Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.45737404363 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.541942926\) \(a_{3}=-1.290162023\) \(a_{4}=+1.377587988\) \(a_{5}=+0.696409401\)
\(a_{6}=+1.989356205\) \(a_{7}=-0.322690884\) \(a_{8}=-0.582219127\) \(a_{9}=+0.664518046\) \(a_{10}=-1.073823550\)
\(a_{11}=+0.035997179\) \(a_{12}=-1.777311705\) \(a_{13}=+1.957379458\) \(a_{14}=+0.497570925\) \(a_{15}=-0.898480962\)
\(a_{16}=-0.479839324\) \(a_{17}=-0.942457198\) \(a_{18}=-1.024648900\) \(a_{19}=-0.229415734\) \(a_{20}=+0.959365226\)
\(a_{21}=+0.416323523\) \(a_{22}=-0.055505595\) \(a_{23}=+0.313845313\) \(a_{24}=+0.751157006\) \(a_{25}=-0.515013946\)
\(a_{26}=-3.018167409\) \(a_{27}=+0.432826077\) \(a_{28}=-0.444535085\) \(a_{29}=+1.274398253\) \(a_{30}=+1.385406364\)
\(a_{31}=-1.936982584\) \(a_{32}=+1.322103978\) \(a_{33}=-0.046442193\) \(a_{34}=+1.453215210\) \(a_{35}=-0.224724965\)
\(a_{36}=+0.915432078\) \(a_{37}=+0.086245113\) \(a_{38}=+0.353745968\) \(a_{39}=-2.525336642\) \(a_{40}=-0.405462873\)
\(a_{41}=-0.497241716\) \(a_{42}=-0.641947112\) \(a_{43}=-0.341508988\) \(a_{44}=+0.049589281\) \(a_{45}=+0.462776614\)
\(a_{46}=-0.483931561\) \(a_{47}=-0.887950626\) \(a_{48}=+0.619070473\) \(a_{49}=-0.895870594\) \(a_{50}=+0.794122111\)
\(a_{51}=+1.215922486\) \(a_{52}=+2.696462429\) \(a_{53}=+1.058768151\) \(a_{54}=-0.667393107\) \(a_{55}=+0.025068774\)
\(a_{56}=+0.187876804\) \(a_{57}=+0.295983467\) \(a_{58}=-1.965049372\) \(a_{59}=+0.179971607\) \(a_{60}=-1.237736580\)
\(a_{61}=-1.000225649\) \(a_{62}=+2.986716594\) \(a_{63}=-0.214433915\) \(a_{64}=-1.558769552\) \(a_{65}=+1.363137456\)
\(a_{66}=+0.071611211\) \(a_{67}=-1.935153633\) \(a_{68}=-1.298317715\) \(a_{69}=-0.404911304\) \(a_{70}=+0.346513070\)
\(a_{71}=-0.248984348\) \(a_{72}=-0.386895116\) \(a_{73}=+0.638123775\) \(a_{74}=-0.132985041\) \(a_{75}=+0.664451434\)
\(a_{76}=-0.316040359\) \(a_{77}=-0.011615961\) \(a_{78}=+3.893924971\) \(a_{79}=-0.701528165\) \(a_{80}=-0.334164616\)
\(a_{81}=-1.222933813\) \(a_{82}=+0.766718347\) \(a_{83}=+0.701532518\) \(a_{84}=+0.573522285\) \(a_{85}=-0.656336053\)
\(a_{86}=+0.526587369\) \(a_{87}=-1.644180229\) \(a_{88}=-0.020958246\) \(a_{89}=-1.421883876\) \(a_{90}=-0.713575127\)
\(a_{91}=-0.631628507\) \(a_{92}=+0.432349534\) \(a_{93}=+2.499021369\) \(a_{94}=+1.369169187\) \(a_{95}=-0.159767274\)
\(a_{96}=-1.705728343\) \(a_{97}=+1.118857878\) \(a_{98}=+1.381381325\) \(a_{99}=+0.023920775\) \(a_{100}=-0.709477025\)

Showing 100 of 546 available coefficients

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