Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(733,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.el
\(\chi_{7098}(31,\cdot)\) \(\chi_{7098}(73,\cdot)\) \(\chi_{7098}(187,\cdot)\) \(\chi_{7098}(229,\cdot)\) \(\chi_{7098}(619,\cdot)\) \(\chi_{7098}(733,\cdot)\) \(\chi_{7098}(1123,\cdot)\) \(\chi_{7098}(1165,\cdot)\) \(\chi_{7098}(1279,\cdot)\) \(\chi_{7098}(1321,\cdot)\) \(\chi_{7098}(1669,\cdot)\) \(\chi_{7098}(1711,\cdot)\) \(\chi_{7098}(1825,\cdot)\) \(\chi_{7098}(1867,\cdot)\) \(\chi_{7098}(2215,\cdot)\) \(\chi_{7098}(2257,\cdot)\) \(\chi_{7098}(2371,\cdot)\) \(\chi_{7098}(2413,\cdot)\) \(\chi_{7098}(2761,\cdot)\) \(\chi_{7098}(2917,\cdot)\) \(\chi_{7098}(2959,\cdot)\) \(\chi_{7098}(3307,\cdot)\) \(\chi_{7098}(3349,\cdot)\) \(\chi_{7098}(3463,\cdot)\) \(\chi_{7098}(3505,\cdot)\) \(\chi_{7098}(3853,\cdot)\) \(\chi_{7098}(3895,\cdot)\) \(\chi_{7098}(4009,\cdot)\) \(\chi_{7098}(4051,\cdot)\) \(\chi_{7098}(4399,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{11}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(733, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) |