Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 42.9222277836 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.384185328\) \(a_{3}=+0.186518932\) \(a_{4}=-0.852401634\) \(a_{5}=-1.512560796\)
\(a_{6}=+0.071657837\) \(a_{7}=+1.345910109\) \(a_{8}=-0.711665529\) \(a_{9}=-0.965210688\) \(a_{10}=-0.581103665\)
\(a_{11}=-1.186440711\) \(a_{12}=-0.158989043\) \(a_{13}=-0.513866323\) \(a_{14}=+0.517078917\) \(a_{15}=-0.282121224\)
\(a_{16}=+0.578990179\) \(a_{17}=+0.020143500\) \(a_{18}=-0.370819785\) \(a_{19}=-0.735363909\) \(a_{20}=+1.289309294\)
\(a_{21}=+0.251037714\) \(a_{22}=-0.455813114\) \(a_{23}=+0.606086262\) \(a_{24}=-0.132739095\) \(a_{25}=+1.287840160\)
\(a_{26}=-0.197419902\) \(a_{27}=-0.366548999\) \(a_{28}=-1.147255975\) \(a_{29}=+0.820316899\) \(a_{30}=-0.108386835\)
\(a_{31}=+0.598602272\) \(a_{32}=+0.934105061\) \(a_{33}=-0.221293654\) \(a_{34}=+0.007738837\) \(a_{35}=-2.035770865\)
\(a_{36}=+0.822747167\) \(a_{37}=-1.146272815\) \(a_{38}=-0.282516025\) \(a_{39}=-0.095845798\) \(a_{40}=+1.076437379\)
\(a_{41}=+1.224759293\) \(a_{42}=+0.096445007\) \(a_{43}=+1.033881148\) \(a_{44}=+1.011324000\) \(a_{45}=+1.459939846\)
\(a_{46}=+0.232849449\) \(a_{47}=+0.583982353\) \(a_{48}=+0.107992630\) \(a_{49}=+0.811474020\) \(a_{50}=+0.494769294\)
\(a_{51}=+0.003757144\) \(a_{52}=+0.438020493\) \(a_{53}=-0.703208661\) \(a_{54}=-0.140822747\) \(a_{55}=+1.794563705\)
\(a_{56}=-0.957837830\) \(a_{57}=-0.137159291\) \(a_{58}=+0.315153717\) \(a_{59}=-0.724362234\) \(a_{60}=+0.240480593\)
\(a_{61}=+0.961598129\) \(a_{62}=+0.229974211\) \(a_{63}=-1.299086823\) \(a_{64}=-0.220120719\) \(a_{65}=+0.777254055\)
\(a_{66}=-0.085017779\) \(a_{67}=+0.256754653\) \(a_{68}=-0.017170355\) \(a_{69}=+0.113046551\) \(a_{70}=-0.782113297\)
\(a_{71}=-0.180201214\) \(a_{72}=+0.686907175\) \(a_{73}=+0.303919196\) \(a_{74}=-0.440381197\) \(a_{75}=+0.240206572\)
\(a_{76}=+0.626825398\) \(a_{77}=-1.596842546\) \(a_{78}=-0.036822549\) \(a_{79}=+1.320905238\) \(a_{80}=-0.875757846\)
\(a_{81}=+0.896842360\) \(a_{82}=+0.470534551\) \(a_{83}=-1.289457407\) \(a_{84}=-0.213984959\) \(a_{85}=-0.030468268\)
\(a_{86}=+0.397201968\) \(a_{87}=+0.153004632\) \(a_{88}=+0.844348956\) \(a_{89}=-0.873312890\) \(a_{90}=+0.560887469\)
\(a_{91}=-0.691617878\) \(a_{92}=-0.516628920\) \(a_{93}=+0.111650657\) \(a_{94}=+0.224357452\) \(a_{95}=+1.112282620\)
\(a_{96}=+0.174228279\) \(a_{97}=-1.528765421\) \(a_{98}=+0.311756413\) \(a_{99}=+1.145165255\) \(a_{100}=-1.097757057\)

Showing 100 of 5000 available coefficients

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