Basic properties
| Modulus: | \(1029\) | |
| Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(98\) | 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 1029.t
\(\chi_{1029}(8,\cdot)\) \(\chi_{1029}(29,\cdot)\) \(\chi_{1029}(71,\cdot)\) \(\chi_{1029}(92,\cdot)\) \(\chi_{1029}(113,\cdot)\) \(\chi_{1029}(134,\cdot)\) \(\chi_{1029}(155,\cdot)\) \(\chi_{1029}(176,\cdot)\) \(\chi_{1029}(218,\cdot)\) \(\chi_{1029}(239,\cdot)\) \(\chi_{1029}(260,\cdot)\) \(\chi_{1029}(281,\cdot)\) \(\chi_{1029}(302,\cdot)\) \(\chi_{1029}(323,\cdot)\) \(\chi_{1029}(365,\cdot)\) \(\chi_{1029}(386,\cdot)\) \(\chi_{1029}(407,\cdot)\) \(\chi_{1029}(428,\cdot)\) \(\chi_{1029}(449,\cdot)\) \(\chi_{1029}(470,\cdot)\) \(\chi_{1029}(512,\cdot)\) \(\chi_{1029}(533,\cdot)\) \(\chi_{1029}(554,\cdot)\) \(\chi_{1029}(575,\cdot)\) \(\chi_{1029}(596,\cdot)\) \(\chi_{1029}(617,\cdot)\) \(\chi_{1029}(659,\cdot)\) \(\chi_{1029}(680,\cdot)\) \(\chi_{1029}(701,\cdot)\) \(\chi_{1029}(722,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 98 polynomial |
Values on generators
\((344,346)\) → \((-1,e\left(\frac{30}{49}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1029 }(281, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{27}{49}\right)\) | \(e\left(\frac{25}{98}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{83}{98}\right)\) | \(e\left(\frac{24}{49}\right)\) | \(e\left(\frac{5}{49}\right)\) | \(e\left(\frac{79}{98}\right)\) | \(1\) |