Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 26.0905993987 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.667918271\) \(a_{3}=+0.577350269\) \(a_{4}=-0.553885183\) \(a_{5}=-1.608750682\)
\(a_{6}=-0.385622794\) \(a_{7}=-0.652161078\) \(a_{8}=+1.037868305\) \(a_{9}=+0.333333333\) \(a_{10}=+1.074513974\)
\(a_{11}=+1.366983788\) \(a_{12}=-0.319785759\) \(a_{13}=+0.963276550\) \(a_{14}=+0.435590300\) \(a_{15}=-0.928812639\)
\(a_{16}=-0.139326021\) \(a_{17}=-0.335008847\) \(a_{18}=-0.222639424\) \(a_{19}=-0.832126221\) \(a_{20}=+0.891063165\)
\(a_{21}=-0.376525374\) \(a_{22}=-0.913033449\) \(a_{23}=+1.519506769\) \(a_{24}=+0.599213545\) \(a_{25}=+1.588078755\)
\(a_{26}=-0.643390008\) \(a_{27}=+0.192450090\) \(a_{28}=+0.361222358\) \(a_{29}=-1.358277520\) \(a_{30}=+0.620370932\)
\(a_{31}=+0.066171594\) \(a_{32}=-0.944809910\) \(a_{33}=+0.789228458\) \(a_{34}=+0.223758530\) \(a_{35}=+1.049164578\)
\(a_{36}=-0.184628394\) \(a_{37}=+0.917510907\) \(a_{38}=+0.555792307\) \(a_{39}=+0.556147976\) \(a_{40}=-1.669671343\)
\(a_{41}=-0.532182516\) \(a_{42}=+0.251488177\) \(a_{43}=+0.224918068\) \(a_{44}=-0.757152066\) \(a_{45}=-0.536250227\)
\(a_{46}=-1.014906335\) \(a_{47}=-1.355862121\) \(a_{48}=-0.080439916\) \(a_{49}=-0.574685929\) \(a_{50}=-1.060706817\)
\(a_{51}=-0.193417448\) \(a_{52}=-0.533544608\) \(a_{53}=+1.372695304\) \(a_{54}=-0.128540931\) \(a_{55}=-2.199136101\)
\(a_{56}=-0.676857312\) \(a_{57}=-0.480428297\) \(a_{58}=+0.907218373\) \(a_{59}=-0.305092042\) \(a_{60}=+0.514455558\)
\(a_{61}=-0.116023549\) \(a_{62}=-0.044197216\) \(a_{63}=-0.217387026\) \(a_{64}=+0.770381823\) \(a_{65}=-1.549671807\)
\(a_{66}=-0.527140107\) \(a_{67}=+0.419257410\) \(a_{68}=+0.185556437\) \(a_{69}=+0.877287642\) \(a_{70}=-0.700756191\)
\(a_{71}=+0.002119882\) \(a_{72}=+0.345956102\) \(a_{73}=-0.044642724\) \(a_{74}=-0.612822299\) \(a_{75}=+0.916877697\)
\(a_{76}=+0.460902384\) \(a_{77}=-0.891493621\) \(a_{78}=-0.371461394\) \(a_{79}=-0.642376378\) \(a_{80}=+0.224140832\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.355454426\) \(a_{83}=+0.311230094\) \(a_{84}=+0.208551825\) \(a_{85}=+0.538945711\)
\(a_{86}=-0.150226887\) \(a_{87}=-0.784201892\) \(a_{88}=+1.418749148\) \(a_{89}=-1.659306701\) \(a_{90}=+0.358171325\)
\(a_{91}=-0.628211473\) \(a_{92}=-0.841632285\) \(a_{93}=+0.038204187\) \(a_{94}=+0.905605084\) \(a_{95}=+1.338683624\)
\(a_{96}=-0.545486256\) \(a_{97}=+0.086968213\) \(a_{98}=+0.383843232\) \(a_{99}=+0.455661263\) \(a_{100}=-0.879613292\)

Showing 100 of 1228 available coefficients

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