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: \( 15.9393601653 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.420989746\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.004791486\) \(a_{7}=-0.394830749\) \(a_{8}=-0.353553391\) \(a_{9}=+1.019211859\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.131834667\) \(a_{12}=-0.710494873\) \(a_{13}=-0.767647507\) \(a_{14}=+0.279187500\) \(a_{15}=-0.635485934\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.255856777\) \(a_{18}=-0.720691617\) \(a_{19}=-0.026215830\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.561050445\) \(a_{22}=+0.800327968\) \(a_{23}=+1.049709624\) \(a_{24}=+0.502395743\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.542808758\) \(a_{27}=-0.027299854\) \(a_{28}=-0.197415374\) \(a_{29}=-1.226978986\) \(a_{30}=+0.449356413\)
\(a_{31}=+1.353849162\) \(a_{32}=-0.176776695\) \(a_{33}=+1.608325456\) \(a_{34}=-0.888024843\) \(a_{35}=-0.176573679\)
\(a_{36}=+0.509605929\) \(a_{37}=+0.860837401\) \(a_{38}=+0.018537391\) \(a_{39}=+1.090819236\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.284876939\) \(a_{42}=-0.396722574\) \(a_{43}=+1.400908897\) \(a_{44}=-0.565917333\) \(a_{45}=+0.455805400\)
\(a_{46}=-0.742256793\) \(a_{47}=+1.666427998\) \(a_{48}=-0.355247437\) \(a_{49}=-0.844108680\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.784559603\) \(a_{52}=-0.383823754\) \(a_{53}=-1.927616064\) \(a_{54}=+0.019303912\) \(a_{55}=-0.506171851\)
\(a_{56}=+0.139593750\) \(a_{57}=+0.037252425\) \(a_{58}=+0.867605162\) \(a_{59}=+0.416231643\) \(a_{60}=-0.317742967\)
\(a_{61}=-1.010060885\) \(a_{62}=-0.957315923\) \(a_{63}=-0.402416181\) \(a_{64}=+0.125000000\) \(a_{65}=-0.343302402\)
\(a_{66}=-1.137257836\) \(a_{67}=-1.289641466\) \(a_{68}=+0.627928388\) \(a_{69}=-1.491626612\) \(a_{70}=+0.124856446\)
\(a_{71}=+1.504573662\) \(a_{72}=-0.360345808\) \(a_{73}=+0.753453894\) \(a_{74}=-0.608703964\) \(a_{75}=-0.284197949\)
\(a_{76}=-0.013107915\) \(a_{77}=+0.446883129\) \(a_{78}=-0.771325679\) \(a_{79}=+0.014345946\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.980419046\) \(a_{82}=+0.201438415\) \(a_{83}=-0.076734075\) \(a_{84}=+0.280525223\) \(a_{85}=+0.561636225\)
\(a_{86}=-0.990592181\) \(a_{87}=+1.743524559\) \(a_{88}=+0.400163984\) \(a_{89}=-1.526831273\) \(a_{90}=-0.322303089\)
\(a_{91}=+0.303090840\) \(a_{92}=+0.524854812\) \(a_{93}=-1.923805777\) \(a_{94}=-1.178342537\) \(a_{95}=-0.011724076\)
\(a_{96}=+0.251197871\) \(a_{97}=+1.829016213\) \(a_{98}=+0.596874972\) \(a_{99}=-1.153579311\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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