Properties

Label 845.2.b.d.339.6
Level $845$
Weight $2$
Character 845.339
Analytic conductor $6.747$
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] = [845,2,Mod(339,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.339");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.49843600.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 8x^{4} + 10x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 339.6
Root \(2.54574i\) of defining polynomial
Character \(\chi\) \(=\) 845.339
Dual form 845.2.b.d.339.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.54574i q^{2} -2.15293i q^{3} -4.48079 q^{4} +(-0.817544 + 2.08125i) q^{5} +5.48079 q^{6} +2.93855i q^{7} -6.31544i q^{8} -1.63509 q^{9} +O(q^{10})\) \(q+2.54574i q^{2} -2.15293i q^{3} -4.48079 q^{4} +(-0.817544 + 2.08125i) q^{5} +5.48079 q^{6} +2.93855i q^{7} -6.31544i q^{8} -1.63509 q^{9} +(-5.29833 - 2.08125i) q^{10} -0.635089 q^{11} +9.64680i q^{12} -7.48079 q^{14} +(4.48079 + 1.76011i) q^{15} +7.11588 q^{16} +1.22396i q^{17} -4.16251i q^{18} -1.36491 q^{19} +(3.66324 - 9.32566i) q^{20} +6.32648 q^{21} -1.61677i q^{22} +2.15293i q^{23} -13.5967 q^{24} +(-3.66324 - 3.40304i) q^{25} -2.93855i q^{27} -13.1670i q^{28} -3.00000 q^{29} +(-4.48079 + 11.4069i) q^{30} -8.96157 q^{31} +5.48429i q^{32} +1.36730i q^{33} -3.11588 q^{34} +(-6.11588 - 2.40240i) q^{35} +7.32648 q^{36} -1.22396i q^{37} -3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} -9.96157 q^{41} +16.1056i q^{42} -1.36730i q^{43} +2.84570 q^{44} +(1.33676 - 3.40304i) q^{45} -5.48079 q^{46} +6.16379i q^{47} -15.3200i q^{48} -1.63509 q^{49} +(8.66324 - 9.32566i) q^{50} +2.63509 q^{51} +0.642285i q^{53} +7.48079 q^{54} +(0.519213 - 1.32178i) q^{55} +18.5582 q^{56} +2.93855i q^{57} -7.63722i q^{58} -7.59666 q^{59} +(-20.0774 - 7.88669i) q^{60} -2.27018 q^{61} -22.8138i q^{62} -4.80479i q^{63} +0.270178 q^{64} -3.48079 q^{66} -8.03003i q^{67} -5.48429i q^{68} +4.63509 q^{69} +(6.11588 - 15.5694i) q^{70} +2.63509 q^{71} +10.3263i q^{72} -10.3263i q^{73} +3.11588 q^{74} +(-7.32648 + 7.88669i) q^{75} +6.11588 q^{76} -1.86624i q^{77} -1.03843 q^{79} +(-5.81754 + 14.8099i) q^{80} -11.2318 q^{81} -25.3596i q^{82} +11.8452i q^{83} -28.3476 q^{84} +(-2.54737 - 1.00064i) q^{85} +3.48079 q^{86} +6.45878i q^{87} +4.01086i q^{88} +12.5582 q^{89} +(8.66324 + 3.40304i) q^{90} -9.64680i q^{92} +19.2936i q^{93} -15.6914 q^{94} +(1.11588 - 2.84073i) q^{95} +11.8073 q^{96} +14.7838i q^{97} -4.16251i q^{98} +1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9} - 7 q^{10} - 22 q^{14} + 4 q^{15} + 16 q^{16} - 12 q^{19} + q^{20} - 4 q^{21} - 32 q^{24} - q^{25} - 18 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{36} + 35 q^{40} - 14 q^{41} - 2 q^{44} + 29 q^{45} - 10 q^{46} - 6 q^{49} + 31 q^{50} + 12 q^{51} + 22 q^{54} + 26 q^{55} + 16 q^{56} + 4 q^{59} - 48 q^{60} - 6 q^{61} - 6 q^{64} + 2 q^{66} + 24 q^{69} + 10 q^{70} + 12 q^{71} - 8 q^{74} - 2 q^{75} + 10 q^{76} - 52 q^{79} - 33 q^{80} - 14 q^{81} - 90 q^{84} - 21 q^{85} - 2 q^{86} - 20 q^{89} + 31 q^{90} - 56 q^{94} - 20 q^{95} + 6 q^{96} + 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.54574i 1.80011i 0.435777 + 0.900055i \(0.356474\pi\)
−0.435777 + 0.900055i \(0.643526\pi\)
\(3\) 2.15293i 1.24299i −0.783417 0.621496i \(-0.786525\pi\)
0.783417 0.621496i \(-0.213475\pi\)
\(4\) −4.48079 −2.24039
\(5\) −0.817544 + 2.08125i −0.365617 + 0.930765i
\(6\) 5.48079 2.23752
\(7\) 2.93855i 1.11067i 0.831627 + 0.555334i \(0.187410\pi\)
−0.831627 + 0.555334i \(0.812590\pi\)
\(8\) 6.31544i 2.23284i
\(9\) −1.63509 −0.545030
\(10\) −5.29833 2.08125i −1.67548 0.658151i
\(11\) −0.635089 −0.191487 −0.0957433 0.995406i \(-0.530523\pi\)
−0.0957433 + 0.995406i \(0.530523\pi\)
\(12\) 9.64680i 2.78479i
\(13\) 0 0
\(14\) −7.48079 −1.99932
\(15\) 4.48079 + 1.76011i 1.15693 + 0.454459i
\(16\) 7.11588 1.77897
\(17\) 1.22396i 0.296853i 0.988923 + 0.148427i \(0.0474209\pi\)
−0.988923 + 0.148427i \(0.952579\pi\)
\(18\) 4.16251i 0.981113i
\(19\) −1.36491 −0.313132 −0.156566 0.987667i \(-0.550042\pi\)
−0.156566 + 0.987667i \(0.550042\pi\)
\(20\) 3.66324 9.32566i 0.819126 2.08528i
\(21\) 6.32648 1.38055
\(22\) 1.61677i 0.344697i
\(23\) 2.15293i 0.448916i 0.974484 + 0.224458i \(0.0720612\pi\)
−0.974484 + 0.224458i \(0.927939\pi\)
\(24\) −13.5967 −2.77541
\(25\) −3.66324 3.40304i −0.732648 0.680607i
\(26\) 0 0
\(27\) 2.93855i 0.565525i
\(28\) 13.1670i 2.48833i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) −4.48079 + 11.4069i −0.818076 + 2.08261i
\(31\) −8.96157 −1.60955 −0.804773 0.593583i \(-0.797713\pi\)
−0.804773 + 0.593583i \(0.797713\pi\)
\(32\) 5.48429i 0.969495i
\(33\) 1.36730i 0.238016i
\(34\) −3.11588 −0.534368
\(35\) −6.11588 2.40240i −1.03377 0.406079i
\(36\) 7.32648 1.22108
\(37\) 1.22396i 0.201217i −0.994926 0.100609i \(-0.967921\pi\)
0.994926 0.100609i \(-0.0320790\pi\)
\(38\) 3.47471i 0.563672i
\(39\) 0 0
\(40\) 13.1440 + 5.16315i 2.07825 + 0.816366i
\(41\) −9.96157 −1.55574 −0.777868 0.628427i \(-0.783699\pi\)
−0.777868 + 0.628427i \(0.783699\pi\)
\(42\) 16.1056i 2.48514i
\(43\) 1.36730i 0.208511i −0.994551 0.104256i \(-0.966754\pi\)
0.994551 0.104256i \(-0.0332460\pi\)
\(44\) 2.84570 0.429005
\(45\) 1.33676 3.40304i 0.199272 0.507295i
\(46\) −5.48079 −0.808098
\(47\) 6.16379i 0.899081i 0.893260 + 0.449540i \(0.148412\pi\)
−0.893260 + 0.449540i \(0.851588\pi\)
\(48\) 15.3200i 2.21124i
\(49\) −1.63509 −0.233584
\(50\) 8.66324 9.32566i 1.22517 1.31885i
\(51\) 2.63509 0.368986
\(52\) 0 0
\(53\) 0.642285i 0.0882246i 0.999027 + 0.0441123i \(0.0140459\pi\)
−0.999027 + 0.0441123i \(0.985954\pi\)
\(54\) 7.48079 1.01801
\(55\) 0.519213 1.32178i 0.0700107 0.178229i
\(56\) 18.5582 2.47995
\(57\) 2.93855i 0.389221i
\(58\) 7.63722i 1.00282i
\(59\) −7.59666 −0.989001 −0.494501 0.869177i \(-0.664649\pi\)
−0.494501 + 0.869177i \(0.664649\pi\)
\(60\) −20.0774 7.88669i −2.59199 1.01817i
\(61\) −2.27018 −0.290666 −0.145333 0.989383i \(-0.546425\pi\)
−0.145333 + 0.989383i \(0.546425\pi\)
\(62\) 22.8138i 2.89736i
\(63\) 4.80479i 0.605347i
\(64\) 0.270178 0.0337722
\(65\) 0 0
\(66\) −3.48079 −0.428455
\(67\) 8.03003i 0.981024i −0.871434 0.490512i \(-0.836810\pi\)
0.871434 0.490512i \(-0.163190\pi\)
\(68\) 5.48429i 0.665068i
\(69\) 4.63509 0.557999
\(70\) 6.11588 15.5694i 0.730987 1.86090i
\(71\) 2.63509 0.312728 0.156364 0.987700i \(-0.450023\pi\)
0.156364 + 0.987700i \(0.450023\pi\)
\(72\) 10.3263i 1.21697i
\(73\) 10.3263i 1.20860i −0.796756 0.604301i \(-0.793453\pi\)
0.796756 0.604301i \(-0.206547\pi\)
\(74\) 3.11588 0.362213
\(75\) −7.32648 + 7.88669i −0.845990 + 0.910676i
\(76\) 6.11588 0.701539
\(77\) 1.86624i 0.212678i
\(78\) 0 0
\(79\) −1.03843 −0.116832 −0.0584161 0.998292i \(-0.518605\pi\)
−0.0584161 + 0.998292i \(0.518605\pi\)
\(80\) −5.81754 + 14.8099i −0.650421 + 1.65580i
\(81\) −11.2318 −1.24797
\(82\) 25.3596i 2.80050i
\(83\) 11.8452i 1.30018i 0.759855 + 0.650092i \(0.225270\pi\)
−0.759855 + 0.650092i \(0.774730\pi\)
\(84\) −28.3476 −3.09298
\(85\) −2.54737 1.00064i −0.276301 0.108535i
\(86\) 3.48079 0.375343
\(87\) 6.45878i 0.692454i
\(88\) 4.01086i 0.427559i
\(89\) 12.5582 1.33117 0.665585 0.746322i \(-0.268182\pi\)
0.665585 + 0.746322i \(0.268182\pi\)
\(90\) 8.66324 + 3.40304i 0.913186 + 0.358712i
\(91\) 0 0
\(92\) 9.64680i 1.00575i
\(93\) 19.2936i 2.00065i
\(94\) −15.6914 −1.61844
\(95\) 1.11588 2.84073i 0.114486 0.291453i
\(96\) 11.8073 1.20507
\(97\) 14.7838i 1.50107i 0.660832 + 0.750534i \(0.270203\pi\)
−0.660832 + 0.750534i \(0.729797\pi\)
\(98\) 4.16251i 0.420477i
\(99\) 1.03843 0.104366
\(100\) 16.4142 + 15.2483i 1.64142 + 1.52483i
\(101\) 13.2318 1.31661 0.658304 0.752752i \(-0.271274\pi\)
0.658304 + 0.752752i \(0.271274\pi\)
\(102\) 6.70825i 0.664216i
\(103\) 10.9686i 1.08077i 0.841419 + 0.540383i \(0.181721\pi\)
−0.841419 + 0.540383i \(0.818279\pi\)
\(104\) 0 0
\(105\) −5.17218 + 13.1670i −0.504753 + 1.28497i
\(106\) −1.63509 −0.158814
\(107\) 10.6736i 1.03186i 0.856632 + 0.515928i \(0.172553\pi\)
−0.856632 + 0.515928i \(0.827447\pi\)
\(108\) 13.1670i 1.26700i
\(109\) 3.27018 0.313226 0.156613 0.987660i \(-0.449942\pi\)
0.156613 + 0.987660i \(0.449942\pi\)
\(110\) 3.36491 + 1.32178i 0.320832 + 0.126027i
\(111\) −2.63509 −0.250112
\(112\) 20.9104i 1.97584i
\(113\) 5.52981i 0.520201i −0.965582 0.260100i \(-0.916244\pi\)
0.965582 0.260100i \(-0.0837556\pi\)
\(114\) −7.48079 −0.700640
\(115\) −4.48079 1.76011i −0.417836 0.164131i
\(116\) 13.4424 1.24809
\(117\) 0 0
\(118\) 19.3391i 1.78031i
\(119\) −3.59666 −0.329705
\(120\) 11.1159 28.2981i 1.01474 2.58325i
\(121\) −10.5967 −0.963333
\(122\) 5.77928i 0.523231i
\(123\) 21.4465i 1.93377i
\(124\) 40.1549 3.60602
\(125\) 10.0774 4.84201i 0.901354 0.433082i
\(126\) 12.2318 1.08969
\(127\) 17.2317i 1.52907i 0.644584 + 0.764534i \(0.277031\pi\)
−0.644584 + 0.764534i \(0.722969\pi\)
\(128\) 11.6564i 1.03029i
\(129\) −2.94369 −0.259178
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 6.12658i 0.533250i
\(133\) 4.01086i 0.347786i
\(134\) 20.4424 1.76595
\(135\) 6.11588 + 2.40240i 0.526371 + 0.206765i
\(136\) 7.72982 0.662827
\(137\) 8.67231i 0.740926i 0.928847 + 0.370463i \(0.120801\pi\)
−0.928847 + 0.370463i \(0.879199\pi\)
\(138\) 11.7997i 1.00446i
\(139\) −14.3265 −1.21516 −0.607578 0.794260i \(-0.707859\pi\)
−0.607578 + 0.794260i \(0.707859\pi\)
\(140\) 27.4039 + 10.7646i 2.31606 + 0.909777i
\(141\) 13.2702 1.11755
\(142\) 6.70825i 0.562944i
\(143\) 0 0
\(144\) −11.6351 −0.969591
\(145\) 2.45263 6.24376i 0.203680 0.518516i
\(146\) 26.2881 2.17562
\(147\) 3.52022i 0.290343i
\(148\) 5.48429i 0.450806i
\(149\) 17.1549 1.40538 0.702692 0.711494i \(-0.251981\pi\)
0.702692 + 0.711494i \(0.251981\pi\)
\(150\) −20.0774 18.6513i −1.63932 1.52287i
\(151\) −21.3828 −1.74011 −0.870053 0.492957i \(-0.835916\pi\)
−0.870053 + 0.492957i \(0.835916\pi\)
\(152\) 8.62001i 0.699175i
\(153\) 2.00128i 0.161794i
\(154\) 4.75096 0.382844
\(155\) 7.32648 18.6513i 0.588477 1.49811i
\(156\) 0 0
\(157\) 18.3646i 1.46566i 0.680413 + 0.732829i \(0.261800\pi\)
−0.680413 + 0.732829i \(0.738200\pi\)
\(158\) 2.64356i 0.210311i
\(159\) 1.38279 0.109662
\(160\) −11.4142 4.48365i −0.902372 0.354464i
\(161\) −6.32648 −0.498597
\(162\) 28.5931i 2.24649i
\(163\) 4.01086i 0.314155i −0.987586 0.157078i \(-0.949793\pi\)
0.987586 0.157078i \(-0.0502072\pi\)
\(164\) 44.6357 3.48546
\(165\) −2.84570 1.11783i −0.221537 0.0870228i
\(166\) −30.1549 −2.34047
\(167\) 2.93855i 0.227392i −0.993516 0.113696i \(-0.963731\pi\)
0.993516 0.113696i \(-0.0362690\pi\)
\(168\) 39.9545i 3.08256i
\(169\) 0 0
\(170\) 2.54737 6.48493i 0.195374 0.497371i
\(171\) 2.23175 0.170666
\(172\) 6.12658i 0.467147i
\(173\) 1.36730i 0.103954i 0.998648 + 0.0519769i \(0.0165522\pi\)
−0.998648 + 0.0519769i \(0.983448\pi\)
\(174\) −16.4424 −1.24649
\(175\) 10.0000 10.7646i 0.755929 0.813729i
\(176\) −4.51921 −0.340649
\(177\) 16.3550i 1.22932i
\(178\) 31.9700i 2.39625i
\(179\) −7.78613 −0.581963 −0.290981 0.956729i \(-0.593982\pi\)
−0.290981 + 0.956729i \(0.593982\pi\)
\(180\) −5.98973 + 15.2483i −0.446448 + 1.13654i
\(181\) −3.86684 −0.287420 −0.143710 0.989620i \(-0.545903\pi\)
−0.143710 + 0.989620i \(0.545903\pi\)
\(182\) 0 0
\(183\) 4.88752i 0.361296i
\(184\) 13.5967 1.00236
\(185\) 2.54737 + 1.00064i 0.187286 + 0.0735685i
\(186\) −49.1165 −3.60139
\(187\) 0.777322i 0.0568434i
\(188\) 27.6186i 2.01429i
\(189\) 8.63509 0.628110
\(190\) 7.23175 + 2.84073i 0.524646 + 0.206088i
\(191\) 4.94369 0.357713 0.178857 0.983875i \(-0.442760\pi\)
0.178857 + 0.983875i \(0.442760\pi\)
\(192\) 0.581673i 0.0419786i
\(193\) 4.95644i 0.356772i 0.983961 + 0.178386i \(0.0570876\pi\)
−0.983961 + 0.178386i \(0.942912\pi\)
\(194\) −37.6357 −2.70208
\(195\) 0 0
\(196\) 7.32648 0.523320
\(197\) 6.74546i 0.480594i −0.970699 0.240297i \(-0.922755\pi\)
0.970699 0.240297i \(-0.0772449\pi\)
\(198\) 2.64356i 0.187870i
\(199\) −5.17544 −0.366878 −0.183439 0.983031i \(-0.558723\pi\)
−0.183439 + 0.983031i \(0.558723\pi\)
\(200\) −21.4917 + 23.1350i −1.51969 + 1.63589i
\(201\) −17.2881 −1.21941
\(202\) 33.6846i 2.37004i
\(203\) 8.81566i 0.618738i
\(204\) −11.8073 −0.826674
\(205\) 8.14403 20.7326i 0.568804 1.44803i
\(206\) −27.9231 −1.94550
\(207\) 3.52022i 0.244673i
\(208\) 0 0
\(209\) 0.866840 0.0599606
\(210\) −33.5198 13.1670i −2.31309 0.908611i
\(211\) −14.0179 −0.965031 −0.482515 0.875888i \(-0.660277\pi\)
−0.482515 + 0.875888i \(0.660277\pi\)
\(212\) 2.87794i 0.197658i
\(213\) 5.67315i 0.388718i
\(214\) −27.1722 −1.85745
\(215\) 2.84570 + 1.11783i 0.194075 + 0.0762352i
\(216\) −18.5582 −1.26273
\(217\) 26.3341i 1.78767i
\(218\) 8.32502i 0.563841i
\(219\) −22.2318 −1.50228
\(220\) −2.32648 + 5.92262i −0.156852 + 0.399303i
\(221\) 0 0
\(222\) 6.70825i 0.450228i
\(223\) 0.00830491i 0.000556138i −1.00000 0.000278069i \(-0.999911\pi\)
1.00000 0.000278069i \(-8.85121e-5\pi\)
\(224\) −16.1159 −1.07679
\(225\) 5.98973 + 5.56427i 0.399315 + 0.370951i
\(226\) 14.0774 0.936418
\(227\) 11.2636i 0.747589i −0.927511 0.373795i \(-0.878056\pi\)
0.927511 0.373795i \(-0.121944\pi\)
\(228\) 13.1670i 0.872008i
\(229\) 16.5404 1.09302 0.546509 0.837453i \(-0.315957\pi\)
0.546509 + 0.837453i \(0.315957\pi\)
\(230\) 4.48079 11.4069i 0.295454 0.752150i
\(231\) −4.01788 −0.264357
\(232\) 18.9463i 1.24389i
\(233\) 6.94941i 0.455271i 0.973746 + 0.227636i \(0.0730995\pi\)
−0.973746 + 0.227636i \(0.926900\pi\)
\(234\) 0 0
\(235\) −12.8284 5.03917i −0.836833 0.328719i
\(236\) 34.0390 2.21575
\(237\) 2.23566i 0.145221i
\(238\) 9.15616i 0.593506i
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 31.8847 + 12.5247i 2.05815 + 0.808469i
\(241\) 19.7721 1.27363 0.636817 0.771015i \(-0.280251\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(242\) 26.9763i 1.73410i
\(243\) 15.3655i 0.985695i
\(244\) 10.1722 0.651207
\(245\) 1.33676 3.40304i 0.0854023 0.217412i
\(246\) −54.5973 −3.48099
\(247\) 0 0
\(248\) 56.5962i 3.59386i
\(249\) 25.5019 1.61612
\(250\) 12.3265 + 25.6546i 0.779595 + 1.62254i
\(251\) 3.67352 0.231870 0.115935 0.993257i \(-0.463014\pi\)
0.115935 + 0.993257i \(0.463014\pi\)
\(252\) 21.5293i 1.35622i
\(253\) 1.36730i 0.0859614i
\(254\) −43.8674 −2.75249
\(255\) −2.15430 + 5.48429i −0.134908 + 0.343440i
\(256\) −29.1338 −1.82086
\(257\) 13.2648i 0.827439i 0.910404 + 0.413719i \(0.135771\pi\)
−0.910404 + 0.413719i \(0.864229\pi\)
\(258\) 7.49387i 0.466548i
\(259\) 3.59666 0.223486
\(260\) 0 0
\(261\) 4.90527 0.303628
\(262\) 25.4574i 1.57276i
\(263\) 30.2705i 1.86656i −0.359152 0.933279i \(-0.616934\pi\)
0.359152 0.933279i \(-0.383066\pi\)
\(264\) 8.63509 0.531453
\(265\) −1.33676 0.525096i −0.0821164 0.0322564i
\(266\) 10.2106 0.626053
\(267\) 27.0369i 1.65463i
\(268\) 35.9809i 2.19788i
\(269\) 22.2496 1.35658 0.678292 0.734792i \(-0.262720\pi\)
0.678292 + 0.734792i \(0.262720\pi\)
\(270\) −6.11588 + 15.5694i −0.372200 + 0.947525i
\(271\) −11.8284 −0.718525 −0.359262 0.933237i \(-0.616972\pi\)
−0.359262 + 0.933237i \(0.616972\pi\)
\(272\) 8.70953i 0.528093i
\(273\) 0 0
\(274\) −22.0774 −1.33375
\(275\) 2.32648 + 2.16123i 0.140292 + 0.130327i
\(276\) −20.7688 −1.25014
\(277\) 16.7851i 1.00852i 0.863553 + 0.504259i \(0.168234\pi\)
−0.863553 + 0.504259i \(0.831766\pi\)
\(278\) 36.4715i 2.18741i
\(279\) 14.6530 0.877250
\(280\) −15.1722 + 38.6244i −0.906711 + 2.30825i
\(281\) −10.5967 −0.632144 −0.316072 0.948735i \(-0.602364\pi\)
−0.316072 + 0.948735i \(0.602364\pi\)
\(282\) 33.7824i 2.01171i
\(283\) 8.81566i 0.524036i 0.965063 + 0.262018i \(0.0843880\pi\)
−0.965063 + 0.262018i \(0.915612\pi\)
\(284\) −11.8073 −0.700633
\(285\) −6.11588 2.40240i −0.362273 0.142306i
\(286\) 0 0
\(287\) 29.2726i 1.72791i
\(288\) 8.96730i 0.528403i
\(289\) 15.5019 0.911878
\(290\) 15.8950 + 6.24376i 0.933386 + 0.366646i
\(291\) 31.8284 1.86581
\(292\) 46.2699i 2.70774i
\(293\) 28.2526i 1.65053i 0.564742 + 0.825267i \(0.308976\pi\)
−0.564742 + 0.825267i \(0.691024\pi\)
\(294\) −8.96157 −0.522650
\(295\) 6.21061 15.8106i 0.361596 0.920528i
\(296\) −7.72982 −0.449287
\(297\) 1.86624i 0.108290i
\(298\) 43.6719i 2.52984i
\(299\) 0 0
\(300\) 32.8284 35.3386i 1.89535 2.04027i
\(301\) 4.01788 0.231587
\(302\) 54.4350i 3.13238i
\(303\) 28.4870i 1.63653i
\(304\) −9.71254 −0.557052
\(305\) 1.85597 4.72482i 0.106273 0.270542i
\(306\) 5.09473 0.291247
\(307\) 12.7219i 0.726077i 0.931774 + 0.363039i \(0.118261\pi\)
−0.931774 + 0.363039i \(0.881739\pi\)
\(308\) 8.36223i 0.476482i
\(309\) 23.6145 1.34338
\(310\) 47.4814 + 18.6513i 2.69676 + 1.05932i
\(311\) 27.9231 1.58338 0.791688 0.610925i \(-0.209202\pi\)
0.791688 + 0.610925i \(0.209202\pi\)
\(312\) 0 0
\(313\) 24.5807i 1.38938i −0.719307 0.694692i \(-0.755540\pi\)
0.719307 0.694692i \(-0.244460\pi\)
\(314\) −46.7516 −2.63834
\(315\) 10.0000 + 3.92813i 0.563436 + 0.221325i
\(316\) 4.65297 0.261750
\(317\) 0.234377i 0.0131639i −0.999978 0.00658196i \(-0.997905\pi\)
0.999978 0.00658196i \(-0.00209512\pi\)
\(318\) 3.52022i 0.197404i
\(319\) 1.90527 0.106674
\(320\) −0.220882 + 0.562309i −0.0123477 + 0.0314340i
\(321\) 22.9795 1.28259
\(322\) 16.1056i 0.897529i
\(323\) 1.67059i 0.0929543i
\(324\) 50.3271 2.79595
\(325\) 0 0
\(326\) 10.2106 0.565513
\(327\) 7.04045i 0.389338i
\(328\) 62.9117i 3.47372i
\(329\) −18.1126 −0.998581
\(330\) 2.84570 7.24440i 0.156651 0.398791i
\(331\) −18.3265 −1.00731 −0.503657 0.863904i \(-0.668013\pi\)
−0.503657 + 0.863904i \(0.668013\pi\)
\(332\) 53.0760i 2.91292i
\(333\) 2.00128i 0.109669i
\(334\) 7.48079 0.409330
\(335\) 16.7125 + 6.56491i 0.913103 + 0.358679i
\(336\) 45.0185 2.45596
\(337\) 21.2949i 1.16001i −0.814614 0.580003i \(-0.803051\pi\)
0.814614 0.580003i \(-0.196949\pi\)
\(338\) 0 0
\(339\) −11.9053 −0.646605
\(340\) 11.4142 + 4.48365i 0.619022 + 0.243160i
\(341\) 5.69140 0.308206
\(342\) 5.68146i 0.307218i
\(343\) 15.7651i 0.851234i
\(344\) −8.63509 −0.465573
\(345\) −3.78939 + 9.64680i −0.204014 + 0.519366i
\(346\) −3.48079 −0.187128
\(347\) 3.81521i 0.204811i −0.994743 0.102406i \(-0.967346\pi\)
0.994743 0.102406i \(-0.0326540\pi\)
\(348\) 28.9404i 1.55137i
\(349\) −24.3265 −1.30217 −0.651083 0.759006i \(-0.725685\pi\)
−0.651083 + 0.759006i \(0.725685\pi\)
\(350\) 27.4039 + 25.4574i 1.46480 + 1.36075i
\(351\) 0 0
\(352\) 3.48301i 0.185645i
\(353\) 27.0591i 1.44021i 0.693866 + 0.720104i \(0.255906\pi\)
−0.693866 + 0.720104i \(0.744094\pi\)
\(354\) −41.6357 −2.21291
\(355\) −2.15430 + 5.48429i −0.114338 + 0.291076i
\(356\) −56.2708 −2.98235
\(357\) 7.74335i 0.409821i
\(358\) 19.8215i 1.04760i
\(359\) −27.0039 −1.42521 −0.712605 0.701566i \(-0.752485\pi\)
−0.712605 + 0.701566i \(0.752485\pi\)
\(360\) −21.4917 8.44221i −1.13271 0.444943i
\(361\) −17.1370 −0.901948
\(362\) 9.84396i 0.517387i
\(363\) 22.8138i 1.19742i
\(364\) 0 0
\(365\) 21.4917 + 8.44221i 1.12492 + 0.441885i
\(366\) −12.4424 −0.650373
\(367\) 6.94111i 0.362323i −0.983453 0.181161i \(-0.942014\pi\)
0.983453 0.181161i \(-0.0579857\pi\)
\(368\) 15.3200i 0.798608i
\(369\) 16.2881 0.847922
\(370\) −2.54737 + 6.48493i −0.132431 + 0.337135i
\(371\) −1.88739 −0.0979882
\(372\) 86.4505i 4.48225i
\(373\) 2.31288i 0.119756i −0.998206 0.0598781i \(-0.980929\pi\)
0.998206 0.0598781i \(-0.0190712\pi\)
\(374\) 1.97886 0.102324
\(375\) −10.4245 21.6960i −0.538318 1.12038i
\(376\) 38.9270 2.00751
\(377\) 0 0
\(378\) 21.9827i 1.13067i
\(379\) −5.17544 −0.265845 −0.132922 0.991126i \(-0.542436\pi\)
−0.132922 + 0.991126i \(0.542436\pi\)
\(380\) −5.00000 + 12.7287i −0.256495 + 0.652968i
\(381\) 37.0986 1.90062
\(382\) 12.5854i 0.643923i
\(383\) 20.6609i 1.05572i 0.849331 + 0.527861i \(0.177006\pi\)
−0.849331 + 0.527861i \(0.822994\pi\)
\(384\) 25.0953 1.28064
\(385\) 3.88412 + 1.52574i 0.197953 + 0.0777587i
\(386\) −12.6178 −0.642229
\(387\) 2.23566i 0.113645i
\(388\) 66.2430i 3.36298i
\(389\) −19.7477 −1.00125 −0.500624 0.865665i \(-0.666896\pi\)
−0.500624 + 0.865665i \(0.666896\pi\)
\(390\) 0 0
\(391\) −2.63509 −0.133262
\(392\) 10.3263i 0.521557i
\(393\) 21.5293i 1.08601i
\(394\) 17.1722 0.865122
\(395\) 0.848960 2.16123i 0.0427158 0.108743i
\(396\) −4.65297 −0.233820
\(397\) 9.38902i 0.471222i −0.971847 0.235611i \(-0.924291\pi\)
0.971847 0.235611i \(-0.0757091\pi\)
\(398\) 13.1753i 0.660420i
\(399\) −8.63509 −0.432295
\(400\) −26.0672 24.2156i −1.30336 1.21078i
\(401\) 24.5019 1.22357 0.611784 0.791025i \(-0.290452\pi\)
0.611784 + 0.791025i \(0.290452\pi\)
\(402\) 44.0109i 2.19506i
\(403\) 0 0
\(404\) −59.2887 −2.94972
\(405\) 9.18246 23.3761i 0.456280 1.16157i
\(406\) 22.4424 1.11380
\(407\) 0.777322i 0.0385304i
\(408\) 16.6417i 0.823889i
\(409\) −36.1165 −1.78584 −0.892922 0.450211i \(-0.851349\pi\)
−0.892922 + 0.450211i \(0.851349\pi\)
\(410\) 52.7797 + 20.7326i 2.60660 + 1.02391i
\(411\) 18.6708 0.920965
\(412\) 49.1479i 2.42134i
\(413\) 22.3232i 1.09845i
\(414\) 8.96157 0.440437
\(415\) −24.6530 9.68401i −1.21017 0.475370i
\(416\) 0 0
\(417\) 30.8439i 1.51043i
\(418\) 2.20675i 0.107936i
\(419\) 6.86684 0.335467 0.167734 0.985832i \(-0.446355\pi\)
0.167734 + 0.985832i \(0.446355\pi\)
\(420\) 23.1754 58.9986i 1.13085 2.87884i
\(421\) 33.9795 1.65606 0.828029 0.560686i \(-0.189462\pi\)
0.828029 + 0.560686i \(0.189462\pi\)
\(422\) 35.6859i 1.73716i
\(423\) 10.0783i 0.490026i
\(424\) 4.05631 0.196992
\(425\) 4.16517 4.48365i 0.202040 0.217489i
\(426\) 14.4424 0.699735
\(427\) 6.67104i 0.322834i
\(428\) 47.8261i 2.31176i
\(429\) 0 0
\(430\) −2.84570 + 7.24440i −0.137232 + 0.349356i
\(431\) −16.2496 −0.782717 −0.391359 0.920238i \(-0.627995\pi\)
−0.391359 + 0.920238i \(0.627995\pi\)
\(432\) 20.9104i 1.00605i
\(433\) 0.256261i 0.0123151i −0.999981 0.00615756i \(-0.998040\pi\)
0.999981 0.00615756i \(-0.00196002\pi\)
\(434\) 67.0396 3.21800
\(435\) −13.4424 5.28034i −0.644512 0.253173i
\(436\) −14.6530 −0.701750
\(437\) 2.93855i 0.140570i
\(438\) 56.5962i 2.70427i
\(439\) 7.59666 0.362569 0.181284 0.983431i \(-0.441975\pi\)
0.181284 + 0.983431i \(0.441975\pi\)
\(440\) −8.34763 3.27906i −0.397957 0.156323i
\(441\) 2.67352 0.127310
\(442\) 0 0
\(443\) 4.32246i 0.205366i −0.994714 0.102683i \(-0.967257\pi\)
0.994714 0.102683i \(-0.0327428\pi\)
\(444\) 11.8073 0.560348
\(445\) −10.2669 + 26.1369i −0.486698 + 1.23901i
\(446\) 0.0211421 0.00100111
\(447\) 36.9332i 1.74688i
\(448\) 0.793931i 0.0375097i
\(449\) −3.28806 −0.155173 −0.0775865 0.996986i \(-0.524721\pi\)
−0.0775865 + 0.996986i \(0.524721\pi\)
\(450\) −14.1652 + 15.2483i −0.667753 + 0.718811i
\(451\) 6.32648 0.297903
\(452\) 24.7779i 1.16545i
\(453\) 46.0356i 2.16294i
\(454\) 28.6741 1.34574
\(455\) 0 0
\(456\) 18.5582 0.869069
\(457\) 15.4261i 0.721602i −0.932643 0.360801i \(-0.882503\pi\)
0.932643 0.360801i \(-0.117497\pi\)
\(458\) 42.1074i 1.96755i
\(459\) 3.59666 0.167878
\(460\) 20.0774 + 7.88669i 0.936116 + 0.367719i
\(461\) 25.8847 1.20557 0.602786 0.797903i \(-0.294057\pi\)
0.602786 + 0.797903i \(0.294057\pi\)
\(462\) 10.2285i 0.475872i
\(463\) 7.04045i 0.327197i −0.986527 0.163599i \(-0.947690\pi\)
0.986527 0.163599i \(-0.0523102\pi\)
\(464\) −21.3476 −0.991039
\(465\) −40.1549 15.7734i −1.86214 0.731473i
\(466\) −17.6914 −0.819538
\(467\) 18.8113i 0.870482i 0.900314 + 0.435241i \(0.143337\pi\)
−0.900314 + 0.435241i \(0.856663\pi\)
\(468\) 0 0
\(469\) 23.5967 1.08959
\(470\) 12.8284 32.6578i 0.591731 1.50639i
\(471\) 39.5377 1.82180
\(472\) 47.9762i 2.20828i
\(473\) 0.868356i 0.0399271i
\(474\) −5.69140 −0.261414
\(475\) 5.00000 + 4.64484i 0.229416 + 0.213120i
\(476\) 16.1159 0.738670
\(477\) 1.05019i 0.0480850i
\(478\) 10.1830i 0.465758i
\(479\) 19.4775 0.889951 0.444975 0.895543i \(-0.353212\pi\)
0.444975 + 0.895543i \(0.353212\pi\)
\(480\) −9.65297 + 24.5739i −0.440596 + 1.12164i
\(481\) 0 0
\(482\) 50.3346i 2.29268i
\(483\) 13.6205i 0.619752i
\(484\) 47.4814 2.15824
\(485\) −30.7688 12.0864i −1.39714 0.548816i
\(486\) −39.1165 −1.77436
\(487\) 32.3241i 1.46474i −0.680905 0.732372i \(-0.738413\pi\)
0.680905 0.732372i \(-0.261587\pi\)
\(488\) 14.3372i 0.649013i
\(489\) −8.63509 −0.390492
\(490\) 8.66324 + 3.40304i 0.391365 + 0.153734i
\(491\) 28.6708 1.29390 0.646949 0.762534i \(-0.276045\pi\)
0.646949 + 0.762534i \(0.276045\pi\)
\(492\) 96.0973i 4.33240i
\(493\) 3.67187i 0.165373i
\(494\) 0 0
\(495\) −0.848960 + 2.16123i −0.0381579 + 0.0971401i
\(496\) −63.7694 −2.86333
\(497\) 7.74335i 0.347337i
\(498\) 64.9213i 2.90919i
\(499\) −28.9616 −1.29650 −0.648249 0.761428i \(-0.724498\pi\)
−0.648249 + 0.761428i \(0.724498\pi\)
\(500\) −45.1549 + 21.6960i −2.01939 + 0.970275i
\(501\) −6.32648 −0.282646
\(502\) 9.35181i 0.417392i
\(503\) 28.1093i 1.25333i 0.779289 + 0.626665i \(0.215581\pi\)
−0.779289 + 0.626665i \(0.784419\pi\)
\(504\) −30.3444 −1.35165
\(505\) −10.8175 + 27.5386i −0.481374 + 1.22545i
\(506\) 3.48079 0.154740
\(507\) 0 0
\(508\) 77.2116i 3.42571i
\(509\) −21.1126 −0.935800 −0.467900 0.883781i \(-0.654989\pi\)
−0.467900 + 0.883781i \(0.654989\pi\)
\(510\) −13.9616 5.48429i −0.618229 0.242848i
\(511\) 30.3444 1.34236
\(512\) 50.8542i 2.24746i
\(513\) 4.01086i 0.177084i
\(514\) −33.7688 −1.48948
\(515\) −22.8284 8.96730i −1.00594 0.395147i
\(516\) 13.1901 0.580660
\(517\) 3.91455i 0.172162i
\(518\) 9.15616i 0.402299i
\(519\) 2.94369 0.129214
\(520\) 0 0
\(521\) 0.673516 0.0295073 0.0147536 0.999891i \(-0.495304\pi\)
0.0147536 + 0.999891i \(0.495304\pi\)
\(522\) 12.4875i 0.546564i
\(523\) 29.8626i 1.30580i 0.757444 + 0.652900i \(0.226448\pi\)
−0.757444 + 0.652900i \(0.773552\pi\)
\(524\) −44.8079 −1.95744
\(525\) −23.1754 21.5293i −1.01146 0.939614i
\(526\) 77.0608 3.36001
\(527\) 10.9686i 0.477799i
\(528\) 9.72953i 0.423423i
\(529\) 18.3649 0.798474
\(530\) 1.33676 3.40304i 0.0580650 0.147818i
\(531\) 12.4212 0.539035
\(532\) 17.9718i 0.779177i
\(533\) 0 0
\(534\) 68.8290 2.97852
\(535\) −22.2145 8.72614i −0.960415 0.377264i
\(536\) −50.7131 −2.19047
\(537\) 16.7630i 0.723375i
\(538\) 56.6418i 2.44200i
\(539\) 1.03843 0.0447282
\(540\) −27.4039 10.7646i −1.17928 0.463236i
\(541\) 6.28806 0.270345 0.135172 0.990822i \(-0.456841\pi\)
0.135172 + 0.990822i \(0.456841\pi\)
\(542\) 30.1121i 1.29342i
\(543\) 8.32502i 0.357261i
\(544\) −6.71254 −0.287798
\(545\) −2.67352 + 6.80607i −0.114521 + 0.291540i
\(546\) 0 0
\(547\) 3.03789i 0.129891i −0.997889 0.0649454i \(-0.979313\pi\)
0.997889 0.0649454i \(-0.0206873\pi\)
\(548\) 38.8588i 1.65997i
\(549\) 3.71194 0.158422
\(550\) −5.50193 + 5.92262i −0.234603 + 0.252541i
\(551\) 4.09473 0.174442
\(552\) 29.2726i 1.24592i
\(553\) 3.05147i 0.129762i
\(554\) −42.7304 −1.81544
\(555\) 2.15430 5.48429i 0.0914450 0.232795i
\(556\) 64.1939 2.72243
\(557\) 20.6996i 0.877071i 0.898714 + 0.438536i \(0.144503\pi\)
−0.898714 + 0.438536i \(0.855497\pi\)
\(558\) 37.3026i 1.57915i
\(559\) 0 0
\(560\) −43.5198 17.0952i −1.83905 0.722402i
\(561\) −1.67352 −0.0706559
\(562\) 26.9763i 1.13793i
\(563\) 10.9603i 0.461921i −0.972963 0.230960i \(-0.925813\pi\)
0.972963 0.230960i \(-0.0741868\pi\)
\(564\) −59.4608 −2.50375
\(565\) 11.5089 + 4.52086i 0.484185 + 0.190194i
\(566\) −22.4424 −0.943323
\(567\) 33.0051i 1.38608i
\(568\) 16.6417i 0.698272i
\(569\) −42.7131 −1.79063 −0.895314 0.445436i \(-0.853049\pi\)
−0.895314 + 0.445436i \(0.853049\pi\)
\(570\) 6.11588 15.5694i 0.256166 0.652131i
\(571\) −23.6145 −0.988238 −0.494119 0.869394i \(-0.664509\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(572\) 0 0
\(573\) 10.6434i 0.444635i
\(574\) 74.5204 3.11042
\(575\) 7.32648 7.88669i 0.305536 0.328898i
\(576\) −0.441765 −0.0184069
\(577\) 18.3646i 0.764530i −0.924053 0.382265i \(-0.875144\pi\)
0.924053 0.382265i \(-0.124856\pi\)
\(578\) 39.4639i 1.64148i
\(579\) 10.6708 0.443465
\(580\) −10.9897 + 27.9770i −0.456324 + 1.16168i
\(581\) −34.8079 −1.44407
\(582\) 81.0268i 3.35867i
\(583\) 0.407908i 0.0168938i
\(584\) −65.2151 −2.69862
\(585\) 0 0
\(586\) −71.9237 −2.97114
\(587\) 0.702897i 0.0290116i −0.999895 0.0145058i \(-0.995382\pi\)
0.999895 0.0145058i \(-0.00461751\pi\)
\(588\) 15.7734i 0.650483i
\(589\) 12.2318 0.504001
\(590\) 40.2496 + 15.8106i 1.65705 + 0.650912i
\(591\) −14.5225 −0.597375
\(592\) 8.70953i 0.357959i
\(593\) 37.1593i 1.52595i 0.646428 + 0.762975i \(0.276262\pi\)
−0.646428 + 0.762975i \(0.723738\pi\)
\(594\) −4.75096 −0.194934
\(595\) 2.94043 7.48557i 0.120546 0.306878i
\(596\) −76.8674 −3.14861
\(597\) 11.1423i 0.456026i
\(598\) 0 0
\(599\) 15.6914 0.641133 0.320567 0.947226i \(-0.396127\pi\)
0.320567 + 0.947226i \(0.396127\pi\)
\(600\) 49.8079 + 46.2699i 2.03340 + 1.88896i
\(601\) 12.0039 0.489648 0.244824 0.969568i \(-0.421270\pi\)
0.244824 + 0.969568i \(0.421270\pi\)
\(602\) 10.2285i 0.416881i
\(603\) 13.1298i 0.534687i
\(604\) 95.8117 3.89852
\(605\) 8.66324 22.0544i 0.352211 0.896637i
\(606\) 72.5204 2.94594
\(607\) 38.6865i 1.57024i 0.619345 + 0.785119i \(0.287398\pi\)
−0.619345 + 0.785119i \(0.712602\pi\)
\(608\) 7.48557i 0.303580i
\(609\) −18.9795 −0.769086
\(610\) 12.0282 + 4.72482i 0.487006 + 0.191302i
\(611\) 0 0
\(612\) 8.96730i 0.362482i
\(613\) 17.2840i 0.698095i 0.937105 + 0.349047i \(0.113495\pi\)
−0.937105 + 0.349047i \(0.886505\pi\)
\(614\) −32.3866 −1.30702
\(615\) −44.6357 17.5335i −1.79988 0.707018i
\(616\) −11.7861 −0.474877
\(617\) 26.4691i 1.06561i 0.846240 + 0.532803i \(0.178861\pi\)
−0.846240 + 0.532803i \(0.821139\pi\)
\(618\) 60.1165i 2.41824i
\(619\) 31.0039 1.24615 0.623075 0.782162i \(-0.285883\pi\)
0.623075 + 0.782162i \(0.285883\pi\)
\(620\) −32.8284 + 83.5726i −1.31842 + 3.35636i
\(621\) 6.32648 0.253873
\(622\) 71.0850i 2.85025i
\(623\) 36.9030i 1.47849i
\(624\) 0 0
\(625\) 1.83869 + 24.9323i 0.0735475 + 0.997292i
\(626\) 62.5761 2.50104
\(627\) 1.86624i 0.0745305i
\(628\) 82.2880i 3.28365i
\(629\) 1.49807 0.0597320
\(630\) −10.0000 + 25.4574i −0.398410 + 1.01425i
\(631\) −20.7131 −0.824577 −0.412288 0.911053i \(-0.635270\pi\)
−0.412288 + 0.911053i \(0.635270\pi\)
\(632\) 6.55812i 0.260868i
\(633\) 30.1795i 1.19953i
\(634\) 0.596662 0.0236965
\(635\) −35.8636 14.0877i −1.42320 0.559053i
\(636\) −6.19599 −0.245687
\(637\) 0 0
\(638\) 4.85031i 0.192026i
\(639\) −4.30860 −0.170446
\(640\) −24.2599 9.52961i −0.958957 0.376691i
\(641\) 21.1895 0.836934 0.418467 0.908232i \(-0.362568\pi\)
0.418467 + 0.908232i \(0.362568\pi\)
\(642\) 58.4997i 2.30880i
\(643\) 11.5336i 0.454843i 0.973796 + 0.227421i \(0.0730294\pi\)
−0.973796 + 0.227421i \(0.926971\pi\)
\(644\) 28.3476 1.11705
\(645\) 2.40660 6.12658i 0.0947598 0.241234i
\(646\) 4.25289 0.167328
\(647\) 34.8464i 1.36995i −0.728565 0.684977i \(-0.759812\pi\)
0.728565 0.684977i \(-0.240188\pi\)
\(648\) 70.9334i 2.78653i
\(649\) 4.82456 0.189380
\(650\) 0 0
\(651\) −56.6953 −2.22206
\(652\) 17.9718i 0.703831i
\(653\) 22.3232i 0.873574i −0.899565 0.436787i \(-0.856116\pi\)
0.899565 0.436787i \(-0.143884\pi\)
\(654\) 17.9231 0.700850
\(655\) −8.17544 + 20.8125i −0.319441 + 0.813214i
\(656\) −70.8853 −2.76761
\(657\) 16.8844i 0.658724i
\(658\) 46.1100i 1.79755i
\(659\) 0.866840 0.0337673 0.0168836 0.999857i \(-0.494626\pi\)
0.0168836 + 0.999857i \(0.494626\pi\)
\(660\) 12.7510 + 5.00875i 0.496331 + 0.194965i
\(661\) 13.3086 0.517645 0.258822 0.965925i \(-0.416666\pi\)
0.258822 + 0.965925i \(0.416666\pi\)
\(662\) 46.6544i 1.81328i
\(663\) 0 0
\(664\) 74.8079 2.90311
\(665\) 8.34763 + 3.27906i 0.323707 + 0.127156i
\(666\) −5.09473 −0.197417
\(667\) 6.45878i 0.250085i
\(668\) 13.1670i 0.509448i
\(669\) −0.0178799 −0.000691275
\(670\) −16.7125 + 42.5458i −0.645662 + 1.64369i
\(671\) 1.44176 0.0556587
\(672\) 34.6963i 1.33844i
\(673\) 5.51320i 0.212518i 0.994338 + 0.106259i \(0.0338873\pi\)
−0.994338 + 0.106259i \(0.966113\pi\)
\(674\) 54.2112 2.08814
\(675\) −10.0000 + 10.7646i −0.384900 + 0.414331i
\(676\) 0 0
\(677\) 4.80479i 0.184663i −0.995728 0.0923316i \(-0.970568\pi\)
0.995728 0.0923316i \(-0.0294320\pi\)
\(678\) 30.3077i 1.16396i
\(679\) −43.4430 −1.66719
\(680\) −6.31947 + 16.0877i −0.242341 + 0.616936i
\(681\) −24.2496 −0.929248
\(682\) 14.4888i 0.554805i
\(683\) 11.7625i 0.450080i −0.974350 0.225040i \(-0.927749\pi\)
0.974350 0.225040i \(-0.0722513\pi\)
\(684\) −10.0000 −0.382360
\(685\) −18.0493 7.09000i −0.689628 0.270895i
\(686\) −40.1338 −1.53231
\(687\) 35.6102i 1.35861i
\(688\) 9.72953i 0.370935i
\(689\) 0 0
\(690\) −24.5582 9.64680i −0.934916 0.367247i
\(691\) 4.86684 0.185143 0.0925717 0.995706i \(-0.470491\pi\)
0.0925717 + 0.995706i \(0.470491\pi\)
\(692\) 6.12658i 0.232897i
\(693\) 3.05147i 0.115916i
\(694\) 9.71254 0.368683
\(695\) 11.7125 29.8171i 0.444282 1.13103i
\(696\) 40.7900 1.54614
\(697\) 12.1925i 0.461825i
\(698\) 61.9289i 2.34404i
\(699\) 14.9616 0.565899
\(700\) −44.8079 + 48.2340i −1.69358 + 1.82307i
\(701\) 21.3828 0.807617 0.403808 0.914844i \(-0.367686\pi\)
0.403808 + 0.914844i \(0.367686\pi\)
\(702\) 0 0
\(703\) 1.67059i 0.0630076i
\(704\) −0.171587 −0.00646692
\(705\) −10.8490 + 27.6186i −0.408595 + 1.04018i
\(706\) −68.8853 −2.59253
\(707\) 38.8822i 1.46232i
\(708\) 73.2835i 2.75416i
\(709\) 26.1165 0.980825 0.490412 0.871491i \(-0.336846\pi\)
0.490412 + 0.871491i \(0.336846\pi\)
\(710\) −13.9616 5.48429i −0.523969 0.205822i
\(711\) 1.69792 0.0636770
\(712\) 79.3107i 2.97229i
\(713\) 19.2936i 0.722551i
\(714\) −19.7125 −0.737723
\(715\) 0 0
\(716\) 34.8880 1.30383
\(717\) 8.61170i 0.321610i
\(718\) 68.7448i 2.56553i
\(719\) −36.6774 −1.36784 −0.683918 0.729559i \(-0.739725\pi\)
−0.683918 + 0.729559i \(0.739725\pi\)
\(720\) 9.51220 24.2156i 0.354499 0.902462i
\(721\) −32.2318 −1.20037
\(722\) 43.6264i 1.62361i
\(723\) 42.5679i 1.58312i
\(724\) 17.3265 0.643934
\(725\) 10.9897 + 10.2091i 0.408148 + 0.379157i
\(726\) −58.0780 −2.15548
\(727\) 26.2596i 0.973916i −0.873425 0.486958i \(-0.838107\pi\)
0.873425 0.486958i \(-0.161893\pi\)
\(728\) 0 0
\(729\) −0.614542 −0.0227608
\(730\) −21.4917 + 54.7121i −0.795442 + 2.02499i
\(731\) 1.67352 0.0618972
\(732\) 21.9000i 0.809446i
\(733\) 31.7811i 1.17386i −0.809637 0.586931i \(-0.800336\pi\)
0.809637 0.586931i \(-0.199664\pi\)
\(734\) 17.6703 0.652221
\(735\) −7.32648 2.87794i −0.270241 0.106154i
\(736\) −11.8073 −0.435222
\(737\) 5.09978i 0.187853i
\(738\) 41.4651i 1.52635i
\(739\) 34.1370 1.25575 0.627875 0.778314i \(-0.283925\pi\)
0.627875 + 0.778314i \(0.283925\pi\)
\(740\) −11.4142 4.48365i −0.419595 0.164822i
\(741\) 0 0
\(742\) 4.80479i 0.176390i
\(743\) 3.12062i 0.114485i −0.998360 0.0572423i \(-0.981769\pi\)
0.998360 0.0572423i \(-0.0182307\pi\)
\(744\) 121.847 4.46715
\(745\) −14.0249 + 35.7037i −0.513832 + 1.30808i
\(746\) 5.88798 0.215574
\(747\) 19.3680i 0.708639i
\(748\) 3.48301i 0.127352i
\(749\) −31.3649 −1.14605
\(750\) 55.2323 26.5380i 2.01680 0.969031i
\(751\) 1.48405 0.0541537 0.0270769 0.999633i \(-0.491380\pi\)
0.0270769 + 0.999633i \(0.491380\pi\)
\(752\) 43.8607i 1.59944i
\(753\) 7.90881i 0.288213i
\(754\) 0 0
\(755\) 17.4814 44.5030i 0.636213 1.61963i
\(756\) −38.6920 −1.40721
\(757\) 5.09978i 0.185355i 0.995696 + 0.0926774i \(0.0295425\pi\)
−0.995696 + 0.0926774i \(0.970457\pi\)
\(758\) 13.1753i 0.478550i
\(759\) −2.94369 −0.106849
\(760\) −17.9404 7.04724i −0.650768 0.255630i
\(761\) −29.7861 −1.07975 −0.539873 0.841746i \(-0.681528\pi\)
−0.539873 + 0.841746i \(0.681528\pi\)
\(762\) 94.4433i 3.42132i
\(763\) 9.60959i 0.347890i
\(764\) −22.1516 −0.801418
\(765\) 4.16517 + 1.63613i 0.150592 + 0.0591546i
\(766\) −52.5973 −1.90042
\(767\) 0 0
\(768\) 62.7228i 2.26331i
\(769\) −19.0986 −0.688713 −0.344356 0.938839i \(-0.611903\pi\)
−0.344356 + 0.938839i \(0.611903\pi\)
\(770\) −3.88412 + 9.88797i −0.139974 + 0.356338i
\(771\) 28.5582 1.02850
\(772\) 22.2088i 0.799311i
\(773\) 49.2306i 1.77070i −0.464923 0.885351i \(-0.653918\pi\)
0.464923 0.885351i \(-0.346082\pi\)
\(774\) −5.69140 −0.204573
\(775\) 32.8284 + 30.4966i 1.17923 + 1.09547i
\(776\) 93.3661 3.35165
\(777\) 7.74335i 0.277791i
\(778\) 50.2725i 1.80236i
\(779\) 13.5967 0.487151
\(780\) 0 0
\(781\) −1.67352 −0.0598831
\(782\) 6.70825i 0.239886i
\(783\) 8.81566i 0.315046i
\(784\) −11.6351 −0.415539
\(785\) −38.2215 15.0139i −1.36418 0.535869i
\(786\) 54.8079 1.95493
\(787\) 9.78335i 0.348739i −0.984680 0.174369i \(-0.944211\pi\)
0.984680 0.174369i \(-0.0557887\pi\)
\(788\) 30.2250i 1.07672i
\(789\) −65.1701 −2.32012
\(790\) 5.50193 + 2.16123i 0.195750 + 0.0768931i
\(791\) 16.2496 0.577770
\(792\) 6.55812i 0.233033i
\(793\) 0 0
\(794\) 23.9020 0.848250
\(795\) −1.13049 + 2.87794i −0.0400945 + 0.102070i
\(796\) 23.1901 0.821950
\(797\) 16.5371i 0.585775i 0.956147 + 0.292887i \(0.0946161\pi\)
−0.956147 + 0.292887i \(0.905384\pi\)
\(798\) 21.9827i 0.778178i
\(799\) −7.54421 −0.266895
\(800\) 18.6632 20.0903i 0.659845 0.710299i
\(801\) −20.5338 −0.725527
\(802\) 62.3755i 2.20256i
\(803\) 6.55812i 0.231431i
\(804\) 77.4641 2.73195
\(805\) 5.17218 13.1670i 0.182295 0.464077i
\(806\) 0 0
\(807\) 47.9018i 1.68622i
\(808\) 83.5643i 2.93978i
\(809\) 31.8424 1.11952 0.559760 0.828655i \(-0.310893\pi\)
0.559760 + 0.828655i \(0.310893\pi\)
\(810\) 59.5095 + 23.3761i 2.09095 + 0.821354i
\(811\) 13.3470 0.468678 0.234339 0.972155i \(-0.424707\pi\)
0.234339 + 0.972155i \(0.424707\pi\)
\(812\) 39.5011i 1.38622i
\(813\) 25.4657i 0.893121i
\(814\) −1.97886 −0.0693589
\(815\) 8.34763 + 3.27906i 0.292405 + 0.114860i
\(816\) 18.7510 0.656415
\(817\) 1.86624i 0.0652915i
\(818\) 91.9431i 3.21472i
\(819\) 0 0
\(820\) −36.4917 + 92.8982i −1.27434 + 3.24415i
\(821\) 11.6735 0.407409 0.203704 0.979032i \(-0.434702\pi\)
0.203704 + 0.979032i \(0.434702\pi\)
\(822\) 47.5311i 1.65784i
\(823\) 32.4317i 1.13050i −0.824920 0.565249i \(-0.808780\pi\)
0.824920 0.565249i \(-0.191220\pi\)
\(824\) 69.2714 2.41318
\(825\) 4.65297 5.00875i 0.161996 0.174382i
\(826\) 56.8290 1.97733
\(827\) 27.3319i 0.950425i 0.879871 + 0.475212i \(0.157629\pi\)
−0.879871 + 0.475212i \(0.842371\pi\)
\(828\) 15.7734i 0.548163i
\(829\) −3.54036 −0.122962 −0.0614808 0.998108i \(-0.519582\pi\)
−0.0614808 + 0.998108i \(0.519582\pi\)
\(830\) 24.6530 62.7600i 0.855717 2.17843i
\(831\) 36.1370 1.25358
\(832\) 0 0
\(833\) 2.00128i 0.0693402i
\(834\) −78.5204 −2.71894
\(835\) 6.11588 + 2.40240i 0.211649 + 0.0831384i
\(836\) −3.88412 −0.134335
\(837\) 26.3341i 0.910238i
\(838\) 17.4812i 0.603877i
\(839\) −44.7900 −1.54632 −0.773161 0.634210i \(-0.781326\pi\)
−0.773161 + 0.634210i \(0.781326\pi\)
\(840\) 83.1555 + 32.6646i 2.86914 + 1.12704i
\(841\) −20.0000 −0.689655
\(842\) 86.5028i 2.98108i
\(843\) 22.8138i 0.785750i
\(844\) 62.8111 2.16205
\(845\) 0 0
\(846\) 25.6568 0.882100
\(847\) 31.1388i 1.06994i
\(848\) 4.57042i 0.156949i
\(849\) 18.9795 0.651373
\(850\) 11.4142 + 10.6034i 0.391504 + 0.363695i
\(851\) 2.63509 0.0903297
\(852\) 25.4202i 0.870881i
\(853\) 31.3732i 1.07420i 0.843519 + 0.537099i \(0.180480\pi\)
−0.843519 + 0.537099i \(0.819520\pi\)
\(854\) 16.9827 0.581137
\(855\) −1.82456 + 4.64484i −0.0623985 + 0.158850i
\(856\) 67.4084 2.30397
\(857\) 21.2813i 0.726955i −0.931603 0.363478i \(-0.881589\pi\)
0.931603 0.363478i \(-0.118411\pi\)
\(858\) 0 0
\(859\) −56.8502 −1.93970 −0.969851 0.243698i \(-0.921639\pi\)
−0.969851 + 0.243698i \(0.921639\pi\)
\(860\) −12.7510 5.00875i −0.434804 0.170797i
\(861\) −63.0217 −2.14778
\(862\) 41.3673i 1.40898i
\(863\) 32.8011i 1.11656i −0.829651 0.558282i \(-0.811461\pi\)
0.829651 0.558282i \(-0.188539\pi\)
\(864\) 16.1159 0.548273
\(865\) −2.84570 1.11783i −0.0967566 0.0380073i
\(866\) 0.652374 0.0221686
\(867\) 33.3745i 1.13346i
\(868\) 117.997i 4.00509i
\(869\) 0.659493 0.0223718
\(870\) 13.4424 34.2207i 0.455739 1.16019i
\(871\) 0 0
\(872\) 20.6526i 0.699385i
\(873\) 24.1728i 0.818126i
\(874\) 7.48079 0.253041
\(875\) 14.2285 + 29.6131i 0.481011 + 1.00111i
\(876\) 99.6157 3.36570
\(877\) 36.0651i 1.21783i −0.793235 0.608916i \(-0.791605\pi\)
0.793235 0.608916i \(-0.208395\pi\)
\(878\) 19.3391i 0.652664i
\(879\) 60.8257 2.05160
\(880\) 3.69466 9.40563i 0.124547 0.317064i
\(881\) −46.0396 −1.55111 −0.775557 0.631277i \(-0.782531\pi\)
−0.775557 + 0.631277i \(0.782531\pi\)
\(882\) 6.80607i 0.229172i
\(883\) 0.802236i 0.0269974i −0.999909 0.0134987i \(-0.995703\pi\)
0.999909 0.0134987i \(-0.00429690\pi\)
\(884\) 0 0
\(885\) −34.0390 13.3710i −1.14421 0.449461i
\(886\) 11.0039 0.369682
\(887\) 8.22568i 0.276191i 0.990419 + 0.138096i \(0.0440981\pi\)
−0.990419 + 0.138096i \(0.955902\pi\)
\(888\) 16.6417i 0.558460i
\(889\) −50.6363 −1.69829
\(890\) −66.5377 26.1369i −2.23035 0.876110i
\(891\) 7.13316 0.238970
\(892\) 0.0372125i 0.00124597i
\(893\) 8.41302i 0.281531i
\(894\) 94.0223 3.14458
\(895\) 6.36551 16.2049i 0.212775 0.541671i
\(896\) −34.2529 −1.14431
\(897\) 0 0
\(898\) 8.37054i 0.279328i
\(899\) 26.8847 0.896656
\(900\) −26.8387 24.9323i −0.894623 0.831076i
\(901\) −0.786129 −0.0261897
\(902\) 16.1056i 0.536257i
\(903\) 8.65020i 0.287861i
\(904\) −34.9231 −1.16153
\(905\) 3.16131 8.04788i 0.105086 0.267521i
\(906\) −117.195 −3.89353
\(907\) 30.4359i 1.01061i −0.862941 0.505305i \(-0.831380\pi\)
0.862941 0.505305i \(-0.168620\pi\)
\(908\) 50.4697i 1.67489i
\(909\) −21.6351 −0.717591
\(910\) 0 0
\(911\) 43.6145 1.44501 0.722507 0.691363i \(-0.242990\pi\)
0.722507 + 0.691363i \(0.242990\pi\)
\(912\) 20.9104i 0.692412i
\(913\) 7.52278i 0.248968i
\(914\) 39.2708 1.29896
\(915\) −10.1722 3.99577i −0.336282 0.132096i
\(916\) −74.1138 −2.44879
\(917\) 29.3855i 0.970395i
\(918\) 9.15616i 0.302198i
\(919\) 37.0217 1.22123 0.610617 0.791926i \(-0.290921\pi\)
0.610617 + 0.791926i \(0.290921\pi\)
\(920\) −11.1159 + 28.2981i −0.366480 + 0.932961i
\(921\) 27.3893 0.902509
\(922\) 65.8957i 2.17016i
\(923\) 0 0
\(924\) 18.0033 0.592264
\(925\) −4.16517 + 4.48365i −0.136950 + 0.147422i
\(926\) 17.9231 0.588991
\(927\) 17.9346i 0.589050i
\(928\) 16.4529i 0.540092i
\(929\) 4.76825 0.156441 0.0782206 0.996936i \(-0.475076\pi\)
0.0782206 + 0.996936i \(0.475076\pi\)
\(930\) 40.1549 102.224i 1.31673 3.35205i
\(931\) 2.23175 0.0731427
\(932\) 31.1388i 1.01999i
\(933\) 60.1165i 1.96812i
\(934\) −47.8886 −1.56696
\(935\) 1.61780 + 0.635495i 0.0529079 + 0.0207829i
\(936\) 0 0
\(937\) 43.6264i 1.42521i 0.701565 + 0.712606i \(0.252485\pi\)
−0.701565 + 0.712606i \(0.747515\pi\)
\(938\) 60.0709i 1.96139i
\(939\) −52.9205 −1.72699
\(940\) 57.4814 + 22.5794i 1.87484 + 0.736460i
\(941\) 18.2675 0.595504 0.297752 0.954643i \(-0.403763\pi\)
0.297752 + 0.954643i \(0.403763\pi\)
\(942\) 100.653i 3.27944i
\(943\) 21.4465i 0.698395i
\(944\) −54.0569 −1.75940
\(945\) −7.05957 + 17.9718i −0.229648 + 0.584623i
\(946\) −2.21061 −0.0718731
\(947\) 19.9829i 0.649358i −0.945824 0.324679i \(-0.894744\pi\)
0.945824 0.324679i \(-0.105256\pi\)
\(948\) 10.0175i 0.325353i
\(949\) 0 0
\(950\) −11.8246 + 12.7287i −0.383639 + 0.412973i
\(951\) −0.504596 −0.0163626
\(952\) 22.7145i 0.736181i
\(953\) 39.8635i 1.29130i 0.763632 + 0.645652i \(0.223414\pi\)
−0.763632 + 0.645652i \(0.776586\pi\)
\(954\) 2.67352 0.0865583
\(955\) −4.04169 + 10.2891i −0.130786 + 0.332947i
\(956\) 17.9231 0.579676
\(957\) 4.10190i 0.132596i
\(958\) 49.5847i 1.60201i
\(959\) −25.4840 −0.822923
\(960\) 1.21061 + 0.475543i 0.0390722 + 0.0153481i
\(961\) 49.3098 1.59064
\(962\) 0 0
\(963\) 17.4523i 0.562392i
\(964\) −88.5946 −2.85344
\(965\) −10.3156 4.05211i −0.332071 0.130442i
\(966\) −34.6741 −1.11562
\(967\) 43.8607i 1.41047i −0.708975 0.705233i \(-0.750842\pi\)
0.708975 0.705233i \(-0.249158\pi\)
\(968\) 66.9225i 2.15097i
\(969\) −3.59666 −0.115541
\(970\) 30.7688 78.3294i 0.987928 2.51501i
\(971\) 60.9795 1.95692 0.978462 0.206428i \(-0.0661838\pi\)
0.978462 + 0.206428i \(0.0661838\pi\)
\(972\) 68.8494i 2.20835i
\(973\) 42.0991i 1.34964i
\(974\) 82.2887 2.63670
\(975\) 0 0
\(976\) −16.1543 −0.517087
\(977\) 51.3697i 1.64346i 0.569875 + 0.821731i \(0.306992\pi\)
−0.569875 + 0.821731i \(0.693008\pi\)
\(978\) 21.9827i 0.702929i
\(979\) −7.97560 −0.254901
\(980\) −5.98973 + 15.2483i −0.191335 + 0.487088i
\(981\) −5.34703 −0.170718
\(982\) 72.9885i 2.32916i
\(983\) 37.3026i 1.18977i −0.803811 0.594885i \(-0.797198\pi\)
0.803811 0.594885i \(-0.202802\pi\)
\(984\) 135.444 4.31780
\(985\) 14.0390 + 5.51471i 0.447320 + 0.175713i
\(986\) 9.34763 0.297689
\(987\) 38.9951i 1.24123i
\(988\) 0 0
\(989\) 2.94369 0.0936040
\(990\) −5.50193 2.16123i −0.174863 0.0686884i
\(991\) −51.5621 −1.63792 −0.818962 0.573848i \(-0.805450\pi\)
−0.818962 + 0.573848i \(0.805450\pi\)
\(992\) 49.1479i 1.56045i
\(993\) 39.4556i 1.25208i
\(994\) −19.7125 −0.625244
\(995\) 4.23116 10.7714i 0.134137 0.341477i
\(996\) −114.269 −3.62074
\(997\) 22.9489i 0.726798i 0.931634 + 0.363399i \(0.118384\pi\)
−0.931634 + 0.363399i \(0.881616\pi\)
\(998\) 73.7286i 2.33384i
\(999\) −3.59666 −0.113793
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 845.2.b.d.339.6 6
5.2 odd 4 4225.2.a.br.1.1 6
5.3 odd 4 4225.2.a.br.1.6 6
5.4 even 2 inner 845.2.b.d.339.1 6
13.2 odd 12 845.2.l.f.654.2 24
13.3 even 3 65.2.n.a.9.1 12
13.4 even 6 845.2.n.e.484.1 12
13.5 odd 4 845.2.d.d.844.11 12
13.6 odd 12 845.2.l.f.699.1 24
13.7 odd 12 845.2.l.f.699.11 24
13.8 odd 4 845.2.d.d.844.1 12
13.9 even 3 65.2.n.a.29.6 yes 12
13.10 even 6 845.2.n.e.529.6 12
13.11 odd 12 845.2.l.f.654.12 24
13.12 even 2 845.2.b.e.339.1 6
39.29 odd 6 585.2.bs.a.334.6 12
39.35 odd 6 585.2.bs.a.289.1 12
52.3 odd 6 1040.2.dh.a.529.2 12
52.35 odd 6 1040.2.dh.a.289.5 12
65.3 odd 12 325.2.e.e.126.1 12
65.4 even 6 845.2.n.e.484.6 12
65.9 even 6 65.2.n.a.29.1 yes 12
65.12 odd 4 4225.2.a.bq.1.6 6
65.19 odd 12 845.2.l.f.699.12 24
65.22 odd 12 325.2.e.e.276.6 12
65.24 odd 12 845.2.l.f.654.1 24
65.29 even 6 65.2.n.a.9.6 yes 12
65.34 odd 4 845.2.d.d.844.12 12
65.38 odd 4 4225.2.a.bq.1.1 6
65.42 odd 12 325.2.e.e.126.6 12
65.44 odd 4 845.2.d.d.844.2 12
65.48 odd 12 325.2.e.e.276.1 12
65.49 even 6 845.2.n.e.529.1 12
65.54 odd 12 845.2.l.f.654.11 24
65.59 odd 12 845.2.l.f.699.2 24
65.64 even 2 845.2.b.e.339.6 6
195.29 odd 6 585.2.bs.a.334.1 12
195.74 odd 6 585.2.bs.a.289.6 12
260.139 odd 6 1040.2.dh.a.289.2 12
260.159 odd 6 1040.2.dh.a.529.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.n.a.9.1 12 13.3 even 3
65.2.n.a.9.6 yes 12 65.29 even 6
65.2.n.a.29.1 yes 12 65.9 even 6
65.2.n.a.29.6 yes 12 13.9 even 3
325.2.e.e.126.1 12 65.3 odd 12
325.2.e.e.126.6 12 65.42 odd 12
325.2.e.e.276.1 12 65.48 odd 12
325.2.e.e.276.6 12 65.22 odd 12
585.2.bs.a.289.1 12 39.35 odd 6
585.2.bs.a.289.6 12 195.74 odd 6
585.2.bs.a.334.1 12 195.29 odd 6
585.2.bs.a.334.6 12 39.29 odd 6
845.2.b.d.339.1 6 5.4 even 2 inner
845.2.b.d.339.6 6 1.1 even 1 trivial
845.2.b.e.339.1 6 13.12 even 2
845.2.b.e.339.6 6 65.64 even 2
845.2.d.d.844.1 12 13.8 odd 4
845.2.d.d.844.2 12 65.44 odd 4
845.2.d.d.844.11 12 13.5 odd 4
845.2.d.d.844.12 12 65.34 odd 4
845.2.l.f.654.1 24 65.24 odd 12
845.2.l.f.654.2 24 13.2 odd 12
845.2.l.f.654.11 24 65.54 odd 12
845.2.l.f.654.12 24 13.11 odd 12
845.2.l.f.699.1 24 13.6 odd 12
845.2.l.f.699.2 24 65.59 odd 12
845.2.l.f.699.11 24 13.7 odd 12
845.2.l.f.699.12 24 65.19 odd 12
845.2.n.e.484.1 12 13.4 even 6
845.2.n.e.484.6 12 65.4 even 6
845.2.n.e.529.1 12 65.49 even 6
845.2.n.e.529.6 12 13.10 even 6
1040.2.dh.a.289.2 12 260.139 odd 6
1040.2.dh.a.289.5 12 52.35 odd 6
1040.2.dh.a.529.2 12 52.3 odd 6
1040.2.dh.a.529.5 12 260.159 odd 6
4225.2.a.bq.1.1 6 65.38 odd 4
4225.2.a.bq.1.6 6 65.12 odd 4
4225.2.a.br.1.1 6 5.2 odd 4
4225.2.a.br.1.6 6 5.3 odd 4