Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 9.91827612186 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.683974816\) \(a_{4}=+0.500000000\) \(a_{5}=-0.416111725\)
\(a_{6}=+0.483643230\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.532178452\) \(a_{10}=-0.294235422\)
\(a_{11}=-0.672589118\) \(a_{12}=+0.341987408\) \(a_{13}=-1.781792109\) \(a_{14}=-0.267261242\) \(a_{15}=-0.284609940\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.207147416\) \(a_{18}=-0.376306992\) \(a_{19}=-0.184851647\) \(a_{20}=-0.208055862\)
\(a_{21}=-0.258518181\) \(a_{22}=-0.475592327\) \(a_{23}=+0.363094962\) \(a_{24}=+0.241821615\) \(a_{25}=-0.826851032\)
\(a_{26}=-1.259917283\) \(a_{27}=-1.047971474\) \(a_{28}=-0.188982237\) \(a_{29}=+0.338365764\) \(a_{30}=-0.201249619\)
\(a_{31}=-1.165641989\) \(a_{32}=+0.176776695\) \(a_{33}=-0.460034018\) \(a_{34}=+0.853582124\) \(a_{35}=+0.157275449\)
\(a_{36}=-0.266089226\) \(a_{37}=-1.537344039\) \(a_{38}=-0.130709853\) \(a_{39}=-1.218700929\) \(a_{40}=-0.147117711\)
\(a_{41}=-0.114334467\) \(a_{42}=-0.182799959\) \(a_{43}=-0.024143739\) \(a_{44}=-0.336294559\) \(a_{45}=+0.221445693\)
\(a_{46}=+0.256746910\) \(a_{47}=+1.025450438\) \(a_{48}=+0.170993704\) \(a_{49}=+0.142857143\) \(a_{50}=-0.584671972\)
\(a_{51}=+0.825658432\) \(a_{52}=-0.890896054\) \(a_{53}=+0.275028848\) \(a_{54}=-0.741027736\) \(a_{55}=+0.279872218\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.126433871\) \(a_{58}=+0.239260726\) \(a_{59}=-1.639787820\) \(a_{60}=-0.142304970\)
\(a_{61}=+0.932607493\) \(a_{62}=-0.824233355\) \(a_{63}=+0.201144548\) \(a_{64}=+0.125000000\) \(a_{65}=+0.741424588\)
\(a_{66}=-0.325293174\) \(a_{67}=-0.770467908\) \(a_{68}=+0.603573708\) \(a_{69}=+0.248347810\) \(a_{70}=+0.111210536\)
\(a_{71}=+1.532940636\) \(a_{72}=-0.188153496\) \(a_{73}=+1.417342817\) \(a_{74}=-1.087066395\) \(a_{75}=-0.565545282\)
\(a_{76}=-0.092425824\) \(a_{77}=+0.254214792\) \(a_{78}=-0.861751691\) \(a_{79}=+0.388510127\) \(a_{80}=-0.104027931\)
\(a_{81}=-0.184607644\) \(a_{82}=-0.080846677\) \(a_{83}=-0.991659683\) \(a_{84}=-0.129259090\) \(a_{85}=-0.502308193\)
\(a_{86}=-0.017072202\) \(a_{87}=+0.231433662\) \(a_{88}=-0.237796163\) \(a_{89}=+0.563112596\) \(a_{90}=+0.156585751\)
\(a_{91}=+0.673454115\) \(a_{92}=+0.181547481\) \(a_{93}=-0.797269762\) \(a_{94}=+0.725102958\) \(a_{95}=+0.076918939\)
\(a_{96}=+0.120910808\) \(a_{97}=+0.058400192\) \(a_{98}=+0.101015254\) \(a_{99}=+0.357937436\) \(a_{100}=-0.413425516\)

Showing 100 of 198 available coefficients

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