Properties

Label 1035.2.a.k.1.2
Level $1035$
Weight $2$
Character 1035.1
Self dual yes
Analytic conductor $8.265$
Analytic rank $0$
Dimension $2$
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] = [1035,2,Mod(1,1035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1035, 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("1035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1035.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: \(8.26451660920\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 345)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.44949\) of defining polynomial
Character \(\chi\) \(=\) 1035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.44949 q^{2} +4.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +4.89898 q^{8} +O(q^{10})\) \(q+2.44949 q^{2} +4.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +4.89898 q^{8} +2.44949 q^{10} -2.44949 q^{11} +4.44949 q^{13} -2.44949 q^{14} +4.00000 q^{16} +5.44949 q^{17} +4.44949 q^{19} +4.00000 q^{20} -6.00000 q^{22} +1.00000 q^{23} +1.00000 q^{25} +10.8990 q^{26} -4.00000 q^{28} -10.3485 q^{29} +0.101021 q^{31} +13.3485 q^{34} -1.00000 q^{35} +3.89898 q^{37} +10.8990 q^{38} +4.89898 q^{40} -5.44949 q^{41} +2.00000 q^{43} -9.79796 q^{44} +2.44949 q^{46} -8.44949 q^{47} -6.00000 q^{49} +2.44949 q^{50} +17.7980 q^{52} -0.550510 q^{53} -2.44949 q^{55} -4.89898 q^{56} -25.3485 q^{58} -10.3485 q^{59} +0.651531 q^{61} +0.247449 q^{62} -8.00000 q^{64} +4.44949 q^{65} -7.00000 q^{67} +21.7980 q^{68} -2.44949 q^{70} +4.34847 q^{71} -5.34847 q^{73} +9.55051 q^{74} +17.7980 q^{76} +2.44949 q^{77} -4.00000 q^{79} +4.00000 q^{80} -13.3485 q^{82} -15.2474 q^{83} +5.44949 q^{85} +4.89898 q^{86} -12.0000 q^{88} +16.8990 q^{89} -4.44949 q^{91} +4.00000 q^{92} -20.6969 q^{94} +4.44949 q^{95} +3.10102 q^{97} -14.6969 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8 q^{4} + 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 8 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{13} + 8 q^{16} + 6 q^{17} + 4 q^{19} + 8 q^{20} - 12 q^{22} + 2 q^{23} + 2 q^{25} + 12 q^{26} - 8 q^{28} - 6 q^{29} + 10 q^{31} + 12 q^{34} - 2 q^{35} - 2 q^{37} + 12 q^{38} - 6 q^{41} + 4 q^{43} - 12 q^{47} - 12 q^{49} + 16 q^{52} - 6 q^{53} - 36 q^{58} - 6 q^{59} + 16 q^{61} - 24 q^{62} - 16 q^{64} + 4 q^{65} - 14 q^{67} + 24 q^{68} - 6 q^{71} + 4 q^{73} + 24 q^{74} + 16 q^{76} - 8 q^{79} + 8 q^{80} - 12 q^{82} - 6 q^{83} + 6 q^{85} - 24 q^{88} + 24 q^{89} - 4 q^{91} + 8 q^{92} - 12 q^{94} + 4 q^{95} + 16 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44949 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0 0
\(4\) 4.00000 2.00000
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 4.89898 1.73205
\(9\) 0 0
\(10\) 2.44949 0.774597
\(11\) −2.44949 −0.738549 −0.369274 0.929320i \(-0.620394\pi\)
−0.369274 + 0.929320i \(0.620394\pi\)
\(12\) 0 0
\(13\) 4.44949 1.23407 0.617033 0.786937i \(-0.288334\pi\)
0.617033 + 0.786937i \(0.288334\pi\)
\(14\) −2.44949 −0.654654
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 5.44949 1.32170 0.660848 0.750520i \(-0.270197\pi\)
0.660848 + 0.750520i \(0.270197\pi\)
\(18\) 0 0
\(19\) 4.44949 1.02078 0.510391 0.859942i \(-0.329501\pi\)
0.510391 + 0.859942i \(0.329501\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 10.8990 2.13747
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) −10.3485 −1.92166 −0.960831 0.277134i \(-0.910615\pi\)
−0.960831 + 0.277134i \(0.910615\pi\)
\(30\) 0 0
\(31\) 0.101021 0.0181438 0.00907191 0.999959i \(-0.497112\pi\)
0.00907191 + 0.999959i \(0.497112\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 13.3485 2.28924
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 3.89898 0.640988 0.320494 0.947250i \(-0.396151\pi\)
0.320494 + 0.947250i \(0.396151\pi\)
\(38\) 10.8990 1.76805
\(39\) 0 0
\(40\) 4.89898 0.774597
\(41\) −5.44949 −0.851067 −0.425534 0.904943i \(-0.639914\pi\)
−0.425534 + 0.904943i \(0.639914\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −9.79796 −1.47710
\(45\) 0 0
\(46\) 2.44949 0.361158
\(47\) −8.44949 −1.23248 −0.616242 0.787557i \(-0.711346\pi\)
−0.616242 + 0.787557i \(0.711346\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 2.44949 0.346410
\(51\) 0 0
\(52\) 17.7980 2.46813
\(53\) −0.550510 −0.0756184 −0.0378092 0.999285i \(-0.512038\pi\)
−0.0378092 + 0.999285i \(0.512038\pi\)
\(54\) 0 0
\(55\) −2.44949 −0.330289
\(56\) −4.89898 −0.654654
\(57\) 0 0
\(58\) −25.3485 −3.32842
\(59\) −10.3485 −1.34726 −0.673628 0.739071i \(-0.735265\pi\)
−0.673628 + 0.739071i \(0.735265\pi\)
\(60\) 0 0
\(61\) 0.651531 0.0834200 0.0417100 0.999130i \(-0.486719\pi\)
0.0417100 + 0.999130i \(0.486719\pi\)
\(62\) 0.247449 0.0314260
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 4.44949 0.551891
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 21.7980 2.64339
\(69\) 0 0
\(70\) −2.44949 −0.292770
\(71\) 4.34847 0.516068 0.258034 0.966136i \(-0.416925\pi\)
0.258034 + 0.966136i \(0.416925\pi\)
\(72\) 0 0
\(73\) −5.34847 −0.625991 −0.312995 0.949755i \(-0.601332\pi\)
−0.312995 + 0.949755i \(0.601332\pi\)
\(74\) 9.55051 1.11022
\(75\) 0 0
\(76\) 17.7980 2.04157
\(77\) 2.44949 0.279145
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 4.00000 0.447214
\(81\) 0 0
\(82\) −13.3485 −1.47409
\(83\) −15.2474 −1.67362 −0.836812 0.547490i \(-0.815584\pi\)
−0.836812 + 0.547490i \(0.815584\pi\)
\(84\) 0 0
\(85\) 5.44949 0.591080
\(86\) 4.89898 0.528271
\(87\) 0 0
\(88\) −12.0000 −1.27920
\(89\) 16.8990 1.79129 0.895644 0.444771i \(-0.146715\pi\)
0.895644 + 0.444771i \(0.146715\pi\)
\(90\) 0 0
\(91\) −4.44949 −0.466433
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) −20.6969 −2.13473
\(95\) 4.44949 0.456508
\(96\) 0 0
\(97\) 3.10102 0.314861 0.157430 0.987530i \(-0.449679\pi\)
0.157430 + 0.987530i \(0.449679\pi\)
\(98\) −14.6969 −1.48461
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) 12.5505 1.24882 0.624411 0.781096i \(-0.285339\pi\)
0.624411 + 0.781096i \(0.285339\pi\)
\(102\) 0 0
\(103\) −12.6969 −1.25107 −0.625533 0.780198i \(-0.715119\pi\)
−0.625533 + 0.780198i \(0.715119\pi\)
\(104\) 21.7980 2.13747
\(105\) 0 0
\(106\) −1.34847 −0.130975
\(107\) 5.44949 0.526822 0.263411 0.964684i \(-0.415152\pi\)
0.263411 + 0.964684i \(0.415152\pi\)
\(108\) 0 0
\(109\) 11.5505 1.10634 0.553169 0.833069i \(-0.313418\pi\)
0.553169 + 0.833069i \(0.313418\pi\)
\(110\) −6.00000 −0.572078
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) 1.65153 0.155363 0.0776815 0.996978i \(-0.475248\pi\)
0.0776815 + 0.996978i \(0.475248\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) −41.3939 −3.84332
\(117\) 0 0
\(118\) −25.3485 −2.33352
\(119\) −5.44949 −0.499554
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) 1.59592 0.144488
\(123\) 0 0
\(124\) 0.404082 0.0362876
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.55051 −0.137586 −0.0687928 0.997631i \(-0.521915\pi\)
−0.0687928 + 0.997631i \(0.521915\pi\)
\(128\) −19.5959 −1.73205
\(129\) 0 0
\(130\) 10.8990 0.955904
\(131\) 19.5959 1.71210 0.856052 0.516890i \(-0.172910\pi\)
0.856052 + 0.516890i \(0.172910\pi\)
\(132\) 0 0
\(133\) −4.44949 −0.385820
\(134\) −17.1464 −1.48123
\(135\) 0 0
\(136\) 26.6969 2.28924
\(137\) 16.8990 1.44378 0.721889 0.692009i \(-0.243274\pi\)
0.721889 + 0.692009i \(0.243274\pi\)
\(138\) 0 0
\(139\) −4.79796 −0.406958 −0.203479 0.979079i \(-0.565225\pi\)
−0.203479 + 0.979079i \(0.565225\pi\)
\(140\) −4.00000 −0.338062
\(141\) 0 0
\(142\) 10.6515 0.893857
\(143\) −10.8990 −0.911418
\(144\) 0 0
\(145\) −10.3485 −0.859394
\(146\) −13.1010 −1.08425
\(147\) 0 0
\(148\) 15.5959 1.28198
\(149\) 1.34847 0.110471 0.0552355 0.998473i \(-0.482409\pi\)
0.0552355 + 0.998473i \(0.482409\pi\)
\(150\) 0 0
\(151\) 14.0000 1.13930 0.569652 0.821886i \(-0.307078\pi\)
0.569652 + 0.821886i \(0.307078\pi\)
\(152\) 21.7980 1.76805
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 0.101021 0.00811416
\(156\) 0 0
\(157\) 18.5959 1.48412 0.742058 0.670336i \(-0.233850\pi\)
0.742058 + 0.670336i \(0.233850\pi\)
\(158\) −9.79796 −0.779484
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −21.7980 −1.70213
\(165\) 0 0
\(166\) −37.3485 −2.89880
\(167\) −13.3485 −1.03294 −0.516468 0.856307i \(-0.672753\pi\)
−0.516468 + 0.856307i \(0.672753\pi\)
\(168\) 0 0
\(169\) 6.79796 0.522920
\(170\) 13.3485 1.02378
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −19.5959 −1.48985 −0.744925 0.667148i \(-0.767515\pi\)
−0.744925 + 0.667148i \(0.767515\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) −9.79796 −0.738549
\(177\) 0 0
\(178\) 41.3939 3.10260
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) −8.89898 −0.661456 −0.330728 0.943726i \(-0.607294\pi\)
−0.330728 + 0.943726i \(0.607294\pi\)
\(182\) −10.8990 −0.807886
\(183\) 0 0
\(184\) 4.89898 0.361158
\(185\) 3.89898 0.286659
\(186\) 0 0
\(187\) −13.3485 −0.976137
\(188\) −33.7980 −2.46497
\(189\) 0 0
\(190\) 10.8990 0.790695
\(191\) 18.2474 1.32034 0.660170 0.751117i \(-0.270484\pi\)
0.660170 + 0.751117i \(0.270484\pi\)
\(192\) 0 0
\(193\) −6.69694 −0.482056 −0.241028 0.970518i \(-0.577485\pi\)
−0.241028 + 0.970518i \(0.577485\pi\)
\(194\) 7.59592 0.545355
\(195\) 0 0
\(196\) −24.0000 −1.71429
\(197\) 22.8990 1.63148 0.815742 0.578415i \(-0.196329\pi\)
0.815742 + 0.578415i \(0.196329\pi\)
\(198\) 0 0
\(199\) −2.89898 −0.205503 −0.102752 0.994707i \(-0.532765\pi\)
−0.102752 + 0.994707i \(0.532765\pi\)
\(200\) 4.89898 0.346410
\(201\) 0 0
\(202\) 30.7423 2.16302
\(203\) 10.3485 0.726320
\(204\) 0 0
\(205\) −5.44949 −0.380609
\(206\) −31.1010 −2.16691
\(207\) 0 0
\(208\) 17.7980 1.23407
\(209\) −10.8990 −0.753898
\(210\) 0 0
\(211\) 11.0000 0.757271 0.378636 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(212\) −2.20204 −0.151237
\(213\) 0 0
\(214\) 13.3485 0.912483
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) −0.101021 −0.00685772
\(218\) 28.2929 1.91623
\(219\) 0 0
\(220\) −9.79796 −0.660578
\(221\) 24.2474 1.63106
\(222\) 0 0
\(223\) 21.5959 1.44617 0.723085 0.690759i \(-0.242724\pi\)
0.723085 + 0.690759i \(0.242724\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 4.04541 0.269097
\(227\) −21.7980 −1.44678 −0.723391 0.690439i \(-0.757417\pi\)
−0.723391 + 0.690439i \(0.757417\pi\)
\(228\) 0 0
\(229\) −28.4949 −1.88300 −0.941498 0.337019i \(-0.890581\pi\)
−0.941498 + 0.337019i \(0.890581\pi\)
\(230\) 2.44949 0.161515
\(231\) 0 0
\(232\) −50.6969 −3.32842
\(233\) −21.7980 −1.42803 −0.714016 0.700129i \(-0.753126\pi\)
−0.714016 + 0.700129i \(0.753126\pi\)
\(234\) 0 0
\(235\) −8.44949 −0.551184
\(236\) −41.3939 −2.69451
\(237\) 0 0
\(238\) −13.3485 −0.865253
\(239\) −6.55051 −0.423717 −0.211859 0.977300i \(-0.567952\pi\)
−0.211859 + 0.977300i \(0.567952\pi\)
\(240\) 0 0
\(241\) −29.3485 −1.89050 −0.945251 0.326346i \(-0.894183\pi\)
−0.945251 + 0.326346i \(0.894183\pi\)
\(242\) −12.2474 −0.787296
\(243\) 0 0
\(244\) 2.60612 0.166840
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 19.7980 1.25971
\(248\) 0.494897 0.0314260
\(249\) 0 0
\(250\) 2.44949 0.154919
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −2.44949 −0.153998
\(254\) −3.79796 −0.238305
\(255\) 0 0
\(256\) −32.0000 −2.00000
\(257\) 25.3485 1.58119 0.790597 0.612337i \(-0.209770\pi\)
0.790597 + 0.612337i \(0.209770\pi\)
\(258\) 0 0
\(259\) −3.89898 −0.242271
\(260\) 17.7980 1.10378
\(261\) 0 0
\(262\) 48.0000 2.96545
\(263\) −27.2474 −1.68015 −0.840075 0.542471i \(-0.817489\pi\)
−0.840075 + 0.542471i \(0.817489\pi\)
\(264\) 0 0
\(265\) −0.550510 −0.0338176
\(266\) −10.8990 −0.668259
\(267\) 0 0
\(268\) −28.0000 −1.71037
\(269\) 5.44949 0.332261 0.166131 0.986104i \(-0.446873\pi\)
0.166131 + 0.986104i \(0.446873\pi\)
\(270\) 0 0
\(271\) 31.6969 1.92545 0.962726 0.270479i \(-0.0871820\pi\)
0.962726 + 0.270479i \(0.0871820\pi\)
\(272\) 21.7980 1.32170
\(273\) 0 0
\(274\) 41.3939 2.50070
\(275\) −2.44949 −0.147710
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −11.7526 −0.704871
\(279\) 0 0
\(280\) −4.89898 −0.292770
\(281\) 19.3485 1.15423 0.577116 0.816662i \(-0.304178\pi\)
0.577116 + 0.816662i \(0.304178\pi\)
\(282\) 0 0
\(283\) −2.10102 −0.124893 −0.0624464 0.998048i \(-0.519890\pi\)
−0.0624464 + 0.998048i \(0.519890\pi\)
\(284\) 17.3939 1.03214
\(285\) 0 0
\(286\) −26.6969 −1.57862
\(287\) 5.44949 0.321673
\(288\) 0 0
\(289\) 12.6969 0.746879
\(290\) −25.3485 −1.48851
\(291\) 0 0
\(292\) −21.3939 −1.25198
\(293\) 21.2474 1.24129 0.620645 0.784092i \(-0.286871\pi\)
0.620645 + 0.784092i \(0.286871\pi\)
\(294\) 0 0
\(295\) −10.3485 −0.602511
\(296\) 19.1010 1.11022
\(297\) 0 0
\(298\) 3.30306 0.191341
\(299\) 4.44949 0.257321
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 34.2929 1.97333
\(303\) 0 0
\(304\) 17.7980 1.02078
\(305\) 0.651531 0.0373065
\(306\) 0 0
\(307\) −2.65153 −0.151331 −0.0756654 0.997133i \(-0.524108\pi\)
−0.0756654 + 0.997133i \(0.524108\pi\)
\(308\) 9.79796 0.558291
\(309\) 0 0
\(310\) 0.247449 0.0140541
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 19.6969 1.11334 0.556668 0.830735i \(-0.312079\pi\)
0.556668 + 0.830735i \(0.312079\pi\)
\(314\) 45.5505 2.57056
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −6.24745 −0.350892 −0.175446 0.984489i \(-0.556137\pi\)
−0.175446 + 0.984489i \(0.556137\pi\)
\(318\) 0 0
\(319\) 25.3485 1.41924
\(320\) −8.00000 −0.447214
\(321\) 0 0
\(322\) −2.44949 −0.136505
\(323\) 24.2474 1.34916
\(324\) 0 0
\(325\) 4.44949 0.246813
\(326\) −24.4949 −1.35665
\(327\) 0 0
\(328\) −26.6969 −1.47409
\(329\) 8.44949 0.465835
\(330\) 0 0
\(331\) 24.5959 1.35191 0.675957 0.736941i \(-0.263731\pi\)
0.675957 + 0.736941i \(0.263731\pi\)
\(332\) −60.9898 −3.34725
\(333\) 0 0
\(334\) −32.6969 −1.78910
\(335\) −7.00000 −0.382451
\(336\) 0 0
\(337\) −19.7980 −1.07846 −0.539232 0.842157i \(-0.681285\pi\)
−0.539232 + 0.842157i \(0.681285\pi\)
\(338\) 16.6515 0.905724
\(339\) 0 0
\(340\) 21.7980 1.18216
\(341\) −0.247449 −0.0134001
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 9.79796 0.528271
\(345\) 0 0
\(346\) −48.0000 −2.58050
\(347\) 28.8990 1.55138 0.775689 0.631115i \(-0.217402\pi\)
0.775689 + 0.631115i \(0.217402\pi\)
\(348\) 0 0
\(349\) 23.4949 1.25765 0.628827 0.777546i \(-0.283536\pi\)
0.628827 + 0.777546i \(0.283536\pi\)
\(350\) −2.44949 −0.130931
\(351\) 0 0
\(352\) 0 0
\(353\) 15.5505 0.827670 0.413835 0.910352i \(-0.364189\pi\)
0.413835 + 0.910352i \(0.364189\pi\)
\(354\) 0 0
\(355\) 4.34847 0.230793
\(356\) 67.5959 3.58258
\(357\) 0 0
\(358\) 14.6969 0.776757
\(359\) 3.55051 0.187389 0.0936944 0.995601i \(-0.470132\pi\)
0.0936944 + 0.995601i \(0.470132\pi\)
\(360\) 0 0
\(361\) 0.797959 0.0419978
\(362\) −21.7980 −1.14568
\(363\) 0 0
\(364\) −17.7980 −0.932867
\(365\) −5.34847 −0.279952
\(366\) 0 0
\(367\) 13.6969 0.714974 0.357487 0.933918i \(-0.383634\pi\)
0.357487 + 0.933918i \(0.383634\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) 9.55051 0.496507
\(371\) 0.550510 0.0285811
\(372\) 0 0
\(373\) 27.5959 1.42886 0.714431 0.699706i \(-0.246686\pi\)
0.714431 + 0.699706i \(0.246686\pi\)
\(374\) −32.6969 −1.69072
\(375\) 0 0
\(376\) −41.3939 −2.13473
\(377\) −46.0454 −2.37146
\(378\) 0 0
\(379\) 25.3939 1.30440 0.652198 0.758049i \(-0.273847\pi\)
0.652198 + 0.758049i \(0.273847\pi\)
\(380\) 17.7980 0.913016
\(381\) 0 0
\(382\) 44.6969 2.28689
\(383\) −1.65153 −0.0843893 −0.0421946 0.999109i \(-0.513435\pi\)
−0.0421946 + 0.999109i \(0.513435\pi\)
\(384\) 0 0
\(385\) 2.44949 0.124838
\(386\) −16.4041 −0.834946
\(387\) 0 0
\(388\) 12.4041 0.629722
\(389\) 3.30306 0.167472 0.0837359 0.996488i \(-0.473315\pi\)
0.0837359 + 0.996488i \(0.473315\pi\)
\(390\) 0 0
\(391\) 5.44949 0.275593
\(392\) −29.3939 −1.48461
\(393\) 0 0
\(394\) 56.0908 2.82581
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) −13.7980 −0.692500 −0.346250 0.938142i \(-0.612545\pi\)
−0.346250 + 0.938142i \(0.612545\pi\)
\(398\) −7.10102 −0.355942
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 13.1010 0.654234 0.327117 0.944984i \(-0.393923\pi\)
0.327117 + 0.944984i \(0.393923\pi\)
\(402\) 0 0
\(403\) 0.449490 0.0223907
\(404\) 50.2020 2.49764
\(405\) 0 0
\(406\) 25.3485 1.25802
\(407\) −9.55051 −0.473401
\(408\) 0 0
\(409\) 21.8990 1.08283 0.541417 0.840754i \(-0.317888\pi\)
0.541417 + 0.840754i \(0.317888\pi\)
\(410\) −13.3485 −0.659234
\(411\) 0 0
\(412\) −50.7878 −2.50213
\(413\) 10.3485 0.509215
\(414\) 0 0
\(415\) −15.2474 −0.748468
\(416\) 0 0
\(417\) 0 0
\(418\) −26.6969 −1.30579
\(419\) −33.5505 −1.63905 −0.819525 0.573044i \(-0.805763\pi\)
−0.819525 + 0.573044i \(0.805763\pi\)
\(420\) 0 0
\(421\) −22.2474 −1.08427 −0.542137 0.840290i \(-0.682385\pi\)
−0.542137 + 0.840290i \(0.682385\pi\)
\(422\) 26.9444 1.31163
\(423\) 0 0
\(424\) −2.69694 −0.130975
\(425\) 5.44949 0.264339
\(426\) 0 0
\(427\) −0.651531 −0.0315298
\(428\) 21.7980 1.05364
\(429\) 0 0
\(430\) 4.89898 0.236250
\(431\) 24.4949 1.17988 0.589939 0.807448i \(-0.299152\pi\)
0.589939 + 0.807448i \(0.299152\pi\)
\(432\) 0 0
\(433\) 2.79796 0.134461 0.0672307 0.997737i \(-0.478584\pi\)
0.0672307 + 0.997737i \(0.478584\pi\)
\(434\) −0.247449 −0.0118779
\(435\) 0 0
\(436\) 46.2020 2.21268
\(437\) 4.44949 0.212848
\(438\) 0 0
\(439\) −36.6969 −1.75145 −0.875725 0.482811i \(-0.839616\pi\)
−0.875725 + 0.482811i \(0.839616\pi\)
\(440\) −12.0000 −0.572078
\(441\) 0 0
\(442\) 59.3939 2.82508
\(443\) 20.4495 0.971585 0.485792 0.874074i \(-0.338531\pi\)
0.485792 + 0.874074i \(0.338531\pi\)
\(444\) 0 0
\(445\) 16.8990 0.801088
\(446\) 52.8990 2.50484
\(447\) 0 0
\(448\) 8.00000 0.377964
\(449\) 21.2474 1.00273 0.501365 0.865236i \(-0.332832\pi\)
0.501365 + 0.865236i \(0.332832\pi\)
\(450\) 0 0
\(451\) 13.3485 0.628555
\(452\) 6.60612 0.310726
\(453\) 0 0
\(454\) −53.3939 −2.50590
\(455\) −4.44949 −0.208595
\(456\) 0 0
\(457\) 0.101021 0.00472554 0.00236277 0.999997i \(-0.499248\pi\)
0.00236277 + 0.999997i \(0.499248\pi\)
\(458\) −69.7980 −3.26144
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) 18.4949 0.861393 0.430697 0.902497i \(-0.358268\pi\)
0.430697 + 0.902497i \(0.358268\pi\)
\(462\) 0 0
\(463\) −24.9444 −1.15926 −0.579632 0.814878i \(-0.696804\pi\)
−0.579632 + 0.814878i \(0.696804\pi\)
\(464\) −41.3939 −1.92166
\(465\) 0 0
\(466\) −53.3939 −2.47342
\(467\) 34.8434 1.61236 0.806179 0.591671i \(-0.201532\pi\)
0.806179 + 0.591671i \(0.201532\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) −20.6969 −0.954679
\(471\) 0 0
\(472\) −50.6969 −2.33352
\(473\) −4.89898 −0.225255
\(474\) 0 0
\(475\) 4.44949 0.204157
\(476\) −21.7980 −0.999108
\(477\) 0 0
\(478\) −16.0454 −0.733900
\(479\) −32.9444 −1.50527 −0.752634 0.658439i \(-0.771217\pi\)
−0.752634 + 0.658439i \(0.771217\pi\)
\(480\) 0 0
\(481\) 17.3485 0.791022
\(482\) −71.8888 −3.27444
\(483\) 0 0
\(484\) −20.0000 −0.909091
\(485\) 3.10102 0.140810
\(486\) 0 0
\(487\) −18.9444 −0.858452 −0.429226 0.903197i \(-0.641214\pi\)
−0.429226 + 0.903197i \(0.641214\pi\)
\(488\) 3.19184 0.144488
\(489\) 0 0
\(490\) −14.6969 −0.663940
\(491\) −12.5505 −0.566397 −0.283198 0.959061i \(-0.591395\pi\)
−0.283198 + 0.959061i \(0.591395\pi\)
\(492\) 0 0
\(493\) −56.3939 −2.53985
\(494\) 48.4949 2.18189
\(495\) 0 0
\(496\) 0.404082 0.0181438
\(497\) −4.34847 −0.195056
\(498\) 0 0
\(499\) −1.00000 −0.0447661 −0.0223831 0.999749i \(-0.507125\pi\)
−0.0223831 + 0.999749i \(0.507125\pi\)
\(500\) 4.00000 0.178885
\(501\) 0 0
\(502\) −44.0908 −1.96787
\(503\) −7.04541 −0.314139 −0.157070 0.987588i \(-0.550205\pi\)
−0.157070 + 0.987588i \(0.550205\pi\)
\(504\) 0 0
\(505\) 12.5505 0.558490
\(506\) −6.00000 −0.266733
\(507\) 0 0
\(508\) −6.20204 −0.275171
\(509\) −28.8990 −1.28092 −0.640462 0.767990i \(-0.721257\pi\)
−0.640462 + 0.767990i \(0.721257\pi\)
\(510\) 0 0
\(511\) 5.34847 0.236602
\(512\) −39.1918 −1.73205
\(513\) 0 0
\(514\) 62.0908 2.73871
\(515\) −12.6969 −0.559494
\(516\) 0 0
\(517\) 20.6969 0.910250
\(518\) −9.55051 −0.419625
\(519\) 0 0
\(520\) 21.7980 0.955904
\(521\) 43.8434 1.92081 0.960406 0.278603i \(-0.0898713\pi\)
0.960406 + 0.278603i \(0.0898713\pi\)
\(522\) 0 0
\(523\) −33.3939 −1.46021 −0.730106 0.683334i \(-0.760529\pi\)
−0.730106 + 0.683334i \(0.760529\pi\)
\(524\) 78.3837 3.42421
\(525\) 0 0
\(526\) −66.7423 −2.91010
\(527\) 0.550510 0.0239806
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −1.34847 −0.0585738
\(531\) 0 0
\(532\) −17.7980 −0.771639
\(533\) −24.2474 −1.05027
\(534\) 0 0
\(535\) 5.44949 0.235602
\(536\) −34.2929 −1.48123
\(537\) 0 0
\(538\) 13.3485 0.575493
\(539\) 14.6969 0.633042
\(540\) 0 0
\(541\) 12.8990 0.554570 0.277285 0.960788i \(-0.410565\pi\)
0.277285 + 0.960788i \(0.410565\pi\)
\(542\) 77.6413 3.33498
\(543\) 0 0
\(544\) 0 0
\(545\) 11.5505 0.494769
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 67.5959 2.88755
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) −46.0454 −1.96160
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) −24.4949 −1.04069
\(555\) 0 0
\(556\) −19.1918 −0.813915
\(557\) 19.0454 0.806980 0.403490 0.914984i \(-0.367797\pi\)
0.403490 + 0.914984i \(0.367797\pi\)
\(558\) 0 0
\(559\) 8.89898 0.376387
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 47.3939 1.99919
\(563\) −5.44949 −0.229669 −0.114834 0.993385i \(-0.536634\pi\)
−0.114834 + 0.993385i \(0.536634\pi\)
\(564\) 0 0
\(565\) 1.65153 0.0694804
\(566\) −5.14643 −0.216321
\(567\) 0 0
\(568\) 21.3031 0.893857
\(569\) 28.2929 1.18610 0.593049 0.805166i \(-0.297924\pi\)
0.593049 + 0.805166i \(0.297924\pi\)
\(570\) 0 0
\(571\) 13.1464 0.550161 0.275080 0.961421i \(-0.411296\pi\)
0.275080 + 0.961421i \(0.411296\pi\)
\(572\) −43.5959 −1.82284
\(573\) 0 0
\(574\) 13.3485 0.557154
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −28.0000 −1.16566 −0.582828 0.812596i \(-0.698054\pi\)
−0.582828 + 0.812596i \(0.698054\pi\)
\(578\) 31.1010 1.29363
\(579\) 0 0
\(580\) −41.3939 −1.71879
\(581\) 15.2474 0.632571
\(582\) 0 0
\(583\) 1.34847 0.0558479
\(584\) −26.2020 −1.08425
\(585\) 0 0
\(586\) 52.0454 2.14998
\(587\) 6.00000 0.247647 0.123823 0.992304i \(-0.460484\pi\)
0.123823 + 0.992304i \(0.460484\pi\)
\(588\) 0 0
\(589\) 0.449490 0.0185209
\(590\) −25.3485 −1.04358
\(591\) 0 0
\(592\) 15.5959 0.640988
\(593\) −27.5505 −1.13136 −0.565682 0.824624i \(-0.691387\pi\)
−0.565682 + 0.824624i \(0.691387\pi\)
\(594\) 0 0
\(595\) −5.44949 −0.223407
\(596\) 5.39388 0.220942
\(597\) 0 0
\(598\) 10.8990 0.445692
\(599\) 2.69694 0.110194 0.0550970 0.998481i \(-0.482453\pi\)
0.0550970 + 0.998481i \(0.482453\pi\)
\(600\) 0 0
\(601\) 5.00000 0.203954 0.101977 0.994787i \(-0.467483\pi\)
0.101977 + 0.994787i \(0.467483\pi\)
\(602\) −4.89898 −0.199667
\(603\) 0 0
\(604\) 56.0000 2.27861
\(605\) −5.00000 −0.203279
\(606\) 0 0
\(607\) −16.2474 −0.659464 −0.329732 0.944075i \(-0.606958\pi\)
−0.329732 + 0.944075i \(0.606958\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.59592 0.0646168
\(611\) −37.5959 −1.52097
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −6.49490 −0.262113
\(615\) 0 0
\(616\) 12.0000 0.483494
\(617\) −12.5505 −0.505265 −0.252632 0.967562i \(-0.581296\pi\)
−0.252632 + 0.967562i \(0.581296\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0.404082 0.0162283
\(621\) 0 0
\(622\) −29.3939 −1.17859
\(623\) −16.8990 −0.677043
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 48.2474 1.92836
\(627\) 0 0
\(628\) 74.3837 2.96823
\(629\) 21.2474 0.847191
\(630\) 0 0
\(631\) 29.5505 1.17639 0.588194 0.808720i \(-0.299839\pi\)
0.588194 + 0.808720i \(0.299839\pi\)
\(632\) −19.5959 −0.779484
\(633\) 0 0
\(634\) −15.3031 −0.607762
\(635\) −1.55051 −0.0615301
\(636\) 0 0
\(637\) −26.6969 −1.05777
\(638\) 62.0908 2.45820
\(639\) 0 0
\(640\) −19.5959 −0.774597
\(641\) −26.9444 −1.06424 −0.532120 0.846669i \(-0.678604\pi\)
−0.532120 + 0.846669i \(0.678604\pi\)
\(642\) 0 0
\(643\) −9.69694 −0.382410 −0.191205 0.981550i \(-0.561240\pi\)
−0.191205 + 0.981550i \(0.561240\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) 59.3939 2.33682
\(647\) −1.95459 −0.0768430 −0.0384215 0.999262i \(-0.512233\pi\)
−0.0384215 + 0.999262i \(0.512233\pi\)
\(648\) 0 0
\(649\) 25.3485 0.995014
\(650\) 10.8990 0.427493
\(651\) 0 0
\(652\) −40.0000 −1.56652
\(653\) −43.8434 −1.71572 −0.857862 0.513881i \(-0.828207\pi\)
−0.857862 + 0.513881i \(0.828207\pi\)
\(654\) 0 0
\(655\) 19.5959 0.765676
\(656\) −21.7980 −0.851067
\(657\) 0 0
\(658\) 20.6969 0.806851
\(659\) 5.14643 0.200476 0.100238 0.994963i \(-0.468040\pi\)
0.100238 + 0.994963i \(0.468040\pi\)
\(660\) 0 0
\(661\) 46.0908 1.79272 0.896362 0.443322i \(-0.146200\pi\)
0.896362 + 0.443322i \(0.146200\pi\)
\(662\) 60.2474 2.34158
\(663\) 0 0
\(664\) −74.6969 −2.89880
\(665\) −4.44949 −0.172544
\(666\) 0 0
\(667\) −10.3485 −0.400694
\(668\) −53.3939 −2.06587
\(669\) 0 0
\(670\) −17.1464 −0.662424
\(671\) −1.59592 −0.0616097
\(672\) 0 0
\(673\) 22.4495 0.865364 0.432682 0.901547i \(-0.357567\pi\)
0.432682 + 0.901547i \(0.357567\pi\)
\(674\) −48.4949 −1.86795
\(675\) 0 0
\(676\) 27.1918 1.04584
\(677\) 12.5505 0.482355 0.241178 0.970481i \(-0.422466\pi\)
0.241178 + 0.970481i \(0.422466\pi\)
\(678\) 0 0
\(679\) −3.10102 −0.119006
\(680\) 26.6969 1.02378
\(681\) 0 0
\(682\) −0.606123 −0.0232097
\(683\) −18.2474 −0.698219 −0.349110 0.937082i \(-0.613516\pi\)
−0.349110 + 0.937082i \(0.613516\pi\)
\(684\) 0 0
\(685\) 16.8990 0.645677
\(686\) 31.8434 1.21579
\(687\) 0 0
\(688\) 8.00000 0.304997
\(689\) −2.44949 −0.0933181
\(690\) 0 0
\(691\) 16.2020 0.616355 0.308177 0.951329i \(-0.400281\pi\)
0.308177 + 0.951329i \(0.400281\pi\)
\(692\) −78.3837 −2.97970
\(693\) 0 0
\(694\) 70.7878 2.68707
\(695\) −4.79796 −0.181997
\(696\) 0 0
\(697\) −29.6969 −1.12485
\(698\) 57.5505 2.17832
\(699\) 0 0
\(700\) −4.00000 −0.151186
\(701\) 52.0454 1.96573 0.982864 0.184332i \(-0.0590123\pi\)
0.982864 + 0.184332i \(0.0590123\pi\)
\(702\) 0 0
\(703\) 17.3485 0.654310
\(704\) 19.5959 0.738549
\(705\) 0 0
\(706\) 38.0908 1.43357
\(707\) −12.5505 −0.472011
\(708\) 0 0
\(709\) −28.7423 −1.07944 −0.539721 0.841844i \(-0.681470\pi\)
−0.539721 + 0.841844i \(0.681470\pi\)
\(710\) 10.6515 0.399745
\(711\) 0 0
\(712\) 82.7878 3.10260
\(713\) 0.101021 0.00378325
\(714\) 0 0
\(715\) −10.8990 −0.407599
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 8.69694 0.324567
\(719\) 11.9444 0.445450 0.222725 0.974881i \(-0.428505\pi\)
0.222725 + 0.974881i \(0.428505\pi\)
\(720\) 0 0
\(721\) 12.6969 0.472859
\(722\) 1.95459 0.0727424
\(723\) 0 0
\(724\) −35.5959 −1.32291
\(725\) −10.3485 −0.384332
\(726\) 0 0
\(727\) −16.3031 −0.604647 −0.302324 0.953205i \(-0.597762\pi\)
−0.302324 + 0.953205i \(0.597762\pi\)
\(728\) −21.7980 −0.807886
\(729\) 0 0
\(730\) −13.1010 −0.484891
\(731\) 10.8990 0.403113
\(732\) 0 0
\(733\) −8.59592 −0.317497 −0.158749 0.987319i \(-0.550746\pi\)
−0.158749 + 0.987319i \(0.550746\pi\)
\(734\) 33.5505 1.23837
\(735\) 0 0
\(736\) 0 0
\(737\) 17.1464 0.631597
\(738\) 0 0
\(739\) −9.20204 −0.338503 −0.169251 0.985573i \(-0.554135\pi\)
−0.169251 + 0.985573i \(0.554135\pi\)
\(740\) 15.5959 0.573317
\(741\) 0 0
\(742\) 1.34847 0.0495039
\(743\) 21.7980 0.799690 0.399845 0.916583i \(-0.369064\pi\)
0.399845 + 0.916583i \(0.369064\pi\)
\(744\) 0 0
\(745\) 1.34847 0.0494041
\(746\) 67.5959 2.47486
\(747\) 0 0
\(748\) −53.3939 −1.95227
\(749\) −5.44949 −0.199120
\(750\) 0 0
\(751\) 30.6515 1.11849 0.559245 0.829002i \(-0.311091\pi\)
0.559245 + 0.829002i \(0.311091\pi\)
\(752\) −33.7980 −1.23248
\(753\) 0 0
\(754\) −112.788 −4.10749
\(755\) 14.0000 0.509512
\(756\) 0 0
\(757\) −3.69694 −0.134368 −0.0671838 0.997741i \(-0.521401\pi\)
−0.0671838 + 0.997741i \(0.521401\pi\)
\(758\) 62.2020 2.25928
\(759\) 0 0
\(760\) 21.7980 0.790695
\(761\) −14.1464 −0.512808 −0.256404 0.966570i \(-0.582538\pi\)
−0.256404 + 0.966570i \(0.582538\pi\)
\(762\) 0 0
\(763\) −11.5505 −0.418157
\(764\) 72.9898 2.64068
\(765\) 0 0
\(766\) −4.04541 −0.146167
\(767\) −46.0454 −1.66260
\(768\) 0 0
\(769\) 10.4495 0.376818 0.188409 0.982091i \(-0.439667\pi\)
0.188409 + 0.982091i \(0.439667\pi\)
\(770\) 6.00000 0.216225
\(771\) 0 0
\(772\) −26.7878 −0.964112
\(773\) 16.2929 0.586013 0.293007 0.956110i \(-0.405344\pi\)
0.293007 + 0.956110i \(0.405344\pi\)
\(774\) 0 0
\(775\) 0.101021 0.00362876
\(776\) 15.1918 0.545355
\(777\) 0 0
\(778\) 8.09082 0.290070
\(779\) −24.2474 −0.868755
\(780\) 0 0
\(781\) −10.6515 −0.381142
\(782\) 13.3485 0.477340
\(783\) 0 0
\(784\) −24.0000 −0.857143
\(785\) 18.5959 0.663717
\(786\) 0 0
\(787\) −21.6969 −0.773412 −0.386706 0.922203i \(-0.626387\pi\)
−0.386706 + 0.922203i \(0.626387\pi\)
\(788\) 91.5959 3.26297
\(789\) 0 0
\(790\) −9.79796 −0.348596
\(791\) −1.65153 −0.0587217
\(792\) 0 0
\(793\) 2.89898 0.102946
\(794\) −33.7980 −1.19944
\(795\) 0 0
\(796\) −11.5959 −0.411006
\(797\) −9.24745 −0.327561 −0.163781 0.986497i \(-0.552369\pi\)
−0.163781 + 0.986497i \(0.552369\pi\)
\(798\) 0 0
\(799\) −46.0454 −1.62897
\(800\) 0 0
\(801\) 0 0
\(802\) 32.0908 1.13317
\(803\) 13.1010 0.462325
\(804\) 0 0
\(805\) −1.00000 −0.0352454
\(806\) 1.10102 0.0387818
\(807\) 0 0
\(808\) 61.4847 2.16302
\(809\) −6.55051 −0.230304 −0.115152 0.993348i \(-0.536735\pi\)
−0.115152 + 0.993348i \(0.536735\pi\)
\(810\) 0 0
\(811\) −42.3939 −1.48865 −0.744325 0.667817i \(-0.767229\pi\)
−0.744325 + 0.667817i \(0.767229\pi\)
\(812\) 41.3939 1.45264
\(813\) 0 0
\(814\) −23.3939 −0.819955
\(815\) −10.0000 −0.350285
\(816\) 0 0
\(817\) 8.89898 0.311336
\(818\) 53.6413 1.87552
\(819\) 0 0
\(820\) −21.7980 −0.761218
\(821\) −21.3031 −0.743482 −0.371741 0.928336i \(-0.621239\pi\)
−0.371741 + 0.928336i \(0.621239\pi\)
\(822\) 0 0
\(823\) 3.59592 0.125346 0.0626729 0.998034i \(-0.480038\pi\)
0.0626729 + 0.998034i \(0.480038\pi\)
\(824\) −62.2020 −2.16691
\(825\) 0 0
\(826\) 25.3485 0.881986
\(827\) −32.1464 −1.11784 −0.558920 0.829221i \(-0.688784\pi\)
−0.558920 + 0.829221i \(0.688784\pi\)
\(828\) 0 0
\(829\) −27.6969 −0.961954 −0.480977 0.876733i \(-0.659718\pi\)
−0.480977 + 0.876733i \(0.659718\pi\)
\(830\) −37.3485 −1.29638
\(831\) 0 0
\(832\) −35.5959 −1.23407
\(833\) −32.6969 −1.13288
\(834\) 0 0
\(835\) −13.3485 −0.461943
\(836\) −43.5959 −1.50780
\(837\) 0 0
\(838\) −82.1816 −2.83892
\(839\) 45.1918 1.56020 0.780098 0.625658i \(-0.215169\pi\)
0.780098 + 0.625658i \(0.215169\pi\)
\(840\) 0 0
\(841\) 78.0908 2.69279
\(842\) −54.4949 −1.87802
\(843\) 0 0
\(844\) 44.0000 1.51454
\(845\) 6.79796 0.233857
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) −2.20204 −0.0756184
\(849\) 0 0
\(850\) 13.3485 0.457849
\(851\) 3.89898 0.133655
\(852\) 0 0
\(853\) 46.0908 1.57812 0.789060 0.614316i \(-0.210568\pi\)
0.789060 + 0.614316i \(0.210568\pi\)
\(854\) −1.59592 −0.0546112
\(855\) 0 0
\(856\) 26.6969 0.912483
\(857\) 13.5959 0.464428 0.232214 0.972665i \(-0.425403\pi\)
0.232214 + 0.972665i \(0.425403\pi\)
\(858\) 0 0
\(859\) 38.1918 1.30309 0.651544 0.758611i \(-0.274121\pi\)
0.651544 + 0.758611i \(0.274121\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) 60.0000 2.04361
\(863\) −6.49490 −0.221089 −0.110544 0.993871i \(-0.535259\pi\)
−0.110544 + 0.993871i \(0.535259\pi\)
\(864\) 0 0
\(865\) −19.5959 −0.666281
\(866\) 6.85357 0.232894
\(867\) 0 0
\(868\) −0.404082 −0.0137154
\(869\) 9.79796 0.332373
\(870\) 0 0
\(871\) −31.1464 −1.05536
\(872\) 56.5857 1.91623
\(873\) 0 0
\(874\) 10.8990 0.368663
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) −10.4949 −0.354388 −0.177194 0.984176i \(-0.556702\pi\)
−0.177194 + 0.984176i \(0.556702\pi\)
\(878\) −89.8888 −3.03360
\(879\) 0 0
\(880\) −9.79796 −0.330289
\(881\) −8.44949 −0.284671 −0.142335 0.989819i \(-0.545461\pi\)
−0.142335 + 0.989819i \(0.545461\pi\)
\(882\) 0 0
\(883\) −37.5505 −1.26368 −0.631838 0.775101i \(-0.717699\pi\)
−0.631838 + 0.775101i \(0.717699\pi\)
\(884\) 96.9898 3.26212
\(885\) 0 0
\(886\) 50.0908 1.68283
\(887\) 6.49490 0.218077 0.109039 0.994038i \(-0.465223\pi\)
0.109039 + 0.994038i \(0.465223\pi\)
\(888\) 0 0
\(889\) 1.55051 0.0520024
\(890\) 41.3939 1.38753
\(891\) 0 0
\(892\) 86.3837 2.89234
\(893\) −37.5959 −1.25810
\(894\) 0 0
\(895\) 6.00000 0.200558
\(896\) 19.5959 0.654654
\(897\) 0 0
\(898\) 52.0454 1.73678
\(899\) −1.04541 −0.0348663
\(900\) 0 0
\(901\) −3.00000 −0.0999445
\(902\) 32.6969 1.08869
\(903\) 0 0
\(904\) 8.09082 0.269097
\(905\) −8.89898 −0.295812
\(906\) 0 0
\(907\) 38.7980 1.28827 0.644133 0.764914i \(-0.277219\pi\)
0.644133 + 0.764914i \(0.277219\pi\)
\(908\) −87.1918 −2.89356
\(909\) 0 0
\(910\) −10.8990 −0.361298
\(911\) 14.2020 0.470535 0.235267 0.971931i \(-0.424403\pi\)
0.235267 + 0.971931i \(0.424403\pi\)
\(912\) 0 0
\(913\) 37.3485 1.23605
\(914\) 0.247449 0.00818488
\(915\) 0 0
\(916\) −113.980 −3.76599
\(917\) −19.5959 −0.647114
\(918\) 0 0
\(919\) −45.3939 −1.49741 −0.748703 0.662906i \(-0.769323\pi\)
−0.748703 + 0.662906i \(0.769323\pi\)
\(920\) 4.89898 0.161515
\(921\) 0 0
\(922\) 45.3031 1.49198
\(923\) 19.3485 0.636863
\(924\) 0 0
\(925\) 3.89898 0.128198
\(926\) −61.1010 −2.00790
\(927\) 0 0
\(928\) 0 0
\(929\) −22.8434 −0.749467 −0.374733 0.927133i \(-0.622266\pi\)
−0.374733 + 0.927133i \(0.622266\pi\)
\(930\) 0 0
\(931\) −26.6969 −0.874957
\(932\) −87.1918 −2.85606
\(933\) 0 0
\(934\) 85.3485 2.79269
\(935\) −13.3485 −0.436542
\(936\) 0 0
\(937\) −8.89898 −0.290717 −0.145358 0.989379i \(-0.546434\pi\)
−0.145358 + 0.989379i \(0.546434\pi\)
\(938\) 17.1464 0.559851
\(939\) 0 0
\(940\) −33.7980 −1.10237
\(941\) 24.8536 0.810203 0.405102 0.914272i \(-0.367236\pi\)
0.405102 + 0.914272i \(0.367236\pi\)
\(942\) 0 0
\(943\) −5.44949 −0.177460
\(944\) −41.3939 −1.34726
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) 0.494897 0.0160820 0.00804100 0.999968i \(-0.497440\pi\)
0.00804100 + 0.999968i \(0.497440\pi\)
\(948\) 0 0
\(949\) −23.7980 −0.772514
\(950\) 10.8990 0.353610
\(951\) 0 0
\(952\) −26.6969 −0.865253
\(953\) −10.4041 −0.337021 −0.168511 0.985700i \(-0.553896\pi\)
−0.168511 + 0.985700i \(0.553896\pi\)
\(954\) 0 0
\(955\) 18.2474 0.590474
\(956\) −26.2020 −0.847435
\(957\) 0 0
\(958\) −80.6969 −2.60720
\(959\) −16.8990 −0.545697
\(960\) 0 0
\(961\) −30.9898 −0.999671
\(962\) 42.4949 1.37009
\(963\) 0 0
\(964\) −117.394 −3.78100
\(965\) −6.69694 −0.215582
\(966\) 0 0
\(967\) 54.0454 1.73798 0.868992 0.494827i \(-0.164769\pi\)
0.868992 + 0.494827i \(0.164769\pi\)
\(968\) −24.4949 −0.787296
\(969\) 0 0
\(970\) 7.59592 0.243890
\(971\) −22.2929 −0.715412 −0.357706 0.933834i \(-0.616441\pi\)
−0.357706 + 0.933834i \(0.616441\pi\)
\(972\) 0 0
\(973\) 4.79796 0.153816
\(974\) −46.4041 −1.48688
\(975\) 0 0
\(976\) 2.60612 0.0834200
\(977\) −19.6515 −0.628708 −0.314354 0.949306i \(-0.601788\pi\)
−0.314354 + 0.949306i \(0.601788\pi\)
\(978\) 0 0
\(979\) −41.3939 −1.32295
\(980\) −24.0000 −0.766652
\(981\) 0 0
\(982\) −30.7423 −0.981028
\(983\) 33.7423 1.07621 0.538107 0.842877i \(-0.319140\pi\)
0.538107 + 0.842877i \(0.319140\pi\)
\(984\) 0 0
\(985\) 22.8990 0.729622
\(986\) −138.136 −4.39915
\(987\) 0 0
\(988\) 79.1918 2.51943
\(989\) 2.00000 0.0635963
\(990\) 0 0
\(991\) 57.7878 1.83569 0.917844 0.396941i \(-0.129928\pi\)
0.917844 + 0.396941i \(0.129928\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −10.6515 −0.337846
\(995\) −2.89898 −0.0919038
\(996\) 0 0
\(997\) 40.0908 1.26969 0.634844 0.772640i \(-0.281064\pi\)
0.634844 + 0.772640i \(0.281064\pi\)
\(998\) −2.44949 −0.0775372
\(999\) 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 1035.2.a.k.1.2 2
3.2 odd 2 345.2.a.i.1.1 2
5.4 even 2 5175.2.a.bl.1.1 2
12.11 even 2 5520.2.a.bi.1.1 2
15.2 even 4 1725.2.b.m.1174.1 4
15.8 even 4 1725.2.b.m.1174.4 4
15.14 odd 2 1725.2.a.y.1.2 2
69.68 even 2 7935.2.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
345.2.a.i.1.1 2 3.2 odd 2
1035.2.a.k.1.2 2 1.1 even 1 trivial
1725.2.a.y.1.2 2 15.14 odd 2
1725.2.b.m.1174.1 4 15.2 even 4
1725.2.b.m.1174.4 4 15.8 even 4
5175.2.a.bl.1.1 2 5.4 even 2
5520.2.a.bi.1.1 2 12.11 even 2
7935.2.a.t.1.1 2 69.68 even 2