Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 31.4604723426 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.260311809\) \(a_{4}=+0.500000000\) \(a_{5}=-1.144664377\)
\(a_{6}=+0.184068245\) \(a_{7}=+1.862610984\) \(a_{8}=+0.353553391\) \(a_{9}=-0.932237762\) \(a_{10}=-0.809399943\)
\(a_{11}=+0.592446335\) \(a_{12}=+0.130155905\) \(a_{13}=-0.736979556\) \(a_{14}=+1.317064857\) \(a_{15}=-0.297969655\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.545751148\) \(a_{18}=-0.659191643\) \(a_{19}=+0.062985833\) \(a_{20}=-0.572332188\)
\(a_{21}=+0.484859635\) \(a_{22}=+0.418922821\) \(a_{23}=+1.694008177\) \(a_{24}=+0.092034123\) \(a_{25}=+0.310256536\)
\(a_{26}=-0.521123241\) \(a_{27}=-0.502984307\) \(a_{28}=+0.931305492\) \(a_{29}=+0.449259826\) \(a_{30}=-0.210696363\)
\(a_{31}=+0.906364450\) \(a_{32}=+0.176776695\) \(a_{33}=+0.154220777\) \(a_{34}=+0.385904338\) \(a_{35}=-2.132064441\)
\(a_{36}=-0.466118881\) \(a_{37}=+0.113624612\) \(a_{38}=+0.044537710\) \(a_{39}=-0.191844481\) \(a_{40}=-0.404699972\)
\(a_{41}=+0.177094535\) \(a_{42}=+0.342847536\) \(a_{43}=+1.605883592\) \(a_{44}=+0.296223167\) \(a_{45}=+1.067099357\)
\(a_{46}=+1.197844669\) \(a_{47}=-0.639894554\) \(a_{48}=+0.065077952\) \(a_{49}=+2.469319677\) \(a_{50}=+0.219384500\)
\(a_{51}=+0.142065469\) \(a_{52}=-0.368489778\) \(a_{53}=+1.770651596\) \(a_{54}=-0.355663614\) \(a_{55}=-0.678152214\)
\(a_{56}=+0.658532429\) \(a_{57}=+0.016395956\) \(a_{58}=+0.317674669\) \(a_{59}=+0.681583285\) \(a_{60}=-0.148984827\)
\(a_{61}=-0.114009597\) \(a_{62}=+0.640896449\) \(a_{63}=-1.736396295\) \(a_{64}=+0.125000000\) \(a_{65}=+0.843594244\)
\(a_{66}=+0.109050557\) \(a_{67}=+0.388471307\) \(a_{68}=+0.272875574\) \(a_{69}=+0.440970333\) \(a_{70}=-1.507597224\)
\(a_{71}=-0.168286181\) \(a_{72}=-0.329595822\) \(a_{73}=+0.782478094\) \(a_{74}=+0.080344734\) \(a_{75}=+0.080763440\)
\(a_{76}=+0.031492917\) \(a_{77}=+1.103497050\) \(a_{78}=-0.135654534\) \(a_{79}=-1.661742055\) \(a_{80}=-0.286166094\)
\(a_{81}=+0.801305007\) \(a_{82}=+0.125224746\) \(a_{83}=-0.241354168\) \(a_{84}=+0.242429817\) \(a_{85}=-0.624701898\)
\(a_{86}=+1.135531178\) \(a_{87}=+0.116947638\) \(a_{88}=+0.209461410\) \(a_{89}=-1.179393308\) \(a_{90}=+0.754553192\)
\(a_{91}=-1.372706215\) \(a_{92}=+0.847004088\) \(a_{93}=+0.235937370\) \(a_{94}=-0.452473778\) \(a_{95}=-0.072097639\)
\(a_{96}=+0.046017061\) \(a_{97}=-0.156986309\) \(a_{98}=+1.746072689\) \(a_{99}=-0.552300845\) \(a_{100}=+0.155128268\)

Showing 100 of 1228 available coefficients

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