Basic properties
Modulus: | \(9702\) | |
Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4851}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fy
\(\chi_{9702}(29,\cdot)\) \(\chi_{9702}(239,\cdot)\) \(\chi_{9702}(281,\cdot)\) \(\chi_{9702}(365,\cdot)\) \(\chi_{9702}(743,\cdot)\) \(\chi_{9702}(1163,\cdot)\) \(\chi_{9702}(1289,\cdot)\) \(\chi_{9702}(1415,\cdot)\) \(\chi_{9702}(1625,\cdot)\) \(\chi_{9702}(1751,\cdot)\) \(\chi_{9702}(1877,\cdot)\) \(\chi_{9702}(2129,\cdot)\) \(\chi_{9702}(2675,\cdot)\) \(\chi_{9702}(2801,\cdot)\) \(\chi_{9702}(3011,\cdot)\) \(\chi_{9702}(3053,\cdot)\) \(\chi_{9702}(3263,\cdot)\) \(\chi_{9702}(3515,\cdot)\) \(\chi_{9702}(3935,\cdot)\) \(\chi_{9702}(4061,\cdot)\) \(\chi_{9702}(4187,\cdot)\) \(\chi_{9702}(4397,\cdot)\) \(\chi_{9702}(4439,\cdot)\) \(\chi_{9702}(4523,\cdot)\) \(\chi_{9702}(4649,\cdot)\) \(\chi_{9702}(5321,\cdot)\) \(\chi_{9702}(5447,\cdot)\) \(\chi_{9702}(5573,\cdot)\) \(\chi_{9702}(5825,\cdot)\) \(\chi_{9702}(5909,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{7}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 9702 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{210}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) |