Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 14.2889756764 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.524966100\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.078313870\) \(a_{7}=-1.518993009\) \(a_{8}=+0.353553391\) \(a_{9}=+1.325521606\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.926068865\) \(a_{12}=+0.762483050\) \(a_{13}=-0.941576124\) \(a_{14}=-1.074090257\) \(a_{15}=-0.681985573\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.806468489\) \(a_{18}=+0.937285317\) \(a_{19}=-0.930661903\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.316412844\) \(a_{22}=-0.654829575\) \(a_{23}=-0.670638832\) \(a_{24}=+0.539156935\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.665794862\) \(a_{27}=+0.496409415\) \(a_{28}=-0.759496504\) \(a_{29}=+1.379714834\) \(a_{30}=-0.482236623\)
\(a_{31}=+0.963770806\) \(a_{32}=+0.176776695\) \(a_{33}=-1.412223626\) \(a_{34}=-0.570259338\) \(a_{35}=+0.679314325\)
\(a_{36}=+0.662760803\) \(a_{37}=+0.620019665\) \(a_{38}=-0.658077342\) \(a_{39}=-1.435871670\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.574165051\) \(a_{42}=-1.637951230\) \(a_{43}=-1.769246360\) \(a_{44}=-0.463034433\) \(a_{45}=-0.592791284\)
\(a_{46}=-0.474213266\) \(a_{47}=-1.018376440\) \(a_{48}=+0.381241525\) \(a_{49}=+1.307339760\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.229837107\) \(a_{52}=-0.470788062\) \(a_{53}=-0.966923181\) \(a_{54}=+0.351014463\) \(a_{55}=+0.414150587\)
\(a_{56}=-0.537045128\) \(a_{57}=-1.419227852\) \(a_{58}=+0.975605715\) \(a_{59}=-1.325170167\) \(a_{60}=-0.340992786\)
\(a_{61}=+1.461249324\) \(a_{62}=+0.681488872\) \(a_{63}=-2.013458053\) \(a_{64}=+0.125000000\) \(a_{65}=+0.421085644\)
\(a_{66}=-0.998592903\) \(a_{67}=+0.875321535\) \(a_{68}=-0.403234245\) \(a_{69}=-1.022701484\) \(a_{70}=+0.480347766\)
\(a_{71}=+0.745098081\) \(a_{72}=+0.468642658\) \(a_{73}=-0.137900674\) \(a_{74}=+0.438420109\) \(a_{75}=+0.304993220\)
\(a_{76}=-0.465330951\) \(a_{77}=+1.406692132\) \(a_{78}=-1.015314595\) \(a_{79}=-1.174931225\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.568514078\) \(a_{82}=+1.113102782\) \(a_{83}=-1.326394092\) \(a_{84}=-1.158206422\) \(a_{85}=+0.360663673\)
\(a_{86}=-1.251046099\) \(a_{87}=+2.104018349\) \(a_{88}=-0.327414787\) \(a_{89}=+0.947336531\) \(a_{90}=-0.419166736\)
\(a_{91}=+1.430247548\) \(a_{92}=-0.335319416\) \(a_{93}=+1.469717803\) \(a_{94}=-0.720100887\) \(a_{95}=+0.416204656\)
\(a_{96}=+0.269578468\) \(a_{97}=-0.713847901\) \(a_{98}=+0.924428810\) \(a_{99}=-1.227524261\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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