Properties

Label 592.2.bc.d.81.1
Level $592$
Weight $2$
Character 592.81
Analytic conductor $4.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [592,2,Mod(33,592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(592, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("592.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.bc (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.72714379966\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 74)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 81.1
Root \(2.00752 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 592.81
Dual form 592.2.bc.d.497.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.72328 - 0.627223i) q^{3} +(-0.326352 - 1.85083i) q^{5} +(-0.598489 - 3.39420i) q^{7} +(0.278152 + 0.233397i) q^{9} +O(q^{10})\) \(q+(-1.72328 - 0.627223i) q^{3} +(-0.326352 - 1.85083i) q^{5} +(-0.598489 - 3.39420i) q^{7} +(0.278152 + 0.233397i) q^{9} +(-1.40483 + 2.43324i) q^{11} +(-2.65877 + 2.23097i) q^{13} +(-0.598489 + 3.39420i) q^{15} +(-2.37417 - 1.99217i) q^{17} +(6.99748 + 2.54687i) q^{19} +(-1.09755 + 6.22454i) q^{21} +(-0.321769 - 0.557320i) q^{23} +(1.37939 - 0.502055i) q^{25} +(2.41787 + 4.18788i) q^{27} +(-1.08449 + 1.87840i) q^{29} -9.90716 q^{31} +(3.94710 - 3.31201i) q^{33} +(-6.08678 + 2.21541i) q^{35} +(-2.56368 + 5.51612i) q^{37} +(5.98112 - 2.17695i) q^{39} +(-8.13803 + 6.82862i) q^{41} -8.30465 q^{43} +(0.341204 - 0.590982i) q^{45} +(-3.92821 - 6.80387i) q^{47} +(-4.58455 + 1.66864i) q^{49} +(2.84183 + 4.92220i) q^{51} +(0.839394 - 4.76044i) q^{53} +(4.96199 + 1.80602i) q^{55} +(-10.4612 - 8.77795i) q^{57} +(-0.0961039 + 0.545032i) q^{59} +(5.37102 - 4.50682i) q^{61} +(0.625726 - 1.08379i) q^{63} +(4.99685 + 4.19285i) q^{65} +(-0.0366435 - 0.207815i) q^{67} +(0.204934 + 1.16224i) q^{69} +(4.75197 + 1.72957i) q^{71} +10.2297 q^{73} -2.69197 q^{75} +(9.09967 + 3.31201i) q^{77} +(0.330775 + 1.87592i) q^{79} +(-1.72910 - 9.80619i) q^{81} +(-5.21650 - 4.37717i) q^{83} +(-2.91235 + 5.04435i) q^{85} +(3.04706 - 2.55679i) q^{87} +(-1.68226 + 9.54055i) q^{89} +(9.16360 + 7.68917i) q^{91} +(17.0728 + 6.21400i) q^{93} +(2.43020 - 13.7823i) q^{95} +(-8.52990 - 14.7742i) q^{97} +(-0.958667 + 0.348926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/592\mathbb{Z}\right)^\times\).

\(n\) \(113\) \(149\) \(223\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72328 0.627223i −0.994936 0.362127i −0.207306 0.978276i \(-0.566470\pi\)
−0.787630 + 0.616149i \(0.788692\pi\)
\(4\) 0 0
\(5\) −0.326352 1.85083i −0.145949 0.827718i −0.966600 0.256289i \(-0.917500\pi\)
0.820651 0.571429i \(-0.193611\pi\)
\(6\) 0 0
\(7\) −0.598489 3.39420i −0.226208 1.28289i −0.860363 0.509681i \(-0.829763\pi\)
0.634156 0.773205i \(-0.281348\pi\)
\(8\) 0 0
\(9\) 0.278152 + 0.233397i 0.0927173 + 0.0777991i
\(10\) 0 0
\(11\) −1.40483 + 2.43324i −0.423572 + 0.733649i −0.996286 0.0861067i \(-0.972557\pi\)
0.572714 + 0.819756i \(0.305891\pi\)
\(12\) 0 0
\(13\) −2.65877 + 2.23097i −0.737409 + 0.618760i −0.932141 0.362097i \(-0.882061\pi\)
0.194731 + 0.980857i \(0.437617\pi\)
\(14\) 0 0
\(15\) −0.598489 + 3.39420i −0.154529 + 0.876378i
\(16\) 0 0
\(17\) −2.37417 1.99217i −0.575822 0.483172i 0.307750 0.951467i \(-0.400424\pi\)
−0.883572 + 0.468295i \(0.844868\pi\)
\(18\) 0 0
\(19\) 6.99748 + 2.54687i 1.60533 + 0.584293i 0.980509 0.196474i \(-0.0629492\pi\)
0.624822 + 0.780767i \(0.285171\pi\)
\(20\) 0 0
\(21\) −1.09755 + 6.22454i −0.239506 + 1.35831i
\(22\) 0 0
\(23\) −0.321769 0.557320i −0.0670934 0.116209i 0.830527 0.556978i \(-0.188039\pi\)
−0.897621 + 0.440769i \(0.854706\pi\)
\(24\) 0 0
\(25\) 1.37939 0.502055i 0.275877 0.100411i
\(26\) 0 0
\(27\) 2.41787 + 4.18788i 0.465320 + 0.805958i
\(28\) 0 0
\(29\) −1.08449 + 1.87840i −0.201385 + 0.348810i −0.948975 0.315351i \(-0.897878\pi\)
0.747590 + 0.664161i \(0.231211\pi\)
\(30\) 0 0
\(31\) −9.90716 −1.77938 −0.889690 0.456566i \(-0.849079\pi\)
−0.889690 + 0.456566i \(0.849079\pi\)
\(32\) 0 0
\(33\) 3.94710 3.31201i 0.687102 0.576547i
\(34\) 0 0
\(35\) −6.08678 + 2.21541i −1.02885 + 0.374472i
\(36\) 0 0
\(37\) −2.56368 + 5.51612i −0.421466 + 0.906844i
\(38\) 0 0
\(39\) 5.98112 2.17695i 0.957745 0.348591i
\(40\) 0 0
\(41\) −8.13803 + 6.82862i −1.27095 + 1.06645i −0.276521 + 0.961008i \(0.589182\pi\)
−0.994425 + 0.105443i \(0.966374\pi\)
\(42\) 0 0
\(43\) −8.30465 −1.26645 −0.633224 0.773969i \(-0.718269\pi\)
−0.633224 + 0.773969i \(0.718269\pi\)
\(44\) 0 0
\(45\) 0.341204 0.590982i 0.0508637 0.0880984i
\(46\) 0 0
\(47\) −3.92821 6.80387i −0.572989 0.992446i −0.996257 0.0864413i \(-0.972450\pi\)
0.423268 0.906004i \(-0.360883\pi\)
\(48\) 0 0
\(49\) −4.58455 + 1.66864i −0.654935 + 0.238377i
\(50\) 0 0
\(51\) 2.84183 + 4.92220i 0.397936 + 0.689246i
\(52\) 0 0
\(53\) 0.839394 4.76044i 0.115300 0.653897i −0.871302 0.490748i \(-0.836724\pi\)
0.986601 0.163149i \(-0.0521651\pi\)
\(54\) 0 0
\(55\) 4.96199 + 1.80602i 0.669074 + 0.243523i
\(56\) 0 0
\(57\) −10.4612 8.77795i −1.38561 1.16267i
\(58\) 0 0
\(59\) −0.0961039 + 0.545032i −0.0125117 + 0.0709572i −0.990424 0.138057i \(-0.955914\pi\)
0.977913 + 0.209014i \(0.0670254\pi\)
\(60\) 0 0
\(61\) 5.37102 4.50682i 0.687689 0.577039i −0.230553 0.973060i \(-0.574053\pi\)
0.918242 + 0.396020i \(0.129609\pi\)
\(62\) 0 0
\(63\) 0.625726 1.08379i 0.0788340 0.136545i
\(64\) 0 0
\(65\) 4.99685 + 4.19285i 0.619783 + 0.520060i
\(66\) 0 0
\(67\) −0.0366435 0.207815i −0.00447671 0.0253887i 0.982488 0.186328i \(-0.0596587\pi\)
−0.986964 + 0.160939i \(0.948548\pi\)
\(68\) 0 0
\(69\) 0.204934 + 1.16224i 0.0246711 + 0.139917i
\(70\) 0 0
\(71\) 4.75197 + 1.72957i 0.563955 + 0.205263i 0.608236 0.793756i \(-0.291877\pi\)
−0.0442811 + 0.999019i \(0.514100\pi\)
\(72\) 0 0
\(73\) 10.2297 1.19730 0.598648 0.801012i \(-0.295705\pi\)
0.598648 + 0.801012i \(0.295705\pi\)
\(74\) 0 0
\(75\) −2.69197 −0.310842
\(76\) 0 0
\(77\) 9.09967 + 3.31201i 1.03700 + 0.377438i
\(78\) 0 0
\(79\) 0.330775 + 1.87592i 0.0372151 + 0.211057i 0.997745 0.0671197i \(-0.0213809\pi\)
−0.960530 + 0.278177i \(0.910270\pi\)
\(80\) 0 0
\(81\) −1.72910 9.80619i −0.192122 1.08958i
\(82\) 0 0
\(83\) −5.21650 4.37717i −0.572586 0.480456i 0.309917 0.950764i \(-0.399699\pi\)
−0.882503 + 0.470307i \(0.844143\pi\)
\(84\) 0 0
\(85\) −2.91235 + 5.04435i −0.315889 + 0.547136i
\(86\) 0 0
\(87\) 3.04706 2.55679i 0.326679 0.274116i
\(88\) 0 0
\(89\) −1.68226 + 9.54055i −0.178319 + 1.01130i 0.755924 + 0.654659i \(0.227188\pi\)
−0.934243 + 0.356637i \(0.883923\pi\)
\(90\) 0 0
\(91\) 9.16360 + 7.68917i 0.960606 + 0.806044i
\(92\) 0 0
\(93\) 17.0728 + 6.21400i 1.77037 + 0.644361i
\(94\) 0 0
\(95\) 2.43020 13.7823i 0.249333 1.41404i
\(96\) 0 0
\(97\) −8.52990 14.7742i −0.866080 1.50009i −0.865971 0.500095i \(-0.833298\pi\)
−0.000109562 1.00000i \(-0.500035\pi\)
\(98\) 0 0
\(99\) −0.958667 + 0.348926i −0.0963497 + 0.0350684i
\(100\) 0 0
\(101\) −5.98911 10.3734i −0.595938 1.03220i −0.993414 0.114583i \(-0.963447\pi\)
0.397475 0.917613i \(-0.369886\pi\)
\(102\) 0 0
\(103\) 6.47233 11.2104i 0.637737 1.10459i −0.348191 0.937424i \(-0.613204\pi\)
0.985928 0.167170i \(-0.0534628\pi\)
\(104\) 0 0
\(105\) 11.8788 1.15925
\(106\) 0 0
\(107\) −11.9706 + 10.0445i −1.15724 + 0.971037i −0.999864 0.0165017i \(-0.994747\pi\)
−0.157374 + 0.987539i \(0.550303\pi\)
\(108\) 0 0
\(109\) −1.45663 + 0.530170i −0.139520 + 0.0507810i −0.410836 0.911709i \(-0.634763\pi\)
0.271317 + 0.962490i \(0.412541\pi\)
\(110\) 0 0
\(111\) 7.87777 7.89781i 0.747725 0.749627i
\(112\) 0 0
\(113\) 4.80629 1.74935i 0.452138 0.164565i −0.105906 0.994376i \(-0.533774\pi\)
0.558044 + 0.829811i \(0.311552\pi\)
\(114\) 0 0
\(115\) −0.926496 + 0.777422i −0.0863962 + 0.0724950i
\(116\) 0 0
\(117\) −1.26024 −0.116510
\(118\) 0 0
\(119\) −5.34090 + 9.25071i −0.489599 + 0.848011i
\(120\) 0 0
\(121\) 1.55290 + 2.68971i 0.141173 + 0.244519i
\(122\) 0 0
\(123\) 18.3072 6.66326i 1.65070 0.600806i
\(124\) 0 0
\(125\) −6.07785 10.5271i −0.543619 0.941576i
\(126\) 0 0
\(127\) 1.23207 6.98740i 0.109328 0.620032i −0.880075 0.474836i \(-0.842508\pi\)
0.989403 0.145196i \(-0.0463814\pi\)
\(128\) 0 0
\(129\) 14.3112 + 5.20886i 1.26003 + 0.458615i
\(130\) 0 0
\(131\) −13.3781 11.2256i −1.16885 0.980781i −0.168861 0.985640i \(-0.554009\pi\)
−0.999988 + 0.00485874i \(0.998453\pi\)
\(132\) 0 0
\(133\) 4.45668 25.2751i 0.386443 2.19163i
\(134\) 0 0
\(135\) 6.96199 5.84180i 0.599192 0.502782i
\(136\) 0 0
\(137\) −4.92852 + 8.53645i −0.421072 + 0.729318i −0.996045 0.0888546i \(-0.971679\pi\)
0.574973 + 0.818173i \(0.305013\pi\)
\(138\) 0 0
\(139\) 6.89049 + 5.78181i 0.584444 + 0.490407i 0.886403 0.462914i \(-0.153196\pi\)
−0.301959 + 0.953321i \(0.597641\pi\)
\(140\) 0 0
\(141\) 2.50187 + 14.1888i 0.210696 + 1.19491i
\(142\) 0 0
\(143\) −1.69337 9.60355i −0.141606 0.803089i
\(144\) 0 0
\(145\) 3.83053 + 1.39420i 0.318108 + 0.115782i
\(146\) 0 0
\(147\) 8.94707 0.737942
\(148\) 0 0
\(149\) −9.97301 −0.817021 −0.408511 0.912754i \(-0.633952\pi\)
−0.408511 + 0.912754i \(0.633952\pi\)
\(150\) 0 0
\(151\) 9.07997 + 3.30484i 0.738918 + 0.268944i 0.683935 0.729543i \(-0.260267\pi\)
0.0549831 + 0.998487i \(0.482490\pi\)
\(152\) 0 0
\(153\) −0.195414 1.10825i −0.0157983 0.0895968i
\(154\) 0 0
\(155\) 3.23322 + 18.3365i 0.259699 + 1.47282i
\(156\) 0 0
\(157\) −6.73320 5.64982i −0.537368 0.450905i 0.333269 0.942832i \(-0.391848\pi\)
−0.870637 + 0.491927i \(0.836293\pi\)
\(158\) 0 0
\(159\) −4.43236 + 7.67708i −0.351509 + 0.608832i
\(160\) 0 0
\(161\) −1.69908 + 1.42570i −0.133906 + 0.112361i
\(162\) 0 0
\(163\) 0.331175 1.87819i 0.0259397 0.147111i −0.969087 0.246719i \(-0.920648\pi\)
0.995027 + 0.0996076i \(0.0317587\pi\)
\(164\) 0 0
\(165\) −7.41812 6.22454i −0.577500 0.484580i
\(166\) 0 0
\(167\) 6.22793 + 2.26678i 0.481932 + 0.175409i 0.571550 0.820567i \(-0.306342\pi\)
−0.0896181 + 0.995976i \(0.528565\pi\)
\(168\) 0 0
\(169\) −0.165612 + 0.939235i −0.0127394 + 0.0722488i
\(170\) 0 0
\(171\) 1.35193 + 2.34161i 0.103385 + 0.179067i
\(172\) 0 0
\(173\) −23.8769 + 8.69049i −1.81533 + 0.660725i −0.819130 + 0.573608i \(0.805543\pi\)
−0.996198 + 0.0871179i \(0.972234\pi\)
\(174\) 0 0
\(175\) −2.52962 4.38143i −0.191221 0.331205i
\(176\) 0 0
\(177\) 0.507471 0.878965i 0.0381438 0.0660670i
\(178\) 0 0
\(179\) −8.12492 −0.607285 −0.303643 0.952786i \(-0.598203\pi\)
−0.303643 + 0.952786i \(0.598203\pi\)
\(180\) 0 0
\(181\) 9.12118 7.65358i 0.677972 0.568886i −0.237441 0.971402i \(-0.576309\pi\)
0.915413 + 0.402516i \(0.131864\pi\)
\(182\) 0 0
\(183\) −12.0826 + 4.39769i −0.893168 + 0.325087i
\(184\) 0 0
\(185\) 11.0461 + 2.94475i 0.812123 + 0.216502i
\(186\) 0 0
\(187\) 8.18273 2.97827i 0.598381 0.217793i
\(188\) 0 0
\(189\) 12.7674 10.7131i 0.928693 0.779266i
\(190\) 0 0
\(191\) −0.266722 −0.0192993 −0.00964965 0.999953i \(-0.503072\pi\)
−0.00964965 + 0.999953i \(0.503072\pi\)
\(192\) 0 0
\(193\) −3.96417 + 6.86615i −0.285348 + 0.494236i −0.972693 0.232094i \(-0.925442\pi\)
0.687346 + 0.726330i \(0.258776\pi\)
\(194\) 0 0
\(195\) −5.98112 10.3596i −0.428317 0.741866i
\(196\) 0 0
\(197\) 0.386805 0.140786i 0.0275587 0.0100306i −0.328204 0.944607i \(-0.606443\pi\)
0.355763 + 0.934576i \(0.384221\pi\)
\(198\) 0 0
\(199\) −1.01751 1.76239i −0.0721297 0.124932i 0.827705 0.561164i \(-0.189646\pi\)
−0.899834 + 0.436232i \(0.856313\pi\)
\(200\) 0 0
\(201\) −0.0671996 + 0.381108i −0.00473989 + 0.0268813i
\(202\) 0 0
\(203\) 7.02471 + 2.55679i 0.493038 + 0.179451i
\(204\) 0 0
\(205\) 15.2945 + 12.8336i 1.06821 + 0.896338i
\(206\) 0 0
\(207\) 0.0405763 0.230119i 0.00282024 0.0159944i
\(208\) 0 0
\(209\) −16.0274 + 13.4486i −1.10864 + 0.930259i
\(210\) 0 0
\(211\) −7.87052 + 13.6321i −0.541829 + 0.938475i 0.456970 + 0.889482i \(0.348935\pi\)
−0.998799 + 0.0489932i \(0.984399\pi\)
\(212\) 0 0
\(213\) −7.10414 5.96108i −0.486768 0.408447i
\(214\) 0 0
\(215\) 2.71024 + 15.3705i 0.184837 + 1.04826i
\(216\) 0 0
\(217\) 5.92933 + 33.6269i 0.402509 + 2.28274i
\(218\) 0 0
\(219\) −17.6286 6.41630i −1.19123 0.433573i
\(220\) 0 0
\(221\) 10.7568 0.723584
\(222\) 0 0
\(223\) 3.43531 0.230045 0.115023 0.993363i \(-0.463306\pi\)
0.115023 + 0.993363i \(0.463306\pi\)
\(224\) 0 0
\(225\) 0.500857 + 0.182297i 0.0333905 + 0.0121531i
\(226\) 0 0
\(227\) 0.401614 + 2.27767i 0.0266561 + 0.151174i 0.995231 0.0975489i \(-0.0311002\pi\)
−0.968575 + 0.248723i \(0.919989\pi\)
\(228\) 0 0
\(229\) −1.02642 5.82114i −0.0678280 0.384672i −0.999757 0.0220316i \(-0.992987\pi\)
0.931929 0.362640i \(-0.118125\pi\)
\(230\) 0 0
\(231\) −13.6039 11.4150i −0.895071 0.751054i
\(232\) 0 0
\(233\) 14.1679 24.5395i 0.928168 1.60763i 0.141782 0.989898i \(-0.454717\pi\)
0.786386 0.617736i \(-0.211950\pi\)
\(234\) 0 0
\(235\) −11.3108 + 9.49092i −0.737838 + 0.619120i
\(236\) 0 0
\(237\) 0.606600 3.44020i 0.0394029 0.223465i
\(238\) 0 0
\(239\) −18.5674 15.5799i −1.20103 1.00778i −0.999600 0.0282780i \(-0.990998\pi\)
−0.201427 0.979504i \(-0.564558\pi\)
\(240\) 0 0
\(241\) −8.31692 3.02711i −0.535740 0.194993i 0.0599594 0.998201i \(-0.480903\pi\)
−0.595700 + 0.803207i \(0.703125\pi\)
\(242\) 0 0
\(243\) −0.651791 + 3.69649i −0.0418124 + 0.237130i
\(244\) 0 0
\(245\) 4.58455 + 7.94067i 0.292896 + 0.507311i
\(246\) 0 0
\(247\) −24.2867 + 8.83962i −1.54532 + 0.562452i
\(248\) 0 0
\(249\) 6.24404 + 10.8150i 0.395700 + 0.685372i
\(250\) 0 0
\(251\) 3.29525 5.70754i 0.207994 0.360257i −0.743088 0.669193i \(-0.766640\pi\)
0.951083 + 0.308937i \(0.0999731\pi\)
\(252\) 0 0
\(253\) 1.80812 0.113676
\(254\) 0 0
\(255\) 8.18273 6.86613i 0.512422 0.429973i
\(256\) 0 0
\(257\) −9.04522 + 3.29219i −0.564225 + 0.205361i −0.608356 0.793665i \(-0.708171\pi\)
0.0441304 + 0.999026i \(0.485948\pi\)
\(258\) 0 0
\(259\) 20.2571 + 5.40031i 1.25872 + 0.335559i
\(260\) 0 0
\(261\) −0.740067 + 0.269362i −0.0458090 + 0.0166731i
\(262\) 0 0
\(263\) 1.21898 1.02284i 0.0751654 0.0630712i −0.604431 0.796658i \(-0.706599\pi\)
0.679596 + 0.733586i \(0.262155\pi\)
\(264\) 0 0
\(265\) −9.08472 −0.558070
\(266\) 0 0
\(267\) 8.88305 15.3859i 0.543634 0.941601i
\(268\) 0 0
\(269\) −11.5599 20.0223i −0.704819 1.22078i −0.966757 0.255697i \(-0.917695\pi\)
0.261938 0.965085i \(-0.415638\pi\)
\(270\) 0 0
\(271\) 0.172362 0.0627348i 0.0104703 0.00381087i −0.336780 0.941583i \(-0.609338\pi\)
0.347250 + 0.937773i \(0.387116\pi\)
\(272\) 0 0
\(273\) −10.9686 18.9982i −0.663851 1.14982i
\(274\) 0 0
\(275\) −0.716183 + 4.06167i −0.0431875 + 0.244928i
\(276\) 0 0
\(277\) 11.9260 + 4.34070i 0.716562 + 0.260807i 0.674466 0.738306i \(-0.264374\pi\)
0.0420965 + 0.999114i \(0.486596\pi\)
\(278\) 0 0
\(279\) −2.75570 2.31230i −0.164979 0.138434i
\(280\) 0 0
\(281\) 3.02774 17.1712i 0.180620 1.02435i −0.750835 0.660490i \(-0.770349\pi\)
0.931455 0.363857i \(-0.118540\pi\)
\(282\) 0 0
\(283\) 10.0612 8.44232i 0.598074 0.501844i −0.292752 0.956188i \(-0.594571\pi\)
0.890826 + 0.454345i \(0.150127\pi\)
\(284\) 0 0
\(285\) −12.8325 + 22.2266i −0.760132 + 1.31659i
\(286\) 0 0
\(287\) 28.0482 + 23.5352i 1.65563 + 1.38924i
\(288\) 0 0
\(289\) −1.28405 7.28223i −0.0755325 0.428366i
\(290\) 0 0
\(291\) 5.43268 + 30.8103i 0.318469 + 1.80613i
\(292\) 0 0
\(293\) −6.37791 2.32137i −0.372602 0.135616i 0.148930 0.988848i \(-0.452417\pi\)
−0.521532 + 0.853232i \(0.674639\pi\)
\(294\) 0 0
\(295\) 1.04013 0.0605586
\(296\) 0 0
\(297\) −13.5868 −0.788386
\(298\) 0 0
\(299\) 2.09887 + 0.763927i 0.121381 + 0.0441790i
\(300\) 0 0
\(301\) 4.97024 + 28.1876i 0.286480 + 1.62471i
\(302\) 0 0
\(303\) 3.81445 + 21.6328i 0.219135 + 1.24277i
\(304\) 0 0
\(305\) −10.0942 8.47006i −0.577993 0.484994i
\(306\) 0 0
\(307\) 4.10242 7.10560i 0.234138 0.405538i −0.724884 0.688871i \(-0.758107\pi\)
0.959022 + 0.283333i \(0.0914400\pi\)
\(308\) 0 0
\(309\) −18.1850 + 15.2591i −1.03451 + 0.868058i
\(310\) 0 0
\(311\) 1.88461 10.6882i 0.106867 0.606070i −0.883592 0.468258i \(-0.844882\pi\)
0.990458 0.137812i \(-0.0440071\pi\)
\(312\) 0 0
\(313\) −6.63058 5.56372i −0.374783 0.314480i 0.435867 0.900011i \(-0.356442\pi\)
−0.810650 + 0.585531i \(0.800886\pi\)
\(314\) 0 0
\(315\) −2.21012 0.804417i −0.124526 0.0453238i
\(316\) 0 0
\(317\) −4.41505 + 25.0390i −0.247974 + 1.40633i 0.565510 + 0.824741i \(0.308679\pi\)
−0.813484 + 0.581587i \(0.802432\pi\)
\(318\) 0 0
\(319\) −3.04706 5.27766i −0.170603 0.295492i
\(320\) 0 0
\(321\) 26.9287 9.80126i 1.50302 0.547053i
\(322\) 0 0
\(323\) −11.5394 19.9869i −0.642071 1.11210i
\(324\) 0 0
\(325\) −2.54739 + 4.41222i −0.141304 + 0.244746i
\(326\) 0 0
\(327\) 2.84271 0.157202
\(328\) 0 0
\(329\) −20.7427 + 17.4052i −1.14358 + 0.959578i
\(330\) 0 0
\(331\) −19.5470 + 7.11454i −1.07440 + 0.391050i −0.817821 0.575473i \(-0.804818\pi\)
−0.256581 + 0.966523i \(0.582596\pi\)
\(332\) 0 0
\(333\) −2.00054 + 0.935963i −0.109629 + 0.0512904i
\(334\) 0 0
\(335\) −0.372673 + 0.135642i −0.0203613 + 0.00741091i
\(336\) 0 0
\(337\) −1.89385 + 1.58913i −0.103165 + 0.0865653i −0.692911 0.721023i \(-0.743672\pi\)
0.589746 + 0.807588i \(0.299228\pi\)
\(338\) 0 0
\(339\) −9.37981 −0.509442
\(340\) 0 0
\(341\) 13.9179 24.1065i 0.753696 1.30544i
\(342\) 0 0
\(343\) −3.65547 6.33145i −0.197377 0.341866i
\(344\) 0 0
\(345\) 2.08423 0.758597i 0.112211 0.0408415i
\(346\) 0 0
\(347\) −2.92690 5.06953i −0.157124 0.272147i 0.776706 0.629863i \(-0.216889\pi\)
−0.933830 + 0.357716i \(0.883556\pi\)
\(348\) 0 0
\(349\) 0.545283 3.09246i 0.0291883 0.165535i −0.966729 0.255801i \(-0.917661\pi\)
0.995918 + 0.0902661i \(0.0287718\pi\)
\(350\) 0 0
\(351\) −15.7716 5.74039i −0.841825 0.306399i
\(352\) 0 0
\(353\) −8.61667 7.23024i −0.458619 0.384827i 0.384004 0.923332i \(-0.374545\pi\)
−0.842623 + 0.538505i \(0.818989\pi\)
\(354\) 0 0
\(355\) 1.65034 9.35955i 0.0875910 0.496753i
\(356\) 0 0
\(357\) 15.0061 12.5916i 0.794208 0.666419i
\(358\) 0 0
\(359\) −11.5467 + 19.9994i −0.609410 + 1.05553i 0.381927 + 0.924192i \(0.375260\pi\)
−0.991338 + 0.131337i \(0.958073\pi\)
\(360\) 0 0
\(361\) 27.9233 + 23.4304i 1.46965 + 1.23318i
\(362\) 0 0
\(363\) −0.989041 5.60913i −0.0519112 0.294403i
\(364\) 0 0
\(365\) −3.33848 18.9335i −0.174744 0.991023i
\(366\) 0 0
\(367\) 1.47673 + 0.537487i 0.0770848 + 0.0280566i 0.380275 0.924874i \(-0.375829\pi\)
−0.303190 + 0.952930i \(0.598052\pi\)
\(368\) 0 0
\(369\) −3.85739 −0.200808
\(370\) 0 0
\(371\) −16.6602 −0.864957
\(372\) 0 0
\(373\) −6.28835 2.28877i −0.325599 0.118508i 0.174049 0.984737i \(-0.444315\pi\)
−0.499647 + 0.866229i \(0.666537\pi\)
\(374\) 0 0
\(375\) 3.87097 + 21.9534i 0.199896 + 1.13367i
\(376\) 0 0
\(377\) −1.30723 7.41370i −0.0673260 0.381825i
\(378\) 0 0
\(379\) 8.40501 + 7.05264i 0.431737 + 0.362270i 0.832606 0.553865i \(-0.186848\pi\)
−0.400870 + 0.916135i \(0.631292\pi\)
\(380\) 0 0
\(381\) −6.50586 + 11.2685i −0.333305 + 0.577301i
\(382\) 0 0
\(383\) 19.3480 16.2349i 0.988638 0.829566i 0.00326840 0.999995i \(-0.498960\pi\)
0.985370 + 0.170429i \(0.0545152\pi\)
\(384\) 0 0
\(385\) 3.16028 17.9228i 0.161063 0.913433i
\(386\) 0 0
\(387\) −2.30995 1.93828i −0.117422 0.0985284i
\(388\) 0 0
\(389\) 10.1599 + 3.69792i 0.515130 + 0.187492i 0.586487 0.809959i \(-0.300511\pi\)
−0.0713568 + 0.997451i \(0.522733\pi\)
\(390\) 0 0
\(391\) −0.346340 + 1.96419i −0.0175152 + 0.0993334i
\(392\) 0 0
\(393\) 16.0133 + 27.7358i 0.807763 + 1.39909i
\(394\) 0 0
\(395\) 3.36406 1.22442i 0.169264 0.0616072i
\(396\) 0 0
\(397\) 5.40570 + 9.36295i 0.271304 + 0.469913i 0.969196 0.246290i \(-0.0792117\pi\)
−0.697892 + 0.716203i \(0.745878\pi\)
\(398\) 0 0
\(399\) −23.5332 + 40.7607i −1.17813 + 2.04059i
\(400\) 0 0
\(401\) −34.6974 −1.73271 −0.866353 0.499432i \(-0.833542\pi\)
−0.866353 + 0.499432i \(0.833542\pi\)
\(402\) 0 0
\(403\) 26.3408 22.1026i 1.31213 1.10101i
\(404\) 0 0
\(405\) −17.5853 + 6.40053i −0.873822 + 0.318045i
\(406\) 0 0
\(407\) −9.82049 13.9873i −0.486783 0.693322i
\(408\) 0 0
\(409\) −1.77330 + 0.645428i −0.0876840 + 0.0319144i −0.385490 0.922712i \(-0.625967\pi\)
0.297806 + 0.954627i \(0.403745\pi\)
\(410\) 0 0
\(411\) 13.8475 11.6194i 0.683046 0.573143i
\(412\) 0 0
\(413\) 1.90747 0.0938602
\(414\) 0 0
\(415\) −6.39899 + 11.0834i −0.314114 + 0.544061i
\(416\) 0 0
\(417\) −8.24777 14.2856i −0.403895 0.699566i
\(418\) 0 0
\(419\) −16.3766 + 5.96059i −0.800048 + 0.291194i −0.709507 0.704699i \(-0.751082\pi\)
−0.0905419 + 0.995893i \(0.528860\pi\)
\(420\) 0 0
\(421\) 9.07719 + 15.7222i 0.442395 + 0.766251i 0.997867 0.0652845i \(-0.0207955\pi\)
−0.555471 + 0.831536i \(0.687462\pi\)
\(422\) 0 0
\(423\) 0.495363 2.80934i 0.0240854 0.136595i
\(424\) 0 0
\(425\) −4.27508 1.55600i −0.207372 0.0754771i
\(426\) 0 0
\(427\) −18.5115 15.5330i −0.895837 0.751696i
\(428\) 0 0
\(429\) −3.10542 + 17.6117i −0.149931 + 0.850302i
\(430\) 0 0
\(431\) −21.7480 + 18.2487i −1.04756 + 0.879011i −0.992835 0.119491i \(-0.961874\pi\)
−0.0547286 + 0.998501i \(0.517429\pi\)
\(432\) 0 0
\(433\) 3.73468 6.46865i 0.179477 0.310864i −0.762224 0.647313i \(-0.775893\pi\)
0.941702 + 0.336449i \(0.109226\pi\)
\(434\) 0 0
\(435\) −5.72660 4.80519i −0.274569 0.230391i
\(436\) 0 0
\(437\) −0.832146 4.71934i −0.0398069 0.225756i
\(438\) 0 0
\(439\) 5.99873 + 34.0205i 0.286304 + 1.62371i 0.700590 + 0.713564i \(0.252920\pi\)
−0.414287 + 0.910146i \(0.635969\pi\)
\(440\) 0 0
\(441\) −1.66466 0.605885i −0.0792693 0.0288517i
\(442\) 0 0
\(443\) 2.89849 0.137712 0.0688558 0.997627i \(-0.478065\pi\)
0.0688558 + 0.997627i \(0.478065\pi\)
\(444\) 0 0
\(445\) 18.2070 0.863094
\(446\) 0 0
\(447\) 17.1863 + 6.25530i 0.812884 + 0.295866i
\(448\) 0 0
\(449\) 4.84053 + 27.4520i 0.228439 + 1.29554i 0.856002 + 0.516973i \(0.172941\pi\)
−0.627563 + 0.778566i \(0.715948\pi\)
\(450\) 0 0
\(451\) −5.18310 29.3948i −0.244063 1.38415i
\(452\) 0 0
\(453\) −13.5745 11.3903i −0.637784 0.535164i
\(454\) 0 0
\(455\) 11.2408 19.4697i 0.526978 0.912752i
\(456\) 0 0
\(457\) 7.48390 6.27974i 0.350082 0.293754i −0.450741 0.892655i \(-0.648840\pi\)
0.800823 + 0.598901i \(0.204396\pi\)
\(458\) 0 0
\(459\) 2.60251 14.7596i 0.121475 0.688917i
\(460\) 0 0
\(461\) 11.8337 + 9.92965i 0.551150 + 0.462470i 0.875330 0.483525i \(-0.160644\pi\)
−0.324180 + 0.945995i \(0.605088\pi\)
\(462\) 0 0
\(463\) 17.2009 + 6.26063i 0.799395 + 0.290956i 0.709236 0.704971i \(-0.249040\pi\)
0.0901595 + 0.995927i \(0.471262\pi\)
\(464\) 0 0
\(465\) 5.92933 33.6269i 0.274966 1.55941i
\(466\) 0 0
\(467\) 11.8035 + 20.4443i 0.546201 + 0.946048i 0.998530 + 0.0541966i \(0.0172598\pi\)
−0.452329 + 0.891851i \(0.649407\pi\)
\(468\) 0 0
\(469\) −0.683436 + 0.248750i −0.0315581 + 0.0114862i
\(470\) 0 0
\(471\) 8.05949 + 13.9594i 0.371362 + 0.643217i
\(472\) 0 0
\(473\) 11.6666 20.2072i 0.536432 0.929128i
\(474\) 0 0
\(475\) 10.9309 0.501544
\(476\) 0 0
\(477\) 1.34455 1.12821i 0.0615628 0.0516573i
\(478\) 0 0
\(479\) −8.16238 + 2.97086i −0.372949 + 0.135742i −0.521693 0.853134i \(-0.674699\pi\)
0.148744 + 0.988876i \(0.452477\pi\)
\(480\) 0 0
\(481\) −5.49006 20.3856i −0.250325 0.929502i
\(482\) 0 0
\(483\) 3.82222 1.39117i 0.173917 0.0633006i
\(484\) 0 0
\(485\) −24.5609 + 20.6090i −1.11525 + 0.935807i
\(486\) 0 0
\(487\) −20.9350 −0.948654 −0.474327 0.880349i \(-0.657309\pi\)
−0.474327 + 0.880349i \(0.657309\pi\)
\(488\) 0 0
\(489\) −1.74875 + 3.02892i −0.0790812 + 0.136973i
\(490\) 0 0
\(491\) 21.6055 + 37.4219i 0.975044 + 1.68883i 0.679791 + 0.733406i \(0.262070\pi\)
0.295253 + 0.955419i \(0.404596\pi\)
\(492\) 0 0
\(493\) 6.31686 2.29915i 0.284497 0.103548i
\(494\) 0 0
\(495\) 0.958667 + 1.66046i 0.0430889 + 0.0746321i
\(496\) 0 0
\(497\) 3.02652 17.1643i 0.135758 0.769922i
\(498\) 0 0
\(499\) −6.35892 2.31446i −0.284664 0.103609i 0.195742 0.980655i \(-0.437289\pi\)
−0.480406 + 0.877046i \(0.659511\pi\)
\(500\) 0 0
\(501\) −9.31069 7.81260i −0.415971 0.349041i
\(502\) 0 0
\(503\) 4.76565 27.0274i 0.212490 1.20509i −0.672719 0.739898i \(-0.734874\pi\)
0.885209 0.465193i \(-0.154015\pi\)
\(504\) 0 0
\(505\) −17.2449 + 14.4702i −0.767390 + 0.643917i
\(506\) 0 0
\(507\) 0.874506 1.51469i 0.0388382 0.0672697i
\(508\) 0 0
\(509\) 16.0780 + 13.4910i 0.712643 + 0.597978i 0.925339 0.379140i \(-0.123780\pi\)
−0.212696 + 0.977118i \(0.568225\pi\)
\(510\) 0 0
\(511\) −6.12236 34.7216i −0.270837 1.53599i
\(512\) 0 0
\(513\) 6.25301 + 35.4626i 0.276077 + 1.56571i
\(514\) 0 0
\(515\) −22.8608 8.32066i −1.00737 0.366652i
\(516\) 0 0
\(517\) 22.0739 0.970809
\(518\) 0 0
\(519\) 46.5975 2.04540
\(520\) 0 0
\(521\) 35.3011 + 12.8486i 1.54657 + 0.562906i 0.967610 0.252449i \(-0.0812361\pi\)
0.578961 + 0.815355i \(0.303458\pi\)
\(522\) 0 0
\(523\) −3.28508 18.6306i −0.143647 0.814660i −0.968444 0.249232i \(-0.919822\pi\)
0.824797 0.565428i \(-0.191289\pi\)
\(524\) 0 0
\(525\) 1.61111 + 9.13707i 0.0703147 + 0.398774i
\(526\) 0 0
\(527\) 23.5213 + 19.7367i 1.02460 + 0.859746i
\(528\) 0 0
\(529\) 11.2929 19.5599i 0.490997 0.850432i
\(530\) 0 0
\(531\) −0.153940 + 0.129171i −0.00668045 + 0.00560556i
\(532\) 0 0
\(533\) 6.40268 36.3114i 0.277331 1.57282i
\(534\) 0 0
\(535\) 22.4973 + 18.8775i 0.972643 + 0.816144i
\(536\) 0 0
\(537\) 14.0015 + 5.09613i 0.604210 + 0.219914i
\(538\) 0 0
\(539\) 2.38032 13.4994i 0.102528 0.581462i
\(540\) 0 0
\(541\) −8.23739 14.2676i −0.354153 0.613411i 0.632820 0.774299i \(-0.281897\pi\)
−0.986973 + 0.160888i \(0.948564\pi\)
\(542\) 0 0
\(543\) −20.5188 + 7.46825i −0.880548 + 0.320493i
\(544\) 0 0
\(545\) 1.45663 + 2.52296i 0.0623951 + 0.108072i
\(546\) 0 0
\(547\) −6.00067 + 10.3935i −0.256570 + 0.444392i −0.965321 0.261067i \(-0.915926\pi\)
0.708751 + 0.705459i \(0.249259\pi\)
\(548\) 0 0
\(549\) 2.54584 0.108654
\(550\) 0 0
\(551\) −12.3728 + 10.3820i −0.527097 + 0.442287i
\(552\) 0 0
\(553\) 6.16927 2.24543i 0.262344 0.0954855i
\(554\) 0 0
\(555\) −17.1885 12.0030i −0.729610 0.509498i
\(556\) 0 0
\(557\) 40.2026 14.6325i 1.70344 0.620001i 0.707229 0.706985i \(-0.249945\pi\)
0.996210 + 0.0869842i \(0.0277230\pi\)
\(558\) 0 0
\(559\) 22.0801 18.5274i 0.933890 0.783627i
\(560\) 0 0
\(561\) −15.9692 −0.674219
\(562\) 0 0
\(563\) 11.8738 20.5660i 0.500421 0.866754i −0.499579 0.866268i \(-0.666512\pi\)
1.00000 0.000486132i \(-0.000154741\pi\)
\(564\) 0 0
\(565\) −4.80629 8.32474i −0.202202 0.350224i
\(566\) 0 0
\(567\) −32.2493 + 11.7378i −1.35434 + 0.492941i
\(568\) 0 0
\(569\) 2.64332 + 4.57837i 0.110814 + 0.191935i 0.916099 0.400953i \(-0.131321\pi\)
−0.805285 + 0.592888i \(0.797988\pi\)
\(570\) 0 0
\(571\) 4.21057 23.8793i 0.176207 0.999318i −0.760535 0.649297i \(-0.775063\pi\)
0.936742 0.350021i \(-0.113826\pi\)
\(572\) 0 0
\(573\) 0.459636 + 0.167294i 0.0192016 + 0.00698880i
\(574\) 0 0
\(575\) −0.723648 0.607213i −0.0301782 0.0253225i
\(576\) 0 0
\(577\) −0.296836 + 1.68344i −0.0123574 + 0.0700825i −0.990363 0.138497i \(-0.955773\pi\)
0.978005 + 0.208579i \(0.0668840\pi\)
\(578\) 0 0
\(579\) 11.1380 9.34588i 0.462879 0.388402i
\(580\) 0 0
\(581\) −11.7350 + 20.3255i −0.486848 + 0.843245i
\(582\) 0 0
\(583\) 10.4041 + 8.73005i 0.430893 + 0.361562i
\(584\) 0 0
\(585\) 0.411283 + 2.33250i 0.0170044 + 0.0964370i
\(586\) 0 0
\(587\) −4.51530 25.6076i −0.186366 1.05694i −0.924187 0.381940i \(-0.875256\pi\)
0.737821 0.674997i \(-0.235855\pi\)
\(588\) 0 0
\(589\) −69.3251 25.2323i −2.85649 1.03968i
\(590\) 0 0
\(591\) −0.754877 −0.0310515
\(592\) 0 0
\(593\) 19.5933 0.804601 0.402300 0.915508i \(-0.368211\pi\)
0.402300 + 0.915508i \(0.368211\pi\)
\(594\) 0 0
\(595\) 18.8645 + 6.86613i 0.773370 + 0.281484i
\(596\) 0 0
\(597\) 0.648053 + 3.67529i 0.0265231 + 0.150420i
\(598\) 0 0
\(599\) −6.43804 36.5119i −0.263051 1.49184i −0.774528 0.632540i \(-0.782012\pi\)
0.511477 0.859297i \(-0.329099\pi\)
\(600\) 0 0
\(601\) −14.1667 11.8873i −0.577871 0.484892i 0.306376 0.951911i \(-0.400884\pi\)
−0.884247 + 0.467019i \(0.845328\pi\)
\(602\) 0 0
\(603\) 0.0383111 0.0663567i 0.00156015 0.00270226i
\(604\) 0 0
\(605\) 4.47140 3.75195i 0.181788 0.152539i
\(606\) 0 0
\(607\) −0.923385 + 5.23678i −0.0374791 + 0.212554i −0.997796 0.0663569i \(-0.978862\pi\)
0.960317 + 0.278911i \(0.0899735\pi\)
\(608\) 0 0
\(609\) −10.5019 8.81212i −0.425557 0.357085i
\(610\) 0 0
\(611\) 25.6234 + 9.32617i 1.03661 + 0.377296i
\(612\) 0 0
\(613\) 7.01848 39.8038i 0.283474 1.60766i −0.427213 0.904151i \(-0.640505\pi\)
0.710687 0.703508i \(-0.248384\pi\)
\(614\) 0 0
\(615\) −18.3072 31.7089i −0.738216 1.27863i
\(616\) 0 0
\(617\) 30.8191 11.2172i 1.24073 0.451589i 0.363470 0.931606i \(-0.381592\pi\)
0.877259 + 0.480017i \(0.159370\pi\)
\(618\) 0 0
\(619\) −2.07537 3.59465i −0.0834163 0.144481i 0.821299 0.570498i \(-0.193250\pi\)
−0.904715 + 0.426017i \(0.859916\pi\)
\(620\) 0 0
\(621\) 1.55599 2.69506i 0.0624398 0.108149i
\(622\) 0 0
\(623\) 33.3893 1.33772
\(624\) 0 0
\(625\) −11.8780 + 9.96686i −0.475122 + 0.398674i
\(626\) 0 0
\(627\) 36.0550 13.1229i 1.43990 0.524080i
\(628\) 0 0
\(629\) 17.0757 7.98893i 0.680851 0.318540i
\(630\) 0 0
\(631\) 28.1162 10.2335i 1.11929 0.407387i 0.284896 0.958559i \(-0.408041\pi\)
0.834392 + 0.551171i \(0.185819\pi\)
\(632\) 0 0
\(633\) 22.1135 18.5554i 0.878932 0.737512i
\(634\) 0 0
\(635\) −13.3346 −0.529168
\(636\) 0 0
\(637\) 8.46656 14.6645i 0.335457 0.581029i
\(638\) 0 0
\(639\) 0.918091 + 1.59018i 0.0363191 + 0.0629065i
\(640\) 0 0
\(641\) −6.42331 + 2.33789i −0.253705 + 0.0923412i −0.465742 0.884920i \(-0.654213\pi\)
0.212037 + 0.977262i \(0.431990\pi\)
\(642\) 0 0
\(643\) 18.7592 + 32.4920i 0.739792 + 1.28136i 0.952589 + 0.304262i \(0.0984097\pi\)
−0.212796 + 0.977097i \(0.568257\pi\)
\(644\) 0 0
\(645\) 4.97024 28.1876i 0.195703 1.10989i
\(646\) 0 0
\(647\) 2.48480 + 0.904395i 0.0976877 + 0.0355554i 0.390402 0.920645i \(-0.372336\pi\)
−0.292714 + 0.956200i \(0.594558\pi\)
\(648\) 0 0
\(649\) −1.19118 0.999522i −0.0467580 0.0392347i
\(650\) 0 0
\(651\) 10.8736 61.6675i 0.426172 2.41694i
\(652\) 0 0
\(653\) −34.2792 + 28.7636i −1.34145 + 1.12561i −0.360197 + 0.932876i \(0.617290\pi\)
−0.981251 + 0.192732i \(0.938265\pi\)
\(654\) 0 0
\(655\) −16.4107 + 28.4241i −0.641218 + 1.11062i
\(656\) 0 0
\(657\) 2.84541 + 2.38758i 0.111010 + 0.0931485i
\(658\) 0 0
\(659\) 0.790306 + 4.48205i 0.0307859 + 0.174596i 0.996324 0.0856667i \(-0.0273020\pi\)
−0.965538 + 0.260262i \(0.916191\pi\)
\(660\) 0 0
\(661\) −7.56467 42.9014i −0.294231 1.66867i −0.670310 0.742082i \(-0.733839\pi\)
0.376078 0.926588i \(-0.377272\pi\)
\(662\) 0 0
\(663\) −18.5371 6.74694i −0.719919 0.262029i
\(664\) 0 0
\(665\) −48.2344 −1.87045
\(666\) 0 0
\(667\) 1.39582 0.0540465
\(668\) 0 0
\(669\) −5.92000 2.15470i −0.228880 0.0833057i
\(670\) 0 0
\(671\) 3.42080 + 19.4003i 0.132058 + 0.748940i
\(672\) 0 0
\(673\) 6.60813 + 37.4766i 0.254725 + 1.44462i 0.796778 + 0.604272i \(0.206536\pi\)
−0.542053 + 0.840344i \(0.682353\pi\)
\(674\) 0 0
\(675\) 5.43772 + 4.56279i 0.209298 + 0.175622i
\(676\) 0 0
\(677\) −22.0131 + 38.1278i −0.846032 + 1.46537i 0.0386894 + 0.999251i \(0.487682\pi\)
−0.884722 + 0.466120i \(0.845652\pi\)
\(678\) 0 0
\(679\) −45.0416 + 37.7944i −1.72854 + 1.45042i
\(680\) 0 0
\(681\) 0.736510 4.17696i 0.0282231 0.160061i
\(682\) 0 0
\(683\) −14.4021 12.0848i −0.551081 0.462412i 0.324226 0.945980i \(-0.394896\pi\)
−0.875307 + 0.483568i \(0.839341\pi\)
\(684\) 0 0
\(685\) 17.4080 + 6.33598i 0.665125 + 0.242086i
\(686\) 0 0
\(687\) −1.88233 + 10.6752i −0.0718155 + 0.407286i
\(688\) 0 0
\(689\) 8.38865 + 14.5296i 0.319582 + 0.553532i
\(690\) 0 0
\(691\) 25.3128 9.21310i 0.962944 0.350483i 0.187757 0.982215i \(-0.439878\pi\)
0.775186 + 0.631733i \(0.217656\pi\)
\(692\) 0 0
\(693\) 1.75808 + 3.04508i 0.0667838 + 0.115673i
\(694\) 0 0
\(695\) 8.45244 14.6401i 0.320619 0.555329i
\(696\) 0 0
\(697\) 32.9248 1.24712
\(698\) 0 0
\(699\) −39.8069 + 33.4020i −1.50564 + 1.26338i
\(700\) 0 0
\(701\) −6.98332 + 2.54172i −0.263756 + 0.0959995i −0.470513 0.882393i \(-0.655931\pi\)
0.206757 + 0.978392i \(0.433709\pi\)
\(702\) 0 0
\(703\) −31.9881 + 32.0695i −1.20646 + 1.20953i
\(704\) 0 0
\(705\) 25.4447 9.26110i 0.958302 0.348793i
\(706\) 0 0
\(707\) −31.6251 + 26.5366i −1.18938 + 0.998012i
\(708\) 0 0
\(709\) 0.834473 0.0313393 0.0156697 0.999877i \(-0.495012\pi\)
0.0156697 + 0.999877i \(0.495012\pi\)
\(710\) 0 0
\(711\) −0.345828 + 0.598992i −0.0129696 + 0.0224640i
\(712\) 0 0
\(713\) 3.18781 + 5.52146i 0.119385 + 0.206780i
\(714\) 0 0
\(715\) −17.2219 + 6.26827i −0.644064 + 0.234420i
\(716\) 0 0
\(717\) 22.2248 + 38.4945i 0.830000 + 1.43760i
\(718\) 0 0
\(719\) 0.874879 4.96169i 0.0326275 0.185040i −0.964138 0.265400i \(-0.914496\pi\)
0.996766 + 0.0803603i \(0.0256071\pi\)
\(720\) 0 0
\(721\) −41.9239 15.2591i −1.56133 0.568277i
\(722\) 0 0
\(723\) 12.4337 + 10.4331i 0.462415 + 0.388012i
\(724\) 0 0
\(725\) −0.552875 + 3.13551i −0.0205333 + 0.116450i
\(726\) 0 0
\(727\) −14.2591 + 11.9648i −0.528842 + 0.443751i −0.867701 0.497086i \(-0.834403\pi\)
0.338860 + 0.940837i \(0.389959\pi\)
\(728\) 0 0
\(729\) −11.4945 + 19.9090i −0.425720 + 0.737369i
\(730\) 0 0
\(731\) 19.7167 + 16.5443i 0.729248 + 0.611912i
\(732\) 0 0
\(733\) 0.797139 + 4.52080i 0.0294430 + 0.166980i 0.995984 0.0895332i \(-0.0285375\pi\)
−0.966541 + 0.256513i \(0.917426\pi\)
\(734\) 0 0
\(735\) −2.91989 16.5595i −0.107702 0.610807i
\(736\) 0 0
\(737\) 0.557142 + 0.202783i 0.0205226 + 0.00746961i
\(738\) 0 0
\(739\) 46.9098 1.72560 0.862802 0.505542i \(-0.168708\pi\)
0.862802 + 0.505542i \(0.168708\pi\)
\(740\) 0 0
\(741\) 47.3971 1.74118
\(742\) 0 0
\(743\) 4.69037 + 1.70716i 0.172073 + 0.0626295i 0.426620 0.904431i \(-0.359704\pi\)
−0.254547 + 0.967060i \(0.581926\pi\)
\(744\) 0 0
\(745\) 3.25471 + 18.4584i 0.119243 + 0.676263i
\(746\) 0 0
\(747\) −0.429362 2.43503i −0.0157095 0.0890932i
\(748\) 0 0
\(749\) 41.2572 + 34.6189i 1.50751 + 1.26495i
\(750\) 0 0
\(751\) 9.41422 16.3059i 0.343530 0.595011i −0.641556 0.767077i \(-0.721711\pi\)
0.985086 + 0.172065i \(0.0550440\pi\)
\(752\) 0 0
\(753\) −9.25853 + 7.76883i −0.337400 + 0.283112i
\(754\) 0 0
\(755\) 3.15344 17.8841i 0.114766 0.650867i
\(756\) 0 0
\(757\) 0.598778 + 0.502435i 0.0217630 + 0.0182613i 0.653604 0.756837i \(-0.273256\pi\)
−0.631841 + 0.775098i \(0.717701\pi\)
\(758\) 0 0
\(759\) −3.11590 1.13409i −0.113100 0.0411650i
\(760\) 0 0
\(761\) −5.27399 + 29.9103i −0.191182 + 1.08425i 0.726570 + 0.687092i \(0.241113\pi\)
−0.917752 + 0.397154i \(0.869998\pi\)
\(762\) 0 0
\(763\) 2.67128 + 4.62679i 0.0967067 + 0.167501i
\(764\) 0 0
\(765\) −1.98741 + 0.723359i −0.0718551 + 0.0261531i
\(766\) 0 0
\(767\) −0.960433 1.66352i −0.0346792 0.0600662i
\(768\) 0 0
\(769\) 7.98228 13.8257i 0.287848 0.498568i −0.685448 0.728122i \(-0.740393\pi\)
0.973296 + 0.229554i \(0.0737268\pi\)
\(770\) 0 0
\(771\) 17.6524 0.635735
\(772\) 0 0
\(773\) 20.2985 17.0324i 0.730086 0.612615i −0.200069 0.979782i \(-0.564117\pi\)
0.930155 + 0.367167i \(0.119672\pi\)
\(774\) 0 0
\(775\) −13.6658 + 4.97394i −0.490890 + 0.178669i
\(776\) 0 0
\(777\) −31.5215 22.0120i −1.13083 0.789675i
\(778\) 0 0
\(779\) −74.3373 + 27.0566i −2.66341 + 0.969402i
\(780\) 0 0
\(781\) −10.8842 + 9.13291i −0.389466 + 0.326801i
\(782\) 0 0
\(783\) −10.4887 −0.374834
\(784\) 0 0
\(785\) −8.25949 + 14.3059i −0.294794 + 0.510598i
\(786\) 0 0
\(787\) −24.1869 41.8930i −0.862171 1.49332i −0.869829 0.493353i \(-0.835771\pi\)
0.00765866 0.999971i \(-0.497562\pi\)
\(788\) 0 0
\(789\) −2.74219 + 0.998076i −0.0976246 + 0.0355324i
\(790\) 0 0
\(791\) −8.81414 15.2665i −0.313395 0.542816i
\(792\) 0 0
\(793\) −4.22571 + 23.9652i −0.150059 + 0.851029i
\(794\) 0 0
\(795\) 15.6555 + 5.69814i 0.555244 + 0.202092i
\(796\) 0 0
\(797\) 18.1488 + 15.2286i 0.642863 + 0.539426i 0.904896 0.425633i \(-0.139948\pi\)
−0.262033 + 0.965059i \(0.584393\pi\)
\(798\) 0 0
\(799\) −4.22818 + 23.9792i −0.149582 + 0.848324i
\(800\) 0 0
\(801\) −2.69466 + 2.26109i −0.0952112 + 0.0798917i
\(802\) 0 0
\(803\) −14.3710 + 24.8913i −0.507141 + 0.878395i
\(804\) 0 0
\(805\) 3.19322 + 2.67943i 0.112546 + 0.0944376i
\(806\) 0 0
\(807\) 7.36248 + 41.7547i 0.259171 + 1.46983i
\(808\) 0 0
\(809\) 0.138317 + 0.784433i 0.00486295 + 0.0275792i 0.987143 0.159842i \(-0.0510983\pi\)
−0.982280 + 0.187421i \(0.939987\pi\)
\(810\) 0 0
\(811\) 13.0191 + 4.73855i 0.457161 + 0.166393i 0.560328 0.828271i \(-0.310675\pi\)
−0.103166 + 0.994664i \(0.532897\pi\)
\(812\) 0 0
\(813\) −0.336377 −0.0117973
\(814\) 0 0
\(815\) −3.58429 −0.125552
\(816\) 0 0
\(817\) −58.1116 21.1509i −2.03307 0.739976i
\(818\) 0 0
\(819\) 0.754242 + 4.27752i 0.0263553 + 0.149469i
\(820\) 0 0
\(821\) −3.79631 21.5300i −0.132492 0.751401i −0.976573 0.215185i \(-0.930965\pi\)
0.844081 0.536216i \(-0.180147\pi\)
\(822\) 0 0
\(823\) −26.4467 22.1914i −0.921873 0.773544i 0.0524672 0.998623i \(-0.483292\pi\)
−0.974341 + 0.225079i \(0.927736\pi\)
\(824\) 0 0
\(825\) 3.78176 6.55020i 0.131664 0.228049i
\(826\) 0 0
\(827\) −3.04336 + 2.55369i −0.105828 + 0.0888003i −0.694166 0.719815i \(-0.744227\pi\)
0.588338 + 0.808615i \(0.299782\pi\)
\(828\) 0 0
\(829\) −2.91749 + 16.5459i −0.101329 + 0.574664i 0.891295 + 0.453425i \(0.149798\pi\)
−0.992623 + 0.121239i \(0.961313\pi\)
\(830\) 0 0
\(831\) −17.8292 14.9605i −0.618488 0.518973i
\(832\) 0 0
\(833\) 14.2087 + 5.17155i 0.492303 + 0.179184i
\(834\) 0 0
\(835\) 2.16294 12.2666i 0.0748515 0.424504i
\(836\) 0 0
\(837\) −23.9543 41.4900i −0.827980 1.43410i
\(838\) 0 0
\(839\) 6.33057 2.30414i 0.218556 0.0795478i −0.230422 0.973091i \(-0.574011\pi\)
0.448977 + 0.893543i \(0.351788\pi\)
\(840\) 0 0
\(841\) 12.1477 + 21.0405i 0.418888 + 0.725535i
\(842\) 0 0
\(843\) −15.9878 + 27.6917i −0.550649 + 0.953752i
\(844\) 0 0
\(845\) 1.79241 0.0616609
\(846\) 0 0
\(847\) 8.20000 6.88062i 0.281755 0.236421i
\(848\) 0 0
\(849\) −22.6334 + 8.23789i −0.776777 + 0.282724i
\(850\) 0 0
\(851\) 3.89915 0.346124i 0.133661 0.0118650i
\(852\) 0 0
\(853\) −40.3273 + 14.6779i −1.38078 + 0.502563i −0.922415 0.386201i \(-0.873787\pi\)
−0.458365 + 0.888764i \(0.651565\pi\)
\(854\) 0 0
\(855\) 3.89272 3.26638i 0.133128 0.111708i
\(856\) 0 0
\(857\) −27.6910 −0.945906 −0.472953 0.881088i \(-0.656812\pi\)
−0.472953 + 0.881088i \(0.656812\pi\)
\(858\) 0 0
\(859\) 9.42711 16.3282i 0.321649 0.557112i −0.659179 0.751986i \(-0.729096\pi\)
0.980828 + 0.194873i \(0.0624296\pi\)
\(860\) 0 0
\(861\) −33.5731 58.1503i −1.14417 1.98176i
\(862\) 0 0
\(863\) 28.0177 10.1976i 0.953734 0.347131i 0.182159 0.983269i \(-0.441691\pi\)
0.771575 + 0.636138i \(0.219469\pi\)
\(864\) 0 0
\(865\) 23.8769 + 41.3560i 0.811839 + 1.40615i
\(866\) 0 0
\(867\) −2.35479 + 13.3547i −0.0799730 + 0.453549i
\(868\) 0 0
\(869\) −5.02924 1.83049i −0.170605 0.0620952i
\(870\) 0 0
\(871\) 0.561057 + 0.470782i 0.0190107 + 0.0159519i
\(872\) 0 0
\(873\) 1.07565 6.10033i 0.0364053 0.206465i
\(874\) 0 0
\(875\) −32.0937 + 26.9298i −1.08496 + 0.910393i
\(876\) 0 0
\(877\) −2.11792 + 3.66834i −0.0715170 + 0.123871i −0.899566 0.436784i \(-0.856117\pi\)
0.828049 + 0.560655i \(0.189451\pi\)
\(878\) 0 0
\(879\) 9.53491 + 8.00074i 0.321605 + 0.269858i
\(880\) 0 0
\(881\) 1.14459 + 6.49127i 0.0385621 + 0.218697i 0.997999 0.0632261i \(-0.0201389\pi\)
−0.959437 + 0.281923i \(0.909028\pi\)
\(882\) 0 0
\(883\) 2.14960 + 12.1910i 0.0723397 + 0.410259i 0.999377 + 0.0352901i \(0.0112355\pi\)
−0.927037 + 0.374969i \(0.877653\pi\)
\(884\) 0 0
\(885\) −1.79243 0.652392i −0.0602519 0.0219299i
\(886\) 0 0
\(887\) 25.0422 0.840833 0.420417 0.907331i \(-0.361884\pi\)
0.420417 + 0.907331i \(0.361884\pi\)
\(888\) 0 0
\(889\) −24.4540 −0.820161
\(890\) 0 0
\(891\) 26.2899 + 9.56873i 0.880744 + 0.320565i
\(892\) 0 0
\(893\) −10.1590 57.6146i −0.339958 1.92800i
\(894\) 0 0
\(895\) 2.65158 + 15.0379i 0.0886326 + 0.502661i
\(896\) 0 0
\(897\) −3.13779 2.63292i −0.104768 0.0879106i
\(898\) 0 0
\(899\) 10.7443 18.6096i 0.358341 0.620665i
\(900\) 0 0
\(901\) −11.4765 + 9.62989i −0.382336 + 0.320818i
\(902\) 0 0
\(903\) 9.11481 51.6926i 0.303322 1.72022i
\(904\) 0 0
\(905\) −17.1422 14.3840i −0.569826 0.478141i
\(906\) 0 0
\(907\) −54.3968 19.7988i −1.80622 0.657409i −0.997613 0.0690533i \(-0.978002\pi\)
−0.808602 0.588355i \(-0.799776\pi\)
\(908\) 0 0
\(909\) 0.755249 4.28323i 0.0250500 0.142066i
\(910\) 0 0
\(911\) −4.18373 7.24644i −0.138613 0.240085i 0.788359 0.615216i \(-0.210931\pi\)
−0.926972 + 0.375131i \(0.877598\pi\)
\(912\) 0 0
\(913\) 17.9790 6.54382i 0.595018 0.216569i
\(914\) 0 0
\(915\) 12.0826 + 20.9276i 0.399437 + 0.691845i
\(916\) 0 0
\(917\) −30.0951 + 52.1263i −0.993828 + 1.72136i
\(918\) 0 0
\(919\) −3.64798 −0.120336 −0.0601678 0.998188i \(-0.519164\pi\)
−0.0601678 + 0.998188i \(0.519164\pi\)
\(920\) 0 0
\(921\) −11.5264 + 9.67181i −0.379808 + 0.318697i
\(922\) 0 0
\(923\) −16.4930 + 6.00296i −0.542874 + 0.197590i
\(924\) 0 0
\(925\) −0.766908 + 8.89596i −0.0252158 + 0.292497i
\(926\) 0 0
\(927\) 4.41677 1.60757i 0.145066 0.0527996i
\(928\) 0 0
\(929\) 40.7198 34.1679i 1.33597 1.12101i 0.353331 0.935498i \(-0.385049\pi\)
0.982641 0.185516i \(-0.0593956\pi\)
\(930\) 0 0
\(931\) −36.3301 −1.19067
\(932\) 0 0
\(933\) −9.95157 + 17.2366i −0.325800 + 0.564302i
\(934\) 0 0
\(935\) −8.18273 14.1729i −0.267604 0.463504i
\(936\) 0 0
\(937\) −0.433752 + 0.157873i −0.0141701 + 0.00515748i −0.349095 0.937087i \(-0.613511\pi\)
0.334925 + 0.942245i \(0.391289\pi\)
\(938\) 0 0
\(939\) 7.93666 + 13.7467i 0.259003 + 0.448607i
\(940\) 0 0
\(941\) 7.83670 44.4441i 0.255469 1.44884i −0.539396 0.842052i \(-0.681347\pi\)
0.794865 0.606786i \(-0.207541\pi\)
\(942\) 0 0
\(943\) 6.42429 + 2.33825i 0.209204 + 0.0761439i
\(944\) 0 0
\(945\) −23.9949 20.1341i −0.780554 0.654963i
\(946\) 0 0
\(947\) 0.192264 1.09038i 0.00624773 0.0354326i −0.981525 0.191336i \(-0.938718\pi\)
0.987772 + 0.155904i \(0.0498290\pi\)
\(948\) 0 0
\(949\) −27.1984 + 22.8222i −0.882897 + 0.740839i
\(950\) 0 0
\(951\) 23.3134 40.3799i 0.755988 1.30941i
\(952\) 0 0
\(953\) −3.46116 2.90426i −0.112118 0.0940782i 0.585005 0.811030i \(-0.301092\pi\)
−0.697123 + 0.716951i \(0.745537\pi\)
\(954\) 0 0
\(955\) 0.0870451 + 0.493657i 0.00281671 + 0.0159744i
\(956\) 0 0
\(957\) 1.94067 + 11.0061i 0.0627329 + 0.355776i
\(958\) 0 0
\(959\) 31.9241 + 11.6194i 1.03088 + 0.375210i
\(960\) 0 0
\(961\) 67.1519 2.16619
\(962\) 0 0
\(963\) −5.67399 −0.182842
\(964\) 0 0
\(965\) 14.0018 + 5.09624i 0.450734 + 0.164054i
\(966\) 0 0
\(967\) 5.99944 + 34.0245i 0.192929 + 1.09415i 0.915338 + 0.402688i \(0.131924\pi\)
−0.722409 + 0.691466i \(0.756965\pi\)
\(968\) 0 0
\(969\) 7.34944 + 41.6808i 0.236098 + 1.33898i
\(970\) 0 0
\(971\) 7.54292 + 6.32926i 0.242064 + 0.203116i 0.755746 0.654865i \(-0.227274\pi\)
−0.513682 + 0.857981i \(0.671719\pi\)
\(972\) 0 0
\(973\) 15.5007 26.8481i 0.496931 0.860709i
\(974\) 0 0
\(975\) 7.15731 6.00570i 0.229218 0.192336i
\(976\) 0 0
\(977\) 6.85364 38.8689i 0.219267 1.24353i −0.654079 0.756427i \(-0.726943\pi\)
0.873346 0.487100i \(-0.161945\pi\)
\(978\) 0 0
\(979\) −20.8512 17.4962i −0.666406 0.559181i
\(980\) 0 0
\(981\) −0.528904 0.192505i −0.0168866 0.00614622i
\(982\) 0 0
\(983\) −2.68903 + 15.2502i −0.0857666 + 0.486407i 0.911422 + 0.411473i \(0.134986\pi\)
−0.997189 + 0.0749336i \(0.976126\pi\)
\(984\) 0 0
\(985\) −0.386805 0.669966i −0.0123246 0.0213469i
\(986\) 0 0
\(987\) 46.6624 16.9837i 1.48528 0.540597i
\(988\) 0 0
\(989\) 2.67218 + 4.62834i 0.0849703 + 0.147173i
\(990\) 0 0
\(991\) 2.60235 4.50740i 0.0826663 0.143182i −0.821728 0.569880i \(-0.806990\pi\)
0.904394 + 0.426698i \(0.140323\pi\)
\(992\) 0 0
\(993\) 38.1474 1.21057
\(994\) 0 0
\(995\) −2.92982 + 2.45841i −0.0928814 + 0.0779367i
\(996\) 0 0
\(997\) −35.0496 + 12.7570i −1.11003 + 0.404018i −0.831005 0.556265i \(-0.812234\pi\)
−0.279026 + 0.960284i \(0.590012\pi\)
\(998\) 0 0
\(999\) −29.2995 + 2.60089i −0.926994 + 0.0822884i
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 592.2.bc.d.81.1 12
4.3 odd 2 74.2.f.b.7.2 12
12.11 even 2 666.2.x.g.451.2 12
37.16 even 9 inner 592.2.bc.d.497.1 12
148.107 odd 18 2738.2.a.t.1.2 6
148.115 odd 18 2738.2.a.q.1.2 6
148.127 odd 18 74.2.f.b.53.2 yes 12
444.275 even 18 666.2.x.g.127.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.f.b.7.2 12 4.3 odd 2
74.2.f.b.53.2 yes 12 148.127 odd 18
592.2.bc.d.81.1 12 1.1 even 1 trivial
592.2.bc.d.497.1 12 37.16 even 9 inner
666.2.x.g.127.2 12 444.275 even 18
666.2.x.g.451.2 12 12.11 even 2
2738.2.a.q.1.2 6 148.115 odd 18
2738.2.a.t.1.2 6 148.107 odd 18