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: \( 7.15749058532 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.281192790\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.345819450\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.905940110\)
\(a_{11}=-0.873364006\) \(a_{12}=-0.288675135\) \(a_{13}=+0.261182608\) \(a_{14}=+0.951638059\) \(a_{15}=-0.739697002\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.467851775\) \(a_{18}=+0.235702260\) \(a_{19}=-1.163930955\) \(a_{20}=+0.640596395\)
\(a_{21}=-0.777009222\) \(a_{22}=-0.617561611\) \(a_{23}=+1.271118963\) \(a_{24}=-0.204124145\) \(a_{25}=+0.641454965\)
\(a_{26}=+0.184683994\) \(a_{27}=-0.192450090\) \(a_{28}=+0.672909725\) \(a_{29}=-0.730471546\) \(a_{30}=-0.523044766\)
\(a_{31}=-1.559835373\) \(a_{32}=+0.176776695\) \(a_{33}=+0.504236944\) \(a_{34}=+0.330821163\) \(a_{35}=+1.724254176\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.424446610\) \(a_{38}=-0.823023471\) \(a_{39}=-0.150793849\) \(a_{40}=+0.452970055\)
\(a_{41}=+0.570642691\) \(a_{42}=-0.549428490\) \(a_{43}=-0.823071893\) \(a_{44}=-0.436682003\) \(a_{45}=+0.427064263\)
\(a_{46}=+0.898816838\) \(a_{47}=-1.319576350\) \(a_{48}=-0.144337567\) \(a_{49}=+0.811229992\) \(a_{50}=+0.453577155\)
\(a_{51}=-0.270114348\) \(a_{52}=+0.130591304\) \(a_{53}=+1.100693300\) \(a_{54}=-0.136082763\) \(a_{55}=-1.118947667\)
\(a_{56}=+0.475819030\) \(a_{57}=+0.671995850\) \(a_{58}=-0.516521384\) \(a_{59}=-0.241833000\) \(a_{60}=-0.369848501\)
\(a_{61}=-0.296227000\) \(a_{62}=-1.102970170\) \(a_{63}=+0.448606483\) \(a_{64}=+0.125000000\) \(a_{65}=+0.334625275\)
\(a_{66}=+0.356549362\) \(a_{67}=-0.264690000\) \(a_{68}=+0.233925887\) \(a_{69}=-0.733880875\) \(a_{70}=+1.219231820\)
\(a_{71}=+0.533630013\) \(a_{72}=+0.117851130\) \(a_{73}=+1.378299713\) \(a_{74}=-0.300129076\) \(a_{75}=-0.370344197\)
\(a_{76}=-0.581965478\) \(a_{77}=-1.175390266\) \(a_{78}=-0.106627353\) \(a_{79}=-1.640000000\) \(a_{80}=+0.320298197\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.403505316\) \(a_{83}=+0.789978027\) \(a_{84}=-0.388504611\) \(a_{85}=+0.599408321\)
\(a_{86}=-0.581999717\) \(a_{87}=+0.421737944\) \(a_{88}=-0.308780805\)

Showing all 88 available coefficients

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