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: \( 23.6301398227 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.536438016\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.086425740\) \(a_{7}=-1.607143809\) \(a_{8}=-0.353553391\) \(a_{9}=+1.360641777\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.774488593\) \(a_{12}=+0.768219008\) \(a_{13}=+0.395386063\) \(a_{14}=+1.136422286\) \(a_{15}=-0.687115969\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.590866845\) \(a_{18}=-0.962119028\) \(a_{19}=-0.609504646\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.469276846\) \(a_{22}=+1.254752917\) \(a_{23}=-1.909570455\) \(a_{24}=-0.543212870\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.279580166\) \(a_{27}=+0.554103737\) \(a_{28}=-0.803571905\) \(a_{29}=-1.040599005\) \(a_{30}=+0.485864361\)
\(a_{31}=+1.788556732\) \(a_{32}=-0.176776695\) \(a_{33}=-2.726391734\) \(a_{34}=-0.417805953\) \(a_{35}=+0.718736561\)
\(a_{36}=+0.680320889\) \(a_{37}=+0.454885359\) \(a_{38}=+0.430984868\) \(a_{39}=+0.607486178\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.227705608\) \(a_{42}=+1.746042402\) \(a_{43}=+0.998952824\) \(a_{44}=-0.887244297\) \(a_{45}=-0.608497501\)
\(a_{46}=+1.350270218\) \(a_{47}=+0.633873559\) \(a_{48}=+0.384109504\) \(a_{49}=+1.582911224\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.907830283\) \(a_{52}=+0.197693031\) \(a_{53}=-0.149703343\) \(a_{54}=-0.391810510\) \(a_{55}=+0.793575424\)
\(a_{56}=+0.568211143\) \(a_{57}=-0.936466108\) \(a_{58}=+0.735814613\) \(a_{59}=-0.760649746\) \(a_{60}=-0.343557985\)
\(a_{61}=+0.788084318\) \(a_{62}=-1.264700594\) \(a_{63}=-2.186747009\) \(a_{64}=+0.125000000\) \(a_{65}=-0.176822023\)
\(a_{66}=+1.927850083\) \(a_{67}=-1.078076323\) \(a_{68}=+0.295433422\) \(a_{69}=-2.933936642\) \(a_{70}=-0.508223496\)
\(a_{71}=+0.666865121\) \(a_{72}=-0.481059514\) \(a_{73}=+0.977784572\) \(a_{74}=-0.321652522\) \(a_{75}=+0.307287603\)
\(a_{76}=-0.304752323\) \(a_{77}=+2.851858357\) \(a_{78}=-0.429557596\) \(a_{79}=+0.447725892\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.509295731\) \(a_{82}=-0.161012180\) \(a_{83}=+0.763392343\) \(a_{84}=-1.234638423\) \(a_{85}=-0.264243686\)
\(a_{86}=-0.706366316\) \(a_{87}=-1.598815870\) \(a_{88}=+0.627376459\) \(a_{89}=+0.226117090\) \(a_{90}=+0.430272710\)
\(a_{91}=-0.635442263\) \(a_{92}=-0.954785228\) \(a_{93}=+2.748006557\) \(a_{94}=-0.448216292\) \(a_{95}=+0.272578764\)
\(a_{96}=-0.271606435\) \(a_{97}=-0.512872281\) \(a_{98}=-1.119287260\) \(a_{99}=-2.414443313\) \(a_{100}=+0.099975586\)

Showing 100 of 218 available coefficients

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