Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 38.3032761525 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.758960092\) \(a_{3}=+1.501969424\) \(a_{4}=+2.093940606\) \(a_{5}=+0.267394981\)
\(a_{6}=+2.641904277\) \(a_{7}=-0.689138148\) \(a_{8}=+1.924197869\) \(a_{9}=+1.255912152\) \(a_{10}=+0.470337100\)
\(a_{11}=+0.634198827\) \(a_{12}=+3.145034767\) \(a_{13}=-0.238802115\) \(a_{14}=-1.212166500\) \(a_{15}=+0.401619086\)
\(a_{16}=+1.290646655\) \(a_{17}=+0.945176400\) \(a_{18}=+2.209099354\) \(a_{19}=+1.251908829\) \(a_{20}=+0.559909208\)
\(a_{21}=-1.035064428\) \(a_{22}=+1.115530428\) \(a_{23}=-1.413600030\) \(a_{24}=+2.890086366\) \(a_{25}=-0.928499924\)
\(a_{26}=-0.420043390\) \(a_{27}=+0.384372227\) \(a_{28}=-1.443014351\) \(a_{29}=-0.954184820\) \(a_{30}=+0.706431944\)
\(a_{31}=+0.327097440\) \(a_{32}=+0.345998091\) \(a_{33}=+0.952547247\) \(a_{34}=+1.662527568\) \(a_{35}=-0.184272082\)
\(a_{36}=+2.629805452\) \(a_{37}=-1.546167109\) \(a_{38}=+2.202057662\) \(a_{39}=-0.358673475\) \(a_{40}=+0.514520853\)
\(a_{41}=+1.126268684\) \(a_{42}=-1.820637021\) \(a_{43}=+0.726768036\) \(a_{44}=+1.327974676\) \(a_{45}=+0.335824606\)
\(a_{46}=-2.486466038\) \(a_{47}=+0.648992582\) \(a_{48}=+1.938511814\) \(a_{49}=-0.525088613\) \(a_{50}=-1.633194312\)
\(a_{51}=+1.419626054\) \(a_{52}=-0.500037446\) \(a_{53}=-0.247959250\) \(a_{54}=+0.676095408\) \(a_{55}=+0.169581583\)
\(a_{56}=-1.326038156\) \(a_{57}=+1.880328777\) \(a_{58}=-1.678373019\) \(a_{59}=+0.085256288\) \(a_{60}=+0.840966511\)
\(a_{61}=-0.087323248\) \(a_{62}=+0.575351344\) \(a_{63}=-0.865496976\) \(a_{64}=-0.682049820\) \(a_{65}=-0.063854486\)
\(a_{66}=+1.675492590\) \(a_{67}=-1.119040110\) \(a_{68}=+1.979143244\) \(a_{69}=-2.123184023\) \(a_{70}=-0.324127238\)
\(a_{71}=-0.984119072\) \(a_{72}=+2.416623486\) \(a_{73}=+1.634418242\) \(a_{74}=-2.719646241\) \(a_{75}=-1.394578497\)
\(a_{76}=+2.621422723\) \(a_{77}=-0.437050605\) \(a_{78}=-0.630892329\) \(a_{79}=-0.121743673\) \(a_{80}=+0.345112438\)
\(a_{81}=-0.678596819\) \(a_{82}=+1.981061669\) \(a_{83}=-0.180460847\) \(a_{84}=-2.167363435\) \(a_{85}=+0.252735425\)
\(a_{86}=+1.278355971\) \(a_{87}=-1.433156425\) \(a_{88}=+1.220324032\) \(a_{89}=+0.206130483\) \(a_{90}=+0.590702080\)
\(a_{91}=+0.164567647\) \(a_{92}=-2.959994503\) \(a_{93}=+0.491290354\) \(a_{94}=+1.141552053\) \(a_{95}=+0.334754136\)
\(a_{96}=+0.519678553\) \(a_{97}=+0.097340856\) \(a_{98}=-0.923609915\) \(a_{99}=+0.796498014\) \(a_{100}=-1.944223694\)

Showing 100 of 5000 available coefficients

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