Basic properties
| Modulus: | \(8673\) | |
| Conductor: | \(413\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{413}(132,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8673.bn
\(\chi_{8673}(97,\cdot)\) \(\chi_{8673}(244,\cdot)\) \(\chi_{8673}(391,\cdot)\) \(\chi_{8673}(832,\cdot)\) \(\chi_{8673}(1273,\cdot)\) \(\chi_{8673}(1567,\cdot)\) \(\chi_{8673}(1861,\cdot)\) \(\chi_{8673}(2008,\cdot)\) \(\chi_{8673}(2155,\cdot)\) \(\chi_{8673}(2449,\cdot)\) \(\chi_{8673}(3478,\cdot)\) \(\chi_{8673}(3772,\cdot)\) \(\chi_{8673}(4066,\cdot)\) \(\chi_{8673}(4213,\cdot)\) \(\chi_{8673}(4507,\cdot)\) \(\chi_{8673}(4654,\cdot)\) \(\chi_{8673}(5242,\cdot)\) \(\chi_{8673}(5977,\cdot)\) \(\chi_{8673}(6124,\cdot)\) \(\chi_{8673}(7006,\cdot)\) \(\chi_{8673}(7153,\cdot)\) \(\chi_{8673}(7300,\cdot)\) \(\chi_{8673}(7447,\cdot)\) \(\chi_{8673}(7594,\cdot)\) \(\chi_{8673}(8035,\cdot)\) \(\chi_{8673}(8182,\cdot)\) \(\chi_{8673}(8329,\cdot)\) \(\chi_{8673}(8476,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((5783,6373,8380)\) → \((1,-1,e\left(\frac{19}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8673 }(7153, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) |