Properties

Label 4014.2.a.w.1.7
Level $4014$
Weight $2$
Character 4014.1
Self dual yes
Analytic conductor $32.052$
Analytic rank $0$
Dimension $7$
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] = [4014,2,Mod(1,4014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4014.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: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 14x^{5} + 12x^{4} + 50x^{3} - 36x^{2} - 38x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 446)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.90898\) of defining polynomial
Character \(\chi\) \(=\) 4014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.52361 q^{5} -0.552246 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.52361 q^{5} -0.552246 q^{7} -1.00000 q^{8} -3.52361 q^{10} -4.67688 q^{11} +4.98313 q^{13} +0.552246 q^{14} +1.00000 q^{16} +5.42398 q^{17} +5.81795 q^{19} +3.52361 q^{20} +4.67688 q^{22} -1.00816 q^{23} +7.41582 q^{25} -4.98313 q^{26} -0.552246 q^{28} -1.30022 q^{29} -2.55507 q^{31} -1.00000 q^{32} -5.42398 q^{34} -1.94590 q^{35} +6.51958 q^{37} -5.81795 q^{38} -3.52361 q^{40} +1.43947 q^{41} -2.12633 q^{43} -4.67688 q^{44} +1.00816 q^{46} -9.21193 q^{47} -6.69502 q^{49} -7.41582 q^{50} +4.98313 q^{52} +11.7307 q^{53} -16.4795 q^{55} +0.552246 q^{56} +1.30022 q^{58} -10.2734 q^{59} +10.3437 q^{61} +2.55507 q^{62} +1.00000 q^{64} +17.5586 q^{65} +14.7510 q^{67} +5.42398 q^{68} +1.94590 q^{70} -13.2562 q^{71} -1.22665 q^{73} -6.51958 q^{74} +5.81795 q^{76} +2.58279 q^{77} +7.86075 q^{79} +3.52361 q^{80} -1.43947 q^{82} +1.03632 q^{83} +19.1120 q^{85} +2.12633 q^{86} +4.67688 q^{88} -6.94988 q^{89} -2.75191 q^{91} -1.00816 q^{92} +9.21193 q^{94} +20.5002 q^{95} -15.1636 q^{97} +6.69502 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{2} + 7 q^{4} - 2 q^{5} + 6 q^{7} - 7 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 7 q^{2} + 7 q^{4} - 2 q^{5} + 6 q^{7} - 7 q^{8} + 2 q^{10} - 9 q^{11} - 2 q^{13} - 6 q^{14} + 7 q^{16} + 7 q^{17} - 2 q^{19} - 2 q^{20} + 9 q^{22} - 15 q^{23} + 13 q^{25} + 2 q^{26} + 6 q^{28} - 9 q^{29} - 2 q^{31} - 7 q^{32} - 7 q^{34} + 4 q^{35} + 5 q^{37} + 2 q^{38} + 2 q^{40} + 33 q^{41} + 20 q^{43} - 9 q^{44} + 15 q^{46} + 2 q^{47} + 3 q^{49} - 13 q^{50} - 2 q^{52} + 13 q^{53} - 18 q^{55} - 6 q^{56} + 9 q^{58} - 9 q^{59} + 8 q^{61} + 2 q^{62} + 7 q^{64} + 44 q^{65} + 29 q^{67} + 7 q^{68} - 4 q^{70} - 37 q^{73} - 5 q^{74} - 2 q^{76} + 18 q^{77} + 32 q^{79} - 2 q^{80} - 33 q^{82} + 6 q^{83} - 4 q^{85} - 20 q^{86} + 9 q^{88} + 17 q^{89} - 4 q^{91} - 15 q^{92} - 2 q^{94} + 12 q^{95} + 12 q^{97} - 3 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 3.52361 1.57581 0.787903 0.615800i \(-0.211167\pi\)
0.787903 + 0.615800i \(0.211167\pi\)
\(6\) 0 0
\(7\) −0.552246 −0.208729 −0.104365 0.994539i \(-0.533281\pi\)
−0.104365 + 0.994539i \(0.533281\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −3.52361 −1.11426
\(11\) −4.67688 −1.41013 −0.705066 0.709142i \(-0.749082\pi\)
−0.705066 + 0.709142i \(0.749082\pi\)
\(12\) 0 0
\(13\) 4.98313 1.38207 0.691036 0.722821i \(-0.257155\pi\)
0.691036 + 0.722821i \(0.257155\pi\)
\(14\) 0.552246 0.147594
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.42398 1.31551 0.657754 0.753233i \(-0.271507\pi\)
0.657754 + 0.753233i \(0.271507\pi\)
\(18\) 0 0
\(19\) 5.81795 1.33473 0.667365 0.744731i \(-0.267422\pi\)
0.667365 + 0.744731i \(0.267422\pi\)
\(20\) 3.52361 0.787903
\(21\) 0 0
\(22\) 4.67688 0.997113
\(23\) −1.00816 −0.210216 −0.105108 0.994461i \(-0.533519\pi\)
−0.105108 + 0.994461i \(0.533519\pi\)
\(24\) 0 0
\(25\) 7.41582 1.48316
\(26\) −4.98313 −0.977272
\(27\) 0 0
\(28\) −0.552246 −0.104365
\(29\) −1.30022 −0.241444 −0.120722 0.992686i \(-0.538521\pi\)
−0.120722 + 0.992686i \(0.538521\pi\)
\(30\) 0 0
\(31\) −2.55507 −0.458904 −0.229452 0.973320i \(-0.573693\pi\)
−0.229452 + 0.973320i \(0.573693\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −5.42398 −0.930205
\(35\) −1.94590 −0.328917
\(36\) 0 0
\(37\) 6.51958 1.07181 0.535906 0.844278i \(-0.319970\pi\)
0.535906 + 0.844278i \(0.319970\pi\)
\(38\) −5.81795 −0.943797
\(39\) 0 0
\(40\) −3.52361 −0.557131
\(41\) 1.43947 0.224807 0.112404 0.993663i \(-0.464145\pi\)
0.112404 + 0.993663i \(0.464145\pi\)
\(42\) 0 0
\(43\) −2.12633 −0.324263 −0.162131 0.986769i \(-0.551837\pi\)
−0.162131 + 0.986769i \(0.551837\pi\)
\(44\) −4.67688 −0.705066
\(45\) 0 0
\(46\) 1.00816 0.148645
\(47\) −9.21193 −1.34370 −0.671849 0.740688i \(-0.734500\pi\)
−0.671849 + 0.740688i \(0.734500\pi\)
\(48\) 0 0
\(49\) −6.69502 −0.956432
\(50\) −7.41582 −1.04876
\(51\) 0 0
\(52\) 4.98313 0.691036
\(53\) 11.7307 1.61133 0.805666 0.592370i \(-0.201808\pi\)
0.805666 + 0.592370i \(0.201808\pi\)
\(54\) 0 0
\(55\) −16.4795 −2.22209
\(56\) 0.552246 0.0737970
\(57\) 0 0
\(58\) 1.30022 0.170727
\(59\) −10.2734 −1.33748 −0.668741 0.743495i \(-0.733166\pi\)
−0.668741 + 0.743495i \(0.733166\pi\)
\(60\) 0 0
\(61\) 10.3437 1.32438 0.662190 0.749336i \(-0.269627\pi\)
0.662190 + 0.749336i \(0.269627\pi\)
\(62\) 2.55507 0.324494
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 17.5586 2.17788
\(66\) 0 0
\(67\) 14.7510 1.80212 0.901058 0.433699i \(-0.142792\pi\)
0.901058 + 0.433699i \(0.142792\pi\)
\(68\) 5.42398 0.657754
\(69\) 0 0
\(70\) 1.94590 0.232579
\(71\) −13.2562 −1.57322 −0.786611 0.617449i \(-0.788166\pi\)
−0.786611 + 0.617449i \(0.788166\pi\)
\(72\) 0 0
\(73\) −1.22665 −0.143569 −0.0717844 0.997420i \(-0.522869\pi\)
−0.0717844 + 0.997420i \(0.522869\pi\)
\(74\) −6.51958 −0.757886
\(75\) 0 0
\(76\) 5.81795 0.667365
\(77\) 2.58279 0.294336
\(78\) 0 0
\(79\) 7.86075 0.884403 0.442202 0.896916i \(-0.354198\pi\)
0.442202 + 0.896916i \(0.354198\pi\)
\(80\) 3.52361 0.393951
\(81\) 0 0
\(82\) −1.43947 −0.158963
\(83\) 1.03632 0.113751 0.0568755 0.998381i \(-0.481886\pi\)
0.0568755 + 0.998381i \(0.481886\pi\)
\(84\) 0 0
\(85\) 19.1120 2.07299
\(86\) 2.12633 0.229288
\(87\) 0 0
\(88\) 4.67688 0.498557
\(89\) −6.94988 −0.736686 −0.368343 0.929690i \(-0.620075\pi\)
−0.368343 + 0.929690i \(0.620075\pi\)
\(90\) 0 0
\(91\) −2.75191 −0.288479
\(92\) −1.00816 −0.105108
\(93\) 0 0
\(94\) 9.21193 0.950138
\(95\) 20.5002 2.10328
\(96\) 0 0
\(97\) −15.1636 −1.53964 −0.769818 0.638264i \(-0.779653\pi\)
−0.769818 + 0.638264i \(0.779653\pi\)
\(98\) 6.69502 0.676300
\(99\) 0 0
\(100\) 7.41582 0.741582
\(101\) 5.37759 0.535090 0.267545 0.963545i \(-0.413788\pi\)
0.267545 + 0.963545i \(0.413788\pi\)
\(102\) 0 0
\(103\) 3.48947 0.343828 0.171914 0.985112i \(-0.445005\pi\)
0.171914 + 0.985112i \(0.445005\pi\)
\(104\) −4.98313 −0.488636
\(105\) 0 0
\(106\) −11.7307 −1.13938
\(107\) 19.0825 1.84478 0.922389 0.386263i \(-0.126234\pi\)
0.922389 + 0.386263i \(0.126234\pi\)
\(108\) 0 0
\(109\) −3.42944 −0.328481 −0.164240 0.986420i \(-0.552517\pi\)
−0.164240 + 0.986420i \(0.552517\pi\)
\(110\) 16.4795 1.57126
\(111\) 0 0
\(112\) −0.552246 −0.0521823
\(113\) 11.2528 1.05857 0.529287 0.848443i \(-0.322459\pi\)
0.529287 + 0.848443i \(0.322459\pi\)
\(114\) 0 0
\(115\) −3.55237 −0.331260
\(116\) −1.30022 −0.120722
\(117\) 0 0
\(118\) 10.2734 0.945743
\(119\) −2.99537 −0.274585
\(120\) 0 0
\(121\) 10.8732 0.988470
\(122\) −10.3437 −0.936478
\(123\) 0 0
\(124\) −2.55507 −0.229452
\(125\) 8.51240 0.761372
\(126\) 0 0
\(127\) −1.66213 −0.147490 −0.0737452 0.997277i \(-0.523495\pi\)
−0.0737452 + 0.997277i \(0.523495\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −17.5586 −1.53999
\(131\) 17.8952 1.56351 0.781754 0.623586i \(-0.214325\pi\)
0.781754 + 0.623586i \(0.214325\pi\)
\(132\) 0 0
\(133\) −3.21294 −0.278597
\(134\) −14.7510 −1.27429
\(135\) 0 0
\(136\) −5.42398 −0.465102
\(137\) −8.80332 −0.752118 −0.376059 0.926596i \(-0.622721\pi\)
−0.376059 + 0.926596i \(0.622721\pi\)
\(138\) 0 0
\(139\) 8.48773 0.719920 0.359960 0.932968i \(-0.382790\pi\)
0.359960 + 0.932968i \(0.382790\pi\)
\(140\) −1.94590 −0.164458
\(141\) 0 0
\(142\) 13.2562 1.11244
\(143\) −23.3055 −1.94890
\(144\) 0 0
\(145\) −4.58146 −0.380469
\(146\) 1.22665 0.101518
\(147\) 0 0
\(148\) 6.51958 0.535906
\(149\) −19.1172 −1.56614 −0.783069 0.621934i \(-0.786347\pi\)
−0.783069 + 0.621934i \(0.786347\pi\)
\(150\) 0 0
\(151\) −4.99709 −0.406657 −0.203329 0.979111i \(-0.565176\pi\)
−0.203329 + 0.979111i \(0.565176\pi\)
\(152\) −5.81795 −0.471898
\(153\) 0 0
\(154\) −2.58279 −0.208127
\(155\) −9.00307 −0.723144
\(156\) 0 0
\(157\) 17.2136 1.37380 0.686898 0.726754i \(-0.258972\pi\)
0.686898 + 0.726754i \(0.258972\pi\)
\(158\) −7.86075 −0.625367
\(159\) 0 0
\(160\) −3.52361 −0.278566
\(161\) 0.556753 0.0438783
\(162\) 0 0
\(163\) 4.92931 0.386093 0.193047 0.981190i \(-0.438163\pi\)
0.193047 + 0.981190i \(0.438163\pi\)
\(164\) 1.43947 0.112404
\(165\) 0 0
\(166\) −1.03632 −0.0804341
\(167\) 6.43760 0.498157 0.249078 0.968483i \(-0.419872\pi\)
0.249078 + 0.968483i \(0.419872\pi\)
\(168\) 0 0
\(169\) 11.8316 0.910121
\(170\) −19.1120 −1.46582
\(171\) 0 0
\(172\) −2.12633 −0.162131
\(173\) 0.967478 0.0735560 0.0367780 0.999323i \(-0.488291\pi\)
0.0367780 + 0.999323i \(0.488291\pi\)
\(174\) 0 0
\(175\) −4.09535 −0.309580
\(176\) −4.67688 −0.352533
\(177\) 0 0
\(178\) 6.94988 0.520915
\(179\) 22.2380 1.66215 0.831073 0.556163i \(-0.187727\pi\)
0.831073 + 0.556163i \(0.187727\pi\)
\(180\) 0 0
\(181\) −6.64066 −0.493597 −0.246798 0.969067i \(-0.579379\pi\)
−0.246798 + 0.969067i \(0.579379\pi\)
\(182\) 2.75191 0.203985
\(183\) 0 0
\(184\) 1.00816 0.0743227
\(185\) 22.9724 1.68897
\(186\) 0 0
\(187\) −25.3673 −1.85504
\(188\) −9.21193 −0.671849
\(189\) 0 0
\(190\) −20.5002 −1.48724
\(191\) −16.0979 −1.16480 −0.582400 0.812902i \(-0.697886\pi\)
−0.582400 + 0.812902i \(0.697886\pi\)
\(192\) 0 0
\(193\) −9.49577 −0.683520 −0.341760 0.939787i \(-0.611023\pi\)
−0.341760 + 0.939787i \(0.611023\pi\)
\(194\) 15.1636 1.08869
\(195\) 0 0
\(196\) −6.69502 −0.478216
\(197\) −18.2762 −1.30213 −0.651063 0.759024i \(-0.725676\pi\)
−0.651063 + 0.759024i \(0.725676\pi\)
\(198\) 0 0
\(199\) 8.57295 0.607721 0.303860 0.952717i \(-0.401724\pi\)
0.303860 + 0.952717i \(0.401724\pi\)
\(200\) −7.41582 −0.524378
\(201\) 0 0
\(202\) −5.37759 −0.378366
\(203\) 0.718040 0.0503965
\(204\) 0 0
\(205\) 5.07213 0.354253
\(206\) −3.48947 −0.243123
\(207\) 0 0
\(208\) 4.98313 0.345518
\(209\) −27.2098 −1.88214
\(210\) 0 0
\(211\) −6.80449 −0.468441 −0.234220 0.972184i \(-0.575254\pi\)
−0.234220 + 0.972184i \(0.575254\pi\)
\(212\) 11.7307 0.805666
\(213\) 0 0
\(214\) −19.0825 −1.30445
\(215\) −7.49236 −0.510975
\(216\) 0 0
\(217\) 1.41103 0.0957867
\(218\) 3.42944 0.232271
\(219\) 0 0
\(220\) −16.4795 −1.11105
\(221\) 27.0284 1.81813
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) 0.552246 0.0368985
\(225\) 0 0
\(226\) −11.2528 −0.748525
\(227\) −27.8830 −1.85066 −0.925330 0.379163i \(-0.876212\pi\)
−0.925330 + 0.379163i \(0.876212\pi\)
\(228\) 0 0
\(229\) 10.6798 0.705739 0.352869 0.935673i \(-0.385206\pi\)
0.352869 + 0.935673i \(0.385206\pi\)
\(230\) 3.55237 0.234236
\(231\) 0 0
\(232\) 1.30022 0.0853634
\(233\) 26.2101 1.71708 0.858541 0.512745i \(-0.171371\pi\)
0.858541 + 0.512745i \(0.171371\pi\)
\(234\) 0 0
\(235\) −32.4592 −2.11741
\(236\) −10.2734 −0.668741
\(237\) 0 0
\(238\) 2.99537 0.194161
\(239\) 8.82406 0.570781 0.285390 0.958411i \(-0.407877\pi\)
0.285390 + 0.958411i \(0.407877\pi\)
\(240\) 0 0
\(241\) −14.7867 −0.952497 −0.476248 0.879311i \(-0.658004\pi\)
−0.476248 + 0.879311i \(0.658004\pi\)
\(242\) −10.8732 −0.698954
\(243\) 0 0
\(244\) 10.3437 0.662190
\(245\) −23.5906 −1.50715
\(246\) 0 0
\(247\) 28.9916 1.84469
\(248\) 2.55507 0.162247
\(249\) 0 0
\(250\) −8.51240 −0.538371
\(251\) −5.31532 −0.335500 −0.167750 0.985830i \(-0.553650\pi\)
−0.167750 + 0.985830i \(0.553650\pi\)
\(252\) 0 0
\(253\) 4.71505 0.296433
\(254\) 1.66213 0.104291
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −25.7340 −1.60524 −0.802620 0.596491i \(-0.796561\pi\)
−0.802620 + 0.596491i \(0.796561\pi\)
\(258\) 0 0
\(259\) −3.60041 −0.223719
\(260\) 17.5586 1.08894
\(261\) 0 0
\(262\) −17.8952 −1.10557
\(263\) 17.6294 1.08708 0.543539 0.839384i \(-0.317084\pi\)
0.543539 + 0.839384i \(0.317084\pi\)
\(264\) 0 0
\(265\) 41.3343 2.53915
\(266\) 3.21294 0.196998
\(267\) 0 0
\(268\) 14.7510 0.901058
\(269\) 21.5522 1.31406 0.657030 0.753864i \(-0.271812\pi\)
0.657030 + 0.753864i \(0.271812\pi\)
\(270\) 0 0
\(271\) −16.1455 −0.980768 −0.490384 0.871506i \(-0.663144\pi\)
−0.490384 + 0.871506i \(0.663144\pi\)
\(272\) 5.42398 0.328877
\(273\) 0 0
\(274\) 8.80332 0.531828
\(275\) −34.6829 −2.09146
\(276\) 0 0
\(277\) −2.90050 −0.174274 −0.0871369 0.996196i \(-0.527772\pi\)
−0.0871369 + 0.996196i \(0.527772\pi\)
\(278\) −8.48773 −0.509060
\(279\) 0 0
\(280\) 1.94590 0.116290
\(281\) 27.2079 1.62309 0.811543 0.584293i \(-0.198628\pi\)
0.811543 + 0.584293i \(0.198628\pi\)
\(282\) 0 0
\(283\) 15.6305 0.929139 0.464570 0.885537i \(-0.346209\pi\)
0.464570 + 0.885537i \(0.346209\pi\)
\(284\) −13.2562 −0.786611
\(285\) 0 0
\(286\) 23.3055 1.37808
\(287\) −0.794941 −0.0469239
\(288\) 0 0
\(289\) 12.4196 0.730562
\(290\) 4.58146 0.269032
\(291\) 0 0
\(292\) −1.22665 −0.0717844
\(293\) 5.47540 0.319876 0.159938 0.987127i \(-0.448871\pi\)
0.159938 + 0.987127i \(0.448871\pi\)
\(294\) 0 0
\(295\) −36.1994 −2.10761
\(296\) −6.51958 −0.378943
\(297\) 0 0
\(298\) 19.1172 1.10743
\(299\) −5.02380 −0.290534
\(300\) 0 0
\(301\) 1.17426 0.0676831
\(302\) 4.99709 0.287550
\(303\) 0 0
\(304\) 5.81795 0.333682
\(305\) 36.4473 2.08697
\(306\) 0 0
\(307\) −18.4616 −1.05366 −0.526829 0.849971i \(-0.676619\pi\)
−0.526829 + 0.849971i \(0.676619\pi\)
\(308\) 2.58279 0.147168
\(309\) 0 0
\(310\) 9.00307 0.511340
\(311\) 17.6340 0.999931 0.499965 0.866045i \(-0.333346\pi\)
0.499965 + 0.866045i \(0.333346\pi\)
\(312\) 0 0
\(313\) 9.93775 0.561715 0.280857 0.959750i \(-0.409381\pi\)
0.280857 + 0.959750i \(0.409381\pi\)
\(314\) −17.2136 −0.971421
\(315\) 0 0
\(316\) 7.86075 0.442202
\(317\) −8.14935 −0.457713 −0.228857 0.973460i \(-0.573499\pi\)
−0.228857 + 0.973460i \(0.573499\pi\)
\(318\) 0 0
\(319\) 6.08096 0.340468
\(320\) 3.52361 0.196976
\(321\) 0 0
\(322\) −0.556753 −0.0310266
\(323\) 31.5565 1.75585
\(324\) 0 0
\(325\) 36.9540 2.04984
\(326\) −4.92931 −0.273009
\(327\) 0 0
\(328\) −1.43947 −0.0794814
\(329\) 5.08725 0.280469
\(330\) 0 0
\(331\) 18.0504 0.992138 0.496069 0.868283i \(-0.334776\pi\)
0.496069 + 0.868283i \(0.334776\pi\)
\(332\) 1.03632 0.0568755
\(333\) 0 0
\(334\) −6.43760 −0.352250
\(335\) 51.9766 2.83978
\(336\) 0 0
\(337\) 24.3184 1.32471 0.662355 0.749191i \(-0.269557\pi\)
0.662355 + 0.749191i \(0.269557\pi\)
\(338\) −11.8316 −0.643553
\(339\) 0 0
\(340\) 19.1120 1.03649
\(341\) 11.9497 0.647115
\(342\) 0 0
\(343\) 7.56302 0.408365
\(344\) 2.12633 0.114644
\(345\) 0 0
\(346\) −0.967478 −0.0520119
\(347\) 20.6234 1.10712 0.553560 0.832809i \(-0.313269\pi\)
0.553560 + 0.832809i \(0.313269\pi\)
\(348\) 0 0
\(349\) 15.4414 0.826557 0.413278 0.910605i \(-0.364384\pi\)
0.413278 + 0.910605i \(0.364384\pi\)
\(350\) 4.09535 0.218906
\(351\) 0 0
\(352\) 4.67688 0.249278
\(353\) −8.29029 −0.441247 −0.220624 0.975359i \(-0.570809\pi\)
−0.220624 + 0.975359i \(0.570809\pi\)
\(354\) 0 0
\(355\) −46.7097 −2.47909
\(356\) −6.94988 −0.368343
\(357\) 0 0
\(358\) −22.2380 −1.17532
\(359\) −5.43143 −0.286660 −0.143330 0.989675i \(-0.545781\pi\)
−0.143330 + 0.989675i \(0.545781\pi\)
\(360\) 0 0
\(361\) 14.8486 0.781504
\(362\) 6.64066 0.349026
\(363\) 0 0
\(364\) −2.75191 −0.144239
\(365\) −4.32224 −0.226236
\(366\) 0 0
\(367\) −29.7690 −1.55393 −0.776965 0.629543i \(-0.783242\pi\)
−0.776965 + 0.629543i \(0.783242\pi\)
\(368\) −1.00816 −0.0525541
\(369\) 0 0
\(370\) −22.9724 −1.19428
\(371\) −6.47822 −0.336332
\(372\) 0 0
\(373\) −21.2795 −1.10181 −0.550906 0.834567i \(-0.685718\pi\)
−0.550906 + 0.834567i \(0.685718\pi\)
\(374\) 25.3673 1.31171
\(375\) 0 0
\(376\) 9.21193 0.475069
\(377\) −6.47915 −0.333693
\(378\) 0 0
\(379\) 21.9952 1.12982 0.564910 0.825153i \(-0.308911\pi\)
0.564910 + 0.825153i \(0.308911\pi\)
\(380\) 20.5002 1.05164
\(381\) 0 0
\(382\) 16.0979 0.823638
\(383\) 6.33678 0.323794 0.161897 0.986808i \(-0.448239\pi\)
0.161897 + 0.986808i \(0.448239\pi\)
\(384\) 0 0
\(385\) 9.10072 0.463816
\(386\) 9.49577 0.483322
\(387\) 0 0
\(388\) −15.1636 −0.769818
\(389\) 15.1173 0.766479 0.383239 0.923649i \(-0.374808\pi\)
0.383239 + 0.923649i \(0.374808\pi\)
\(390\) 0 0
\(391\) −5.46825 −0.276541
\(392\) 6.69502 0.338150
\(393\) 0 0
\(394\) 18.2762 0.920742
\(395\) 27.6982 1.39365
\(396\) 0 0
\(397\) 0.598725 0.0300492 0.0150246 0.999887i \(-0.495217\pi\)
0.0150246 + 0.999887i \(0.495217\pi\)
\(398\) −8.57295 −0.429723
\(399\) 0 0
\(400\) 7.41582 0.370791
\(401\) −5.71303 −0.285295 −0.142648 0.989774i \(-0.545562\pi\)
−0.142648 + 0.989774i \(0.545562\pi\)
\(402\) 0 0
\(403\) −12.7322 −0.634238
\(404\) 5.37759 0.267545
\(405\) 0 0
\(406\) −0.718040 −0.0356357
\(407\) −30.4913 −1.51140
\(408\) 0 0
\(409\) −18.4094 −0.910285 −0.455142 0.890419i \(-0.650412\pi\)
−0.455142 + 0.890419i \(0.650412\pi\)
\(410\) −5.07213 −0.250495
\(411\) 0 0
\(412\) 3.48947 0.171914
\(413\) 5.67344 0.279172
\(414\) 0 0
\(415\) 3.65159 0.179249
\(416\) −4.98313 −0.244318
\(417\) 0 0
\(418\) 27.2098 1.33088
\(419\) 2.26470 0.110638 0.0553189 0.998469i \(-0.482382\pi\)
0.0553189 + 0.998469i \(0.482382\pi\)
\(420\) 0 0
\(421\) 0.936904 0.0456619 0.0228309 0.999739i \(-0.492732\pi\)
0.0228309 + 0.999739i \(0.492732\pi\)
\(422\) 6.80449 0.331237
\(423\) 0 0
\(424\) −11.7307 −0.569692
\(425\) 40.2232 1.95111
\(426\) 0 0
\(427\) −5.71229 −0.276437
\(428\) 19.0825 0.922389
\(429\) 0 0
\(430\) 7.49236 0.361314
\(431\) −3.93486 −0.189536 −0.0947678 0.995499i \(-0.530211\pi\)
−0.0947678 + 0.995499i \(0.530211\pi\)
\(432\) 0 0
\(433\) −28.0634 −1.34864 −0.674320 0.738439i \(-0.735563\pi\)
−0.674320 + 0.738439i \(0.735563\pi\)
\(434\) −1.41103 −0.0677315
\(435\) 0 0
\(436\) −3.42944 −0.164240
\(437\) −5.86544 −0.280582
\(438\) 0 0
\(439\) 5.19677 0.248028 0.124014 0.992280i \(-0.460423\pi\)
0.124014 + 0.992280i \(0.460423\pi\)
\(440\) 16.4795 0.785628
\(441\) 0 0
\(442\) −27.0284 −1.28561
\(443\) 40.3997 1.91945 0.959724 0.280945i \(-0.0906480\pi\)
0.959724 + 0.280945i \(0.0906480\pi\)
\(444\) 0 0
\(445\) −24.4886 −1.16087
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) −0.552246 −0.0260912
\(449\) −21.0560 −0.993693 −0.496847 0.867838i \(-0.665509\pi\)
−0.496847 + 0.867838i \(0.665509\pi\)
\(450\) 0 0
\(451\) −6.73222 −0.317008
\(452\) 11.2528 0.529287
\(453\) 0 0
\(454\) 27.8830 1.30861
\(455\) −9.69666 −0.454587
\(456\) 0 0
\(457\) −22.4763 −1.05140 −0.525698 0.850671i \(-0.676196\pi\)
−0.525698 + 0.850671i \(0.676196\pi\)
\(458\) −10.6798 −0.499033
\(459\) 0 0
\(460\) −3.55237 −0.165630
\(461\) 40.9480 1.90714 0.953570 0.301173i \(-0.0973781\pi\)
0.953570 + 0.301173i \(0.0973781\pi\)
\(462\) 0 0
\(463\) 33.1771 1.54187 0.770935 0.636914i \(-0.219789\pi\)
0.770935 + 0.636914i \(0.219789\pi\)
\(464\) −1.30022 −0.0603611
\(465\) 0 0
\(466\) −26.2101 −1.21416
\(467\) 5.18020 0.239711 0.119856 0.992791i \(-0.461757\pi\)
0.119856 + 0.992791i \(0.461757\pi\)
\(468\) 0 0
\(469\) −8.14615 −0.376154
\(470\) 32.4592 1.49723
\(471\) 0 0
\(472\) 10.2734 0.472871
\(473\) 9.94459 0.457253
\(474\) 0 0
\(475\) 43.1449 1.97962
\(476\) −2.99537 −0.137293
\(477\) 0 0
\(478\) −8.82406 −0.403603
\(479\) 22.1006 1.00980 0.504902 0.863177i \(-0.331529\pi\)
0.504902 + 0.863177i \(0.331529\pi\)
\(480\) 0 0
\(481\) 32.4879 1.48132
\(482\) 14.7867 0.673517
\(483\) 0 0
\(484\) 10.8732 0.494235
\(485\) −53.4308 −2.42617
\(486\) 0 0
\(487\) −7.33737 −0.332488 −0.166244 0.986085i \(-0.553164\pi\)
−0.166244 + 0.986085i \(0.553164\pi\)
\(488\) −10.3437 −0.468239
\(489\) 0 0
\(490\) 23.5906 1.06572
\(491\) −23.5057 −1.06080 −0.530399 0.847748i \(-0.677958\pi\)
−0.530399 + 0.847748i \(0.677958\pi\)
\(492\) 0 0
\(493\) −7.05235 −0.317622
\(494\) −28.9916 −1.30439
\(495\) 0 0
\(496\) −2.55507 −0.114726
\(497\) 7.32068 0.328377
\(498\) 0 0
\(499\) 20.0215 0.896284 0.448142 0.893962i \(-0.352086\pi\)
0.448142 + 0.893962i \(0.352086\pi\)
\(500\) 8.51240 0.380686
\(501\) 0 0
\(502\) 5.31532 0.237234
\(503\) −21.7880 −0.971480 −0.485740 0.874103i \(-0.661450\pi\)
−0.485740 + 0.874103i \(0.661450\pi\)
\(504\) 0 0
\(505\) 18.9485 0.843199
\(506\) −4.71505 −0.209609
\(507\) 0 0
\(508\) −1.66213 −0.0737452
\(509\) −39.6437 −1.75718 −0.878588 0.477580i \(-0.841514\pi\)
−0.878588 + 0.477580i \(0.841514\pi\)
\(510\) 0 0
\(511\) 0.677413 0.0299670
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 25.7340 1.13508
\(515\) 12.2955 0.541806
\(516\) 0 0
\(517\) 43.0831 1.89479
\(518\) 3.60041 0.158193
\(519\) 0 0
\(520\) −17.5586 −0.769995
\(521\) −13.2341 −0.579796 −0.289898 0.957058i \(-0.593621\pi\)
−0.289898 + 0.957058i \(0.593621\pi\)
\(522\) 0 0
\(523\) −0.619536 −0.0270904 −0.0135452 0.999908i \(-0.504312\pi\)
−0.0135452 + 0.999908i \(0.504312\pi\)
\(524\) 17.8952 0.781754
\(525\) 0 0
\(526\) −17.6294 −0.768680
\(527\) −13.8586 −0.603692
\(528\) 0 0
\(529\) −21.9836 −0.955809
\(530\) −41.3343 −1.79545
\(531\) 0 0
\(532\) −3.21294 −0.139299
\(533\) 7.17306 0.310700
\(534\) 0 0
\(535\) 67.2394 2.90701
\(536\) −14.7510 −0.637144
\(537\) 0 0
\(538\) −21.5522 −0.929181
\(539\) 31.3118 1.34869
\(540\) 0 0
\(541\) −28.9524 −1.24476 −0.622380 0.782715i \(-0.713834\pi\)
−0.622380 + 0.782715i \(0.713834\pi\)
\(542\) 16.1455 0.693508
\(543\) 0 0
\(544\) −5.42398 −0.232551
\(545\) −12.0840 −0.517622
\(546\) 0 0
\(547\) −40.8559 −1.74687 −0.873436 0.486938i \(-0.838114\pi\)
−0.873436 + 0.486938i \(0.838114\pi\)
\(548\) −8.80332 −0.376059
\(549\) 0 0
\(550\) 34.6829 1.47888
\(551\) −7.56460 −0.322263
\(552\) 0 0
\(553\) −4.34106 −0.184601
\(554\) 2.90050 0.123230
\(555\) 0 0
\(556\) 8.48773 0.359960
\(557\) −20.5129 −0.869161 −0.434580 0.900633i \(-0.643103\pi\)
−0.434580 + 0.900633i \(0.643103\pi\)
\(558\) 0 0
\(559\) −10.5958 −0.448154
\(560\) −1.94590 −0.0822292
\(561\) 0 0
\(562\) −27.2079 −1.14770
\(563\) −6.76288 −0.285021 −0.142511 0.989793i \(-0.545518\pi\)
−0.142511 + 0.989793i \(0.545518\pi\)
\(564\) 0 0
\(565\) 39.6505 1.66811
\(566\) −15.6305 −0.657001
\(567\) 0 0
\(568\) 13.2562 0.556218
\(569\) −29.3112 −1.22879 −0.614394 0.788999i \(-0.710600\pi\)
−0.614394 + 0.788999i \(0.710600\pi\)
\(570\) 0 0
\(571\) −15.1295 −0.633148 −0.316574 0.948568i \(-0.602533\pi\)
−0.316574 + 0.948568i \(0.602533\pi\)
\(572\) −23.3055 −0.974451
\(573\) 0 0
\(574\) 0.794941 0.0331802
\(575\) −7.47635 −0.311785
\(576\) 0 0
\(577\) 19.0457 0.792883 0.396441 0.918060i \(-0.370245\pi\)
0.396441 + 0.918060i \(0.370245\pi\)
\(578\) −12.4196 −0.516585
\(579\) 0 0
\(580\) −4.58146 −0.190235
\(581\) −0.572304 −0.0237432
\(582\) 0 0
\(583\) −54.8629 −2.27219
\(584\) 1.22665 0.0507592
\(585\) 0 0
\(586\) −5.47540 −0.226187
\(587\) 21.9243 0.904915 0.452457 0.891786i \(-0.350547\pi\)
0.452457 + 0.891786i \(0.350547\pi\)
\(588\) 0 0
\(589\) −14.8653 −0.612513
\(590\) 36.1994 1.49031
\(591\) 0 0
\(592\) 6.51958 0.267953
\(593\) −36.3422 −1.49240 −0.746198 0.665725i \(-0.768123\pi\)
−0.746198 + 0.665725i \(0.768123\pi\)
\(594\) 0 0
\(595\) −10.5545 −0.432693
\(596\) −19.1172 −0.783069
\(597\) 0 0
\(598\) 5.02380 0.205439
\(599\) −4.75160 −0.194145 −0.0970725 0.995277i \(-0.530948\pi\)
−0.0970725 + 0.995277i \(0.530948\pi\)
\(600\) 0 0
\(601\) 11.5124 0.469600 0.234800 0.972044i \(-0.424557\pi\)
0.234800 + 0.972044i \(0.424557\pi\)
\(602\) −1.17426 −0.0478592
\(603\) 0 0
\(604\) −4.99709 −0.203329
\(605\) 38.3128 1.55764
\(606\) 0 0
\(607\) 19.3437 0.785137 0.392569 0.919723i \(-0.371587\pi\)
0.392569 + 0.919723i \(0.371587\pi\)
\(608\) −5.81795 −0.235949
\(609\) 0 0
\(610\) −36.4473 −1.47571
\(611\) −45.9042 −1.85709
\(612\) 0 0
\(613\) −2.72707 −0.110145 −0.0550727 0.998482i \(-0.517539\pi\)
−0.0550727 + 0.998482i \(0.517539\pi\)
\(614\) 18.4616 0.745049
\(615\) 0 0
\(616\) −2.58279 −0.104063
\(617\) 19.4135 0.781557 0.390779 0.920485i \(-0.372206\pi\)
0.390779 + 0.920485i \(0.372206\pi\)
\(618\) 0 0
\(619\) 22.0336 0.885605 0.442803 0.896619i \(-0.353984\pi\)
0.442803 + 0.896619i \(0.353984\pi\)
\(620\) −9.00307 −0.361572
\(621\) 0 0
\(622\) −17.6340 −0.707058
\(623\) 3.83804 0.153768
\(624\) 0 0
\(625\) −7.08474 −0.283389
\(626\) −9.93775 −0.397192
\(627\) 0 0
\(628\) 17.2136 0.686898
\(629\) 35.3621 1.40998
\(630\) 0 0
\(631\) 28.0832 1.11798 0.558988 0.829176i \(-0.311190\pi\)
0.558988 + 0.829176i \(0.311190\pi\)
\(632\) −7.86075 −0.312684
\(633\) 0 0
\(634\) 8.14935 0.323652
\(635\) −5.85670 −0.232416
\(636\) 0 0
\(637\) −33.3622 −1.32186
\(638\) −6.08096 −0.240747
\(639\) 0 0
\(640\) −3.52361 −0.139283
\(641\) −38.4899 −1.52026 −0.760129 0.649772i \(-0.774864\pi\)
−0.760129 + 0.649772i \(0.774864\pi\)
\(642\) 0 0
\(643\) −27.7998 −1.09632 −0.548158 0.836375i \(-0.684671\pi\)
−0.548158 + 0.836375i \(0.684671\pi\)
\(644\) 0.556753 0.0219392
\(645\) 0 0
\(646\) −31.5565 −1.24157
\(647\) 39.2430 1.54280 0.771401 0.636349i \(-0.219556\pi\)
0.771401 + 0.636349i \(0.219556\pi\)
\(648\) 0 0
\(649\) 48.0474 1.88603
\(650\) −36.9540 −1.44945
\(651\) 0 0
\(652\) 4.92931 0.193047
\(653\) 26.8999 1.05268 0.526338 0.850276i \(-0.323565\pi\)
0.526338 + 0.850276i \(0.323565\pi\)
\(654\) 0 0
\(655\) 63.0556 2.46379
\(656\) 1.43947 0.0562019
\(657\) 0 0
\(658\) −5.08725 −0.198322
\(659\) 4.28280 0.166834 0.0834170 0.996515i \(-0.473417\pi\)
0.0834170 + 0.996515i \(0.473417\pi\)
\(660\) 0 0
\(661\) −0.991244 −0.0385549 −0.0192775 0.999814i \(-0.506137\pi\)
−0.0192775 + 0.999814i \(0.506137\pi\)
\(662\) −18.0504 −0.701548
\(663\) 0 0
\(664\) −1.03632 −0.0402170
\(665\) −11.3211 −0.439015
\(666\) 0 0
\(667\) 1.31083 0.0507555
\(668\) 6.43760 0.249078
\(669\) 0 0
\(670\) −51.9766 −2.00803
\(671\) −48.3764 −1.86755
\(672\) 0 0
\(673\) −44.1899 −1.70339 −0.851697 0.524035i \(-0.824426\pi\)
−0.851697 + 0.524035i \(0.824426\pi\)
\(674\) −24.3184 −0.936711
\(675\) 0 0
\(676\) 11.8316 0.455061
\(677\) −15.0897 −0.579945 −0.289973 0.957035i \(-0.593646\pi\)
−0.289973 + 0.957035i \(0.593646\pi\)
\(678\) 0 0
\(679\) 8.37406 0.321367
\(680\) −19.1120 −0.732911
\(681\) 0 0
\(682\) −11.9497 −0.457579
\(683\) 10.1984 0.390230 0.195115 0.980780i \(-0.437492\pi\)
0.195115 + 0.980780i \(0.437492\pi\)
\(684\) 0 0
\(685\) −31.0195 −1.18519
\(686\) −7.56302 −0.288757
\(687\) 0 0
\(688\) −2.12633 −0.0810657
\(689\) 58.4555 2.22698
\(690\) 0 0
\(691\) −33.7250 −1.28296 −0.641479 0.767140i \(-0.721679\pi\)
−0.641479 + 0.767140i \(0.721679\pi\)
\(692\) 0.967478 0.0367780
\(693\) 0 0
\(694\) −20.6234 −0.782852
\(695\) 29.9074 1.13445
\(696\) 0 0
\(697\) 7.80765 0.295736
\(698\) −15.4414 −0.584464
\(699\) 0 0
\(700\) −4.09535 −0.154790
\(701\) −5.58673 −0.211008 −0.105504 0.994419i \(-0.533646\pi\)
−0.105504 + 0.994419i \(0.533646\pi\)
\(702\) 0 0
\(703\) 37.9306 1.43058
\(704\) −4.67688 −0.176266
\(705\) 0 0
\(706\) 8.29029 0.312009
\(707\) −2.96975 −0.111689
\(708\) 0 0
\(709\) −4.63305 −0.173998 −0.0869989 0.996208i \(-0.527728\pi\)
−0.0869989 + 0.996208i \(0.527728\pi\)
\(710\) 46.7097 1.75298
\(711\) 0 0
\(712\) 6.94988 0.260458
\(713\) 2.57592 0.0964691
\(714\) 0 0
\(715\) −82.1194 −3.07109
\(716\) 22.2380 0.831073
\(717\) 0 0
\(718\) 5.43143 0.202699
\(719\) −23.8702 −0.890207 −0.445103 0.895479i \(-0.646833\pi\)
−0.445103 + 0.895479i \(0.646833\pi\)
\(720\) 0 0
\(721\) −1.92705 −0.0717670
\(722\) −14.8486 −0.552607
\(723\) 0 0
\(724\) −6.64066 −0.246798
\(725\) −9.64217 −0.358101
\(726\) 0 0
\(727\) 30.4145 1.12801 0.564005 0.825771i \(-0.309260\pi\)
0.564005 + 0.825771i \(0.309260\pi\)
\(728\) 2.75191 0.101993
\(729\) 0 0
\(730\) 4.32224 0.159973
\(731\) −11.5332 −0.426570
\(732\) 0 0
\(733\) 12.9252 0.477404 0.238702 0.971093i \(-0.423278\pi\)
0.238702 + 0.971093i \(0.423278\pi\)
\(734\) 29.7690 1.09879
\(735\) 0 0
\(736\) 1.00816 0.0371613
\(737\) −68.9884 −2.54122
\(738\) 0 0
\(739\) −34.4826 −1.26846 −0.634231 0.773144i \(-0.718683\pi\)
−0.634231 + 0.773144i \(0.718683\pi\)
\(740\) 22.9724 0.844484
\(741\) 0 0
\(742\) 6.47822 0.237823
\(743\) −43.0222 −1.57833 −0.789166 0.614180i \(-0.789487\pi\)
−0.789166 + 0.614180i \(0.789487\pi\)
\(744\) 0 0
\(745\) −67.3614 −2.46793
\(746\) 21.2795 0.779099
\(747\) 0 0
\(748\) −25.3673 −0.927520
\(749\) −10.5382 −0.385059
\(750\) 0 0
\(751\) 0.0251921 0.000919274 0 0.000459637 1.00000i \(-0.499854\pi\)
0.000459637 1.00000i \(0.499854\pi\)
\(752\) −9.21193 −0.335925
\(753\) 0 0
\(754\) 6.47915 0.235957
\(755\) −17.6078 −0.640813
\(756\) 0 0
\(757\) 28.9990 1.05399 0.526994 0.849869i \(-0.323319\pi\)
0.526994 + 0.849869i \(0.323319\pi\)
\(758\) −21.9952 −0.798903
\(759\) 0 0
\(760\) −20.5002 −0.743620
\(761\) −4.62723 −0.167737 −0.0838686 0.996477i \(-0.526728\pi\)
−0.0838686 + 0.996477i \(0.526728\pi\)
\(762\) 0 0
\(763\) 1.89389 0.0685636
\(764\) −16.0979 −0.582400
\(765\) 0 0
\(766\) −6.33678 −0.228957
\(767\) −51.1936 −1.84850
\(768\) 0 0
\(769\) −9.41324 −0.339450 −0.169725 0.985491i \(-0.554288\pi\)
−0.169725 + 0.985491i \(0.554288\pi\)
\(770\) −9.10072 −0.327967
\(771\) 0 0
\(772\) −9.49577 −0.341760
\(773\) 46.4250 1.66979 0.834895 0.550409i \(-0.185528\pi\)
0.834895 + 0.550409i \(0.185528\pi\)
\(774\) 0 0
\(775\) −18.9479 −0.680630
\(776\) 15.1636 0.544343
\(777\) 0 0
\(778\) −15.1173 −0.541982
\(779\) 8.37477 0.300057
\(780\) 0 0
\(781\) 61.9976 2.21845
\(782\) 5.46825 0.195544
\(783\) 0 0
\(784\) −6.69502 −0.239108
\(785\) 60.6540 2.16484
\(786\) 0 0
\(787\) 17.0666 0.608360 0.304180 0.952615i \(-0.401618\pi\)
0.304180 + 0.952615i \(0.401618\pi\)
\(788\) −18.2762 −0.651063
\(789\) 0 0
\(790\) −27.6982 −0.985458
\(791\) −6.21431 −0.220955
\(792\) 0 0
\(793\) 51.5442 1.83039
\(794\) −0.598725 −0.0212480
\(795\) 0 0
\(796\) 8.57295 0.303860
\(797\) −45.2805 −1.60392 −0.801959 0.597380i \(-0.796209\pi\)
−0.801959 + 0.597380i \(0.796209\pi\)
\(798\) 0 0
\(799\) −49.9653 −1.76765
\(800\) −7.41582 −0.262189
\(801\) 0 0
\(802\) 5.71303 0.201734
\(803\) 5.73690 0.202451
\(804\) 0 0
\(805\) 1.96178 0.0691437
\(806\) 12.7322 0.448474
\(807\) 0 0
\(808\) −5.37759 −0.189183
\(809\) 1.67580 0.0589181 0.0294590 0.999566i \(-0.490622\pi\)
0.0294590 + 0.999566i \(0.490622\pi\)
\(810\) 0 0
\(811\) 2.23025 0.0783146 0.0391573 0.999233i \(-0.487533\pi\)
0.0391573 + 0.999233i \(0.487533\pi\)
\(812\) 0.718040 0.0251982
\(813\) 0 0
\(814\) 30.4913 1.06872
\(815\) 17.3690 0.608408
\(816\) 0 0
\(817\) −12.3709 −0.432803
\(818\) 18.4094 0.643669
\(819\) 0 0
\(820\) 5.07213 0.177126
\(821\) −6.28415 −0.219318 −0.109659 0.993969i \(-0.534976\pi\)
−0.109659 + 0.993969i \(0.534976\pi\)
\(822\) 0 0
\(823\) −18.4870 −0.644415 −0.322207 0.946669i \(-0.604425\pi\)
−0.322207 + 0.946669i \(0.604425\pi\)
\(824\) −3.48947 −0.121562
\(825\) 0 0
\(826\) −5.67344 −0.197404
\(827\) −16.2279 −0.564299 −0.282150 0.959370i \(-0.591047\pi\)
−0.282150 + 0.959370i \(0.591047\pi\)
\(828\) 0 0
\(829\) 17.7274 0.615698 0.307849 0.951435i \(-0.400391\pi\)
0.307849 + 0.951435i \(0.400391\pi\)
\(830\) −3.65159 −0.126748
\(831\) 0 0
\(832\) 4.98313 0.172759
\(833\) −36.3137 −1.25819
\(834\) 0 0
\(835\) 22.6836 0.784998
\(836\) −27.2098 −0.941072
\(837\) 0 0
\(838\) −2.26470 −0.0782327
\(839\) 27.7284 0.957291 0.478646 0.878008i \(-0.341128\pi\)
0.478646 + 0.878008i \(0.341128\pi\)
\(840\) 0 0
\(841\) −27.3094 −0.941705
\(842\) −0.936904 −0.0322878
\(843\) 0 0
\(844\) −6.80449 −0.234220
\(845\) 41.6898 1.43417
\(846\) 0 0
\(847\) −6.00466 −0.206323
\(848\) 11.7307 0.402833
\(849\) 0 0
\(850\) −40.2232 −1.37965
\(851\) −6.57279 −0.225312
\(852\) 0 0
\(853\) −19.1483 −0.655625 −0.327812 0.944743i \(-0.606311\pi\)
−0.327812 + 0.944743i \(0.606311\pi\)
\(854\) 5.71229 0.195470
\(855\) 0 0
\(856\) −19.0825 −0.652227
\(857\) −29.8037 −1.01807 −0.509037 0.860745i \(-0.669998\pi\)
−0.509037 + 0.860745i \(0.669998\pi\)
\(858\) 0 0
\(859\) −10.4840 −0.357709 −0.178855 0.983876i \(-0.557239\pi\)
−0.178855 + 0.983876i \(0.557239\pi\)
\(860\) −7.49236 −0.255487
\(861\) 0 0
\(862\) 3.93486 0.134022
\(863\) −8.13754 −0.277005 −0.138502 0.990362i \(-0.544229\pi\)
−0.138502 + 0.990362i \(0.544229\pi\)
\(864\) 0 0
\(865\) 3.40901 0.115910
\(866\) 28.0634 0.953633
\(867\) 0 0
\(868\) 1.41103 0.0478934
\(869\) −36.7637 −1.24712
\(870\) 0 0
\(871\) 73.5059 2.49065
\(872\) 3.42944 0.116135
\(873\) 0 0
\(874\) 5.86544 0.198401
\(875\) −4.70094 −0.158921
\(876\) 0 0
\(877\) 44.5659 1.50488 0.752442 0.658659i \(-0.228876\pi\)
0.752442 + 0.658659i \(0.228876\pi\)
\(878\) −5.19677 −0.175382
\(879\) 0 0
\(880\) −16.4795 −0.555523
\(881\) 7.17323 0.241672 0.120836 0.992672i \(-0.461442\pi\)
0.120836 + 0.992672i \(0.461442\pi\)
\(882\) 0 0
\(883\) −33.5763 −1.12993 −0.564967 0.825114i \(-0.691111\pi\)
−0.564967 + 0.825114i \(0.691111\pi\)
\(884\) 27.0284 0.909063
\(885\) 0 0
\(886\) −40.3997 −1.35725
\(887\) −21.7630 −0.730730 −0.365365 0.930864i \(-0.619056\pi\)
−0.365365 + 0.930864i \(0.619056\pi\)
\(888\) 0 0
\(889\) 0.917905 0.0307856
\(890\) 24.4886 0.820861
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −53.5946 −1.79347
\(894\) 0 0
\(895\) 78.3580 2.61922
\(896\) 0.552246 0.0184492
\(897\) 0 0
\(898\) 21.0560 0.702647
\(899\) 3.32215 0.110800
\(900\) 0 0
\(901\) 63.6269 2.11972
\(902\) 6.73222 0.224158
\(903\) 0 0
\(904\) −11.2528 −0.374262
\(905\) −23.3991 −0.777812
\(906\) 0 0
\(907\) 26.9243 0.894008 0.447004 0.894532i \(-0.352491\pi\)
0.447004 + 0.894532i \(0.352491\pi\)
\(908\) −27.8830 −0.925330
\(909\) 0 0
\(910\) 9.69666 0.321441
\(911\) 24.3104 0.805439 0.402719 0.915323i \(-0.368065\pi\)
0.402719 + 0.915323i \(0.368065\pi\)
\(912\) 0 0
\(913\) −4.84674 −0.160404
\(914\) 22.4763 0.743449
\(915\) 0 0
\(916\) 10.6798 0.352869
\(917\) −9.88254 −0.326350
\(918\) 0 0
\(919\) −41.1810 −1.35844 −0.679219 0.733936i \(-0.737681\pi\)
−0.679219 + 0.733936i \(0.737681\pi\)
\(920\) 3.55237 0.117118
\(921\) 0 0
\(922\) −40.9480 −1.34855
\(923\) −66.0574 −2.17430
\(924\) 0 0
\(925\) 48.3480 1.58967
\(926\) −33.1771 −1.09027
\(927\) 0 0
\(928\) 1.30022 0.0426817
\(929\) 0.772006 0.0253287 0.0126643 0.999920i \(-0.495969\pi\)
0.0126643 + 0.999920i \(0.495969\pi\)
\(930\) 0 0
\(931\) −38.9513 −1.27658
\(932\) 26.2101 0.858541
\(933\) 0 0
\(934\) −5.18020 −0.169501
\(935\) −89.3844 −2.92318
\(936\) 0 0
\(937\) −16.1568 −0.527819 −0.263909 0.964547i \(-0.585012\pi\)
−0.263909 + 0.964547i \(0.585012\pi\)
\(938\) 8.14615 0.265981
\(939\) 0 0
\(940\) −32.4592 −1.05870
\(941\) 42.1770 1.37493 0.687465 0.726218i \(-0.258724\pi\)
0.687465 + 0.726218i \(0.258724\pi\)
\(942\) 0 0
\(943\) −1.45122 −0.0472582
\(944\) −10.2734 −0.334371
\(945\) 0 0
\(946\) −9.94459 −0.323327
\(947\) 6.20082 0.201499 0.100750 0.994912i \(-0.467876\pi\)
0.100750 + 0.994912i \(0.467876\pi\)
\(948\) 0 0
\(949\) −6.11256 −0.198422
\(950\) −43.1449 −1.39980
\(951\) 0 0
\(952\) 2.99537 0.0970805
\(953\) 2.34293 0.0758950 0.0379475 0.999280i \(-0.487918\pi\)
0.0379475 + 0.999280i \(0.487918\pi\)
\(954\) 0 0
\(955\) −56.7226 −1.83550
\(956\) 8.82406 0.285390
\(957\) 0 0
\(958\) −22.1006 −0.714040
\(959\) 4.86160 0.156989
\(960\) 0 0
\(961\) −24.4716 −0.789407
\(962\) −32.4879 −1.04745
\(963\) 0 0
\(964\) −14.7867 −0.476248
\(965\) −33.4594 −1.07710
\(966\) 0 0
\(967\) 0.0757963 0.00243744 0.00121872 0.999999i \(-0.499612\pi\)
0.00121872 + 0.999999i \(0.499612\pi\)
\(968\) −10.8732 −0.349477
\(969\) 0 0
\(970\) 53.4308 1.71556
\(971\) 29.9768 0.962001 0.481001 0.876720i \(-0.340273\pi\)
0.481001 + 0.876720i \(0.340273\pi\)
\(972\) 0 0
\(973\) −4.68732 −0.150268
\(974\) 7.33737 0.235104
\(975\) 0 0
\(976\) 10.3437 0.331095
\(977\) 3.26298 0.104392 0.0521960 0.998637i \(-0.483378\pi\)
0.0521960 + 0.998637i \(0.483378\pi\)
\(978\) 0 0
\(979\) 32.5037 1.03882
\(980\) −23.5906 −0.753576
\(981\) 0 0
\(982\) 23.5057 0.750098
\(983\) 26.6268 0.849264 0.424632 0.905366i \(-0.360403\pi\)
0.424632 + 0.905366i \(0.360403\pi\)
\(984\) 0 0
\(985\) −64.3982 −2.05190
\(986\) 7.05235 0.224593
\(987\) 0 0
\(988\) 28.9916 0.922346
\(989\) 2.14369 0.0681653
\(990\) 0 0
\(991\) 2.34679 0.0745482 0.0372741 0.999305i \(-0.488133\pi\)
0.0372741 + 0.999305i \(0.488133\pi\)
\(992\) 2.55507 0.0811236
\(993\) 0 0
\(994\) −7.32068 −0.232198
\(995\) 30.2077 0.957650
\(996\) 0 0
\(997\) −3.39888 −0.107644 −0.0538218 0.998551i \(-0.517140\pi\)
−0.0538218 + 0.998551i \(0.517140\pi\)
\(998\) −20.0215 −0.633769
\(999\) 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 4014.2.a.w.1.7 7
3.2 odd 2 446.2.a.e.1.1 7
12.11 even 2 3568.2.a.l.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
446.2.a.e.1.1 7 3.2 odd 2
3568.2.a.l.1.7 7 12.11 even 2
4014.2.a.w.1.7 7 1.1 even 1 trivial