Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 25.2414671674 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.157760968\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.818660631\) \(a_{7}=+0.671707953\) \(a_{8}=+0.353553391\) \(a_{9}=+0.340410458\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.860610460\) \(a_{12}=-0.578880484\) \(a_{13}=-1.088383077\) \(a_{14}=+0.474969249\) \(a_{15}=-0.517766445\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.247051675\) \(a_{18}=+0.240706543\) \(a_{19}=-1.577930627\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.777677250\) \(a_{22}=+1.315650273\) \(a_{23}=-0.260886212\) \(a_{24}=-0.409330316\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.769603054\) \(a_{27}=+0.763647026\) \(a_{28}=+0.335853976\) \(a_{29}=+0.241284454\) \(a_{30}=-0.366116164\)
\(a_{31}=+1.584391473\) \(a_{32}=+0.176776695\) \(a_{33}=-2.154142167\) \(a_{34}=-0.881798696\) \(a_{35}=+0.300396929\)
\(a_{36}=+0.170205229\) \(a_{37}=-0.937306825\) \(a_{38}=-1.115765447\) \(a_{39}=+1.260087444\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.116361084\) \(a_{42}=-0.549900857\) \(a_{43}=+0.526882548\) \(a_{44}=+0.930305230\) \(a_{45}=+0.152236185\)
\(a_{46}=-0.184474409\) \(a_{47}=+0.489511001\) \(a_{48}=-0.289440242\) \(a_{49}=-0.548808426\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.443787754\) \(a_{52}=-0.544191539\) \(a_{53}=+1.866570306\) \(a_{54}=+0.539979991\) \(a_{55}=+0.832090294\)
\(a_{56}=+0.237484624\) \(a_{57}=+1.826866490\) \(a_{58}=+0.170613874\) \(a_{59}=-0.619919594\) \(a_{60}=-0.258883223\)
\(a_{61}=-1.580906329\) \(a_{62}=+1.120333955\) \(a_{63}=+0.228656412\) \(a_{64}=+0.125000000\) \(a_{65}=-0.486739709\)
\(a_{66}=-1.523208534\) \(a_{67}=+0.347856722\) \(a_{68}=-0.623525837\) \(a_{69}=+0.302043873\) \(a_{70}=+0.212412705\)
\(a_{71}=-0.376585848\) \(a_{72}=+0.120353272\) \(a_{73}=+0.240761625\) \(a_{74}=-0.662776012\) \(a_{75}=-0.231552194\)
\(a_{76}=-0.788965314\) \(a_{77}=+1.249786843\) \(a_{78}=+0.891016377\) \(a_{79}=-0.384208182\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.224531178\) \(a_{82}=-0.789386493\) \(a_{83}=-0.139218818\) \(a_{84}=-0.388838625\) \(a_{85}=-0.557698463\)
\(a_{86}=+0.372562223\) \(a_{87}=-0.279349723\) \(a_{88}=+0.657825137\) \(a_{89}=+0.071016062\) \(a_{90}=+0.107647239\)
\(a_{91}=-0.731075569\) \(a_{92}=-0.130443106\) \(a_{93}=-1.834346605\) \(a_{94}=+0.346136548\) \(a_{95}=-0.705672029\)
\(a_{96}=-0.204665158\) \(a_{97}=-0.739563001\) \(a_{98}=-0.388066160\) \(a_{99}=+0.633371259\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

Rows: Cols: