Basic properties
Modulus: | \(8100\) | |
Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2700}(2347,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.df
\(\chi_{8100}(127,\cdot)\) \(\chi_{8100}(523,\cdot)\) \(\chi_{8100}(667,\cdot)\) \(\chi_{8100}(847,\cdot)\) \(\chi_{8100}(883,\cdot)\) \(\chi_{8100}(1063,\cdot)\) \(\chi_{8100}(1387,\cdot)\) \(\chi_{8100}(1423,\cdot)\) \(\chi_{8100}(1603,\cdot)\) \(\chi_{8100}(1747,\cdot)\) \(\chi_{8100}(1927,\cdot)\) \(\chi_{8100}(1963,\cdot)\) \(\chi_{8100}(2287,\cdot)\) \(\chi_{8100}(2467,\cdot)\) \(\chi_{8100}(2503,\cdot)\) \(\chi_{8100}(2683,\cdot)\) \(\chi_{8100}(2827,\cdot)\) \(\chi_{8100}(3223,\cdot)\) \(\chi_{8100}(3367,\cdot)\) \(\chi_{8100}(3547,\cdot)\) \(\chi_{8100}(3583,\cdot)\) \(\chi_{8100}(3763,\cdot)\) \(\chi_{8100}(4087,\cdot)\) \(\chi_{8100}(4123,\cdot)\) \(\chi_{8100}(4303,\cdot)\) \(\chi_{8100}(4447,\cdot)\) \(\chi_{8100}(4627,\cdot)\) \(\chi_{8100}(4663,\cdot)\) \(\chi_{8100}(4987,\cdot)\) \(\chi_{8100}(5167,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{17}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8100 }(4447, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{38}{45}\right)\) |