Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 24.5205749989 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.307644007\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.217537164\) \(a_{7}=+1.297139422\) \(a_{8}=+0.353553391\) \(a_{9}=-0.905355165\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.265655220\) \(a_{12}=+0.153822004\) \(a_{13}=+0.314872980\) \(a_{14}=+0.917216081\) \(a_{15}=+0.137582583\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.868102028\) \(a_{18}=-0.640182776\) \(a_{19}=-1.490637936\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.399057169\) \(a_{22}=-0.894953389\) \(a_{23}=-1.151842851\) \(a_{24}=+0.108768582\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.222648819\) \(a_{27}=-0.586171098\) \(a_{28}=+0.648569711\) \(a_{29}=-1.069605235\) \(a_{30}=+0.097285577\)
\(a_{31}=-1.488377447\) \(a_{32}=+0.176776695\) \(a_{33}=-0.389371243\) \(a_{34}=+0.613840830\) \(a_{35}=+0.580098385\)
\(a_{36}=-0.452677582\) \(a_{37}=+0.257724390\) \(a_{38}=-1.054040193\) \(a_{39}=+0.096868785\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.102199609\) \(a_{42}=+0.282176031\) \(a_{43}=-1.304451382\) \(a_{44}=-0.632827610\) \(a_{45}=-0.404887138\)
\(a_{46}=-0.814475891\) \(a_{47}=+0.505493829\) \(a_{48}=+0.076911002\) \(a_{49}=+0.682570679\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.267066386\) \(a_{52}=+0.157436490\) \(a_{53}=+1.526317168\) \(a_{54}=-0.414485558\) \(a_{55}=-0.566018222\)
\(a_{56}=+0.458608041\) \(a_{57}=-0.458585828\) \(a_{58}=-0.756325115\) \(a_{59}=-1.464822104\) \(a_{60}=+0.068791291\)
\(a_{61}=+1.660794204\) \(a_{62}=-1.052441786\) \(a_{63}=-1.174371875\) \(a_{64}=+0.125000000\) \(a_{65}=+0.140815478\)
\(a_{66}=-0.275327047\) \(a_{67}=-0.113102814\) \(a_{68}=+0.434051014\) \(a_{69}=-0.354357550\) \(a_{70}=+0.410191502\)
\(a_{71}=-0.299937068\) \(a_{72}=-0.320091388\) \(a_{73}=+0.136383461\) \(a_{74}=+0.182238664\) \(a_{75}=+0.061528801\)
\(a_{76}=-0.745318968\) \(a_{77}=-1.641731280\) \(a_{78}=+0.068496575\) \(a_{79}=+0.193122744\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.725023140\) \(a_{82}=-0.072266036\) \(a_{83}=-1.997945183\) \(a_{84}=+0.199528585\) \(a_{85}=+0.388227029\)
\(a_{86}=-0.922386418\) \(a_{87}=-0.329057641\) \(a_{88}=-0.447476694\) \(a_{89}=+0.043827246\) \(a_{90}=-0.286298441\)
\(a_{91}=+0.408434155\) \(a_{92}=-0.575921425\) \(a_{93}=-0.457890402\) \(a_{94}=+0.357438114\) \(a_{95}=-0.666633551\)
\(a_{96}=+0.054384291\) \(a_{97}=+0.843933276\) \(a_{98}=+0.482650356\) \(a_{99}=+1.145867490\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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