Basic properties
| Modulus: | \(5625\) | |
| Conductor: | \(1125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1125}(752,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5625.bn
\(\chi_{5625}(32,\cdot)\) \(\chi_{5625}(218,\cdot)\) \(\chi_{5625}(257,\cdot)\) \(\chi_{5625}(293,\cdot)\) \(\chi_{5625}(407,\cdot)\) \(\chi_{5625}(482,\cdot)\) \(\chi_{5625}(518,\cdot)\) \(\chi_{5625}(632,\cdot)\) \(\chi_{5625}(668,\cdot)\) \(\chi_{5625}(707,\cdot)\) \(\chi_{5625}(743,\cdot)\) \(\chi_{5625}(857,\cdot)\) \(\chi_{5625}(893,\cdot)\) \(\chi_{5625}(968,\cdot)\) \(\chi_{5625}(1082,\cdot)\) \(\chi_{5625}(1118,\cdot)\) \(\chi_{5625}(1157,\cdot)\) \(\chi_{5625}(1343,\cdot)\) \(\chi_{5625}(1382,\cdot)\) \(\chi_{5625}(1418,\cdot)\) \(\chi_{5625}(1532,\cdot)\) \(\chi_{5625}(1607,\cdot)\) \(\chi_{5625}(1643,\cdot)\) \(\chi_{5625}(1757,\cdot)\) \(\chi_{5625}(1793,\cdot)\) \(\chi_{5625}(1832,\cdot)\) \(\chi_{5625}(1868,\cdot)\) \(\chi_{5625}(1982,\cdot)\) \(\chi_{5625}(2018,\cdot)\) \(\chi_{5625}(2093,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((4376,1252)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5625 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{300}\right)\) | \(e\left(\frac{103}{150}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{89}{150}\right)\) | \(e\left(\frac{17}{300}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) |