Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(141\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5077.o
\(\chi_{5077}(89,\cdot)\) \(\chi_{5077}(97,\cdot)\) \(\chi_{5077}(134,\cdot)\) \(\chi_{5077}(188,\cdot)\) \(\chi_{5077}(232,\cdot)\) \(\chi_{5077}(284,\cdot)\) \(\chi_{5077}(341,\cdot)\) \(\chi_{5077}(377,\cdot)\) \(\chi_{5077}(467,\cdot)\) \(\chi_{5077}(473,\cdot)\) \(\chi_{5077}(484,\cdot)\) \(\chi_{5077}(550,\cdot)\) \(\chi_{5077}(675,\cdot)\) \(\chi_{5077}(714,\cdot)\) \(\chi_{5077}(729,\cdot)\) \(\chi_{5077}(917,\cdot)\) \(\chi_{5077}(941,\cdot)\) \(\chi_{5077}(974,\cdot)\) \(\chi_{5077}(1035,\cdot)\) \(\chi_{5077}(1155,\cdot)\) \(\chi_{5077}(1159,\cdot)\) \(\chi_{5077}(1255,\cdot)\) \(\chi_{5077}(1393,\cdot)\) \(\chi_{5077}(1418,\cdot)\) \(\chi_{5077}(1459,\cdot)\) \(\chi_{5077}(1481,\cdot)\) \(\chi_{5077}(1487,\cdot)\) \(\chi_{5077}(1587,\cdot)\) \(\chi_{5077}(1611,\cdot)\) \(\chi_{5077}(1632,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{141})$ |
Fixed field: | Number field defined by a degree 141 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{95}{141}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{141}\right)\) | \(e\left(\frac{44}{47}\right)\) | \(e\left(\frac{49}{141}\right)\) | \(e\left(\frac{5}{47}\right)\) | \(e\left(\frac{86}{141}\right)\) | \(e\left(\frac{56}{141}\right)\) | \(e\left(\frac{1}{47}\right)\) | \(e\left(\frac{41}{47}\right)\) | \(e\left(\frac{110}{141}\right)\) | \(e\left(\frac{7}{141}\right)\) |