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: \( 7.2945513252 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.558958242\) \(a_{3}=+1.254536446\) \(a_{4}=+1.430350800\) \(a_{5}=+1.643938167\)
\(a_{6}=+1.955769932\) \(a_{7}=-1.102947398\) \(a_{8}=+0.670898926\) \(a_{9}=+0.573861694\) \(a_{10}=+2.562830955\)
\(a_{11}=-1.154792686\) \(a_{12}=+1.794427209\) \(a_{13}=+0.277350098\) \(a_{14}=-1.719448936\) \(a_{15}=+2.062380345\)
\(a_{16}=-0.384447390\) \(a_{17}=+0.892149923\) \(a_{18}=+0.894626417\) \(a_{19}=+0.544567145\) \(a_{20}=+2.351408272\)
\(a_{21}=-1.383687709\) \(a_{22}=-1.800273575\) \(a_{23}=-0.902397940\) \(a_{24}=+0.841667154\) \(a_{25}=+1.702532697\)
\(a_{26}=+0.432377221\) \(a_{27}=-0.534606036\) \(a_{28}=-1.577601693\) \(a_{29}=+0.198404429\) \(a_{30}=+3.215164837\)
\(a_{31}=-0.748173954\) \(a_{32}=-1.270236352\) \(a_{33}=-1.448729511\) \(a_{34}=+1.390824475\) \(a_{35}=-1.813177324\)
\(a_{36}=+0.820823533\) \(a_{37}=+1.209851108\) \(a_{38}=+0.848957439\) \(a_{39}=+0.347945806\) \(a_{40}=+1.102916351\)
\(a_{41}=+0.857368729\) \(a_{42}=-2.157111357\) \(a_{43}=-1.032499152\) \(a_{44}=-1.651758641\) \(a_{45}=+0.943393141\)
\(a_{46}=-1.406800706\) \(a_{47}=-0.349693909\) \(a_{48}=-0.482303262\) \(a_{49}=+0.216492963\) \(a_{50}=+2.654177380\)
\(a_{51}=+1.119234594\) \(a_{52}=+0.396707935\) \(a_{53}=+0.921457078\) \(a_{54}=-0.833428486\) \(a_{55}=-1.898407771\)
\(a_{56}=-0.739966225\) \(a_{57}=+0.683179330\) \(a_{58}=+0.309304219\) \(a_{59}=-0.412081579\) \(a_{60}=+2.949927376\)
\(a_{61}=+0.818214902\) \(a_{62}=-1.166371951\) \(a_{63}=-0.632939262\) \(a_{64}=-1.595798041\) \(a_{65}=+0.455946412\)
\(a_{66}=-2.258508812\) \(a_{67}=+0.900281130\) \(a_{68}=+1.276087356\) \(a_{69}=-1.132091104\) \(a_{70}=-2.826667733\)
\(a_{71}=+0.970633013\) \(a_{72}=+0.385003194\) \(a_{73}=-1.381733797\) \(a_{74}=+1.886107357\) \(a_{75}=+2.135889319\)
\(a_{76}=+0.778922051\) \(a_{77}=+1.273675588\) \(a_{78}=+0.542432982\) \(a_{79}=-1.226004764\) \(a_{80}=-0.632007737\)
\(a_{81}=-1.244544450\) \(a_{82}=+1.336602047\) \(a_{83}=+1.072714974\) \(a_{84}=-1.979158821\) \(a_{85}=+1.466639309\)
\(a_{86}=-1.609623062\) \(a_{87}=+0.248905587\) \(a_{88}=-0.774749173\) \(a_{89}=+0.528040239\) \(a_{90}=+1.470710513\)
\(a_{91}=-0.305902569\) \(a_{92}=-1.290745615\) \(a_{93}=-0.938611493\) \(a_{94}=-0.545158201\) \(a_{95}=+0.895234714\)
\(a_{96}=-1.593557799\) \(a_{97}=-0.055816657\) \(a_{98}=+0.337503489\) \(a_{99}=-0.662691287\) \(a_{100}=+2.435219005\)

Showing 100 of 546 available coefficients

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