Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.0252843957 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.689670885\) \(a_{3}=+1.137346862\) \(a_{4}=+1.854987699\) \(a_{5}=-0.412895371\)
\(a_{6}=-1.921741879\) \(a_{7}=+1.054373693\) \(a_{8}=-1.444647822\) \(a_{9}=+0.293557885\) \(a_{10}=+0.697657286\)
\(a_{11}=-0.203268200\) \(a_{12}=+2.109764439\) \(a_{13}=-0.277350098\) \(a_{14}=-1.781544531\) \(a_{15}=-0.469605254\)
\(a_{16}=+0.585991664\) \(a_{17}=+1.178496583\) \(a_{18}=-0.496016211\) \(a_{19}=-0.235862380\) \(a_{20}=-0.765915833\)
\(a_{21}=+1.199188611\) \(a_{22}=+0.343456360\) \(a_{23}=-0.543100976\) \(a_{24}=-1.643065667\) \(a_{25}=-0.829517413\)
\(a_{26}=+0.468630386\) \(a_{27}=-0.803469723\) \(a_{28}=+1.955850231\) \(a_{29}=+1.418600530\) \(a_{30}=+0.793478325\)
\(a_{31}=-0.193421529\) \(a_{32}=+0.454514768\) \(a_{33}=-0.231186450\) \(a_{34}=-1.991271363\) \(a_{35}=-0.435346017\)
\(a_{36}=+0.544546265\) \(a_{37}=+0.858542839\) \(a_{38}=+0.398529796\) \(a_{39}=-0.315443264\) \(a_{40}=+0.596488398\)
\(a_{41}=-1.897764667\) \(a_{42}=-2.026234082\) \(a_{43}=+0.227378333\) \(a_{44}=-0.377060011\) \(a_{45}=-0.121208692\)
\(a_{46}=+0.917661907\) \(a_{47}=+0.576799937\) \(a_{48}=+0.666475781\) \(a_{49}=+0.111703885\) \(a_{50}=+1.401611421\)
\(a_{51}=+1.340359390\) \(a_{52}=-0.514481020\) \(a_{53}=+0.197407739\) \(a_{54}=+1.357599398\) \(a_{55}=+0.083928499\)
\(a_{56}=-1.523198659\) \(a_{57}=-0.268257338\) \(a_{58}=-2.396968013\) \(a_{59}=-0.211276282\) \(a_{60}=-0.871111970\)
\(a_{61}=+0.774254930\) \(a_{62}=+0.326818726\) \(a_{63}=+0.309519711\) \(a_{64}=-1.353972034\) \(a_{65}=+0.114516572\)
\(a_{66}=+0.390629013\) \(a_{67}=+0.024966587\) \(a_{68}=+2.186096664\) \(a_{69}=-0.617694191\) \(a_{70}=+0.735591489\)
\(a_{71}=+0.077072499\) \(a_{72}=-0.424087759\) \(a_{73}=+0.929509586\) \(a_{74}=-1.450654839\) \(a_{75}=-0.943449027\)
\(a_{76}=-0.437521813\) \(a_{77}=-0.214320643\) \(a_{78}=+0.532995299\) \(a_{79}=-0.185721901\) \(a_{80}=-0.241953245\)
\(a_{81}=-1.207381653\) \(a_{82}=+3.206597704\) \(a_{83}=-1.331479432\) \(a_{84}=+2.224480123\) \(a_{85}=-0.486595783\)
\(a_{86}=-0.384194549\) \(a_{87}=+1.613440861\) \(a_{88}=+0.293650963\) \(a_{89}=-0.919270637\) \(a_{90}=+0.204802797\)
\(a_{91}=-0.292430647\) \(a_{92}=-1.007445630\) \(a_{93}=-0.219987369\) \(a_{94}=-0.974602060\) \(a_{95}=+0.097386485\)
\(a_{96}=+0.516940945\) \(a_{97}=+1.660072977\) \(a_{98}=-0.188742802\) \(a_{99}=-0.059670983\) \(a_{100}=-1.538744597\)

Showing 100 of 546 available coefficients

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