Properties

Level $757$
Weight $0$
Character 757.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 757 \)
Weight: \( 0 \)
Character: 757.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.31531289679 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.464507559\) \(a_{3}=+0.057024254\) \(a_{4}=-0.784232730\) \(a_{5}=+0.485728909\)
\(a_{6}=-0.026488203\) \(a_{7}=+0.137433725\) \(a_{8}=+0.828789594\) \(a_{9}=-0.996748232\) \(a_{10}=-0.225624752\)
\(a_{11}=+0.925944661\) \(a_{12}=-0.044720279\) \(a_{13}=-1.444628598\) \(a_{14}=-0.063839010\) \(a_{15}=+0.027698328\)
\(a_{16}=+0.399253715\) \(a_{17}=-0.309432511\) \(a_{18}=+0.462997073\) \(a_{19}=+0.491790003\) \(a_{20}=-0.380924512\)
\(a_{21}=+0.007837056\) \(a_{22}=-0.430108300\) \(a_{23}=-0.454770092\) \(a_{24}=+0.047261120\) \(a_{25}=-0.764067427\)
\(a_{26}=+0.671040894\) \(a_{27}=-0.113863073\) \(a_{28}=-0.107780036\) \(a_{29}=+0.800814877\) \(a_{30}=-0.012866095\)
\(a_{31}=+0.218720926\) \(a_{32}=-1.014245960\) \(a_{33}=+0.052801297\) \(a_{34}=+0.143733741\) \(a_{35}=+0.066755543\)
\(a_{36}=+0.781682603\) \(a_{37}=-1.750793585\) \(a_{38}=-0.228440179\) \(a_{39}=-0.082378859\) \(a_{40}=+0.402567046\)
\(a_{41}=+0.562567408\) \(a_{42}=-0.003640367\) \(a_{43}=-1.726773818\) \(a_{44}=-0.726156104\) \(a_{45}=-0.484149415\)
\(a_{46}=+0.211244144\) \(a_{47}=+0.138987251\) \(a_{48}=+0.022767140\) \(a_{49}=-0.981111955\) \(a_{50}=+0.354915089\)
\(a_{51}=-0.017645148\) \(a_{52}=+1.132925042\) \(a_{53}=-0.972734726\) \(a_{54}=+0.052890248\) \(a_{55}=+0.449758109\)
\(a_{56}=+0.113903645\) \(a_{57}=+0.028043955\) \(a_{58}=-0.371984557\) \(a_{59}=+0.856366174\) \(a_{60}=-0.021721930\)
\(a_{61}=-1.835522160\) \(a_{62}=-0.101597460\) \(a_{63}=-0.136986839\) \(a_{64}=+0.071871199\) \(a_{65}=-0.701697890\)
\(a_{66}=-0.024526610\) \(a_{67}=-0.699247742\) \(a_{68}=+0.242667085\) \(a_{69}=-0.025932898\) \(a_{70}=-0.031008463\)
\(a_{71}=-1.180358679\) \(a_{72}=-0.826094531\) \(a_{73}=-0.208523444\) \(a_{74}=+0.813256817\) \(a_{75}=-0.043570367\)
\(a_{76}=-0.385677793\) \(a_{77}=+0.127256027\) \(a_{78}=+0.038265576\) \(a_{79}=+0.153008605\) \(a_{80}=+0.193929093\)
\(a_{81}=+0.990255254\) \(a_{82}=-0.261316808\) \(a_{83}=+1.078515812\) \(a_{84}=-0.006146049\) \(a_{85}=-0.150300354\)
\(a_{86}=+0.802099433\) \(a_{87}=+0.045665903\) \(a_{88}=+0.767413311\) \(a_{89}=-1.045790811\) \(a_{90}=+0.224891047\)
\(a_{91}=-0.198540701\) \(a_{92}=+0.356645589\) \(a_{93}=+0.012472425\) \(a_{94}=-0.064560642\) \(a_{95}=+0.238876607\)
\(a_{96}=-0.057836623\) \(a_{97}=+0.681733446\) \(a_{98}=+0.455733963\) \(a_{99}=-0.922933723\) \(a_{100}=+0.599206657\)

Showing 100 of 2178 available coefficients

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