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: \( 27.7811733014 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.888933341\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.335677574\) \(a_{7}=+1.425814481\) \(a_{8}=+0.353553391\) \(a_{9}=+2.568069166\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.547098872\) \(a_{12}=+0.944466670\) \(a_{13}=+0.196599776\) \(a_{14}=+1.008203089\) \(a_{15}=-0.844756671\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.081535607\) \(a_{18}=+1.815899122\) \(a_{19}=+0.126888676\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.693268512\) \(a_{22}=-0.386857323\) \(a_{23}=-0.219799897\) \(a_{24}=+0.667838787\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.139017035\) \(a_{27}=+2.961978128\) \(a_{28}=+0.712907241\) \(a_{29}=+1.441137589\) \(a_{30}=-0.597333170\)
\(a_{31}=+1.500924759\) \(a_{32}=+0.176776695\) \(a_{33}=-1.033433301\) \(a_{34}=-0.764761161\) \(a_{35}=-0.637643621\)
\(a_{36}=+1.284034583\) \(a_{37}=+1.347272785\) \(a_{38}=+0.089723843\) \(a_{39}=+0.371363871\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.506010654\) \(a_{42}=+1.904428428\) \(a_{43}=-0.013592671\) \(a_{44}=-0.273549436\) \(a_{45}=-1.148475445\)
\(a_{46}=-0.155421998\) \(a_{47}=-1.335198917\) \(a_{48}=+0.472233335\) \(a_{49}=+1.032946935\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.042948666\) \(a_{52}=+0.098299888\) \(a_{53}=+1.286683829\) \(a_{54}=+2.094434820\) \(a_{55}=+0.244670054\)
\(a_{56}=+0.504101544\) \(a_{57}=+0.239684250\) \(a_{58}=+1.019038162\) \(a_{59}=-0.164983574\) \(a_{60}=-0.422378335\)
\(a_{61}=+1.775098679\) \(a_{62}=+1.061314075\) \(a_{63}=+3.661590206\) \(a_{64}=+0.125000000\) \(a_{65}=-0.087922093\)
\(a_{66}=-0.730747695\) \(a_{67}=-0.199123675\) \(a_{68}=-0.540767803\) \(a_{69}=-0.415187354\) \(a_{70}=-0.450882128\)
\(a_{71}=+0.371573233\) \(a_{72}=+0.907949561\) \(a_{73}=-1.219932981\) \(a_{74}=+0.952665723\) \(a_{75}=+0.377786668\)
\(a_{76}=+0.063444338\) \(a_{77}=-0.780061495\) \(a_{78}=+0.262593912\) \(a_{79}=+0.660592311\) \(a_{80}=-0.111803399\)
\(a_{81}=+3.026910074\) \(a_{82}=-1.064910346\) \(a_{83}=-1.072189900\) \(a_{84}=+1.346634256\) \(a_{85}=+0.483677427\)
\(a_{86}=-0.009611470\) \(a_{87}=+2.722212841\) \(a_{88}=-0.193428661\) \(a_{89}=-1.908060421\) \(a_{90}=-0.812094775\)
\(a_{91}=+0.280314807\) \(a_{92}=-0.109899949\) \(a_{93}=+2.835146819\) \(a_{94}=-0.944128208\) \(a_{95}=-0.056746341\)
\(a_{96}=+0.333919394\) \(a_{97}=+0.454552645\) \(a_{98}=+0.730403783\) \(a_{99}=-1.404987745\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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