Properties

Label 380.2.bh.a.33.1
Level $380$
Weight $2$
Character 380.33
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 33.1
Character \(\chi\) \(=\) 380.33
Dual form 380.2.bh.a.357.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +O(q^{10})\) \(q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +(1.71018 - 2.96212i) q^{11} +(1.74848 + 1.22430i) q^{13} +(-5.54820 - 2.94613i) q^{15} +(-2.63830 + 5.65786i) q^{17} +(1.56004 - 4.07017i) q^{19} +(-4.88905 - 13.4325i) q^{21} +(-2.25262 - 0.197079i) q^{23} +(2.93449 - 4.04831i) q^{25} +(5.13536 - 1.37602i) q^{27} +(-5.51312 - 2.00661i) q^{29} +(-0.923557 + 0.533216i) q^{31} +(-9.57244 + 0.837480i) q^{33} +(11.1277 - 2.37165i) q^{35} +(-2.20652 - 2.20652i) q^{37} -5.99656i q^{39} +(-2.29610 - 0.404865i) q^{41} +(-0.102775 - 1.17473i) q^{43} +(1.33919 + 10.8575i) q^{45} +(-2.83672 + 1.32278i) q^{47} +(16.3593 + 9.44505i) q^{49} +(17.2716 - 3.04546i) q^{51} +(-1.09089 + 12.4689i) q^{53} +(0.396085 - 7.63791i) q^{55} +(-11.8804 + 2.96849i) q^{57} +(1.32531 - 0.482374i) q^{59} +(-8.84468 + 7.42157i) q^{61} +(-14.2785 + 20.3919i) q^{63} +(4.72681 + 0.661666i) q^{65} +(2.33207 + 5.00114i) q^{67} +(3.17628 + 5.50149i) q^{69} +(-2.27536 + 2.71167i) q^{71} +(-1.61028 + 1.12753i) q^{73} +(-14.0449 - 0.229741i) q^{75} +(12.3062 - 12.3062i) q^{77} +(1.00143 - 5.67937i) q^{79} +(-0.198129 - 0.166250i) q^{81} +(0.0567325 - 0.211729i) q^{83} +(0.494822 + 13.9505i) q^{85} +(4.26593 + 15.9207i) q^{87} +(-2.79291 - 15.8394i) q^{89} +(6.98122 + 8.31989i) q^{91} +(2.71528 + 1.26616i) q^{93} +(-1.02903 - 9.69232i) q^{95} +(12.8386 + 5.98673i) q^{97} +(10.7564 + 12.8189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 6 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −1.61138 2.30128i −0.930328 1.32865i −0.944418 0.328746i \(-0.893374\pi\)
0.0140900 0.999901i \(-0.495515\pi\)
\(4\) 0 0
\(5\) 1.99179 1.01625i 0.890757 0.454479i
\(6\) 0 0
\(7\) 4.91485 + 1.31693i 1.85764 + 0.497753i 0.999868 0.0162764i \(-0.00518117\pi\)
0.857772 + 0.514030i \(0.171848\pi\)
\(8\) 0 0
\(9\) −1.67331 + 4.59739i −0.557771 + 1.53246i
\(10\) 0 0
\(11\) 1.71018 2.96212i 0.515640 0.893114i −0.484195 0.874960i \(-0.660888\pi\)
0.999835 0.0181543i \(-0.00577902\pi\)
\(12\) 0 0
\(13\) 1.74848 + 1.22430i 0.484942 + 0.339560i 0.790344 0.612664i \(-0.209902\pi\)
−0.305402 + 0.952224i \(0.598791\pi\)
\(14\) 0 0
\(15\) −5.54820 2.94613i −1.43254 0.760687i
\(16\) 0 0
\(17\) −2.63830 + 5.65786i −0.639882 + 1.37223i 0.272206 + 0.962239i \(0.412247\pi\)
−0.912089 + 0.409993i \(0.865531\pi\)
\(18\) 0 0
\(19\) 1.56004 4.07017i 0.357897 0.933761i
\(20\) 0 0
\(21\) −4.88905 13.4325i −1.06688 2.93122i
\(22\) 0 0
\(23\) −2.25262 0.197079i −0.469704 0.0410938i −0.150153 0.988663i \(-0.547977\pi\)
−0.319551 + 0.947569i \(0.603532\pi\)
\(24\) 0 0
\(25\) 2.93449 4.04831i 0.586897 0.809661i
\(26\) 0 0
\(27\) 5.13536 1.37602i 0.988301 0.264814i
\(28\) 0 0
\(29\) −5.51312 2.00661i −1.02376 0.372618i −0.225059 0.974345i \(-0.572257\pi\)
−0.798702 + 0.601727i \(0.794480\pi\)
\(30\) 0 0
\(31\) −0.923557 + 0.533216i −0.165876 + 0.0957684i −0.580640 0.814161i \(-0.697197\pi\)
0.414764 + 0.909929i \(0.363864\pi\)
\(32\) 0 0
\(33\) −9.57244 + 0.837480i −1.66635 + 0.145787i
\(34\) 0 0
\(35\) 11.1277 2.37165i 1.88092 0.400881i
\(36\) 0 0
\(37\) −2.20652 2.20652i −0.362749 0.362749i 0.502075 0.864824i \(-0.332570\pi\)
−0.864824 + 0.502075i \(0.832570\pi\)
\(38\) 0 0
\(39\) 5.99656i 0.960219i
\(40\) 0 0
\(41\) −2.29610 0.404865i −0.358591 0.0632293i −0.00854966 0.999963i \(-0.502721\pi\)
−0.350042 + 0.936734i \(0.613833\pi\)
\(42\) 0 0
\(43\) −0.102775 1.17473i −0.0156731 0.179144i −0.999996 0.00276953i \(-0.999118\pi\)
0.984323 0.176375i \(-0.0564371\pi\)
\(44\) 0 0
\(45\) 1.33919 + 10.8575i 0.199634 + 1.61855i
\(46\) 0 0
\(47\) −2.83672 + 1.32278i −0.413778 + 0.192948i −0.618349 0.785904i \(-0.712198\pi\)
0.204570 + 0.978852i \(0.434420\pi\)
\(48\) 0 0
\(49\) 16.3593 + 9.44505i 2.33704 + 1.34929i
\(50\) 0 0
\(51\) 17.2716 3.04546i 2.41851 0.426449i
\(52\) 0 0
\(53\) −1.09089 + 12.4689i −0.149845 + 1.71274i 0.434030 + 0.900898i \(0.357091\pi\)
−0.583876 + 0.811843i \(0.698465\pi\)
\(54\) 0 0
\(55\) 0.396085 7.63791i 0.0534081 1.02990i
\(56\) 0 0
\(57\) −11.8804 + 2.96849i −1.57360 + 0.393186i
\(58\) 0 0
\(59\) 1.32531 0.482374i 0.172541 0.0627998i −0.254305 0.967124i \(-0.581847\pi\)
0.426846 + 0.904324i \(0.359625\pi\)
\(60\) 0 0
\(61\) −8.84468 + 7.42157i −1.13244 + 0.950234i −0.999166 0.0408444i \(-0.986995\pi\)
−0.133279 + 0.991079i \(0.542551\pi\)
\(62\) 0 0
\(63\) −14.2785 + 20.3919i −1.79893 + 2.56913i
\(64\) 0 0
\(65\) 4.72681 + 0.661666i 0.586289 + 0.0820696i
\(66\) 0 0
\(67\) 2.33207 + 5.00114i 0.284907 + 0.610986i 0.995723 0.0923928i \(-0.0294516\pi\)
−0.710815 + 0.703379i \(0.751674\pi\)
\(68\) 0 0
\(69\) 3.17628 + 5.50149i 0.382380 + 0.662301i
\(70\) 0 0
\(71\) −2.27536 + 2.71167i −0.270036 + 0.321816i −0.883972 0.467539i \(-0.845141\pi\)
0.613937 + 0.789355i \(0.289585\pi\)
\(72\) 0 0
\(73\) −1.61028 + 1.12753i −0.188468 + 0.131967i −0.664003 0.747730i \(-0.731144\pi\)
0.475534 + 0.879697i \(0.342255\pi\)
\(74\) 0 0
\(75\) −14.0449 0.229741i −1.62176 0.0265282i
\(76\) 0 0
\(77\) 12.3062 12.3062i 1.40242 1.40242i
\(78\) 0 0
\(79\) 1.00143 5.67937i 0.112669 0.638979i −0.875209 0.483746i \(-0.839276\pi\)
0.987878 0.155233i \(-0.0496129\pi\)
\(80\) 0 0
\(81\) −0.198129 0.166250i −0.0220144 0.0184722i
\(82\) 0 0
\(83\) 0.0567325 0.211729i 0.00622720 0.0232402i −0.962742 0.270420i \(-0.912837\pi\)
0.968970 + 0.247180i \(0.0795040\pi\)
\(84\) 0 0
\(85\) 0.494822 + 13.9505i 0.0536710 + 1.51314i
\(86\) 0 0
\(87\) 4.26593 + 15.9207i 0.457355 + 1.70687i
\(88\) 0 0
\(89\) −2.79291 15.8394i −0.296048 1.67897i −0.662912 0.748697i \(-0.730680\pi\)
0.366864 0.930275i \(-0.380432\pi\)
\(90\) 0 0
\(91\) 6.98122 + 8.31989i 0.731831 + 0.872162i
\(92\) 0 0
\(93\) 2.71528 + 1.26616i 0.281561 + 0.131294i
\(94\) 0 0
\(95\) −1.02903 9.69232i −0.105576 0.994411i
\(96\) 0 0
\(97\) 12.8386 + 5.98673i 1.30356 + 0.607860i 0.945434 0.325813i \(-0.105638\pi\)
0.358126 + 0.933673i \(0.383416\pi\)
\(98\) 0 0
\(99\) 10.7564 + 12.8189i 1.08106 + 1.28835i
\(100\) 0 0
\(101\) −2.10879 11.9595i −0.209832 1.19002i −0.889652 0.456639i \(-0.849053\pi\)
0.679820 0.733379i \(-0.262058\pi\)
\(102\) 0 0
\(103\) −4.25223 15.8695i −0.418984 1.56367i −0.776719 0.629848i \(-0.783117\pi\)
0.357734 0.933823i \(-0.383549\pi\)
\(104\) 0 0
\(105\) −23.3887 21.7864i −2.28251 2.12613i
\(106\) 0 0
\(107\) 1.05878 3.95143i 0.102356 0.381999i −0.895676 0.444708i \(-0.853307\pi\)
0.998032 + 0.0627092i \(0.0199741\pi\)
\(108\) 0 0
\(109\) 1.02714 + 0.861870i 0.0983818 + 0.0825522i 0.690652 0.723187i \(-0.257324\pi\)
−0.592270 + 0.805740i \(0.701768\pi\)
\(110\) 0 0
\(111\) −1.52229 + 8.63335i −0.144490 + 0.819441i
\(112\) 0 0
\(113\) 1.49986 1.49986i 0.141095 0.141095i −0.633031 0.774126i \(-0.718190\pi\)
0.774126 + 0.633031i \(0.218190\pi\)
\(114\) 0 0
\(115\) −4.68704 + 1.89668i −0.437068 + 0.176866i
\(116\) 0 0
\(117\) −8.55435 + 5.98982i −0.790850 + 0.553759i
\(118\) 0 0
\(119\) −20.4179 + 24.3331i −1.87170 + 2.23061i
\(120\) 0 0
\(121\) −0.349455 0.605274i −0.0317686 0.0550249i
\(122\) 0 0
\(123\) 2.76818 + 5.93638i 0.249598 + 0.535265i
\(124\) 0 0
\(125\) 1.73082 11.0456i 0.154809 0.987944i
\(126\) 0 0
\(127\) −8.69236 + 12.4140i −0.771322 + 1.10156i 0.220681 + 0.975346i \(0.429172\pi\)
−0.992003 + 0.126216i \(0.959717\pi\)
\(128\) 0 0
\(129\) −2.53777 + 2.12945i −0.223439 + 0.187487i
\(130\) 0 0
\(131\) −0.988864 + 0.359917i −0.0863974 + 0.0314461i −0.384857 0.922976i \(-0.625749\pi\)
0.298460 + 0.954422i \(0.403527\pi\)
\(132\) 0 0
\(133\) 13.0275 17.9498i 1.12963 1.55645i
\(134\) 0 0
\(135\) 8.83021 7.95954i 0.759984 0.685048i
\(136\) 0 0
\(137\) −1.29449 + 14.7961i −0.110596 + 1.26412i 0.714705 + 0.699426i \(0.246561\pi\)
−0.825301 + 0.564692i \(0.808995\pi\)
\(138\) 0 0
\(139\) −5.53858 + 0.976601i −0.469776 + 0.0828342i −0.403525 0.914969i \(-0.632215\pi\)
−0.0662515 + 0.997803i \(0.521104\pi\)
\(140\) 0 0
\(141\) 7.61513 + 4.39660i 0.641309 + 0.370260i
\(142\) 0 0
\(143\) 6.61676 3.08545i 0.553321 0.258018i
\(144\) 0 0
\(145\) −13.0202 + 1.60593i −1.08127 + 0.133365i
\(146\) 0 0
\(147\) −4.62526 52.8669i −0.381485 4.36039i
\(148\) 0 0
\(149\) 14.2507 + 2.51279i 1.16746 + 0.205856i 0.723588 0.690232i \(-0.242492\pi\)
0.443877 + 0.896088i \(0.353603\pi\)
\(150\) 0 0
\(151\) 10.6963i 0.870457i 0.900320 + 0.435228i \(0.143332\pi\)
−0.900320 + 0.435228i \(0.856668\pi\)
\(152\) 0 0
\(153\) −21.5967 21.5967i −1.74599 1.74599i
\(154\) 0 0
\(155\) −1.29766 + 2.00062i −0.104230 + 0.160694i
\(156\) 0 0
\(157\) 11.8321 1.03517i 0.944303 0.0826159i 0.395407 0.918506i \(-0.370604\pi\)
0.548897 + 0.835890i \(0.315048\pi\)
\(158\) 0 0
\(159\) 30.4524 17.5817i 2.41503 1.39432i
\(160\) 0 0
\(161\) −10.8118 3.93516i −0.852086 0.310134i
\(162\) 0 0
\(163\) −3.09224 + 0.828563i −0.242203 + 0.0648981i −0.377878 0.925855i \(-0.623346\pi\)
0.135675 + 0.990753i \(0.456680\pi\)
\(164\) 0 0
\(165\) −18.2152 + 11.3960i −1.41805 + 0.887181i
\(166\) 0 0
\(167\) −1.39419 0.121976i −0.107886 0.00943880i 0.0330849 0.999453i \(-0.489467\pi\)
−0.140971 + 0.990014i \(0.545022\pi\)
\(168\) 0 0
\(169\) −2.88798 7.93466i −0.222152 0.610359i
\(170\) 0 0
\(171\) 16.1017 + 13.9828i 1.23133 + 1.06929i
\(172\) 0 0
\(173\) −8.28676 + 17.7710i −0.630031 + 1.35111i 0.289155 + 0.957282i \(0.406626\pi\)
−0.919186 + 0.393823i \(0.871152\pi\)
\(174\) 0 0
\(175\) 19.7539 16.0323i 1.49326 1.21193i
\(176\) 0 0
\(177\) −3.24566 2.27263i −0.243959 0.170822i
\(178\) 0 0
\(179\) −5.18896 + 8.98755i −0.387841 + 0.671761i −0.992159 0.124983i \(-0.960112\pi\)
0.604318 + 0.796743i \(0.293446\pi\)
\(180\) 0 0
\(181\) 0.294087 0.807997i 0.0218593 0.0600579i −0.928283 0.371874i \(-0.878715\pi\)
0.950142 + 0.311816i \(0.100937\pi\)
\(182\) 0 0
\(183\) 31.3312 + 8.39518i 2.31607 + 0.620589i
\(184\) 0 0
\(185\) −6.63729 2.15256i −0.487983 0.158260i
\(186\) 0 0
\(187\) 12.2473 + 17.4910i 0.895611 + 1.27907i
\(188\) 0 0
\(189\) 27.0517 1.96772
\(190\) 0 0
\(191\) −12.3532 −0.893844 −0.446922 0.894573i \(-0.647480\pi\)
−0.446922 + 0.894573i \(0.647480\pi\)
\(192\) 0 0
\(193\) 14.4146 + 20.5862i 1.03759 + 1.48183i 0.868159 + 0.496287i \(0.165304\pi\)
0.169429 + 0.985542i \(0.445808\pi\)
\(194\) 0 0
\(195\) −6.09399 11.9439i −0.436399 0.855322i
\(196\) 0 0
\(197\) 2.73612 + 0.733141i 0.194940 + 0.0522341i 0.354968 0.934878i \(-0.384492\pi\)
−0.160028 + 0.987113i \(0.551158\pi\)
\(198\) 0 0
\(199\) −3.69566 + 10.1538i −0.261979 + 0.719781i 0.737055 + 0.675833i \(0.236216\pi\)
−0.999034 + 0.0439479i \(0.986006\pi\)
\(200\) 0 0
\(201\) 7.75119 13.4255i 0.546727 0.946959i
\(202\) 0 0
\(203\) −24.4536 17.1226i −1.71631 1.20177i
\(204\) 0 0
\(205\) −4.98481 + 1.52700i −0.348154 + 0.106650i
\(206\) 0 0
\(207\) 4.67539 10.0264i 0.324962 0.696883i
\(208\) 0 0
\(209\) −9.38841 11.5818i −0.649410 0.801127i
\(210\) 0 0
\(211\) 3.91671 + 10.7611i 0.269637 + 0.740822i 0.998426 + 0.0560837i \(0.0178614\pi\)
−0.728789 + 0.684739i \(0.759916\pi\)
\(212\) 0 0
\(213\) 9.90678 + 0.866731i 0.678801 + 0.0593874i
\(214\) 0 0
\(215\) −1.39852 2.23537i −0.0953784 0.152451i
\(216\) 0 0
\(217\) −5.24136 + 1.40442i −0.355807 + 0.0953381i
\(218\) 0 0
\(219\) 5.18952 + 1.88883i 0.350675 + 0.127635i
\(220\) 0 0
\(221\) −11.5399 + 6.66259i −0.776261 + 0.448174i
\(222\) 0 0
\(223\) 7.31669 0.640127i 0.489962 0.0428661i 0.160502 0.987036i \(-0.448689\pi\)
0.329460 + 0.944170i \(0.393133\pi\)
\(224\) 0 0
\(225\) 13.7013 + 20.2651i 0.913422 + 1.35100i
\(226\) 0 0
\(227\) −17.3630 17.3630i −1.15243 1.15243i −0.986065 0.166361i \(-0.946798\pi\)
−0.166361 0.986065i \(-0.553202\pi\)
\(228\) 0 0
\(229\) 23.0335i 1.52210i −0.648695 0.761049i \(-0.724685\pi\)
0.648695 0.761049i \(-0.275315\pi\)
\(230\) 0 0
\(231\) −48.1500 8.49015i −3.16804 0.558611i
\(232\) 0 0
\(233\) −0.808518 9.24140i −0.0529678 0.605424i −0.975573 0.219678i \(-0.929499\pi\)
0.922605 0.385747i \(-0.126056\pi\)
\(234\) 0 0
\(235\) −4.30589 + 5.51752i −0.280885 + 0.359923i
\(236\) 0 0
\(237\) −14.6835 + 6.84703i −0.953796 + 0.444763i
\(238\) 0 0
\(239\) 1.41871 + 0.819094i 0.0917689 + 0.0529828i 0.545182 0.838318i \(-0.316460\pi\)
−0.453413 + 0.891300i \(0.649794\pi\)
\(240\) 0 0
\(241\) 19.4770 3.43432i 1.25462 0.221224i 0.493450 0.869774i \(-0.335736\pi\)
0.761172 + 0.648550i \(0.224624\pi\)
\(242\) 0 0
\(243\) 1.32677 15.1650i 0.0851122 0.972837i
\(244\) 0 0
\(245\) 42.1828 + 2.18751i 2.69496 + 0.139755i
\(246\) 0 0
\(247\) 7.71081 5.20667i 0.490627 0.331293i
\(248\) 0 0
\(249\) −0.578665 + 0.210617i −0.0366714 + 0.0133473i
\(250\) 0 0
\(251\) 7.88691 6.61790i 0.497817 0.417718i −0.359001 0.933337i \(-0.616882\pi\)
0.856818 + 0.515619i \(0.172438\pi\)
\(252\) 0 0
\(253\) −4.43617 + 6.33550i −0.278899 + 0.398310i
\(254\) 0 0
\(255\) 31.3066 23.6182i 1.96050 1.47903i
\(256\) 0 0
\(257\) −2.50140 5.36428i −0.156033 0.334615i 0.812715 0.582662i \(-0.197989\pi\)
−0.968748 + 0.248047i \(0.920211\pi\)
\(258\) 0 0
\(259\) −7.93888 13.7505i −0.493298 0.854417i
\(260\) 0 0
\(261\) 18.4503 21.9883i 1.14205 1.36104i
\(262\) 0 0
\(263\) −4.51813 + 3.16363i −0.278600 + 0.195078i −0.704522 0.709682i \(-0.748839\pi\)
0.425922 + 0.904760i \(0.359950\pi\)
\(264\) 0 0
\(265\) 10.4987 + 25.9442i 0.644929 + 1.59374i
\(266\) 0 0
\(267\) −31.9505 + 31.9505i −1.95534 + 1.95534i
\(268\) 0 0
\(269\) −2.13669 + 12.1178i −0.130276 + 0.738832i 0.847757 + 0.530384i \(0.177952\pi\)
−0.978033 + 0.208448i \(0.933159\pi\)
\(270\) 0 0
\(271\) −5.15712 4.32734i −0.313273 0.262867i 0.472570 0.881293i \(-0.343326\pi\)
−0.785843 + 0.618426i \(0.787771\pi\)
\(272\) 0 0
\(273\) 7.89706 29.4722i 0.477952 1.78374i
\(274\) 0 0
\(275\) −6.97308 15.6157i −0.420492 0.941660i
\(276\) 0 0
\(277\) 6.11754 + 22.8310i 0.367567 + 1.37178i 0.863907 + 0.503652i \(0.168011\pi\)
−0.496339 + 0.868129i \(0.665323\pi\)
\(278\) 0 0
\(279\) −0.906001 5.13819i −0.0542409 0.307615i
\(280\) 0 0
\(281\) −0.197508 0.235381i −0.0117824 0.0140417i 0.760121 0.649781i \(-0.225140\pi\)
−0.771903 + 0.635740i \(0.780695\pi\)
\(282\) 0 0
\(283\) −18.6762 8.70885i −1.11018 0.517687i −0.221017 0.975270i \(-0.570938\pi\)
−0.889167 + 0.457583i \(0.848715\pi\)
\(284\) 0 0
\(285\) −20.6466 + 17.9861i −1.22300 + 1.06540i
\(286\) 0 0
\(287\) −10.7518 5.01367i −0.634661 0.295947i
\(288\) 0 0
\(289\) −14.1233 16.8315i −0.830784 0.990090i
\(290\) 0 0
\(291\) −6.91062 39.1921i −0.405108 2.29748i
\(292\) 0 0
\(293\) 1.62270 + 6.05601i 0.0947993 + 0.353796i 0.996989 0.0775438i \(-0.0247078\pi\)
−0.902190 + 0.431340i \(0.858041\pi\)
\(294\) 0 0
\(295\) 2.14954 2.30763i 0.125151 0.134356i
\(296\) 0 0
\(297\) 4.70648 17.5648i 0.273098 1.01921i
\(298\) 0 0
\(299\) −3.69739 3.10247i −0.213825 0.179421i
\(300\) 0 0
\(301\) 1.04191 5.90897i 0.0600547 0.340587i
\(302\) 0 0
\(303\) −24.1242 + 24.1242i −1.38590 + 1.38590i
\(304\) 0 0
\(305\) −10.0746 + 23.7706i −0.576872 + 1.36110i
\(306\) 0 0
\(307\) −19.6087 + 13.7302i −1.11913 + 0.783621i −0.978460 0.206436i \(-0.933814\pi\)
−0.140667 + 0.990057i \(0.544925\pi\)
\(308\) 0 0
\(309\) −29.6683 + 35.3574i −1.68777 + 2.01141i
\(310\) 0 0
\(311\) 1.54478 + 2.67563i 0.0875963 + 0.151721i 0.906495 0.422217i \(-0.138748\pi\)
−0.818898 + 0.573939i \(0.805415\pi\)
\(312\) 0 0
\(313\) 1.10064 + 2.36034i 0.0622121 + 0.133414i 0.934956 0.354765i \(-0.115439\pi\)
−0.872744 + 0.488179i \(0.837661\pi\)
\(314\) 0 0
\(315\) −7.71674 + 55.1269i −0.434789 + 3.10605i
\(316\) 0 0
\(317\) 16.8842 24.1131i 0.948310 1.35433i 0.0132217 0.999913i \(-0.495791\pi\)
0.935088 0.354415i \(-0.115320\pi\)
\(318\) 0 0
\(319\) −15.3723 + 12.8989i −0.860682 + 0.722198i
\(320\) 0 0
\(321\) −10.7995 + 3.93068i −0.602767 + 0.219389i
\(322\) 0 0
\(323\) 18.9126 + 19.5648i 1.05233 + 1.08861i
\(324\) 0 0
\(325\) 10.0872 3.48570i 0.559540 0.193352i
\(326\) 0 0
\(327\) 0.328304 3.75253i 0.0181552 0.207515i
\(328\) 0 0
\(329\) −15.6841 + 2.76553i −0.864692 + 0.152468i
\(330\) 0 0
\(331\) 12.6138 + 7.28259i 0.693318 + 0.400288i 0.804854 0.593473i \(-0.202244\pi\)
−0.111536 + 0.993760i \(0.535577\pi\)
\(332\) 0 0
\(333\) 13.8364 6.45202i 0.758231 0.353569i
\(334\) 0 0
\(335\) 9.72739 + 7.59128i 0.531464 + 0.414756i
\(336\) 0 0
\(337\) −0.211469 2.41711i −0.0115195 0.131668i 0.988257 0.152799i \(-0.0488288\pi\)
−0.999777 + 0.0211311i \(0.993273\pi\)
\(338\) 0 0
\(339\) −5.86844 1.03476i −0.318730 0.0562007i
\(340\) 0 0
\(341\) 3.64759i 0.197528i
\(342\) 0 0
\(343\) 42.7796 + 42.7796i 2.30988 + 2.30988i
\(344\) 0 0
\(345\) 11.9174 + 7.72994i 0.641610 + 0.416166i
\(346\) 0 0
\(347\) 20.0577 1.75482i 1.07675 0.0942037i 0.465045 0.885287i \(-0.346038\pi\)
0.611708 + 0.791083i \(0.290483\pi\)
\(348\) 0 0
\(349\) −12.2272 + 7.05939i −0.654509 + 0.377881i −0.790181 0.612873i \(-0.790014\pi\)
0.135673 + 0.990754i \(0.456680\pi\)
\(350\) 0 0
\(351\) 10.6638 + 3.88129i 0.569189 + 0.207168i
\(352\) 0 0
\(353\) −16.1175 + 4.31866i −0.857846 + 0.229859i −0.660825 0.750540i \(-0.729793\pi\)
−0.197021 + 0.980399i \(0.563127\pi\)
\(354\) 0 0
\(355\) −1.77633 + 7.71341i −0.0942776 + 0.409385i
\(356\) 0 0
\(357\) 88.8982 + 7.77758i 4.70499 + 0.411633i
\(358\) 0 0
\(359\) −7.37703 20.2682i −0.389345 1.06972i −0.967297 0.253645i \(-0.918370\pi\)
0.577953 0.816070i \(-0.303852\pi\)
\(360\) 0 0
\(361\) −14.1326 12.6992i −0.743820 0.668380i
\(362\) 0 0
\(363\) −0.829803 + 1.77952i −0.0435534 + 0.0934005i
\(364\) 0 0
\(365\) −2.06149 + 3.88224i −0.107903 + 0.203206i
\(366\) 0 0
\(367\) 6.66787 + 4.66890i 0.348060 + 0.243714i 0.734513 0.678595i \(-0.237411\pi\)
−0.386453 + 0.922309i \(0.626300\pi\)
\(368\) 0 0
\(369\) 5.70342 9.87862i 0.296908 0.514260i
\(370\) 0 0
\(371\) −21.7823 + 59.8464i −1.13088 + 3.10707i
\(372\) 0 0
\(373\) −23.0493 6.17604i −1.19345 0.319783i −0.393200 0.919453i \(-0.628632\pi\)
−0.800248 + 0.599670i \(0.795299\pi\)
\(374\) 0 0
\(375\) −28.2079 + 13.8154i −1.45665 + 0.713426i
\(376\) 0 0
\(377\) −7.18290 10.2582i −0.369938 0.528326i
\(378\) 0 0
\(379\) 36.8691 1.89384 0.946918 0.321474i \(-0.104178\pi\)
0.946918 + 0.321474i \(0.104178\pi\)
\(380\) 0 0
\(381\) 42.5747 2.18117
\(382\) 0 0
\(383\) 3.36428 + 4.80470i 0.171907 + 0.245508i 0.895856 0.444345i \(-0.146564\pi\)
−0.723949 + 0.689854i \(0.757675\pi\)
\(384\) 0 0
\(385\) 12.0053 37.0176i 0.611847 1.88659i
\(386\) 0 0
\(387\) 5.57266 + 1.49319i 0.283274 + 0.0759031i
\(388\) 0 0
\(389\) 2.40116 6.59712i 0.121743 0.334487i −0.863818 0.503803i \(-0.831934\pi\)
0.985562 + 0.169316i \(0.0541558\pi\)
\(390\) 0 0
\(391\) 7.05814 12.2251i 0.356945 0.618248i
\(392\) 0 0
\(393\) 2.42170 + 1.69569i 0.122159 + 0.0855364i
\(394\) 0 0
\(395\) −3.77700 12.3298i −0.190042 0.620381i
\(396\) 0 0
\(397\) 7.81017 16.7490i 0.391981 0.840607i −0.606966 0.794728i \(-0.707613\pi\)
0.998947 0.0458786i \(-0.0146087\pi\)
\(398\) 0 0
\(399\) −62.2998 1.05600i −3.11889 0.0528660i
\(400\) 0 0
\(401\) 12.5239 + 34.4092i 0.625414 + 1.71831i 0.693329 + 0.720621i \(0.256143\pi\)
−0.0679151 + 0.997691i \(0.521635\pi\)
\(402\) 0 0
\(403\) −2.26764 0.198393i −0.112959 0.00988265i
\(404\) 0 0
\(405\) −0.563584 0.129788i −0.0280047 0.00644921i
\(406\) 0 0
\(407\) −10.3095 + 2.76243i −0.511024 + 0.136929i
\(408\) 0 0
\(409\) −30.6038 11.1389i −1.51326 0.550783i −0.553808 0.832645i \(-0.686826\pi\)
−0.959455 + 0.281862i \(0.909048\pi\)
\(410\) 0 0
\(411\) 36.1360 20.8631i 1.78246 1.02910i
\(412\) 0 0
\(413\) 7.14897 0.625454i 0.351778 0.0307766i
\(414\) 0 0
\(415\) −0.102169 0.479374i −0.00501528 0.0235315i
\(416\) 0 0
\(417\) 11.1722 + 11.1722i 0.547104 + 0.547104i
\(418\) 0 0
\(419\) 6.65117i 0.324931i −0.986714 0.162465i \(-0.948055\pi\)
0.986714 0.162465i \(-0.0519446\pi\)
\(420\) 0 0
\(421\) −10.5514 1.86049i −0.514243 0.0906749i −0.0894963 0.995987i \(-0.528526\pi\)
−0.424747 + 0.905312i \(0.639637\pi\)
\(422\) 0 0
\(423\) −1.33463 15.2549i −0.0648921 0.741721i
\(424\) 0 0
\(425\) 15.1627 + 27.2836i 0.735498 + 1.32345i
\(426\) 0 0
\(427\) −53.2440 + 24.8281i −2.57666 + 1.20151i
\(428\) 0 0
\(429\) −17.7626 10.2552i −0.857585 0.495127i
\(430\) 0 0
\(431\) 27.1926 4.79479i 1.30982 0.230957i 0.525225 0.850963i \(-0.323981\pi\)
0.784597 + 0.620006i \(0.212870\pi\)
\(432\) 0 0
\(433\) 2.80661 32.0797i 0.134877 1.54165i −0.563616 0.826037i \(-0.690590\pi\)
0.698493 0.715616i \(-0.253854\pi\)
\(434\) 0 0
\(435\) 24.6762 + 27.3754i 1.18313 + 1.31255i
\(436\) 0 0
\(437\) −4.31631 + 8.86110i −0.206477 + 0.423884i
\(438\) 0 0
\(439\) −16.0863 + 5.85492i −0.767756 + 0.279440i −0.696057 0.717986i \(-0.745064\pi\)
−0.0716983 + 0.997426i \(0.522842\pi\)
\(440\) 0 0
\(441\) −70.7968 + 59.4055i −3.37127 + 2.82884i
\(442\) 0 0
\(443\) 14.2838 20.3994i 0.678643 0.969203i −0.321111 0.947042i \(-0.604056\pi\)
0.999754 0.0221615i \(-0.00705480\pi\)
\(444\) 0 0
\(445\) −21.6596 28.7105i −1.02676 1.36101i
\(446\) 0 0
\(447\) −17.1806 36.8440i −0.812616 1.74266i
\(448\) 0 0
\(449\) 12.4835 + 21.6220i 0.589131 + 1.02041i 0.994347 + 0.106184i \(0.0338632\pi\)
−0.405215 + 0.914221i \(0.632803\pi\)
\(450\) 0 0
\(451\) −5.12602 + 6.10896i −0.241375 + 0.287659i
\(452\) 0 0
\(453\) 24.6153 17.2358i 1.15653 0.809810i
\(454\) 0 0
\(455\) 22.3602 + 9.47687i 1.04826 + 0.444283i
\(456\) 0 0
\(457\) −0.449839 + 0.449839i −0.0210426 + 0.0210426i −0.717550 0.696507i \(-0.754736\pi\)
0.696507 + 0.717550i \(0.254736\pi\)
\(458\) 0 0
\(459\) −5.76334 + 32.6855i −0.269010 + 1.52563i
\(460\) 0 0
\(461\) 12.3104 + 10.3297i 0.573353 + 0.481101i 0.882757 0.469830i \(-0.155685\pi\)
−0.309403 + 0.950931i \(0.600129\pi\)
\(462\) 0 0
\(463\) −5.79341 + 21.6213i −0.269243 + 1.00483i 0.690359 + 0.723467i \(0.257453\pi\)
−0.959602 + 0.281361i \(0.909214\pi\)
\(464\) 0 0
\(465\) 6.69500 0.237472i 0.310473 0.0110125i
\(466\) 0 0
\(467\) −7.20514 26.8899i −0.333414 1.24432i −0.905578 0.424179i \(-0.860563\pi\)
0.572165 0.820139i \(-0.306104\pi\)
\(468\) 0 0
\(469\) 4.87562 + 27.6510i 0.225135 + 1.27681i
\(470\) 0 0
\(471\) −21.4482 25.5609i −0.988280 1.17779i
\(472\) 0 0
\(473\) −3.65546 1.70457i −0.168078 0.0783761i
\(474\) 0 0
\(475\) −11.8994 18.2594i −0.545982 0.837797i
\(476\) 0 0
\(477\) −55.4992 25.8797i −2.54113 1.18495i
\(478\) 0 0
\(479\) 13.5112 + 16.1020i 0.617340 + 0.735718i 0.980611 0.195966i \(-0.0627843\pi\)
−0.363270 + 0.931684i \(0.618340\pi\)
\(480\) 0 0
\(481\) −1.15662 6.55950i −0.0527372 0.299087i
\(482\) 0 0
\(483\) 8.36590 + 31.2220i 0.380661 + 1.42065i
\(484\) 0 0
\(485\) 31.6558 1.12283i 1.43742 0.0509851i
\(486\) 0 0
\(487\) 8.79135 32.8098i 0.398374 1.48675i −0.417583 0.908639i \(-0.637123\pi\)
0.815957 0.578113i \(-0.196211\pi\)
\(488\) 0 0
\(489\) 6.88952 + 5.78099i 0.311555 + 0.261426i
\(490\) 0 0
\(491\) −0.327892 + 1.85957i −0.0147975 + 0.0839210i −0.991312 0.131530i \(-0.958011\pi\)
0.976515 + 0.215451i \(0.0691222\pi\)
\(492\) 0 0
\(493\) 25.8984 25.8984i 1.16641 1.16641i
\(494\) 0 0
\(495\) 34.4517 + 14.6016i 1.54849 + 0.656292i
\(496\) 0 0
\(497\) −14.7541 + 10.3310i −0.661814 + 0.463407i
\(498\) 0 0
\(499\) 8.60591 10.2561i 0.385254 0.459127i −0.538211 0.842810i \(-0.680900\pi\)
0.923465 + 0.383682i \(0.125344\pi\)
\(500\) 0 0
\(501\) 1.96587 + 3.40498i 0.0878285 + 0.152123i
\(502\) 0 0
\(503\) −14.6602 31.4389i −0.653667 1.40179i −0.901410 0.432967i \(-0.857467\pi\)
0.247743 0.968826i \(-0.420311\pi\)
\(504\) 0 0
\(505\) −16.3541 21.6779i −0.727748 0.964653i
\(506\) 0 0
\(507\) −13.6063 + 19.4318i −0.604276 + 0.862996i
\(508\) 0 0
\(509\) 1.65253 1.38664i 0.0732471 0.0614616i −0.605429 0.795899i \(-0.706998\pi\)
0.678676 + 0.734438i \(0.262554\pi\)
\(510\) 0 0
\(511\) −9.39914 + 3.42101i −0.415794 + 0.151336i
\(512\) 0 0
\(513\) 2.41073 23.0484i 0.106436 1.01761i
\(514\) 0 0
\(515\) −24.5969 27.2875i −1.08387 1.20243i
\(516\) 0 0
\(517\) −0.933060 + 10.6649i −0.0410359 + 0.469043i
\(518\) 0 0
\(519\) 54.2493 9.56561i 2.38128 0.419884i
\(520\) 0 0
\(521\) 1.56446 + 0.903239i 0.0685401 + 0.0395716i 0.533878 0.845561i \(-0.320734\pi\)
−0.465338 + 0.885133i \(0.654067\pi\)
\(522\) 0 0
\(523\) 4.32062 2.01474i 0.188928 0.0880984i −0.325853 0.945421i \(-0.605651\pi\)
0.514780 + 0.857322i \(0.327874\pi\)
\(524\) 0 0
\(525\) −68.7259 19.6253i −2.99944 0.856517i
\(526\) 0 0
\(527\) −0.580237 6.63214i −0.0252755 0.288901i
\(528\) 0 0
\(529\) −17.6151 3.10602i −0.765875 0.135044i
\(530\) 0 0
\(531\) 6.90014i 0.299441i
\(532\) 0 0
\(533\) −3.51902 3.51902i −0.152426 0.152426i
\(534\) 0 0
\(535\) −1.90675 8.94641i −0.0824359 0.386787i
\(536\) 0 0
\(537\) 29.0443 2.54104i 1.25335 0.109654i
\(538\) 0 0
\(539\) 55.9548 32.3055i 2.41014 1.39150i
\(540\) 0 0
\(541\) −15.3734 5.59548i −0.660956 0.240568i −0.0103070 0.999947i \(-0.503281\pi\)
−0.650649 + 0.759379i \(0.725503\pi\)
\(542\) 0 0
\(543\) −2.33331 + 0.625210i −0.100132 + 0.0268303i
\(544\) 0 0
\(545\) 2.92172 + 0.672843i 0.125153 + 0.0288214i
\(546\) 0 0
\(547\) 2.89754 + 0.253502i 0.123890 + 0.0108390i 0.148932 0.988847i \(-0.452416\pi\)
−0.0250420 + 0.999686i \(0.507972\pi\)
\(548\) 0 0
\(549\) −19.3199 53.0810i −0.824554 2.26544i
\(550\) 0 0
\(551\) −16.7679 + 19.3089i −0.714337 + 0.822589i
\(552\) 0 0
\(553\) 12.4012 26.5945i 0.527353 1.13091i
\(554\) 0 0
\(555\) 5.74152 + 18.7429i 0.243714 + 0.795591i
\(556\) 0 0
\(557\) −16.9680 11.8811i −0.718959 0.503420i 0.155916 0.987770i \(-0.450167\pi\)
−0.874874 + 0.484350i \(0.839056\pi\)
\(558\) 0 0
\(559\) 1.25852 2.17982i 0.0532298 0.0921966i
\(560\) 0 0
\(561\) 20.5166 56.3690i 0.866213 2.37990i
\(562\) 0 0
\(563\) −13.2883 3.56059i −0.560035 0.150061i −0.0323123 0.999478i \(-0.510287\pi\)
−0.527722 + 0.849417i \(0.676954\pi\)
\(564\) 0 0
\(565\) 1.46318 4.51164i 0.0615566 0.189806i
\(566\) 0 0
\(567\) −0.754836 1.07802i −0.0317001 0.0452725i
\(568\) 0 0
\(569\) 20.1440 0.844479 0.422239 0.906484i \(-0.361244\pi\)
0.422239 + 0.906484i \(0.361244\pi\)
\(570\) 0 0
\(571\) −22.1344 −0.926295 −0.463148 0.886281i \(-0.653280\pi\)
−0.463148 + 0.886281i \(0.653280\pi\)
\(572\) 0 0
\(573\) 19.9056 + 28.4282i 0.831569 + 1.18760i
\(574\) 0 0
\(575\) −7.40812 + 8.54097i −0.308940 + 0.356183i
\(576\) 0 0
\(577\) 8.47640 + 2.27124i 0.352877 + 0.0945531i 0.430903 0.902398i \(-0.358195\pi\)
−0.0780261 + 0.996951i \(0.524862\pi\)
\(578\) 0 0
\(579\) 24.1474 66.3443i 1.00353 2.75718i
\(580\) 0 0
\(581\) 0.557664 0.965902i 0.0231358 0.0400724i
\(582\) 0 0
\(583\) 35.0689 + 24.5555i 1.45241 + 1.01699i
\(584\) 0 0
\(585\) −10.9514 + 20.6238i −0.452783 + 0.852689i
\(586\) 0 0
\(587\) −1.32881 + 2.84965i −0.0548460 + 0.117618i −0.931821 0.362919i \(-0.881780\pi\)
0.876975 + 0.480536i \(0.159558\pi\)
\(588\) 0 0
\(589\) 0.729498 + 4.59087i 0.0300584 + 0.189164i
\(590\) 0 0
\(591\) −2.72175 7.47795i −0.111958 0.307602i
\(592\) 0 0
\(593\) 20.9146 + 1.82979i 0.858861 + 0.0751406i 0.508073 0.861314i \(-0.330358\pi\)
0.350788 + 0.936455i \(0.385914\pi\)
\(594\) 0 0
\(595\) −15.9398 + 69.2161i −0.653468 + 2.83758i
\(596\) 0 0
\(597\) 29.3218 7.85675i 1.20006 0.321555i
\(598\) 0 0
\(599\) 7.54429 + 2.74590i 0.308252 + 0.112194i 0.491514 0.870870i \(-0.336444\pi\)
−0.183263 + 0.983064i \(0.558666\pi\)
\(600\) 0 0
\(601\) 24.2230 13.9851i 0.988075 0.570466i 0.0833769 0.996518i \(-0.473429\pi\)
0.904698 + 0.426053i \(0.140096\pi\)
\(602\) 0 0
\(603\) −26.8944 + 2.35296i −1.09523 + 0.0958199i
\(604\) 0 0
\(605\) −1.31115 0.850448i −0.0533058 0.0345756i
\(606\) 0 0
\(607\) −25.5906 25.5906i −1.03869 1.03869i −0.999221 0.0394685i \(-0.987434\pi\)
−0.0394685 0.999221i \(-0.512566\pi\)
\(608\) 0 0
\(609\) 83.8656i 3.39841i
\(610\) 0 0
\(611\) −6.57945 1.16013i −0.266176 0.0469340i
\(612\) 0 0
\(613\) 0.797871 + 9.11970i 0.0322257 + 0.368341i 0.995135 + 0.0985173i \(0.0314100\pi\)
−0.962910 + 0.269824i \(0.913034\pi\)
\(614\) 0 0
\(615\) 11.5465 + 9.01089i 0.465598 + 0.363354i
\(616\) 0 0
\(617\) 0.712827 0.332397i 0.0286973 0.0133818i −0.408217 0.912885i \(-0.633849\pi\)
0.436914 + 0.899503i \(0.356071\pi\)
\(618\) 0 0
\(619\) −11.9011 6.87112i −0.478347 0.276174i 0.241380 0.970431i \(-0.422400\pi\)
−0.719727 + 0.694257i \(0.755733\pi\)
\(620\) 0 0
\(621\) −11.8392 + 2.08757i −0.475091 + 0.0837714i
\(622\) 0 0
\(623\) 7.13263 81.5264i 0.285763 3.26628i
\(624\) 0 0
\(625\) −7.77758 23.7594i −0.311103 0.950376i
\(626\) 0 0
\(627\) −11.5247 + 40.2680i −0.460251 + 1.60815i
\(628\) 0 0
\(629\) 18.3056 6.66270i 0.729893 0.265659i
\(630\) 0 0
\(631\) 6.05675 5.08222i 0.241115 0.202320i −0.514220 0.857658i \(-0.671918\pi\)
0.755335 + 0.655339i \(0.227474\pi\)
\(632\) 0 0
\(633\) 18.4530 26.3536i 0.733440 1.04746i
\(634\) 0 0
\(635\) −4.69773 + 33.5597i −0.186424 + 1.33177i
\(636\) 0 0
\(637\) 17.0404 + 36.5432i 0.675164 + 1.44789i
\(638\) 0 0
\(639\) −8.65921 14.9982i −0.342553 0.593319i
\(640\) 0 0
\(641\) −6.04488 + 7.20401i −0.238758 + 0.284541i −0.872096 0.489334i \(-0.837240\pi\)
0.633338 + 0.773875i \(0.281684\pi\)
\(642\) 0 0
\(643\) −19.4660 + 13.6303i −0.767666 + 0.537525i −0.890544 0.454896i \(-0.849676\pi\)
0.122879 + 0.992422i \(0.460787\pi\)
\(644\) 0 0
\(645\) −2.89068 + 6.82042i −0.113821 + 0.268554i
\(646\) 0 0
\(647\) 24.9929 24.9929i 0.982571 0.982571i −0.0172799 0.999851i \(-0.505501\pi\)
0.999851 + 0.0172799i \(0.00550063\pi\)
\(648\) 0 0
\(649\) 0.837675 4.75069i 0.0328816 0.186481i
\(650\) 0 0
\(651\) 11.6778 + 9.79881i 0.457688 + 0.384045i
\(652\) 0 0
\(653\) −1.60286 + 5.98196i −0.0627248 + 0.234092i −0.990170 0.139866i \(-0.955333\pi\)
0.927446 + 0.373958i \(0.122000\pi\)
\(654\) 0 0
\(655\) −1.60385 + 1.72181i −0.0626675 + 0.0672767i
\(656\) 0 0
\(657\) −2.48919 9.28977i −0.0971124 0.362428i
\(658\) 0 0
\(659\) −4.09855 23.2441i −0.159657 0.905460i −0.954404 0.298519i \(-0.903507\pi\)
0.794747 0.606941i \(-0.207604\pi\)
\(660\) 0 0
\(661\) 12.7152 + 15.1534i 0.494566 + 0.589401i 0.954373 0.298618i \(-0.0965258\pi\)
−0.459807 + 0.888019i \(0.652081\pi\)
\(662\) 0 0
\(663\) 33.9277 + 15.8208i 1.31764 + 0.614427i
\(664\) 0 0
\(665\) 7.70661 48.9915i 0.298849 1.89981i
\(666\) 0 0
\(667\) 12.0235 + 5.60665i 0.465552 + 0.217090i
\(668\) 0 0
\(669\) −13.2630 15.8063i −0.512779 0.611106i
\(670\) 0 0
\(671\) 6.85758 + 38.8913i 0.264734 + 1.50138i
\(672\) 0 0
\(673\) −4.86798 18.1676i −0.187647 0.700308i −0.994048 0.108940i \(-0.965255\pi\)
0.806401 0.591369i \(-0.201412\pi\)
\(674\) 0 0
\(675\) 9.49912 24.8274i 0.365621 0.955608i
\(676\) 0 0
\(677\) −10.0879 + 37.6486i −0.387710 + 1.44695i 0.446141 + 0.894963i \(0.352798\pi\)
−0.833850 + 0.551990i \(0.813869\pi\)
\(678\) 0 0
\(679\) 55.2156 + 46.3314i 2.11898 + 1.77804i
\(680\) 0 0
\(681\) −11.9789 + 67.9357i −0.459032 + 2.60330i
\(682\) 0 0
\(683\) 18.0735 18.0735i 0.691562 0.691562i −0.271013 0.962576i \(-0.587359\pi\)
0.962576 + 0.271013i \(0.0873588\pi\)
\(684\) 0 0
\(685\) 12.4581 + 30.7864i 0.476001 + 1.17629i
\(686\) 0 0
\(687\) −53.0066 + 37.1156i −2.02233 + 1.41605i
\(688\) 0 0
\(689\) −17.1731 + 20.4662i −0.654245 + 0.779699i
\(690\) 0 0
\(691\) 0.633938 + 1.09801i 0.0241161 + 0.0417704i 0.877832 0.478969i \(-0.158990\pi\)
−0.853715 + 0.520740i \(0.825656\pi\)
\(692\) 0 0
\(693\) 35.9843 + 77.1686i 1.36693 + 2.93139i
\(694\) 0 0
\(695\) −10.0392 + 7.57375i −0.380810 + 0.287289i
\(696\) 0 0
\(697\) 8.34849 11.9229i 0.316222 0.451611i
\(698\) 0 0
\(699\) −19.9643 + 16.7520i −0.755117 + 0.633619i
\(700\) 0 0
\(701\) −37.4222 + 13.6206i −1.41342 + 0.514441i −0.932130 0.362123i \(-0.882052\pi\)
−0.481285 + 0.876564i \(0.659830\pi\)
\(702\) 0 0
\(703\) −12.4231 + 5.53866i −0.468548 + 0.208894i
\(704\) 0 0
\(705\) 19.6358 + 1.01827i 0.739527 + 0.0383502i
\(706\) 0 0
\(707\) 5.38549 61.5565i 0.202542 2.31507i
\(708\) 0 0
\(709\) −37.2819 + 6.57380i −1.40015 + 0.246884i −0.822205 0.569192i \(-0.807256\pi\)
−0.577945 + 0.816076i \(0.696145\pi\)
\(710\) 0 0
\(711\) 24.4346 + 14.1073i 0.916368 + 0.529065i
\(712\) 0 0
\(713\) 2.18551 1.01912i 0.0818480 0.0381663i
\(714\) 0 0
\(715\) 10.0436 12.8698i 0.375611 0.481304i
\(716\) 0 0
\(717\) −0.401112 4.58473i −0.0149798 0.171220i
\(718\) 0 0
\(719\) 15.7089 + 2.76990i 0.585842 + 0.103300i 0.458710 0.888586i \(-0.348312\pi\)
0.127132 + 0.991886i \(0.459423\pi\)
\(720\) 0 0
\(721\) 83.5963i 3.11329i
\(722\) 0 0
\(723\) −39.2881 39.2881i −1.46114 1.46114i
\(724\) 0 0
\(725\) −24.3016 + 16.4304i −0.902537 + 0.610211i
\(726\) 0 0
\(727\) 10.6694 0.933450i 0.395705 0.0346197i 0.112433 0.993659i \(-0.464136\pi\)
0.283272 + 0.959040i \(0.408580\pi\)
\(728\) 0 0
\(729\) −37.7089 + 21.7712i −1.39663 + 0.806342i
\(730\) 0 0
\(731\) 6.91760 + 2.51780i 0.255857 + 0.0931243i
\(732\) 0 0
\(733\) −4.08675 + 1.09504i −0.150948 + 0.0404463i −0.333502 0.942750i \(-0.608230\pi\)
0.182554 + 0.983196i \(0.441564\pi\)
\(734\) 0 0
\(735\) −62.9384 100.600i −2.32152 3.71067i
\(736\) 0 0
\(737\) 18.8023 + 1.64498i 0.692590 + 0.0605938i
\(738\) 0 0
\(739\) −10.5906 29.0974i −0.389581 1.07037i −0.967190 0.254052i \(-0.918236\pi\)
0.577609 0.816313i \(-0.303986\pi\)
\(740\) 0 0
\(741\) −24.4070 9.35486i −0.896615 0.343659i
\(742\) 0 0
\(743\) −11.6395 + 24.9609i −0.427011 + 0.915728i 0.568642 + 0.822585i \(0.307469\pi\)
−0.995653 + 0.0931428i \(0.970309\pi\)
\(744\) 0 0
\(745\) 30.9381 9.47729i 1.13349 0.347221i
\(746\) 0 0
\(747\) 0.878467 + 0.615109i 0.0321414 + 0.0225057i
\(748\) 0 0
\(749\) 10.4075 18.0263i 0.380282 0.658668i
\(750\) 0 0
\(751\) 0.801864 2.20310i 0.0292604 0.0803924i −0.924202 0.381903i \(-0.875269\pi\)
0.953463 + 0.301511i \(0.0974910\pi\)
\(752\) 0 0
\(753\) −27.9385 7.48609i −1.01813 0.272808i
\(754\) 0 0
\(755\) 10.8701 + 21.3049i 0.395604 + 0.775366i
\(756\) 0 0
\(757\) −19.3741 27.6691i −0.704163 1.00565i −0.998748 0.0500237i \(-0.984070\pi\)
0.294585 0.955625i \(-0.404819\pi\)
\(758\) 0 0
\(759\) 21.7281 0.788681
\(760\) 0 0
\(761\) −40.7538 −1.47733 −0.738663 0.674075i \(-0.764542\pi\)
−0.738663 + 0.674075i \(0.764542\pi\)
\(762\) 0 0
\(763\) 3.91320 + 5.58863i 0.141667 + 0.202322i
\(764\) 0 0
\(765\) −64.9636 21.0686i −2.34877 0.761736i
\(766\) 0 0
\(767\) 2.90786 + 0.779158i 0.104997 + 0.0281338i
\(768\) 0 0
\(769\) 3.46321 9.51510i 0.124887 0.343123i −0.861455 0.507833i \(-0.830447\pi\)
0.986342 + 0.164710i \(0.0526688\pi\)
\(770\) 0 0
\(771\) −8.31403 + 14.4003i −0.299422 + 0.518615i
\(772\) 0 0
\(773\) 4.12919 + 2.89129i 0.148517 + 0.103992i 0.645473 0.763783i \(-0.276660\pi\)
−0.496956 + 0.867775i \(0.665549\pi\)
\(774\) 0 0
\(775\) −0.551544 + 5.30356i −0.0198121 + 0.190509i
\(776\) 0 0
\(777\) −18.8514 + 40.4269i −0.676289 + 1.45031i
\(778\) 0 0
\(779\) −5.22988 + 8.71393i −0.187380 + 0.312209i
\(780\) 0 0
\(781\) 4.14102 + 11.3774i 0.148177 + 0.407114i
\(782\) 0 0
\(783\) −31.0730 2.71853i −1.11046 0.0971525i
\(784\) 0 0
\(785\) 22.5151 14.0862i 0.803598 0.502757i
\(786\) 0 0
\(787\) 43.7226 11.7154i 1.55854 0.417611i 0.626342 0.779549i \(-0.284551\pi\)
0.932202 + 0.361938i \(0.117885\pi\)
\(788\) 0 0
\(789\) 14.5608 + 5.29970i 0.518379 + 0.188674i
\(790\) 0 0
\(791\) 9.34680 5.39638i 0.332334 0.191873i
\(792\) 0 0
\(793\) −24.5510 + 2.14793i −0.871832 + 0.0762754i
\(794\) 0 0
\(795\) 42.7876 65.9663i 1.51752 2.33958i
\(796\) 0 0
\(797\) −7.21332 7.21332i −0.255509 0.255509i 0.567716 0.823225i \(-0.307827\pi\)
−0.823225 + 0.567716i \(0.807827\pi\)
\(798\) 0 0
\(799\) 19.5397i 0.691264i
\(800\) 0 0
\(801\) 77.4933 + 13.6642i 2.73809 + 0.482799i
\(802\) 0 0
\(803\) 0.586009 + 6.69811i 0.0206798 + 0.236371i
\(804\) 0 0
\(805\) −25.5339 + 3.14939i −0.899951 + 0.111001i
\(806\) 0 0
\(807\) 31.3294 14.6091i 1.10285 0.514266i
\(808\) 0 0
\(809\) 46.9863 + 27.1276i 1.65195 + 0.953754i 0.976269 + 0.216561i \(0.0694841\pi\)
0.675682 + 0.737193i \(0.263849\pi\)
\(810\) 0 0
\(811\) 15.2535 2.68960i 0.535621 0.0944445i 0.100707 0.994916i \(-0.467890\pi\)
0.434915 + 0.900472i \(0.356779\pi\)
\(812\) 0 0
\(813\) −1.64837 + 18.8410i −0.0578109 + 0.660781i
\(814\) 0 0
\(815\) −5.31708 + 4.79280i −0.186249 + 0.167885i
\(816\) 0 0
\(817\) −4.94168 1.41431i −0.172888 0.0494803i
\(818\) 0 0
\(819\) −49.9315 + 18.1736i −1.74475 + 0.635037i
\(820\) 0 0
\(821\) 18.6596 15.6572i 0.651224 0.546442i −0.256218 0.966619i \(-0.582477\pi\)
0.907442 + 0.420177i \(0.138032\pi\)
\(822\) 0 0
\(823\) −5.89287 + 8.41588i −0.205412 + 0.293359i −0.908619 0.417626i \(-0.862862\pi\)
0.703206 + 0.710986i \(0.251751\pi\)
\(824\) 0 0
\(825\) −24.6998 + 41.2097i −0.859937 + 1.43474i
\(826\) 0 0
\(827\) 8.54511 + 18.3250i 0.297143 + 0.637224i 0.997029 0.0770301i \(-0.0245438\pi\)
−0.699886 + 0.714254i \(0.746766\pi\)
\(828\) 0 0
\(829\) 6.25984 + 10.8424i 0.217413 + 0.376571i 0.954016 0.299754i \(-0.0969048\pi\)
−0.736603 + 0.676325i \(0.763571\pi\)
\(830\) 0 0
\(831\) 42.6829 50.8675i 1.48065 1.76457i
\(832\) 0 0
\(833\) −96.5995 + 67.6397i −3.34697 + 2.34358i
\(834\) 0 0
\(835\) −2.90090 + 1.17389i −0.100390 + 0.0406242i
\(836\) 0 0
\(837\) −4.00909 + 4.00909i −0.138574 + 0.138574i
\(838\) 0 0
\(839\) −0.603354 + 3.42179i −0.0208301 + 0.118133i −0.993450 0.114269i \(-0.963547\pi\)
0.972620 + 0.232402i \(0.0746586\pi\)
\(840\) 0 0
\(841\) 4.15270 + 3.48453i 0.143197 + 0.120156i
\(842\) 0 0
\(843\) −0.223419 + 0.833811i −0.00769496 + 0.0287180i
\(844\) 0 0
\(845\) −13.8158 12.8693i −0.475279 0.442718i
\(846\) 0 0
\(847\) −0.920416 3.43504i −0.0316259 0.118029i
\(848\) 0 0
\(849\) 10.0528 + 57.0124i 0.345012 + 1.95666i
\(850\) 0 0
\(851\) 4.53559 + 5.40530i 0.155478 + 0.185291i
\(852\) 0 0
\(853\) 6.52387 + 3.04213i 0.223373 + 0.104161i 0.531083 0.847320i \(-0.321785\pi\)
−0.307711 + 0.951480i \(0.599563\pi\)
\(854\) 0 0
\(855\) 46.2813 + 11.4875i 1.58279 + 0.392863i
\(856\) 0 0
\(857\) 32.2156 + 15.0224i 1.10046 + 0.513155i 0.886051 0.463588i \(-0.153438\pi\)
0.214414 + 0.976743i \(0.431216\pi\)
\(858\) 0 0
\(859\) −13.9057 16.5722i −0.474457 0.565435i 0.474737 0.880128i \(-0.342543\pi\)
−0.949194 + 0.314692i \(0.898099\pi\)
\(860\) 0 0
\(861\) 5.78739 + 32.8219i 0.197234 + 1.11857i
\(862\) 0 0
\(863\) 6.41950 + 23.9579i 0.218522 + 0.815536i 0.984897 + 0.173142i \(0.0553920\pi\)
−0.766375 + 0.642394i \(0.777941\pi\)
\(864\) 0 0
\(865\) 1.55421 + 43.8176i 0.0528447 + 1.48984i
\(866\) 0 0
\(867\) −15.9761 + 59.6237i −0.542578 + 2.02493i
\(868\) 0 0
\(869\) −15.1104 12.6791i −0.512584 0.430109i
\(870\) 0 0
\(871\) −2.04531 + 11.5996i −0.0693028 + 0.393036i
\(872\) 0 0
\(873\) −49.0063 + 49.0063i −1.65861 + 1.65861i
\(874\) 0 0
\(875\) 23.0529 52.0079i 0.779332 1.75819i
\(876\) 0 0
\(877\) 5.39529 3.77783i 0.182186 0.127568i −0.478926 0.877855i \(-0.658974\pi\)
0.661112 + 0.750287i \(0.270085\pi\)
\(878\) 0 0
\(879\) 11.3218 13.4928i 0.381875 0.455101i
\(880\) 0 0
\(881\) −18.7714 32.5130i −0.632425 1.09539i −0.987055 0.160385i \(-0.948726\pi\)
0.354630 0.935007i \(-0.384607\pi\)
\(882\) 0 0
\(883\) −6.53362 14.0114i −0.219874 0.471521i 0.765169 0.643829i \(-0.222655\pi\)
−0.985043 + 0.172308i \(0.944877\pi\)
\(884\) 0 0
\(885\) −8.77424 1.22823i −0.294943 0.0412865i
\(886\) 0 0
\(887\) −21.0059 + 29.9995i −0.705309 + 1.00729i 0.293375 + 0.955998i \(0.405222\pi\)
−0.998684 + 0.0512883i \(0.983667\pi\)
\(888\) 0 0
\(889\) −59.0700 + 49.5656i −1.98115 + 1.66238i
\(890\) 0 0
\(891\) −0.831291 + 0.302565i −0.0278493 + 0.0101363i
\(892\) 0 0
\(893\) 0.958573 + 13.6095i 0.0320774 + 0.455426i
\(894\) 0 0
\(895\) −1.20178 + 23.1746i −0.0401712 + 0.774642i
\(896\) 0 0
\(897\) −1.18180 + 13.5080i −0.0394590 + 0.451019i
\(898\) 0 0
\(899\) 6.16164 1.08646i 0.205502 0.0362356i
\(900\) 0 0
\(901\) −67.6694 39.0690i −2.25440 1.30158i
\(902\) 0 0
\(903\) −15.2771 + 7.12384i −0.508391 + 0.237067i
\(904\) 0 0
\(905\) −0.235364 1.90823i −0.00782375 0.0634317i
\(906\) 0 0
\(907\) −3.49095 39.9017i −0.115915 1.32492i −0.801969 0.597365i \(-0.796214\pi\)
0.686054 0.727550i \(-0.259341\pi\)
\(908\) 0 0
\(909\) 58.5113 + 10.3171i 1.94070 + 0.342197i
\(910\) 0 0
\(911\) 20.2994i 0.672548i 0.941764 + 0.336274i \(0.109167\pi\)
−0.941764 + 0.336274i \(0.890833\pi\)
\(912\) 0 0
\(913\) −0.530143 0.530143i −0.0175452 0.0175452i
\(914\) 0 0
\(915\) 70.9369 15.1188i 2.34510 0.499812i
\(916\) 0 0
\(917\) −5.33411 + 0.466674i −0.176148 + 0.0154109i
\(918\) 0 0
\(919\) −32.2390 + 18.6132i −1.06347 + 0.613993i −0.926389 0.376567i \(-0.877105\pi\)
−0.137078 + 0.990560i \(0.543771\pi\)
\(920\) 0 0
\(921\) 63.1939 + 23.0007i 2.08231 + 0.757899i
\(922\) 0 0
\(923\) −7.29833 + 1.95558i −0.240227 + 0.0643687i
\(924\) 0 0
\(925\) −15.4077 + 2.45766i −0.506601 + 0.0808075i
\(926\) 0 0
\(927\) 80.0737 + 7.00554i 2.62997 + 0.230092i
\(928\) 0 0
\(929\) −2.40026 6.59467i −0.0787501 0.216364i 0.894070 0.447928i \(-0.147838\pi\)
−0.972820 + 0.231564i \(0.925616\pi\)
\(930\) 0 0
\(931\) 63.9640 51.8505i 2.09634 1.69933i
\(932\) 0 0
\(933\) 3.66817 7.86642i 0.120091 0.257535i
\(934\) 0 0
\(935\) 42.1692 + 22.3921i 1.37908 + 0.732300i
\(936\) 0 0
\(937\) −13.7249 9.61029i −0.448373 0.313954i 0.327491 0.944854i \(-0.393797\pi\)
−0.775864 + 0.630900i \(0.782686\pi\)
\(938\) 0 0
\(939\) 3.65826 6.33628i 0.119383 0.206777i
\(940\) 0 0
\(941\) 12.6283 34.6959i 0.411670 1.13105i −0.544633 0.838674i \(-0.683331\pi\)
0.956303 0.292379i \(-0.0944467\pi\)
\(942\) 0 0
\(943\) 5.09246 + 1.36452i 0.165833 + 0.0444349i
\(944\) 0 0
\(945\) 53.8814 27.4912i 1.75276 0.894288i
\(946\) 0 0
\(947\) −9.51983 13.5957i −0.309353 0.441802i 0.634128 0.773228i \(-0.281359\pi\)
−0.943481 + 0.331426i \(0.892470\pi\)
\(948\) 0 0
\(949\) −4.19597 −0.136207
\(950\) 0 0
\(951\) −82.6979 −2.68166
\(952\) 0 0
\(953\) −19.7227 28.1669i −0.638881 0.912417i 0.360915 0.932599i \(-0.382464\pi\)
−0.999796 + 0.0201819i \(0.993575\pi\)
\(954\) 0 0
\(955\) −24.6050 + 12.5539i −0.796198 + 0.406234i
\(956\) 0 0
\(957\) 54.4545 + 14.5910i 1.76026 + 0.471661i
\(958\) 0 0
\(959\) −25.8477 + 71.0160i −0.834666 + 2.29323i
\(960\) 0 0
\(961\) −14.9314 + 25.8619i −0.481657 + 0.834254i
\(962\) 0 0
\(963\) 16.3946 + 11.4796i 0.528308 + 0.369925i
\(964\) 0 0
\(965\) 49.6317 + 26.3547i 1.59770 + 0.848388i
\(966\) 0 0
\(967\) −24.6593 + 52.8819i −0.792988 + 1.70057i −0.0827896 + 0.996567i \(0.526383\pi\)
−0.710199 + 0.704001i \(0.751395\pi\)
\(968\) 0 0
\(969\) 14.5488 75.0495i 0.467376 2.41094i
\(970\) 0 0
\(971\) −7.18370 19.7370i −0.230536 0.633392i 0.769450 0.638707i \(-0.220530\pi\)
−0.999986 + 0.00531508i \(0.998308\pi\)
\(972\) 0 0
\(973\) −28.5074 2.49408i −0.913906 0.0799564i
\(974\) 0 0
\(975\) −24.2759 17.5968i −0.777452 0.563550i
\(976\) 0 0
\(977\) −41.3020 + 11.0668i −1.32137 + 0.354060i −0.849490 0.527604i \(-0.823090\pi\)
−0.471878 + 0.881664i \(0.656424\pi\)
\(978\) 0 0
\(979\) −51.6946 18.8153i −1.65217 0.601340i
\(980\) 0 0
\(981\) −5.68107 + 3.27997i −0.181383 + 0.104721i
\(982\) 0 0
\(983\) −40.4772 + 3.54130i −1.29102 + 0.112950i −0.711894 0.702287i \(-0.752162\pi\)
−0.579128 + 0.815237i \(0.696607\pi\)
\(984\) 0 0
\(985\) 6.19484 1.32031i 0.197384 0.0420684i
\(986\) 0 0
\(987\) 31.6372 + 31.6372i 1.00702 + 1.00702i
\(988\) 0 0
\(989\) 2.66647i 0.0847889i
\(990\) 0 0
\(991\) 10.3145 + 1.81872i 0.327650 + 0.0577735i 0.335053 0.942199i \(-0.391246\pi\)
−0.00740383 + 0.999973i \(0.502357\pi\)
\(992\) 0 0
\(993\) −3.56630 40.7630i −0.113173 1.29357i
\(994\) 0 0
\(995\) 2.95771 + 23.9799i 0.0937658 + 0.760214i
\(996\) 0 0
\(997\) −30.8957 + 14.4069i −0.978478 + 0.456272i −0.844992 0.534779i \(-0.820395\pi\)
−0.133486 + 0.991051i \(0.542617\pi\)
\(998\) 0 0
\(999\) −14.3675 8.29506i −0.454567 0.262444i
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.33.1 120
5.2 odd 4 inner 380.2.bh.a.337.1 yes 120
19.15 odd 18 inner 380.2.bh.a.53.1 yes 120
95.72 even 36 inner 380.2.bh.a.357.1 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.bh.a.33.1 120 1.1 even 1 trivial
380.2.bh.a.53.1 yes 120 19.15 odd 18 inner
380.2.bh.a.337.1 yes 120 5.2 odd 4 inner
380.2.bh.a.357.1 yes 120 95.72 even 36 inner