LMFDB - Embedded newform 968.2.i.b.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.i (of order $5$ , degree $4$ , 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	968.729
Dual form			968.2.i.b.81.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 3.07768i) q^{3} +(-1.80902 - 1.31433i) q^{5} +(1.00000 - 3.07768i) q^{7} +(-6.04508 + 4.39201i) q^{9} +(-1.42705 + 1.03681i) q^{13} +(-2.23607 + 6.88191i) q^{15} +(-0.809017 - 0.587785i) q^{17} +(-1.76393 - 5.42882i) q^{19} -10.4721 q^{21} +0.763932 q^{23} +(11.7082 + 8.50651i) q^{27} +(0.545085 - 1.67760i) q^{29} +(-3.85410 + 2.80017i) q^{31} +(-5.85410 + 4.25325i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(4.61803 + 3.35520i) q^{39} +(2.30902 + 7.10642i) q^{41} +10.4721 q^{43} +16.7082 q^{45} +(1.76393 + 5.42882i) q^{47} +(-2.80902 - 2.04087i) q^{49} +(-1.00000 + 3.07768i) q^{51} +(10.6631 - 7.74721i) q^{53} +(-14.9443 + 10.8576i) q^{57} +(-1.70820 + 5.25731i) q^{59} +(-12.0902 - 8.78402i) q^{61} +(7.47214 + 22.9969i) q^{63} +3.94427 q^{65} -0.763932 q^{67} +(-0.763932 - 2.35114i) q^{69} +(3.23607 + 2.35114i) q^{71} +(1.09017 - 3.35520i) q^{73} +(5.85410 - 4.25325i) q^{79} +(7.54508 - 23.2214i) q^{81} +(-9.85410 - 7.15942i) q^{83} +(0.690983 + 2.12663i) q^{85} -5.70820 q^{87} -12.4164 q^{89} +(1.76393 + 5.42882i) q^{91} +(12.4721 + 9.06154i) q^{93} +(-3.94427 + 12.1392i) q^{95} +(-9.66312 + 7.02067i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{3} - 5 q^{5} + 4 q^{7} - 13 q^{9} + q^{13} - q^{17} - 16 q^{19} - 24 q^{21} + 12 q^{23} + 20 q^{27} - 9 q^{29} - 2 q^{31} - 10 q^{35} - 7 q^{37} + 14 q^{39} + 7 q^{41} + 24 q^{43} + 40 q^{45}+ \cdots - 23 q^{97}+O(q^{100})$ 4 * q - 4 * q^3 - 5 * q^5 + 4 * q^7 - 13 * q^9 + q^13 - q^17 - 16 * q^19 - 24 * q^21 + 12 * q^23 + 20 * q^27 - 9 * q^29 - 2 * q^31 - 10 * q^35 - 7 * q^37 + 14 * q^39 + 7 * q^41 + 24 * q^43 + 40 * q^45 + 16 * q^47 - 9 * q^49 - 4 * q^51 + 27 * q^53 - 24 * q^57 + 20 * q^59 - 26 * q^61 + 12 * q^63 - 20 * q^65 - 12 * q^67 - 12 * q^69 + 4 * q^71 - 18 * q^73 + 10 * q^79 + 19 * q^81 - 26 * q^83 + 5 * q^85 + 4 * q^87 + 4 * q^89 + 16 * q^91 + 32 * q^93 + 20 * q^95 - 23 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−1.00000	−	3.07768i	−0.577350	−	1.77690i	−0.628033	−	0.778187i	$-0.716140\pi$
$3$	−1.00000	−	3.07768i	−0.577350	−	1.77690i	0.0506828	−	0.998715i	$-0.483860\pi$
$4$		0			0
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$6$		0			0
$7$	1.00000	−	3.07768i	0.377964	−	1.16326i	−0.563492	−	0.826121i	$-0.690543\pi$
$7$	1.00000	−	3.07768i	0.377964	−	1.16326i	0.941457	−	0.337134i	$-0.109457\pi$
$8$		0			0
$9$	−6.04508	+	4.39201i	−2.01503	+	1.46400i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−1.42705	+	1.03681i	−0.395793	+	0.287560i	−0.767825	−	0.640660i	$-0.778661\pi$
$13$	−1.42705	+	1.03681i	−0.395793	+	0.287560i	0.372032	+	0.928220i	$0.378661\pi$
$14$		0			0
$15$	−2.23607	+	6.88191i	−0.577350	+	1.77690i
$16$		0			0
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i	0.485340	−	0.874326i	$-0.338696\pi$
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i	−0.681555	+	0.731767i	$0.738696\pi$
$18$		0			0
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	−0.921167	−	0.389167i	$-0.872763\pi$
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	0.516494	−	0.856291i	$-0.327237\pi$
$20$		0			0
$21$	−10.4721			−2.28521
$22$		0			0
$23$	0.763932			0.159291			0.0796454	−	0.996823i	$-0.474621\pi$
$23$	0.763932			0.159291			0.0796454	+	0.996823i	$0.474621\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	11.7082	+	8.50651i	2.25324	+	1.63708i
$28$		0			0
$29$	0.545085	−	1.67760i	0.101220	−	0.311522i	−0.887605	−	0.460606i	$-0.847632\pi$
$29$	0.545085	−	1.67760i	0.101220	−	0.311522i	0.988825	+	0.149083i	$0.0476323\pi$
$30$		0			0
$31$	−3.85410	+	2.80017i	−0.692217	+	0.502925i	−0.877388	−	0.479781i	$-0.840716\pi$
$31$	−3.85410	+	2.80017i	−0.692217	+	0.502925i	0.185171	+	0.982706i	$0.440716\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.85410	+	4.25325i	−0.989524	+	0.718931i
$36$		0			0
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	−0.956874	−	0.290504i	$-0.906177\pi$
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	0.944881	+	0.327414i	$0.106177\pi$
$38$		0			0
$39$	4.61803	+	3.35520i	0.739477	+	0.537262i
$40$		0			0
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	0.952686	+	0.303956i	$0.0983077\pi$
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	−0.592078	+	0.805881i	$0.701692\pi$
$42$		0			0
$43$	10.4721			1.59699			0.798493	−	0.602004i	$-0.205631\pi$
$43$	10.4721			1.59699			0.798493	+	0.602004i	$0.205631\pi$
$44$		0			0
$45$	16.7082			2.49071
$46$		0			0
$47$	1.76393	+	5.42882i	0.257296	+	0.791875i	0.993369	+	0.114973i	$0.0366781\pi$
$47$	1.76393	+	5.42882i	0.257296	+	0.791875i	−0.736073	+	0.676902i	$0.763322\pi$
$48$		0			0
$49$	−2.80902	−	2.04087i	−0.401288	−	0.291553i
$50$		0			0
$51$	−1.00000	+	3.07768i	−0.140028	+	0.430962i
$52$		0			0
$53$	10.6631	−	7.74721i	1.46469	−	1.06416i	0.482582	−	0.875851i	$-0.339699\pi$
$53$	10.6631	−	7.74721i	1.46469	−	1.06416i	0.982110	−	0.188311i	$-0.0603011\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−14.9443	+	10.8576i	−1.97942	+	1.43813i
$58$		0			0
$59$	−1.70820	+	5.25731i	−0.222389	+	0.684444i	0.776157	+	0.630540i	$0.217166\pi$
$59$	−1.70820	+	5.25731i	−0.222389	+	0.684444i	−0.998546	+	0.0539038i	$0.982834\pi$
$60$		0			0
$61$	−12.0902	−	8.78402i	−1.54799	−	1.12468i	−0.945067	−	0.326878i	$-0.894003\pi$
$61$	−12.0902	−	8.78402i	−1.54799	−	1.12468i	−0.602921	−	0.797801i	$-0.705997\pi$
$62$		0			0
$63$	7.47214	+	22.9969i	0.941401	+	2.89733i
$64$		0			0
$65$	3.94427			0.489227
$66$		0			0
$67$	−0.763932			−0.0933292			−0.0466646	−	0.998911i	$-0.514859\pi$
$67$	−0.763932			−0.0933292			−0.0466646	+	0.998911i	$0.514859\pi$
$68$		0			0
$69$	−0.763932	−	2.35114i	−0.0919666	−	0.283044i
$70$		0			0
$71$	3.23607	+	2.35114i	0.384051	+	0.279029i	0.763013	−	0.646383i	$-0.223719\pi$
$71$	3.23607	+	2.35114i	0.384051	+	0.279029i	−0.378963	+	0.925412i	$0.623719\pi$
$72$		0			0
$73$	1.09017	−	3.35520i	0.127595	−	0.392696i	−0.866770	−	0.498708i	$-0.833808\pi$
$73$	1.09017	−	3.35520i	0.127595	−	0.392696i	0.994365	+	0.106012i	$0.0338081\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.85410	−	4.25325i	0.658638	−	0.478528i	−0.207565	−	0.978221i	$-0.566554\pi$
$79$	5.85410	−	4.25325i	0.658638	−	0.478528i	0.866203	+	0.499693i	$0.166554\pi$
$80$		0			0
$81$	7.54508	−	23.2214i	0.838343	−	2.58015i
$82$		0			0
$83$	−9.85410	−	7.15942i	−1.08163	−	0.785849i	−0.103662	−	0.994613i	$-0.533056\pi$
$83$	−9.85410	−	7.15942i	−1.08163	−	0.785849i	−0.977966	+	0.208764i	$0.933056\pi$
$84$		0			0
$85$	0.690983	+	2.12663i	0.0749476	+	0.230665i
$86$		0			0
$87$	−5.70820			−0.611984
$88$		0			0
$89$	−12.4164			−1.31614			−0.658068	−	0.752958i	$-0.728626\pi$
$89$	−12.4164			−1.31614			−0.658068	+	0.752958i	$0.728626\pi$
$90$		0			0
$91$	1.76393	+	5.42882i	0.184910	+	0.569095i
$92$		0			0
$93$	12.4721	+	9.06154i	1.29330	+	0.939638i
$94$		0			0
$95$	−3.94427	+	12.1392i	−0.404674	+	1.24546i
$96$		0			0
$97$	−9.66312	+	7.02067i	−0.981141	+	0.712841i	−0.957963	−	0.286891i	$-0.907378\pi$
$97$	−9.66312	+	7.02067i	−0.981141	+	0.712841i	−0.0231777	+	0.999731i	$0.507378\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	−0.665368	−	0.746515i	$-0.731726\pi$
$101$	−1.61803	+	1.17557i	−0.161000	+	0.116974i	0.504368	+	0.863489i	$0.331726\pi$
$102$		0			0
$103$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$103$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$104$		0			0
$105$	18.9443	+	13.7638i	1.84877	+	1.34321i
$106$		0			0
$107$	0.527864	+	1.62460i	0.0510305	+	0.157056i	0.973324	−	0.229434i	$-0.0736875\pi$
$107$	0.527864	+	1.62460i	0.0510305	+	0.157056i	−0.922294	+	0.386490i	$0.873687\pi$
$108$		0			0
$109$	−6.23607			−0.597307			−0.298653	−	0.954362i	$-0.596537\pi$
$109$	−6.23607			−0.597307			−0.298653	+	0.954362i	$0.596537\pi$
$110$		0			0
$111$	0.763932			0.0725092
$112$		0			0
$113$	6.16312	+	18.9681i	0.579777	+	1.78437i	0.619302	+	0.785153i	$0.287416\pi$
$113$	6.16312	+	18.9681i	0.579777	+	1.78437i	−0.0395244	+	0.999219i	$0.512584\pi$
$114$		0			0
$115$	−1.38197	−	1.00406i	−0.128869	−	0.0936288i
$116$		0			0
$117$	4.07295	−	12.5352i	0.376544	−	1.15888i
$118$		0			0
$119$	−2.61803	+	1.90211i	−0.239995	+	0.174366i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	19.5623	−	14.2128i	1.76387	−	1.28153i
$124$		0			0
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$		0			0
$127$	−14.9443	−	10.8576i	−1.32609	−	0.963461i	−0.999835	−	0.0181787i	$-0.994213\pi$
$127$	−14.9443	−	10.8576i	−1.32609	−	0.963461i	−0.326255	−	0.945282i	$-0.605787\pi$
$128$		0			0
$129$	−10.4721	−	32.2299i	−0.922020	−	2.83769i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	−18.4721			−1.60174
$134$		0			0
$135$	−10.0000	−	30.7768i	−0.860663	−	2.64885i
$136$		0			0
$137$	−6.09017	−	4.42477i	−0.520318	−	0.378033i	0.296405	−	0.955062i	$-0.404212\pi$
$137$	−6.09017	−	4.42477i	−0.520318	−	0.378033i	−0.816724	+	0.577029i	$0.804212\pi$
$138$		0			0
$139$	4.70820	−	14.4904i	0.399345	−	1.22906i	−0.526181	−	0.850372i	$-0.676377\pi$
$139$	4.70820	−	14.4904i	0.399345	−	1.22906i	0.925526	−	0.378684i	$-0.123623\pi$
$140$		0			0
$141$	14.9443	−	10.8576i	1.25853	−	0.914379i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−3.19098	+	2.31838i	−0.264997	+	0.192531i
$146$		0			0
$147$	−3.47214	+	10.6861i	−0.286377	+	0.881378i
$148$		0			0
$149$	8.28115	+	6.01661i	0.678418	+	0.492900i	0.872833	−	0.488020i	$-0.162281\pi$
$149$	8.28115	+	6.01661i	0.678418	+	0.492900i	−0.194414	+	0.980920i	$0.562281\pi$
$150$		0			0
$151$	−2.29180	−	7.05342i	−0.186504	−	0.573999i	0.813467	−	0.581611i	$-0.197577\pi$
$151$	−2.29180	−	7.05342i	−0.186504	−	0.573999i	−0.999971	+	0.00761121i	$0.997577\pi$
$152$		0			0
$153$	7.47214			0.604086
$154$		0			0
$155$	10.6525			0.855627
$156$		0			0
$157$	−3.85410	−	11.8617i	−0.307591	−	0.946667i	−0.978698	−	0.205307i	$-0.934181\pi$
$157$	−3.85410	−	11.8617i	−0.307591	−	0.946667i	0.671107	−	0.741361i	$-0.265819\pi$
$158$		0			0
$159$	−34.5066	−	25.0705i	−2.73655	−	1.98822i
$160$		0			0
$161$	0.763932	−	2.35114i	0.0602063	−	0.185296i
$162$		0			0
$163$	−4.61803	+	3.35520i	−0.361712	+	0.262799i	−0.753766	−	0.657143i	$-0.771765\pi$
$163$	−4.61803	+	3.35520i	−0.361712	+	0.262799i	0.392054	+	0.919942i	$0.371765\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.23607	+	6.71040i	−0.714708	+	0.519266i	−0.884689	−	0.466181i	$-0.845629\pi$
$167$	−9.23607	+	6.71040i	−0.714708	+	0.519266i	0.169981	+	0.985447i	$0.445629\pi$
$168$		0			0
$169$	−3.05573	+	9.40456i	−0.235056	+	0.723428i
$170$		0			0
$171$	34.5066	+	25.0705i	2.63878	+	1.91719i
$172$		0			0
$173$	−5.85410	−	18.0171i	−0.445079	−	1.36981i	−0.882397	−	0.470506i	$-0.844072\pi$
$173$	−5.85410	−	18.0171i	−0.445079	−	1.36981i	0.437318	−	0.899307i	$-0.355928\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	17.8885			1.34459
$178$		0			0
$179$	−0.763932	−	2.35114i	−0.0570990	−	0.175733i	0.918439	−	0.395562i	$-0.129450\pi$
$179$	−0.763932	−	2.35114i	−0.0570990	−	0.175733i	−0.975538	+	0.219829i	$0.929450\pi$
$180$		0			0
$181$	−10.2812	−	7.46969i	−0.764192	−	0.555218i	0.136001	−	0.990709i	$-0.456575\pi$
$181$	−10.2812	−	7.46969i	−0.764192	−	0.555218i	−0.900193	+	0.435491i	$0.856575\pi$
$182$		0			0
$183$	−14.9443	+	45.9937i	−1.10471	+	3.39996i
$184$		0			0
$185$	0.427051	−	0.310271i	0.0313974	−	0.0228116i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	37.8885	−	27.5276i	2.75599	−	2.00234i
$190$		0			0
$191$	1.70820	−	5.25731i	0.123601	−	0.380406i	−0.870042	−	0.492977i	$-0.835909\pi$
$191$	1.70820	−	5.25731i	0.123601	−	0.380406i	0.993644	+	0.112571i	$0.0359087\pi$
$192$		0			0
$193$	3.19098	+	2.31838i	0.229692	+	0.166881i	0.696679	−	0.717383i	$-0.254660\pi$
$193$	3.19098	+	2.31838i	0.229692	+	0.166881i	−0.466987	+	0.884264i	$0.654660\pi$
$194$		0			0
$195$	−3.94427	−	12.1392i	−0.282455	−	0.869308i
$196$		0			0
$197$	−17.6525			−1.25769			−0.628843	−	0.777532i	$-0.716471\pi$
$197$	−17.6525			−1.25769			−0.628843	+	0.777532i	$0.716471\pi$
$198$		0			0
$199$	−18.4721			−1.30945			−0.654727	−	0.755865i	$-0.727217\pi$
$199$	−18.4721			−1.30945			−0.654727	+	0.755865i	$0.727217\pi$
$200$		0			0
$201$	0.763932	+	2.35114i	0.0538836	+	0.165837i
$202$		0			0
$203$	−4.61803	−	3.35520i	−0.324122	−	0.235489i
$204$		0			0
$205$	5.16312	−	15.8904i	0.360608	−	1.10984i
$206$		0			0
$207$	−4.61803	+	3.35520i	−0.320976	+	0.233202i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	5.70820	−	4.14725i	0.392969	−	0.285509i	−0.373702	−	0.927549i	$-0.621912\pi$
$211$	5.70820	−	4.14725i	0.392969	−	0.285509i	0.766671	+	0.642040i	$0.221912\pi$
$212$		0			0
$213$	4.00000	−	12.3107i	0.274075	−	0.843518i
$214$		0			0
$215$	−18.9443	−	13.7638i	−1.29199	−	0.938685i
$216$		0			0
$217$	4.76393	+	14.6619i	0.323397	+	0.995313i
$218$		0			0
$219$	−11.4164			−0.771449
$220$		0			0
$221$	1.76393			0.118655
$222$		0			0
$223$	2.76393	+	8.50651i	0.185087	+	0.569638i	0.999950	−	0.0100153i	$-0.00318802\pi$
$223$	2.76393	+	8.50651i	0.185087	+	0.569638i	−0.814863	+	0.579653i	$0.803188\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.763932	+	2.35114i	−0.0507039	+	0.156051i	−0.973202	−	0.229950i	$-0.926144\pi$
$227$	−0.763932	+	2.35114i	−0.0507039	+	0.156051i	0.922499	+	0.386001i	$0.126144\pi$
$228$		0			0
$229$	2.19098	−	1.59184i	0.144784	−	0.105192i	−0.513035	−	0.858368i	$-0.671479\pi$
$229$	2.19098	−	1.59184i	0.144784	−	0.105192i	0.657819	+	0.753176i	$0.271479\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.89919	−	6.46564i	0.583005	−	0.423578i	−0.256801	−	0.966464i	$-0.582669\pi$
$233$	8.89919	−	6.46564i	0.583005	−	0.423578i	0.839806	+	0.542886i	$0.182669\pi$
$234$		0			0
$235$	3.94427	−	12.1392i	0.257296	−	0.791875i
$236$		0			0
$237$	−18.9443	−	13.7638i	−1.23056	−	0.894056i
$238$		0			0
$239$	−6.23607	−	19.1926i	−0.403378	−	1.24147i	−0.922242	−	0.386612i	$-0.873645\pi$
$239$	−6.23607	−	19.1926i	−0.403378	−	1.24147i	0.518865	−	0.854856i	$-0.326355\pi$
$240$		0			0
$241$	3.52786			0.227250			0.113625	−	0.993524i	$-0.463754\pi$
$241$	3.52786			0.227250			0.113625	+	0.993524i	$0.463754\pi$
$242$		0			0
$243$	−35.5967			−2.28353
$244$		0			0
$245$	2.39919	+	7.38394i	0.153278	+	0.471743i
$246$		0			0
$247$	8.14590	+	5.91834i	0.518311	+	0.376575i
$248$		0			0
$249$	−12.1803	+	37.4872i	−0.771898	+	2.37566i
$250$		0			0
$251$	16.7984	−	12.2047i	1.06030	−	0.770356i	0.0861594	−	0.996281i	$-0.472541\pi$
$251$	16.7984	−	12.2047i	1.06030	−	0.770356i	0.974145	+	0.225925i	$0.0725406\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	5.85410	−	4.25325i	0.366598	−	0.266349i
$256$		0			0
$257$	−4.48936	+	13.8168i	−0.280038	+	0.861870i	0.707804	+	0.706409i	$0.249686\pi$
$257$	−4.48936	+	13.8168i	−0.280038	+	0.861870i	−0.987842	+	0.155460i	$0.950314\pi$
$258$		0			0
$259$	0.618034	+	0.449028i	0.0384028	+	0.0279012i
$260$		0			0
$261$	4.07295	+	12.5352i	0.252109	+	0.775912i
$262$		0			0
$263$	6.65248			0.410209			0.205105	−	0.978740i	$-0.434247\pi$
$263$	6.65248			0.410209			0.205105	+	0.978740i	$0.434247\pi$
$264$		0			0
$265$	−29.4721			−1.81046
$266$		0			0
$267$	12.4164	+	38.2138i	0.759872	+	2.33864i
$268$		0			0
$269$	−13.5172	−	9.82084i	−0.824160	−	0.598787i	0.0937414	−	0.995597i	$-0.470117\pi$
$269$	−13.5172	−	9.82084i	−0.824160	−	0.598787i	−0.917901	+	0.396810i	$0.870117\pi$
$270$		0			0
$271$	9.23607	−	28.4257i	0.561051	−	1.72674i	−0.118351	−	0.992972i	$-0.537761\pi$
$271$	9.23607	−	28.4257i	0.561051	−	1.72674i	0.679402	−	0.733766i	$-0.262239\pi$
$272$		0			0
$273$	14.9443	−	10.8576i	0.904468	−	0.657135i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−21.1353	+	15.3557i	−1.26989	+	0.922632i	−0.999198	−	0.0400326i	$-0.987254\pi$
$277$	−21.1353	+	15.3557i	−1.26989	+	0.922632i	−0.270696	+	0.962665i	$0.587254\pi$
$278$		0			0
$279$	11.0000	−	33.8545i	0.658553	−	2.02682i
$280$		0			0
$281$	12.5623	+	9.12705i	0.749404	+	0.544474i	0.895642	−	0.444775i	$-0.146716\pi$
$281$	12.5623	+	9.12705i	0.749404	+	0.544474i	−0.146238	+	0.989249i	$0.546716\pi$
$282$		0			0
$283$	3.52786	+	10.8576i	0.209710	+	0.645420i	0.999487	+	0.0320265i	$0.0101961\pi$
$283$	3.52786	+	10.8576i	0.209710	+	0.645420i	−0.789777	+	0.613394i	$0.789804\pi$
$284$		0			0
$285$	41.3050			2.44669
$286$		0			0
$287$	24.1803			1.42732
$288$		0			0
$289$	−4.94427	−	15.2169i	−0.290840	−	0.895112i
$290$		0			0
$291$	31.2705	+	22.7194i	1.83311	+	1.33183i
$292$		0			0
$293$	−1.63525	+	5.03280i	−0.0955326	+	0.294019i	−0.987392	−	0.158293i	$-0.949401\pi$
$293$	−1.63525	+	5.03280i	−0.0955326	+	0.294019i	0.891860	+	0.452313i	$0.149401\pi$
$294$		0			0
$295$	10.0000	−	7.26543i	0.582223	−	0.423009i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.09017	+	0.792055i	−0.0630462	+	0.0458057i
$300$		0			0
$301$	10.4721	−	32.2299i	0.603604	−	1.85770i
$302$		0			0
$303$	5.23607	+	3.80423i	0.300804	+	0.218547i
$304$		0			0
$305$	10.3262	+	31.7809i	0.591279	+	1.81977i
$306$		0			0
$307$	24.1803			1.38004			0.690022	−	0.723788i	$-0.257601\pi$
$307$	24.1803			1.38004			0.690022	+	0.723788i	$0.257601\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.18034	−	12.8658i	−0.237045	−	0.729551i	−0.996844	−	0.0793915i	$-0.974702\pi$
$311$	−4.18034	−	12.8658i	−0.237045	−	0.729551i	0.759798	−	0.650159i	$-0.225298\pi$
$312$		0			0
$313$	−6.42705	−	4.66953i	−0.363278	−	0.263937i	0.391140	−	0.920331i	$-0.372081\pi$
$313$	−6.42705	−	4.66953i	−0.363278	−	0.263937i	−0.754418	+	0.656394i	$0.772081\pi$
$314$		0			0
$315$	16.7082	−	51.4226i	0.941401	−	2.89733i
$316$		0			0
$317$	−12.8541	+	9.33905i	−0.721958	+	0.524533i	−0.887009	−	0.461752i	$-0.847221\pi$
$317$	−12.8541	+	9.33905i	−0.721958	+	0.524533i	0.165051	+	0.986285i	$0.447221\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	4.47214	−	3.24920i	0.249610	−	0.181352i
$322$		0			0
$323$	−1.76393	+	5.42882i	−0.0981478	+	0.302068i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.23607	+	19.1926i	0.344855	+	1.06136i
$328$		0			0
$329$	18.4721			1.01840
$330$		0			0
$331$	−6.47214			−0.355741			−0.177870	−	0.984054i	$-0.556921\pi$
$331$	−6.47214			−0.355741			−0.177870	+	0.984054i	$0.556921\pi$
$332$		0			0
$333$	−0.545085	−	1.67760i	−0.0298705	−	0.0919319i
$334$		0			0
$335$	1.38197	+	1.00406i	0.0755049	+	0.0548575i
$336$		0			0
$337$	−1.98278	+	6.10237i	−0.108009	+	0.332417i	−0.990425	−	0.138053i	$-0.955916\pi$
$337$	−1.98278	+	6.10237i	−0.108009	+	0.332417i	0.882416	+	0.470470i	$0.155916\pi$
$338$		0			0
$339$	52.2148	−	37.9363i	2.83592	−	2.06041i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	9.23607	−	6.71040i	0.498701	−	0.362327i
$344$		0			0
$345$	−1.70820	+	5.25731i	−0.0919666	+	0.283044i
$346$		0			0
$347$	9.23607	+	6.71040i	0.495818	+	0.360233i	0.807417	−	0.589981i	$-0.200865\pi$
$347$	9.23607	+	6.71040i	0.495818	+	0.360233i	−0.311599	+	0.950214i	$0.600865\pi$
$348$		0			0
$349$	8.54508	+	26.2991i	0.457408	+	1.40776i	0.868285	+	0.496066i	$0.165223\pi$
$349$	8.54508	+	26.2991i	0.457408	+	1.40776i	−0.410877	+	0.911691i	$0.634777\pi$
$350$		0			0
$351$	−25.5279			−1.36258
$352$		0			0
$353$	23.0000			1.22417			0.612083	−	0.790793i	$-0.290332\pi$
$353$	23.0000			1.22417			0.612083	+	0.790793i	$0.290332\pi$
$354$		0			0
$355$	−2.76393	−	8.50651i	−0.146694	−	0.451479i
$356$		0			0
$357$	8.47214	+	6.15537i	0.448393	+	0.325777i
$358$		0			0
$359$	−3.94427	+	12.1392i	−0.208171	+	0.640684i	0.791398	+	0.611302i	$0.209354\pi$
$359$	−3.94427	+	12.1392i	−0.208171	+	0.640684i	−0.999568	+	0.0293817i	$0.990646\pi$
$360$		0			0
$361$	−10.9894	+	7.98424i	−0.578387	+	0.420223i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.38197	+	4.63677i	−0.334047	+	0.242700i
$366$		0			0
$367$	−1.29180	+	3.97574i	−0.0674312	+	0.207532i	−0.979094	−	0.203406i	$-0.934799\pi$
$367$	−1.29180	+	3.97574i	−0.0674312	+	0.207532i	0.911663	+	0.410938i	$0.134799\pi$
$368$		0			0
$369$	−45.1697	−	32.8177i	−2.35144	−	1.70842i
$370$		0			0
$371$	−13.1803	−	40.5649i	−0.684289	−	2.10603i
$372$		0			0
$373$	0.111456			0.00577098			0.00288549	−	0.999996i	$-0.499082\pi$
$373$	0.111456			0.00577098			0.00288549	+	0.999996i	$0.499082\pi$
$374$		0			0
$375$	36.1803			1.86834
$376$		0			0
$377$	0.961493	+	2.95917i	0.0495194	+	0.152405i
$378$		0			0
$379$	2.47214	+	1.79611i	0.126985	+	0.0922601i	0.649465	−	0.760392i	$-0.274993\pi$
$379$	2.47214	+	1.79611i	0.126985	+	0.0922601i	−0.522480	+	0.852652i	$0.674993\pi$
$380$		0			0
$381$	−18.4721	+	56.8514i	−0.946356	+	2.91258i
$382$		0			0
$383$	−15.7082	+	11.4127i	−0.802652	+	0.583161i	−0.911691	−	0.410877i	$-0.865223\pi$
$383$	−15.7082	+	11.4127i	−0.802652	+	0.583161i	0.109039	+	0.994037i	$0.465223\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−63.3050	+	45.9937i	−3.21797	+	2.33799i
$388$		0			0
$389$	−6.72542	+	20.6987i	−0.340993	+	1.04947i	0.622702	+	0.782459i	$0.286035\pi$
$389$	−6.72542	+	20.6987i	−0.340993	+	1.04947i	−0.963694	+	0.267008i	$0.913965\pi$
$390$		0			0
$391$	−0.618034	−	0.449028i	−0.0312553	−	0.0227083i
$392$		0			0
$393$	−8.00000	−	24.6215i	−0.403547	−	1.24199i
$394$		0			0
$395$	−16.1803			−0.814121
$396$		0			0
$397$	−20.2361			−1.01562			−0.507810	−	0.861469i	$-0.669545\pi$
$397$	−20.2361			−1.01562			−0.507810	+	0.861469i	$0.669545\pi$
$398$		0			0
$399$	18.4721	+	56.8514i	0.924763	+	2.84613i
$400$		0			0
$401$	11.7533	+	8.53926i	0.586931	+	0.426431i	0.841216	−	0.540699i	$-0.181840\pi$
$401$	11.7533	+	8.53926i	0.586931	+	0.426431i	−0.254285	+	0.967129i	$0.581840\pi$
$402$		0			0
$403$	2.59675	−	7.99197i	0.129353	−	0.398108i
$404$		0			0
$405$	−44.1697	+	32.0912i	−2.19481	+	1.59462i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	22.8992	−	16.6372i	1.13229	−	0.822658i	0.146265	−	0.989245i	$-0.453275\pi$
$409$	22.8992	−	16.6372i	1.13229	−	0.822658i	0.986027	+	0.166587i	$0.0532747\pi$
$410$		0			0
$411$	−7.52786	+	23.1684i	−0.371322	+	1.14281i
$412$		0			0
$413$	14.4721	+	10.5146i	0.712127	+	0.517391i
$414$		0			0
$415$	8.41641	+	25.9030i	0.413145	+	1.27153i
$416$		0			0
$417$	−49.3050			−2.41447
$418$		0			0
$419$	−24.1803			−1.18129			−0.590643	−	0.806933i	$-0.701126\pi$
$419$	−24.1803			−1.18129			−0.590643	+	0.806933i	$0.701126\pi$
$420$		0			0
$421$	−2.72542	−	8.38800i	−0.132829	−	0.408806i	0.862417	−	0.506199i	$-0.168950\pi$
$421$	−2.72542	−	8.38800i	−0.132829	−	0.408806i	−0.995246	+	0.0973927i	$0.968950\pi$
$422$		0			0
$423$	−34.5066	−	25.0705i	−1.67777	−	1.21897i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−39.1246	+	28.4257i	−1.89337	+	1.37562i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.2361	−	12.5227i	0.830232	−	0.603199i	−0.0893928	−	0.995996i	$-0.528493\pi$
$431$	17.2361	−	12.5227i	0.830232	−	0.603199i	0.919625	+	0.392797i	$0.128493\pi$
$432$		0			0
$433$	−2.78115	+	8.55951i	−0.133654	+	0.411344i	−0.995378	−	0.0960328i	$-0.969385\pi$
$433$	−2.78115	+	8.55951i	−0.133654	+	0.411344i	0.861724	+	0.507376i	$0.169385\pi$
$434$		0			0
$435$	10.3262	+	7.50245i	0.495105	+	0.359715i
$436$		0			0
$437$	−1.34752	−	4.14725i	−0.0644608	−	0.198390i
$438$		0			0
$439$	−12.7639			−0.609189			−0.304595	−	0.952482i	$-0.598521\pi$
$439$	−12.7639			−0.609189			−0.304595	+	0.952482i	$0.598521\pi$
$440$		0			0
$441$	25.9443			1.23544
$442$		0			0
$443$	−8.47214	−	26.0746i	−0.402523	−	1.23884i	−0.922946	−	0.384930i	$-0.874225\pi$
$443$	−8.47214	−	26.0746i	−0.402523	−	1.23884i	0.520422	−	0.853909i	$-0.325775\pi$
$444$		0			0
$445$	22.4615	+	16.3192i	1.06478	+	0.773606i
$446$		0			0
$447$	10.2361	−	31.5034i	0.484149	−	1.49006i
$448$		0			0
$449$	21.7533	−	15.8047i	1.02660	−	0.745869i	0.0589756	−	0.998259i	$-0.481217\pi$
$449$	21.7533	−	15.8047i	1.02660	−	0.745869i	0.967626	+	0.252390i	$0.0812166\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−19.4164	+	14.1068i	−0.912262	+	0.662797i
$454$		0			0
$455$	3.94427	−	12.1392i	0.184910	−	0.569095i
$456$		0			0
$457$	−20.9894	−	15.2497i	−0.981841	−	0.713349i	−0.0237215	−	0.999719i	$-0.507551\pi$
$457$	−20.9894	−	15.2497i	−0.981841	−	0.713349i	−0.958119	+	0.286370i	$0.907551\pi$
$458$		0			0
$459$	−4.47214	−	13.7638i	−0.208741	−	0.642440i
$460$		0			0
$461$	−35.1803			−1.63851			−0.819256	−	0.573428i	$-0.805613\pi$
$461$	−35.1803			−1.63851			−0.819256	+	0.573428i	$0.805613\pi$
$462$		0			0
$463$	34.8328			1.61882			0.809409	−	0.587245i	$-0.199788\pi$
$463$	34.8328			1.61882			0.809409	+	0.587245i	$0.199788\pi$
$464$		0			0
$465$	−10.6525	−	32.7849i	−0.493997	−	1.52037i
$466$		0			0
$467$	18.1803	+	13.2088i	0.841286	+	0.611230i	0.922730	−	0.385448i	$-0.125953\pi$
$467$	18.1803	+	13.2088i	0.841286	+	0.611230i	−0.0814437	+	0.996678i	$0.525953\pi$
$468$		0			0
$469$	−0.763932	+	2.35114i	−0.0352751	+	0.108566i
$470$		0			0
$471$	−32.6525	+	23.7234i	−1.50455	+	1.09312i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−30.4336	+	93.6651i	−1.39346	+	4.28863i
$478$		0			0
$479$	18.4721	+	13.4208i	0.844013	+	0.613212i	0.923489	−	0.383625i	$-0.125325\pi$
$479$	18.4721	+	13.4208i	0.844013	+	0.613212i	−0.0794755	+	0.996837i	$0.525325\pi$
$480$		0			0
$481$	−0.128677	−	0.396027i	−0.00586717	−	0.0180573i
$482$		0			0
$483$	−8.00000			−0.364013
$484$		0			0
$485$	26.7082			1.21276
$486$		0			0
$487$	−6.05573	−	18.6376i	−0.274411	−	0.844551i	−0.989375	−	0.145389i	$-0.953557\pi$
$487$	−6.05573	−	18.6376i	−0.274411	−	0.844551i	0.714963	−	0.699162i	$-0.246443\pi$
$488$		0			0
$489$	14.9443	+	10.8576i	0.675803	+	0.491000i
$490$		0			0
$491$	−7.47214	+	22.9969i	−0.337213	+	1.03783i	0.628409	+	0.777883i	$0.283706\pi$
$491$	−7.47214	+	22.9969i	−0.337213	+	1.03783i	−0.965622	+	0.259951i	$0.916294\pi$
$492$		0			0
$493$	−1.42705	+	1.03681i	−0.0642711	+	0.0466957i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.4721	−	7.60845i	0.469739	−	0.341286i
$498$		0			0
$499$	12.7639	−	39.2833i	0.571392	−	1.75856i	−0.0767563	−	0.997050i	$-0.524456\pi$
$499$	12.7639	−	39.2833i	0.571392	−	1.75856i	0.648148	−	0.761514i	$-0.275544\pi$
$500$		0			0
$501$	29.8885	+	21.7153i	1.33532	+	0.970168i
$502$		0			0
$503$	−9.76393	−	30.0503i	−0.435352	−	1.33988i	−0.892725	−	0.450601i	$-0.851210\pi$
$503$	−9.76393	−	30.0503i	−0.435352	−	1.33988i	0.457373	−	0.889275i	$-0.348790\pi$
$504$		0			0
$505$	4.47214			0.199007
$506$		0			0
$507$	32.0000			1.42117
$508$		0			0
$509$	0.326238	+	1.00406i	0.0144602	+	0.0445040i	0.958026	−	0.286680i	$-0.0925518\pi$
$509$	0.326238	+	1.00406i	0.0144602	+	0.0445040i	−0.943566	+	0.331184i	$0.892552\pi$
$510$		0			0
$511$	−9.23607	−	6.71040i	−0.408580	−	0.296850i
$512$		0			0
$513$	25.5279	−	78.5667i	1.12708	−	3.46880i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−49.5967	+	36.0341i	−2.17706	+	1.58172i
$520$		0			0
$521$	−4.14590	+	12.7598i	−0.181635	+	0.559015i	−0.999874	−	0.0158627i	$-0.994951\pi$
$521$	−4.14590	+	12.7598i	−0.181635	+	0.559015i	0.818239	+	0.574878i	$0.194951\pi$
$522$		0			0
$523$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$523$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.76393			0.207520
$528$		0			0
$529$	−22.4164			−0.974626
$530$		0			0
$531$	−12.7639	−	39.2833i	−0.553907	−	1.70475i
$532$		0			0
$533$	−10.6631	−	7.74721i	−0.461871	−	0.335569i
$534$		0			0
$535$	1.18034	−	3.63271i	0.0510305	−	0.157056i
$536$		0			0
$537$	−6.47214	+	4.70228i	−0.279293	+	0.202918i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.85410	−	2.07363i	0.122707	−	0.0891522i	−0.524739	−	0.851263i	$-0.675837\pi$
$541$	2.85410	−	2.07363i	0.122707	−	0.0891522i	0.647446	+	0.762111i	$0.275837\pi$
$542$		0			0
$543$	−12.7082	+	39.1118i	−0.545361	+	1.67845i
$544$		0			0
$545$	11.2812	+	8.19624i	0.483231	+	0.351088i
$546$		0			0
$547$	−5.70820	−	17.5680i	−0.244065	−	0.751155i	−0.995789	−	0.0916771i	$-0.970777\pi$
$547$	−5.70820	−	17.5680i	−0.244065	−	0.751155i	0.751724	−	0.659478i	$-0.229223\pi$
$548$		0			0
$549$	111.666			4.76577
$550$		0			0
$551$	−10.0689			−0.428949
$552$		0			0
$553$	−7.23607	−	22.2703i	−0.307709	−	0.947031i
$554$		0			0
$555$	−1.38197	−	1.00406i	−0.0586612	−	0.0426198i
$556$		0			0
$557$	11.0902	−	34.1320i	0.469906	−	1.44622i	−0.382801	−	0.923831i	$-0.625041\pi$
$557$	11.0902	−	34.1320i	0.469906	−	1.44622i	0.852707	−	0.522390i	$-0.174959\pi$
$558$		0			0
$559$	−14.9443	+	10.8576i	−0.632075	+	0.459230i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.0344	+	11.6497i	−0.675771	+	0.490976i	−0.871952	−	0.489591i	$-0.837146\pi$
$563$	−16.0344	+	11.6497i	−0.675771	+	0.490976i	0.196181	+	0.980568i	$0.437146\pi$
$564$		0			0
$565$	13.7812	−	42.4140i	0.579777	−	1.78437i
$566$		0			0
$567$	−63.9230	−	46.4428i	−2.68451	−	1.95041i
$568$		0			0
$569$	8.14590	+	25.0705i	0.341494	+	1.05101i	0.963434	+	0.267945i	$0.0863446\pi$
$569$	8.14590	+	25.0705i	0.341494	+	1.05101i	−0.621940	+	0.783065i	$0.713655\pi$
$570$		0			0
$571$	−12.7639			−0.534154			−0.267077	−	0.963675i	$-0.586058\pi$
$571$	−12.7639			−0.534154			−0.267077	+	0.963675i	$0.586058\pi$
$572$		0			0
$573$	−17.8885			−0.747305
$574$		0			0
$575$		0			0
$576$		0			0
$577$	27.7533	+	20.1639i	1.15538	+	0.839436i	0.989187	−	0.146657i	$-0.0468512\pi$
$577$	27.7533	+	20.1639i	1.15538	+	0.839436i	0.166197	+	0.986093i	$0.446851\pi$
$578$		0			0
$579$	3.94427	−	12.1392i	0.163918	−	0.504489i
$580$		0			0
$581$	−31.8885	+	23.1684i	−1.32296	+	0.961186i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−23.8435	+	17.3233i	−0.985806	+	0.716230i
$586$		0			0
$587$	−0.416408	+	1.28157i	−0.0171870	+	0.0528961i	−0.959282	−	0.282449i	$-0.908853\pi$
$587$	−0.416408	+	1.28157i	−0.0171870	+	0.0528961i	0.942095	+	0.335346i	$0.108853\pi$
$588$		0			0
$589$	22.0000	+	15.9839i	0.906494	+	0.658607i
$590$		0			0
$591$	17.6525	+	54.3287i	0.726126	+	2.23479i
$592$		0			0
$593$	−22.4164			−0.920532			−0.460266	−	0.887781i	$-0.652246\pi$
$593$	−22.4164			−0.920532			−0.460266	+	0.887781i	$0.652246\pi$
$594$		0			0
$595$	7.23607			0.296650
$596$		0			0
$597$	18.4721	+	56.8514i	0.756014	+	2.32677i
$598$		0			0
$599$	−4.61803	−	3.35520i	−0.188688	−	0.137090i	0.489431	−	0.872042i	$-0.337205\pi$
$599$	−4.61803	−	3.35520i	−0.188688	−	0.137090i	−0.678119	+	0.734952i	$0.737205\pi$
$600$		0			0
$601$	10.1287	−	31.1729i	0.413157	−	1.27157i	−0.500731	−	0.865603i	$-0.666936\pi$
$601$	10.1287	−	31.1729i	0.413157	−	1.27157i	0.913889	−	0.405965i	$-0.133064\pi$
$602$		0			0
$603$	4.61803	−	3.35520i	0.188061	−	0.136634i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.3262	−	13.3148i	0.743839	−	0.540431i	−0.150072	−	0.988675i	$-0.547951\pi$
$607$	18.3262	−	13.3148i	0.743839	−	0.540431i	0.893911	+	0.448244i	$0.147951\pi$
$608$		0			0
$609$	−5.70820	+	17.5680i	−0.231308	+	0.711893i
$610$		0			0
$611$	−8.14590	−	5.91834i	−0.329548	−	0.239430i
$612$		0			0
$613$	−14.3992	−	44.3161i	−0.581578	−	1.78991i	−0.612600	−	0.790393i	$-0.709876\pi$
$613$	−14.3992	−	44.3161i	−0.581578	−	1.78991i	0.0310220	−	0.999519i	$-0.490124\pi$
$614$		0			0
$615$	−54.0689			−2.18027
$616$		0			0
$617$	15.3607			0.618398			0.309199	−	0.950997i	$-0.399939\pi$
$617$	15.3607			0.618398			0.309199	+	0.950997i	$0.399939\pi$
$618$		0			0
$619$	11.7639	+	36.2057i	0.472832	+	1.45523i	0.848859	+	0.528619i	$0.177290\pi$
$619$	11.7639	+	36.2057i	0.472832	+	1.45523i	−0.376027	+	0.926609i	$0.622710\pi$
$620$		0			0
$621$	8.94427	+	6.49839i	0.358921	+	0.260772i
$622$		0			0
$623$	−12.4164	+	38.2138i	−0.497453	+	1.53100i
$624$		0			0
$625$	20.2254	−	14.6946i	0.809017	−	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.190983	−	0.138757i	0.00761499	−	0.00553261i
$630$		0			0
$631$	9.18034	−	28.2542i	0.365464	−	1.12478i	−0.584227	−	0.811591i	$-0.698602\pi$
$631$	9.18034	−	28.2542i	0.365464	−	1.12478i	0.949690	−	0.313191i	$-0.101398\pi$
$632$		0			0
$633$	−18.4721	−	13.4208i	−0.734201	−	0.533429i
$634$		0			0
$635$	12.7639	+	39.2833i	0.506521	+	1.55891i
$636$		0			0
$637$	6.12461			0.242666
$638$		0			0
$639$	−29.8885			−1.18237
$640$		0			0
$641$	0.454915	+	1.40008i	0.0179681	+	0.0553000i	0.959639	−	0.281236i	$-0.0907445\pi$
$641$	0.454915	+	1.40008i	0.0179681	+	0.0553000i	−0.941670	+	0.336536i	$0.890744\pi$
$642$		0			0
$643$	16.3262	+	11.8617i	0.643844	+	0.467780i	0.861169	−	0.508319i	$-0.169733\pi$
$643$	16.3262	+	11.8617i	0.643844	+	0.467780i	−0.217325	+	0.976099i	$0.569733\pi$
$644$		0			0
$645$	−23.4164	+	72.0683i	−0.922020	+	2.83769i
$646$		0			0
$647$	30.6525	−	22.2703i	1.20507	−	0.875537i	0.210299	−	0.977637i	$-0.432556\pi$
$647$	30.6525	−	22.2703i	1.20507	−	0.875537i	0.994774	+	0.102100i	$0.0325562\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	40.3607	−	29.3238i	1.58186	−	1.14929i
$652$		0			0
$653$	12.1459	−	37.3812i	0.475306	−	1.46284i	−0.370239	−	0.928936i	$-0.620724\pi$
$653$	12.1459	−	37.3812i	0.475306	−	1.46284i	0.845545	−	0.533904i	$-0.179276\pi$
$654$		0			0
$655$	−14.4721	−	10.5146i	−0.565473	−	0.410840i
$656$		0			0
$657$	8.14590	+	25.0705i	0.317802	+	0.978093i
$658$		0			0
$659$	−32.1803			−1.25357			−0.626784	−	0.779193i	$-0.715629\pi$
$659$	−32.1803			−1.25357			−0.626784	+	0.779193i	$0.715629\pi$
$660$		0			0
$661$	23.1803			0.901611			0.450805	−	0.892622i	$-0.351137\pi$
$661$	23.1803			0.901611			0.450805	+	0.892622i	$0.351137\pi$
$662$		0			0
$663$	−1.76393	−	5.42882i	−0.0685054	−	0.210838i
$664$		0			0
$665$	33.4164	+	24.2784i	1.29583	+	0.941478i
$666$		0			0
$667$	0.416408	−	1.28157i	0.0161234	−	0.0496227i
$668$		0			0
$669$	23.4164	−	17.0130i	0.905331	−	0.657761i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	16.5623	−	12.0332i	0.638430	−	0.463847i	−0.220880	−	0.975301i	$-0.570893\pi$
$673$	16.5623	−	12.0332i	0.638430	−	0.463847i	0.859310	+	0.511454i	$0.170893\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.2254	+	16.8743i	0.892626	+	0.648530i	0.936561	−	0.350504i	$-0.113990\pi$
$677$	23.2254	+	16.8743i	0.892626	+	0.648530i	−0.0439357	+	0.999034i	$0.513990\pi$
$678$		0			0
$679$	11.9443	+	36.7607i	0.458379	+	1.41075i
$680$		0			0
$681$	8.00000			0.306561
$682$		0			0
$683$	−6.87539			−0.263079			−0.131540	−	0.991311i	$-0.541992\pi$
$683$	−6.87539			−0.263079			−0.131540	+	0.991311i	$0.541992\pi$
$684$		0			0
$685$	5.20163	+	16.0090i	0.198744	+	0.611671i
$686$		0			0
$687$	−7.09017	−	5.15131i	−0.270507	−	0.196535i
$688$		0			0
$689$	−7.18441	+	22.1113i	−0.273704	+	0.842374i
$690$		0			0
$691$	−15.7082	+	11.4127i	−0.597568	+	0.434159i	−0.845015	−	0.534743i	$-0.820409\pi$
$691$	−15.7082	+	11.4127i	−0.597568	+	0.434159i	0.247447	+	0.968902i	$0.420409\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−27.5623	+	20.0252i	−1.04550	+	0.759599i
$696$		0			0
$697$	2.30902	−	7.10642i	0.0874603	−	0.269175i
$698$		0			0
$699$	−28.7984	−	20.9232i	−1.08925	−	0.791390i
$700$		0			0
$701$	11.0172	+	33.9075i	0.416115	+	1.28067i	0.911250	+	0.411854i	$0.135118\pi$
$701$	11.0172	+	33.9075i	0.416115	+	1.28067i	−0.495135	+	0.868816i	$0.664882\pi$
$702$		0			0
$703$	1.34752			0.0508228
$704$		0			0
$705$	−41.3050			−1.55563
$706$		0			0
$707$	2.00000	+	6.15537i	0.0752177	+	0.231496i
$708$		0			0
$709$	3.14590	+	2.28563i	0.118147	+	0.0858386i	0.645290	−	0.763938i	$-0.276737\pi$
$709$	3.14590	+	2.28563i	0.118147	+	0.0858386i	−0.527143	+	0.849777i	$0.676737\pi$
$710$		0			0
$711$	−16.7082	+	51.4226i	−0.626607	+	1.92850i
$712$		0			0
$713$	−2.94427	+	2.13914i	−0.110264	+	0.0801114i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−52.8328	+	38.3853i	−1.97308	+	1.43352i
$718$		0			0
$719$	15.0000	−	46.1653i	0.559406	−	1.72167i	−0.124610	−	0.992206i	$-0.539768\pi$
$719$	15.0000	−	46.1653i	0.559406	−	1.72167i	0.684015	−	0.729468i	$-0.260232\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.52786	−	10.8576i	−0.131203	−	0.403800i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−6.29180			−0.233350			−0.116675	−	0.993170i	$-0.537224\pi$
$727$	−6.29180			−0.233350			−0.116675	+	0.993170i	$0.537224\pi$
$728$		0			0
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$		0			0
$731$	−8.47214	−	6.15537i	−0.313353	−	0.227664i
$732$		0			0
$733$	6.25329	−	19.2456i	0.230970	−	0.710854i	−0.766660	−	0.642053i	$-0.778083\pi$
$733$	6.25329	−	19.2456i	0.230970	−	0.710854i	0.997630	−	0.0688007i	$-0.0219173\pi$
$734$		0			0
$735$	20.3262	−	14.7679i	0.749745	−	0.544721i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	11.5623	−	8.40051i	0.425326	−	0.309018i	−0.354451	−	0.935075i	$-0.615332\pi$
$739$	11.5623	−	8.40051i	0.425326	−	0.309018i	0.779777	+	0.626057i	$0.215332\pi$
$740$		0			0
$741$	10.0689	−	30.9888i	0.369890	−	1.13840i
$742$		0			0
$743$	23.0902	+	16.7760i	0.847096	+	0.615451i	0.924344	−	0.381561i	$-0.124613\pi$
$743$	23.0902	+	16.7760i	0.847096	+	0.615451i	−0.0772477	+	0.997012i	$0.524613\pi$
$744$		0			0
$745$	−7.07295	−	21.7683i	−0.259133	−	0.797529i
$746$		0			0
$747$	91.0132			3.33000
$748$		0			0
$749$	5.52786			0.201984
$750$		0			0
$751$	−14.1803	−	43.6426i	−0.517448	−	1.59254i	−0.778783	−	0.627293i	$-0.784163\pi$
$751$	−14.1803	−	43.6426i	−0.517448	−	1.59254i	0.261335	−	0.965248i	$-0.415837\pi$
$752$		0			0
$753$	−54.3607	−	39.4953i	−1.98101	−	1.43929i
$754$		0			0
$755$	−5.12461	+	15.7719i	−0.186504	+	0.573999i
$756$		0			0
$757$	12.6631	−	9.20029i	0.460249	−	0.334390i	−0.333380	−	0.942793i	$-0.608189\pi$
$757$	12.6631	−	9.20029i	0.460249	−	0.334390i	0.793629	+	0.608402i	$0.208189\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.8435	−	17.3233i	0.864325	−	0.627969i	−0.0647334	−	0.997903i	$-0.520620\pi$
$761$	23.8435	−	17.3233i	0.864325	−	0.627969i	0.929058	+	0.369934i	$0.120620\pi$
$762$		0			0
$763$	−6.23607	+	19.1926i	−0.225761	+	0.694820i
$764$		0			0
$765$	−13.5172	−	9.82084i	−0.488716	−	0.355073i
$766$		0			0
$767$	−3.01316	−	9.27354i	−0.108799	−	0.334848i
$768$		0			0
$769$	18.8885			0.681138			0.340569	−	0.940219i	$-0.389380\pi$
$769$	18.8885			0.681138			0.340569	+	0.940219i	$0.389380\pi$
$770$		0			0
$771$	47.0132			1.69314
$772$		0			0
$773$	6.79837	+	20.9232i	0.244521	+	0.752557i	0.995715	+	0.0924757i	$0.0294781\pi$
$773$	6.79837	+	20.9232i	0.244521	+	0.752557i	−0.751194	+	0.660081i	$0.770522\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.763932	−	2.35114i	0.0274059	−	0.0843467i
$778$		0			0
$779$	34.5066	−	25.0705i	1.23633	−	0.898244i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	20.6525	−	15.0049i	0.738059	−	0.536231i
$784$		0			0
$785$	−8.61803	+	26.5236i	−0.307591	+	0.946667i
$786$		0			0
$787$	12.7639	+	9.27354i	0.454985	+	0.330566i	0.791561	−	0.611090i	$-0.209269\pi$
$787$	12.7639	+	9.27354i	0.454985	+	0.330566i	−0.336576	+	0.941656i	$0.609269\pi$
$788$		0			0
$789$	−6.65248	−	20.4742i	−0.236834	−	0.728901i
$790$		0			0
$791$	64.5410			2.29481
$792$		0			0
$793$	26.3607			0.936095
$794$		0			0
$795$	29.4721	+	90.7059i	1.04527	+	3.21701i
$796$		0			0
$797$	−20.2705	−	14.7274i	−0.718018	−	0.521671i	0.167732	−	0.985833i	$-0.446356\pi$
$797$	−20.2705	−	14.7274i	−0.718018	−	0.521671i	−0.885750	+	0.464162i	$0.846356\pi$
$798$		0			0
$799$	1.76393	−	5.42882i	0.0624034	−	0.192058i
$800$		0			0
$801$	75.0582	−	54.5330i	2.65205	−	1.92683i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−4.47214	+	3.24920i	−0.157622	+	0.114519i
$806$		0			0
$807$	−16.7082	+	51.4226i	−0.588157	+	1.81016i
$808$		0			0
$809$	−21.3262	−	15.4944i	−0.749791	−	0.544755i	0.145971	−	0.989289i	$-0.453369\pi$
$809$	−21.3262	−	15.4944i	−0.749791	−	0.544755i	−0.895762	+	0.444534i	$0.853369\pi$
$810$		0			0
$811$	6.94427	+	21.3723i	0.243846	+	0.750482i	0.995824	+	0.0912934i	$0.0291001\pi$
$811$	6.94427	+	21.3723i	0.243846	+	0.750482i	−0.751978	+	0.659189i	$0.770900\pi$
$812$		0			0
$813$	−96.7214			−3.39217
$814$		0			0
$815$	12.7639			0.447101
$816$		0			0
$817$	−18.4721	−	56.8514i	−0.646258	−	1.98898i
$818$		0			0
$819$	−34.5066	−	25.0705i	−1.20576	−	0.876034i
$820$		0			0
$821$	9.56231	−	29.4298i	0.333727	−	1.02711i	−0.633619	−	0.773645i	$-0.718431\pi$
$821$	9.56231	−	29.4298i	0.333727	−	1.02711i	0.967346	−	0.253460i	$-0.0815687\pi$
$822$		0			0
$823$	8.47214	−	6.15537i	0.295320	−	0.214563i	−0.430252	−	0.902709i	$-0.641575\pi$
$823$	8.47214	−	6.15537i	0.295320	−	0.214563i	0.725572	+	0.688146i	$0.241575\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.61803	−	3.35520i	0.160585	−	0.116672i	−0.504591	−	0.863359i	$-0.668357\pi$
$827$	4.61803	−	3.35520i	0.160585	−	0.116672i	0.665176	+	0.746687i	$0.268357\pi$
$828$		0			0
$829$	−3.60081	+	11.0822i	−0.125061	+	0.384899i	−0.993912	−	0.110174i	$-0.964859\pi$
$829$	−3.60081	+	11.0822i	−0.125061	+	0.384899i	0.868851	+	0.495074i	$0.164859\pi$
$830$		0			0
$831$	68.3951	+	49.6920i	2.37260	+	1.72380i
$832$		0			0
$833$	1.07295	+	3.30220i	0.0371755	+	0.114414i
$834$		0			0
$835$	25.5279			0.883428
$836$		0			0
$837$	−68.9443			−2.38306
$838$		0			0
$839$	−12.4164	−	38.2138i	−0.428662	−	1.31929i	−0.899444	−	0.437036i	$-0.856028\pi$
$839$	−12.4164	−	38.2138i	−0.428662	−	1.31929i	0.470782	−	0.882250i	$-0.343972\pi$
$840$		0			0
$841$	20.9443	+	15.2169i	0.722216	+	0.524721i
$842$		0			0
$843$	15.5279	−	47.7899i	0.534808	−	1.64597i
$844$		0			0
$845$	17.8885	−	12.9968i	0.615385	−	0.447103i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	29.8885	−	21.7153i	1.02577	−	0.745267i
$850$		0			0
$851$	−0.0557281	+	0.171513i	−0.00191033	+	0.00587940i
$852$		0			0
$853$	−10.1910	−	7.40418i	−0.348933	−	0.253514i	0.399488	−	0.916738i	$-0.369188\pi$
$853$	−10.1910	−	7.40418i	−0.348933	−	0.253514i	−0.748421	+	0.663224i	$0.769188\pi$
$854$		0			0
$855$	−29.4721	−	90.7059i	−1.00793	−	3.10208i
$856$		0			0
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	−0.583592			−0.0199119			−0.00995595	−	0.999950i	$-0.503169\pi$
$859$	−0.583592			−0.0199119			−0.00995595	+	0.999950i	$0.503169\pi$
$860$		0			0
$861$	−24.1803	−	74.4194i	−0.824064	−	2.53621i
$862$		0			0
$863$	28.7984	+	20.9232i	0.980308	+	0.712235i	0.957777	−	0.287511i	$-0.0928277\pi$
$863$	28.7984	+	20.9232i	0.980308	+	0.712235i	0.0225306	+	0.999746i	$0.492828\pi$
$864$		0			0
$865$	−13.0902	+	40.2874i	−0.445079	+	1.36981i
$866$		0			0
$867$	−41.8885	+	30.4338i	−1.42261	+	1.03359i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	1.09017	−	0.792055i	0.0369390	−	0.0268378i
$872$		0			0
$873$	27.5795	−	84.8811i	0.933426	−	2.87279i
$874$		0			0
$875$	29.2705	+	21.2663i	0.989524	+	0.718931i
$876$		0			0
$877$	−5.16312	−	15.8904i	−0.174346	−	0.536582i	0.825257	−	0.564758i	$-0.191030\pi$
$877$	−5.16312	−	15.8904i	−0.174346	−	0.536582i	−0.999603	+	0.0281753i	$0.991030\pi$
$878$		0			0
$879$	17.1246			0.577599
$880$		0			0
$881$	4.52786			0.152548			0.0762738	−	0.997087i	$-0.475698\pi$
$881$	4.52786			0.152548			0.0762738	+	0.997087i	$0.475698\pi$
$882$		0			0
$883$	2.18034	+	6.71040i	0.0733743	+	0.225823i	0.981017	−	0.193920i	$-0.0621202\pi$
$883$	2.18034	+	6.71040i	0.0733743	+	0.225823i	−0.907643	+	0.419743i	$0.862120\pi$
$884$		0			0
$885$	−32.3607	−	23.5114i	−1.08779	−	0.790327i
$886$		0			0
$887$	6.05573	−	18.6376i	0.203331	−	0.625790i	−0.796446	−	0.604709i	$-0.793289\pi$
$887$	6.05573	−	18.6376i	0.203331	−	0.625790i	0.999778	−	0.0210806i	$-0.00671067\pi$
$888$		0			0
$889$	−48.3607	+	35.1361i	−1.62197	+	1.17843i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	26.3607	−	19.1522i	0.882127	−	0.640902i
$894$		0			0
$895$	−1.70820	+	5.25731i	−0.0570990	+	0.175733i
$896$		0			0
$897$	3.52786	+	2.56314i	0.117792	+	0.0855809i
$898$		0			0
$899$	2.59675	+	7.99197i	0.0866064	+	0.266547i
$900$		0			0
$901$	−13.1803			−0.439101
$902$		0			0
$903$	−109.666			−3.64944
$904$		0			0
$905$	8.78115	+	27.0256i	0.291895	+	0.898362i
$906$		0			0
$907$	−24.1803	−	17.5680i	−0.802895	−	0.583337i	0.108867	−	0.994056i	$-0.465278\pi$
$907$	−24.1803	−	17.5680i	−0.802895	−	0.583337i	−0.911762	+	0.410719i	$0.865278\pi$
$908$		0			0
$909$	4.61803	−	14.2128i	0.153171	−	0.471410i
$910$		0			0
$911$	−12.9443	+	9.40456i	−0.428863	+	0.311587i	−0.781194	−	0.624288i	$-0.785389\pi$
$911$	−12.9443	+	9.40456i	−0.428863	+	0.311587i	0.352331	+	0.935875i	$0.385389\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	87.4853	−	63.5618i	2.89217	−	2.10129i
$916$		0			0
$917$	8.00000	−	24.6215i	0.264183	−	0.813073i
$918$		0			0
$919$	16.6525	+	12.0987i	0.549314	+	0.399100i	0.827533	−	0.561418i	$-0.189744\pi$
$919$	16.6525	+	12.0987i	0.549314	+	0.399100i	−0.278218	+	0.960518i	$0.589744\pi$
$920$		0			0
$921$	−24.1803	−	74.4194i	−0.796769	−	2.45220i
$922$		0			0
$923$	−7.05573			−0.232242
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.6074	−	10.6129i	−0.479253	−	0.348198i	0.321783	−	0.946813i	$-0.395718\pi$
$929$	−14.6074	−	10.6129i	−0.479253	−	0.348198i	−0.801036	+	0.598616i	$0.795718\pi$
$930$		0			0
$931$	−6.12461	+	18.8496i	−0.200726	+	0.617771i
$932$		0			0
$933$	−35.4164	+	25.7315i	−1.15948	+	0.842412i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.4615	+	12.6865i	−0.570442	+	0.414450i	−0.835266	−	0.549846i	$-0.814686\pi$
$937$	−17.4615	+	12.6865i	−0.570442	+	0.414450i	0.264824	+	0.964297i	$0.414686\pi$
$938$		0			0
$939$	−7.94427	+	24.4500i	−0.259252	+	0.797894i
$940$		0			0
$941$	−8.95492	−	6.50613i	−0.291922	−	0.212094i	0.432179	−	0.901788i	$-0.357745\pi$
$941$	−8.95492	−	6.50613i	−0.291922	−	0.212094i	−0.724101	+	0.689694i	$0.757745\pi$
$942$		0			0
$943$	1.76393	+	5.42882i	0.0574415	+	0.176787i
$944$		0			0
$945$	−104.721			−3.40659
$946$		0			0
$947$	−49.1246			−1.59634			−0.798168	−	0.602435i	$-0.794197\pi$
$947$	−49.1246			−1.59634			−0.798168	+	0.602435i	$0.794197\pi$
$948$		0			0
$949$	1.92299	+	5.91834i	0.0624228	+	0.192117i
$950$		0			0
$951$	41.5967	+	30.2218i	1.34887	+	0.980009i
$952$		0			0
$953$	−16.9271	+	52.0961i	−0.548321	+	1.68756i	0.164639	+	0.986354i	$0.447354\pi$
$953$	−16.9271	+	52.0961i	−0.548321	+	1.68756i	−0.712960	+	0.701205i	$0.752646\pi$
$954$		0			0
$955$	−10.0000	+	7.26543i	−0.323592	+	0.235104i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.7082	+	14.3188i	−0.636411	+	0.462380i
$960$		0			0
$961$	−2.56637	+	7.89848i	−0.0827862	+	0.254790i
$962$		0			0
$963$	−10.3262	−	7.50245i	−0.332758	−	0.241763i
$964$		0			0
$965$	−2.72542	−	8.38800i	−0.0877345	−	0.270019i
$966$		0			0
$967$	−39.9574			−1.28494			−0.642472	−	0.766309i	$-0.722091\pi$
$967$	−39.9574			−1.28494			−0.642472	+	0.766309i	$0.722091\pi$
$968$		0			0
$969$	18.4721			0.593411
$970$		0			0
$971$	−12.5967	−	38.7688i	−0.404249	−	1.24415i	−0.921521	−	0.388329i	$-0.873052\pi$
$971$	−12.5967	−	38.7688i	−0.404249	−	1.24415i	0.517272	−	0.855821i	$-0.326948\pi$
$972$		0			0
$973$	−39.8885	−	28.9807i	−1.27877	−	0.929079i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.1910	+	9.58381i	−0.422017	+	0.306613i	−0.778449	−	0.627708i	$-0.783993\pi$
$977$	−13.1910	+	9.58381i	−0.422017	+	0.306613i	0.356432	+	0.934321i	$0.383993\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	37.6976	−	27.3889i	1.20359	−	0.874460i
$982$		0			0
$983$	−16.6525	+	51.2511i	−0.531131	+	1.63465i	0.220731	+	0.975335i	$0.429156\pi$
$983$	−16.6525	+	51.2511i	−0.531131	+	1.63465i	−0.751863	+	0.659320i	$0.770844\pi$
$984$		0			0
$985$	31.9336	+	23.2011i	1.01749	+	0.739250i
$986$		0			0
$987$	−18.4721	−	56.8514i	−0.587975	−	1.80960i
$988$		0			0
$989$	8.00000			0.254385
$990$		0			0
$991$	−29.8885			−0.949441			−0.474720	−	0.880137i	$-0.657451\pi$
$991$	−29.8885			−0.949441			−0.474720	+	0.880137i	$0.657451\pi$
$992$		0			0
$993$	6.47214	+	19.9192i	0.205387	+	0.632116i
$994$		0			0
$995$	33.4164	+	24.2784i	1.05937	+	0.769678i
$996$		0			0
$997$	−0.871323	+	2.68166i	−0.0275951	+	0.0849289i	−0.963906	−	0.266244i	$-0.914217\pi$
$997$	−0.871323	+	2.68166i	−0.0275951	+	0.0849289i	0.936310	+	0.351173i	$0.114217\pi$
$998$		0			0
$999$	−2.76393	+	2.00811i	−0.0874469	+	0.0635339i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.b.729.1		4
11.2	odd	10		968.2.a.f.1.1	✓	2
11.3	even	5		968.2.i.l.753.1		4
11.4	even	5	inner	968.2.i.b.81.1		4
11.5	even	5		968.2.i.l.9.1		4
11.6	odd	10		968.2.i.m.9.1		4
11.7	odd	10		968.2.i.a.81.1		4
11.8	odd	10		968.2.i.m.753.1		4
11.9	even	5		968.2.a.g.1.1	yes	2
11.10	odd	2		968.2.i.a.729.1		4
33.2	even	10		8712.2.a.bj.1.1		2
33.20	odd	10		8712.2.a.bk.1.1		2
44.31	odd	10		1936.2.a.w.1.2		2
44.35	even	10		1936.2.a.x.1.2		2
88.13	odd	10		7744.2.a.ct.1.2		2
88.35	even	10		7744.2.a.bs.1.1		2
88.53	even	10		7744.2.a.cu.1.2		2
88.75	odd	10		7744.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.a.f.1.1	✓	2	11.2	odd	10
968.2.a.g.1.1	yes	2	11.9	even	5
968.2.i.a.81.1		4	11.7	odd	10
968.2.i.a.729.1		4	11.10	odd	2
968.2.i.b.81.1		4	11.4	even	5	inner
968.2.i.b.729.1		4	1.1	even	1	trivial
968.2.i.l.9.1		4	11.5	even	5
968.2.i.l.753.1		4	11.3	even	5
968.2.i.m.9.1		4	11.6	odd	10
968.2.i.m.753.1		4	11.8	odd	10
1936.2.a.w.1.2		2	44.31	odd	10
1936.2.a.x.1.2		2	44.35	even	10
7744.2.a.br.1.1		2	88.75	odd	10
7744.2.a.bs.1.1		2	88.35	even	10
7744.2.a.ct.1.2		2	88.13	odd	10
7744.2.a.cu.1.2		2	88.53	even	10
8712.2.a.bj.1.1		2	33.2	even	10
8712.2.a.bk.1.1		2	33.20	odd	10

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

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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	968.2.i.b.729.1

Level	$968$
Weight	$2$
Character	968.729
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$