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: \( 3.59362788512 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.795237893\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.562318107\) \(a_{7}=-0.899804719\) \(a_{8}=-0.353553391\) \(a_{9}=-0.367596694\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.496840608\) \(a_{12}=-0.397618946\) \(a_{13}=-1.122252763\) \(a_{14}=+0.636258019\) \(a_{15}=+0.355641197\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.665073354\) \(a_{18}=+0.259930115\) \(a_{19}=-1.124694256\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.715558809\) \(a_{22}=-1.058426144\) \(a_{23}=+1.079808371\) \(a_{24}=+0.281159053\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.793552539\) \(a_{27}=+1.087564713\) \(a_{28}=-0.449902360\) \(a_{29}=-1.150055048\) \(a_{30}=-0.251476302\)
\(a_{31}=-0.430292792\) \(a_{32}=-0.176776695\) \(a_{33}=-1.190344371\) \(a_{34}=+0.470277879\) \(a_{35}=+0.402404904\)
\(a_{36}=-0.183798347\) \(a_{37}=-0.367025503\) \(a_{38}=+0.795278935\) \(a_{39}=+0.892457923\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.366062478\) \(a_{42}=-0.505976486\) \(a_{43}=-0.283147974\) \(a_{44}=+0.748420304\) \(a_{45}=+0.164394239\)
\(a_{46}=-0.763539822\) \(a_{47}=+0.242440107\) \(a_{48}=-0.198809473\) \(a_{49}=-0.190351467\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.528891533\) \(a_{52}=-0.561126382\) \(a_{53}=-0.297510285\) \(a_{54}=-0.769024384\) \(a_{55}=-0.669407470\)
\(a_{56}=+0.318129009\) \(a_{57}=+0.894399490\) \(a_{58}=+0.813211723\) \(a_{59}=-0.926145770\) \(a_{60}=+0.177820599\)
\(a_{61}=-0.174208400\) \(a_{62}=+0.304262951\) \(a_{63}=+0.330765240\) \(a_{64}=+0.125000000\) \(a_{65}=+0.501886693\)
\(a_{66}=+0.841700577\) \(a_{67}=+0.070025068\) \(a_{68}=-0.332536677\) \(a_{69}=-0.858704534\) \(a_{70}=-0.284543236\)
\(a_{71}=-0.360023000\) \(a_{72}=+0.129965058\) \(a_{73}=+1.470124006\) \(a_{74}=+0.259526222\) \(a_{75}=-0.159047579\)
\(a_{76}=-0.562347128\) \(a_{77}=-1.346864243\) \(a_{78}=-0.631063049\) \(a_{79}=+0.814990997\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.497275977\) \(a_{82}=-0.258845261\) \(a_{83}=-1.372229993\) \(a_{84}=+0.357779404\) \(a_{85}=+0.297429846\)
\(a_{86}=+0.200215852\) \(a_{87}=+0.914567353\) \(a_{88}=-0.529213072\) \(a_{89}=+1.572800000\) \(a_{90}=-0.116244281\)
\(a_{91}=+1.009808333\) \(a_{92}=+0.539904186\) \(a_{93}=+0.342185133\) \(a_{94}=-0.171431044\) \(a_{95}=+0.502978562\)
\(a_{96}=+0.140579527\) \(a_{97}=-0.913999557\) \(a_{98}=+0.134598813\) \(a_{99}=-0.550233659\) \(a_{100}=+0.099975586\)

Showing 100 of 112 available coefficients

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