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: \( 18.8098346996 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.313428919\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.221627714\) \(a_{7}=-1.289815370\) \(a_{8}=+0.353553391\) \(a_{9}=-0.901762313\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.203781532\) \(a_{12}=+0.156714460\) \(a_{13}=+0.613609766\) \(a_{14}=-0.912037194\) \(a_{15}=+0.140169674\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.545444408\) \(a_{18}=-0.637642246\) \(a_{19}=-1.116286135\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.404265437\) \(a_{22}=+0.851202085\) \(a_{23}=-1.669542315\) \(a_{24}=+0.110813857\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.433887626\) \(a_{27}=-0.596067306\) \(a_{28}=-0.644907685\) \(a_{29}=+0.670754659\) \(a_{30}=+0.099114927\)
\(a_{31}=-0.849035000\) \(a_{32}=+0.176776695\) \(a_{33}=+0.377299944\) \(a_{34}=+0.385687439\) \(a_{35}=-0.576822969\)
\(a_{36}=-0.450881156\) \(a_{37}=+0.569733211\) \(a_{38}=-0.789333496\) \(a_{39}=+0.192323046\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.784489594\) \(a_{42}=-0.285858832\) \(a_{43}=-1.877784897\) \(a_{44}=+0.601890766\) \(a_{45}=-0.403280366\)
\(a_{46}=-1.180544693\) \(a_{47}=-0.927620462\) \(a_{48}=+0.078357230\) \(a_{49}=+0.663623688\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.170958051\) \(a_{52}=+0.306804883\) \(a_{53}=+1.194931416\) \(a_{54}=-0.421483234\) \(a_{55}=+0.538347467\)
\(a_{56}=-0.456018597\) \(a_{57}=-0.349876357\) \(a_{58}=+0.474295168\) \(a_{59}=+0.998047263\) \(a_{60}=+0.070084837\)
\(a_{61}=-1.184417416\) \(a_{62}=-0.600358406\) \(a_{63}=+1.163106891\) \(a_{64}=+0.125000000\) \(a_{65}=+0.274414630\)
\(a_{66}=+0.266791349\) \(a_{67}=+0.705659907\) \(a_{68}=+0.272722204\) \(a_{69}=-0.523282843\) \(a_{70}=-0.407875433\)
\(a_{71}=-1.615610160\) \(a_{72}=-0.318821123\) \(a_{73}=-1.742108989\) \(a_{74}=+0.402862217\) \(a_{75}=+0.062685784\)
\(a_{76}=-0.558143068\) \(a_{77}=-1.552655922\) \(a_{78}=+0.135992930\) \(a_{79}=-0.707115052\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.714937581\) \(a_{82}=-0.554717912\) \(a_{83}=-0.218719587\) \(a_{84}=-0.202132719\) \(a_{85}=+0.243930155\)
\(a_{86}=-1.327794434\) \(a_{87}=+0.210233908\) \(a_{88}=+0.425601042\) \(a_{89}=-1.012620023\) \(a_{90}=-0.285162282\)
\(a_{91}=-0.791443307\) \(a_{92}=-0.834771158\) \(a_{93}=-0.266112122\) \(a_{94}=-0.655926719\) \(a_{95}=-0.499218336\)
\(a_{96}=+0.055406929\) \(a_{97}=+1.156219554\) \(a_{98}=+0.469252810\) \(a_{99}=-1.085524819\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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