Properties

Label 1805.2.b.l.1084.10
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $24$
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] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, 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("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.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: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.10
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.l.1084.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.449373i q^{2} -1.95684i q^{3} +1.79806 q^{4} +(1.87757 + 1.21438i) q^{5} -0.879352 q^{6} +2.06079i q^{7} -1.70675i q^{8} -0.829224 q^{9} +O(q^{10})\) \(q-0.449373i q^{2} -1.95684i q^{3} +1.79806 q^{4} +(1.87757 + 1.21438i) q^{5} -0.879352 q^{6} +2.06079i q^{7} -1.70675i q^{8} -0.829224 q^{9} +(0.545709 - 0.843732i) q^{10} -2.30599 q^{11} -3.51852i q^{12} +4.39611i q^{13} +0.926065 q^{14} +(2.37634 - 3.67411i) q^{15} +2.82916 q^{16} +5.47185i q^{17} +0.372631i q^{18} +(3.37600 + 2.18353i) q^{20} +4.03264 q^{21} +1.03625i q^{22} -5.81755i q^{23} -3.33983 q^{24} +(2.05058 + 4.56017i) q^{25} +1.97549 q^{26} -4.24786i q^{27} +3.70544i q^{28} +5.50466 q^{29} +(-1.65105 - 1.06786i) q^{30} -0.757832 q^{31} -4.68485i q^{32} +4.51245i q^{33} +2.45890 q^{34} +(-2.50258 + 3.86929i) q^{35} -1.49100 q^{36} -6.22555i q^{37} +8.60248 q^{39} +(2.07264 - 3.20455i) q^{40} +6.53829 q^{41} -1.81216i q^{42} +3.16680i q^{43} -4.14632 q^{44} +(-1.55693 - 1.00699i) q^{45} -2.61425 q^{46} -6.36116i q^{47} -5.53621i q^{48} +2.75314 q^{49} +(2.04922 - 0.921474i) q^{50} +10.7075 q^{51} +7.90448i q^{52} +3.85028i q^{53} -1.90888 q^{54} +(-4.32967 - 2.80034i) q^{55} +3.51725 q^{56} -2.47365i q^{58} +2.55023 q^{59} +(4.27282 - 6.60629i) q^{60} +9.94010 q^{61} +0.340550i q^{62} -1.70886i q^{63} +3.55308 q^{64} +(-5.33853 + 8.25402i) q^{65} +2.02778 q^{66} +1.70269i q^{67} +9.83874i q^{68} -11.3840 q^{69} +(1.73876 + 1.12459i) q^{70} -9.85909 q^{71} +1.41528i q^{72} +10.2167i q^{73} -2.79760 q^{74} +(8.92352 - 4.01265i) q^{75} -4.75216i q^{77} -3.86572i q^{78} +2.41187 q^{79} +(5.31196 + 3.43567i) q^{80} -10.8001 q^{81} -2.93813i q^{82} -7.06253i q^{83} +7.25095 q^{84} +(-6.64489 + 10.2738i) q^{85} +1.42307 q^{86} -10.7717i q^{87} +3.93574i q^{88} -2.33452 q^{89} +(-0.452514 + 0.699642i) q^{90} -9.05946 q^{91} -10.4603i q^{92} +1.48296i q^{93} -2.85854 q^{94} -9.16749 q^{96} +6.81539i q^{97} -1.23719i q^{98} +1.91218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} - 12 q^{40} - 60 q^{41} + 30 q^{44} + 9 q^{45} - 6 q^{46} - 12 q^{49} - 18 q^{50} - 30 q^{51} + 24 q^{54} + 33 q^{55} - 18 q^{56} + 60 q^{59} + 42 q^{60} + 30 q^{61} - 18 q^{65} + 36 q^{66} + 66 q^{69} - 9 q^{70} - 96 q^{71} - 24 q^{74} - 36 q^{75} + 72 q^{79} - 42 q^{80} - 96 q^{81} - 54 q^{84} - 27 q^{85} - 108 q^{86} + 84 q^{89} + 93 q^{90} - 96 q^{91} + 36 q^{94} - 120 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.449373i 0.317755i −0.987298 0.158877i \(-0.949213\pi\)
0.987298 0.158877i \(-0.0507875\pi\)
\(3\) 1.95684i 1.12978i −0.825165 0.564891i \(-0.808918\pi\)
0.825165 0.564891i \(-0.191082\pi\)
\(4\) 1.79806 0.899032
\(5\) 1.87757 + 1.21438i 0.839677 + 0.543086i
\(6\) −0.879352 −0.358994
\(7\) 2.06079i 0.778906i 0.921046 + 0.389453i \(0.127336\pi\)
−0.921046 + 0.389453i \(0.872664\pi\)
\(8\) 1.70675i 0.603427i
\(9\) −0.829224 −0.276408
\(10\) 0.545709 0.843732i 0.172568 0.266811i
\(11\) −2.30599 −0.695282 −0.347641 0.937628i \(-0.613017\pi\)
−0.347641 + 0.937628i \(0.613017\pi\)
\(12\) 3.51852i 1.01571i
\(13\) 4.39611i 1.21926i 0.792686 + 0.609630i \(0.208682\pi\)
−0.792686 + 0.609630i \(0.791318\pi\)
\(14\) 0.926065 0.247501
\(15\) 2.37634 3.67411i 0.613569 0.948652i
\(16\) 2.82916 0.707290
\(17\) 5.47185i 1.32712i 0.748123 + 0.663560i \(0.230955\pi\)
−0.748123 + 0.663560i \(0.769045\pi\)
\(18\) 0.372631i 0.0878299i
\(19\) 0 0
\(20\) 3.37600 + 2.18353i 0.754896 + 0.488252i
\(21\) 4.03264 0.879994
\(22\) 1.03625i 0.220929i
\(23\) 5.81755i 1.21304i −0.795067 0.606522i \(-0.792564\pi\)
0.795067 0.606522i \(-0.207436\pi\)
\(24\) −3.33983 −0.681741
\(25\) 2.05058 + 4.56017i 0.410115 + 0.912034i
\(26\) 1.97549 0.387426
\(27\) 4.24786i 0.817502i
\(28\) 3.70544i 0.700262i
\(29\) 5.50466 1.02219 0.511095 0.859524i \(-0.329240\pi\)
0.511095 + 0.859524i \(0.329240\pi\)
\(30\) −1.65105 1.06786i −0.301439 0.194965i
\(31\) −0.757832 −0.136111 −0.0680553 0.997682i \(-0.521679\pi\)
−0.0680553 + 0.997682i \(0.521679\pi\)
\(32\) 4.68485i 0.828171i
\(33\) 4.51245i 0.785517i
\(34\) 2.45890 0.421699
\(35\) −2.50258 + 3.86929i −0.423013 + 0.654030i
\(36\) −1.49100 −0.248499
\(37\) 6.22555i 1.02347i −0.859142 0.511737i \(-0.829002\pi\)
0.859142 0.511737i \(-0.170998\pi\)
\(38\) 0 0
\(39\) 8.60248 1.37750
\(40\) 2.07264 3.20455i 0.327713 0.506683i
\(41\) 6.53829 1.02111 0.510554 0.859845i \(-0.329440\pi\)
0.510554 + 0.859845i \(0.329440\pi\)
\(42\) 1.81216i 0.279623i
\(43\) 3.16680i 0.482932i 0.970409 + 0.241466i \(0.0776282\pi\)
−0.970409 + 0.241466i \(0.922372\pi\)
\(44\) −4.14632 −0.625081
\(45\) −1.55693 1.00699i −0.232093 0.150113i
\(46\) −2.61425 −0.385451
\(47\) 6.36116i 0.927871i −0.885869 0.463936i \(-0.846437\pi\)
0.885869 0.463936i \(-0.153563\pi\)
\(48\) 5.53621i 0.799084i
\(49\) 2.75314 0.393305
\(50\) 2.04922 0.921474i 0.289803 0.130316i
\(51\) 10.7075 1.49936
\(52\) 7.90448i 1.09615i
\(53\) 3.85028i 0.528876i 0.964403 + 0.264438i \(0.0851865\pi\)
−0.964403 + 0.264438i \(0.914813\pi\)
\(54\) −1.90888 −0.259765
\(55\) −4.32967 2.80034i −0.583812 0.377598i
\(56\) 3.51725 0.470013
\(57\) 0 0
\(58\) 2.47365i 0.324806i
\(59\) 2.55023 0.332012 0.166006 0.986125i \(-0.446913\pi\)
0.166006 + 0.986125i \(0.446913\pi\)
\(60\) 4.27282 6.60629i 0.551618 0.852869i
\(61\) 9.94010 1.27270 0.636350 0.771401i \(-0.280444\pi\)
0.636350 + 0.771401i \(0.280444\pi\)
\(62\) 0.340550i 0.0432498i
\(63\) 1.70886i 0.215296i
\(64\) 3.55308 0.444135
\(65\) −5.33853 + 8.25402i −0.662163 + 1.02378i
\(66\) 2.02778 0.249602
\(67\) 1.70269i 0.208017i 0.994576 + 0.104009i \(0.0331669\pi\)
−0.994576 + 0.104009i \(0.966833\pi\)
\(68\) 9.83874i 1.19312i
\(69\) −11.3840 −1.37048
\(70\) 1.73876 + 1.12459i 0.207821 + 0.134414i
\(71\) −9.85909 −1.17006 −0.585029 0.811012i \(-0.698917\pi\)
−0.585029 + 0.811012i \(0.698917\pi\)
\(72\) 1.41528i 0.166792i
\(73\) 10.2167i 1.19577i 0.801581 + 0.597886i \(0.203993\pi\)
−0.801581 + 0.597886i \(0.796007\pi\)
\(74\) −2.79760 −0.325214
\(75\) 8.92352 4.01265i 1.03040 0.463341i
\(76\) 0 0
\(77\) 4.75216i 0.541559i
\(78\) 3.86572i 0.437707i
\(79\) 2.41187 0.271357 0.135679 0.990753i \(-0.456679\pi\)
0.135679 + 0.990753i \(0.456679\pi\)
\(80\) 5.31196 + 3.43567i 0.593895 + 0.384119i
\(81\) −10.8001 −1.20001
\(82\) 2.93813i 0.324462i
\(83\) 7.06253i 0.775213i −0.921825 0.387607i \(-0.873302\pi\)
0.921825 0.387607i \(-0.126698\pi\)
\(84\) 7.25095 0.791143
\(85\) −6.64489 + 10.2738i −0.720740 + 1.11435i
\(86\) 1.42307 0.153454
\(87\) 10.7717i 1.15485i
\(88\) 3.93574i 0.419552i
\(89\) −2.33452 −0.247458 −0.123729 0.992316i \(-0.539485\pi\)
−0.123729 + 0.992316i \(0.539485\pi\)
\(90\) −0.452514 + 0.699642i −0.0476992 + 0.0737488i
\(91\) −9.05946 −0.949689
\(92\) 10.4603i 1.09056i
\(93\) 1.48296i 0.153775i
\(94\) −2.85854 −0.294836
\(95\) 0 0
\(96\) −9.16749 −0.935653
\(97\) 6.81539i 0.691998i 0.938235 + 0.345999i \(0.112460\pi\)
−0.938235 + 0.345999i \(0.887540\pi\)
\(98\) 1.23719i 0.124975i
\(99\) 1.91218 0.192181
\(100\) 3.68706 + 8.19947i 0.368706 + 0.819947i
\(101\) 12.1976 1.21370 0.606851 0.794816i \(-0.292433\pi\)
0.606851 + 0.794816i \(0.292433\pi\)
\(102\) 4.81168i 0.476428i
\(103\) 12.9197i 1.27302i 0.771269 + 0.636509i \(0.219622\pi\)
−0.771269 + 0.636509i \(0.780378\pi\)
\(104\) 7.50304 0.735734
\(105\) 7.57159 + 4.89715i 0.738911 + 0.477913i
\(106\) 1.73021 0.168053
\(107\) 15.1729i 1.46682i 0.679785 + 0.733412i \(0.262073\pi\)
−0.679785 + 0.733412i \(0.737927\pi\)
\(108\) 7.63793i 0.734960i
\(109\) −19.1794 −1.83705 −0.918527 0.395359i \(-0.870620\pi\)
−0.918527 + 0.395359i \(0.870620\pi\)
\(110\) −1.25840 + 1.94564i −0.119984 + 0.185509i
\(111\) −12.1824 −1.15630
\(112\) 5.83031i 0.550913i
\(113\) 1.91146i 0.179815i −0.995950 0.0899075i \(-0.971343\pi\)
0.995950 0.0899075i \(-0.0286571\pi\)
\(114\) 0 0
\(115\) 7.06470 10.9229i 0.658787 1.01856i
\(116\) 9.89773 0.918981
\(117\) 3.64535i 0.337013i
\(118\) 1.14601i 0.105498i
\(119\) −11.2764 −1.03370
\(120\) −6.27079 4.05582i −0.572442 0.370244i
\(121\) −5.68241 −0.516583
\(122\) 4.46682i 0.404406i
\(123\) 12.7944i 1.15363i
\(124\) −1.36263 −0.122368
\(125\) −1.68766 + 11.0522i −0.150949 + 0.988542i
\(126\) −0.767915 −0.0684113
\(127\) 21.2359i 1.88438i −0.335077 0.942191i \(-0.608762\pi\)
0.335077 0.942191i \(-0.391238\pi\)
\(128\) 10.9663i 0.969297i
\(129\) 6.19692 0.545608
\(130\) 3.70913 + 2.39899i 0.325313 + 0.210406i
\(131\) −1.67271 −0.146146 −0.0730728 0.997327i \(-0.523281\pi\)
−0.0730728 + 0.997327i \(0.523281\pi\)
\(132\) 8.11368i 0.706205i
\(133\) 0 0
\(134\) 0.765145 0.0660984
\(135\) 5.15851 7.97568i 0.443974 0.686437i
\(136\) 9.33908 0.800819
\(137\) 17.2880i 1.47701i −0.674247 0.738506i \(-0.735532\pi\)
0.674247 0.738506i \(-0.264468\pi\)
\(138\) 5.11567i 0.435475i
\(139\) −12.3265 −1.04552 −0.522761 0.852479i \(-0.675098\pi\)
−0.522761 + 0.852479i \(0.675098\pi\)
\(140\) −4.49980 + 6.95723i −0.380302 + 0.587994i
\(141\) −12.4478 −1.04829
\(142\) 4.43041i 0.371792i
\(143\) 10.1374i 0.847730i
\(144\) −2.34601 −0.195501
\(145\) 10.3354 + 6.68473i 0.858309 + 0.555137i
\(146\) 4.59111 0.379963
\(147\) 5.38745i 0.444349i
\(148\) 11.1939i 0.920136i
\(149\) −4.35901 −0.357104 −0.178552 0.983930i \(-0.557141\pi\)
−0.178552 + 0.983930i \(0.557141\pi\)
\(150\) −1.80318 4.00999i −0.147229 0.327414i
\(151\) −4.44628 −0.361833 −0.180917 0.983498i \(-0.557906\pi\)
−0.180917 + 0.983498i \(0.557906\pi\)
\(152\) 0 0
\(153\) 4.53739i 0.366826i
\(154\) −2.13550 −0.172083
\(155\) −1.42289 0.920294i −0.114289 0.0739198i
\(156\) 15.4678 1.23841
\(157\) 19.8432i 1.58366i −0.610740 0.791831i \(-0.709128\pi\)
0.610740 0.791831i \(-0.290872\pi\)
\(158\) 1.08383i 0.0862250i
\(159\) 7.53438 0.597515
\(160\) 5.68917 8.79615i 0.449768 0.695397i
\(161\) 11.9888 0.944847
\(162\) 4.85326i 0.381308i
\(163\) 1.28088i 0.100326i −0.998741 0.0501632i \(-0.984026\pi\)
0.998741 0.0501632i \(-0.0159742\pi\)
\(164\) 11.7563 0.918009
\(165\) −5.47982 + 8.47247i −0.426603 + 0.659581i
\(166\) −3.17371 −0.246328
\(167\) 8.03589i 0.621836i −0.950437 0.310918i \(-0.899364\pi\)
0.950437 0.310918i \(-0.100636\pi\)
\(168\) 6.88270i 0.531012i
\(169\) −6.32574 −0.486595
\(170\) 4.61678 + 2.98604i 0.354091 + 0.229019i
\(171\) 0 0
\(172\) 5.69410i 0.434171i
\(173\) 2.65910i 0.202167i −0.994878 0.101084i \(-0.967769\pi\)
0.994878 0.101084i \(-0.0322310\pi\)
\(174\) −4.84053 −0.366960
\(175\) −9.39756 + 4.22581i −0.710389 + 0.319441i
\(176\) −6.52401 −0.491766
\(177\) 4.99040i 0.375101i
\(178\) 1.04907i 0.0786311i
\(179\) 8.10201 0.605572 0.302786 0.953059i \(-0.402083\pi\)
0.302786 + 0.953059i \(0.402083\pi\)
\(180\) −2.79946 1.81063i −0.208659 0.134957i
\(181\) −21.5023 −1.59826 −0.799128 0.601161i \(-0.794705\pi\)
−0.799128 + 0.601161i \(0.794705\pi\)
\(182\) 4.07108i 0.301768i
\(183\) 19.4512i 1.43787i
\(184\) −9.92910 −0.731983
\(185\) 7.56017 11.6889i 0.555835 0.859388i
\(186\) 0.666401 0.0488629
\(187\) 12.6180i 0.922722i
\(188\) 11.4378i 0.834186i
\(189\) 8.75396 0.636757
\(190\) 0 0
\(191\) −19.5939 −1.41777 −0.708884 0.705326i \(-0.750801\pi\)
−0.708884 + 0.705326i \(0.750801\pi\)
\(192\) 6.95280i 0.501775i
\(193\) 0.483357i 0.0347928i −0.999849 0.0173964i \(-0.994462\pi\)
0.999849 0.0173964i \(-0.00553773\pi\)
\(194\) 3.06265 0.219886
\(195\) 16.1518 + 10.4467i 1.15665 + 0.748100i
\(196\) 4.95031 0.353594
\(197\) 1.26189i 0.0899060i 0.998989 + 0.0449530i \(0.0143138\pi\)
−0.998989 + 0.0449530i \(0.985686\pi\)
\(198\) 0.859283i 0.0610666i
\(199\) −20.6554 −1.46423 −0.732113 0.681183i \(-0.761466\pi\)
−0.732113 + 0.681183i \(0.761466\pi\)
\(200\) 7.78306 3.49982i 0.550345 0.247474i
\(201\) 3.33190 0.235014
\(202\) 5.48125i 0.385660i
\(203\) 11.3440i 0.796190i
\(204\) 19.2528 1.34797
\(205\) 12.2761 + 7.93995i 0.857402 + 0.554550i
\(206\) 5.80578 0.404508
\(207\) 4.82405i 0.335295i
\(208\) 12.4373i 0.862371i
\(209\) 0 0
\(210\) 2.20065 3.40247i 0.151859 0.234793i
\(211\) −7.01196 −0.482723 −0.241361 0.970435i \(-0.577594\pi\)
−0.241361 + 0.970435i \(0.577594\pi\)
\(212\) 6.92305i 0.475477i
\(213\) 19.2927i 1.32191i
\(214\) 6.81831 0.466090
\(215\) −3.84569 + 5.94590i −0.262274 + 0.405507i
\(216\) −7.25003 −0.493302
\(217\) 1.56173i 0.106017i
\(218\) 8.61871i 0.583733i
\(219\) 19.9924 1.35096
\(220\) −7.78502 5.03519i −0.524866 0.339473i
\(221\) −24.0548 −1.61810
\(222\) 5.47445i 0.367421i
\(223\) 19.4374i 1.30162i 0.759239 + 0.650812i \(0.225571\pi\)
−0.759239 + 0.650812i \(0.774429\pi\)
\(224\) 9.65449 0.645068
\(225\) −1.70039 3.78140i −0.113359 0.252093i
\(226\) −0.858959 −0.0571371
\(227\) 6.53998i 0.434074i −0.976163 0.217037i \(-0.930361\pi\)
0.976163 0.217037i \(-0.0696392\pi\)
\(228\) 0 0
\(229\) 20.4005 1.34810 0.674052 0.738684i \(-0.264552\pi\)
0.674052 + 0.738684i \(0.264552\pi\)
\(230\) −4.90846 3.17469i −0.323654 0.209333i
\(231\) −9.29923 −0.611844
\(232\) 9.39507i 0.616816i
\(233\) 12.0490i 0.789357i −0.918819 0.394679i \(-0.870856\pi\)
0.918819 0.394679i \(-0.129144\pi\)
\(234\) −1.63812 −0.107088
\(235\) 7.72485 11.9436i 0.503914 0.779112i
\(236\) 4.58548 0.298489
\(237\) 4.71965i 0.306574i
\(238\) 5.06729i 0.328464i
\(239\) 6.12499 0.396193 0.198096 0.980183i \(-0.436524\pi\)
0.198096 + 0.980183i \(0.436524\pi\)
\(240\) 6.72305 10.3947i 0.433971 0.670972i
\(241\) 7.27309 0.468501 0.234250 0.972176i \(-0.424736\pi\)
0.234250 + 0.972176i \(0.424736\pi\)
\(242\) 2.55352i 0.164147i
\(243\) 8.39040i 0.538244i
\(244\) 17.8729 1.14420
\(245\) 5.16922 + 3.34335i 0.330249 + 0.213598i
\(246\) −5.74945 −0.366572
\(247\) 0 0
\(248\) 1.29343i 0.0821328i
\(249\) −13.8202 −0.875822
\(250\) 4.96658 + 0.758388i 0.314114 + 0.0479647i
\(251\) −24.1866 −1.52664 −0.763321 0.646019i \(-0.776433\pi\)
−0.763321 + 0.646019i \(0.776433\pi\)
\(252\) 3.07263i 0.193558i
\(253\) 13.4152i 0.843407i
\(254\) −9.54285 −0.598771
\(255\) 20.1042 + 13.0030i 1.25897 + 0.814279i
\(256\) 2.17817 0.136136
\(257\) 12.2379i 0.763382i −0.924290 0.381691i \(-0.875342\pi\)
0.924290 0.381691i \(-0.124658\pi\)
\(258\) 2.78473i 0.173370i
\(259\) 12.8296 0.797191
\(260\) −9.59902 + 14.8412i −0.595306 + 0.920415i
\(261\) −4.56459 −0.282541
\(262\) 0.751673i 0.0464385i
\(263\) 12.3859i 0.763746i 0.924215 + 0.381873i \(0.124721\pi\)
−0.924215 + 0.381873i \(0.875279\pi\)
\(264\) 7.70162 0.474002
\(265\) −4.67569 + 7.22919i −0.287225 + 0.444085i
\(266\) 0 0
\(267\) 4.56828i 0.279574i
\(268\) 3.06155i 0.187014i
\(269\) −4.93880 −0.301124 −0.150562 0.988601i \(-0.548108\pi\)
−0.150562 + 0.988601i \(0.548108\pi\)
\(270\) −3.58406 2.31810i −0.218119 0.141075i
\(271\) −6.90194 −0.419263 −0.209631 0.977780i \(-0.567226\pi\)
−0.209631 + 0.977780i \(0.567226\pi\)
\(272\) 15.4808i 0.938658i
\(273\) 17.7279i 1.07294i
\(274\) −7.76876 −0.469328
\(275\) −4.72860 10.5157i −0.285146 0.634121i
\(276\) −20.4692 −1.23210
\(277\) 3.96325i 0.238129i −0.992887 0.119064i \(-0.962011\pi\)
0.992887 0.119064i \(-0.0379895\pi\)
\(278\) 5.53921i 0.332220i
\(279\) 0.628412 0.0376221
\(280\) 6.60391 + 4.27127i 0.394659 + 0.255257i
\(281\) −31.1993 −1.86119 −0.930597 0.366045i \(-0.880711\pi\)
−0.930597 + 0.366045i \(0.880711\pi\)
\(282\) 5.59370i 0.333100i
\(283\) 10.6270i 0.631711i −0.948807 0.315855i \(-0.897709\pi\)
0.948807 0.315855i \(-0.102291\pi\)
\(284\) −17.7273 −1.05192
\(285\) 0 0
\(286\) −4.55546 −0.269370
\(287\) 13.4741i 0.795348i
\(288\) 3.88478i 0.228913i
\(289\) −12.9412 −0.761246
\(290\) 3.00394 4.64446i 0.176397 0.272732i
\(291\) 13.3366 0.781807
\(292\) 18.3703i 1.07504i
\(293\) 19.6263i 1.14658i −0.819353 0.573289i \(-0.805667\pi\)
0.819353 0.573289i \(-0.194333\pi\)
\(294\) −2.42097 −0.141194
\(295\) 4.78825 + 3.09695i 0.278783 + 0.180311i
\(296\) −10.6255 −0.617592
\(297\) 9.79553i 0.568394i
\(298\) 1.95882i 0.113472i
\(299\) 25.5746 1.47902
\(300\) 16.0451 7.21500i 0.926362 0.416558i
\(301\) −6.52611 −0.376159
\(302\) 1.99804i 0.114974i
\(303\) 23.8687i 1.37122i
\(304\) 0 0
\(305\) 18.6633 + 12.0710i 1.06866 + 0.691185i
\(306\) −2.03898 −0.116561
\(307\) 22.6258i 1.29132i 0.763623 + 0.645662i \(0.223419\pi\)
−0.763623 + 0.645662i \(0.776581\pi\)
\(308\) 8.54469i 0.486879i
\(309\) 25.2818 1.43823
\(310\) −0.413556 + 0.639407i −0.0234884 + 0.0363159i
\(311\) 24.8577 1.40955 0.704776 0.709430i \(-0.251047\pi\)
0.704776 + 0.709430i \(0.251047\pi\)
\(312\) 14.6823i 0.831219i
\(313\) 22.2026i 1.25497i 0.778630 + 0.627484i \(0.215915\pi\)
−0.778630 + 0.627484i \(0.784085\pi\)
\(314\) −8.91701 −0.503216
\(315\) 2.07520 3.20851i 0.116924 0.180779i
\(316\) 4.33670 0.243959
\(317\) 2.03957i 0.114554i 0.998358 + 0.0572769i \(0.0182418\pi\)
−0.998358 + 0.0572769i \(0.981758\pi\)
\(318\) 3.38575i 0.189863i
\(319\) −12.6937 −0.710710
\(320\) 6.67117 + 4.31478i 0.372930 + 0.241203i
\(321\) 29.6910 1.65719
\(322\) 5.38743i 0.300230i
\(323\) 0 0
\(324\) −19.4192 −1.07884
\(325\) −20.0470 + 9.01454i −1.11201 + 0.500037i
\(326\) −0.575594 −0.0318792
\(327\) 37.5310i 2.07547i
\(328\) 11.1592i 0.616164i
\(329\) 13.1090 0.722725
\(330\) 3.80730 + 2.46248i 0.209585 + 0.135555i
\(331\) −33.6525 −1.84971 −0.924855 0.380321i \(-0.875814\pi\)
−0.924855 + 0.380321i \(0.875814\pi\)
\(332\) 12.6989i 0.696941i
\(333\) 5.16237i 0.282896i
\(334\) −3.61111 −0.197591
\(335\) −2.06771 + 3.19693i −0.112971 + 0.174667i
\(336\) 11.4090 0.622411
\(337\) 2.58877i 0.141019i −0.997511 0.0705096i \(-0.977537\pi\)
0.997511 0.0705096i \(-0.0224625\pi\)
\(338\) 2.84262i 0.154618i
\(339\) −3.74042 −0.203152
\(340\) −11.9479 + 18.4730i −0.647968 + 1.00184i
\(341\) 1.74755 0.0946353
\(342\) 0 0
\(343\) 20.0992i 1.08525i
\(344\) 5.40493 0.291414
\(345\) −21.3744 13.8245i −1.15076 0.744286i
\(346\) −1.19493 −0.0642397
\(347\) 23.8033i 1.27783i 0.769279 + 0.638913i \(0.220616\pi\)
−0.769279 + 0.638913i \(0.779384\pi\)
\(348\) 19.3683i 1.03825i
\(349\) 2.48241 0.132880 0.0664402 0.997790i \(-0.478836\pi\)
0.0664402 + 0.997790i \(0.478836\pi\)
\(350\) 1.89897 + 4.22301i 0.101504 + 0.225730i
\(351\) 18.6741 0.996747
\(352\) 10.8032i 0.575813i
\(353\) 35.7434i 1.90243i −0.308527 0.951216i \(-0.599836\pi\)
0.308527 0.951216i \(-0.400164\pi\)
\(354\) −2.24255 −0.119190
\(355\) −18.5112 11.9727i −0.982471 0.635442i
\(356\) −4.19761 −0.222473
\(357\) 22.0660i 1.16786i
\(358\) 3.64082i 0.192424i
\(359\) 5.76436 0.304231 0.152116 0.988363i \(-0.451391\pi\)
0.152116 + 0.988363i \(0.451391\pi\)
\(360\) −1.71868 + 2.65729i −0.0905823 + 0.140051i
\(361\) 0 0
\(362\) 9.66258i 0.507854i
\(363\) 11.1196i 0.583626i
\(364\) −16.2895 −0.853801
\(365\) −12.4069 + 19.1826i −0.649407 + 1.00406i
\(366\) −8.74084 −0.456891
\(367\) 5.95729i 0.310968i −0.987838 0.155484i \(-0.950306\pi\)
0.987838 0.155484i \(-0.0496937\pi\)
\(368\) 16.4588i 0.857974i
\(369\) −5.42170 −0.282243
\(370\) −5.25270 3.39734i −0.273075 0.176619i
\(371\) −7.93462 −0.411945
\(372\) 2.66645i 0.138249i
\(373\) 4.46841i 0.231365i −0.993286 0.115683i \(-0.963094\pi\)
0.993286 0.115683i \(-0.0369056\pi\)
\(374\) −5.67021 −0.293199
\(375\) 21.6274 + 3.30248i 1.11684 + 0.170539i
\(376\) −10.8569 −0.559902
\(377\) 24.1991i 1.24631i
\(378\) 3.93380i 0.202333i
\(379\) 13.3179 0.684095 0.342047 0.939683i \(-0.388880\pi\)
0.342047 + 0.939683i \(0.388880\pi\)
\(380\) 0 0
\(381\) −41.5553 −2.12894
\(382\) 8.80499i 0.450502i
\(383\) 10.1737i 0.519849i 0.965629 + 0.259925i \(0.0836977\pi\)
−0.965629 + 0.259925i \(0.916302\pi\)
\(384\) −21.4594 −1.09509
\(385\) 5.77092 8.92255i 0.294113 0.454735i
\(386\) −0.217208 −0.0110556
\(387\) 2.62598i 0.133486i
\(388\) 12.2545i 0.622128i
\(389\) 11.4104 0.578530 0.289265 0.957249i \(-0.406589\pi\)
0.289265 + 0.957249i \(0.406589\pi\)
\(390\) 4.69445 7.25818i 0.237712 0.367532i
\(391\) 31.8328 1.60985
\(392\) 4.69891i 0.237331i
\(393\) 3.27323i 0.165113i
\(394\) 0.567060 0.0285681
\(395\) 4.52848 + 2.92893i 0.227852 + 0.147370i
\(396\) 3.43822 0.172777
\(397\) 5.14253i 0.258096i 0.991638 + 0.129048i \(0.0411921\pi\)
−0.991638 + 0.129048i \(0.958808\pi\)
\(398\) 9.28201i 0.465265i
\(399\) 0 0
\(400\) 5.80141 + 12.9014i 0.290070 + 0.645072i
\(401\) −17.0822 −0.853043 −0.426522 0.904477i \(-0.640261\pi\)
−0.426522 + 0.904477i \(0.640261\pi\)
\(402\) 1.49727i 0.0746768i
\(403\) 3.33151i 0.165954i
\(404\) 21.9320 1.09116
\(405\) −20.2779 13.1153i −1.00762 0.651707i
\(406\) 5.09767 0.252993
\(407\) 14.3561i 0.711603i
\(408\) 18.2751i 0.904751i
\(409\) −26.0696 −1.28906 −0.644529 0.764580i \(-0.722947\pi\)
−0.644529 + 0.764580i \(0.722947\pi\)
\(410\) 3.56800 5.51656i 0.176211 0.272444i
\(411\) −33.8298 −1.66870
\(412\) 23.2305i 1.14448i
\(413\) 5.25550i 0.258606i
\(414\) 2.16780 0.106542
\(415\) 8.57657 13.2604i 0.421007 0.650929i
\(416\) 20.5951 1.00976
\(417\) 24.1211i 1.18121i
\(418\) 0 0
\(419\) −5.77281 −0.282020 −0.141010 0.990008i \(-0.545035\pi\)
−0.141010 + 0.990008i \(0.545035\pi\)
\(420\) 13.6142 + 8.80538i 0.664305 + 0.429659i
\(421\) −25.3007 −1.23308 −0.616540 0.787323i \(-0.711466\pi\)
−0.616540 + 0.787323i \(0.711466\pi\)
\(422\) 3.15099i 0.153388i
\(423\) 5.27483i 0.256471i
\(424\) 6.57146 0.319138
\(425\) −24.9526 + 11.2204i −1.21038 + 0.544272i
\(426\) 8.66960 0.420044
\(427\) 20.4845i 0.991314i
\(428\) 27.2819i 1.31872i
\(429\) −19.8372 −0.957750
\(430\) 2.67193 + 1.72815i 0.128852 + 0.0833387i
\(431\) 18.7629 0.903777 0.451888 0.892074i \(-0.350751\pi\)
0.451888 + 0.892074i \(0.350751\pi\)
\(432\) 12.0179i 0.578211i
\(433\) 8.51298i 0.409108i −0.978855 0.204554i \(-0.934426\pi\)
0.978855 0.204554i \(-0.0655743\pi\)
\(434\) −0.701802 −0.0336876
\(435\) 13.0810 20.2247i 0.627184 0.969702i
\(436\) −34.4858 −1.65157
\(437\) 0 0
\(438\) 8.98406i 0.429275i
\(439\) −2.05530 −0.0980941 −0.0490470 0.998796i \(-0.515618\pi\)
−0.0490470 + 0.998796i \(0.515618\pi\)
\(440\) −4.77948 + 7.38965i −0.227853 + 0.352288i
\(441\) −2.28296 −0.108713
\(442\) 10.8096i 0.514160i
\(443\) 12.0403i 0.572054i −0.958222 0.286027i \(-0.907665\pi\)
0.958222 0.286027i \(-0.0923347\pi\)
\(444\) −21.9048 −1.03955
\(445\) −4.38323 2.83498i −0.207785 0.134391i
\(446\) 8.73464 0.413597
\(447\) 8.52989i 0.403450i
\(448\) 7.32215i 0.345939i
\(449\) 7.49400 0.353664 0.176832 0.984241i \(-0.443415\pi\)
0.176832 + 0.984241i \(0.443415\pi\)
\(450\) −1.69926 + 0.764108i −0.0801039 + 0.0360204i
\(451\) −15.0772 −0.709959
\(452\) 3.43693i 0.161659i
\(453\) 8.70066i 0.408793i
\(454\) −2.93889 −0.137929
\(455\) −17.0098 11.0016i −0.797432 0.515763i
\(456\) 0 0
\(457\) 14.0052i 0.655137i −0.944827 0.327568i \(-0.893771\pi\)
0.944827 0.327568i \(-0.106229\pi\)
\(458\) 9.16745i 0.428367i
\(459\) 23.2437 1.08492
\(460\) 12.7028 19.6401i 0.592271 0.915722i
\(461\) −17.6751 −0.823210 −0.411605 0.911362i \(-0.635032\pi\)
−0.411605 + 0.911362i \(0.635032\pi\)
\(462\) 4.17882i 0.194416i
\(463\) 16.5926i 0.771123i −0.922682 0.385562i \(-0.874008\pi\)
0.922682 0.385562i \(-0.125992\pi\)
\(464\) 15.5736 0.722984
\(465\) −1.80087 + 2.78436i −0.0835133 + 0.129122i
\(466\) −5.41451 −0.250822
\(467\) 15.9904i 0.739949i 0.929042 + 0.369975i \(0.120634\pi\)
−0.929042 + 0.369975i \(0.879366\pi\)
\(468\) 6.55458i 0.302985i
\(469\) −3.50890 −0.162026
\(470\) −5.36712 3.47134i −0.247567 0.160121i
\(471\) −38.8300 −1.78919
\(472\) 4.35261i 0.200345i
\(473\) 7.30260i 0.335774i
\(474\) −2.12089 −0.0974155
\(475\) 0 0
\(476\) −20.2756 −0.929331
\(477\) 3.19274i 0.146186i
\(478\) 2.75241i 0.125892i
\(479\) −7.39591 −0.337928 −0.168964 0.985622i \(-0.554042\pi\)
−0.168964 + 0.985622i \(0.554042\pi\)
\(480\) −17.2127 11.1328i −0.785647 0.508140i
\(481\) 27.3682 1.24788
\(482\) 3.26833i 0.148868i
\(483\) 23.4601i 1.06747i
\(484\) −10.2173 −0.464425
\(485\) −8.27645 + 12.7964i −0.375814 + 0.581055i
\(486\) 3.77042 0.171030
\(487\) 20.1881i 0.914811i −0.889258 0.457406i \(-0.848779\pi\)
0.889258 0.457406i \(-0.151221\pi\)
\(488\) 16.9652i 0.767981i
\(489\) −2.50648 −0.113347
\(490\) 1.50241 2.32291i 0.0678720 0.104938i
\(491\) 9.33307 0.421195 0.210598 0.977573i \(-0.432459\pi\)
0.210598 + 0.977573i \(0.432459\pi\)
\(492\) 23.0051i 1.03715i
\(493\) 30.1207i 1.35657i
\(494\) 0 0
\(495\) 3.59026 + 2.32211i 0.161370 + 0.104371i
\(496\) −2.14403 −0.0962697
\(497\) 20.3175i 0.911366i
\(498\) 6.21044i 0.278297i
\(499\) 23.9612 1.07265 0.536326 0.844011i \(-0.319812\pi\)
0.536326 + 0.844011i \(0.319812\pi\)
\(500\) −3.03452 + 19.8726i −0.135708 + 0.888730i
\(501\) −15.7249 −0.702539
\(502\) 10.8688i 0.485098i
\(503\) 10.3338i 0.460763i −0.973100 0.230382i \(-0.926003\pi\)
0.973100 0.230382i \(-0.0739974\pi\)
\(504\) −2.91659 −0.129915
\(505\) 22.9018 + 14.8124i 1.01912 + 0.659144i
\(506\) 6.02844 0.267997
\(507\) 12.3785i 0.549747i
\(508\) 38.1835i 1.69412i
\(509\) 27.7116 1.22829 0.614147 0.789192i \(-0.289500\pi\)
0.614147 + 0.789192i \(0.289500\pi\)
\(510\) 5.84320 9.03430i 0.258741 0.400045i
\(511\) −21.0545 −0.931395
\(512\) 22.9115i 1.01256i
\(513\) 0 0
\(514\) −5.49940 −0.242568
\(515\) −15.6894 + 24.2577i −0.691358 + 1.06892i
\(516\) 11.1424 0.490519
\(517\) 14.6688i 0.645132i
\(518\) 5.76527i 0.253311i
\(519\) −5.20343 −0.228405
\(520\) 14.0875 + 9.11153i 0.617779 + 0.399567i
\(521\) 10.5729 0.463209 0.231604 0.972810i \(-0.425602\pi\)
0.231604 + 0.972810i \(0.425602\pi\)
\(522\) 2.05121i 0.0897788i
\(523\) 18.1596i 0.794065i −0.917805 0.397032i \(-0.870040\pi\)
0.917805 0.397032i \(-0.129960\pi\)
\(524\) −3.00765 −0.131390
\(525\) 8.26923 + 18.3895i 0.360899 + 0.802585i
\(526\) 5.56588 0.242684
\(527\) 4.14675i 0.180635i
\(528\) 12.7665i 0.555588i
\(529\) −10.8439 −0.471475
\(530\) 3.24860 + 2.10113i 0.141110 + 0.0912673i
\(531\) −2.11471 −0.0917707
\(532\) 0 0
\(533\) 28.7430i 1.24500i
\(534\) 2.05286 0.0888360
\(535\) −18.4257 + 28.4883i −0.796612 + 1.23166i
\(536\) 2.90607 0.125523
\(537\) 15.8543i 0.684165i
\(538\) 2.21936i 0.0956835i
\(539\) −6.34870 −0.273458
\(540\) 9.27533 14.3408i 0.399147 0.617129i
\(541\) 6.10507 0.262478 0.131239 0.991351i \(-0.458105\pi\)
0.131239 + 0.991351i \(0.458105\pi\)
\(542\) 3.10155i 0.133223i
\(543\) 42.0766i 1.80568i
\(544\) 25.6348 1.09908
\(545\) −36.0108 23.2910i −1.54253 0.997678i
\(546\) 7.96645 0.340933
\(547\) 10.9019i 0.466132i −0.972461 0.233066i \(-0.925124\pi\)
0.972461 0.233066i \(-0.0748759\pi\)
\(548\) 31.0849i 1.32788i
\(549\) −8.24256 −0.351784
\(550\) −4.72547 + 2.12491i −0.201495 + 0.0906064i
\(551\) 0 0
\(552\) 19.4297i 0.826981i
\(553\) 4.97037i 0.211362i
\(554\) −1.78098 −0.0756665
\(555\) −22.8734 14.7940i −0.970921 0.627972i
\(556\) −22.1639 −0.939958
\(557\) 12.2157i 0.517595i −0.965932 0.258798i \(-0.916674\pi\)
0.965932 0.258798i \(-0.0833263\pi\)
\(558\) 0.282392i 0.0119546i
\(559\) −13.9216 −0.588820
\(560\) −7.08020 + 10.9468i −0.299193 + 0.462589i
\(561\) −24.6915 −1.04247
\(562\) 14.0201i 0.591403i
\(563\) 18.3200i 0.772095i 0.922479 + 0.386048i \(0.126160\pi\)
−0.922479 + 0.386048i \(0.873840\pi\)
\(564\) −22.3819 −0.942448
\(565\) 2.32123 3.58891i 0.0976550 0.150987i
\(566\) −4.77550 −0.200729
\(567\) 22.2567i 0.934693i
\(568\) 16.8270i 0.706044i
\(569\) 32.3240 1.35509 0.677546 0.735480i \(-0.263043\pi\)
0.677546 + 0.735480i \(0.263043\pi\)
\(570\) 0 0
\(571\) −13.2641 −0.555083 −0.277542 0.960714i \(-0.589520\pi\)
−0.277542 + 0.960714i \(0.589520\pi\)
\(572\) 18.2276i 0.762136i
\(573\) 38.3422i 1.60177i
\(574\) 6.05488 0.252726
\(575\) 26.5290 11.9293i 1.10634 0.497487i
\(576\) −2.94629 −0.122762
\(577\) 21.7627i 0.905993i −0.891512 0.452996i \(-0.850355\pi\)
0.891512 0.452996i \(-0.149645\pi\)
\(578\) 5.81542i 0.241890i
\(579\) −0.945853 −0.0393083
\(580\) 18.5837 + 12.0196i 0.771647 + 0.499086i
\(581\) 14.5544 0.603818
\(582\) 5.99312i 0.248423i
\(583\) 8.87870i 0.367718i
\(584\) 17.4373 0.721561
\(585\) 4.42684 6.84442i 0.183027 0.282982i
\(586\) −8.81952 −0.364331
\(587\) 41.5762i 1.71604i −0.513620 0.858018i \(-0.671696\pi\)
0.513620 0.858018i \(-0.328304\pi\)
\(588\) 9.68697i 0.399484i
\(589\) 0 0
\(590\) 1.39168 2.15171i 0.0572947 0.0885846i
\(591\) 2.46932 0.101574
\(592\) 17.6131i 0.723893i
\(593\) 8.58712i 0.352631i −0.984334 0.176315i \(-0.943582\pi\)
0.984334 0.176315i \(-0.0564179\pi\)
\(594\) 4.40185 0.180610
\(595\) −21.1722 13.6937i −0.867975 0.561389i
\(596\) −7.83778 −0.321048
\(597\) 40.4194i 1.65426i
\(598\) 11.4925i 0.469964i
\(599\) 41.2980 1.68739 0.843696 0.536822i \(-0.180375\pi\)
0.843696 + 0.536822i \(0.180375\pi\)
\(600\) −6.84858 15.2302i −0.279592 0.621771i
\(601\) 1.60121 0.0653145 0.0326573 0.999467i \(-0.489603\pi\)
0.0326573 + 0.999467i \(0.489603\pi\)
\(602\) 2.93266i 0.119526i
\(603\) 1.41191i 0.0574975i
\(604\) −7.99470 −0.325300
\(605\) −10.6692 6.90060i −0.433763 0.280549i
\(606\) −10.7259 −0.435711
\(607\) 32.4708i 1.31795i 0.752165 + 0.658975i \(0.229010\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(608\) 0 0
\(609\) 22.1983 0.899521
\(610\) 5.42440 8.38678i 0.219628 0.339571i
\(611\) 27.9643 1.13132
\(612\) 8.15852i 0.329788i
\(613\) 13.9352i 0.562839i 0.959585 + 0.281420i \(0.0908053\pi\)
−0.959585 + 0.281420i \(0.909195\pi\)
\(614\) 10.1674 0.410325
\(615\) 15.5372 24.0224i 0.626521 0.968677i
\(616\) −8.11075 −0.326791
\(617\) 14.4224i 0.580625i 0.956932 + 0.290313i \(0.0937593\pi\)
−0.956932 + 0.290313i \(0.906241\pi\)
\(618\) 11.3610i 0.457005i
\(619\) 4.71305 0.189434 0.0947168 0.995504i \(-0.469805\pi\)
0.0947168 + 0.995504i \(0.469805\pi\)
\(620\) −2.55844 1.65475i −0.102749 0.0664563i
\(621\) −24.7122 −0.991665
\(622\) 11.1704i 0.447892i
\(623\) 4.81095i 0.192747i
\(624\) 24.3378 0.974291
\(625\) −16.5903 + 18.7019i −0.663611 + 0.748078i
\(626\) 9.97728 0.398772
\(627\) 0 0
\(628\) 35.6794i 1.42376i
\(629\) 34.0653 1.35827
\(630\) −1.44182 0.932538i −0.0574434 0.0371532i
\(631\) 3.31273 0.131878 0.0659388 0.997824i \(-0.478996\pi\)
0.0659388 + 0.997824i \(0.478996\pi\)
\(632\) 4.11646i 0.163744i
\(633\) 13.7213i 0.545372i
\(634\) 0.916530 0.0364000
\(635\) 25.7884 39.8720i 1.02338 1.58227i
\(636\) 13.5473 0.537185
\(637\) 12.1031i 0.479541i
\(638\) 5.70420i 0.225831i
\(639\) 8.17539 0.323413
\(640\) 13.3173 20.5901i 0.526412 0.813897i
\(641\) 0.0491989 0.00194324 0.000971620 1.00000i \(-0.499691\pi\)
0.000971620 1.00000i \(0.499691\pi\)
\(642\) 13.3424i 0.526581i
\(643\) 12.0003i 0.473246i −0.971602 0.236623i \(-0.923959\pi\)
0.971602 0.236623i \(-0.0760406\pi\)
\(644\) 21.5566 0.849448
\(645\) 11.6352 + 7.52539i 0.458135 + 0.296312i
\(646\) 0 0
\(647\) 36.3971i 1.43092i −0.698656 0.715458i \(-0.746218\pi\)
0.698656 0.715458i \(-0.253782\pi\)
\(648\) 18.4330i 0.724116i
\(649\) −5.88081 −0.230842
\(650\) 4.05089 + 9.00858i 0.158889 + 0.353345i
\(651\) −3.05607 −0.119777
\(652\) 2.30311i 0.0901967i
\(653\) 31.7999i 1.24443i 0.782847 + 0.622214i \(0.213767\pi\)
−0.782847 + 0.622214i \(0.786233\pi\)
\(654\) 16.8654 0.659491
\(655\) −3.14065 2.03131i −0.122715 0.0793697i
\(656\) 18.4979 0.722220
\(657\) 8.47192i 0.330521i
\(658\) 5.89085i 0.229649i
\(659\) 26.8414 1.04559 0.522796 0.852458i \(-0.324889\pi\)
0.522796 + 0.852458i \(0.324889\pi\)
\(660\) −9.85307 + 15.2340i −0.383530 + 0.592984i
\(661\) 34.2970 1.33400 0.667000 0.745057i \(-0.267578\pi\)
0.667000 + 0.745057i \(0.267578\pi\)
\(662\) 15.1225i 0.587754i
\(663\) 47.0715i 1.82810i
\(664\) −12.0540 −0.467784
\(665\) 0 0
\(666\) 2.31983 0.0898917
\(667\) 32.0236i 1.23996i
\(668\) 14.4490i 0.559050i
\(669\) 38.0358 1.47055
\(670\) 1.43662 + 0.929174i 0.0555013 + 0.0358971i
\(671\) −22.9218 −0.884885
\(672\) 18.8923i 0.728786i
\(673\) 21.7196i 0.837230i 0.908164 + 0.418615i \(0.137484\pi\)
−0.908164 + 0.418615i \(0.862516\pi\)
\(674\) −1.16332 −0.0448096
\(675\) 19.3710 8.71056i 0.745589 0.335270i
\(676\) −11.3741 −0.437465
\(677\) 8.53064i 0.327859i −0.986472 0.163930i \(-0.947583\pi\)
0.986472 0.163930i \(-0.0524170\pi\)
\(678\) 1.68085i 0.0645525i
\(679\) −14.0451 −0.539001
\(680\) 17.5348 + 11.3412i 0.672429 + 0.434914i
\(681\) −12.7977 −0.490409
\(682\) 0.785303i 0.0300708i
\(683\) 17.3190i 0.662695i −0.943509 0.331347i \(-0.892497\pi\)
0.943509 0.331347i \(-0.107503\pi\)
\(684\) 0 0
\(685\) 20.9941 32.4595i 0.802145 1.24021i
\(686\) 9.03204 0.344845
\(687\) 39.9206i 1.52306i
\(688\) 8.95938i 0.341573i
\(689\) −16.9262 −0.644838
\(690\) −6.21236 + 9.60506i −0.236500 + 0.365658i
\(691\) 17.2709 0.657014 0.328507 0.944501i \(-0.393454\pi\)
0.328507 + 0.944501i \(0.393454\pi\)
\(692\) 4.78122i 0.181755i
\(693\) 3.94061i 0.149691i
\(694\) 10.6966 0.406036
\(695\) −23.1440 14.9691i −0.877902 0.567809i
\(696\) −18.3846 −0.696868
\(697\) 35.7765i 1.35513i
\(698\) 1.11553i 0.0422234i
\(699\) −23.5780 −0.891802
\(700\) −16.8974 + 7.59827i −0.638662 + 0.287188i
\(701\) 21.8816 0.826457 0.413228 0.910627i \(-0.364401\pi\)
0.413228 + 0.910627i \(0.364401\pi\)
\(702\) 8.39162i 0.316721i
\(703\) 0 0
\(704\) −8.19336 −0.308799
\(705\) −23.3716 15.1163i −0.880227 0.569313i
\(706\) −16.0621 −0.604507
\(707\) 25.1366i 0.945360i
\(708\) 8.97305i 0.337228i
\(709\) −20.5621 −0.772224 −0.386112 0.922452i \(-0.626182\pi\)
−0.386112 + 0.922452i \(0.626182\pi\)
\(710\) −5.38019 + 8.31843i −0.201915 + 0.312185i
\(711\) −1.99998 −0.0750052
\(712\) 3.98443i 0.149323i
\(713\) 4.40873i 0.165108i
\(714\) 9.91588 0.371092
\(715\) 12.3106 19.0337i 0.460390 0.711819i
\(716\) 14.5679 0.544429
\(717\) 11.9856i 0.447612i
\(718\) 2.59035i 0.0966709i
\(719\) −15.6722 −0.584473 −0.292237 0.956346i \(-0.594400\pi\)
−0.292237 + 0.956346i \(0.594400\pi\)
\(720\) −4.40480 2.84894i −0.164157 0.106174i
\(721\) −26.6249 −0.991561
\(722\) 0 0
\(723\) 14.2323i 0.529304i
\(724\) −38.6626 −1.43688
\(725\) 11.2877 + 25.1022i 0.419215 + 0.932271i
\(726\) 4.99684 0.185450
\(727\) 43.5233i 1.61419i 0.590421 + 0.807095i \(0.298962\pi\)
−0.590421 + 0.807095i \(0.701038\pi\)
\(728\) 15.4622i 0.573068i
\(729\) −15.9815 −0.591907
\(730\) 8.62014 + 5.57533i 0.319046 + 0.206352i
\(731\) −17.3282 −0.640908
\(732\) 34.9745i 1.29269i
\(733\) 12.6904i 0.468729i −0.972149 0.234364i \(-0.924699\pi\)
0.972149 0.234364i \(-0.0753009\pi\)
\(734\) −2.67705 −0.0988116
\(735\) 6.54239 10.1153i 0.241320 0.373110i
\(736\) −27.2543 −1.00461
\(737\) 3.92639i 0.144630i
\(738\) 2.43637i 0.0896839i
\(739\) −28.1664 −1.03612 −0.518059 0.855345i \(-0.673345\pi\)
−0.518059 + 0.855345i \(0.673345\pi\)
\(740\) 13.5937 21.0175i 0.499713 0.772617i
\(741\) 0 0
\(742\) 3.56561i 0.130898i
\(743\) 25.5639i 0.937849i 0.883238 + 0.468924i \(0.155358\pi\)
−0.883238 + 0.468924i \(0.844642\pi\)
\(744\) 2.53103 0.0927922
\(745\) −8.18437 5.29348i −0.299852 0.193938i
\(746\) −2.00798 −0.0735175
\(747\) 5.85641i 0.214275i
\(748\) 22.6880i 0.829557i
\(749\) −31.2683 −1.14252
\(750\) 1.48404 9.71880i 0.0541896 0.354880i
\(751\) −34.6687 −1.26508 −0.632539 0.774529i \(-0.717987\pi\)
−0.632539 + 0.774529i \(0.717987\pi\)
\(752\) 17.9968i 0.656274i
\(753\) 47.3293i 1.72477i
\(754\) 10.8744 0.396023
\(755\) −8.34823 5.39946i −0.303823 0.196507i
\(756\) 15.7402 0.572465
\(757\) 45.7467i 1.66269i 0.555755 + 0.831346i \(0.312429\pi\)
−0.555755 + 0.831346i \(0.687571\pi\)
\(758\) 5.98471i 0.217374i
\(759\) 26.2514 0.952867
\(760\) 0 0
\(761\) 2.85442 0.103472 0.0517362 0.998661i \(-0.483524\pi\)
0.0517362 + 0.998661i \(0.483524\pi\)
\(762\) 18.6738i 0.676481i
\(763\) 39.5248i 1.43089i
\(764\) −35.2311 −1.27462
\(765\) 5.51010 8.51929i 0.199218 0.308016i
\(766\) 4.57177 0.165185
\(767\) 11.2111i 0.404809i
\(768\) 4.26233i 0.153804i
\(769\) −19.5208 −0.703937 −0.351969 0.936012i \(-0.614488\pi\)
−0.351969 + 0.936012i \(0.614488\pi\)
\(770\) −4.00955 2.59330i −0.144494 0.0934560i
\(771\) −23.9477 −0.862455
\(772\) 0.869107i 0.0312798i
\(773\) 7.24881i 0.260722i 0.991467 + 0.130361i \(0.0416136\pi\)
−0.991467 + 0.130361i \(0.958386\pi\)
\(774\) −1.18005 −0.0424159
\(775\) −1.55399 3.45584i −0.0558210 0.124138i
\(776\) 11.6322 0.417570
\(777\) 25.1054i 0.900652i
\(778\) 5.12753i 0.183831i
\(779\) 0 0
\(780\) 29.0419 + 18.7837i 1.03987 + 0.672566i
\(781\) 22.7349 0.813520
\(782\) 14.3048i 0.511539i
\(783\) 23.3830i 0.835641i
\(784\) 7.78906 0.278181
\(785\) 24.0972 37.2571i 0.860065 1.32976i
\(786\) 1.47090 0.0524654
\(787\) 4.20711i 0.149967i −0.997185 0.0749837i \(-0.976110\pi\)
0.997185 0.0749837i \(-0.0238905\pi\)
\(788\) 2.26896i 0.0808283i
\(789\) 24.2372 0.862867
\(790\) 1.31618 2.03498i 0.0468276 0.0724012i
\(791\) 3.93912 0.140059
\(792\) 3.26361i 0.115967i
\(793\) 43.6977i 1.55175i
\(794\) 2.31091 0.0820113
\(795\) 14.1464 + 9.14958i 0.501720 + 0.324502i
\(796\) −37.1398 −1.31639
\(797\) 25.6411i 0.908253i −0.890937 0.454127i \(-0.849951\pi\)
0.890937 0.454127i \(-0.150049\pi\)
\(798\) 0 0
\(799\) 34.8074 1.23140
\(800\) 21.3637 9.60663i 0.755320 0.339646i
\(801\) 1.93584 0.0683994
\(802\) 7.67627i 0.271059i
\(803\) 23.5596i 0.831399i
\(804\) 5.99096 0.211285
\(805\) 22.5098 + 14.5589i 0.793367 + 0.513133i
\(806\) −1.49709 −0.0527328
\(807\) 9.66444i 0.340204i
\(808\) 20.8181i 0.732380i
\(809\) 0.516056 0.0181436 0.00907179 0.999959i \(-0.497112\pi\)
0.00907179 + 0.999959i \(0.497112\pi\)
\(810\) −5.89369 + 9.11235i −0.207083 + 0.320176i
\(811\) 24.0377 0.844078 0.422039 0.906578i \(-0.361315\pi\)
0.422039 + 0.906578i \(0.361315\pi\)
\(812\) 20.3972i 0.715800i
\(813\) 13.5060i 0.473676i
\(814\) 6.45123 0.226115
\(815\) 1.55547 2.40495i 0.0544859 0.0842418i
\(816\) 30.2934 1.06048
\(817\) 0 0
\(818\) 11.7150i 0.409605i
\(819\) 7.51232 0.262502
\(820\) 22.0733 + 14.2765i 0.770831 + 0.498558i
\(821\) 38.7573 1.35264 0.676320 0.736608i \(-0.263574\pi\)
0.676320 + 0.736608i \(0.263574\pi\)
\(822\) 15.2022i 0.530238i
\(823\) 3.48827i 0.121593i 0.998150 + 0.0607967i \(0.0193641\pi\)
−0.998150 + 0.0607967i \(0.980636\pi\)
\(824\) 22.0507 0.768173
\(825\) −20.5775 + 9.25312i −0.716418 + 0.322152i
\(826\) 2.36168 0.0821734
\(827\) 27.4821i 0.955645i −0.878456 0.477823i \(-0.841426\pi\)
0.878456 0.477823i \(-0.158574\pi\)
\(828\) 8.67395i 0.301441i
\(829\) −8.60945 −0.299019 −0.149509 0.988760i \(-0.547769\pi\)
−0.149509 + 0.988760i \(0.547769\pi\)
\(830\) −5.95888 3.85408i −0.206836 0.133777i
\(831\) −7.75545 −0.269034
\(832\) 15.6197i 0.541516i
\(833\) 15.0648i 0.521963i
\(834\) 10.8394 0.375336
\(835\) 9.75860 15.0880i 0.337710 0.522141i
\(836\) 0 0
\(837\) 3.21917i 0.111271i
\(838\) 2.59415i 0.0896133i
\(839\) 11.9397 0.412206 0.206103 0.978530i \(-0.433922\pi\)
0.206103 + 0.978530i \(0.433922\pi\)
\(840\) 8.35820 12.9228i 0.288385 0.445879i
\(841\) 1.30126 0.0448710
\(842\) 11.3695i 0.391817i
\(843\) 61.0520i 2.10274i
\(844\) −12.6079 −0.433983
\(845\) −11.8771 7.68184i −0.408583 0.264263i
\(846\) 2.37037 0.0814949
\(847\) 11.7103i 0.402370i
\(848\) 10.8931i 0.374069i
\(849\) −20.7954 −0.713695
\(850\) 5.04217 + 11.2130i 0.172945 + 0.384603i
\(851\) −36.2175 −1.24152
\(852\) 34.6894i 1.18844i
\(853\) 28.9175i 0.990117i 0.868860 + 0.495059i \(0.164853\pi\)
−0.868860 + 0.495059i \(0.835147\pi\)
\(854\) 9.20518 0.314995
\(855\) 0 0
\(856\) 25.8964 0.885121
\(857\) 55.2147i 1.88610i −0.332651 0.943050i \(-0.607943\pi\)
0.332651 0.943050i \(-0.392057\pi\)
\(858\) 8.91431i 0.304330i
\(859\) 26.6572 0.909532 0.454766 0.890611i \(-0.349723\pi\)
0.454766 + 0.890611i \(0.349723\pi\)
\(860\) −6.91479 + 10.6911i −0.235792 + 0.364564i
\(861\) 26.3666 0.898570
\(862\) 8.43154i 0.287180i
\(863\) 1.21123i 0.0412307i 0.999787 + 0.0206154i \(0.00656254\pi\)
−0.999787 + 0.0206154i \(0.993437\pi\)
\(864\) −19.9006 −0.677031
\(865\) 3.22915 4.99265i 0.109794 0.169755i
\(866\) −3.82551 −0.129996
\(867\) 25.3238i 0.860042i
\(868\) 2.80810i 0.0953131i
\(869\) −5.56176 −0.188670
\(870\) −9.08846 5.87823i −0.308128 0.199291i
\(871\) −7.48522 −0.253627
\(872\) 32.7344i 1.10853i
\(873\) 5.65148i 0.191274i
\(874\) 0 0
\(875\) −22.7764 3.47791i −0.769981 0.117575i
\(876\) 35.9476 1.21456
\(877\) 49.5420i 1.67291i 0.548032 + 0.836457i \(0.315377\pi\)
−0.548032 + 0.836457i \(0.684623\pi\)
\(878\) 0.923597i 0.0311699i
\(879\) −38.4055 −1.29538
\(880\) −12.2493 7.92261i −0.412925 0.267071i
\(881\) −30.5639 −1.02972 −0.514861 0.857273i \(-0.672157\pi\)
−0.514861 + 0.857273i \(0.672157\pi\)
\(882\) 1.02590i 0.0345440i
\(883\) 5.57841i 0.187729i 0.995585 + 0.0938643i \(0.0299220\pi\)
−0.995585 + 0.0938643i \(0.970078\pi\)
\(884\) −43.2521 −1.45473
\(885\) 6.06023 9.36985i 0.203712 0.314964i
\(886\) −5.41061 −0.181773
\(887\) 0.666360i 0.0223742i −0.999937 0.0111871i \(-0.996439\pi\)
0.999937 0.0111871i \(-0.00356104\pi\)
\(888\) 20.7923i 0.697744i
\(889\) 43.7628 1.46776
\(890\) −1.27397 + 1.96971i −0.0427034 + 0.0660247i
\(891\) 24.9048 0.834343
\(892\) 34.9497i 1.17020i
\(893\) 0 0
\(894\) 3.83310 0.128198
\(895\) 15.2121 + 9.83889i 0.508485 + 0.328878i
\(896\) 22.5994 0.754992
\(897\) 50.0454i 1.67097i
\(898\) 3.36760i 0.112378i
\(899\) −4.17161 −0.139131
\(900\) −3.05740 6.79920i −0.101913 0.226640i
\(901\) −21.0682 −0.701882
\(902\) 6.77530i 0.225593i
\(903\) 12.7706i 0.424978i
\(904\) −3.26238 −0.108505
\(905\) −40.3723 26.1120i −1.34202 0.867991i
\(906\) 3.90984 0.129896
\(907\) 52.7812i 1.75257i 0.481792 + 0.876286i \(0.339986\pi\)
−0.481792 + 0.876286i \(0.660014\pi\)
\(908\) 11.7593i 0.390246i
\(909\) −10.1145 −0.335477
\(910\) −4.94383 + 7.64376i −0.163886 + 0.253388i
\(911\) 13.0586 0.432650 0.216325 0.976321i \(-0.430593\pi\)
0.216325 + 0.976321i \(0.430593\pi\)
\(912\) 0 0
\(913\) 16.2861i 0.538992i
\(914\) −6.29357 −0.208173
\(915\) 23.6211 36.5211i 0.780889 1.20735i
\(916\) 36.6814 1.21199
\(917\) 3.44712i 0.113834i
\(918\) 10.4451i 0.344739i
\(919\) 46.0539 1.51918 0.759589 0.650403i \(-0.225400\pi\)
0.759589 + 0.650403i \(0.225400\pi\)
\(920\) −18.6426 12.0577i −0.614629 0.397530i
\(921\) 44.2751 1.45892
\(922\) 7.94271i 0.261579i
\(923\) 43.3416i 1.42661i
\(924\) −16.7206 −0.550067
\(925\) 28.3896 12.7660i 0.933443 0.419742i
\(926\) −7.45627 −0.245028
\(927\) 10.7133i 0.351872i
\(928\) 25.7885i 0.846548i
\(929\) −30.9736 −1.01621 −0.508105 0.861295i \(-0.669654\pi\)
−0.508105 + 0.861295i \(0.669654\pi\)
\(930\) 1.25122 + 0.809262i 0.0410290 + 0.0265368i
\(931\) 0 0
\(932\) 21.6649i 0.709657i
\(933\) 48.6426i 1.59249i
\(934\) 7.18568 0.235123
\(935\) 15.3231 23.6913i 0.501118 0.774789i
\(936\) −6.22170 −0.203363
\(937\) 34.8133i 1.13730i 0.822580 + 0.568650i \(0.192534\pi\)
−0.822580 + 0.568650i \(0.807466\pi\)
\(938\) 1.57680i 0.0514845i
\(939\) 43.4470 1.41784
\(940\) 13.8898 21.4753i 0.453035 0.700447i
\(941\) 16.2153 0.528604 0.264302 0.964440i \(-0.414858\pi\)
0.264302 + 0.964440i \(0.414858\pi\)
\(942\) 17.4492i 0.568525i
\(943\) 38.0368i 1.23865i
\(944\) 7.21502 0.234829
\(945\) 16.4362 + 10.6306i 0.534670 + 0.345814i
\(946\) −3.28159 −0.106694
\(947\) 14.6403i 0.475746i −0.971296 0.237873i \(-0.923550\pi\)
0.971296 0.237873i \(-0.0764502\pi\)
\(948\) 8.48624i 0.275620i
\(949\) −44.9136 −1.45796
\(950\) 0 0
\(951\) 3.99112 0.129421
\(952\) 19.2459i 0.623763i
\(953\) 40.8271i 1.32252i −0.750156 0.661260i \(-0.770022\pi\)
0.750156 0.661260i \(-0.229978\pi\)
\(954\) −1.43473 −0.0464512
\(955\) −36.7891 23.7944i −1.19047 0.769970i
\(956\) 11.0131 0.356190
\(957\) 24.8395i 0.802947i
\(958\) 3.32352i 0.107378i
\(959\) 35.6269 1.15045
\(960\) 8.44333 13.0544i 0.272507 0.421329i
\(961\) −30.4257 −0.981474
\(962\) 12.2985i 0.396520i
\(963\) 12.5818i 0.405442i
\(964\) 13.0775 0.421197
\(965\) 0.586978 0.907539i 0.0188955 0.0292147i
\(966\) −10.5423 −0.339194
\(967\) 24.1608i 0.776958i 0.921458 + 0.388479i \(0.126999\pi\)
−0.921458 + 0.388479i \(0.873001\pi\)
\(968\) 9.69845i 0.311720i
\(969\) 0 0
\(970\) 5.75036 + 3.71922i 0.184633 + 0.119417i
\(971\) −27.7592 −0.890836 −0.445418 0.895323i \(-0.646945\pi\)
−0.445418 + 0.895323i \(0.646945\pi\)
\(972\) 15.0865i 0.483899i
\(973\) 25.4024i 0.814364i
\(974\) −9.07201 −0.290686
\(975\) 17.6400 + 39.2287i 0.564933 + 1.25633i
\(976\) 28.1221 0.900168
\(977\) 3.56499i 0.114054i −0.998373 0.0570270i \(-0.981838\pi\)
0.998373 0.0570270i \(-0.0181621\pi\)
\(978\) 1.12635i 0.0360166i
\(979\) 5.38337 0.172053
\(980\) 9.29458 + 6.01155i 0.296905 + 0.192032i
\(981\) 15.9040 0.507776
\(982\) 4.19403i 0.133837i
\(983\) 1.63550i 0.0521643i −0.999660 0.0260822i \(-0.991697\pi\)
0.999660 0.0260822i \(-0.00830315\pi\)
\(984\) −21.8368 −0.696131
\(985\) −1.53241 + 2.36929i −0.0488267 + 0.0754920i
\(986\) 13.5354 0.431056
\(987\) 25.6523i 0.816521i
\(988\) 0 0
\(989\) 18.4230 0.585818
\(990\) 1.04349 1.61337i 0.0331644 0.0512762i
\(991\) −1.50405 −0.0477778 −0.0238889 0.999715i \(-0.507605\pi\)
−0.0238889 + 0.999715i \(0.507605\pi\)
\(992\) 3.55033i 0.112723i
\(993\) 65.8526i 2.08977i
\(994\) −9.13015 −0.289591
\(995\) −38.7822 25.0835i −1.22948 0.795201i
\(996\) −24.8497 −0.787392
\(997\) 51.4138i 1.62829i −0.580660 0.814146i \(-0.697205\pi\)
0.580660 0.814146i \(-0.302795\pi\)
\(998\) 10.7675i 0.340841i
\(999\) −26.4453 −0.836692
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 1805.2.b.l.1084.10 24
5.2 odd 4 9025.2.a.ct.1.15 24
5.3 odd 4 9025.2.a.ct.1.10 24
5.4 even 2 inner 1805.2.b.l.1084.15 24
19.14 odd 18 95.2.p.a.44.5 yes 48
19.15 odd 18 95.2.p.a.54.4 yes 48
19.18 odd 2 1805.2.b.k.1084.15 24
57.14 even 18 855.2.da.b.424.4 48
57.53 even 18 855.2.da.b.244.5 48
95.14 odd 18 95.2.p.a.44.4 48
95.18 even 4 9025.2.a.cu.1.15 24
95.33 even 36 475.2.l.f.101.5 48
95.34 odd 18 95.2.p.a.54.5 yes 48
95.37 even 4 9025.2.a.cu.1.10 24
95.52 even 36 475.2.l.f.101.4 48
95.53 even 36 475.2.l.f.301.5 48
95.72 even 36 475.2.l.f.301.4 48
95.94 odd 2 1805.2.b.k.1084.10 24
285.14 even 18 855.2.da.b.424.5 48
285.224 even 18 855.2.da.b.244.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.44.4 48 95.14 odd 18
95.2.p.a.44.5 yes 48 19.14 odd 18
95.2.p.a.54.4 yes 48 19.15 odd 18
95.2.p.a.54.5 yes 48 95.34 odd 18
475.2.l.f.101.4 48 95.52 even 36
475.2.l.f.101.5 48 95.33 even 36
475.2.l.f.301.4 48 95.72 even 36
475.2.l.f.301.5 48 95.53 even 36
855.2.da.b.244.4 48 285.224 even 18
855.2.da.b.244.5 48 57.53 even 18
855.2.da.b.424.4 48 57.14 even 18
855.2.da.b.424.5 48 285.14 even 18
1805.2.b.k.1084.10 24 95.94 odd 2
1805.2.b.k.1084.15 24 19.18 odd 2
1805.2.b.l.1084.10 24 1.1 even 1 trivial
1805.2.b.l.1084.15 24 5.4 even 2 inner
9025.2.a.ct.1.10 24 5.3 odd 4
9025.2.a.ct.1.15 24 5.2 odd 4
9025.2.a.cu.1.10 24 95.37 even 4
9025.2.a.cu.1.15 24 95.18 even 4