Properties

Level $69$
Weight $0$
Character 69.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 69 = 3 \cdot 23 \)
Weight: \( 0 \)
Character: 69.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.4907717072 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.028848227\) \(a_{3}=-0.577350269\) \(a_{4}=+0.058528674\) \(a_{5}=+0.119118666\)
\(a_{6}=-0.594005801\) \(a_{7}=+1.090193183\) \(a_{8}=-0.968631105\) \(a_{9}=+0.333333333\) \(a_{10}=+0.122555028\)
\(a_{11}=+0.986454459\) \(a_{12}=-0.033791546\) \(a_{13}=+0.055806618\) \(a_{14}=+1.121643323\) \(a_{15}=-0.068773194\)
\(a_{16}=-1.055103068\) \(a_{17}=+0.833528939\) \(a_{18}=+0.342949409\) \(a_{19}=-0.673523680\) \(a_{20}=+0.006971858\)
\(a_{21}=-0.629423328\) \(a_{22}=+1.014911921\) \(a_{23}=-0.208514414\) \(a_{24}=+0.559239429\) \(a_{25}=-0.985810743\)
\(a_{26}=+0.057416540\) \(a_{27}=-0.192450090\) \(a_{28}=+0.063807561\) \(a_{29}=+1.164175592\) \(a_{30}=-0.070757178\)
\(a_{31}=-0.890518608\) \(a_{32}=-0.116909816\) \(a_{33}=-0.569529747\) \(a_{34}=+0.857574771\) \(a_{35}=+0.129862357\)
\(a_{36}=+0.019509558\) \(a_{37}=+0.967739515\) \(a_{38}=-0.692953644\) \(a_{39}=-0.032219966\) \(a_{40}=-0.115382045\)
\(a_{41}=+1.118930680\) \(a_{42}=-0.647581074\) \(a_{43}=-1.411872710\) \(a_{44}=+0.057735871\) \(a_{45}=+0.039706222\)
\(a_{46}=-0.214529685\) \(a_{47}=-1.055100369\) \(a_{48}=+0.609164040\) \(a_{49}=+0.188521176\) \(a_{50}=-1.014249635\)
\(a_{51}=-0.481238157\) \(a_{52}=+0.003266287\) \(a_{53}=-1.398256115\) \(a_{54}=-0.198001934\) \(a_{55}=+0.117505139\)
\(a_{56}=-1.055995027\) \(a_{57}=+0.388859078\) \(a_{58}=+1.197759993\) \(a_{59}=+1.918470100\) \(a_{60}=-0.004025204\)
\(a_{61}=+1.673513849\) \(a_{62}=-0.916208491\) \(a_{63}=+0.363397728\) \(a_{64}=+0.934820611\) \(a_{65}=+0.006647610\)
\(a_{66}=-0.585959671\) \(a_{67}=+0.140237357\) \(a_{68}=+0.048785343\) \(a_{69}=+0.120385853\) \(a_{70}=+0.133608656\)
\(a_{71}=-0.279491018\) \(a_{72}=-0.322877035\) \(a_{73}=+0.523548999\) \(a_{74}=+0.995657084\) \(a_{75}=+0.569158098\)
\(a_{76}=-0.039420448\) \(a_{77}=+1.075425926\) \(a_{78}=-0.033149455\) \(a_{79}=-1.436007451\) \(a_{80}=-0.125682470\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.151209846\) \(a_{83}=+1.690637957\) \(a_{84}=-0.036839313\) \(a_{85}=+0.099288855\)
\(a_{86}=-1.452602734\) \(a_{87}=-0.672137091\) \(a_{88}=-0.955510472\) \(a_{89}=+0.457272787\) \(a_{90}=+0.040851676\)
\(a_{91}=+0.060839995\) \(a_{92}=-0.012204072\) \(a_{93}=+0.514141158\) \(a_{94}=-1.085538144\) \(a_{95}=-0.080229242\)
\(a_{96}=+0.067497914\) \(a_{97}=-0.784405155\) \(a_{98}=+0.193959677\) \(a_{99}=+0.328818153\) \(a_{100}=-0.057698195\)

Showing 100 of 556 available coefficients

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