Properties

Level $35$
Weight $0$
Character 35.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 35 = 5 \cdot 7 \)
Weight: \( 0 \)
Character: 35.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.69515745048 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.924162110\) \(a_{3}=+1.714624983\) \(a_{4}=-0.145924395\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.584591442\) \(a_{7}=-0.377964473\) \(a_{8}=+1.059019906\) \(a_{9}=+1.939938831\) \(a_{10}=+0.413297860\)
\(a_{11}=+0.604455720\) \(a_{12}=-0.250205613\) \(a_{13}=+0.082830808\) \(a_{14}=+0.349300445\) \(a_{15}=-0.766803603\)
\(a_{16}=-0.832781676\) \(a_{17}=+1.163840185\) \(a_{18}=-1.792817963\) \(a_{19}=-1.248591136\) \(a_{20}=+0.065259373\)
\(a_{21}=-0.648067328\) \(a_{22}=-0.558615073\) \(a_{23}=-0.159640232\) \(a_{24}=+1.815821988\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.076549094\) \(a_{27}=+1.611642601\) \(a_{28}=+0.055154237\) \(a_{29}=-0.126685589\) \(a_{30}=+0.708650836\)
\(a_{31}=-0.408006416\) \(a_{32}=-0.289394635\) \(a_{33}=+1.036414878\) \(a_{34}=-1.075577001\) \(a_{35}=+0.169030851\)
\(a_{36}=-0.283084400\) \(a_{37}=-1.671639199\) \(a_{38}=+1.153900618\) \(a_{39}=+0.142023772\) \(a_{40}=-0.473608100\)
\(a_{41}=-0.472346664\) \(a_{42}=+0.598919269\) \(a_{43}=+1.740260055\) \(a_{44}=-0.088204835\) \(a_{45}=-0.867567020\)
\(a_{46}=+0.147533454\) \(a_{47}=+1.119429697\) \(a_{48}=-1.427908268\) \(a_{49}=+0.142857143\) \(a_{50}=-0.184832422\)
\(a_{51}=+1.995549457\) \(a_{52}=-0.012087036\) \(a_{53}=-0.355820199\) \(a_{54}=-1.489419026\) \(a_{55}=-0.270320816\)
\(a_{56}=-0.400271901\) \(a_{57}=-2.140865553\) \(a_{58}=+0.117078021\) \(a_{59}=-0.223484688\) \(a_{60}=+0.111895352\)
\(a_{61}=+1.109885988\) \(a_{62}=+0.377064064\) \(a_{63}=-0.733227963\) \(a_{64}=+1.100229235\) \(a_{65}=-0.037043052\)
\(a_{66}=-0.957815357\) \(a_{67}=-0.219014740\) \(a_{68}=-0.169832704\) \(a_{69}=-0.273723172\) \(a_{70}=-0.156211894\)
\(a_{71}=-0.684268443\) \(a_{72}=+2.054433835\) \(a_{73}=+0.232837451\) \(a_{74}=+1.544865580\) \(a_{75}=+0.342924868\)
\(a_{76}=+0.182199366\) \(a_{77}=-0.228462342\) \(a_{78}=-0.131252222\) \(a_{79}=-0.716043527\) \(a_{80}=+0.372430761\)
\(a_{81}=+0.823426946\) \(a_{82}=+0.436526046\) \(a_{83}=+1.044411321\) \(a_{84}=+0.094565033\) \(a_{85}=-0.520474850\)
\(a_{86}=-1.608273042\) \(a_{87}=-0.217251468\) \(a_{88}=+0.640153391\) \(a_{89}=-0.662927870\) \(a_{90}=+0.801769746\)
\(a_{91}=-0.031310203\) \(a_{92}=+0.023348972\) \(a_{93}=-0.699583588\) \(a_{94}=-1.034550259\) \(a_{95}=+0.558484439\)
\(a_{96}=-0.496342242\) \(a_{97}=+0.475516888\) \(a_{98}=-0.132028249\) \(a_{99}=+1.172608984\) \(a_{100}=-0.029185080\)

Showing 100 of 1500 available coefficients

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