Properties

Level $5$
Weight $0$
Character 5.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.02837629307 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.593266803\) \(a_{3}=+1.113764923\) \(a_{4}=-0.648034500\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.660759755\) \(a_{7}=-0.290618431\) \(a_{8}=+0.977724159\) \(a_{9}=+0.240472303\) \(a_{10}=-0.265316974\)
\(a_{11}=-0.130606636\) \(a_{12}=-0.721758096\) \(a_{13}=-0.072219223\) \(a_{14}=+0.172414267\) \(a_{15}=+0.498090816\)
\(a_{16}=+0.067983214\) \(a_{17}=+1.042157348\) \(a_{18}=-0.142664235\) \(a_{19}=-1.246440947\) \(a_{20}=-0.289809839\)
\(a_{21}=-0.323680614\) \(a_{22}=+0.077484574\) \(a_{23}=+0.122194817\) \(a_{24}=+1.088954873\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.042845268\) \(a_{27}=-0.845935306\) \(a_{28}=+0.188330769\) \(a_{29}=+0.445957793\) \(a_{30}=-0.295500746\)
\(a_{31}=+0.535011205\) \(a_{32}=-1.018056343\) \(a_{33}=-0.145465075\) \(a_{34}=-0.618277358\) \(a_{35}=-0.129968514\)
\(a_{36}=-0.155834349\) \(a_{37}=+1.643232530\) \(a_{38}=+0.739472035\) \(a_{39}=-0.080435239\) \(a_{40}=+0.437251543\)
\(a_{41}=-0.687183508\) \(a_{42}=+0.192028931\) \(a_{43}=-1.471077758\) \(a_{44}=+0.084637610\) \(a_{45}=+0.107542559\)
\(a_{46}=-0.072494167\) \(a_{47}=+0.067950485\) \(a_{48}=+0.075717268\) \(a_{49}=-0.915538192\) \(a_{50}=-0.118653862\)
\(a_{51}=+1.160718298\) \(a_{52}=+0.046800548\) \(a_{53}=+1.204957779\) \(a_{54}=+0.501865335\) \(a_{55}=-0.058409057\)
\(a_{56}=-0.284144661\) \(a_{57}=-1.388242206\) \(a_{58}=-0.264571953\) \(a_{59}=+0.791887015\) \(a_{60}=-0.322780035\)
\(a_{61}=-0.655041370\) \(a_{62}=-0.317404382\) \(a_{63}=-0.069885690\) \(a_{64}=+0.535995817\) \(a_{65}=-0.032297414\)
\(a_{66}=+0.086299601\) \(a_{67}=+0.804563706\) \(a_{68}=-0.675353978\) \(a_{69}=+0.136096333\) \(a_{70}=+0.077105988\)
\(a_{71}=+0.056681272\) \(a_{72}=+0.235115316\) \(a_{73}=+1.007451357\) \(a_{74}=-0.974875657\) \(a_{75}=+0.222753151\)
\(a_{76}=+0.807736777\) \(a_{77}=+0.037956710\) \(a_{78}=+0.047719429\) \(a_{79}=-1.512329771\) \(a_{80}=+0.030403569\)
\(a_{81}=-1.182645366\) \(a_{82}=+0.407683162\) \(a_{83}=-1.306106823\) \(a_{84}=+0.209756205\) \(a_{85}=+0.466066966\)
\(a_{86}=+0.872741616\) \(a_{87}=+0.496692143\) \(a_{88}=-0.127697211\) \(a_{89}=+1.424150801\) \(a_{90}=-0.063801286\)
\(a_{91}=+0.020988251\) \(a_{92}=-0.079186357\) \(a_{93}=+0.595876816\) \(a_{94}=-0.040312768\) \(a_{95}=-0.557425444\)
\(a_{96}=-1.133875812\) \(a_{97}=-0.736996757\) \(a_{98}=+0.543160263\) \(a_{99}=-0.031409167\) \(a_{100}=-0.129606942\)

Showing 100 of 5000 available coefficients

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