Basic properties
Modulus: | \(668\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{167}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 668.e
\(\chi_{668}(9,\cdot)\) \(\chi_{668}(21,\cdot)\) \(\chi_{668}(25,\cdot)\) \(\chi_{668}(29,\cdot)\) \(\chi_{668}(33,\cdot)\) \(\chi_{668}(49,\cdot)\) \(\chi_{668}(57,\cdot)\) \(\chi_{668}(61,\cdot)\) \(\chi_{668}(65,\cdot)\) \(\chi_{668}(77,\cdot)\) \(\chi_{668}(81,\cdot)\) \(\chi_{668}(85,\cdot)\) \(\chi_{668}(89,\cdot)\) \(\chi_{668}(93,\cdot)\) \(\chi_{668}(97,\cdot)\) \(\chi_{668}(121,\cdot)\) \(\chi_{668}(133,\cdot)\) \(\chi_{668}(137,\cdot)\) \(\chi_{668}(141,\cdot)\) \(\chi_{668}(157,\cdot)\) \(\chi_{668}(169,\cdot)\) \(\chi_{668}(173,\cdot)\) \(\chi_{668}(181,\cdot)\) \(\chi_{668}(185,\cdot)\) \(\chi_{668}(189,\cdot)\) \(\chi_{668}(205,\cdot)\) \(\chi_{668}(209,\cdot)\) \(\chi_{668}(217,\cdot)\) \(\chi_{668}(221,\cdot)\) \(\chi_{668}(225,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((335,5)\) → \((1,e\left(\frac{75}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 668 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{73}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) |