Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 21.1086958873 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.001924504\) \(a_{3}=-0.577350269\) \(a_{4}=+0.003852711\) \(a_{5}=+0.529885472\)
\(a_{6}=-0.578461382\) \(a_{7}=+0.467278894\) \(a_{8}=-0.998064378\) \(a_{9}=+0.333333333\) \(a_{10}=+0.530905238\)
\(a_{11}=+1.084381071\) \(a_{12}=-0.002224364\) \(a_{13}=-0.768237086\) \(a_{14}=+0.468178174\) \(a_{15}=-0.305929520\)
\(a_{16}=-1.003837868\) \(a_{17}=-1.721615129\) \(a_{18}=+0.333974835\) \(a_{19}=-0.416155815\) \(a_{20}=+0.002041496\)
\(a_{21}=-0.269783595\) \(a_{22}=+1.086467967\) \(a_{23}=+0.602927571\) \(a_{24}=+0.576232737\) \(a_{25}=-0.719221387\)
\(a_{26}=-0.769715561\) \(a_{27}=-0.192450090\) \(a_{28}=+0.001800291\) \(a_{29}=-1.430493939\) \(a_{30}=-0.306518282\)
\(a_{31}=-0.990199833\) \(a_{32}=-0.007705379\) \(a_{33}=-0.626067703\) \(a_{34}=-1.724928383\) \(a_{35}=+0.247604297\)
\(a_{36}=+0.001284237\) \(a_{37}=+0.147757025\) \(a_{38}=-0.416956708\) \(a_{39}=+0.443541888\) \(a_{40}=-0.528859814\)
\(a_{41}=-1.614423584\) \(a_{42}=-0.270302795\) \(a_{43}=+1.538347390\) \(a_{44}=+0.004177807\) \(a_{45}=+0.176628491\)
\(a_{46}=+0.604087907\) \(a_{47}=-1.449905995\) \(a_{48}=+0.579566063\) \(a_{49}=-0.781650435\) \(a_{50}=-0.720605531\)
\(a_{51}=+0.993974958\) \(a_{52}=-0.002959795\) \(a_{53}=+0.617944113\) \(a_{54}=-0.192820461\) \(a_{55}=+0.574597776\)
\(a_{56}=-0.466374419\) \(a_{57}=+0.240267672\) \(a_{58}=-1.433246929\) \(a_{59}=+0.166822934\) \(a_{60}=-0.001178658\)
\(a_{61}=+1.231051089\) \(a_{62}=-0.992105476\) \(a_{63}=+0.155759631\) \(a_{64}=+0.996117659\) \(a_{65}=-0.407077671\)
\(a_{66}=-0.627272573\) \(a_{67}=+0.686597705\) \(a_{68}=-0.006632885\) \(a_{69}=-0.348100396\) \(a_{70}=+0.248080812\)
\(a_{71}=-0.186211582\) \(a_{72}=-0.332688126\) \(a_{73}=-0.664165627\) \(a_{74}=+0.148041384\) \(a_{75}=+0.415242661\)
\(a_{76}=-0.001603328\) \(a_{77}=+0.506708387\) \(a_{78}=+0.444395486\) \(a_{79}=+1.007655280\) \(a_{80}=-0.531919102\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.617530548\) \(a_{83}=-0.612658860\) \(a_{84}=-0.001039398\) \(a_{85}=-0.912258845\)
\(a_{86}=+1.541307945\) \(a_{87}=+0.825896061\) \(a_{88}=-1.082282120\) \(a_{89}=+1.519780751\) \(a_{90}=+0.176968413\)
\(a_{91}=-0.358980976\) \(a_{92}=+0.002322906\) \(a_{93}=+0.571692140\) \(a_{94}=-1.452696344\) \(a_{95}=-0.220514920\)
\(a_{96}=+0.004448703\) \(a_{97}=+0.172208054\) \(a_{98}=-0.783154725\) \(a_{99}=+0.361460357\) \(a_{100}=-0.002770952\)

Showing 100 of 1228 available coefficients

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