Properties

Label 324.2.b.b.323.2
Level $324$
Weight $2$
Character 324.323
Analytic conductor $2.587$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,2,Mod(323,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.b (of order \(2\), degree \(1\), 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: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.170772624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.2
Root \(-1.02187 + 0.977642i\) of defining polynomial
Character \(\chi\) \(=\) 324.323
Dual form 324.2.b.b.323.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35760 + 0.396143i) q^{2} +(1.68614 - 1.07561i) q^{4} +2.52434i q^{5} +1.27582i q^{7} +(-1.86301 + 2.12819i) q^{8} +O(q^{10})\) \(q+(-1.35760 + 0.396143i) q^{2} +(1.68614 - 1.07561i) q^{4} +2.52434i q^{5} +1.27582i q^{7} +(-1.86301 + 2.12819i) q^{8} +(-1.00000 - 3.42703i) q^{10} -0.505408 q^{11} -2.37228 q^{13} +(-0.505408 - 1.73205i) q^{14} +(1.68614 - 3.62725i) q^{16} +0.792287i q^{17} +4.70285i q^{19} +(2.71519 + 4.25639i) q^{20} +(0.686141 - 0.200214i) q^{22} -3.22060 q^{23} -1.37228 q^{25} +(3.22060 - 0.939764i) q^{26} +(1.37228 + 2.15121i) q^{28} +2.52434i q^{29} +8.12989i q^{31} +(-0.852189 + 5.59230i) q^{32} +(-0.313859 - 1.07561i) q^{34} -3.22060 q^{35} -6.74456 q^{37} +(-1.86301 - 6.38458i) q^{38} +(-5.37228 - 4.70285i) q^{40} -6.78073i q^{41} +7.72946i q^{43} +(-0.852189 + 0.543620i) q^{44} +(4.37228 - 1.27582i) q^{46} -1.19897 q^{47} +5.37228 q^{49} +(1.86301 - 0.543620i) q^{50} +(-4.00000 + 2.55164i) q^{52} +1.87953i q^{53} -1.27582i q^{55} +(-2.71519 - 2.37686i) q^{56} +(-1.00000 - 3.42703i) q^{58} +12.3770 q^{59} -2.37228 q^{61} +(-3.22060 - 11.0371i) q^{62} +(-1.05842 - 7.92967i) q^{64} -5.98844i q^{65} -7.72946i q^{67} +(0.852189 + 1.33591i) q^{68} +(4.37228 - 1.27582i) q^{70} +11.8716 q^{71} +3.37228 q^{73} +(9.15640 - 2.67181i) q^{74} +(5.05842 + 7.92967i) q^{76} -0.644810i q^{77} -9.88067i q^{79} +(9.15640 + 4.25639i) q^{80} +(2.68614 + 9.20550i) q^{82} +7.64018 q^{83} -2.00000 q^{85} +(-3.06198 - 10.4935i) q^{86} +(0.941578 - 1.07561i) q^{88} -11.9769i q^{89} -3.02661i q^{91} +(-5.43039 + 3.46410i) q^{92} +(1.62772 - 0.474964i) q^{94} -11.8716 q^{95} +10.4891 q^{97} +(-7.29339 + 2.12819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 8 q^{10} + 4 q^{13} + 2 q^{16} - 6 q^{22} + 12 q^{25} - 12 q^{28} - 14 q^{34} - 8 q^{37} - 20 q^{40} + 12 q^{46} + 20 q^{49} - 32 q^{52} - 8 q^{58} + 4 q^{61} + 26 q^{64} + 12 q^{70} + 4 q^{73} + 6 q^{76} + 10 q^{82} - 16 q^{85} + 42 q^{88} + 36 q^{94} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35760 + 0.396143i −0.959966 + 0.280116i
\(3\) 0 0
\(4\) 1.68614 1.07561i 0.843070 0.537803i
\(5\) 2.52434i 1.12892i 0.825461 + 0.564459i \(0.190915\pi\)
−0.825461 + 0.564459i \(0.809085\pi\)
\(6\) 0 0
\(7\) 1.27582i 0.482215i 0.970498 + 0.241107i \(0.0775106\pi\)
−0.970498 + 0.241107i \(0.922489\pi\)
\(8\) −1.86301 + 2.12819i −0.658672 + 0.752430i
\(9\) 0 0
\(10\) −1.00000 3.42703i −0.316228 1.08372i
\(11\) −0.505408 −0.152386 −0.0761931 0.997093i \(-0.524277\pi\)
−0.0761931 + 0.997093i \(0.524277\pi\)
\(12\) 0 0
\(13\) −2.37228 −0.657952 −0.328976 0.944338i \(-0.606704\pi\)
−0.328976 + 0.944338i \(0.606704\pi\)
\(14\) −0.505408 1.73205i −0.135076 0.462910i
\(15\) 0 0
\(16\) 1.68614 3.62725i 0.421535 0.906812i
\(17\) 0.792287i 0.192158i 0.995374 + 0.0960789i \(0.0306301\pi\)
−0.995374 + 0.0960789i \(0.969370\pi\)
\(18\) 0 0
\(19\) 4.70285i 1.07891i 0.842015 + 0.539454i \(0.181369\pi\)
−0.842015 + 0.539454i \(0.818631\pi\)
\(20\) 2.71519 + 4.25639i 0.607136 + 0.951757i
\(21\) 0 0
\(22\) 0.686141 0.200214i 0.146286 0.0426858i
\(23\) −3.22060 −0.671542 −0.335771 0.941944i \(-0.608997\pi\)
−0.335771 + 0.941944i \(0.608997\pi\)
\(24\) 0 0
\(25\) −1.37228 −0.274456
\(26\) 3.22060 0.939764i 0.631612 0.184303i
\(27\) 0 0
\(28\) 1.37228 + 2.15121i 0.259337 + 0.406541i
\(29\) 2.52434i 0.468758i 0.972145 + 0.234379i \(0.0753056\pi\)
−0.972145 + 0.234379i \(0.924694\pi\)
\(30\) 0 0
\(31\) 8.12989i 1.46017i 0.683356 + 0.730086i \(0.260520\pi\)
−0.683356 + 0.730086i \(0.739480\pi\)
\(32\) −0.852189 + 5.59230i −0.150647 + 0.988588i
\(33\) 0 0
\(34\) −0.313859 1.07561i −0.0538264 0.184465i
\(35\) −3.22060 −0.544381
\(36\) 0 0
\(37\) −6.74456 −1.10880 −0.554400 0.832251i \(-0.687052\pi\)
−0.554400 + 0.832251i \(0.687052\pi\)
\(38\) −1.86301 6.38458i −0.302219 1.03572i
\(39\) 0 0
\(40\) −5.37228 4.70285i −0.849432 0.743587i
\(41\) 6.78073i 1.05897i −0.848319 0.529486i \(-0.822385\pi\)
0.848319 0.529486i \(-0.177615\pi\)
\(42\) 0 0
\(43\) 7.72946i 1.17873i 0.807866 + 0.589366i \(0.200622\pi\)
−0.807866 + 0.589366i \(0.799378\pi\)
\(44\) −0.852189 + 0.543620i −0.128472 + 0.0819538i
\(45\) 0 0
\(46\) 4.37228 1.27582i 0.644658 0.188110i
\(47\) −1.19897 −0.174888 −0.0874439 0.996169i \(-0.527870\pi\)
−0.0874439 + 0.996169i \(0.527870\pi\)
\(48\) 0 0
\(49\) 5.37228 0.767469
\(50\) 1.86301 0.543620i 0.263469 0.0768795i
\(51\) 0 0
\(52\) −4.00000 + 2.55164i −0.554700 + 0.353849i
\(53\) 1.87953i 0.258173i 0.991633 + 0.129086i \(0.0412045\pi\)
−0.991633 + 0.129086i \(0.958796\pi\)
\(54\) 0 0
\(55\) 1.27582i 0.172032i
\(56\) −2.71519 2.37686i −0.362833 0.317621i
\(57\) 0 0
\(58\) −1.00000 3.42703i −0.131306 0.449992i
\(59\) 12.3770 1.61135 0.805674 0.592359i \(-0.201803\pi\)
0.805674 + 0.592359i \(0.201803\pi\)
\(60\) 0 0
\(61\) −2.37228 −0.303739 −0.151870 0.988401i \(-0.548529\pi\)
−0.151870 + 0.988401i \(0.548529\pi\)
\(62\) −3.22060 11.0371i −0.409017 1.40172i
\(63\) 0 0
\(64\) −1.05842 7.92967i −0.132303 0.991209i
\(65\) 5.98844i 0.742774i
\(66\) 0 0
\(67\) 7.72946i 0.944304i −0.881517 0.472152i \(-0.843477\pi\)
0.881517 0.472152i \(-0.156523\pi\)
\(68\) 0.852189 + 1.33591i 0.103343 + 0.162003i
\(69\) 0 0
\(70\) 4.37228 1.27582i 0.522588 0.152490i
\(71\) 11.8716 1.40890 0.704450 0.709754i \(-0.251194\pi\)
0.704450 + 0.709754i \(0.251194\pi\)
\(72\) 0 0
\(73\) 3.37228 0.394696 0.197348 0.980334i \(-0.436767\pi\)
0.197348 + 0.980334i \(0.436767\pi\)
\(74\) 9.15640 2.67181i 1.06441 0.310592i
\(75\) 0 0
\(76\) 5.05842 + 7.92967i 0.580241 + 0.909596i
\(77\) 0.644810i 0.0734829i
\(78\) 0 0
\(79\) 9.88067i 1.11166i −0.831295 0.555831i \(-0.812400\pi\)
0.831295 0.555831i \(-0.187600\pi\)
\(80\) 9.15640 + 4.25639i 1.02372 + 0.475879i
\(81\) 0 0
\(82\) 2.68614 + 9.20550i 0.296635 + 1.01658i
\(83\) 7.64018 0.838618 0.419309 0.907844i \(-0.362272\pi\)
0.419309 + 0.907844i \(0.362272\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) −3.06198 10.4935i −0.330181 1.13154i
\(87\) 0 0
\(88\) 0.941578 1.07561i 0.100373 0.114660i
\(89\) 11.9769i 1.26955i −0.772698 0.634773i \(-0.781093\pi\)
0.772698 0.634773i \(-0.218907\pi\)
\(90\) 0 0
\(91\) 3.02661i 0.317274i
\(92\) −5.43039 + 3.46410i −0.566157 + 0.361158i
\(93\) 0 0
\(94\) 1.62772 0.474964i 0.167886 0.0489888i
\(95\) −11.8716 −1.21800
\(96\) 0 0
\(97\) 10.4891 1.06501 0.532505 0.846427i \(-0.321251\pi\)
0.532505 + 0.846427i \(0.321251\pi\)
\(98\) −7.29339 + 2.12819i −0.736744 + 0.214980i
\(99\) 0 0
\(100\) −2.31386 + 1.47603i −0.231386 + 0.147603i
\(101\) 1.23472i 0.122859i 0.998111 + 0.0614295i \(0.0195659\pi\)
−0.998111 + 0.0614295i \(0.980434\pi\)
\(102\) 0 0
\(103\) 0.474964i 0.0467996i 0.999726 + 0.0233998i \(0.00744907\pi\)
−0.999726 + 0.0233998i \(0.992551\pi\)
\(104\) 4.41957 5.04868i 0.433375 0.495063i
\(105\) 0 0
\(106\) −0.744563 2.55164i −0.0723183 0.247837i
\(107\) −12.5652 −1.21472 −0.607360 0.794427i \(-0.707771\pi\)
−0.607360 + 0.794427i \(0.707771\pi\)
\(108\) 0 0
\(109\) 13.4891 1.29202 0.646012 0.763327i \(-0.276436\pi\)
0.646012 + 0.763327i \(0.276436\pi\)
\(110\) 0.505408 + 1.73205i 0.0481888 + 0.165145i
\(111\) 0 0
\(112\) 4.62772 + 2.15121i 0.437278 + 0.203271i
\(113\) 7.27806i 0.684662i 0.939579 + 0.342331i \(0.111216\pi\)
−0.939579 + 0.342331i \(0.888784\pi\)
\(114\) 0 0
\(115\) 8.12989i 0.758116i
\(116\) 2.71519 + 4.25639i 0.252099 + 0.395196i
\(117\) 0 0
\(118\) −16.8030 + 4.90307i −1.54684 + 0.451364i
\(119\) −1.01082 −0.0926614
\(120\) 0 0
\(121\) −10.7446 −0.976778
\(122\) 3.22060 0.939764i 0.291580 0.0850822i
\(123\) 0 0
\(124\) 8.74456 + 13.7081i 0.785285 + 1.23103i
\(125\) 9.15759i 0.819080i
\(126\) 0 0
\(127\) 7.65492i 0.679265i −0.940558 0.339632i \(-0.889697\pi\)
0.940558 0.339632i \(-0.110303\pi\)
\(128\) 4.57820 + 10.3460i 0.404660 + 0.914467i
\(129\) 0 0
\(130\) 2.37228 + 8.12989i 0.208063 + 0.713038i
\(131\) −7.64018 −0.667525 −0.333763 0.942657i \(-0.608318\pi\)
−0.333763 + 0.942657i \(0.608318\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 3.06198 + 10.4935i 0.264514 + 0.906500i
\(135\) 0 0
\(136\) −1.68614 1.47603i −0.144585 0.126569i
\(137\) 5.49111i 0.469137i −0.972100 0.234568i \(-0.924632\pi\)
0.972100 0.234568i \(-0.0753677\pi\)
\(138\) 0 0
\(139\) 15.3844i 1.30489i −0.757838 0.652443i \(-0.773744\pi\)
0.757838 0.652443i \(-0.226256\pi\)
\(140\) −5.43039 + 3.46410i −0.458952 + 0.292770i
\(141\) 0 0
\(142\) −16.1168 + 4.70285i −1.35250 + 0.394655i
\(143\) 1.19897 0.100263
\(144\) 0 0
\(145\) −6.37228 −0.529189
\(146\) −4.57820 + 1.33591i −0.378895 + 0.110560i
\(147\) 0 0
\(148\) −11.3723 + 7.25450i −0.934796 + 0.596316i
\(149\) 12.9166i 1.05817i 0.848568 + 0.529086i \(0.177465\pi\)
−0.848568 + 0.529086i \(0.822535\pi\)
\(150\) 0 0
\(151\) 3.02661i 0.246302i 0.992388 + 0.123151i \(0.0392999\pi\)
−0.992388 + 0.123151i \(0.960700\pi\)
\(152\) −10.0086 8.76144i −0.811804 0.710647i
\(153\) 0 0
\(154\) 0.255437 + 0.875393i 0.0205837 + 0.0705411i
\(155\) −20.5226 −1.64841
\(156\) 0 0
\(157\) 11.8614 0.946643 0.473322 0.880890i \(-0.343055\pi\)
0.473322 + 0.880890i \(0.343055\pi\)
\(158\) 3.91416 + 13.4140i 0.311394 + 1.06716i
\(159\) 0 0
\(160\) −14.1168 2.15121i −1.11603 0.170068i
\(161\) 4.10891i 0.323828i
\(162\) 0 0
\(163\) 1.75079i 0.137132i 0.997647 + 0.0685660i \(0.0218424\pi\)
−0.997647 + 0.0685660i \(0.978158\pi\)
\(164\) −7.29339 11.4333i −0.569518 0.892787i
\(165\) 0 0
\(166\) −10.3723 + 3.02661i −0.805045 + 0.234910i
\(167\) 17.4901 1.35343 0.676714 0.736246i \(-0.263403\pi\)
0.676714 + 0.736246i \(0.263403\pi\)
\(168\) 0 0
\(169\) −7.37228 −0.567099
\(170\) 2.71519 0.792287i 0.208246 0.0607656i
\(171\) 0 0
\(172\) 8.31386 + 13.0330i 0.633926 + 0.993754i
\(173\) 17.6704i 1.34345i 0.740799 + 0.671726i \(0.234447\pi\)
−0.740799 + 0.671726i \(0.765553\pi\)
\(174\) 0 0
\(175\) 1.75079i 0.132347i
\(176\) −0.852189 + 1.83324i −0.0642362 + 0.138186i
\(177\) 0 0
\(178\) 4.74456 + 16.2598i 0.355620 + 1.21872i
\(179\) 8.83915 0.660669 0.330334 0.943864i \(-0.392838\pi\)
0.330334 + 0.943864i \(0.392838\pi\)
\(180\) 0 0
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 1.19897 + 4.10891i 0.0888736 + 0.304573i
\(183\) 0 0
\(184\) 6.00000 6.85407i 0.442326 0.505289i
\(185\) 17.0256i 1.25174i
\(186\) 0 0
\(187\) 0.400428i 0.0292822i
\(188\) −2.02163 + 1.28962i −0.147443 + 0.0940552i
\(189\) 0 0
\(190\) 16.1168 4.70285i 1.16924 0.341181i
\(191\) 15.0922 1.09203 0.546017 0.837774i \(-0.316144\pi\)
0.546017 + 0.837774i \(0.316144\pi\)
\(192\) 0 0
\(193\) 7.74456 0.557466 0.278733 0.960369i \(-0.410086\pi\)
0.278733 + 0.960369i \(0.410086\pi\)
\(194\) −14.2400 + 4.15520i −1.02237 + 0.298326i
\(195\) 0 0
\(196\) 9.05842 5.77846i 0.647030 0.412747i
\(197\) 23.9538i 1.70663i 0.521392 + 0.853317i \(0.325413\pi\)
−0.521392 + 0.853317i \(0.674587\pi\)
\(198\) 0 0
\(199\) 12.9073i 0.914973i −0.889217 0.457486i \(-0.848750\pi\)
0.889217 0.457486i \(-0.151250\pi\)
\(200\) 2.55657 2.92048i 0.180777 0.206509i
\(201\) 0 0
\(202\) −0.489125 1.67625i −0.0344147 0.117940i
\(203\) −3.22060 −0.226042
\(204\) 0 0
\(205\) 17.1168 1.19549
\(206\) −0.188154 0.644810i −0.0131093 0.0449261i
\(207\) 0 0
\(208\) −4.00000 + 8.60485i −0.277350 + 0.596639i
\(209\) 2.37686i 0.164411i
\(210\) 0 0
\(211\) 17.5356i 1.20720i 0.797287 + 0.603600i \(0.206268\pi\)
−0.797287 + 0.603600i \(0.793732\pi\)
\(212\) 2.02163 + 3.16915i 0.138846 + 0.217658i
\(213\) 0 0
\(214\) 17.0584 4.97760i 1.16609 0.340262i
\(215\) −19.5118 −1.33069
\(216\) 0 0
\(217\) −10.3723 −0.704116
\(218\) −18.3128 + 5.34363i −1.24030 + 0.361916i
\(219\) 0 0
\(220\) −1.37228 2.15121i −0.0925192 0.145035i
\(221\) 1.87953i 0.126431i
\(222\) 0 0
\(223\) 8.12989i 0.544418i −0.962238 0.272209i \(-0.912246\pi\)
0.962238 0.272209i \(-0.0877541\pi\)
\(224\) −7.13477 1.08724i −0.476712 0.0726443i
\(225\) 0 0
\(226\) −2.88316 9.88067i −0.191785 0.657253i
\(227\) 14.3986 0.955671 0.477835 0.878449i \(-0.341422\pi\)
0.477835 + 0.878449i \(0.341422\pi\)
\(228\) 0 0
\(229\) 3.62772 0.239726 0.119863 0.992790i \(-0.461754\pi\)
0.119863 + 0.992790i \(0.461754\pi\)
\(230\) 3.22060 + 11.0371i 0.212360 + 0.727766i
\(231\) 0 0
\(232\) −5.37228 4.70285i −0.352708 0.308758i
\(233\) 4.84630i 0.317491i −0.987320 0.158746i \(-0.949255\pi\)
0.987320 0.158746i \(-0.0507450\pi\)
\(234\) 0 0
\(235\) 3.02661i 0.197434i
\(236\) 20.8694 13.3128i 1.35848 0.866589i
\(237\) 0 0
\(238\) 1.37228 0.400428i 0.0889518 0.0259559i
\(239\) −12.0597 −0.780080 −0.390040 0.920798i \(-0.627539\pi\)
−0.390040 + 0.920798i \(0.627539\pi\)
\(240\) 0 0
\(241\) −6.48913 −0.418001 −0.209001 0.977916i \(-0.567021\pi\)
−0.209001 + 0.977916i \(0.567021\pi\)
\(242\) 14.5868 4.25639i 0.937674 0.273611i
\(243\) 0 0
\(244\) −4.00000 + 2.55164i −0.256074 + 0.163352i
\(245\) 13.5615i 0.866409i
\(246\) 0 0
\(247\) 11.1565i 0.709871i
\(248\) −17.3020 15.1460i −1.09868 0.961774i
\(249\) 0 0
\(250\) −3.62772 12.4323i −0.229437 0.786289i
\(251\) 11.1780 0.705551 0.352776 0.935708i \(-0.385238\pi\)
0.352776 + 0.935708i \(0.385238\pi\)
\(252\) 0 0
\(253\) 1.62772 0.102334
\(254\) 3.03245 + 10.3923i 0.190273 + 0.652071i
\(255\) 0 0
\(256\) −10.3139 12.2321i −0.644616 0.764506i
\(257\) 14.9985i 0.935584i −0.883839 0.467792i \(-0.845050\pi\)
0.883839 0.467792i \(-0.154950\pi\)
\(258\) 0 0
\(259\) 8.60485i 0.534680i
\(260\) −6.44121 10.0974i −0.399467 0.626211i
\(261\) 0 0
\(262\) 10.3723 3.02661i 0.640802 0.186984i
\(263\) −27.9746 −1.72499 −0.862494 0.506067i \(-0.831099\pi\)
−0.862494 + 0.506067i \(0.831099\pi\)
\(264\) 0 0
\(265\) −4.74456 −0.291456
\(266\) 8.14558 2.37686i 0.499438 0.145735i
\(267\) 0 0
\(268\) −8.31386 13.0330i −0.507850 0.796115i
\(269\) 21.4843i 1.30992i −0.755663 0.654961i \(-0.772685\pi\)
0.755663 0.654961i \(-0.227315\pi\)
\(270\) 0 0
\(271\) 29.9679i 1.82042i 0.414146 + 0.910211i \(0.364080\pi\)
−0.414146 + 0.910211i \(0.635920\pi\)
\(272\) 2.87382 + 1.33591i 0.174251 + 0.0810013i
\(273\) 0 0
\(274\) 2.17527 + 7.45471i 0.131413 + 0.450356i
\(275\) 0.693562 0.0418234
\(276\) 0 0
\(277\) 6.37228 0.382873 0.191437 0.981505i \(-0.438685\pi\)
0.191437 + 0.981505i \(0.438685\pi\)
\(278\) 6.09442 + 20.8858i 0.365519 + 1.25265i
\(279\) 0 0
\(280\) 6.00000 6.85407i 0.358569 0.409609i
\(281\) 23.0140i 1.37290i −0.727177 0.686450i \(-0.759168\pi\)
0.727177 0.686450i \(-0.240832\pi\)
\(282\) 0 0
\(283\) 9.88067i 0.587345i 0.955906 + 0.293673i \(0.0948775\pi\)
−0.955906 + 0.293673i \(0.905122\pi\)
\(284\) 20.0172 12.7692i 1.18780 0.757711i
\(285\) 0 0
\(286\) −1.62772 + 0.474964i −0.0962490 + 0.0280852i
\(287\) 8.65099 0.510652
\(288\) 0 0
\(289\) 16.3723 0.963075
\(290\) 8.65099 2.52434i 0.508004 0.148234i
\(291\) 0 0
\(292\) 5.68614 3.62725i 0.332756 0.212269i
\(293\) 23.3089i 1.36172i 0.732412 + 0.680862i \(0.238395\pi\)
−0.732412 + 0.680862i \(0.761605\pi\)
\(294\) 0 0
\(295\) 31.2437i 1.81908i
\(296\) 12.5652 14.3537i 0.730335 0.834294i
\(297\) 0 0
\(298\) −5.11684 17.5356i −0.296411 1.01581i
\(299\) 7.64018 0.441843
\(300\) 0 0
\(301\) −9.86141 −0.568402
\(302\) −1.19897 4.10891i −0.0689930 0.236441i
\(303\) 0 0
\(304\) 17.0584 + 7.92967i 0.978368 + 0.454798i
\(305\) 5.98844i 0.342897i
\(306\) 0 0
\(307\) 1.20128i 0.0685609i −0.999412 0.0342805i \(-0.989086\pi\)
0.999412 0.0342805i \(-0.0109140\pi\)
\(308\) −0.693562 1.08724i −0.0395194 0.0619513i
\(309\) 0 0
\(310\) 27.8614 8.12989i 1.58242 0.461747i
\(311\) 19.1355 1.08507 0.542536 0.840032i \(-0.317464\pi\)
0.542536 + 0.840032i \(0.317464\pi\)
\(312\) 0 0
\(313\) −18.4891 −1.04507 −0.522534 0.852619i \(-0.675013\pi\)
−0.522534 + 0.852619i \(0.675013\pi\)
\(314\) −16.1030 + 4.69882i −0.908746 + 0.265170i
\(315\) 0 0
\(316\) −10.6277 16.6602i −0.597856 0.937210i
\(317\) 32.5214i 1.82659i −0.407303 0.913293i \(-0.633531\pi\)
0.407303 0.913293i \(-0.366469\pi\)
\(318\) 0 0
\(319\) 1.27582i 0.0714323i
\(320\) 20.0172 2.67181i 1.11899 0.149359i
\(321\) 0 0
\(322\) 1.62772 + 5.57825i 0.0907092 + 0.310864i
\(323\) −3.72601 −0.207321
\(324\) 0 0
\(325\) 3.25544 0.180579
\(326\) −0.693562 2.37686i −0.0384129 0.131642i
\(327\) 0 0
\(328\) 14.4307 + 12.6325i 0.796802 + 0.697515i
\(329\) 1.52967i 0.0843335i
\(330\) 0 0
\(331\) 27.7422i 1.52485i 0.647078 + 0.762424i \(0.275991\pi\)
−0.647078 + 0.762424i \(0.724009\pi\)
\(332\) 12.8824 8.21782i 0.707014 0.451012i
\(333\) 0 0
\(334\) −23.7446 + 6.92860i −1.29924 + 0.379116i
\(335\) 19.5118 1.06604
\(336\) 0 0
\(337\) −15.7446 −0.857661 −0.428830 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(338\) 10.0086 2.92048i 0.544395 0.158853i
\(339\) 0 0
\(340\) −3.37228 + 2.15121i −0.182888 + 0.116666i
\(341\) 4.10891i 0.222510i
\(342\) 0 0
\(343\) 15.7848i 0.852300i
\(344\) −16.4498 14.4000i −0.886913 0.776397i
\(345\) 0 0
\(346\) −7.00000 23.9892i −0.376322 1.28967i
\(347\) −6.94661 −0.372914 −0.186457 0.982463i \(-0.559700\pi\)
−0.186457 + 0.982463i \(0.559700\pi\)
\(348\) 0 0
\(349\) −5.62772 −0.301245 −0.150622 0.988591i \(-0.548128\pi\)
−0.150622 + 0.988591i \(0.548128\pi\)
\(350\) 0.693562 + 2.37686i 0.0370725 + 0.127049i
\(351\) 0 0
\(352\) 0.430703 2.82639i 0.0229566 0.150647i
\(353\) 8.36530i 0.445240i 0.974905 + 0.222620i \(0.0714609\pi\)
−0.974905 + 0.222620i \(0.928539\pi\)
\(354\) 0 0
\(355\) 29.9679i 1.59053i
\(356\) −12.8824 20.1947i −0.682766 1.07032i
\(357\) 0 0
\(358\) −12.0000 + 3.50157i −0.634220 + 0.185064i
\(359\) −1.38712 −0.0732096 −0.0366048 0.999330i \(-0.511654\pi\)
−0.0366048 + 0.999330i \(0.511654\pi\)
\(360\) 0 0
\(361\) −3.11684 −0.164044
\(362\) 5.43039 1.58457i 0.285415 0.0832834i
\(363\) 0 0
\(364\) −3.25544 5.10328i −0.170631 0.267485i
\(365\) 8.51278i 0.445579i
\(366\) 0 0
\(367\) 6.37910i 0.332987i −0.986043 0.166493i \(-0.946756\pi\)
0.986043 0.166493i \(-0.0532444\pi\)
\(368\) −5.43039 + 11.6819i −0.283079 + 0.608962i
\(369\) 0 0
\(370\) 6.74456 + 23.1138i 0.350633 + 1.20163i
\(371\) −2.39794 −0.124495
\(372\) 0 0
\(373\) −19.8614 −1.02838 −0.514192 0.857675i \(-0.671908\pi\)
−0.514192 + 0.857675i \(0.671908\pi\)
\(374\) 0.158627 + 0.543620i 0.00820241 + 0.0281099i
\(375\) 0 0
\(376\) 2.23369 2.55164i 0.115194 0.131591i
\(377\) 5.98844i 0.308420i
\(378\) 0 0
\(379\) 6.45364i 0.331501i −0.986168 0.165751i \(-0.946995\pi\)
0.986168 0.165751i \(-0.0530047\pi\)
\(380\) −20.0172 + 12.7692i −1.02686 + 0.655044i
\(381\) 0 0
\(382\) −20.4891 + 5.97868i −1.04831 + 0.305896i
\(383\) 8.65099 0.442045 0.221023 0.975269i \(-0.429061\pi\)
0.221023 + 0.975269i \(0.429061\pi\)
\(384\) 0 0
\(385\) 1.62772 0.0829562
\(386\) −10.5140 + 3.06796i −0.535148 + 0.156155i
\(387\) 0 0
\(388\) 17.6861 11.2822i 0.897878 0.572766i
\(389\) 31.5268i 1.59847i 0.601018 + 0.799235i \(0.294762\pi\)
−0.601018 + 0.799235i \(0.705238\pi\)
\(390\) 0 0
\(391\) 2.55164i 0.129042i
\(392\) −10.0086 + 11.4333i −0.505510 + 0.577467i
\(393\) 0 0
\(394\) −9.48913 32.5196i −0.478055 1.63831i
\(395\) 24.9422 1.25498
\(396\) 0 0
\(397\) −18.7446 −0.940763 −0.470381 0.882463i \(-0.655884\pi\)
−0.470381 + 0.882463i \(0.655884\pi\)
\(398\) 5.11313 + 17.5229i 0.256298 + 0.878343i
\(399\) 0 0
\(400\) −2.31386 + 4.97760i −0.115693 + 0.248880i
\(401\) 4.60625i 0.230025i −0.993364 0.115012i \(-0.963309\pi\)
0.993364 0.115012i \(-0.0366908\pi\)
\(402\) 0 0
\(403\) 19.2864i 0.960723i
\(404\) 1.32807 + 2.08191i 0.0660740 + 0.103579i
\(405\) 0 0
\(406\) 4.37228 1.27582i 0.216993 0.0633179i
\(407\) 3.40876 0.168966
\(408\) 0 0
\(409\) 13.7446 0.679625 0.339812 0.940493i \(-0.389636\pi\)
0.339812 + 0.940493i \(0.389636\pi\)
\(410\) −23.2378 + 6.78073i −1.14763 + 0.334876i
\(411\) 0 0
\(412\) 0.510875 + 0.800857i 0.0251690 + 0.0394554i
\(413\) 15.7908i 0.777016i
\(414\) 0 0
\(415\) 19.2864i 0.946731i
\(416\) 2.02163 13.2665i 0.0991187 0.650444i
\(417\) 0 0
\(418\) 0.941578 + 3.22682i 0.0460541 + 0.157829i
\(419\) −26.9638 −1.31727 −0.658634 0.752464i \(-0.728865\pi\)
−0.658634 + 0.752464i \(0.728865\pi\)
\(420\) 0 0
\(421\) −10.6060 −0.516903 −0.258452 0.966024i \(-0.583212\pi\)
−0.258452 + 0.966024i \(0.583212\pi\)
\(422\) −6.94661 23.8063i −0.338156 1.15887i
\(423\) 0 0
\(424\) −4.00000 3.50157i −0.194257 0.170051i
\(425\) 1.08724i 0.0527389i
\(426\) 0 0
\(427\) 3.02661i 0.146468i
\(428\) −21.1866 + 13.5152i −1.02409 + 0.653280i
\(429\) 0 0
\(430\) 26.4891 7.72946i 1.27742 0.372748i
\(431\) −31.1952 −1.50262 −0.751310 0.659949i \(-0.770578\pi\)
−0.751310 + 0.659949i \(0.770578\pi\)
\(432\) 0 0
\(433\) −8.62772 −0.414622 −0.207311 0.978275i \(-0.566471\pi\)
−0.207311 + 0.978275i \(0.566471\pi\)
\(434\) 14.0814 4.10891i 0.675928 0.197234i
\(435\) 0 0
\(436\) 22.7446 14.5090i 1.08927 0.694855i
\(437\) 15.1460i 0.724533i
\(438\) 0 0
\(439\) 6.52818i 0.311573i 0.987791 + 0.155786i \(0.0497912\pi\)
−0.987791 + 0.155786i \(0.950209\pi\)
\(440\) 2.71519 + 2.37686i 0.129442 + 0.113312i
\(441\) 0 0
\(442\) 0.744563 + 2.55164i 0.0354152 + 0.121369i
\(443\) −12.3770 −0.588049 −0.294025 0.955798i \(-0.594995\pi\)
−0.294025 + 0.955798i \(0.594995\pi\)
\(444\) 0 0
\(445\) 30.2337 1.43321
\(446\) 3.22060 + 11.0371i 0.152500 + 0.522623i
\(447\) 0 0
\(448\) 10.1168 1.35036i 0.477976 0.0637984i
\(449\) 19.4024i 0.915657i 0.889041 + 0.457828i \(0.151373\pi\)
−0.889041 + 0.457828i \(0.848627\pi\)
\(450\) 0 0
\(451\) 3.42703i 0.161373i
\(452\) 7.82833 + 12.2718i 0.368214 + 0.577218i
\(453\) 0 0
\(454\) −19.5475 + 5.70393i −0.917412 + 0.267698i
\(455\) 7.64018 0.358177
\(456\) 0 0
\(457\) 39.9783 1.87010 0.935052 0.354511i \(-0.115353\pi\)
0.935052 + 0.354511i \(0.115353\pi\)
\(458\) −4.92498 + 1.43710i −0.230129 + 0.0671511i
\(459\) 0 0
\(460\) −8.74456 13.7081i −0.407717 0.639145i
\(461\) 0.349857i 0.0162944i 0.999967 + 0.00814722i \(0.00259337\pi\)
−0.999967 + 0.00814722i \(0.997407\pi\)
\(462\) 0 0
\(463\) 4.77739i 0.222024i −0.993819 0.111012i \(-0.964591\pi\)
0.993819 0.111012i \(-0.0354092\pi\)
\(464\) 9.15640 + 4.25639i 0.425075 + 0.197598i
\(465\) 0 0
\(466\) 1.91983 + 6.57932i 0.0889343 + 0.304781i
\(467\) 5.11313 0.236608 0.118304 0.992977i \(-0.462254\pi\)
0.118304 + 0.992977i \(0.462254\pi\)
\(468\) 0 0
\(469\) 9.86141 0.455357
\(470\) 1.19897 + 4.10891i 0.0553044 + 0.189530i
\(471\) 0 0
\(472\) −23.0584 + 26.3407i −1.06135 + 1.21243i
\(473\) 3.90653i 0.179623i
\(474\) 0 0
\(475\) 6.45364i 0.296113i
\(476\) −1.70438 + 1.08724i −0.0781201 + 0.0498336i
\(477\) 0 0
\(478\) 16.3723 4.77739i 0.748851 0.218513i
\(479\) −13.0706 −0.597209 −0.298605 0.954377i \(-0.596521\pi\)
−0.298605 + 0.954377i \(0.596521\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 8.80962 2.57062i 0.401267 0.117089i
\(483\) 0 0
\(484\) −18.1168 + 11.5569i −0.823493 + 0.525315i
\(485\) 26.4781i 1.20231i
\(486\) 0 0
\(487\) 42.8752i 1.94286i −0.237325 0.971430i \(-0.576271\pi\)
0.237325 0.971430i \(-0.423729\pi\)
\(488\) 4.41957 5.04868i 0.200065 0.228543i
\(489\) 0 0
\(490\) −5.37228 18.4110i −0.242695 0.831724i
\(491\) 13.7641 0.621166 0.310583 0.950546i \(-0.399476\pi\)
0.310583 + 0.950546i \(0.399476\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 4.41957 + 15.1460i 0.198846 + 0.681452i
\(495\) 0 0
\(496\) 29.4891 + 13.7081i 1.32410 + 0.615513i
\(497\) 15.1460i 0.679392i
\(498\) 0 0
\(499\) 3.42703i 0.153415i 0.997054 + 0.0767076i \(0.0244408\pi\)
−0.997054 + 0.0767076i \(0.975559\pi\)
\(500\) 9.84996 + 15.4410i 0.440504 + 0.690542i
\(501\) 0 0
\(502\) −15.1753 + 4.42810i −0.677305 + 0.197636i
\(503\) −19.3236 −0.861597 −0.430799 0.902448i \(-0.641768\pi\)
−0.430799 + 0.902448i \(0.641768\pi\)
\(504\) 0 0
\(505\) −3.11684 −0.138698
\(506\) −2.20979 + 0.644810i −0.0982370 + 0.0286653i
\(507\) 0 0
\(508\) −8.23369 12.9073i −0.365311 0.572668i
\(509\) 14.7962i 0.655829i −0.944707 0.327914i \(-0.893654\pi\)
0.944707 0.327914i \(-0.106346\pi\)
\(510\) 0 0
\(511\) 4.30243i 0.190328i
\(512\) 18.8477 + 12.5205i 0.832960 + 0.553333i
\(513\) 0 0
\(514\) 5.94158 + 20.3620i 0.262072 + 0.898129i
\(515\) −1.19897 −0.0528329
\(516\) 0 0
\(517\) 0.605969 0.0266505
\(518\) 3.40876 + 11.6819i 0.149772 + 0.513274i
\(519\) 0 0
\(520\) 12.7446 + 11.1565i 0.558886 + 0.489245i
\(521\) 26.0357i 1.14064i −0.821421 0.570322i \(-0.806819\pi\)
0.821421 0.570322i \(-0.193181\pi\)
\(522\) 0 0
\(523\) 9.40571i 0.411283i −0.978627 0.205641i \(-0.934072\pi\)
0.978627 0.205641i \(-0.0659281\pi\)
\(524\) −12.8824 + 8.21782i −0.562771 + 0.358997i
\(525\) 0 0
\(526\) 37.9783 11.0820i 1.65593 0.483196i
\(527\) −6.44121 −0.280583
\(528\) 0 0
\(529\) −12.6277 −0.549031
\(530\) 6.44121 1.87953i 0.279788 0.0816415i
\(531\) 0 0
\(532\) −10.1168 + 6.45364i −0.438621 + 0.279801i
\(533\) 16.0858i 0.696753i
\(534\) 0 0
\(535\) 31.7187i 1.37132i
\(536\) 16.4498 + 14.4000i 0.710523 + 0.621986i
\(537\) 0 0
\(538\) 8.51087 + 29.1671i 0.366930 + 1.25748i
\(539\) −2.71519 −0.116952
\(540\) 0 0
\(541\) −8.97825 −0.386005 −0.193003 0.981198i \(-0.561823\pi\)
−0.193003 + 0.981198i \(0.561823\pi\)
\(542\) −11.8716 40.6844i −0.509929 1.74754i
\(543\) 0 0
\(544\) −4.43070 0.675178i −0.189965 0.0289480i
\(545\) 34.0511i 1.45859i
\(546\) 0 0
\(547\) 22.2385i 0.950848i −0.879757 0.475424i \(-0.842295\pi\)
0.879757 0.475424i \(-0.157705\pi\)
\(548\) −5.90627 9.25878i −0.252303 0.395515i
\(549\) 0 0
\(550\) −0.941578 + 0.274750i −0.0401490 + 0.0117154i
\(551\) −11.8716 −0.505747
\(552\) 0 0
\(553\) 12.6060 0.536060
\(554\) −8.65099 + 2.52434i −0.367545 + 0.107249i
\(555\) 0 0
\(556\) −16.5475 25.9402i −0.701772 1.10011i
\(557\) 7.22316i 0.306055i −0.988222 0.153027i \(-0.951098\pi\)
0.988222 0.153027i \(-0.0489023\pi\)
\(558\) 0 0
\(559\) 18.3365i 0.775549i
\(560\) −5.43039 + 11.6819i −0.229476 + 0.493651i
\(561\) 0 0
\(562\) 9.11684 + 31.2437i 0.384571 + 1.31794i
\(563\) −15.7858 −0.665290 −0.332645 0.943052i \(-0.607941\pi\)
−0.332645 + 0.943052i \(0.607941\pi\)
\(564\) 0 0
\(565\) −18.3723 −0.772928
\(566\) −3.91416 13.4140i −0.164525 0.563831i
\(567\) 0 0
\(568\) −22.1168 + 25.2651i −0.928002 + 1.06010i
\(569\) 25.3909i 1.06444i −0.846606 0.532220i \(-0.821358\pi\)
0.846606 0.532220i \(-0.178642\pi\)
\(570\) 0 0
\(571\) 4.22789i 0.176932i −0.996079 0.0884659i \(-0.971804\pi\)
0.996079 0.0884659i \(-0.0281964\pi\)
\(572\) 2.02163 1.28962i 0.0845287 0.0539217i
\(573\) 0 0
\(574\) −11.7446 + 3.42703i −0.490209 + 0.143042i
\(575\) 4.41957 0.184309
\(576\) 0 0
\(577\) 31.8397 1.32550 0.662751 0.748840i \(-0.269389\pi\)
0.662751 + 0.748840i \(0.269389\pi\)
\(578\) −22.2270 + 6.48577i −0.924520 + 0.269773i
\(579\) 0 0
\(580\) −10.7446 + 6.85407i −0.446144 + 0.284600i
\(581\) 9.74749i 0.404394i
\(582\) 0 0
\(583\) 0.949929i 0.0393420i
\(584\) −6.28258 + 7.17687i −0.259975 + 0.296981i
\(585\) 0 0
\(586\) −9.23369 31.6442i −0.381440 1.30721i
\(587\) 3.91416 0.161555 0.0807774 0.996732i \(-0.474260\pi\)
0.0807774 + 0.996732i \(0.474260\pi\)
\(588\) 0 0
\(589\) −38.2337 −1.57539
\(590\) −12.3770 42.4164i −0.509553 1.74626i
\(591\) 0 0
\(592\) −11.3723 + 24.4642i −0.467398 + 1.00547i
\(593\) 8.80773i 0.361690i 0.983512 + 0.180845i \(0.0578833\pi\)
−0.983512 + 0.180845i \(0.942117\pi\)
\(594\) 0 0
\(595\) 2.55164i 0.104607i
\(596\) 13.8932 + 21.7793i 0.569089 + 0.892114i
\(597\) 0 0
\(598\) −10.3723 + 3.02661i −0.424154 + 0.123767i
\(599\) −0.188154 −0.00768776 −0.00384388 0.999993i \(-0.501224\pi\)
−0.00384388 + 0.999993i \(0.501224\pi\)
\(600\) 0 0
\(601\) 15.9783 0.651766 0.325883 0.945410i \(-0.394338\pi\)
0.325883 + 0.945410i \(0.394338\pi\)
\(602\) 13.3878 3.90653i 0.545647 0.159218i
\(603\) 0 0
\(604\) 3.25544 + 5.10328i 0.132462 + 0.207650i
\(605\) 27.1229i 1.10270i
\(606\) 0 0
\(607\) 3.97653i 0.161403i 0.996738 + 0.0807013i \(0.0257160\pi\)
−0.996738 + 0.0807013i \(0.974284\pi\)
\(608\) −26.2998 4.00772i −1.06660 0.162535i
\(609\) 0 0
\(610\) 2.37228 + 8.12989i 0.0960509 + 0.329170i
\(611\) 2.84429 0.115068
\(612\) 0 0
\(613\) 4.23369 0.170997 0.0854985 0.996338i \(-0.472752\pi\)
0.0854985 + 0.996338i \(0.472752\pi\)
\(614\) 0.475881 + 1.63086i 0.0192050 + 0.0658162i
\(615\) 0 0
\(616\) 1.37228 + 1.20128i 0.0552908 + 0.0484011i
\(617\) 4.90120i 0.197315i 0.995121 + 0.0986574i \(0.0314548\pi\)
−0.995121 + 0.0986574i \(0.968545\pi\)
\(618\) 0 0
\(619\) 9.33117i 0.375052i −0.982260 0.187526i \(-0.939953\pi\)
0.982260 0.187526i \(-0.0600468\pi\)
\(620\) −34.6040 + 22.0742i −1.38973 + 0.886522i
\(621\) 0 0
\(622\) −25.9783 + 7.58039i −1.04163 + 0.303946i
\(623\) 15.2804 0.612194
\(624\) 0 0
\(625\) −29.9783 −1.19913
\(626\) 25.1008 7.32435i 1.00323 0.292740i
\(627\) 0 0
\(628\) 20.0000 12.7582i 0.798087 0.509108i
\(629\) 5.34363i 0.213064i
\(630\) 0 0
\(631\) 42.8752i 1.70683i 0.521228 + 0.853417i \(0.325474\pi\)
−0.521228 + 0.853417i \(0.674526\pi\)
\(632\) 21.0280 + 18.4077i 0.836449 + 0.732221i
\(633\) 0 0
\(634\) 12.8832 + 44.1510i 0.511655 + 1.75346i
\(635\) 19.3236 0.766834
\(636\) 0 0
\(637\) −12.7446 −0.504958
\(638\) 0.505408 + 1.73205i 0.0200093 + 0.0685725i
\(639\) 0 0
\(640\) −26.1168 + 11.5569i −1.03236 + 0.456827i
\(641\) 20.9321i 0.826768i 0.910557 + 0.413384i \(0.135653\pi\)
−0.910557 + 0.413384i \(0.864347\pi\)
\(642\) 0 0
\(643\) 35.9466i 1.41760i −0.705412 0.708798i \(-0.749238\pi\)
0.705412 0.708798i \(-0.250762\pi\)
\(644\) −4.41957 6.92820i −0.174156 0.273009i
\(645\) 0 0
\(646\) 5.05842 1.47603i 0.199021 0.0580738i
\(647\) 46.0993 1.81235 0.906174 0.422904i \(-0.138989\pi\)
0.906174 + 0.422904i \(0.138989\pi\)
\(648\) 0 0
\(649\) −6.25544 −0.245547
\(650\) −4.41957 + 1.28962i −0.173350 + 0.0505831i
\(651\) 0 0
\(652\) 1.88316 + 2.95207i 0.0737501 + 0.115612i
\(653\) 4.40387i 0.172337i −0.996281 0.0861683i \(-0.972538\pi\)
0.996281 0.0861683i \(-0.0274623\pi\)
\(654\) 0 0
\(655\) 19.2864i 0.753581i
\(656\) −24.5954 11.4333i −0.960288 0.446394i
\(657\) 0 0
\(658\) 0.605969 + 2.07668i 0.0236231 + 0.0809573i
\(659\) 12.0597 0.469781 0.234891 0.972022i \(-0.424527\pi\)
0.234891 + 0.972022i \(0.424527\pi\)
\(660\) 0 0
\(661\) 15.6277 0.607848 0.303924 0.952696i \(-0.401703\pi\)
0.303924 + 0.952696i \(0.401703\pi\)
\(662\) −10.9899 37.6627i −0.427134 1.46380i
\(663\) 0 0
\(664\) −14.2337 + 16.2598i −0.552374 + 0.631002i
\(665\) 15.1460i 0.587338i
\(666\) 0 0
\(667\) 8.12989i 0.314791i
\(668\) 29.4908 18.8125i 1.14103 0.727878i
\(669\) 0 0
\(670\) −26.4891 + 7.72946i −1.02336 + 0.298615i
\(671\) 1.19897 0.0462857
\(672\) 0 0
\(673\) 29.8614 1.15107 0.575536 0.817776i \(-0.304793\pi\)
0.575536 + 0.817776i \(0.304793\pi\)
\(674\) 21.3748 6.23711i 0.823326 0.240244i
\(675\) 0 0
\(676\) −12.4307 + 7.92967i −0.478104 + 0.304987i
\(677\) 3.51900i 0.135246i −0.997711 0.0676232i \(-0.978458\pi\)
0.997711 0.0676232i \(-0.0215416\pi\)
\(678\) 0 0
\(679\) 13.3822i 0.513563i
\(680\) 3.72601 4.25639i 0.142886 0.163225i
\(681\) 0 0
\(682\) 1.62772 + 5.57825i 0.0623286 + 0.213602i
\(683\) −20.0172 −0.765936 −0.382968 0.923762i \(-0.625098\pi\)
−0.382968 + 0.923762i \(0.625098\pi\)
\(684\) 0 0
\(685\) 13.8614 0.529617
\(686\) −6.25305 21.4294i −0.238743 0.818179i
\(687\) 0 0
\(688\) 28.0367 + 13.0330i 1.06889 + 0.496877i
\(689\) 4.45877i 0.169866i
\(690\) 0 0
\(691\) 20.0872i 0.764155i 0.924130 + 0.382077i \(0.124791\pi\)
−0.924130 + 0.382077i \(0.875209\pi\)
\(692\) 19.0064 + 29.7947i 0.722513 + 1.13263i
\(693\) 0 0
\(694\) 9.43070 2.75186i 0.357985 0.104459i
\(695\) 38.8354 1.47311
\(696\) 0 0
\(697\) 5.37228 0.203490
\(698\) 7.64018 2.22938i 0.289185 0.0843834i
\(699\) 0 0
\(700\) −1.88316 2.95207i −0.0711766 0.111578i
\(701\) 32.7615i 1.23738i −0.785634 0.618692i \(-0.787663\pi\)
0.785634 0.618692i \(-0.212337\pi\)
\(702\) 0 0
\(703\) 31.7187i 1.19629i
\(704\) 0.534935 + 4.00772i 0.0201611 + 0.151047i
\(705\) 0 0
\(706\) −3.31386 11.3567i −0.124719 0.427415i
\(707\) −1.57528 −0.0592444
\(708\) 0 0
\(709\) 23.8614 0.896134 0.448067 0.894000i \(-0.352113\pi\)
0.448067 + 0.894000i \(0.352113\pi\)
\(710\) −11.8716 40.6844i −0.445533 1.52686i
\(711\) 0 0
\(712\) 25.4891 + 22.3130i 0.955245 + 0.836215i
\(713\) 26.1831i 0.980566i
\(714\) 0 0
\(715\) 3.02661i 0.113189i
\(716\) 14.9040 9.50744i 0.556990 0.355310i
\(717\) 0 0
\(718\) 1.88316 0.549500i 0.0702788 0.0205072i
\(719\) 16.2912 0.607558 0.303779 0.952743i \(-0.401752\pi\)
0.303779 + 0.952743i \(0.401752\pi\)
\(720\) 0 0
\(721\) −0.605969 −0.0225675
\(722\) 4.23142 1.23472i 0.157477 0.0459514i
\(723\) 0 0
\(724\) −6.74456 + 4.30243i −0.250660 + 0.159898i
\(725\) 3.46410i 0.128654i
\(726\) 0 0
\(727\) 38.0978i 1.41297i −0.707728 0.706485i \(-0.750280\pi\)
0.707728 0.706485i \(-0.249720\pi\)
\(728\) 6.44121 + 5.63858i 0.238727 + 0.208980i
\(729\) 0 0
\(730\) −3.37228 11.5569i −0.124814 0.427741i
\(731\) −6.12395 −0.226503
\(732\) 0 0
\(733\) 0.372281 0.0137505 0.00687526 0.999976i \(-0.497812\pi\)
0.00687526 + 0.999976i \(0.497812\pi\)
\(734\) 2.52704 + 8.66025i 0.0932748 + 0.319656i
\(735\) 0 0
\(736\) 2.74456 18.0106i 0.101166 0.663878i
\(737\) 3.90653i 0.143899i
\(738\) 0 0
\(739\) 6.45364i 0.237401i 0.992930 + 0.118700i \(0.0378728\pi\)
−0.992930 + 0.118700i \(0.962127\pi\)
\(740\) −18.3128 28.7075i −0.673192 1.05531i
\(741\) 0 0
\(742\) 3.25544 0.949929i 0.119511 0.0348730i
\(743\) −21.1571 −0.776179 −0.388089 0.921622i \(-0.626865\pi\)
−0.388089 + 0.921622i \(0.626865\pi\)
\(744\) 0 0
\(745\) −32.6060 −1.19459
\(746\) 26.9638 7.86797i 0.987215 0.288067i
\(747\) 0 0
\(748\) −0.430703 0.675178i −0.0157481 0.0246870i
\(749\) 16.0309i 0.585756i
\(750\) 0 0
\(751\) 21.6890i 0.791441i 0.918371 + 0.395721i \(0.129505\pi\)
−0.918371 + 0.395721i \(0.870495\pi\)
\(752\) −2.02163 + 4.34896i −0.0737213 + 0.158590i
\(753\) 0 0
\(754\) 2.37228 + 8.12989i 0.0863934 + 0.296073i
\(755\) −7.64018 −0.278054
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 2.55657 + 8.76144i 0.0928587 + 0.318230i
\(759\) 0 0
\(760\) 22.1168 25.2651i 0.802262 0.916460i
\(761\) 17.3754i 0.629858i −0.949115 0.314929i \(-0.898019\pi\)
0.949115 0.314929i \(-0.101981\pi\)
\(762\) 0 0
\(763\) 17.2097i 0.623033i
\(764\) 25.4476 16.2333i 0.920661 0.587299i
\(765\) 0 0
\(766\) −11.7446 + 3.42703i −0.424348 + 0.123824i
\(767\) −29.3617 −1.06019
\(768\) 0 0
\(769\) 8.09509 0.291917 0.145958 0.989291i \(-0.453373\pi\)
0.145958 + 0.989291i \(0.453373\pi\)
\(770\) −2.20979 + 0.644810i −0.0796352 + 0.0232373i
\(771\) 0 0
\(772\) 13.0584 8.33010i 0.469983 0.299807i
\(773\) 0.699713i 0.0251669i −0.999921 0.0125835i \(-0.995994\pi\)
0.999921 0.0125835i \(-0.00400555\pi\)
\(774\) 0 0
\(775\) 11.1565i 0.400753i
\(776\) −19.5413 + 22.3229i −0.701492 + 0.801345i
\(777\) 0 0
\(778\) −12.4891 42.8007i −0.447757 1.53448i
\(779\) 31.8888 1.14253
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) 1.01082 + 3.46410i 0.0361467 + 0.123876i
\(783\) 0 0
\(784\) 9.05842 19.4866i 0.323515 0.695950i
\(785\) 29.9422i 1.06868i
\(786\) 0 0
\(787\) 34.7453i 1.23854i −0.785180 0.619268i \(-0.787429\pi\)
0.785180 0.619268i \(-0.212571\pi\)
\(788\) 25.7648 + 40.3894i 0.917834 + 1.43881i
\(789\) 0 0
\(790\) −33.8614 + 9.88067i −1.20473 + 0.351539i
\(791\) −9.28550 −0.330154
\(792\) 0 0
\(793\) 5.62772 0.199846
\(794\) 25.4476 7.42554i 0.903100 0.263522i
\(795\) 0 0
\(796\) −13.8832 21.7635i −0.492075 0.771386i
\(797\) 23.8989i 0.846541i −0.906003 0.423270i \(-0.860882\pi\)
0.906003 0.423270i \(-0.139118\pi\)
\(798\) 0 0
\(799\) 0.949929i 0.0336061i
\(800\) 1.16944 7.67420i 0.0413461 0.271324i
\(801\) 0 0
\(802\) 1.82473 + 6.25343i 0.0644336 + 0.220816i
\(803\) −1.70438 −0.0601462
\(804\) 0 0
\(805\) 10.3723 0.365575
\(806\) 7.64018 + 26.1831i 0.269114 + 0.922262i
\(807\) 0 0
\(808\) −2.62772 2.30029i −0.0924428 0.0809238i
\(809\) 35.8381i 1.26000i 0.776595 + 0.630000i \(0.216945\pi\)
−0.776595 + 0.630000i \(0.783055\pi\)
\(810\) 0 0
\(811\) 1.20128i 0.0421828i 0.999778 + 0.0210914i \(0.00671410\pi\)
−0.999778 + 0.0210914i \(0.993286\pi\)
\(812\) −5.43039 + 3.46410i −0.190569 + 0.121566i
\(813\) 0 0
\(814\) −4.62772 + 1.35036i −0.162201 + 0.0473300i
\(815\) −4.41957 −0.154811
\(816\) 0 0
\(817\) −36.3505 −1.27174
\(818\) −18.6596 + 5.44482i −0.652417 + 0.190374i
\(819\) 0 0
\(820\) 28.8614 18.4110i 1.00788 0.642940i
\(821\) 18.2603i 0.637288i −0.947874 0.318644i \(-0.896773\pi\)
0.947874 0.318644i \(-0.103227\pi\)
\(822\) 0 0
\(823\) 14.0340i 0.489195i 0.969625 + 0.244598i \(0.0786559\pi\)
−0.969625 + 0.244598i \(0.921344\pi\)
\(824\) −1.01082 0.884861i −0.0352135 0.0308256i
\(825\) 0 0
\(826\) −6.25544 21.4376i −0.217655 0.745909i
\(827\) −47.4864 −1.65126 −0.825632 0.564210i \(-0.809181\pi\)
−0.825632 + 0.564210i \(0.809181\pi\)
\(828\) 0 0
\(829\) −48.2337 −1.67523 −0.837613 0.546265i \(-0.816049\pi\)
−0.837613 + 0.546265i \(0.816049\pi\)
\(830\) −7.64018 26.1831i −0.265194 0.908830i
\(831\) 0 0
\(832\) 2.51087 + 18.8114i 0.0870489 + 0.652169i
\(833\) 4.25639i 0.147475i
\(834\) 0 0
\(835\) 44.1510i 1.52791i
\(836\) −2.55657 4.00772i −0.0884207 0.138610i
\(837\) 0 0
\(838\) 36.6060 10.6815i 1.26453 0.368987i
\(839\) −42.6205 −1.47142 −0.735711 0.677296i \(-0.763152\pi\)
−0.735711 + 0.677296i \(0.763152\pi\)
\(840\) 0 0
\(841\) 22.6277 0.780266
\(842\) 14.3986 4.20149i 0.496210 0.144793i
\(843\) 0 0
\(844\) 18.8614 + 29.5675i 0.649236 + 1.01775i
\(845\) 18.6101i 0.640208i
\(846\) 0 0
\(847\) 13.7081i 0.471017i
\(848\) 6.81751 + 3.16915i 0.234114 + 0.108829i
\(849\) 0 0
\(850\) 0.430703 + 1.47603i 0.0147730 + 0.0506276i
\(851\) 21.7216 0.744605
\(852\) 0 0
\(853\) 44.6060 1.52728 0.763640 0.645643i \(-0.223410\pi\)
0.763640 + 0.645643i \(0.223410\pi\)
\(854\) 1.19897 + 4.10891i 0.0410279 + 0.140604i
\(855\) 0 0
\(856\) 23.4090 26.7411i 0.800102 0.913992i
\(857\) 37.5701i 1.28337i 0.766968 + 0.641685i \(0.221764\pi\)
−0.766968 + 0.641685i \(0.778236\pi\)
\(858\) 0 0
\(859\) 1.82532i 0.0622791i −0.999515 0.0311396i \(-0.990086\pi\)
0.999515 0.0311396i \(-0.00991364\pi\)
\(860\) −32.8996 + 20.9870i −1.12187 + 0.715650i
\(861\) 0 0
\(862\) 42.3505 12.3578i 1.44246 0.420908i
\(863\) 40.0344 1.36279 0.681393 0.731918i \(-0.261375\pi\)
0.681393 + 0.731918i \(0.261375\pi\)
\(864\) 0 0
\(865\) −44.6060 −1.51665
\(866\) 11.7130 3.41781i 0.398023 0.116142i
\(867\) 0 0
\(868\) −17.4891 + 11.1565i −0.593620 + 0.378676i
\(869\) 4.99377i 0.169402i
\(870\) 0 0
\(871\) 18.3365i 0.621307i
\(872\) −25.1303 + 28.7075i −0.851020 + 0.972158i
\(873\) 0 0
\(874\) 6.00000 + 20.5622i 0.202953 + 0.695527i
\(875\) −11.6834 −0.394972
\(876\) 0 0
\(877\) 21.6277 0.730316 0.365158 0.930946i \(-0.381015\pi\)
0.365158 + 0.930946i \(0.381015\pi\)
\(878\) −2.58609 8.86263i −0.0872765 0.299099i
\(879\) 0 0
\(880\) −4.62772 2.15121i −0.156000 0.0725174i
\(881\) 52.9562i 1.78414i 0.451898 + 0.892070i \(0.350747\pi\)
−0.451898 + 0.892070i \(0.649253\pi\)
\(882\) 0 0
\(883\) 20.0127i 0.673481i 0.941597 + 0.336741i \(0.109325\pi\)
−0.941597 + 0.336741i \(0.890675\pi\)
\(884\) −2.02163 3.16915i −0.0679949 0.106590i
\(885\) 0 0
\(886\) 16.8030 4.90307i 0.564507 0.164722i
\(887\) −19.5118 −0.655141 −0.327571 0.944827i \(-0.606230\pi\)
−0.327571 + 0.944827i \(0.606230\pi\)
\(888\) 0 0
\(889\) 9.76631 0.327552
\(890\) −41.0452 + 11.9769i −1.37584 + 0.401466i
\(891\) 0 0
\(892\) −8.74456 13.7081i −0.292790 0.458982i
\(893\) 5.63858i 0.188688i
\(894\) 0 0
\(895\) 22.3130i 0.745841i
\(896\) −13.1997 + 5.84096i −0.440970 + 0.195133i
\(897\) 0 0
\(898\) −7.68614 26.3407i −0.256490 0.878999i
\(899\) −20.5226 −0.684467
\(900\) 0 0
\(901\) −1.48913 −0.0496100
\(902\) −1.35760 4.65253i −0.0452030 0.154912i
\(903\) 0 0
\(904\) −15.4891 13.5591i −0.515161 0.450968i
\(905\) 10.0974i 0.335647i
\(906\) 0 0
\(907\) 29.8934i 0.992593i −0.868153 0.496297i \(-0.834693\pi\)
0.868153 0.496297i \(-0.165307\pi\)
\(908\) 24.2781 15.4873i 0.805698 0.513963i
\(909\) 0 0
\(910\) −10.3723 + 3.02661i −0.343838 + 0.100331i
\(911\) 35.8029 1.18620 0.593102 0.805127i \(-0.297903\pi\)
0.593102 + 0.805127i \(0.297903\pi\)
\(912\) 0 0
\(913\) −3.86141 −0.127794
\(914\) −54.2744 + 15.8371i −1.79524 + 0.523846i
\(915\) 0 0
\(916\) 6.11684 3.90200i 0.202106 0.128926i
\(917\) 9.74749i 0.321891i
\(918\) 0 0
\(919\) 36.9711i 1.21956i 0.792570 + 0.609781i \(0.208743\pi\)
−0.792570 + 0.609781i \(0.791257\pi\)
\(920\) 17.3020 + 15.1460i 0.570429 + 0.499350i
\(921\) 0 0
\(922\) −0.138593 0.474964i −0.00456433 0.0156421i
\(923\) −28.1628 −0.926989
\(924\) 0 0
\(925\) 9.25544 0.304317
\(926\) 1.89253 + 6.48577i 0.0621925 + 0.213136i
\(927\) 0 0
\(928\) −14.1168 2.15121i −0.463408 0.0706170i
\(929\) 18.5552i 0.608777i 0.952548 + 0.304389i \(0.0984521\pi\)
−0.952548 + 0.304389i \(0.901548\pi\)
\(930\) 0 0
\(931\) 25.2651i 0.828029i
\(932\) −5.21271 8.17154i −0.170748 0.267668i
\(933\) 0 0
\(934\) −6.94158 + 2.02554i −0.227135 + 0.0662775i
\(935\) 1.01082 0.0330572
\(936\) 0 0
\(937\) 45.7228 1.49370 0.746850 0.664993i \(-0.231565\pi\)
0.746850 + 0.664993i \(0.231565\pi\)
\(938\) −13.3878 + 3.90653i −0.437128 + 0.127553i
\(939\) 0 0
\(940\) −3.25544 5.10328i −0.106181 0.166451i
\(941\) 13.5065i 0.440301i −0.975466 0.220150i \(-0.929345\pi\)
0.975466 0.220150i \(-0.0706548\pi\)
\(942\) 0 0
\(943\) 21.8380i 0.711144i
\(944\) 20.8694 44.8945i 0.679240 1.46119i
\(945\) 0 0
\(946\) 1.54755 + 5.30350i 0.0503151 + 0.172432i
\(947\) −6.57031 −0.213506 −0.106753 0.994286i \(-0.534045\pi\)
−0.106753 + 0.994286i \(0.534045\pi\)
\(948\) 0 0
\(949\) −8.00000 −0.259691
\(950\) 2.55657 + 8.76144i 0.0829460 + 0.284259i
\(951\) 0 0
\(952\) 1.88316 2.15121i 0.0610334 0.0697212i
\(953\) 10.2997i 0.333641i 0.985987 + 0.166821i \(0.0533500\pi\)
−0.985987 + 0.166821i \(0.946650\pi\)
\(954\) 0 0
\(955\) 38.0978i 1.23282i
\(956\) −20.3344 + 12.9715i −0.657663 + 0.419530i
\(957\) 0 0
\(958\) 17.7446 5.17782i 0.573301 0.167288i
\(959\) 7.00567 0.226225
\(960\) 0 0
\(961\) −35.0951 −1.13210
\(962\) −21.7216 + 6.33830i −0.700331 + 0.204355i
\(963\) 0 0
\(964\) −10.9416 + 6.97975i −0.352404 + 0.224802i
\(965\) 19.5499i 0.629333i
\(966\) 0 0
\(967\) 46.8517i 1.50665i 0.657648 + 0.753325i \(0.271551\pi\)
−0.657648 + 0.753325i \(0.728449\pi\)
\(968\) 20.0172 22.8665i 0.643376 0.734958i
\(969\) 0 0
\(970\) −10.4891 35.9466i −0.336786 1.15418i
\(971\) 37.0019 1.18745 0.593724 0.804669i \(-0.297657\pi\)
0.593724 + 0.804669i \(0.297657\pi\)
\(972\) 0 0
\(973\) 19.6277 0.629236
\(974\) 16.9847 + 58.2072i 0.544226 + 1.86508i
\(975\) 0 0
\(976\) −4.00000 + 8.60485i −0.128037 + 0.275435i
\(977\) 54.6882i 1.74963i 0.484455 + 0.874816i \(0.339018\pi\)
−0.484455 + 0.874816i \(0.660982\pi\)
\(978\) 0 0
\(979\) 6.05321i 0.193461i
\(980\) 14.5868 + 22.8665i 0.465958 + 0.730444i
\(981\) 0 0
\(982\) −18.6861 + 5.45257i −0.596299 + 0.173998i
\(983\) 34.4158 1.09769 0.548847 0.835923i \(-0.315067\pi\)
0.548847 + 0.835923i \(0.315067\pi\)
\(984\) 0 0
\(985\) −60.4674 −1.92665
\(986\) 2.71519 0.792287i 0.0864694 0.0252316i
\(987\) 0 0
\(988\) −12.0000 18.8114i −0.381771 0.598471i
\(989\) 24.8935i 0.791568i
\(990\) 0 0
\(991\) 7.65492i 0.243167i 0.992581 + 0.121583i \(0.0387972\pi\)
−0.992581 + 0.121583i \(0.961203\pi\)
\(992\) −45.4647 6.92820i −1.44351 0.219971i
\(993\) 0 0
\(994\) −6.00000 20.5622i −0.190308 0.652194i
\(995\) 32.5823 1.03293
\(996\) 0 0
\(997\) −24.1386 −0.764477 −0.382238 0.924064i \(-0.624847\pi\)
−0.382238 + 0.924064i \(0.624847\pi\)
\(998\) −1.35760 4.65253i −0.0429740 0.147273i
\(999\) 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 324.2.b.b.323.2 8
3.2 odd 2 inner 324.2.b.b.323.7 8
4.3 odd 2 inner 324.2.b.b.323.8 8
8.3 odd 2 5184.2.c.j.5183.1 8
8.5 even 2 5184.2.c.j.5183.2 8
9.2 odd 6 108.2.h.a.71.1 8
9.4 even 3 108.2.h.a.35.2 8
9.5 odd 6 36.2.h.a.11.3 8
9.7 even 3 36.2.h.a.23.4 yes 8
12.11 even 2 inner 324.2.b.b.323.1 8
24.5 odd 2 5184.2.c.j.5183.8 8
24.11 even 2 5184.2.c.j.5183.7 8
36.7 odd 6 36.2.h.a.23.3 yes 8
36.11 even 6 108.2.h.a.71.2 8
36.23 even 6 36.2.h.a.11.4 yes 8
36.31 odd 6 108.2.h.a.35.1 8
45.7 odd 12 900.2.o.a.599.3 16
45.14 odd 6 900.2.r.c.551.2 8
45.23 even 12 900.2.o.a.299.8 16
45.32 even 12 900.2.o.a.299.1 16
45.34 even 6 900.2.r.c.851.1 8
45.43 odd 12 900.2.o.a.599.6 16
72.5 odd 6 576.2.s.f.191.1 8
72.11 even 6 1728.2.s.f.1151.1 8
72.13 even 6 1728.2.s.f.575.1 8
72.29 odd 6 1728.2.s.f.1151.2 8
72.43 odd 6 576.2.s.f.383.1 8
72.59 even 6 576.2.s.f.191.4 8
72.61 even 6 576.2.s.f.383.4 8
72.67 odd 6 1728.2.s.f.575.2 8
180.7 even 12 900.2.o.a.599.8 16
180.23 odd 12 900.2.o.a.299.3 16
180.43 even 12 900.2.o.a.599.1 16
180.59 even 6 900.2.r.c.551.1 8
180.79 odd 6 900.2.r.c.851.2 8
180.167 odd 12 900.2.o.a.299.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.2.h.a.11.3 8 9.5 odd 6
36.2.h.a.11.4 yes 8 36.23 even 6
36.2.h.a.23.3 yes 8 36.7 odd 6
36.2.h.a.23.4 yes 8 9.7 even 3
108.2.h.a.35.1 8 36.31 odd 6
108.2.h.a.35.2 8 9.4 even 3
108.2.h.a.71.1 8 9.2 odd 6
108.2.h.a.71.2 8 36.11 even 6
324.2.b.b.323.1 8 12.11 even 2 inner
324.2.b.b.323.2 8 1.1 even 1 trivial
324.2.b.b.323.7 8 3.2 odd 2 inner
324.2.b.b.323.8 8 4.3 odd 2 inner
576.2.s.f.191.1 8 72.5 odd 6
576.2.s.f.191.4 8 72.59 even 6
576.2.s.f.383.1 8 72.43 odd 6
576.2.s.f.383.4 8 72.61 even 6
900.2.o.a.299.1 16 45.32 even 12
900.2.o.a.299.3 16 180.23 odd 12
900.2.o.a.299.6 16 180.167 odd 12
900.2.o.a.299.8 16 45.23 even 12
900.2.o.a.599.1 16 180.43 even 12
900.2.o.a.599.3 16 45.7 odd 12
900.2.o.a.599.6 16 45.43 odd 12
900.2.o.a.599.8 16 180.7 even 12
900.2.r.c.551.1 8 180.59 even 6
900.2.r.c.551.2 8 45.14 odd 6
900.2.r.c.851.1 8 45.34 even 6
900.2.r.c.851.2 8 180.79 odd 6
1728.2.s.f.575.1 8 72.13 even 6
1728.2.s.f.575.2 8 72.67 odd 6
1728.2.s.f.1151.1 8 72.11 even 6
1728.2.s.f.1151.2 8 72.29 odd 6
5184.2.c.j.5183.1 8 8.3 odd 2
5184.2.c.j.5183.2 8 8.5 even 2
5184.2.c.j.5183.7 8 24.11 even 2
5184.2.c.j.5183.8 8 24.5 odd 2