Basic properties
Modulus: | \(4020\) | |
Conductor: | \(1005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1005}(548,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.do
\(\chi_{4020}(113,\cdot)\) \(\chi_{4020}(197,\cdot)\) \(\chi_{4020}(233,\cdot)\) \(\chi_{4020}(353,\cdot)\) \(\chi_{4020}(413,\cdot)\) \(\chi_{4020}(497,\cdot)\) \(\chi_{4020}(593,\cdot)\) \(\chi_{4020}(653,\cdot)\) \(\chi_{4020}(677,\cdot)\) \(\chi_{4020}(917,\cdot)\) \(\chi_{4020}(1037,\cdot)\) \(\chi_{4020}(1133,\cdot)\) \(\chi_{4020}(1157,\cdot)\) \(\chi_{4020}(1217,\cdot)\) \(\chi_{4020}(1397,\cdot)\) \(\chi_{4020}(1457,\cdot)\) \(\chi_{4020}(1553,\cdot)\) \(\chi_{4020}(1793,\cdot)\) \(\chi_{4020}(1853,\cdot)\) \(\chi_{4020}(1937,\cdot)\) \(\chi_{4020}(2213,\cdot)\) \(\chi_{4020}(2357,\cdot)\) \(\chi_{4020}(2393,\cdot)\) \(\chi_{4020}(2453,\cdot)\) \(\chi_{4020}(2513,\cdot)\) \(\chi_{4020}(2597,\cdot)\) \(\chi_{4020}(2633,\cdot)\) \(\chi_{4020}(2657,\cdot)\) \(\chi_{4020}(2693,\cdot)\) \(\chi_{4020}(3017,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2011,2681,3217,1141)\) → \((1,-1,-i,e\left(\frac{41}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4020 }(1553, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{14}{33}\right)\) |