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: \( 19.1674767534 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.102003939\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.779234459\) \(a_{7}=-0.528289597\) \(a_{8}=+0.353553391\) \(a_{9}=+0.214412683\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.216692743\) \(a_{12}=+0.551001970\) \(a_{13}=-0.217811952\) \(a_{14}=-0.373557156\) \(a_{15}=-0.492831144\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.165945379\) \(a_{18}=+0.151612662\) \(a_{19}=+1.329556327\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.582177217\) \(a_{22}=-0.153224908\) \(a_{23}=-1.328768311\) \(a_{24}=+0.389617229\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.154016308\) \(a_{27}=-0.865720319\) \(a_{28}=-0.264144798\) \(a_{29}=-0.644519343\) \(a_{30}=-0.348484244\)
\(a_{31}=-0.664714029\) \(a_{32}=+0.176776695\) \(a_{33}=-0.238796256\) \(a_{34}=-0.117341103\) \(a_{35}=+0.236258290\)
\(a_{36}=+0.107206341\) \(a_{37}=-1.008226440\) \(a_{38}=+0.940138294\) \(a_{39}=-0.240029629\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.912519403\) \(a_{42}=-0.411661458\) \(a_{43}=-1.213931587\) \(a_{44}=-0.108346371\) \(a_{45}=-0.095888267\)
\(a_{46}=-0.939581083\) \(a_{47}=+0.086433663\) \(a_{48}=+0.275500985\) \(a_{49}=-0.720910102\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.182872461\) \(a_{52}=-0.108905976\) \(a_{53}=-0.464373346\) \(a_{54}=-0.612156708\) \(a_{55}=+0.096907941\)
\(a_{56}=-0.186778578\) \(a_{57}=+1.465176310\) \(a_{58}=-0.455743998\) \(a_{59}=+1.900718430\) \(a_{60}=-0.246415572\)
\(a_{61}=+1.753473755\) \(a_{62}=-0.470023798\) \(a_{63}=-0.113271990\) \(a_{64}=+0.125000000\) \(a_{65}=+0.097408466\)
\(a_{66}=-0.168854452\) \(a_{67}=-1.068220762\) \(a_{68}=-0.082972689\) \(a_{69}=-1.464307913\) \(a_{70}=+0.167059839\)
\(a_{71}=+0.727487821\) \(a_{72}=+0.075806331\) \(a_{73}=-0.358233791\) \(a_{74}=-0.712923753\) \(a_{75}=+0.220400788\)
\(a_{76}=+0.664778163\) \(a_{77}=+0.114476522\) \(a_{78}=-0.169726578\) \(a_{79}=-1.300883805\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.168439884\) \(a_{82}=-0.645248658\) \(a_{83}=-1.308401684\) \(a_{84}=-0.291088608\) \(a_{85}=+0.074213030\)
\(a_{86}=-0.858379257\) \(a_{87}=-0.710262855\) \(a_{88}=-0.076612454\) \(a_{89}=+0.606305123\) \(a_{90}=-0.067803244\)
\(a_{91}=+0.115067788\) \(a_{92}=-0.664384155\) \(a_{93}=-0.732517478\) \(a_{94}=+0.061117829\) \(a_{95}=-0.594595665\)
\(a_{96}=+0.194808615\) \(a_{97}=-0.651510786\) \(a_{98}=-0.509760422\) \(a_{99}=-0.046461673\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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