Properties

Label 380.2.bh.a.13.1
Level $380$
Weight $2$
Character 380.13
Analytic conductor $3.034$
Analytic rank $0$
Dimension $120$
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] = [380,2,Mod(13,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([0, 27, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.bh (of order \(36\), degree \(12\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 13.1
Character \(\chi\) \(=\) 380.13
Dual form 380.2.bh.a.117.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +O(q^{10})\) \(q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +(2.73107 + 4.73035i) q^{11} +(-0.160884 + 0.345016i) q^{13} +(5.63692 + 3.76578i) q^{15} +(-0.0144528 + 0.165196i) q^{17} +(1.45553 + 4.10870i) q^{19} +(2.78783 + 3.32240i) q^{21} +(0.363161 - 0.254288i) q^{23} +(-2.30799 + 4.43544i) q^{25} +(-2.50399 + 9.34503i) q^{27} +(1.09856 + 0.921802i) q^{29} +(6.67979 + 3.85658i) q^{31} +(-13.5648 - 9.49816i) q^{33} +(-2.21187 + 2.31094i) q^{35} +(6.77341 + 6.77341i) q^{37} -1.15412i q^{39} +(2.40119 - 6.59722i) q^{41} +(6.61211 - 9.44307i) q^{43} +(-13.6830 - 2.10482i) q^{45} +(-3.11441 + 0.272476i) q^{47} +(4.28980 - 2.47672i) q^{49} +(-0.171947 - 0.472419i) q^{51} +(6.56681 + 9.37838i) q^{53} +(5.87375 - 10.7086i) q^{55} +(-9.26357 - 9.42437i) q^{57} +(-8.39207 + 7.04179i) q^{59} +(2.07149 - 11.7480i) q^{61} +(-8.02716 - 3.74313i) q^{63} +(0.846167 - 0.0927428i) q^{65} +(0.773226 + 8.83802i) q^{67} +(-0.672034 + 1.16400i) q^{69} +(-0.325803 + 0.0574478i) q^{71} +(-0.964863 - 2.06915i) q^{73} +(0.658643 - 15.1442i) q^{75} +(5.52535 - 5.52535i) q^{77} +(-2.57267 - 0.936374i) q^{79} +(-1.86796 - 10.5937i) q^{81} +(-11.1195 + 2.97945i) q^{83} +(0.332548 - 0.164029i) q^{85} +(-4.19952 - 1.12526i) q^{87} +(-5.02263 + 1.82809i) q^{89} +(0.536325 + 0.0945686i) q^{91} +(-23.2950 - 2.03804i) q^{93} +(6.16528 - 7.54912i) q^{95} +(0.497197 + 0.0434991i) q^{97} +(33.3033 + 5.87227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −2.74765 + 1.28125i −1.58636 + 0.739730i −0.997643 0.0686122i \(-0.978143\pi\)
−0.588713 + 0.808342i \(0.700365\pi\)
\(4\) 0 0
\(5\) −1.16017 1.91154i −0.518846 0.854868i
\(6\) 0 0
\(7\) −0.370262 1.38184i −0.139946 0.522285i −0.999928 0.0119616i \(-0.996192\pi\)
0.859983 0.510323i \(-0.170474\pi\)
\(8\) 0 0
\(9\) 3.97961 4.74272i 1.32654 1.58091i
\(10\) 0 0
\(11\) 2.73107 + 4.73035i 0.823448 + 1.42625i 0.903100 + 0.429431i \(0.141286\pi\)
−0.0796521 + 0.996823i \(0.525381\pi\)
\(12\) 0 0
\(13\) −0.160884 + 0.345016i −0.0446211 + 0.0956903i −0.927355 0.374184i \(-0.877923\pi\)
0.882733 + 0.469874i \(0.155701\pi\)
\(14\) 0 0
\(15\) 5.63692 + 3.76578i 1.45545 + 0.972320i
\(16\) 0 0
\(17\) −0.0144528 + 0.165196i −0.00350532 + 0.0400660i −0.997746 0.0671051i \(-0.978624\pi\)
0.994241 + 0.107171i \(0.0341793\pi\)
\(18\) 0 0
\(19\) 1.45553 + 4.10870i 0.333922 + 0.942601i
\(20\) 0 0
\(21\) 2.78783 + 3.32240i 0.608354 + 0.725008i
\(22\) 0 0
\(23\) 0.363161 0.254288i 0.0757244 0.0530228i −0.535101 0.844788i \(-0.679727\pi\)
0.610826 + 0.791765i \(0.290838\pi\)
\(24\) 0 0
\(25\) −2.30799 + 4.43544i −0.461599 + 0.887089i
\(26\) 0 0
\(27\) −2.50399 + 9.34503i −0.481894 + 1.79845i
\(28\) 0 0
\(29\) 1.09856 + 0.921802i 0.203998 + 0.171174i 0.739063 0.673636i \(-0.235269\pi\)
−0.535065 + 0.844811i \(0.679713\pi\)
\(30\) 0 0
\(31\) 6.67979 + 3.85658i 1.19973 + 0.692662i 0.960494 0.278301i \(-0.0897712\pi\)
0.239231 + 0.970963i \(0.423105\pi\)
\(32\) 0 0
\(33\) −13.5648 9.49816i −2.36132 1.65342i
\(34\) 0 0
\(35\) −2.21187 + 2.31094i −0.373874 + 0.390620i
\(36\) 0 0
\(37\) 6.77341 + 6.77341i 1.11354 + 1.11354i 0.992668 + 0.120874i \(0.0385699\pi\)
0.120874 + 0.992668i \(0.461430\pi\)
\(38\) 0 0
\(39\) 1.15412i 0.184807i
\(40\) 0 0
\(41\) 2.40119 6.59722i 0.375003 1.03031i −0.598397 0.801200i \(-0.704195\pi\)
0.973400 0.229112i \(-0.0735824\pi\)
\(42\) 0 0
\(43\) 6.61211 9.44307i 1.00834 1.44005i 0.113565 0.993531i \(-0.463773\pi\)
0.894772 0.446524i \(-0.147338\pi\)
\(44\) 0 0
\(45\) −13.6830 2.10482i −2.03973 0.313769i
\(46\) 0 0
\(47\) −3.11441 + 0.272476i −0.454284 + 0.0397447i −0.312002 0.950081i \(-0.601000\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(48\) 0 0
\(49\) 4.28980 2.47672i 0.612829 0.353817i
\(50\) 0 0
\(51\) −0.171947 0.472419i −0.0240773 0.0661519i
\(52\) 0 0
\(53\) 6.56681 + 9.37838i 0.902021 + 1.28822i 0.957106 + 0.289738i \(0.0935681\pi\)
−0.0550851 + 0.998482i \(0.517543\pi\)
\(54\) 0 0
\(55\) 5.87375 10.7086i 0.792016 1.44394i
\(56\) 0 0
\(57\) −9.26357 9.42437i −1.22699 1.24829i
\(58\) 0 0
\(59\) −8.39207 + 7.04179i −1.09255 + 0.916762i −0.996902 0.0786523i \(-0.974938\pi\)
−0.0956529 + 0.995415i \(0.530494\pi\)
\(60\) 0 0
\(61\) 2.07149 11.7480i 0.265227 1.50418i −0.503159 0.864194i \(-0.667829\pi\)
0.768387 0.639986i \(-0.221060\pi\)
\(62\) 0 0
\(63\) −8.02716 3.74313i −1.01133 0.471589i
\(64\) 0 0
\(65\) 0.846167 0.0927428i 0.104954 0.0115033i
\(66\) 0 0
\(67\) 0.773226 + 8.83802i 0.0944646 + 1.07974i 0.884458 + 0.466620i \(0.154528\pi\)
−0.789993 + 0.613116i \(0.789916\pi\)
\(68\) 0 0
\(69\) −0.672034 + 1.16400i −0.0809033 + 0.140129i
\(70\) 0 0
\(71\) −0.325803 + 0.0574478i −0.0386657 + 0.00681780i −0.192948 0.981209i \(-0.561805\pi\)
0.154282 + 0.988027i \(0.450694\pi\)
\(72\) 0 0
\(73\) −0.964863 2.06915i −0.112929 0.242176i 0.841718 0.539917i \(-0.181545\pi\)
−0.954647 + 0.297741i \(0.903767\pi\)
\(74\) 0 0
\(75\) 0.658643 15.1442i 0.0760535 1.74870i
\(76\) 0 0
\(77\) 5.52535 5.52535i 0.629672 0.629672i
\(78\) 0 0
\(79\) −2.57267 0.936374i −0.289447 0.105350i 0.193216 0.981156i \(-0.438108\pi\)
−0.482663 + 0.875806i \(0.660330\pi\)
\(80\) 0 0
\(81\) −1.86796 10.5937i −0.207551 1.17708i
\(82\) 0 0
\(83\) −11.1195 + 2.97945i −1.22052 + 0.327037i −0.810881 0.585211i \(-0.801012\pi\)
−0.409638 + 0.912248i \(0.634345\pi\)
\(84\) 0 0
\(85\) 0.332548 0.164029i 0.0360698 0.0177915i
\(86\) 0 0
\(87\) −4.19952 1.12526i −0.450236 0.120640i
\(88\) 0 0
\(89\) −5.02263 + 1.82809i −0.532397 + 0.193777i −0.594208 0.804311i \(-0.702535\pi\)
0.0618111 + 0.998088i \(0.480312\pi\)
\(90\) 0 0
\(91\) 0.536325 + 0.0945686i 0.0562222 + 0.00991348i
\(92\) 0 0
\(93\) −23.2950 2.03804i −2.41557 0.211335i
\(94\) 0 0
\(95\) 6.16528 7.54912i 0.632545 0.774524i
\(96\) 0 0
\(97\) 0.497197 + 0.0434991i 0.0504827 + 0.00441667i 0.112369 0.993667i \(-0.464156\pi\)
−0.0618864 + 0.998083i \(0.519712\pi\)
\(98\) 0 0
\(99\) 33.3033 + 5.87227i 3.34711 + 0.590185i
\(100\) 0 0
\(101\) 1.05706 0.384738i 0.105181 0.0382828i −0.288893 0.957361i \(-0.593287\pi\)
0.394075 + 0.919078i \(0.371065\pi\)
\(102\) 0 0
\(103\) 14.9080 + 3.99460i 1.46893 + 0.393599i 0.902565 0.430554i \(-0.141682\pi\)
0.566367 + 0.824153i \(0.308348\pi\)
\(104\) 0 0
\(105\) 3.11655 9.18362i 0.304144 0.896229i
\(106\) 0 0
\(107\) −7.95396 + 2.13126i −0.768938 + 0.206036i −0.621902 0.783095i \(-0.713640\pi\)
−0.147036 + 0.989131i \(0.546973\pi\)
\(108\) 0 0
\(109\) 1.54408 + 8.75691i 0.147896 + 0.838760i 0.964996 + 0.262264i \(0.0844692\pi\)
−0.817100 + 0.576496i \(0.804420\pi\)
\(110\) 0 0
\(111\) −27.2894 9.93253i −2.59020 0.942754i
\(112\) 0 0
\(113\) −6.62544 + 6.62544i −0.623269 + 0.623269i −0.946366 0.323097i \(-0.895276\pi\)
0.323097 + 0.946366i \(0.395276\pi\)
\(114\) 0 0
\(115\) −0.907414 0.399180i −0.0846168 0.0372237i
\(116\) 0 0
\(117\) 0.996061 + 2.13606i 0.0920858 + 0.197479i
\(118\) 0 0
\(119\) 0.233625 0.0411945i 0.0214164 0.00377629i
\(120\) 0 0
\(121\) −9.41746 + 16.3115i −0.856132 + 1.48286i
\(122\) 0 0
\(123\) 1.85505 + 21.2034i 0.167265 + 1.91184i
\(124\) 0 0
\(125\) 11.1562 0.734059i 0.997842 0.0656562i
\(126\) 0 0
\(127\) 4.55705 + 2.12499i 0.404373 + 0.188562i 0.614154 0.789186i \(-0.289497\pi\)
−0.209781 + 0.977748i \(0.567275\pi\)
\(128\) 0 0
\(129\) −6.06882 + 34.4180i −0.534330 + 3.03034i
\(130\) 0 0
\(131\) −8.78769 + 7.37375i −0.767784 + 0.644247i −0.940140 0.340787i \(-0.889306\pi\)
0.172356 + 0.985035i \(0.444862\pi\)
\(132\) 0 0
\(133\) 5.13862 3.53260i 0.445575 0.306316i
\(134\) 0 0
\(135\) 20.7685 6.05537i 1.78747 0.521163i
\(136\) 0 0
\(137\) 0.732633 + 1.04631i 0.0625931 + 0.0893922i 0.849228 0.528026i \(-0.177068\pi\)
−0.786635 + 0.617418i \(0.788179\pi\)
\(138\) 0 0
\(139\) −1.80645 4.96319i −0.153222 0.420973i 0.839205 0.543816i \(-0.183021\pi\)
−0.992426 + 0.122843i \(0.960799\pi\)
\(140\) 0 0
\(141\) 8.20821 4.73901i 0.691256 0.399097i
\(142\) 0 0
\(143\) −2.07143 + 0.181227i −0.173222 + 0.0151549i
\(144\) 0 0
\(145\) 0.487542 3.16940i 0.0404882 0.263204i
\(146\) 0 0
\(147\) −8.61358 + 12.3015i −0.710436 + 1.01461i
\(148\) 0 0
\(149\) 4.81272 13.2229i 0.394274 1.08326i −0.570756 0.821119i \(-0.693350\pi\)
0.965030 0.262139i \(-0.0844278\pi\)
\(150\) 0 0
\(151\) 20.4283i 1.66243i −0.555948 0.831217i \(-0.687644\pi\)
0.555948 0.831217i \(-0.312356\pi\)
\(152\) 0 0
\(153\) 0.725963 + 0.725963i 0.0586906 + 0.0586906i
\(154\) 0 0
\(155\) −0.377702 17.2430i −0.0303378 1.38499i
\(156\) 0 0
\(157\) 13.4852 + 9.44244i 1.07624 + 0.753589i 0.970572 0.240813i \(-0.0774140\pi\)
0.105665 + 0.994402i \(0.466303\pi\)
\(158\) 0 0
\(159\) −30.0593 17.3548i −2.38386 1.37632i
\(160\) 0 0
\(161\) −0.485850 0.407676i −0.0382903 0.0321294i
\(162\) 0 0
\(163\) 2.35672 8.79540i 0.184593 0.688909i −0.810125 0.586258i \(-0.800601\pi\)
0.994717 0.102652i \(-0.0327327\pi\)
\(164\) 0 0
\(165\) −2.41864 + 36.9492i −0.188291 + 2.87649i
\(166\) 0 0
\(167\) 5.11551 3.58192i 0.395850 0.277177i −0.358657 0.933469i \(-0.616765\pi\)
0.754507 + 0.656293i \(0.227876\pi\)
\(168\) 0 0
\(169\) 8.26309 + 9.84756i 0.635622 + 0.757505i
\(170\) 0 0
\(171\) 25.2789 + 9.44785i 1.93312 + 0.722495i
\(172\) 0 0
\(173\) 1.37458 15.7116i 0.104508 1.19453i −0.745041 0.667019i \(-0.767570\pi\)
0.849549 0.527510i \(-0.176874\pi\)
\(174\) 0 0
\(175\) 6.98362 + 1.54699i 0.527912 + 0.116942i
\(176\) 0 0
\(177\) 14.0362 30.1007i 1.05502 2.26251i
\(178\) 0 0
\(179\) −10.6511 18.4482i −0.796099 1.37888i −0.922139 0.386858i \(-0.873560\pi\)
0.126041 0.992025i \(-0.459773\pi\)
\(180\) 0 0
\(181\) −5.65911 + 6.74426i −0.420638 + 0.501297i −0.934197 0.356757i \(-0.883882\pi\)
0.513559 + 0.858054i \(0.328327\pi\)
\(182\) 0 0
\(183\) 9.36041 + 34.9335i 0.691942 + 2.58236i
\(184\) 0 0
\(185\) 5.08933 20.8060i 0.374175 1.52969i
\(186\) 0 0
\(187\) −0.820907 + 0.382795i −0.0600307 + 0.0279928i
\(188\) 0 0
\(189\) 13.8404 1.00674
\(190\) 0 0
\(191\) 11.8629 0.858369 0.429185 0.903217i \(-0.358801\pi\)
0.429185 + 0.903217i \(0.358801\pi\)
\(192\) 0 0
\(193\) −2.98330 + 1.39114i −0.214743 + 0.100136i −0.527013 0.849857i \(-0.676688\pi\)
0.312271 + 0.949993i \(0.398910\pi\)
\(194\) 0 0
\(195\) −2.20614 + 1.33898i −0.157985 + 0.0958861i
\(196\) 0 0
\(197\) 5.05223 + 18.8552i 0.359956 + 1.34338i 0.874131 + 0.485690i \(0.161432\pi\)
−0.514175 + 0.857685i \(0.671902\pi\)
\(198\) 0 0
\(199\) −7.32786 + 8.73301i −0.519458 + 0.619066i −0.960453 0.278443i \(-0.910182\pi\)
0.440994 + 0.897510i \(0.354626\pi\)
\(200\) 0 0
\(201\) −13.4483 23.2931i −0.948568 1.64297i
\(202\) 0 0
\(203\) 0.867024 1.85934i 0.0608531 0.130500i
\(204\) 0 0
\(205\) −15.3967 + 3.06394i −1.07535 + 0.213995i
\(206\) 0 0
\(207\) 0.239224 2.73434i 0.0166272 0.190050i
\(208\) 0 0
\(209\) −15.4604 + 18.1063i −1.06942 + 1.25244i
\(210\) 0 0
\(211\) 7.39450 + 8.81242i 0.509058 + 0.606672i 0.957957 0.286910i \(-0.0926282\pi\)
−0.448899 + 0.893582i \(0.648184\pi\)
\(212\) 0 0
\(213\) 0.821587 0.575281i 0.0562942 0.0394176i
\(214\) 0 0
\(215\) −25.7220 1.68373i −1.75423 0.114829i
\(216\) 0 0
\(217\) 2.85589 10.6583i 0.193870 0.723534i
\(218\) 0 0
\(219\) 5.30221 + 4.44908i 0.358290 + 0.300641i
\(220\) 0 0
\(221\) −0.0546702 0.0315639i −0.00367752 0.00212322i
\(222\) 0 0
\(223\) −12.8084 8.96853i −0.857713 0.600577i 0.0598325 0.998208i \(-0.480943\pi\)
−0.917545 + 0.397632i \(0.869832\pi\)
\(224\) 0 0
\(225\) 11.8511 + 28.5975i 0.790076 + 1.90650i
\(226\) 0 0
\(227\) 6.34919 + 6.34919i 0.421410 + 0.421410i 0.885689 0.464279i \(-0.153686\pi\)
−0.464279 + 0.885689i \(0.653686\pi\)
\(228\) 0 0
\(229\) 1.24193i 0.0820690i −0.999158 0.0410345i \(-0.986935\pi\)
0.999158 0.0410345i \(-0.0130654\pi\)
\(230\) 0 0
\(231\) −8.10238 + 22.2611i −0.533097 + 1.46467i
\(232\) 0 0
\(233\) 10.3258 14.7467i 0.676465 0.966091i −0.323339 0.946283i \(-0.604806\pi\)
0.999804 0.0198083i \(-0.00630560\pi\)
\(234\) 0 0
\(235\) 4.13411 + 5.63722i 0.269680 + 0.367731i
\(236\) 0 0
\(237\) 8.26851 0.723401i 0.537098 0.0469899i
\(238\) 0 0
\(239\) −11.0995 + 6.40830i −0.717967 + 0.414518i −0.814004 0.580859i \(-0.802717\pi\)
0.0960369 + 0.995378i \(0.469383\pi\)
\(240\) 0 0
\(241\) −4.12415 11.3310i −0.265660 0.729894i −0.998760 0.0497742i \(-0.984150\pi\)
0.733101 0.680120i \(-0.238072\pi\)
\(242\) 0 0
\(243\) 2.05823 + 2.93945i 0.132035 + 0.188566i
\(244\) 0 0
\(245\) −9.71127 5.32672i −0.620430 0.340311i
\(246\) 0 0
\(247\) −1.65174 0.158840i −0.105098 0.0101068i
\(248\) 0 0
\(249\) 26.7350 22.4333i 1.69426 1.42165i
\(250\) 0 0
\(251\) −2.27798 + 12.9190i −0.143785 + 0.815443i 0.824550 + 0.565789i \(0.191428\pi\)
−0.968335 + 0.249654i \(0.919683\pi\)
\(252\) 0 0
\(253\) 2.19469 + 1.02340i 0.137979 + 0.0643407i
\(254\) 0 0
\(255\) −0.703562 + 0.876772i −0.0440587 + 0.0549056i
\(256\) 0 0
\(257\) 2.27311 + 25.9817i 0.141792 + 1.62070i 0.650328 + 0.759654i \(0.274632\pi\)
−0.508535 + 0.861041i \(0.669813\pi\)
\(258\) 0 0
\(259\) 6.85181 11.8677i 0.425751 0.737422i
\(260\) 0 0
\(261\) 8.74369 1.54175i 0.541221 0.0954319i
\(262\) 0 0
\(263\) 6.36796 + 13.6561i 0.392665 + 0.842073i 0.998905 + 0.0467907i \(0.0148994\pi\)
−0.606240 + 0.795282i \(0.707323\pi\)
\(264\) 0 0
\(265\) 10.3085 23.4333i 0.633248 1.43950i
\(266\) 0 0
\(267\) 11.4582 11.4582i 0.701229 0.701229i
\(268\) 0 0
\(269\) −15.9217 5.79504i −0.970765 0.353330i −0.192522 0.981293i \(-0.561667\pi\)
−0.778243 + 0.627963i \(0.783889\pi\)
\(270\) 0 0
\(271\) 5.49996 + 31.1918i 0.334099 + 1.89477i 0.435956 + 0.899968i \(0.356410\pi\)
−0.101857 + 0.994799i \(0.532479\pi\)
\(272\) 0 0
\(273\) −1.59480 + 0.427325i −0.0965217 + 0.0258629i
\(274\) 0 0
\(275\) −27.2845 + 1.19589i −1.64532 + 0.0721148i
\(276\) 0 0
\(277\) 6.55193 + 1.75558i 0.393667 + 0.105483i 0.450222 0.892917i \(-0.351345\pi\)
−0.0565546 + 0.998400i \(0.518012\pi\)
\(278\) 0 0
\(279\) 44.8736 16.3327i 2.68651 0.977811i
\(280\) 0 0
\(281\) 23.1123 + 4.07533i 1.37877 + 0.243114i 0.813389 0.581720i \(-0.197620\pi\)
0.565376 + 0.824833i \(0.308731\pi\)
\(282\) 0 0
\(283\) −13.9218 1.21800i −0.827564 0.0724025i −0.334500 0.942396i \(-0.608568\pi\)
−0.493064 + 0.869993i \(0.664123\pi\)
\(284\) 0 0
\(285\) −7.26773 + 28.6416i −0.430503 + 1.69658i
\(286\) 0 0
\(287\) −10.0053 0.875354i −0.590597 0.0516705i
\(288\) 0 0
\(289\) 16.7147 + 2.94724i 0.983215 + 0.173367i
\(290\) 0 0
\(291\) −1.42186 + 0.517514i −0.0833507 + 0.0303372i
\(292\) 0 0
\(293\) −0.339935 0.0910852i −0.0198592 0.00532126i 0.248876 0.968535i \(-0.419939\pi\)
−0.268735 + 0.963214i \(0.586606\pi\)
\(294\) 0 0
\(295\) 23.1969 + 7.87211i 1.35058 + 0.458332i
\(296\) 0 0
\(297\) −51.0438 + 13.6771i −2.96186 + 0.793629i
\(298\) 0 0
\(299\) 0.0293069 + 0.166208i 0.00169486 + 0.00961203i
\(300\) 0 0
\(301\) −15.4970 5.64044i −0.893231 0.325110i
\(302\) 0 0
\(303\) −2.41148 + 2.41148i −0.138536 + 0.138536i
\(304\) 0 0
\(305\) −24.8601 + 9.67000i −1.42349 + 0.553702i
\(306\) 0 0
\(307\) −1.53013 3.28138i −0.0873292 0.187278i 0.857793 0.513996i \(-0.171835\pi\)
−0.945122 + 0.326717i \(0.894057\pi\)
\(308\) 0 0
\(309\) −46.0801 + 8.12517i −2.62141 + 0.462225i
\(310\) 0 0
\(311\) 12.3076 21.3174i 0.697901 1.20880i −0.271291 0.962497i \(-0.587451\pi\)
0.969193 0.246303i \(-0.0792160\pi\)
\(312\) 0 0
\(313\) −1.42067 16.2383i −0.0803008 0.917842i −0.924342 0.381564i \(-0.875386\pi\)
0.844042 0.536278i \(-0.180170\pi\)
\(314\) 0 0
\(315\) 2.15775 + 19.6869i 0.121576 + 1.10923i
\(316\) 0 0
\(317\) −16.7901 7.82936i −0.943027 0.439741i −0.110593 0.993866i \(-0.535275\pi\)
−0.832433 + 0.554125i \(0.813053\pi\)
\(318\) 0 0
\(319\) −1.36020 + 7.71407i −0.0761565 + 0.431905i
\(320\) 0 0
\(321\) 19.1240 16.0470i 1.06740 0.895654i
\(322\) 0 0
\(323\) −0.699779 + 0.181067i −0.0389367 + 0.0100748i
\(324\) 0 0
\(325\) −1.15898 1.50989i −0.0642888 0.0837534i
\(326\) 0 0
\(327\) −15.4624 22.0826i −0.855072 1.22117i
\(328\) 0 0
\(329\) 1.52967 + 4.20272i 0.0843332 + 0.231704i
\(330\) 0 0
\(331\) −11.8874 + 6.86318i −0.653389 + 0.377235i −0.789754 0.613424i \(-0.789792\pi\)
0.136364 + 0.990659i \(0.456458\pi\)
\(332\) 0 0
\(333\) 59.0800 5.16883i 3.23756 0.283250i
\(334\) 0 0
\(335\) 15.9972 11.7317i 0.874019 0.640971i
\(336\) 0 0
\(337\) 12.9431 18.4847i 0.705056 1.00692i −0.293642 0.955915i \(-0.594867\pi\)
0.998698 0.0510088i \(-0.0162437\pi\)
\(338\) 0 0
\(339\) 9.71555 26.6932i 0.527676 1.44978i
\(340\) 0 0
\(341\) 42.1303i 2.28148i
\(342\) 0 0
\(343\) −12.0918 12.0918i −0.652895 0.652895i
\(344\) 0 0
\(345\) 3.00470 0.0658171i 0.161768 0.00354347i
\(346\) 0 0
\(347\) −29.5562 20.6955i −1.58666 1.11099i −0.936207 0.351448i \(-0.885689\pi\)
−0.650455 0.759545i \(-0.725422\pi\)
\(348\) 0 0
\(349\) 4.78794 + 2.76432i 0.256292 + 0.147970i 0.622642 0.782507i \(-0.286059\pi\)
−0.366350 + 0.930477i \(0.619393\pi\)
\(350\) 0 0
\(351\) −2.82134 2.36738i −0.150592 0.126362i
\(352\) 0 0
\(353\) −1.95531 + 7.29731i −0.104071 + 0.388397i −0.998238 0.0593360i \(-0.981102\pi\)
0.894168 + 0.447733i \(0.147768\pi\)
\(354\) 0 0
\(355\) 0.487802 + 0.556137i 0.0258898 + 0.0295167i
\(356\) 0 0
\(357\) −0.589141 + 0.412521i −0.0311806 + 0.0218329i
\(358\) 0 0
\(359\) −2.56312 3.05461i −0.135276 0.161216i 0.694153 0.719827i \(-0.255779\pi\)
−0.829430 + 0.558611i \(0.811335\pi\)
\(360\) 0 0
\(361\) −14.7628 + 11.9607i −0.776992 + 0.629511i
\(362\) 0 0
\(363\) 4.97674 56.8844i 0.261211 2.98566i
\(364\) 0 0
\(365\) −2.83587 + 4.24496i −0.148436 + 0.222191i
\(366\) 0 0
\(367\) 14.6703 31.4606i 0.765784 1.64223i −0.000727542 1.00000i \(-0.500232\pi\)
0.766512 0.642230i \(-0.221991\pi\)
\(368\) 0 0
\(369\) −21.7329 37.6426i −1.13137 1.95959i
\(370\) 0 0
\(371\) 10.5279 12.5467i 0.546583 0.651393i
\(372\) 0 0
\(373\) 0.766310 + 2.85991i 0.0396781 + 0.148081i 0.982923 0.184017i \(-0.0589103\pi\)
−0.943245 + 0.332098i \(0.892244\pi\)
\(374\) 0 0
\(375\) −29.7129 + 16.3108i −1.53437 + 0.842288i
\(376\) 0 0
\(377\) −0.494777 + 0.230718i −0.0254823 + 0.0118826i
\(378\) 0 0
\(379\) −31.3437 −1.61002 −0.805010 0.593262i \(-0.797840\pi\)
−0.805010 + 0.593262i \(0.797840\pi\)
\(380\) 0 0
\(381\) −15.2438 −0.780965
\(382\) 0 0
\(383\) 8.61928 4.01924i 0.440425 0.205373i −0.189741 0.981834i \(-0.560765\pi\)
0.630166 + 0.776461i \(0.282987\pi\)
\(384\) 0 0
\(385\) −16.9723 4.15158i −0.864990 0.211584i
\(386\) 0 0
\(387\) −18.4722 68.9391i −0.938994 3.50437i
\(388\) 0 0
\(389\) 6.11064 7.28238i 0.309822 0.369231i −0.588555 0.808457i \(-0.700303\pi\)
0.898377 + 0.439226i \(0.144747\pi\)
\(390\) 0 0
\(391\) 0.0367588 + 0.0636681i 0.00185897 + 0.00321983i
\(392\) 0 0
\(393\) 14.6979 31.5197i 0.741410 1.58996i
\(394\) 0 0
\(395\) 1.19482 + 6.00412i 0.0601180 + 0.302100i
\(396\) 0 0
\(397\) −0.411018 + 4.69796i −0.0206284 + 0.235784i 0.978880 + 0.204435i \(0.0655358\pi\)
−0.999509 + 0.0313487i \(0.990020\pi\)
\(398\) 0 0
\(399\) −9.59298 + 16.2902i −0.480250 + 0.815531i
\(400\) 0 0
\(401\) 3.05550 + 3.64140i 0.152584 + 0.181843i 0.836922 0.547323i \(-0.184353\pi\)
−0.684338 + 0.729165i \(0.739908\pi\)
\(402\) 0 0
\(403\) −2.40525 + 1.68418i −0.119814 + 0.0838948i
\(404\) 0 0
\(405\) −18.0832 + 15.8613i −0.898563 + 0.788153i
\(406\) 0 0
\(407\) −13.5419 + 50.5392i −0.671250 + 2.50514i
\(408\) 0 0
\(409\) −16.9851 14.2522i −0.839858 0.704724i 0.117674 0.993052i \(-0.462456\pi\)
−0.957532 + 0.288328i \(0.906901\pi\)
\(410\) 0 0
\(411\) −3.35360 1.93620i −0.165421 0.0955059i
\(412\) 0 0
\(413\) 12.8379 + 8.98916i 0.631710 + 0.442328i
\(414\) 0 0
\(415\) 18.5958 + 17.7986i 0.912834 + 0.873701i
\(416\) 0 0
\(417\) 11.3226 + 11.3226i 0.554470 + 0.554470i
\(418\) 0 0
\(419\) 27.3929i 1.33823i −0.743159 0.669115i \(-0.766673\pi\)
0.743159 0.669115i \(-0.233327\pi\)
\(420\) 0 0
\(421\) −4.48082 + 12.3109i −0.218382 + 0.599999i −0.999709 0.0241228i \(-0.992321\pi\)
0.781327 + 0.624121i \(0.214543\pi\)
\(422\) 0 0
\(423\) −11.1019 + 15.8551i −0.539792 + 0.770903i
\(424\) 0 0
\(425\) −0.699362 0.445376i −0.0339240 0.0216039i
\(426\) 0 0
\(427\) −17.0008 + 1.48738i −0.822728 + 0.0719793i
\(428\) 0 0
\(429\) 5.45937 3.15197i 0.263581 0.152179i
\(430\) 0 0
\(431\) −10.1249 27.8180i −0.487701 1.33995i −0.902757 0.430151i \(-0.858460\pi\)
0.415056 0.909796i \(-0.363762\pi\)
\(432\) 0 0
\(433\) 0.999898 + 1.42800i 0.0480520 + 0.0686254i 0.842459 0.538760i \(-0.181107\pi\)
−0.794407 + 0.607386i \(0.792218\pi\)
\(434\) 0 0
\(435\) 2.72119 + 9.33305i 0.130471 + 0.447486i
\(436\) 0 0
\(437\) 1.57339 + 1.12200i 0.0752654 + 0.0536724i
\(438\) 0 0
\(439\) −6.39461 + 5.36572i −0.305198 + 0.256092i −0.782504 0.622646i \(-0.786058\pi\)
0.477306 + 0.878737i \(0.341613\pi\)
\(440\) 0 0
\(441\) 5.32538 30.2017i 0.253589 1.43818i
\(442\) 0 0
\(443\) −21.4646 10.0091i −1.01981 0.475547i −0.160522 0.987032i \(-0.551318\pi\)
−0.859292 + 0.511485i \(0.829095\pi\)
\(444\) 0 0
\(445\) 9.32159 + 7.48007i 0.441886 + 0.354589i
\(446\) 0 0
\(447\) 3.71810 + 42.4981i 0.175860 + 2.01009i
\(448\) 0 0
\(449\) 2.36294 4.09274i 0.111514 0.193148i −0.804867 0.593455i \(-0.797763\pi\)
0.916381 + 0.400307i \(0.131097\pi\)
\(450\) 0 0
\(451\) 37.7649 6.65898i 1.77828 0.313559i
\(452\) 0 0
\(453\) 26.1738 + 56.1299i 1.22975 + 2.63721i
\(454\) 0 0
\(455\) −0.441459 1.13492i −0.0206959 0.0532061i
\(456\) 0 0
\(457\) −13.9975 + 13.9975i −0.654773 + 0.654773i −0.954139 0.299365i \(-0.903225\pi\)
0.299365 + 0.954139i \(0.403225\pi\)
\(458\) 0 0
\(459\) −1.50757 0.548712i −0.0703676 0.0256117i
\(460\) 0 0
\(461\) −0.975172 5.53048i −0.0454183 0.257580i 0.953641 0.300947i \(-0.0973027\pi\)
−0.999059 + 0.0433669i \(0.986192\pi\)
\(462\) 0 0
\(463\) 12.6185 3.38111i 0.586430 0.157133i 0.0466088 0.998913i \(-0.485159\pi\)
0.539821 + 0.841780i \(0.318492\pi\)
\(464\) 0 0
\(465\) 23.1304 + 46.8938i 1.07265 + 2.17465i
\(466\) 0 0
\(467\) 30.4453 + 8.15779i 1.40884 + 0.377498i 0.881511 0.472164i \(-0.156527\pi\)
0.527329 + 0.849661i \(0.323194\pi\)
\(468\) 0 0
\(469\) 11.9264 4.34085i 0.550710 0.200442i
\(470\) 0 0
\(471\) −49.1507 8.66660i −2.26475 0.399336i
\(472\) 0 0
\(473\) 62.7271 + 5.48791i 2.88420 + 0.252334i
\(474\) 0 0
\(475\) −21.5833 3.02691i −0.990309 0.138884i
\(476\) 0 0
\(477\) 70.6124 + 6.17778i 3.23312 + 0.282861i
\(478\) 0 0
\(479\) 28.5377 + 5.03196i 1.30392 + 0.229916i 0.782107 0.623144i \(-0.214145\pi\)
0.521813 + 0.853060i \(0.325256\pi\)
\(480\) 0 0
\(481\) −3.42667 + 1.24721i −0.156243 + 0.0568677i
\(482\) 0 0
\(483\) 1.85728 + 0.497657i 0.0845092 + 0.0226442i
\(484\) 0 0
\(485\) −0.493685 1.00088i −0.0224171 0.0454476i
\(486\) 0 0
\(487\) 26.8569 7.19630i 1.21700 0.326095i 0.407498 0.913206i \(-0.366401\pi\)
0.809507 + 0.587111i \(0.199735\pi\)
\(488\) 0 0
\(489\) 4.79367 + 27.1862i 0.216777 + 1.22940i
\(490\) 0 0
\(491\) 19.2426 + 7.00372i 0.868404 + 0.316073i 0.737521 0.675324i \(-0.235996\pi\)
0.130883 + 0.991398i \(0.458219\pi\)
\(492\) 0 0
\(493\) −0.168155 + 0.168155i −0.00757334 + 0.00757334i
\(494\) 0 0
\(495\) −27.4125 70.4735i −1.23210 3.16755i
\(496\) 0 0
\(497\) 0.200016 + 0.428935i 0.00897194 + 0.0192404i
\(498\) 0 0
\(499\) −11.8732 + 2.09357i −0.531519 + 0.0937211i −0.432965 0.901411i \(-0.642533\pi\)
−0.0985537 + 0.995132i \(0.531422\pi\)
\(500\) 0 0
\(501\) −9.46629 + 16.3961i −0.422923 + 0.732523i
\(502\) 0 0
\(503\) 2.40329 + 27.4697i 0.107157 + 1.22481i 0.839302 + 0.543666i \(0.182964\pi\)
−0.732145 + 0.681149i \(0.761480\pi\)
\(504\) 0 0
\(505\) −1.96181 1.57425i −0.0872996 0.0700532i
\(506\) 0 0
\(507\) −35.3213 16.4706i −1.56867 0.731484i
\(508\) 0 0
\(509\) 2.22736 12.6320i 0.0987260 0.559903i −0.894816 0.446436i \(-0.852693\pi\)
0.993542 0.113467i \(-0.0361957\pi\)
\(510\) 0 0
\(511\) −2.50198 + 2.09941i −0.110681 + 0.0928725i
\(512\) 0 0
\(513\) −42.0406 + 3.31385i −1.85614 + 0.146310i
\(514\) 0 0
\(515\) −9.66007 33.1318i −0.425674 1.45996i
\(516\) 0 0
\(517\) −9.79458 13.9881i −0.430765 0.615196i
\(518\) 0 0
\(519\) 16.3536 + 44.9311i 0.717842 + 1.97226i
\(520\) 0 0
\(521\) −14.6741 + 8.47209i −0.642884 + 0.371169i −0.785725 0.618577i \(-0.787710\pi\)
0.142841 + 0.989746i \(0.454376\pi\)
\(522\) 0 0
\(523\) 24.1464 2.11254i 1.05585 0.0923748i 0.454013 0.890995i \(-0.349992\pi\)
0.601836 + 0.798620i \(0.294436\pi\)
\(524\) 0 0
\(525\) −21.1706 + 4.69717i −0.923962 + 0.205001i
\(526\) 0 0
\(527\) −0.733634 + 1.04774i −0.0319576 + 0.0456402i
\(528\) 0 0
\(529\) −7.79924 + 21.4282i −0.339097 + 0.931662i
\(530\) 0 0
\(531\) 67.8248i 2.94335i
\(532\) 0 0
\(533\) 1.88984 + 1.88984i 0.0818579 + 0.0818579i
\(534\) 0 0
\(535\) 13.3020 + 12.7317i 0.575094 + 0.550439i
\(536\) 0 0
\(537\) 52.9022 + 37.0425i 2.28290 + 1.59850i
\(538\) 0 0
\(539\) 23.4315 + 13.5282i 1.00926 + 0.582699i
\(540\) 0 0
\(541\) −27.0758 22.7193i −1.16408 0.976779i −0.164126 0.986439i \(-0.552480\pi\)
−0.999953 + 0.00966081i \(0.996925\pi\)
\(542\) 0 0
\(543\) 6.90816 25.7816i 0.296457 1.10639i
\(544\) 0 0
\(545\) 14.9478 13.1111i 0.640294 0.561619i
\(546\) 0 0
\(547\) 18.0598 12.6456i 0.772183 0.540689i −0.119778 0.992801i \(-0.538218\pi\)
0.891961 + 0.452112i \(0.149329\pi\)
\(548\) 0 0
\(549\) −47.4738 56.5771i −2.02613 2.41465i
\(550\) 0 0
\(551\) −2.18841 + 5.85537i −0.0932296 + 0.249447i
\(552\) 0 0
\(553\) −0.341355 + 3.90170i −0.0145159 + 0.165917i
\(554\) 0 0
\(555\) 12.6740 + 63.6883i 0.537981 + 2.70342i
\(556\) 0 0
\(557\) 10.4168 22.3390i 0.441376 0.946534i −0.552237 0.833687i \(-0.686225\pi\)
0.993612 0.112846i \(-0.0359968\pi\)
\(558\) 0 0
\(559\) 2.19423 + 3.80052i 0.0928062 + 0.160745i
\(560\) 0 0
\(561\) 1.76511 2.10358i 0.0745230 0.0888130i
\(562\) 0 0
\(563\) 0.147798 + 0.551590i 0.00622894 + 0.0232467i 0.968970 0.247177i \(-0.0795029\pi\)
−0.962741 + 0.270424i \(0.912836\pi\)
\(564\) 0 0
\(565\) 20.3515 + 4.97815i 0.856193 + 0.209432i
\(566\) 0 0
\(567\) −13.9472 + 6.50368i −0.585727 + 0.273129i
\(568\) 0 0
\(569\) −34.0442 −1.42721 −0.713603 0.700551i \(-0.752938\pi\)
−0.713603 + 0.700551i \(0.752938\pi\)
\(570\) 0 0
\(571\) 26.6659 1.11593 0.557967 0.829863i \(-0.311582\pi\)
0.557967 + 0.829863i \(0.311582\pi\)
\(572\) 0 0
\(573\) −32.5951 + 15.1993i −1.36168 + 0.634962i
\(574\) 0 0
\(575\) 0.289708 + 2.19768i 0.0120817 + 0.0916495i
\(576\) 0 0
\(577\) 1.99204 + 7.43441i 0.0829298 + 0.309498i 0.994914 0.100727i \(-0.0321168\pi\)
−0.911984 + 0.410225i \(0.865450\pi\)
\(578\) 0 0
\(579\) 6.41467 7.64471i 0.266585 0.317703i
\(580\) 0 0
\(581\) 8.23422 + 14.2621i 0.341613 + 0.591691i
\(582\) 0 0
\(583\) −26.4286 + 56.6763i −1.09456 + 2.34729i
\(584\) 0 0
\(585\) 2.92756 4.38221i 0.121040 0.181182i
\(586\) 0 0
\(587\) −0.646976 + 7.39497i −0.0267036 + 0.305223i 0.971084 + 0.238739i \(0.0767339\pi\)
−0.997787 + 0.0664847i \(0.978822\pi\)
\(588\) 0 0
\(589\) −6.12286 + 33.0586i −0.252288 + 1.36216i
\(590\) 0 0
\(591\) −38.0399 45.3342i −1.56475 1.86480i
\(592\) 0 0
\(593\) −9.53664 + 6.67763i −0.391623 + 0.274217i −0.752760 0.658296i \(-0.771278\pi\)
0.361137 + 0.932513i \(0.382389\pi\)
\(594\) 0 0
\(595\) −0.349791 0.398792i −0.0143400 0.0163489i
\(596\) 0 0
\(597\) 8.94523 33.3841i 0.366104 1.36632i
\(598\) 0 0
\(599\) −1.68646 1.41511i −0.0689069 0.0578197i 0.607684 0.794179i \(-0.292099\pi\)
−0.676591 + 0.736359i \(0.736543\pi\)
\(600\) 0 0
\(601\) −12.0611 6.96346i −0.491981 0.284045i 0.233415 0.972377i \(-0.425010\pi\)
−0.725396 + 0.688332i \(0.758343\pi\)
\(602\) 0 0
\(603\) 44.9934 + 31.5047i 1.83227 + 1.28297i
\(604\) 0 0
\(605\) 42.1060 0.922319i 1.71185 0.0374976i
\(606\) 0 0
\(607\) −27.3635 27.3635i −1.11065 1.11065i −0.993062 0.117588i \(-0.962484\pi\)
−0.117588 0.993062i \(-0.537516\pi\)
\(608\) 0 0
\(609\) 6.21968i 0.252034i
\(610\) 0 0
\(611\) 0.407050 1.11836i 0.0164675 0.0452440i
\(612\) 0 0
\(613\) −16.0911 + 22.9805i −0.649913 + 0.928172i −0.999963 0.00855863i \(-0.997276\pi\)
0.350050 + 0.936731i \(0.386165\pi\)
\(614\) 0 0
\(615\) 38.3790 28.1456i 1.54759 1.13494i
\(616\) 0 0
\(617\) 1.72373 0.150807i 0.0693949 0.00607127i −0.0524054 0.998626i \(-0.516689\pi\)
0.121800 + 0.992555i \(0.461133\pi\)
\(618\) 0 0
\(619\) 16.7870 9.69196i 0.674725 0.389553i −0.123140 0.992389i \(-0.539296\pi\)
0.797865 + 0.602837i \(0.205963\pi\)
\(620\) 0 0
\(621\) 1.46698 + 4.03049i 0.0588678 + 0.161738i
\(622\) 0 0
\(623\) 4.38580 + 6.26357i 0.175713 + 0.250945i
\(624\) 0 0
\(625\) −14.3463 20.4740i −0.573853 0.818958i
\(626\) 0 0
\(627\) 19.2811 69.5585i 0.770013 2.77790i
\(628\) 0 0
\(629\) −1.21684 + 1.02105i −0.0485185 + 0.0407118i
\(630\) 0 0
\(631\) −1.43123 + 8.11694i −0.0569766 + 0.323130i −0.999953 0.00973032i \(-0.996903\pi\)
0.942976 + 0.332860i \(0.108014\pi\)
\(632\) 0 0
\(633\) −31.6084 14.7392i −1.25632 0.585832i
\(634\) 0 0
\(635\) −1.22497 11.1764i −0.0486113 0.443520i
\(636\) 0 0
\(637\) 0.164349 + 1.87852i 0.00651174 + 0.0744295i
\(638\) 0 0
\(639\) −1.02411 + 1.77381i −0.0405132 + 0.0701709i
\(640\) 0 0
\(641\) 3.01863 0.532266i 0.119229 0.0210232i −0.113715 0.993513i \(-0.536275\pi\)
0.232944 + 0.972490i \(0.425164\pi\)
\(642\) 0 0
\(643\) −11.3967 24.4403i −0.449442 0.963832i −0.992283 0.123996i \(-0.960429\pi\)
0.542840 0.839836i \(-0.317349\pi\)
\(644\) 0 0
\(645\) 72.8324 28.3301i 2.86777 1.11549i
\(646\) 0 0
\(647\) −9.43474 + 9.43474i −0.370918 + 0.370918i −0.867812 0.496894i \(-0.834474\pi\)
0.496894 + 0.867812i \(0.334474\pi\)
\(648\) 0 0
\(649\) −56.2294 20.4658i −2.20720 0.803354i
\(650\) 0 0
\(651\) 5.80899 + 32.9444i 0.227672 + 1.29119i
\(652\) 0 0
\(653\) 25.7176 6.89102i 1.00641 0.269666i 0.282281 0.959332i \(-0.408909\pi\)
0.724128 + 0.689665i \(0.242242\pi\)
\(654\) 0 0
\(655\) 24.2905 + 8.24322i 0.949108 + 0.322089i
\(656\) 0 0
\(657\) −13.6532 3.65836i −0.532662 0.142726i
\(658\) 0 0
\(659\) 8.38583 3.05219i 0.326666 0.118897i −0.173481 0.984837i \(-0.555502\pi\)
0.500147 + 0.865941i \(0.333279\pi\)
\(660\) 0 0
\(661\) −15.1515 2.67162i −0.589325 0.103914i −0.128970 0.991649i \(-0.541167\pi\)
−0.460356 + 0.887735i \(0.652278\pi\)
\(662\) 0 0
\(663\) 0.190656 + 0.0166802i 0.00740446 + 0.000647806i
\(664\) 0 0
\(665\) −12.7144 5.72426i −0.493044 0.221977i
\(666\) 0 0
\(667\) 0.633358 + 0.0554117i 0.0245237 + 0.00214555i
\(668\) 0 0
\(669\) 46.6839 + 8.23163i 1.80490 + 0.318253i
\(670\) 0 0
\(671\) 61.2296 22.2857i 2.36374 0.860332i
\(672\) 0 0
\(673\) 1.76147 + 0.471984i 0.0678996 + 0.0181936i 0.292609 0.956232i \(-0.405477\pi\)
−0.224709 + 0.974426i \(0.572143\pi\)
\(674\) 0 0
\(675\) −35.6702 32.6746i −1.37295 1.25765i
\(676\) 0 0
\(677\) 2.89080 0.774587i 0.111102 0.0297698i −0.202839 0.979212i \(-0.565017\pi\)
0.313942 + 0.949442i \(0.398350\pi\)
\(678\) 0 0
\(679\) −0.123984 0.703151i −0.00475809 0.0269845i
\(680\) 0 0
\(681\) −25.5802 9.31045i −0.980237 0.356777i
\(682\) 0 0
\(683\) 16.7520 16.7520i 0.640998 0.640998i −0.309803 0.950801i \(-0.600263\pi\)
0.950801 + 0.309803i \(0.100263\pi\)
\(684\) 0 0
\(685\) 1.15008 2.61436i 0.0439424 0.0998896i
\(686\) 0 0
\(687\) 1.59122 + 3.41239i 0.0607089 + 0.130191i
\(688\) 0 0
\(689\) −4.29219 + 0.756829i −0.163519 + 0.0288329i
\(690\) 0 0
\(691\) −4.79488 + 8.30497i −0.182406 + 0.315936i −0.942699 0.333644i \(-0.891722\pi\)
0.760294 + 0.649580i \(0.225055\pi\)
\(692\) 0 0
\(693\) −4.21643 48.1940i −0.160169 1.83074i
\(694\) 0 0
\(695\) −7.39156 + 9.21128i −0.280378 + 0.349404i
\(696\) 0 0
\(697\) 1.05513 + 0.492016i 0.0399660 + 0.0186364i
\(698\) 0 0
\(699\) −9.47736 + 53.7488i −0.358467 + 2.03297i
\(700\) 0 0
\(701\) −30.5097 + 25.6007i −1.15234 + 0.966925i −0.999772 0.0213689i \(-0.993198\pi\)
−0.152564 + 0.988294i \(0.548753\pi\)
\(702\) 0 0
\(703\) −17.9710 + 37.6889i −0.677789 + 1.42146i
\(704\) 0 0
\(705\) −18.5818 10.1923i −0.699830 0.383863i
\(706\) 0 0
\(707\) −0.923033 1.31823i −0.0347142 0.0495770i
\(708\) 0 0
\(709\) −0.312288 0.858004i −0.0117282 0.0322230i 0.933690 0.358081i \(-0.116569\pi\)
−0.945419 + 0.325858i \(0.894347\pi\)
\(710\) 0 0
\(711\) −14.6792 + 8.47502i −0.550512 + 0.317838i
\(712\) 0 0
\(713\) 3.40653 0.298032i 0.127575 0.0111614i
\(714\) 0 0
\(715\) 2.74964 + 3.74938i 0.102831 + 0.140219i
\(716\) 0 0
\(717\) 22.2869 31.8290i 0.832320 1.18868i
\(718\) 0 0
\(719\) 0.148862 0.408995i 0.00555161 0.0152529i −0.936886 0.349635i \(-0.886305\pi\)
0.942437 + 0.334382i \(0.108528\pi\)
\(720\) 0 0
\(721\) 22.0795i 0.822284i
\(722\) 0 0
\(723\) 25.8496 + 25.8496i 0.961356 + 0.961356i
\(724\) 0 0
\(725\) −6.62407 + 2.74509i −0.246012 + 0.101950i
\(726\) 0 0
\(727\) 17.2496 + 12.0783i 0.639752 + 0.447959i 0.847913 0.530135i \(-0.177859\pi\)
−0.208161 + 0.978095i \(0.566748\pi\)
\(728\) 0 0
\(729\) 18.5265 + 10.6963i 0.686166 + 0.396158i
\(730\) 0 0
\(731\) 1.46440 + 1.22877i 0.0541627 + 0.0454479i
\(732\) 0 0
\(733\) 3.37563 12.5980i 0.124682 0.465318i −0.875147 0.483858i \(-0.839235\pi\)
0.999828 + 0.0185400i \(0.00590180\pi\)
\(734\) 0 0
\(735\) 33.5080 + 2.19339i 1.23596 + 0.0809043i
\(736\) 0 0
\(737\) −39.6952 + 27.7949i −1.46219 + 1.02384i
\(738\) 0 0
\(739\) 2.05518 + 2.44926i 0.0756009 + 0.0900976i 0.802519 0.596626i \(-0.203493\pi\)
−0.726918 + 0.686724i \(0.759048\pi\)
\(740\) 0 0
\(741\) 4.74192 1.67986i 0.174199 0.0617111i
\(742\) 0 0
\(743\) −1.79419 + 20.5077i −0.0658225 + 0.752355i 0.889528 + 0.456880i \(0.151033\pi\)
−0.955351 + 0.295474i \(0.904522\pi\)
\(744\) 0 0
\(745\) −30.8596 + 6.14108i −1.13061 + 0.224992i
\(746\) 0 0
\(747\) −30.1205 + 64.5935i −1.10205 + 2.36335i
\(748\) 0 0
\(749\) 5.89009 + 10.2019i 0.215219 + 0.372771i
\(750\) 0 0
\(751\) 9.43710 11.2467i 0.344365 0.410398i −0.565867 0.824496i \(-0.691459\pi\)
0.910232 + 0.414098i \(0.135903\pi\)
\(752\) 0 0
\(753\) −10.2934 38.4157i −0.375114 1.39994i
\(754\) 0 0
\(755\) −39.0496 + 23.7004i −1.42116 + 0.862547i
\(756\) 0 0
\(757\) −27.4326 + 12.7920i −0.997055 + 0.464935i −0.851466 0.524411i \(-0.824286\pi\)
−0.145590 + 0.989345i \(0.546508\pi\)
\(758\) 0 0
\(759\) −7.34147 −0.266479
\(760\) 0 0
\(761\) 45.9564 1.66592 0.832958 0.553336i \(-0.186645\pi\)
0.832958 + 0.553336i \(0.186645\pi\)
\(762\) 0 0
\(763\) 11.5289 5.37602i 0.417374 0.194625i
\(764\) 0 0
\(765\) 0.545466 2.22995i 0.0197214 0.0806241i
\(766\) 0 0
\(767\) −1.07938 4.02831i −0.0389743 0.145454i
\(768\) 0 0
\(769\) −20.5141 + 24.4477i −0.739757 + 0.881608i −0.996389 0.0849013i \(-0.972943\pi\)
0.256633 + 0.966509i \(0.417387\pi\)
\(770\) 0 0
\(771\) −39.5348 68.4762i −1.42381 2.46611i
\(772\) 0 0
\(773\) 1.37825 2.95567i 0.0495722 0.106308i −0.879962 0.475045i \(-0.842432\pi\)
0.929534 + 0.368737i \(0.120210\pi\)
\(774\) 0 0
\(775\) −32.5225 + 20.7269i −1.16824 + 0.744531i
\(776\) 0 0
\(777\) −3.62090 + 41.3871i −0.129899 + 1.48475i
\(778\) 0 0
\(779\) 30.6010 + 0.263299i 1.09639 + 0.00943366i
\(780\) 0 0
\(781\) −1.16154 1.38427i −0.0415631 0.0495330i
\(782\) 0 0
\(783\) −11.3651 + 7.95790i −0.406154 + 0.284392i
\(784\) 0 0
\(785\) 2.40445 36.7324i 0.0858185 1.31104i
\(786\) 0 0
\(787\) −8.61435 + 32.1492i −0.307068 + 1.14599i 0.624082 + 0.781359i \(0.285473\pi\)
−0.931150 + 0.364636i \(0.881194\pi\)
\(788\) 0 0
\(789\) −34.9938 29.3633i −1.24581 1.04536i
\(790\) 0 0
\(791\) 11.6084 + 6.70213i 0.412748 + 0.238300i
\(792\) 0 0
\(793\) 3.71999 + 2.60476i 0.132101 + 0.0924979i
\(794\) 0 0
\(795\) 1.69968 + 77.5943i 0.0602813 + 2.75199i
\(796\) 0 0
\(797\) −24.8027 24.8027i −0.878558 0.878558i 0.114828 0.993385i \(-0.463368\pi\)
−0.993385 + 0.114828i \(0.963368\pi\)
\(798\) 0 0
\(799\) 0.518428i 0.0183407i
\(800\) 0 0
\(801\) −11.3180 + 31.0960i −0.399902 + 1.09872i
\(802\) 0 0
\(803\) 7.15271 10.2151i 0.252414 0.360484i
\(804\) 0 0
\(805\) −0.215621 + 1.40170i −0.00759963 + 0.0494034i
\(806\) 0 0
\(807\) 51.1722 4.47699i 1.80135 0.157597i
\(808\) 0 0
\(809\) 43.2476 24.9690i 1.52050 0.877864i 0.520797 0.853680i \(-0.325635\pi\)
0.999708 0.0241837i \(-0.00769865\pi\)
\(810\) 0 0
\(811\) −4.57286 12.5638i −0.160575 0.441176i 0.833147 0.553051i \(-0.186536\pi\)
−0.993722 + 0.111875i \(0.964314\pi\)
\(812\) 0 0
\(813\) −55.0765 78.6573i −1.93162 2.75863i
\(814\) 0 0
\(815\) −19.5470 + 5.69922i −0.684701 + 0.199635i
\(816\) 0 0
\(817\) 48.4229 + 13.4225i 1.69410 + 0.469593i
\(818\) 0 0
\(819\) 2.58288 2.16729i 0.0902531 0.0757314i
\(820\) 0 0
\(821\) 7.37576 41.8300i 0.257416 1.45988i −0.532379 0.846506i \(-0.678702\pi\)
0.789795 0.613371i \(-0.210187\pi\)
\(822\) 0 0
\(823\) −5.82682 2.71709i −0.203110 0.0947119i 0.318402 0.947956i \(-0.396854\pi\)
−0.521512 + 0.853244i \(0.674632\pi\)
\(824\) 0 0
\(825\) 73.4359 38.2441i 2.55671 1.33149i
\(826\) 0 0
\(827\) 3.71091 + 42.4159i 0.129041 + 1.47495i 0.734250 + 0.678879i \(0.237534\pi\)
−0.605209 + 0.796067i \(0.706910\pi\)
\(828\) 0 0
\(829\) 6.49254 11.2454i 0.225495 0.390569i −0.730973 0.682407i \(-0.760933\pi\)
0.956468 + 0.291837i \(0.0942666\pi\)
\(830\) 0 0
\(831\) −20.2518 + 3.57093i −0.702526 + 0.123874i
\(832\) 0 0
\(833\) 0.347145 + 0.744455i 0.0120279 + 0.0257938i
\(834\) 0 0
\(835\) −12.7819 5.62286i −0.442335 0.194587i
\(836\) 0 0
\(837\) −52.7660 + 52.7660i −1.82386 + 1.82386i
\(838\) 0 0
\(839\) 10.1482 + 3.69363i 0.350354 + 0.127518i 0.511201 0.859461i \(-0.329201\pi\)
−0.160848 + 0.986979i \(0.551423\pi\)
\(840\) 0 0
\(841\) −4.67868 26.5341i −0.161334 0.914969i
\(842\) 0 0
\(843\) −68.7261 + 18.4151i −2.36705 + 0.634250i
\(844\) 0 0
\(845\) 9.23742 27.2201i 0.317777 0.936401i
\(846\) 0 0
\(847\) 26.0268 + 6.97385i 0.894290 + 0.239624i
\(848\) 0 0
\(849\) 39.8127 14.4907i 1.36637 0.497318i
\(850\) 0 0
\(851\) 4.18224 + 0.737442i 0.143365 + 0.0252792i
\(852\) 0 0
\(853\) 31.1952 + 2.72923i 1.06810 + 0.0934469i 0.607625 0.794224i \(-0.292122\pi\)
0.460478 + 0.887671i \(0.347678\pi\)
\(854\) 0 0
\(855\) −11.2679 59.2828i −0.385355 2.02743i
\(856\) 0 0
\(857\) −19.4140 1.69851i −0.663171 0.0580199i −0.249399 0.968401i \(-0.580233\pi\)
−0.413772 + 0.910381i \(0.635789\pi\)
\(858\) 0 0
\(859\) −5.61823 0.990645i −0.191691 0.0338004i 0.0769781 0.997033i \(-0.475473\pi\)
−0.268670 + 0.963232i \(0.586584\pi\)
\(860\) 0 0
\(861\) 28.6127 10.4142i 0.975119 0.354914i
\(862\) 0 0
\(863\) −15.9626 4.27717i −0.543374 0.145597i −0.0233169 0.999728i \(-0.507423\pi\)
−0.520057 + 0.854131i \(0.674089\pi\)
\(864\) 0 0
\(865\) −31.6281 + 15.6006i −1.07539 + 0.530436i
\(866\) 0 0
\(867\) −49.7022 + 13.3177i −1.68797 + 0.452291i
\(868\) 0 0
\(869\) −2.59675 14.7269i −0.0880887 0.499576i
\(870\) 0 0
\(871\) −3.17366 1.15512i −0.107535 0.0391397i
\(872\) 0 0
\(873\) 2.18496 2.18496i 0.0739496 0.0739496i
\(874\) 0 0
\(875\) −5.14507 15.1443i −0.173935 0.511970i
\(876\) 0 0
\(877\) −23.2792 49.9224i −0.786082 1.68576i −0.726130 0.687557i \(-0.758683\pi\)
−0.0599519 0.998201i \(-0.519095\pi\)
\(878\) 0 0
\(879\) 1.05072 0.185271i 0.0354401 0.00624904i
\(880\) 0 0
\(881\) −5.41082 + 9.37181i −0.182295 + 0.315744i −0.942662 0.333750i \(-0.891686\pi\)
0.760367 + 0.649494i \(0.225019\pi\)
\(882\) 0 0
\(883\) −2.30914 26.3935i −0.0777086 0.888213i −0.930579 0.366091i \(-0.880696\pi\)
0.852870 0.522123i \(-0.174860\pi\)
\(884\) 0 0
\(885\) −73.8232 + 8.09127i −2.48154 + 0.271985i
\(886\) 0 0
\(887\) −13.6051 6.34415i −0.456814 0.213016i 0.180570 0.983562i \(-0.442206\pi\)
−0.637384 + 0.770546i \(0.719983\pi\)
\(888\) 0 0
\(889\) 1.24908 7.08390i 0.0418929 0.237587i
\(890\) 0 0
\(891\) 45.0106 37.7683i 1.50791 1.26529i
\(892\) 0 0
\(893\) −5.65266 12.3996i −0.189159 0.414937i
\(894\) 0 0
\(895\) −22.9074 + 41.7631i −0.765711 + 1.39599i
\(896\) 0 0
\(897\) −0.293479 0.419131i −0.00979896 0.0139944i
\(898\) 0 0
\(899\) 3.78315 + 10.3941i 0.126175 + 0.346663i
\(900\) 0 0
\(901\) −1.64418 + 0.949269i −0.0547757 + 0.0316247i
\(902\) 0 0
\(903\) 49.8071 4.35756i 1.65748 0.145010i
\(904\) 0 0
\(905\) 19.4575 + 2.99311i 0.646789 + 0.0994943i
\(906\) 0 0
\(907\) 0.341941 0.488342i 0.0113540 0.0162151i −0.813435 0.581656i \(-0.802405\pi\)
0.824789 + 0.565441i \(0.191294\pi\)
\(908\) 0 0
\(909\) 2.38198 6.54444i 0.0790053 0.217065i
\(910\) 0 0
\(911\) 8.85098i 0.293246i 0.989192 + 0.146623i \(0.0468404\pi\)
−0.989192 + 0.146623i \(0.953160\pi\)
\(912\) 0 0
\(913\) −44.4618 44.4618i −1.47147 1.47147i
\(914\) 0 0
\(915\) 55.9172 58.4218i 1.84857 1.93137i
\(916\) 0 0
\(917\) 13.4431 + 9.41293i 0.443929 + 0.310842i
\(918\) 0 0
\(919\) −19.2508 11.1144i −0.635025 0.366632i 0.147671 0.989037i \(-0.452822\pi\)
−0.782695 + 0.622405i \(0.786156\pi\)
\(920\) 0 0
\(921\) 8.40853 + 7.05560i 0.277071 + 0.232490i
\(922\) 0 0
\(923\) 0.0325960 0.121650i 0.00107291 0.00400415i
\(924\) 0 0
\(925\) −45.6761 + 14.4101i −1.50182 + 0.473801i
\(926\) 0 0
\(927\) 78.2735 54.8077i 2.57084 1.80012i
\(928\) 0 0
\(929\) 19.0299 + 22.6790i 0.624352 + 0.744074i 0.981812 0.189855i \(-0.0608017\pi\)
−0.357460 + 0.933928i \(0.616357\pi\)
\(930\) 0 0
\(931\) 16.4200 + 14.0206i 0.538145 + 0.459505i
\(932\) 0 0
\(933\) −6.50408 + 74.3420i −0.212934 + 2.43385i
\(934\) 0 0
\(935\) 1.68413 + 1.12509i 0.0550768 + 0.0367944i
\(936\) 0 0
\(937\) 7.65894 16.4246i 0.250207 0.536570i −0.740585 0.671962i \(-0.765452\pi\)
0.990792 + 0.135392i \(0.0432295\pi\)
\(938\) 0 0
\(939\) 24.7088 + 42.7969i 0.806341 + 1.39662i
\(940\) 0 0
\(941\) 15.3669 18.3136i 0.500948 0.597006i −0.455019 0.890482i \(-0.650367\pi\)
0.955967 + 0.293475i \(0.0948119\pi\)
\(942\) 0 0
\(943\) −0.805576 3.00645i −0.0262332 0.0979035i
\(944\) 0 0
\(945\) −16.0573 26.4566i −0.522344 0.860633i
\(946\) 0 0
\(947\) −43.5035 + 20.2860i −1.41367 + 0.659207i −0.971351 0.237649i \(-0.923623\pi\)
−0.442323 + 0.896856i \(0.645845\pi\)
\(948\) 0 0
\(949\) 0.869123 0.0282129
\(950\) 0 0
\(951\) 56.1647 1.82127
\(952\) 0 0
\(953\) −18.6957 + 8.71794i −0.605612 + 0.282402i −0.701138 0.713025i \(-0.747324\pi\)
0.0955259 + 0.995427i \(0.469547\pi\)
\(954\) 0 0
\(955\) −13.7630 22.6764i −0.445361 0.733793i
\(956\) 0 0
\(957\) −6.14631 22.9383i −0.198682 0.741491i
\(958\) 0 0
\(959\) 1.17456 1.39979i 0.0379285 0.0452015i
\(960\) 0 0
\(961\) 14.2464 + 24.6755i 0.459561 + 0.795983i
\(962\) 0 0
\(963\) −21.5457 + 46.2050i −0.694301 + 1.48893i
\(964\) 0 0
\(965\) 6.12036 + 4.08875i 0.197021 + 0.131621i
\(966\) 0 0
\(967\) 3.10021 35.4356i 0.0996961 1.13953i −0.767325 0.641259i \(-0.778412\pi\)
0.867021 0.498272i \(-0.166032\pi\)
\(968\) 0 0
\(969\) 1.69075 1.39410i 0.0543149 0.0447849i
\(970\) 0 0
\(971\) −11.8621 14.1367i −0.380674 0.453670i 0.541353 0.840796i \(-0.317912\pi\)
−0.922027 + 0.387126i \(0.873468\pi\)
\(972\) 0 0
\(973\) −6.18946 + 4.33391i −0.198425 + 0.138939i
\(974\) 0 0
\(975\) 5.11902 + 2.66369i 0.163940 + 0.0853065i
\(976\) 0 0
\(977\) 4.55193 16.9880i 0.145629 0.543495i −0.854097 0.520113i \(-0.825890\pi\)
0.999727 0.0233823i \(-0.00744348\pi\)
\(978\) 0 0
\(979\) −22.3646 18.7661i −0.714776 0.599768i
\(980\) 0 0
\(981\) 47.6764 + 27.5260i 1.52219 + 0.878837i
\(982\) 0 0
\(983\) −27.7628 19.4397i −0.885494 0.620030i 0.0398299 0.999206i \(-0.487318\pi\)
−0.925324 + 0.379177i \(0.876207\pi\)
\(984\) 0 0
\(985\) 30.1810 31.5328i 0.961647 1.00472i
\(986\) 0 0
\(987\) −9.58772 9.58772i −0.305181 0.305181i
\(988\) 0 0
\(989\) 5.11074i 0.162512i
\(990\) 0 0
\(991\) −1.98331 + 5.44910i −0.0630019 + 0.173096i −0.967199 0.254018i \(-0.918248\pi\)
0.904198 + 0.427115i \(0.140470\pi\)
\(992\) 0 0
\(993\) 23.8689 34.0883i 0.757457 1.08176i
\(994\) 0 0
\(995\) 25.1951 + 3.87572i 0.798739 + 0.122869i
\(996\) 0 0
\(997\) −29.9828 + 2.62315i −0.949565 + 0.0830761i −0.551403 0.834239i \(-0.685907\pi\)
−0.398162 + 0.917315i \(0.630352\pi\)
\(998\) 0 0
\(999\) −80.2583 + 46.3372i −2.53926 + 1.46604i
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 380.2.bh.a.13.1 120
5.2 odd 4 inner 380.2.bh.a.317.10 yes 120
19.3 odd 18 inner 380.2.bh.a.193.10 yes 120
95.22 even 36 inner 380.2.bh.a.117.1 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.bh.a.13.1 120 1.1 even 1 trivial
380.2.bh.a.117.1 yes 120 95.22 even 36 inner
380.2.bh.a.193.10 yes 120 19.3 odd 18 inner
380.2.bh.a.317.10 yes 120 5.2 odd 4 inner