Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 8041 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 840 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 8041.fw |
| Orbit index | = | 153 |
Galois orbit
\(\chi_{8041}(19,\cdot)\) \(\chi_{8041}(134,\cdot)\) \(\chi_{8041}(162,\cdot)\) \(\chi_{8041}(206,\cdot)\) \(\chi_{8041}(270,\cdot)\) \(\chi_{8041}(304,\cdot)\) \(\chi_{8041}(321,\cdot)\) \(\chi_{8041}(349,\cdot)\) \(\chi_{8041}(491,\cdot)\) \(\chi_{8041}(501,\cdot)\) \(\chi_{8041}(502,\cdot)\) \(\chi_{8041}(519,\cdot)\) \(\chi_{8041}(535,\cdot)\) \(\chi_{8041}(536,\cdot)\) \(\chi_{8041}(546,\cdot)\) \(\chi_{8041}(678,\cdot)\) \(\chi_{8041}(706,\cdot)\) \(\chi_{8041}(722,\cdot)\) \(\chi_{8041}(750,\cdot)\) \(\chi_{8041}(865,\cdot)\) \(\chi_{8041}(886,\cdot)\) \(\chi_{8041}(893,\cdot)\) \(\chi_{8041}(937,\cdot)\) \(\chi_{8041}(1018,\cdot)\) \(\chi_{8041}(1052,\cdot)\) \(\chi_{8041}(1062,\cdot)\) \(\chi_{8041}(1080,\cdot)\) \(\chi_{8041}(1130,\cdot)\) \(\chi_{8041}(1216,\cdot)\) \(\chi_{8041}(1250,\cdot)\) ...
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{7}{8}\right),e\left(\frac{19}{42}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 |
| \(1\) | \(1\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{611}{840}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{743}{840}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{191}{420}\right)\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{43}{168}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{840})\) |