Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.eu
\(\chi_{8018}(3,\cdot)\) \(\chi_{8018}(29,\cdot)\) \(\chi_{8018}(155,\cdot)\) \(\chi_{8018}(167,\cdot)\) \(\chi_{8018}(181,\cdot)\) \(\chi_{8018}(205,\cdot)\) \(\chi_{8018}(317,\cdot)\) \(\chi_{8018}(319,\cdot)\) \(\chi_{8018}(363,\cdot)\) \(\chi_{8018}(371,\cdot)\) \(\chi_{8018}(375,\cdot)\) \(\chi_{8018}(439,\cdot)\) \(\chi_{8018}(497,\cdot)\) \(\chi_{8018}(553,\cdot)\) \(\chi_{8018}(751,\cdot)\) \(\chi_{8018}(763,\cdot)\) \(\chi_{8018}(971,\cdot)\) \(\chi_{8018}(1003,\cdot)\) \(\chi_{8018}(1009,\cdot)\) \(\chi_{8018}(1219,\cdot)\) \(\chi_{8018}(1307,\cdot)\) \(\chi_{8018}(1351,\cdot)\) \(\chi_{8018}(1457,\cdot)\) \(\chi_{8018}(1473,\cdot)\) \(\chi_{8018}(1549,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{315})$ |
Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{43}{210}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{315}\right)\) | \(e\left(\frac{184}{315}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{122}{315}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{61}{630}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{611}{630}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) |