Properties

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

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 16.6328704615 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.855015980\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.899951723\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.311694379\)
\(a_{11}=-1.012862510\) \(a_{12}=-0.288675135\) \(a_{13}=+0.875393235\) \(a_{14}=-0.636361966\) \(a_{15}=+1.070993975\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.448535432\) \(a_{18}=-0.235702260\) \(a_{19}=+1.373418008\) \(a_{20}=-0.927507990\)
\(a_{21}=-0.519587370\) \(a_{22}=+0.716201949\) \(a_{23}=+0.347628496\) \(a_{24}=+0.204124145\) \(a_{25}=+2.441084286\)
\(a_{26}=-0.618996492\) \(a_{27}=-0.192450090\) \(a_{28}=+0.449975862\) \(a_{29}=-0.217449250\) \(a_{30}=-0.757307103\)
\(a_{31}=+0.173392858\) \(a_{32}=-0.176776695\) \(a_{33}=+0.584776443\) \(a_{34}=-0.317162446\) \(a_{35}=-1.669424827\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.784079571\) \(a_{38}=-0.971153187\) \(a_{39}=-0.505408520\) \(a_{40}=+0.655847189\)
\(a_{41}=+0.139754863\) \(a_{42}=+0.367403752\) \(a_{43}=-1.558394555\) \(a_{44}=-0.506431255\) \(a_{45}=-0.618338660\)
\(a_{46}=-0.245810467\) \(a_{47}=+1.306397836\) \(a_{48}=-0.144337567\) \(a_{49}=-0.190086896\) \(a_{50}=-1.726107252\)
\(a_{51}=-0.258962052\) \(a_{52}=+0.437696617\) \(a_{53}=-0.655337362\) \(a_{54}=+0.136082763\) \(a_{55}=+1.878876142\)
\(a_{56}=-0.318180983\) \(a_{57}=-0.792943257\) \(a_{58}=+0.153759840\) \(a_{59}=-0.152924380\) \(a_{60}=+0.535496988\)
\(a_{61}=-0.429190140\) \(a_{62}=-0.122607266\) \(a_{63}=+0.299983908\) \(a_{64}=+0.125000000\) \(a_{65}=-1.623868439\)
\(a_{66}=-0.413499388\) \(a_{67}=+0.313643410\) \(a_{68}=+0.224267716\) \(a_{69}=-0.200703406\) \(a_{70}=+1.180461616\)
\(a_{71}=+1.544352200\) \(a_{72}=-0.117851130\) \(a_{73}=-1.343119800\) \(a_{74}=+1.261534763\) \(a_{75}=-1.409360669\)
\(a_{76}=+0.686709004\) \(a_{77}=-0.911527361\) \(a_{78}=+0.357377792\) \(a_{79}=-0.444078000\) \(a_{80}=-0.463753995\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.098821611\) \(a_{83}=+0.360761002\) \(a_{84}=-0.259793685\) \(a_{85}=-0.832040394\)
\(a_{86}=+1.101951358\) \(a_{87}=+0.125544383\) \(a_{88}=+0.358100975\) \(a_{89}=+0.405900002\) \(a_{90}=+0.437231460\)
\(a_{91}=+0.787811650\) \(a_{92}=+0.173814248\) \(a_{93}=-0.100108413\) \(a_{94}=-0.923762768\) \(a_{95}=-2.547712352\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.969001770\) \(a_{98}=+0.134411733\) \(a_{99}=-0.337620837\) \(a_{100}=+1.220542143\)

Showing 100 of 112 available coefficients

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