Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.51842933602 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.174714797\) \(a_{3}=+0.577350269\) \(a_{4}=-0.969474740\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.100871635\) \(a_{7}=+1.167376728\) \(a_{8}=+0.344096380\) \(a_{9}=+0.333333333\) \(a_{10}=+0.078134833\)
\(a_{11}=-0.370527938\) \(a_{12}=-0.559726502\) \(a_{13}=-0.164314669\) \(a_{14}=-0.203957989\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.909356010\) \(a_{17}=-0.726972733\) \(a_{18}=-0.058238266\) \(a_{19}=-0.903090891\) \(a_{20}=+0.433562284\)
\(a_{21}=+0.673985268\) \(a_{22}=+0.064736714\) \(a_{23}=+1.009173862\) \(a_{24}=+0.198664138\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.028708204\) \(a_{27}=+0.192450090\) \(a_{28}=-1.131742250\) \(a_{29}=+0.192624117\) \(a_{30}=+0.045111167\)
\(a_{31}=-0.444868264\) \(a_{32}=-0.502974331\) \(a_{33}=-0.213924405\) \(a_{34}=+0.127012894\) \(a_{35}=-0.522066745\)
\(a_{36}=-0.323158246\) \(a_{37}=+0.845661158\) \(a_{38}=+0.157783344\) \(a_{39}=-0.094867118\) \(a_{40}=-0.153884580\)
\(a_{41}=-0.495414876\) \(a_{42}=-0.117755203\) \(a_{43}=+1.205978122\) \(a_{44}=+0.359217476\) \(a_{45}=-0.149071191\)
\(a_{46}=-0.176317606\) \(a_{47}=+1.095635278\) \(a_{48}=+0.525016924\) \(a_{49}=+0.362768418\) \(a_{50}=-0.034942959\)
\(a_{51}=-0.419717898\) \(a_{52}=+0.159298965\) \(a_{53}=-1.944175160\) \(a_{54}=-0.033623862\) \(a_{55}=+0.165705044\)
\(a_{56}=+0.401690081\) \(a_{57}=-0.521399773\) \(a_{58}=-0.033654211\) \(a_{59}=-0.293984462\) \(a_{60}=+0.250317315\)
\(a_{61}=-0.641853372\) \(a_{62}=+0.077724959\) \(a_{63}=+0.389126385\) \(a_{64}=-0.821478965\) \(a_{65}=+0.073483767\)
\(a_{66}=+0.037374657\) \(a_{67}=-1.286937903\) \(a_{68}=+0.704781676\) \(a_{69}=+0.582646497\) \(a_{70}=+0.091214302\)
\(a_{71}=+1.877977558\) \(a_{72}=+0.114695612\) \(a_{73}=+0.059434035\) \(a_{74}=-0.147740016\) \(a_{75}=+0.115451147\)
\(a_{76}=+0.875520124\) \(a_{77}=-0.432542313\) \(a_{78}=+0.016557078\) \(a_{79}=-0.039049780\) \(a_{80}=-0.406645717\)
\(a_{81}=+0.110911488\) \(a_{82}=+0.086610879\) \(a_{83}=-0.603261242\) \(a_{84}=-0.653418214\) \(a_{85}=+0.325605403\)
\(a_{86}=-0.210065302\) \(a_{87}=+0.109640355\) \(a_{88}=-0.127626891\) \(a_{89}=+0.671328211\) \(a_{90}=+0.027633888\)
\(a_{91}=-0.193282492\) \(a_{92}=-0.978371501\) \(a_{93}=-0.256909698\) \(a_{94}=-0.191403701\) \(a_{95}=+0.403703324\)
\(a_{96}=-0.290377366\) \(a_{97}=+0.751291043\) \(a_{98}=-0.063267410\) \(a_{99}=-0.123072061\) \(a_{100}=-0.193902489\)

Showing 100 of 1500 available coefficients

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