Properties

Level $5$
Weight $0$
Character 5.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.45847643848 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.325358039\) \(a_{3}=-0.044190818\) \(a_{4}=+0.756573932\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.058568656\) \(a_{7}=+0.946099446\) \(a_{8}=+0.322626696\) \(a_{9}=-0.998047172\) \(a_{10}=-0.592718134\)
\(a_{11}=+1.377456591\) \(a_{12}=-0.033433621\) \(a_{13}=+0.893377340\) \(a_{14}=-1.253920500\) \(a_{15}=-0.019762750\)
\(a_{16}=-1.184169805\) \(a_{17}=+0.660749201\) \(a_{18}=+1.322769843\) \(a_{19}=-0.308995655\) \(a_{20}=+0.338350149\)
\(a_{21}=-0.041808908\) \(a_{22}=-1.825623166\) \(a_{23}=+1.339350779\) \(a_{24}=-0.014257138\) \(a_{25}=+0.200000000\)
\(a_{26}=-1.184044842\) \(a_{27}=+0.088295339\) \(a_{28}=+0.715794178\) \(a_{29}=+0.135882574\) \(a_{30}=+0.026192699\)
\(a_{31}=-0.311941186\) \(a_{32}=+1.246822291\) \(a_{33}=-0.060870934\) \(a_{34}=-0.875729265\) \(a_{35}=+0.423108535\)
\(a_{36}=-0.755096473\) \(a_{37}=-1.372063810\) \(a_{38}=+0.409529876\) \(a_{39}=-0.039479075\) \(a_{40}=+0.144283045\)
\(a_{41}=+1.745690170\) \(a_{42}=+0.055411773\) \(a_{43}=+0.248884367\) \(a_{44}=+1.042147747\) \(a_{45}=-0.446340264\)
\(a_{46}=-1.775119319\) \(a_{47}=-0.515075454\) \(a_{48}=+0.052329433\) \(a_{49}=-0.104895833\) \(a_{50}=-0.265071610\)
\(a_{51}=-0.029199056\) \(a_{52}=+0.675906008\) \(a_{53}=+0.269539864\) \(a_{54}=-0.117022917\) \(a_{55}=+0.616017282\)
\(a_{56}=+0.305236914\) \(a_{57}=+0.013654879\) \(a_{58}=-0.180093177\) \(a_{59}=-0.691337075\) \(a_{60}=-0.014951970\)
\(a_{61}=+0.693956327\) \(a_{62}=+0.413433759\) \(a_{63}=-0.944251876\) \(a_{64}=-0.468316130\) \(a_{65}=+0.399530493\)
\(a_{66}=+0.080675781\) \(a_{67}=-0.388942576\) \(a_{68}=+0.499905621\) \(a_{69}=-0.059187007\) \(a_{70}=-0.560770298\)
\(a_{71}=-1.165864167\) \(a_{72}=-0.321996662\) \(a_{73}=+0.829565148\) \(a_{74}=+1.818475802\) \(a_{75}=-0.008838165\)
\(a_{76}=-0.233778060\) \(a_{77}=+1.303210919\) \(a_{78}=+0.052323915\) \(a_{79}=-0.257462125\) \(a_{80}=-0.529576843\)
\(a_{81}=+0.994145336\) \(a_{82}=-2.313664504\) \(a_{83}=-0.875877522\) \(a_{84}=-0.031631517\) \(a_{85}=+0.295496051\)
\(a_{86}=-0.329860925\) \(a_{87}=-0.006004779\) \(a_{88}=+0.444404301\) \(a_{89}=-0.969651548\) \(a_{90}=+0.591560578\)
\(a_{91}=+0.845223840\) \(a_{92}=+1.013317991\) \(a_{93}=+0.013784936\) \(a_{94}=+0.682659389\) \(a_{95}=-0.138187059\)
\(a_{96}=-0.055098095\) \(a_{97}=+0.518138242\) \(a_{98}=+0.139024544\) \(a_{99}=-1.374766654\) \(a_{100}=+0.151314787\)

Showing 100 of 5000 available coefficients

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