Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 29.1335076947 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.864227195\) \(a_{3}=-0.577350269\) \(a_{4}=+2.475343035\) \(a_{5}=+0.449629615\)
\(a_{6}=-1.076312073\) \(a_{7}=+1.813807739\) \(a_{8}=+2.750374607\) \(a_{9}=+0.333333333\) \(a_{10}=+0.838211756\)
\(a_{11}=-0.713929247\) \(a_{12}=-1.429139967\) \(a_{13}=+0.480463665\) \(a_{14}=+3.381349714\) \(a_{15}=-0.259593779\)
\(a_{16}=+2.651980105\) \(a_{17}=-0.731783830\) \(a_{18}=+0.621409065\) \(a_{19}=+0.197026079\) \(a_{20}=+1.112987535\)
\(a_{21}=-1.047202386\) \(a_{22}=-1.330926317\) \(a_{23}=+0.222497208\) \(a_{24}=-1.587929520\) \(a_{25}=-0.797833209\)
\(a_{26}=+0.895693430\) \(a_{27}=-0.192450090\) \(a_{28}=+4.489796353\) \(a_{29}=+0.342074126\) \(a_{30}=-0.483941783\)
\(a_{31}=+0.738791554\) \(a_{32}=+2.193518825\) \(a_{33}=+0.412187243\) \(a_{34}=-1.364211317\) \(a_{35}=+0.815541675\)
\(a_{36}=+0.825114345\) \(a_{37}=+1.019547013\) \(a_{38}=+0.367301375\) \(a_{39}=-0.277395826\) \(a_{40}=+1.236649875\)
\(a_{41}=+0.703989672\) \(a_{42}=-1.952223167\) \(a_{43}=+1.098684258\) \(a_{44}=-1.767219788\) \(a_{45}=+0.149876538\)
\(a_{46}=+0.414785347\) \(a_{47}=-1.196398868\) \(a_{48}=-1.531121427\) \(a_{49}=+2.289898514\) \(a_{50}=-1.487342366\)
\(a_{51}=+0.422495591\) \(a_{52}=+1.189312386\) \(a_{53}=-1.000027175\) \(a_{54}=-0.358770691\) \(a_{55}=-0.321003732\)
\(a_{56}=+4.988650748\) \(a_{57}=-0.113753060\) \(a_{58}=+0.637703889\) \(a_{59}=-1.284703775\) \(a_{60}=-0.642583653\)
\(a_{61}=+1.129754178\) \(a_{62}=+1.377275306\) \(a_{63}=+0.604602580\) \(a_{64}=+1.437237341\) \(a_{65}=+0.216030693\)
\(a_{66}=+0.768410668\) \(a_{67}=+0.392242213\) \(a_{68}=-1.811416006\) \(a_{69}=-0.128458823\) \(a_{70}=+1.520354969\)
\(a_{71}=-0.554643518\) \(a_{72}=+0.916791536\) \(a_{73}=-0.951831955\) \(a_{74}=+1.900667268\) \(a_{75}=+0.460629218\)
\(a_{76}=+0.487707133\) \(a_{77}=-1.294930393\) \(a_{78}=-0.517128843\) \(a_{79}=-1.334937521\) \(a_{80}=+1.192408793\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.312396692\) \(a_{83}=+1.010629687\) \(a_{84}=-2.592185133\) \(a_{85}=-0.329031682\)
\(a_{86}=+2.048197073\) \(a_{87}=-0.197496589\) \(a_{88}=-1.963572872\) \(a_{89}=+1.149679294\) \(a_{90}=+0.279403919\)
\(a_{91}=+0.871468714\) \(a_{92}=+0.550756915\) \(a_{93}=-0.426541503\) \(a_{94}=-2.230359307\) \(a_{95}=+0.088588760\)
\(a_{96}=-1.266428684\) \(a_{97}=+0.356576230\) \(a_{98}=+4.268891083\) \(a_{99}=-0.237976416\) \(a_{100}=-1.974910878\)

Showing 100 of 1228 available coefficients

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