Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 45.3616136021 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.003273830\) \(a_{3}=+0.524617549\) \(a_{4}=-0.999989282\) \(a_{5}=-0.737181170\)
\(a_{6}=-0.001717509\) \(a_{7}=-1.743715747\) \(a_{8}=+0.006547626\) \(a_{9}=-0.724776427\) \(a_{10}=+0.002413406\)
\(a_{11}=-0.642657332\) \(a_{12}=-0.524611926\) \(a_{13}=-1.294932147\) \(a_{14}=+0.005708630\) \(a_{15}=-0.386738179\)
\(a_{16}=+0.999967846\) \(a_{17}=+0.234043507\) \(a_{18}=+0.002372795\) \(a_{19}=+0.148461628\) \(a_{20}=+0.737173268\)
\(a_{21}=-0.914783880\) \(a_{22}=+0.002103931\) \(a_{23}=+0.705949815\) \(a_{24}=+0.003434999\) \(a_{25}=-0.456563923\)
\(a_{26}=+0.004239388\) \(a_{27}=-0.904847982\) \(a_{28}=+1.743697058\) \(a_{29}=-0.246527182\) \(a_{30}=+0.001266115\)
\(a_{31}=-0.898178367\) \(a_{32}=-0.009821351\) \(a_{33}=-0.337149315\) \(a_{34}=-0.000766219\) \(a_{35}=+1.285434414\)
\(a_{36}=+0.724768659\) \(a_{37}=-0.481745192\) \(a_{38}=-0.000486038\) \(a_{39}=-0.679344129\) \(a_{40}=-0.004826786\)
\(a_{41}=-1.782117725\) \(a_{42}=+0.002994847\) \(a_{43}=-0.109841690\) \(a_{44}=+0.642650444\) \(a_{45}=+0.534291534\)
\(a_{46}=-0.002311160\) \(a_{47}=+1.558233187\) \(a_{48}=+0.524600681\) \(a_{49}=+2.040544607\) \(a_{50}=+0.001494713\)
\(a_{51}=+0.122783331\) \(a_{52}=+1.294918268\) \(a_{53}=+0.972914732\) \(a_{54}=+0.002962319\) \(a_{55}=+0.473754884\)
\(a_{56}=-0.011417198\) \(a_{57}=+0.077885576\) \(a_{58}=+0.000807088\) \(a_{59}=+1.022610033\) \(a_{60}=+0.386734034\)
\(a_{61}=-1.398617462\) \(a_{62}=+0.002940484\) \(a_{63}=+1.263804069\) \(a_{64}=-0.999935693\) \(a_{65}=+0.954599595\)
\(a_{66}=+0.001103769\) \(a_{67}=-0.715369679\) \(a_{68}=-0.234041001\) \(a_{69}=+0.370353658\) \(a_{70}=-0.004208294\)
\(a_{71}=+0.607567659\) \(a_{72}=-0.004745565\) \(a_{73}=-0.638905070\) \(a_{74}=+0.001577152\) \(a_{75}=-0.239521446\)
\(a_{76}=-0.148460037\) \(a_{77}=+1.120611710\) \(a_{78}=+0.002224057\) \(a_{79}=-0.281282063\) \(a_{80}=-0.737157467\)
\(a_{81}=+0.250077296\) \(a_{82}=+0.005834351\) \(a_{83}=-0.261114654\) \(a_{84}=+0.914774077\) \(a_{85}=-0.172532466\)
\(a_{86}=+0.000359603\) \(a_{87}=-0.129332486\) \(a_{88}=-0.004207880\) \(a_{89}=-1.195950109\) \(a_{90}=-0.001749180\)
\(a_{91}=+2.257993576\) \(a_{92}=-0.705942248\) \(a_{93}=-0.471200134\) \(a_{94}=-0.005101391\) \(a_{95}=-0.109443117\)
\(a_{96}=-0.005152453\) \(a_{97}=-0.381377884\) \(a_{98}=-0.006680397\) \(a_{99}=+0.465782885\) \(a_{100}=+0.456559029\)

Showing 100 of 5000 available coefficients

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