Properties

Level $89$
Weight $0$
Character 89.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 89 \)
Weight: \( 0 \)
Character: 89.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.990622716 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.426424807\) \(a_{3}=-0.741233722\) \(a_{4}=+1.034687730\) \(a_{5}=+1.373900640\)
\(a_{6}=-1.057314169\) \(a_{7}=+0.658919727\) \(a_{8}=+0.049479439\) \(a_{9}=-0.450572569\) \(a_{10}=+1.959765955\)
\(a_{11}=-1.373809030\) \(a_{12}=-0.766945437\) \(a_{13}=+0.037936406\) \(a_{14}=+0.939899444\) \(a_{15}=-1.018381485\)
\(a_{16}=-0.964109031\) \(a_{17}=+1.124017007\) \(a_{18}=-0.642707890\) \(a_{19}=-1.762438300\) \(a_{20}=+1.421558134\)
\(a_{21}=-0.488413522\) \(a_{22}=-1.959635280\) \(a_{23}=+0.812785060\) \(a_{24}=-0.036675828\) \(a_{25}=+0.887602969\)
\(a_{26}=+0.054113431\) \(a_{27}=+1.075213305\) \(a_{28}=+0.681776157\) \(a_{29}=+1.509611992\) \(a_{30}=-1.452644613\)
\(a_{31}=+0.392210935\) \(a_{32}=-1.424708478\) \(a_{33}=+1.018313581\) \(a_{34}=+1.603325742\) \(a_{35}=+0.905290235\)
\(a_{36}=-0.466201909\) \(a_{37}=-0.526546916\) \(a_{38}=-2.513985712\) \(a_{39}=-0.028119743\) \(a_{40}=+0.067979832\)
\(a_{41}=-0.339722266\) \(a_{42}=-0.696685163\) \(a_{43}=+0.795730114\) \(a_{44}=-1.421463347\) \(a_{45}=-0.619041941\)
\(a_{46}=+1.159376773\) \(a_{47}=+0.382115236\) \(a_{48}=+0.714630126\) \(a_{49}=-0.565824793\) \(a_{50}=+1.266098893\)
\(a_{51}=-0.833159310\) \(a_{52}=+0.039252334\) \(a_{53}=-1.287021722\) \(a_{54}=+1.533710931\) \(a_{55}=-1.887477106\)
\(a_{56}=+0.032602978\) \(a_{57}=+1.306378701\) \(a_{58}=+2.153347995\) \(a_{59}=+1.291453600\) \(a_{60}=-1.053706827\)
\(a_{61}=+1.163483302\) \(a_{62}=+0.559459407\) \(a_{63}=-0.296891154\) \(a_{64}=-1.068130484\) \(a_{65}=+0.052120852\)
\(a_{66}=+1.452547753\) \(a_{67}=+0.022923781\) \(a_{68}=+1.163006605\) \(a_{69}=-0.602463695\) \(a_{70}=+1.291328448\)
\(a_{71}=+1.176521232\) \(a_{72}=-0.022294078\) \(a_{73}=-0.979297522\) \(a_{74}=-0.751079583\) \(a_{75}=-0.657921252\)
\(a_{76}=-1.823573284\) \(a_{77}=-0.905229871\) \(a_{78}=-0.040110700\) \(a_{79}=-0.440400412\) \(a_{80}=-1.324590015\)
\(a_{81}=-0.346411790\) \(a_{82}=-0.484588268\) \(a_{83}=-0.621014380\) \(a_{84}=-0.505355478\) \(a_{85}=+1.544287685\)
\(a_{86}=+1.135049174\) \(a_{87}=-1.118975316\) \(a_{88}=-0.067975300\) \(a_{89}=+0.105999788\) \(a_{90}=-0.883016782\)
\(a_{91}=+0.024997046\) \(a_{92}=+0.840978729\) \(a_{93}=-0.290719971\) \(a_{94}=+0.545058652\) \(a_{95}=-2.421415108\)
\(a_{96}=+1.056041968\) \(a_{97}=+1.402161539\) \(a_{98}=-0.807106522\) \(a_{99}=+0.619000664\) \(a_{100}=+0.918391901\)

Showing 100 of 546 available coefficients

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