Basic properties
Modulus: | \(4235\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 4235.dd
\(\chi_{4235}(48,\cdot)\) \(\chi_{4235}(97,\cdot)\) \(\chi_{4235}(223,\cdot)\) \(\chi_{4235}(258,\cdot)\) \(\chi_{4235}(328,\cdot)\) \(\chi_{4235}(377,\cdot)\) \(\chi_{4235}(412,\cdot)\) \(\chi_{4235}(433,\cdot)\) \(\chi_{4235}(482,\cdot)\) \(\chi_{4235}(587,\cdot)\) \(\chi_{4235}(643,\cdot)\) \(\chi_{4235}(713,\cdot)\) \(\chi_{4235}(762,\cdot)\) \(\chi_{4235}(797,\cdot)\) \(\chi_{4235}(818,\cdot)\) \(\chi_{4235}(867,\cdot)\) \(\chi_{4235}(972,\cdot)\) \(\chi_{4235}(993,\cdot)\) \(\chi_{4235}(1028,\cdot)\) \(\chi_{4235}(1147,\cdot)\) \(\chi_{4235}(1182,\cdot)\) \(\chi_{4235}(1203,\cdot)\) \(\chi_{4235}(1252,\cdot)\) \(\chi_{4235}(1357,\cdot)\) \(\chi_{4235}(1378,\cdot)\) \(\chi_{4235}(1413,\cdot)\) \(\chi_{4235}(1483,\cdot)\) \(\chi_{4235}(1532,\cdot)\) \(\chi_{4235}(1567,\cdot)\) \(\chi_{4235}(1588,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-i,-1,e\left(\frac{42}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 4235 }(643, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{220}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{147}{220}\right)\) |