Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.98429702517 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.242342475\) \(a_{3}=+0.795334646\) \(a_{4}=-0.941270125\) \(a_{5}=+1.280598338\)
\(a_{6}=+0.192743367\) \(a_{7}=+0.377964473\) \(a_{8}=-0.470452207\) \(a_{9}=-0.367442800\) \(a_{10}=+0.310343371\)
\(a_{11}=+0.591140338\) \(a_{12}=-0.748624742\) \(a_{13}=+1.282029264\) \(a_{14}=+0.091596846\) \(a_{15}=+1.018504227\)
\(a_{16}=+0.827259573\) \(a_{17}=+0.668307666\) \(a_{18}=-0.089046998\) \(a_{19}=+0.807534996\) \(a_{20}=-1.205388957\)
\(a_{21}=+0.300608241\) \(a_{22}=+0.143258413\) \(a_{23}=+1.426437341\) \(a_{24}=-0.374166940\) \(a_{25}=+0.639932103\)
\(a_{26}=+0.310690145\) \(a_{27}=-1.087574636\) \(a_{28}=-0.355766667\) \(a_{29}=+0.749971123\) \(a_{30}=+0.246826835\)
\(a_{31}=-1.802807558\) \(a_{32}=+0.670932339\) \(a_{33}=+0.470154392\) \(a_{34}=+0.161959334\) \(a_{35}=+0.484020676\)
\(a_{36}=+0.345862930\) \(a_{37}=-0.681591349\) \(a_{38}=+0.195700030\) \(a_{39}=+1.019642292\) \(a_{40}=-0.602460314\)
\(a_{41}=-0.793667546\) \(a_{42}=+0.072850145\) \(a_{43}=-0.430186370\) \(a_{44}=-0.556422740\) \(a_{45}=-0.470546639\)
\(a_{46}=+0.345686356\) \(a_{47}=+1.076724198\) \(a_{48}=+0.657948200\) \(a_{49}=+0.142857143\) \(a_{50}=+0.155082730\)
\(a_{51}=+0.531528241\) \(a_{52}=-1.206735846\) \(a_{53}=-0.472588476\) \(a_{54}=-0.263565529\) \(a_{55}=+0.757013335\)
\(a_{56}=-0.177814220\) \(a_{57}=+0.642260560\) \(a_{58}=+0.181749858\) \(a_{59}=-0.167523763\) \(a_{60}=-0.958687600\)
\(a_{61}=-0.576178471\) \(a_{62}=-0.436896846\) \(a_{63}=-0.138880324\) \(a_{64}=-0.664664169\) \(a_{65}=+1.641764545\)
\(a_{66}=+0.113938379\) \(a_{67}=+1.275897248\) \(a_{68}=-0.629058040\) \(a_{69}=+1.134495039\) \(a_{70}=+0.117298769\)
\(a_{71}=-0.434897409\) \(a_{72}=+0.172864276\) \(a_{73}=-1.215902153\) \(a_{74}=-0.165178535\) \(a_{75}=+0.508960173\)
\(a_{76}=-0.760108566\) \(a_{77}=+0.223430046\) \(a_{78}=+0.247102637\) \(a_{79}=-1.490356403\) \(a_{80}=+1.059387234\)
\(a_{81}=-0.497542989\) \(a_{82}=-0.192339357\) \(a_{83}=-0.054850075\) \(a_{84}=-0.282953556\) \(a_{85}=+0.855833687\)
\(a_{86}=-0.104252430\) \(a_{87}=+0.596478018\) \(a_{88}=-0.278103277\) \(a_{89}=+1.976118192\) \(a_{90}=-0.114033437\)
\(a_{91}=+0.484561515\) \(a_{92}=-1.342662854\) \(a_{93}=-1.433835312\) \(a_{94}=+0.260936007\) \(a_{95}=+1.034127973\)
\(a_{96}=+0.533615735\) \(a_{97}=-0.636525983\) \(a_{98}=+0.034620354\) \(a_{99}=-0.217210261\) \(a_{100}=-0.602348971\)

Showing 100 of 1228 available coefficients

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