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: \( 31.0251790778 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.971471977\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.686934423\) \(a_{7}=+0.037007469\) \(a_{8}=+0.353553391\) \(a_{9}=-0.056242197\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.466463625\) \(a_{12}=-0.485735989\) \(a_{13}=-0.733878212\) \(a_{14}=+0.026168233\) \(a_{15}=+0.434455476\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.160011739\) \(a_{18}=-0.039769239\) \(a_{19}=-1.567548268\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.035951719\) \(a_{22}=-1.036946374\) \(a_{23}=-0.960182168\) \(a_{24}=-0.343467211\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.518930260\) \(a_{27}=+1.026109696\) \(a_{28}=+0.018503735\) \(a_{29}=-0.342897425\) \(a_{30}=+0.307206413\)
\(a_{31}=-0.778542018\) \(a_{32}=+0.176776695\) \(a_{33}=+1.424628317\) \(a_{34}=-0.113145385\) \(a_{35}=-0.016550243\)
\(a_{36}=-0.028121099\) \(a_{37}=-1.416288280\) \(a_{38}=-1.108424010\) \(a_{39}=+0.712942117\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.071943576\) \(a_{42}=-0.025421705\) \(a_{43}=-0.723524381\) \(a_{44}=-0.733231813\) \(a_{45}=+0.025152275\)
\(a_{46}=-0.678951322\) \(a_{47}=-0.320100114\) \(a_{48}=-0.242867994\) \(a_{49}=-0.998630447\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.155446920\) \(a_{52}=-0.366939106\) \(a_{53}=+0.068213295\) \(a_{54}=+0.725569124\) \(a_{55}=+0.655822470\)
\(a_{56}=+0.013084116\) \(a_{57}=+1.522829215\) \(a_{58}=-0.242465095\) \(a_{59}=+1.084307724\) \(a_{60}=+0.217227738\)
\(a_{61}=-1.304006896\) \(a_{62}=-0.550512340\) \(a_{63}=-0.002081381\) \(a_{64}=+0.125000000\) \(a_{65}=+0.328200314\)
\(a_{66}=+1.007364344\) \(a_{67}=-0.677985434\) \(a_{68}=-0.080005869\) \(a_{69}=+0.932790069\) \(a_{70}=-0.011702789\)
\(a_{71}=-0.689675714\) \(a_{72}=-0.019884620\) \(a_{73}=-1.211021612\) \(a_{74}=-1.001467047\) \(a_{75}=-0.194294395\)
\(a_{76}=-0.783774134\) \(a_{77}=-0.054270108\) \(a_{78}=+0.504126206\) \(a_{79}=+0.244640072\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.940594618\) \(a_{82}=+0.757978571\) \(a_{83}=-0.742955245\) \(a_{84}=-0.017975860\) \(a_{85}=+0.071559425\)
\(a_{86}=-0.511608996\) \(a_{87}=+0.333115240\) \(a_{88}=-0.518473187\) \(a_{89}=-1.643647305\) \(a_{90}=+0.017785344\)
\(a_{91}=-0.027158975\) \(a_{92}=-0.480091084\) \(a_{93}=+0.756331754\) \(a_{94}=-0.226344962\) \(a_{95}=+0.701028897\)
\(a_{96}=-0.171733606\) \(a_{97}=-1.940759427\) \(a_{98}=-0.706138361\) \(a_{99}=+0.082477137\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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