Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 21.4790575447 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.656250008\) \(a_{3}=+0.226441881\) \(a_{4}=-0.569335927\) \(a_{5}=+1.082293347\)
\(a_{6}=-0.148602487\) \(a_{7}=+0.423534131\) \(a_{8}=+1.029876715\) \(a_{9}=-0.948724074\) \(a_{10}=-0.710255018\)
\(a_{11}=-1.658529269\) \(a_{12}=-0.128921498\) \(a_{13}=-0.661095730\) \(a_{14}=-0.277944277\) \(a_{15}=+0.245076542\)
\(a_{16}=-0.106520676\) \(a_{17}=-0.494627437\) \(a_{18}=+0.622600182\) \(a_{19}=+0.001399322\) \(a_{20}=-0.616188486\)
\(a_{21}=+0.095905866\) \(a_{22}=+1.088409846\) \(a_{23}=-1.245546121\) \(a_{24}=+0.233207221\) \(a_{25}=+0.171358889\)
\(a_{26}=+0.433844078\) \(a_{27}=-0.441272746\) \(a_{28}=-0.241133197\) \(a_{29}=+0.219809656\) \(a_{30}=-0.160831483\)
\(a_{31}=+1.017542220\) \(a_{32}=-0.959972520\) \(a_{33}=-0.375560488\) \(a_{34}=+0.324599259\) \(a_{35}=+0.458388173\)
\(a_{36}=+0.540142700\) \(a_{37}=-1.160330879\) \(a_{38}=-0.000918305\) \(a_{39}=-0.149699761\) \(a_{40}=+1.114628717\)
\(a_{41}=-0.313557925\) \(a_{42}=-0.062938225\) \(a_{43}=-0.836537339\) \(a_{44}=+0.944260298\) \(a_{45}=-1.026797754\)
\(a_{46}=+0.817389652\) \(a_{47}=+0.421679414\) \(a_{48}=-0.024120742\) \(a_{49}=-0.820618840\) \(a_{50}=-0.112454273\)
\(a_{51}=-0.112004367\) \(a_{52}=+0.376385550\) \(a_{53}=+0.911475271\) \(a_{54}=+0.289585242\) \(a_{55}=-1.795015194\)
\(a_{56}=+0.436187942\) \(a_{57}=+0.000316862\) \(a_{58}=-0.144250090\) \(a_{59}=+0.966347721\) \(a_{60}=-0.139530902\)
\(a_{61}=+0.134282570\) \(a_{62}=-0.667762090\) \(a_{63}=-0.401817027\) \(a_{64}=+0.736502650\) \(a_{65}=-0.715499510\)
\(a_{66}=+0.246461573\) \(a_{67}=+0.696754565\) \(a_{68}=+0.281609170\) \(a_{69}=-0.282043807\) \(a_{70}=-0.300817242\)
\(a_{71}=-0.501067930\) \(a_{72}=-0.977068833\) \(a_{73}=+1.209699986\) \(a_{74}=+0.761467149\) \(a_{75}=+0.038802829\)
\(a_{76}=-0.000796684\) \(a_{77}=-0.702443753\) \(a_{78}=+0.098240469\) \(a_{79}=-0.717711609\) \(a_{80}=-0.115286619\)
\(a_{81}=+0.848801444\) \(a_{82}=+0.205772391\) \(a_{83}=+0.204486321\) \(a_{84}=-0.054602655\) \(a_{85}=-0.535331984\)
\(a_{86}=+0.548977635\) \(a_{87}=+0.049774112\) \(a_{88}=-1.708080675\) \(a_{89}=+0.635464330\) \(a_{90}=+0.673836034\)
\(a_{91}=-0.279996605\) \(a_{92}=+0.709134155\) \(a_{93}=+0.230414175\) \(a_{94}=-0.276727120\) \(a_{95}=+0.001514478\)
\(a_{96}=-0.217377984\) \(a_{97}=-1.953693055\) \(a_{98}=+0.538531119\) \(a_{99}=+1.573486643\) \(a_{100}=-0.097560771\)

Showing 100 of 5000 available coefficients

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