Properties

Label 1134.2.d.b.1133.6
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 1133.6
Root \(0.500000 - 0.612384i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.b.1133.14

$q$-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 \(-0.385581\pi\)
0.351767 + 0.936088i \(0.385581\pi\)
\(6\) 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 \(-0.959801\pi\)
0.992036 0.125953i \(-0.0401987\pi\)
\(12\) 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 \(-0.490008\pi\)
0.0313868 + 0.999507i \(0.490008\pi\)
\(18\) 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 \(0.177594\pi\)
−0.848354 + 0.529430i \(0.822406\pi\)
\(24\) 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 \(0.0871957\pi\)
−0.962714 + 0.270520i \(0.912804\pi\)
\(30\) 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 \(-0.221818\pi\)
0.766860 + 0.641814i \(0.221818\pi\)
\(42\) 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 \(-0.215382\pi\)
0.779679 + 0.626179i \(0.215382\pi\)
\(48\) 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 \(-0.809680\pi\)
0.826515 0.562914i \(-0.190320\pi\)
\(54\) 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 \(-0.461951\pi\)
0.119251 + 0.992864i \(0.461951\pi\)
\(60\) 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 \(0.0913029\pi\)
−0.959144 + 0.282919i \(0.908697\pi\)
\(72\) 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 \(-0.403809\pi\)
0.297614 + 0.954686i \(0.403809\pi\)
\(84\) 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 \(-0.603612\pi\)
−0.319789 + 0.947489i \(0.603612\pi\)
\(90\) 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 \(-0.123494\pi\)
0.925679 + 0.378309i \(0.123494\pi\)
\(102\) 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 \(-0.946179\pi\)
0.985740 0.168278i \(-0.0538207\pi\)
\(108\) 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 \(-0.765558\pi\)
0.740811 0.671714i \(-0.234442\pi\)
\(114\) 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 \(-0.802060\pi\)
−0.812803 + 0.582538i \(0.802060\pi\)
\(132\) 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 \(-0.728700\pi\)
0.658242 0.752806i \(-0.271300\pi\)
\(138\) 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 \(0.347102\pi\)
−0.462082 + 0.886837i \(0.652898\pi\)
\(150\) 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 \(-0.641777\pi\)
−0.430823 + 0.902436i \(0.641777\pi\)
\(168\) 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 \(-0.595861\pi\)
−0.296623 + 0.954995i \(0.595861\pi\)
\(174\) 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 \(-0.796048\pi\)
0.801657 0.597784i \(-0.203952\pi\)
\(180\) 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 \(0.0687757\pi\)
−0.976749 + 0.214388i \(0.931224\pi\)
\(192\) 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 \(0.0114162\pi\)
−0.999357 + 0.0358575i \(0.988584\pi\)
\(198\) 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 \(-0.666040\pi\)
−0.498294 + 0.867008i \(0.666040\pi\)
\(228\) 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 \(-0.864463\pi\)
0.910708 0.413051i \(-0.135537\pi\)
\(234\) 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 \(-0.708113\pi\)
0.608213 0.793774i \(-0.291887\pi\)
\(240\) 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 \(-0.310898\pi\)
0.559747 + 0.828664i \(0.310898\pi\)
\(252\) 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 \(-0.0689116\pi\)
0.976657 + 0.214805i \(0.0689116\pi\)
\(258\) 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 \(-0.732037\pi\)
0.666098 0.745864i \(-0.267963\pi\)
\(264\) 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 \(-0.789560\pi\)
−0.789308 + 0.613998i \(0.789560\pi\)
\(270\) 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 \(-0.913369\pi\)
0.963193 0.268812i \(-0.0866309\pi\)
\(282\) 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 \(-0.705918\pi\)
−0.602723 + 0.797950i \(0.705918\pi\)
\(294\) 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 \(-0.497388\pi\)
0.00820440 + 0.999966i \(0.497388\pi\)
\(312\) 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 \(0.138700\pi\)
−0.906558 + 0.422082i \(0.861300\pi\)
\(318\) 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 \(-0.874765\pi\)
0.923597 0.383364i \(-0.125235\pi\)
\(348\) 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 \(-0.774857\pi\)
−0.760113 + 0.649791i \(0.774857\pi\)
\(354\) 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 \(0.216443\pi\)
−0.777587 + 0.628775i \(0.783557\pi\)
\(360\) 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 \(-0.640255\pi\)
−0.426503 + 0.904486i \(0.640255\pi\)
\(384\) 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 \(-0.740409\pi\)
0.685484 0.728088i \(-0.259591\pi\)
\(390\) 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 \(0.0727622\pi\)
−0.973987 + 0.226604i \(0.927238\pi\)
\(402\) 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 \(-0.432238\pi\)
0.211275 + 0.977427i \(0.432238\pi\)
\(420\) 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 \(-0.773923\pi\)
0.758204 0.652018i \(-0.226077\pi\)
\(432\) 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 \(0.0236670\pi\)
−0.997237 + 0.0742835i \(0.976333\pi\)
\(444\) 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 \(-0.859842\pi\)
0.904615 0.426229i \(-0.140158\pi\)
\(450\) 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 \(-0.372318\pi\)
0.390453 + 0.920623i \(0.372318\pi\)
\(462\) 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 \(-0.155658\pi\)
0.882797 + 0.469755i \(0.155658\pi\)
\(468\) 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 \(-0.393648\pi\)
0.327934 + 0.944701i \(0.393648\pi\)
\(480\) 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 \(-0.778659\pi\)
0.767822 0.640663i \(-0.221341\pi\)
\(492\) 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 \(-0.243387\pi\)
0.721643 + 0.692266i \(0.243387\pi\)
\(504\) 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 \(-0.464154\pi\)
0.112375 + 0.993666i \(0.464154\pi\)
\(510\) 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 \(-0.288131\pi\)
0.617537 + 0.786542i \(0.288131\pi\)
\(522\) 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 \(0.157404\pi\)
−0.880206 + 0.474592i \(0.842596\pi\)
\(558\) 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 \(-0.797524\pi\)
−0.804421 + 0.594059i \(0.797524\pi\)
\(564\) 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 \(0.0452528\pi\)
−0.989911 + 0.141688i \(0.954747\pi\)
\(570\) 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 \(-0.379686\pi\)
0.369042 + 0.929413i \(0.379686\pi\)
\(588\) 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 \(-0.564215\pi\)
−0.200373 + 0.979720i \(0.564215\pi\)
\(594\) 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 \(0.135053\pi\)
−0.911335 + 0.411665i \(0.864947\pi\)
\(600\) 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 \(0.0694045\pi\)
−0.976323 + 0.216317i \(0.930595\pi\)
\(618\) 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 \(-0.790130\pi\)
0.790406 0.612584i \(-0.209870\pi\)
\(642\) 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 \(-0.413724\pi\)
0.267738 + 0.963492i \(0.413724\pi\)
\(648\) 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 \(-0.727492\pi\)
0.655381 0.755299i \(-0.272508\pi\)
\(654\) 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 \(0.0204710\pi\)
−0.997933 + 0.0642673i \(0.979529\pi\)
\(660\) 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 \(-0.295891\pi\)
0.598179 + 0.801362i \(0.295891\pi\)
\(678\) 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 \(0.0214204\pi\)
−0.997737 + 0.0672435i \(0.978580\pi\)
\(684\) 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 \(0.126726\pi\)
−0.921791 + 0.387687i \(0.873274\pi\)
\(702\) 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 \(-0.506820\pi\)
−0.0214226 + 0.999771i \(0.506820\pi\)
\(720\) 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 \(-0.996481\pi\)
0.999939 0.0110550i \(-0.00351898\pi\)
\(744\) 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 \(-0.404983\pi\)
0.294092 + 0.955777i \(0.404983\pi\)
\(762\) 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 \(-0.610133\pi\)
−0.339130 + 0.940740i \(0.610133\pi\)
\(774\) 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 \(-0.455869\pi\)
0.138197 + 0.990405i \(0.455869\pi\)
\(798\) 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 \(-0.990552\pi\)
0.999560 0.0296762i \(-0.00944761\pi\)
\(810\) 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 \(0.193573\pi\)
−0.820720 + 0.571330i \(0.806427\pi\)
\(822\) 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 \(-0.834775\pi\)
0.868281 0.496073i \(-0.165225\pi\)
\(828\) 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 \(-0.597435\pi\)
−0.301342 + 0.953516i \(0.597435\pi\)
\(840\) 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 \(-0.628718\pi\)
−0.393447 + 0.919347i \(0.628718\pi\)
\(858\) 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 \(0.00371560\pi\)
−0.999932 + 0.0116726i \(0.996284\pi\)
\(864\) 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 \(-0.476829\pi\)
0.0727305 + 0.997352i \(0.476829\pi\)
\(882\) 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 \(-0.517371\pi\)
−0.0545448 + 0.998511i \(0.517371\pi\)
\(888\) 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 \(0.389432\pi\)
−0.340417 + 0.940275i \(0.610568\pi\)
\(912\) 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 \(-0.545118\pi\)
−0.141270 + 0.989971i \(0.545118\pi\)
\(930\) 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 \(-0.671748\pi\)
−0.513760 + 0.857934i \(0.671748\pi\)
\(942\) 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 \(-0.898593\pi\)
0.949681 0.313218i \(-0.101407\pi\)
\(948\) 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 \(-0.872277\pi\)
0.920572 0.390574i \(-0.127723\pi\)
\(954\) 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 \(-0.496946\pi\)
0.00959455 + 0.999954i \(0.496946\pi\)
\(972\) 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 \(0.0845828\pi\)
−0.964902 + 0.262609i \(0.915417\pi\)
\(978\) 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 \(-0.535012\pi\)
−0.109773 + 0.993957i \(0.535012\pi\)
\(984\) 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.1133.6 yes 16
3.2 odd 2 inner 1134.2.d.b.1133.11 yes 16
7.6 odd 2 inner 1134.2.d.b.1133.3 16
9.2 odd 6 1134.2.m.i.377.7 16
9.4 even 3 1134.2.m.i.755.6 16
9.5 odd 6 1134.2.m.h.755.3 16
9.7 even 3 1134.2.m.h.377.2 16
21.20 even 2 inner 1134.2.d.b.1133.14 yes 16
63.13 odd 6 1134.2.m.i.755.7 16
63.20 even 6 1134.2.m.i.377.6 16
63.34 odd 6 1134.2.m.h.377.3 16
63.41 even 6 1134.2.m.h.755.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.d.b.1133.3 16 7.6 odd 2 inner
1134.2.d.b.1133.6 yes 16 1.1 even 1 trivial
1134.2.d.b.1133.11 yes 16 3.2 odd 2 inner
1134.2.d.b.1133.14 yes 16 21.20 even 2 inner
1134.2.m.h.377.2 16 9.7 even 3
1134.2.m.h.377.3 16 63.34 odd 6
1134.2.m.h.755.2 16 63.41 even 6
1134.2.m.h.755.3 16 9.5 odd 6
1134.2.m.i.377.6 16 63.20 even 6
1134.2.m.i.377.7 16 9.2 odd 6
1134.2.m.i.755.6 16 9.4 even 3
1134.2.m.i.755.7 16 63.13 odd 6