Properties

Label 1805.2.b.l.1084.2
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 1084.2
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.l.1084.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 - 1.90301i) q^{5} -5.41794 q^{6} -1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +O(q^{10})\) \(q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 - 1.90301i) q^{5} -5.41794 q^{6} -1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +(-4.51198 - 2.78378i) q^{10} +2.72748 q^{11} +8.27553i q^{12} -6.19933i q^{13} -3.88073 q^{14} +(-4.34861 - 2.68298i) q^{15} +1.87222 q^{16} +3.12451i q^{17} +5.26771i q^{18} +(-4.25204 + 6.89175i) q^{20} -3.74021 q^{21} -6.46676i q^{22} +7.29904i q^{23} +8.78514 q^{24} +(-2.24292 - 4.46870i) q^{25} -14.6984 q^{26} -1.77838i q^{27} +5.92756i q^{28} +2.22572 q^{29} +(-6.36127 + 10.3104i) q^{30} -4.42666 q^{31} +3.25005i q^{32} -6.23260i q^{33} +7.40811 q^{34} +(-3.11480 - 1.92175i) q^{35} +8.04607 q^{36} -2.04016i q^{37} -14.1662 q^{39} +(7.31614 + 4.51388i) q^{40} -3.92482 q^{41} +8.86793i q^{42} +0.472856i q^{43} -9.87754 q^{44} +(-2.60859 + 4.22803i) q^{45} +17.3058 q^{46} -2.30160i q^{47} -4.27823i q^{48} +4.32098 q^{49} +(-10.5952 + 5.31789i) q^{50} +7.13986 q^{51} +22.4508i q^{52} +6.36387i q^{53} -4.21648 q^{54} +(3.20237 - 5.19043i) q^{55} +6.29258 q^{56} -5.27711i q^{58} +12.2661 q^{59} +(15.7484 + 9.71640i) q^{60} -4.79076 q^{61} +10.4955i q^{62} +3.63651i q^{63} +11.4502 q^{64} +(-11.7974 - 7.27871i) q^{65} -14.7773 q^{66} -0.670960i q^{67} -11.3154i q^{68} +16.6791 q^{69} +(-4.55642 + 7.38509i) q^{70} -2.63494 q^{71} -8.54155i q^{72} -6.51298i q^{73} -4.83714 q^{74} +(-10.2115 + 5.12533i) q^{75} -4.46426i q^{77} +33.5876i q^{78} +4.12016 q^{79} +(2.19819 - 3.56285i) q^{80} -10.7291 q^{81} +9.30563i q^{82} +6.42396i q^{83} +13.5452 q^{84} +(5.94598 + 3.66852i) q^{85} +1.12113 q^{86} -5.08603i q^{87} +10.4858i q^{88} +17.3044 q^{89} +(10.0245 + 6.18489i) q^{90} -10.1469 q^{91} -26.4334i q^{92} +10.1154i q^{93} -5.45702 q^{94} +7.42673 q^{96} -0.129944i q^{97} -10.2449i q^{98} -6.05979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.37097i 1.67653i −0.545265 0.838264i \(-0.683571\pi\)
0.545265 0.838264i \(-0.316429\pi\)
\(3\) 2.28512i 1.31931i −0.751567 0.659656i \(-0.770702\pi\)
0.751567 0.659656i \(-0.229298\pi\)
\(4\) −3.62149 −1.81075
\(5\) 1.17411 1.90301i 0.525079 0.851053i
\(6\) −5.41794 −2.21186
\(7\) 1.63677i 0.618642i −0.950958 0.309321i \(-0.899898\pi\)
0.950958 0.309321i \(-0.100102\pi\)
\(8\) 3.84450i 1.35924i
\(9\) −2.22176 −0.740585
\(10\) −4.51198 2.78378i −1.42681 0.880310i
\(11\) 2.72748 0.822365 0.411183 0.911553i \(-0.365116\pi\)
0.411183 + 0.911553i \(0.365116\pi\)
\(12\) 8.27553i 2.38894i
\(13\) 6.19933i 1.71938i −0.510812 0.859692i \(-0.670655\pi\)
0.510812 0.859692i \(-0.329345\pi\)
\(14\) −3.88073 −1.03717
\(15\) −4.34861 2.68298i −1.12281 0.692743i
\(16\) 1.87222 0.468054
\(17\) 3.12451i 0.757804i 0.925437 + 0.378902i \(0.123698\pi\)
−0.925437 + 0.378902i \(0.876302\pi\)
\(18\) 5.26771i 1.24161i
\(19\) 0 0
\(20\) −4.25204 + 6.89175i −0.950785 + 1.54104i
\(21\) −3.74021 −0.816182
\(22\) 6.46676i 1.37872i
\(23\) 7.29904i 1.52195i 0.648779 + 0.760977i \(0.275280\pi\)
−0.648779 + 0.760977i \(0.724720\pi\)
\(24\) 8.78514 1.79326
\(25\) −2.24292 4.46870i −0.448584 0.893741i
\(26\) −14.6984 −2.88260
\(27\) 1.77838i 0.342249i
\(28\) 5.92756i 1.12020i
\(29\) 2.22572 0.413306 0.206653 0.978414i \(-0.433743\pi\)
0.206653 + 0.978414i \(0.433743\pi\)
\(30\) −6.36127 + 10.3104i −1.16140 + 1.88241i
\(31\) −4.42666 −0.795051 −0.397526 0.917591i \(-0.630131\pi\)
−0.397526 + 0.917591i \(0.630131\pi\)
\(32\) 3.25005i 0.574532i
\(33\) 6.23260i 1.08496i
\(34\) 7.40811 1.27048
\(35\) −3.11480 1.92175i −0.526497 0.324836i
\(36\) 8.04607 1.34101
\(37\) 2.04016i 0.335400i −0.985838 0.167700i \(-0.946366\pi\)
0.985838 0.167700i \(-0.0536339\pi\)
\(38\) 0 0
\(39\) −14.1662 −2.26841
\(40\) 7.31614 + 4.51388i 1.15678 + 0.713707i
\(41\) −3.92482 −0.612954 −0.306477 0.951878i \(-0.599150\pi\)
−0.306477 + 0.951878i \(0.599150\pi\)
\(42\) 8.86793i 1.36835i
\(43\) 0.472856i 0.0721099i 0.999350 + 0.0360549i \(0.0114791\pi\)
−0.999350 + 0.0360549i \(0.988521\pi\)
\(44\) −9.87754 −1.48909
\(45\) −2.60859 + 4.22803i −0.388866 + 0.630278i
\(46\) 17.3058 2.55160
\(47\) 2.30160i 0.335723i −0.985811 0.167862i \(-0.946314\pi\)
0.985811 0.167862i \(-0.0536862\pi\)
\(48\) 4.27823i 0.617509i
\(49\) 4.32098 0.617282
\(50\) −10.5952 + 5.31789i −1.49838 + 0.752063i
\(51\) 7.13986 0.999781
\(52\) 22.4508i 3.11337i
\(53\) 6.36387i 0.874145i 0.899426 + 0.437072i \(0.143985\pi\)
−0.899426 + 0.437072i \(0.856015\pi\)
\(54\) −4.21648 −0.573790
\(55\) 3.20237 5.19043i 0.431807 0.699877i
\(56\) 6.29258 0.840881
\(57\) 0 0
\(58\) 5.27711i 0.692919i
\(59\) 12.2661 1.59691 0.798454 0.602056i \(-0.205652\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(60\) 15.7484 + 9.71640i 2.03311 + 1.25438i
\(61\) −4.79076 −0.613393 −0.306697 0.951807i \(-0.599224\pi\)
−0.306697 + 0.951807i \(0.599224\pi\)
\(62\) 10.4955i 1.33293i
\(63\) 3.63651i 0.458157i
\(64\) 11.4502 1.43127
\(65\) −11.7974 7.27871i −1.46329 0.902813i
\(66\) −14.7773 −1.81896
\(67\) 0.670960i 0.0819708i −0.999160 0.0409854i \(-0.986950\pi\)
0.999160 0.0409854i \(-0.0130497\pi\)
\(68\) 11.3154i 1.37219i
\(69\) 16.6791 2.00793
\(70\) −4.55642 + 7.38509i −0.544596 + 0.882687i
\(71\) −2.63494 −0.312710 −0.156355 0.987701i \(-0.549974\pi\)
−0.156355 + 0.987701i \(0.549974\pi\)
\(72\) 8.54155i 1.00663i
\(73\) 6.51298i 0.762287i −0.924516 0.381143i \(-0.875530\pi\)
0.924516 0.381143i \(-0.124470\pi\)
\(74\) −4.83714 −0.562307
\(75\) −10.2115 + 5.12533i −1.17912 + 0.591822i
\(76\) 0 0
\(77\) 4.46426i 0.508750i
\(78\) 33.5876i 3.80305i
\(79\) 4.12016 0.463555 0.231777 0.972769i \(-0.425546\pi\)
0.231777 + 0.972769i \(0.425546\pi\)
\(80\) 2.19819 3.56285i 0.245765 0.398339i
\(81\) −10.7291 −1.19212
\(82\) 9.30563i 1.02763i
\(83\) 6.42396i 0.705121i 0.935789 + 0.352560i \(0.114689\pi\)
−0.935789 + 0.352560i \(0.885311\pi\)
\(84\) 13.5452 1.47790
\(85\) 5.94598 + 3.66852i 0.644932 + 0.397907i
\(86\) 1.12113 0.120894
\(87\) 5.08603i 0.545280i
\(88\) 10.4858i 1.11779i
\(89\) 17.3044 1.83426 0.917130 0.398589i \(-0.130500\pi\)
0.917130 + 0.398589i \(0.130500\pi\)
\(90\) 10.0245 + 6.18489i 1.05668 + 0.651945i
\(91\) −10.1469 −1.06368
\(92\) 26.4334i 2.75587i
\(93\) 10.1154i 1.04892i
\(94\) −5.45702 −0.562849
\(95\) 0 0
\(96\) 7.42673 0.757988
\(97\) 0.129944i 0.0131938i −0.999978 0.00659689i \(-0.997900\pi\)
0.999978 0.00659689i \(-0.00209987\pi\)
\(98\) 10.2449i 1.03489i
\(99\) −6.05979 −0.609032
\(100\) 8.12271 + 16.1834i 0.812271 + 1.61834i
\(101\) 3.73547 0.371693 0.185846 0.982579i \(-0.440497\pi\)
0.185846 + 0.982579i \(0.440497\pi\)
\(102\) 16.9284i 1.67616i
\(103\) 6.59954i 0.650272i 0.945667 + 0.325136i \(0.105410\pi\)
−0.945667 + 0.325136i \(0.894590\pi\)
\(104\) 23.8333 2.33705
\(105\) −4.39143 + 7.11768i −0.428560 + 0.694614i
\(106\) 15.0885 1.46553
\(107\) 11.7953i 1.14029i −0.821543 0.570146i \(-0.806886\pi\)
0.821543 0.570146i \(-0.193114\pi\)
\(108\) 6.44038i 0.619726i
\(109\) 7.23806 0.693281 0.346640 0.937998i \(-0.387322\pi\)
0.346640 + 0.937998i \(0.387322\pi\)
\(110\) −12.3063 7.59271i −1.17336 0.723936i
\(111\) −4.66199 −0.442497
\(112\) 3.06439i 0.289558i
\(113\) 13.2879i 1.25002i −0.780616 0.625010i \(-0.785095\pi\)
0.780616 0.625010i \(-0.214905\pi\)
\(114\) 0 0
\(115\) 13.8902 + 8.56989i 1.29526 + 0.799146i
\(116\) −8.06043 −0.748392
\(117\) 13.7734i 1.27335i
\(118\) 29.0825i 2.67726i
\(119\) 5.11411 0.468809
\(120\) 10.3147 16.7182i 0.941603 1.52616i
\(121\) −3.56087 −0.323715
\(122\) 11.3587i 1.02837i
\(123\) 8.96867i 0.808678i
\(124\) 16.0311 1.43964
\(125\) −11.1374 0.978456i −0.996163 0.0875158i
\(126\) 8.62205 0.768113
\(127\) 8.69369i 0.771440i −0.922616 0.385720i \(-0.873953\pi\)
0.922616 0.385720i \(-0.126047\pi\)
\(128\) 20.6479i 1.82504i
\(129\) 1.08053 0.0951355
\(130\) −17.2576 + 27.9713i −1.51359 + 2.45324i
\(131\) 10.5459 0.921402 0.460701 0.887555i \(-0.347598\pi\)
0.460701 + 0.887555i \(0.347598\pi\)
\(132\) 22.5713i 1.96458i
\(133\) 0 0
\(134\) −1.59083 −0.137426
\(135\) −3.38428 2.08801i −0.291272 0.179708i
\(136\) −12.0122 −1.03004
\(137\) 0.397219i 0.0339367i −0.999856 0.0169683i \(-0.994599\pi\)
0.999856 0.0169683i \(-0.00540145\pi\)
\(138\) 39.5457i 3.36636i
\(139\) 7.50543 0.636602 0.318301 0.947990i \(-0.396888\pi\)
0.318301 + 0.947990i \(0.396888\pi\)
\(140\) 11.2802 + 6.95962i 0.953352 + 0.588195i
\(141\) −5.25943 −0.442924
\(142\) 6.24735i 0.524266i
\(143\) 16.9085i 1.41396i
\(144\) −4.15961 −0.346634
\(145\) 2.61325 4.23558i 0.217018 0.351745i
\(146\) −15.4421 −1.27800
\(147\) 9.87393i 0.814388i
\(148\) 7.38841i 0.607323i
\(149\) 3.68581 0.301953 0.150977 0.988537i \(-0.451758\pi\)
0.150977 + 0.988537i \(0.451758\pi\)
\(150\) 12.1520 + 24.2112i 0.992207 + 1.97683i
\(151\) 4.49051 0.365433 0.182716 0.983166i \(-0.441511\pi\)
0.182716 + 0.983166i \(0.441511\pi\)
\(152\) 0 0
\(153\) 6.94189i 0.561219i
\(154\) −10.5846 −0.852933
\(155\) −5.19740 + 8.42399i −0.417465 + 0.676631i
\(156\) 51.3027 4.10751
\(157\) 20.2651i 1.61733i 0.588266 + 0.808667i \(0.299811\pi\)
−0.588266 + 0.808667i \(0.700189\pi\)
\(158\) 9.76878i 0.777162i
\(159\) 14.5422 1.15327
\(160\) 6.18488 + 3.81592i 0.488958 + 0.301675i
\(161\) 11.9469 0.941544
\(162\) 25.4383i 1.99862i
\(163\) 15.6590i 1.22651i −0.789887 0.613253i \(-0.789861\pi\)
0.789887 0.613253i \(-0.210139\pi\)
\(164\) 14.2137 1.10990
\(165\) −11.8607 7.31778i −0.923356 0.569688i
\(166\) 15.2310 1.18215
\(167\) 6.04571i 0.467831i −0.972257 0.233915i \(-0.924846\pi\)
0.972257 0.233915i \(-0.0751539\pi\)
\(168\) 14.3793i 1.10938i
\(169\) −25.4317 −1.95628
\(170\) 8.69795 14.0977i 0.667103 1.08125i
\(171\) 0 0
\(172\) 1.71244i 0.130573i
\(173\) 1.64040i 0.124717i 0.998054 + 0.0623586i \(0.0198623\pi\)
−0.998054 + 0.0623586i \(0.980138\pi\)
\(174\) −12.0588 −0.914177
\(175\) −7.31425 + 3.67115i −0.552905 + 0.277513i
\(176\) 5.10642 0.384911
\(177\) 28.0294i 2.10682i
\(178\) 41.0281i 3.07519i
\(179\) −14.1885 −1.06050 −0.530248 0.847842i \(-0.677901\pi\)
−0.530248 + 0.847842i \(0.677901\pi\)
\(180\) 9.44699 15.3118i 0.704137 1.14127i
\(181\) −22.9459 −1.70555 −0.852776 0.522277i \(-0.825083\pi\)
−0.852776 + 0.522277i \(0.825083\pi\)
\(182\) 24.0580i 1.78329i
\(183\) 10.9474i 0.809258i
\(184\) −28.0612 −2.06870
\(185\) −3.88244 2.39537i −0.285443 0.176111i
\(186\) 23.9834 1.75855
\(187\) 8.52202i 0.623192i
\(188\) 8.33523i 0.607909i
\(189\) −2.91080 −0.211729
\(190\) 0 0
\(191\) 10.2099 0.738762 0.369381 0.929278i \(-0.379570\pi\)
0.369381 + 0.929278i \(0.379570\pi\)
\(192\) 26.1650i 1.88830i
\(193\) 11.8312i 0.851631i −0.904810 0.425816i \(-0.859987\pi\)
0.904810 0.425816i \(-0.140013\pi\)
\(194\) −0.308092 −0.0221197
\(195\) −16.6327 + 26.9584i −1.19109 + 1.93053i
\(196\) −15.6484 −1.11774
\(197\) 2.72674i 0.194273i 0.995271 + 0.0971363i \(0.0309683\pi\)
−0.995271 + 0.0971363i \(0.969032\pi\)
\(198\) 14.3676i 1.02106i
\(199\) −4.47838 −0.317464 −0.158732 0.987322i \(-0.550741\pi\)
−0.158732 + 0.987322i \(0.550741\pi\)
\(200\) 17.1799 8.62291i 1.21481 0.609732i
\(201\) −1.53322 −0.108145
\(202\) 8.85667i 0.623153i
\(203\) 3.64300i 0.255688i
\(204\) −25.8569 −1.81035
\(205\) −4.60818 + 7.46899i −0.321849 + 0.521657i
\(206\) 15.6473 1.09020
\(207\) 16.2167i 1.12714i
\(208\) 11.6065i 0.804764i
\(209\) 0 0
\(210\) 16.8758 + 10.4119i 1.16454 + 0.718493i
\(211\) 7.34023 0.505322 0.252661 0.967555i \(-0.418694\pi\)
0.252661 + 0.967555i \(0.418694\pi\)
\(212\) 23.0467i 1.58285i
\(213\) 6.02114i 0.412562i
\(214\) −27.9662 −1.91173
\(215\) 0.899852 + 0.555186i 0.0613694 + 0.0378634i
\(216\) 6.83698 0.465197
\(217\) 7.24543i 0.491852i
\(218\) 17.1612i 1.16230i
\(219\) −14.8829 −1.00569
\(220\) −11.5973 + 18.7971i −0.781892 + 1.26730i
\(221\) 19.3699 1.30296
\(222\) 11.0534i 0.741858i
\(223\) 16.5811i 1.11035i 0.831733 + 0.555176i \(0.187349\pi\)
−0.831733 + 0.555176i \(0.812651\pi\)
\(224\) 5.31958 0.355430
\(225\) 4.98322 + 9.92837i 0.332215 + 0.661891i
\(226\) −31.5052 −2.09569
\(227\) 11.7828i 0.782052i 0.920380 + 0.391026i \(0.127880\pi\)
−0.920380 + 0.391026i \(0.872120\pi\)
\(228\) 0 0
\(229\) 7.82331 0.516979 0.258490 0.966014i \(-0.416775\pi\)
0.258490 + 0.966014i \(0.416775\pi\)
\(230\) 20.3189 32.9331i 1.33979 2.17155i
\(231\) −10.2014 −0.671200
\(232\) 8.55679i 0.561781i
\(233\) 6.71975i 0.440225i −0.975474 0.220113i \(-0.929358\pi\)
0.975474 0.220113i \(-0.0706425\pi\)
\(234\) 32.6563 2.13481
\(235\) −4.37998 2.70234i −0.285718 0.176281i
\(236\) −44.4215 −2.89159
\(237\) 9.41505i 0.611573i
\(238\) 12.1254i 0.785972i
\(239\) 15.9746 1.03331 0.516654 0.856194i \(-0.327177\pi\)
0.516654 + 0.856194i \(0.327177\pi\)
\(240\) −8.14153 5.02312i −0.525533 0.324241i
\(241\) −10.4554 −0.673493 −0.336747 0.941595i \(-0.609327\pi\)
−0.336747 + 0.941595i \(0.609327\pi\)
\(242\) 8.44270i 0.542717i
\(243\) 19.1820i 1.23053i
\(244\) 17.3497 1.11070
\(245\) 5.07331 8.22288i 0.324122 0.525340i
\(246\) 21.2644 1.35577
\(247\) 0 0
\(248\) 17.0183i 1.08066i
\(249\) 14.6795 0.930275
\(250\) −2.31989 + 26.4065i −0.146723 + 1.67010i
\(251\) −11.8661 −0.748984 −0.374492 0.927230i \(-0.622183\pi\)
−0.374492 + 0.927230i \(0.622183\pi\)
\(252\) 13.1696i 0.829606i
\(253\) 19.9080i 1.25160i
\(254\) −20.6125 −1.29334
\(255\) 8.38300 13.5873i 0.524964 0.850867i
\(256\) −26.0552 −1.62845
\(257\) 3.81629i 0.238053i 0.992891 + 0.119027i \(0.0379774\pi\)
−0.992891 + 0.119027i \(0.962023\pi\)
\(258\) 2.56191i 0.159497i
\(259\) −3.33927 −0.207492
\(260\) 42.7242 + 26.3598i 2.64964 + 1.63476i
\(261\) −4.94501 −0.306088
\(262\) 25.0041i 1.54476i
\(263\) 2.11957i 0.130699i 0.997862 + 0.0653493i \(0.0208161\pi\)
−0.997862 + 0.0653493i \(0.979184\pi\)
\(264\) 23.9613 1.47471
\(265\) 12.1105 + 7.47190i 0.743944 + 0.458995i
\(266\) 0 0
\(267\) 39.5425i 2.41996i
\(268\) 2.42988i 0.148428i
\(269\) −3.92827 −0.239511 −0.119755 0.992803i \(-0.538211\pi\)
−0.119755 + 0.992803i \(0.538211\pi\)
\(270\) −4.95062 + 8.02401i −0.301285 + 0.488326i
\(271\) 18.9358 1.15027 0.575135 0.818058i \(-0.304949\pi\)
0.575135 + 0.818058i \(0.304949\pi\)
\(272\) 5.84975i 0.354693i
\(273\) 23.1868i 1.40333i
\(274\) −0.941793 −0.0568958
\(275\) −6.11751 12.1883i −0.368900 0.734982i
\(276\) −60.4034 −3.63586
\(277\) 15.0274i 0.902909i 0.892294 + 0.451454i \(0.149095\pi\)
−0.892294 + 0.451454i \(0.850905\pi\)
\(278\) 17.7951i 1.06728i
\(279\) 9.83496 0.588803
\(280\) 7.38819 11.9749i 0.441529 0.715635i
\(281\) −27.4830 −1.63950 −0.819750 0.572722i \(-0.805888\pi\)
−0.819750 + 0.572722i \(0.805888\pi\)
\(282\) 12.4699i 0.742574i
\(283\) 20.3357i 1.20883i −0.796669 0.604415i \(-0.793407\pi\)
0.796669 0.604415i \(-0.206593\pi\)
\(284\) 9.54240 0.566237
\(285\) 0 0
\(286\) −40.0896 −2.37055
\(287\) 6.42404i 0.379199i
\(288\) 7.22081i 0.425490i
\(289\) 7.23745 0.425732
\(290\) −10.0424 6.19593i −0.589711 0.363837i
\(291\) −0.296936 −0.0174067
\(292\) 23.5867i 1.38031i
\(293\) 4.58659i 0.267951i 0.990985 + 0.133976i \(0.0427744\pi\)
−0.990985 + 0.133976i \(0.957226\pi\)
\(294\) −23.4108 −1.36534
\(295\) 14.4018 23.3425i 0.838503 1.35905i
\(296\) 7.84339 0.455888
\(297\) 4.85048i 0.281454i
\(298\) 8.73893i 0.506233i
\(299\) 45.2491 2.61682
\(300\) 36.9809 18.5613i 2.13509 1.07164i
\(301\) 0.773958 0.0446102
\(302\) 10.6469i 0.612658i
\(303\) 8.53597i 0.490379i
\(304\) 0 0
\(305\) −5.62489 + 9.11687i −0.322080 + 0.522031i
\(306\) −16.4590 −0.940899
\(307\) 24.3228i 1.38818i 0.719890 + 0.694088i \(0.244192\pi\)
−0.719890 + 0.694088i \(0.755808\pi\)
\(308\) 16.1673i 0.921216i
\(309\) 15.0807 0.857911
\(310\) 19.9730 + 12.3229i 1.13439 + 0.699891i
\(311\) 22.0205 1.24867 0.624334 0.781157i \(-0.285370\pi\)
0.624334 + 0.781157i \(0.285370\pi\)
\(312\) 54.4620i 3.08330i
\(313\) 29.4817i 1.66640i 0.552969 + 0.833202i \(0.313495\pi\)
−0.552969 + 0.833202i \(0.686505\pi\)
\(314\) 48.0480 2.71151
\(315\) 6.92032 + 4.26967i 0.389916 + 0.240569i
\(316\) −14.9211 −0.839379
\(317\) 8.04314i 0.451748i −0.974157 0.225874i \(-0.927476\pi\)
0.974157 0.225874i \(-0.0725237\pi\)
\(318\) 34.4791i 1.93349i
\(319\) 6.07060 0.339889
\(320\) 13.4438 21.7899i 0.751532 1.21809i
\(321\) −26.9536 −1.50440
\(322\) 28.3256i 1.57853i
\(323\) 0 0
\(324\) 38.8552 2.15862
\(325\) −27.7030 + 13.9046i −1.53668 + 0.771288i
\(326\) −37.1269 −2.05627
\(327\) 16.5398i 0.914654i
\(328\) 15.0890i 0.833150i
\(329\) −3.76720 −0.207692
\(330\) −17.3502 + 28.1214i −0.955098 + 1.54803i
\(331\) −18.2183 −1.00137 −0.500685 0.865630i \(-0.666918\pi\)
−0.500685 + 0.865630i \(0.666918\pi\)
\(332\) 23.2643i 1.27679i
\(333\) 4.53273i 0.248392i
\(334\) −14.3342 −0.784331
\(335\) −1.27685 0.787783i −0.0697615 0.0430412i
\(336\) −7.00249 −0.382017
\(337\) 9.60328i 0.523124i 0.965187 + 0.261562i \(0.0842376\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(338\) 60.2977i 3.27976i
\(339\) −30.3644 −1.64917
\(340\) −21.5333 13.2855i −1.16781 0.720509i
\(341\) −12.0736 −0.653823
\(342\) 0 0
\(343\) 18.5299i 1.00052i
\(344\) −1.81790 −0.0980144
\(345\) 19.5832 31.7406i 1.05432 1.70886i
\(346\) 3.88934 0.209092
\(347\) 1.26627i 0.0679771i −0.999422 0.0339885i \(-0.989179\pi\)
0.999422 0.0339885i \(-0.0108210\pi\)
\(348\) 18.4190i 0.987363i
\(349\) −26.6148 −1.42466 −0.712330 0.701845i \(-0.752360\pi\)
−0.712330 + 0.701845i \(0.752360\pi\)
\(350\) 8.70418 + 17.3419i 0.465258 + 0.926961i
\(351\) −11.0247 −0.588457
\(352\) 8.86443i 0.472475i
\(353\) 26.8743i 1.43037i −0.698934 0.715187i \(-0.746342\pi\)
0.698934 0.715187i \(-0.253658\pi\)
\(354\) −66.4568 −3.53214
\(355\) −3.09371 + 5.01432i −0.164197 + 0.266133i
\(356\) −62.6676 −3.32138
\(357\) 11.6863i 0.618506i
\(358\) 33.6404i 1.77795i
\(359\) 21.0567 1.11133 0.555664 0.831407i \(-0.312464\pi\)
0.555664 + 0.831407i \(0.312464\pi\)
\(360\) −16.2547 10.0287i −0.856697 0.528561i
\(361\) 0 0
\(362\) 54.4039i 2.85940i
\(363\) 8.13699i 0.427081i
\(364\) 36.7469 1.92606
\(365\) −12.3943 7.64697i −0.648747 0.400261i
\(366\) 25.9560 1.35674
\(367\) 11.0177i 0.575118i 0.957763 + 0.287559i \(0.0928437\pi\)
−0.957763 + 0.287559i \(0.907156\pi\)
\(368\) 13.6654i 0.712356i
\(369\) 8.72000 0.453945
\(370\) −5.67935 + 9.20515i −0.295255 + 0.478553i
\(371\) 10.4162 0.540782
\(372\) 36.6329i 1.89933i
\(373\) 4.83309i 0.250248i −0.992141 0.125124i \(-0.960067\pi\)
0.992141 0.125124i \(-0.0399328\pi\)
\(374\) 20.2055 1.04480
\(375\) −2.23589 + 25.4504i −0.115461 + 1.31425i
\(376\) 8.84852 0.456327
\(377\) 13.7980i 0.710632i
\(378\) 6.90141i 0.354970i
\(379\) 2.03721 0.104644 0.0523221 0.998630i \(-0.483338\pi\)
0.0523221 + 0.998630i \(0.483338\pi\)
\(380\) 0 0
\(381\) −19.8661 −1.01777
\(382\) 24.2073i 1.23856i
\(383\) 34.5805i 1.76698i 0.468451 + 0.883489i \(0.344812\pi\)
−0.468451 + 0.883489i \(0.655188\pi\)
\(384\) −47.1829 −2.40779
\(385\) −8.49554 5.24154i −0.432973 0.267134i
\(386\) −28.0515 −1.42778
\(387\) 1.05057i 0.0534035i
\(388\) 0.470590i 0.0238906i
\(389\) 4.53021 0.229691 0.114845 0.993383i \(-0.463363\pi\)
0.114845 + 0.993383i \(0.463363\pi\)
\(390\) 63.9176 + 39.4356i 3.23659 + 1.99690i
\(391\) −22.8059 −1.15334
\(392\) 16.6120i 0.839033i
\(393\) 24.0987i 1.21562i
\(394\) 6.46503 0.325703
\(395\) 4.83754 7.84073i 0.243403 0.394510i
\(396\) 21.9455 1.10280
\(397\) 25.1348i 1.26148i 0.775995 + 0.630739i \(0.217248\pi\)
−0.775995 + 0.630739i \(0.782752\pi\)
\(398\) 10.6181i 0.532237i
\(399\) 0 0
\(400\) −4.19923 8.36637i −0.209961 0.418319i
\(401\) −28.9116 −1.44378 −0.721888 0.692010i \(-0.756725\pi\)
−0.721888 + 0.692010i \(0.756725\pi\)
\(402\) 3.63522i 0.181308i
\(403\) 27.4423i 1.36700i
\(404\) −13.5280 −0.673041
\(405\) −12.5971 + 20.4176i −0.625957 + 1.01456i
\(406\) −8.63743 −0.428669
\(407\) 5.56448i 0.275821i
\(408\) 27.4492i 1.35894i
\(409\) −22.9616 −1.13538 −0.567689 0.823243i \(-0.692163\pi\)
−0.567689 + 0.823243i \(0.692163\pi\)
\(410\) 17.7087 + 10.9259i 0.874572 + 0.539589i
\(411\) −0.907691 −0.0447731
\(412\) 23.9002i 1.17748i
\(413\) 20.0768i 0.987913i
\(414\) −38.4492 −1.88968
\(415\) 12.2249 + 7.54245i 0.600096 + 0.370244i
\(416\) 20.1481 0.987842
\(417\) 17.1508i 0.839877i
\(418\) 0 0
\(419\) −8.98058 −0.438730 −0.219365 0.975643i \(-0.570399\pi\)
−0.219365 + 0.975643i \(0.570399\pi\)
\(420\) 15.9035 25.7766i 0.776013 1.25777i
\(421\) 34.0406 1.65904 0.829519 0.558478i \(-0.188615\pi\)
0.829519 + 0.558478i \(0.188615\pi\)
\(422\) 17.4034i 0.847187i
\(423\) 5.11360i 0.248632i
\(424\) −24.4659 −1.18817
\(425\) 13.9625 7.00802i 0.677281 0.339939i
\(426\) 14.2759 0.691671
\(427\) 7.84138i 0.379471i
\(428\) 42.7165i 2.06478i
\(429\) −38.6380 −1.86546
\(430\) 1.31633 2.13352i 0.0634790 0.102887i
\(431\) −37.9730 −1.82909 −0.914547 0.404480i \(-0.867453\pi\)
−0.914547 + 0.404480i \(0.867453\pi\)
\(432\) 3.32950i 0.160191i
\(433\) 36.9800i 1.77714i −0.458738 0.888572i \(-0.651698\pi\)
0.458738 0.888572i \(-0.348302\pi\)
\(434\) 17.1787 0.824603
\(435\) −9.67878 5.97157i −0.464062 0.286315i
\(436\) −26.2126 −1.25535
\(437\) 0 0
\(438\) 35.2869i 1.68607i
\(439\) 22.1830 1.05874 0.529369 0.848392i \(-0.322429\pi\)
0.529369 + 0.848392i \(0.322429\pi\)
\(440\) 19.9546 + 12.3115i 0.951299 + 0.586928i
\(441\) −9.60016 −0.457150
\(442\) 45.9253i 2.18444i
\(443\) 9.84880i 0.467931i 0.972245 + 0.233965i \(0.0751702\pi\)
−0.972245 + 0.233965i \(0.924830\pi\)
\(444\) 16.8834 0.801249
\(445\) 20.3173 32.9304i 0.963131 1.56105i
\(446\) 39.3133 1.86154
\(447\) 8.42250i 0.398370i
\(448\) 18.7413i 0.885445i
\(449\) −37.3039 −1.76048 −0.880240 0.474528i \(-0.842619\pi\)
−0.880240 + 0.474528i \(0.842619\pi\)
\(450\) 23.5399 11.8151i 1.10968 0.556967i
\(451\) −10.7049 −0.504072
\(452\) 48.1220i 2.26347i
\(453\) 10.2613i 0.482120i
\(454\) 27.9367 1.31113
\(455\) −11.9136 + 19.3097i −0.558518 + 0.905251i
\(456\) 0 0
\(457\) 14.0343i 0.656498i 0.944591 + 0.328249i \(0.106458\pi\)
−0.944591 + 0.328249i \(0.893542\pi\)
\(458\) 18.5488i 0.866730i
\(459\) 5.55655 0.259358
\(460\) −50.3031 31.0358i −2.34539 1.44705i
\(461\) −10.1359 −0.472077 −0.236039 0.971744i \(-0.575849\pi\)
−0.236039 + 0.971744i \(0.575849\pi\)
\(462\) 24.1871i 1.12528i
\(463\) 0.722130i 0.0335602i 0.999859 + 0.0167801i \(0.00534153\pi\)
−0.999859 + 0.0167801i \(0.994658\pi\)
\(464\) 4.16703 0.193449
\(465\) 19.2498 + 11.8767i 0.892688 + 0.550767i
\(466\) −15.9323 −0.738050
\(467\) 35.0172i 1.62040i −0.586152 0.810201i \(-0.699358\pi\)
0.586152 0.810201i \(-0.300642\pi\)
\(468\) 49.8802i 2.30572i
\(469\) −1.09821 −0.0507106
\(470\) −6.40716 + 10.3848i −0.295540 + 0.479015i
\(471\) 46.3082 2.13377
\(472\) 47.1570i 2.17058i
\(473\) 1.28970i 0.0593007i
\(474\) −22.3228 −1.02532
\(475\) 0 0
\(476\) −18.5207 −0.848895
\(477\) 14.1390i 0.647379i
\(478\) 37.8752i 1.73237i
\(479\) 26.9601 1.23184 0.615920 0.787809i \(-0.288784\pi\)
0.615920 + 0.787809i \(0.288784\pi\)
\(480\) 8.71982 14.1332i 0.398003 0.645088i
\(481\) −12.6476 −0.576681
\(482\) 24.7895i 1.12913i
\(483\) 27.3000i 1.24219i
\(484\) 12.8956 0.586166
\(485\) −0.247285 0.152569i −0.0112286 0.00692778i
\(486\) 45.4800 2.06301
\(487\) 3.06758i 0.139005i −0.997582 0.0695026i \(-0.977859\pi\)
0.997582 0.0695026i \(-0.0221412\pi\)
\(488\) 18.4181i 0.833747i
\(489\) −35.7826 −1.61814
\(490\) −19.4962 12.0287i −0.880748 0.543400i
\(491\) 1.24888 0.0563613 0.0281806 0.999603i \(-0.491029\pi\)
0.0281806 + 0.999603i \(0.491029\pi\)
\(492\) 32.4800i 1.46431i
\(493\) 6.95428i 0.313205i
\(494\) 0 0
\(495\) −7.11488 + 11.5319i −0.319790 + 0.518319i
\(496\) −8.28766 −0.372127
\(497\) 4.31279i 0.193455i
\(498\) 34.8046i 1.55963i
\(499\) −19.5720 −0.876165 −0.438083 0.898935i \(-0.644342\pi\)
−0.438083 + 0.898935i \(0.644342\pi\)
\(500\) 40.3341 + 3.54347i 1.80380 + 0.158469i
\(501\) −13.8151 −0.617215
\(502\) 28.1342i 1.25569i
\(503\) 5.11859i 0.228227i 0.993468 + 0.114113i \(0.0364027\pi\)
−0.993468 + 0.114113i \(0.963597\pi\)
\(504\) −13.9806 −0.622744
\(505\) 4.38586 7.10864i 0.195168 0.316330i
\(506\) 47.2011 2.09835
\(507\) 58.1144i 2.58095i
\(508\) 31.4841i 1.39688i
\(509\) −15.8349 −0.701871 −0.350935 0.936400i \(-0.614136\pi\)
−0.350935 + 0.936400i \(0.614136\pi\)
\(510\) −32.2150 19.8758i −1.42650 0.880117i
\(511\) −10.6603 −0.471582
\(512\) 20.4803i 0.905108i
\(513\) 0 0
\(514\) 9.04830 0.399103
\(515\) 12.5590 + 7.74860i 0.553416 + 0.341444i
\(516\) −3.91313 −0.172266
\(517\) 6.27757i 0.276087i
\(518\) 7.91730i 0.347866i
\(519\) 3.74850 0.164541
\(520\) 27.9830 45.3552i 1.22714 1.98896i
\(521\) 29.9732 1.31315 0.656575 0.754261i \(-0.272004\pi\)
0.656575 + 0.754261i \(0.272004\pi\)
\(522\) 11.7245i 0.513166i
\(523\) 30.3765i 1.32827i 0.747611 + 0.664136i \(0.231201\pi\)
−0.747611 + 0.664136i \(0.768799\pi\)
\(524\) −38.1920 −1.66843
\(525\) 8.38900 + 16.7139i 0.366126 + 0.729455i
\(526\) 5.02544 0.219120
\(527\) 13.8311i 0.602493i
\(528\) 11.6688i 0.507818i
\(529\) −30.2759 −1.31635
\(530\) 17.7156 28.7137i 0.769518 1.24724i
\(531\) −27.2522 −1.18265
\(532\) 0 0
\(533\) 24.3313i 1.05390i
\(534\) −93.7540 −4.05713
\(535\) −22.4466 13.8490i −0.970450 0.598744i
\(536\) 2.57951 0.111418
\(537\) 32.4223i 1.39913i
\(538\) 9.31380i 0.401546i
\(539\) 11.7854 0.507632
\(540\) 12.2561 + 7.56173i 0.527420 + 0.325405i
\(541\) −23.8593 −1.02579 −0.512895 0.858451i \(-0.671427\pi\)
−0.512895 + 0.858451i \(0.671427\pi\)
\(542\) 44.8963i 1.92846i
\(543\) 52.4339i 2.25016i
\(544\) −10.1548 −0.435383
\(545\) 8.49830 13.7741i 0.364027 0.590019i
\(546\) 54.9752 2.35272
\(547\) 13.7402i 0.587489i 0.955884 + 0.293745i \(0.0949015\pi\)
−0.955884 + 0.293745i \(0.905098\pi\)
\(548\) 1.43852i 0.0614507i
\(549\) 10.6439 0.454270
\(550\) −28.8980 + 14.5044i −1.23222 + 0.618471i
\(551\) 0 0
\(552\) 64.1230i 2.72926i
\(553\) 6.74377i 0.286774i
\(554\) 35.6295 1.51375
\(555\) −5.47370 + 8.87183i −0.232346 + 0.376588i
\(556\) −27.1808 −1.15272
\(557\) 27.0314i 1.14536i −0.819780 0.572679i \(-0.805904\pi\)
0.819780 0.572679i \(-0.194096\pi\)
\(558\) 23.3184i 0.987145i
\(559\) 2.93139 0.123985
\(560\) −5.83157 3.59794i −0.246429 0.152041i
\(561\) 19.4738 0.822185
\(562\) 65.1614i 2.74867i
\(563\) 38.1678i 1.60858i 0.594237 + 0.804290i \(0.297454\pi\)
−0.594237 + 0.804290i \(0.702546\pi\)
\(564\) 19.0470 0.802022
\(565\) −25.2871 15.6015i −1.06383 0.656360i
\(566\) −48.2153 −2.02664
\(567\) 17.5610i 0.737494i
\(568\) 10.1300i 0.425046i
\(569\) 2.28061 0.0956082 0.0478041 0.998857i \(-0.484778\pi\)
0.0478041 + 0.998857i \(0.484778\pi\)
\(570\) 0 0
\(571\) −14.4656 −0.605367 −0.302683 0.953091i \(-0.597883\pi\)
−0.302683 + 0.953091i \(0.597883\pi\)
\(572\) 61.2341i 2.56033i
\(573\) 23.3308i 0.974658i
\(574\) 15.2312 0.635738
\(575\) 32.6172 16.3712i 1.36023 0.682724i
\(576\) −25.4395 −1.05998
\(577\) 8.17830i 0.340467i 0.985404 + 0.170234i \(0.0544522\pi\)
−0.985404 + 0.170234i \(0.945548\pi\)
\(578\) 17.1598i 0.713752i
\(579\) −27.0358 −1.12357
\(580\) −9.46385 + 15.3391i −0.392965 + 0.636922i
\(581\) 10.5146 0.436217
\(582\) 0.704027i 0.0291829i
\(583\) 17.3573i 0.718867i
\(584\) 25.0392 1.03613
\(585\) 26.2110 + 16.1715i 1.08369 + 0.668610i
\(586\) 10.8746 0.449228
\(587\) 34.4354i 1.42130i 0.703544 + 0.710651i \(0.251600\pi\)
−0.703544 + 0.710651i \(0.748400\pi\)
\(588\) 35.7584i 1.47465i
\(589\) 0 0
\(590\) −55.3443 34.1461i −2.27849 1.40577i
\(591\) 6.23093 0.256306
\(592\) 3.81961i 0.156985i
\(593\) 2.65119i 0.108871i 0.998517 + 0.0544357i \(0.0173360\pi\)
−0.998517 + 0.0544357i \(0.982664\pi\)
\(594\) −11.5003 −0.471865
\(595\) 6.00454 9.73221i 0.246162 0.398982i
\(596\) −13.3481 −0.546760
\(597\) 10.2336i 0.418834i
\(598\) 107.284i 4.38718i
\(599\) −2.45464 −0.100294 −0.0501469 0.998742i \(-0.515969\pi\)
−0.0501469 + 0.998742i \(0.515969\pi\)
\(600\) −19.7044 39.2582i −0.804427 1.60271i
\(601\) −14.9631 −0.610356 −0.305178 0.952295i \(-0.598716\pi\)
−0.305178 + 0.952295i \(0.598716\pi\)
\(602\) 1.83503i 0.0747902i
\(603\) 1.49071i 0.0607064i
\(604\) −16.2623 −0.661705
\(605\) −4.18086 + 6.77638i −0.169976 + 0.275499i
\(606\) −20.2385 −0.822134
\(607\) 43.0431i 1.74706i −0.486767 0.873532i \(-0.661824\pi\)
0.486767 0.873532i \(-0.338176\pi\)
\(608\) 0 0
\(609\) −8.32467 −0.337333
\(610\) 21.6158 + 13.3364i 0.875199 + 0.539976i
\(611\) −14.2684 −0.577237
\(612\) 25.1400i 1.01622i
\(613\) 39.1922i 1.58296i −0.611198 0.791478i \(-0.709312\pi\)
0.611198 0.791478i \(-0.290688\pi\)
\(614\) 57.6686 2.32732
\(615\) 17.0675 + 10.5302i 0.688228 + 0.424620i
\(616\) 17.1629 0.691511
\(617\) 27.9028i 1.12332i −0.827367 0.561662i \(-0.810162\pi\)
0.827367 0.561662i \(-0.189838\pi\)
\(618\) 35.7559i 1.43831i
\(619\) 24.8596 0.999193 0.499597 0.866258i \(-0.333482\pi\)
0.499597 + 0.866258i \(0.333482\pi\)
\(620\) 18.8223 30.5074i 0.755923 1.22521i
\(621\) 12.9804 0.520887
\(622\) 52.2099i 2.09343i
\(623\) 28.3233i 1.13475i
\(624\) −26.5222 −1.06174
\(625\) −14.9386 + 20.0459i −0.597545 + 0.801835i
\(626\) 69.9001 2.79377
\(627\) 0 0
\(628\) 73.3901i 2.92858i
\(629\) 6.37448 0.254167
\(630\) 10.1233 16.4079i 0.403320 0.653705i
\(631\) 44.2670 1.76224 0.881120 0.472893i \(-0.156790\pi\)
0.881120 + 0.472893i \(0.156790\pi\)
\(632\) 15.8400i 0.630081i
\(633\) 16.7733i 0.666678i
\(634\) −19.0700 −0.757368
\(635\) −16.5442 10.2074i −0.656537 0.405067i
\(636\) −52.6644 −2.08828
\(637\) 26.7872i 1.06135i
\(638\) 14.3932i 0.569833i
\(639\) 5.85419 0.231588
\(640\) −39.2933 24.2430i −1.55320 0.958289i
\(641\) −20.3402 −0.803389 −0.401695 0.915774i \(-0.631579\pi\)
−0.401695 + 0.915774i \(0.631579\pi\)
\(642\) 63.9061i 2.52217i
\(643\) 30.3707i 1.19770i −0.800860 0.598852i \(-0.795624\pi\)
0.800860 0.598852i \(-0.204376\pi\)
\(644\) −43.2654 −1.70490
\(645\) 1.26867 2.05627i 0.0499536 0.0809654i
\(646\) 0 0
\(647\) 48.5913i 1.91032i −0.296087 0.955161i \(-0.595682\pi\)
0.296087 0.955161i \(-0.404318\pi\)
\(648\) 41.2479i 1.62037i
\(649\) 33.4554 1.31324
\(650\) 32.9674 + 65.6829i 1.29309 + 2.57629i
\(651\) 16.5567 0.648906
\(652\) 56.7088i 2.22089i
\(653\) 19.9555i 0.780918i 0.920620 + 0.390459i \(0.127684\pi\)
−0.920620 + 0.390459i \(0.872316\pi\)
\(654\) −39.2154 −1.53344
\(655\) 12.3821 20.0690i 0.483809 0.784163i
\(656\) −7.34811 −0.286895
\(657\) 14.4703i 0.564539i
\(658\) 8.93191i 0.348202i
\(659\) −17.0285 −0.663335 −0.331667 0.943396i \(-0.607611\pi\)
−0.331667 + 0.943396i \(0.607611\pi\)
\(660\) 42.9535 + 26.5013i 1.67196 + 1.03156i
\(661\) 27.5335 1.07093 0.535464 0.844558i \(-0.320137\pi\)
0.535464 + 0.844558i \(0.320137\pi\)
\(662\) 43.1951i 1.67882i
\(663\) 44.2624i 1.71901i
\(664\) −24.6969 −0.958427
\(665\) 0 0
\(666\) 10.7470 0.416436
\(667\) 16.2456i 0.629033i
\(668\) 21.8945i 0.847122i
\(669\) 37.8897 1.46490
\(670\) −1.86781 + 3.02736i −0.0721597 + 0.116957i
\(671\) −13.0667 −0.504434
\(672\) 12.1559i 0.468923i
\(673\) 37.2560i 1.43611i −0.695984 0.718057i \(-0.745032\pi\)
0.695984 0.718057i \(-0.254968\pi\)
\(674\) 22.7691 0.877032
\(675\) −7.94704 + 3.98876i −0.305882 + 0.153527i
\(676\) 92.1006 3.54233
\(677\) 22.7880i 0.875815i −0.899020 0.437907i \(-0.855720\pi\)
0.899020 0.437907i \(-0.144280\pi\)
\(678\) 71.9930i 2.76488i
\(679\) −0.212688 −0.00816223
\(680\) −14.1037 + 22.8593i −0.540850 + 0.876616i
\(681\) 26.9251 1.03177
\(682\) 28.6262i 1.09615i
\(683\) 4.61408i 0.176553i −0.996096 0.0882764i \(-0.971864\pi\)
0.996096 0.0882764i \(-0.0281359\pi\)
\(684\) 0 0
\(685\) −0.755912 0.466379i −0.0288819 0.0178194i
\(686\) −43.9337 −1.67740
\(687\) 17.8772i 0.682057i
\(688\) 0.885288i 0.0337513i
\(689\) 39.4517 1.50299
\(690\) −75.2561 46.4311i −2.86495 1.76760i
\(691\) 35.7599 1.36037 0.680186 0.733040i \(-0.261899\pi\)
0.680186 + 0.733040i \(0.261899\pi\)
\(692\) 5.94069i 0.225831i
\(693\) 9.91850i 0.376773i
\(694\) −3.00229 −0.113965
\(695\) 8.81222 14.2829i 0.334267 0.541783i
\(696\) 19.5533 0.741165
\(697\) 12.2631i 0.464499i
\(698\) 63.1030i 2.38848i
\(699\) −15.3554 −0.580795
\(700\) 26.4885 13.2950i 1.00117 0.502505i
\(701\) 32.8766 1.24173 0.620865 0.783917i \(-0.286781\pi\)
0.620865 + 0.783917i \(0.286781\pi\)
\(702\) 26.1393i 0.986565i
\(703\) 0 0
\(704\) 31.2301 1.17703
\(705\) −6.17516 + 10.0088i −0.232570 + 0.376952i
\(706\) −63.7180 −2.39806
\(707\) 6.11411i 0.229945i
\(708\) 101.508i 3.81491i
\(709\) −44.4229 −1.66834 −0.834169 0.551510i \(-0.814052\pi\)
−0.834169 + 0.551510i \(0.814052\pi\)
\(710\) 11.8888 + 7.33510i 0.446179 + 0.275281i
\(711\) −9.15400 −0.343302
\(712\) 66.5267i 2.49319i
\(713\) 32.3103i 1.21003i
\(714\) −27.7079 −1.03694
\(715\) −32.1772 19.8525i −1.20336 0.742442i
\(716\) 51.3834 1.92029
\(717\) 36.5037i 1.36326i
\(718\) 49.9247i 1.86317i
\(719\) 20.0859 0.749079 0.374540 0.927211i \(-0.377801\pi\)
0.374540 + 0.927211i \(0.377801\pi\)
\(720\) −4.88385 + 7.91579i −0.182010 + 0.295004i
\(721\) 10.8019 0.402285
\(722\) 0 0
\(723\) 23.8919i 0.888548i
\(724\) 83.0982 3.08832
\(725\) −4.99211 9.94609i −0.185402 0.369388i
\(726\) 19.2926 0.716014
\(727\) 0.729793i 0.0270665i −0.999908 0.0135333i \(-0.995692\pi\)
0.999908 0.0135333i \(-0.00430790\pi\)
\(728\) 39.0098i 1.44580i
\(729\) 11.6460 0.431333
\(730\) −18.1307 + 29.3865i −0.671049 + 1.08764i
\(731\) −1.47744 −0.0546452
\(732\) 39.6460i 1.46536i
\(733\) 29.4948i 1.08941i 0.838626 + 0.544707i \(0.183359\pi\)
−0.838626 + 0.544707i \(0.816641\pi\)
\(734\) 26.1226 0.964201
\(735\) −18.7902 11.5931i −0.693088 0.427618i
\(736\) −23.7222 −0.874412
\(737\) 1.83003i 0.0674100i
\(738\) 20.6748i 0.761051i
\(739\) 40.4996 1.48980 0.744901 0.667175i \(-0.232497\pi\)
0.744901 + 0.667175i \(0.232497\pi\)
\(740\) 14.0602 + 8.67482i 0.516864 + 0.318893i
\(741\) 0 0
\(742\) 24.6965i 0.906637i
\(743\) 19.4337i 0.712955i −0.934304 0.356477i \(-0.883978\pi\)
0.934304 0.356477i \(-0.116022\pi\)
\(744\) −38.8888 −1.42573
\(745\) 4.32755 7.01414i 0.158549 0.256978i
\(746\) −11.4591 −0.419547
\(747\) 14.2725i 0.522202i
\(748\) 30.8624i 1.12844i
\(749\) −19.3062 −0.705433
\(750\) 60.3420 + 5.30122i 2.20338 + 0.193573i
\(751\) −5.66378 −0.206674 −0.103337 0.994646i \(-0.532952\pi\)
−0.103337 + 0.994646i \(0.532952\pi\)
\(752\) 4.30909i 0.157136i
\(753\) 27.1155i 0.988144i
\(754\) −32.7146 −1.19139
\(755\) 5.27236 8.54550i 0.191881 0.311003i
\(756\) 10.5414 0.383388
\(757\) 12.5786i 0.457176i −0.973523 0.228588i \(-0.926589\pi\)
0.973523 0.228588i \(-0.0734109\pi\)
\(758\) 4.83015i 0.175439i
\(759\) 45.4920 1.65126
\(760\) 0 0
\(761\) 50.0335 1.81371 0.906857 0.421439i \(-0.138475\pi\)
0.906857 + 0.421439i \(0.138475\pi\)
\(762\) 47.1019i 1.70632i
\(763\) 11.8471i 0.428892i
\(764\) −36.9750 −1.33771
\(765\) −13.2105 8.15057i −0.477627 0.294684i
\(766\) 81.9892 2.96239
\(767\) 76.0414i 2.74570i
\(768\) 59.5392i 2.14844i
\(769\) 31.7447 1.14474 0.572371 0.819994i \(-0.306024\pi\)
0.572371 + 0.819994i \(0.306024\pi\)
\(770\) −12.4275 + 20.1427i −0.447857 + 0.725891i
\(771\) 8.72066 0.314067
\(772\) 42.8467i 1.54209i
\(773\) 11.4374i 0.411373i −0.978618 0.205687i \(-0.934057\pi\)
0.978618 0.205687i \(-0.0659428\pi\)
\(774\) −2.49087 −0.0895325
\(775\) 9.92864 + 19.7814i 0.356647 + 0.710570i
\(776\) 0.499569 0.0179335
\(777\) 7.63062i 0.273747i
\(778\) 10.7410i 0.385083i
\(779\) 0 0
\(780\) 60.2352 97.6298i 2.15677 3.49571i
\(781\) −7.18673 −0.257162
\(782\) 54.0721i 1.93361i
\(783\) 3.95817i 0.141453i
\(784\) 8.08980 0.288921
\(785\) 38.5648 + 23.7936i 1.37644 + 0.849229i
\(786\) −57.1372 −2.03802
\(787\) 6.64024i 0.236699i 0.992972 + 0.118350i \(0.0377603\pi\)
−0.992972 + 0.118350i \(0.962240\pi\)
\(788\) 9.87488i 0.351778i
\(789\) 4.84347 0.172432
\(790\) −18.5901 11.4696i −0.661407 0.408072i
\(791\) −21.7493 −0.773315
\(792\) 23.2969i 0.827819i
\(793\) 29.6995i 1.05466i
\(794\) 59.5938 2.11490
\(795\) 17.0742 27.6740i 0.605558 0.981495i
\(796\) 16.2184 0.574847
\(797\) 0.186468i 0.00660502i −0.999995 0.00330251i \(-0.998949\pi\)
0.999995 0.00330251i \(-0.00105122\pi\)
\(798\) 0 0
\(799\) 7.19137 0.254412
\(800\) 14.5235 7.28959i 0.513483 0.257726i
\(801\) −38.4461 −1.35843
\(802\) 68.5485i 2.42053i
\(803\) 17.7640i 0.626878i
\(804\) 5.55255 0.195823
\(805\) 14.0270 22.7350i 0.494385 0.801305i
\(806\) 65.0649 2.29181
\(807\) 8.97655i 0.315989i
\(808\) 14.3610i 0.505219i
\(809\) −1.21997 −0.0428918 −0.0214459 0.999770i \(-0.506827\pi\)
−0.0214459 + 0.999770i \(0.506827\pi\)
\(810\) 48.4094 + 29.8674i 1.70093 + 1.04943i
\(811\) 19.0938 0.670474 0.335237 0.942134i \(-0.391184\pi\)
0.335237 + 0.942134i \(0.391184\pi\)
\(812\) 13.1931i 0.462986i
\(813\) 43.2706i 1.51757i
\(814\) −13.1932 −0.462422
\(815\) −29.7992 18.3854i −1.04382 0.644012i
\(816\) 13.3674 0.467951
\(817\) 0 0
\(818\) 54.4413i 1.90349i
\(819\) 22.5439 0.787748
\(820\) 16.6885 27.0489i 0.582787 0.944587i
\(821\) −9.97729 −0.348210 −0.174105 0.984727i \(-0.555703\pi\)
−0.174105 + 0.984727i \(0.555703\pi\)
\(822\) 2.15211i 0.0750633i
\(823\) 28.2077i 0.983260i −0.870804 0.491630i \(-0.836401\pi\)
0.870804 0.491630i \(-0.163599\pi\)
\(824\) −25.3719 −0.883873
\(825\) −27.8517 + 13.9792i −0.969670 + 0.486694i
\(826\) −47.6014 −1.65626
\(827\) 8.85297i 0.307848i 0.988083 + 0.153924i \(0.0491911\pi\)
−0.988083 + 0.153924i \(0.950809\pi\)
\(828\) 58.7286i 2.04096i
\(829\) 45.6892 1.58685 0.793425 0.608668i \(-0.208296\pi\)
0.793425 + 0.608668i \(0.208296\pi\)
\(830\) 17.8829 28.9848i 0.620725 1.00608i
\(831\) 34.3393 1.19122
\(832\) 70.9835i 2.46091i
\(833\) 13.5009i 0.467779i
\(834\) −40.6640 −1.40808
\(835\) −11.5051 7.09834i −0.398149 0.245648i
\(836\) 0 0
\(837\) 7.87227i 0.272105i
\(838\) 21.2927i 0.735543i
\(839\) 0.182558 0.00630259 0.00315130 0.999995i \(-0.498997\pi\)
0.00315130 + 0.999995i \(0.498997\pi\)
\(840\) −27.3639 16.8829i −0.944146 0.582515i
\(841\) −24.0462 −0.829178
\(842\) 80.7092i 2.78142i
\(843\) 62.8019i 2.16301i
\(844\) −26.5826 −0.915010
\(845\) −29.8597 + 48.3968i −1.02720 + 1.66490i
\(846\) 12.1242 0.416838
\(847\) 5.82833i 0.200264i
\(848\) 11.9145i 0.409147i
\(849\) −46.4694 −1.59483
\(850\) −16.6158 33.1046i −0.569917 1.13548i
\(851\) 14.8912 0.510463
\(852\) 21.8055i 0.747044i
\(853\) 49.2184i 1.68520i 0.538537 + 0.842602i \(0.318977\pi\)
−0.538537 + 0.842602i \(0.681023\pi\)
\(854\) 18.5917 0.636193
\(855\) 0 0
\(856\) 45.3470 1.54993
\(857\) 31.5699i 1.07841i −0.842175 0.539204i \(-0.818725\pi\)
0.842175 0.539204i \(-0.181275\pi\)
\(858\) 91.6094i 3.12749i
\(859\) 10.6896 0.364723 0.182362 0.983232i \(-0.441626\pi\)
0.182362 + 0.983232i \(0.441626\pi\)
\(860\) −3.25880 2.01060i −0.111124 0.0685610i
\(861\) 14.6797 0.500282
\(862\) 90.0327i 3.06653i
\(863\) 25.5826i 0.870841i 0.900227 + 0.435420i \(0.143400\pi\)
−0.900227 + 0.435420i \(0.856600\pi\)
\(864\) 5.77981 0.196633
\(865\) 3.12170 + 1.92601i 0.106141 + 0.0654864i
\(866\) −87.6783 −2.97943
\(867\) 16.5384i 0.561674i
\(868\) 26.2393i 0.890619i
\(869\) 11.2377 0.381211
\(870\) −14.1584 + 22.9481i −0.480015 + 0.778013i
\(871\) −4.15950 −0.140939
\(872\) 27.8268i 0.942333i
\(873\) 0.288703i 0.00977113i
\(874\) 0 0
\(875\) −1.60151 + 18.2295i −0.0541409 + 0.616268i
\(876\) 53.8984 1.82106
\(877\) 31.0952i 1.05001i 0.851099 + 0.525005i \(0.175937\pi\)
−0.851099 + 0.525005i \(0.824063\pi\)
\(878\) 52.5953i 1.77500i
\(879\) 10.4809 0.353511
\(880\) 5.99552 9.71759i 0.202109 0.327580i
\(881\) −47.4465 −1.59851 −0.799257 0.600990i \(-0.794773\pi\)
−0.799257 + 0.600990i \(0.794773\pi\)
\(882\) 22.7617i 0.766425i
\(883\) 14.5332i 0.489082i −0.969639 0.244541i \(-0.921363\pi\)
0.969639 0.244541i \(-0.0786372\pi\)
\(884\) −70.1477 −2.35932
\(885\) −53.3403 32.9097i −1.79302 1.10625i
\(886\) 23.3512 0.784498
\(887\) 37.1270i 1.24660i 0.781982 + 0.623301i \(0.214209\pi\)
−0.781982 + 0.623301i \(0.785791\pi\)
\(888\) 17.9230i 0.601458i
\(889\) −14.2296 −0.477245
\(890\) −78.0770 48.1716i −2.61715 1.61472i
\(891\) −29.2633 −0.980357
\(892\) 60.0483i 2.01057i
\(893\) 0 0
\(894\) −19.9695 −0.667879
\(895\) −16.6589 + 27.0009i −0.556845 + 0.902539i
\(896\) −33.7960 −1.12904
\(897\) 103.400i 3.45241i
\(898\) 88.4464i 2.95150i
\(899\) −9.85251 −0.328600
\(900\) −18.0467 35.9555i −0.601556 1.19852i
\(901\) −19.8840 −0.662431
\(902\) 25.3809i 0.845091i
\(903\) 1.76858i 0.0588548i
\(904\) 51.0854 1.69907
\(905\) −26.9410 + 43.6663i −0.895550 + 1.45152i
\(906\) −24.3293 −0.808287
\(907\) 10.8657i 0.360789i −0.983594 0.180394i \(-0.942263\pi\)
0.983594 0.180394i \(-0.0577374\pi\)
\(908\) 42.6713i 1.41610i
\(909\) −8.29929 −0.275270
\(910\) 45.7826 + 28.2467i 1.51768 + 0.936371i
\(911\) 39.5522 1.31042 0.655211 0.755446i \(-0.272580\pi\)
0.655211 + 0.755446i \(0.272580\pi\)
\(912\) 0 0
\(913\) 17.5212i 0.579867i
\(914\) 33.2749 1.10064
\(915\) 20.8331 + 12.8535i 0.688722 + 0.424924i
\(916\) −28.3321 −0.936117
\(917\) 17.2613i 0.570018i
\(918\) 13.1744i 0.434820i
\(919\) −32.1565 −1.06074 −0.530372 0.847765i \(-0.677948\pi\)
−0.530372 + 0.847765i \(0.677948\pi\)
\(920\) −32.9470 + 53.4008i −1.08623 + 1.76057i
\(921\) 55.5805 1.83144
\(922\) 24.0320i 0.791451i
\(923\) 16.3348i 0.537668i
\(924\) 36.9441 1.21537
\(925\) −9.11685 + 4.57590i −0.299760 + 0.150455i
\(926\) 1.71215 0.0562647
\(927\) 14.6626i 0.481582i
\(928\) 7.23369i 0.237458i
\(929\) 10.9336 0.358719 0.179359 0.983784i \(-0.442598\pi\)
0.179359 + 0.983784i \(0.442598\pi\)
\(930\) 28.1592 45.6407i 0.923376 1.49662i
\(931\) 0 0
\(932\) 24.3355i 0.797136i
\(933\) 50.3194i 1.64738i
\(934\) −83.0247 −2.71665
\(935\) 16.2175 + 10.0058i 0.530370 + 0.327225i
\(936\) −52.9519 −1.73079
\(937\) 45.0301i 1.47107i −0.677487 0.735535i \(-0.736931\pi\)
0.677487 0.735535i \(-0.263069\pi\)
\(938\) 2.60382i 0.0850177i
\(939\) 67.3691 2.19851
\(940\) 15.8621 + 9.78650i 0.517363 + 0.319200i
\(941\) 42.6516 1.39040 0.695201 0.718816i \(-0.255315\pi\)
0.695201 + 0.718816i \(0.255315\pi\)
\(942\) 109.795i 3.57733i
\(943\) 28.6474i 0.932888i
\(944\) 22.9647 0.747438
\(945\) −3.41760 + 5.53929i −0.111175 + 0.180193i
\(946\) 3.05785 0.0994192
\(947\) 24.7131i 0.803069i −0.915844 0.401535i \(-0.868477\pi\)
0.915844 0.401535i \(-0.131523\pi\)
\(948\) 34.0965i 1.10740i
\(949\) −40.3761 −1.31066
\(950\) 0 0
\(951\) −18.3795 −0.595996
\(952\) 19.6612i 0.637223i
\(953\) 15.5170i 0.502646i 0.967903 + 0.251323i \(0.0808657\pi\)
−0.967903 + 0.251323i \(0.919134\pi\)
\(954\) −33.5231 −1.08535
\(955\) 11.9876 19.4296i 0.387909 0.628726i
\(956\) −57.8517 −1.87106
\(957\) 13.8720i 0.448419i
\(958\) 63.9217i 2.06521i
\(959\) −0.650157 −0.0209946
\(960\) −49.7923 30.7207i −1.60704 0.991505i
\(961\) −11.4047 −0.367893
\(962\) 29.9871i 0.966821i
\(963\) 26.2062i 0.844484i
\(964\) 37.8642 1.21952
\(965\) −22.5150 13.8912i −0.724784 0.447174i
\(966\) −64.7274 −2.08257
\(967\) 16.0510i 0.516166i −0.966123 0.258083i \(-0.916909\pi\)
0.966123 0.258083i \(-0.0830909\pi\)
\(968\) 13.6898i 0.440006i
\(969\) 0 0
\(970\) −0.361735 + 0.586304i −0.0116146 + 0.0188251i
\(971\) 5.76925 0.185144 0.0925720 0.995706i \(-0.470491\pi\)
0.0925720 + 0.995706i \(0.470491\pi\)
\(972\) 69.4676i 2.22817i
\(973\) 12.2847i 0.393829i
\(974\) −7.27312 −0.233046
\(975\) 31.7736 + 63.3045i 1.01757 + 2.02737i
\(976\) −8.96933 −0.287101
\(977\) 46.7724i 1.49638i 0.663484 + 0.748190i \(0.269077\pi\)
−0.663484 + 0.748190i \(0.730923\pi\)
\(978\) 84.8394i 2.71286i
\(979\) 47.1973 1.50843
\(980\) −18.3730 + 29.7791i −0.586903 + 0.951258i
\(981\) −16.0812 −0.513434
\(982\) 2.96106i 0.0944912i
\(983\) 33.6039i 1.07180i 0.844282 + 0.535900i \(0.180028\pi\)
−0.844282 + 0.535900i \(0.819972\pi\)
\(984\) −34.4801 −1.09919
\(985\) 5.18903 + 3.20151i 0.165336 + 0.102008i
\(986\) 16.4884 0.525097
\(987\) 8.60848i 0.274011i
\(988\) 0 0
\(989\) −3.45139 −0.109748
\(990\) 27.3417 + 16.8691i 0.868976 + 0.536137i
\(991\) 45.6040 1.44866 0.724329 0.689454i \(-0.242150\pi\)
0.724329 + 0.689454i \(0.242150\pi\)
\(992\) 14.3868i 0.456783i
\(993\) 41.6310i 1.32112i
\(994\) 10.2255 0.324333
\(995\) −5.25812 + 8.52242i −0.166694 + 0.270179i
\(996\) −53.1616 −1.68449
\(997\) 4.80126i 0.152057i −0.997106 0.0760287i \(-0.975776\pi\)
0.997106 0.0760287i \(-0.0242241\pi\)
\(998\) 46.4047i 1.46892i
\(999\) −3.62817 −0.114790
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.1084.2 24
5.2 odd 4 9025.2.a.ct.1.23 24
5.3 odd 4 9025.2.a.ct.1.2 24
5.4 even 2 inner 1805.2.b.l.1084.23 24
19.2 odd 18 95.2.p.a.4.8 yes 48
19.10 odd 18 95.2.p.a.24.1 yes 48
19.18 odd 2 1805.2.b.k.1084.23 24
57.2 even 18 855.2.da.b.289.1 48
57.29 even 18 855.2.da.b.784.8 48
95.2 even 36 475.2.l.f.251.8 48
95.18 even 4 9025.2.a.cu.1.23 24
95.29 odd 18 95.2.p.a.24.8 yes 48
95.37 even 4 9025.2.a.cu.1.2 24
95.48 even 36 475.2.l.f.176.1 48
95.59 odd 18 95.2.p.a.4.1 48
95.67 even 36 475.2.l.f.176.8 48
95.78 even 36 475.2.l.f.251.1 48
95.94 odd 2 1805.2.b.k.1084.2 24
285.29 even 18 855.2.da.b.784.1 48
285.59 even 18 855.2.da.b.289.8 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.4.1 48 95.59 odd 18
95.2.p.a.4.8 yes 48 19.2 odd 18
95.2.p.a.24.1 yes 48 19.10 odd 18
95.2.p.a.24.8 yes 48 95.29 odd 18
475.2.l.f.176.1 48 95.48 even 36
475.2.l.f.176.8 48 95.67 even 36
475.2.l.f.251.1 48 95.78 even 36
475.2.l.f.251.8 48 95.2 even 36
855.2.da.b.289.1 48 57.2 even 18
855.2.da.b.289.8 48 285.59 even 18
855.2.da.b.784.1 48 285.29 even 18
855.2.da.b.784.8 48 57.29 even 18
1805.2.b.k.1084.2 24 95.94 odd 2
1805.2.b.k.1084.23 24 19.18 odd 2
1805.2.b.l.1084.2 24 1.1 even 1 trivial
1805.2.b.l.1084.23 24 5.4 even 2 inner
9025.2.a.ct.1.2 24 5.3 odd 4
9025.2.a.ct.1.23 24 5.2 odd 4
9025.2.a.cu.1.2 24 95.37 even 4
9025.2.a.cu.1.23 24 95.18 even 4