Properties

Label 2900.2.c.f.349.6
Level $2900$
Weight $2$
Character 2900.349
Analytic conductor $23.157$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2900,2,Mod(349,2900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2900.349");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.c (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: \(23.1566165862\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5089536.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 580)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.6
Root \(1.66044 - 1.66044i\) of defining polynomial
Character \(\chi\) \(=\) 2900.349
Dual form 2900.2.c.f.349.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.32088i q^{3} -1.32088i q^{7} -8.02827 q^{9} +O(q^{10})\) \(q+3.32088i q^{3} -1.32088i q^{7} -8.02827 q^{9} +5.32088 q^{11} -5.02827i q^{13} +6.34916i q^{17} +4.34916 q^{19} +4.38650 q^{21} -1.70739i q^{23} -16.6983i q^{27} +1.00000 q^{29} +8.34916 q^{31} +17.6700i q^{33} +6.93438i q^{37} +16.6983 q^{39} -1.02827 q^{41} +10.7357i q^{43} +0.679116i q^{47} +5.25526 q^{49} -21.0848 q^{51} +2.38650i q^{53} +14.4431i q^{57} -10.4431 q^{59} -6.38650 q^{61} +10.6044i q^{63} +5.70739i q^{67} +5.67004 q^{69} -3.61350 q^{71} -6.73566i q^{73} -7.02827i q^{77} +11.3774 q^{79} +31.3684 q^{81} -3.96265i q^{83} +3.32088i q^{87} -2.58522 q^{89} -6.64177 q^{91} +27.7266i q^{93} +15.3209i q^{97} -42.7175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 22 q^{9} + 16 q^{11} - 16 q^{19} + 32 q^{21} + 6 q^{29} + 8 q^{31} + 16 q^{39} + 20 q^{41} - 6 q^{49} - 48 q^{51} - 16 q^{59} - 44 q^{61} - 24 q^{69} - 16 q^{71} + 46 q^{81} - 36 q^{89} - 8 q^{91} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).

\(n\) \(901\) \(1277\) \(1451\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 3.32088i 1.91731i 0.284565 + 0.958657i \(0.408151\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 1.32088i − 0.499247i −0.968343 0.249624i \(-0.919693\pi\)
0.968343 0.249624i \(-0.0803069\pi\)
\(8\) 0 0
\(9\) −8.02827 −2.67609
\(10\) 0 0
\(11\) 5.32088 1.60431 0.802154 0.597118i \(-0.203688\pi\)
0.802154 + 0.597118i \(0.203688\pi\)
\(12\) 0 0
\(13\) − 5.02827i − 1.39459i −0.716783 0.697296i \(-0.754386\pi\)
0.716783 0.697296i \(-0.245614\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.34916i 1.53990i 0.638106 + 0.769949i \(0.279718\pi\)
−0.638106 + 0.769949i \(0.720282\pi\)
\(18\) 0 0
\(19\) 4.34916 0.997765 0.498883 0.866670i \(-0.333744\pi\)
0.498883 + 0.866670i \(0.333744\pi\)
\(20\) 0 0
\(21\) 4.38650 0.957214
\(22\) 0 0
\(23\) − 1.70739i − 0.356015i −0.984029 0.178008i \(-0.943035\pi\)
0.984029 0.178008i \(-0.0569652\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 16.6983i − 3.21359i
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 8.34916 1.49955 0.749777 0.661691i \(-0.230161\pi\)
0.749777 + 0.661691i \(0.230161\pi\)
\(32\) 0 0
\(33\) 17.6700i 3.07596i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.93438i 1.14000i 0.821643 + 0.570002i \(0.193058\pi\)
−0.821643 + 0.570002i \(0.806942\pi\)
\(38\) 0 0
\(39\) 16.6983 2.67387
\(40\) 0 0
\(41\) −1.02827 −0.160589 −0.0802947 0.996771i \(-0.525586\pi\)
−0.0802947 + 0.996771i \(0.525586\pi\)
\(42\) 0 0
\(43\) 10.7357i 1.63717i 0.574383 + 0.818587i \(0.305242\pi\)
−0.574383 + 0.818587i \(0.694758\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.679116i 0.0990592i 0.998773 + 0.0495296i \(0.0157722\pi\)
−0.998773 + 0.0495296i \(0.984228\pi\)
\(48\) 0 0
\(49\) 5.25526 0.750752
\(50\) 0 0
\(51\) −21.0848 −2.95247
\(52\) 0 0
\(53\) 2.38650i 0.327812i 0.986476 + 0.163906i \(0.0524093\pi\)
−0.986476 + 0.163906i \(0.947591\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 14.4431i 1.91303i
\(58\) 0 0
\(59\) −10.4431 −1.35957 −0.679785 0.733412i \(-0.737927\pi\)
−0.679785 + 0.733412i \(0.737927\pi\)
\(60\) 0 0
\(61\) −6.38650 −0.817708 −0.408854 0.912600i \(-0.634072\pi\)
−0.408854 + 0.912600i \(0.634072\pi\)
\(62\) 0 0
\(63\) 10.6044i 1.33603i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.70739i 0.697269i 0.937259 + 0.348634i \(0.113354\pi\)
−0.937259 + 0.348634i \(0.886646\pi\)
\(68\) 0 0
\(69\) 5.67004 0.682593
\(70\) 0 0
\(71\) −3.61350 −0.428843 −0.214421 0.976741i \(-0.568787\pi\)
−0.214421 + 0.976741i \(0.568787\pi\)
\(72\) 0 0
\(73\) − 6.73566i − 0.788350i −0.919035 0.394175i \(-0.871030\pi\)
0.919035 0.394175i \(-0.128970\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 7.02827i − 0.800946i
\(78\) 0 0
\(79\) 11.3774 1.28006 0.640031 0.768349i \(-0.278922\pi\)
0.640031 + 0.768349i \(0.278922\pi\)
\(80\) 0 0
\(81\) 31.3684 3.48537
\(82\) 0 0
\(83\) − 3.96265i − 0.434958i −0.976065 0.217479i \(-0.930217\pi\)
0.976065 0.217479i \(-0.0697833\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.32088i 0.356036i
\(88\) 0 0
\(89\) −2.58522 −0.274033 −0.137016 0.990569i \(-0.543751\pi\)
−0.137016 + 0.990569i \(0.543751\pi\)
\(90\) 0 0
\(91\) −6.64177 −0.696247
\(92\) 0 0
\(93\) 27.7266i 2.87511i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 15.3209i 1.55560i 0.628512 + 0.777800i \(0.283664\pi\)
−0.628512 + 0.777800i \(0.716336\pi\)
\(98\) 0 0
\(99\) −42.7175 −4.29327
\(100\) 0 0
\(101\) 11.8688 1.18099 0.590493 0.807043i \(-0.298933\pi\)
0.590493 + 0.807043i \(0.298933\pi\)
\(102\) 0 0
\(103\) − 3.65084i − 0.359728i −0.983691 0.179864i \(-0.942434\pi\)
0.983691 0.179864i \(-0.0575658\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.32088i 0.514389i 0.966360 + 0.257195i \(0.0827982\pi\)
−0.966360 + 0.257195i \(0.917202\pi\)
\(108\) 0 0
\(109\) 14.3118 1.37082 0.685411 0.728156i \(-0.259622\pi\)
0.685411 + 0.728156i \(0.259622\pi\)
\(110\) 0 0
\(111\) −23.0283 −2.18575
\(112\) 0 0
\(113\) 2.03735i 0.191657i 0.995398 + 0.0958287i \(0.0305501\pi\)
−0.995398 + 0.0958287i \(0.969450\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 40.3684i 3.73206i
\(118\) 0 0
\(119\) 8.38650 0.768790
\(120\) 0 0
\(121\) 17.3118 1.57380
\(122\) 0 0
\(123\) − 3.41478i − 0.307900i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.26434i 0.112192i 0.998425 + 0.0560959i \(0.0178652\pi\)
−0.998425 + 0.0560959i \(0.982135\pi\)
\(128\) 0 0
\(129\) −35.6519 −3.13897
\(130\) 0 0
\(131\) −1.70739 −0.149175 −0.0745877 0.997214i \(-0.523764\pi\)
−0.0745877 + 0.997214i \(0.523764\pi\)
\(132\) 0 0
\(133\) − 5.74474i − 0.498132i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 21.7639i − 1.85942i −0.368294 0.929709i \(-0.620058\pi\)
0.368294 0.929709i \(-0.379942\pi\)
\(138\) 0 0
\(139\) 16.6983 1.41633 0.708166 0.706046i \(-0.249523\pi\)
0.708166 + 0.706046i \(0.249523\pi\)
\(140\) 0 0
\(141\) −2.25526 −0.189928
\(142\) 0 0
\(143\) − 26.7549i − 2.23735i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 17.4521i 1.43943i
\(148\) 0 0
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 6.44305 0.524328 0.262164 0.965023i \(-0.415564\pi\)
0.262164 + 0.965023i \(0.415564\pi\)
\(152\) 0 0
\(153\) − 50.9728i − 4.12091i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 10.7357i − 0.856799i −0.903589 0.428400i \(-0.859078\pi\)
0.903589 0.428400i \(-0.140922\pi\)
\(158\) 0 0
\(159\) −7.92531 −0.628518
\(160\) 0 0
\(161\) −2.25526 −0.177740
\(162\) 0 0
\(163\) 3.90611i 0.305950i 0.988230 + 0.152975i \(0.0488854\pi\)
−0.988230 + 0.152975i \(0.951115\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.51960i 0.427120i 0.976930 + 0.213560i \(0.0685058\pi\)
−0.976930 + 0.213560i \(0.931494\pi\)
\(168\) 0 0
\(169\) −12.2835 −0.944888
\(170\) 0 0
\(171\) −34.9162 −2.67011
\(172\) 0 0
\(173\) 5.80128i 0.441063i 0.975380 + 0.220532i \(0.0707792\pi\)
−0.975380 + 0.220532i \(0.929221\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) − 34.6802i − 2.60672i
\(178\) 0 0
\(179\) −14.0565 −1.05064 −0.525318 0.850906i \(-0.676054\pi\)
−0.525318 + 0.850906i \(0.676054\pi\)
\(180\) 0 0
\(181\) −7.08482 −0.526611 −0.263305 0.964713i \(-0.584813\pi\)
−0.263305 + 0.964713i \(0.584813\pi\)
\(182\) 0 0
\(183\) − 21.2088i − 1.56780i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 33.7831i 2.47047i
\(188\) 0 0
\(189\) −22.0565 −1.60438
\(190\) 0 0
\(191\) −0.547875 −0.0396428 −0.0198214 0.999804i \(-0.506310\pi\)
−0.0198214 + 0.999804i \(0.506310\pi\)
\(192\) 0 0
\(193\) 4.40571i 0.317130i 0.987349 + 0.158565i \(0.0506867\pi\)
−0.987349 + 0.158565i \(0.949313\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.64177i 0.330712i 0.986234 + 0.165356i \(0.0528774\pi\)
−0.986234 + 0.165356i \(0.947123\pi\)
\(198\) 0 0
\(199\) −18.4431 −1.30739 −0.653697 0.756757i \(-0.726783\pi\)
−0.653697 + 0.756757i \(0.726783\pi\)
\(200\) 0 0
\(201\) −18.9536 −1.33688
\(202\) 0 0
\(203\) − 1.32088i − 0.0927079i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 13.7074i 0.952729i
\(208\) 0 0
\(209\) 23.1414 1.60072
\(210\) 0 0
\(211\) −4.54787 −0.313089 −0.156544 0.987671i \(-0.550035\pi\)
−0.156544 + 0.987671i \(0.550035\pi\)
\(212\) 0 0
\(213\) − 12.0000i − 0.822226i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 11.0283i − 0.748648i
\(218\) 0 0
\(219\) 22.3684 1.51151
\(220\) 0 0
\(221\) 31.9253 2.14753
\(222\) 0 0
\(223\) 1.12217i 0.0751459i 0.999294 + 0.0375730i \(0.0119627\pi\)
−0.999294 + 0.0375730i \(0.988037\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 9.63270i − 0.639345i −0.947528 0.319672i \(-0.896427\pi\)
0.947528 0.319672i \(-0.103573\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 23.3401 1.53566
\(232\) 0 0
\(233\) − 8.05655i − 0.527802i −0.964550 0.263901i \(-0.914991\pi\)
0.964550 0.263901i \(-0.0850092\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 37.7831i 2.45428i
\(238\) 0 0
\(239\) −15.6135 −1.00995 −0.504977 0.863133i \(-0.668499\pi\)
−0.504977 + 0.863133i \(0.668499\pi\)
\(240\) 0 0
\(241\) 18.5105 1.19237 0.596184 0.802848i \(-0.296683\pi\)
0.596184 + 0.802848i \(0.296683\pi\)
\(242\) 0 0
\(243\) 54.0757i 3.46896i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 21.8688i − 1.39148i
\(248\) 0 0
\(249\) 13.1595 0.833950
\(250\) 0 0
\(251\) −6.67912 −0.421582 −0.210791 0.977531i \(-0.567604\pi\)
−0.210791 + 0.977531i \(0.567604\pi\)
\(252\) 0 0
\(253\) − 9.08482i − 0.571158i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 26.4249i 1.64834i 0.566342 + 0.824170i \(0.308358\pi\)
−0.566342 + 0.824170i \(0.691642\pi\)
\(258\) 0 0
\(259\) 9.15951 0.569145
\(260\) 0 0
\(261\) −8.02827 −0.496938
\(262\) 0 0
\(263\) 27.4340i 1.69165i 0.533459 + 0.845826i \(0.320892\pi\)
−0.533459 + 0.845826i \(0.679108\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 8.58522i − 0.525407i
\(268\) 0 0
\(269\) 10.9717 0.668958 0.334479 0.942403i \(-0.391440\pi\)
0.334479 + 0.942403i \(0.391440\pi\)
\(270\) 0 0
\(271\) 20.1504 1.22405 0.612026 0.790838i \(-0.290355\pi\)
0.612026 + 0.790838i \(0.290355\pi\)
\(272\) 0 0
\(273\) − 22.0565i − 1.33492i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 3.15951i − 0.189837i −0.995485 0.0949184i \(-0.969741\pi\)
0.995485 0.0949184i \(-0.0302590\pi\)
\(278\) 0 0
\(279\) −67.0293 −4.01294
\(280\) 0 0
\(281\) −10.3118 −0.615151 −0.307576 0.951524i \(-0.599518\pi\)
−0.307576 + 0.951524i \(0.599518\pi\)
\(282\) 0 0
\(283\) 0.423851i 0.0251953i 0.999921 + 0.0125977i \(0.00401007\pi\)
−0.999921 + 0.0125977i \(0.995990\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.35823i 0.0801738i
\(288\) 0 0
\(289\) −23.3118 −1.37128
\(290\) 0 0
\(291\) −50.8789 −2.98257
\(292\) 0 0
\(293\) 19.2462i 1.12437i 0.827010 + 0.562187i \(0.190040\pi\)
−0.827010 + 0.562187i \(0.809960\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) − 88.8498i − 5.15559i
\(298\) 0 0
\(299\) −8.58522 −0.496496
\(300\) 0 0
\(301\) 14.1806 0.817355
\(302\) 0 0
\(303\) 39.4148i 2.26432i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 22.7357i − 1.29759i −0.760962 0.648796i \(-0.775273\pi\)
0.760962 0.648796i \(-0.224727\pi\)
\(308\) 0 0
\(309\) 12.1240 0.689712
\(310\) 0 0
\(311\) 14.8031 0.839409 0.419704 0.907661i \(-0.362134\pi\)
0.419704 + 0.907661i \(0.362134\pi\)
\(312\) 0 0
\(313\) − 14.9717i − 0.846252i −0.906071 0.423126i \(-0.860933\pi\)
0.906071 0.423126i \(-0.139067\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 23.1222i − 1.29867i −0.760502 0.649335i \(-0.775047\pi\)
0.760502 0.649335i \(-0.224953\pi\)
\(318\) 0 0
\(319\) 5.32088 0.297912
\(320\) 0 0
\(321\) −17.6700 −0.986246
\(322\) 0 0
\(323\) 27.6135i 1.53646i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 47.5279i 2.62830i
\(328\) 0 0
\(329\) 0.897033 0.0494550
\(330\) 0 0
\(331\) −9.82048 −0.539783 −0.269891 0.962891i \(-0.586988\pi\)
−0.269891 + 0.962891i \(0.586988\pi\)
\(332\) 0 0
\(333\) − 55.6711i − 3.05076i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.09389i 0.440903i 0.975398 + 0.220451i \(0.0707530\pi\)
−0.975398 + 0.220451i \(0.929247\pi\)
\(338\) 0 0
\(339\) −6.76579 −0.367467
\(340\) 0 0
\(341\) 44.4249 2.40574
\(342\) 0 0
\(343\) − 16.1878i − 0.874058i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.37743i 0.396041i 0.980198 + 0.198021i \(0.0634513\pi\)
−0.980198 + 0.198021i \(0.936549\pi\)
\(348\) 0 0
\(349\) −8.82956 −0.472635 −0.236318 0.971676i \(-0.575941\pi\)
−0.236318 + 0.971676i \(0.575941\pi\)
\(350\) 0 0
\(351\) −83.9637 −4.48165
\(352\) 0 0
\(353\) 13.7266i 0.730593i 0.930891 + 0.365296i \(0.119032\pi\)
−0.930891 + 0.365296i \(0.880968\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 27.8506i 1.47401i
\(358\) 0 0
\(359\) 1.70739 0.0901126 0.0450563 0.998984i \(-0.485653\pi\)
0.0450563 + 0.998984i \(0.485653\pi\)
\(360\) 0 0
\(361\) −0.0848216 −0.00446429
\(362\) 0 0
\(363\) 57.4905i 3.01747i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 25.9627i 1.35524i 0.735412 + 0.677620i \(0.236988\pi\)
−0.735412 + 0.677620i \(0.763012\pi\)
\(368\) 0 0
\(369\) 8.25526 0.429752
\(370\) 0 0
\(371\) 3.15230 0.163659
\(372\) 0 0
\(373\) 9.92531i 0.513913i 0.966423 + 0.256956i \(0.0827197\pi\)
−0.966423 + 0.256956i \(0.917280\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 5.02827i − 0.258969i
\(378\) 0 0
\(379\) −34.2070 −1.75710 −0.878548 0.477655i \(-0.841487\pi\)
−0.878548 + 0.477655i \(0.841487\pi\)
\(380\) 0 0
\(381\) −4.19872 −0.215107
\(382\) 0 0
\(383\) − 21.4340i − 1.09523i −0.836732 0.547613i \(-0.815537\pi\)
0.836732 0.547613i \(-0.184463\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 86.1888i − 4.38123i
\(388\) 0 0
\(389\) 36.3684 1.84395 0.921975 0.387251i \(-0.126575\pi\)
0.921975 + 0.387251i \(0.126575\pi\)
\(390\) 0 0
\(391\) 10.8405 0.548227
\(392\) 0 0
\(393\) − 5.67004i − 0.286016i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 27.4713i 1.37875i 0.724406 + 0.689373i \(0.242114\pi\)
−0.724406 + 0.689373i \(0.757886\pi\)
\(398\) 0 0
\(399\) 19.0776 0.955075
\(400\) 0 0
\(401\) 22.3118 1.11420 0.557099 0.830446i \(-0.311914\pi\)
0.557099 + 0.830446i \(0.311914\pi\)
\(402\) 0 0
\(403\) − 41.9819i − 2.09127i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 36.8970i 1.82892i
\(408\) 0 0
\(409\) −4.95358 −0.244939 −0.122469 0.992472i \(-0.539081\pi\)
−0.122469 + 0.992472i \(0.539081\pi\)
\(410\) 0 0
\(411\) 72.2755 3.56509
\(412\) 0 0
\(413\) 13.7941i 0.678762i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 55.4532i 2.71555i
\(418\) 0 0
\(419\) 0.198716 0.00970793 0.00485397 0.999988i \(-0.498455\pi\)
0.00485397 + 0.999988i \(0.498455\pi\)
\(420\) 0 0
\(421\) 26.4996 1.29151 0.645756 0.763544i \(-0.276542\pi\)
0.645756 + 0.763544i \(0.276542\pi\)
\(422\) 0 0
\(423\) − 5.45213i − 0.265091i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.43584i 0.408239i
\(428\) 0 0
\(429\) 88.8498 4.28971
\(430\) 0 0
\(431\) −21.2835 −1.02519 −0.512596 0.858630i \(-0.671316\pi\)
−0.512596 + 0.858630i \(0.671316\pi\)
\(432\) 0 0
\(433\) − 24.8031i − 1.19196i −0.802998 0.595981i \(-0.796763\pi\)
0.802998 0.595981i \(-0.203237\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 7.42571i − 0.355220i
\(438\) 0 0
\(439\) 32.3118 1.54216 0.771079 0.636739i \(-0.219717\pi\)
0.771079 + 0.636739i \(0.219717\pi\)
\(440\) 0 0
\(441\) −42.1907 −2.00908
\(442\) 0 0
\(443\) 25.3774i 1.20572i 0.797848 + 0.602859i \(0.205972\pi\)
−0.797848 + 0.602859i \(0.794028\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 59.7759i − 2.82730i
\(448\) 0 0
\(449\) −13.7266 −0.647798 −0.323899 0.946092i \(-0.604994\pi\)
−0.323899 + 0.946092i \(0.604994\pi\)
\(450\) 0 0
\(451\) −5.47133 −0.257635
\(452\) 0 0
\(453\) 21.3966i 1.00530i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 15.0101i 0.702144i 0.936348 + 0.351072i \(0.114183\pi\)
−0.936348 + 0.351072i \(0.885817\pi\)
\(458\) 0 0
\(459\) 106.020 4.94860
\(460\) 0 0
\(461\) 32.7549 1.52555 0.762773 0.646666i \(-0.223837\pi\)
0.762773 + 0.646666i \(0.223837\pi\)
\(462\) 0 0
\(463\) − 24.5369i − 1.14033i −0.821531 0.570164i \(-0.806880\pi\)
0.821531 0.570164i \(-0.193120\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.60442i 0.398165i 0.979983 + 0.199083i \(0.0637962\pi\)
−0.979983 + 0.199083i \(0.936204\pi\)
\(468\) 0 0
\(469\) 7.53880 0.348110
\(470\) 0 0
\(471\) 35.6519 1.64275
\(472\) 0 0
\(473\) 57.1232i 2.62653i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 19.1595i − 0.877254i
\(478\) 0 0
\(479\) −3.26434 −0.149151 −0.0745757 0.997215i \(-0.523760\pi\)
−0.0745757 + 0.997215i \(0.523760\pi\)
\(480\) 0 0
\(481\) 34.8680 1.58984
\(482\) 0 0
\(483\) − 7.48947i − 0.340783i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 34.2070i − 1.55007i −0.631920 0.775033i \(-0.717733\pi\)
0.631920 0.775033i \(-0.282267\pi\)
\(488\) 0 0
\(489\) −12.9717 −0.586602
\(490\) 0 0
\(491\) −8.93438 −0.403203 −0.201601 0.979468i \(-0.564615\pi\)
−0.201601 + 0.979468i \(0.564615\pi\)
\(492\) 0 0
\(493\) 6.34916i 0.285952i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.77301i 0.214099i
\(498\) 0 0
\(499\) −28.6236 −1.28137 −0.640685 0.767804i \(-0.721349\pi\)
−0.640685 + 0.767804i \(0.721349\pi\)
\(500\) 0 0
\(501\) −18.3300 −0.818922
\(502\) 0 0
\(503\) − 0.0192012i 0 0.000856140i −1.00000 0.000428070i \(-0.999864\pi\)
1.00000 0.000428070i \(-0.000136259\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 40.7922i − 1.81165i
\(508\) 0 0
\(509\) 8.25526 0.365908 0.182954 0.983121i \(-0.441434\pi\)
0.182954 + 0.983121i \(0.441434\pi\)
\(510\) 0 0
\(511\) −8.89703 −0.393582
\(512\) 0 0
\(513\) − 72.6236i − 3.20641i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3.61350i 0.158921i
\(518\) 0 0
\(519\) −19.2654 −0.845657
\(520\) 0 0
\(521\) −20.2553 −0.887399 −0.443700 0.896176i \(-0.646334\pi\)
−0.443700 + 0.896176i \(0.646334\pi\)
\(522\) 0 0
\(523\) 1.82048i 0.0796042i 0.999208 + 0.0398021i \(0.0126728\pi\)
−0.999208 + 0.0398021i \(0.987327\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 53.0101i 2.30916i
\(528\) 0 0
\(529\) 20.0848 0.873253
\(530\) 0 0
\(531\) 83.8397 3.63833
\(532\) 0 0
\(533\) 5.17044i 0.223957i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 46.6802i − 2.01440i
\(538\) 0 0
\(539\) 27.9627 1.20444
\(540\) 0 0
\(541\) 1.03920 0.0446788 0.0223394 0.999750i \(-0.492889\pi\)
0.0223394 + 0.999750i \(0.492889\pi\)
\(542\) 0 0
\(543\) − 23.5279i − 1.00968i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 37.7567i − 1.61436i −0.590305 0.807180i \(-0.700992\pi\)
0.590305 0.807180i \(-0.299008\pi\)
\(548\) 0 0
\(549\) 51.2726 2.18826
\(550\) 0 0
\(551\) 4.34916 0.185280
\(552\) 0 0
\(553\) − 15.0283i − 0.639067i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 45.8506i − 1.94275i −0.237545 0.971376i \(-0.576343\pi\)
0.237545 0.971376i \(-0.423657\pi\)
\(558\) 0 0
\(559\) 53.9819 2.28319
\(560\) 0 0
\(561\) −112.190 −4.73666
\(562\) 0 0
\(563\) 33.3027i 1.40354i 0.712402 + 0.701772i \(0.247607\pi\)
−0.712402 + 0.701772i \(0.752393\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 41.4340i − 1.74006i
\(568\) 0 0
\(569\) 23.6700 0.992300 0.496150 0.868237i \(-0.334747\pi\)
0.496150 + 0.868237i \(0.334747\pi\)
\(570\) 0 0
\(571\) 14.5671 0.609613 0.304807 0.952414i \(-0.401408\pi\)
0.304807 + 0.952414i \(0.401408\pi\)
\(572\) 0 0
\(573\) − 1.81943i − 0.0760077i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 13.7639i 0.573000i 0.958080 + 0.286500i \(0.0924919\pi\)
−0.958080 + 0.286500i \(0.907508\pi\)
\(578\) 0 0
\(579\) −14.6308 −0.608037
\(580\) 0 0
\(581\) −5.23421 −0.217152
\(582\) 0 0
\(583\) 12.6983i 0.525911i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.04748i 0.0432339i 0.999766 + 0.0216170i \(0.00688143\pi\)
−0.999766 + 0.0216170i \(0.993119\pi\)
\(588\) 0 0
\(589\) 36.3118 1.49620
\(590\) 0 0
\(591\) −15.4148 −0.634079
\(592\) 0 0
\(593\) 14.3865i 0.590783i 0.955376 + 0.295391i \(0.0954501\pi\)
−0.955376 + 0.295391i \(0.904550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 61.2472i − 2.50668i
\(598\) 0 0
\(599\) 5.98080 0.244369 0.122184 0.992507i \(-0.461010\pi\)
0.122184 + 0.992507i \(0.461010\pi\)
\(600\) 0 0
\(601\) −7.08482 −0.288996 −0.144498 0.989505i \(-0.546157\pi\)
−0.144498 + 0.989505i \(0.546157\pi\)
\(602\) 0 0
\(603\) − 45.8205i − 1.86595i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 32.7175i − 1.32796i −0.747749 0.663982i \(-0.768865\pi\)
0.747749 0.663982i \(-0.231135\pi\)
\(608\) 0 0
\(609\) 4.38650 0.177750
\(610\) 0 0
\(611\) 3.41478 0.138147
\(612\) 0 0
\(613\) 9.22699i 0.372675i 0.982486 + 0.186337i \(0.0596617\pi\)
−0.982486 + 0.186337i \(0.940338\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 0.281683i − 0.0113401i −0.999984 0.00567006i \(-0.998195\pi\)
0.999984 0.00567006i \(-0.00180485\pi\)
\(618\) 0 0
\(619\) −21.2462 −0.853957 −0.426978 0.904262i \(-0.640422\pi\)
−0.426978 + 0.904262i \(0.640422\pi\)
\(620\) 0 0
\(621\) −28.5105 −1.14409
\(622\) 0 0
\(623\) 3.41478i 0.136810i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 76.8498i 3.06909i
\(628\) 0 0
\(629\) −44.0275 −1.75549
\(630\) 0 0
\(631\) 37.8688 1.50753 0.753766 0.657143i \(-0.228235\pi\)
0.753766 + 0.657143i \(0.228235\pi\)
\(632\) 0 0
\(633\) − 15.1030i − 0.600289i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 26.4249i − 1.04699i
\(638\) 0 0
\(639\) 29.0101 1.14762
\(640\) 0 0
\(641\) −36.7658 −1.45216 −0.726081 0.687609i \(-0.758660\pi\)
−0.726081 + 0.687609i \(0.758660\pi\)
\(642\) 0 0
\(643\) − 24.9728i − 0.984830i −0.870360 0.492415i \(-0.836114\pi\)
0.870360 0.492415i \(-0.163886\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.56522i 0.140163i 0.997541 + 0.0700816i \(0.0223260\pi\)
−0.997541 + 0.0700816i \(0.977674\pi\)
\(648\) 0 0
\(649\) −55.5663 −2.18117
\(650\) 0 0
\(651\) 36.6236 1.43539
\(652\) 0 0
\(653\) − 21.5652i − 0.843912i −0.906616 0.421956i \(-0.861344\pi\)
0.906616 0.421956i \(-0.138656\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 54.0757i 2.10970i
\(658\) 0 0
\(659\) 40.4623 1.57619 0.788093 0.615556i \(-0.211069\pi\)
0.788093 + 0.615556i \(0.211069\pi\)
\(660\) 0 0
\(661\) 26.1987 1.01901 0.509506 0.860467i \(-0.329828\pi\)
0.509506 + 0.860467i \(0.329828\pi\)
\(662\) 0 0
\(663\) 106.020i 4.11749i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 1.70739i − 0.0661104i
\(668\) 0 0
\(669\) −3.72659 −0.144078
\(670\) 0 0
\(671\) −33.9819 −1.31185
\(672\) 0 0
\(673\) 3.35823i 0.129450i 0.997903 + 0.0647251i \(0.0206171\pi\)
−0.997903 + 0.0647251i \(0.979383\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.6965i 0.603264i 0.953424 + 0.301632i \(0.0975314\pi\)
−0.953424 + 0.301632i \(0.902469\pi\)
\(678\) 0 0
\(679\) 20.2371 0.776629
\(680\) 0 0
\(681\) 31.9891 1.22582
\(682\) 0 0
\(683\) − 40.1998i − 1.53820i −0.639128 0.769101i \(-0.720704\pi\)
0.639128 0.769101i \(-0.279296\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 6.64177i − 0.253399i
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 25.7084 0.977995 0.488998 0.872285i \(-0.337363\pi\)
0.488998 + 0.872285i \(0.337363\pi\)
\(692\) 0 0
\(693\) 56.4249i 2.14340i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 6.52867i − 0.247291i
\(698\) 0 0
\(699\) 26.7549 1.01196
\(700\) 0 0
\(701\) −8.51775 −0.321711 −0.160855 0.986978i \(-0.551425\pi\)
−0.160855 + 0.986978i \(0.551425\pi\)
\(702\) 0 0
\(703\) 30.1587i 1.13746i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 15.6773i − 0.589604i
\(708\) 0 0
\(709\) −35.0848 −1.31764 −0.658819 0.752301i \(-0.728944\pi\)
−0.658819 + 0.752301i \(0.728944\pi\)
\(710\) 0 0
\(711\) −91.3411 −3.42556
\(712\) 0 0
\(713\) − 14.2553i − 0.533864i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) − 51.8506i − 1.93640i
\(718\) 0 0
\(719\) −31.3292 −1.16838 −0.584190 0.811617i \(-0.698588\pi\)
−0.584190 + 0.811617i \(0.698588\pi\)
\(720\) 0 0
\(721\) −4.82234 −0.179593
\(722\) 0 0
\(723\) 61.4713i 2.28614i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 13.9627i 0.517846i 0.965898 + 0.258923i \(0.0833676\pi\)
−0.965898 + 0.258923i \(0.916632\pi\)
\(728\) 0 0
\(729\) −85.4742 −3.16571
\(730\) 0 0
\(731\) −68.1624 −2.52108
\(732\) 0 0
\(733\) − 29.5761i − 1.09242i −0.837648 0.546210i \(-0.816070\pi\)
0.837648 0.546210i \(-0.183930\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 30.3684i 1.11863i
\(738\) 0 0
\(739\) 6.66819 0.245293 0.122647 0.992450i \(-0.460862\pi\)
0.122647 + 0.992450i \(0.460862\pi\)
\(740\) 0 0
\(741\) 72.6236 2.66790
\(742\) 0 0
\(743\) − 33.7002i − 1.23634i −0.786045 0.618170i \(-0.787874\pi\)
0.786045 0.618170i \(-0.212126\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 31.8133i 1.16399i
\(748\) 0 0
\(749\) 7.02827 0.256808
\(750\) 0 0
\(751\) −48.3129 −1.76296 −0.881481 0.472220i \(-0.843453\pi\)
−0.881481 + 0.472220i \(0.843453\pi\)
\(752\) 0 0
\(753\) − 22.1806i − 0.808305i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 42.3985i − 1.54100i −0.637440 0.770500i \(-0.720007\pi\)
0.637440 0.770500i \(-0.279993\pi\)
\(758\) 0 0
\(759\) 30.1696 1.09509
\(760\) 0 0
\(761\) −44.7933 −1.62375 −0.811877 0.583828i \(-0.801554\pi\)
−0.811877 + 0.583828i \(0.801554\pi\)
\(762\) 0 0
\(763\) − 18.9043i − 0.684380i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 52.5105i 1.89605i
\(768\) 0 0
\(769\) 52.2080 1.88267 0.941335 0.337473i \(-0.109572\pi\)
0.941335 + 0.337473i \(0.109572\pi\)
\(770\) 0 0
\(771\) −87.7541 −3.16039
\(772\) 0 0
\(773\) − 24.2179i − 0.871058i −0.900175 0.435529i \(-0.856561\pi\)
0.900175 0.435529i \(-0.143439\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 30.4177i 1.09123i
\(778\) 0 0
\(779\) −4.47213 −0.160231
\(780\) 0 0
\(781\) −19.2270 −0.687996
\(782\) 0 0
\(783\) − 16.6983i − 0.596749i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.43398i 0.0511159i 0.999673 + 0.0255579i \(0.00813623\pi\)
−0.999673 + 0.0255579i \(0.991864\pi\)
\(788\) 0 0
\(789\) −91.1051 −3.24343
\(790\) 0 0
\(791\) 2.69110 0.0956845
\(792\) 0 0
\(793\) 32.1131i 1.14037i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14.4732i 0.512666i 0.966588 + 0.256333i \(0.0825144\pi\)
−0.966588 + 0.256333i \(0.917486\pi\)
\(798\) 0 0
\(799\) −4.31181 −0.152541
\(800\) 0 0
\(801\) 20.7549 0.733337
\(802\) 0 0
\(803\) − 35.8397i − 1.26476i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 36.4358i 1.28260i
\(808\) 0 0
\(809\) −49.2654 −1.73208 −0.866039 0.499976i \(-0.833342\pi\)
−0.866039 + 0.499976i \(0.833342\pi\)
\(810\) 0 0
\(811\) −4.69832 −0.164980 −0.0824901 0.996592i \(-0.526287\pi\)
−0.0824901 + 0.996592i \(0.526287\pi\)
\(812\) 0 0
\(813\) 66.9173i 2.34689i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 46.6911i 1.63351i
\(818\) 0 0
\(819\) 53.3219 1.86322
\(820\) 0 0
\(821\) 34.7730 1.21359 0.606793 0.794860i \(-0.292456\pi\)
0.606793 + 0.794860i \(0.292456\pi\)
\(822\) 0 0
\(823\) − 44.1323i − 1.53836i −0.639035 0.769178i \(-0.720666\pi\)
0.639035 0.769178i \(-0.279334\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 22.6610i − 0.787999i −0.919111 0.394000i \(-0.871091\pi\)
0.919111 0.394000i \(-0.128909\pi\)
\(828\) 0 0
\(829\) 37.9144 1.31682 0.658410 0.752659i \(-0.271229\pi\)
0.658410 + 0.752659i \(0.271229\pi\)
\(830\) 0 0
\(831\) 10.4924 0.363977
\(832\) 0 0
\(833\) 33.3665i 1.15608i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 139.417i − 4.81895i
\(838\) 0 0
\(839\) −30.7175 −1.06049 −0.530243 0.847846i \(-0.677899\pi\)
−0.530243 + 0.847846i \(0.677899\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) − 34.2443i − 1.17944i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 22.8669i − 0.785716i
\(848\) 0 0
\(849\) −1.40756 −0.0483074
\(850\) 0 0
\(851\) 11.8397 0.405859
\(852\) 0 0
\(853\) 1.25341i 0.0429159i 0.999770 + 0.0214579i \(0.00683080\pi\)
−0.999770 + 0.0214579i \(0.993169\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7.85783i 0.268418i 0.990953 + 0.134209i \(0.0428494\pi\)
−0.990953 + 0.134209i \(0.957151\pi\)
\(858\) 0 0
\(859\) 14.4913 0.494438 0.247219 0.968960i \(-0.420483\pi\)
0.247219 + 0.968960i \(0.420483\pi\)
\(860\) 0 0
\(861\) −4.51053 −0.153718
\(862\) 0 0
\(863\) − 9.69646i − 0.330071i −0.986288 0.165036i \(-0.947226\pi\)
0.986288 0.165036i \(-0.0527739\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 77.4158i − 2.62918i
\(868\) 0 0
\(869\) 60.5380 2.05361
\(870\) 0 0
\(871\) 28.6983 0.972405
\(872\) 0 0
\(873\) − 123.000i − 4.16293i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 6.27341i − 0.211838i −0.994375 0.105919i \(-0.966222\pi\)
0.994375 0.105919i \(-0.0337784\pi\)
\(878\) 0 0
\(879\) −63.9144 −2.15578
\(880\) 0 0
\(881\) 19.5953 0.660184 0.330092 0.943949i \(-0.392920\pi\)
0.330092 + 0.943949i \(0.392920\pi\)
\(882\) 0 0
\(883\) − 5.24619i − 0.176548i −0.996096 0.0882742i \(-0.971865\pi\)
0.996096 0.0882742i \(-0.0281352\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32.6044i 1.09475i 0.836888 + 0.547375i \(0.184373\pi\)
−0.836888 + 0.547375i \(0.815627\pi\)
\(888\) 0 0
\(889\) 1.67004 0.0560114
\(890\) 0 0
\(891\) 166.907 5.59161
\(892\) 0 0
\(893\) 2.95358i 0.0988378i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 28.5105i − 0.951939i
\(898\) 0 0
\(899\) 8.34916 0.278460
\(900\) 0 0
\(901\) −15.1523 −0.504796
\(902\) 0 0
\(903\) 47.0920i 1.56712i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.96265i 0.0651688i 0.999469 + 0.0325844i \(0.0103738\pi\)
−0.999469 + 0.0325844i \(0.989626\pi\)
\(908\) 0 0
\(909\) −95.2856 −3.16043
\(910\) 0 0
\(911\) 50.7066 1.67998 0.839992 0.542599i \(-0.182560\pi\)
0.839992 + 0.542599i \(0.182560\pi\)
\(912\) 0 0
\(913\) − 21.0848i − 0.697806i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.25526i 0.0744754i
\(918\) 0 0
\(919\) −56.2371 −1.85509 −0.927546 0.373710i \(-0.878086\pi\)
−0.927546 + 0.373710i \(0.878086\pi\)
\(920\) 0 0
\(921\) 75.5025 2.48789
\(922\) 0 0
\(923\) 18.1696i 0.598061i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 29.3100i 0.962665i
\(928\) 0 0
\(929\) 5.34009 0.175203 0.0876013 0.996156i \(-0.472080\pi\)
0.0876013 + 0.996156i \(0.472080\pi\)
\(930\) 0 0
\(931\) 22.8560 0.749074
\(932\) 0 0
\(933\) 49.1595i 1.60941i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 3.01013i 0.0983366i 0.998791 + 0.0491683i \(0.0156571\pi\)
−0.998791 + 0.0491683i \(0.984343\pi\)
\(938\) 0 0
\(939\) 49.7194 1.62253
\(940\) 0 0
\(941\) −0.829557 −0.0270428 −0.0135214 0.999909i \(-0.504304\pi\)
−0.0135214 + 0.999909i \(0.504304\pi\)
\(942\) 0 0
\(943\) 1.75566i 0.0571723i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 21.3027i − 0.692246i −0.938189 0.346123i \(-0.887498\pi\)
0.938189 0.346123i \(-0.112502\pi\)
\(948\) 0 0
\(949\) −33.8688 −1.09943
\(950\) 0 0
\(951\) 76.7860 2.48996
\(952\) 0 0
\(953\) − 40.0203i − 1.29638i −0.761477 0.648192i \(-0.775526\pi\)
0.761477 0.648192i \(-0.224474\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 17.6700i 0.571191i
\(958\) 0 0
\(959\) −28.7476 −0.928310
\(960\) 0 0
\(961\) 38.7084 1.24866
\(962\) 0 0
\(963\) − 42.7175i − 1.37655i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 31.0365i 0.998068i 0.866582 + 0.499034i \(0.166312\pi\)
−0.866582 + 0.499034i \(0.833688\pi\)
\(968\) 0 0
\(969\) −91.7012 −2.94587
\(970\) 0 0
\(971\) −2.66819 −0.0856262 −0.0428131 0.999083i \(-0.513632\pi\)
−0.0428131 + 0.999083i \(0.513632\pi\)
\(972\) 0 0
\(973\) − 22.0565i − 0.707100i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 45.6519i − 1.46053i −0.683162 0.730267i \(-0.739396\pi\)
0.683162 0.730267i \(-0.260604\pi\)
\(978\) 0 0
\(979\) −13.7557 −0.439633
\(980\) 0 0
\(981\) −114.899 −3.66845
\(982\) 0 0
\(983\) − 17.4521i − 0.556636i −0.960489 0.278318i \(-0.910223\pi\)
0.960489 0.278318i \(-0.0897770\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.97894i 0.0948208i
\(988\) 0 0
\(989\) 18.3300 0.582859
\(990\) 0 0
\(991\) −4.49960 −0.142935 −0.0714673 0.997443i \(-0.522768\pi\)
−0.0714673 + 0.997443i \(0.522768\pi\)
\(992\) 0 0
\(993\) − 32.6127i − 1.03493i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 21.1896i 0.671083i 0.942025 + 0.335541i \(0.108919\pi\)
−0.942025 + 0.335541i \(0.891081\pi\)
\(998\) 0 0
\(999\) 115.792 3.66351
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 2900.2.c.f.349.6 6
5.2 odd 4 580.2.a.c.1.3 3
5.3 odd 4 2900.2.a.g.1.1 3
5.4 even 2 inner 2900.2.c.f.349.1 6
15.2 even 4 5220.2.a.x.1.3 3
20.7 even 4 2320.2.a.m.1.1 3
40.27 even 4 9280.2.a.bw.1.3 3
40.37 odd 4 9280.2.a.bk.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.2.a.c.1.3 3 5.2 odd 4
2320.2.a.m.1.1 3 20.7 even 4
2900.2.a.g.1.1 3 5.3 odd 4
2900.2.c.f.349.1 6 5.4 even 2 inner
2900.2.c.f.349.6 6 1.1 even 1 trivial
5220.2.a.x.1.3 3 15.2 even 4
9280.2.a.bk.1.1 3 40.37 odd 4
9280.2.a.bw.1.3 3 40.27 even 4