Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.35406838073 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.343653790\) \(a_{4}=+0.500000000\) \(a_{5}=+1.056803809\)
\(a_{6}=-0.242999925\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.881902073\) \(a_{10}=+0.747273140\)
\(a_{11}=+0.940998643\) \(a_{12}=-0.171826895\) \(a_{13}=-0.160847193\) \(a_{14}=+0.267261242\) \(a_{15}=-0.363174634\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.432871994\) \(a_{18}=-0.623598936\) \(a_{19}=+0.969724163\) \(a_{20}=+0.528401905\)
\(a_{21}=-0.129888924\) \(a_{22}=+0.665386522\) \(a_{23}=+1.760138207\) \(a_{24}=-0.121499963\) \(a_{25}=+0.116834291\)
\(a_{26}=-0.113736141\) \(a_{27}=+0.646722779\) \(a_{28}=+0.188982237\) \(a_{29}=+0.584434704\) \(a_{30}=-0.256803247\)
\(a_{31}=+1.210169445\) \(a_{32}=+0.176776695\) \(a_{33}=-0.323377750\) \(a_{34}=-0.306086722\) \(a_{35}=+0.399434295\)
\(a_{36}=-0.440951036\) \(a_{37}=+1.634945416\) \(a_{38}=+0.685698532\) \(a_{39}=+0.055275747\) \(a_{40}=+0.373636570\)
\(a_{41}=+0.088149614\) \(a_{42}=-0.091845339\) \(a_{43}=-1.163340628\) \(a_{44}=+0.470499322\) \(a_{45}=-0.931997470\)
\(a_{46}=+1.244605662\) \(a_{47}=-1.346529841\) \(a_{48}=-0.085913447\) \(a_{49}=+0.142857143\) \(a_{50}=+0.082614320\)
\(a_{51}=+0.148758101\) \(a_{52}=-0.080423596\) \(a_{53}=+0.041276197\) \(a_{54}=+0.457302063\) \(a_{55}=+0.994450951\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.333249384\) \(a_{58}=+0.413257742\) \(a_{59}=+0.273058235\) \(a_{60}=-0.181587317\)
\(a_{61}=-0.274726565\) \(a_{62}=+0.855719021\) \(a_{63}=-0.333327652\) \(a_{64}=+0.125000000\) \(a_{65}=-0.169983926\)
\(a_{66}=-0.228662600\) \(a_{67}=-1.935256987\) \(a_{68}=-0.216435997\) \(a_{69}=-0.604878166\) \(a_{70}=+0.282442699\)
\(a_{71}=-0.979046581\) \(a_{72}=-0.311799468\) \(a_{73}=+1.697561559\) \(a_{74}=+1.156080990\) \(a_{75}=-0.040150547\)
\(a_{76}=+0.484862082\) \(a_{77}=+0.355664056\) \(a_{78}=+0.039085856\) \(a_{79}=-0.688569772\) \(a_{80}=+0.264200952\)
\(a_{81}=+0.659653338\) \(a_{82}=+0.062331190\) \(a_{83}=+0.171270851\) \(a_{84}=-0.064944462\) \(a_{85}=-0.457460772\)
\(a_{86}=-0.822606047\) \(a_{87}=-0.200843202\) \(a_{88}=+0.332693261\) \(a_{89}=+0.673877182\) \(a_{90}=-0.659021731\)
\(a_{91}=-0.060794524\) \(a_{92}=+0.880069104\) \(a_{93}=-0.415879314\) \(a_{94}=-0.952140381\) \(a_{95}=+1.024808191\)
\(a_{96}=-0.060749981\) \(a_{97}=-0.773297175\) \(a_{98}=+0.101015254\) \(a_{99}=-0.829868668\) \(a_{100}=+0.058417146\)

Showing 100 of 198 available coefficients

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