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: \( 21.5655607109 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.788068859\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.557248834\) \(a_{7}=-0.675668959\) \(a_{8}=+0.353553391\) \(a_{9}=-0.378947474\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.811809684\) \(a_{12}=-0.394034429\) \(a_{13}=-0.097716149\) \(a_{14}=-0.477770103\) \(a_{15}=+0.352435108\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.488166280\) \(a_{18}=-0.267956328\) \(a_{19}=-1.794877268\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.532473666\) \(a_{22}=+0.574036133\) \(a_{23}=-1.235382281\) \(a_{24}=-0.278624417\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.069095751\) \(a_{27}=+1.086705562\) \(a_{28}=-0.337834480\) \(a_{29}=+1.341179447\) \(a_{30}=+0.249209255\)
\(a_{31}=-0.785044508\) \(a_{32}=+0.176776695\) \(a_{33}=-0.639761931\) \(a_{34}=-0.345185687\) \(a_{35}=+0.302168345\)
\(a_{36}=-0.189473737\) \(a_{37}=-1.022430841\) \(a_{38}=-1.269169888\) \(a_{39}=+0.077007054\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.068669115\) \(a_{42}=+0.376515740\) \(a_{43}=+1.208159433\) \(a_{44}=+0.405904842\) \(a_{45}=+0.169470462\)
\(a_{46}=-0.873547189\) \(a_{47}=+0.464430226\) \(a_{48}=-0.197017215\) \(a_{49}=-0.543471458\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.384708643\) \(a_{52}=-0.048858074\) \(a_{53}=-0.547859033\) \(a_{54}=+0.768416872\) \(a_{55}=-0.363052328\)
\(a_{56}=-0.238885051\) \(a_{57}=+1.414486880\) \(a_{58}=+0.948357082\) \(a_{59}=+1.352256415\) \(a_{60}=+0.176217554\)
\(a_{61}=+0.312382853\) \(a_{62}=-0.555110295\) \(a_{63}=+0.256043045\) \(a_{64}=+0.125000000\) \(a_{65}=+0.043699990\)
\(a_{66}=-0.452380000\) \(a_{67}=+0.359368660\) \(a_{68}=-0.244083140\) \(a_{69}=+0.973566305\) \(a_{70}=+0.213665285\)
\(a_{71}=-0.027398339\) \(a_{72}=-0.133978164\) \(a_{73}=+0.499460260\) \(a_{74}=-0.722967781\) \(a_{75}=-0.157613772\)
\(a_{76}=-0.897438634\) \(a_{77}=-0.548514604\) \(a_{78}=+0.054452210\) \(a_{79}=-0.999973834\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.477451338\) \(a_{82}=-0.755663178\) \(a_{83}=+0.274878127\) \(a_{84}=+0.266236833\) \(a_{85}=+0.218314597\)
\(a_{86}=+0.854297728\) \(a_{87}=-1.056941756\) \(a_{88}=+0.287018066\) \(a_{89}=+0.808124802\) \(a_{90}=+0.119833713\)
\(a_{91}=+0.066023769\) \(a_{92}=-0.617691141\) \(a_{93}=+0.618669130\) \(a_{94}=+0.328401762\) \(a_{95}=+0.802693517\)
\(a_{96}=-0.139312209\) \(a_{97}=+1.253833279\) \(a_{98}=-0.384292353\) \(a_{99}=-0.307633229\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

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