Properties

Label 920.2.bv.a.217.27
Level $920$
Weight $2$
Character 920.217
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
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] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 217.27
Character \(\chi\) \(=\) 920.217
Dual form 920.2.bv.a.513.27

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.45300 - 0.316080i) q^{3} +(-1.46408 - 1.69011i) q^{5} +(3.74304 - 2.04386i) q^{7} +(-0.717605 + 0.327719i) q^{9} +O(q^{10})\) \(q+(1.45300 - 0.316080i) q^{3} +(-1.46408 - 1.69011i) q^{5} +(3.74304 - 2.04386i) q^{7} +(-0.717605 + 0.327719i) q^{9} +(3.97107 + 3.44095i) q^{11} +(1.16993 - 2.14256i) q^{13} +(-2.66152 - 1.99295i) q^{15} +(-4.94978 - 3.70536i) q^{17} +(0.582115 - 4.04870i) q^{19} +(4.79260 - 4.15281i) q^{21} +(2.02482 + 4.34742i) q^{23} +(-0.712923 + 4.94891i) q^{25} +(-4.51025 + 3.37633i) q^{27} +(6.20765 - 0.892526i) q^{29} +(4.73538 - 3.04325i) q^{31} +(6.85756 + 3.74451i) q^{33} +(-8.93446 - 3.33377i) q^{35} +(-9.55279 - 3.56301i) q^{37} +(1.02268 - 3.48292i) q^{39} +(0.166757 - 0.365147i) q^{41} +(-1.81424 - 8.33991i) q^{43} +(1.60451 + 0.733021i) q^{45} +(-0.536764 - 0.536764i) q^{47} +(6.04853 - 9.41169i) q^{49} +(-8.36319 - 3.81934i) q^{51} +(1.45425 + 2.66327i) q^{53} +(0.00160101 - 11.7494i) q^{55} +(-0.433902 - 6.06674i) q^{57} +(-0.860416 - 2.93031i) q^{59} +(4.49955 + 7.00143i) q^{61} +(-2.01621 + 2.69335i) q^{63} +(-5.33402 + 1.15958i) q^{65} +(7.51381 + 0.537398i) q^{67} +(4.31619 + 5.67678i) q^{69} +(1.45881 + 1.68355i) q^{71} +(1.44576 + 1.93131i) q^{73} +(0.528378 + 7.41609i) q^{75} +(21.8967 + 4.76333i) q^{77} +(-7.24346 + 2.12687i) q^{79} +(-3.93634 + 4.54278i) q^{81} +(-4.44169 + 11.9086i) q^{83} +(0.984434 + 13.7906i) q^{85} +(8.73759 - 3.25895i) q^{87} +(-1.18949 - 0.764437i) q^{89} -10.4108i q^{91} +(5.91859 - 5.91859i) q^{93} +(-7.69500 + 4.94379i) q^{95} +(-3.95206 - 10.5959i) q^{97} +(-3.97732 - 1.16785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q+O(q^{10}) \) Copy content Toggle raw display \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 1.45300 0.316080i 0.838888 0.182489i 0.227458 0.973788i \(-0.426958\pi\)
0.611429 + 0.791299i \(0.290595\pi\)
\(4\) 0 0
\(5\) −1.46408 1.69011i −0.654758 0.755839i
\(6\) 0 0
\(7\) 3.74304 2.04386i 1.41474 0.772505i 0.423663 0.905820i \(-0.360744\pi\)
0.991074 + 0.133315i \(0.0425623\pi\)
\(8\) 0 0
\(9\) −0.717605 + 0.327719i −0.239202 + 0.109240i
\(10\) 0 0
\(11\) 3.97107 + 3.44095i 1.19732 + 1.03749i 0.998347 + 0.0574805i \(0.0183067\pi\)
0.198975 + 0.980005i \(0.436239\pi\)
\(12\) 0 0
\(13\) 1.16993 2.14256i 0.324479 0.594239i −0.663618 0.748072i \(-0.730980\pi\)
0.988097 + 0.153833i \(0.0491617\pi\)
\(14\) 0 0
\(15\) −2.66152 1.99295i −0.687200 0.514578i
\(16\) 0 0
\(17\) −4.94978 3.70536i −1.20050 0.898681i −0.203730 0.979027i \(-0.565306\pi\)
−0.996767 + 0.0803463i \(0.974397\pi\)
\(18\) 0 0
\(19\) 0.582115 4.04870i 0.133546 0.928835i −0.807334 0.590095i \(-0.799090\pi\)
0.940880 0.338740i \(-0.110001\pi\)
\(20\) 0 0
\(21\) 4.79260 4.15281i 1.04583 0.906218i
\(22\) 0 0
\(23\) 2.02482 + 4.34742i 0.422205 + 0.906501i
\(24\) 0 0
\(25\) −0.712923 + 4.94891i −0.142585 + 0.989783i
\(26\) 0 0
\(27\) −4.51025 + 3.37633i −0.867999 + 0.649776i
\(28\) 0 0
\(29\) 6.20765 0.892526i 1.15273 0.165738i 0.460667 0.887573i \(-0.347610\pi\)
0.692065 + 0.721835i \(0.256701\pi\)
\(30\) 0 0
\(31\) 4.73538 3.04325i 0.850500 0.546583i −0.0412306 0.999150i \(-0.513128\pi\)
0.891731 + 0.452566i \(0.149491\pi\)
\(32\) 0 0
\(33\) 6.85756 + 3.74451i 1.19375 + 0.651836i
\(34\) 0 0
\(35\) −8.93446 3.33377i −1.51020 0.563509i
\(36\) 0 0
\(37\) −9.55279 3.56301i −1.57047 0.585755i −0.594583 0.804034i \(-0.702683\pi\)
−0.975886 + 0.218280i \(0.929956\pi\)
\(38\) 0 0
\(39\) 1.02268 3.48292i 0.163760 0.557714i
\(40\) 0 0
\(41\) 0.166757 0.365147i 0.0260431 0.0570264i −0.896163 0.443724i \(-0.853657\pi\)
0.922207 + 0.386698i \(0.126384\pi\)
\(42\) 0 0
\(43\) −1.81424 8.33991i −0.276669 1.27183i −0.880245 0.474520i \(-0.842622\pi\)
0.603576 0.797305i \(-0.293742\pi\)
\(44\) 0 0
\(45\) 1.60451 + 0.733021i 0.239187 + 0.109272i
\(46\) 0 0
\(47\) −0.536764 0.536764i −0.0782950 0.0782950i 0.666875 0.745170i \(-0.267632\pi\)
−0.745170 + 0.666875i \(0.767632\pi\)
\(48\) 0 0
\(49\) 6.04853 9.41169i 0.864075 1.34453i
\(50\) 0 0
\(51\) −8.36319 3.81934i −1.17108 0.534815i
\(52\) 0 0
\(53\) 1.45425 + 2.66327i 0.199757 + 0.365828i 0.958286 0.285812i \(-0.0922633\pi\)
−0.758529 + 0.651640i \(0.774081\pi\)
\(54\) 0 0
\(55\) 0.00160101 11.7494i 0.000215880 1.58428i
\(56\) 0 0
\(57\) −0.433902 6.06674i −0.0574717 0.803559i
\(58\) 0 0
\(59\) −0.860416 2.93031i −0.112017 0.381494i 0.884333 0.466856i \(-0.154613\pi\)
−0.996350 + 0.0853625i \(0.972795\pi\)
\(60\) 0 0
\(61\) 4.49955 + 7.00143i 0.576108 + 0.896441i 0.999957 0.00929148i \(-0.00295761\pi\)
−0.423849 + 0.905733i \(0.639321\pi\)
\(62\) 0 0
\(63\) −2.01621 + 2.69335i −0.254019 + 0.339330i
\(64\) 0 0
\(65\) −5.33402 + 1.15958i −0.661604 + 0.143829i
\(66\) 0 0
\(67\) 7.51381 + 0.537398i 0.917958 + 0.0656537i 0.522317 0.852751i \(-0.325068\pi\)
0.395641 + 0.918405i \(0.370522\pi\)
\(68\) 0 0
\(69\) 4.31619 + 5.67678i 0.519608 + 0.683405i
\(70\) 0 0
\(71\) 1.45881 + 1.68355i 0.173128 + 0.199801i 0.835682 0.549214i \(-0.185073\pi\)
−0.662553 + 0.749015i \(0.730527\pi\)
\(72\) 0 0
\(73\) 1.44576 + 1.93131i 0.169214 + 0.226043i 0.877130 0.480254i \(-0.159455\pi\)
−0.707916 + 0.706297i \(0.750364\pi\)
\(74\) 0 0
\(75\) 0.528378 + 7.41609i 0.0610118 + 0.856337i
\(76\) 0 0
\(77\) 21.8967 + 4.76333i 2.49536 + 0.542832i
\(78\) 0 0
\(79\) −7.24346 + 2.12687i −0.814953 + 0.239292i −0.662541 0.749025i \(-0.730522\pi\)
−0.152411 + 0.988317i \(0.548704\pi\)
\(80\) 0 0
\(81\) −3.93634 + 4.54278i −0.437371 + 0.504753i
\(82\) 0 0
\(83\) −4.44169 + 11.9086i −0.487539 + 1.30714i 0.427586 + 0.903975i \(0.359364\pi\)
−0.915126 + 0.403169i \(0.867909\pi\)
\(84\) 0 0
\(85\) 0.984434 + 13.7906i 0.106777 + 1.49580i
\(86\) 0 0
\(87\) 8.73759 3.25895i 0.936768 0.349396i
\(88\) 0 0
\(89\) −1.18949 0.764437i −0.126085 0.0810301i 0.476078 0.879403i \(-0.342058\pi\)
−0.602163 + 0.798373i \(0.705694\pi\)
\(90\) 0 0
\(91\) 10.4108i 1.09135i
\(92\) 0 0
\(93\) 5.91859 5.91859i 0.613729 0.613729i
\(94\) 0 0
\(95\) −7.69500 + 4.94379i −0.789490 + 0.507222i
\(96\) 0 0
\(97\) −3.95206 10.5959i −0.401270 1.07585i −0.967781 0.251793i \(-0.918980\pi\)
0.566511 0.824054i \(-0.308293\pi\)
\(98\) 0 0
\(99\) −3.97732 1.16785i −0.399736 0.117373i
\(100\) 0 0
\(101\) 7.18881 + 15.7413i 0.715313 + 1.56632i 0.820358 + 0.571851i \(0.193774\pi\)
−0.105044 + 0.994468i \(0.533498\pi\)
\(102\) 0 0
\(103\) 3.62936 0.259577i 0.357611 0.0255769i 0.108622 0.994083i \(-0.465356\pi\)
0.248989 + 0.968506i \(0.419902\pi\)
\(104\) 0 0
\(105\) −14.0355 2.01995i −1.36972 0.197127i
\(106\) 0 0
\(107\) −0.615753 + 2.83057i −0.0595271 + 0.273642i −0.997284 0.0736503i \(-0.976535\pi\)
0.937757 + 0.347292i \(0.112899\pi\)
\(108\) 0 0
\(109\) 0.287334 + 1.99845i 0.0275216 + 0.191417i 0.998944 0.0459396i \(-0.0146282\pi\)
−0.971423 + 0.237356i \(0.923719\pi\)
\(110\) 0 0
\(111\) −15.0064 2.15759i −1.42434 0.204789i
\(112\) 0 0
\(113\) 0.133081 1.86071i 0.0125192 0.175041i −0.987345 0.158585i \(-0.949307\pi\)
0.999865 0.0164565i \(-0.00523851\pi\)
\(114\) 0 0
\(115\) 4.38310 9.78715i 0.408727 0.912657i
\(116\) 0 0
\(117\) −0.137387 + 1.92092i −0.0127014 + 0.177589i
\(118\) 0 0
\(119\) −26.1004 3.75267i −2.39262 0.344007i
\(120\) 0 0
\(121\) 2.36378 + 16.4404i 0.214889 + 1.49459i
\(122\) 0 0
\(123\) 0.126882 0.583266i 0.0114405 0.0525914i
\(124\) 0 0
\(125\) 9.40797 6.04070i 0.841474 0.540297i
\(126\) 0 0
\(127\) −2.02443 + 0.144790i −0.179639 + 0.0128480i −0.160869 0.986976i \(-0.551430\pi\)
−0.0187700 + 0.999824i \(0.505975\pi\)
\(128\) 0 0
\(129\) −5.27216 11.5444i −0.464188 1.01643i
\(130\) 0 0
\(131\) 18.4586 + 5.41993i 1.61274 + 0.473542i 0.959053 0.283227i \(-0.0914051\pi\)
0.653682 + 0.756769i \(0.273223\pi\)
\(132\) 0 0
\(133\) −6.09607 16.3442i −0.528596 1.41722i
\(134\) 0 0
\(135\) 12.3097 + 2.67958i 1.05945 + 0.230621i
\(136\) 0 0
\(137\) −5.50730 + 5.50730i −0.470520 + 0.470520i −0.902083 0.431563i \(-0.857962\pi\)
0.431563 + 0.902083i \(0.357962\pi\)
\(138\) 0 0
\(139\) 21.0107i 1.78210i 0.453900 + 0.891052i \(0.350032\pi\)
−0.453900 + 0.891052i \(0.649968\pi\)
\(140\) 0 0
\(141\) −0.949576 0.610255i −0.0799687 0.0513928i
\(142\) 0 0
\(143\) 12.0183 4.48259i 1.00502 0.374853i
\(144\) 0 0
\(145\) −10.5970 9.18487i −0.880031 0.762762i
\(146\) 0 0
\(147\) 5.81364 15.5870i 0.479501 1.28559i
\(148\) 0 0
\(149\) 0.792767 0.914902i 0.0649460 0.0749517i −0.722347 0.691531i \(-0.756937\pi\)
0.787293 + 0.616579i \(0.211482\pi\)
\(150\) 0 0
\(151\) −12.8935 + 3.78588i −1.04926 + 0.308090i −0.760518 0.649317i \(-0.775055\pi\)
−0.288741 + 0.957407i \(0.593237\pi\)
\(152\) 0 0
\(153\) 4.76630 + 1.03684i 0.385332 + 0.0838239i
\(154\) 0 0
\(155\) −12.0764 3.54774i −0.970000 0.284961i
\(156\) 0 0
\(157\) 6.82980 + 9.12354i 0.545077 + 0.728138i 0.985504 0.169651i \(-0.0542639\pi\)
−0.440427 + 0.897788i \(0.645173\pi\)
\(158\) 0 0
\(159\) 2.95483 + 3.41005i 0.234333 + 0.270435i
\(160\) 0 0
\(161\) 16.4645 + 12.1341i 1.29758 + 0.956305i
\(162\) 0 0
\(163\) −21.1614 1.51349i −1.65749 0.118546i −0.789044 0.614337i \(-0.789424\pi\)
−0.868442 + 0.495791i \(0.834878\pi\)
\(164\) 0 0
\(165\) −3.71141 17.0723i −0.288933 1.32908i
\(166\) 0 0
\(167\) −8.30582 + 11.0953i −0.642724 + 0.858578i −0.997067 0.0765372i \(-0.975614\pi\)
0.354343 + 0.935115i \(0.384705\pi\)
\(168\) 0 0
\(169\) 3.80650 + 5.92302i 0.292807 + 0.455617i
\(170\) 0 0
\(171\) 0.909107 + 3.09613i 0.0695212 + 0.236767i
\(172\) 0 0
\(173\) 0.621670 + 8.69208i 0.0472647 + 0.660847i 0.964765 + 0.263112i \(0.0847490\pi\)
−0.917500 + 0.397735i \(0.869796\pi\)
\(174\) 0 0
\(175\) 7.44636 + 19.9811i 0.562892 + 1.51043i
\(176\) 0 0
\(177\) −2.17639 3.98577i −0.163588 0.299588i
\(178\) 0 0
\(179\) −2.25810 1.03124i −0.168778 0.0770785i 0.329234 0.944248i \(-0.393209\pi\)
−0.498013 + 0.867170i \(0.665937\pi\)
\(180\) 0 0
\(181\) −2.90018 + 4.51278i −0.215569 + 0.335432i −0.932150 0.362072i \(-0.882070\pi\)
0.716581 + 0.697504i \(0.245706\pi\)
\(182\) 0 0
\(183\) 8.75084 + 8.75084i 0.646880 + 0.646880i
\(184\) 0 0
\(185\) 7.96421 + 21.3618i 0.585541 + 1.57055i
\(186\) 0 0
\(187\) −6.90595 31.7461i −0.505013 2.32151i
\(188\) 0 0
\(189\) −9.98133 + 21.8561i −0.726035 + 1.58979i
\(190\) 0 0
\(191\) 2.55576 8.70414i 0.184929 0.629809i −0.813881 0.581032i \(-0.802649\pi\)
0.998810 0.0487776i \(-0.0155326\pi\)
\(192\) 0 0
\(193\) −22.7563 8.48766i −1.63803 0.610955i −0.649286 0.760544i \(-0.724932\pi\)
−0.988748 + 0.149589i \(0.952205\pi\)
\(194\) 0 0
\(195\) −7.38379 + 3.37085i −0.528764 + 0.241392i
\(196\) 0 0
\(197\) −5.58998 3.05236i −0.398270 0.217472i 0.267616 0.963526i \(-0.413764\pi\)
−0.665885 + 0.746054i \(0.731946\pi\)
\(198\) 0 0
\(199\) −1.65726 + 1.06506i −0.117480 + 0.0754998i −0.598061 0.801450i \(-0.704062\pi\)
0.480581 + 0.876950i \(0.340426\pi\)
\(200\) 0 0
\(201\) 11.0874 1.59413i 0.782045 0.112441i
\(202\) 0 0
\(203\) 21.4113 16.0283i 1.50278 1.12497i
\(204\) 0 0
\(205\) −0.861284 + 0.252768i −0.0601547 + 0.0176541i
\(206\) 0 0
\(207\) −2.87776 2.45616i −0.200018 0.170715i
\(208\) 0 0
\(209\) 16.2430 14.0746i 1.12355 0.973562i
\(210\) 0 0
\(211\) 0.873331 6.07415i 0.0601226 0.418162i −0.937426 0.348185i \(-0.886798\pi\)
0.997549 0.0699773i \(-0.0222927\pi\)
\(212\) 0 0
\(213\) 2.65178 + 1.98510i 0.181697 + 0.136017i
\(214\) 0 0
\(215\) −11.4392 + 15.2766i −0.780144 + 1.04185i
\(216\) 0 0
\(217\) 11.5048 21.0694i 0.780995 1.43029i
\(218\) 0 0
\(219\) 2.71114 + 2.34921i 0.183202 + 0.158745i
\(220\) 0 0
\(221\) −13.7298 + 6.27020i −0.923567 + 0.421779i
\(222\) 0 0
\(223\) 14.6574 8.00355i 0.981533 0.535957i 0.0934414 0.995625i \(-0.470213\pi\)
0.888091 + 0.459667i \(0.152031\pi\)
\(224\) 0 0
\(225\) −1.11026 3.78500i −0.0740171 0.252333i
\(226\) 0 0
\(227\) 24.7471 5.38340i 1.64252 0.357309i 0.706080 0.708132i \(-0.250462\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(228\) 0 0
\(229\) 25.1054 1.65901 0.829505 0.558500i \(-0.188623\pi\)
0.829505 + 0.558500i \(0.188623\pi\)
\(230\) 0 0
\(231\) 33.3214 2.19238
\(232\) 0 0
\(233\) −18.1278 + 3.94347i −1.18759 + 0.258345i −0.762612 0.646856i \(-0.776083\pi\)
−0.424982 + 0.905202i \(0.639720\pi\)
\(234\) 0 0
\(235\) −0.121322 + 1.69305i −0.00791415 + 0.110443i
\(236\) 0 0
\(237\) −9.85246 + 5.37985i −0.639986 + 0.349459i
\(238\) 0 0
\(239\) −22.9826 + 10.4958i −1.48662 + 0.678918i −0.982764 0.184867i \(-0.940815\pi\)
−0.503860 + 0.863785i \(0.668087\pi\)
\(240\) 0 0
\(241\) 0.874396 + 0.757668i 0.0563248 + 0.0488057i 0.682568 0.730822i \(-0.260863\pi\)
−0.626244 + 0.779628i \(0.715408\pi\)
\(242\) 0 0
\(243\) 3.81667 6.98971i 0.244839 0.448390i
\(244\) 0 0
\(245\) −24.7623 + 3.55684i −1.58201 + 0.227238i
\(246\) 0 0
\(247\) −7.99355 5.98389i −0.508617 0.380746i
\(248\) 0 0
\(249\) −2.68968 + 18.7071i −0.170452 + 1.18552i
\(250\) 0 0
\(251\) −6.44290 + 5.58281i −0.406672 + 0.352384i −0.834049 0.551690i \(-0.813983\pi\)
0.427377 + 0.904074i \(0.359438\pi\)
\(252\) 0 0
\(253\) −6.91856 + 24.2312i −0.434966 + 1.52340i
\(254\) 0 0
\(255\) 5.78931 + 19.7265i 0.362541 + 1.23532i
\(256\) 0 0
\(257\) −19.9526 + 14.9363i −1.24461 + 0.931703i −0.999288 0.0377381i \(-0.987985\pi\)
−0.245322 + 0.969442i \(0.578894\pi\)
\(258\) 0 0
\(259\) −43.0388 + 6.18804i −2.67430 + 0.384506i
\(260\) 0 0
\(261\) −4.16214 + 2.67485i −0.257630 + 0.165569i
\(262\) 0 0
\(263\) 11.5413 + 6.30202i 0.711666 + 0.388599i 0.793928 0.608012i \(-0.208033\pi\)
−0.0822619 + 0.996611i \(0.526214\pi\)
\(264\) 0 0
\(265\) 2.37206 6.35708i 0.145714 0.390513i
\(266\) 0 0
\(267\) −1.96994 0.734751i −0.120559 0.0449660i
\(268\) 0 0
\(269\) −2.09716 + 7.14228i −0.127866 + 0.435473i −0.998394 0.0566462i \(-0.981959\pi\)
0.870528 + 0.492119i \(0.163777\pi\)
\(270\) 0 0
\(271\) −0.668877 + 1.46464i −0.0406314 + 0.0889703i −0.928859 0.370433i \(-0.879209\pi\)
0.888228 + 0.459403i \(0.151937\pi\)
\(272\) 0 0
\(273\) −3.29066 15.1269i −0.199160 0.915523i
\(274\) 0 0
\(275\) −19.8600 + 17.1993i −1.19760 + 1.03716i
\(276\) 0 0
\(277\) 14.0946 + 14.0946i 0.846863 + 0.846863i 0.989740 0.142877i \(-0.0456354\pi\)
−0.142877 + 0.989740i \(0.545635\pi\)
\(278\) 0 0
\(279\) −2.40080 + 3.73572i −0.143732 + 0.223652i
\(280\) 0 0
\(281\) −23.1437 10.5694i −1.38064 0.630516i −0.419797 0.907618i \(-0.637899\pi\)
−0.960841 + 0.277102i \(0.910626\pi\)
\(282\) 0 0
\(283\) 13.1924 + 24.1600i 0.784204 + 1.43616i 0.896760 + 0.442518i \(0.145915\pi\)
−0.112555 + 0.993645i \(0.535904\pi\)
\(284\) 0 0
\(285\) −9.61817 + 9.61555i −0.569731 + 0.569576i
\(286\) 0 0
\(287\) −0.122129 1.70759i −0.00720906 0.100796i
\(288\) 0 0
\(289\) 5.98117 + 20.3700i 0.351833 + 1.19823i
\(290\) 0 0
\(291\) −9.09146 14.1466i −0.532951 0.829288i
\(292\) 0 0
\(293\) 4.77099 6.37329i 0.278724 0.372332i −0.639232 0.769014i \(-0.720748\pi\)
0.917956 + 0.396682i \(0.129839\pi\)
\(294\) 0 0
\(295\) −3.69281 + 5.74441i −0.215004 + 0.334452i
\(296\) 0 0
\(297\) −29.5283 2.11191i −1.71341 0.122545i
\(298\) 0 0
\(299\) 11.6835 + 0.747863i 0.675675 + 0.0432500i
\(300\) 0 0
\(301\) −23.8363 27.5086i −1.37390 1.58557i
\(302\) 0 0
\(303\) 15.4208 + 20.5998i 0.885903 + 1.18343i
\(304\) 0 0
\(305\) 5.24546 17.8554i 0.300354 1.02240i
\(306\) 0 0
\(307\) −8.89536 1.93507i −0.507685 0.110440i −0.0485749 0.998820i \(-0.515468\pi\)
−0.459110 + 0.888379i \(0.651832\pi\)
\(308\) 0 0
\(309\) 5.19140 1.52433i 0.295328 0.0867162i
\(310\) 0 0
\(311\) 3.39765 3.92110i 0.192663 0.222345i −0.651196 0.758909i \(-0.725733\pi\)
0.843860 + 0.536564i \(0.180278\pi\)
\(312\) 0 0
\(313\) −3.65240 + 9.79246i −0.206446 + 0.553502i −0.998367 0.0571204i \(-0.981808\pi\)
0.791922 + 0.610623i \(0.209081\pi\)
\(314\) 0 0
\(315\) 7.50395 0.535665i 0.422799 0.0301813i
\(316\) 0 0
\(317\) 30.2023 11.2649i 1.69633 0.632699i 0.699678 0.714458i \(-0.253327\pi\)
0.996652 + 0.0817594i \(0.0260539\pi\)
\(318\) 0 0
\(319\) 27.7221 + 17.8159i 1.55214 + 0.997501i
\(320\) 0 0
\(321\) 4.30744i 0.240418i
\(322\) 0 0
\(323\) −17.8832 + 17.8832i −0.995048 + 0.995048i
\(324\) 0 0
\(325\) 9.76927 + 7.31734i 0.541902 + 0.405893i
\(326\) 0 0
\(327\) 1.04916 + 2.81292i 0.0580190 + 0.155555i
\(328\) 0 0
\(329\) −3.10620 0.912061i −0.171250 0.0502836i
\(330\) 0 0
\(331\) 9.41892 + 20.6246i 0.517711 + 1.13363i 0.970299 + 0.241909i \(0.0777735\pi\)
−0.452588 + 0.891720i \(0.649499\pi\)
\(332\) 0 0
\(333\) 8.02279 0.573801i 0.439646 0.0314441i
\(334\) 0 0
\(335\) −10.0926 13.4859i −0.551417 0.736816i
\(336\) 0 0
\(337\) 7.32691 33.6813i 0.399122 1.83474i −0.136968 0.990575i \(-0.543736\pi\)
0.536091 0.844160i \(-0.319900\pi\)
\(338\) 0 0
\(339\) −0.394768 2.74567i −0.0214409 0.149124i
\(340\) 0 0
\(341\) 29.2762 + 4.20928i 1.58539 + 0.227945i
\(342\) 0 0
\(343\) 1.27407 17.8138i 0.0687932 0.961854i
\(344\) 0 0
\(345\) 3.27511 15.6061i 0.176326 0.840205i
\(346\) 0 0
\(347\) 0.0661572 0.924999i 0.00355151 0.0496566i −0.995367 0.0961454i \(-0.969349\pi\)
0.998919 + 0.0464888i \(0.0148032\pi\)
\(348\) 0 0
\(349\) −22.8023 3.27847i −1.22058 0.175492i −0.498243 0.867037i \(-0.666021\pi\)
−0.722333 + 0.691545i \(0.756930\pi\)
\(350\) 0 0
\(351\) 1.95733 + 13.6135i 0.104475 + 0.726637i
\(352\) 0 0
\(353\) 0.374809 1.72297i 0.0199491 0.0917045i −0.966096 0.258183i \(-0.916876\pi\)
0.986045 + 0.166479i \(0.0532398\pi\)
\(354\) 0 0
\(355\) 0.709570 4.93040i 0.0376601 0.261678i
\(356\) 0 0
\(357\) −39.1100 + 2.79720i −2.06992 + 0.148044i
\(358\) 0 0
\(359\) 5.76528 + 12.6242i 0.304280 + 0.666279i 0.998572 0.0534131i \(-0.0170100\pi\)
−0.694293 + 0.719693i \(0.744283\pi\)
\(360\) 0 0
\(361\) 2.17727 + 0.639304i 0.114593 + 0.0336476i
\(362\) 0 0
\(363\) 8.63105 + 23.1407i 0.453013 + 1.21457i
\(364\) 0 0
\(365\) 1.14741 5.27109i 0.0600581 0.275902i
\(366\) 0 0
\(367\) 11.2472 11.2472i 0.587098 0.587098i −0.349747 0.936844i \(-0.613732\pi\)
0.936844 + 0.349747i \(0.113732\pi\)
\(368\) 0 0
\(369\) 0.316681i 0.0164858i
\(370\) 0 0
\(371\) 10.8867 + 6.99643i 0.565207 + 0.363237i
\(372\) 0 0
\(373\) 25.1957 9.39750i 1.30458 0.486584i 0.401424 0.915892i \(-0.368515\pi\)
0.903158 + 0.429308i \(0.141243\pi\)
\(374\) 0 0
\(375\) 11.7604 11.7508i 0.607304 0.606808i
\(376\) 0 0
\(377\) 5.35021 14.3445i 0.275550 0.738777i
\(378\) 0 0
\(379\) −1.35798 + 1.56719i −0.0697546 + 0.0805011i −0.789554 0.613681i \(-0.789688\pi\)
0.719800 + 0.694182i \(0.244234\pi\)
\(380\) 0 0
\(381\) −2.89572 + 0.850259i −0.148352 + 0.0435601i
\(382\) 0 0
\(383\) −12.2127 2.65670i −0.624038 0.135751i −0.110582 0.993867i \(-0.535271\pi\)
−0.513456 + 0.858116i \(0.671635\pi\)
\(384\) 0 0
\(385\) −24.0080 43.9816i −1.22356 2.24151i
\(386\) 0 0
\(387\) 4.03505 + 5.39020i 0.205113 + 0.273999i
\(388\) 0 0
\(389\) −9.03003 10.4212i −0.457841 0.528377i 0.479149 0.877734i \(-0.340945\pi\)
−0.936990 + 0.349357i \(0.886400\pi\)
\(390\) 0 0
\(391\) 6.08634 29.0215i 0.307799 1.46768i
\(392\) 0 0
\(393\) 28.5334 + 2.04075i 1.43932 + 0.102942i
\(394\) 0 0
\(395\) 14.1997 + 9.12830i 0.714463 + 0.459295i
\(396\) 0 0
\(397\) 2.70180 3.60919i 0.135600 0.181140i −0.727602 0.686000i \(-0.759365\pi\)
0.863201 + 0.504860i \(0.168456\pi\)
\(398\) 0 0
\(399\) −14.0236 21.8212i −0.702060 1.09243i
\(400\) 0 0
\(401\) −5.66497 19.2931i −0.282895 0.963452i −0.971247 0.238075i \(-0.923484\pi\)
0.688352 0.725377i \(-0.258335\pi\)
\(402\) 0 0
\(403\) −0.980288 13.7062i −0.0488316 0.682755i
\(404\) 0 0
\(405\) 13.4409 + 0.00183150i 0.667884 + 9.10081e-5i
\(406\) 0 0
\(407\) −25.6746 47.0196i −1.27264 2.33068i
\(408\) 0 0
\(409\) −12.3191 5.62595i −0.609141 0.278185i 0.0868666 0.996220i \(-0.472315\pi\)
−0.696007 + 0.718035i \(0.745042\pi\)
\(410\) 0 0
\(411\) −6.26134 + 9.74283i −0.308849 + 0.480578i
\(412\) 0 0
\(413\) −9.20970 9.20970i −0.453179 0.453179i
\(414\) 0 0
\(415\) 26.6299 9.92830i 1.30721 0.487361i
\(416\) 0 0
\(417\) 6.64106 + 30.5285i 0.325214 + 1.49499i
\(418\) 0 0
\(419\) 10.1080 22.1335i 0.493809 1.08129i −0.484623 0.874723i \(-0.661043\pi\)
0.978432 0.206568i \(-0.0662295\pi\)
\(420\) 0 0
\(421\) 8.34777 28.4299i 0.406845 1.38559i −0.460402 0.887710i \(-0.652295\pi\)
0.867247 0.497877i \(-0.165887\pi\)
\(422\) 0 0
\(423\) 0.561092 + 0.209276i 0.0272812 + 0.0101754i
\(424\) 0 0
\(425\) 21.8663 21.8544i 1.06067 1.06009i
\(426\) 0 0
\(427\) 31.1519 + 17.0102i 1.50755 + 0.823182i
\(428\) 0 0
\(429\) 16.0457 10.3119i 0.774692 0.497865i
\(430\) 0 0
\(431\) −2.93829 + 0.422463i −0.141533 + 0.0203493i −0.212717 0.977114i \(-0.568231\pi\)
0.0711844 + 0.997463i \(0.477322\pi\)
\(432\) 0 0
\(433\) −6.31522 + 4.72751i −0.303490 + 0.227190i −0.740158 0.672433i \(-0.765249\pi\)
0.436668 + 0.899623i \(0.356158\pi\)
\(434\) 0 0
\(435\) −18.3005 9.99608i −0.877443 0.479275i
\(436\) 0 0
\(437\) 18.7801 5.66719i 0.898373 0.271099i
\(438\) 0 0
\(439\) 0.597120 0.517408i 0.0284990 0.0246945i −0.640495 0.767962i \(-0.721271\pi\)
0.668994 + 0.743268i \(0.266725\pi\)
\(440\) 0 0
\(441\) −1.25606 + 8.73609i −0.0598124 + 0.416004i
\(442\) 0 0
\(443\) −10.0231 7.50322i −0.476213 0.356489i 0.334050 0.942555i \(-0.391585\pi\)
−0.810263 + 0.586067i \(0.800676\pi\)
\(444\) 0 0
\(445\) 0.449527 + 3.12956i 0.0213096 + 0.148355i
\(446\) 0 0
\(447\) 0.862705 1.57993i 0.0408045 0.0747279i
\(448\) 0 0
\(449\) 2.03870 + 1.76655i 0.0962124 + 0.0833685i 0.701639 0.712533i \(-0.252452\pi\)
−0.605427 + 0.795901i \(0.706997\pi\)
\(450\) 0 0
\(451\) 1.91866 0.876221i 0.0903460 0.0412597i
\(452\) 0 0
\(453\) −17.5376 + 9.57624i −0.823987 + 0.449931i
\(454\) 0 0
\(455\) −17.5954 + 15.2423i −0.824887 + 0.714572i
\(456\) 0 0
\(457\) −23.7944 + 5.17616i −1.11306 + 0.242130i −0.731248 0.682111i \(-0.761062\pi\)
−0.381808 + 0.924242i \(0.624698\pi\)
\(458\) 0 0
\(459\) 34.8353 1.62597
\(460\) 0 0
\(461\) −12.2517 −0.570620 −0.285310 0.958435i \(-0.592097\pi\)
−0.285310 + 0.958435i \(0.592097\pi\)
\(462\) 0 0
\(463\) 31.1122 6.76805i 1.44591 0.314538i 0.579949 0.814653i \(-0.303073\pi\)
0.865959 + 0.500115i \(0.166709\pi\)
\(464\) 0 0
\(465\) −18.6683 1.33774i −0.865724 0.0620363i
\(466\) 0 0
\(467\) −7.08984 + 3.87134i −0.328078 + 0.179144i −0.634843 0.772641i \(-0.718935\pi\)
0.306765 + 0.951785i \(0.400754\pi\)
\(468\) 0 0
\(469\) 29.2229 13.3456i 1.34939 0.616244i
\(470\) 0 0
\(471\) 12.8074 + 11.0977i 0.590135 + 0.511355i
\(472\) 0 0
\(473\) 21.4928 39.3611i 0.988238 1.80982i
\(474\) 0 0
\(475\) 19.6217 + 5.76725i 0.900303 + 0.264619i
\(476\) 0 0
\(477\) −1.91638 1.43459i −0.0877451 0.0656852i
\(478\) 0 0
\(479\) 1.40277 9.75651i 0.0640944 0.445786i −0.932352 0.361553i \(-0.882247\pi\)
0.996446 0.0842335i \(-0.0268442\pi\)
\(480\) 0 0
\(481\) −18.8100 + 16.2990i −0.857663 + 0.743169i
\(482\) 0 0
\(483\) 27.7582 + 12.4268i 1.26304 + 0.565438i
\(484\) 0 0
\(485\) −12.1220 + 22.1926i −0.550432 + 1.00772i
\(486\) 0 0
\(487\) −15.8514 + 11.8662i −0.718298 + 0.537711i −0.894733 0.446601i \(-0.852634\pi\)
0.176435 + 0.984312i \(0.443543\pi\)
\(488\) 0 0
\(489\) −31.2258 + 4.48959i −1.41208 + 0.203026i
\(490\) 0 0
\(491\) −22.1221 + 14.2170i −0.998358 + 0.641606i −0.934355 0.356344i \(-0.884023\pi\)
−0.0640030 + 0.997950i \(0.520387\pi\)
\(492\) 0 0
\(493\) −34.0336 18.5838i −1.53280 0.836971i
\(494\) 0 0
\(495\) 3.84934 + 8.43192i 0.173015 + 0.378987i
\(496\) 0 0
\(497\) 8.90131 + 3.32002i 0.399278 + 0.148923i
\(498\) 0 0
\(499\) 5.79227 19.7267i 0.259298 0.883087i −0.722212 0.691672i \(-0.756874\pi\)
0.981509 0.191414i \(-0.0613075\pi\)
\(500\) 0 0
\(501\) −8.56133 + 18.7467i −0.382492 + 0.837541i
\(502\) 0 0
\(503\) −8.61835 39.6179i −0.384273 1.76647i −0.610117 0.792311i \(-0.708878\pi\)
0.225844 0.974163i \(-0.427486\pi\)
\(504\) 0 0
\(505\) 16.0795 35.1964i 0.715527 1.56622i
\(506\) 0 0
\(507\) 7.40297 + 7.40297i 0.328778 + 0.328778i
\(508\) 0 0
\(509\) −3.81281 + 5.93285i −0.169000 + 0.262969i −0.915415 0.402512i \(-0.868137\pi\)
0.746415 + 0.665481i \(0.231774\pi\)
\(510\) 0 0
\(511\) 9.35887 + 4.27405i 0.414012 + 0.189073i
\(512\) 0 0
\(513\) 11.0443 + 20.2261i 0.487616 + 0.893003i
\(514\) 0 0
\(515\) −5.75240 5.75396i −0.253481 0.253550i
\(516\) 0 0
\(517\) −0.284548 3.97850i −0.0125144 0.174974i
\(518\) 0 0
\(519\) 3.65068 + 12.4331i 0.160247 + 0.545751i
\(520\) 0 0
\(521\) 21.4200 + 33.3302i 0.938427 + 1.46022i 0.887120 + 0.461538i \(0.152702\pi\)
0.0513070 + 0.998683i \(0.483661\pi\)
\(522\) 0 0
\(523\) 19.4096 25.9282i 0.848722 1.13376i −0.140894 0.990025i \(-0.544998\pi\)
0.989616 0.143735i \(-0.0459113\pi\)
\(524\) 0 0
\(525\) 17.1352 + 26.6788i 0.747840 + 1.16436i
\(526\) 0 0
\(527\) −34.7154 2.48289i −1.51223 0.108157i
\(528\) 0 0
\(529\) −14.8002 + 17.6055i −0.643487 + 0.765457i
\(530\) 0 0
\(531\) 1.57776 + 1.82083i 0.0684688 + 0.0790172i
\(532\) 0 0
\(533\) −0.587256 0.784483i −0.0254369 0.0339797i
\(534\) 0 0
\(535\) 5.68548 3.10350i 0.245805 0.134176i
\(536\) 0 0
\(537\) −3.60697 0.784648i −0.155652 0.0338600i
\(538\) 0 0
\(539\) 56.4042 16.5618i 2.42950 0.713366i
\(540\) 0 0
\(541\) 13.6123 15.7095i 0.585240 0.675403i −0.383483 0.923548i \(-0.625276\pi\)
0.968723 + 0.248145i \(0.0798210\pi\)
\(542\) 0 0
\(543\) −2.78756 + 7.47374i −0.119626 + 0.320729i
\(544\) 0 0
\(545\) 2.95691 3.41152i 0.126660 0.146134i
\(546\) 0 0
\(547\) 15.0516 5.61395i 0.643559 0.240035i −0.00642931 0.999979i \(-0.502047\pi\)
0.649988 + 0.759944i \(0.274774\pi\)
\(548\) 0 0
\(549\) −5.52340 3.54967i −0.235733 0.151496i
\(550\) 0 0
\(551\) 25.6525i 1.09283i
\(552\) 0 0
\(553\) −22.7655 + 22.7655i −0.968089 + 0.968089i
\(554\) 0 0
\(555\) 18.3240 + 28.5212i 0.777811 + 1.21066i
\(556\) 0 0
\(557\) 6.49203 + 17.4058i 0.275076 + 0.737507i 0.998872 + 0.0474929i \(0.0151231\pi\)
−0.723796 + 0.690014i \(0.757604\pi\)
\(558\) 0 0
\(559\) −19.9913 5.86997i −0.845541 0.248273i
\(560\) 0 0
\(561\) −20.0686 43.9442i −0.847299 1.85533i
\(562\) 0 0
\(563\) −20.5000 + 1.46619i −0.863970 + 0.0617924i −0.496287 0.868159i \(-0.665304\pi\)
−0.367683 + 0.929951i \(0.619849\pi\)
\(564\) 0 0
\(565\) −3.33964 + 2.49932i −0.140500 + 0.105147i
\(566\) 0 0
\(567\) −5.44910 + 25.0491i −0.228841 + 1.05196i
\(568\) 0 0
\(569\) 3.00500 + 20.9002i 0.125976 + 0.876183i 0.950582 + 0.310475i \(0.100488\pi\)
−0.824605 + 0.565708i \(0.808603\pi\)
\(570\) 0 0
\(571\) 1.24090 + 0.178414i 0.0519300 + 0.00746641i 0.168231 0.985748i \(-0.446195\pi\)
−0.116301 + 0.993214i \(0.537104\pi\)
\(572\) 0 0
\(573\) 0.962314 13.4549i 0.0402012 0.562087i
\(574\) 0 0
\(575\) −22.9586 + 6.92129i −0.957438 + 0.288638i
\(576\) 0 0
\(577\) −0.000913547 0.0127731i −3.80315e−5 0.000531749i −0.997471 0.0710733i \(-0.977358\pi\)
0.997433 + 0.0716051i \(0.0228121\pi\)
\(578\) 0 0
\(579\) −35.7476 5.13973i −1.48562 0.213600i
\(580\) 0 0
\(581\) 7.71410 + 53.6527i 0.320035 + 2.22589i
\(582\) 0 0
\(583\) −3.38922 + 15.5800i −0.140367 + 0.645258i
\(584\) 0 0
\(585\) 3.44770 2.58018i 0.142545 0.106677i
\(586\) 0 0
\(587\) −0.768689 + 0.0549777i −0.0317272 + 0.00226917i −0.0871938 0.996191i \(-0.527790\pi\)
0.0554666 + 0.998461i \(0.482335\pi\)
\(588\) 0 0
\(589\) −9.56465 20.9437i −0.394104 0.862968i
\(590\) 0 0
\(591\) −9.08701 2.66819i −0.373790 0.109755i
\(592\) 0 0
\(593\) −8.06882 21.6333i −0.331347 0.888375i −0.990641 0.136490i \(-0.956418\pi\)
0.659295 0.751885i \(-0.270855\pi\)
\(594\) 0 0
\(595\) 31.8708 + 49.6067i 1.30657 + 2.03368i
\(596\) 0 0
\(597\) −2.07135 + 2.07135i −0.0847746 + 0.0847746i
\(598\) 0 0
\(599\) 14.2597i 0.582637i −0.956626 0.291318i \(-0.905906\pi\)
0.956626 0.291318i \(-0.0940939\pi\)
\(600\) 0 0
\(601\) 29.0088 + 18.6428i 1.18329 + 0.760457i 0.975989 0.217819i \(-0.0698942\pi\)
0.207305 + 0.978276i \(0.433531\pi\)
\(602\) 0 0
\(603\) −5.56806 + 2.07678i −0.226749 + 0.0845730i
\(604\) 0 0
\(605\) 24.3253 28.0652i 0.988965 1.14101i
\(606\) 0 0
\(607\) 11.5430 30.9480i 0.468516 1.25614i −0.461013 0.887393i \(-0.652514\pi\)
0.929530 0.368748i \(-0.120213\pi\)
\(608\) 0 0
\(609\) 26.0443 30.0567i 1.05537 1.21796i
\(610\) 0 0
\(611\) −1.77802 + 0.522074i −0.0719311 + 0.0211209i
\(612\) 0 0
\(613\) 40.9030 + 8.89790i 1.65206 + 0.359383i 0.939584 0.342317i \(-0.111212\pi\)
0.712472 + 0.701700i \(0.247575\pi\)
\(614\) 0 0
\(615\) −1.17155 + 0.639506i −0.0472414 + 0.0257874i
\(616\) 0 0
\(617\) −3.14163 4.19672i −0.126477 0.168954i 0.732833 0.680409i \(-0.238198\pi\)
−0.859310 + 0.511455i \(0.829107\pi\)
\(618\) 0 0
\(619\) −23.9499 27.6397i −0.962630 1.11093i −0.993774 0.111419i \(-0.964460\pi\)
0.0311438 0.999515i \(-0.490085\pi\)
\(620\) 0 0
\(621\) −23.8108 12.7715i −0.955495 0.512503i
\(622\) 0 0
\(623\) −6.01469 0.430179i −0.240974 0.0172348i
\(624\) 0 0
\(625\) −23.9835 7.05639i −0.959339 0.282255i
\(626\) 0 0
\(627\) 19.1523 25.5845i 0.764868 1.02174i
\(628\) 0 0
\(629\) 34.0820 + 53.0326i 1.35894 + 2.11455i
\(630\) 0 0
\(631\) −12.6272 43.0044i −0.502682 1.71198i −0.684826 0.728707i \(-0.740122\pi\)
0.182144 0.983272i \(-0.441696\pi\)
\(632\) 0 0
\(633\) −0.650971 9.10176i −0.0258738 0.361763i
\(634\) 0 0
\(635\) 3.20864 + 3.20951i 0.127331 + 0.127366i
\(636\) 0 0
\(637\) −13.0888 23.9703i −0.518596 0.949738i
\(638\) 0 0
\(639\) −1.59858 0.730046i −0.0632388 0.0288802i
\(640\) 0 0
\(641\) −19.6615 + 30.5938i −0.776581 + 1.20838i 0.197081 + 0.980387i \(0.436854\pi\)
−0.973662 + 0.227996i \(0.926783\pi\)
\(642\) 0 0
\(643\) 4.57170 + 4.57170i 0.180290 + 0.180290i 0.791482 0.611192i \(-0.209310\pi\)
−0.611192 + 0.791482i \(0.709310\pi\)
\(644\) 0 0
\(645\) −11.7924 + 25.8125i −0.464326 + 1.01637i
\(646\) 0 0
\(647\) −2.86552 13.1726i −0.112655 0.517867i −0.998543 0.0539672i \(-0.982813\pi\)
0.885888 0.463900i \(-0.153550\pi\)
\(648\) 0 0
\(649\) 6.66627 14.5971i 0.261674 0.572986i
\(650\) 0 0
\(651\) 10.0568 34.2502i 0.394156 1.34237i
\(652\) 0 0
\(653\) 34.5955 + 12.9034i 1.35383 + 0.504951i 0.918535 0.395340i \(-0.129373\pi\)
0.435290 + 0.900290i \(0.356646\pi\)
\(654\) 0 0
\(655\) −17.8646 39.1322i −0.698030 1.52902i
\(656\) 0 0
\(657\) −1.67041 0.912115i −0.0651690 0.0355850i
\(658\) 0 0
\(659\) −22.7076 + 14.5933i −0.884561 + 0.568473i −0.902174 0.431372i \(-0.858030\pi\)
0.0176130 + 0.999845i \(0.494393\pi\)
\(660\) 0 0
\(661\) 18.9130 2.71928i 0.735631 0.105768i 0.235691 0.971828i \(-0.424265\pi\)
0.499940 + 0.866060i \(0.333355\pi\)
\(662\) 0 0
\(663\) −17.9675 + 13.4503i −0.697799 + 0.522366i
\(664\) 0 0
\(665\) −18.6983 + 34.2323i −0.725089 + 1.32747i
\(666\) 0 0
\(667\) 16.4496 + 25.1801i 0.636930 + 0.974977i
\(668\) 0 0
\(669\) 18.7674 16.2620i 0.725589 0.628727i
\(670\) 0 0
\(671\) −6.22357 + 43.2859i −0.240258 + 1.67103i
\(672\) 0 0
\(673\) −9.92038 7.42631i −0.382403 0.286263i 0.390733 0.920504i \(-0.372222\pi\)
−0.773135 + 0.634241i \(0.781313\pi\)
\(674\) 0 0
\(675\) −13.4937 24.7279i −0.519373 0.951778i
\(676\) 0 0
\(677\) −12.6135 + 23.0999i −0.484775 + 0.887800i 0.514761 + 0.857334i \(0.327881\pi\)
−0.999536 + 0.0304657i \(0.990301\pi\)
\(678\) 0 0
\(679\) −36.4491 31.5833i −1.39879 1.21206i
\(680\) 0 0
\(681\) 34.2558 15.6441i 1.31269 0.599484i
\(682\) 0 0
\(683\) −38.3443 + 20.9376i −1.46720 + 0.801154i −0.996695 0.0812403i \(-0.974112\pi\)
−0.470510 + 0.882395i \(0.655930\pi\)
\(684\) 0 0
\(685\) 17.3711 + 1.24478i 0.663714 + 0.0475607i
\(686\) 0 0
\(687\) 36.4780 7.93530i 1.39172 0.302751i
\(688\) 0 0
\(689\) 7.40757 0.282206
\(690\) 0 0
\(691\) −17.4276 −0.662975 −0.331488 0.943460i \(-0.607551\pi\)
−0.331488 + 0.943460i \(0.607551\pi\)
\(692\) 0 0
\(693\) −17.2742 + 3.75777i −0.656192 + 0.142746i
\(694\) 0 0
\(695\) 35.5103 30.7614i 1.34698 1.16685i
\(696\) 0 0
\(697\) −2.17841 + 1.18950i −0.0825132 + 0.0450556i
\(698\) 0 0
\(699\) −25.0932 + 11.4597i −0.949113 + 0.433445i
\(700\) 0 0
\(701\) −26.1061 22.6211i −0.986015 0.854387i 0.00332702 0.999994i \(-0.498941\pi\)
−0.989342 + 0.145607i \(0.953486\pi\)
\(702\) 0 0
\(703\) −19.9864 + 36.6023i −0.753800 + 1.38048i
\(704\) 0 0
\(705\) 0.358861 + 2.49835i 0.0135155 + 0.0940933i
\(706\) 0 0
\(707\) 59.0810 + 44.2274i 2.22197 + 1.66334i
\(708\) 0 0
\(709\) −1.54932 + 10.7757i −0.0581859 + 0.404692i 0.939825 + 0.341655i \(0.110988\pi\)
−0.998011 + 0.0630365i \(0.979922\pi\)
\(710\) 0 0
\(711\) 4.50092 3.90007i 0.168798 0.146264i
\(712\) 0 0
\(713\) 22.8186 + 14.4247i 0.854563 + 0.540209i
\(714\) 0 0
\(715\) −25.1718 13.7493i −0.941373 0.514195i
\(716\) 0 0
\(717\) −30.0762 + 22.5147i −1.12322 + 0.840829i
\(718\) 0 0
\(719\) 24.1459 3.47166i 0.900492 0.129471i 0.323507 0.946226i \(-0.395138\pi\)
0.576985 + 0.816755i \(0.304229\pi\)
\(720\) 0 0
\(721\) 13.0543 8.38949i 0.486168 0.312441i
\(722\) 0 0
\(723\) 1.50998 + 0.824510i 0.0561567 + 0.0306639i
\(724\) 0 0
\(725\) −0.00854574 + 31.3574i −0.000317381 + 1.16459i
\(726\) 0 0
\(727\) 6.53292 + 2.43665i 0.242292 + 0.0903704i 0.467677 0.883899i \(-0.345091\pi\)
−0.225384 + 0.974270i \(0.572364\pi\)
\(728\) 0 0
\(729\) 8.41675 28.6648i 0.311731 1.06166i
\(730\) 0 0
\(731\) −21.9223 + 48.0031i −0.810825 + 1.77546i
\(732\) 0 0
\(733\) −8.52003 39.1659i −0.314694 1.44663i −0.814335 0.580394i \(-0.802898\pi\)
0.499641 0.866233i \(-0.333465\pi\)
\(734\) 0 0
\(735\) −34.8553 + 12.9949i −1.28566 + 0.479326i
\(736\) 0 0
\(737\) 27.9887 + 27.9887i 1.03098 + 1.03098i
\(738\) 0 0
\(739\) −13.7464 + 21.3899i −0.505671 + 0.786839i −0.996427 0.0844580i \(-0.973084\pi\)
0.490756 + 0.871297i \(0.336720\pi\)
\(740\) 0 0
\(741\) −13.5060 6.16797i −0.496155 0.226586i
\(742\) 0 0
\(743\) −25.4618 46.6298i −0.934103 1.71068i −0.663807 0.747904i \(-0.731060\pi\)
−0.270296 0.962777i \(-0.587122\pi\)
\(744\) 0 0
\(745\) −2.70696 0.000368859i −0.0991752 1.35139e-5i
\(746\) 0 0
\(747\) −0.715309 10.0013i −0.0261718 0.365929i
\(748\) 0 0
\(749\) 3.48049 + 11.8535i 0.127174 + 0.433116i
\(750\) 0 0
\(751\) 4.29615 + 6.68495i 0.156769 + 0.243937i 0.910749 0.412960i \(-0.135505\pi\)
−0.753980 + 0.656897i \(0.771869\pi\)
\(752\) 0 0
\(753\) −7.59690 + 10.1483i −0.276846 + 0.369823i
\(754\) 0 0
\(755\) 25.2757 + 16.2486i 0.919877 + 0.591346i
\(756\) 0 0
\(757\) −3.05710 0.218648i −0.111112 0.00794691i 0.0156723 0.999877i \(-0.495011\pi\)
−0.126785 + 0.991930i \(0.540466\pi\)
\(758\) 0 0
\(759\) −2.39364 + 37.3947i −0.0868836 + 1.35734i
\(760\) 0 0
\(761\) −11.5470 13.3259i −0.418577 0.483063i 0.506826 0.862048i \(-0.330819\pi\)
−0.925403 + 0.378985i \(0.876273\pi\)
\(762\) 0 0
\(763\) 5.16004 + 6.89301i 0.186806 + 0.249544i
\(764\) 0 0
\(765\) −5.22588 9.57358i −0.188942 0.346134i
\(766\) 0 0
\(767\) −7.28498 1.58475i −0.263045 0.0572220i
\(768\) 0 0
\(769\) −9.57042 + 2.81013i −0.345118 + 0.101336i −0.449698 0.893181i \(-0.648468\pi\)
0.104580 + 0.994516i \(0.466650\pi\)
\(770\) 0 0
\(771\) −24.2700 + 28.0091i −0.874063 + 1.00872i
\(772\) 0 0
\(773\) 13.4734 36.1237i 0.484606 1.29928i −0.432858 0.901462i \(-0.642495\pi\)
0.917464 0.397818i \(-0.130232\pi\)
\(774\) 0 0
\(775\) 11.6848 + 25.6046i 0.419730 + 0.919744i
\(776\) 0 0
\(777\) −60.5792 + 22.5949i −2.17327 + 0.810587i
\(778\) 0 0
\(779\) −1.38130 0.887707i −0.0494902 0.0318054i
\(780\) 0 0
\(781\) 11.7052i 0.418844i
\(782\) 0 0
\(783\) −24.9846 + 24.9846i −0.892878 + 0.892878i
\(784\) 0 0
\(785\) 5.42037 24.9007i 0.193461 0.888744i
\(786\) 0 0
\(787\) −12.8124 34.3514i −0.456713 1.22449i −0.937601 0.347712i \(-0.886959\pi\)
0.480889 0.876782i \(-0.340314\pi\)
\(788\) 0 0
\(789\) 18.7614 + 5.50884i 0.667923 + 0.196120i
\(790\) 0 0
\(791\) −3.30490 7.23672i −0.117509 0.257308i
\(792\) 0 0
\(793\) 20.2651 1.44939i 0.719636 0.0514693i
\(794\) 0 0
\(795\) 1.43724 9.98658i 0.0509737 0.354187i
\(796\) 0 0
\(797\) −6.50463 + 29.9013i −0.230406 + 1.05916i 0.705993 + 0.708219i \(0.250501\pi\)
−0.936398 + 0.350939i \(0.885863\pi\)
\(798\) 0 0
\(799\) 0.667960 + 4.64576i 0.0236307 + 0.164355i
\(800\) 0 0
\(801\) 1.10410 + 0.158746i 0.0390115 + 0.00560901i
\(802\) 0 0
\(803\) −0.904328 + 12.6442i −0.0319131 + 0.446203i
\(804\) 0 0
\(805\) −3.59738 45.5922i −0.126791 1.60691i
\(806\) 0 0
\(807\) −0.789638 + 11.0406i −0.0277966 + 0.388647i
\(808\) 0 0
\(809\) −7.19238 1.03411i −0.252871 0.0363573i 0.0147137 0.999892i \(-0.495316\pi\)
−0.267584 + 0.963534i \(0.586225\pi\)
\(810\) 0 0
\(811\) −4.75480 33.0703i −0.166963 1.16126i −0.885116 0.465371i \(-0.845921\pi\)
0.718152 0.695886i \(-0.244988\pi\)
\(812\) 0 0
\(813\) −0.508934 + 2.33953i −0.0178491 + 0.0820509i
\(814\) 0 0
\(815\) 28.4240 + 37.9808i 0.995650 + 1.33041i
\(816\) 0 0
\(817\) −34.8219 + 2.49051i −1.21826 + 0.0871319i
\(818\) 0 0
\(819\) 3.41183 + 7.47087i 0.119219 + 0.261053i
\(820\) 0 0
\(821\) 27.7861 + 8.15874i 0.969742 + 0.284742i 0.727984 0.685594i \(-0.240458\pi\)
0.241759 + 0.970336i \(0.422276\pi\)
\(822\) 0 0
\(823\) 7.17527 + 19.2376i 0.250114 + 0.670582i 0.999960 + 0.00896932i \(0.00285506\pi\)
−0.749846 + 0.661613i \(0.769872\pi\)
\(824\) 0 0
\(825\) −23.4202 + 31.2679i −0.815386 + 1.08861i
\(826\) 0 0
\(827\) −21.0208 + 21.0208i −0.730964 + 0.730964i −0.970811 0.239847i \(-0.922903\pi\)
0.239847 + 0.970811i \(0.422903\pi\)
\(828\) 0 0
\(829\) 23.8762i 0.829256i −0.909991 0.414628i \(-0.863912\pi\)
0.909991 0.414628i \(-0.136088\pi\)
\(830\) 0 0
\(831\) 24.9344 + 16.0244i 0.864966 + 0.555880i
\(832\) 0 0
\(833\) −64.8125 + 24.1738i −2.24562 + 0.837573i
\(834\) 0 0
\(835\) 30.9126 2.20668i 1.06978 0.0763653i
\(836\) 0 0
\(837\) −11.0828 + 29.7140i −0.383076 + 1.02707i
\(838\) 0 0
\(839\) 1.46125 1.68637i 0.0504480 0.0582201i −0.729965 0.683485i \(-0.760464\pi\)
0.780413 + 0.625265i \(0.215009\pi\)
\(840\) 0 0
\(841\) 9.91306 2.91074i 0.341830 0.100370i
\(842\) 0 0
\(843\) −36.9685 8.04200i −1.27326 0.276981i
\(844\) 0 0
\(845\) 4.43752 15.1052i 0.152655 0.519634i
\(846\) 0 0
\(847\) 42.4496 + 56.7060i 1.45858 + 1.94844i
\(848\) 0 0
\(849\) 26.8049 + 30.9346i 0.919943 + 1.06167i
\(850\) 0 0
\(851\) −3.85280 48.7445i −0.132072 1.67094i
\(852\) 0 0
\(853\) −27.7288 1.98321i −0.949417 0.0679037i −0.411967 0.911199i \(-0.635158\pi\)
−0.537451 + 0.843295i \(0.680613\pi\)
\(854\) 0 0
\(855\) 3.90179 6.06949i 0.133438 0.207572i
\(856\) 0 0
\(857\) 12.5739 16.7968i 0.429517 0.573768i −0.532613 0.846359i \(-0.678790\pi\)
0.962130 + 0.272591i \(0.0878807\pi\)
\(858\) 0 0
\(859\) −6.69163 10.4124i −0.228316 0.355266i 0.708128 0.706084i \(-0.249540\pi\)
−0.936444 + 0.350818i \(0.885904\pi\)
\(860\) 0 0
\(861\) −0.717188 2.44252i −0.0244417 0.0832408i
\(862\) 0 0
\(863\) −1.23174 17.2219i −0.0419288 0.586241i −0.974375 0.224931i \(-0.927784\pi\)
0.932446 0.361310i \(-0.117670\pi\)
\(864\) 0 0
\(865\) 13.7804 13.7766i 0.468547 0.468419i
\(866\) 0 0
\(867\) 15.1292 + 27.7070i 0.513813 + 0.940978i
\(868\) 0 0
\(869\) −36.0827 16.4784i −1.22402 0.558992i
\(870\) 0 0
\(871\) 9.94201 15.4701i 0.336872 0.524183i
\(872\) 0 0
\(873\) 6.30848 + 6.30848i 0.213510 + 0.213510i
\(874\) 0 0
\(875\) 22.8681 41.8391i 0.773083 1.41442i
\(876\) 0 0
\(877\) 11.8532 + 54.4882i 0.400254 + 1.83994i 0.529482 + 0.848321i \(0.322386\pi\)
−0.129228 + 0.991615i \(0.541250\pi\)
\(878\) 0 0
\(879\) 4.91776 10.7684i 0.165872 0.363209i
\(880\) 0 0
\(881\) −5.85817 + 19.9511i −0.197367 + 0.672169i 0.800024 + 0.599969i \(0.204820\pi\)
−0.997390 + 0.0722003i \(0.976998\pi\)
\(882\) 0 0
\(883\) −20.9903 7.82897i −0.706379 0.263466i −0.0295049 0.999565i \(-0.509393\pi\)
−0.676874 + 0.736099i \(0.736666\pi\)
\(884\) 0 0
\(885\) −3.54995 + 9.51383i −0.119330 + 0.319804i
\(886\) 0 0
\(887\) −17.3296 9.46266i −0.581870 0.317725i 0.161218 0.986919i \(-0.448458\pi\)
−0.743088 + 0.669194i \(0.766640\pi\)
\(888\) 0 0
\(889\) −7.28158 + 4.67959i −0.244216 + 0.156948i
\(890\) 0 0
\(891\) −31.2629 + 4.49493i −1.04735 + 0.150586i
\(892\) 0 0
\(893\) −2.48565 + 1.86074i −0.0831792 + 0.0622672i
\(894\) 0 0
\(895\) 1.56314 + 5.32625i 0.0522500 + 0.178037i
\(896\) 0 0
\(897\) 17.2125 2.60628i 0.574708 0.0870212i
\(898\) 0 0
\(899\) 26.6794 23.1179i 0.889809 0.771024i
\(900\) 0 0
\(901\) 2.67012 18.5711i 0.0889546 0.618693i
\(902\) 0 0
\(903\) −43.3290 32.4357i −1.44190 1.07939i
\(904\) 0 0
\(905\) 11.8732 1.70545i 0.394678 0.0566912i
\(906\) 0 0
\(907\) −12.8017 + 23.4445i −0.425073 + 0.778463i −0.999187 0.0403122i \(-0.987165\pi\)
0.574114 + 0.818775i \(0.305347\pi\)
\(908\) 0 0
\(909\) −10.3174 8.94012i −0.342208 0.296525i
\(910\) 0 0
\(911\) 21.4398 9.79124i 0.710333 0.324398i −0.0272743 0.999628i \(-0.508683\pi\)
0.737608 + 0.675230i \(0.235955\pi\)
\(912\) 0 0
\(913\) −58.6153 + 32.0064i −1.93988 + 1.05926i
\(914\) 0 0
\(915\) 1.97790 27.6018i 0.0653874 0.912487i
\(916\) 0 0
\(917\) 80.1688 17.4397i 2.64741 0.575908i
\(918\) 0 0
\(919\) −4.33631 −0.143042 −0.0715208 0.997439i \(-0.522785\pi\)
−0.0715208 + 0.997439i \(0.522785\pi\)
\(920\) 0 0
\(921\) −13.5366 −0.446045
\(922\) 0 0
\(923\) 5.31381 1.15595i 0.174906 0.0380485i
\(924\) 0 0
\(925\) 24.4434 44.7358i 0.803695 1.47090i
\(926\) 0 0
\(927\) −2.51938 + 1.37568i −0.0827472 + 0.0451834i
\(928\) 0 0
\(929\) 45.8991 20.9614i 1.50590 0.687722i 0.519864 0.854249i \(-0.325983\pi\)
0.986037 + 0.166527i \(0.0532553\pi\)
\(930\) 0 0
\(931\) −34.5842 29.9673i −1.13345 0.982140i
\(932\) 0 0
\(933\) 3.69740 6.77128i 0.121047 0.221682i
\(934\) 0 0
\(935\) −43.5435 + 58.1508i −1.42402 + 1.90173i
\(936\) 0 0
\(937\) 25.7827 + 19.3007i 0.842285 + 0.630526i 0.930792 0.365549i \(-0.119119\pi\)
−0.0885074 + 0.996076i \(0.528210\pi\)
\(938\) 0 0
\(939\) −2.21172 + 15.3829i −0.0721768 + 0.502000i
\(940\) 0 0
\(941\) −4.14588 + 3.59242i −0.135152 + 0.117110i −0.719813 0.694168i \(-0.755773\pi\)
0.584662 + 0.811277i \(0.301227\pi\)
\(942\) 0 0
\(943\) 1.92510 0.0143940i 0.0626900 0.000468734i
\(944\) 0 0
\(945\) 51.5526 15.1296i 1.67701 0.492165i
\(946\) 0 0
\(947\) −41.2655 + 30.8910i −1.34095 + 1.00382i −0.343032 + 0.939324i \(0.611454\pi\)
−0.997918 + 0.0644983i \(0.979455\pi\)
\(948\) 0 0
\(949\) 5.82939 0.838139i 0.189230 0.0272071i
\(950\) 0 0
\(951\) 40.3232 25.9142i 1.30757 0.840324i
\(952\) 0 0
\(953\) −10.8110 5.90326i −0.350203 0.191225i 0.294513 0.955647i \(-0.404843\pi\)
−0.644716 + 0.764422i \(0.723024\pi\)
\(954\) 0 0
\(955\) −18.4528 + 8.42406i −0.597118 + 0.272596i
\(956\) 0 0
\(957\) 45.9114 + 17.1241i 1.48411 + 0.553543i
\(958\) 0 0
\(959\) −9.35792 + 31.8702i −0.302183 + 1.02914i
\(960\) 0 0
\(961\) 0.284645 0.623287i 0.00918211 0.0201060i
\(962\) 0 0
\(963\) −0.485765 2.23303i −0.0156536 0.0719583i
\(964\) 0 0
\(965\) 18.9721 + 50.8872i 0.610732 + 1.63812i
\(966\) 0 0
\(967\) 15.8904 + 15.8904i 0.511000 + 0.511000i 0.914833 0.403833i \(-0.132322\pi\)
−0.403833 + 0.914833i \(0.632322\pi\)
\(968\) 0 0
\(969\) −20.3317 + 31.6368i −0.653149 + 1.01632i
\(970\) 0 0
\(971\) 8.51859 + 3.89031i 0.273375 + 0.124846i 0.547386 0.836881i \(-0.315623\pi\)
−0.274011 + 0.961727i \(0.588350\pi\)
\(972\) 0 0
\(973\) 42.9428 + 78.6439i 1.37668 + 2.52121i
\(974\) 0 0
\(975\) 16.5076 + 7.54420i 0.528666 + 0.241608i
\(976\) 0 0
\(977\) 1.72135 + 24.0676i 0.0550709 + 0.769991i 0.947692 + 0.319185i \(0.103409\pi\)
−0.892622 + 0.450807i \(0.851136\pi\)
\(978\) 0 0
\(979\) −2.09314 7.12859i −0.0668971 0.227831i
\(980\) 0 0
\(981\) −0.861122 1.33993i −0.0274935 0.0427808i
\(982\) 0 0
\(983\) −15.6437 + 20.8976i −0.498958 + 0.666529i −0.977353 0.211615i \(-0.932128\pi\)
0.478395 + 0.878145i \(0.341219\pi\)
\(984\) 0 0
\(985\) 3.02538 + 13.9166i 0.0963966 + 0.443419i
\(986\) 0 0
\(987\) −4.80158 0.343415i −0.152836 0.0109310i
\(988\) 0 0
\(989\) 32.5836 24.7741i 1.03610 0.787771i
\(990\) 0 0
\(991\) −20.2266 23.3428i −0.642521 0.741508i 0.337298 0.941398i \(-0.390487\pi\)
−0.979818 + 0.199890i \(0.935942\pi\)
\(992\) 0 0
\(993\) 20.2047 + 26.9903i 0.641176 + 0.856510i
\(994\) 0 0
\(995\) 4.22642 + 1.24162i 0.133987 + 0.0393619i
\(996\) 0 0
\(997\) −12.2891 2.67334i −0.389201 0.0846655i 0.0137068 0.999906i \(-0.495637\pi\)
−0.402908 + 0.915241i \(0.632000\pi\)
\(998\) 0 0
\(999\) 55.1154 16.1833i 1.74377 0.512018i
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 920.2.bv.a.217.27 yes 720
5.3 odd 4 inner 920.2.bv.a.33.27 720
23.7 odd 22 inner 920.2.bv.a.697.27 yes 720
115.53 even 44 inner 920.2.bv.a.513.27 yes 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.33.27 720 5.3 odd 4 inner
920.2.bv.a.217.27 yes 720 1.1 even 1 trivial
920.2.bv.a.513.27 yes 720 115.53 even 44 inner
920.2.bv.a.697.27 yes 720 23.7 odd 22 inner