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: \( 3.61565926071 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.188993495\) \(a_{4}=+0.500000000\) \(a_{5}=-0.844124952\)
\(a_{6}=-0.133638582\) \(a_{7}=-1.425372263\) \(a_{8}=+0.353553391\) \(a_{9}=-0.964281459\) \(a_{10}=-0.596886478\)
\(a_{11}=+0.035719096\) \(a_{12}=-0.094496748\) \(a_{13}=-0.109498040\) \(a_{14}=-1.007890393\) \(a_{15}=+0.159534125\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.242535625\) \(a_{18}=-0.681849958\) \(a_{19}=+1.641862799\) \(a_{20}=-0.422062476\)
\(a_{21}=+0.269386086\) \(a_{22}=+0.025257215\) \(a_{23}=-0.635765316\) \(a_{24}=-0.066819291\) \(a_{25}=-0.287453065\)
\(a_{26}=-0.077426806\) \(a_{27}=+0.371236418\) \(a_{28}=-0.712686131\) \(a_{29}=-1.211268820\) \(a_{30}=+0.112807662\)
\(a_{31}=-1.518465181\) \(a_{32}=+0.176776695\) \(a_{33}=-0.006750677\) \(a_{34}=+0.171498585\) \(a_{35}=+1.203192293\)
\(a_{36}=-0.482140729\) \(a_{37}=+1.348415826\) \(a_{38}=+1.160972319\) \(a_{39}=+0.020694417\) \(a_{40}=-0.298443239\)
\(a_{41}=+0.425318834\) \(a_{42}=+0.190484728\) \(a_{43}=-0.537958057\) \(a_{44}=+0.017859548\) \(a_{45}=+0.813974040\)
\(a_{46}=-0.449553966\) \(a_{47}=-1.137257253\) \(a_{48}=-0.047248374\) \(a_{49}=+1.031686088\) \(a_{50}=-0.203260012\)
\(a_{51}=-0.045837655\) \(a_{52}=-0.054749020\) \(a_{53}=+0.929918906\) \(a_{54}=+0.262503789\) \(a_{55}=-0.030151380\)
\(a_{56}=-0.503945196\) \(a_{57}=-0.310301389\) \(a_{58}=-0.856496397\) \(a_{59}=-1.139610575\) \(a_{60}=+0.079767062\)
\(a_{61}=-1.568145256\) \(a_{62}=-1.073717026\) \(a_{63}=+1.374460045\) \(a_{64}=+0.125000000\) \(a_{65}=+0.092430027\)
\(a_{66}=-0.004773449\) \(a_{67}=+0.059712766\) \(a_{68}=+0.121267813\) \(a_{69}=+0.120155509\) \(a_{70}=+0.850785429\)
\(a_{71}=+0.433768920\) \(a_{72}=-0.340924979\) \(a_{73}=-0.517379115\) \(a_{74}=+0.953473974\) \(a_{75}=+0.054326760\)
\(a_{76}=+0.820931399\) \(a_{77}=-0.050913008\) \(a_{78}=+0.014633163\) \(a_{79}=-1.017956567\) \(a_{80}=-0.211031238\)
\(a_{81}=+0.894120191\) \(a_{82}=+0.300745832\) \(a_{83}=+0.251789661\) \(a_{84}=+0.134693043\) \(a_{85}=-0.204730373\)
\(a_{86}=-0.380393790\) \(a_{87}=+0.228921928\) \(a_{88}=+0.012628607\) \(a_{89}=+0.668190534\) \(a_{90}=+0.575566563\)
\(a_{91}=+0.156075468\) \(a_{92}=-0.317882658\) \(a_{93}=+0.286980042\) \(a_{94}=-0.804162315\) \(a_{95}=-1.385937356\)
\(a_{96}=-0.033409645\) \(a_{97}=-0.233231336\) \(a_{98}=+0.729512229\) \(a_{99}=-0.034443262\) \(a_{100}=-0.143726533\)

Showing 100 of 330 available coefficients

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