Properties

Label 5929.2.a.y.1.3
Level $5929$
Weight $2$
Character 5929.1
Self dual yes
Analytic conductor $47.343$
Analytic rank $0$
Dimension $3$
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] = [5929,2,Mod(1,5929)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5929.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5929.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: \(47.3433033584\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 847)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.76156\) of defining polynomial
Character \(\chi\) \(=\) 5929.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.76156 q^{2} -1.76156 q^{3} +5.62620 q^{4} +2.62620 q^{5} -4.86464 q^{6} +10.0140 q^{8} +0.103084 q^{9} +O(q^{10})\) \(q+2.76156 q^{2} -1.76156 q^{3} +5.62620 q^{4} +2.62620 q^{5} -4.86464 q^{6} +10.0140 q^{8} +0.103084 q^{9} +7.25240 q^{10} -9.91087 q^{12} +2.38776 q^{13} -4.62620 q^{15} +16.4017 q^{16} +2.38776 q^{17} +0.284672 q^{18} +1.72928 q^{19} +14.7755 q^{20} -0.626198 q^{23} -17.6402 q^{24} +1.89692 q^{25} +6.59392 q^{26} +5.10308 q^{27} +1.72928 q^{29} -12.7755 q^{30} +2.23844 q^{31} +25.2663 q^{32} +6.59392 q^{34} +0.579969 q^{36} -6.89692 q^{37} +4.77551 q^{38} -4.20617 q^{39} +26.2986 q^{40} -10.3878 q^{41} +7.25240 q^{43} +0.270718 q^{45} -1.72928 q^{46} -6.38776 q^{47} -28.8925 q^{48} +5.23844 q^{50} -4.20617 q^{51} +13.4340 q^{52} -9.25240 q^{53} +14.0925 q^{54} -3.04623 q^{57} +4.77551 q^{58} +1.76156 q^{59} -26.0279 q^{60} +10.3878 q^{61} +6.18159 q^{62} +36.9711 q^{64} +6.27072 q^{65} -6.42003 q^{67} +13.4340 q^{68} +1.10308 q^{69} +8.08476 q^{71} +1.03228 q^{72} -10.3878 q^{73} -19.0462 q^{74} -3.34153 q^{75} +9.72928 q^{76} -11.6156 q^{78} +15.2524 q^{79} +43.0741 q^{80} -9.29862 q^{81} -28.6864 q^{82} -12.7755 q^{83} +6.27072 q^{85} +20.0279 q^{86} -3.04623 q^{87} +14.1493 q^{89} +0.747604 q^{90} -3.52311 q^{92} -3.94315 q^{93} -17.6402 q^{94} +4.54144 q^{95} -44.5081 q^{96} +8.35548 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9} + 4 q^{10} - 2 q^{12} - 8 q^{13} - 5 q^{15} + 10 q^{16} - 8 q^{17} - 18 q^{18} + 14 q^{20} + 7 q^{23} - 20 q^{24} + 2 q^{25} + 12 q^{26} + 19 q^{27} - 8 q^{30} + 13 q^{31} + 34 q^{32} + 12 q^{34} + 18 q^{36} - 17 q^{37} - 16 q^{38} - 20 q^{39} + 36 q^{40} - 16 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{47} - 36 q^{48} + 22 q^{50} - 20 q^{51} - 10 q^{53} - 8 q^{54} + 16 q^{57} - 16 q^{58} - q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} + 34 q^{64} + 24 q^{65} - 3 q^{67} + 7 q^{69} + 5 q^{71} + 2 q^{72} - 16 q^{73} - 32 q^{74} - 20 q^{75} + 24 q^{76} + 28 q^{78} + 28 q^{79} + 56 q^{80} + 15 q^{81} - 28 q^{82} - 8 q^{83} + 24 q^{85} + 12 q^{86} + 16 q^{87} + 21 q^{89} + 20 q^{90} + 2 q^{92} + 17 q^{93} - 20 q^{94} + 24 q^{95} - 20 q^{96} + 11 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.76156 1.95272 0.976358 0.216160i \(-0.0693534\pi\)
0.976358 + 0.216160i \(0.0693534\pi\)
\(3\) −1.76156 −1.01704 −0.508518 0.861052i \(-0.669806\pi\)
−0.508518 + 0.861052i \(0.669806\pi\)
\(4\) 5.62620 2.81310
\(5\) 2.62620 1.17447 0.587236 0.809416i \(-0.300216\pi\)
0.587236 + 0.809416i \(0.300216\pi\)
\(6\) −4.86464 −1.98598
\(7\) 0 0
\(8\) 10.0140 3.54047
\(9\) 0.103084 0.0343612
\(10\) 7.25240 2.29341
\(11\) 0 0
\(12\) −9.91087 −2.86102
\(13\) 2.38776 0.662244 0.331122 0.943588i \(-0.392573\pi\)
0.331122 + 0.943588i \(0.392573\pi\)
\(14\) 0 0
\(15\) −4.62620 −1.19448
\(16\) 16.4017 4.10043
\(17\) 2.38776 0.579116 0.289558 0.957161i \(-0.406492\pi\)
0.289558 + 0.957161i \(0.406492\pi\)
\(18\) 0.284672 0.0670977
\(19\) 1.72928 0.396724 0.198362 0.980129i \(-0.436438\pi\)
0.198362 + 0.980129i \(0.436438\pi\)
\(20\) 14.7755 3.30390
\(21\) 0 0
\(22\) 0 0
\(23\) −0.626198 −0.130571 −0.0652857 0.997867i \(-0.520796\pi\)
−0.0652857 + 0.997867i \(0.520796\pi\)
\(24\) −17.6402 −3.60078
\(25\) 1.89692 0.379383
\(26\) 6.59392 1.29317
\(27\) 5.10308 0.982089
\(28\) 0 0
\(29\) 1.72928 0.321120 0.160560 0.987026i \(-0.448670\pi\)
0.160560 + 0.987026i \(0.448670\pi\)
\(30\) −12.7755 −2.33248
\(31\) 2.23844 0.402036 0.201018 0.979588i \(-0.435575\pi\)
0.201018 + 0.979588i \(0.435575\pi\)
\(32\) 25.2663 4.46650
\(33\) 0 0
\(34\) 6.59392 1.13085
\(35\) 0 0
\(36\) 0.579969 0.0966616
\(37\) −6.89692 −1.13385 −0.566923 0.823771i \(-0.691866\pi\)
−0.566923 + 0.823771i \(0.691866\pi\)
\(38\) 4.77551 0.774690
\(39\) −4.20617 −0.673526
\(40\) 26.2986 4.15818
\(41\) −10.3878 −1.62229 −0.811147 0.584842i \(-0.801157\pi\)
−0.811147 + 0.584842i \(0.801157\pi\)
\(42\) 0 0
\(43\) 7.25240 1.10598 0.552990 0.833188i \(-0.313487\pi\)
0.552990 + 0.833188i \(0.313487\pi\)
\(44\) 0 0
\(45\) 0.270718 0.0403563
\(46\) −1.72928 −0.254969
\(47\) −6.38776 −0.931750 −0.465875 0.884851i \(-0.654260\pi\)
−0.465875 + 0.884851i \(0.654260\pi\)
\(48\) −28.8925 −4.17028
\(49\) 0 0
\(50\) 5.23844 0.740828
\(51\) −4.20617 −0.588981
\(52\) 13.4340 1.86296
\(53\) −9.25240 −1.27091 −0.635457 0.772136i \(-0.719188\pi\)
−0.635457 + 0.772136i \(0.719188\pi\)
\(54\) 14.0925 1.91774
\(55\) 0 0
\(56\) 0 0
\(57\) −3.04623 −0.403483
\(58\) 4.77551 0.627055
\(59\) 1.76156 0.229335 0.114668 0.993404i \(-0.463420\pi\)
0.114668 + 0.993404i \(0.463420\pi\)
\(60\) −26.0279 −3.36019
\(61\) 10.3878 1.33002 0.665008 0.746836i \(-0.268428\pi\)
0.665008 + 0.746836i \(0.268428\pi\)
\(62\) 6.18159 0.785062
\(63\) 0 0
\(64\) 36.9711 4.62138
\(65\) 6.27072 0.777787
\(66\) 0 0
\(67\) −6.42003 −0.784332 −0.392166 0.919895i \(-0.628274\pi\)
−0.392166 + 0.919895i \(0.628274\pi\)
\(68\) 13.4340 1.62911
\(69\) 1.10308 0.132796
\(70\) 0 0
\(71\) 8.08476 0.959485 0.479742 0.877409i \(-0.340730\pi\)
0.479742 + 0.877409i \(0.340730\pi\)
\(72\) 1.03228 0.121655
\(73\) −10.3878 −1.21579 −0.607897 0.794016i \(-0.707987\pi\)
−0.607897 + 0.794016i \(0.707987\pi\)
\(74\) −19.0462 −2.21408
\(75\) −3.34153 −0.385846
\(76\) 9.72928 1.11603
\(77\) 0 0
\(78\) −11.6156 −1.31520
\(79\) 15.2524 1.71603 0.858014 0.513626i \(-0.171698\pi\)
0.858014 + 0.513626i \(0.171698\pi\)
\(80\) 43.0741 4.81583
\(81\) −9.29862 −1.03318
\(82\) −28.6864 −3.16788
\(83\) −12.7755 −1.40229 −0.701147 0.713017i \(-0.747328\pi\)
−0.701147 + 0.713017i \(0.747328\pi\)
\(84\) 0 0
\(85\) 6.27072 0.680155
\(86\) 20.0279 2.15966
\(87\) −3.04623 −0.326590
\(88\) 0 0
\(89\) 14.1493 1.49982 0.749912 0.661538i \(-0.230096\pi\)
0.749912 + 0.661538i \(0.230096\pi\)
\(90\) 0.747604 0.0788044
\(91\) 0 0
\(92\) −3.52311 −0.367310
\(93\) −3.94315 −0.408885
\(94\) −17.6402 −1.81944
\(95\) 4.54144 0.465942
\(96\) −44.5081 −4.54259
\(97\) 8.35548 0.848370 0.424185 0.905575i \(-0.360561\pi\)
0.424185 + 0.905575i \(0.360561\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 10.6724 1.06724
\(101\) 13.8463 1.37776 0.688880 0.724875i \(-0.258103\pi\)
0.688880 + 0.724875i \(0.258103\pi\)
\(102\) −11.6156 −1.15011
\(103\) 2.92919 0.288622 0.144311 0.989532i \(-0.453903\pi\)
0.144311 + 0.989532i \(0.453903\pi\)
\(104\) 23.9109 2.34465
\(105\) 0 0
\(106\) −25.5510 −2.48173
\(107\) 3.45856 0.334352 0.167176 0.985927i \(-0.446535\pi\)
0.167176 + 0.985927i \(0.446535\pi\)
\(108\) 28.7110 2.76271
\(109\) −16.2341 −1.55494 −0.777471 0.628919i \(-0.783498\pi\)
−0.777471 + 0.628919i \(0.783498\pi\)
\(110\) 0 0
\(111\) 12.1493 1.15316
\(112\) 0 0
\(113\) 7.10308 0.668202 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(114\) −8.41233 −0.787887
\(115\) −1.64452 −0.153352
\(116\) 9.72928 0.903341
\(117\) 0.246139 0.0227555
\(118\) 4.86464 0.447826
\(119\) 0 0
\(120\) −46.3265 −4.22901
\(121\) 0 0
\(122\) 28.6864 2.59714
\(123\) 18.2986 1.64993
\(124\) 12.5939 1.13097
\(125\) −8.14931 −0.728897
\(126\) 0 0
\(127\) −4.54144 −0.402987 −0.201494 0.979490i \(-0.564580\pi\)
−0.201494 + 0.979490i \(0.564580\pi\)
\(128\) 51.5650 4.55774
\(129\) −12.7755 −1.12482
\(130\) 17.3169 1.51880
\(131\) 6.27072 0.547875 0.273938 0.961747i \(-0.411674\pi\)
0.273938 + 0.961747i \(0.411674\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −17.7293 −1.53158
\(135\) 13.4017 1.15344
\(136\) 23.9109 2.05034
\(137\) 9.40171 0.803242 0.401621 0.915806i \(-0.368447\pi\)
0.401621 + 0.915806i \(0.368447\pi\)
\(138\) 3.04623 0.259312
\(139\) −15.8217 −1.34198 −0.670991 0.741465i \(-0.734131\pi\)
−0.670991 + 0.741465i \(0.734131\pi\)
\(140\) 0 0
\(141\) 11.2524 0.947623
\(142\) 22.3265 1.87360
\(143\) 0 0
\(144\) 1.69075 0.140896
\(145\) 4.54144 0.377146
\(146\) −28.6864 −2.37410
\(147\) 0 0
\(148\) −38.8034 −3.18962
\(149\) 3.45856 0.283337 0.141668 0.989914i \(-0.454753\pi\)
0.141668 + 0.989914i \(0.454753\pi\)
\(150\) −9.22782 −0.753448
\(151\) −10.2986 −0.838090 −0.419045 0.907965i \(-0.637635\pi\)
−0.419045 + 0.907965i \(0.637635\pi\)
\(152\) 17.3169 1.40459
\(153\) 0.246139 0.0198991
\(154\) 0 0
\(155\) 5.87859 0.472180
\(156\) −23.6647 −1.89469
\(157\) −11.3372 −0.904804 −0.452402 0.891814i \(-0.649433\pi\)
−0.452402 + 0.891814i \(0.649433\pi\)
\(158\) 42.1204 3.35092
\(159\) 16.2986 1.29257
\(160\) 66.3544 5.24578
\(161\) 0 0
\(162\) −25.6787 −2.01751
\(163\) −9.72928 −0.762056 −0.381028 0.924563i \(-0.624430\pi\)
−0.381028 + 0.924563i \(0.624430\pi\)
\(164\) −58.4436 −4.56368
\(165\) 0 0
\(166\) −35.2803 −2.73828
\(167\) −22.5048 −1.74147 −0.870737 0.491750i \(-0.836357\pi\)
−0.870737 + 0.491750i \(0.836357\pi\)
\(168\) 0 0
\(169\) −7.29862 −0.561433
\(170\) 17.3169 1.32815
\(171\) 0.178261 0.0136319
\(172\) 40.8034 3.11123
\(173\) −6.92919 −0.526817 −0.263408 0.964684i \(-0.584847\pi\)
−0.263408 + 0.964684i \(0.584847\pi\)
\(174\) −8.41233 −0.637737
\(175\) 0 0
\(176\) 0 0
\(177\) −3.10308 −0.233242
\(178\) 39.0741 2.92873
\(179\) 13.9431 1.04216 0.521080 0.853508i \(-0.325529\pi\)
0.521080 + 0.853508i \(0.325529\pi\)
\(180\) 1.52311 0.113526
\(181\) −3.16763 −0.235448 −0.117724 0.993046i \(-0.537560\pi\)
−0.117724 + 0.993046i \(0.537560\pi\)
\(182\) 0 0
\(183\) −18.2986 −1.35267
\(184\) −6.27072 −0.462283
\(185\) −18.1127 −1.33167
\(186\) −10.8892 −0.798436
\(187\) 0 0
\(188\) −35.9388 −2.62110
\(189\) 0 0
\(190\) 12.5414 0.909851
\(191\) 18.3555 1.32816 0.664078 0.747663i \(-0.268824\pi\)
0.664078 + 0.747663i \(0.268824\pi\)
\(192\) −65.1266 −4.70011
\(193\) −3.04623 −0.219272 −0.109636 0.993972i \(-0.534969\pi\)
−0.109636 + 0.993972i \(0.534969\pi\)
\(194\) 23.0741 1.65663
\(195\) −11.0462 −0.791037
\(196\) 0 0
\(197\) 4.95377 0.352942 0.176471 0.984306i \(-0.443532\pi\)
0.176471 + 0.984306i \(0.443532\pi\)
\(198\) 0 0
\(199\) −15.7047 −1.11328 −0.556638 0.830755i \(-0.687909\pi\)
−0.556638 + 0.830755i \(0.687909\pi\)
\(200\) 18.9956 1.34319
\(201\) 11.3093 0.797693
\(202\) 38.2374 2.69037
\(203\) 0 0
\(204\) −23.6647 −1.65686
\(205\) −27.2803 −1.90534
\(206\) 8.08913 0.563596
\(207\) −0.0645508 −0.00448659
\(208\) 39.1633 2.71548
\(209\) 0 0
\(210\) 0 0
\(211\) 17.5510 1.20826 0.604131 0.796885i \(-0.293520\pi\)
0.604131 + 0.796885i \(0.293520\pi\)
\(212\) −52.0558 −3.57521
\(213\) −14.2418 −0.975830
\(214\) 9.55102 0.652894
\(215\) 19.0462 1.29894
\(216\) 51.1020 3.47705
\(217\) 0 0
\(218\) −44.8313 −3.03636
\(219\) 18.2986 1.23651
\(220\) 0 0
\(221\) 5.70138 0.383516
\(222\) 33.5510 2.25180
\(223\) 22.2943 1.49293 0.746467 0.665423i \(-0.231749\pi\)
0.746467 + 0.665423i \(0.231749\pi\)
\(224\) 0 0
\(225\) 0.195541 0.0130361
\(226\) 19.6156 1.30481
\(227\) −14.2707 −0.947181 −0.473590 0.880745i \(-0.657042\pi\)
−0.473590 + 0.880745i \(0.657042\pi\)
\(228\) −17.1387 −1.13504
\(229\) 3.87859 0.256305 0.128152 0.991754i \(-0.459095\pi\)
0.128152 + 0.991754i \(0.459095\pi\)
\(230\) −4.54144 −0.299453
\(231\) 0 0
\(232\) 17.3169 1.13691
\(233\) 6.68305 0.437821 0.218911 0.975745i \(-0.429750\pi\)
0.218911 + 0.975745i \(0.429750\pi\)
\(234\) 0.679726 0.0444351
\(235\) −16.7755 −1.09431
\(236\) 9.91087 0.645143
\(237\) −26.8680 −1.74526
\(238\) 0 0
\(239\) −4.54144 −0.293761 −0.146881 0.989154i \(-0.546923\pi\)
−0.146881 + 0.989154i \(0.546923\pi\)
\(240\) −75.8776 −4.89787
\(241\) 3.70470 0.238641 0.119320 0.992856i \(-0.461928\pi\)
0.119320 + 0.992856i \(0.461928\pi\)
\(242\) 0 0
\(243\) 1.07081 0.0686924
\(244\) 58.4436 3.74147
\(245\) 0 0
\(246\) 50.5327 3.22185
\(247\) 4.12910 0.262728
\(248\) 22.4157 1.42340
\(249\) 22.5048 1.42618
\(250\) −22.5048 −1.42333
\(251\) −8.50916 −0.537093 −0.268547 0.963267i \(-0.586543\pi\)
−0.268547 + 0.963267i \(0.586543\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −12.5414 −0.786920
\(255\) −11.0462 −0.691742
\(256\) 68.4575 4.27860
\(257\) 2.95377 0.184251 0.0921256 0.995747i \(-0.470634\pi\)
0.0921256 + 0.995747i \(0.470634\pi\)
\(258\) −35.2803 −2.19646
\(259\) 0 0
\(260\) 35.2803 2.18799
\(261\) 0.178261 0.0110341
\(262\) 17.3169 1.06984
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) −24.2986 −1.49265
\(266\) 0 0
\(267\) −24.9248 −1.52537
\(268\) −36.1204 −2.20640
\(269\) 6.77551 0.413110 0.206555 0.978435i \(-0.433775\pi\)
0.206555 + 0.978435i \(0.433775\pi\)
\(270\) 37.0096 2.25233
\(271\) −3.45856 −0.210093 −0.105046 0.994467i \(-0.533499\pi\)
−0.105046 + 0.994467i \(0.533499\pi\)
\(272\) 39.1633 2.37462
\(273\) 0 0
\(274\) 25.9634 1.56850
\(275\) 0 0
\(276\) 6.20617 0.373567
\(277\) −11.4586 −0.688478 −0.344239 0.938882i \(-0.611863\pi\)
−0.344239 + 0.938882i \(0.611863\pi\)
\(278\) −43.6926 −2.62051
\(279\) 0.230747 0.0138145
\(280\) 0 0
\(281\) −22.3265 −1.33189 −0.665945 0.746001i \(-0.731971\pi\)
−0.665945 + 0.746001i \(0.731971\pi\)
\(282\) 31.0741 1.85044
\(283\) 12.3632 0.734915 0.367457 0.930040i \(-0.380228\pi\)
0.367457 + 0.930040i \(0.380228\pi\)
\(284\) 45.4865 2.69913
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) 0 0
\(288\) 2.60455 0.153475
\(289\) −11.2986 −0.664625
\(290\) 12.5414 0.736459
\(291\) −14.7187 −0.862823
\(292\) −58.4436 −3.42015
\(293\) −2.15368 −0.125819 −0.0629097 0.998019i \(-0.520038\pi\)
−0.0629097 + 0.998019i \(0.520038\pi\)
\(294\) 0 0
\(295\) 4.62620 0.269348
\(296\) −69.0654 −4.01434
\(297\) 0 0
\(298\) 9.55102 0.553276
\(299\) −1.49521 −0.0864701
\(300\) −18.8001 −1.08542
\(301\) 0 0
\(302\) −28.4402 −1.63655
\(303\) −24.3911 −1.40123
\(304\) 28.3632 1.62674
\(305\) 27.2803 1.56207
\(306\) 0.679726 0.0388573
\(307\) 31.8217 1.81616 0.908081 0.418794i \(-0.137547\pi\)
0.908081 + 0.418794i \(0.137547\pi\)
\(308\) 0 0
\(309\) −5.15994 −0.293539
\(310\) 16.2341 0.922033
\(311\) 10.9292 0.619738 0.309869 0.950779i \(-0.399715\pi\)
0.309869 + 0.950779i \(0.399715\pi\)
\(312\) −42.1204 −2.38460
\(313\) −7.40171 −0.418369 −0.209185 0.977876i \(-0.567081\pi\)
−0.209185 + 0.977876i \(0.567081\pi\)
\(314\) −31.3082 −1.76682
\(315\) 0 0
\(316\) 85.8130 4.82736
\(317\) −8.89692 −0.499701 −0.249850 0.968284i \(-0.580381\pi\)
−0.249850 + 0.968284i \(0.580381\pi\)
\(318\) 45.0096 2.52401
\(319\) 0 0
\(320\) 97.0933 5.42768
\(321\) −6.09246 −0.340048
\(322\) 0 0
\(323\) 4.12910 0.229749
\(324\) −52.3159 −2.90644
\(325\) 4.52937 0.251244
\(326\) −26.8680 −1.48808
\(327\) 28.5972 1.58143
\(328\) −104.022 −5.74368
\(329\) 0 0
\(330\) 0 0
\(331\) 8.56165 0.470591 0.235295 0.971924i \(-0.424394\pi\)
0.235295 + 0.971924i \(0.424394\pi\)
\(332\) −71.8776 −3.94479
\(333\) −0.710960 −0.0389604
\(334\) −62.1483 −3.40060
\(335\) −16.8603 −0.921175
\(336\) 0 0
\(337\) −9.72928 −0.529988 −0.264994 0.964250i \(-0.585370\pi\)
−0.264994 + 0.964250i \(0.585370\pi\)
\(338\) −20.1556 −1.09632
\(339\) −12.5125 −0.679585
\(340\) 35.2803 1.91334
\(341\) 0 0
\(342\) 0.492277 0.0266193
\(343\) 0 0
\(344\) 72.6252 3.91569
\(345\) 2.89692 0.155965
\(346\) −19.1354 −1.02872
\(347\) 14.8401 0.796656 0.398328 0.917243i \(-0.369591\pi\)
0.398328 + 0.917243i \(0.369591\pi\)
\(348\) −17.1387 −0.918730
\(349\) −16.2461 −0.869636 −0.434818 0.900518i \(-0.643187\pi\)
−0.434818 + 0.900518i \(0.643187\pi\)
\(350\) 0 0
\(351\) 12.1849 0.650383
\(352\) 0 0
\(353\) −30.8603 −1.64253 −0.821263 0.570549i \(-0.806730\pi\)
−0.821263 + 0.570549i \(0.806730\pi\)
\(354\) −8.56934 −0.455455
\(355\) 21.2322 1.12689
\(356\) 79.6068 4.21915
\(357\) 0 0
\(358\) 38.5048 2.03504
\(359\) −11.7938 −0.622455 −0.311227 0.950335i \(-0.600740\pi\)
−0.311227 + 0.950335i \(0.600740\pi\)
\(360\) 2.71096 0.142880
\(361\) −16.0096 −0.842610
\(362\) −8.74760 −0.459764
\(363\) 0 0
\(364\) 0 0
\(365\) −27.2803 −1.42792
\(366\) −50.5327 −2.64139
\(367\) 3.55539 0.185590 0.0927949 0.995685i \(-0.470420\pi\)
0.0927949 + 0.995685i \(0.470420\pi\)
\(368\) −10.2707 −0.535398
\(369\) −1.07081 −0.0557441
\(370\) −50.0192 −2.60037
\(371\) 0 0
\(372\) −22.1849 −1.15023
\(373\) 22.5048 1.16525 0.582627 0.812740i \(-0.302025\pi\)
0.582627 + 0.812740i \(0.302025\pi\)
\(374\) 0 0
\(375\) 14.3555 0.741314
\(376\) −63.9667 −3.29883
\(377\) 4.12910 0.212660
\(378\) 0 0
\(379\) 23.4296 1.20350 0.601749 0.798685i \(-0.294471\pi\)
0.601749 + 0.798685i \(0.294471\pi\)
\(380\) 25.5510 1.31074
\(381\) 8.00000 0.409852
\(382\) 50.6897 2.59351
\(383\) 3.42629 0.175075 0.0875376 0.996161i \(-0.472100\pi\)
0.0875376 + 0.996161i \(0.472100\pi\)
\(384\) −90.8347 −4.63539
\(385\) 0 0
\(386\) −8.41233 −0.428177
\(387\) 0.747604 0.0380028
\(388\) 47.0096 2.38655
\(389\) 8.05685 0.408499 0.204249 0.978919i \(-0.434525\pi\)
0.204249 + 0.978919i \(0.434525\pi\)
\(390\) −30.5048 −1.54467
\(391\) −1.49521 −0.0756159
\(392\) 0 0
\(393\) −11.0462 −0.557209
\(394\) 13.6801 0.689195
\(395\) 40.0558 2.01543
\(396\) 0 0
\(397\) 26.3632 1.32313 0.661565 0.749888i \(-0.269893\pi\)
0.661565 + 0.749888i \(0.269893\pi\)
\(398\) −43.3694 −2.17391
\(399\) 0 0
\(400\) 31.1127 1.55563
\(401\) −22.5972 −1.12845 −0.564226 0.825620i \(-0.690825\pi\)
−0.564226 + 0.825620i \(0.690825\pi\)
\(402\) 31.2311 1.55767
\(403\) 5.34485 0.266246
\(404\) 77.9021 3.87578
\(405\) −24.4200 −1.21344
\(406\) 0 0
\(407\) 0 0
\(408\) −42.1204 −2.08527
\(409\) −9.30488 −0.460097 −0.230048 0.973179i \(-0.573888\pi\)
−0.230048 + 0.973179i \(0.573888\pi\)
\(410\) −75.3361 −3.72059
\(411\) −16.5616 −0.816926
\(412\) 16.4802 0.811922
\(413\) 0 0
\(414\) −0.178261 −0.00876104
\(415\) −33.5510 −1.64695
\(416\) 60.3299 2.95791
\(417\) 27.8709 1.36484
\(418\) 0 0
\(419\) 13.8463 0.676437 0.338218 0.941068i \(-0.390176\pi\)
0.338218 + 0.941068i \(0.390176\pi\)
\(420\) 0 0
\(421\) −35.7572 −1.74270 −0.871349 0.490663i \(-0.836755\pi\)
−0.871349 + 0.490663i \(0.836755\pi\)
\(422\) 48.4681 2.35939
\(423\) −0.658473 −0.0320161
\(424\) −92.6531 −4.49963
\(425\) 4.52937 0.219707
\(426\) −39.3295 −1.90552
\(427\) 0 0
\(428\) 19.4586 0.940565
\(429\) 0 0
\(430\) 52.5972 2.53646
\(431\) −31.3082 −1.50806 −0.754032 0.656838i \(-0.771894\pi\)
−0.754032 + 0.656838i \(0.771894\pi\)
\(432\) 83.6993 4.02698
\(433\) −21.6079 −1.03841 −0.519204 0.854650i \(-0.673772\pi\)
−0.519204 + 0.854650i \(0.673772\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) −91.3361 −4.37421
\(437\) −1.08287 −0.0518008
\(438\) 50.5327 2.41455
\(439\) −15.5877 −0.743959 −0.371979 0.928241i \(-0.621321\pi\)
−0.371979 + 0.928241i \(0.621321\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 15.7447 0.748898
\(443\) 23.4942 1.11624 0.558121 0.829760i \(-0.311523\pi\)
0.558121 + 0.829760i \(0.311523\pi\)
\(444\) 68.3544 3.24396
\(445\) 37.1589 1.76150
\(446\) 61.5669 2.91528
\(447\) −6.09246 −0.288163
\(448\) 0 0
\(449\) 22.7832 1.07521 0.537603 0.843198i \(-0.319330\pi\)
0.537603 + 0.843198i \(0.319330\pi\)
\(450\) 0.539998 0.0254558
\(451\) 0 0
\(452\) 39.9634 1.87972
\(453\) 18.1416 0.852368
\(454\) −39.4094 −1.84957
\(455\) 0 0
\(456\) −30.5048 −1.42852
\(457\) −14.5048 −0.678506 −0.339253 0.940695i \(-0.610174\pi\)
−0.339253 + 0.940695i \(0.610174\pi\)
\(458\) 10.7110 0.500490
\(459\) 12.1849 0.568743
\(460\) −9.25240 −0.431395
\(461\) 31.1633 1.45142 0.725709 0.688002i \(-0.241512\pi\)
0.725709 + 0.688002i \(0.241512\pi\)
\(462\) 0 0
\(463\) −5.87859 −0.273201 −0.136601 0.990626i \(-0.543618\pi\)
−0.136601 + 0.990626i \(0.543618\pi\)
\(464\) 28.3632 1.31673
\(465\) −10.3555 −0.480224
\(466\) 18.4556 0.854941
\(467\) 23.7249 1.09786 0.548929 0.835869i \(-0.315036\pi\)
0.548929 + 0.835869i \(0.315036\pi\)
\(468\) 1.38482 0.0640136
\(469\) 0 0
\(470\) −46.3265 −2.13688
\(471\) 19.9711 0.920217
\(472\) 17.6402 0.811954
\(473\) 0 0
\(474\) −74.1974 −3.40800
\(475\) 3.28030 0.150511
\(476\) 0 0
\(477\) −0.953771 −0.0436702
\(478\) −12.5414 −0.573632
\(479\) −8.41233 −0.384369 −0.192185 0.981359i \(-0.561557\pi\)
−0.192185 + 0.981359i \(0.561557\pi\)
\(480\) −116.887 −5.33514
\(481\) −16.4681 −0.750883
\(482\) 10.2307 0.465998
\(483\) 0 0
\(484\) 0 0
\(485\) 21.9431 0.996387
\(486\) 2.95710 0.134137
\(487\) 24.7957 1.12360 0.561801 0.827273i \(-0.310109\pi\)
0.561801 + 0.827273i \(0.310109\pi\)
\(488\) 104.022 4.70888
\(489\) 17.1387 0.775038
\(490\) 0 0
\(491\) 12.2062 0.550857 0.275428 0.961322i \(-0.411180\pi\)
0.275428 + 0.961322i \(0.411180\pi\)
\(492\) 102.952 4.64142
\(493\) 4.12910 0.185965
\(494\) 11.4028 0.513034
\(495\) 0 0
\(496\) 36.7143 1.64852
\(497\) 0 0
\(498\) 62.1483 2.78493
\(499\) 22.3265 0.999473 0.499736 0.866178i \(-0.333430\pi\)
0.499736 + 0.866178i \(0.333430\pi\)
\(500\) −45.8496 −2.05046
\(501\) 39.6435 1.77114
\(502\) −23.4985 −1.04879
\(503\) 4.54144 0.202493 0.101246 0.994861i \(-0.467717\pi\)
0.101246 + 0.994861i \(0.467717\pi\)
\(504\) 0 0
\(505\) 36.3632 1.61814
\(506\) 0 0
\(507\) 12.8569 0.570997
\(508\) −25.5510 −1.13364
\(509\) −4.12141 −0.182678 −0.0913391 0.995820i \(-0.529115\pi\)
−0.0913391 + 0.995820i \(0.529115\pi\)
\(510\) −30.5048 −1.35077
\(511\) 0 0
\(512\) 85.9194 3.79714
\(513\) 8.82467 0.389619
\(514\) 8.15701 0.359790
\(515\) 7.69264 0.338978
\(516\) −71.8776 −3.16423
\(517\) 0 0
\(518\) 0 0
\(519\) 12.2062 0.535791
\(520\) 62.7947 2.75373
\(521\) −39.2880 −1.72124 −0.860619 0.509249i \(-0.829923\pi\)
−0.860619 + 0.509249i \(0.829923\pi\)
\(522\) 0.492277 0.0215464
\(523\) 2.14162 0.0936464 0.0468232 0.998903i \(-0.485090\pi\)
0.0468232 + 0.998903i \(0.485090\pi\)
\(524\) 35.2803 1.54123
\(525\) 0 0
\(526\) −44.1849 −1.92655
\(527\) 5.34485 0.232825
\(528\) 0 0
\(529\) −22.6079 −0.982951
\(530\) −67.1020 −2.91473
\(531\) 0.181588 0.00788024
\(532\) 0 0
\(533\) −24.8034 −1.07436
\(534\) −68.8313 −2.97862
\(535\) 9.08287 0.392687
\(536\) −64.2899 −2.77690
\(537\) −24.5616 −1.05991
\(538\) 18.7110 0.806687
\(539\) 0 0
\(540\) 75.4007 3.24473
\(541\) −43.0462 −1.85070 −0.925351 0.379112i \(-0.876230\pi\)
−0.925351 + 0.379112i \(0.876230\pi\)
\(542\) −9.55102 −0.410251
\(543\) 5.57997 0.239459
\(544\) 60.3299 2.58662
\(545\) −42.6339 −1.82624
\(546\) 0 0
\(547\) −29.0096 −1.24036 −0.620180 0.784459i \(-0.712940\pi\)
−0.620180 + 0.784459i \(0.712940\pi\)
\(548\) 52.8959 2.25960
\(549\) 1.07081 0.0457010
\(550\) 0 0
\(551\) 2.99042 0.127396
\(552\) 11.0462 0.470159
\(553\) 0 0
\(554\) −31.6435 −1.34440
\(555\) 31.9065 1.35436
\(556\) −89.0162 −3.77513
\(557\) −1.49521 −0.0633540 −0.0316770 0.999498i \(-0.510085\pi\)
−0.0316770 + 0.999498i \(0.510085\pi\)
\(558\) 0.637221 0.0269757
\(559\) 17.3169 0.732429
\(560\) 0 0
\(561\) 0 0
\(562\) −61.6560 −2.60080
\(563\) −6.27072 −0.264279 −0.132140 0.991231i \(-0.542185\pi\)
−0.132140 + 0.991231i \(0.542185\pi\)
\(564\) 63.3082 2.66576
\(565\) 18.6541 0.784784
\(566\) 34.1416 1.43508
\(567\) 0 0
\(568\) 80.9604 3.39702
\(569\) 7.82174 0.327904 0.163952 0.986468i \(-0.447576\pi\)
0.163952 + 0.986468i \(0.447576\pi\)
\(570\) −22.0925 −0.925351
\(571\) −15.1753 −0.635068 −0.317534 0.948247i \(-0.602855\pi\)
−0.317534 + 0.948247i \(0.602855\pi\)
\(572\) 0 0
\(573\) −32.3342 −1.35078
\(574\) 0 0
\(575\) −1.18785 −0.0495366
\(576\) 3.81111 0.158796
\(577\) −23.6445 −0.984334 −0.492167 0.870501i \(-0.663795\pi\)
−0.492167 + 0.870501i \(0.663795\pi\)
\(578\) −31.2018 −1.29782
\(579\) 5.36611 0.223008
\(580\) 25.5510 1.06095
\(581\) 0 0
\(582\) −40.6464 −1.68485
\(583\) 0 0
\(584\) −104.022 −4.30448
\(585\) 0.646409 0.0267257
\(586\) −5.94751 −0.245690
\(587\) 10.1537 0.419087 0.209544 0.977799i \(-0.432802\pi\)
0.209544 + 0.977799i \(0.432802\pi\)
\(588\) 0 0
\(589\) 3.87090 0.159498
\(590\) 12.7755 0.525959
\(591\) −8.72635 −0.358954
\(592\) −113.121 −4.64925
\(593\) −33.7972 −1.38788 −0.693942 0.720031i \(-0.744127\pi\)
−0.693942 + 0.720031i \(0.744127\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 19.4586 0.797054
\(597\) 27.6647 1.13224
\(598\) −4.12910 −0.168852
\(599\) −18.3265 −0.748802 −0.374401 0.927267i \(-0.622152\pi\)
−0.374401 + 0.927267i \(0.622152\pi\)
\(600\) −33.4619 −1.36608
\(601\) −48.4802 −1.97755 −0.988775 0.149415i \(-0.952261\pi\)
−0.988775 + 0.149415i \(0.952261\pi\)
\(602\) 0 0
\(603\) −0.661801 −0.0269506
\(604\) −57.9421 −2.35763
\(605\) 0 0
\(606\) −67.3574 −2.73621
\(607\) 20.5972 0.836017 0.418008 0.908443i \(-0.362728\pi\)
0.418008 + 0.908443i \(0.362728\pi\)
\(608\) 43.6926 1.77197
\(609\) 0 0
\(610\) 75.3361 3.05027
\(611\) −15.2524 −0.617046
\(612\) 1.38482 0.0559782
\(613\) 18.8122 0.759816 0.379908 0.925024i \(-0.375956\pi\)
0.379908 + 0.925024i \(0.375956\pi\)
\(614\) 87.8776 3.54645
\(615\) 48.0558 1.93780
\(616\) 0 0
\(617\) −14.2062 −0.571919 −0.285959 0.958242i \(-0.592312\pi\)
−0.285959 + 0.958242i \(0.592312\pi\)
\(618\) −14.2495 −0.573198
\(619\) 16.0235 0.644040 0.322020 0.946733i \(-0.395638\pi\)
0.322020 + 0.946733i \(0.395638\pi\)
\(620\) 33.0741 1.32829
\(621\) −3.19554 −0.128233
\(622\) 30.1816 1.21017
\(623\) 0 0
\(624\) −68.9883 −2.76174
\(625\) −30.8863 −1.23545
\(626\) −20.4402 −0.816956
\(627\) 0 0
\(628\) −63.7851 −2.54530
\(629\) −16.4681 −0.656628
\(630\) 0 0
\(631\) 15.1955 0.604925 0.302462 0.953161i \(-0.402191\pi\)
0.302462 + 0.953161i \(0.402191\pi\)
\(632\) 152.737 6.07554
\(633\) −30.9171 −1.22885
\(634\) −24.5693 −0.975773
\(635\) −11.9267 −0.473297
\(636\) 91.6993 3.63611
\(637\) 0 0
\(638\) 0 0
\(639\) 0.833407 0.0329691
\(640\) 135.420 5.35294
\(641\) −10.2264 −0.403918 −0.201959 0.979394i \(-0.564731\pi\)
−0.201959 + 0.979394i \(0.564731\pi\)
\(642\) −16.8247 −0.664017
\(643\) −20.5650 −0.811003 −0.405502 0.914094i \(-0.632903\pi\)
−0.405502 + 0.914094i \(0.632903\pi\)
\(644\) 0 0
\(645\) −33.5510 −1.32107
\(646\) 11.4028 0.448635
\(647\) 25.4542 1.00071 0.500354 0.865821i \(-0.333203\pi\)
0.500354 + 0.865821i \(0.333203\pi\)
\(648\) −93.1160 −3.65794
\(649\) 0 0
\(650\) 12.5081 0.490609
\(651\) 0 0
\(652\) −54.7389 −2.14374
\(653\) −45.2514 −1.77082 −0.885411 0.464809i \(-0.846123\pi\)
−0.885411 + 0.464809i \(0.846123\pi\)
\(654\) 78.9729 3.08809
\(655\) 16.4681 0.643464
\(656\) −170.377 −6.65210
\(657\) −1.07081 −0.0417762
\(658\) 0 0
\(659\) −50.3544 −1.96153 −0.980765 0.195191i \(-0.937467\pi\)
−0.980765 + 0.195191i \(0.937467\pi\)
\(660\) 0 0
\(661\) 23.2234 0.903287 0.451644 0.892198i \(-0.350838\pi\)
0.451644 + 0.892198i \(0.350838\pi\)
\(662\) 23.6435 0.918930
\(663\) −10.0433 −0.390049
\(664\) −127.933 −4.96478
\(665\) 0 0
\(666\) −1.96336 −0.0760785
\(667\) −1.08287 −0.0419290
\(668\) −126.616 −4.89894
\(669\) −39.2726 −1.51837
\(670\) −46.5606 −1.79879
\(671\) 0 0
\(672\) 0 0
\(673\) −3.22449 −0.124295 −0.0621475 0.998067i \(-0.519795\pi\)
−0.0621475 + 0.998067i \(0.519795\pi\)
\(674\) −26.8680 −1.03492
\(675\) 9.68012 0.372588
\(676\) −41.0635 −1.57937
\(677\) −42.6218 −1.63809 −0.819045 0.573729i \(-0.805496\pi\)
−0.819045 + 0.573729i \(0.805496\pi\)
\(678\) −34.5540 −1.32704
\(679\) 0 0
\(680\) 62.7947 2.40807
\(681\) 25.1387 0.963317
\(682\) 0 0
\(683\) 15.5877 0.596445 0.298223 0.954496i \(-0.403606\pi\)
0.298223 + 0.954496i \(0.403606\pi\)
\(684\) 1.00293 0.0383480
\(685\) 24.6907 0.943385
\(686\) 0 0
\(687\) −6.83237 −0.260671
\(688\) 118.952 4.53499
\(689\) −22.0925 −0.841656
\(690\) 8.00000 0.304555
\(691\) −41.9311 −1.59513 −0.797567 0.603231i \(-0.793880\pi\)
−0.797567 + 0.603231i \(0.793880\pi\)
\(692\) −38.9850 −1.48199
\(693\) 0 0
\(694\) 40.9817 1.55564
\(695\) −41.5510 −1.57612
\(696\) −30.5048 −1.15628
\(697\) −24.8034 −0.939496
\(698\) −44.8646 −1.69815
\(699\) −11.7726 −0.445280
\(700\) 0 0
\(701\) −15.4094 −0.582005 −0.291003 0.956722i \(-0.593989\pi\)
−0.291003 + 0.956722i \(0.593989\pi\)
\(702\) 33.6493 1.27001
\(703\) −11.9267 −0.449824
\(704\) 0 0
\(705\) 29.5510 1.11296
\(706\) −85.2224 −3.20739
\(707\) 0 0
\(708\) −17.4586 −0.656133
\(709\) 2.86027 0.107420 0.0537099 0.998557i \(-0.482895\pi\)
0.0537099 + 0.998557i \(0.482895\pi\)
\(710\) 58.6339 2.20049
\(711\) 1.57227 0.0589649
\(712\) 141.691 5.31008
\(713\) −1.40171 −0.0524944
\(714\) 0 0
\(715\) 0 0
\(716\) 78.4469 2.93170
\(717\) 8.00000 0.298765
\(718\) −32.5693 −1.21548
\(719\) 34.4725 1.28561 0.642804 0.766031i \(-0.277771\pi\)
0.642804 + 0.766031i \(0.277771\pi\)
\(720\) 4.44024 0.165478
\(721\) 0 0
\(722\) −44.2114 −1.64538
\(723\) −6.52604 −0.242706
\(724\) −17.8217 −0.662340
\(725\) 3.28030 0.121827
\(726\) 0 0
\(727\) 40.3309 1.49579 0.747895 0.663817i \(-0.231065\pi\)
0.747895 + 0.663817i \(0.231065\pi\)
\(728\) 0 0
\(729\) 26.0096 0.963318
\(730\) −75.3361 −2.78831
\(731\) 17.3169 0.640490
\(732\) −102.952 −3.80520
\(733\) 28.7634 1.06240 0.531201 0.847246i \(-0.321741\pi\)
0.531201 + 0.847246i \(0.321741\pi\)
\(734\) 9.81841 0.362404
\(735\) 0 0
\(736\) −15.8217 −0.583197
\(737\) 0 0
\(738\) −2.95710 −0.108852
\(739\) 35.1020 1.29125 0.645625 0.763655i \(-0.276597\pi\)
0.645625 + 0.763655i \(0.276597\pi\)
\(740\) −101.905 −3.74612
\(741\) −7.27365 −0.267204
\(742\) 0 0
\(743\) −32.4681 −1.19114 −0.595570 0.803303i \(-0.703074\pi\)
−0.595570 + 0.803303i \(0.703074\pi\)
\(744\) −39.4865 −1.44764
\(745\) 9.08287 0.332771
\(746\) 62.1483 2.27541
\(747\) −1.31695 −0.0481846
\(748\) 0 0
\(749\) 0 0
\(750\) 39.6435 1.44758
\(751\) −28.3834 −1.03572 −0.517862 0.855464i \(-0.673272\pi\)
−0.517862 + 0.855464i \(0.673272\pi\)
\(752\) −104.770 −3.82057
\(753\) 14.9894 0.546243
\(754\) 11.4028 0.415264
\(755\) −27.0462 −0.984313
\(756\) 0 0
\(757\) −17.0462 −0.619556 −0.309778 0.950809i \(-0.600255\pi\)
−0.309778 + 0.950809i \(0.600255\pi\)
\(758\) 64.7022 2.35009
\(759\) 0 0
\(760\) 45.4777 1.64965
\(761\) −27.9388 −1.01278 −0.506390 0.862305i \(-0.669020\pi\)
−0.506390 + 0.862305i \(0.669020\pi\)
\(762\) 22.0925 0.800325
\(763\) 0 0
\(764\) 103.272 3.73623
\(765\) 0.646409 0.0233710
\(766\) 9.46189 0.341872
\(767\) 4.20617 0.151876
\(768\) −120.592 −4.35148
\(769\) −6.69512 −0.241432 −0.120716 0.992687i \(-0.538519\pi\)
−0.120716 + 0.992687i \(0.538519\pi\)
\(770\) 0 0
\(771\) −5.20324 −0.187390
\(772\) −17.1387 −0.616835
\(773\) −27.9142 −1.00400 −0.502002 0.864866i \(-0.667403\pi\)
−0.502002 + 0.864866i \(0.667403\pi\)
\(774\) 2.06455 0.0742087
\(775\) 4.24614 0.152526
\(776\) 83.6714 3.00363
\(777\) 0 0
\(778\) 22.2495 0.797682
\(779\) −17.9634 −0.643604
\(780\) −62.1483 −2.22527
\(781\) 0 0
\(782\) −4.12910 −0.147656
\(783\) 8.82467 0.315368
\(784\) 0 0
\(785\) −29.7736 −1.06267
\(786\) −30.5048 −1.08807
\(787\) −21.8584 −0.779167 −0.389584 0.920991i \(-0.627381\pi\)
−0.389584 + 0.920991i \(0.627381\pi\)
\(788\) 27.8709 0.992860
\(789\) 28.1849 1.00341
\(790\) 110.616 3.93556
\(791\) 0 0
\(792\) 0 0
\(793\) 24.8034 0.880795
\(794\) 72.8034 2.58370
\(795\) 42.8034 1.51808
\(796\) −88.3578 −3.13176
\(797\) 34.6262 1.22652 0.613261 0.789880i \(-0.289857\pi\)
0.613261 + 0.789880i \(0.289857\pi\)
\(798\) 0 0
\(799\) −15.2524 −0.539591
\(800\) 47.9282 1.69452
\(801\) 1.45856 0.0515358
\(802\) −62.4036 −2.20355
\(803\) 0 0
\(804\) 63.6281 2.24399
\(805\) 0 0
\(806\) 14.7601 0.519903
\(807\) −11.9354 −0.420148
\(808\) 138.656 4.87791
\(809\) 35.0462 1.23216 0.616080 0.787684i \(-0.288720\pi\)
0.616080 + 0.787684i \(0.288720\pi\)
\(810\) −67.4373 −2.36951
\(811\) 18.1416 0.637038 0.318519 0.947916i \(-0.396814\pi\)
0.318519 + 0.947916i \(0.396814\pi\)
\(812\) 0 0
\(813\) 6.09246 0.213672
\(814\) 0 0
\(815\) −25.5510 −0.895013
\(816\) −68.9883 −2.41507
\(817\) 12.5414 0.438769
\(818\) −25.6960 −0.898438
\(819\) 0 0
\(820\) −153.484 −5.35991
\(821\) −3.45856 −0.120705 −0.0603524 0.998177i \(-0.519222\pi\)
−0.0603524 + 0.998177i \(0.519222\pi\)
\(822\) −45.7359 −1.59522
\(823\) −33.5308 −1.16881 −0.584405 0.811462i \(-0.698672\pi\)
−0.584405 + 0.811462i \(0.698672\pi\)
\(824\) 29.3328 1.02186
\(825\) 0 0
\(826\) 0 0
\(827\) −26.2986 −0.914493 −0.457246 0.889340i \(-0.651164\pi\)
−0.457246 + 0.889340i \(0.651164\pi\)
\(828\) −0.363176 −0.0126212
\(829\) 29.0019 1.00728 0.503639 0.863914i \(-0.331994\pi\)
0.503639 + 0.863914i \(0.331994\pi\)
\(830\) −92.6531 −3.21603
\(831\) 20.1849 0.700207
\(832\) 88.2778 3.06048
\(833\) 0 0
\(834\) 76.9671 2.66515
\(835\) −59.1020 −2.04531
\(836\) 0 0
\(837\) 11.4230 0.394835
\(838\) 38.2374 1.32089
\(839\) −29.1710 −1.00709 −0.503547 0.863968i \(-0.667972\pi\)
−0.503547 + 0.863968i \(0.667972\pi\)
\(840\) 0 0
\(841\) −26.0096 −0.896882
\(842\) −98.7455 −3.40300
\(843\) 39.3295 1.35458
\(844\) 98.7455 3.39896
\(845\) −19.1676 −0.659387
\(846\) −1.81841 −0.0625183
\(847\) 0 0
\(848\) −151.755 −5.21129
\(849\) −21.7784 −0.747434
\(850\) 12.5081 0.429025
\(851\) 4.31884 0.148048
\(852\) −80.1270 −2.74511
\(853\) −10.6218 −0.363685 −0.181842 0.983328i \(-0.558206\pi\)
−0.181842 + 0.983328i \(0.558206\pi\)
\(854\) 0 0
\(855\) 0.468148 0.0160103
\(856\) 34.6339 1.18376
\(857\) −37.8463 −1.29281 −0.646403 0.762996i \(-0.723727\pi\)
−0.646403 + 0.762996i \(0.723727\pi\)
\(858\) 0 0
\(859\) 19.0785 0.650950 0.325475 0.945551i \(-0.394476\pi\)
0.325475 + 0.945551i \(0.394476\pi\)
\(860\) 107.158 3.65405
\(861\) 0 0
\(862\) −86.4594 −2.94482
\(863\) 11.1753 0.380413 0.190206 0.981744i \(-0.439084\pi\)
0.190206 + 0.981744i \(0.439084\pi\)
\(864\) 128.936 4.38650
\(865\) −18.1974 −0.618731
\(866\) −59.6714 −2.02772
\(867\) 19.9032 0.675947
\(868\) 0 0
\(869\) 0 0
\(870\) −22.0925 −0.749004
\(871\) −15.3295 −0.519419
\(872\) −162.567 −5.50522
\(873\) 0.861314 0.0291511
\(874\) −2.99042 −0.101152
\(875\) 0 0
\(876\) 102.952 3.47842
\(877\) −5.85838 −0.197824 −0.0989118 0.995096i \(-0.531536\pi\)
−0.0989118 + 0.995096i \(0.531536\pi\)
\(878\) −43.0462 −1.45274
\(879\) 3.79383 0.127963
\(880\) 0 0
\(881\) 25.9065 0.872812 0.436406 0.899750i \(-0.356251\pi\)
0.436406 + 0.899750i \(0.356251\pi\)
\(882\) 0 0
\(883\) 13.4219 0.451684 0.225842 0.974164i \(-0.427487\pi\)
0.225842 + 0.974164i \(0.427487\pi\)
\(884\) 32.0771 1.07887
\(885\) −8.14931 −0.273936
\(886\) 64.8805 2.17970
\(887\) 49.6068 1.66563 0.832817 0.553548i \(-0.186726\pi\)
0.832817 + 0.553548i \(0.186726\pi\)
\(888\) 121.663 4.08273
\(889\) 0 0
\(890\) 102.616 3.43971
\(891\) 0 0
\(892\) 125.432 4.19977
\(893\) −11.0462 −0.369648
\(894\) −16.8247 −0.562701
\(895\) 36.6175 1.22399
\(896\) 0 0
\(897\) 2.63389 0.0879432
\(898\) 62.9171 2.09957
\(899\) 3.87090 0.129102
\(900\) 1.10015 0.0366718
\(901\) −22.0925 −0.736006
\(902\) 0 0
\(903\) 0 0
\(904\) 71.1299 2.36575
\(905\) −8.31884 −0.276527
\(906\) 50.0991 1.66443
\(907\) −47.8776 −1.58975 −0.794874 0.606775i \(-0.792463\pi\)
−0.794874 + 0.606775i \(0.792463\pi\)
\(908\) −80.2899 −2.66451
\(909\) 1.42733 0.0473415
\(910\) 0 0
\(911\) 22.8122 0.755800 0.377900 0.925846i \(-0.376646\pi\)
0.377900 + 0.925846i \(0.376646\pi\)
\(912\) −49.9634 −1.65445
\(913\) 0 0
\(914\) −40.0558 −1.32493
\(915\) −48.0558 −1.58868
\(916\) 21.8217 0.721011
\(917\) 0 0
\(918\) 33.6493 1.11059
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) −16.4681 −0.542939
\(921\) −56.0558 −1.84710
\(922\) 86.0591 2.83421
\(923\) 19.3044 0.635413
\(924\) 0 0
\(925\) −13.0829 −0.430162
\(926\) −16.2341 −0.533485
\(927\) 0.301952 0.00991740
\(928\) 43.6926 1.43428
\(929\) 16.0366 0.526145 0.263073 0.964776i \(-0.415264\pi\)
0.263073 + 0.964776i \(0.415264\pi\)
\(930\) −28.5972 −0.937741
\(931\) 0 0
\(932\) 37.6002 1.23163
\(933\) −19.2524 −0.630295
\(934\) 65.5177 2.14380
\(935\) 0 0
\(936\) 2.46482 0.0805652
\(937\) 25.3049 0.826674 0.413337 0.910578i \(-0.364363\pi\)
0.413337 + 0.910578i \(0.364363\pi\)
\(938\) 0 0
\(939\) 13.0385 0.425496
\(940\) −94.3823 −3.07841
\(941\) −20.5294 −0.669238 −0.334619 0.942353i \(-0.608608\pi\)
−0.334619 + 0.942353i \(0.608608\pi\)
\(942\) 55.1512 1.79692
\(943\) 6.50479 0.211825
\(944\) 28.8925 0.940372
\(945\) 0 0
\(946\) 0 0
\(947\) −16.6907 −0.542376 −0.271188 0.962526i \(-0.587417\pi\)
−0.271188 + 0.962526i \(0.587417\pi\)
\(948\) −151.165 −4.90960
\(949\) −24.8034 −0.805153
\(950\) 9.05874 0.293904
\(951\) 15.6724 0.508213
\(952\) 0 0
\(953\) 56.4681 1.82918 0.914591 0.404379i \(-0.132512\pi\)
0.914591 + 0.404379i \(0.132512\pi\)
\(954\) −2.63389 −0.0852755
\(955\) 48.2051 1.55988
\(956\) −25.5510 −0.826379
\(957\) 0 0
\(958\) −23.2311 −0.750564
\(959\) 0 0
\(960\) −171.035 −5.52014
\(961\) −25.9894 −0.838367
\(962\) −45.4777 −1.46626
\(963\) 0.356522 0.0114887
\(964\) 20.8434 0.671320
\(965\) −8.00000 −0.257529
\(966\) 0 0
\(967\) 47.3082 1.52133 0.760665 0.649145i \(-0.224873\pi\)
0.760665 + 0.649145i \(0.224873\pi\)
\(968\) 0 0
\(969\) −7.27365 −0.233663
\(970\) 60.5972 1.94566
\(971\) 25.2355 0.809846 0.404923 0.914351i \(-0.367298\pi\)
0.404923 + 0.914351i \(0.367298\pi\)
\(972\) 6.02458 0.193238
\(973\) 0 0
\(974\) 68.4748 2.19407
\(975\) −7.97875 −0.255524
\(976\) 170.377 5.45363
\(977\) 7.10308 0.227248 0.113624 0.993524i \(-0.463754\pi\)
0.113624 + 0.993524i \(0.463754\pi\)
\(978\) 47.3295 1.51343
\(979\) 0 0
\(980\) 0 0
\(981\) −1.67347 −0.0534297
\(982\) 33.7080 1.07567
\(983\) 14.1893 0.452568 0.226284 0.974061i \(-0.427342\pi\)
0.226284 + 0.974061i \(0.427342\pi\)
\(984\) 183.242 5.84153
\(985\) 13.0096 0.414520
\(986\) 11.4028 0.363138
\(987\) 0 0
\(988\) 23.2311 0.739081
\(989\) −4.54144 −0.144409
\(990\) 0 0
\(991\) 4.23407 0.134500 0.0672499 0.997736i \(-0.478578\pi\)
0.0672499 + 0.997736i \(0.478578\pi\)
\(992\) 56.5573 1.79570
\(993\) −15.0818 −0.478607
\(994\) 0 0
\(995\) −41.2437 −1.30751
\(996\) 126.616 4.01199
\(997\) 27.7047 0.877417 0.438708 0.898629i \(-0.355436\pi\)
0.438708 + 0.898629i \(0.355436\pi\)
\(998\) 61.6560 1.95169
\(999\) −35.1955 −1.11354
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 5929.2.a.y.1.3 3
7.6 odd 2 847.2.a.j.1.3 yes 3
11.10 odd 2 5929.2.a.t.1.1 3
21.20 even 2 7623.2.a.bz.1.1 3
77.6 even 10 847.2.f.u.729.3 12
77.13 even 10 847.2.f.u.323.3 12
77.20 odd 10 847.2.f.t.323.1 12
77.27 odd 10 847.2.f.t.729.1 12
77.41 even 10 847.2.f.u.372.1 12
77.48 odd 10 847.2.f.t.148.3 12
77.62 even 10 847.2.f.u.148.1 12
77.69 odd 10 847.2.f.t.372.3 12
77.76 even 2 847.2.a.i.1.1 3
231.230 odd 2 7623.2.a.ce.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.i.1.1 3 77.76 even 2
847.2.a.j.1.3 yes 3 7.6 odd 2
847.2.f.t.148.3 12 77.48 odd 10
847.2.f.t.323.1 12 77.20 odd 10
847.2.f.t.372.3 12 77.69 odd 10
847.2.f.t.729.1 12 77.27 odd 10
847.2.f.u.148.1 12 77.62 even 10
847.2.f.u.323.3 12 77.13 even 10
847.2.f.u.372.1 12 77.41 even 10
847.2.f.u.729.3 12 77.6 even 10
5929.2.a.t.1.1 3 11.10 odd 2
5929.2.a.y.1.3 3 1.1 even 1 trivial
7623.2.a.bz.1.1 3 21.20 even 2
7623.2.a.ce.1.3 3 231.230 odd 2