Properties

Label 9800.2.a.dc.1.7
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9800,2,Mod(1,9800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9800.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.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: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 1960)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.92302\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.12212 q^{3} -1.74084 q^{9} +O(q^{10})\) \(q+1.12212 q^{3} -1.74084 q^{9} -4.94252 q^{11} -4.64101 q^{13} +5.72505 q^{17} -7.53763 q^{19} -6.87122 q^{23} -5.31980 q^{27} +8.11636 q^{29} +3.87614 q^{31} -5.54611 q^{33} +5.18786 q^{37} -5.20778 q^{39} +9.45170 q^{41} -0.706904 q^{43} -2.20616 q^{47} +6.42420 q^{51} -1.32166 q^{53} -8.45814 q^{57} +3.94064 q^{59} +6.07542 q^{61} -8.24674 q^{67} -7.71035 q^{69} -4.50952 q^{71} -2.93470 q^{73} -11.0249 q^{79} -0.746943 q^{81} +5.27356 q^{83} +9.10755 q^{87} +9.49970 q^{89} +4.34950 q^{93} +1.74808 q^{97} +8.60415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 14 q^{9} - 12 q^{11} + 16 q^{23} + 12 q^{29} + 36 q^{37} - 20 q^{39} + 24 q^{43} - 36 q^{51} + 8 q^{53} + 16 q^{57} + 40 q^{67} - 8 q^{71} - 4 q^{79} + 50 q^{81} + 48 q^{93} - 72 q^{99}+O(q^{100}) \) 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
\(3\) 1.12212 0.647857 0.323929 0.946081i \(-0.394996\pi\)
0.323929 + 0.946081i \(0.394996\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.74084 −0.580281
\(10\) 0 0
\(11\) −4.94252 −1.49023 −0.745113 0.666938i \(-0.767604\pi\)
−0.745113 + 0.666938i \(0.767604\pi\)
\(12\) 0 0
\(13\) −4.64101 −1.28718 −0.643592 0.765369i \(-0.722557\pi\)
−0.643592 + 0.765369i \(0.722557\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.72505 1.38853 0.694264 0.719720i \(-0.255730\pi\)
0.694264 + 0.719720i \(0.255730\pi\)
\(18\) 0 0
\(19\) −7.53763 −1.72925 −0.864625 0.502417i \(-0.832444\pi\)
−0.864625 + 0.502417i \(0.832444\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.87122 −1.43275 −0.716374 0.697716i \(-0.754200\pi\)
−0.716374 + 0.697716i \(0.754200\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.31980 −1.02380
\(28\) 0 0
\(29\) 8.11636 1.50717 0.753585 0.657350i \(-0.228323\pi\)
0.753585 + 0.657350i \(0.228323\pi\)
\(30\) 0 0
\(31\) 3.87614 0.696175 0.348087 0.937462i \(-0.386831\pi\)
0.348087 + 0.937462i \(0.386831\pi\)
\(32\) 0 0
\(33\) −5.54611 −0.965454
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.18786 0.852879 0.426439 0.904516i \(-0.359768\pi\)
0.426439 + 0.904516i \(0.359768\pi\)
\(38\) 0 0
\(39\) −5.20778 −0.833912
\(40\) 0 0
\(41\) 9.45170 1.47611 0.738054 0.674742i \(-0.235745\pi\)
0.738054 + 0.674742i \(0.235745\pi\)
\(42\) 0 0
\(43\) −0.706904 −0.107802 −0.0539009 0.998546i \(-0.517166\pi\)
−0.0539009 + 0.998546i \(0.517166\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.20616 −0.321802 −0.160901 0.986971i \(-0.551440\pi\)
−0.160901 + 0.986971i \(0.551440\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 6.42420 0.899568
\(52\) 0 0
\(53\) −1.32166 −0.181544 −0.0907721 0.995872i \(-0.528933\pi\)
−0.0907721 + 0.995872i \(0.528933\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8.45814 −1.12031
\(58\) 0 0
\(59\) 3.94064 0.513027 0.256514 0.966541i \(-0.417426\pi\)
0.256514 + 0.966541i \(0.417426\pi\)
\(60\) 0 0
\(61\) 6.07542 0.777878 0.388939 0.921264i \(-0.372842\pi\)
0.388939 + 0.921264i \(0.372842\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −8.24674 −1.00750 −0.503750 0.863850i \(-0.668047\pi\)
−0.503750 + 0.863850i \(0.668047\pi\)
\(68\) 0 0
\(69\) −7.71035 −0.928217
\(70\) 0 0
\(71\) −4.50952 −0.535182 −0.267591 0.963533i \(-0.586228\pi\)
−0.267591 + 0.963533i \(0.586228\pi\)
\(72\) 0 0
\(73\) −2.93470 −0.343481 −0.171741 0.985142i \(-0.554939\pi\)
−0.171741 + 0.985142i \(0.554939\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.0249 −1.24040 −0.620201 0.784443i \(-0.712949\pi\)
−0.620201 + 0.784443i \(0.712949\pi\)
\(80\) 0 0
\(81\) −0.746943 −0.0829937
\(82\) 0 0
\(83\) 5.27356 0.578848 0.289424 0.957201i \(-0.406536\pi\)
0.289424 + 0.957201i \(0.406536\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 9.10755 0.976432
\(88\) 0 0
\(89\) 9.49970 1.00697 0.503483 0.864005i \(-0.332052\pi\)
0.503483 + 0.864005i \(0.332052\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.34950 0.451022
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.74808 0.177491 0.0887454 0.996054i \(-0.471714\pi\)
0.0887454 + 0.996054i \(0.471714\pi\)
\(98\) 0 0
\(99\) 8.60415 0.864749
\(100\) 0 0
\(101\) −5.22585 −0.519991 −0.259996 0.965610i \(-0.583721\pi\)
−0.259996 + 0.965610i \(0.583721\pi\)
\(102\) 0 0
\(103\) 4.15144 0.409053 0.204527 0.978861i \(-0.434434\pi\)
0.204527 + 0.978861i \(0.434434\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.7234 1.61671 0.808356 0.588694i \(-0.200358\pi\)
0.808356 + 0.588694i \(0.200358\pi\)
\(108\) 0 0
\(109\) 11.3182 1.08409 0.542045 0.840349i \(-0.317650\pi\)
0.542045 + 0.840349i \(0.317650\pi\)
\(110\) 0 0
\(111\) 5.82141 0.552544
\(112\) 0 0
\(113\) −0.614757 −0.0578315 −0.0289157 0.999582i \(-0.509205\pi\)
−0.0289157 + 0.999582i \(0.509205\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 8.07926 0.746928
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 13.4285 1.22077
\(122\) 0 0
\(123\) 10.6060 0.956307
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.32166 0.472221 0.236111 0.971726i \(-0.424127\pi\)
0.236111 + 0.971726i \(0.424127\pi\)
\(128\) 0 0
\(129\) −0.793233 −0.0698402
\(130\) 0 0
\(131\) 7.30041 0.637840 0.318920 0.947782i \(-0.396680\pi\)
0.318920 + 0.947782i \(0.396680\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.9675 1.87681 0.938403 0.345542i \(-0.112305\pi\)
0.938403 + 0.345542i \(0.112305\pi\)
\(138\) 0 0
\(139\) −9.46849 −0.803107 −0.401553 0.915836i \(-0.631530\pi\)
−0.401553 + 0.915836i \(0.631530\pi\)
\(140\) 0 0
\(141\) −2.47558 −0.208482
\(142\) 0 0
\(143\) 22.9383 1.91820
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.7823 −1.29293 −0.646467 0.762942i \(-0.723754\pi\)
−0.646467 + 0.762942i \(0.723754\pi\)
\(150\) 0 0
\(151\) 11.2669 0.916884 0.458442 0.888724i \(-0.348408\pi\)
0.458442 + 0.888724i \(0.348408\pi\)
\(152\) 0 0
\(153\) −9.96640 −0.805736
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.66981 0.691926 0.345963 0.938248i \(-0.387552\pi\)
0.345963 + 0.938248i \(0.387552\pi\)
\(158\) 0 0
\(159\) −1.48307 −0.117615
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 24.1275 1.88981 0.944905 0.327344i \(-0.106154\pi\)
0.944905 + 0.327344i \(0.106154\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.9825 1.31414 0.657071 0.753829i \(-0.271795\pi\)
0.657071 + 0.753829i \(0.271795\pi\)
\(168\) 0 0
\(169\) 8.53896 0.656843
\(170\) 0 0
\(171\) 13.1218 1.00345
\(172\) 0 0
\(173\) −19.7691 −1.50302 −0.751509 0.659723i \(-0.770673\pi\)
−0.751509 + 0.659723i \(0.770673\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.42188 0.332368
\(178\) 0 0
\(179\) −2.11496 −0.158080 −0.0790398 0.996871i \(-0.525185\pi\)
−0.0790398 + 0.996871i \(0.525185\pi\)
\(180\) 0 0
\(181\) −9.23706 −0.686585 −0.343293 0.939229i \(-0.611542\pi\)
−0.343293 + 0.939229i \(0.611542\pi\)
\(182\) 0 0
\(183\) 6.81736 0.503954
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −28.2962 −2.06922
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.75734 −0.488944 −0.244472 0.969656i \(-0.578615\pi\)
−0.244472 + 0.969656i \(0.578615\pi\)
\(192\) 0 0
\(193\) 2.71570 0.195480 0.0977402 0.995212i \(-0.468839\pi\)
0.0977402 + 0.995212i \(0.468839\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2189 1.22680 0.613398 0.789774i \(-0.289802\pi\)
0.613398 + 0.789774i \(0.289802\pi\)
\(198\) 0 0
\(199\) 14.0215 0.993956 0.496978 0.867763i \(-0.334443\pi\)
0.496978 + 0.867763i \(0.334443\pi\)
\(200\) 0 0
\(201\) −9.25385 −0.652716
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 11.9617 0.831396
\(208\) 0 0
\(209\) 37.2549 2.57697
\(210\) 0 0
\(211\) −9.78518 −0.673639 −0.336820 0.941569i \(-0.609351\pi\)
−0.336820 + 0.941569i \(0.609351\pi\)
\(212\) 0 0
\(213\) −5.06023 −0.346721
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.29310 −0.222527
\(220\) 0 0
\(221\) −26.5700 −1.78729
\(222\) 0 0
\(223\) −7.13608 −0.477867 −0.238934 0.971036i \(-0.576798\pi\)
−0.238934 + 0.971036i \(0.576798\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.773180 0.0513178 0.0256589 0.999671i \(-0.491832\pi\)
0.0256589 + 0.999671i \(0.491832\pi\)
\(228\) 0 0
\(229\) −14.2336 −0.940580 −0.470290 0.882512i \(-0.655851\pi\)
−0.470290 + 0.882512i \(0.655851\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.7275 −0.768294 −0.384147 0.923272i \(-0.625504\pi\)
−0.384147 + 0.923272i \(0.625504\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −12.3713 −0.803604
\(238\) 0 0
\(239\) −14.3330 −0.927124 −0.463562 0.886065i \(-0.653429\pi\)
−0.463562 + 0.886065i \(0.653429\pi\)
\(240\) 0 0
\(241\) −2.07456 −0.133634 −0.0668171 0.997765i \(-0.521284\pi\)
−0.0668171 + 0.997765i \(0.521284\pi\)
\(242\) 0 0
\(243\) 15.1212 0.970029
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 34.9822 2.22586
\(248\) 0 0
\(249\) 5.91758 0.375011
\(250\) 0 0
\(251\) 2.81192 0.177487 0.0887435 0.996055i \(-0.471715\pi\)
0.0887435 + 0.996055i \(0.471715\pi\)
\(252\) 0 0
\(253\) 33.9611 2.13512
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −21.5852 −1.34644 −0.673222 0.739440i \(-0.735090\pi\)
−0.673222 + 0.739440i \(0.735090\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −14.1293 −0.874582
\(262\) 0 0
\(263\) 16.9163 1.04310 0.521551 0.853220i \(-0.325354\pi\)
0.521551 + 0.853220i \(0.325354\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.6598 0.652370
\(268\) 0 0
\(269\) 11.3325 0.690953 0.345477 0.938427i \(-0.387717\pi\)
0.345477 + 0.938427i \(0.387717\pi\)
\(270\) 0 0
\(271\) 3.11364 0.189140 0.0945701 0.995518i \(-0.469852\pi\)
0.0945701 + 0.995518i \(0.469852\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 26.6607 1.60189 0.800945 0.598739i \(-0.204331\pi\)
0.800945 + 0.598739i \(0.204331\pi\)
\(278\) 0 0
\(279\) −6.74774 −0.403977
\(280\) 0 0
\(281\) 28.2579 1.68572 0.842861 0.538131i \(-0.180869\pi\)
0.842861 + 0.538131i \(0.180869\pi\)
\(282\) 0 0
\(283\) −13.9531 −0.829428 −0.414714 0.909952i \(-0.636118\pi\)
−0.414714 + 0.909952i \(0.636118\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 15.7762 0.928011
\(290\) 0 0
\(291\) 1.96156 0.114989
\(292\) 0 0
\(293\) −6.50405 −0.379970 −0.189985 0.981787i \(-0.560844\pi\)
−0.189985 + 0.981787i \(0.560844\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 26.2932 1.52569
\(298\) 0 0
\(299\) 31.8894 1.84421
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −5.86404 −0.336880
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −28.4580 −1.62418 −0.812091 0.583531i \(-0.801671\pi\)
−0.812091 + 0.583531i \(0.801671\pi\)
\(308\) 0 0
\(309\) 4.65842 0.265008
\(310\) 0 0
\(311\) 6.10465 0.346163 0.173081 0.984908i \(-0.444628\pi\)
0.173081 + 0.984908i \(0.444628\pi\)
\(312\) 0 0
\(313\) −4.42029 −0.249850 −0.124925 0.992166i \(-0.539869\pi\)
−0.124925 + 0.992166i \(0.539869\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.67611 −0.318802 −0.159401 0.987214i \(-0.550956\pi\)
−0.159401 + 0.987214i \(0.550956\pi\)
\(318\) 0 0
\(319\) −40.1153 −2.24602
\(320\) 0 0
\(321\) 18.7657 1.04740
\(322\) 0 0
\(323\) −43.1533 −2.40111
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 12.7004 0.702336
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −24.4091 −1.34165 −0.670823 0.741618i \(-0.734059\pi\)
−0.670823 + 0.741618i \(0.734059\pi\)
\(332\) 0 0
\(333\) −9.03124 −0.494909
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.84018 0.154714 0.0773572 0.997003i \(-0.475352\pi\)
0.0773572 + 0.997003i \(0.475352\pi\)
\(338\) 0 0
\(339\) −0.689832 −0.0374666
\(340\) 0 0
\(341\) −19.1579 −1.03746
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.47921 0.294139 0.147070 0.989126i \(-0.453016\pi\)
0.147070 + 0.989126i \(0.453016\pi\)
\(348\) 0 0
\(349\) 11.5197 0.616637 0.308318 0.951283i \(-0.400234\pi\)
0.308318 + 0.951283i \(0.400234\pi\)
\(350\) 0 0
\(351\) 24.6893 1.31781
\(352\) 0 0
\(353\) 11.1927 0.595726 0.297863 0.954609i \(-0.403726\pi\)
0.297863 + 0.954609i \(0.403726\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 35.2726 1.86161 0.930807 0.365511i \(-0.119106\pi\)
0.930807 + 0.365511i \(0.119106\pi\)
\(360\) 0 0
\(361\) 37.8159 1.99031
\(362\) 0 0
\(363\) 15.0684 0.790887
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 31.1383 1.62541 0.812704 0.582677i \(-0.197995\pi\)
0.812704 + 0.582677i \(0.197995\pi\)
\(368\) 0 0
\(369\) −16.4539 −0.856557
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.9531 0.567131 0.283565 0.958953i \(-0.408483\pi\)
0.283565 + 0.958953i \(0.408483\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −37.6681 −1.94001
\(378\) 0 0
\(379\) 7.34338 0.377204 0.188602 0.982054i \(-0.439604\pi\)
0.188602 + 0.982054i \(0.439604\pi\)
\(380\) 0 0
\(381\) 5.97155 0.305932
\(382\) 0 0
\(383\) 3.73491 0.190845 0.0954224 0.995437i \(-0.469580\pi\)
0.0954224 + 0.995437i \(0.469580\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.23061 0.0625553
\(388\) 0 0
\(389\) 9.29745 0.471399 0.235700 0.971826i \(-0.424262\pi\)
0.235700 + 0.971826i \(0.424262\pi\)
\(390\) 0 0
\(391\) −39.3381 −1.98941
\(392\) 0 0
\(393\) 8.19195 0.413229
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −13.2764 −0.666325 −0.333163 0.942869i \(-0.608116\pi\)
−0.333163 + 0.942869i \(0.608116\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.01019 −0.200260 −0.100130 0.994974i \(-0.531926\pi\)
−0.100130 + 0.994974i \(0.531926\pi\)
\(402\) 0 0
\(403\) −17.9892 −0.896105
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −25.6411 −1.27098
\(408\) 0 0
\(409\) −29.2260 −1.44513 −0.722567 0.691301i \(-0.757038\pi\)
−0.722567 + 0.691301i \(0.757038\pi\)
\(410\) 0 0
\(411\) 24.6502 1.21590
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.6248 −0.520299
\(418\) 0 0
\(419\) −29.8552 −1.45852 −0.729260 0.684237i \(-0.760136\pi\)
−0.729260 + 0.684237i \(0.760136\pi\)
\(420\) 0 0
\(421\) −9.81281 −0.478247 −0.239124 0.970989i \(-0.576860\pi\)
−0.239124 + 0.970989i \(0.576860\pi\)
\(422\) 0 0
\(423\) 3.84058 0.186735
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 25.7395 1.24272
\(430\) 0 0
\(431\) −17.0840 −0.822908 −0.411454 0.911430i \(-0.634979\pi\)
−0.411454 + 0.911430i \(0.634979\pi\)
\(432\) 0 0
\(433\) 9.70709 0.466493 0.233246 0.972418i \(-0.425065\pi\)
0.233246 + 0.972418i \(0.425065\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 51.7927 2.47758
\(438\) 0 0
\(439\) 10.4222 0.497425 0.248713 0.968577i \(-0.419993\pi\)
0.248713 + 0.968577i \(0.419993\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 34.8412 1.65535 0.827677 0.561205i \(-0.189662\pi\)
0.827677 + 0.561205i \(0.189662\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −17.7096 −0.837637
\(448\) 0 0
\(449\) −8.64043 −0.407767 −0.203883 0.978995i \(-0.565356\pi\)
−0.203883 + 0.978995i \(0.565356\pi\)
\(450\) 0 0
\(451\) −46.7152 −2.19973
\(452\) 0 0
\(453\) 12.6428 0.594010
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.6058 1.19779 0.598893 0.800829i \(-0.295607\pi\)
0.598893 + 0.800829i \(0.295607\pi\)
\(458\) 0 0
\(459\) −30.4561 −1.42157
\(460\) 0 0
\(461\) −23.8105 −1.10896 −0.554482 0.832196i \(-0.687083\pi\)
−0.554482 + 0.832196i \(0.687083\pi\)
\(462\) 0 0
\(463\) 3.27660 0.152276 0.0761382 0.997097i \(-0.475741\pi\)
0.0761382 + 0.997097i \(0.475741\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −29.1321 −1.34807 −0.674036 0.738699i \(-0.735441\pi\)
−0.674036 + 0.738699i \(0.735441\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 9.72859 0.448270
\(472\) 0 0
\(473\) 3.49389 0.160649
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.30080 0.105347
\(478\) 0 0
\(479\) 7.58771 0.346692 0.173346 0.984861i \(-0.444542\pi\)
0.173346 + 0.984861i \(0.444542\pi\)
\(480\) 0 0
\(481\) −24.0769 −1.09781
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 4.86118 0.220281 0.110140 0.993916i \(-0.464870\pi\)
0.110140 + 0.993916i \(0.464870\pi\)
\(488\) 0 0
\(489\) 27.0740 1.22433
\(490\) 0 0
\(491\) 5.95002 0.268521 0.134260 0.990946i \(-0.457134\pi\)
0.134260 + 0.990946i \(0.457134\pi\)
\(492\) 0 0
\(493\) 46.4666 2.09275
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.08297 −0.0932467 −0.0466234 0.998913i \(-0.514846\pi\)
−0.0466234 + 0.998913i \(0.514846\pi\)
\(500\) 0 0
\(501\) 19.0564 0.851377
\(502\) 0 0
\(503\) 2.22949 0.0994081 0.0497041 0.998764i \(-0.484172\pi\)
0.0497041 + 0.998764i \(0.484172\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 9.58176 0.425541
\(508\) 0 0
\(509\) 1.75149 0.0776334 0.0388167 0.999246i \(-0.487641\pi\)
0.0388167 + 0.999246i \(0.487641\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 40.0987 1.77040
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.9040 0.479557
\(518\) 0 0
\(519\) −22.1833 −0.973741
\(520\) 0 0
\(521\) −16.7933 −0.735727 −0.367864 0.929880i \(-0.619911\pi\)
−0.367864 + 0.929880i \(0.619911\pi\)
\(522\) 0 0
\(523\) −20.3763 −0.890995 −0.445497 0.895283i \(-0.646973\pi\)
−0.445497 + 0.895283i \(0.646973\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.1911 0.966658
\(528\) 0 0
\(529\) 24.2137 1.05277
\(530\) 0 0
\(531\) −6.86002 −0.297700
\(532\) 0 0
\(533\) −43.8654 −1.90002
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.37324 −0.102413
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.4407 −0.534867 −0.267434 0.963576i \(-0.586176\pi\)
−0.267434 + 0.963576i \(0.586176\pi\)
\(542\) 0 0
\(543\) −10.3651 −0.444809
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 33.2004 1.41955 0.709773 0.704431i \(-0.248798\pi\)
0.709773 + 0.704431i \(0.248798\pi\)
\(548\) 0 0
\(549\) −10.5763 −0.451388
\(550\) 0 0
\(551\) −61.1781 −2.60628
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −26.0813 −1.10510 −0.552551 0.833479i \(-0.686345\pi\)
−0.552551 + 0.833479i \(0.686345\pi\)
\(558\) 0 0
\(559\) 3.28075 0.138761
\(560\) 0 0
\(561\) −31.7517 −1.34056
\(562\) 0 0
\(563\) 39.4346 1.66197 0.830986 0.556294i \(-0.187777\pi\)
0.830986 + 0.556294i \(0.187777\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.09101 −0.255348 −0.127674 0.991816i \(-0.540751\pi\)
−0.127674 + 0.991816i \(0.540751\pi\)
\(570\) 0 0
\(571\) −24.9957 −1.04604 −0.523019 0.852321i \(-0.675194\pi\)
−0.523019 + 0.852321i \(0.675194\pi\)
\(572\) 0 0
\(573\) −7.58256 −0.316766
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −23.4463 −0.976083 −0.488042 0.872820i \(-0.662289\pi\)
−0.488042 + 0.872820i \(0.662289\pi\)
\(578\) 0 0
\(579\) 3.04735 0.126643
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 6.53234 0.270542
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −27.6033 −1.13931 −0.569656 0.821884i \(-0.692923\pi\)
−0.569656 + 0.821884i \(0.692923\pi\)
\(588\) 0 0
\(589\) −29.2169 −1.20386
\(590\) 0 0
\(591\) 19.3217 0.794789
\(592\) 0 0
\(593\) −5.40275 −0.221864 −0.110932 0.993828i \(-0.535384\pi\)
−0.110932 + 0.993828i \(0.535384\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 15.7338 0.643942
\(598\) 0 0
\(599\) 42.1269 1.72126 0.860628 0.509234i \(-0.170071\pi\)
0.860628 + 0.509234i \(0.170071\pi\)
\(600\) 0 0
\(601\) −1.70777 −0.0696615 −0.0348307 0.999393i \(-0.511089\pi\)
−0.0348307 + 0.999393i \(0.511089\pi\)
\(602\) 0 0
\(603\) 14.3563 0.584632
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.1419 0.533412 0.266706 0.963778i \(-0.414065\pi\)
0.266706 + 0.963778i \(0.414065\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.2388 0.414218
\(612\) 0 0
\(613\) 38.3179 1.54764 0.773822 0.633403i \(-0.218342\pi\)
0.773822 + 0.633403i \(0.218342\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.55459 −0.384653 −0.192327 0.981331i \(-0.561603\pi\)
−0.192327 + 0.981331i \(0.561603\pi\)
\(618\) 0 0
\(619\) −30.6354 −1.23134 −0.615670 0.788004i \(-0.711115\pi\)
−0.615670 + 0.788004i \(0.711115\pi\)
\(620\) 0 0
\(621\) 36.5535 1.46684
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 41.8045 1.66951
\(628\) 0 0
\(629\) 29.7007 1.18425
\(630\) 0 0
\(631\) −31.4786 −1.25314 −0.626571 0.779364i \(-0.715542\pi\)
−0.626571 + 0.779364i \(0.715542\pi\)
\(632\) 0 0
\(633\) −10.9802 −0.436422
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 7.85036 0.310556
\(640\) 0 0
\(641\) 21.4201 0.846041 0.423021 0.906120i \(-0.360970\pi\)
0.423021 + 0.906120i \(0.360970\pi\)
\(642\) 0 0
\(643\) 5.83210 0.229996 0.114998 0.993366i \(-0.463314\pi\)
0.114998 + 0.993366i \(0.463314\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.1428 1.02778 0.513890 0.857856i \(-0.328204\pi\)
0.513890 + 0.857856i \(0.328204\pi\)
\(648\) 0 0
\(649\) −19.4767 −0.764526
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −37.1019 −1.45191 −0.725955 0.687742i \(-0.758602\pi\)
−0.725955 + 0.687742i \(0.758602\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.10886 0.199315
\(658\) 0 0
\(659\) −49.4758 −1.92730 −0.963652 0.267159i \(-0.913915\pi\)
−0.963652 + 0.267159i \(0.913915\pi\)
\(660\) 0 0
\(661\) 28.1885 1.09640 0.548202 0.836346i \(-0.315313\pi\)
0.548202 + 0.836346i \(0.315313\pi\)
\(662\) 0 0
\(663\) −29.8148 −1.15791
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −55.7693 −2.15940
\(668\) 0 0
\(669\) −8.00755 −0.309590
\(670\) 0 0
\(671\) −30.0279 −1.15921
\(672\) 0 0
\(673\) −14.0752 −0.542558 −0.271279 0.962501i \(-0.587447\pi\)
−0.271279 + 0.962501i \(0.587447\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −27.9999 −1.07612 −0.538062 0.842906i \(-0.680843\pi\)
−0.538062 + 0.842906i \(0.680843\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.867603 0.0332466
\(682\) 0 0
\(683\) −25.1558 −0.962562 −0.481281 0.876566i \(-0.659828\pi\)
−0.481281 + 0.876566i \(0.659828\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −15.9718 −0.609362
\(688\) 0 0
\(689\) 6.13384 0.233681
\(690\) 0 0
\(691\) 18.6990 0.711344 0.355672 0.934611i \(-0.384252\pi\)
0.355672 + 0.934611i \(0.384252\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 54.1114 2.04962
\(698\) 0 0
\(699\) −13.1597 −0.497745
\(700\) 0 0
\(701\) 25.1354 0.949351 0.474676 0.880161i \(-0.342565\pi\)
0.474676 + 0.880161i \(0.342565\pi\)
\(702\) 0 0
\(703\) −39.1042 −1.47484
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 17.6659 0.663458 0.331729 0.943375i \(-0.392368\pi\)
0.331729 + 0.943375i \(0.392368\pi\)
\(710\) 0 0
\(711\) 19.1927 0.719782
\(712\) 0 0
\(713\) −26.6338 −0.997443
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −16.0834 −0.600644
\(718\) 0 0
\(719\) 4.06812 0.151715 0.0758576 0.997119i \(-0.475831\pi\)
0.0758576 + 0.997119i \(0.475831\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −2.32791 −0.0865760
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 35.5626 1.31894 0.659471 0.751730i \(-0.270780\pi\)
0.659471 + 0.751730i \(0.270780\pi\)
\(728\) 0 0
\(729\) 19.2087 0.711434
\(730\) 0 0
\(731\) −4.04706 −0.149686
\(732\) 0 0
\(733\) 1.90581 0.0703929 0.0351964 0.999380i \(-0.488794\pi\)
0.0351964 + 0.999380i \(0.488794\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 40.7597 1.50140
\(738\) 0 0
\(739\) −5.44004 −0.200115 −0.100058 0.994982i \(-0.531903\pi\)
−0.100058 + 0.994982i \(0.531903\pi\)
\(740\) 0 0
\(741\) 39.2543 1.44204
\(742\) 0 0
\(743\) 42.7120 1.56695 0.783475 0.621423i \(-0.213445\pi\)
0.783475 + 0.621423i \(0.213445\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −9.18043 −0.335895
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −15.9029 −0.580306 −0.290153 0.956980i \(-0.593706\pi\)
−0.290153 + 0.956980i \(0.593706\pi\)
\(752\) 0 0
\(753\) 3.15532 0.114986
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.28840 0.0468277 0.0234138 0.999726i \(-0.492546\pi\)
0.0234138 + 0.999726i \(0.492546\pi\)
\(758\) 0 0
\(759\) 38.1085 1.38325
\(760\) 0 0
\(761\) 18.7660 0.680266 0.340133 0.940377i \(-0.389528\pi\)
0.340133 + 0.940377i \(0.389528\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.2885 −0.660360
\(768\) 0 0
\(769\) −39.3190 −1.41788 −0.708939 0.705269i \(-0.750826\pi\)
−0.708939 + 0.705269i \(0.750826\pi\)
\(770\) 0 0
\(771\) −24.2212 −0.872304
\(772\) 0 0
\(773\) −11.9516 −0.429868 −0.214934 0.976629i \(-0.568954\pi\)
−0.214934 + 0.976629i \(0.568954\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −71.2434 −2.55256
\(780\) 0 0
\(781\) 22.2884 0.797541
\(782\) 0 0
\(783\) −43.1774 −1.54304
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 36.6318 1.30578 0.652892 0.757451i \(-0.273555\pi\)
0.652892 + 0.757451i \(0.273555\pi\)
\(788\) 0 0
\(789\) 18.9821 0.675782
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −28.1961 −1.00127
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.35871 0.0481281 0.0240641 0.999710i \(-0.492339\pi\)
0.0240641 + 0.999710i \(0.492339\pi\)
\(798\) 0 0
\(799\) −12.6304 −0.446831
\(800\) 0 0
\(801\) −16.5375 −0.584323
\(802\) 0 0
\(803\) 14.5048 0.511864
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12.7164 0.447639
\(808\) 0 0
\(809\) 55.6391 1.95617 0.978084 0.208211i \(-0.0667642\pi\)
0.978084 + 0.208211i \(0.0667642\pi\)
\(810\) 0 0
\(811\) 54.1690 1.90213 0.951065 0.308990i \(-0.0999909\pi\)
0.951065 + 0.308990i \(0.0999909\pi\)
\(812\) 0 0
\(813\) 3.49389 0.122536
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 5.32838 0.186416
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46.2489 1.61410 0.807048 0.590486i \(-0.201064\pi\)
0.807048 + 0.590486i \(0.201064\pi\)
\(822\) 0 0
\(823\) 54.1540 1.88769 0.943845 0.330388i \(-0.107179\pi\)
0.943845 + 0.330388i \(0.107179\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10.0834 0.350632 0.175316 0.984512i \(-0.443905\pi\)
0.175316 + 0.984512i \(0.443905\pi\)
\(828\) 0 0
\(829\) −39.0572 −1.35651 −0.678256 0.734825i \(-0.737264\pi\)
−0.678256 + 0.734825i \(0.737264\pi\)
\(830\) 0 0
\(831\) 29.9166 1.03780
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −20.6203 −0.712741
\(838\) 0 0
\(839\) −44.4278 −1.53382 −0.766909 0.641756i \(-0.778206\pi\)
−0.766909 + 0.641756i \(0.778206\pi\)
\(840\) 0 0
\(841\) 36.8753 1.27156
\(842\) 0 0
\(843\) 31.7088 1.09211
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −15.6571 −0.537351
\(850\) 0 0
\(851\) −35.6469 −1.22196
\(852\) 0 0
\(853\) 49.0774 1.68038 0.840189 0.542293i \(-0.182444\pi\)
0.840189 + 0.542293i \(0.182444\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.7257 −1.15205 −0.576025 0.817432i \(-0.695397\pi\)
−0.576025 + 0.817432i \(0.695397\pi\)
\(858\) 0 0
\(859\) 27.8680 0.950843 0.475421 0.879758i \(-0.342296\pi\)
0.475421 + 0.879758i \(0.342296\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −23.3459 −0.794702 −0.397351 0.917667i \(-0.630070\pi\)
−0.397351 + 0.917667i \(0.630070\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 17.7028 0.601219
\(868\) 0 0
\(869\) 54.4910 1.84848
\(870\) 0 0
\(871\) 38.2732 1.29684
\(872\) 0 0
\(873\) −3.04313 −0.102994
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 22.4536 0.758206 0.379103 0.925355i \(-0.376233\pi\)
0.379103 + 0.925355i \(0.376233\pi\)
\(878\) 0 0
\(879\) −7.29833 −0.246167
\(880\) 0 0
\(881\) 2.44467 0.0823629 0.0411814 0.999152i \(-0.486888\pi\)
0.0411814 + 0.999152i \(0.486888\pi\)
\(882\) 0 0
\(883\) 42.2730 1.42260 0.711299 0.702889i \(-0.248107\pi\)
0.711299 + 0.702889i \(0.248107\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.29839 0.0771725 0.0385863 0.999255i \(-0.487715\pi\)
0.0385863 + 0.999255i \(0.487715\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3.69178 0.123679
\(892\) 0 0
\(893\) 16.6292 0.556476
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 35.7838 1.19479
\(898\) 0 0
\(899\) 31.4601 1.04925
\(900\) 0 0
\(901\) −7.56657 −0.252079
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 54.1626 1.79844 0.899220 0.437497i \(-0.144135\pi\)
0.899220 + 0.437497i \(0.144135\pi\)
\(908\) 0 0
\(909\) 9.09738 0.301741
\(910\) 0 0
\(911\) 7.71481 0.255603 0.127801 0.991800i \(-0.459208\pi\)
0.127801 + 0.991800i \(0.459208\pi\)
\(912\) 0 0
\(913\) −26.0647 −0.862615
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 6.86010 0.226294 0.113147 0.993578i \(-0.463907\pi\)
0.113147 + 0.993578i \(0.463907\pi\)
\(920\) 0 0
\(921\) −31.9333 −1.05224
\(922\) 0 0
\(923\) 20.9287 0.688877
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7.22700 −0.237366
\(928\) 0 0
\(929\) −19.2013 −0.629975 −0.314988 0.949096i \(-0.602000\pi\)
−0.314988 + 0.949096i \(0.602000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 6.85016 0.224264
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −20.3868 −0.666009 −0.333004 0.942925i \(-0.608062\pi\)
−0.333004 + 0.942925i \(0.608062\pi\)
\(938\) 0 0
\(939\) −4.96011 −0.161867
\(940\) 0 0
\(941\) −44.2362 −1.44206 −0.721030 0.692904i \(-0.756331\pi\)
−0.721030 + 0.692904i \(0.756331\pi\)
\(942\) 0 0
\(943\) −64.9447 −2.11489
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.4842 1.18558 0.592788 0.805359i \(-0.298027\pi\)
0.592788 + 0.805359i \(0.298027\pi\)
\(948\) 0 0
\(949\) 13.6200 0.442123
\(950\) 0 0
\(951\) −6.36929 −0.206538
\(952\) 0 0
\(953\) 2.51474 0.0814606 0.0407303 0.999170i \(-0.487032\pi\)
0.0407303 + 0.999170i \(0.487032\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −45.0142 −1.45510
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −15.9756 −0.515341
\(962\) 0 0
\(963\) −29.1128 −0.938147
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 2.49369 0.0801915 0.0400958 0.999196i \(-0.487234\pi\)
0.0400958 + 0.999196i \(0.487234\pi\)
\(968\) 0 0
\(969\) −48.4233 −1.55558
\(970\) 0 0
\(971\) −15.3021 −0.491069 −0.245534 0.969388i \(-0.578963\pi\)
−0.245534 + 0.969388i \(0.578963\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −38.5170 −1.23227 −0.616134 0.787641i \(-0.711302\pi\)
−0.616134 + 0.787641i \(0.711302\pi\)
\(978\) 0 0
\(979\) −46.9524 −1.50061
\(980\) 0 0
\(981\) −19.7033 −0.629077
\(982\) 0 0
\(983\) −19.9438 −0.636107 −0.318054 0.948073i \(-0.603029\pi\)
−0.318054 + 0.948073i \(0.603029\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.85729 0.154453
\(990\) 0 0
\(991\) −1.09531 −0.0347937 −0.0173968 0.999849i \(-0.505538\pi\)
−0.0173968 + 0.999849i \(0.505538\pi\)
\(992\) 0 0
\(993\) −27.3900 −0.869195
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 43.8274 1.38803 0.694014 0.719961i \(-0.255841\pi\)
0.694014 + 0.719961i \(0.255841\pi\)
\(998\) 0 0
\(999\) −27.5984 −0.873175
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 9800.2.a.dc.1.7 10
5.2 odd 4 1960.2.g.g.1569.7 20
5.3 odd 4 1960.2.g.g.1569.13 yes 20
5.4 even 2 9800.2.a.db.1.4 10
7.6 odd 2 inner 9800.2.a.dc.1.4 10
35.13 even 4 1960.2.g.g.1569.8 yes 20
35.27 even 4 1960.2.g.g.1569.14 yes 20
35.34 odd 2 9800.2.a.db.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1960.2.g.g.1569.7 20 5.2 odd 4
1960.2.g.g.1569.8 yes 20 35.13 even 4
1960.2.g.g.1569.13 yes 20 5.3 odd 4
1960.2.g.g.1569.14 yes 20 35.27 even 4
9800.2.a.db.1.4 10 5.4 even 2
9800.2.a.db.1.7 10 35.34 odd 2
9800.2.a.dc.1.4 10 7.6 odd 2 inner
9800.2.a.dc.1.7 10 1.1 even 1 trivial