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: \( 13.7422588437 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.550334060\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.389144946\) \(a_{7}=-0.880993645\) \(a_{8}=+0.353553391\) \(a_{9}=-0.697132423\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.664911728\) \(a_{12}=+0.275167030\) \(a_{13}=-0.327949010\) \(a_{14}=-0.622956581\) \(a_{15}=-0.246116874\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.597636852\) \(a_{18}=-0.492947063\) \(a_{19}=+1.664547310\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.484840809\) \(a_{22}=+1.177270373\) \(a_{23}=+0.459804834\) \(a_{24}=+0.194572473\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.231894969\) \(a_{27}=-0.933989776\) \(a_{28}=-0.440496823\) \(a_{29}=+0.461960032\) \(a_{30}=-0.174030910\)
\(a_{31}=-1.266909459\) \(a_{32}=+0.176776695\) \(a_{33}=+0.916257631\) \(a_{34}=+1.129699852\) \(a_{35}=+0.393992336\)
\(a_{36}=-0.348566211\) \(a_{37}=+0.790853319\) \(a_{38}=+1.177012690\) \(a_{39}=-0.180481510\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.756522785\) \(a_{42}=-0.342834224\) \(a_{43}=+0.094012795\) \(a_{44}=+0.832455864\) \(a_{45}=+0.311767097\)
\(a_{46}=+0.325131116\) \(a_{47}=+1.745087957\) \(a_{48}=+0.137583515\) \(a_{49}=-0.223850197\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.879233975\) \(a_{52}=-0.163974505\) \(a_{53}=+0.877609165\) \(a_{54}=-0.660430504\) \(a_{55}=-0.744571160\)
\(a_{56}=-0.311478290\) \(a_{57}=+0.916057079\) \(a_{58}=+0.326655071\) \(a_{59}=+0.696835405\) \(a_{60}=-0.123058437\)
\(a_{61}=-0.543097797\) \(a_{62}=-0.895840269\) \(a_{63}=+0.614169234\) \(a_{64}=+0.125000000\) \(a_{65}=+0.146663256\)
\(a_{66}=+0.647891984\) \(a_{67}=-0.555203600\) \(a_{68}=+0.798818426\) \(a_{69}=+0.253046261\) \(a_{70}=+0.278594652\)
\(a_{71}=-0.475185029\) \(a_{72}=-0.246473532\) \(a_{73}=+0.015515500\) \(a_{74}=+0.559217745\) \(a_{75}=+0.110066812\)
\(a_{76}=+0.832273655\) \(a_{77}=-1.466776653\) \(a_{78}=-0.127619700\) \(a_{79}=-1.155410027\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.183126037\) \(a_{82}=+0.534942391\) \(a_{83}=+0.121813849\) \(a_{84}=-0.242420405\) \(a_{85}=-0.714484921\)
\(a_{86}=+0.066477085\) \(a_{87}=+0.254232335\) \(a_{88}=+0.588635187\) \(a_{89}=+1.250836963\) \(a_{90}=+0.220452629\)
\(a_{91}=+0.288920996\) \(a_{92}=+0.229902417\) \(a_{93}=-0.697223435\) \(a_{94}=+1.233963528\) \(a_{95}=-0.744408187\)
\(a_{96}=+0.097286236\) \(a_{97}=-0.218507329\) \(a_{98}=-0.158285992\) \(a_{99}=-1.160663982\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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