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: \( 3.81509389117 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.762260748\) \(a_{3}=-0.577350269\) \(a_{4}=-0.418958552\) \(a_{5}=+1.961870756\)
\(a_{6}=+0.440091448\) \(a_{7}=-0.850953602\) \(a_{8}=+1.081616407\) \(a_{9}=+0.333333333\) \(a_{10}=-1.495457071\)
\(a_{11}=+0.155585490\) \(a_{12}=+0.241885833\) \(a_{13}=-0.874051087\) \(a_{14}=+0.648648529\) \(a_{15}=-1.132686609\)
\(a_{16}=-0.405515180\) \(a_{17}=-0.242535625\) \(a_{18}=-0.254086916\) \(a_{19}=-0.630959036\) \(a_{20}=-0.821942531\)
\(a_{21}=+0.491298291\) \(a_{22}=-0.118596712\) \(a_{23}=+0.307850799\) \(a_{24}=-0.624471524\) \(a_{25}=+2.848936865\)
\(a_{26}=+0.666254836\) \(a_{27}=-0.192450090\) \(a_{28}=+0.356514289\) \(a_{29}=-1.525986498\) \(a_{30}=+0.863402542\)
\(a_{31}=-1.481099613\) \(a_{32}=-0.772508103\) \(a_{33}=-0.089827325\) \(a_{34}=+0.184875387\) \(a_{35}=-1.669460987\)
\(a_{36}=-0.139652851\) \(a_{37}=-0.611017104\) \(a_{38}=+0.480955307\) \(a_{39}=+0.504633631\) \(a_{40}=+2.121991599\)
\(a_{41}=+0.204378017\) \(a_{42}=-0.374497403\) \(a_{43}=-1.751993560\) \(a_{44}=-0.065183872\) \(a_{45}=+0.653956919\)
\(a_{46}=-0.234662580\) \(a_{47}=+0.079841669\) \(a_{48}=+0.234124298\) \(a_{49}=-0.275877967\) \(a_{50}=-2.171632746\)
\(a_{51}=+0.140028008\) \(a_{52}=+0.366191178\) \(a_{53}=+1.035766642\) \(a_{54}=+0.146697149\) \(a_{55}=+0.305238623\)
\(a_{56}=-0.920405378\) \(a_{57}=+0.364284369\) \(a_{58}=+1.163199609\) \(a_{59}=-0.233821438\) \(a_{60}=+0.474548741\)
\(a_{61}=-0.052643412\) \(a_{62}=+1.128984099\) \(a_{63}=-0.283651201\) \(a_{64}=+0.994367785\) \(a_{65}=-1.714775268\)
\(a_{66}=+0.068471844\) \(a_{67}=-1.664784488\) \(a_{68}=+0.101612374\) \(a_{69}=-0.177737742\) \(a_{70}=+1.272564581\)
\(a_{71}=+0.980725961\) \(a_{72}=+0.360538802\) \(a_{73}=+1.223349002\) \(a_{74}=+0.465754355\) \(a_{75}=-1.644834466\)
\(a_{76}=+0.264345684\) \(a_{77}=-0.132396033\) \(a_{78}=-0.384662409\) \(a_{79}=-0.297738326\) \(a_{80}=-0.795568373\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.155789340\) \(a_{83}=-0.894599693\) \(a_{84}=-0.205833621\) \(a_{85}=-0.475823550\)
\(a_{86}=+1.335475922\) \(a_{87}=+0.881028715\) \(a_{88}=+0.168283819\) \(a_{89}=-1.080669126\) \(a_{90}=-0.498485690\)
\(a_{91}=+0.743776921\) \(a_{92}=-0.128976725\) \(a_{93}=+0.855113260\) \(a_{94}=-0.060860171\) \(a_{95}=-1.237860082\)
\(a_{96}=+0.446007761\) \(a_{97}=+1.256292756\) \(a_{98}=+0.210290946\) \(a_{99}=+0.051861830\) \(a_{100}=-1.193586463\)

Showing 100 of 400 available coefficients

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