Basic properties
| Modulus: | \(810\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{405}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 810.w
\(\chi_{810}(23,\cdot)\) \(\chi_{810}(47,\cdot)\) \(\chi_{810}(77,\cdot)\) \(\chi_{810}(83,\cdot)\) \(\chi_{810}(113,\cdot)\) \(\chi_{810}(137,\cdot)\) \(\chi_{810}(167,\cdot)\) \(\chi_{810}(173,\cdot)\) \(\chi_{810}(203,\cdot)\) \(\chi_{810}(227,\cdot)\) \(\chi_{810}(257,\cdot)\) \(\chi_{810}(263,\cdot)\) \(\chi_{810}(293,\cdot)\) \(\chi_{810}(317,\cdot)\) \(\chi_{810}(347,\cdot)\) \(\chi_{810}(353,\cdot)\) \(\chi_{810}(383,\cdot)\) \(\chi_{810}(407,\cdot)\) \(\chi_{810}(437,\cdot)\) \(\chi_{810}(443,\cdot)\) \(\chi_{810}(473,\cdot)\) \(\chi_{810}(497,\cdot)\) \(\chi_{810}(527,\cdot)\) \(\chi_{810}(533,\cdot)\) \(\chi_{810}(563,\cdot)\) \(\chi_{810}(587,\cdot)\) \(\chi_{810}(617,\cdot)\) \(\chi_{810}(623,\cdot)\) \(\chi_{810}(653,\cdot)\) \(\chi_{810}(677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((731,487)\) → \((e\left(\frac{11}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 810 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{43}{54}\right)\) |