Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.92775246896 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.327174879\) \(a_{3}=-0.577350269\) \(a_{4}=-0.892956599\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.188894504\) \(a_{7}=-1.293166619\) \(a_{8}=-0.619327846\) \(a_{9}=+0.333333333\) \(a_{10}=+0.146317054\)
\(a_{11}=-0.764262986\) \(a_{12}=+0.515548733\) \(a_{13}=+1.284046343\) \(a_{14}=-0.423091632\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.690328085\) \(a_{17}=-0.820623501\) \(a_{18}=+0.109058293\) \(a_{19}=-1.494562327\) \(a_{20}=-0.399342331\)
\(a_{21}=+0.746610096\) \(a_{22}=-0.250047650\) \(a_{23}=+0.404276571\) \(a_{24}=+0.357569099\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.420107707\) \(a_{27}=-0.192450090\) \(a_{28}=+1.154741666\) \(a_{29}=-1.240571585\) \(a_{30}=-0.084476191\)
\(a_{31}=-0.080297135\) \(a_{32}=+0.845185854\) \(a_{33}=+0.441247441\) \(a_{34}=-0.268487395\) \(a_{35}=-0.578321693\)
\(a_{36}=-0.297652200\) \(a_{37}=+0.078001488\) \(a_{38}=-0.488983249\) \(a_{39}=-0.741344502\) \(a_{40}=-0.276971833\)
\(a_{41}=-0.763348906\) \(a_{42}=+0.244272068\) \(a_{43}=+0.911444757\) \(a_{44}=+0.682453676\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.132269138\) \(a_{47}=+0.328507642\) \(a_{48}=-0.398561106\) \(a_{49}=+0.672279905\) \(a_{50}=+0.065434976\)
\(a_{51}=+0.473787199\) \(a_{52}=-1.146597654\) \(a_{53}=+0.449419092\) \(a_{54}=-0.062964835\) \(a_{55}=-0.341788798\)
\(a_{56}=+0.800894097\) \(a_{57}=+0.862885962\) \(a_{58}=-0.405883858\) \(a_{59}=-1.664255879\) \(a_{60}=+0.230560402\)
\(a_{61}=+0.501944250\) \(a_{62}=-0.026271205\) \(a_{63}=-0.431055540\) \(a_{64}=-0.413804506\) \(a_{65}=+0.574242982\)
\(a_{66}=+0.144365078\) \(a_{67}=-1.547352705\) \(a_{68}=+0.732781170\) \(a_{69}=-0.233409187\) \(a_{70}=-0.189212330\)
\(a_{71}=-1.365591564\) \(a_{72}=-0.206442615\) \(a_{73}=+0.653014406\) \(a_{74}=+0.025520128\) \(a_{75}=-0.115470054\)
\(a_{76}=+1.334579292\) \(a_{77}=+0.988319382\) \(a_{78}=-0.242549298\) \(a_{79}=+1.973481520\) \(a_{80}=+0.308724105\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.249748586\) \(a_{83}=-1.015079720\) \(a_{84}=-0.666690412\) \(a_{85}=-0.366993986\)
\(a_{86}=+0.298201828\) \(a_{87}=+0.716244339\) \(a_{88}=+0.473329349\) \(a_{89}=+0.095942800\) \(a_{90}=+0.048772351\)
\(a_{91}=-1.660485868\) \(a_{92}=-0.361001432\) \(a_{93}=+0.046359572\) \(a_{94}=+0.107479448\) \(a_{95}=-0.668388592\)
\(a_{96}=-0.487968280\) \(a_{97}=+0.401601002\) \(a_{98}=+0.219953097\) \(a_{99}=-0.254754329\) \(a_{100}=-0.178591320\)

Showing 100 of 192 available coefficients

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