Basic properties
| Modulus: | \(1476\) | |
| Conductor: | \(369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{369}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1476.ci
\(\chi_{1476}(13,\cdot)\) \(\chi_{1476}(97,\cdot)\) \(\chi_{1476}(157,\cdot)\) \(\chi_{1476}(193,\cdot)\) \(\chi_{1476}(229,\cdot)\) \(\chi_{1476}(265,\cdot)\) \(\chi_{1476}(313,\cdot)\) \(\chi_{1476}(421,\cdot)\) \(\chi_{1476}(445,\cdot)\) \(\chi_{1476}(457,\cdot)\) \(\chi_{1476}(481,\cdot)\) \(\chi_{1476}(589,\cdot)\) \(\chi_{1476}(637,\cdot)\) \(\chi_{1476}(673,\cdot)\) \(\chi_{1476}(709,\cdot)\) \(\chi_{1476}(745,\cdot)\) \(\chi_{1476}(805,\cdot)\) \(\chi_{1476}(889,\cdot)\) \(\chi_{1476}(913,\cdot)\) \(\chi_{1476}(949,\cdot)\) \(\chi_{1476}(997,\cdot)\) \(\chi_{1476}(1129,\cdot)\) \(\chi_{1476}(1141,\cdot)\) \(\chi_{1476}(1165,\cdot)\) \(\chi_{1476}(1177,\cdot)\) \(\chi_{1476}(1201,\cdot)\) \(\chi_{1476}(1213,\cdot)\) \(\chi_{1476}(1237,\cdot)\) \(\chi_{1476}(1249,\cdot)\) \(\chi_{1476}(1381,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((739,821,1441)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{31}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1476 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |