Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.90114750377 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.258800550\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.663358372\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.182999624\)
\(a_{11}=+1.066268599\) \(a_{12}=+0.288675135\) \(a_{13}=-0.755939676\) \(a_{14}=+1.176171984\) \(a_{15}=-0.149418567\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.210216702\) \(a_{18}=+0.235702260\) \(a_{19}=+0.043215561\) \(a_{20}=-0.129400275\)
\(a_{21}=+0.960340404\) \(a_{22}=+0.753965757\) \(a_{23}=-0.664860730\) \(a_{24}=+0.204124145\) \(a_{25}=-0.933022272\)
\(a_{26}=-0.534530069\) \(a_{27}=+0.192450076\) \(a_{28}=+0.831679186\) \(a_{29}=-1.320966787\) \(a_{30}=-0.105654882\)
\(a_{31}=+1.850833486\) \(a_{32}=+0.176776695\) \(a_{33}=+0.615610463\) \(a_{34}=-0.855752437\) \(a_{35}=-0.430478061\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.729389016\) \(a_{38}=+0.030558016\) \(a_{39}=-0.436441976\) \(a_{40}=-0.091499812\)
\(a_{41}=-0.017640560\) \(a_{42}=+0.679063212\) \(a_{43}=+0.469858714\) \(a_{44}=+0.533134299\) \(a_{45}=-0.086266850\)
\(a_{46}=-0.470127530\) \(a_{47}=-0.604902419\) \(a_{48}=+0.144337567\) \(a_{49}=+1.766761073\) \(a_{50}=-0.659746378\)
\(a_{51}=-0.698718939\) \(a_{52}=-0.377969838\) \(a_{53}=-0.236605830\) \(a_{54}=+0.136082763\) \(a_{55}=-0.275950900\)
\(a_{56}=+0.588085992\) \(a_{57}=+0.024950516\) \(a_{58}=-0.934064573\) \(a_{59}=-0.352452024\) \(a_{60}=-0.074709284\)
\(a_{61}=+0.616701736\) \(a_{62}=+1.308736909\) \(a_{63}=+0.554452791\) \(a_{64}=+0.124999999\) \(a_{65}=+0.195637603\)
\(a_{66}=+0.435302338\) \(a_{67}=-0.822883718\) \(a_{68}=-0.605108355\) \(a_{69}=-0.383857521\) \(a_{70}=-0.304393967\)
\(a_{71}=-1.258820656\) \(a_{72}=+0.117851130\) \(a_{73}=+0.892327538\) \(a_{74}=-0.515755919\) \(a_{75}=-0.538680662\)
\(a_{76}=+0.021607781\) \(a_{77}=+1.773586801\) \(a_{78}=-0.308611081\) \(a_{79}=+0.552592925\) \(a_{80}=-0.064700137\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.012473760\) \(a_{83}=-0.283906065\) \(a_{84}=+0.480170202\) \(a_{85}=+0.313204748\)
\(a_{86}=+0.332240283\) \(a_{87}=-0.762660530\) \(a_{88}=+0.376982878\) \(a_{89}=-0.805409779\) \(a_{90}=-0.060999874\)
\(a_{91}=-1.257398589\) \(a_{92}=-0.332430365\) \(a_{93}=+1.068579211\) \(a_{94}=-0.427730602\) \(a_{95}=-0.011184211\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.579331131\) \(a_{98}=+1.249288734\) \(a_{99}=+0.355422868\) \(a_{100}=-0.466511139\)

Showing 100 of 1000 available coefficients

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