Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 34.0278842001 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.171191559\) \(a_{3}=-0.947721476\) \(a_{4}=+0.371689668\) \(a_{5}=-1.034349685\)
\(a_{6}=-1.109963393\) \(a_{7}=+1.141576104\) \(a_{8}=-0.735871757\) \(a_{9}=-0.101824004\) \(a_{10}=-1.211421621\)
\(a_{11}=-0.382965738\) \(a_{12}=-0.352258281\) \(a_{13}=+1.471190362\) \(a_{14}=+1.337004296\) \(a_{15}=+0.980275410\)
\(a_{16}=-1.233536459\) \(a_{17}=+1.326886645\) \(a_{18}=-0.119255449\) \(a_{19}=+1.019199263\) \(a_{20}=-0.384457091\)
\(a_{21}=-1.081896190\) \(a_{22}=-0.448526239\) \(a_{23}=-0.355491125\) \(a_{24}=+0.697401468\) \(a_{25}=+0.069879271\)
\(a_{26}=+1.723045733\) \(a_{27}=+1.044222271\) \(a_{28}=+0.424312043\) \(a_{29}=+0.734231831\) \(a_{30}=+1.148090286\)
\(a_{31}=+0.504529585\) \(a_{32}=-0.708835731\) \(a_{33}=+0.362944854\) \(a_{34}=+1.554038435\) \(a_{35}=-1.180788883\)
\(a_{36}=-0.037846930\) \(a_{37}=+0.031973460\) \(a_{38}=+1.193677574\) \(a_{39}=-1.394278701\) \(a_{40}=+0.761148720\)
\(a_{41}=+0.159024123\) \(a_{42}=-1.267107685\) \(a_{43}=+1.285061040\) \(a_{44}=-0.142344408\) \(a_{45}=+0.105321627\)
\(a_{46}=-0.416348205\) \(a_{47}=-0.863641515\) \(a_{48}=+1.169048993\) \(a_{49}=+0.303196000\) \(a_{50}=+0.081842013\)
\(a_{51}=-1.257518967\) \(a_{52}=+0.546826257\) \(a_{53}=-0.625054905\) \(a_{54}=+1.222984310\) \(a_{55}=+0.396120490\)
\(a_{56}=-0.840053613\) \(a_{57}=-0.965917030\) \(a_{58}=+0.859926123\) \(a_{59}=+0.123964104\) \(a_{60}=+0.364358241\)
\(a_{61}=-0.773008142\) \(a_{62}=+0.590900794\) \(a_{63}=-0.116239850\) \(a_{64}=+0.403354029\) \(a_{65}=-1.521725254\)
\(a_{66}=+0.425077882\) \(a_{67}=+0.752276251\) \(a_{68}=+0.493190056\) \(a_{69}=+0.336906574\) \(a_{70}=-1.382929973\)
\(a_{71}=-0.488113323\) \(a_{72}=+0.074929409\) \(a_{73}=+1.109230738\) \(a_{74}=+0.037447047\) \(a_{75}=-0.066226086\)
\(a_{76}=+0.378825836\) \(a_{77}=-0.437184535\) \(a_{78}=-1.632967446\) \(a_{79}=+0.850856163\) \(a_{80}=+1.275908048\)
\(a_{81}=-0.887807868\) \(a_{82}=+0.186247710\) \(a_{83}=+0.690539685\) \(a_{84}=-0.402129636\) \(a_{85}=-1.372464781\)
\(a_{86}=+1.505052642\) \(a_{87}=-0.695847275\) \(a_{88}=+0.281813670\) \(a_{89}=-0.718385118\) \(a_{90}=+0.123351800\)
\(a_{91}=+1.679475761\) \(a_{92}=-0.132132378\) \(a_{93}=-0.478153523\) \(a_{94}=-1.011489652\) \(a_{95}=-1.054208437\)
\(a_{96}=+0.671778845\) \(a_{97}=+1.229845489\) \(a_{98}=+0.355100596\) \(a_{99}=+0.038995105\) \(a_{100}=+0.025973403\)

Showing 100 of 5000 available coefficients

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