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: \( 25.5713135417 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.794687081\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.561928624\) \(a_{7}=+1.798162437\) \(a_{8}=-0.353553391\) \(a_{9}=-0.368472443\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.750067742\) \(a_{12}=+0.397343541\) \(a_{13}=+0.408821741\) \(a_{14}=-1.271492853\) \(a_{15}=-0.355394867\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.595469288\) \(a_{18}=+0.260549363\) \(a_{19}=-0.187359204\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.428976459\) \(a_{22}=+1.237484768\) \(a_{23}=+0.330802981\) \(a_{24}=-0.280964312\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.289080626\) \(a_{27}=-1.087507371\) \(a_{28}=+0.899081219\) \(a_{29}=-0.427080532\) \(a_{30}=+0.251302120\)
\(a_{31}=-0.088514813\) \(a_{32}=-0.176776695\) \(a_{33}=-1.390756226\) \(a_{34}=+1.128167153\) \(a_{35}=-0.804162689\)
\(a_{36}=-0.184236221\) \(a_{37}=+1.140031364\) \(a_{38}=+0.132482964\) \(a_{39}=+0.324885356\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.477125033\) \(a_{42}=-1.010438944\) \(a_{43}=+1.267645163\) \(a_{44}=-0.875033871\) \(a_{45}=+0.164785886\)
\(a_{46}=-0.233913031\) \(a_{47}=+1.005658074\) \(a_{48}=+0.198671770\) \(a_{49}=+2.233388151\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.267898832\) \(a_{52}=+0.204410871\) \(a_{53}=+0.558482576\) \(a_{54}=+0.768983837\) \(a_{55}=+0.782654087\)
\(a_{56}=-0.635746427\) \(a_{57}=-0.148891939\) \(a_{58}=+0.301991540\) \(a_{59}=+0.729012039\) \(a_{60}=-0.177697433\)
\(a_{61}=+1.361132856\) \(a_{62}=+0.062589424\) \(a_{63}=-0.662573306\) \(a_{64}=+0.125000000\) \(a_{65}=-0.182830641\)
\(a_{66}=+0.983413158\) \(a_{67}=-1.122628176\) \(a_{68}=-0.797734644\) \(a_{69}=+0.262884856\) \(a_{70}=+0.568628890\)
\(a_{71}=+1.042750881\) \(a_{72}=+0.130274681\) \(a_{73}=-0.461254738\) \(a_{74}=-0.806123908\) \(a_{75}=+0.158937416\)
\(a_{76}=-0.093679602\) \(a_{77}=-3.146906076\) \(a_{78}=-0.229728639\) \(a_{79}=-1.119180268\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.495755616\) \(a_{82}=+0.337378346\) \(a_{83}=-0.102349481\) \(a_{84}=+0.714488230\) \(a_{85}=+0.713515557\)
\(a_{86}=-0.896360491\) \(a_{87}=-0.339395381\) \(a_{88}=+0.618742384\) \(a_{89}=+0.056302482\) \(a_{90}=-0.116521217\)
\(a_{91}=+0.735127899\) \(a_{92}=+0.165401491\) \(a_{93}=-0.070341578\) \(a_{94}=-0.711107644\) \(a_{95}=+0.083789583\)
\(a_{96}=-0.140482156\) \(a_{97}=+1.294550014\) \(a_{98}=-1.579243907\) \(a_{99}=+0.644851736\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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