Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 8.27366588959 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.198212710\) \(a_{4}=+0.500000000\) \(a_{5}=-0.213106436\)
\(a_{6}=+0.847264333\) \(a_{7}=-0.941436187\) \(a_{8}=+0.353553391\) \(a_{9}=+0.435713699\) \(a_{10}=-0.150689006\)
\(a_{11}=-0.848628416\) \(a_{12}=+0.599106355\) \(a_{13}=+0.685984750\) \(a_{14}=-0.665695912\) \(a_{15}=-0.255346841\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.247079926\) \(a_{18}=+0.308096111\) \(a_{19}=+0.587317133\) \(a_{20}=-0.106553218\)
\(a_{21}=-1.128040805\) \(a_{22}=-0.600070908\) \(a_{23}=+1.676069992\) \(a_{24}=+0.423632166\) \(a_{25}=-0.954585647\)
\(a_{26}=+0.485064468\) \(a_{27}=-0.676135018\) \(a_{28}=-0.470718094\) \(a_{29}=+0.588859861\) \(a_{30}=-0.180557483\)
\(a_{31}=+1.012940051\) \(a_{32}=+0.176776695\) \(a_{33}=-1.016837355\) \(a_{34}=-0.174711891\) \(a_{35}=+0.200626111\)
\(a_{36}=+0.217856849\) \(a_{37}=-0.901020465\) \(a_{38}=+0.415295927\) \(a_{39}=+0.821955646\) \(a_{40}=-0.075344503\)
\(a_{41}=+0.939390000\) \(a_{42}=-0.797645303\) \(a_{43}=-1.137417896\) \(a_{44}=-0.424314208\) \(a_{45}=-0.092853394\)
\(a_{46}=+1.185160457\) \(a_{47}=+0.500688557\) \(a_{48}=+0.299553178\) \(a_{49}=-0.113697906\) \(a_{50}=-0.674993984\)
\(a_{51}=-0.296054308\) \(a_{52}=+0.342992375\) \(a_{53}=-0.180070650\) \(a_{54}=-0.478099656\) \(a_{55}=+0.180848178\)
\(a_{56}=-0.332847956\) \(a_{57}=+0.703730854\) \(a_{58}=+0.416386801\) \(a_{59}=+0.745624199\) \(a_{60}=-0.127673420\)
\(a_{61}=-1.572244909\) \(a_{62}=+0.716256779\) \(a_{63}=-0.410196643\) \(a_{64}=+0.125000000\) \(a_{65}=-0.146187765\)
\(a_{66}=-0.719012589\) \(a_{67}=+0.282376671\) \(a_{68}=-0.123539963\) \(a_{69}=+2.008288367\) \(a_{70}=+0.141864084\)
\(a_{71}=-0.488922596\) \(a_{72}=+0.154048056\) \(a_{73}=-0.781014231\) \(a_{74}=-0.637117681\) \(a_{75}=-1.143796655\)
\(a_{76}=+0.293658566\) \(a_{77}=+0.798929500\) \(a_{78}=+0.581210411\) \(a_{79}=+0.711177174\) \(a_{80}=-0.053276609\)
\(a_{81}=-1.245867272\) \(a_{82}=+0.664249039\) \(a_{83}=+0.735441422\) \(a_{84}=-0.564020403\) \(a_{85}=+0.052654323\)
\(a_{86}=-0.804275907\) \(a_{87}=+0.705579370\) \(a_{88}=-0.300035454\) \(a_{89}=-0.737871573\) \(a_{90}=-0.065657264\)
\(a_{91}=-0.645810867\) \(a_{92}=+0.838034996\) \(a_{93}=+1.213717644\) \(a_{94}=+0.354040274\) \(a_{95}=-0.125161061\)
\(a_{96}=+0.211816083\) \(a_{97}=-0.519795473\) \(a_{98}=-0.080396560\) \(a_{99}=-0.369759026\) \(a_{100}=-0.477292823\)

Showing 100 of 1228 available coefficients

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