Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 26.0780963826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.705430246\) \(a_{3}=+0.577350269\) \(a_{4}=+1.908492323\) \(a_{5}=+0.429887527\)
\(a_{6}=-0.984630611\) \(a_{7}=+0.403833428\) \(a_{8}=-1.549370286\) \(a_{9}=+0.333333333\) \(a_{10}=-0.733143191\)
\(a_{11}=+1.582156918\) \(a_{12}=+1.101868556\) \(a_{13}=+1.572407594\) \(a_{14}=-0.688709743\) \(a_{15}=+0.248195680\)
\(a_{16}=+0.733850624\) \(a_{17}=+1.758351450\) \(a_{18}=-0.568476749\) \(a_{19}=+0.614141817\) \(a_{20}=+0.820437046\)
\(a_{21}=+0.233153339\) \(a_{22}=-2.698258262\) \(a_{23}=-0.512000799\) \(a_{24}=-0.894529352\) \(a_{25}=-0.815196714\)
\(a_{26}=-2.681631469\) \(a_{27}=+0.192450090\) \(a_{28}=+0.770712998\) \(a_{29}=+0.262754356\) \(a_{30}=-0.423280419\)
\(a_{31}=-0.133712347\) \(a_{32}=+0.297839235\) \(a_{33}=+0.913458723\) \(a_{34}=-2.998745745\) \(a_{35}=+0.173602954\)
\(a_{36}=+0.636164108\) \(a_{37}=-0.715436651\) \(a_{38}=-1.047376030\) \(a_{39}=+0.907829947\) \(a_{40}=-0.666054961\)
\(a_{41}=+0.847562508\) \(a_{42}=-0.397626755\) \(a_{43}=-0.241477675\) \(a_{44}=+3.019534333\) \(a_{45}=+0.143295842\)
\(a_{46}=+0.873181648\) \(a_{47}=-0.149583579\) \(a_{48}=+0.423688855\) \(a_{49}=-0.836918562\) \(a_{50}=+1.390261132\)
\(a_{51}=+1.015184683\) \(a_{52}=+3.000927821\) \(a_{53}=-1.574950034\) \(a_{54}=-0.328210204\) \(a_{55}=+0.680149526\)
\(a_{56}=-0.625687514\) \(a_{57}=+0.354574943\) \(a_{58}=-0.448109225\) \(a_{59}=+1.181761872\) \(a_{60}=+0.473679549\)
\(a_{61}=+0.400772168\) \(a_{62}=+0.228037081\) \(a_{63}=+0.134611143\) \(a_{64}=-1.241794665\) \(a_{65}=+0.675958412\)
\(a_{66}=-1.557840134\) \(a_{67}=-0.690111120\) \(a_{68}=+3.355800243\) \(a_{69}=-0.295603799\) \(a_{70}=-0.296067728\)
\(a_{71}=-0.563770560\) \(a_{72}=-0.516456762\) \(a_{73}=-0.528838025\) \(a_{74}=+1.220127303\) \(a_{75}=-0.470654042\)
\(a_{76}=+1.172084943\) \(a_{77}=+0.638927853\) \(a_{78}=-1.548240650\) \(a_{79}=-0.881955077\) \(a_{80}=+0.315473230\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.445458737\) \(a_{83}=+1.829340221\) \(a_{84}=+0.444971357\) \(a_{85}=+0.755893357\)
\(a_{86}=+0.411823331\) \(a_{87}=+0.151701298\) \(a_{88}=-2.451346917\) \(a_{89}=+0.437202856\) \(a_{90}=-0.244381064\)
\(a_{91}=+0.634990749\) \(a_{92}=-0.977149594\) \(a_{93}=-0.077198860\) \(a_{94}=+0.255104359\) \(a_{95}=+0.264011907\)
\(a_{96}=+0.171957563\) \(a_{97}=+0.538295052\) \(a_{98}=+1.427306229\) \(a_{99}=+0.527385639\) \(a_{100}=-1.555796670\)

Showing 100 of 1228 available coefficients

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