Basic properties
Modulus: | \(4235\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{605}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.de
\(\chi_{4235}(8,\cdot)\) \(\chi_{4235}(57,\cdot)\) \(\chi_{4235}(127,\cdot)\) \(\chi_{4235}(162,\cdot)\) \(\chi_{4235}(183,\cdot)\) \(\chi_{4235}(288,\cdot)\) \(\chi_{4235}(337,\cdot)\) \(\chi_{4235}(358,\cdot)\) \(\chi_{4235}(393,\cdot)\) \(\chi_{4235}(442,\cdot)\) \(\chi_{4235}(512,\cdot)\) \(\chi_{4235}(547,\cdot)\) \(\chi_{4235}(568,\cdot)\) \(\chi_{4235}(673,\cdot)\) \(\chi_{4235}(722,\cdot)\) \(\chi_{4235}(743,\cdot)\) \(\chi_{4235}(778,\cdot)\) \(\chi_{4235}(827,\cdot)\) \(\chi_{4235}(897,\cdot)\) \(\chi_{4235}(932,\cdot)\) \(\chi_{4235}(953,\cdot)\) \(\chi_{4235}(1058,\cdot)\) \(\chi_{4235}(1107,\cdot)\) \(\chi_{4235}(1128,\cdot)\) \(\chi_{4235}(1163,\cdot)\) \(\chi_{4235}(1212,\cdot)\) \(\chi_{4235}(1282,\cdot)\) \(\chi_{4235}(1317,\cdot)\) \(\chi_{4235}(1338,\cdot)\) \(\chi_{4235}(1513,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-i,1,e\left(\frac{3}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 4235 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{171}{220}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{19}{220}\right)\) |