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: \( 47.9265583306 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.511058434\) \(a_{3}=+1.700681263\) \(a_{4}=-0.738819277\) \(a_{5}=-1.358582751\)
\(a_{6}=+0.869147502\) \(a_{7}=+0.028925946\) \(a_{8}=-0.888638256\) \(a_{9}=+1.892316756\) \(a_{10}=-0.694315173\)
\(a_{11}=-0.295544126\) \(a_{12}=-1.256496101\) \(a_{13}=-0.087366865\) \(a_{14}=+0.014782849\) \(a_{15}=-2.310516229\)
\(a_{16}=+0.284673202\) \(a_{17}=+0.937817000\) \(a_{18}=+0.967084438\) \(a_{19}=+1.795503232\) \(a_{20}=+1.003747133\)
\(a_{21}=+0.049193769\) \(a_{22}=-0.151039948\) \(a_{23}=+0.834397327\) \(a_{24}=-1.511290432\) \(a_{25}=+0.845747092\)
\(a_{26}=-0.044649573\) \(a_{27}=+1.517546388\) \(a_{28}=-0.021371046\) \(a_{29}=+0.457702082\) \(a_{30}=-1.180808801\)
\(a_{31}=+0.983544353\) \(a_{32}=+1.034122897\) \(a_{33}=-0.502626357\) \(a_{34}=+0.479279287\) \(a_{35}=-0.039298291\)
\(a_{36}=-1.398080099\) \(a_{37}=-0.281997063\) \(a_{38}=+0.917607070\) \(a_{39}=-0.148583191\) \(a_{40}=+1.207288608\)
\(a_{41}=+0.106615524\) \(a_{42}=+0.025140913\) \(a_{43}=-0.056789382\) \(a_{44}=+0.218353697\) \(a_{45}=-2.570868906\)
\(a_{46}=+0.426425791\) \(a_{47}=-0.594028135\) \(a_{48}=+0.484138380\) \(a_{49}=-0.999163290\) \(a_{50}=+0.432226185\)
\(a_{51}=+1.594927800\) \(a_{52}=+0.064548324\) \(a_{53}=+1.570495982\) \(a_{54}=+0.775554880\) \(a_{55}=+0.401521152\)
\(a_{56}=-0.025704701\) \(a_{57}=+3.053578703\) \(a_{58}=+0.233912511\) \(a_{59}=-1.438940091\) \(a_{60}=+1.707053924\)
\(a_{61}=+0.238236479\) \(a_{62}=+0.502648620\) \(a_{63}=+0.054737048\) \(a_{64}=+0.243824096\) \(a_{65}=+0.118694939\)
\(a_{66}=-0.256871204\) \(a_{67}=+0.333596780\) \(a_{68}=-0.692877278\) \(a_{69}=+1.419043899\) \(a_{70}=-0.020083723\)
\(a_{71}=-0.217222531\) \(a_{72}=-1.681585063\) \(a_{73}=+1.273568777\) \(a_{74}=-0.144116977\) \(a_{75}=+1.438346233\)
\(a_{76}=-1.326552401\) \(a_{77}=-0.008548893\) \(a_{78}=-0.075934693\) \(a_{79}=+0.095472770\) \(a_{80}=-0.386752101\)
\(a_{81}=+0.688545951\) \(a_{82}=+0.054486763\) \(a_{83}=+0.285832380\) \(a_{84}=-0.036345338\) \(a_{85}=-1.274102001\)
\(a_{86}=-0.029022693\) \(a_{87}=+0.778405355\) \(a_{88}=+0.262631817\) \(a_{89}=+0.879120870\) \(a_{90}=-1.313864236\)
\(a_{91}=-0.002527169\) \(a_{92}=-0.616468831\) \(a_{93}=+1.672695453\) \(a_{94}=-0.303583089\) \(a_{95}=-2.439339723\)
\(a_{96}=+1.758713436\) \(a_{97}=+1.398034242\) \(a_{98}=-0.510630825\) \(a_{99}=-0.559263099\) \(a_{100}=-0.624854262\)

Showing 100 of 5000 available coefficients

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