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: \( 25.2347442706 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.098430564\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.069600919\) \(a_{7}=-1.245260930\) \(a_{8}=-0.353553391\) \(a_{9}=-0.990311424\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.167556540\) \(a_{12}=-0.049215282\) \(a_{13}=+0.371141815\) \(a_{14}=+0.880532448\) \(a_{15}=-0.044019487\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.387856699\) \(a_{18}=+0.700255923\) \(a_{19}=+1.093450136\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.122571736\) \(a_{22}=+0.825587147\) \(a_{23}=+0.896104448\) \(a_{24}=+0.034800460\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.262436894\) \(a_{27}=+0.195907477\) \(a_{28}=-0.622630465\) \(a_{29}=+0.089785225\) \(a_{30}=+0.031126477\)
\(a_{31}=+0.455674594\) \(a_{32}=-0.176776695\) \(a_{33}=+0.114923249\) \(a_{34}=-0.274256102\) \(a_{35}=-0.556897618\)
\(a_{36}=-0.495155712\) \(a_{37}=-0.812384049\) \(a_{38}=-0.773186006\) \(a_{39}=-0.036531698\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.272370301\) \(a_{42}=-0.086671306\) \(a_{43}=+0.762557800\) \(a_{44}=-0.583778270\) \(a_{45}=-0.442880733\)
\(a_{46}=-0.633641532\) \(a_{47}=+0.094830286\) \(a_{48}=-0.024607641\) \(a_{49}=+0.550674784\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.038176954\) \(a_{52}=+0.185570907\) \(a_{53}=+0.285193362\) \(a_{54}=-0.138527505\) \(a_{55}=-0.522147158\)
\(a_{56}=+0.440266224\) \(a_{57}=-0.107628914\) \(a_{58}=-0.063487741\) \(a_{59}=-1.401253022\) \(a_{60}=-0.022009743\)
\(a_{61}=+0.455205797\) \(a_{62}=-0.322210595\) \(a_{63}=+1.233196125\) \(a_{64}=+0.125000000\) \(a_{65}=+0.165979665\)
\(a_{66}=-0.081263009\) \(a_{67}=-1.668675254\) \(a_{68}=+0.193928350\) \(a_{69}=-0.088204066\) \(a_{70}=+0.393786082\)
\(a_{71}=+1.654583834\) \(a_{72}=+0.350127962\) \(a_{73}=-0.089966362\) \(a_{74}=+0.574442270\) \(a_{75}=-0.019686113\)
\(a_{76}=+0.546725068\) \(a_{77}=+1.453912543\) \(a_{78}=+0.025831812\) \(a_{79}=+1.607442707\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.971028141\) \(a_{82}=-0.899701668\) \(a_{83}=-1.666882486\) \(a_{84}=+0.061285868\) \(a_{85}=+0.173454789\)
\(a_{86}=-0.539209792\) \(a_{87}=-0.008837610\) \(a_{88}=+0.412793573\) \(a_{89}=-0.637358757\) \(a_{90}=+0.313163969\)
\(a_{91}=-0.462168402\) \(a_{92}=+0.448052224\) \(a_{93}=-0.044852307\) \(a_{94}=-0.067055138\) \(a_{95}=+0.489005767\)
\(a_{96}=+0.017400230\) \(a_{97}=-1.027196905\) \(a_{98}=-0.389385874\) \(a_{99}=+1.156244579\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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