Properties

Label 3332.2.a.o.1.1
Level $3332$
Weight $2$
Character 3332.1
Self dual yes
Analytic conductor $26.606$
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] = [3332,2,Mod(1,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, 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("3332.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.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: \(26.6061539535\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 3332.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.381966 q^{3} +1.38197 q^{5} -2.85410 q^{9} +O(q^{10})\) \(q+0.381966 q^{3} +1.38197 q^{5} -2.85410 q^{9} -3.23607 q^{13} +0.527864 q^{15} +1.00000 q^{17} -2.47214 q^{19} +5.23607 q^{23} -3.09017 q^{25} -2.23607 q^{27} +2.76393 q^{29} +9.56231 q^{31} +3.70820 q^{37} -1.23607 q^{39} -1.14590 q^{41} +4.85410 q^{43} -3.94427 q^{45} +10.9443 q^{47} +0.381966 q^{51} +12.3262 q^{53} -0.944272 q^{57} +5.23607 q^{59} +12.5623 q^{61} -4.47214 q^{65} -5.09017 q^{67} +2.00000 q^{69} -4.76393 q^{71} -2.85410 q^{73} -1.18034 q^{75} -1.70820 q^{79} +7.70820 q^{81} -1.52786 q^{83} +1.38197 q^{85} +1.05573 q^{87} +13.2361 q^{89} +3.65248 q^{93} -3.41641 q^{95} +3.85410 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 5 q^{5} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 5 q^{5} + q^{9} - 2 q^{13} + 10 q^{15} + 2 q^{17} + 4 q^{19} + 6 q^{23} + 5 q^{25} + 10 q^{29} - q^{31} - 6 q^{37} + 2 q^{39} - 9 q^{41} + 3 q^{43} + 10 q^{45} + 4 q^{47} + 3 q^{51} + 9 q^{53} + 16 q^{57} + 6 q^{59} + 5 q^{61} + q^{67} + 4 q^{69} - 14 q^{71} + q^{73} + 20 q^{75} + 10 q^{79} + 2 q^{81} - 12 q^{83} + 5 q^{85} + 20 q^{87} + 22 q^{89} - 24 q^{93} + 20 q^{95} + q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.381966 0.220528 0.110264 0.993902i \(-0.464830\pi\)
0.110264 + 0.993902i \(0.464830\pi\)
\(4\) 0 0
\(5\) 1.38197 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.85410 −0.951367
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −3.23607 −0.897524 −0.448762 0.893651i \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 0 0
\(15\) 0.527864 0.136294
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) −2.47214 −0.567147 −0.283573 0.958951i \(-0.591520\pi\)
−0.283573 + 0.958951i \(0.591520\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.23607 1.09180 0.545898 0.837852i \(-0.316189\pi\)
0.545898 + 0.837852i \(0.316189\pi\)
\(24\) 0 0
\(25\) −3.09017 −0.618034
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) 2.76393 0.513249 0.256625 0.966511i \(-0.417390\pi\)
0.256625 + 0.966511i \(0.417390\pi\)
\(30\) 0 0
\(31\) 9.56231 1.71744 0.858720 0.512444i \(-0.171260\pi\)
0.858720 + 0.512444i \(0.171260\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.70820 0.609625 0.304812 0.952412i \(-0.401406\pi\)
0.304812 + 0.952412i \(0.401406\pi\)
\(38\) 0 0
\(39\) −1.23607 −0.197929
\(40\) 0 0
\(41\) −1.14590 −0.178959 −0.0894796 0.995989i \(-0.528520\pi\)
−0.0894796 + 0.995989i \(0.528520\pi\)
\(42\) 0 0
\(43\) 4.85410 0.740244 0.370122 0.928983i \(-0.379316\pi\)
0.370122 + 0.928983i \(0.379316\pi\)
\(44\) 0 0
\(45\) −3.94427 −0.587977
\(46\) 0 0
\(47\) 10.9443 1.59639 0.798193 0.602402i \(-0.205789\pi\)
0.798193 + 0.602402i \(0.205789\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.381966 0.0534859
\(52\) 0 0
\(53\) 12.3262 1.69314 0.846569 0.532278i \(-0.178664\pi\)
0.846569 + 0.532278i \(0.178664\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.944272 −0.125072
\(58\) 0 0
\(59\) 5.23607 0.681678 0.340839 0.940122i \(-0.389289\pi\)
0.340839 + 0.940122i \(0.389289\pi\)
\(60\) 0 0
\(61\) 12.5623 1.60844 0.804219 0.594333i \(-0.202584\pi\)
0.804219 + 0.594333i \(0.202584\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.47214 −0.554700
\(66\) 0 0
\(67\) −5.09017 −0.621863 −0.310932 0.950432i \(-0.600641\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(68\) 0 0
\(69\) 2.00000 0.240772
\(70\) 0 0
\(71\) −4.76393 −0.565375 −0.282687 0.959212i \(-0.591226\pi\)
−0.282687 + 0.959212i \(0.591226\pi\)
\(72\) 0 0
\(73\) −2.85410 −0.334047 −0.167024 0.985953i \(-0.553416\pi\)
−0.167024 + 0.985953i \(0.553416\pi\)
\(74\) 0 0
\(75\) −1.18034 −0.136294
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.70820 −0.192188 −0.0960940 0.995372i \(-0.530635\pi\)
−0.0960940 + 0.995372i \(0.530635\pi\)
\(80\) 0 0
\(81\) 7.70820 0.856467
\(82\) 0 0
\(83\) −1.52786 −0.167705 −0.0838524 0.996478i \(-0.526722\pi\)
−0.0838524 + 0.996478i \(0.526722\pi\)
\(84\) 0 0
\(85\) 1.38197 0.149895
\(86\) 0 0
\(87\) 1.05573 0.113186
\(88\) 0 0
\(89\) 13.2361 1.40302 0.701510 0.712659i \(-0.252509\pi\)
0.701510 + 0.712659i \(0.252509\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.65248 0.378744
\(94\) 0 0
\(95\) −3.41641 −0.350516
\(96\) 0 0
\(97\) 3.85410 0.391325 0.195662 0.980671i \(-0.437314\pi\)
0.195662 + 0.980671i \(0.437314\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.4721 1.63904 0.819519 0.573051i \(-0.194240\pi\)
0.819519 + 0.573051i \(0.194240\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −10.1803 −0.975100 −0.487550 0.873095i \(-0.662109\pi\)
−0.487550 + 0.873095i \(0.662109\pi\)
\(110\) 0 0
\(111\) 1.41641 0.134439
\(112\) 0 0
\(113\) −4.94427 −0.465118 −0.232559 0.972582i \(-0.574710\pi\)
−0.232559 + 0.972582i \(0.574710\pi\)
\(114\) 0 0
\(115\) 7.23607 0.674767
\(116\) 0 0
\(117\) 9.23607 0.853875
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −0.437694 −0.0394655
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) −13.3820 −1.18746 −0.593729 0.804665i \(-0.702345\pi\)
−0.593729 + 0.804665i \(0.702345\pi\)
\(128\) 0 0
\(129\) 1.85410 0.163245
\(130\) 0 0
\(131\) −2.47214 −0.215992 −0.107996 0.994151i \(-0.534443\pi\)
−0.107996 + 0.994151i \(0.534443\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −3.09017 −0.265959
\(136\) 0 0
\(137\) −0.0901699 −0.00770374 −0.00385187 0.999993i \(-0.501226\pi\)
−0.00385187 + 0.999993i \(0.501226\pi\)
\(138\) 0 0
\(139\) −11.3820 −0.965406 −0.482703 0.875784i \(-0.660345\pi\)
−0.482703 + 0.875784i \(0.660345\pi\)
\(140\) 0 0
\(141\) 4.18034 0.352048
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 3.81966 0.317206
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.61803 −0.460247 −0.230124 0.973161i \(-0.573913\pi\)
−0.230124 + 0.973161i \(0.573913\pi\)
\(150\) 0 0
\(151\) 12.2705 0.998560 0.499280 0.866441i \(-0.333598\pi\)
0.499280 + 0.866441i \(0.333598\pi\)
\(152\) 0 0
\(153\) −2.85410 −0.230740
\(154\) 0 0
\(155\) 13.2148 1.06144
\(156\) 0 0
\(157\) 10.2918 0.821375 0.410687 0.911776i \(-0.365289\pi\)
0.410687 + 0.911776i \(0.365289\pi\)
\(158\) 0 0
\(159\) 4.70820 0.373385
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.5623 −1.59116 −0.795580 0.605849i \(-0.792833\pi\)
−0.795580 + 0.605849i \(0.792833\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) 0 0
\(171\) 7.05573 0.539565
\(172\) 0 0
\(173\) 6.67376 0.507397 0.253698 0.967283i \(-0.418353\pi\)
0.253698 + 0.967283i \(0.418353\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.00000 0.150329
\(178\) 0 0
\(179\) 8.09017 0.604688 0.302344 0.953199i \(-0.402231\pi\)
0.302344 + 0.953199i \(0.402231\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 4.79837 0.354706
\(184\) 0 0
\(185\) 5.12461 0.376769
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.9098 0.789408 0.394704 0.918808i \(-0.370847\pi\)
0.394704 + 0.918808i \(0.370847\pi\)
\(192\) 0 0
\(193\) −14.4721 −1.04173 −0.520864 0.853640i \(-0.674390\pi\)
−0.520864 + 0.853640i \(0.674390\pi\)
\(194\) 0 0
\(195\) −1.70820 −0.122327
\(196\) 0 0
\(197\) −2.29180 −0.163284 −0.0816419 0.996662i \(-0.526016\pi\)
−0.0816419 + 0.996662i \(0.526016\pi\)
\(198\) 0 0
\(199\) 18.8541 1.33653 0.668266 0.743922i \(-0.267037\pi\)
0.668266 + 0.743922i \(0.267037\pi\)
\(200\) 0 0
\(201\) −1.94427 −0.137138
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.58359 −0.110603
\(206\) 0 0
\(207\) −14.9443 −1.03870
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −25.5967 −1.76215 −0.881076 0.472974i \(-0.843180\pi\)
−0.881076 + 0.472974i \(0.843180\pi\)
\(212\) 0 0
\(213\) −1.81966 −0.124681
\(214\) 0 0
\(215\) 6.70820 0.457496
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.09017 −0.0736669
\(220\) 0 0
\(221\) −3.23607 −0.217681
\(222\) 0 0
\(223\) −19.8885 −1.33184 −0.665918 0.746025i \(-0.731960\pi\)
−0.665918 + 0.746025i \(0.731960\pi\)
\(224\) 0 0
\(225\) 8.81966 0.587977
\(226\) 0 0
\(227\) −13.8541 −0.919529 −0.459765 0.888041i \(-0.652066\pi\)
−0.459765 + 0.888041i \(0.652066\pi\)
\(228\) 0 0
\(229\) 9.41641 0.622254 0.311127 0.950368i \(-0.399294\pi\)
0.311127 + 0.950368i \(0.399294\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.1803 1.32206 0.661029 0.750360i \(-0.270120\pi\)
0.661029 + 0.750360i \(0.270120\pi\)
\(234\) 0 0
\(235\) 15.1246 0.986621
\(236\) 0 0
\(237\) −0.652476 −0.0423829
\(238\) 0 0
\(239\) −21.6180 −1.39835 −0.699177 0.714948i \(-0.746450\pi\)
−0.699177 + 0.714948i \(0.746450\pi\)
\(240\) 0 0
\(241\) 1.38197 0.0890203 0.0445101 0.999009i \(-0.485827\pi\)
0.0445101 + 0.999009i \(0.485827\pi\)
\(242\) 0 0
\(243\) 9.65248 0.619207
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 0 0
\(249\) −0.583592 −0.0369836
\(250\) 0 0
\(251\) 2.18034 0.137622 0.0688109 0.997630i \(-0.478079\pi\)
0.0688109 + 0.997630i \(0.478079\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0.527864 0.0330561
\(256\) 0 0
\(257\) 10.4721 0.653234 0.326617 0.945157i \(-0.394091\pi\)
0.326617 + 0.945157i \(0.394091\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −7.88854 −0.488289
\(262\) 0 0
\(263\) −7.41641 −0.457315 −0.228658 0.973507i \(-0.573434\pi\)
−0.228658 + 0.973507i \(0.573434\pi\)
\(264\) 0 0
\(265\) 17.0344 1.04642
\(266\) 0 0
\(267\) 5.05573 0.309406
\(268\) 0 0
\(269\) −13.4164 −0.818013 −0.409006 0.912532i \(-0.634125\pi\)
−0.409006 + 0.912532i \(0.634125\pi\)
\(270\) 0 0
\(271\) −11.5279 −0.700268 −0.350134 0.936700i \(-0.613864\pi\)
−0.350134 + 0.936700i \(0.613864\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.12461 0.548245 0.274122 0.961695i \(-0.411613\pi\)
0.274122 + 0.961695i \(0.411613\pi\)
\(278\) 0 0
\(279\) −27.2918 −1.63392
\(280\) 0 0
\(281\) 14.5066 0.865390 0.432695 0.901540i \(-0.357563\pi\)
0.432695 + 0.901540i \(0.357563\pi\)
\(282\) 0 0
\(283\) 25.8541 1.53687 0.768433 0.639930i \(-0.221037\pi\)
0.768433 + 0.639930i \(0.221037\pi\)
\(284\) 0 0
\(285\) −1.30495 −0.0772987
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 1.47214 0.0862981
\(292\) 0 0
\(293\) 21.5967 1.26170 0.630848 0.775907i \(-0.282707\pi\)
0.630848 + 0.775907i \(0.282707\pi\)
\(294\) 0 0
\(295\) 7.23607 0.421300
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −16.9443 −0.979913
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 6.29180 0.361454
\(304\) 0 0
\(305\) 17.3607 0.994070
\(306\) 0 0
\(307\) 17.4164 0.994007 0.497003 0.867749i \(-0.334434\pi\)
0.497003 + 0.867749i \(0.334434\pi\)
\(308\) 0 0
\(309\) 2.29180 0.130376
\(310\) 0 0
\(311\) 11.7426 0.665864 0.332932 0.942951i \(-0.391962\pi\)
0.332932 + 0.942951i \(0.391962\pi\)
\(312\) 0 0
\(313\) 23.8541 1.34831 0.674157 0.738588i \(-0.264507\pi\)
0.674157 + 0.738588i \(0.264507\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.8885 −0.667727 −0.333864 0.942621i \(-0.608352\pi\)
−0.333864 + 0.942621i \(0.608352\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.47214 −0.137553
\(324\) 0 0
\(325\) 10.0000 0.554700
\(326\) 0 0
\(327\) −3.88854 −0.215037
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.32624 −0.127862 −0.0639308 0.997954i \(-0.520364\pi\)
−0.0639308 + 0.997954i \(0.520364\pi\)
\(332\) 0 0
\(333\) −10.5836 −0.579977
\(334\) 0 0
\(335\) −7.03444 −0.384333
\(336\) 0 0
\(337\) 13.4164 0.730838 0.365419 0.930843i \(-0.380926\pi\)
0.365419 + 0.930843i \(0.380926\pi\)
\(338\) 0 0
\(339\) −1.88854 −0.102572
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2.76393 0.148805
\(346\) 0 0
\(347\) −9.88854 −0.530845 −0.265422 0.964132i \(-0.585511\pi\)
−0.265422 + 0.964132i \(0.585511\pi\)
\(348\) 0 0
\(349\) −0.472136 −0.0252729 −0.0126364 0.999920i \(-0.504022\pi\)
−0.0126364 + 0.999920i \(0.504022\pi\)
\(350\) 0 0
\(351\) 7.23607 0.386233
\(352\) 0 0
\(353\) −24.0689 −1.28106 −0.640529 0.767934i \(-0.721285\pi\)
−0.640529 + 0.767934i \(0.721285\pi\)
\(354\) 0 0
\(355\) −6.58359 −0.349421
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.14590 0.218812 0.109406 0.993997i \(-0.465105\pi\)
0.109406 + 0.993997i \(0.465105\pi\)
\(360\) 0 0
\(361\) −12.8885 −0.678344
\(362\) 0 0
\(363\) −4.20163 −0.220528
\(364\) 0 0
\(365\) −3.94427 −0.206453
\(366\) 0 0
\(367\) −15.6180 −0.815255 −0.407627 0.913148i \(-0.633644\pi\)
−0.407627 + 0.913148i \(0.633644\pi\)
\(368\) 0 0
\(369\) 3.27051 0.170256
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 7.50658 0.388676 0.194338 0.980935i \(-0.437744\pi\)
0.194338 + 0.980935i \(0.437744\pi\)
\(374\) 0 0
\(375\) −4.27051 −0.220528
\(376\) 0 0
\(377\) −8.94427 −0.460653
\(378\) 0 0
\(379\) 31.1246 1.59876 0.799382 0.600823i \(-0.205160\pi\)
0.799382 + 0.600823i \(0.205160\pi\)
\(380\) 0 0
\(381\) −5.11146 −0.261868
\(382\) 0 0
\(383\) 25.8885 1.32284 0.661421 0.750014i \(-0.269954\pi\)
0.661421 + 0.750014i \(0.269954\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.8541 −0.704244
\(388\) 0 0
\(389\) −10.5066 −0.532705 −0.266352 0.963876i \(-0.585818\pi\)
−0.266352 + 0.963876i \(0.585818\pi\)
\(390\) 0 0
\(391\) 5.23607 0.264799
\(392\) 0 0
\(393\) −0.944272 −0.0476322
\(394\) 0 0
\(395\) −2.36068 −0.118779
\(396\) 0 0
\(397\) −1.67376 −0.0840037 −0.0420019 0.999118i \(-0.513374\pi\)
−0.0420019 + 0.999118i \(0.513374\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 28.9443 1.44541 0.722704 0.691158i \(-0.242899\pi\)
0.722704 + 0.691158i \(0.242899\pi\)
\(402\) 0 0
\(403\) −30.9443 −1.54144
\(404\) 0 0
\(405\) 10.6525 0.529326
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 16.0000 0.791149 0.395575 0.918434i \(-0.370545\pi\)
0.395575 + 0.918434i \(0.370545\pi\)
\(410\) 0 0
\(411\) −0.0344419 −0.00169889
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2.11146 −0.103647
\(416\) 0 0
\(417\) −4.34752 −0.212899
\(418\) 0 0
\(419\) −2.50658 −0.122454 −0.0612272 0.998124i \(-0.519501\pi\)
−0.0612272 + 0.998124i \(0.519501\pi\)
\(420\) 0 0
\(421\) −16.8541 −0.821419 −0.410709 0.911766i \(-0.634719\pi\)
−0.410709 + 0.911766i \(0.634719\pi\)
\(422\) 0 0
\(423\) −31.2361 −1.51875
\(424\) 0 0
\(425\) −3.09017 −0.149895
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14.9443 0.719840 0.359920 0.932983i \(-0.382804\pi\)
0.359920 + 0.932983i \(0.382804\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) 1.45898 0.0699528
\(436\) 0 0
\(437\) −12.9443 −0.619208
\(438\) 0 0
\(439\) −22.8541 −1.09077 −0.545383 0.838187i \(-0.683616\pi\)
−0.545383 + 0.838187i \(0.683616\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −24.9443 −1.18514 −0.592569 0.805520i \(-0.701886\pi\)
−0.592569 + 0.805520i \(0.701886\pi\)
\(444\) 0 0
\(445\) 18.2918 0.867114
\(446\) 0 0
\(447\) −2.14590 −0.101497
\(448\) 0 0
\(449\) −16.9443 −0.799650 −0.399825 0.916592i \(-0.630929\pi\)
−0.399825 + 0.916592i \(0.630929\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 4.68692 0.220211
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −21.2705 −0.994992 −0.497496 0.867466i \(-0.665747\pi\)
−0.497496 + 0.867466i \(0.665747\pi\)
\(458\) 0 0
\(459\) −2.23607 −0.104371
\(460\) 0 0
\(461\) 26.8328 1.24973 0.624864 0.780733i \(-0.285154\pi\)
0.624864 + 0.780733i \(0.285154\pi\)
\(462\) 0 0
\(463\) 21.7984 1.01306 0.506528 0.862223i \(-0.330929\pi\)
0.506528 + 0.862223i \(0.330929\pi\)
\(464\) 0 0
\(465\) 5.04760 0.234077
\(466\) 0 0
\(467\) −33.2361 −1.53798 −0.768991 0.639260i \(-0.779241\pi\)
−0.768991 + 0.639260i \(0.779241\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.93112 0.181136
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 7.63932 0.350516
\(476\) 0 0
\(477\) −35.1803 −1.61080
\(478\) 0 0
\(479\) −8.38197 −0.382982 −0.191491 0.981494i \(-0.561332\pi\)
−0.191491 + 0.981494i \(0.561332\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.32624 0.241852
\(486\) 0 0
\(487\) 36.9443 1.67410 0.837052 0.547123i \(-0.184277\pi\)
0.837052 + 0.547123i \(0.184277\pi\)
\(488\) 0 0
\(489\) −2.29180 −0.103639
\(490\) 0 0
\(491\) −15.2016 −0.686040 −0.343020 0.939328i \(-0.611450\pi\)
−0.343020 + 0.939328i \(0.611450\pi\)
\(492\) 0 0
\(493\) 2.76393 0.124481
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 27.3050 1.22234 0.611169 0.791500i \(-0.290700\pi\)
0.611169 + 0.791500i \(0.290700\pi\)
\(500\) 0 0
\(501\) −7.85410 −0.350895
\(502\) 0 0
\(503\) −21.2705 −0.948405 −0.474203 0.880416i \(-0.657264\pi\)
−0.474203 + 0.880416i \(0.657264\pi\)
\(504\) 0 0
\(505\) 22.7639 1.01298
\(506\) 0 0
\(507\) −0.965558 −0.0428819
\(508\) 0 0
\(509\) −18.7639 −0.831697 −0.415848 0.909434i \(-0.636515\pi\)
−0.415848 + 0.909434i \(0.636515\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 5.52786 0.244061
\(514\) 0 0
\(515\) 8.29180 0.365380
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.54915 0.111895
\(520\) 0 0
\(521\) −1.90983 −0.0836712 −0.0418356 0.999125i \(-0.513321\pi\)
−0.0418356 + 0.999125i \(0.513321\pi\)
\(522\) 0 0
\(523\) −38.6525 −1.69015 −0.845077 0.534644i \(-0.820446\pi\)
−0.845077 + 0.534644i \(0.820446\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.56231 0.416541
\(528\) 0 0
\(529\) 4.41641 0.192018
\(530\) 0 0
\(531\) −14.9443 −0.648526
\(532\) 0 0
\(533\) 3.70820 0.160620
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.09017 0.133351
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) 5.34752 0.229484
\(544\) 0 0
\(545\) −14.0689 −0.602645
\(546\) 0 0
\(547\) 27.1246 1.15976 0.579882 0.814700i \(-0.303099\pi\)
0.579882 + 0.814700i \(0.303099\pi\)
\(548\) 0 0
\(549\) −35.8541 −1.53022
\(550\) 0 0
\(551\) −6.83282 −0.291088
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.95743 0.0830882
\(556\) 0 0
\(557\) 15.5279 0.657937 0.328968 0.944341i \(-0.393299\pi\)
0.328968 + 0.944341i \(0.393299\pi\)
\(558\) 0 0
\(559\) −15.7082 −0.664386
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.1246 0.974586 0.487293 0.873238i \(-0.337984\pi\)
0.487293 + 0.873238i \(0.337984\pi\)
\(564\) 0 0
\(565\) −6.83282 −0.287459
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.09017 −0.171469 −0.0857344 0.996318i \(-0.527324\pi\)
−0.0857344 + 0.996318i \(0.527324\pi\)
\(570\) 0 0
\(571\) −2.65248 −0.111003 −0.0555013 0.998459i \(-0.517676\pi\)
−0.0555013 + 0.998459i \(0.517676\pi\)
\(572\) 0 0
\(573\) 4.16718 0.174087
\(574\) 0 0
\(575\) −16.1803 −0.674767
\(576\) 0 0
\(577\) 18.5836 0.773645 0.386823 0.922154i \(-0.373573\pi\)
0.386823 + 0.922154i \(0.373573\pi\)
\(578\) 0 0
\(579\) −5.52786 −0.229730
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 12.7639 0.527724
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) −23.6393 −0.974041
\(590\) 0 0
\(591\) −0.875388 −0.0360087
\(592\) 0 0
\(593\) −19.5967 −0.804742 −0.402371 0.915477i \(-0.631814\pi\)
−0.402371 + 0.915477i \(0.631814\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.20163 0.294743
\(598\) 0 0
\(599\) 17.0344 0.696008 0.348004 0.937493i \(-0.386859\pi\)
0.348004 + 0.937493i \(0.386859\pi\)
\(600\) 0 0
\(601\) 32.4721 1.32457 0.662283 0.749254i \(-0.269588\pi\)
0.662283 + 0.749254i \(0.269588\pi\)
\(602\) 0 0
\(603\) 14.5279 0.591620
\(604\) 0 0
\(605\) −15.2016 −0.618034
\(606\) 0 0
\(607\) −18.1459 −0.736519 −0.368260 0.929723i \(-0.620046\pi\)
−0.368260 + 0.929723i \(0.620046\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −35.4164 −1.43279
\(612\) 0 0
\(613\) 5.85410 0.236445 0.118222 0.992987i \(-0.462280\pi\)
0.118222 + 0.992987i \(0.462280\pi\)
\(614\) 0 0
\(615\) −0.604878 −0.0243911
\(616\) 0 0
\(617\) −3.59675 −0.144800 −0.0723998 0.997376i \(-0.523066\pi\)
−0.0723998 + 0.997376i \(0.523066\pi\)
\(618\) 0 0
\(619\) −6.83282 −0.274634 −0.137317 0.990527i \(-0.543848\pi\)
−0.137317 + 0.990527i \(0.543848\pi\)
\(620\) 0 0
\(621\) −11.7082 −0.469834
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.70820 0.147856
\(630\) 0 0
\(631\) −30.9787 −1.23324 −0.616622 0.787260i \(-0.711499\pi\)
−0.616622 + 0.787260i \(0.711499\pi\)
\(632\) 0 0
\(633\) −9.77709 −0.388604
\(634\) 0 0
\(635\) −18.4934 −0.733889
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 13.5967 0.537879
\(640\) 0 0
\(641\) −29.7771 −1.17612 −0.588062 0.808816i \(-0.700109\pi\)
−0.588062 + 0.808816i \(0.700109\pi\)
\(642\) 0 0
\(643\) 31.6180 1.24689 0.623447 0.781866i \(-0.285732\pi\)
0.623447 + 0.781866i \(0.285732\pi\)
\(644\) 0 0
\(645\) 2.56231 0.100891
\(646\) 0 0
\(647\) −21.5967 −0.849056 −0.424528 0.905415i \(-0.639560\pi\)
−0.424528 + 0.905415i \(0.639560\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20.7639 −0.812555 −0.406278 0.913750i \(-0.633173\pi\)
−0.406278 + 0.913750i \(0.633173\pi\)
\(654\) 0 0
\(655\) −3.41641 −0.133490
\(656\) 0 0
\(657\) 8.14590 0.317802
\(658\) 0 0
\(659\) −21.0902 −0.821556 −0.410778 0.911735i \(-0.634743\pi\)
−0.410778 + 0.911735i \(0.634743\pi\)
\(660\) 0 0
\(661\) −31.4164 −1.22196 −0.610978 0.791647i \(-0.709224\pi\)
−0.610978 + 0.791647i \(0.709224\pi\)
\(662\) 0 0
\(663\) −1.23607 −0.0480049
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 14.4721 0.560363
\(668\) 0 0
\(669\) −7.59675 −0.293707
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.9443 −0.653154 −0.326577 0.945171i \(-0.605895\pi\)
−0.326577 + 0.945171i \(0.605895\pi\)
\(674\) 0 0
\(675\) 6.90983 0.265959
\(676\) 0 0
\(677\) 32.8328 1.26187 0.630934 0.775837i \(-0.282672\pi\)
0.630934 + 0.775837i \(0.282672\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5.29180 −0.202782
\(682\) 0 0
\(683\) −10.1115 −0.386904 −0.193452 0.981110i \(-0.561968\pi\)
−0.193452 + 0.981110i \(0.561968\pi\)
\(684\) 0 0
\(685\) −0.124612 −0.00476117
\(686\) 0 0
\(687\) 3.59675 0.137224
\(688\) 0 0
\(689\) −39.8885 −1.51963
\(690\) 0 0
\(691\) −35.9787 −1.36869 −0.684347 0.729156i \(-0.739913\pi\)
−0.684347 + 0.729156i \(0.739913\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15.7295 −0.596654
\(696\) 0 0
\(697\) −1.14590 −0.0434040
\(698\) 0 0
\(699\) 7.70820 0.291551
\(700\) 0 0
\(701\) 39.3050 1.48453 0.742264 0.670108i \(-0.233752\pi\)
0.742264 + 0.670108i \(0.233752\pi\)
\(702\) 0 0
\(703\) −9.16718 −0.345747
\(704\) 0 0
\(705\) 5.77709 0.217578
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 28.6525 1.07607 0.538033 0.842924i \(-0.319168\pi\)
0.538033 + 0.842924i \(0.319168\pi\)
\(710\) 0 0
\(711\) 4.87539 0.182841
\(712\) 0 0
\(713\) 50.0689 1.87509
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.25735 −0.308377
\(718\) 0 0
\(719\) −22.0902 −0.823824 −0.411912 0.911224i \(-0.635139\pi\)
−0.411912 + 0.911224i \(0.635139\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0.527864 0.0196315
\(724\) 0 0
\(725\) −8.54102 −0.317206
\(726\) 0 0
\(727\) −0.291796 −0.0108221 −0.00541106 0.999985i \(-0.501722\pi\)
−0.00541106 + 0.999985i \(0.501722\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) 0 0
\(731\) 4.85410 0.179535
\(732\) 0 0
\(733\) −34.2492 −1.26502 −0.632512 0.774551i \(-0.717976\pi\)
−0.632512 + 0.774551i \(0.717976\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 9.61803 0.353805 0.176903 0.984228i \(-0.443392\pi\)
0.176903 + 0.984228i \(0.443392\pi\)
\(740\) 0 0
\(741\) 3.05573 0.112255
\(742\) 0 0
\(743\) 35.8885 1.31662 0.658311 0.752746i \(-0.271271\pi\)
0.658311 + 0.752746i \(0.271271\pi\)
\(744\) 0 0
\(745\) −7.76393 −0.284448
\(746\) 0 0
\(747\) 4.36068 0.159549
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.83282 −0.103371 −0.0516855 0.998663i \(-0.516459\pi\)
−0.0516855 + 0.998663i \(0.516459\pi\)
\(752\) 0 0
\(753\) 0.832816 0.0303495
\(754\) 0 0
\(755\) 16.9574 0.617144
\(756\) 0 0
\(757\) 14.5623 0.529276 0.264638 0.964348i \(-0.414748\pi\)
0.264638 + 0.964348i \(0.414748\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 53.8885 1.95346 0.976729 0.214477i \(-0.0688046\pi\)
0.976729 + 0.214477i \(0.0688046\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −3.94427 −0.142605
\(766\) 0 0
\(767\) −16.9443 −0.611822
\(768\) 0 0
\(769\) −13.5967 −0.490311 −0.245156 0.969484i \(-0.578839\pi\)
−0.245156 + 0.969484i \(0.578839\pi\)
\(770\) 0 0
\(771\) 4.00000 0.144056
\(772\) 0 0
\(773\) −20.4721 −0.736332 −0.368166 0.929760i \(-0.620014\pi\)
−0.368166 + 0.929760i \(0.620014\pi\)
\(774\) 0 0
\(775\) −29.5492 −1.06144
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.83282 0.101496
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −6.18034 −0.220867
\(784\) 0 0
\(785\) 14.2229 0.507638
\(786\) 0 0
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) 0 0
\(789\) −2.83282 −0.100851
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −40.6525 −1.44361
\(794\) 0 0
\(795\) 6.50658 0.230765
\(796\) 0 0
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 10.9443 0.387181
\(800\) 0 0
\(801\) −37.7771 −1.33479
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.12461 −0.180395
\(808\) 0 0
\(809\) −0.875388 −0.0307770 −0.0153885 0.999882i \(-0.504899\pi\)
−0.0153885 + 0.999882i \(0.504899\pi\)
\(810\) 0 0
\(811\) 31.9787 1.12292 0.561462 0.827502i \(-0.310239\pi\)
0.561462 + 0.827502i \(0.310239\pi\)
\(812\) 0 0
\(813\) −4.40325 −0.154429
\(814\) 0 0
\(815\) −8.29180 −0.290449
\(816\) 0 0
\(817\) −12.0000 −0.419827
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46.4721 1.62189 0.810944 0.585123i \(-0.198954\pi\)
0.810944 + 0.585123i \(0.198954\pi\)
\(822\) 0 0
\(823\) 24.5410 0.855446 0.427723 0.903910i \(-0.359316\pi\)
0.427723 + 0.903910i \(0.359316\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −41.2361 −1.43392 −0.716959 0.697115i \(-0.754467\pi\)
−0.716959 + 0.697115i \(0.754467\pi\)
\(828\) 0 0
\(829\) 37.5967 1.30579 0.652895 0.757449i \(-0.273554\pi\)
0.652895 + 0.757449i \(0.273554\pi\)
\(830\) 0 0
\(831\) 3.48529 0.120903
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −28.4164 −0.983390
\(836\) 0 0
\(837\) −21.3820 −0.739069
\(838\) 0 0
\(839\) −15.0557 −0.519781 −0.259891 0.965638i \(-0.583687\pi\)
−0.259891 + 0.965638i \(0.583687\pi\)
\(840\) 0 0
\(841\) −21.3607 −0.736575
\(842\) 0 0
\(843\) 5.54102 0.190843
\(844\) 0 0
\(845\) −3.49342 −0.120177
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 9.87539 0.338922
\(850\) 0 0
\(851\) 19.4164 0.665586
\(852\) 0 0
\(853\) 45.7771 1.56738 0.783689 0.621154i \(-0.213336\pi\)
0.783689 + 0.621154i \(0.213336\pi\)
\(854\) 0 0
\(855\) 9.75078 0.333470
\(856\) 0 0
\(857\) −44.7984 −1.53028 −0.765142 0.643862i \(-0.777331\pi\)
−0.765142 + 0.643862i \(0.777331\pi\)
\(858\) 0 0
\(859\) −36.8328 −1.25672 −0.628360 0.777923i \(-0.716273\pi\)
−0.628360 + 0.777923i \(0.716273\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26.3262 −0.896156 −0.448078 0.893995i \(-0.647891\pi\)
−0.448078 + 0.893995i \(0.647891\pi\)
\(864\) 0 0
\(865\) 9.22291 0.313588
\(866\) 0 0
\(867\) 0.381966 0.0129722
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 16.4721 0.558137
\(872\) 0 0
\(873\) −11.0000 −0.372294
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −17.3050 −0.584347 −0.292173 0.956365i \(-0.594378\pi\)
−0.292173 + 0.956365i \(0.594378\pi\)
\(878\) 0 0
\(879\) 8.24922 0.278239
\(880\) 0 0
\(881\) −21.1591 −0.712867 −0.356433 0.934321i \(-0.616007\pi\)
−0.356433 + 0.934321i \(0.616007\pi\)
\(882\) 0 0
\(883\) −14.6869 −0.494254 −0.247127 0.968983i \(-0.579487\pi\)
−0.247127 + 0.968983i \(0.579487\pi\)
\(884\) 0 0
\(885\) 2.76393 0.0929086
\(886\) 0 0
\(887\) −11.7426 −0.394279 −0.197140 0.980375i \(-0.563165\pi\)
−0.197140 + 0.980375i \(0.563165\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −27.0557 −0.905385
\(894\) 0 0
\(895\) 11.1803 0.373718
\(896\) 0 0
\(897\) −6.47214 −0.216098
\(898\) 0 0
\(899\) 26.4296 0.881475
\(900\) 0 0
\(901\) 12.3262 0.410647
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.3475 0.643133
\(906\) 0 0
\(907\) −36.1803 −1.20135 −0.600674 0.799494i \(-0.705101\pi\)
−0.600674 + 0.799494i \(0.705101\pi\)
\(908\) 0 0
\(909\) −47.0132 −1.55933
\(910\) 0 0
\(911\) 50.7214 1.68047 0.840237 0.542220i \(-0.182416\pi\)
0.840237 + 0.542220i \(0.182416\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 6.63119 0.219220
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −23.6869 −0.781359 −0.390680 0.920527i \(-0.627760\pi\)
−0.390680 + 0.920527i \(0.627760\pi\)
\(920\) 0 0
\(921\) 6.65248 0.219207
\(922\) 0 0
\(923\) 15.4164 0.507437
\(924\) 0 0
\(925\) −11.4590 −0.376769
\(926\) 0 0
\(927\) −17.1246 −0.562446
\(928\) 0 0
\(929\) −44.7984 −1.46979 −0.734893 0.678183i \(-0.762768\pi\)
−0.734893 + 0.678183i \(0.762768\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 4.48529 0.146842
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 31.4164 1.02633 0.513165 0.858290i \(-0.328473\pi\)
0.513165 + 0.858290i \(0.328473\pi\)
\(938\) 0 0
\(939\) 9.11146 0.297341
\(940\) 0 0
\(941\) −43.7984 −1.42779 −0.713893 0.700255i \(-0.753070\pi\)
−0.713893 + 0.700255i \(0.753070\pi\)
\(942\) 0 0
\(943\) −6.00000 −0.195387
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 57.1935 1.85854 0.929269 0.369403i \(-0.120438\pi\)
0.929269 + 0.369403i \(0.120438\pi\)
\(948\) 0 0
\(949\) 9.23607 0.299815
\(950\) 0 0
\(951\) −4.54102 −0.147253
\(952\) 0 0
\(953\) −31.0902 −1.00711 −0.503555 0.863963i \(-0.667975\pi\)
−0.503555 + 0.863963i \(0.667975\pi\)
\(954\) 0 0
\(955\) 15.0770 0.487881
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 60.4377 1.94960
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −20.0000 −0.643823
\(966\) 0 0
\(967\) −36.0902 −1.16058 −0.580291 0.814409i \(-0.697061\pi\)
−0.580291 + 0.814409i \(0.697061\pi\)
\(968\) 0 0
\(969\) −0.944272 −0.0303344
\(970\) 0 0
\(971\) 27.2361 0.874047 0.437024 0.899450i \(-0.356033\pi\)
0.437024 + 0.899450i \(0.356033\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 3.81966 0.122327
\(976\) 0 0
\(977\) 19.4508 0.622288 0.311144 0.950363i \(-0.399288\pi\)
0.311144 + 0.950363i \(0.399288\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 29.0557 0.927678
\(982\) 0 0
\(983\) −33.2705 −1.06116 −0.530582 0.847633i \(-0.678027\pi\)
−0.530582 + 0.847633i \(0.678027\pi\)
\(984\) 0 0
\(985\) −3.16718 −0.100915
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.4164 0.808195
\(990\) 0 0
\(991\) −58.5410 −1.85962 −0.929808 0.368044i \(-0.880028\pi\)
−0.929808 + 0.368044i \(0.880028\pi\)
\(992\) 0 0
\(993\) −0.888544 −0.0281971
\(994\) 0 0
\(995\) 26.0557 0.826022
\(996\) 0 0
\(997\) −12.7426 −0.403564 −0.201782 0.979430i \(-0.564673\pi\)
−0.201782 + 0.979430i \(0.564673\pi\)
\(998\) 0 0
\(999\) −8.29180 −0.262341
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 3332.2.a.o.1.1 yes 2
7.6 odd 2 3332.2.a.g.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.2.a.g.1.2 2 7.6 odd 2
3332.2.a.o.1.1 yes 2 1.1 even 1 trivial