Properties

Label 912.2.f.i.113.3
Level $912$
Weight $2$
Character 912.113
Analytic conductor $7.282$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [912,2,Mod(113,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("912.113");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: 10.0.20322144469993472.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 113.3
Root \(-0.729858 - 1.57077i\) of defining polynomial
Character \(\chi\) \(=\) 912.113
Dual form 912.2.f.i.113.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.729858 - 1.57077i) q^{3} +1.22502i q^{5} +2.80880 q^{7} +(-1.93462 + 2.29287i) q^{9} +O(q^{10})\) \(q+(-0.729858 - 1.57077i) q^{3} +1.22502i q^{5} +2.80880 q^{7} +(-1.93462 + 2.29287i) q^{9} -2.49828i q^{11} -1.86827i q^{13} +(1.92421 - 0.894087i) q^{15} +4.88146i q^{17} +(4.12897 - 1.39700i) q^{19} +(-2.05003 - 4.41197i) q^{21} -0.424059i q^{23} +3.49934 q^{25} +(5.01356 + 1.36536i) q^{27} +3.86923 q^{29} +0.514909i q^{31} +(-3.92421 + 1.82339i) q^{33} +3.44083i q^{35} -5.16750i q^{37} +(-2.93462 + 1.36357i) q^{39} +2.40952 q^{41} -0.420092 q^{43} +(-2.80880 - 2.36993i) q^{45} -10.7405i q^{47} +0.889372 q^{49} +(7.66763 - 3.56277i) q^{51} +7.71766 q^{53} +3.06043 q^{55} +(-5.20792 - 5.46604i) q^{57} +3.63841 q^{59} -1.85900 q^{61} +(-5.43395 + 6.44022i) q^{63} +2.28866 q^{65} -14.1012i q^{67} +(-0.666098 + 0.309503i) q^{69} -15.5869 q^{71} +11.9862 q^{73} +(-2.55402 - 5.49664i) q^{75} -7.01717i q^{77} -1.61516i q^{79} +(-1.51452 - 8.87165i) q^{81} +5.68241i q^{83} -5.97986 q^{85} +(-2.82399 - 6.07766i) q^{87} +11.4660 q^{89} -5.24760i q^{91} +(0.808803 - 0.375811i) q^{93} +(1.71134 + 5.05805i) q^{95} -2.48325i q^{97} +(5.72823 + 4.83321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{3} + 2 q^{7} + 3 q^{9} - 10 q^{15} - 2 q^{19} + 5 q^{21} - 14 q^{25} + 10 q^{27} - 6 q^{29} - 10 q^{33} - 7 q^{39} - 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} - q^{51} - 26 q^{53} + 12 q^{55} + 9 q^{57} - 2 q^{59} - 4 q^{61} + 17 q^{63} + 32 q^{65} - 27 q^{69} - 8 q^{71} - 26 q^{73} - 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} + 4 q^{89} - 18 q^{93} + 8 q^{95} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.729858 1.57077i −0.421383 0.906883i
\(4\) 0 0
\(5\) 1.22502i 0.547843i 0.961752 + 0.273922i \(0.0883209\pi\)
−0.961752 + 0.273922i \(0.911679\pi\)
\(6\) 0 0
\(7\) 2.80880 1.06163 0.530814 0.847488i \(-0.321886\pi\)
0.530814 + 0.847488i \(0.321886\pi\)
\(8\) 0 0
\(9\) −1.93462 + 2.29287i −0.644872 + 0.764291i
\(10\) 0 0
\(11\) 2.49828i 0.753259i −0.926364 0.376630i \(-0.877083\pi\)
0.926364 0.376630i \(-0.122917\pi\)
\(12\) 0 0
\(13\) 1.86827i 0.518165i −0.965855 0.259082i \(-0.916580\pi\)
0.965855 0.259082i \(-0.0834201\pi\)
\(14\) 0 0
\(15\) 1.92421 0.894087i 0.496830 0.230852i
\(16\) 0 0
\(17\) 4.88146i 1.18393i 0.805965 + 0.591964i \(0.201647\pi\)
−0.805965 + 0.591964i \(0.798353\pi\)
\(18\) 0 0
\(19\) 4.12897 1.39700i 0.947251 0.320493i
\(20\) 0 0
\(21\) −2.05003 4.41197i −0.447352 0.962772i
\(22\) 0 0
\(23\) 0.424059i 0.0884224i −0.999022 0.0442112i \(-0.985923\pi\)
0.999022 0.0442112i \(-0.0140775\pi\)
\(24\) 0 0
\(25\) 3.49934 0.699868
\(26\) 0 0
\(27\) 5.01356 + 1.36536i 0.964860 + 0.262764i
\(28\) 0 0
\(29\) 3.86923 0.718498 0.359249 0.933242i \(-0.383033\pi\)
0.359249 + 0.933242i \(0.383033\pi\)
\(30\) 0 0
\(31\) 0.514909i 0.0924805i 0.998930 + 0.0462402i \(0.0147240\pi\)
−0.998930 + 0.0462402i \(0.985276\pi\)
\(32\) 0 0
\(33\) −3.92421 + 1.82339i −0.683118 + 0.317411i
\(34\) 0 0
\(35\) 3.44083i 0.581606i
\(36\) 0 0
\(37\) 5.16750i 0.849532i −0.905303 0.424766i \(-0.860356\pi\)
0.905303 0.424766i \(-0.139644\pi\)
\(38\) 0 0
\(39\) −2.93462 + 1.36357i −0.469915 + 0.218346i
\(40\) 0 0
\(41\) 2.40952 0.376303 0.188152 0.982140i \(-0.439750\pi\)
0.188152 + 0.982140i \(0.439750\pi\)
\(42\) 0 0
\(43\) −0.420092 −0.0640635 −0.0320317 0.999487i \(-0.510198\pi\)
−0.0320317 + 0.999487i \(0.510198\pi\)
\(44\) 0 0
\(45\) −2.80880 2.36993i −0.418712 0.353289i
\(46\) 0 0
\(47\) 10.7405i 1.56666i −0.621607 0.783329i \(-0.713520\pi\)
0.621607 0.783329i \(-0.286480\pi\)
\(48\) 0 0
\(49\) 0.889372 0.127053
\(50\) 0 0
\(51\) 7.66763 3.56277i 1.07368 0.498887i
\(52\) 0 0
\(53\) 7.71766 1.06010 0.530051 0.847966i \(-0.322173\pi\)
0.530051 + 0.847966i \(0.322173\pi\)
\(54\) 0 0
\(55\) 3.06043 0.412668
\(56\) 0 0
\(57\) −5.20792 5.46604i −0.689805 0.723995i
\(58\) 0 0
\(59\) 3.63841 0.473681 0.236840 0.971549i \(-0.423888\pi\)
0.236840 + 0.971549i \(0.423888\pi\)
\(60\) 0 0
\(61\) −1.85900 −0.238021 −0.119010 0.992893i \(-0.537972\pi\)
−0.119010 + 0.992893i \(0.537972\pi\)
\(62\) 0 0
\(63\) −5.43395 + 6.44022i −0.684614 + 0.811392i
\(64\) 0 0
\(65\) 2.28866 0.283873
\(66\) 0 0
\(67\) 14.1012i 1.72274i −0.507982 0.861368i \(-0.669608\pi\)
0.507982 0.861368i \(-0.330392\pi\)
\(68\) 0 0
\(69\) −0.666098 + 0.309503i −0.0801888 + 0.0372598i
\(70\) 0 0
\(71\) −15.5869 −1.84982 −0.924912 0.380182i \(-0.875861\pi\)
−0.924912 + 0.380182i \(0.875861\pi\)
\(72\) 0 0
\(73\) 11.9862 1.40288 0.701438 0.712731i \(-0.252542\pi\)
0.701438 + 0.712731i \(0.252542\pi\)
\(74\) 0 0
\(75\) −2.55402 5.49664i −0.294913 0.634698i
\(76\) 0 0
\(77\) 7.01717i 0.799681i
\(78\) 0 0
\(79\) 1.61516i 0.181719i −0.995864 0.0908597i \(-0.971039\pi\)
0.995864 0.0908597i \(-0.0289615\pi\)
\(80\) 0 0
\(81\) −1.51452 8.87165i −0.168280 0.985739i
\(82\) 0 0
\(83\) 5.68241i 0.623726i 0.950127 + 0.311863i \(0.100953\pi\)
−0.950127 + 0.311863i \(0.899047\pi\)
\(84\) 0 0
\(85\) −5.97986 −0.648607
\(86\) 0 0
\(87\) −2.82399 6.07766i −0.302763 0.651594i
\(88\) 0 0
\(89\) 11.4660 1.21540 0.607698 0.794168i \(-0.292093\pi\)
0.607698 + 0.794168i \(0.292093\pi\)
\(90\) 0 0
\(91\) 5.24760i 0.550098i
\(92\) 0 0
\(93\) 0.808803 0.375811i 0.0838689 0.0389697i
\(94\) 0 0
\(95\) 1.71134 + 5.05805i 0.175580 + 0.518945i
\(96\) 0 0
\(97\) 2.48325i 0.252136i −0.992022 0.126068i \(-0.959764\pi\)
0.992022 0.126068i \(-0.0402358\pi\)
\(98\) 0 0
\(99\) 5.72823 + 4.83321i 0.575709 + 0.485756i
\(100\) 0 0
\(101\) 15.9455i 1.58663i −0.608809 0.793317i \(-0.708353\pi\)
0.608809 0.793317i \(-0.291647\pi\)
\(102\) 0 0
\(103\) 17.8913i 1.76289i 0.472290 + 0.881443i \(0.343427\pi\)
−0.472290 + 0.881443i \(0.656573\pi\)
\(104\) 0 0
\(105\) 5.40473 2.51131i 0.527448 0.245079i
\(106\) 0 0
\(107\) −1.33220 −0.128788 −0.0643941 0.997925i \(-0.520511\pi\)
−0.0643941 + 0.997925i \(0.520511\pi\)
\(108\) 0 0
\(109\) 16.5645i 1.58659i 0.608838 + 0.793294i \(0.291636\pi\)
−0.608838 + 0.793294i \(0.708364\pi\)
\(110\) 0 0
\(111\) −8.11694 + 3.77154i −0.770426 + 0.357979i
\(112\) 0 0
\(113\) −16.7157 −1.57248 −0.786242 0.617919i \(-0.787976\pi\)
−0.786242 + 0.617919i \(0.787976\pi\)
\(114\) 0 0
\(115\) 0.519479 0.0484417
\(116\) 0 0
\(117\) 4.28370 + 3.61438i 0.396029 + 0.334150i
\(118\) 0 0
\(119\) 13.7111i 1.25689i
\(120\) 0 0
\(121\) 4.75860 0.432600
\(122\) 0 0
\(123\) −1.75860 3.78479i −0.158568 0.341263i
\(124\) 0 0
\(125\) 10.4118i 0.931261i
\(126\) 0 0
\(127\) 7.20314i 0.639176i 0.947557 + 0.319588i \(0.103544\pi\)
−0.947557 + 0.319588i \(0.896456\pi\)
\(128\) 0 0
\(129\) 0.306608 + 0.659867i 0.0269953 + 0.0580980i
\(130\) 0 0
\(131\) 0.0482485i 0.00421550i −0.999998 0.00210775i \(-0.999329\pi\)
0.999998 0.00210775i \(-0.000670917\pi\)
\(132\) 0 0
\(133\) 11.5975 3.92389i 1.00563 0.340244i
\(134\) 0 0
\(135\) −1.67259 + 6.14169i −0.143953 + 0.528592i
\(136\) 0 0
\(137\) 16.8562i 1.44012i 0.693912 + 0.720060i \(0.255886\pi\)
−0.693912 + 0.720060i \(0.744114\pi\)
\(138\) 0 0
\(139\) −10.5169 −0.892031 −0.446016 0.895025i \(-0.647157\pi\)
−0.446016 + 0.895025i \(0.647157\pi\)
\(140\) 0 0
\(141\) −16.8708 + 7.83901i −1.42077 + 0.660164i
\(142\) 0 0
\(143\) −4.66746 −0.390312
\(144\) 0 0
\(145\) 4.73987i 0.393625i
\(146\) 0 0
\(147\) −0.649115 1.39700i −0.0535381 0.115222i
\(148\) 0 0
\(149\) 4.61966i 0.378457i −0.981933 0.189229i \(-0.939401\pi\)
0.981933 0.189229i \(-0.0605987\pi\)
\(150\) 0 0
\(151\) 17.9811i 1.46328i 0.681690 + 0.731641i \(0.261245\pi\)
−0.681690 + 0.731641i \(0.738755\pi\)
\(152\) 0 0
\(153\) −11.1926 9.44375i −0.904865 0.763482i
\(154\) 0 0
\(155\) −0.630772 −0.0506648
\(156\) 0 0
\(157\) −1.77874 −0.141959 −0.0709796 0.997478i \(-0.522613\pi\)
−0.0709796 + 0.997478i \(0.522613\pi\)
\(158\) 0 0
\(159\) −5.63279 12.1226i −0.446709 0.961388i
\(160\) 0 0
\(161\) 1.19110i 0.0938717i
\(162\) 0 0
\(163\) 15.4565 1.21064 0.605322 0.795981i \(-0.293044\pi\)
0.605322 + 0.795981i \(0.293044\pi\)
\(164\) 0 0
\(165\) −2.23368 4.80722i −0.173892 0.374242i
\(166\) 0 0
\(167\) 4.46164 0.345252 0.172626 0.984987i \(-0.444775\pi\)
0.172626 + 0.984987i \(0.444775\pi\)
\(168\) 0 0
\(169\) 9.50957 0.731505
\(170\) 0 0
\(171\) −4.78484 + 12.1699i −0.365906 + 0.930652i
\(172\) 0 0
\(173\) −19.0529 −1.44857 −0.724283 0.689502i \(-0.757829\pi\)
−0.724283 + 0.689502i \(0.757829\pi\)
\(174\) 0 0
\(175\) 9.82895 0.742999
\(176\) 0 0
\(177\) −2.65552 5.71510i −0.199601 0.429573i
\(178\) 0 0
\(179\) −15.9759 −1.19410 −0.597049 0.802205i \(-0.703660\pi\)
−0.597049 + 0.802205i \(0.703660\pi\)
\(180\) 0 0
\(181\) 5.25727i 0.390770i −0.980727 0.195385i \(-0.937404\pi\)
0.980727 0.195385i \(-0.0625956\pi\)
\(182\) 0 0
\(183\) 1.35681 + 2.92006i 0.100298 + 0.215857i
\(184\) 0 0
\(185\) 6.33027 0.465411
\(186\) 0 0
\(187\) 12.1952 0.891804
\(188\) 0 0
\(189\) 14.0821 + 3.83503i 1.02432 + 0.278957i
\(190\) 0 0
\(191\) 5.33309i 0.385889i −0.981210 0.192945i \(-0.938196\pi\)
0.981210 0.192945i \(-0.0618038\pi\)
\(192\) 0 0
\(193\) 21.2027i 1.52621i 0.646277 + 0.763103i \(0.276325\pi\)
−0.646277 + 0.763103i \(0.723675\pi\)
\(194\) 0 0
\(195\) −1.67039 3.59495i −0.119619 0.257440i
\(196\) 0 0
\(197\) 20.6853i 1.47377i 0.676019 + 0.736884i \(0.263704\pi\)
−0.676019 + 0.736884i \(0.736296\pi\)
\(198\) 0 0
\(199\) −3.09080 −0.219101 −0.109550 0.993981i \(-0.534941\pi\)
−0.109550 + 0.993981i \(0.534941\pi\)
\(200\) 0 0
\(201\) −22.1497 + 10.2919i −1.56232 + 0.725932i
\(202\) 0 0
\(203\) 10.8679 0.762778
\(204\) 0 0
\(205\) 2.95169i 0.206155i
\(206\) 0 0
\(207\) 0.972313 + 0.820392i 0.0675804 + 0.0570212i
\(208\) 0 0
\(209\) −3.49009 10.3153i −0.241414 0.713526i
\(210\) 0 0
\(211\) 6.02995i 0.415119i 0.978222 + 0.207560i \(0.0665521\pi\)
−0.978222 + 0.207560i \(0.933448\pi\)
\(212\) 0 0
\(213\) 11.3762 + 24.4834i 0.779485 + 1.67757i
\(214\) 0 0
\(215\) 0.514619i 0.0350967i
\(216\) 0 0
\(217\) 1.44628i 0.0981798i
\(218\) 0 0
\(219\) −8.74820 18.8275i −0.591149 1.27224i
\(220\) 0 0
\(221\) 9.11988 0.613470
\(222\) 0 0
\(223\) 12.5462i 0.840153i 0.907489 + 0.420076i \(0.137997\pi\)
−0.907489 + 0.420076i \(0.862003\pi\)
\(224\) 0 0
\(225\) −6.76987 + 8.02353i −0.451325 + 0.534902i
\(226\) 0 0
\(227\) 23.0562 1.53029 0.765146 0.643857i \(-0.222667\pi\)
0.765146 + 0.643857i \(0.222667\pi\)
\(228\) 0 0
\(229\) −11.4971 −0.759748 −0.379874 0.925038i \(-0.624033\pi\)
−0.379874 + 0.925038i \(0.624033\pi\)
\(230\) 0 0
\(231\) −11.0223 + 5.12154i −0.725217 + 0.336972i
\(232\) 0 0
\(233\) 14.7204i 0.964369i −0.876070 0.482184i \(-0.839844\pi\)
0.876070 0.482184i \(-0.160156\pi\)
\(234\) 0 0
\(235\) 13.1572 0.858283
\(236\) 0 0
\(237\) −2.53704 + 1.17884i −0.164798 + 0.0765736i
\(238\) 0 0
\(239\) 25.6025i 1.65609i −0.560663 0.828044i \(-0.689454\pi\)
0.560663 0.828044i \(-0.310546\pi\)
\(240\) 0 0
\(241\) 3.66611i 0.236155i 0.993004 + 0.118077i \(0.0376731\pi\)
−0.993004 + 0.118077i \(0.962327\pi\)
\(242\) 0 0
\(243\) −12.8299 + 8.85401i −0.823039 + 0.567985i
\(244\) 0 0
\(245\) 1.08949i 0.0696052i
\(246\) 0 0
\(247\) −2.60997 7.71403i −0.166068 0.490832i
\(248\) 0 0
\(249\) 8.92575 4.14735i 0.565646 0.262828i
\(250\) 0 0
\(251\) 27.2774i 1.72173i −0.508832 0.860866i \(-0.669923\pi\)
0.508832 0.860866i \(-0.330077\pi\)
\(252\) 0 0
\(253\) −1.05942 −0.0666050
\(254\) 0 0
\(255\) 4.36445 + 9.39296i 0.273312 + 0.588210i
\(256\) 0 0
\(257\) −10.5562 −0.658476 −0.329238 0.944247i \(-0.606792\pi\)
−0.329238 + 0.944247i \(0.606792\pi\)
\(258\) 0 0
\(259\) 14.5145i 0.901887i
\(260\) 0 0
\(261\) −7.48548 + 8.87165i −0.463339 + 0.549142i
\(262\) 0 0
\(263\) 13.8784i 0.855780i 0.903831 + 0.427890i \(0.140743\pi\)
−0.903831 + 0.427890i \(0.859257\pi\)
\(264\) 0 0
\(265\) 9.45425i 0.580770i
\(266\) 0 0
\(267\) −8.36857 18.0105i −0.512148 1.10222i
\(268\) 0 0
\(269\) −9.60804 −0.585813 −0.292906 0.956141i \(-0.594622\pi\)
−0.292906 + 0.956141i \(0.594622\pi\)
\(270\) 0 0
\(271\) −18.5859 −1.12901 −0.564507 0.825428i \(-0.690934\pi\)
−0.564507 + 0.825428i \(0.690934\pi\)
\(272\) 0 0
\(273\) −8.24276 + 3.83000i −0.498874 + 0.231802i
\(274\) 0 0
\(275\) 8.74232i 0.527182i
\(276\) 0 0
\(277\) −11.4363 −0.687142 −0.343571 0.939127i \(-0.611637\pi\)
−0.343571 + 0.939127i \(0.611637\pi\)
\(278\) 0 0
\(279\) −1.18062 0.996152i −0.0706820 0.0596381i
\(280\) 0 0
\(281\) −21.1774 −1.26334 −0.631668 0.775239i \(-0.717629\pi\)
−0.631668 + 0.775239i \(0.717629\pi\)
\(282\) 0 0
\(283\) −4.67803 −0.278080 −0.139040 0.990287i \(-0.544402\pi\)
−0.139040 + 0.990287i \(0.544402\pi\)
\(284\) 0 0
\(285\) 6.69598 6.37978i 0.396636 0.377905i
\(286\) 0 0
\(287\) 6.76786 0.399494
\(288\) 0 0
\(289\) −6.82863 −0.401684
\(290\) 0 0
\(291\) −3.90061 + 1.81242i −0.228658 + 0.106246i
\(292\) 0 0
\(293\) −13.4049 −0.783125 −0.391563 0.920151i \(-0.628065\pi\)
−0.391563 + 0.920151i \(0.628065\pi\)
\(294\) 0 0
\(295\) 4.45711i 0.259503i
\(296\) 0 0
\(297\) 3.41105 12.5253i 0.197929 0.726790i
\(298\) 0 0
\(299\) −0.792257 −0.0458174
\(300\) 0 0
\(301\) −1.17996 −0.0680115
\(302\) 0 0
\(303\) −25.0466 + 11.6379i −1.43889 + 0.668581i
\(304\) 0 0
\(305\) 2.27730i 0.130398i
\(306\) 0 0
\(307\) 26.2565i 1.49854i 0.662266 + 0.749269i \(0.269595\pi\)
−0.662266 + 0.749269i \(0.730405\pi\)
\(308\) 0 0
\(309\) 28.1031 13.0581i 1.59873 0.742851i
\(310\) 0 0
\(311\) 10.4261i 0.591213i −0.955310 0.295606i \(-0.904478\pi\)
0.955310 0.295606i \(-0.0955217\pi\)
\(312\) 0 0
\(313\) −11.0678 −0.625587 −0.312793 0.949821i \(-0.601265\pi\)
−0.312793 + 0.949821i \(0.601265\pi\)
\(314\) 0 0
\(315\) −7.88937 6.65668i −0.444516 0.375061i
\(316\) 0 0
\(317\) −2.95937 −0.166215 −0.0831073 0.996541i \(-0.526484\pi\)
−0.0831073 + 0.996541i \(0.526484\pi\)
\(318\) 0 0
\(319\) 9.66642i 0.541216i
\(320\) 0 0
\(321\) 0.972313 + 2.09257i 0.0542692 + 0.116796i
\(322\) 0 0
\(323\) 6.81938 + 20.1554i 0.379440 + 1.12148i
\(324\) 0 0
\(325\) 6.53771i 0.362647i
\(326\) 0 0
\(327\) 26.0189 12.0897i 1.43885 0.668562i
\(328\) 0 0
\(329\) 30.1678i 1.66321i
\(330\) 0 0
\(331\) 4.55718i 0.250485i −0.992126 0.125243i \(-0.960029\pi\)
0.992126 0.125243i \(-0.0399710\pi\)
\(332\) 0 0
\(333\) 11.8484 + 9.99714i 0.649290 + 0.547840i
\(334\) 0 0
\(335\) 17.2742 0.943789
\(336\) 0 0
\(337\) 8.27943i 0.451009i −0.974242 0.225505i \(-0.927597\pi\)
0.974242 0.225505i \(-0.0724031\pi\)
\(338\) 0 0
\(339\) 12.2001 + 26.2565i 0.662619 + 1.42606i
\(340\) 0 0
\(341\) 1.28639 0.0696618
\(342\) 0 0
\(343\) −17.1635 −0.926744
\(344\) 0 0
\(345\) −0.379146 0.815980i −0.0204125 0.0439309i
\(346\) 0 0
\(347\) 18.3626i 0.985754i 0.870099 + 0.492877i \(0.164055\pi\)
−0.870099 + 0.492877i \(0.835945\pi\)
\(348\) 0 0
\(349\) 3.25535 0.174255 0.0871275 0.996197i \(-0.472231\pi\)
0.0871275 + 0.996197i \(0.472231\pi\)
\(350\) 0 0
\(351\) 2.55086 9.36668i 0.136155 0.499957i
\(352\) 0 0
\(353\) 2.48890i 0.132471i 0.997804 + 0.0662354i \(0.0210988\pi\)
−0.997804 + 0.0662354i \(0.978901\pi\)
\(354\) 0 0
\(355\) 19.0942i 1.01341i
\(356\) 0 0
\(357\) 21.5369 10.0071i 1.13985 0.529633i
\(358\) 0 0
\(359\) 26.8512i 1.41715i 0.705634 + 0.708577i \(0.250662\pi\)
−0.705634 + 0.708577i \(0.749338\pi\)
\(360\) 0 0
\(361\) 15.0968 11.5363i 0.794569 0.607174i
\(362\) 0 0
\(363\) −3.47310 7.47466i −0.182291 0.392318i
\(364\) 0 0
\(365\) 14.6832i 0.768556i
\(366\) 0 0
\(367\) −6.67905 −0.348643 −0.174322 0.984689i \(-0.555773\pi\)
−0.174322 + 0.984689i \(0.555773\pi\)
\(368\) 0 0
\(369\) −4.66149 + 5.52471i −0.242667 + 0.287605i
\(370\) 0 0
\(371\) 21.6774 1.12543
\(372\) 0 0
\(373\) 29.6103i 1.53317i −0.642146 0.766583i \(-0.721956\pi\)
0.642146 0.766583i \(-0.278044\pi\)
\(374\) 0 0
\(375\) 16.3545 7.59914i 0.844545 0.392418i
\(376\) 0 0
\(377\) 7.22877i 0.372301i
\(378\) 0 0
\(379\) 3.41300i 0.175314i −0.996151 0.0876570i \(-0.972062\pi\)
0.996151 0.0876570i \(-0.0279379\pi\)
\(380\) 0 0
\(381\) 11.3145 5.25727i 0.579657 0.269338i
\(382\) 0 0
\(383\) −4.40661 −0.225167 −0.112584 0.993642i \(-0.535913\pi\)
−0.112584 + 0.993642i \(0.535913\pi\)
\(384\) 0 0
\(385\) 8.59614 0.438100
\(386\) 0 0
\(387\) 0.812717 0.963218i 0.0413127 0.0489631i
\(388\) 0 0
\(389\) 3.20661i 0.162581i 0.996690 + 0.0812907i \(0.0259042\pi\)
−0.996690 + 0.0812907i \(0.974096\pi\)
\(390\) 0 0
\(391\) 2.07003 0.104686
\(392\) 0 0
\(393\) −0.0757872 + 0.0352146i −0.00382296 + 0.00177634i
\(394\) 0 0
\(395\) 1.97859 0.0995538
\(396\) 0 0
\(397\) −15.9925 −0.802640 −0.401320 0.915938i \(-0.631448\pi\)
−0.401320 + 0.915938i \(0.631448\pi\)
\(398\) 0 0
\(399\) −14.6280 15.3530i −0.732316 0.768613i
\(400\) 0 0
\(401\) 30.7131 1.53374 0.766869 0.641804i \(-0.221814\pi\)
0.766869 + 0.641804i \(0.221814\pi\)
\(402\) 0 0
\(403\) 0.961990 0.0479201
\(404\) 0 0
\(405\) 10.8679 1.85531i 0.540031 0.0921913i
\(406\) 0 0
\(407\) −12.9099 −0.639918
\(408\) 0 0
\(409\) 36.9136i 1.82526i −0.408789 0.912629i \(-0.634049\pi\)
0.408789 0.912629i \(-0.365951\pi\)
\(410\) 0 0
\(411\) 26.4771 12.3026i 1.30602 0.606842i
\(412\) 0 0
\(413\) 10.2196 0.502873
\(414\) 0 0
\(415\) −6.96104 −0.341704
\(416\) 0 0
\(417\) 7.67584 + 16.5196i 0.375887 + 0.808968i
\(418\) 0 0
\(419\) 14.7287i 0.719546i 0.933040 + 0.359773i \(0.117146\pi\)
−0.933040 + 0.359773i \(0.882854\pi\)
\(420\) 0 0
\(421\) 23.4457i 1.14267i 0.820716 + 0.571337i \(0.193575\pi\)
−0.820716 + 0.571337i \(0.806425\pi\)
\(422\) 0 0
\(423\) 24.6265 + 20.7787i 1.19738 + 1.01029i
\(424\) 0 0
\(425\) 17.0819i 0.828592i
\(426\) 0 0
\(427\) −5.22157 −0.252689
\(428\) 0 0
\(429\) 3.40658 + 7.33149i 0.164471 + 0.353968i
\(430\) 0 0
\(431\) −25.4449 −1.22564 −0.612818 0.790224i \(-0.709964\pi\)
−0.612818 + 0.790224i \(0.709964\pi\)
\(432\) 0 0
\(433\) 21.2027i 1.01894i 0.860489 + 0.509469i \(0.170158\pi\)
−0.860489 + 0.509469i \(0.829842\pi\)
\(434\) 0 0
\(435\) 7.44522 3.45943i 0.356971 0.165867i
\(436\) 0 0
\(437\) −0.592409 1.75093i −0.0283388 0.0837582i
\(438\) 0 0
\(439\) 27.5578i 1.31526i −0.753341 0.657630i \(-0.771559\pi\)
0.753341 0.657630i \(-0.228441\pi\)
\(440\) 0 0
\(441\) −1.72059 + 2.03922i −0.0819330 + 0.0971056i
\(442\) 0 0
\(443\) 23.8168i 1.13157i 0.824552 + 0.565786i \(0.191427\pi\)
−0.824552 + 0.565786i \(0.808573\pi\)
\(444\) 0 0
\(445\) 14.0461i 0.665847i
\(446\) 0 0
\(447\) −7.25641 + 3.37169i −0.343216 + 0.159476i
\(448\) 0 0
\(449\) 35.3561 1.66856 0.834278 0.551344i \(-0.185885\pi\)
0.834278 + 0.551344i \(0.185885\pi\)
\(450\) 0 0
\(451\) 6.01964i 0.283454i
\(452\) 0 0
\(453\) 28.2441 13.1236i 1.32702 0.616603i
\(454\) 0 0
\(455\) 6.42839 0.301368
\(456\) 0 0
\(457\) 26.1233 1.22199 0.610997 0.791633i \(-0.290769\pi\)
0.610997 + 0.791633i \(0.290769\pi\)
\(458\) 0 0
\(459\) −6.66495 + 24.4735i −0.311093 + 1.14232i
\(460\) 0 0
\(461\) 17.1158i 0.797162i −0.917133 0.398581i \(-0.869503\pi\)
0.917133 0.398581i \(-0.130497\pi\)
\(462\) 0 0
\(463\) −0.341102 −0.0158524 −0.00792618 0.999969i \(-0.502523\pi\)
−0.00792618 + 0.999969i \(0.502523\pi\)
\(464\) 0 0
\(465\) 0.460374 + 0.990795i 0.0213493 + 0.0459470i
\(466\) 0 0
\(467\) 30.7092i 1.42105i −0.703671 0.710526i \(-0.748457\pi\)
0.703671 0.710526i \(-0.251543\pi\)
\(468\) 0 0
\(469\) 39.6075i 1.82890i
\(470\) 0 0
\(471\) 1.29823 + 2.79399i 0.0598193 + 0.128740i
\(472\) 0 0
\(473\) 1.04951i 0.0482564i
\(474\) 0 0
\(475\) 14.4487 4.88856i 0.662950 0.224303i
\(476\) 0 0
\(477\) −14.9307 + 17.6956i −0.683630 + 0.810226i
\(478\) 0 0
\(479\) 30.2160i 1.38060i 0.723522 + 0.690302i \(0.242522\pi\)
−0.723522 + 0.690302i \(0.757478\pi\)
\(480\) 0 0
\(481\) −9.65429 −0.440198
\(482\) 0 0
\(483\) −1.87094 + 0.869332i −0.0851306 + 0.0395560i
\(484\) 0 0
\(485\) 3.04202 0.138131
\(486\) 0 0
\(487\) 35.1534i 1.59295i −0.604670 0.796476i \(-0.706695\pi\)
0.604670 0.796476i \(-0.293305\pi\)
\(488\) 0 0
\(489\) −11.2810 24.2785i −0.510145 1.09791i
\(490\) 0 0
\(491\) 26.8286i 1.21076i 0.795937 + 0.605379i \(0.206978\pi\)
−0.795937 + 0.605379i \(0.793022\pi\)
\(492\) 0 0
\(493\) 18.8875i 0.850650i
\(494\) 0 0
\(495\) −5.92075 + 7.01717i −0.266118 + 0.315398i
\(496\) 0 0
\(497\) −43.7805 −1.96382
\(498\) 0 0
\(499\) −40.1309 −1.79651 −0.898253 0.439479i \(-0.855163\pi\)
−0.898253 + 0.439479i \(0.855163\pi\)
\(500\) 0 0
\(501\) −3.25636 7.00820i −0.145484 0.313103i
\(502\) 0 0
\(503\) 29.4746i 1.31421i −0.753801 0.657103i \(-0.771782\pi\)
0.753801 0.657103i \(-0.228218\pi\)
\(504\) 0 0
\(505\) 19.5334 0.869226
\(506\) 0 0
\(507\) −6.94063 14.9373i −0.308244 0.663389i
\(508\) 0 0
\(509\) −5.81464 −0.257729 −0.128865 0.991662i \(-0.541133\pi\)
−0.128865 + 0.991662i \(0.541133\pi\)
\(510\) 0 0
\(511\) 33.6668 1.48933
\(512\) 0 0
\(513\) 22.6082 1.36639i 0.998179 0.0603278i
\(514\) 0 0
\(515\) −21.9172 −0.965785
\(516\) 0 0
\(517\) −26.8327 −1.18010
\(518\) 0 0
\(519\) 13.9059 + 29.9277i 0.610402 + 1.31368i
\(520\) 0 0
\(521\) 38.2332 1.67503 0.837513 0.546417i \(-0.184009\pi\)
0.837513 + 0.546417i \(0.184009\pi\)
\(522\) 0 0
\(523\) 2.17499i 0.0951055i −0.998869 0.0475528i \(-0.984858\pi\)
0.998869 0.0475528i \(-0.0151422\pi\)
\(524\) 0 0
\(525\) −7.17373 15.4390i −0.313087 0.673813i
\(526\) 0 0
\(527\) −2.51351 −0.109490
\(528\) 0 0
\(529\) 22.8202 0.992181
\(530\) 0 0
\(531\) −7.03893 + 8.34241i −0.305463 + 0.362030i
\(532\) 0 0
\(533\) 4.50163i 0.194987i
\(534\) 0 0
\(535\) 1.63196i 0.0705558i
\(536\) 0 0
\(537\) 11.6602 + 25.0945i 0.503173 + 1.08291i
\(538\) 0 0
\(539\) 2.22190i 0.0957040i
\(540\) 0 0
\(541\) −26.8781 −1.15558 −0.577791 0.816185i \(-0.696085\pi\)
−0.577791 + 0.816185i \(0.696085\pi\)
\(542\) 0 0
\(543\) −8.25794 + 3.83706i −0.354382 + 0.164664i
\(544\) 0 0
\(545\) −20.2917 −0.869202
\(546\) 0 0
\(547\) 29.0152i 1.24060i 0.784364 + 0.620300i \(0.212989\pi\)
−0.784364 + 0.620300i \(0.787011\pi\)
\(548\) 0 0
\(549\) 3.59645 4.26245i 0.153493 0.181917i
\(550\) 0 0
\(551\) 15.9759 5.40530i 0.680598 0.230274i
\(552\) 0 0
\(553\) 4.53666i 0.192918i
\(554\) 0 0
\(555\) −4.62020 9.94338i −0.196116 0.422073i
\(556\) 0 0
\(557\) 19.5680i 0.829122i −0.910021 0.414561i \(-0.863935\pi\)
0.910021 0.414561i \(-0.136065\pi\)
\(558\) 0 0
\(559\) 0.784846i 0.0331954i
\(560\) 0 0
\(561\) −8.90079 19.1559i −0.375792 0.808762i
\(562\) 0 0
\(563\) −18.3253 −0.772321 −0.386161 0.922432i \(-0.626199\pi\)
−0.386161 + 0.922432i \(0.626199\pi\)
\(564\) 0 0
\(565\) 20.4770i 0.861475i
\(566\) 0 0
\(567\) −4.25400 24.9187i −0.178651 1.04649i
\(568\) 0 0
\(569\) −17.7539 −0.744282 −0.372141 0.928176i \(-0.621376\pi\)
−0.372141 + 0.928176i \(0.621376\pi\)
\(570\) 0 0
\(571\) −8.25794 −0.345584 −0.172792 0.984958i \(-0.555279\pi\)
−0.172792 + 0.984958i \(0.555279\pi\)
\(572\) 0 0
\(573\) −8.37705 + 3.89240i −0.349956 + 0.162607i
\(574\) 0 0
\(575\) 1.48393i 0.0618840i
\(576\) 0 0
\(577\) −9.96477 −0.414839 −0.207419 0.978252i \(-0.566506\pi\)
−0.207419 + 0.978252i \(0.566506\pi\)
\(578\) 0 0
\(579\) 33.3045 15.4750i 1.38409 0.643118i
\(580\) 0 0
\(581\) 15.9608i 0.662165i
\(582\) 0 0
\(583\) 19.2809i 0.798532i
\(584\) 0 0
\(585\) −4.42767 + 5.24760i −0.183062 + 0.216962i
\(586\) 0 0
\(587\) 33.1772i 1.36937i −0.728840 0.684685i \(-0.759940\pi\)
0.728840 0.684685i \(-0.240060\pi\)
\(588\) 0 0
\(589\) 0.719327 + 2.12605i 0.0296393 + 0.0876022i
\(590\) 0 0
\(591\) 32.4918 15.0973i 1.33654 0.621022i
\(592\) 0 0
\(593\) 23.1507i 0.950684i 0.879801 + 0.475342i \(0.157676\pi\)
−0.879801 + 0.475342i \(0.842324\pi\)
\(594\) 0 0
\(595\) −16.7962 −0.688579
\(596\) 0 0
\(597\) 2.25584 + 4.85493i 0.0923255 + 0.198699i
\(598\) 0 0
\(599\) 42.9672 1.75559 0.877796 0.479035i \(-0.159013\pi\)
0.877796 + 0.479035i \(0.159013\pi\)
\(600\) 0 0
\(601\) 34.0425i 1.38862i −0.719675 0.694311i \(-0.755709\pi\)
0.719675 0.694311i \(-0.244291\pi\)
\(602\) 0 0
\(603\) 32.3322 + 27.2804i 1.31667 + 1.11094i
\(604\) 0 0
\(605\) 5.82936i 0.236997i
\(606\) 0 0
\(607\) 20.7358i 0.841641i 0.907144 + 0.420821i \(0.138258\pi\)
−0.907144 + 0.420821i \(0.861742\pi\)
\(608\) 0 0
\(609\) −7.93203 17.0709i −0.321422 0.691750i
\(610\) 0 0
\(611\) −20.0661 −0.811787
\(612\) 0 0
\(613\) −37.2732 −1.50545 −0.752724 0.658336i \(-0.771261\pi\)
−0.752724 + 0.658336i \(0.771261\pi\)
\(614\) 0 0
\(615\) 4.63642 2.15432i 0.186959 0.0868704i
\(616\) 0 0
\(617\) 31.6733i 1.27512i 0.770402 + 0.637559i \(0.220056\pi\)
−0.770402 + 0.637559i \(0.779944\pi\)
\(618\) 0 0
\(619\) 28.2177 1.13416 0.567082 0.823662i \(-0.308072\pi\)
0.567082 + 0.823662i \(0.308072\pi\)
\(620\) 0 0
\(621\) 0.578993 2.12605i 0.0232342 0.0853153i
\(622\) 0 0
\(623\) 32.2058 1.29030
\(624\) 0 0
\(625\) 4.74206 0.189682
\(626\) 0 0
\(627\) −13.6557 + 13.0108i −0.545356 + 0.519602i
\(628\) 0 0
\(629\) 25.2250 1.00578
\(630\) 0 0
\(631\) −12.0994 −0.481669 −0.240834 0.970566i \(-0.577421\pi\)
−0.240834 + 0.970566i \(0.577421\pi\)
\(632\) 0 0
\(633\) 9.47165 4.40101i 0.376464 0.174924i
\(634\) 0 0
\(635\) −8.82396 −0.350168
\(636\) 0 0
\(637\) 1.66159i 0.0658345i
\(638\) 0 0
\(639\) 30.1546 35.7387i 1.19290 1.41380i
\(640\) 0 0
\(641\) 24.2308 0.957060 0.478530 0.878071i \(-0.341170\pi\)
0.478530 + 0.878071i \(0.341170\pi\)
\(642\) 0 0
\(643\) −21.0981 −0.832026 −0.416013 0.909359i \(-0.636573\pi\)
−0.416013 + 0.909359i \(0.636573\pi\)
\(644\) 0 0
\(645\) −0.808347 + 0.375599i −0.0318286 + 0.0147892i
\(646\) 0 0
\(647\) 0.254891i 0.0100208i −0.999987 0.00501039i \(-0.998405\pi\)
0.999987 0.00501039i \(-0.00159486\pi\)
\(648\) 0 0
\(649\) 9.08977i 0.356804i
\(650\) 0 0
\(651\) 2.27177 1.05558i 0.0890376 0.0413714i
\(652\) 0 0
\(653\) 24.0777i 0.942232i −0.882071 0.471116i \(-0.843851\pi\)
0.882071 0.471116i \(-0.156149\pi\)
\(654\) 0 0
\(655\) 0.0591052 0.00230943
\(656\) 0 0
\(657\) −23.1886 + 27.4828i −0.904675 + 1.07220i
\(658\) 0 0
\(659\) 8.53072 0.332310 0.166155 0.986100i \(-0.446865\pi\)
0.166155 + 0.986100i \(0.446865\pi\)
\(660\) 0 0
\(661\) 38.4286i 1.49470i −0.664430 0.747350i \(-0.731326\pi\)
0.664430 0.747350i \(-0.268674\pi\)
\(662\) 0 0
\(663\) −6.65621 14.3252i −0.258506 0.556345i
\(664\) 0 0
\(665\) 4.80682 + 14.2071i 0.186401 + 0.550926i
\(666\) 0 0
\(667\) 1.64078i 0.0635314i
\(668\) 0 0
\(669\) 19.7071 9.15691i 0.761920 0.354026i
\(670\) 0 0
\(671\) 4.64430i 0.179291i
\(672\) 0 0
\(673\) 46.8954i 1.80768i 0.427867 + 0.903842i \(0.359265\pi\)
−0.427867 + 0.903842i \(0.640735\pi\)
\(674\) 0 0
\(675\) 17.5441 + 4.77786i 0.675274 + 0.183900i
\(676\) 0 0
\(677\) 21.6890 0.833575 0.416787 0.909004i \(-0.363156\pi\)
0.416787 + 0.909004i \(0.363156\pi\)
\(678\) 0 0
\(679\) 6.97497i 0.267675i
\(680\) 0 0
\(681\) −16.8277 36.2159i −0.644840 1.38779i
\(682\) 0 0
\(683\) −38.8523 −1.48664 −0.743321 0.668935i \(-0.766750\pi\)
−0.743321 + 0.668935i \(0.766750\pi\)
\(684\) 0 0
\(685\) −20.6491 −0.788960
\(686\) 0 0
\(687\) 8.39122 + 18.0592i 0.320145 + 0.689002i
\(688\) 0 0
\(689\) 14.4187i 0.549307i
\(690\) 0 0
\(691\) 7.39377 0.281272 0.140636 0.990061i \(-0.455085\pi\)
0.140636 + 0.990061i \(0.455085\pi\)
\(692\) 0 0
\(693\) 16.0895 + 13.5755i 0.611189 + 0.515692i
\(694\) 0 0
\(695\) 12.8834i 0.488693i
\(696\) 0 0
\(697\) 11.7620i 0.445516i
\(698\) 0 0
\(699\) −23.1224 + 10.7438i −0.874569 + 0.406369i
\(700\) 0 0
\(701\) 31.8613i 1.20338i 0.798728 + 0.601692i \(0.205507\pi\)
−0.798728 + 0.601692i \(0.794493\pi\)
\(702\) 0 0
\(703\) −7.21898 21.3365i −0.272269 0.804720i
\(704\) 0 0
\(705\) −9.60291 20.6669i −0.361666 0.778362i
\(706\) 0 0
\(707\) 44.7877i 1.68441i
\(708\) 0 0
\(709\) 14.7371 0.553465 0.276732 0.960947i \(-0.410748\pi\)
0.276732 + 0.960947i \(0.410748\pi\)
\(710\) 0 0
\(711\) 3.70335 + 3.12471i 0.138886 + 0.117186i
\(712\) 0 0
\(713\) 0.218352 0.00817735
\(714\) 0 0
\(715\) 5.71771i 0.213830i
\(716\) 0 0
\(717\) −40.2156 + 18.6862i −1.50188 + 0.697848i
\(718\) 0 0
\(719\) 21.7645i 0.811678i −0.913945 0.405839i \(-0.866979\pi\)
0.913945 0.405839i \(-0.133021\pi\)
\(720\) 0 0
\(721\) 50.2532i 1.87153i
\(722\) 0 0
\(723\) 5.75860 2.67574i 0.214165 0.0995118i
\(724\) 0 0
\(725\) 13.5397 0.502854
\(726\) 0 0
\(727\) 1.44554 0.0536123 0.0268061 0.999641i \(-0.491466\pi\)
0.0268061 + 0.999641i \(0.491466\pi\)
\(728\) 0 0
\(729\) 23.2716 + 13.6906i 0.861911 + 0.507060i
\(730\) 0 0
\(731\) 2.05066i 0.0758465i
\(732\) 0 0
\(733\) −15.6302 −0.577316 −0.288658 0.957432i \(-0.593209\pi\)
−0.288658 + 0.957432i \(0.593209\pi\)
\(734\) 0 0
\(735\) 1.71134 0.795176i 0.0631238 0.0293305i
\(736\) 0 0
\(737\) −35.2287 −1.29767
\(738\) 0 0
\(739\) −41.1663 −1.51433 −0.757163 0.653226i \(-0.773415\pi\)
−0.757163 + 0.653226i \(0.773415\pi\)
\(740\) 0 0
\(741\) −10.2120 + 9.72979i −0.375149 + 0.357433i
\(742\) 0 0
\(743\) −42.2089 −1.54849 −0.774247 0.632884i \(-0.781871\pi\)
−0.774247 + 0.632884i \(0.781871\pi\)
\(744\) 0 0
\(745\) 5.65915 0.207335
\(746\) 0 0
\(747\) −13.0290 10.9933i −0.476708 0.402223i
\(748\) 0 0
\(749\) −3.74188 −0.136725
\(750\) 0 0
\(751\) 0.203487i 0.00742536i −0.999993 0.00371268i \(-0.998818\pi\)
0.999993 0.00371268i \(-0.00118178\pi\)
\(752\) 0 0
\(753\) −42.8464 + 19.9086i −1.56141 + 0.725509i
\(754\) 0 0
\(755\) −22.0271 −0.801649
\(756\) 0 0
\(757\) −43.0897 −1.56612 −0.783060 0.621946i \(-0.786342\pi\)
−0.783060 + 0.621946i \(0.786342\pi\)
\(758\) 0 0
\(759\) 0.773224 + 1.66410i 0.0280663 + 0.0604029i
\(760\) 0 0
\(761\) 17.4848i 0.633823i 0.948455 + 0.316912i \(0.102646\pi\)
−0.948455 + 0.316912i \(0.897354\pi\)
\(762\) 0 0
\(763\) 46.5263i 1.68437i
\(764\) 0 0
\(765\) 11.5687 13.7111i 0.418268 0.495724i
\(766\) 0 0
\(767\) 6.79753i 0.245445i
\(768\) 0 0
\(769\) −31.9862 −1.15345 −0.576725 0.816938i \(-0.695670\pi\)
−0.576725 + 0.816938i \(0.695670\pi\)
\(770\) 0 0
\(771\) 7.70450 + 16.5813i 0.277471 + 0.597160i
\(772\) 0 0
\(773\) 47.1338 1.69529 0.847643 0.530567i \(-0.178021\pi\)
0.847643 + 0.530567i \(0.178021\pi\)
\(774\) 0 0
\(775\) 1.80184i 0.0647241i
\(776\) 0 0
\(777\) −22.7989 + 10.5935i −0.817906 + 0.380040i
\(778\) 0 0
\(779\) 9.94882 3.36609i 0.356454 0.120603i
\(780\) 0 0
\(781\) 38.9404i 1.39340i
\(782\) 0 0
\(783\) 19.3986 + 5.28289i 0.693250 + 0.188795i
\(784\) 0 0
\(785\) 2.17899i 0.0777714i
\(786\) 0 0
\(787\) 28.4779i 1.01513i 0.861614 + 0.507564i \(0.169454\pi\)
−0.861614 + 0.507564i \(0.830546\pi\)
\(788\) 0 0
\(789\) 21.7998 10.1293i 0.776092 0.360612i
\(790\) 0 0
\(791\) −46.9512 −1.66939
\(792\) 0 0
\(793\) 3.47312i 0.123334i
\(794\) 0 0
\(795\) 14.8504 6.90025i 0.526690 0.244727i
\(796\) 0 0
\(797\) −42.8013 −1.51610 −0.758050 0.652197i \(-0.773848\pi\)
−0.758050 + 0.652197i \(0.773848\pi\)
\(798\) 0 0
\(799\) 52.4291 1.85481
\(800\) 0 0
\(801\) −22.1824 + 26.2901i −0.783775 + 0.928916i
\(802\) 0 0
\(803\) 29.9448i 1.05673i
\(804\) 0 0
\(805\) 1.45911 0.0514270
\(806\) 0 0
\(807\) 7.01250 + 15.0920i 0.246852 + 0.531263i
\(808\) 0 0
\(809\) 0.248801i 0.00874739i −0.999990 0.00437369i \(-0.998608\pi\)
0.999990 0.00437369i \(-0.00139219\pi\)
\(810\) 0 0
\(811\) 9.07141i 0.318540i 0.987235 + 0.159270i \(0.0509141\pi\)
−0.987235 + 0.159270i \(0.949086\pi\)
\(812\) 0 0
\(813\) 13.5651 + 29.1941i 0.475748 + 1.02388i
\(814\) 0 0
\(815\) 18.9344i 0.663243i
\(816\) 0 0
\(817\) −1.73455 + 0.586867i −0.0606842 + 0.0205319i
\(818\) 0 0
\(819\) 12.0321 + 10.1521i 0.420435 + 0.354743i
\(820\) 0 0
\(821\) 6.31807i 0.220502i −0.993904 0.110251i \(-0.964835\pi\)
0.993904 0.110251i \(-0.0351655\pi\)
\(822\) 0 0
\(823\) −9.46537 −0.329942 −0.164971 0.986298i \(-0.552753\pi\)
−0.164971 + 0.986298i \(0.552753\pi\)
\(824\) 0 0
\(825\) −13.7321 + 6.38065i −0.478092 + 0.222146i
\(826\) 0 0
\(827\) 0.938117 0.0326215 0.0163108 0.999867i \(-0.494808\pi\)
0.0163108 + 0.999867i \(0.494808\pi\)
\(828\) 0 0
\(829\) 47.9726i 1.66616i −0.553153 0.833079i \(-0.686576\pi\)
0.553153 0.833079i \(-0.313424\pi\)
\(830\) 0 0
\(831\) 8.34689 + 17.9638i 0.289550 + 0.623157i
\(832\) 0 0
\(833\) 4.34143i 0.150422i
\(834\) 0 0
\(835\) 5.46558i 0.189144i
\(836\) 0 0
\(837\) −0.703037 + 2.58153i −0.0243005 + 0.0892307i
\(838\) 0 0
\(839\) 14.7186 0.508144 0.254072 0.967185i \(-0.418230\pi\)
0.254072 + 0.967185i \(0.418230\pi\)
\(840\) 0 0
\(841\) −14.0290 −0.483760
\(842\) 0 0
\(843\) 15.4565 + 33.2647i 0.532349 + 1.14570i
\(844\) 0 0
\(845\) 11.6494i 0.400750i
\(846\) 0 0
\(847\) 13.3660 0.459260
\(848\) 0 0
\(849\) 3.41430 + 7.34810i 0.117178 + 0.252186i
\(850\) 0 0
\(851\) −2.19133 −0.0751177
\(852\) 0 0
\(853\) 41.4691 1.41987 0.709937 0.704265i \(-0.248723\pi\)
0.709937 + 0.704265i \(0.248723\pi\)
\(854\) 0 0
\(855\) −14.9083 5.86150i −0.509851 0.200459i
\(856\) 0 0
\(857\) 39.4595 1.34791 0.673956 0.738772i \(-0.264594\pi\)
0.673956 + 0.738772i \(0.264594\pi\)
\(858\) 0 0
\(859\) −38.5338 −1.31475 −0.657377 0.753561i \(-0.728334\pi\)
−0.657377 + 0.753561i \(0.728334\pi\)
\(860\) 0 0
\(861\) −4.93957 10.6307i −0.168340 0.362294i
\(862\) 0 0
\(863\) −25.8874 −0.881217 −0.440609 0.897699i \(-0.645237\pi\)
−0.440609 + 0.897699i \(0.645237\pi\)
\(864\) 0 0
\(865\) 23.3401i 0.793588i
\(866\) 0 0
\(867\) 4.98393 + 10.7262i 0.169263 + 0.364280i
\(868\) 0 0
\(869\) −4.03511 −0.136882
\(870\) 0 0
\(871\) −26.3448 −0.892661
\(872\) 0 0
\(873\) 5.69378 + 4.80414i 0.192705 + 0.162596i
\(874\) 0 0
\(875\) 29.2447i 0.988653i
\(876\) 0 0
\(877\) 14.1823i 0.478901i 0.970909 + 0.239451i \(0.0769673\pi\)
−0.970909 + 0.239451i \(0.923033\pi\)
\(878\) 0 0
\(879\) 9.78370 + 21.0560i 0.329996 + 0.710203i
\(880\) 0 0
\(881\) 26.2348i 0.883871i −0.897047 0.441936i \(-0.854292\pi\)
0.897047 0.441936i \(-0.145708\pi\)
\(882\) 0 0
\(883\) −22.2365 −0.748317 −0.374158 0.927365i \(-0.622068\pi\)
−0.374158 + 0.927365i \(0.622068\pi\)
\(884\) 0 0
\(885\) 7.00108 3.25305i 0.235339 0.109350i
\(886\) 0 0
\(887\) 48.4735 1.62758 0.813790 0.581159i \(-0.197400\pi\)
0.813790 + 0.581159i \(0.197400\pi\)
\(888\) 0 0
\(889\) 20.2322i 0.678566i
\(890\) 0 0
\(891\) −22.1639 + 3.78370i −0.742517 + 0.126759i
\(892\) 0 0
\(893\) −15.0044 44.3471i −0.502103 1.48402i
\(894\) 0 0
\(895\) 19.5708i 0.654179i
\(896\) 0 0
\(897\) 0.578235 + 1.24445i 0.0193067 + 0.0415510i
\(898\) 0 0
\(899\) 1.99230i 0.0664471i
\(900\) 0 0
\(901\) 37.6734i 1.25508i
\(902\) 0 0
\(903\) 0.861200 + 1.85344i 0.0286589 + 0.0616785i
\(904\) 0 0
\(905\) 6.44023 0.214081
\(906\) 0 0
\(907\) 41.9850i 1.39409i 0.717028 + 0.697045i \(0.245502\pi\)
−0.717028 + 0.697045i \(0.754498\pi\)
\(908\) 0 0
\(909\) 36.5609 + 30.8483i 1.21265 + 1.02318i
\(910\) 0 0
\(911\) −24.8668 −0.823873 −0.411937 0.911213i \(-0.635147\pi\)
−0.411937 + 0.911213i \(0.635147\pi\)
\(912\) 0 0
\(913\) 14.1963 0.469827
\(914\) 0 0
\(915\) −3.57711 + 1.66211i −0.118256 + 0.0549476i
\(916\) 0 0
\(917\) 0.135521i 0.00447529i
\(918\) 0 0
\(919\) −36.4355 −1.20190 −0.600948 0.799288i \(-0.705210\pi\)
−0.600948 + 0.799288i \(0.705210\pi\)
\(920\) 0 0
\(921\) 41.2429 19.1635i 1.35900 0.631459i
\(922\) 0 0
\(923\) 29.1205i 0.958513i
\(924\) 0 0
\(925\) 18.0828i 0.594560i
\(926\) 0 0
\(927\) −41.0225 34.6129i −1.34736 1.13684i
\(928\) 0 0
\(929\) 20.7869i 0.681997i −0.940064 0.340999i \(-0.889235\pi\)
0.940064 0.340999i \(-0.110765\pi\)
\(930\) 0 0
\(931\) 3.67219 1.24245i 0.120351 0.0407196i
\(932\) 0 0
\(933\) −16.3770 + 7.60960i −0.536160 + 0.249127i
\(934\) 0 0
\(935\) 14.9394i 0.488569i
\(936\) 0 0
\(937\) 29.1210 0.951341 0.475671 0.879623i \(-0.342205\pi\)
0.475671 + 0.879623i \(0.342205\pi\)
\(938\) 0 0
\(939\) 8.07789 + 17.3849i 0.263612 + 0.567334i
\(940\) 0 0
\(941\) −20.7848 −0.677565 −0.338783 0.940865i \(-0.610015\pi\)
−0.338783 + 0.940865i \(0.610015\pi\)
\(942\) 0 0
\(943\) 1.02178i 0.0332737i
\(944\) 0 0
\(945\) −4.69797 + 17.2508i −0.152825 + 0.561168i
\(946\) 0 0
\(947\) 16.5344i 0.537294i 0.963239 + 0.268647i \(0.0865766\pi\)
−0.963239 + 0.268647i \(0.913423\pi\)
\(948\) 0 0
\(949\) 22.3934i 0.726921i
\(950\) 0 0
\(951\) 2.15992 + 4.64847i 0.0700401 + 0.150737i
\(952\) 0 0
\(953\) −1.99710 −0.0646923 −0.0323462 0.999477i \(-0.510298\pi\)
−0.0323462 + 0.999477i \(0.510298\pi\)
\(954\) 0 0
\(955\) 6.53312 0.211407
\(956\) 0 0
\(957\) −15.1837 + 7.05511i −0.490819 + 0.228059i
\(958\) 0 0
\(959\) 47.3456i 1.52887i
\(960\) 0 0
\(961\) 30.7349 0.991447
\(962\) 0 0
\(963\) 2.57729 3.05455i 0.0830519 0.0984316i
\(964\) 0 0
\(965\) −25.9737 −0.836122
\(966\) 0 0
\(967\) 36.0754 1.16011 0.580053 0.814579i \(-0.303032\pi\)
0.580053 + 0.814579i \(0.303032\pi\)
\(968\) 0 0
\(969\) 26.6823 25.4222i 0.857157 0.816679i
\(970\) 0 0
\(971\) 14.9370 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(972\) 0 0
\(973\) −29.5399 −0.947005
\(974\) 0 0
\(975\) −10.2692 + 4.77160i −0.328878 + 0.152813i
\(976\) 0 0
\(977\) −20.0411 −0.641171 −0.320586 0.947220i \(-0.603880\pi\)
−0.320586 + 0.947220i \(0.603880\pi\)
\(978\) 0 0
\(979\) 28.6453i 0.915509i
\(980\) 0 0
\(981\) −37.9802 32.0459i −1.21261 1.02315i
\(982\) 0 0
\(983\) −16.3031 −0.519990 −0.259995 0.965610i \(-0.583721\pi\)
−0.259995 + 0.965610i \(0.583721\pi\)
\(984\) 0 0
\(985\) −25.3398 −0.807395
\(986\) 0 0
\(987\) −47.3866 + 22.0182i −1.50833 + 0.700848i
\(988\) 0 0
\(989\) 0.178144i 0.00566465i
\(990\) 0 0
\(991\) 17.5862i 0.558645i 0.960197 + 0.279322i \(0.0901098\pi\)
−0.960197 + 0.279322i \(0.909890\pi\)
\(992\) 0 0
\(993\) −7.15827 + 3.32610i −0.227161 + 0.105550i
\(994\) 0 0
\(995\) 3.78628i 0.120033i
\(996\) 0 0
\(997\) 44.8255 1.41964 0.709819 0.704384i \(-0.248777\pi\)
0.709819 + 0.704384i \(0.248777\pi\)
\(998\) 0 0
\(999\) 7.05550 25.9076i 0.223226 0.819680i
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 912.2.f.i.113.3 10
3.2 odd 2 912.2.f.h.113.7 10
4.3 odd 2 456.2.f.a.113.8 yes 10
12.11 even 2 456.2.f.b.113.4 yes 10
19.18 odd 2 912.2.f.h.113.8 10
57.56 even 2 inner 912.2.f.i.113.4 10
76.75 even 2 456.2.f.b.113.3 yes 10
228.227 odd 2 456.2.f.a.113.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.f.a.113.7 10 228.227 odd 2
456.2.f.a.113.8 yes 10 4.3 odd 2
456.2.f.b.113.3 yes 10 76.75 even 2
456.2.f.b.113.4 yes 10 12.11 even 2
912.2.f.h.113.7 10 3.2 odd 2
912.2.f.h.113.8 10 19.18 odd 2
912.2.f.i.113.3 10 1.1 even 1 trivial
912.2.f.i.113.4 10 57.56 even 2 inner