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: \( 14.3176285454 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.160633473\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.820691799\) \(a_{7}=+0.665508123\) \(a_{8}=+0.353553391\) \(a_{9}=+0.347070059\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.573124021\) \(a_{12}=-0.580316737\) \(a_{13}=+0.976349294\) \(a_{14}=+0.470585306\) \(a_{15}=+0.519051069\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.379250791\) \(a_{18}=+0.245415592\) \(a_{19}=+0.136126990\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.772411004\) \(a_{22}=-0.405259882\) \(a_{23}=-1.614962375\) \(a_{24}=-0.410345900\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.690383207\) \(a_{27}=+0.757812345\) \(a_{28}=+0.332754061\) \(a_{29}=-0.137627386\) \(a_{30}=+0.367024530\)
\(a_{31}=-1.808827957\) \(a_{32}=+0.176776695\) \(a_{33}=+0.665186923\) \(a_{34}=+0.975277587\) \(a_{35}=-0.297624280\)
\(a_{36}=+0.173535030\) \(a_{37}=-0.107111548\) \(a_{38}=+0.096256318\) \(a_{39}=-1.133183672\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.887345999\) \(a_{42}=-0.546177059\) \(a_{43}=-0.699649966\) \(a_{44}=-0.286562011\) \(a_{45}=-0.155214449\)
\(a_{46}=-1.141950846\) \(a_{47}=+0.499697815\) \(a_{48}=-0.290158368\) \(a_{49}=-0.557098939\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.600804636\) \(a_{52}=+0.488174647\) \(a_{53}=-1.123531123\) \(a_{54}=+0.535854248\) \(a_{55}=+0.256308854\)
\(a_{56}=+0.235292653\) \(a_{57}=-0.157993541\) \(a_{58}=-0.097317258\) \(a_{59}=-0.847668357\) \(a_{60}=+0.259525534\)
\(a_{61}=-0.779804393\) \(a_{62}=-1.279034514\) \(a_{63}=+0.230977943\) \(a_{64}=+0.125000000\) \(a_{65}=-0.436636678\)
\(a_{66}=+0.470358184\) \(a_{67}=-1.243203858\) \(a_{68}=+0.689625396\) \(a_{69}=+1.874379390\) \(a_{70}=-0.210452147\)
\(a_{71}=+1.056044753\) \(a_{72}=+0.122707796\) \(a_{73}=-1.654937232\) \(a_{74}=-0.075739302\) \(a_{75}=-0.232126695\)
\(a_{76}=+0.068063495\) \(a_{77}=-0.381418691\) \(a_{78}=-0.801281859\) \(a_{79}=+1.824881355\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.226612433\) \(a_{82}=-0.627448373\) \(a_{83}=+1.373406276\) \(a_{84}=-0.386205502\) \(a_{85}=-0.616819705\)
\(a_{86}=-0.494727236\) \(a_{87}=+0.159734950\) \(a_{88}=-0.202629941\) \(a_{89}=+0.551377838\) \(a_{90}=-0.109753189\)
\(a_{91}=+0.649768382\) \(a_{92}=-0.807481187\) \(a_{93}=+2.099386267\) \(a_{94}=+0.353339714\) \(a_{95}=-0.060877841\)
\(a_{96}=-0.205172950\) \(a_{97}=+0.025634965\) \(a_{98}=-0.393928437\) \(a_{99}=-0.198914198\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

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