Properties

Level $641$
Weight $0$
Character 641.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 641 \)
Weight: \( 0 \)
Character: 641.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.4309549703 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.593046686\) \(a_{3}=+1.374573299\) \(a_{4}=+1.537798320\) \(a_{5}=-0.741336181\)
\(a_{6}=+2.189758231\) \(a_{7}=+0.281633255\) \(a_{8}=+0.856737379\) \(a_{9}=+0.889450350\) \(a_{10}=-1.180983738\)
\(a_{11}=+1.826966446\) \(a_{12}=+2.113814730\) \(a_{13}=-0.984752475\) \(a_{14}=+0.448654923\) \(a_{15}=-1.019020407\)
\(a_{16}=-0.172976005\) \(a_{17}=-0.249673823\) \(a_{18}=+1.416934862\) \(a_{19}=-0.470994752\) \(a_{20}=-1.140025721\)
\(a_{21}=+0.387124980\) \(a_{22}=+2.910442977\) \(a_{23}=+1.150081800\) \(a_{24}=+1.177647748\) \(a_{25}=-0.450420308\)
\(a_{26}=-1.568756724\) \(a_{27}=-0.151959064\) \(a_{28}=+0.433094652\) \(a_{29}=-0.684534750\) \(a_{30}=-1.623348342\)
\(a_{31}=-1.141324153\) \(a_{32}=-1.132295223\) \(a_{33}=+2.511297953\) \(a_{34}=-0.397742119\) \(a_{35}=-0.208785450\)
\(a_{36}=+1.367794521\) \(a_{37}=+0.361392438\) \(a_{38}=-0.750317108\) \(a_{39}=-1.353614072\) \(a_{40}=-0.635130637\)
\(a_{41}=+1.802119162\) \(a_{42}=+0.616708645\) \(a_{43}=-0.492620895\) \(a_{44}=+2.809505180\) \(a_{45}=-0.659381271\)
\(a_{46}=+1.832134047\) \(a_{47}=+1.576067843\) \(a_{48}=-0.237767653\) \(a_{49}=-0.920682891\) \(a_{50}=-0.717540496\)
\(a_{51}=-0.343194442\) \(a_{52}=-1.514350564\) \(a_{53}=+0.827646724\) \(a_{54}=-0.242078697\) \(a_{55}=-1.354396420\)
\(a_{56}=+0.241285365\) \(a_{57}=-0.647417547\) \(a_{58}=-1.090495877\) \(a_{59}=-1.488958823\) \(a_{60}=-1.567048051\)
\(a_{61}=-1.515825982\) \(a_{62}=-1.818181821\) \(a_{63}=+0.250498079\) \(a_{64}=-1.630823508\) \(a_{65}=+0.730033071\)
\(a_{66}=+4.000615242\) \(a_{67}=+1.096149492\) \(a_{68}=-0.383947784\) \(a_{69}=+1.580871283\) \(a_{70}=-0.332604247\)
\(a_{71}=-1.392118514\) \(a_{72}=+0.762025103\) \(a_{73}=+0.786189175\) \(a_{74}=+0.575715179\) \(a_{75}=-0.619134724\)
\(a_{76}=-0.724295637\) \(a_{77}=+0.514534754\) \(a_{78}=-2.156370360\) \(a_{79}=-0.794911918\) \(a_{80}=+0.128232746\)
\(a_{81}=-1.098327957\) \(a_{82}=+2.870860086\) \(a_{83}=-0.245071955\) \(a_{84}=+0.595320414\) \(a_{85}=+0.185092779\)
\(a_{86}=-0.784768455\) \(a_{87}=-0.940942028\) \(a_{88}=+1.565230246\) \(a_{89}=+1.071573771\) \(a_{90}=-1.050426459\)
\(a_{91}=-0.277339103\) \(a_{92}=+1.768593439\) \(a_{93}=-1.568832996\) \(a_{94}=+2.510750429\) \(a_{95}=+0.349165892\)
\(a_{96}=-1.556422160\) \(a_{97}=+1.255800542\) \(a_{98}=-1.466690854\) \(a_{99}=+1.624995361\) \(a_{100}=-0.692655123\)

Showing 100 of 1662 available coefficients

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