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: \( 24.1201522922 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.390128346\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.982969180\) \(a_{7}=+1.223013618\) \(a_{8}=-0.353553391\) \(a_{9}=+0.932456818\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.147513719\) \(a_{12}=-0.695064173\) \(a_{13}=-0.556862475\) \(a_{14}=-0.864801223\) \(a_{15}=+0.621684296\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.958102804\) \(a_{18}=-0.659346539\) \(a_{19}=+0.459270964\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.700145898\) \(a_{22}=-0.811414732\) \(a_{23}=-1.407141041\) \(a_{24}=+0.491484590\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.393761232\) \(a_{27}=+0.093893692\) \(a_{28}=+0.611506809\) \(a_{29}=+1.116834372\) \(a_{30}=-0.439597181\)
\(a_{31}=-1.711524336\) \(a_{32}=-0.176776695\) \(a_{33}=-1.595191348\) \(a_{34}=+0.677480990\) \(a_{35}=-0.546948318\)
\(a_{36}=+0.466228409\) \(a_{37}=-0.598756245\) \(a_{38}=-0.324753613\) \(a_{39}=+0.774110311\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.120504117\) \(a_{42}=+1.202184694\) \(a_{43}=+0.890928028\) \(a_{44}=+0.573756859\) \(a_{45}=-0.417007366\)
\(a_{46}=+0.994998972\) \(a_{47}=+0.220874611\) \(a_{48}=-0.347532086\) \(a_{49}=+0.495762311\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.331885866\) \(a_{52}=-0.278431237\) \(a_{53}=+1.238383548\) \(a_{54}=-0.066392866\) \(a_{55}=-0.513183736\)
\(a_{56}=-0.432400612\) \(a_{57}=-0.638445586\) \(a_{58}=-0.789721158\) \(a_{59}=-1.025050880\) \(a_{60}=+0.310842148\)
\(a_{61}=+1.911993174\) \(a_{62}=+1.210230464\) \(a_{63}=+1.140407387\) \(a_{64}=+0.125000000\) \(a_{65}=+0.249036470\)
\(a_{66}=+1.127970619\) \(a_{67}=-1.310036125\) \(a_{68}=-0.479051402\) \(a_{69}=+1.956106647\) \(a_{70}=+0.386750864\)
\(a_{71}=+1.197192227\) \(a_{72}=-0.329673270\) \(a_{73}=-1.225878725\) \(a_{74}=+0.423384601\) \(a_{75}=-0.278025669\)
\(a_{76}=+0.229635482\) \(a_{77}=+1.403424905\) \(a_{78}=-0.547378650\) \(a_{79}=+0.206259341\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.062981101\) \(a_{82}=+0.085209278\) \(a_{83}=+0.694630274\) \(a_{84}=-0.850072949\) \(a_{85}=+0.428476600\)
\(a_{86}=-0.629981250\) \(a_{87}=-1.552543118\) \(a_{88}=-0.405707366\) \(a_{89}=+1.881952919\) \(a_{90}=+0.294868736\)
\(a_{91}=-0.681050390\) \(a_{92}=-0.703570520\) \(a_{93}=+2.379238495\) \(a_{94}=-0.156181935\) \(a_{95}=-0.205392219\)
\(a_{96}=+0.245742295\) \(a_{97}=+1.108770757\) \(a_{98}=-0.350556892\) \(a_{99}=+1.070006991\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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