Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 28.3445409049 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.858428957\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.314107718\) \(a_{7}=-1.602168079\) \(a_{8}=-0.353553391\) \(a_{9}=+2.453758187\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.700041884\) \(a_{12}=+0.929214478\) \(a_{13}=-0.831642425\) \(a_{14}=+1.132903914\) \(a_{15}=-0.831114696\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.392434901\) \(a_{18}=-1.735069053\) \(a_{19}=-0.445400129\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.977515552\) \(a_{22}=-1.202111144\) \(a_{23}=+0.483577292\) \(a_{24}=-0.657053859\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.588059998\) \(a_{27}=+2.701706310\) \(a_{28}=-0.801084040\) \(a_{29}=-0.949400481\) \(a_{30}=+0.587686837\)
\(a_{31}=+0.829710470\) \(a_{32}=-0.176776695\) \(a_{33}=+3.159407064\) \(a_{34}=+0.277493380\) \(a_{35}=+0.716511347\)
\(a_{36}=+1.226879093\) \(a_{37}=-0.586024100\) \(a_{38}=+0.314945451\) \(a_{39}=-1.545548365\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.554742023\) \(a_{42}=+2.105421438\) \(a_{43}=+0.232063762\) \(a_{44}=+0.850020942\) \(a_{45}=-1.097354021\)
\(a_{46}=-0.341940782\) \(a_{47}=+0.669853331\) \(a_{48}=+0.464607239\) \(a_{49}=+1.566942555\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.729312383\) \(a_{52}=-0.415821213\) \(a_{53}=+0.253008918\) \(a_{54}=-1.910394852\) \(a_{55}=-0.760281843\)
\(a_{56}=+0.566451957\) \(a_{57}=-0.827744497\) \(a_{58}=+0.671327518\) \(a_{59}=+0.861961817\) \(a_{60}=-0.415557348\)
\(a_{61}=+0.018338498\) \(a_{62}=-0.586693900\) \(a_{63}=-3.931333041\) \(a_{64}=+0.125000000\) \(a_{65}=+0.371921799\)
\(a_{66}=-2.234038160\) \(a_{67}=-0.847652358\) \(a_{68}=-0.196217450\) \(a_{69}=+0.898694042\) \(a_{70}=-0.506650033\)
\(a_{71}=-1.573297964\) \(a_{72}=-0.867534527\) \(a_{73}=+0.795999333\) \(a_{74}=+0.414381615\) \(a_{75}=+0.371685791\)
\(a_{76}=-0.222700064\) \(a_{77}=-2.723752840\) \(a_{78}=+1.092867729\) \(a_{79}=-1.109631553\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.567171052\) \(a_{82}=+1.099368628\) \(a_{83}=-0.479983683\) \(a_{84}=-1.488757776\) \(a_{85}=+0.175502223\)
\(a_{86}=-0.164093860\) \(a_{87}=-1.764393345\) \(a_{88}=-0.601055572\) \(a_{89}=+0.888567577\) \(a_{90}=+0.775946470\)
\(a_{91}=+1.332430947\) \(a_{92}=+0.241788646\) \(a_{93}=+1.541957963\) \(a_{94}=-0.473657833\) \(a_{95}=+0.199188993\)
\(a_{96}=-0.328526929\) \(a_{97}=-1.124660015\) \(a_{98}=-1.107995706\) \(a_{99}=+4.171491690\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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