Basic properties
| Modulus: | \(3017\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(430\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3017.ba
\(\chi_{3017}(20,\cdot)\) \(\chi_{3017}(41,\cdot)\) \(\chi_{3017}(69,\cdot)\) \(\chi_{3017}(76,\cdot)\) \(\chi_{3017}(90,\cdot)\) \(\chi_{3017}(97,\cdot)\) \(\chi_{3017}(118,\cdot)\) \(\chi_{3017}(125,\cdot)\) \(\chi_{3017}(132,\cdot)\) \(\chi_{3017}(139,\cdot)\) \(\chi_{3017}(160,\cdot)\) \(\chi_{3017}(174,\cdot)\) \(\chi_{3017}(209,\cdot)\) \(\chi_{3017}(223,\cdot)\) \(\chi_{3017}(230,\cdot)\) \(\chi_{3017}(244,\cdot)\) \(\chi_{3017}(265,\cdot)\) \(\chi_{3017}(300,\cdot)\) \(\chi_{3017}(307,\cdot)\) \(\chi_{3017}(314,\cdot)\) \(\chi_{3017}(328,\cdot)\) \(\chi_{3017}(342,\cdot)\) \(\chi_{3017}(363,\cdot)\) \(\chi_{3017}(454,\cdot)\) \(\chi_{3017}(461,\cdot)\) \(\chi_{3017}(475,\cdot)\) \(\chi_{3017}(489,\cdot)\) \(\chi_{3017}(531,\cdot)\) \(\chi_{3017}(545,\cdot)\) \(\chi_{3017}(552,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{215})$ |
| Fixed field: | Number field defined by a degree 430 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((-1,e\left(\frac{2}{215}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3017 }(1539, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{9}{86}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{293}{430}\right)\) | \(e\left(\frac{13}{86}\right)\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{313}{430}\right)\) | \(e\left(\frac{191}{215}\right)\) | \(e\left(\frac{17}{86}\right)\) |