Properties

Label 1008.2.q.h.625.3
Level $1008$
Weight $2$
Character 1008.625
Analytic conductor $8.049$
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] = [1008,2,Mod(529,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.q (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: \(8.04892052375\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1008.625
Dual form 1008.2.q.h.529.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.29418 + 1.15113i) q^{3} +(-1.84981 - 3.20397i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +O(q^{10})\) \(q+(1.29418 + 1.15113i) q^{3} +(-1.84981 - 3.20397i) q^{5} +(-2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +(-0.738550 + 1.27921i) q^{11} +(-1.34981 + 2.33795i) q^{13} +(1.29418 - 6.27589i) q^{15} +(3.28799 + 5.69497i) q^{17} +(0.444368 - 0.769668i) q^{19} +(-3.53273 - 2.91887i) q^{21} +(3.14400 + 5.44556i) q^{23} +(-4.34362 + 7.52338i) q^{25} +(-2.97710 + 4.25874i) q^{27} +(1.25526 + 2.17417i) q^{29} -6.81089 q^{31} +(-2.42835 + 0.805361i) q^{33} +(5.19963 + 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} +(-4.43818 + 1.47192i) q^{39} +(-2.05563 + 3.56046i) q^{41} +(-0.00618986 - 0.0107211i) q^{43} +(8.89926 - 6.63238i) q^{45} +6.98762 q^{47} +(6.98143 - 0.509538i) q^{49} +(-2.30037 + 11.1552i) q^{51} +(-1.60507 - 2.78007i) q^{53} +5.46472 q^{55} +(1.46108 - 0.484566i) q^{57} -6.90978 q^{59} -5.73305 q^{61} +(-1.21201 - 7.84417i) q^{63} +9.98762 q^{65} +9.46472 q^{67} +(-2.19963 + 10.6667i) q^{69} +5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} +(-14.2818 + 4.73656i) q^{75} +(1.82946 - 3.45338i) q^{77} -11.4523 q^{79} +(-8.75526 + 2.08457i) q^{81} +(-2.23855 - 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(-0.878215 + 4.25874i) q^{87} +(-4.43818 + 7.68715i) q^{89} +(3.34362 - 6.31159i) q^{91} +(-8.81453 - 7.84020i) q^{93} -3.28799 q^{95} +(-6.58836 - 11.4114i) q^{97} +(-4.06979 - 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} - 2 q^{25} - 7 q^{27} - 5 q^{29} - 28 q^{31} - 19 q^{33} + 19 q^{35} - 9 q^{37} - 9 q^{39} - 12 q^{41} - 18 q^{43} + 29 q^{45} + 6 q^{47} - 12 q^{49} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} + 8 q^{59} - 8 q^{61} - 31 q^{63} + 24 q^{65} + 10 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} - 44 q^{75} + 52 q^{77} + 14 q^{79} - 40 q^{81} - 8 q^{83} + 14 q^{85} - 31 q^{87} - 9 q^{89} - 4 q^{91} + 4 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.29418 + 1.15113i 0.747196 + 0.664603i
\(4\) 0 0
\(5\) −1.84981 3.20397i −0.827262 1.43286i −0.900178 0.435522i \(-0.856564\pi\)
0.0729162 0.997338i \(-0.476769\pi\)
\(6\) 0 0
\(7\) −2.64400 + 0.0963576i −0.999337 + 0.0364197i
\(8\) 0 0
\(9\) 0.349814 + 2.97954i 0.116605 + 0.993178i
\(10\) 0 0
\(11\) −0.738550 + 1.27921i −0.222681 + 0.385695i −0.955621 0.294598i \(-0.904814\pi\)
0.732940 + 0.680293i \(0.238148\pi\)
\(12\) 0 0
\(13\) −1.34981 + 2.33795i −0.374371 + 0.648430i −0.990233 0.139425i \(-0.955475\pi\)
0.615862 + 0.787854i \(0.288808\pi\)
\(14\) 0 0
\(15\) 1.29418 6.27589i 0.334156 1.62043i
\(16\) 0 0
\(17\) 3.28799 + 5.69497i 0.797455 + 1.38123i 0.921268 + 0.388927i \(0.127154\pi\)
−0.123813 + 0.992306i \(0.539512\pi\)
\(18\) 0 0
\(19\) 0.444368 0.769668i 0.101945 0.176574i −0.810541 0.585682i \(-0.800827\pi\)
0.912486 + 0.409108i \(0.134160\pi\)
\(20\) 0 0
\(21\) −3.53273 2.91887i −0.770905 0.636950i
\(22\) 0 0
\(23\) 3.14400 + 5.44556i 0.655568 + 1.13548i 0.981751 + 0.190171i \(0.0609043\pi\)
−0.326182 + 0.945307i \(0.605762\pi\)
\(24\) 0 0
\(25\) −4.34362 + 7.52338i −0.868725 + 1.50468i
\(26\) 0 0
\(27\) −2.97710 + 4.25874i −0.572943 + 0.819595i
\(28\) 0 0
\(29\) 1.25526 + 2.17417i 0.233096 + 0.403734i 0.958718 0.284360i \(-0.0917810\pi\)
−0.725622 + 0.688094i \(0.758448\pi\)
\(30\) 0 0
\(31\) −6.81089 −1.22327 −0.611636 0.791139i \(-0.709488\pi\)
−0.611636 + 0.791139i \(0.709488\pi\)
\(32\) 0 0
\(33\) −2.42835 + 0.805361i −0.422721 + 0.140195i
\(34\) 0 0
\(35\) 5.19963 + 8.29305i 0.878898 + 1.40178i
\(36\) 0 0
\(37\) −1.38874 + 2.40536i −0.228307 + 0.395439i −0.957306 0.289075i \(-0.906652\pi\)
0.729000 + 0.684514i \(0.239986\pi\)
\(38\) 0 0
\(39\) −4.43818 + 1.47192i −0.710677 + 0.235696i
\(40\) 0 0
\(41\) −2.05563 + 3.56046i −0.321036 + 0.556050i −0.980702 0.195508i \(-0.937364\pi\)
0.659666 + 0.751559i \(0.270698\pi\)
\(42\) 0 0
\(43\) −0.00618986 0.0107211i −0.000943944 0.00163496i 0.865553 0.500817i \(-0.166967\pi\)
−0.866497 + 0.499182i \(0.833634\pi\)
\(44\) 0 0
\(45\) 8.89926 6.63238i 1.32662 0.988697i
\(46\) 0 0
\(47\) 6.98762 1.01925 0.509625 0.860397i \(-0.329784\pi\)
0.509625 + 0.860397i \(0.329784\pi\)
\(48\) 0 0
\(49\) 6.98143 0.509538i 0.997347 0.0727912i
\(50\) 0 0
\(51\) −2.30037 + 11.1552i −0.322116 + 1.56204i
\(52\) 0 0
\(53\) −1.60507 2.78007i −0.220474 0.381872i 0.734478 0.678632i \(-0.237427\pi\)
−0.954952 + 0.296760i \(0.904094\pi\)
\(54\) 0 0
\(55\) 5.46472 0.736863
\(56\) 0 0
\(57\) 1.46108 0.484566i 0.193525 0.0641824i
\(58\) 0 0
\(59\) −6.90978 −0.899576 −0.449788 0.893135i \(-0.648501\pi\)
−0.449788 + 0.893135i \(0.648501\pi\)
\(60\) 0 0
\(61\) −5.73305 −0.734042 −0.367021 0.930213i \(-0.619622\pi\)
−0.367021 + 0.930213i \(0.619622\pi\)
\(62\) 0 0
\(63\) −1.21201 7.84417i −0.152699 0.988273i
\(64\) 0 0
\(65\) 9.98762 1.23881
\(66\) 0 0
\(67\) 9.46472 1.15630 0.578150 0.815931i \(-0.303775\pi\)
0.578150 + 0.815931i \(0.303775\pi\)
\(68\) 0 0
\(69\) −2.19963 + 10.6667i −0.264804 + 1.28412i
\(70\) 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 −0.966301 0.257414i \(-0.917130\pi\)
0.260223 0.965548i \(-0.416204\pi\)
\(74\) 0 0
\(75\) −14.2818 + 4.73656i −1.64912 + 0.546931i
\(76\) 0 0
\(77\) 1.82946 3.45338i 0.208487 0.393549i
\(78\) 0 0
\(79\) −11.4523 −1.28849 −0.644244 0.764820i \(-0.722828\pi\)
−0.644244 + 0.764820i \(0.722828\pi\)
\(80\) 0 0
\(81\) −8.75526 + 2.08457i −0.972807 + 0.231619i
\(82\) 0 0
\(83\) −2.23855 3.87728i −0.245713 0.425587i 0.716619 0.697465i \(-0.245689\pi\)
−0.962332 + 0.271878i \(0.912355\pi\)
\(84\) 0 0
\(85\) 12.1643 21.0693i 1.31941 2.28528i
\(86\) 0 0
\(87\) −0.878215 + 4.25874i −0.0941546 + 0.456585i
\(88\) 0 0
\(89\) −4.43818 + 7.68715i −0.470446 + 0.814836i −0.999429 0.0337963i \(-0.989240\pi\)
0.528983 + 0.848633i \(0.322574\pi\)
\(90\) 0 0
\(91\) 3.34362 6.31159i 0.350507 0.661634i
\(92\) 0 0
\(93\) −8.81453 7.84020i −0.914025 0.812991i
\(94\) 0 0
\(95\) −3.28799 −0.337341
\(96\) 0 0
\(97\) −6.58836 11.4114i −0.668947 1.15865i −0.978199 0.207670i \(-0.933412\pi\)
0.309252 0.950980i \(-0.399921\pi\)
\(98\) 0 0
\(99\) −4.06979 1.75305i −0.409030 0.176188i
\(100\) 0 0
\(101\) −2.62729 + 4.55059i −0.261425 + 0.452801i −0.966621 0.256212i \(-0.917526\pi\)
0.705196 + 0.709012i \(0.250859\pi\)
\(102\) 0 0
\(103\) 0.833104 + 1.44298i 0.0820882 + 0.142181i 0.904147 0.427222i \(-0.140508\pi\)
−0.822059 + 0.569403i \(0.807174\pi\)
\(104\) 0 0
\(105\) −2.81708 + 16.7181i −0.274919 + 1.63152i
\(106\) 0 0
\(107\) 5.38255 9.32284i 0.520350 0.901273i −0.479370 0.877613i \(-0.659135\pi\)
0.999720 0.0236602i \(-0.00753198\pi\)
\(108\) 0 0
\(109\) −0.0945538 0.163772i −0.00905662 0.0156865i 0.861462 0.507823i \(-0.169550\pi\)
−0.870518 + 0.492136i \(0.836216\pi\)
\(110\) 0 0
\(111\) −4.56615 + 1.51436i −0.433400 + 0.143737i
\(112\) 0 0
\(113\) −6.78180 + 11.7464i −0.637978 + 1.10501i 0.347897 + 0.937533i \(0.386896\pi\)
−0.985876 + 0.167478i \(0.946438\pi\)
\(114\) 0 0
\(115\) 11.6316 20.1466i 1.08465 1.87868i
\(116\) 0 0
\(117\) −7.43818 3.20397i −0.687660 0.296207i
\(118\) 0 0
\(119\) −9.24219 14.7407i −0.847230 1.35127i
\(120\) 0 0
\(121\) 4.40909 + 7.63676i 0.400826 + 0.694251i
\(122\) 0 0
\(123\) −6.75890 + 2.24159i −0.609430 + 0.202117i
\(124\) 0 0
\(125\) 13.6414 1.22013
\(126\) 0 0
\(127\) 2.85669 0.253490 0.126745 0.991935i \(-0.459547\pi\)
0.126745 + 0.991935i \(0.459547\pi\)
\(128\) 0 0
\(129\) 0.00433060 0.0210004i 0.000381288 0.00184898i
\(130\) 0 0
\(131\) 0.0778435 + 0.134829i 0.00680122 + 0.0117801i 0.869406 0.494098i \(-0.164502\pi\)
−0.862605 + 0.505878i \(0.831168\pi\)
\(132\) 0 0
\(133\) −1.10074 + 2.07782i −0.0954466 + 0.180170i
\(134\) 0 0
\(135\) 19.1520 + 1.66066i 1.64834 + 0.142927i
\(136\) 0 0
\(137\) 1.70582 2.95456i 0.145738 0.252425i −0.783910 0.620874i \(-0.786778\pi\)
0.929648 + 0.368449i \(0.120111\pi\)
\(138\) 0 0
\(139\) 6.75526 11.7005i 0.572974 0.992420i −0.423285 0.905997i \(-0.639123\pi\)
0.996259 0.0864229i \(-0.0275436\pi\)
\(140\) 0 0
\(141\) 9.04325 + 8.04364i 0.761579 + 0.677396i
\(142\) 0 0
\(143\) −1.99381 3.45338i −0.166731 0.288786i
\(144\) 0 0
\(145\) 4.64400 8.04364i 0.385663 0.667988i
\(146\) 0 0
\(147\) 9.62178 + 7.37708i 0.793591 + 0.608451i
\(148\) 0 0
\(149\) −0.166896 0.289073i −0.0136727 0.0236818i 0.859108 0.511794i \(-0.171019\pi\)
−0.872781 + 0.488112i \(0.837686\pi\)
\(150\) 0 0
\(151\) −9.95489 + 17.2424i −0.810117 + 1.40316i 0.102664 + 0.994716i \(0.467263\pi\)
−0.912781 + 0.408448i \(0.866070\pi\)
\(152\) 0 0
\(153\) −15.8182 + 11.7889i −1.27882 + 0.953074i
\(154\) 0 0
\(155\) 12.5989 + 21.8219i 1.01197 + 1.75278i
\(156\) 0 0
\(157\) −6.96286 −0.555697 −0.277848 0.960625i \(-0.589621\pi\)
−0.277848 + 0.960625i \(0.589621\pi\)
\(158\) 0 0
\(159\) 1.12296 5.44556i 0.0890561 0.431861i
\(160\) 0 0
\(161\) −8.83743 14.0951i −0.696487 1.11085i
\(162\) 0 0
\(163\) −4.03706 + 6.99240i −0.316207 + 0.547687i −0.979693 0.200502i \(-0.935743\pi\)
0.663486 + 0.748189i \(0.269076\pi\)
\(164\) 0 0
\(165\) 7.07234 + 6.29059i 0.550581 + 0.489721i
\(166\) 0 0
\(167\) −9.74288 + 16.8752i −0.753927 + 1.30584i 0.191979 + 0.981399i \(0.438509\pi\)
−0.945906 + 0.324440i \(0.894824\pi\)
\(168\) 0 0
\(169\) 2.85600 + 4.94674i 0.219693 + 0.380519i
\(170\) 0 0
\(171\) 2.44870 + 1.05477i 0.187257 + 0.0806602i
\(172\) 0 0
\(173\) 22.5636 1.71548 0.857740 0.514085i \(-0.171868\pi\)
0.857740 + 0.514085i \(0.171868\pi\)
\(174\) 0 0
\(175\) 10.7596 20.3103i 0.813349 1.53532i
\(176\) 0 0
\(177\) −8.94251 7.95403i −0.672160 0.597861i
\(178\) 0 0
\(179\) −0.166896 0.289073i −0.0124744 0.0216063i 0.859721 0.510764i \(-0.170637\pi\)
−0.872195 + 0.489158i \(0.837304\pi\)
\(180\) 0 0
\(181\) 23.2422 1.72758 0.863789 0.503853i \(-0.168085\pi\)
0.863789 + 0.503853i \(0.168085\pi\)
\(182\) 0 0
\(183\) −7.41961 6.59947i −0.548473 0.487847i
\(184\) 0 0
\(185\) 10.2756 0.755478
\(186\) 0 0
\(187\) −9.71339 −0.710313
\(188\) 0 0
\(189\) 7.46108 11.5470i 0.542714 0.839918i
\(190\) 0 0
\(191\) 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 \(0.672371\pi\)
\(194\) 0 0
\(195\) 12.9258 + 11.4970i 0.925636 + 0.823319i
\(196\) 0 0
\(197\) 2.42402 0.172704 0.0863520 0.996265i \(-0.472479\pi\)
0.0863520 + 0.996265i \(0.472479\pi\)
\(198\) 0 0
\(199\) 3.05563 + 5.29251i 0.216608 + 0.375176i 0.953769 0.300541i \(-0.0971673\pi\)
−0.737161 + 0.675717i \(0.763834\pi\)
\(200\) 0 0
\(201\) 12.2491 + 10.8951i 0.863983 + 0.768481i
\(202\) 0 0
\(203\) −3.52840 5.62755i −0.247645 0.394977i
\(204\) 0 0
\(205\) 15.2101 1.06232
\(206\) 0 0
\(207\) −15.1254 + 11.2726i −1.05129 + 0.783499i
\(208\) 0 0
\(209\) 0.656376 + 1.13688i 0.0454025 + 0.0786394i
\(210\) 0 0
\(211\) −5.72253 + 9.91171i −0.393955 + 0.682350i −0.992967 0.118390i \(-0.962227\pi\)
0.599012 + 0.800740i \(0.295560\pi\)
\(212\) 0 0
\(213\) 7.07234 + 6.29059i 0.484589 + 0.431024i
\(214\) 0 0
\(215\) −0.0229002 + 0.0396643i −0.00156178 + 0.00270508i
\(216\) 0 0
\(217\) 18.0080 0.656281i 1.22246 0.0445513i
\(218\) 0 0
\(219\) 4.22067 20.4673i 0.285206 1.38305i
\(220\) 0 0
\(221\) −17.7527 −1.19418
\(222\) 0 0
\(223\) 3.61126 + 6.25489i 0.241828 + 0.418859i 0.961235 0.275730i \(-0.0889196\pi\)
−0.719407 + 0.694589i \(0.755586\pi\)
\(224\) 0 0
\(225\) −23.9356 10.3102i −1.59571 0.687347i
\(226\) 0 0
\(227\) 6.82760 11.8258i 0.453164 0.784903i −0.545417 0.838165i \(-0.683629\pi\)
0.998581 + 0.0532622i \(0.0169619\pi\)
\(228\) 0 0
\(229\) −8.68725 15.0468i −0.574070 0.994318i −0.996142 0.0877555i \(-0.972031\pi\)
0.422073 0.906562i \(-0.361303\pi\)
\(230\) 0 0
\(231\) 6.34294 2.36336i 0.417335 0.155498i
\(232\) 0 0
\(233\) 7.62110 13.2001i 0.499275 0.864769i −0.500725 0.865606i \(-0.666933\pi\)
1.00000 0.000837426i \(0.000266561\pi\)
\(234\) 0 0
\(235\) −12.9258 22.3881i −0.843186 1.46044i
\(236\) 0 0
\(237\) −14.8214 13.1831i −0.962754 0.856334i
\(238\) 0 0
\(239\) −9.47524 + 16.4116i −0.612902 + 1.06158i 0.377846 + 0.925868i \(0.376665\pi\)
−0.990749 + 0.135710i \(0.956669\pi\)
\(240\) 0 0
\(241\) 12.2527 21.2223i 0.789267 1.36705i −0.137150 0.990550i \(-0.543794\pi\)
0.926417 0.376500i \(-0.122872\pi\)
\(242\) 0 0
\(243\) −13.7305 7.38061i −0.880812 0.473466i
\(244\) 0 0
\(245\) −14.5469 21.4258i −0.929367 1.36884i
\(246\) 0 0
\(247\) 1.19963 + 2.07782i 0.0763305 + 0.132208i
\(248\) 0 0
\(249\) 1.56615 7.59476i 0.0992509 0.481299i
\(250\) 0 0
\(251\) 12.1236 0.765238 0.382619 0.923906i \(-0.375022\pi\)
0.382619 + 0.923906i \(0.375022\pi\)
\(252\) 0 0
\(253\) −9.28799 −0.583931
\(254\) 0 0
\(255\) 39.9963 13.2648i 2.50466 0.830672i
\(256\) 0 0
\(257\) 4.10439 + 7.10900i 0.256025 + 0.443448i 0.965173 0.261611i \(-0.0842539\pi\)
−0.709149 + 0.705059i \(0.750921\pi\)
\(258\) 0 0
\(259\) 3.44004 6.49358i 0.213754 0.403491i
\(260\) 0 0
\(261\) −6.03892 + 4.50065i −0.373800 + 0.278583i
\(262\) 0 0
\(263\) −2.67309 + 4.62992i −0.164830 + 0.285493i −0.936595 0.350414i \(-0.886041\pi\)
0.771765 + 0.635908i \(0.219374\pi\)
\(264\) 0 0
\(265\) −5.93818 + 10.2852i −0.364779 + 0.631816i
\(266\) 0 0
\(267\) −14.5927 + 4.83967i −0.893058 + 0.296183i
\(268\) 0 0
\(269\) 9.24219 + 16.0079i 0.563506 + 0.976022i 0.997187 + 0.0749550i \(0.0238813\pi\)
−0.433681 + 0.901067i \(0.642785\pi\)
\(270\) 0 0
\(271\) 3.67742 6.36947i 0.223387 0.386918i −0.732447 0.680824i \(-0.761622\pi\)
0.955834 + 0.293906i \(0.0949552\pi\)
\(272\) 0 0
\(273\) 11.5927 4.31941i 0.701622 0.261422i
\(274\) 0 0
\(275\) −6.41597 11.1128i −0.386897 0.670126i
\(276\) 0 0
\(277\) 4.54944 7.87987i 0.273349 0.473455i −0.696368 0.717685i \(-0.745202\pi\)
0.969717 + 0.244230i \(0.0785351\pi\)
\(278\) 0 0
\(279\) −2.38255 20.2933i −0.142639 1.21493i
\(280\) 0 0
\(281\) 6.00433 + 10.3998i 0.358188 + 0.620400i 0.987658 0.156624i \(-0.0500612\pi\)
−0.629470 + 0.777025i \(0.716728\pi\)
\(282\) 0 0
\(283\) −9.84294 −0.585102 −0.292551 0.956250i \(-0.594504\pi\)
−0.292551 + 0.956250i \(0.594504\pi\)
\(284\) 0 0
\(285\) −4.25526 3.78490i −0.252060 0.224198i
\(286\) 0 0
\(287\) 5.09201 9.61192i 0.300572 0.567373i
\(288\) 0 0
\(289\) −13.1218 + 22.7276i −0.771870 + 1.33692i
\(290\) 0 0
\(291\) 4.60940 22.3524i 0.270208 1.31032i
\(292\) 0 0
\(293\) 10.7101 18.5505i 0.625694 1.08373i −0.362713 0.931901i \(-0.618149\pi\)
0.988406 0.151832i \(-0.0485173\pi\)
\(294\) 0 0
\(295\) 12.7818 + 22.1387i 0.744185 + 1.28897i
\(296\) 0 0
\(297\) −3.24907 6.95362i −0.188530 0.403490i
\(298\) 0 0
\(299\) −16.9752 −0.981704
\(300\) 0 0
\(301\) 0.0173990 + 0.0277502i 0.00100286 + 0.00159950i
\(302\) 0 0
\(303\) −8.63849 + 2.86496i −0.496269 + 0.164587i
\(304\) 0 0
\(305\) 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
\(309\) −0.582863 + 2.82648i −0.0331579 + 0.160793i
\(310\) 0 0
\(311\) 11.7207 0.664618 0.332309 0.943171i \(-0.392172\pi\)
0.332309 + 0.943171i \(0.392172\pi\)
\(312\) 0 0
\(313\) −26.7738 −1.51334 −0.756671 0.653796i \(-0.773176\pi\)
−0.756671 + 0.653796i \(0.773176\pi\)
\(314\) 0 0
\(315\) −22.8905 + 18.3935i −1.28973 + 1.03636i
\(316\) 0 0
\(317\) 1.90249 0.106855 0.0534273 0.998572i \(-0.482985\pi\)
0.0534273 + 0.998572i \(0.482985\pi\)
\(318\) 0 0
\(319\) −3.70829 −0.207624
\(320\) 0 0
\(321\) 17.6978 5.86946i 0.987793 0.327601i
\(322\) 0 0
\(323\) 5.84431 0.325186
\(324\) 0 0
\(325\) −11.7262 20.3103i −0.650451 1.12661i
\(326\) 0 0
\(327\) 0.0661525 0.320794i 0.00365824 0.0177400i
\(328\) 0 0
\(329\) −18.4752 + 0.673310i −1.01857 + 0.0371208i
\(330\) 0 0
\(331\) −5.56732 −0.306008 −0.153004 0.988226i \(-0.548895\pi\)
−0.153004 + 0.988226i \(0.548895\pi\)
\(332\) 0 0
\(333\) −7.65266 3.29636i −0.419363 0.180639i
\(334\) 0 0
\(335\) −17.5080 30.3247i −0.956563 1.65682i
\(336\) 0 0
\(337\) −16.8869 + 29.2489i −0.919887 + 1.59329i −0.120302 + 0.992737i \(0.538386\pi\)
−0.799585 + 0.600553i \(0.794947\pi\)
\(338\) 0 0
\(339\) −22.2985 + 7.39530i −1.21109 + 0.401657i
\(340\) 0 0
\(341\) 5.03018 8.71253i 0.272400 0.471810i
\(342\) 0 0
\(343\) −18.4098 + 2.01993i −0.994035 + 0.109066i
\(344\) 0 0
\(345\) 38.2447 12.6838i 2.05902 0.682875i
\(346\) 0 0
\(347\) 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 \(-0.276118\pi\)
−0.983889 + 0.178782i \(0.942784\pi\)
\(350\) 0 0
\(351\) −5.93818 12.7088i −0.316956 0.678346i
\(352\) 0 0
\(353\) 3.76578 6.52252i 0.200432 0.347159i −0.748235 0.663433i \(-0.769099\pi\)
0.948668 + 0.316274i \(0.102432\pi\)
\(354\) 0 0
\(355\) −10.1087 17.5088i −0.536515 0.929271i
\(356\) 0 0
\(357\) 5.00728 29.7160i 0.265014 1.57274i
\(358\) 0 0
\(359\) 3.44801 5.97213i 0.181979 0.315197i −0.760575 0.649250i \(-0.775083\pi\)
0.942554 + 0.334053i \(0.108416\pi\)
\(360\) 0 0
\(361\) 9.10507 + 15.7705i 0.479214 + 0.830024i
\(362\) 0 0
\(363\) −3.08472 + 14.9588i −0.161906 + 0.785132i
\(364\) 0 0
\(365\) −22.3189 + 38.6574i −1.16822 + 2.02342i
\(366\) 0 0
\(367\) 11.5618 20.0257i 0.603522 1.04533i −0.388761 0.921339i \(-0.627097\pi\)
0.992283 0.123992i \(-0.0395699\pi\)
\(368\) 0 0
\(369\) −11.3276 4.87933i −0.589691 0.254008i
\(370\) 0 0
\(371\) 4.51169 + 7.19583i 0.234235 + 0.373589i
\(372\) 0 0
\(373\) −14.5822 25.2571i −0.755036 1.30776i −0.945356 0.326039i \(-0.894286\pi\)
0.190320 0.981722i \(-0.439047\pi\)
\(374\) 0 0
\(375\) 17.6545 + 15.7030i 0.911675 + 0.810901i
\(376\) 0 0
\(377\) −6.77747 −0.349058
\(378\) 0 0
\(379\) 13.5622 0.696645 0.348322 0.937375i \(-0.386751\pi\)
0.348322 + 0.937375i \(0.386751\pi\)
\(380\) 0 0
\(381\) 3.69708 + 3.28842i 0.189407 + 0.168471i
\(382\) 0 0
\(383\) −1.41783 2.45575i −0.0724475 0.125483i 0.827526 0.561428i \(-0.189748\pi\)
−0.899973 + 0.435945i \(0.856414\pi\)
\(384\) 0 0
\(385\) −14.4487 + 0.526567i −0.736374 + 0.0268364i
\(386\) 0 0
\(387\) 0.0297787 0.0221933i 0.00151374 0.00112815i
\(388\) 0 0
\(389\) 9.30401 16.1150i 0.471732 0.817064i −0.527745 0.849403i \(-0.676962\pi\)
0.999477 + 0.0323388i \(0.0102956\pi\)
\(390\) 0 0
\(391\) −20.6749 + 35.8099i −1.04557 + 1.81099i
\(392\) 0 0
\(393\) −0.0544615 + 0.264101i −0.00274722 + 0.0133221i
\(394\) 0 0
\(395\) 21.1847 + 36.6930i 1.06592 + 1.84622i
\(396\) 0 0
\(397\) −10.2880 + 17.8193i −0.516340 + 0.894326i 0.483481 + 0.875355i \(0.339372\pi\)
−0.999820 + 0.0189712i \(0.993961\pi\)
\(398\) 0 0
\(399\) −3.81639 + 1.42198i −0.191059 + 0.0711879i
\(400\) 0 0
\(401\) 3.37704 + 5.84921i 0.168642 + 0.292096i 0.937942 0.346791i \(-0.112729\pi\)
−0.769301 + 0.638887i \(0.779395\pi\)
\(402\) 0 0
\(403\) 9.19344 15.9235i 0.457958 0.793206i
\(404\) 0 0
\(405\) 22.8745 + 24.1955i 1.13664 + 1.20229i
\(406\) 0 0
\(407\) −2.05130 3.55296i −0.101679 0.176114i
\(408\) 0 0
\(409\) 15.3214 0.757595 0.378798 0.925480i \(-0.376338\pi\)
0.378798 + 0.925480i \(0.376338\pi\)
\(410\) 0 0
\(411\) 5.60872 1.86013i 0.276658 0.0917534i
\(412\) 0 0
\(413\) 18.2694 0.665809i 0.898980 0.0327623i
\(414\) 0 0
\(415\) −8.28180 + 14.3445i −0.406538 + 0.704144i
\(416\) 0 0
\(417\) 22.2112 7.36636i 1.08769 0.360732i
\(418\) 0 0
\(419\) 4.32141 7.48491i 0.211115 0.365662i −0.740949 0.671561i \(-0.765624\pi\)
0.952064 + 0.305900i \(0.0989573\pi\)
\(420\) 0 0
\(421\) 18.5636 + 32.1531i 0.904735 + 1.56705i 0.821273 + 0.570536i \(0.193264\pi\)
0.0834618 + 0.996511i \(0.473402\pi\)
\(422\) 0 0
\(423\) 2.44437 + 20.8199i 0.118849 + 1.01230i
\(424\) 0 0
\(425\) −57.1272 −2.77108
\(426\) 0 0
\(427\) 15.1582 0.552423i 0.733555 0.0267336i
\(428\) 0 0
\(429\) 1.39493 6.76443i 0.0673476 0.326590i
\(430\) 0 0
\(431\) 4.71015 + 8.15822i 0.226880 + 0.392967i 0.956882 0.290478i \(-0.0938142\pi\)
−0.730002 + 0.683445i \(0.760481\pi\)
\(432\) 0 0
\(433\) −0.208771 −0.0100329 −0.00501645 0.999987i \(-0.501597\pi\)
−0.00501645 + 0.999987i \(0.501597\pi\)
\(434\) 0 0
\(435\) 15.2694 5.06410i 0.732113 0.242805i
\(436\) 0 0
\(437\) 5.58836 0.267328
\(438\) 0 0
\(439\) 9.96796 0.475745 0.237872 0.971296i \(-0.423550\pi\)
0.237872 + 0.971296i \(0.423550\pi\)
\(440\) 0 0
\(441\) 3.96039 + 20.6232i 0.188590 + 0.982056i
\(442\) 0 0
\(443\) 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
\(446\) 0 0
\(447\) 0.116765 0.566231i 0.00552281 0.0267818i
\(448\) 0 0
\(449\) 33.6253 1.58688 0.793439 0.608650i \(-0.208288\pi\)
0.793439 + 0.608650i \(0.208288\pi\)
\(450\) 0 0
\(451\) −3.03637 5.25915i −0.142977 0.247644i
\(452\) 0 0
\(453\) −32.7316 + 10.8554i −1.53786 + 0.510033i
\(454\) 0 0
\(455\) −26.4072 + 0.962383i −1.23799 + 0.0451172i
\(456\) 0 0
\(457\) 32.7083 1.53003 0.765015 0.644013i \(-0.222732\pi\)
0.765015 + 0.644013i \(0.222732\pi\)
\(458\) 0 0
\(459\) −34.0421 2.95178i −1.58895 0.137778i
\(460\) 0 0
\(461\) −2.07165 3.58821i −0.0964865 0.167120i 0.813742 0.581227i \(-0.197427\pi\)
−0.910228 + 0.414107i \(0.864094\pi\)
\(462\) 0 0
\(463\) 8.34176 14.4484i 0.387675 0.671472i −0.604462 0.796634i \(-0.706612\pi\)
0.992136 + 0.125162i \(0.0399451\pi\)
\(464\) 0 0
\(465\) −8.81453 + 42.7444i −0.408764 + 1.98223i
\(466\) 0 0
\(467\) −14.9585 + 25.9089i −0.692198 + 1.19892i 0.278918 + 0.960315i \(0.410024\pi\)
−0.971116 + 0.238608i \(0.923309\pi\)
\(468\) 0 0
\(469\) −25.0247 + 0.911998i −1.15553 + 0.0421121i
\(470\) 0 0
\(471\) −9.01121 8.01514i −0.415215 0.369318i
\(472\) 0 0
\(473\) 0.0182861 0.000840794
\(474\) 0 0
\(475\) 3.86033 + 6.68630i 0.177124 + 0.306788i
\(476\) 0 0
\(477\) 7.72184 5.75488i 0.353559 0.263498i
\(478\) 0 0
\(479\) −1.47965 + 2.56283i −0.0676068 + 0.117098i −0.897847 0.440307i \(-0.854870\pi\)
0.830241 + 0.557405i \(0.188203\pi\)
\(480\) 0 0
\(481\) −3.74907 6.49358i −0.170943 0.296082i
\(482\) 0 0
\(483\) 4.78799 28.4146i 0.217861 1.29291i
\(484\) 0 0
\(485\) −24.3745 + 42.2179i −1.10679 + 1.91701i
\(486\) 0 0
\(487\) 14.0309 + 24.3022i 0.635800 + 1.10124i 0.986345 + 0.164691i \(0.0526628\pi\)
−0.350546 + 0.936546i \(0.614004\pi\)
\(488\) 0 0
\(489\) −13.2738 + 4.40226i −0.600263 + 0.199077i
\(490\) 0 0
\(491\) −17.0734 + 29.5721i −0.770513 + 1.33457i 0.166769 + 0.985996i \(0.446667\pi\)
−0.937282 + 0.348572i \(0.886667\pi\)
\(492\) 0 0
\(493\) −8.25457 + 14.2973i −0.371767 + 0.643920i
\(494\) 0 0
\(495\) 1.91164 + 16.2823i 0.0859216 + 0.731836i
\(496\) 0 0
\(497\) −14.4487 + 0.526567i −0.648113 + 0.0236198i
\(498\) 0 0
\(499\) −1.14035 1.97515i −0.0510493 0.0884199i 0.839372 0.543558i \(-0.182923\pi\)
−0.890421 + 0.455138i \(0.849590\pi\)
\(500\) 0 0
\(501\) −32.0345 + 10.6242i −1.43120 + 0.474656i
\(502\) 0 0
\(503\) −13.9890 −0.623739 −0.311869 0.950125i \(-0.600955\pi\)
−0.311869 + 0.950125i \(0.600955\pi\)
\(504\) 0 0
\(505\) 19.4400 0.865067
\(506\) 0 0
\(507\) −1.99814 + 9.68961i −0.0887405 + 0.430331i
\(508\) 0 0
\(509\) −12.8090 22.1859i −0.567750 0.983373i −0.996788 0.0800859i \(-0.974481\pi\)
0.429038 0.903287i \(-0.358853\pi\)
\(510\) 0 0
\(511\) 16.9574 + 27.0458i 0.750149 + 1.19644i
\(512\) 0 0
\(513\) 1.95489 + 4.18383i 0.0863104 + 0.184720i
\(514\) 0 0
\(515\) 3.08217 5.33848i 0.135817 0.235242i
\(516\) 0 0
\(517\) −5.16071 + 8.93861i −0.226968 + 0.393119i
\(518\) 0 0
\(519\) 29.2014 + 25.9736i 1.28180 + 1.14011i
\(520\) 0 0
\(521\) −20.9127 36.2219i −0.916203 1.58691i −0.805130 0.593099i \(-0.797904\pi\)
−0.111073 0.993812i \(-0.535429\pi\)
\(522\) 0 0
\(523\) −7.88323 + 13.6542i −0.344710 + 0.597055i −0.985301 0.170827i \(-0.945356\pi\)
0.640591 + 0.767882i \(0.278689\pi\)
\(524\) 0 0
\(525\) 37.3046 13.8996i 1.62811 0.606628i
\(526\) 0 0
\(527\) −22.3942 38.7878i −0.975505 1.68962i
\(528\) 0 0
\(529\) −8.26942 + 14.3231i −0.359540 + 0.622742i
\(530\) 0 0
\(531\) −2.41714 20.5879i −0.104895 0.893440i
\(532\) 0 0
\(533\) −5.54944 9.61192i −0.240373 0.416338i
\(534\) 0 0
\(535\) −39.8268 −1.72186
\(536\) 0 0
\(537\) 0.116765 0.566231i 0.00503879 0.0244347i
\(538\) 0 0
\(539\) −4.50433 + 9.30701i −0.194015 + 0.400881i
\(540\) 0 0
\(541\) −21.0963 + 36.5399i −0.907002 + 1.57097i −0.0887957 + 0.996050i \(0.528302\pi\)
−0.818207 + 0.574924i \(0.805031\pi\)
\(542\) 0 0
\(543\) 30.0796 + 26.7547i 1.29084 + 1.14815i
\(544\) 0 0
\(545\) −0.349814 + 0.605896i −0.0149844 + 0.0259537i
\(546\) 0 0
\(547\) −20.3356 35.2222i −0.869486 1.50599i −0.862522 0.506019i \(-0.831117\pi\)
−0.00696400 0.999976i \(-0.502217\pi\)
\(548\) 0 0
\(549\) −2.00550 17.0818i −0.0855927 0.729034i
\(550\) 0 0
\(551\) 2.23119 0.0950519
\(552\) 0 0
\(553\) 30.2799 1.10352i 1.28763 0.0469264i
\(554\) 0 0
\(555\) 13.2985 + 11.8285i 0.564490 + 0.502093i
\(556\) 0 0
\(557\) 6.68794 + 11.5838i 0.283377 + 0.490823i 0.972214 0.234093i \(-0.0752119\pi\)
−0.688837 + 0.724916i \(0.741879\pi\)
\(558\) 0 0
\(559\) 0.0334206 0.00141354
\(560\) 0 0
\(561\) −12.5709 11.1813i −0.530743 0.472076i
\(562\) 0 0
\(563\) 32.7614 1.38073 0.690364 0.723463i \(-0.257451\pi\)
0.690364 + 0.723463i \(0.257451\pi\)
\(564\) 0 0
\(565\) 50.1803 2.11110
\(566\) 0 0
\(567\) 22.9480 6.35522i 0.963726 0.266894i
\(568\) 0 0
\(569\) −16.7280 −0.701272 −0.350636 0.936512i \(-0.614035\pi\)
−0.350636 + 0.936512i \(0.614035\pi\)
\(570\) 0 0
\(571\) 27.4734 1.14973 0.574863 0.818250i \(-0.305055\pi\)
0.574863 + 0.818250i \(0.305055\pi\)
\(572\) 0 0
\(573\) 21.1229 + 18.7880i 0.882421 + 0.784881i
\(574\) 0 0
\(575\) −54.6253 −2.27803
\(576\) 0 0
\(577\) 1.41714 + 2.45455i 0.0589962 + 0.102184i 0.894015 0.448037i \(-0.147877\pi\)
−0.835019 + 0.550221i \(0.814543\pi\)
\(578\) 0 0
\(579\) −18.5345 16.4858i −0.770268 0.685125i
\(580\) 0 0
\(581\) 6.29232 + 10.0358i 0.261050 + 0.416356i
\(582\) 0 0
\(583\) 4.74171 0.196382
\(584\) 0 0
\(585\) 3.49381 + 29.7585i 0.144451 + 1.23036i
\(586\) 0 0
\(587\) 2.34795 + 4.06678i 0.0969105 + 0.167854i 0.910404 0.413720i \(-0.135771\pi\)
−0.813494 + 0.581573i \(0.802437\pi\)
\(588\) 0 0
\(589\) −3.02654 + 5.24212i −0.124706 + 0.215998i
\(590\) 0 0
\(591\) 3.13712 + 2.79035i 0.129044 + 0.114780i
\(592\) 0 0
\(593\) 0.636024 1.10163i 0.0261184 0.0452383i −0.852671 0.522449i \(-0.825019\pi\)
0.878789 + 0.477210i \(0.158352\pi\)
\(594\) 0 0
\(595\) −30.1323 + 56.8792i −1.23530 + 2.33182i
\(596\) 0 0
\(597\) −2.13781 + 10.3669i −0.0874946 + 0.424289i
\(598\) 0 0
\(599\) −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 \(-0.255002\pi\)
−0.969874 + 0.243609i \(0.921669\pi\)
\(602\) 0 0
\(603\) 3.31089 + 28.2005i 0.134830 + 1.14841i
\(604\) 0 0
\(605\) 16.3120 28.2532i 0.663177 1.14866i
\(606\) 0 0
\(607\) −2.29232 3.97042i −0.0930425 0.161154i 0.815747 0.578408i \(-0.196326\pi\)
−0.908790 + 0.417254i \(0.862993\pi\)
\(608\) 0 0
\(609\) 1.91164 11.3447i 0.0774634 0.459711i
\(610\) 0 0
\(611\) −9.43199 + 16.3367i −0.381577 + 0.660911i
\(612\) 0 0
\(613\) −11.0538 19.1457i −0.446458 0.773287i 0.551695 0.834046i \(-0.313981\pi\)
−0.998152 + 0.0607587i \(0.980648\pi\)
\(614\) 0 0
\(615\) 19.6847 + 17.5088i 0.793764 + 0.706023i
\(616\) 0 0
\(617\) 6.00433 10.3998i 0.241725 0.418680i −0.719481 0.694513i \(-0.755620\pi\)
0.961206 + 0.275832i \(0.0889534\pi\)
\(618\) 0 0
\(619\) −8.78180 + 15.2105i −0.352970 + 0.611363i −0.986768 0.162136i \(-0.948162\pi\)
0.633798 + 0.773499i \(0.281495\pi\)
\(620\) 0 0
\(621\) −32.5512 2.82251i −1.30624 0.113264i
\(622\) 0 0
\(623\) 10.9938 20.7524i 0.440458 0.831429i
\(624\) 0 0
\(625\) −3.51602 6.08993i −0.140641 0.243597i
\(626\) 0 0
\(627\) −0.459219 + 2.22690i −0.0183394 + 0.0889337i
\(628\) 0 0
\(629\) −18.2646 −0.728258
\(630\) 0 0
\(631\) 44.9381 1.78896 0.894479 0.447110i \(-0.147547\pi\)
0.894479 + 0.447110i \(0.147547\pi\)
\(632\) 0 0
\(633\) −18.8156 + 6.24020i −0.747854 + 0.248026i
\(634\) 0 0
\(635\) −5.28435 9.15276i −0.209703 0.363216i
\(636\) 0 0
\(637\) −8.23236 + 17.0100i −0.326178 + 0.673960i
\(638\) 0 0
\(639\) 1.91164 + 16.2823i 0.0756232 + 0.644119i
\(640\) 0 0
\(641\) 14.4920 25.1008i 0.572398 0.991422i −0.423921 0.905699i \(-0.639347\pi\)
0.996319 0.0857228i \(-0.0273199\pi\)
\(642\) 0 0
\(643\) −6.03087 + 10.4458i −0.237834 + 0.411941i −0.960093 0.279682i \(-0.909771\pi\)
0.722258 + 0.691623i \(0.243104\pi\)
\(644\) 0 0
\(645\) −0.0752956 + 0.0249718i −0.00296476 + 0.000983262i
\(646\) 0 0
\(647\) −18.8825 32.7055i −0.742349 1.28579i −0.951423 0.307887i \(-0.900378\pi\)
0.209073 0.977900i \(-0.432955\pi\)
\(648\) 0 0
\(649\) 5.10322 8.83903i 0.200319 0.346962i
\(650\) 0 0
\(651\) 24.0611 + 19.8801i 0.943027 + 0.779163i
\(652\) 0 0
\(653\) −18.7040 32.3962i −0.731942 1.26776i −0.956052 0.293198i \(-0.905281\pi\)
0.224109 0.974564i \(-0.428053\pi\)
\(654\) 0 0
\(655\) 0.287992 0.498817i 0.0112528 0.0194904i
\(656\) 0 0
\(657\) 29.0228 21.6299i 1.13229 0.843864i
\(658\) 0 0
\(659\) −14.9356 25.8693i −0.581810 1.00772i −0.995265 0.0971993i \(-0.969012\pi\)
0.413455 0.910524i \(-0.364322\pi\)
\(660\) 0 0
\(661\) 5.60803 0.218127 0.109063 0.994035i \(-0.465215\pi\)
0.109063 + 0.994035i \(0.465215\pi\)
\(662\) 0 0
\(663\) −22.9752 20.4356i −0.892284 0.793654i
\(664\) 0 0
\(665\) 8.69344 0.316823i 0.337117 0.0122859i
\(666\) 0 0
\(667\) −7.89307 + 13.6712i −0.305621 + 0.529351i
\(668\) 0 0
\(669\) −2.52654 + 12.2520i −0.0976818 + 0.473689i
\(670\) 0 0
\(671\) 4.23414 7.33375i 0.163457 0.283116i
\(672\) 0 0
\(673\) −4.72253 8.17966i −0.182040 0.315303i 0.760535 0.649297i \(-0.224937\pi\)
−0.942575 + 0.333994i \(0.891603\pi\)
\(674\) 0 0
\(675\) −19.1087 40.8962i −0.735495 1.57410i
\(676\) 0 0
\(677\) 11.0617 0.425137 0.212569 0.977146i \(-0.431817\pi\)
0.212569 + 0.977146i \(0.431817\pi\)
\(678\) 0 0
\(679\) 18.5192 + 29.5368i 0.710701 + 1.13352i
\(680\) 0 0
\(681\) 22.4491 7.44524i 0.860252 0.285302i
\(682\) 0 0
\(683\) 4.41961 + 7.65499i 0.169112 + 0.292910i 0.938108 0.346343i \(-0.112577\pi\)
−0.768996 + 0.639253i \(0.779243\pi\)
\(684\) 0 0
\(685\) −12.6218 −0.482254
\(686\) 0 0
\(687\) 6.07784 29.4734i 0.231884 1.12448i
\(688\) 0 0
\(689\) 8.66621 0.330156
\(690\) 0 0
\(691\) −25.0617 −0.953394 −0.476697 0.879068i \(-0.658166\pi\)
−0.476697 + 0.879068i \(0.658166\pi\)
\(692\) 0 0
\(693\) 10.9294 + 4.24290i 0.415175 + 0.161175i
\(694\) 0 0
\(695\) −49.9839 −1.89600
\(696\) 0 0
\(697\) −27.0356 −1.02405
\(698\) 0 0
\(699\) 25.0581 8.31052i 0.947785 0.314333i
\(700\) 0 0
\(701\) −43.4858 −1.64243 −0.821217 0.570616i \(-0.806705\pi\)
−0.821217 + 0.570616i \(0.806705\pi\)
\(702\) 0 0
\(703\) 1.23422 + 2.13773i 0.0465495 + 0.0806260i
\(704\) 0 0
\(705\) 9.04325 43.8536i 0.340589 1.65162i
\(706\) 0 0
\(707\) 6.50805 12.2849i 0.244760 0.462021i
\(708\) 0 0
\(709\) −22.7403 −0.854031 −0.427016 0.904244i \(-0.640435\pi\)
−0.427016 + 0.904244i \(0.640435\pi\)
\(710\) 0 0
\(711\) −4.00619 34.1227i −0.150244 1.27970i
\(712\) 0 0
\(713\) −21.4134 37.0891i −0.801939 1.38900i
\(714\) 0 0
\(715\) −7.37636 + 12.7762i −0.275860 + 0.477804i
\(716\) 0 0
\(717\) −31.1545 + 10.3324i −1.16349 + 0.385870i
\(718\) 0 0
\(719\) −6.06182 + 10.4994i −0.226068 + 0.391561i −0.956639 0.291275i \(-0.905920\pi\)
0.730571 + 0.682836i \(0.239254\pi\)
\(720\) 0 0
\(721\) −2.34176 3.73495i −0.0872119 0.139097i
\(722\) 0 0
\(723\) 40.2868 13.3611i 1.49828 0.496905i
\(724\) 0 0
\(725\) −21.8095 −0.809985
\(726\) 0 0
\(727\) −23.0908 39.9945i −0.856392 1.48331i −0.875348 0.483494i \(-0.839368\pi\)
0.0189562 0.999820i \(-0.493966\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) 0 0
\(731\) 0.0407044 0.0705021i 0.00150551 0.00260761i
\(732\) 0 0
\(733\) 18.0149 + 31.2026i 0.665394 + 1.15250i 0.979178 + 0.203002i \(0.0650696\pi\)
−0.313785 + 0.949494i \(0.601597\pi\)
\(734\) 0 0
\(735\) 5.83743 44.4741i 0.215317 1.64045i
\(736\) 0 0
\(737\) −6.99017 + 12.1073i −0.257486 + 0.445979i
\(738\) 0 0
\(739\) −23.2119 40.2042i −0.853865 1.47894i −0.877694 0.479221i \(-0.840919\pi\)
0.0238296 0.999716i \(-0.492414\pi\)
\(740\) 0 0
\(741\) −0.839294 + 4.07000i −0.0308322 + 0.149515i
\(742\) 0 0
\(743\) −0.598884 + 1.03730i −0.0219709 + 0.0380548i −0.876802 0.480852i \(-0.840327\pi\)
0.854831 + 0.518907i \(0.173661\pi\)
\(744\) 0 0
\(745\) −0.617454 + 1.06946i −0.0226218 + 0.0391820i
\(746\) 0 0
\(747\) 10.7694 8.02617i 0.394033 0.293662i
\(748\) 0 0
\(749\) −13.3331 + 25.1682i −0.487181 + 0.919626i
\(750\) 0 0
\(751\) 24.0600 + 41.6731i 0.877961 + 1.52067i 0.853575 + 0.520970i \(0.174430\pi\)
0.0243853 + 0.999703i \(0.492237\pi\)
\(752\) 0 0
\(753\) 15.6902 + 13.9559i 0.571783 + 0.508580i
\(754\) 0 0
\(755\) 73.6588 2.68072
\(756\) 0 0
\(757\) 49.6006 1.80276 0.901382 0.433025i \(-0.142554\pi\)
0.901382 + 0.433025i \(0.142554\pi\)
\(758\) 0 0
\(759\) −12.0204 10.6917i −0.436311 0.388083i
\(760\) 0 0
\(761\) 18.7701 + 32.5108i 0.680416 + 1.17852i 0.974854 + 0.222845i \(0.0715342\pi\)
−0.294438 + 0.955671i \(0.595132\pi\)
\(762\) 0 0
\(763\) 0.265781 + 0.423902i 0.00962191 + 0.0153463i
\(764\) 0 0
\(765\) 67.0319 + 28.8738i 2.42354 + 1.04393i
\(766\) 0 0
\(767\) 9.32691 16.1547i 0.336775 0.583312i
\(768\) 0 0
\(769\) −13.4592 + 23.3121i −0.485352 + 0.840654i −0.999858 0.0168324i \(-0.994642\pi\)
0.514506 + 0.857486i \(0.327975\pi\)
\(770\) 0 0
\(771\) −2.87154 + 13.9250i −0.103416 + 0.501497i
\(772\) 0 0
\(773\) 25.1130 + 43.4971i 0.903254 + 1.56448i 0.823245 + 0.567687i \(0.192162\pi\)
0.0800089 + 0.996794i \(0.474505\pi\)
\(774\) 0 0
\(775\) 29.5840 51.2409i 1.06269 1.84063i
\(776\) 0 0
\(777\) 11.9270 4.44396i 0.427878 0.159426i
\(778\) 0 0
\(779\) 1.82691 + 3.16431i 0.0654560 + 0.113373i
\(780\) 0 0
\(781\) −4.03597 + 6.99050i −0.144418 + 0.250140i
\(782\) 0 0
\(783\) −12.9963 1.12691i −0.464449 0.0402723i
\(784\) 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 \(0.490587\pi\)
\(788\) 0 0
\(789\) −8.78909 + 2.91490i −0.312900 + 0.103773i
\(790\) 0 0
\(791\) 16.7992 31.7110i 0.597311 1.12751i
\(792\) 0 0
\(793\) 7.73855 13.4036i 0.274804 0.475974i
\(794\) 0 0
\(795\) −19.5247 + 6.47536i −0.692469 + 0.229657i
\(796\) 0 0
\(797\) −15.3702 + 26.6219i −0.544439 + 0.942996i 0.454203 + 0.890898i \(0.349924\pi\)
−0.998642 + 0.0520981i \(0.983409\pi\)
\(798\) 0 0
\(799\) 22.9752 + 39.7943i 0.812806 + 1.40782i
\(800\) 0 0
\(801\) −24.4567 10.5346i −0.864134 0.372223i
\(802\) 0 0
\(803\) 17.8219 0.628921
\(804\) 0 0
\(805\) −28.8127 + 54.3882i −1.01551 + 1.91693i
\(806\) 0 0
\(807\) −6.46610 + 31.3561i −0.227617 + 1.10379i
\(808\) 0 0
\(809\) −1.44251 2.49850i −0.0507159 0.0878425i 0.839553 0.543278i \(-0.182817\pi\)
−0.890269 + 0.455435i \(0.849484\pi\)
\(810\) 0 0
\(811\) −28.5461 −1.00239 −0.501195 0.865334i \(-0.667106\pi\)
−0.501195 + 0.865334i \(0.667106\pi\)
\(812\) 0 0
\(813\) 12.0913 4.01008i 0.424061 0.140640i
\(814\) 0 0
\(815\) 29.8713 1.04634
\(816\) 0 0
\(817\) −0.0110023 −0.000384922
\(818\) 0 0
\(819\) 19.9752 + 7.75456i 0.697991 + 0.270966i
\(820\) 0 0
\(821\) 7.96658 0.278036 0.139018 0.990290i \(-0.455605\pi\)
0.139018 + 0.990290i \(0.455605\pi\)
\(822\) 0 0
\(823\) −40.5461 −1.41335 −0.706675 0.707539i \(-0.749806\pi\)
−0.706675 + 0.707539i \(0.749806\pi\)
\(824\) 0 0
\(825\) 4.48879 21.7676i 0.156280 0.757849i
\(826\) 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 \(-0.245696\pi\)
−0.962338 + 0.271856i \(0.912363\pi\)
\(830\) 0 0
\(831\) 14.9585 4.96099i 0.518906 0.172095i
\(832\) 0 0
\(833\) 25.8567 + 38.0837i 0.895881 + 1.31952i
\(834\) 0 0
\(835\) 72.0901 2.49478
\(836\) 0 0
\(837\) 20.2767 29.0058i 0.700866 1.00259i
\(838\) 0 0
\(839\) −1.19599 2.07151i −0.0412900 0.0715164i 0.844642 0.535332i \(-0.179813\pi\)
−0.885932 + 0.463815i \(0.846480\pi\)
\(840\) 0 0
\(841\) 11.3486 19.6564i 0.391333 0.677808i
\(842\) 0 0
\(843\) −4.20080 + 20.3710i −0.144683 + 0.701614i
\(844\) 0 0
\(845\) 10.5662 18.3011i 0.363487 0.629577i
\(846\) 0 0
\(847\) −12.3935 19.7667i −0.425845 0.679193i
\(848\) 0 0
\(849\) −12.7385 11.3305i −0.437186 0.388861i
\(850\) 0 0
\(851\) −17.4647 −0.598683
\(852\) 0 0
\(853\) −8.33998 14.4453i −0.285556 0.494597i 0.687188 0.726479i \(-0.258845\pi\)
−0.972744 + 0.231883i \(0.925511\pi\)
\(854\) 0 0
\(855\) −1.15019 9.79669i −0.0393355 0.335040i
\(856\) 0 0
\(857\) 6.92580 11.9958i 0.236581 0.409770i −0.723150 0.690691i \(-0.757307\pi\)
0.959731 + 0.280921i \(0.0906399\pi\)
\(858\) 0 0
\(859\) 24.2472 + 41.9974i 0.827304 + 1.43293i 0.900146 + 0.435589i \(0.143460\pi\)
−0.0728414 + 0.997344i \(0.523207\pi\)
\(860\) 0 0
\(861\) 17.6545 6.57802i 0.601664 0.224178i
\(862\) 0 0
\(863\) −2.96541 + 5.13624i −0.100944 + 0.174840i −0.912074 0.410026i \(-0.865520\pi\)
0.811130 + 0.584866i \(0.198853\pi\)
\(864\) 0 0
\(865\) −41.7385 72.2932i −1.41915 2.45804i
\(866\) 0 0
\(867\) −43.1443 + 14.3088i −1.46526 + 0.485953i
\(868\) 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 0
\(873\) 31.6959 23.6221i 1.07274 0.799488i
\(874\) 0 0
\(875\) −36.0679 + 1.31446i −1.21932 + 0.0444368i
\(876\) 0 0
\(877\) −1.96472 3.40300i −0.0663439 0.114911i 0.830945 0.556354i \(-0.187800\pi\)
−0.897289 + 0.441443i \(0.854467\pi\)
\(878\) 0 0
\(879\) 35.2149 11.6790i 1.18777 0.393923i
\(880\) 0 0
\(881\) 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 \(-0.146659\pi\)
0.895723 + 0.444613i \(0.146659\pi\)
\(884\) 0 0
\(885\) −8.94251 + 43.3650i −0.300599 + 1.45770i
\(886\) 0 0
\(887\) −18.4938 32.0322i −0.620961 1.07554i −0.989307 0.145848i \(-0.953409\pi\)
0.368346 0.929689i \(-0.379924\pi\)
\(888\) 0 0
\(889\) −7.55308 + 0.275264i −0.253322 + 0.00923206i
\(890\) 0 0
\(891\) 3.79961 12.7393i 0.127292 0.426784i
\(892\) 0 0
\(893\) 3.10507 5.37815i 0.103907 0.179973i
\(894\) 0 0
\(895\) −0.617454 + 1.06946i −0.0206392 + 0.0357482i
\(896\) 0 0
\(897\) −21.9691 19.5407i −0.733525 0.652443i
\(898\) 0 0
\(899\) −8.54944 14.8081i −0.285140 0.493877i
\(900\) 0 0
\(901\) 10.5549 18.2817i 0.351636 0.609052i
\(902\) 0 0
\(903\) −0.00942653 + 0.0559423i −0.000313695 + 0.00186164i
\(904\) 0 0
\(905\) −42.9937 74.4673i −1.42916 2.47538i
\(906\) 0 0
\(907\) −19.5080 + 33.7888i −0.647752 + 1.12194i 0.335907 + 0.941895i \(0.390957\pi\)
−0.983659 + 0.180044i \(0.942376\pi\)
\(908\) 0 0
\(909\) −14.4777 6.23623i −0.480195 0.206843i
\(910\) 0 0
\(911\) 12.8090 + 22.1859i 0.424382 + 0.735052i 0.996363 0.0852158i \(-0.0271580\pi\)
−0.571980 + 0.820267i \(0.693825\pi\)
\(912\) 0 0
\(913\) 6.61312 0.218862
\(914\) 0 0
\(915\) −7.41961 + 35.9800i −0.245285 + 1.18946i
\(916\) 0 0
\(917\) −0.218810 0.348986i −0.00722574 0.0115245i
\(918\) 0 0
\(919\) −10.3367 + 17.9038i −0.340978 + 0.590591i −0.984615 0.174740i \(-0.944091\pi\)
0.643637 + 0.765331i \(0.277425\pi\)
\(920\) 0 0
\(921\) 7.36033 + 6.54674i 0.242531 + 0.215723i
\(922\) 0 0
\(923\) −7.37636 + 12.7762i −0.242796 + 0.420535i
\(924\) 0 0
\(925\) −12.0643 20.8960i −0.396672 0.687055i
\(926\) 0 0
\(927\) −4.00797 + 2.98704i −0.131639 + 0.0981071i
\(928\) 0 0
\(929\) −3.74033 −0.122716 −0.0613582 0.998116i \(-0.519543\pi\)
−0.0613582 + 0.998116i \(0.519543\pi\)
\(930\) 0 0
\(931\) 2.71015 5.59980i 0.0888215 0.183526i
\(932\) 0 0
\(933\) 15.1687 + 13.4920i 0.496600 + 0.441707i
\(934\) 0 0
\(935\) 17.9680 + 31.1214i 0.587615 + 1.01778i
\(936\) 0 0
\(937\) −27.1345 −0.886445 −0.443223 0.896412i \(-0.646165\pi\)
−0.443223 + 0.896412i \(0.646165\pi\)
\(938\) 0 0
\(939\) −34.6501 30.8200i −1.13076 1.00577i
\(940\) 0 0
\(941\) 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
\(944\) 0 0
\(945\) −50.7977 2.54535i −1.65245 0.0828004i
\(946\) 0 0
\(947\) −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
\(950\) 0 0
\(951\) 2.46217 + 2.19001i 0.0798414 + 0.0710160i
\(952\) 0 0
\(953\) 4.28937 0.138946 0.0694732 0.997584i \(-0.477868\pi\)
0.0694732 + 0.997584i \(0.477868\pi\)
\(954\) 0 0
\(955\) −30.1916 52.2933i −0.976977 1.69217i
\(956\) 0 0
\(957\) −4.79920 4.26871i −0.155136 0.137988i
\(958\) 0 0
\(959\) −4.22548 + 7.97622i −0.136448 + 0.257566i
\(960\) 0 0
\(961\) 15.3883 0.496395
\(962\) 0 0
\(963\) 29.6606 + 12.7762i 0.955800 + 0.411708i
\(964\) 0 0
\(965\) 26.4920 + 45.8854i 0.852806 + 1.47710i
\(966\) 0 0
\(967\) 7.59201 13.1497i 0.244142 0.422867i −0.717748 0.696303i \(-0.754827\pi\)
0.961890 + 0.273436i \(0.0881602\pi\)
\(968\) 0 0
\(969\) 7.56360 + 6.72755i 0.242978 + 0.216120i
\(970\) 0 0
\(971\) −1.62364 + 2.81223i −0.0521052 + 0.0902489i −0.890902 0.454196i \(-0.849926\pi\)
0.838796 + 0.544445i \(0.183260\pi\)
\(972\) 0 0
\(973\) −16.7335 + 31.5869i −0.536450 + 1.01263i
\(974\) 0 0
\(975\) 8.20396 39.7836i 0.262737 1.27409i
\(976\) 0 0
\(977\) 15.5439 0.497295 0.248647 0.968594i \(-0.420014\pi\)
0.248647 + 0.968594i \(0.420014\pi\)
\(978\) 0 0
\(979\) −6.55563 11.3547i −0.209519 0.362897i
\(980\) 0 0
\(981\) 0.454888 0.339016i 0.0145235 0.0108240i
\(982\) 0 0
\(983\) 6.19158 10.7241i 0.197481 0.342047i −0.750230 0.661177i \(-0.770057\pi\)
0.947711 + 0.319130i \(0.103391\pi\)
\(984\) 0 0
\(985\) −4.48398 7.76648i −0.142871 0.247461i
\(986\) 0 0
\(987\) −24.6854 20.3960i −0.785745 0.649211i
\(988\) 0 0
\(989\) 0.0389218 0.0674145i 0.00123764 0.00214366i
\(990\) 0 0
\(991\) 3.32760 + 5.76358i 0.105705 + 0.183086i 0.914026 0.405656i \(-0.132957\pi\)
−0.808321 + 0.588742i \(0.799623\pi\)
\(992\) 0 0
\(993\) −7.20513 6.40869i −0.228648 0.203374i
\(994\) 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 \(-0.857562\pi\)
0.825497 + 0.564406i \(0.190895\pi\)
\(998\) 0 0
\(999\) −6.10940 13.0753i −0.193293 0.413683i
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 1008.2.q.h.625.3 6
3.2 odd 2 3024.2.q.h.2305.3 6
4.3 odd 2 126.2.e.d.121.1 yes 6
7.4 even 3 1008.2.t.g.193.3 6
9.2 odd 6 3024.2.t.g.289.1 6
9.7 even 3 1008.2.t.g.961.3 6
12.11 even 2 378.2.e.c.37.3 6
21.11 odd 6 3024.2.t.g.1873.1 6
28.3 even 6 882.2.h.o.67.3 6
28.11 odd 6 126.2.h.c.67.1 yes 6
28.19 even 6 882.2.f.m.589.1 6
28.23 odd 6 882.2.f.l.589.3 6
28.27 even 2 882.2.e.p.373.3 6
36.7 odd 6 126.2.h.c.79.1 yes 6
36.11 even 6 378.2.h.d.289.1 6
36.23 even 6 1134.2.g.n.163.3 6
36.31 odd 6 1134.2.g.k.163.1 6
63.11 odd 6 3024.2.q.h.2881.3 6
63.25 even 3 inner 1008.2.q.h.529.3 6
84.11 even 6 378.2.h.d.361.1 6
84.23 even 6 2646.2.f.o.1765.3 6
84.47 odd 6 2646.2.f.n.1765.1 6
84.59 odd 6 2646.2.h.p.361.3 6
84.83 odd 2 2646.2.e.o.1549.1 6
252.11 even 6 378.2.e.c.235.3 6
252.23 even 6 7938.2.a.bu.1.1 3
252.47 odd 6 2646.2.f.n.883.1 6
252.67 odd 6 1134.2.g.k.487.1 6
252.79 odd 6 882.2.f.l.295.3 6
252.83 odd 6 2646.2.h.p.667.3 6
252.95 even 6 1134.2.g.n.487.3 6
252.103 even 6 7938.2.a.by.1.1 3
252.115 even 6 882.2.e.p.655.3 6
252.131 odd 6 7938.2.a.bx.1.3 3
252.151 odd 6 126.2.e.d.25.1 6
252.187 even 6 882.2.f.m.295.1 6
252.191 even 6 2646.2.f.o.883.3 6
252.223 even 6 882.2.h.o.79.3 6
252.227 odd 6 2646.2.e.o.2125.1 6
252.247 odd 6 7938.2.a.cb.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.1 6 252.151 odd 6
126.2.e.d.121.1 yes 6 4.3 odd 2
126.2.h.c.67.1 yes 6 28.11 odd 6
126.2.h.c.79.1 yes 6 36.7 odd 6
378.2.e.c.37.3 6 12.11 even 2
378.2.e.c.235.3 6 252.11 even 6
378.2.h.d.289.1 6 36.11 even 6
378.2.h.d.361.1 6 84.11 even 6
882.2.e.p.373.3 6 28.27 even 2
882.2.e.p.655.3 6 252.115 even 6
882.2.f.l.295.3 6 252.79 odd 6
882.2.f.l.589.3 6 28.23 odd 6
882.2.f.m.295.1 6 252.187 even 6
882.2.f.m.589.1 6 28.19 even 6
882.2.h.o.67.3 6 28.3 even 6
882.2.h.o.79.3 6 252.223 even 6
1008.2.q.h.529.3 6 63.25 even 3 inner
1008.2.q.h.625.3 6 1.1 even 1 trivial
1008.2.t.g.193.3 6 7.4 even 3
1008.2.t.g.961.3 6 9.7 even 3
1134.2.g.k.163.1 6 36.31 odd 6
1134.2.g.k.487.1 6 252.67 odd 6
1134.2.g.n.163.3 6 36.23 even 6
1134.2.g.n.487.3 6 252.95 even 6
2646.2.e.o.1549.1 6 84.83 odd 2
2646.2.e.o.2125.1 6 252.227 odd 6
2646.2.f.n.883.1 6 252.47 odd 6
2646.2.f.n.1765.1 6 84.47 odd 6
2646.2.f.o.883.3 6 252.191 even 6
2646.2.f.o.1765.3 6 84.23 even 6
2646.2.h.p.361.3 6 84.59 odd 6
2646.2.h.p.667.3 6 252.83 odd 6
3024.2.q.h.2305.3 6 3.2 odd 2
3024.2.q.h.2881.3 6 63.11 odd 6
3024.2.t.g.289.1 6 9.2 odd 6
3024.2.t.g.1873.1 6 21.11 odd 6
7938.2.a.bu.1.1 3 252.23 even 6
7938.2.a.bx.1.3 3 252.131 odd 6
7938.2.a.by.1.1 3 252.103 even 6
7938.2.a.cb.1.3 3 252.247 odd 6