Properties

Label 1805.2.b.l.1084.12
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 1084.12
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.l.1084.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.244477i q^{2} +2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} -0.963297i q^{8} -4.49866 q^{9} +O(q^{10})\) \(q-0.244477i q^{2} +2.73837i q^{3} +1.94023 q^{4} +(0.750459 - 2.10637i) q^{5} +0.669469 q^{6} +1.94027i q^{7} -0.963297i q^{8} -4.49866 q^{9} +(-0.514961 - 0.183470i) q^{10} +4.23333 q^{11} +5.31307i q^{12} +1.26982i q^{13} +0.474352 q^{14} +(5.76803 + 2.05503i) q^{15} +3.64496 q^{16} +2.46021i q^{17} +1.09982i q^{18} +(1.45606 - 4.08685i) q^{20} -5.31318 q^{21} -1.03495i q^{22} -5.13716i q^{23} +2.63786 q^{24} +(-3.87362 - 3.16149i) q^{25} +0.310443 q^{26} -4.10387i q^{27} +3.76457i q^{28} +8.64123 q^{29} +(0.502409 - 1.41015i) q^{30} -5.10084 q^{31} -2.81770i q^{32} +11.5924i q^{33} +0.601466 q^{34} +(4.08694 + 1.45609i) q^{35} -8.72843 q^{36} +11.0305i q^{37} -3.47724 q^{39} +(-2.02906 - 0.722915i) q^{40} -2.49838 q^{41} +1.29895i q^{42} +4.46879i q^{43} +8.21364 q^{44} +(-3.37606 + 9.47585i) q^{45} -1.25592 q^{46} -6.76901i q^{47} +9.98123i q^{48} +3.23535 q^{49} +(-0.772913 + 0.947013i) q^{50} -6.73697 q^{51} +2.46375i q^{52} -0.689802i q^{53} -1.00330 q^{54} +(3.17694 - 8.91697i) q^{55} +1.86906 q^{56} -2.11258i q^{58} +5.19336 q^{59} +(11.1913 + 3.98724i) q^{60} +2.80281 q^{61} +1.24704i q^{62} -8.72862i q^{63} +6.60105 q^{64} +(2.67472 + 0.952950i) q^{65} +2.83408 q^{66} -5.21227i q^{67} +4.77338i q^{68} +14.0674 q^{69} +(0.355982 - 0.999163i) q^{70} -0.791916 q^{71} +4.33354i q^{72} +1.41576i q^{73} +2.69671 q^{74} +(8.65733 - 10.6074i) q^{75} +8.21381i q^{77} +0.850107i q^{78} -6.06294 q^{79} +(2.73539 - 7.67764i) q^{80} -2.25806 q^{81} +0.610798i q^{82} +11.8522i q^{83} -10.3088 q^{84} +(5.18213 + 1.84629i) q^{85} +1.09252 q^{86} +23.6629i q^{87} -4.07795i q^{88} -2.23291 q^{89} +(2.31663 + 0.825369i) q^{90} -2.46380 q^{91} -9.96727i q^{92} -13.9680i q^{93} -1.65487 q^{94} +7.71591 q^{96} -8.60981i q^{97} -0.790969i q^{98} -19.0443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.244477i 0.172872i −0.996257 0.0864358i \(-0.972452\pi\)
0.996257 0.0864358i \(-0.0275477\pi\)
\(3\) 2.73837i 1.58100i 0.612464 + 0.790499i \(0.290179\pi\)
−0.612464 + 0.790499i \(0.709821\pi\)
\(4\) 1.94023 0.970115
\(5\) 0.750459 2.10637i 0.335615 0.941999i
\(6\) 0.669469 0.273309
\(7\) 1.94027i 0.733354i 0.930348 + 0.366677i \(0.119505\pi\)
−0.930348 + 0.366677i \(0.880495\pi\)
\(8\) 0.963297i 0.340577i
\(9\) −4.49866 −1.49955
\(10\) −0.514961 0.183470i −0.162845 0.0580184i
\(11\) 4.23333 1.27640 0.638198 0.769872i \(-0.279680\pi\)
0.638198 + 0.769872i \(0.279680\pi\)
\(12\) 5.31307i 1.53375i
\(13\) 1.26982i 0.352186i 0.984374 + 0.176093i \(0.0563459\pi\)
−0.984374 + 0.176093i \(0.943654\pi\)
\(14\) 0.474352 0.126776
\(15\) 5.76803 + 2.05503i 1.48930 + 0.530607i
\(16\) 3.64496 0.911239
\(17\) 2.46021i 0.596689i 0.954458 + 0.298345i \(0.0964345\pi\)
−0.954458 + 0.298345i \(0.903566\pi\)
\(18\) 1.09982i 0.259230i
\(19\) 0 0
\(20\) 1.45606 4.08685i 0.325586 0.913848i
\(21\) −5.31318 −1.15943
\(22\) 1.03495i 0.220653i
\(23\) 5.13716i 1.07117i −0.844481 0.535586i \(-0.820091\pi\)
0.844481 0.535586i \(-0.179909\pi\)
\(24\) 2.63786 0.538451
\(25\) −3.87362 3.16149i −0.774725 0.632299i
\(26\) 0.310443 0.0608829
\(27\) 4.10387i 0.789791i
\(28\) 3.76457i 0.711438i
\(29\) 8.64123 1.60464 0.802318 0.596897i \(-0.203600\pi\)
0.802318 + 0.596897i \(0.203600\pi\)
\(30\) 0.502409 1.41015i 0.0917269 0.257457i
\(31\) −5.10084 −0.916138 −0.458069 0.888917i \(-0.651459\pi\)
−0.458069 + 0.888917i \(0.651459\pi\)
\(32\) 2.81770i 0.498104i
\(33\) 11.5924i 2.01798i
\(34\) 0.601466 0.103151
\(35\) 4.08694 + 1.45609i 0.690819 + 0.246125i
\(36\) −8.72843 −1.45474
\(37\) 11.0305i 1.81341i 0.421770 + 0.906703i \(0.361409\pi\)
−0.421770 + 0.906703i \(0.638591\pi\)
\(38\) 0 0
\(39\) −3.47724 −0.556805
\(40\) −2.02906 0.722915i −0.320823 0.114303i
\(41\) −2.49838 −0.390182 −0.195091 0.980785i \(-0.562500\pi\)
−0.195091 + 0.980785i \(0.562500\pi\)
\(42\) 1.29895i 0.200432i
\(43\) 4.46879i 0.681484i 0.940157 + 0.340742i \(0.110678\pi\)
−0.940157 + 0.340742i \(0.889322\pi\)
\(44\) 8.21364 1.23825
\(45\) −3.37606 + 9.47585i −0.503273 + 1.41258i
\(46\) −1.25592 −0.185175
\(47\) 6.76901i 0.987362i −0.869643 0.493681i \(-0.835651\pi\)
0.869643 0.493681i \(-0.164349\pi\)
\(48\) 9.98123i 1.44067i
\(49\) 3.23535 0.462192
\(50\) −0.772913 + 0.947013i −0.109306 + 0.133928i
\(51\) −6.73697 −0.943364
\(52\) 2.46375i 0.341661i
\(53\) 0.689802i 0.0947515i −0.998877 0.0473758i \(-0.984914\pi\)
0.998877 0.0473758i \(-0.0150858\pi\)
\(54\) −1.00330 −0.136532
\(55\) 3.17694 8.91697i 0.428378 1.20236i
\(56\) 1.86906 0.249763
\(57\) 0 0
\(58\) 2.11258i 0.277396i
\(59\) 5.19336 0.676118 0.338059 0.941125i \(-0.390230\pi\)
0.338059 + 0.941125i \(0.390230\pi\)
\(60\) 11.1913 + 3.98724i 1.44479 + 0.514750i
\(61\) 2.80281 0.358864 0.179432 0.983770i \(-0.442574\pi\)
0.179432 + 0.983770i \(0.442574\pi\)
\(62\) 1.24704i 0.158374i
\(63\) 8.72862i 1.09970i
\(64\) 6.60105 0.825131
\(65\) 2.67472 + 0.952950i 0.331759 + 0.118199i
\(66\) 2.83408 0.348851
\(67\) 5.21227i 0.636780i −0.947960 0.318390i \(-0.896858\pi\)
0.947960 0.318390i \(-0.103142\pi\)
\(68\) 4.77338i 0.578858i
\(69\) 14.0674 1.69352
\(70\) 0.355982 0.999163i 0.0425480 0.119423i
\(71\) −0.791916 −0.0939832 −0.0469916 0.998895i \(-0.514963\pi\)
−0.0469916 + 0.998895i \(0.514963\pi\)
\(72\) 4.33354i 0.510713i
\(73\) 1.41576i 0.165702i 0.996562 + 0.0828512i \(0.0264026\pi\)
−0.996562 + 0.0828512i \(0.973597\pi\)
\(74\) 2.69671 0.313486
\(75\) 8.65733 10.6074i 0.999663 1.22484i
\(76\) 0 0
\(77\) 8.21381i 0.936050i
\(78\) 0.850107i 0.0962557i
\(79\) −6.06294 −0.682134 −0.341067 0.940039i \(-0.610788\pi\)
−0.341067 + 0.940039i \(0.610788\pi\)
\(80\) 2.73539 7.67764i 0.305826 0.858387i
\(81\) −2.25806 −0.250895
\(82\) 0.610798i 0.0674514i
\(83\) 11.8522i 1.30095i 0.759527 + 0.650476i \(0.225430\pi\)
−0.759527 + 0.650476i \(0.774570\pi\)
\(84\) −10.3088 −1.12478
\(85\) 5.18213 + 1.84629i 0.562081 + 0.200258i
\(86\) 1.09252 0.117809
\(87\) 23.6629i 2.53692i
\(88\) 4.07795i 0.434711i
\(89\) −2.23291 −0.236688 −0.118344 0.992973i \(-0.537759\pi\)
−0.118344 + 0.992973i \(0.537759\pi\)
\(90\) 2.31663 + 0.825369i 0.244194 + 0.0870016i
\(91\) −2.46380 −0.258277
\(92\) 9.96727i 1.03916i
\(93\) 13.9680i 1.44841i
\(94\) −1.65487 −0.170687
\(95\) 0 0
\(96\) 7.71591 0.787501
\(97\) 8.60981i 0.874194i −0.899414 0.437097i \(-0.856007\pi\)
0.899414 0.437097i \(-0.143993\pi\)
\(98\) 0.790969i 0.0798999i
\(99\) −19.0443 −1.91402
\(100\) −7.51572 6.13403i −0.751572 0.613403i
\(101\) −13.4510 −1.33842 −0.669212 0.743071i \(-0.733368\pi\)
−0.669212 + 0.743071i \(0.733368\pi\)
\(102\) 1.64704i 0.163081i
\(103\) 4.03579i 0.397658i −0.980034 0.198829i \(-0.936286\pi\)
0.980034 0.198829i \(-0.0637139\pi\)
\(104\) 1.22322 0.119946
\(105\) −3.98732 + 11.1915i −0.389123 + 1.09218i
\(106\) −0.168641 −0.0163798
\(107\) 16.9589i 1.63948i 0.572734 + 0.819741i \(0.305883\pi\)
−0.572734 + 0.819741i \(0.694117\pi\)
\(108\) 7.96246i 0.766188i
\(109\) 6.83567 0.654739 0.327369 0.944896i \(-0.393838\pi\)
0.327369 + 0.944896i \(0.393838\pi\)
\(110\) −2.18000 0.776689i −0.207855 0.0740544i
\(111\) −30.2056 −2.86699
\(112\) 7.07221i 0.668261i
\(113\) 5.92416i 0.557298i −0.960393 0.278649i \(-0.910113\pi\)
0.960393 0.278649i \(-0.0898867\pi\)
\(114\) 0 0
\(115\) −10.8208 3.85523i −1.00904 0.359502i
\(116\) 16.7660 1.55668
\(117\) 5.71250i 0.528121i
\(118\) 1.26966i 0.116882i
\(119\) −4.77348 −0.437584
\(120\) 1.97961 5.55632i 0.180712 0.507221i
\(121\) 6.92107 0.629188
\(122\) 0.685224i 0.0620373i
\(123\) 6.84150i 0.616877i
\(124\) −9.89681 −0.888759
\(125\) −9.56628 + 5.78673i −0.855634 + 0.517581i
\(126\) −2.13395 −0.190107
\(127\) 19.1802i 1.70197i −0.525193 0.850983i \(-0.676007\pi\)
0.525193 0.850983i \(-0.323993\pi\)
\(128\) 7.24921i 0.640746i
\(129\) −12.2372 −1.07742
\(130\) 0.232975 0.653909i 0.0204332 0.0573516i
\(131\) −0.307990 −0.0269092 −0.0134546 0.999909i \(-0.504283\pi\)
−0.0134546 + 0.999909i \(0.504283\pi\)
\(132\) 22.4920i 1.95767i
\(133\) 0 0
\(134\) −1.27428 −0.110081
\(135\) −8.64429 3.07979i −0.743982 0.265066i
\(136\) 2.36992 0.203219
\(137\) 14.4994i 1.23876i 0.785090 + 0.619382i \(0.212617\pi\)
−0.785090 + 0.619382i \(0.787383\pi\)
\(138\) 3.43917i 0.292761i
\(139\) −15.7973 −1.33991 −0.669955 0.742401i \(-0.733687\pi\)
−0.669955 + 0.742401i \(0.733687\pi\)
\(140\) 7.92960 + 2.82516i 0.670174 + 0.238769i
\(141\) 18.5360 1.56102
\(142\) 0.193606i 0.0162470i
\(143\) 5.37558i 0.449529i
\(144\) −16.3974 −1.36645
\(145\) 6.48489 18.2017i 0.538540 1.51157i
\(146\) 0.346122 0.0286452
\(147\) 8.85957i 0.730725i
\(148\) 21.4017i 1.75921i
\(149\) 12.4650 1.02117 0.510585 0.859827i \(-0.329429\pi\)
0.510585 + 0.859827i \(0.329429\pi\)
\(150\) −2.59327 2.11652i −0.211740 0.172813i
\(151\) −13.8400 −1.12629 −0.563143 0.826360i \(-0.690408\pi\)
−0.563143 + 0.826360i \(0.690408\pi\)
\(152\) 0 0
\(153\) 11.0677i 0.894767i
\(154\) 2.00809 0.161816
\(155\) −3.82797 + 10.7443i −0.307470 + 0.863001i
\(156\) −6.74666 −0.540165
\(157\) 18.1970i 1.45228i 0.687549 + 0.726138i \(0.258687\pi\)
−0.687549 + 0.726138i \(0.741313\pi\)
\(158\) 1.48225i 0.117922i
\(159\) 1.88893 0.149802
\(160\) −5.93514 2.11457i −0.469214 0.167171i
\(161\) 9.96748 0.785548
\(162\) 0.552043i 0.0433726i
\(163\) 15.3337i 1.20103i −0.799613 0.600516i \(-0.794962\pi\)
0.799613 0.600516i \(-0.205038\pi\)
\(164\) −4.84744 −0.378522
\(165\) 24.4180 + 8.69963i 1.90094 + 0.677265i
\(166\) 2.89760 0.224897
\(167\) 6.21690i 0.481079i −0.970639 0.240539i \(-0.922676\pi\)
0.970639 0.240539i \(-0.0773243\pi\)
\(168\) 5.11817i 0.394875i
\(169\) 11.3875 0.875965
\(170\) 0.451376 1.26691i 0.0346189 0.0971678i
\(171\) 0 0
\(172\) 8.67048i 0.661118i
\(173\) 2.76604i 0.210298i −0.994456 0.105149i \(-0.966468\pi\)
0.994456 0.105149i \(-0.0335319\pi\)
\(174\) 5.78503 0.438562
\(175\) 6.13416 7.51588i 0.463699 0.568147i
\(176\) 15.4303 1.16310
\(177\) 14.2213i 1.06894i
\(178\) 0.545896i 0.0409167i
\(179\) −11.3783 −0.850456 −0.425228 0.905086i \(-0.639806\pi\)
−0.425228 + 0.905086i \(0.639806\pi\)
\(180\) −6.55033 + 18.3853i −0.488233 + 1.37036i
\(181\) −3.56654 −0.265099 −0.132549 0.991176i \(-0.542316\pi\)
−0.132549 + 0.991176i \(0.542316\pi\)
\(182\) 0.602344i 0.0446487i
\(183\) 7.67513i 0.567362i
\(184\) −4.94861 −0.364816
\(185\) 23.2344 + 8.27795i 1.70823 + 0.608607i
\(186\) −3.41485 −0.250389
\(187\) 10.4149i 0.761612i
\(188\) 13.1334i 0.957855i
\(189\) 7.96263 0.579196
\(190\) 0 0
\(191\) −8.67323 −0.627573 −0.313786 0.949494i \(-0.601598\pi\)
−0.313786 + 0.949494i \(0.601598\pi\)
\(192\) 18.0761i 1.30453i
\(193\) 0.422110i 0.0303841i 0.999885 + 0.0151921i \(0.00483597\pi\)
−0.999885 + 0.0151921i \(0.995164\pi\)
\(194\) −2.10490 −0.151123
\(195\) −2.60953 + 7.32438i −0.186872 + 0.524510i
\(196\) 6.27732 0.448380
\(197\) 15.2415i 1.08591i −0.839761 0.542956i \(-0.817305\pi\)
0.839761 0.542956i \(-0.182695\pi\)
\(198\) 4.65590i 0.330880i
\(199\) −12.9264 −0.916331 −0.458166 0.888867i \(-0.651493\pi\)
−0.458166 + 0.888867i \(0.651493\pi\)
\(200\) −3.04546 + 3.73145i −0.215346 + 0.263853i
\(201\) 14.2731 1.00675
\(202\) 3.28846i 0.231376i
\(203\) 16.7663i 1.17677i
\(204\) −13.0713 −0.915172
\(205\) −1.87493 + 5.26253i −0.130951 + 0.367551i
\(206\) −0.986659 −0.0687438
\(207\) 23.1103i 1.60628i
\(208\) 4.62845i 0.320926i
\(209\) 0 0
\(210\) 2.73608 + 0.974809i 0.188807 + 0.0672682i
\(211\) 4.44619 0.306089 0.153044 0.988219i \(-0.451092\pi\)
0.153044 + 0.988219i \(0.451092\pi\)
\(212\) 1.33837i 0.0919199i
\(213\) 2.16856i 0.148587i
\(214\) 4.14608 0.283420
\(215\) 9.41294 + 3.35364i 0.641957 + 0.228717i
\(216\) −3.95325 −0.268985
\(217\) 9.89701i 0.671853i
\(218\) 1.67117i 0.113186i
\(219\) −3.87688 −0.261975
\(220\) 6.16399 17.3010i 0.415576 1.16643i
\(221\) −3.12404 −0.210146
\(222\) 7.38459i 0.495621i
\(223\) 9.19893i 0.616006i −0.951385 0.308003i \(-0.900339\pi\)
0.951385 0.308003i \(-0.0996607\pi\)
\(224\) 5.46711 0.365287
\(225\) 17.4261 + 14.2225i 1.16174 + 0.948165i
\(226\) −1.44832 −0.0963411
\(227\) 0.600308i 0.0398438i 0.999802 + 0.0199219i \(0.00634176\pi\)
−0.999802 + 0.0199219i \(0.993658\pi\)
\(228\) 0 0
\(229\) 7.11499 0.470172 0.235086 0.971975i \(-0.424463\pi\)
0.235086 + 0.971975i \(0.424463\pi\)
\(230\) −0.942515 + 2.64543i −0.0621476 + 0.174435i
\(231\) −22.4924 −1.47989
\(232\) 8.32407i 0.546502i
\(233\) 20.1662i 1.32113i −0.750767 0.660567i \(-0.770316\pi\)
0.750767 0.660567i \(-0.229684\pi\)
\(234\) −1.39658 −0.0912971
\(235\) −14.2581 5.07986i −0.930094 0.331374i
\(236\) 10.0763 0.655912
\(237\) 16.6026i 1.07845i
\(238\) 1.16701i 0.0756459i
\(239\) 11.6342 0.752554 0.376277 0.926507i \(-0.377204\pi\)
0.376277 + 0.926507i \(0.377204\pi\)
\(240\) 21.0242 + 7.49050i 1.35711 + 0.483510i
\(241\) −25.5301 −1.64454 −0.822269 0.569100i \(-0.807292\pi\)
−0.822269 + 0.569100i \(0.807292\pi\)
\(242\) 1.69205i 0.108769i
\(243\) 18.4950i 1.18646i
\(244\) 5.43811 0.348139
\(245\) 2.42799 6.81485i 0.155119 0.435385i
\(246\) −1.67259 −0.106640
\(247\) 0 0
\(248\) 4.91362i 0.312015i
\(249\) −32.4558 −2.05680
\(250\) 1.41472 + 2.33874i 0.0894750 + 0.147915i
\(251\) 15.3783 0.970669 0.485335 0.874328i \(-0.338698\pi\)
0.485335 + 0.874328i \(0.338698\pi\)
\(252\) 16.9355i 1.06684i
\(253\) 21.7473i 1.36724i
\(254\) −4.68912 −0.294221
\(255\) −5.05582 + 14.1906i −0.316608 + 0.888648i
\(256\) 11.4298 0.714365
\(257\) 16.0534i 1.00139i −0.865625 0.500693i \(-0.833079\pi\)
0.865625 0.500693i \(-0.166921\pi\)
\(258\) 2.99172i 0.186256i
\(259\) −21.4022 −1.32987
\(260\) 5.18958 + 1.84894i 0.321844 + 0.114667i
\(261\) −38.8739 −2.40624
\(262\) 0.0752965i 0.00465183i
\(263\) 14.2397i 0.878055i −0.898474 0.439027i \(-0.855323\pi\)
0.898474 0.439027i \(-0.144677\pi\)
\(264\) 11.1669 0.687277
\(265\) −1.45298 0.517668i −0.0892559 0.0318001i
\(266\) 0 0
\(267\) 6.11453i 0.374203i
\(268\) 10.1130i 0.617750i
\(269\) 16.2414 0.990254 0.495127 0.868821i \(-0.335121\pi\)
0.495127 + 0.868821i \(0.335121\pi\)
\(270\) −0.752938 + 2.11333i −0.0458224 + 0.128613i
\(271\) −5.92530 −0.359936 −0.179968 0.983672i \(-0.557599\pi\)
−0.179968 + 0.983672i \(0.557599\pi\)
\(272\) 8.96737i 0.543727i
\(273\) 6.74680i 0.408335i
\(274\) 3.54476 0.214147
\(275\) −16.3983 13.3836i −0.988856 0.807064i
\(276\) 27.2941 1.64291
\(277\) 6.30936i 0.379093i −0.981872 0.189546i \(-0.939298\pi\)
0.981872 0.189546i \(-0.0607017\pi\)
\(278\) 3.86208i 0.231632i
\(279\) 22.9469 1.37380
\(280\) 1.40265 3.93693i 0.0838244 0.235277i
\(281\) 2.67961 0.159852 0.0799261 0.996801i \(-0.474532\pi\)
0.0799261 + 0.996801i \(0.474532\pi\)
\(282\) 4.53164i 0.269855i
\(283\) 31.0643i 1.84658i 0.384105 + 0.923290i \(0.374510\pi\)
−0.384105 + 0.923290i \(0.625490\pi\)
\(284\) −1.53650 −0.0911745
\(285\) 0 0
\(286\) 1.31421 0.0777107
\(287\) 4.84754i 0.286142i
\(288\) 12.6759i 0.746933i
\(289\) 10.9474 0.643962
\(290\) −4.44989 1.58541i −0.261307 0.0930983i
\(291\) 23.5768 1.38210
\(292\) 2.74690i 0.160750i
\(293\) 0.865650i 0.0505718i −0.999680 0.0252859i \(-0.991950\pi\)
0.999680 0.0252859i \(-0.00804961\pi\)
\(294\) 2.16596 0.126322
\(295\) 3.89740 10.9392i 0.226916 0.636902i
\(296\) 10.6257 0.617604
\(297\) 17.3730i 1.00809i
\(298\) 3.04740i 0.176531i
\(299\) 6.52329 0.377251
\(300\) 16.7972 20.5808i 0.969788 1.18823i
\(301\) −8.67067 −0.499769
\(302\) 3.38357i 0.194703i
\(303\) 36.8338i 2.11605i
\(304\) 0 0
\(305\) 2.10340 5.90377i 0.120440 0.338049i
\(306\) −2.70579 −0.154680
\(307\) 8.99201i 0.513201i −0.966518 0.256601i \(-0.917397\pi\)
0.966518 0.256601i \(-0.0826025\pi\)
\(308\) 15.9367i 0.908077i
\(309\) 11.0515 0.628696
\(310\) 2.62673 + 0.935852i 0.149188 + 0.0531528i
\(311\) −11.4407 −0.648742 −0.324371 0.945930i \(-0.605153\pi\)
−0.324371 + 0.945930i \(0.605153\pi\)
\(312\) 3.34962i 0.189635i
\(313\) 7.86521i 0.444568i 0.974982 + 0.222284i \(0.0713512\pi\)
−0.974982 + 0.222284i \(0.928649\pi\)
\(314\) 4.44875 0.251057
\(315\) −18.3857 6.55047i −1.03592 0.369077i
\(316\) −11.7635 −0.661749
\(317\) 16.5265i 0.928218i 0.885778 + 0.464109i \(0.153625\pi\)
−0.885778 + 0.464109i \(0.846375\pi\)
\(318\) 0.461801i 0.0258965i
\(319\) 36.5812 2.04815
\(320\) 4.95382 13.9043i 0.276927 0.777273i
\(321\) −46.4398 −2.59202
\(322\) 2.43682i 0.135799i
\(323\) 0 0
\(324\) −4.38115 −0.243397
\(325\) 4.01454 4.91882i 0.222687 0.272847i
\(326\) −3.74875 −0.207624
\(327\) 18.7186i 1.03514i
\(328\) 2.40669i 0.132887i
\(329\) 13.1337 0.724085
\(330\) 2.12686 5.96963i 0.117080 0.328618i
\(331\) −7.91446 −0.435018 −0.217509 0.976058i \(-0.569793\pi\)
−0.217509 + 0.976058i \(0.569793\pi\)
\(332\) 22.9961i 1.26207i
\(333\) 49.6225i 2.71930i
\(334\) −1.51989 −0.0831648
\(335\) −10.9790 3.91159i −0.599846 0.213713i
\(336\) −19.3663 −1.05652
\(337\) 19.0361i 1.03696i −0.855090 0.518480i \(-0.826498\pi\)
0.855090 0.518480i \(-0.173502\pi\)
\(338\) 2.78400i 0.151429i
\(339\) 16.2225 0.881087
\(340\) 10.0545 + 3.58223i 0.545283 + 0.194274i
\(341\) −21.5935 −1.16936
\(342\) 0 0
\(343\) 19.8594i 1.07230i
\(344\) 4.30477 0.232098
\(345\) 10.5570 29.6313i 0.568371 1.59529i
\(346\) −0.676233 −0.0363545
\(347\) 5.46420i 0.293334i 0.989186 + 0.146667i \(0.0468545\pi\)
−0.989186 + 0.146667i \(0.953145\pi\)
\(348\) 45.9114i 2.46111i
\(349\) 6.26435 0.335323 0.167662 0.985845i \(-0.446378\pi\)
0.167662 + 0.985845i \(0.446378\pi\)
\(350\) −1.83746 1.49966i −0.0982165 0.0801603i
\(351\) 5.21120 0.278153
\(352\) 11.9283i 0.635779i
\(353\) 8.29398i 0.441444i −0.975337 0.220722i \(-0.929159\pi\)
0.975337 0.220722i \(-0.0708414\pi\)
\(354\) 3.47679 0.184789
\(355\) −0.594300 + 1.66807i −0.0315422 + 0.0885321i
\(356\) −4.33237 −0.229615
\(357\) 13.0715i 0.691820i
\(358\) 2.78174i 0.147020i
\(359\) −13.0857 −0.690637 −0.345318 0.938486i \(-0.612229\pi\)
−0.345318 + 0.938486i \(0.612229\pi\)
\(360\) 9.12806 + 3.25215i 0.481091 + 0.171403i
\(361\) 0 0
\(362\) 0.871938i 0.0458281i
\(363\) 18.9524i 0.994745i
\(364\) −4.78035 −0.250558
\(365\) 2.98212 + 1.06247i 0.156091 + 0.0556123i
\(366\) 1.87640 0.0980808
\(367\) 26.0942i 1.36211i −0.732234 0.681053i \(-0.761522\pi\)
0.732234 0.681053i \(-0.238478\pi\)
\(368\) 18.7247i 0.976094i
\(369\) 11.2394 0.585099
\(370\) 2.02377 5.68028i 0.105211 0.295304i
\(371\) 1.33840 0.0694864
\(372\) 27.1011i 1.40513i
\(373\) 27.1969i 1.40820i −0.710101 0.704100i \(-0.751351\pi\)
0.710101 0.704100i \(-0.248649\pi\)
\(374\) 2.54620 0.131661
\(375\) −15.8462 26.1960i −0.818294 1.35276i
\(376\) −6.52057 −0.336273
\(377\) 10.9728i 0.565130i
\(378\) 1.94668i 0.100127i
\(379\) 13.6999 0.703714 0.351857 0.936054i \(-0.385550\pi\)
0.351857 + 0.936054i \(0.385550\pi\)
\(380\) 0 0
\(381\) 52.5224 2.69080
\(382\) 2.12041i 0.108490i
\(383\) 10.2515i 0.523827i −0.965091 0.261913i \(-0.915647\pi\)
0.965091 0.261913i \(-0.0843535\pi\)
\(384\) 19.8510 1.01302
\(385\) 17.3014 + 6.16412i 0.881758 + 0.314153i
\(386\) 0.103196 0.00525255
\(387\) 20.1036i 1.02192i
\(388\) 16.7050i 0.848069i
\(389\) 5.05671 0.256385 0.128193 0.991749i \(-0.459082\pi\)
0.128193 + 0.991749i \(0.459082\pi\)
\(390\) 1.79064 + 0.637971i 0.0906728 + 0.0323049i
\(391\) 12.6385 0.639157
\(392\) 3.11660i 0.157412i
\(393\) 0.843389i 0.0425434i
\(394\) −3.72620 −0.187723
\(395\) −4.54999 + 12.7708i −0.228935 + 0.642570i
\(396\) −36.9503 −1.85682
\(397\) 23.8758i 1.19829i −0.800640 0.599146i \(-0.795507\pi\)
0.800640 0.599146i \(-0.204493\pi\)
\(398\) 3.16022i 0.158408i
\(399\) 0 0
\(400\) −14.1192 11.5235i −0.705960 0.576176i
\(401\) 24.7655 1.23673 0.618366 0.785891i \(-0.287795\pi\)
0.618366 + 0.785891i \(0.287795\pi\)
\(402\) 3.48945i 0.174038i
\(403\) 6.47717i 0.322651i
\(404\) −26.0981 −1.29843
\(405\) −1.69458 + 4.75631i −0.0842042 + 0.236343i
\(406\) 4.09899 0.203429
\(407\) 46.6958i 2.31463i
\(408\) 6.48970i 0.321288i
\(409\) −9.89998 −0.489523 −0.244761 0.969583i \(-0.578710\pi\)
−0.244761 + 0.969583i \(0.578710\pi\)
\(410\) 1.28657 + 0.458379i 0.0635392 + 0.0226377i
\(411\) −39.7046 −1.95848
\(412\) 7.83036i 0.385774i
\(413\) 10.0765i 0.495833i
\(414\) 5.64995 0.277680
\(415\) 24.9652 + 8.89461i 1.22549 + 0.436619i
\(416\) 3.57799 0.175425
\(417\) 43.2588i 2.11839i
\(418\) 0 0
\(419\) −4.00810 −0.195808 −0.0979042 0.995196i \(-0.531214\pi\)
−0.0979042 + 0.995196i \(0.531214\pi\)
\(420\) −7.73632 + 21.7142i −0.377494 + 1.05954i
\(421\) −20.2781 −0.988294 −0.494147 0.869378i \(-0.664520\pi\)
−0.494147 + 0.869378i \(0.664520\pi\)
\(422\) 1.08699i 0.0529140i
\(423\) 30.4515i 1.48060i
\(424\) −0.664484 −0.0322702
\(425\) 7.77795 9.52994i 0.377286 0.462270i
\(426\) −0.530163 −0.0256865
\(427\) 5.43822i 0.263174i
\(428\) 32.9043i 1.59049i
\(429\) −14.7203 −0.710704
\(430\) 0.819890 2.30125i 0.0395386 0.110976i
\(431\) −13.4783 −0.649229 −0.324615 0.945846i \(-0.605235\pi\)
−0.324615 + 0.945846i \(0.605235\pi\)
\(432\) 14.9584i 0.719689i
\(433\) 34.3776i 1.65208i −0.563611 0.826040i \(-0.690588\pi\)
0.563611 0.826040i \(-0.309412\pi\)
\(434\) −2.41959 −0.116144
\(435\) 49.8428 + 17.7580i 2.38978 + 0.851431i
\(436\) 13.2628 0.635172
\(437\) 0 0
\(438\) 0.947808i 0.0452880i
\(439\) 23.4179 1.11768 0.558838 0.829277i \(-0.311247\pi\)
0.558838 + 0.829277i \(0.311247\pi\)
\(440\) −8.58969 3.06034i −0.409498 0.145896i
\(441\) −14.5547 −0.693082
\(442\) 0.763756i 0.0363282i
\(443\) 2.39888i 0.113974i −0.998375 0.0569871i \(-0.981851\pi\)
0.998375 0.0569871i \(-0.0181494\pi\)
\(444\) −58.6059 −2.78131
\(445\) −1.67571 + 4.70335i −0.0794362 + 0.222960i
\(446\) −2.24893 −0.106490
\(447\) 34.1337i 1.61447i
\(448\) 12.8078i 0.605113i
\(449\) 38.2019 1.80286 0.901430 0.432924i \(-0.142518\pi\)
0.901430 + 0.432924i \(0.142518\pi\)
\(450\) 3.47707 4.26029i 0.163911 0.200832i
\(451\) −10.5765 −0.498027
\(452\) 11.4942i 0.540644i
\(453\) 37.8991i 1.78065i
\(454\) 0.146762 0.00688786
\(455\) −1.84898 + 5.18969i −0.0866816 + 0.243296i
\(456\) 0 0
\(457\) 1.87605i 0.0877581i −0.999037 0.0438790i \(-0.986028\pi\)
0.999037 0.0438790i \(-0.0139716\pi\)
\(458\) 1.73945i 0.0812793i
\(459\) 10.0964 0.471260
\(460\) −20.9948 7.48003i −0.978888 0.348758i
\(461\) 16.8204 0.783402 0.391701 0.920092i \(-0.371887\pi\)
0.391701 + 0.920092i \(0.371887\pi\)
\(462\) 5.49889i 0.255831i
\(463\) 24.3641i 1.13230i −0.824303 0.566148i \(-0.808433\pi\)
0.824303 0.566148i \(-0.191567\pi\)
\(464\) 31.4969 1.46221
\(465\) −29.4218 10.4824i −1.36440 0.486109i
\(466\) −4.93019 −0.228386
\(467\) 13.6511i 0.631696i −0.948810 0.315848i \(-0.897711\pi\)
0.948810 0.315848i \(-0.102289\pi\)
\(468\) 11.0836i 0.512338i
\(469\) 10.1132 0.466985
\(470\) −1.24191 + 3.48577i −0.0572851 + 0.160787i
\(471\) −49.8300 −2.29604
\(472\) 5.00275i 0.230270i
\(473\) 18.9179i 0.869844i
\(474\) −4.05895 −0.186434
\(475\) 0 0
\(476\) −9.26166 −0.424507
\(477\) 3.10318i 0.142085i
\(478\) 2.84430i 0.130095i
\(479\) 21.7405 0.993351 0.496675 0.867936i \(-0.334554\pi\)
0.496675 + 0.867936i \(0.334554\pi\)
\(480\) 5.79047 16.2526i 0.264298 0.741826i
\(481\) −14.0068 −0.638656
\(482\) 6.24153i 0.284294i
\(483\) 27.2946i 1.24195i
\(484\) 13.4285 0.610385
\(485\) −18.1355 6.46131i −0.823490 0.293393i
\(486\) −4.52161 −0.205104
\(487\) 29.2454i 1.32524i −0.748957 0.662618i \(-0.769445\pi\)
0.748957 0.662618i \(-0.230555\pi\)
\(488\) 2.69994i 0.122221i
\(489\) 41.9894 1.89883
\(490\) −1.66608 0.593589i −0.0752656 0.0268156i
\(491\) −18.3556 −0.828375 −0.414188 0.910191i \(-0.635934\pi\)
−0.414188 + 0.910191i \(0.635934\pi\)
\(492\) 13.2741i 0.598442i
\(493\) 21.2593i 0.957469i
\(494\) 0 0
\(495\) −14.2920 + 40.1144i −0.642376 + 1.80301i
\(496\) −18.5923 −0.834821
\(497\) 1.53653i 0.0689229i
\(498\) 7.93470i 0.355562i
\(499\) −10.4159 −0.466279 −0.233140 0.972443i \(-0.574900\pi\)
−0.233140 + 0.972443i \(0.574900\pi\)
\(500\) −18.5608 + 11.2276i −0.830064 + 0.502113i
\(501\) 17.0242 0.760584
\(502\) 3.75964i 0.167801i
\(503\) 4.35731i 0.194283i 0.995271 + 0.0971413i \(0.0309699\pi\)
−0.995271 + 0.0971413i \(0.969030\pi\)
\(504\) −8.40825 −0.374533
\(505\) −10.0944 + 28.3328i −0.449196 + 1.26079i
\(506\) −5.31672 −0.236357
\(507\) 31.1833i 1.38490i
\(508\) 37.2140i 1.65110i
\(509\) −38.2608 −1.69588 −0.847941 0.530091i \(-0.822158\pi\)
−0.847941 + 0.530091i \(0.822158\pi\)
\(510\) 3.46927 + 1.23603i 0.153622 + 0.0547324i
\(511\) −2.74696 −0.121518
\(512\) 17.2928i 0.764239i
\(513\) 0 0
\(514\) −3.92470 −0.173111
\(515\) −8.50088 3.02869i −0.374594 0.133460i
\(516\) −23.7430 −1.04523
\(517\) 28.6555i 1.26027i
\(518\) 5.23235i 0.229896i
\(519\) 7.57442 0.332480
\(520\) 0.917974 2.57655i 0.0402558 0.112989i
\(521\) 2.48812 0.109007 0.0545033 0.998514i \(-0.482642\pi\)
0.0545033 + 0.998514i \(0.482642\pi\)
\(522\) 9.50379i 0.415970i
\(523\) 19.4533i 0.850635i −0.905044 0.425317i \(-0.860163\pi\)
0.905044 0.425317i \(-0.139837\pi\)
\(524\) −0.597571 −0.0261050
\(525\) 20.5812 + 16.7976i 0.898239 + 0.733106i
\(526\) −3.48127 −0.151791
\(527\) 12.5492i 0.546650i
\(528\) 42.2538i 1.83886i
\(529\) −3.39040 −0.147409
\(530\) −0.126558 + 0.355221i −0.00549733 + 0.0154298i
\(531\) −23.3631 −1.01387
\(532\) 0 0
\(533\) 3.17251i 0.137417i
\(534\) −1.49486 −0.0646891
\(535\) 35.7219 + 12.7270i 1.54439 + 0.550236i
\(536\) −5.02096 −0.216873
\(537\) 31.1580i 1.34457i
\(538\) 3.97065i 0.171187i
\(539\) 13.6963 0.589941
\(540\) −16.7719 5.97550i −0.721749 0.257145i
\(541\) 14.4565 0.621535 0.310768 0.950486i \(-0.399414\pi\)
0.310768 + 0.950486i \(0.399414\pi\)
\(542\) 1.44860i 0.0622228i
\(543\) 9.76650i 0.419121i
\(544\) 6.93215 0.297214
\(545\) 5.12989 14.3985i 0.219740 0.616763i
\(546\) −1.64944 −0.0705895
\(547\) 31.3961i 1.34240i 0.741276 + 0.671200i \(0.234221\pi\)
−0.741276 + 0.671200i \(0.765779\pi\)
\(548\) 28.1321i 1.20174i
\(549\) −12.6089 −0.538135
\(550\) −3.27200 + 4.00902i −0.139518 + 0.170945i
\(551\) 0 0
\(552\) 13.5511i 0.576774i
\(553\) 11.7637i 0.500245i
\(554\) −1.54250 −0.0655343
\(555\) −22.6681 + 63.6243i −0.962206 + 2.70070i
\(556\) −30.6504 −1.29987
\(557\) 30.4484i 1.29014i 0.764124 + 0.645070i \(0.223172\pi\)
−0.764124 + 0.645070i \(0.776828\pi\)
\(558\) 5.61000i 0.237490i
\(559\) −5.67458 −0.240009
\(560\) 14.8967 + 5.30740i 0.629501 + 0.224279i
\(561\) −28.5198 −1.20411
\(562\) 0.655104i 0.0276339i
\(563\) 26.7012i 1.12532i 0.826687 + 0.562661i \(0.190223\pi\)
−0.826687 + 0.562661i \(0.809777\pi\)
\(564\) 35.9642 1.51437
\(565\) −12.4785 4.44584i −0.524975 0.187038i
\(566\) 7.59451 0.319221
\(567\) 4.38124i 0.183995i
\(568\) 0.762850i 0.0320085i
\(569\) −25.6513 −1.07536 −0.537679 0.843150i \(-0.680699\pi\)
−0.537679 + 0.843150i \(0.680699\pi\)
\(570\) 0 0
\(571\) 2.93559 0.122851 0.0614253 0.998112i \(-0.480435\pi\)
0.0614253 + 0.998112i \(0.480435\pi\)
\(572\) 10.4299i 0.436095i
\(573\) 23.7505i 0.992191i
\(574\) −1.18511 −0.0494657
\(575\) −16.2411 + 19.8994i −0.677301 + 0.829863i
\(576\) −29.6959 −1.23733
\(577\) 17.7732i 0.739908i 0.929050 + 0.369954i \(0.120627\pi\)
−0.929050 + 0.369954i \(0.879373\pi\)
\(578\) 2.67638i 0.111323i
\(579\) −1.15589 −0.0480373
\(580\) 12.5822 35.3154i 0.522446 1.46639i
\(581\) −22.9965 −0.954057
\(582\) 5.76400i 0.238925i
\(583\) 2.92016i 0.120941i
\(584\) 1.36380 0.0564344
\(585\) −12.0327 4.28700i −0.497490 0.177246i
\(586\) −0.211632 −0.00874243
\(587\) 23.1236i 0.954415i −0.878791 0.477207i \(-0.841649\pi\)
0.878791 0.477207i \(-0.158351\pi\)
\(588\) 17.1896i 0.708887i
\(589\) 0 0
\(590\) −2.67438 0.952826i −0.110102 0.0392272i
\(591\) 41.7368 1.71682
\(592\) 40.2058i 1.65245i
\(593\) 17.1574i 0.704569i 0.935893 + 0.352284i \(0.114595\pi\)
−0.935893 + 0.352284i \(0.885405\pi\)
\(594\) −4.24732 −0.174269
\(595\) −3.58230 + 10.0547i −0.146860 + 0.412204i
\(596\) 24.1849 0.990653
\(597\) 35.3973i 1.44872i
\(598\) 1.59480i 0.0652160i
\(599\) −13.3967 −0.547376 −0.273688 0.961819i \(-0.588244\pi\)
−0.273688 + 0.961819i \(0.588244\pi\)
\(600\) −10.2181 8.33958i −0.417151 0.340462i
\(601\) −8.26251 −0.337035 −0.168517 0.985699i \(-0.553898\pi\)
−0.168517 + 0.985699i \(0.553898\pi\)
\(602\) 2.11978i 0.0863958i
\(603\) 23.4482i 0.954885i
\(604\) −26.8528 −1.09263
\(605\) 5.19398 14.5784i 0.211165 0.592695i
\(606\) −9.00503 −0.365804
\(607\) 23.5191i 0.954612i −0.878737 0.477306i \(-0.841613\pi\)
0.878737 0.477306i \(-0.158387\pi\)
\(608\) 0 0
\(609\) −45.9124 −1.86046
\(610\) −1.44334 0.514233i −0.0584391 0.0208207i
\(611\) 8.59545 0.347735
\(612\) 21.4738i 0.868027i
\(613\) 29.8313i 1.20488i −0.798166 0.602438i \(-0.794196\pi\)
0.798166 0.602438i \(-0.205804\pi\)
\(614\) −2.19834 −0.0887179
\(615\) −14.4107 5.13426i −0.581098 0.207033i
\(616\) 7.91234 0.318797
\(617\) 11.5902i 0.466605i −0.972404 0.233303i \(-0.925047\pi\)
0.972404 0.233303i \(-0.0749533\pi\)
\(618\) 2.70183i 0.108684i
\(619\) −29.6697 −1.19253 −0.596264 0.802789i \(-0.703349\pi\)
−0.596264 + 0.802789i \(0.703349\pi\)
\(620\) −7.42714 + 20.8464i −0.298281 + 0.837211i
\(621\) −21.0823 −0.846002
\(622\) 2.79699i 0.112149i
\(623\) 4.33246i 0.173576i
\(624\) −12.6744 −0.507382
\(625\) 5.00991 + 24.4929i 0.200397 + 0.979715i
\(626\) 1.92287 0.0768532
\(627\) 0 0
\(628\) 35.3063i 1.40888i
\(629\) −27.1374 −1.08204
\(630\) −1.60144 + 4.49489i −0.0638029 + 0.179081i
\(631\) −24.4964 −0.975187 −0.487593 0.873071i \(-0.662125\pi\)
−0.487593 + 0.873071i \(0.662125\pi\)
\(632\) 5.84041i 0.232319i
\(633\) 12.1753i 0.483925i
\(634\) 4.04034 0.160463
\(635\) −40.4006 14.3939i −1.60325 0.571206i
\(636\) 3.66496 0.145325
\(637\) 4.10832i 0.162778i
\(638\) 8.94326i 0.354067i
\(639\) 3.56256 0.140933
\(640\) −15.2696 5.44024i −0.603582 0.215044i
\(641\) −12.3802 −0.488989 −0.244495 0.969651i \(-0.578622\pi\)
−0.244495 + 0.969651i \(0.578622\pi\)
\(642\) 11.3535i 0.448086i
\(643\) 45.9092i 1.81048i 0.424898 + 0.905241i \(0.360310\pi\)
−0.424898 + 0.905241i \(0.639690\pi\)
\(644\) 19.3392 0.762072
\(645\) −9.18351 + 25.7761i −0.361600 + 1.01493i
\(646\) 0 0
\(647\) 33.6773i 1.32399i −0.749508 0.661996i \(-0.769710\pi\)
0.749508 0.661996i \(-0.230290\pi\)
\(648\) 2.17518i 0.0854491i
\(649\) 21.9852 0.862994
\(650\) −1.20254 0.981464i −0.0471675 0.0384962i
\(651\) 27.1017 1.06220
\(652\) 29.7510i 1.16514i
\(653\) 19.6365i 0.768437i 0.923242 + 0.384219i \(0.125529\pi\)
−0.923242 + 0.384219i \(0.874471\pi\)
\(654\) 4.57627 0.178946
\(655\) −0.231134 + 0.648742i −0.00903114 + 0.0253484i
\(656\) −9.10651 −0.355549
\(657\) 6.36903i 0.248479i
\(658\) 3.21090i 0.125174i
\(659\) 20.7693 0.809059 0.404529 0.914525i \(-0.367435\pi\)
0.404529 + 0.914525i \(0.367435\pi\)
\(660\) 47.3765 + 16.8793i 1.84413 + 0.657025i
\(661\) −13.2561 −0.515603 −0.257802 0.966198i \(-0.582998\pi\)
−0.257802 + 0.966198i \(0.582998\pi\)
\(662\) 1.93490i 0.0752022i
\(663\) 8.55476i 0.332239i
\(664\) 11.4172 0.443074
\(665\) 0 0
\(666\) −12.1316 −0.470089
\(667\) 44.3914i 1.71884i
\(668\) 12.0622i 0.466702i
\(669\) 25.1901 0.973904
\(670\) −0.956296 + 2.68411i −0.0369449 + 0.103696i
\(671\) 11.8652 0.458052
\(672\) 14.9710i 0.577517i
\(673\) 12.8576i 0.495624i −0.968808 0.247812i \(-0.920289\pi\)
0.968808 0.247812i \(-0.0797115\pi\)
\(674\) −4.65388 −0.179261
\(675\) −12.9744 + 15.8969i −0.499384 + 0.611871i
\(676\) 22.0945 0.849787
\(677\) 25.5573i 0.982245i −0.871091 0.491122i \(-0.836587\pi\)
0.871091 0.491122i \(-0.163413\pi\)
\(678\) 3.96604i 0.152315i
\(679\) 16.7054 0.641093
\(680\) 1.77852 4.99193i 0.0682033 0.191432i
\(681\) −1.64386 −0.0629930
\(682\) 5.27913i 0.202148i
\(683\) 22.8692i 0.875064i 0.899203 + 0.437532i \(0.144147\pi\)
−0.899203 + 0.437532i \(0.855853\pi\)
\(684\) 0 0
\(685\) 30.5411 + 10.8812i 1.16691 + 0.415748i
\(686\) 4.85516 0.185371
\(687\) 19.4835i 0.743340i
\(688\) 16.2886i 0.620995i
\(689\) 0.875927 0.0333701
\(690\) −7.24417 2.58095i −0.275781 0.0982552i
\(691\) −32.3148 −1.22931 −0.614657 0.788795i \(-0.710705\pi\)
−0.614657 + 0.788795i \(0.710705\pi\)
\(692\) 5.36675i 0.204013i
\(693\) 36.9511i 1.40366i
\(694\) 1.33587 0.0507091
\(695\) −11.8552 + 33.2750i −0.449695 + 1.26219i
\(696\) 22.7944 0.864018
\(697\) 6.14656i 0.232818i
\(698\) 1.53149i 0.0579678i
\(699\) 55.2226 2.08871
\(700\) 11.9017 14.5825i 0.449841 0.551168i
\(701\) 34.7457 1.31233 0.656164 0.754618i \(-0.272178\pi\)
0.656164 + 0.754618i \(0.272178\pi\)
\(702\) 1.27402i 0.0480848i
\(703\) 0 0
\(704\) 27.9444 1.05319
\(705\) 13.9105 39.0438i 0.523901 1.47048i
\(706\) −2.02769 −0.0763131
\(707\) 26.0986i 0.981539i
\(708\) 27.5927i 1.03700i
\(709\) −8.00778 −0.300738 −0.150369 0.988630i \(-0.548046\pi\)
−0.150369 + 0.988630i \(0.548046\pi\)
\(710\) 0.407806 + 0.145293i 0.0153047 + 0.00545275i
\(711\) 27.2751 1.02290
\(712\) 2.15096i 0.0806105i
\(713\) 26.2038i 0.981341i
\(714\) −3.19570 −0.119596
\(715\) 11.3230 + 4.03415i 0.423456 + 0.150869i
\(716\) −22.0766 −0.825040
\(717\) 31.8587i 1.18979i
\(718\) 3.19916i 0.119391i
\(719\) −14.2690 −0.532143 −0.266071 0.963953i \(-0.585726\pi\)
−0.266071 + 0.963953i \(0.585726\pi\)
\(720\) −12.3056 + 34.5391i −0.458602 + 1.28720i
\(721\) 7.83053 0.291624
\(722\) 0 0
\(723\) 69.9107i 2.60001i
\(724\) −6.91991 −0.257177
\(725\) −33.4729 27.3192i −1.24315 1.01461i
\(726\) 4.63344 0.171963
\(727\) 3.13639i 0.116322i −0.998307 0.0581612i \(-0.981476\pi\)
0.998307 0.0581612i \(-0.0185237\pi\)
\(728\) 2.37337i 0.0879631i
\(729\) 43.8720 1.62489
\(730\) 0.259750 0.729061i 0.00961378 0.0269838i
\(731\) −10.9942 −0.406634
\(732\) 14.8915i 0.550407i
\(733\) 12.4004i 0.458020i 0.973424 + 0.229010i \(0.0735488\pi\)
−0.973424 + 0.229010i \(0.926451\pi\)
\(734\) −6.37944 −0.235469
\(735\) 18.6616 + 6.64874i 0.688342 + 0.245243i
\(736\) −14.4750 −0.533555
\(737\) 22.0653i 0.812784i
\(738\) 2.74777i 0.101147i
\(739\) 9.34314 0.343693 0.171846 0.985124i \(-0.445027\pi\)
0.171846 + 0.985124i \(0.445027\pi\)
\(740\) 45.0801 + 16.0611i 1.65718 + 0.590419i
\(741\) 0 0
\(742\) 0.327209i 0.0120122i
\(743\) 38.3186i 1.40577i 0.711302 + 0.702887i \(0.248106\pi\)
−0.711302 + 0.702887i \(0.751894\pi\)
\(744\) −13.4553 −0.493295
\(745\) 9.35445 26.2559i 0.342720 0.961942i
\(746\) −6.64901 −0.243438
\(747\) 53.3191i 1.95084i
\(748\) 20.2073i 0.738852i
\(749\) −32.9050 −1.20232
\(750\) −6.40433 + 3.87403i −0.233853 + 0.141460i
\(751\) 49.0370 1.78939 0.894693 0.446681i \(-0.147394\pi\)
0.894693 + 0.446681i \(0.147394\pi\)
\(752\) 24.6728i 0.899723i
\(753\) 42.1114i 1.53463i
\(754\) 2.68261 0.0976949
\(755\) −10.3864 + 29.1523i −0.377999 + 1.06096i
\(756\) 15.4493 0.561887
\(757\) 36.7936i 1.33728i 0.743584 + 0.668642i \(0.233124\pi\)
−0.743584 + 0.668642i \(0.766876\pi\)
\(758\) 3.34930i 0.121652i
\(759\) 59.5521 2.16160
\(760\) 0 0
\(761\) −0.255560 −0.00926406 −0.00463203 0.999989i \(-0.501474\pi\)
−0.00463203 + 0.999989i \(0.501474\pi\)
\(762\) 12.8405i 0.465163i
\(763\) 13.2631i 0.480155i
\(764\) −16.8281 −0.608818
\(765\) −23.3126 8.30582i −0.842870 0.300298i
\(766\) −2.50626 −0.0905548
\(767\) 6.59465i 0.238119i
\(768\) 31.2991i 1.12941i
\(769\) 9.45643 0.341008 0.170504 0.985357i \(-0.445460\pi\)
0.170504 + 0.985357i \(0.445460\pi\)
\(770\) 1.50699 4.22979i 0.0543081 0.152431i
\(771\) 43.9602 1.58319
\(772\) 0.818991i 0.0294761i
\(773\) 30.2259i 1.08715i 0.839360 + 0.543575i \(0.182930\pi\)
−0.839360 + 0.543575i \(0.817070\pi\)
\(774\) −4.91486 −0.176661
\(775\) 19.7587 + 16.1263i 0.709754 + 0.579273i
\(776\) −8.29381 −0.297730
\(777\) 58.6071i 2.10252i
\(778\) 1.23625i 0.0443217i
\(779\) 0 0
\(780\) −5.06309 + 14.2110i −0.181288 + 0.508835i
\(781\) −3.35244 −0.119960
\(782\) 3.08983i 0.110492i
\(783\) 35.4625i 1.26733i
\(784\) 11.7927 0.421168
\(785\) 38.3296 + 13.6561i 1.36804 + 0.487406i
\(786\) −0.206190 −0.00735454
\(787\) 36.3976i 1.29743i 0.761030 + 0.648717i \(0.224694\pi\)
−0.761030 + 0.648717i \(0.775306\pi\)
\(788\) 29.5720i 1.05346i
\(789\) 38.9934 1.38820
\(790\) 3.12217 + 1.11237i 0.111082 + 0.0395763i
\(791\) 11.4945 0.408697
\(792\) 18.3453i 0.651872i
\(793\) 3.55908i 0.126387i
\(794\) −5.83709 −0.207151
\(795\) 1.41756 3.97879i 0.0502758 0.141113i
\(796\) −25.0803 −0.888947
\(797\) 19.2118i 0.680517i −0.940332 0.340258i \(-0.889485\pi\)
0.940332 0.340258i \(-0.110515\pi\)
\(798\) 0 0
\(799\) 16.6532 0.589148
\(800\) −8.90815 + 10.9147i −0.314951 + 0.385894i
\(801\) 10.0451 0.354926
\(802\) 6.05461i 0.213796i
\(803\) 5.99338i 0.211502i
\(804\) 27.6931 0.976661
\(805\) 7.48019 20.9952i 0.263642 0.739985i
\(806\) −1.58352 −0.0557771
\(807\) 44.4749i 1.56559i
\(808\) 12.9573i 0.455837i
\(809\) 43.0501 1.51356 0.756781 0.653669i \(-0.226771\pi\)
0.756781 + 0.653669i \(0.226771\pi\)
\(810\) 1.16281 + 0.414286i 0.0408570 + 0.0145565i
\(811\) 31.3282 1.10008 0.550040 0.835138i \(-0.314612\pi\)
0.550040 + 0.835138i \(0.314612\pi\)
\(812\) 32.5305i 1.14160i
\(813\) 16.2257i 0.569058i
\(814\) 11.4161 0.400133
\(815\) −32.2986 11.5073i −1.13137 0.403085i
\(816\) −24.5560 −0.859631
\(817\) 0 0
\(818\) 2.42032i 0.0846245i
\(819\) 11.0838 0.387299
\(820\) −3.63781 + 10.2105i −0.127038 + 0.356567i
\(821\) 17.0708 0.595776 0.297888 0.954601i \(-0.403718\pi\)
0.297888 + 0.954601i \(0.403718\pi\)
\(822\) 9.70686i 0.338566i
\(823\) 36.3136i 1.26581i −0.774228 0.632907i \(-0.781862\pi\)
0.774228 0.632907i \(-0.218138\pi\)
\(824\) −3.88766 −0.135433
\(825\) 36.6493 44.9046i 1.27597 1.56338i
\(826\) 2.46348 0.0857155
\(827\) 19.3430i 0.672623i 0.941751 + 0.336311i \(0.109179\pi\)
−0.941751 + 0.336311i \(0.890821\pi\)
\(828\) 44.8393i 1.55828i
\(829\) −20.1843 −0.701029 −0.350514 0.936557i \(-0.613993\pi\)
−0.350514 + 0.936557i \(0.613993\pi\)
\(830\) 2.17453 6.10343i 0.0754790 0.211853i
\(831\) 17.2773 0.599345
\(832\) 8.38217i 0.290600i
\(833\) 7.95964i 0.275785i
\(834\) −10.5758 −0.366210
\(835\) −13.0951 4.66553i −0.453176 0.161457i
\(836\) 0 0
\(837\) 20.9332i 0.723557i
\(838\) 0.979889i 0.0338497i
\(839\) 25.8209 0.891437 0.445719 0.895173i \(-0.352948\pi\)
0.445719 + 0.895173i \(0.352948\pi\)
\(840\) 10.7808 + 3.84097i 0.371972 + 0.132526i
\(841\) 45.6708 1.57486
\(842\) 4.95753i 0.170848i
\(843\) 7.33776i 0.252726i
\(844\) 8.62664 0.296941
\(845\) 8.54589 23.9864i 0.293987 0.825158i
\(846\) 7.44469 0.255954
\(847\) 13.4288i 0.461418i
\(848\) 2.51430i 0.0863413i
\(849\) −85.0654 −2.91944
\(850\) −2.32985 1.90153i −0.0799133 0.0652220i
\(851\) 56.6655 1.94247
\(852\) 4.20750i 0.144147i
\(853\) 14.3234i 0.490425i 0.969469 + 0.245212i \(0.0788577\pi\)
−0.969469 + 0.245212i \(0.921142\pi\)
\(854\) 1.32952 0.0454953
\(855\) 0 0
\(856\) 16.3365 0.558370
\(857\) 24.2649i 0.828874i 0.910078 + 0.414437i \(0.136021\pi\)
−0.910078 + 0.414437i \(0.863979\pi\)
\(858\) 3.59878i 0.122860i
\(859\) −40.5232 −1.38263 −0.691317 0.722551i \(-0.742969\pi\)
−0.691317 + 0.722551i \(0.742969\pi\)
\(860\) 18.2633 + 6.50684i 0.622773 + 0.221881i
\(861\) 13.2744 0.452389
\(862\) 3.29515i 0.112233i
\(863\) 22.9160i 0.780069i −0.920800 0.390035i \(-0.872463\pi\)
0.920800 0.390035i \(-0.127537\pi\)
\(864\) −11.5635 −0.393398
\(865\) −5.82631 2.07580i −0.198100 0.0705792i
\(866\) −8.40453 −0.285598
\(867\) 29.9779i 1.01810i
\(868\) 19.2025i 0.651775i
\(869\) −25.6664 −0.870673
\(870\) 4.34143 12.1854i 0.147188 0.413125i
\(871\) 6.61866 0.224265
\(872\) 6.58478i 0.222989i
\(873\) 38.7326i 1.31090i
\(874\) 0 0
\(875\) −11.2278 18.5612i −0.379570 0.627483i
\(876\) −7.52203 −0.254146
\(877\) 49.6951i 1.67808i 0.544067 + 0.839042i \(0.316884\pi\)
−0.544067 + 0.839042i \(0.683116\pi\)
\(878\) 5.72515i 0.193214i
\(879\) 2.37047 0.0799539
\(880\) 11.5798 32.5020i 0.390355 1.09564i
\(881\) −11.0358 −0.371804 −0.185902 0.982568i \(-0.559521\pi\)
−0.185902 + 0.982568i \(0.559521\pi\)
\(882\) 3.55830i 0.119814i
\(883\) 22.1244i 0.744547i 0.928123 + 0.372273i \(0.121422\pi\)
−0.928123 + 0.372273i \(0.878578\pi\)
\(884\) −6.06135 −0.203865
\(885\) 29.9554 + 10.6725i 1.00694 + 0.358753i
\(886\) −0.586472 −0.0197029
\(887\) 20.0329i 0.672640i −0.941748 0.336320i \(-0.890818\pi\)
0.941748 0.336320i \(-0.109182\pi\)
\(888\) 29.0970i 0.976430i
\(889\) 37.2148 1.24814
\(890\) 1.14986 + 0.409673i 0.0385435 + 0.0137323i
\(891\) −9.55909 −0.320242
\(892\) 17.8481i 0.597597i
\(893\) 0 0
\(894\) 8.34491 0.279095
\(895\) −8.53896 + 23.9670i −0.285426 + 0.801129i
\(896\) 14.0654 0.469893
\(897\) 17.8632i 0.596433i
\(898\) 9.33951i 0.311663i
\(899\) −44.0775 −1.47007
\(900\) 33.8107 + 27.5949i 1.12702 + 0.919830i
\(901\) 1.69706 0.0565372
\(902\) 2.58571i 0.0860947i
\(903\) 23.7435i 0.790133i
\(904\) −5.70673 −0.189803
\(905\) −2.67654 + 7.51247i −0.0889713 + 0.249723i
\(906\) −9.26546 −0.307824
\(907\) 0.681366i 0.0226244i 0.999936 + 0.0113122i \(0.00360086\pi\)
−0.999936 + 0.0113122i \(0.996399\pi\)
\(908\) 1.16474i 0.0386531i
\(909\) 60.5114 2.00704
\(910\) 1.26876 + 0.452034i 0.0420590 + 0.0149848i
\(911\) −28.7169 −0.951433 −0.475716 0.879599i \(-0.657811\pi\)
−0.475716 + 0.879599i \(0.657811\pi\)
\(912\) 0 0
\(913\) 50.1744i 1.66053i
\(914\) −0.458652 −0.0151709
\(915\) 16.1667 + 5.75987i 0.534455 + 0.190416i
\(916\) 13.8047 0.456121
\(917\) 0.597584i 0.0197340i
\(918\) 2.46834i 0.0814674i
\(919\) −6.91259 −0.228025 −0.114013 0.993479i \(-0.536370\pi\)
−0.114013 + 0.993479i \(0.536370\pi\)
\(920\) −3.71373 + 10.4236i −0.122438 + 0.343657i
\(921\) 24.6234 0.811370
\(922\) 4.11220i 0.135428i
\(923\) 1.00559i 0.0330995i
\(924\) −43.6405 −1.43567
\(925\) 34.8729 42.7281i 1.14661 1.40489i
\(926\) −5.95647 −0.195742
\(927\) 18.1556i 0.596309i
\(928\) 24.3484i 0.799276i
\(929\) −40.8302 −1.33960 −0.669798 0.742544i \(-0.733619\pi\)
−0.669798 + 0.742544i \(0.733619\pi\)
\(930\) −2.56271 + 7.19296i −0.0840344 + 0.235866i
\(931\) 0 0
\(932\) 39.1272i 1.28165i
\(933\) 31.3288i 1.02566i
\(934\) −3.33737 −0.109202
\(935\) 21.9377 + 7.81595i 0.717438 + 0.255609i
\(936\) −5.50284 −0.179866
\(937\) 14.7439i 0.481664i −0.970567 0.240832i \(-0.922580\pi\)
0.970567 0.240832i \(-0.0774202\pi\)
\(938\) 2.47245i 0.0807284i
\(939\) −21.5378 −0.702861
\(940\) −27.6639 9.85611i −0.902298 0.321471i
\(941\) 52.2137 1.70212 0.851059 0.525071i \(-0.175961\pi\)
0.851059 + 0.525071i \(0.175961\pi\)
\(942\) 12.1823i 0.396921i
\(943\) 12.8346i 0.417952i
\(944\) 18.9296 0.616105
\(945\) 5.97563 16.7723i 0.194387 0.545602i
\(946\) 4.62499 0.150371
\(947\) 57.3403i 1.86331i −0.363343 0.931655i \(-0.618365\pi\)
0.363343 0.931655i \(-0.381635\pi\)
\(948\) 32.2128i 1.04622i
\(949\) −1.79777 −0.0583580
\(950\) 0 0
\(951\) −45.2555 −1.46751
\(952\) 4.59828i 0.149031i
\(953\) 9.31765i 0.301828i −0.988547 0.150914i \(-0.951778\pi\)
0.988547 0.150914i \(-0.0482217\pi\)
\(954\) 0.758657 0.0245624
\(955\) −6.50890 + 18.2691i −0.210623 + 0.591173i
\(956\) 22.5731 0.730065
\(957\) 100.173i 3.23812i
\(958\) 5.31507i 0.171722i
\(959\) −28.1327 −0.908452
\(960\) 38.0750 + 13.5654i 1.22887 + 0.437820i
\(961\) −4.98144 −0.160692
\(962\) 3.42435i 0.110405i
\(963\) 76.2925i 2.45849i
\(964\) −49.5343 −1.59539
\(965\) 0.889122 + 0.316776i 0.0286218 + 0.0101974i
\(966\) 6.67292 0.214698
\(967\) 8.82697i 0.283856i 0.989877 + 0.141928i \(0.0453302\pi\)
−0.989877 + 0.141928i \(0.954670\pi\)
\(968\) 6.66705i 0.214287i
\(969\) 0 0
\(970\) −1.57964 + 4.43371i −0.0507193 + 0.142358i
\(971\) −55.9918 −1.79686 −0.898431 0.439114i \(-0.855292\pi\)
−0.898431 + 0.439114i \(0.855292\pi\)
\(972\) 35.8846i 1.15100i
\(973\) 30.6511i 0.982628i
\(974\) −7.14984 −0.229096
\(975\) 13.4695 + 10.9933i 0.431370 + 0.352067i
\(976\) 10.2161 0.327011
\(977\) 41.1034i 1.31501i −0.753449 0.657506i \(-0.771611\pi\)
0.753449 0.657506i \(-0.228389\pi\)
\(978\) 10.2655i 0.328253i
\(979\) −9.45265 −0.302108
\(980\) 4.71087 13.2224i 0.150483 0.422374i
\(981\) −30.7513 −0.981815
\(982\) 4.48752i 0.143203i
\(983\) 2.49864i 0.0796941i −0.999206 0.0398471i \(-0.987313\pi\)
0.999206 0.0398471i \(-0.0126871\pi\)
\(984\) −6.59039 −0.210094
\(985\) −32.1043 11.4381i −1.02293 0.364449i
\(986\) 5.19741 0.165519
\(987\) 35.9650i 1.14478i
\(988\) 0 0
\(989\) 22.9569 0.729986
\(990\) 9.80706 + 3.49406i 0.311689 + 0.111048i
\(991\) −17.4234 −0.553471 −0.276736 0.960946i \(-0.589253\pi\)
−0.276736 + 0.960946i \(0.589253\pi\)
\(992\) 14.3727i 0.456332i
\(993\) 21.6727i 0.687762i
\(994\) −0.375647 −0.0119148
\(995\) −9.70076 + 27.2279i −0.307535 + 0.863183i
\(996\) −62.9717 −1.99533
\(997\) 12.8010i 0.405412i −0.979240 0.202706i \(-0.935026\pi\)
0.979240 0.202706i \(-0.0649736\pi\)
\(998\) 2.54645i 0.0806065i
\(999\) 45.2679 1.43221
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.1084.12 24
5.2 odd 4 9025.2.a.ct.1.13 24
5.3 odd 4 9025.2.a.ct.1.12 24
5.4 even 2 inner 1805.2.b.l.1084.13 24
19.3 odd 18 95.2.p.a.9.4 48
19.13 odd 18 95.2.p.a.74.5 yes 48
19.18 odd 2 1805.2.b.k.1084.13 24
57.32 even 18 855.2.da.b.739.4 48
57.41 even 18 855.2.da.b.199.5 48
95.3 even 36 475.2.l.f.351.5 48
95.13 even 36 475.2.l.f.226.5 48
95.18 even 4 9025.2.a.cu.1.13 24
95.22 even 36 475.2.l.f.351.4 48
95.32 even 36 475.2.l.f.226.4 48
95.37 even 4 9025.2.a.cu.1.12 24
95.79 odd 18 95.2.p.a.9.5 yes 48
95.89 odd 18 95.2.p.a.74.4 yes 48
95.94 odd 2 1805.2.b.k.1084.12 24
285.89 even 18 855.2.da.b.739.5 48
285.269 even 18 855.2.da.b.199.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.4 48 19.3 odd 18
95.2.p.a.9.5 yes 48 95.79 odd 18
95.2.p.a.74.4 yes 48 95.89 odd 18
95.2.p.a.74.5 yes 48 19.13 odd 18
475.2.l.f.226.4 48 95.32 even 36
475.2.l.f.226.5 48 95.13 even 36
475.2.l.f.351.4 48 95.22 even 36
475.2.l.f.351.5 48 95.3 even 36
855.2.da.b.199.4 48 285.269 even 18
855.2.da.b.199.5 48 57.41 even 18
855.2.da.b.739.4 48 57.32 even 18
855.2.da.b.739.5 48 285.89 even 18
1805.2.b.k.1084.12 24 95.94 odd 2
1805.2.b.k.1084.13 24 19.18 odd 2
1805.2.b.l.1084.12 24 1.1 even 1 trivial
1805.2.b.l.1084.13 24 5.4 even 2 inner
9025.2.a.ct.1.12 24 5.3 odd 4
9025.2.a.ct.1.13 24 5.2 odd 4
9025.2.a.cu.1.12 24 95.37 even 4
9025.2.a.cu.1.13 24 95.18 even 4