LMFDB - Embedded newform 1568.2.q.h.815.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(815,1568)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1568.815"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9640188644209402576896.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			815.7
Root			$-0.349313 + 1.37039i$ of defining polynomial
Character	$\chi$	$=$	1568.815
Dual form			1568.2.q.h.1391.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60021 + 0.923880i) q^{3} +(-1.92538 - 3.33486i) q^{5} +(0.207107 + 0.358719i) q^{9} +(-2.12132 + 3.67423i) q^{11} -3.85077 q^{13} -7.11529i q^{15} +(0.274552 + 0.158513i) q^{17} +(-2.53759 + 1.46508i) q^{19} +(2.55239 - 1.47363i) q^{23} +(-4.91421 + 8.51167i) q^{25} -4.77791i q^{27} +2.94725i q^{29} +(-1.12786 + 1.95352i) q^{31} +(-6.78910 + 3.91969i) q^{33} +(-6.16203 + 3.55765i) q^{37} +(-6.16203 - 3.55765i) q^{39} +1.39942i q^{41} -5.41421 q^{43} +(0.797521 - 1.38135i) q^{45} +(-3.85077 - 6.66973i) q^{47} +(0.292893 + 0.507306i) q^{51} +(-8.71442 - 5.03127i) q^{53} +16.3374 q^{55} -5.41421 q^{57} +(0.113723 + 0.0656581i) q^{59} +(0.797521 + 1.38135i) q^{61} +(7.41421 + 12.8418i) q^{65} +(-1.00000 + 1.73205i) q^{67} +5.44581 q^{69} +15.9570i q^{71} +(-2.53759 - 1.46508i) q^{73} +(-15.7275 + 9.08028i) q^{75} +(-5.10479 + 2.94725i) q^{79} +(5.03553 - 8.72180i) q^{81} -3.82683i q^{83} -1.22079i q^{85} +(-2.72291 + 4.71621i) q^{87} +(-8.38931 + 4.84357i) q^{89} +(-3.60963 + 2.08402i) q^{93} +(9.77166 + 5.64167i) q^{95} -16.6298i q^{97} -1.75736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} - 56 q^{25} - 64 q^{43} + 16 q^{51} - 64 q^{57} + 96 q^{65} - 16 q^{67} + 24 q^{81} - 96 q^{99}+O(q^{100}) $ 16 * q - 8 * q^9 - 56 * q^25 - 64 * q^43 + 16 * q^51 - 64 * q^57 + 96 * q^65 - 16 * q^67 + 24 * q^81 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.60021	+	0.923880i	0.923880	+	0.533402i	0.884871	−	0.465837i	$-0.154247\pi$
$3$	1.60021	+	0.923880i	0.923880	+	0.533402i	0.0390089	+	0.999239i	$0.487580\pi$
$4$		0			0
$5$	−1.92538	−	3.33486i	−0.861058	−	1.49140i	−0.870909	−	0.491445i	$-0.836469\pi$
$5$	−1.92538	−	3.33486i	−0.861058	−	1.49140i	0.00985022	−	0.999951i	$-0.496865\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.207107	+	0.358719i	0.0690356	+	0.119573i
$10$		0			0
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$		0			0
$13$	−3.85077			−1.06801			−0.534006	−	0.845481i	$-0.679314\pi$
$13$	−3.85077			−1.06801			−0.534006	+	0.845481i	$0.679314\pi$
$14$		0			0
$15$		−	7.11529i		−	1.83716i
$16$		0			0
$17$	0.274552	+	0.158513i	0.0665886	+	0.0384450i	0.532925	−	0.846163i	$-0.321093\pi$
$17$	0.274552	+	0.158513i	0.0665886	+	0.0384450i	−0.466336	+	0.884608i	$0.654426\pi$
$18$		0			0
$19$	−2.53759	+	1.46508i	−0.582162	+	0.336111i	−0.761992	−	0.647586i	$-0.775779\pi$
$19$	−2.53759	+	1.46508i	−0.582162	+	0.336111i	0.179830	+	0.983698i	$0.442445\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.55239	−	1.47363i	0.532211	−	0.307272i	−0.209705	−	0.977765i	$-0.567250\pi$
$23$	2.55239	−	1.47363i	0.532211	−	0.307272i	0.741916	+	0.670492i	$0.233917\pi$
$24$		0			0
$25$	−4.91421	+	8.51167i	−0.982843	+	1.70233i
$26$		0			0
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$			2.94725i			0.547291i	0.961831	+	0.273645i	$0.0882295\pi$
$29$			2.94725i			0.547291i	−0.961831	+	0.273645i	$0.911771\pi$
$30$		0			0
$31$	−1.12786	+	1.95352i	−0.202570	+	0.350862i	−0.949356	−	0.314203i	$-0.898263\pi$
$31$	−1.12786	+	1.95352i	−0.202570	+	0.350862i	0.746785	+	0.665065i	$0.231596\pi$
$32$		0			0
$33$	−6.78910	+	3.91969i	−1.18183	+	0.682330i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.16203	+	3.55765i	−1.01303	+	0.584874i	−0.912078	−	0.410018i	$-0.865523\pi$
$37$	−6.16203	+	3.55765i	−1.01303	+	0.584874i	−0.100953	+	0.994891i	$0.532189\pi$
$38$		0			0
$39$	−6.16203	−	3.55765i	−0.986714	−	0.569679i
$40$		0			0
$41$			1.39942i			0.218552i	0.994011	+	0.109276i	$0.0348533\pi$
$41$			1.39942i			0.218552i	−0.994011	+	0.109276i	$0.965147\pi$
$42$		0			0
$43$	−5.41421			−0.825660			−0.412830	−	0.910808i	$-0.635460\pi$
$43$	−5.41421			−0.825660			−0.412830	+	0.910808i	$0.635460\pi$
$44$		0			0
$45$	0.797521	−	1.38135i	0.118887	−	0.205919i
$46$		0			0
$47$	−3.85077	−	6.66973i	−0.561692	−	0.972880i	−0.997349	−	0.0727669i	$-0.976817\pi$
$47$	−3.85077	−	6.66973i	−0.561692	−	0.972880i	0.435656	−	0.900113i	$-0.356516\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.292893	+	0.507306i	0.0410133	+	0.0710370i
$52$		0			0
$53$	−8.71442	−	5.03127i	−1.19702	−	0.691099i	−0.237129	−	0.971478i	$-0.576206\pi$
$53$	−8.71442	−	5.03127i	−1.19702	−	0.691099i	−0.959889	+	0.280380i	$0.909540\pi$
$54$		0			0
$55$	16.3374			2.20294
$56$		0			0
$57$	−5.41421			−0.717130
$58$		0			0
$59$	0.113723	+	0.0656581i	0.0148055	+	0.00854796i	0.507384	−	0.861720i	$-0.330612\pi$
$59$	0.113723	+	0.0656581i	0.0148055	+	0.00854796i	−0.492579	+	0.870268i	$0.663946\pi$
$60$		0			0
$61$	0.797521	+	1.38135i	0.102112	+	0.176863i	0.912555	−	0.408955i	$-0.134107\pi$
$61$	0.797521	+	1.38135i	0.102112	+	0.176863i	−0.810443	+	0.585818i	$0.800773\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.41421	+	12.8418i	0.919620	+	1.59283i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	5.44581			0.655599
$70$		0			0
$71$			15.9570i			1.89375i	0.321597	+	0.946877i	$0.395780\pi$
$71$			15.9570i			1.89375i	−0.321597	+	0.946877i	$0.604220\pi$
$72$		0			0
$73$	−2.53759	−	1.46508i	−0.297002	−	0.171474i	0.344093	−	0.938935i	$-0.388186\pi$
$73$	−2.53759	−	1.46508i	−0.297002	−	0.171474i	−0.641095	+	0.767461i	$0.721520\pi$
$74$		0			0
$75$	−15.7275	+	9.08028i	−1.81606	+	1.04850i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.10479	+	2.94725i	−0.574334	+	0.331592i	−0.758878	−	0.651232i	$-0.774252\pi$
$79$	−5.10479	+	2.94725i	−0.574334	+	0.331592i	0.184545	+	0.982824i	$0.440919\pi$
$80$		0			0
$81$	5.03553	−	8.72180i	0.559504	−	0.969089i
$82$		0			0
$83$		−	3.82683i		−	0.420050i	−0.977696	−	0.210025i	$-0.932646\pi$
$83$		−	3.82683i		−	0.420050i	0.977696	−	0.210025i	$-0.0673545\pi$
$84$		0			0
$85$		−	1.22079i		−	0.132413i
$86$		0			0
$87$	−2.72291	+	4.71621i	−0.291926	+	0.505631i
$88$		0			0
$89$	−8.38931	+	4.84357i	−0.889265	+	0.513417i	−0.873702	−	0.486462i	$-0.838287\pi$
$89$	−8.38931	+	4.84357i	−0.889265	+	0.513417i	−0.0155628	+	0.999879i	$0.504954\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.60963	+	2.08402i	−0.374301	+	0.216103i
$94$		0			0
$95$	9.77166	+	5.64167i	1.00255	+	0.578823i
$96$		0			0
$97$		−	16.6298i		−	1.68850i	−0.535947	−	0.844252i	$-0.680045\pi$
$97$		−	16.6298i		−	1.68850i	0.535947	−	0.844252i	$-0.319955\pi$
$98$		0			0
$99$	−1.75736			−0.176621
$100$		0			0
$101$	3.52043	−	6.09756i	0.350295	−	0.606730i	−0.636006	−	0.771684i	$-0.719415\pi$
$101$	3.52043	−	6.09756i	0.350295	−	0.606730i	0.986301	+	0.164955i	$0.0527478\pi$
$102$		0			0
$103$	2.72291	+	4.71621i	0.268296	+	0.464702i	0.968422	−	0.249317i	$-0.0802062\pi$
$103$	2.72291	+	4.71621i	0.268296	+	0.464702i	−0.700126	+	0.714019i	$0.746873\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.65685	+	16.7262i	0.933563	+	1.61698i	0.777176	+	0.629283i	$0.216651\pi$
$107$	9.65685	+	16.7262i	0.933563	+	1.61698i	0.156387	+	0.987696i	$0.450015\pi$
$108$		0			0
$109$	−2.55239	−	1.47363i	−0.244475	−	0.141148i	0.372757	−	0.927929i	$-0.378413\pi$
$109$	−2.55239	−	1.47363i	−0.244475	−	0.141148i	−0.617232	+	0.786781i	$0.711746\pi$
$110$		0			0
$111$	−13.1474			−1.24789
$112$		0			0
$113$	1.41421			0.133038			0.0665190	−	0.997785i	$-0.478811\pi$
$113$	1.41421			0.133038			0.0665190	+	0.997785i	$0.478811\pi$
$114$		0			0
$115$	−9.82868	−	5.67459i	−0.916530	−	0.529159i
$116$		0			0
$117$	−0.797521	−	1.38135i	−0.0737308	−	0.127705i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		0			0
$123$	−1.29289	+	2.23936i	−0.116576	+	0.201916i
$124$		0			0
$125$	18.5932			1.66302
$126$		0			0
$127$		−	17.1778i		−	1.52429i	−0.647408	−	0.762143i	$-0.724147\pi$
$127$		−	17.1778i		−	1.52429i	0.647408	−	0.762143i	$-0.275853\pi$
$128$		0			0
$129$	−8.66386	−	5.00208i	−0.762810	−	0.440409i
$130$		0			0
$131$	14.4019	−	8.31492i	1.25830	−	0.726478i	0.285553	−	0.958363i	$-0.407823\pi$
$131$	14.4019	−	8.31492i	1.25830	−	0.726478i	0.972743	+	0.231885i	$0.0744894\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−15.9337	+	9.19932i	−1.37135	+	0.791751i
$136$		0			0
$137$	−5.77817	+	10.0081i	−0.493663	+	0.855049i	−0.999973	−	0.00730221i	$-0.997676\pi$
$137$	−5.77817	+	10.0081i	−0.493663	+	0.855049i	0.506311	+	0.862351i	$0.331009\pi$
$138$		0			0
$139$		−	14.4650i		−	1.22691i	−0.789730	−	0.613455i	$-0.789779\pi$
$139$		−	14.4650i		−	1.22691i	0.789730	−	0.613455i	$-0.210221\pi$
$140$		0			0
$141$		−	14.2306i		−	1.19843i
$142$		0			0
$143$	8.16872	−	14.1486i	0.683102	−	1.18317i
$144$		0			0
$145$	9.82868	−	5.67459i	0.816228	−	0.471249i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.3241	−	7.11529i	1.00963	−	0.582908i	0.0985436	−	0.995133i	$-0.468582\pi$
$149$	12.3241	−	7.11529i	1.00963	−	0.582908i	0.911082	+	0.412225i	$0.135248\pi$
$150$		0			0
$151$	−9.77166	−	5.64167i	−0.795206	−	0.459112i	0.0465860	−	0.998914i	$-0.485166\pi$
$151$	−9.77166	−	5.64167i	−0.795206	−	0.459112i	−0.841792	+	0.539802i	$0.818499\pi$
$152$		0			0
$153$			0.131316i			0.0106163i
$154$		0			0
$155$	8.68629			0.697700
$156$		0			0
$157$	−0.797521	+	1.38135i	−0.0636491	+	0.110243i	−0.896094	−	0.443864i	$-0.853607\pi$
$157$	−0.797521	+	1.38135i	−0.0636491	+	0.110243i	0.832445	+	0.554108i	$0.186940\pi$
$158$		0			0
$159$	−9.29658	−	16.1021i	−0.737267	−	1.27698i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.29289	−	2.23936i	−0.101267	−	0.175400i	0.810940	−	0.585130i	$-0.198956\pi$
$163$	−1.29289	−	2.23936i	−0.101267	−	0.175400i	−0.912207	+	0.409730i	$0.865623\pi$
$164$		0			0
$165$	26.1433	+	15.0938i	2.03525	+	1.17505i
$166$		0			0
$167$	−10.8916			−0.842819			−0.421409	−	0.906870i	$-0.638464\pi$
$167$	−10.8916			−0.842819			−0.421409	+	0.906870i	$0.638464\pi$
$168$		0			0
$169$	1.82843			0.140648
$170$		0			0
$171$	−1.05110	−	0.606854i	−0.0803798	−	0.0464073i
$172$		0			0
$173$	−10.0941	−	17.4835i	−0.767440	−	1.32925i	−0.938947	−	0.344063i	$-0.888197\pi$
$173$	−10.0941	−	17.4835i	−0.767440	−	1.32925i	0.171506	−	0.985183i	$-0.445137\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.121320	+	0.210133i	0.00911900	+	0.0157946i
$178$		0			0
$179$	6.82843	−	11.8272i	0.510381	−	0.884005i	−0.489547	−	0.871977i	$-0.662838\pi$
$179$	6.82843	−	11.8272i	0.510381	−	0.884005i	0.999928	−	0.0120283i	$-0.00382881\pi$
$180$		0			0
$181$	−11.5523			−0.858676			−0.429338	−	0.903144i	$-0.641253\pi$
$181$	−11.5523			−0.858676			−0.429338	+	0.903144i	$0.641253\pi$
$182$		0			0
$183$			2.94725i			0.217867i
$184$		0			0
$185$	23.7285	+	13.6997i	1.74456	+	1.00722i
$186$		0			0
$187$	−1.16483	+	0.672512i	−0.0851805	+	0.0491790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.71442	−	5.03127i	0.630553	−	0.364050i	−0.150413	−	0.988623i	$-0.548060\pi$
$191$	8.71442	−	5.03127i	0.630553	−	0.364050i	0.780966	+	0.624573i	$0.214727\pi$
$192$		0			0
$193$	3.29289	−	5.70346i	0.237028	−	0.410544i	−0.722832	−	0.691023i	$-0.757160\pi$
$193$	3.29289	−	5.70346i	0.237028	−	0.410544i	0.959860	+	0.280479i	$0.0904935\pi$
$194$		0			0
$195$			27.3994i			1.96211i
$196$		0			0
$197$		−	1.72646i		−	0.123005i	−0.998107	−	0.0615026i	$-0.980411\pi$
$197$		−	1.72646i		−	0.123005i	0.998107	−	0.0615026i	$-0.0195892\pi$
$198$		0			0
$199$	4.97863	−	8.62325i	0.352926	−	0.611286i	−0.633835	−	0.773469i	$-0.718520\pi$
$199$	4.97863	−	8.62325i	0.352926	−	0.611286i	0.986761	+	0.162183i	$0.0518534\pi$
$200$		0			0
$201$	−3.20041	+	1.84776i	−0.225740	+	0.130331i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	4.66687	−	2.69442i	0.325948	−	0.188186i
$206$		0			0
$207$	1.05724	+	0.610396i	0.0734830	+	0.0424254i
$208$		0			0
$209$		−	12.4316i		−	0.859910i
$210$		0			0
$211$	14.9706			1.03062			0.515308	−	0.857005i	$-0.327678\pi$
$211$	14.9706			1.03062			0.515308	+	0.857005i	$0.327678\pi$
$212$		0			0
$213$	−14.7424	+	25.5346i	−1.01013	+	1.74960i
$214$		0			0
$215$	10.4244	+	18.0557i	0.710941	+	1.23139i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.70711	−	4.68885i	−0.182929	−	0.316843i
$220$		0			0
$221$	−1.05724	−	0.610396i	−0.0711174	−	0.0410597i
$222$		0			0
$223$	−5.44581			−0.364678			−0.182339	−	0.983236i	$-0.558367\pi$
$223$	−5.44581			−0.364678			−0.182339	+	0.983236i	$0.558367\pi$
$224$		0			0
$225$	−4.07107			−0.271405
$226$		0			0
$227$	18.9279	+	10.9280i	1.25629	+	0.725320i	0.972351	−	0.233523i	$-0.0750253\pi$
$227$	18.9279	+	10.9280i	1.25629	+	0.725320i	0.283939	+	0.958842i	$0.408359\pi$
$228$		0			0
$229$	11.6891	+	20.2462i	0.772440	+	1.33791i	0.936222	+	0.351409i	$0.114297\pi$
$229$	11.6891	+	20.2462i	0.772440	+	1.33791i	−0.163782	+	0.986497i	$0.552369\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.94975	−	8.57321i	−0.324269	−	0.561650i	0.657095	−	0.753807i	$-0.271785\pi$
$233$	−4.94975	−	8.57321i	−0.324269	−	0.561650i	−0.981364	+	0.192158i	$0.938452\pi$
$234$		0			0
$235$	−14.8284	+	25.6836i	−0.967300	+	1.67541i
$236$		0			0
$237$	−10.8916			−0.707487
$238$		0			0
$239$			15.4514i			0.999467i	0.866179	+	0.499733i	$0.166569\pi$
$239$			15.4514i			0.999467i	−0.866179	+	0.499733i	$0.833431\pi$
$240$		0			0
$241$	−15.8883	−	9.17314i	−1.02346	−	0.590894i	−0.108354	−	0.994112i	$-0.534558\pi$
$241$	−15.8883	−	9.17314i	−1.02346	−	0.590894i	−0.915104	+	0.403219i	$0.867891\pi$
$242$		0			0
$243$	3.70241	−	2.13759i	0.237510	−	0.137126i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.77166	−	5.64167i	0.621756	−	0.358971i
$248$		0			0
$249$	3.53553	−	6.12372i	0.224055	−	0.388075i
$250$		0			0
$251$			11.0322i			0.696344i	0.937431	+	0.348172i	$0.113197\pi$
$251$			11.0322i			0.696344i	−0.937431	+	0.348172i	$0.886803\pi$
$252$		0			0
$253$			12.5041i			0.786128i
$254$		0			0
$255$	1.12786	−	1.95352i	0.0706296	−	0.122334i
$256$		0			0
$257$	13.3036	−	7.68087i	0.829859	−	0.479119i	−0.0239455	−	0.999713i	$-0.507623\pi$
$257$	13.3036	−	7.68087i	0.829859	−	0.479119i	0.853804	+	0.520594i	$0.174289\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.05724	+	0.610396i	−0.0654413	+	0.0377825i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$			38.7485i			2.38030i
$266$		0			0
$267$	−17.8995			−1.09543
$268$		0			0
$269$	−7.37120	+	12.7673i	−0.449430	+	0.778435i	−0.998349	−	0.0574403i	$-0.981706\pi$
$269$	−7.37120	+	12.7673i	−0.449430	+	0.778435i	0.548919	+	0.835875i	$0.315039\pi$
$270$		0			0
$271$	6.57368	+	11.3859i	0.399322	+	0.691647i	0.993642	−	0.112582i	$-0.0359121\pi$
$271$	6.57368	+	11.3859i	0.399322	+	0.691647i	−0.594320	+	0.804229i	$0.702579\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.8492	−	36.1119i	−1.25726	−	2.17763i
$276$		0			0
$277$	−26.1433	−	15.0938i	−1.57080	−	0.906900i	−0.996071	−	0.0885530i	$-0.971776\pi$
$277$	−26.1433	−	15.0938i	−1.57080	−	0.906900i	−0.574725	−	0.818347i	$-0.694891\pi$
$278$		0			0
$279$	−0.934353			−0.0559383
$280$		0			0
$281$	3.07107			0.183205			0.0916023	−	0.995796i	$-0.470801\pi$
$281$	3.07107			0.183205			0.0916023	+	0.995796i	$0.470801\pi$
$282$		0			0
$283$	−13.2370	−	7.64240i	−0.786860	−	0.454294i	0.0519961	−	0.998647i	$-0.483442\pi$
$283$	−13.2370	−	7.64240i	−0.786860	−	0.454294i	−0.838856	+	0.544354i	$0.816775\pi$
$284$		0			0
$285$	10.4244	+	18.0557i	0.617491	+	1.06953i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.44975	−	14.6354i	−0.497044	−	0.860905i
$290$		0			0
$291$	15.3640	−	26.6112i	0.900651	−	1.55997i
$292$		0			0
$293$	16.0638			0.938455			0.469228	−	0.883077i	$-0.344532\pi$
$293$	16.0638			0.938455			0.469228	+	0.883077i	$0.344532\pi$
$294$		0			0
$295$		−	0.505668i		−	0.0294412i
$296$		0			0
$297$	17.5552	+	10.1355i	1.01865	+	0.588120i
$298$		0			0
$299$	−9.82868	+	5.67459i	−0.568407	+	0.328170i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.2668	−	6.50490i	0.647262	−	0.373697i
$304$		0			0
$305$	3.07107	−	5.31925i	0.175849	−	0.304579i
$306$		0			0
$307$			14.2024i			0.810575i	0.914189	+	0.405287i	$0.132829\pi$
$307$			14.2024i			0.810575i	−0.914189	+	0.405287i	$0.867171\pi$
$308$		0			0
$309$			10.0625i			0.572438i
$310$		0			0
$311$	−13.1474	+	22.7719i	−0.745518	+	1.29127i	0.204435	+	0.978880i	$0.434464\pi$
$311$	−13.1474	+	22.7719i	−0.745518	+	1.29127i	−0.949952	+	0.312395i	$0.898869\pi$
$312$		0			0
$313$	13.7861	−	7.95943i	0.779238	−	0.449894i	−0.0569219	−	0.998379i	$-0.518129\pi$
$313$	13.7861	−	7.95943i	0.779238	−	0.449894i	0.836160	+	0.548485i	$0.184795\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.21926	+	4.16804i	−0.405474	+	0.234101i	−0.688843	−	0.724910i	$-0.741881\pi$
$317$	−7.21926	+	4.16804i	−0.405474	+	0.234101i	0.283369	+	0.959011i	$0.408548\pi$
$318$		0			0
$319$	−10.8289	−	6.25206i	−0.606302	−	0.350048i
$320$		0			0
$321$			35.6871i			1.99186i
$322$		0			0
$323$	−0.928932			−0.0516872
$324$		0			0
$325$	18.9235	−	32.7765i	1.04969	−	1.81811i
$326$		0			0
$327$	−2.72291	−	4.71621i	−0.150577	−	0.260807i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.53553	+	9.58783i	0.304260	+	0.526995i	0.977096	−	0.212797i	$-0.0682574\pi$
$331$	5.53553	+	9.58783i	0.304260	+	0.526995i	−0.672836	+	0.739792i	$0.734924\pi$
$332$		0			0
$333$	−2.55239	−	1.47363i	−0.139870	−	0.0807542i
$334$		0			0
$335$	7.70154			0.420780
$336$		0			0
$337$	−14.1421			−0.770371			−0.385186	−	0.922839i	$-0.625863\pi$
$337$	−14.1421			−0.770371			−0.385186	+	0.922839i	$0.625863\pi$
$338$		0			0
$339$	2.26303	+	1.30656i	0.122911	+	0.0709628i
$340$		0			0
$341$	−4.78512	−	8.28808i	−0.259129	−	0.448824i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−10.4853	−	18.1610i	−0.564509	−	0.977758i
$346$		0			0
$347$	6.12132	−	10.6024i	0.328610	−	0.569169i	−0.653627	−	0.756817i	$-0.726753\pi$
$347$	6.12132	−	10.6024i	0.328610	−	0.569169i	0.982236	+	0.187649i	$0.0600866\pi$
$348$		0			0
$349$	−14.7424			−0.789142			−0.394571	−	0.918865i	$-0.629107\pi$
$349$	−14.7424			−0.789142			−0.394571	+	0.918865i	$0.629107\pi$
$350$		0			0
$351$			18.3986i			0.982046i
$352$		0			0
$353$	−4.09069	−	2.36176i	−0.217725	−	0.125704i	0.387171	−	0.922008i	$-0.373452\pi$
$353$	−4.09069	−	2.36176i	−0.217725	−	0.125704i	−0.604897	+	0.796304i	$0.706786\pi$
$354$		0			0
$355$	53.2146	−	30.7235i	2.82434	−	1.63063i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.3813	−	7.72569i	0.706237	−	0.407746i	−0.103429	−	0.994637i	$-0.532981\pi$
$359$	13.3813	−	7.72569i	0.706237	−	0.407746i	0.809666	+	0.586891i	$0.199648\pi$
$360$		0			0
$361$	−5.20711	+	9.01897i	−0.274058	+	0.474683i
$362$		0			0
$363$		−	12.9343i		−	0.678875i
$364$		0			0
$365$			11.2833i			0.590597i
$366$		0			0
$367$	−15.2096	+	26.3437i	−0.793933	+	1.37513i	0.129582	+	0.991569i	$0.458637\pi$
$367$	−15.2096	+	26.3437i	−0.793933	+	1.37513i	−0.923515	+	0.383563i	$0.874697\pi$
$368$		0			0
$369$	−0.501998	+	0.289829i	−0.0261330	+	0.0150879i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.4385	−	8.33609i	0.747598	−	0.431626i	−0.0772271	−	0.997014i	$-0.524607\pi$
$373$	14.4385	−	8.33609i	0.747598	−	0.431626i	0.824826	+	0.565387i	$0.191273\pi$
$374$		0			0
$375$	29.7529	+	17.1778i	1.53643	+	0.887060i
$376$		0			0
$377$		−	11.3492i		−	0.584513i
$378$		0			0
$379$	−10.3848			−0.533430			−0.266715	−	0.963775i	$-0.585938\pi$
$379$	−10.3848			−0.533430			−0.266715	+	0.963775i	$0.585938\pi$
$380$		0			0
$381$	15.8703	−	27.4881i	0.813058	−	1.40826i
$382$		0			0
$383$	16.9981	+	29.4416i	0.868563	+	1.50440i	0.863465	+	0.504409i	$0.168290\pi$
$383$	16.9981	+	29.4416i	0.868563	+	1.50440i	0.00509839	+	0.999987i	$0.498377\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.12132	−	1.94218i	−0.0569999	−	0.0987268i
$388$		0			0
$389$	14.8764	+	8.58892i	0.754266	+	0.435476i	0.827233	−	0.561859i	$-0.189914\pi$
$389$	14.8764	+	8.58892i	0.754266	+	0.435476i	−0.0729674	+	0.997334i	$0.523247\pi$
$390$		0			0
$391$	0.934353			0.0472523
$392$		0			0
$393$	30.7279			1.55002
$394$		0			0
$395$	19.6574	+	11.3492i	0.989070	+	0.571040i
$396$		0			0
$397$	13.9449	+	24.1532i	0.699873	+	1.21222i	0.968510	+	0.248974i	$0.0800934\pi$
$397$	13.9449	+	24.1532i	0.699873	+	1.21222i	−0.268637	+	0.963241i	$0.586573\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.07107	+	10.5154i	0.303175	+	0.525114i	0.976853	−	0.213911i	$-0.0686201\pi$
$401$	6.07107	+	10.5154i	0.303175	+	0.525114i	−0.673679	+	0.739024i	$0.735287\pi$
$402$		0			0
$403$	4.34315	−	7.52255i	0.216347	−	0.374725i
$404$		0			0
$405$	−38.7814			−1.92706
$406$		0			0
$407$		−	30.1876i		−	1.49635i
$408$		0			0
$409$	−18.6063	−	10.7423i	−0.920021	−	0.531174i	−0.0363790	−	0.999338i	$-0.511582\pi$
$409$	−18.6063	−	10.7423i	−0.920021	−	0.531174i	−0.883642	+	0.468164i	$0.844916\pi$
$410$		0			0
$411$	−18.4925	+	10.6767i	−0.912170	+	0.526642i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.7620	+	7.36813i	−0.626461	+	0.361687i
$416$		0			0
$417$	13.3640	−	23.1471i	0.654436	−	1.13352i
$418$		0			0
$419$			9.94977i			0.486078i	0.970017	+	0.243039i	$0.0781443\pi$
$419$			9.94977i			0.486078i	−0.970017	+	0.243039i	$0.921856\pi$
$420$		0			0
$421$		−	7.62096i		−	0.371423i	−0.982604	−	0.185712i	$-0.940541\pi$
$421$		−	7.62096i		−	0.371423i	0.982604	−	0.185712i	$-0.0594590\pi$
$422$		0			0
$423$	1.59504	−	2.76269i	0.0775535	−	0.134327i
$424$		0			0
$425$	−2.69841	+	1.55793i	−0.130892	+	0.0755707i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	26.1433	−	15.0938i	1.26221	−	0.728736i
$430$		0			0
$431$	16.3716	+	9.45215i	0.788592	+	0.455294i	0.839467	−	0.543411i	$-0.182867\pi$
$431$	16.3716	+	9.45215i	0.788592	+	0.455294i	−0.0508743	+	0.998705i	$0.516201\pi$
$432$		0			0
$433$		−	18.1606i		−	0.872741i	−0.899767	−	0.436371i	$-0.856264\pi$
$433$		−	18.1606i		−	0.872741i	0.899767	−	0.436371i	$-0.143736\pi$
$434$		0			0
$435$	20.9706			1.00546
$436$		0			0
$437$	−4.31795	+	7.47890i	−0.206555	+	0.357764i
$438$		0			0
$439$	−19.7210	−	34.1578i	−0.941233	−	1.63026i	−0.763123	−	0.646253i	$-0.776335\pi$
$439$	−19.7210	−	34.1578i	−0.941233	−	1.63026i	−0.178110	−	0.984011i	$-0.556998\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.514719	−	0.891519i	−0.0244550	−	0.0423573i	0.853539	−	0.521029i	$-0.174452\pi$
$443$	−0.514719	−	0.891519i	−0.0244550	−	0.0423573i	−0.877994	+	0.478672i	$0.841118\pi$
$444$		0			0
$445$	32.3053	+	18.6515i	1.53142	+	0.884164i
$446$		0			0
$447$	26.2947			1.24370
$448$		0			0
$449$	36.2843			1.71236			0.856180	−	0.516677i	$-0.172831\pi$
$449$	36.2843			1.71236			0.856180	+	0.516677i	$0.172831\pi$
$450$		0			0
$451$	−5.14179	−	2.96861i	−0.242117	−	0.139787i
$452$		0			0
$453$	−10.4244	−	18.0557i	−0.489783	−	0.848329i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.0208	+	20.8207i	0.562310	+	0.973950i	0.997294	+	0.0735115i	$0.0234206\pi$
$457$	12.0208	+	20.8207i	0.562310	+	0.973950i	−0.434984	+	0.900438i	$0.643246\pi$
$458$		0			0
$459$	0.757359	−	1.31178i	0.0353505	−	0.0612289i
$460$		0			0
$461$	−25.6340			−1.19389			−0.596947	−	0.802280i	$-0.703620\pi$
$461$	−25.6340			−1.19389			−0.596947	+	0.802280i	$0.703620\pi$
$462$		0			0
$463$		−	12.5041i		−	0.581116i	−0.956857	−	0.290558i	$-0.906159\pi$
$463$		−	12.5041i		−	0.581116i	0.956857	−	0.290558i	$-0.0938409\pi$
$464$		0			0
$465$	13.8999	+	8.02509i	0.644590	+	0.372154i
$466$		0			0
$467$	20.6419	−	11.9176i	0.955191	−	0.551480i	0.0605014	−	0.998168i	$-0.480730\pi$
$467$	20.6419	−	11.9176i	0.955191	−	0.551480i	0.894690	+	0.446688i	$0.147397\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.55239	+	1.47363i	−0.117608	+	0.0679011i
$472$		0			0
$473$	11.4853	−	19.8931i	0.528094	−	0.914685i
$474$		0			0
$475$		−	28.7988i		−	1.32138i
$476$		0			0
$477$		−	4.16804i		−	0.190842i
$478$		0			0
$479$	−4.31795	+	7.47890i	−0.197292	+	0.341720i	−0.947649	−	0.319312i	$-0.896548\pi$
$479$	−4.31795	+	7.47890i	−0.197292	+	0.341720i	0.750357	+	0.661032i	$0.229881\pi$
$480$		0			0
$481$	23.7285	−	13.6997i	1.08193	−	0.624652i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−55.4582	+	32.0188i	−2.51823	+	1.45390i
$486$		0			0
$487$	20.6006	+	11.8937i	0.933500	+	0.538957i	0.887917	−	0.460004i	$-0.152152\pi$
$487$	20.6006	+	11.8937i	0.933500	+	0.538957i	0.0455832	+	0.998961i	$0.485485\pi$
$488$		0			0
$489$		−	4.77791i		−	0.216065i
$490$		0			0
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$		0			0
$493$	−0.467177	+	0.809174i	−0.0210406	+	0.0364434i
$494$		0			0
$495$	3.38359	+	5.86055i	0.152081	+	0.263412i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−20.3137	−	35.1844i	−0.909366	−	1.57507i	−0.814946	−	0.579537i	$-0.803234\pi$
$499$	−20.3137	−	35.1844i	−0.909366	−	1.57507i	−0.0944202	−	0.995532i	$-0.530100\pi$
$500$		0			0
$501$	−17.4288	−	10.0625i	−0.778663	−	0.449561i
$502$		0			0
$503$	−34.9306			−1.55748			−0.778739	−	0.627348i	$-0.784140\pi$
$503$	−34.9306			−1.55748			−0.778739	+	0.627348i	$0.784140\pi$
$504$		0			0
$505$	−27.1127			−1.20650
$506$		0			0
$507$	2.92586	+	1.68925i	0.129942	+	0.0750221i
$508$		0			0
$509$	−3.05325	−	5.28838i	−0.135333	−	0.234403i	0.790392	−	0.612602i	$-0.209877\pi$
$509$	−3.05325	−	5.28838i	−0.135333	−	0.234403i	−0.925725	+	0.378198i	$0.876544\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	7.00000	+	12.1244i	0.309058	+	0.535303i
$514$		0			0
$515$	10.4853	−	18.1610i	0.462037	−	0.800271i
$516$		0			0
$517$	32.6749			1.43704
$518$		0			0
$519$		−	37.3029i		−	1.63742i
$520$		0			0
$521$	−39.4561	−	22.7800i	−1.72860	−	0.998008i	−0.895842	−	0.444373i	$-0.853427\pi$
$521$	−39.4561	−	22.7800i	−1.72860	−	0.998008i	−0.832759	−	0.553635i	$-0.813240\pi$
$522$		0			0
$523$	−3.47496	+	2.00627i	−0.151950	+	0.0877281i	−0.574047	−	0.818822i	$-0.694627\pi$
$523$	−3.47496	+	2.00627i	−0.151950	+	0.0877281i	0.422097	+	0.906550i	$0.361294\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.619315	+	0.357562i	−0.0269778	+	0.0155756i
$528$		0			0
$529$	−7.15685	+	12.3960i	−0.311168	+	0.538958i
$530$		0			0
$531$			0.0543929i			0.00236045i
$532$		0			0
$533$		−	5.38883i		−	0.233416i
$534$		0			0
$535$	37.1863	−	64.4086i	1.60770	−	2.78463i
$536$		0			0
$537$	21.8538	−	12.6173i	0.943060	−	0.544476i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−6.59995	+	3.81048i	−0.283754	+	0.163825i	−0.635122	−	0.772412i	$-0.719050\pi$
$541$	−6.59995	+	3.81048i	−0.283754	+	0.163825i	0.351368	+	0.936238i	$0.385717\pi$
$542$		0			0
$543$	−18.4861	−	10.6729i	−0.793314	−	0.458020i
$544$		0			0
$545$			11.3492i			0.486146i
$546$		0			0
$547$	−37.4142			−1.59972			−0.799858	−	0.600189i	$-0.795092\pi$
$547$	−37.4142			−1.59972			−0.799858	+	0.600189i	$0.795092\pi$
$548$		0			0
$549$	−0.330344	+	0.572172i	−0.0140987	+	0.0244197i
$550$		0			0
$551$	−4.31795	−	7.47890i	−0.183951	−	0.318612i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	25.3137	+	43.8446i	1.07451	+	1.86110i
$556$		0			0
$557$	−6.59995	−	3.81048i	−0.279649	−	0.161455i	0.353616	−	0.935391i	$-0.384952\pi$
$557$	−6.59995	−	3.81048i	−0.279649	−	0.161455i	−0.633264	+	0.773936i	$0.718285\pi$
$558$		0			0
$559$	20.8489			0.881814
$560$		0			0
$561$	−2.48528			−0.104929
$562$		0			0
$563$	−29.5332	−	17.0510i	−1.24467	−	0.718613i	−0.274632	−	0.961549i	$-0.588556\pi$
$563$	−29.5332	−	17.0510i	−1.24467	−	0.718613i	−0.970042	+	0.242936i	$0.921889\pi$
$564$		0			0
$565$	−2.72291	−	4.71621i	−0.114553	−	0.198412i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	0.694319	−	0.719667i	$-0.255706\pi$
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	−0.970410	+	0.241464i	$0.922372\pi$
$570$		0			0
$571$	−17.1924	+	29.7781i	−0.719479	+	1.24617i	0.241727	+	0.970344i	$0.422286\pi$
$571$	−17.1924	+	29.7781i	−0.719479	+	1.24617i	−0.961206	+	0.275830i	$0.911047\pi$
$572$		0			0
$573$	18.5932			0.776740
$574$		0			0
$575$			28.9668i			1.20800i
$576$		0			0
$577$	13.5311	+	7.81218i	0.563307	+	0.325225i	0.754472	−	0.656333i	$-0.227893\pi$
$577$	13.5311	+	7.81218i	0.563307	+	0.325225i	−0.191165	+	0.981558i	$0.561227\pi$
$578$		0			0
$579$	10.5386	−	6.08447i	0.437970	−	0.252862i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	36.9722	−	21.3459i	1.53123	−	0.884056i
$584$		0			0
$585$	−3.07107	+	5.31925i	−0.126973	+	0.219924i
$586$		0			0
$587$		−	20.6968i		−	0.854247i	−0.904193	−	0.427124i	$-0.859527\pi$
$587$		−	20.6968i		−	0.854247i	0.904193	−	0.427124i	$-0.140473\pi$
$588$		0			0
$589$		−	6.60963i		−	0.272345i
$590$		0			0
$591$	1.59504	−	2.76269i	0.0656112	−	0.113642i
$592$		0			0
$593$	−36.8714	+	21.2877i	−1.51413	+	0.874181i	−0.514262	+	0.857633i	$0.671934\pi$
$593$	−36.8714	+	21.2877i	−1.51413	+	0.874181i	−0.999863	+	0.0165477i	$0.994732\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.9337	−	9.19932i	0.652122	−	0.376503i
$598$		0			0
$599$	−6.59995	−	3.81048i	−0.269667	−	0.155692i	0.359070	−	0.933311i	$-0.383094\pi$
$599$	−6.59995	−	3.81048i	−0.269667	−	0.155692i	−0.628736	+	0.777619i	$0.716427\pi$
$600$		0			0
$601$		−	20.2166i		−	0.824651i	−0.911037	−	0.412325i	$-0.864717\pi$
$601$		−	20.2166i		−	0.824651i	0.911037	−	0.412325i	$-0.135283\pi$
$602$		0			0
$603$	−0.828427			−0.0337362
$604$		0			0
$605$	−13.4777	+	23.3441i	−0.547946	+	0.949071i
$606$		0			0
$607$	17.9325	+	31.0600i	0.727857	+	1.26068i	0.957787	+	0.287478i	$0.0928167\pi$
$607$	17.9325	+	31.0600i	0.727857	+	1.26068i	−0.229931	+	0.973207i	$0.573850\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.8284	+	25.6836i	0.599894	+	1.03905i
$612$		0			0
$613$	26.5812	+	15.3467i	1.07360	+	0.619845i	0.929164	−	0.369668i	$-0.120529\pi$
$613$	26.5812	+	15.3467i	1.07360	+	0.619845i	0.144440	+	0.989514i	$0.453862\pi$
$614$		0			0
$615$	9.95727			0.401516
$616$		0			0
$617$	−23.1716			−0.932852			−0.466426	−	0.884560i	$-0.654459\pi$
$617$	−23.1716			−0.932852			−0.466426	+	0.884560i	$0.654459\pi$
$618$		0			0
$619$	−24.5522	−	14.1752i	−0.986836	−	0.569750i	−0.0825091	−	0.996590i	$-0.526293\pi$
$619$	−24.5522	−	14.1752i	−0.986836	−	0.569750i	−0.904327	+	0.426840i	$0.859627\pi$
$620$		0			0
$621$	−7.04085	−	12.1951i	−0.282540	−	0.489373i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−11.2279	−	19.4473i	−0.449117	−	0.777893i
$626$		0			0
$627$	11.4853	−	19.8931i	0.458678	−	0.794454i
$628$		0			0
$629$	−2.25573			−0.0899418
$630$		0			0
$631$			32.6292i			1.29895i	0.760383	+	0.649474i	$0.225011\pi$
$631$			32.6292i			1.29895i	−0.760383	+	0.649474i	$0.774989\pi$
$632$		0			0
$633$	23.9560	+	13.8310i	0.952165	+	0.549733i
$634$		0			0
$635$	−57.2858	+	33.0740i	−2.27332	+	1.31250i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.72410	+	3.30481i	−0.226442	+	0.130736i
$640$		0			0
$641$	−11.0711	+	19.1757i	−0.437281	+	0.757393i	−0.997479	−	0.0709661i	$-0.977392\pi$
$641$	−11.0711	+	19.1757i	−0.437281	+	0.757393i	0.560198	+	0.828359i	$0.310725\pi$
$642$		0			0
$643$			25.0263i			0.986942i	0.869762	+	0.493471i	$0.164272\pi$
$643$			25.0263i			0.986942i	−0.869762	+	0.493471i	$0.835728\pi$
$644$		0			0
$645$			38.5237i			1.51687i
$646$		0			0
$647$	−16.5309	+	28.6324i	−0.649898	+	1.12566i	0.333248	+	0.942839i	$0.391855\pi$
$647$	−16.5309	+	28.6324i	−0.649898	+	1.12566i	−0.983147	+	0.182818i	$0.941478\pi$
$648$		0			0
$649$	−0.482487	+	0.278564i	−0.0189393	+	0.0109346i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.5909	+	13.6202i	−0.923182	+	0.532999i	−0.884649	−	0.466258i	$-0.845602\pi$
$653$	−23.5909	+	13.6202i	−0.923182	+	0.532999i	−0.0385332	+	0.999257i	$0.512269\pi$
$654$		0			0
$655$	−55.4582	−	32.0188i	−2.16693	−	1.25108i
$656$		0			0
$657$		−	1.21371i		−	0.0473513i
$658$		0			0
$659$	33.6985			1.31271			0.656353	−	0.754454i	$-0.272098\pi$
$659$	33.6985			1.31271			0.656353	+	0.754454i	$0.272098\pi$
$660$		0			0
$661$	−6.90402	+	11.9581i	−0.268535	+	0.465117i	−0.968484	−	0.249077i	$-0.919873\pi$
$661$	−6.90402	+	11.9581i	−0.268535	+	0.465117i	0.699949	+	0.714193i	$0.253206\pi$
$662$		0			0
$663$	−1.12786	−	1.95352i	−0.0438026	−	0.0758684i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.34315	+	7.52255i	0.168167	+	0.291274i
$668$		0			0
$669$	−8.71442	−	5.03127i	−0.336919	−	0.194520i
$670$		0			0
$671$	−6.76719			−0.261244
$672$		0			0
$673$	−10.1005			−0.389346			−0.194673	−	0.980868i	$-0.562365\pi$
$673$	−10.1005			−0.389346			−0.194673	+	0.980868i	$0.562365\pi$
$674$		0			0
$675$	40.6680	+	23.4797i	1.56531	+	0.903733i
$676$		0			0
$677$	16.0071	+	27.7251i	0.615202	+	1.06556i	0.990349	+	0.138596i	$0.0442590\pi$
$677$	16.0071	+	27.7251i	0.615202	+	1.06556i	−0.375147	+	0.926966i	$0.622408\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	20.1924	+	34.9742i	0.773774	+	1.34022i
$682$		0			0
$683$	−8.51472	+	14.7479i	−0.325807	+	0.564314i	−0.981675	−	0.190561i	$-0.938969\pi$
$683$	−8.51472	+	14.7479i	−0.325807	+	0.564314i	0.655869	+	0.754875i	$0.272303\pi$
$684$		0			0
$685$	44.5008			1.70029
$686$		0			0
$687$			43.1974i			1.64808i
$688$		0			0
$689$	33.5572	+	19.3743i	1.27843	+	0.738101i
$690$		0			0
$691$	−27.6584	+	15.9686i	−1.05218	+	0.607474i	−0.923257	−	0.384182i	$-0.874484\pi$
$691$	−27.6584	+	15.9686i	−1.05218	+	0.607474i	−0.128918	+	0.991655i	$0.541150\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−48.2390	+	27.8508i	−1.82981	+	1.05644i
$696$		0			0
$697$	−0.221825	+	0.384213i	−0.00840224	+	0.0145531i
$698$		0			0
$699$		−	18.2919i		−	0.691862i
$700$		0			0
$701$		−	8.84175i		−	0.333948i	−0.985961	−	0.166974i	$-0.946600\pi$
$701$		−	8.84175i		−	0.333948i	0.985961	−	0.166974i	$-0.0533997\pi$
$702$		0			0
$703$	10.4244	−	18.0557i	0.393165	−	0.680982i
$704$		0			0
$705$	−47.4571	+	27.3994i	−1.78734	+	1.03192i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	41.0197	−	23.6827i	1.54053	−	0.889424i	0.541722	−	0.840558i	$-0.317773\pi$
$709$	41.0197	−	23.6827i	1.54053	−	0.889424i	0.998805	−	0.0488663i	$-0.0155608\pi$
$710$		0			0
$711$	−2.11447	−	1.22079i	−0.0792989	−	0.0457833i
$712$		0			0
$713$			6.64820i			0.248977i
$714$		0			0
$715$	−62.9117			−2.35276
$716$		0			0
$717$	−14.2752	+	24.7254i	−0.533118	+	0.923387i
$718$		0			0
$719$	−7.70154	−	13.3395i	−0.287219	−	0.497478i	0.685926	−	0.727671i	$-0.259397\pi$
$719$	−7.70154	−	13.3395i	−0.287219	−	0.497478i	−0.973145	+	0.230194i	$0.926064\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−16.9497	−	29.3578i	−0.630368	−	1.09183i
$724$		0			0
$725$	−25.0860	−	14.4834i	−0.931672	−	0.537901i
$726$		0			0
$727$	−27.6161			−1.02422			−0.512112	−	0.858919i	$-0.671137\pi$
$727$	−27.6161			−1.02422			−0.512112	+	0.858919i	$0.671137\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$		0			0
$731$	−1.48648	−	0.858221i	−0.0549796	−	0.0317425i
$732$		0			0
$733$	−17.3285	−	30.0138i	−0.640041	−	1.10858i	−0.985423	−	0.170122i	$-0.945584\pi$
$733$	−17.3285	−	30.0138i	−0.640041	−	1.10858i	0.345382	−	0.938462i	$-0.387749\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.24264	−	7.34847i	−0.156280	−	0.270684i
$738$		0			0
$739$	−7.87868	+	13.6463i	−0.289822	+	0.501986i	−0.973767	−	0.227547i	$-0.926929\pi$
$739$	−7.87868	+	13.6463i	−0.289822	+	0.501986i	0.683945	+	0.729533i	$0.260263\pi$
$740$		0			0
$741$	20.8489			0.765903
$742$		0			0
$743$		−	38.0181i		−	1.39475i	−0.716708	−	0.697374i	$-0.754352\pi$
$743$		−	38.0181i		−	1.39475i	0.716708	−	0.697374i	$-0.245648\pi$
$744$		0			0
$745$	−47.4571	−	27.3994i	−1.73869	−	1.00383i
$746$		0			0
$747$	1.37276	−	0.792563i	0.0502267	−	0.0289984i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−38.9052	+	22.4619i	−1.41967	+	0.819648i	−0.996270	−	0.0862936i	$-0.972498\pi$
$751$	−38.9052	+	22.4619i	−1.41967	+	0.819648i	−0.423402	+	0.905942i	$0.639164\pi$
$752$		0			0
$753$	−10.1924	+	17.6537i	−0.371431	+	0.643338i
$754$		0			0
$755$			43.4495i			1.58129i
$756$		0			0
$757$		−	43.9126i		−	1.59603i	−0.602638	−	0.798015i	$-0.705884\pi$
$757$		−	43.9126i		−	1.59603i	0.602638	−	0.798015i	$-0.294116\pi$
$758$		0			0
$759$	−11.5523	+	20.0092i	−0.419322	+	0.726287i
$760$		0			0
$761$	−38.1304	+	22.0146i	−1.38223	+	0.798028i	−0.992423	−	0.122870i	$-0.960790\pi$
$761$	−38.1304	+	22.0146i	−1.38223	+	0.798028i	−0.389803	+	0.920898i	$0.627457\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.437922	−	0.252834i	0.0158331	−	0.00914124i
$766$		0			0
$767$	−0.437922	−	0.252834i	−0.0158124	−	0.00912931i
$768$		0			0
$769$		−	8.15640i		−	0.294127i	−0.989127	−	0.147064i	$-0.953018\pi$
$769$		−	8.15640i		−	0.294127i	0.989127	−	0.147064i	$-0.0469822\pi$
$770$		0			0
$771$	28.3848			1.02225
$772$		0			0
$773$	−0.330344	+	0.572172i	−0.0118816	+	0.0205796i	−0.871905	−	0.489675i	$-0.837115\pi$
$773$	−0.330344	+	0.572172i	−0.0118816	+	0.0205796i	0.860023	+	0.510255i	$0.170449\pi$
$774$		0			0
$775$	−11.0851	−	19.2000i	−0.398190	−	0.689685i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.05025	−	3.55114i	−0.0734579	−	0.127233i
$780$		0			0
$781$	−58.6299	−	33.8500i	−2.09794	−	1.21125i
$782$		0			0
$783$	14.0817			0.503239
$784$		0			0
$785$	6.14214			0.219222
$786$		0			0
$787$	8.93841	+	5.16059i	0.318620	+	0.183955i	0.650777	−	0.759269i	$-0.274443\pi$
$787$	8.93841	+	5.16059i	0.318620	+	0.183955i	−0.332157	+	0.943224i	$0.607776\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.07107	−	5.31925i	−0.109057	−	0.188892i
$794$		0			0
$795$	−35.7990	+	62.0057i	−1.26966	+	2.19911i
$796$		0			0
$797$	8.36223			0.296205			0.148103	−	0.988972i	$-0.452683\pi$
$797$	8.36223			0.296205			0.148103	+	0.988972i	$0.452683\pi$
$798$		0			0
$799$		−	2.44158i		−	0.0863770i
$800$		0			0
$801$	−3.47496	−	2.00627i	−0.122782	−	0.0708881i
$802$		0			0
$803$	10.7661	−	6.21579i	0.379926	−	0.219350i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−23.5909	+	13.6202i	−0.830438	+	0.479454i
$808$		0			0
$809$	10.4645	−	18.1250i	0.367911	−	0.637241i	−0.621328	−	0.783551i	$-0.713406\pi$
$809$	10.4645	−	18.1250i	0.367911	−	0.637241i	0.989239	+	0.146310i	$0.0467398\pi$
$810$		0			0
$811$			30.8548i			1.08346i	0.840553	+	0.541729i	$0.182230\pi$
$811$			30.8548i			1.08346i	−0.840553	+	0.541729i	$0.817770\pi$
$812$		0			0
$813$			24.2931i			0.851997i
$814$		0			0
$815$	−4.97863	+	8.62325i	−0.174394	+	0.302059i
$816$		0			0
$817$	13.7390	−	7.93223i	0.480668	−	0.277514i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	27.6384	−	15.9570i	0.964588	−	0.556905i	0.0670056	−	0.997753i	$-0.478655\pi$
$821$	27.6384	−	15.9570i	0.964588	−	0.556905i	0.897582	+	0.440848i	$0.145322\pi$
$822$		0			0
$823$	−18.9240	−	10.9258i	−0.659649	−	0.380849i	0.132494	−	0.991184i	$-0.457701\pi$
$823$	−18.9240	−	10.9258i	−0.659649	−	0.380849i	−0.792143	+	0.610335i	$0.791035\pi$
$824$		0			0
$825$		−	77.0488i		−	2.68249i
$826$		0			0
$827$	−9.65685			−0.335802			−0.167901	−	0.985804i	$-0.553699\pi$
$827$	−9.65685			−0.335802			−0.167901	+	0.985804i	$0.553699\pi$
$828$		0			0
$829$	20.9857	−	36.3483i	0.728864	−	1.26243i	−0.228499	−	0.973544i	$-0.573382\pi$
$829$	20.9857	−	36.3483i	0.728864	−	1.26243i	0.957364	−	0.288886i	$-0.0932848\pi$
$830$		0			0
$831$	−27.8897	−	48.3064i	−0.967484	−	1.67573i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	20.9706	+	36.3221i	0.725716	+	1.25698i
$836$		0			0
$837$	9.33374	+	5.38883i	0.322621	+	0.186265i
$838$		0			0
$839$	9.95727			0.343763			0.171882	−	0.985118i	$-0.445015\pi$
$839$	9.95727			0.343763			0.171882	+	0.985118i	$0.445015\pi$
$840$		0			0
$841$	20.3137			0.700473
$842$		0			0
$843$	4.91434	+	2.83730i	0.169259	+	0.0977217i
$844$		0			0
$845$	−3.52043	−	6.09756i	−0.121106	−	0.209762i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.1213	−	24.4588i	−0.484642	−	0.839425i
$850$		0			0
$851$	−10.4853	+	18.1610i	−0.359431	+	0.622552i
$852$		0			0
$853$	−13.8080			−0.472778			−0.236389	−	0.971658i	$-0.575964\pi$
$853$	−13.8080			−0.472778			−0.236389	+	0.971658i	$0.575964\pi$
$854$		0			0
$855$			4.67371i			0.159838i
$856$		0			0
$857$	31.1139	+	17.9636i	1.06283	+	0.613625i	0.926213	−	0.377000i	$-0.123044\pi$
$857$	31.1139	+	17.9636i	1.06283	+	0.613625i	0.136616	+	0.990624i	$0.456378\pi$
$858$		0			0
$859$	−28.9174	+	16.6955i	−0.986650	+	0.569643i	−0.904271	−	0.426958i	$-0.859585\pi$
$859$	−28.9174	+	16.6955i	−0.986650	+	0.569643i	−0.0823789	+	0.996601i	$0.526252\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.3144	−	8.84175i	0.521307	−	0.300977i	−0.216162	−	0.976357i	$-0.569354\pi$
$863$	15.3144	−	8.84175i	0.521307	−	0.300977i	0.737469	+	0.675381i	$0.236021\pi$
$864$		0			0
$865$	−38.8701	+	67.3249i	−1.32162	+	2.28912i
$866$		0			0
$867$		−	31.2262i		−	1.06050i
$868$		0			0
$869$		−	25.0083i		−	0.848347i
$870$		0			0
$871$	3.85077	−	6.66973i	0.130478	−	0.225995i
$872$		0			0
$873$	5.96544	−	3.44415i	0.201900	−	0.116567i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.7620	−	7.36813i	0.430941	−	0.248804i	−0.268806	−	0.963194i	$-0.586629\pi$
$877$	12.7620	−	7.36813i	0.430941	−	0.248804i	0.699748	+	0.714390i	$0.253296\pi$
$878$		0			0
$879$	25.7053	+	14.8410i	0.867020	+	0.500574i
$880$		0			0
$881$			21.2220i			0.714988i	0.933915	+	0.357494i	$0.116369\pi$
$881$			21.2220i			0.714988i	−0.933915	+	0.357494i	$0.883631\pi$
$882$		0			0
$883$	2.34315			0.0788531			0.0394266	−	0.999222i	$-0.487447\pi$
$883$	2.34315			0.0788531			0.0394266	+	0.999222i	$0.487447\pi$
$884$		0			0
$885$	0.467177	−	0.809174i	0.0157040	−	0.0272001i
$886$		0			0
$887$	−6.10650	−	10.5768i	−0.205036	−	0.355133i	0.745108	−	0.666944i	$-0.232398\pi$
$887$	−6.10650	−	10.5768i	−0.205036	−	0.355133i	−0.950144	+	0.311811i	$0.899065\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	21.3640	+	37.0035i	0.715720	+	1.23966i
$892$		0			0
$893$	19.5433	+	11.2833i	0.653992	+	0.377582i
$894$		0			0
$895$	−52.5894			−1.75787
$896$		0			0
$897$	−20.9706			−0.700187
$898$		0			0
$899$	−5.75751	−	3.32410i	−0.192024	−	0.110865i
$900$		0			0
$901$	−1.59504	−	2.76269i	−0.0531385	−	0.0920386i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	22.2426	+	38.5254i	0.739370	+	1.28063i
$906$		0			0
$907$	1.51472	−	2.62357i	0.0502954	−	0.0871142i	−0.839782	−	0.542924i	$-0.817317\pi$
$907$	1.51472	−	2.62357i	0.0502954	−	0.0871142i	0.890077	+	0.455810i	$0.150650\pi$
$908$		0			0
$909$	2.91642			0.0967314
$910$		0			0
$911$		−	14.7363i		−	0.488234i	−0.969746	−	0.244117i	$-0.921502\pi$
$911$		−	14.7363i		−	0.488234i	0.969746	−	0.244117i	$-0.0784981\pi$
$912$		0			0
$913$	14.0607	+	8.11794i	0.465341	+	0.268665i
$914$		0			0
$915$	9.82868	−	5.67459i	0.324926	−	0.187596i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	13.8192	−	7.97852i	0.455854	−	0.263187i	−0.254446	−	0.967087i	$-0.581893\pi$
$919$	13.8192	−	7.97852i	0.455854	−	0.263187i	0.710299	+	0.703900i	$0.248560\pi$
$920$		0			0
$921$	−13.1213	+	22.7268i	−0.432362	+	0.748873i
$922$		0			0
$923$		−	61.4469i		−	2.02255i
$924$		0			0
$925$		−	69.9322i		−	2.29936i
$926$		0			0
$927$	−1.12786	+	1.95352i	−0.0370439	+	0.0641620i
$928$		0			0
$929$	−6.67538	+	3.85403i	−0.219012	+	0.126447i	−0.605493	−	0.795851i	$-0.707024\pi$
$929$	−6.67538	+	3.85403i	−0.219012	+	0.126447i	0.386481	+	0.922297i	$0.373691\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−42.0769	+	24.2931i	−1.37754	+	0.795322i
$934$		0			0
$935$	4.48547	+	2.58969i	0.146691	+	0.0846919i
$936$		0			0
$937$			17.9749i			0.587213i	0.955926	+	0.293606i	$0.0948555\pi$
$937$			17.9749i			0.587213i	−0.955926	+	0.293606i	$0.905144\pi$
$938$		0			0
$939$	29.4142			0.959897
$940$		0			0
$941$	22.1136	−	38.3019i	0.720882	−	1.24860i	−0.239764	−	0.970831i	$-0.577070\pi$
$941$	22.1136	−	38.3019i	0.720882	−	1.24860i	0.960647	−	0.277774i	$-0.0895965\pi$
$942$		0			0
$943$	2.06222	+	3.57187i	0.0671550	+	0.116316i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.6066	−	21.8353i	−0.409660	−	0.709551i	0.585192	−	0.810895i	$-0.301019\pi$
$947$	−12.6066	−	21.8353i	−0.409660	−	0.709551i	−0.994851	+	0.101344i	$0.967686\pi$
$948$		0			0
$949$	9.77166	+	5.64167i	0.317201	+	0.183136i
$950$		0			0
$951$	−15.4031			−0.499479
$952$		0			0
$953$	5.37258			0.174035			0.0870175	−	0.996207i	$-0.472266\pi$
$953$	5.37258			0.174035			0.0870175	+	0.996207i	$0.472266\pi$
$954$		0			0
$955$	−33.5572	−	19.3743i	−1.08589	−	0.626937i
$956$		0			0
$957$	−11.5523	−	20.0092i	−0.373433	−	0.646805i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.9558	+	22.4402i	0.417930	+	0.723877i
$962$		0			0
$963$	−4.00000	+	6.92820i	−0.128898	+	0.223258i
$964$		0			0
$965$	−25.3603			−0.816378
$966$		0			0
$967$			8.84175i			0.284332i	0.989843	+	0.142166i	$0.0454066\pi$
$967$			8.84175i			0.284332i	−0.989843	+	0.142166i	$0.954593\pi$
$968$		0			0
$969$	−1.48648	−	0.858221i	−0.0477527	−	0.0275700i
$970$		0			0
$971$	−25.7170	+	14.8477i	−0.825299	+	0.476486i	−0.852240	−	0.523151i	$-0.824757\pi$
$971$	−25.7170	+	14.8477i	−0.825299	+	0.476486i	0.0269416	+	0.999637i	$0.491423\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	60.5630	−	34.9661i	1.93957	−	1.11981i
$976$		0			0
$977$	−1.87868	+	3.25397i	−0.0601043	+	0.104104i	−0.894512	−	0.447044i	$-0.852477\pi$
$977$	−1.87868	+	3.25397i	−0.0601043	+	0.104104i	0.834408	+	0.551148i	$0.185810\pi$
$978$		0			0
$979$		−	41.0990i		−	1.31353i
$980$		0			0
$981$		−	1.22079i		−	0.0389769i
$982$		0			0
$983$	1.12786	−	1.95352i	0.0359733	−	0.0623076i	−0.847478	−	0.530830i	$-0.821880\pi$
$983$	1.12786	−	1.95352i	0.0359733	−	0.0623076i	0.883452	+	0.468523i	$0.155214\pi$
$984$		0			0
$985$	−5.75751	+	3.32410i	−0.183450	+	0.105915i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.8192	+	7.97852i	−0.439425	+	0.253702i
$990$		0			0
$991$	31.2481	+	18.0411i	0.992627	+	0.573093i	0.906059	−	0.423152i	$-0.139077\pi$
$991$	31.2481	+	18.0411i	0.992627	+	0.573093i	0.0865685	+	0.996246i	$0.472410\pi$
$992$		0			0
$993$			20.4567i			0.649173i
$994$		0			0
$995$	−38.3431			−1.21556
$996$		0			0
$997$	−5.11547	+	8.86025i	−0.162008	+	0.280607i	−0.935589	−	0.353091i	$-0.885131\pi$
$997$	−5.11547	+	8.86025i	−0.162008	+	0.280607i	0.773580	+	0.633698i	$0.218464\pi$
$998$		0			0
$999$	16.9981	+	29.4416i	0.537797	+	0.931491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.q.h.815.7		16
4.3	odd	2		392.2.m.h.227.1		16
7.2	even	3	inner	1568.2.q.h.1391.1		16
7.3	odd	6		1568.2.e.d.783.7		8
7.4	even	3		1568.2.e.d.783.2		8
7.5	odd	6	inner	1568.2.q.h.1391.8		16
7.6	odd	2	inner	1568.2.q.h.815.2		16
8.3	odd	2	inner	1568.2.q.h.815.8		16
8.5	even	2		392.2.m.h.227.5		16
28.3	even	6		392.2.e.d.195.5	✓	8
28.11	odd	6		392.2.e.d.195.6	yes	8
28.19	even	6		392.2.m.h.19.5		16
28.23	odd	6		392.2.m.h.19.6		16
28.27	even	2		392.2.m.h.227.2		16
56.3	even	6		1568.2.e.d.783.8		8
56.5	odd	6		392.2.m.h.19.1		16
56.11	odd	6		1568.2.e.d.783.1		8
56.13	odd	2		392.2.m.h.227.6		16
56.19	even	6	inner	1568.2.q.h.1391.7		16
56.27	even	2	inner	1568.2.q.h.815.1		16
56.37	even	6		392.2.m.h.19.2		16
56.45	odd	6		392.2.e.d.195.7	yes	8
56.51	odd	6	inner	1568.2.q.h.1391.2		16
56.53	even	6		392.2.e.d.195.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.5	✓	8	28.3	even	6
392.2.e.d.195.6	yes	8	28.11	odd	6
392.2.e.d.195.7	yes	8	56.45	odd	6
392.2.e.d.195.8	yes	8	56.53	even	6
392.2.m.h.19.1		16	56.5	odd	6
392.2.m.h.19.2		16	56.37	even	6
392.2.m.h.19.5		16	28.19	even	6
392.2.m.h.19.6		16	28.23	odd	6
392.2.m.h.227.1		16	4.3	odd	2
392.2.m.h.227.2		16	28.27	even	2
392.2.m.h.227.5		16	8.5	even	2
392.2.m.h.227.6		16	56.13	odd	2
1568.2.e.d.783.1		8	56.11	odd	6
1568.2.e.d.783.2		8	7.4	even	3
1568.2.e.d.783.7		8	7.3	odd	6
1568.2.e.d.783.8		8	56.3	even	6
1568.2.q.h.815.1		16	56.27	even	2	inner
1568.2.q.h.815.2		16	7.6	odd	2	inner
1568.2.q.h.815.7		16	1.1	even	1	trivial
1568.2.q.h.815.8		16	8.3	odd	2	inner
1568.2.q.h.1391.1		16	7.2	even	3	inner
1568.2.q.h.1391.2		16	56.51	odd	6	inner
1568.2.q.h.1391.7		16	56.19	even	6	inner
1568.2.q.h.1391.8		16	7.5	odd	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60021 + 0.923880i) q^{3} +(-1.92538 - 3.33486i) q^{5} +(0.207107 + 0.358719i) q^{9} +(-2.12132 + 3.67423i) q^{11} -3.85077 q^{13} -7.11529i q^{15} +(0.274552 + 0.158513i) q^{17} +(-2.53759 + 1.46508i) q^{19} +(2.55239 - 1.47363i) q^{23} +(-4.91421 + 8.51167i) q^{25} -4.77791i q^{27} +2.94725i q^{29} +(-1.12786 + 1.95352i) q^{31} +(-6.78910 + 3.91969i) q^{33} +(-6.16203 + 3.55765i) q^{37} +(-6.16203 - 3.55765i) q^{39} +1.39942i q^{41} -5.41421 q^{43} +(0.797521 - 1.38135i) q^{45} +(-3.85077 - 6.66973i) q^{47} +(0.292893 + 0.507306i) q^{51} +(-8.71442 - 5.03127i) q^{53} +16.3374 q^{55} -5.41421 q^{57} +(0.113723 + 0.0656581i) q^{59} +(0.797521 + 1.38135i) q^{61} +(7.41421 + 12.8418i) q^{65} +(-1.00000 + 1.73205i) q^{67} +5.44581 q^{69} +15.9570i q^{71} +(-2.53759 - 1.46508i) q^{73} +(-15.7275 + 9.08028i) q^{75} +(-5.10479 + 2.94725i) q^{79} +(5.03553 - 8.72180i) q^{81} -3.82683i q^{83} -1.22079i q^{85} +(-2.72291 + 4.71621i) q^{87} +(-8.38931 + 4.84357i) q^{89} +(-3.60963 + 2.08402i) q^{93} +(9.77166 + 5.64167i) q^{95} -16.6298i q^{97} -1.75736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} - 56 q^{25} - 64 q^{43} + 16 q^{51} - 64 q^{57} + 96 q^{65} - 16 q^{67} + 24 q^{81} - 96 q^{99}+O(q^{100}) \) 16 * q - 8 * q^9 - 56 * q^25 - 64 * q^43 + 16 * q^51 - 64 * q^57 + 96 * q^65 - 16 * q^67 + 24 * q^81 - 96 * q^99

Introduction

L-functions

Modular forms

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Database

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