Properties

Label 2100.4.k.d.1849.1
Level $2100$
Weight $4$
Character 2100.1849
Analytic conductor $123.904$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,4,Mod(1849,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.1849");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.k (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(123.904011012\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1849.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1849
Dual form 2100.4.k.d.1849.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000i q^{3} -7.00000i q^{7} -9.00000 q^{9} -26.0000 q^{11} -39.0000i q^{13} +101.000i q^{17} +48.0000 q^{19} -21.0000 q^{21} +57.0000i q^{23} +27.0000i q^{27} +291.000 q^{29} -79.0000 q^{31} +78.0000i q^{33} -322.000i q^{37} -117.000 q^{39} +455.000 q^{41} -307.000i q^{43} -508.000i q^{47} -49.0000 q^{49} +303.000 q^{51} -31.0000i q^{53} -144.000i q^{57} -211.000 q^{59} -797.000 q^{61} +63.0000i q^{63} +924.000i q^{67} +171.000 q^{69} +212.000 q^{71} +22.0000i q^{73} +182.000i q^{77} -874.000 q^{79} +81.0000 q^{81} -587.000i q^{83} -873.000i q^{87} +266.000 q^{89} -273.000 q^{91} +237.000i q^{93} -1822.00i q^{97} +234.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 18 q^{9} - 52 q^{11} + 96 q^{19} - 42 q^{21} + 582 q^{29} - 158 q^{31} - 234 q^{39} + 910 q^{41} - 98 q^{49} + 606 q^{51} - 422 q^{59} - 1594 q^{61} + 342 q^{69} + 424 q^{71} - 1748 q^{79} + 162 q^{81}+ \cdots + 468 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) − 3.00000i − 0.577350i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 7.00000i − 0.377964i
\(8\) 0 0
\(9\) −9.00000 −0.333333
\(10\) 0 0
\(11\) −26.0000 −0.712663 −0.356332 0.934360i \(-0.615973\pi\)
−0.356332 + 0.934360i \(0.615973\pi\)
\(12\) 0 0
\(13\) − 39.0000i − 0.832050i −0.909353 0.416025i \(-0.863423\pi\)
0.909353 0.416025i \(-0.136577\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 101.000i 1.44095i 0.693482 + 0.720473i \(0.256075\pi\)
−0.693482 + 0.720473i \(0.743925\pi\)
\(18\) 0 0
\(19\) 48.0000 0.579577 0.289788 0.957091i \(-0.406415\pi\)
0.289788 + 0.957091i \(0.406415\pi\)
\(20\) 0 0
\(21\) −21.0000 −0.218218
\(22\) 0 0
\(23\) 57.0000i 0.516753i 0.966044 + 0.258377i \(0.0831875\pi\)
−0.966044 + 0.258377i \(0.916812\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000i 0.192450i
\(28\) 0 0
\(29\) 291.000 1.86336 0.931678 0.363284i \(-0.118345\pi\)
0.931678 + 0.363284i \(0.118345\pi\)
\(30\) 0 0
\(31\) −79.0000 −0.457704 −0.228852 0.973461i \(-0.573497\pi\)
−0.228852 + 0.973461i \(0.573497\pi\)
\(32\) 0 0
\(33\) 78.0000i 0.411456i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 322.000i − 1.43072i −0.698758 0.715358i \(-0.746264\pi\)
0.698758 0.715358i \(-0.253736\pi\)
\(38\) 0 0
\(39\) −117.000 −0.480384
\(40\) 0 0
\(41\) 455.000 1.73315 0.866574 0.499049i \(-0.166317\pi\)
0.866574 + 0.499049i \(0.166317\pi\)
\(42\) 0 0
\(43\) − 307.000i − 1.08877i −0.838836 0.544384i \(-0.816763\pi\)
0.838836 0.544384i \(-0.183237\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 508.000i − 1.57658i −0.615302 0.788292i \(-0.710966\pi\)
0.615302 0.788292i \(-0.289034\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 303.000 0.831931
\(52\) 0 0
\(53\) − 31.0000i − 0.0803430i −0.999193 0.0401715i \(-0.987210\pi\)
0.999193 0.0401715i \(-0.0127904\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) − 144.000i − 0.334619i
\(58\) 0 0
\(59\) −211.000 −0.465591 −0.232795 0.972526i \(-0.574787\pi\)
−0.232795 + 0.972526i \(0.574787\pi\)
\(60\) 0 0
\(61\) −797.000 −1.67288 −0.836438 0.548062i \(-0.815366\pi\)
−0.836438 + 0.548062i \(0.815366\pi\)
\(62\) 0 0
\(63\) 63.0000i 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 924.000i 1.68484i 0.538818 + 0.842422i \(0.318871\pi\)
−0.538818 + 0.842422i \(0.681129\pi\)
\(68\) 0 0
\(69\) 171.000 0.298348
\(70\) 0 0
\(71\) 212.000 0.354363 0.177181 0.984178i \(-0.443302\pi\)
0.177181 + 0.984178i \(0.443302\pi\)
\(72\) 0 0
\(73\) 22.0000i 0.0352727i 0.999844 + 0.0176363i \(0.00561411\pi\)
−0.999844 + 0.0176363i \(0.994386\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 182.000i 0.269361i
\(78\) 0 0
\(79\) −874.000 −1.24472 −0.622359 0.782732i \(-0.713825\pi\)
−0.622359 + 0.782732i \(0.713825\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) − 587.000i − 0.776285i −0.921599 0.388142i \(-0.873117\pi\)
0.921599 0.388142i \(-0.126883\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 873.000i − 1.07581i
\(88\) 0 0
\(89\) 266.000 0.316808 0.158404 0.987374i \(-0.449365\pi\)
0.158404 + 0.987374i \(0.449365\pi\)
\(90\) 0 0
\(91\) −273.000 −0.314485
\(92\) 0 0
\(93\) 237.000i 0.264255i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 1822.00i − 1.90718i −0.301114 0.953588i \(-0.597359\pi\)
0.301114 0.953588i \(-0.402641\pi\)
\(98\) 0 0
\(99\) 234.000 0.237554
\(100\) 0 0
\(101\) −1872.00 −1.84427 −0.922133 0.386872i \(-0.873556\pi\)
−0.922133 + 0.386872i \(0.873556\pi\)
\(102\) 0 0
\(103\) 1595.00i 1.52583i 0.646501 + 0.762913i \(0.276231\pi\)
−0.646501 + 0.762913i \(0.723769\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 1026.00i − 0.926983i −0.886101 0.463491i \(-0.846596\pi\)
0.886101 0.463491i \(-0.153404\pi\)
\(108\) 0 0
\(109\) 588.000 0.516699 0.258349 0.966052i \(-0.416821\pi\)
0.258349 + 0.966052i \(0.416821\pi\)
\(110\) 0 0
\(111\) −966.000 −0.826024
\(112\) 0 0
\(113\) 22.0000i 0.0183149i 0.999958 + 0.00915746i \(0.00291495\pi\)
−0.999958 + 0.00915746i \(0.997085\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 351.000i 0.277350i
\(118\) 0 0
\(119\) 707.000 0.544627
\(120\) 0 0
\(121\) −655.000 −0.492111
\(122\) 0 0
\(123\) − 1365.00i − 1.00063i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1750.00i 1.22274i 0.791347 + 0.611368i \(0.209380\pi\)
−0.791347 + 0.611368i \(0.790620\pi\)
\(128\) 0 0
\(129\) −921.000 −0.628601
\(130\) 0 0
\(131\) 1664.00 1.10980 0.554902 0.831916i \(-0.312756\pi\)
0.554902 + 0.831916i \(0.312756\pi\)
\(132\) 0 0
\(133\) − 336.000i − 0.219059i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 1080.00i − 0.673508i −0.941593 0.336754i \(-0.890671\pi\)
0.941593 0.336754i \(-0.109329\pi\)
\(138\) 0 0
\(139\) 896.000 0.546746 0.273373 0.961908i \(-0.411861\pi\)
0.273373 + 0.961908i \(0.411861\pi\)
\(140\) 0 0
\(141\) −1524.00 −0.910241
\(142\) 0 0
\(143\) 1014.00i 0.592972i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 147.000i 0.0824786i
\(148\) 0 0
\(149\) 591.000 0.324944 0.162472 0.986713i \(-0.448053\pi\)
0.162472 + 0.986713i \(0.448053\pi\)
\(150\) 0 0
\(151\) −1606.00 −0.865526 −0.432763 0.901508i \(-0.642461\pi\)
−0.432763 + 0.901508i \(0.642461\pi\)
\(152\) 0 0
\(153\) − 909.000i − 0.480316i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 3554.00i − 1.80662i −0.428983 0.903312i \(-0.641128\pi\)
0.428983 0.903312i \(-0.358872\pi\)
\(158\) 0 0
\(159\) −93.0000 −0.0463860
\(160\) 0 0
\(161\) 399.000 0.195314
\(162\) 0 0
\(163\) − 2897.00i − 1.39209i −0.717999 0.696045i \(-0.754942\pi\)
0.717999 0.696045i \(-0.245058\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 66.0000i 0.0305822i 0.999883 + 0.0152911i \(0.00486750\pi\)
−0.999883 + 0.0152911i \(0.995132\pi\)
\(168\) 0 0
\(169\) 676.000 0.307692
\(170\) 0 0
\(171\) −432.000 −0.193192
\(172\) 0 0
\(173\) 1672.00i 0.734797i 0.930064 + 0.367398i \(0.119751\pi\)
−0.930064 + 0.367398i \(0.880249\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 633.000i 0.268809i
\(178\) 0 0
\(179\) −4710.00 −1.96671 −0.983357 0.181682i \(-0.941846\pi\)
−0.983357 + 0.181682i \(0.941846\pi\)
\(180\) 0 0
\(181\) 2842.00 1.16710 0.583548 0.812079i \(-0.301664\pi\)
0.583548 + 0.812079i \(0.301664\pi\)
\(182\) 0 0
\(183\) 2391.00i 0.965835i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 2626.00i − 1.02691i
\(188\) 0 0
\(189\) 189.000 0.0727393
\(190\) 0 0
\(191\) −4197.00 −1.58997 −0.794985 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(192\) 0 0
\(193\) 2662.00i 0.992824i 0.868087 + 0.496412i \(0.165349\pi\)
−0.868087 + 0.496412i \(0.834651\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 3601.00i − 1.30234i −0.758933 0.651169i \(-0.774279\pi\)
0.758933 0.651169i \(-0.225721\pi\)
\(198\) 0 0
\(199\) 1840.00 0.655448 0.327724 0.944774i \(-0.393718\pi\)
0.327724 + 0.944774i \(0.393718\pi\)
\(200\) 0 0
\(201\) 2772.00 0.972745
\(202\) 0 0
\(203\) − 2037.00i − 0.704283i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 513.000i − 0.172251i
\(208\) 0 0
\(209\) −1248.00 −0.413043
\(210\) 0 0
\(211\) −1733.00 −0.565425 −0.282712 0.959205i \(-0.591234\pi\)
−0.282712 + 0.959205i \(0.591234\pi\)
\(212\) 0 0
\(213\) − 636.000i − 0.204592i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 553.000i 0.172996i
\(218\) 0 0
\(219\) 66.0000 0.0203647
\(220\) 0 0
\(221\) 3939.00 1.19894
\(222\) 0 0
\(223\) 4727.00i 1.41948i 0.704465 + 0.709738i \(0.251187\pi\)
−0.704465 + 0.709738i \(0.748813\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 2863.00i − 0.837110i −0.908191 0.418555i \(-0.862537\pi\)
0.908191 0.418555i \(-0.137463\pi\)
\(228\) 0 0
\(229\) −5578.00 −1.60963 −0.804814 0.593528i \(-0.797735\pi\)
−0.804814 + 0.593528i \(0.797735\pi\)
\(230\) 0 0
\(231\) 546.000 0.155516
\(232\) 0 0
\(233\) 5016.00i 1.41034i 0.709039 + 0.705170i \(0.249129\pi\)
−0.709039 + 0.705170i \(0.750871\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2622.00i 0.718638i
\(238\) 0 0
\(239\) −2992.00 −0.809776 −0.404888 0.914366i \(-0.632689\pi\)
−0.404888 + 0.914366i \(0.632689\pi\)
\(240\) 0 0
\(241\) −1574.00 −0.420706 −0.210353 0.977625i \(-0.567461\pi\)
−0.210353 + 0.977625i \(0.567461\pi\)
\(242\) 0 0
\(243\) − 243.000i − 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 1872.00i − 0.482237i
\(248\) 0 0
\(249\) −1761.00 −0.448188
\(250\) 0 0
\(251\) −5697.00 −1.43264 −0.716318 0.697774i \(-0.754174\pi\)
−0.716318 + 0.697774i \(0.754174\pi\)
\(252\) 0 0
\(253\) − 1482.00i − 0.368271i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 2599.00i − 0.630822i −0.948955 0.315411i \(-0.897858\pi\)
0.948955 0.315411i \(-0.102142\pi\)
\(258\) 0 0
\(259\) −2254.00 −0.540760
\(260\) 0 0
\(261\) −2619.00 −0.621119
\(262\) 0 0
\(263\) − 1115.00i − 0.261421i −0.991421 0.130711i \(-0.958274\pi\)
0.991421 0.130711i \(-0.0417259\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 798.000i − 0.182909i
\(268\) 0 0
\(269\) −4194.00 −0.950605 −0.475302 0.879822i \(-0.657661\pi\)
−0.475302 + 0.879822i \(0.657661\pi\)
\(270\) 0 0
\(271\) −3972.00 −0.890339 −0.445169 0.895446i \(-0.646857\pi\)
−0.445169 + 0.895446i \(0.646857\pi\)
\(272\) 0 0
\(273\) 819.000i 0.181568i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1842.00i 0.399549i 0.979842 + 0.199774i \(0.0640209\pi\)
−0.979842 + 0.199774i \(0.935979\pi\)
\(278\) 0 0
\(279\) 711.000 0.152568
\(280\) 0 0
\(281\) −2680.00 −0.568952 −0.284476 0.958683i \(-0.591820\pi\)
−0.284476 + 0.958683i \(0.591820\pi\)
\(282\) 0 0
\(283\) 2680.00i 0.562931i 0.959571 + 0.281465i \(0.0908205\pi\)
−0.959571 + 0.281465i \(0.909180\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 3185.00i − 0.655068i
\(288\) 0 0
\(289\) −5288.00 −1.07633
\(290\) 0 0
\(291\) −5466.00 −1.10111
\(292\) 0 0
\(293\) − 5656.00i − 1.12774i −0.825864 0.563869i \(-0.809312\pi\)
0.825864 0.563869i \(-0.190688\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) − 702.000i − 0.137152i
\(298\) 0 0
\(299\) 2223.00 0.429965
\(300\) 0 0
\(301\) −2149.00 −0.411516
\(302\) 0 0
\(303\) 5616.00i 1.06479i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 6998.00i − 1.30097i −0.759520 0.650484i \(-0.774566\pi\)
0.759520 0.650484i \(-0.225434\pi\)
\(308\) 0 0
\(309\) 4785.00 0.880936
\(310\) 0 0
\(311\) 5610.00 1.02287 0.511437 0.859321i \(-0.329113\pi\)
0.511437 + 0.859321i \(0.329113\pi\)
\(312\) 0 0
\(313\) 166.000i 0.0299772i 0.999888 + 0.0149886i \(0.00477120\pi\)
−0.999888 + 0.0149886i \(0.995229\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 5333.00i − 0.944893i −0.881359 0.472447i \(-0.843371\pi\)
0.881359 0.472447i \(-0.156629\pi\)
\(318\) 0 0
\(319\) −7566.00 −1.32795
\(320\) 0 0
\(321\) −3078.00 −0.535194
\(322\) 0 0
\(323\) 4848.00i 0.835139i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 1764.00i − 0.298316i
\(328\) 0 0
\(329\) −3556.00 −0.595892
\(330\) 0 0
\(331\) 6481.00 1.07622 0.538109 0.842875i \(-0.319139\pi\)
0.538109 + 0.842875i \(0.319139\pi\)
\(332\) 0 0
\(333\) 2898.00i 0.476905i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 9221.00i − 1.49050i −0.666783 0.745252i \(-0.732329\pi\)
0.666783 0.745252i \(-0.267671\pi\)
\(338\) 0 0
\(339\) 66.0000 0.0105741
\(340\) 0 0
\(341\) 2054.00 0.326189
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 1910.00i − 0.295488i −0.989026 0.147744i \(-0.952799\pi\)
0.989026 0.147744i \(-0.0472011\pi\)
\(348\) 0 0
\(349\) −3409.00 −0.522864 −0.261432 0.965222i \(-0.584195\pi\)
−0.261432 + 0.965222i \(0.584195\pi\)
\(350\) 0 0
\(351\) 1053.00 0.160128
\(352\) 0 0
\(353\) 2130.00i 0.321157i 0.987023 + 0.160579i \(0.0513360\pi\)
−0.987023 + 0.160579i \(0.948664\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 2121.00i − 0.314440i
\(358\) 0 0
\(359\) −647.000 −0.0951180 −0.0475590 0.998868i \(-0.515144\pi\)
−0.0475590 + 0.998868i \(0.515144\pi\)
\(360\) 0 0
\(361\) −4555.00 −0.664091
\(362\) 0 0
\(363\) 1965.00i 0.284121i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 11503.0i 1.63611i 0.575141 + 0.818054i \(0.304947\pi\)
−0.575141 + 0.818054i \(0.695053\pi\)
\(368\) 0 0
\(369\) −4095.00 −0.577716
\(370\) 0 0
\(371\) −217.000 −0.0303668
\(372\) 0 0
\(373\) − 3692.00i − 0.512505i −0.966610 0.256253i \(-0.917512\pi\)
0.966610 0.256253i \(-0.0824879\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 11349.0i − 1.55041i
\(378\) 0 0
\(379\) −8103.00 −1.09821 −0.549107 0.835752i \(-0.685032\pi\)
−0.549107 + 0.835752i \(0.685032\pi\)
\(380\) 0 0
\(381\) 5250.00 0.705947
\(382\) 0 0
\(383\) − 2664.00i − 0.355415i −0.984083 0.177708i \(-0.943132\pi\)
0.984083 0.177708i \(-0.0568681\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2763.00i 0.362923i
\(388\) 0 0
\(389\) 2050.00 0.267196 0.133598 0.991036i \(-0.457347\pi\)
0.133598 + 0.991036i \(0.457347\pi\)
\(390\) 0 0
\(391\) −5757.00 −0.744614
\(392\) 0 0
\(393\) − 4992.00i − 0.640746i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1213.00i 0.153347i 0.997056 + 0.0766735i \(0.0244299\pi\)
−0.997056 + 0.0766735i \(0.975570\pi\)
\(398\) 0 0
\(399\) −1008.00 −0.126474
\(400\) 0 0
\(401\) 10876.0 1.35442 0.677209 0.735791i \(-0.263189\pi\)
0.677209 + 0.735791i \(0.263189\pi\)
\(402\) 0 0
\(403\) 3081.00i 0.380833i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8372.00i 1.01962i
\(408\) 0 0
\(409\) 12534.0 1.51532 0.757661 0.652649i \(-0.226342\pi\)
0.757661 + 0.652649i \(0.226342\pi\)
\(410\) 0 0
\(411\) −3240.00 −0.388850
\(412\) 0 0
\(413\) 1477.00i 0.175977i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 2688.00i − 0.315664i
\(418\) 0 0
\(419\) −4569.00 −0.532721 −0.266361 0.963873i \(-0.585821\pi\)
−0.266361 + 0.963873i \(0.585821\pi\)
\(420\) 0 0
\(421\) −9262.00 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 4572.00i 0.525528i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5579.00i 0.632287i
\(428\) 0 0
\(429\) 3042.00 0.342352
\(430\) 0 0
\(431\) −9429.00 −1.05378 −0.526890 0.849934i \(-0.676642\pi\)
−0.526890 + 0.849934i \(0.676642\pi\)
\(432\) 0 0
\(433\) 418.000i 0.0463921i 0.999731 + 0.0231961i \(0.00738420\pi\)
−0.999731 + 0.0231961i \(0.992616\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2736.00i 0.299498i
\(438\) 0 0
\(439\) 419.000 0.0455530 0.0227765 0.999741i \(-0.492749\pi\)
0.0227765 + 0.999741i \(0.492749\pi\)
\(440\) 0 0
\(441\) 441.000 0.0476190
\(442\) 0 0
\(443\) − 9628.00i − 1.03260i −0.856409 0.516298i \(-0.827310\pi\)
0.856409 0.516298i \(-0.172690\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 1773.00i − 0.187606i
\(448\) 0 0
\(449\) −14052.0 −1.47696 −0.738480 0.674276i \(-0.764456\pi\)
−0.738480 + 0.674276i \(0.764456\pi\)
\(450\) 0 0
\(451\) −11830.0 −1.23515
\(452\) 0 0
\(453\) 4818.00i 0.499712i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 12089.0i − 1.23742i −0.785621 0.618708i \(-0.787656\pi\)
0.785621 0.618708i \(-0.212344\pi\)
\(458\) 0 0
\(459\) −2727.00 −0.277310
\(460\) 0 0
\(461\) −2744.00 −0.277225 −0.138613 0.990347i \(-0.544264\pi\)
−0.138613 + 0.990347i \(0.544264\pi\)
\(462\) 0 0
\(463\) 592.000i 0.0594224i 0.999559 + 0.0297112i \(0.00945876\pi\)
−0.999559 + 0.0297112i \(0.990541\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 3361.00i − 0.333038i −0.986038 0.166519i \(-0.946747\pi\)
0.986038 0.166519i \(-0.0532526\pi\)
\(468\) 0 0
\(469\) 6468.00 0.636811
\(470\) 0 0
\(471\) −10662.0 −1.04306
\(472\) 0 0
\(473\) 7982.00i 0.775925i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 279.000i 0.0267810i
\(478\) 0 0
\(479\) −8604.00 −0.820724 −0.410362 0.911923i \(-0.634598\pi\)
−0.410362 + 0.911923i \(0.634598\pi\)
\(480\) 0 0
\(481\) −12558.0 −1.19043
\(482\) 0 0
\(483\) − 1197.00i − 0.112765i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 9826.00i − 0.914289i −0.889393 0.457144i \(-0.848872\pi\)
0.889393 0.457144i \(-0.151128\pi\)
\(488\) 0 0
\(489\) −8691.00 −0.803723
\(490\) 0 0
\(491\) 4758.00 0.437323 0.218661 0.975801i \(-0.429831\pi\)
0.218661 + 0.975801i \(0.429831\pi\)
\(492\) 0 0
\(493\) 29391.0i 2.68500i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 1484.00i − 0.133937i
\(498\) 0 0
\(499\) 20631.0 1.85084 0.925421 0.378940i \(-0.123711\pi\)
0.925421 + 0.378940i \(0.123711\pi\)
\(500\) 0 0
\(501\) 198.000 0.0176567
\(502\) 0 0
\(503\) − 7566.00i − 0.670678i −0.942097 0.335339i \(-0.891149\pi\)
0.942097 0.335339i \(-0.108851\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 2028.00i − 0.177646i
\(508\) 0 0
\(509\) −12028.0 −1.04741 −0.523705 0.851900i \(-0.675451\pi\)
−0.523705 + 0.851900i \(0.675451\pi\)
\(510\) 0 0
\(511\) 154.000 0.0133318
\(512\) 0 0
\(513\) 1296.00i 0.111540i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 13208.0i 1.12357i
\(518\) 0 0
\(519\) 5016.00 0.424235
\(520\) 0 0
\(521\) 21317.0 1.79254 0.896271 0.443506i \(-0.146266\pi\)
0.896271 + 0.443506i \(0.146266\pi\)
\(522\) 0 0
\(523\) 15416.0i 1.28890i 0.764647 + 0.644450i \(0.222914\pi\)
−0.764647 + 0.644450i \(0.777086\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 7979.00i − 0.659527i
\(528\) 0 0
\(529\) 8918.00 0.732966
\(530\) 0 0
\(531\) 1899.00 0.155197
\(532\) 0 0
\(533\) − 17745.0i − 1.44207i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 14130.0i 1.13548i
\(538\) 0 0
\(539\) 1274.00 0.101809
\(540\) 0 0
\(541\) 17520.0 1.39232 0.696159 0.717888i \(-0.254891\pi\)
0.696159 + 0.717888i \(0.254891\pi\)
\(542\) 0 0
\(543\) − 8526.00i − 0.673823i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 17379.0i − 1.35845i −0.733930 0.679225i \(-0.762316\pi\)
0.733930 0.679225i \(-0.237684\pi\)
\(548\) 0 0
\(549\) 7173.00 0.557625
\(550\) 0 0
\(551\) 13968.0 1.07996
\(552\) 0 0
\(553\) 6118.00i 0.470459i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 15830.0i − 1.20420i −0.798421 0.602099i \(-0.794331\pi\)
0.798421 0.602099i \(-0.205669\pi\)
\(558\) 0 0
\(559\) −11973.0 −0.905910
\(560\) 0 0
\(561\) −7878.00 −0.592887
\(562\) 0 0
\(563\) − 7343.00i − 0.549681i −0.961490 0.274841i \(-0.911375\pi\)
0.961490 0.274841i \(-0.0886251\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 567.000i − 0.0419961i
\(568\) 0 0
\(569\) 10806.0 0.796153 0.398077 0.917352i \(-0.369678\pi\)
0.398077 + 0.917352i \(0.369678\pi\)
\(570\) 0 0
\(571\) −1593.00 −0.116751 −0.0583756 0.998295i \(-0.518592\pi\)
−0.0583756 + 0.998295i \(0.518592\pi\)
\(572\) 0 0
\(573\) 12591.0i 0.917970i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 9314.00i − 0.672005i −0.941861 0.336003i \(-0.890925\pi\)
0.941861 0.336003i \(-0.109075\pi\)
\(578\) 0 0
\(579\) 7986.00 0.573207
\(580\) 0 0
\(581\) −4109.00 −0.293408
\(582\) 0 0
\(583\) 806.000i 0.0572575i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3083.00i 0.216779i 0.994109 + 0.108389i \(0.0345693\pi\)
−0.994109 + 0.108389i \(0.965431\pi\)
\(588\) 0 0
\(589\) −3792.00 −0.265274
\(590\) 0 0
\(591\) −10803.0 −0.751905
\(592\) 0 0
\(593\) − 18882.0i − 1.30757i −0.756679 0.653787i \(-0.773179\pi\)
0.756679 0.653787i \(-0.226821\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 5520.00i − 0.378423i
\(598\) 0 0
\(599\) −1707.00 −0.116438 −0.0582188 0.998304i \(-0.518542\pi\)
−0.0582188 + 0.998304i \(0.518542\pi\)
\(600\) 0 0
\(601\) 1440.00 0.0977352 0.0488676 0.998805i \(-0.484439\pi\)
0.0488676 + 0.998805i \(0.484439\pi\)
\(602\) 0 0
\(603\) − 8316.00i − 0.561615i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 8284.00i 0.553933i 0.960880 + 0.276966i \(0.0893291\pi\)
−0.960880 + 0.276966i \(0.910671\pi\)
\(608\) 0 0
\(609\) −6111.00 −0.406618
\(610\) 0 0
\(611\) −19812.0 −1.31180
\(612\) 0 0
\(613\) − 24042.0i − 1.58409i −0.610463 0.792045i \(-0.709016\pi\)
0.610463 0.792045i \(-0.290984\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 862.000i − 0.0562444i −0.999604 0.0281222i \(-0.991047\pi\)
0.999604 0.0281222i \(-0.00895276\pi\)
\(618\) 0 0
\(619\) −9890.00 −0.642185 −0.321093 0.947048i \(-0.604050\pi\)
−0.321093 + 0.947048i \(0.604050\pi\)
\(620\) 0 0
\(621\) −1539.00 −0.0994492
\(622\) 0 0
\(623\) − 1862.00i − 0.119742i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3744.00i 0.238470i
\(628\) 0 0
\(629\) 32522.0 2.06159
\(630\) 0 0
\(631\) −21646.0 −1.36563 −0.682816 0.730590i \(-0.739245\pi\)
−0.682816 + 0.730590i \(0.739245\pi\)
\(632\) 0 0
\(633\) 5199.00i 0.326448i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1911.00i 0.118864i
\(638\) 0 0
\(639\) −1908.00 −0.118121
\(640\) 0 0
\(641\) 19658.0 1.21130 0.605651 0.795731i \(-0.292913\pi\)
0.605651 + 0.795731i \(0.292913\pi\)
\(642\) 0 0
\(643\) − 23818.0i − 1.46079i −0.683023 0.730397i \(-0.739335\pi\)
0.683023 0.730397i \(-0.260665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 28490.0i − 1.73116i −0.500775 0.865578i \(-0.666951\pi\)
0.500775 0.865578i \(-0.333049\pi\)
\(648\) 0 0
\(649\) 5486.00 0.331809
\(650\) 0 0
\(651\) 1659.00 0.0998792
\(652\) 0 0
\(653\) 11002.0i 0.659329i 0.944098 + 0.329664i \(0.106936\pi\)
−0.944098 + 0.329664i \(0.893064\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 198.000i − 0.0117576i
\(658\) 0 0
\(659\) −11506.0 −0.680137 −0.340068 0.940401i \(-0.610450\pi\)
−0.340068 + 0.940401i \(0.610450\pi\)
\(660\) 0 0
\(661\) 8398.00 0.494167 0.247083 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(662\) 0 0
\(663\) − 11817.0i − 0.692209i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16587.0i 0.962895i
\(668\) 0 0
\(669\) 14181.0 0.819535
\(670\) 0 0
\(671\) 20722.0 1.19220
\(672\) 0 0
\(673\) 1901.00i 0.108883i 0.998517 + 0.0544414i \(0.0173378\pi\)
−0.998517 + 0.0544414i \(0.982662\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 19896.0i − 1.12949i −0.825265 0.564745i \(-0.808974\pi\)
0.825265 0.564745i \(-0.191026\pi\)
\(678\) 0 0
\(679\) −12754.0 −0.720845
\(680\) 0 0
\(681\) −8589.00 −0.483306
\(682\) 0 0
\(683\) − 15662.0i − 0.877437i −0.898624 0.438719i \(-0.855432\pi\)
0.898624 0.438719i \(-0.144568\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 16734.0i 0.929319i
\(688\) 0 0
\(689\) −1209.00 −0.0668494
\(690\) 0 0
\(691\) 1162.00 0.0639719 0.0319859 0.999488i \(-0.489817\pi\)
0.0319859 + 0.999488i \(0.489817\pi\)
\(692\) 0 0
\(693\) − 1638.00i − 0.0897871i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 45955.0i 2.49737i
\(698\) 0 0
\(699\) 15048.0 0.814260
\(700\) 0 0
\(701\) 13501.0 0.727426 0.363713 0.931511i \(-0.381509\pi\)
0.363713 + 0.931511i \(0.381509\pi\)
\(702\) 0 0
\(703\) − 15456.0i − 0.829209i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13104.0i 0.697067i
\(708\) 0 0
\(709\) 20672.0 1.09500 0.547499 0.836806i \(-0.315580\pi\)
0.547499 + 0.836806i \(0.315580\pi\)
\(710\) 0 0
\(711\) 7866.00 0.414906
\(712\) 0 0
\(713\) − 4503.00i − 0.236520i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8976.00i 0.467524i
\(718\) 0 0
\(719\) 7098.00 0.368165 0.184083 0.982911i \(-0.441069\pi\)
0.184083 + 0.982911i \(0.441069\pi\)
\(720\) 0 0
\(721\) 11165.0 0.576708
\(722\) 0 0
\(723\) 4722.00i 0.242895i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4053.00i 0.206764i 0.994642 + 0.103382i \(0.0329664\pi\)
−0.994642 + 0.103382i \(0.967034\pi\)
\(728\) 0 0
\(729\) −729.000 −0.0370370
\(730\) 0 0
\(731\) 31007.0 1.56886
\(732\) 0 0
\(733\) 10331.0i 0.520579i 0.965531 + 0.260289i \(0.0838180\pi\)
−0.965531 + 0.260289i \(0.916182\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 24024.0i − 1.20073i
\(738\) 0 0
\(739\) 8969.00 0.446455 0.223227 0.974766i \(-0.428341\pi\)
0.223227 + 0.974766i \(0.428341\pi\)
\(740\) 0 0
\(741\) −5616.00 −0.278420
\(742\) 0 0
\(743\) − 11613.0i − 0.573405i −0.958020 0.286702i \(-0.907441\pi\)
0.958020 0.286702i \(-0.0925591\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5283.00i 0.258762i
\(748\) 0 0
\(749\) −7182.00 −0.350367
\(750\) 0 0
\(751\) −32476.0 −1.57798 −0.788992 0.614403i \(-0.789397\pi\)
−0.788992 + 0.614403i \(0.789397\pi\)
\(752\) 0 0
\(753\) 17091.0i 0.827132i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 29914.0i 1.43625i 0.695913 + 0.718126i \(0.255000\pi\)
−0.695913 + 0.718126i \(0.745000\pi\)
\(758\) 0 0
\(759\) −4446.00 −0.212621
\(760\) 0 0
\(761\) −3090.00 −0.147191 −0.0735955 0.997288i \(-0.523447\pi\)
−0.0735955 + 0.997288i \(0.523447\pi\)
\(762\) 0 0
\(763\) − 4116.00i − 0.195294i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8229.00i 0.387395i
\(768\) 0 0
\(769\) 7760.00 0.363892 0.181946 0.983309i \(-0.441760\pi\)
0.181946 + 0.983309i \(0.441760\pi\)
\(770\) 0 0
\(771\) −7797.00 −0.364205
\(772\) 0 0
\(773\) 34020.0i 1.58294i 0.611207 + 0.791471i \(0.290684\pi\)
−0.611207 + 0.791471i \(0.709316\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6762.00i 0.312208i
\(778\) 0 0
\(779\) 21840.0 1.00449
\(780\) 0 0
\(781\) −5512.00 −0.252541
\(782\) 0 0
\(783\) 7857.00i 0.358603i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 15154.0i 0.686381i 0.939266 + 0.343190i \(0.111508\pi\)
−0.939266 + 0.343190i \(0.888492\pi\)
\(788\) 0 0
\(789\) −3345.00 −0.150932
\(790\) 0 0
\(791\) 154.000 0.00692239
\(792\) 0 0
\(793\) 31083.0i 1.39192i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13386.0i 0.594927i 0.954733 + 0.297463i \(0.0961406\pi\)
−0.954733 + 0.297463i \(0.903859\pi\)
\(798\) 0 0
\(799\) 51308.0 2.27177
\(800\) 0 0
\(801\) −2394.00 −0.105603
\(802\) 0 0
\(803\) − 572.000i − 0.0251375i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12582.0i 0.548832i
\(808\) 0 0
\(809\) −36468.0 −1.58485 −0.792427 0.609967i \(-0.791183\pi\)
−0.792427 + 0.609967i \(0.791183\pi\)
\(810\) 0 0
\(811\) −38422.0 −1.66360 −0.831800 0.555076i \(-0.812689\pi\)
−0.831800 + 0.555076i \(0.812689\pi\)
\(812\) 0 0
\(813\) 11916.0i 0.514037i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 14736.0i − 0.631025i
\(818\) 0 0
\(819\) 2457.00 0.104828
\(820\) 0 0
\(821\) 19194.0 0.815926 0.407963 0.912998i \(-0.366239\pi\)
0.407963 + 0.912998i \(0.366239\pi\)
\(822\) 0 0
\(823\) − 7426.00i − 0.314525i −0.987557 0.157263i \(-0.949733\pi\)
0.987557 0.157263i \(-0.0502669\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33170.0i 1.39472i 0.716721 + 0.697360i \(0.245642\pi\)
−0.716721 + 0.697360i \(0.754358\pi\)
\(828\) 0 0
\(829\) −16397.0 −0.686962 −0.343481 0.939160i \(-0.611606\pi\)
−0.343481 + 0.939160i \(0.611606\pi\)
\(830\) 0 0
\(831\) 5526.00 0.230680
\(832\) 0 0
\(833\) − 4949.00i − 0.205850i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 2133.00i − 0.0880851i
\(838\) 0 0
\(839\) −14996.0 −0.617067 −0.308534 0.951213i \(-0.599838\pi\)
−0.308534 + 0.951213i \(0.599838\pi\)
\(840\) 0 0
\(841\) 60292.0 2.47210
\(842\) 0 0
\(843\) 8040.00i 0.328484i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 4585.00i 0.186001i
\(848\) 0 0
\(849\) 8040.00 0.325008
\(850\) 0 0
\(851\) 18354.0 0.739327
\(852\) 0 0
\(853\) − 21053.0i − 0.845066i −0.906348 0.422533i \(-0.861141\pi\)
0.906348 0.422533i \(-0.138859\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6390.00i 0.254700i 0.991858 + 0.127350i \(0.0406472\pi\)
−0.991858 + 0.127350i \(0.959353\pi\)
\(858\) 0 0
\(859\) −22176.0 −0.880833 −0.440416 0.897794i \(-0.645169\pi\)
−0.440416 + 0.897794i \(0.645169\pi\)
\(860\) 0 0
\(861\) −9555.00 −0.378204
\(862\) 0 0
\(863\) − 42472.0i − 1.67528i −0.546225 0.837638i \(-0.683936\pi\)
0.546225 0.837638i \(-0.316064\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 15864.0i 0.621418i
\(868\) 0 0
\(869\) 22724.0 0.887064
\(870\) 0 0
\(871\) 36036.0 1.40188
\(872\) 0 0
\(873\) 16398.0i 0.635725i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 3472.00i − 0.133684i −0.997764 0.0668421i \(-0.978708\pi\)
0.997764 0.0668421i \(-0.0212924\pi\)
\(878\) 0 0
\(879\) −16968.0 −0.651099
\(880\) 0 0
\(881\) 32639.0 1.24817 0.624084 0.781357i \(-0.285472\pi\)
0.624084 + 0.781357i \(0.285472\pi\)
\(882\) 0 0
\(883\) − 45513.0i − 1.73458i −0.497803 0.867290i \(-0.665860\pi\)
0.497803 0.867290i \(-0.334140\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 27626.0i 1.04576i 0.852406 + 0.522881i \(0.175143\pi\)
−0.852406 + 0.522881i \(0.824857\pi\)
\(888\) 0 0
\(889\) 12250.0 0.462151
\(890\) 0 0
\(891\) −2106.00 −0.0791848
\(892\) 0 0
\(893\) − 24384.0i − 0.913751i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 6669.00i − 0.248240i
\(898\) 0 0
\(899\) −22989.0 −0.852865
\(900\) 0 0
\(901\) 3131.00 0.115770
\(902\) 0 0
\(903\) 6447.00i 0.237589i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 11561.0i 0.423238i 0.977352 + 0.211619i \(0.0678736\pi\)
−0.977352 + 0.211619i \(0.932126\pi\)
\(908\) 0 0
\(909\) 16848.0 0.614756
\(910\) 0 0
\(911\) 25773.0 0.937319 0.468659 0.883379i \(-0.344737\pi\)
0.468659 + 0.883379i \(0.344737\pi\)
\(912\) 0 0
\(913\) 15262.0i 0.553229i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 11648.0i − 0.419467i
\(918\) 0 0
\(919\) 13240.0 0.475242 0.237621 0.971358i \(-0.423632\pi\)
0.237621 + 0.971358i \(0.423632\pi\)
\(920\) 0 0
\(921\) −20994.0 −0.751114
\(922\) 0 0
\(923\) − 8268.00i − 0.294848i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 14355.0i − 0.508608i
\(928\) 0 0
\(929\) 30653.0 1.08255 0.541277 0.840844i \(-0.317941\pi\)
0.541277 + 0.840844i \(0.317941\pi\)
\(930\) 0 0
\(931\) −2352.00 −0.0827967
\(932\) 0 0
\(933\) − 16830.0i − 0.590557i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 19030.0i − 0.663482i −0.943370 0.331741i \(-0.892364\pi\)
0.943370 0.331741i \(-0.107636\pi\)
\(938\) 0 0
\(939\) 498.000 0.0173074
\(940\) 0 0
\(941\) −5320.00 −0.184301 −0.0921504 0.995745i \(-0.529374\pi\)
−0.0921504 + 0.995745i \(0.529374\pi\)
\(942\) 0 0
\(943\) 25935.0i 0.895610i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 14524.0i − 0.498381i −0.968455 0.249190i \(-0.919836\pi\)
0.968455 0.249190i \(-0.0801645\pi\)
\(948\) 0 0
\(949\) 858.000 0.0293486
\(950\) 0 0
\(951\) −15999.0 −0.545534
\(952\) 0 0
\(953\) − 8688.00i − 0.295312i −0.989039 0.147656i \(-0.952827\pi\)
0.989039 0.147656i \(-0.0471728\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 22698.0i 0.766690i
\(958\) 0 0
\(959\) −7560.00 −0.254562
\(960\) 0 0
\(961\) −23550.0 −0.790507
\(962\) 0 0
\(963\) 9234.00i 0.308994i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 19672.0i 0.654197i 0.944990 + 0.327099i \(0.106071\pi\)
−0.944990 + 0.327099i \(0.893929\pi\)
\(968\) 0 0
\(969\) 14544.0 0.482168
\(970\) 0 0
\(971\) 45996.0 1.52017 0.760083 0.649826i \(-0.225158\pi\)
0.760083 + 0.649826i \(0.225158\pi\)
\(972\) 0 0
\(973\) − 6272.00i − 0.206651i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32454.0i 1.06274i 0.847140 + 0.531369i \(0.178322\pi\)
−0.847140 + 0.531369i \(0.821678\pi\)
\(978\) 0 0
\(979\) −6916.00 −0.225778
\(980\) 0 0
\(981\) −5292.00 −0.172233
\(982\) 0 0
\(983\) 34048.0i 1.10474i 0.833598 + 0.552372i \(0.186277\pi\)
−0.833598 + 0.552372i \(0.813723\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 10668.0i 0.344039i
\(988\) 0 0
\(989\) 17499.0 0.562625
\(990\) 0 0
\(991\) −14804.0 −0.474535 −0.237268 0.971444i \(-0.576252\pi\)
−0.237268 + 0.971444i \(0.576252\pi\)
\(992\) 0 0
\(993\) − 19443.0i − 0.621354i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 35546.0i 1.12914i 0.825385 + 0.564570i \(0.190958\pi\)
−0.825385 + 0.564570i \(0.809042\pi\)
\(998\) 0 0
\(999\) 8694.00 0.275341
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 2100.4.k.d.1849.1 2
5.2 odd 4 2100.4.a.e.1.1 1
5.3 odd 4 2100.4.a.j.1.1 yes 1
5.4 even 2 inner 2100.4.k.d.1849.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.4.a.e.1.1 1 5.2 odd 4
2100.4.a.j.1.1 yes 1 5.3 odd 4
2100.4.k.d.1849.1 2 1.1 even 1 trivial
2100.4.k.d.1849.2 2 5.4 even 2 inner