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: \( 25.2524967393 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.520180571\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.074929991\) \(a_{7}=+1.508623190\) \(a_{8}=-0.353553391\) \(a_{9}=+1.310948969\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.205261312\) \(a_{12}=+0.760090286\) \(a_{13}=+1.227673000\) \(a_{14}=-1.066757688\) \(a_{15}=+0.679845419\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.734915693\) \(a_{18}=-0.926980906\) \(a_{19}=+1.250532490\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.293379663\) \(a_{22}=-0.145141665\) \(a_{23}=-1.043233520\) \(a_{24}=-0.537464995\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.868095904\) \(a_{27}=+0.472698582\) \(a_{28}=+0.754311595\) \(a_{29}=-0.435004329\) \(a_{30}=-0.480723306\)
\(a_{31}=+1.157136061\) \(a_{32}=-0.176776695\) \(a_{33}=+0.312034258\) \(a_{34}=-0.519663870\) \(a_{35}=+0.674676801\)
\(a_{36}=+0.655474485\) \(a_{37}=-1.382501553\) \(a_{38}=-0.884260004\) \(a_{39}=+1.866284643\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.235412385\) \(a_{42}=-1.621664312\) \(a_{43}=+1.174052147\) \(a_{44}=+0.102630656\) \(a_{45}=+0.586274202\)
\(a_{46}=+0.737677496\) \(a_{47}=+0.491983752\) \(a_{48}=+0.380045143\) \(a_{49}=+1.275943930\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.117204558\) \(a_{52}=+0.613836500\) \(a_{53}=+1.111326034\) \(a_{54}=-0.334248373\) \(a_{55}=+0.091795649\)
\(a_{56}=-0.533378844\) \(a_{57}=+1.901035196\) \(a_{58}=+0.307594511\) \(a_{59}=-1.629201677\) \(a_{60}=+0.339922710\)
\(a_{61}=+1.196726691\) \(a_{62}=-0.818218756\) \(a_{63}=+1.977728017\) \(a_{64}=+0.125000000\) \(a_{65}=+0.549032057\)
\(a_{66}=-0.220641540\) \(a_{67}=+0.372958279\) \(a_{68}=+0.367457846\) \(a_{69}=-1.585903328\) \(a_{70}=-0.477068541\)
\(a_{71}=-1.842624394\) \(a_{72}=-0.463490453\) \(a_{73}=-1.343626376\) \(a_{74}=+0.977576223\) \(a_{75}=+0.304036114\)
\(a_{76}=+0.625266245\) \(a_{77}=+0.309661975\) \(a_{78}=-1.319662527\) \(a_{79}=-0.631336345\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.592361769\) \(a_{82}=-0.166461694\) \(a_{83}=-1.581302553\) \(a_{84}=+1.146689832\) \(a_{85}=+0.328664289\)
\(a_{86}=-0.830180234\) \(a_{87}=-0.661285129\) \(a_{88}=-0.072570833\) \(a_{89}=+1.418901926\) \(a_{90}=-0.414558464\)
\(a_{91}=+1.852095959\) \(a_{92}=-0.521616760\) \(a_{93}=+1.759055759\) \(a_{94}=-0.347885047\) \(a_{95}=+0.559255131\)
\(a_{96}=-0.268732498\) \(a_{97}=-0.650575348\) \(a_{98}=-0.902228606\) \(a_{99}=+0.269087105\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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