Properties

Level $85$
Weight $0$
Character 85.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 85 = 5 \cdot 17 \)
Weight: \( 0 \)
Character: 85.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.578461236089 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.745780755\) \(a_{3}=-0.717393730\) \(a_{4}=+2.047750444\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.252412167\) \(a_{7}=-0.240093200\) \(a_{8}=+1.829142562\) \(a_{9}=-0.485346236\) \(a_{10}=-0.780736888\)
\(a_{11}=-0.647485389\) \(a_{12}=-1.469043329\) \(a_{13}=+1.254102006\) \(a_{14}=-0.419150089\) \(a_{15}=+0.320828229\)
\(a_{16}=+1.145531438\) \(a_{17}=+0.242535625\) \(a_{18}=-0.847308119\) \(a_{19}=-0.654995559\) \(a_{20}=-0.915781839\)
\(a_{21}=+0.172241357\) \(a_{22}=-1.130367531\) \(a_{23}=+0.041887471\) \(a_{24}=-1.312215405\) \(a_{25}=+0.199951172\)
\(a_{26}=+2.189387147\) \(a_{27}=+1.065578077\) \(a_{28}=-0.491650958\) \(a_{29}=+0.596685390\) \(a_{30}=+0.560095748\)
\(a_{31}=+1.273560002\) \(a_{32}=+0.170704177\) \(a_{33}=+0.464501958\) \(a_{34}=+0.423414027\) \(a_{35}=+0.107372943\)
\(a_{36}=-0.993867971\) \(a_{37}=+0.619141841\) \(a_{38}=-1.143478641\) \(a_{39}=-0.899684916\) \(a_{40}=-0.818017422\)
\(a_{41}=-1.898329622\) \(a_{42}=+0.300695646\) \(a_{43}=+0.772755905\) \(a_{44}=-1.325888492\) \(a_{45}=+0.217053435\)
\(a_{46}=+0.073126342\) \(a_{47}=+0.211278240\) \(a_{48}=-0.821797071\) \(a_{49}=-0.942355255\) \(a_{50}=+0.349156151\)
\(a_{51}=-0.173993537\) \(a_{52}=+2.568087940\) \(a_{53}=-0.151152972\) \(a_{54}=+1.860265699\) \(a_{55}=+0.289564269\)
\(a_{56}=-0.439164692\) \(a_{57}=+0.469889707\) \(a_{58}=+1.041681871\) \(a_{59}=+0.878074893\) \(a_{60}=+0.656976149\)
\(a_{61}=-1.367655192\) \(a_{62}=+2.223356542\) \(a_{63}=+0.116528331\) \(a_{64}=-0.847519371\) \(a_{65}=-0.560851467\)
\(a_{66}=+0.810918579\) \(a_{67}=-1.186990036\) \(a_{68}=+0.496652434\) \(a_{69}=-0.030049809\) \(a_{70}=+0.187449618\)
\(a_{71}=+0.382774760\) \(a_{72}=-0.887767458\) \(a_{73}=+0.849908765\) \(a_{74}=+1.080885911\) \(a_{75}=-0.143478746\)
\(a_{76}=-1.341267446\) \(a_{77}=+0.155456839\) \(a_{78}=-1.570652612\) \(a_{79}=-0.937043047\) \(a_{80}=-0.512297233\)
\(a_{81}=-0.279092795\) \(a_{82}=-3.314067320\) \(a_{83}=+0.021315822\) \(a_{84}=+0.352707315\) \(a_{85}=-0.108465229\)
\(a_{86}=+1.349062387\) \(a_{87}=-0.428058357\) \(a_{88}=-1.184343083\) \(a_{89}=-0.817859509\) \(a_{90}=+0.378927710\)
\(a_{91}=-0.301101364\) \(a_{92}=+0.085775088\) \(a_{93}=-0.913643960\) \(a_{94}=+0.368845485\) \(a_{95}=+0.292922919\)
\(a_{96}=-0.122462106\) \(a_{97}=-1.079406457\) \(a_{98}=-1.645145669\) \(a_{99}=+0.314254597\) \(a_{100}=+0.409550089\)

Showing 100 of 646 available coefficients

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