LMFDB - Embedded newform 2028.2.q.h.1837.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2028,2,Mod(361,2028)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2028, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2028.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2028 = 2^{2} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2028.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.1936615299$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1837.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2028.1837
Dual form			2028.2.q.h.361.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +4.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +4.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.46410 + 2.00000i) q^{11} +(3.46410 + 2.00000i) q^{15} +(1.00000 + 1.73205i) q^{17} +(1.73205 - 1.00000i) q^{19} +2.00000i q^{21} -11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} +10.0000i q^{31} +(3.46410 - 2.00000i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(-8.66025 - 5.00000i) q^{37} +(6.92820 + 4.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} +(3.46410 - 2.00000i) q^{45} -4.00000i q^{47} +(-1.50000 + 2.59808i) q^{49} +2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} -2.00000i q^{57} +(-6.92820 + 4.00000i) q^{59} +(7.00000 + 12.1244i) q^{61} +(1.73205 + 1.00000i) q^{63} +(1.73205 + 1.00000i) q^{67} +(-13.8564 + 8.00000i) q^{71} -10.0000i q^{73} +(-5.50000 + 9.52628i) q^{75} -8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.92820 + 4.00000i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(3.46410 + 2.00000i) q^{89} +(8.66025 + 5.00000i) q^{93} +(4.00000 + 6.92820i) q^{95} +(1.73205 - 1.00000i) q^{97} -4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{9} + 4 q^{17} - 44 q^{25} - 4 q^{27} + 12 q^{29} - 16 q^{35} + 8 q^{43} - 6 q^{49} + 8 q^{51} - 40 q^{53} - 32 q^{55} + 28 q^{61} - 22 q^{75} - 32 q^{77} - 64 q^{79} - 2 q^{81} - 12 q^{87} + 16 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^9 + 4 * q^17 - 44 * q^25 - 4 * q^27 + 12 * q^29 - 16 * q^35 + 8 * q^43 - 6 * q^49 + 8 * q^51 - 40 * q^53 - 32 * q^55 + 28 * q^61 - 22 * q^75 - 32 * q^77 - 64 * q^79 - 2 * q^81 - 12 * q^87 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1861$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$			4.00000i			1.78885i	0.447214	+	0.894427i	$0.352416\pi$
$5$			4.00000i			1.78885i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.46410	+	2.00000i	1.04447	+	0.603023i	0.921095	−	0.389338i	$-0.127296\pi$
$11$	3.46410	+	2.00000i	1.04447	+	0.603023i	0.123371	+	0.992361i	$0.460630\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	3.46410	+	2.00000i	0.894427	+	0.516398i
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	1.73205	−	1.00000i	0.397360	−	0.229416i	−0.287984	−	0.957635i	$-0.592985\pi$
$19$	1.73205	−	1.00000i	0.397360	−	0.229416i	0.685344	+	0.728219i	$0.259652\pi$
$20$		0			0
$21$			2.00000i			0.436436i
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−11.0000			−2.20000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$		0			0
$33$	3.46410	−	2.00000i	0.603023	−	0.348155i
$34$		0			0
$35$	−4.00000	−	6.92820i	−0.676123	−	1.17108i
$36$		0			0
$37$	−8.66025	−	5.00000i	−1.42374	−	0.821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	−8.66025	−	5.00000i	−1.42374	−	0.821995i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.92820	+	4.00000i	1.08200	+	0.624695i	0.931436	−	0.363905i	$-0.118557\pi$
$41$	6.92820	+	4.00000i	1.08200	+	0.624695i	0.150567	+	0.988600i	$0.451890\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$		0			0
$45$	3.46410	−	2.00000i	0.516398	−	0.298142i
$46$		0			0
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		0			0
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$	2.00000			0.280056
$52$		0			0
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$	−8.00000	+	13.8564i	−1.07872	+	1.86840i
$56$		0			0
$57$		−	2.00000i		−	0.264906i
$58$		0			0
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	0.602056	−	0.798454i	$-0.294348\pi$
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	−0.390453	+	0.920623i	$0.627682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.8564	+	8.00000i	−1.64445	+	0.949425i	−0.665230	+	0.746639i	$0.731667\pi$
$71$	−13.8564	+	8.00000i	−1.64445	+	0.949425i	−0.979223	+	0.202787i	$0.935000\pi$
$72$		0			0
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$		0			0
$75$	−5.50000	+	9.52628i	−0.635085	+	1.10000i
$76$		0			0
$77$	−8.00000			−0.911685
$78$		0			0
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	−6.92820	+	4.00000i	−0.751469	+	0.433861i
$86$		0			0
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	3.46410	+	2.00000i	0.367194	+	0.212000i	0.672232	−	0.740341i	$-0.265336\pi$
$89$	3.46410	+	2.00000i	0.367194	+	0.212000i	−0.305038	+	0.952340i	$0.598669\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	8.66025	+	5.00000i	0.898027	+	0.518476i
$94$		0			0
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$		0			0
$99$		−	4.00000i		−	0.402015i
$100$		0			0
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	−8.66025	+	5.00000i	−0.821995	+	0.474579i
$112$		0			0
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.46410	−	2.00000i	−0.317554	−	0.183340i
$120$		0			0
$121$	2.50000	+	4.33013i	0.227273	+	0.393648i
$122$		0			0
$123$	6.92820	−	4.00000i	0.624695	−	0.360668i
$124$		0			0
$125$		−	24.0000i		−	2.14663i
$126$		0			0
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	−0.466870	−	0.884326i	$-0.654618\pi$
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	0.999284	−	0.0378419i	$-0.0120483\pi$
$128$		0			0
$129$	4.00000			0.352180
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$		0			0
$135$		−	4.00000i		−	0.344265i
$136$		0			0
$137$	6.92820	−	4.00000i	0.591916	−	0.341743i	−0.173939	−	0.984757i	$-0.555649\pi$
$137$	6.92820	−	4.00000i	0.591916	−	0.341743i	0.765855	+	0.643013i	$0.222316\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	−3.46410	−	2.00000i	−0.291730	−	0.168430i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	20.7846	+	12.0000i	1.72607	+	0.996546i
$146$		0			0
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$		0			0
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$		0			0
$155$	−40.0000			−3.21288
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.73205	−	1.00000i	0.135665	−	0.0783260i	−0.430632	−	0.902528i	$-0.641709\pi$
$163$	1.73205	−	1.00000i	0.135665	−	0.0783260i	0.566296	+	0.824202i	$0.308376\pi$
$164$		0			0
$165$	8.00000	+	13.8564i	0.622799	+	1.07872i
$166$		0			0
$167$	10.3923	+	6.00000i	0.804181	+	0.464294i	0.844931	−	0.534875i	$-0.179641\pi$
$167$	10.3923	+	6.00000i	0.804181	+	0.464294i	−0.0407502	+	0.999169i	$0.512975\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−1.73205	−	1.00000i	−0.132453	−	0.0764719i
$172$		0			0
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	−0.825505	+	0.564396i	$0.809109\pi$
$174$		0			0
$175$	19.0526	−	11.0000i	1.44024	−	0.831522i
$176$		0			0
$177$			8.00000i			0.601317i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$	20.0000	−	34.6410i	1.47043	−	2.54686i
$186$		0			0
$187$			8.00000i			0.585018i
$188$		0			0
$189$	1.73205	−	1.00000i	0.125988	−	0.0727393i
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.868255	−	0.496119i	$-0.165242\pi$
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.00447566	+	0.999990i	$0.498575\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.3923	−	6.00000i	−0.740421	−	0.427482i	0.0818013	−	0.996649i	$-0.473933\pi$
$197$	−10.3923	−	6.00000i	−0.740421	−	0.427482i	−0.822222	+	0.569166i	$0.807266\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	1.73205	−	1.00000i	0.122169	−	0.0705346i
$202$		0			0
$203$			12.0000i			0.842235i
$204$		0			0
$205$	−16.0000	+	27.7128i	−1.11749	+	1.93555i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$		0			0
$213$			16.0000i			1.09630i
$214$		0			0
$215$	−13.8564	+	8.00000i	−0.944999	+	0.545595i
$216$		0			0
$217$	−10.0000	−	17.3205i	−0.678844	−	1.17579i
$218$		0			0
$219$	−8.66025	−	5.00000i	−0.585206	−	0.337869i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	12.1244	+	7.00000i	0.811907	+	0.468755i	0.847618	−	0.530607i	$-0.178036\pi$
$223$	12.1244	+	7.00000i	0.811907	+	0.468755i	−0.0357107	+	0.999362i	$0.511370\pi$
$224$		0			0
$225$	5.50000	+	9.52628i	0.366667	+	0.635085i
$226$		0			0
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	−0.380615	−	0.924734i	$-0.624288\pi$
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	0.610535	+	0.791989i	$0.290954\pi$
$228$		0			0
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$		0			0
$231$	−4.00000	+	6.92820i	−0.263181	+	0.455842i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$		0			0
$237$	−8.00000	+	13.8564i	−0.519656	+	0.900070i
$238$		0			0
$239$			24.0000i			1.55243i	0.630468	+	0.776215i	$0.282863\pi$
$239$			24.0000i			1.55243i	−0.630468	+	0.776215i	$0.717137\pi$
$240$		0			0
$241$	−1.73205	+	1.00000i	−0.111571	+	0.0644157i	−0.554747	−	0.832019i	$-0.687185\pi$
$241$	−1.73205	+	1.00000i	−0.111571	+	0.0644157i	0.443176	+	0.896435i	$0.353852\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−10.3923	−	6.00000i	−0.663940	−	0.383326i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.0000	−	17.3205i	−0.631194	−	1.09326i	−0.987308	−	0.158818i	$-0.949232\pi$
$251$	−10.0000	−	17.3205i	−0.631194	−	1.09326i	0.356113	−	0.934443i	$-0.384102\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$			8.00000i			0.500979i
$256$		0			0
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$		0			0
$259$	20.0000			1.24274
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$		−	40.0000i		−	2.45718i
$266$		0			0
$267$	3.46410	−	2.00000i	0.212000	−	0.122398i
$268$		0			0
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	8.66025	+	5.00000i	0.526073	+	0.303728i	0.739416	−	0.673249i	$-0.235102\pi$
$271$	8.66025	+	5.00000i	0.526073	+	0.303728i	−0.213343	+	0.976977i	$0.568435\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−38.1051	−	22.0000i	−2.29783	−	1.32665i
$276$		0			0
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$		0			0
$279$	8.66025	−	5.00000i	0.518476	−	0.299342i
$280$		0			0
$281$		−	8.00000i		−	0.477240i	−0.971113	−	0.238620i	$-0.923305\pi$
$281$		−	8.00000i		−	0.477240i	0.971113	−	0.238620i	$-0.0766950\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$		0			0
$285$	8.00000			0.473879
$286$		0			0
$287$	−16.0000			−0.944450
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		−	2.00000i		−	0.117242i
$292$		0			0
$293$	6.92820	−	4.00000i	0.404750	−	0.233682i	−0.283782	−	0.958889i	$-0.591589\pi$
$293$	6.92820	−	4.00000i	0.404750	−	0.233682i	0.688531	+	0.725206i	$0.258256\pi$
$294$		0			0
$295$	−16.0000	−	27.7128i	−0.931556	−	1.61350i
$296$		0			0
$297$	−3.46410	−	2.00000i	−0.201008	−	0.116052i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−6.92820	−	4.00000i	−0.399335	−	0.230556i
$302$		0			0
$303$	−5.00000	−	8.66025i	−0.287242	−	0.497519i
$304$		0			0
$305$	−48.4974	+	28.0000i	−2.77695	+	1.60328i
$306$		0			0
$307$			22.0000i			1.25561i	0.778372	+	0.627803i	$0.216046\pi$
$307$			22.0000i			1.25561i	−0.778372	+	0.627803i	$0.783954\pi$
$308$		0			0
$309$	4.00000	−	6.92820i	0.227552	−	0.394132i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$	−4.00000	+	6.92820i	−0.225374	+	0.390360i
$316$		0			0
$317$			12.0000i			0.673987i	0.941507	+	0.336994i	$0.109410\pi$
$317$			12.0000i			0.673987i	−0.941507	+	0.336994i	$0.890590\pi$
$318$		0			0
$319$	20.7846	−	12.0000i	1.16371	−	0.671871i
$320$		0			0
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	3.46410	+	2.00000i	0.192748	+	0.111283i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.73205	+	1.00000i	0.0957826	+	0.0553001i
$328$		0			0
$329$	4.00000	+	6.92820i	0.220527	+	0.381964i
$330$		0			0
$331$	−1.73205	+	1.00000i	−0.0952021	+	0.0549650i	−0.546845	−	0.837234i	$-0.684171\pi$
$331$	−1.73205	+	1.00000i	−0.0952021	+	0.0549650i	0.451643	+	0.892199i	$0.350838\pi$
$332$		0			0
$333$			10.0000i			0.547997i
$334$		0			0
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	30.0000			1.63420			0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000			1.63420			0.817102	+	0.576493i	$0.195579\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$		0			0
$341$	−20.0000	+	34.6410i	−1.08306	+	1.87592i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	−15.5885	−	9.00000i	−0.834431	−	0.481759i	0.0209364	−	0.999781i	$-0.493335\pi$
$349$	−15.5885	−	9.00000i	−0.834431	−	0.481759i	−0.855367	+	0.518022i	$0.826669\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.8564	−	8.00000i	−0.737502	−	0.425797i	0.0836583	−	0.996495i	$-0.473340\pi$
$353$	−13.8564	−	8.00000i	−0.737502	−	0.425797i	−0.821160	+	0.570697i	$0.806673\pi$
$354$		0			0
$355$	−32.0000	−	55.4256i	−1.69838	−	2.94169i
$356$		0			0
$357$	−3.46410	+	2.00000i	−0.183340	+	0.105851i
$358$		0			0
$359$		−	12.0000i		−	0.633336i	−0.948536	−	0.316668i	$-0.897436\pi$
$359$		−	12.0000i		−	0.633336i	0.948536	−	0.316668i	$-0.102564\pi$
$360$		0			0
$361$	−7.50000	+	12.9904i	−0.394737	+	0.683704i
$362$		0			0
$363$	5.00000			0.262432
$364$		0			0
$365$	40.0000			2.09370
$366$		0			0
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$		−	8.00000i		−	0.416463i
$370$		0			0
$371$	17.3205	−	10.0000i	0.899236	−	0.519174i
$372$		0			0
$373$	9.00000	+	15.5885i	0.466002	+	0.807140i	0.999246	−	0.0388219i	$-0.0123605\pi$
$373$	9.00000	+	15.5885i	0.466002	+	0.807140i	−0.533244	+	0.845962i	$0.679027\pi$
$374$		0			0
$375$	−20.7846	−	12.0000i	−1.07331	−	0.619677i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	5.19615	+	3.00000i	0.266908	+	0.154100i	0.627482	−	0.778631i	$-0.284086\pi$
$379$	5.19615	+	3.00000i	0.266908	+	0.154100i	−0.360573	+	0.932731i	$0.617419\pi$
$380$		0			0
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$		0			0
$383$	−10.3923	+	6.00000i	−0.531022	+	0.306586i	−0.741433	−	0.671027i	$-0.765853\pi$
$383$	−10.3923	+	6.00000i	−0.531022	+	0.306586i	0.210411	+	0.977613i	$0.432520\pi$
$384$		0			0
$385$		−	32.0000i		−	1.63087i
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$		0			0
$389$	26.0000			1.31825			0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000			1.31825			0.659126	+	0.752032i	$0.270926\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	2.00000	−	3.46410i	0.100887	−	0.174741i
$394$		0			0
$395$		−	64.0000i		−	3.22019i
$396$		0			0
$397$	15.5885	−	9.00000i	0.782362	−	0.451697i	−0.0549046	−	0.998492i	$-0.517485\pi$
$397$	15.5885	−	9.00000i	0.782362	−	0.451697i	0.837267	+	0.546795i	$0.184152\pi$
$398$		0			0
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$		0			0
$401$	10.3923	+	6.00000i	0.518967	+	0.299626i	0.736512	−	0.676425i	$-0.236472\pi$
$401$	10.3923	+	6.00000i	0.518967	+	0.299626i	−0.217545	+	0.976050i	$0.569805\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−3.46410	−	2.00000i	−0.172133	−	0.0993808i
$406$		0			0
$407$	−20.0000	−	34.6410i	−0.991363	−	1.71709i
$408$		0			0
$409$	−12.1244	+	7.00000i	−0.599511	+	0.346128i	−0.768849	−	0.639430i	$-0.779170\pi$
$409$	−12.1244	+	7.00000i	−0.599511	+	0.346128i	0.169338	+	0.985558i	$0.445837\pi$
$410$		0			0
$411$		−	8.00000i		−	0.394611i
$412$		0			0
$413$	8.00000	−	13.8564i	0.393654	−	0.681829i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	−0.511381	−	0.859354i	$-0.670866\pi$
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	0.999913	+	0.0131919i	$0.00419923\pi$
$420$		0			0
$421$			2.00000i			0.0974740i	0.998812	+	0.0487370i	$0.0155196\pi$
$421$			2.00000i			0.0974740i	−0.998812	+	0.0487370i	$0.984480\pi$
$422$		0			0
$423$	−3.46410	+	2.00000i	−0.168430	+	0.0972433i
$424$		0			0
$425$	−11.0000	−	19.0526i	−0.533578	−	0.924185i
$426$		0			0
$427$	−24.2487	−	14.0000i	−1.17348	−	0.677507i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.3205	−	10.0000i	−0.834300	−	0.481683i	0.0210230	−	0.999779i	$-0.493308\pi$
$431$	−17.3205	−	10.0000i	−0.834300	−	0.481683i	−0.855323	+	0.518096i	$0.826641\pi$
$432$		0			0
$433$	−9.00000	−	15.5885i	−0.432512	−	0.749133i	0.564577	−	0.825381i	$-0.309039\pi$
$433$	−9.00000	−	15.5885i	−0.432512	−	0.749133i	−0.997089	+	0.0762473i	$0.975706\pi$
$434$		0			0
$435$	20.7846	−	12.0000i	0.996546	−	0.575356i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$		0			0
$445$	−8.00000	+	13.8564i	−0.379236	+	0.656857i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	10.3923	−	6.00000i	0.490443	−	0.283158i	−0.234315	−	0.972161i	$-0.575285\pi$
$449$	10.3923	−	6.00000i	0.490443	−	0.283158i	0.724758	+	0.689003i	$0.241951\pi$
$450$		0			0
$451$	16.0000	+	27.7128i	0.753411	+	1.30495i
$452$		0			0
$453$	15.5885	+	9.00000i	0.732410	+	0.422857i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	0.0889312	−	0.996038i	$-0.471655\pi$
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	−0.818128	+	0.575036i	$0.804988\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	−10.3923	+	6.00000i	−0.484018	+	0.279448i	−0.722089	−	0.691800i	$-0.756818\pi$
$461$	−10.3923	+	6.00000i	−0.484018	+	0.279448i	0.238071	+	0.971248i	$0.423485\pi$
$462$		0			0
$463$			22.0000i			1.02243i	0.859454	+	0.511213i	$0.170804\pi$
$463$			22.0000i			1.02243i	−0.859454	+	0.511213i	$0.829196\pi$
$464$		0			0
$465$	−20.0000	+	34.6410i	−0.927478	+	1.60644i
$466$		0			0
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$		0			0
$473$			16.0000i			0.735681i
$474$		0			0
$475$	−19.0526	+	11.0000i	−0.874191	+	0.504715i
$476$		0			0
$477$	5.00000	+	8.66025i	0.228934	+	0.396526i
$478$		0			0
$479$	13.8564	+	8.00000i	0.633115	+	0.365529i	0.781958	−	0.623332i	$-0.214221\pi$
$479$	13.8564	+	8.00000i	0.633115	+	0.365529i	−0.148842	+	0.988861i	$0.547555\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$		0			0
$487$	22.5167	−	13.0000i	1.02033	−	0.589086i	0.106129	−	0.994352i	$-0.466154\pi$
$487$	22.5167	−	13.0000i	1.02033	−	0.589086i	0.914199	+	0.405266i	$0.132821\pi$
$488$		0			0
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$		0			0
$493$	12.0000			0.540453
$494$		0			0
$495$	16.0000			0.719147
$496$		0			0
$497$	16.0000	−	27.7128i	0.717698	−	1.24309i
$498$		0			0
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$		0			0
$501$	10.3923	−	6.00000i	0.464294	−	0.268060i
$502$		0			0
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	0.630705	−	0.776022i	$-0.282766\pi$
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	−0.987408	+	0.158196i	$0.949432\pi$
$504$		0			0
$505$	34.6410	+	20.0000i	1.54150	+	0.889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.3923	+	6.00000i	0.460631	+	0.265945i	0.712309	−	0.701866i	$-0.247649\pi$
$509$	10.3923	+	6.00000i	0.460631	+	0.265945i	−0.251679	+	0.967811i	$0.580983\pi$
$510$		0			0
$511$	10.0000	+	17.3205i	0.442374	+	0.766214i
$512$		0			0
$513$	−1.73205	+	1.00000i	−0.0764719	+	0.0441511i
$514$		0			0
$515$			32.0000i			1.41009i
$516$		0			0
$517$	8.00000	−	13.8564i	0.351840	−	0.609404i
$518$		0			0
$519$	2.00000			0.0877903
$520$		0			0
$521$	−2.00000			−0.0876216			−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000			−0.0876216			−0.0438108	+	0.999040i	$0.513950\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$		0			0
$525$		−	22.0000i		−	0.960159i
$526$		0			0
$527$	−17.3205	+	10.0000i	−0.754493	+	0.435607i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	6.92820	+	4.00000i	0.300658	+	0.173585i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−41.5692	−	24.0000i	−1.79719	−	1.03761i
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	−10.3923	+	6.00000i	−0.447628	+	0.258438i
$540$		0			0
$541$			38.0000i			1.63375i	0.576816	+	0.816874i	$0.304295\pi$
$541$			38.0000i			1.63375i	−0.576816	+	0.816874i	$0.695705\pi$
$542$		0			0
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$		0			0
$545$	−8.00000			−0.342682
$546$		0			0
$547$	32.0000			1.36822			0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000			1.36822			0.684111	+	0.729378i	$0.260191\pi$
$548$		0			0
$549$	7.00000	−	12.1244i	0.298753	−	0.517455i
$550$		0			0
$551$		−	12.0000i		−	0.511217i
$552$		0			0
$553$	27.7128	−	16.0000i	1.17847	−	0.680389i
$554$		0			0
$555$	−20.0000	−	34.6410i	−0.848953	−	1.47043i
$556$		0			0
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.00979220	−	0.999952i	$-0.503117\pi$
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.870880	+	0.491496i	$0.836450\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	6.92820	+	4.00000i	0.292509	+	0.168880i
$562$		0			0
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	0.994228	+	0.107290i	$0.0342173\pi$
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	−0.404198	+	0.914671i	$0.632449\pi$
$564$		0			0
$565$	20.7846	−	12.0000i	0.874415	−	0.504844i
$566$		0			0
$567$		−	2.00000i		−	0.0839921i
$568$		0			0
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$		0			0
$575$		0			0
$576$		0			0
$577$			30.0000i			1.24892i	0.781058	+	0.624458i	$0.214680\pi$
$577$			30.0000i			1.24892i	−0.781058	+	0.624458i	$0.785320\pi$
$578$		0			0
$579$	12.1244	−	7.00000i	0.503871	−	0.290910i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−34.6410	−	20.0000i	−1.43468	−	0.828315i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.92820	−	4.00000i	−0.285958	−	0.165098i	0.350160	−	0.936690i	$-0.386127\pi$
$587$	−6.92820	−	4.00000i	−0.285958	−	0.165098i	−0.636117	+	0.771592i	$0.719461\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	−10.3923	+	6.00000i	−0.427482	+	0.246807i
$592$		0			0
$593$		−	36.0000i		−	1.47834i	−0.673517	−	0.739171i	$-0.735217\pi$
$593$		−	36.0000i		−	1.47834i	0.673517	−	0.739171i	$-0.264783\pi$
$594$		0			0
$595$	8.00000	−	13.8564i	0.327968	−	0.568057i
$596$		0			0
$597$	4.00000			0.163709
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$		0			0
$603$		−	2.00000i		−	0.0814463i
$604$		0			0
$605$	−17.3205	+	10.0000i	−0.704179	+	0.406558i
$606$		0			0
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$		0			0
$609$	10.3923	+	6.00000i	0.421117	+	0.243132i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	0.234751	−	0.972056i	$-0.424572\pi$
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	−0.724449	+	0.689328i	$0.757906\pi$
$614$		0			0
$615$	16.0000	+	27.7128i	0.645182	+	1.11749i
$616$		0			0
$617$	41.5692	−	24.0000i	1.67351	−	0.966204i	0.707867	−	0.706346i	$-0.249658\pi$
$617$	41.5692	−	24.0000i	1.67351	−	0.966204i	0.965647	−	0.259858i	$-0.0836757\pi$
$618$		0			0
$619$			14.0000i			0.562708i	0.959604	+	0.281354i	$0.0907834\pi$
$619$			14.0000i			0.562708i	−0.959604	+	0.281354i	$0.909217\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.00000			−0.320513
$624$		0			0
$625$	41.0000			1.64000
$626$		0			0
$627$	4.00000	−	6.92820i	0.159745	−	0.276686i
$628$		0			0
$629$		−	20.0000i		−	0.797452i
$630$		0			0
$631$	−25.9808	+	15.0000i	−1.03428	+	0.597141i	−0.918207	−	0.396100i	$-0.870363\pi$
$631$	−25.9808	+	15.0000i	−1.03428	+	0.597141i	−0.116071	+	0.993241i	$0.537030\pi$
$632$		0			0
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$		0			0
$635$	41.5692	+	24.0000i	1.64962	+	0.952411i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	13.8564	+	8.00000i	0.548151	+	0.316475i
$640$		0			0
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$		0			0
$643$	−22.5167	+	13.0000i	−0.887970	+	0.512670i	−0.873278	−	0.487222i	$-0.838010\pi$
$643$	−22.5167	+	13.0000i	−0.887970	+	0.512670i	−0.0146923	+	0.999892i	$0.504677\pi$
$644$		0			0
$645$			16.0000i			0.629999i
$646$		0			0
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$		0			0
$649$	−32.0000			−1.25611
$650$		0			0
$651$	−20.0000			−0.783862
$652$		0			0
$653$	23.0000	−	39.8372i	0.900060	−	1.55895i	0.0726446	−	0.997358i	$-0.476856\pi$
$653$	23.0000	−	39.8372i	0.900060	−	1.55895i	0.827415	−	0.561591i	$-0.189811\pi$
$654$		0			0
$655$			16.0000i			0.625172i
$656$		0			0
$657$	−8.66025	+	5.00000i	−0.337869	+	0.195069i
$658$		0			0
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	−8.66025	−	5.00000i	−0.336845	−	0.194477i	0.322031	−	0.946729i	$-0.395634\pi$
$661$	−8.66025	−	5.00000i	−0.336845	−	0.194477i	−0.658876	+	0.752252i	$0.728968\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−13.8564	−	8.00000i	−0.537328	−	0.310227i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	12.1244	−	7.00000i	0.468755	−	0.270636i
$670$		0			0
$671$			56.0000i			2.16186i
$672$		0			0
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$		0			0
$675$	11.0000			0.423390
$676$		0			0
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$		0			0
$681$		−	4.00000i		−	0.153280i
$682$		0			0
$683$	17.3205	−	10.0000i	0.662751	−	0.382639i	−0.130573	−	0.991439i	$-0.541682\pi$
$683$	17.3205	−	10.0000i	0.662751	−	0.382639i	0.793324	+	0.608799i	$0.208349\pi$
$684$		0			0
$685$	16.0000	+	27.7128i	0.611329	+	1.05885i
$686$		0			0
$687$	−1.73205	−	1.00000i	−0.0660819	−	0.0381524i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	8.66025	+	5.00000i	0.329452	+	0.190209i	0.655598	−	0.755110i	$-0.272417\pi$
$691$	8.66025	+	5.00000i	0.329452	+	0.190209i	−0.326146	+	0.945319i	$0.605750\pi$
$692$		0			0
$693$	4.00000	+	6.92820i	0.151947	+	0.263181i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			16.0000i			0.606043i
$698$		0			0
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$		0			0
$705$	8.00000	−	13.8564i	0.301297	−	0.521862i
$706$		0			0
$707$			20.0000i			0.752177i
$708$		0			0
$709$	5.19615	−	3.00000i	0.195146	−	0.112667i	−0.399244	−	0.916845i	$-0.630727\pi$
$709$	5.19615	−	3.00000i	0.195146	−	0.112667i	0.594389	+	0.804178i	$0.297394\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	20.7846	+	12.0000i	0.776215	+	0.448148i
$718$		0			0
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$	−13.8564	+	8.00000i	−0.516040	+	0.297936i
$722$		0			0
$723$			2.00000i			0.0743808i
$724$		0			0
$725$	−33.0000	+	57.1577i	−1.22559	+	2.12278i
$726$		0			0
$727$	−44.0000			−1.63187			−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000			−1.63187			−0.815935	+	0.578144i	$0.803777\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$		−	22.0000i		−	0.812589i	−0.913742	−	0.406294i	$-0.866821\pi$
$733$		−	22.0000i		−	0.812589i	0.913742	−	0.406294i	$-0.133179\pi$
$734$		0			0
$735$	−10.3923	+	6.00000i	−0.383326	+	0.221313i
$736$		0			0
$737$	4.00000	+	6.92820i	0.147342	+	0.255204i
$738$		0			0
$739$	−19.0526	−	11.0000i	−0.700860	−	0.404642i	0.106808	−	0.994280i	$-0.465937\pi$
$739$	−19.0526	−	11.0000i	−0.700860	−	0.404642i	−0.807668	+	0.589638i	$0.799270\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	41.5692	+	24.0000i	1.52503	+	0.880475i	0.999560	+	0.0296605i	$0.00944260\pi$
$743$	41.5692	+	24.0000i	1.52503	+	0.880475i	0.525467	+	0.850814i	$0.323891\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	24.0000i		−	0.876941i
$750$		0			0
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$		0			0
$753$	−20.0000			−0.728841
$754$		0			0
$755$	−72.0000			−2.62035
$756$		0			0
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	0.654827	+	0.755779i	$0.272742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	34.6410	−	20.0000i	1.25574	−	0.724999i	0.283493	−	0.958974i	$-0.408507\pi$
$761$	34.6410	−	20.0000i	1.25574	−	0.724999i	0.972243	+	0.233975i	$0.0751733\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$	6.92820	+	4.00000i	0.250490	+	0.144620i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−19.0526	−	11.0000i	−0.687053	−	0.396670i	0.115454	−	0.993313i	$-0.463168\pi$
$769$	−19.0526	−	11.0000i	−0.687053	−	0.396670i	−0.802507	+	0.596643i	$0.796501\pi$
$770$		0			0
$771$	−15.0000	−	25.9808i	−0.540212	−	0.935674i
$772$		0			0
$773$	41.5692	−	24.0000i	1.49514	−	0.863220i	0.495156	−	0.868804i	$-0.335111\pi$
$773$	41.5692	−	24.0000i	1.49514	−	0.863220i	0.999984	+	0.00558380i	$0.00177739\pi$
$774$		0			0
$775$		−	110.000i		−	3.95132i
$776$		0			0
$777$	10.0000	−	17.3205i	0.358748	−	0.621370i
$778$		0			0
$779$	16.0000			0.573259
$780$		0			0
$781$	−64.0000			−2.29010
$782$		0			0
$783$	−3.00000	+	5.19615i	−0.107211	+	0.185695i
$784$		0			0
$785$			8.00000i			0.285532i
$786$		0			0
$787$	−43.3013	+	25.0000i	−1.54352	+	0.891154i	−0.544911	+	0.838494i	$0.683437\pi$
$787$	−43.3013	+	25.0000i	−1.54352	+	0.891154i	−0.998613	+	0.0526599i	$0.983230\pi$
$788$		0			0
$789$	−8.00000	−	13.8564i	−0.284808	−	0.493301i
$790$		0			0
$791$	10.3923	+	6.00000i	0.369508	+	0.213335i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−34.6410	−	20.0000i	−1.22859	−	0.709327i
$796$		0			0
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	0.538501	−	0.842625i	$-0.318991\pi$
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	−0.998985	+	0.0450436i	$0.985657\pi$
$798$		0			0
$799$	6.92820	−	4.00000i	0.245102	−	0.141510i
$800$		0			0
$801$		−	4.00000i		−	0.141333i
$802$		0			0
$803$	20.0000	−	34.6410i	0.705785	−	1.22245i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.0000			0.492823
$808$		0			0
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	0.310457	+	0.950587i	$0.399518\pi$
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	−0.978461	+	0.206430i	$0.933815\pi$
$810$		0			0
$811$		−	6.00000i		−	0.210688i	−0.994436	−	0.105344i	$-0.966406\pi$
$811$		−	6.00000i		−	0.210688i	0.994436	−	0.105344i	$-0.0335944\pi$
$812$		0			0
$813$	8.66025	−	5.00000i	0.303728	−	0.175358i
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	6.92820	+	4.00000i	0.242387	+	0.139942i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.7846	+	12.0000i	0.725388	+	0.418803i	0.816733	−	0.577016i	$-0.195783\pi$
$821$	20.7846	+	12.0000i	0.725388	+	0.418803i	−0.0913446	+	0.995819i	$0.529116\pi$
$822$		0			0
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	0.997686	+	0.0679910i	$0.0216589\pi$
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	−0.439961	+	0.898017i	$0.645008\pi$
$824$		0			0
$825$	−38.1051	+	22.0000i	−1.32665	+	0.765942i
$826$		0			0
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$		0			0
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		0			0
$831$	22.0000			0.763172
$832$		0			0
$833$	−6.00000			−0.207888
$834$		0			0
$835$	−24.0000	+	41.5692i	−0.830554	+	1.43856i
$836$		0			0
$837$		−	10.0000i		−	0.345651i
$838$		0			0
$839$	−13.8564	+	8.00000i	−0.478376	+	0.276191i	−0.719740	−	0.694244i	$-0.755739\pi$
$839$	−13.8564	+	8.00000i	−0.478376	+	0.276191i	0.241363	+	0.970435i	$0.422405\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	−6.92820	−	4.00000i	−0.238620	−	0.137767i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.66025	−	5.00000i	−0.297570	−	0.171802i
$848$		0			0
$849$	8.00000	+	13.8564i	0.274559	+	0.475551i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	14.0000i		−	0.479351i	−0.970853	−	0.239675i	$-0.922959\pi$
$853$		−	14.0000i		−	0.479351i	0.970853	−	0.239675i	$-0.0770410\pi$
$854$		0			0
$855$	4.00000	−	6.92820i	0.136797	−	0.236940i
$856$		0			0
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	52.0000			1.77422			0.887109	−	0.461561i	$-0.152710\pi$
$859$	52.0000			1.77422			0.887109	+	0.461561i	$0.152710\pi$
$860$		0			0
$861$	−8.00000	+	13.8564i	−0.272639	+	0.472225i
$862$		0			0
$863$		−	4.00000i		−	0.136162i	−0.997680	−	0.0680808i	$-0.978312\pi$
$863$		−	4.00000i		−	0.136162i	0.997680	−	0.0680808i	$-0.0216876\pi$
$864$		0			0
$865$	−6.92820	+	4.00000i	−0.235566	+	0.136004i
$866$		0			0
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$		0			0
$869$	−55.4256	−	32.0000i	−1.88019	−	1.08553i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.73205	−	1.00000i	−0.0586210	−	0.0338449i
$874$		0			0
$875$	24.0000	+	41.5692i	0.811348	+	1.40530i
$876$		0			0
$877$	−8.66025	+	5.00000i	−0.292436	+	0.168838i	−0.639040	−	0.769174i	$-0.720668\pi$
$877$	−8.66025	+	5.00000i	−0.292436	+	0.168838i	0.346604	+	0.938012i	$0.387335\pi$
$878$		0			0
$879$		−	8.00000i		−	0.269833i
$880$		0			0
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	−0.723679	−	0.690136i	$-0.757551\pi$
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	0.959515	+	0.281656i	$0.0908839\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$	−32.0000			−1.07567
$886$		0			0
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$			24.0000i			0.804934i
$890$		0			0
$891$	−3.46410	+	2.00000i	−0.116052	+	0.0670025i
$892$		0			0
$893$	−4.00000	−	6.92820i	−0.133855	−	0.231843i
$894$		0			0
$895$	41.5692	+	24.0000i	1.38951	+	0.802232i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	51.9615	+	30.0000i	1.73301	+	1.00056i
$900$		0			0
$901$	−10.0000	−	17.3205i	−0.333148	−	0.577030i
$902$		0			0
$903$	−6.92820	+	4.00000i	−0.230556	+	0.133112i
$904$		0			0
$905$		−	8.00000i		−	0.265929i
$906$		0			0
$907$	−28.0000	+	48.4974i	−0.929725	+	1.61033i	−0.145944	+	0.989293i	$0.546622\pi$
$907$	−28.0000	+	48.4974i	−0.929725	+	1.61033i	−0.783781	+	0.621038i	$0.786711\pi$
$908$		0			0
$909$	−10.0000			−0.331679
$910$		0			0
$911$	−56.0000			−1.85536			−0.927681	−	0.373373i	$-0.878201\pi$
$911$	−56.0000			−1.85536			−0.927681	+	0.373373i	$0.878201\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$			56.0000i			1.85130i
$916$		0			0
$917$	−6.92820	+	4.00000i	−0.228789	+	0.132092i
$918$		0			0
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.793742	−	0.608254i	$-0.791870\pi$
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.129893	−	0.991528i	$-0.541463\pi$
$920$		0			0
$921$	19.0526	+	11.0000i	0.627803	+	0.362462i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	95.2628	+	55.0000i	3.13222	+	1.80839i
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$	−13.8564	+	8.00000i	−0.454614	+	0.262471i	−0.709777	−	0.704427i	$-0.751204\pi$
$929$	−13.8564	+	8.00000i	−0.454614	+	0.262471i	0.255163	+	0.966898i	$0.417871\pi$
$930$		0			0
$931$			6.00000i			0.196642i
$932$		0			0
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$	−32.0000			−1.04651
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$		0			0
$941$		−	8.00000i		−	0.260793i	−0.991462	−	0.130396i	$-0.958375\pi$
$941$		−	8.00000i		−	0.260793i	0.991462	−	0.130396i	$-0.0416250\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.00000	+	6.92820i	0.130120	+	0.225374i
$946$		0			0
$947$	−6.92820	−	4.00000i	−0.225136	−	0.129983i	0.383190	−	0.923670i	$-0.374825\pi$
$947$	−6.92820	−	4.00000i	−0.225136	−	0.129983i	−0.608326	+	0.793687i	$0.708159\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	10.3923	+	6.00000i	0.336994	+	0.194563i
$952$		0			0
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	−0.974902	−	0.222633i	$-0.928535\pi$
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	0.294646	−	0.955607i	$-0.404798\pi$
$954$		0			0
$955$	−27.7128	+	16.0000i	−0.896766	+	0.517748i
$956$		0			0
$957$		−	24.0000i		−	0.775810i
$958$		0			0
$959$	−8.00000	+	13.8564i	−0.258333	+	0.447447i
$960$		0			0
$961$	−69.0000			−2.22581
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−28.0000	+	48.4974i	−0.901352	+	1.56119i
$966$		0			0
$967$		−	22.0000i		−	0.707472i	−0.935345	−	0.353736i	$-0.884911\pi$
$967$		−	22.0000i		−	0.707472i	0.935345	−	0.353736i	$-0.115089\pi$
$968$		0			0
$969$	3.46410	−	2.00000i	0.111283	−	0.0642493i
$970$		0			0
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	0.998339	−	0.0576061i	$-0.0183467\pi$
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	−0.549058	+	0.835784i	$0.685013\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	0.324462	−	0.945899i	$-0.394817\pi$
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	−0.656941	+	0.753942i	$0.728150\pi$
$978$		0			0
$979$	8.00000	+	13.8564i	0.255681	+	0.442853i
$980$		0			0
$981$	1.73205	−	1.00000i	0.0553001	−	0.0319275i
$982$		0			0
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$		0			0
$985$	24.0000	−	41.5692i	0.764704	−	1.32451i
$986$		0			0
$987$	8.00000			0.254643
$988$		0			0
$989$		0			0
$990$		0			0
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	0.996382	−	0.0849833i	$-0.0270837\pi$
$992$		0			0
$993$			2.00000i			0.0634681i
$994$		0			0
$995$	−13.8564	+	8.00000i	−0.439278	+	0.253617i
$996$		0			0
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$		0			0
$999$	8.66025	+	5.00000i	0.273998	+	0.158193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.q.h.1837.2		4
13.2	odd	12		2028.2.i.g.2005.1		2
13.3	even	3	inner	2028.2.q.h.361.2		4
13.4	even	6		2028.2.b.a.337.1		2
13.5	odd	4		2028.2.i.g.529.1		2
13.6	odd	12		2028.2.a.c.1.1		1
13.7	odd	12		156.2.a.a.1.1	✓	1
13.8	odd	4		2028.2.i.e.529.1		2
13.9	even	3		2028.2.b.a.337.2		2
13.10	even	6	inner	2028.2.q.h.361.1		4
13.11	odd	12		2028.2.i.e.2005.1		2
13.12	even	2	inner	2028.2.q.h.1837.1		4
39.17	odd	6		6084.2.b.j.4393.2		2
39.20	even	12		468.2.a.d.1.1		1
39.32	even	12		6084.2.a.b.1.1		1
39.35	odd	6		6084.2.b.j.4393.1		2
52.7	even	12		624.2.a.e.1.1		1
52.19	even	12		8112.2.a.bi.1.1		1
65.7	even	12		3900.2.h.b.1249.2		2
65.33	even	12		3900.2.h.b.1249.1		2
65.59	odd	12		3900.2.a.m.1.1		1
91.20	even	12		7644.2.a.k.1.1		1
104.59	even	12		2496.2.a.o.1.1		1
104.85	odd	12		2496.2.a.bc.1.1		1
117.7	odd	12		4212.2.i.l.1405.1		2
117.20	even	12		4212.2.i.b.1405.1		2
117.59	even	12		4212.2.i.b.2809.1		2
117.85	odd	12		4212.2.i.l.2809.1		2
156.59	odd	12		1872.2.a.s.1.1		1
312.59	odd	12		7488.2.a.d.1.1		1
312.293	even	12		7488.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.a.a.1.1	✓	1	13.7	odd	12
468.2.a.d.1.1		1	39.20	even	12
624.2.a.e.1.1		1	52.7	even	12
1872.2.a.s.1.1		1	156.59	odd	12
2028.2.a.c.1.1		1	13.6	odd	12
2028.2.b.a.337.1		2	13.4	even	6
2028.2.b.a.337.2		2	13.9	even	3
2028.2.i.e.529.1		2	13.8	odd	4
2028.2.i.e.2005.1		2	13.11	odd	12
2028.2.i.g.529.1		2	13.5	odd	4
2028.2.i.g.2005.1		2	13.2	odd	12
2028.2.q.h.361.1		4	13.10	even	6	inner
2028.2.q.h.361.2		4	13.3	even	3	inner
2028.2.q.h.1837.1		4	13.12	even	2	inner
2028.2.q.h.1837.2		4	1.1	even	1	trivial
2496.2.a.o.1.1		1	104.59	even	12
2496.2.a.bc.1.1		1	104.85	odd	12
3900.2.a.m.1.1		1	65.59	odd	12
3900.2.h.b.1249.1		2	65.33	even	12
3900.2.h.b.1249.2		2	65.7	even	12
4212.2.i.b.1405.1		2	117.20	even	12
4212.2.i.b.2809.1		2	117.59	even	12
4212.2.i.l.1405.1		2	117.7	odd	12
4212.2.i.l.2809.1		2	117.85	odd	12
6084.2.a.b.1.1		1	39.32	even	12
6084.2.b.j.4393.1		2	39.35	odd	6
6084.2.b.j.4393.2		2	39.17	odd	6
7488.2.a.c.1.1		1	312.293	even	12
7488.2.a.d.1.1		1	312.59	odd	12
7644.2.a.k.1.1		1	91.20	even	12
8112.2.a.bi.1.1		1	52.19	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +4.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +4.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.46410 + 2.00000i) q^{11} +(3.46410 + 2.00000i) q^{15} +(1.00000 + 1.73205i) q^{17} +(1.73205 - 1.00000i) q^{19} +2.00000i q^{21} -11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} +10.0000i q^{31} +(3.46410 - 2.00000i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(-8.66025 - 5.00000i) q^{37} +(6.92820 + 4.00000i) q^{41} +(2.00000 + 3.46410i) q^{43} +(3.46410 - 2.00000i) q^{45} -4.00000i q^{47} +(-1.50000 + 2.59808i) q^{49} +2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} -2.00000i q^{57} +(-6.92820 + 4.00000i) q^{59} +(7.00000 + 12.1244i) q^{61} +(1.73205 + 1.00000i) q^{63} +(1.73205 + 1.00000i) q^{67} +(-13.8564 + 8.00000i) q^{71} -10.0000i q^{73} +(-5.50000 + 9.52628i) q^{75} -8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.92820 + 4.00000i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(3.46410 + 2.00000i) q^{89} +(8.66025 + 5.00000i) q^{93} +(4.00000 + 6.92820i) q^{95} +(1.73205 - 1.00000i) q^{97} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{9} + 4 q^{17} - 44 q^{25} - 4 q^{27} + 12 q^{29} - 16 q^{35} + 8 q^{43} - 6 q^{49} + 8 q^{51} - 40 q^{53} - 32 q^{55} + 28 q^{61} - 22 q^{75} - 32 q^{77} - 64 q^{79} - 2 q^{81} - 12 q^{87} + 16 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^9 + 4 * q^17 - 44 * q^25 - 4 * q^27 + 12 * q^29 - 16 * q^35 + 8 * q^43 - 6 * q^49 + 8 * q^51 - 40 * q^53 - 32 * q^55 + 28 * q^61 - 22 * q^75 - 32 * q^77 - 64 * q^79 - 2 * q^81 - 12 * q^87 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more