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: \( 14.20455634 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.967336646\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.684010302\) \(a_{7}=+1.901307143\) \(a_{8}=+0.353553391\) \(a_{9}=-0.064259813\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.085480676\) \(a_{12}=+0.483668323\) \(a_{13}=-0.610875358\) \(a_{14}=+1.344427174\) \(a_{15}=+0.432606100\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.955875025\) \(a_{18}=-0.045438549\) \(a_{19}=+1.132614345\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.839204076\) \(a_{22}=+0.767550747\) \(a_{23}=-0.073825246\) \(a_{24}=+0.342005151\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.431954108\) \(a_{27}=-1.029497518\) \(a_{28}=+0.950653572\) \(a_{29}=-0.294241136\) \(a_{30}=+0.305898707\)
\(a_{31}=-1.269636896\) \(a_{32}=+0.176776695\) \(a_{33}=+1.050025237\) \(a_{34}=-0.675905712\) \(a_{35}=+0.850290404\)
\(a_{36}=-0.032129906\) \(a_{37}=-1.070331678\) \(a_{38}=+0.800879284\) \(a_{39}=-0.590922120\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.677552721\) \(a_{42}=+1.300513674\) \(a_{43}=+1.007525484\) \(a_{44}=+0.542740338\) \(a_{45}=-0.028737862\)
\(a_{46}=-0.052202332\) \(a_{47}=-0.880984706\) \(a_{48}=+0.241834162\) \(a_{49}=+2.614968853\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.924652941\) \(a_{52}=-0.305437679\) \(a_{53}=+0.871404123\) \(a_{54}=-0.727964676\) \(a_{55}=+0.485441716\)
\(a_{56}=+0.672213587\) \(a_{57}=+1.095619362\) \(a_{58}=-0.208059902\) \(a_{59}=+0.215766011\) \(a_{60}=+0.216303050\)
\(a_{61}=+0.623727770\) \(a_{62}=-0.897768859\) \(a_{63}=-0.122177641\) \(a_{64}=+0.125000000\) \(a_{65}=-0.273191765\)
\(a_{66}=+0.742479965\) \(a_{67}=+1.063784821\) \(a_{68}=-0.477937512\) \(a_{69}=-0.071413866\) \(a_{70}=+0.601246110\)
\(a_{71}=-1.088585106\) \(a_{72}=-0.022719275\) \(a_{73}=-1.283538094\) \(a_{74}=-0.756838788\) \(a_{75}=+0.193467329\)
\(a_{76}=+0.566307173\) \(a_{77}=+2.063832163\) \(a_{78}=-0.417845038\) \(a_{79}=-0.062929466\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.931610865\) \(a_{82}=+1.186208905\) \(a_{83}=+0.118835028\) \(a_{84}=+0.919602038\) \(a_{85}=-0.427480307\)
\(a_{86}=+0.712428102\) \(a_{87}=-0.284630233\) \(a_{88}=+0.383775373\) \(a_{89}=-1.440664996\) \(a_{90}=-0.020320737\)
\(a_{91}=-1.161461683\) \(a_{92}=-0.036912623\) \(a_{93}=-1.228166287\) \(a_{94}=-0.622950260\) \(a_{95}=+0.506520534\)
\(a_{96}=+0.171002576\) \(a_{97}=+0.364997544\) \(a_{98}=+1.849062208\) \(a_{99}=-0.069752761\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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