Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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 38025.nv
\(\chi_{38025}(67,\cdot)\) \(\chi_{38025}(97,\cdot)\) \(\chi_{38025}(358,\cdot)\) \(\chi_{38025}(652,\cdot)\) \(\chi_{38025}(778,\cdot)\) \(\chi_{38025}(1237,\cdot)\) \(\chi_{38025}(1267,\cdot)\) \(\chi_{38025}(1363,\cdot)\) \(\chi_{38025}(1528,\cdot)\) \(\chi_{38025}(1822,\cdot)\) \(\chi_{38025}(1852,\cdot)\) \(\chi_{38025}(2113,\cdot)\) \(\chi_{38025}(2437,\cdot)\) \(\chi_{38025}(2533,\cdot)\) \(\chi_{38025}(2698,\cdot)\) \(\chi_{38025}(2992,\cdot)\) \(\chi_{38025}(3022,\cdot)\) \(\chi_{38025}(3283,\cdot)\) \(\chi_{38025}(3577,\cdot)\) \(\chi_{38025}(3703,\cdot)\) \(\chi_{38025}(4162,\cdot)\) \(\chi_{38025}(4192,\cdot)\) \(\chi_{38025}(4288,\cdot)\) \(\chi_{38025}(4453,\cdot)\) \(\chi_{38025}(4747,\cdot)\) \(\chi_{38025}(4777,\cdot)\) \(\chi_{38025}(4873,\cdot)\) \(\chi_{38025}(5038,\cdot)\) \(\chi_{38025}(5362,\cdot)\) \(\chi_{38025}(5458,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{13}{20}\right),e\left(\frac{37}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{127}{780}\right)\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{61}{780}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) |