Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.40345084102 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.860590285\) \(a_{4}=+0.500000000\) \(a_{5}=-0.080603723\)
\(a_{6}=+0.608529226\) \(a_{7}=-1.136661811\) \(a_{8}=+0.353553391\) \(a_{9}=-0.259384361\) \(a_{10}=-0.056995439\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.430295143\) \(a_{13}=+1.536064096\) \(a_{14}=-0.803741274\) \(a_{15}=-0.069366781\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.156487602\) \(a_{18}=-0.183412441\) \(a_{19}=+1.201838804\) \(a_{20}=-0.040301861\)
\(a_{21}=-0.978200112\) \(a_{22}=-0.213200716\) \(a_{23}=-1.085898433\) \(a_{24}=+0.304264613\) \(a_{25}=-0.993503040\)
\(a_{26}=+1.086161339\) \(a_{27}=-1.083813946\) \(a_{28}=-0.568330905\) \(a_{29}=+1.281573185\) \(a_{30}=-0.049049721\)
\(a_{31}=+0.293909033\) \(a_{32}=+0.176776695\) \(a_{33}=-0.259477734\) \(a_{34}=+0.110653444\) \(a_{35}=+0.091619173\)
\(a_{36}=-0.129692180\) \(a_{37}=+1.655214411\) \(a_{38}=+0.849828368\) \(a_{39}=+1.321921838\) \(a_{40}=-0.028497721\)
\(a_{41}=-1.016603280\) \(a_{42}=-0.691691930\) \(a_{43}=-1.154084468\) \(a_{44}=-0.150755674\) \(a_{45}=+0.020907340\)
\(a_{46}=-0.767846146\) \(a_{47}=-0.942393924\) \(a_{48}=+0.215147574\) \(a_{49}=+0.292000075\) \(a_{50}=-0.702512743\)
\(a_{51}=+0.134671695\) \(a_{52}=+0.768032059\) \(a_{53}=+0.361431923\) \(a_{54}=-0.766372204\) \(a_{55}=+0.024302896\)
\(a_{56}=-0.401870632\) \(a_{57}=+1.034290854\) \(a_{58}=+0.906209128\) \(a_{59}=-0.978756653\) \(a_{60}=-0.034683391\)
\(a_{61}=+0.404734422\) \(a_{62}=+0.207825062\) \(a_{63}=+0.294832301\) \(a_{64}=+0.124999983\) \(a_{65}=-0.123812447\)
\(a_{66}=-0.183478486\) \(a_{67}=+0.352957168\) \(a_{68}=+0.078243797\) \(a_{69}=-0.934513602\) \(a_{70}=+0.064784705\)
\(a_{71}=-0.243360526\) \(a_{72}=-0.091705963\) \(a_{73}=+0.249388313\) \(a_{74}=+1.170413523\) \(a_{75}=-0.854999144\)
\(a_{76}=+0.600920142\) \(a_{77}=+0.342712528\) \(a_{78}=+0.934737892\) \(a_{79}=+1.175905568\) \(a_{80}=-0.020145435\)
\(a_{81}=-0.673332980\) \(a_{82}=-0.718844666\) \(a_{83}=-0.781320632\) \(a_{84}=-0.489100039\) \(a_{85}=-0.012613862\)
\(a_{86}=-0.816060981\) \(a_{87}=+1.102910001\) \(a_{88}=-0.106600629\) \(a_{89}=-0.511829759\) \(a_{90}=+0.014783915\)
\(a_{91}=-1.745985592\) \(a_{92}=-0.542949968\) \(a_{93}=+0.252936140\) \(a_{94}=-0.666377264\) \(a_{95}=-0.096875715\)
\(a_{96}=+0.152132389\) \(a_{97}=+1.533660713\) \(a_{98}=+0.206471362\) \(a_{99}=+0.078195416\) \(a_{100}=-0.496752981\)

Showing 100 of 1500 available coefficients

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