Properties

Label 9196.2.a.n.1.4
Level $9196$
Weight $2$
Character 9196.1
Self dual yes
Analytic conductor $73.430$
Analytic rank $0$
Dimension $6$
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] = [9196,2,Mod(1,9196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9196, 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("9196.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9196.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: \(73.4304296988\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.744786576.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 836)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.837309\) of defining polynomial
Character \(\chi\) \(=\) 9196.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.837309 q^{3} +3.44987 q^{5} -0.535976 q^{7} -2.29891 q^{9} +O(q^{10})\) \(q+0.837309 q^{3} +3.44987 q^{5} -0.535976 q^{7} -2.29891 q^{9} -5.54895 q^{13} +2.88861 q^{15} -1.49993 q^{17} +1.00000 q^{19} -0.448778 q^{21} +3.26301 q^{23} +6.90158 q^{25} -4.43683 q^{27} +3.17227 q^{29} -0.888605 q^{31} -1.84905 q^{35} +11.0600 q^{37} -4.64619 q^{39} +8.44868 q^{41} +7.61261 q^{43} -7.93094 q^{45} +3.39981 q^{47} -6.71273 q^{49} -1.25590 q^{51} +7.22511 q^{53} +0.837309 q^{57} -1.36560 q^{59} +2.57435 q^{61} +1.23216 q^{63} -19.1431 q^{65} -10.8862 q^{67} +2.73215 q^{69} +2.66509 q^{71} -9.82294 q^{73} +5.77876 q^{75} +2.17469 q^{79} +3.18174 q^{81} -4.71288 q^{83} -5.17454 q^{85} +2.65617 q^{87} -4.66282 q^{89} +2.97411 q^{91} -0.744038 q^{93} +3.44987 q^{95} +6.93516 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 5 q^{5} + 2 q^{7} + 17 q^{9} - 8 q^{13} + 9 q^{15} + 2 q^{17} + 6 q^{19} - 18 q^{21} + 5 q^{23} + 13 q^{25} + 7 q^{27} - 10 q^{29} + 3 q^{31} + 4 q^{35} + 7 q^{37} + 10 q^{39} - 6 q^{41} - 16 q^{43} + 42 q^{45} + 12 q^{49} - 8 q^{51} + 20 q^{53} + q^{57} + 15 q^{59} - 24 q^{61} + 20 q^{63} + 28 q^{65} + 25 q^{67} - 33 q^{69} - 9 q^{71} + 26 q^{73} + 28 q^{75} + 16 q^{79} + 58 q^{81} + 2 q^{83} - 12 q^{85} + 36 q^{87} + 7 q^{89} + 8 q^{91} - 55 q^{93} + 5 q^{95} + 37 q^{97}+O(q^{100}) \) 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
\(3\) 0.837309 0.483421 0.241710 0.970348i \(-0.422292\pi\)
0.241710 + 0.970348i \(0.422292\pi\)
\(4\) 0 0
\(5\) 3.44987 1.54283 0.771414 0.636334i \(-0.219550\pi\)
0.771414 + 0.636334i \(0.219550\pi\)
\(6\) 0 0
\(7\) −0.535976 −0.202580 −0.101290 0.994857i \(-0.532297\pi\)
−0.101290 + 0.994857i \(0.532297\pi\)
\(8\) 0 0
\(9\) −2.29891 −0.766304
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −5.54895 −1.53900 −0.769501 0.638646i \(-0.779495\pi\)
−0.769501 + 0.638646i \(0.779495\pi\)
\(14\) 0 0
\(15\) 2.88861 0.745835
\(16\) 0 0
\(17\) −1.49993 −0.363785 −0.181893 0.983318i \(-0.558222\pi\)
−0.181893 + 0.983318i \(0.558222\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −0.448778 −0.0979314
\(22\) 0 0
\(23\) 3.26301 0.680385 0.340192 0.940356i \(-0.389508\pi\)
0.340192 + 0.940356i \(0.389508\pi\)
\(24\) 0 0
\(25\) 6.90158 1.38032
\(26\) 0 0
\(27\) −4.43683 −0.853868
\(28\) 0 0
\(29\) 3.17227 0.589076 0.294538 0.955640i \(-0.404834\pi\)
0.294538 + 0.955640i \(0.404834\pi\)
\(30\) 0 0
\(31\) −0.888605 −0.159598 −0.0797991 0.996811i \(-0.525428\pi\)
−0.0797991 + 0.996811i \(0.525428\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.84905 −0.312546
\(36\) 0 0
\(37\) 11.0600 1.81825 0.909127 0.416520i \(-0.136750\pi\)
0.909127 + 0.416520i \(0.136750\pi\)
\(38\) 0 0
\(39\) −4.64619 −0.743985
\(40\) 0 0
\(41\) 8.44868 1.31946 0.659731 0.751502i \(-0.270670\pi\)
0.659731 + 0.751502i \(0.270670\pi\)
\(42\) 0 0
\(43\) 7.61261 1.16091 0.580456 0.814292i \(-0.302874\pi\)
0.580456 + 0.814292i \(0.302874\pi\)
\(44\) 0 0
\(45\) −7.93094 −1.18228
\(46\) 0 0
\(47\) 3.39981 0.495913 0.247956 0.968771i \(-0.420241\pi\)
0.247956 + 0.968771i \(0.420241\pi\)
\(48\) 0 0
\(49\) −6.71273 −0.958961
\(50\) 0 0
\(51\) −1.25590 −0.175861
\(52\) 0 0
\(53\) 7.22511 0.992446 0.496223 0.868195i \(-0.334720\pi\)
0.496223 + 0.868195i \(0.334720\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.837309 0.110904
\(58\) 0 0
\(59\) −1.36560 −0.177786 −0.0888932 0.996041i \(-0.528333\pi\)
−0.0888932 + 0.996041i \(0.528333\pi\)
\(60\) 0 0
\(61\) 2.57435 0.329612 0.164806 0.986326i \(-0.447300\pi\)
0.164806 + 0.986326i \(0.447300\pi\)
\(62\) 0 0
\(63\) 1.23216 0.155238
\(64\) 0 0
\(65\) −19.1431 −2.37441
\(66\) 0 0
\(67\) −10.8862 −1.32997 −0.664983 0.746859i \(-0.731561\pi\)
−0.664983 + 0.746859i \(0.731561\pi\)
\(68\) 0 0
\(69\) 2.73215 0.328912
\(70\) 0 0
\(71\) 2.66509 0.316288 0.158144 0.987416i \(-0.449449\pi\)
0.158144 + 0.987416i \(0.449449\pi\)
\(72\) 0 0
\(73\) −9.82294 −1.14969 −0.574844 0.818263i \(-0.694937\pi\)
−0.574844 + 0.818263i \(0.694937\pi\)
\(74\) 0 0
\(75\) 5.77876 0.667273
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.17469 0.244672 0.122336 0.992489i \(-0.460961\pi\)
0.122336 + 0.992489i \(0.460961\pi\)
\(80\) 0 0
\(81\) 3.18174 0.353527
\(82\) 0 0
\(83\) −4.71288 −0.517305 −0.258653 0.965970i \(-0.583279\pi\)
−0.258653 + 0.965970i \(0.583279\pi\)
\(84\) 0 0
\(85\) −5.17454 −0.561258
\(86\) 0 0
\(87\) 2.65617 0.284772
\(88\) 0 0
\(89\) −4.66282 −0.494258 −0.247129 0.968983i \(-0.579487\pi\)
−0.247129 + 0.968983i \(0.579487\pi\)
\(90\) 0 0
\(91\) 2.97411 0.311771
\(92\) 0 0
\(93\) −0.744038 −0.0771531
\(94\) 0 0
\(95\) 3.44987 0.353949
\(96\) 0 0
\(97\) 6.93516 0.704158 0.352079 0.935970i \(-0.385475\pi\)
0.352079 + 0.935970i \(0.385475\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.274812 −0.0273448 −0.0136724 0.999907i \(-0.504352\pi\)
−0.0136724 + 0.999907i \(0.504352\pi\)
\(102\) 0 0
\(103\) 16.0745 1.58387 0.791933 0.610608i \(-0.209075\pi\)
0.791933 + 0.610608i \(0.209075\pi\)
\(104\) 0 0
\(105\) −1.54822 −0.151091
\(106\) 0 0
\(107\) 10.8689 1.05074 0.525370 0.850874i \(-0.323927\pi\)
0.525370 + 0.850874i \(0.323927\pi\)
\(108\) 0 0
\(109\) 12.2947 1.17762 0.588809 0.808272i \(-0.299597\pi\)
0.588809 + 0.808272i \(0.299597\pi\)
\(110\) 0 0
\(111\) 9.26064 0.878981
\(112\) 0 0
\(113\) 7.54030 0.709331 0.354666 0.934993i \(-0.384595\pi\)
0.354666 + 0.934993i \(0.384595\pi\)
\(114\) 0 0
\(115\) 11.2570 1.04972
\(116\) 0 0
\(117\) 12.7566 1.17934
\(118\) 0 0
\(119\) 0.803925 0.0736957
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 7.07416 0.637856
\(124\) 0 0
\(125\) 6.56019 0.586762
\(126\) 0 0
\(127\) 13.8753 1.23123 0.615615 0.788047i \(-0.288908\pi\)
0.615615 + 0.788047i \(0.288908\pi\)
\(128\) 0 0
\(129\) 6.37411 0.561209
\(130\) 0 0
\(131\) 22.7894 1.99112 0.995558 0.0941505i \(-0.0300135\pi\)
0.995558 + 0.0941505i \(0.0300135\pi\)
\(132\) 0 0
\(133\) −0.535976 −0.0464750
\(134\) 0 0
\(135\) −15.3065 −1.31737
\(136\) 0 0
\(137\) −17.4238 −1.48861 −0.744306 0.667839i \(-0.767220\pi\)
−0.744306 + 0.667839i \(0.767220\pi\)
\(138\) 0 0
\(139\) 13.7540 1.16660 0.583301 0.812256i \(-0.301761\pi\)
0.583301 + 0.812256i \(0.301761\pi\)
\(140\) 0 0
\(141\) 2.84669 0.239735
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 10.9439 0.908843
\(146\) 0 0
\(147\) −5.62063 −0.463582
\(148\) 0 0
\(149\) 12.4471 1.01971 0.509855 0.860261i \(-0.329699\pi\)
0.509855 + 0.860261i \(0.329699\pi\)
\(150\) 0 0
\(151\) −8.67447 −0.705918 −0.352959 0.935639i \(-0.614825\pi\)
−0.352959 + 0.935639i \(0.614825\pi\)
\(152\) 0 0
\(153\) 3.44820 0.278770
\(154\) 0 0
\(155\) −3.06557 −0.246233
\(156\) 0 0
\(157\) 15.7729 1.25881 0.629406 0.777076i \(-0.283298\pi\)
0.629406 + 0.777076i \(0.283298\pi\)
\(158\) 0 0
\(159\) 6.04966 0.479769
\(160\) 0 0
\(161\) −1.74890 −0.137832
\(162\) 0 0
\(163\) −11.6248 −0.910523 −0.455261 0.890358i \(-0.650454\pi\)
−0.455261 + 0.890358i \(0.650454\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.39744 −0.727196 −0.363598 0.931556i \(-0.618452\pi\)
−0.363598 + 0.931556i \(0.618452\pi\)
\(168\) 0 0
\(169\) 17.7908 1.36853
\(170\) 0 0
\(171\) −2.29891 −0.175802
\(172\) 0 0
\(173\) −9.00005 −0.684261 −0.342131 0.939652i \(-0.611149\pi\)
−0.342131 + 0.939652i \(0.611149\pi\)
\(174\) 0 0
\(175\) −3.69908 −0.279624
\(176\) 0 0
\(177\) −1.14343 −0.0859456
\(178\) 0 0
\(179\) −0.439101 −0.0328200 −0.0164100 0.999865i \(-0.505224\pi\)
−0.0164100 + 0.999865i \(0.505224\pi\)
\(180\) 0 0
\(181\) −19.1343 −1.42224 −0.711120 0.703071i \(-0.751812\pi\)
−0.711120 + 0.703071i \(0.751812\pi\)
\(182\) 0 0
\(183\) 2.15553 0.159341
\(184\) 0 0
\(185\) 38.1555 2.80525
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 2.37804 0.172977
\(190\) 0 0
\(191\) −22.2325 −1.60869 −0.804343 0.594165i \(-0.797482\pi\)
−0.804343 + 0.594165i \(0.797482\pi\)
\(192\) 0 0
\(193\) 20.6415 1.48581 0.742904 0.669397i \(-0.233448\pi\)
0.742904 + 0.669397i \(0.233448\pi\)
\(194\) 0 0
\(195\) −16.0287 −1.14784
\(196\) 0 0
\(197\) 2.25328 0.160540 0.0802698 0.996773i \(-0.474422\pi\)
0.0802698 + 0.996773i \(0.474422\pi\)
\(198\) 0 0
\(199\) −3.27743 −0.232331 −0.116166 0.993230i \(-0.537060\pi\)
−0.116166 + 0.993230i \(0.537060\pi\)
\(200\) 0 0
\(201\) −9.11515 −0.642933
\(202\) 0 0
\(203\) −1.70026 −0.119335
\(204\) 0 0
\(205\) 29.1468 2.03570
\(206\) 0 0
\(207\) −7.50138 −0.521382
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −8.60267 −0.592232 −0.296116 0.955152i \(-0.595691\pi\)
−0.296116 + 0.955152i \(0.595691\pi\)
\(212\) 0 0
\(213\) 2.23150 0.152900
\(214\) 0 0
\(215\) 26.2625 1.79109
\(216\) 0 0
\(217\) 0.476271 0.0323314
\(218\) 0 0
\(219\) −8.22484 −0.555783
\(220\) 0 0
\(221\) 8.32301 0.559867
\(222\) 0 0
\(223\) 17.1038 1.14535 0.572677 0.819781i \(-0.305905\pi\)
0.572677 + 0.819781i \(0.305905\pi\)
\(224\) 0 0
\(225\) −15.8661 −1.05774
\(226\) 0 0
\(227\) −0.0197823 −0.00131300 −0.000656499 1.00000i \(-0.500209\pi\)
−0.000656499 1.00000i \(0.500209\pi\)
\(228\) 0 0
\(229\) 23.3471 1.54282 0.771410 0.636338i \(-0.219552\pi\)
0.771410 + 0.636338i \(0.219552\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.6262 0.696149 0.348074 0.937467i \(-0.386836\pi\)
0.348074 + 0.937467i \(0.386836\pi\)
\(234\) 0 0
\(235\) 11.7289 0.765108
\(236\) 0 0
\(237\) 1.82089 0.118280
\(238\) 0 0
\(239\) 10.0843 0.652297 0.326148 0.945319i \(-0.394249\pi\)
0.326148 + 0.945319i \(0.394249\pi\)
\(240\) 0 0
\(241\) −19.7997 −1.27541 −0.637704 0.770281i \(-0.720116\pi\)
−0.637704 + 0.770281i \(0.720116\pi\)
\(242\) 0 0
\(243\) 15.9746 1.02477
\(244\) 0 0
\(245\) −23.1580 −1.47951
\(246\) 0 0
\(247\) −5.54895 −0.353071
\(248\) 0 0
\(249\) −3.94614 −0.250076
\(250\) 0 0
\(251\) −13.5342 −0.854273 −0.427137 0.904187i \(-0.640478\pi\)
−0.427137 + 0.904187i \(0.640478\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −4.33269 −0.271324
\(256\) 0 0
\(257\) 1.47161 0.0917966 0.0458983 0.998946i \(-0.485385\pi\)
0.0458983 + 0.998946i \(0.485385\pi\)
\(258\) 0 0
\(259\) −5.92790 −0.368342
\(260\) 0 0
\(261\) −7.29278 −0.451412
\(262\) 0 0
\(263\) 30.2847 1.86744 0.933718 0.358010i \(-0.116545\pi\)
0.933718 + 0.358010i \(0.116545\pi\)
\(264\) 0 0
\(265\) 24.9257 1.53117
\(266\) 0 0
\(267\) −3.90422 −0.238934
\(268\) 0 0
\(269\) 7.12385 0.434349 0.217174 0.976133i \(-0.430316\pi\)
0.217174 + 0.976133i \(0.430316\pi\)
\(270\) 0 0
\(271\) 29.8853 1.81540 0.907702 0.419616i \(-0.137835\pi\)
0.907702 + 0.419616i \(0.137835\pi\)
\(272\) 0 0
\(273\) 2.49025 0.150717
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −13.5222 −0.812469 −0.406235 0.913769i \(-0.633158\pi\)
−0.406235 + 0.913769i \(0.633158\pi\)
\(278\) 0 0
\(279\) 2.04283 0.122301
\(280\) 0 0
\(281\) −4.37760 −0.261146 −0.130573 0.991439i \(-0.541682\pi\)
−0.130573 + 0.991439i \(0.541682\pi\)
\(282\) 0 0
\(283\) −20.6608 −1.22816 −0.614079 0.789244i \(-0.710472\pi\)
−0.614079 + 0.789244i \(0.710472\pi\)
\(284\) 0 0
\(285\) 2.88861 0.171106
\(286\) 0 0
\(287\) −4.52829 −0.267297
\(288\) 0 0
\(289\) −14.7502 −0.867660
\(290\) 0 0
\(291\) 5.80687 0.340405
\(292\) 0 0
\(293\) 10.5734 0.617706 0.308853 0.951110i \(-0.400055\pi\)
0.308853 + 0.951110i \(0.400055\pi\)
\(294\) 0 0
\(295\) −4.71115 −0.274294
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −18.1063 −1.04711
\(300\) 0 0
\(301\) −4.08018 −0.235178
\(302\) 0 0
\(303\) −0.230102 −0.0132190
\(304\) 0 0
\(305\) 8.88117 0.508534
\(306\) 0 0
\(307\) −4.45392 −0.254199 −0.127099 0.991890i \(-0.540567\pi\)
−0.127099 + 0.991890i \(0.540567\pi\)
\(308\) 0 0
\(309\) 13.4593 0.765673
\(310\) 0 0
\(311\) 5.02138 0.284736 0.142368 0.989814i \(-0.454528\pi\)
0.142368 + 0.989814i \(0.454528\pi\)
\(312\) 0 0
\(313\) 15.1246 0.854892 0.427446 0.904041i \(-0.359413\pi\)
0.427446 + 0.904041i \(0.359413\pi\)
\(314\) 0 0
\(315\) 4.25080 0.239505
\(316\) 0 0
\(317\) −17.8288 −1.00137 −0.500683 0.865630i \(-0.666918\pi\)
−0.500683 + 0.865630i \(0.666918\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 9.10067 0.507950
\(322\) 0 0
\(323\) −1.49993 −0.0834581
\(324\) 0 0
\(325\) −38.2965 −2.12431
\(326\) 0 0
\(327\) 10.2945 0.569285
\(328\) 0 0
\(329\) −1.82222 −0.100462
\(330\) 0 0
\(331\) 32.7851 1.80203 0.901016 0.433786i \(-0.142823\pi\)
0.901016 + 0.433786i \(0.142823\pi\)
\(332\) 0 0
\(333\) −25.4260 −1.39334
\(334\) 0 0
\(335\) −37.5561 −2.05191
\(336\) 0 0
\(337\) −17.0964 −0.931298 −0.465649 0.884970i \(-0.654179\pi\)
−0.465649 + 0.884970i \(0.654179\pi\)
\(338\) 0 0
\(339\) 6.31356 0.342905
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 7.34970 0.396846
\(344\) 0 0
\(345\) 9.42555 0.507455
\(346\) 0 0
\(347\) −1.52587 −0.0819132 −0.0409566 0.999161i \(-0.513041\pi\)
−0.0409566 + 0.999161i \(0.513041\pi\)
\(348\) 0 0
\(349\) −3.37139 −0.180466 −0.0902331 0.995921i \(-0.528761\pi\)
−0.0902331 + 0.995921i \(0.528761\pi\)
\(350\) 0 0
\(351\) 24.6197 1.31410
\(352\) 0 0
\(353\) 6.08870 0.324069 0.162034 0.986785i \(-0.448194\pi\)
0.162034 + 0.986785i \(0.448194\pi\)
\(354\) 0 0
\(355\) 9.19420 0.487978
\(356\) 0 0
\(357\) 0.673134 0.0356260
\(358\) 0 0
\(359\) 20.8084 1.09823 0.549113 0.835748i \(-0.314966\pi\)
0.549113 + 0.835748i \(0.314966\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −33.8878 −1.77377
\(366\) 0 0
\(367\) −17.8042 −0.929372 −0.464686 0.885476i \(-0.653833\pi\)
−0.464686 + 0.885476i \(0.653833\pi\)
\(368\) 0 0
\(369\) −19.4228 −1.01111
\(370\) 0 0
\(371\) −3.87249 −0.201050
\(372\) 0 0
\(373\) −17.2736 −0.894395 −0.447198 0.894435i \(-0.647578\pi\)
−0.447198 + 0.894435i \(0.647578\pi\)
\(374\) 0 0
\(375\) 5.49291 0.283653
\(376\) 0 0
\(377\) −17.6028 −0.906589
\(378\) 0 0
\(379\) 17.9061 0.919773 0.459886 0.887978i \(-0.347890\pi\)
0.459886 + 0.887978i \(0.347890\pi\)
\(380\) 0 0
\(381\) 11.6179 0.595202
\(382\) 0 0
\(383\) 3.83449 0.195933 0.0979667 0.995190i \(-0.468766\pi\)
0.0979667 + 0.995190i \(0.468766\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −17.5007 −0.889612
\(388\) 0 0
\(389\) 2.75314 0.139590 0.0697949 0.997561i \(-0.477766\pi\)
0.0697949 + 0.997561i \(0.477766\pi\)
\(390\) 0 0
\(391\) −4.89427 −0.247514
\(392\) 0 0
\(393\) 19.0817 0.962547
\(394\) 0 0
\(395\) 7.50240 0.377487
\(396\) 0 0
\(397\) 7.78879 0.390908 0.195454 0.980713i \(-0.437382\pi\)
0.195454 + 0.980713i \(0.437382\pi\)
\(398\) 0 0
\(399\) −0.448778 −0.0224670
\(400\) 0 0
\(401\) −2.64767 −0.132218 −0.0661092 0.997812i \(-0.521059\pi\)
−0.0661092 + 0.997812i \(0.521059\pi\)
\(402\) 0 0
\(403\) 4.93083 0.245622
\(404\) 0 0
\(405\) 10.9766 0.545431
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −32.0043 −1.58251 −0.791256 0.611485i \(-0.790572\pi\)
−0.791256 + 0.611485i \(0.790572\pi\)
\(410\) 0 0
\(411\) −14.5891 −0.719626
\(412\) 0 0
\(413\) 0.731931 0.0360160
\(414\) 0 0
\(415\) −16.2588 −0.798113
\(416\) 0 0
\(417\) 11.5164 0.563960
\(418\) 0 0
\(419\) −17.0000 −0.830502 −0.415251 0.909707i \(-0.636306\pi\)
−0.415251 + 0.909707i \(0.636306\pi\)
\(420\) 0 0
\(421\) 17.5236 0.854050 0.427025 0.904240i \(-0.359562\pi\)
0.427025 + 0.904240i \(0.359562\pi\)
\(422\) 0 0
\(423\) −7.81586 −0.380020
\(424\) 0 0
\(425\) −10.3519 −0.502139
\(426\) 0 0
\(427\) −1.37979 −0.0667728
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −29.8949 −1.43998 −0.719992 0.693982i \(-0.755855\pi\)
−0.719992 + 0.693982i \(0.755855\pi\)
\(432\) 0 0
\(433\) −11.0433 −0.530708 −0.265354 0.964151i \(-0.585489\pi\)
−0.265354 + 0.964151i \(0.585489\pi\)
\(434\) 0 0
\(435\) 9.16344 0.439354
\(436\) 0 0
\(437\) 3.26301 0.156091
\(438\) 0 0
\(439\) −13.7529 −0.656389 −0.328195 0.944610i \(-0.606440\pi\)
−0.328195 + 0.944610i \(0.606440\pi\)
\(440\) 0 0
\(441\) 15.4320 0.734856
\(442\) 0 0
\(443\) 40.2861 1.91405 0.957026 0.290001i \(-0.0936557\pi\)
0.957026 + 0.290001i \(0.0936557\pi\)
\(444\) 0 0
\(445\) −16.0861 −0.762554
\(446\) 0 0
\(447\) 10.4221 0.492949
\(448\) 0 0
\(449\) 0.932979 0.0440300 0.0220150 0.999758i \(-0.492992\pi\)
0.0220150 + 0.999758i \(0.492992\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −7.26322 −0.341256
\(454\) 0 0
\(455\) 10.2603 0.481009
\(456\) 0 0
\(457\) 24.6463 1.15290 0.576452 0.817131i \(-0.304437\pi\)
0.576452 + 0.817131i \(0.304437\pi\)
\(458\) 0 0
\(459\) 6.65492 0.310625
\(460\) 0 0
\(461\) −31.5768 −1.47068 −0.735339 0.677700i \(-0.762977\pi\)
−0.735339 + 0.677700i \(0.762977\pi\)
\(462\) 0 0
\(463\) 35.4243 1.64631 0.823154 0.567818i \(-0.192212\pi\)
0.823154 + 0.567818i \(0.192212\pi\)
\(464\) 0 0
\(465\) −2.56683 −0.119034
\(466\) 0 0
\(467\) −42.9301 −1.98657 −0.993285 0.115696i \(-0.963090\pi\)
−0.993285 + 0.115696i \(0.963090\pi\)
\(468\) 0 0
\(469\) 5.83477 0.269424
\(470\) 0 0
\(471\) 13.2068 0.608536
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 6.90158 0.316666
\(476\) 0 0
\(477\) −16.6099 −0.760516
\(478\) 0 0
\(479\) −26.4557 −1.20879 −0.604397 0.796683i \(-0.706586\pi\)
−0.604397 + 0.796683i \(0.706586\pi\)
\(480\) 0 0
\(481\) −61.3714 −2.79830
\(482\) 0 0
\(483\) −1.46437 −0.0666310
\(484\) 0 0
\(485\) 23.9254 1.08639
\(486\) 0 0
\(487\) −2.95751 −0.134017 −0.0670087 0.997752i \(-0.521346\pi\)
−0.0670087 + 0.997752i \(0.521346\pi\)
\(488\) 0 0
\(489\) −9.73353 −0.440165
\(490\) 0 0
\(491\) 9.73732 0.439439 0.219720 0.975563i \(-0.429486\pi\)
0.219720 + 0.975563i \(0.429486\pi\)
\(492\) 0 0
\(493\) −4.75817 −0.214297
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.42842 −0.0640736
\(498\) 0 0
\(499\) 38.3394 1.71631 0.858154 0.513393i \(-0.171612\pi\)
0.858154 + 0.513393i \(0.171612\pi\)
\(500\) 0 0
\(501\) −7.86856 −0.351542
\(502\) 0 0
\(503\) −42.0185 −1.87351 −0.936757 0.349980i \(-0.886188\pi\)
−0.936757 + 0.349980i \(0.886188\pi\)
\(504\) 0 0
\(505\) −0.948063 −0.0421883
\(506\) 0 0
\(507\) 14.8964 0.661574
\(508\) 0 0
\(509\) −39.3516 −1.74423 −0.872115 0.489301i \(-0.837252\pi\)
−0.872115 + 0.489301i \(0.837252\pi\)
\(510\) 0 0
\(511\) 5.26486 0.232904
\(512\) 0 0
\(513\) −4.43683 −0.195891
\(514\) 0 0
\(515\) 55.4548 2.44363
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −7.53583 −0.330786
\(520\) 0 0
\(521\) −12.9100 −0.565599 −0.282800 0.959179i \(-0.591263\pi\)
−0.282800 + 0.959179i \(0.591263\pi\)
\(522\) 0 0
\(523\) −4.51924 −0.197612 −0.0988062 0.995107i \(-0.531502\pi\)
−0.0988062 + 0.995107i \(0.531502\pi\)
\(524\) 0 0
\(525\) −3.09728 −0.135176
\(526\) 0 0
\(527\) 1.33284 0.0580595
\(528\) 0 0
\(529\) −12.3528 −0.537077
\(530\) 0 0
\(531\) 3.13940 0.136238
\(532\) 0 0
\(533\) −46.8813 −2.03066
\(534\) 0 0
\(535\) 37.4964 1.62111
\(536\) 0 0
\(537\) −0.367664 −0.0158659
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 18.5678 0.798291 0.399145 0.916888i \(-0.369307\pi\)
0.399145 + 0.916888i \(0.369307\pi\)
\(542\) 0 0
\(543\) −16.0213 −0.687540
\(544\) 0 0
\(545\) 42.4151 1.81686
\(546\) 0 0
\(547\) −4.82176 −0.206164 −0.103082 0.994673i \(-0.532870\pi\)
−0.103082 + 0.994673i \(0.532870\pi\)
\(548\) 0 0
\(549\) −5.91821 −0.252583
\(550\) 0 0
\(551\) 3.17227 0.135143
\(552\) 0 0
\(553\) −1.16558 −0.0495657
\(554\) 0 0
\(555\) 31.9480 1.35612
\(556\) 0 0
\(557\) 15.4258 0.653610 0.326805 0.945092i \(-0.394028\pi\)
0.326805 + 0.945092i \(0.394028\pi\)
\(558\) 0 0
\(559\) −42.2420 −1.78665
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −29.2902 −1.23444 −0.617218 0.786792i \(-0.711740\pi\)
−0.617218 + 0.786792i \(0.711740\pi\)
\(564\) 0 0
\(565\) 26.0130 1.09438
\(566\) 0 0
\(567\) −1.70534 −0.0716174
\(568\) 0 0
\(569\) −6.50295 −0.272618 −0.136309 0.990666i \(-0.543524\pi\)
−0.136309 + 0.990666i \(0.543524\pi\)
\(570\) 0 0
\(571\) 10.8414 0.453700 0.226850 0.973930i \(-0.427157\pi\)
0.226850 + 0.973930i \(0.427157\pi\)
\(572\) 0 0
\(573\) −18.6155 −0.777672
\(574\) 0 0
\(575\) 22.5199 0.939146
\(576\) 0 0
\(577\) −12.7957 −0.532694 −0.266347 0.963877i \(-0.585817\pi\)
−0.266347 + 0.963877i \(0.585817\pi\)
\(578\) 0 0
\(579\) 17.2833 0.718271
\(580\) 0 0
\(581\) 2.52599 0.104796
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 44.0084 1.81952
\(586\) 0 0
\(587\) 34.9956 1.44442 0.722212 0.691671i \(-0.243125\pi\)
0.722212 + 0.691671i \(0.243125\pi\)
\(588\) 0 0
\(589\) −0.888605 −0.0366143
\(590\) 0 0
\(591\) 1.88669 0.0776082
\(592\) 0 0
\(593\) 11.8232 0.485522 0.242761 0.970086i \(-0.421947\pi\)
0.242761 + 0.970086i \(0.421947\pi\)
\(594\) 0 0
\(595\) 2.77343 0.113700
\(596\) 0 0
\(597\) −2.74422 −0.112314
\(598\) 0 0
\(599\) 13.1662 0.537957 0.268978 0.963146i \(-0.413314\pi\)
0.268978 + 0.963146i \(0.413314\pi\)
\(600\) 0 0
\(601\) 4.97707 0.203019 0.101509 0.994835i \(-0.467633\pi\)
0.101509 + 0.994835i \(0.467633\pi\)
\(602\) 0 0
\(603\) 25.0265 1.01916
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −5.87279 −0.238369 −0.119185 0.992872i \(-0.538028\pi\)
−0.119185 + 0.992872i \(0.538028\pi\)
\(608\) 0 0
\(609\) −1.42365 −0.0576890
\(610\) 0 0
\(611\) −18.8654 −0.763211
\(612\) 0 0
\(613\) −35.7193 −1.44269 −0.721345 0.692576i \(-0.756476\pi\)
−0.721345 + 0.692576i \(0.756476\pi\)
\(614\) 0 0
\(615\) 24.4049 0.984101
\(616\) 0 0
\(617\) −44.6231 −1.79646 −0.898230 0.439526i \(-0.855146\pi\)
−0.898230 + 0.439526i \(0.855146\pi\)
\(618\) 0 0
\(619\) 19.9642 0.802427 0.401214 0.915985i \(-0.368589\pi\)
0.401214 + 0.915985i \(0.368589\pi\)
\(620\) 0 0
\(621\) −14.4774 −0.580959
\(622\) 0 0
\(623\) 2.49916 0.100127
\(624\) 0 0
\(625\) −11.8761 −0.475044
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −16.5892 −0.661454
\(630\) 0 0
\(631\) 26.9609 1.07330 0.536649 0.843806i \(-0.319690\pi\)
0.536649 + 0.843806i \(0.319690\pi\)
\(632\) 0 0
\(633\) −7.20309 −0.286297
\(634\) 0 0
\(635\) 47.8678 1.89958
\(636\) 0 0
\(637\) 37.2486 1.47584
\(638\) 0 0
\(639\) −6.12681 −0.242373
\(640\) 0 0
\(641\) −38.3564 −1.51499 −0.757494 0.652843i \(-0.773576\pi\)
−0.757494 + 0.652843i \(0.773576\pi\)
\(642\) 0 0
\(643\) −5.26918 −0.207796 −0.103898 0.994588i \(-0.533132\pi\)
−0.103898 + 0.994588i \(0.533132\pi\)
\(644\) 0 0
\(645\) 21.9898 0.865849
\(646\) 0 0
\(647\) 23.8457 0.937471 0.468736 0.883338i \(-0.344710\pi\)
0.468736 + 0.883338i \(0.344710\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.398786 0.0156297
\(652\) 0 0
\(653\) −10.2029 −0.399269 −0.199635 0.979870i \(-0.563975\pi\)
−0.199635 + 0.979870i \(0.563975\pi\)
\(654\) 0 0
\(655\) 78.6203 3.07195
\(656\) 0 0
\(657\) 22.5821 0.881011
\(658\) 0 0
\(659\) −19.2704 −0.750666 −0.375333 0.926890i \(-0.622472\pi\)
−0.375333 + 0.926890i \(0.622472\pi\)
\(660\) 0 0
\(661\) −49.7415 −1.93472 −0.967360 0.253408i \(-0.918449\pi\)
−0.967360 + 0.253408i \(0.918449\pi\)
\(662\) 0 0
\(663\) 6.96894 0.270651
\(664\) 0 0
\(665\) −1.84905 −0.0717030
\(666\) 0 0
\(667\) 10.3512 0.400799
\(668\) 0 0
\(669\) 14.3212 0.553688
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −20.7375 −0.799372 −0.399686 0.916652i \(-0.630881\pi\)
−0.399686 + 0.916652i \(0.630881\pi\)
\(674\) 0 0
\(675\) −30.6211 −1.17861
\(676\) 0 0
\(677\) −47.5162 −1.82620 −0.913098 0.407740i \(-0.866317\pi\)
−0.913098 + 0.407740i \(0.866317\pi\)
\(678\) 0 0
\(679\) −3.71708 −0.142648
\(680\) 0 0
\(681\) −0.0165639 −0.000634731 0
\(682\) 0 0
\(683\) 0.951416 0.0364049 0.0182025 0.999834i \(-0.494206\pi\)
0.0182025 + 0.999834i \(0.494206\pi\)
\(684\) 0 0
\(685\) −60.1096 −2.29667
\(686\) 0 0
\(687\) 19.5488 0.745832
\(688\) 0 0
\(689\) −40.0918 −1.52738
\(690\) 0 0
\(691\) 44.1537 1.67969 0.839843 0.542829i \(-0.182647\pi\)
0.839843 + 0.542829i \(0.182647\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 47.4496 1.79987
\(696\) 0 0
\(697\) −12.6724 −0.480001
\(698\) 0 0
\(699\) 8.89746 0.336533
\(700\) 0 0
\(701\) 34.9736 1.32093 0.660467 0.750855i \(-0.270358\pi\)
0.660467 + 0.750855i \(0.270358\pi\)
\(702\) 0 0
\(703\) 11.0600 0.417136
\(704\) 0 0
\(705\) 9.82070 0.369869
\(706\) 0 0
\(707\) 0.147292 0.00553950
\(708\) 0 0
\(709\) 21.9016 0.822531 0.411266 0.911516i \(-0.365087\pi\)
0.411266 + 0.911516i \(0.365087\pi\)
\(710\) 0 0
\(711\) −4.99943 −0.187493
\(712\) 0 0
\(713\) −2.89953 −0.108588
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8.44365 0.315334
\(718\) 0 0
\(719\) −21.7324 −0.810482 −0.405241 0.914210i \(-0.632812\pi\)
−0.405241 + 0.914210i \(0.632812\pi\)
\(720\) 0 0
\(721\) −8.61554 −0.320859
\(722\) 0 0
\(723\) −16.5784 −0.616559
\(724\) 0 0
\(725\) 21.8937 0.813111
\(726\) 0 0
\(727\) 0.468343 0.0173699 0.00868494 0.999962i \(-0.497235\pi\)
0.00868494 + 0.999962i \(0.497235\pi\)
\(728\) 0 0
\(729\) 3.83045 0.141868
\(730\) 0 0
\(731\) −11.4184 −0.422323
\(732\) 0 0
\(733\) 25.5434 0.943468 0.471734 0.881741i \(-0.343628\pi\)
0.471734 + 0.881741i \(0.343628\pi\)
\(734\) 0 0
\(735\) −19.3904 −0.715227
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −39.9284 −1.46879 −0.734395 0.678722i \(-0.762534\pi\)
−0.734395 + 0.678722i \(0.762534\pi\)
\(740\) 0 0
\(741\) −4.64619 −0.170682
\(742\) 0 0
\(743\) −33.2994 −1.22164 −0.610818 0.791771i \(-0.709159\pi\)
−0.610818 + 0.791771i \(0.709159\pi\)
\(744\) 0 0
\(745\) 42.9410 1.57324
\(746\) 0 0
\(747\) 10.8345 0.396413
\(748\) 0 0
\(749\) −5.82550 −0.212859
\(750\) 0 0
\(751\) 7.88424 0.287700 0.143850 0.989600i \(-0.454052\pi\)
0.143850 + 0.989600i \(0.454052\pi\)
\(752\) 0 0
\(753\) −11.3323 −0.412974
\(754\) 0 0
\(755\) −29.9258 −1.08911
\(756\) 0 0
\(757\) 46.8309 1.70210 0.851049 0.525086i \(-0.175967\pi\)
0.851049 + 0.525086i \(0.175967\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.5091 0.489704 0.244852 0.969561i \(-0.421261\pi\)
0.244852 + 0.969561i \(0.421261\pi\)
\(762\) 0 0
\(763\) −6.58967 −0.238562
\(764\) 0 0
\(765\) 11.8958 0.430095
\(766\) 0 0
\(767\) 7.57766 0.273614
\(768\) 0 0
\(769\) 45.9453 1.65683 0.828415 0.560114i \(-0.189243\pi\)
0.828415 + 0.560114i \(0.189243\pi\)
\(770\) 0 0
\(771\) 1.23219 0.0443764
\(772\) 0 0
\(773\) 14.6262 0.526070 0.263035 0.964786i \(-0.415277\pi\)
0.263035 + 0.964786i \(0.415277\pi\)
\(774\) 0 0
\(775\) −6.13278 −0.220296
\(776\) 0 0
\(777\) −4.96349 −0.178064
\(778\) 0 0
\(779\) 8.44868 0.302705
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −14.0748 −0.502993
\(784\) 0 0
\(785\) 54.4143 1.94213
\(786\) 0 0
\(787\) −20.6203 −0.735035 −0.367517 0.930017i \(-0.619792\pi\)
−0.367517 + 0.930017i \(0.619792\pi\)
\(788\) 0 0
\(789\) 25.3577 0.902757
\(790\) 0 0
\(791\) −4.04142 −0.143696
\(792\) 0 0
\(793\) −14.2849 −0.507273
\(794\) 0 0
\(795\) 20.8705 0.740201
\(796\) 0 0
\(797\) −30.5069 −1.08061 −0.540305 0.841469i \(-0.681691\pi\)
−0.540305 + 0.841469i \(0.681691\pi\)
\(798\) 0 0
\(799\) −5.09946 −0.180406
\(800\) 0 0
\(801\) 10.7194 0.378752
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −6.03346 −0.212651
\(806\) 0 0
\(807\) 5.96486 0.209973
\(808\) 0 0
\(809\) 5.15845 0.181362 0.0906808 0.995880i \(-0.471096\pi\)
0.0906808 + 0.995880i \(0.471096\pi\)
\(810\) 0 0
\(811\) 27.8881 0.979283 0.489641 0.871924i \(-0.337128\pi\)
0.489641 + 0.871924i \(0.337128\pi\)
\(812\) 0 0
\(813\) 25.0233 0.877604
\(814\) 0 0
\(815\) −40.1039 −1.40478
\(816\) 0 0
\(817\) 7.61261 0.266332
\(818\) 0 0
\(819\) −6.83721 −0.238911
\(820\) 0 0
\(821\) −28.9562 −1.01058 −0.505289 0.862950i \(-0.668614\pi\)
−0.505289 + 0.862950i \(0.668614\pi\)
\(822\) 0 0
\(823\) −12.6621 −0.441373 −0.220686 0.975345i \(-0.570830\pi\)
−0.220686 + 0.975345i \(0.570830\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 46.3476 1.61166 0.805832 0.592144i \(-0.201718\pi\)
0.805832 + 0.592144i \(0.201718\pi\)
\(828\) 0 0
\(829\) 0.681275 0.0236616 0.0118308 0.999930i \(-0.496234\pi\)
0.0118308 + 0.999930i \(0.496234\pi\)
\(830\) 0 0
\(831\) −11.3222 −0.392764
\(832\) 0 0
\(833\) 10.0686 0.348856
\(834\) 0 0
\(835\) −32.4199 −1.12194
\(836\) 0 0
\(837\) 3.94259 0.136276
\(838\) 0 0
\(839\) 7.58503 0.261864 0.130932 0.991391i \(-0.458203\pi\)
0.130932 + 0.991391i \(0.458203\pi\)
\(840\) 0 0
\(841\) −18.9367 −0.652989
\(842\) 0 0
\(843\) −3.66541 −0.126243
\(844\) 0 0
\(845\) 61.3760 2.11140
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −17.2995 −0.593717
\(850\) 0 0
\(851\) 36.0889 1.23711
\(852\) 0 0
\(853\) −21.0662 −0.721293 −0.360646 0.932703i \(-0.617444\pi\)
−0.360646 + 0.932703i \(0.617444\pi\)
\(854\) 0 0
\(855\) −7.93094 −0.271233
\(856\) 0 0
\(857\) −29.2288 −0.998438 −0.499219 0.866476i \(-0.666380\pi\)
−0.499219 + 0.866476i \(0.666380\pi\)
\(858\) 0 0
\(859\) 40.1410 1.36959 0.684797 0.728734i \(-0.259891\pi\)
0.684797 + 0.728734i \(0.259891\pi\)
\(860\) 0 0
\(861\) −3.79158 −0.129217
\(862\) 0 0
\(863\) 13.5487 0.461204 0.230602 0.973048i \(-0.425931\pi\)
0.230602 + 0.973048i \(0.425931\pi\)
\(864\) 0 0
\(865\) −31.0490 −1.05570
\(866\) 0 0
\(867\) −12.3505 −0.419445
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 60.4072 2.04682
\(872\) 0 0
\(873\) −15.9433 −0.539600
\(874\) 0 0
\(875\) −3.51611 −0.118866
\(876\) 0 0
\(877\) −31.2008 −1.05358 −0.526788 0.849997i \(-0.676604\pi\)
−0.526788 + 0.849997i \(0.676604\pi\)
\(878\) 0 0
\(879\) 8.85323 0.298612
\(880\) 0 0
\(881\) 17.5664 0.591827 0.295914 0.955215i \(-0.404376\pi\)
0.295914 + 0.955215i \(0.404376\pi\)
\(882\) 0 0
\(883\) −8.30172 −0.279375 −0.139688 0.990196i \(-0.544610\pi\)
−0.139688 + 0.990196i \(0.544610\pi\)
\(884\) 0 0
\(885\) −3.94469 −0.132599
\(886\) 0 0
\(887\) 39.8748 1.33886 0.669432 0.742873i \(-0.266538\pi\)
0.669432 + 0.742873i \(0.266538\pi\)
\(888\) 0 0
\(889\) −7.43681 −0.249423
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.39981 0.113770
\(894\) 0 0
\(895\) −1.51484 −0.0506355
\(896\) 0 0
\(897\) −15.1606 −0.506196
\(898\) 0 0
\(899\) −2.81890 −0.0940155
\(900\) 0 0
\(901\) −10.8371 −0.361037
\(902\) 0 0
\(903\) −3.41637 −0.113690
\(904\) 0 0
\(905\) −66.0107 −2.19427
\(906\) 0 0
\(907\) 30.5058 1.01293 0.506463 0.862261i \(-0.330953\pi\)
0.506463 + 0.862261i \(0.330953\pi\)
\(908\) 0 0
\(909\) 0.631768 0.0209544
\(910\) 0 0
\(911\) 42.5459 1.40961 0.704804 0.709402i \(-0.251035\pi\)
0.704804 + 0.709402i \(0.251035\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 7.43629 0.245836
\(916\) 0 0
\(917\) −12.2146 −0.403360
\(918\) 0 0
\(919\) 55.8366 1.84188 0.920939 0.389706i \(-0.127423\pi\)
0.920939 + 0.389706i \(0.127423\pi\)
\(920\) 0 0
\(921\) −3.72931 −0.122885
\(922\) 0 0
\(923\) −14.7885 −0.486768
\(924\) 0 0
\(925\) 76.3315 2.50976
\(926\) 0 0
\(927\) −36.9538 −1.21372
\(928\) 0 0
\(929\) 27.1283 0.890052 0.445026 0.895518i \(-0.353194\pi\)
0.445026 + 0.895518i \(0.353194\pi\)
\(930\) 0 0
\(931\) −6.71273 −0.220001
\(932\) 0 0
\(933\) 4.20445 0.137648
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1.34615 0.0439767 0.0219883 0.999758i \(-0.493000\pi\)
0.0219883 + 0.999758i \(0.493000\pi\)
\(938\) 0 0
\(939\) 12.6640 0.413273
\(940\) 0 0
\(941\) −32.1301 −1.04741 −0.523706 0.851899i \(-0.675451\pi\)
−0.523706 + 0.851899i \(0.675451\pi\)
\(942\) 0 0
\(943\) 27.5681 0.897742
\(944\) 0 0
\(945\) 8.20390 0.266873
\(946\) 0 0
\(947\) −47.8773 −1.55580 −0.777901 0.628387i \(-0.783716\pi\)
−0.777901 + 0.628387i \(0.783716\pi\)
\(948\) 0 0
\(949\) 54.5070 1.76937
\(950\) 0 0
\(951\) −14.9282 −0.484082
\(952\) 0 0
\(953\) 4.67682 0.151497 0.0757485 0.997127i \(-0.475865\pi\)
0.0757485 + 0.997127i \(0.475865\pi\)
\(954\) 0 0
\(955\) −76.6991 −2.48192
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 9.33872 0.301563
\(960\) 0 0
\(961\) −30.2104 −0.974528
\(962\) 0 0
\(963\) −24.9868 −0.805187
\(964\) 0 0
\(965\) 71.2105 2.29235
\(966\) 0 0
\(967\) −17.3817 −0.558957 −0.279478 0.960152i \(-0.590162\pi\)
−0.279478 + 0.960152i \(0.590162\pi\)
\(968\) 0 0
\(969\) −1.25590 −0.0403454
\(970\) 0 0
\(971\) 20.9338 0.671799 0.335899 0.941898i \(-0.390960\pi\)
0.335899 + 0.941898i \(0.390960\pi\)
\(972\) 0 0
\(973\) −7.37184 −0.236330
\(974\) 0 0
\(975\) −32.0660 −1.02693
\(976\) 0 0
\(977\) −55.7692 −1.78422 −0.892108 0.451823i \(-0.850774\pi\)
−0.892108 + 0.451823i \(0.850774\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −28.2644 −0.902414
\(982\) 0 0
\(983\) 46.8831 1.49534 0.747670 0.664070i \(-0.231172\pi\)
0.747670 + 0.664070i \(0.231172\pi\)
\(984\) 0 0
\(985\) 7.77352 0.247685
\(986\) 0 0
\(987\) −1.52576 −0.0485654
\(988\) 0 0
\(989\) 24.8400 0.789867
\(990\) 0 0
\(991\) −35.2300 −1.11912 −0.559559 0.828791i \(-0.689029\pi\)
−0.559559 + 0.828791i \(0.689029\pi\)
\(992\) 0 0
\(993\) 27.4513 0.871140
\(994\) 0 0
\(995\) −11.3067 −0.358447
\(996\) 0 0
\(997\) 28.6068 0.905986 0.452993 0.891514i \(-0.350356\pi\)
0.452993 + 0.891514i \(0.350356\pi\)
\(998\) 0 0
\(999\) −49.0713 −1.55255
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 9196.2.a.n.1.4 6
11.10 odd 2 836.2.a.e.1.4 6
33.32 even 2 7524.2.a.q.1.2 6
44.43 even 2 3344.2.a.w.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.a.e.1.4 6 11.10 odd 2
3344.2.a.w.1.3 6 44.43 even 2
7524.2.a.q.1.2 6 33.32 even 2
9196.2.a.n.1.4 6 1.1 even 1 trivial