Basic properties
| Modulus: | \(9702\) | |
| Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4851}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9702.fc
\(\chi_{9702}(61,\cdot)\) \(\chi_{9702}(283,\cdot)\) \(\chi_{9702}(409,\cdot)\) \(\chi_{9702}(535,\cdot)\) \(\chi_{9702}(787,\cdot)\) \(\chi_{9702}(943,\cdot)\) \(\chi_{9702}(1069,\cdot)\) \(\chi_{9702}(1447,\cdot)\) \(\chi_{9702}(1669,\cdot)\) \(\chi_{9702}(1921,\cdot)\) \(\chi_{9702}(2173,\cdot)\) \(\chi_{9702}(2329,\cdot)\) \(\chi_{9702}(2455,\cdot)\) \(\chi_{9702}(2581,\cdot)\) \(\chi_{9702}(2833,\cdot)\) \(\chi_{9702}(3055,\cdot)\) \(\chi_{9702}(3181,\cdot)\) \(\chi_{9702}(3307,\cdot)\) \(\chi_{9702}(3715,\cdot)\) \(\chi_{9702}(3967,\cdot)\) \(\chi_{9702}(4219,\cdot)\) \(\chi_{9702}(4567,\cdot)\) \(\chi_{9702}(4693,\cdot)\) \(\chi_{9702}(4945,\cdot)\) \(\chi_{9702}(5101,\cdot)\) \(\chi_{9702}(5227,\cdot)\) \(\chi_{9702}(5353,\cdot)\) \(\chi_{9702}(5827,\cdot)\) \(\chi_{9702}(5953,\cdot)\) \(\chi_{9702}(6079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,5293)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9702 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) |