Properties

Level $409$
Weight $0$
Character 409.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 409 \)
Weight: \( 0 \)
Character: 409.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.50125736753 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.294209755\) \(a_{3}=+1.775680885\) \(a_{4}=-0.913440607\) \(a_{5}=-1.355918677\)
\(a_{6}=-0.522422626\) \(a_{7}=+1.383698176\) \(a_{8}=+0.562952857\) \(a_{9}=+2.153042605\) \(a_{10}=+0.398924480\)
\(a_{11}=+0.703881883\) \(a_{12}=-1.621979018\) \(a_{13}=-0.038205071\) \(a_{14}=-0.407097483\) \(a_{15}=-2.407678936\)
\(a_{16}=+0.747814402\) \(a_{17}=-0.339367323\) \(a_{18}=-0.633446116\) \(a_{19}=+0.719860151\) \(a_{20}=+1.238551157\)
\(a_{21}=+2.457006379\) \(a_{22}=-0.207088945\) \(a_{23}=+1.174573894\) \(a_{24}=+0.999624672\) \(a_{25}=+0.838515510\)
\(a_{26}=+0.011240320\) \(a_{27}=+2.047435701\) \(a_{28}=-1.263926105\) \(a_{29}=-0.507414688\) \(a_{30}=+0.708362627\)
\(a_{31}=+1.333498336\) \(a_{32}=-0.782967164\) \(a_{33}=+1.249869606\) \(a_{34}=+0.099845145\) \(a_{35}=-1.876182221\)
\(a_{36}=-1.966676638\) \(a_{37}=-1.952367351\) \(a_{38}=-0.211789878\) \(a_{39}=-0.067839988\) \(a_{40}=-0.763318308\)
\(a_{41}=+0.982841502\) \(a_{42}=-0.722875202\) \(a_{43}=-0.361945462\) \(a_{44}=-0.642954291\) \(a_{45}=-2.919350723\)
\(a_{46}=-0.345571115\) \(a_{47}=-0.061470344\) \(a_{48}=+1.327879726\) \(a_{49}=+0.914620625\) \(a_{50}=-0.246699481\)
\(a_{51}=-0.602608067\) \(a_{52}=+0.034898051\) \(a_{53}=-0.739590816\) \(a_{54}=-0.602375529\) \(a_{55}=-0.954406665\)
\(a_{56}=+0.778956916\) \(a_{57}=+1.278241835\) \(a_{58}=+0.149286319\) \(a_{59}=-0.011994947\) \(a_{60}=+2.199271717\)
\(a_{61}=+0.532833894\) \(a_{62}=-0.392328249\) \(a_{63}=+2.979161059\) \(a_{64}=-0.517457794\) \(a_{65}=+0.051802919\)
\(a_{66}=-0.367723801\) \(a_{67}=-1.642124549\) \(a_{68}=+0.309991962\) \(a_{69}=+2.085668328\) \(a_{70}=+0.551991142\)
\(a_{71}=-1.460204380\) \(a_{72}=+1.212061587\) \(a_{73}=+0.183392200\) \(a_{74}=+0.574405534\) \(a_{75}=+1.488936003\)
\(a_{76}=-0.657549435\) \(a_{77}=+0.973960062\) \(a_{78}=+0.019959194\) \(a_{79}=-0.882297137\) \(a_{80}=-1.013975549\)
\(a_{81}=+1.482549865\) \(a_{82}=-0.289161530\) \(a_{83}=-1.624006415\) \(a_{84}=-2.244329362\) \(a_{85}=+0.460154376\)
\(a_{86}=+0.106487962\) \(a_{87}=-0.901006692\) \(a_{88}=+0.396252335\) \(a_{89}=+0.927563164\) \(a_{90}=+0.858901423\)
\(a_{91}=-0.052864193\) \(a_{92}=-1.072903566\) \(a_{93}=+2.367867567\) \(a_{94}=+0.018085192\) \(a_{95}=-0.976071790\)
\(a_{96}=-1.390299794\) \(a_{97}=+0.887627580\) \(a_{98}=-0.269090163\) \(a_{99}=+1.515487585\) \(a_{100}=-0.765934118\)

Showing 100 of 1170 available coefficients

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