Properties

Level $29$
Weight $0$
Character 29.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.87021845266 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.821074049\) \(a_{3}=-0.080179570\) \(a_{4}=-0.325837406\) \(a_{5}=+1.062376904\)
\(a_{6}=-0.065833364\) \(a_{7}=-0.683618747\) \(a_{8}=-1.088610687\) \(a_{9}=-0.993571237\) \(a_{10}=+0.872290106\)
\(a_{11}=-0.704937708\) \(a_{12}=+0.026125503\) \(a_{13}=-0.206909145\) \(a_{14}=-0.561301613\) \(a_{15}=-0.085180923\)
\(a_{16}=-0.567992578\) \(a_{17}=-0.159542978\) \(a_{18}=-0.815795558\) \(a_{19}=-0.702185567\) \(a_{20}=-0.346162135\)
\(a_{21}=+0.054812257\) \(a_{22}=-0.578806058\) \(a_{23}=-0.224741889\) \(a_{24}=+0.087284337\) \(a_{25}=+0.128644687\)
\(a_{26}=-0.169887729\) \(a_{27}=+0.159843685\) \(a_{28}=+0.222748560\) \(a_{29}=+0.185695338\) \(a_{30}=-0.069939846\)
\(a_{31}=+1.494827083\) \(a_{32}=+0.622246722\) \(a_{33}=+0.056521602\) \(a_{34}=-0.130996599\) \(a_{35}=-0.726260769\)
\(a_{36}=+0.323742675\) \(a_{37}=-1.561359018\) \(a_{38}=-0.576546346\) \(a_{39}=+0.016589886\) \(a_{40}=-1.156514852\)
\(a_{41}=+0.235638701\) \(a_{42}=+0.045004922\) \(a_{43}=+0.210255100\) \(a_{44}=+0.229695075\) \(a_{45}=-1.055547135\)
\(a_{46}=-0.184529733\) \(a_{47}=+1.492238294\) \(a_{48}=+0.045541401\) \(a_{49}=-0.532665408\) \(a_{50}=+0.105626814\)
\(a_{51}=+0.012792087\) \(a_{52}=+0.067418739\) \(a_{53}=+1.479295114\) \(a_{54}=+0.131243502\) \(a_{55}=-0.748909540\)
\(a_{56}=+0.744194674\) \(a_{57}=+0.056300937\) \(a_{58}=+0.152469623\) \(a_{59}=-0.571546840\) \(a_{60}=+0.027755131\)
\(a_{61}=-1.720384562\) \(a_{62}=+1.227363727\) \(a_{63}=+0.679223922\) \(a_{64}=+1.078903215\) \(a_{65}=-0.219815495\)
\(a_{66}=+0.046408418\) \(a_{67}=-0.343279675\) \(a_{68}=+0.051985068\) \(a_{69}=+0.018019712\) \(a_{70}=-0.596313871\)
\(a_{71}=-0.293701419\) \(a_{72}=+1.081612273\) \(a_{73}=-1.786259880\) \(a_{74}=-1.281991376\) \(a_{75}=-0.010314670\)
\(a_{76}=+0.228798326\) \(a_{77}=+0.481908627\) \(a_{78}=+0.013621530\) \(a_{79}=+0.210799528\) \(a_{80}=-0.603422191\)
\(a_{81}=+0.980755028\) \(a_{82}=+0.193476814\) \(a_{83}=-0.346407071\) \(a_{84}=-0.017859885\) \(a_{85}=-0.169494789\)
\(a_{86}=+0.172635011\) \(a_{87}=-0.014888984\) \(a_{88}=+0.767402736\) \(a_{89}=-0.675266631\) \(a_{90}=-0.866682372\)
\(a_{91}=+0.141446934\) \(a_{92}=+0.073229316\) \(a_{93}=-0.119854583\) \(a_{94}=+1.225238183\) \(a_{95}=-0.745985740\)
\(a_{96}=-0.049891535\) \(a_{97}=-0.039978230\) \(a_{98}=-0.437357762\) \(a_{99}=+0.700405854\) \(a_{100}=-0.041917214\)

Showing 100 of 1500 available coefficients

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