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: \( 30.546564283 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.387731549\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.274167607\) \(a_{7}=+0.392039866\) \(a_{8}=+0.353553391\) \(a_{9}=-0.849664246\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.577606176\) \(a_{12}=+0.193865774\) \(a_{13}=+0.912818868\) \(a_{14}=+0.277214048\) \(a_{15}=-0.173398820\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.286089794\) \(a_{18}=-0.600803350\) \(a_{19}=+1.787955296\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.152006224\) \(a_{22}=+0.408429244\) \(a_{23}=-1.805988041\) \(a_{24}=+0.137083804\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.645460412\) \(a_{27}=-0.717173183\) \(a_{28}=+0.196019933\) \(a_{29}=-0.976692090\) \(a_{30}=-0.122611481\)
\(a_{31}=+1.057521758\) \(a_{32}=+0.176776695\) \(a_{33}=+0.223956137\) \(a_{34}=+0.909402814\) \(a_{35}=-0.175325558\)
\(a_{36}=-0.424832123\) \(a_{37}=-0.188776592\) \(a_{38}=+1.264275314\) \(a_{39}=+0.353928673\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.645723160\) \(a_{42}=+0.107484632\) \(a_{43}=-1.509961721\) \(a_{44}=+0.288803088\) \(a_{45}=+0.379981403\)
\(a_{46}=-1.277026391\) \(a_{47}=+1.130176015\) \(a_{48}=+0.096932887\) \(a_{49}=-0.846304744\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.498657587\) \(a_{52}=+0.456409434\) \(a_{53}=+1.169169419\) \(a_{54}=-0.507118021\) \(a_{55}=-0.258313335\)
\(a_{56}=+0.138607024\) \(a_{57}=+0.693246676\) \(a_{58}=-0.690625600\) \(a_{59}=-1.641972143\) \(a_{60}=-0.086699410\)
\(a_{61}=+1.025056054\) \(a_{62}=+0.747780806\) \(a_{63}=-0.333102257\) \(a_{64}=+0.125000000\) \(a_{65}=-0.408225008\)
\(a_{66}=+0.158360903\) \(a_{67}=+1.816360891\) \(a_{68}=+0.643044897\) \(a_{69}=-0.700238540\) \(a_{70}=-0.123973891\)
\(a_{71}=+0.399723967\) \(a_{72}=-0.300401675\) \(a_{73}=-0.500299280\) \(a_{74}=-0.133485208\) \(a_{75}=+0.077546310\)
\(a_{76}=+0.893977648\) \(a_{77}=+0.226444648\) \(a_{78}=+0.250265365\) \(a_{79}=+1.045245196\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.571593578\) \(a_{82}=-0.456595225\) \(a_{83}=+0.018103676\) \(a_{84}=+0.076003112\) \(a_{85}=-0.575156841\)
\(a_{86}=-1.067704172\) \(a_{87}=-0.378694337\) \(a_{88}=+0.204214622\) \(a_{89}=-0.490282468\) \(a_{90}=+0.268687426\)
\(a_{91}=+0.357861387\) \(a_{92}=-0.902994021\) \(a_{93}=+0.410034549\) \(a_{94}=+0.799155124\) \(a_{95}=-0.799597917\)
\(a_{96}=+0.068541902\) \(a_{97}=+0.936326816\) \(a_{98}=-0.598427823\) \(a_{99}=-0.490771316\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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