Basic properties
| Modulus: | \(100010\) | |
| Conductor: | \(73\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{73}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100010.ks
\(\chi_{100010}(2741,\cdot)\) \(\chi_{100010}(6851,\cdot)\) \(\chi_{100010}(8221,\cdot)\) \(\chi_{100010}(9591,\cdot)\) \(\chi_{100010}(10961,\cdot)\) \(\chi_{100010}(15071,\cdot)\) \(\chi_{100010}(24661,\cdot)\) \(\chi_{100010}(27401,\cdot)\) \(\chi_{100010}(32881,\cdot)\) \(\chi_{100010}(34251,\cdot)\) \(\chi_{100010}(36991,\cdot)\) \(\chi_{100010}(42471,\cdot)\) \(\chi_{100010}(50691,\cdot)\) \(\chi_{100010}(53431,\cdot)\) \(\chi_{100010}(56171,\cdot)\) \(\chi_{100010}(61651,\cdot)\) \(\chi_{100010}(64391,\cdot)\) \(\chi_{100010}(67131,\cdot)\) \(\chi_{100010}(75351,\cdot)\) \(\chi_{100010}(80831,\cdot)\) \(\chi_{100010}(83571,\cdot)\) \(\chi_{100010}(84941,\cdot)\) \(\chi_{100010}(90421,\cdot)\) \(\chi_{100010}(93161,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((60007,64391,97821)\) → \((1,e\left(\frac{1}{72}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 100010 }(64391, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(i\) |