Basic properties
| Modulus: | \(5070\) | |
| Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2535}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.cu
\(\chi_{5070}(59,\cdot)\) \(\chi_{5070}(119,\cdot)\) \(\chi_{5070}(149,\cdot)\) \(\chi_{5070}(449,\cdot)\) \(\chi_{5070}(479,\cdot)\) \(\chi_{5070}(509,\cdot)\) \(\chi_{5070}(539,\cdot)\) \(\chi_{5070}(839,\cdot)\) \(\chi_{5070}(869,\cdot)\) \(\chi_{5070}(899,\cdot)\) \(\chi_{5070}(929,\cdot)\) \(\chi_{5070}(1229,\cdot)\) \(\chi_{5070}(1259,\cdot)\) \(\chi_{5070}(1289,\cdot)\) \(\chi_{5070}(1319,\cdot)\) \(\chi_{5070}(1619,\cdot)\) \(\chi_{5070}(1649,\cdot)\) \(\chi_{5070}(1679,\cdot)\) \(\chi_{5070}(2039,\cdot)\) \(\chi_{5070}(2069,\cdot)\) \(\chi_{5070}(2099,\cdot)\) \(\chi_{5070}(2399,\cdot)\) \(\chi_{5070}(2429,\cdot)\) \(\chi_{5070}(2459,\cdot)\) \(\chi_{5070}(2489,\cdot)\) \(\chi_{5070}(2789,\cdot)\) \(\chi_{5070}(2819,\cdot)\) \(\chi_{5070}(2849,\cdot)\) \(\chi_{5070}(2879,\cdot)\) \(\chi_{5070}(3179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,4057,1861)\) → \((-1,-1,e\left(\frac{35}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5070 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) |