Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(1493,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dp
\(\chi_{8470}(107,\cdot)\) \(\chi_{8470}(123,\cdot)\) \(\chi_{8470}(193,\cdot)\) \(\chi_{8470}(277,\cdot)\) \(\chi_{8470}(303,\cdot)\) \(\chi_{8470}(347,\cdot)\) \(\chi_{8470}(387,\cdot)\) \(\chi_{8470}(513,\cdot)\) \(\chi_{8470}(557,\cdot)\) \(\chi_{8470}(613,\cdot)\) \(\chi_{8470}(667,\cdot)\) \(\chi_{8470}(767,\cdot)\) \(\chi_{8470}(877,\cdot)\) \(\chi_{8470}(893,\cdot)\) \(\chi_{8470}(963,\cdot)\) \(\chi_{8470}(1003,\cdot)\) \(\chi_{8470}(1047,\cdot)\) \(\chi_{8470}(1073,\cdot)\) \(\chi_{8470}(1117,\cdot)\) \(\chi_{8470}(1157,\cdot)\) \(\chi_{8470}(1173,\cdot)\) \(\chi_{8470}(1227,\cdot)\) \(\chi_{8470}(1283,\cdot)\) \(\chi_{8470}(1327,\cdot)\) \(\chi_{8470}(1383,\cdot)\) \(\chi_{8470}(1437,\cdot)\) \(\chi_{8470}(1493,\cdot)\) \(\chi_{8470}(1537,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{660})$ |
Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-i,e\left(\frac{1}{3}\right),e\left(\frac{23}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(1493, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{217}{660}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{131}{660}\right)\) |