Properties

Label 2100.2.s.c.1457.9
Level $2100$
Weight $2$
Character 2100.1457
Analytic conductor $16.769$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,2,Mod(1457,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 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("2100.1457");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.s (of order \(4\), degree \(2\), 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: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1457.9
Character \(\chi\) \(=\) 2100.1457
Dual form 2100.2.s.c.1793.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0412661 + 1.73156i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +O(q^{10})\) \(q+(0.0412661 + 1.73156i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.99659 + 0.142909i) q^{9} +1.76542i q^{11} +(-0.719742 + 0.719742i) q^{13} +(1.55115 - 1.55115i) q^{17} +5.12249i q^{19} +(-1.19522 + 1.25358i) q^{21} +(1.47001 + 1.47001i) q^{23} +(-0.371114 - 5.18288i) q^{27} -7.63621 q^{29} -0.104617 q^{31} +(-3.05693 + 0.0728519i) q^{33} +(-0.0126355 - 0.0126355i) q^{37} +(-1.27598 - 1.21658i) q^{39} +9.35682i q^{41} +(-2.66423 + 2.66423i) q^{43} +(3.98447 - 3.98447i) q^{47} +1.00000i q^{49} +(2.74992 + 2.62190i) q^{51} +(-5.44907 - 5.44907i) q^{53} +(-8.86989 + 0.211385i) q^{57} -5.32780 q^{59} -4.82359 q^{61} +(-2.21996 - 2.01786i) q^{63} +(-3.01428 - 3.01428i) q^{67} +(-2.48475 + 2.60608i) q^{69} +5.20665i q^{71} +(-7.10198 + 7.10198i) q^{73} +(-1.24834 + 1.24834i) q^{77} +15.4899i q^{79} +(8.95915 - 0.856482i) q^{81} +(-3.76280 - 3.76280i) q^{83} +(-0.315116 - 13.2225i) q^{87} -2.98785 q^{89} -1.01787 q^{91} +(-0.00431713 - 0.181150i) q^{93} +(6.41605 + 6.41605i) q^{97} +(-0.252295 - 5.29024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0412661 + 1.73156i 0.0238250 + 0.999716i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) −2.99659 + 0.142909i −0.998865 + 0.0476364i
\(10\) 0 0
\(11\) 1.76542i 0.532294i 0.963933 + 0.266147i \(0.0857506\pi\)
−0.963933 + 0.266147i \(0.914249\pi\)
\(12\) 0 0
\(13\) −0.719742 + 0.719742i −0.199621 + 0.199621i −0.799837 0.600217i \(-0.795081\pi\)
0.600217 + 0.799837i \(0.295081\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.55115 1.55115i 0.376209 0.376209i −0.493523 0.869733i \(-0.664291\pi\)
0.869733 + 0.493523i \(0.164291\pi\)
\(18\) 0 0
\(19\) 5.12249i 1.17518i 0.809159 + 0.587589i \(0.199923\pi\)
−0.809159 + 0.587589i \(0.800077\pi\)
\(20\) 0 0
\(21\) −1.19522 + 1.25358i −0.260818 + 0.273553i
\(22\) 0 0
\(23\) 1.47001 + 1.47001i 0.306519 + 0.306519i 0.843558 0.537039i \(-0.180457\pi\)
−0.537039 + 0.843558i \(0.680457\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.371114 5.18288i −0.0714208 0.997446i
\(28\) 0 0
\(29\) −7.63621 −1.41801 −0.709004 0.705204i \(-0.750855\pi\)
−0.709004 + 0.705204i \(0.750855\pi\)
\(30\) 0 0
\(31\) −0.104617 −0.0187897 −0.00939487 0.999956i \(-0.502991\pi\)
−0.00939487 + 0.999956i \(0.502991\pi\)
\(32\) 0 0
\(33\) −3.05693 + 0.0728519i −0.532142 + 0.0126819i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.0126355 0.0126355i −0.00207727 0.00207727i 0.706067 0.708145i \(-0.250468\pi\)
−0.708145 + 0.706067i \(0.750468\pi\)
\(38\) 0 0
\(39\) −1.27598 1.21658i −0.204320 0.194808i
\(40\) 0 0
\(41\) 9.35682i 1.46129i 0.682757 + 0.730645i \(0.260781\pi\)
−0.682757 + 0.730645i \(0.739219\pi\)
\(42\) 0 0
\(43\) −2.66423 + 2.66423i −0.406291 + 0.406291i −0.880443 0.474152i \(-0.842755\pi\)
0.474152 + 0.880443i \(0.342755\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.98447 3.98447i 0.581195 0.581195i −0.354037 0.935232i \(-0.615191\pi\)
0.935232 + 0.354037i \(0.115191\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 2.74992 + 2.62190i 0.385066 + 0.367139i
\(52\) 0 0
\(53\) −5.44907 5.44907i −0.748488 0.748488i 0.225707 0.974195i \(-0.427531\pi\)
−0.974195 + 0.225707i \(0.927531\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8.86989 + 0.211385i −1.17485 + 0.0279986i
\(58\) 0 0
\(59\) −5.32780 −0.693621 −0.346810 0.937935i \(-0.612735\pi\)
−0.346810 + 0.937935i \(0.612735\pi\)
\(60\) 0 0
\(61\) −4.82359 −0.617597 −0.308798 0.951127i \(-0.599927\pi\)
−0.308798 + 0.951127i \(0.599927\pi\)
\(62\) 0 0
\(63\) −2.21996 2.01786i −0.279689 0.254226i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.01428 3.01428i −0.368253 0.368253i 0.498587 0.866840i \(-0.333853\pi\)
−0.866840 + 0.498587i \(0.833853\pi\)
\(68\) 0 0
\(69\) −2.48475 + 2.60608i −0.299129 + 0.313735i
\(70\) 0 0
\(71\) 5.20665i 0.617916i 0.951076 + 0.308958i \(0.0999802\pi\)
−0.951076 + 0.308958i \(0.900020\pi\)
\(72\) 0 0
\(73\) −7.10198 + 7.10198i −0.831224 + 0.831224i −0.987684 0.156461i \(-0.949992\pi\)
0.156461 + 0.987684i \(0.449992\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.24834 + 1.24834i −0.142261 + 0.142261i
\(78\) 0 0
\(79\) 15.4899i 1.74275i 0.490613 + 0.871377i \(0.336773\pi\)
−0.490613 + 0.871377i \(0.663227\pi\)
\(80\) 0 0
\(81\) 8.95915 0.856482i 0.995462 0.0951647i
\(82\) 0 0
\(83\) −3.76280 3.76280i −0.413021 0.413021i 0.469769 0.882789i \(-0.344337\pi\)
−0.882789 + 0.469769i \(0.844337\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.315116 13.2225i −0.0337840 1.41761i
\(88\) 0 0
\(89\) −2.98785 −0.316711 −0.158356 0.987382i \(-0.550619\pi\)
−0.158356 + 0.987382i \(0.550619\pi\)
\(90\) 0 0
\(91\) −1.01787 −0.106702
\(92\) 0 0
\(93\) −0.00431713 0.181150i −0.000447665 0.0187844i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.41605 + 6.41605i 0.651451 + 0.651451i 0.953342 0.301891i \(-0.0976179\pi\)
−0.301891 + 0.953342i \(0.597618\pi\)
\(98\) 0 0
\(99\) −0.252295 5.29024i −0.0253566 0.531689i
\(100\) 0 0
\(101\) 19.5014i 1.94047i −0.242175 0.970233i \(-0.577861\pi\)
0.242175 0.970233i \(-0.422139\pi\)
\(102\) 0 0
\(103\) −2.55799 + 2.55799i −0.252046 + 0.252046i −0.821809 0.569763i \(-0.807035\pi\)
0.569763 + 0.821809i \(0.307035\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.7892 12.7892i 1.23638 1.23638i 0.274908 0.961471i \(-0.411353\pi\)
0.961471 0.274908i \(-0.0886474\pi\)
\(108\) 0 0
\(109\) 7.24497i 0.693943i 0.937876 + 0.346971i \(0.112790\pi\)
−0.937876 + 0.346971i \(0.887210\pi\)
\(110\) 0 0
\(111\) 0.0213578 0.0224006i 0.00202719 0.00212617i
\(112\) 0 0
\(113\) −6.56229 6.56229i −0.617328 0.617328i 0.327517 0.944845i \(-0.393788\pi\)
−0.944845 + 0.327517i \(0.893788\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.05392 2.25963i 0.189885 0.208903i
\(118\) 0 0
\(119\) 2.19366 0.201092
\(120\) 0 0
\(121\) 7.88330 0.716664
\(122\) 0 0
\(123\) −16.2019 + 0.386119i −1.46088 + 0.0348152i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.16223 3.16223i −0.280603 0.280603i 0.552746 0.833349i \(-0.313580\pi\)
−0.833349 + 0.552746i \(0.813580\pi\)
\(128\) 0 0
\(129\) −4.72321 4.50333i −0.415856 0.396496i
\(130\) 0 0
\(131\) 12.4846i 1.09078i −0.838182 0.545391i \(-0.816381\pi\)
0.838182 0.545391i \(-0.183619\pi\)
\(132\) 0 0
\(133\) −3.62214 + 3.62214i −0.314080 + 0.314080i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.5780 + 11.5780i −0.989171 + 0.989171i −0.999942 0.0107709i \(-0.996571\pi\)
0.0107709 + 0.999942i \(0.496571\pi\)
\(138\) 0 0
\(139\) 14.9719i 1.26990i 0.772553 + 0.634951i \(0.218980\pi\)
−0.772553 + 0.634951i \(0.781020\pi\)
\(140\) 0 0
\(141\) 7.06377 + 6.73492i 0.594877 + 0.567183i
\(142\) 0 0
\(143\) −1.27065 1.27065i −0.106257 0.106257i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.73156 + 0.0412661i −0.142817 + 0.00340357i
\(148\) 0 0
\(149\) −5.94073 −0.486684 −0.243342 0.969941i \(-0.578244\pi\)
−0.243342 + 0.969941i \(0.578244\pi\)
\(150\) 0 0
\(151\) −17.0306 −1.38593 −0.692967 0.720970i \(-0.743697\pi\)
−0.692967 + 0.720970i \(0.743697\pi\)
\(152\) 0 0
\(153\) −4.42650 + 4.86984i −0.357861 + 0.393704i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.04726 + 8.04726i 0.642241 + 0.642241i 0.951106 0.308865i \(-0.0999491\pi\)
−0.308865 + 0.951106i \(0.599949\pi\)
\(158\) 0 0
\(159\) 9.21053 9.66025i 0.730443 0.766108i
\(160\) 0 0
\(161\) 2.07891i 0.163841i
\(162\) 0 0
\(163\) 6.10483 6.10483i 0.478167 0.478167i −0.426378 0.904545i \(-0.640211\pi\)
0.904545 + 0.426378i \(0.140211\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.71835 + 2.71835i −0.210352 + 0.210352i −0.804417 0.594065i \(-0.797522\pi\)
0.594065 + 0.804417i \(0.297522\pi\)
\(168\) 0 0
\(169\) 11.9639i 0.920303i
\(170\) 0 0
\(171\) −0.732051 15.3500i −0.0559813 1.17384i
\(172\) 0 0
\(173\) −16.0058 16.0058i −1.21690 1.21690i −0.968713 0.248183i \(-0.920167\pi\)
−0.248183 0.968713i \(-0.579833\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.219857 9.22540i −0.0165255 0.693424i
\(178\) 0 0
\(179\) 0.351893 0.0263017 0.0131509 0.999914i \(-0.495814\pi\)
0.0131509 + 0.999914i \(0.495814\pi\)
\(180\) 0 0
\(181\) 5.32474 0.395785 0.197893 0.980224i \(-0.436590\pi\)
0.197893 + 0.980224i \(0.436590\pi\)
\(182\) 0 0
\(183\) −0.199050 8.35233i −0.0147142 0.617422i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.73843 + 2.73843i 0.200254 + 0.200254i
\(188\) 0 0
\(189\) 3.40243 3.92727i 0.247491 0.285667i
\(190\) 0 0
\(191\) 7.84604i 0.567720i 0.958866 + 0.283860i \(0.0916151\pi\)
−0.958866 + 0.283860i \(0.908385\pi\)
\(192\) 0 0
\(193\) 0.268377 0.268377i 0.0193182 0.0193182i −0.697382 0.716700i \(-0.745652\pi\)
0.716700 + 0.697382i \(0.245652\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.41576 + 9.41576i −0.670845 + 0.670845i −0.957911 0.287066i \(-0.907320\pi\)
0.287066 + 0.957911i \(0.407320\pi\)
\(198\) 0 0
\(199\) 2.21621i 0.157103i 0.996910 + 0.0785515i \(0.0250295\pi\)
−0.996910 + 0.0785515i \(0.974970\pi\)
\(200\) 0 0
\(201\) 5.09502 5.34380i 0.359375 0.376923i
\(202\) 0 0
\(203\) −5.39961 5.39961i −0.378979 0.378979i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.61511 4.19495i −0.320772 0.291569i
\(208\) 0 0
\(209\) −9.04333 −0.625540
\(210\) 0 0
\(211\) 0.433151 0.0298193 0.0149097 0.999889i \(-0.495254\pi\)
0.0149097 + 0.999889i \(0.495254\pi\)
\(212\) 0 0
\(213\) −9.01563 + 0.214858i −0.617740 + 0.0147218i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.0739753 0.0739753i −0.00502177 0.00502177i
\(218\) 0 0
\(219\) −12.5906 12.0044i −0.850792 0.811184i
\(220\) 0 0
\(221\) 2.23286i 0.150198i
\(222\) 0 0
\(223\) 16.2689 16.2689i 1.08944 1.08944i 0.0938585 0.995586i \(-0.470080\pi\)
0.995586 0.0938585i \(-0.0299201\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.6647 18.6647i 1.23882 1.23882i 0.278338 0.960483i \(-0.410216\pi\)
0.960483 0.278338i \(-0.0897836\pi\)
\(228\) 0 0
\(229\) 4.85673i 0.320941i 0.987041 + 0.160471i \(0.0513012\pi\)
−0.987041 + 0.160471i \(0.948699\pi\)
\(230\) 0 0
\(231\) −2.21309 2.11006i −0.145610 0.138832i
\(232\) 0 0
\(233\) 19.4471 + 19.4471i 1.27402 + 1.27402i 0.943959 + 0.330062i \(0.107070\pi\)
0.330062 + 0.943959i \(0.392930\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −26.8218 + 0.639209i −1.74226 + 0.0415211i
\(238\) 0 0
\(239\) 17.7348 1.14717 0.573583 0.819147i \(-0.305553\pi\)
0.573583 + 0.819147i \(0.305553\pi\)
\(240\) 0 0
\(241\) −21.9071 −1.41116 −0.705580 0.708630i \(-0.749313\pi\)
−0.705580 + 0.708630i \(0.749313\pi\)
\(242\) 0 0
\(243\) 1.85276 + 15.4780i 0.118855 + 0.992912i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.68687 3.68687i −0.234590 0.234590i
\(248\) 0 0
\(249\) 6.36023 6.67078i 0.403063 0.422744i
\(250\) 0 0
\(251\) 5.13030i 0.323822i 0.986805 + 0.161911i \(0.0517657\pi\)
−0.986805 + 0.161911i \(0.948234\pi\)
\(252\) 0 0
\(253\) −2.59519 + 2.59519i −0.163158 + 0.163158i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.23056 1.23056i 0.0767602 0.0767602i −0.667684 0.744445i \(-0.732714\pi\)
0.744445 + 0.667684i \(0.232714\pi\)
\(258\) 0 0
\(259\) 0.0178694i 0.00111035i
\(260\) 0 0
\(261\) 22.8826 1.09128i 1.41640 0.0675488i
\(262\) 0 0
\(263\) 0.370051 + 0.370051i 0.0228183 + 0.0228183i 0.718424 0.695606i \(-0.244864\pi\)
−0.695606 + 0.718424i \(0.744864\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.123297 5.17364i −0.00754564 0.316621i
\(268\) 0 0
\(269\) 15.2276 0.928444 0.464222 0.885719i \(-0.346334\pi\)
0.464222 + 0.885719i \(0.346334\pi\)
\(270\) 0 0
\(271\) −16.2887 −0.989467 −0.494734 0.869045i \(-0.664734\pi\)
−0.494734 + 0.869045i \(0.664734\pi\)
\(272\) 0 0
\(273\) −0.0420035 1.76250i −0.00254217 0.106671i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.4653 + 16.4653i 0.989306 + 0.989306i 0.999943 0.0106374i \(-0.00338604\pi\)
−0.0106374 + 0.999943i \(0.503386\pi\)
\(278\) 0 0
\(279\) 0.313494 0.0149507i 0.0187684 0.000895076i
\(280\) 0 0
\(281\) 26.5619i 1.58455i 0.610166 + 0.792274i \(0.291103\pi\)
−0.610166 + 0.792274i \(0.708897\pi\)
\(282\) 0 0
\(283\) 6.64836 6.64836i 0.395204 0.395204i −0.481334 0.876538i \(-0.659847\pi\)
0.876538 + 0.481334i \(0.159847\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.61627 + 6.61627i −0.390546 + 0.390546i
\(288\) 0 0
\(289\) 12.1879i 0.716933i
\(290\) 0 0
\(291\) −10.8450 + 11.3745i −0.635746 + 0.666787i
\(292\) 0 0
\(293\) 6.20064 + 6.20064i 0.362245 + 0.362245i 0.864639 0.502394i \(-0.167547\pi\)
−0.502394 + 0.864639i \(0.667547\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.14996 0.655171i 0.530934 0.0380169i
\(298\) 0 0
\(299\) −2.11606 −0.122375
\(300\) 0 0
\(301\) −3.76779 −0.217172
\(302\) 0 0
\(303\) 33.7679 0.804748i 1.93991 0.0462315i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.71993 + 2.71993i 0.155235 + 0.155235i 0.780451 0.625217i \(-0.214989\pi\)
−0.625217 + 0.780451i \(0.714989\pi\)
\(308\) 0 0
\(309\) −4.53486 4.32375i −0.257979 0.245969i
\(310\) 0 0
\(311\) 31.8252i 1.80464i −0.431065 0.902321i \(-0.641862\pi\)
0.431065 0.902321i \(-0.358138\pi\)
\(312\) 0 0
\(313\) −14.2759 + 14.2759i −0.806922 + 0.806922i −0.984167 0.177245i \(-0.943281\pi\)
0.177245 + 0.984167i \(0.443281\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.71018 + 7.71018i −0.433047 + 0.433047i −0.889663 0.456617i \(-0.849061\pi\)
0.456617 + 0.889663i \(0.349061\pi\)
\(318\) 0 0
\(319\) 13.4811i 0.754797i
\(320\) 0 0
\(321\) 22.6730 + 21.6175i 1.26548 + 1.20657i
\(322\) 0 0
\(323\) 7.94575 + 7.94575i 0.442113 + 0.442113i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −12.5451 + 0.298972i −0.693746 + 0.0165332i
\(328\) 0 0
\(329\) 5.63489 0.310662
\(330\) 0 0
\(331\) 15.6380 0.859543 0.429771 0.902938i \(-0.358594\pi\)
0.429771 + 0.902938i \(0.358594\pi\)
\(332\) 0 0
\(333\) 0.0396693 + 0.0360579i 0.00217387 + 0.00197596i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 21.5849 + 21.5849i 1.17581 + 1.17581i 0.980803 + 0.195003i \(0.0624716\pi\)
0.195003 + 0.980803i \(0.437528\pi\)
\(338\) 0 0
\(339\) 11.0922 11.6338i 0.602445 0.631861i
\(340\) 0 0
\(341\) 0.184692i 0.0100017i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.11458 5.11458i 0.274565 0.274565i −0.556370 0.830935i \(-0.687806\pi\)
0.830935 + 0.556370i \(0.187806\pi\)
\(348\) 0 0
\(349\) 25.9034i 1.38657i −0.720661 0.693287i \(-0.756162\pi\)
0.720661 0.693287i \(-0.243838\pi\)
\(350\) 0 0
\(351\) 3.99745 + 3.46323i 0.213368 + 0.184854i
\(352\) 0 0
\(353\) 13.6228 + 13.6228i 0.725068 + 0.725068i 0.969633 0.244565i \(-0.0786451\pi\)
−0.244565 + 0.969633i \(0.578645\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.0905237 + 3.79845i 0.00479102 + 0.201035i
\(358\) 0 0
\(359\) −26.9640 −1.42311 −0.711554 0.702632i \(-0.752008\pi\)
−0.711554 + 0.702632i \(0.752008\pi\)
\(360\) 0 0
\(361\) −7.23987 −0.381046
\(362\) 0 0
\(363\) 0.325313 + 13.6504i 0.0170745 + 0.716460i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 9.56565 + 9.56565i 0.499323 + 0.499323i 0.911227 0.411904i \(-0.135136\pi\)
−0.411904 + 0.911227i \(0.635136\pi\)
\(368\) 0 0
\(369\) −1.33718 28.0386i −0.0696107 1.45963i
\(370\) 0 0
\(371\) 7.70615i 0.400084i
\(372\) 0 0
\(373\) 14.3181 14.3181i 0.741364 0.741364i −0.231476 0.972841i \(-0.574356\pi\)
0.972841 + 0.231476i \(0.0743555\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.49610 5.49610i 0.283064 0.283064i
\(378\) 0 0
\(379\) 29.1422i 1.49694i 0.663171 + 0.748468i \(0.269210\pi\)
−0.663171 + 0.748468i \(0.730790\pi\)
\(380\) 0 0
\(381\) 5.34510 5.60609i 0.273838 0.287209i
\(382\) 0 0
\(383\) 17.5964 + 17.5964i 0.899136 + 0.899136i 0.995360 0.0962236i \(-0.0306764\pi\)
−0.0962236 + 0.995360i \(0.530676\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.60287 8.36436i 0.386476 0.425184i
\(388\) 0 0
\(389\) 29.6512 1.50338 0.751688 0.659519i \(-0.229240\pi\)
0.751688 + 0.659519i \(0.229240\pi\)
\(390\) 0 0
\(391\) 4.56043 0.230631
\(392\) 0 0
\(393\) 21.6178 0.515189i 1.09047 0.0259878i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.22593 + 8.22593i 0.412847 + 0.412847i 0.882729 0.469882i \(-0.155703\pi\)
−0.469882 + 0.882729i \(0.655703\pi\)
\(398\) 0 0
\(399\) −6.42143 6.12249i −0.321474 0.306508i
\(400\) 0 0
\(401\) 32.2078i 1.60838i 0.594370 + 0.804191i \(0.297401\pi\)
−0.594370 + 0.804191i \(0.702599\pi\)
\(402\) 0 0
\(403\) 0.0752972 0.0752972i 0.00375082 0.00375082i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.0223070 0.0223070i 0.00110572 0.00110572i
\(408\) 0 0
\(409\) 7.75602i 0.383511i −0.981443 0.191755i \(-0.938582\pi\)
0.981443 0.191755i \(-0.0614180\pi\)
\(410\) 0 0
\(411\) −20.5257 19.5701i −1.01246 0.965323i
\(412\) 0 0
\(413\) −3.76732 3.76732i −0.185378 0.185378i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −25.9248 + 0.617832i −1.26954 + 0.0302554i
\(418\) 0 0
\(419\) 0.442296 0.0216076 0.0108038 0.999942i \(-0.496561\pi\)
0.0108038 + 0.999942i \(0.496561\pi\)
\(420\) 0 0
\(421\) −15.5754 −0.759097 −0.379549 0.925172i \(-0.623921\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(422\) 0 0
\(423\) −11.3704 + 12.5093i −0.552849 + 0.608221i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.41079 3.41079i −0.165060 0.165060i
\(428\) 0 0
\(429\) 2.14776 2.25263i 0.103695 0.108758i
\(430\) 0 0
\(431\) 4.29772i 0.207014i −0.994629 0.103507i \(-0.966994\pi\)
0.994629 0.103507i \(-0.0330064\pi\)
\(432\) 0 0
\(433\) 25.3909 25.3909i 1.22021 1.22021i 0.252649 0.967558i \(-0.418698\pi\)
0.967558 0.252649i \(-0.0813016\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.53012 + 7.53012i −0.360215 + 0.360215i
\(438\) 0 0
\(439\) 16.3148i 0.778665i −0.921097 0.389333i \(-0.872706\pi\)
0.921097 0.389333i \(-0.127294\pi\)
\(440\) 0 0
\(441\) −0.142909 2.99659i −0.00680520 0.142695i
\(442\) 0 0
\(443\) 25.0050 + 25.0050i 1.18802 + 1.18802i 0.977613 + 0.210411i \(0.0674804\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.245151 10.2867i −0.0115952 0.486546i
\(448\) 0 0
\(449\) −10.7127 −0.505566 −0.252783 0.967523i \(-0.581346\pi\)
−0.252783 + 0.967523i \(0.581346\pi\)
\(450\) 0 0
\(451\) −16.5187 −0.777836
\(452\) 0 0
\(453\) −0.702787 29.4895i −0.0330198 1.38554i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.78419 + 6.78419i 0.317351 + 0.317351i 0.847749 0.530398i \(-0.177957\pi\)
−0.530398 + 0.847749i \(0.677957\pi\)
\(458\) 0 0
\(459\) −8.61509 7.46378i −0.402118 0.348380i
\(460\) 0 0
\(461\) 13.2962i 0.619268i 0.950856 + 0.309634i \(0.100207\pi\)
−0.950856 + 0.309634i \(0.899793\pi\)
\(462\) 0 0
\(463\) 25.5971 25.5971i 1.18960 1.18960i 0.212419 0.977179i \(-0.431866\pi\)
0.977179 0.212419i \(-0.0681341\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −19.7182 + 19.7182i −0.912451 + 0.912451i −0.996465 0.0840140i \(-0.973226\pi\)
0.0840140 + 0.996465i \(0.473226\pi\)
\(468\) 0 0
\(469\) 4.26284i 0.196840i
\(470\) 0 0
\(471\) −13.6022 + 14.2664i −0.626757 + 0.657360i
\(472\) 0 0
\(473\) −4.70348 4.70348i −0.216266 0.216266i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 17.1074 + 15.5499i 0.783293 + 0.711983i
\(478\) 0 0
\(479\) 15.7258 0.718530 0.359265 0.933236i \(-0.383027\pi\)
0.359265 + 0.933236i \(0.383027\pi\)
\(480\) 0 0
\(481\) 0.0181887 0.000829332
\(482\) 0 0
\(483\) −3.59976 + 0.0857885i −0.163795 + 0.00390351i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.1070 + 15.1070i 0.684564 + 0.684564i 0.961025 0.276461i \(-0.0891617\pi\)
−0.276461 + 0.961025i \(0.589162\pi\)
\(488\) 0 0
\(489\) 10.8228 + 10.3190i 0.489424 + 0.466639i
\(490\) 0 0
\(491\) 1.69331i 0.0764179i 0.999270 + 0.0382090i \(0.0121652\pi\)
−0.999270 + 0.0382090i \(0.987835\pi\)
\(492\) 0 0
\(493\) −11.8449 + 11.8449i −0.533468 + 0.533468i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.68166 + 3.68166i −0.165145 + 0.165145i
\(498\) 0 0
\(499\) 42.9129i 1.92104i 0.278203 + 0.960522i \(0.410261\pi\)
−0.278203 + 0.960522i \(0.589739\pi\)
\(500\) 0 0
\(501\) −4.81916 4.59481i −0.215304 0.205281i
\(502\) 0 0
\(503\) 26.6274 + 26.6274i 1.18726 + 1.18726i 0.977823 + 0.209433i \(0.0671617\pi\)
0.209433 + 0.977823i \(0.432838\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −20.7163 + 0.493705i −0.920042 + 0.0219262i
\(508\) 0 0
\(509\) 24.5004 1.08596 0.542981 0.839745i \(-0.317295\pi\)
0.542981 + 0.839745i \(0.317295\pi\)
\(510\) 0 0
\(511\) −10.0437 −0.444308
\(512\) 0 0
\(513\) 26.5492 1.90102i 1.17218 0.0839323i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.03426 + 7.03426i 0.309366 + 0.309366i
\(518\) 0 0
\(519\) 27.0544 28.3754i 1.18756 1.24554i
\(520\) 0 0
\(521\) 0.487097i 0.0213401i 0.999943 + 0.0106701i \(0.00339645\pi\)
−0.999943 + 0.0106701i \(0.996604\pi\)
\(522\) 0 0
\(523\) 1.98037 1.98037i 0.0865954 0.0865954i −0.662482 0.749078i \(-0.730497\pi\)
0.749078 + 0.662482i \(0.230497\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.162277 + 0.162277i −0.00706888 + 0.00706888i
\(528\) 0 0
\(529\) 18.6781i 0.812092i
\(530\) 0 0
\(531\) 15.9653 0.761392i 0.692833 0.0330416i
\(532\) 0 0
\(533\) −6.73450 6.73450i −0.291704 0.291704i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.0145212 + 0.609324i 0.000626638 + 0.0262943i
\(538\) 0 0
\(539\) −1.76542 −0.0760419
\(540\) 0 0
\(541\) 39.1538 1.68335 0.841677 0.539982i \(-0.181569\pi\)
0.841677 + 0.539982i \(0.181569\pi\)
\(542\) 0 0
\(543\) 0.219731 + 9.22011i 0.00942957 + 0.395673i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −21.3666 21.3666i −0.913568 0.913568i 0.0829826 0.996551i \(-0.473555\pi\)
−0.996551 + 0.0829826i \(0.973555\pi\)
\(548\) 0 0
\(549\) 14.4543 0.689335i 0.616896 0.0294201i
\(550\) 0 0
\(551\) 39.1164i 1.66641i
\(552\) 0 0
\(553\) −10.9530 + 10.9530i −0.465771 + 0.465771i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.13033 + 8.13033i −0.344493 + 0.344493i −0.858054 0.513560i \(-0.828326\pi\)
0.513560 + 0.858054i \(0.328326\pi\)
\(558\) 0 0
\(559\) 3.83512i 0.162208i
\(560\) 0 0
\(561\) −4.62875 + 4.85476i −0.195426 + 0.204968i
\(562\) 0 0
\(563\) −26.5393 26.5393i −1.11850 1.11850i −0.991962 0.126535i \(-0.959614\pi\)
−0.126535 0.991962i \(-0.540386\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.94070 + 5.72945i 0.291482 + 0.240614i
\(568\) 0 0
\(569\) 12.3882 0.519341 0.259671 0.965697i \(-0.416386\pi\)
0.259671 + 0.965697i \(0.416386\pi\)
\(570\) 0 0
\(571\) 1.56580 0.0655267 0.0327633 0.999463i \(-0.489569\pi\)
0.0327633 + 0.999463i \(0.489569\pi\)
\(572\) 0 0
\(573\) −13.5859 + 0.323775i −0.567559 + 0.0135259i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.04688 + 6.04688i 0.251735 + 0.251735i 0.821682 0.569947i \(-0.193036\pi\)
−0.569947 + 0.821682i \(0.693036\pi\)
\(578\) 0 0
\(579\) 0.475786 + 0.453636i 0.0197730 + 0.0188525i
\(580\) 0 0
\(581\) 5.32140i 0.220769i
\(582\) 0 0
\(583\) 9.61989 9.61989i 0.398415 0.398415i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.0640 + 19.0640i −0.786857 + 0.786857i −0.980978 0.194121i \(-0.937815\pi\)
0.194121 + 0.980978i \(0.437815\pi\)
\(588\) 0 0
\(589\) 0.535898i 0.0220813i
\(590\) 0 0
\(591\) −16.6925 15.9154i −0.686638 0.654672i
\(592\) 0 0
\(593\) −18.5595 18.5595i −0.762148 0.762148i 0.214562 0.976710i \(-0.431167\pi\)
−0.976710 + 0.214562i \(0.931167\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3.83750 + 0.0914543i −0.157058 + 0.00374298i
\(598\) 0 0
\(599\) −3.58329 −0.146409 −0.0732046 0.997317i \(-0.523323\pi\)
−0.0732046 + 0.997317i \(0.523323\pi\)
\(600\) 0 0
\(601\) −17.2133 −0.702145 −0.351072 0.936348i \(-0.614183\pi\)
−0.351072 + 0.936348i \(0.614183\pi\)
\(602\) 0 0
\(603\) 9.46336 + 8.60182i 0.385378 + 0.350293i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.02293 + 6.02293i 0.244463 + 0.244463i 0.818694 0.574230i \(-0.194699\pi\)
−0.574230 + 0.818694i \(0.694699\pi\)
\(608\) 0 0
\(609\) 9.12693 9.57257i 0.369842 0.387900i
\(610\) 0 0
\(611\) 5.73558i 0.232037i
\(612\) 0 0
\(613\) −4.01752 + 4.01752i −0.162266 + 0.162266i −0.783570 0.621304i \(-0.786603\pi\)
0.621304 + 0.783570i \(0.286603\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.421041 0.421041i 0.0169505 0.0169505i −0.698581 0.715531i \(-0.746185\pi\)
0.715531 + 0.698581i \(0.246185\pi\)
\(618\) 0 0
\(619\) 29.0434i 1.16735i −0.811986 0.583676i \(-0.801614\pi\)
0.811986 0.583676i \(-0.198386\pi\)
\(620\) 0 0
\(621\) 7.07336 8.16445i 0.283844 0.327628i
\(622\) 0 0
\(623\) −2.11273 2.11273i −0.0846446 0.0846446i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.373183 15.6591i −0.0149035 0.625363i
\(628\) 0 0
\(629\) −0.0391993 −0.00156298
\(630\) 0 0
\(631\) 27.4797 1.09395 0.546975 0.837149i \(-0.315779\pi\)
0.546975 + 0.837149i \(0.315779\pi\)
\(632\) 0 0
\(633\) 0.0178744 + 0.750027i 0.000710445 + 0.0298109i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.719742 0.719742i −0.0285172 0.0285172i
\(638\) 0 0
\(639\) −0.744079 15.6022i −0.0294353 0.617214i
\(640\) 0 0
\(641\) 33.3722i 1.31812i −0.752089 0.659062i \(-0.770954\pi\)
0.752089 0.659062i \(-0.229046\pi\)
\(642\) 0 0
\(643\) 29.8928 29.8928i 1.17886 1.17886i 0.198824 0.980035i \(-0.436288\pi\)
0.980035 0.198824i \(-0.0637121\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.4656 + 10.4656i −0.411446 + 0.411446i −0.882242 0.470796i \(-0.843967\pi\)
0.470796 + 0.882242i \(0.343967\pi\)
\(648\) 0 0
\(649\) 9.40580i 0.369210i
\(650\) 0 0
\(651\) 0.125040 0.131145i 0.00490070 0.00513999i
\(652\) 0 0
\(653\) 15.3707 + 15.3707i 0.601500 + 0.601500i 0.940711 0.339210i \(-0.110160\pi\)
−0.339210 + 0.940711i \(0.610160\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 20.2668 22.2967i 0.790683 0.869876i
\(658\) 0 0
\(659\) −2.70465 −0.105358 −0.0526791 0.998611i \(-0.516776\pi\)
−0.0526791 + 0.998611i \(0.516776\pi\)
\(660\) 0 0
\(661\) −30.8272 −1.19904 −0.599519 0.800360i \(-0.704642\pi\)
−0.599519 + 0.800360i \(0.704642\pi\)
\(662\) 0 0
\(663\) −3.86633 + 0.0921413i −0.150156 + 0.00357847i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −11.2253 11.2253i −0.434646 0.434646i
\(668\) 0 0
\(669\) 28.8419 + 27.4992i 1.11509 + 1.06318i
\(670\) 0 0
\(671\) 8.51565i 0.328743i
\(672\) 0 0
\(673\) −20.1553 + 20.1553i −0.776930 + 0.776930i −0.979308 0.202378i \(-0.935133\pi\)
0.202378 + 0.979308i \(0.435133\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.7572 22.7572i 0.874629 0.874629i −0.118344 0.992973i \(-0.537758\pi\)
0.992973 + 0.118344i \(0.0377584\pi\)
\(678\) 0 0
\(679\) 9.07367i 0.348215i
\(680\) 0 0
\(681\) 33.0893 + 31.5489i 1.26798 + 1.20895i
\(682\) 0 0
\(683\) −25.1450 25.1450i −0.962146 0.962146i 0.0371629 0.999309i \(-0.488168\pi\)
−0.999309 + 0.0371629i \(0.988168\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8.40971 + 0.200418i −0.320850 + 0.00764642i
\(688\) 0 0
\(689\) 7.84386 0.298827
\(690\) 0 0
\(691\) −22.6399 −0.861261 −0.430631 0.902528i \(-0.641709\pi\)
−0.430631 + 0.902528i \(0.641709\pi\)
\(692\) 0 0
\(693\) 3.56237 3.91917i 0.135323 0.148877i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 14.5139 + 14.5139i 0.549751 + 0.549751i
\(698\) 0 0
\(699\) −32.8713 + 34.4763i −1.24331 + 1.30401i
\(700\) 0 0
\(701\) 32.6250i 1.23223i −0.787657 0.616114i \(-0.788706\pi\)
0.787657 0.616114i \(-0.211294\pi\)
\(702\) 0 0
\(703\) 0.0647254 0.0647254i 0.00244117 0.00244117i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.7896 13.7896i 0.518611 0.518611i
\(708\) 0 0
\(709\) 0.338874i 0.0127267i 0.999980 + 0.00636333i \(0.00202553\pi\)
−0.999980 + 0.00636333i \(0.997974\pi\)
\(710\) 0 0
\(711\) −2.21366 46.4171i −0.0830186 1.74078i
\(712\) 0 0
\(713\) −0.153788 0.153788i −0.00575941 0.00575941i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.731844 + 30.7088i 0.0273312 + 1.14684i
\(718\) 0 0
\(719\) 51.0469 1.90373 0.951863 0.306523i \(-0.0991657\pi\)
0.951863 + 0.306523i \(0.0991657\pi\)
\(720\) 0 0
\(721\) −3.61754 −0.134724
\(722\) 0 0
\(723\) −0.904020 37.9334i −0.0336209 1.41076i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 14.3223 + 14.3223i 0.531185 + 0.531185i 0.920925 0.389740i \(-0.127435\pi\)
−0.389740 + 0.920925i \(0.627435\pi\)
\(728\) 0 0
\(729\) −26.7245 + 3.84688i −0.989798 + 0.142477i
\(730\) 0 0
\(731\) 8.26525i 0.305701i
\(732\) 0 0
\(733\) −29.8460 + 29.8460i −1.10239 + 1.10239i −0.108264 + 0.994122i \(0.534529\pi\)
−0.994122 + 0.108264i \(0.965471\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.32147 5.32147i 0.196019 0.196019i
\(738\) 0 0
\(739\) 12.5764i 0.462631i −0.972879 0.231316i \(-0.925697\pi\)
0.972879 0.231316i \(-0.0743030\pi\)
\(740\) 0 0
\(741\) 6.23189 6.53618i 0.228934 0.240112i
\(742\) 0 0
\(743\) 29.8270 + 29.8270i 1.09425 + 1.09425i 0.995070 + 0.0991785i \(0.0316215\pi\)
0.0991785 + 0.995070i \(0.468379\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 11.8133 + 10.7378i 0.432227 + 0.392877i
\(748\) 0 0
\(749\) 18.0867 0.660872
\(750\) 0 0
\(751\) 37.9527 1.38491 0.692456 0.721460i \(-0.256528\pi\)
0.692456 + 0.721460i \(0.256528\pi\)
\(752\) 0 0
\(753\) −8.88342 + 0.211707i −0.323730 + 0.00771505i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −17.5520 17.5520i −0.637938 0.637938i 0.312108 0.950047i \(-0.398965\pi\)
−0.950047 + 0.312108i \(0.898965\pi\)
\(758\) 0 0
\(759\) −4.60081 4.38663i −0.166999 0.159224i
\(760\) 0 0
\(761\) 8.56045i 0.310316i 0.987890 + 0.155158i \(0.0495887\pi\)
−0.987890 + 0.155158i \(0.950411\pi\)
\(762\) 0 0
\(763\) −5.12297 + 5.12297i −0.185464 + 0.185464i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.83464 3.83464i 0.138461 0.138461i
\(768\) 0 0
\(769\) 9.71231i 0.350235i −0.984548 0.175117i \(-0.943969\pi\)
0.984548 0.175117i \(-0.0560305\pi\)
\(770\) 0 0
\(771\) 2.18157 + 2.08001i 0.0785672 + 0.0749096i
\(772\) 0 0
\(773\) −30.1398 30.1398i −1.08405 1.08405i −0.996127 0.0879261i \(-0.971976\pi\)
−0.0879261 0.996127i \(-0.528024\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.0309419 0.000737398i 0.00111003 2.64540e-5i
\(778\) 0 0
\(779\) −47.9302 −1.71728
\(780\) 0 0
\(781\) −9.19192 −0.328913
\(782\) 0 0
\(783\) 2.83390 + 39.5776i 0.101275 + 1.41439i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −8.55996 8.55996i −0.305130 0.305130i 0.537887 0.843017i \(-0.319223\pi\)
−0.843017 + 0.537887i \(0.819223\pi\)
\(788\) 0 0
\(789\) −0.625495 + 0.656036i −0.0222682 + 0.0233555i
\(790\) 0 0
\(791\) 9.28048i 0.329976i
\(792\) 0 0
\(793\) 3.47174 3.47174i 0.123285 0.123285i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.9179 11.9179i 0.422152 0.422152i −0.463792 0.885944i \(-0.653512\pi\)
0.885944 + 0.463792i \(0.153512\pi\)
\(798\) 0 0
\(799\) 12.3610i 0.437302i
\(800\) 0 0
\(801\) 8.95337 0.426991i 0.316352 0.0150870i
\(802\) 0 0
\(803\) −12.5380 12.5380i −0.442455 0.442455i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.628384 + 26.3675i 0.0221202 + 0.928180i
\(808\) 0 0
\(809\) −2.44921 −0.0861097 −0.0430549 0.999073i \(-0.513709\pi\)
−0.0430549 + 0.999073i \(0.513709\pi\)
\(810\) 0 0
\(811\) 1.32051 0.0463693 0.0231847 0.999731i \(-0.492619\pi\)
0.0231847 + 0.999731i \(0.492619\pi\)
\(812\) 0 0
\(813\) −0.672170 28.2048i −0.0235740 0.989186i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −13.6475 13.6475i −0.477465 0.477465i
\(818\) 0 0
\(819\) 3.05014 0.145463i 0.106581 0.00508289i
\(820\) 0 0
\(821\) 40.5038i 1.41359i 0.707417 + 0.706797i \(0.249860\pi\)
−0.707417 + 0.706797i \(0.750140\pi\)
\(822\) 0 0
\(823\) 28.1227 28.1227i 0.980296 0.980296i −0.0195133 0.999810i \(-0.506212\pi\)
0.999810 + 0.0195133i \(0.00621167\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.9005 25.9005i 0.900649 0.900649i −0.0948428 0.995492i \(-0.530235\pi\)
0.995492 + 0.0948428i \(0.0302349\pi\)
\(828\) 0 0
\(829\) 3.31951i 0.115291i −0.998337 0.0576457i \(-0.981641\pi\)
0.998337 0.0576457i \(-0.0183594\pi\)
\(830\) 0 0
\(831\) −27.8312 + 29.1902i −0.965455 + 1.01260i
\(832\) 0 0
\(833\) 1.55115 + 1.55115i 0.0537442 + 0.0537442i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.0388247 + 0.542217i 0.00134198 + 0.0187418i
\(838\) 0 0
\(839\) −20.4082 −0.704570 −0.352285 0.935893i \(-0.614595\pi\)
−0.352285 + 0.935893i \(0.614595\pi\)
\(840\) 0 0
\(841\) 29.3117 1.01075
\(842\) 0 0
\(843\) −45.9934 + 1.09610i −1.58410 + 0.0377518i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 5.57433 + 5.57433i 0.191536 + 0.191536i
\(848\) 0 0
\(849\) 11.7864 + 11.2377i 0.404508 + 0.385676i
\(850\) 0 0
\(851\) 0.0371488i 0.00127345i
\(852\) 0 0
\(853\) −6.05842 + 6.05842i −0.207436 + 0.207436i −0.803177 0.595741i \(-0.796859\pi\)
0.595741 + 0.803177i \(0.296859\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −31.2305 + 31.2305i −1.06681 + 1.06681i −0.0692109 + 0.997602i \(0.522048\pi\)
−0.997602 + 0.0692109i \(0.977952\pi\)
\(858\) 0 0
\(859\) 50.7305i 1.73090i 0.500992 + 0.865452i \(0.332969\pi\)
−0.500992 + 0.865452i \(0.667031\pi\)
\(860\) 0 0
\(861\) −11.7295 11.1834i −0.399740 0.381131i
\(862\) 0 0
\(863\) −9.99997 9.99997i −0.340403 0.340403i 0.516116 0.856519i \(-0.327377\pi\)
−0.856519 + 0.516116i \(0.827377\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −21.1040 + 0.502945i −0.716729 + 0.0170809i
\(868\) 0 0
\(869\) −27.3462 −0.927657
\(870\) 0 0
\(871\) 4.33902 0.147022
\(872\) 0 0
\(873\) −20.1432 18.3094i −0.681745 0.619679i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −33.6199 33.6199i −1.13526 1.13526i −0.989288 0.145974i \(-0.953368\pi\)
−0.145974 0.989288i \(-0.546632\pi\)
\(878\) 0 0
\(879\) −10.4809 + 10.9927i −0.353512 + 0.370773i
\(880\) 0 0
\(881\) 34.9376i 1.17708i 0.808469 + 0.588539i \(0.200297\pi\)
−0.808469 + 0.588539i \(0.799703\pi\)
\(882\) 0 0
\(883\) −27.3663 + 27.3663i −0.920948 + 0.920948i −0.997096 0.0761487i \(-0.975738\pi\)
0.0761487 + 0.997096i \(0.475738\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −24.2242 + 24.2242i −0.813369 + 0.813369i −0.985137 0.171769i \(-0.945052\pi\)
0.171769 + 0.985137i \(0.445052\pi\)
\(888\) 0 0
\(889\) 4.47208i 0.149989i
\(890\) 0 0
\(891\) 1.51205 + 15.8167i 0.0506556 + 0.529878i
\(892\) 0 0
\(893\) 20.4104 + 20.4104i 0.683008 + 0.683008i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.0873215 3.66409i −0.00291558 0.122340i
\(898\) 0 0
\(899\) 0.798876 0.0266440
\(900\) 0 0
\(901\) −16.9047 −0.563176
\(902\) 0 0
\(903\) −0.155482 6.52415i −0.00517411 0.217110i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −24.2907 24.2907i −0.806558 0.806558i 0.177553 0.984111i \(-0.443182\pi\)
−0.984111 + 0.177553i \(0.943182\pi\)
\(908\) 0 0
\(909\) 2.78694 + 58.4379i 0.0924368 + 1.93826i
\(910\) 0 0
\(911\) 4.30457i 0.142617i 0.997454 + 0.0713083i \(0.0227174\pi\)
−0.997454 + 0.0713083i \(0.977283\pi\)
\(912\) 0 0
\(913\) 6.64291 6.64291i 0.219848 0.219848i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.82792 8.82792i 0.291524 0.291524i
\(918\) 0 0
\(919\) 28.6567i 0.945299i 0.881251 + 0.472649i \(0.156702\pi\)
−0.881251 + 0.472649i \(0.843298\pi\)
\(920\) 0 0
\(921\) −4.59748 + 4.82196i −0.151492 + 0.158889i
\(922\) 0 0
\(923\) −3.74745 3.74745i −0.123349 0.123349i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 7.29969 8.03081i 0.239753 0.263766i
\(928\) 0 0
\(929\) −30.1698 −0.989840 −0.494920 0.868938i \(-0.664803\pi\)
−0.494920 + 0.868938i \(0.664803\pi\)
\(930\) 0 0
\(931\) −5.12249 −0.167883
\(932\) 0 0
\(933\) 55.1072 1.31330i 1.80413 0.0429955i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 7.29925 + 7.29925i 0.238456 + 0.238456i 0.816211 0.577755i \(-0.196071\pi\)
−0.577755 + 0.816211i \(0.696071\pi\)
\(938\) 0 0
\(939\) −25.3087 24.1305i −0.825918 0.787468i
\(940\) 0 0
\(941\) 15.2822i 0.498187i 0.968480 + 0.249093i \(0.0801326\pi\)
−0.968480 + 0.249093i \(0.919867\pi\)
\(942\) 0 0
\(943\) −13.7547 + 13.7547i −0.447913 + 0.447913i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.4664 12.4664i 0.405104 0.405104i −0.474923 0.880027i \(-0.657524\pi\)
0.880027 + 0.474923i \(0.157524\pi\)
\(948\) 0 0
\(949\) 10.2232i 0.331859i
\(950\) 0 0
\(951\) −13.6688 13.0325i −0.443241 0.422606i
\(952\) 0 0
\(953\) 19.7282 + 19.7282i 0.639058 + 0.639058i 0.950323 0.311265i \(-0.100753\pi\)
−0.311265 + 0.950323i \(0.600753\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 23.3433 0.556312i 0.754582 0.0179830i
\(958\) 0 0
\(959\) −16.3737 −0.528734
\(960\) 0 0
\(961\) −30.9891 −0.999647
\(962\) 0 0
\(963\) −36.4963 + 40.1517i −1.17608 + 1.29387i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −27.4624 27.4624i −0.883130 0.883130i 0.110721 0.993852i \(-0.464684\pi\)
−0.993852 + 0.110721i \(0.964684\pi\)
\(968\) 0 0
\(969\) −13.4306 + 14.0864i −0.431455 + 0.452521i
\(970\) 0 0
\(971\) 12.8693i 0.412994i −0.978447 0.206497i \(-0.933794\pi\)
0.978447 0.206497i \(-0.0662064\pi\)
\(972\) 0 0
\(973\) −10.5867 + 10.5867i −0.339395 + 0.339395i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 15.3733 15.3733i 0.491836 0.491836i −0.417048 0.908884i \(-0.636935\pi\)
0.908884 + 0.417048i \(0.136935\pi\)
\(978\) 0 0
\(979\) 5.27480i 0.168583i
\(980\) 0 0
\(981\) −1.03537 21.7102i −0.0330569 0.693155i
\(982\) 0 0
\(983\) −16.1811 16.1811i −0.516096 0.516096i 0.400292 0.916388i \(-0.368909\pi\)
−0.916388 + 0.400292i \(0.868909\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0.232530 + 9.75715i 0.00740151 + 0.310574i
\(988\) 0 0
\(989\) −7.83290 −0.249072
\(990\) 0 0
\(991\) 14.4737 0.459772 0.229886 0.973218i \(-0.426165\pi\)
0.229886 + 0.973218i \(0.426165\pi\)
\(992\) 0 0
\(993\) 0.645319 + 27.0781i 0.0204786 + 0.859299i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −11.9234 11.9234i −0.377617 0.377617i 0.492625 0.870242i \(-0.336037\pi\)
−0.870242 + 0.492625i \(0.836037\pi\)
\(998\) 0 0
\(999\) −0.0607993 + 0.0701778i −0.00192361 + 0.00222033i
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 2100.2.s.c.1457.9 yes 32
3.2 odd 2 inner 2100.2.s.c.1457.1 32
5.2 odd 4 inner 2100.2.s.c.1793.16 yes 32
5.3 odd 4 inner 2100.2.s.c.1793.1 yes 32
5.4 even 2 inner 2100.2.s.c.1457.8 yes 32
15.2 even 4 inner 2100.2.s.c.1793.8 yes 32
15.8 even 4 inner 2100.2.s.c.1793.9 yes 32
15.14 odd 2 inner 2100.2.s.c.1457.16 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.2.s.c.1457.1 32 3.2 odd 2 inner
2100.2.s.c.1457.8 yes 32 5.4 even 2 inner
2100.2.s.c.1457.9 yes 32 1.1 even 1 trivial
2100.2.s.c.1457.16 yes 32 15.14 odd 2 inner
2100.2.s.c.1793.1 yes 32 5.3 odd 4 inner
2100.2.s.c.1793.8 yes 32 15.2 even 4 inner
2100.2.s.c.1793.9 yes 32 15.8 even 4 inner
2100.2.s.c.1793.16 yes 32 5.2 odd 4 inner