Properties

Label 688.2.bg.c.369.2
Level $688$
Weight $2$
Character 688.369
Analytic conductor $5.494$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [688,2,Mod(17,688)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(688, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 0, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("688.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 688.bg (of order \(21\), degree \(12\), not 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: \(5.49370765906\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(3\) over \(\Q(\zeta_{21})\)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 369.2
Character \(\chi\) \(=\) 688.369
Dual form 688.2.bg.c.289.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.90223 + 1.29692i) q^{3} +(2.37710 - 2.20563i) q^{5} +(1.38418 - 2.39748i) q^{7} +(0.840455 + 2.14144i) q^{9} +O(q^{10})\) \(q+(1.90223 + 1.29692i) q^{3} +(2.37710 - 2.20563i) q^{5} +(1.38418 - 2.39748i) q^{7} +(0.840455 + 2.14144i) q^{9} +(-3.47915 + 4.36271i) q^{11} +(1.57105 + 0.484606i) q^{13} +(7.38231 - 1.11270i) q^{15} +(0.555777 + 0.515686i) q^{17} +(0.795961 - 2.02807i) q^{19} +(5.74237 - 2.76538i) q^{21} +(-0.00139480 - 0.000210232i) q^{23} +(0.412168 - 5.50000i) q^{25} +(0.358374 - 1.57014i) q^{27} +(-3.87133 + 2.63943i) q^{29} +(-0.301429 - 4.02229i) q^{31} +(-12.2762 + 3.78671i) q^{33} +(-1.99760 - 8.75205i) q^{35} +(-0.999506 - 1.73120i) q^{37} +(2.36001 + 2.95936i) q^{39} +(6.30781 + 3.03768i) q^{41} +(-6.54912 - 0.330261i) q^{43} +(6.72108 + 3.23670i) q^{45} +(4.90255 + 6.14760i) q^{47} +(-0.331936 - 0.574929i) q^{49} +(0.388413 + 1.70175i) q^{51} +(-3.76860 + 1.16246i) q^{53} +(1.35223 + 18.0443i) q^{55} +(4.14434 - 2.82557i) q^{57} +(0.811036 - 3.55338i) q^{59} +(-0.639001 + 8.52687i) q^{61} +(6.29741 + 0.949182i) q^{63} +(4.80342 - 2.31320i) q^{65} +(-3.43004 + 8.73959i) q^{67} +(-0.00238057 - 0.00220885i) q^{69} +(-6.83052 + 1.02953i) q^{71} +(-10.6150 - 3.27429i) q^{73} +(7.91708 - 9.92771i) q^{75} +(5.64372 + 14.3800i) q^{77} +(3.26980 - 5.66346i) q^{79} +(7.77713 - 7.21613i) q^{81} +(4.71578 + 3.21516i) q^{83} +2.45855 q^{85} -10.7873 q^{87} +(-7.13427 - 4.86406i) q^{89} +(3.33646 - 3.09578i) q^{91} +(4.64319 - 8.04224i) q^{93} +(-2.58110 - 6.57654i) q^{95} +(-11.0143 + 13.8115i) q^{97} +(-12.2666 - 3.78373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9} + 4 q^{11} + 3 q^{15} - 10 q^{17} - 10 q^{19} - 21 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 9 q^{29} - 40 q^{31} - 11 q^{33} - 11 q^{35} - 19 q^{37} + q^{39} - 28 q^{41} + 8 q^{43} - 46 q^{45} + 30 q^{47} + 6 q^{49} - 57 q^{51} - 24 q^{53} - 14 q^{55} + 52 q^{57} + q^{59} - 14 q^{61} - 47 q^{63} + 38 q^{65} - 66 q^{67} - 7 q^{69} + 33 q^{71} + 29 q^{73} + 55 q^{75} - 27 q^{77} + 17 q^{79} + 38 q^{81} + 23 q^{83} - 56 q^{85} + 86 q^{87} - 19 q^{89} + 13 q^{91} - 30 q^{93} - q^{95} - 31 q^{97} + 31 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).

\(n\) \(431\) \(433\) \(517\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{21}\right)\) \(1\)

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
\(3\) 1.90223 + 1.29692i 1.09825 + 0.748775i 0.970034 0.242970i \(-0.0781218\pi\)
0.128218 + 0.991746i \(0.459074\pi\)
\(4\) 0 0
\(5\) 2.37710 2.20563i 1.06307 0.986388i 0.0631405 0.998005i \(-0.479888\pi\)
0.999933 + 0.0116171i \(0.00369791\pi\)
\(6\) 0 0
\(7\) 1.38418 2.39748i 0.523173 0.906162i −0.476464 0.879194i \(-0.658082\pi\)
0.999636 0.0269675i \(-0.00858507\pi\)
\(8\) 0 0
\(9\) 0.840455 + 2.14144i 0.280152 + 0.713814i
\(10\) 0 0
\(11\) −3.47915 + 4.36271i −1.04900 + 1.31541i −0.101787 + 0.994806i \(0.532456\pi\)
−0.947215 + 0.320600i \(0.896115\pi\)
\(12\) 0 0
\(13\) 1.57105 + 0.484606i 0.435732 + 0.134406i 0.504858 0.863202i \(-0.331545\pi\)
−0.0691260 + 0.997608i \(0.522021\pi\)
\(14\) 0 0
\(15\) 7.38231 1.11270i 1.90610 0.287299i
\(16\) 0 0
\(17\) 0.555777 + 0.515686i 0.134796 + 0.125072i 0.744690 0.667411i \(-0.232597\pi\)
−0.609894 + 0.792483i \(0.708788\pi\)
\(18\) 0 0
\(19\) 0.795961 2.02807i 0.182606 0.465272i −0.810033 0.586384i \(-0.800551\pi\)
0.992639 + 0.121112i \(0.0386461\pi\)
\(20\) 0 0
\(21\) 5.74237 2.76538i 1.25309 0.603455i
\(22\) 0 0
\(23\) −0.00139480 0.000210232i −0.000290836 4.38364e-5i 0.148897 0.988853i \(-0.452428\pi\)
−0.149188 + 0.988809i \(0.547666\pi\)
\(24\) 0 0
\(25\) 0.412168 5.50000i 0.0824336 1.10000i
\(26\) 0 0
\(27\) 0.358374 1.57014i 0.0689691 0.302174i
\(28\) 0 0
\(29\) −3.87133 + 2.63943i −0.718888 + 0.490129i −0.866665 0.498891i \(-0.833741\pi\)
0.147777 + 0.989021i \(0.452788\pi\)
\(30\) 0 0
\(31\) −0.301429 4.02229i −0.0541382 0.722424i −0.956553 0.291557i \(-0.905827\pi\)
0.902415 0.430867i \(-0.141792\pi\)
\(32\) 0 0
\(33\) −12.2762 + 3.78671i −2.13701 + 0.659181i
\(34\) 0 0
\(35\) −1.99760 8.75205i −0.337656 1.47937i
\(36\) 0 0
\(37\) −0.999506 1.73120i −0.164318 0.284607i 0.772095 0.635507i \(-0.219209\pi\)
−0.936413 + 0.350900i \(0.885876\pi\)
\(38\) 0 0
\(39\) 2.36001 + 2.95936i 0.377904 + 0.473877i
\(40\) 0 0
\(41\) 6.30781 + 3.03768i 0.985115 + 0.474406i 0.855861 0.517205i \(-0.173028\pi\)
0.129253 + 0.991612i \(0.458742\pi\)
\(42\) 0 0
\(43\) −6.54912 0.330261i −0.998731 0.0503643i
\(44\) 0 0
\(45\) 6.72108 + 3.23670i 1.00192 + 0.482499i
\(46\) 0 0
\(47\) 4.90255 + 6.14760i 0.715110 + 0.896720i 0.998050 0.0624180i \(-0.0198812\pi\)
−0.282940 + 0.959138i \(0.591310\pi\)
\(48\) 0 0
\(49\) −0.331936 0.574929i −0.0474194 0.0821328i
\(50\) 0 0
\(51\) 0.388413 + 1.70175i 0.0543887 + 0.238293i
\(52\) 0 0
\(53\) −3.76860 + 1.16246i −0.517657 + 0.159676i −0.542565 0.840014i \(-0.682547\pi\)
0.0249081 + 0.999690i \(0.492071\pi\)
\(54\) 0 0
\(55\) 1.35223 + 18.0443i 0.182335 + 2.43310i
\(56\) 0 0
\(57\) 4.14434 2.82557i 0.548932 0.374255i
\(58\) 0 0
\(59\) 0.811036 3.55338i 0.105588 0.462611i −0.894297 0.447473i \(-0.852324\pi\)
0.999885 0.0151380i \(-0.00481876\pi\)
\(60\) 0 0
\(61\) −0.639001 + 8.52687i −0.0818157 + 1.09175i 0.793618 + 0.608416i \(0.208195\pi\)
−0.875434 + 0.483338i \(0.839424\pi\)
\(62\) 0 0
\(63\) 6.29741 + 0.949182i 0.793399 + 0.119586i
\(64\) 0 0
\(65\) 4.80342 2.31320i 0.595791 0.286918i
\(66\) 0 0
\(67\) −3.43004 + 8.73959i −0.419046 + 1.06771i 0.553054 + 0.833145i \(0.313462\pi\)
−0.972100 + 0.234566i \(0.924633\pi\)
\(68\) 0 0
\(69\) −0.00238057 0.00220885i −0.000286587 0.000265914i
\(70\) 0 0
\(71\) −6.83052 + 1.02953i −0.810633 + 0.122183i −0.541263 0.840853i \(-0.682054\pi\)
−0.269370 + 0.963037i \(0.586816\pi\)
\(72\) 0 0
\(73\) −10.6150 3.27429i −1.24239 0.383226i −0.397220 0.917724i \(-0.630025\pi\)
−0.845170 + 0.534497i \(0.820501\pi\)
\(74\) 0 0
\(75\) 7.91708 9.92771i 0.914186 1.14635i
\(76\) 0 0
\(77\) 5.64372 + 14.3800i 0.643162 + 1.63875i
\(78\) 0 0
\(79\) 3.26980 5.66346i 0.367882 0.637190i −0.621353 0.783531i \(-0.713417\pi\)
0.989234 + 0.146342i \(0.0467498\pi\)
\(80\) 0 0
\(81\) 7.77713 7.21613i 0.864126 0.801792i
\(82\) 0 0
\(83\) 4.71578 + 3.21516i 0.517624 + 0.352910i 0.793782 0.608202i \(-0.208109\pi\)
−0.276158 + 0.961112i \(0.589061\pi\)
\(84\) 0 0
\(85\) 2.45855 0.266667
\(86\) 0 0
\(87\) −10.7873 −1.15652
\(88\) 0 0
\(89\) −7.13427 4.86406i −0.756231 0.515590i 0.122755 0.992437i \(-0.460827\pi\)
−0.878986 + 0.476847i \(0.841779\pi\)
\(90\) 0 0
\(91\) 3.33646 3.09578i 0.349756 0.324526i
\(92\) 0 0
\(93\) 4.64319 8.04224i 0.481476 0.833941i
\(94\) 0 0
\(95\) −2.58110 6.57654i −0.264815 0.674739i
\(96\) 0 0
\(97\) −11.0143 + 13.8115i −1.11833 + 1.40234i −0.213306 + 0.976986i \(0.568423\pi\)
−0.905026 + 0.425357i \(0.860148\pi\)
\(98\) 0 0
\(99\) −12.2666 3.78373i −1.23284 0.380279i
\(100\) 0 0
\(101\) −9.98838 + 1.50551i −0.993881 + 0.149803i −0.625794 0.779988i \(-0.715225\pi\)
−0.368086 + 0.929792i \(0.619987\pi\)
\(102\) 0 0
\(103\) −10.2237 9.48624i −1.00737 0.934707i −0.00950588 0.999955i \(-0.503026\pi\)
−0.997869 + 0.0652474i \(0.979216\pi\)
\(104\) 0 0
\(105\) 7.55080 19.2391i 0.736883 1.87755i
\(106\) 0 0
\(107\) −6.73185 + 3.24189i −0.650793 + 0.313405i −0.729994 0.683453i \(-0.760477\pi\)
0.0792013 + 0.996859i \(0.474763\pi\)
\(108\) 0 0
\(109\) 7.53258 + 1.13535i 0.721490 + 0.108747i 0.499515 0.866305i \(-0.333512\pi\)
0.221975 + 0.975052i \(0.428750\pi\)
\(110\) 0 0
\(111\) 0.343928 4.58941i 0.0326442 0.435607i
\(112\) 0 0
\(113\) 1.43538 6.28879i 0.135029 0.591600i −0.861456 0.507831i \(-0.830447\pi\)
0.996485 0.0837684i \(-0.0266956\pi\)
\(114\) 0 0
\(115\) −0.00377927 + 0.00257667i −0.000352419 + 0.000240275i
\(116\) 0 0
\(117\) 0.282643 + 3.77161i 0.0261304 + 0.348686i
\(118\) 0 0
\(119\) 2.00564 0.618659i 0.183857 0.0567124i
\(120\) 0 0
\(121\) −4.48106 19.6328i −0.407369 1.78480i
\(122\) 0 0
\(123\) 8.05927 + 13.9591i 0.726680 + 1.25865i
\(124\) 0 0
\(125\) −1.04209 1.30674i −0.0932077 0.116879i
\(126\) 0 0
\(127\) 6.89399 + 3.31997i 0.611743 + 0.294600i 0.713986 0.700159i \(-0.246888\pi\)
−0.102243 + 0.994759i \(0.532602\pi\)
\(128\) 0 0
\(129\) −12.0296 9.12189i −1.05915 0.803138i
\(130\) 0 0
\(131\) 15.7172 + 7.56902i 1.37322 + 0.661308i 0.967543 0.252708i \(-0.0813211\pi\)
0.405678 + 0.914016i \(0.367035\pi\)
\(132\) 0 0
\(133\) −3.76051 4.71553i −0.326077 0.408888i
\(134\) 0 0
\(135\) −2.61125 4.52283i −0.224741 0.389263i
\(136\) 0 0
\(137\) −0.579094 2.53718i −0.0494753 0.216766i 0.944147 0.329524i \(-0.106888\pi\)
−0.993622 + 0.112759i \(0.964031\pi\)
\(138\) 0 0
\(139\) −7.59006 + 2.34122i −0.643780 + 0.198580i −0.599419 0.800436i \(-0.704602\pi\)
−0.0443616 + 0.999016i \(0.514125\pi\)
\(140\) 0 0
\(141\) 1.35284 + 18.0523i 0.113929 + 1.52028i
\(142\) 0 0
\(143\) −7.58012 + 5.16804i −0.633881 + 0.432173i
\(144\) 0 0
\(145\) −3.38095 + 14.8129i −0.280773 + 1.23015i
\(146\) 0 0
\(147\) 0.114219 1.52414i 0.00942058 0.125709i
\(148\) 0 0
\(149\) 18.4553 + 2.78168i 1.51191 + 0.227884i 0.852034 0.523487i \(-0.175369\pi\)
0.659880 + 0.751371i \(0.270607\pi\)
\(150\) 0 0
\(151\) 8.42384 4.05671i 0.685522 0.330130i −0.0584978 0.998288i \(-0.518631\pi\)
0.744020 + 0.668158i \(0.232917\pi\)
\(152\) 0 0
\(153\) −0.637207 + 1.62358i −0.0515151 + 0.131258i
\(154\) 0 0
\(155\) −9.58821 8.89656i −0.770143 0.714589i
\(156\) 0 0
\(157\) −1.46599 + 0.220962i −0.116999 + 0.0176347i −0.207280 0.978282i \(-0.566461\pi\)
0.0902820 + 0.995916i \(0.471223\pi\)
\(158\) 0 0
\(159\) −8.67635 2.67630i −0.688080 0.212244i
\(160\) 0 0
\(161\) −0.00243469 + 0.00305300i −0.000191880 + 0.000240610i
\(162\) 0 0
\(163\) −5.31184 13.5344i −0.416056 1.06009i −0.973258 0.229715i \(-0.926220\pi\)
0.557202 0.830377i \(-0.311875\pi\)
\(164\) 0 0
\(165\) −20.8297 + 36.0781i −1.62159 + 2.80868i
\(166\) 0 0
\(167\) 5.81721 5.39758i 0.450149 0.417677i −0.422244 0.906482i \(-0.638757\pi\)
0.872393 + 0.488805i \(0.162567\pi\)
\(168\) 0 0
\(169\) −8.50774 5.80048i −0.654441 0.446191i
\(170\) 0 0
\(171\) 5.01198 0.383275
\(172\) 0 0
\(173\) −1.73137 −0.131634 −0.0658169 0.997832i \(-0.520965\pi\)
−0.0658169 + 0.997832i \(0.520965\pi\)
\(174\) 0 0
\(175\) −12.6156 8.60118i −0.953651 0.650188i
\(176\) 0 0
\(177\) 6.15122 5.70750i 0.462354 0.429002i
\(178\) 0 0
\(179\) −4.07203 + 7.05296i −0.304358 + 0.527163i −0.977118 0.212698i \(-0.931775\pi\)
0.672761 + 0.739860i \(0.265108\pi\)
\(180\) 0 0
\(181\) −4.70194 11.9804i −0.349493 0.890493i −0.992231 0.124407i \(-0.960297\pi\)
0.642739 0.766086i \(-0.277798\pi\)
\(182\) 0 0
\(183\) −12.2742 + 15.3913i −0.907333 + 1.13776i
\(184\) 0 0
\(185\) −6.19431 1.91069i −0.455414 0.140477i
\(186\) 0 0
\(187\) −4.18342 + 0.630549i −0.305922 + 0.0461103i
\(188\) 0 0
\(189\) −3.26832 3.03256i −0.237735 0.220586i
\(190\) 0 0
\(191\) 5.39153 13.7374i 0.390118 0.994003i −0.592034 0.805913i \(-0.701675\pi\)
0.982152 0.188090i \(-0.0602298\pi\)
\(192\) 0 0
\(193\) −15.7520 + 7.58576i −1.13385 + 0.546035i −0.904145 0.427225i \(-0.859491\pi\)
−0.229708 + 0.973260i \(0.573777\pi\)
\(194\) 0 0
\(195\) 12.1372 + 1.82939i 0.869165 + 0.131006i
\(196\) 0 0
\(197\) −0.204205 + 2.72492i −0.0145490 + 0.194143i 0.985193 + 0.171447i \(0.0548441\pi\)
−0.999742 + 0.0226962i \(0.992775\pi\)
\(198\) 0 0
\(199\) −0.867208 + 3.79949i −0.0614747 + 0.269338i −0.996319 0.0857186i \(-0.972681\pi\)
0.934845 + 0.355057i \(0.115539\pi\)
\(200\) 0 0
\(201\) −17.8592 + 12.1762i −1.25969 + 0.858845i
\(202\) 0 0
\(203\) 0.969336 + 12.9349i 0.0680340 + 0.907851i
\(204\) 0 0
\(205\) 21.6943 6.69181i 1.51520 0.467376i
\(206\) 0 0
\(207\) −0.000722065 0.00316357i −5.01870e−5 0.000219883i
\(208\) 0 0
\(209\) 6.07864 + 10.5285i 0.420468 + 0.728272i
\(210\) 0 0
\(211\) 6.26808 + 7.85992i 0.431512 + 0.541099i 0.949284 0.314419i \(-0.101810\pi\)
−0.517772 + 0.855519i \(0.673238\pi\)
\(212\) 0 0
\(213\) −14.3284 6.90020i −0.981767 0.472794i
\(214\) 0 0
\(215\) −16.2964 + 13.6599i −1.11140 + 0.931595i
\(216\) 0 0
\(217\) −10.0606 4.84492i −0.682957 0.328895i
\(218\) 0 0
\(219\) −15.9456 19.9952i −1.07751 1.35115i
\(220\) 0 0
\(221\) 0.623252 + 1.07950i 0.0419244 + 0.0726152i
\(222\) 0 0
\(223\) −3.33401 14.6072i −0.223262 0.978173i −0.955004 0.296592i \(-0.904150\pi\)
0.731743 0.681581i \(-0.238707\pi\)
\(224\) 0 0
\(225\) 12.1244 3.73987i 0.808290 0.249324i
\(226\) 0 0
\(227\) 0.663861 + 8.85861i 0.0440620 + 0.587966i 0.974916 + 0.222574i \(0.0714460\pi\)
−0.930854 + 0.365392i \(0.880935\pi\)
\(228\) 0 0
\(229\) 16.7625 11.4285i 1.10770 0.755217i 0.135829 0.990732i \(-0.456630\pi\)
0.971871 + 0.235515i \(0.0756778\pi\)
\(230\) 0 0
\(231\) −7.91398 + 34.6734i −0.520702 + 2.28134i
\(232\) 0 0
\(233\) 0.762419 10.1738i 0.0499477 0.666506i −0.914897 0.403687i \(-0.867729\pi\)
0.964845 0.262819i \(-0.0846524\pi\)
\(234\) 0 0
\(235\) 25.2132 + 3.80028i 1.64473 + 0.247903i
\(236\) 0 0
\(237\) 13.5650 6.53254i 0.881139 0.424334i
\(238\) 0 0
\(239\) 2.91886 7.43713i 0.188805 0.481068i −0.804858 0.593468i \(-0.797759\pi\)
0.993663 + 0.112400i \(0.0358538\pi\)
\(240\) 0 0
\(241\) 6.16388 + 5.71925i 0.397051 + 0.368409i 0.853280 0.521453i \(-0.174610\pi\)
−0.456229 + 0.889862i \(0.650800\pi\)
\(242\) 0 0
\(243\) 19.3750 2.92031i 1.24291 0.187338i
\(244\) 0 0
\(245\) −2.05713 0.634540i −0.131425 0.0405392i
\(246\) 0 0
\(247\) 2.23331 2.80049i 0.142102 0.178191i
\(248\) 0 0
\(249\) 4.80069 + 12.2320i 0.304231 + 0.775168i
\(250\) 0 0
\(251\) −9.14704 + 15.8431i −0.577356 + 1.00001i 0.418425 + 0.908251i \(0.362582\pi\)
−0.995781 + 0.0917585i \(0.970751\pi\)
\(252\) 0 0
\(253\) 0.00576989 0.00535367i 0.000362750 0.000336583i
\(254\) 0 0
\(255\) 4.67673 + 3.18854i 0.292868 + 0.199674i
\(256\) 0 0
\(257\) 19.1765 1.19620 0.598098 0.801423i \(-0.295923\pi\)
0.598098 + 0.801423i \(0.295923\pi\)
\(258\) 0 0
\(259\) −5.53401 −0.343866
\(260\) 0 0
\(261\) −8.90586 6.07191i −0.551259 0.375842i
\(262\) 0 0
\(263\) −10.1950 + 9.45955i −0.628649 + 0.583301i −0.928796 0.370592i \(-0.879155\pi\)
0.300147 + 0.953893i \(0.402964\pi\)
\(264\) 0 0
\(265\) −6.39440 + 11.0754i −0.392805 + 0.680358i
\(266\) 0 0
\(267\) −7.26272 18.5051i −0.444471 1.13249i
\(268\) 0 0
\(269\) −16.8908 + 21.1804i −1.02985 + 1.29139i −0.0740861 + 0.997252i \(0.523604\pi\)
−0.955763 + 0.294138i \(0.904967\pi\)
\(270\) 0 0
\(271\) −19.3810 5.97823i −1.17731 0.363152i −0.356467 0.934308i \(-0.616019\pi\)
−0.820842 + 0.571156i \(0.806495\pi\)
\(272\) 0 0
\(273\) 10.3617 1.56177i 0.627118 0.0945228i
\(274\) 0 0
\(275\) 22.5609 + 20.9335i 1.36047 + 1.26234i
\(276\) 0 0
\(277\) 6.37801 16.2509i 0.383218 0.976423i −0.600966 0.799274i \(-0.705217\pi\)
0.984184 0.177149i \(-0.0566873\pi\)
\(278\) 0 0
\(279\) 8.36017 4.02604i 0.500510 0.241033i
\(280\) 0 0
\(281\) −15.2324 2.29591i −0.908688 0.136963i −0.321966 0.946751i \(-0.604344\pi\)
−0.586722 + 0.809789i \(0.699582\pi\)
\(282\) 0 0
\(283\) 1.21194 16.1722i 0.0720423 0.961338i −0.837691 0.546144i \(-0.816095\pi\)
0.909733 0.415193i \(-0.136286\pi\)
\(284\) 0 0
\(285\) 3.61938 15.8575i 0.214394 0.939320i
\(286\) 0 0
\(287\) 16.0140 10.9181i 0.945274 0.644477i
\(288\) 0 0
\(289\) −1.22746 16.3793i −0.0722032 0.963485i
\(290\) 0 0
\(291\) −38.8640 + 11.9880i −2.27825 + 0.702747i
\(292\) 0 0
\(293\) 4.51144 + 19.7659i 0.263561 + 1.15474i 0.917357 + 0.398066i \(0.130318\pi\)
−0.653796 + 0.756671i \(0.726824\pi\)
\(294\) 0 0
\(295\) −5.90953 10.2356i −0.344066 0.595940i
\(296\) 0 0
\(297\) 5.60323 + 7.02623i 0.325132 + 0.407703i
\(298\) 0 0
\(299\) −0.00208942 0.00100621i −0.000120835 5.81908e-5i
\(300\) 0 0
\(301\) −9.85698 + 15.2442i −0.568147 + 0.878663i
\(302\) 0 0
\(303\) −20.9527 10.0903i −1.20370 0.579672i
\(304\) 0 0
\(305\) 17.2882 + 21.6787i 0.989917 + 1.24132i
\(306\) 0 0
\(307\) 4.14771 + 7.18404i 0.236722 + 0.410015i 0.959772 0.280781i \(-0.0905936\pi\)
−0.723050 + 0.690796i \(0.757260\pi\)
\(308\) 0 0
\(309\) −7.14501 31.3043i −0.406466 1.78084i
\(310\) 0 0
\(311\) 28.6492 8.83711i 1.62455 0.501107i 0.657021 0.753872i \(-0.271816\pi\)
0.967528 + 0.252766i \(0.0813402\pi\)
\(312\) 0 0
\(313\) −0.488509 6.51870i −0.0276122 0.368459i −0.993844 0.110786i \(-0.964663\pi\)
0.966232 0.257673i \(-0.0829558\pi\)
\(314\) 0 0
\(315\) 17.0631 11.6334i 0.961399 0.655471i
\(316\) 0 0
\(317\) 1.74389 7.64049i 0.0979468 0.429133i −0.902050 0.431631i \(-0.857938\pi\)
0.999997 + 0.00249843i \(0.000795277\pi\)
\(318\) 0 0
\(319\) 1.95386 26.0724i 0.109395 1.45978i
\(320\) 0 0
\(321\) −17.0100 2.56384i −0.949405 0.143100i
\(322\) 0 0
\(323\) 1.48823 0.716692i 0.0828071 0.0398778i
\(324\) 0 0
\(325\) 3.31287 8.44106i 0.183765 0.468226i
\(326\) 0 0
\(327\) 12.8562 + 11.9288i 0.710951 + 0.659666i
\(328\) 0 0
\(329\) 21.5248 3.24434i 1.18670 0.178866i
\(330\) 0 0
\(331\) 23.1834 + 7.15112i 1.27427 + 0.393061i 0.856810 0.515633i \(-0.172443\pi\)
0.417463 + 0.908694i \(0.362919\pi\)
\(332\) 0 0
\(333\) 2.86722 3.59538i 0.157123 0.197025i
\(334\) 0 0
\(335\) 11.1228 + 28.3403i 0.607701 + 1.54840i
\(336\) 0 0
\(337\) 16.5673 28.6953i 0.902476 1.56313i 0.0782058 0.996937i \(-0.475081\pi\)
0.824270 0.566197i \(-0.191586\pi\)
\(338\) 0 0
\(339\) 10.8865 10.1012i 0.591271 0.548619i
\(340\) 0 0
\(341\) 18.5968 + 12.6791i 1.00707 + 0.686611i
\(342\) 0 0
\(343\) 17.5407 0.947111
\(344\) 0 0
\(345\) −0.0105308 −0.000566957
\(346\) 0 0
\(347\) 3.01977 + 2.05885i 0.162110 + 0.110525i 0.641658 0.766991i \(-0.278247\pi\)
−0.479548 + 0.877516i \(0.659199\pi\)
\(348\) 0 0
\(349\) 4.09206 3.79688i 0.219043 0.203242i −0.563017 0.826445i \(-0.690359\pi\)
0.782060 + 0.623203i \(0.214169\pi\)
\(350\) 0 0
\(351\) 1.32392 2.29310i 0.0706659 0.122397i
\(352\) 0 0
\(353\) −1.50000 3.82194i −0.0798369 0.203421i 0.885382 0.464864i \(-0.153897\pi\)
−0.965219 + 0.261443i \(0.915802\pi\)
\(354\) 0 0
\(355\) −13.9661 + 17.5129i −0.741242 + 0.929488i
\(356\) 0 0
\(357\) 4.61754 + 1.42432i 0.244386 + 0.0753832i
\(358\) 0 0
\(359\) 2.63409 0.397026i 0.139022 0.0209542i −0.0791625 0.996862i \(-0.525225\pi\)
0.218185 + 0.975908i \(0.429986\pi\)
\(360\) 0 0
\(361\) 10.4485 + 9.69475i 0.549919 + 0.510250i
\(362\) 0 0
\(363\) 16.9381 43.1576i 0.889021 2.26519i
\(364\) 0 0
\(365\) −32.4548 + 15.6294i −1.69876 + 0.818080i
\(366\) 0 0
\(367\) −2.72302 0.410430i −0.142141 0.0214243i 0.0775865 0.996986i \(-0.475279\pi\)
−0.219727 + 0.975561i \(0.570517\pi\)
\(368\) 0 0
\(369\) −1.20359 + 16.0609i −0.0626566 + 0.836095i
\(370\) 0 0
\(371\) −2.42947 + 10.6442i −0.126132 + 0.552619i
\(372\) 0 0
\(373\) 27.6542 18.8543i 1.43188 0.976241i 0.434751 0.900551i \(-0.356836\pi\)
0.997131 0.0756903i \(-0.0241160\pi\)
\(374\) 0 0
\(375\) −0.287561 3.83724i −0.0148496 0.198154i
\(376\) 0 0
\(377\) −7.36115 + 2.27061i −0.379118 + 0.116943i
\(378\) 0 0
\(379\) −3.61567 15.8413i −0.185725 0.813713i −0.978838 0.204638i \(-0.934398\pi\)
0.793113 0.609074i \(-0.208459\pi\)
\(380\) 0 0
\(381\) 8.80822 + 15.2563i 0.451259 + 0.781603i
\(382\) 0 0
\(383\) 21.5546 + 27.0287i 1.10139 + 1.38110i 0.917303 + 0.398191i \(0.130362\pi\)
0.184088 + 0.982910i \(0.441067\pi\)
\(384\) 0 0
\(385\) 45.1326 + 21.7347i 2.30017 + 1.10770i
\(386\) 0 0
\(387\) −4.79700 14.3021i −0.243845 0.727018i
\(388\) 0 0
\(389\) −16.7611 8.07174i −0.849823 0.409253i −0.0423114 0.999104i \(-0.513472\pi\)
−0.807512 + 0.589851i \(0.799186\pi\)
\(390\) 0 0
\(391\) −0.000666784 0 0.000836120i −3.37207e−5 0 4.22844e-5i
\(392\) 0 0
\(393\) 20.0814 + 34.7819i 1.01297 + 1.75452i
\(394\) 0 0
\(395\) −4.71885 20.6746i −0.237431 1.04025i
\(396\) 0 0
\(397\) 29.0394 8.95748i 1.45745 0.449563i 0.538057 0.842909i \(-0.319159\pi\)
0.919391 + 0.393346i \(0.128682\pi\)
\(398\) 0 0
\(399\) −1.03770 13.8471i −0.0519497 0.693221i
\(400\) 0 0
\(401\) −31.2339 + 21.2949i −1.55975 + 1.06342i −0.593820 + 0.804598i \(0.702381\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(402\) 0 0
\(403\) 1.47566 6.46531i 0.0735081 0.322060i
\(404\) 0 0
\(405\) 2.57095 34.3070i 0.127752 1.70473i
\(406\) 0 0
\(407\) 11.0301 + 1.66252i 0.546743 + 0.0824083i
\(408\) 0 0
\(409\) −3.84798 + 1.85309i −0.190271 + 0.0916294i −0.526593 0.850117i \(-0.676531\pi\)
0.336323 + 0.941747i \(0.390817\pi\)
\(410\) 0 0
\(411\) 2.18894 5.57733i 0.107972 0.275109i
\(412\) 0 0
\(413\) −7.39653 6.86298i −0.363960 0.337705i
\(414\) 0 0
\(415\) 18.3014 2.75849i 0.898378 0.135409i
\(416\) 0 0
\(417\) −17.4744 5.39014i −0.855725 0.263956i
\(418\) 0 0
\(419\) −7.59816 + 9.52780i −0.371195 + 0.465463i −0.931986 0.362494i \(-0.881925\pi\)
0.560792 + 0.827957i \(0.310497\pi\)
\(420\) 0 0
\(421\) −3.62044 9.22474i −0.176450 0.449586i 0.815099 0.579322i \(-0.196682\pi\)
−0.991549 + 0.129735i \(0.958587\pi\)
\(422\) 0 0
\(423\) −9.04437 + 15.6653i −0.439752 + 0.761673i
\(424\) 0 0
\(425\) 3.06535 2.84423i 0.148691 0.137965i
\(426\) 0 0
\(427\) 19.5585 + 13.3348i 0.946502 + 0.645314i
\(428\) 0 0
\(429\) −21.1216 −1.01976
\(430\) 0 0
\(431\) 20.4652 0.985772 0.492886 0.870094i \(-0.335942\pi\)
0.492886 + 0.870094i \(0.335942\pi\)
\(432\) 0 0
\(433\) −1.14039 0.777507i −0.0548038 0.0373646i 0.535608 0.844467i \(-0.320082\pi\)
−0.590412 + 0.807102i \(0.701035\pi\)
\(434\) 0 0
\(435\) −25.6425 + 23.7927i −1.22946 + 1.14077i
\(436\) 0 0
\(437\) −0.00153657 + 0.00266142i −7.35042e−5 + 0.000127313i
\(438\) 0 0
\(439\) 3.75806 + 9.57538i 0.179362 + 0.457008i 0.992074 0.125659i \(-0.0401045\pi\)
−0.812711 + 0.582667i \(0.802009\pi\)
\(440\) 0 0
\(441\) 0.952202 1.19402i 0.0453430 0.0568583i
\(442\) 0 0
\(443\) −5.22921 1.61300i −0.248447 0.0766358i 0.168030 0.985782i \(-0.446259\pi\)
−0.416477 + 0.909146i \(0.636736\pi\)
\(444\) 0 0
\(445\) −27.6872 + 4.17318i −1.31250 + 0.197828i
\(446\) 0 0
\(447\) 31.4985 + 29.2263i 1.48983 + 1.38236i
\(448\) 0 0
\(449\) 10.2240 26.0503i 0.482499 1.22939i −0.457805 0.889053i \(-0.651364\pi\)
0.940304 0.340335i \(-0.110541\pi\)
\(450\) 0 0
\(451\) −35.1983 + 16.9506i −1.65742 + 0.798173i
\(452\) 0 0
\(453\) 21.2853 + 3.20824i 1.00007 + 0.150736i
\(454\) 0 0
\(455\) 1.10296 14.7180i 0.0517076 0.689990i
\(456\) 0 0
\(457\) −8.19722 + 35.9144i −0.383450 + 1.68000i 0.303131 + 0.952949i \(0.401968\pi\)
−0.686581 + 0.727054i \(0.740889\pi\)
\(458\) 0 0
\(459\) 1.00888 0.687840i 0.0470903 0.0321056i
\(460\) 0 0
\(461\) 0.984869 + 13.1422i 0.0458699 + 0.612092i 0.972014 + 0.234922i \(0.0754836\pi\)
−0.926144 + 0.377170i \(0.876897\pi\)
\(462\) 0 0
\(463\) −27.5468 + 8.49706i −1.28021 + 0.394892i −0.858955 0.512052i \(-0.828886\pi\)
−0.421253 + 0.906943i \(0.638409\pi\)
\(464\) 0 0
\(465\) −6.70086 29.3584i −0.310745 1.36146i
\(466\) 0 0
\(467\) −1.62410 2.81302i −0.0751544 0.130171i 0.825999 0.563672i \(-0.190612\pi\)
−0.901153 + 0.433500i \(0.857278\pi\)
\(468\) 0 0
\(469\) 16.2052 + 20.3207i 0.748286 + 0.938321i
\(470\) 0 0
\(471\) −3.07521 1.48094i −0.141698 0.0682383i
\(472\) 0 0
\(473\) 24.2262 27.4229i 1.11392 1.26090i
\(474\) 0 0
\(475\) −10.8263 5.21369i −0.496747 0.239221i
\(476\) 0 0
\(477\) −5.65668 7.09325i −0.259002 0.324778i
\(478\) 0 0
\(479\) −11.1630 19.3348i −0.510049 0.883431i −0.999932 0.0116426i \(-0.996294\pi\)
0.489883 0.871788i \(-0.337039\pi\)
\(480\) 0 0
\(481\) −0.731330 3.20417i −0.0333458 0.146097i
\(482\) 0 0
\(483\) −0.00859082 + 0.00264992i −0.000390896 + 0.000120575i
\(484\) 0 0
\(485\) 4.28091 + 57.1247i 0.194386 + 2.59390i
\(486\) 0 0
\(487\) 11.1751 7.61906i 0.506393 0.345253i −0.283022 0.959114i \(-0.591337\pi\)
0.789414 + 0.613861i \(0.210384\pi\)
\(488\) 0 0
\(489\) 7.44860 32.6344i 0.336837 1.47578i
\(490\) 0 0
\(491\) −0.751481 + 10.0278i −0.0339139 + 0.452549i 0.954236 + 0.299055i \(0.0966715\pi\)
−0.988150 + 0.153494i \(0.950948\pi\)
\(492\) 0 0
\(493\) −3.51271 0.529456i −0.158205 0.0238455i
\(494\) 0 0
\(495\) −37.5044 + 18.0612i −1.68570 + 0.811789i
\(496\) 0 0
\(497\) −6.98641 + 17.8011i −0.313383 + 0.798488i
\(498\) 0 0
\(499\) 17.9853 + 16.6880i 0.805135 + 0.747056i 0.970997 0.239093i \(-0.0768502\pi\)
−0.165862 + 0.986149i \(0.553041\pi\)
\(500\) 0 0
\(501\) 18.0659 2.72299i 0.807124 0.121654i
\(502\) 0 0
\(503\) 18.7167 + 5.77333i 0.834535 + 0.257420i 0.682436 0.730945i \(-0.260921\pi\)
0.152099 + 0.988365i \(0.451397\pi\)
\(504\) 0 0
\(505\) −20.4228 + 25.6094i −0.908803 + 1.13960i
\(506\) 0 0
\(507\) −8.66092 22.0677i −0.384645 0.980059i
\(508\) 0 0
\(509\) 2.13596 3.69959i 0.0946747 0.163981i −0.814798 0.579745i \(-0.803152\pi\)
0.909473 + 0.415763i \(0.136486\pi\)
\(510\) 0 0
\(511\) −22.5431 + 20.9170i −0.997250 + 0.925312i
\(512\) 0 0
\(513\) −2.89911 1.97658i −0.127999 0.0872681i
\(514\) 0 0
\(515\) −45.2260 −1.99290
\(516\) 0 0
\(517\) −43.8769 −1.92970
\(518\) 0 0
\(519\) −3.29347 2.24545i −0.144567 0.0985642i
\(520\) 0 0
\(521\) 2.62150 2.43239i 0.114850 0.106565i −0.620658 0.784082i \(-0.713134\pi\)
0.735507 + 0.677517i \(0.236944\pi\)
\(522\) 0 0
\(523\) 0.344694 0.597027i 0.0150724 0.0261062i −0.858391 0.512996i \(-0.828535\pi\)
0.873463 + 0.486890i \(0.161869\pi\)
\(524\) 0 0
\(525\) −12.8428 32.7228i −0.560504 1.42814i
\(526\) 0 0
\(527\) 1.90671 2.39094i 0.0830576 0.104151i
\(528\) 0 0
\(529\) −21.9782 6.77937i −0.955573 0.294755i
\(530\) 0 0
\(531\) 8.29100 1.24967i 0.359799 0.0542310i
\(532\) 0 0
\(533\) 8.43783 + 7.82916i 0.365483 + 0.339119i
\(534\) 0 0
\(535\) −8.85191 + 22.5543i −0.382701 + 0.975107i
\(536\) 0 0
\(537\) −16.8930 + 8.13525i −0.728988 + 0.351062i
\(538\) 0 0
\(539\) 3.66310 + 0.552124i 0.157781 + 0.0237817i
\(540\) 0 0
\(541\) −2.98772 + 39.8684i −0.128452 + 1.71408i 0.445579 + 0.895243i \(0.352998\pi\)
−0.574031 + 0.818834i \(0.694621\pi\)
\(542\) 0 0
\(543\) 6.59336 28.8874i 0.282948 1.23968i
\(544\) 0 0
\(545\) 20.4099 13.9152i 0.874263 0.596063i
\(546\) 0 0
\(547\) −2.84068 37.9062i −0.121459 1.62075i −0.641853 0.766828i \(-0.721834\pi\)
0.520394 0.853926i \(-0.325785\pi\)
\(548\) 0 0
\(549\) −18.7969 + 5.79806i −0.802231 + 0.247455i
\(550\) 0 0
\(551\) 2.27153 + 9.95222i 0.0967704 + 0.423979i
\(552\) 0 0
\(553\) −9.05202 15.6786i −0.384931 0.666720i
\(554\) 0 0
\(555\) −9.30498 11.6681i −0.394974 0.495282i
\(556\) 0 0
\(557\) −33.9643 16.3563i −1.43911 0.693040i −0.458445 0.888723i \(-0.651593\pi\)
−0.980667 + 0.195683i \(0.937308\pi\)
\(558\) 0 0
\(559\) −10.1290 3.69260i −0.428410 0.156180i
\(560\) 0 0
\(561\) −8.77558 4.22610i −0.370505 0.178426i
\(562\) 0 0
\(563\) 22.6446 + 28.3955i 0.954357 + 1.19673i 0.980391 + 0.197065i \(0.0631409\pi\)
−0.0260336 + 0.999661i \(0.508288\pi\)
\(564\) 0 0
\(565\) −10.4587 18.1150i −0.440001 0.762105i
\(566\) 0 0
\(567\) −6.53552 28.6340i −0.274466 1.20251i
\(568\) 0 0
\(569\) 27.5039 8.48383i 1.15302 0.355661i 0.341444 0.939902i \(-0.389084\pi\)
0.811580 + 0.584241i \(0.198608\pi\)
\(570\) 0 0
\(571\) 1.35501 + 18.0813i 0.0567052 + 0.756679i 0.950998 + 0.309197i \(0.100060\pi\)
−0.894293 + 0.447482i \(0.852321\pi\)
\(572\) 0 0
\(573\) 28.0722 19.1393i 1.17273 0.799556i
\(574\) 0 0
\(575\) −0.00173117 + 0.00758474i −7.21947e−5 + 0.000316306i
\(576\) 0 0
\(577\) −0.994996 + 13.2773i −0.0414222 + 0.552741i 0.937430 + 0.348173i \(0.113198\pi\)
−0.978852 + 0.204568i \(0.934421\pi\)
\(578\) 0 0
\(579\) −39.8020 5.99918i −1.65411 0.249318i
\(580\) 0 0
\(581\) 14.2358 6.85560i 0.590600 0.284418i
\(582\) 0 0
\(583\) 8.04004 20.4857i 0.332984 0.848430i
\(584\) 0 0
\(585\) 8.99065 + 8.34211i 0.371718 + 0.344904i
\(586\) 0 0
\(587\) −6.55180 + 0.987525i −0.270422 + 0.0407595i −0.282853 0.959163i \(-0.591281\pi\)
0.0124315 + 0.999923i \(0.496043\pi\)
\(588\) 0 0
\(589\) −8.39743 2.59026i −0.346010 0.106730i
\(590\) 0 0
\(591\) −3.92244 + 4.91859i −0.161348 + 0.202324i
\(592\) 0 0
\(593\) 1.57645 + 4.01673i 0.0647371 + 0.164947i 0.959582 0.281431i \(-0.0908089\pi\)
−0.894844 + 0.446378i \(0.852714\pi\)
\(594\) 0 0
\(595\) 3.40309 5.89433i 0.139513 0.241644i
\(596\) 0 0
\(597\) −6.57725 + 6.10279i −0.269189 + 0.249771i
\(598\) 0 0
\(599\) −18.5509 12.6478i −0.757968 0.516774i 0.121581 0.992581i \(-0.461203\pi\)
−0.879549 + 0.475808i \(0.842156\pi\)
\(600\) 0 0
\(601\) 3.82446 0.156003 0.0780015 0.996953i \(-0.475146\pi\)
0.0780015 + 0.996953i \(0.475146\pi\)
\(602\) 0 0
\(603\) −21.5981 −0.879544
\(604\) 0 0
\(605\) −53.9546 36.7856i −2.19357 1.49555i
\(606\) 0 0
\(607\) 17.0366 15.8077i 0.691495 0.641613i −0.254018 0.967200i \(-0.581752\pi\)
0.945512 + 0.325586i \(0.105562\pi\)
\(608\) 0 0
\(609\) −14.9316 + 25.8622i −0.605058 + 1.04799i
\(610\) 0 0
\(611\) 4.72300 + 12.0340i 0.191072 + 0.486844i
\(612\) 0 0
\(613\) 2.06228 2.58602i 0.0832947 0.104448i −0.738438 0.674321i \(-0.764436\pi\)
0.821733 + 0.569873i \(0.193008\pi\)
\(614\) 0 0
\(615\) 49.9463 + 15.4064i 2.01403 + 0.621245i
\(616\) 0 0
\(617\) 34.6142 5.21724i 1.39351 0.210038i 0.591000 0.806672i \(-0.298733\pi\)
0.802514 + 0.596633i \(0.203495\pi\)
\(618\) 0 0
\(619\) 13.1838 + 12.2328i 0.529903 + 0.491678i 0.899142 0.437656i \(-0.144191\pi\)
−0.369239 + 0.929334i \(0.620382\pi\)
\(620\) 0 0
\(621\) −0.000829954 0.00211469i −3.33049e−5 8.48595e-5i
\(622\) 0 0
\(623\) −21.5366 + 10.3715i −0.862847 + 0.415525i
\(624\) 0 0
\(625\) 21.9097 + 3.30236i 0.876390 + 0.132094i
\(626\) 0 0
\(627\) −2.09165 + 27.9111i −0.0835324 + 1.11466i
\(628\) 0 0
\(629\) 0.337250 1.47759i 0.0134471 0.0589154i
\(630\) 0 0
\(631\) −20.8020 + 14.1826i −0.828114 + 0.564599i −0.901537 0.432702i \(-0.857560\pi\)
0.0734225 + 0.997301i \(0.476608\pi\)
\(632\) 0 0
\(633\) 1.72965 + 23.0805i 0.0687473 + 0.917369i
\(634\) 0 0
\(635\) 23.7104 7.31368i 0.940917 0.290235i
\(636\) 0 0
\(637\) −0.242875 1.06410i −0.00962304 0.0421613i
\(638\) 0 0
\(639\) −7.94543 13.7619i −0.314316 0.544412i
\(640\) 0 0
\(641\) 22.6472 + 28.3987i 0.894511 + 1.12168i 0.991974 + 0.126442i \(0.0403557\pi\)
−0.0974634 + 0.995239i \(0.531073\pi\)
\(642\) 0 0
\(643\) 2.99826 + 1.44389i 0.118240 + 0.0569413i 0.492069 0.870556i \(-0.336241\pi\)
−0.373829 + 0.927498i \(0.621955\pi\)
\(644\) 0 0
\(645\) −48.7151 + 4.84914i −1.91816 + 0.190935i
\(646\) 0 0
\(647\) −37.9436 18.2727i −1.49172 0.718372i −0.502464 0.864598i \(-0.667573\pi\)
−0.989251 + 0.146226i \(0.953287\pi\)
\(648\) 0 0
\(649\) 12.6807 + 15.9010i 0.497759 + 0.624171i
\(650\) 0 0
\(651\) −12.8541 22.2639i −0.503791 0.872591i
\(652\) 0 0
\(653\) −5.31138 23.2707i −0.207850 0.910652i −0.965994 0.258564i \(-0.916751\pi\)
0.758144 0.652088i \(-0.226107\pi\)
\(654\) 0 0
\(655\) 54.0559 16.6740i 2.11214 0.651509i
\(656\) 0 0
\(657\) −1.90971 25.4833i −0.0745048 0.994197i
\(658\) 0 0
\(659\) 3.95025 2.69323i 0.153880 0.104913i −0.483932 0.875105i \(-0.660792\pi\)
0.637812 + 0.770192i \(0.279840\pi\)
\(660\) 0 0
\(661\) 3.18440 13.9518i 0.123859 0.542662i −0.874481 0.485060i \(-0.838798\pi\)
0.998340 0.0576012i \(-0.0183452\pi\)
\(662\) 0 0
\(663\) −0.214460 + 2.86177i −0.00832893 + 0.111142i
\(664\) 0 0
\(665\) −19.3398 2.91501i −0.749966 0.113039i
\(666\) 0 0
\(667\) 0.00595462 0.00286759i 0.000230564 0.000111034i
\(668\) 0 0
\(669\) 12.6023 32.1102i 0.487234 1.24145i
\(670\) 0 0
\(671\) −34.9771 32.4540i −1.35028 1.25287i
\(672\) 0 0
\(673\) −22.9150 + 3.45387i −0.883307 + 0.133137i −0.575003 0.818151i \(-0.694999\pi\)
−0.308303 + 0.951288i \(0.599761\pi\)
\(674\) 0 0
\(675\) −8.48806 2.61822i −0.326706 0.100775i
\(676\) 0 0
\(677\) 8.82015 11.0601i 0.338986 0.425075i −0.582895 0.812547i \(-0.698080\pi\)
0.921881 + 0.387472i \(0.126652\pi\)
\(678\) 0 0
\(679\) 17.8669 + 45.5241i 0.685669 + 1.74706i
\(680\) 0 0
\(681\) −10.2261 + 17.7121i −0.391864 + 0.678728i
\(682\) 0 0
\(683\) 34.9013 32.3837i 1.33546 1.23913i 0.387060 0.922054i \(-0.373491\pi\)
0.948401 0.317073i \(-0.102700\pi\)
\(684\) 0 0
\(685\) −6.97264 4.75386i −0.266411 0.181636i
\(686\) 0 0
\(687\) 46.7080 1.78202
\(688\) 0 0
\(689\) −6.48401 −0.247021
\(690\) 0 0
\(691\) −34.1689 23.2959i −1.29985 0.886220i −0.302096 0.953277i \(-0.597686\pi\)
−0.997749 + 0.0670578i \(0.978639\pi\)
\(692\) 0 0
\(693\) −26.0506 + 24.1714i −0.989581 + 0.918197i
\(694\) 0 0
\(695\) −12.8785 + 22.3062i −0.488509 + 0.846122i
\(696\) 0 0
\(697\) 1.93925 + 4.94112i 0.0734543 + 0.187158i
\(698\) 0 0
\(699\) 14.6448 18.3640i 0.553919 0.694592i
\(700\) 0 0
\(701\) 45.7066 + 14.0986i 1.72632 + 0.532498i 0.989618 0.143725i \(-0.0459079\pi\)
0.736698 + 0.676222i \(0.236384\pi\)
\(702\) 0 0
\(703\) −4.30656 + 0.649110i −0.162425 + 0.0244816i
\(704\) 0 0
\(705\) 43.0326 + 39.9284i 1.62070 + 1.50379i
\(706\) 0 0
\(707\) −10.2163 + 26.0308i −0.384225 + 0.978990i
\(708\) 0 0
\(709\) −26.2688 + 12.6504i −0.986547 + 0.475096i −0.856352 0.516392i \(-0.827275\pi\)
−0.130195 + 0.991488i \(0.541560\pi\)
\(710\) 0 0
\(711\) 14.8761 + 2.24221i 0.557898 + 0.0840896i
\(712\) 0 0
\(713\) −0.000425181 0.00567365i −1.59232e−5 0.000212480i
\(714\) 0 0
\(715\) −6.61995 + 29.0039i −0.247572 + 1.08468i
\(716\) 0 0
\(717\) 15.1977 10.3616i 0.567567 0.386961i
\(718\) 0 0
\(719\) −0.145367 1.93979i −0.00542127 0.0723418i 0.993837 0.110852i \(-0.0353579\pi\)
−0.999258 + 0.0385100i \(0.987739\pi\)
\(720\) 0 0
\(721\) −36.8946 + 11.3805i −1.37403 + 0.423831i
\(722\) 0 0
\(723\) 4.30772 + 18.8734i 0.160206 + 0.701908i
\(724\) 0 0
\(725\) 12.9212 + 22.3802i 0.479882 + 0.831180i
\(726\) 0 0
\(727\) −5.86302 7.35200i −0.217447 0.272670i 0.661129 0.750272i \(-0.270078\pi\)
−0.878576 + 0.477602i \(0.841506\pi\)
\(728\) 0 0
\(729\) 11.9673 + 5.76313i 0.443232 + 0.213449i
\(730\) 0 0
\(731\) −3.46954 3.56084i −0.128326 0.131702i
\(732\) 0 0
\(733\) 11.3172 + 5.45007i 0.418010 + 0.201303i 0.631053 0.775740i \(-0.282623\pi\)
−0.213043 + 0.977043i \(0.568337\pi\)
\(734\) 0 0
\(735\) −3.09018 3.87496i −0.113983 0.142930i
\(736\) 0 0
\(737\) −26.1947 45.3706i −0.964895 1.67125i
\(738\) 0 0
\(739\) 9.29738 + 40.7345i 0.342010 + 1.49844i 0.794825 + 0.606838i \(0.207563\pi\)
−0.452815 + 0.891604i \(0.649580\pi\)
\(740\) 0 0
\(741\) 7.88027 2.43074i 0.289489 0.0892955i
\(742\) 0 0
\(743\) −0.118093 1.57585i −0.00433243 0.0578122i 0.994619 0.103605i \(-0.0330377\pi\)
−0.998951 + 0.0457926i \(0.985419\pi\)
\(744\) 0 0
\(745\) 50.0054 34.0931i 1.83206 1.24908i
\(746\) 0 0
\(747\) −2.92169 + 12.8008i −0.106899 + 0.468356i
\(748\) 0 0
\(749\) −1.54577 + 20.6269i −0.0564812 + 0.753689i
\(750\) 0 0
\(751\) 6.12248 + 0.922815i 0.223412 + 0.0336740i 0.259794 0.965664i \(-0.416345\pi\)
−0.0363820 + 0.999338i \(0.511583\pi\)
\(752\) 0 0
\(753\) −37.9470 + 18.2743i −1.38286 + 0.665953i
\(754\) 0 0
\(755\) 11.0767 28.2231i 0.403124 1.02714i
\(756\) 0 0
\(757\) 4.19269 + 3.89025i 0.152386 + 0.141394i 0.752682 0.658385i \(-0.228760\pi\)
−0.600296 + 0.799778i \(0.704950\pi\)
\(758\) 0 0
\(759\) 0.0179189 0.00270084i 0.000650415 9.80343e-5i
\(760\) 0 0
\(761\) 16.3236 + 5.03516i 0.591729 + 0.182524i 0.576136 0.817354i \(-0.304560\pi\)
0.0155937 + 0.999878i \(0.495036\pi\)
\(762\) 0 0
\(763\) 13.1485 16.4877i 0.476006 0.596893i
\(764\) 0 0
\(765\) 2.06630 + 5.26485i 0.0747073 + 0.190351i
\(766\) 0 0
\(767\) 2.99617 5.18952i 0.108185 0.187383i
\(768\) 0 0
\(769\) 1.75024 1.62399i 0.0631153 0.0585624i −0.647985 0.761653i \(-0.724388\pi\)
0.711100 + 0.703091i \(0.248197\pi\)
\(770\) 0 0
\(771\) 36.4780 + 24.8703i 1.31372 + 0.895682i
\(772\) 0 0
\(773\) 1.76858 0.0636114 0.0318057 0.999494i \(-0.489874\pi\)
0.0318057 + 0.999494i \(0.489874\pi\)
\(774\) 0 0
\(775\) −22.2468 −0.799130
\(776\) 0 0
\(777\) −10.5269 7.17715i −0.377652 0.257479i
\(778\) 0 0
\(779\) 11.1814 10.3748i 0.400616 0.371717i
\(780\) 0 0
\(781\) 19.2728 33.3815i 0.689635 1.19448i
\(782\) 0 0
\(783\) 2.75689 + 7.02443i 0.0985231 + 0.251033i
\(784\) 0 0
\(785\) −2.99744 + 3.75867i −0.106983 + 0.134153i
\(786\) 0 0
\(787\) −31.5189 9.72230i −1.12353 0.346563i −0.323323 0.946289i \(-0.604800\pi\)
−0.800205 + 0.599726i \(0.795276\pi\)
\(788\) 0 0
\(789\) −31.6614 + 4.77219i −1.12718 + 0.169894i
\(790\) 0 0
\(791\) −13.0904 12.1461i −0.465442 0.431867i
\(792\) 0 0
\(793\) −5.13608 + 13.0865i −0.182387 + 0.464716i
\(794\) 0 0
\(795\) −26.5275 + 12.7750i −0.940834 + 0.453082i
\(796\) 0 0
\(797\) 22.3286 + 3.36550i 0.790921 + 0.119212i 0.532065 0.846704i \(-0.321416\pi\)
0.258856 + 0.965916i \(0.416654\pi\)
\(798\) 0 0
\(799\) −0.445506 + 5.94487i −0.0157609 + 0.210314i
\(800\) 0 0
\(801\) 4.42008 19.3657i 0.156176 0.684252i
\(802\) 0 0
\(803\) 51.2158 34.9184i 1.80737 1.23224i
\(804\) 0 0
\(805\) 0.000946286 0.0126273i 3.33522e−5 0.000445054i
\(806\) 0 0
\(807\) −59.5993 + 18.3839i −2.09799 + 0.647146i
\(808\) 0 0
\(809\) 2.39510 + 10.4936i 0.0842072 + 0.368936i 0.999421 0.0340335i \(-0.0108353\pi\)
−0.915213 + 0.402969i \(0.867978\pi\)
\(810\) 0 0
\(811\) 9.44394 + 16.3574i 0.331621 + 0.574385i 0.982830 0.184514i \(-0.0590710\pi\)
−0.651208 + 0.758899i \(0.725738\pi\)
\(812\) 0 0
\(813\) −29.1137 36.5074i −1.02106 1.28037i
\(814\) 0 0
\(815\) −42.4786 20.4566i −1.48796 0.716563i
\(816\) 0 0
\(817\) −5.88263 + 13.0192i −0.205807 + 0.455485i
\(818\) 0 0
\(819\) 9.43359 + 4.54298i 0.329636 + 0.158744i
\(820\) 0 0
\(821\) −29.5066 37.0001i −1.02979 1.29131i −0.955789 0.294053i \(-0.904996\pi\)
−0.0739969 0.997258i \(-0.523576\pi\)
\(822\) 0 0
\(823\) 0.551677 + 0.955532i 0.0192302 + 0.0333078i 0.875480 0.483254i \(-0.160545\pi\)
−0.856250 + 0.516561i \(0.827212\pi\)
\(824\) 0 0
\(825\) 15.7670 + 69.0799i 0.548938 + 2.40505i
\(826\) 0 0
\(827\) −21.0646 + 6.49756i −0.732487 + 0.225942i −0.638490 0.769630i \(-0.720441\pi\)
−0.0939973 + 0.995572i \(0.529965\pi\)
\(828\) 0 0
\(829\) −3.82921 51.0972i −0.132994 1.77468i −0.521518 0.853241i \(-0.674634\pi\)
0.388524 0.921439i \(-0.372985\pi\)
\(830\) 0 0
\(831\) 33.2085 22.6412i 1.15199 0.785414i
\(832\) 0 0
\(833\) 0.112001 0.490707i 0.00388060 0.0170020i
\(834\) 0 0
\(835\) 1.92304 25.6612i 0.0665496 0.888043i
\(836\) 0 0
\(837\) −6.42358 0.968199i −0.222031 0.0334659i
\(838\) 0 0
\(839\) −10.0756 + 4.85214i −0.347847 + 0.167514i −0.599646 0.800265i \(-0.704692\pi\)
0.251799 + 0.967780i \(0.418978\pi\)
\(840\) 0 0
\(841\) −2.57428 + 6.55915i −0.0887682 + 0.226178i
\(842\) 0 0
\(843\) −25.9979 24.1225i −0.895414 0.830823i
\(844\) 0 0
\(845\) −33.0175 + 4.97658i −1.13584 + 0.171200i
\(846\) 0 0
\(847\) −53.2718 16.4322i −1.83044 0.564616i
\(848\) 0 0
\(849\) 23.2794 29.1914i 0.798947 1.00185i
\(850\) 0 0
\(851\) 0.00103016 + 0.00262480i 3.53133e−5 + 8.99769e-5i
\(852\) 0 0
\(853\) −10.4719 + 18.1379i −0.358553 + 0.621031i −0.987719 0.156239i \(-0.950063\pi\)
0.629167 + 0.777270i \(0.283396\pi\)
\(854\) 0 0
\(855\) 11.9140 11.0546i 0.407450 0.378058i
\(856\) 0 0
\(857\) 6.50785 + 4.43698i 0.222304 + 0.151564i 0.669351 0.742946i \(-0.266572\pi\)
−0.447047 + 0.894510i \(0.647524\pi\)
\(858\) 0 0
\(859\) 42.8104 1.46067 0.730337 0.683087i \(-0.239363\pi\)
0.730337 + 0.683087i \(0.239363\pi\)
\(860\) 0 0
\(861\) 44.6221 1.52072
\(862\) 0 0
\(863\) −0.563855 0.384430i −0.0191939 0.0130861i 0.553685 0.832726i \(-0.313221\pi\)
−0.572879 + 0.819640i \(0.694174\pi\)
\(864\) 0 0
\(865\) −4.11565 + 3.81877i −0.139936 + 0.129842i
\(866\) 0 0
\(867\) 18.9076 32.7490i 0.642137 1.11221i
\(868\) 0 0
\(869\) 13.3319 + 33.9692i 0.452255 + 1.15233i
\(870\) 0 0
\(871\) −9.62403 + 12.0682i −0.326098 + 0.408914i
\(872\) 0 0
\(873\) −38.8335 11.9785i −1.31431 0.405412i
\(874\) 0 0
\(875\) −4.57534 + 0.689622i −0.154675 + 0.0233135i
\(876\) 0 0
\(877\) −25.4736 23.6361i −0.860183 0.798133i 0.120709 0.992688i \(-0.461483\pi\)
−0.980892 + 0.194555i \(0.937674\pi\)
\(878\) 0 0
\(879\) −17.0530 + 43.4502i −0.575182 + 1.46554i
\(880\) 0 0
\(881\) 3.50466 1.68776i 0.118075 0.0568620i −0.373914 0.927463i \(-0.621984\pi\)
0.491989 + 0.870602i \(0.336270\pi\)
\(882\) 0 0
\(883\) −36.9489 5.56915i −1.24343 0.187417i −0.505817 0.862641i \(-0.668809\pi\)
−0.737613 + 0.675224i \(0.764047\pi\)
\(884\) 0 0
\(885\) 2.03346 27.1346i 0.0683540 0.912120i
\(886\) 0 0
\(887\) −0.0666391 + 0.291965i −0.00223752 + 0.00980322i −0.976034 0.217617i \(-0.930172\pi\)
0.973797 + 0.227420i \(0.0730289\pi\)
\(888\) 0 0
\(889\) 17.5021 11.9327i 0.587002 0.400211i
\(890\) 0 0
\(891\) 4.42409 + 59.0353i 0.148212 + 1.97776i
\(892\) 0 0
\(893\) 16.3700 5.04948i 0.547802 0.168975i
\(894\) 0 0
\(895\) 5.87658 + 25.7470i 0.196432 + 0.860627i
\(896\) 0 0
\(897\) −0.00266959 0.00462386i −8.91349e−5 0.000154386i
\(898\) 0 0
\(899\) 11.7835 + 14.7760i 0.393001 + 0.492807i
\(900\) 0 0
\(901\) −2.69397 1.29735i −0.0897490 0.0432209i
\(902\) 0 0
\(903\) −38.5207 + 16.2143i −1.28189 + 0.539578i
\(904\) 0 0
\(905\) −37.6012 18.1078i −1.24991 0.601924i
\(906\) 0 0
\(907\) 19.3860 + 24.3092i 0.643700 + 0.807175i 0.991460 0.130409i \(-0.0416290\pi\)
−0.347760 + 0.937584i \(0.613058\pi\)
\(908\) 0 0
\(909\) −11.6187 20.1242i −0.385369 0.667479i
\(910\) 0 0
\(911\) −6.55930 28.7382i −0.217319 0.952139i −0.959449 0.281882i \(-0.909041\pi\)
0.742130 0.670256i \(-0.233816\pi\)
\(912\) 0 0
\(913\) −30.4337 + 9.38756i −1.00721 + 0.310683i
\(914\) 0 0
\(915\) 4.77059 + 63.6590i 0.157711 + 2.10450i
\(916\) 0 0
\(917\) 39.9021 27.2048i 1.31768 0.898382i
\(918\) 0 0
\(919\) 3.58384 15.7018i 0.118220 0.517956i −0.880792 0.473504i \(-0.842989\pi\)
0.999012 0.0444515i \(-0.0141540\pi\)
\(920\) 0 0
\(921\) −1.42722 + 19.0449i −0.0470285 + 0.627551i
\(922\) 0 0
\(923\) −11.2300 1.69265i −0.369641 0.0557144i
\(924\) 0 0
\(925\) −9.93354 + 4.78374i −0.326613 + 0.157288i
\(926\) 0 0
\(927\) 11.7217 29.8663i 0.384990 0.980939i
\(928\) 0 0
\(929\) −16.5691 15.3739i −0.543616 0.504402i 0.359880 0.932999i \(-0.382818\pi\)
−0.903496 + 0.428597i \(0.859008\pi\)
\(930\) 0 0
\(931\) −1.43021 + 0.215569i −0.0468732 + 0.00706499i
\(932\) 0 0
\(933\) 65.9584 + 20.3455i 2.15938 + 0.666080i
\(934\) 0 0
\(935\) −8.55366 + 10.7260i −0.279735 + 0.350776i
\(936\) 0 0
\(937\) 11.9474 + 30.4414i 0.390304 + 0.994478i 0.982095 + 0.188387i \(0.0603258\pi\)
−0.591791 + 0.806091i \(0.701579\pi\)
\(938\) 0 0
\(939\) 7.52496 13.0336i 0.245568 0.425336i
\(940\) 0 0
\(941\) −0.214487 + 0.199015i −0.00699209 + 0.00648771i −0.683661 0.729800i \(-0.739613\pi\)
0.676669 + 0.736287i \(0.263423\pi\)
\(942\) 0 0
\(943\) −0.00815951 0.00556306i −0.000265710 0.000181158i
\(944\) 0 0
\(945\) −14.4578 −0.470313
\(946\) 0 0
\(947\) −13.5390 −0.439959 −0.219979 0.975504i \(-0.570599\pi\)
−0.219979 + 0.975504i \(0.570599\pi\)
\(948\) 0 0
\(949\) −15.0900 10.2882i −0.489841 0.333968i
\(950\) 0 0
\(951\) 13.2264 12.2723i 0.428894 0.397956i
\(952\) 0 0
\(953\) −6.90661 + 11.9626i −0.223727 + 0.387507i −0.955937 0.293573i \(-0.905156\pi\)
0.732210 + 0.681079i \(0.238489\pi\)
\(954\) 0 0
\(955\) −17.4834 44.5469i −0.565749 1.44151i
\(956\) 0 0
\(957\) 37.5305 47.0617i 1.21319 1.52129i
\(958\) 0 0
\(959\) −6.88440 2.12356i −0.222309 0.0685732i
\(960\) 0 0
\(961\) 14.5658 2.19544i 0.469865 0.0708207i
\(962\) 0 0
\(963\) −12.6001 11.6912i −0.406034 0.376744i
\(964\) 0 0
\(965\) −20.7127 + 52.7752i −0.666767 + 1.69889i
\(966\) 0 0
\(967\) −10.3525 + 4.98550i −0.332914 + 0.160323i −0.592871 0.805297i \(-0.702006\pi\)
0.259958 + 0.965620i \(0.416291\pi\)
\(968\) 0 0
\(969\) 3.76044 + 0.566795i 0.120803 + 0.0182081i
\(970\) 0 0
\(971\) −3.68142 + 49.1251i −0.118142 + 1.57650i 0.551729 + 0.834023i \(0.313968\pi\)
−0.669872 + 0.742477i \(0.733651\pi\)
\(972\) 0 0
\(973\) −4.89301 + 21.4377i −0.156863 + 0.687261i
\(974\) 0 0
\(975\) 17.2492 11.7603i 0.552416 0.376631i
\(976\) 0 0
\(977\) −2.57239 34.3262i −0.0822982 1.09819i −0.873560 0.486716i \(-0.838195\pi\)
0.791262 0.611477i \(-0.209424\pi\)
\(978\) 0 0
\(979\) 46.0416 14.2020i 1.47150 0.453897i
\(980\) 0 0
\(981\) 3.89949 + 17.0848i 0.124501 + 0.545476i
\(982\) 0 0
\(983\) 23.3956 + 40.5224i 0.746205 + 1.29247i 0.949630 + 0.313375i \(0.101460\pi\)
−0.203424 + 0.979091i \(0.565207\pi\)
\(984\) 0 0
\(985\) 5.52476 + 6.92783i 0.176033 + 0.220739i
\(986\) 0 0
\(987\) 45.1527 + 21.7444i 1.43723 + 0.692131i
\(988\) 0 0
\(989\) 0.00906527 + 0.00183748i 0.000288259 + 5.84285e-5i
\(990\) 0 0
\(991\) 21.0704 + 10.1470i 0.669325 + 0.322330i 0.737503 0.675343i \(-0.236005\pi\)
−0.0681788 + 0.997673i \(0.521719\pi\)
\(992\) 0 0
\(993\) 34.8256 + 43.6700i 1.10516 + 1.38582i
\(994\) 0 0
\(995\) 6.31882 + 10.9445i 0.200320 + 0.346964i
\(996\) 0 0
\(997\) 11.0399 + 48.3689i 0.349637 + 1.53186i 0.778007 + 0.628255i \(0.216231\pi\)
−0.428370 + 0.903603i \(0.640912\pi\)
\(998\) 0 0
\(999\) −3.07642 + 0.948949i −0.0973335 + 0.0300234i
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 688.2.bg.c.369.2 36
4.3 odd 2 43.2.g.a.25.1 36
12.11 even 2 387.2.y.c.154.3 36
43.31 even 21 inner 688.2.bg.c.289.2 36
172.31 odd 42 43.2.g.a.31.1 yes 36
172.103 odd 42 1849.2.a.n.1.14 18
172.155 even 42 1849.2.a.o.1.5 18
516.203 even 42 387.2.y.c.289.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.2.g.a.25.1 36 4.3 odd 2
43.2.g.a.31.1 yes 36 172.31 odd 42
387.2.y.c.154.3 36 12.11 even 2
387.2.y.c.289.3 36 516.203 even 42
688.2.bg.c.289.2 36 43.31 even 21 inner
688.2.bg.c.369.2 36 1.1 even 1 trivial
1849.2.a.n.1.14 18 172.103 odd 42
1849.2.a.o.1.5 18 172.155 even 42