Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 9.66612934925 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.468157111\) \(a_{3}=+1.200761714\) \(a_{4}=-0.780828919\) \(a_{5}=-0.223470190\)
\(a_{6}=-0.562145135\) \(a_{7}=+0.377964473\) \(a_{8}=+0.833707722\) \(a_{9}=+0.441828694\) \(a_{10}=+0.104619159\)
\(a_{11}=-0.512855162\) \(a_{12}=-0.937589472\) \(a_{13}=-0.807123628\) \(a_{14}=-0.176946756\) \(a_{15}=-0.268334448\)
\(a_{16}=+0.390522721\) \(a_{17}=-1.229512498\) \(a_{18}=-0.206845245\) \(a_{19}=-1.427056444\) \(a_{20}=+0.174491987\)
\(a_{21}=+0.453845268\) \(a_{22}=+0.240096791\) \(a_{23}=-0.377619501\) \(a_{24}=+1.001084314\) \(a_{25}=-0.950061074\)
\(a_{26}=+0.377860666\) \(a_{27}=-0.670230734\) \(a_{28}=-0.295125591\) \(a_{29}=-0.262173603\) \(a_{30}=+0.125622680\)
\(a_{31}=+1.421839530\) \(a_{32}=-1.016533711\) \(a_{33}=-0.615816843\) \(a_{34}=+0.575605019\) \(a_{35}=-0.084463793\)
\(a_{36}=-0.344992622\) \(a_{37}=+1.630513361\) \(a_{38}=+0.668086622\) \(a_{39}=-0.969163151\) \(a_{40}=-0.186308823\)
\(a_{41}=-0.638218446\) \(a_{42}=-0.212470890\) \(a_{43}=-1.363633871\) \(a_{44}=+0.400452142\) \(a_{45}=-0.098735542\)
\(a_{46}=+0.176785255\) \(a_{47}=+1.589030641\) \(a_{48}=+0.468924731\) \(a_{49}=+0.142857143\) \(a_{50}=+0.444777848\)
\(a_{51}=-1.476351535\) \(a_{52}=+0.630225470\) \(a_{53}=-0.634045266\) \(a_{54}=+0.313773284\) \(a_{55}=+0.114607840\)
\(a_{56}=+0.315111900\) \(a_{57}=-1.713554741\) \(a_{58}=+0.122738437\) \(a_{59}=+0.536898816\) \(a_{60}=+0.209523297\)
\(a_{61}=-0.307167487\) \(a_{62}=-0.665644287\) \(a_{63}=+0.166995550\) \(a_{64}=+0.085374765\) \(a_{65}=+0.180368070\)
\(a_{66}=+0.288299034\) \(a_{67}=+1.125667901\) \(a_{68}=+0.960038915\) \(a_{69}=-0.453431040\) \(a_{70}=+0.039542325\)
\(a_{71}=-0.287698830\) \(a_{72}=+0.368355994\) \(a_{73}=-1.117962627\) \(a_{74}=-0.763336424\) \(a_{75}=-1.140796964\)
\(a_{76}=+1.114286941\) \(a_{77}=-0.193841031\) \(a_{78}=+0.453720621\) \(a_{79}=+0.248888803\) \(a_{80}=-0.087270187\)
\(a_{81}=-1.246616099\) \(a_{82}=+0.298786504\) \(a_{83}=+1.017621562\) \(a_{84}=-0.354375511\) \(a_{85}=+0.274759392\)
\(a_{86}=+0.638394894\) \(a_{87}=-0.314808025\) \(a_{88}=-0.427571309\) \(a_{89}=+0.333418535\) \(a_{90}=+0.046223746\)
\(a_{91}=-0.305064057\) \(a_{92}=+0.294856227\) \(a_{93}=+1.707290472\) \(a_{94}=-0.743915994\) \(a_{95}=+0.318904575\)
\(a_{96}=-1.220614761\) \(a_{97}=+0.214215075\) \(a_{98}=-0.066879587\) \(a_{99}=-0.226594126\) \(a_{100}=+0.741835162\)

Showing 100 of 1228 available coefficients

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