Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.43077741663 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.538304219\) \(a_{3}=+1.717537075\) \(a_{4}=+1.366379869\) \(a_{5}=+1.352091494\)
\(a_{6}=-2.642094529\) \(a_{7}=-0.481894310\) \(a_{8}=-0.563603699\) \(a_{9}=+1.949933605\) \(a_{10}=-2.079928049\)
\(a_{11}=-0.033793761\) \(a_{12}=+2.346808084\) \(a_{13}=-0.590930722\) \(a_{14}=+0.741300049\) \(a_{15}=+2.322267270\)
\(a_{16}=-0.499385922\) \(a_{17}=-0.808429645\) \(a_{18}=-2.999591090\) \(a_{19}=-0.327440226\) \(a_{20}=+1.847470599\)
\(a_{21}=-0.827671343\) \(a_{22}=+0.051985085\) \(a_{23}=+0.208514414\) \(a_{24}=-0.968010248\) \(a_{25}=+0.828151408\)
\(a_{26}=+0.909031223\) \(a_{27}=+1.631546185\) \(a_{28}=-0.658450684\) \(a_{29}=+0.323393584\) \(a_{30}=-3.572353539\)
\(a_{31}=-1.017487605\) \(a_{32}=+1.331811169\) \(a_{33}=-0.058042038\) \(a_{34}=+1.243610733\) \(a_{35}=-0.651565197\)
\(a_{36}=+2.664350024\) \(a_{37}=-0.822877568\) \(a_{38}=+0.503702682\) \(a_{39}=-1.014945425\) \(a_{40}=-0.762043767\)
\(a_{41}=-1.571688518\) \(a_{42}=+1.273210319\) \(a_{43}=+1.294625439\) \(a_{44}=-0.046175115\) \(a_{45}=+2.636488641\)
\(a_{46}=-0.320758603\) \(a_{47}=+0.884680275\) \(a_{48}=-0.857713836\) \(a_{49}=-0.767777874\) \(a_{50}=-1.273948805\)
\(a_{51}=-1.388507887\) \(a_{52}=-0.807435843\) \(a_{53}=+1.643718964\) \(a_{54}=-2.509814379\) \(a_{55}=-0.045692257\)
\(a_{56}=+0.271597415\) \(a_{57}=-0.562390729\) \(a_{58}=-0.497477715\) \(a_{59}=-0.479312292\) \(a_{60}=+3.173099249\)
\(a_{61}=+0.789216570\) \(a_{62}=+1.565205475\) \(a_{63}=-0.939661908\) \(a_{64}=-1.549344818\) \(a_{65}=-0.798992403\)
\(a_{66}=+0.089286312\) \(a_{67}=+0.880963088\) \(a_{68}=-1.104621992\) \(a_{69}=+0.358131237\) \(a_{70}=+1.002305491\)
\(a_{71}=+1.211652530\) \(a_{72}=-1.098989792\) \(a_{73}=-1.501842487\) \(a_{74}=+1.265836034\) \(a_{75}=+1.422380748\)
\(a_{76}=-0.447407734\) \(a_{77}=+0.016285021\) \(a_{78}=+1.561294829\) \(a_{79}=+0.361106746\) \(a_{80}=-0.675215457\)
\(a_{81}=+0.852307458\) \(a_{82}=+2.417735078\) \(a_{83}=+0.117365883\) \(a_{84}=-1.130913462\) \(a_{85}=-1.093070846\)
\(a_{86}=-1.991527775\) \(a_{87}=+0.555440471\) \(a_{88}=+0.019046289\) \(a_{89}=-1.158709469\) \(a_{90}=-4.055721599\)
\(a_{91}=+0.284766152\) \(a_{92}=+0.284909898\) \(a_{93}=-1.747572685\) \(a_{94}=-1.360907399\) \(a_{95}=-0.442729145\)
\(a_{96}=+2.287435060\) \(a_{97}=+0.255202157\) \(a_{98}=+1.181075943\) \(a_{99}=-0.065895591\) \(a_{100}=+1.131569413\)

Showing 100 of 546 available coefficients

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