Basic properties
| Modulus: | \(2019\) | |
| Conductor: | \(2019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(672\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 2019.bu
\(\chi_{2019}(5,\cdot)\) \(\chi_{2019}(11,\cdot)\) \(\chi_{2019}(17,\cdot)\) \(\chi_{2019}(20,\cdot)\) \(\chi_{2019}(35,\cdot)\) \(\chi_{2019}(38,\cdot)\) \(\chi_{2019}(44,\cdot)\) \(\chi_{2019}(47,\cdot)\) \(\chi_{2019}(101,\cdot)\) \(\chi_{2019}(119,\cdot)\) \(\chi_{2019}(134,\cdot)\) \(\chi_{2019}(137,\cdot)\) \(\chi_{2019}(140,\cdot)\) \(\chi_{2019}(152,\cdot)\) \(\chi_{2019}(158,\cdot)\) \(\chi_{2019}(164,\cdot)\) \(\chi_{2019}(173,\cdot)\) \(\chi_{2019}(185,\cdot)\) \(\chi_{2019}(188,\cdot)\) \(\chi_{2019}(221,\cdot)\) \(\chi_{2019}(248,\cdot)\) \(\chi_{2019}(251,\cdot)\) \(\chi_{2019}(260,\cdot)\) \(\chi_{2019}(266,\cdot)\) \(\chi_{2019}(269,\cdot)\) \(\chi_{2019}(272,\cdot)\) \(\chi_{2019}(284,\cdot)\) \(\chi_{2019}(290,\cdot)\) \(\chi_{2019}(311,\cdot)\) \(\chi_{2019}(320,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{672})$ |
| Fixed field: | Number field defined by a degree 672 polynomial (not computed) |
Values on generators
\((674,1351)\) → \((-1,e\left(\frac{1}{672}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2019 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{337}{672}\right)\) | \(e\left(\frac{81}{112}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{61}{224}\right)\) | \(e\left(\frac{319}{672}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{83}{168}\right)\) | \(e\left(\frac{1}{12}\right)\) |