Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.36133422204 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.641789405\) \(a_{3}=-0.577350269\) \(a_{4}=+1.695472449\) \(a_{5}=-0.447213596\)
\(a_{6}=+0.947887555\) \(a_{7}=-1.049668977\) \(a_{8}=-1.141819298\) \(a_{9}=+0.333333333\) \(a_{10}=+0.734230543\)
\(a_{11}=-0.892205132\) \(a_{12}=-0.978881475\) \(a_{13}=+0.778578753\) \(a_{14}=+1.723335405\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.179154377\) \(a_{17}=-0.325438379\) \(a_{18}=-0.547263135\) \(a_{19}=-1.126623830\) \(a_{20}=-0.758238330\)
\(a_{21}=+0.606026667\) \(a_{22}=+1.464812932\) \(a_{23}=-0.070828598\) \(a_{24}=+0.659229679\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.278262348\) \(a_{27}=-0.192450090\) \(a_{28}=-1.779684832\) \(a_{29}=+0.663908386\) \(a_{30}=-0.423908201\)
\(a_{31}=-0.268650106\) \(a_{32}=+0.847685541\) \(a_{33}=+0.515114873\) \(a_{34}=+0.534301283\) \(a_{35}=+0.469426237\)
\(a_{36}=+0.565157483\) \(a_{37}=-0.708806332\) \(a_{38}=+1.849679067\) \(a_{39}=-0.449512653\) \(a_{40}=+0.510637114\)
\(a_{41}=-0.323933510\) \(a_{42}=-0.994968160\) \(a_{43}=+0.422821423\) \(a_{44}=-1.512709220\) \(a_{45}=-0.149071199\)
\(a_{46}=+0.116285642\) \(a_{47}=-1.704896394\) \(a_{48}=-0.103434827\) \(a_{49}=+0.101804961\) \(a_{50}=-0.328357881\)
\(a_{51}=+0.187891936\) \(a_{52}=+1.320058825\) \(a_{53}=-1.225102932\) \(a_{54}=+0.315962514\) \(a_{55}=+0.399006271\)
\(a_{56}=+1.198532294\) \(a_{57}=+0.650456569\) \(a_{58}=-1.089997752\) \(a_{59}=+1.765014447\) \(a_{60}=+0.437769099\)
\(a_{61}=+1.271624699\) \(a_{62}=+0.441066916\) \(a_{63}=-0.349889674\) \(a_{64}=-1.570875487\) \(a_{65}=-0.348191059\)
\(a_{66}=-0.845710114\) \(a_{67}=-0.525464413\) \(a_{68}=-0.551771807\) \(a_{69}=+0.040892912\) \(a_{70}=-0.770699022\)
\(a_{71}=-0.161431947\) \(a_{72}=-0.380606409\) \(a_{73}=+1.890456195\) \(a_{74}=+1.163710717\) \(a_{75}=-0.115470013\)
\(a_{76}=-1.910159537\) \(a_{77}=+0.936519954\) \(a_{78}=+0.738005090\) \(a_{79}=-1.608016971\) \(a_{80}=-0.080120119\)
\(a_{81}=+0.111110880\) \(a_{82}=+0.531830938\) \(a_{83}=-0.548618068\) \(a_{84}=+1.027501302\) \(a_{85}=+0.145539983\)
\(a_{86}=-0.694184902\) \(a_{87}=-0.383306687\) \(a_{88}=+1.018739959\) \(a_{89}=-1.173116535\) \(a_{90}=+0.244740094\)
\(a_{91}=-0.817242299\) \(a_{92}=-0.120090101\) \(a_{93}=+0.155106433\) \(a_{94}=+2.799072240\) \(a_{95}=+0.503863668\)
\(a_{96}=-0.489297005\) \(a_{97}=-0.161002829\) \(a_{98}=-0.167205510\) \(a_{99}=-0.297387951\) \(a_{100}=+0.338850809\)

Showing 100 of 1500 available coefficients

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