Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.25178553271 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.785724918\) \(a_{3}=-1.628027770\) \(a_{4}=+2.188813482\) \(a_{5}=+0.425884838\)
\(a_{6}=+2.907209756\) \(a_{7}=-0.377964473\) \(a_{8}=-2.122893858\) \(a_{9}=+1.650474420\) \(a_{10}=-0.760513167\)
\(a_{11}=+0.717867114\) \(a_{12}=-3.563449133\) \(a_{13}=+0.280851862\) \(a_{14}=+0.674940578\) \(a_{15}=-0.693352343\)
\(a_{16}=+1.602090978\) \(a_{17}=+0.867583163\) \(a_{18}=-2.947293299\) \(a_{19}=-0.548809554\) \(a_{20}=+0.932182475\)
\(a_{21}=+0.615336658\) \(a_{22}=-1.281913194\) \(a_{23}=-0.611304297\) \(a_{24}=+3.456130154\) \(a_{25}=-0.818622105\)
\(a_{26}=-0.501524168\) \(a_{27}=-1.058990420\) \(a_{28}=-0.827293734\) \(a_{29}=+0.679560436\) \(a_{30}=+1.238136555\)
\(a_{31}=+0.742566609\) \(a_{32}=-0.737999923\) \(a_{33}=-1.168707597\) \(a_{34}=-1.549264872\) \(a_{35}=-0.160969338\)
\(a_{36}=+3.612580664\) \(a_{37}=-1.394974470\) \(a_{38}=+0.980022896\) \(a_{39}=-0.457234631\) \(a_{40}=-0.904108306\)
\(a_{41}=+1.473381452\) \(a_{42}=-1.098822003\) \(a_{43}=-1.114685791\) \(a_{44}=+1.571277218\) \(a_{45}=+0.702912031\)
\(a_{46}=+1.091621316\) \(a_{47}=-1.979383208\) \(a_{48}=-2.608248603\) \(a_{49}=+0.142857143\) \(a_{50}=+1.461833891\)
\(a_{51}=-1.412449482\) \(a_{52}=+0.614732342\) \(a_{53}=+0.822678310\) \(a_{54}=+1.891065581\) \(a_{55}=+0.305728719\)
\(a_{56}=+0.802378458\) \(a_{57}=+0.893477195\) \(a_{58}=-1.213508004\) \(a_{59}=-0.152149549\) \(a_{60}=-1.517618956\)
\(a_{61}=-1.060534266\) \(a_{62}=-1.326019697\) \(a_{63}=-0.623820695\) \(a_{64}=-0.284226127\) \(a_{65}=+0.119610550\)
\(a_{66}=+2.086990278\) \(a_{67}=+0.485472997\) \(a_{68}=+1.898977724\) \(a_{69}=+0.995220372\) \(a_{70}=+0.287446958\)
\(a_{71}=-1.556317822\) \(a_{72}=-3.503782010\) \(a_{73}=-0.145092571\) \(a_{74}=+2.491040671\) \(a_{75}=+1.332739520\)
\(a_{76}=-1.201241752\) \(a_{77}=-0.271328266\) \(a_{78}=+0.816495273\) \(a_{79}=-0.551107891\) \(a_{80}=+0.682306256\)
\(a_{81}=+0.073591392\) \(a_{82}=-2.631053972\) \(a_{83}=-0.191688943\) \(a_{84}=+1.346857174\) \(a_{85}=+0.369490514\)
\(a_{86}=+1.990522193\) \(a_{87}=-1.106343262\) \(a_{88}=-1.523955688\) \(a_{89}=+1.109930729\) \(a_{90}=-1.255207528\)
\(a_{91}=-0.106152026\) \(a_{92}=-1.338031088\) \(a_{93}=-1.208919061\) \(a_{94}=+3.534633916\) \(a_{95}=-0.233729668\)
\(a_{96}=+1.201484368\) \(a_{97}=-0.150795286\) \(a_{98}=-0.255103560\) \(a_{99}=+1.184821309\) \(a_{100}=-1.791811100\)

Showing 100 of 1228 available coefficients

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