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: \( 7.34617187347 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.837394968\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.299234442\) \(a_{7}=+0.093895882\) \(a_{8}=-0.353553391\) \(a_{9}=+2.376020268\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.998431122\) \(a_{12}=+0.918697484\) \(a_{13}=+1.068928144\) \(a_{14}=-0.066394415\) \(a_{15}=+0.821708010\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.547579042\) \(a_{18}=-1.680100044\) \(a_{19}=-0.439384659\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.172523822\) \(a_{22}=+0.705997417\) \(a_{23}=-0.265674490\) \(a_{24}=-0.649617221\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.755846339\) \(a_{27}=+2.528292717\) \(a_{28}=+0.046947941\) \(a_{29}=+0.021062094\) \(a_{30}=-0.581035306\)
\(a_{31}=+0.266709983\) \(a_{32}=-0.176776695\) \(a_{33}=-1.834512319\) \(a_{34}=-1.094303635\) \(a_{35}=+0.041991515\)
\(a_{36}=+1.188010134\) \(a_{37}=+0.234065550\) \(a_{38}=+0.310691872\) \(a_{39}=+1.964043192\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.768301796\) \(a_{42}=-0.121992764\) \(a_{43}=-0.450691833\) \(a_{44}=-0.499215561\) \(a_{45}=+1.062588567\)
\(a_{46}=+0.187860233\) \(a_{47}=-1.436095557\) \(a_{48}=+0.459348742\) \(a_{49}=-0.991183563\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.843513944\) \(a_{52}=+0.534464072\) \(a_{53}=-0.970514144\) \(a_{54}=-1.787772925\) \(a_{55}=-0.446511972\)
\(a_{56}=-0.033197208\) \(a_{57}=-0.807323162\) \(a_{58}=-0.014893150\) \(a_{59}=+0.911335472\) \(a_{60}=+0.410854005\)
\(a_{61}=+1.120710589\) \(a_{62}=-0.188592438\) \(a_{63}=+0.223098520\) \(a_{64}=+0.125000000\) \(a_{65}=+0.478039198\)
\(a_{66}=+1.297196101\) \(a_{67}=-1.300954352\) \(a_{68}=+0.773789521\) \(a_{69}=-0.488148971\) \(a_{70}=-0.029692485\)
\(a_{71}=-1.579023410\) \(a_{72}=-0.840050022\) \(a_{73}=+0.063984230\) \(a_{74}=-0.165509337\) \(a_{75}=+0.367478994\)
\(a_{76}=-0.219692330\) \(a_{77}=-0.093748571\) \(a_{78}=-1.388788260\) \(a_{79}=+0.592925300\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.269452047\) \(a_{82}=+0.543271410\) \(a_{83}=-1.215801480\) \(a_{84}=+0.086261911\) \(a_{85}=+0.692098388\)
\(a_{86}=+0.318687251\) \(a_{87}=+0.038699386\) \(a_{88}=+0.352998708\) \(a_{89}=-0.690510600\) \(a_{90}=-0.751363581\)
\(a_{91}=+0.100367951\) \(a_{92}=-0.132837245\) \(a_{93}=+0.490051581\) \(a_{94}=+1.015472907\) \(a_{95}=-0.196498793\)
\(a_{96}=-0.324808610\) \(a_{97}=+0.965361997\) \(a_{98}=+0.700872619\) \(a_{99}=-2.372292582\) \(a_{100}=+0.099975586\)

Showing 100 of 136 available coefficients

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