Properties

Level $34$
Weight $0$
Character 34.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 34 = 2 \cdot 17 \)
Weight: \( 0 \)
Character: 34.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.31878442521 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.799385654\) \(a_{4}=+0.500000000\) \(a_{5}=+1.107731194\)
\(a_{6}=-0.565251017\) \(a_{7}=+1.724572144\) \(a_{8}=-0.353553391\) \(a_{9}=-0.360982576\) \(a_{10}=-0.783284239\)
\(a_{11}=-1.466914437\) \(a_{12}=+0.399692827\) \(a_{13}=+0.817453935\) \(a_{14}=-1.219456658\) \(a_{15}=+0.885504426\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.255253227\) \(a_{19}=-0.607187952\) \(a_{20}=+0.553865597\)
\(a_{21}=+1.378598232\) \(a_{22}=+1.037265146\) \(a_{23}=-0.520802600\) \(a_{24}=-0.282625508\) \(a_{25}=+0.227068399\)
\(a_{26}=-0.578027221\) \(a_{27}=-1.087949947\) \(a_{28}=+0.862286072\) \(a_{29}=-0.430760063\) \(a_{30}=-0.626146184\)
\(a_{31}=-0.182774673\) \(a_{32}=-0.176776695\) \(a_{33}=-1.172630357\) \(a_{34}=-0.171498585\) \(a_{35}=+1.910362361\)
\(a_{36}=-0.180491288\) \(a_{37}=+0.658462580\) \(a_{38}=+0.429346719\) \(a_{39}=+0.653460949\) \(a_{40}=-0.391642120\)
\(a_{41}=-1.541898864\) \(a_{42}=-0.974816158\) \(a_{43}=+0.273301885\) \(a_{44}=-0.733457218\) \(a_{45}=-0.399871660\)
\(a_{46}=+0.368263050\) \(a_{47}=-0.410657362\) \(a_{48}=+0.199846414\) \(a_{49}=+1.974149079\) \(a_{50}=-0.160561605\)
\(a_{51}=+0.193879499\) \(a_{52}=+0.408726968\) \(a_{53}=+1.342381151\) \(a_{54}=+0.769296785\) \(a_{55}=-1.624946881\)
\(a_{56}=-0.609728329\) \(a_{57}=-0.485377339\) \(a_{58}=+0.304593361\) \(a_{59}=-0.397571565\) \(a_{60}=+0.442752213\)
\(a_{61}=+1.041932960\) \(a_{62}=+0.129241211\) \(a_{63}=-0.622540494\) \(a_{64}=+0.125000000\) \(a_{65}=+0.905519224\)
\(a_{66}=+0.829174877\) \(a_{67}=-0.963539036\) \(a_{68}=+0.121267813\) \(a_{69}=-0.416322127\) \(a_{70}=-1.350830180\)
\(a_{71}=+1.705705805\) \(a_{72}=+0.127626614\) \(a_{73}=+0.569965226\) \(a_{74}=-0.465603355\) \(a_{75}=+0.181515221\)
\(a_{76}=-0.303593976\) \(a_{77}=-2.529799775\) \(a_{78}=-0.462066668\) \(a_{79}=-1.559896197\) \(a_{80}=+0.276932799\)
\(a_{81}=-0.508709004\) \(a_{82}=+1.090287143\) \(a_{83}=-0.923131407\) \(a_{84}=+0.689299116\) \(a_{85}=+0.268664278\)
\(a_{86}=-0.193253616\) \(a_{87}=-0.344343415\) \(a_{88}=+0.518632573\) \(a_{89}=+0.694646259\) \(a_{90}=+0.282751962\)
\(a_{91}=+1.409758286\) \(a_{92}=-0.260401300\) \(a_{93}=-0.146107452\) \(a_{94}=+0.290378606\) \(a_{95}=-0.672601036\)
\(a_{96}=-0.141312754\) \(a_{97}=+0.069249876\) \(a_{98}=-1.395934201\) \(a_{99}=+0.529530552\) \(a_{100}=+0.113534199\)

Showing 100 of 346 available coefficients

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