Basic properties
| Modulus: | \(375\) | |
| Conductor: | \(375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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 375.r
\(\chi_{375}(2,\cdot)\) \(\chi_{375}(8,\cdot)\) \(\chi_{375}(17,\cdot)\) \(\chi_{375}(23,\cdot)\) \(\chi_{375}(38,\cdot)\) \(\chi_{375}(47,\cdot)\) \(\chi_{375}(53,\cdot)\) \(\chi_{375}(62,\cdot)\) \(\chi_{375}(77,\cdot)\) \(\chi_{375}(83,\cdot)\) \(\chi_{375}(92,\cdot)\) \(\chi_{375}(98,\cdot)\) \(\chi_{375}(113,\cdot)\) \(\chi_{375}(122,\cdot)\) \(\chi_{375}(128,\cdot)\) \(\chi_{375}(137,\cdot)\) \(\chi_{375}(152,\cdot)\) \(\chi_{375}(158,\cdot)\) \(\chi_{375}(167,\cdot)\) \(\chi_{375}(173,\cdot)\) \(\chi_{375}(188,\cdot)\) \(\chi_{375}(197,\cdot)\) \(\chi_{375}(203,\cdot)\) \(\chi_{375}(212,\cdot)\) \(\chi_{375}(227,\cdot)\) \(\chi_{375}(233,\cdot)\) \(\chi_{375}(242,\cdot)\) \(\chi_{375}(248,\cdot)\) \(\chi_{375}(263,\cdot)\) \(\chi_{375}(272,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((251,127)\) → \((-1,e\left(\frac{1}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 375 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) |