Properties

Level $491$
Weight $0$
Character 491.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 491 \)
Weight: \( 0 \)
Character: 491.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.92107012241 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.788285321\) \(a_{3}=-1.698683728\) \(a_{4}=+2.197964417\) \(a_{5}=-0.770830120\)
\(a_{6}=-3.037731163\) \(a_{7}=+0.550770031\) \(a_{8}=+2.142302178\) \(a_{9}=+1.885526808\) \(a_{10}=-1.378464245\)
\(a_{11}=+1.421299896\) \(a_{12}=-3.733646389\) \(a_{13}=+0.219455787\) \(a_{14}=+0.984933993\) \(a_{15}=+1.309396445\)
\(a_{16}=+1.633083159\) \(a_{17}=+0.803581495\) \(a_{18}=+3.371859992\) \(a_{19}=+1.741782173\) \(a_{20}=-1.694257258\)
\(a_{21}=-0.935584223\) \(a_{22}=+2.541689678\) \(a_{23}=+0.841234476\) \(a_{24}=-3.639093778\) \(a_{25}=-0.405820899\)
\(a_{26}=+0.392449639\) \(a_{27}=-1.504229954\) \(a_{28}=+1.210572837\) \(a_{29}=-1.005909646\) \(a_{30}=+2.341574527\)
\(a_{31}=-1.481931442\) \(a_{32}=+0.778116403\) \(a_{33}=-2.414338994\) \(a_{34}=+1.437032930\) \(a_{35}=-0.424550081\)
\(a_{36}=+4.144320824\) \(a_{37}=-1.051238757\) \(a_{38}=+3.114803372\) \(a_{39}=-0.372786122\) \(a_{40}=-1.651351155\)
\(a_{41}=+1.615738164\) \(a_{42}=-1.673091464\) \(a_{43}=+1.445375045\) \(a_{44}=+3.123966616\) \(a_{45}=-1.453420883\)
\(a_{46}=+1.504367482\) \(a_{47}=-0.256177768\) \(a_{48}=-2.774091548\) \(a_{49}=-0.696652279\) \(a_{50}=-0.725723502\)
\(a_{51}=-1.365030880\) \(a_{52}=+0.482356054\) \(a_{53}=+1.446359301\) \(a_{54}=-2.689992374\) \(a_{55}=-1.095580752\)
\(a_{56}=+1.179915839\) \(a_{57}=-2.958737359\) \(a_{58}=-1.798853541\) \(a_{59}=+0.635920356\) \(a_{60}=+2.878006767\)
\(a_{61}=-0.234728188\) \(a_{62}=-2.650116358\) \(a_{63}=+1.038491697\) \(a_{64}=-0.241588934\) \(a_{65}=-0.169163185\)
\(a_{66}=-4.317526942\) \(a_{67}=+0.445189528\) \(a_{68}=+1.766243437\) \(a_{69}=-1.428991761\) \(a_{70}=-0.759216690\)
\(a_{71}=-0.641680853\) \(a_{72}=+4.039368242\) \(a_{73}=-0.713868337\) \(a_{74}=-1.879914853\) \(a_{75}=+0.689361632\)
\(a_{76}=+3.828375164\) \(a_{77}=+0.782809357\) \(a_{78}=-0.666647919\) \(a_{79}=+0.133884057\) \(a_{80}=-1.258829780\)
\(a_{81}=+0.669684609\) \(a_{82}=+2.889400949\) \(a_{83}=-1.288831084\) \(a_{84}=-2.056380841\) \(a_{85}=-0.619424743\)
\(a_{86}=+2.584742972\) \(a_{87}=+1.708722579\) \(a_{88}=+3.044853791\) \(a_{89}=+1.516424097\) \(a_{90}=-2.599131192\)
\(a_{91}=+0.120869693\) \(a_{92}=+1.849003496\) \(a_{93}=+2.517332981\) \(a_{94}=-0.458118957\) \(a_{95}=-1.342618022\)
\(a_{96}=-1.321773507\) \(a_{97}=-0.504305192\) \(a_{98}=-1.245813215\) \(a_{99}=+2.679899009\) \(a_{100}=-0.891979773\)

Showing 100 of 1452 available coefficients

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