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: \( 14.3794514696 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.370650455\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.415382814\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.262089450\)
\(a_{11}=+0.651558702\) \(a_{12}=-0.288675135\) \(a_{13}=+0.399343592\) \(a_{14}=+0.293720005\) \(a_{15}=+0.213995140\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.839648886\) \(a_{18}=-0.235702260\) \(a_{19}=+1.789620848\) \(a_{20}=-0.185325227\)
\(a_{21}=+0.239821380\) \(a_{22}=-0.460721577\) \(a_{23}=-1.264373312\) \(a_{24}=+0.204124145\) \(a_{25}=-0.862618240\)
\(a_{26}=-0.282378562\) \(a_{27}=-0.192450090\) \(a_{28}=-0.207691407\) \(a_{29}=-0.755773371\) \(a_{30}=-0.151317415\)
\(a_{31}=-1.609554981\) \(a_{32}=-0.176776695\) \(a_{33}=-0.376177593\) \(a_{34}=-0.593721419\) \(a_{35}=+0.153961827\)
\(a_{36}=+0.166666662\) \(a_{37}=+1.778821135\) \(a_{38}=-1.265453038\) \(a_{39}=-0.230561130\) \(a_{40}=+0.131044725\)
\(a_{41}=-1.651790126\) \(a_{42}=-0.169579324\) \(a_{43}=+0.140267807\) \(a_{44}=+0.325779351\) \(a_{45}=-0.123550152\)
\(a_{46}=+0.894046943\) \(a_{47}=+0.353199309\) \(a_{48}=-0.144337567\) \(a_{49}=-0.827457118\) \(a_{50}=+0.609963207\)
\(a_{51}=-0.484771511\) \(a_{52}=+0.199671796\) \(a_{53}=+0.032758400\) \(a_{54}=+0.136082763\) \(a_{55}=-0.241500529\)
\(a_{56}=+0.146860002\) \(a_{57}=-1.033238079\) \(a_{58}=+0.534412475\) \(a_{59}=-0.552420507\) \(a_{60}=+0.106997570\)
\(a_{61}=+0.053664193\) \(a_{62}=+1.138127242\) \(a_{63}=-0.138460938\) \(a_{64}=+0.125000000\) \(a_{65}=-0.148016884\)
\(a_{66}=+0.265997726\) \(a_{67}=-0.478616152\) \(a_{68}=+0.419824443\) \(a_{69}=+0.729986272\) \(a_{70}=-0.108867453\)
\(a_{71}=-1.684747224\) \(a_{72}=-0.117851131\) \(a_{73}=+0.159216189\) \(a_{74}=-1.257816487\) \(a_{75}=+0.498032873\)
\(a_{76}=+0.894810425\) \(a_{77}=-0.270646288\) \(a_{78}=+0.163031345\) \(a_{79}=+0.772472603\) \(a_{80}=-0.092662614\)
\(a_{81}=+0.111111122\) \(a_{82}=+1.167991999\) \(a_{83}=-0.676104647\) \(a_{84}=+0.119910690\) \(a_{85}=-0.311216242\)
\(a_{86}=-0.099184318\) \(a_{87}=+0.436345959\) \(a_{88}=-0.230360788\) \(a_{89}=-1.497849857\) \(a_{90}=+0.087363150\)
\(a_{91}=-0.165880465\) \(a_{92}=-0.632186656\) \(a_{93}=+0.929277002\) \(a_{94}=-0.249749627\) \(a_{95}=-0.663323782\)
\(a_{96}=+0.102062073\) \(a_{97}=+1.325013142\) \(a_{98}=+0.585100539\) \(a_{99}=+0.217186234\) \(a_{100}=-0.431309120\)

Showing 100 of 1000 available coefficients

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