Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 6.27191087352 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.270896712\) \(a_{3}=-1.376017124\) \(a_{4}=+0.615178453\) \(a_{5}=-1.256649954\)
\(a_{6}=-1.748775638\) \(a_{7}=+0.377964473\) \(a_{8}=-0.489068439\) \(a_{9}=+0.893423124\) \(a_{10}=-1.597072295\)
\(a_{11}=+1.055666792\) \(a_{12}=-0.846496086\) \(a_{13}=-0.875640044\) \(a_{14}=+0.480353806\) \(a_{15}=+1.729171855\)
\(a_{16}=-1.236733924\) \(a_{17}=-0.402044155\) \(a_{18}=+1.135448512\) \(a_{19}=-0.122300174\) \(a_{20}=-0.773063975\)
\(a_{21}=-0.520085587\) \(a_{22}=+1.341643456\) \(a_{23}=-1.559362395\) \(a_{24}=+0.672966546\) \(a_{25}=+0.579169106\)
\(a_{26}=-1.112848054\) \(a_{27}=+0.146651606\) \(a_{28}=+0.232515600\) \(a_{29}=+0.877067887\) \(a_{30}=+2.197598825\)
\(a_{31}=-0.922917388\) \(a_{32}=-1.082692639\) \(a_{33}=-1.452615583\) \(a_{34}=-0.510956595\) \(a_{35}=-0.474969038\)
\(a_{36}=+0.549614656\) \(a_{37}=+0.294566240\) \(a_{38}=-0.155430889\) \(a_{39}=+1.204895695\) \(a_{40}=+0.614587831\)
\(a_{41}=+1.036790303\) \(a_{42}=-0.660975063\) \(a_{43}=+0.090226688\) \(a_{44}=+0.649423464\) \(a_{45}=-1.122720128\)
\(a_{46}=-1.981788541\) \(a_{47}=-1.146205087\) \(a_{48}=+1.701767057\) \(a_{49}=+0.142857143\) \(a_{50}=+0.736064113\)
\(a_{51}=+0.553219642\) \(a_{52}=-0.538674888\) \(a_{53}=-0.263094643\) \(a_{54}=+0.186379044\) \(a_{55}=-1.326603626\)
\(a_{56}=-0.184850495\) \(a_{57}=+0.168287133\) \(a_{58}=+1.114662695\) \(a_{59}=+1.177415305\) \(a_{60}=+1.063749267\)
\(a_{61}=-0.889289956\) \(a_{62}=-1.172932674\) \(a_{63}=+0.337682200\) \(a_{64}=-0.139256592\) \(a_{65}=+1.100373021\)
\(a_{66}=-1.846124369\) \(a_{67}=-0.238636581\) \(a_{68}=-0.247328901\) \(a_{69}=+2.145709358\) \(a_{70}=-0.603636588\)
\(a_{71}=-1.350498891\) \(a_{72}=-0.436945052\) \(a_{73}=+0.290038813\) \(a_{74}=+0.374363266\) \(a_{75}=-0.796946608\)
\(a_{76}=-0.075236432\) \(a_{77}=+0.399004543\) \(a_{78}=+1.531297978\) \(a_{79}=-1.178993630\) \(a_{80}=+1.554141628\)
\(a_{81}=-1.095218245\) \(a_{82}=+1.317653388\) \(a_{83}=+0.886602558\) \(a_{84}=-0.319945447\) \(a_{85}=+0.505228769\)
\(a_{86}=+0.114668801\) \(a_{87}=-1.206860432\) \(a_{88}=-0.516293310\) \(a_{89}=-0.180518754\) \(a_{90}=-1.426861320\)
\(a_{91}=-0.330960828\) \(a_{92}=-0.959286146\) \(a_{93}=+1.269950130\) \(a_{94}=-1.456708277\) \(a_{95}=+0.153688508\)
\(a_{96}=+1.489803611\) \(a_{97}=-0.427572054\) \(a_{98}=+0.181556673\) \(a_{99}=+0.943157124\) \(a_{100}=+0.356292355\)

Showing 100 of 1228 available coefficients

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