Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.98696108952 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.412141395\) \(a_{4}=+0.500000000\) \(a_{5}=+0.625923933\)
\(a_{6}=+0.291427975\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.830139470\) \(a_{10}=-0.442595057\)
\(a_{11}=-0.477218543\) \(a_{12}=-0.206070698\) \(a_{13}=-0.161787832\) \(a_{14}=+0.267261242\) \(a_{15}=-0.257969163\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.918641037\) \(a_{18}=+0.586997249\) \(a_{19}=+1.320228882\) \(a_{20}=+0.312961966\)
\(a_{21}=+0.155774805\) \(a_{22}=+0.337444468\) \(a_{23}=-0.575840224\) \(a_{24}=+0.145713988\) \(a_{25}=-0.608219230\)
\(a_{26}=+0.114401273\) \(a_{27}=+0.754276235\) \(a_{28}=-0.188982237\) \(a_{29}=+1.192354285\) \(a_{30}=+0.182411745\)
\(a_{31}=+1.158843638\) \(a_{32}=-0.176776695\) \(a_{33}=+0.196681516\) \(a_{34}=-0.649577307\) \(a_{35}=-0.236577009\)
\(a_{36}=-0.415069735\) \(a_{37}=+0.775947033\) \(a_{38}=-0.933542795\) \(a_{39}=+0.066679462\) \(a_{40}=-0.221297529\)
\(a_{41}=-0.650640832\) \(a_{42}=-0.110149421\) \(a_{43}=+1.083971898\) \(a_{44}=-0.238609273\) \(a_{45}=-0.519604163\)
\(a_{46}=+0.407180529\) \(a_{47}=+1.369139061\) \(a_{48}=-0.103035350\) \(a_{49}=+0.142857133\) \(a_{50}=+0.430075948\)
\(a_{51}=-0.378610000\) \(a_{52}=-0.080893915\) \(a_{53}=+0.170966108\) \(a_{54}=-0.533353825\) \(a_{55}=-0.298702552\)
\(a_{56}=+0.133630612\) \(a_{57}=-0.544120903\) \(a_{58}=-0.843121800\) \(a_{59}=+1.896350230\) \(a_{60}=-0.128984582\)
\(a_{61}=-0.318045112\) \(a_{62}=-0.819426195\) \(a_{63}=+0.313763228\) \(a_{64}=+0.125000000\) \(a_{65}=-0.101266877\)
\(a_{66}=-0.139074835\) \(a_{67}=-1.305997036\) \(a_{68}=+0.459320518\) \(a_{69}=+0.237327596\) \(a_{70}=+0.167285204\)
\(a_{71}=+0.021689265\) \(a_{72}=+0.293498626\) \(a_{73}=+1.301100625\) \(a_{74}=-0.548677413\) \(a_{75}=+0.250672320\)
\(a_{76}=+0.660114440\) \(a_{77}=+0.180371666\) \(a_{78}=-0.047149493\) \(a_{79}=-1.271536941\) \(a_{80}=+0.156480971\)
\(a_{81}=+0.519271002\) \(a_{82}=+0.460072613\) \(a_{83}=-0.667087941\) \(a_{84}=+0.077887370\) \(a_{85}=+0.574999411\)
\(a_{86}=-0.766483881\) \(a_{87}=-0.491418559\) \(a_{88}=+0.168722231\) \(a_{89}=-0.326327280\) \(a_{90}=+0.367415630\)
\(a_{91}=+0.061150051\) \(a_{92}=-0.287920115\) \(a_{93}=-0.477607427\) \(a_{94}=-0.968127517\) \(a_{95}=+0.826362853\)
\(a_{96}=+0.072856990\) \(a_{97}=-0.868968227\) \(a_{98}=-0.101015248\) \(a_{99}=+0.396157941\) \(a_{100}=-0.304109607\)

Showing 100 of 2000 available coefficients

Rows: Cols: