Properties

Level $37$
Weight $0$
Character 37.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 37 \)
Weight: \( 0 \)
Character: 37.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.903734503358 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.567249413\) \(a_{3}=+0.867138590\) \(a_{4}=+1.456270814\) \(a_{5}=+1.420271307\)
\(a_{6}=-1.359022503\) \(a_{7}=-0.308042639\) \(a_{8}=-0.715090200\) \(a_{9}=-0.248070628\) \(a_{10}=-2.225919417\)
\(a_{11}=-1.007512716\) \(a_{12}=+1.262788639\) \(a_{13}=+0.697415394\) \(a_{14}=+0.482779662\) \(a_{15}=+1.231572089\)
\(a_{16}=-0.335546118\) \(a_{17}=+0.168774818\) \(a_{18}=+0.388788550\) \(a_{19}=-0.942210719\) \(a_{20}=+2.068299670\)
\(a_{21}=-0.267115678\) \(a_{22}=+1.579023794\) \(a_{23}=-0.431033326\) \(a_{24}=-0.620082297\) \(a_{25}=+1.017170594\)
\(a_{26}=-1.093023829\) \(a_{27}=-1.082250175\) \(a_{28}=-0.448593567\) \(a_{29}=-1.125183124\) \(a_{30}=-1.930180599\)
\(a_{31}=+1.383709332\) \(a_{32}=+1.240974709\) \(a_{33}=-0.873653175\) \(a_{34}=-0.264512257\) \(a_{35}=-0.437504163\)
\(a_{36}=-0.361258063\) \(a_{37}=+0.164398892\) \(a_{38}=+1.476679220\) \(a_{39}=+0.604755827\) \(a_{40}=-1.015622035\)
\(a_{41}=+0.527769625\) \(a_{42}=+0.418636863\) \(a_{43}=+1.659379981\) \(a_{44}=-1.467211369\) \(a_{45}=-0.352327636\)
\(a_{46}=+0.675536737\) \(a_{47}=+0.114177308\) \(a_{48}=-0.290964959\) \(a_{49}=-0.905109729\) \(a_{50}=-1.594160089\)
\(a_{51}=+0.146351143\) \(a_{52}=+1.015625646\) \(a_{53}=+0.421727939\) \(a_{54}=+1.696156020\) \(a_{55}=-1.430941444\)
\(a_{56}=+0.220278357\) \(a_{57}=-0.817027219\) \(a_{58}=+1.763442459\) \(a_{59}=+0.045056122\) \(a_{60}=+1.793502537\)
\(a_{61}=-1.178285498\) \(a_{62}=-2.168617875\) \(a_{63}=+0.076416415\) \(a_{64}=-1.609370729\) \(a_{65}=+0.990519014\)
\(a_{66}=+1.369232441\) \(a_{67}=+0.402090215\) \(a_{68}=+0.245781942\) \(a_{69}=-0.373765643\) \(a_{70}=+0.685678137\)
\(a_{71}=+1.167184160\) \(a_{72}=+0.177392885\) \(a_{73}=+0.085480386\) \(a_{74}=-0.257654187\) \(a_{75}=+0.882027891\)
\(a_{76}=-1.372113965\) \(a_{77}=+0.310356899\) \(a_{78}=-0.947803161\) \(a_{79}=+0.671707902\) \(a_{80}=-0.476566569\)
\(a_{81}=-0.690390282\) \(a_{82}=-0.827146600\) \(a_{83}=-0.436155851\) \(a_{84}=-0.388992703\) \(a_{85}=+0.239706000\)
\(a_{86}=-2.600662515\) \(a_{87}=-0.975689664\) \(a_{88}=+0.720462421\) \(a_{89}=+0.034763121\) \(a_{90}=+0.552185272\)
\(a_{91}=-0.214833617\) \(a_{92}=-0.627701203\) \(a_{93}=+1.199867922\) \(a_{94}=-0.178944249\) \(a_{95}=-1.338194870\)
\(a_{96}=+1.076096970\) \(a_{97}=+0.551400621\) \(a_{98}=+1.418532694\) \(a_{99}=+0.249934285\) \(a_{100}=+1.481275977\)

Showing 100 of 2000 available coefficients

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