Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.20820733505 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.392342069\) \(a_{3}=-1.793969231\) \(a_{4}=-0.846067701\) \(a_{5}=-0.560843178\)
\(a_{6}=-0.703849599\) \(a_{7}=-1.365424500\) \(a_{8}=-0.724290021\) \(a_{9}=+2.218325600\) \(a_{10}=-0.220042373\)
\(a_{11}=-0.694598731\) \(a_{12}=+1.517819422\) \(a_{13}=+0.277350098\) \(a_{14}=-0.535713473\) \(a_{15}=+1.006135404\)
\(a_{16}=+0.561898256\) \(a_{17}=+0.432928368\) \(a_{18}=+0.870342455\) \(a_{19}=-1.453000484\) \(a_{20}=+0.474511298\)
\(a_{21}=+2.449529539\) \(a_{22}=-0.272520303\) \(a_{23}=-1.319525569\) \(a_{24}=+1.299354012\) \(a_{25}=-0.685454930\)
\(a_{26}=+0.108816111\) \(a_{27}=-2.185638639\) \(a_{28}=+1.155241567\) \(a_{29}=-0.025696833\) \(a_{30}=+0.394749246\)
\(a_{31}=-0.379678518\) \(a_{32}=+0.944746345\) \(a_{33}=+1.246088752\) \(a_{34}=+0.169856011\) \(a_{35}=+0.765789015\)
\(a_{36}=-1.876853640\) \(a_{37}=+0.040747799\) \(a_{38}=-0.570073217\) \(a_{39}=-0.497557542\) \(a_{40}=+0.406213118\)
\(a_{41}=-0.426924146\) \(a_{42}=+0.961053484\) \(a_{43}=+0.298655366\) \(a_{44}=+0.587677557\) \(a_{45}=-1.244132786\)
\(a_{46}=-0.517705396\) \(a_{47}=+0.669212315\) \(a_{48}=-1.008028173\) \(a_{49}=+0.864384039\) \(a_{50}=-0.268932829\)
\(a_{51}=-0.776660081\) \(a_{52}=-0.234656967\) \(a_{53}=+1.068091393\) \(a_{54}=-0.857517986\) \(a_{55}=+0.389560960\)
\(a_{56}=+0.988963340\) \(a_{57}=+2.606638161\) \(a_{58}=-0.010081949\) \(a_{59}=+1.391783090\) \(a_{60}=-0.851258668\)
\(a_{61}=-1.799110224\) \(a_{62}=-0.148963855\) \(a_{63}=-3.028956123\) \(a_{64}=-0.191234520\) \(a_{65}=-0.155549910\)
\(a_{66}=+0.488893039\) \(a_{67}=-0.116774353\) \(a_{68}=-0.366286709\) \(a_{69}=+2.367188269\) \(a_{70}=+0.300451247\)
\(a_{71}=-0.990856164\) \(a_{72}=-1.606711095\) \(a_{73}=+0.265749160\) \(a_{74}=+0.015987075\) \(a_{75}=+1.229685059\)
\(a_{76}=+1.229336779\) \(a_{77}=+0.948422122\) \(a_{78}=-0.195212758\) \(a_{79}=-1.338759442\) \(a_{80}=-0.315136792\)
\(a_{81}=+1.702642861\) \(a_{82}=-0.167500309\) \(a_{83}=+0.932121876\) \(a_{84}=-2.072467831\) \(a_{85}=-0.242804894\)
\(a_{86}=+0.117175055\) \(a_{87}=+0.046099290\) \(a_{88}=+0.503090942\) \(a_{89}=-0.837317914\) \(a_{90}=-0.488125543\)
\(a_{91}=-0.378700615\) \(a_{92}=+1.116407964\) \(a_{93}=+0.681131579\) \(a_{94}=+0.262560140\) \(a_{95}=+0.814905409\)
\(a_{96}=-1.694845873\) \(a_{97}=-0.535162501\) \(a_{98}=+0.339134231\) \(a_{99}=-1.540846147\) \(a_{100}=+0.579941277\)

Showing 100 of 1000 available coefficients

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