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: \( 29.1157220269 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.726479496\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.513698578\) \(a_{7}=+0.099131933\) \(a_{8}=-0.353553391\) \(a_{9}=-0.472227542\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.141330545\) \(a_{12}=+0.363239748\) \(a_{13}=+0.278639654\) \(a_{14}=-0.070096862\) \(a_{15}=-0.324891508\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.137880862\) \(a_{18}=+0.333915297\) \(a_{19}=+1.142092965\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.072017317\) \(a_{22}=-0.807042568\) \(a_{23}=+0.850235772\) \(a_{24}=-0.256849289\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.197027989\) \(a_{27}=-1.069543123\) \(a_{28}=+0.049565967\) \(a_{29}=+0.518345432\) \(a_{30}=+0.229732988\)
\(a_{31}=-0.220978291\) \(a_{32}=-0.176776695\) \(a_{33}=+0.829153240\) \(a_{34}=-0.804603274\) \(a_{35}=-0.044333148\)
\(a_{36}=-0.236113771\) \(a_{37}=-1.275310457\) \(a_{38}=-0.807581680\) \(a_{39}=+0.202425996\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.827598811\) \(a_{42}=-0.050923933\) \(a_{43}=+1.603028890\) \(a_{44}=+0.570665273\) \(a_{45}=+0.211186577\)
\(a_{46}=-0.601207480\) \(a_{47}=-1.304594172\) \(a_{48}=+0.181619874\) \(a_{49}=-0.990172860\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.826647115\) \(a_{52}=+0.139319827\) \(a_{53}=+0.947197707\) \(a_{54}=+0.756281195\) \(a_{55}=-0.510418537\)
\(a_{56}=-0.035048431\) \(a_{57}=+0.829707122\) \(a_{58}=-0.366525570\) \(a_{59}=-0.527460481\) \(a_{60}=-0.162445754\)
\(a_{61}=+1.056836243\) \(a_{62}=+0.156255248\) \(a_{63}=-0.046812829\) \(a_{64}=+0.125000000\) \(a_{65}=-0.124611442\)
\(a_{66}=-0.586299878\) \(a_{67}=+0.005345699\) \(a_{68}=+0.568940431\) \(a_{69}=+0.617678855\) \(a_{70}=+0.031348270\)
\(a_{71}=+1.632290006\) \(a_{72}=+0.166957648\) \(a_{73}=-0.126702648\) \(a_{74}=+0.901780672\) \(a_{75}=+0.145295899\)
\(a_{76}=+0.571046482\) \(a_{77}=+0.113142303\) \(a_{78}=-0.143136794\) \(a_{79}=-0.293691635\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.304773607\) \(a_{82}=+0.585200731\) \(a_{83}=+0.464127332\) \(a_{84}=+0.036008658\) \(a_{85}=-0.508875792\)
\(a_{86}=-1.133512598\) \(a_{87}=+0.376567328\) \(a_{88}=-0.403521284\) \(a_{89}=+0.153753041\) \(a_{90}=-0.149331461\)
\(a_{91}=+0.027622088\) \(a_{92}=+0.425117886\) \(a_{93}=-0.160536197\) \(a_{94}=+0.922487386\) \(a_{95}=-0.510759501\)
\(a_{96}=-0.128424645\) \(a_{97}=-0.080232105\) \(a_{98}=+0.700157944\) \(a_{99}=-0.538967718\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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