Basic properties
| Modulus: | \(1151\) | |
| Conductor: | \(1151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1151.l
\(\chi_{1151}(17,\cdot)\) \(\chi_{1151}(23,\cdot)\) \(\chi_{1151}(26,\cdot)\) \(\chi_{1151}(31,\cdot)\) \(\chi_{1151}(34,\cdot)\) \(\chi_{1151}(38,\cdot)\) \(\chi_{1151}(39,\cdot)\) \(\chi_{1151}(41,\cdot)\) \(\chi_{1151}(46,\cdot)\) \(\chi_{1151}(51,\cdot)\) \(\chi_{1151}(52,\cdot)\) \(\chi_{1151}(57,\cdot)\) \(\chi_{1151}(61,\cdot)\) \(\chi_{1151}(62,\cdot)\) \(\chi_{1151}(65,\cdot)\) \(\chi_{1151}(68,\cdot)\) \(\chi_{1151}(69,\cdot)\) \(\chi_{1151}(71,\cdot)\) \(\chi_{1151}(73,\cdot)\) \(\chi_{1151}(76,\cdot)\) \(\chi_{1151}(79,\cdot)\) \(\chi_{1151}(82,\cdot)\) \(\chi_{1151}(85,\cdot)\) \(\chi_{1151}(97,\cdot)\) \(\chi_{1151}(101,\cdot)\) \(\chi_{1151}(102,\cdot)\) \(\chi_{1151}(103,\cdot)\) \(\chi_{1151}(104,\cdot)\) \(\chi_{1151}(107,\cdot)\) \(\chi_{1151}(113,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{575})$ |
| Fixed field: | Number field defined by a degree 1150 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{1003}{1150}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1151 }(1149, a) \) | \(-1\) | \(1\) | \(e\left(\frac{167}{575}\right)\) | \(e\left(\frac{278}{575}\right)\) | \(e\left(\frac{334}{575}\right)\) | \(e\left(\frac{187}{575}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{501}{575}\right)\) | \(e\left(\frac{556}{575}\right)\) | \(e\left(\frac{354}{575}\right)\) | \(e\left(\frac{359}{575}\right)\) |