Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 14.9169973013 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.731532439\) \(a_{3}=+0.577350269\) \(a_{4}=+1.998204587\) \(a_{5}=-0.628846374\)
\(a_{6}=+0.999700720\) \(a_{7}=+1.517758778\) \(a_{8}=+1.728423624\) \(a_{9}=+0.333333333\) \(a_{10}=-1.088867896\)
\(a_{11}=+0.516304521\) \(a_{12}=+1.153663954\) \(a_{13}=-1.138383918\) \(a_{14}=+2.628048525\) \(a_{15}=-0.363064474\)
\(a_{16}=+0.994616288\) \(a_{17}=+0.590422053\) \(a_{18}=+0.577161205\) \(a_{19}=+0.474222361\) \(a_{20}=-1.256563709\)
\(a_{21}=+0.876278439\) \(a_{22}=+0.893998026\) \(a_{23}=-0.526781693\) \(a_{24}=+0.997905844\) \(a_{25}=-0.604552238\)
\(a_{26}=-1.971148695\) \(a_{27}=+0.192450090\) \(a_{28}=+3.032792552\) \(a_{29}=-0.327366787\) \(a_{30}=-0.628658173\)
\(a_{31}=-1.336388032\) \(a_{32}=-0.006212049\) \(a_{33}=+0.298088554\) \(a_{34}=+1.022329117\) \(a_{35}=-0.954437104\)
\(a_{36}=+0.666068196\) \(a_{37}=-0.166404648\) \(a_{38}=+0.821131401\) \(a_{39}=-0.657246266\) \(a_{40}=-1.086912929\)
\(a_{41}=+0.197469459\) \(a_{42}=+1.517304543\) \(a_{43}=-1.626857193\) \(a_{44}=+1.031682061\) \(a_{45}=-0.209615458\)
\(a_{46}=-0.912139590\) \(a_{47}=+0.589723668\) \(a_{48}=+0.574242384\) \(a_{49}=+1.303591707\) \(a_{50}=-1.046801810\)
\(a_{51}=+0.340878392\) \(a_{52}=-2.274723984\) \(a_{53}=-0.121397908\) \(a_{54}=+0.333233576\) \(a_{55}=-0.324676215\)
\(a_{56}=+2.623330125\) \(a_{57}=+0.273792385\) \(a_{58}=-0.566846222\) \(a_{59}=-0.009767325\) \(a_{60}=-0.725477348\)
\(a_{61}=+0.956469177\) \(a_{62}=-2.313999375\) \(a_{63}=+0.505919707\) \(a_{64}=-1.005372899\) \(a_{65}=+0.715868604\)
\(a_{66}=+0.516150001\) \(a_{67}=+1.127775850\) \(a_{68}=+1.179777338\) \(a_{69}=-0.304137553\) \(a_{70}=-1.652638806\)
\(a_{71}=-0.578368087\) \(a_{72}=+0.576141208\) \(a_{73}=+0.209923040\) \(a_{74}=-0.288135047\) \(a_{75}=-0.349038397\)
\(a_{76}=+0.947593297\) \(a_{77}=+0.783625718\) \(a_{78}=-1.138043231\) \(a_{79}=-0.779889362\) \(a_{80}=-0.625461283\)
\(a_{81}=+0.111111113\) \(a_{82}=+0.341924774\) \(a_{83}=+1.565043216\) \(a_{84}=+1.750983596\) \(a_{85}=-0.371282648\)
\(a_{86}=-2.816955999\) \(a_{87}=-0.189005309\) \(a_{88}=+0.892392921\) \(a_{89}=+1.847346184\) \(a_{90}=-0.362955951\)
\(a_{91}=-1.727792194\) \(a_{92}=-1.052617620\) \(a_{93}=-0.771564002\) \(a_{94}=+1.021125691\) \(a_{95}=-0.298212986\)
\(a_{96}=-0.003586551\) \(a_{97}=+1.532852137\) \(a_{98}=+2.257211358\) \(a_{99}=+0.172101595\) \(a_{100}=-1.208019076\)

Showing 100 of 5000 available coefficients

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