Basic properties
Modulus: | \(9196\) | |
Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2299}(1766,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9196.cr
\(\chi_{9196}(189,\cdot)\) \(\chi_{9196}(569,\cdot)\) \(\chi_{9196}(721,\cdot)\) \(\chi_{9196}(1025,\cdot)\) \(\chi_{9196}(1405,\cdot)\) \(\chi_{9196}(1481,\cdot)\) \(\chi_{9196}(1557,\cdot)\) \(\chi_{9196}(1861,\cdot)\) \(\chi_{9196}(2241,\cdot)\) \(\chi_{9196}(2317,\cdot)\) \(\chi_{9196}(2697,\cdot)\) \(\chi_{9196}(3077,\cdot)\) \(\chi_{9196}(3153,\cdot)\) \(\chi_{9196}(3229,\cdot)\) \(\chi_{9196}(3533,\cdot)\) \(\chi_{9196}(3913,\cdot)\) \(\chi_{9196}(3989,\cdot)\) \(\chi_{9196}(4065,\cdot)\) \(\chi_{9196}(4369,\cdot)\) \(\chi_{9196}(4749,\cdot)\) \(\chi_{9196}(4825,\cdot)\) \(\chi_{9196}(4901,\cdot)\) \(\chi_{9196}(5205,\cdot)\) \(\chi_{9196}(5585,\cdot)\) \(\chi_{9196}(5661,\cdot)\) \(\chi_{9196}(5737,\cdot)\) \(\chi_{9196}(6421,\cdot)\) \(\chi_{9196}(6497,\cdot)\) \(\chi_{9196}(6573,\cdot)\) \(\chi_{9196}(6877,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((4599,3269,8229)\) → \((1,e\left(\frac{69}{110}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 9196 }(4065, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{46}{55}\right)\) |