Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 10.0194866131 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.253035905\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.886030186\) \(a_{7}=-0.893722120\) \(a_{8}=+0.353553391\) \(a_{9}=+0.570098980\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.329916289\) \(a_{12}=-0.626517953\) \(a_{13}=+1.057885983\) \(a_{14}=-0.631956971\) \(a_{15}=+0.560374693\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.551080054\) \(a_{18}=+0.403120855\) \(a_{19}=+1.357396346\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.119865906\) \(a_{22}=-0.233286045\) \(a_{23}=+1.921486576\) \(a_{24}=-0.443015093\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.748038352\) \(a_{27}=+0.538681413\) \(a_{28}=-0.446861060\) \(a_{29}=-0.477763158\) \(a_{30}=+0.396244745\)
\(a_{31}=+0.008308874\) \(a_{32}=+0.176776695\) \(a_{33}=+0.413396956\) \(a_{34}=-0.389672443\) \(a_{35}=+0.399684683\)
\(a_{36}=+0.285049490\) \(a_{37}=+1.575270024\) \(a_{38}=+0.959824161\) \(a_{39}=-1.325569120\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.678504844\) \(a_{42}=+0.791864776\) \(a_{43}=-1.577387670\) \(a_{44}=-0.164958145\) \(a_{45}=-0.254956015\)
\(a_{46}=+1.358696188\) \(a_{47}=+1.324534668\) \(a_{48}=-0.313258976\) \(a_{49}=-0.201260773\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.690523095\) \(a_{52}=+0.528942991\) \(a_{53}=-0.798869694\) \(a_{54}=+0.380905280\) \(a_{55}=+0.147543050\)
\(a_{56}=-0.315978486\) \(a_{57}=-1.700866359\) \(a_{58}=-0.337829569\) \(a_{59}=-0.149275447\) \(a_{60}=+0.280187346\)
\(a_{61}=+1.457638226\) \(a_{62}=+0.005875261\) \(a_{63}=-0.509510069\) \(a_{64}=+0.125000000\) \(a_{65}=-0.473100994\)
\(a_{66}=+0.292315791\) \(a_{67}=+0.824074741\) \(a_{68}=-0.275540027\) \(a_{69}=-2.407691671\) \(a_{70}=+0.282619749\)
\(a_{71}=+1.343070038\) \(a_{72}=+0.201560427\) \(a_{73}=+0.352114766\) \(a_{74}=+1.113884116\) \(a_{75}=-0.250607181\)
\(a_{76}=+0.678698173\) \(a_{77}=+0.294853484\) \(a_{78}=-0.937318914\) \(a_{79}=+0.074892097\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.245086127\) \(a_{82}=-1.186882157\) \(a_{83}=+0.450508576\) \(a_{84}=+0.559932953\) \(a_{85}=+0.246450492\)
\(a_{86}=-1.115381518\) \(a_{87}=+0.598654392\) \(a_{88}=-0.116643023\) \(a_{89}=+0.472457707\) \(a_{90}=-0.180281127\)
\(a_{91}=-0.945456114\) \(a_{92}=+0.960743288\) \(a_{93}=-0.010411332\) \(a_{94}=+0.936587446\) \(a_{95}=-0.607046100\)
\(a_{96}=-0.221507546\) \(a_{97}=+0.907270885\) \(a_{98}=-0.142312857\) \(a_{99}=-0.188085194\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

Rows: Cols: