Properties

Level $29$
Weight $0$
Character 29.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.31985783319 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.661277412\) \(a_{3}=+0.399051384\) \(a_{4}=-0.562712184\) \(a_{5}=-0.005472655\)
\(a_{6}=+0.263883667\) \(a_{7}=-0.248063707\) \(a_{8}=-1.033386269\) \(a_{9}=-0.840757993\) \(a_{10}=-0.003618943\)
\(a_{11}=-1.847640568\) \(a_{12}=-0.224551076\) \(a_{13}=+0.678364454\) \(a_{14}=-0.164038926\) \(a_{15}=-0.002183870\)
\(a_{16}=-0.120642814\) \(a_{17}=-0.638187333\) \(a_{18}=-0.555974270\) \(a_{19}=+1.669459153\) \(a_{20}=+0.003079529\)
\(a_{21}=-0.098990166\) \(a_{22}=-1.221802973\) \(a_{23}=+0.745295370\) \(a_{24}=-0.412374221\) \(a_{25}=-0.999970050\)
\(a_{26}=+0.448587091\) \(a_{27}=-0.734557025\) \(a_{28}=+0.139588471\) \(a_{29}=-0.185695338\) \(a_{30}=-0.001444144\)
\(a_{31}=-1.039928872\) \(a_{32}=+0.953607901\) \(a_{33}=-0.737303526\) \(a_{34}=-0.422018868\) \(a_{35}=+0.001357567\)
\(a_{36}=+0.473104766\) \(a_{37}=+1.816107861\) \(a_{38}=+1.103975629\) \(a_{39}=+0.270702274\) \(a_{40}=+0.005655366\)
\(a_{41}=-0.496628230\) \(a_{42}=-0.065459961\) \(a_{43}=-0.856967730\) \(a_{44}=+1.039689859\) \(a_{45}=+0.004601178\)
\(a_{46}=+0.492846994\) \(a_{47}=-0.336465695\) \(a_{48}=-0.048142682\) \(a_{49}=-0.938464397\) \(a_{50}=-0.661257607\)
\(a_{51}=-0.254669538\) \(a_{52}=-0.381723944\) \(a_{53}=-0.562817650\) \(a_{54}=-0.485745968\) \(a_{55}=+0.010111498\)
\(a_{56}=+0.256345629\) \(a_{57}=+0.666199986\) \(a_{58}=-0.122796134\) \(a_{59}=-0.604043874\) \(a_{60}=+0.001228891\)
\(a_{61}=+1.359630761\) \(a_{62}=-0.687681473\) \(a_{63}=+0.208561543\) \(a_{64}=+0.751242181\) \(a_{65}=-0.003712455\)
\(a_{66}=-0.487562170\) \(a_{67}=-0.660405415\) \(a_{68}=+0.359115784\) \(a_{69}=+0.297411149\) \(a_{70}=+0.000897730\)
\(a_{71}=+0.108105589\) \(a_{72}=+0.868827776\) \(a_{73}=-0.491063686\) \(a_{74}=+1.200951104\) \(a_{75}=-0.399039428\)
\(a_{76}=-0.939425025\) \(a_{77}=+0.458332596\) \(a_{78}=+0.179009309\) \(a_{79}=+0.022724066\) \(a_{80}=+0.000660242\)
\(a_{81}=+0.547631973\) \(a_{82}=-0.328408989\) \(a_{83}=-0.096406006\) \(a_{84}=+0.055702892\) \(a_{85}=+0.003492587\)
\(a_{86}=-0.566693400\) \(a_{87}=-0.074101993\) \(a_{88}=+1.909326410\) \(a_{89}=-0.889120111\) \(a_{90}=+0.003042655\)
\(a_{91}=-0.168277592\) \(a_{92}=-0.419386810\) \(a_{93}=-0.414985061\) \(a_{94}=-0.222497143\) \(a_{95}=-0.009136383\)
\(a_{96}=+0.380538568\) \(a_{97}=-1.726901177\) \(a_{98}=-0.620585320\) \(a_{99}=+1.553418598\) \(a_{100}=+0.562695320\)

Showing 100 of 1500 available coefficients

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