Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 22.3041595536 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.334248997\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.943456514\) \(a_{7}=+0.577841096\) \(a_{8}=+0.353553391\) \(a_{9}=+0.780220387\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.634075764\) \(a_{12}=+0.667124499\) \(a_{13}=-0.059446685\) \(a_{14}=+0.408595358\) \(a_{15}=+0.596694291\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.180106958\) \(a_{18}=+0.551699126\) \(a_{19}=-0.851025273\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.770983904\) \(a_{22}=+1.155466053\) \(a_{23}=+0.511672395\) \(a_{24}=+0.471728257\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.042035154\) \(a_{27}=-0.293240729\) \(a_{28}=+0.288920548\) \(a_{29}=-1.803195326\) \(a_{30}=+0.421926580\)
\(a_{31}=+0.291724139\) \(a_{32}=+0.176776695\) \(a_{33}=+2.180263949\) \(a_{34}=+0.834461633\) \(a_{35}=+0.258418394\)
\(a_{36}=+0.390110193\) \(a_{37}=+0.785008072\) \(a_{38}=-0.601765742\) \(a_{39}=-0.079316680\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.623190680\) \(a_{42}=+0.545167946\) \(a_{43}=+1.569604425\) \(a_{44}=+0.817037882\) \(a_{45}=+0.348925164\)
\(a_{46}=+0.361807020\) \(a_{47}=-1.097751399\) \(a_{48}=+0.333562249\) \(a_{49}=-0.666099667\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.574556526\) \(a_{52}=-0.029723342\) \(a_{53}=+0.882909349\) \(a_{54}=-0.207352508\) \(a_{55}=+0.730780898\)
\(a_{56}=+0.204297679\) \(a_{57}=-1.135479617\) \(a_{58}=-1.275051643\) \(a_{59}=+1.205483708\) \(a_{60}=+0.298347146\)
\(a_{61}=+0.511977237\) \(a_{62}=+0.206280117\) \(a_{63}=+0.450843404\) \(a_{64}=+0.125000000\) \(a_{65}=-0.026585366\)
\(a_{66}=+1.541679423\) \(a_{67}=+0.643610249\) \(a_{68}=+0.590053479\) \(a_{69}=+0.682698379\) \(a_{70}=+0.182729399\)
\(a_{71}=-1.327089930\) \(a_{72}=+0.275849563\) \(a_{73}=-0.403483721\) \(a_{74}=+0.555084531\) \(a_{75}=+0.266849799\)
\(a_{76}=-0.425512637\) \(a_{77}=+0.944236131\) \(a_{78}=-0.056085362\) \(a_{79}=-1.509626820\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.171476535\) \(a_{82}=-0.440662356\) \(a_{83}=-0.595804248\) \(a_{84}=+0.385491952\) \(a_{85}=+0.527759876\)
\(a_{86}=+1.109877933\) \(a_{87}=-2.405911556\) \(a_{88}=+0.577733027\) \(a_{89}=-0.151129876\) \(a_{90}=+0.246727350\)
\(a_{91}=-0.034350738\) \(a_{92}=+0.255836197\) \(a_{93}=+0.389232640\) \(a_{94}=-0.776227458\) \(a_{95}=-0.380590072\)
\(a_{96}=+0.235864128\) \(a_{97}=-1.447792347\) \(a_{98}=-0.471003592\) \(a_{99}=+1.274939224\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

Rows: Cols: