Properties

Label 2100.2.bi.j.1601.2
Level $2100$
Weight $2$
Character 2100.1601
Analytic conductor $16.769$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,2,Mod(101,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.101");
 
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.bi (of order \(6\), 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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.29471584693248.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.2
Root \(1.72689 + 0.133595i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1601
Dual form 2100.2.bi.j.101.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.979142 - 1.42873i) q^{3} +(0.456468 - 2.60608i) q^{7} +(-1.08256 + 2.79787i) q^{9} +O(q^{10})\) \(q+(-0.979142 - 1.42873i) q^{3} +(0.456468 - 2.60608i) q^{7} +(-1.08256 + 2.79787i) q^{9} +(0.698384 - 0.403212i) q^{11} -3.86649i q^{13} +(1.05989 + 1.83578i) q^{17} +(2.70603 + 1.56233i) q^{19} +(-4.17034 + 1.89955i) q^{21} +(-4.21989 - 2.43635i) q^{23} +(5.05739 - 1.19282i) q^{27} -6.67701i q^{29} +(5.65010 - 3.26209i) q^{31} +(-1.25990 - 0.603003i) q^{33} +(3.89991 - 6.75485i) q^{37} +(-5.52419 + 3.78585i) q^{39} -8.44841 q^{41} +0.819076 q^{43} +(-1.38776 + 2.40368i) q^{47} +(-6.58327 - 2.37918i) q^{49} +(1.58506 - 3.31179i) q^{51} +(-11.5565 + 6.67216i) q^{53} +(-0.417438 - 5.39594i) q^{57} +(2.86351 + 4.95974i) q^{59} +(1.79397 + 1.03575i) q^{61} +(6.79730 + 4.09838i) q^{63} +(5.45110 + 9.44157i) q^{67} +(0.650969 + 8.41464i) q^{69} -10.3850i q^{71} +(-2.67203 + 1.54270i) q^{73} +(-0.732012 - 2.00410i) q^{77} +(6.76342 - 11.7146i) q^{79} +(-6.65612 - 6.05773i) q^{81} -12.8948 q^{83} +(-9.53968 + 6.53775i) q^{87} +(-1.60530 + 2.78046i) q^{89} +(-10.0764 - 1.76493i) q^{91} +(-10.1929 - 4.87844i) q^{93} +1.01388i q^{97} +(0.372090 + 2.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{3} + 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{3} + 5 q^{7} + 3 q^{9} + 6 q^{11} + 6 q^{17} + 3 q^{19} + 12 q^{21} + 24 q^{23} + 8 q^{27} + 15 q^{31} + 4 q^{33} + q^{37} - 21 q^{39} + 8 q^{41} + 26 q^{43} + 14 q^{47} - 13 q^{49} + 40 q^{51} - 24 q^{53} - 18 q^{57} + 42 q^{61} + 49 q^{63} - 7 q^{67} + 14 q^{69} + 3 q^{73} - 26 q^{77} + q^{79} - 13 q^{81} - 8 q^{83} - 8 q^{87} - 28 q^{89} - 11 q^{91} - 25 q^{93} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) −0.979142 1.42873i −0.565308 0.824880i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.456468 2.60608i 0.172529 0.985004i
\(8\) 0 0
\(9\) −1.08256 + 2.79787i −0.360854 + 0.932622i
\(10\) 0 0
\(11\) 0.698384 0.403212i 0.210571 0.121573i −0.391006 0.920388i \(-0.627873\pi\)
0.601577 + 0.798815i \(0.294539\pi\)
\(12\) 0 0
\(13\) 3.86649i 1.07237i −0.844100 0.536186i \(-0.819864\pi\)
0.844100 0.536186i \(-0.180136\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.05989 + 1.83578i 0.257061 + 0.445242i 0.965453 0.260577i \(-0.0839127\pi\)
−0.708393 + 0.705819i \(0.750579\pi\)
\(18\) 0 0
\(19\) 2.70603 + 1.56233i 0.620807 + 0.358423i 0.777183 0.629275i \(-0.216648\pi\)
−0.156376 + 0.987698i \(0.549981\pi\)
\(20\) 0 0
\(21\) −4.17034 + 1.89955i −0.910042 + 0.414515i
\(22\) 0 0
\(23\) −4.21989 2.43635i −0.879908 0.508015i −0.00927994 0.999957i \(-0.502954\pi\)
−0.870628 + 0.491942i \(0.836287\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.05739 1.19282i 0.973295 0.229558i
\(28\) 0 0
\(29\) 6.67701i 1.23989i −0.784645 0.619945i \(-0.787155\pi\)
0.784645 0.619945i \(-0.212845\pi\)
\(30\) 0 0
\(31\) 5.65010 3.26209i 1.01479 0.585888i 0.102198 0.994764i \(-0.467413\pi\)
0.912590 + 0.408876i \(0.134079\pi\)
\(32\) 0 0
\(33\) −1.25990 0.603003i −0.219320 0.104969i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.89991 6.75485i 0.641142 1.11049i −0.344036 0.938956i \(-0.611794\pi\)
0.985178 0.171534i \(-0.0548724\pi\)
\(38\) 0 0
\(39\) −5.52419 + 3.78585i −0.884579 + 0.606221i
\(40\) 0 0
\(41\) −8.44841 −1.31942 −0.659710 0.751520i \(-0.729321\pi\)
−0.659710 + 0.751520i \(0.729321\pi\)
\(42\) 0 0
\(43\) 0.819076 0.124908 0.0624540 0.998048i \(-0.480107\pi\)
0.0624540 + 0.998048i \(0.480107\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.38776 + 2.40368i −0.202426 + 0.350612i −0.949310 0.314343i \(-0.898216\pi\)
0.746883 + 0.664955i \(0.231549\pi\)
\(48\) 0 0
\(49\) −6.58327 2.37918i −0.940468 0.339883i
\(50\) 0 0
\(51\) 1.58506 3.31179i 0.221953 0.463743i
\(52\) 0 0
\(53\) −11.5565 + 6.67216i −1.58741 + 0.916492i −0.593678 + 0.804703i \(0.702325\pi\)
−0.993732 + 0.111789i \(0.964342\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.417438 5.39594i −0.0552910 0.714710i
\(58\) 0 0
\(59\) 2.86351 + 4.95974i 0.372797 + 0.645703i 0.989995 0.141105i \(-0.0450655\pi\)
−0.617198 + 0.786808i \(0.711732\pi\)
\(60\) 0 0
\(61\) 1.79397 + 1.03575i 0.229694 + 0.132614i 0.610431 0.792070i \(-0.290996\pi\)
−0.380737 + 0.924683i \(0.624330\pi\)
\(62\) 0 0
\(63\) 6.79730 + 4.09838i 0.856380 + 0.516347i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.45110 + 9.44157i 0.665957 + 1.15347i 0.979025 + 0.203741i \(0.0653101\pi\)
−0.313067 + 0.949731i \(0.601357\pi\)
\(68\) 0 0
\(69\) 0.650969 + 8.41464i 0.0783674 + 1.01300i
\(70\) 0 0
\(71\) 10.3850i 1.23248i −0.787559 0.616239i \(-0.788656\pi\)
0.787559 0.616239i \(-0.211344\pi\)
\(72\) 0 0
\(73\) −2.67203 + 1.54270i −0.312737 + 0.180559i −0.648151 0.761512i \(-0.724457\pi\)
0.335413 + 0.942071i \(0.391124\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.732012 2.00410i −0.0834205 0.228388i
\(78\) 0 0
\(79\) 6.76342 11.7146i 0.760944 1.31799i −0.181420 0.983406i \(-0.558069\pi\)
0.942364 0.334589i \(-0.108597\pi\)
\(80\) 0 0
\(81\) −6.65612 6.05773i −0.739569 0.673081i
\(82\) 0 0
\(83\) −12.8948 −1.41539 −0.707694 0.706519i \(-0.750265\pi\)
−0.707694 + 0.706519i \(0.750265\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.53968 + 6.53775i −1.02276 + 0.700920i
\(88\) 0 0
\(89\) −1.60530 + 2.78046i −0.170161 + 0.294728i −0.938476 0.345344i \(-0.887762\pi\)
0.768315 + 0.640072i \(0.221096\pi\)
\(90\) 0 0
\(91\) −10.0764 1.76493i −1.05629 0.185015i
\(92\) 0 0
\(93\) −10.1929 4.87844i −1.05695 0.505871i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.01388i 0.102944i 0.998674 + 0.0514721i \(0.0163913\pi\)
−0.998674 + 0.0514721i \(0.983609\pi\)
\(98\) 0 0
\(99\) 0.372090 + 2.39049i 0.0373965 + 0.240253i
\(100\) 0 0
\(101\) −4.27796 7.40965i −0.425673 0.737288i 0.570810 0.821082i \(-0.306629\pi\)
−0.996483 + 0.0837947i \(0.973296\pi\)
\(102\) 0 0
\(103\) −8.46835 4.88921i −0.834411 0.481748i 0.0209492 0.999781i \(-0.493331\pi\)
−0.855361 + 0.518033i \(0.826664\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.8336 + 9.14150i 1.53069 + 0.883743i 0.999330 + 0.0365946i \(0.0116510\pi\)
0.531357 + 0.847148i \(0.321682\pi\)
\(108\) 0 0
\(109\) −8.74840 15.1527i −0.837945 1.45136i −0.891610 0.452804i \(-0.850424\pi\)
0.0536658 0.998559i \(-0.482909\pi\)
\(110\) 0 0
\(111\) −13.4695 + 1.04202i −1.27846 + 0.0989039i
\(112\) 0 0
\(113\) 6.96021i 0.654761i −0.944893 0.327381i \(-0.893834\pi\)
0.944893 0.327381i \(-0.106166\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 10.8179 + 4.18572i 1.00012 + 0.386970i
\(118\) 0 0
\(119\) 5.26799 1.92417i 0.482916 0.176389i
\(120\) 0 0
\(121\) −5.17484 + 8.96309i −0.470440 + 0.814826i
\(122\) 0 0
\(123\) 8.27219 + 12.0705i 0.745879 + 1.08836i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.77139 −0.689600 −0.344800 0.938676i \(-0.612053\pi\)
−0.344800 + 0.938676i \(0.612053\pi\)
\(128\) 0 0
\(129\) −0.801992 1.17024i −0.0706114 0.103034i
\(130\) 0 0
\(131\) −5.93761 + 10.2842i −0.518772 + 0.898539i 0.480990 + 0.876726i \(0.340277\pi\)
−0.999762 + 0.0218131i \(0.993056\pi\)
\(132\) 0 0
\(133\) 5.30677 6.33898i 0.460155 0.549659i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.12894 1.22915i 0.181888 0.105013i −0.406291 0.913744i \(-0.633178\pi\)
0.588179 + 0.808730i \(0.299845\pi\)
\(138\) 0 0
\(139\) 2.81335i 0.238625i 0.992857 + 0.119313i \(0.0380691\pi\)
−0.992857 + 0.119313i \(0.961931\pi\)
\(140\) 0 0
\(141\) 4.79303 0.370796i 0.403646 0.0312267i
\(142\) 0 0
\(143\) −1.55902 2.70030i −0.130372 0.225810i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.04674 + 11.7353i 0.251291 + 0.967912i
\(148\) 0 0
\(149\) −12.8234 7.40357i −1.05053 0.606524i −0.127733 0.991809i \(-0.540770\pi\)
−0.922798 + 0.385285i \(0.874103\pi\)
\(150\) 0 0
\(151\) 0.427898 + 0.741141i 0.0348218 + 0.0603132i 0.882911 0.469540i \(-0.155580\pi\)
−0.848089 + 0.529853i \(0.822247\pi\)
\(152\) 0 0
\(153\) −6.28366 + 0.978080i −0.508004 + 0.0790731i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −21.1042 + 12.1845i −1.68430 + 0.972428i −0.725547 + 0.688173i \(0.758413\pi\)
−0.958748 + 0.284256i \(0.908254\pi\)
\(158\) 0 0
\(159\) 20.8482 + 9.97820i 1.65337 + 0.791323i
\(160\) 0 0
\(161\) −8.27557 + 9.88524i −0.652207 + 0.779066i
\(162\) 0 0
\(163\) 0.789402 1.36728i 0.0618307 0.107094i −0.833453 0.552590i \(-0.813639\pi\)
0.895284 + 0.445496i \(0.146973\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16.9264 −1.30980 −0.654902 0.755714i \(-0.727290\pi\)
−0.654902 + 0.755714i \(0.727290\pi\)
\(168\) 0 0
\(169\) −1.94978 −0.149983
\(170\) 0 0
\(171\) −7.30064 + 5.87980i −0.558294 + 0.449640i
\(172\) 0 0
\(173\) 2.33037 4.03633i 0.177175 0.306876i −0.763737 0.645528i \(-0.776637\pi\)
0.940912 + 0.338652i \(0.109971\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.28237 8.94748i 0.321883 0.672534i
\(178\) 0 0
\(179\) 3.11674 1.79945i 0.232956 0.134497i −0.378979 0.925405i \(-0.623725\pi\)
0.611935 + 0.790908i \(0.290391\pi\)
\(180\) 0 0
\(181\) 22.5821i 1.67851i 0.543737 + 0.839256i \(0.317009\pi\)
−0.543737 + 0.839256i \(0.682991\pi\)
\(182\) 0 0
\(183\) −0.276741 3.57725i −0.0204573 0.264438i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.48042 + 0.854719i 0.108259 + 0.0625033i
\(188\) 0 0
\(189\) −0.800034 13.7244i −0.0581939 0.998305i
\(190\) 0 0
\(191\) −2.92355 1.68791i −0.211541 0.122133i 0.390486 0.920609i \(-0.372307\pi\)
−0.602027 + 0.798475i \(0.705640\pi\)
\(192\) 0 0
\(193\) −5.54524 9.60463i −0.399155 0.691357i 0.594467 0.804120i \(-0.297363\pi\)
−0.993622 + 0.112763i \(0.964030\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2585i 1.15837i −0.815197 0.579184i \(-0.803371\pi\)
0.815197 0.579184i \(-0.196629\pi\)
\(198\) 0 0
\(199\) −1.07964 + 0.623332i −0.0765338 + 0.0441868i −0.537779 0.843086i \(-0.680736\pi\)
0.461245 + 0.887273i \(0.347403\pi\)
\(200\) 0 0
\(201\) 8.15210 17.0328i 0.575005 1.20140i
\(202\) 0 0
\(203\) −17.4008 3.04784i −1.22130 0.213917i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 11.3849 9.16919i 0.791305 0.637303i
\(208\) 0 0
\(209\) 2.51980 0.174298
\(210\) 0 0
\(211\) −7.65466 −0.526968 −0.263484 0.964664i \(-0.584872\pi\)
−0.263484 + 0.964664i \(0.584872\pi\)
\(212\) 0 0
\(213\) −14.8375 + 10.1684i −1.01665 + 0.696730i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.92216 16.2136i −0.402022 1.10065i
\(218\) 0 0
\(219\) 4.82040 + 2.30710i 0.325732 + 0.155899i
\(220\) 0 0
\(221\) 7.09803 4.09805i 0.477465 0.275665i
\(222\) 0 0
\(223\) 20.9369i 1.40204i −0.713143 0.701019i \(-0.752729\pi\)
0.713143 0.701019i \(-0.247271\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.29103 + 3.96818i 0.152061 + 0.263377i 0.931985 0.362497i \(-0.118076\pi\)
−0.779924 + 0.625874i \(0.784742\pi\)
\(228\) 0 0
\(229\) 0.845272 + 0.488018i 0.0558572 + 0.0322492i 0.527669 0.849450i \(-0.323066\pi\)
−0.471811 + 0.881700i \(0.656400\pi\)
\(230\) 0 0
\(231\) −2.14658 + 3.00814i −0.141234 + 0.197921i
\(232\) 0 0
\(233\) 17.2382 + 9.95247i 1.12931 + 0.652008i 0.943762 0.330627i \(-0.107260\pi\)
0.185550 + 0.982635i \(0.440593\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −23.3594 + 1.80712i −1.51736 + 0.117385i
\(238\) 0 0
\(239\) 28.2703i 1.82865i 0.404977 + 0.914327i \(0.367279\pi\)
−0.404977 + 0.914327i \(0.632721\pi\)
\(240\) 0 0
\(241\) 11.0949 6.40567i 0.714688 0.412625i −0.0981065 0.995176i \(-0.531279\pi\)
0.812794 + 0.582551i \(0.197945\pi\)
\(242\) 0 0
\(243\) −2.13760 + 15.4412i −0.137127 + 0.990553i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.04074 10.4629i 0.384363 0.665736i
\(248\) 0 0
\(249\) 12.6258 + 18.4232i 0.800130 + 1.16753i
\(250\) 0 0
\(251\) −10.3349 −0.652335 −0.326167 0.945312i \(-0.605757\pi\)
−0.326167 + 0.945312i \(0.605757\pi\)
\(252\) 0 0
\(253\) −3.92947 −0.247044
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.2527 26.4185i 0.951439 1.64794i 0.209124 0.977889i \(-0.432939\pi\)
0.742315 0.670052i \(-0.233728\pi\)
\(258\) 0 0
\(259\) −15.8235 13.2469i −0.983223 0.823119i
\(260\) 0 0
\(261\) 18.6814 + 7.22828i 1.15635 + 0.447419i
\(262\) 0 0
\(263\) 17.9054 10.3377i 1.10409 0.637447i 0.166799 0.985991i \(-0.446657\pi\)
0.937293 + 0.348543i \(0.113324\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 5.54435 0.428919i 0.339309 0.0262494i
\(268\) 0 0
\(269\) −12.4095 21.4938i −0.756618 1.31050i −0.944566 0.328322i \(-0.893517\pi\)
0.187948 0.982179i \(-0.439816\pi\)
\(270\) 0 0
\(271\) 18.8571 + 10.8871i 1.14548 + 0.661346i 0.947783 0.318916i \(-0.103319\pi\)
0.197702 + 0.980262i \(0.436652\pi\)
\(272\) 0 0
\(273\) 7.34459 + 16.1246i 0.444515 + 0.975905i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.61126 + 13.1831i 0.457316 + 0.792095i 0.998818 0.0486048i \(-0.0154775\pi\)
−0.541502 + 0.840699i \(0.682144\pi\)
\(278\) 0 0
\(279\) 3.01030 + 19.3396i 0.180222 + 1.15783i
\(280\) 0 0
\(281\) 17.9488i 1.07073i −0.844619 0.535367i \(-0.820173\pi\)
0.844619 0.535367i \(-0.179827\pi\)
\(282\) 0 0
\(283\) 23.3730 13.4944i 1.38938 0.802159i 0.396135 0.918192i \(-0.370351\pi\)
0.993245 + 0.116033i \(0.0370178\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.85643 + 22.0172i −0.227638 + 1.29963i
\(288\) 0 0
\(289\) 6.25328 10.8310i 0.367840 0.637117i
\(290\) 0 0
\(291\) 1.44857 0.992735i 0.0849166 0.0581951i
\(292\) 0 0
\(293\) 14.4450 0.843887 0.421944 0.906622i \(-0.361348\pi\)
0.421944 + 0.906622i \(0.361348\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.05104 2.87224i 0.177039 0.166665i
\(298\) 0 0
\(299\) −9.42015 + 16.3162i −0.544782 + 0.943589i
\(300\) 0 0
\(301\) 0.373882 2.13457i 0.0215502 0.123035i
\(302\) 0 0
\(303\) −6.39768 + 13.3672i −0.367537 + 0.767924i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.34543i 0.533372i −0.963783 0.266686i \(-0.914071\pi\)
0.963783 0.266686i \(-0.0859287\pi\)
\(308\) 0 0
\(309\) 1.30635 + 16.8862i 0.0743154 + 0.960625i
\(310\) 0 0
\(311\) 14.6664 + 25.4029i 0.831654 + 1.44047i 0.896726 + 0.442586i \(0.145939\pi\)
−0.0650722 + 0.997881i \(0.520728\pi\)
\(312\) 0 0
\(313\) −9.55728 5.51790i −0.540209 0.311890i 0.204954 0.978772i \(-0.434295\pi\)
−0.745164 + 0.666881i \(0.767629\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.6987 + 8.48631i 0.825563 + 0.476639i 0.852331 0.523003i \(-0.175188\pi\)
−0.0267682 + 0.999642i \(0.508522\pi\)
\(318\) 0 0
\(319\) −2.69225 4.66312i −0.150737 0.261085i
\(320\) 0 0
\(321\) −2.44252 31.5728i −0.136328 1.76222i
\(322\) 0 0
\(323\) 6.62357i 0.368546i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.0832 + 27.3357i −0.723503 + 1.51167i
\(328\) 0 0
\(329\) 5.63070 + 4.71382i 0.310430 + 0.259881i
\(330\) 0 0
\(331\) 5.82739 10.0933i 0.320302 0.554780i −0.660248 0.751048i \(-0.729549\pi\)
0.980550 + 0.196268i \(0.0628822\pi\)
\(332\) 0 0
\(333\) 14.6773 + 18.2240i 0.804310 + 0.998668i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −10.1753 −0.554286 −0.277143 0.960829i \(-0.589388\pi\)
−0.277143 + 0.960829i \(0.589388\pi\)
\(338\) 0 0
\(339\) −9.94428 + 6.81503i −0.540099 + 0.370142i
\(340\) 0 0
\(341\) 2.63063 4.55638i 0.142456 0.246742i
\(342\) 0 0
\(343\) −9.20538 + 16.0705i −0.497044 + 0.867725i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.38025 + 0.796887i −0.0740956 + 0.0427791i −0.536590 0.843843i \(-0.680288\pi\)
0.462494 + 0.886622i \(0.346955\pi\)
\(348\) 0 0
\(349\) 15.4812i 0.828690i −0.910120 0.414345i \(-0.864011\pi\)
0.910120 0.414345i \(-0.135989\pi\)
\(350\) 0 0
\(351\) −4.61202 19.5544i −0.246171 1.04374i
\(352\) 0 0
\(353\) 6.40056 + 11.0861i 0.340668 + 0.590054i 0.984557 0.175065i \(-0.0560136\pi\)
−0.643889 + 0.765119i \(0.722680\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.90724 5.64251i −0.418496 0.298633i
\(358\) 0 0
\(359\) 5.66697 + 3.27183i 0.299091 + 0.172680i 0.642035 0.766676i \(-0.278091\pi\)
−0.342943 + 0.939356i \(0.611424\pi\)
\(360\) 0 0
\(361\) −4.61826 7.99906i −0.243066 0.421003i
\(362\) 0 0
\(363\) 17.8728 1.38266i 0.938077 0.0725710i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 15.0004 8.66046i 0.783012 0.452072i −0.0544847 0.998515i \(-0.517352\pi\)
0.837497 + 0.546442i \(0.184018\pi\)
\(368\) 0 0
\(369\) 9.14593 23.6375i 0.476118 1.23052i
\(370\) 0 0
\(371\) 12.1130 + 33.1628i 0.628875 + 1.72173i
\(372\) 0 0
\(373\) −0.497933 + 0.862445i −0.0257820 + 0.0446557i −0.878629 0.477506i \(-0.841541\pi\)
0.852847 + 0.522162i \(0.174874\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −25.8166 −1.32962
\(378\) 0 0
\(379\) −20.2985 −1.04266 −0.521331 0.853355i \(-0.674564\pi\)
−0.521331 + 0.853355i \(0.674564\pi\)
\(380\) 0 0
\(381\) 7.60930 + 11.1033i 0.389836 + 0.568837i
\(382\) 0 0
\(383\) 9.93736 17.2120i 0.507776 0.879493i −0.492184 0.870491i \(-0.663801\pi\)
0.999959 0.00900178i \(-0.00286539\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.886700 + 2.29167i −0.0450735 + 0.116492i
\(388\) 0 0
\(389\) −1.56923 + 0.905994i −0.0795630 + 0.0459357i −0.539254 0.842143i \(-0.681294\pi\)
0.459691 + 0.888079i \(0.347960\pi\)
\(390\) 0 0
\(391\) 10.3291i 0.522363i
\(392\) 0 0
\(393\) 20.5072 1.58647i 1.03445 0.0800268i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 30.1320 + 17.3967i 1.51228 + 0.873116i 0.999897 + 0.0143590i \(0.00457078\pi\)
0.512384 + 0.858757i \(0.328763\pi\)
\(398\) 0 0
\(399\) −14.2528 1.37520i −0.713532 0.0688461i
\(400\) 0 0
\(401\) 32.5121 + 18.7709i 1.62358 + 0.937374i 0.985952 + 0.167029i \(0.0534173\pi\)
0.637627 + 0.770345i \(0.279916\pi\)
\(402\) 0 0
\(403\) −12.6128 21.8461i −0.628290 1.08823i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.28997i 0.311782i
\(408\) 0 0
\(409\) 3.24769 1.87505i 0.160588 0.0927154i −0.417552 0.908653i \(-0.637112\pi\)
0.578140 + 0.815937i \(0.303779\pi\)
\(410\) 0 0
\(411\) −3.84066 1.83819i −0.189446 0.0906710i
\(412\) 0 0
\(413\) 14.2326 5.19856i 0.700339 0.255804i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.01953 2.75467i 0.196837 0.134897i
\(418\) 0 0
\(419\) 30.0547 1.46827 0.734134 0.679005i \(-0.237589\pi\)
0.734134 + 0.679005i \(0.237589\pi\)
\(420\) 0 0
\(421\) 20.5447 1.00129 0.500643 0.865654i \(-0.333097\pi\)
0.500643 + 0.865654i \(0.333097\pi\)
\(422\) 0 0
\(423\) −5.22283 6.48491i −0.253943 0.315307i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.51813 4.20243i 0.170254 0.203370i
\(428\) 0 0
\(429\) −2.33151 + 4.87140i −0.112566 + 0.235193i
\(430\) 0 0
\(431\) 31.7400 18.3251i 1.52886 0.882688i 0.529451 0.848340i \(-0.322398\pi\)
0.999410 0.0343478i \(-0.0109354\pi\)
\(432\) 0 0
\(433\) 36.4397i 1.75118i 0.483057 + 0.875589i \(0.339526\pi\)
−0.483057 + 0.875589i \(0.660474\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.61278 13.1857i −0.364168 0.630758i
\(438\) 0 0
\(439\) −7.96135 4.59649i −0.379975 0.219378i 0.297833 0.954618i \(-0.403736\pi\)
−0.677807 + 0.735240i \(0.737070\pi\)
\(440\) 0 0
\(441\) 13.7834 15.8435i 0.656354 0.754453i
\(442\) 0 0
\(443\) 20.7332 + 11.9703i 0.985063 + 0.568727i 0.903795 0.427966i \(-0.140770\pi\)
0.0812683 + 0.996692i \(0.474103\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.97816 + 25.5703i 0.0935636 + 1.20943i
\(448\) 0 0
\(449\) 24.0126i 1.13322i −0.823985 0.566611i \(-0.808254\pi\)
0.823985 0.566611i \(-0.191746\pi\)
\(450\) 0 0
\(451\) −5.90023 + 3.40650i −0.277831 + 0.160406i
\(452\) 0 0
\(453\) 0.639920 1.33703i 0.0300661 0.0628193i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.33585 5.77786i 0.156044 0.270277i −0.777394 0.629013i \(-0.783459\pi\)
0.933439 + 0.358737i \(0.116792\pi\)
\(458\) 0 0
\(459\) 7.55001 + 8.02000i 0.352404 + 0.374342i
\(460\) 0 0
\(461\) −26.6895 −1.24305 −0.621527 0.783393i \(-0.713487\pi\)
−0.621527 + 0.783393i \(0.713487\pi\)
\(462\) 0 0
\(463\) −10.9550 −0.509123 −0.254562 0.967057i \(-0.581931\pi\)
−0.254562 + 0.967057i \(0.581931\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.549726 0.952153i 0.0254383 0.0440604i −0.853026 0.521868i \(-0.825235\pi\)
0.878464 + 0.477808i \(0.158569\pi\)
\(468\) 0 0
\(469\) 27.0937 9.89620i 1.25107 0.456964i
\(470\) 0 0
\(471\) 38.0724 + 18.2219i 1.75428 + 0.839620i
\(472\) 0 0
\(473\) 0.572029 0.330261i 0.0263019 0.0151854i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.15717 39.5566i −0.281917 1.81117i
\(478\) 0 0
\(479\) −6.91657 11.9798i −0.316026 0.547373i 0.663629 0.748062i \(-0.269015\pi\)
−0.979655 + 0.200689i \(0.935682\pi\)
\(480\) 0 0
\(481\) −26.1176 15.0790i −1.19086 0.687543i
\(482\) 0 0
\(483\) 22.2263 + 2.14454i 1.01133 + 0.0975799i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −15.8416 27.4385i −0.717854 1.24336i −0.961849 0.273582i \(-0.911791\pi\)
0.243995 0.969776i \(-0.421542\pi\)
\(488\) 0 0
\(489\) −2.72642 + 0.210920i −0.123293 + 0.00953813i
\(490\) 0 0
\(491\) 37.3388i 1.68508i −0.538636 0.842538i \(-0.681060\pi\)
0.538636 0.842538i \(-0.318940\pi\)
\(492\) 0 0
\(493\) 12.2575 7.07689i 0.552051 0.318727i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.0642 4.74044i −1.21400 0.212638i
\(498\) 0 0
\(499\) 5.50065 9.52740i 0.246243 0.426505i −0.716237 0.697857i \(-0.754137\pi\)
0.962480 + 0.271352i \(0.0874706\pi\)
\(500\) 0 0
\(501\) 16.5734 + 24.1833i 0.740443 + 1.08043i
\(502\) 0 0
\(503\) 20.2246 0.901772 0.450886 0.892582i \(-0.351108\pi\)
0.450886 + 0.892582i \(0.351108\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.90911 + 2.78572i 0.0847867 + 0.123718i
\(508\) 0 0
\(509\) −5.24557 + 9.08560i −0.232506 + 0.402712i −0.958545 0.284941i \(-0.908026\pi\)
0.726039 + 0.687654i \(0.241359\pi\)
\(510\) 0 0
\(511\) 2.80069 + 7.66771i 0.123895 + 0.339199i
\(512\) 0 0
\(513\) 15.5490 + 4.67351i 0.686507 + 0.206340i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2.23825i 0.0984383i
\(518\) 0 0
\(519\) −8.04860 + 0.622652i −0.353295 + 0.0273314i
\(520\) 0 0
\(521\) 6.00130 + 10.3946i 0.262922 + 0.455394i 0.967017 0.254712i \(-0.0819806\pi\)
−0.704095 + 0.710105i \(0.748647\pi\)
\(522\) 0 0
\(523\) 7.74038 + 4.46891i 0.338463 + 0.195412i 0.659592 0.751624i \(-0.270729\pi\)
−0.321129 + 0.947035i \(0.604062\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.9769 + 6.91489i 0.521724 + 0.301217i
\(528\) 0 0
\(529\) 0.371651 + 0.643719i 0.0161587 + 0.0279878i
\(530\) 0 0
\(531\) −16.9766 + 2.64249i −0.736723 + 0.114674i
\(532\) 0 0
\(533\) 32.6657i 1.41491i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.62266 2.69107i −0.242636 0.116128i
\(538\) 0 0
\(539\) −5.55697 + 0.992874i −0.239356 + 0.0427661i
\(540\) 0 0
\(541\) −15.9695 + 27.6599i −0.686581 + 1.18919i 0.286357 + 0.958123i \(0.407556\pi\)
−0.972937 + 0.231069i \(0.925778\pi\)
\(542\) 0 0
\(543\) 32.2638 22.1110i 1.38457 0.948876i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 33.6313 1.43797 0.718984 0.695026i \(-0.244607\pi\)
0.718984 + 0.695026i \(0.244607\pi\)
\(548\) 0 0
\(549\) −4.83996 + 3.89802i −0.206565 + 0.166363i
\(550\) 0 0
\(551\) 10.4317 18.0682i 0.444405 0.769732i
\(552\) 0 0
\(553\) −27.4418 22.9733i −1.16695 0.976926i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.17988 + 5.30000i −0.388964 + 0.224568i −0.681711 0.731621i \(-0.738764\pi\)
0.292747 + 0.956190i \(0.405431\pi\)
\(558\) 0 0
\(559\) 3.16695i 0.133948i
\(560\) 0 0
\(561\) −0.228372 2.95201i −0.00964188 0.124634i
\(562\) 0 0
\(563\) 1.14796 + 1.98833i 0.0483808 + 0.0837980i 0.889202 0.457515i \(-0.151261\pi\)
−0.840821 + 0.541313i \(0.817927\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −18.8252 + 14.5812i −0.790585 + 0.612353i
\(568\) 0 0
\(569\) −24.1648 13.9515i −1.01304 0.584878i −0.100959 0.994891i \(-0.532191\pi\)
−0.912080 + 0.410012i \(0.865524\pi\)
\(570\) 0 0
\(571\) 3.11649 + 5.39791i 0.130421 + 0.225896i 0.923839 0.382782i \(-0.125034\pi\)
−0.793418 + 0.608677i \(0.791700\pi\)
\(572\) 0 0
\(573\) 0.450993 + 5.82969i 0.0188405 + 0.243539i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.4776 + 6.62662i −0.477820 + 0.275870i −0.719508 0.694484i \(-0.755632\pi\)
0.241687 + 0.970354i \(0.422299\pi\)
\(578\) 0 0
\(579\) −8.29289 + 17.3270i −0.344641 + 0.720084i
\(580\) 0 0
\(581\) −5.88606 + 33.6048i −0.244195 + 1.39416i
\(582\) 0 0
\(583\) −5.38059 + 9.31946i −0.222841 + 0.385973i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.6209 −0.768568 −0.384284 0.923215i \(-0.625552\pi\)
−0.384284 + 0.923215i \(0.625552\pi\)
\(588\) 0 0
\(589\) 20.3858 0.839982
\(590\) 0 0
\(591\) −23.2290 + 15.9193i −0.955514 + 0.654834i
\(592\) 0 0
\(593\) 1.37822 2.38715i 0.0565967 0.0980284i −0.836339 0.548213i \(-0.815308\pi\)
0.892936 + 0.450184i \(0.148642\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.94770 + 0.932191i 0.0797140 + 0.0381520i
\(598\) 0 0
\(599\) 16.2530 9.38368i 0.664080 0.383407i −0.129750 0.991547i \(-0.541417\pi\)
0.793830 + 0.608140i \(0.208084\pi\)
\(600\) 0 0
\(601\) 16.5669i 0.675779i 0.941186 + 0.337890i \(0.109713\pi\)
−0.941186 + 0.337890i \(0.890287\pi\)
\(602\) 0 0
\(603\) −32.3174 + 5.03035i −1.31607 + 0.204852i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −28.9773 16.7301i −1.17615 0.679053i −0.221032 0.975266i \(-0.570943\pi\)
−0.955122 + 0.296213i \(0.904276\pi\)
\(608\) 0 0
\(609\) 12.6833 + 27.8454i 0.513954 + 1.12835i
\(610\) 0 0
\(611\) 9.29381 + 5.36578i 0.375987 + 0.217076i
\(612\) 0 0
\(613\) −18.7772 32.5231i −0.758404 1.31359i −0.943664 0.330905i \(-0.892646\pi\)
0.185260 0.982690i \(-0.440687\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22.5088i 0.906172i −0.891467 0.453086i \(-0.850323\pi\)
0.891467 0.453086i \(-0.149677\pi\)
\(618\) 0 0
\(619\) −23.3812 + 13.4991i −0.939770 + 0.542576i −0.889888 0.456179i \(-0.849218\pi\)
−0.0498816 + 0.998755i \(0.515884\pi\)
\(620\) 0 0
\(621\) −24.2478 7.28804i −0.973029 0.292459i
\(622\) 0 0
\(623\) 6.51332 + 5.45272i 0.260951 + 0.218459i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.46724 3.60012i −0.0985322 0.143775i
\(628\) 0 0
\(629\) 16.5339 0.659249
\(630\) 0 0
\(631\) 9.17965 0.365436 0.182718 0.983165i \(-0.441510\pi\)
0.182718 + 0.983165i \(0.441510\pi\)
\(632\) 0 0
\(633\) 7.49499 + 10.9365i 0.297899 + 0.434686i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −9.19909 + 25.4542i −0.364481 + 1.00853i
\(638\) 0 0
\(639\) 29.0560 + 11.2425i 1.14944 + 0.444745i
\(640\) 0 0
\(641\) 26.6664 15.3959i 1.05326 0.608100i 0.129700 0.991553i \(-0.458599\pi\)
0.923560 + 0.383453i \(0.125265\pi\)
\(642\) 0 0
\(643\) 3.42929i 0.135238i 0.997711 + 0.0676189i \(0.0215402\pi\)
−0.997711 + 0.0676189i \(0.978460\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25.2967 + 43.8152i 0.994516 + 1.72255i 0.587828 + 0.808986i \(0.299983\pi\)
0.406689 + 0.913567i \(0.366683\pi\)
\(648\) 0 0
\(649\) 3.99966 + 2.30920i 0.157000 + 0.0906441i
\(650\) 0 0
\(651\) −17.3663 + 24.3366i −0.680640 + 0.953828i
\(652\) 0 0
\(653\) −4.57643 2.64220i −0.179090 0.103397i 0.407775 0.913082i \(-0.366305\pi\)
−0.586865 + 0.809685i \(0.699638\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.42362 9.14605i −0.0555408 0.356821i
\(658\) 0 0
\(659\) 26.0502i 1.01477i 0.861719 + 0.507385i \(0.169388\pi\)
−0.861719 + 0.507385i \(0.830612\pi\)
\(660\) 0 0
\(661\) −28.3751 + 16.3823i −1.10366 + 0.637199i −0.937180 0.348845i \(-0.886574\pi\)
−0.166481 + 0.986045i \(0.553241\pi\)
\(662\) 0 0
\(663\) −12.8050 6.12863i −0.497305 0.238016i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −16.2676 + 28.1763i −0.629883 + 1.09099i
\(668\) 0 0
\(669\) −29.9132 + 20.5002i −1.15651 + 0.792583i
\(670\) 0 0
\(671\) 1.67050 0.0644891
\(672\) 0 0
\(673\) 38.5194 1.48481 0.742406 0.669950i \(-0.233685\pi\)
0.742406 + 0.669950i \(0.233685\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.58044 + 16.5938i −0.368206 + 0.637752i −0.989285 0.145996i \(-0.953361\pi\)
0.621079 + 0.783748i \(0.286695\pi\)
\(678\) 0 0
\(679\) 2.64225 + 0.462805i 0.101400 + 0.0177608i
\(680\) 0 0
\(681\) 3.42623 7.15868i 0.131293 0.274321i
\(682\) 0 0
\(683\) −25.0821 + 14.4812i −0.959741 + 0.554107i −0.896093 0.443866i \(-0.853607\pi\)
−0.0636479 + 0.997972i \(0.520273\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.130393 1.68551i −0.00497482 0.0643062i
\(688\) 0 0
\(689\) 25.7979 + 44.6832i 0.982821 + 1.70230i
\(690\) 0 0
\(691\) 39.4572 + 22.7806i 1.50102 + 0.866616i 0.999999 + 0.00118303i \(0.000376571\pi\)
0.501024 + 0.865433i \(0.332957\pi\)
\(692\) 0 0
\(693\) 6.39964 + 0.121486i 0.243102 + 0.00461485i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −8.95437 15.5094i −0.339171 0.587461i
\(698\) 0 0
\(699\) −2.65920 34.3737i −0.100580 1.30013i
\(700\) 0 0
\(701\) 39.2878i 1.48388i −0.670466 0.741940i \(-0.733906\pi\)
0.670466 0.741940i \(-0.266094\pi\)
\(702\) 0 0
\(703\) 21.1066 12.1859i 0.796050 0.459600i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.2629 + 7.76643i −0.799672 + 0.292087i
\(708\) 0 0
\(709\) −9.88537 + 17.1220i −0.371253 + 0.643029i −0.989759 0.142752i \(-0.954405\pi\)
0.618506 + 0.785780i \(0.287738\pi\)
\(710\) 0 0
\(711\) 25.4540 + 31.6049i 0.954601 + 1.18528i
\(712\) 0 0
\(713\) −31.7904 −1.19056
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 40.3907 27.6806i 1.50842 1.03375i
\(718\) 0 0
\(719\) −0.740641 + 1.28283i −0.0276212 + 0.0478414i −0.879506 0.475889i \(-0.842127\pi\)
0.851884 + 0.523730i \(0.175460\pi\)
\(720\) 0 0
\(721\) −16.6072 + 19.8374i −0.618484 + 0.738784i
\(722\) 0 0
\(723\) −20.0155 9.57966i −0.744385 0.356271i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 6.35193i 0.235580i 0.993039 + 0.117790i \(0.0375810\pi\)
−0.993039 + 0.117790i \(0.962419\pi\)
\(728\) 0 0
\(729\) 24.1544 12.0651i 0.894607 0.446855i
\(730\) 0 0
\(731\) 0.868129 + 1.50364i 0.0321089 + 0.0556142i
\(732\) 0 0
\(733\) 34.0100 + 19.6357i 1.25619 + 0.725261i 0.972331 0.233605i \(-0.0750524\pi\)
0.283857 + 0.958866i \(0.408386\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.61392 + 4.39590i 0.280462 + 0.161925i
\(738\) 0 0
\(739\) 11.2904 + 19.5555i 0.415324 + 0.719362i 0.995462 0.0951558i \(-0.0303349\pi\)
−0.580139 + 0.814518i \(0.697002\pi\)
\(740\) 0 0
\(741\) −20.8634 + 1.61402i −0.766436 + 0.0592926i
\(742\) 0 0
\(743\) 26.6330i 0.977070i −0.872544 0.488535i \(-0.837532\pi\)
0.872544 0.488535i \(-0.162468\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 13.9594 36.0779i 0.510748 1.32002i
\(748\) 0 0
\(749\) 31.0510 37.0906i 1.13458 1.35526i
\(750\) 0 0
\(751\) 8.62709 14.9426i 0.314807 0.545262i −0.664589 0.747209i \(-0.731393\pi\)
0.979396 + 0.201947i \(0.0647268\pi\)
\(752\) 0 0
\(753\) 10.1194 + 14.7659i 0.368770 + 0.538098i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −25.1712 −0.914863 −0.457431 0.889245i \(-0.651230\pi\)
−0.457431 + 0.889245i \(0.651230\pi\)
\(758\) 0 0
\(759\) 3.84751 + 5.61417i 0.139656 + 0.203781i
\(760\) 0 0
\(761\) −0.00796126 + 0.0137893i −0.000288596 + 0.000499862i −0.866170 0.499750i \(-0.833425\pi\)
0.865881 + 0.500250i \(0.166759\pi\)
\(762\) 0 0
\(763\) −43.4824 + 15.8823i −1.57417 + 0.574977i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 19.1768 11.0717i 0.692435 0.399777i
\(768\) 0 0
\(769\) 13.0356i 0.470075i −0.971986 0.235037i \(-0.924479\pi\)
0.971986 0.235037i \(-0.0755213\pi\)
\(770\) 0 0
\(771\) −52.6796 + 4.07537i −1.89721 + 0.146771i
\(772\) 0 0
\(773\) 14.7085 + 25.4758i 0.529027 + 0.916301i 0.999427 + 0.0338481i \(0.0107762\pi\)
−0.470400 + 0.882453i \(0.655890\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −3.43280 + 35.5781i −0.123151 + 1.27636i
\(778\) 0 0
\(779\) −22.8617 13.1992i −0.819105 0.472910i
\(780\) 0 0
\(781\) −4.18738 7.25275i −0.149836 0.259524i
\(782\) 0 0
\(783\) −7.96445 33.7683i −0.284626 1.20678i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.95977 + 1.13148i −0.0698584 + 0.0403327i −0.534522 0.845154i \(-0.679508\pi\)
0.464664 + 0.885487i \(0.346175\pi\)
\(788\) 0 0
\(789\) −32.3017 15.4600i −1.14997 0.550389i
\(790\) 0 0
\(791\) −18.1388 3.17711i −0.644943 0.112965i
\(792\) 0 0
\(793\) 4.00471 6.93636i 0.142211 0.246318i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19.6277 −0.695250 −0.347625 0.937634i \(-0.613012\pi\)
−0.347625 + 0.937634i \(0.613012\pi\)
\(798\) 0 0
\(799\) −5.88350 −0.208143
\(800\) 0 0
\(801\) −6.04152 7.50143i −0.213467 0.265050i
\(802\) 0 0
\(803\) −1.24407 + 2.15479i −0.0439022 + 0.0760409i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −18.5583 + 38.7753i −0.653284 + 1.36496i
\(808\) 0 0
\(809\) −21.2506 + 12.2690i −0.747130 + 0.431356i −0.824656 0.565635i \(-0.808631\pi\)
0.0775260 + 0.996990i \(0.475298\pi\)
\(810\) 0 0
\(811\) 38.7927i 1.36220i −0.732192 0.681098i \(-0.761503\pi\)
0.732192 0.681098i \(-0.238497\pi\)
\(812\) 0 0
\(813\) −2.90893 37.6018i −0.102021 1.31875i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.21645 + 1.27967i 0.0775436 + 0.0447698i
\(818\) 0 0
\(819\) 15.8464 26.2817i 0.553716 0.918358i
\(820\) 0 0
\(821\) 11.8734 + 6.85513i 0.414386 + 0.239246i 0.692672 0.721252i \(-0.256433\pi\)
−0.278287 + 0.960498i \(0.589767\pi\)
\(822\) 0 0
\(823\) 4.04168 + 7.00040i 0.140884 + 0.244019i 0.927830 0.373004i \(-0.121672\pi\)
−0.786946 + 0.617022i \(0.788339\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 37.6581i 1.30950i −0.755845 0.654751i \(-0.772774\pi\)
0.755845 0.654751i \(-0.227226\pi\)
\(828\) 0 0
\(829\) 15.4475 8.91864i 0.536515 0.309757i −0.207150 0.978309i \(-0.566419\pi\)
0.743665 + 0.668552i \(0.233086\pi\)
\(830\) 0 0
\(831\) 11.3826 23.7826i 0.394859 0.825008i
\(832\) 0 0
\(833\) −2.60988 14.6071i −0.0904269 0.506106i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 24.6837 23.2372i 0.853193 0.803194i
\(838\) 0 0
\(839\) 4.49497 0.155183 0.0775917 0.996985i \(-0.475277\pi\)
0.0775917 + 0.996985i \(0.475277\pi\)
\(840\) 0 0
\(841\) −15.5825 −0.537329
\(842\) 0 0
\(843\) −25.6440 + 17.5744i −0.883228 + 0.605295i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 20.9963 + 17.5774i 0.721443 + 0.603966i
\(848\) 0 0
\(849\) −42.1654 20.1809i −1.44711 0.692605i
\(850\) 0 0
\(851\) −32.9144 + 19.0032i −1.12829 + 0.651420i
\(852\) 0 0
\(853\) 33.0503i 1.13162i 0.824535 + 0.565811i \(0.191437\pi\)
−0.824535 + 0.565811i \(0.808563\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.210762 + 0.365051i 0.00719949 + 0.0124699i 0.869603 0.493752i \(-0.164375\pi\)
−0.862403 + 0.506222i \(0.831042\pi\)
\(858\) 0 0
\(859\) −17.0294 9.83192i −0.581035 0.335461i 0.180509 0.983573i \(-0.442225\pi\)
−0.761545 + 0.648112i \(0.775559\pi\)
\(860\) 0 0
\(861\) 35.2327 16.0482i 1.20073 0.546920i
\(862\) 0 0
\(863\) 0.782575 + 0.451820i 0.0266392 + 0.0153801i 0.513260 0.858233i \(-0.328437\pi\)
−0.486621 + 0.873613i \(0.661771\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −21.5974 + 1.67081i −0.733488 + 0.0567437i
\(868\) 0 0
\(869\) 10.9084i 0.370041i
\(870\) 0 0
\(871\) 36.5058 21.0766i 1.23695 0.714154i
\(872\) 0 0
\(873\) −2.83671 1.09759i −0.0960080 0.0371478i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −7.65916 + 13.2661i −0.258632 + 0.447963i −0.965876 0.259006i \(-0.916605\pi\)
0.707244 + 0.706970i \(0.249938\pi\)
\(878\) 0 0
\(879\) −14.1437 20.6381i −0.477056 0.696106i
\(880\) 0 0
\(881\) −43.8614 −1.47773 −0.738863 0.673855i \(-0.764637\pi\)
−0.738863 + 0.673855i \(0.764637\pi\)
\(882\) 0 0
\(883\) 2.91300 0.0980304 0.0490152 0.998798i \(-0.484392\pi\)
0.0490152 + 0.998798i \(0.484392\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.44790 12.9001i 0.250076 0.433145i −0.713470 0.700685i \(-0.752878\pi\)
0.963547 + 0.267541i \(0.0862110\pi\)
\(888\) 0 0
\(889\) −3.54739 + 20.2528i −0.118976 + 0.679259i
\(890\) 0 0
\(891\) −7.09108 1.54679i −0.237560 0.0518195i
\(892\) 0 0
\(893\) −7.51067 + 4.33629i −0.251335 + 0.145108i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 32.5352 2.51697i 1.08632 0.0840391i
\(898\) 0 0
\(899\) −21.7810 37.7258i −0.726437 1.25823i
\(900\) 0 0
\(901\) −24.4972 14.1435i −0.816121 0.471188i
\(902\) 0 0
\(903\) −3.41582 + 1.55587i −0.113671 + 0.0517762i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 9.54899 + 16.5393i 0.317069 + 0.549180i 0.979875 0.199611i \(-0.0639679\pi\)
−0.662806 + 0.748791i \(0.730635\pi\)
\(908\) 0 0
\(909\) 25.3624 3.94777i 0.841217 0.130939i
\(910\) 0 0
\(911\) 6.16915i 0.204393i −0.994764 0.102197i \(-0.967413\pi\)
0.994764 0.102197i \(-0.0325871\pi\)
\(912\) 0 0
\(913\) −9.00552 + 5.19934i −0.298039 + 0.172073i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 24.0912 + 20.1683i 0.795562 + 0.666016i
\(918\) 0 0
\(919\) −14.8318 + 25.6894i −0.489255 + 0.847415i −0.999924 0.0123630i \(-0.996065\pi\)
0.510668 + 0.859778i \(0.329398\pi\)
\(920\) 0 0
\(921\) −13.3521 + 9.15051i −0.439968 + 0.301519i
\(922\) 0 0
\(923\) −40.1537 −1.32168
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 22.8469 18.4005i 0.750389 0.604350i
\(928\) 0 0
\(929\) 16.8256 29.1428i 0.552030 0.956144i −0.446098 0.894984i \(-0.647187\pi\)
0.998128 0.0611601i \(-0.0194800\pi\)
\(930\) 0 0
\(931\) −14.0975 16.7234i −0.462027 0.548087i
\(932\) 0 0
\(933\) 21.9335 45.8274i 0.718072 1.50032i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 7.99276i 0.261112i −0.991441 0.130556i \(-0.958324\pi\)
0.991441 0.130556i \(-0.0416762\pi\)
\(938\) 0 0
\(939\) 1.47433 + 19.0576i 0.0481128 + 0.621922i
\(940\) 0 0
\(941\) −8.69431 15.0590i −0.283426 0.490909i 0.688800 0.724951i \(-0.258138\pi\)
−0.972226 + 0.234043i \(0.924804\pi\)
\(942\) 0 0
\(943\) 35.6514 + 20.5833i 1.16097 + 0.670285i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.6302 + 21.1485i 1.19032 + 0.687233i 0.958380 0.285496i \(-0.0921583\pi\)
0.231943 + 0.972729i \(0.425492\pi\)
\(948\) 0 0
\(949\) 5.96483 + 10.3314i 0.193627 + 0.335371i
\(950\) 0 0
\(951\) −2.26746 29.3099i −0.0735273 0.950438i
\(952\) 0 0
\(953\) 40.5612i 1.31391i −0.753932 0.656953i \(-0.771845\pi\)
0.753932 0.656953i \(-0.228155\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −4.02626 + 8.41237i −0.130150 + 0.271933i
\(958\) 0 0
\(959\) −2.23145 6.10926i −0.0720574 0.197278i
\(960\) 0 0
\(961\) 5.78241 10.0154i 0.186529 0.323078i
\(962\) 0 0
\(963\) −42.7175 + 34.4039i −1.37655 + 1.10865i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 37.6713 1.21143 0.605714 0.795682i \(-0.292888\pi\)
0.605714 + 0.795682i \(0.292888\pi\)
\(968\) 0 0
\(969\) 9.46333 6.48542i 0.304006 0.208342i
\(970\) 0 0
\(971\) −21.5452 + 37.3173i −0.691418 + 1.19757i 0.279956 + 0.960013i \(0.409680\pi\)
−0.971373 + 0.237558i \(0.923653\pi\)
\(972\) 0 0
\(973\) 7.33180 + 1.28420i 0.235047 + 0.0411697i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 19.7402 11.3970i 0.631545 0.364622i −0.149805 0.988716i \(-0.547865\pi\)
0.781350 + 0.624093i \(0.214531\pi\)
\(978\) 0 0
\(979\) 2.58910i 0.0827481i
\(980\) 0 0
\(981\) 51.8658 8.07315i 1.65595 0.257756i
\(982\) 0 0
\(983\) −22.5929 39.1321i −0.720602 1.24812i −0.960759 0.277385i \(-0.910532\pi\)
0.240157 0.970734i \(-0.422801\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.22154 12.6603i 0.0388822 0.402981i
\(988\) 0 0
\(989\) −3.45641 1.99556i −0.109907 0.0634551i
\(990\) 0 0
\(991\) −25.2760 43.7793i −0.802919 1.39070i −0.917687 0.397304i \(-0.869946\pi\)
0.114768 0.993392i \(-0.463388\pi\)
\(992\) 0 0
\(993\) −20.1265 + 1.55702i −0.638696 + 0.0494105i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 22.5635 13.0271i 0.714595 0.412571i −0.0981654 0.995170i \(-0.531297\pi\)
0.812760 + 0.582599i \(0.197964\pi\)
\(998\) 0 0
\(999\) 11.6661 38.8138i 0.369099 1.22801i
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.bi.j.1601.2 10
3.2 odd 2 2100.2.bi.k.1601.4 10
5.2 odd 4 2100.2.bo.g.1349.2 20
5.3 odd 4 2100.2.bo.g.1349.9 20
5.4 even 2 420.2.bh.b.341.4 yes 10
7.3 odd 6 2100.2.bi.k.101.4 10
15.2 even 4 2100.2.bo.h.1349.8 20
15.8 even 4 2100.2.bo.h.1349.3 20
15.14 odd 2 420.2.bh.a.341.2 yes 10
21.17 even 6 inner 2100.2.bi.j.101.2 10
35.3 even 12 2100.2.bo.h.1949.8 20
35.9 even 6 2940.2.d.a.881.2 10
35.17 even 12 2100.2.bo.h.1949.3 20
35.19 odd 6 2940.2.d.b.881.9 10
35.24 odd 6 420.2.bh.a.101.2 10
105.17 odd 12 2100.2.bo.g.1949.9 20
105.38 odd 12 2100.2.bo.g.1949.2 20
105.44 odd 6 2940.2.d.b.881.10 10
105.59 even 6 420.2.bh.b.101.4 yes 10
105.89 even 6 2940.2.d.a.881.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
420.2.bh.a.101.2 10 35.24 odd 6
420.2.bh.a.341.2 yes 10 15.14 odd 2
420.2.bh.b.101.4 yes 10 105.59 even 6
420.2.bh.b.341.4 yes 10 5.4 even 2
2100.2.bi.j.101.2 10 21.17 even 6 inner
2100.2.bi.j.1601.2 10 1.1 even 1 trivial
2100.2.bi.k.101.4 10 7.3 odd 6
2100.2.bi.k.1601.4 10 3.2 odd 2
2100.2.bo.g.1349.2 20 5.2 odd 4
2100.2.bo.g.1349.9 20 5.3 odd 4
2100.2.bo.g.1949.2 20 105.38 odd 12
2100.2.bo.g.1949.9 20 105.17 odd 12
2100.2.bo.h.1349.3 20 15.8 even 4
2100.2.bo.h.1349.8 20 15.2 even 4
2100.2.bo.h.1949.3 20 35.17 even 12
2100.2.bo.h.1949.8 20 35.3 even 12
2940.2.d.a.881.1 10 105.89 even 6
2940.2.d.a.881.2 10 35.9 even 6
2940.2.d.b.881.9 10 35.19 odd 6
2940.2.d.b.881.10 10 105.44 odd 6