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: \( 3.96466554946 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.073349160\) \(a_{3}=+1.687864910\) \(a_{4}=+0.152078420\) \(a_{5}=+1.204341031\)
\(a_{6}=-1.811668384\) \(a_{7}=+0.209283667\) \(a_{8}=+0.910115916\) \(a_{9}=+1.848887956\) \(a_{10}=-1.292678435\)
\(a_{11}=-0.626415717\) \(a_{12}=+0.256687829\) \(a_{13}=+0.277350098\) \(a_{14}=-0.224634449\) \(a_{15}=+2.032764967\)
\(a_{16}=-1.128950574\) \(a_{17}=-0.691573828\) \(a_{18}=-1.984502335\) \(a_{19}=+1.259968328\) \(a_{20}=+0.183154281\)
\(a_{21}=+0.353242559\) \(a_{22}=+0.672362784\) \(a_{23}=-1.815008771\) \(a_{24}=+1.536152719\) \(a_{25}=+0.450437319\)
\(a_{26}=-0.297693495\) \(a_{27}=+1.432808193\) \(a_{28}=+0.031827529\) \(a_{29}=-0.227385246\) \(a_{30}=-2.181866570\)
\(a_{31}=+0.100303204\) \(a_{32}=+0.301642235\) \(a_{33}=-1.057305108\) \(a_{34}=+0.742300187\) \(a_{35}=+0.252048908\)
\(a_{36}=+0.281175959\) \(a_{37}=-0.489635811\) \(a_{38}=-1.352385946\) \(a_{39}=+0.468129498\) \(a_{40}=+1.096089941\)
\(a_{41}=-0.033856983\) \(a_{42}=-0.379152604\) \(a_{43}=-0.069953643\) \(a_{44}=-0.095264312\) \(a_{45}=+2.226691627\)
\(a_{46}=+1.948138141\) \(a_{47}=+0.830190359\) \(a_{48}=-1.905516059\) \(a_{49}=-0.956200347\) \(a_{50}=-0.483476519\)
\(a_{51}=-1.167283197\) \(a_{52}=+0.042178965\) \(a_{53}=-0.087077394\) \(a_{54}=-1.537903471\) \(a_{55}=-0.754418151\)
\(a_{56}=+0.190472397\) \(a_{57}=+2.126656328\) \(a_{58}=+0.244063763\) \(a_{59}=-1.246443336\) \(a_{60}=+0.309139684\)
\(a_{61}=+0.632007823\) \(a_{62}=-0.107660360\) \(a_{63}=+0.386942052\) \(a_{64}=+0.805183135\) \(a_{65}=+0.334024103\)
\(a_{66}=+1.134857550\) \(a_{67}=+0.100314406\) \(a_{68}=-0.105173455\) \(a_{69}=-3.063489617\) \(a_{70}=-0.270536484\)
\(a_{71}=-1.533918969\) \(a_{72}=+1.682702355\) \(a_{73}=+0.824146020\) \(a_{74}=+0.525550187\) \(a_{75}=+0.760277346\)
\(a_{76}=+0.191613992\) \(a_{77}=-0.131098579\) \(a_{78}=-0.502466404\) \(a_{79}=+1.201197528\) \(a_{80}=-1.359641499\)
\(a_{81}=+0.569498717\) \(a_{82}=+0.036340364\) \(a_{83}=-0.237410647\) \(a_{84}=+0.053720570\) \(a_{85}=-0.832890737\)
\(a_{86}=+0.075084684\) \(a_{87}=-0.383795578\) \(a_{88}=-0.570110914\) \(a_{89}=+0.898506284\) \(a_{90}=-2.390017588\)
\(a_{91}=+0.058044846\) \(a_{92}=-0.276023666\) \(a_{93}=+0.169298258\) \(a_{94}=-0.891084125\) \(a_{95}=+1.517431555\)
\(a_{96}=+0.509131343\) \(a_{97}=+0.658889579\) \(a_{98}=+1.026336839\) \(a_{99}=-1.158172475\) \(a_{100}=+0.068501796\)

Showing 100 of 546 available coefficients

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