Properties

Label 804.2.ba.b.353.3
Level $804$
Weight $2$
Character 804.353
Analytic conductor $6.420$
Analytic rank $0$
Dimension $440$
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] = [804,2,Mod(41,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 33, 53]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.ba (of order \(66\), degree \(20\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 353.3
Character \(\chi\) \(=\) 804.353
Dual form 804.2.ba.b.41.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.68954 + 0.381398i) q^{3} +(0.606307 + 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(2.70907 - 1.28877i) q^{9} +O(q^{10})\) \(q+(-1.68954 + 0.381398i) q^{3} +(0.606307 + 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(2.70907 - 1.28877i) q^{9} +(5.34850 + 2.14122i) q^{11} +(1.06287 - 1.11471i) q^{13} +(-2.63272 - 6.89346i) q^{15} +(3.13592 + 1.08535i) q^{17} +(0.373168 - 0.0356332i) q^{19} +(-0.679910 - 5.33244i) q^{21} +(-3.36039 - 0.160075i) q^{23} +(-12.6176 + 3.70487i) q^{25} +(-4.08554 + 3.21067i) q^{27} +(5.55526 + 3.20733i) q^{29} +(-5.06664 - 5.31374i) q^{31} +(-9.85315 - 1.57776i) q^{33} +(-13.2074 + 0.629146i) q^{35} +(2.92489 + 5.06605i) q^{37} +(-1.37061 + 2.28871i) q^{39} +(10.4018 - 2.00479i) q^{41} +(0.118743 - 0.102891i) q^{43} +(7.07723 + 10.6426i) q^{45} +(-2.91118 - 5.64690i) q^{47} +(-2.58483 - 0.498185i) q^{49} +(-5.71220 - 0.637708i) q^{51} +(-1.39615 + 1.61125i) q^{53} +(-5.78658 + 23.8526i) q^{55} +(-0.616890 + 0.202529i) q^{57} +(-0.864195 + 2.94318i) q^{59} +(-5.18649 - 12.9552i) q^{61} +(3.18252 + 8.75004i) q^{63} +(5.34509 + 3.80622i) q^{65} +(1.49951 - 8.04683i) q^{67} +(5.73856 - 1.01119i) q^{69} +(-4.54395 + 1.57268i) q^{71} +(2.76888 - 1.10849i) q^{73} +(19.9049 - 11.0719i) q^{75} +(-8.19331 + 15.8928i) q^{77} +(0.363719 + 0.0882373i) q^{79} +(5.67813 - 6.98276i) q^{81} +(-6.94036 - 8.82538i) q^{83} +(-2.67555 + 13.8821i) q^{85} +(-10.6091 - 3.30014i) q^{87} +(1.23838 + 1.92696i) q^{89} +(3.13038 + 3.61265i) q^{91} +(10.5869 + 7.04535i) q^{93} +(0.376518 + 1.55203i) q^{95} +(-0.393962 + 0.227454i) q^{97} +(17.2490 - 1.09230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{66}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.68954 + 0.381398i −0.975455 + 0.220200i
\(4\) 0 0
\(5\) 0.606307 + 4.21696i 0.271149 + 1.88588i 0.436590 + 0.899660i \(0.356186\pi\)
−0.165442 + 0.986220i \(0.552905\pi\)
\(6\) 0 0
\(7\) −0.295017 + 3.08956i −0.111506 + 1.16774i 0.750509 + 0.660860i \(0.229808\pi\)
−0.862015 + 0.506883i \(0.830798\pi\)
\(8\) 0 0
\(9\) 2.70907 1.28877i 0.903024 0.429591i
\(10\) 0 0
\(11\) 5.34850 + 2.14122i 1.61263 + 0.645601i 0.990525 0.137330i \(-0.0438522\pi\)
0.622108 + 0.782931i \(0.286276\pi\)
\(12\) 0 0
\(13\) 1.06287 1.11471i 0.294787 0.309164i −0.559639 0.828736i \(-0.689060\pi\)
0.854426 + 0.519573i \(0.173909\pi\)
\(14\) 0 0
\(15\) −2.63272 6.89346i −0.679765 1.77988i
\(16\) 0 0
\(17\) 3.13592 + 1.08535i 0.760572 + 0.263236i 0.679702 0.733488i \(-0.262109\pi\)
0.0808697 + 0.996725i \(0.474230\pi\)
\(18\) 0 0
\(19\) 0.373168 0.0356332i 0.0856105 0.00817481i −0.0521629 0.998639i \(-0.516611\pi\)
0.137773 + 0.990464i \(0.456005\pi\)
\(20\) 0 0
\(21\) −0.679910 5.33244i −0.148369 1.16363i
\(22\) 0 0
\(23\) −3.36039 0.160075i −0.700690 0.0333780i −0.305786 0.952100i \(-0.598919\pi\)
−0.394904 + 0.918722i \(0.629222\pi\)
\(24\) 0 0
\(25\) −12.6176 + 3.70487i −2.52353 + 0.740975i
\(26\) 0 0
\(27\) −4.08554 + 3.21067i −0.786262 + 0.617893i
\(28\) 0 0
\(29\) 5.55526 + 3.20733i 1.03159 + 0.595586i 0.917438 0.397878i \(-0.130253\pi\)
0.114147 + 0.993464i \(0.463586\pi\)
\(30\) 0 0
\(31\) −5.06664 5.31374i −0.909996 0.954376i 0.0891369 0.996019i \(-0.471589\pi\)
−0.999133 + 0.0416434i \(0.986741\pi\)
\(32\) 0 0
\(33\) −9.85315 1.57776i −1.71521 0.274652i
\(34\) 0 0
\(35\) −13.2074 + 0.629146i −2.23246 + 0.106345i
\(36\) 0 0
\(37\) 2.92489 + 5.06605i 0.480848 + 0.832854i 0.999759 0.0219750i \(-0.00699543\pi\)
−0.518910 + 0.854829i \(0.673662\pi\)
\(38\) 0 0
\(39\) −1.37061 + 2.28871i −0.219473 + 0.366487i
\(40\) 0 0
\(41\) 10.4018 2.00479i 1.62449 0.313095i 0.705903 0.708308i \(-0.250541\pi\)
0.918590 + 0.395213i \(0.129329\pi\)
\(42\) 0 0
\(43\) 0.118743 0.102891i 0.0181081 0.0156908i −0.645760 0.763541i \(-0.723459\pi\)
0.663868 + 0.747850i \(0.268914\pi\)
\(44\) 0 0
\(45\) 7.07723 + 10.6426i 1.05501 + 1.58651i
\(46\) 0 0
\(47\) −2.91118 5.64690i −0.424639 0.823685i −0.999983 0.00577368i \(-0.998162\pi\)
0.575344 0.817911i \(-0.304868\pi\)
\(48\) 0 0
\(49\) −2.58483 0.498185i −0.369261 0.0711692i
\(50\) 0 0
\(51\) −5.71220 0.637708i −0.799868 0.0892970i
\(52\) 0 0
\(53\) −1.39615 + 1.61125i −0.191776 + 0.221322i −0.843492 0.537142i \(-0.819504\pi\)
0.651716 + 0.758463i \(0.274050\pi\)
\(54\) 0 0
\(55\) −5.78658 + 23.8526i −0.780263 + 3.21629i
\(56\) 0 0
\(57\) −0.616890 + 0.202529i −0.0817091 + 0.0268256i
\(58\) 0 0
\(59\) −0.864195 + 2.94318i −0.112509 + 0.383169i −0.996426 0.0844747i \(-0.973079\pi\)
0.883917 + 0.467644i \(0.154897\pi\)
\(60\) 0 0
\(61\) −5.18649 12.9552i −0.664062 1.65875i −0.749173 0.662375i \(-0.769549\pi\)
0.0851109 0.996371i \(-0.472876\pi\)
\(62\) 0 0
\(63\) 3.18252 + 8.75004i 0.400959 + 1.10240i
\(64\) 0 0
\(65\) 5.34509 + 3.80622i 0.662977 + 0.472104i
\(66\) 0 0
\(67\) 1.49951 8.04683i 0.183194 0.983077i
\(68\) 0 0
\(69\) 5.73856 1.01119i 0.690841 0.121734i
\(70\) 0 0
\(71\) −4.54395 + 1.57268i −0.539268 + 0.186642i −0.583106 0.812396i \(-0.698163\pi\)
0.0438379 + 0.999039i \(0.486041\pi\)
\(72\) 0 0
\(73\) 2.76888 1.10849i 0.324073 0.129739i −0.203921 0.978987i \(-0.565369\pi\)
0.527994 + 0.849248i \(0.322944\pi\)
\(74\) 0 0
\(75\) 19.9049 11.0719i 2.29842 1.27847i
\(76\) 0 0
\(77\) −8.19331 + 15.8928i −0.933714 + 1.81115i
\(78\) 0 0
\(79\) 0.363719 + 0.0882373i 0.0409216 + 0.00992748i 0.256167 0.966632i \(-0.417540\pi\)
−0.215246 + 0.976560i \(0.569055\pi\)
\(80\) 0 0
\(81\) 5.67813 6.98276i 0.630903 0.775862i
\(82\) 0 0
\(83\) −6.94036 8.82538i −0.761803 0.968712i 0.238194 0.971218i \(-0.423445\pi\)
−0.999997 + 0.00250596i \(0.999202\pi\)
\(84\) 0 0
\(85\) −2.67555 + 13.8821i −0.290204 + 1.50572i
\(86\) 0 0
\(87\) −10.6091 3.30014i −1.13741 0.353812i
\(88\) 0 0
\(89\) 1.23838 + 1.92696i 0.131268 + 0.204258i 0.900665 0.434513i \(-0.143080\pi\)
−0.769397 + 0.638771i \(0.779443\pi\)
\(90\) 0 0
\(91\) 3.13038 + 3.61265i 0.328153 + 0.378709i
\(92\) 0 0
\(93\) 10.5869 + 7.04535i 1.09781 + 0.730569i
\(94\) 0 0
\(95\) 0.376518 + 1.55203i 0.0386299 + 0.159235i
\(96\) 0 0
\(97\) −0.393962 + 0.227454i −0.0400008 + 0.0230945i −0.519867 0.854247i \(-0.674019\pi\)
0.479866 + 0.877342i \(0.340685\pi\)
\(98\) 0 0
\(99\) 17.2490 1.09230i 1.73359 0.109780i
\(100\) 0 0
\(101\) −7.12702 10.0085i −0.709165 0.995882i −0.999244 0.0388797i \(-0.987621\pi\)
0.290079 0.957003i \(-0.406318\pi\)
\(102\) 0 0
\(103\) −13.1880 + 12.5747i −1.29945 + 1.23902i −0.345726 + 0.938336i \(0.612367\pi\)
−0.953723 + 0.300686i \(0.902784\pi\)
\(104\) 0 0
\(105\) 22.0744 6.10024i 2.15424 0.595323i
\(106\) 0 0
\(107\) 1.02067 + 0.146751i 0.0986721 + 0.0141869i 0.191474 0.981498i \(-0.438673\pi\)
−0.0928019 + 0.995685i \(0.529582\pi\)
\(108\) 0 0
\(109\) −3.29791 11.2316i −0.315882 1.07580i −0.952480 0.304601i \(-0.901477\pi\)
0.636598 0.771196i \(-0.280341\pi\)
\(110\) 0 0
\(111\) −6.87389 7.44373i −0.652441 0.706528i
\(112\) 0 0
\(113\) 7.84294 + 6.16776i 0.737802 + 0.580214i 0.914757 0.404005i \(-0.132382\pi\)
−0.176955 + 0.984219i \(0.556625\pi\)
\(114\) 0 0
\(115\) −1.36240 14.2677i −0.127044 1.33047i
\(116\) 0 0
\(117\) 1.44279 4.38961i 0.133386 0.405820i
\(118\) 0 0
\(119\) −4.27841 + 9.36840i −0.392201 + 0.858800i
\(120\) 0 0
\(121\) 16.0606 + 15.3137i 1.46005 + 1.39216i
\(122\) 0 0
\(123\) −16.8097 + 7.35440i −1.51568 + 0.663124i
\(124\) 0 0
\(125\) −14.4244 31.5851i −1.29016 2.82506i
\(126\) 0 0
\(127\) 6.65841 + 0.635801i 0.590839 + 0.0564183i 0.386193 0.922418i \(-0.373790\pi\)
0.204645 + 0.978836i \(0.434396\pi\)
\(128\) 0 0
\(129\) −0.161378 + 0.219127i −0.0142085 + 0.0192930i
\(130\) 0 0
\(131\) 2.72329 4.23752i 0.237935 0.370234i −0.701666 0.712506i \(-0.747560\pi\)
0.939601 + 0.342272i \(0.111197\pi\)
\(132\) 0 0
\(133\) 1.16343i 0.100883i
\(134\) 0 0
\(135\) −16.0163 15.2819i −1.37847 1.31526i
\(136\) 0 0
\(137\) −14.7333 9.46850i −1.25875 0.808948i −0.270636 0.962682i \(-0.587234\pi\)
−0.988112 + 0.153734i \(0.950870\pi\)
\(138\) 0 0
\(139\) 8.55641 1.23023i 0.725746 0.104346i 0.230466 0.973080i \(-0.425975\pi\)
0.495279 + 0.868734i \(0.335066\pi\)
\(140\) 0 0
\(141\) 7.07226 + 8.43033i 0.595592 + 0.709962i
\(142\) 0 0
\(143\) 8.07158 3.68617i 0.674980 0.308253i
\(144\) 0 0
\(145\) −10.1570 + 25.3709i −0.843491 + 2.10694i
\(146\) 0 0
\(147\) 4.55717 0.144147i 0.375869 0.0118891i
\(148\) 0 0
\(149\) 9.94457 + 4.54153i 0.814691 + 0.372057i 0.778779 0.627298i \(-0.215839\pi\)
0.0359117 + 0.999355i \(0.488567\pi\)
\(150\) 0 0
\(151\) 3.03650 8.77339i 0.247107 0.713968i −0.751426 0.659817i \(-0.770634\pi\)
0.998533 0.0541507i \(-0.0172452\pi\)
\(152\) 0 0
\(153\) 9.89420 1.10119i 0.799898 0.0890262i
\(154\) 0 0
\(155\) 19.3359 24.5876i 1.55309 1.97492i
\(156\) 0 0
\(157\) −0.126031 + 2.64571i −0.0100584 + 0.211151i 0.988243 + 0.152891i \(0.0488583\pi\)
−0.998301 + 0.0582601i \(0.981445\pi\)
\(158\) 0 0
\(159\) 1.74433 3.25475i 0.138334 0.258119i
\(160\) 0 0
\(161\) 1.48593 10.3349i 0.117108 0.814504i
\(162\) 0 0
\(163\) 7.59768 13.1596i 0.595096 1.03074i −0.398437 0.917196i \(-0.630447\pi\)
0.993533 0.113541i \(-0.0362194\pi\)
\(164\) 0 0
\(165\) 0.679296 42.5069i 0.0528831 3.30916i
\(166\) 0 0
\(167\) 9.89558 7.04661i 0.765743 0.545283i −0.129117 0.991629i \(-0.541214\pi\)
0.894860 + 0.446346i \(0.147275\pi\)
\(168\) 0 0
\(169\) 0.505688 + 10.6157i 0.0388991 + 0.816592i
\(170\) 0 0
\(171\) 0.965014 0.577461i 0.0737965 0.0441596i
\(172\) 0 0
\(173\) 6.27092 1.52131i 0.476769 0.115663i 0.00982875 0.999952i \(-0.496871\pi\)
0.466941 + 0.884289i \(0.345356\pi\)
\(174\) 0 0
\(175\) −7.72400 40.0759i −0.583880 3.02946i
\(176\) 0 0
\(177\) 0.337566 5.30221i 0.0253730 0.398538i
\(178\) 0 0
\(179\) 19.2913 12.3978i 1.44190 0.926653i 0.442344 0.896845i \(-0.354147\pi\)
0.999556 0.0298077i \(-0.00948948\pi\)
\(180\) 0 0
\(181\) −11.7407 + 6.05273i −0.872677 + 0.449896i −0.835550 0.549414i \(-0.814851\pi\)
−0.0371268 + 0.999311i \(0.511821\pi\)
\(182\) 0 0
\(183\) 13.7039 + 19.9102i 1.01302 + 1.47180i
\(184\) 0 0
\(185\) −19.5899 + 15.4057i −1.44028 + 1.13265i
\(186\) 0 0
\(187\) 14.4485 + 12.5197i 1.05658 + 0.915530i
\(188\) 0 0
\(189\) −8.71423 13.5697i −0.633867 0.987051i
\(190\) 0 0
\(191\) −2.68091 1.38211i −0.193984 0.100006i 0.358498 0.933530i \(-0.383289\pi\)
−0.552482 + 0.833525i \(0.686319\pi\)
\(192\) 0 0
\(193\) 6.64319 + 1.95062i 0.478187 + 0.140408i 0.511939 0.859022i \(-0.328927\pi\)
−0.0337517 + 0.999430i \(0.510746\pi\)
\(194\) 0 0
\(195\) −10.4824 4.39214i −0.750661 0.314528i
\(196\) 0 0
\(197\) −3.87942 11.2088i −0.276397 0.798596i −0.994696 0.102862i \(-0.967200\pi\)
0.718299 0.695735i \(-0.244921\pi\)
\(198\) 0 0
\(199\) −11.6192 + 16.3169i −0.823663 + 1.15667i 0.161807 + 0.986822i \(0.448268\pi\)
−0.985470 + 0.169850i \(0.945672\pi\)
\(200\) 0 0
\(201\) 0.535570 + 14.1673i 0.0377762 + 0.999286i
\(202\) 0 0
\(203\) −11.5481 + 16.2171i −0.810519 + 1.13822i
\(204\) 0 0
\(205\) 14.7608 + 42.6485i 1.03094 + 2.97870i
\(206\) 0 0
\(207\) −9.30984 + 3.89713i −0.647079 + 0.270869i
\(208\) 0 0
\(209\) 2.07219 + 0.608449i 0.143336 + 0.0420873i
\(210\) 0 0
\(211\) 22.8993 + 11.8054i 1.57645 + 0.812718i 0.999990 0.00440540i \(-0.00140229\pi\)
0.576463 + 0.817123i \(0.304433\pi\)
\(212\) 0 0
\(213\) 7.07736 4.39015i 0.484933 0.300808i
\(214\) 0 0
\(215\) 0.505882 + 0.438350i 0.0345009 + 0.0298952i
\(216\) 0 0
\(217\) 17.9118 14.0860i 1.21594 0.956222i
\(218\) 0 0
\(219\) −4.25534 + 2.92888i −0.287550 + 0.197916i
\(220\) 0 0
\(221\) 4.54292 2.34204i 0.305590 0.157543i
\(222\) 0 0
\(223\) −11.7753 + 7.56750i −0.788530 + 0.506757i −0.871854 0.489765i \(-0.837083\pi\)
0.0833246 + 0.996522i \(0.473446\pi\)
\(224\) 0 0
\(225\) −29.4073 + 26.2980i −1.96049 + 1.75320i
\(226\) 0 0
\(227\) 4.97463 + 25.8108i 0.330178 + 1.71312i 0.645177 + 0.764033i \(0.276784\pi\)
−0.314999 + 0.949092i \(0.602004\pi\)
\(228\) 0 0
\(229\) 6.42665 1.55909i 0.424685 0.103027i −0.0177199 0.999843i \(-0.505641\pi\)
0.442405 + 0.896816i \(0.354126\pi\)
\(230\) 0 0
\(231\) 7.78141 29.9764i 0.511979 1.97230i
\(232\) 0 0
\(233\) 0.980955 + 20.5928i 0.0642645 + 1.34908i 0.768837 + 0.639445i \(0.220836\pi\)
−0.704572 + 0.709632i \(0.748861\pi\)
\(234\) 0 0
\(235\) 22.0477 15.7001i 1.43823 1.02416i
\(236\) 0 0
\(237\) −0.648171 0.0103583i −0.0421032 0.000672845i
\(238\) 0 0
\(239\) −3.37469 + 5.84513i −0.218290 + 0.378090i −0.954285 0.298897i \(-0.903381\pi\)
0.735995 + 0.676987i \(0.236715\pi\)
\(240\) 0 0
\(241\) 3.90362 27.1503i 0.251454 1.74890i −0.338042 0.941131i \(-0.609765\pi\)
0.589496 0.807771i \(-0.299326\pi\)
\(242\) 0 0
\(243\) −6.93019 + 13.9633i −0.444572 + 0.895743i
\(244\) 0 0
\(245\) 0.533624 11.2022i 0.0340920 0.715679i
\(246\) 0 0
\(247\) 0.356908 0.453845i 0.0227095 0.0288775i
\(248\) 0 0
\(249\) 15.0920 + 12.2638i 0.956415 + 0.777185i
\(250\) 0 0
\(251\) 3.62965 10.4872i 0.229101 0.661945i −0.770595 0.637325i \(-0.780041\pi\)
0.999697 0.0246205i \(-0.00783774\pi\)
\(252\) 0 0
\(253\) −17.6303 8.05149i −1.10841 0.506193i
\(254\) 0 0
\(255\) −0.774159 24.4747i −0.0484797 1.53267i
\(256\) 0 0
\(257\) −7.02930 + 17.5583i −0.438475 + 1.09526i 0.530408 + 0.847742i \(0.322039\pi\)
−0.968884 + 0.247516i \(0.920386\pi\)
\(258\) 0 0
\(259\) −16.5147 + 7.54203i −1.02618 + 0.468639i
\(260\) 0 0
\(261\) 19.1831 + 1.52941i 1.18740 + 0.0946684i
\(262\) 0 0
\(263\) 13.9779 2.00973i 0.861917 0.123925i 0.302841 0.953041i \(-0.402065\pi\)
0.559076 + 0.829116i \(0.311156\pi\)
\(264\) 0 0
\(265\) −7.64106 4.91061i −0.469386 0.301656i
\(266\) 0 0
\(267\) −2.82724 2.78336i −0.173024 0.170339i
\(268\) 0 0
\(269\) 16.1978i 0.987597i 0.869576 + 0.493799i \(0.164392\pi\)
−0.869576 + 0.493799i \(0.835608\pi\)
\(270\) 0 0
\(271\) 2.88664 4.49170i 0.175351 0.272851i −0.742442 0.669910i \(-0.766333\pi\)
0.917793 + 0.397059i \(0.129969\pi\)
\(272\) 0 0
\(273\) −6.66676 4.90979i −0.403490 0.297154i
\(274\) 0 0
\(275\) −75.4184 7.20158i −4.54790 0.434272i
\(276\) 0 0
\(277\) −10.0366 21.9772i −0.603043 1.32048i −0.927232 0.374487i \(-0.877819\pi\)
0.324189 0.945992i \(-0.394909\pi\)
\(278\) 0 0
\(279\) −20.5741 7.86555i −1.23174 0.470898i
\(280\) 0 0
\(281\) 13.0301 + 12.4242i 0.777312 + 0.741166i 0.970788 0.239939i \(-0.0771275\pi\)
−0.193476 + 0.981105i \(0.561976\pi\)
\(282\) 0 0
\(283\) 1.76612 3.86727i 0.104985 0.229885i −0.849848 0.527028i \(-0.823306\pi\)
0.954833 + 0.297142i \(0.0960336\pi\)
\(284\) 0 0
\(285\) −1.22808 2.47860i −0.0727452 0.146820i
\(286\) 0 0
\(287\) 3.12519 + 32.7285i 0.184474 + 1.93190i
\(288\) 0 0
\(289\) −4.70691 3.70155i −0.276877 0.217738i
\(290\) 0 0
\(291\) 0.578863 0.534549i 0.0339335 0.0313358i
\(292\) 0 0
\(293\) 2.18836 + 7.45288i 0.127845 + 0.435402i 0.998392 0.0566841i \(-0.0180528\pi\)
−0.870547 + 0.492086i \(0.836235\pi\)
\(294\) 0 0
\(295\) −12.9352 1.85980i −0.753117 0.108282i
\(296\) 0 0
\(297\) −28.7262 + 8.42422i −1.66687 + 0.488823i
\(298\) 0 0
\(299\) −3.75010 + 3.57571i −0.216874 + 0.206789i
\(300\) 0 0
\(301\) 0.282857 + 0.397217i 0.0163036 + 0.0228952i
\(302\) 0 0
\(303\) 15.8586 + 14.1915i 0.911052 + 0.815280i
\(304\) 0 0
\(305\) 51.4870 29.7260i 2.94814 1.70211i
\(306\) 0 0
\(307\) 1.30583 + 5.38272i 0.0745279 + 0.307208i 0.996859 0.0791913i \(-0.0252338\pi\)
−0.922332 + 0.386399i \(0.873719\pi\)
\(308\) 0 0
\(309\) 17.4856 26.2753i 0.994720 1.49475i
\(310\) 0 0
\(311\) 7.91488 + 9.13426i 0.448812 + 0.517956i 0.934397 0.356233i \(-0.115939\pi\)
−0.485586 + 0.874189i \(0.661394\pi\)
\(312\) 0 0
\(313\) −15.9193 24.7709i −0.899813 1.40014i −0.916396 0.400274i \(-0.868915\pi\)
0.0165828 0.999862i \(-0.494721\pi\)
\(314\) 0 0
\(315\) −34.9689 + 18.7257i −1.97028 + 1.05508i
\(316\) 0 0
\(317\) 2.77787 14.4130i 0.156021 0.809514i −0.816616 0.577182i \(-0.804152\pi\)
0.972637 0.232332i \(-0.0746355\pi\)
\(318\) 0 0
\(319\) 22.8447 + 29.0494i 1.27906 + 1.62646i
\(320\) 0 0
\(321\) −1.78043 + 0.141342i −0.0993742 + 0.00788896i
\(322\) 0 0
\(323\) 1.20890 + 0.293275i 0.0672649 + 0.0163183i
\(324\) 0 0
\(325\) −9.28107 + 18.0028i −0.514821 + 0.998613i
\(326\) 0 0
\(327\) 9.85567 + 17.7185i 0.545020 + 0.979833i
\(328\) 0 0
\(329\) 18.3053 7.32832i 1.00920 0.404024i
\(330\) 0 0
\(331\) 4.93615 1.70842i 0.271315 0.0939031i −0.188023 0.982165i \(-0.560208\pi\)
0.459338 + 0.888262i \(0.348087\pi\)
\(332\) 0 0
\(333\) 14.4527 + 9.95478i 0.792004 + 0.545518i
\(334\) 0 0
\(335\) 34.8423 + 1.44452i 1.90364 + 0.0789226i
\(336\) 0 0
\(337\) 15.9342 + 11.3467i 0.867990 + 0.618093i 0.924868 0.380288i \(-0.124175\pi\)
−0.0568779 + 0.998381i \(0.518115\pi\)
\(338\) 0 0
\(339\) −15.6033 7.42937i −0.847455 0.403508i
\(340\) 0 0
\(341\) −15.7211 39.2693i −0.851343 2.12655i
\(342\) 0 0
\(343\) −3.81898 + 13.0062i −0.206206 + 0.702271i
\(344\) 0 0
\(345\) 7.74349 + 23.5862i 0.416896 + 1.26984i
\(346\) 0 0
\(347\) −1.90110 + 7.83645i −0.102056 + 0.420683i −0.999803 0.0198291i \(-0.993688\pi\)
0.897747 + 0.440512i \(0.145203\pi\)
\(348\) 0 0
\(349\) 3.25401 3.75533i 0.174183 0.201018i −0.661945 0.749553i \(-0.730269\pi\)
0.836128 + 0.548535i \(0.184814\pi\)
\(350\) 0 0
\(351\) −0.763449 + 7.96669i −0.0407499 + 0.425231i
\(352\) 0 0
\(353\) −26.5842 5.12369i −1.41493 0.272706i −0.576228 0.817289i \(-0.695476\pi\)
−0.838707 + 0.544583i \(0.816688\pi\)
\(354\) 0 0
\(355\) −9.38694 18.2081i −0.498207 0.966387i
\(356\) 0 0
\(357\) 3.65543 17.4600i 0.193466 0.924083i
\(358\) 0 0
\(359\) −15.4265 + 13.3671i −0.814177 + 0.705489i −0.958826 0.283995i \(-0.908340\pi\)
0.144649 + 0.989483i \(0.453795\pi\)
\(360\) 0 0
\(361\) −18.5187 + 3.56918i −0.974666 + 0.187852i
\(362\) 0 0
\(363\) −32.9756 19.7476i −1.73077 1.03648i
\(364\) 0 0
\(365\) 6.35325 + 11.0041i 0.332544 + 0.575984i
\(366\) 0 0
\(367\) −17.2173 + 0.820159i −0.898734 + 0.0428120i −0.491862 0.870673i \(-0.663684\pi\)
−0.406872 + 0.913485i \(0.633381\pi\)
\(368\) 0 0
\(369\) 25.5956 18.8367i 1.33245 0.980600i
\(370\) 0 0
\(371\) −4.56615 4.78884i −0.237063 0.248624i
\(372\) 0 0
\(373\) −6.10626 3.52545i −0.316170 0.182541i 0.333514 0.942745i \(-0.391765\pi\)
−0.649684 + 0.760204i \(0.725099\pi\)
\(374\) 0 0
\(375\) 36.4172 + 47.8628i 1.88057 + 2.47162i
\(376\) 0 0
\(377\) 9.47974 2.78350i 0.488232 0.143358i
\(378\) 0 0
\(379\) −0.768266 0.0365970i −0.0394632 0.00187986i 0.0278410 0.999612i \(-0.491137\pi\)
−0.0673042 + 0.997732i \(0.521440\pi\)
\(380\) 0 0
\(381\) −11.4921 + 1.46530i −0.588760 + 0.0750695i
\(382\) 0 0
\(383\) 7.47379 0.713661i 0.381893 0.0364663i 0.0976555 0.995220i \(-0.468866\pi\)
0.284237 + 0.958754i \(0.408260\pi\)
\(384\) 0 0
\(385\) −71.9869 24.9149i −3.66879 1.26978i
\(386\) 0 0
\(387\) 0.189079 0.431772i 0.00961144 0.0219482i
\(388\) 0 0
\(389\) −11.1481 + 11.6917i −0.565229 + 0.592795i −0.942872 0.333156i \(-0.891886\pi\)
0.377643 + 0.925951i \(0.376735\pi\)
\(390\) 0 0
\(391\) −10.3642 4.14919i −0.524139 0.209834i
\(392\) 0 0
\(393\) −2.98491 + 8.19810i −0.150569 + 0.413539i
\(394\) 0 0
\(395\) −0.151568 + 1.58729i −0.00762619 + 0.0798651i
\(396\) 0 0
\(397\) 3.11736 + 21.6817i 0.156456 + 1.08818i 0.905099 + 0.425202i \(0.139797\pi\)
−0.748643 + 0.662974i \(0.769294\pi\)
\(398\) 0 0
\(399\) −0.443732 1.96567i −0.0222144 0.0984064i
\(400\) 0 0
\(401\) 27.5475 1.37566 0.687829 0.725873i \(-0.258564\pi\)
0.687829 + 0.725873i \(0.258564\pi\)
\(402\) 0 0
\(403\) −11.3084 −0.563313
\(404\) 0 0
\(405\) 32.8887 + 19.7107i 1.63425 + 0.979433i
\(406\) 0 0
\(407\) 4.79624 + 33.3586i 0.237741 + 1.65352i
\(408\) 0 0
\(409\) 2.08694 21.8554i 0.103193 1.08068i −0.784464 0.620175i \(-0.787062\pi\)
0.887656 0.460507i \(-0.152332\pi\)
\(410\) 0 0
\(411\) 28.5037 + 10.3781i 1.40598 + 0.511915i
\(412\) 0 0
\(413\) −8.83816 3.53827i −0.434897 0.174107i
\(414\) 0 0
\(415\) 33.0083 34.6181i 1.62031 1.69933i
\(416\) 0 0
\(417\) −13.9872 + 5.34192i −0.684955 + 0.261595i
\(418\) 0 0
\(419\) −20.6175 7.13577i −1.00723 0.348605i −0.226862 0.973927i \(-0.572847\pi\)
−0.780367 + 0.625322i \(0.784968\pi\)
\(420\) 0 0
\(421\) 9.37835 0.895524i 0.457073 0.0436452i 0.136019 0.990706i \(-0.456569\pi\)
0.321054 + 0.947061i \(0.395963\pi\)
\(422\) 0 0
\(423\) −15.1642 11.5460i −0.737307 0.561386i
\(424\) 0 0
\(425\) −43.5890 2.07640i −2.11438 0.100720i
\(426\) 0 0
\(427\) 41.5560 12.2019i 2.01104 0.590493i
\(428\) 0 0
\(429\) −12.2313 + 9.30641i −0.590535 + 0.449318i
\(430\) 0 0
\(431\) −23.2702 13.4351i −1.12089 0.647144i −0.179260 0.983802i \(-0.557370\pi\)
−0.941627 + 0.336657i \(0.890704\pi\)
\(432\) 0 0
\(433\) −23.0976 24.2241i −1.11000 1.16414i −0.985103 0.171967i \(-0.944988\pi\)
−0.124899 0.992169i \(-0.539861\pi\)
\(434\) 0 0
\(435\) 7.48417 46.7389i 0.358838 2.24096i
\(436\) 0 0
\(437\) −1.25969 + 0.0600066i −0.0602593 + 0.00287050i
\(438\) 0 0
\(439\) −7.23239 12.5269i −0.345183 0.597875i 0.640204 0.768205i \(-0.278850\pi\)
−0.985387 + 0.170330i \(0.945517\pi\)
\(440\) 0 0
\(441\) −7.64453 + 1.98164i −0.364025 + 0.0943637i
\(442\) 0 0
\(443\) 36.6488 7.06347i 1.74124 0.335596i 0.783097 0.621900i \(-0.213639\pi\)
0.958139 + 0.286304i \(0.0924268\pi\)
\(444\) 0 0
\(445\) −7.37508 + 6.39054i −0.349612 + 0.302941i
\(446\) 0 0
\(447\) −18.5339 3.88025i −0.876621 0.183529i
\(448\) 0 0
\(449\) 2.78293 + 5.39814i 0.131335 + 0.254754i 0.945328 0.326120i \(-0.105741\pi\)
−0.813994 + 0.580874i \(0.802711\pi\)
\(450\) 0 0
\(451\) 59.9269 + 11.5500i 2.82185 + 0.543866i
\(452\) 0 0
\(453\) −1.78412 + 15.9811i −0.0838254 + 0.750857i
\(454\) 0 0
\(455\) −13.3364 + 15.3911i −0.625221 + 0.721544i
\(456\) 0 0
\(457\) −2.94610 + 12.1440i −0.137813 + 0.568073i 0.860470 + 0.509501i \(0.170170\pi\)
−0.998283 + 0.0585720i \(0.981345\pi\)
\(458\) 0 0
\(459\) −16.2966 + 5.63414i −0.760661 + 0.262979i
\(460\) 0 0
\(461\) 3.50252 11.9285i 0.163129 0.555566i −0.836838 0.547450i \(-0.815599\pi\)
0.999967 0.00811540i \(-0.00258324\pi\)
\(462\) 0 0
\(463\) 7.60634 + 18.9997i 0.353497 + 0.882992i 0.993417 + 0.114551i \(0.0365429\pi\)
−0.639921 + 0.768441i \(0.721033\pi\)
\(464\) 0 0
\(465\) −23.2910 + 48.9163i −1.08009 + 2.26844i
\(466\) 0 0
\(467\) 7.51464 + 5.35115i 0.347736 + 0.247622i 0.740557 0.671993i \(-0.234562\pi\)
−0.392821 + 0.919615i \(0.628501\pi\)
\(468\) 0 0
\(469\) 24.4188 + 7.00677i 1.12755 + 0.323543i
\(470\) 0 0
\(471\) −0.796137 4.51810i −0.0366841 0.208183i
\(472\) 0 0
\(473\) 0.855409 0.296060i 0.0393317 0.0136128i
\(474\) 0 0
\(475\) −4.57648 + 1.83215i −0.209983 + 0.0840646i
\(476\) 0 0
\(477\) −1.70575 + 6.16431i −0.0781008 + 0.282244i
\(478\) 0 0
\(479\) −8.80975 + 17.0885i −0.402528 + 0.780795i −0.999774 0.0212630i \(-0.993231\pi\)
0.597246 + 0.802058i \(0.296262\pi\)
\(480\) 0 0
\(481\) 8.75593 + 2.12417i 0.399236 + 0.0968536i
\(482\) 0 0
\(483\) 1.43117 + 18.0279i 0.0651206 + 0.820299i
\(484\) 0 0
\(485\) −1.19803 1.52341i −0.0543995 0.0691747i
\(486\) 0 0
\(487\) 0.0504807 0.261919i 0.00228750 0.0118687i −0.980767 0.195182i \(-0.937470\pi\)
0.983055 + 0.183313i \(0.0586823\pi\)
\(488\) 0 0
\(489\) −7.81752 + 25.1313i −0.353521 + 1.13648i
\(490\) 0 0
\(491\) 4.10090 + 6.38112i 0.185071 + 0.287976i 0.921375 0.388675i \(-0.127067\pi\)
−0.736304 + 0.676651i \(0.763431\pi\)
\(492\) 0 0
\(493\) 13.9398 + 16.0873i 0.627815 + 0.724537i
\(494\) 0 0
\(495\) 15.0644 + 72.0760i 0.677093 + 3.23958i
\(496\) 0 0
\(497\) −3.51833 14.5028i −0.157819 0.650538i
\(498\) 0 0
\(499\) −28.5894 + 16.5061i −1.27984 + 0.738915i −0.976818 0.214070i \(-0.931328\pi\)
−0.303019 + 0.952984i \(0.597995\pi\)
\(500\) 0 0
\(501\) −14.0314 + 15.6797i −0.626876 + 0.700516i
\(502\) 0 0
\(503\) 12.8092 + 17.9880i 0.571133 + 0.802045i 0.994591 0.103871i \(-0.0331230\pi\)
−0.423457 + 0.905916i \(0.639184\pi\)
\(504\) 0 0
\(505\) 37.8842 36.1225i 1.68583 1.60743i
\(506\) 0 0
\(507\) −4.90319 17.7428i −0.217758 0.787983i
\(508\) 0 0
\(509\) 11.2173 + 1.61280i 0.497197 + 0.0714861i 0.386352 0.922352i \(-0.373735\pi\)
0.110845 + 0.993838i \(0.464644\pi\)
\(510\) 0 0
\(511\) 2.60788 + 8.88163i 0.115366 + 0.392900i
\(512\) 0 0
\(513\) −1.41018 + 1.34370i −0.0622612 + 0.0593257i
\(514\) 0 0
\(515\) −61.0229 47.9889i −2.68899 2.11465i
\(516\) 0 0
\(517\) −3.47921 36.4359i −0.153015 1.60245i
\(518\) 0 0
\(519\) −10.0147 + 4.96203i −0.439598 + 0.217809i
\(520\) 0 0
\(521\) −11.8525 + 25.9534i −0.519269 + 1.13704i 0.450446 + 0.892804i \(0.351265\pi\)
−0.969715 + 0.244238i \(0.921462\pi\)
\(522\) 0 0
\(523\) −9.57913 9.13368i −0.418866 0.399388i 0.451121 0.892463i \(-0.351024\pi\)
−0.869987 + 0.493075i \(0.835873\pi\)
\(524\) 0 0
\(525\) 28.3349 + 64.7638i 1.23664 + 2.82653i
\(526\) 0 0
\(527\) −10.1213 22.1625i −0.440890 0.965416i
\(528\) 0 0
\(529\) −11.6292 1.11046i −0.505619 0.0482808i
\(530\) 0 0
\(531\) 1.45192 + 9.08702i 0.0630081 + 0.394343i
\(532\) 0 0
\(533\) 8.82104 13.7258i 0.382082 0.594531i
\(534\) 0 0
\(535\) 4.39311i 0.189931i
\(536\) 0 0
\(537\) −27.8649 + 28.3042i −1.20246 + 1.22141i
\(538\) 0 0
\(539\) −12.7582 8.19921i −0.549536 0.353165i
\(540\) 0 0
\(541\) 29.6342 4.26075i 1.27407 0.183184i 0.528112 0.849175i \(-0.322900\pi\)
0.745960 + 0.665991i \(0.231991\pi\)
\(542\) 0 0
\(543\) 17.5278 14.7042i 0.752189 0.631017i
\(544\) 0 0
\(545\) 45.3638 20.7170i 1.94317 0.887417i
\(546\) 0 0
\(547\) 12.9717 32.4018i 0.554631 1.38540i −0.340773 0.940146i \(-0.610689\pi\)
0.895404 0.445255i \(-0.146887\pi\)
\(548\) 0 0
\(549\) −30.7469 28.4124i −1.31225 1.21261i
\(550\) 0 0
\(551\) 2.18733 + 0.998920i 0.0931834 + 0.0425554i
\(552\) 0 0
\(553\) −0.379918 + 1.09770i −0.0161557 + 0.0466789i
\(554\) 0 0
\(555\) 27.2222 33.5001i 1.15552 1.42200i
\(556\) 0 0
\(557\) −13.7885 + 17.5335i −0.584238 + 0.742919i −0.984865 0.173322i \(-0.944550\pi\)
0.400627 + 0.916241i \(0.368792\pi\)
\(558\) 0 0
\(559\) 0.0115147 0.241723i 0.000487020 0.0102238i
\(560\) 0 0
\(561\) −29.1862 15.6418i −1.23224 0.660399i
\(562\) 0 0
\(563\) −1.75169 + 12.1833i −0.0738250 + 0.513464i 0.919035 + 0.394176i \(0.128970\pi\)
−0.992860 + 0.119288i \(0.961939\pi\)
\(564\) 0 0
\(565\) −21.2539 + 36.8129i −0.894159 + 1.54873i
\(566\) 0 0
\(567\) 19.8985 + 19.6029i 0.835658 + 0.823246i
\(568\) 0 0
\(569\) −26.8976 + 19.1537i −1.12761 + 0.802965i −0.982465 0.186446i \(-0.940303\pi\)
−0.145141 + 0.989411i \(0.546364\pi\)
\(570\) 0 0
\(571\) 0.0868183 + 1.82254i 0.00363323 + 0.0762710i 0.999956 0.00941174i \(-0.00299589\pi\)
−0.996322 + 0.0856827i \(0.972693\pi\)
\(572\) 0 0
\(573\) 5.05663 + 1.31262i 0.211244 + 0.0548357i
\(574\) 0 0
\(575\) 42.9933 10.4301i 1.79294 0.434963i
\(576\) 0 0
\(577\) −0.209927 1.08920i −0.00873936 0.0453441i 0.977297 0.211873i \(-0.0679563\pi\)
−0.986037 + 0.166529i \(0.946744\pi\)
\(578\) 0 0
\(579\) −11.9679 0.761937i −0.497368 0.0316650i
\(580\) 0 0
\(581\) 29.3141 18.8390i 1.21615 0.781573i
\(582\) 0 0
\(583\) −10.9174 + 5.62829i −0.452151 + 0.233100i
\(584\) 0 0
\(585\) 19.3856 + 3.42271i 0.801495 + 0.141512i
\(586\) 0 0
\(587\) 14.1258 11.1087i 0.583036 0.458505i −0.282559 0.959250i \(-0.591183\pi\)
0.865595 + 0.500746i \(0.166941\pi\)
\(588\) 0 0
\(589\) −2.08005 1.80238i −0.0857070 0.0742656i
\(590\) 0 0
\(591\) 10.8294 + 17.4581i 0.445464 + 0.718132i
\(592\) 0 0
\(593\) 9.58828 + 4.94310i 0.393744 + 0.202989i 0.643717 0.765264i \(-0.277392\pi\)
−0.249973 + 0.968253i \(0.580422\pi\)
\(594\) 0 0
\(595\) −42.1002 12.3617i −1.72594 0.506781i
\(596\) 0 0
\(597\) 13.4078 31.9995i 0.548746 1.30965i
\(598\) 0 0
\(599\) −1.04442 3.01765i −0.0426738 0.123298i 0.921651 0.388020i \(-0.126841\pi\)
−0.964325 + 0.264722i \(0.914720\pi\)
\(600\) 0 0
\(601\) −3.69220 + 5.18497i −0.150608 + 0.211499i −0.882986 0.469399i \(-0.844471\pi\)
0.732379 + 0.680898i \(0.238410\pi\)
\(602\) 0 0
\(603\) −6.30826 23.7320i −0.256892 0.966440i
\(604\) 0 0
\(605\) −54.8397 + 77.0115i −2.22955 + 3.13096i
\(606\) 0 0
\(607\) 4.49809 + 12.9964i 0.182572 + 0.527506i 0.998733 0.0503174i \(-0.0160233\pi\)
−0.816162 + 0.577824i \(0.803902\pi\)
\(608\) 0 0
\(609\) 13.3258 31.8038i 0.539989 1.28875i
\(610\) 0 0
\(611\) −9.38884 2.75681i −0.379832 0.111529i
\(612\) 0 0
\(613\) −23.7393 12.2385i −0.958823 0.494308i −0.0935533 0.995614i \(-0.529823\pi\)
−0.865270 + 0.501307i \(0.832853\pi\)
\(614\) 0 0
\(615\) −41.2050 66.4265i −1.66155 2.67858i
\(616\) 0 0
\(617\) −4.81268 4.17021i −0.193751 0.167886i 0.552583 0.833458i \(-0.313642\pi\)
−0.746334 + 0.665572i \(0.768188\pi\)
\(618\) 0 0
\(619\) −12.7834 + 10.0530i −0.513809 + 0.404064i −0.841116 0.540854i \(-0.818101\pi\)
0.327308 + 0.944918i \(0.393859\pi\)
\(620\) 0 0
\(621\) 14.2430 10.1351i 0.571550 0.406708i
\(622\) 0 0
\(623\) −6.31881 + 3.25757i −0.253158 + 0.130512i
\(624\) 0 0
\(625\) 69.1337 44.4295i 2.76535 1.77718i
\(626\) 0 0
\(627\) −3.73310 0.237668i −0.149085 0.00949155i
\(628\) 0 0
\(629\) 3.67376 + 19.0613i 0.146482 + 0.760022i
\(630\) 0 0
\(631\) 34.7069 8.41980i 1.38166 0.335187i 0.525014 0.851093i \(-0.324060\pi\)
0.856645 + 0.515906i \(0.172545\pi\)
\(632\) 0 0
\(633\) −43.1918 11.2119i −1.71672 0.445634i
\(634\) 0 0
\(635\) 1.35589 + 28.4637i 0.0538070 + 1.12955i
\(636\) 0 0
\(637\) −3.30266 + 2.35182i −0.130856 + 0.0931823i
\(638\) 0 0
\(639\) −10.2831 + 10.1166i −0.406792 + 0.400207i
\(640\) 0 0
\(641\) −1.91537 + 3.31751i −0.0756524 + 0.131034i −0.901370 0.433050i \(-0.857437\pi\)
0.825717 + 0.564084i \(0.190771\pi\)
\(642\) 0 0
\(643\) −4.05839 + 28.2267i −0.160047 + 1.11315i 0.738492 + 0.674262i \(0.235538\pi\)
−0.898540 + 0.438892i \(0.855371\pi\)
\(644\) 0 0
\(645\) −1.02189 0.547665i −0.0402370 0.0215643i
\(646\) 0 0
\(647\) 1.47317 30.9257i 0.0579164 1.21581i −0.763623 0.645663i \(-0.776581\pi\)
0.821539 0.570152i \(-0.193116\pi\)
\(648\) 0 0
\(649\) −10.9241 + 13.8912i −0.428809 + 0.545275i
\(650\) 0 0
\(651\) −24.8903 + 30.6304i −0.975529 + 1.20050i
\(652\) 0 0
\(653\) −4.31635 + 12.4713i −0.168912 + 0.488038i −0.997408 0.0719565i \(-0.977076\pi\)
0.828496 + 0.559995i \(0.189197\pi\)
\(654\) 0 0
\(655\) 19.5206 + 8.91475i 0.762732 + 0.348328i
\(656\) 0 0
\(657\) 6.07249 6.57144i 0.236910 0.256376i
\(658\) 0 0
\(659\) 4.60925 11.5134i 0.179551 0.448497i −0.811102 0.584905i \(-0.801132\pi\)
0.990653 + 0.136408i \(0.0435560\pi\)
\(660\) 0 0
\(661\) −38.1537 + 17.4242i −1.48401 + 0.677723i −0.982300 0.187314i \(-0.940022\pi\)
−0.501707 + 0.865038i \(0.667294\pi\)
\(662\) 0 0
\(663\) −6.78218 + 5.68962i −0.263398 + 0.220967i
\(664\) 0 0
\(665\) −4.90615 + 0.705398i −0.190252 + 0.0273542i
\(666\) 0 0
\(667\) −18.1544 11.6671i −0.702942 0.451754i
\(668\) 0 0
\(669\) 17.0085 17.2766i 0.657587 0.667953i
\(670\) 0 0
\(671\) 80.3964i 3.10367i
\(672\) 0 0
\(673\) −3.70299 + 5.76197i −0.142740 + 0.222107i −0.905261 0.424856i \(-0.860325\pi\)
0.762521 + 0.646963i \(0.223961\pi\)
\(674\) 0 0
\(675\) 39.6548 55.6474i 1.52631 2.14187i
\(676\) 0 0
\(677\) −14.1584 1.35197i −0.544153 0.0519603i −0.180640 0.983549i \(-0.557817\pi\)
−0.363513 + 0.931589i \(0.618423\pi\)
\(678\) 0 0
\(679\) −0.586507 1.28427i −0.0225081 0.0492858i
\(680\) 0 0
\(681\) −18.2490 41.7110i −0.699304 1.59837i
\(682\) 0 0
\(683\) 25.8052 + 24.6052i 0.987407 + 0.941490i 0.998290 0.0584504i \(-0.0186160\pi\)
−0.0108837 + 0.999941i \(0.503464\pi\)
\(684\) 0 0
\(685\) 30.9953 67.8703i 1.18427 2.59319i
\(686\) 0 0
\(687\) −10.2634 + 5.08525i −0.391574 + 0.194014i
\(688\) 0 0
\(689\) 0.312137 + 3.26885i 0.0118915 + 0.124533i
\(690\) 0 0
\(691\) −19.2125 15.1089i −0.730879 0.574770i 0.181854 0.983325i \(-0.441790\pi\)
−0.912733 + 0.408556i \(0.866033\pi\)
\(692\) 0 0
\(693\) −1.71403 + 53.6140i −0.0651108 + 2.03663i
\(694\) 0 0
\(695\) 10.3756 + 35.3361i 0.393570 + 1.34038i
\(696\) 0 0
\(697\) 34.7952 + 5.00279i 1.31796 + 0.189494i
\(698\) 0 0
\(699\) −9.51141 34.4181i −0.359755 1.30181i
\(700\) 0 0
\(701\) 18.2783 17.4283i 0.690361 0.658258i −0.261353 0.965243i \(-0.584169\pi\)
0.951714 + 0.306986i \(0.0993203\pi\)
\(702\) 0 0
\(703\) 1.27199 + 1.78626i 0.0479741 + 0.0673702i
\(704\) 0 0
\(705\) −31.2624 + 34.9348i −1.17741 + 1.31572i
\(706\) 0 0
\(707\) 33.0244 19.0666i 1.24201 0.717075i
\(708\) 0 0
\(709\) −4.47237 18.4354i −0.167964 0.692355i −0.992045 0.125884i \(-0.959823\pi\)
0.824081 0.566471i \(-0.191692\pi\)
\(710\) 0 0
\(711\) 1.09906 0.229710i 0.0412179 0.00861482i
\(712\) 0 0
\(713\) 16.1753 + 18.6673i 0.605770 + 0.699096i
\(714\) 0 0
\(715\) 20.4383 + 31.8026i 0.764348 + 1.18935i
\(716\) 0 0
\(717\) 3.47234 11.1627i 0.129677 0.416878i
\(718\) 0 0
\(719\) 1.18605 6.15381i 0.0442322 0.229498i −0.953085 0.302704i \(-0.902111\pi\)
0.997317 + 0.0732054i \(0.0233229\pi\)
\(720\) 0 0
\(721\) −34.9596 44.4547i −1.30196 1.65558i
\(722\) 0 0
\(723\) 3.75976 + 47.3602i 0.139827 + 1.76135i
\(724\) 0 0
\(725\) −81.9770 19.8874i −3.04455 0.738600i
\(726\) 0 0
\(727\) 21.9554 42.5875i 0.814279 1.57948i −0.000705458 1.00000i \(-0.500225\pi\)
0.814985 0.579482i \(-0.196745\pi\)
\(728\) 0 0
\(729\) 6.38326 26.2346i 0.236417 0.971652i
\(730\) 0 0
\(731\) 0.484041 0.193781i 0.0179029 0.00716724i
\(732\) 0 0
\(733\) 22.7614 7.87781i 0.840713 0.290973i 0.127428 0.991848i \(-0.459328\pi\)
0.713285 + 0.700874i \(0.247207\pi\)
\(734\) 0 0
\(735\) 3.37090 + 19.1300i 0.124338 + 0.705620i
\(736\) 0 0
\(737\) 25.2501 39.8277i 0.930101 1.46707i
\(738\) 0 0
\(739\) 14.7241 + 10.4850i 0.541635 + 0.385696i 0.817878 0.575391i \(-0.195150\pi\)
−0.276244 + 0.961088i \(0.589090\pi\)
\(740\) 0 0
\(741\) −0.429913 + 0.902913i −0.0157933 + 0.0331693i
\(742\) 0 0
\(743\) −0.522599 1.30539i −0.0191723 0.0478901i 0.918473 0.395484i \(-0.129423\pi\)
−0.937645 + 0.347594i \(0.886999\pi\)
\(744\) 0 0
\(745\) −13.1220 + 44.6894i −0.480752 + 1.63729i
\(746\) 0 0
\(747\) −30.1758 14.9640i −1.10408 0.547506i
\(748\) 0 0
\(749\) −0.754510 + 3.11013i −0.0275692 + 0.113642i
\(750\) 0 0
\(751\) 24.2455 27.9808i 0.884732 1.02104i −0.114885 0.993379i \(-0.536650\pi\)
0.999617 0.0276568i \(-0.00880456\pi\)
\(752\) 0 0
\(753\) −2.13263 + 19.1028i −0.0777175 + 0.696146i
\(754\) 0 0
\(755\) 38.8380 + 7.48542i 1.41346 + 0.272422i
\(756\) 0 0
\(757\) 3.14182 + 6.09427i 0.114191 + 0.221500i 0.939004 0.343905i \(-0.111750\pi\)
−0.824813 + 0.565406i \(0.808720\pi\)
\(758\) 0 0
\(759\) 32.8579 + 6.87912i 1.19267 + 0.249696i
\(760\) 0 0
\(761\) 36.1610 31.3337i 1.31084 1.13585i 0.329371 0.944201i \(-0.393163\pi\)
0.981464 0.191645i \(-0.0613821\pi\)
\(762\) 0 0
\(763\) 35.6738 6.87555i 1.29148 0.248912i
\(764\) 0 0
\(765\) 10.6426 + 41.0557i 0.384784 + 1.48437i
\(766\) 0 0
\(767\) 2.36225 + 4.09154i 0.0852959 + 0.147737i
\(768\) 0 0
\(769\) −20.6084 + 0.981699i −0.743158 + 0.0354010i −0.415746 0.909481i \(-0.636479\pi\)
−0.327412 + 0.944882i \(0.606176\pi\)
\(770\) 0 0
\(771\) 5.17954 32.3464i 0.186536 1.16493i
\(772\) 0 0
\(773\) 28.8887 + 30.2976i 1.03905 + 1.08973i 0.995882 + 0.0906604i \(0.0288978\pi\)
0.0431718 + 0.999068i \(0.486254\pi\)
\(774\) 0 0
\(775\) 83.6158 + 48.2756i 3.00357 + 1.73411i
\(776\) 0 0
\(777\) 25.0258 19.0412i 0.897794 0.683101i
\(778\) 0 0
\(779\) 3.81019 1.11877i 0.136514 0.0400842i
\(780\) 0 0
\(781\) −27.6708 1.31812i −0.990138 0.0471661i
\(782\) 0 0
\(783\) −32.9939 + 4.73240i −1.17911 + 0.169122i
\(784\) 0 0
\(785\) −11.2333 + 1.07265i −0.400933 + 0.0382844i
\(786\) 0 0
\(787\) 13.3927 + 4.63524i 0.477397 + 0.165229i 0.555161 0.831743i \(-0.312657\pi\)
−0.0777638 + 0.996972i \(0.524778\pi\)
\(788\) 0 0
\(789\) −22.8498 + 8.72667i −0.813473 + 0.310678i
\(790\) 0 0
\(791\) −21.3694 + 22.4116i −0.759810 + 0.796865i
\(792\) 0 0
\(793\) −19.9538 7.98830i −0.708581 0.283673i
\(794\) 0 0
\(795\) 14.7827 + 5.38237i 0.524290 + 0.190893i
\(796\) 0 0
\(797\) −0.0339439 + 0.355477i −0.00120236 + 0.0125916i −0.996053 0.0887583i \(-0.971710\pi\)
0.994851 + 0.101350i \(0.0323162\pi\)
\(798\) 0 0
\(799\) −3.00035 20.8679i −0.106145 0.738252i
\(800\) 0 0
\(801\) 5.83829 + 3.62428i 0.206286 + 0.128058i
\(802\) 0 0
\(803\) 17.1829 0.606370
\(804\) 0 0
\(805\) 44.4827 1.56781
\(806\) 0 0
\(807\) −6.17781 27.3668i −0.217469 0.963356i
\(808\) 0 0
\(809\) 2.85633 + 19.8662i 0.100423 + 0.698459i 0.976379 + 0.216067i \(0.0693228\pi\)
−0.875955 + 0.482392i \(0.839768\pi\)
\(810\) 0 0
\(811\) 4.90615 51.3796i 0.172278 1.80418i −0.334809 0.942286i \(-0.608672\pi\)
0.507088 0.861894i \(-0.330722\pi\)
\(812\) 0 0
\(813\) −3.16396 + 8.68985i −0.110965 + 0.304766i
\(814\) 0 0
\(815\) 60.0998 + 24.0603i 2.10521 + 0.842797i
\(816\) 0 0
\(817\) 0.0406446 0.0426269i 0.00142198 0.00149133i
\(818\) 0 0
\(819\) 13.1363 + 5.75258i 0.459020 + 0.201011i
\(820\) 0 0
\(821\) −21.7404 7.52442i −0.758744 0.262604i −0.0798172 0.996810i \(-0.525434\pi\)
−0.678927 + 0.734206i \(0.737555\pi\)
\(822\) 0 0
\(823\) −31.5999 + 3.01742i −1.10150 + 0.105181i −0.629934 0.776648i \(-0.716918\pi\)
−0.471569 + 0.881829i \(0.656312\pi\)
\(824\) 0 0
\(825\) 130.169 16.5971i 4.53190 0.577837i
\(826\) 0 0
\(827\) −43.2640 2.06092i −1.50444 0.0716651i −0.720912 0.693027i \(-0.756277\pi\)
−0.783524 + 0.621362i \(0.786580\pi\)
\(828\) 0 0
\(829\) −33.1925 + 9.74620i −1.15282 + 0.338499i −0.801640 0.597807i \(-0.796039\pi\)
−0.351183 + 0.936307i \(0.614221\pi\)
\(830\) 0 0
\(831\) 25.3393 + 33.3033i 0.879011 + 1.15528i
\(832\) 0 0
\(833\) −7.56510 4.36771i −0.262115 0.151332i
\(834\) 0 0
\(835\) 35.7150 + 37.4568i 1.23597 + 1.29625i
\(836\) 0 0
\(837\) 37.7606 + 5.44221i 1.30520 + 0.188110i
\(838\) 0 0
\(839\) 30.6174 1.45849i 1.05703 0.0503525i 0.488139 0.872766i \(-0.337676\pi\)
0.568890 + 0.822413i \(0.307373\pi\)
\(840\) 0 0
\(841\) 6.07393 + 10.5204i 0.209446 + 0.362771i
\(842\) 0 0
\(843\) −26.7535 16.0215i −0.921438 0.551809i
\(844\) 0 0
\(845\) −44.4593 + 8.56884i −1.52945 + 0.294777i
\(846\) 0 0
\(847\) −52.0508 + 45.1022i −1.78849 + 1.54973i
\(848\) 0 0
\(849\) −1.50896 + 7.20749i −0.0517874 + 0.247361i
\(850\) 0 0
\(851\) −9.01781 17.4921i −0.309127 0.599622i
\(852\) 0 0
\(853\) 8.39092 + 1.61722i 0.287300 + 0.0553725i 0.330865 0.943678i \(-0.392660\pi\)
−0.0435653 + 0.999051i \(0.513872\pi\)
\(854\) 0 0
\(855\) 3.02022 + 3.71930i 0.103289 + 0.127198i
\(856\) 0 0
\(857\) 29.8887 34.4934i 1.02098 1.17827i 0.0371221 0.999311i \(-0.488181\pi\)
0.983856 0.178961i \(-0.0572736\pi\)
\(858\) 0 0
\(859\) 2.75206 11.3441i 0.0938990 0.387057i −0.905397 0.424565i \(-0.860427\pi\)
0.999296 + 0.0375083i \(0.0119421\pi\)
\(860\) 0 0
\(861\) −17.7627 54.1041i −0.605352 1.84386i
\(862\) 0 0
\(863\) 4.01477 13.6730i 0.136664 0.465436i −0.862511 0.506038i \(-0.831109\pi\)
0.999175 + 0.0406022i \(0.0129276\pi\)
\(864\) 0 0
\(865\) 10.2174 + 25.5218i 0.347402 + 0.867768i
\(866\) 0 0
\(867\) 9.36426 + 4.45871i 0.318027 + 0.151426i
\(868\) 0 0
\(869\) 1.75642 + 1.25074i 0.0595824 + 0.0424284i
\(870\) 0 0
\(871\) −7.37606 10.2242i −0.249928 0.346435i
\(872\) 0 0
\(873\) −0.774134 + 1.12392i −0.0262005 + 0.0380388i
\(874\) 0 0
\(875\) 101.840 35.2470i 3.44280 1.19157i
\(876\) 0 0
\(877\) −22.8715 + 9.15635i −0.772314 + 0.309188i −0.724142 0.689651i \(-0.757764\pi\)
−0.0481723 + 0.998839i \(0.515340\pi\)
\(878\) 0 0
\(879\) −6.53983 11.7573i −0.220583 0.396563i
\(880\) 0 0
\(881\) −11.0138 + 21.3637i −0.371063 + 0.719762i −0.998252 0.0591053i \(-0.981175\pi\)
0.627189 + 0.778867i \(0.284206\pi\)
\(882\) 0 0
\(883\) 0.596955 + 0.144820i 0.0200891 + 0.00487357i 0.245791 0.969323i \(-0.420952\pi\)
−0.225702 + 0.974196i \(0.572467\pi\)
\(884\) 0 0
\(885\) 22.5638 1.79126i 0.758475 0.0602127i
\(886\) 0 0
\(887\) −30.6086 38.9220i −1.02774 1.30687i −0.950790 0.309836i \(-0.899726\pi\)
−0.0769450 0.997035i \(-0.524517\pi\)
\(888\) 0 0
\(889\) −3.92869 + 20.3840i −0.131764 + 0.683657i
\(890\) 0 0
\(891\) 45.3211 25.1892i 1.51831 0.843869i
\(892\) 0 0
\(893\) −1.28757 2.00351i −0.0430871 0.0670448i
\(894\) 0 0
\(895\) 63.9773 + 73.8337i 2.13853 + 2.46799i
\(896\) 0 0
\(897\) 4.97216 7.47157i 0.166015 0.249469i
\(898\) 0 0
\(899\) −11.1036 45.7696i −0.370325 1.52650i
\(900\) 0 0
\(901\) −6.12699 + 3.53742i −0.204120 + 0.117849i
\(902\) 0 0
\(903\) −0.629396 0.563232i −0.0209450 0.0187432i
\(904\) 0 0
\(905\) −32.6426 45.8401i −1.08508 1.52378i
\(906\) 0 0
\(907\) −17.6881 + 16.8655i −0.587323 + 0.560011i −0.924380 0.381473i \(-0.875417\pi\)
0.337057 + 0.941484i \(0.390568\pi\)
\(908\) 0 0
\(909\) −32.2063 17.9286i −1.06821 0.594654i
\(910\) 0 0
\(911\) 9.70330 + 1.39512i 0.321485 + 0.0462225i 0.301168 0.953571i \(-0.402624\pi\)
0.0203166 + 0.999794i \(0.493533\pi\)
\(912\) 0 0
\(913\) −18.2235 62.0634i −0.603108 2.05400i
\(914\) 0 0
\(915\) −75.6517 + 69.8603i −2.50097 + 2.30951i
\(916\) 0 0
\(917\) 12.2886 + 9.66389i 0.405807 + 0.319130i
\(918\) 0 0
\(919\) 1.71168 + 17.9255i 0.0564632 + 0.591309i 0.978785 + 0.204888i \(0.0656829\pi\)
−0.922322 + 0.386422i \(0.873711\pi\)
\(920\) 0 0
\(921\) −4.25922 8.59626i −0.140346 0.283257i
\(922\) 0 0
\(923\) −3.07656 + 6.73672i −0.101266 + 0.221742i
\(924\) 0 0
\(925\) −55.6743 53.0853i −1.83056 1.74543i
\(926\) 0 0
\(927\) −19.5212 + 51.0620i −0.641160 + 1.67710i
\(928\) 0 0
\(929\) −22.5808 49.4450i −0.740851 1.62224i −0.782149 0.623091i \(-0.785877\pi\)
0.0412978 0.999147i \(-0.486851\pi\)
\(930\) 0 0
\(931\) −0.982326 0.0938007i −0.0321944 0.00307419i
\(932\) 0 0
\(933\) −16.8563 12.4139i −0.551849 0.406414i
\(934\) 0 0
\(935\) −44.0347 + 68.5194i −1.44009 + 2.24082i
\(936\) 0 0
\(937\) 46.2095i 1.50960i −0.655956 0.754799i \(-0.727734\pi\)
0.655956 0.754799i \(-0.272266\pi\)
\(938\) 0 0
\(939\) 36.3439 + 35.7798i 1.18604 + 1.16763i
\(940\) 0 0
\(941\) 3.19084 + 2.05063i 0.104018 + 0.0668485i 0.591616 0.806220i \(-0.298490\pi\)
−0.487597 + 0.873069i \(0.662127\pi\)
\(942\) 0 0
\(943\) −35.2751 + 5.07180i −1.14872 + 0.165161i
\(944\) 0 0
\(945\) 51.9394 44.9749i 1.68959 1.46303i
\(946\) 0 0
\(947\) 19.4327 8.87460i 0.631477 0.288386i −0.0738487 0.997269i \(-0.523528\pi\)
0.705325 + 0.708884i \(0.250801\pi\)
\(948\) 0 0
\(949\) 1.70731 4.26467i 0.0554218 0.138437i
\(950\) 0 0
\(951\) 0.803766 + 25.4107i 0.0260639 + 0.824000i
\(952\) 0 0
\(953\) −11.1843 5.10770i −0.362295 0.165454i 0.225947 0.974140i \(-0.427452\pi\)
−0.588242 + 0.808685i \(0.700180\pi\)
\(954\) 0 0
\(955\) 4.20283 12.1433i 0.136000 0.392947i
\(956\) 0 0
\(957\) −49.6764 40.3671i −1.60581 1.30488i
\(958\) 0 0
\(959\) 33.6000 42.7259i 1.08500 1.37969i
\(960\) 0 0
\(961\) −1.08994 + 22.8807i −0.0351595 + 0.738088i
\(962\) 0 0
\(963\) 2.95420 0.917858i 0.0951978 0.0295776i
\(964\) 0 0
\(965\) −4.19785 + 29.1967i −0.135134 + 0.939876i
\(966\) 0 0
\(967\) −20.4017 + 35.3368i −0.656075 + 1.13636i 0.325548 + 0.945526i \(0.394451\pi\)
−0.981623 + 0.190830i \(0.938882\pi\)
\(968\) 0 0
\(969\) −2.15433 0.0344281i −0.0692071 0.00110599i
\(970\) 0 0
\(971\) −26.4067 + 18.8041i −0.847432 + 0.603453i −0.919122 0.393974i \(-0.871100\pi\)
0.0716902 + 0.997427i \(0.477161\pi\)
\(972\) 0 0
\(973\) 1.27657 + 26.7985i 0.0409249 + 0.859119i
\(974\) 0 0
\(975\) 8.81448 33.9561i 0.282289 1.08747i
\(976\) 0 0
\(977\) −9.02418 + 2.18924i −0.288709 + 0.0700401i −0.377498 0.926010i \(-0.623216\pi\)
0.0887889 + 0.996050i \(0.471700\pi\)
\(978\) 0 0
\(979\) 2.49745 + 12.9580i 0.0798189 + 0.414140i
\(980\) 0 0
\(981\) −23.4093 26.1771i −0.747402 0.835769i
\(982\) 0 0
\(983\) 15.6773 10.0752i 0.500030 0.321350i −0.266198 0.963918i \(-0.585768\pi\)
0.766228 + 0.642569i \(0.222131\pi\)
\(984\) 0 0
\(985\) 44.9150 23.1553i 1.43111 0.737790i
\(986\) 0 0
\(987\) −28.1324 + 19.3631i −0.895465 + 0.616333i
\(988\) 0 0
\(989\) −0.415493 + 0.326747i −0.0132119 + 0.0103900i
\(990\) 0 0
\(991\) 16.3701 + 14.1848i 0.520015 + 0.450595i 0.874892 0.484317i \(-0.160932\pi\)
−0.354878 + 0.934913i \(0.615477\pi\)
\(992\) 0 0
\(993\) −7.68822 + 4.76907i −0.243978 + 0.151342i
\(994\) 0 0
\(995\) −75.8523 39.1046i −2.40468 1.23970i
\(996\) 0 0
\(997\) 42.9340 + 12.6066i 1.35973 + 0.399254i 0.878669 0.477431i \(-0.158432\pi\)
0.481065 + 0.876685i \(0.340250\pi\)
\(998\) 0 0
\(999\) −28.2151 11.3067i −0.892687 0.357729i
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 804.2.ba.b.353.3 yes 440
3.2 odd 2 inner 804.2.ba.b.353.13 yes 440
67.41 odd 66 inner 804.2.ba.b.41.13 yes 440
201.41 even 66 inner 804.2.ba.b.41.3 440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.ba.b.41.3 440 201.41 even 66 inner
804.2.ba.b.41.13 yes 440 67.41 odd 66 inner
804.2.ba.b.353.3 yes 440 1.1 even 1 trivial
804.2.ba.b.353.13 yes 440 3.2 odd 2 inner