Basic properties
Modulus: | \(8670\) | |
Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4335}(353,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.cd
\(\chi_{8670}(353,\cdot)\) \(\chi_{8670}(497,\cdot)\) \(\chi_{8670}(863,\cdot)\) \(\chi_{8670}(1007,\cdot)\) \(\chi_{8670}(1373,\cdot)\) \(\chi_{8670}(1517,\cdot)\) \(\chi_{8670}(1883,\cdot)\) \(\chi_{8670}(2027,\cdot)\) \(\chi_{8670}(2393,\cdot)\) \(\chi_{8670}(2537,\cdot)\) \(\chi_{8670}(2903,\cdot)\) \(\chi_{8670}(3047,\cdot)\) \(\chi_{8670}(3413,\cdot)\) \(\chi_{8670}(3557,\cdot)\) \(\chi_{8670}(3923,\cdot)\) \(\chi_{8670}(4067,\cdot)\) \(\chi_{8670}(4433,\cdot)\) \(\chi_{8670}(4577,\cdot)\) \(\chi_{8670}(4943,\cdot)\) \(\chi_{8670}(5087,\cdot)\) \(\chi_{8670}(5597,\cdot)\) \(\chi_{8670}(5963,\cdot)\) \(\chi_{8670}(6473,\cdot)\) \(\chi_{8670}(6617,\cdot)\) \(\chi_{8670}(6983,\cdot)\) \(\chi_{8670}(7127,\cdot)\) \(\chi_{8670}(7493,\cdot)\) \(\chi_{8670}(7637,\cdot)\) \(\chi_{8670}(8003,\cdot)\) \(\chi_{8670}(8147,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,6937,6361)\) → \((-1,-i,e\left(\frac{13}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8670 }(353, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{31}{68}\right)\) |