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: \( 12.5585779181 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.310754002\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.926843044\) \(a_{7}=-1.140461797\) \(a_{8}=-0.353553391\) \(a_{9}=+0.718076055\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.134668306\) \(a_{12}=+0.655377001\) \(a_{13}=-0.139079786\) \(a_{14}=+0.806428270\) \(a_{15}=-0.586187010\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.447269868\) \(a_{18}=-0.507756448\) \(a_{19}=-1.410888254\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.494864865\) \(a_{22}=-0.802331653\) \(a_{23}=+1.261763310\) \(a_{24}=-0.463421522\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.098344260\) \(a_{27}=-0.369532939\) \(a_{28}=-0.570230899\) \(a_{29}=+0.735851137\) \(a_{30}=+0.414496810\)
\(a_{31}=+1.148191441\) \(a_{32}=-0.176776695\) \(a_{33}=+1.487271023\) \(a_{34}=-1.023374338\) \(a_{35}=+0.510030021\)
\(a_{36}=+0.359038028\) \(a_{37}=+0.999639221\) \(a_{38}=+0.997648652\) \(a_{39}=-0.182299386\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.508845785\) \(a_{42}=+1.057029083\) \(a_{43}=-0.212214729\) \(a_{44}=+0.567334153\) \(a_{45}=-0.321133374\)
\(a_{46}=-0.892201393\) \(a_{47}=-1.060242977\) \(a_{48}=+0.327688501\) \(a_{49}=+0.300653111\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.897014772\) \(a_{52}=-0.069539893\) \(a_{53}=+1.625443194\) \(a_{54}=+0.261299247\) \(a_{55}=-0.507439093\)
\(a_{56}=+0.403214135\) \(a_{57}=-1.849327426\) \(a_{58}=-0.520325329\) \(a_{59}=+0.461218786\) \(a_{60}=-0.293093505\)
\(a_{61}=+1.287216886\) \(a_{62}=-0.811893954\) \(a_{63}=-0.818938308\) \(a_{64}=+0.125000000\) \(a_{65}=+0.062198371\)
\(a_{66}=-1.051659426\) \(a_{67}=+0.525970594\) \(a_{68}=+0.723634934\) \(a_{69}=+1.653861309\) \(a_{70}=-0.360645686\)
\(a_{71}=-0.360402638\) \(a_{72}=-0.253878224\) \(a_{73}=+1.603784668\) \(a_{74}=-0.706851672\) \(a_{75}=+0.262150800\)
\(a_{76}=-0.705444127\) \(a_{77}=-1.294045854\) \(a_{78}=+0.128905132\) \(a_{79}=+1.810092326\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.202442840\) \(a_{82}=-0.359808305\) \(a_{83}=+0.864124282\) \(a_{84}=-0.747432433\) \(a_{85}=-0.647238761\)
\(a_{86}=+0.150058474\) \(a_{87}=+0.964519806\) \(a_{88}=-0.401165827\) \(a_{89}=-1.644987029\) \(a_{90}=+0.227075587\)
\(a_{91}=+0.158615177\) \(a_{92}=+0.630881655\) \(a_{93}=+1.504996528\) \(a_{94}=+0.749704998\) \(a_{95}=+0.630968409\)
\(a_{96}=-0.231710761\) \(a_{97}=-1.439380225\) \(a_{98}=-0.212593853\) \(a_{99}=+0.814778661\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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