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: \( 30.9373388598 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.618422771\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.437290935\) \(a_{7}=-1.250716297\) \(a_{8}=-0.353553391\) \(a_{9}=-0.617553276\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.248280960\) \(a_{12}=-0.309211386\) \(a_{13}=+0.824960885\) \(a_{14}=+0.884389975\) \(a_{15}=+0.276567071\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.168174659\) \(a_{18}=+0.436676109\) \(a_{19}=+1.624442024\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.773471438\) \(a_{22}=-0.882667931\) \(a_{23}=+1.359895077\) \(a_{24}=+0.218645468\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.583335436\) \(a_{27}=+1.000331780\) \(a_{28}=-0.625358148\) \(a_{29}=-1.537757692\) \(a_{30}=-0.195562451\)
\(a_{31}=-0.768370445\) \(a_{32}=-0.176776695\) \(a_{33}=-0.771965370\) \(a_{34}=-0.118917442\) \(a_{35}=+0.559337332\)
\(a_{36}=-0.308776638\) \(a_{37}=+1.064543508\) \(a_{38}=-1.148653971\) \(a_{39}=-0.510174596\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.578969234\) \(a_{42}=-0.546926899\) \(a_{43}=-1.396934061\) \(a_{44}=+0.624140480\) \(a_{45}=+0.276178221\)
\(a_{46}=-0.961591031\) \(a_{47}=-0.870825034\) \(a_{48}=-0.154605693\) \(a_{49}=+0.564291254\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.104003039\) \(a_{52}=+0.412480442\) \(a_{53}=+1.366140727\) \(a_{54}=-0.707341385\) \(a_{55}=-0.558248216\)
\(a_{56}=+0.442194987\) \(a_{57}=-1.004591938\) \(a_{58}=+1.087358892\) \(a_{59}=+0.598702248\) \(a_{60}=+0.138283536\)
\(a_{61}=-0.174336911\) \(a_{62}=+0.543319952\) \(a_{63}=+0.772383946\) \(a_{64}=+0.125000000\) \(a_{65}=-0.368933723\)
\(a_{66}=+0.545861948\) \(a_{67}=+0.691019783\) \(a_{68}=+0.084087330\) \(a_{69}=-0.840990082\) \(a_{70}=-0.395511220\)
\(a_{71}=-1.319640250\) \(a_{72}=+0.218338055\) \(a_{73}=-0.671979152\) \(a_{74}=-0.752745933\) \(a_{75}=-0.123684554\)
\(a_{76}=+0.812221012\) \(a_{77}=-1.561245339\) \(a_{78}=+0.360747917\) \(a_{79}=-0.506489491\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.001074675\) \(a_{82}=-1.116499852\) \(a_{83}=+1.401042200\) \(a_{84}=+0.386735719\) \(a_{85}=-0.075209994\)
\(a_{86}=+0.987781547\) \(a_{87}=+0.950984373\) \(a_{88}=-0.441333966\) \(a_{89}=-0.126964292\) \(a_{90}=-0.195287493\)
\(a_{91}=-1.031792023\) \(a_{92}=+0.679947538\) \(a_{93}=+0.475177780\) \(a_{94}=+0.615766287\) \(a_{95}=-0.726472558\)
\(a_{96}=+0.109322734\) \(a_{97}=-1.377037906\) \(a_{98}=-0.399014173\) \(a_{99}=-0.770879996\) \(a_{100}=+0.099975586\)

Showing 100 of 254 available coefficients

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