Properties

Label 460.2.m.b.41.3
Level $460$
Weight $2$
Character 460.41
Analytic conductor $3.673$
Analytic rank $0$
Dimension $50$
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] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 41.3
Character \(\chi\) \(=\) 460.41
Dual form 460.2.m.b.101.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.249442 + 0.287871i) q^{3} +(0.142315 - 0.989821i) q^{5} +(0.948129 + 2.07611i) q^{7} +(0.406296 + 2.82585i) q^{9} +O(q^{10})\) \(q+(-0.249442 + 0.287871i) q^{3} +(0.142315 - 0.989821i) q^{5} +(0.948129 + 2.07611i) q^{7} +(0.406296 + 2.82585i) q^{9} +(-1.15200 + 0.338258i) q^{11} +(-0.598825 + 1.31124i) q^{13} +(0.249442 + 0.287871i) q^{15} +(2.71926 - 1.74756i) q^{17} +(3.45147 + 2.21813i) q^{19} +(-0.834156 - 0.244930i) q^{21} +(0.285852 + 4.78730i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(-1.87615 - 1.20573i) q^{27} +(7.48167 - 4.80818i) q^{29} +(3.34367 + 3.85880i) q^{31} +(0.189983 - 0.416004i) q^{33} +(2.18991 - 0.643017i) q^{35} +(0.528714 + 3.67728i) q^{37} +(-0.228097 - 0.499464i) q^{39} +(-0.982571 + 6.83393i) q^{41} +(-6.09554 + 7.03463i) q^{43} +2.85491 q^{45} -5.96396 q^{47} +(1.17273 - 1.35340i) q^{49} +(-0.175225 + 1.21871i) q^{51} +(-5.25446 - 11.5057i) q^{53} +(0.170868 + 1.18841i) q^{55} +(-1.49948 + 0.440286i) q^{57} +(2.77695 - 6.08067i) q^{59} +(-8.39220 - 9.68511i) q^{61} +(-5.48156 + 3.52279i) q^{63} +(1.21268 + 0.779340i) q^{65} +(6.69305 + 1.96526i) q^{67} +(-1.44943 - 1.11187i) q^{69} +(7.66043 + 2.24931i) q^{71} +(-3.23766 - 2.08072i) q^{73} +(0.320440 - 0.205935i) q^{75} +(-1.79451 - 2.07097i) q^{77} +(3.99170 - 8.74061i) q^{79} +(-7.40271 + 2.17363i) q^{81} +(0.0525008 + 0.365151i) q^{83} +(-1.34279 - 2.94029i) q^{85} +(-0.482106 + 3.35312i) q^{87} +(6.81641 - 7.86656i) q^{89} -3.29006 q^{91} -1.94489 q^{93} +(2.68675 - 3.10067i) q^{95} +(1.48856 - 10.3532i) q^{97} +(-1.42392 - 3.11795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\)

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 0
\(3\) −0.249442 + 0.287871i −0.144015 + 0.166203i −0.823174 0.567789i \(-0.807799\pi\)
0.679159 + 0.733991i \(0.262345\pi\)
\(4\) 0 0
\(5\) 0.142315 0.989821i 0.0636451 0.442662i
\(6\) 0 0
\(7\) 0.948129 + 2.07611i 0.358359 + 0.784697i 0.999846 + 0.0175627i \(0.00559067\pi\)
−0.641487 + 0.767134i \(0.721682\pi\)
\(8\) 0 0
\(9\) 0.406296 + 2.82585i 0.135432 + 0.941950i
\(10\) 0 0
\(11\) −1.15200 + 0.338258i −0.347341 + 0.101989i −0.450750 0.892650i \(-0.648843\pi\)
0.103408 + 0.994639i \(0.467025\pi\)
\(12\) 0 0
\(13\) −0.598825 + 1.31124i −0.166084 + 0.363674i −0.974314 0.225193i \(-0.927699\pi\)
0.808230 + 0.588867i \(0.200426\pi\)
\(14\) 0 0
\(15\) 0.249442 + 0.287871i 0.0644056 + 0.0743280i
\(16\) 0 0
\(17\) 2.71926 1.74756i 0.659518 0.423847i −0.167615 0.985853i \(-0.553607\pi\)
0.827133 + 0.562006i \(0.189970\pi\)
\(18\) 0 0
\(19\) 3.45147 + 2.21813i 0.791822 + 0.508873i 0.872938 0.487831i \(-0.162212\pi\)
−0.0811156 + 0.996705i \(0.525848\pi\)
\(20\) 0 0
\(21\) −0.834156 0.244930i −0.182028 0.0534482i
\(22\) 0 0
\(23\) 0.285852 + 4.78730i 0.0596043 + 0.998222i
\(24\) 0 0
\(25\) −0.959493 0.281733i −0.191899 0.0563465i
\(26\) 0 0
\(27\) −1.87615 1.20573i −0.361065 0.232042i
\(28\) 0 0
\(29\) 7.48167 4.80818i 1.38931 0.892857i 0.389706 0.920939i \(-0.372576\pi\)
0.999606 + 0.0280825i \(0.00894013\pi\)
\(30\) 0 0
\(31\) 3.34367 + 3.85880i 0.600541 + 0.693062i 0.971891 0.235431i \(-0.0756503\pi\)
−0.371350 + 0.928493i \(0.621105\pi\)
\(32\) 0 0
\(33\) 0.189983 0.416004i 0.0330717 0.0724170i
\(34\) 0 0
\(35\) 2.18991 0.643017i 0.370163 0.108690i
\(36\) 0 0
\(37\) 0.528714 + 3.67728i 0.0869200 + 0.604542i 0.985998 + 0.166754i \(0.0533287\pi\)
−0.899078 + 0.437788i \(0.855762\pi\)
\(38\) 0 0
\(39\) −0.228097 0.499464i −0.0365248 0.0799782i
\(40\) 0 0
\(41\) −0.982571 + 6.83393i −0.153452 + 1.06728i 0.756925 + 0.653501i \(0.226701\pi\)
−0.910377 + 0.413780i \(0.864208\pi\)
\(42\) 0 0
\(43\) −6.09554 + 7.03463i −0.929561 + 1.07277i 0.0676182 + 0.997711i \(0.478460\pi\)
−0.997179 + 0.0750592i \(0.976085\pi\)
\(44\) 0 0
\(45\) 2.85491 0.425585
\(46\) 0 0
\(47\) −5.96396 −0.869933 −0.434966 0.900447i \(-0.643240\pi\)
−0.434966 + 0.900447i \(0.643240\pi\)
\(48\) 0 0
\(49\) 1.17273 1.35340i 0.167533 0.193343i
\(50\) 0 0
\(51\) −0.175225 + 1.21871i −0.0245363 + 0.170654i
\(52\) 0 0
\(53\) −5.25446 11.5057i −0.721756 1.58042i −0.811428 0.584453i \(-0.801309\pi\)
0.0896720 0.995971i \(-0.471418\pi\)
\(54\) 0 0
\(55\) 0.170868 + 1.18841i 0.0230399 + 0.160246i
\(56\) 0 0
\(57\) −1.49948 + 0.440286i −0.198611 + 0.0583173i
\(58\) 0 0
\(59\) 2.77695 6.08067i 0.361528 0.791636i −0.638235 0.769842i \(-0.720335\pi\)
0.999762 0.0217937i \(-0.00693770\pi\)
\(60\) 0 0
\(61\) −8.39220 9.68511i −1.07451 1.24005i −0.969373 0.245594i \(-0.921017\pi\)
−0.105138 0.994458i \(-0.533528\pi\)
\(62\) 0 0
\(63\) −5.48156 + 3.52279i −0.690612 + 0.443829i
\(64\) 0 0
\(65\) 1.21268 + 0.779340i 0.150414 + 0.0966652i
\(66\) 0 0
\(67\) 6.69305 + 1.96526i 0.817687 + 0.240094i 0.663720 0.747981i \(-0.268977\pi\)
0.153967 + 0.988076i \(0.450795\pi\)
\(68\) 0 0
\(69\) −1.44943 1.11187i −0.174491 0.133853i
\(70\) 0 0
\(71\) 7.66043 + 2.24931i 0.909126 + 0.266944i 0.702673 0.711513i \(-0.251990\pi\)
0.206453 + 0.978456i \(0.433808\pi\)
\(72\) 0 0
\(73\) −3.23766 2.08072i −0.378940 0.243530i 0.337280 0.941404i \(-0.390493\pi\)
−0.716220 + 0.697874i \(0.754129\pi\)
\(74\) 0 0
\(75\) 0.320440 0.205935i 0.0370013 0.0237793i
\(76\) 0 0
\(77\) −1.79451 2.07097i −0.204503 0.236009i
\(78\) 0 0
\(79\) 3.99170 8.74061i 0.449102 0.983395i −0.540736 0.841192i \(-0.681854\pi\)
0.989838 0.142203i \(-0.0454186\pi\)
\(80\) 0 0
\(81\) −7.40271 + 2.17363i −0.822523 + 0.241515i
\(82\) 0 0
\(83\) 0.0525008 + 0.365151i 0.00576271 + 0.0400805i 0.992500 0.122245i \(-0.0390095\pi\)
−0.986737 + 0.162326i \(0.948100\pi\)
\(84\) 0 0
\(85\) −1.34279 2.94029i −0.145646 0.318919i
\(86\) 0 0
\(87\) −0.482106 + 3.35312i −0.0516872 + 0.359492i
\(88\) 0 0
\(89\) 6.81641 7.86656i 0.722538 0.833854i −0.269072 0.963120i \(-0.586717\pi\)
0.991610 + 0.129267i \(0.0412623\pi\)
\(90\) 0 0
\(91\) −3.29006 −0.344891
\(92\) 0 0
\(93\) −1.94489 −0.201676
\(94\) 0 0
\(95\) 2.68675 3.10067i 0.275654 0.318122i
\(96\) 0 0
\(97\) 1.48856 10.3532i 0.151141 1.05121i −0.763171 0.646196i \(-0.776359\pi\)
0.914312 0.405011i \(-0.132732\pi\)
\(98\) 0 0
\(99\) −1.42392 3.11795i −0.143109 0.313366i
\(100\) 0 0
\(101\) −1.26265 8.78191i −0.125638 0.873832i −0.950992 0.309216i \(-0.899933\pi\)
0.825354 0.564616i \(-0.190976\pi\)
\(102\) 0 0
\(103\) −8.21066 + 2.41087i −0.809021 + 0.237550i −0.659982 0.751281i \(-0.729436\pi\)
−0.149039 + 0.988831i \(0.547618\pi\)
\(104\) 0 0
\(105\) −0.361150 + 0.790808i −0.0352446 + 0.0771750i
\(106\) 0 0
\(107\) −0.173877 0.200665i −0.0168093 0.0193990i 0.747283 0.664506i \(-0.231358\pi\)
−0.764092 + 0.645107i \(0.776813\pi\)
\(108\) 0 0
\(109\) 1.81220 1.16463i 0.173577 0.111551i −0.450968 0.892540i \(-0.648921\pi\)
0.624545 + 0.780989i \(0.285285\pi\)
\(110\) 0 0
\(111\) −1.19047 0.765067i −0.112994 0.0726169i
\(112\) 0 0
\(113\) −1.08121 0.317471i −0.101711 0.0298651i 0.230481 0.973077i \(-0.425970\pi\)
−0.332192 + 0.943212i \(0.607788\pi\)
\(114\) 0 0
\(115\) 4.77926 + 0.398362i 0.445668 + 0.0371474i
\(116\) 0 0
\(117\) −3.94868 1.15944i −0.365056 0.107190i
\(118\) 0 0
\(119\) 6.20635 + 3.98858i 0.568935 + 0.365633i
\(120\) 0 0
\(121\) −8.04110 + 5.16770i −0.731009 + 0.469791i
\(122\) 0 0
\(123\) −1.72220 1.98752i −0.155285 0.179209i
\(124\) 0 0
\(125\) −0.415415 + 0.909632i −0.0371558 + 0.0813600i
\(126\) 0 0
\(127\) −18.4646 + 5.42168i −1.63846 + 0.481096i −0.965894 0.258937i \(-0.916628\pi\)
−0.672570 + 0.740034i \(0.734810\pi\)
\(128\) 0 0
\(129\) −0.504584 3.50946i −0.0444262 0.308991i
\(130\) 0 0
\(131\) −2.24027 4.90550i −0.195733 0.428596i 0.786162 0.618020i \(-0.212065\pi\)
−0.981895 + 0.189425i \(0.939338\pi\)
\(132\) 0 0
\(133\) −1.33264 + 9.26872i −0.115555 + 0.803700i
\(134\) 0 0
\(135\) −1.46046 + 1.68546i −0.125696 + 0.145061i
\(136\) 0 0
\(137\) −1.66235 −0.142024 −0.0710120 0.997475i \(-0.522623\pi\)
−0.0710120 + 0.997475i \(0.522623\pi\)
\(138\) 0 0
\(139\) −0.330904 −0.0280669 −0.0140335 0.999902i \(-0.504467\pi\)
−0.0140335 + 0.999902i \(0.504467\pi\)
\(140\) 0 0
\(141\) 1.48766 1.71685i 0.125284 0.144585i
\(142\) 0 0
\(143\) 0.246308 1.71311i 0.0205973 0.143258i
\(144\) 0 0
\(145\) −3.69449 8.08980i −0.306810 0.671821i
\(146\) 0 0
\(147\) 0.0970777 + 0.675190i 0.00800683 + 0.0556887i
\(148\) 0 0
\(149\) 6.67270 1.95928i 0.546649 0.160511i 0.00326460 0.999995i \(-0.498961\pi\)
0.543384 + 0.839484i \(0.317143\pi\)
\(150\) 0 0
\(151\) 1.15611 2.53153i 0.0940831 0.206013i −0.856739 0.515750i \(-0.827513\pi\)
0.950823 + 0.309736i \(0.100241\pi\)
\(152\) 0 0
\(153\) 6.04318 + 6.97420i 0.488562 + 0.563831i
\(154\) 0 0
\(155\) 4.29538 2.76047i 0.345013 0.221727i
\(156\) 0 0
\(157\) 9.09701 + 5.84629i 0.726020 + 0.466585i 0.850726 0.525609i \(-0.176162\pi\)
−0.124706 + 0.992194i \(0.539799\pi\)
\(158\) 0 0
\(159\) 4.62283 + 1.35739i 0.366614 + 0.107648i
\(160\) 0 0
\(161\) −9.66796 + 5.13244i −0.761942 + 0.404493i
\(162\) 0 0
\(163\) −19.1124 5.61190i −1.49700 0.439558i −0.572231 0.820092i \(-0.693922\pi\)
−0.924767 + 0.380534i \(0.875740\pi\)
\(164\) 0 0
\(165\) −0.384732 0.247252i −0.0299514 0.0192486i
\(166\) 0 0
\(167\) 12.8546 8.26114i 0.994718 0.639267i 0.0613235 0.998118i \(-0.480468\pi\)
0.933395 + 0.358851i \(0.116832\pi\)
\(168\) 0 0
\(169\) 7.15242 + 8.25433i 0.550186 + 0.634949i
\(170\) 0 0
\(171\) −4.86578 + 10.6546i −0.372095 + 0.814775i
\(172\) 0 0
\(173\) 3.08418 0.905596i 0.234486 0.0688512i −0.162379 0.986729i \(-0.551917\pi\)
0.396864 + 0.917877i \(0.370098\pi\)
\(174\) 0 0
\(175\) −0.324814 2.25913i −0.0245537 0.170775i
\(176\) 0 0
\(177\) 1.05776 + 2.31618i 0.0795063 + 0.174094i
\(178\) 0 0
\(179\) −2.38199 + 16.5671i −0.178038 + 1.23828i 0.683257 + 0.730178i \(0.260563\pi\)
−0.861295 + 0.508105i \(0.830346\pi\)
\(180\) 0 0
\(181\) 9.29775 10.7302i 0.691096 0.797567i −0.296425 0.955056i \(-0.595794\pi\)
0.987521 + 0.157489i \(0.0503399\pi\)
\(182\) 0 0
\(183\) 4.88143 0.360846
\(184\) 0 0
\(185\) 3.71510 0.273140
\(186\) 0 0
\(187\) −2.54147 + 2.93301i −0.185851 + 0.214483i
\(188\) 0 0
\(189\) 0.724396 5.03828i 0.0526920 0.366481i
\(190\) 0 0
\(191\) −1.36632 2.99183i −0.0988637 0.216481i 0.853737 0.520704i \(-0.174331\pi\)
−0.952601 + 0.304223i \(0.901603\pi\)
\(192\) 0 0
\(193\) 1.76885 + 12.3027i 0.127325 + 0.885564i 0.948925 + 0.315501i \(0.102172\pi\)
−0.821600 + 0.570064i \(0.806919\pi\)
\(194\) 0 0
\(195\) −0.526842 + 0.154695i −0.0377279 + 0.0110779i
\(196\) 0 0
\(197\) 9.21268 20.1729i 0.656376 1.43726i −0.229485 0.973312i \(-0.573704\pi\)
0.885861 0.463951i \(-0.153569\pi\)
\(198\) 0 0
\(199\) 0.265343 + 0.306222i 0.0188097 + 0.0217075i 0.765076 0.643939i \(-0.222701\pi\)
−0.746267 + 0.665647i \(0.768156\pi\)
\(200\) 0 0
\(201\) −2.23527 + 1.43652i −0.157664 + 0.101324i
\(202\) 0 0
\(203\) 17.0759 + 10.9740i 1.19849 + 0.770226i
\(204\) 0 0
\(205\) 6.62454 + 1.94514i 0.462678 + 0.135854i
\(206\) 0 0
\(207\) −13.4121 + 2.75284i −0.932203 + 0.191336i
\(208\) 0 0
\(209\) −4.72640 1.38780i −0.326932 0.0959959i
\(210\) 0 0
\(211\) 9.10777 + 5.85321i 0.627005 + 0.402952i 0.815200 0.579180i \(-0.196627\pi\)
−0.188195 + 0.982132i \(0.560264\pi\)
\(212\) 0 0
\(213\) −2.55834 + 1.64415i −0.175295 + 0.112655i
\(214\) 0 0
\(215\) 6.09554 + 7.03463i 0.415712 + 0.479758i
\(216\) 0 0
\(217\) −4.84108 + 10.6005i −0.328634 + 0.719608i
\(218\) 0 0
\(219\) 1.40659 0.413012i 0.0950484 0.0279087i
\(220\) 0 0
\(221\) 0.663121 + 4.61211i 0.0446063 + 0.310244i
\(222\) 0 0
\(223\) 0.923781 + 2.02280i 0.0618610 + 0.135457i 0.938038 0.346534i \(-0.112641\pi\)
−0.876177 + 0.481990i \(0.839914\pi\)
\(224\) 0 0
\(225\) 0.406296 2.82585i 0.0270864 0.188390i
\(226\) 0 0
\(227\) 5.79090 6.68306i 0.384356 0.443570i −0.530296 0.847812i \(-0.677919\pi\)
0.914652 + 0.404242i \(0.132465\pi\)
\(228\) 0 0
\(229\) 17.4428 1.15265 0.576327 0.817219i \(-0.304485\pi\)
0.576327 + 0.817219i \(0.304485\pi\)
\(230\) 0 0
\(231\) 1.04380 0.0686769
\(232\) 0 0
\(233\) −14.4825 + 16.7137i −0.948779 + 1.09495i 0.0465992 + 0.998914i \(0.485162\pi\)
−0.995378 + 0.0960354i \(0.969384\pi\)
\(234\) 0 0
\(235\) −0.848760 + 5.90326i −0.0553670 + 0.385086i
\(236\) 0 0
\(237\) 1.52047 + 3.32937i 0.0987653 + 0.216266i
\(238\) 0 0
\(239\) −3.20880 22.3177i −0.207560 1.44361i −0.781085 0.624425i \(-0.785333\pi\)
0.573525 0.819188i \(-0.305576\pi\)
\(240\) 0 0
\(241\) −17.0555 + 5.00793i −1.09864 + 0.322589i −0.780311 0.625391i \(-0.784939\pi\)
−0.318327 + 0.947981i \(0.603121\pi\)
\(242\) 0 0
\(243\) 4.00017 8.75916i 0.256611 0.561900i
\(244\) 0 0
\(245\) −1.17273 1.35340i −0.0749229 0.0864657i
\(246\) 0 0
\(247\) −4.97534 + 3.19745i −0.316573 + 0.203449i
\(248\) 0 0
\(249\) −0.118212 0.0759704i −0.00749140 0.00481443i
\(250\) 0 0
\(251\) 26.4033 + 7.75270i 1.66656 + 0.489346i 0.972952 0.231007i \(-0.0742020\pi\)
0.693608 + 0.720353i \(0.256020\pi\)
\(252\) 0 0
\(253\) −1.94865 5.41829i −0.122510 0.340645i
\(254\) 0 0
\(255\) 1.18137 + 0.346882i 0.0739804 + 0.0217226i
\(256\) 0 0
\(257\) 8.99614 + 5.78147i 0.561164 + 0.360638i 0.790266 0.612764i \(-0.209943\pi\)
−0.229102 + 0.973402i \(0.573579\pi\)
\(258\) 0 0
\(259\) −7.13317 + 4.58421i −0.443234 + 0.284849i
\(260\) 0 0
\(261\) 16.6270 + 19.1885i 1.02918 + 1.18774i
\(262\) 0 0
\(263\) 8.67645 18.9988i 0.535013 1.17152i −0.428423 0.903578i \(-0.640931\pi\)
0.963436 0.267937i \(-0.0863420\pi\)
\(264\) 0 0
\(265\) −12.1363 + 3.56355i −0.745529 + 0.218907i
\(266\) 0 0
\(267\) 0.564258 + 3.92450i 0.0345320 + 0.240175i
\(268\) 0 0
\(269\) 4.62193 + 10.1206i 0.281804 + 0.617065i 0.996611 0.0822567i \(-0.0262127\pi\)
−0.714807 + 0.699322i \(0.753485\pi\)
\(270\) 0 0
\(271\) −0.857736 + 5.96569i −0.0521038 + 0.362390i 0.947044 + 0.321105i \(0.104054\pi\)
−0.999147 + 0.0412848i \(0.986855\pi\)
\(272\) 0 0
\(273\) 0.820677 0.947112i 0.0496696 0.0573218i
\(274\) 0 0
\(275\) 1.20064 0.0724010
\(276\) 0 0
\(277\) 8.75353 0.525949 0.262974 0.964803i \(-0.415297\pi\)
0.262974 + 0.964803i \(0.415297\pi\)
\(278\) 0 0
\(279\) −9.54588 + 11.0165i −0.571497 + 0.659543i
\(280\) 0 0
\(281\) −0.338311 + 2.35301i −0.0201820 + 0.140369i −0.997421 0.0717723i \(-0.977135\pi\)
0.977239 + 0.212141i \(0.0680436\pi\)
\(282\) 0 0
\(283\) −1.33659 2.92673i −0.0794522 0.173976i 0.865737 0.500499i \(-0.166850\pi\)
−0.945189 + 0.326523i \(0.894123\pi\)
\(284\) 0 0
\(285\) 0.222407 + 1.54687i 0.0131742 + 0.0916289i
\(286\) 0 0
\(287\) −15.1196 + 4.43952i −0.892483 + 0.262057i
\(288\) 0 0
\(289\) −2.72164 + 5.95957i −0.160097 + 0.350563i
\(290\) 0 0
\(291\) 2.60907 + 3.01103i 0.152947 + 0.176510i
\(292\) 0 0
\(293\) 7.85391 5.04740i 0.458830 0.294872i −0.290734 0.956804i \(-0.593899\pi\)
0.749564 + 0.661932i \(0.230263\pi\)
\(294\) 0 0
\(295\) −5.62358 3.61405i −0.327417 0.210418i
\(296\) 0 0
\(297\) 2.56917 + 0.754377i 0.149079 + 0.0437734i
\(298\) 0 0
\(299\) −6.44850 2.49194i −0.372927 0.144112i
\(300\) 0 0
\(301\) −20.3840 5.98529i −1.17492 0.344987i
\(302\) 0 0
\(303\) 2.84301 + 1.82709i 0.163327 + 0.104964i
\(304\) 0 0
\(305\) −10.7809 + 6.92844i −0.617311 + 0.396721i
\(306\) 0 0
\(307\) 6.40257 + 7.38896i 0.365414 + 0.421710i 0.908446 0.418001i \(-0.137269\pi\)
−0.543032 + 0.839712i \(0.682724\pi\)
\(308\) 0 0
\(309\) 1.35406 2.96498i 0.0770300 0.168672i
\(310\) 0 0
\(311\) 9.12404 2.67906i 0.517377 0.151916i −0.0126115 0.999920i \(-0.504014\pi\)
0.529988 + 0.848005i \(0.322196\pi\)
\(312\) 0 0
\(313\) −0.823298 5.72616i −0.0465355 0.323662i −0.999770 0.0214310i \(-0.993178\pi\)
0.953235 0.302231i \(-0.0977313\pi\)
\(314\) 0 0
\(315\) 2.70682 + 5.92711i 0.152512 + 0.333955i
\(316\) 0 0
\(317\) 1.47624 10.2675i 0.0829137 0.576678i −0.905437 0.424482i \(-0.860456\pi\)
0.988350 0.152196i \(-0.0486345\pi\)
\(318\) 0 0
\(319\) −6.99249 + 8.06977i −0.391504 + 0.451820i
\(320\) 0 0
\(321\) 0.101138 0.00564496
\(322\) 0 0
\(323\) 13.2618 0.737905
\(324\) 0 0
\(325\) 0.943989 1.08942i 0.0523631 0.0604302i
\(326\) 0 0
\(327\) −0.116775 + 0.812186i −0.00645766 + 0.0449140i
\(328\) 0 0
\(329\) −5.65460 12.3819i −0.311748 0.682634i
\(330\) 0 0
\(331\) −4.55688 31.6938i −0.250469 1.74205i −0.595407 0.803424i \(-0.703009\pi\)
0.344938 0.938625i \(-0.387900\pi\)
\(332\) 0 0
\(333\) −10.1766 + 2.98813i −0.557676 + 0.163749i
\(334\) 0 0
\(335\) 2.89778 6.34524i 0.158322 0.346678i
\(336\) 0 0
\(337\) 20.4541 + 23.6053i 1.11421 + 1.28586i 0.954340 + 0.298723i \(0.0965605\pi\)
0.159865 + 0.987139i \(0.448894\pi\)
\(338\) 0 0
\(339\) 0.361089 0.232058i 0.0196116 0.0126036i
\(340\) 0 0
\(341\) −5.15719 3.31432i −0.279277 0.179481i
\(342\) 0 0
\(343\) 19.2511 + 5.65264i 1.03946 + 0.305214i
\(344\) 0 0
\(345\) −1.30682 + 1.27644i −0.0703570 + 0.0687214i
\(346\) 0 0
\(347\) −24.1609 7.09427i −1.29702 0.380841i −0.440874 0.897569i \(-0.645332\pi\)
−0.856149 + 0.516728i \(0.827150\pi\)
\(348\) 0 0
\(349\) 15.5978 + 10.0241i 0.834931 + 0.536577i 0.886841 0.462074i \(-0.152895\pi\)
−0.0519104 + 0.998652i \(0.516531\pi\)
\(350\) 0 0
\(351\) 2.70449 1.73807i 0.144355 0.0927713i
\(352\) 0 0
\(353\) 8.95678 + 10.3367i 0.476721 + 0.550166i 0.942269 0.334857i \(-0.108688\pi\)
−0.465547 + 0.885023i \(0.654143\pi\)
\(354\) 0 0
\(355\) 3.31660 7.26235i 0.176027 0.385446i
\(356\) 0 0
\(357\) −2.69632 + 0.791711i −0.142704 + 0.0419018i
\(358\) 0 0
\(359\) −0.941910 6.55113i −0.0497121 0.345755i −0.999464 0.0327503i \(-0.989573\pi\)
0.949751 0.313005i \(-0.101336\pi\)
\(360\) 0 0
\(361\) −0.900307 1.97140i −0.0473846 0.103758i
\(362\) 0 0
\(363\) 0.518154 3.60384i 0.0271960 0.189153i
\(364\) 0 0
\(365\) −2.52031 + 2.90859i −0.131919 + 0.152243i
\(366\) 0 0
\(367\) 22.8576 1.19316 0.596579 0.802555i \(-0.296526\pi\)
0.596579 + 0.802555i \(0.296526\pi\)
\(368\) 0 0
\(369\) −19.7109 −1.02611
\(370\) 0 0
\(371\) 18.9051 21.8177i 0.981506 1.13272i
\(372\) 0 0
\(373\) 2.59111 18.0216i 0.134163 0.933121i −0.805884 0.592074i \(-0.798309\pi\)
0.940046 0.341047i \(-0.110782\pi\)
\(374\) 0 0
\(375\) −0.158235 0.346486i −0.00817122 0.0178925i
\(376\) 0 0
\(377\) 1.82448 + 12.6896i 0.0939657 + 0.653546i
\(378\) 0 0
\(379\) −30.6967 + 9.01336i −1.57678 + 0.462985i −0.948967 0.315376i \(-0.897869\pi\)
−0.627816 + 0.778362i \(0.716051\pi\)
\(380\) 0 0
\(381\) 3.04509 6.66781i 0.156004 0.341602i
\(382\) 0 0
\(383\) −23.5506 27.1788i −1.20338 1.38877i −0.899992 0.435905i \(-0.856428\pi\)
−0.303386 0.952868i \(-0.598117\pi\)
\(384\) 0 0
\(385\) −2.30528 + 1.48151i −0.117488 + 0.0755049i
\(386\) 0 0
\(387\) −22.3554 14.3669i −1.13639 0.730313i
\(388\) 0 0
\(389\) −17.0561 5.00812i −0.864779 0.253922i −0.180885 0.983504i \(-0.557896\pi\)
−0.683893 + 0.729582i \(0.739715\pi\)
\(390\) 0 0
\(391\) 9.14343 + 12.5184i 0.462403 + 0.633083i
\(392\) 0 0
\(393\) 1.97097 + 0.578729i 0.0994222 + 0.0291930i
\(394\) 0 0
\(395\) −8.08356 5.19499i −0.406728 0.261388i
\(396\) 0 0
\(397\) −6.92101 + 4.44786i −0.347356 + 0.223232i −0.702672 0.711514i \(-0.748010\pi\)
0.355316 + 0.934746i \(0.384373\pi\)
\(398\) 0 0
\(399\) −2.33578 2.69563i −0.116935 0.134951i
\(400\) 0 0
\(401\) 5.10692 11.1826i 0.255027 0.558432i −0.738205 0.674577i \(-0.764326\pi\)
0.993232 + 0.116144i \(0.0370535\pi\)
\(402\) 0 0
\(403\) −7.06211 + 2.07362i −0.351789 + 0.103295i
\(404\) 0 0
\(405\) 1.09799 + 7.63670i 0.0545597 + 0.379471i
\(406\) 0 0
\(407\) −1.85295 4.05740i −0.0918473 0.201118i
\(408\) 0 0
\(409\) −3.02856 + 21.0641i −0.149752 + 1.04155i 0.766871 + 0.641801i \(0.221812\pi\)
−0.916624 + 0.399751i \(0.869097\pi\)
\(410\) 0 0
\(411\) 0.414659 0.478542i 0.0204536 0.0236048i
\(412\) 0 0
\(413\) 15.2571 0.750751
\(414\) 0 0
\(415\) 0.368906 0.0181089
\(416\) 0 0
\(417\) 0.0825414 0.0952578i 0.00404207 0.00466480i
\(418\) 0 0
\(419\) 2.70677 18.8260i 0.132234 0.919709i −0.810399 0.585879i \(-0.800750\pi\)
0.942633 0.333831i \(-0.108341\pi\)
\(420\) 0 0
\(421\) −10.3374 22.6357i −0.503813 1.10320i −0.975211 0.221275i \(-0.928978\pi\)
0.471399 0.881920i \(-0.343749\pi\)
\(422\) 0 0
\(423\) −2.42313 16.8533i −0.117817 0.819433i
\(424\) 0 0
\(425\) −3.10146 + 0.910671i −0.150443 + 0.0441740i
\(426\) 0 0
\(427\) 12.1505 26.6059i 0.588004 1.28755i
\(428\) 0 0
\(429\) 0.431716 + 0.498227i 0.0208435 + 0.0240546i
\(430\) 0 0
\(431\) −14.5298 + 9.33776i −0.699878 + 0.449784i −0.841585 0.540124i \(-0.818377\pi\)
0.141707 + 0.989909i \(0.454741\pi\)
\(432\) 0 0
\(433\) 21.4304 + 13.7725i 1.02988 + 0.661863i 0.942464 0.334309i \(-0.108503\pi\)
0.0874154 + 0.996172i \(0.472139\pi\)
\(434\) 0 0
\(435\) 3.25038 + 0.954397i 0.155844 + 0.0457598i
\(436\) 0 0
\(437\) −9.63224 + 17.1573i −0.460772 + 0.820745i
\(438\) 0 0
\(439\) −20.8609 6.12531i −0.995636 0.292345i −0.256972 0.966419i \(-0.582725\pi\)
−0.738664 + 0.674074i \(0.764543\pi\)
\(440\) 0 0
\(441\) 4.30099 + 2.76408i 0.204809 + 0.131623i
\(442\) 0 0
\(443\) −18.9779 + 12.1964i −0.901669 + 0.579468i −0.907285 0.420517i \(-0.861849\pi\)
0.00561558 + 0.999984i \(0.498212\pi\)
\(444\) 0 0
\(445\) −6.81641 7.86656i −0.323129 0.372911i
\(446\) 0 0
\(447\) −1.10043 + 2.40960i −0.0520485 + 0.113970i
\(448\) 0 0
\(449\) −21.6615 + 6.36040i −1.02227 + 0.300166i −0.749565 0.661931i \(-0.769737\pi\)
−0.272707 + 0.962097i \(0.587919\pi\)
\(450\) 0 0
\(451\) −1.17971 8.20506i −0.0555504 0.386361i
\(452\) 0 0
\(453\) 0.440373 + 0.964282i 0.0206905 + 0.0453059i
\(454\) 0 0
\(455\) −0.468224 + 3.25657i −0.0219507 + 0.152670i
\(456\) 0 0
\(457\) 16.6944 19.2663i 0.780930 0.901241i −0.216247 0.976339i \(-0.569382\pi\)
0.997176 + 0.0750980i \(0.0239270\pi\)
\(458\) 0 0
\(459\) −7.20883 −0.336479
\(460\) 0 0
\(461\) −21.2768 −0.990959 −0.495479 0.868620i \(-0.665008\pi\)
−0.495479 + 0.868620i \(0.665008\pi\)
\(462\) 0 0
\(463\) −0.899349 + 1.03790i −0.0417963 + 0.0482355i −0.776263 0.630409i \(-0.782887\pi\)
0.734467 + 0.678645i \(0.237432\pi\)
\(464\) 0 0
\(465\) −0.276787 + 1.92509i −0.0128357 + 0.0892741i
\(466\) 0 0
\(467\) −10.7378 23.5126i −0.496888 1.08803i −0.977468 0.211083i \(-0.932301\pi\)
0.480580 0.876951i \(-0.340426\pi\)
\(468\) 0 0
\(469\) 2.26578 + 15.7589i 0.104624 + 0.727676i
\(470\) 0 0
\(471\) −3.95215 + 1.16046i −0.182106 + 0.0534710i
\(472\) 0 0
\(473\) 4.64255 10.1658i 0.213465 0.467422i
\(474\) 0 0
\(475\) −2.68675 3.10067i −0.123276 0.142268i
\(476\) 0 0
\(477\) 30.3784 19.5230i 1.39093 0.893898i
\(478\) 0 0
\(479\) 28.8828 + 18.5619i 1.31969 + 0.848114i 0.995208 0.0977779i \(-0.0311735\pi\)
0.324483 + 0.945892i \(0.394810\pi\)
\(480\) 0 0
\(481\) −5.13843 1.50878i −0.234292 0.0687944i
\(482\) 0 0
\(483\) 0.934111 4.06337i 0.0425035 0.184890i
\(484\) 0 0
\(485\) −10.0360 2.94682i −0.455710 0.133808i
\(486\) 0 0
\(487\) −32.3917 20.8169i −1.46781 0.943302i −0.998172 0.0604421i \(-0.980749\pi\)
−0.469636 0.882860i \(-0.655615\pi\)
\(488\) 0 0
\(489\) 6.38293 4.10206i 0.288646 0.185502i
\(490\) 0 0
\(491\) 16.2128 + 18.7106i 0.731675 + 0.844398i 0.992659 0.120945i \(-0.0385926\pi\)
−0.260984 + 0.965343i \(0.584047\pi\)
\(492\) 0 0
\(493\) 11.9420 26.1494i 0.537842 1.17771i
\(494\) 0 0
\(495\) −3.28886 + 0.965696i −0.147823 + 0.0434048i
\(496\) 0 0
\(497\) 2.59327 + 18.0366i 0.116324 + 0.809050i
\(498\) 0 0
\(499\) −0.401632 0.879452i −0.0179795 0.0393697i 0.900429 0.435003i \(-0.143253\pi\)
−0.918409 + 0.395633i \(0.870525\pi\)
\(500\) 0 0
\(501\) −0.828327 + 5.76114i −0.0370069 + 0.257389i
\(502\) 0 0
\(503\) 16.7636 19.3462i 0.747450 0.862603i −0.246868 0.969049i \(-0.579402\pi\)
0.994319 + 0.106446i \(0.0339470\pi\)
\(504\) 0 0
\(505\) −8.87221 −0.394808
\(506\) 0 0
\(507\) −4.16030 −0.184765
\(508\) 0 0
\(509\) −22.4372 + 25.8939i −0.994510 + 1.14773i −0.00548361 + 0.999985i \(0.501745\pi\)
−0.989026 + 0.147740i \(0.952800\pi\)
\(510\) 0 0
\(511\) 1.25009 8.69455i 0.0553006 0.384624i
\(512\) 0 0
\(513\) −3.80102 8.32307i −0.167819 0.367473i
\(514\) 0 0
\(515\) 1.21783 + 8.47019i 0.0536640 + 0.373241i
\(516\) 0 0
\(517\) 6.87049 2.01736i 0.302164 0.0887233i
\(518\) 0 0
\(519\) −0.508628 + 1.11374i −0.0223263 + 0.0488877i
\(520\) 0 0
\(521\) 14.7482 + 17.0203i 0.646129 + 0.745673i 0.980446 0.196788i \(-0.0630510\pi\)
−0.334317 + 0.942461i \(0.608506\pi\)
\(522\) 0 0
\(523\) 7.86834 5.05668i 0.344059 0.221113i −0.357187 0.934033i \(-0.616264\pi\)
0.701245 + 0.712920i \(0.252628\pi\)
\(524\) 0 0
\(525\) 0.731362 + 0.470018i 0.0319193 + 0.0205133i
\(526\) 0 0
\(527\) 15.8358 + 4.64982i 0.689820 + 0.202549i
\(528\) 0 0
\(529\) −22.8366 + 2.73693i −0.992895 + 0.118997i
\(530\) 0 0
\(531\) 18.3113 + 5.37669i 0.794644 + 0.233328i
\(532\) 0 0
\(533\) −8.37257 5.38072i −0.362656 0.233065i
\(534\) 0 0
\(535\) −0.223368 + 0.143550i −0.00965703 + 0.00620619i
\(536\) 0 0
\(537\) −4.17502 4.81823i −0.180166 0.207922i
\(538\) 0 0
\(539\) −0.893187 + 1.95581i −0.0384723 + 0.0842425i
\(540\) 0 0
\(541\) 3.34395 0.981873i 0.143768 0.0422140i −0.209057 0.977903i \(-0.567039\pi\)
0.352825 + 0.935689i \(0.385221\pi\)
\(542\) 0 0
\(543\) 0.769660 + 5.35311i 0.0330293 + 0.229724i
\(544\) 0 0
\(545\) −0.894871 1.95950i −0.0383321 0.0839355i
\(546\) 0 0
\(547\) −3.15274 + 21.9278i −0.134801 + 0.937565i 0.804373 + 0.594125i \(0.202501\pi\)
−0.939175 + 0.343440i \(0.888408\pi\)
\(548\) 0 0
\(549\) 23.9590 27.6501i 1.02254 1.18008i
\(550\) 0 0
\(551\) 36.4880 1.55444
\(552\) 0 0
\(553\) 21.9311 0.932607
\(554\) 0 0
\(555\) −0.926701 + 1.06947i −0.0393363 + 0.0453965i
\(556\) 0 0
\(557\) 3.43243 23.8731i 0.145437 1.01154i −0.778131 0.628102i \(-0.783832\pi\)
0.923568 0.383434i \(-0.125259\pi\)
\(558\) 0 0
\(559\) −5.57395 12.2053i −0.235753 0.516227i
\(560\) 0 0
\(561\) −0.210381 1.46323i −0.00888228 0.0617776i
\(562\) 0 0
\(563\) −7.87716 + 2.31294i −0.331983 + 0.0974789i −0.443476 0.896286i \(-0.646255\pi\)
0.111493 + 0.993765i \(0.464437\pi\)
\(564\) 0 0
\(565\) −0.468111 + 1.02502i −0.0196936 + 0.0431229i
\(566\) 0 0
\(567\) −11.5314 13.3080i −0.484275 0.558883i
\(568\) 0 0
\(569\) −22.6646 + 14.5657i −0.950150 + 0.610624i −0.921255 0.388958i \(-0.872835\pi\)
−0.0288943 + 0.999582i \(0.509199\pi\)
\(570\) 0 0
\(571\) −6.01994 3.86878i −0.251927 0.161903i 0.408583 0.912721i \(-0.366023\pi\)
−0.660509 + 0.750818i \(0.729660\pi\)
\(572\) 0 0
\(573\) 1.20208 + 0.352962i 0.0502176 + 0.0147452i
\(574\) 0 0
\(575\) 1.07447 4.67392i 0.0448083 0.194916i
\(576\) 0 0
\(577\) −19.0125 5.58257i −0.791500 0.232405i −0.139098 0.990279i \(-0.544420\pi\)
−0.652402 + 0.757873i \(0.726239\pi\)
\(578\) 0 0
\(579\) −3.98281 2.55959i −0.165520 0.106373i
\(580\) 0 0
\(581\) −0.708317 + 0.455208i −0.0293859 + 0.0188852i
\(582\) 0 0
\(583\) 9.94503 + 11.4772i 0.411881 + 0.475336i
\(584\) 0 0
\(585\) −1.70959 + 3.74348i −0.0706829 + 0.154774i
\(586\) 0 0
\(587\) −14.1431 + 4.15278i −0.583747 + 0.171404i −0.560255 0.828320i \(-0.689297\pi\)
−0.0234923 + 0.999724i \(0.507479\pi\)
\(588\) 0 0
\(589\) 2.98128 + 20.7353i 0.122841 + 0.854381i
\(590\) 0 0
\(591\) 3.50918 + 7.68404i 0.144349 + 0.316079i
\(592\) 0 0
\(593\) −3.68519 + 25.6311i −0.151333 + 1.05254i 0.762657 + 0.646804i \(0.223895\pi\)
−0.913989 + 0.405738i \(0.867014\pi\)
\(594\) 0 0
\(595\) 4.83124 5.57555i 0.198062 0.228575i
\(596\) 0 0
\(597\) −0.154340 −0.00631673
\(598\) 0 0
\(599\) −18.9146 −0.772828 −0.386414 0.922325i \(-0.626286\pi\)
−0.386414 + 0.922325i \(0.626286\pi\)
\(600\) 0 0
\(601\) −12.0436 + 13.8991i −0.491270 + 0.566955i −0.946204 0.323569i \(-0.895117\pi\)
0.454935 + 0.890525i \(0.349663\pi\)
\(602\) 0 0
\(603\) −2.83416 + 19.7120i −0.115416 + 0.802737i
\(604\) 0 0
\(605\) 3.97073 + 8.69469i 0.161433 + 0.353490i
\(606\) 0 0
\(607\) 5.75260 + 40.0102i 0.233491 + 1.62396i 0.682812 + 0.730594i \(0.260757\pi\)
−0.449321 + 0.893370i \(0.648334\pi\)
\(608\) 0 0
\(609\) −7.41855 + 2.17828i −0.300615 + 0.0882685i
\(610\) 0 0
\(611\) 3.57137 7.82021i 0.144482 0.316372i
\(612\) 0 0
\(613\) 9.32405 + 10.7605i 0.376595 + 0.434613i 0.912131 0.409899i \(-0.134436\pi\)
−0.535536 + 0.844512i \(0.679891\pi\)
\(614\) 0 0
\(615\) −2.21239 + 1.42181i −0.0892120 + 0.0573331i
\(616\) 0 0
\(617\) 8.78985 + 5.64890i 0.353866 + 0.227416i 0.705481 0.708729i \(-0.250731\pi\)
−0.351615 + 0.936145i \(0.614367\pi\)
\(618\) 0 0
\(619\) −37.4503 10.9964i −1.50526 0.441983i −0.577882 0.816120i \(-0.696121\pi\)
−0.927373 + 0.374137i \(0.877939\pi\)
\(620\) 0 0
\(621\) 5.23588 9.32636i 0.210109 0.374254i
\(622\) 0 0
\(623\) 22.7947 + 6.69313i 0.913250 + 0.268155i
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.0336501 + 0.0216256i
\(626\) 0 0
\(627\) 1.57847 1.01442i 0.0630380 0.0405120i
\(628\) 0 0
\(629\) 7.86400 + 9.07554i 0.313558 + 0.361866i
\(630\) 0 0
\(631\) 14.1605 31.0072i 0.563722 1.23438i −0.386351 0.922352i \(-0.626265\pi\)
0.950073 0.312027i \(-0.101008\pi\)
\(632\) 0 0
\(633\) −3.95683 + 1.16183i −0.157270 + 0.0461786i
\(634\) 0 0
\(635\) 2.73872 + 19.0482i 0.108683 + 0.755905i
\(636\) 0 0
\(637\) 1.07238 + 2.34819i 0.0424893 + 0.0930385i
\(638\) 0 0
\(639\) −3.24380 + 22.5611i −0.128323 + 0.892504i
\(640\) 0 0
\(641\) −13.4810 + 15.5579i −0.532467 + 0.614499i −0.956708 0.291050i \(-0.905995\pi\)
0.424241 + 0.905549i \(0.360541\pi\)
\(642\) 0 0
\(643\) 28.7329 1.13312 0.566558 0.824022i \(-0.308275\pi\)
0.566558 + 0.824022i \(0.308275\pi\)
\(644\) 0 0
\(645\) −3.54555 −0.139606
\(646\) 0 0
\(647\) 14.6691 16.9291i 0.576702 0.665550i −0.390190 0.920734i \(-0.627591\pi\)
0.966892 + 0.255184i \(0.0821362\pi\)
\(648\) 0 0
\(649\) −1.14221 + 7.94426i −0.0448358 + 0.311840i
\(650\) 0 0
\(651\) −1.84401 4.03781i −0.0722723 0.158254i
\(652\) 0 0
\(653\) −4.57266 31.8035i −0.178942 1.24457i −0.859217 0.511611i \(-0.829049\pi\)
0.680275 0.732957i \(-0.261860\pi\)
\(654\) 0 0
\(655\) −5.17439 + 1.51934i −0.202180 + 0.0593655i
\(656\) 0 0
\(657\) 4.56435 9.99454i 0.178072 0.389924i
\(658\) 0 0
\(659\) 10.7632 + 12.4214i 0.419275 + 0.483870i 0.925616 0.378464i \(-0.123548\pi\)
−0.506341 + 0.862334i \(0.669002\pi\)
\(660\) 0 0
\(661\) 2.19554 1.41099i 0.0853965 0.0548810i −0.497246 0.867610i \(-0.665655\pi\)
0.582642 + 0.812729i \(0.302019\pi\)
\(662\) 0 0
\(663\) −1.49310 0.959559i −0.0579873 0.0372662i
\(664\) 0 0
\(665\) 8.98472 + 2.63815i 0.348413 + 0.102303i
\(666\) 0 0
\(667\) 25.1569 + 34.4426i 0.974078 + 1.33362i
\(668\) 0 0
\(669\) −0.812735 0.238641i −0.0314222 0.00922638i
\(670\) 0 0
\(671\) 12.9439 + 8.31853i 0.499693 + 0.321133i
\(672\) 0 0
\(673\) 42.3034 27.1868i 1.63068 1.04797i 0.682181 0.731183i \(-0.261032\pi\)
0.948496 0.316789i \(-0.102605\pi\)
\(674\) 0 0
\(675\) 1.46046 + 1.68546i 0.0562131 + 0.0648734i
\(676\) 0 0
\(677\) −12.9603 + 28.3792i −0.498106 + 1.09070i 0.478974 + 0.877829i \(0.341009\pi\)
−0.977080 + 0.212872i \(0.931718\pi\)
\(678\) 0 0
\(679\) 22.9057 6.72573i 0.879041 0.258110i
\(680\) 0 0
\(681\) 0.479367 + 3.33407i 0.0183694 + 0.127762i
\(682\) 0 0
\(683\) −2.18646 4.78769i −0.0836627 0.183196i 0.863177 0.504901i \(-0.168471\pi\)
−0.946840 + 0.321706i \(0.895744\pi\)
\(684\) 0 0
\(685\) −0.236577 + 1.64543i −0.00903914 + 0.0628686i
\(686\) 0 0
\(687\) −4.35097 + 5.02129i −0.166000 + 0.191574i
\(688\) 0 0
\(689\) 18.2332 0.694631
\(690\) 0 0
\(691\) −9.41804 −0.358279 −0.179140 0.983824i \(-0.557331\pi\)
−0.179140 + 0.983824i \(0.557331\pi\)
\(692\) 0 0
\(693\) 5.12316 5.91244i 0.194613 0.224595i
\(694\) 0 0
\(695\) −0.0470926 + 0.327536i −0.00178632 + 0.0124242i
\(696\) 0 0
\(697\) 9.27087 + 20.3004i 0.351159 + 0.768931i
\(698\) 0 0
\(699\) −1.19885 8.33818i −0.0453446 0.315379i
\(700\) 0 0
\(701\) −29.1860 + 8.56977i −1.10234 + 0.323676i −0.781781 0.623553i \(-0.785688\pi\)
−0.320558 + 0.947229i \(0.603870\pi\)
\(702\) 0 0
\(703\) −6.33184 + 13.8648i −0.238810 + 0.522921i
\(704\) 0 0
\(705\) −1.48766 1.71685i −0.0560285 0.0646604i
\(706\) 0 0
\(707\) 17.0351 10.9478i 0.640670 0.411734i
\(708\) 0 0
\(709\) 24.4856 + 15.7360i 0.919577 + 0.590976i 0.912535 0.408999i \(-0.134122\pi\)
0.00704223 + 0.999975i \(0.497758\pi\)
\(710\) 0 0
\(711\) 26.3215 + 7.72868i 0.987132 + 0.289848i
\(712\) 0 0
\(713\) −17.5175 + 17.1102i −0.656035 + 0.640783i
\(714\) 0 0
\(715\) −1.66062 0.487603i −0.0621038 0.0182353i
\(716\) 0 0
\(717\) 7.22504 + 4.64325i 0.269824 + 0.173405i
\(718\) 0 0
\(719\) −31.5047 + 20.2468i −1.17493 + 0.755079i −0.974447 0.224619i \(-0.927886\pi\)
−0.200479 + 0.979698i \(0.564250\pi\)
\(720\) 0 0
\(721\) −12.7900 14.7604i −0.476324 0.549708i
\(722\) 0 0
\(723\) 2.81270 6.15896i 0.104606 0.229054i
\(724\) 0 0
\(725\) −8.53323 + 2.50558i −0.316916 + 0.0930550i
\(726\) 0 0
\(727\) 0.186058 + 1.29406i 0.00690051 + 0.0479941i 0.992981 0.118276i \(-0.0377367\pi\)
−0.986080 + 0.166270i \(0.946828\pi\)
\(728\) 0 0
\(729\) −8.09137 17.7176i −0.299680 0.656209i
\(730\) 0 0
\(731\) −4.28191 + 29.7814i −0.158372 + 1.10150i
\(732\) 0 0
\(733\) −8.39350 + 9.68662i −0.310021 + 0.357783i −0.889282 0.457359i \(-0.848796\pi\)
0.579261 + 0.815142i \(0.303341\pi\)
\(734\) 0 0
\(735\) 0.682133 0.0251609
\(736\) 0 0
\(737\) −8.37517 −0.308503
\(738\) 0 0
\(739\) 24.0184 27.7187i 0.883532 1.01965i −0.116119 0.993235i \(-0.537045\pi\)
0.999651 0.0264153i \(-0.00840924\pi\)
\(740\) 0 0
\(741\) 0.320602 2.22983i 0.0117776 0.0819150i
\(742\) 0 0
\(743\) 6.49549 + 14.2231i 0.238296 + 0.521796i 0.990562 0.137063i \(-0.0437664\pi\)
−0.752266 + 0.658860i \(0.771039\pi\)
\(744\) 0 0
\(745\) −0.989715 6.88362i −0.0362603 0.252196i
\(746\) 0 0
\(747\) −1.01053 + 0.296719i −0.0369734 + 0.0108564i
\(748\) 0 0
\(749\) 0.251745 0.551245i 0.00919856 0.0201420i
\(750\) 0 0
\(751\) −25.0913 28.9569i −0.915596 1.05665i −0.998194 0.0600712i \(-0.980867\pi\)
0.0825981 0.996583i \(-0.473678\pi\)
\(752\) 0 0
\(753\) −8.81786 + 5.66689i −0.321341 + 0.206513i
\(754\) 0 0
\(755\) −2.34123 1.50462i −0.0852062 0.0547587i
\(756\) 0 0
\(757\) 47.7878 + 14.0318i 1.73688 + 0.509993i 0.988230 0.152977i \(-0.0488861\pi\)
0.748646 + 0.662970i \(0.230704\pi\)
\(758\) 0 0
\(759\) 2.04584 + 0.790589i 0.0742594 + 0.0286966i
\(760\) 0 0
\(761\) 14.3538 + 4.21467i 0.520326 + 0.152782i 0.531341 0.847158i \(-0.321688\pi\)
−0.0110153 + 0.999939i \(0.503506\pi\)
\(762\) 0 0
\(763\) 4.13610 + 2.65811i 0.149737 + 0.0962299i
\(764\) 0 0
\(765\) 7.76325 4.98914i 0.280681 0.180383i
\(766\) 0 0
\(767\) 6.31034 + 7.28252i 0.227853 + 0.262956i
\(768\) 0 0
\(769\) 20.1449 44.1113i 0.726445 1.59069i −0.0782001 0.996938i \(-0.524917\pi\)
0.804645 0.593756i \(-0.202355\pi\)
\(770\) 0 0
\(771\) −3.90833 + 1.14759i −0.140755 + 0.0413294i
\(772\) 0 0
\(773\) −0.941508 6.54833i −0.0338637 0.235527i 0.965859 0.259068i \(-0.0834152\pi\)
−0.999723 + 0.0235405i \(0.992506\pi\)
\(774\) 0 0
\(775\) −2.12108 4.64452i −0.0761914 0.166836i
\(776\) 0 0
\(777\) 0.459649 3.19693i 0.0164898 0.114689i
\(778\) 0 0
\(779\) −18.5498 + 21.4077i −0.664617 + 0.767009i
\(780\) 0 0
\(781\) −9.58568 −0.343002
\(782\) 0 0
\(783\) −19.8341 −0.708813
\(784\) 0 0
\(785\) 7.08142 8.17240i 0.252747 0.291685i
\(786\) 0 0
\(787\) −1.18809 + 8.26333i −0.0423507 + 0.294556i 0.957628 + 0.288009i \(0.0929932\pi\)
−0.999979 + 0.00654730i \(0.997916\pi\)
\(788\) 0 0
\(789\) 3.30493 + 7.23679i 0.117659 + 0.257637i
\(790\) 0 0
\(791\) −0.366018 2.54571i −0.0130141 0.0905150i
\(792\) 0 0
\(793\) 17.7250 5.20453i 0.629434 0.184818i
\(794\) 0 0
\(795\) 2.00147 4.38260i 0.0709847 0.155435i
\(796\) 0 0
\(797\) −9.10091 10.5030i −0.322371 0.372036i 0.571314 0.820732i \(-0.306434\pi\)
−0.893684 + 0.448696i \(0.851889\pi\)
\(798\) 0 0
\(799\) −16.2176 + 10.4224i −0.573737 + 0.368718i
\(800\) 0 0
\(801\) 24.9992 + 16.0660i 0.883303 + 0.567665i
\(802\) 0 0
\(803\) 4.43361 + 1.30183i 0.156459 + 0.0459405i
\(804\) 0 0
\(805\) 3.70431 + 10.3000i 0.130560 + 0.363026i
\(806\) 0 0
\(807\) −4.06634 1.19398i −0.143142 0.0420302i
\(808\) 0 0
\(809\) −18.6538 11.9880i −0.655831 0.421477i 0.169962 0.985451i \(-0.445636\pi\)
−0.825793 + 0.563974i \(0.809272\pi\)
\(810\) 0 0
\(811\) 1.08109 0.694775i 0.0379622 0.0243968i −0.521522 0.853238i \(-0.674636\pi\)
0.559484 + 0.828841i \(0.310999\pi\)
\(812\) 0 0
\(813\) −1.50339 1.73501i −0.0527263 0.0608494i
\(814\) 0 0
\(815\) −8.27476 + 18.1192i −0.289852 + 0.634688i
\(816\) 0 0
\(817\) −36.6423 + 10.7591i −1.28195 + 0.376415i
\(818\) 0 0
\(819\) −1.33674 9.29720i −0.0467093 0.324871i
\(820\) 0 0
\(821\) −0.239706 0.524882i −0.00836578 0.0183185i 0.905403 0.424553i \(-0.139569\pi\)
−0.913769 + 0.406235i \(0.866842\pi\)
\(822\) 0 0
\(823\) −4.21292 + 29.3015i −0.146853 + 1.02139i 0.774476 + 0.632604i \(0.218014\pi\)
−0.921329 + 0.388784i \(0.872895\pi\)
\(824\) 0 0
\(825\) −0.299489 + 0.345628i −0.0104269 + 0.0120332i
\(826\) 0 0
\(827\) −45.0861 −1.56780 −0.783898 0.620890i \(-0.786772\pi\)
−0.783898 + 0.620890i \(0.786772\pi\)
\(828\) 0 0
\(829\) 25.4899 0.885300 0.442650 0.896694i \(-0.354038\pi\)
0.442650 + 0.896694i \(0.354038\pi\)
\(830\) 0 0
\(831\) −2.18350 + 2.51989i −0.0757447 + 0.0874140i
\(832\) 0 0
\(833\) 0.823803 5.72968i 0.0285431 0.198522i
\(834\) 0 0
\(835\) −6.34766 13.8994i −0.219670 0.481010i
\(836\) 0 0
\(837\) −1.62056 11.2713i −0.0560148 0.389591i
\(838\) 0 0
\(839\) 13.9704 4.10208i 0.482311 0.141619i −0.0315332 0.999503i \(-0.510039\pi\)
0.513845 + 0.857883i \(0.328221\pi\)
\(840\) 0 0
\(841\) 20.8098 45.5671i 0.717580 1.57128i
\(842\) 0 0
\(843\) −0.592974 0.684328i −0.0204231 0.0235695i
\(844\) 0 0
\(845\) 9.18821 5.90490i 0.316084 0.203135i
\(846\) 0 0
\(847\) −18.3527 11.7946i −0.630607 0.405267i
\(848\) 0 0
\(849\) 1.17592 + 0.345282i 0.0403576 + 0.0118501i
\(850\) 0 0
\(851\) −17.4531 + 3.58227i −0.598286 + 0.122799i
\(852\) 0 0
\(853\) −41.2422 12.1098i −1.41211 0.414632i −0.515282 0.857020i \(-0.672313\pi\)
−0.896823 + 0.442389i \(0.854131\pi\)
\(854\) 0 0
\(855\) 9.85364 + 6.33255i 0.336987 + 0.216569i
\(856\) 0 0
\(857\) 2.33470 1.50042i 0.0797520 0.0512535i −0.500157 0.865935i \(-0.666724\pi\)
0.579909 + 0.814681i \(0.303088\pi\)
\(858\) 0 0
\(859\) 36.6739 + 42.3239i 1.25130 + 1.44407i 0.848852 + 0.528630i \(0.177294\pi\)
0.402445 + 0.915444i \(0.368160\pi\)
\(860\) 0 0
\(861\) 2.49346 5.45990i 0.0849767 0.186073i
\(862\) 0 0
\(863\) 0.601182 0.176523i 0.0204645 0.00600891i −0.271484 0.962443i \(-0.587515\pi\)
0.291949 + 0.956434i \(0.405696\pi\)
\(864\) 0 0
\(865\) −0.457454 3.18166i −0.0155539 0.108180i
\(866\) 0 0
\(867\) −1.03670 2.27005i −0.0352080 0.0770949i
\(868\) 0 0
\(869\) −1.64186 + 11.4194i −0.0556965 + 0.387377i
\(870\) 0 0
\(871\) −6.58490 + 7.59938i −0.223121 + 0.257495i
\(872\) 0 0
\(873\) 29.8614 1.01065
\(874\) 0 0
\(875\) −2.28237 −0.0771580
\(876\) 0 0
\(877\) −5.16860 + 5.96488i −0.174531 + 0.201420i −0.836275 0.548310i \(-0.815271\pi\)
0.661744 + 0.749730i \(0.269817\pi\)
\(878\) 0 0
\(879\) −0.506092 + 3.51995i −0.0170701 + 0.118725i
\(880\) 0 0
\(881\) 5.36376 + 11.7450i 0.180710 + 0.395699i 0.978209 0.207620i \(-0.0665719\pi\)
−0.797500 + 0.603319i \(0.793845\pi\)
\(882\) 0 0
\(883\) −1.49137 10.3727i −0.0501887 0.349070i −0.999406 0.0344502i \(-0.989032\pi\)
0.949218 0.314620i \(-0.101877\pi\)
\(884\) 0 0
\(885\) 2.44314 0.717370i 0.0821251 0.0241141i
\(886\) 0 0
\(887\) 1.97943 4.33436i 0.0664629 0.145533i −0.873485 0.486850i \(-0.838146\pi\)
0.939948 + 0.341317i \(0.110873\pi\)
\(888\) 0 0
\(889\) −28.7628 33.1940i −0.964673 1.11329i
\(890\) 0 0
\(891\) 7.79268 5.00805i 0.261065 0.167776i
\(892\) 0 0
\(893\) −20.5844 13.2288i −0.688832 0.442686i
\(894\) 0 0
\(895\) 16.0595 + 4.71549i 0.536809 + 0.157621i
\(896\) 0 0
\(897\) 2.32588 1.23475i 0.0776590 0.0412269i
\(898\) 0 0
\(899\) 43.5701 + 12.7933i 1.45314 + 0.426682i
\(900\) 0 0
\(901\) −34.3952 22.1044i −1.14587 0.736405i
\(902\) 0 0
\(903\) 6.80762 4.37499i 0.226544 0.145591i
\(904\) 0 0
\(905\) −9.29775 10.7302i −0.309068 0.356683i
\(906\) 0 0
\(907\) −1.87504 + 4.10577i −0.0622597 + 0.136330i −0.938204 0.346082i \(-0.887512\pi\)
0.875945 + 0.482412i \(0.160239\pi\)
\(908\) 0 0
\(909\) 24.3033 7.13610i 0.806091 0.236690i
\(910\) 0 0
\(911\) 2.48769 + 17.3023i 0.0824210 + 0.573251i 0.988624 + 0.150408i \(0.0480587\pi\)
−0.906203 + 0.422843i \(0.861032\pi\)
\(912\) 0 0
\(913\) −0.183996 0.402895i −0.00608939 0.0133339i
\(914\) 0 0
\(915\) 0.694700 4.83174i 0.0229661 0.159733i
\(916\) 0 0
\(917\) 8.06031 9.30209i 0.266175 0.307182i
\(918\) 0 0
\(919\) −5.72003 −0.188686 −0.0943431 0.995540i \(-0.530075\pi\)
−0.0943431 + 0.995540i \(0.530075\pi\)
\(920\) 0 0
\(921\) −3.72414 −0.122715
\(922\) 0 0
\(923\) −7.53665 + 8.69776i −0.248072 + 0.286290i
\(924\) 0 0
\(925\) 0.528714 3.67728i 0.0173840 0.120908i
\(926\) 0 0
\(927\) −10.1487 22.2226i −0.333327 0.729885i
\(928\) 0 0
\(929\) −5.71568 39.7534i −0.187525 1.30427i −0.838389 0.545072i \(-0.816502\pi\)
0.650864 0.759195i \(-0.274407\pi\)
\(930\) 0 0
\(931\) 7.04966 2.06997i 0.231043 0.0678404i
\(932\) 0 0
\(933\) −1.50469 + 3.29482i −0.0492614 + 0.107868i
\(934\) 0 0
\(935\) 2.54147 + 2.93301i 0.0831149 + 0.0959197i
\(936\) 0 0
\(937\) 39.2521 25.2258i 1.28231 0.824090i 0.291138 0.956681i \(-0.405966\pi\)
0.991171 + 0.132591i \(0.0423297\pi\)
\(938\) 0 0
\(939\) 1.85376 + 1.19134i 0.0604952 + 0.0388779i
\(940\) 0 0
\(941\) −12.1122 3.55648i −0.394848 0.115938i 0.0782803 0.996931i \(-0.475057\pi\)
−0.473128 + 0.880994i \(0.656875\pi\)
\(942\) 0 0
\(943\) −32.9970 2.75037i −1.07453 0.0895644i
\(944\) 0 0
\(945\) −4.88391 1.43404i −0.158874 0.0466495i
\(946\) 0 0
\(947\) −4.95977 3.18745i −0.161171 0.103578i 0.457569 0.889174i \(-0.348720\pi\)
−0.618740 + 0.785596i \(0.712357\pi\)
\(948\) 0 0
\(949\) 4.66713 2.99938i 0.151501 0.0973640i
\(950\) 0 0
\(951\) 2.58747 + 2.98610i 0.0839044 + 0.0968309i
\(952\) 0 0
\(953\) −16.0419 + 35.1269i −0.519649 + 1.13787i 0.449923 + 0.893067i \(0.351451\pi\)
−0.969572 + 0.244806i \(0.921276\pi\)
\(954\) 0 0
\(955\) −3.15583 + 0.926634i −0.102120 + 0.0299852i
\(956\) 0 0
\(957\) −0.578833 4.02587i −0.0187110 0.130138i
\(958\) 0 0
\(959\) −1.57612 3.45122i −0.0508956 0.111446i
\(960\) 0 0
\(961\) 0.701537 4.87930i 0.0226302 0.157397i
\(962\) 0 0
\(963\) 0.496403 0.572880i 0.0159964 0.0184608i
\(964\) 0 0
\(965\) 12.4292 0.400109
\(966\) 0 0
\(967\) 39.5246 1.27103 0.635513 0.772090i \(-0.280789\pi\)
0.635513 + 0.772090i \(0.280789\pi\)
\(968\) 0 0
\(969\) −3.30804 + 3.81769i −0.106270 + 0.122642i
\(970\) 0 0
\(971\) −1.79629 + 12.4935i −0.0576458 + 0.400935i 0.940486 + 0.339833i \(0.110371\pi\)
−0.998132 + 0.0611022i \(0.980538\pi\)
\(972\) 0 0
\(973\) −0.313740 0.686995i −0.0100580 0.0220240i
\(974\) 0 0
\(975\) 0.0781427 + 0.543494i 0.00250257 + 0.0174058i
\(976\) 0 0
\(977\) −32.6342 + 9.58226i −1.04406 + 0.306564i −0.758415 0.651772i \(-0.774026\pi\)
−0.285645 + 0.958336i \(0.592208\pi\)
\(978\) 0 0
\(979\) −5.19159 + 11.3680i −0.165924 + 0.363323i
\(980\) 0 0
\(981\) 4.02735 + 4.64781i 0.128583 + 0.148393i
\(982\) 0 0
\(983\) −25.8434 + 16.6085i −0.824275 + 0.529729i −0.883454 0.468518i \(-0.844788\pi\)
0.0591789 + 0.998247i \(0.481152\pi\)
\(984\) 0 0
\(985\) −18.6565 11.9898i −0.594446 0.382027i
\(986\) 0 0
\(987\) 4.97487 + 1.46075i 0.158352 + 0.0464963i
\(988\) 0 0
\(989\) −35.4193 27.1703i −1.12627 0.863966i
\(990\) 0 0
\(991\) −51.0971 15.0035i −1.62315 0.476601i −0.661290 0.750131i \(-0.729991\pi\)
−0.961864 + 0.273530i \(0.911809\pi\)
\(992\) 0 0
\(993\) 10.2604 + 6.59397i 0.325604 + 0.209253i
\(994\) 0 0
\(995\) 0.340868 0.219062i 0.0108062 0.00694475i
\(996\) 0 0
\(997\) −16.1577 18.6469i −0.511718 0.590555i 0.439819 0.898086i \(-0.355042\pi\)
−0.951538 + 0.307532i \(0.900497\pi\)
\(998\) 0 0
\(999\) 3.44186 7.53662i 0.108896 0.238448i
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 460.2.m.b.41.3 50
23.9 even 11 inner 460.2.m.b.101.3 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.b.41.3 50 1.1 even 1 trivial
460.2.m.b.101.3 yes 50 23.9 even 11 inner