Properties

Level $58$
Weight $0$
Character 58.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 58 = 2 \cdot 29 \)
Weight: \( 0 \)
Character: 58.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.859385049143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.933335169\) \(a_{4}=+0.500000000\) \(a_{5}=-1.868572314\)
\(a_{6}=+0.659967627\) \(a_{7}=-0.097681500\) \(a_{8}=+0.353553391\) \(a_{9}=-0.128885462\) \(a_{10}=-1.321280154\)
\(a_{11}=+1.053968115\) \(a_{12}=+0.466667585\) \(a_{13}=+0.655072500\) \(a_{14}=-0.069071251\) \(a_{15}=-1.744004257\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.632374761\) \(a_{18}=-0.091135784\) \(a_{19}=-0.614804878\) \(a_{20}=-0.934286157\)
\(a_{21}=-0.091169579\) \(a_{22}=+0.745268002\) \(a_{23}=+0.639423101\) \(a_{24}=+0.329983814\) \(a_{25}=+2.491562492\)
\(a_{26}=+0.463206207\) \(a_{27}=-1.053628504\) \(a_{28}=-0.048840750\) \(a_{29}=-0.185695338\) \(a_{30}=-1.233197236\)
\(a_{31}=+0.818346478\) \(a_{32}=+0.176776695\) \(a_{33}=+0.983705509\) \(a_{34}=-0.447156481\) \(a_{35}=+0.182524946\)
\(a_{36}=-0.064442731\) \(a_{37}=-0.101743954\) \(a_{38}=-0.434732699\) \(a_{39}=+0.611402203\) \(a_{40}=-0.660640077\)
\(a_{41}=+0.573524871\) \(a_{42}=-0.064466628\) \(a_{43}=-0.809559958\) \(a_{44}=+0.526984058\) \(a_{45}=+0.240831806\)
\(a_{46}=+0.452140411\) \(a_{47}=+0.147670580\) \(a_{48}=+0.233333792\) \(a_{49}=-0.990458325\) \(a_{50}=+1.761800734\)
\(a_{51}=-0.590217604\) \(a_{52}=+0.327536250\) \(a_{53}=-0.308315302\) \(a_{54}=-0.745027860\) \(a_{55}=-1.969415640\)
\(a_{56}=-0.034535625\) \(a_{57}=-0.573819015\) \(a_{58}=-0.131306433\) \(a_{59}=+0.777965229\) \(a_{60}=-0.872002128\)
\(a_{61}=-1.685943916\) \(a_{62}=+0.578658344\) \(a_{63}=+0.012589725\) \(a_{64}=+0.125000000\) \(a_{65}=-1.224050337\)
\(a_{66}=+0.695584836\) \(a_{67}=+0.708074042\) \(a_{68}=-0.316187380\) \(a_{69}=+0.596796068\) \(a_{70}=+0.129064627\)
\(a_{71}=+0.503439429\) \(a_{72}=-0.045567892\) \(a_{73}=+0.354791685\) \(a_{74}=-0.071943840\) \(a_{75}=+2.325462900\)
\(a_{76}=-0.307402439\) \(a_{77}=-0.102953186\) \(a_{78}=+0.432326644\) \(a_{79}=-0.235663156\) \(a_{80}=-0.467143078\)
\(a_{81}=-0.854503076\) \(a_{82}=+0.405543325\) \(a_{83}=-1.477723275\) \(a_{84}=-0.045584789\) \(a_{85}=+1.181637970\)
\(a_{86}=-0.572445336\) \(a_{87}=-0.173315990\) \(a_{88}=+0.372634001\) \(a_{89}=+0.482322579\) \(a_{90}=+0.170293803\)
\(a_{91}=-0.063988464\) \(a_{92}=+0.319711551\) \(a_{93}=+0.763791549\) \(a_{94}=+0.104418869\) \(a_{95}=+1.148807374\)
\(a_{96}=+0.164991907\) \(a_{97}=+1.691658460\) \(a_{98}=-0.700359798\) \(a_{99}=-0.135841167\) \(a_{100}=+1.245781246\)

Showing 100 of 568 available coefficients

Rows: Cols: