Properties

Label 2646.2.e.o.2125.1
Level $2646$
Weight $2$
Character 2646.2125
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
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] = [2646,2,Mod(1549,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.1549");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.e (of order \(3\), degree \(2\), 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: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2125.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2125
Dual form 2646.2.e.o.1549.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +(-1.84981 + 3.20397i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +(-1.84981 + 3.20397i) q^{5} -1.00000 q^{8} +(1.84981 - 3.20397i) q^{10} +(-0.738550 - 1.27921i) q^{11} +(1.34981 + 2.33795i) q^{13} +1.00000 q^{16} +(3.28799 - 5.69497i) q^{17} +(0.444368 + 0.769668i) q^{19} +(-1.84981 + 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} +(3.14400 - 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +(-1.34981 - 2.33795i) q^{26} +(-1.25526 + 2.17417i) q^{29} -6.81089 q^{31} -1.00000 q^{32} +(-3.28799 + 5.69497i) q^{34} +(-1.38874 - 2.40536i) q^{37} +(-0.444368 - 0.769668i) q^{38} +(1.84981 - 3.20397i) q^{40} +(-2.05563 - 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(-0.738550 - 1.27921i) q^{44} +(-3.14400 + 5.44556i) q^{46} -6.98762 q^{47} +(4.34362 + 7.52338i) q^{50} +(1.34981 + 2.33795i) q^{52} +(1.60507 - 2.78007i) q^{53} +5.46472 q^{55} +(1.25526 - 2.17417i) q^{58} +6.90978 q^{59} +5.73305 q^{61} +6.81089 q^{62} +1.00000 q^{64} -9.98762 q^{65} -9.46472 q^{67} +(3.28799 - 5.69497i) q^{68} +5.46472 q^{71} +(6.03273 - 10.4490i) q^{73} +(1.38874 + 2.40536i) q^{74} +(0.444368 + 0.769668i) q^{76} +11.4523 q^{79} +(-1.84981 + 3.20397i) q^{80} +(2.05563 + 3.56046i) q^{82} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +(-0.00618986 + 0.0107211i) q^{86} +(0.738550 + 1.27921i) q^{88} +(-4.43818 - 7.68715i) q^{89} +(3.14400 - 5.44556i) q^{92} +6.98762 q^{94} -3.28799 q^{95} +(6.58836 - 11.4114i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} - 5 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} - 5 q^{5} - 6 q^{8} + 5 q^{10} + q^{11} + 2 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} - 2 q^{26} + 5 q^{29} - 28 q^{31} - 6 q^{32} + 4 q^{34} - 9 q^{37} - 3 q^{38} + 5 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} - 6 q^{47} + 2 q^{50} + 2 q^{52} - 9 q^{53} - 14 q^{55} - 5 q^{58} - 8 q^{59} + 8 q^{61} + 28 q^{62} + 6 q^{64} - 24 q^{65} - 10 q^{67} - 4 q^{68} - 14 q^{71} + 25 q^{73} + 9 q^{74} + 3 q^{76} - 14 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} - 9 q^{89} + 7 q^{92} + 6 q^{94} + 4 q^{95} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.84981 + 3.20397i −0.827262 + 1.43286i 0.0729162 + 0.997338i \(0.476769\pi\)
−0.900178 + 0.435522i \(0.856564\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.84981 3.20397i 0.584963 1.01318i
\(11\) −0.738550 1.27921i −0.222681 0.385695i 0.732940 0.680293i \(-0.238148\pi\)
−0.955621 + 0.294598i \(0.904814\pi\)
\(12\) 0 0
\(13\) 1.34981 + 2.33795i 0.374371 + 0.648430i 0.990233 0.139425i \(-0.0445253\pi\)
−0.615862 + 0.787854i \(0.711192\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.28799 5.69497i 0.797455 1.38123i −0.123813 0.992306i \(-0.539512\pi\)
0.921268 0.388927i \(-0.127154\pi\)
\(18\) 0 0
\(19\) 0.444368 + 0.769668i 0.101945 + 0.176574i 0.912486 0.409108i \(-0.134160\pi\)
−0.810541 + 0.585682i \(0.800827\pi\)
\(20\) −1.84981 + 3.20397i −0.413631 + 0.716430i
\(21\) 0 0
\(22\) 0.738550 + 1.27921i 0.157459 + 0.272728i
\(23\) 3.14400 5.44556i 0.655568 1.13548i −0.326182 0.945307i \(-0.605762\pi\)
0.981751 0.190171i \(-0.0609043\pi\)
\(24\) 0 0
\(25\) −4.34362 7.52338i −0.868725 1.50468i
\(26\) −1.34981 2.33795i −0.264720 0.458509i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.25526 + 2.17417i −0.233096 + 0.403734i −0.958718 0.284360i \(-0.908219\pi\)
0.725622 + 0.688094i \(0.241552\pi\)
\(30\) 0 0
\(31\) −6.81089 −1.22327 −0.611636 0.791139i \(-0.709488\pi\)
−0.611636 + 0.791139i \(0.709488\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.28799 + 5.69497i −0.563886 + 0.976679i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.38874 2.40536i −0.228307 0.395439i 0.729000 0.684514i \(-0.239986\pi\)
−0.957306 + 0.289075i \(0.906652\pi\)
\(38\) −0.444368 0.769668i −0.0720860 0.124857i
\(39\) 0 0
\(40\) 1.84981 3.20397i 0.292481 0.506592i
\(41\) −2.05563 3.56046i −0.321036 0.556050i 0.659666 0.751559i \(-0.270698\pi\)
−0.980702 + 0.195508i \(0.937364\pi\)
\(42\) 0 0
\(43\) 0.00618986 0.0107211i 0.000943944 0.00163496i −0.865553 0.500817i \(-0.833033\pi\)
0.866497 + 0.499182i \(0.166366\pi\)
\(44\) −0.738550 1.27921i −0.111341 0.192848i
\(45\) 0 0
\(46\) −3.14400 + 5.44556i −0.463557 + 0.802904i
\(47\) −6.98762 −1.01925 −0.509625 0.860397i \(-0.670216\pi\)
−0.509625 + 0.860397i \(0.670216\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.34362 + 7.52338i 0.614281 + 1.06397i
\(51\) 0 0
\(52\) 1.34981 + 2.33795i 0.187186 + 0.324215i
\(53\) 1.60507 2.78007i 0.220474 0.381872i −0.734478 0.678632i \(-0.762573\pi\)
0.954952 + 0.296760i \(0.0959063\pi\)
\(54\) 0 0
\(55\) 5.46472 0.736863
\(56\) 0 0
\(57\) 0 0
\(58\) 1.25526 2.17417i 0.164824 0.285483i
\(59\) 6.90978 0.899576 0.449788 0.893135i \(-0.351499\pi\)
0.449788 + 0.893135i \(0.351499\pi\)
\(60\) 0 0
\(61\) 5.73305 0.734042 0.367021 0.930213i \(-0.380378\pi\)
0.367021 + 0.930213i \(0.380378\pi\)
\(62\) 6.81089 0.864984
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −9.98762 −1.23881
\(66\) 0 0
\(67\) −9.46472 −1.15630 −0.578150 0.815931i \(-0.696225\pi\)
−0.578150 + 0.815931i \(0.696225\pi\)
\(68\) 3.28799 5.69497i 0.398728 0.690616i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.46472 0.648543 0.324271 0.945964i \(-0.394881\pi\)
0.324271 + 0.945964i \(0.394881\pi\)
\(72\) 0 0
\(73\) 6.03273 10.4490i 0.706078 1.22296i −0.260223 0.965548i \(-0.583796\pi\)
0.966301 0.257414i \(-0.0828705\pi\)
\(74\) 1.38874 + 2.40536i 0.161437 + 0.279618i
\(75\) 0 0
\(76\) 0.444368 + 0.769668i 0.0509725 + 0.0882870i
\(77\) 0 0
\(78\) 0 0
\(79\) 11.4523 1.28849 0.644244 0.764820i \(-0.277172\pi\)
0.644244 + 0.764820i \(0.277172\pi\)
\(80\) −1.84981 + 3.20397i −0.206816 + 0.358215i
\(81\) 0 0
\(82\) 2.05563 + 3.56046i 0.227007 + 0.393187i
\(83\) 2.23855 3.87728i 0.245713 0.425587i −0.716619 0.697465i \(-0.754311\pi\)
0.962332 + 0.271878i \(0.0876447\pi\)
\(84\) 0 0
\(85\) 12.1643 + 21.0693i 1.31941 + 2.28528i
\(86\) −0.00618986 + 0.0107211i −0.000667469 + 0.00115609i
\(87\) 0 0
\(88\) 0.738550 + 1.27921i 0.0787297 + 0.136364i
\(89\) −4.43818 7.68715i −0.470446 0.814836i 0.528983 0.848633i \(-0.322574\pi\)
−0.999429 + 0.0337963i \(0.989240\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.14400 5.44556i 0.327784 0.567739i
\(93\) 0 0
\(94\) 6.98762 0.720718
\(95\) −3.28799 −0.337341
\(96\) 0 0
\(97\) 6.58836 11.4114i 0.668947 1.15865i −0.309252 0.950980i \(-0.600079\pi\)
0.978199 0.207670i \(-0.0665880\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −4.34362 7.52338i −0.434362 0.752338i
\(101\) −2.62729 4.55059i −0.261425 0.452801i 0.705196 0.709012i \(-0.250859\pi\)
−0.966621 + 0.256212i \(0.917526\pi\)
\(102\) 0 0
\(103\) 0.833104 1.44298i 0.0820882 0.142181i −0.822059 0.569403i \(-0.807174\pi\)
0.904147 + 0.427222i \(0.140508\pi\)
\(104\) −1.34981 2.33795i −0.132360 0.229255i
\(105\) 0 0
\(106\) −1.60507 + 2.78007i −0.155899 + 0.270024i
\(107\) 5.38255 + 9.32284i 0.520350 + 0.901273i 0.999720 + 0.0236602i \(0.00753198\pi\)
−0.479370 + 0.877613i \(0.659135\pi\)
\(108\) 0 0
\(109\) −0.0945538 + 0.163772i −0.00905662 + 0.0156865i −0.870518 0.492136i \(-0.836216\pi\)
0.861462 + 0.507823i \(0.169550\pi\)
\(110\) −5.46472 −0.521041
\(111\) 0 0
\(112\) 0 0
\(113\) 6.78180 + 11.7464i 0.637978 + 1.10501i 0.985876 + 0.167478i \(0.0535624\pi\)
−0.347897 + 0.937533i \(0.613104\pi\)
\(114\) 0 0
\(115\) 11.6316 + 20.1466i 1.08465 + 1.87868i
\(116\) −1.25526 + 2.17417i −0.116548 + 0.201867i
\(117\) 0 0
\(118\) −6.90978 −0.636097
\(119\) 0 0
\(120\) 0 0
\(121\) 4.40909 7.63676i 0.400826 0.694251i
\(122\) −5.73305 −0.519046
\(123\) 0 0
\(124\) −6.81089 −0.611636
\(125\) 13.6414 1.22013
\(126\) 0 0
\(127\) −2.85669 −0.253490 −0.126745 0.991935i \(-0.540453\pi\)
−0.126745 + 0.991935i \(0.540453\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 9.98762 0.875972
\(131\) −0.0778435 + 0.134829i −0.00680122 + 0.0117801i −0.869406 0.494098i \(-0.835498\pi\)
0.862605 + 0.505878i \(0.168832\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 9.46472 0.817627
\(135\) 0 0
\(136\) −3.28799 + 5.69497i −0.281943 + 0.488340i
\(137\) −1.70582 2.95456i −0.145738 0.252425i 0.783910 0.620874i \(-0.213222\pi\)
−0.929648 + 0.368449i \(0.879889\pi\)
\(138\) 0 0
\(139\) 6.75526 + 11.7005i 0.572974 + 0.992420i 0.996259 + 0.0864229i \(0.0275436\pi\)
−0.423285 + 0.905997i \(0.639123\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.46472 −0.458589
\(143\) 1.99381 3.45338i 0.166731 0.288786i
\(144\) 0 0
\(145\) −4.64400 8.04364i −0.385663 0.667988i
\(146\) −6.03273 + 10.4490i −0.499272 + 0.864765i
\(147\) 0 0
\(148\) −1.38874 2.40536i −0.114153 0.197719i
\(149\) 0.166896 0.289073i 0.0136727 0.0236818i −0.859108 0.511794i \(-0.828981\pi\)
0.872781 + 0.488112i \(0.162314\pi\)
\(150\) 0 0
\(151\) 9.95489 + 17.2424i 0.810117 + 1.40316i 0.912781 + 0.408448i \(0.133930\pi\)
−0.102664 + 0.994716i \(0.532737\pi\)
\(152\) −0.444368 0.769668i −0.0360430 0.0624283i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.5989 21.8219i 1.01197 1.75278i
\(156\) 0 0
\(157\) 6.96286 0.555697 0.277848 0.960625i \(-0.410379\pi\)
0.277848 + 0.960625i \(0.410379\pi\)
\(158\) −11.4523 −0.911099
\(159\) 0 0
\(160\) 1.84981 3.20397i 0.146241 0.253296i
\(161\) 0 0
\(162\) 0 0
\(163\) 4.03706 + 6.99240i 0.316207 + 0.547687i 0.979693 0.200502i \(-0.0642572\pi\)
−0.663486 + 0.748189i \(0.730924\pi\)
\(164\) −2.05563 3.56046i −0.160518 0.278025i
\(165\) 0 0
\(166\) −2.23855 + 3.87728i −0.173745 + 0.300935i
\(167\) 9.74288 + 16.8752i 0.753927 + 1.30584i 0.945906 + 0.324440i \(0.105176\pi\)
−0.191979 + 0.981399i \(0.561491\pi\)
\(168\) 0 0
\(169\) 2.85600 4.94674i 0.219693 0.380519i
\(170\) −12.1643 21.0693i −0.932963 1.61594i
\(171\) 0 0
\(172\) 0.00618986 0.0107211i 0.000471972 0.000817480i
\(173\) 22.5636 1.71548 0.857740 0.514085i \(-0.171868\pi\)
0.857740 + 0.514085i \(0.171868\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.738550 1.27921i −0.0556703 0.0964238i
\(177\) 0 0
\(178\) 4.43818 + 7.68715i 0.332656 + 0.576176i
\(179\) −0.166896 + 0.289073i −0.0124744 + 0.0216063i −0.872195 0.489158i \(-0.837304\pi\)
0.859721 + 0.510764i \(0.170637\pi\)
\(180\) 0 0
\(181\) −23.2422 −1.72758 −0.863789 0.503853i \(-0.831915\pi\)
−0.863789 + 0.503853i \(0.831915\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.14400 + 5.44556i −0.231778 + 0.401452i
\(185\) 10.2756 0.755478
\(186\) 0 0
\(187\) −9.71339 −0.710313
\(188\) −6.98762 −0.509625
\(189\) 0 0
\(190\) 3.28799 0.238536
\(191\) 16.3214 1.18098 0.590488 0.807046i \(-0.298935\pi\)
0.590488 + 0.807046i \(0.298935\pi\)
\(192\) 0 0
\(193\) −14.3214 −1.03088 −0.515439 0.856926i \(-0.672371\pi\)
−0.515439 + 0.856926i \(0.672371\pi\)
\(194\) −6.58836 + 11.4114i −0.473017 + 0.819289i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.42402 −0.172704 −0.0863520 0.996265i \(-0.527521\pi\)
−0.0863520 + 0.996265i \(0.527521\pi\)
\(198\) 0 0
\(199\) 3.05563 5.29251i 0.216608 0.375176i −0.737161 0.675717i \(-0.763834\pi\)
0.953769 + 0.300541i \(0.0971673\pi\)
\(200\) 4.34362 + 7.52338i 0.307141 + 0.531983i
\(201\) 0 0
\(202\) 2.62729 + 4.55059i 0.184855 + 0.320179i
\(203\) 0 0
\(204\) 0 0
\(205\) 15.2101 1.06232
\(206\) −0.833104 + 1.44298i −0.0580451 + 0.100537i
\(207\) 0 0
\(208\) 1.34981 + 2.33795i 0.0935928 + 0.162107i
\(209\) 0.656376 1.13688i 0.0454025 0.0786394i
\(210\) 0 0
\(211\) 5.72253 + 9.91171i 0.393955 + 0.682350i 0.992967 0.118390i \(-0.0377732\pi\)
−0.599012 + 0.800740i \(0.704440\pi\)
\(212\) 1.60507 2.78007i 0.110237 0.190936i
\(213\) 0 0
\(214\) −5.38255 9.32284i −0.367943 0.637296i
\(215\) 0.0229002 + 0.0396643i 0.00156178 + 0.00270508i
\(216\) 0 0
\(217\) 0 0
\(218\) 0.0945538 0.163772i 0.00640399 0.0110920i
\(219\) 0 0
\(220\) 5.46472 0.368431
\(221\) 17.7527 1.19418
\(222\) 0 0
\(223\) 3.61126 6.25489i 0.241828 0.418859i −0.719407 0.694589i \(-0.755586\pi\)
0.961235 + 0.275730i \(0.0889196\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.78180 11.7464i −0.451119 0.781361i
\(227\) −6.82760 11.8258i −0.453164 0.784903i 0.545417 0.838165i \(-0.316371\pi\)
−0.998581 + 0.0532622i \(0.983038\pi\)
\(228\) 0 0
\(229\) 8.68725 15.0468i 0.574070 0.994318i −0.422073 0.906562i \(-0.638697\pi\)
0.996142 0.0877555i \(-0.0279694\pi\)
\(230\) −11.6316 20.1466i −0.766966 1.32842i
\(231\) 0 0
\(232\) 1.25526 2.17417i 0.0824119 0.142742i
\(233\) −7.62110 13.2001i −0.499275 0.864769i 0.500725 0.865606i \(-0.333067\pi\)
−1.00000 0.000837426i \(0.999733\pi\)
\(234\) 0 0
\(235\) 12.9258 22.3881i 0.843186 1.46044i
\(236\) 6.90978 0.449788
\(237\) 0 0
\(238\) 0 0
\(239\) −9.47524 16.4116i −0.612902 1.06158i −0.990749 0.135710i \(-0.956669\pi\)
0.377846 0.925868i \(-0.376665\pi\)
\(240\) 0 0
\(241\) −12.2527 21.2223i −0.789267 1.36705i −0.926417 0.376500i \(-0.877128\pi\)
0.137150 0.990550i \(-0.456206\pi\)
\(242\) −4.40909 + 7.63676i −0.283427 + 0.490910i
\(243\) 0 0
\(244\) 5.73305 0.367021
\(245\) 0 0
\(246\) 0 0
\(247\) −1.19963 + 2.07782i −0.0763305 + 0.132208i
\(248\) 6.81089 0.432492
\(249\) 0 0
\(250\) −13.6414 −0.862761
\(251\) −12.1236 −0.765238 −0.382619 0.923906i \(-0.624978\pi\)
−0.382619 + 0.923906i \(0.624978\pi\)
\(252\) 0 0
\(253\) −9.28799 −0.583931
\(254\) 2.85669 0.179245
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 4.10439 7.10900i 0.256025 0.443448i −0.709149 0.705059i \(-0.750921\pi\)
0.965173 + 0.261611i \(0.0842539\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −9.98762 −0.619406
\(261\) 0 0
\(262\) 0.0778435 0.134829i 0.00480919 0.00832976i
\(263\) −2.67309 4.62992i −0.164830 0.285493i 0.771765 0.635908i \(-0.219374\pi\)
−0.936595 + 0.350414i \(0.886041\pi\)
\(264\) 0 0
\(265\) 5.93818 + 10.2852i 0.364779 + 0.631816i
\(266\) 0 0
\(267\) 0 0
\(268\) −9.46472 −0.578150
\(269\) 9.24219 16.0079i 0.563506 0.976022i −0.433681 0.901067i \(-0.642785\pi\)
0.997187 0.0749550i \(-0.0238813\pi\)
\(270\) 0 0
\(271\) 3.67742 + 6.36947i 0.223387 + 0.386918i 0.955834 0.293906i \(-0.0949552\pi\)
−0.732447 + 0.680824i \(0.761622\pi\)
\(272\) 3.28799 5.69497i 0.199364 0.345308i
\(273\) 0 0
\(274\) 1.70582 + 2.95456i 0.103052 + 0.178492i
\(275\) −6.41597 + 11.1128i −0.386897 + 0.670126i
\(276\) 0 0
\(277\) 4.54944 + 7.87987i 0.273349 + 0.473455i 0.969717 0.244230i \(-0.0785351\pi\)
−0.696368 + 0.717685i \(0.745202\pi\)
\(278\) −6.75526 11.7005i −0.405154 0.701747i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00433 + 10.3998i −0.358188 + 0.620400i −0.987658 0.156624i \(-0.949939\pi\)
0.629470 + 0.777025i \(0.283272\pi\)
\(282\) 0 0
\(283\) −9.84294 −0.585102 −0.292551 0.956250i \(-0.594504\pi\)
−0.292551 + 0.956250i \(0.594504\pi\)
\(284\) 5.46472 0.324271
\(285\) 0 0
\(286\) −1.99381 + 3.45338i −0.117896 + 0.204203i
\(287\) 0 0
\(288\) 0 0
\(289\) −13.1218 22.7276i −0.771870 1.33692i
\(290\) 4.64400 + 8.04364i 0.272705 + 0.472339i
\(291\) 0 0
\(292\) 6.03273 10.4490i 0.353039 0.611481i
\(293\) 10.7101 + 18.5505i 0.625694 + 1.08373i 0.988406 + 0.151832i \(0.0485173\pi\)
−0.362713 + 0.931901i \(0.618149\pi\)
\(294\) 0 0
\(295\) −12.7818 + 22.1387i −0.744185 + 1.28897i
\(296\) 1.38874 + 2.40536i 0.0807186 + 0.139809i
\(297\) 0 0
\(298\) −0.166896 + 0.289073i −0.00966804 + 0.0167455i
\(299\) 16.9752 0.981704
\(300\) 0 0
\(301\) 0 0
\(302\) −9.95489 17.2424i −0.572839 0.992187i
\(303\) 0 0
\(304\) 0.444368 + 0.769668i 0.0254862 + 0.0441435i
\(305\) −10.6051 + 18.3685i −0.607245 + 1.05178i
\(306\) 0 0
\(307\) 5.68725 0.324588 0.162294 0.986742i \(-0.448111\pi\)
0.162294 + 0.986742i \(0.448111\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.5989 + 21.8219i −0.715569 + 1.23940i
\(311\) −11.7207 −0.664618 −0.332309 0.943171i \(-0.607828\pi\)
−0.332309 + 0.943171i \(0.607828\pi\)
\(312\) 0 0
\(313\) 26.7738 1.51334 0.756671 0.653796i \(-0.226824\pi\)
0.756671 + 0.653796i \(0.226824\pi\)
\(314\) −6.96286 −0.392937
\(315\) 0 0
\(316\) 11.4523 0.644244
\(317\) −1.90249 −0.106855 −0.0534273 0.998572i \(-0.517015\pi\)
−0.0534273 + 0.998572i \(0.517015\pi\)
\(318\) 0 0
\(319\) 3.70829 0.207624
\(320\) −1.84981 + 3.20397i −0.103408 + 0.179107i
\(321\) 0 0
\(322\) 0 0
\(323\) 5.84431 0.325186
\(324\) 0 0
\(325\) 11.7262 20.3103i 0.650451 1.12661i
\(326\) −4.03706 6.99240i −0.223592 0.387273i
\(327\) 0 0
\(328\) 2.05563 + 3.56046i 0.113503 + 0.196593i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.56732 0.306008 0.153004 0.988226i \(-0.451105\pi\)
0.153004 + 0.988226i \(0.451105\pi\)
\(332\) 2.23855 3.87728i 0.122856 0.212794i
\(333\) 0 0
\(334\) −9.74288 16.8752i −0.533107 0.923368i
\(335\) 17.5080 30.3247i 0.956563 1.65682i
\(336\) 0 0
\(337\) −16.8869 29.2489i −0.919887 1.59329i −0.799585 0.600553i \(-0.794947\pi\)
−0.120302 0.992737i \(-0.538386\pi\)
\(338\) −2.85600 + 4.94674i −0.155346 + 0.269067i
\(339\) 0 0
\(340\) 12.1643 + 21.0693i 0.659704 + 1.14264i
\(341\) 5.03018 + 8.71253i 0.272400 + 0.471810i
\(342\) 0 0
\(343\) 0 0
\(344\) −0.00618986 + 0.0107211i −0.000333735 + 0.000578045i
\(345\) 0 0
\(346\) −22.5636 −1.21303
\(347\) 30.4065 1.63231 0.816154 0.577834i \(-0.196102\pi\)
0.816154 + 0.577834i \(0.196102\pi\)
\(348\) 0 0
\(349\) 6.29782 10.9082i 0.337115 0.583900i −0.646774 0.762682i \(-0.723882\pi\)
0.983889 + 0.178782i \(0.0572156\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.738550 + 1.27921i 0.0393648 + 0.0681819i
\(353\) 3.76578 + 6.52252i 0.200432 + 0.347159i 0.948668 0.316274i \(-0.102432\pi\)
−0.748235 + 0.663433i \(0.769099\pi\)
\(354\) 0 0
\(355\) −10.1087 + 17.5088i −0.536515 + 0.929271i
\(356\) −4.43818 7.68715i −0.235223 0.407418i
\(357\) 0 0
\(358\) 0.166896 0.289073i 0.00882074 0.0152780i
\(359\) 3.44801 + 5.97213i 0.181979 + 0.315197i 0.942554 0.334053i \(-0.108416\pi\)
−0.760575 + 0.649250i \(0.775083\pi\)
\(360\) 0 0
\(361\) 9.10507 15.7705i 0.479214 0.830024i
\(362\) 23.2422 1.22158
\(363\) 0 0
\(364\) 0 0
\(365\) 22.3189 + 38.6574i 1.16822 + 2.02342i
\(366\) 0 0
\(367\) 11.5618 + 20.0257i 0.603522 + 1.04533i 0.992283 + 0.123992i \(0.0395699\pi\)
−0.388761 + 0.921339i \(0.627097\pi\)
\(368\) 3.14400 5.44556i 0.163892 0.283869i
\(369\) 0 0
\(370\) −10.2756 −0.534204
\(371\) 0 0
\(372\) 0 0
\(373\) −14.5822 + 25.2571i −0.755036 + 1.30776i 0.190320 + 0.981722i \(0.439047\pi\)
−0.945356 + 0.326039i \(0.894286\pi\)
\(374\) 9.71339 0.502267
\(375\) 0 0
\(376\) 6.98762 0.360359
\(377\) −6.77747 −0.349058
\(378\) 0 0
\(379\) −13.5622 −0.696645 −0.348322 0.937375i \(-0.613249\pi\)
−0.348322 + 0.937375i \(0.613249\pi\)
\(380\) −3.28799 −0.168670
\(381\) 0 0
\(382\) −16.3214 −0.835076
\(383\) 1.41783 2.45575i 0.0724475 0.125483i −0.827526 0.561428i \(-0.810252\pi\)
0.899973 + 0.435945i \(0.143586\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.3214 0.728941
\(387\) 0 0
\(388\) 6.58836 11.4114i 0.334474 0.579325i
\(389\) −9.30401 16.1150i −0.471732 0.817064i 0.527745 0.849403i \(-0.323038\pi\)
−0.999477 + 0.0323388i \(0.989704\pi\)
\(390\) 0 0
\(391\) −20.6749 35.8099i −1.04557 1.81099i
\(392\) 0 0
\(393\) 0 0
\(394\) 2.42402 0.122120
\(395\) −21.1847 + 36.6930i −1.06592 + 1.84622i
\(396\) 0 0
\(397\) 10.2880 + 17.8193i 0.516340 + 0.894326i 0.999820 + 0.0189712i \(0.00603907\pi\)
−0.483481 + 0.875355i \(0.660628\pi\)
\(398\) −3.05563 + 5.29251i −0.153165 + 0.265290i
\(399\) 0 0
\(400\) −4.34362 7.52338i −0.217181 0.376169i
\(401\) −3.37704 + 5.84921i −0.168642 + 0.292096i −0.937942 0.346791i \(-0.887271\pi\)
0.769301 + 0.638887i \(0.220605\pi\)
\(402\) 0 0
\(403\) −9.19344 15.9235i −0.457958 0.793206i
\(404\) −2.62729 4.55059i −0.130712 0.226400i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.05130 + 3.55296i −0.101679 + 0.176114i
\(408\) 0 0
\(409\) −15.3214 −0.757595 −0.378798 0.925480i \(-0.623662\pi\)
−0.378798 + 0.925480i \(0.623662\pi\)
\(410\) −15.2101 −0.751176
\(411\) 0 0
\(412\) 0.833104 1.44298i 0.0410441 0.0710904i
\(413\) 0 0
\(414\) 0 0
\(415\) 8.28180 + 14.3445i 0.406538 + 0.704144i
\(416\) −1.34981 2.33795i −0.0661801 0.114627i
\(417\) 0 0
\(418\) −0.656376 + 1.13688i −0.0321044 + 0.0556064i
\(419\) −4.32141 7.48491i −0.211115 0.365662i 0.740949 0.671561i \(-0.234376\pi\)
−0.952064 + 0.305900i \(0.901043\pi\)
\(420\) 0 0
\(421\) 18.5636 32.1531i 0.904735 1.56705i 0.0834618 0.996511i \(-0.473402\pi\)
0.821273 0.570536i \(-0.193264\pi\)
\(422\) −5.72253 9.91171i −0.278568 0.482494i
\(423\) 0 0
\(424\) −1.60507 + 2.78007i −0.0779493 + 0.135012i
\(425\) −57.1272 −2.77108
\(426\) 0 0
\(427\) 0 0
\(428\) 5.38255 + 9.32284i 0.260175 + 0.450637i
\(429\) 0 0
\(430\) −0.0229002 0.0396643i −0.00110434 0.00191278i
\(431\) 4.71015 8.15822i 0.226880 0.392967i −0.730002 0.683445i \(-0.760481\pi\)
0.956882 + 0.290478i \(0.0938142\pi\)
\(432\) 0 0
\(433\) 0.208771 0.0100329 0.00501645 0.999987i \(-0.498403\pi\)
0.00501645 + 0.999987i \(0.498403\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.0945538 + 0.163772i −0.00452831 + 0.00784326i
\(437\) 5.58836 0.267328
\(438\) 0 0
\(439\) 9.96796 0.475745 0.237872 0.971296i \(-0.423550\pi\)
0.237872 + 0.971296i \(0.423550\pi\)
\(440\) −5.46472 −0.260520
\(441\) 0 0
\(442\) −17.7527 −0.844410
\(443\) 15.6996 0.745912 0.372956 0.927849i \(-0.378344\pi\)
0.372956 + 0.927849i \(0.378344\pi\)
\(444\) 0 0
\(445\) 32.8392 1.55673
\(446\) −3.61126 + 6.25489i −0.170998 + 0.296178i
\(447\) 0 0
\(448\) 0 0
\(449\) −33.6253 −1.58688 −0.793439 0.608650i \(-0.791712\pi\)
−0.793439 + 0.608650i \(0.791712\pi\)
\(450\) 0 0
\(451\) −3.03637 + 5.25915i −0.142977 + 0.247644i
\(452\) 6.78180 + 11.7464i 0.318989 + 0.552505i
\(453\) 0 0
\(454\) 6.82760 + 11.8258i 0.320435 + 0.555010i
\(455\) 0 0
\(456\) 0 0
\(457\) 32.7083 1.53003 0.765015 0.644013i \(-0.222732\pi\)
0.765015 + 0.644013i \(0.222732\pi\)
\(458\) −8.68725 + 15.0468i −0.405928 + 0.703089i
\(459\) 0 0
\(460\) 11.6316 + 20.1466i 0.542327 + 0.939338i
\(461\) −2.07165 + 3.58821i −0.0964865 + 0.167120i −0.910228 0.414107i \(-0.864094\pi\)
0.813742 + 0.581227i \(0.197427\pi\)
\(462\) 0 0
\(463\) −8.34176 14.4484i −0.387675 0.671472i 0.604462 0.796634i \(-0.293388\pi\)
−0.992136 + 0.125162i \(0.960055\pi\)
\(464\) −1.25526 + 2.17417i −0.0582740 + 0.100934i
\(465\) 0 0
\(466\) 7.62110 + 13.2001i 0.353040 + 0.611484i
\(467\) 14.9585 + 25.9089i 0.692198 + 1.19892i 0.971116 + 0.238608i \(0.0766909\pi\)
−0.278918 + 0.960315i \(0.589976\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −12.9258 + 22.3881i −0.596223 + 1.03269i
\(471\) 0 0
\(472\) −6.90978 −0.318048
\(473\) −0.0182861 −0.000840794
\(474\) 0 0
\(475\) 3.86033 6.68630i 0.177124 0.306788i
\(476\) 0 0
\(477\) 0 0
\(478\) 9.47524 + 16.4116i 0.433387 + 0.750649i
\(479\) 1.47965 + 2.56283i 0.0676068 + 0.117098i 0.897847 0.440307i \(-0.145130\pi\)
−0.830241 + 0.557405i \(0.811797\pi\)
\(480\) 0 0
\(481\) 3.74907 6.49358i 0.170943 0.296082i
\(482\) 12.2527 + 21.2223i 0.558096 + 0.966650i
\(483\) 0 0
\(484\) 4.40909 7.63676i 0.200413 0.347126i
\(485\) 24.3745 + 42.2179i 1.10679 + 1.91701i
\(486\) 0 0
\(487\) −14.0309 + 24.3022i −0.635800 + 1.10124i 0.350546 + 0.936546i \(0.385996\pi\)
−0.986345 + 0.164691i \(0.947337\pi\)
\(488\) −5.73305 −0.259523
\(489\) 0 0
\(490\) 0 0
\(491\) −17.0734 29.5721i −0.770513 1.33457i −0.937282 0.348572i \(-0.886667\pi\)
0.166769 0.985996i \(-0.446667\pi\)
\(492\) 0 0
\(493\) 8.25457 + 14.2973i 0.371767 + 0.643920i
\(494\) 1.19963 2.07782i 0.0539738 0.0934854i
\(495\) 0 0
\(496\) −6.81089 −0.305818
\(497\) 0 0
\(498\) 0 0
\(499\) 1.14035 1.97515i 0.0510493 0.0884199i −0.839372 0.543558i \(-0.817077\pi\)
0.890421 + 0.455138i \(0.150410\pi\)
\(500\) 13.6414 0.610064
\(501\) 0 0
\(502\) 12.1236 0.541105
\(503\) 13.9890 0.623739 0.311869 0.950125i \(-0.399045\pi\)
0.311869 + 0.950125i \(0.399045\pi\)
\(504\) 0 0
\(505\) 19.4400 0.865067
\(506\) 9.28799 0.412902
\(507\) 0 0
\(508\) −2.85669 −0.126745
\(509\) −12.8090 + 22.1859i −0.567750 + 0.983373i 0.429038 + 0.903287i \(0.358853\pi\)
−0.996788 + 0.0800859i \(0.974481\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −4.10439 + 7.10900i −0.181037 + 0.313565i
\(515\) 3.08217 + 5.33848i 0.135817 + 0.235242i
\(516\) 0 0
\(517\) 5.16071 + 8.93861i 0.226968 + 0.393119i
\(518\) 0 0
\(519\) 0 0
\(520\) 9.98762 0.437986
\(521\) −20.9127 + 36.2219i −0.916203 + 1.58691i −0.111073 + 0.993812i \(0.535429\pi\)
−0.805130 + 0.593099i \(0.797904\pi\)
\(522\) 0 0
\(523\) −7.88323 13.6542i −0.344710 0.597055i 0.640591 0.767882i \(-0.278689\pi\)
−0.985301 + 0.170827i \(0.945356\pi\)
\(524\) −0.0778435 + 0.134829i −0.00340061 + 0.00589003i
\(525\) 0 0
\(526\) 2.67309 + 4.62992i 0.116552 + 0.201874i
\(527\) −22.3942 + 38.7878i −0.975505 + 1.68962i
\(528\) 0 0
\(529\) −8.26942 14.3231i −0.359540 0.622742i
\(530\) −5.93818 10.2852i −0.257938 0.446762i
\(531\) 0 0
\(532\) 0 0
\(533\) 5.54944 9.61192i 0.240373 0.416338i
\(534\) 0 0
\(535\) −39.8268 −1.72186
\(536\) 9.46472 0.408814
\(537\) 0 0
\(538\) −9.24219 + 16.0079i −0.398459 + 0.690152i
\(539\) 0 0
\(540\) 0 0
\(541\) −21.0963 36.5399i −0.907002 1.57097i −0.818207 0.574924i \(-0.805031\pi\)
−0.0887957 0.996050i \(-0.528302\pi\)
\(542\) −3.67742 6.36947i −0.157959 0.273592i
\(543\) 0 0
\(544\) −3.28799 + 5.69497i −0.140971 + 0.244170i
\(545\) −0.349814 0.605896i −0.0149844 0.0259537i
\(546\) 0 0
\(547\) 20.3356 35.2222i 0.869486 1.50599i 0.00696400 0.999976i \(-0.497783\pi\)
0.862522 0.506019i \(-0.168883\pi\)
\(548\) −1.70582 2.95456i −0.0728689 0.126213i
\(549\) 0 0
\(550\) 6.41597 11.1128i 0.273578 0.473851i
\(551\) −2.23119 −0.0950519
\(552\) 0 0
\(553\) 0 0
\(554\) −4.54944 7.87987i −0.193287 0.334783i
\(555\) 0 0
\(556\) 6.75526 + 11.7005i 0.286487 + 0.496210i
\(557\) −6.68794 + 11.5838i −0.283377 + 0.490823i −0.972214 0.234093i \(-0.924788\pi\)
0.688837 + 0.724916i \(0.258121\pi\)
\(558\) 0 0
\(559\) 0.0334206 0.00141354
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00433 10.3998i 0.253277 0.438689i
\(563\) −32.7614 −1.38073 −0.690364 0.723463i \(-0.742549\pi\)
−0.690364 + 0.723463i \(0.742549\pi\)
\(564\) 0 0
\(565\) −50.1803 −2.11110
\(566\) 9.84294 0.413729
\(567\) 0 0
\(568\) −5.46472 −0.229295
\(569\) 16.7280 0.701272 0.350636 0.936512i \(-0.385965\pi\)
0.350636 + 0.936512i \(0.385965\pi\)
\(570\) 0 0
\(571\) −27.4734 −1.14973 −0.574863 0.818250i \(-0.694945\pi\)
−0.574863 + 0.818250i \(0.694945\pi\)
\(572\) 1.99381 3.45338i 0.0833654 0.144393i
\(573\) 0 0
\(574\) 0 0
\(575\) −54.6253 −2.27803
\(576\) 0 0
\(577\) −1.41714 + 2.45455i −0.0589962 + 0.102184i −0.894015 0.448037i \(-0.852123\pi\)
0.835019 + 0.550221i \(0.185457\pi\)
\(578\) 13.1218 + 22.7276i 0.545794 + 0.945343i
\(579\) 0 0
\(580\) −4.64400 8.04364i −0.192831 0.333994i
\(581\) 0 0
\(582\) 0 0
\(583\) −4.74171 −0.196382
\(584\) −6.03273 + 10.4490i −0.249636 + 0.432383i
\(585\) 0 0
\(586\) −10.7101 18.5505i −0.442432 0.766315i
\(587\) −2.34795 + 4.06678i −0.0969105 + 0.167854i −0.910404 0.413720i \(-0.864229\pi\)
0.813494 + 0.581573i \(0.197563\pi\)
\(588\) 0 0
\(589\) −3.02654 5.24212i −0.124706 0.215998i
\(590\) 12.7818 22.1387i 0.526218 0.911437i
\(591\) 0 0
\(592\) −1.38874 2.40536i −0.0570767 0.0988597i
\(593\) 0.636024 + 1.10163i 0.0261184 + 0.0452383i 0.878789 0.477210i \(-0.158352\pi\)
−0.852671 + 0.522449i \(0.825019\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.166896 0.289073i 0.00683634 0.0118409i
\(597\) 0 0
\(598\) −16.9752 −0.694169
\(599\) −43.8516 −1.79173 −0.895864 0.444329i \(-0.853442\pi\)
−0.895864 + 0.444329i \(0.853442\pi\)
\(600\) 0 0
\(601\) 6.71634 11.6330i 0.273965 0.474522i −0.695908 0.718131i \(-0.744998\pi\)
0.969874 + 0.243609i \(0.0783314\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 9.95489 + 17.2424i 0.405059 + 0.701582i
\(605\) 16.3120 + 28.2532i 0.663177 + 1.14866i
\(606\) 0 0
\(607\) −2.29232 + 3.97042i −0.0930425 + 0.161154i −0.908790 0.417254i \(-0.862993\pi\)
0.815747 + 0.578408i \(0.196326\pi\)
\(608\) −0.444368 0.769668i −0.0180215 0.0312142i
\(609\) 0 0
\(610\) 10.6051 18.3685i 0.429387 0.743720i
\(611\) −9.43199 16.3367i −0.381577 0.660911i
\(612\) 0 0
\(613\) −11.0538 + 19.1457i −0.446458 + 0.773287i −0.998152 0.0607587i \(-0.980648\pi\)
0.551695 + 0.834046i \(0.313981\pi\)
\(614\) −5.68725 −0.229519
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00433 10.3998i −0.241725 0.418680i 0.719481 0.694513i \(-0.244380\pi\)
−0.961206 + 0.275832i \(0.911047\pi\)
\(618\) 0 0
\(619\) −8.78180 15.2105i −0.352970 0.611363i 0.633798 0.773499i \(-0.281495\pi\)
−0.986768 + 0.162136i \(0.948162\pi\)
\(620\) 12.5989 21.8219i 0.505983 0.876389i
\(621\) 0 0
\(622\) 11.7207 0.469956
\(623\) 0 0
\(624\) 0 0
\(625\) −3.51602 + 6.08993i −0.140641 + 0.243597i
\(626\) −26.7738 −1.07009
\(627\) 0 0
\(628\) 6.96286 0.277848
\(629\) −18.2646 −0.728258
\(630\) 0 0
\(631\) −44.9381 −1.78896 −0.894479 0.447110i \(-0.852453\pi\)
−0.894479 + 0.447110i \(0.852453\pi\)
\(632\) −11.4523 −0.455550
\(633\) 0 0
\(634\) 1.90249 0.0755576
\(635\) 5.28435 9.15276i 0.209703 0.363216i
\(636\) 0 0
\(637\) 0 0
\(638\) −3.70829 −0.146813
\(639\) 0 0
\(640\) 1.84981 3.20397i 0.0731203 0.126648i
\(641\) −14.4920 25.1008i −0.572398 0.991422i −0.996319 0.0857228i \(-0.972680\pi\)
0.423921 0.905699i \(-0.360653\pi\)
\(642\) 0 0
\(643\) −6.03087 10.4458i −0.237834 0.411941i 0.722258 0.691623i \(-0.243104\pi\)
−0.960093 + 0.279682i \(0.909771\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.84431 −0.229941
\(647\) 18.8825 32.7055i 0.742349 1.28579i −0.209073 0.977900i \(-0.567045\pi\)
0.951423 0.307887i \(-0.0996219\pi\)
\(648\) 0 0
\(649\) −5.10322 8.83903i −0.200319 0.346962i
\(650\) −11.7262 + 20.3103i −0.459938 + 0.796636i
\(651\) 0 0
\(652\) 4.03706 + 6.99240i 0.158104 + 0.273843i
\(653\) 18.7040 32.3962i 0.731942 1.26776i −0.224109 0.974564i \(-0.571947\pi\)
0.956052 0.293198i \(-0.0947194\pi\)
\(654\) 0 0
\(655\) −0.287992 0.498817i −0.0112528 0.0194904i
\(656\) −2.05563 3.56046i −0.0802589 0.139013i
\(657\) 0 0
\(658\) 0 0
\(659\) −14.9356 + 25.8693i −0.581810 + 1.00772i 0.413455 + 0.910524i \(0.364322\pi\)
−0.995265 + 0.0971993i \(0.969012\pi\)
\(660\) 0 0
\(661\) −5.60803 −0.218127 −0.109063 0.994035i \(-0.534785\pi\)
−0.109063 + 0.994035i \(0.534785\pi\)
\(662\) −5.56732 −0.216380
\(663\) 0 0
\(664\) −2.23855 + 3.87728i −0.0868726 + 0.150468i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.89307 + 13.6712i 0.305621 + 0.529351i
\(668\) 9.74288 + 16.8752i 0.376963 + 0.652920i
\(669\) 0 0
\(670\) −17.5080 + 30.3247i −0.676392 + 1.17155i
\(671\) −4.23414 7.33375i −0.163457 0.283116i
\(672\) 0 0
\(673\) −4.72253 + 8.17966i −0.182040 + 0.315303i −0.942575 0.333994i \(-0.891603\pi\)
0.760535 + 0.649297i \(0.224937\pi\)
\(674\) 16.8869 + 29.2489i 0.650458 + 1.12663i
\(675\) 0 0
\(676\) 2.85600 4.94674i 0.109846 0.190259i
\(677\) 11.0617 0.425137 0.212569 0.977146i \(-0.431817\pi\)
0.212569 + 0.977146i \(0.431817\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −12.1643 21.0693i −0.466481 0.807970i
\(681\) 0 0
\(682\) −5.03018 8.71253i −0.192616 0.333620i
\(683\) 4.41961 7.65499i 0.169112 0.292910i −0.768996 0.639253i \(-0.779243\pi\)
0.938108 + 0.346343i \(0.112577\pi\)
\(684\) 0 0
\(685\) 12.6218 0.482254
\(686\) 0 0
\(687\) 0 0
\(688\) 0.00618986 0.0107211i 0.000235986 0.000408740i
\(689\) 8.66621 0.330156
\(690\) 0 0
\(691\) −25.0617 −0.953394 −0.476697 0.879068i \(-0.658166\pi\)
−0.476697 + 0.879068i \(0.658166\pi\)
\(692\) 22.5636 0.857740
\(693\) 0 0
\(694\) −30.4065 −1.15422
\(695\) −49.9839 −1.89600
\(696\) 0 0
\(697\) −27.0356 −1.02405
\(698\) −6.29782 + 10.9082i −0.238376 + 0.412880i
\(699\) 0 0
\(700\) 0 0
\(701\) 43.4858 1.64243 0.821217 0.570616i \(-0.193295\pi\)
0.821217 + 0.570616i \(0.193295\pi\)
\(702\) 0 0
\(703\) 1.23422 2.13773i 0.0465495 0.0806260i
\(704\) −0.738550 1.27921i −0.0278351 0.0482119i
\(705\) 0 0
\(706\) −3.76578 6.52252i −0.141727 0.245478i
\(707\) 0 0
\(708\) 0 0
\(709\) −22.7403 −0.854031 −0.427016 0.904244i \(-0.640435\pi\)
−0.427016 + 0.904244i \(0.640435\pi\)
\(710\) 10.1087 17.5088i 0.379373 0.657094i
\(711\) 0 0
\(712\) 4.43818 + 7.68715i 0.166328 + 0.288088i
\(713\) −21.4134 + 37.0891i −0.801939 + 1.38900i
\(714\) 0 0
\(715\) 7.37636 + 12.7762i 0.275860 + 0.477804i
\(716\) −0.166896 + 0.289073i −0.00623721 + 0.0108032i
\(717\) 0 0
\(718\) −3.44801 5.97213i −0.128679 0.222878i
\(719\) 6.06182 + 10.4994i 0.226068 + 0.391561i 0.956639 0.291275i \(-0.0940796\pi\)
−0.730571 + 0.682836i \(0.760746\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.10507 + 15.7705i −0.338856 + 0.586915i
\(723\) 0 0
\(724\) −23.2422 −0.863789
\(725\) 21.8095 0.809985
\(726\) 0 0
\(727\) −23.0908 + 39.9945i −0.856392 + 1.48331i 0.0189562 + 0.999820i \(0.493966\pi\)
−0.875348 + 0.483494i \(0.839368\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −22.3189 38.6574i −0.826058 1.43077i
\(731\) −0.0407044 0.0705021i −0.00150551 0.00260761i
\(732\) 0 0
\(733\) −18.0149 + 31.2026i −0.665394 + 1.15250i 0.313785 + 0.949494i \(0.398403\pi\)
−0.979178 + 0.203002i \(0.934930\pi\)
\(734\) −11.5618 20.0257i −0.426755 0.739161i
\(735\) 0 0
\(736\) −3.14400 + 5.44556i −0.115889 + 0.200726i
\(737\) 6.99017 + 12.1073i 0.257486 + 0.445979i
\(738\) 0 0
\(739\) 23.2119 40.2042i 0.853865 1.47894i −0.0238296 0.999716i \(-0.507586\pi\)
0.877694 0.479221i \(-0.159081\pi\)
\(740\) 10.2756 0.377739
\(741\) 0 0
\(742\) 0 0
\(743\) −0.598884 1.03730i −0.0219709 0.0380548i 0.854831 0.518907i \(-0.173661\pi\)
−0.876802 + 0.480852i \(0.840327\pi\)
\(744\) 0 0
\(745\) 0.617454 + 1.06946i 0.0226218 + 0.0391820i
\(746\) 14.5822 25.2571i 0.533891 0.924727i
\(747\) 0 0
\(748\) −9.71339 −0.355157
\(749\) 0 0
\(750\) 0 0
\(751\) −24.0600 + 41.6731i −0.877961 + 1.52067i −0.0243853 + 0.999703i \(0.507763\pi\)
−0.853575 + 0.520970i \(0.825570\pi\)
\(752\) −6.98762 −0.254812
\(753\) 0 0
\(754\) 6.77747 0.246821
\(755\) −73.6588 −2.68072
\(756\) 0 0
\(757\) 49.6006 1.80276 0.901382 0.433025i \(-0.142554\pi\)
0.901382 + 0.433025i \(0.142554\pi\)
\(758\) 13.5622 0.492602
\(759\) 0 0
\(760\) 3.28799 0.119268
\(761\) 18.7701 32.5108i 0.680416 1.17852i −0.294438 0.955671i \(-0.595132\pi\)
0.974854 0.222845i \(-0.0715342\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16.3214 0.590488
\(765\) 0 0
\(766\) −1.41783 + 2.45575i −0.0512281 + 0.0887297i
\(767\) 9.32691 + 16.1547i 0.336775 + 0.583312i
\(768\) 0 0
\(769\) 13.4592 + 23.3121i 0.485352 + 0.840654i 0.999858 0.0168324i \(-0.00535818\pi\)
−0.514506 + 0.857486i \(0.672025\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.3214 −0.515439
\(773\) 25.1130 43.4971i 0.903254 1.56448i 0.0800089 0.996794i \(-0.474505\pi\)
0.823245 0.567687i \(-0.192162\pi\)
\(774\) 0 0
\(775\) 29.5840 + 51.2409i 1.06269 + 1.84063i
\(776\) −6.58836 + 11.4114i −0.236508 + 0.409645i
\(777\) 0 0
\(778\) 9.30401 + 16.1150i 0.333565 + 0.577752i
\(779\) 1.82691 3.16431i 0.0654560 0.113373i
\(780\) 0 0
\(781\) −4.03597 6.99050i −0.144418 0.250140i
\(782\) 20.6749 + 35.8099i 0.739332 + 1.28056i
\(783\) 0 0
\(784\) 0 0
\(785\) −12.8800 + 22.3088i −0.459707 + 0.796236i
\(786\) 0 0
\(787\) 1.65892 0.0591342 0.0295671 0.999563i \(-0.490587\pi\)
0.0295671 + 0.999563i \(0.490587\pi\)
\(788\) −2.42402 −0.0863520
\(789\) 0 0
\(790\) 21.1847 36.6930i 0.753718 1.30548i
\(791\) 0 0
\(792\) 0 0
\(793\) 7.73855 + 13.4036i 0.274804 + 0.475974i
\(794\) −10.2880 17.8193i −0.365107 0.632384i
\(795\) 0 0
\(796\) 3.05563 5.29251i 0.108304 0.187588i
\(797\) −15.3702 26.6219i −0.544439 0.942996i −0.998642 0.0520981i \(-0.983409\pi\)
0.454203 0.890898i \(-0.349924\pi\)
\(798\) 0 0
\(799\) −22.9752 + 39.7943i −0.812806 + 1.40782i
\(800\) 4.34362 + 7.52338i 0.153570 + 0.265992i
\(801\) 0 0
\(802\) 3.37704 5.84921i 0.119248 0.206543i
\(803\) −17.8219 −0.628921
\(804\) 0 0
\(805\) 0 0
\(806\) 9.19344 + 15.9235i 0.323825 + 0.560881i
\(807\) 0 0
\(808\) 2.62729 + 4.55059i 0.0924276 + 0.160089i
\(809\) 1.44251 2.49850i 0.0507159 0.0878425i −0.839553 0.543278i \(-0.817183\pi\)
0.890269 + 0.455435i \(0.150516\pi\)
\(810\) 0 0
\(811\) −28.5461 −1.00239 −0.501195 0.865334i \(-0.667106\pi\)
−0.501195 + 0.865334i \(0.667106\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 2.05130 3.55296i 0.0718981 0.124531i
\(815\) −29.8713 −1.04634
\(816\) 0 0
\(817\) 0.0110023 0.000384922
\(818\) 15.3214 0.535701
\(819\) 0 0
\(820\) 15.2101 0.531161
\(821\) −7.96658 −0.278036 −0.139018 0.990290i \(-0.544395\pi\)
−0.139018 + 0.990290i \(0.544395\pi\)
\(822\) 0 0
\(823\) 40.5461 1.41335 0.706675 0.707539i \(-0.250194\pi\)
0.706675 + 0.707539i \(0.250194\pi\)
\(824\) −0.833104 + 1.44298i −0.0290225 + 0.0502685i
\(825\) 0 0
\(826\) 0 0
\(827\) −1.22115 −0.0424636 −0.0212318 0.999775i \(-0.506759\pi\)
−0.0212318 + 0.999775i \(0.506759\pi\)
\(828\) 0 0
\(829\) 7.07530 12.2548i 0.245735 0.425626i −0.716603 0.697481i \(-0.754304\pi\)
0.962338 + 0.271856i \(0.0876373\pi\)
\(830\) −8.28180 14.3445i −0.287466 0.497905i
\(831\) 0 0
\(832\) 1.34981 + 2.33795i 0.0467964 + 0.0810537i
\(833\) 0 0
\(834\) 0 0
\(835\) −72.0901 −2.49478
\(836\) 0.656376 1.13688i 0.0227012 0.0393197i
\(837\) 0 0
\(838\) 4.32141 + 7.48491i 0.149281 + 0.258562i
\(839\) 1.19599 2.07151i 0.0412900 0.0715164i −0.844642 0.535332i \(-0.820187\pi\)
0.885932 + 0.463815i \(0.153520\pi\)
\(840\) 0 0
\(841\) 11.3486 + 19.6564i 0.391333 + 0.677808i
\(842\) −18.5636 + 32.1531i −0.639744 + 1.10807i
\(843\) 0 0
\(844\) 5.72253 + 9.91171i 0.196978 + 0.341175i
\(845\) 10.5662 + 18.3011i 0.363487 + 0.629577i
\(846\) 0 0
\(847\) 0 0
\(848\) 1.60507 2.78007i 0.0551185 0.0954680i
\(849\) 0 0
\(850\) 57.1272 1.95945
\(851\) −17.4647 −0.598683
\(852\) 0 0
\(853\) 8.33998 14.4453i 0.285556 0.494597i −0.687188 0.726479i \(-0.741155\pi\)
0.972744 + 0.231883i \(0.0744886\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −5.38255 9.32284i −0.183972 0.318648i
\(857\) 6.92580 + 11.9958i 0.236581 + 0.409770i 0.959731 0.280921i \(-0.0906399\pi\)
−0.723150 + 0.690691i \(0.757307\pi\)
\(858\) 0 0
\(859\) 24.2472 41.9974i 0.827304 1.43293i −0.0728414 0.997344i \(-0.523207\pi\)
0.900146 0.435589i \(-0.143460\pi\)
\(860\) 0.0229002 + 0.0396643i 0.000780889 + 0.00135254i
\(861\) 0 0
\(862\) −4.71015 + 8.15822i −0.160428 + 0.277870i
\(863\) −2.96541 5.13624i −0.100944 0.174840i 0.811130 0.584866i \(-0.198853\pi\)
−0.912074 + 0.410026i \(0.865520\pi\)
\(864\) 0 0
\(865\) −41.7385 + 72.2932i −1.41915 + 2.45804i
\(866\) −0.208771 −0.00709433
\(867\) 0 0
\(868\) 0 0
\(869\) −8.45813 14.6499i −0.286922 0.496964i
\(870\) 0 0
\(871\) −12.7756 22.1280i −0.432885 0.749779i
\(872\) 0.0945538 0.163772i 0.00320200 0.00554602i
\(873\) 0 0
\(874\) −5.58836 −0.189029
\(875\) 0 0
\(876\) 0 0
\(877\) −1.96472 + 3.40300i −0.0663439 + 0.114911i −0.897289 0.441443i \(-0.854467\pi\)
0.830945 + 0.556354i \(0.187800\pi\)
\(878\) −9.96796 −0.336402
\(879\) 0 0
\(880\) 5.46472 0.184216
\(881\) 37.6552 1.26864 0.634318 0.773072i \(-0.281281\pi\)
0.634318 + 0.773072i \(0.281281\pi\)
\(882\) 0 0
\(883\) −53.2334 −1.79145 −0.895723 0.444613i \(-0.853341\pi\)
−0.895723 + 0.444613i \(0.853341\pi\)
\(884\) 17.7527 0.597088
\(885\) 0 0
\(886\) −15.6996 −0.527439
\(887\) 18.4938 32.0322i 0.620961 1.07554i −0.368346 0.929689i \(-0.620076\pi\)
0.989307 0.145848i \(-0.0465910\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −32.8392 −1.10077
\(891\) 0 0
\(892\) 3.61126 6.25489i 0.120914 0.209429i
\(893\) −3.10507 5.37815i −0.103907 0.179973i
\(894\) 0 0
\(895\) −0.617454 1.06946i −0.0206392 0.0357482i
\(896\) 0 0
\(897\) 0 0
\(898\) 33.6253 1.12209
\(899\) 8.54944 14.8081i 0.285140 0.493877i
\(900\) 0 0
\(901\) −10.5549 18.2817i −0.351636 0.609052i
\(902\) 3.03637 5.25915i 0.101100 0.175111i
\(903\) 0 0
\(904\) −6.78180 11.7464i −0.225559 0.390680i
\(905\) 42.9937 74.4673i 1.42916 2.47538i
\(906\) 0 0
\(907\) 19.5080 + 33.7888i 0.647752 + 1.12194i 0.983659 + 0.180044i \(0.0576239\pi\)
−0.335907 + 0.941895i \(0.609043\pi\)
\(908\) −6.82760 11.8258i −0.226582 0.392451i
\(909\) 0 0
\(910\) 0 0
\(911\) 12.8090 22.1859i 0.424382 0.735052i −0.571980 0.820267i \(-0.693825\pi\)
0.996363 + 0.0852158i \(0.0271580\pi\)
\(912\) 0 0
\(913\) −6.61312 −0.218862
\(914\) −32.7083 −1.08189
\(915\) 0 0
\(916\) 8.68725 15.0468i 0.287035 0.497159i
\(917\) 0 0
\(918\) 0 0
\(919\) 10.3367 + 17.9038i 0.340978 + 0.590591i 0.984615 0.174740i \(-0.0559086\pi\)
−0.643637 + 0.765331i \(0.722575\pi\)
\(920\) −11.6316 20.1466i −0.383483 0.664212i
\(921\) 0 0
\(922\) 2.07165 3.58821i 0.0682263 0.118171i
\(923\) 7.37636 + 12.7762i 0.242796 + 0.420535i
\(924\) 0 0
\(925\) −12.0643 + 20.8960i −0.396672 + 0.687055i
\(926\) 8.34176 + 14.4484i 0.274127 + 0.474803i
\(927\) 0 0
\(928\) 1.25526 2.17417i 0.0412059 0.0713708i
\(929\) −3.74033 −0.122716 −0.0613582 0.998116i \(-0.519543\pi\)
−0.0613582 + 0.998116i \(0.519543\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7.62110 13.2001i −0.249637 0.432384i
\(933\) 0 0
\(934\) −14.9585 25.9089i −0.489458 0.847766i
\(935\) 17.9680 31.1214i 0.587615 1.01778i
\(936\) 0 0
\(937\) 27.1345 0.886445 0.443223 0.896412i \(-0.353835\pi\)
0.443223 + 0.896412i \(0.353835\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 12.9258 22.3881i 0.421593 0.730221i
\(941\) 6.32870 0.206310 0.103155 0.994665i \(-0.467106\pi\)
0.103155 + 0.994665i \(0.467106\pi\)
\(942\) 0 0
\(943\) −25.8516 −0.841844
\(944\) 6.90978 0.224894
\(945\) 0 0
\(946\) 0.0182861 0.000594531
\(947\) −31.2792 −1.01644 −0.508218 0.861228i \(-0.669696\pi\)
−0.508218 + 0.861228i \(0.669696\pi\)
\(948\) 0 0
\(949\) 32.5723 1.05734
\(950\) −3.86033 + 6.68630i −0.125246 + 0.216932i
\(951\) 0 0
\(952\) 0 0
\(953\) −4.28937 −0.138946 −0.0694732 0.997584i \(-0.522132\pi\)
−0.0694732 + 0.997584i \(0.522132\pi\)
\(954\) 0 0
\(955\) −30.1916 + 52.2933i −0.976977 + 1.69217i
\(956\) −9.47524 16.4116i −0.306451 0.530789i
\(957\) 0 0
\(958\) −1.47965 2.56283i −0.0478053 0.0828011i
\(959\) 0 0
\(960\) 0 0
\(961\) 15.3883 0.496395
\(962\) −3.74907 + 6.49358i −0.120875 + 0.209361i
\(963\) 0 0
\(964\) −12.2527 21.2223i −0.394633 0.683525i
\(965\) 26.4920 45.8854i 0.852806 1.47710i
\(966\) 0 0
\(967\) −7.59201 13.1497i −0.244142 0.422867i 0.717748 0.696303i \(-0.245173\pi\)
−0.961890 + 0.273436i \(0.911840\pi\)
\(968\) −4.40909 + 7.63676i −0.141713 + 0.245455i
\(969\) 0 0
\(970\) −24.3745 42.2179i −0.782618 1.35553i
\(971\) 1.62364 + 2.81223i 0.0521052 + 0.0902489i 0.890902 0.454196i \(-0.150074\pi\)
−0.838796 + 0.544445i \(0.816740\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 14.0309 24.3022i 0.449578 0.778692i
\(975\) 0 0
\(976\) 5.73305 0.183510
\(977\) −15.5439 −0.497295 −0.248647 0.968594i \(-0.579986\pi\)
−0.248647 + 0.968594i \(0.579986\pi\)
\(978\) 0 0
\(979\) −6.55563 + 11.3547i −0.209519 + 0.362897i
\(980\) 0 0
\(981\) 0 0
\(982\) 17.0734 + 29.5721i 0.544835 + 0.943682i
\(983\) −6.19158 10.7241i −0.197481 0.342047i 0.750230 0.661177i \(-0.229943\pi\)
−0.947711 + 0.319130i \(0.896609\pi\)
\(984\) 0 0
\(985\) 4.48398 7.76648i 0.142871 0.247461i
\(986\) −8.25457 14.2973i −0.262879 0.455320i
\(987\) 0 0
\(988\) −1.19963 + 2.07782i −0.0381653 + 0.0661042i
\(989\) −0.0389218 0.0674145i −0.00123764 0.00214366i
\(990\) 0 0
\(991\) −3.32760 + 5.76358i −0.105705 + 0.183086i −0.914026 0.405656i \(-0.867043\pi\)
0.808321 + 0.588742i \(0.200377\pi\)
\(992\) 6.81089 0.216246
\(993\) 0 0
\(994\) 0 0
\(995\) 11.3047 + 19.5803i 0.358383 + 0.620738i
\(996\) 0 0
\(997\) 2.40104 + 4.15872i 0.0760417 + 0.131708i 0.901539 0.432698i \(-0.142438\pi\)
−0.825497 + 0.564406i \(0.809105\pi\)
\(998\) −1.14035 + 1.97515i −0.0360973 + 0.0625223i
\(999\) 0 0
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 2646.2.e.o.2125.1 6
3.2 odd 2 882.2.e.p.655.3 6
7.2 even 3 2646.2.h.p.667.3 6
7.3 odd 6 2646.2.f.o.883.3 6
7.4 even 3 2646.2.f.n.883.1 6
7.5 odd 6 378.2.h.d.289.1 6
7.6 odd 2 378.2.e.c.235.3 6
9.4 even 3 2646.2.h.p.361.3 6
9.5 odd 6 882.2.h.o.67.3 6
21.2 odd 6 882.2.h.o.79.3 6
21.5 even 6 126.2.h.c.79.1 yes 6
21.11 odd 6 882.2.f.m.295.1 6
21.17 even 6 882.2.f.l.295.3 6
21.20 even 2 126.2.e.d.25.1 6
28.19 even 6 3024.2.t.g.289.1 6
28.27 even 2 3024.2.q.h.2881.3 6
63.4 even 3 2646.2.f.n.1765.1 6
63.5 even 6 126.2.e.d.121.1 yes 6
63.11 odd 6 7938.2.a.by.1.1 3
63.13 odd 6 378.2.h.d.361.1 6
63.20 even 6 1134.2.g.k.487.1 6
63.23 odd 6 882.2.e.p.373.3 6
63.25 even 3 7938.2.a.bx.1.3 3
63.31 odd 6 2646.2.f.o.1765.3 6
63.32 odd 6 882.2.f.m.589.1 6
63.34 odd 6 1134.2.g.n.487.3 6
63.38 even 6 7938.2.a.cb.1.3 3
63.40 odd 6 378.2.e.c.37.3 6
63.41 even 6 126.2.h.c.67.1 yes 6
63.47 even 6 1134.2.g.k.163.1 6
63.52 odd 6 7938.2.a.bu.1.1 3
63.58 even 3 inner 2646.2.e.o.1549.1 6
63.59 even 6 882.2.f.l.589.3 6
63.61 odd 6 1134.2.g.n.163.3 6
84.47 odd 6 1008.2.t.g.961.3 6
84.83 odd 2 1008.2.q.h.529.3 6
252.103 even 6 3024.2.q.h.2305.3 6
252.131 odd 6 1008.2.q.h.625.3 6
252.139 even 6 3024.2.t.g.1873.1 6
252.167 odd 6 1008.2.t.g.193.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.1 6 21.20 even 2
126.2.e.d.121.1 yes 6 63.5 even 6
126.2.h.c.67.1 yes 6 63.41 even 6
126.2.h.c.79.1 yes 6 21.5 even 6
378.2.e.c.37.3 6 63.40 odd 6
378.2.e.c.235.3 6 7.6 odd 2
378.2.h.d.289.1 6 7.5 odd 6
378.2.h.d.361.1 6 63.13 odd 6
882.2.e.p.373.3 6 63.23 odd 6
882.2.e.p.655.3 6 3.2 odd 2
882.2.f.l.295.3 6 21.17 even 6
882.2.f.l.589.3 6 63.59 even 6
882.2.f.m.295.1 6 21.11 odd 6
882.2.f.m.589.1 6 63.32 odd 6
882.2.h.o.67.3 6 9.5 odd 6
882.2.h.o.79.3 6 21.2 odd 6
1008.2.q.h.529.3 6 84.83 odd 2
1008.2.q.h.625.3 6 252.131 odd 6
1008.2.t.g.193.3 6 252.167 odd 6
1008.2.t.g.961.3 6 84.47 odd 6
1134.2.g.k.163.1 6 63.47 even 6
1134.2.g.k.487.1 6 63.20 even 6
1134.2.g.n.163.3 6 63.61 odd 6
1134.2.g.n.487.3 6 63.34 odd 6
2646.2.e.o.1549.1 6 63.58 even 3 inner
2646.2.e.o.2125.1 6 1.1 even 1 trivial
2646.2.f.n.883.1 6 7.4 even 3
2646.2.f.n.1765.1 6 63.4 even 3
2646.2.f.o.883.3 6 7.3 odd 6
2646.2.f.o.1765.3 6 63.31 odd 6
2646.2.h.p.361.3 6 9.4 even 3
2646.2.h.p.667.3 6 7.2 even 3
3024.2.q.h.2305.3 6 252.103 even 6
3024.2.q.h.2881.3 6 28.27 even 2
3024.2.t.g.289.1 6 28.19 even 6
3024.2.t.g.1873.1 6 252.139 even 6
7938.2.a.bu.1.1 3 63.52 odd 6
7938.2.a.bx.1.3 3 63.25 even 3
7938.2.a.by.1.1 3 63.11 odd 6
7938.2.a.cb.1.3 3 63.38 even 6