Basic properties
| Modulus: | \(5625\) | |
| Conductor: | \(1125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1125}(1084,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5625.bg
\(\chi_{5625}(49,\cdot)\) \(\chi_{5625}(274,\cdot)\) \(\chi_{5625}(349,\cdot)\) \(\chi_{5625}(574,\cdot)\) \(\chi_{5625}(724,\cdot)\) \(\chi_{5625}(799,\cdot)\) \(\chi_{5625}(949,\cdot)\) \(\chi_{5625}(1024,\cdot)\) \(\chi_{5625}(1174,\cdot)\) \(\chi_{5625}(1399,\cdot)\) \(\chi_{5625}(1474,\cdot)\) \(\chi_{5625}(1699,\cdot)\) \(\chi_{5625}(1849,\cdot)\) \(\chi_{5625}(1924,\cdot)\) \(\chi_{5625}(2074,\cdot)\) \(\chi_{5625}(2149,\cdot)\) \(\chi_{5625}(2299,\cdot)\) \(\chi_{5625}(2524,\cdot)\) \(\chi_{5625}(2599,\cdot)\) \(\chi_{5625}(2824,\cdot)\) \(\chi_{5625}(2974,\cdot)\) \(\chi_{5625}(3049,\cdot)\) \(\chi_{5625}(3199,\cdot)\) \(\chi_{5625}(3274,\cdot)\) \(\chi_{5625}(3424,\cdot)\) \(\chi_{5625}(3649,\cdot)\) \(\chi_{5625}(3724,\cdot)\) \(\chi_{5625}(3949,\cdot)\) \(\chi_{5625}(4099,\cdot)\) \(\chi_{5625}(4174,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((4376,1252)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{47}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5625 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{150}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{49}{150}\right)\) | \(e\left(\frac{38}{75}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) |