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: \( 6.70252321169 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.076247173\) \(a_{3}=+0.429321892\) \(a_{4}=+0.158307978\) \(a_{5}=-1.177873528\)
\(a_{6}=-0.462056473\) \(a_{7}=-1.081520017\) \(a_{8}=+0.905868659\) \(a_{9}=-0.815682713\) \(a_{10}=+1.267683055\)
\(a_{11}=+0.323566851\) \(a_{12}=+0.067965081\) \(a_{13}=+0.277350098\) \(a_{14}=+1.163982862\) \(a_{15}=-0.505686891\)
\(a_{16}=-1.133246562\) \(a_{17}=+1.255153999\) \(a_{18}=+0.877876214\) \(a_{19}=+1.465641840\) \(a_{20}=-0.186466776\)
\(a_{21}=-0.464320220\) \(a_{22}=-0.348237908\) \(a_{23}=-0.811703042\) \(a_{24}=+0.388909247\) \(a_{25}=+0.387386047\)
\(a_{26}=-0.298497259\) \(a_{27}=-0.779512338\) \(a_{28}=-0.171213247\) \(a_{29}=+0.013609964\) \(a_{30}=+0.544244087\)
\(a_{31}=+1.556455976\) \(a_{32}=+0.313784750\) \(a_{33}=+0.138914333\) \(a_{34}=-1.350855943\) \(a_{35}=+1.273893798\)
\(a_{36}=-0.129129081\) \(a_{37}=+0.833337104\) \(a_{38}=-1.577392887\) \(a_{39}=+0.119072469\) \(a_{40}=-1.066998714\)
\(a_{41}=-1.201244506\) \(a_{42}=+0.499723324\) \(a_{43}=-0.517836443\) \(a_{44}=+0.051223214\) \(a_{45}=+0.960771075\)
\(a_{46}=+0.873593105\) \(a_{47}=+0.703822888\) \(a_{48}=-0.486527558\) \(a_{49}=+0.169685548\) \(a_{50}=-0.416923138\)
\(a_{51}=+0.538865089\) \(a_{52}=+0.043906733\) \(a_{53}=+0.017075937\) \(a_{54}=+0.838947950\) \(a_{55}=-0.381120828\)
\(a_{56}=-0.979715088\) \(a_{57}=+0.629232128\) \(a_{58}=-0.014647685\) \(a_{59}=-0.791486666\) \(a_{60}=-0.080054269\)
\(a_{61}=+0.154598196\) \(a_{62}=-1.675131344\) \(a_{63}=+0.882177182\) \(a_{64}=+0.795536612\) \(a_{65}=-0.326683338\)
\(a_{66}=-0.149506158\) \(a_{67}=+0.967937206\) \(a_{68}=+0.198700892\) \(a_{69}=-0.348481886\) \(a_{70}=-1.371024599\)
\(a_{71}=+1.775361444\) \(a_{72}=-0.738901406\) \(a_{73}=-0.732787779\) \(a_{74}=-0.896876703\) \(a_{75}=+0.166313311\)
\(a_{76}=+0.232022796\) \(a_{77}=-0.349944026\) \(a_{78}=-0.128151408\) \(a_{79}=+1.680922749\) \(a_{80}=+1.334821126\)
\(a_{81}=+0.481021002\) \(a_{82}=+1.292836004\) \(a_{83}=-1.169247155\) \(a_{84}=-0.073505595\) \(a_{85}=-1.478412668\)
\(a_{86}=+0.557320008\) \(a_{87}=+0.005843055\) \(a_{88}=+0.293109069\) \(a_{89}=+0.158651234\) \(a_{90}=-1.034027153\)
\(a_{91}=-0.299959683\) \(a_{92}=-0.128499067\) \(a_{93}=+0.668220624\) \(a_{94}=-0.757487394\) \(a_{95}=-1.726340724\)
\(a_{96}=+0.134714662\) \(a_{97}=+1.120770123\) \(a_{98}=-0.182623591\) \(a_{99}=-0.263927887\) \(a_{100}=+0.061326302\)

Showing 100 of 546 available coefficients

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