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: \( 21.2155846326 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.740318863\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.523484489\) \(a_{7}=-0.732756677\) \(a_{8}=-0.353553391\) \(a_{9}=-0.451927981\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.643660424\) \(a_{12}=-0.370159432\) \(a_{13}=-1.917572836\) \(a_{14}=+0.518137215\) \(a_{15}=-0.331080661\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.444153554\) \(a_{18}=+0.319561340\) \(a_{19}=-0.379200737\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.542473590\) \(a_{22}=-0.455136651\) \(a_{23}=+0.699597179\) \(a_{24}=+0.261742244\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.355928755\) \(a_{27}=+1.074889672\) \(a_{28}=-0.366378339\) \(a_{29}=-1.337505508\) \(a_{30}=+0.234109380\)
\(a_{31}=-0.181755861\) \(a_{32}=-0.176776695\) \(a_{33}=-0.476513954\) \(a_{34}=+0.314063990\) \(a_{35}=-0.327698748\)
\(a_{36}=-0.225963990\) \(a_{37}=-1.249336043\) \(a_{38}=+0.268135413\) \(a_{39}=+1.419615342\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.042232307\) \(a_{42}=-0.383586754\) \(a_{43}=-0.808228530\) \(a_{44}=+0.321830212\) \(a_{45}=-0.202108337\)
\(a_{46}=-0.494689909\) \(a_{47}=-1.678400914\) \(a_{48}=-0.185079716\) \(a_{49}=-0.463067652\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.328815254\) \(a_{52}=-0.958786418\) \(a_{53}=-0.533632301\) \(a_{54}=-0.760061776\) \(a_{55}=+0.287853693\)
\(a_{56}=+0.259068608\) \(a_{57}=+0.280729459\) \(a_{58}=+0.945759214\) \(a_{59}=+0.249771312\) \(a_{60}=-0.165540330\)
\(a_{61}=-0.674938949\) \(a_{62}=+0.128520802\) \(a_{63}=+0.331153245\) \(a_{64}=+0.125000000\) \(a_{65}=-0.857564642\)
\(a_{66}=+0.336946248\) \(a_{67}=-0.921665974\) \(a_{68}=-0.222076777\) \(a_{69}=-0.517924988\) \(a_{70}=+0.231718007\)
\(a_{71}=+0.956286210\) \(a_{72}=+0.159780670\) \(a_{73}=-1.857066058\) \(a_{74}=+0.883413988\) \(a_{75}=-0.148063773\)
\(a_{76}=-0.189600369\) \(a_{77}=-0.471646474\) \(a_{78}=-1.003819635\) \(a_{79}=-1.496918895\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.343833120\) \(a_{82}=-0.736969532\) \(a_{83}=+1.328657709\) \(a_{84}=+0.271236795\) \(a_{85}=-0.198631508\)
\(a_{86}=+0.571503874\) \(a_{87}=+0.990180557\) \(a_{88}=-0.227568325\) \(a_{89}=-0.380414575\) \(a_{90}=+0.142912176\)
\(a_{91}=+1.405114299\) \(a_{92}=+0.349798589\) \(a_{93}=+0.134557293\) \(a_{94}=+1.186808668\) \(a_{95}=-0.169583725\)
\(a_{96}=+0.130871122\) \(a_{97}=-0.647226696\) \(a_{98}=+0.327438277\) \(a_{99}=-0.290888156\) \(a_{100}=+0.099975586\)

Showing 100 of 206 available coefficients

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