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: \( 26.671211243 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.065480741\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.753408657\) \(a_{7}=-1.516246480\) \(a_{8}=-0.353553391\) \(a_{9}=+0.135249210\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.035386170\) \(a_{12}=+0.532740371\) \(a_{13}=+1.155845690\) \(a_{14}=+1.072148168\) \(a_{15}=+0.476497473\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.097780550\) \(a_{18}=-0.095635634\) \(a_{19}=+1.694079684\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.615531424\) \(a_{22}=-0.732128582\) \(a_{23}=-0.323893237\) \(a_{24}=-0.376704329\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.817306325\) \(a_{27}=-0.921375313\) \(a_{28}=-0.758123240\) \(a_{29}=-1.303730048\) \(a_{30}=-0.336934595\)
\(a_{31}=+0.893858891\) \(a_{32}=-0.176776695\) \(a_{33}=+1.103184024\) \(a_{34}=-0.069141290\) \(a_{35}=-0.678086040\)
\(a_{36}=+0.067624605\) \(a_{37}=+1.047506226\) \(a_{38}=-1.197895232\) \(a_{39}=+1.231531322\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.255700657\) \(a_{42}=+1.142353225\) \(a_{43}=+0.093383324\) \(a_{44}=+0.517693085\) \(a_{45}=+0.060485286\)
\(a_{46}=+0.229027104\) \(a_{47}=-1.175424689\) \(a_{48}=+0.266370185\) \(a_{49}=+1.299003389\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.104183293\) \(a_{52}=+0.577922845\) \(a_{53}=-1.302010012\) \(a_{54}=+0.651510732\) \(a_{55}=+0.463038772\)
\(a_{56}=+0.536074084\) \(a_{57}=+1.805009277\) \(a_{58}=+0.921876358\) \(a_{59}=+1.160238005\) \(a_{60}=+0.238248737\)
\(a_{61}=-0.616580877\) \(a_{62}=-0.632053683\) \(a_{63}=-0.205071139\) \(a_{64}=+0.125000000\) \(a_{65}=+0.516909907\)
\(a_{66}=-0.780068904\) \(a_{67}=+1.310186549\) \(a_{68}=+0.048890275\) \(a_{69}=-0.345102006\) \(a_{70}=+0.479479237\)
\(a_{71}=+1.638017239\) \(a_{72}=-0.047817817\) \(a_{73}=-0.350289583\) \(a_{74}=-0.740698755\) \(a_{75}=+0.213096148\)
\(a_{76}=+0.847039842\) \(a_{77}=-1.569900636\) \(a_{78}=-0.870824149\) \(a_{79}=+0.180580865\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.116956861\) \(a_{82}=+0.887914450\) \(a_{83}=+0.321203148\) \(a_{84}=-0.807765712\) \(a_{85}=+0.043728791\)
\(a_{86}=-0.066031981\) \(a_{87}=-1.389099258\) \(a_{88}=-0.366064291\) \(a_{89}=-1.157368280\) \(a_{90}=-0.042769556\)
\(a_{91}=-1.752546959\) \(a_{92}=-0.161946618\) \(a_{93}=+0.952389433\) \(a_{94}=+0.831150769\) \(a_{95}=+0.757615466\)
\(a_{96}=-0.188352164\) \(a_{97}=-0.818049094\) \(a_{98}=-0.918534105\) \(a_{99}=+0.140035162\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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