Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 25.0508548508 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.053871711\) \(a_{3}=+0.552021891\) \(a_{4}=+0.110645584\) \(a_{5}=-0.733656950\)
\(a_{6}=-0.581760254\) \(a_{7}=+1.547031599\) \(a_{8}=+0.937265461\) \(a_{9}=-0.695271832\) \(a_{10}=+0.773180306\)
\(a_{11}=+0.721992684\) \(a_{12}=+0.061078784\) \(a_{13}=-0.684843782\) \(a_{14}=-1.630372839\) \(a_{15}=-0.404994697\)
\(a_{16}=-1.098403139\) \(a_{17}=-0.782683886\) \(a_{18}=+0.732727316\) \(a_{19}=-1.063243505\) \(a_{20}=-0.081175902\)
\(a_{21}=+0.853995308\) \(a_{22}=-0.760887665\) \(a_{23}=-0.107648851\) \(a_{24}=+0.517391051\) \(a_{25}=-0.461747479\)
\(a_{26}=+0.721737489\) \(a_{27}=-0.935827162\) \(a_{28}=+0.171172214\) \(a_{29}=+0.478977269\) \(a_{30}=+0.426812454\)
\(a_{31}=-1.232800183\) \(a_{32}=+0.220310535\) \(a_{33}=+0.398555766\) \(a_{34}=+0.824848406\) \(a_{35}=-1.134990485\)
\(a_{36}=-0.076928758\) \(a_{37}=-0.128098768\) \(a_{38}=+1.120522252\) \(a_{39}=-0.378048759\) \(a_{40}=-0.687631320\)
\(a_{41}=+0.812190173\) \(a_{42}=-0.900001496\) \(a_{43}=+0.411490198\) \(a_{44}=+0.079885302\) \(a_{45}=+0.510091012\)
\(a_{46}=+0.113448079\) \(a_{47}=-1.125408854\) \(a_{48}=-0.606342577\) \(a_{49}=+1.393306767\) \(a_{50}=+0.486622606\)
\(a_{51}=-0.432058638\) \(a_{52}=-0.075774940\) \(a_{53}=-1.241566203\) \(a_{54}=+0.986241773\) \(a_{55}=-0.529694950\)
\(a_{56}=+1.449979284\) \(a_{57}=-0.586933690\) \(a_{58}=-0.504780594\) \(a_{59}=+0.170051504\) \(a_{60}=-0.044810874\)
\(a_{61}=-0.701580826\) \(a_{62}=+1.299213238\) \(a_{63}=-1.075607494\) \(a_{64}=+0.866224098\) \(a_{65}=+0.502440401\)
\(a_{66}=-0.420026647\) \(a_{67}=-1.090963684\) \(a_{68}=-0.086600515\) \(a_{69}=-0.059424522\) \(a_{70}=+1.196134365\)
\(a_{71}=+0.920414164\) \(a_{72}=-0.651654274\) \(a_{73}=-1.099984786\) \(a_{74}=+0.134999668\) \(a_{75}=-0.254894716\)
\(a_{76}=-0.117643198\) \(a_{77}=+1.116945496\) \(a_{78}=+0.398414893\) \(a_{79}=-1.241600675\) \(a_{80}=+0.805851097\)
\(a_{81}=+0.178674753\) \(a_{82}=-0.855944248\) \(a_{83}=-0.244800153\) \(a_{84}=+0.094490809\) \(a_{85}=+0.574221473\)
\(a_{86}=-0.433657879\) \(a_{87}=+0.264405938\) \(a_{88}=+0.676698805\) \(a_{89}=+0.317560823\) \(a_{90}=-0.537570488\)
\(a_{91}=-1.059474971\) \(a_{92}=-0.011910870\) \(a_{93}=-0.680532688\) \(a_{94}=+1.186036555\) \(a_{95}=+0.780055987\)
\(a_{96}=+0.121616238\) \(a_{97}=+0.622708042\) \(a_{98}=-1.468366586\) \(a_{99}=-0.501981178\) \(a_{100}=-0.051090318\)

Showing 100 of 5000 available coefficients

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