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: \( 28.7503926305 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.724976045\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.219742259\) \(a_{7}=-1.743768734\) \(a_{8}=-0.353553391\) \(a_{9}=+1.975542356\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.072475230\) \(a_{12}=-0.862488023\) \(a_{13}=-0.204222371\) \(a_{14}=+1.233030696\) \(a_{15}=-0.771432739\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.570379947\) \(a_{18}=-1.396919396\) \(a_{19}=+1.113727742\) \(a_{20}=+0.223606798\)
\(a_{21}=+3.007959294\) \(a_{22}=+0.051247727\) \(a_{23}=-1.475706062\) \(a_{24}=+0.609871129\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.144407023\) \(a_{27}=-1.682787195\) \(a_{28}=-0.871884367\) \(a_{29}=-0.747098064\) \(a_{30}=+0.545485321\)
\(a_{31}=+0.475181173\) \(a_{32}=-0.176776695\) \(a_{33}=+0.125018036\) \(a_{34}=+1.110426310\) \(a_{35}=-0.779837085\)
\(a_{36}=+0.987771178\) \(a_{37}=+1.009449990\) \(a_{38}=-0.787524439\) \(a_{39}=+0.352278698\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.913639029\) \(a_{42}=-2.126948414\) \(a_{43}=+0.817307443\) \(a_{44}=-0.036237615\) \(a_{45}=+0.883489400\)
\(a_{46}=+1.043481763\) \(a_{47}=-1.164048503\) \(a_{48}=-0.431244011\) \(a_{49}=+2.040729397\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.708867791\) \(a_{52}=-0.102111186\) \(a_{53}=-0.434003038\) \(a_{54}=+1.189910237\) \(a_{55}=-0.032411908\)
\(a_{56}=+0.616515348\) \(a_{57}=-1.921153675\) \(a_{58}=+0.528278107\) \(a_{59}=-1.448947034\) \(a_{60}=-0.385716370\)
\(a_{61}=-0.587437625\) \(a_{62}=-0.336003830\) \(a_{63}=-3.444888992\) \(a_{64}=+0.125000000\) \(a_{65}=-0.091331021\)
\(a_{66}=-0.088401101\) \(a_{67}=-1.024053039\) \(a_{68}=-0.785189974\) \(a_{69}=+2.545557606\) \(a_{70}=+0.551428091\)
\(a_{71}=-1.149961434\) \(a_{72}=-0.698459698\) \(a_{73}=-0.527991324\) \(a_{74}=-0.713788934\) \(a_{75}=-0.344995209\)
\(a_{76}=+0.556863871\) \(a_{77}=+0.126380041\) \(a_{78}=-0.249098656\) \(a_{79}=-1.367473224\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.927225244\) \(a_{82}=-0.646040353\) \(a_{83}=-0.969861899\) \(a_{84}=+1.503979647\) \(a_{85}=-0.702295263\)
\(a_{86}=-0.577923635\) \(a_{87}=+1.288726263\) \(a_{88}=+0.025623863\) \(a_{89}=-1.218302166\) \(a_{90}=-0.624721346\)
\(a_{91}=+0.356116585\) \(a_{92}=-0.737853031\) \(a_{93}=-0.819676140\) \(a_{94}=+0.823106590\) \(a_{95}=+0.498074188\)
\(a_{96}=+0.304935565\) \(a_{97}=+0.931587770\) \(a_{98}=-1.443013595\) \(a_{99}=-0.143177887\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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