Properties

Label 1134.2.d.b.1133.11
Level $1134$
Weight $2$
Character 1134.1133
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(1133,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.1133");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.d (of order \(2\), degree \(1\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + 26533 x^{8} - 38796 x^{7} + 47500 x^{6} - 47396 x^{5} + 38144 x^{4} + \cdots + 457 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1133.11
Root \(0.500000 - 1.61238i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.b.1133.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} -1.57315 q^{5} +(0.858719 + 2.50252i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} -1.57315 q^{5} +(0.858719 + 2.50252i) q^{7} -1.00000i q^{8} -1.57315i q^{10} +0.835475i q^{11} +4.55675i q^{13} +(-2.50252 + 0.858719i) q^{14} +1.00000 q^{16} -0.258822 q^{17} -2.46595i q^{19} +1.57315 q^{20} -0.835475 q^{22} -5.07812i q^{23} -2.52520 q^{25} -4.55675 q^{26} +(-0.858719 - 2.50252i) q^{28} -2.91359i q^{29} +9.98331i q^{31} +1.00000i q^{32} -0.258822i q^{34} +(-1.35089 - 3.93684i) q^{35} +0.400597 q^{37} +2.46595 q^{38} +1.57315i q^{40} -9.82060 q^{41} -6.15623 q^{43} -0.835475i q^{44} +5.07812 q^{46} -10.6904 q^{47} +(-5.52520 + 4.29792i) q^{49} -2.52520i q^{50} -4.55675i q^{52} +8.19615i q^{53} -1.31433i q^{55} +(2.50252 - 0.858719i) q^{56} +2.91359 q^{58} -1.83197 q^{59} -0.703333i q^{61} -9.98331 q^{62} -1.00000 q^{64} -7.16844i q^{65} -8.46651 q^{67} +0.258822 q^{68} +(3.93684 - 1.35089i) q^{70} -4.76784i q^{71} -7.72981i q^{73} +0.400597i q^{74} +2.46595i q^{76} +(-2.09079 + 0.717439i) q^{77} +12.9917 q^{79} -1.57315 q^{80} -9.82060i q^{82} -5.42278 q^{83} +0.407165 q^{85} -6.15623i q^{86} +0.835475 q^{88} +6.03377 q^{89} +(-11.4033 + 3.91297i) q^{91} +5.07812i q^{92} -10.6904i q^{94} +3.87931i q^{95} +1.15163i q^{97} +(-4.29792 - 5.52520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 8 q^{7} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{37} + 64 q^{43} - 32 q^{49} - 48 q^{58} - 16 q^{64} - 16 q^{67} - 24 q^{70} + 32 q^{79} - 48 q^{85} + 24 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.57315 −0.703534 −0.351767 0.936088i \(-0.614419\pi\)
−0.351767 + 0.936088i \(0.614419\pi\)
\(6\) 0 0
\(7\) 0.858719 + 2.50252i 0.324565 + 0.945863i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.57315i 0.497473i
\(11\) 0.835475i 0.251905i 0.992036 + 0.125953i \(0.0401987\pi\)
−0.992036 + 0.125953i \(0.959801\pi\)
\(12\) 0 0
\(13\) 4.55675i 1.26381i 0.775044 + 0.631907i \(0.217727\pi\)
−0.775044 + 0.631907i \(0.782273\pi\)
\(14\) −2.50252 + 0.858719i −0.668826 + 0.229502i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.258822 −0.0627735 −0.0313868 0.999507i \(-0.509992\pi\)
−0.0313868 + 0.999507i \(0.509992\pi\)
\(18\) 0 0
\(19\) 2.46595i 0.565728i −0.959160 0.282864i \(-0.908715\pi\)
0.959160 0.282864i \(-0.0912846\pi\)
\(20\) 1.57315 0.351767
\(21\) 0 0
\(22\) −0.835475 −0.178124
\(23\) 5.07812i 1.05886i −0.848354 0.529430i \(-0.822406\pi\)
0.848354 0.529430i \(-0.177594\pi\)
\(24\) 0 0
\(25\) −2.52520 −0.505040
\(26\) −4.55675 −0.893651
\(27\) 0 0
\(28\) −0.858719 2.50252i −0.162283 0.472932i
\(29\) 2.91359i 0.541040i −0.962714 0.270520i \(-0.912804\pi\)
0.962714 0.270520i \(-0.0871957\pi\)
\(30\) 0 0
\(31\) 9.98331i 1.79305i 0.442988 + 0.896527i \(0.353918\pi\)
−0.442988 + 0.896527i \(0.646082\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0.258822i 0.0443876i
\(35\) −1.35089 3.93684i −0.228343 0.665447i
\(36\) 0 0
\(37\) 0.400597 0.0658578 0.0329289 0.999458i \(-0.489517\pi\)
0.0329289 + 0.999458i \(0.489517\pi\)
\(38\) 2.46595 0.400030
\(39\) 0 0
\(40\) 1.57315i 0.248737i
\(41\) −9.82060 −1.53372 −0.766860 0.641814i \(-0.778182\pi\)
−0.766860 + 0.641814i \(0.778182\pi\)
\(42\) 0 0
\(43\) −6.15623 −0.938817 −0.469408 0.882981i \(-0.655533\pi\)
−0.469408 + 0.882981i \(0.655533\pi\)
\(44\) 0.835475i 0.125953i
\(45\) 0 0
\(46\) 5.07812 0.748727
\(47\) −10.6904 −1.55936 −0.779679 0.626179i \(-0.784618\pi\)
−0.779679 + 0.626179i \(0.784618\pi\)
\(48\) 0 0
\(49\) −5.52520 + 4.29792i −0.789315 + 0.613989i
\(50\) 2.52520i 0.357117i
\(51\) 0 0
\(52\) 4.55675i 0.631907i
\(53\) 8.19615i 1.12583i 0.826515 + 0.562914i \(0.190320\pi\)
−0.826515 + 0.562914i \(0.809680\pi\)
\(54\) 0 0
\(55\) 1.31433i 0.177224i
\(56\) 2.50252 0.858719i 0.334413 0.114751i
\(57\) 0 0
\(58\) 2.91359 0.382573
\(59\) −1.83197 −0.238502 −0.119251 0.992864i \(-0.538049\pi\)
−0.119251 + 0.992864i \(0.538049\pi\)
\(60\) 0 0
\(61\) 0.703333i 0.0900525i −0.998986 0.0450263i \(-0.985663\pi\)
0.998986 0.0450263i \(-0.0143371\pi\)
\(62\) −9.98331 −1.26788
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 7.16844i 0.889136i
\(66\) 0 0
\(67\) −8.46651 −1.03435 −0.517174 0.855880i \(-0.673016\pi\)
−0.517174 + 0.855880i \(0.673016\pi\)
\(68\) 0.258822 0.0313868
\(69\) 0 0
\(70\) 3.93684 1.35089i 0.470542 0.161463i
\(71\) 4.76784i 0.565839i −0.959144 0.282919i \(-0.908697\pi\)
0.959144 0.282919i \(-0.0913029\pi\)
\(72\) 0 0
\(73\) 7.72981i 0.904706i −0.891839 0.452353i \(-0.850585\pi\)
0.891839 0.452353i \(-0.149415\pi\)
\(74\) 0.400597i 0.0465685i
\(75\) 0 0
\(76\) 2.46595i 0.282864i
\(77\) −2.09079 + 0.717439i −0.238268 + 0.0817598i
\(78\) 0 0
\(79\) 12.9917 1.46168 0.730841 0.682548i \(-0.239128\pi\)
0.730841 + 0.682548i \(0.239128\pi\)
\(80\) −1.57315 −0.175883
\(81\) 0 0
\(82\) 9.82060i 1.08450i
\(83\) −5.42278 −0.595227 −0.297614 0.954686i \(-0.596191\pi\)
−0.297614 + 0.954686i \(0.596191\pi\)
\(84\) 0 0
\(85\) 0.407165 0.0441633
\(86\) 6.15623i 0.663844i
\(87\) 0 0
\(88\) 0.835475 0.0890620
\(89\) 6.03377 0.639579 0.319789 0.947489i \(-0.396388\pi\)
0.319789 + 0.947489i \(0.396388\pi\)
\(90\) 0 0
\(91\) −11.4033 + 3.91297i −1.19539 + 0.410190i
\(92\) 5.07812i 0.529430i
\(93\) 0 0
\(94\) 10.6904i 1.10263i
\(95\) 3.87931i 0.398009i
\(96\) 0 0
\(97\) 1.15163i 0.116930i 0.998289 + 0.0584649i \(0.0186206\pi\)
−0.998289 + 0.0584649i \(0.981379\pi\)
\(98\) −4.29792 5.52520i −0.434156 0.558130i
\(99\) 0 0
\(100\) 2.52520 0.252520
\(101\) −18.6059 −1.85136 −0.925679 0.378309i \(-0.876506\pi\)
−0.925679 + 0.378309i \(0.876506\pi\)
\(102\) 0 0
\(103\) 3.66394i 0.361019i 0.983573 + 0.180509i \(0.0577746\pi\)
−0.983573 + 0.180509i \(0.942225\pi\)
\(104\) 4.55675 0.446826
\(105\) 0 0
\(106\) −8.19615 −0.796081
\(107\) 3.48137i 0.336556i 0.985740 + 0.168278i \(0.0538207\pi\)
−0.985740 + 0.168278i \(0.946179\pi\)
\(108\) 0 0
\(109\) 17.6692 1.69240 0.846202 0.532862i \(-0.178883\pi\)
0.846202 + 0.532862i \(0.178883\pi\)
\(110\) 1.31433 0.125316
\(111\) 0 0
\(112\) 0.858719 + 2.50252i 0.0811414 + 0.236466i
\(113\) 14.2808i 1.34343i 0.740811 + 0.671714i \(0.234442\pi\)
−0.740811 + 0.671714i \(0.765558\pi\)
\(114\) 0 0
\(115\) 7.98863i 0.744944i
\(116\) 2.91359i 0.270520i
\(117\) 0 0
\(118\) 1.83197i 0.168647i
\(119\) −0.222255 0.647707i −0.0203741 0.0593752i
\(120\) 0 0
\(121\) 10.3020 0.936544
\(122\) 0.703333 0.0636767
\(123\) 0 0
\(124\) 9.98331i 0.896527i
\(125\) 11.8383 1.05885
\(126\) 0 0
\(127\) 2.82327 0.250524 0.125262 0.992124i \(-0.460023\pi\)
0.125262 + 0.992124i \(0.460023\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 7.16844 0.628714
\(131\) 18.6059 1.62561 0.812803 0.582538i \(-0.197940\pi\)
0.812803 + 0.582538i \(0.197940\pi\)
\(132\) 0 0
\(133\) 6.17109 2.11756i 0.535102 0.183616i
\(134\) 8.46651i 0.731395i
\(135\) 0 0
\(136\) 0.258822i 0.0221938i
\(137\) 17.6227i 1.50561i 0.658242 + 0.752806i \(0.271300\pi\)
−0.658242 + 0.752806i \(0.728700\pi\)
\(138\) 0 0
\(139\) 2.02144i 0.171456i 0.996319 + 0.0857282i \(0.0273217\pi\)
−0.996319 + 0.0857282i \(0.972678\pi\)
\(140\) 1.35089 + 3.93684i 0.114171 + 0.332723i
\(141\) 0 0
\(142\) 4.76784 0.400108
\(143\) −3.80705 −0.318361
\(144\) 0 0
\(145\) 4.58351i 0.380640i
\(146\) 7.72981 0.639724
\(147\) 0 0
\(148\) −0.400597 −0.0329289
\(149\) 21.6505i 1.77367i −0.462082 0.886837i \(-0.652898\pi\)
0.462082 0.886837i \(-0.347102\pi\)
\(150\) 0 0
\(151\) −17.5235 −1.42604 −0.713020 0.701144i \(-0.752673\pi\)
−0.713020 + 0.701144i \(0.752673\pi\)
\(152\) −2.46595 −0.200015
\(153\) 0 0
\(154\) −0.717439 2.09079i −0.0578129 0.168481i
\(155\) 15.7052i 1.26147i
\(156\) 0 0
\(157\) 10.8493i 0.865872i −0.901425 0.432936i \(-0.857478\pi\)
0.901425 0.432936i \(-0.142522\pi\)
\(158\) 12.9917i 1.03356i
\(159\) 0 0
\(160\) 1.57315i 0.124368i
\(161\) 12.7081 4.36068i 1.00154 0.343669i
\(162\) 0 0
\(163\) −11.6376 −0.911527 −0.455764 0.890101i \(-0.650634\pi\)
−0.455764 + 0.890101i \(0.650634\pi\)
\(164\) 9.82060 0.766860
\(165\) 0 0
\(166\) 5.42278i 0.420889i
\(167\) 11.1349 0.861647 0.430823 0.902436i \(-0.358223\pi\)
0.430823 + 0.902436i \(0.358223\pi\)
\(168\) 0 0
\(169\) −7.76393 −0.597225
\(170\) 0.407165i 0.0312282i
\(171\) 0 0
\(172\) 6.15623 0.469408
\(173\) 7.80295 0.593247 0.296623 0.954995i \(-0.404139\pi\)
0.296623 + 0.954995i \(0.404139\pi\)
\(174\) 0 0
\(175\) −2.16844 6.31937i −0.163919 0.477699i
\(176\) 0.835475i 0.0629763i
\(177\) 0 0
\(178\) 6.03377i 0.452251i
\(179\) 15.9956i 1.19557i 0.801657 + 0.597784i \(0.203952\pi\)
−0.801657 + 0.597784i \(0.796048\pi\)
\(180\) 0 0
\(181\) 1.92154i 0.142827i 0.997447 + 0.0714135i \(0.0227510\pi\)
−0.997447 + 0.0714135i \(0.977249\pi\)
\(182\) −3.91297 11.4033i −0.290048 0.845272i
\(183\) 0 0
\(184\) −5.07812 −0.374364
\(185\) −0.630200 −0.0463332
\(186\) 0 0
\(187\) 0.216239i 0.0158130i
\(188\) 10.6904 0.779679
\(189\) 0 0
\(190\) −3.87931 −0.281435
\(191\) 5.92580i 0.428776i −0.976749 0.214388i \(-0.931224\pi\)
0.976749 0.214388i \(-0.0687757\pi\)
\(192\) 0 0
\(193\) 2.98450 0.214829 0.107414 0.994214i \(-0.465743\pi\)
0.107414 + 0.994214i \(0.465743\pi\)
\(194\) −1.15163 −0.0826819
\(195\) 0 0
\(196\) 5.52520 4.29792i 0.394657 0.306995i
\(197\) 1.00657i 0.0717150i −0.999357 0.0358575i \(-0.988584\pi\)
0.999357 0.0358575i \(-0.0114162\pi\)
\(198\) 0 0
\(199\) 17.6170i 1.24884i 0.781090 + 0.624418i \(0.214664\pi\)
−0.781090 + 0.624418i \(0.785336\pi\)
\(200\) 2.52520i 0.178559i
\(201\) 0 0
\(202\) 18.6059i 1.30911i
\(203\) 7.29132 2.50196i 0.511750 0.175603i
\(204\) 0 0
\(205\) 15.4493 1.07902
\(206\) −3.66394 −0.255279
\(207\) 0 0
\(208\) 4.55675i 0.315953i
\(209\) 2.06024 0.142510
\(210\) 0 0
\(211\) 2.87540 0.197950 0.0989752 0.995090i \(-0.468444\pi\)
0.0989752 + 0.995090i \(0.468444\pi\)
\(212\) 8.19615i 0.562914i
\(213\) 0 0
\(214\) −3.48137 −0.237981
\(215\) 9.68467 0.660489
\(216\) 0 0
\(217\) −24.9834 + 8.57286i −1.69598 + 0.581964i
\(218\) 17.6692i 1.19671i
\(219\) 0 0
\(220\) 1.31433i 0.0886119i
\(221\) 1.17939i 0.0793340i
\(222\) 0 0
\(223\) 17.3380i 1.16104i 0.814248 + 0.580518i \(0.197150\pi\)
−0.814248 + 0.580518i \(0.802850\pi\)
\(224\) −2.50252 + 0.858719i −0.167207 + 0.0573756i
\(225\) 0 0
\(226\) −14.2808 −0.949947
\(227\) 15.0151 0.996588 0.498294 0.867008i \(-0.333960\pi\)
0.498294 + 0.867008i \(0.333960\pi\)
\(228\) 0 0
\(229\) 18.7484i 1.23893i −0.785024 0.619465i \(-0.787350\pi\)
0.785024 0.619465i \(-0.212650\pi\)
\(230\) −7.98863 −0.526755
\(231\) 0 0
\(232\) −2.91359 −0.191287
\(233\) 12.6099i 0.826101i 0.910708 + 0.413051i \(0.135537\pi\)
−0.910708 + 0.413051i \(0.864463\pi\)
\(234\) 0 0
\(235\) 16.8176 1.09706
\(236\) 1.83197 0.119251
\(237\) 0 0
\(238\) 0.647707 0.222255i 0.0419846 0.0144067i
\(239\) 24.5429i 1.58755i 0.608213 + 0.793774i \(0.291887\pi\)
−0.608213 + 0.793774i \(0.708113\pi\)
\(240\) 0 0
\(241\) 18.0653i 1.16369i −0.813300 0.581844i \(-0.802331\pi\)
0.813300 0.581844i \(-0.197669\pi\)
\(242\) 10.3020i 0.662236i
\(243\) 0 0
\(244\) 0.703333i 0.0450263i
\(245\) 8.69197 6.76127i 0.555309 0.431962i
\(246\) 0 0
\(247\) 11.2367 0.714975
\(248\) 9.98331 0.633941
\(249\) 0 0
\(250\) 11.8383i 0.748718i
\(251\) −17.7361 −1.11949 −0.559747 0.828664i \(-0.689102\pi\)
−0.559747 + 0.828664i \(0.689102\pi\)
\(252\) 0 0
\(253\) 4.24264 0.266733
\(254\) 2.82327i 0.177148i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −31.3140 −1.95331 −0.976657 0.214805i \(-0.931088\pi\)
−0.976657 + 0.214805i \(0.931088\pi\)
\(258\) 0 0
\(259\) 0.344001 + 1.00250i 0.0213752 + 0.0622925i
\(260\) 7.16844i 0.444568i
\(261\) 0 0
\(262\) 18.6059i 1.14948i
\(263\) 24.1918i 1.49173i 0.666098 + 0.745864i \(0.267963\pi\)
−0.666098 + 0.745864i \(0.732037\pi\)
\(264\) 0 0
\(265\) 12.8938i 0.792058i
\(266\) 2.11756 + 6.17109i 0.129836 + 0.378374i
\(267\) 0 0
\(268\) 8.46651 0.517174
\(269\) 25.8912 1.57862 0.789308 0.613998i \(-0.210440\pi\)
0.789308 + 0.613998i \(0.210440\pi\)
\(270\) 0 0
\(271\) 29.8768i 1.81489i 0.420176 + 0.907443i \(0.361968\pi\)
−0.420176 + 0.907443i \(0.638032\pi\)
\(272\) −0.258822 −0.0156934
\(273\) 0 0
\(274\) −17.6227 −1.06463
\(275\) 2.10974i 0.127222i
\(276\) 0 0
\(277\) −25.5113 −1.53282 −0.766412 0.642350i \(-0.777960\pi\)
−0.766412 + 0.642350i \(0.777960\pi\)
\(278\) −2.02144 −0.121238
\(279\) 0 0
\(280\) −3.93684 + 1.35089i −0.235271 + 0.0807313i
\(281\) 9.01221i 0.537623i 0.963193 + 0.268812i \(0.0866309\pi\)
−0.963193 + 0.268812i \(0.913369\pi\)
\(282\) 0 0
\(283\) 5.07817i 0.301866i 0.988544 + 0.150933i \(0.0482278\pi\)
−0.988544 + 0.150933i \(0.951772\pi\)
\(284\) 4.76784i 0.282919i
\(285\) 0 0
\(286\) 3.80705i 0.225115i
\(287\) −8.43314 24.5762i −0.497793 1.45069i
\(288\) 0 0
\(289\) −16.9330 −0.996059
\(290\) −4.58351 −0.269153
\(291\) 0 0
\(292\) 7.72981i 0.452353i
\(293\) 20.6339 1.20545 0.602723 0.797950i \(-0.294082\pi\)
0.602723 + 0.797950i \(0.294082\pi\)
\(294\) 0 0
\(295\) 2.88196 0.167794
\(296\) 0.400597i 0.0232843i
\(297\) 0 0
\(298\) 21.6505 1.25418
\(299\) 23.1397 1.33820
\(300\) 0 0
\(301\) −5.28648 15.4061i −0.304707 0.887992i
\(302\) 17.5235i 1.00836i
\(303\) 0 0
\(304\) 2.46595i 0.141432i
\(305\) 1.10645i 0.0633550i
\(306\) 0 0
\(307\) 21.8254i 1.24564i 0.782366 + 0.622819i \(0.214013\pi\)
−0.782366 + 0.622819i \(0.785987\pi\)
\(308\) 2.09079 0.717439i 0.119134 0.0408799i
\(309\) 0 0
\(310\) 15.7052 0.891997
\(311\) −0.289372 −0.0164088 −0.00820440 0.999966i \(-0.502612\pi\)
−0.00820440 + 0.999966i \(0.502612\pi\)
\(312\) 0 0
\(313\) 18.8915i 1.06781i 0.845544 + 0.533906i \(0.179276\pi\)
−0.845544 + 0.533906i \(0.820724\pi\)
\(314\) 10.8493 0.612264
\(315\) 0 0
\(316\) −12.9917 −0.730841
\(317\) 15.0299i 0.844163i −0.906558 0.422082i \(-0.861300\pi\)
0.906558 0.422082i \(-0.138700\pi\)
\(318\) 0 0
\(319\) 2.43423 0.136291
\(320\) 1.57315 0.0879417
\(321\) 0 0
\(322\) 4.36068 + 12.7081i 0.243011 + 0.708194i
\(323\) 0.638242i 0.0355128i
\(324\) 0 0
\(325\) 11.5067i 0.638277i
\(326\) 11.6376i 0.644547i
\(327\) 0 0
\(328\) 9.82060i 0.542252i
\(329\) −9.18007 26.7530i −0.506114 1.47494i
\(330\) 0 0
\(331\) 21.8182 1.19924 0.599620 0.800285i \(-0.295319\pi\)
0.599620 + 0.800285i \(0.295319\pi\)
\(332\) 5.42278 0.297614
\(333\) 0 0
\(334\) 11.1349i 0.609276i
\(335\) 13.3191 0.727699
\(336\) 0 0
\(337\) 9.09032 0.495181 0.247591 0.968865i \(-0.420361\pi\)
0.247591 + 0.968865i \(0.420361\pi\)
\(338\) 7.76393i 0.422302i
\(339\) 0 0
\(340\) −0.407165 −0.0220816
\(341\) −8.34081 −0.451680
\(342\) 0 0
\(343\) −15.5002 10.1362i −0.836934 0.547304i
\(344\) 6.15623i 0.331922i
\(345\) 0 0
\(346\) 7.80295i 0.419489i
\(347\) 14.2826i 0.766728i 0.923597 + 0.383364i \(0.125235\pi\)
−0.923597 + 0.383364i \(0.874765\pi\)
\(348\) 0 0
\(349\) 33.5047i 1.79347i −0.442573 0.896733i \(-0.645934\pi\)
0.442573 0.896733i \(-0.354066\pi\)
\(350\) 6.31937 2.16844i 0.337784 0.115908i
\(351\) 0 0
\(352\) −0.835475 −0.0445310
\(353\) 28.5625 1.52023 0.760113 0.649791i \(-0.225143\pi\)
0.760113 + 0.649791i \(0.225143\pi\)
\(354\) 0 0
\(355\) 7.50053i 0.398087i
\(356\) −6.03377 −0.319789
\(357\) 0 0
\(358\) −15.9956 −0.845395
\(359\) 23.8272i 1.25755i −0.777587 0.628775i \(-0.783557\pi\)
0.777587 0.628775i \(-0.216443\pi\)
\(360\) 0 0
\(361\) 12.9191 0.679952
\(362\) −1.92154 −0.100994
\(363\) 0 0
\(364\) 11.4033 3.91297i 0.597697 0.205095i
\(365\) 12.1601i 0.636491i
\(366\) 0 0
\(367\) 11.2709i 0.588334i 0.955754 + 0.294167i \(0.0950423\pi\)
−0.955754 + 0.294167i \(0.904958\pi\)
\(368\) 5.07812i 0.264715i
\(369\) 0 0
\(370\) 0.630200i 0.0327625i
\(371\) −20.5110 + 7.03820i −1.06488 + 0.365405i
\(372\) 0 0
\(373\) −2.65153 −0.137291 −0.0686455 0.997641i \(-0.521868\pi\)
−0.0686455 + 0.997641i \(0.521868\pi\)
\(374\) 0.216239 0.0111815
\(375\) 0 0
\(376\) 10.6904i 0.551316i
\(377\) 13.2765 0.683774
\(378\) 0 0
\(379\) 14.0820 0.723345 0.361673 0.932305i \(-0.382206\pi\)
0.361673 + 0.932305i \(0.382206\pi\)
\(380\) 3.87931i 0.199004i
\(381\) 0 0
\(382\) 5.92580 0.303190
\(383\) 16.6936 0.853005 0.426503 0.904486i \(-0.359745\pi\)
0.426503 + 0.904486i \(0.359745\pi\)
\(384\) 0 0
\(385\) 3.28913 1.12864i 0.167630 0.0575207i
\(386\) 2.98450i 0.151907i
\(387\) 0 0
\(388\) 1.15163i 0.0584649i
\(389\) 28.7203i 1.45618i 0.685484 + 0.728088i \(0.259591\pi\)
−0.685484 + 0.728088i \(0.740409\pi\)
\(390\) 0 0
\(391\) 1.31433i 0.0664684i
\(392\) 4.29792 + 5.52520i 0.217078 + 0.279065i
\(393\) 0 0
\(394\) 1.00657 0.0507102
\(395\) −20.4379 −1.02834
\(396\) 0 0
\(397\) 23.6343i 1.18617i −0.805139 0.593087i \(-0.797909\pi\)
0.805139 0.593087i \(-0.202091\pi\)
\(398\) −17.6170 −0.883060
\(399\) 0 0
\(400\) −2.52520 −0.126260
\(401\) 9.07546i 0.453207i −0.973987 0.226604i \(-0.927238\pi\)
0.973987 0.226604i \(-0.0727622\pi\)
\(402\) 0 0
\(403\) −45.4914 −2.26609
\(404\) 18.6059 0.925679
\(405\) 0 0
\(406\) 2.50196 + 7.29132i 0.124170 + 0.361862i
\(407\) 0.334689i 0.0165899i
\(408\) 0 0
\(409\) 3.36909i 0.166591i −0.996525 0.0832953i \(-0.973456\pi\)
0.996525 0.0832953i \(-0.0265445\pi\)
\(410\) 15.4493i 0.762985i
\(411\) 0 0
\(412\) 3.66394i 0.180509i
\(413\) −1.57315 4.58454i −0.0774096 0.225591i
\(414\) 0 0
\(415\) 8.53084 0.418763
\(416\) −4.55675 −0.223413
\(417\) 0 0
\(418\) 2.06024i 0.100770i
\(419\) −8.64938 −0.422550 −0.211275 0.977427i \(-0.567762\pi\)
−0.211275 + 0.977427i \(0.567762\pi\)
\(420\) 0 0
\(421\) 32.2112 1.56988 0.784939 0.619573i \(-0.212694\pi\)
0.784939 + 0.619573i \(0.212694\pi\)
\(422\) 2.87540i 0.139972i
\(423\) 0 0
\(424\) 8.19615 0.398040
\(425\) 0.653577 0.0317032
\(426\) 0 0
\(427\) 1.76010 0.603965i 0.0851774 0.0292279i
\(428\) 3.48137i 0.168278i
\(429\) 0 0
\(430\) 9.68467i 0.467036i
\(431\) 27.0725i 1.30404i 0.758204 + 0.652018i \(0.226077\pi\)
−0.758204 + 0.652018i \(0.773923\pi\)
\(432\) 0 0
\(433\) 23.3909i 1.12410i −0.827104 0.562048i \(-0.810013\pi\)
0.827104 0.562048i \(-0.189987\pi\)
\(434\) −8.57286 24.9834i −0.411510 1.19924i
\(435\) 0 0
\(436\) −17.6692 −0.846202
\(437\) −12.5224 −0.599027
\(438\) 0 0
\(439\) 10.0297i 0.478690i −0.970935 0.239345i \(-0.923067\pi\)
0.970935 0.239345i \(-0.0769327\pi\)
\(440\) −1.31433 −0.0626581
\(441\) 0 0
\(442\) 1.17939 0.0560976
\(443\) 3.12697i 0.148567i −0.997237 0.0742835i \(-0.976333\pi\)
0.997237 0.0742835i \(-0.0236670\pi\)
\(444\) 0 0
\(445\) −9.49203 −0.449965
\(446\) −17.3380 −0.820976
\(447\) 0 0
\(448\) −0.858719 2.50252i −0.0405707 0.118233i
\(449\) 18.0633i 0.852458i 0.904615 + 0.426229i \(0.140158\pi\)
−0.904615 + 0.426229i \(0.859842\pi\)
\(450\) 0 0
\(451\) 8.20487i 0.386352i
\(452\) 14.2808i 0.671714i
\(453\) 0 0
\(454\) 15.0151i 0.704694i
\(455\) 17.9392 6.15568i 0.841001 0.288583i
\(456\) 0 0
\(457\) 24.1822 1.13120 0.565598 0.824681i \(-0.308645\pi\)
0.565598 + 0.824681i \(0.308645\pi\)
\(458\) 18.7484 0.876056
\(459\) 0 0
\(460\) 7.98863i 0.372472i
\(461\) −16.7668 −0.780907 −0.390453 0.920623i \(-0.627682\pi\)
−0.390453 + 0.920623i \(0.627682\pi\)
\(462\) 0 0
\(463\) −13.7052 −0.636936 −0.318468 0.947934i \(-0.603168\pi\)
−0.318468 + 0.947934i \(0.603168\pi\)
\(464\) 2.91359i 0.135260i
\(465\) 0 0
\(466\) −12.6099 −0.584142
\(467\) −38.1548 −1.76559 −0.882797 0.469755i \(-0.844342\pi\)
−0.882797 + 0.469755i \(0.844342\pi\)
\(468\) 0 0
\(469\) −7.27035 21.1876i −0.335714 0.978352i
\(470\) 16.8176i 0.775739i
\(471\) 0 0
\(472\) 1.83197i 0.0843233i
\(473\) 5.14338i 0.236493i
\(474\) 0 0
\(475\) 6.22703i 0.285716i
\(476\) 0.222255 + 0.647707i 0.0101871 + 0.0296876i
\(477\) 0 0
\(478\) −24.5429 −1.12257
\(479\) −14.3544 −0.655868 −0.327934 0.944701i \(-0.606352\pi\)
−0.327934 + 0.944701i \(0.606352\pi\)
\(480\) 0 0
\(481\) 1.82542i 0.0832320i
\(482\) 18.0653 0.822852
\(483\) 0 0
\(484\) −10.3020 −0.468272
\(485\) 1.81168i 0.0822641i
\(486\) 0 0
\(487\) 10.3633 0.469607 0.234804 0.972043i \(-0.424555\pi\)
0.234804 + 0.972043i \(0.424555\pi\)
\(488\) −0.703333 −0.0318384
\(489\) 0 0
\(490\) 6.76127 + 8.69197i 0.305443 + 0.392663i
\(491\) 28.3923i 1.28133i 0.767822 + 0.640663i \(0.221341\pi\)
−0.767822 + 0.640663i \(0.778659\pi\)
\(492\) 0 0
\(493\) 0.754101i 0.0339630i
\(494\) 11.2367i 0.505564i
\(495\) 0 0
\(496\) 9.98331i 0.448264i
\(497\) 11.9316 4.09424i 0.535206 0.183652i
\(498\) 0 0
\(499\) −5.40717 −0.242058 −0.121029 0.992649i \(-0.538619\pi\)
−0.121029 + 0.992649i \(0.538619\pi\)
\(500\) −11.8383 −0.529423
\(501\) 0 0
\(502\) 17.7361i 0.791601i
\(503\) −32.3695 −1.44329 −0.721643 0.692266i \(-0.756613\pi\)
−0.721643 + 0.692266i \(0.756613\pi\)
\(504\) 0 0
\(505\) 29.2699 1.30249
\(506\) 4.24264i 0.188608i
\(507\) 0 0
\(508\) −2.82327 −0.125262
\(509\) −5.07061 −0.224751 −0.112375 0.993666i \(-0.535846\pi\)
−0.112375 + 0.993666i \(0.535846\pi\)
\(510\) 0 0
\(511\) 19.3440 6.63774i 0.855728 0.293636i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 31.3140i 1.38120i
\(515\) 5.76393i 0.253989i
\(516\) 0 0
\(517\) 8.93158i 0.392811i
\(518\) −1.00250 + 0.344001i −0.0440474 + 0.0151145i
\(519\) 0 0
\(520\) −7.16844 −0.314357
\(521\) −28.1911 −1.23507 −0.617537 0.786542i \(-0.711869\pi\)
−0.617537 + 0.786542i \(0.711869\pi\)
\(522\) 0 0
\(523\) 29.4515i 1.28782i −0.765100 0.643912i \(-0.777310\pi\)
0.765100 0.643912i \(-0.222690\pi\)
\(524\) −18.6059 −0.812803
\(525\) 0 0
\(526\) −24.1918 −1.05481
\(527\) 2.58390i 0.112556i
\(528\) 0 0
\(529\) −2.78726 −0.121185
\(530\) 12.8938 0.560070
\(531\) 0 0
\(532\) −6.17109 + 2.11756i −0.267551 + 0.0918079i
\(533\) 44.7500i 1.93834i
\(534\) 0 0
\(535\) 5.47671i 0.236779i
\(536\) 8.46651i 0.365697i
\(537\) 0 0
\(538\) 25.8912i 1.11625i
\(539\) −3.59081 4.61617i −0.154667 0.198833i
\(540\) 0 0
\(541\) −22.7052 −0.976174 −0.488087 0.872795i \(-0.662305\pi\)
−0.488087 + 0.872795i \(0.662305\pi\)
\(542\) −29.8768 −1.28332
\(543\) 0 0
\(544\) 0.258822i 0.0110969i
\(545\) −27.7963 −1.19066
\(546\) 0 0
\(547\) 6.70258 0.286582 0.143291 0.989681i \(-0.454232\pi\)
0.143291 + 0.989681i \(0.454232\pi\)
\(548\) 17.6227i 0.752806i
\(549\) 0 0
\(550\) 2.10974 0.0899598
\(551\) −7.18478 −0.306082
\(552\) 0 0
\(553\) 11.1562 + 32.5120i 0.474411 + 1.38255i
\(554\) 25.5113i 1.08387i
\(555\) 0 0
\(556\) 2.02144i 0.0857282i
\(557\) 22.4015i 0.949183i −0.880206 0.474592i \(-0.842596\pi\)
0.880206 0.474592i \(-0.157404\pi\)
\(558\) 0 0
\(559\) 28.0524i 1.18649i
\(560\) −1.35089 3.93684i −0.0570857 0.166362i
\(561\) 0 0
\(562\) −9.01221 −0.380157
\(563\) 38.1740 1.60884 0.804421 0.594059i \(-0.202476\pi\)
0.804421 + 0.594059i \(0.202476\pi\)
\(564\) 0 0
\(565\) 22.4659i 0.945147i
\(566\) −5.07817 −0.213451
\(567\) 0 0
\(568\) −4.76784 −0.200054
\(569\) 6.75955i 0.283375i −0.989911 0.141688i \(-0.954747\pi\)
0.989911 0.141688i \(-0.0452528\pi\)
\(570\) 0 0
\(571\) −17.0484 −0.713453 −0.356727 0.934209i \(-0.616107\pi\)
−0.356727 + 0.934209i \(0.616107\pi\)
\(572\) 3.80705 0.159181
\(573\) 0 0
\(574\) 24.5762 8.43314i 1.02579 0.351993i
\(575\) 12.8233i 0.534767i
\(576\) 0 0
\(577\) 0.919572i 0.0382823i −0.999817 0.0191411i \(-0.993907\pi\)
0.999817 0.0191411i \(-0.00609319\pi\)
\(578\) 16.9330i 0.704320i
\(579\) 0 0
\(580\) 4.58351i 0.190320i
\(581\) −4.65665 13.5706i −0.193190 0.563004i
\(582\) 0 0
\(583\) −6.84768 −0.283602
\(584\) −7.72981 −0.319862
\(585\) 0 0
\(586\) 20.6339i 0.852379i
\(587\) −17.8824 −0.738084 −0.369042 0.929413i \(-0.620314\pi\)
−0.369042 + 0.929413i \(0.620314\pi\)
\(588\) 0 0
\(589\) 24.6184 1.01438
\(590\) 2.88196i 0.118649i
\(591\) 0 0
\(592\) 0.400597 0.0164645
\(593\) 9.75882 0.400747 0.200373 0.979720i \(-0.435785\pi\)
0.200373 + 0.979720i \(0.435785\pi\)
\(594\) 0 0
\(595\) 0.349641 + 1.01894i 0.0143339 + 0.0417724i
\(596\) 21.6505i 0.886837i
\(597\) 0 0
\(598\) 23.1397i 0.946252i
\(599\) 20.1506i 0.823331i −0.911335 0.411665i \(-0.864947\pi\)
0.911335 0.411665i \(-0.135053\pi\)
\(600\) 0 0
\(601\) 15.3831i 0.627490i −0.949507 0.313745i \(-0.898416\pi\)
0.949507 0.313745i \(-0.101584\pi\)
\(602\) 15.4061 5.28648i 0.627905 0.215461i
\(603\) 0 0
\(604\) 17.5235 0.713020
\(605\) −16.2066 −0.658890
\(606\) 0 0
\(607\) 46.3793i 1.88248i 0.337744 + 0.941238i \(0.390336\pi\)
−0.337744 + 0.941238i \(0.609664\pi\)
\(608\) 2.46595 0.100008
\(609\) 0 0
\(610\) −1.10645 −0.0447987
\(611\) 48.7135i 1.97074i
\(612\) 0 0
\(613\) 42.7977 1.72858 0.864292 0.502990i \(-0.167767\pi\)
0.864292 + 0.502990i \(0.167767\pi\)
\(614\) −21.8254 −0.880800
\(615\) 0 0
\(616\) 0.717439 + 2.09079i 0.0289064 + 0.0842404i
\(617\) 10.7464i 0.432634i −0.976323 0.216317i \(-0.930595\pi\)
0.976323 0.216317i \(-0.0694045\pi\)
\(618\) 0 0
\(619\) 14.0650i 0.565320i −0.959220 0.282660i \(-0.908783\pi\)
0.959220 0.282660i \(-0.0912168\pi\)
\(620\) 15.7052i 0.630737i
\(621\) 0 0
\(622\) 0.289372i 0.0116028i
\(623\) 5.18132 + 15.0996i 0.207585 + 0.604954i
\(624\) 0 0
\(625\) −5.99735 −0.239894
\(626\) −18.8915 −0.755057
\(627\) 0 0
\(628\) 10.8493i 0.432936i
\(629\) −0.103683 −0.00413413
\(630\) 0 0
\(631\) 8.27818 0.329549 0.164775 0.986331i \(-0.447310\pi\)
0.164775 + 0.986331i \(0.447310\pi\)
\(632\) 12.9917i 0.516782i
\(633\) 0 0
\(634\) 15.0299 0.596914
\(635\) −4.44142 −0.176252
\(636\) 0 0
\(637\) −19.5845 25.1769i −0.775968 0.997547i
\(638\) 2.43423i 0.0963722i
\(639\) 0 0
\(640\) 1.57315i 0.0621842i
\(641\) 31.0188i 1.22517i 0.790406 + 0.612584i \(0.209870\pi\)
−0.790406 + 0.612584i \(0.790130\pi\)
\(642\) 0 0
\(643\) 4.33672i 0.171024i 0.996337 + 0.0855119i \(0.0272525\pi\)
−0.996337 + 0.0855119i \(0.972747\pi\)
\(644\) −12.7081 + 4.36068i −0.500769 + 0.171835i
\(645\) 0 0
\(646\) −0.638242 −0.0251113
\(647\) −13.6205 −0.535476 −0.267738 0.963492i \(-0.586276\pi\)
−0.267738 + 0.963492i \(0.586276\pi\)
\(648\) 0 0
\(649\) 1.53057i 0.0600800i
\(650\) 11.5067 0.451330
\(651\) 0 0
\(652\) 11.6376 0.455764
\(653\) 38.6016i 1.51060i 0.655381 + 0.755299i \(0.272508\pi\)
−0.655381 + 0.755299i \(0.727492\pi\)
\(654\) 0 0
\(655\) −29.2699 −1.14367
\(656\) −9.82060 −0.383430
\(657\) 0 0
\(658\) 26.7530 9.18007i 1.04294 0.357877i
\(659\) 3.29961i 0.128535i −0.997933 0.0642673i \(-0.979529\pi\)
0.997933 0.0642673i \(-0.0204710\pi\)
\(660\) 0 0
\(661\) 10.2885i 0.400176i −0.979778 0.200088i \(-0.935877\pi\)
0.979778 0.200088i \(-0.0641228\pi\)
\(662\) 21.8182i 0.847990i
\(663\) 0 0
\(664\) 5.42278i 0.210445i
\(665\) −9.70805 + 3.33124i −0.376462 + 0.129180i
\(666\) 0 0
\(667\) −14.7956 −0.572886
\(668\) −11.1349 −0.430823
\(669\) 0 0
\(670\) 13.3191i 0.514561i
\(671\) 0.587617 0.0226847
\(672\) 0 0
\(673\) 3.58063 0.138023 0.0690115 0.997616i \(-0.478015\pi\)
0.0690115 + 0.997616i \(0.478015\pi\)
\(674\) 9.09032i 0.350146i
\(675\) 0 0
\(676\) 7.76393 0.298613
\(677\) −31.1283 −1.19636 −0.598179 0.801362i \(-0.704109\pi\)
−0.598179 + 0.801362i \(0.704109\pi\)
\(678\) 0 0
\(679\) −2.88196 + 0.988923i −0.110600 + 0.0379514i
\(680\) 0.407165i 0.0156141i
\(681\) 0 0
\(682\) 8.34081i 0.319386i
\(683\) 3.51472i 0.134487i −0.997737 0.0672435i \(-0.978580\pi\)
0.997737 0.0672435i \(-0.0214204\pi\)
\(684\) 0 0
\(685\) 27.7232i 1.05925i
\(686\) 10.1362 15.5002i 0.387002 0.591802i
\(687\) 0 0
\(688\) −6.15623 −0.234704
\(689\) −37.3478 −1.42284
\(690\) 0 0
\(691\) 25.2239i 0.959563i −0.877388 0.479782i \(-0.840716\pi\)
0.877388 0.479782i \(-0.159284\pi\)
\(692\) −7.80295 −0.296623
\(693\) 0 0
\(694\) −14.2826 −0.542159
\(695\) 3.18003i 0.120625i
\(696\) 0 0
\(697\) 2.54179 0.0962770
\(698\) 33.5047 1.26817
\(699\) 0 0
\(700\) 2.16844 + 6.31937i 0.0819593 + 0.238850i
\(701\) 20.5291i 0.775374i −0.921791 0.387687i \(-0.873274\pi\)
0.921791 0.387687i \(-0.126726\pi\)
\(702\) 0 0
\(703\) 0.987854i 0.0372576i
\(704\) 0.835475i 0.0314882i
\(705\) 0 0
\(706\) 28.5625i 1.07496i
\(707\) −15.9773 46.5617i −0.600887 1.75113i
\(708\) 0 0
\(709\) 8.79821 0.330424 0.165212 0.986258i \(-0.447169\pi\)
0.165212 + 0.986258i \(0.447169\pi\)
\(710\) −7.50053 −0.281490
\(711\) 0 0
\(712\) 6.03377i 0.226125i
\(713\) 50.6964 1.89859
\(714\) 0 0
\(715\) 5.98905 0.223978
\(716\) 15.9956i 0.597784i
\(717\) 0 0
\(718\) 23.8272 0.889223
\(719\) 1.14886 0.0428451 0.0214226 0.999771i \(-0.493180\pi\)
0.0214226 + 0.999771i \(0.493180\pi\)
\(720\) 0 0
\(721\) −9.16908 + 3.14630i −0.341475 + 0.117174i
\(722\) 12.9191i 0.480798i
\(723\) 0 0
\(724\) 1.92154i 0.0714135i
\(725\) 7.35741i 0.273247i
\(726\) 0 0
\(727\) 10.7200i 0.397581i 0.980042 + 0.198791i \(0.0637014\pi\)
−0.980042 + 0.198791i \(0.936299\pi\)
\(728\) 3.91297 + 11.4033i 0.145024 + 0.422636i
\(729\) 0 0
\(730\) −12.1601 −0.450067
\(731\) 1.59337 0.0589328
\(732\) 0 0
\(733\) 26.1768i 0.966863i −0.875382 0.483431i \(-0.839390\pi\)
0.875382 0.483431i \(-0.160610\pi\)
\(734\) −11.2709 −0.416015
\(735\) 0 0
\(736\) 5.07812 0.187182
\(737\) 7.07356i 0.260558i
\(738\) 0 0
\(739\) −41.6267 −1.53126 −0.765631 0.643280i \(-0.777573\pi\)
−0.765631 + 0.643280i \(0.777573\pi\)
\(740\) 0.630200 0.0231666
\(741\) 0 0
\(742\) −7.03820 20.5110i −0.258380 0.752983i
\(743\) 0.602674i 0.0221100i 0.999939 + 0.0110550i \(0.00351898\pi\)
−0.999939 + 0.0110550i \(0.996481\pi\)
\(744\) 0 0
\(745\) 34.0594i 1.24784i
\(746\) 2.65153i 0.0970794i
\(747\) 0 0
\(748\) 0.216239i 0.00790649i
\(749\) −8.71218 + 2.98952i −0.318336 + 0.109235i
\(750\) 0 0
\(751\) 15.3550 0.560313 0.280157 0.959954i \(-0.409614\pi\)
0.280157 + 0.959954i \(0.409614\pi\)
\(752\) −10.6904 −0.389840
\(753\) 0 0
\(754\) 13.2765i 0.483501i
\(755\) 27.5670 1.00327
\(756\) 0 0
\(757\) 26.1331 0.949823 0.474911 0.880034i \(-0.342480\pi\)
0.474911 + 0.880034i \(0.342480\pi\)
\(758\) 14.0820i 0.511482i
\(759\) 0 0
\(760\) 3.87931 0.140717
\(761\) −16.2258 −0.588183 −0.294092 0.955777i \(-0.595017\pi\)
−0.294092 + 0.955777i \(0.595017\pi\)
\(762\) 0 0
\(763\) 15.1729 + 44.2176i 0.549296 + 1.60078i
\(764\) 5.92580i 0.214388i
\(765\) 0 0
\(766\) 16.6936i 0.603166i
\(767\) 8.34783i 0.301422i
\(768\) 0 0
\(769\) 36.9170i 1.33126i 0.746282 + 0.665630i \(0.231837\pi\)
−0.746282 + 0.665630i \(0.768163\pi\)
\(770\) 1.12864 + 3.28913i 0.0406733 + 0.118532i
\(771\) 0 0
\(772\) −2.98450 −0.107414
\(773\) 18.8576 0.678260 0.339130 0.940740i \(-0.389867\pi\)
0.339130 + 0.940740i \(0.389867\pi\)
\(774\) 0 0
\(775\) 25.2099i 0.905565i
\(776\) 1.15163 0.0413409
\(777\) 0 0
\(778\) −28.7203 −1.02967
\(779\) 24.2171i 0.867669i
\(780\) 0 0
\(781\) 3.98341 0.142538
\(782\) −1.31433 −0.0470002
\(783\) 0 0
\(784\) −5.52520 + 4.29792i −0.197329 + 0.153497i
\(785\) 17.0676i 0.609170i
\(786\) 0 0
\(787\) 13.1760i 0.469673i 0.972035 + 0.234836i \(0.0754554\pi\)
−0.972035 + 0.234836i \(0.924545\pi\)
\(788\) 1.00657i 0.0358575i
\(789\) 0 0
\(790\) 20.4379i 0.727148i
\(791\) −35.7381 + 12.2632i −1.27070 + 0.436030i
\(792\) 0 0
\(793\) 3.20491 0.113810
\(794\) 23.6343 0.838751
\(795\) 0 0
\(796\) 17.6170i 0.624418i
\(797\) −7.80295 −0.276394 −0.138197 0.990405i \(-0.544131\pi\)
−0.138197 + 0.990405i \(0.544131\pi\)
\(798\) 0 0
\(799\) 2.76691 0.0978864
\(800\) 2.52520i 0.0892794i
\(801\) 0 0
\(802\) 9.07546 0.320466
\(803\) 6.45807 0.227900
\(804\) 0 0
\(805\) −19.9917 + 6.86000i −0.704615 + 0.241783i
\(806\) 45.4914i 1.60237i
\(807\) 0 0
\(808\) 18.6059i 0.654554i
\(809\) 1.68815i 0.0593523i 0.999560 + 0.0296762i \(0.00944761\pi\)
−0.999560 + 0.0296762i \(0.990552\pi\)
\(810\) 0 0
\(811\) 40.7131i 1.42963i 0.699314 + 0.714815i \(0.253489\pi\)
−0.699314 + 0.714815i \(0.746511\pi\)
\(812\) −7.29132 + 2.50196i −0.255875 + 0.0878015i
\(813\) 0 0
\(814\) −0.334689 −0.0117309
\(815\) 18.3077 0.641290
\(816\) 0 0
\(817\) 15.1810i 0.531115i
\(818\) 3.36909 0.117797
\(819\) 0 0
\(820\) −15.4493 −0.539512
\(821\) 32.7408i 1.14266i −0.820720 0.571330i \(-0.806427\pi\)
0.820720 0.571330i \(-0.193573\pi\)
\(822\) 0 0
\(823\) −51.6210 −1.79940 −0.899698 0.436514i \(-0.856213\pi\)
−0.899698 + 0.436514i \(0.856213\pi\)
\(824\) 3.66394 0.127639
\(825\) 0 0
\(826\) 4.58454 1.57315i 0.159517 0.0547369i
\(827\) 28.5318i 0.992147i 0.868281 + 0.496073i \(0.165225\pi\)
−0.868281 + 0.496073i \(0.834775\pi\)
\(828\) 0 0
\(829\) 12.1211i 0.420983i 0.977596 + 0.210491i \(0.0675064\pi\)
−0.977596 + 0.210491i \(0.932494\pi\)
\(830\) 8.53084i 0.296110i
\(831\) 0 0
\(832\) 4.55675i 0.157977i
\(833\) 1.43004 1.11240i 0.0495480 0.0385423i
\(834\) 0 0
\(835\) −17.5169 −0.606198
\(836\) −2.06024 −0.0712550
\(837\) 0 0
\(838\) 8.64938i 0.298788i
\(839\) 17.4571 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(840\) 0 0
\(841\) 20.5110 0.707275
\(842\) 32.2112i 1.11007i
\(843\) 0 0
\(844\) −2.87540 −0.0989752
\(845\) 12.2138 0.420168
\(846\) 0 0
\(847\) 8.84651 + 25.7809i 0.303970 + 0.885842i
\(848\) 8.19615i 0.281457i
\(849\) 0 0
\(850\) 0.653577i 0.0224175i
\(851\) 2.03428i 0.0697342i
\(852\) 0 0
\(853\) 28.9338i 0.990676i 0.868700 + 0.495338i \(0.164956\pi\)
−0.868700 + 0.495338i \(0.835044\pi\)
\(854\) 0.603965 + 1.76010i 0.0206673 + 0.0602295i
\(855\) 0 0
\(856\) 3.48137 0.118991
\(857\) 23.0360 0.786895 0.393447 0.919347i \(-0.371282\pi\)
0.393447 + 0.919347i \(0.371282\pi\)
\(858\) 0 0
\(859\) 25.3966i 0.866520i −0.901269 0.433260i \(-0.857363\pi\)
0.901269 0.433260i \(-0.142637\pi\)
\(860\) −9.68467 −0.330245
\(861\) 0 0
\(862\) −27.0725 −0.922092
\(863\) 0.685811i 0.0233453i −0.999932 0.0116726i \(-0.996284\pi\)
0.999932 0.0116726i \(-0.00371560\pi\)
\(864\) 0 0
\(865\) −12.2752 −0.417369
\(866\) 23.3909 0.794856
\(867\) 0 0
\(868\) 24.9834 8.57286i 0.847992 0.290982i
\(869\) 10.8543i 0.368205i
\(870\) 0 0
\(871\) 38.5797i 1.30722i
\(872\) 17.6692i 0.598355i
\(873\) 0 0
\(874\) 12.5224i 0.423576i
\(875\) 10.1657 + 29.6255i 0.343665 + 1.00152i
\(876\) 0 0
\(877\) −29.3236 −0.990187 −0.495094 0.868840i \(-0.664866\pi\)
−0.495094 + 0.868840i \(0.664866\pi\)
\(878\) 10.0297 0.338485
\(879\) 0 0
\(880\) 1.31433i 0.0443060i
\(881\) −4.31752 −0.145461 −0.0727305 0.997352i \(-0.523171\pi\)
−0.0727305 + 0.997352i \(0.523171\pi\)
\(882\) 0 0
\(883\) 12.9773 0.436721 0.218361 0.975868i \(-0.429929\pi\)
0.218361 + 0.975868i \(0.429929\pi\)
\(884\) 1.17939i 0.0396670i
\(885\) 0 0
\(886\) 3.12697 0.105053
\(887\) 3.24897 0.109090 0.0545448 0.998511i \(-0.482629\pi\)
0.0545448 + 0.998511i \(0.482629\pi\)
\(888\) 0 0
\(889\) 2.42439 + 7.06528i 0.0813116 + 0.236962i
\(890\) 9.49203i 0.318173i
\(891\) 0 0
\(892\) 17.3380i 0.580518i
\(893\) 26.3621i 0.882173i
\(894\) 0 0
\(895\) 25.1635i 0.841123i
\(896\) 2.50252 0.858719i 0.0836033 0.0286878i
\(897\) 0 0
\(898\) −18.0633 −0.602779
\(899\) 29.0873 0.970115
\(900\) 0 0
\(901\) 2.12134i 0.0706722i
\(902\) 8.20487 0.273192
\(903\) 0 0
\(904\) 14.2808 0.474974
\(905\) 3.02287i 0.100484i
\(906\) 0 0
\(907\) 22.1395 0.735129 0.367564 0.929998i \(-0.380192\pi\)
0.367564 + 0.929998i \(0.380192\pi\)
\(908\) −15.0151 −0.498294
\(909\) 0 0
\(910\) 6.15568 + 17.9392i 0.204059 + 0.594677i
\(911\) 56.7602i 1.88055i −0.340417 0.940275i \(-0.610568\pi\)
0.340417 0.940275i \(-0.389432\pi\)
\(912\) 0 0
\(913\) 4.53060i 0.149941i
\(914\) 24.1822i 0.799877i
\(915\) 0 0
\(916\) 18.7484i 0.619465i
\(917\) 15.9773 + 46.5617i 0.527616 + 1.53760i
\(918\) 0 0
\(919\) −17.1180 −0.564672 −0.282336 0.959316i \(-0.591109\pi\)
−0.282336 + 0.959316i \(0.591109\pi\)
\(920\) 7.98863 0.263377
\(921\) 0 0
\(922\) 16.7668i 0.552184i
\(923\) 21.7258 0.715115
\(924\) 0 0
\(925\) −1.01159 −0.0332609
\(926\) 13.7052i 0.450382i
\(927\) 0 0
\(928\) 2.91359 0.0956433
\(929\) 8.61166 0.282539 0.141270 0.989971i \(-0.454882\pi\)
0.141270 + 0.989971i \(0.454882\pi\)
\(930\) 0 0
\(931\) 10.5985 + 13.6249i 0.347351 + 0.446538i
\(932\) 12.6099i 0.413051i
\(933\) 0 0
\(934\) 38.1548i 1.24846i
\(935\) 0.340177i 0.0111250i
\(936\) 0 0
\(937\) 59.3424i 1.93863i 0.245820 + 0.969316i \(0.420943\pi\)
−0.245820 + 0.969316i \(0.579057\pi\)
\(938\) 21.1876 7.27035i 0.691799 0.237385i
\(939\) 0 0
\(940\) −16.8176 −0.548531
\(941\) 31.5199 1.02752 0.513760 0.857934i \(-0.328252\pi\)
0.513760 + 0.857934i \(0.328252\pi\)
\(942\) 0 0
\(943\) 49.8702i 1.62400i
\(944\) −1.83197 −0.0596256
\(945\) 0 0
\(946\) 5.14338 0.167226
\(947\) 19.2775i 0.626436i 0.949681 + 0.313218i \(0.101407\pi\)
−0.949681 + 0.313218i \(0.898593\pi\)
\(948\) 0 0
\(949\) 35.2228 1.14338
\(950\) −6.22703 −0.202031
\(951\) 0 0
\(952\) −0.647707 + 0.222255i −0.0209923 + 0.00720334i
\(953\) 24.1146i 0.781148i 0.920572 + 0.390574i \(0.127723\pi\)
−0.920572 + 0.390574i \(0.872277\pi\)
\(954\) 0 0
\(955\) 9.32217i 0.301658i
\(956\) 24.5429i 0.793774i
\(957\) 0 0
\(958\) 14.3544i 0.463768i
\(959\) −44.1012 + 15.1330i −1.42410 + 0.488670i
\(960\) 0 0
\(961\) −68.6664 −2.21505
\(962\) −1.82542 −0.0588539
\(963\) 0 0
\(964\) 18.0653i 0.581844i
\(965\) −4.69506 −0.151139
\(966\) 0 0
\(967\) 36.5196 1.17439 0.587195 0.809446i \(-0.300232\pi\)
0.587195 + 0.809446i \(0.300232\pi\)
\(968\) 10.3020i 0.331118i
\(969\) 0 0
\(970\) 1.81168 0.0581695
\(971\) −0.597949 −0.0191891 −0.00959455 0.999954i \(-0.503054\pi\)
−0.00959455 + 0.999954i \(0.503054\pi\)
\(972\) 0 0
\(973\) −5.05870 + 1.73585i −0.162174 + 0.0556488i
\(974\) 10.3633i 0.332063i
\(975\) 0 0
\(976\) 0.703333i 0.0225131i
\(977\) 16.4167i 0.525217i −0.964902 0.262609i \(-0.915417\pi\)
0.964902 0.262609i \(-0.0845828\pi\)
\(978\) 0 0
\(979\) 5.04107i 0.161113i
\(980\) −8.69197 + 6.76127i −0.277655 + 0.215981i
\(981\) 0 0
\(982\) −28.3923 −0.906035
\(983\) 6.88337 0.219546 0.109773 0.993957i \(-0.464988\pi\)
0.109773 + 0.993957i \(0.464988\pi\)
\(984\) 0 0
\(985\) 1.58348i 0.0504539i
\(986\) −0.754101 −0.0240155
\(987\) 0 0
\(988\) −11.2367 −0.357488
\(989\) 31.2621i 0.994076i
\(990\) 0 0
\(991\) −40.6240 −1.29046 −0.645232 0.763987i \(-0.723239\pi\)
−0.645232 + 0.763987i \(0.723239\pi\)
\(992\) −9.98331 −0.316970
\(993\) 0 0
\(994\) 4.09424 + 11.9316i 0.129861 + 0.378448i
\(995\) 27.7142i 0.878598i
\(996\) 0 0
\(997\) 32.9805i 1.04450i −0.852792 0.522252i \(-0.825092\pi\)
0.852792 0.522252i \(-0.174908\pi\)
\(998\) 5.40717i 0.171161i
\(999\) 0 0
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 1134.2.d.b.1133.11 yes 16
3.2 odd 2 inner 1134.2.d.b.1133.6 yes 16
7.6 odd 2 inner 1134.2.d.b.1133.14 yes 16
9.2 odd 6 1134.2.m.h.377.2 16
9.4 even 3 1134.2.m.h.755.3 16
9.5 odd 6 1134.2.m.i.755.6 16
9.7 even 3 1134.2.m.i.377.7 16
21.20 even 2 inner 1134.2.d.b.1133.3 16
63.13 odd 6 1134.2.m.h.755.2 16
63.20 even 6 1134.2.m.h.377.3 16
63.34 odd 6 1134.2.m.i.377.6 16
63.41 even 6 1134.2.m.i.755.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.d.b.1133.3 16 21.20 even 2 inner
1134.2.d.b.1133.6 yes 16 3.2 odd 2 inner
1134.2.d.b.1133.11 yes 16 1.1 even 1 trivial
1134.2.d.b.1133.14 yes 16 7.6 odd 2 inner
1134.2.m.h.377.2 16 9.2 odd 6
1134.2.m.h.377.3 16 63.20 even 6
1134.2.m.h.755.2 16 63.13 odd 6
1134.2.m.h.755.3 16 9.4 even 3
1134.2.m.i.377.6 16 63.34 odd 6
1134.2.m.i.377.7 16 9.7 even 3
1134.2.m.i.755.6 16 9.5 odd 6
1134.2.m.i.755.7 16 63.41 even 6