Properties

Label 5225.2.a.x.1.9
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 5 x^{14} - 11 x^{13} + 85 x^{12} + 6 x^{11} - 537 x^{10} + 327 x^{9} + 1556 x^{8} - 1451 x^{7} + \cdots - 13 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(1.10124\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.10124 q^{2} -1.12617 q^{3} -0.787279 q^{4} -1.24018 q^{6} -1.81708 q^{7} -3.06945 q^{8} -1.73174 q^{9} +O(q^{10})\) \(q+1.10124 q^{2} -1.12617 q^{3} -0.787279 q^{4} -1.24018 q^{6} -1.81708 q^{7} -3.06945 q^{8} -1.73174 q^{9} +1.00000 q^{11} +0.886611 q^{12} -3.00590 q^{13} -2.00104 q^{14} -1.80563 q^{16} -0.396094 q^{17} -1.90705 q^{18} -1.00000 q^{19} +2.04635 q^{21} +1.10124 q^{22} -2.47213 q^{23} +3.45673 q^{24} -3.31020 q^{26} +5.32875 q^{27} +1.43055 q^{28} -4.66419 q^{29} -10.5803 q^{31} +4.15048 q^{32} -1.12617 q^{33} -0.436192 q^{34} +1.36336 q^{36} +3.18261 q^{37} -1.10124 q^{38} +3.38516 q^{39} -9.74534 q^{41} +2.25351 q^{42} +3.52635 q^{43} -0.787279 q^{44} -2.72240 q^{46} -3.07500 q^{47} +2.03345 q^{48} -3.69820 q^{49} +0.446069 q^{51} +2.36648 q^{52} +1.32628 q^{53} +5.86821 q^{54} +5.57745 q^{56} +1.12617 q^{57} -5.13637 q^{58} -6.08186 q^{59} +13.2731 q^{61} -11.6514 q^{62} +3.14672 q^{63} +8.18192 q^{64} -1.24018 q^{66} +9.86746 q^{67} +0.311836 q^{68} +2.78404 q^{69} +3.14591 q^{71} +5.31549 q^{72} -10.7607 q^{73} +3.50480 q^{74} +0.787279 q^{76} -1.81708 q^{77} +3.72786 q^{78} +2.48793 q^{79} -0.805865 q^{81} -10.7319 q^{82} -8.40591 q^{83} -1.61105 q^{84} +3.88335 q^{86} +5.25268 q^{87} -3.06945 q^{88} -4.18002 q^{89} +5.46197 q^{91} +1.94626 q^{92} +11.9152 q^{93} -3.38630 q^{94} -4.67415 q^{96} +5.66478 q^{97} -4.07260 q^{98} -1.73174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 15 q^{7} + 15 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 15 q^{7} + 15 q^{8} + 19 q^{9} + 15 q^{11} + 9 q^{12} + 13 q^{13} + 9 q^{14} + 21 q^{16} + 11 q^{17} + 16 q^{18} - 15 q^{19} + 5 q^{22} + 10 q^{23} + 17 q^{24} - 17 q^{26} + 13 q^{27} + 30 q^{28} + 5 q^{29} + 6 q^{31} + 40 q^{32} + 4 q^{33} + 17 q^{34} + 28 q^{36} + 13 q^{37} - 5 q^{38} - 22 q^{39} + 30 q^{42} + 36 q^{43} + 17 q^{44} + 13 q^{46} - 6 q^{47} + 14 q^{48} + 16 q^{49} + 4 q^{51} + 50 q^{52} + 9 q^{53} + 9 q^{54} - 18 q^{56} - 4 q^{57} + 2 q^{58} - 7 q^{59} - 2 q^{61} + 11 q^{62} + 39 q^{63} + 17 q^{64} - q^{66} + 35 q^{67} - 18 q^{68} - 9 q^{69} + 13 q^{71} + 68 q^{72} + 2 q^{73} + 13 q^{74} - 17 q^{76} + 15 q^{77} - 10 q^{78} + 6 q^{79} + 11 q^{81} + 14 q^{82} + 30 q^{83} - 6 q^{84} - 25 q^{86} + 19 q^{87} + 15 q^{88} + 55 q^{89} + 26 q^{91} - 18 q^{92} + 14 q^{93} - 22 q^{94} - 17 q^{96} + 28 q^{97} - 22 q^{98} + 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10124 0.778691 0.389346 0.921092i \(-0.372701\pi\)
0.389346 + 0.921092i \(0.372701\pi\)
\(3\) −1.12617 −0.650195 −0.325098 0.945680i \(-0.605397\pi\)
−0.325098 + 0.945680i \(0.605397\pi\)
\(4\) −0.787279 −0.393640
\(5\) 0 0
\(6\) −1.24018 −0.506301
\(7\) −1.81708 −0.686793 −0.343397 0.939190i \(-0.611578\pi\)
−0.343397 + 0.939190i \(0.611578\pi\)
\(8\) −3.06945 −1.08522
\(9\) −1.73174 −0.577246
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0.886611 0.255943
\(13\) −3.00590 −0.833687 −0.416843 0.908978i \(-0.636864\pi\)
−0.416843 + 0.908978i \(0.636864\pi\)
\(14\) −2.00104 −0.534800
\(15\) 0 0
\(16\) −1.80563 −0.451408
\(17\) −0.396094 −0.0960668 −0.0480334 0.998846i \(-0.515295\pi\)
−0.0480334 + 0.998846i \(0.515295\pi\)
\(18\) −1.90705 −0.449497
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.04635 0.446550
\(22\) 1.10124 0.234784
\(23\) −2.47213 −0.515475 −0.257737 0.966215i \(-0.582977\pi\)
−0.257737 + 0.966215i \(0.582977\pi\)
\(24\) 3.45673 0.705602
\(25\) 0 0
\(26\) −3.31020 −0.649185
\(27\) 5.32875 1.02552
\(28\) 1.43055 0.270349
\(29\) −4.66419 −0.866118 −0.433059 0.901366i \(-0.642566\pi\)
−0.433059 + 0.901366i \(0.642566\pi\)
\(30\) 0 0
\(31\) −10.5803 −1.90027 −0.950135 0.311838i \(-0.899055\pi\)
−0.950135 + 0.311838i \(0.899055\pi\)
\(32\) 4.15048 0.733708
\(33\) −1.12617 −0.196041
\(34\) −0.436192 −0.0748064
\(35\) 0 0
\(36\) 1.36336 0.227227
\(37\) 3.18261 0.523217 0.261609 0.965174i \(-0.415747\pi\)
0.261609 + 0.965174i \(0.415747\pi\)
\(38\) −1.10124 −0.178644
\(39\) 3.38516 0.542059
\(40\) 0 0
\(41\) −9.74534 −1.52197 −0.760983 0.648772i \(-0.775283\pi\)
−0.760983 + 0.648772i \(0.775283\pi\)
\(42\) 2.25351 0.347724
\(43\) 3.52635 0.537764 0.268882 0.963173i \(-0.413346\pi\)
0.268882 + 0.963173i \(0.413346\pi\)
\(44\) −0.787279 −0.118687
\(45\) 0 0
\(46\) −2.72240 −0.401396
\(47\) −3.07500 −0.448535 −0.224267 0.974528i \(-0.571999\pi\)
−0.224267 + 0.974528i \(0.571999\pi\)
\(48\) 2.03345 0.293503
\(49\) −3.69820 −0.528315
\(50\) 0 0
\(51\) 0.446069 0.0624622
\(52\) 2.36648 0.328172
\(53\) 1.32628 0.182179 0.0910893 0.995843i \(-0.470965\pi\)
0.0910893 + 0.995843i \(0.470965\pi\)
\(54\) 5.86821 0.798562
\(55\) 0 0
\(56\) 5.57745 0.745319
\(57\) 1.12617 0.149165
\(58\) −5.13637 −0.674439
\(59\) −6.08186 −0.791791 −0.395895 0.918296i \(-0.629566\pi\)
−0.395895 + 0.918296i \(0.629566\pi\)
\(60\) 0 0
\(61\) 13.2731 1.69944 0.849721 0.527233i \(-0.176770\pi\)
0.849721 + 0.527233i \(0.176770\pi\)
\(62\) −11.6514 −1.47972
\(63\) 3.14672 0.396449
\(64\) 8.18192 1.02274
\(65\) 0 0
\(66\) −1.24018 −0.152656
\(67\) 9.86746 1.20550 0.602751 0.797930i \(-0.294071\pi\)
0.602751 + 0.797930i \(0.294071\pi\)
\(68\) 0.311836 0.0378157
\(69\) 2.78404 0.335159
\(70\) 0 0
\(71\) 3.14591 0.373351 0.186675 0.982422i \(-0.440229\pi\)
0.186675 + 0.982422i \(0.440229\pi\)
\(72\) 5.31549 0.626436
\(73\) −10.7607 −1.25944 −0.629720 0.776822i \(-0.716830\pi\)
−0.629720 + 0.776822i \(0.716830\pi\)
\(74\) 3.50480 0.407425
\(75\) 0 0
\(76\) 0.787279 0.0903071
\(77\) −1.81708 −0.207076
\(78\) 3.72786 0.422097
\(79\) 2.48793 0.279914 0.139957 0.990158i \(-0.455304\pi\)
0.139957 + 0.990158i \(0.455304\pi\)
\(80\) 0 0
\(81\) −0.805865 −0.0895405
\(82\) −10.7319 −1.18514
\(83\) −8.40591 −0.922668 −0.461334 0.887227i \(-0.652629\pi\)
−0.461334 + 0.887227i \(0.652629\pi\)
\(84\) −1.61105 −0.175780
\(85\) 0 0
\(86\) 3.88335 0.418752
\(87\) 5.25268 0.563146
\(88\) −3.06945 −0.327205
\(89\) −4.18002 −0.443081 −0.221540 0.975151i \(-0.571108\pi\)
−0.221540 + 0.975151i \(0.571108\pi\)
\(90\) 0 0
\(91\) 5.46197 0.572570
\(92\) 1.94626 0.202911
\(93\) 11.9152 1.23555
\(94\) −3.38630 −0.349270
\(95\) 0 0
\(96\) −4.67415 −0.477053
\(97\) 5.66478 0.575172 0.287586 0.957755i \(-0.407147\pi\)
0.287586 + 0.957755i \(0.407147\pi\)
\(98\) −4.07260 −0.411394
\(99\) −1.73174 −0.174046
\(100\) 0 0
\(101\) 8.17189 0.813134 0.406567 0.913621i \(-0.366726\pi\)
0.406567 + 0.913621i \(0.366726\pi\)
\(102\) 0.491227 0.0486388
\(103\) −5.11727 −0.504219 −0.252110 0.967699i \(-0.581124\pi\)
−0.252110 + 0.967699i \(0.581124\pi\)
\(104\) 9.22647 0.904729
\(105\) 0 0
\(106\) 1.46055 0.141861
\(107\) 11.0610 1.06931 0.534653 0.845072i \(-0.320442\pi\)
0.534653 + 0.845072i \(0.320442\pi\)
\(108\) −4.19521 −0.403684
\(109\) 1.77465 0.169981 0.0849904 0.996382i \(-0.472914\pi\)
0.0849904 + 0.996382i \(0.472914\pi\)
\(110\) 0 0
\(111\) −3.58416 −0.340193
\(112\) 3.28099 0.310024
\(113\) 17.0343 1.60245 0.801225 0.598363i \(-0.204182\pi\)
0.801225 + 0.598363i \(0.204182\pi\)
\(114\) 1.24018 0.116154
\(115\) 0 0
\(116\) 3.67202 0.340938
\(117\) 5.20543 0.481242
\(118\) −6.69756 −0.616561
\(119\) 0.719735 0.0659780
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 14.6168 1.32334
\(123\) 10.9749 0.989575
\(124\) 8.32962 0.748022
\(125\) 0 0
\(126\) 3.46528 0.308711
\(127\) 8.14604 0.722844 0.361422 0.932402i \(-0.382291\pi\)
0.361422 + 0.932402i \(0.382291\pi\)
\(128\) 0.709272 0.0626913
\(129\) −3.97128 −0.349651
\(130\) 0 0
\(131\) −10.3533 −0.904569 −0.452284 0.891874i \(-0.649391\pi\)
−0.452284 + 0.891874i \(0.649391\pi\)
\(132\) 0.886611 0.0771696
\(133\) 1.81708 0.157561
\(134\) 10.8664 0.938714
\(135\) 0 0
\(136\) 1.21579 0.104253
\(137\) −0.222099 −0.0189752 −0.00948761 0.999955i \(-0.503020\pi\)
−0.00948761 + 0.999955i \(0.503020\pi\)
\(138\) 3.06589 0.260986
\(139\) 1.52039 0.128958 0.0644790 0.997919i \(-0.479461\pi\)
0.0644790 + 0.997919i \(0.479461\pi\)
\(140\) 0 0
\(141\) 3.46298 0.291635
\(142\) 3.46439 0.290725
\(143\) −3.00590 −0.251366
\(144\) 3.12688 0.260574
\(145\) 0 0
\(146\) −11.8500 −0.980715
\(147\) 4.16481 0.343508
\(148\) −2.50560 −0.205959
\(149\) 13.4208 1.09947 0.549737 0.835338i \(-0.314728\pi\)
0.549737 + 0.835338i \(0.314728\pi\)
\(150\) 0 0
\(151\) −1.77240 −0.144236 −0.0721180 0.997396i \(-0.522976\pi\)
−0.0721180 + 0.997396i \(0.522976\pi\)
\(152\) 3.06945 0.248965
\(153\) 0.685931 0.0554542
\(154\) −2.00104 −0.161248
\(155\) 0 0
\(156\) −2.66506 −0.213376
\(157\) 17.6002 1.40465 0.702326 0.711856i \(-0.252145\pi\)
0.702326 + 0.711856i \(0.252145\pi\)
\(158\) 2.73980 0.217967
\(159\) −1.49362 −0.118452
\(160\) 0 0
\(161\) 4.49207 0.354024
\(162\) −0.887447 −0.0697244
\(163\) 13.7583 1.07763 0.538816 0.842423i \(-0.318872\pi\)
0.538816 + 0.842423i \(0.318872\pi\)
\(164\) 7.67230 0.599106
\(165\) 0 0
\(166\) −9.25689 −0.718474
\(167\) −4.42753 −0.342612 −0.171306 0.985218i \(-0.554799\pi\)
−0.171306 + 0.985218i \(0.554799\pi\)
\(168\) −6.28117 −0.484603
\(169\) −3.96457 −0.304967
\(170\) 0 0
\(171\) 1.73174 0.132429
\(172\) −2.77622 −0.211685
\(173\) 8.62772 0.655953 0.327977 0.944686i \(-0.393633\pi\)
0.327977 + 0.944686i \(0.393633\pi\)
\(174\) 5.78444 0.438517
\(175\) 0 0
\(176\) −1.80563 −0.136105
\(177\) 6.84922 0.514819
\(178\) −4.60319 −0.345023
\(179\) 4.62285 0.345528 0.172764 0.984963i \(-0.444730\pi\)
0.172764 + 0.984963i \(0.444730\pi\)
\(180\) 0 0
\(181\) −3.43691 −0.255464 −0.127732 0.991809i \(-0.540770\pi\)
−0.127732 + 0.991809i \(0.540770\pi\)
\(182\) 6.01492 0.445856
\(183\) −14.9477 −1.10497
\(184\) 7.58808 0.559401
\(185\) 0 0
\(186\) 13.1214 0.962110
\(187\) −0.396094 −0.0289652
\(188\) 2.42088 0.176561
\(189\) −9.68278 −0.704319
\(190\) 0 0
\(191\) 5.94862 0.430427 0.215213 0.976567i \(-0.430955\pi\)
0.215213 + 0.976567i \(0.430955\pi\)
\(192\) −9.21424 −0.664981
\(193\) −6.33082 −0.455702 −0.227851 0.973696i \(-0.573170\pi\)
−0.227851 + 0.973696i \(0.573170\pi\)
\(194\) 6.23826 0.447881
\(195\) 0 0
\(196\) 2.91152 0.207966
\(197\) −10.9220 −0.778163 −0.389082 0.921203i \(-0.627208\pi\)
−0.389082 + 0.921203i \(0.627208\pi\)
\(198\) −1.90705 −0.135528
\(199\) −17.0111 −1.20588 −0.602941 0.797786i \(-0.706005\pi\)
−0.602941 + 0.797786i \(0.706005\pi\)
\(200\) 0 0
\(201\) −11.1124 −0.783811
\(202\) 8.99918 0.633180
\(203\) 8.47523 0.594844
\(204\) −0.351181 −0.0245876
\(205\) 0 0
\(206\) −5.63532 −0.392631
\(207\) 4.28108 0.297556
\(208\) 5.42755 0.376333
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 4.62775 0.318588 0.159294 0.987231i \(-0.449078\pi\)
0.159294 + 0.987231i \(0.449078\pi\)
\(212\) −1.04415 −0.0717127
\(213\) −3.54283 −0.242751
\(214\) 12.1808 0.832659
\(215\) 0 0
\(216\) −16.3563 −1.11291
\(217\) 19.2252 1.30509
\(218\) 1.95431 0.132363
\(219\) 12.1183 0.818882
\(220\) 0 0
\(221\) 1.19062 0.0800896
\(222\) −3.94700 −0.264906
\(223\) −6.92101 −0.463465 −0.231733 0.972780i \(-0.574439\pi\)
−0.231733 + 0.972780i \(0.574439\pi\)
\(224\) −7.54177 −0.503905
\(225\) 0 0
\(226\) 18.7588 1.24781
\(227\) 20.9784 1.39238 0.696192 0.717855i \(-0.254876\pi\)
0.696192 + 0.717855i \(0.254876\pi\)
\(228\) −0.886611 −0.0587173
\(229\) −4.01914 −0.265592 −0.132796 0.991143i \(-0.542396\pi\)
−0.132796 + 0.991143i \(0.542396\pi\)
\(230\) 0 0
\(231\) 2.04635 0.134640
\(232\) 14.3165 0.939925
\(233\) 6.92311 0.453548 0.226774 0.973947i \(-0.427182\pi\)
0.226774 + 0.973947i \(0.427182\pi\)
\(234\) 5.73241 0.374739
\(235\) 0 0
\(236\) 4.78812 0.311680
\(237\) −2.80184 −0.181999
\(238\) 0.792598 0.0513765
\(239\) 19.6937 1.27388 0.636941 0.770913i \(-0.280200\pi\)
0.636941 + 0.770913i \(0.280200\pi\)
\(240\) 0 0
\(241\) 0.140555 0.00905396 0.00452698 0.999990i \(-0.498559\pi\)
0.00452698 + 0.999990i \(0.498559\pi\)
\(242\) 1.10124 0.0707901
\(243\) −15.0787 −0.967299
\(244\) −10.4496 −0.668968
\(245\) 0 0
\(246\) 12.0860 0.770574
\(247\) 3.00590 0.191261
\(248\) 32.4756 2.06220
\(249\) 9.46649 0.599914
\(250\) 0 0
\(251\) 2.70575 0.170786 0.0853928 0.996347i \(-0.472785\pi\)
0.0853928 + 0.996347i \(0.472785\pi\)
\(252\) −2.47734 −0.156058
\(253\) −2.47213 −0.155421
\(254\) 8.97071 0.562872
\(255\) 0 0
\(256\) −15.5828 −0.973923
\(257\) 10.3982 0.648622 0.324311 0.945950i \(-0.394868\pi\)
0.324311 + 0.945950i \(0.394868\pi\)
\(258\) −4.37331 −0.272271
\(259\) −5.78306 −0.359342
\(260\) 0 0
\(261\) 8.07716 0.499964
\(262\) −11.4014 −0.704380
\(263\) −23.0218 −1.41959 −0.709793 0.704410i \(-0.751211\pi\)
−0.709793 + 0.704410i \(0.751211\pi\)
\(264\) 3.45673 0.212747
\(265\) 0 0
\(266\) 2.00104 0.122692
\(267\) 4.70741 0.288089
\(268\) −7.76844 −0.474533
\(269\) −5.97611 −0.364370 −0.182185 0.983264i \(-0.558317\pi\)
−0.182185 + 0.983264i \(0.558317\pi\)
\(270\) 0 0
\(271\) −30.7969 −1.87078 −0.935388 0.353623i \(-0.884950\pi\)
−0.935388 + 0.353623i \(0.884950\pi\)
\(272\) 0.715200 0.0433653
\(273\) −6.15112 −0.372282
\(274\) −0.244584 −0.0147758
\(275\) 0 0
\(276\) −2.19182 −0.131932
\(277\) −14.0355 −0.843311 −0.421655 0.906756i \(-0.638551\pi\)
−0.421655 + 0.906756i \(0.638551\pi\)
\(278\) 1.67431 0.100419
\(279\) 18.3222 1.09692
\(280\) 0 0
\(281\) −12.9615 −0.773221 −0.386610 0.922243i \(-0.626354\pi\)
−0.386610 + 0.922243i \(0.626354\pi\)
\(282\) 3.81355 0.227094
\(283\) 25.3050 1.50423 0.752114 0.659033i \(-0.229034\pi\)
0.752114 + 0.659033i \(0.229034\pi\)
\(284\) −2.47671 −0.146966
\(285\) 0 0
\(286\) −3.31020 −0.195737
\(287\) 17.7081 1.04528
\(288\) −7.18754 −0.423530
\(289\) −16.8431 −0.990771
\(290\) 0 0
\(291\) −6.37952 −0.373974
\(292\) 8.47164 0.495765
\(293\) 22.9413 1.34025 0.670123 0.742250i \(-0.266241\pi\)
0.670123 + 0.742250i \(0.266241\pi\)
\(294\) 4.58644 0.267487
\(295\) 0 0
\(296\) −9.76886 −0.567803
\(297\) 5.32875 0.309205
\(298\) 14.7795 0.856151
\(299\) 7.43097 0.429744
\(300\) 0 0
\(301\) −6.40768 −0.369333
\(302\) −1.95183 −0.112315
\(303\) −9.20295 −0.528696
\(304\) 1.80563 0.103560
\(305\) 0 0
\(306\) 0.755371 0.0431817
\(307\) 11.0205 0.628971 0.314485 0.949262i \(-0.398168\pi\)
0.314485 + 0.949262i \(0.398168\pi\)
\(308\) 1.43055 0.0815133
\(309\) 5.76292 0.327841
\(310\) 0 0
\(311\) 14.0537 0.796913 0.398456 0.917187i \(-0.369546\pi\)
0.398456 + 0.917187i \(0.369546\pi\)
\(312\) −10.3906 −0.588251
\(313\) −15.0295 −0.849519 −0.424759 0.905306i \(-0.639641\pi\)
−0.424759 + 0.905306i \(0.639641\pi\)
\(314\) 19.3820 1.09379
\(315\) 0 0
\(316\) −1.95870 −0.110185
\(317\) −26.7125 −1.50033 −0.750163 0.661253i \(-0.770025\pi\)
−0.750163 + 0.661253i \(0.770025\pi\)
\(318\) −1.64483 −0.0922373
\(319\) −4.66419 −0.261144
\(320\) 0 0
\(321\) −12.4566 −0.695257
\(322\) 4.94683 0.275676
\(323\) 0.396094 0.0220392
\(324\) 0.634441 0.0352467
\(325\) 0 0
\(326\) 15.1511 0.839143
\(327\) −1.99856 −0.110521
\(328\) 29.9129 1.65166
\(329\) 5.58753 0.308051
\(330\) 0 0
\(331\) 18.3065 1.00622 0.503109 0.864223i \(-0.332190\pi\)
0.503109 + 0.864223i \(0.332190\pi\)
\(332\) 6.61780 0.363199
\(333\) −5.51144 −0.302025
\(334\) −4.87575 −0.266789
\(335\) 0 0
\(336\) −3.69495 −0.201576
\(337\) 3.55269 0.193527 0.0967636 0.995307i \(-0.469151\pi\)
0.0967636 + 0.995307i \(0.469151\pi\)
\(338\) −4.36592 −0.237475
\(339\) −19.1835 −1.04191
\(340\) 0 0
\(341\) −10.5803 −0.572953
\(342\) 1.90705 0.103122
\(343\) 19.4395 1.04964
\(344\) −10.8240 −0.583589
\(345\) 0 0
\(346\) 9.50116 0.510785
\(347\) −13.9284 −0.747713 −0.373857 0.927486i \(-0.621965\pi\)
−0.373857 + 0.927486i \(0.621965\pi\)
\(348\) −4.13532 −0.221677
\(349\) −2.94165 −0.157463 −0.0787313 0.996896i \(-0.525087\pi\)
−0.0787313 + 0.996896i \(0.525087\pi\)
\(350\) 0 0
\(351\) −16.0177 −0.854960
\(352\) 4.15048 0.221221
\(353\) −3.34914 −0.178257 −0.0891283 0.996020i \(-0.528408\pi\)
−0.0891283 + 0.996020i \(0.528408\pi\)
\(354\) 7.54260 0.400885
\(355\) 0 0
\(356\) 3.29084 0.174414
\(357\) −0.810545 −0.0428986
\(358\) 5.09085 0.269060
\(359\) −17.3050 −0.913321 −0.456660 0.889641i \(-0.650955\pi\)
−0.456660 + 0.889641i \(0.650955\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −3.78485 −0.198927
\(363\) −1.12617 −0.0591087
\(364\) −4.30010 −0.225386
\(365\) 0 0
\(366\) −16.4610 −0.860430
\(367\) 2.84237 0.148370 0.0741851 0.997244i \(-0.476364\pi\)
0.0741851 + 0.997244i \(0.476364\pi\)
\(368\) 4.46376 0.232689
\(369\) 16.8764 0.878549
\(370\) 0 0
\(371\) −2.40996 −0.125119
\(372\) −9.38057 −0.486360
\(373\) 31.3251 1.62195 0.810976 0.585079i \(-0.198936\pi\)
0.810976 + 0.585079i \(0.198936\pi\)
\(374\) −0.436192 −0.0225550
\(375\) 0 0
\(376\) 9.43856 0.486757
\(377\) 14.0201 0.722071
\(378\) −10.6630 −0.548447
\(379\) 15.3932 0.790697 0.395349 0.918531i \(-0.370624\pi\)
0.395349 + 0.918531i \(0.370624\pi\)
\(380\) 0 0
\(381\) −9.17383 −0.469990
\(382\) 6.55083 0.335170
\(383\) 18.8395 0.962654 0.481327 0.876541i \(-0.340155\pi\)
0.481327 + 0.876541i \(0.340155\pi\)
\(384\) −0.798761 −0.0407616
\(385\) 0 0
\(386\) −6.97173 −0.354852
\(387\) −6.10672 −0.310422
\(388\) −4.45977 −0.226410
\(389\) −30.9839 −1.57095 −0.785473 0.618896i \(-0.787580\pi\)
−0.785473 + 0.618896i \(0.787580\pi\)
\(390\) 0 0
\(391\) 0.979194 0.0495200
\(392\) 11.3515 0.573335
\(393\) 11.6595 0.588146
\(394\) −12.0277 −0.605949
\(395\) 0 0
\(396\) 1.36336 0.0685115
\(397\) 9.73881 0.488777 0.244388 0.969677i \(-0.421413\pi\)
0.244388 + 0.969677i \(0.421413\pi\)
\(398\) −18.7332 −0.939010
\(399\) −2.04635 −0.102446
\(400\) 0 0
\(401\) −16.8539 −0.841642 −0.420821 0.907144i \(-0.638258\pi\)
−0.420821 + 0.907144i \(0.638258\pi\)
\(402\) −12.2374 −0.610347
\(403\) 31.8032 1.58423
\(404\) −6.43356 −0.320082
\(405\) 0 0
\(406\) 9.33322 0.463200
\(407\) 3.18261 0.157756
\(408\) −1.36919 −0.0677849
\(409\) 14.4968 0.716822 0.358411 0.933564i \(-0.383319\pi\)
0.358411 + 0.933564i \(0.383319\pi\)
\(410\) 0 0
\(411\) 0.250122 0.0123376
\(412\) 4.02872 0.198481
\(413\) 11.0513 0.543797
\(414\) 4.71448 0.231704
\(415\) 0 0
\(416\) −12.4759 −0.611682
\(417\) −1.71222 −0.0838479
\(418\) −1.10124 −0.0538632
\(419\) 23.5582 1.15089 0.575447 0.817839i \(-0.304828\pi\)
0.575447 + 0.817839i \(0.304828\pi\)
\(420\) 0 0
\(421\) 3.16377 0.154193 0.0770964 0.997024i \(-0.475435\pi\)
0.0770964 + 0.997024i \(0.475435\pi\)
\(422\) 5.09625 0.248081
\(423\) 5.32510 0.258915
\(424\) −4.07095 −0.197703
\(425\) 0 0
\(426\) −3.90149 −0.189028
\(427\) −24.1183 −1.16717
\(428\) −8.70808 −0.420921
\(429\) 3.38516 0.163437
\(430\) 0 0
\(431\) −22.3848 −1.07824 −0.539120 0.842229i \(-0.681243\pi\)
−0.539120 + 0.842229i \(0.681243\pi\)
\(432\) −9.62176 −0.462927
\(433\) −33.0415 −1.58787 −0.793937 0.608000i \(-0.791972\pi\)
−0.793937 + 0.608000i \(0.791972\pi\)
\(434\) 21.1715 1.01626
\(435\) 0 0
\(436\) −1.39715 −0.0669111
\(437\) 2.47213 0.118258
\(438\) 13.3452 0.637656
\(439\) −13.5183 −0.645193 −0.322597 0.946537i \(-0.604556\pi\)
−0.322597 + 0.946537i \(0.604556\pi\)
\(440\) 0 0
\(441\) 6.40432 0.304968
\(442\) 1.31115 0.0623651
\(443\) 26.2368 1.24655 0.623273 0.782004i \(-0.285803\pi\)
0.623273 + 0.782004i \(0.285803\pi\)
\(444\) 2.82173 0.133914
\(445\) 0 0
\(446\) −7.62167 −0.360896
\(447\) −15.1141 −0.714873
\(448\) −14.8672 −0.702411
\(449\) −37.8759 −1.78747 −0.893737 0.448591i \(-0.851926\pi\)
−0.893737 + 0.448591i \(0.851926\pi\)
\(450\) 0 0
\(451\) −9.74534 −0.458890
\(452\) −13.4107 −0.630788
\(453\) 1.99603 0.0937815
\(454\) 23.1022 1.08424
\(455\) 0 0
\(456\) −3.45673 −0.161876
\(457\) −8.11897 −0.379789 −0.189895 0.981804i \(-0.560815\pi\)
−0.189895 + 0.981804i \(0.560815\pi\)
\(458\) −4.42602 −0.206814
\(459\) −2.11068 −0.0985182
\(460\) 0 0
\(461\) 2.99911 0.139683 0.0698413 0.997558i \(-0.477751\pi\)
0.0698413 + 0.997558i \(0.477751\pi\)
\(462\) 2.25351 0.104843
\(463\) 20.0068 0.929795 0.464897 0.885365i \(-0.346091\pi\)
0.464897 + 0.885365i \(0.346091\pi\)
\(464\) 8.42181 0.390973
\(465\) 0 0
\(466\) 7.62397 0.353174
\(467\) 2.07746 0.0961333 0.0480667 0.998844i \(-0.484694\pi\)
0.0480667 + 0.998844i \(0.484694\pi\)
\(468\) −4.09813 −0.189436
\(469\) −17.9300 −0.827930
\(470\) 0 0
\(471\) −19.8209 −0.913298
\(472\) 18.6680 0.859264
\(473\) 3.52635 0.162142
\(474\) −3.08548 −0.141721
\(475\) 0 0
\(476\) −0.566633 −0.0259716
\(477\) −2.29677 −0.105162
\(478\) 21.6874 0.991960
\(479\) 39.1671 1.78959 0.894795 0.446478i \(-0.147322\pi\)
0.894795 + 0.446478i \(0.147322\pi\)
\(480\) 0 0
\(481\) −9.56659 −0.436199
\(482\) 0.154784 0.00705024
\(483\) −5.05884 −0.230185
\(484\) −0.787279 −0.0357854
\(485\) 0 0
\(486\) −16.6052 −0.753228
\(487\) −40.8687 −1.85194 −0.925968 0.377603i \(-0.876749\pi\)
−0.925968 + 0.377603i \(0.876749\pi\)
\(488\) −40.7410 −1.84426
\(489\) −15.4942 −0.700671
\(490\) 0 0
\(491\) −6.86419 −0.309777 −0.154888 0.987932i \(-0.549502\pi\)
−0.154888 + 0.987932i \(0.549502\pi\)
\(492\) −8.64033 −0.389536
\(493\) 1.84746 0.0832052
\(494\) 3.31020 0.148933
\(495\) 0 0
\(496\) 19.1041 0.857798
\(497\) −5.71638 −0.256415
\(498\) 10.4248 0.467148
\(499\) −28.2774 −1.26587 −0.632936 0.774204i \(-0.718150\pi\)
−0.632936 + 0.774204i \(0.718150\pi\)
\(500\) 0 0
\(501\) 4.98615 0.222765
\(502\) 2.97967 0.132989
\(503\) −0.0217862 −0.000971397 0 −0.000485698 1.00000i \(-0.500155\pi\)
−0.000485698 1.00000i \(0.500155\pi\)
\(504\) −9.65869 −0.430232
\(505\) 0 0
\(506\) −2.72240 −0.121025
\(507\) 4.46478 0.198288
\(508\) −6.41321 −0.284540
\(509\) 12.8569 0.569873 0.284936 0.958546i \(-0.408028\pi\)
0.284936 + 0.958546i \(0.408028\pi\)
\(510\) 0 0
\(511\) 19.5530 0.864975
\(512\) −18.5788 −0.821077
\(513\) −5.32875 −0.235270
\(514\) 11.4509 0.505077
\(515\) 0 0
\(516\) 3.12650 0.137637
\(517\) −3.07500 −0.135238
\(518\) −6.36852 −0.279817
\(519\) −9.71629 −0.426498
\(520\) 0 0
\(521\) 35.4800 1.55441 0.777203 0.629250i \(-0.216638\pi\)
0.777203 + 0.629250i \(0.216638\pi\)
\(522\) 8.89486 0.389317
\(523\) −31.9759 −1.39821 −0.699104 0.715020i \(-0.746417\pi\)
−0.699104 + 0.715020i \(0.746417\pi\)
\(524\) 8.15091 0.356074
\(525\) 0 0
\(526\) −25.3524 −1.10542
\(527\) 4.19077 0.182553
\(528\) 2.03345 0.0884946
\(529\) −16.8886 −0.734286
\(530\) 0 0
\(531\) 10.5322 0.457058
\(532\) −1.43055 −0.0620223
\(533\) 29.2935 1.26884
\(534\) 5.18397 0.224333
\(535\) 0 0
\(536\) −30.2877 −1.30823
\(537\) −5.20612 −0.224661
\(538\) −6.58111 −0.283732
\(539\) −3.69820 −0.159293
\(540\) 0 0
\(541\) 19.1990 0.825432 0.412716 0.910860i \(-0.364580\pi\)
0.412716 + 0.910860i \(0.364580\pi\)
\(542\) −33.9146 −1.45676
\(543\) 3.87055 0.166101
\(544\) −1.64398 −0.0704849
\(545\) 0 0
\(546\) −6.77383 −0.289893
\(547\) 19.1493 0.818764 0.409382 0.912363i \(-0.365744\pi\)
0.409382 + 0.912363i \(0.365744\pi\)
\(548\) 0.174854 0.00746940
\(549\) −22.9855 −0.980996
\(550\) 0 0
\(551\) 4.66419 0.198701
\(552\) −8.54548 −0.363720
\(553\) −4.52078 −0.192243
\(554\) −15.4564 −0.656679
\(555\) 0 0
\(556\) −1.19697 −0.0507630
\(557\) −20.7708 −0.880085 −0.440043 0.897977i \(-0.645037\pi\)
−0.440043 + 0.897977i \(0.645037\pi\)
\(558\) 20.1771 0.854165
\(559\) −10.5999 −0.448326
\(560\) 0 0
\(561\) 0.446069 0.0188331
\(562\) −14.2737 −0.602100
\(563\) 2.56588 0.108139 0.0540694 0.998537i \(-0.482781\pi\)
0.0540694 + 0.998537i \(0.482781\pi\)
\(564\) −2.72633 −0.114799
\(565\) 0 0
\(566\) 27.8668 1.17133
\(567\) 1.46432 0.0614958
\(568\) −9.65621 −0.405166
\(569\) 32.6425 1.36844 0.684221 0.729274i \(-0.260142\pi\)
0.684221 + 0.729274i \(0.260142\pi\)
\(570\) 0 0
\(571\) 26.8048 1.12175 0.560873 0.827902i \(-0.310465\pi\)
0.560873 + 0.827902i \(0.310465\pi\)
\(572\) 2.36648 0.0989476
\(573\) −6.69916 −0.279861
\(574\) 19.5008 0.813948
\(575\) 0 0
\(576\) −14.1689 −0.590373
\(577\) −35.1268 −1.46235 −0.731174 0.682191i \(-0.761027\pi\)
−0.731174 + 0.682191i \(0.761027\pi\)
\(578\) −18.5482 −0.771505
\(579\) 7.12959 0.296295
\(580\) 0 0
\(581\) 15.2742 0.633682
\(582\) −7.02535 −0.291210
\(583\) 1.32628 0.0549289
\(584\) 33.0293 1.36676
\(585\) 0 0
\(586\) 25.2638 1.04364
\(587\) −23.9743 −0.989523 −0.494762 0.869029i \(-0.664745\pi\)
−0.494762 + 0.869029i \(0.664745\pi\)
\(588\) −3.27887 −0.135218
\(589\) 10.5803 0.435952
\(590\) 0 0
\(591\) 12.3001 0.505958
\(592\) −5.74662 −0.236185
\(593\) 2.13888 0.0878333 0.0439166 0.999035i \(-0.486016\pi\)
0.0439166 + 0.999035i \(0.486016\pi\)
\(594\) 5.86821 0.240776
\(595\) 0 0
\(596\) −10.5659 −0.432796
\(597\) 19.1574 0.784059
\(598\) 8.18325 0.334638
\(599\) 34.6600 1.41617 0.708084 0.706128i \(-0.249560\pi\)
0.708084 + 0.706128i \(0.249560\pi\)
\(600\) 0 0
\(601\) −40.8041 −1.66443 −0.832216 0.554451i \(-0.812928\pi\)
−0.832216 + 0.554451i \(0.812928\pi\)
\(602\) −7.05637 −0.287596
\(603\) −17.0879 −0.695871
\(604\) 1.39537 0.0567770
\(605\) 0 0
\(606\) −10.1346 −0.411691
\(607\) 35.9560 1.45941 0.729704 0.683763i \(-0.239658\pi\)
0.729704 + 0.683763i \(0.239658\pi\)
\(608\) −4.15048 −0.168324
\(609\) −9.54455 −0.386765
\(610\) 0 0
\(611\) 9.24314 0.373937
\(612\) −0.540019 −0.0218290
\(613\) 37.5253 1.51563 0.757816 0.652468i \(-0.226266\pi\)
0.757816 + 0.652468i \(0.226266\pi\)
\(614\) 12.1361 0.489774
\(615\) 0 0
\(616\) 5.57745 0.224722
\(617\) 10.0204 0.403404 0.201702 0.979447i \(-0.435353\pi\)
0.201702 + 0.979447i \(0.435353\pi\)
\(618\) 6.34633 0.255287
\(619\) −29.6702 −1.19255 −0.596274 0.802781i \(-0.703353\pi\)
−0.596274 + 0.802781i \(0.703353\pi\)
\(620\) 0 0
\(621\) −13.1734 −0.528628
\(622\) 15.4764 0.620549
\(623\) 7.59544 0.304305
\(624\) −6.11235 −0.244690
\(625\) 0 0
\(626\) −16.5511 −0.661513
\(627\) 1.12617 0.0449749
\(628\) −13.8563 −0.552927
\(629\) −1.26061 −0.0502638
\(630\) 0 0
\(631\) 18.7254 0.745447 0.372723 0.927943i \(-0.378424\pi\)
0.372723 + 0.927943i \(0.378424\pi\)
\(632\) −7.63658 −0.303767
\(633\) −5.21164 −0.207144
\(634\) −29.4168 −1.16829
\(635\) 0 0
\(636\) 1.17590 0.0466273
\(637\) 11.1164 0.440449
\(638\) −5.13637 −0.203351
\(639\) −5.44789 −0.215515
\(640\) 0 0
\(641\) −25.4242 −1.00420 −0.502098 0.864811i \(-0.667438\pi\)
−0.502098 + 0.864811i \(0.667438\pi\)
\(642\) −13.7176 −0.541391
\(643\) 17.8870 0.705395 0.352697 0.935737i \(-0.385265\pi\)
0.352697 + 0.935737i \(0.385265\pi\)
\(644\) −3.53651 −0.139358
\(645\) 0 0
\(646\) 0.436192 0.0171618
\(647\) −7.30694 −0.287265 −0.143633 0.989631i \(-0.545878\pi\)
−0.143633 + 0.989631i \(0.545878\pi\)
\(648\) 2.47356 0.0971708
\(649\) −6.08186 −0.238734
\(650\) 0 0
\(651\) −21.6509 −0.848565
\(652\) −10.8316 −0.424199
\(653\) 4.36571 0.170843 0.0854217 0.996345i \(-0.472776\pi\)
0.0854217 + 0.996345i \(0.472776\pi\)
\(654\) −2.20089 −0.0860615
\(655\) 0 0
\(656\) 17.5965 0.687028
\(657\) 18.6346 0.727007
\(658\) 6.15319 0.239876
\(659\) −41.6526 −1.62255 −0.811277 0.584662i \(-0.801227\pi\)
−0.811277 + 0.584662i \(0.801227\pi\)
\(660\) 0 0
\(661\) 5.30624 0.206389 0.103194 0.994661i \(-0.467094\pi\)
0.103194 + 0.994661i \(0.467094\pi\)
\(662\) 20.1598 0.783533
\(663\) −1.34084 −0.0520739
\(664\) 25.8015 1.00129
\(665\) 0 0
\(666\) −6.06940 −0.235184
\(667\) 11.5305 0.446462
\(668\) 3.48570 0.134866
\(669\) 7.79424 0.301343
\(670\) 0 0
\(671\) 13.2731 0.512401
\(672\) 8.49332 0.327637
\(673\) 30.5025 1.17578 0.587892 0.808940i \(-0.299958\pi\)
0.587892 + 0.808940i \(0.299958\pi\)
\(674\) 3.91235 0.150698
\(675\) 0 0
\(676\) 3.12122 0.120047
\(677\) 30.1893 1.16027 0.580134 0.814521i \(-0.303000\pi\)
0.580134 + 0.814521i \(0.303000\pi\)
\(678\) −21.1256 −0.811323
\(679\) −10.2934 −0.395024
\(680\) 0 0
\(681\) −23.6253 −0.905322
\(682\) −11.6514 −0.446154
\(683\) 20.2522 0.774929 0.387464 0.921885i \(-0.373351\pi\)
0.387464 + 0.921885i \(0.373351\pi\)
\(684\) −1.36336 −0.0521294
\(685\) 0 0
\(686\) 21.4075 0.817343
\(687\) 4.52624 0.172687
\(688\) −6.36730 −0.242751
\(689\) −3.98667 −0.151880
\(690\) 0 0
\(691\) −5.43936 −0.206923 −0.103462 0.994633i \(-0.532992\pi\)
−0.103462 + 0.994633i \(0.532992\pi\)
\(692\) −6.79243 −0.258209
\(693\) 3.14672 0.119534
\(694\) −15.3384 −0.582238
\(695\) 0 0
\(696\) −16.1228 −0.611135
\(697\) 3.86007 0.146210
\(698\) −3.23945 −0.122615
\(699\) −7.79660 −0.294895
\(700\) 0 0
\(701\) −19.7193 −0.744789 −0.372394 0.928075i \(-0.621463\pi\)
−0.372394 + 0.928075i \(0.621463\pi\)
\(702\) −17.6392 −0.665750
\(703\) −3.18261 −0.120034
\(704\) 8.18192 0.308368
\(705\) 0 0
\(706\) −3.68819 −0.138807
\(707\) −14.8490 −0.558455
\(708\) −5.39225 −0.202653
\(709\) 18.2446 0.685191 0.342595 0.939483i \(-0.388694\pi\)
0.342595 + 0.939483i \(0.388694\pi\)
\(710\) 0 0
\(711\) −4.30845 −0.161579
\(712\) 12.8304 0.480838
\(713\) 26.1558 0.979541
\(714\) −0.892601 −0.0334048
\(715\) 0 0
\(716\) −3.63947 −0.136013
\(717\) −22.1785 −0.828271
\(718\) −19.0568 −0.711195
\(719\) 36.8064 1.37265 0.686323 0.727296i \(-0.259223\pi\)
0.686323 + 0.727296i \(0.259223\pi\)
\(720\) 0 0
\(721\) 9.29851 0.346295
\(722\) 1.10124 0.0409838
\(723\) −0.158289 −0.00588684
\(724\) 2.70581 0.100561
\(725\) 0 0
\(726\) −1.24018 −0.0460274
\(727\) 41.1500 1.52617 0.763085 0.646299i \(-0.223684\pi\)
0.763085 + 0.646299i \(0.223684\pi\)
\(728\) −16.7653 −0.621362
\(729\) 19.3988 0.718474
\(730\) 0 0
\(731\) −1.39677 −0.0516612
\(732\) 11.7680 0.434960
\(733\) −41.1579 −1.52020 −0.760100 0.649806i \(-0.774850\pi\)
−0.760100 + 0.649806i \(0.774850\pi\)
\(734\) 3.13012 0.115535
\(735\) 0 0
\(736\) −10.2605 −0.378208
\(737\) 9.86746 0.363472
\(738\) 18.5849 0.684119
\(739\) −29.5872 −1.08838 −0.544192 0.838961i \(-0.683164\pi\)
−0.544192 + 0.838961i \(0.683164\pi\)
\(740\) 0 0
\(741\) −3.38516 −0.124357
\(742\) −2.65394 −0.0974291
\(743\) 15.0223 0.551113 0.275557 0.961285i \(-0.411138\pi\)
0.275557 + 0.961285i \(0.411138\pi\)
\(744\) −36.5731 −1.34083
\(745\) 0 0
\(746\) 34.4963 1.26300
\(747\) 14.5568 0.532607
\(748\) 0.311836 0.0114019
\(749\) −20.0987 −0.734392
\(750\) 0 0
\(751\) 38.6495 1.41034 0.705171 0.709038i \(-0.250870\pi\)
0.705171 + 0.709038i \(0.250870\pi\)
\(752\) 5.55232 0.202472
\(753\) −3.04714 −0.111044
\(754\) 15.4394 0.562271
\(755\) 0 0
\(756\) 7.62305 0.277248
\(757\) 17.8737 0.649631 0.324815 0.945777i \(-0.394698\pi\)
0.324815 + 0.945777i \(0.394698\pi\)
\(758\) 16.9516 0.615709
\(759\) 2.78404 0.101054
\(760\) 0 0
\(761\) −39.7350 −1.44039 −0.720195 0.693771i \(-0.755948\pi\)
−0.720195 + 0.693771i \(0.755948\pi\)
\(762\) −10.1026 −0.365977
\(763\) −3.22469 −0.116742
\(764\) −4.68322 −0.169433
\(765\) 0 0
\(766\) 20.7467 0.749610
\(767\) 18.2815 0.660105
\(768\) 17.5489 0.633240
\(769\) −27.3872 −0.987609 −0.493804 0.869573i \(-0.664394\pi\)
−0.493804 + 0.869573i \(0.664394\pi\)
\(770\) 0 0
\(771\) −11.7102 −0.421731
\(772\) 4.98412 0.179382
\(773\) −35.8608 −1.28982 −0.644911 0.764258i \(-0.723106\pi\)
−0.644911 + 0.764258i \(0.723106\pi\)
\(774\) −6.72494 −0.241723
\(775\) 0 0
\(776\) −17.3878 −0.624185
\(777\) 6.51272 0.233642
\(778\) −34.1206 −1.22328
\(779\) 9.74534 0.349163
\(780\) 0 0
\(781\) 3.14591 0.112569
\(782\) 1.07832 0.0385608
\(783\) −24.8543 −0.888220
\(784\) 6.67760 0.238486
\(785\) 0 0
\(786\) 12.8399 0.457984
\(787\) −10.1175 −0.360649 −0.180324 0.983607i \(-0.557715\pi\)
−0.180324 + 0.983607i \(0.557715\pi\)
\(788\) 8.59870 0.306316
\(789\) 25.9265 0.923008
\(790\) 0 0
\(791\) −30.9527 −1.10055
\(792\) 5.31549 0.188878
\(793\) −39.8975 −1.41680
\(794\) 10.7247 0.380606
\(795\) 0 0
\(796\) 13.3925 0.474683
\(797\) −41.7207 −1.47782 −0.738911 0.673803i \(-0.764660\pi\)
−0.738911 + 0.673803i \(0.764660\pi\)
\(798\) −2.25351 −0.0797735
\(799\) 1.21799 0.0430893
\(800\) 0 0
\(801\) 7.23870 0.255767
\(802\) −18.5601 −0.655379
\(803\) −10.7607 −0.379735
\(804\) 8.74860 0.308539
\(805\) 0 0
\(806\) 35.0228 1.23363
\(807\) 6.73013 0.236912
\(808\) −25.0832 −0.882425
\(809\) 48.0804 1.69042 0.845209 0.534436i \(-0.179476\pi\)
0.845209 + 0.534436i \(0.179476\pi\)
\(810\) 0 0
\(811\) −33.1054 −1.16249 −0.581243 0.813730i \(-0.697434\pi\)
−0.581243 + 0.813730i \(0.697434\pi\)
\(812\) −6.67237 −0.234154
\(813\) 34.6825 1.21637
\(814\) 3.50480 0.122843
\(815\) 0 0
\(816\) −0.805437 −0.0281959
\(817\) −3.52635 −0.123371
\(818\) 15.9644 0.558183
\(819\) −9.45871 −0.330514
\(820\) 0 0
\(821\) 36.5920 1.27707 0.638535 0.769593i \(-0.279541\pi\)
0.638535 + 0.769593i \(0.279541\pi\)
\(822\) 0.275443 0.00960718
\(823\) −12.9128 −0.450110 −0.225055 0.974346i \(-0.572256\pi\)
−0.225055 + 0.974346i \(0.572256\pi\)
\(824\) 15.7072 0.547187
\(825\) 0 0
\(826\) 12.1700 0.423450
\(827\) −14.2210 −0.494512 −0.247256 0.968950i \(-0.579529\pi\)
−0.247256 + 0.968950i \(0.579529\pi\)
\(828\) −3.37041 −0.117130
\(829\) −49.9790 −1.73584 −0.867922 0.496701i \(-0.834545\pi\)
−0.867922 + 0.496701i \(0.834545\pi\)
\(830\) 0 0
\(831\) 15.8064 0.548317
\(832\) −24.5940 −0.852645
\(833\) 1.46484 0.0507535
\(834\) −1.88556 −0.0652916
\(835\) 0 0
\(836\) 0.787279 0.0272286
\(837\) −56.3795 −1.94876
\(838\) 25.9431 0.896191
\(839\) −35.3809 −1.22149 −0.610743 0.791829i \(-0.709129\pi\)
−0.610743 + 0.791829i \(0.709129\pi\)
\(840\) 0 0
\(841\) −7.24533 −0.249839
\(842\) 3.48406 0.120069
\(843\) 14.5969 0.502744
\(844\) −3.64333 −0.125409
\(845\) 0 0
\(846\) 5.86419 0.201615
\(847\) −1.81708 −0.0624358
\(848\) −2.39478 −0.0822369
\(849\) −28.4978 −0.978042
\(850\) 0 0
\(851\) −7.86781 −0.269705
\(852\) 2.78920 0.0955563
\(853\) 20.9094 0.715924 0.357962 0.933736i \(-0.383472\pi\)
0.357962 + 0.933736i \(0.383472\pi\)
\(854\) −26.5599 −0.908862
\(855\) 0 0
\(856\) −33.9512 −1.16043
\(857\) −21.5067 −0.734654 −0.367327 0.930092i \(-0.619727\pi\)
−0.367327 + 0.930092i \(0.619727\pi\)
\(858\) 3.72786 0.127267
\(859\) 47.9041 1.63447 0.817233 0.576307i \(-0.195507\pi\)
0.817233 + 0.576307i \(0.195507\pi\)
\(860\) 0 0
\(861\) −19.9424 −0.679633
\(862\) −24.6510 −0.839616
\(863\) −46.5232 −1.58367 −0.791834 0.610737i \(-0.790873\pi\)
−0.791834 + 0.610737i \(0.790873\pi\)
\(864\) 22.1168 0.752430
\(865\) 0 0
\(866\) −36.3865 −1.23646
\(867\) 18.9682 0.644195
\(868\) −15.1356 −0.513736
\(869\) 2.48793 0.0843973
\(870\) 0 0
\(871\) −29.6606 −1.00501
\(872\) −5.44721 −0.184466
\(873\) −9.80993 −0.332016
\(874\) 2.72240 0.0920865
\(875\) 0 0
\(876\) −9.54052 −0.322344
\(877\) 9.27067 0.313048 0.156524 0.987674i \(-0.449971\pi\)
0.156524 + 0.987674i \(0.449971\pi\)
\(878\) −14.8868 −0.502406
\(879\) −25.8358 −0.871421
\(880\) 0 0
\(881\) −16.1306 −0.543454 −0.271727 0.962374i \(-0.587595\pi\)
−0.271727 + 0.962374i \(0.587595\pi\)
\(882\) 7.05267 0.237476
\(883\) −0.0216069 −0.000727130 0 −0.000363565 1.00000i \(-0.500116\pi\)
−0.000363565 1.00000i \(0.500116\pi\)
\(884\) −0.937348 −0.0315264
\(885\) 0 0
\(886\) 28.8929 0.970674
\(887\) −42.0739 −1.41270 −0.706352 0.707860i \(-0.749661\pi\)
−0.706352 + 0.707860i \(0.749661\pi\)
\(888\) 11.0014 0.369183
\(889\) −14.8020 −0.496444
\(890\) 0 0
\(891\) −0.805865 −0.0269975
\(892\) 5.44877 0.182438
\(893\) 3.07500 0.102901
\(894\) −16.6442 −0.556665
\(895\) 0 0
\(896\) −1.28881 −0.0430560
\(897\) −8.36855 −0.279418
\(898\) −41.7103 −1.39189
\(899\) 49.3483 1.64586
\(900\) 0 0
\(901\) −0.525331 −0.0175013
\(902\) −10.7319 −0.357334
\(903\) 7.21614 0.240138
\(904\) −52.2859 −1.73900
\(905\) 0 0
\(906\) 2.19810 0.0730269
\(907\) −4.10956 −0.136456 −0.0682279 0.997670i \(-0.521735\pi\)
−0.0682279 + 0.997670i \(0.521735\pi\)
\(908\) −16.5159 −0.548098
\(909\) −14.1516 −0.469378
\(910\) 0 0
\(911\) 10.7860 0.357356 0.178678 0.983908i \(-0.442818\pi\)
0.178678 + 0.983908i \(0.442818\pi\)
\(912\) −2.03345 −0.0673343
\(913\) −8.40591 −0.278195
\(914\) −8.94090 −0.295739
\(915\) 0 0
\(916\) 3.16418 0.104548
\(917\) 18.8127 0.621252
\(918\) −2.32436 −0.0767153
\(919\) −32.3453 −1.06697 −0.533486 0.845809i \(-0.679118\pi\)
−0.533486 + 0.845809i \(0.679118\pi\)
\(920\) 0 0
\(921\) −12.4109 −0.408954
\(922\) 3.30273 0.108770
\(923\) −9.45628 −0.311257
\(924\) −1.61105 −0.0529996
\(925\) 0 0
\(926\) 22.0322 0.724023
\(927\) 8.86177 0.291059
\(928\) −19.3586 −0.635478
\(929\) −41.8124 −1.37182 −0.685910 0.727686i \(-0.740596\pi\)
−0.685910 + 0.727686i \(0.740596\pi\)
\(930\) 0 0
\(931\) 3.69820 0.121204
\(932\) −5.45042 −0.178534
\(933\) −15.8269 −0.518149
\(934\) 2.28777 0.0748582
\(935\) 0 0
\(936\) −15.9778 −0.522252
\(937\) −18.0548 −0.589825 −0.294913 0.955524i \(-0.595291\pi\)
−0.294913 + 0.955524i \(0.595291\pi\)
\(938\) −19.7452 −0.644702
\(939\) 16.9258 0.552353
\(940\) 0 0
\(941\) 19.9391 0.649997 0.324999 0.945714i \(-0.394636\pi\)
0.324999 + 0.945714i \(0.394636\pi\)
\(942\) −21.8275 −0.711177
\(943\) 24.0917 0.784535
\(944\) 10.9816 0.357421
\(945\) 0 0
\(946\) 3.88335 0.126259
\(947\) 7.78827 0.253085 0.126542 0.991961i \(-0.459612\pi\)
0.126542 + 0.991961i \(0.459612\pi\)
\(948\) 2.20583 0.0716419
\(949\) 32.3455 1.04998
\(950\) 0 0
\(951\) 30.0829 0.975504
\(952\) −2.20919 −0.0716004
\(953\) 47.5841 1.54140 0.770700 0.637199i \(-0.219907\pi\)
0.770700 + 0.637199i \(0.219907\pi\)
\(954\) −2.52929 −0.0818887
\(955\) 0 0
\(956\) −15.5045 −0.501450
\(957\) 5.25268 0.169795
\(958\) 43.1322 1.39354
\(959\) 0.403573 0.0130321
\(960\) 0 0
\(961\) 80.9419 2.61103
\(962\) −10.5351 −0.339664
\(963\) −19.1547 −0.617253
\(964\) −0.110656 −0.00356400
\(965\) 0 0
\(966\) −5.57097 −0.179243
\(967\) 52.8234 1.69869 0.849343 0.527841i \(-0.176998\pi\)
0.849343 + 0.527841i \(0.176998\pi\)
\(968\) −3.06945 −0.0986559
\(969\) −0.446069 −0.0143298
\(970\) 0 0
\(971\) 13.9120 0.446456 0.223228 0.974766i \(-0.428341\pi\)
0.223228 + 0.974766i \(0.428341\pi\)
\(972\) 11.8711 0.380767
\(973\) −2.76268 −0.0885675
\(974\) −45.0060 −1.44209
\(975\) 0 0
\(976\) −23.9663 −0.767142
\(977\) −6.97874 −0.223270 −0.111635 0.993749i \(-0.535609\pi\)
−0.111635 + 0.993749i \(0.535609\pi\)
\(978\) −17.0628 −0.545607
\(979\) −4.18002 −0.133594
\(980\) 0 0
\(981\) −3.07323 −0.0981207
\(982\) −7.55910 −0.241220
\(983\) −28.5372 −0.910197 −0.455098 0.890441i \(-0.650396\pi\)
−0.455098 + 0.890441i \(0.650396\pi\)
\(984\) −33.6870 −1.07390
\(985\) 0 0
\(986\) 2.03448 0.0647912
\(987\) −6.29252 −0.200293
\(988\) −2.36648 −0.0752878
\(989\) −8.71760 −0.277204
\(990\) 0 0
\(991\) 20.5503 0.652802 0.326401 0.945231i \(-0.394164\pi\)
0.326401 + 0.945231i \(0.394164\pi\)
\(992\) −43.9131 −1.39424
\(993\) −20.6163 −0.654238
\(994\) −6.29508 −0.199668
\(995\) 0 0
\(996\) −7.45277 −0.236150
\(997\) −17.1671 −0.543688 −0.271844 0.962341i \(-0.587634\pi\)
−0.271844 + 0.962341i \(0.587634\pi\)
\(998\) −31.1401 −0.985724
\(999\) 16.9593 0.536569
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 5225.2.a.x.1.9 yes 15
5.4 even 2 5225.2.a.s.1.7 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5225.2.a.s.1.7 15 5.4 even 2
5225.2.a.x.1.9 yes 15 1.1 even 1 trivial