Basic properties
| Modulus: | \(7600\) | |
| Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3800}(2179,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7600.hz
\(\chi_{7600}(279,\cdot)\) \(\chi_{7600}(439,\cdot)\) \(\chi_{7600}(679,\cdot)\) \(\chi_{7600}(839,\cdot)\) \(\chi_{7600}(1079,\cdot)\) \(\chi_{7600}(1959,\cdot)\) \(\chi_{7600}(2119,\cdot)\) \(\chi_{7600}(2359,\cdot)\) \(\chi_{7600}(3319,\cdot)\) \(\chi_{7600}(3479,\cdot)\) \(\chi_{7600}(3639,\cdot)\) \(\chi_{7600}(3719,\cdot)\) \(\chi_{7600}(3879,\cdot)\) \(\chi_{7600}(4119,\cdot)\) \(\chi_{7600}(4839,\cdot)\) \(\chi_{7600}(5159,\cdot)\) \(\chi_{7600}(5239,\cdot)\) \(\chi_{7600}(5639,\cdot)\) \(\chi_{7600}(6359,\cdot)\) \(\chi_{7600}(6519,\cdot)\) \(\chi_{7600}(6679,\cdot)\) \(\chi_{7600}(6759,\cdot)\) \(\chi_{7600}(6919,\cdot)\) \(\chi_{7600}(7159,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4751,5701,5777,401)\) → \((-1,-1,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7600 }(279, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) |