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: \( 10.1454558365 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.753825434\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.773335560\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.240141858\)
\(a_{11}=-0.083456402\) \(a_{12}=+0.288675135\) \(a_{13}=-1.755763306\) \(a_{14}=-0.546830818\) \(a_{15}=-1.012571587\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.094258459\) \(a_{18}=+0.235702260\) \(a_{19}=-0.099425441\) \(a_{20}=-0.876912717\)
\(a_{21}=-0.446485494\) \(a_{22}=-0.059012588\) \(a_{23}=-0.550499919\) \(a_{24}=+0.204124145\) \(a_{25}=+2.075903654\)
\(a_{26}=-1.241512139\) \(a_{27}=+0.192450088\) \(a_{28}=-0.386667779\) \(a_{29}=+0.848055671\) \(a_{30}=-0.715996260\)
\(a_{31}=-1.117357778\) \(a_{32}=+0.176776695\) \(a_{33}=-0.048183576\) \(a_{34}=-0.066650796\) \(a_{35}=+1.356295574\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.342152196\) \(a_{38}=-0.070304404\) \(a_{39}=-1.013690417\) \(a_{40}=-0.620070929\)
\(a_{41}=+1.097496691\) \(a_{42}=-0.315712920\) \(a_{43}=+0.054454095\) \(a_{44}=-0.041728201\) \(a_{45}=-0.584608478\)
\(a_{46}=-0.389262225\) \(a_{47}=+0.413671465\) \(a_{48}=+0.144337567\) \(a_{49}=-0.401952112\) \(a_{50}=+1.467885551\)
\(a_{51}=-0.054420147\) \(a_{52}=-0.877881653\) \(a_{53}=+0.681932812\) \(a_{54}=+0.136082764\) \(a_{55}=+0.146367960\)
\(a_{56}=-0.273415409\) \(a_{57}=-0.057403305\) \(a_{58}=+0.599665913\) \(a_{59}=-1.127522823\) \(a_{60}=-0.506285793\)
\(a_{61}=-0.564235450\) \(a_{62}=-0.790091262\) \(a_{63}=-0.257778520\) \(a_{64}=+0.125000001\) \(a_{65}=+3.079302341\)
\(a_{66}=-0.034070934\) \(a_{67}=+0.345628634\) \(a_{68}=-0.047129229\) \(a_{69}=-0.317831276\) \(a_{70}=+0.959045795\)
\(a_{71}=-1.629549225\) \(a_{72}=+0.117851136\) \(a_{73}=-1.318073425\) \(a_{74}=+0.241938132\) \(a_{75}=+1.198523533\)
\(a_{76}=-0.049712720\) \(a_{77}=+0.064539803\) \(a_{78}=-0.716787368\) \(a_{79}=-1.354221855\) \(a_{80}=-0.438456359\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.776047352\) \(a_{83}=+1.680649543\) \(a_{84}=-0.223242747\) \(a_{85}=+0.165312883\)
\(a_{86}=+0.038504860\) \(a_{87}=+0.489625168\) \(a_{88}=-0.029506294\) \(a_{89}=-0.881596209\) \(a_{90}=-0.413380619\)
\(a_{91}=+1.357794198\) \(a_{92}=-0.275249959\) \(a_{93}=-0.645106814\) \(a_{94}=+0.292509898\) \(a_{95}=+0.174374867\)
\(a_{96}=+0.102062072\) \(a_{97}=-1.632301332\) \(a_{98}=-0.284223064\) \(a_{99}=-0.027818801\) \(a_{100}=+1.037951828\)

Showing 100 of 1000 available coefficients

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