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: \( 30.0454030918 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.279273749\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.197476361\) \(a_{7}=+0.796976750\) \(a_{8}=+0.353553391\) \(a_{9}=-0.922006173\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.078086981\) \(a_{12}=-0.139636874\) \(a_{13}=-0.805443794\) \(a_{14}=+0.563547665\) \(a_{15}=-0.124895017\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.911701525\) \(a_{18}=-0.651956817\) \(a_{19}=-1.636093991\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.222574685\) \(a_{22}=+0.762322615\) \(a_{23}=+0.314110801\) \(a_{24}=-0.098738181\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.569534769\) \(a_{27}=+0.536765869\) \(a_{28}=+0.398488375\) \(a_{29}=-1.890943969\) \(a_{30}=-0.088314114\)
\(a_{31}=-0.078828161\) \(a_{32}=+0.176776695\) \(a_{33}=-0.301081393\) \(a_{34}=+0.644670331\) \(a_{35}=+0.356418838\)
\(a_{36}=-0.461003087\) \(a_{37}=-0.343904263\) \(a_{38}=-1.156893156\) \(a_{39}=+0.224939308\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.668291642\) \(a_{42}=-0.157384069\) \(a_{43}=-0.215150622\) \(a_{44}=+0.539043491\) \(a_{45}=-0.412333696\)
\(a_{46}=+0.222109878\) \(a_{47}=-0.784223024\) \(a_{48}=-0.069818437\) \(a_{49}=-0.364828059\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.254614303\) \(a_{52}=-0.402721897\) \(a_{53}=-1.743572529\) \(a_{54}=+0.379550786\) \(a_{55}=+0.482135155\)
\(a_{56}=+0.281773832\) \(a_{57}=+0.456918102\) \(a_{58}=-1.337099303\) \(a_{59}=+1.048191932\) \(a_{60}=-0.062447509\)
\(a_{61}=-0.564431630\) \(a_{62}=-0.055739927\) \(a_{63}=-0.734817484\) \(a_{64}=+0.125000000\) \(a_{65}=-0.360205415\)
\(a_{66}=-0.212896694\) \(a_{67}=+0.736783656\) \(a_{68}=+0.455850763\) \(a_{69}=-0.087722901\) \(a_{70}=+0.252026177\)
\(a_{71}=+1.609859813\) \(a_{72}=-0.325978409\) \(a_{73}=-1.346796760\) \(a_{74}=-0.243177037\) \(a_{75}=-0.055854750\)
\(a_{76}=-0.818046995\) \(a_{77}=+0.859210259\) \(a_{78}=+0.159056110\) \(a_{79}=-0.638276956\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.772101557\) \(a_{82}=+0.472553552\) \(a_{83}=+1.021345009\) \(a_{84}=-0.111287342\) \(a_{85}=+0.407725317\)
\(a_{86}=-0.152134464\) \(a_{87}=+0.528091010\) \(a_{88}=+0.381161308\) \(a_{89}=+0.330356080\) \(a_{90}=-0.291563952\)
\(a_{91}=-0.641919978\) \(a_{92}=+0.157055401\) \(a_{93}=+0.022014636\) \(a_{94}=-0.554529418\) \(a_{95}=-0.731683476\)
\(a_{96}=-0.049369090\) \(a_{97}=+1.720788277\) \(a_{98}=-0.257972395\) \(a_{99}=-0.994002852\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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