Properties

Label 552.2.q.d.121.3
Level $552$
Weight $2$
Character 552.121
Analytic conductor $4.408$
Analytic rank $0$
Dimension $30$
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] = [552,2,Mod(25,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.q (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 121.3
Character \(\chi\) \(=\) 552.121
Dual form 552.2.q.d.73.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.959493 + 0.281733i) q^{3} +(1.92120 - 1.23468i) q^{5} +(0.378426 - 2.63201i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(0.959493 + 0.281733i) q^{3} +(1.92120 - 1.23468i) q^{5} +(0.378426 - 2.63201i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-1.90442 - 4.17009i) q^{11} +(-0.246103 - 1.71169i) q^{13} +(2.19122 - 0.643401i) q^{15} +(-1.99661 + 2.30421i) q^{17} +(-1.69713 - 1.95859i) q^{19} +(1.10462 - 2.41878i) q^{21} +(4.51927 + 1.60506i) q^{23} +(0.0894893 - 0.195954i) q^{25} +(0.654861 + 0.755750i) q^{27} +(-5.02332 + 5.79722i) q^{29} +(1.10129 - 0.323369i) q^{31} +(-0.652424 - 4.53771i) q^{33} +(-2.52266 - 5.52384i) q^{35} +(7.40338 + 4.75787i) q^{37} +(0.246103 - 1.71169i) q^{39} +(4.83341 - 3.10624i) q^{41} +(4.05546 + 1.19079i) q^{43} +2.28373 q^{45} -2.43774 q^{47} +(-0.0678292 - 0.0199164i) q^{49} +(-2.56490 + 1.64836i) q^{51} +(-1.13221 + 7.87469i) q^{53} +(-8.80747 - 5.66022i) q^{55} +(-1.07658 - 2.35739i) q^{57} +(0.762525 + 5.30348i) q^{59} +(10.2607 - 3.01281i) q^{61} +(1.74133 - 2.00960i) q^{63} +(-2.58619 - 2.98463i) q^{65} +(6.67408 - 14.6142i) q^{67} +(3.88401 + 2.81326i) q^{69} +(-6.49235 + 14.2163i) q^{71} +(6.10673 + 7.04754i) q^{73} +(0.141071 - 0.162805i) q^{75} +(-11.6964 + 3.43437i) q^{77} +(-0.841256 - 5.85107i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-3.82619 - 2.45894i) q^{83} +(-0.990920 + 6.89200i) q^{85} +(-6.45311 + 4.14716i) q^{87} +(4.57162 + 1.34235i) q^{89} -4.59831 q^{91} +1.14779 q^{93} +(-5.67873 - 1.66743i) q^{95} +(-9.16603 + 5.89065i) q^{97} +(0.652424 - 4.53771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(1\) \(1\) \(1\)

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 0
\(3\) 0.959493 + 0.281733i 0.553964 + 0.162658i
\(4\) 0 0
\(5\) 1.92120 1.23468i 0.859185 0.552165i −0.0352420 0.999379i \(-0.511220\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) 0.378426 2.63201i 0.143032 0.994807i −0.784251 0.620444i \(-0.786952\pi\)
0.927282 0.374363i \(-0.122139\pi\)
\(8\) 0 0
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) 0 0
\(11\) −1.90442 4.17009i −0.574203 1.25733i −0.944529 0.328427i \(-0.893481\pi\)
0.370326 0.928902i \(-0.379246\pi\)
\(12\) 0 0
\(13\) −0.246103 1.71169i −0.0682568 0.474736i −0.995067 0.0992060i \(-0.968370\pi\)
0.926810 0.375530i \(-0.122539\pi\)
\(14\) 0 0
\(15\) 2.19122 0.643401i 0.565771 0.166125i
\(16\) 0 0
\(17\) −1.99661 + 2.30421i −0.484248 + 0.558852i −0.944320 0.329030i \(-0.893278\pi\)
0.460071 + 0.887882i \(0.347824\pi\)
\(18\) 0 0
\(19\) −1.69713 1.95859i −0.389347 0.449331i 0.526910 0.849921i \(-0.323351\pi\)
−0.916257 + 0.400590i \(0.868805\pi\)
\(20\) 0 0
\(21\) 1.10462 2.41878i 0.241048 0.527821i
\(22\) 0 0
\(23\) 4.51927 + 1.60506i 0.942333 + 0.334677i
\(24\) 0 0
\(25\) 0.0894893 0.195954i 0.0178979 0.0391909i
\(26\) 0 0
\(27\) 0.654861 + 0.755750i 0.126028 + 0.145444i
\(28\) 0 0
\(29\) −5.02332 + 5.79722i −0.932807 + 1.07652i 0.0641012 + 0.997943i \(0.479582\pi\)
−0.996908 + 0.0785734i \(0.974963\pi\)
\(30\) 0 0
\(31\) 1.10129 0.323369i 0.197798 0.0580789i −0.181333 0.983422i \(-0.558041\pi\)
0.379131 + 0.925343i \(0.376223\pi\)
\(32\) 0 0
\(33\) −0.652424 4.53771i −0.113572 0.789913i
\(34\) 0 0
\(35\) −2.52266 5.52384i −0.426407 0.933700i
\(36\) 0 0
\(37\) 7.40338 + 4.75787i 1.21711 + 0.782188i 0.981834 0.189741i \(-0.0607647\pi\)
0.235275 + 0.971929i \(0.424401\pi\)
\(38\) 0 0
\(39\) 0.246103 1.71169i 0.0394081 0.274089i
\(40\) 0 0
\(41\) 4.83341 3.10624i 0.754851 0.485113i −0.105750 0.994393i \(-0.533724\pi\)
0.860601 + 0.509279i \(0.170088\pi\)
\(42\) 0 0
\(43\) 4.05546 + 1.19079i 0.618451 + 0.181594i 0.575926 0.817502i \(-0.304642\pi\)
0.0425252 + 0.999095i \(0.486460\pi\)
\(44\) 0 0
\(45\) 2.28373 0.340438
\(46\) 0 0
\(47\) −2.43774 −0.355581 −0.177790 0.984068i \(-0.556895\pi\)
−0.177790 + 0.984068i \(0.556895\pi\)
\(48\) 0 0
\(49\) −0.0678292 0.0199164i −0.00968988 0.00284521i
\(50\) 0 0
\(51\) −2.56490 + 1.64836i −0.359158 + 0.230817i
\(52\) 0 0
\(53\) −1.13221 + 7.87469i −0.155521 + 1.08167i 0.751241 + 0.660028i \(0.229456\pi\)
−0.906762 + 0.421643i \(0.861453\pi\)
\(54\) 0 0
\(55\) −8.80747 5.66022i −1.18760 0.763224i
\(56\) 0 0
\(57\) −1.07658 2.35739i −0.142597 0.312243i
\(58\) 0 0
\(59\) 0.762525 + 5.30348i 0.0992723 + 0.690454i 0.977302 + 0.211849i \(0.0679484\pi\)
−0.878030 + 0.478605i \(0.841143\pi\)
\(60\) 0 0
\(61\) 10.2607 3.01281i 1.31375 0.385751i 0.451514 0.892264i \(-0.350884\pi\)
0.862232 + 0.506514i \(0.169066\pi\)
\(62\) 0 0
\(63\) 1.74133 2.00960i 0.219386 0.253185i
\(64\) 0 0
\(65\) −2.58619 2.98463i −0.320778 0.370197i
\(66\) 0 0
\(67\) 6.67408 14.6142i 0.815369 1.78541i 0.233016 0.972473i \(-0.425141\pi\)
0.582353 0.812936i \(-0.302132\pi\)
\(68\) 0 0
\(69\) 3.88401 + 2.81326i 0.467580 + 0.338677i
\(70\) 0 0
\(71\) −6.49235 + 14.2163i −0.770501 + 1.68716i −0.0449529 + 0.998989i \(0.514314\pi\)
−0.725548 + 0.688172i \(0.758414\pi\)
\(72\) 0 0
\(73\) 6.10673 + 7.04754i 0.714739 + 0.824852i 0.990664 0.136327i \(-0.0435297\pi\)
−0.275925 + 0.961179i \(0.588984\pi\)
\(74\) 0 0
\(75\) 0.141071 0.162805i 0.0162895 0.0187991i
\(76\) 0 0
\(77\) −11.6964 + 3.43437i −1.33293 + 0.391383i
\(78\) 0 0
\(79\) −0.841256 5.85107i −0.0946487 0.658296i −0.980817 0.194932i \(-0.937551\pi\)
0.886168 0.463364i \(-0.153358\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 0 0
\(83\) −3.82619 2.45894i −0.419979 0.269904i 0.313537 0.949576i \(-0.398486\pi\)
−0.733516 + 0.679672i \(0.762122\pi\)
\(84\) 0 0
\(85\) −0.990920 + 6.89200i −0.107480 + 0.747542i
\(86\) 0 0
\(87\) −6.45311 + 4.14716i −0.691846 + 0.444622i
\(88\) 0 0
\(89\) 4.57162 + 1.34235i 0.484591 + 0.142289i 0.514897 0.857252i \(-0.327830\pi\)
−0.0303064 + 0.999541i \(0.509648\pi\)
\(90\) 0 0
\(91\) −4.59831 −0.482034
\(92\) 0 0
\(93\) 1.14779 0.119020
\(94\) 0 0
\(95\) −5.67873 1.66743i −0.582626 0.171074i
\(96\) 0 0
\(97\) −9.16603 + 5.89065i −0.930669 + 0.598105i −0.915735 0.401784i \(-0.868390\pi\)
−0.0149348 + 0.999888i \(0.504754\pi\)
\(98\) 0 0
\(99\) 0.652424 4.53771i 0.0655711 0.456057i
\(100\) 0 0
\(101\) −7.43646 4.77912i −0.739956 0.475541i 0.115571 0.993299i \(-0.463130\pi\)
−0.855527 + 0.517759i \(0.826767\pi\)
\(102\) 0 0
\(103\) −1.38134 3.02471i −0.136107 0.298033i 0.829289 0.558820i \(-0.188746\pi\)
−0.965397 + 0.260786i \(0.916018\pi\)
\(104\) 0 0
\(105\) −0.864223 6.01080i −0.0843395 0.586594i
\(106\) 0 0
\(107\) −13.0919 + 3.84414i −1.26565 + 0.371627i −0.844593 0.535409i \(-0.820157\pi\)
−0.421052 + 0.907036i \(0.638339\pi\)
\(108\) 0 0
\(109\) −1.32429 + 1.52831i −0.126844 + 0.146385i −0.815619 0.578590i \(-0.803603\pi\)
0.688775 + 0.724975i \(0.258149\pi\)
\(110\) 0 0
\(111\) 5.76305 + 6.65091i 0.547004 + 0.631277i
\(112\) 0 0
\(113\) 1.78410 3.90663i 0.167834 0.367504i −0.806962 0.590603i \(-0.798890\pi\)
0.974796 + 0.223099i \(0.0716172\pi\)
\(114\) 0 0
\(115\) 10.6641 2.49621i 0.994435 0.232773i
\(116\) 0 0
\(117\) 0.718372 1.57302i 0.0664135 0.145425i
\(118\) 0 0
\(119\) 5.30913 + 6.12707i 0.486687 + 0.561667i
\(120\) 0 0
\(121\) −6.55937 + 7.56992i −0.596307 + 0.688174i
\(122\) 0 0
\(123\) 5.51275 1.61869i 0.497068 0.145952i
\(124\) 0 0
\(125\) 1.55503 + 10.8155i 0.139086 + 0.967365i
\(126\) 0 0
\(127\) 3.64707 + 7.98597i 0.323625 + 0.708640i 0.999600 0.0282847i \(-0.00900449\pi\)
−0.675975 + 0.736925i \(0.736277\pi\)
\(128\) 0 0
\(129\) 3.55570 + 2.28511i 0.313062 + 0.201193i
\(130\) 0 0
\(131\) 0.0499416 0.347351i 0.00436342 0.0303482i −0.987523 0.157472i \(-0.949666\pi\)
0.991887 + 0.127124i \(0.0405746\pi\)
\(132\) 0 0
\(133\) −5.79726 + 3.72567i −0.502686 + 0.323057i
\(134\) 0 0
\(135\) 2.19122 + 0.643401i 0.188590 + 0.0553751i
\(136\) 0 0
\(137\) −6.59758 −0.563669 −0.281835 0.959463i \(-0.590943\pi\)
−0.281835 + 0.959463i \(0.590943\pi\)
\(138\) 0 0
\(139\) −4.68361 −0.397259 −0.198629 0.980075i \(-0.563649\pi\)
−0.198629 + 0.980075i \(0.563649\pi\)
\(140\) 0 0
\(141\) −2.33899 0.686790i −0.196979 0.0578382i
\(142\) 0 0
\(143\) −6.66920 + 4.28603i −0.557706 + 0.358416i
\(144\) 0 0
\(145\) −2.49308 + 17.3398i −0.207039 + 1.43999i
\(146\) 0 0
\(147\) −0.0594705 0.0382194i −0.00490505 0.00315228i
\(148\) 0 0
\(149\) 1.81118 + 3.96592i 0.148377 + 0.324901i 0.969197 0.246286i \(-0.0792103\pi\)
−0.820820 + 0.571187i \(0.806483\pi\)
\(150\) 0 0
\(151\) 0.408413 + 2.84057i 0.0332361 + 0.231162i 0.999668 0.0257600i \(-0.00820059\pi\)
−0.966432 + 0.256922i \(0.917291\pi\)
\(152\) 0 0
\(153\) −2.92540 + 0.858975i −0.236505 + 0.0694440i
\(154\) 0 0
\(155\) 1.71655 1.98100i 0.137876 0.159118i
\(156\) 0 0
\(157\) 2.76681 + 3.19307i 0.220816 + 0.254835i 0.855339 0.518069i \(-0.173349\pi\)
−0.634523 + 0.772904i \(0.718803\pi\)
\(158\) 0 0
\(159\) −3.30490 + 7.23673i −0.262096 + 0.573910i
\(160\) 0 0
\(161\) 5.93474 11.2874i 0.467723 0.889570i
\(162\) 0 0
\(163\) 3.53236 7.73480i 0.276676 0.605836i −0.719375 0.694622i \(-0.755572\pi\)
0.996051 + 0.0887862i \(0.0282988\pi\)
\(164\) 0 0
\(165\) −6.85604 7.91229i −0.533742 0.615971i
\(166\) 0 0
\(167\) −11.6311 + 13.4230i −0.900042 + 1.03870i 0.0990059 + 0.995087i \(0.468434\pi\)
−0.999048 + 0.0436174i \(0.986112\pi\)
\(168\) 0 0
\(169\) 9.60411 2.82002i 0.738777 0.216925i
\(170\) 0 0
\(171\) −0.368821 2.56520i −0.0282044 0.196166i
\(172\) 0 0
\(173\) −7.13558 15.6247i −0.542508 1.18793i −0.960194 0.279335i \(-0.909886\pi\)
0.417686 0.908592i \(-0.362841\pi\)
\(174\) 0 0
\(175\) −0.481889 0.309691i −0.0364274 0.0234105i
\(176\) 0 0
\(177\) −0.762525 + 5.30348i −0.0573149 + 0.398634i
\(178\) 0 0
\(179\) 6.74318 4.33358i 0.504009 0.323907i −0.263809 0.964575i \(-0.584979\pi\)
0.767818 + 0.640668i \(0.221343\pi\)
\(180\) 0 0
\(181\) −16.3840 4.81077i −1.21781 0.357582i −0.391174 0.920317i \(-0.627931\pi\)
−0.826637 + 0.562735i \(0.809749\pi\)
\(182\) 0 0
\(183\) 10.6939 0.790513
\(184\) 0 0
\(185\) 20.0978 1.47762
\(186\) 0 0
\(187\) 13.4111 + 3.93786i 0.980718 + 0.287965i
\(188\) 0 0
\(189\) 2.23696 1.43761i 0.162715 0.104570i
\(190\) 0 0
\(191\) −2.00632 + 13.9543i −0.145173 + 1.00970i 0.778809 + 0.627261i \(0.215824\pi\)
−0.923982 + 0.382436i \(0.875085\pi\)
\(192\) 0 0
\(193\) −18.0079 11.5730i −1.29624 0.833041i −0.303441 0.952850i \(-0.598135\pi\)
−0.992797 + 0.119809i \(0.961772\pi\)
\(194\) 0 0
\(195\) −1.64057 3.59234i −0.117483 0.257253i
\(196\) 0 0
\(197\) −3.64384 25.3434i −0.259613 1.80565i −0.535587 0.844480i \(-0.679910\pi\)
0.275974 0.961165i \(-0.411000\pi\)
\(198\) 0 0
\(199\) −24.0826 + 7.07128i −1.70717 + 0.501270i −0.982252 0.187568i \(-0.939940\pi\)
−0.724916 + 0.688837i \(0.758121\pi\)
\(200\) 0 0
\(201\) 10.5210 12.1419i 0.742096 0.856425i
\(202\) 0 0
\(203\) 13.3574 + 15.4153i 0.937505 + 1.08194i
\(204\) 0 0
\(205\) 5.45071 11.9354i 0.380694 0.833604i
\(206\) 0 0
\(207\) 2.93409 + 3.79356i 0.203934 + 0.263671i
\(208\) 0 0
\(209\) −4.93545 + 10.8071i −0.341392 + 0.747545i
\(210\) 0 0
\(211\) −8.99494 10.3807i −0.619237 0.714638i 0.356325 0.934362i \(-0.384030\pi\)
−0.975562 + 0.219724i \(0.929484\pi\)
\(212\) 0 0
\(213\) −10.2346 + 11.8113i −0.701260 + 0.809297i
\(214\) 0 0
\(215\) 9.26157 2.71944i 0.631634 0.185464i
\(216\) 0 0
\(217\) −0.434353 3.02099i −0.0294858 0.205078i
\(218\) 0 0
\(219\) 3.87384 + 8.48253i 0.261770 + 0.573196i
\(220\) 0 0
\(221\) 4.43545 + 2.85049i 0.298361 + 0.191745i
\(222\) 0 0
\(223\) −2.17025 + 15.0944i −0.145331 + 1.01080i 0.778404 + 0.627764i \(0.216030\pi\)
−0.923734 + 0.383034i \(0.874879\pi\)
\(224\) 0 0
\(225\) 0.181224 0.116466i 0.0120816 0.00776438i
\(226\) 0 0
\(227\) 22.8920 + 6.72170i 1.51940 + 0.446135i 0.931785 0.363010i \(-0.118251\pi\)
0.587610 + 0.809144i \(0.300069\pi\)
\(228\) 0 0
\(229\) 15.2019 1.00457 0.502284 0.864703i \(-0.332493\pi\)
0.502284 + 0.864703i \(0.332493\pi\)
\(230\) 0 0
\(231\) −12.1902 −0.802056
\(232\) 0 0
\(233\) −9.58489 2.81438i −0.627927 0.184376i −0.0477406 0.998860i \(-0.515202\pi\)
−0.580186 + 0.814484i \(0.697020\pi\)
\(234\) 0 0
\(235\) −4.68337 + 3.00982i −0.305510 + 0.196339i
\(236\) 0 0
\(237\) 0.841256 5.85107i 0.0546455 0.380068i
\(238\) 0 0
\(239\) 17.7339 + 11.3969i 1.14711 + 0.737204i 0.969062 0.246818i \(-0.0793849\pi\)
0.178050 + 0.984022i \(0.443021\pi\)
\(240\) 0 0
\(241\) −3.37068 7.38075i −0.217124 0.475436i 0.769459 0.638697i \(-0.220526\pi\)
−0.986583 + 0.163261i \(0.947799\pi\)
\(242\) 0 0
\(243\) 0.142315 + 0.989821i 0.00912950 + 0.0634971i
\(244\) 0 0
\(245\) −0.154904 + 0.0454838i −0.00989642 + 0.00290585i
\(246\) 0 0
\(247\) −2.93482 + 3.38696i −0.186738 + 0.215507i
\(248\) 0 0
\(249\) −2.97844 3.43730i −0.188751 0.217830i
\(250\) 0 0
\(251\) 12.5252 27.4264i 0.790583 1.73114i 0.115610 0.993295i \(-0.463118\pi\)
0.674974 0.737842i \(-0.264155\pi\)
\(252\) 0 0
\(253\) −1.91334 21.9024i −0.120291 1.37700i
\(254\) 0 0
\(255\) −2.89248 + 6.33365i −0.181134 + 0.396629i
\(256\) 0 0
\(257\) −15.3516 17.7167i −0.957609 1.10514i −0.994386 0.105816i \(-0.966255\pi\)
0.0367771 0.999323i \(-0.488291\pi\)
\(258\) 0 0
\(259\) 15.3244 17.6853i 0.952212 1.09891i
\(260\) 0 0
\(261\) −7.36010 + 2.16112i −0.455579 + 0.133770i
\(262\) 0 0
\(263\) 0.445501 + 3.09853i 0.0274708 + 0.191063i 0.998936 0.0461187i \(-0.0146853\pi\)
−0.971465 + 0.237182i \(0.923776\pi\)
\(264\) 0 0
\(265\) 7.54750 + 16.5267i 0.463639 + 1.01523i
\(266\) 0 0
\(267\) 4.00825 + 2.57595i 0.245301 + 0.157645i
\(268\) 0 0
\(269\) −0.711178 + 4.94635i −0.0433613 + 0.301584i 0.956587 + 0.291446i \(0.0941363\pi\)
−0.999949 + 0.0101385i \(0.996773\pi\)
\(270\) 0 0
\(271\) −5.62965 + 3.61795i −0.341977 + 0.219775i −0.700344 0.713806i \(-0.746970\pi\)
0.358367 + 0.933581i \(0.383334\pi\)
\(272\) 0 0
\(273\) −4.41205 1.29549i −0.267029 0.0784068i
\(274\) 0 0
\(275\) −0.987572 −0.0595528
\(276\) 0 0
\(277\) 29.1628 1.75222 0.876112 0.482107i \(-0.160128\pi\)
0.876112 + 0.482107i \(0.160128\pi\)
\(278\) 0 0
\(279\) 1.10129 + 0.323369i 0.0659328 + 0.0193596i
\(280\) 0 0
\(281\) 16.5582 10.6413i 0.987777 0.634806i 0.0562268 0.998418i \(-0.482093\pi\)
0.931550 + 0.363612i \(0.118457\pi\)
\(282\) 0 0
\(283\) 3.93443 27.3646i 0.233878 1.62666i −0.447192 0.894438i \(-0.647576\pi\)
0.681070 0.732218i \(-0.261515\pi\)
\(284\) 0 0
\(285\) −4.97894 3.19977i −0.294927 0.189538i
\(286\) 0 0
\(287\) −6.34658 13.8971i −0.374627 0.820318i
\(288\) 0 0
\(289\) 1.09642 + 7.62577i 0.0644953 + 0.448575i
\(290\) 0 0
\(291\) −10.4543 + 3.06967i −0.612844 + 0.179947i
\(292\) 0 0
\(293\) 8.53167 9.84607i 0.498425 0.575213i −0.449672 0.893194i \(-0.648459\pi\)
0.948097 + 0.317980i \(0.103005\pi\)
\(294\) 0 0
\(295\) 8.01304 + 9.24754i 0.466537 + 0.538413i
\(296\) 0 0
\(297\) 1.90442 4.17009i 0.110505 0.241973i
\(298\) 0 0
\(299\) 1.63514 8.13058i 0.0945628 0.470204i
\(300\) 0 0
\(301\) 4.66886 10.2234i 0.269109 0.589266i
\(302\) 0 0
\(303\) −5.78880 6.68063i −0.332558 0.383792i
\(304\) 0 0
\(305\) 15.9929 18.4568i 0.915753 1.05683i
\(306\) 0 0
\(307\) −21.1246 + 6.20274i −1.20564 + 0.354009i −0.822009 0.569475i \(-0.807147\pi\)
−0.383636 + 0.923484i \(0.625328\pi\)
\(308\) 0 0
\(309\) −0.473225 3.29135i −0.0269209 0.187239i
\(310\) 0 0
\(311\) −5.13763 11.2498i −0.291328 0.637919i 0.706213 0.707999i \(-0.250402\pi\)
−0.997541 + 0.0700797i \(0.977675\pi\)
\(312\) 0 0
\(313\) 15.1033 + 9.70633i 0.853692 + 0.548634i 0.892724 0.450604i \(-0.148791\pi\)
−0.0390325 + 0.999238i \(0.512428\pi\)
\(314\) 0 0
\(315\) 0.864223 6.01080i 0.0486935 0.338670i
\(316\) 0 0
\(317\) −0.999649 + 0.642435i −0.0561459 + 0.0360828i −0.568413 0.822744i \(-0.692442\pi\)
0.512267 + 0.858826i \(0.328806\pi\)
\(318\) 0 0
\(319\) 33.7414 + 9.90737i 1.88916 + 0.554706i
\(320\) 0 0
\(321\) −13.6446 −0.761569
\(322\) 0 0
\(323\) 7.90148 0.439650
\(324\) 0 0
\(325\) −0.357436 0.104953i −0.0198270 0.00582173i
\(326\) 0 0
\(327\) −1.70122 + 1.09331i −0.0940775 + 0.0604599i
\(328\) 0 0
\(329\) −0.922504 + 6.41616i −0.0508593 + 0.353734i
\(330\) 0 0
\(331\) −20.3996 13.1100i −1.12126 0.720591i −0.157543 0.987512i \(-0.550357\pi\)
−0.963718 + 0.266921i \(0.913994\pi\)
\(332\) 0 0
\(333\) 3.65583 + 8.00514i 0.200338 + 0.438679i
\(334\) 0 0
\(335\) −5.22161 36.3171i −0.285287 1.98421i
\(336\) 0 0
\(337\) −28.1809 + 8.27465i −1.53511 + 0.450749i −0.936610 0.350374i \(-0.886054\pi\)
−0.598500 + 0.801123i \(0.704236\pi\)
\(338\) 0 0
\(339\) 2.81245 3.24574i 0.152751 0.176285i
\(340\) 0 0
\(341\) −3.44580 3.97667i −0.186601 0.215349i
\(342\) 0 0
\(343\) 7.65426 16.7605i 0.413291 0.904981i
\(344\) 0 0
\(345\) 10.9354 + 0.609332i 0.588743 + 0.0328053i
\(346\) 0 0
\(347\) 3.97900 8.71279i 0.213604 0.467727i −0.772253 0.635315i \(-0.780870\pi\)
0.985857 + 0.167588i \(0.0535977\pi\)
\(348\) 0 0
\(349\) −1.39106 1.60537i −0.0744619 0.0859337i 0.717296 0.696768i \(-0.245379\pi\)
−0.791758 + 0.610835i \(0.790834\pi\)
\(350\) 0 0
\(351\) 1.13244 1.30691i 0.0604453 0.0697576i
\(352\) 0 0
\(353\) −17.3881 + 5.10561i −0.925476 + 0.271744i −0.709542 0.704664i \(-0.751098\pi\)
−0.215934 + 0.976408i \(0.569280\pi\)
\(354\) 0 0
\(355\) 5.07943 + 35.3282i 0.269588 + 1.87503i
\(356\) 0 0
\(357\) 3.36788 + 7.37463i 0.178247 + 0.390307i
\(358\) 0 0
\(359\) 15.5991 + 10.0249i 0.823287 + 0.529094i 0.883138 0.469113i \(-0.155426\pi\)
−0.0598515 + 0.998207i \(0.519063\pi\)
\(360\) 0 0
\(361\) 1.74815 12.1587i 0.0920080 0.639930i
\(362\) 0 0
\(363\) −8.42636 + 5.41530i −0.442269 + 0.284229i
\(364\) 0 0
\(365\) 20.4337 + 5.99987i 1.06955 + 0.314047i
\(366\) 0 0
\(367\) 20.2707 1.05812 0.529061 0.848584i \(-0.322544\pi\)
0.529061 + 0.848584i \(0.322544\pi\)
\(368\) 0 0
\(369\) 5.74548 0.299098
\(370\) 0 0
\(371\) 20.2978 + 5.95998i 1.05381 + 0.309426i
\(372\) 0 0
\(373\) −4.72549 + 3.03689i −0.244676 + 0.157244i −0.657232 0.753689i \(-0.728273\pi\)
0.412555 + 0.910933i \(0.364636\pi\)
\(374\) 0 0
\(375\) −1.55503 + 10.8155i −0.0803014 + 0.558508i
\(376\) 0 0
\(377\) 11.1593 + 7.17163i 0.574732 + 0.369358i
\(378\) 0 0
\(379\) 10.2302 + 22.4011i 0.525492 + 1.15067i 0.967318 + 0.253566i \(0.0816036\pi\)
−0.441826 + 0.897101i \(0.645669\pi\)
\(380\) 0 0
\(381\) 1.24943 + 8.68998i 0.0640102 + 0.445201i
\(382\) 0 0
\(383\) −3.72748 + 1.09449i −0.190466 + 0.0559257i −0.375574 0.926792i \(-0.622554\pi\)
0.185109 + 0.982718i \(0.440736\pi\)
\(384\) 0 0
\(385\) −18.2307 + 21.0394i −0.929124 + 1.07227i
\(386\) 0 0
\(387\) 2.76788 + 3.19430i 0.140699 + 0.162375i
\(388\) 0 0
\(389\) −11.6566 + 25.5244i −0.591012 + 1.29414i 0.343816 + 0.939037i \(0.388280\pi\)
−0.934829 + 0.355099i \(0.884447\pi\)
\(390\) 0 0
\(391\) −12.7216 + 7.20867i −0.643358 + 0.364558i
\(392\) 0 0
\(393\) 0.145779 0.319211i 0.00735357 0.0161021i
\(394\) 0 0
\(395\) −8.84040 10.2024i −0.444809 0.513337i
\(396\) 0 0
\(397\) 17.7145 20.4436i 0.889063 1.02603i −0.110420 0.993885i \(-0.535219\pi\)
0.999483 0.0321489i \(-0.0102351\pi\)
\(398\) 0 0
\(399\) −6.61208 + 1.94148i −0.331018 + 0.0971956i
\(400\) 0 0
\(401\) −1.12636 7.83403i −0.0562479 0.391213i −0.998425 0.0560982i \(-0.982134\pi\)
0.942177 0.335115i \(-0.108775\pi\)
\(402\) 0 0
\(403\) −0.824539 1.80549i −0.0410732 0.0899378i
\(404\) 0 0
\(405\) 1.92120 + 1.23468i 0.0954650 + 0.0613516i
\(406\) 0 0
\(407\) 5.74160 39.9337i 0.284601 1.97944i
\(408\) 0 0
\(409\) −27.0593 + 17.3900i −1.33800 + 0.859878i −0.996786 0.0801091i \(-0.974473\pi\)
−0.341210 + 0.939987i \(0.610837\pi\)
\(410\) 0 0
\(411\) −6.33033 1.85875i −0.312252 0.0916855i
\(412\) 0 0
\(413\) 14.2474 0.701067
\(414\) 0 0
\(415\) −10.3869 −0.509871
\(416\) 0 0
\(417\) −4.49389 1.31953i −0.220067 0.0646174i
\(418\) 0 0
\(419\) −8.13577 + 5.22854i −0.397458 + 0.255431i −0.724068 0.689728i \(-0.757730\pi\)
0.326610 + 0.945159i \(0.394094\pi\)
\(420\) 0 0
\(421\) −4.59917 + 31.9880i −0.224150 + 1.55900i 0.497948 + 0.867207i \(0.334087\pi\)
−0.722098 + 0.691791i \(0.756822\pi\)
\(422\) 0 0
\(423\) −2.05076 1.31794i −0.0997112 0.0640805i
\(424\) 0 0
\(425\) 0.272844 + 0.597446i 0.0132349 + 0.0289804i
\(426\) 0 0
\(427\) −4.04684 28.1464i −0.195840 1.36210i
\(428\) 0 0
\(429\) −7.60657 + 2.23349i −0.367248 + 0.107834i
\(430\) 0 0
\(431\) −15.6514 + 18.0626i −0.753900 + 0.870047i −0.994940 0.100468i \(-0.967966\pi\)
0.241040 + 0.970515i \(0.422511\pi\)
\(432\) 0 0
\(433\) −10.9333 12.6177i −0.525420 0.606367i 0.429560 0.903038i \(-0.358669\pi\)
−0.954980 + 0.296672i \(0.904123\pi\)
\(434\) 0 0
\(435\) −7.27728 + 15.9350i −0.348919 + 0.764025i
\(436\) 0 0
\(437\) −4.52613 11.5754i −0.216514 0.553725i
\(438\) 0 0
\(439\) −10.5838 + 23.1754i −0.505139 + 1.10610i 0.469626 + 0.882866i \(0.344389\pi\)
−0.974765 + 0.223235i \(0.928338\pi\)
\(440\) 0 0
\(441\) −0.0462939 0.0534260i −0.00220447 0.00254410i
\(442\) 0 0
\(443\) −10.1209 + 11.6802i −0.480860 + 0.554941i −0.943400 0.331657i \(-0.892392\pi\)
0.462541 + 0.886598i \(0.346938\pi\)
\(444\) 0 0
\(445\) 10.4403 3.06556i 0.494920 0.145322i
\(446\) 0 0
\(447\) 0.620481 + 4.31554i 0.0293478 + 0.204118i
\(448\) 0 0
\(449\) 8.49848 + 18.6091i 0.401068 + 0.878216i 0.997161 + 0.0753007i \(0.0239917\pi\)
−0.596093 + 0.802915i \(0.703281\pi\)
\(450\) 0 0
\(451\) −22.1581 14.2402i −1.04339 0.670543i
\(452\) 0 0
\(453\) −0.408413 + 2.84057i −0.0191889 + 0.133462i
\(454\) 0 0
\(455\) −8.83425 + 5.67743i −0.414156 + 0.266162i
\(456\) 0 0
\(457\) 6.86581 + 2.01598i 0.321169 + 0.0943037i 0.438343 0.898808i \(-0.355565\pi\)
−0.117174 + 0.993111i \(0.537384\pi\)
\(458\) 0 0
\(459\) −3.04890 −0.142311
\(460\) 0 0
\(461\) 9.32069 0.434108 0.217054 0.976160i \(-0.430355\pi\)
0.217054 + 0.976160i \(0.430355\pi\)
\(462\) 0 0
\(463\) −7.07182 2.07647i −0.328655 0.0965019i 0.113242 0.993567i \(-0.463876\pi\)
−0.441898 + 0.897065i \(0.645695\pi\)
\(464\) 0 0
\(465\) 2.20513 1.41715i 0.102260 0.0657187i
\(466\) 0 0
\(467\) −0.556229 + 3.86866i −0.0257392 + 0.179020i −0.998636 0.0522217i \(-0.983370\pi\)
0.972896 + 0.231242i \(0.0742788\pi\)
\(468\) 0 0
\(469\) −35.9391 23.0967i −1.65951 1.06650i
\(470\) 0 0
\(471\) 1.75515 + 3.84323i 0.0808728 + 0.177087i
\(472\) 0 0
\(473\) −2.75758 19.1794i −0.126794 0.881869i
\(474\) 0 0
\(475\) −0.535668 + 0.157286i −0.0245781 + 0.00721680i
\(476\) 0 0
\(477\) −5.20985 + 6.01249i −0.238543 + 0.275293i
\(478\) 0 0
\(479\) 6.41186 + 7.39968i 0.292966 + 0.338100i 0.883083 0.469217i \(-0.155464\pi\)
−0.590117 + 0.807318i \(0.700918\pi\)
\(480\) 0 0
\(481\) 6.32198 13.8432i 0.288257 0.631195i
\(482\) 0 0
\(483\) 8.87436 9.15815i 0.403797 0.416710i
\(484\) 0 0
\(485\) −10.3367 + 22.6342i −0.469365 + 1.02777i
\(486\) 0 0
\(487\) −7.40740 8.54860i −0.335661 0.387374i 0.562678 0.826676i \(-0.309771\pi\)
−0.898339 + 0.439302i \(0.855226\pi\)
\(488\) 0 0
\(489\) 5.56842 6.42630i 0.251813 0.290607i
\(490\) 0 0
\(491\) −24.7044 + 7.25387i −1.11489 + 0.327363i −0.786754 0.617266i \(-0.788240\pi\)
−0.328140 + 0.944629i \(0.606422\pi\)
\(492\) 0 0
\(493\) −3.32840 23.1495i −0.149904 1.04260i
\(494\) 0 0
\(495\) −4.34917 9.52336i −0.195481 0.428043i
\(496\) 0 0
\(497\) 34.9605 + 22.4678i 1.56819 + 1.00782i
\(498\) 0 0
\(499\) −4.66202 + 32.4251i −0.208701 + 1.45155i 0.568702 + 0.822544i \(0.307446\pi\)
−0.777403 + 0.629003i \(0.783463\pi\)
\(500\) 0 0
\(501\) −14.9417 + 9.60243i −0.667545 + 0.429005i
\(502\) 0 0
\(503\) 19.9771 + 5.86581i 0.890735 + 0.261544i 0.694911 0.719096i \(-0.255444\pi\)
0.195824 + 0.980639i \(0.437262\pi\)
\(504\) 0 0
\(505\) −20.1876 −0.898335
\(506\) 0 0
\(507\) 10.0096 0.444540
\(508\) 0 0
\(509\) 20.4103 + 5.99301i 0.904671 + 0.265635i 0.700796 0.713362i \(-0.252828\pi\)
0.203875 + 0.978997i \(0.434646\pi\)
\(510\) 0 0
\(511\) 20.8602 13.4060i 0.922799 0.593047i
\(512\) 0 0
\(513\) 0.368821 2.56520i 0.0162838 0.113257i
\(514\) 0 0
\(515\) −6.38836 4.10555i −0.281505 0.180912i
\(516\) 0 0
\(517\) 4.64247 + 10.1656i 0.204176 + 0.447082i
\(518\) 0 0
\(519\) −2.44454 17.0022i −0.107303 0.746312i
\(520\) 0 0
\(521\) 5.13935 1.50905i 0.225159 0.0661127i −0.167207 0.985922i \(-0.553475\pi\)
0.392366 + 0.919809i \(0.371657\pi\)
\(522\) 0 0
\(523\) −29.6108 + 34.1726i −1.29479 + 1.49427i −0.533595 + 0.845740i \(0.679159\pi\)
−0.761193 + 0.648525i \(0.775386\pi\)
\(524\) 0 0
\(525\) −0.375119 0.432910i −0.0163715 0.0188938i
\(526\) 0 0
\(527\) −1.45374 + 3.18325i −0.0633260 + 0.138665i
\(528\) 0 0
\(529\) 17.8476 + 14.5074i 0.775982 + 0.630755i
\(530\) 0 0
\(531\) −2.22580 + 4.87382i −0.0965914 + 0.211506i
\(532\) 0 0
\(533\) −6.50643 7.50882i −0.281825 0.325243i
\(534\) 0 0
\(535\) −20.4059 + 23.5497i −0.882224 + 1.01814i
\(536\) 0 0
\(537\) 7.69094 2.25826i 0.331889 0.0974513i
\(538\) 0 0
\(539\) 0.0461216 + 0.320783i 0.00198660 + 0.0138171i
\(540\) 0 0
\(541\) 3.52068 + 7.70922i 0.151366 + 0.331445i 0.970091 0.242740i \(-0.0780462\pi\)
−0.818725 + 0.574185i \(0.805319\pi\)
\(542\) 0 0
\(543\) −14.3650 9.23180i −0.616459 0.396174i
\(544\) 0 0
\(545\) −0.657246 + 4.57124i −0.0281533 + 0.195811i
\(546\) 0 0
\(547\) 12.7677 8.20530i 0.545907 0.350833i −0.238438 0.971158i \(-0.576635\pi\)
0.784345 + 0.620325i \(0.212999\pi\)
\(548\) 0 0
\(549\) 10.2607 + 3.01281i 0.437915 + 0.128584i
\(550\) 0 0
\(551\) 19.8796 0.846898
\(552\) 0 0
\(553\) −15.7184 −0.668416
\(554\) 0 0
\(555\) 19.2837 + 5.66220i 0.818547 + 0.240347i
\(556\) 0 0
\(557\) 25.6320 16.4727i 1.08606 0.697971i 0.130113 0.991499i \(-0.458466\pi\)
0.955950 + 0.293528i \(0.0948295\pi\)
\(558\) 0 0
\(559\) 1.04020 7.23473i 0.0439956 0.305996i
\(560\) 0 0
\(561\) 11.7585 + 7.55670i 0.496442 + 0.319044i
\(562\) 0 0
\(563\) −7.15695 15.6715i −0.301629 0.660476i 0.696754 0.717310i \(-0.254627\pi\)
−0.998384 + 0.0568338i \(0.981899\pi\)
\(564\) 0 0
\(565\) −1.39582 9.70818i −0.0587228 0.408426i
\(566\) 0 0
\(567\) 2.55137 0.749149i 0.107147 0.0314613i
\(568\) 0 0
\(569\) 1.30394 1.50483i 0.0546641 0.0630858i −0.727759 0.685833i \(-0.759438\pi\)
0.782423 + 0.622747i \(0.213984\pi\)
\(570\) 0 0
\(571\) 0.0843731 + 0.0973718i 0.00353090 + 0.00407488i 0.757512 0.652821i \(-0.226415\pi\)
−0.753981 + 0.656896i \(0.771869\pi\)
\(572\) 0 0
\(573\) −5.85643 + 12.8238i −0.244656 + 0.535722i
\(574\) 0 0
\(575\) 0.718944 0.741935i 0.0299820 0.0309408i
\(576\) 0 0
\(577\) −14.0510 + 30.7675i −0.584953 + 1.28087i 0.353492 + 0.935438i \(0.384994\pi\)
−0.938444 + 0.345430i \(0.887733\pi\)
\(578\) 0 0
\(579\) −14.0180 16.1776i −0.582567 0.672318i
\(580\) 0 0
\(581\) −7.91990 + 9.14005i −0.328573 + 0.379193i
\(582\) 0 0
\(583\) 34.9943 10.2753i 1.44932 0.425558i
\(584\) 0 0
\(585\) −0.562033 3.90903i −0.0232372 0.161618i
\(586\) 0 0
\(587\) −4.65842 10.2005i −0.192274 0.421021i 0.788801 0.614648i \(-0.210702\pi\)
−0.981075 + 0.193627i \(0.937975\pi\)
\(588\) 0 0
\(589\) −2.50238 1.60818i −0.103109 0.0662641i
\(590\) 0 0
\(591\) 3.64384 25.3434i 0.149887 1.04249i
\(592\) 0 0
\(593\) −34.5384 + 22.1965i −1.41832 + 0.911500i −0.418327 + 0.908296i \(0.637384\pi\)
−0.999995 + 0.00320409i \(0.998980\pi\)
\(594\) 0 0
\(595\) 17.7648 + 5.21623i 0.728287 + 0.213844i
\(596\) 0 0
\(597\) −25.0993 −1.02724
\(598\) 0 0
\(599\) −13.8948 −0.567727 −0.283863 0.958865i \(-0.591616\pi\)
−0.283863 + 0.958865i \(0.591616\pi\)
\(600\) 0 0
\(601\) 36.4668 + 10.7076i 1.48751 + 0.436773i 0.921746 0.387793i \(-0.126762\pi\)
0.565766 + 0.824566i \(0.308581\pi\)
\(602\) 0 0
\(603\) 13.5156 8.68597i 0.550399 0.353720i
\(604\) 0 0
\(605\) −3.25543 + 22.6420i −0.132352 + 0.920528i
\(606\) 0 0
\(607\) −7.82890 5.03133i −0.317765 0.204215i 0.372028 0.928221i \(-0.378662\pi\)
−0.689794 + 0.724006i \(0.742299\pi\)
\(608\) 0 0
\(609\) 8.47335 + 18.5540i 0.343357 + 0.751848i
\(610\) 0 0
\(611\) 0.599936 + 4.17264i 0.0242708 + 0.168807i
\(612\) 0 0
\(613\) −34.4865 + 10.1261i −1.39290 + 0.408991i −0.890238 0.455495i \(-0.849462\pi\)
−0.502657 + 0.864486i \(0.667644\pi\)
\(614\) 0 0
\(615\) 8.59251 9.91629i 0.346483 0.399863i
\(616\) 0 0
\(617\) −12.3944 14.3039i −0.498978 0.575851i 0.449264 0.893399i \(-0.351686\pi\)
−0.948242 + 0.317548i \(0.897141\pi\)
\(618\) 0 0
\(619\) 5.02572 11.0048i 0.202001 0.442320i −0.781337 0.624110i \(-0.785462\pi\)
0.983337 + 0.181790i \(0.0581891\pi\)
\(620\) 0 0
\(621\) 1.74647 + 4.46652i 0.0700835 + 0.179235i
\(622\) 0 0
\(623\) 5.26310 11.5246i 0.210862 0.461722i
\(624\) 0 0
\(625\) 17.0465 + 19.6727i 0.681859 + 0.786908i
\(626\) 0 0
\(627\) −7.78025 + 8.97889i −0.310713 + 0.358582i
\(628\) 0 0
\(629\) −25.7448 + 7.55934i −1.02651 + 0.301411i
\(630\) 0 0
\(631\) −3.77021 26.2224i −0.150090 1.04390i −0.916066 0.401028i \(-0.868653\pi\)
0.765976 0.642869i \(-0.222256\pi\)
\(632\) 0 0
\(633\) −5.70600 12.4944i −0.226793 0.496607i
\(634\) 0 0
\(635\) 16.8668 + 10.8397i 0.669340 + 0.430158i
\(636\) 0 0
\(637\) −0.0173977 + 0.121004i −0.000689323 + 0.00479434i
\(638\) 0 0
\(639\) −13.1476 + 8.44946i −0.520111 + 0.334255i
\(640\) 0 0
\(641\) 7.37655 + 2.16595i 0.291356 + 0.0855499i 0.424145 0.905594i \(-0.360575\pi\)
−0.132788 + 0.991144i \(0.542393\pi\)
\(642\) 0 0
\(643\) −10.8542 −0.428048 −0.214024 0.976828i \(-0.568657\pi\)
−0.214024 + 0.976828i \(0.568657\pi\)
\(644\) 0 0
\(645\) 9.65256 0.380069
\(646\) 0 0
\(647\) 15.4575 + 4.53873i 0.607697 + 0.178436i 0.571081 0.820893i \(-0.306524\pi\)
0.0366156 + 0.999329i \(0.488342\pi\)
\(648\) 0 0
\(649\) 20.6638 13.2798i 0.811125 0.521278i
\(650\) 0 0
\(651\) 0.434353 3.02099i 0.0170236 0.118402i
\(652\) 0 0
\(653\) −41.1474 26.4438i −1.61022 1.03483i −0.961878 0.273479i \(-0.911826\pi\)
−0.648344 0.761348i \(-0.724538\pi\)
\(654\) 0 0
\(655\) −0.332919 0.728992i −0.0130082 0.0284841i
\(656\) 0 0
\(657\) 1.32712 + 9.23032i 0.0517759 + 0.360109i
\(658\) 0 0
\(659\) −26.7961 + 7.86805i −1.04383 + 0.306496i −0.758321 0.651881i \(-0.773980\pi\)
−0.285507 + 0.958377i \(0.592162\pi\)
\(660\) 0 0
\(661\) 20.5437 23.7087i 0.799057 0.922161i −0.199272 0.979944i \(-0.563858\pi\)
0.998329 + 0.0577830i \(0.0184032\pi\)
\(662\) 0 0
\(663\) 3.45271 + 3.98464i 0.134092 + 0.154750i
\(664\) 0 0
\(665\) −6.53767 + 14.3155i −0.253520 + 0.555131i
\(666\) 0 0
\(667\) −32.0066 + 18.1365i −1.23930 + 0.702248i
\(668\) 0 0
\(669\) −6.33493 + 13.8716i −0.244923 + 0.536306i
\(670\) 0 0
\(671\) −32.1043 37.0503i −1.23937 1.43031i
\(672\) 0 0
\(673\) 26.0490 30.0622i 1.00412 1.15881i 0.0168310 0.999858i \(-0.494642\pi\)
0.987286 0.158954i \(-0.0508123\pi\)
\(674\) 0 0
\(675\) 0.206695 0.0606913i 0.00795571 0.00233601i
\(676\) 0 0
\(677\) 1.87722 + 13.0564i 0.0721475 + 0.501797i 0.993569 + 0.113231i \(0.0361201\pi\)
−0.921421 + 0.388565i \(0.872971\pi\)
\(678\) 0 0
\(679\) 12.0356 + 26.3543i 0.461884 + 1.01138i
\(680\) 0 0
\(681\) 20.0710 + 12.8988i 0.769122 + 0.494285i
\(682\) 0 0
\(683\) 5.45627 37.9492i 0.208778 1.45208i −0.568373 0.822771i \(-0.692427\pi\)
0.777152 0.629313i \(-0.216664\pi\)
\(684\) 0 0
\(685\) −12.6752 + 8.14588i −0.484296 + 0.311238i
\(686\) 0 0
\(687\) 14.5861 + 4.28286i 0.556494 + 0.163401i
\(688\) 0 0
\(689\) 13.7576 0.524124
\(690\) 0 0
\(691\) 27.4084 1.04266 0.521331 0.853354i \(-0.325436\pi\)
0.521331 + 0.853354i \(0.325436\pi\)
\(692\) 0 0
\(693\) −11.6964 3.43437i −0.444310 0.130461i
\(694\) 0 0
\(695\) −8.99813 + 5.78275i −0.341319 + 0.219352i
\(696\) 0 0
\(697\) −2.49299 + 17.3391i −0.0944287 + 0.656766i
\(698\) 0 0
\(699\) −8.40373 5.40075i −0.317858 0.204275i
\(700\) 0 0
\(701\) 5.84805 + 12.8055i 0.220878 + 0.483655i 0.987337 0.158638i \(-0.0507103\pi\)
−0.766459 + 0.642293i \(0.777983\pi\)
\(702\) 0 0
\(703\) −3.24578 22.5749i −0.122417 0.851427i
\(704\) 0 0
\(705\) −5.34163 + 1.56844i −0.201177 + 0.0590710i
\(706\) 0 0
\(707\) −15.3929 + 17.7643i −0.578908 + 0.668096i
\(708\) 0 0
\(709\) −12.2640 14.1534i −0.460584 0.531542i 0.477185 0.878803i \(-0.341657\pi\)
−0.937769 + 0.347261i \(0.887112\pi\)
\(710\) 0 0
\(711\) 2.45562 5.37705i 0.0920928 0.201655i
\(712\) 0 0
\(713\) 5.49607 + 0.306246i 0.205830 + 0.0114690i
\(714\) 0 0
\(715\) −7.52097 + 16.4686i −0.281268 + 0.615892i
\(716\) 0 0
\(717\) 13.8047 + 15.9315i 0.515546 + 0.594971i
\(718\) 0 0
\(719\) −8.16681 + 9.42501i −0.304571 + 0.351493i −0.887316 0.461161i \(-0.847433\pi\)
0.582746 + 0.812655i \(0.301978\pi\)
\(720\) 0 0
\(721\) −8.48380 + 2.49107i −0.315953 + 0.0927723i
\(722\) 0 0
\(723\) −1.15474 8.03141i −0.0429453 0.298691i
\(724\) 0 0
\(725\) 0.686457 + 1.50313i 0.0254944 + 0.0558249i
\(726\) 0 0
\(727\) −24.6161 15.8198i −0.912959 0.586723i −0.00235247 0.999997i \(-0.500749\pi\)
−0.910607 + 0.413274i \(0.864385\pi\)
\(728\) 0 0
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) 0 0
\(731\) −10.8410 + 6.96708i −0.400968 + 0.257687i
\(732\) 0 0
\(733\) 24.6789 + 7.24639i 0.911537 + 0.267652i 0.703688 0.710509i \(-0.251535\pi\)
0.207850 + 0.978161i \(0.433354\pi\)
\(734\) 0 0
\(735\) −0.161443 −0.00595492
\(736\) 0 0
\(737\) −73.6527 −2.71303
\(738\) 0 0
\(739\) 41.4600 + 12.1738i 1.52513 + 0.447819i 0.933557 0.358430i \(-0.116688\pi\)
0.591576 + 0.806249i \(0.298506\pi\)
\(740\) 0 0
\(741\) −3.77015 + 2.42293i −0.138500 + 0.0890086i
\(742\) 0 0
\(743\) −3.18052 + 22.1210i −0.116682 + 0.811540i 0.844486 + 0.535577i \(0.179906\pi\)
−0.961168 + 0.275963i \(0.911003\pi\)
\(744\) 0 0
\(745\) 8.37626 + 5.38310i 0.306882 + 0.197221i
\(746\) 0 0
\(747\) −1.88939 4.13719i −0.0691292 0.151372i
\(748\) 0 0
\(749\) 5.16349 + 35.9129i 0.188670 + 1.31223i
\(750\) 0 0
\(751\) −11.6763 + 3.42848i −0.426075 + 0.125107i −0.487738 0.872990i \(-0.662178\pi\)
0.0616629 + 0.998097i \(0.480360\pi\)
\(752\) 0 0
\(753\) 19.7447 22.7866i 0.719538 0.830391i
\(754\) 0 0
\(755\) 4.29183 + 4.95304i 0.156196 + 0.180259i
\(756\) 0 0
\(757\) 13.2656 29.0475i 0.482145 1.05575i −0.499723 0.866185i \(-0.666565\pi\)
0.981868 0.189566i \(-0.0607080\pi\)
\(758\) 0 0
\(759\) 4.33479 21.5543i 0.157343 0.782371i
\(760\) 0 0
\(761\) 13.9210 30.4828i 0.504637 1.10500i −0.470297 0.882508i \(-0.655853\pi\)
0.974934 0.222493i \(-0.0714196\pi\)
\(762\) 0 0
\(763\) 3.52138 + 4.06389i 0.127482 + 0.147123i
\(764\) 0 0
\(765\) −4.55971 + 5.26219i −0.164857 + 0.190255i
\(766\) 0 0
\(767\) 8.89023 2.61041i 0.321007 0.0942563i
\(768\) 0 0
\(769\) −5.57273 38.7592i −0.200958 1.39769i −0.801451 0.598061i \(-0.795938\pi\)
0.600493 0.799630i \(-0.294971\pi\)
\(770\) 0 0
\(771\) −9.73841 21.3241i −0.350720 0.767970i
\(772\) 0 0
\(773\) 20.9969 + 13.4939i 0.755207 + 0.485342i 0.860722 0.509076i \(-0.170013\pi\)
−0.105515 + 0.994418i \(0.533649\pi\)
\(774\) 0 0
\(775\) 0.0351885 0.244742i 0.00126401 0.00879138i
\(776\) 0 0
\(777\) 19.6862 12.6515i 0.706238 0.453871i
\(778\) 0 0
\(779\) −14.2867 4.19497i −0.511876 0.150300i
\(780\) 0 0
\(781\) 71.6472 2.56374
\(782\) 0 0
\(783\) −7.67082 −0.274133
\(784\) 0 0
\(785\) 9.25801 + 2.71840i 0.330432 + 0.0970237i
\(786\) 0 0
\(787\) 37.7028 24.2301i 1.34396 0.863710i 0.346720 0.937969i \(-0.387295\pi\)
0.997239 + 0.0742587i \(0.0236591\pi\)
\(788\) 0 0
\(789\) −0.445501 + 3.09853i −0.0158603 + 0.110311i
\(790\) 0 0
\(791\) −9.60714 6.17413i −0.341590 0.219527i
\(792\) 0 0
\(793\) −7.68217 16.8216i −0.272802 0.597353i
\(794\) 0 0
\(795\) 2.58566 + 17.9837i 0.0917039 + 0.637815i
\(796\) 0 0
\(797\) 36.3094 10.6614i 1.28615 0.377647i 0.433982 0.900921i \(-0.357108\pi\)
0.852164 + 0.523275i \(0.175290\pi\)
\(798\) 0 0
\(799\) 4.86721 5.61706i 0.172189 0.198717i
\(800\) 0 0
\(801\) 3.12016 + 3.60086i 0.110246 + 0.127230i
\(802\) 0 0
\(803\) 17.7591 38.8871i 0.626706 1.37229i
\(804\) 0 0
\(805\) −2.53448 29.0127i −0.0893287 1.02256i
\(806\) 0 0
\(807\) −2.07592 + 4.54563i −0.0730758 + 0.160014i
\(808\) 0 0
\(809\) −9.49764 10.9609i −0.333919 0.385363i 0.563815 0.825901i \(-0.309333\pi\)
−0.897734 + 0.440538i \(0.854788\pi\)
\(810\) 0 0
\(811\) −2.27878 + 2.62985i −0.0800188 + 0.0923466i −0.794347 0.607464i \(-0.792187\pi\)
0.714328 + 0.699811i \(0.246732\pi\)
\(812\) 0 0
\(813\) −6.42090 + 1.88535i −0.225191 + 0.0661220i
\(814\) 0 0
\(815\) −2.76362 19.2214i −0.0968053 0.673296i
\(816\) 0 0
\(817\) −4.55035 9.96389i −0.159197 0.348592i
\(818\) 0 0
\(819\) −3.86834 2.48603i −0.135171 0.0868691i
\(820\) 0 0
\(821\) −5.43073 + 37.7715i −0.189534 + 1.31824i 0.643684 + 0.765291i \(0.277405\pi\)
−0.833218 + 0.552945i \(0.813504\pi\)
\(822\) 0 0
\(823\) 25.3708 16.3049i 0.884372 0.568351i −0.0177452 0.999843i \(-0.505649\pi\)
0.902117 + 0.431491i \(0.142012\pi\)
\(824\) 0 0
\(825\) −0.947568 0.278231i −0.0329901 0.00968676i
\(826\) 0 0
\(827\) −41.2905 −1.43581 −0.717905 0.696141i \(-0.754899\pi\)
−0.717905 + 0.696141i \(0.754899\pi\)
\(828\) 0 0
\(829\) 47.8835 1.66306 0.831532 0.555477i \(-0.187464\pi\)
0.831532 + 0.555477i \(0.187464\pi\)
\(830\) 0 0
\(831\) 27.9815 + 8.21612i 0.970668 + 0.285014i
\(832\) 0 0
\(833\) 0.181320 0.116527i 0.00628236 0.00403743i
\(834\) 0 0
\(835\) −5.77254 + 40.1489i −0.199767 + 1.38941i
\(836\) 0 0
\(837\) 0.965581 + 0.620541i 0.0333754 + 0.0214490i
\(838\) 0 0
\(839\) 13.6188 + 29.8210i 0.470174 + 1.02954i 0.985049 + 0.172272i \(0.0551108\pi\)
−0.514876 + 0.857265i \(0.672162\pi\)
\(840\) 0 0
\(841\) −4.24689 29.5378i −0.146444 1.01854i
\(842\) 0 0
\(843\) 18.8854 5.54527i 0.650449 0.190989i
\(844\) 0 0
\(845\) 14.9696 17.2758i 0.514968 0.594305i
\(846\) 0 0
\(847\) 17.4419 + 20.1290i 0.599310 + 0.691641i
\(848\) 0 0
\(849\) 11.4846 25.1477i 0.394149 0.863066i
\(850\) 0 0
\(851\) 25.8213 + 33.3849i 0.885141 + 1.14442i
\(852\) 0 0
\(853\) 5.41389 11.8548i 0.185368 0.405900i −0.794019 0.607893i \(-0.792015\pi\)
0.979387 + 0.201994i \(0.0647420\pi\)
\(854\) 0 0
\(855\) −3.87578 4.47288i −0.132549 0.152969i
\(856\) 0 0
\(857\) 29.9948 34.6158i 1.02460 1.18245i 0.0415477 0.999137i \(-0.486771\pi\)
0.983054 0.183317i \(-0.0586834\pi\)
\(858\) 0 0
\(859\) 17.6706 5.18857i 0.602915 0.177032i 0.0339912 0.999422i \(-0.489178\pi\)
0.568924 + 0.822390i \(0.307360\pi\)
\(860\) 0 0
\(861\) −2.17424 15.1222i −0.0740979 0.515362i
\(862\) 0 0
\(863\) 5.05264 + 11.0637i 0.171994 + 0.376614i 0.975924 0.218109i \(-0.0699889\pi\)
−0.803931 + 0.594723i \(0.797262\pi\)
\(864\) 0 0
\(865\) −33.0004 21.2080i −1.12205 0.721095i
\(866\) 0 0
\(867\) −1.09642 + 7.62577i −0.0372364 + 0.258985i
\(868\) 0 0
\(869\) −22.7974 + 14.6510i −0.773348 + 0.497000i
\(870\) 0 0
\(871\) −26.6574 7.82733i −0.903253 0.265219i
\(872\) 0 0
\(873\) −10.8957 −0.368763
\(874\) 0 0
\(875\) 29.0549 0.982235
\(876\) 0 0
\(877\) −46.0155 13.5114i −1.55383 0.456247i −0.611589 0.791175i \(-0.709470\pi\)
−0.942243 + 0.334929i \(0.891288\pi\)
\(878\) 0 0
\(879\) 10.9600 7.04358i 0.369673 0.237574i
\(880\) 0 0
\(881\) −1.65041 + 11.4789i −0.0556039 + 0.386733i 0.942948 + 0.332940i \(0.108040\pi\)
−0.998552 + 0.0537939i \(0.982869\pi\)
\(882\) 0 0
\(883\) −17.1384 11.0142i −0.576754 0.370657i 0.219507 0.975611i \(-0.429555\pi\)
−0.796261 + 0.604954i \(0.793192\pi\)
\(884\) 0 0
\(885\) 5.08312 + 11.1305i 0.170867 + 0.374147i
\(886\) 0 0
\(887\) −4.19871 29.2027i −0.140979 0.980529i −0.930366 0.366633i \(-0.880510\pi\)
0.789387 0.613896i \(-0.210399\pi\)
\(888\) 0 0
\(889\) 22.3993 6.57703i 0.751249 0.220587i
\(890\) 0 0
\(891\) 3.00212 3.46463i 0.100575 0.116070i
\(892\) 0 0
\(893\) 4.13715 + 4.77452i 0.138444 + 0.159773i
\(894\) 0 0
\(895\) 7.60439 16.6513i 0.254187 0.556592i
\(896\) 0 0
\(897\) 3.85956 7.34056i 0.128867 0.245094i
\(898\) 0 0
\(899\) −3.65751 + 8.00884i −0.121985 + 0.267110i
\(900\) 0 0
\(901\) −15.8843 18.3315i −0.529184 0.610711i
\(902\) 0 0
\(903\) 7.36000 8.49390i 0.244926 0.282659i
\(904\) 0 0
\(905\) −37.4166 + 10.9865i −1.24377 + 0.365203i
\(906\) 0 0
\(907\) 6.81379 + 47.3909i 0.226248 + 1.57359i 0.713707 + 0.700444i \(0.247015\pi\)
−0.487459 + 0.873146i \(0.662076\pi\)
\(908\) 0 0
\(909\) −3.67216 8.04091i −0.121798 0.266700i
\(910\) 0 0
\(911\) −37.6247 24.1799i −1.24656 0.801116i −0.260175 0.965562i \(-0.583780\pi\)
−0.986386 + 0.164446i \(0.947417\pi\)
\(912\) 0 0
\(913\) −2.96735 + 20.6384i −0.0982051 + 0.683032i
\(914\) 0 0
\(915\) 20.5450 13.2035i 0.679197 0.436493i
\(916\) 0 0
\(917\) −0.895333 0.262894i −0.0295665 0.00868151i
\(918\) 0 0
\(919\) 15.1051 0.498273 0.249136 0.968468i \(-0.419853\pi\)
0.249136 + 0.968468i \(0.419853\pi\)
\(920\) 0 0
\(921\) −22.0164 −0.725466
\(922\) 0 0
\(923\) 25.9316 + 7.61420i 0.853548 + 0.250624i
\(924\) 0 0
\(925\) 1.59485 1.02495i 0.0524383 0.0337000i
\(926\) 0 0
\(927\) 0.473225 3.29135i 0.0155428 0.108102i
\(928\) 0 0
\(929\) 23.4545 + 15.0733i 0.769517 + 0.494539i 0.865540 0.500840i \(-0.166976\pi\)
−0.0960223 + 0.995379i \(0.530612\pi\)
\(930\) 0 0
\(931\) 0.0761065 + 0.166650i 0.00249429 + 0.00546174i
\(932\) 0 0
\(933\) −1.76007 12.2416i −0.0576222 0.400771i
\(934\) 0 0
\(935\) 30.6274 8.99301i 1.00162 0.294103i
\(936\) 0 0
\(937\) −37.7275 + 43.5399i −1.23250 + 1.42238i −0.360590 + 0.932724i \(0.617425\pi\)
−0.871913 + 0.489661i \(0.837121\pi\)
\(938\) 0 0
\(939\) 11.7570 + 13.5683i 0.383674 + 0.442783i
\(940\) 0 0
\(941\) 20.4813 44.8477i 0.667670 1.46199i −0.207528 0.978229i \(-0.566542\pi\)
0.875198 0.483765i \(-0.160731\pi\)
\(942\) 0 0
\(943\) 26.8292 6.28006i 0.873678 0.204507i
\(944\) 0 0
\(945\) 2.52266 5.52384i 0.0820620 0.179691i
\(946\) 0 0
\(947\) −22.9779 26.5179i −0.746680 0.861715i 0.247562 0.968872i \(-0.420371\pi\)
−0.994242 + 0.107157i \(0.965825\pi\)
\(948\) 0 0
\(949\) 10.5603 12.1872i 0.342802 0.395614i
\(950\) 0 0
\(951\) −1.14015 + 0.334778i −0.0369719 + 0.0108559i
\(952\) 0 0
\(953\) 0.340098 + 2.36544i 0.0110169 + 0.0766240i 0.994588 0.103896i \(-0.0331310\pi\)
−0.983571 + 0.180520i \(0.942222\pi\)
\(954\) 0 0
\(955\) 13.3745 + 29.2861i 0.432789 + 0.947676i
\(956\) 0 0
\(957\) 29.5834 + 19.0121i 0.956296 + 0.614574i
\(958\) 0 0
\(959\) −2.49670 + 17.3649i −0.0806225 + 0.560742i
\(960\) 0 0
\(961\) −24.9706 + 16.0476i −0.805502 + 0.517665i
\(962\) 0 0
\(963\) −13.0919 3.84414i −0.421882 0.123876i
\(964\) 0 0
\(965\) −48.8856 −1.57368
\(966\) 0 0
\(967\) −37.4419 −1.20405 −0.602026 0.798477i \(-0.705640\pi\)
−0.602026 + 0.798477i \(0.705640\pi\)
\(968\) 0 0
\(969\) 7.58142 + 2.22611i 0.243550 + 0.0715128i
\(970\) 0 0
\(971\) −39.7745 + 25.5615i −1.27643 + 0.820309i −0.990443 0.137926i \(-0.955956\pi\)
−0.285983 + 0.958235i \(0.592320\pi\)
\(972\) 0 0
\(973\) −1.77240 + 12.3273i −0.0568206 + 0.395196i
\(974\) 0 0
\(975\) −0.313389 0.201403i −0.0100365 0.00645005i
\(976\) 0 0
\(977\) −12.4140 27.1829i −0.397159 0.869657i −0.997550 0.0699507i \(-0.977716\pi\)
0.600391 0.799706i \(-0.295011\pi\)
\(978\) 0 0
\(979\) −3.10855 21.6205i −0.0993497 0.690993i
\(980\) 0 0
\(981\) −1.94033 + 0.569731i −0.0619498 + 0.0181901i
\(982\) 0 0
\(983\) 16.7460 19.3259i 0.534114 0.616400i −0.422994 0.906132i \(-0.639021\pi\)
0.957108 + 0.289732i \(0.0935663\pi\)
\(984\) 0 0
\(985\) −38.2915 44.1907i −1.22007 1.40803i
\(986\) 0 0
\(987\) −2.69278 + 5.89636i −0.0857120 + 0.187683i
\(988\) 0 0
\(989\) 16.4164 + 11.8907i 0.522012 + 0.378103i
\(990\) 0 0
\(991\) 0.990728 2.16939i 0.0314715 0.0689130i −0.893243 0.449573i \(-0.851576\pi\)
0.924715 + 0.380660i \(0.124303\pi\)
\(992\) 0 0
\(993\) −15.8797 18.3262i −0.503928 0.581564i
\(994\) 0 0
\(995\) −37.5366 + 43.3195i −1.18999 + 1.37332i
\(996\) 0 0
\(997\) 3.22836 0.947932i 0.102243 0.0300213i −0.230211 0.973141i \(-0.573942\pi\)
0.332454 + 0.943119i \(0.392123\pi\)
\(998\) 0 0
\(999\) 1.25243 + 8.71084i 0.0396251 + 0.275599i
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 552.2.q.d.121.3 yes 30
23.4 even 11 inner 552.2.q.d.73.3 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.q.d.73.3 30 23.4 even 11 inner
552.2.q.d.121.3 yes 30 1.1 even 1 trivial