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: \( 6.99327291741 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.518345577\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=+1.073632453\) \(a_{7}=-0.624319743\) \(a_{8}=+0.353553391\) \(a_{9}=+1.305373290\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.596496810\) \(a_{12}=+0.759172788\) \(a_{13}=-1.289415233\) \(a_{14}=-0.441460724\) \(a_{15}=+0.679024785\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.888406269\) \(a_{18}=+0.923038306\) \(a_{19}=-0.937993232\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.947933120\) \(a_{22}=+1.128893721\) \(a_{23}=-0.576961704\) \(a_{24}=+0.536816227\) \(a_{25}=+0.200000000\)
\(a_{26}=-0.911754255\) \(a_{27}=+0.463662185\) \(a_{28}=-0.312159871\) \(a_{29}=-0.693614104\) \(a_{30}=+0.480143030\)
\(a_{31}=-1.052641752\) \(a_{32}=+0.176776694\) \(a_{33}=+2.424033867\) \(a_{34}=+0.628198099\) \(a_{35}=-0.279204270\)
\(a_{36}=+0.652686644\) \(a_{37}=-1.073363071\) \(a_{38}=-0.663261375\) \(a_{39}=-1.957777794\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.640924160\) \(a_{42}=-0.670289937\) \(a_{43}=-0.976465077\) \(a_{44}=+0.798248405\) \(a_{45}=+0.583780683\)
\(a_{46}=-0.407973533\) \(a_{47}=+0.243644351\) \(a_{48}=+0.379586394\) \(a_{49}=-0.610224858\) \(a_{50}=+0.141421357\)
\(a_{51}=+1.348907728\) \(a_{52}=-0.644707616\) \(a_{53}=+0.467902591\) \(a_{54}=+0.327858675\) \(a_{55}=+0.713975080\)
\(a_{56}=-0.220730362\) \(a_{57}=-1.424197874\) \(a_{58}=-0.490459238\) \(a_{59}=-0.278626607\) \(a_{60}=+0.339512396\)
\(a_{61}=+0.056335367\) \(a_{62}=-0.744330121\) \(a_{63}=-0.814970320\) \(a_{64}=+0.125000004\) \(a_{65}=-0.576644017\)
\(a_{66}=+1.714050772\) \(a_{67}=+0.076801650\) \(a_{68}=+0.444203128\) \(a_{69}=-0.876027260\) \(a_{70}=-0.197427199\)
\(a_{71}=+1.477895510\) \(a_{72}=+0.461519194\) \(a_{73}=+1.488386034\) \(a_{74}=-0.758982249\) \(a_{75}=+0.303669213\)
\(a_{76}=-0.468996617\) \(a_{77}=-0.996724478\) \(a_{78}=-1.384358040\) \(a_{79}=+0.180771775\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.601373863\) \(a_{82}=+1.160308602\) \(a_{83}=+0.775142718\) \(a_{84}=-0.473966561\) \(a_{85}=+0.397307359\)
\(a_{86}=-0.690465079\) \(a_{87}=-1.053145901\) \(a_{88}=+0.564446860\) \(a_{89}=+0.007113582\) \(a_{90}=+0.412795276\)
\(a_{91}=+0.805007386\) \(a_{92}=-0.288480848\) \(a_{93}=-1.598273963\) \(a_{94}=+0.172282576\) \(a_{95}=-0.419483324\)
\(a_{96}=+0.268408115\) \(a_{97}=-0.844255010\) \(a_{98}=-0.431494158\) \(a_{99}=+2.084024292\) \(a_{100}=+0.099999979\)

Showing 100 of 2000 available coefficients

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