Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.97548743286 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.032517718\) \(a_{3}=-0.444111488\) \(a_{4}=+0.066092839\) \(a_{5}=+0.449944814\)
\(a_{6}=-0.458552980\) \(a_{7}=-1.338581527\) \(a_{8}=-0.964275691\) \(a_{9}=-0.802764986\) \(a_{10}=+0.464575993\)
\(a_{11}=-0.031919103\) \(a_{12}=-0.029352589\) \(a_{13}=-0.277350098\) \(a_{14}=-1.382109144\) \(a_{15}=-0.199825661\)
\(a_{16}=-1.061724575\) \(a_{17}=+1.131512275\) \(a_{18}=-0.828869072\) \(a_{19}=+0.702718241\) \(a_{20}=+0.029738130\)
\(a_{21}=+0.594479434\) \(a_{22}=-0.032957040\) \(a_{23}=-0.222374011\) \(a_{24}=+0.428245912\) \(a_{25}=-0.797549664\)
\(a_{26}=-0.286368890\) \(a_{27}=+0.800628641\) \(a_{28}=-0.088470653\) \(a_{29}=-1.410380653\) \(a_{30}=-0.206323536\)
\(a_{31}=+0.637706992\) \(a_{32}=-0.131973745\) \(a_{33}=+0.014175640\) \(a_{34}=+1.168306472\) \(a_{35}=-0.602287817\)
\(a_{36}=-0.053057017\) \(a_{37}=-0.436971731\) \(a_{38}=+0.725569035\) \(a_{39}=+0.123174365\) \(a_{40}=-0.433870848\)
\(a_{41}=-0.397412631\) \(a_{42}=+0.613810551\) \(a_{43}=+1.231639842\) \(a_{44}=-0.002109630\) \(a_{45}=-0.361199944\)
\(a_{46}=-0.229605092\) \(a_{47}=-1.194757442\) \(a_{48}=+0.471524050\) \(a_{49}=+0.791800519\) \(a_{50}=-0.823484092\)
\(a_{51}=-0.502517655\) \(a_{52}=-0.018330855\) \(a_{53}=-1.637151221\) \(a_{54}=+0.826663257\) \(a_{55}=-0.014361835\)
\(a_{56}=+1.290761628\) \(a_{57}=-0.312085244\) \(a_{58}=-1.456243014\) \(a_{59}=+0.318251515\) \(a_{60}=-0.013207045\)
\(a_{61}=+1.466899303\) \(a_{62}=+0.658443768\) \(a_{63}=+1.074566381\) \(a_{64}=+0.925459346\) \(a_{65}=-0.124792238\)
\(a_{66}=+0.014636600\) \(a_{67}=-1.190605735\) \(a_{68}=+0.074784858\) \(a_{69}=+0.098758853\) \(a_{70}=-0.621872843\)
\(a_{71}=-1.331863088\) \(a_{72}=+0.774086762\) \(a_{73}=-1.313883921\) \(a_{74}=-0.451181054\) \(a_{75}=+0.354200968\)
\(a_{76}=+0.046444644\) \(a_{77}=+0.042726322\) \(a_{78}=+0.127179714\) \(a_{79}=-0.994718798\) \(a_{80}=-0.477717470\)
\(a_{81}=+0.447196612\) \(a_{82}=-0.410335577\) \(a_{83}=+1.837324384\) \(a_{84}=+0.039290834\) \(a_{85}=+0.509118088\)
\(a_{86}=+1.271689966\) \(a_{87}=+0.626366260\) \(a_{88}=+0.030778817\) \(a_{89}=-1.093242752\) \(a_{90}=-0.372945480\)
\(a_{91}=+0.371255803\) \(a_{92}=-0.014697326\) \(a_{93}=-0.283213001\) \(a_{94}=-1.233608226\) \(a_{95}=+0.316184428\)
\(a_{96}=+0.058611056\) \(a_{97}=+0.708727054\) \(a_{98}=+0.817548051\) \(a_{99}=+0.025623539\) \(a_{100}=-0.052712321\)

Showing 100 of 1000 available coefficients

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