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: \( 1.61189615978 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.905869325\) \(a_{3}=-0.577350269\) \(a_{4}=+2.632337885\) \(a_{5}=-0.690311319\)
\(a_{6}=-1.100354168\) \(a_{7}=-1.043119566\) \(a_{8}=+3.111022703\) \(a_{9}=+0.333333333\) \(a_{10}=-1.315643168\)
\(a_{11}=+0.785246549\) \(a_{12}=-1.519780986\) \(a_{13}=-1.052018750\) \(a_{14}=-1.988049584\) \(a_{15}=+0.398551426\)
\(a_{16}=+3.296864855\) \(a_{17}=+0.242535625\) \(a_{18}=+0.635289775\) \(a_{19}=+0.793706550\) \(a_{20}=-1.817132638\)
\(a_{21}=+0.602245362\) \(a_{22}=+1.496577311\) \(a_{23}=+0.585964140\) \(a_{24}=-1.796149795\) \(a_{25}=-0.523470283\)
\(a_{26}=-2.005010266\) \(a_{27}=-0.192450090\) \(a_{28}=-2.745843153\) \(a_{29}=+0.137955158\) \(a_{30}=+0.759586937\)
\(a_{31}=+1.301044714\) \(a_{32}=+3.172370894\) \(a_{33}=-0.453362307\) \(a_{34}=+0.462241208\) \(a_{35}=+0.720077244\)
\(a_{36}=+0.877445962\) \(a_{37}=-1.069673343\) \(a_{38}=+1.512700967\) \(a_{39}=+0.607383309\) \(a_{40}=-2.147574186\)
\(a_{41}=-0.128084660\) \(a_{42}=+1.147800963\) \(a_{43}=-0.017246247\) \(a_{44}=+2.067034241\) \(a_{45}=-0.230103773\)
\(a_{46}=+1.116771079\) \(a_{47}=-1.682000382\) \(a_{48}=-1.903445812\) \(a_{49}=+0.088098430\) \(a_{50}=-0.997665954\)
\(a_{51}=-0.140028008\) \(a_{52}=-2.769268812\) \(a_{53}=+0.454824115\) \(a_{54}=-0.366784723\) \(a_{55}=-0.542064581\)
\(a_{56}=-3.245168653\) \(a_{57}=-0.458246690\) \(a_{58}=+0.262924503\) \(a_{59}=-0.161319704\) \(a_{60}=+1.049122018\)
\(a_{61}=-0.221103613\) \(a_{62}=+2.479621211\) \(a_{63}=-0.347706522\) \(a_{64}=+2.749259520\) \(a_{65}=+0.726220451\)
\(a_{66}=-0.864049313\) \(a_{67}=+0.116091328\) \(a_{68}=+0.638435714\) \(a_{69}=-0.338306554\) \(a_{70}=+1.372373131\)
\(a_{71}=-0.059547504\) \(a_{72}=+1.037007568\) \(a_{73}=-0.030875944\) \(a_{74}=-2.038657612\) \(a_{75}=+0.302225709\)
\(a_{76}=+2.089303822\) \(a_{77}=-0.819106040\) \(a_{78}=+1.157593217\) \(a_{79}=-1.807775135\) \(a_{80}=-2.275863127\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.244112624\) \(a_{83}=+1.137822534\) \(a_{84}=+1.585313284\) \(a_{85}=-0.167425087\)
\(a_{86}=-0.032869094\) \(a_{87}=-0.079648447\) \(a_{88}=+2.442919843\) \(a_{89}=+1.192118053\) \(a_{90}=-0.438547723\)
\(a_{91}=+1.097381343\) \(a_{92}=+1.542455604\) \(a_{93}=-0.751158516\) \(a_{94}=-3.205672934\) \(a_{95}=-0.547904616\)
\(a_{96}=-1.831569190\) \(a_{97}=+0.465368303\) \(a_{98}=+0.167904095\) \(a_{99}=+0.261748850\) \(a_{100}=-1.377950656\)

Showing 100 of 442 available coefficients

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