Properties

Level $51$
Weight $0$
Character 51.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.35857801489 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.898381498\) \(a_{3}=+0.577350269\) \(a_{4}=+2.603852313\) \(a_{5}=+0.306429291\)
\(a_{6}=+1.096031069\) \(a_{7}=-1.017293494\) \(a_{8}=+3.044723556\) \(a_{9}=+0.333333333\) \(a_{10}=+0.581719696\)
\(a_{11}=+0.855369286\) \(a_{12}=+1.503334834\) \(a_{13}=-1.009630322\) \(a_{14}=-1.931211147\) \(a_{15}=+0.176917033\)
\(a_{16}=+3.176194554\) \(a_{17}=-0.242535625\) \(a_{18}=+0.632793833\) \(a_{19}=-1.464552271\) \(a_{20}=+0.797896617\)
\(a_{21}=-0.587334673\) \(a_{22}=+1.623817226\) \(a_{23}=+0.594311456\) \(a_{24}=+1.757871965\) \(a_{25}=-0.906101090\)
\(a_{26}=-1.916663522\) \(a_{27}=+0.192450090\) \(a_{28}=-2.648882017\) \(a_{29}=-0.316768091\) \(a_{30}=+0.335856023\)
\(a_{31}=-1.601176923\) \(a_{32}=+2.984905420\) \(a_{33}=+0.493847687\) \(a_{34}=-0.460425143\) \(a_{35}=-0.311728524\)
\(a_{36}=+0.867950771\) \(a_{37}=+1.434550420\) \(a_{38}=-2.780278934\) \(a_{39}=-0.582910338\) \(a_{40}=+0.932992480\)
\(a_{41}=+1.376540265\) \(a_{42}=-1.114985276\) \(a_{43}=+1.655848400\) \(a_{44}=+2.227255293\) \(a_{45}=+0.102143097\)
\(a_{46}=+1.128229872\) \(a_{47}=+0.421487253\) \(a_{48}=+1.833776781\) \(a_{49}=+0.034886053\) \(a_{50}=-1.720125544\)
\(a_{51}=-0.140028008\) \(a_{52}=-2.628928248\) \(a_{53}=-0.772462524\) \(a_{54}=+0.365343690\) \(a_{55}=+0.262110204\)
\(a_{56}=-3.097377465\) \(a_{57}=-0.845559648\) \(a_{58}=-0.601346684\) \(a_{59}=+1.272450945\) \(a_{60}=+0.460665827\)
\(a_{61}=+0.772190171\) \(a_{62}=-3.039644647\) \(a_{63}=-0.339097831\) \(a_{64}=+2.490294669\) \(a_{65}=-0.309380303\)
\(a_{66}=+0.937511313\) \(a_{67}=-0.648300380\) \(a_{68}=-0.631526948\) \(a_{69}=+0.343125879\) \(a_{70}=-0.591779662\)
\(a_{71}=+0.355599500\) \(a_{72}=+1.014907852\) \(a_{73}=+1.117391609\) \(a_{74}=+2.723323975\) \(a_{75}=-0.523137708\)
\(a_{76}=-3.813477817\) \(a_{77}=-0.870161609\) \(a_{78}=-1.106586201\) \(a_{79}=-0.663124585\) \(a_{80}=+0.973279044\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.613198570\) \(a_{83}=-1.291501525\) \(a_{84}=-1.529332746\) \(a_{85}=-0.074320020\)
\(a_{86}=+3.143431966\) \(a_{87}=-0.182886143\) \(a_{88}=+2.604363014\) \(a_{89}=+0.048211757\) \(a_{90}=+0.193906565\)
\(a_{91}=+1.027090357\) \(a_{92}=+1.547499258\) \(a_{93}=-0.924439928\) \(a_{94}=+0.800143602\) \(a_{95}=-0.448781713\)
\(a_{96}=+1.723335948\) \(a_{97}=-0.091833160\) \(a_{98}=+0.066227037\) \(a_{99}=+0.285123095\) \(a_{100}=-2.359353418\)

Showing 100 of 478 available coefficients

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