Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.178819528 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.390839392\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.276365185\) \(a_{7}=-0.829623523\) \(a_{8}=-0.353553391\) \(a_{9}=-0.847244569\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.539713824\) \(a_{12}=-0.195419696\) \(a_{13}=-1.484850587\) \(a_{14}=+0.586632419\) \(a_{15}=-0.174788690\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.043020487\) \(a_{18}=+0.599092380\) \(a_{19}=+0.918857294\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.324249553\) \(a_{22}=+1.088742086\) \(a_{23}=-0.096265243\) \(a_{24}=+0.138182592\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.049947919\) \(a_{27}=+0.721975945\) \(a_{28}=-0.414811761\) \(a_{29}=+0.901082604\) \(a_{30}=+0.123594268\)
\(a_{31}=+0.449668769\) \(a_{32}=-0.176776695\) \(a_{33}=+0.601780815\) \(a_{34}=-0.737526859\) \(a_{35}=-0.371018918\)
\(a_{36}=-0.423622285\) \(a_{37}=+1.078779194\) \(a_{38}=-0.649730224\) \(a_{39}=+0.580338101\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.136420471\) \(a_{42}=-0.229279058\) \(a_{43}=-0.500456229\) \(a_{44}=-0.769856912\) \(a_{45}=-0.378899290\)
\(a_{46}=+0.068069806\) \(a_{47}=+1.251776568\) \(a_{48}=-0.097709848\) \(a_{49}=-0.311724811\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.407653493\) \(a_{52}=-0.742425294\) \(a_{53}=-0.555591098\) \(a_{54}=-0.510514087\) \(a_{55}=-0.688580955\)
\(a_{56}=+0.293316209\) \(a_{57}=-0.359125627\) \(a_{58}=-0.637161620\) \(a_{59}=+0.661406909\) \(a_{60}=-0.087394345\)
\(a_{61}=+1.815464549\) \(a_{62}=-0.317963836\) \(a_{63}=+0.702894024\) \(a_{64}=+0.125000000\) \(a_{65}=-0.664045370\)
\(a_{66}=-0.425523295\) \(a_{67}=+1.524780724\) \(a_{68}=+0.521510243\) \(a_{69}=+0.037624249\) \(a_{70}=+0.262349993\)
\(a_{71}=-1.019828612\) \(a_{72}=+0.299546190\) \(a_{73}=-1.069125478\) \(a_{74}=-0.762812083\) \(a_{75}=-0.078167878\)
\(a_{76}=+0.459428647\) \(a_{77}=+1.277382806\) \(a_{78}=-0.410361007\) \(a_{79}=-1.553219903\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.565067930\) \(a_{82}=+0.096463840\) \(a_{83}=+0.752103277\) \(a_{84}=+0.162124777\) \(a_{85}=+0.466452942\)
\(a_{86}=+0.353875993\) \(a_{87}=-0.352178577\) \(a_{88}=+0.544371043\) \(a_{89}=-1.368374971\) \(a_{90}=+0.267922257\)
\(a_{91}=+1.231866975\) \(a_{92}=-0.048132622\) \(a_{93}=-0.175748269\) \(a_{94}=-0.885139700\) \(a_{95}=+0.410925474\)
\(a_{96}=+0.069091296\) \(a_{97}=-1.174446082\) \(a_{98}=+0.220422728\) \(a_{99}=+1.304514176\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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