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: \( 20.9322050353 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.840643956\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.301531823\) \(a_{7}=+0.344453269\) \(a_{8}=-0.353553391\) \(a_{9}=+2.387970172\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.238751879\) \(a_{12}=+0.920321978\) \(a_{13}=+1.801287181\) \(a_{14}=-0.243565242\) \(a_{15}=-0.823161001\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.478918028\) \(a_{18}=-1.688549902\) \(a_{19}=+0.753451360\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.634015828\) \(a_{22}=-0.875929854\) \(a_{23}=-0.817737090\) \(a_{24}=-0.650765911\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.273702381\) \(a_{27}=+2.554758907\) \(a_{28}=+0.172226635\) \(a_{29}=-1.115834509\) \(a_{30}=+0.582062726\)
\(a_{31}=+0.827433949\) \(a_{32}=-0.176776695\) \(a_{33}=+2.280101158\) \(a_{34}=+0.338646185\) \(a_{35}=-0.154044185\)
\(a_{36}=+1.193985086\) \(a_{37}=+1.395706291\) \(a_{38}=-0.532770566\) \(a_{39}=+3.315528363\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.816935094\) \(a_{42}=-0.448316891\) \(a_{43}=-0.565934166\) \(a_{44}=+0.619375939\) \(a_{45}=-1.067932726\)
\(a_{46}=+0.578227442\) \(a_{47}=-1.126530866\) \(a_{48}=+0.460160989\) \(a_{49}=-0.881351945\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.881517574\) \(a_{52}=+0.900643591\) \(a_{53}=+0.651189767\) \(a_{54}=-1.806487348\) \(a_{55}=-0.553986682\)
\(a_{56}=-0.121782621\) \(a_{57}=+1.386835691\) \(a_{58}=+0.789014148\) \(a_{59}=-0.615505008\) \(a_{60}=-0.411580501\)
\(a_{61}=+1.324923419\) \(a_{62}=-0.585084157\) \(a_{63}=+0.822544132\) \(a_{64}=+0.125000000\) \(a_{65}=-0.805560117\)
\(a_{66}=-1.612274991\) \(a_{67}=+0.526721245\) \(a_{68}=-0.239459014\) \(a_{69}=-1.505162832\) \(a_{70}=+0.108925688\)
\(a_{71}=+0.352190719\) \(a_{72}=-0.844274951\) \(a_{73}=+0.571037657\) \(a_{74}=-0.986913383\) \(a_{75}=+0.368128791\)
\(a_{76}=+0.376725680\) \(a_{77}=+0.426692134\) \(a_{78}=-2.344432589\) \(a_{79}=-1.341448686\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.314431369\) \(a_{82}=+0.577660345\) \(a_{83}=+0.754385453\) \(a_{84}=+0.317007914\) \(a_{85}=+0.214178653\)
\(a_{86}=+0.400175887\) \(a_{87}=-2.053854044\) \(a_{88}=-0.437964927\) \(a_{89}=+0.041267466\) \(a_{90}=+0.755142473\)
\(a_{91}=+0.620459258\) \(a_{92}=-0.408868545\) \(a_{93}=+1.523011298\) \(a_{94}=+0.796577614\) \(a_{95}=-0.336953692\)
\(a_{96}=-0.325382956\) \(a_{97}=+0.665369101\) \(a_{98}=+0.623209937\) \(a_{99}=+2.958102537\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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