Properties

Level $51$
Weight $0$
Character 51.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.58157256423 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.619320989\) \(a_{3}=+0.577350269\) \(a_{4}=-0.616441513\) \(a_{5}=-0.110794769\)
\(a_{6}=-0.357565139\) \(a_{7}=-1.537071954\) \(a_{8}=+1.001096156\) \(a_{9}=+0.333333333\) \(a_{10}=+0.068617526\)
\(a_{11}=+1.131003824\) \(a_{12}=-0.355902674\) \(a_{13}=+1.325200524\) \(a_{14}=+0.951940922\) \(a_{15}=-0.063967389\)
\(a_{16}=-0.003558348\) \(a_{17}=-0.242535625\) \(a_{18}=-0.206440330\) \(a_{19}=+1.552447762\) \(a_{20}=+0.068298495\)
\(a_{21}=-0.887428906\) \(a_{22}=-0.700454406\) \(a_{23}=-0.902422666\) \(a_{24}=+0.577983135\) \(a_{25}=-0.987724519\)
\(a_{26}=-0.820724499\) \(a_{27}=+0.192450090\) \(a_{28}=+0.947514961\) \(a_{29}=+1.073908048\) \(a_{30}=+0.039616347\)
\(a_{31}=+1.630773480\) \(a_{32}=-0.998892396\) \(a_{33}=+0.652985362\) \(a_{34}=+0.150207403\) \(a_{35}=+0.170299531\)
\(a_{36}=-0.205480504\) \(a_{37}=+0.717607717\) \(a_{38}=-0.961463482\) \(a_{39}=+0.765104879\) \(a_{40}=-0.110916217\)
\(a_{41}=-0.197748605\) \(a_{42}=+0.549603348\) \(a_{43}=-1.552513010\) \(a_{44}=-0.697197709\) \(a_{45}=-0.036931590\)
\(a_{46}=+0.558889297\) \(a_{47}=+0.706191019\) \(a_{48}=-0.002054413\) \(a_{49}=+1.362590191\) \(a_{50}=+0.611718526\)
\(a_{51}=-0.140028008\) \(a_{52}=-0.816908616\) \(a_{53}=+0.022783656\) \(a_{54}=-0.119188380\) \(a_{55}=-0.125309307\)
\(a_{56}=-1.538756824\) \(a_{57}=+0.896306133\) \(a_{58}=-0.665093794\) \(a_{59}=+0.798461807\) \(a_{60}=+0.039432154\)
\(a_{61}=-0.168100197\) \(a_{62}=-1.009972244\) \(a_{63}=-0.512357318\) \(a_{64}=+0.622193374\) \(a_{65}=-0.146825285\)
\(a_{66}=-0.404407540\) \(a_{67}=+1.247484285\) \(a_{68}=+0.149509028\) \(a_{69}=-0.521013969\) \(a_{70}=-0.105470074\)
\(a_{71}=-0.851757357\) \(a_{72}=+0.333698719\) \(a_{73}=+1.528304065\) \(a_{74}=-0.444429521\) \(a_{75}=-0.570263017\)
\(a_{76}=-0.956993247\) \(a_{77}=-1.738434257\) \(a_{78}=-0.473845510\) \(a_{79}=+0.858373739\) \(a_{80}=+0.000394246\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.122469861\) \(a_{83}=+0.714181485\) \(a_{84}=+0.547048018\) \(a_{85}=+0.026871678\)
\(a_{86}=+0.961503892\) \(a_{87}=+0.620021101\) \(a_{88}=+1.132243580\) \(a_{89}=+1.056470551\) \(a_{90}=+0.022872509\)
\(a_{91}=-2.036928559\) \(a_{92}=+0.556290793\) \(a_{93}=+0.941527508\) \(a_{94}=-0.437358920\) \(a_{95}=-0.172003090\)
\(a_{96}=-0.576710794\) \(a_{97}=+0.954736681\) \(a_{98}=-0.843880704\) \(a_{99}=+0.377001275\) \(a_{100}=+0.608874397\)

Showing 100 of 498 available coefficients

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