Properties

Label 7200.2.k.u.3601.6
Level $7200$
Weight $2$
Character 7200.3601
Analytic conductor $57.492$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7200,2,Mod(3601,7200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 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("7200.3601");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.k (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(57.4922894553\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.180227832610816.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{53}]\)
Coefficient ring index: \( 2^{17} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3601.6
Root \(0.806504 + 1.16170i\) of defining polynomial
Character \(\chi\) \(=\) 7200.3601
Dual form 7200.2.k.u.3601.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.746175 q^{7} +O(q^{10})\) \(q-0.746175 q^{7} +5.36068i q^{11} +2.92520i q^{13} -2.13466 q^{17} -1.73367i q^{19} +7.49534 q^{23} -6.74916i q^{29} -2.64681 q^{31} -1.07480i q^{37} +11.2936 q^{41} +7.44322i q^{43} +1.73367 q^{47} -6.44322 q^{49} +7.72161i q^{53} +6.85302i q^{59} -6.45203i q^{61} +7.44322i q^{67} +13.2936 q^{71} -0.690358 q^{73} -4.00000i q^{77} -2.64681 q^{79} +5.85039i q^{83} -7.59283 q^{89} -2.18271i q^{91} -14.1887 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 32 q^{31} + 8 q^{41} + 12 q^{49} + 32 q^{71} + 32 q^{79} - 40 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7200\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(6401\) \(6751\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.746175 −0.282028 −0.141014 0.990008i \(-0.545036\pi\)
−0.141014 + 0.990008i \(0.545036\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.36068i 1.61630i 0.588974 + 0.808152i \(0.299532\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(12\) 0 0
\(13\) 2.92520i 0.811304i 0.914028 + 0.405652i \(0.132955\pi\)
−0.914028 + 0.405652i \(0.867045\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.13466 −0.517731 −0.258866 0.965913i \(-0.583349\pi\)
−0.258866 + 0.965913i \(0.583349\pi\)
\(18\) 0 0
\(19\) − 1.73367i − 0.397730i −0.980027 0.198865i \(-0.936274\pi\)
0.980027 0.198865i \(-0.0637255\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.49534 1.56289 0.781443 0.623977i \(-0.214484\pi\)
0.781443 + 0.623977i \(0.214484\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 6.74916i − 1.25329i −0.779306 0.626644i \(-0.784428\pi\)
0.779306 0.626644i \(-0.215572\pi\)
\(30\) 0 0
\(31\) −2.64681 −0.475381 −0.237690 0.971341i \(-0.576390\pi\)
−0.237690 + 0.971341i \(0.576390\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 1.07480i − 0.176697i −0.996090 0.0883483i \(-0.971841\pi\)
0.996090 0.0883483i \(-0.0281588\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.2936 1.76377 0.881883 0.471468i \(-0.156276\pi\)
0.881883 + 0.471468i \(0.156276\pi\)
\(42\) 0 0
\(43\) 7.44322i 1.13508i 0.823346 + 0.567540i \(0.192105\pi\)
−0.823346 + 0.567540i \(0.807895\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.73367 0.252881 0.126441 0.991974i \(-0.459645\pi\)
0.126441 + 0.991974i \(0.459645\pi\)
\(48\) 0 0
\(49\) −6.44322 −0.920460
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.72161i 1.06064i 0.847796 + 0.530322i \(0.177929\pi\)
−0.847796 + 0.530322i \(0.822071\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.85302i 0.892188i 0.894986 + 0.446094i \(0.147185\pi\)
−0.894986 + 0.446094i \(0.852815\pi\)
\(60\) 0 0
\(61\) − 6.45203i − 0.826098i −0.910709 0.413049i \(-0.864464\pi\)
0.910709 0.413049i \(-0.135536\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.44322i 0.909334i 0.890661 + 0.454667i \(0.150242\pi\)
−0.890661 + 0.454667i \(0.849758\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.2936 1.57766 0.788831 0.614610i \(-0.210687\pi\)
0.788831 + 0.614610i \(0.210687\pi\)
\(72\) 0 0
\(73\) −0.690358 −0.0808003 −0.0404002 0.999184i \(-0.512863\pi\)
−0.0404002 + 0.999184i \(0.512863\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.00000i − 0.455842i
\(78\) 0 0
\(79\) −2.64681 −0.297789 −0.148895 0.988853i \(-0.547572\pi\)
−0.148895 + 0.988853i \(0.547572\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.85039i 0.642164i 0.947051 + 0.321082i \(0.104047\pi\)
−0.947051 + 0.321082i \(0.895953\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.59283 −0.804838 −0.402419 0.915456i \(-0.631831\pi\)
−0.402419 + 0.915456i \(0.631831\pi\)
\(90\) 0 0
\(91\) − 2.18271i − 0.228810i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.1887 −1.44064 −0.720321 0.693641i \(-0.756006\pi\)
−0.720321 + 0.693641i \(0.756006\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.43952i 0.740260i 0.928980 + 0.370130i \(0.120687\pi\)
−0.928980 + 0.370130i \(0.879313\pi\)
\(102\) 0 0
\(103\) −7.19820 −0.709260 −0.354630 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 4.00000i − 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0 0
\(109\) − 19.9504i − 1.91090i −0.295158 0.955449i \(-0.595372\pi\)
0.295158 0.955449i \(-0.404628\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −12.0540 −1.13395 −0.566973 0.823736i \(-0.691886\pi\)
−0.566973 + 0.823736i \(0.691886\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.59283 0.146014
\(120\) 0 0
\(121\) −17.7368 −1.61244
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 4.21351 0.373888 0.186944 0.982371i \(-0.440142\pi\)
0.186944 + 0.982371i \(0.440142\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.3204i 0.901694i 0.892601 + 0.450847i \(0.148878\pi\)
−0.892601 + 0.450847i \(0.851122\pi\)
\(132\) 0 0
\(133\) 1.29362i 0.112171i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.0387 −1.28484 −0.642422 0.766351i \(-0.722070\pi\)
−0.642422 + 0.766351i \(0.722070\pi\)
\(138\) 0 0
\(139\) 9.47032i 0.803262i 0.915802 + 0.401631i \(0.131557\pi\)
−0.915802 + 0.401631i \(0.868443\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −15.6810 −1.31131
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 1.78948i − 0.146600i −0.997310 0.0733000i \(-0.976647\pi\)
0.997310 0.0733000i \(-0.0233531\pi\)
\(150\) 0 0
\(151\) −10.6468 −0.866425 −0.433212 0.901292i \(-0.642620\pi\)
−0.433212 + 0.901292i \(0.642620\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.92520i 0.552691i 0.961058 + 0.276345i \(0.0891234\pi\)
−0.961058 + 0.276345i \(0.910877\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.59283 −0.440777
\(162\) 0 0
\(163\) 7.70079i 0.603172i 0.953439 + 0.301586i \(0.0975161\pi\)
−0.953439 + 0.301586i \(0.902484\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.22601 −0.249637 −0.124818 0.992180i \(-0.539835\pi\)
−0.124818 + 0.992180i \(0.539835\pi\)
\(168\) 0 0
\(169\) 4.44322 0.341786
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 6.42799i − 0.488711i −0.969686 0.244356i \(-0.921424\pi\)
0.969686 0.244356i \(-0.0785764\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.13765i 0.608236i 0.952634 + 0.304118i \(0.0983618\pi\)
−0.952634 + 0.304118i \(0.901638\pi\)
\(180\) 0 0
\(181\) − 1.49235i − 0.110925i −0.998461 0.0554627i \(-0.982337\pi\)
0.998461 0.0554627i \(-0.0176634\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 11.4432i − 0.836811i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.88645 0.498286 0.249143 0.968467i \(-0.419851\pi\)
0.249143 + 0.968467i \(0.419851\pi\)
\(192\) 0 0
\(193\) −16.4830 −1.18647 −0.593237 0.805028i \(-0.702150\pi\)
−0.593237 + 0.805028i \(0.702150\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.5720i 0.966965i 0.875354 + 0.483483i \(0.160628\pi\)
−0.875354 + 0.483483i \(0.839372\pi\)
\(198\) 0 0
\(199\) −9.05398 −0.641820 −0.320910 0.947110i \(-0.603989\pi\)
−0.320910 + 0.947110i \(0.603989\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.03605i 0.353462i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 9.29362 0.642853
\(210\) 0 0
\(211\) − 2.53566i − 0.174562i −0.996184 0.0872809i \(-0.972182\pi\)
0.996184 0.0872809i \(-0.0278178\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.97498 0.134070
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 6.24430i − 0.420037i
\(222\) 0 0
\(223\) −12.1579 −0.814152 −0.407076 0.913394i \(-0.633452\pi\)
−0.407076 + 0.913394i \(0.633452\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.7368i 1.37635i 0.725544 + 0.688176i \(0.241588\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(228\) 0 0
\(229\) 19.9504i 1.31836i 0.751987 + 0.659178i \(0.229096\pi\)
−0.751987 + 0.659178i \(0.770904\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.3386 0.873844 0.436922 0.899499i \(-0.356069\pi\)
0.436922 + 0.899499i \(0.356069\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.8864 1.48040 0.740201 0.672386i \(-0.234731\pi\)
0.740201 + 0.672386i \(0.234731\pi\)
\(240\) 0 0
\(241\) 3.59283 0.231435 0.115717 0.993282i \(-0.463083\pi\)
0.115717 + 0.993282i \(0.463083\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.07131 0.322680
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 8.82801i − 0.557219i −0.960404 0.278609i \(-0.910127\pi\)
0.960404 0.278609i \(-0.0898735\pi\)
\(252\) 0 0
\(253\) 40.1801i 2.52610i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.2927 1.39058 0.695291 0.718728i \(-0.255275\pi\)
0.695291 + 0.718728i \(0.255275\pi\)
\(258\) 0 0
\(259\) 0.801991i 0.0498333i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −21.2014 −1.30733 −0.653667 0.756783i \(-0.726770\pi\)
−0.653667 + 0.756783i \(0.726770\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 14.6935i − 0.895881i −0.894063 0.447940i \(-0.852158\pi\)
0.894063 0.447940i \(-0.147842\pi\)
\(270\) 0 0
\(271\) 20.2396 1.22947 0.614735 0.788734i \(-0.289263\pi\)
0.614735 + 0.788734i \(0.289263\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.518027i 0.0311252i 0.999879 + 0.0155626i \(0.00495393\pi\)
−0.999879 + 0.0155626i \(0.995046\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.7008 −0.817320 −0.408660 0.912687i \(-0.634004\pi\)
−0.408660 + 0.912687i \(0.634004\pi\)
\(282\) 0 0
\(283\) 18.0305i 1.07180i 0.844282 + 0.535900i \(0.180027\pi\)
−0.844282 + 0.535900i \(0.819973\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.42701 −0.497431
\(288\) 0 0
\(289\) −12.4432 −0.731954
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 15.9792i 0.933513i 0.884386 + 0.466757i \(0.154578\pi\)
−0.884386 + 0.466757i \(0.845422\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 21.9253i 1.26797i
\(300\) 0 0
\(301\) − 5.55394i − 0.320124i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 22.5872i 1.28912i 0.764553 + 0.644561i \(0.222960\pi\)
−0.764553 + 0.644561i \(0.777040\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.5872 −1.05399 −0.526993 0.849870i \(-0.676680\pi\)
−0.526993 + 0.849870i \(0.676680\pi\)
\(312\) 0 0
\(313\) −29.3871 −1.66106 −0.830528 0.556977i \(-0.811961\pi\)
−0.830528 + 0.556977i \(0.811961\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.57201i 0.312955i 0.987682 + 0.156478i \(0.0500139\pi\)
−0.987682 + 0.156478i \(0.949986\pi\)
\(318\) 0 0
\(319\) 36.1801 2.02569
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.70079i 0.205917i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.29362 −0.0713194
\(330\) 0 0
\(331\) − 13.7396i − 0.755199i −0.925969 0.377599i \(-0.876750\pi\)
0.925969 0.377599i \(-0.123250\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 20.7523 1.13045 0.565226 0.824936i \(-0.308789\pi\)
0.565226 + 0.824936i \(0.308789\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 14.1887i − 0.768360i
\(342\) 0 0
\(343\) 10.0310 0.541623
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 4.73684i − 0.254287i −0.991884 0.127143i \(-0.959419\pi\)
0.991884 0.127143i \(-0.0405809\pi\)
\(348\) 0 0
\(349\) 0.482632i 0.0258347i 0.999917 + 0.0129174i \(0.00411184\pi\)
−0.999917 + 0.0129174i \(0.995888\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.13466 0.113617 0.0568083 0.998385i \(-0.481908\pi\)
0.0568083 + 0.998385i \(0.481908\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.59283 −0.506290 −0.253145 0.967428i \(-0.581465\pi\)
−0.253145 + 0.967428i \(0.581465\pi\)
\(360\) 0 0
\(361\) 15.9944 0.841811
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −34.0832 −1.77913 −0.889565 0.456809i \(-0.848992\pi\)
−0.889565 + 0.456809i \(0.848992\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 5.76167i − 0.299131i
\(372\) 0 0
\(373\) − 4.33796i − 0.224611i −0.993674 0.112306i \(-0.964176\pi\)
0.993674 0.112306i \(-0.0358236\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 19.7426 1.01680
\(378\) 0 0
\(379\) 6.90107i 0.354484i 0.984167 + 0.177242i \(0.0567176\pi\)
−0.984167 + 0.177242i \(0.943282\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 22.3744 1.14328 0.571639 0.820506i \(-0.306308\pi\)
0.571639 + 0.820506i \(0.306308\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.0185i 0.558659i 0.960195 + 0.279330i \(0.0901122\pi\)
−0.960195 + 0.279330i \(0.909888\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 25.2549i 1.26751i 0.773536 + 0.633753i \(0.218486\pi\)
−0.773536 + 0.633753i \(0.781514\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.29362 −0.364226 −0.182113 0.983278i \(-0.558294\pi\)
−0.182113 + 0.983278i \(0.558294\pi\)
\(402\) 0 0
\(403\) − 7.74244i − 0.385678i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.76167 0.285595
\(408\) 0 0
\(409\) 15.8504 0.783752 0.391876 0.920018i \(-0.371826\pi\)
0.391876 + 0.920018i \(0.371826\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 5.11355i − 0.251622i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 8.02602i − 0.392097i −0.980594 0.196048i \(-0.937189\pi\)
0.980594 0.196048i \(-0.0628109\pi\)
\(420\) 0 0
\(421\) 22.9351i 1.11779i 0.829240 + 0.558893i \(0.188774\pi\)
−0.829240 + 0.558893i \(0.811226\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.81434i 0.232982i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −35.0665 −1.68909 −0.844547 0.535481i \(-0.820130\pi\)
−0.844547 + 0.535481i \(0.820130\pi\)
\(432\) 0 0
\(433\) 17.0773 0.820682 0.410341 0.911932i \(-0.365410\pi\)
0.410341 + 0.911932i \(0.365410\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 12.9944i − 0.621607i
\(438\) 0 0
\(439\) −8.53885 −0.407537 −0.203769 0.979019i \(-0.565319\pi\)
−0.203769 + 0.979019i \(0.565319\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 20.7368i 0.985237i 0.870245 + 0.492619i \(0.163960\pi\)
−0.870245 + 0.492619i \(0.836040\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 60.5414i 2.85078i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.28462 0.0600921 0.0300461 0.999549i \(-0.490435\pi\)
0.0300461 + 0.999549i \(0.490435\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 15.7033i − 0.731374i −0.930738 0.365687i \(-0.880834\pi\)
0.930738 0.365687i \(-0.119166\pi\)
\(462\) 0 0
\(463\) −18.7215 −0.870064 −0.435032 0.900415i \(-0.643263\pi\)
−0.435032 + 0.900415i \(0.643263\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 2.14961i − 0.0994719i −0.998762 0.0497360i \(-0.984162\pi\)
0.998762 0.0497360i \(-0.0158380\pi\)
\(468\) 0 0
\(469\) − 5.55394i − 0.256457i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −39.9007 −1.83464
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.1801 −0.556521 −0.278261 0.960506i \(-0.589758\pi\)
−0.278261 + 0.960506i \(0.589758\pi\)
\(480\) 0 0
\(481\) 3.14401 0.143355
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −25.7678 −1.16765 −0.583826 0.811879i \(-0.698445\pi\)
−0.583826 + 0.811879i \(0.698445\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 16.7724i − 0.756927i −0.925616 0.378464i \(-0.876453\pi\)
0.925616 0.378464i \(-0.123547\pi\)
\(492\) 0 0
\(493\) 14.4072i 0.648866i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.91936 −0.444944
\(498\) 0 0
\(499\) − 17.6224i − 0.788888i −0.918920 0.394444i \(-0.870937\pi\)
0.918920 0.394444i \(-0.129063\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.1263 −1.20950 −0.604752 0.796414i \(-0.706728\pi\)
−0.604752 + 0.796414i \(0.706728\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.9782i 0.708220i 0.935204 + 0.354110i \(0.115216\pi\)
−0.935204 + 0.354110i \(0.884784\pi\)
\(510\) 0 0
\(511\) 0.515128 0.0227879
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.29362i 0.408733i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.886447 −0.0388359 −0.0194180 0.999811i \(-0.506181\pi\)
−0.0194180 + 0.999811i \(0.506181\pi\)
\(522\) 0 0
\(523\) 41.7729i 1.82660i 0.407286 + 0.913301i \(0.366475\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.65004 0.246120
\(528\) 0 0
\(529\) 33.1801 1.44261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 33.0361i 1.43095i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 34.5400i − 1.48774i
\(540\) 0 0
\(541\) − 4.47705i − 0.192483i −0.995358 0.0962417i \(-0.969318\pi\)
0.995358 0.0962417i \(-0.0306822\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14.3297i 0.612692i 0.951920 + 0.306346i \(0.0991065\pi\)
−0.951920 + 0.306346i \(0.900893\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.7008 −0.498470
\(552\) 0 0
\(553\) 1.97498 0.0839848
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 2.68556i − 0.113791i −0.998380 0.0568954i \(-0.981880\pi\)
0.998380 0.0568954i \(-0.0181201\pi\)
\(558\) 0 0
\(559\) −21.7729 −0.920895
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 20.7368i − 0.873954i −0.899473 0.436977i \(-0.856049\pi\)
0.899473 0.436977i \(-0.143951\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.40717 −0.184758 −0.0923791 0.995724i \(-0.529447\pi\)
−0.0923791 + 0.995724i \(0.529447\pi\)
\(570\) 0 0
\(571\) − 23.6590i − 0.990098i −0.868865 0.495049i \(-0.835150\pi\)
0.868865 0.495049i \(-0.164850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −6.56366 −0.273249 −0.136624 0.990623i \(-0.543625\pi\)
−0.136624 + 0.990623i \(0.543625\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 4.36542i − 0.181108i
\(582\) 0 0
\(583\) −41.3931 −1.71433
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 16.2992i − 0.672741i −0.941730 0.336370i \(-0.890801\pi\)
0.941730 0.336370i \(-0.109199\pi\)
\(588\) 0 0
\(589\) 4.58868i 0.189073i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.3233 0.670319 0.335160 0.942161i \(-0.391210\pi\)
0.335160 + 0.942161i \(0.391210\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −25.5928 −1.04569 −0.522847 0.852426i \(-0.675130\pi\)
−0.522847 + 0.852426i \(0.675130\pi\)
\(600\) 0 0
\(601\) 29.9225 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 20.6965 0.840046 0.420023 0.907513i \(-0.362022\pi\)
0.420023 + 0.907513i \(0.362022\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.07131i 0.205163i
\(612\) 0 0
\(613\) − 22.6676i − 0.915537i −0.889071 0.457769i \(-0.848649\pi\)
0.889071 0.457769i \(-0.151351\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.1966 −0.893603 −0.446802 0.894633i \(-0.647437\pi\)
−0.446802 + 0.894633i \(0.647437\pi\)
\(618\) 0 0
\(619\) 16.8204i 0.676070i 0.941133 + 0.338035i \(0.109762\pi\)
−0.941133 + 0.338035i \(0.890238\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.66558 0.226987
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.29434i 0.0914813i
\(630\) 0 0
\(631\) 44.1205 1.75641 0.878204 0.478285i \(-0.158742\pi\)
0.878204 + 0.478285i \(0.158742\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 18.8477i − 0.746773i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.18566 0.0468307 0.0234154 0.999726i \(-0.492546\pi\)
0.0234154 + 0.999726i \(0.492546\pi\)
\(642\) 0 0
\(643\) − 22.5872i − 0.890754i −0.895343 0.445377i \(-0.853070\pi\)
0.895343 0.445377i \(-0.146930\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −19.7090 −0.774842 −0.387421 0.921903i \(-0.626634\pi\)
−0.387421 + 0.921903i \(0.626634\pi\)
\(648\) 0 0
\(649\) −36.7368 −1.44205
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 44.4585i − 1.73979i −0.493234 0.869897i \(-0.664185\pi\)
0.493234 0.869897i \(-0.335815\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 41.5863i − 1.61997i −0.586448 0.809987i \(-0.699474\pi\)
0.586448 0.809987i \(-0.300526\pi\)
\(660\) 0 0
\(661\) − 12.0060i − 0.466978i −0.972359 0.233489i \(-0.924986\pi\)
0.972359 0.233489i \(-0.0750143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 50.5872i − 1.95875i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 34.5872 1.33523
\(672\) 0 0
\(673\) 14.5080 0.559244 0.279622 0.960110i \(-0.409791\pi\)
0.279622 + 0.960110i \(0.409791\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 43.8600i 1.68568i 0.538166 + 0.842839i \(0.319117\pi\)
−0.538166 + 0.842839i \(0.680883\pi\)
\(678\) 0 0
\(679\) 10.5872 0.406301
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 5.33527i − 0.204148i −0.994777 0.102074i \(-0.967452\pi\)
0.994777 0.102074i \(-0.0325479\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −22.5872 −0.860505
\(690\) 0 0
\(691\) − 39.7710i − 1.51296i −0.654016 0.756480i \(-0.726917\pi\)
0.654016 0.756480i \(-0.273083\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −24.1080 −0.913157
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27.5015i 1.03872i 0.854556 + 0.519359i \(0.173829\pi\)
−0.854556 + 0.519359i \(0.826171\pi\)
\(702\) 0 0
\(703\) −1.86335 −0.0702775
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 5.55118i − 0.208774i
\(708\) 0 0
\(709\) 0.111632i 0.00419244i 0.999998 + 0.00209622i \(0.000667249\pi\)
−0.999998 + 0.00209622i \(0.999333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −19.8387 −0.742966
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.7064 0.399281 0.199640 0.979869i \(-0.436023\pi\)
0.199640 + 0.979869i \(0.436023\pi\)
\(720\) 0 0
\(721\) 5.37112 0.200031
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 25.6562 0.951536 0.475768 0.879571i \(-0.342170\pi\)
0.475768 + 0.879571i \(0.342170\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 15.8888i − 0.587667i
\(732\) 0 0
\(733\) 30.3684i 1.12168i 0.827923 + 0.560842i \(0.189522\pi\)
−0.827923 + 0.560842i \(0.810478\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −39.9007 −1.46976
\(738\) 0 0
\(739\) − 20.1917i − 0.742763i −0.928480 0.371381i \(-0.878884\pi\)
0.928480 0.371381i \(-0.121116\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 46.3863 1.70175 0.850875 0.525369i \(-0.176073\pi\)
0.850875 + 0.525369i \(0.176073\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.98470i 0.109059i
\(750\) 0 0
\(751\) 27.1261 0.989845 0.494922 0.868937i \(-0.335196\pi\)
0.494922 + 0.868937i \(0.335196\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 45.2549i − 1.64482i −0.568898 0.822408i \(-0.692630\pi\)
0.568898 0.822408i \(-0.307370\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.8864 −0.612133 −0.306067 0.952010i \(-0.599013\pi\)
−0.306067 + 0.952010i \(0.599013\pi\)
\(762\) 0 0
\(763\) 14.8864i 0.538926i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −20.0464 −0.723835
\(768\) 0 0
\(769\) 16.3297 0.588863 0.294431 0.955673i \(-0.404870\pi\)
0.294431 + 0.955673i \(0.404870\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 41.3144i 1.48598i 0.669304 + 0.742989i \(0.266592\pi\)
−0.669304 + 0.742989i \(0.733408\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 19.5794i − 0.701503i
\(780\) 0 0
\(781\) 71.2628i 2.54998i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 11.4849i 0.409391i 0.978826 + 0.204696i \(0.0656205\pi\)
−0.978826 + 0.204696i \(0.934380\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.99440 0.319804
\(792\) 0 0
\(793\) 18.8735 0.670216
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 45.4945i − 1.61150i −0.592257 0.805749i \(-0.701763\pi\)
0.592257 0.805749i \(-0.298237\pi\)
\(798\) 0 0
\(799\) −3.70079 −0.130924
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 3.70079i − 0.130598i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 36.0721 1.26823 0.634114 0.773240i \(-0.281365\pi\)
0.634114 + 0.773240i \(0.281365\pi\)
\(810\) 0 0
\(811\) 44.5230i 1.56341i 0.623646 + 0.781707i \(0.285651\pi\)
−0.623646 + 0.781707i \(0.714349\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 12.9041 0.451456
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 34.1613i 1.19224i 0.802897 + 0.596118i \(0.203291\pi\)
−0.802897 + 0.596118i \(0.796709\pi\)
\(822\) 0 0
\(823\) 2.12689 0.0741388 0.0370694 0.999313i \(-0.488198\pi\)
0.0370694 + 0.999313i \(0.488198\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 38.5872i 1.34181i 0.741543 + 0.670905i \(0.234094\pi\)
−0.741543 + 0.670905i \(0.765906\pi\)
\(828\) 0 0
\(829\) 34.2351i 1.18904i 0.804083 + 0.594518i \(0.202657\pi\)
−0.804083 + 0.594518i \(0.797343\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 13.7541 0.476551
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −41.5928 −1.43594 −0.717972 0.696072i \(-0.754929\pi\)
−0.717972 + 0.696072i \(0.754929\pi\)
\(840\) 0 0
\(841\) −16.5512 −0.570730
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 13.2348 0.454752
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 8.05601i − 0.276156i
\(852\) 0 0
\(853\) − 23.1828i − 0.793763i −0.917870 0.396881i \(-0.870092\pi\)
0.917870 0.396881i \(-0.129908\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.38868 −0.320711 −0.160356 0.987059i \(-0.551264\pi\)
−0.160356 + 0.987059i \(0.551264\pi\)
\(858\) 0 0
\(859\) − 8.98769i − 0.306656i −0.988175 0.153328i \(-0.951001\pi\)
0.988175 0.153328i \(-0.0489991\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −12.2473 −0.416903 −0.208451 0.978033i \(-0.566842\pi\)
−0.208451 + 0.978033i \(0.566842\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 14.1887i − 0.481318i
\(870\) 0 0
\(871\) −21.7729 −0.737746
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 26.1109i 0.881701i 0.897581 + 0.440850i \(0.145323\pi\)
−0.897581 + 0.440850i \(0.854677\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 38.4793 1.29640 0.648200 0.761470i \(-0.275522\pi\)
0.648200 + 0.761470i \(0.275522\pi\)
\(882\) 0 0
\(883\) − 6.58723i − 0.221678i −0.993838 0.110839i \(-0.964646\pi\)
0.993838 0.110839i \(-0.0353538\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 50.9595 1.71105 0.855526 0.517760i \(-0.173234\pi\)
0.855526 + 0.517760i \(0.173234\pi\)
\(888\) 0 0
\(889\) −3.14401 −0.105447
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 3.00560i − 0.100578i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 17.8637i 0.595789i
\(900\) 0 0
\(901\) − 16.4830i − 0.549129i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 24.5568i 0.815394i 0.913117 + 0.407697i \(0.133668\pi\)
−0.913117 + 0.407697i \(0.866332\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 16.0000 0.530104 0.265052 0.964234i \(-0.414611\pi\)
0.265052 + 0.964234i \(0.414611\pi\)
\(912\) 0 0
\(913\) −31.3621 −1.03793
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 7.70079i − 0.254302i
\(918\) 0 0
\(919\) −28.7548 −0.948532 −0.474266 0.880382i \(-0.657287\pi\)
−0.474266 + 0.880382i \(0.657287\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 38.8864i 1.27996i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −28.2880 −0.928100 −0.464050 0.885809i \(-0.653604\pi\)
−0.464050 + 0.885809i \(0.653604\pi\)
\(930\) 0 0
\(931\) 11.1704i 0.366095i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −33.9313 −1.10849 −0.554244 0.832354i \(-0.686992\pi\)
−0.554244 + 0.832354i \(0.686992\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 38.8016i 1.26490i 0.774603 + 0.632448i \(0.217950\pi\)
−0.774603 + 0.632448i \(0.782050\pi\)
\(942\) 0 0
\(943\) 84.6495 2.75657
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17.7729i 0.577541i 0.957398 + 0.288771i \(0.0932465\pi\)
−0.957398 + 0.288771i \(0.906753\pi\)
\(948\) 0 0
\(949\) − 2.01943i − 0.0655536i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 46.3047 1.49996 0.749978 0.661463i \(-0.230064\pi\)
0.749978 + 0.661463i \(0.230064\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 11.2215 0.362361
\(960\) 0 0
\(961\) −23.9944 −0.774013
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −9.28482 −0.298580 −0.149290 0.988793i \(-0.547699\pi\)
−0.149290 + 0.988793i \(0.547699\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 20.9301i 0.671678i 0.941919 + 0.335839i \(0.109020\pi\)
−0.941919 + 0.335839i \(0.890980\pi\)
\(972\) 0 0
\(973\) − 7.06651i − 0.226542i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.8314 0.986383 0.493192 0.869921i \(-0.335830\pi\)
0.493192 + 0.869921i \(0.335830\pi\)
\(978\) 0 0
\(979\) − 40.7027i − 1.30086i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 31.3285 0.999223 0.499612 0.866250i \(-0.333476\pi\)
0.499612 + 0.866250i \(0.333476\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 55.7895i 1.77400i
\(990\) 0 0
\(991\) −31.3420 −0.995611 −0.497806 0.867289i \(-0.665861\pi\)
−0.497806 + 0.867289i \(0.665861\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 20.9557i 0.663672i 0.943337 + 0.331836i \(0.107668\pi\)
−0.943337 + 0.331836i \(0.892332\pi\)
\(998\) 0 0
\(999\) 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 7200.2.k.u.3601.6 12
3.2 odd 2 2400.2.k.f.1201.9 12
4.3 odd 2 1800.2.k.u.901.3 12
5.2 odd 4 1440.2.d.f.1009.1 6
5.3 odd 4 1440.2.d.e.1009.5 6
5.4 even 2 inner 7200.2.k.u.3601.8 12
8.3 odd 2 1800.2.k.u.901.4 12
8.5 even 2 inner 7200.2.k.u.3601.5 12
12.11 even 2 600.2.k.f.301.10 12
15.2 even 4 480.2.d.b.49.6 6
15.8 even 4 480.2.d.a.49.2 6
15.14 odd 2 2400.2.k.f.1201.4 12
20.3 even 4 360.2.d.f.109.2 6
20.7 even 4 360.2.d.e.109.5 6
20.19 odd 2 1800.2.k.u.901.10 12
24.5 odd 2 2400.2.k.f.1201.3 12
24.11 even 2 600.2.k.f.301.9 12
40.3 even 4 360.2.d.e.109.6 6
40.13 odd 4 1440.2.d.f.1009.2 6
40.19 odd 2 1800.2.k.u.901.9 12
40.27 even 4 360.2.d.f.109.1 6
40.29 even 2 inner 7200.2.k.u.3601.7 12
40.37 odd 4 1440.2.d.e.1009.6 6
60.23 odd 4 120.2.d.a.109.5 6
60.47 odd 4 120.2.d.b.109.2 yes 6
60.59 even 2 600.2.k.f.301.3 12
120.29 odd 2 2400.2.k.f.1201.10 12
120.53 even 4 480.2.d.b.49.5 6
120.59 even 2 600.2.k.f.301.4 12
120.77 even 4 480.2.d.a.49.1 6
120.83 odd 4 120.2.d.b.109.1 yes 6
120.107 odd 4 120.2.d.a.109.6 yes 6
240.53 even 4 3840.2.f.m.769.8 12
240.77 even 4 3840.2.f.m.769.11 12
240.83 odd 4 3840.2.f.l.769.11 12
240.107 odd 4 3840.2.f.l.769.8 12
240.173 even 4 3840.2.f.m.769.5 12
240.197 even 4 3840.2.f.m.769.2 12
240.203 odd 4 3840.2.f.l.769.2 12
240.227 odd 4 3840.2.f.l.769.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.d.a.109.5 6 60.23 odd 4
120.2.d.a.109.6 yes 6 120.107 odd 4
120.2.d.b.109.1 yes 6 120.83 odd 4
120.2.d.b.109.2 yes 6 60.47 odd 4
360.2.d.e.109.5 6 20.7 even 4
360.2.d.e.109.6 6 40.3 even 4
360.2.d.f.109.1 6 40.27 even 4
360.2.d.f.109.2 6 20.3 even 4
480.2.d.a.49.1 6 120.77 even 4
480.2.d.a.49.2 6 15.8 even 4
480.2.d.b.49.5 6 120.53 even 4
480.2.d.b.49.6 6 15.2 even 4
600.2.k.f.301.3 12 60.59 even 2
600.2.k.f.301.4 12 120.59 even 2
600.2.k.f.301.9 12 24.11 even 2
600.2.k.f.301.10 12 12.11 even 2
1440.2.d.e.1009.5 6 5.3 odd 4
1440.2.d.e.1009.6 6 40.37 odd 4
1440.2.d.f.1009.1 6 5.2 odd 4
1440.2.d.f.1009.2 6 40.13 odd 4
1800.2.k.u.901.3 12 4.3 odd 2
1800.2.k.u.901.4 12 8.3 odd 2
1800.2.k.u.901.9 12 40.19 odd 2
1800.2.k.u.901.10 12 20.19 odd 2
2400.2.k.f.1201.3 12 24.5 odd 2
2400.2.k.f.1201.4 12 15.14 odd 2
2400.2.k.f.1201.9 12 3.2 odd 2
2400.2.k.f.1201.10 12 120.29 odd 2
3840.2.f.l.769.2 12 240.203 odd 4
3840.2.f.l.769.5 12 240.227 odd 4
3840.2.f.l.769.8 12 240.107 odd 4
3840.2.f.l.769.11 12 240.83 odd 4
3840.2.f.m.769.2 12 240.197 even 4
3840.2.f.m.769.5 12 240.173 even 4
3840.2.f.m.769.8 12 240.53 even 4
3840.2.f.m.769.11 12 240.77 even 4
7200.2.k.u.3601.5 12 8.5 even 2 inner
7200.2.k.u.3601.6 12 1.1 even 1 trivial
7200.2.k.u.3601.7 12 40.29 even 2 inner
7200.2.k.u.3601.8 12 5.4 even 2 inner