Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 15.2144704333 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.397646030\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.988284985\) \(a_{7}=+1.721595566\) \(a_{8}=-0.353553391\) \(a_{9}=+0.953414424\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.167843124\) \(a_{12}=-0.698823015\) \(a_{13}=+1.035417293\) \(a_{14}=-1.217351899\) \(a_{15}=+0.625046306\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.149975153\) \(a_{18}=-0.674165805\) \(a_{19}=+0.717670425\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.406181208\) \(a_{22}=-0.825789792\) \(a_{23}=+0.570245442\) \(a_{24}=+0.494142493\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.732150590\) \(a_{27}=+0.065110145\) \(a_{28}=+0.860797783\) \(a_{29}=-1.887463089\) \(a_{30}=-0.441974482\)
\(a_{31}=+0.114975179\) \(a_{32}=-0.176776695\) \(a_{33}=-1.632231305\) \(a_{34}=+0.813155229\) \(a_{35}=-0.769920943\)
\(a_{36}=+0.476707212\) \(a_{37}=+0.212696596\) \(a_{38}=-0.507469624\) \(a_{39}=-1.447146869\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.101233292\) \(a_{42}=+1.701427049\) \(a_{43}=-0.648265949\) \(a_{44}=+0.583921562\) \(a_{45}=-0.426379893\)
\(a_{46}=-0.403224419\) \(a_{47}=+1.737502123\) \(a_{48}=-0.349411507\) \(a_{49}=+1.963891293\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.607258207\) \(a_{52}=+0.517708647\) \(a_{53}=+0.376352078\) \(a_{54}=-0.046039825\) \(a_{55}=-0.522275322\)
\(a_{56}=-0.608675950\) \(a_{57}=-1.003049220\) \(a_{58}=+1.334637949\) \(a_{59}=+0.544862457\) \(a_{60}=+0.312523153\)
\(a_{61}=+0.727513575\) \(a_{62}=-0.081299729\) \(a_{63}=+1.641394046\) \(a_{64}=+0.125000000\) \(a_{65}=-0.463052691\)
\(a_{66}=+1.154161824\) \(a_{67}=+1.091081157\) \(a_{68}=-0.574987577\) \(a_{69}=-0.797001278\) \(a_{70}=+0.544416320\)
\(a_{71}=-1.195093307\) \(a_{72}=-0.337082902\) \(a_{73}=-0.640505623\) \(a_{74}=-0.150399206\) \(a_{75}=-0.279529206\)
\(a_{76}=+0.358835212\) \(a_{77}=+2.010553544\) \(a_{78}=+1.023287365\) \(a_{79}=+0.303077888\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.044415360\) \(a_{82}=+0.071582747\) \(a_{83}=-1.055439192\) \(a_{84}=-1.203090604\) \(a_{85}=+0.514284523\)
\(a_{86}=+0.458393249\) \(a_{87}=+2.638005291\) \(a_{88}=-0.412894896\) \(a_{89}=-1.905710210\) \(a_{90}=+0.301496113\)
\(a_{91}=+1.782569822\) \(a_{92}=+0.285122721\) \(a_{93}=-0.160694596\) \(a_{94}=-1.228599534\) \(a_{95}=-0.320951971\)
\(a_{96}=+0.247071246\) \(a_{97}=+0.023919867\) \(a_{98}=-1.388680851\) \(a_{99}=+1.113438463\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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