Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.23019956539 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.639360506\) \(a_{3}=-1.021074831\) \(a_{4}=-0.591218143\) \(a_{5}=+0.274167326\)
\(a_{6}=-0.652834921\) \(a_{7}=-0.609897846\) \(a_{8}=-1.017362037\) \(a_{9}=+0.042593811\) \(a_{10}=+0.175291761\)
\(a_{11}=+0.501355431\) \(a_{12}=+0.603677966\) \(a_{13}=+0.277350098\) \(a_{14}=-0.389944596\) \(a_{15}=-0.279945356\)
\(a_{16}=-0.059242964\) \(a_{17}=-1.814973557\) \(a_{18}=+0.027232801\) \(a_{19}=+0.964640129\) \(a_{20}=-0.162092698\)
\(a_{21}=+0.622751341\) \(a_{22}=+0.320546862\) \(a_{23}=-0.669323795\) \(a_{24}=+1.038802771\) \(a_{25}=-0.924832277\)
\(a_{26}=+0.177326699\) \(a_{27}=+0.977583362\) \(a_{28}=+0.360582672\) \(a_{29}=-0.479687443\) \(a_{30}=-0.178986005\)
\(a_{31}=-1.103230895\) \(a_{32}=+0.979484426\) \(a_{33}=-0.511921410\) \(a_{34}=-1.160422415\) \(a_{35}=-0.167214064\)
\(a_{36}=-0.025182225\) \(a_{37}=+0.431120113\) \(a_{38}=+0.616752782\) \(a_{39}=-0.283195205\) \(a_{40}=-0.278927430\)
\(a_{41}=+1.381502025\) \(a_{42}=+0.398162612\) \(a_{43}=-0.376310706\) \(a_{44}=-0.296410427\) \(a_{45}=+0.011677832\)
\(a_{46}=-0.427939201\) \(a_{47}=+0.903496305\) \(a_{48}=+0.060491501\) \(a_{49}=-0.628024617\) \(a_{50}=-0.591301233\)
\(a_{51}=+1.853223819\) \(a_{52}=-0.163974411\) \(a_{53}=-1.511774210\) \(a_{54}=+0.625028197\) \(a_{55}=+0.137455279\)
\(a_{56}=+0.620486908\) \(a_{57}=-0.984969760\) \(a_{58}=-0.306693195\) \(a_{59}=-0.992043488\) \(a_{60}=+0.165508764\)
\(a_{61}=-0.703062276\) \(a_{62}=-0.705362265\) \(a_{63}=-0.025977848\) \(a_{64}=+0.685486650\) \(a_{65}=+0.076040280\)
\(a_{66}=-0.327302403\) \(a_{67}=+1.687808402\) \(a_{68}=+1.073045406\) \(a_{69}=+0.683429604\) \(a_{70}=-0.106910065\)
\(a_{71}=+1.180784913\) \(a_{72}=-0.043333325\) \(a_{73}=-1.781260341\) \(a_{74}=+0.275641169\) \(a_{75}=+0.944322957\)
\(a_{76}=-0.570312730\) \(a_{77}=-0.305775593\) \(a_{78}=-0.181063839\) \(a_{79}=-0.316997519\) \(a_{80}=-0.016242483\)
\(a_{81}=-1.040779573\) \(a_{82}=+0.883277844\) \(a_{83}=-1.142074378\) \(a_{84}=-0.368181919\) \(a_{85}=-0.497606467\)
\(a_{86}=-0.240598232\) \(a_{87}=+0.489796818\) \(a_{88}=-0.510059931\) \(a_{89}=+0.830063917\) \(a_{90}=+0.007466211\)
\(a_{91}=-0.169155359\) \(a_{92}=+0.395716435\) \(a_{93}=+1.126481304\) \(a_{94}=+0.577659860\) \(a_{95}=+0.264472794\)
\(a_{96}=-1.000126890\) \(a_{97}=-1.058477118\) \(a_{98}=-0.401534109\) \(a_{99}=+0.021354619\) \(a_{100}=+0.546777607\)

Showing 100 of 1000 available coefficients

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