Basic properties
| Modulus: | \(2070\) | |
| Conductor: | \(1035\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1035}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2070.bt
\(\chi_{2070}(77,\cdot)\) \(\chi_{2070}(167,\cdot)\) \(\chi_{2070}(173,\cdot)\) \(\chi_{2070}(257,\cdot)\) \(\chi_{2070}(317,\cdot)\) \(\chi_{2070}(347,\cdot)\) \(\chi_{2070}(353,\cdot)\) \(\chi_{2070}(407,\cdot)\) \(\chi_{2070}(443,\cdot)\) \(\chi_{2070}(473,\cdot)\) \(\chi_{2070}(533,\cdot)\) \(\chi_{2070}(587,\cdot)\) \(\chi_{2070}(623,\cdot)\) \(\chi_{2070}(653,\cdot)\) \(\chi_{2070}(767,\cdot)\) \(\chi_{2070}(857,\cdot)\) \(\chi_{2070}(887,\cdot)\) \(\chi_{2070}(923,\cdot)\) \(\chi_{2070}(947,\cdot)\) \(\chi_{2070}(1037,\cdot)\) \(\chi_{2070}(1067,\cdot)\) \(\chi_{2070}(1163,\cdot)\) \(\chi_{2070}(1283,\cdot)\) \(\chi_{2070}(1337,\cdot)\) \(\chi_{2070}(1343,\cdot)\) \(\chi_{2070}(1373,\cdot)\) \(\chi_{2070}(1553,\cdot)\) \(\chi_{2070}(1577,\cdot)\) \(\chi_{2070}(1613,\cdot)\) \(\chi_{2070}(1697,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((461,1657,1891)\) → \((e\left(\frac{5}{6}\right),i,e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2070 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{59}{132}\right)\) |