Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1337}(292,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.cf
\(\chi_{4011}(19,\cdot)\) \(\chi_{4011}(61,\cdot)\) \(\chi_{4011}(73,\cdot)\) \(\chi_{4011}(94,\cdot)\) \(\chi_{4011}(124,\cdot)\) \(\chi_{4011}(145,\cdot)\) \(\chi_{4011}(157,\cdot)\) \(\chi_{4011}(178,\cdot)\) \(\chi_{4011}(187,\cdot)\) \(\chi_{4011}(220,\cdot)\) \(\chi_{4011}(262,\cdot)\) \(\chi_{4011}(292,\cdot)\) \(\chi_{4011}(304,\cdot)\) \(\chi_{4011}(334,\cdot)\) \(\chi_{4011}(355,\cdot)\) \(\chi_{4011}(367,\cdot)\) \(\chi_{4011}(439,\cdot)\) \(\chi_{4011}(481,\cdot)\) \(\chi_{4011}(493,\cdot)\) \(\chi_{4011}(514,\cdot)\) \(\chi_{4011}(523,\cdot)\) \(\chi_{4011}(556,\cdot)\) \(\chi_{4011}(565,\cdot)\) \(\chi_{4011}(649,\cdot)\) \(\chi_{4011}(661,\cdot)\) \(\chi_{4011}(724,\cdot)\) \(\chi_{4011}(754,\cdot)\) \(\chi_{4011}(808,\cdot)\) \(\chi_{4011}(817,\cdot)\) \(\chi_{4011}(838,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{41}{190}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(292, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{285}\right)\) | \(e\left(\frac{92}{285}\right)\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{46}{95}\right)\) | \(e\left(\frac{67}{570}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{127}{190}\right)\) | \(e\left(\frac{184}{285}\right)\) | \(e\left(\frac{559}{570}\right)\) | \(e\left(\frac{109}{285}\right)\) |