Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(70,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.ea
\(\chi_{4017}(70,\cdot)\) \(\chi_{4017}(109,\cdot)\) \(\chi_{4017}(148,\cdot)\) \(\chi_{4017}(151,\cdot)\) \(\chi_{4017}(187,\cdot)\) \(\chi_{4017}(190,\cdot)\) \(\chi_{4017}(226,\cdot)\) \(\chi_{4017}(268,\cdot)\) \(\chi_{4017}(307,\cdot)\) \(\chi_{4017}(424,\cdot)\) \(\chi_{4017}(460,\cdot)\) \(\chi_{4017}(463,\cdot)\) \(\chi_{4017}(499,\cdot)\) \(\chi_{4017}(577,\cdot)\) \(\chi_{4017}(580,\cdot)\) \(\chi_{4017}(616,\cdot)\) \(\chi_{4017}(658,\cdot)\) \(\chi_{4017}(733,\cdot)\) \(\chi_{4017}(772,\cdot)\) \(\chi_{4017}(775,\cdot)\) \(\chi_{4017}(889,\cdot)\) \(\chi_{4017}(967,\cdot)\) \(\chi_{4017}(970,\cdot)\) \(\chi_{4017}(1084,\cdot)\) \(\chi_{4017}(1126,\cdot)\) \(\chi_{4017}(1204,\cdot)\) \(\chi_{4017}(1279,\cdot)\) \(\chi_{4017}(1321,\cdot)\) \(\chi_{4017}(1360,\cdot)\) \(\chi_{4017}(1435,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,-i,e\left(\frac{49}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(70, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{204}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{47}{204}\right)\) | \(e\left(\frac{35}{204}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{113}{204}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{13}{102}\right)\) |