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: \( 23.0718574707 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.741488781\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.524311745\) \(a_{7}=+0.600114760\) \(a_{8}=-0.353553391\) \(a_{9}=-0.450194388\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.611565664\) \(a_{12}=-0.370744390\) \(a_{13}=+1.456877721\) \(a_{14}=-0.424345216\) \(a_{15}=+0.331603864\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.069291465\) \(a_{18}=+0.318335505\) \(a_{19}=-1.852947711\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.444978362\) \(a_{22}=+0.432442228\) \(a_{23}=+0.833614372\) \(a_{24}=+0.262155872\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.030168116\) \(a_{27}=+1.075302869\) \(a_{28}=+0.300057380\) \(a_{29}=-1.691390760\) \(a_{30}=-0.234479341\)
\(a_{31}=-0.374819939\) \(a_{32}=-0.176776695\) \(a_{33}=+0.453469079\) \(a_{34}=-0.048996465\) \(a_{35}=-0.268379480\)
\(a_{36}=-0.225097194\) \(a_{37}=+0.327163391\) \(a_{38}=+1.310231891\) \(a_{39}=-1.080258485\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.584375190\) \(a_{42}=+0.314647217\) \(a_{43}=-0.208276834\) \(a_{44}=-0.305782832\) \(a_{45}=+0.201333051\)
\(a_{46}=-0.589454376\) \(a_{47}=+1.075884310\) \(a_{48}=-0.185372195\) \(a_{49}=-0.639862275\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.051378844\) \(a_{52}=+0.728438861\) \(a_{53}=-0.614216661\) \(a_{54}=-0.760353950\) \(a_{55}=+0.273500480\)
\(a_{56}=-0.212172608\) \(a_{57}=+1.373939938\) \(a_{58}=+1.195993876\) \(a_{59}=+1.179240809\) \(a_{60}=+0.165801932\)
\(a_{61}=+1.269898857\) \(a_{62}=+0.265037721\) \(a_{63}=-0.270168297\) \(a_{64}=+0.125000000\) \(a_{65}=-0.651535524\)
\(a_{66}=-0.320651061\) \(a_{67}=+0.719942070\) \(a_{68}=+0.034645733\) \(a_{69}=-0.618115704\) \(a_{70}=+0.189772950\)
\(a_{71}=+0.670774300\) \(a_{72}=+0.159167752\) \(a_{73}=+0.121731551\) \(a_{74}=-0.231339452\) \(a_{75}=-0.148297756\)
\(a_{76}=-0.926473855\) \(a_{77}=-0.367009582\) \(a_{78}=+0.763858100\) \(a_{79}=+0.468684426\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.347130625\) \(a_{82}=-1.120322441\) \(a_{83}=+0.952798346\) \(a_{84}=-0.222489181\) \(a_{85}=-0.030988085\)
\(a_{86}=+0.147273962\) \(a_{87}=+1.254147272\) \(a_{88}=+0.216221114\) \(a_{89}=+1.591902063\) \(a_{90}=-0.142363966\)
\(a_{91}=+0.874293824\) \(a_{92}=+0.416807186\) \(a_{93}=+0.277924780\) \(a_{94}=-0.760765091\) \(a_{95}=+0.828663408\)
\(a_{96}=+0.131077936\) \(a_{97}=-1.408198838\) \(a_{98}=+0.452450953\) \(a_{99}=+0.275323430\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

Rows: Cols: