Basic properties
Modulus: | \(1617\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.cc
\(\chi_{1617}(8,\cdot)\) \(\chi_{1617}(29,\cdot)\) \(\chi_{1617}(134,\cdot)\) \(\chi_{1617}(239,\cdot)\) \(\chi_{1617}(260,\cdot)\) \(\chi_{1617}(281,\cdot)\) \(\chi_{1617}(365,\cdot)\) \(\chi_{1617}(470,\cdot)\) \(\chi_{1617}(512,\cdot)\) \(\chi_{1617}(596,\cdot)\) \(\chi_{1617}(701,\cdot)\) \(\chi_{1617}(722,\cdot)\) \(\chi_{1617}(743,\cdot)\) \(\chi_{1617}(827,\cdot)\) \(\chi_{1617}(953,\cdot)\) \(\chi_{1617}(974,\cdot)\) \(\chi_{1617}(1058,\cdot)\) \(\chi_{1617}(1163,\cdot)\) \(\chi_{1617}(1184,\cdot)\) \(\chi_{1617}(1205,\cdot)\) \(\chi_{1617}(1289,\cdot)\) \(\chi_{1617}(1394,\cdot)\) \(\chi_{1617}(1415,\cdot)\) \(\chi_{1617}(1436,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{3}{7}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{70}\right)\) |