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: \( 24.7649515125 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.862315621\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.609749223\) \(a_{7}=-1.635497425\) \(a_{8}=-0.353553391\) \(a_{9}=-0.256411770\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.749333396\) \(a_{12}=+0.431157810\) \(a_{13}=-1.174847409\) \(a_{14}=+1.156471320\) \(a_{15}=+0.385639269\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.135408852\) \(a_{18}=+0.181310501\) \(a_{19}=-0.849114014\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.410314977\) \(a_{22}=-0.529858726\) \(a_{23}=-1.579316320\) \(a_{24}=-0.304874611\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.830742570\) \(a_{27}=-1.083423496\) \(a_{28}=-0.817748713\) \(a_{29}=+1.407067685\) \(a_{30}=-0.272688142\)
\(a_{31}=+0.073637642\) \(a_{32}=-0.176776695\) \(a_{33}=+0.646161893\) \(a_{34}=+0.802855299\) \(a_{35}=-0.731416684\)
\(a_{36}=-0.128205885\) \(a_{37}=+0.384217303\) \(a_{38}=+0.600414277\) \(a_{39}=-1.013089273\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.042421189\) \(a_{42}=+0.997243284\) \(a_{43}=-1.275362147\) \(a_{44}=+0.374666698\) \(a_{45}=-0.114670830\)
\(a_{46}=+1.116745279\) \(a_{47}=+0.658272606\) \(a_{48}=+0.215578905\) \(a_{49}=+1.674851828\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.979080789\) \(a_{52}=-0.587423704\) \(a_{53}=+1.029636059\) \(a_{54}=+0.766096101\) \(a_{55}=+0.335112082\)
\(a_{56}=+0.578235660\) \(a_{57}=-0.732204278\) \(a_{58}=-0.994947102\) \(a_{59}=+1.290567871\) \(a_{60}=+0.192819635\)
\(a_{61}=+1.386540971\) \(a_{62}=-0.052069676\) \(a_{63}=+0.419360790\) \(a_{64}=+0.125000000\) \(a_{65}=-0.525407734\)
\(a_{66}=-0.456905456\) \(a_{67}=-1.419509196\) \(a_{68}=-0.567704426\) \(a_{69}=-1.361869133\) \(a_{70}=+0.517189697\)
\(a_{71}=-0.877981269\) \(a_{72}=+0.090655251\) \(a_{73}=+0.069536583\) \(a_{74}=-0.271682660\) \(a_{75}=+0.172463124\)
\(a_{76}=-0.424557007\) \(a_{77}=-1.225532840\) \(a_{78}=+0.716362295\) \(a_{79}=+0.297628383\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.677841234\) \(a_{82}=-0.737103092\) \(a_{83}=+0.267154531\) \(a_{84}=-0.705157489\) \(a_{85}=-0.507770275\)
\(a_{86}=+0.901817222\) \(a_{87}=+1.213336444\) \(a_{88}=-0.264929363\) \(a_{89}=+0.997009681\) \(a_{90}=+0.081084521\)
\(a_{91}=+1.921459912\) \(a_{92}=-0.789658160\) \(a_{93}=+0.063498889\) \(a_{94}=-0.465469024\) \(a_{95}=-0.379735331\)
\(a_{96}=-0.152437306\) \(a_{97}=-0.927371614\) \(a_{98}=-1.184299085\) \(a_{99}=-0.192137903\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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