Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.81472029634 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.508803988\) \(a_{3}=-1.796206045\) \(a_{4}=+1.276489475\) \(a_{5}=-1.142256999\)
\(a_{6}=-2.710122845\) \(a_{7}=-0.150835673\) \(a_{8}=+0.417168422\) \(a_{9}=+2.226356157\) \(a_{10}=-1.723441916\)
\(a_{11}=+0.238208627\) \(a_{12}=-2.292838111\) \(a_{13}=-0.277350098\) \(a_{14}=-0.227581464\) \(a_{15}=+2.051728927\)
\(a_{16}=-0.647064096\) \(a_{17}=-1.021175265\) \(a_{18}=+3.359135049\) \(a_{19}=-1.198158668\) \(a_{20}=-1.458079037\)
\(a_{21}=+0.270931947\) \(a_{22}=+0.359410126\) \(a_{23}=+0.736245180\) \(a_{24}=-0.749320442\) \(a_{25}=+0.304751052\)
\(a_{26}=-0.418466934\) \(a_{27}=-2.202788343\) \(a_{28}=-0.192540148\) \(a_{29}=-0.079294134\) \(a_{30}=+3.095656788\)
\(a_{31}=+1.394825955\) \(a_{32}=-1.393461310\) \(a_{33}=-0.427871775\) \(a_{34}=-1.540753313\) \(a_{35}=+0.172293103\)
\(a_{36}=+2.841920201\) \(a_{37}=-0.353242203\) \(a_{38}=-1.807786577\) \(a_{39}=+0.498177923\) \(a_{40}=-0.476513550\)
\(a_{41}=+0.584564966\) \(a_{42}=+0.408783202\) \(a_{43}=+0.220990242\) \(a_{44}=+0.304070805\) \(a_{45}=-2.543070903\)
\(a_{46}=+1.110849664\) \(a_{47}=-0.804685966\) \(a_{48}=+1.162260440\) \(a_{49}=-0.977248600\) \(a_{50}=+0.459809603\)
\(a_{51}=+1.834241185\) \(a_{52}=-0.354034481\) \(a_{53}=-0.609274141\) \(a_{54}=-3.323575836\) \(a_{55}=-0.272095471\)
\(a_{56}=-0.062923880\) \(a_{57}=+2.152139843\) \(a_{58}=-0.119639305\) \(a_{59}=+0.615908521\) \(a_{60}=+2.619010381\)
\(a_{61}=-0.197544540\) \(a_{62}=+2.104518964\) \(a_{63}=-0.335813928\) \(a_{64}=-1.455395887\) \(a_{65}=+0.316805091\)
\(a_{66}=-0.645574641\) \(a_{67}=-0.642484239\) \(a_{68}=-1.303519478\) \(a_{69}=-1.322448043\) \(a_{70}=+0.259956521\)
\(a_{71}=+0.353328508\) \(a_{72}=+0.928765485\) \(a_{73}=-1.334415982\) \(a_{74}=-0.532973245\) \(a_{75}=-0.547395682\)
\(a_{76}=-1.529436929\) \(a_{77}=-0.035930358\) \(a_{78}=+0.751652837\) \(a_{79}=+1.050029907\) \(a_{80}=+0.739113492\)
\(a_{81}=+1.730305580\) \(a_{82}=+0.881993953\) \(a_{83}=-0.004271561\) \(a_{84}=+0.345841779\) \(a_{85}=+1.166444594\)
\(a_{86}=+0.333430958\) \(a_{87}=+0.142428602\) \(a_{88}=+0.099373117\) \(a_{89}=-0.074124681\) \(a_{90}=-3.836995521\)
\(a_{91}=+0.041834289\) \(a_{92}=+0.939809223\) \(a_{93}=-2.505394812\) \(a_{94}=-1.214113395\) \(a_{95}=+1.368605125\)
\(a_{96}=+2.502943629\) \(a_{97}=-0.178249397\) \(a_{98}=-1.474476585\) \(a_{99}=+0.530337242\) \(a_{100}=+0.389011511\)

Showing 100 of 546 available coefficients

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