Properties

Level $70$
Weight $0$
Character 70.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( 0 \)
Character: 70.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.98650522948 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.782187724\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.260197025\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+2.176193082\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.127418827\) \(a_{12}=+0.891093862\) \(a_{13}=-1.133759791\) \(a_{14}=+0.267261242\) \(a_{15}=-0.797018580\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.363520428\) \(a_{18}=-1.538800885\) \(a_{19}=+1.034989761\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.673603644\) \(a_{22}=-0.797205498\) \(a_{23}=+1.088945081\) \(a_{24}=-0.630098512\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.801689237\) \(a_{27}=+2.096196871\) \(a_{28}=-0.188982237\) \(a_{29}=-0.949203661\) \(a_{30}=+0.563577242\)
\(a_{31}=+1.131002631\) \(a_{32}=-0.176776695\) \(a_{33}=+2.009271993\) \(a_{34}=-0.964154541\) \(a_{35}=+0.169030851\)
\(a_{36}=+1.088096541\) \(a_{37}=+1.078582768\) \(a_{38}=-0.731848279\) \(a_{39}=-2.020572781\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.243805448\) \(a_{42}=+0.476309704\) \(a_{43}=-0.423674238\) \(a_{44}=+0.563709414\) \(a_{45}=-0.973223133\)
\(a_{46}=-0.770000451\) \(a_{47}=-1.748789968\) \(a_{48}=+0.445546931\) \(a_{49}=+0.142857143\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.430049367\) \(a_{52}=-0.566879896\) \(a_{53}=+0.059433286\) \(a_{54}=-1.482235022\) \(a_{55}=-0.504197027\)
\(a_{56}=+0.133630621\) \(a_{57}=+1.844546047\) \(a_{58}=+0.671188345\) \(a_{59}=-0.444629421\) \(a_{60}=-0.398509290\)
\(a_{61}=+0.331251690\) \(a_{62}=-0.799739630\) \(a_{63}=-0.822523671\) \(a_{64}=+0.125000000\) \(a_{65}=+0.507032793\)
\(a_{66}=-1.420769852\) \(a_{67}=+1.348624440\) \(a_{68}=+0.681760214\) \(a_{69}=+1.940704554\) \(a_{70}=-0.119522861\)
\(a_{71}=-0.668952308\) \(a_{72}=-0.769400443\) \(a_{73}=-0.580866288\) \(a_{74}=-0.762673190\) \(a_{75}=+0.356437545\)
\(a_{76}=+0.517494881\) \(a_{77}=-0.426124263\) \(a_{78}=+1.428760716\) \(a_{79}=-1.861199633\) \(a_{80}=-0.111803399\)
\(a_{81}=+1.559623248\) \(a_{82}=-0.879503267\) \(a_{83}=-0.505676185\) \(a_{84}=-0.336801822\) \(a_{85}=-0.609784873\)
\(a_{86}=+0.299582927\) \(a_{87}=-1.691659112\) \(a_{88}=-0.398602749\) \(a_{89}=+0.713941130\) \(a_{90}=+0.688172677\)
\(a_{91}=+0.428520922\) \(a_{92}=+0.544472540\) \(a_{93}=+2.015659005\) \(a_{94}=+1.236581245\) \(a_{95}=-0.462861492\)
\(a_{96}=-0.315049256\) \(a_{97}=-0.286829017\) \(a_{98}=-0.101015254\) \(a_{99}=+2.453481052\) \(a_{100}=+0.099975586\)

Showing 100 of 1300 available coefficients

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