Basic properties
Modulus: | \(950\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 950.bi
\(\chi_{950}(3,\cdot)\) \(\chi_{950}(13,\cdot)\) \(\chi_{950}(33,\cdot)\) \(\chi_{950}(53,\cdot)\) \(\chi_{950}(67,\cdot)\) \(\chi_{950}(97,\cdot)\) \(\chi_{950}(117,\cdot)\) \(\chi_{950}(127,\cdot)\) \(\chi_{950}(147,\cdot)\) \(\chi_{950}(167,\cdot)\) \(\chi_{950}(173,\cdot)\) \(\chi_{950}(203,\cdot)\) \(\chi_{950}(223,\cdot)\) \(\chi_{950}(287,\cdot)\) \(\chi_{950}(317,\cdot)\) \(\chi_{950}(333,\cdot)\) \(\chi_{950}(337,\cdot)\) \(\chi_{950}(363,\cdot)\) \(\chi_{950}(383,\cdot)\) \(\chi_{950}(413,\cdot)\) \(\chi_{950}(433,\cdot)\) \(\chi_{950}(447,\cdot)\) \(\chi_{950}(477,\cdot)\) \(\chi_{950}(497,\cdot)\) \(\chi_{950}(523,\cdot)\) \(\chi_{950}(527,\cdot)\) \(\chi_{950}(547,\cdot)\) \(\chi_{950}(553,\cdot)\) \(\chi_{950}(573,\cdot)\) \(\chi_{950}(583,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((77,401)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 950 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{151}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{41}{45}\right)\) |