Properties

Label 9405.2.a.v.1.5
Level $9405$
Weight $2$
Character 9405.1
Self dual yes
Analytic conductor $75.099$
Analytic rank $0$
Dimension $5$
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] = [9405,2,Mod(1,9405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9405, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9405.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9405.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: \(75.0993031010\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\Q(\zeta_{22})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.91899\) of defining polynomial
Character \(\chi\) \(=\) 9405.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.39788 q^{2} +3.74982 q^{4} -1.00000 q^{5} -2.89389 q^{7} +4.19584 q^{8} +O(q^{10})\) \(q+2.39788 q^{2} +3.74982 q^{4} -1.00000 q^{5} -2.89389 q^{7} +4.19584 q^{8} -2.39788 q^{10} +1.00000 q^{11} +4.73780 q^{13} -6.93920 q^{14} +2.56149 q^{16} +5.65389 q^{17} +1.00000 q^{19} -3.74982 q^{20} +2.39788 q^{22} +4.00714 q^{23} +1.00000 q^{25} +11.3607 q^{26} -10.8516 q^{28} -9.32825 q^{29} -6.60270 q^{31} -2.24955 q^{32} +13.5573 q^{34} +2.89389 q^{35} +6.07686 q^{37} +2.39788 q^{38} -4.19584 q^{40} -5.47333 q^{41} +10.9515 q^{43} +3.74982 q^{44} +9.60863 q^{46} +0.295438 q^{47} +1.37462 q^{49} +2.39788 q^{50} +17.7659 q^{52} +3.81149 q^{53} -1.00000 q^{55} -12.1423 q^{56} -22.3680 q^{58} +5.54910 q^{59} -1.01018 q^{61} -15.8325 q^{62} -10.5171 q^{64} -4.73780 q^{65} +6.98807 q^{67} +21.2010 q^{68} +6.93920 q^{70} +1.02085 q^{71} -0.202033 q^{73} +14.5716 q^{74} +3.74982 q^{76} -2.89389 q^{77} +7.28690 q^{79} -2.56149 q^{80} -13.1244 q^{82} +13.7041 q^{83} -5.65389 q^{85} +26.2603 q^{86} +4.19584 q^{88} +15.8152 q^{89} -13.7107 q^{91} +15.0260 q^{92} +0.708423 q^{94} -1.00000 q^{95} +4.81308 q^{97} +3.29618 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 3 q^{2} + 5 q^{4} - 5 q^{5} - 11 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 3 q^{2} + 5 q^{4} - 5 q^{5} - 11 q^{7} - 3 q^{8} - 3 q^{10} + 5 q^{11} + q^{13} - 3 q^{16} + 3 q^{17} + 5 q^{19} - 5 q^{20} + 3 q^{22} + 8 q^{23} + 5 q^{25} + 16 q^{26} - 22 q^{28} - 11 q^{29} - 5 q^{31} + 2 q^{32} + 4 q^{34} + 11 q^{35} - 9 q^{37} + 3 q^{38} + 3 q^{40} - 15 q^{41} - 13 q^{43} + 5 q^{44} + 18 q^{46} + 20 q^{47} + 20 q^{49} + 3 q^{50} + q^{52} + 5 q^{53} - 5 q^{55} - 33 q^{58} + 17 q^{59} + 3 q^{61} - 14 q^{62} - 17 q^{64} - q^{65} - 28 q^{67} + 25 q^{68} + 6 q^{71} - 16 q^{73} + 21 q^{74} + 5 q^{76} - 11 q^{77} + 3 q^{79} + 3 q^{80} + 2 q^{82} + 33 q^{83} - 3 q^{85} - 10 q^{86} - 3 q^{88} + 16 q^{89} - 22 q^{91} + 19 q^{92} - 10 q^{94} - 5 q^{95} - 14 q^{97} - 10 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.39788 1.69556 0.847778 0.530352i \(-0.177940\pi\)
0.847778 + 0.530352i \(0.177940\pi\)
\(3\) 0 0
\(4\) 3.74982 1.87491
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.89389 −1.09379 −0.546895 0.837201i \(-0.684190\pi\)
−0.546895 + 0.837201i \(0.684190\pi\)
\(8\) 4.19584 1.48345
\(9\) 0 0
\(10\) −2.39788 −0.758275
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 4.73780 1.31403 0.657015 0.753878i \(-0.271819\pi\)
0.657015 + 0.753878i \(0.271819\pi\)
\(14\) −6.93920 −1.85458
\(15\) 0 0
\(16\) 2.56149 0.640372
\(17\) 5.65389 1.37127 0.685635 0.727946i \(-0.259525\pi\)
0.685635 + 0.727946i \(0.259525\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) −3.74982 −0.838484
\(21\) 0 0
\(22\) 2.39788 0.511229
\(23\) 4.00714 0.835547 0.417773 0.908551i \(-0.362811\pi\)
0.417773 + 0.908551i \(0.362811\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 11.3607 2.22801
\(27\) 0 0
\(28\) −10.8516 −2.05075
\(29\) −9.32825 −1.73221 −0.866106 0.499860i \(-0.833385\pi\)
−0.866106 + 0.499860i \(0.833385\pi\)
\(30\) 0 0
\(31\) −6.60270 −1.18588 −0.592940 0.805247i \(-0.702033\pi\)
−0.592940 + 0.805247i \(0.702033\pi\)
\(32\) −2.24955 −0.397669
\(33\) 0 0
\(34\) 13.5573 2.32506
\(35\) 2.89389 0.489157
\(36\) 0 0
\(37\) 6.07686 0.999029 0.499515 0.866305i \(-0.333512\pi\)
0.499515 + 0.866305i \(0.333512\pi\)
\(38\) 2.39788 0.388987
\(39\) 0 0
\(40\) −4.19584 −0.663421
\(41\) −5.47333 −0.854791 −0.427395 0.904065i \(-0.640569\pi\)
−0.427395 + 0.904065i \(0.640569\pi\)
\(42\) 0 0
\(43\) 10.9515 1.67009 0.835043 0.550185i \(-0.185443\pi\)
0.835043 + 0.550185i \(0.185443\pi\)
\(44\) 3.74982 0.565306
\(45\) 0 0
\(46\) 9.60863 1.41672
\(47\) 0.295438 0.0430940 0.0215470 0.999768i \(-0.493141\pi\)
0.0215470 + 0.999768i \(0.493141\pi\)
\(48\) 0 0
\(49\) 1.37462 0.196375
\(50\) 2.39788 0.339111
\(51\) 0 0
\(52\) 17.7659 2.46368
\(53\) 3.81149 0.523549 0.261774 0.965129i \(-0.415692\pi\)
0.261774 + 0.965129i \(0.415692\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) −12.1423 −1.62259
\(57\) 0 0
\(58\) −22.3680 −2.93706
\(59\) 5.54910 0.722431 0.361215 0.932482i \(-0.382362\pi\)
0.361215 + 0.932482i \(0.382362\pi\)
\(60\) 0 0
\(61\) −1.01018 −0.129340 −0.0646700 0.997907i \(-0.520599\pi\)
−0.0646700 + 0.997907i \(0.520599\pi\)
\(62\) −15.8325 −2.01073
\(63\) 0 0
\(64\) −10.5171 −1.31464
\(65\) −4.73780 −0.587652
\(66\) 0 0
\(67\) 6.98807 0.853729 0.426864 0.904316i \(-0.359618\pi\)
0.426864 + 0.904316i \(0.359618\pi\)
\(68\) 21.2010 2.57100
\(69\) 0 0
\(70\) 6.93920 0.829393
\(71\) 1.02085 0.121152 0.0605761 0.998164i \(-0.480706\pi\)
0.0605761 + 0.998164i \(0.480706\pi\)
\(72\) 0 0
\(73\) −0.202033 −0.0236462 −0.0118231 0.999930i \(-0.503763\pi\)
−0.0118231 + 0.999930i \(0.503763\pi\)
\(74\) 14.5716 1.69391
\(75\) 0 0
\(76\) 3.74982 0.430133
\(77\) −2.89389 −0.329790
\(78\) 0 0
\(79\) 7.28690 0.819840 0.409920 0.912121i \(-0.365557\pi\)
0.409920 + 0.912121i \(0.365557\pi\)
\(80\) −2.56149 −0.286383
\(81\) 0 0
\(82\) −13.1244 −1.44935
\(83\) 13.7041 1.50422 0.752109 0.659039i \(-0.229037\pi\)
0.752109 + 0.659039i \(0.229037\pi\)
\(84\) 0 0
\(85\) −5.65389 −0.613250
\(86\) 26.2603 2.83172
\(87\) 0 0
\(88\) 4.19584 0.447278
\(89\) 15.8152 1.67641 0.838203 0.545359i \(-0.183606\pi\)
0.838203 + 0.545359i \(0.183606\pi\)
\(90\) 0 0
\(91\) −13.7107 −1.43727
\(92\) 15.0260 1.56657
\(93\) 0 0
\(94\) 0.708423 0.0730683
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 4.81308 0.488694 0.244347 0.969688i \(-0.421426\pi\)
0.244347 + 0.969688i \(0.421426\pi\)
\(98\) 3.29618 0.332964
\(99\) 0 0
\(100\) 3.74982 0.374982
\(101\) −1.76221 −0.175346 −0.0876730 0.996149i \(-0.527943\pi\)
−0.0876730 + 0.996149i \(0.527943\pi\)
\(102\) 0 0
\(103\) −5.53571 −0.545450 −0.272725 0.962092i \(-0.587925\pi\)
−0.272725 + 0.962092i \(0.587925\pi\)
\(104\) 19.8791 1.94930
\(105\) 0 0
\(106\) 9.13949 0.887706
\(107\) 4.32073 0.417701 0.208851 0.977948i \(-0.433028\pi\)
0.208851 + 0.977948i \(0.433028\pi\)
\(108\) 0 0
\(109\) −13.0039 −1.24555 −0.622776 0.782400i \(-0.713995\pi\)
−0.622776 + 0.782400i \(0.713995\pi\)
\(110\) −2.39788 −0.228629
\(111\) 0 0
\(112\) −7.41267 −0.700432
\(113\) 17.0047 1.59967 0.799833 0.600223i \(-0.204922\pi\)
0.799833 + 0.600223i \(0.204922\pi\)
\(114\) 0 0
\(115\) −4.00714 −0.373668
\(116\) −34.9792 −3.24774
\(117\) 0 0
\(118\) 13.3061 1.22492
\(119\) −16.3618 −1.49988
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −2.42228 −0.219303
\(123\) 0 0
\(124\) −24.7589 −2.22342
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.80245 −0.869826 −0.434913 0.900472i \(-0.643221\pi\)
−0.434913 + 0.900472i \(0.643221\pi\)
\(128\) −20.7197 −1.83138
\(129\) 0 0
\(130\) −11.3607 −0.996396
\(131\) 13.4383 1.17411 0.587053 0.809549i \(-0.300288\pi\)
0.587053 + 0.809549i \(0.300288\pi\)
\(132\) 0 0
\(133\) −2.89389 −0.250932
\(134\) 16.7565 1.44754
\(135\) 0 0
\(136\) 23.7228 2.03422
\(137\) 16.2122 1.38510 0.692549 0.721371i \(-0.256488\pi\)
0.692549 + 0.721371i \(0.256488\pi\)
\(138\) 0 0
\(139\) 19.0373 1.61472 0.807359 0.590060i \(-0.200896\pi\)
0.807359 + 0.590060i \(0.200896\pi\)
\(140\) 10.8516 0.917125
\(141\) 0 0
\(142\) 2.44787 0.205420
\(143\) 4.73780 0.396195
\(144\) 0 0
\(145\) 9.32825 0.774669
\(146\) −0.484451 −0.0400934
\(147\) 0 0
\(148\) 22.7871 1.87309
\(149\) 15.3234 1.25534 0.627670 0.778480i \(-0.284009\pi\)
0.627670 + 0.778480i \(0.284009\pi\)
\(150\) 0 0
\(151\) −1.25936 −0.102485 −0.0512426 0.998686i \(-0.516318\pi\)
−0.0512426 + 0.998686i \(0.516318\pi\)
\(152\) 4.19584 0.340328
\(153\) 0 0
\(154\) −6.93920 −0.559177
\(155\) 6.60270 0.530342
\(156\) 0 0
\(157\) 12.1861 0.972559 0.486279 0.873803i \(-0.338354\pi\)
0.486279 + 0.873803i \(0.338354\pi\)
\(158\) 17.4731 1.39008
\(159\) 0 0
\(160\) 2.24955 0.177843
\(161\) −11.5962 −0.913912
\(162\) 0 0
\(163\) 6.09722 0.477571 0.238786 0.971072i \(-0.423251\pi\)
0.238786 + 0.971072i \(0.423251\pi\)
\(164\) −20.5240 −1.60265
\(165\) 0 0
\(166\) 32.8607 2.55048
\(167\) −1.06720 −0.0825826 −0.0412913 0.999147i \(-0.513147\pi\)
−0.0412913 + 0.999147i \(0.513147\pi\)
\(168\) 0 0
\(169\) 9.44675 0.726673
\(170\) −13.5573 −1.03980
\(171\) 0 0
\(172\) 41.0661 3.13126
\(173\) 13.0289 0.990571 0.495286 0.868730i \(-0.335063\pi\)
0.495286 + 0.868730i \(0.335063\pi\)
\(174\) 0 0
\(175\) −2.89389 −0.218758
\(176\) 2.56149 0.193079
\(177\) 0 0
\(178\) 37.9229 2.84244
\(179\) −20.6273 −1.54176 −0.770878 0.636983i \(-0.780182\pi\)
−0.770878 + 0.636983i \(0.780182\pi\)
\(180\) 0 0
\(181\) −20.5908 −1.53050 −0.765251 0.643732i \(-0.777385\pi\)
−0.765251 + 0.643732i \(0.777385\pi\)
\(182\) −32.8766 −2.43697
\(183\) 0 0
\(184\) 16.8133 1.23950
\(185\) −6.07686 −0.446779
\(186\) 0 0
\(187\) 5.65389 0.413453
\(188\) 1.10784 0.0807973
\(189\) 0 0
\(190\) −2.39788 −0.173960
\(191\) −8.40047 −0.607837 −0.303918 0.952698i \(-0.598295\pi\)
−0.303918 + 0.952698i \(0.598295\pi\)
\(192\) 0 0
\(193\) 11.4982 0.827661 0.413830 0.910354i \(-0.364191\pi\)
0.413830 + 0.910354i \(0.364191\pi\)
\(194\) 11.5412 0.828607
\(195\) 0 0
\(196\) 5.15458 0.368185
\(197\) −27.0376 −1.92635 −0.963173 0.268883i \(-0.913345\pi\)
−0.963173 + 0.268883i \(0.913345\pi\)
\(198\) 0 0
\(199\) −5.18460 −0.367526 −0.183763 0.982971i \(-0.558828\pi\)
−0.183763 + 0.982971i \(0.558828\pi\)
\(200\) 4.19584 0.296691
\(201\) 0 0
\(202\) −4.22555 −0.297309
\(203\) 26.9950 1.89468
\(204\) 0 0
\(205\) 5.47333 0.382274
\(206\) −13.2740 −0.924840
\(207\) 0 0
\(208\) 12.1358 0.841467
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −21.5427 −1.48306 −0.741529 0.670921i \(-0.765899\pi\)
−0.741529 + 0.670921i \(0.765899\pi\)
\(212\) 14.2924 0.981606
\(213\) 0 0
\(214\) 10.3606 0.708235
\(215\) −10.9515 −0.746885
\(216\) 0 0
\(217\) 19.1075 1.29710
\(218\) −31.1818 −2.11190
\(219\) 0 0
\(220\) −3.74982 −0.252813
\(221\) 26.7870 1.80189
\(222\) 0 0
\(223\) −26.9600 −1.80537 −0.902687 0.430298i \(-0.858408\pi\)
−0.902687 + 0.430298i \(0.858408\pi\)
\(224\) 6.50997 0.434966
\(225\) 0 0
\(226\) 40.7751 2.71232
\(227\) −9.02570 −0.599057 −0.299528 0.954087i \(-0.596829\pi\)
−0.299528 + 0.954087i \(0.596829\pi\)
\(228\) 0 0
\(229\) −13.7697 −0.909926 −0.454963 0.890510i \(-0.650347\pi\)
−0.454963 + 0.890510i \(0.650347\pi\)
\(230\) −9.60863 −0.633575
\(231\) 0 0
\(232\) −39.1399 −2.56966
\(233\) 2.45587 0.160890 0.0804448 0.996759i \(-0.474366\pi\)
0.0804448 + 0.996759i \(0.474366\pi\)
\(234\) 0 0
\(235\) −0.295438 −0.0192722
\(236\) 20.8081 1.35449
\(237\) 0 0
\(238\) −39.2335 −2.54313
\(239\) 22.8439 1.47765 0.738825 0.673897i \(-0.235381\pi\)
0.738825 + 0.673897i \(0.235381\pi\)
\(240\) 0 0
\(241\) 16.1181 1.03826 0.519129 0.854696i \(-0.326256\pi\)
0.519129 + 0.854696i \(0.326256\pi\)
\(242\) 2.39788 0.154141
\(243\) 0 0
\(244\) −3.78798 −0.242501
\(245\) −1.37462 −0.0878215
\(246\) 0 0
\(247\) 4.73780 0.301459
\(248\) −27.7039 −1.75920
\(249\) 0 0
\(250\) −2.39788 −0.151655
\(251\) 18.8758 1.19143 0.595716 0.803195i \(-0.296868\pi\)
0.595716 + 0.803195i \(0.296868\pi\)
\(252\) 0 0
\(253\) 4.00714 0.251927
\(254\) −23.5051 −1.47484
\(255\) 0 0
\(256\) −28.6490 −1.79056
\(257\) −7.48029 −0.466608 −0.233304 0.972404i \(-0.574954\pi\)
−0.233304 + 0.972404i \(0.574954\pi\)
\(258\) 0 0
\(259\) −17.5858 −1.09273
\(260\) −17.7659 −1.10179
\(261\) 0 0
\(262\) 32.2233 1.99076
\(263\) 17.7703 1.09577 0.547883 0.836555i \(-0.315434\pi\)
0.547883 + 0.836555i \(0.315434\pi\)
\(264\) 0 0
\(265\) −3.81149 −0.234138
\(266\) −6.93920 −0.425470
\(267\) 0 0
\(268\) 26.2040 1.60066
\(269\) −25.9320 −1.58110 −0.790550 0.612398i \(-0.790205\pi\)
−0.790550 + 0.612398i \(0.790205\pi\)
\(270\) 0 0
\(271\) −16.2686 −0.988248 −0.494124 0.869391i \(-0.664511\pi\)
−0.494124 + 0.869391i \(0.664511\pi\)
\(272\) 14.4824 0.878122
\(273\) 0 0
\(274\) 38.8748 2.34851
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) −17.9217 −1.07681 −0.538405 0.842686i \(-0.680973\pi\)
−0.538405 + 0.842686i \(0.680973\pi\)
\(278\) 45.6490 2.73784
\(279\) 0 0
\(280\) 12.1423 0.725643
\(281\) 28.8563 1.72142 0.860712 0.509093i \(-0.170019\pi\)
0.860712 + 0.509093i \(0.170019\pi\)
\(282\) 0 0
\(283\) −10.7620 −0.639736 −0.319868 0.947462i \(-0.603639\pi\)
−0.319868 + 0.947462i \(0.603639\pi\)
\(284\) 3.82799 0.227149
\(285\) 0 0
\(286\) 11.3607 0.671770
\(287\) 15.8392 0.934961
\(288\) 0 0
\(289\) 14.9665 0.880380
\(290\) 22.3680 1.31349
\(291\) 0 0
\(292\) −0.757587 −0.0443345
\(293\) −5.14307 −0.300462 −0.150231 0.988651i \(-0.548002\pi\)
−0.150231 + 0.988651i \(0.548002\pi\)
\(294\) 0 0
\(295\) −5.54910 −0.323081
\(296\) 25.4975 1.48201
\(297\) 0 0
\(298\) 36.7436 2.12850
\(299\) 18.9850 1.09793
\(300\) 0 0
\(301\) −31.6924 −1.82672
\(302\) −3.01979 −0.173769
\(303\) 0 0
\(304\) 2.56149 0.146911
\(305\) 1.01018 0.0578427
\(306\) 0 0
\(307\) 28.1017 1.60385 0.801925 0.597425i \(-0.203809\pi\)
0.801925 + 0.597425i \(0.203809\pi\)
\(308\) −10.8516 −0.618326
\(309\) 0 0
\(310\) 15.8325 0.899224
\(311\) 14.1909 0.804692 0.402346 0.915488i \(-0.368195\pi\)
0.402346 + 0.915488i \(0.368195\pi\)
\(312\) 0 0
\(313\) −9.46083 −0.534758 −0.267379 0.963591i \(-0.586158\pi\)
−0.267379 + 0.963591i \(0.586158\pi\)
\(314\) 29.2208 1.64903
\(315\) 0 0
\(316\) 27.3245 1.53712
\(317\) 23.8673 1.34052 0.670260 0.742126i \(-0.266182\pi\)
0.670260 + 0.742126i \(0.266182\pi\)
\(318\) 0 0
\(319\) −9.32825 −0.522282
\(320\) 10.5171 0.587926
\(321\) 0 0
\(322\) −27.8064 −1.54959
\(323\) 5.65389 0.314591
\(324\) 0 0
\(325\) 4.73780 0.262806
\(326\) 14.6204 0.809748
\(327\) 0 0
\(328\) −22.9652 −1.26804
\(329\) −0.854966 −0.0471358
\(330\) 0 0
\(331\) −13.1843 −0.724674 −0.362337 0.932047i \(-0.618021\pi\)
−0.362337 + 0.932047i \(0.618021\pi\)
\(332\) 51.3877 2.82027
\(333\) 0 0
\(334\) −2.55902 −0.140023
\(335\) −6.98807 −0.381799
\(336\) 0 0
\(337\) 17.0148 0.926854 0.463427 0.886135i \(-0.346620\pi\)
0.463427 + 0.886135i \(0.346620\pi\)
\(338\) 22.6521 1.23211
\(339\) 0 0
\(340\) −21.2010 −1.14979
\(341\) −6.60270 −0.357556
\(342\) 0 0
\(343\) 16.2792 0.878997
\(344\) 45.9507 2.47750
\(345\) 0 0
\(346\) 31.2418 1.67957
\(347\) 30.2606 1.62447 0.812236 0.583329i \(-0.198250\pi\)
0.812236 + 0.583329i \(0.198250\pi\)
\(348\) 0 0
\(349\) 5.13463 0.274851 0.137425 0.990512i \(-0.456117\pi\)
0.137425 + 0.990512i \(0.456117\pi\)
\(350\) −6.93920 −0.370916
\(351\) 0 0
\(352\) −2.24955 −0.119902
\(353\) 10.5661 0.562376 0.281188 0.959653i \(-0.409272\pi\)
0.281188 + 0.959653i \(0.409272\pi\)
\(354\) 0 0
\(355\) −1.02085 −0.0541809
\(356\) 59.3040 3.14311
\(357\) 0 0
\(358\) −49.4617 −2.61413
\(359\) −16.5178 −0.871778 −0.435889 0.900000i \(-0.643566\pi\)
−0.435889 + 0.900000i \(0.643566\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −49.3742 −2.59505
\(363\) 0 0
\(364\) −51.4126 −2.69475
\(365\) 0.202033 0.0105749
\(366\) 0 0
\(367\) 19.8761 1.03752 0.518762 0.854919i \(-0.326393\pi\)
0.518762 + 0.854919i \(0.326393\pi\)
\(368\) 10.2642 0.535061
\(369\) 0 0
\(370\) −14.5716 −0.757539
\(371\) −11.0301 −0.572652
\(372\) 0 0
\(373\) −11.4151 −0.591052 −0.295526 0.955335i \(-0.595495\pi\)
−0.295526 + 0.955335i \(0.595495\pi\)
\(374\) 13.5573 0.701033
\(375\) 0 0
\(376\) 1.23961 0.0639280
\(377\) −44.1954 −2.27618
\(378\) 0 0
\(379\) 1.99925 0.102695 0.0513474 0.998681i \(-0.483648\pi\)
0.0513474 + 0.998681i \(0.483648\pi\)
\(380\) −3.74982 −0.192362
\(381\) 0 0
\(382\) −20.1433 −1.03062
\(383\) 7.07007 0.361264 0.180632 0.983551i \(-0.442186\pi\)
0.180632 + 0.983551i \(0.442186\pi\)
\(384\) 0 0
\(385\) 2.89389 0.147487
\(386\) 27.5713 1.40334
\(387\) 0 0
\(388\) 18.0481 0.916256
\(389\) −17.0237 −0.863135 −0.431568 0.902081i \(-0.642039\pi\)
−0.431568 + 0.902081i \(0.642039\pi\)
\(390\) 0 0
\(391\) 22.6559 1.14576
\(392\) 5.76771 0.291313
\(393\) 0 0
\(394\) −64.8327 −3.26623
\(395\) −7.28690 −0.366644
\(396\) 0 0
\(397\) −25.3590 −1.27273 −0.636366 0.771387i \(-0.719563\pi\)
−0.636366 + 0.771387i \(0.719563\pi\)
\(398\) −12.4320 −0.623161
\(399\) 0 0
\(400\) 2.56149 0.128074
\(401\) −19.6449 −0.981019 −0.490509 0.871436i \(-0.663189\pi\)
−0.490509 + 0.871436i \(0.663189\pi\)
\(402\) 0 0
\(403\) −31.2823 −1.55828
\(404\) −6.60795 −0.328758
\(405\) 0 0
\(406\) 64.7306 3.21253
\(407\) 6.07686 0.301219
\(408\) 0 0
\(409\) −28.6527 −1.41678 −0.708392 0.705819i \(-0.750579\pi\)
−0.708392 + 0.705819i \(0.750579\pi\)
\(410\) 13.1244 0.648167
\(411\) 0 0
\(412\) −20.7579 −1.02267
\(413\) −16.0585 −0.790187
\(414\) 0 0
\(415\) −13.7041 −0.672706
\(416\) −10.6579 −0.522548
\(417\) 0 0
\(418\) 2.39788 0.117284
\(419\) 2.80518 0.137042 0.0685211 0.997650i \(-0.478172\pi\)
0.0685211 + 0.997650i \(0.478172\pi\)
\(420\) 0 0
\(421\) 3.26165 0.158963 0.0794815 0.996836i \(-0.474674\pi\)
0.0794815 + 0.996836i \(0.474674\pi\)
\(422\) −51.6566 −2.51461
\(423\) 0 0
\(424\) 15.9924 0.776661
\(425\) 5.65389 0.274254
\(426\) 0 0
\(427\) 2.92335 0.141471
\(428\) 16.2020 0.783151
\(429\) 0 0
\(430\) −26.2603 −1.26639
\(431\) −32.7606 −1.57802 −0.789012 0.614378i \(-0.789407\pi\)
−0.789012 + 0.614378i \(0.789407\pi\)
\(432\) 0 0
\(433\) −21.8656 −1.05079 −0.525396 0.850858i \(-0.676083\pi\)
−0.525396 + 0.850858i \(0.676083\pi\)
\(434\) 45.8175 2.19931
\(435\) 0 0
\(436\) −48.7624 −2.33529
\(437\) 4.00714 0.191688
\(438\) 0 0
\(439\) 30.6280 1.46180 0.730898 0.682486i \(-0.239101\pi\)
0.730898 + 0.682486i \(0.239101\pi\)
\(440\) −4.19584 −0.200029
\(441\) 0 0
\(442\) 64.2319 3.05520
\(443\) −4.54914 −0.216136 −0.108068 0.994144i \(-0.534466\pi\)
−0.108068 + 0.994144i \(0.534466\pi\)
\(444\) 0 0
\(445\) −15.8152 −0.749711
\(446\) −64.6467 −3.06111
\(447\) 0 0
\(448\) 30.4355 1.43794
\(449\) −11.5308 −0.544172 −0.272086 0.962273i \(-0.587714\pi\)
−0.272086 + 0.962273i \(0.587714\pi\)
\(450\) 0 0
\(451\) −5.47333 −0.257729
\(452\) 63.7644 2.99923
\(453\) 0 0
\(454\) −21.6425 −1.01573
\(455\) 13.7107 0.642767
\(456\) 0 0
\(457\) 11.3778 0.532231 0.266115 0.963941i \(-0.414260\pi\)
0.266115 + 0.963941i \(0.414260\pi\)
\(458\) −33.0180 −1.54283
\(459\) 0 0
\(460\) −15.0260 −0.700593
\(461\) −4.37265 −0.203655 −0.101827 0.994802i \(-0.532469\pi\)
−0.101827 + 0.994802i \(0.532469\pi\)
\(462\) 0 0
\(463\) −9.31982 −0.433129 −0.216564 0.976268i \(-0.569485\pi\)
−0.216564 + 0.976268i \(0.569485\pi\)
\(464\) −23.8942 −1.10926
\(465\) 0 0
\(466\) 5.88888 0.272797
\(467\) 28.0711 1.29897 0.649487 0.760372i \(-0.274984\pi\)
0.649487 + 0.760372i \(0.274984\pi\)
\(468\) 0 0
\(469\) −20.2227 −0.933799
\(470\) −0.708423 −0.0326771
\(471\) 0 0
\(472\) 23.2831 1.07169
\(473\) 10.9515 0.503550
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) −61.3536 −2.81214
\(477\) 0 0
\(478\) 54.7769 2.50544
\(479\) 5.65184 0.258239 0.129120 0.991629i \(-0.458785\pi\)
0.129120 + 0.991629i \(0.458785\pi\)
\(480\) 0 0
\(481\) 28.7909 1.31275
\(482\) 38.6492 1.76042
\(483\) 0 0
\(484\) 3.74982 0.170446
\(485\) −4.81308 −0.218550
\(486\) 0 0
\(487\) −6.09349 −0.276122 −0.138061 0.990424i \(-0.544087\pi\)
−0.138061 + 0.990424i \(0.544087\pi\)
\(488\) −4.23855 −0.191870
\(489\) 0 0
\(490\) −3.29618 −0.148906
\(491\) −8.56286 −0.386436 −0.193218 0.981156i \(-0.561893\pi\)
−0.193218 + 0.981156i \(0.561893\pi\)
\(492\) 0 0
\(493\) −52.7409 −2.37533
\(494\) 11.3607 0.511140
\(495\) 0 0
\(496\) −16.9127 −0.759404
\(497\) −2.95422 −0.132515
\(498\) 0 0
\(499\) −1.35537 −0.0606749 −0.0303374 0.999540i \(-0.509658\pi\)
−0.0303374 + 0.999540i \(0.509658\pi\)
\(500\) −3.74982 −0.167697
\(501\) 0 0
\(502\) 45.2619 2.02014
\(503\) −13.9030 −0.619903 −0.309952 0.950752i \(-0.600313\pi\)
−0.309952 + 0.950752i \(0.600313\pi\)
\(504\) 0 0
\(505\) 1.76221 0.0784172
\(506\) 9.60863 0.427156
\(507\) 0 0
\(508\) −36.7574 −1.63084
\(509\) 3.21978 0.142714 0.0713572 0.997451i \(-0.477267\pi\)
0.0713572 + 0.997451i \(0.477267\pi\)
\(510\) 0 0
\(511\) 0.584663 0.0258640
\(512\) −27.2574 −1.20462
\(513\) 0 0
\(514\) −17.9368 −0.791160
\(515\) 5.53571 0.243933
\(516\) 0 0
\(517\) 0.295438 0.0129933
\(518\) −42.1686 −1.85278
\(519\) 0 0
\(520\) −19.8791 −0.871755
\(521\) −3.09750 −0.135704 −0.0678520 0.997695i \(-0.521615\pi\)
−0.0678520 + 0.997695i \(0.521615\pi\)
\(522\) 0 0
\(523\) 13.2007 0.577228 0.288614 0.957446i \(-0.406806\pi\)
0.288614 + 0.957446i \(0.406806\pi\)
\(524\) 50.3910 2.20134
\(525\) 0 0
\(526\) 42.6111 1.85793
\(527\) −37.3309 −1.62616
\(528\) 0 0
\(529\) −6.94281 −0.301861
\(530\) −9.13949 −0.396994
\(531\) 0 0
\(532\) −10.8516 −0.470475
\(533\) −25.9316 −1.12322
\(534\) 0 0
\(535\) −4.32073 −0.186802
\(536\) 29.3209 1.26647
\(537\) 0 0
\(538\) −62.1817 −2.68084
\(539\) 1.37462 0.0592092
\(540\) 0 0
\(541\) −6.57608 −0.282728 −0.141364 0.989958i \(-0.545149\pi\)
−0.141364 + 0.989958i \(0.545149\pi\)
\(542\) −39.0102 −1.67563
\(543\) 0 0
\(544\) −12.7187 −0.545311
\(545\) 13.0039 0.557028
\(546\) 0 0
\(547\) −23.9559 −1.02428 −0.512139 0.858902i \(-0.671147\pi\)
−0.512139 + 0.858902i \(0.671147\pi\)
\(548\) 60.7926 2.59693
\(549\) 0 0
\(550\) 2.39788 0.102246
\(551\) −9.32825 −0.397397
\(552\) 0 0
\(553\) −21.0875 −0.896732
\(554\) −42.9740 −1.82579
\(555\) 0 0
\(556\) 71.3862 3.02745
\(557\) 11.2404 0.476271 0.238135 0.971232i \(-0.423464\pi\)
0.238135 + 0.971232i \(0.423464\pi\)
\(558\) 0 0
\(559\) 51.8860 2.19454
\(560\) 7.41267 0.313243
\(561\) 0 0
\(562\) 69.1939 2.91877
\(563\) −44.9880 −1.89602 −0.948009 0.318242i \(-0.896907\pi\)
−0.948009 + 0.318242i \(0.896907\pi\)
\(564\) 0 0
\(565\) −17.0047 −0.715392
\(566\) −25.8060 −1.08471
\(567\) 0 0
\(568\) 4.28331 0.179724
\(569\) −33.2099 −1.39223 −0.696115 0.717930i \(-0.745090\pi\)
−0.696115 + 0.717930i \(0.745090\pi\)
\(570\) 0 0
\(571\) −44.6440 −1.86829 −0.934146 0.356891i \(-0.883837\pi\)
−0.934146 + 0.356891i \(0.883837\pi\)
\(572\) 17.7659 0.742829
\(573\) 0 0
\(574\) 37.9806 1.58528
\(575\) 4.00714 0.167109
\(576\) 0 0
\(577\) −45.6776 −1.90158 −0.950792 0.309831i \(-0.899728\pi\)
−0.950792 + 0.309831i \(0.899728\pi\)
\(578\) 35.8877 1.49273
\(579\) 0 0
\(580\) 34.9792 1.45243
\(581\) −39.6581 −1.64530
\(582\) 0 0
\(583\) 3.81149 0.157856
\(584\) −0.847700 −0.0350781
\(585\) 0 0
\(586\) −12.3325 −0.509449
\(587\) 17.5933 0.726155 0.363078 0.931759i \(-0.381726\pi\)
0.363078 + 0.931759i \(0.381726\pi\)
\(588\) 0 0
\(589\) −6.60270 −0.272060
\(590\) −13.3061 −0.547802
\(591\) 0 0
\(592\) 15.5658 0.639750
\(593\) −32.4709 −1.33342 −0.666710 0.745317i \(-0.732298\pi\)
−0.666710 + 0.745317i \(0.732298\pi\)
\(594\) 0 0
\(595\) 16.3618 0.670767
\(596\) 57.4598 2.35365
\(597\) 0 0
\(598\) 45.5238 1.86161
\(599\) −1.31594 −0.0537679 −0.0268839 0.999639i \(-0.508558\pi\)
−0.0268839 + 0.999639i \(0.508558\pi\)
\(600\) 0 0
\(601\) −4.53331 −0.184918 −0.0924588 0.995717i \(-0.529473\pi\)
−0.0924588 + 0.995717i \(0.529473\pi\)
\(602\) −75.9946 −3.09731
\(603\) 0 0
\(604\) −4.72236 −0.192150
\(605\) −1.00000 −0.0406558
\(606\) 0 0
\(607\) −14.2654 −0.579016 −0.289508 0.957176i \(-0.593492\pi\)
−0.289508 + 0.957176i \(0.593492\pi\)
\(608\) −2.24955 −0.0912315
\(609\) 0 0
\(610\) 2.42228 0.0980754
\(611\) 1.39972 0.0566268
\(612\) 0 0
\(613\) 5.06662 0.204639 0.102319 0.994752i \(-0.467374\pi\)
0.102319 + 0.994752i \(0.467374\pi\)
\(614\) 67.3845 2.71942
\(615\) 0 0
\(616\) −12.1423 −0.489228
\(617\) −19.5460 −0.786893 −0.393446 0.919348i \(-0.628717\pi\)
−0.393446 + 0.919348i \(0.628717\pi\)
\(618\) 0 0
\(619\) 8.78654 0.353161 0.176580 0.984286i \(-0.443496\pi\)
0.176580 + 0.984286i \(0.443496\pi\)
\(620\) 24.7589 0.994342
\(621\) 0 0
\(622\) 34.0280 1.36440
\(623\) −45.7675 −1.83363
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −22.6859 −0.906712
\(627\) 0 0
\(628\) 45.6957 1.82346
\(629\) 34.3579 1.36994
\(630\) 0 0
\(631\) −0.0559751 −0.00222833 −0.00111417 0.999999i \(-0.500355\pi\)
−0.00111417 + 0.999999i \(0.500355\pi\)
\(632\) 30.5747 1.21620
\(633\) 0 0
\(634\) 57.2308 2.27293
\(635\) 9.80245 0.388998
\(636\) 0 0
\(637\) 6.51269 0.258042
\(638\) −22.3680 −0.885558
\(639\) 0 0
\(640\) 20.7197 0.819017
\(641\) −4.49262 −0.177448 −0.0887239 0.996056i \(-0.528279\pi\)
−0.0887239 + 0.996056i \(0.528279\pi\)
\(642\) 0 0
\(643\) −5.48669 −0.216374 −0.108187 0.994131i \(-0.534505\pi\)
−0.108187 + 0.994131i \(0.534505\pi\)
\(644\) −43.4838 −1.71350
\(645\) 0 0
\(646\) 13.5573 0.533406
\(647\) 34.5798 1.35947 0.679736 0.733456i \(-0.262094\pi\)
0.679736 + 0.733456i \(0.262094\pi\)
\(648\) 0 0
\(649\) 5.54910 0.217821
\(650\) 11.3607 0.445602
\(651\) 0 0
\(652\) 22.8635 0.895402
\(653\) −11.3537 −0.444304 −0.222152 0.975012i \(-0.571308\pi\)
−0.222152 + 0.975012i \(0.571308\pi\)
\(654\) 0 0
\(655\) −13.4383 −0.525076
\(656\) −14.0199 −0.547384
\(657\) 0 0
\(658\) −2.05010 −0.0799213
\(659\) −27.1448 −1.05741 −0.528706 0.848805i \(-0.677323\pi\)
−0.528706 + 0.848805i \(0.677323\pi\)
\(660\) 0 0
\(661\) 5.01901 0.195217 0.0976084 0.995225i \(-0.468881\pi\)
0.0976084 + 0.995225i \(0.468881\pi\)
\(662\) −31.6143 −1.22873
\(663\) 0 0
\(664\) 57.5002 2.23144
\(665\) 2.89389 0.112220
\(666\) 0 0
\(667\) −37.3796 −1.44734
\(668\) −4.00181 −0.154835
\(669\) 0 0
\(670\) −16.7565 −0.647362
\(671\) −1.01018 −0.0389975
\(672\) 0 0
\(673\) −38.5035 −1.48420 −0.742100 0.670289i \(-0.766170\pi\)
−0.742100 + 0.670289i \(0.766170\pi\)
\(674\) 40.7994 1.57153
\(675\) 0 0
\(676\) 35.4236 1.36244
\(677\) −17.8660 −0.686647 −0.343324 0.939217i \(-0.611553\pi\)
−0.343324 + 0.939217i \(0.611553\pi\)
\(678\) 0 0
\(679\) −13.9285 −0.534528
\(680\) −23.7228 −0.909729
\(681\) 0 0
\(682\) −15.8325 −0.606257
\(683\) −44.9512 −1.72001 −0.860005 0.510286i \(-0.829540\pi\)
−0.860005 + 0.510286i \(0.829540\pi\)
\(684\) 0 0
\(685\) −16.2122 −0.619435
\(686\) 39.0356 1.49039
\(687\) 0 0
\(688\) 28.0521 1.06948
\(689\) 18.0581 0.687958
\(690\) 0 0
\(691\) 24.1309 0.917983 0.458991 0.888441i \(-0.348211\pi\)
0.458991 + 0.888441i \(0.348211\pi\)
\(692\) 48.8561 1.85723
\(693\) 0 0
\(694\) 72.5611 2.75438
\(695\) −19.0373 −0.722124
\(696\) 0 0
\(697\) −30.9456 −1.17215
\(698\) 12.3122 0.466024
\(699\) 0 0
\(700\) −10.8516 −0.410151
\(701\) 1.53772 0.0580789 0.0290395 0.999578i \(-0.490755\pi\)
0.0290395 + 0.999578i \(0.490755\pi\)
\(702\) 0 0
\(703\) 6.07686 0.229193
\(704\) −10.5171 −0.396379
\(705\) 0 0
\(706\) 25.3362 0.953540
\(707\) 5.09964 0.191792
\(708\) 0 0
\(709\) 5.19348 0.195045 0.0975226 0.995233i \(-0.468908\pi\)
0.0975226 + 0.995233i \(0.468908\pi\)
\(710\) −2.44787 −0.0918668
\(711\) 0 0
\(712\) 66.3580 2.48687
\(713\) −26.4580 −0.990858
\(714\) 0 0
\(715\) −4.73780 −0.177184
\(716\) −77.3485 −2.89065
\(717\) 0 0
\(718\) −39.6077 −1.47815
\(719\) 37.4841 1.39792 0.698960 0.715160i \(-0.253646\pi\)
0.698960 + 0.715160i \(0.253646\pi\)
\(720\) 0 0
\(721\) 16.0198 0.596607
\(722\) 2.39788 0.0892398
\(723\) 0 0
\(724\) −77.2117 −2.86955
\(725\) −9.32825 −0.346443
\(726\) 0 0
\(727\) 28.1916 1.04557 0.522785 0.852464i \(-0.324893\pi\)
0.522785 + 0.852464i \(0.324893\pi\)
\(728\) −57.5279 −2.13213
\(729\) 0 0
\(730\) 0.484451 0.0179303
\(731\) 61.9185 2.29014
\(732\) 0 0
\(733\) −18.1906 −0.671884 −0.335942 0.941883i \(-0.609055\pi\)
−0.335942 + 0.941883i \(0.609055\pi\)
\(734\) 47.6604 1.75918
\(735\) 0 0
\(736\) −9.01428 −0.332271
\(737\) 6.98807 0.257409
\(738\) 0 0
\(739\) 5.65484 0.208017 0.104008 0.994576i \(-0.466833\pi\)
0.104008 + 0.994576i \(0.466833\pi\)
\(740\) −22.7871 −0.837670
\(741\) 0 0
\(742\) −26.4487 −0.970963
\(743\) 44.5565 1.63462 0.817310 0.576198i \(-0.195464\pi\)
0.817310 + 0.576198i \(0.195464\pi\)
\(744\) 0 0
\(745\) −15.3234 −0.561405
\(746\) −27.3720 −1.00216
\(747\) 0 0
\(748\) 21.2010 0.775187
\(749\) −12.5037 −0.456877
\(750\) 0 0
\(751\) −18.8205 −0.686769 −0.343384 0.939195i \(-0.611573\pi\)
−0.343384 + 0.939195i \(0.611573\pi\)
\(752\) 0.756760 0.0275962
\(753\) 0 0
\(754\) −105.975 −3.85939
\(755\) 1.25936 0.0458328
\(756\) 0 0
\(757\) 2.97780 0.108230 0.0541150 0.998535i \(-0.482766\pi\)
0.0541150 + 0.998535i \(0.482766\pi\)
\(758\) 4.79397 0.174125
\(759\) 0 0
\(760\) −4.19584 −0.152199
\(761\) 41.9642 1.52120 0.760601 0.649219i \(-0.224904\pi\)
0.760601 + 0.649219i \(0.224904\pi\)
\(762\) 0 0
\(763\) 37.6320 1.36237
\(764\) −31.5002 −1.13964
\(765\) 0 0
\(766\) 16.9532 0.612542
\(767\) 26.2905 0.949295
\(768\) 0 0
\(769\) −2.33683 −0.0842683 −0.0421341 0.999112i \(-0.513416\pi\)
−0.0421341 + 0.999112i \(0.513416\pi\)
\(770\) 6.93920 0.250072
\(771\) 0 0
\(772\) 43.1162 1.55179
\(773\) −4.40125 −0.158302 −0.0791509 0.996863i \(-0.525221\pi\)
−0.0791509 + 0.996863i \(0.525221\pi\)
\(774\) 0 0
\(775\) −6.60270 −0.237176
\(776\) 20.1949 0.724955
\(777\) 0 0
\(778\) −40.8207 −1.46349
\(779\) −5.47333 −0.196102
\(780\) 0 0
\(781\) 1.02085 0.0365288
\(782\) 54.3262 1.94270
\(783\) 0 0
\(784\) 3.52108 0.125753
\(785\) −12.1861 −0.434942
\(786\) 0 0
\(787\) −13.1902 −0.470180 −0.235090 0.971974i \(-0.575539\pi\)
−0.235090 + 0.971974i \(0.575539\pi\)
\(788\) −101.386 −3.61172
\(789\) 0 0
\(790\) −17.4731 −0.621664
\(791\) −49.2097 −1.74970
\(792\) 0 0
\(793\) −4.78602 −0.169957
\(794\) −60.8078 −2.15799
\(795\) 0 0
\(796\) −19.4413 −0.689078
\(797\) 39.1687 1.38743 0.693713 0.720252i \(-0.255974\pi\)
0.693713 + 0.720252i \(0.255974\pi\)
\(798\) 0 0
\(799\) 1.67037 0.0590935
\(800\) −2.24955 −0.0795338
\(801\) 0 0
\(802\) −47.1060 −1.66337
\(803\) −0.202033 −0.00712960
\(804\) 0 0
\(805\) 11.5962 0.408714
\(806\) −75.0111 −2.64215
\(807\) 0 0
\(808\) −7.39394 −0.260118
\(809\) −18.2003 −0.639887 −0.319944 0.947437i \(-0.603664\pi\)
−0.319944 + 0.947437i \(0.603664\pi\)
\(810\) 0 0
\(811\) −54.6434 −1.91879 −0.959395 0.282065i \(-0.908981\pi\)
−0.959395 + 0.282065i \(0.908981\pi\)
\(812\) 101.226 3.55234
\(813\) 0 0
\(814\) 14.5716 0.510733
\(815\) −6.09722 −0.213576
\(816\) 0 0
\(817\) 10.9515 0.383144
\(818\) −68.7056 −2.40224
\(819\) 0 0
\(820\) 20.5240 0.716729
\(821\) −18.3540 −0.640560 −0.320280 0.947323i \(-0.603777\pi\)
−0.320280 + 0.947323i \(0.603777\pi\)
\(822\) 0 0
\(823\) 9.63416 0.335826 0.167913 0.985802i \(-0.446297\pi\)
0.167913 + 0.985802i \(0.446297\pi\)
\(824\) −23.2270 −0.809150
\(825\) 0 0
\(826\) −38.5063 −1.33981
\(827\) −26.2829 −0.913947 −0.456973 0.889480i \(-0.651067\pi\)
−0.456973 + 0.889480i \(0.651067\pi\)
\(828\) 0 0
\(829\) −45.2690 −1.57226 −0.786128 0.618064i \(-0.787917\pi\)
−0.786128 + 0.618064i \(0.787917\pi\)
\(830\) −32.8607 −1.14061
\(831\) 0 0
\(832\) −49.8281 −1.72748
\(833\) 7.77197 0.269283
\(834\) 0 0
\(835\) 1.06720 0.0369321
\(836\) 3.74982 0.129690
\(837\) 0 0
\(838\) 6.72648 0.232362
\(839\) −23.0656 −0.796315 −0.398157 0.917317i \(-0.630350\pi\)
−0.398157 + 0.917317i \(0.630350\pi\)
\(840\) 0 0
\(841\) 58.0162 2.00056
\(842\) 7.82104 0.269531
\(843\) 0 0
\(844\) −80.7810 −2.78060
\(845\) −9.44675 −0.324978
\(846\) 0 0
\(847\) −2.89389 −0.0994354
\(848\) 9.76309 0.335266
\(849\) 0 0
\(850\) 13.5573 0.465013
\(851\) 24.3508 0.834736
\(852\) 0 0
\(853\) −10.1175 −0.346418 −0.173209 0.984885i \(-0.555414\pi\)
−0.173209 + 0.984885i \(0.555414\pi\)
\(854\) 7.00983 0.239872
\(855\) 0 0
\(856\) 18.1291 0.619641
\(857\) −17.5975 −0.601119 −0.300559 0.953763i \(-0.597173\pi\)
−0.300559 + 0.953763i \(0.597173\pi\)
\(858\) 0 0
\(859\) 51.9873 1.77378 0.886891 0.461978i \(-0.152860\pi\)
0.886891 + 0.461978i \(0.152860\pi\)
\(860\) −41.0661 −1.40034
\(861\) 0 0
\(862\) −78.5560 −2.67563
\(863\) 42.2968 1.43980 0.719900 0.694078i \(-0.244188\pi\)
0.719900 + 0.694078i \(0.244188\pi\)
\(864\) 0 0
\(865\) −13.0289 −0.442997
\(866\) −52.4310 −1.78168
\(867\) 0 0
\(868\) 71.6497 2.43195
\(869\) 7.28690 0.247191
\(870\) 0 0
\(871\) 33.1081 1.12182
\(872\) −54.5625 −1.84772
\(873\) 0 0
\(874\) 9.60863 0.325017
\(875\) 2.89389 0.0978315
\(876\) 0 0
\(877\) −4.60606 −0.155535 −0.0777677 0.996972i \(-0.524779\pi\)
−0.0777677 + 0.996972i \(0.524779\pi\)
\(878\) 73.4423 2.47856
\(879\) 0 0
\(880\) −2.56149 −0.0863477
\(881\) −45.1124 −1.51987 −0.759937 0.649997i \(-0.774770\pi\)
−0.759937 + 0.649997i \(0.774770\pi\)
\(882\) 0 0
\(883\) −40.3849 −1.35906 −0.679530 0.733648i \(-0.737816\pi\)
−0.679530 + 0.733648i \(0.737816\pi\)
\(884\) 100.446 3.37837
\(885\) 0 0
\(886\) −10.9083 −0.366471
\(887\) −50.2462 −1.68710 −0.843551 0.537050i \(-0.819539\pi\)
−0.843551 + 0.537050i \(0.819539\pi\)
\(888\) 0 0
\(889\) 28.3672 0.951407
\(890\) −37.9229 −1.27118
\(891\) 0 0
\(892\) −101.095 −3.38491
\(893\) 0.295438 0.00988645
\(894\) 0 0
\(895\) 20.6273 0.689494
\(896\) 59.9606 2.00314
\(897\) 0 0
\(898\) −27.6495 −0.922674
\(899\) 61.5916 2.05420
\(900\) 0 0
\(901\) 21.5498 0.717926
\(902\) −13.1244 −0.436994
\(903\) 0 0
\(904\) 71.3490 2.37303
\(905\) 20.5908 0.684462
\(906\) 0 0
\(907\) 58.4194 1.93979 0.969893 0.243532i \(-0.0783062\pi\)
0.969893 + 0.243532i \(0.0783062\pi\)
\(908\) −33.8447 −1.12318
\(909\) 0 0
\(910\) 32.8766 1.08985
\(911\) 39.2409 1.30011 0.650054 0.759888i \(-0.274746\pi\)
0.650054 + 0.759888i \(0.274746\pi\)
\(912\) 0 0
\(913\) 13.7041 0.453539
\(914\) 27.2826 0.902427
\(915\) 0 0
\(916\) −51.6337 −1.70603
\(917\) −38.8889 −1.28422
\(918\) 0 0
\(919\) 18.4113 0.607334 0.303667 0.952778i \(-0.401789\pi\)
0.303667 + 0.952778i \(0.401789\pi\)
\(920\) −16.8133 −0.554319
\(921\) 0 0
\(922\) −10.4851 −0.345308
\(923\) 4.83657 0.159198
\(924\) 0 0
\(925\) 6.07686 0.199806
\(926\) −22.3478 −0.734393
\(927\) 0 0
\(928\) 20.9844 0.688847
\(929\) 32.8679 1.07836 0.539180 0.842191i \(-0.318734\pi\)
0.539180 + 0.842191i \(0.318734\pi\)
\(930\) 0 0
\(931\) 1.37462 0.0450515
\(932\) 9.20907 0.301653
\(933\) 0 0
\(934\) 67.3110 2.20248
\(935\) −5.65389 −0.184902
\(936\) 0 0
\(937\) 4.34616 0.141983 0.0709914 0.997477i \(-0.477384\pi\)
0.0709914 + 0.997477i \(0.477384\pi\)
\(938\) −48.4917 −1.58331
\(939\) 0 0
\(940\) −1.10784 −0.0361337
\(941\) 55.1238 1.79699 0.898493 0.438989i \(-0.144663\pi\)
0.898493 + 0.438989i \(0.144663\pi\)
\(942\) 0 0
\(943\) −21.9324 −0.714218
\(944\) 14.2139 0.462625
\(945\) 0 0
\(946\) 26.2603 0.853797
\(947\) −16.6794 −0.542007 −0.271004 0.962578i \(-0.587356\pi\)
−0.271004 + 0.962578i \(0.587356\pi\)
\(948\) 0 0
\(949\) −0.957193 −0.0310718
\(950\) 2.39788 0.0777974
\(951\) 0 0
\(952\) −68.6514 −2.22500
\(953\) −51.8274 −1.67885 −0.839427 0.543472i \(-0.817109\pi\)
−0.839427 + 0.543472i \(0.817109\pi\)
\(954\) 0 0
\(955\) 8.40047 0.271833
\(956\) 85.6605 2.77046
\(957\) 0 0
\(958\) 13.5524 0.437859
\(959\) −46.9163 −1.51501
\(960\) 0 0
\(961\) 12.5957 0.406312
\(962\) 69.0371 2.22585
\(963\) 0 0
\(964\) 60.4399 1.94664
\(965\) −11.4982 −0.370141
\(966\) 0 0
\(967\) −28.7146 −0.923398 −0.461699 0.887037i \(-0.652760\pi\)
−0.461699 + 0.887037i \(0.652760\pi\)
\(968\) 4.19584 0.134860
\(969\) 0 0
\(970\) −11.5412 −0.370564
\(971\) −43.9744 −1.41121 −0.705603 0.708607i \(-0.749324\pi\)
−0.705603 + 0.708607i \(0.749324\pi\)
\(972\) 0 0
\(973\) −55.0918 −1.76616
\(974\) −14.6114 −0.468180
\(975\) 0 0
\(976\) −2.58756 −0.0828258
\(977\) −19.2496 −0.615848 −0.307924 0.951411i \(-0.599634\pi\)
−0.307924 + 0.951411i \(0.599634\pi\)
\(978\) 0 0
\(979\) 15.8152 0.505455
\(980\) −5.15458 −0.164657
\(981\) 0 0
\(982\) −20.5327 −0.655224
\(983\) 12.7410 0.406373 0.203187 0.979140i \(-0.434870\pi\)
0.203187 + 0.979140i \(0.434870\pi\)
\(984\) 0 0
\(985\) 27.0376 0.861488
\(986\) −126.466 −4.02750
\(987\) 0 0
\(988\) 17.7659 0.565208
\(989\) 43.8842 1.39544
\(990\) 0 0
\(991\) 27.9827 0.888900 0.444450 0.895804i \(-0.353399\pi\)
0.444450 + 0.895804i \(0.353399\pi\)
\(992\) 14.8531 0.471588
\(993\) 0 0
\(994\) −7.08387 −0.224687
\(995\) 5.18460 0.164363
\(996\) 0 0
\(997\) −47.7121 −1.51106 −0.755528 0.655116i \(-0.772620\pi\)
−0.755528 + 0.655116i \(0.772620\pi\)
\(998\) −3.25002 −0.102878
\(999\) 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 9405.2.a.v.1.5 5
3.2 odd 2 1045.2.a.d.1.1 5
15.14 odd 2 5225.2.a.j.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.d.1.1 5 3.2 odd 2
5225.2.a.j.1.5 5 15.14 odd 2
9405.2.a.v.1.5 5 1.1 even 1 trivial