Properties

Label 693.4.a.e.1.1
Level $693$
Weight $4$
Character 693.1
Self dual yes
Analytic conductor $40.888$
Analytic rank $0$
Dimension $1$
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] = [693,4,Mod(1,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 693.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: \(40.8883236340\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 231)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 693.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -24.0000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} -4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -24.0000 q^{8} -2.00000 q^{10} +11.0000 q^{11} +7.00000 q^{13} -14.0000 q^{14} -16.0000 q^{16} +14.0000 q^{17} -45.0000 q^{19} +4.00000 q^{20} +22.0000 q^{22} +88.0000 q^{23} -124.000 q^{25} +14.0000 q^{26} +28.0000 q^{28} +69.0000 q^{29} +22.0000 q^{31} +160.000 q^{32} +28.0000 q^{34} +7.00000 q^{35} +57.0000 q^{37} -90.0000 q^{38} +24.0000 q^{40} +380.000 q^{41} +48.0000 q^{43} -44.0000 q^{44} +176.000 q^{46} +385.000 q^{47} +49.0000 q^{49} -248.000 q^{50} -28.0000 q^{52} +672.000 q^{53} -11.0000 q^{55} +168.000 q^{56} +138.000 q^{58} +469.000 q^{59} -342.000 q^{61} +44.0000 q^{62} +448.000 q^{64} -7.00000 q^{65} -139.000 q^{67} -56.0000 q^{68} +14.0000 q^{70} -132.000 q^{71} +145.000 q^{73} +114.000 q^{74} +180.000 q^{76} -77.0000 q^{77} +1244.00 q^{79} +16.0000 q^{80} +760.000 q^{82} -522.000 q^{83} -14.0000 q^{85} +96.0000 q^{86} -264.000 q^{88} -822.000 q^{89} -49.0000 q^{91} -352.000 q^{92} +770.000 q^{94} +45.0000 q^{95} +272.000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 0 0
\(4\) −4.00000 −0.500000
\(5\) −1.00000 −0.0894427 −0.0447214 0.998999i \(-0.514240\pi\)
−0.0447214 + 0.998999i \(0.514240\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) −24.0000 −1.06066
\(9\) 0 0
\(10\) −2.00000 −0.0632456
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 7.00000 0.149342 0.0746712 0.997208i \(-0.476209\pi\)
0.0746712 + 0.997208i \(0.476209\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) −16.0000 −0.250000
\(17\) 14.0000 0.199735 0.0998676 0.995001i \(-0.468158\pi\)
0.0998676 + 0.995001i \(0.468158\pi\)
\(18\) 0 0
\(19\) −45.0000 −0.543353 −0.271677 0.962389i \(-0.587578\pi\)
−0.271677 + 0.962389i \(0.587578\pi\)
\(20\) 4.00000 0.0447214
\(21\) 0 0
\(22\) 22.0000 0.213201
\(23\) 88.0000 0.797794 0.398897 0.916996i \(-0.369393\pi\)
0.398897 + 0.916996i \(0.369393\pi\)
\(24\) 0 0
\(25\) −124.000 −0.992000
\(26\) 14.0000 0.105601
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) 69.0000 0.441827 0.220913 0.975293i \(-0.429096\pi\)
0.220913 + 0.975293i \(0.429096\pi\)
\(30\) 0 0
\(31\) 22.0000 0.127462 0.0637309 0.997967i \(-0.479700\pi\)
0.0637309 + 0.997967i \(0.479700\pi\)
\(32\) 160.000 0.883883
\(33\) 0 0
\(34\) 28.0000 0.141234
\(35\) 7.00000 0.0338062
\(36\) 0 0
\(37\) 57.0000 0.253263 0.126632 0.991950i \(-0.459583\pi\)
0.126632 + 0.991950i \(0.459583\pi\)
\(38\) −90.0000 −0.384209
\(39\) 0 0
\(40\) 24.0000 0.0948683
\(41\) 380.000 1.44746 0.723732 0.690081i \(-0.242425\pi\)
0.723732 + 0.690081i \(0.242425\pi\)
\(42\) 0 0
\(43\) 48.0000 0.170231 0.0851155 0.996371i \(-0.472874\pi\)
0.0851155 + 0.996371i \(0.472874\pi\)
\(44\) −44.0000 −0.150756
\(45\) 0 0
\(46\) 176.000 0.564126
\(47\) 385.000 1.19485 0.597426 0.801924i \(-0.296190\pi\)
0.597426 + 0.801924i \(0.296190\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −248.000 −0.701450
\(51\) 0 0
\(52\) −28.0000 −0.0746712
\(53\) 672.000 1.74163 0.870814 0.491612i \(-0.163592\pi\)
0.870814 + 0.491612i \(0.163592\pi\)
\(54\) 0 0
\(55\) −11.0000 −0.0269680
\(56\) 168.000 0.400892
\(57\) 0 0
\(58\) 138.000 0.312419
\(59\) 469.000 1.03489 0.517446 0.855716i \(-0.326883\pi\)
0.517446 + 0.855716i \(0.326883\pi\)
\(60\) 0 0
\(61\) −342.000 −0.717846 −0.358923 0.933367i \(-0.616856\pi\)
−0.358923 + 0.933367i \(0.616856\pi\)
\(62\) 44.0000 0.0901291
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) −7.00000 −0.0133576
\(66\) 0 0
\(67\) −139.000 −0.253456 −0.126728 0.991938i \(-0.540448\pi\)
−0.126728 + 0.991938i \(0.540448\pi\)
\(68\) −56.0000 −0.0998676
\(69\) 0 0
\(70\) 14.0000 0.0239046
\(71\) −132.000 −0.220641 −0.110321 0.993896i \(-0.535188\pi\)
−0.110321 + 0.993896i \(0.535188\pi\)
\(72\) 0 0
\(73\) 145.000 0.232479 0.116239 0.993221i \(-0.462916\pi\)
0.116239 + 0.993221i \(0.462916\pi\)
\(74\) 114.000 0.179084
\(75\) 0 0
\(76\) 180.000 0.271677
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) 1244.00 1.77166 0.885829 0.464012i \(-0.153591\pi\)
0.885829 + 0.464012i \(0.153591\pi\)
\(80\) 16.0000 0.0223607
\(81\) 0 0
\(82\) 760.000 1.02351
\(83\) −522.000 −0.690325 −0.345162 0.938543i \(-0.612176\pi\)
−0.345162 + 0.938543i \(0.612176\pi\)
\(84\) 0 0
\(85\) −14.0000 −0.0178649
\(86\) 96.0000 0.120371
\(87\) 0 0
\(88\) −264.000 −0.319801
\(89\) −822.000 −0.979009 −0.489505 0.872001i \(-0.662822\pi\)
−0.489505 + 0.872001i \(0.662822\pi\)
\(90\) 0 0
\(91\) −49.0000 −0.0564461
\(92\) −352.000 −0.398897
\(93\) 0 0
\(94\) 770.000 0.844888
\(95\) 45.0000 0.0485990
\(96\) 0 0
\(97\) 272.000 0.284716 0.142358 0.989815i \(-0.454532\pi\)
0.142358 + 0.989815i \(0.454532\pi\)
\(98\) 98.0000 0.101015
\(99\) 0 0
\(100\) 496.000 0.496000
\(101\) 874.000 0.861052 0.430526 0.902578i \(-0.358328\pi\)
0.430526 + 0.902578i \(0.358328\pi\)
\(102\) 0 0
\(103\) −826.000 −0.790177 −0.395088 0.918643i \(-0.629286\pi\)
−0.395088 + 0.918643i \(0.629286\pi\)
\(104\) −168.000 −0.158401
\(105\) 0 0
\(106\) 1344.00 1.23152
\(107\) −219.000 −0.197865 −0.0989324 0.995094i \(-0.531543\pi\)
−0.0989324 + 0.995094i \(0.531543\pi\)
\(108\) 0 0
\(109\) 1426.00 1.25308 0.626541 0.779388i \(-0.284470\pi\)
0.626541 + 0.779388i \(0.284470\pi\)
\(110\) −22.0000 −0.0190693
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) −882.000 −0.734262 −0.367131 0.930169i \(-0.619660\pi\)
−0.367131 + 0.930169i \(0.619660\pi\)
\(114\) 0 0
\(115\) −88.0000 −0.0713569
\(116\) −276.000 −0.220913
\(117\) 0 0
\(118\) 938.000 0.731779
\(119\) −98.0000 −0.0754928
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) −684.000 −0.507594
\(123\) 0 0
\(124\) −88.0000 −0.0637309
\(125\) 249.000 0.178170
\(126\) 0 0
\(127\) 1826.00 1.27584 0.637918 0.770104i \(-0.279796\pi\)
0.637918 + 0.770104i \(0.279796\pi\)
\(128\) −384.000 −0.265165
\(129\) 0 0
\(130\) −14.0000 −0.00944524
\(131\) −84.0000 −0.0560238 −0.0280119 0.999608i \(-0.508918\pi\)
−0.0280119 + 0.999608i \(0.508918\pi\)
\(132\) 0 0
\(133\) 315.000 0.205368
\(134\) −278.000 −0.179220
\(135\) 0 0
\(136\) −336.000 −0.211851
\(137\) 1834.00 1.14372 0.571858 0.820352i \(-0.306223\pi\)
0.571858 + 0.820352i \(0.306223\pi\)
\(138\) 0 0
\(139\) 2416.00 1.47426 0.737131 0.675750i \(-0.236180\pi\)
0.737131 + 0.675750i \(0.236180\pi\)
\(140\) −28.0000 −0.0169031
\(141\) 0 0
\(142\) −264.000 −0.156017
\(143\) 77.0000 0.0450284
\(144\) 0 0
\(145\) −69.0000 −0.0395182
\(146\) 290.000 0.164387
\(147\) 0 0
\(148\) −228.000 −0.126632
\(149\) −1895.00 −1.04191 −0.520955 0.853584i \(-0.674424\pi\)
−0.520955 + 0.853584i \(0.674424\pi\)
\(150\) 0 0
\(151\) −3478.00 −1.87441 −0.937204 0.348782i \(-0.886596\pi\)
−0.937204 + 0.348782i \(0.886596\pi\)
\(152\) 1080.00 0.576313
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) −22.0000 −0.0114005
\(156\) 0 0
\(157\) −952.000 −0.483935 −0.241968 0.970284i \(-0.577793\pi\)
−0.241968 + 0.970284i \(0.577793\pi\)
\(158\) 2488.00 1.25275
\(159\) 0 0
\(160\) −160.000 −0.0790569
\(161\) −616.000 −0.301538
\(162\) 0 0
\(163\) −2483.00 −1.19315 −0.596575 0.802557i \(-0.703472\pi\)
−0.596575 + 0.802557i \(0.703472\pi\)
\(164\) −1520.00 −0.723732
\(165\) 0 0
\(166\) −1044.00 −0.488133
\(167\) −468.000 −0.216856 −0.108428 0.994104i \(-0.534582\pi\)
−0.108428 + 0.994104i \(0.534582\pi\)
\(168\) 0 0
\(169\) −2148.00 −0.977697
\(170\) −28.0000 −0.0126324
\(171\) 0 0
\(172\) −192.000 −0.0851155
\(173\) 2148.00 0.943985 0.471993 0.881603i \(-0.343535\pi\)
0.471993 + 0.881603i \(0.343535\pi\)
\(174\) 0 0
\(175\) 868.000 0.374941
\(176\) −176.000 −0.0753778
\(177\) 0 0
\(178\) −1644.00 −0.692264
\(179\) 1464.00 0.611310 0.305655 0.952142i \(-0.401125\pi\)
0.305655 + 0.952142i \(0.401125\pi\)
\(180\) 0 0
\(181\) 1432.00 0.588065 0.294032 0.955795i \(-0.405003\pi\)
0.294032 + 0.955795i \(0.405003\pi\)
\(182\) −98.0000 −0.0399134
\(183\) 0 0
\(184\) −2112.00 −0.846189
\(185\) −57.0000 −0.0226526
\(186\) 0 0
\(187\) 154.000 0.0602224
\(188\) −1540.00 −0.597426
\(189\) 0 0
\(190\) 90.0000 0.0343647
\(191\) 1330.00 0.503850 0.251925 0.967747i \(-0.418936\pi\)
0.251925 + 0.967747i \(0.418936\pi\)
\(192\) 0 0
\(193\) −2540.00 −0.947322 −0.473661 0.880707i \(-0.657068\pi\)
−0.473661 + 0.880707i \(0.657068\pi\)
\(194\) 544.000 0.201324
\(195\) 0 0
\(196\) −196.000 −0.0714286
\(197\) −1606.00 −0.580826 −0.290413 0.956901i \(-0.593793\pi\)
−0.290413 + 0.956901i \(0.593793\pi\)
\(198\) 0 0
\(199\) 288.000 0.102592 0.0512959 0.998683i \(-0.483665\pi\)
0.0512959 + 0.998683i \(0.483665\pi\)
\(200\) 2976.00 1.05217
\(201\) 0 0
\(202\) 1748.00 0.608856
\(203\) −483.000 −0.166995
\(204\) 0 0
\(205\) −380.000 −0.129465
\(206\) −1652.00 −0.558739
\(207\) 0 0
\(208\) −112.000 −0.0373356
\(209\) −495.000 −0.163827
\(210\) 0 0
\(211\) 1482.00 0.483531 0.241766 0.970335i \(-0.422273\pi\)
0.241766 + 0.970335i \(0.422273\pi\)
\(212\) −2688.00 −0.870814
\(213\) 0 0
\(214\) −438.000 −0.139912
\(215\) −48.0000 −0.0152259
\(216\) 0 0
\(217\) −154.000 −0.0481760
\(218\) 2852.00 0.886063
\(219\) 0 0
\(220\) 44.0000 0.0134840
\(221\) 98.0000 0.0298289
\(222\) 0 0
\(223\) 3502.00 1.05162 0.525810 0.850602i \(-0.323762\pi\)
0.525810 + 0.850602i \(0.323762\pi\)
\(224\) −1120.00 −0.334077
\(225\) 0 0
\(226\) −1764.00 −0.519201
\(227\) −1830.00 −0.535072 −0.267536 0.963548i \(-0.586209\pi\)
−0.267536 + 0.963548i \(0.586209\pi\)
\(228\) 0 0
\(229\) −2268.00 −0.654470 −0.327235 0.944943i \(-0.606117\pi\)
−0.327235 + 0.944943i \(0.606117\pi\)
\(230\) −176.000 −0.0504569
\(231\) 0 0
\(232\) −1656.00 −0.468628
\(233\) −2430.00 −0.683239 −0.341619 0.939838i \(-0.610975\pi\)
−0.341619 + 0.939838i \(0.610975\pi\)
\(234\) 0 0
\(235\) −385.000 −0.106871
\(236\) −1876.00 −0.517446
\(237\) 0 0
\(238\) −196.000 −0.0533815
\(239\) 2151.00 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) 2803.00 0.749200 0.374600 0.927187i \(-0.377780\pi\)
0.374600 + 0.927187i \(0.377780\pi\)
\(242\) 242.000 0.0642824
\(243\) 0 0
\(244\) 1368.00 0.358923
\(245\) −49.0000 −0.0127775
\(246\) 0 0
\(247\) −315.000 −0.0811456
\(248\) −528.000 −0.135194
\(249\) 0 0
\(250\) 498.000 0.125985
\(251\) 5339.00 1.34261 0.671304 0.741182i \(-0.265734\pi\)
0.671304 + 0.741182i \(0.265734\pi\)
\(252\) 0 0
\(253\) 968.000 0.240544
\(254\) 3652.00 0.902153
\(255\) 0 0
\(256\) −4352.00 −1.06250
\(257\) 4439.00 1.07742 0.538711 0.842491i \(-0.318912\pi\)
0.538711 + 0.842491i \(0.318912\pi\)
\(258\) 0 0
\(259\) −399.000 −0.0957245
\(260\) 28.0000 0.00667879
\(261\) 0 0
\(262\) −168.000 −0.0396148
\(263\) −1271.00 −0.297997 −0.148999 0.988837i \(-0.547605\pi\)
−0.148999 + 0.988837i \(0.547605\pi\)
\(264\) 0 0
\(265\) −672.000 −0.155776
\(266\) 630.000 0.145217
\(267\) 0 0
\(268\) 556.000 0.126728
\(269\) −3682.00 −0.834556 −0.417278 0.908779i \(-0.637016\pi\)
−0.417278 + 0.908779i \(0.637016\pi\)
\(270\) 0 0
\(271\) 4127.00 0.925083 0.462541 0.886598i \(-0.346938\pi\)
0.462541 + 0.886598i \(0.346938\pi\)
\(272\) −224.000 −0.0499338
\(273\) 0 0
\(274\) 3668.00 0.808730
\(275\) −1364.00 −0.299099
\(276\) 0 0
\(277\) −44.0000 −0.00954406 −0.00477203 0.999989i \(-0.501519\pi\)
−0.00477203 + 0.999989i \(0.501519\pi\)
\(278\) 4832.00 1.04246
\(279\) 0 0
\(280\) −168.000 −0.0358569
\(281\) 561.000 0.119098 0.0595489 0.998225i \(-0.481034\pi\)
0.0595489 + 0.998225i \(0.481034\pi\)
\(282\) 0 0
\(283\) −3845.00 −0.807638 −0.403819 0.914839i \(-0.632317\pi\)
−0.403819 + 0.914839i \(0.632317\pi\)
\(284\) 528.000 0.110321
\(285\) 0 0
\(286\) 154.000 0.0318399
\(287\) −2660.00 −0.547090
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) −138.000 −0.0279436
\(291\) 0 0
\(292\) −580.000 −0.116239
\(293\) −912.000 −0.181842 −0.0909208 0.995858i \(-0.528981\pi\)
−0.0909208 + 0.995858i \(0.528981\pi\)
\(294\) 0 0
\(295\) −469.000 −0.0925635
\(296\) −1368.00 −0.268626
\(297\) 0 0
\(298\) −3790.00 −0.736741
\(299\) 616.000 0.119144
\(300\) 0 0
\(301\) −336.000 −0.0643413
\(302\) −6956.00 −1.32541
\(303\) 0 0
\(304\) 720.000 0.135838
\(305\) 342.000 0.0642061
\(306\) 0 0
\(307\) 6860.00 1.27531 0.637656 0.770321i \(-0.279904\pi\)
0.637656 + 0.770321i \(0.279904\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) −44.0000 −0.00806139
\(311\) −5472.00 −0.997713 −0.498856 0.866685i \(-0.666246\pi\)
−0.498856 + 0.866685i \(0.666246\pi\)
\(312\) 0 0
\(313\) 6422.00 1.15972 0.579861 0.814716i \(-0.303107\pi\)
0.579861 + 0.814716i \(0.303107\pi\)
\(314\) −1904.00 −0.342194
\(315\) 0 0
\(316\) −4976.00 −0.885829
\(317\) 6476.00 1.14741 0.573704 0.819063i \(-0.305506\pi\)
0.573704 + 0.819063i \(0.305506\pi\)
\(318\) 0 0
\(319\) 759.000 0.133216
\(320\) −448.000 −0.0782624
\(321\) 0 0
\(322\) −1232.00 −0.213219
\(323\) −630.000 −0.108527
\(324\) 0 0
\(325\) −868.000 −0.148148
\(326\) −4966.00 −0.843685
\(327\) 0 0
\(328\) −9120.00 −1.53527
\(329\) −2695.00 −0.451611
\(330\) 0 0
\(331\) −11840.0 −1.96612 −0.983059 0.183288i \(-0.941326\pi\)
−0.983059 + 0.183288i \(0.941326\pi\)
\(332\) 2088.00 0.345162
\(333\) 0 0
\(334\) −936.000 −0.153340
\(335\) 139.000 0.0226698
\(336\) 0 0
\(337\) 1640.00 0.265093 0.132547 0.991177i \(-0.457685\pi\)
0.132547 + 0.991177i \(0.457685\pi\)
\(338\) −4296.00 −0.691336
\(339\) 0 0
\(340\) 56.0000 0.00893243
\(341\) 242.000 0.0384312
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) −1152.00 −0.180557
\(345\) 0 0
\(346\) 4296.00 0.667498
\(347\) −2032.00 −0.314362 −0.157181 0.987570i \(-0.550241\pi\)
−0.157181 + 0.987570i \(0.550241\pi\)
\(348\) 0 0
\(349\) 1755.00 0.269178 0.134589 0.990902i \(-0.457029\pi\)
0.134589 + 0.990902i \(0.457029\pi\)
\(350\) 1736.00 0.265123
\(351\) 0 0
\(352\) 1760.00 0.266501
\(353\) 1101.00 0.166007 0.0830033 0.996549i \(-0.473549\pi\)
0.0830033 + 0.996549i \(0.473549\pi\)
\(354\) 0 0
\(355\) 132.000 0.0197347
\(356\) 3288.00 0.489505
\(357\) 0 0
\(358\) 2928.00 0.432261
\(359\) −5020.00 −0.738010 −0.369005 0.929427i \(-0.620301\pi\)
−0.369005 + 0.929427i \(0.620301\pi\)
\(360\) 0 0
\(361\) −4834.00 −0.704767
\(362\) 2864.00 0.415825
\(363\) 0 0
\(364\) 196.000 0.0282231
\(365\) −145.000 −0.0207936
\(366\) 0 0
\(367\) 11638.0 1.65531 0.827655 0.561237i \(-0.189675\pi\)
0.827655 + 0.561237i \(0.189675\pi\)
\(368\) −1408.00 −0.199449
\(369\) 0 0
\(370\) −114.000 −0.0160178
\(371\) −4704.00 −0.658274
\(372\) 0 0
\(373\) −8834.00 −1.22629 −0.613146 0.789969i \(-0.710096\pi\)
−0.613146 + 0.789969i \(0.710096\pi\)
\(374\) 308.000 0.0425837
\(375\) 0 0
\(376\) −9240.00 −1.26733
\(377\) 483.000 0.0659835
\(378\) 0 0
\(379\) 7507.00 1.01744 0.508719 0.860933i \(-0.330119\pi\)
0.508719 + 0.860933i \(0.330119\pi\)
\(380\) −180.000 −0.0242995
\(381\) 0 0
\(382\) 2660.00 0.356276
\(383\) −3608.00 −0.481358 −0.240679 0.970605i \(-0.577370\pi\)
−0.240679 + 0.970605i \(0.577370\pi\)
\(384\) 0 0
\(385\) 77.0000 0.0101929
\(386\) −5080.00 −0.669858
\(387\) 0 0
\(388\) −1088.00 −0.142358
\(389\) 7896.00 1.02916 0.514580 0.857442i \(-0.327948\pi\)
0.514580 + 0.857442i \(0.327948\pi\)
\(390\) 0 0
\(391\) 1232.00 0.159348
\(392\) −1176.00 −0.151523
\(393\) 0 0
\(394\) −3212.00 −0.410706
\(395\) −1244.00 −0.158462
\(396\) 0 0
\(397\) 6934.00 0.876593 0.438297 0.898830i \(-0.355582\pi\)
0.438297 + 0.898830i \(0.355582\pi\)
\(398\) 576.000 0.0725434
\(399\) 0 0
\(400\) 1984.00 0.248000
\(401\) 700.000 0.0871729 0.0435864 0.999050i \(-0.486122\pi\)
0.0435864 + 0.999050i \(0.486122\pi\)
\(402\) 0 0
\(403\) 154.000 0.0190355
\(404\) −3496.00 −0.430526
\(405\) 0 0
\(406\) −966.000 −0.118083
\(407\) 627.000 0.0763618
\(408\) 0 0
\(409\) −11550.0 −1.39636 −0.698179 0.715923i \(-0.746006\pi\)
−0.698179 + 0.715923i \(0.746006\pi\)
\(410\) −760.000 −0.0915457
\(411\) 0 0
\(412\) 3304.00 0.395088
\(413\) −3283.00 −0.391152
\(414\) 0 0
\(415\) 522.000 0.0617445
\(416\) 1120.00 0.132001
\(417\) 0 0
\(418\) −990.000 −0.115843
\(419\) 4555.00 0.531089 0.265545 0.964099i \(-0.414448\pi\)
0.265545 + 0.964099i \(0.414448\pi\)
\(420\) 0 0
\(421\) −161.000 −0.0186381 −0.00931907 0.999957i \(-0.502966\pi\)
−0.00931907 + 0.999957i \(0.502966\pi\)
\(422\) 2964.00 0.341908
\(423\) 0 0
\(424\) −16128.0 −1.84728
\(425\) −1736.00 −0.198137
\(426\) 0 0
\(427\) 2394.00 0.271320
\(428\) 876.000 0.0989324
\(429\) 0 0
\(430\) −96.0000 −0.0107664
\(431\) 3249.00 0.363106 0.181553 0.983381i \(-0.441888\pi\)
0.181553 + 0.983381i \(0.441888\pi\)
\(432\) 0 0
\(433\) 1792.00 0.198887 0.0994434 0.995043i \(-0.468294\pi\)
0.0994434 + 0.995043i \(0.468294\pi\)
\(434\) −308.000 −0.0340656
\(435\) 0 0
\(436\) −5704.00 −0.626541
\(437\) −3960.00 −0.433484
\(438\) 0 0
\(439\) 9319.00 1.01315 0.506574 0.862197i \(-0.330912\pi\)
0.506574 + 0.862197i \(0.330912\pi\)
\(440\) 264.000 0.0286039
\(441\) 0 0
\(442\) 196.000 0.0210922
\(443\) −5608.00 −0.601454 −0.300727 0.953710i \(-0.597229\pi\)
−0.300727 + 0.953710i \(0.597229\pi\)
\(444\) 0 0
\(445\) 822.000 0.0875653
\(446\) 7004.00 0.743608
\(447\) 0 0
\(448\) −3136.00 −0.330719
\(449\) 4384.00 0.460788 0.230394 0.973097i \(-0.425999\pi\)
0.230394 + 0.973097i \(0.425999\pi\)
\(450\) 0 0
\(451\) 4180.00 0.436427
\(452\) 3528.00 0.367131
\(453\) 0 0
\(454\) −3660.00 −0.378353
\(455\) 49.0000 0.00504869
\(456\) 0 0
\(457\) 324.000 0.0331643 0.0165821 0.999863i \(-0.494721\pi\)
0.0165821 + 0.999863i \(0.494721\pi\)
\(458\) −4536.00 −0.462780
\(459\) 0 0
\(460\) 352.000 0.0356784
\(461\) 18360.0 1.85490 0.927452 0.373943i \(-0.121994\pi\)
0.927452 + 0.373943i \(0.121994\pi\)
\(462\) 0 0
\(463\) −1667.00 −0.167326 −0.0836631 0.996494i \(-0.526662\pi\)
−0.0836631 + 0.996494i \(0.526662\pi\)
\(464\) −1104.00 −0.110457
\(465\) 0 0
\(466\) −4860.00 −0.483123
\(467\) −10839.0 −1.07402 −0.537012 0.843575i \(-0.680447\pi\)
−0.537012 + 0.843575i \(0.680447\pi\)
\(468\) 0 0
\(469\) 973.000 0.0957974
\(470\) −770.000 −0.0755690
\(471\) 0 0
\(472\) −11256.0 −1.09767
\(473\) 528.000 0.0513266
\(474\) 0 0
\(475\) 5580.00 0.539006
\(476\) 392.000 0.0377464
\(477\) 0 0
\(478\) 4302.00 0.411650
\(479\) 910.000 0.0868037 0.0434018 0.999058i \(-0.486180\pi\)
0.0434018 + 0.999058i \(0.486180\pi\)
\(480\) 0 0
\(481\) 399.000 0.0378229
\(482\) 5606.00 0.529764
\(483\) 0 0
\(484\) −484.000 −0.0454545
\(485\) −272.000 −0.0254657
\(486\) 0 0
\(487\) 12032.0 1.11955 0.559776 0.828644i \(-0.310887\pi\)
0.559776 + 0.828644i \(0.310887\pi\)
\(488\) 8208.00 0.761391
\(489\) 0 0
\(490\) −98.0000 −0.00903508
\(491\) −4243.00 −0.389988 −0.194994 0.980804i \(-0.562469\pi\)
−0.194994 + 0.980804i \(0.562469\pi\)
\(492\) 0 0
\(493\) 966.000 0.0882484
\(494\) −630.000 −0.0573786
\(495\) 0 0
\(496\) −352.000 −0.0318655
\(497\) 924.000 0.0833945
\(498\) 0 0
\(499\) −5869.00 −0.526518 −0.263259 0.964725i \(-0.584797\pi\)
−0.263259 + 0.964725i \(0.584797\pi\)
\(500\) −996.000 −0.0890849
\(501\) 0 0
\(502\) 10678.0 0.949367
\(503\) −148.000 −0.0131193 −0.00655964 0.999978i \(-0.502088\pi\)
−0.00655964 + 0.999978i \(0.502088\pi\)
\(504\) 0 0
\(505\) −874.000 −0.0770148
\(506\) 1936.00 0.170090
\(507\) 0 0
\(508\) −7304.00 −0.637918
\(509\) −12114.0 −1.05490 −0.527450 0.849586i \(-0.676852\pi\)
−0.527450 + 0.849586i \(0.676852\pi\)
\(510\) 0 0
\(511\) −1015.00 −0.0878688
\(512\) −5632.00 −0.486136
\(513\) 0 0
\(514\) 8878.00 0.761852
\(515\) 826.000 0.0706756
\(516\) 0 0
\(517\) 4235.00 0.360261
\(518\) −798.000 −0.0676875
\(519\) 0 0
\(520\) 168.000 0.0141679
\(521\) 14943.0 1.25655 0.628277 0.777990i \(-0.283760\pi\)
0.628277 + 0.777990i \(0.283760\pi\)
\(522\) 0 0
\(523\) 16589.0 1.38697 0.693486 0.720470i \(-0.256074\pi\)
0.693486 + 0.720470i \(0.256074\pi\)
\(524\) 336.000 0.0280119
\(525\) 0 0
\(526\) −2542.00 −0.210716
\(527\) 308.000 0.0254586
\(528\) 0 0
\(529\) −4423.00 −0.363524
\(530\) −1344.00 −0.110150
\(531\) 0 0
\(532\) −1260.00 −0.102684
\(533\) 2660.00 0.216168
\(534\) 0 0
\(535\) 219.000 0.0176976
\(536\) 3336.00 0.268831
\(537\) 0 0
\(538\) −7364.00 −0.590120
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 3232.00 0.256848 0.128424 0.991719i \(-0.459008\pi\)
0.128424 + 0.991719i \(0.459008\pi\)
\(542\) 8254.00 0.654132
\(543\) 0 0
\(544\) 2240.00 0.176543
\(545\) −1426.00 −0.112079
\(546\) 0 0
\(547\) −16468.0 −1.28724 −0.643621 0.765345i \(-0.722568\pi\)
−0.643621 + 0.765345i \(0.722568\pi\)
\(548\) −7336.00 −0.571858
\(549\) 0 0
\(550\) −2728.00 −0.211495
\(551\) −3105.00 −0.240068
\(552\) 0 0
\(553\) −8708.00 −0.669624
\(554\) −88.0000 −0.00674867
\(555\) 0 0
\(556\) −9664.00 −0.737131
\(557\) −14143.0 −1.07587 −0.537934 0.842987i \(-0.680795\pi\)
−0.537934 + 0.842987i \(0.680795\pi\)
\(558\) 0 0
\(559\) 336.000 0.0254227
\(560\) −112.000 −0.00845154
\(561\) 0 0
\(562\) 1122.00 0.0842148
\(563\) 22916.0 1.71544 0.857721 0.514115i \(-0.171879\pi\)
0.857721 + 0.514115i \(0.171879\pi\)
\(564\) 0 0
\(565\) 882.000 0.0656744
\(566\) −7690.00 −0.571086
\(567\) 0 0
\(568\) 3168.00 0.234025
\(569\) 294.000 0.0216610 0.0108305 0.999941i \(-0.496552\pi\)
0.0108305 + 0.999941i \(0.496552\pi\)
\(570\) 0 0
\(571\) 13292.0 0.974173 0.487087 0.873354i \(-0.338060\pi\)
0.487087 + 0.873354i \(0.338060\pi\)
\(572\) −308.000 −0.0225142
\(573\) 0 0
\(574\) −5320.00 −0.386851
\(575\) −10912.0 −0.791412
\(576\) 0 0
\(577\) 9630.00 0.694804 0.347402 0.937716i \(-0.387064\pi\)
0.347402 + 0.937716i \(0.387064\pi\)
\(578\) −9434.00 −0.678897
\(579\) 0 0
\(580\) 276.000 0.0197591
\(581\) 3654.00 0.260918
\(582\) 0 0
\(583\) 7392.00 0.525121
\(584\) −3480.00 −0.246581
\(585\) 0 0
\(586\) −1824.00 −0.128581
\(587\) 17015.0 1.19640 0.598198 0.801348i \(-0.295884\pi\)
0.598198 + 0.801348i \(0.295884\pi\)
\(588\) 0 0
\(589\) −990.000 −0.0692568
\(590\) −938.000 −0.0654523
\(591\) 0 0
\(592\) −912.000 −0.0633158
\(593\) 12028.0 0.832936 0.416468 0.909150i \(-0.363268\pi\)
0.416468 + 0.909150i \(0.363268\pi\)
\(594\) 0 0
\(595\) 98.0000 0.00675228
\(596\) 7580.00 0.520955
\(597\) 0 0
\(598\) 1232.00 0.0842479
\(599\) −1252.00 −0.0854012 −0.0427006 0.999088i \(-0.513596\pi\)
−0.0427006 + 0.999088i \(0.513596\pi\)
\(600\) 0 0
\(601\) −19699.0 −1.33700 −0.668502 0.743711i \(-0.733064\pi\)
−0.668502 + 0.743711i \(0.733064\pi\)
\(602\) −672.000 −0.0454961
\(603\) 0 0
\(604\) 13912.0 0.937204
\(605\) −121.000 −0.00813116
\(606\) 0 0
\(607\) 29855.0 1.99634 0.998169 0.0604881i \(-0.0192657\pi\)
0.998169 + 0.0604881i \(0.0192657\pi\)
\(608\) −7200.00 −0.480261
\(609\) 0 0
\(610\) 684.000 0.0454006
\(611\) 2695.00 0.178442
\(612\) 0 0
\(613\) −3178.00 −0.209393 −0.104697 0.994504i \(-0.533387\pi\)
−0.104697 + 0.994504i \(0.533387\pi\)
\(614\) 13720.0 0.901782
\(615\) 0 0
\(616\) 1848.00 0.120873
\(617\) 14394.0 0.939191 0.469595 0.882882i \(-0.344400\pi\)
0.469595 + 0.882882i \(0.344400\pi\)
\(618\) 0 0
\(619\) 3878.00 0.251809 0.125905 0.992042i \(-0.459817\pi\)
0.125905 + 0.992042i \(0.459817\pi\)
\(620\) 88.0000 0.00570027
\(621\) 0 0
\(622\) −10944.0 −0.705489
\(623\) 5754.00 0.370031
\(624\) 0 0
\(625\) 15251.0 0.976064
\(626\) 12844.0 0.820047
\(627\) 0 0
\(628\) 3808.00 0.241968
\(629\) 798.000 0.0505856
\(630\) 0 0
\(631\) 18100.0 1.14192 0.570958 0.820979i \(-0.306572\pi\)
0.570958 + 0.820979i \(0.306572\pi\)
\(632\) −29856.0 −1.87913
\(633\) 0 0
\(634\) 12952.0 0.811340
\(635\) −1826.00 −0.114114
\(636\) 0 0
\(637\) 343.000 0.0213346
\(638\) 1518.00 0.0941978
\(639\) 0 0
\(640\) 384.000 0.0237171
\(641\) 7470.00 0.460292 0.230146 0.973156i \(-0.426080\pi\)
0.230146 + 0.973156i \(0.426080\pi\)
\(642\) 0 0
\(643\) 25400.0 1.55782 0.778910 0.627136i \(-0.215773\pi\)
0.778910 + 0.627136i \(0.215773\pi\)
\(644\) 2464.00 0.150769
\(645\) 0 0
\(646\) −1260.00 −0.0767400
\(647\) −25061.0 −1.52280 −0.761398 0.648284i \(-0.775487\pi\)
−0.761398 + 0.648284i \(0.775487\pi\)
\(648\) 0 0
\(649\) 5159.00 0.312032
\(650\) −1736.00 −0.104756
\(651\) 0 0
\(652\) 9932.00 0.596575
\(653\) 1832.00 0.109788 0.0548941 0.998492i \(-0.482518\pi\)
0.0548941 + 0.998492i \(0.482518\pi\)
\(654\) 0 0
\(655\) 84.0000 0.00501092
\(656\) −6080.00 −0.361866
\(657\) 0 0
\(658\) −5390.00 −0.319338
\(659\) 27809.0 1.64383 0.821916 0.569609i \(-0.192905\pi\)
0.821916 + 0.569609i \(0.192905\pi\)
\(660\) 0 0
\(661\) −29612.0 −1.74247 −0.871235 0.490865i \(-0.836681\pi\)
−0.871235 + 0.490865i \(0.836681\pi\)
\(662\) −23680.0 −1.39026
\(663\) 0 0
\(664\) 12528.0 0.732200
\(665\) −315.000 −0.0183687
\(666\) 0 0
\(667\) 6072.00 0.352487
\(668\) 1872.00 0.108428
\(669\) 0 0
\(670\) 278.000 0.0160300
\(671\) −3762.00 −0.216439
\(672\) 0 0
\(673\) −3892.00 −0.222921 −0.111460 0.993769i \(-0.535553\pi\)
−0.111460 + 0.993769i \(0.535553\pi\)
\(674\) 3280.00 0.187449
\(675\) 0 0
\(676\) 8592.00 0.488848
\(677\) −10518.0 −0.597104 −0.298552 0.954393i \(-0.596504\pi\)
−0.298552 + 0.954393i \(0.596504\pi\)
\(678\) 0 0
\(679\) −1904.00 −0.107612
\(680\) 336.000 0.0189485
\(681\) 0 0
\(682\) 484.000 0.0271750
\(683\) −12902.0 −0.722813 −0.361407 0.932408i \(-0.617703\pi\)
−0.361407 + 0.932408i \(0.617703\pi\)
\(684\) 0 0
\(685\) −1834.00 −0.102297
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −768.000 −0.0425577
\(689\) 4704.00 0.260099
\(690\) 0 0
\(691\) 30386.0 1.67285 0.836424 0.548083i \(-0.184642\pi\)
0.836424 + 0.548083i \(0.184642\pi\)
\(692\) −8592.00 −0.471993
\(693\) 0 0
\(694\) −4064.00 −0.222287
\(695\) −2416.00 −0.131862
\(696\) 0 0
\(697\) 5320.00 0.289110
\(698\) 3510.00 0.190337
\(699\) 0 0
\(700\) −3472.00 −0.187470
\(701\) 26842.0 1.44623 0.723116 0.690727i \(-0.242709\pi\)
0.723116 + 0.690727i \(0.242709\pi\)
\(702\) 0 0
\(703\) −2565.00 −0.137611
\(704\) 4928.00 0.263822
\(705\) 0 0
\(706\) 2202.00 0.117384
\(707\) −6118.00 −0.325447
\(708\) 0 0
\(709\) −5701.00 −0.301982 −0.150991 0.988535i \(-0.548247\pi\)
−0.150991 + 0.988535i \(0.548247\pi\)
\(710\) 264.000 0.0139546
\(711\) 0 0
\(712\) 19728.0 1.03840
\(713\) 1936.00 0.101688
\(714\) 0 0
\(715\) −77.0000 −0.00402746
\(716\) −5856.00 −0.305655
\(717\) 0 0
\(718\) −10040.0 −0.521852
\(719\) 23919.0 1.24065 0.620326 0.784344i \(-0.287000\pi\)
0.620326 + 0.784344i \(0.287000\pi\)
\(720\) 0 0
\(721\) 5782.00 0.298659
\(722\) −9668.00 −0.498346
\(723\) 0 0
\(724\) −5728.00 −0.294032
\(725\) −8556.00 −0.438292
\(726\) 0 0
\(727\) 19188.0 0.978877 0.489438 0.872038i \(-0.337202\pi\)
0.489438 + 0.872038i \(0.337202\pi\)
\(728\) 1176.00 0.0598701
\(729\) 0 0
\(730\) −290.000 −0.0147033
\(731\) 672.000 0.0340011
\(732\) 0 0
\(733\) −5670.00 −0.285711 −0.142856 0.989744i \(-0.545628\pi\)
−0.142856 + 0.989744i \(0.545628\pi\)
\(734\) 23276.0 1.17048
\(735\) 0 0
\(736\) 14080.0 0.705157
\(737\) −1529.00 −0.0764199
\(738\) 0 0
\(739\) 17276.0 0.859957 0.429978 0.902839i \(-0.358521\pi\)
0.429978 + 0.902839i \(0.358521\pi\)
\(740\) 228.000 0.0113263
\(741\) 0 0
\(742\) −9408.00 −0.465470
\(743\) −15367.0 −0.758763 −0.379381 0.925240i \(-0.623863\pi\)
−0.379381 + 0.925240i \(0.623863\pi\)
\(744\) 0 0
\(745\) 1895.00 0.0931912
\(746\) −17668.0 −0.867120
\(747\) 0 0
\(748\) −616.000 −0.0301112
\(749\) 1533.00 0.0747858
\(750\) 0 0
\(751\) −38123.0 −1.85237 −0.926184 0.377072i \(-0.876931\pi\)
−0.926184 + 0.377072i \(0.876931\pi\)
\(752\) −6160.00 −0.298713
\(753\) 0 0
\(754\) 966.000 0.0466574
\(755\) 3478.00 0.167652
\(756\) 0 0
\(757\) 23417.0 1.12431 0.562157 0.827031i \(-0.309972\pi\)
0.562157 + 0.827031i \(0.309972\pi\)
\(758\) 15014.0 0.719437
\(759\) 0 0
\(760\) −1080.00 −0.0515470
\(761\) 16332.0 0.777969 0.388985 0.921244i \(-0.372826\pi\)
0.388985 + 0.921244i \(0.372826\pi\)
\(762\) 0 0
\(763\) −9982.00 −0.473621
\(764\) −5320.00 −0.251925
\(765\) 0 0
\(766\) −7216.00 −0.340372
\(767\) 3283.00 0.154553
\(768\) 0 0
\(769\) 19523.0 0.915497 0.457749 0.889082i \(-0.348656\pi\)
0.457749 + 0.889082i \(0.348656\pi\)
\(770\) 154.000 0.00720750
\(771\) 0 0
\(772\) 10160.0 0.473661
\(773\) −21525.0 −1.00155 −0.500776 0.865577i \(-0.666952\pi\)
−0.500776 + 0.865577i \(0.666952\pi\)
\(774\) 0 0
\(775\) −2728.00 −0.126442
\(776\) −6528.00 −0.301987
\(777\) 0 0
\(778\) 15792.0 0.727726
\(779\) −17100.0 −0.786484
\(780\) 0 0
\(781\) −1452.00 −0.0665258
\(782\) 2464.00 0.112676
\(783\) 0 0
\(784\) −784.000 −0.0357143
\(785\) 952.000 0.0432845
\(786\) 0 0
\(787\) −3707.00 −0.167904 −0.0839519 0.996470i \(-0.526754\pi\)
−0.0839519 + 0.996470i \(0.526754\pi\)
\(788\) 6424.00 0.290413
\(789\) 0 0
\(790\) −2488.00 −0.112049
\(791\) 6174.00 0.277525
\(792\) 0 0
\(793\) −2394.00 −0.107205
\(794\) 13868.0 0.619845
\(795\) 0 0
\(796\) −1152.00 −0.0512959
\(797\) 7621.00 0.338707 0.169354 0.985555i \(-0.445832\pi\)
0.169354 + 0.985555i \(0.445832\pi\)
\(798\) 0 0
\(799\) 5390.00 0.238654
\(800\) −19840.0 −0.876812
\(801\) 0 0
\(802\) 1400.00 0.0616405
\(803\) 1595.00 0.0700951
\(804\) 0 0
\(805\) 616.000 0.0269704
\(806\) 308.000 0.0134601
\(807\) 0 0
\(808\) −20976.0 −0.913284
\(809\) −23451.0 −1.01915 −0.509576 0.860426i \(-0.670198\pi\)
−0.509576 + 0.860426i \(0.670198\pi\)
\(810\) 0 0
\(811\) −4499.00 −0.194798 −0.0973990 0.995245i \(-0.531052\pi\)
−0.0973990 + 0.995245i \(0.531052\pi\)
\(812\) 1932.00 0.0834974
\(813\) 0 0
\(814\) 1254.00 0.0539959
\(815\) 2483.00 0.106719
\(816\) 0 0
\(817\) −2160.00 −0.0924955
\(818\) −23100.0 −0.987375
\(819\) 0 0
\(820\) 1520.00 0.0647326
\(821\) 30215.0 1.28442 0.642211 0.766528i \(-0.278017\pi\)
0.642211 + 0.766528i \(0.278017\pi\)
\(822\) 0 0
\(823\) −19947.0 −0.844847 −0.422423 0.906399i \(-0.638820\pi\)
−0.422423 + 0.906399i \(0.638820\pi\)
\(824\) 19824.0 0.838109
\(825\) 0 0
\(826\) −6566.00 −0.276586
\(827\) 20341.0 0.855291 0.427646 0.903946i \(-0.359343\pi\)
0.427646 + 0.903946i \(0.359343\pi\)
\(828\) 0 0
\(829\) −14024.0 −0.587544 −0.293772 0.955876i \(-0.594911\pi\)
−0.293772 + 0.955876i \(0.594911\pi\)
\(830\) 1044.00 0.0436600
\(831\) 0 0
\(832\) 3136.00 0.130675
\(833\) 686.000 0.0285336
\(834\) 0 0
\(835\) 468.000 0.0193962
\(836\) 1980.00 0.0819136
\(837\) 0 0
\(838\) 9110.00 0.375537
\(839\) 37193.0 1.53045 0.765223 0.643765i \(-0.222628\pi\)
0.765223 + 0.643765i \(0.222628\pi\)
\(840\) 0 0
\(841\) −19628.0 −0.804789
\(842\) −322.000 −0.0131792
\(843\) 0 0
\(844\) −5928.00 −0.241766
\(845\) 2148.00 0.0874479
\(846\) 0 0
\(847\) −847.000 −0.0343604
\(848\) −10752.0 −0.435407
\(849\) 0 0
\(850\) −3472.00 −0.140104
\(851\) 5016.00 0.202052
\(852\) 0 0
\(853\) −37042.0 −1.48686 −0.743431 0.668812i \(-0.766803\pi\)
−0.743431 + 0.668812i \(0.766803\pi\)
\(854\) 4788.00 0.191852
\(855\) 0 0
\(856\) 5256.00 0.209867
\(857\) 41962.0 1.67257 0.836286 0.548293i \(-0.184722\pi\)
0.836286 + 0.548293i \(0.184722\pi\)
\(858\) 0 0
\(859\) −9372.00 −0.372257 −0.186128 0.982525i \(-0.559594\pi\)
−0.186128 + 0.982525i \(0.559594\pi\)
\(860\) 192.000 0.00761296
\(861\) 0 0
\(862\) 6498.00 0.256755
\(863\) −18096.0 −0.713783 −0.356892 0.934146i \(-0.616163\pi\)
−0.356892 + 0.934146i \(0.616163\pi\)
\(864\) 0 0
\(865\) −2148.00 −0.0844326
\(866\) 3584.00 0.140634
\(867\) 0 0
\(868\) 616.000 0.0240880
\(869\) 13684.0 0.534175
\(870\) 0 0
\(871\) −973.000 −0.0378517
\(872\) −34224.0 −1.32910
\(873\) 0 0
\(874\) −7920.00 −0.306519
\(875\) −1743.00 −0.0673419
\(876\) 0 0
\(877\) −28848.0 −1.11075 −0.555375 0.831600i \(-0.687425\pi\)
−0.555375 + 0.831600i \(0.687425\pi\)
\(878\) 18638.0 0.716403
\(879\) 0 0
\(880\) 176.000 0.00674200
\(881\) −26273.0 −1.00472 −0.502361 0.864658i \(-0.667535\pi\)
−0.502361 + 0.864658i \(0.667535\pi\)
\(882\) 0 0
\(883\) −33821.0 −1.28898 −0.644489 0.764614i \(-0.722930\pi\)
−0.644489 + 0.764614i \(0.722930\pi\)
\(884\) −392.000 −0.0149145
\(885\) 0 0
\(886\) −11216.0 −0.425292
\(887\) 14134.0 0.535032 0.267516 0.963553i \(-0.413797\pi\)
0.267516 + 0.963553i \(0.413797\pi\)
\(888\) 0 0
\(889\) −12782.0 −0.482221
\(890\) 1644.00 0.0619180
\(891\) 0 0
\(892\) −14008.0 −0.525810
\(893\) −17325.0 −0.649226
\(894\) 0 0
\(895\) −1464.00 −0.0546772
\(896\) 2688.00 0.100223
\(897\) 0 0
\(898\) 8768.00 0.325826
\(899\) 1518.00 0.0563161
\(900\) 0 0
\(901\) 9408.00 0.347865
\(902\) 8360.00 0.308600
\(903\) 0 0
\(904\) 21168.0 0.778802
\(905\) −1432.00 −0.0525981
\(906\) 0 0
\(907\) −35748.0 −1.30870 −0.654351 0.756191i \(-0.727058\pi\)
−0.654351 + 0.756191i \(0.727058\pi\)
\(908\) 7320.00 0.267536
\(909\) 0 0
\(910\) 98.0000 0.00356997
\(911\) 9522.00 0.346299 0.173149 0.984896i \(-0.444606\pi\)
0.173149 + 0.984896i \(0.444606\pi\)
\(912\) 0 0
\(913\) −5742.00 −0.208141
\(914\) 648.000 0.0234507
\(915\) 0 0
\(916\) 9072.00 0.327235
\(917\) 588.000 0.0211750
\(918\) 0 0
\(919\) −33260.0 −1.19385 −0.596924 0.802298i \(-0.703611\pi\)
−0.596924 + 0.802298i \(0.703611\pi\)
\(920\) 2112.00 0.0756854
\(921\) 0 0
\(922\) 36720.0 1.31161
\(923\) −924.000 −0.0329511
\(924\) 0 0
\(925\) −7068.00 −0.251237
\(926\) −3334.00 −0.118318
\(927\) 0 0
\(928\) 11040.0 0.390523
\(929\) 55101.0 1.94597 0.972984 0.230871i \(-0.0741574\pi\)
0.972984 + 0.230871i \(0.0741574\pi\)
\(930\) 0 0
\(931\) −2205.00 −0.0776219
\(932\) 9720.00 0.341619
\(933\) 0 0
\(934\) −21678.0 −0.759449
\(935\) −154.000 −0.00538646
\(936\) 0 0
\(937\) −19474.0 −0.678962 −0.339481 0.940613i \(-0.610252\pi\)
−0.339481 + 0.940613i \(0.610252\pi\)
\(938\) 1946.00 0.0677390
\(939\) 0 0
\(940\) 1540.00 0.0534354
\(941\) −52104.0 −1.80504 −0.902520 0.430649i \(-0.858285\pi\)
−0.902520 + 0.430649i \(0.858285\pi\)
\(942\) 0 0
\(943\) 33440.0 1.15478
\(944\) −7504.00 −0.258723
\(945\) 0 0
\(946\) 1056.00 0.0362934
\(947\) −16830.0 −0.577510 −0.288755 0.957403i \(-0.593241\pi\)
−0.288755 + 0.957403i \(0.593241\pi\)
\(948\) 0 0
\(949\) 1015.00 0.0347190
\(950\) 11160.0 0.381135
\(951\) 0 0
\(952\) 2352.00 0.0800722
\(953\) 13997.0 0.475768 0.237884 0.971294i \(-0.423546\pi\)
0.237884 + 0.971294i \(0.423546\pi\)
\(954\) 0 0
\(955\) −1330.00 −0.0450657
\(956\) −8604.00 −0.291081
\(957\) 0 0
\(958\) 1820.00 0.0613795
\(959\) −12838.0 −0.432284
\(960\) 0 0
\(961\) −29307.0 −0.983753
\(962\) 798.000 0.0267449
\(963\) 0 0
\(964\) −11212.0 −0.374600
\(965\) 2540.00 0.0847311
\(966\) 0 0
\(967\) 9574.00 0.318386 0.159193 0.987247i \(-0.449111\pi\)
0.159193 + 0.987247i \(0.449111\pi\)
\(968\) −2904.00 −0.0964237
\(969\) 0 0
\(970\) −544.000 −0.0180070
\(971\) −32585.0 −1.07693 −0.538467 0.842647i \(-0.680996\pi\)
−0.538467 + 0.842647i \(0.680996\pi\)
\(972\) 0 0
\(973\) −16912.0 −0.557219
\(974\) 24064.0 0.791643
\(975\) 0 0
\(976\) 5472.00 0.179462
\(977\) −42036.0 −1.37651 −0.688255 0.725469i \(-0.741623\pi\)
−0.688255 + 0.725469i \(0.741623\pi\)
\(978\) 0 0
\(979\) −9042.00 −0.295182
\(980\) 196.000 0.00638877
\(981\) 0 0
\(982\) −8486.00 −0.275763
\(983\) −42336.0 −1.37366 −0.686830 0.726818i \(-0.740999\pi\)
−0.686830 + 0.726818i \(0.740999\pi\)
\(984\) 0 0
\(985\) 1606.00 0.0519507
\(986\) 1932.00 0.0624010
\(987\) 0 0
\(988\) 1260.00 0.0405728
\(989\) 4224.00 0.135809
\(990\) 0 0
\(991\) −4691.00 −0.150368 −0.0751839 0.997170i \(-0.523954\pi\)
−0.0751839 + 0.997170i \(0.523954\pi\)
\(992\) 3520.00 0.112661
\(993\) 0 0
\(994\) 1848.00 0.0589688
\(995\) −288.000 −0.00917609
\(996\) 0 0
\(997\) 18518.0 0.588236 0.294118 0.955769i \(-0.404974\pi\)
0.294118 + 0.955769i \(0.404974\pi\)
\(998\) −11738.0 −0.372305
\(999\) 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 693.4.a.e.1.1 1
3.2 odd 2 231.4.a.b.1.1 1
21.20 even 2 1617.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.4.a.b.1.1 1 3.2 odd 2
693.4.a.e.1.1 1 1.1 even 1 trivial
1617.4.a.c.1.1 1 21.20 even 2