Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 15.1570371874 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.012888599\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.009113616\) \(a_{7}=-1.674540941\) \(a_{8}=-0.353553391\) \(a_{9}=-0.999833884\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.278293544\) \(a_{12}=-0.006444299\) \(a_{13}=-1.040565369\) \(a_{14}=+1.184079254\) \(a_{15}=+0.005763957\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.634401938\) \(a_{18}=+0.706989319\) \(a_{19}=-1.330632965\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.021582487\) \(a_{22}=+0.196783252\) \(a_{23}=-0.877053353\) \(a_{24}=+0.004556808\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.735790829\) \(a_{27}=+0.025775057\) \(a_{28}=-0.837270470\) \(a_{29}=-0.154548156\) \(a_{30}=-0.004075733\)
\(a_{31}=-1.843445794\) \(a_{32}=-0.176776695\) \(a_{33}=+0.003586814\) \(a_{34}=-0.448589912\) \(a_{35}=+0.748877475\)
\(a_{36}=-0.499916942\) \(a_{37}=-1.263256450\) \(a_{38}=+0.940899593\) \(a_{39}=+0.013411430\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.315107147\) \(a_{42}=-0.015261123\) \(a_{43}=+0.696907032\) \(a_{44}=-0.139146772\) \(a_{45}=+0.447139306\)
\(a_{46}=+0.620170374\) \(a_{47}=+1.632670328\) \(a_{48}=-0.003222150\) \(a_{49}=+1.804087362\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.008176552\) \(a_{52}=-0.520282685\) \(a_{53}=+1.260630194\) \(a_{54}=-0.018225717\) \(a_{55}=+0.124456657\)
\(a_{56}=+0.592039627\) \(a_{57}=+0.017149995\) \(a_{58}=+0.109282049\) \(a_{59}=-1.026719752\) \(a_{60}=+0.002881978\)
\(a_{61}=+0.829957327\) \(a_{62}=+1.303513022\) \(a_{63}=+1.674262773\) \(a_{64}=+0.125000000\) \(a_{65}=+0.465354980\)
\(a_{66}=-0.002536260\) \(a_{67}=-1.026557872\) \(a_{68}=+0.317200969\) \(a_{69}=+0.011303989\) \(a_{70}=-0.529536341\)
\(a_{71}=-0.214088022\) \(a_{72}=+0.353494660\) \(a_{73}=-0.428230434\) \(a_{74}=+0.893257202\) \(a_{75}=-0.002577720\)
\(a_{76}=-0.665316483\) \(a_{77}=+0.466013933\) \(a_{78}=-0.009483313\) \(a_{79}=-0.778025891\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.999501676\) \(a_{82}=+0.929921182\) \(a_{83}=+0.098826113\) \(a_{84}=+0.010791243\) \(a_{85}=-0.283713171\)
\(a_{86}=-0.492787688\) \(a_{87}=+0.001991906\) \(a_{88}=+0.098391626\) \(a_{89}=+0.064785986\) \(a_{90}=-0.316175236\)
\(a_{91}=+1.742469277\) \(a_{92}=-0.438526677\) \(a_{93}=+0.023759406\) \(a_{94}=-1.154472261\) \(a_{95}=+0.595077153\)
\(a_{96}=+0.002278404\) \(a_{97}=-0.689729316\) \(a_{98}=-1.275682407\) \(a_{99}=+0.278247188\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

Rows: Cols: