Properties

Label 432.2.u.b.337.2
Level $432$
Weight $2$
Character 432.337
Analytic conductor $3.450$
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] = [432,2,Mod(49,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.u (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: \(3.44953736732\)
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: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} - 1584 x^{3} + 936 x^{2} - 342 x + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 337.2
Root \(0.500000 - 1.74095i\) of defining polynomial
Character \(\chi\) \(=\) 432.337
Dual form 432.2.u.b.241.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.140451 + 1.72635i) q^{3} +(2.42692 + 2.03643i) q^{5} +(3.46344 + 1.26059i) q^{7} +(-2.96055 - 0.484935i) q^{9} +O(q^{10})\) \(q+(-0.140451 + 1.72635i) q^{3} +(2.42692 + 2.03643i) q^{5} +(3.46344 + 1.26059i) q^{7} +(-2.96055 - 0.484935i) q^{9} +(1.75046 - 1.46881i) q^{11} +(0.538357 - 3.05317i) q^{13} +(-3.85644 + 3.90368i) q^{15} +(-0.862878 + 1.49455i) q^{17} +(-1.69740 - 2.93998i) q^{19} +(-2.66266 + 5.80205i) q^{21} +(-3.15087 + 1.14682i) q^{23} +(0.874658 + 4.96043i) q^{25} +(1.25298 - 5.04282i) q^{27} +(-0.101661 - 0.576550i) q^{29} +(-4.35827 + 1.58628i) q^{31} +(2.28983 + 3.22820i) q^{33} +(5.83839 + 10.1124i) q^{35} +(3.65360 - 6.32822i) q^{37} +(5.19523 + 1.35821i) q^{39} +(-1.22952 + 6.97295i) q^{41} +(-1.27004 + 1.06569i) q^{43} +(-6.19747 - 7.20583i) q^{45} +(-3.61968 - 1.31746i) q^{47} +(5.04404 + 4.23245i) q^{49} +(-2.45892 - 1.69954i) q^{51} -2.58267 q^{53} +7.23936 q^{55} +(5.31383 - 2.51737i) q^{57} +(7.40243 + 6.21138i) q^{59} +(-12.3018 - 4.47750i) q^{61} +(-9.64238 - 5.41158i) q^{63} +(7.52411 - 6.31348i) q^{65} +(1.49490 - 8.47798i) q^{67} +(-1.53727 - 5.60057i) q^{69} +(0.993732 - 1.72119i) q^{71} +(-5.32371 - 9.22094i) q^{73} +(-8.68627 + 0.813264i) q^{75} +(7.91420 - 2.88053i) q^{77} +(-2.44726 - 13.8791i) q^{79} +(8.52968 + 2.87135i) q^{81} +(0.538035 + 3.05135i) q^{83} +(-5.13767 + 1.86996i) q^{85} +(1.00960 - 0.0945255i) q^{87} +(8.67300 + 15.0221i) q^{89} +(5.71337 - 9.89585i) q^{91} +(-2.12635 - 7.74668i) q^{93} +(1.86760 - 10.5917i) q^{95} +(7.04084 - 5.90797i) q^{97} +(-5.89461 + 3.49963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{45} + 9 q^{47} - 39 q^{49} + 27 q^{51} - 12 q^{53} - 18 q^{55} + 18 q^{57} - 12 q^{59} - 36 q^{61} - 3 q^{63} - 15 q^{65} - 36 q^{67} + 18 q^{69} - 12 q^{71} - 21 q^{73} - 30 q^{75} + 3 q^{77} - 39 q^{79} - 18 q^{83} + 45 q^{85} - 27 q^{87} + 12 q^{89} + 6 q^{91} - 33 q^{93} + 15 q^{95} + 39 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\)

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
\(3\) −0.140451 + 1.72635i −0.0810896 + 0.996707i
\(4\) 0 0
\(5\) 2.42692 + 2.03643i 1.08535 + 0.910717i 0.996354 0.0853149i \(-0.0271896\pi\)
0.0889963 + 0.996032i \(0.471634\pi\)
\(6\) 0 0
\(7\) 3.46344 + 1.26059i 1.30906 + 0.476458i 0.899936 0.436021i \(-0.143613\pi\)
0.409122 + 0.912480i \(0.365835\pi\)
\(8\) 0 0
\(9\) −2.96055 0.484935i −0.986849 0.161645i
\(10\) 0 0
\(11\) 1.75046 1.46881i 0.527785 0.442864i −0.339551 0.940588i \(-0.610275\pi\)
0.867336 + 0.497724i \(0.165831\pi\)
\(12\) 0 0
\(13\) 0.538357 3.05317i 0.149313 0.846798i −0.814489 0.580179i \(-0.802982\pi\)
0.963802 0.266619i \(-0.0859065\pi\)
\(14\) 0 0
\(15\) −3.85644 + 3.90368i −0.995728 + 1.00793i
\(16\) 0 0
\(17\) −0.862878 + 1.49455i −0.209279 + 0.362481i −0.951487 0.307687i \(-0.900445\pi\)
0.742209 + 0.670169i \(0.233778\pi\)
\(18\) 0 0
\(19\) −1.69740 2.93998i −0.389410 0.674478i 0.602960 0.797771i \(-0.293988\pi\)
−0.992370 + 0.123293i \(0.960654\pi\)
\(20\) 0 0
\(21\) −2.66266 + 5.80205i −0.581040 + 1.26611i
\(22\) 0 0
\(23\) −3.15087 + 1.14682i −0.657002 + 0.239129i −0.648942 0.760838i \(-0.724788\pi\)
−0.00806071 + 0.999968i \(0.502566\pi\)
\(24\) 0 0
\(25\) 0.874658 + 4.96043i 0.174932 + 0.992086i
\(26\) 0 0
\(27\) 1.25298 5.04282i 0.241136 0.970491i
\(28\) 0 0
\(29\) −0.101661 0.576550i −0.0188780 0.107063i 0.973913 0.226923i \(-0.0728665\pi\)
−0.992791 + 0.119860i \(0.961755\pi\)
\(30\) 0 0
\(31\) −4.35827 + 1.58628i −0.782769 + 0.284904i −0.702327 0.711855i \(-0.747855\pi\)
−0.0804420 + 0.996759i \(0.525633\pi\)
\(32\) 0 0
\(33\) 2.28983 + 3.22820i 0.398608 + 0.561958i
\(34\) 0 0
\(35\) 5.83839 + 10.1124i 0.986868 + 1.70931i
\(36\) 0 0
\(37\) 3.65360 6.32822i 0.600648 1.04035i −0.392075 0.919933i \(-0.628243\pi\)
0.992723 0.120420i \(-0.0384240\pi\)
\(38\) 0 0
\(39\) 5.19523 + 1.35821i 0.831902 + 0.217488i
\(40\) 0 0
\(41\) −1.22952 + 6.97295i −0.192019 + 1.08899i 0.724582 + 0.689188i \(0.242033\pi\)
−0.916601 + 0.399803i \(0.869078\pi\)
\(42\) 0 0
\(43\) −1.27004 + 1.06569i −0.193679 + 0.162516i −0.734470 0.678641i \(-0.762569\pi\)
0.540791 + 0.841157i \(0.318125\pi\)
\(44\) 0 0
\(45\) −6.19747 7.20583i −0.923864 1.07418i
\(46\) 0 0
\(47\) −3.61968 1.31746i −0.527984 0.192171i 0.0642537 0.997934i \(-0.479533\pi\)
−0.592238 + 0.805763i \(0.701756\pi\)
\(48\) 0 0
\(49\) 5.04404 + 4.23245i 0.720577 + 0.604636i
\(50\) 0 0
\(51\) −2.45892 1.69954i −0.344317 0.237983i
\(52\) 0 0
\(53\) −2.58267 −0.354757 −0.177379 0.984143i \(-0.556762\pi\)
−0.177379 + 0.984143i \(0.556762\pi\)
\(54\) 0 0
\(55\) 7.23936 0.976155
\(56\) 0 0
\(57\) 5.31383 2.51737i 0.703834 0.333434i
\(58\) 0 0
\(59\) 7.40243 + 6.21138i 0.963714 + 0.808652i 0.981553 0.191188i \(-0.0612342\pi\)
−0.0178389 + 0.999841i \(0.505679\pi\)
\(60\) 0 0
\(61\) −12.3018 4.47750i −1.57509 0.573285i −0.600960 0.799279i \(-0.705215\pi\)
−0.974129 + 0.225994i \(0.927437\pi\)
\(62\) 0 0
\(63\) −9.64238 5.41158i −1.21483 0.681795i
\(64\) 0 0
\(65\) 7.52411 6.31348i 0.933251 0.783091i
\(66\) 0 0
\(67\) 1.49490 8.47798i 0.182631 1.03575i −0.746331 0.665574i \(-0.768187\pi\)
0.928962 0.370175i \(-0.120702\pi\)
\(68\) 0 0
\(69\) −1.53727 5.60057i −0.185066 0.674230i
\(70\) 0 0
\(71\) 0.993732 1.72119i 0.117934 0.204268i −0.801015 0.598645i \(-0.795706\pi\)
0.918949 + 0.394377i \(0.129039\pi\)
\(72\) 0 0
\(73\) −5.32371 9.22094i −0.623094 1.07923i −0.988906 0.148541i \(-0.952542\pi\)
0.365812 0.930689i \(-0.380791\pi\)
\(74\) 0 0
\(75\) −8.68627 + 0.813264i −1.00300 + 0.0939077i
\(76\) 0 0
\(77\) 7.91420 2.88053i 0.901907 0.328267i
\(78\) 0 0
\(79\) −2.44726 13.8791i −0.275338 1.56152i −0.737886 0.674925i \(-0.764176\pi\)
0.462548 0.886594i \(-0.346935\pi\)
\(80\) 0 0
\(81\) 8.52968 + 2.87135i 0.947742 + 0.319038i
\(82\) 0 0
\(83\) 0.538035 + 3.05135i 0.0590571 + 0.334929i 0.999993 0.00365453i \(-0.00116328\pi\)
−0.940936 + 0.338584i \(0.890052\pi\)
\(84\) 0 0
\(85\) −5.13767 + 1.86996i −0.557258 + 0.202825i
\(86\) 0 0
\(87\) 1.00960 0.0945255i 0.108241 0.0101342i
\(88\) 0 0
\(89\) 8.67300 + 15.0221i 0.919336 + 1.59234i 0.800425 + 0.599432i \(0.204607\pi\)
0.118911 + 0.992905i \(0.462060\pi\)
\(90\) 0 0
\(91\) 5.71337 9.89585i 0.598924 1.03737i
\(92\) 0 0
\(93\) −2.12635 7.74668i −0.220492 0.803294i
\(94\) 0 0
\(95\) 1.86760 10.5917i 0.191612 1.08669i
\(96\) 0 0
\(97\) 7.04084 5.90797i 0.714889 0.599863i −0.211077 0.977469i \(-0.567697\pi\)
0.925966 + 0.377606i \(0.123253\pi\)
\(98\) 0 0
\(99\) −5.89461 + 3.49963i −0.592430 + 0.351726i
\(100\) 0 0
\(101\) −11.2389 4.09062i −1.11831 0.407032i −0.284276 0.958743i \(-0.591753\pi\)
−0.834036 + 0.551710i \(0.813975\pi\)
\(102\) 0 0
\(103\) 9.76437 + 8.19328i 0.962112 + 0.807308i 0.981295 0.192508i \(-0.0616623\pi\)
−0.0191837 + 0.999816i \(0.506107\pi\)
\(104\) 0 0
\(105\) −18.2775 + 8.65879i −1.78370 + 0.845011i
\(106\) 0 0
\(107\) −6.09894 −0.589607 −0.294803 0.955558i \(-0.595254\pi\)
−0.294803 + 0.955558i \(0.595254\pi\)
\(108\) 0 0
\(109\) 11.2390 1.07650 0.538250 0.842785i \(-0.319086\pi\)
0.538250 + 0.842785i \(0.319086\pi\)
\(110\) 0 0
\(111\) 10.4115 + 7.19618i 0.988220 + 0.683032i
\(112\) 0 0
\(113\) −5.39062 4.52327i −0.507107 0.425513i 0.353003 0.935622i \(-0.385161\pi\)
−0.860110 + 0.510109i \(0.829605\pi\)
\(114\) 0 0
\(115\) −9.98233 3.63327i −0.930857 0.338804i
\(116\) 0 0
\(117\) −3.07442 + 8.77800i −0.284230 + 0.811526i
\(118\) 0 0
\(119\) −4.87254 + 4.08855i −0.446665 + 0.374796i
\(120\) 0 0
\(121\) −1.00342 + 5.69068i −0.0912200 + 0.517334i
\(122\) 0 0
\(123\) −11.8650 3.10193i −1.06983 0.279692i
\(124\) 0 0
\(125\) −0.0585380 + 0.101391i −0.00523579 + 0.00906866i
\(126\) 0 0
\(127\) 2.99250 + 5.18316i 0.265541 + 0.459931i 0.967705 0.252084i \(-0.0811160\pi\)
−0.702164 + 0.712015i \(0.747783\pi\)
\(128\) 0 0
\(129\) −1.66137 2.34220i −0.146275 0.206219i
\(130\) 0 0
\(131\) 15.4251 5.61427i 1.34770 0.490521i 0.435468 0.900204i \(-0.356583\pi\)
0.912228 + 0.409683i \(0.134361\pi\)
\(132\) 0 0
\(133\) −2.17273 12.3222i −0.188400 1.06847i
\(134\) 0 0
\(135\) 13.3102 9.68691i 1.14556 0.833717i
\(136\) 0 0
\(137\) −0.0366673 0.207951i −0.00313270 0.0177664i 0.983201 0.182524i \(-0.0584268\pi\)
−0.986334 + 0.164758i \(0.947316\pi\)
\(138\) 0 0
\(139\) 3.45009 1.25573i 0.292633 0.106510i −0.191532 0.981486i \(-0.561346\pi\)
0.484165 + 0.874977i \(0.339123\pi\)
\(140\) 0 0
\(141\) 2.78277 6.06378i 0.234352 0.510663i
\(142\) 0 0
\(143\) −3.54217 6.13522i −0.296211 0.513053i
\(144\) 0 0
\(145\) 0.927377 1.60626i 0.0770145 0.133393i
\(146\) 0 0
\(147\) −8.01512 + 8.11331i −0.661076 + 0.669174i
\(148\) 0 0
\(149\) 2.68710 15.2393i 0.220136 1.24845i −0.651633 0.758535i \(-0.725916\pi\)
0.871769 0.489918i \(-0.162973\pi\)
\(150\) 0 0
\(151\) −15.4325 + 12.9494i −1.25588 + 1.05381i −0.259772 + 0.965670i \(0.583648\pi\)
−0.996108 + 0.0881390i \(0.971908\pi\)
\(152\) 0 0
\(153\) 3.27935 4.00624i 0.265120 0.323885i
\(154\) 0 0
\(155\) −13.8075 5.02552i −1.10905 0.403660i
\(156\) 0 0
\(157\) 13.7868 + 11.5685i 1.10031 + 0.923269i 0.997446 0.0714264i \(-0.0227551\pi\)
0.102863 + 0.994695i \(0.467200\pi\)
\(158\) 0 0
\(159\) 0.362739 4.45859i 0.0287671 0.353589i
\(160\) 0 0
\(161\) −12.3585 −0.973989
\(162\) 0 0
\(163\) −3.05289 −0.239121 −0.119560 0.992827i \(-0.538149\pi\)
−0.119560 + 0.992827i \(0.538149\pi\)
\(164\) 0 0
\(165\) −1.01678 + 12.4976i −0.0791559 + 0.972940i
\(166\) 0 0
\(167\) 3.14170 + 2.63620i 0.243112 + 0.203995i 0.756199 0.654341i \(-0.227054\pi\)
−0.513088 + 0.858336i \(0.671498\pi\)
\(168\) 0 0
\(169\) 3.18396 + 1.15887i 0.244920 + 0.0891435i
\(170\) 0 0
\(171\) 3.59953 + 9.52708i 0.275263 + 0.728554i
\(172\) 0 0
\(173\) −13.0435 + 10.9448i −0.991680 + 0.832118i −0.985810 0.167864i \(-0.946313\pi\)
−0.00586990 + 0.999983i \(0.501868\pi\)
\(174\) 0 0
\(175\) −3.22374 + 18.2828i −0.243692 + 1.38205i
\(176\) 0 0
\(177\) −11.7627 + 11.9068i −0.884137 + 0.894967i
\(178\) 0 0
\(179\) −7.27802 + 12.6059i −0.543985 + 0.942210i 0.454685 + 0.890652i \(0.349752\pi\)
−0.998670 + 0.0515575i \(0.983581\pi\)
\(180\) 0 0
\(181\) 6.51190 + 11.2789i 0.484026 + 0.838357i 0.999832 0.0183482i \(-0.00584075\pi\)
−0.515806 + 0.856706i \(0.672507\pi\)
\(182\) 0 0
\(183\) 9.45753 20.6084i 0.699121 1.52341i
\(184\) 0 0
\(185\) 21.7539 7.91778i 1.59938 0.582127i
\(186\) 0 0
\(187\) 0.684776 + 3.88356i 0.0500758 + 0.283994i
\(188\) 0 0
\(189\) 10.6966 15.8860i 0.778060 1.15554i
\(190\) 0 0
\(191\) −0.625632 3.54814i −0.0452692 0.256734i 0.953771 0.300534i \(-0.0971648\pi\)
−0.999040 + 0.0437996i \(0.986054\pi\)
\(192\) 0 0
\(193\) −1.38592 + 0.504435i −0.0997610 + 0.0363100i −0.391418 0.920213i \(-0.628015\pi\)
0.291657 + 0.956523i \(0.405793\pi\)
\(194\) 0 0
\(195\) 9.84248 + 13.8760i 0.704835 + 0.993678i
\(196\) 0 0
\(197\) −1.26931 2.19851i −0.0904346 0.156637i 0.817259 0.576270i \(-0.195492\pi\)
−0.907694 + 0.419633i \(0.862159\pi\)
\(198\) 0 0
\(199\) −0.925891 + 1.60369i −0.0656347 + 0.113683i −0.896975 0.442081i \(-0.854241\pi\)
0.831341 + 0.555763i \(0.187574\pi\)
\(200\) 0 0
\(201\) 14.4260 + 3.77145i 1.01753 + 0.266018i
\(202\) 0 0
\(203\) 0.374695 2.12500i 0.0262984 0.149146i
\(204\) 0 0
\(205\) −17.1838 + 14.4189i −1.20017 + 1.00706i
\(206\) 0 0
\(207\) 9.88444 1.86726i 0.687016 0.129783i
\(208\) 0 0
\(209\) −7.28951 2.65317i −0.504226 0.183523i
\(210\) 0 0
\(211\) 14.5459 + 12.2054i 1.00138 + 0.840257i 0.987175 0.159642i \(-0.0510340\pi\)
0.0142043 + 0.999899i \(0.495478\pi\)
\(212\) 0 0
\(213\) 2.83181 + 1.95727i 0.194032 + 0.134110i
\(214\) 0 0
\(215\) −5.25247 −0.358215
\(216\) 0 0
\(217\) −17.0943 −1.16043
\(218\) 0 0
\(219\) 16.6663 7.89549i 1.12620 0.533527i
\(220\) 0 0
\(221\) 4.09858 + 3.43912i 0.275700 + 0.231340i
\(222\) 0 0
\(223\) −6.81687 2.48114i −0.456491 0.166149i 0.103532 0.994626i \(-0.466986\pi\)
−0.560023 + 0.828477i \(0.689208\pi\)
\(224\) 0 0
\(225\) −0.183979 15.1097i −0.0122652 1.00732i
\(226\) 0 0
\(227\) 21.8531 18.3369i 1.45044 1.21706i 0.518182 0.855271i \(-0.326609\pi\)
0.932258 0.361793i \(-0.117835\pi\)
\(228\) 0 0
\(229\) 0.322184 1.82720i 0.0212905 0.120744i −0.972310 0.233694i \(-0.924919\pi\)
0.993601 + 0.112949i \(0.0360298\pi\)
\(230\) 0 0
\(231\) 3.86124 + 14.0672i 0.254051 + 0.925556i
\(232\) 0 0
\(233\) −4.26735 + 7.39126i −0.279563 + 0.484218i −0.971276 0.237955i \(-0.923523\pi\)
0.691713 + 0.722172i \(0.256856\pi\)
\(234\) 0 0
\(235\) −6.10176 10.5686i −0.398035 0.689417i
\(236\) 0 0
\(237\) 24.3038 2.27548i 1.57870 0.147808i
\(238\) 0 0
\(239\) −6.84845 + 2.49263i −0.442989 + 0.161235i −0.553878 0.832598i \(-0.686853\pi\)
0.110889 + 0.993833i \(0.464630\pi\)
\(240\) 0 0
\(241\) −0.231806 1.31464i −0.0149319 0.0846833i 0.976431 0.215829i \(-0.0692455\pi\)
−0.991363 + 0.131146i \(0.958134\pi\)
\(242\) 0 0
\(243\) −6.15494 + 14.3219i −0.394840 + 0.918750i
\(244\) 0 0
\(245\) 3.62239 + 20.5436i 0.231426 + 1.31248i
\(246\) 0 0
\(247\) −9.89008 + 3.59969i −0.629291 + 0.229043i
\(248\) 0 0
\(249\) −5.34326 + 0.500270i −0.338615 + 0.0317033i
\(250\) 0 0
\(251\) −1.43928 2.49291i −0.0908466 0.157351i 0.817021 0.576608i \(-0.195624\pi\)
−0.907868 + 0.419257i \(0.862291\pi\)
\(252\) 0 0
\(253\) −3.83102 + 6.63552i −0.240854 + 0.417171i
\(254\) 0 0
\(255\) −2.50660 9.13203i −0.156970 0.571870i
\(256\) 0 0
\(257\) −4.47629 + 25.3863i −0.279223 + 1.58355i 0.445996 + 0.895035i \(0.352850\pi\)
−0.725219 + 0.688518i \(0.758262\pi\)
\(258\) 0 0
\(259\) 20.6313 17.3117i 1.28197 1.07570i
\(260\) 0 0
\(261\) 0.0213838 + 1.75620i 0.00132362 + 0.108706i
\(262\) 0 0
\(263\) −14.1609 5.15414i −0.873197 0.317818i −0.133736 0.991017i \(-0.542697\pi\)
−0.739461 + 0.673199i \(0.764920\pi\)
\(264\) 0 0
\(265\) −6.26793 5.25942i −0.385036 0.323083i
\(266\) 0 0
\(267\) −27.1515 + 12.8627i −1.66164 + 0.787187i
\(268\) 0 0
\(269\) 16.0615 0.979286 0.489643 0.871923i \(-0.337127\pi\)
0.489643 + 0.871923i \(0.337127\pi\)
\(270\) 0 0
\(271\) −9.41446 −0.571888 −0.285944 0.958246i \(-0.592307\pi\)
−0.285944 + 0.958246i \(0.592307\pi\)
\(272\) 0 0
\(273\) 16.2812 + 11.2531i 0.985384 + 0.681071i
\(274\) 0 0
\(275\) 8.81700 + 7.39834i 0.531685 + 0.446137i
\(276\) 0 0
\(277\) −5.23856 1.90668i −0.314755 0.114561i 0.179812 0.983701i \(-0.442451\pi\)
−0.494567 + 0.869140i \(0.664673\pi\)
\(278\) 0 0
\(279\) 13.6721 2.58278i 0.818528 0.154627i
\(280\) 0 0
\(281\) 21.4529 18.0011i 1.27977 1.07386i 0.286499 0.958081i \(-0.407509\pi\)
0.993275 0.115777i \(-0.0369359\pi\)
\(282\) 0 0
\(283\) −1.06884 + 6.06171i −0.0635361 + 0.360331i 0.936419 + 0.350883i \(0.114119\pi\)
−0.999955 + 0.00944797i \(0.996993\pi\)
\(284\) 0 0
\(285\) 18.0227 + 4.71175i 1.06757 + 0.279100i
\(286\) 0 0
\(287\) −13.0484 + 22.6005i −0.770222 + 1.33406i
\(288\) 0 0
\(289\) 7.01088 + 12.1432i 0.412405 + 0.714306i
\(290\) 0 0
\(291\) 9.21031 + 12.9847i 0.539918 + 0.761177i
\(292\) 0 0
\(293\) −2.19428 + 0.798651i −0.128191 + 0.0466577i −0.405319 0.914175i \(-0.632840\pi\)
0.277128 + 0.960833i \(0.410617\pi\)
\(294\) 0 0
\(295\) 5.31608 + 30.1490i 0.309514 + 1.75534i
\(296\) 0 0
\(297\) −5.21367 10.6677i −0.302528 0.619001i
\(298\) 0 0
\(299\) 1.80516 + 10.2376i 0.104395 + 0.592054i
\(300\) 0 0
\(301\) −5.74209 + 2.08995i −0.330969 + 0.120463i
\(302\) 0 0
\(303\) 8.64035 18.8277i 0.496375 1.08162i
\(304\) 0 0
\(305\) −20.7374 35.9183i −1.18742 2.05668i
\(306\) 0 0
\(307\) 3.41265 5.91088i 0.194770 0.337351i −0.752055 0.659100i \(-0.770937\pi\)
0.946825 + 0.321749i \(0.104271\pi\)
\(308\) 0 0
\(309\) −15.5159 + 15.7059i −0.882666 + 0.893479i
\(310\) 0 0
\(311\) −1.49254 + 8.46464i −0.0846344 + 0.479986i 0.912800 + 0.408406i \(0.133915\pi\)
−0.997435 + 0.0715798i \(0.977196\pi\)
\(312\) 0 0
\(313\) −16.5993 + 13.9285i −0.938250 + 0.787285i −0.977280 0.211953i \(-0.932018\pi\)
0.0390299 + 0.999238i \(0.487573\pi\)
\(314\) 0 0
\(315\) −12.3810 32.7694i −0.697589 1.84635i
\(316\) 0 0
\(317\) −33.1899 12.0801i −1.86413 0.678488i −0.975554 0.219760i \(-0.929473\pi\)
−0.888577 0.458728i \(-0.848305\pi\)
\(318\) 0 0
\(319\) −1.02480 0.859908i −0.0573777 0.0481456i
\(320\) 0 0
\(321\) 0.856604 10.5289i 0.0478110 0.587665i
\(322\) 0 0
\(323\) 5.85859 0.325981
\(324\) 0 0
\(325\) 15.6159 0.866217
\(326\) 0 0
\(327\) −1.57853 + 19.4024i −0.0872929 + 1.07296i
\(328\) 0 0
\(329\) −10.8758 9.12586i −0.599601 0.503125i
\(330\) 0 0
\(331\) −24.2569 8.82879i −1.33328 0.485274i −0.425590 0.904916i \(-0.639933\pi\)
−0.907690 + 0.419642i \(0.862156\pi\)
\(332\) 0 0
\(333\) −13.8854 + 16.9632i −0.760917 + 0.929579i
\(334\) 0 0
\(335\) 20.8928 17.5311i 1.14149 0.957826i
\(336\) 0 0
\(337\) −0.587727 + 3.33317i −0.0320156 + 0.181569i −0.996622 0.0821241i \(-0.973830\pi\)
0.964607 + 0.263693i \(0.0849407\pi\)
\(338\) 0 0
\(339\) 8.56585 8.67078i 0.465233 0.470932i
\(340\) 0 0
\(341\) −5.29904 + 9.17821i −0.286959 + 0.497028i
\(342\) 0 0
\(343\) −0.765664 1.32617i −0.0413420 0.0716064i
\(344\) 0 0
\(345\) 7.67431 16.7227i 0.413171 0.900318i
\(346\) 0 0
\(347\) −15.2230 + 5.54073i −0.817216 + 0.297442i −0.716601 0.697483i \(-0.754303\pi\)
−0.100615 + 0.994925i \(0.532081\pi\)
\(348\) 0 0
\(349\) 0.780120 + 4.42428i 0.0417589 + 0.236826i 0.998542 0.0539752i \(-0.0171892\pi\)
−0.956783 + 0.290801i \(0.906078\pi\)
\(350\) 0 0
\(351\) −14.7221 6.54040i −0.785806 0.349101i
\(352\) 0 0
\(353\) −4.03327 22.8738i −0.214669 1.21745i −0.881479 0.472222i \(-0.843452\pi\)
0.666810 0.745228i \(-0.267659\pi\)
\(354\) 0 0
\(355\) 5.91679 2.15353i 0.314030 0.114298i
\(356\) 0 0
\(357\) −6.37389 8.98593i −0.337342 0.475586i
\(358\) 0 0
\(359\) −5.77697 10.0060i −0.304897 0.528097i 0.672341 0.740241i \(-0.265289\pi\)
−0.977238 + 0.212144i \(0.931955\pi\)
\(360\) 0 0
\(361\) 3.73768 6.47385i 0.196720 0.340729i
\(362\) 0 0
\(363\) −9.68315 2.53151i −0.508234 0.132870i
\(364\) 0 0
\(365\) 5.85755 33.2198i 0.306598 1.73880i
\(366\) 0 0
\(367\) −11.9271 + 10.0080i −0.622589 + 0.522414i −0.898616 0.438735i \(-0.855427\pi\)
0.276027 + 0.961150i \(0.410982\pi\)
\(368\) 0 0
\(369\) 7.02147 20.0475i 0.365523 1.04363i
\(370\) 0 0
\(371\) −8.94493 3.25569i −0.464398 0.169027i
\(372\) 0 0
\(373\) −7.47450 6.27185i −0.387015 0.324744i 0.428434 0.903573i \(-0.359065\pi\)
−0.815449 + 0.578829i \(0.803510\pi\)
\(374\) 0 0
\(375\) −0.166814 0.115297i −0.00861423 0.00595392i
\(376\) 0 0
\(377\) −1.81504 −0.0934792
\(378\) 0 0
\(379\) 18.7904 0.965197 0.482599 0.875842i \(-0.339693\pi\)
0.482599 + 0.875842i \(0.339693\pi\)
\(380\) 0 0
\(381\) −9.36823 + 4.43811i −0.479949 + 0.227371i
\(382\) 0 0
\(383\) −23.5697 19.7773i −1.20435 1.01057i −0.999495 0.0317817i \(-0.989882\pi\)
−0.204859 0.978791i \(-0.565674\pi\)
\(384\) 0 0
\(385\) 25.0731 + 9.12586i 1.27784 + 0.465097i
\(386\) 0 0
\(387\) 4.27679 2.53913i 0.217402 0.129071i
\(388\) 0 0
\(389\) 22.6754 19.0269i 1.14969 0.964704i 0.149978 0.988689i \(-0.452080\pi\)
0.999712 + 0.0239850i \(0.00763540\pi\)
\(390\) 0 0
\(391\) 1.00483 5.69870i 0.0508167 0.288196i
\(392\) 0 0
\(393\) 7.52571 + 27.4176i 0.379622 + 1.38303i
\(394\) 0 0
\(395\) 22.3244 38.6670i 1.12326 1.94555i
\(396\) 0 0
\(397\) −8.07134 13.9800i −0.405089 0.701635i 0.589243 0.807956i \(-0.299426\pi\)
−0.994332 + 0.106321i \(0.966093\pi\)
\(398\) 0 0
\(399\) 21.5775 2.02022i 1.08023 0.101138i
\(400\) 0 0
\(401\) −23.8328 + 8.67444i −1.19016 + 0.433181i −0.859778 0.510668i \(-0.829398\pi\)
−0.330377 + 0.943849i \(0.607176\pi\)
\(402\) 0 0
\(403\) 2.49689 + 14.1605i 0.124379 + 0.705387i
\(404\) 0 0
\(405\) 14.8535 + 24.3386i 0.738078 + 1.20939i
\(406\) 0 0
\(407\) −2.89948 16.4438i −0.143722 0.815087i
\(408\) 0 0
\(409\) 21.3980 7.78825i 1.05806 0.385104i 0.246364 0.969177i \(-0.420764\pi\)
0.811701 + 0.584073i \(0.198542\pi\)
\(410\) 0 0
\(411\) 0.364145 0.0340936i 0.0179619 0.00168171i
\(412\) 0 0
\(413\) 17.8079 + 30.8442i 0.876269 + 1.51774i
\(414\) 0 0
\(415\) −4.90808 + 8.50104i −0.240928 + 0.417300i
\(416\) 0 0
\(417\) 1.68326 + 6.13242i 0.0824294 + 0.300306i
\(418\) 0 0
\(419\) 0.854828 4.84797i 0.0417611 0.236839i −0.956782 0.290808i \(-0.906076\pi\)
0.998543 + 0.0539688i \(0.0171872\pi\)
\(420\) 0 0
\(421\) 15.1046 12.6742i 0.736151 0.617704i −0.195650 0.980674i \(-0.562682\pi\)
0.931801 + 0.362970i \(0.118237\pi\)
\(422\) 0 0
\(423\) 10.0773 + 5.65570i 0.489977 + 0.274989i
\(424\) 0 0
\(425\) −8.16833 2.97303i −0.396222 0.144213i
\(426\) 0 0
\(427\) −36.9624 31.0151i −1.78874 1.50093i
\(428\) 0 0
\(429\) 11.0890 5.25331i 0.535383 0.253632i
\(430\) 0 0
\(431\) 6.16323 0.296873 0.148436 0.988922i \(-0.452576\pi\)
0.148436 + 0.988922i \(0.452576\pi\)
\(432\) 0 0
\(433\) −14.7838 −0.710466 −0.355233 0.934778i \(-0.615599\pi\)
−0.355233 + 0.934778i \(0.615599\pi\)
\(434\) 0 0
\(435\) 2.64272 + 1.82658i 0.126709 + 0.0875776i
\(436\) 0 0
\(437\) 8.71993 + 7.31689i 0.417131 + 0.350014i
\(438\) 0 0
\(439\) 27.9719 + 10.1809i 1.33502 + 0.485909i 0.908242 0.418445i \(-0.137425\pi\)
0.426782 + 0.904354i \(0.359647\pi\)
\(440\) 0 0
\(441\) −12.8806 14.9764i −0.613364 0.713162i
\(442\) 0 0
\(443\) −23.3447 + 19.5885i −1.10914 + 0.930680i −0.998006 0.0631253i \(-0.979893\pi\)
−0.111136 + 0.993805i \(0.535449\pi\)
\(444\) 0 0
\(445\) −9.54269 + 54.1193i −0.452367 + 2.56550i
\(446\) 0 0
\(447\) 25.9309 + 6.77925i 1.22649 + 0.320647i
\(448\) 0 0
\(449\) −5.92055 + 10.2547i −0.279408 + 0.483949i −0.971238 0.238112i \(-0.923472\pi\)
0.691830 + 0.722061i \(0.256805\pi\)
\(450\) 0 0
\(451\) 8.08973 + 14.0118i 0.380930 + 0.659791i
\(452\) 0 0
\(453\) −20.1877 28.4606i −0.948500 1.33720i
\(454\) 0 0
\(455\) 34.0180 12.3816i 1.59479 0.580456i
\(456\) 0 0
\(457\) −0.0323668 0.183561i −0.00151406 0.00858664i 0.984041 0.177940i \(-0.0569432\pi\)
−0.985555 + 0.169353i \(0.945832\pi\)
\(458\) 0 0
\(459\) 6.45557 + 6.22397i 0.301320 + 0.290510i
\(460\) 0 0
\(461\) 1.80687 + 10.2473i 0.0841543 + 0.477263i 0.997536 + 0.0701583i \(0.0223505\pi\)
−0.913382 + 0.407105i \(0.866538\pi\)
\(462\) 0 0
\(463\) 24.2332 8.82016i 1.12621 0.409907i 0.289296 0.957240i \(-0.406579\pi\)
0.836915 + 0.547332i \(0.184357\pi\)
\(464\) 0 0
\(465\) 10.6151 23.1307i 0.492262 1.07266i
\(466\) 0 0
\(467\) 10.8506 + 18.7937i 0.502104 + 0.869670i 0.999997 + 0.00243153i \(0.000773982\pi\)
−0.497893 + 0.867239i \(0.665893\pi\)
\(468\) 0 0
\(469\) 15.8647 27.4785i 0.732566 1.26884i
\(470\) 0 0
\(471\) −21.9077 + 22.1760i −1.00945 + 1.02182i
\(472\) 0 0
\(473\) −0.657857 + 3.73089i −0.0302483 + 0.171547i
\(474\) 0 0
\(475\) 13.0989 10.9913i 0.601020 0.504316i
\(476\) 0 0
\(477\) 7.64612 + 1.25243i 0.350092 + 0.0573447i
\(478\) 0 0
\(479\) −36.7619 13.3802i −1.67970 0.611359i −0.686427 0.727199i \(-0.740822\pi\)
−0.993268 + 0.115839i \(0.963044\pi\)
\(480\) 0 0
\(481\) −17.3542 14.5619i −0.791284 0.663966i
\(482\) 0 0
\(483\) 1.73577 21.3351i 0.0789804 0.970782i
\(484\) 0 0
\(485\) 29.1187 1.32221
\(486\) 0 0
\(487\) 10.4833 0.475043 0.237522 0.971382i \(-0.423665\pi\)
0.237522 + 0.971382i \(0.423665\pi\)
\(488\) 0 0
\(489\) 0.428782 5.27035i 0.0193902 0.238334i
\(490\) 0 0
\(491\) −5.25278 4.40761i −0.237055 0.198913i 0.516519 0.856276i \(-0.327227\pi\)
−0.753574 + 0.657363i \(0.771672\pi\)
\(492\) 0 0
\(493\) 0.949403 + 0.345554i 0.0427589 + 0.0155630i
\(494\) 0 0
\(495\) −21.4325 3.51062i −0.963317 0.157791i
\(496\) 0 0
\(497\) 5.61145 4.70857i 0.251708 0.211208i
\(498\) 0 0
\(499\) −3.26002 + 18.4885i −0.145939 + 0.827659i 0.820670 + 0.571402i \(0.193600\pi\)
−0.966609 + 0.256257i \(0.917511\pi\)
\(500\) 0 0
\(501\) −4.99225 + 5.05340i −0.223037 + 0.225769i
\(502\) 0 0
\(503\) −6.21350 + 10.7621i −0.277046 + 0.479858i −0.970649 0.240499i \(-0.922689\pi\)
0.693603 + 0.720357i \(0.256022\pi\)
\(504\) 0 0
\(505\) −18.9456 32.8148i −0.843069 1.46024i
\(506\) 0 0
\(507\) −2.44779 + 5.33385i −0.108710 + 0.236885i
\(508\) 0 0
\(509\) −30.9889 + 11.2790i −1.37356 + 0.499935i −0.920219 0.391403i \(-0.871990\pi\)
−0.453340 + 0.891338i \(0.649768\pi\)
\(510\) 0 0
\(511\) −6.81455 38.6472i −0.301458 1.70965i
\(512\) 0 0
\(513\) −16.9526 + 4.87594i −0.748476 + 0.215278i
\(514\) 0 0
\(515\) 7.01231 + 39.7688i 0.308999 + 1.75242i
\(516\) 0 0
\(517\) −8.27121 + 3.01047i −0.363767 + 0.132400i
\(518\) 0 0
\(519\) −17.0626 24.0548i −0.748963 1.05589i
\(520\) 0 0
\(521\) −7.16598 12.4118i −0.313947 0.543773i 0.665266 0.746607i \(-0.268318\pi\)
−0.979213 + 0.202834i \(0.934985\pi\)
\(522\) 0 0
\(523\) −2.85442 + 4.94400i −0.124815 + 0.216186i −0.921661 0.387997i \(-0.873167\pi\)
0.796846 + 0.604183i \(0.206500\pi\)
\(524\) 0 0
\(525\) −31.1096 8.13313i −1.35773 0.354959i
\(526\) 0 0
\(527\) 1.38988 7.88241i 0.0605442 0.343363i
\(528\) 0 0
\(529\) −9.00623 + 7.55712i −0.391575 + 0.328571i
\(530\) 0 0
\(531\) −18.9031 21.9788i −0.820326 0.953797i
\(532\) 0 0
\(533\) 20.6277 + 7.50787i 0.893485 + 0.325202i
\(534\) 0 0
\(535\) −14.8016 12.4200i −0.639930 0.536965i
\(536\) 0 0
\(537\) −20.7400 14.3349i −0.894995 0.618597i
\(538\) 0 0
\(539\) 15.0461 0.648081
\(540\) 0 0
\(541\) 18.0099 0.774305 0.387153 0.922016i \(-0.373459\pi\)
0.387153 + 0.922016i \(0.373459\pi\)
\(542\) 0 0
\(543\) −20.3860 + 9.65766i −0.874846 + 0.414450i
\(544\) 0 0
\(545\) 27.2761 + 22.8874i 1.16838 + 0.980387i
\(546\) 0 0
\(547\) −19.3837 7.05509i −0.828788 0.301654i −0.107426 0.994213i \(-0.534261\pi\)
−0.721361 + 0.692559i \(0.756483\pi\)
\(548\) 0 0
\(549\) 34.2489 + 19.2214i 1.46171 + 0.820351i
\(550\) 0 0
\(551\) −1.52249 + 1.27752i −0.0648601 + 0.0544241i
\(552\) 0 0
\(553\) 9.01990 51.1544i 0.383565 2.17531i
\(554\) 0 0
\(555\) 10.6135 + 38.6669i 0.450517 + 1.64132i
\(556\) 0 0
\(557\) 1.90209 3.29452i 0.0805942 0.139593i −0.822911 0.568170i \(-0.807652\pi\)
0.903505 + 0.428577i \(0.140985\pi\)
\(558\) 0 0
\(559\) 2.57000 + 4.45136i 0.108699 + 0.188273i
\(560\) 0 0
\(561\) −6.80054 + 0.636710i −0.287119 + 0.0268819i
\(562\) 0 0
\(563\) −10.4037 + 3.78663i −0.438463 + 0.159587i −0.551813 0.833968i \(-0.686064\pi\)
0.113351 + 0.993555i \(0.463842\pi\)
\(564\) 0 0
\(565\) −3.87129 21.9552i −0.162866 0.923662i
\(566\) 0 0
\(567\) 25.9225 + 20.6972i 1.08864 + 0.869199i
\(568\) 0 0
\(569\) 8.11202 + 46.0056i 0.340074 + 1.92865i 0.369836 + 0.929097i \(0.379414\pi\)
−0.0297623 + 0.999557i \(0.509475\pi\)
\(570\) 0 0
\(571\) −29.7753 + 10.8373i −1.24606 + 0.453528i −0.879068 0.476697i \(-0.841834\pi\)
−0.366990 + 0.930225i \(0.619612\pi\)
\(572\) 0 0
\(573\) 6.21319 0.581718i 0.259560 0.0243016i
\(574\) 0 0
\(575\) −8.44468 14.6266i −0.352167 0.609972i
\(576\) 0 0
\(577\) −22.1642 + 38.3895i −0.922707 + 1.59818i −0.127499 + 0.991839i \(0.540695\pi\)
−0.795208 + 0.606336i \(0.792639\pi\)
\(578\) 0 0
\(579\) −0.676175 2.46343i −0.0281009 0.102377i
\(580\) 0 0
\(581\) −1.98305 + 11.2464i −0.0822707 + 0.466580i
\(582\) 0 0
\(583\) −4.52087 + 3.79346i −0.187235 + 0.157109i
\(584\) 0 0
\(585\) −25.3371 + 15.0426i −1.04756 + 0.621937i
\(586\) 0 0
\(587\) 38.5694 + 14.0381i 1.59193 + 0.579414i 0.977754 0.209756i \(-0.0672669\pi\)
0.614174 + 0.789170i \(0.289489\pi\)
\(588\) 0 0
\(589\) 12.0614 + 10.1207i 0.496980 + 0.417015i
\(590\) 0 0
\(591\) 3.97367 1.88249i 0.163455 0.0774351i
\(592\) 0 0
\(593\) −9.69265 −0.398029 −0.199015 0.979996i \(-0.563774\pi\)
−0.199015 + 0.979996i \(0.563774\pi\)
\(594\) 0 0
\(595\) −20.1513 −0.826121
\(596\) 0 0
\(597\) −2.63848 1.82365i −0.107986 0.0746370i
\(598\) 0 0
\(599\) 22.8572 + 19.1794i 0.933918 + 0.783651i 0.976517 0.215442i \(-0.0691191\pi\)
−0.0425983 + 0.999092i \(0.513564\pi\)
\(600\) 0 0
\(601\) −11.7938 4.29259i −0.481079 0.175098i 0.0900856 0.995934i \(-0.471286\pi\)
−0.571165 + 0.820836i \(0.693508\pi\)
\(602\) 0 0
\(603\) −8.53698 + 24.3745i −0.347653 + 0.992607i
\(604\) 0 0
\(605\) −14.0239 + 11.7674i −0.570151 + 0.478413i
\(606\) 0 0
\(607\) 0.482765 2.73790i 0.0195948 0.111128i −0.973442 0.228935i \(-0.926476\pi\)
0.993036 + 0.117808i \(0.0375866\pi\)
\(608\) 0 0
\(609\) 3.61586 + 0.945312i 0.146522 + 0.0383060i
\(610\) 0 0
\(611\) −5.97110 + 10.3422i −0.241565 + 0.418403i
\(612\) 0 0
\(613\) 4.29646 + 7.44168i 0.173532 + 0.300567i 0.939652 0.342131i \(-0.111149\pi\)
−0.766120 + 0.642697i \(0.777815\pi\)
\(614\) 0 0
\(615\) −22.4786 31.6904i −0.906425 1.27788i
\(616\) 0 0
\(617\) 18.8681 6.86743i 0.759602 0.276472i 0.0669615 0.997756i \(-0.478670\pi\)
0.692640 + 0.721283i \(0.256447\pi\)
\(618\) 0 0
\(619\) −1.45723 8.26436i −0.0585710 0.332173i 0.941416 0.337247i \(-0.109496\pi\)
−0.999987 + 0.00507458i \(0.998385\pi\)
\(620\) 0 0
\(621\) 1.83525 + 17.3262i 0.0736461 + 0.695278i
\(622\) 0 0
\(623\) 11.1018 + 62.9612i 0.444783 + 2.52249i
\(624\) 0 0
\(625\) 23.3174 8.48684i 0.932696 0.339474i
\(626\) 0 0
\(627\) 5.60411 12.2116i 0.223806 0.487684i
\(628\) 0 0
\(629\) 6.30522 + 10.9210i 0.251405 + 0.435447i
\(630\) 0 0
\(631\) 8.78157 15.2101i 0.349589 0.605506i −0.636588 0.771204i \(-0.719655\pi\)
0.986176 + 0.165699i \(0.0529879\pi\)
\(632\) 0 0
\(633\) −23.1138 + 23.3970i −0.918691 + 0.929946i
\(634\) 0 0
\(635\) −3.29257 + 18.6731i −0.130662 + 0.741019i
\(636\) 0 0
\(637\) 15.6379 13.1218i 0.619596 0.519903i
\(638\) 0 0
\(639\) −3.77666 + 4.61378i −0.149402 + 0.182518i
\(640\) 0 0
\(641\) 12.6056 + 4.58808i 0.497893 + 0.181218i 0.578746 0.815508i \(-0.303542\pi\)
−0.0808532 + 0.996726i \(0.525765\pi\)
\(642\) 0 0
\(643\) 7.99375 + 6.70755i 0.315243 + 0.264520i 0.786655 0.617393i \(-0.211811\pi\)
−0.471412 + 0.881913i \(0.656256\pi\)
\(644\) 0 0
\(645\) 0.737715 9.06758i 0.0290475 0.357035i
\(646\) 0 0
\(647\) 37.9585 1.49230 0.746152 0.665775i \(-0.231899\pi\)
0.746152 + 0.665775i \(0.231899\pi\)
\(648\) 0 0
\(649\) 22.0810 0.866756
\(650\) 0 0
\(651\) 2.40091 29.5106i 0.0940991 1.15661i
\(652\) 0 0
\(653\) −20.9178 17.5521i −0.818578 0.686868i 0.134061 0.990973i \(-0.457198\pi\)
−0.952639 + 0.304105i \(0.901643\pi\)
\(654\) 0 0
\(655\) 48.8684 + 17.7867i 1.90945 + 0.694982i
\(656\) 0 0
\(657\) 11.2895 + 29.8807i 0.440447 + 1.16576i
\(658\) 0 0
\(659\) 26.3174 22.0829i 1.02518 0.860228i 0.0349104 0.999390i \(-0.488885\pi\)
0.990270 + 0.139162i \(0.0444410\pi\)
\(660\) 0 0
\(661\) −4.26787 + 24.2043i −0.166001 + 0.941439i 0.782025 + 0.623247i \(0.214187\pi\)
−0.948026 + 0.318192i \(0.896924\pi\)
\(662\) 0 0
\(663\) −6.51276 + 6.59254i −0.252935 + 0.256033i
\(664\) 0 0
\(665\) 19.8202 34.3295i 0.768593 1.33124i
\(666\) 0 0
\(667\) 0.981523 + 1.70005i 0.0380047 + 0.0658261i
\(668\) 0 0
\(669\) 5.24074 11.4198i 0.202619 0.441515i
\(670\) 0 0
\(671\) −28.1105 + 10.2314i −1.08519 + 0.394979i
\(672\) 0 0
\(673\) 7.44524 + 42.2241i 0.286993 + 1.62762i 0.698078 + 0.716021i \(0.254039\pi\)
−0.411085 + 0.911597i \(0.634850\pi\)
\(674\) 0 0
\(675\) 26.1105 + 1.80457i 1.00499 + 0.0694580i
\(676\) 0 0
\(677\) 1.30018 + 7.37368i 0.0499699 + 0.283393i 0.999546 0.0301446i \(-0.00959678\pi\)
−0.949576 + 0.313538i \(0.898486\pi\)
\(678\) 0 0
\(679\) 31.8331 11.5863i 1.22164 0.444641i
\(680\) 0 0
\(681\) 28.5866 + 40.3014i 1.09544 + 1.54435i
\(682\) 0 0
\(683\) 8.37724 + 14.5098i 0.320546 + 0.555202i 0.980601 0.196015i \(-0.0628002\pi\)
−0.660055 + 0.751218i \(0.729467\pi\)
\(684\) 0 0
\(685\) 0.334487 0.579349i 0.0127801 0.0221358i
\(686\) 0 0
\(687\) 3.10912 + 0.812833i 0.118620 + 0.0310115i
\(688\) 0 0
\(689\) −1.39040 + 7.88535i −0.0529700 + 0.300408i
\(690\) 0 0
\(691\) 11.4550 9.61189i 0.435769 0.365653i −0.398354 0.917232i \(-0.630419\pi\)
0.834123 + 0.551578i \(0.185974\pi\)
\(692\) 0 0
\(693\) −24.8272 + 4.69008i −0.943109 + 0.178161i
\(694\) 0 0
\(695\) 10.9303 + 3.97830i 0.414609 + 0.150905i
\(696\) 0 0
\(697\) −9.36048 7.85437i −0.354553 0.297506i
\(698\) 0 0
\(699\) −12.1605 8.40503i −0.459953 0.317908i
\(700\) 0 0
\(701\) −42.1025 −1.59019 −0.795094 0.606486i \(-0.792579\pi\)
−0.795094 + 0.606486i \(0.792579\pi\)
\(702\) 0 0
\(703\) −24.8065 −0.935593
\(704\) 0 0
\(705\) 19.1020 9.04939i 0.719423 0.340820i
\(706\) 0 0
\(707\) −33.7687 28.3353i −1.27000 1.06566i
\(708\) 0 0
\(709\) −26.7677 9.74265i −1.00528 0.365893i −0.213663 0.976907i \(-0.568539\pi\)
−0.791619 + 0.611015i \(0.790762\pi\)
\(710\) 0 0
\(711\) 0.514765 + 42.2764i 0.0193052 + 1.58549i
\(712\) 0 0
\(713\) 11.9132 9.99634i 0.446152 0.374366i
\(714\) 0 0
\(715\) 3.89736 22.1030i 0.145753 0.826606i
\(716\) 0 0
\(717\) −3.34127 12.1729i −0.124782 0.454605i
\(718\) 0 0
\(719\) 1.26744 2.19526i 0.0472674 0.0818695i −0.841424 0.540376i \(-0.818282\pi\)
0.888691 + 0.458506i \(0.151615\pi\)
\(720\) 0 0
\(721\) 23.4900 + 40.6858i 0.874812 + 1.51522i
\(722\) 0 0
\(723\) 2.30208 0.215535i 0.0856152 0.00801585i
\(724\) 0 0
\(725\) 2.77102 1.00857i 0.102913 0.0374573i
\(726\) 0 0
\(727\) −3.45271 19.5813i −0.128054 0.726231i −0.979447 0.201702i \(-0.935353\pi\)
0.851393 0.524529i \(-0.175758\pi\)
\(728\) 0 0
\(729\) −23.8601 12.6371i −0.883707 0.468040i
\(730\) 0 0
\(731\) −0.496834 2.81769i −0.0183761 0.104216i
\(732\) 0 0
\(733\) 9.40733 3.42399i 0.347468 0.126468i −0.162390 0.986727i \(-0.551920\pi\)
0.509858 + 0.860259i \(0.329698\pi\)
\(734\) 0 0
\(735\) −35.9742 + 3.36813i −1.32693 + 0.124235i
\(736\) 0 0
\(737\) −9.83580 17.0361i −0.362306 0.627533i
\(738\) 0 0
\(739\) −20.1957 + 34.9800i −0.742911 + 1.28676i 0.208253 + 0.978075i \(0.433222\pi\)
−0.951164 + 0.308685i \(0.900111\pi\)
\(740\) 0 0
\(741\) −4.82525 17.5793i −0.177260 0.645791i
\(742\) 0 0
\(743\) −6.19059 + 35.1086i −0.227111 + 1.28801i 0.631498 + 0.775377i \(0.282440\pi\)
−0.858609 + 0.512631i \(0.828671\pi\)
\(744\) 0 0
\(745\) 37.5551 31.5124i 1.37591 1.15453i
\(746\) 0 0
\(747\) −0.113172 9.29458i −0.00414076 0.340071i
\(748\) 0 0
\(749\) −21.1233 7.68826i −0.771830 0.280923i
\(750\) 0 0
\(751\) 7.25347 + 6.08638i 0.264683 + 0.222095i 0.765464 0.643479i \(-0.222509\pi\)
−0.500781 + 0.865574i \(0.666954\pi\)
\(752\) 0 0
\(753\) 4.50577 2.13457i 0.164199 0.0777879i
\(754\) 0 0
\(755\) −63.8240 −2.32279
\(756\) 0 0
\(757\) −37.9651 −1.37987 −0.689933 0.723873i \(-0.742360\pi\)
−0.689933 + 0.723873i \(0.742360\pi\)
\(758\) 0 0
\(759\) −10.9171 7.54563i −0.396267 0.273889i
\(760\) 0 0
\(761\) 34.3845 + 28.8520i 1.24644 + 1.04588i 0.996993 + 0.0774952i \(0.0246922\pi\)
0.249444 + 0.968389i \(0.419752\pi\)
\(762\) 0 0
\(763\) 38.9256 + 14.1678i 1.40920 + 0.512908i
\(764\) 0 0
\(765\) 16.1171 3.04466i 0.582715 0.110080i
\(766\) 0 0
\(767\) 22.9496 19.2570i 0.828661 0.695329i
\(768\) 0 0
\(769\) 7.94212 45.0420i 0.286400 1.62426i −0.413841 0.910349i \(-0.635813\pi\)
0.700241 0.713906i \(-0.253076\pi\)
\(770\) 0 0
\(771\) −43.1968 11.2932i −1.55570 0.406713i
\(772\) 0 0
\(773\) 10.2853 17.8147i 0.369938 0.640752i −0.619617 0.784904i \(-0.712712\pi\)
0.989556 + 0.144152i \(0.0460455\pi\)
\(774\) 0 0
\(775\) −11.6806 20.2315i −0.419581 0.726735i
\(776\) 0 0
\(777\) 26.9884 + 38.0483i 0.968202 + 1.36497i
\(778\) 0 0
\(779\) 22.5873 8.22111i 0.809274 0.294552i
\(780\) 0 0
\(781\) −0.788621 4.47249i −0.0282191 0.160038i
\(782\) 0 0
\(783\) −3.03482 0.209745i −0.108456 0.00749567i
\(784\) 0 0
\(785\) 9.90106 + 56.1517i 0.353384 + 2.00414i
\(786\) 0 0
\(787\) 41.8760 15.2416i 1.49272 0.543305i 0.538555 0.842590i \(-0.318970\pi\)
0.954164 + 0.299285i \(0.0967483\pi\)
\(788\) 0 0
\(789\) 10.8867 23.7227i 0.387578 0.844550i
\(790\) 0 0
\(791\) −12.9681 22.4614i −0.461093 0.798637i
\(792\) 0 0
\(793\) −20.2934 + 35.1492i −0.720639 + 1.24818i
\(794\) 0 0
\(795\) 9.95992 10.0819i 0.353242 0.357569i
\(796\) 0 0
\(797\) 7.61623 43.1938i 0.269781 1.53000i −0.485287 0.874355i \(-0.661285\pi\)
0.755067 0.655647i \(-0.227604\pi\)
\(798\) 0 0
\(799\) 5.09234 4.27298i 0.180154 0.151167i
\(800\) 0 0
\(801\) −18.3921 48.6794i −0.649853 1.72000i
\(802\) 0 0
\(803\) −22.8628 8.32138i −0.806811 0.293655i
\(804\) 0 0
\(805\) −29.9932 25.1672i −1.05712 0.887029i
\(806\) 0 0
\(807\) −2.25585 + 27.7277i −0.0794098 + 0.976061i
\(808\) 0 0
\(809\) −15.5821 −0.547836 −0.273918 0.961753i \(-0.588320\pi\)
−0.273918 + 0.961753i \(0.588320\pi\)
\(810\) 0 0
\(811\) 30.4691 1.06992 0.534958 0.844879i \(-0.320327\pi\)
0.534958 + 0.844879i \(0.320327\pi\)
\(812\) 0 0
\(813\) 1.32227 16.2526i 0.0463741 0.570004i
\(814\) 0 0
\(815\) −7.40912 6.21699i −0.259530 0.217772i
\(816\) 0 0
\(817\) 5.28886 + 1.92499i 0.185034 + 0.0673468i
\(818\) 0 0
\(819\) −21.7135 + 26.5265i −0.758733 + 0.926911i
\(820\) 0 0
\(821\) −1.45626 + 1.22195i −0.0508240 + 0.0426464i −0.667846 0.744300i \(-0.732783\pi\)
0.617022 + 0.786946i \(0.288339\pi\)
\(822\) 0 0
\(823\) 3.82738 21.7062i 0.133414 0.756629i −0.842537 0.538639i \(-0.818939\pi\)
0.975951 0.217991i \(-0.0699502\pi\)
\(824\) 0 0
\(825\) −14.0105 + 14.1821i −0.487782 + 0.493757i
\(826\) 0 0
\(827\) 24.2488 42.0001i 0.843213 1.46049i −0.0439508 0.999034i \(-0.513994\pi\)
0.887164 0.461454i \(-0.152672\pi\)
\(828\) 0 0
\(829\) 10.1593 + 17.5964i 0.352846 + 0.611148i 0.986747 0.162267i \(-0.0518805\pi\)
−0.633900 + 0.773415i \(0.718547\pi\)
\(830\) 0 0
\(831\) 4.02735 8.77578i 0.139707 0.304428i
\(832\) 0 0
\(833\) −10.6780 + 3.88647i −0.369970 + 0.134658i
\(834\) 0 0
\(835\) 2.25622 + 12.7957i 0.0780797 + 0.442812i
\(836\) 0 0
\(837\) 2.53851 + 23.9656i 0.0877438 + 0.828371i
\(838\) 0 0
\(839\) 0.879762 + 4.98938i 0.0303728 + 0.172253i 0.996221 0.0868566i \(-0.0276822\pi\)
−0.965848 + 0.259109i \(0.916571\pi\)
\(840\) 0 0
\(841\) 26.9290 9.80136i 0.928587 0.337978i
\(842\) 0 0
\(843\) 28.0631 + 39.5635i 0.966545 + 1.36264i
\(844\) 0 0
\(845\) 5.36726 + 9.29636i 0.184639 + 0.319804i
\(846\) 0 0
\(847\) −10.6489 + 18.4444i −0.365901 + 0.633758i
\(848\) 0 0
\(849\) −10.3145 2.69657i −0.353992 0.0925459i
\(850\) 0 0
\(851\) −4.25467 + 24.1294i −0.145848 + 0.827147i
\(852\) 0 0
\(853\) 20.2756 17.0132i 0.694222 0.582521i −0.225902 0.974150i \(-0.572533\pi\)
0.920123 + 0.391629i \(0.128088\pi\)
\(854\) 0 0
\(855\) −10.6654 + 30.4516i −0.364750 + 1.04142i
\(856\) 0 0
\(857\) 17.2073 + 6.26295i 0.587790 + 0.213938i 0.618757 0.785582i \(-0.287636\pi\)
−0.0309669 + 0.999520i \(0.509859\pi\)
\(858\) 0 0
\(859\) 7.23097 + 6.06751i 0.246718 + 0.207021i 0.757757 0.652536i \(-0.226295\pi\)
−0.511040 + 0.859557i \(0.670740\pi\)
\(860\) 0 0
\(861\) −37.1836 25.7003i −1.26721 0.875865i
\(862\) 0 0
\(863\) 14.2154 0.483898 0.241949 0.970289i \(-0.422213\pi\)
0.241949 + 0.970289i \(0.422213\pi\)
\(864\) 0 0
\(865\) −53.9438 −1.83414
\(866\) 0 0
\(867\) −21.9481 + 10.3977i −0.745396 + 0.353124i
\(868\) 0 0
\(869\) −24.6696 20.7003i −0.836859 0.702208i
\(870\) 0 0
\(871\) −25.0800 9.12836i −0.849802 0.309303i
\(872\) 0 0
\(873\) −23.7097 + 14.0765i −0.802452 + 0.476416i
\(874\) 0 0
\(875\) −0.330555 + 0.277369i −0.0111748 + 0.00937677i
\(876\) 0 0
\(877\) 6.79059 38.5113i 0.229302 1.30044i −0.624986 0.780636i \(-0.714895\pi\)
0.854288 0.519800i \(-0.173993\pi\)
\(878\) 0 0
\(879\) −1.07056 3.90025i −0.0361091 0.131552i
\(880\) 0 0
\(881\) 11.4469 19.8266i 0.385657 0.667977i −0.606203 0.795310i \(-0.707308\pi\)
0.991860 + 0.127333i \(0.0406416\pi\)
\(882\) 0 0
\(883\) −8.57546 14.8531i −0.288587 0.499847i 0.684886 0.728651i \(-0.259852\pi\)
−0.973473 + 0.228803i \(0.926519\pi\)
\(884\) 0 0
\(885\) −52.7943 + 4.94294i −1.77466 + 0.166155i
\(886\) 0 0
\(887\) 17.1560 6.24427i 0.576042 0.209662i −0.0375373 0.999295i \(-0.511951\pi\)
0.613579 + 0.789633i \(0.289729\pi\)
\(888\) 0 0
\(889\) 3.83051 + 21.7239i 0.128471 + 0.728596i
\(890\) 0 0
\(891\) 19.1484 7.50231i 0.641494 0.251337i
\(892\) 0 0
\(893\) 2.27074 + 12.8780i 0.0759876 + 0.430947i
\(894\) 0 0
\(895\) −43.3342 + 15.7723i −1.44850 + 0.527211i
\(896\) 0 0
\(897\) −17.9271 + 1.67845i −0.598569 + 0.0560419i
\(898\) 0 0
\(899\) 1.35764 + 2.35150i 0.0452797 + 0.0784268i
\(900\) 0 0
\(901\) 2.22853 3.85993i 0.0742431 0.128593i
\(902\) 0 0
\(903\) −2.80150 10.2064i −0.0932280 0.339647i
\(904\) 0 0
\(905\) −7.16488 + 40.6341i −0.238169 + 1.35072i
\(906\) 0 0
\(907\) −22.3621 + 18.7640i −0.742521 + 0.623049i −0.933513 0.358542i \(-0.883274\pi\)
0.190992 + 0.981592i \(0.438829\pi\)
\(908\) 0 0
\(909\) 31.2896 + 17.5606i 1.03781 + 0.582449i
\(910\) 0 0
\(911\) 51.3409 + 18.6866i 1.70100 + 0.619114i 0.995939 0.0900315i \(-0.0286968\pi\)
0.705062 + 0.709145i \(0.250919\pi\)
\(912\) 0 0
\(913\) 5.42367 + 4.55100i 0.179497 + 0.150616i
\(914\) 0 0
\(915\) 64.9200 30.7552i 2.14619 1.01674i
\(916\) 0 0
\(917\) 60.5012 1.99793
\(918\) 0 0
\(919\) −41.0995 −1.35575 −0.677873 0.735179i \(-0.737098\pi\)
−0.677873 + 0.735179i \(0.737098\pi\)
\(920\) 0 0
\(921\) 9.72491 + 6.72160i 0.320447 + 0.221484i
\(922\) 0 0
\(923\) −4.72012 3.96065i −0.155365 0.130367i
\(924\) 0 0
\(925\) 34.5863 + 12.5884i 1.13719 + 0.413904i
\(926\) 0 0
\(927\) −24.9347 28.9917i −0.818962 0.952211i
\(928\) 0 0
\(929\) 11.1812 9.38218i 0.366845 0.307819i −0.440667 0.897671i \(-0.645258\pi\)
0.807512 + 0.589851i \(0.200814\pi\)
\(930\) 0 0
\(931\) 3.88158 22.0135i 0.127214 0.721464i
\(932\) 0 0
\(933\) −14.4033 3.76552i −0.471542 0.123278i
\(934\) 0 0
\(935\) −6.24668 + 10.8196i −0.204288 + 0.353838i
\(936\) 0 0
\(937\) −12.4641 21.5885i −0.407185 0.705265i 0.587388 0.809305i \(-0.300156\pi\)
−0.994573 + 0.104041i \(0.966823\pi\)
\(938\) 0 0
\(939\) −21.7140 30.6125i −0.708610 0.999001i
\(940\) 0 0
\(941\) −19.5873 + 7.12918i −0.638526 + 0.232405i −0.640938 0.767592i \(-0.721455\pi\)
0.00241179 + 0.999997i \(0.499232\pi\)
\(942\) 0 0
\(943\) −4.12268 23.3809i −0.134253 0.761387i
\(944\) 0 0
\(945\) 58.3104 16.7714i 1.89684 0.545572i
\(946\) 0 0
\(947\) −6.23623 35.3674i −0.202650 1.14929i −0.901095 0.433622i \(-0.857235\pi\)
0.698445 0.715664i \(-0.253876\pi\)
\(948\) 0 0
\(949\) −31.0192 + 11.2901i −1.00693 + 0.366491i
\(950\) 0 0
\(951\) 25.5161 55.6006i 0.827415 1.80297i
\(952\) 0 0
\(953\) −2.90103 5.02474i −0.0939737 0.162767i 0.815206 0.579171i \(-0.196624\pi\)
−0.909180 + 0.416404i \(0.863290\pi\)
\(954\) 0 0
\(955\) 5.70716 9.88509i 0.184679 0.319874i
\(956\) 0 0
\(957\) 1.62843 1.64838i 0.0526398 0.0532846i
\(958\) 0 0
\(959\) 0.135145 0.766447i 0.00436407 0.0247499i
\(960\) 0 0
\(961\) −7.26914 + 6.09953i −0.234488 + 0.196759i
\(962\) 0 0
\(963\) 18.0562 + 2.95759i 0.581853 + 0.0953070i
\(964\) 0 0
\(965\) −4.39077 1.59811i −0.141344 0.0514449i
\(966\) 0 0
\(967\) −22.7200 19.0644i −0.730627 0.613069i 0.199675 0.979862i \(-0.436011\pi\)
−0.930303 + 0.366793i \(0.880456\pi\)
\(968\) 0 0
\(969\) −0.822846 + 10.1140i −0.0264336 + 0.324907i
\(970\) 0 0
\(971\) −47.1522 −1.51318 −0.756592 0.653887i \(-0.773137\pi\)
−0.756592 + 0.653887i \(0.773137\pi\)
\(972\) 0 0
\(973\) 13.5322 0.433821
\(974\) 0 0
\(975\) −2.19328 + 26.9585i −0.0702411 + 0.863364i
\(976\) 0 0
\(977\) −18.2341 15.3002i −0.583361 0.489498i 0.302688 0.953090i \(-0.402116\pi\)
−0.886049 + 0.463592i \(0.846560\pi\)
\(978\) 0 0
\(979\) 37.2464 + 13.5566i 1.19040 + 0.433270i
\(980\) 0 0
\(981\) −33.2736 5.45018i −1.06234 0.174011i
\(982\) 0 0
\(983\) −8.48950 + 7.12353i −0.270773 + 0.227205i −0.768056 0.640383i \(-0.778776\pi\)
0.497283 + 0.867589i \(0.334331\pi\)
\(984\) 0 0
\(985\) 1.39659 7.92046i 0.0444991 0.252367i
\(986\) 0 0
\(987\) 17.2819 17.4936i 0.550090 0.556828i
\(988\) 0 0
\(989\) 2.77957 4.81435i 0.0883851 0.153087i
\(990\) 0 0
\(991\) 5.71846 + 9.90466i 0.181653 + 0.314632i 0.942443 0.334365i \(-0.108522\pi\)
−0.760791 + 0.648997i \(0.775189\pi\)
\(992\) 0 0
\(993\) 18.6485 40.6358i 0.591791 1.28954i
\(994\) 0 0
\(995\) −5.51286 + 2.00652i −0.174769 + 0.0636108i
\(996\) 0 0
\(997\) −4.84383 27.4707i −0.153406 0.870007i −0.960229 0.279214i \(-0.909926\pi\)
0.806823 0.590793i \(-0.201185\pi\)
\(998\) 0 0
\(999\) −27.3342 26.3536i −0.864816 0.833790i
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 432.2.u.b.337.2 12
4.3 odd 2 54.2.e.b.13.1 12
12.11 even 2 162.2.e.b.91.1 12
27.25 even 9 inner 432.2.u.b.241.2 12
36.7 odd 6 486.2.e.h.109.1 12
36.11 even 6 486.2.e.e.109.2 12
36.23 even 6 486.2.e.g.433.1 12
36.31 odd 6 486.2.e.f.433.2 12
108.7 odd 18 486.2.e.h.379.1 12
108.11 even 18 486.2.e.g.55.1 12
108.23 even 18 1458.2.c.g.487.5 12
108.31 odd 18 1458.2.c.f.487.2 12
108.43 odd 18 486.2.e.f.55.2 12
108.47 even 18 486.2.e.e.379.2 12
108.59 even 18 1458.2.a.f.1.2 6
108.67 odd 18 1458.2.c.f.973.2 12
108.79 odd 18 54.2.e.b.25.1 yes 12
108.83 even 18 162.2.e.b.73.1 12
108.95 even 18 1458.2.c.g.973.5 12
108.103 odd 18 1458.2.a.g.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.2.e.b.13.1 12 4.3 odd 2
54.2.e.b.25.1 yes 12 108.79 odd 18
162.2.e.b.73.1 12 108.83 even 18
162.2.e.b.91.1 12 12.11 even 2
432.2.u.b.241.2 12 27.25 even 9 inner
432.2.u.b.337.2 12 1.1 even 1 trivial
486.2.e.e.109.2 12 36.11 even 6
486.2.e.e.379.2 12 108.47 even 18
486.2.e.f.55.2 12 108.43 odd 18
486.2.e.f.433.2 12 36.31 odd 6
486.2.e.g.55.1 12 108.11 even 18
486.2.e.g.433.1 12 36.23 even 6
486.2.e.h.109.1 12 36.7 odd 6
486.2.e.h.379.1 12 108.7 odd 18
1458.2.a.f.1.2 6 108.59 even 18
1458.2.a.g.1.5 6 108.103 odd 18
1458.2.c.f.487.2 12 108.31 odd 18
1458.2.c.f.973.2 12 108.67 odd 18
1458.2.c.g.487.5 12 108.23 even 18
1458.2.c.g.973.5 12 108.95 even 18