Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.31945091149 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.428052857\) \(a_{3}=+0.577350269\) \(a_{4}=+1.039334962\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.824486701\) \(a_{7}=-0.430702289\) \(a_{8}=-0.056172405\) \(a_{9}=+0.333333333\) \(a_{10}=-0.638644653\)
\(a_{11}=-0.767991419\) \(a_{12}=+0.600060320\) \(a_{13}=-1.426793402\) \(a_{14}=+0.615065634\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.959117799\) \(a_{17}=+1.004781966\) \(a_{18}=-0.476017619\) \(a_{19}=-1.401152314\) \(a_{20}=+0.464804725\)
\(a_{21}=-0.248666082\) \(a_{22}=+1.096732340\) \(a_{23}=-0.768511944\) \(a_{24}=-0.032431153\) \(a_{25}=+0.200000000\)
\(a_{26}=+2.037536394\) \(a_{27}=+0.192450089\) \(a_{28}=-0.447643946\) \(a_{29}=-0.612417845\) \(a_{30}=-0.368721664\)
\(a_{31}=-1.840273757\) \(a_{32}=+1.425843321\) \(a_{33}=-0.443400051\) \(a_{34}=-1.434881763\) \(a_{35}=-0.192615918\)
\(a_{36}=+0.346444987\) \(a_{37}=+0.327391408\) \(a_{38}=+2.000919549\) \(a_{39}=-0.823759530\) \(a_{40}=-0.025121026\)
\(a_{41}=-0.530632622\) \(a_{42}=+0.355108310\) \(a_{43}=+1.772313028\) \(a_{44}=-0.798200332\) \(a_{45}=+0.149071197\)
\(a_{46}=+1.097475676\) \(a_{47}=+0.479372378\) \(a_{48}=-0.553746911\) \(a_{49}=-0.814495540\) \(a_{50}=-0.285610571\)
\(a_{51}=+0.580111133\) \(a_{52}=-1.482916272\) \(a_{53}=-1.293438470\) \(a_{54}=-0.274828908\) \(a_{55}=-0.343456176\)
\(a_{56}=+0.024193580\) \(a_{57}=-0.808955667\) \(a_{58}=+0.874565049\) \(a_{59}=+0.087099698\) \(a_{60}=+0.268355146\)
\(a_{61}=+1.264917191\) \(a_{62}=+2.628008173\) \(a_{63}=-0.143567447\) \(a_{64}=-1.077061804\) \(a_{65}=-0.638081407\)
\(a_{66}=+0.633198743\) \(a_{67}=-1.015104591\) \(a_{68}=+1.044305026\) \(a_{69}=-0.443700576\) \(a_{70}=+0.275065724\)
\(a_{71}=-0.368365123\) \(a_{72}=-0.018724156\) \(a_{73}=-0.200837160\) \(a_{74}=-0.467532223\) \(a_{75}=+0.115470022\)
\(a_{76}=-1.456266620\) \(a_{77}=+0.330775724\) \(a_{78}=+1.176372198\) \(a_{79}=+0.684069262\) \(a_{80}=-0.428930470\)
\(a_{81}=+0.111111132\) \(a_{82}=+0.757771408\) \(a_{83}=+0.241581245\) \(a_{84}=-0.258447328\) \(a_{85}=+0.449352075\)
\(a_{86}=-2.530956734\) \(a_{87}=-0.353579447\) \(a_{88}=+0.043139964\) \(a_{89}=+1.178913952\) \(a_{90}=-0.212881578\)
\(a_{91}=+0.614523272\) \(a_{92}=-0.798741344\) \(a_{93}=-1.062482563\) \(a_{94}=-0.684569116\) \(a_{95}=-0.626614351\)
\(a_{96}=+0.823211080\) \(a_{97}=+0.876105826\) \(a_{98}=+1.163142670\) \(a_{99}=-0.255997165\) \(a_{100}=+0.207866972\)

Showing 100 of 1500 available coefficients

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