Basic properties
Modulus: | \(9702\) | |
Conductor: | \(1617\) | 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 \(\chi_{1617}(701,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.es
\(\chi_{9702}(701,\cdot)\) \(\chi_{9702}(827,\cdot)\) \(\chi_{9702}(953,\cdot)\) \(\chi_{9702}(1205,\cdot)\) \(\chi_{9702}(2087,\cdot)\) \(\chi_{9702}(2213,\cdot)\) \(\chi_{9702}(2339,\cdot)\) \(\chi_{9702}(2591,\cdot)\) \(\chi_{9702}(3473,\cdot)\) \(\chi_{9702}(3599,\cdot)\) \(\chi_{9702}(3977,\cdot)\) \(\chi_{9702}(4859,\cdot)\) \(\chi_{9702}(4985,\cdot)\) \(\chi_{9702}(5111,\cdot)\) \(\chi_{9702}(5363,\cdot)\) \(\chi_{9702}(6245,\cdot)\) \(\chi_{9702}(6497,\cdot)\) \(\chi_{9702}(6749,\cdot)\) \(\chi_{9702}(7631,\cdot)\) \(\chi_{9702}(7757,\cdot)\) \(\chi_{9702}(7883,\cdot)\) \(\chi_{9702}(9143,\cdot)\) \(\chi_{9702}(9269,\cdot)\) \(\chi_{9702}(9521,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4313,199,5293)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 9702 }(701, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) |