Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.0095393762 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.176029992\) \(a_{3}=-0.577350269\) \(a_{4}=-0.969013442\) \(a_{5}=+0.895551414\)
\(a_{6}=-0.101630963\) \(a_{7}=+0.112999947\) \(a_{8}=-0.346605420\) \(a_{9}=+0.333333333\) \(a_{10}=+0.157643908\)
\(a_{11}=-1.300344675\) \(a_{12}=+0.559460172\) \(a_{13}=+1.542151048\) \(a_{14}=+0.019891380\) \(a_{15}=-0.517046850\)
\(a_{16}=+0.908000493\) \(a_{17}=-1.538660047\) \(a_{18}=+0.058676664\) \(a_{19}=+0.277306390\) \(a_{20}=-0.867801358\)
\(a_{21}=-0.065240550\) \(a_{22}=-0.228899663\) \(a_{23}=-1.165736592\) \(a_{24}=+0.200112733\) \(a_{25}=-0.197987666\)
\(a_{26}=+0.271464836\) \(a_{27}=-0.192450090\) \(a_{28}=-0.109498467\) \(a_{29}=-1.133081610\) \(a_{30}=-0.091015753\)
\(a_{31}=+0.658999181\) \(a_{32}=+0.506440740\) \(a_{33}=+0.750754348\) \(a_{34}=-0.270850315\) \(a_{35}=+0.101197262\)
\(a_{36}=-0.323004481\) \(a_{37}=+0.186286634\) \(a_{38}=+0.048814242\) \(a_{39}=-0.890361323\) \(a_{40}=-0.310402974\)
\(a_{41}=+0.457196148\) \(a_{42}=-0.011484293\) \(a_{43}=+0.423566795\) \(a_{44}=+1.260051469\) \(a_{45}=+0.298517138\)
\(a_{46}=-0.205204603\) \(a_{47}=+0.511368192\) \(a_{48}=-0.524234329\) \(a_{49}=-0.987231012\) \(a_{50}=-0.034851767\)
\(a_{51}=+0.888345792\) \(a_{52}=-1.494365095\) \(a_{53}=-0.166648821\) \(a_{54}=-0.033876988\) \(a_{55}=-1.164525512\)
\(a_{56}=-0.039166394\) \(a_{57}=-0.160102919\) \(a_{58}=-0.199456347\) \(a_{59}=+0.390366448\) \(a_{60}=+0.501025347\)
\(a_{61}=+1.906102020\) \(a_{62}=+0.116003620\) \(a_{63}=+0.037666649\) \(a_{64}=-0.818851733\) \(a_{65}=+1.381075551\)
\(a_{66}=+0.132155282\) \(a_{67}=+1.052567966\) \(a_{68}=+1.490982268\) \(a_{69}=+0.673038335\) \(a_{70}=+0.017813753\)
\(a_{71}=+0.368214798\) \(a_{72}=-0.115535140\) \(a_{73}=+1.704960183\) \(a_{74}=+0.032792035\) \(a_{75}=+0.114308232\)
\(a_{76}=-0.268713619\) \(a_{77}=-0.146938879\) \(a_{78}=-0.156730296\) \(a_{79}=+1.380425068\) \(a_{80}=+0.813161125\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.080480234\) \(a_{83}=+0.241843205\) \(a_{84}=+0.063218970\) \(a_{85}=-1.377949180\)
\(a_{86}=+0.074560459\) \(a_{87}=+0.654184973\) \(a_{88}=+0.450706513\) \(a_{89}=-0.689252193\) \(a_{90}=+0.052547969\)
\(a_{91}=+0.174262986\) \(a_{92}=+1.129614427\) \(a_{93}=-0.380473354\) \(a_{94}=+0.090016139\) \(a_{95}=+0.248342129\)
\(a_{96}=-0.292393697\) \(a_{97}=-0.189606700\) \(a_{98}=-0.173782267\) \(a_{99}=-0.433448225\) \(a_{100}=+0.191852709\)

Showing 100 of 1228 available coefficients

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