Basic properties
Modulus: | \(8624\) | |
Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4312}(2325,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.fi
\(\chi_{8624}(169,\cdot)\) \(\chi_{8624}(729,\cdot)\) \(\chi_{8624}(841,\cdot)\) \(\chi_{8624}(1065,\cdot)\) \(\chi_{8624}(1401,\cdot)\) \(\chi_{8624}(2073,\cdot)\) \(\chi_{8624}(2297,\cdot)\) \(\chi_{8624}(2633,\cdot)\) \(\chi_{8624}(3193,\cdot)\) \(\chi_{8624}(3305,\cdot)\) \(\chi_{8624}(3865,\cdot)\) \(\chi_{8624}(4425,\cdot)\) \(\chi_{8624}(4537,\cdot)\) \(\chi_{8624}(4761,\cdot)\) \(\chi_{8624}(5657,\cdot)\) \(\chi_{8624}(5769,\cdot)\) \(\chi_{8624}(5993,\cdot)\) \(\chi_{8624}(6329,\cdot)\) \(\chi_{8624}(6889,\cdot)\) \(\chi_{8624}(7001,\cdot)\) \(\chi_{8624}(7225,\cdot)\) \(\chi_{8624}(7561,\cdot)\) \(\chi_{8624}(8121,\cdot)\) \(\chi_{8624}(8457,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-1,e\left(\frac{4}{7}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 8624 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) |