Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 8.69561426476 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.615913893\) \(a_{4}=+0.500000000\) \(a_{5}=-0.963376041\)
\(a_{6}=+0.435516891\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.620650076\) \(a_{10}=+0.681209731\)
\(a_{11}=-1.812654552\) \(a_{12}=-0.307956947\) \(a_{13}=-1.378816234\) \(a_{14}=-0.267261242\) \(a_{15}=+0.593356688\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.805462277\) \(a_{18}=+0.438865878\) \(a_{19}=-0.536367722\) \(a_{20}=-0.481688020\)
\(a_{21}=-0.232793570\) \(a_{22}=+1.281740326\) \(a_{23}=+0.981289534\) \(a_{24}=+0.217758445\) \(a_{25}=-0.071906604\)
\(a_{26}=+0.974970309\) \(a_{27}=+0.998180898\) \(a_{28}=+0.188982237\) \(a_{29}=+1.186204032\) \(a_{30}=-0.419566538\)
\(a_{31}=-1.511056193\) \(a_{32}=-0.176776695\) \(a_{33}=+1.116439122\) \(a_{34}=-0.569547838\) \(a_{35}=-0.364121917\)
\(a_{36}=-0.310325038\) \(a_{37}=+0.386403689\) \(a_{38}=+0.379269254\) \(a_{39}=+0.849232075\) \(a_{40}=+0.340604866\)
\(a_{41}=+1.047133014\) \(a_{42}=+0.164609912\) \(a_{43}=-0.919835255\) \(a_{44}=-0.906327276\) \(a_{45}=+0.597919413\)
\(a_{46}=-0.693876484\) \(a_{47}=+1.190524566\) \(a_{48}=-0.153978473\) \(a_{49}=+0.142857143\) \(a_{50}=+0.050845648\)
\(a_{51}=-0.496095407\) \(a_{52}=-0.689408117\) \(a_{53}=-0.623342131\) \(a_{54}=-0.705820482\) \(a_{55}=+1.746267965\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.330356332\) \(a_{58}=-0.838772915\) \(a_{59}=+0.333105637\) \(a_{60}=+0.296678344\)
\(a_{61}=-1.060466812\) \(a_{62}=+1.068478081\) \(a_{63}=-0.234583679\) \(a_{64}=+0.125000000\) \(a_{65}=+1.328318524\)
\(a_{66}=-0.789441674\) \(a_{67}=+0.405566060\) \(a_{68}=+0.402731139\) \(a_{69}=-0.604389857\) \(a_{70}=+0.257473077\)
\(a_{71}=-0.472080992\) \(a_{72}=+0.219432939\) \(a_{73}=+0.339575981\) \(a_{74}=-0.273228669\) \(a_{75}=+0.044288277\)
\(a_{76}=-0.268183861\) \(a_{77}=-0.685119022\) \(a_{78}=-0.600497759\) \(a_{79}=+0.631250576\) \(a_{80}=-0.240844010\)
\(a_{81}=+0.005856593\) \(a_{82}=-0.740434855\) \(a_{83}=+0.707288678\) \(a_{84}=-0.116396785\) \(a_{85}=-0.775963058\)
\(a_{86}=+0.650421746\) \(a_{87}=-0.730599543\) \(a_{88}=+0.640870163\) \(a_{89}=+1.116292710\) \(a_{90}=-0.422792871\)
\(a_{91}=-0.521143551\) \(a_{92}=+0.490644767\) \(a_{93}=+0.930680510\) \(a_{94}=-0.841827994\) \(a_{95}=+0.516723810\)
\(a_{96}=+0.108879223\) \(a_{97}=+0.275007232\) \(a_{98}=-0.101015254\) \(a_{99}=+1.125024186\) \(a_{100}=-0.035953302\)

Showing 100 of 190 available coefficients

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