Basic properties
Modulus: | \(8020\) | |
Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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)
|
Galois orbit 8020.dg
\(\chi_{8020}(307,\cdot)\) \(\chi_{8020}(383,\cdot)\) \(\chi_{8020}(883,\cdot)\) \(\chi_{8020}(923,\cdot)\) \(\chi_{8020}(1047,\cdot)\) \(\chi_{8020}(1267,\cdot)\) \(\chi_{8020}(1303,\cdot)\) \(\chi_{8020}(1547,\cdot)\) \(\chi_{8020}(1703,\cdot)\) \(\chi_{8020}(1787,\cdot)\) \(\chi_{8020}(2223,\cdot)\) \(\chi_{8020}(2307,\cdot)\) \(\chi_{8020}(2463,\cdot)\) \(\chi_{8020}(2707,\cdot)\) \(\chi_{8020}(2743,\cdot)\) \(\chi_{8020}(2963,\cdot)\) \(\chi_{8020}(3087,\cdot)\) \(\chi_{8020}(3127,\cdot)\) \(\chi_{8020}(3627,\cdot)\) \(\chi_{8020}(3703,\cdot)\) \(\chi_{8020}(4207,\cdot)\) \(\chi_{8020}(4407,\cdot)\) \(\chi_{8020}(4527,\cdot)\) \(\chi_{8020}(4663,\cdot)\) \(\chi_{8020}(4763,\cdot)\) \(\chi_{8020}(5103,\cdot)\) \(\chi_{8020}(5123,\cdot)\) \(\chi_{8020}(5683,\cdot)\) \(\chi_{8020}(5707,\cdot)\) \(\chi_{8020}(5727,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4011,6417,7221)\) → \((-1,i,e\left(\frac{11}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 8020 }(307, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) |