pi\)
\(360\) 0 0
\(361\) 0.682261 0.0359085
\(362\) 27.4289 1.44163
\(363\) 0 0
\(364\) 2.20823 0.115743
\(365\) −0.327460 −0.0171400
\(366\) 0 0
\(367\) 19.8773 1.03759 0.518793 0.854900i \(-0.326382\pi\)
0.518793 + 0.854900i \(0.326382\pi\)
\(368\) −13.7477 −0.716646
\(369\) 0 0
\(370\) −14.3900 −0.748103
\(371\) 31.2831 1.62414
\(372\) 0 0
\(373\) 31.8286 1.64802 0.824011 0.566574i \(-0.191732\pi\)
0.824011 + 0.566574i \(0.191732\pi\)
\(374\) 3.19450 0.165184
\(375\) 0 0
\(376\) 21.0361 1.08485
\(377\) −5.03409 −0.259269
\(378\) 0 0
\(379\) −18.3892 −0.944590 −0.472295 0.881440i \(-0.656574\pi\)
−0.472295 + 0.881440i \(0.656574\pi\)
\(380\) 2.50580 0.128545
\(381\) 0 0
\(382\) −8.09005 −0.413923
\(383\) −31.4493 −1.60699 −0.803493 0.595314i \(-0.797028\pi\)
−0.803493 + 0.595314i \(0.797028\pi\)
\(384\) 0 0
\(385\) 9.49191 0.483753
\(386\) 15.5681 0.792394
\(387\) 0 0
\(388\) −5.07771 −0.257782
\(389\) 36.1960 1.83521 0.917604 0.397496i \(-0.130121\pi\)
0.917604 + 0.397496i \(0.130121\pi\)
\(390\) 0 0
\(391\) 2.95501 0.149441
\(392\) 10.4470 0.527654
\(393\) 0 0
\(394\) −12.7826 −0.643980
\(395\) −9.98846 −0.502574
\(396\) 0 0
\(397\) −16.0708 −0.806569 −0.403284 0.915075i \(-0.632131\pi\)
−0.403284 + 0.915075i \(0.632131\pi\)
\(398\) 0.925454 0.0463888
\(399\) 0 0
\(400\) 14.4480 0.722399
\(401\) −18.3382 −0.915766 −0.457883 0.889013i \(-0.651392\pi\)
−0.457883 + 0.889013i \(0.651392\pi\)
\(402\) 0 0
\(403\) 7.58933 0.378052
\(404\) 6.96352 0.346448
\(405\) 0 0
\(406\) 16.3148 0.809688
\(407\) −13.8561 −0.686821
\(408\) 0 0
\(409\) −21.6593 −1.07098 −0.535491 0.844541i \(-0.679874\pi\)
−0.535491 + 0.844541i \(0.679874\pi\)
\(410\) 19.8321 0.979438
\(411\) 0 0
\(412\) 0.411136 0.0202552
\(413\) −32.9685 −1.62227
\(414\) 0 0
\(415\) 2.96387 0.145491
\(416\) −3.67188 −0.180029
\(417\) 0 0
\(418\) 14.1723 0.693191
\(419\) 0.799500 0.0390581 0.0195291 0.999809i \(-0.493783\pi\)
0.0195291 + 0.999809i \(0.493783\pi\)
\(420\) 0 0
\(421\) −21.4459 −1.04521 −0.522604 0.852576i \(-0.675039\pi\)
−0.522604 + 0.852576i \(0.675039\pi\)
\(422\) 3.28711 0.160014
\(423\) 0 0
\(424\) −23.0357 −1.11871
\(425\) −3.10554 −0.150641
\(426\) 0 0
\(427\) −9.22965 −0.446654
\(428\) −7.07342 −0.341907
\(429\) 0 0
\(430\) 2.13690 0.103050
\(431\) 12.5374 0.603905 0.301953 0.953323i \(-0.402362\pi\)
0.301953 + 0.953323i \(0.402362\pi\)
\(432\) 0 0
\(433\) 0.316199 0.0151956 0.00759778 0.999971i \(-0.497582\pi\)
0.00759778 + 0.999971i \(0.497582\pi\)
\(434\) −24.5959 −1.18064
\(435\) 0 0
\(436\) −3.89072 −0.186332
\(437\) 13.1098 0.627127
\(438\) 0 0
\(439\) −39.0690 −1.86466 −0.932331 0.361607i \(-0.882228\pi\)
−0.932331 + 0.361607i \(0.882228\pi\)
\(440\) −6.98948 −0.333210
\(441\) 0 0
\(442\) 2.49271 0.118566
\(443\) −2.92193 −0.138825 −0.0694125 0.997588i \(-0.522112\pi\)
−0.0694125 + 0.997588i \(0.522112\pi\)
\(444\) 0 0
\(445\) 18.4704 0.875582
\(446\) 33.1480 1.56960
\(447\) 0 0
\(448\) −19.2852 −0.911140
\(449\) −3.14960 −0.148639 −0.0743195 0.997234i \(-0.523678\pi\)
−0.0743195 + 0.997234i \(0.523678\pi\)
\(450\) 0 0
\(451\) 19.0962 0.899206
\(452\) 2.33759 0.109951
\(453\) 0 0
\(454\) 26.7465 1.25528
\(455\) 7.40664 0.347229
\(456\) 0 0
\(457\) −31.7688 −1.48608 −0.743040 0.669247i \(-0.766617\pi\)
−0.743040 + 0.669247i \(0.766617\pi\)
\(458\) 1.28911 0.0602363
\(459\) 0 0
\(460\) 1.66904 0.0778195
\(461\) −27.5045 −1.28101 −0.640505 0.767954i \(-0.721275\pi\)
−0.640505 + 0.767954i \(0.721275\pi\)
\(462\) 0 0
\(463\) −6.28353 −0.292020 −0.146010 0.989283i \(-0.546643\pi\)
−0.146010 + 0.989283i \(0.546643\pi\)
\(464\) −14.5868 −0.677177
\(465\) 0 0
\(466\) −27.5045 −1.27412
\(467\) 15.1305 0.700158 0.350079 0.936720i \(-0.386155\pi\)
0.350079 + 0.936720i \(0.386155\pi\)
\(468\) 0 0
\(469\) −29.6581 −1.36948
\(470\) −18.2142 −0.840156
\(471\) 0 0
\(472\) 24.2767 1.11743
\(473\) 2.05761 0.0946089
\(474\) 0 0
\(475\) −13.7776 −0.632161
\(476\) −1.37535 −0.0630393
\(477\) 0 0
\(478\) −32.1721 −1.47152
\(479\) −18.3840 −0.839984 −0.419992 0.907528i \(-0.637967\pi\)
−0.419992 + 0.907528i \(0.637967\pi\)
\(480\) 0 0
\(481\) −10.8121 −0.492988
\(482\) −12.4509 −0.567121
\(483\) 0 0
\(484\) −2.77661 −0.126209
\(485\) −17.0312 −0.773345
\(486\) 0 0
\(487\) −25.0292 −1.13418 −0.567091 0.823655i \(-0.691931\pi\)
−0.567091 + 0.823655i \(0.691931\pi\)
\(488\) 6.79635 0.307657
\(489\) 0 0
\(490\) −9.04557 −0.408637
\(491\) −8.38193 −0.378271 −0.189136 0.981951i \(-0.560569\pi\)
−0.189136 + 0.981951i \(0.560569\pi\)
\(492\) 0 0
\(493\) 3.13539 0.141211
\(494\) 11.0588 0.497560
\(495\) 0 0
\(496\) 21.9909 0.987422
\(497\) −4.59954 −0.206318
\(498\) 0 0
\(499\) 12.4436 0.557050 0.278525 0.960429i \(-0.410154\pi\)
0.278525 + 0.960429i \(0.410154\pi\)
\(500\) −4.57816 −0.204741
\(501\) 0 0
\(502\) 18.7238 0.835682
\(503\) 16.3260 0.727942 0.363971 0.931410i \(-0.381421\pi\)
0.363971 + 0.931410i \(0.381421\pi\)
\(504\) 0 0
\(505\) 23.3564 1.03935
\(506\) 9.43979 0.419650
\(507\) 0 0
\(508\) −3.70855 −0.164540
\(509\) −18.4749 −0.818887 −0.409443 0.912336i \(-0.634277\pi\)
−0.409443 + 0.912336i \(0.634277\pi\)
\(510\) 0 0
\(511\) 0.797377 0.0352739
\(512\) 12.3239 0.544645
\(513\) 0 0
\(514\) −0.176268 −0.00777485
\(515\) 1.37899 0.0607657
\(516\) 0 0
\(517\) −17.5383 −0.771334
\(518\) 35.0403 1.53958
\(519\) 0 0
\(520\) −5.45396 −0.239172
\(521\) −16.3339 −0.715600 −0.357800 0.933798i \(-0.616473\pi\)
−0.357800 + 0.933798i \(0.616473\pi\)
\(522\) 0 0
\(523\) −10.8949 −0.476399 −0.238200 0.971216i \(-0.576557\pi\)
−0.238200 + 0.971216i \(0.576557\pi\)
\(524\) −5.42001 −0.236774
\(525\) 0 0
\(526\) −1.61976 −0.0706247
\(527\) −4.72687 −0.205906
\(528\) 0 0
\(529\) −14.2679 −0.620345
\(530\) 19.9455 0.866378
\(531\) 0 0
\(532\) −6.10172 −0.264543
\(533\) 14.9010 0.645434
\(534\) 0 0
\(535\) −23.7250 −1.02572
\(536\) 21.8391 0.943304
\(537\) 0 0
\(538\) −5.05839 −0.218083
\(539\) −8.70993 −0.375163
\(540\) 0 0
\(541\) 14.6315 0.629055 0.314528 0.949248i \(-0.398154\pi\)
0.314528 + 0.949248i \(0.398154\pi\)
\(542\) −3.35541 −0.144127
\(543\) 0 0
\(544\) 2.28696 0.0980524
\(545\) −13.0499 −0.558995
\(546\) 0 0
\(547\) 38.8321 1.66034 0.830170 0.557510i \(-0.188243\pi\)
0.830170 + 0.557510i \(0.188243\pi\)
\(548\) −0.204533 −0.00873720
\(549\) 0 0
\(550\) −9.92066 −0.423019
\(551\) 13.9100 0.592588
\(552\) 0 0
\(553\) 24.3223 1.03429
\(554\) 3.19941 0.135930
\(555\) 0 0
\(556\) 5.33960 0.226449
\(557\) 15.0377 0.637167 0.318583 0.947895i \(-0.396793\pi\)
0.318583 + 0.947895i \(0.396793\pi\)
\(558\) 0 0
\(559\) 1.60557 0.0679085
\(560\) 21.4616 0.906917
\(561\) 0 0
\(562\) 30.4690 1.28526
\(563\) −25.9281 −1.09274 −0.546370 0.837544i \(-0.683991\pi\)
−0.546370 + 0.837544i \(0.683991\pi\)
\(564\) 0 0
\(565\) 7.84052 0.329853
\(566\) −46.3295 −1.94737
\(567\) 0 0
\(568\) 3.38692 0.142112
\(569\) −33.5425 −1.40617 −0.703086 0.711104i \(-0.748195\pi\)
−0.703086 + 0.711104i \(0.748195\pi\)
\(570\) 0 0
\(571\) −1.78040 −0.0745073 −0.0372536 0.999306i \(-0.511861\pi\)
−0.0372536 + 0.999306i \(0.511861\pi\)
\(572\) 1.35568 0.0566840
\(573\) 0 0
\(574\) −48.2920 −2.01567
\(575\) −9.17690 −0.382703
\(576\) 0 0
\(577\) −5.31057 −0.221082 −0.110541 0.993872i \(-0.535258\pi\)
−0.110541 + 0.993872i \(0.535258\pi\)
\(578\) −1.55253 −0.0645769
\(579\) 0 0
\(580\) 1.77092 0.0735336
\(581\) −7.21714 −0.299417
\(582\) 0 0
\(583\) 19.2054 0.795408
\(584\) −0.587158 −0.0242968
\(585\) 0 0
\(586\) 15.1533 0.625976
\(587\) 13.6765 0.564488 0.282244 0.959343i \(-0.408921\pi\)
0.282244 + 0.959343i \(0.408921\pi\)
\(588\) 0 0
\(589\) −20.9706 −0.864079
\(590\) −21.0201 −0.865383
\(591\) 0 0
\(592\) −31.3292 −1.28762
\(593\) 23.1903 0.952312 0.476156 0.879361i \(-0.342030\pi\)
0.476156 + 0.879361i \(0.342030\pi\)
\(594\) 0 0
\(595\) −4.61308 −0.189118
\(596\) 7.66204 0.313849
\(597\) 0 0
\(598\) 7.36597 0.301217
\(599\) −3.62388 −0.148068 −0.0740339 0.997256i \(-0.523587\pi\)
−0.0740339 + 0.997256i \(0.523587\pi\)
\(600\) 0 0
\(601\) 10.7756 0.439548 0.219774 0.975551i \(-0.429468\pi\)
0.219774 + 0.975551i \(0.429468\pi\)
\(602\) −5.20343 −0.212076
\(603\) 0 0
\(604\) −6.12131 −0.249073
\(605\) −9.31303 −0.378628
\(606\) 0 0
\(607\) 11.1257 0.451578 0.225789 0.974176i \(-0.427504\pi\)
0.225789 + 0.974176i \(0.427504\pi\)
\(608\) 10.1460 0.411475
\(609\) 0 0
\(610\) −5.88464 −0.238262
\(611\) −13.6853 −0.553650
\(612\) 0 0
\(613\) −33.5257 −1.35409 −0.677046 0.735941i \(-0.736740\pi\)
−0.677046 + 0.735941i \(0.736740\pi\)
\(614\) −8.46488 −0.341615
\(615\) 0 0
\(616\) 17.0197 0.685741
\(617\) −40.9696 −1.64937 −0.824686 0.565591i \(-0.808648\pi\)
−0.824686 + 0.565591i \(0.808648\pi\)
\(618\) 0 0
\(619\) −18.3291 −0.736709 −0.368355 0.929685i \(-0.620079\pi\)
−0.368355 + 0.929685i \(0.620079\pi\)
\(620\) −2.66982 −0.107223
\(621\) 0 0
\(622\) 10.7303 0.430245
\(623\) −44.9762 −1.80193
\(624\) 0 0
\(625\) 0.172088 0.00688353
\(626\) 47.0144 1.87907
\(627\) 0 0
\(628\) 7.89558 0.315068
\(629\) 6.73408 0.268506
\(630\) 0 0
\(631\) 4.31547 0.171796 0.0858981 0.996304i \(-0.472624\pi\)
0.0858981 + 0.996304i \(0.472624\pi\)
\(632\) −17.9100 −0.712422
\(633\) 0 0
\(634\) −1.64313 −0.0652570
\(635\) −12.4389 −0.493622
\(636\) 0 0
\(637\) −6.79646 −0.269285
\(638\) 10.0160 0.396537
\(639\) 0 0
\(640\) −18.5914 −0.734888
\(641\) −39.4483 −1.55811 −0.779057 0.626953i \(-0.784302\pi\)
−0.779057 + 0.626953i \(0.784302\pi\)
\(642\) 0 0
\(643\) 44.4275 1.75205 0.876024 0.482267i \(-0.160186\pi\)
0.876024 + 0.482267i \(0.160186\pi\)
\(644\) −4.06418 −0.160151
\(645\) 0 0
\(646\) −6.88777 −0.270996
\(647\) 14.5542 0.572183 0.286091 0.958202i \(-0.407644\pi\)
0.286091 + 0.958202i \(0.407644\pi\)
\(648\) 0 0
\(649\) −20.2401 −0.794494
\(650\) −7.74120 −0.303635
\(651\) 0 0
\(652\) 2.84269 0.111328
\(653\) 5.75768 0.225315 0.112658 0.993634i \(-0.464064\pi\)
0.112658 + 0.993634i \(0.464064\pi\)
\(654\) 0 0
\(655\) −18.1793 −0.710323
\(656\) 43.1773 1.68579
\(657\) 0 0
\(658\) 44.3522 1.72903
\(659\) −34.6474 −1.34967 −0.674835 0.737969i \(-0.735785\pi\)
−0.674835 + 0.737969i \(0.735785\pi\)
\(660\) 0 0
\(661\) −2.04505 −0.0795432 −0.0397716 0.999209i \(-0.512663\pi\)
−0.0397716 + 0.999209i \(0.512663\pi\)
\(662\) −10.2554 −0.398589
\(663\) 0 0
\(664\) 5.31442 0.206240
\(665\) −20.4658 −0.793630
\(666\) 0 0
\(667\) 9.26509 0.358746
\(668\) −4.63952 −0.179509
\(669\) 0 0
\(670\) −18.9094 −0.730535
\(671\) −5.66629 −0.218745
\(672\) 0 0
\(673\) −37.3113 −1.43825 −0.719123 0.694883i \(-0.755456\pi\)
−0.719123 + 0.694883i \(0.755456\pi\)
\(674\) 12.1085 0.466400
\(675\) 0 0
\(676\) −4.27684 −0.164494
\(677\) −0.572224 −0.0219924 −0.0109962 0.999940i \(-0.503500\pi\)
−0.0109962 + 0.999940i \(0.503500\pi\)
\(678\) 0 0
\(679\) 41.4715 1.59153
\(680\) 3.39690 0.130265
\(681\) 0 0
\(682\) −15.1000 −0.578209
\(683\) 40.0033 1.53069 0.765343 0.643623i \(-0.222570\pi\)
0.765343 + 0.643623i \(0.222570\pi\)
\(684\) 0 0
\(685\) −0.686024 −0.0262116
\(686\) −14.3977 −0.549706
\(687\) 0 0
\(688\) 4.65233 0.177368
\(689\) 14.9862 0.570929
\(690\) 0 0
\(691\) 19.8850 0.756461 0.378231 0.925711i \(-0.376533\pi\)
0.378231 + 0.925711i \(0.376533\pi\)
\(692\) −7.75378 −0.294754
\(693\) 0 0
\(694\) −15.2823 −0.580107
\(695\) 17.9096 0.679348
\(696\) 0 0
\(697\) −9.28079 −0.351535
\(698\) 47.0319 1.78019
\(699\) 0 0
\(700\) 4.27122 0.161437
\(701\) −19.6778 −0.743222 −0.371611 0.928389i \(-0.621194\pi\)
−0.371611 + 0.928389i \(0.621194\pi\)
\(702\) 0 0
\(703\) 29.8756 1.12678
\(704\) −11.8396 −0.446223
\(705\) 0 0
\(706\) −5.18325 −0.195074
\(707\) −56.8737 −2.13896
\(708\) 0 0
\(709\) 19.6415 0.737653 0.368827 0.929498i \(-0.379760\pi\)
0.368827 + 0.929498i \(0.379760\pi\)
\(710\) −2.93258 −0.110058
\(711\) 0 0
\(712\) 33.1187 1.24118
\(713\) −13.9679 −0.523103
\(714\) 0 0
\(715\) 4.54711 0.170052
\(716\) 6.62454 0.247571
\(717\) 0 0
\(718\) 51.1761 1.90987
\(719\) −37.4428 −1.39638 −0.698191 0.715912i \(-0.746011\pi\)
−0.698191 + 0.715912i \(0.746011\pi\)
\(720\) 0 0
\(721\) −3.35790 −0.125055
\(722\) −1.05923 −0.0394206
\(723\) 0 0
\(724\) −7.24993 −0.269442
\(725\) −9.73707 −0.361626
\(726\) 0 0
\(727\) 37.6367 1.39587 0.697933 0.716163i \(-0.254103\pi\)
0.697933 + 0.716163i \(0.254103\pi\)
\(728\) 13.2806 0.492213
\(729\) 0 0
\(730\) 0.508392 0.0188164
\(731\) −1.00000 −0.0369863
\(732\) 0 0
\(733\) 2.42520 0.0895766 0.0447883 0.998996i \(-0.485739\pi\)
0.0447883 + 0.998996i \(0.485739\pi\)
\(734\) −30.8602 −1.13907
\(735\) 0 0
\(736\) 6.75798 0.249102
\(737\) −18.2078 −0.670692
\(738\) 0 0
\(739\) −9.87099 −0.363110 −0.181555 0.983381i \(-0.558113\pi\)
−0.181555 + 0.983381i \(0.558113\pi\)
\(740\) 3.80353 0.139821
\(741\) 0 0
\(742\) −48.5681 −1.78299
\(743\) −25.0556 −0.919202 −0.459601 0.888125i \(-0.652008\pi\)
−0.459601 + 0.888125i \(0.652008\pi\)
\(744\) 0 0
\(745\) 25.6993 0.941548
\(746\) −49.4149 −1.80921
\(747\) 0 0
\(748\) −0.844362 −0.0308729
\(749\) 57.7713 2.11092
\(750\) 0 0
\(751\) −17.8673 −0.651987 −0.325993 0.945372i \(-0.605699\pi\)
−0.325993 + 0.945372i \(0.605699\pi\)
\(752\) −39.6548 −1.44606
\(753\) 0 0
\(754\) 7.81560 0.284627
\(755\) −20.5315 −0.747218
\(756\) 0 0
\(757\) −29.2824 −1.06429 −0.532144 0.846654i \(-0.678614\pi\)
−0.532144 + 0.846654i \(0.678614\pi\)
\(758\) 28.5499 1.03698
\(759\) 0 0
\(760\) 15.0702 0.546654
\(761\) −29.8059 −1.08046 −0.540231 0.841517i \(-0.681663\pi\)
−0.540231 + 0.841517i \(0.681663\pi\)
\(762\) 0 0
\(763\) 31.7770 1.15040
\(764\) 2.13834 0.0773623
\(765\) 0 0
\(766\) 48.8262 1.76416
\(767\) −15.7936 −0.570273
\(768\) 0 0
\(769\) −6.62324 −0.238840 −0.119420 0.992844i \(-0.538104\pi\)
−0.119420 + 0.992844i \(0.538104\pi\)
\(770\) −14.7365 −0.531067
\(771\) 0 0
\(772\) −4.11490 −0.148099
\(773\) −42.7240 −1.53667 −0.768337 0.640045i \(-0.778916\pi\)
−0.768337 + 0.640045i \(0.778916\pi\)
\(774\) 0 0
\(775\) 14.6795 0.527302
\(776\) −30.5380 −1.09625
\(777\) 0 0
\(778\) −56.1954 −2.01470
\(779\) −41.1740 −1.47521
\(780\) 0 0
\(781\) −2.82376 −0.101042
\(782\) −4.58775 −0.164058
\(783\) 0 0
\(784\) −19.6935 −0.703339
\(785\) 26.4826 0.945204
\(786\) 0 0
\(787\) −54.3543 −1.93752 −0.968760 0.247999i \(-0.920227\pi\)
−0.968760 + 0.247999i \(0.920227\pi\)
\(788\) 3.37867 0.120360
\(789\) 0 0
\(790\) 15.5074 0.551730
\(791\) −19.0920 −0.678833
\(792\) 0 0
\(793\) −4.42147 −0.157011
\(794\) 24.9504 0.885457
\(795\) 0 0
\(796\) −0.244613 −0.00867008
\(797\) −39.0251 −1.38234 −0.691171 0.722692i \(-0.742905\pi\)
−0.691171 + 0.722692i \(0.742905\pi\)
\(798\) 0 0
\(799\) 8.52365 0.301545
\(800\) −7.10224 −0.251102
\(801\) 0 0
\(802\) 28.4707 1.00533
\(803\) 0.489528 0.0172751
\(804\) 0 0
\(805\) −13.6317 −0.480454
\(806\) −11.7827 −0.415028
\(807\) 0 0
\(808\) 41.8796 1.47332
\(809\) −1.18490 −0.0416590 −0.0208295 0.999783i \(-0.506631\pi\)
−0.0208295 + 0.999783i \(0.506631\pi\)
\(810\) 0 0
\(811\) 10.4542 0.367098 0.183549 0.983011i \(-0.441241\pi\)
0.183549 + 0.983011i \(0.441241\pi\)
\(812\) −4.31227 −0.151331
\(813\) 0 0
\(814\) 21.5121 0.753997
\(815\) 9.53468 0.333985
\(816\) 0 0
\(817\) −4.43647 −0.155212
\(818\) 33.6268 1.17573
\(819\) 0 0
\(820\) −5.24196 −0.183057
\(821\) −13.1726 −0.459727 −0.229863 0.973223i \(-0.573828\pi\)
−0.229863 + 0.973223i \(0.573828\pi\)
\(822\) 0 0
\(823\) −31.6599 −1.10360 −0.551798 0.833978i \(-0.686058\pi\)
−0.551798 + 0.833978i \(0.686058\pi\)
\(824\) 2.47263 0.0861381
\(825\) 0 0
\(826\) 51.1847 1.78094
\(827\) −3.05427 −0.106208 −0.0531038 0.998589i \(-0.516911\pi\)
−0.0531038 + 0.998589i \(0.516911\pi\)
\(828\) 0 0
\(829\) −1.45481 −0.0505276 −0.0252638 0.999681i \(-0.508043\pi\)
−0.0252638 + 0.999681i \(0.508043\pi\)
\(830\) −4.60151 −0.159721
\(831\) 0 0
\(832\) −9.23859 −0.320290
\(833\) 4.23304 0.146666
\(834\) 0 0
\(835\) −15.5614 −0.538526
\(836\) −3.74598 −0.129558
\(837\) 0 0
\(838\) −1.24125 −0.0428783
\(839\) 6.85018 0.236494 0.118247 0.992984i \(-0.462272\pi\)
0.118247 + 0.992984i \(0.462272\pi\)
\(840\) 0 0
\(841\) −19.1694 −0.661012
\(842\) 33.2954 1.14744
\(843\) 0 0
\(844\) −0.868840 −0.0299067
\(845\) −14.3450 −0.493482
\(846\) 0 0
\(847\) 22.6776 0.779211
\(848\) 43.4242 1.49119
\(849\) 0 0
\(850\) 4.82146 0.165375
\(851\) 19.8993 0.682138
\(852\) 0 0
\(853\) −17.5620 −0.601310 −0.300655 0.953733i \(-0.597205\pi\)
−0.300655 + 0.953733i \(0.597205\pi\)
\(854\) 14.3293 0.490340
\(855\) 0 0
\(856\) −42.5406 −1.45401
\(857\) 6.67420 0.227986 0.113993 0.993482i \(-0.463636\pi\)
0.113993 + 0.993482i \(0.463636\pi\)
\(858\) 0 0
\(859\) −19.3448 −0.660036 −0.330018 0.943975i \(-0.607055\pi\)
−0.330018 + 0.943975i \(0.607055\pi\)
\(860\) −0.564818 −0.0192601
\(861\) 0 0
\(862\) −19.4647 −0.662971
\(863\) 30.8248 1.04929 0.524645 0.851321i \(-0.324198\pi\)
0.524645 + 0.851321i \(0.324198\pi\)
\(864\) 0 0
\(865\) −26.0070 −0.884264
\(866\) −0.490910 −0.0166818
\(867\) 0 0
\(868\) 6.50112 0.220662
\(869\) 14.9320 0.506534
\(870\) 0 0
\(871\) −14.2077 −0.481411
\(872\) −23.3993 −0.792401
\(873\) 0 0
\(874\) −20.3534 −0.688464
\(875\) 37.3915 1.26406
\(876\) 0 0
\(877\) −9.29617 −0.313909 −0.156955 0.987606i \(-0.550168\pi\)
−0.156955 + 0.987606i \(0.550168\pi\)
\(878\) 60.6559 2.04704
\(879\) 0 0
\(880\) 13.1757 0.444154
\(881\) −10.8604 −0.365896 −0.182948 0.983123i \(-0.558564\pi\)
−0.182948 + 0.983123i \(0.558564\pi\)
\(882\) 0 0
\(883\) 5.78586 0.194710 0.0973549 0.995250i \(-0.468962\pi\)
0.0973549 + 0.995250i \(0.468962\pi\)
\(884\) −0.658865 −0.0221600
\(885\) 0 0
\(886\) 4.53639 0.152403
\(887\) −23.4572 −0.787615 −0.393807 0.919193i \(-0.628842\pi\)
−0.393807 + 0.919193i \(0.628842\pi\)
\(888\) 0 0
\(889\) 30.2891 1.01587
\(890\) −28.6760 −0.961220
\(891\) 0 0
\(892\) −8.76157 −0.293359
\(893\) 37.8149 1.26543
\(894\) 0 0
\(895\) 22.2194 0.742713
\(896\) 45.2707 1.51239
\(897\) 0 0
\(898\) 4.88986 0.163177
\(899\) −14.8206 −0.494293
\(900\) 0 0
\(901\) −9.33387 −0.310956
\(902\) −29.6475 −0.987155
\(903\) 0 0
\(904\) 14.0586 0.467582
\(905\) −24.3170 −0.808325
\(906\) 0 0
\(907\) −24.4247 −0.811009 −0.405504 0.914093i \(-0.632904\pi\)
−0.405504 + 0.914093i \(0.632904\pi\)
\(908\) −7.06956 −0.234611
\(909\) 0 0
\(910\) −11.4991 −0.381190
\(911\) 29.5612 0.979406 0.489703 0.871889i \(-0.337105\pi\)
0.489703 + 0.871889i \(0.337105\pi\)
\(912\) 0 0
\(913\) −4.43077 −0.146637
\(914\) 49.3221 1.63143
\(915\) 0 0
\(916\) −0.340735 −0.0112582
\(917\) 44.2672 1.46183
\(918\) 0 0
\(919\) −8.03175 −0.264943 −0.132471 0.991187i \(-0.542291\pi\)
−0.132471 + 0.991187i \(0.542291\pi\)
\(920\) 10.0379 0.330938
\(921\) 0 0
\(922\) 42.7016 1.40630
\(923\) −2.20341 −0.0725262
\(924\) 0 0
\(925\) −20.9130 −0.687614
\(926\) 9.75539 0.320582
\(927\) 0 0
\(928\) 7.17049 0.235383
\(929\) −34.6810 −1.13785 −0.568924 0.822390i \(-0.692640\pi\)
−0.568924 + 0.822390i \(0.692640\pi\)
\(930\) 0 0
\(931\) 18.7798 0.615481
\(932\) 7.26990 0.238134
\(933\) 0 0
\(934\) −23.4907 −0.768638
\(935\) −2.83208 −0.0926188
\(936\) 0 0
\(937\) 35.9363 1.17399 0.586994 0.809591i \(-0.300311\pi\)
0.586994 + 0.809591i \(0.300311\pi\)
\(938\) 46.0452 1.50343
\(939\) 0 0
\(940\) 4.81431 0.157025
\(941\) 48.1664 1.57018 0.785090 0.619382i \(-0.212617\pi\)
0.785090 + 0.619382i \(0.212617\pi\)
\(942\) 0 0
\(943\) −27.4248 −0.893075
\(944\) −45.7636 −1.48948
\(945\) 0 0
\(946\) −3.19450 −0.103862
\(947\) −50.0891 −1.62768 −0.813839 0.581091i \(-0.802626\pi\)
−0.813839 + 0.581091i \(0.802626\pi\)
\(948\) 0 0
\(949\) 0.381984 0.0123997
\(950\) 21.3902 0.693991
\(951\) 0 0
\(952\) −8.27157 −0.268083
\(953\) 47.1986 1.52891 0.764457 0.644675i \(-0.223007\pi\)
0.764457 + 0.644675i \(0.223007\pi\)
\(954\) 0 0
\(955\) 7.17221 0.232087
\(956\) 8.50363 0.275027
\(957\) 0 0
\(958\) 28.5417 0.922141
\(959\) 1.67050 0.0539431
\(960\) 0 0
\(961\) −8.65672 −0.279249
\(962\) 16.7861 0.541206
\(963\) 0 0
\(964\) 3.29097 0.105995
\(965\) −13.8018 −0.444296
\(966\) 0 0
\(967\) 50.7117 1.63078 0.815390 0.578912i \(-0.196523\pi\)
0.815390 + 0.578912i \(0.196523\pi\)
\(968\) −16.6989 −0.536723
\(969\) 0 0
\(970\) 26.4414 0.848984
\(971\) −14.3657 −0.461017 −0.230508 0.973070i \(-0.574039\pi\)
−0.230508 + 0.973070i \(0.574039\pi\)
\(972\) 0 0
\(973\) −43.6105 −1.39809
\(974\) 38.8587 1.24511
\(975\) 0 0
\(976\) −12.8117 −0.410092
\(977\) −3.90889 −0.125056 −0.0625282 0.998043i \(-0.519916\pi\)
−0.0625282 + 0.998043i \(0.519916\pi\)
\(978\) 0 0
\(979\) −27.6119 −0.882481
\(980\) 2.39090 0.0763744
\(981\) 0 0
\(982\) 13.0132 0.415269
\(983\) −46.8969 −1.49578 −0.747889 0.663824i \(-0.768933\pi\)
−0.747889 + 0.663824i \(0.768933\pi\)
\(984\) 0 0
\(985\) 11.3324 0.361081
\(986\) −4.86779 −0.155022
\(987\) 0 0
\(988\) −2.92303 −0.0929941
\(989\) −2.95501 −0.0939638
\(990\) 0 0
\(991\) −31.8168 −1.01069 −0.505347 0.862916i \(-0.668635\pi\)
−0.505347 + 0.862916i \(0.668635\pi\)
\(992\) −10.8101 −0.343222
\(993\) 0 0
\(994\) 7.14094 0.226497
\(995\) −0.820458 −0.0260103
\(996\) 0 0
\(997\) −19.3075 −0.611473 −0.305737 0.952116i \(-0.598903\pi\)
−0.305737 + 0.952116i \(0.598903\pi\)
\(998\) −19.3191 −0.611534
\(999\) 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.1.2 6
3.2 odd 2 731.2.a.c.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.5 6 3.2 odd 2
6579.2.a.j.1.2 6 1.1 even 1 trivial