Properties

Level $67$
Weight $0$
Character 67.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 67 \)
Weight: \( 0 \)
Character: 67.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.6775902092 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.216823707\) \(a_{3}=+1.749590962\) \(a_{4}=+0.480659934\) \(a_{5}=-0.121512586\)
\(a_{6}=-2.128943760\) \(a_{7}=+0.267750854\) \(a_{8}=+0.631945304\) \(a_{9}=+2.061068534\) \(a_{10}=+0.147859395\)
\(a_{11}=+0.262901264\) \(a_{12}=+0.840958276\) \(a_{13}=-1.116826196\) \(a_{14}=-0.325805587\) \(a_{15}=-0.212597322\)
\(a_{16}=-1.249625962\) \(a_{17}=-1.254333186\) \(a_{18}=-2.507957054\) \(a_{19}=+0.180225783\) \(a_{20}=-0.058406231\)
\(a_{21}=+0.468454475\) \(a_{22}=-0.319904490\) \(a_{23}=+0.386576709\) \(a_{24}=+1.105645793\) \(a_{25}=-0.985234692\)
\(a_{26}=+1.358980592\) \(a_{27}=+1.856435918\) \(a_{28}=+0.128697108\) \(a_{29}=-1.290938586\) \(a_{30}=+0.258693461\)
\(a_{31}=-0.246745519\) \(a_{32}=+0.888629191\) \(a_{33}=+0.459969675\) \(a_{34}=+1.526302357\) \(a_{35}=-0.032535099\)
\(a_{36}=+0.990673066\) \(a_{37}=+0.926782244\) \(a_{38}=-0.219303006\) \(a_{39}=-1.953989019\) \(a_{40}=-0.076789308\)
\(a_{41}=+1.192405479\) \(a_{42}=-0.570026511\) \(a_{43}=+1.356675927\) \(a_{44}=+0.126366104\) \(a_{45}=-0.250445767\)
\(a_{46}=-0.470395704\) \(a_{47}=+0.337491921\) \(a_{48}=-2.186334289\) \(a_{49}=-0.928309480\) \(a_{50}=+1.198856930\)
\(a_{51}=-2.194570006\) \(a_{52}=-0.536813606\) \(a_{53}=+0.528076294\) \(a_{54}=-2.258955235\) \(a_{55}=-0.031945812\)
\(a_{56}=+0.169203895\) \(a_{57}=+0.315321401\) \(a_{58}=+1.570844676\) \(a_{59}=-1.606448427\) \(a_{60}=-0.102187015\)
\(a_{61}=+0.675138685\) \(a_{62}=+0.300245797\) \(a_{63}=+0.551852861\) \(a_{64}=+0.168320896\) \(a_{65}=+0.135708439\)
\(a_{66}=-0.559702005\) \(a_{67}=+0.122169444\) \(a_{68}=-0.602907706\) \(a_{69}=+0.676351116\) \(a_{70}=+0.039589479\)
\(a_{71}=+0.972979769\) \(a_{72}=+1.302482582\) \(a_{73}=+0.969875404\) \(a_{74}=-1.127730605\) \(a_{75}=-1.723757712\)
\(a_{76}=+0.086627313\) \(a_{77}=+0.070392038\) \(a_{78}=+2.377660161\) \(a_{79}=-0.221258590\) \(a_{80}=+0.151845282\)
\(a_{81}=+1.186934969\) \(a_{82}=-1.450947255\) \(a_{83}=-0.765240958\) \(a_{84}=+0.225167297\) \(a_{85}=+0.152417269\)
\(a_{86}=-1.650835431\) \(a_{87}=-2.258614483\) \(a_{88}=+0.166139219\) \(a_{89}=+0.079237920\) \(a_{90}=+0.304748346\)
\(a_{91}=-0.299031168\) \(a_{92}=+0.185811935\) \(a_{93}=-0.431703729\) \(a_{94}=-0.410668170\) \(a_{95}=-0.021899701\)
\(a_{96}=+1.554737601\) \(a_{97}=+1.015384304\) \(a_{98}=+1.129588983\) \(a_{99}=+0.541857522\) \(a_{100}=-0.473562842\)

Showing 100 of 546 available coefficients

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