Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 6.75529844582 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.826273547\) \(a_{4}=+0.500000000\) \(a_{5}=+0.648045795\)
\(a_{6}=-0.584263628\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.317272026\) \(a_{10}=+0.458237576\)
\(a_{11}=-1.057025642\) \(a_{12}=-0.413136773\) \(a_{13}=-1.663538217\) \(a_{14}=-0.267261242\) \(a_{15}=-0.535463097\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.003737046\) \(a_{18}=-0.224345201\) \(a_{19}=-0.544071710\) \(a_{20}=+0.324022897\)
\(a_{21}=+0.312302046\) \(a_{22}=-0.747429999\) \(a_{23}=+0.536651004\) \(a_{24}=-0.292131814\) \(a_{25}=-0.580036648\)
\(a_{26}=-1.176299154\) \(a_{27}=+1.088427029\) \(a_{28}=-0.188982237\) \(a_{29}=-0.938546232\) \(a_{30}=-0.378629587\)
\(a_{31}=+1.342961592\) \(a_{32}=+0.176776695\) \(a_{33}=+0.873392326\) \(a_{34}=-0.002642491\) \(a_{35}=-0.244938287\)
\(a_{36}=-0.158636013\) \(a_{37}=-0.948421850\) \(a_{38}=-0.384716795\) \(a_{39}=+1.374537622\) \(a_{40}=+0.229118788\)
\(a_{41}=+0.016772955\) \(a_{42}=+0.220830894\) \(a_{43}=-1.033267080\) \(a_{44}=-0.528512821\) \(a_{45}=-0.205606802\)
\(a_{46}=+0.379469564\) \(a_{47}=-0.112748624\) \(a_{48}=-0.206568387\) \(a_{49}=+0.142857143\) \(a_{50}=-0.410147847\)
\(a_{51}=+0.003087822\) \(a_{52}=-0.831769109\) \(a_{53}=+1.569198386\) \(a_{54}=+0.769634133\) \(a_{55}=-0.685001022\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.449552061\) \(a_{58}=-0.663652405\) \(a_{59}=+1.812934195\) \(a_{60}=-0.267731549\)
\(a_{61}=-0.357867030\) \(a_{62}=+0.949617248\) \(a_{63}=+0.119917554\) \(a_{64}=+0.125000000\) \(a_{65}=-1.078048946\)
\(a_{66}=+0.617581636\) \(a_{67}=-1.687687027\) \(a_{68}=-0.001868523\) \(a_{69}=-0.443420528\) \(a_{70}=-0.173197524\)
\(a_{71}=-1.009249967\) \(a_{72}=-0.112172601\) \(a_{73}=+0.301779250\) \(a_{74}=-0.670635522\) \(a_{75}=+0.479268938\)
\(a_{76}=-0.272035855\) \(a_{77}=+0.399518140\) \(a_{78}=+0.971944874\) \(a_{79}=+1.138817741\) \(a_{80}=+0.162011449\)
\(a_{81}=-0.582066435\) \(a_{82}=+0.011860270\) \(a_{83}=+1.949506599\) \(a_{84}=+0.156151023\) \(a_{85}=-0.002421777\)
\(a_{86}=-0.730630159\) \(a_{87}=+0.775495924\) \(a_{88}=-0.373715000\) \(a_{89}=-1.766450020\) \(a_{90}=-0.145385964\)
\(a_{91}=+0.628758346\) \(a_{92}=+0.268325502\) \(a_{93}=-1.109653637\) \(a_{94}=-0.079725316\) \(a_{95}=-0.352583384\)
\(a_{96}=-0.146065907\) \(a_{97}=+0.976446200\) \(a_{98}=+0.101015254\) \(a_{99}=+0.335364667\) \(a_{100}=-0.290018324\)

Showing 100 of 166 available coefficients

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