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: \( 9.30018385212 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.689879838\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.194925492\) \(a_{7}=-1.423096875\) \(a_{8}=-0.353553391\) \(a_{9}=+1.855693865\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.435256623\) \(a_{12}=+0.844939919\) \(a_{13}=-1.059563716\) \(a_{14}=+1.006281451\) \(a_{15}=-0.755737238\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.890061062\) \(a_{18}=-1.312173716\) \(a_{19}=+0.802236050\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.404862717\) \(a_{22}=+0.307772909\) \(a_{23}=-0.260860650\) \(a_{24}=-0.597462746\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.749224689\) \(a_{27}=+1.446019810\) \(a_{28}=-0.711548438\) \(a_{29}=-1.597965057\) \(a_{30}=+0.534386926\)
\(a_{31}=-1.427355875\) \(a_{32}=-0.176776696\) \(a_{33}=-0.735531392\) \(a_{34}=+0.629368215\) \(a_{35}=+0.636428272\)
\(a_{36}=+0.927846926\) \(a_{37}=+0.865205687\) \(a_{38}=-0.567266538\) \(a_{39}=-1.790535381\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.703540275\) \(a_{42}=+1.700494690\) \(a_{43}=-1.492315795\) \(a_{44}=-0.217628311\) \(a_{45}=-0.829891526\)
\(a_{46}=+0.184456334\) \(a_{47}=+0.618732357\) \(a_{48}=+0.422469959\) \(a_{49}=+1.025204717\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.504096242\) \(a_{52}=-0.529781858\) \(a_{53}=-0.627932019\) \(a_{54}=-1.022490413\) \(a_{55}=+0.194652679\)
\(a_{56}=+0.503140725\) \(a_{57}=+1.355682526\) \(a_{58}=+1.129931928\) \(a_{59}=+1.247906632\) \(a_{60}=-0.377868619\)
\(a_{61}=-0.138903282\) \(a_{62}=+1.009293020\) \(a_{63}=-2.640832141\) \(a_{64}=+0.124999997\) \(a_{65}=+0.473851300\)
\(a_{66}=+0.520099238\) \(a_{67}=-1.075253046\) \(a_{68}=-0.445030530\) \(a_{69}=-0.440823156\) \(a_{70}=-0.450022746\)
\(a_{71}=+0.668831897\) \(a_{72}=-0.656086856\) \(a_{73}=+0.353795695\) \(a_{74}=-0.611792803\) \(a_{75}=+0.337975975\)
\(a_{76}=+0.401118030\) \(a_{77}=+0.619412284\) \(a_{78}=+1.266099781\) \(a_{79}=-0.266295375\) \(a_{80}=-0.111803570\)
\(a_{81}=+0.587905747\) \(a_{82}=-0.497477897\) \(a_{83}=+0.696539285\) \(a_{84}=-1.202431358\) \(a_{85}=+0.398047408\)
\(a_{86}=+1.055226618\) \(a_{87}=-2.700368931\) \(a_{88}=+0.153886454\) \(a_{89}=+1.057665736\) \(a_{90}=+0.586821926\)
\(a_{91}=+1.507861814\) \(a_{92}=-0.130430324\) \(a_{93}=-2.412059916\) \(a_{94}=-0.437509848\) \(a_{95}=-0.358770870\)
\(a_{96}=-0.298731373\) \(a_{97}=+0.620945135\) \(a_{98}=-0.724929206\) \(a_{99}=-0.807703040\) \(a_{100}=+0.100000007\)

Showing 100 of 2000 available coefficients

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