Properties

Label 552.2.q.a.121.1
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 121.1
Character \(\chi\) \(=\) 552.121
Dual form 552.2.q.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.959493 - 0.281733i) q^{3} +(-1.03173 + 0.663053i) q^{5} +(-0.0639556 + 0.444821i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(-0.959493 - 0.281733i) q^{3} +(-1.03173 + 0.663053i) q^{5} +(-0.0639556 + 0.444821i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-0.763378 - 1.67156i) q^{11} +(0.0274548 + 0.190952i) q^{13} +(1.17674 - 0.345523i) q^{15} +(-4.88422 + 5.63669i) q^{17} +(-1.51494 - 1.74833i) q^{19} +(0.186685 - 0.408784i) q^{21} +(-4.79527 - 0.0735064i) q^{23} +(-1.45225 + 3.17998i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-1.04446 + 1.20537i) q^{29} +(-6.45215 + 1.89452i) q^{31} +(0.261522 + 1.81892i) q^{33} +(-0.228955 - 0.501341i) q^{35} +(0.540222 + 0.347179i) q^{37} +(0.0274548 - 0.190952i) q^{39} +(-4.22262 + 2.71371i) q^{41} +(6.95642 + 2.04259i) q^{43} -1.22642 q^{45} -8.78822 q^{47} +(6.52268 + 1.91523i) q^{49} +(6.27441 - 4.03232i) q^{51} +(-1.18533 + 8.24414i) q^{53} +(1.89594 + 1.21844i) q^{55} +(0.961009 + 2.10432i) q^{57} +(-1.37944 - 9.59422i) q^{59} +(-0.818917 + 0.240456i) q^{61} +(-0.294291 + 0.339630i) q^{63} +(-0.154937 - 0.178807i) q^{65} +(1.62187 - 3.55141i) q^{67} +(4.58032 + 1.42151i) q^{69} +(0.316163 - 0.692300i) q^{71} +(-6.35201 - 7.33061i) q^{73} +(2.28932 - 2.64202i) q^{75} +(0.792369 - 0.232661i) q^{77} +(-0.576039 - 4.00644i) q^{79} +(0.415415 + 0.909632i) q^{81} +(6.08490 + 3.91053i) q^{83} +(1.30177 - 9.05404i) q^{85} +(1.34175 - 0.862289i) q^{87} +(2.35651 + 0.691933i) q^{89} -0.0866955 q^{91} +6.72454 q^{93} +(2.72224 + 0.799322i) q^{95} +(9.01157 - 5.79138i) q^{97} +(0.261522 - 1.81892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 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
\(5\) −1.03173 + 0.663053i −0.461404 + 0.296526i −0.750616 0.660739i \(-0.770243\pi\)
0.289212 + 0.957265i \(0.406607\pi\)
\(6\) 0 0
\(7\) −0.0639556 + 0.444821i −0.0241729 + 0.168126i −0.998332 0.0577374i \(-0.981611\pi\)
0.974159 + 0.225864i \(0.0725205\pi\)
\(8\) 0 0
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) 0 0
\(11\) −0.763378 1.67156i −0.230167 0.503996i 0.758946 0.651154i \(-0.225715\pi\)
−0.989113 + 0.147158i \(0.952987\pi\)
\(12\) 0 0
\(13\) 0.0274548 + 0.190952i 0.00761459 + 0.0529607i 0.993274 0.115784i \(-0.0369379\pi\)
−0.985660 + 0.168744i \(0.946029\pi\)
\(14\) 0 0
\(15\) 1.17674 0.345523i 0.303833 0.0892135i
\(16\) 0 0
\(17\) −4.88422 + 5.63669i −1.18460 + 1.36710i −0.269935 + 0.962879i \(0.587002\pi\)
−0.914662 + 0.404219i \(0.867543\pi\)
\(18\) 0 0
\(19\) −1.51494 1.74833i −0.347550 0.401094i 0.554880 0.831930i \(-0.312764\pi\)
−0.902430 + 0.430836i \(0.858219\pi\)
\(20\) 0 0
\(21\) 0.186685 0.408784i 0.0407381 0.0892040i
\(22\) 0 0
\(23\) −4.79527 0.0735064i −0.999883 0.0153271i
\(24\) 0 0
\(25\) −1.45225 + 3.17998i −0.290449 + 0.635995i
\(26\) 0 0
\(27\) −0.654861 0.755750i −0.126028 0.145444i
\(28\) 0 0
\(29\) −1.04446 + 1.20537i −0.193952 + 0.223832i −0.844393 0.535724i \(-0.820039\pi\)
0.650441 + 0.759557i \(0.274584\pi\)
\(30\) 0 0
\(31\) −6.45215 + 1.89452i −1.15884 + 0.340266i −0.803982 0.594654i \(-0.797289\pi\)
−0.354858 + 0.934920i \(0.615471\pi\)
\(32\) 0 0
\(33\) 0.261522 + 1.81892i 0.0455251 + 0.316634i
\(34\) 0 0
\(35\) −0.228955 0.501341i −0.0387004 0.0847421i
\(36\) 0 0
\(37\) 0.540222 + 0.347179i 0.0888119 + 0.0570759i 0.584293 0.811543i \(-0.301372\pi\)
−0.495481 + 0.868619i \(0.665008\pi\)
\(38\) 0 0
\(39\) 0.0274548 0.190952i 0.00439629 0.0305768i
\(40\) 0 0
\(41\) −4.22262 + 2.71371i −0.659463 + 0.423811i −0.827113 0.562036i \(-0.810018\pi\)
0.167650 + 0.985847i \(0.446382\pi\)
\(42\) 0 0
\(43\) 6.95642 + 2.04259i 1.06084 + 0.311492i 0.765191 0.643804i \(-0.222645\pi\)
0.295653 + 0.955295i \(0.404463\pi\)
\(44\) 0 0
\(45\) −1.22642 −0.182824
\(46\) 0 0
\(47\) −8.78822 −1.28189 −0.640947 0.767585i \(-0.721458\pi\)
−0.640947 + 0.767585i \(0.721458\pi\)
\(48\) 0 0
\(49\) 6.52268 + 1.91523i 0.931811 + 0.273604i
\(50\) 0 0
\(51\) 6.27441 4.03232i 0.878594 0.564638i
\(52\) 0 0
\(53\) −1.18533 + 8.24414i −0.162817 + 1.13242i 0.730473 + 0.682941i \(0.239299\pi\)
−0.893291 + 0.449479i \(0.851610\pi\)
\(54\) 0 0
\(55\) 1.89594 + 1.21844i 0.255648 + 0.164295i
\(56\) 0 0
\(57\) 0.961009 + 2.10432i 0.127289 + 0.278724i
\(58\) 0 0
\(59\) −1.37944 9.59422i −0.179588 1.24906i −0.857718 0.514120i \(-0.828119\pi\)
0.678131 0.734941i \(-0.262790\pi\)
\(60\) 0 0
\(61\) −0.818917 + 0.240456i −0.104852 + 0.0307872i −0.333738 0.942666i \(-0.608310\pi\)
0.228886 + 0.973453i \(0.426492\pi\)
\(62\) 0 0
\(63\) −0.294291 + 0.339630i −0.0370772 + 0.0427894i
\(64\) 0 0
\(65\) −0.154937 0.178807i −0.0192176 0.0221783i
\(66\) 0 0
\(67\) 1.62187 3.55141i 0.198143 0.433873i −0.784313 0.620365i \(-0.786984\pi\)
0.982457 + 0.186492i \(0.0597117\pi\)
\(68\) 0 0
\(69\) 4.58032 + 1.42151i 0.551405 + 0.171130i
\(70\) 0 0
\(71\) 0.316163 0.692300i 0.0375216 0.0821609i −0.889943 0.456072i \(-0.849256\pi\)
0.927465 + 0.373911i \(0.121983\pi\)
\(72\) 0 0
\(73\) −6.35201 7.33061i −0.743446 0.857983i 0.250470 0.968124i \(-0.419415\pi\)
−0.993916 + 0.110142i \(0.964869\pi\)
\(74\) 0 0
\(75\) 2.28932 2.64202i 0.264348 0.305074i
\(76\) 0 0
\(77\) 0.792369 0.232661i 0.0902989 0.0265141i
\(78\) 0 0
\(79\) −0.576039 4.00644i −0.0648094 0.450760i −0.996225 0.0868033i \(-0.972335\pi\)
0.931416 0.363956i \(-0.118574\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 0 0
\(83\) 6.08490 + 3.91053i 0.667905 + 0.429236i 0.830170 0.557511i \(-0.188243\pi\)
−0.162265 + 0.986747i \(0.551880\pi\)
\(84\) 0 0
\(85\) 1.30177 9.05404i 0.141197 0.982048i
\(86\) 0 0
\(87\) 1.34175 0.862289i 0.143850 0.0924470i
\(88\) 0 0
\(89\) 2.35651 + 0.691933i 0.249789 + 0.0733447i 0.404230 0.914657i \(-0.367539\pi\)
−0.154441 + 0.988002i \(0.549358\pi\)
\(90\) 0 0
\(91\) −0.0866955 −0.00908816
\(92\) 0 0
\(93\) 6.72454 0.697302
\(94\) 0 0
\(95\) 2.72224 + 0.799322i 0.279296 + 0.0820087i
\(96\) 0 0
\(97\) 9.01157 5.79138i 0.914986 0.588026i 0.00378720 0.999993i \(-0.498794\pi\)
0.911199 + 0.411967i \(0.135158\pi\)
\(98\) 0 0
\(99\) 0.261522 1.81892i 0.0262839 0.182809i
\(100\) 0 0
\(101\) −4.14547 2.66413i −0.412490 0.265091i 0.317896 0.948125i \(-0.397024\pi\)
−0.730386 + 0.683034i \(0.760660\pi\)
\(102\) 0 0
\(103\) 4.65115 + 10.1846i 0.458292 + 1.00352i 0.987874 + 0.155260i \(0.0496216\pi\)
−0.529582 + 0.848259i \(0.677651\pi\)
\(104\) 0 0
\(105\) 0.0784364 + 0.545537i 0.00765461 + 0.0532390i
\(106\) 0 0
\(107\) −3.37777 + 0.991803i −0.326541 + 0.0958812i −0.440894 0.897559i \(-0.645339\pi\)
0.114353 + 0.993440i \(0.463520\pi\)
\(108\) 0 0
\(109\) 3.89746 4.49791i 0.373309 0.430821i −0.537746 0.843107i \(-0.680724\pi\)
0.911055 + 0.412286i \(0.135269\pi\)
\(110\) 0 0
\(111\) −0.420527 0.485314i −0.0399147 0.0460640i
\(112\) 0 0
\(113\) −2.92308 + 6.40066i −0.274980 + 0.602123i −0.995856 0.0909411i \(-0.971012\pi\)
0.720876 + 0.693064i \(0.243740\pi\)
\(114\) 0 0
\(115\) 4.99616 3.10368i 0.465895 0.289419i
\(116\) 0 0
\(117\) −0.0801402 + 0.175483i −0.00740896 + 0.0162234i
\(118\) 0 0
\(119\) −2.19494 2.53310i −0.201210 0.232209i
\(120\) 0 0
\(121\) 4.99208 5.76117i 0.453826 0.523743i
\(122\) 0 0
\(123\) 4.81612 1.41414i 0.434255 0.127509i
\(124\) 0 0
\(125\) −1.48285 10.3135i −0.132631 0.922466i
\(126\) 0 0
\(127\) 1.98875 + 4.35476i 0.176473 + 0.386423i 0.977112 0.212725i \(-0.0682337\pi\)
−0.800639 + 0.599147i \(0.795506\pi\)
\(128\) 0 0
\(129\) −6.09917 3.91970i −0.537002 0.345110i
\(130\) 0 0
\(131\) 1.05444 7.33379i 0.0921269 0.640757i −0.890475 0.455032i \(-0.849628\pi\)
0.982602 0.185724i \(-0.0594631\pi\)
\(132\) 0 0
\(133\) 0.874582 0.562060i 0.0758359 0.0487368i
\(134\) 0 0
\(135\) 1.17674 + 0.345523i 0.101278 + 0.0297378i
\(136\) 0 0
\(137\) 6.38832 0.545791 0.272895 0.962044i \(-0.412019\pi\)
0.272895 + 0.962044i \(0.412019\pi\)
\(138\) 0 0
\(139\) 1.20784 0.102448 0.0512238 0.998687i \(-0.483688\pi\)
0.0512238 + 0.998687i \(0.483688\pi\)
\(140\) 0 0
\(141\) 8.43224 + 2.47593i 0.710122 + 0.208511i
\(142\) 0 0
\(143\) 0.298231 0.191661i 0.0249393 0.0160275i
\(144\) 0 0
\(145\) 0.278377 1.93615i 0.0231180 0.160789i
\(146\) 0 0
\(147\) −5.71888 3.67530i −0.471685 0.303134i
\(148\) 0 0
\(149\) −0.519306 1.13712i −0.0425432 0.0931566i 0.887167 0.461448i \(-0.152670\pi\)
−0.929710 + 0.368292i \(0.879943\pi\)
\(150\) 0 0
\(151\) 1.59368 + 11.0843i 0.129691 + 0.902024i 0.945944 + 0.324329i \(0.105139\pi\)
−0.816253 + 0.577695i \(0.803952\pi\)
\(152\) 0 0
\(153\) −7.15629 + 2.10128i −0.578552 + 0.169878i
\(154\) 0 0
\(155\) 5.40071 6.23275i 0.433795 0.500626i
\(156\) 0 0
\(157\) 7.50836 + 8.66511i 0.599232 + 0.691551i 0.971626 0.236524i \(-0.0760082\pi\)
−0.372393 + 0.928075i \(0.621463\pi\)
\(158\) 0 0
\(159\) 3.45996 7.57625i 0.274393 0.600836i
\(160\) 0 0
\(161\) 0.339381 2.12833i 0.0267470 0.167736i
\(162\) 0 0
\(163\) −1.41158 + 3.09093i −0.110563 + 0.242100i −0.956823 0.290670i \(-0.906122\pi\)
0.846260 + 0.532770i \(0.178849\pi\)
\(164\) 0 0
\(165\) −1.47586 1.70324i −0.114896 0.132597i
\(166\) 0 0
\(167\) 3.80613 4.39250i 0.294527 0.339902i −0.589129 0.808039i \(-0.700529\pi\)
0.883656 + 0.468137i \(0.155075\pi\)
\(168\) 0 0
\(169\) 12.4377 3.65204i 0.956746 0.280926i
\(170\) 0 0
\(171\) −0.329227 2.28983i −0.0251766 0.175107i
\(172\) 0 0
\(173\) 5.81026 + 12.7227i 0.441746 + 0.967288i 0.991275 + 0.131814i \(0.0420800\pi\)
−0.549529 + 0.835475i \(0.685193\pi\)
\(174\) 0 0
\(175\) −1.32164 0.849367i −0.0999066 0.0642061i
\(176\) 0 0
\(177\) −1.37944 + 9.59422i −0.103685 + 0.721146i
\(178\) 0 0
\(179\) −12.8056 + 8.22967i −0.957137 + 0.615114i −0.923204 0.384310i \(-0.874439\pi\)
−0.0339324 + 0.999424i \(0.510803\pi\)
\(180\) 0 0
\(181\) −8.39667 2.46549i −0.624120 0.183258i −0.0456441 0.998958i \(-0.514534\pi\)
−0.578476 + 0.815700i \(0.696352\pi\)
\(182\) 0 0
\(183\) 0.853490 0.0630918
\(184\) 0 0
\(185\) −0.787561 −0.0579027
\(186\) 0 0
\(187\) 13.1506 + 3.86136i 0.961667 + 0.282371i
\(188\) 0 0
\(189\) 0.378055 0.242961i 0.0274995 0.0176728i
\(190\) 0 0
\(191\) −3.38632 + 23.5524i −0.245026 + 1.70419i 0.381153 + 0.924512i \(0.375527\pi\)
−0.626178 + 0.779680i \(0.715382\pi\)
\(192\) 0 0
\(193\) −13.3929 8.60711i −0.964044 0.619553i −0.0389295 0.999242i \(-0.512395\pi\)
−0.925114 + 0.379689i \(0.876031\pi\)
\(194\) 0 0
\(195\) 0.0982855 + 0.215215i 0.00703837 + 0.0154119i
\(196\) 0 0
\(197\) −2.98117 20.7345i −0.212399 1.47727i −0.765112 0.643897i \(-0.777316\pi\)
0.552713 0.833372i \(-0.313593\pi\)
\(198\) 0 0
\(199\) −17.9426 + 5.26842i −1.27192 + 0.373469i −0.846917 0.531725i \(-0.821544\pi\)
−0.425000 + 0.905193i \(0.639726\pi\)
\(200\) 0 0
\(201\) −2.55672 + 2.95062i −0.180337 + 0.208120i
\(202\) 0 0
\(203\) −0.469376 0.541689i −0.0329438 0.0380191i
\(204\) 0 0
\(205\) 2.55727 5.59964i 0.178608 0.391096i
\(206\) 0 0
\(207\) −3.99430 2.65436i −0.277623 0.184490i
\(208\) 0 0
\(209\) −1.76598 + 3.86695i −0.122155 + 0.267483i
\(210\) 0 0
\(211\) −4.58086 5.28660i −0.315360 0.363944i 0.575835 0.817566i \(-0.304677\pi\)
−0.891194 + 0.453622i \(0.850132\pi\)
\(212\) 0 0
\(213\) −0.498399 + 0.575183i −0.0341498 + 0.0394109i
\(214\) 0 0
\(215\) −8.53149 + 2.50507i −0.581843 + 0.170844i
\(216\) 0 0
\(217\) −0.430072 2.99121i −0.0291952 0.203057i
\(218\) 0 0
\(219\) 4.02943 + 8.82323i 0.272284 + 0.596219i
\(220\) 0 0
\(221\) −1.21043 0.777899i −0.0814226 0.0523271i
\(222\) 0 0
\(223\) −1.23386 + 8.58171i −0.0826256 + 0.574674i 0.905885 + 0.423523i \(0.139207\pi\)
−0.988511 + 0.151150i \(0.951702\pi\)
\(224\) 0 0
\(225\) −2.94093 + 1.89002i −0.196062 + 0.126002i
\(226\) 0 0
\(227\) 10.6581 + 3.12950i 0.707402 + 0.207712i 0.615593 0.788064i \(-0.288917\pi\)
0.0918097 + 0.995777i \(0.470735\pi\)
\(228\) 0 0
\(229\) −23.4851 −1.55194 −0.775970 0.630769i \(-0.782739\pi\)
−0.775970 + 0.630769i \(0.782739\pi\)
\(230\) 0 0
\(231\) −0.825821 −0.0543350
\(232\) 0 0
\(233\) 20.1579 + 5.91888i 1.32059 + 0.387759i 0.864704 0.502281i \(-0.167506\pi\)
0.455882 + 0.890040i \(0.349324\pi\)
\(234\) 0 0
\(235\) 9.06707 5.82705i 0.591471 0.380115i
\(236\) 0 0
\(237\) −0.576039 + 4.00644i −0.0374177 + 0.260246i
\(238\) 0 0
\(239\) 2.75140 + 1.76822i 0.177973 + 0.114377i 0.626594 0.779346i \(-0.284448\pi\)
−0.448621 + 0.893722i \(0.648085\pi\)
\(240\) 0 0
\(241\) 2.83312 + 6.20367i 0.182497 + 0.399614i 0.978665 0.205463i \(-0.0658699\pi\)
−0.796167 + 0.605076i \(0.793143\pi\)
\(242\) 0 0
\(243\) −0.142315 0.989821i −0.00912950 0.0634971i
\(244\) 0 0
\(245\) −7.99954 + 2.34888i −0.511072 + 0.150064i
\(246\) 0 0
\(247\) 0.292255 0.337281i 0.0185958 0.0214607i
\(248\) 0 0
\(249\) −4.73670 5.46644i −0.300176 0.346422i
\(250\) 0 0
\(251\) 12.1866 26.6850i 0.769212 1.68434i 0.0408323 0.999166i \(-0.486999\pi\)
0.728380 0.685174i \(-0.240274\pi\)
\(252\) 0 0
\(253\) 3.53773 + 8.07172i 0.222415 + 0.507464i
\(254\) 0 0
\(255\) −3.79986 + 8.32053i −0.237957 + 0.521052i
\(256\) 0 0
\(257\) −13.2637 15.3071i −0.827364 0.954829i 0.172179 0.985066i \(-0.444919\pi\)
−0.999543 + 0.0302368i \(0.990374\pi\)
\(258\) 0 0
\(259\) −0.188983 + 0.218098i −0.0117428 + 0.0135519i
\(260\) 0 0
\(261\) −1.53033 + 0.449346i −0.0947252 + 0.0278138i
\(262\) 0 0
\(263\) 0.799612 + 5.56142i 0.0493062 + 0.342932i 0.999510 + 0.0313027i \(0.00996559\pi\)
−0.950204 + 0.311629i \(0.899125\pi\)
\(264\) 0 0
\(265\) −4.24336 9.29167i −0.260668 0.570783i
\(266\) 0 0
\(267\) −2.06611 1.32781i −0.126444 0.0812606i
\(268\) 0 0
\(269\) −1.12453 + 7.82129i −0.0685639 + 0.476873i 0.926392 + 0.376560i \(0.122893\pi\)
−0.994956 + 0.100312i \(0.968016\pi\)
\(270\) 0 0
\(271\) −25.9791 + 16.6957i −1.57812 + 1.01419i −0.601589 + 0.798806i \(0.705465\pi\)
−0.976528 + 0.215389i \(0.930898\pi\)
\(272\) 0 0
\(273\) 0.0831837 + 0.0244249i 0.00503451 + 0.00147826i
\(274\) 0 0
\(275\) 6.42415 0.387391
\(276\) 0 0
\(277\) −10.6876 −0.642154 −0.321077 0.947053i \(-0.604045\pi\)
−0.321077 + 0.947053i \(0.604045\pi\)
\(278\) 0 0
\(279\) −6.45215 1.89452i −0.386280 0.113422i
\(280\) 0 0
\(281\) 0.926104 0.595171i 0.0552467 0.0355049i −0.512726 0.858552i \(-0.671364\pi\)
0.567973 + 0.823047i \(0.307728\pi\)
\(282\) 0 0
\(283\) −3.82623 + 26.6120i −0.227445 + 1.58192i 0.481366 + 0.876520i \(0.340141\pi\)
−0.708811 + 0.705398i \(0.750768\pi\)
\(284\) 0 0
\(285\) −2.38678 1.53389i −0.141380 0.0908597i
\(286\) 0 0
\(287\) −0.937056 2.05187i −0.0553127 0.121118i
\(288\) 0 0
\(289\) −5.49732 38.2347i −0.323372 2.24910i
\(290\) 0 0
\(291\) −10.2782 + 3.01794i −0.602516 + 0.176915i
\(292\) 0 0
\(293\) −14.3105 + 16.5152i −0.836030 + 0.964830i −0.999765 0.0216745i \(-0.993100\pi\)
0.163735 + 0.986504i \(0.447646\pi\)
\(294\) 0 0
\(295\) 7.78469 + 8.98401i 0.453242 + 0.523069i
\(296\) 0 0
\(297\) −0.763378 + 1.67156i −0.0442957 + 0.0969940i
\(298\) 0 0
\(299\) −0.117617 0.917686i −0.00680196 0.0530711i
\(300\) 0 0
\(301\) −1.35349 + 2.96372i −0.0780137 + 0.170826i
\(302\) 0 0
\(303\) 3.22698 + 3.72413i 0.185385 + 0.213946i
\(304\) 0 0
\(305\) 0.685467 0.791071i 0.0392497 0.0452966i
\(306\) 0 0
\(307\) −32.6304 + 9.58115i −1.86232 + 0.546825i −0.863196 + 0.504869i \(0.831541\pi\)
−0.999119 + 0.0419567i \(0.986641\pi\)
\(308\) 0 0
\(309\) −1.59341 11.0824i −0.0906462 0.630458i
\(310\) 0 0
\(311\) 1.59511 + 3.49281i 0.0904504 + 0.198059i 0.949451 0.313916i \(-0.101641\pi\)
−0.859000 + 0.511975i \(0.828914\pi\)
\(312\) 0 0
\(313\) 27.5657 + 17.7154i 1.55811 + 1.00133i 0.983075 + 0.183202i \(0.0586461\pi\)
0.575030 + 0.818132i \(0.304990\pi\)
\(314\) 0 0
\(315\) 0.0784364 0.545537i 0.00441939 0.0307375i
\(316\) 0 0
\(317\) 29.3282 18.8481i 1.64724 1.05862i 0.713502 0.700654i \(-0.247108\pi\)
0.933736 0.357962i \(-0.116528\pi\)
\(318\) 0 0
\(319\) 2.81218 + 0.825731i 0.157452 + 0.0462320i
\(320\) 0 0
\(321\) 3.52037 0.196488
\(322\) 0 0
\(323\) 17.2541 0.960042
\(324\) 0 0
\(325\) −0.647095 0.190004i −0.0358944 0.0105395i
\(326\) 0 0
\(327\) −5.00679 + 3.21767i −0.276876 + 0.177937i
\(328\) 0 0
\(329\) 0.562056 3.90918i 0.0309871 0.215520i
\(330\) 0 0
\(331\) 7.37109 + 4.73711i 0.405152 + 0.260375i 0.727308 0.686311i \(-0.240771\pi\)
−0.322156 + 0.946687i \(0.604408\pi\)
\(332\) 0 0
\(333\) 0.266764 + 0.584132i 0.0146186 + 0.0320102i
\(334\) 0 0
\(335\) 0.681435 + 4.73948i 0.0372308 + 0.258946i
\(336\) 0 0
\(337\) −8.52316 + 2.50263i −0.464286 + 0.136327i −0.505505 0.862823i \(-0.668694\pi\)
0.0412193 + 0.999150i \(0.486876\pi\)
\(338\) 0 0
\(339\) 4.60795 5.31786i 0.250269 0.288826i
\(340\) 0 0
\(341\) 8.09224 + 9.33895i 0.438220 + 0.505732i
\(342\) 0 0
\(343\) −2.57589 + 5.64042i −0.139085 + 0.304554i
\(344\) 0 0
\(345\) −5.66819 + 1.57038i −0.305165 + 0.0845462i
\(346\) 0 0
\(347\) −3.52530 + 7.71932i −0.189248 + 0.414395i −0.980344 0.197297i \(-0.936784\pi\)
0.791096 + 0.611692i \(0.209511\pi\)
\(348\) 0 0
\(349\) −13.7144 15.8272i −0.734114 0.847213i 0.258814 0.965927i \(-0.416668\pi\)
−0.992928 + 0.118714i \(0.962123\pi\)
\(350\) 0 0
\(351\) 0.126333 0.145796i 0.00674316 0.00778202i
\(352\) 0 0
\(353\) −17.7170 + 5.20219i −0.942982 + 0.276885i −0.716862 0.697215i \(-0.754422\pi\)
−0.226120 + 0.974099i \(0.572604\pi\)
\(354\) 0 0
\(355\) 0.132837 + 0.923899i 0.00705024 + 0.0490355i
\(356\) 0 0
\(357\) 1.39238 + 3.04888i 0.0736924 + 0.161364i
\(358\) 0 0
\(359\) 9.95479 + 6.39755i 0.525394 + 0.337650i 0.776302 0.630361i \(-0.217093\pi\)
−0.250909 + 0.968011i \(0.580729\pi\)
\(360\) 0 0
\(361\) 1.94236 13.5094i 0.102229 0.711021i
\(362\) 0 0
\(363\) −6.41298 + 4.12137i −0.336594 + 0.216316i
\(364\) 0 0
\(365\) 11.4141 + 3.35149i 0.597443 + 0.175425i
\(366\) 0 0
\(367\) −12.9272 −0.674794 −0.337397 0.941362i \(-0.609546\pi\)
−0.337397 + 0.941362i \(0.609546\pi\)
\(368\) 0 0
\(369\) −5.01944 −0.261302
\(370\) 0 0
\(371\) −3.59136 1.05452i −0.186454 0.0547478i
\(372\) 0 0
\(373\) −21.4610 + 13.7921i −1.11121 + 0.714129i −0.961556 0.274610i \(-0.911451\pi\)
−0.149651 + 0.988739i \(0.547815\pi\)
\(374\) 0 0
\(375\) −1.48285 + 10.3135i −0.0765743 + 0.532586i
\(376\) 0 0
\(377\) −0.258844 0.166349i −0.0133312 0.00856742i
\(378\) 0 0
\(379\) −10.8954 23.8575i −0.559657 1.22548i −0.952124 0.305712i \(-0.901106\pi\)
0.392467 0.919766i \(-0.371622\pi\)
\(380\) 0 0
\(381\) −0.681316 4.73866i −0.0349049 0.242769i
\(382\) 0 0
\(383\) 0.938574 0.275590i 0.0479589 0.0140820i −0.257665 0.966234i \(-0.582953\pi\)
0.305624 + 0.952152i \(0.401135\pi\)
\(384\) 0 0
\(385\) −0.663245 + 0.765426i −0.0338021 + 0.0390097i
\(386\) 0 0
\(387\) 4.74780 + 5.47926i 0.241344 + 0.278526i
\(388\) 0 0
\(389\) 14.4819 31.7109i 0.734260 1.60781i −0.0585119 0.998287i \(-0.518636\pi\)
0.792772 0.609518i \(-0.208637\pi\)
\(390\) 0 0
\(391\) 23.8355 26.6704i 1.20541 1.34878i
\(392\) 0 0
\(393\) −3.07790 + 6.73965i −0.155259 + 0.339971i
\(394\) 0 0
\(395\) 3.25080 + 3.75162i 0.163565 + 0.188764i
\(396\) 0 0
\(397\) −22.9471 + 26.4824i −1.15168 + 1.32911i −0.215947 + 0.976405i \(0.569284\pi\)
−0.935734 + 0.352706i \(0.885261\pi\)
\(398\) 0 0
\(399\) −0.997506 + 0.292894i −0.0499378 + 0.0146631i
\(400\) 0 0
\(401\) 3.22175 + 22.4078i 0.160886 + 1.11899i 0.896968 + 0.442096i \(0.145765\pi\)
−0.736081 + 0.676893i \(0.763326\pi\)
\(402\) 0 0
\(403\) −0.538906 1.18004i −0.0268448 0.0587819i
\(404\) 0 0
\(405\) −1.03173 0.663053i −0.0512671 0.0329474i
\(406\) 0 0
\(407\) 0.167939 1.16804i 0.00832445 0.0578978i
\(408\) 0 0
\(409\) 1.97065 1.26646i 0.0974425 0.0626225i −0.491012 0.871153i \(-0.663373\pi\)
0.588455 + 0.808530i \(0.299737\pi\)
\(410\) 0 0
\(411\) −6.12955 1.79980i −0.302348 0.0887775i
\(412\) 0 0
\(413\) 4.35593 0.214341
\(414\) 0 0
\(415\) −8.87087 −0.435454
\(416\) 0 0
\(417\) −1.15891 0.340288i −0.0567523 0.0166640i
\(418\) 0 0
\(419\) 22.1959 14.2645i 1.08434 0.696864i 0.128786 0.991672i \(-0.458892\pi\)
0.955557 + 0.294808i \(0.0952557\pi\)
\(420\) 0 0
\(421\) −3.15644 + 21.9535i −0.153835 + 1.06995i 0.755879 + 0.654712i \(0.227210\pi\)
−0.909714 + 0.415236i \(0.863699\pi\)
\(422\) 0 0
\(423\) −7.39312 4.75127i −0.359466 0.231015i
\(424\) 0 0
\(425\) −10.8314 23.7176i −0.525402 1.15047i
\(426\) 0 0
\(427\) −0.0545854 0.379650i −0.00264157 0.0183726i
\(428\) 0 0
\(429\) −0.340148 + 0.0998764i −0.0164225 + 0.00482208i
\(430\) 0 0
\(431\) −7.60815 + 8.78027i −0.366471 + 0.422931i −0.908797 0.417238i \(-0.862998\pi\)
0.542326 + 0.840168i \(0.317544\pi\)
\(432\) 0 0
\(433\) 4.48304 + 5.17370i 0.215441 + 0.248632i 0.853175 0.521624i \(-0.174674\pi\)
−0.637734 + 0.770256i \(0.720128\pi\)
\(434\) 0 0
\(435\) −0.812579 + 1.77930i −0.0389602 + 0.0853108i
\(436\) 0 0
\(437\) 7.13601 + 8.49507i 0.341362 + 0.406374i
\(438\) 0 0
\(439\) 3.46025 7.57689i 0.165149 0.361625i −0.808906 0.587938i \(-0.799940\pi\)
0.974055 + 0.226313i \(0.0726672\pi\)
\(440\) 0 0
\(441\) 4.45177 + 5.13762i 0.211989 + 0.244649i
\(442\) 0 0
\(443\) 4.67255 5.39241i 0.222000 0.256201i −0.633814 0.773485i \(-0.718512\pi\)
0.855814 + 0.517284i \(0.173057\pi\)
\(444\) 0 0
\(445\) −2.89007 + 0.848600i −0.137002 + 0.0402275i
\(446\) 0 0
\(447\) 0.177906 + 1.23737i 0.00841468 + 0.0585254i
\(448\) 0 0
\(449\) −1.92593 4.21720i −0.0908902 0.199022i 0.858727 0.512433i \(-0.171256\pi\)
−0.949618 + 0.313411i \(0.898528\pi\)
\(450\) 0 0
\(451\) 7.75961 + 4.98680i 0.365386 + 0.234819i
\(452\) 0 0
\(453\) 1.59368 11.0843i 0.0748774 0.520784i
\(454\) 0 0
\(455\) 0.0894464 0.0574837i 0.00419331 0.00269488i
\(456\) 0 0
\(457\) 38.6496 + 11.3485i 1.80795 + 0.530863i 0.998419 0.0562114i \(-0.0179021\pi\)
0.809533 + 0.587074i \(0.199720\pi\)
\(458\) 0 0
\(459\) 7.45841 0.348129
\(460\) 0 0
\(461\) 31.0249 1.44498 0.722488 0.691384i \(-0.242999\pi\)
0.722488 + 0.691384i \(0.242999\pi\)
\(462\) 0 0
\(463\) 15.7784 + 4.63294i 0.733283 + 0.215311i 0.626994 0.779024i \(-0.284285\pi\)
0.106289 + 0.994335i \(0.466103\pi\)
\(464\) 0 0
\(465\) −6.93791 + 4.45872i −0.321738 + 0.206768i
\(466\) 0 0
\(467\) −1.35258 + 9.40737i −0.0625898 + 0.435321i 0.934298 + 0.356492i \(0.116027\pi\)
−0.996888 + 0.0788293i \(0.974882\pi\)
\(468\) 0 0
\(469\) 1.47601 + 0.948575i 0.0681559 + 0.0438011i
\(470\) 0 0
\(471\) −4.76298 10.4295i −0.219466 0.480564i
\(472\) 0 0
\(473\) −1.89606 13.1874i −0.0871808 0.606356i
\(474\) 0 0
\(475\) 7.75971 2.27846i 0.356040 0.104543i
\(476\) 0 0
\(477\) −5.45428 + 6.29458i −0.249734 + 0.288209i
\(478\) 0 0
\(479\) −20.6498 23.8312i −0.943514 1.08887i −0.995919 0.0902472i \(-0.971234\pi\)
0.0524055 0.998626i \(-0.483311\pi\)
\(480\) 0 0
\(481\) −0.0514630 + 0.112688i −0.00234651 + 0.00513815i
\(482\) 0 0
\(483\) −0.925255 + 1.94651i −0.0421006 + 0.0885691i
\(484\) 0 0
\(485\) −5.45751 + 11.9503i −0.247813 + 0.542635i
\(486\) 0 0
\(487\) −12.4212 14.3349i −0.562860 0.649575i 0.400971 0.916091i \(-0.368673\pi\)
−0.963830 + 0.266516i \(0.914127\pi\)
\(488\) 0 0
\(489\) 2.22521 2.56803i 0.100628 0.116131i
\(490\) 0 0
\(491\) −0.617231 + 0.181235i −0.0278553 + 0.00817904i −0.295631 0.955302i \(-0.595530\pi\)
0.267775 + 0.963481i \(0.413712\pi\)
\(492\) 0 0
\(493\) −1.69293 11.7746i −0.0762459 0.530302i
\(494\) 0 0
\(495\) 0.936222 + 2.05004i 0.0420801 + 0.0921425i
\(496\) 0 0
\(497\) 0.287729 + 0.184912i 0.0129064 + 0.00829445i
\(498\) 0 0
\(499\) 4.23154 29.4310i 0.189430 1.31751i −0.644058 0.764976i \(-0.722751\pi\)
0.833488 0.552537i \(-0.186340\pi\)
\(500\) 0 0
\(501\) −4.88946 + 3.14227i −0.218445 + 0.140386i
\(502\) 0 0
\(503\) 23.0023 + 6.75407i 1.02562 + 0.301149i 0.750929 0.660383i \(-0.229606\pi\)
0.274691 + 0.961532i \(0.411424\pi\)
\(504\) 0 0
\(505\) 6.04347 0.268931
\(506\) 0 0
\(507\) −12.9628 −0.575697
\(508\) 0 0
\(509\) 17.9003 + 5.25600i 0.793417 + 0.232968i 0.653233 0.757157i \(-0.273412\pi\)
0.140184 + 0.990125i \(0.455231\pi\)
\(510\) 0 0
\(511\) 3.66705 2.35667i 0.162221 0.104253i
\(512\) 0 0
\(513\) −0.329227 + 2.28983i −0.0145357 + 0.101098i
\(514\) 0 0
\(515\) −11.5517 7.42381i −0.509027 0.327132i
\(516\) 0 0
\(517\) 6.70874 + 14.6901i 0.295050 + 0.646069i
\(518\) 0 0
\(519\) −1.99051 13.8443i −0.0873735 0.607696i
\(520\) 0 0
\(521\) −11.5187 + 3.38220i −0.504645 + 0.148177i −0.524139 0.851633i \(-0.675613\pi\)
0.0194940 + 0.999810i \(0.493794\pi\)
\(522\) 0 0
\(523\) 24.4806 28.2521i 1.07046 1.23538i 0.0997785 0.995010i \(-0.468187\pi\)
0.970682 0.240368i \(-0.0772680\pi\)
\(524\) 0 0
\(525\) 1.02881 + 1.18731i 0.0449010 + 0.0518185i
\(526\) 0 0
\(527\) 20.8349 45.6220i 0.907581 1.98733i
\(528\) 0 0
\(529\) 22.9892 + 0.704966i 0.999530 + 0.0306507i
\(530\) 0 0
\(531\) 4.02657 8.81695i 0.174738 0.382623i
\(532\) 0 0
\(533\) −0.634121 0.731815i −0.0274668 0.0316984i
\(534\) 0 0
\(535\) 2.82733 3.26291i 0.122236 0.141068i
\(536\) 0 0
\(537\) 14.6055 4.28855i 0.630272 0.185065i
\(538\) 0 0
\(539\) −1.77784 12.3651i −0.0765768 0.532603i
\(540\) 0 0
\(541\) 3.27115 + 7.16282i 0.140638 + 0.307954i 0.966824 0.255443i \(-0.0822215\pi\)
−0.826186 + 0.563397i \(0.809494\pi\)
\(542\) 0 0
\(543\) 7.36194 + 4.73123i 0.315931 + 0.203037i
\(544\) 0 0
\(545\) −1.03878 + 7.22485i −0.0444963 + 0.309478i
\(546\) 0 0
\(547\) 1.64163 1.05501i 0.0701909 0.0451089i −0.505075 0.863076i \(-0.668535\pi\)
0.575266 + 0.817967i \(0.304899\pi\)
\(548\) 0 0
\(549\) −0.818917 0.240456i −0.0349505 0.0102624i
\(550\) 0 0
\(551\) 3.68969 0.157186
\(552\) 0 0
\(553\) 1.81899 0.0773512
\(554\) 0 0
\(555\) 0.755659 + 0.221882i 0.0320760 + 0.00941835i
\(556\) 0 0
\(557\) 27.6304 17.7570i 1.17074 0.752389i 0.197078 0.980388i \(-0.436855\pi\)
0.973661 + 0.227999i \(0.0732183\pi\)
\(558\) 0 0
\(559\) −0.199050 + 1.38442i −0.00841892 + 0.0585549i
\(560\) 0 0
\(561\) −11.5300 7.40990i −0.486798 0.312846i
\(562\) 0 0
\(563\) 6.91441 + 15.1404i 0.291408 + 0.638094i 0.997549 0.0699776i \(-0.0222928\pi\)
−0.706141 + 0.708071i \(0.749565\pi\)
\(564\) 0 0
\(565\) −1.22814 8.54191i −0.0516683 0.359361i
\(566\) 0 0
\(567\) −0.431191 + 0.126609i −0.0181083 + 0.00531709i
\(568\) 0 0
\(569\) −7.18145 + 8.28783i −0.301062 + 0.347444i −0.886043 0.463603i \(-0.846556\pi\)
0.584981 + 0.811047i \(0.301102\pi\)
\(570\) 0 0
\(571\) 0.874204 + 1.00888i 0.0365843 + 0.0422205i 0.773747 0.633495i \(-0.218380\pi\)
−0.737163 + 0.675715i \(0.763835\pi\)
\(572\) 0 0
\(573\) 9.88463 21.6443i 0.412936 0.904205i
\(574\) 0 0
\(575\) 7.19766 15.1421i 0.300163 0.631469i
\(576\) 0 0
\(577\) −12.0792 + 26.4497i −0.502863 + 1.10112i 0.472665 + 0.881242i \(0.343292\pi\)
−0.975528 + 0.219875i \(0.929435\pi\)
\(578\) 0 0
\(579\) 10.4255 + 12.0317i 0.433270 + 0.500020i
\(580\) 0 0
\(581\) −2.12865 + 2.45659i −0.0883112 + 0.101917i
\(582\) 0 0
\(583\) 14.6855 4.31204i 0.608210 0.178587i
\(584\) 0 0
\(585\) −0.0336711 0.234188i −0.00139213 0.00968248i
\(586\) 0 0
\(587\) 2.68851 + 5.88703i 0.110967 + 0.242984i 0.956966 0.290201i \(-0.0937223\pi\)
−0.845999 + 0.533185i \(0.820995\pi\)
\(588\) 0 0
\(589\) 13.0868 + 8.41040i 0.539234 + 0.346545i
\(590\) 0 0
\(591\) −2.98117 + 20.7345i −0.122629 + 0.852902i
\(592\) 0 0
\(593\) −1.67320 + 1.07530i −0.0687102 + 0.0441574i −0.574545 0.818473i \(-0.694821\pi\)
0.505835 + 0.862630i \(0.331185\pi\)
\(594\) 0 0
\(595\) 3.94417 + 1.15811i 0.161695 + 0.0474780i
\(596\) 0 0
\(597\) 18.7001 0.765344
\(598\) 0 0
\(599\) 11.2754 0.460699 0.230349 0.973108i \(-0.426013\pi\)
0.230349 + 0.973108i \(0.426013\pi\)
\(600\) 0 0
\(601\) 36.9229 + 10.8415i 1.50612 + 0.442235i 0.927644 0.373467i \(-0.121831\pi\)
0.578472 + 0.815702i \(0.303649\pi\)
\(602\) 0 0
\(603\) 3.28444 2.11078i 0.133753 0.0859577i
\(604\) 0 0
\(605\) −1.33052 + 9.25399i −0.0540935 + 0.376228i
\(606\) 0 0
\(607\) −36.0381 23.1603i −1.46274 0.940046i −0.998523 0.0543243i \(-0.982700\pi\)
−0.464217 0.885722i \(-0.653664\pi\)
\(608\) 0 0
\(609\) 0.297752 + 0.651985i 0.0120655 + 0.0264198i
\(610\) 0 0
\(611\) −0.241279 1.67813i −0.00976110 0.0678899i
\(612\) 0 0
\(613\) −30.3464 + 8.91050i −1.22568 + 0.359892i −0.829617 0.558332i \(-0.811441\pi\)
−0.396061 + 0.918224i \(0.629623\pi\)
\(614\) 0 0
\(615\) −4.03129 + 4.65235i −0.162557 + 0.187601i
\(616\) 0 0
\(617\) 18.6034 + 21.4694i 0.748943 + 0.864327i 0.994465 0.105064i \(-0.0335048\pi\)
−0.245522 + 0.969391i \(0.578959\pi\)
\(618\) 0 0
\(619\) 5.37276 11.7647i 0.215949 0.472863i −0.770393 0.637569i \(-0.779940\pi\)
0.986343 + 0.164706i \(0.0526675\pi\)
\(620\) 0 0
\(621\) 3.08468 + 3.67216i 0.123784 + 0.147359i
\(622\) 0 0
\(623\) −0.458498 + 1.00397i −0.0183693 + 0.0402232i
\(624\) 0 0
\(625\) −3.07833 3.55258i −0.123133 0.142103i
\(626\) 0 0
\(627\) 2.78389 3.21278i 0.111178 0.128306i
\(628\) 0 0
\(629\) −4.59550 + 1.34936i −0.183235 + 0.0538026i
\(630\) 0 0
\(631\) −5.43283 37.7862i −0.216278 1.50424i −0.751613 0.659605i \(-0.770724\pi\)
0.535335 0.844640i \(-0.320185\pi\)
\(632\) 0 0
\(633\) 2.90590 + 6.36303i 0.115499 + 0.252908i
\(634\) 0 0
\(635\) −4.93929 3.17429i −0.196010 0.125968i
\(636\) 0 0
\(637\) −0.186639 + 1.29810i −0.00739491 + 0.0514327i
\(638\) 0 0
\(639\) 0.640258 0.411469i 0.0253282 0.0162775i
\(640\) 0 0
\(641\) −3.87650 1.13824i −0.153112 0.0449578i 0.204278 0.978913i \(-0.434515\pi\)
−0.357391 + 0.933955i \(0.616333\pi\)
\(642\) 0 0
\(643\) −22.6512 −0.893277 −0.446638 0.894715i \(-0.647379\pi\)
−0.446638 + 0.894715i \(0.647379\pi\)
\(644\) 0 0
\(645\) 8.89167 0.350109
\(646\) 0 0
\(647\) −32.3616 9.50223i −1.27227 0.373571i −0.425220 0.905090i \(-0.639803\pi\)
−0.847047 + 0.531519i \(0.821622\pi\)
\(648\) 0 0
\(649\) −14.9843 + 9.62984i −0.588186 + 0.378004i
\(650\) 0 0
\(651\) −0.430072 + 2.99121i −0.0168558 + 0.117235i
\(652\) 0 0
\(653\) −29.2892 18.8230i −1.14617 0.736601i −0.177300 0.984157i \(-0.556736\pi\)
−0.968874 + 0.247555i \(0.920373\pi\)
\(654\) 0 0
\(655\) 3.77479 + 8.26565i 0.147493 + 0.322966i
\(656\) 0 0
\(657\) −1.38042 9.60105i −0.0538554 0.374573i
\(658\) 0 0
\(659\) −39.0980 + 11.4802i −1.52304 + 0.447206i −0.932913 0.360102i \(-0.882742\pi\)
−0.590131 + 0.807308i \(0.700924\pi\)
\(660\) 0 0
\(661\) −10.8123 + 12.4781i −0.420551 + 0.485342i −0.926005 0.377512i \(-0.876780\pi\)
0.505454 + 0.862854i \(0.331325\pi\)
\(662\) 0 0
\(663\) 0.942244 + 1.08741i 0.0365937 + 0.0422314i
\(664\) 0 0
\(665\) −0.529658 + 1.15979i −0.0205392 + 0.0449747i
\(666\) 0 0
\(667\) 5.09708 5.70332i 0.197360 0.220833i
\(668\) 0 0
\(669\) 3.60163 7.88647i 0.139247 0.304909i
\(670\) 0 0
\(671\) 1.02708 + 1.18531i 0.0396500 + 0.0457586i
\(672\) 0 0
\(673\) −17.8229 + 20.5688i −0.687024 + 0.792868i −0.986938 0.161098i \(-0.948496\pi\)
0.299914 + 0.953966i \(0.403042\pi\)
\(674\) 0 0
\(675\) 3.35429 0.984907i 0.129106 0.0379091i
\(676\) 0 0
\(677\) −1.22978 8.55328i −0.0472641 0.328729i −0.999711 0.0240257i \(-0.992352\pi\)
0.952447 0.304704i \(-0.0985574\pi\)
\(678\) 0 0
\(679\) 1.99979 + 4.37892i 0.0767448 + 0.168048i
\(680\) 0 0
\(681\) −9.34468 6.00546i −0.358089 0.230130i
\(682\) 0 0
\(683\) −7.12649 + 49.5658i −0.272688 + 1.89658i 0.147362 + 0.989083i \(0.452922\pi\)
−0.420049 + 0.907501i \(0.637987\pi\)
\(684\) 0 0
\(685\) −6.59102 + 4.23579i −0.251830 + 0.161841i
\(686\) 0 0
\(687\) 22.5338 + 6.61652i 0.859718 + 0.252436i
\(688\) 0 0
\(689\) −1.60678 −0.0612135
\(690\) 0 0
\(691\) 13.0745 0.497376 0.248688 0.968584i \(-0.420001\pi\)
0.248688 + 0.968584i \(0.420001\pi\)
\(692\) 0 0
\(693\) 0.792369 + 0.232661i 0.0300996 + 0.00883805i
\(694\) 0 0
\(695\) −1.24617 + 0.800862i −0.0472698 + 0.0303784i
\(696\) 0 0
\(697\) 5.32785 37.0560i 0.201807 1.40360i
\(698\) 0 0
\(699\) −17.6738 11.3583i −0.668484 0.429609i
\(700\) 0 0
\(701\) −5.39022 11.8029i −0.203586 0.445791i 0.780107 0.625646i \(-0.215164\pi\)
−0.983693 + 0.179855i \(0.942437\pi\)
\(702\) 0 0
\(703\) −0.211417 1.47044i −0.00797376 0.0554587i
\(704\) 0 0
\(705\) −10.3415 + 3.03653i −0.389482 + 0.114362i
\(706\) 0 0
\(707\) 1.45019 1.67361i 0.0545399 0.0629425i
\(708\) 0 0
\(709\) 20.0683 + 23.1600i 0.753680 + 0.869793i 0.994920 0.100672i \(-0.0320994\pi\)
−0.241240 + 0.970466i \(0.577554\pi\)
\(710\) 0 0
\(711\) 1.68145 3.68186i 0.0630593 0.138081i
\(712\) 0 0
\(713\) 31.0790 8.61046i 1.16392 0.322464i
\(714\) 0 0
\(715\) −0.180612 + 0.395486i −0.00675451 + 0.0147903i
\(716\) 0 0
\(717\) −2.14179 2.47175i −0.0799865 0.0923093i
\(718\) 0 0
\(719\) −15.1922 + 17.5328i −0.566574 + 0.653862i −0.964663 0.263485i \(-0.915128\pi\)
0.398089 + 0.917347i \(0.369673\pi\)
\(720\) 0 0
\(721\) −4.82779 + 1.41757i −0.179796 + 0.0527930i
\(722\) 0 0
\(723\) −0.970585 6.75056i −0.0360964 0.251056i
\(724\) 0 0
\(725\) −2.31624 5.07187i −0.0860231 0.188364i
\(726\) 0 0
\(727\) 41.5408 + 26.6967i 1.54066 + 0.990124i 0.987601 + 0.156984i \(0.0501771\pi\)
0.553062 + 0.833140i \(0.313459\pi\)
\(728\) 0 0
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) 0 0
\(731\) −45.4901 + 29.2347i −1.68251 + 1.08128i
\(732\) 0 0
\(733\) −3.31686 0.973917i −0.122511 0.0359724i 0.219902 0.975522i \(-0.429426\pi\)
−0.342413 + 0.939549i \(0.611244\pi\)
\(734\) 0 0
\(735\) 8.33726 0.307524
\(736\) 0 0
\(737\) −7.17451 −0.264277
\(738\) 0 0
\(739\) −48.1697 14.1439i −1.77195 0.520292i −0.777822 0.628484i \(-0.783676\pi\)
−0.994130 + 0.108192i \(0.965494\pi\)
\(740\) 0 0
\(741\) −0.375440 + 0.241281i −0.0137921 + 0.00886367i
\(742\) 0 0
\(743\) −3.64854 + 25.3762i −0.133852 + 0.930961i 0.806615 + 0.591077i \(0.201297\pi\)
−0.940467 + 0.339884i \(0.889612\pi\)
\(744\) 0 0
\(745\) 1.28976 + 0.828876i 0.0472530 + 0.0303676i
\(746\) 0 0
\(747\) 3.00475 + 6.57950i 0.109938 + 0.240731i
\(748\) 0 0
\(749\) −0.225147 1.56593i −0.00822670 0.0572180i
\(750\) 0 0
\(751\) 20.0058 5.87422i 0.730021 0.214353i 0.104460 0.994529i \(-0.466689\pi\)
0.625560 + 0.780176i \(0.284870\pi\)
\(752\) 0 0
\(753\) −19.2110 + 22.1707i −0.700087 + 0.807944i
\(754\) 0 0
\(755\) −8.99369 10.3793i −0.327314 0.377740i
\(756\) 0 0
\(757\) −11.5075 + 25.1980i −0.418248 + 0.915836i 0.576841 + 0.816856i \(0.304285\pi\)
−0.995089 + 0.0989796i \(0.968442\pi\)
\(758\) 0 0
\(759\) −1.12036 8.74145i −0.0406666 0.317294i
\(760\) 0 0
\(761\) −20.5062 + 44.9024i −0.743350 + 1.62771i 0.0346142 + 0.999401i \(0.488980\pi\)
−0.777964 + 0.628309i \(0.783748\pi\)
\(762\) 0 0
\(763\) 1.75150 + 2.02134i 0.0634085 + 0.0731773i
\(764\) 0 0
\(765\) 5.99011 6.91295i 0.216573 0.249938i
\(766\) 0 0
\(767\) 1.79417 0.526815i 0.0647836 0.0190222i
\(768\) 0 0
\(769\) 0.479967 + 3.33825i 0.0173081 + 0.120380i 0.996644 0.0818614i \(-0.0260865\pi\)
−0.979336 + 0.202242i \(0.935177\pi\)
\(770\) 0 0
\(771\) 8.41388 + 18.4238i 0.303019 + 0.663518i
\(772\) 0 0
\(773\) −30.4749 19.5850i −1.09611 0.704424i −0.137883 0.990448i \(-0.544030\pi\)
−0.958222 + 0.286024i \(0.907666\pi\)
\(774\) 0 0
\(775\) 3.34558 23.2690i 0.120177 0.835847i
\(776\) 0 0
\(777\) 0.242773 0.156021i 0.00870943 0.00559721i
\(778\) 0 0
\(779\) 11.1415 + 3.27143i 0.399185 + 0.117211i
\(780\) 0 0
\(781\) −1.39858 −0.0500450
\(782\) 0 0
\(783\) 1.59494 0.0569984
\(784\) 0 0
\(785\) −13.4920 3.96162i −0.481551 0.141396i
\(786\) 0 0
\(787\) −5.89391 + 3.78779i −0.210095 + 0.135020i −0.641457 0.767159i \(-0.721670\pi\)
0.431362 + 0.902179i \(0.358033\pi\)
\(788\) 0 0
\(789\) 0.799612 5.56142i 0.0284669 0.197992i
\(790\) 0 0
\(791\) −2.66020 1.70961i −0.0945858 0.0607866i
\(792\) 0 0
\(793\) −0.0683988 0.149773i −0.00242891 0.00531858i
\(794\) 0 0
\(795\) 1.45371 + 10.1108i 0.0515578 + 0.358593i
\(796\) 0 0
\(797\) −6.16327 + 1.80970i −0.218314 + 0.0641029i −0.389061 0.921212i \(-0.627200\pi\)
0.170746 + 0.985315i \(0.445382\pi\)
\(798\) 0 0
\(799\) 42.9236 49.5365i 1.51853 1.75247i
\(800\) 0 0
\(801\) 1.60833 + 1.85611i 0.0568276 + 0.0655826i
\(802\) 0 0
\(803\) −7.40460 + 16.2138i −0.261303 + 0.572173i
\(804\) 0 0
\(805\) 1.06105 + 2.42089i 0.0373970 + 0.0853253i
\(806\) 0 0
\(807\) 3.28249 7.18766i 0.115549 0.253018i
\(808\) 0 0
\(809\) −4.66046 5.37845i −0.163853 0.189096i 0.667886 0.744264i \(-0.267200\pi\)
−0.831738 + 0.555168i \(0.812654\pi\)
\(810\) 0 0
\(811\) −18.2647 + 21.0786i −0.641361 + 0.740170i −0.979615 0.200885i \(-0.935618\pi\)
0.338254 + 0.941055i \(0.390164\pi\)
\(812\) 0 0
\(813\) 29.6305 8.70030i 1.03919 0.305133i
\(814\) 0 0
\(815\) −0.593079 4.12495i −0.0207746 0.144491i
\(816\) 0 0
\(817\) −6.96741 15.2565i −0.243759 0.533757i
\(818\) 0 0
\(819\) −0.0729329 0.0468711i −0.00254848 0.00163781i
\(820\) 0 0
\(821\) 3.57979 24.8980i 0.124936 0.868946i −0.826902 0.562345i \(-0.809899\pi\)
0.951838 0.306601i \(-0.0991917\pi\)
\(822\) 0 0
\(823\) −34.2618 + 22.0188i −1.19429 + 0.767526i −0.977960 0.208794i \(-0.933046\pi\)
−0.216333 + 0.976320i \(0.569410\pi\)
\(824\) 0 0
\(825\) −6.16393 1.80989i −0.214600 0.0630124i
\(826\) 0 0
\(827\) −21.9602 −0.763631 −0.381815 0.924239i \(-0.624701\pi\)
−0.381815 + 0.924239i \(0.624701\pi\)
\(828\) 0 0
\(829\) −5.11534 −0.177663 −0.0888315 0.996047i \(-0.528313\pi\)
−0.0888315 + 0.996047i \(0.528313\pi\)
\(830\) 0 0
\(831\) 10.2546 + 3.01104i 0.355730 + 0.104452i
\(832\) 0 0
\(833\) −42.6537 + 27.4119i −1.47786 + 0.949766i
\(834\) 0 0
\(835\) −1.01443 + 7.05554i −0.0351059 + 0.244167i
\(836\) 0 0
\(837\) 5.65704 + 3.63556i 0.195536 + 0.125663i
\(838\) 0 0
\(839\) 14.5106 + 31.7738i 0.500962 + 1.09695i 0.976156 + 0.217072i \(0.0696507\pi\)
−0.475194 + 0.879881i \(0.657622\pi\)
\(840\) 0 0
\(841\) 3.76511 + 26.1869i 0.129831 + 0.902996i
\(842\) 0 0
\(843\) −1.05627 + 0.310149i −0.0363799 + 0.0106821i
\(844\) 0 0
\(845\) −10.4109 + 12.0148i −0.358144 + 0.413321i
\(846\) 0 0
\(847\) 2.24342 + 2.58904i 0.0770848 + 0.0889606i
\(848\) 0 0
\(849\) 11.1687 24.4560i 0.383309 0.839329i
\(850\) 0 0
\(851\) −2.56499 1.70453i −0.0879266 0.0584305i
\(852\) 0 0
\(853\) −1.14702 + 2.51163i −0.0392733 + 0.0859966i −0.928252 0.371952i \(-0.878688\pi\)
0.888978 + 0.457949i \(0.151416\pi\)
\(854\) 0 0
\(855\) 1.85795 + 2.14419i 0.0635405 + 0.0733297i
\(856\) 0 0
\(857\) −10.5237 + 12.1450i −0.359482 + 0.414865i −0.906466 0.422279i \(-0.861230\pi\)
0.546984 + 0.837143i \(0.315776\pi\)
\(858\) 0 0
\(859\) −34.3107 + 10.0745i −1.17067 + 0.343738i −0.808568 0.588402i \(-0.799757\pi\)
−0.362097 + 0.932140i \(0.617939\pi\)
\(860\) 0 0
\(861\) 0.321021 + 2.23275i 0.0109404 + 0.0760920i
\(862\) 0 0
\(863\) 0.309210 + 0.677074i 0.0105256 + 0.0230479i 0.914822 0.403858i \(-0.132331\pi\)
−0.904296 + 0.426906i \(0.859604\pi\)
\(864\) 0 0
\(865\) −14.4304 9.27388i −0.490650 0.315321i
\(866\) 0 0
\(867\) −5.49732 + 38.2347i −0.186699 + 1.29852i
\(868\) 0 0
\(869\) −6.25729 + 4.02131i −0.212264 + 0.136414i
\(870\) 0 0
\(871\) 0.722678 + 0.212197i 0.0244870 + 0.00719003i
\(872\) 0 0
\(873\) 10.7121 0.362549
\(874\) 0 0
\(875\) 4.68249 0.158297
\(876\) 0 0
\(877\) 42.6743 + 12.5303i 1.44101 + 0.423118i 0.906558 0.422082i \(-0.138701\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(878\) 0 0
\(879\) 18.3837 11.8145i 0.620068 0.398493i
\(880\) 0 0
\(881\) 2.60160 18.0945i 0.0876502 0.609621i −0.897895 0.440209i \(-0.854904\pi\)
0.985545 0.169411i \(-0.0541867\pi\)
\(882\) 0 0
\(883\) 17.8245 + 11.4551i 0.599843 + 0.385495i 0.805036 0.593226i \(-0.202146\pi\)
−0.205193 + 0.978721i \(0.565782\pi\)
\(884\) 0 0
\(885\) −4.93826 10.8133i −0.165998 0.363485i
\(886\) 0 0
\(887\) −4.74139 32.9771i −0.159200 1.10726i −0.900112 0.435659i \(-0.856515\pi\)
0.740912 0.671602i \(-0.234394\pi\)
\(888\) 0 0
\(889\) −2.06428 + 0.606127i −0.0692337 + 0.0203289i
\(890\) 0 0
\(891\) 1.20339 1.38879i 0.0403151 0.0465261i
\(892\) 0 0
\(893\) 13.3136 + 15.3647i 0.445522 + 0.514160i
\(894\) 0 0
\(895\) 7.75524 16.9816i 0.259229 0.567632i
\(896\) 0 0
\(897\) −0.145689 + 0.913650i −0.00486443 + 0.0305059i
\(898\) 0 0
\(899\) 4.45542 9.75600i 0.148597 0.325381i
\(900\) 0 0
\(901\) −40.6803 46.9475i −1.35526 1.56405i
\(902\) 0 0
\(903\) 2.13364 2.46235i 0.0710031 0.0819419i
\(904\) 0 0
\(905\) 10.2978 3.02372i 0.342312 0.100512i
\(906\) 0 0
\(907\) 7.62263 + 53.0166i 0.253105 + 1.76039i 0.579329 + 0.815094i \(0.303315\pi\)
−0.326223 + 0.945293i \(0.605776\pi\)
\(908\) 0 0
\(909\) −2.04705 4.48242i −0.0678965 0.148673i
\(910\) 0 0
\(911\) 13.2100 + 8.48955i 0.437667 + 0.281271i 0.740862 0.671657i \(-0.234417\pi\)
−0.303195 + 0.952928i \(0.598053\pi\)
\(912\) 0 0
\(913\) 1.89162 13.1565i 0.0626036 0.435417i
\(914\) 0 0
\(915\) −0.880571 + 0.565909i −0.0291108 + 0.0187084i
\(916\) 0 0
\(917\) 3.19479 + 0.938074i 0.105501 + 0.0309779i
\(918\) 0 0
\(919\) 17.9820 0.593172 0.296586 0.955006i \(-0.404152\pi\)
0.296586 + 0.955006i \(0.404152\pi\)
\(920\) 0 0
\(921\) 34.0080 1.12060
\(922\) 0 0
\(923\) 0.140876 + 0.0413651i 0.00463700 + 0.00136155i
\(924\) 0 0
\(925\) −1.88856 + 1.21370i −0.0620954 + 0.0399063i
\(926\) 0 0
\(927\) −1.59341 + 11.0824i −0.0523346 + 0.363995i
\(928\) 0 0
\(929\) −45.1337 29.0057i −1.48079 0.951646i −0.997076 0.0764197i \(-0.975651\pi\)
−0.483714 0.875226i \(-0.660713\pi\)
\(930\) 0 0
\(931\) −6.53298 14.3052i −0.214110 0.468835i
\(932\) 0 0
\(933\) −0.546461 3.80072i −0.0178903 0.124430i
\(934\) 0 0
\(935\) −16.1282 + 4.73566i −0.527447 + 0.154872i
\(936\) 0 0
\(937\) 9.86557 11.3855i 0.322294 0.371947i −0.571363 0.820697i \(-0.693585\pi\)
0.893657 + 0.448750i \(0.148131\pi\)
\(938\) 0 0
\(939\) −21.4581 24.7640i −0.700258 0.808141i
\(940\) 0 0
\(941\) −3.59494 + 7.87182i −0.117192 + 0.256614i −0.959133 0.282955i \(-0.908685\pi\)
0.841942 + 0.539569i \(0.181413\pi\)
\(942\) 0 0
\(943\) 20.4481 12.7026i 0.665881 0.413654i
\(944\) 0 0
\(945\) −0.228955 + 0.501341i −0.00744790 + 0.0163086i
\(946\) 0 0
\(947\) 2.42705 + 2.80097i 0.0788687 + 0.0910193i 0.793812 0.608163i \(-0.208093\pi\)
−0.714944 + 0.699182i \(0.753548\pi\)
\(948\) 0 0
\(949\) 1.22540 1.41419i 0.0397783 0.0459066i
\(950\) 0 0
\(951\) −33.4504 + 9.82191i −1.08470 + 0.318497i
\(952\) 0 0
\(953\) 0.108236 + 0.752799i 0.00350611 + 0.0243855i 0.991499 0.130111i \(-0.0415335\pi\)
−0.987993 + 0.154497i \(0.950624\pi\)
\(954\) 0 0
\(955\) −12.1227 26.5450i −0.392282 0.858977i
\(956\) 0 0
\(957\) −2.46563 1.58457i −0.0797026 0.0512217i
\(958\) 0 0
\(959\) −0.408569 + 2.84166i −0.0131934 + 0.0917619i
\(960\) 0 0
\(961\) 11.9621 7.68759i 0.385875 0.247987i
\(962\) 0 0
\(963\) −3.37777 0.991803i −0.108847 0.0319604i
\(964\) 0 0
\(965\) 19.5249 0.628527
\(966\) 0 0
\(967\) −0.360731 −0.0116003 −0.00580017 0.999983i \(-0.501846\pi\)
−0.00580017 + 0.999983i \(0.501846\pi\)
\(968\) 0 0
\(969\) −16.5552 4.86103i −0.531828 0.156159i
\(970\) 0 0
\(971\) −34.0705 + 21.8958i −1.09337 + 0.702669i −0.957609 0.288072i \(-0.906986\pi\)
−0.135765 + 0.990741i \(0.543349\pi\)
\(972\) 0 0
\(973\) −0.0772481 + 0.537273i −0.00247646 + 0.0172242i
\(974\) 0 0
\(975\) 0.567353 + 0.364616i 0.0181698 + 0.0116770i
\(976\) 0 0
\(977\) −13.0877 28.6580i −0.418712 0.916852i −0.995025 0.0996231i \(-0.968236\pi\)
0.576313 0.817229i \(-0.304491\pi\)
\(978\) 0 0
\(979\) −0.642295 4.46726i −0.0205278 0.142774i
\(980\) 0 0
\(981\) 5.71050 1.67675i 0.182322 0.0535346i
\(982\) 0 0
\(983\) −15.3592 + 17.7255i −0.489883 + 0.565355i −0.945834 0.324650i \(-0.894754\pi\)
0.455951 + 0.890005i \(0.349299\pi\)
\(984\) 0 0
\(985\) 16.8238 + 19.4157i 0.536051 + 0.618636i
\(986\) 0 0
\(987\) −1.64063 + 3.59248i −0.0522219 + 0.114350i
\(988\) 0 0
\(989\) −33.2077 10.3061i −1.05594 0.327715i
\(990\) 0 0
\(991\) −17.3615 + 38.0164i −0.551507 + 1.20763i 0.404568 + 0.914508i \(0.367422\pi\)
−0.956075 + 0.293124i \(0.905305\pi\)
\(992\) 0 0
\(993\) −5.73791 6.62190i −0.182087 0.210140i
\(994\) 0 0
\(995\) 15.0187 17.3325i 0.476124 0.549477i
\(996\) 0 0
\(997\) −37.9812 + 11.1523i −1.20288 + 0.353196i −0.820952 0.570998i \(-0.806557\pi\)
−0.381924 + 0.924194i \(0.624738\pi\)
\(998\) 0 0
\(999\) −0.0913893 0.635626i −0.00289143 0.0201103i
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.a.121.1 yes 30
23.4 even 11 inner 552.2.q.a.73.1 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.q.a.73.1 30 23.4 even 11 inner
552.2.q.a.121.1 yes 30 1.1 even 1 trivial