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: \( 3.8128927243 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.525411704\) \(a_{3}=+0.735952911\) \(a_{4}=+1.326880868\) \(a_{5}=-0.004240250\)
\(a_{6}=+1.122631185\) \(a_{7}=-1.351156636\) \(a_{8}=+0.498627902\) \(a_{9}=-0.458373313\) \(a_{10}=-0.006468127\)
\(a_{11}=+1.556965540\) \(a_{12}=+0.976521837\) \(a_{13}=+0.277350098\) \(a_{14}=-2.061070147\) \(a_{15}=-0.003120624\)
\(a_{16}=-0.566268030\) \(a_{17}=+0.549854048\) \(a_{18}=-0.699208016\) \(a_{19}=-0.120960530\) \(a_{20}=-0.005626306\)
\(a_{21}=-0.994387660\) \(a_{22}=+2.375013457\) \(a_{23}=+1.578869926\) \(a_{24}=+0.366966656\) \(a_{25}=-0.999982025\)
\(a_{26}=+0.423073087\) \(a_{27}=-1.073294074\) \(a_{28}=-1.792823896\) \(a_{29}=+0.603070750\) \(a_{30}=-0.004760213\)
\(a_{31}=+0.200502856\) \(a_{32}=-1.362419853\) \(a_{33}=+1.145853241\) \(a_{34}=+0.838753995\) \(a_{35}=+0.005729242\)
\(a_{36}=-0.608206779\) \(a_{37}=+0.844849073\) \(a_{38}=-0.184514609\) \(a_{39}=+0.204116612\) \(a_{40}=-0.002114307\)
\(a_{41}=-0.629242270\) \(a_{42}=-1.516850575\) \(a_{43}=-1.110257335\) \(a_{44}=+2.065907786\) \(a_{45}=+0.001943616\)
\(a_{46}=+2.408426660\) \(a_{47}=+0.149439491\) \(a_{48}=-0.416746600\) \(a_{49}=+0.825624253\) \(a_{50}=-1.525384283\)
\(a_{51}=+0.404666681\) \(a_{52}=+0.368010544\) \(a_{53}=-0.562391725\) \(a_{54}=-1.637215372\) \(a_{55}=-0.006601953\)
\(a_{56}=-0.673724397\) \(a_{57}=-0.089021212\) \(a_{58}=+0.919931262\) \(a_{59}=-0.821710238\) \(a_{60}=-0.004140785\)
\(a_{61}=+0.151095619\) \(a_{62}=+0.305849335\) \(a_{63}=+0.619334140\) \(a_{64}=-1.511983051\) \(a_{65}=-0.001176032\)
\(a_{66}=+1.747898073\) \(a_{67}=-0.847037057\) \(a_{68}=+0.729590808\) \(a_{69}=+1.161973913\) \(a_{70}=+0.008739455\)
\(a_{71}=-0.146065327\) \(a_{72}=-0.228557723\) \(a_{73}=+1.783993527\) \(a_{74}=+1.288742638\) \(a_{75}=-0.735939675\)
\(a_{76}=-0.160500167\) \(a_{77}=-2.103704303\) \(a_{78}=+0.311361868\) \(a_{79}=-0.910417367\) \(a_{80}=+0.002401104\)
\(a_{81}=-0.331520512\) \(a_{82}=-0.959853512\) \(a_{83}=+0.724748199\) \(a_{84}=-1.319433968\) \(a_{85}=-0.002331522\)
\(a_{86}=-1.693599579\) \(a_{87}=+0.443831708\) \(a_{88}=+0.776346486\) \(a_{89}=+0.947666403\) \(a_{90}=+0.002964811\)
\(a_{91}=-0.374743516\) \(a_{92}=+2.094972305\) \(a_{93}=+0.147560624\) \(a_{94}=+0.227956718\) \(a_{95}=+0.000512907\)
\(a_{96}=-1.002676815\) \(a_{97}=+0.638979817\) \(a_{98}=+1.259416869\) \(a_{99}=-0.713671481\) \(a_{100}=-1.326856894\)

Showing 100 of 1000 available coefficients

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