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: \( 6.71350181149 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.636152657\) \(a_{3}=+0.577350269\) \(a_{4}=+1.676995517\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.944633177\) \(a_{7}=-0.743550679\) \(a_{8}=-1.107668013\) \(a_{9}=+0.333333333\) \(a_{10}=+0.731709712\)
\(a_{11}=-1.647178958\) \(a_{12}=+0.968213813\) \(a_{13}=+0.818501170\) \(a_{14}=+1.216562420\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.135318446\) \(a_{17}=-0.306844616\) \(a_{18}=-0.545384219\) \(a_{19}=+1.541478903\) \(a_{20}=-0.749975195\)
\(a_{21}=-0.429289185\) \(a_{22}=+2.695036228\) \(a_{23}=+1.084399810\) \(a_{24}=-0.639512426\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.339192863\) \(a_{27}=+0.192450090\) \(a_{28}=-1.246931156\) \(a_{29}=-0.639631037\) \(a_{30}=+0.422452799\)
\(a_{31}=+0.349086427\) \(a_{32}=+0.886266378\) \(a_{33}=-0.950999215\) \(a_{34}=+0.502044634\) \(a_{35}=+0.332525973\)
\(a_{36}=+0.558998506\) \(a_{37}=+1.869180820\) \(a_{38}=-2.522094803\) \(a_{39}=+0.472561871\) \(a_{40}=+0.495364195\)
\(a_{41}=+0.629881865\) \(a_{42}=+0.702382641\) \(a_{43}=+1.418040968\) \(a_{44}=-2.762311727\) \(a_{45}=-0.149071198\)
\(a_{46}=-1.774243630\) \(a_{47}=-0.213751247\) \(a_{48}=+0.078126141\) \(a_{49}=-0.447132387\) \(a_{50}=-0.327230531\)
\(a_{51}=-0.177156822\) \(a_{52}=+1.372622792\) \(a_{53}=+0.386543350\) \(a_{54}=-0.314877726\) \(a_{55}=+0.736640824\)
\(a_{56}=+0.823607304\) \(a_{57}=+0.889973260\) \(a_{58}=+1.046534020\) \(a_{59}=+0.297194210\) \(a_{60}=-0.432998381\)
\(a_{61}=-1.294350675\) \(a_{62}=-0.571158685\) \(a_{63}=-0.247850226\) \(a_{64}=-1.585385535\) \(a_{65}=-0.366044851\)
\(a_{66}=+1.555979892\) \(a_{67}=+0.154875659\) \(a_{68}=-0.514577046\) \(a_{69}=+0.626078522\) \(a_{70}=-0.544063254\)
\(a_{71}=+0.650658417\) \(a_{72}=-0.369222671\) \(a_{73}=+1.332198381\) \(a_{74}=-3.058265165\) \(a_{75}=+0.115470054\)
\(a_{76}=+2.585053210\) \(a_{77}=+1.224761033\) \(a_{78}=-0.773183360\) \(a_{79}=-1.215345931\) \(a_{80}=-0.060516249\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.030582887\) \(a_{83}=+0.574423394\) \(a_{84}=-0.719916039\) \(a_{85}=+0.137225084\)
\(a_{86}=-2.320131497\) \(a_{87}=-0.369291151\) \(a_{88}=+1.824527444\) \(a_{89}=+1.820116386\) \(a_{90}=+0.243903237\)
\(a_{91}=-0.608597101\) \(a_{92}=+1.818533620\) \(a_{93}=+0.201545143\) \(a_{94}=+0.349729671\) \(a_{95}=-0.689370323\)
\(a_{96}=+0.511686132\) \(a_{97}=-1.302039211\) \(a_{98}=+0.731576843\) \(a_{99}=-0.549059653\) \(a_{100}=+0.335399103\)

Showing 100 of 190 available coefficients

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