Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 19.4246337363 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.122156859\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.086377943\) \(a_{7}=+1.788721885\) \(a_{8}=+0.353553391\) \(a_{9}=-0.985077702\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.899404373\) \(a_{12}=+0.061078429\) \(a_{13}=+0.079364571\) \(a_{14}=+1.264817374\) \(a_{15}=-0.054630208\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.349519813\) \(a_{18}=-0.696555123\) \(a_{19}=+0.325662782\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.218504647\) \(a_{22}=+1.343081713\) \(a_{23}=-0.477793150\) \(a_{24}=+0.043188972\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.056119226\) \(a_{27}=-0.242490856\) \(a_{28}=+0.894360942\) \(a_{29}=-1.190251116\) \(a_{30}=-0.038629391\)
\(a_{31}=+0.644334086\) \(a_{32}=+0.176776695\) \(a_{33}=+0.232025272\) \(a_{34}=-0.247147830\) \(a_{35}=-0.799940745\)
\(a_{36}=-0.492538851\) \(a_{37}=+1.695017866\) \(a_{38}=+0.230278362\) \(a_{39}=+0.009694927\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.501725649\) \(a_{42}=+0.154506117\) \(a_{43}=+1.357084659\) \(a_{44}=+0.949702187\) \(a_{45}=+0.440540141\)
\(a_{46}=-0.337850777\) \(a_{47}=+0.961467449\) \(a_{48}=+0.030539215\) \(a_{49}=+2.199525981\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.042696242\) \(a_{52}=+0.039682285\) \(a_{53}=-0.959472683\) \(a_{54}=-0.171466929\) \(a_{55}=-0.849439459\)
\(a_{56}=+0.632408687\) \(a_{57}=+0.039781942\) \(a_{58}=-0.841634636\) \(a_{59}=+0.084954196\) \(a_{60}=-0.027315104\)
\(a_{61}=+0.632714297\) \(a_{62}=+0.455613002\) \(a_{63}=-1.762030044\) \(a_{64}=+0.125000000\) \(a_{65}=-0.035492915\)
\(a_{66}=+0.164066643\) \(a_{67}=-0.650421355\) \(a_{68}=-0.174759907\) \(a_{69}=-0.058365710\) \(a_{70}=-0.565643526\)
\(a_{71}=+0.540351028\) \(a_{72}=-0.348277561\) \(a_{73}=-0.604894510\) \(a_{74}=+1.198558627\) \(a_{75}=+0.024431372\)
\(a_{76}=+0.162831391\) \(a_{77}=+3.397506171\) \(a_{78}=+0.006855348\) \(a_{79}=+0.440234117\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.955455781\) \(a_{82}=-1.061880390\) \(a_{83}=-0.129383710\) \(a_{84}=+0.109252323\) \(a_{85}=+0.156310012\)
\(a_{86}=+0.959603765\) \(a_{87}=-0.145397337\) \(a_{88}=+0.671540856\) \(a_{89}=+1.140505231\) \(a_{90}=+0.311508921\)
\(a_{91}=+0.141961145\) \(a_{92}=-0.238896575\) \(a_{93}=+0.078709828\) \(a_{94}=+0.679860153\) \(a_{95}=-0.145640824\)
\(a_{96}=+0.021594486\) \(a_{97}=+1.910193227\) \(a_{98}=+1.555299737\) \(a_{99}=-1.871060895\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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