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: \( 10.7422023202 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.611704537\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.432540426\) \(a_{7}=-0.546838000\) \(a_{8}=+0.353553391\) \(a_{9}=-0.625817559\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.834139533\) \(a_{12}=+0.305852269\) \(a_{13}=+0.367866626\) \(a_{14}=-0.386672858\) \(a_{15}=-0.273562585\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.189851313\) \(a_{18}=-0.442519840\) \(a_{19}=-1.004726038\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.334503286\) \(a_{22}=-1.296932502\) \(a_{23}=-0.660513622\) \(a_{24}=+0.216270213\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.260120986\) \(a_{27}=-0.994519978\) \(a_{28}=-0.273419000\) \(a_{29}=-1.207363655\) \(a_{30}=-0.193437959\)
\(a_{31}=-0.971870492\) \(a_{32}=+0.176776695\) \(a_{33}=-1.121951474\) \(a_{34}=+0.841351932\) \(a_{35}=+0.244553388\)
\(a_{36}=-0.312908780\) \(a_{37}=+0.964072852\) \(a_{38}=-0.710448595\) \(a_{39}=+0.225025684\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.477314362\) \(a_{42}=-0.236529542\) \(a_{43}=-0.628051641\) \(a_{44}=-0.917069767\) \(a_{45}=+0.279874121\)
\(a_{46}=-0.467053661\) \(a_{47}=+0.185239146\) \(a_{48}=+0.152926134\) \(a_{49}=-0.700968201\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.727837447\) \(a_{52}=+0.183933313\) \(a_{53}=+1.336182696\) \(a_{54}=-0.703231820\) \(a_{55}=+0.820252135\)
\(a_{56}=-0.193336429\) \(a_{57}=-0.614595476\) \(a_{58}=-0.853735028\) \(a_{59}=+1.076154205\) \(a_{60}=-0.136781293\)
\(a_{61}=-0.889949478\) \(a_{62}=-0.687216215\) \(a_{63}=+0.342220823\) \(a_{64}=+0.125000000\) \(a_{65}=-0.164514957\)
\(a_{66}=-0.793339496\) \(a_{67}=+1.296152405\) \(a_{68}=+0.594925657\) \(a_{69}=-0.404039180\) \(a_{70}=+0.172925359\)
\(a_{71}=-1.169566229\) \(a_{72}=-0.221259920\) \(a_{73}=+0.850448038\) \(a_{74}=+0.681702451\) \(a_{75}=+0.122340907\)
\(a_{76}=-0.502363019\) \(a_{77}=+1.002977195\) \(a_{78}=+0.159117187\) \(a_{79}=-1.151003788\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.017465176\) \(a_{82}=+0.337512222\) \(a_{83}=+1.240109551\) \(a_{84}=-0.167251643\) \(a_{85}=-0.532117684\)
\(a_{86}=-0.444099574\) \(a_{87}=-0.738549829\) \(a_{88}=-0.648466251\) \(a_{89}=+0.457378900\) \(a_{90}=+0.197900889\)
\(a_{91}=-0.201163450\) \(a_{92}=-0.330256811\) \(a_{93}=-0.594497585\) \(a_{94}=+0.130983856\) \(a_{95}=+0.449327144\)
\(a_{96}=+0.108135107\) \(a_{97}=-0.252835455\) \(a_{98}=-0.495659369\) \(a_{99}=+1.147836726\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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