LMFDB - Embedded newform 1080.2.d.g.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.d (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 3 x^{14} + 36 x^{13} - 78 x^{12} - 96 x^{11} + 1194 x^{10} + 1456 x^{9} + \cdots + 45658 $ x^16 - 3x^15 - 3x^14 + 36x^13 - 78x^12 - 96x^11 + 1194x^10 + 1456x^9 + 2243x^8 + 23019x^7 + 49749x^6 + 37798x^5 + 78784x^4 + 244612x^3 + 302532x^2 + 157882*x + 45658
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.5
Root			$-0.315931 - 0.438405i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.g.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.763079 - 1.19068i) q^{2} +(-0.835421 + 1.81716i) q^{4} +(1.27498 - 1.83696i) q^{5} +1.23231i q^{7} +(2.80114 - 0.391920i) q^{8} +O(q^{10})$	\(q+(-0.763079 - 1.19068i) q^{2} +(-0.835421 + 1.81716i) q^{4} +(1.27498 - 1.83696i) q^{5} +1.23231i q^{7} +(2.80114 - 0.391920i) q^{8} +(-3.16014 - 0.116351i) q^{10} +4.64044i q^{11} -4.85741 q^{13} +(1.46728 - 0.940350i) q^{14} +(-2.60414 - 3.03619i) q^{16} -0.206211i q^{17} +7.40698i q^{19} +(2.27290 + 3.85149i) q^{20} +(5.52527 - 3.54102i) q^{22} -1.04676i q^{23} +(-1.74883 - 4.68419i) q^{25} +(3.70659 + 5.78361i) q^{26} +(-2.23930 - 1.02950i) q^{28} +6.52114i q^{29} -6.41781 q^{31} +(-1.62795 + 5.41754i) q^{32} +(-0.245531 + 0.157356i) q^{34} +(2.26370 + 1.57118i) q^{35} -8.11597 q^{37} +(8.81931 - 5.65211i) q^{38} +(2.85147 - 5.64527i) q^{40} -10.6717 q^{41} +2.55576 q^{43} +(-8.43243 - 3.87673i) q^{44} +(-1.24635 + 0.798757i) q^{46} -4.41816i q^{47} +5.48141 q^{49} +(-4.24286 + 5.65669i) q^{50} +(4.05799 - 8.82669i) q^{52} +3.80300 q^{53} +(8.52430 + 5.91650i) q^{55} +(0.482966 + 3.45188i) q^{56} +(7.76457 - 4.97615i) q^{58} +5.04607i q^{59} +7.09226i q^{61} +(4.89730 + 7.64154i) q^{62} +(7.69280 - 2.19565i) q^{64} +(-6.19313 + 8.92286i) q^{65} -13.9851 q^{67} +(0.374719 + 0.172273i) q^{68} +(0.143381 - 3.89427i) q^{70} +9.12769 q^{71} +8.71998i q^{73} +(6.19313 + 9.66350i) q^{74} +(-13.4597 - 6.18795i) q^{76} -5.71847 q^{77} +6.11122 q^{79} +(-8.89759 + 0.912603i) q^{80} +(8.14338 + 12.7066i) q^{82} +17.3731 q^{83} +(-0.378802 - 0.262916i) q^{85} +(-1.95025 - 3.04309i) q^{86} +(1.81868 + 12.9985i) q^{88} +7.15906 q^{89} -5.98584i q^{91} +(1.90212 + 0.874482i) q^{92} +(-5.26060 + 3.37140i) q^{94} +(13.6063 + 9.44378i) q^{95} +5.82040i q^{97} +(-4.18275 - 6.52659i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−0.763079	−	1.19068i	−0.539578	−	0.841935i
$2$	−0.763079	−	1.19068i	−0.539578	−	0.841935i
$3$		0			0
$3$		0			0
$4$	−0.835421	+	1.81716i	−0.417711	+	0.908580i
$5$	1.27498	−	1.83696i	0.570191	−	0.821512i
$5$	1.27498	−	1.83696i	0.570191	−	0.821512i
$6$		0			0
$7$			1.23231i			0.465769i	0.972504	+	0.232885i	$0.0748165\pi$
$7$			1.23231i			0.465769i	−0.972504	+	0.232885i	$0.925184\pi$
$8$	2.80114	−	0.391920i	0.990353	−	0.138564i
$9$		0			0
$10$	−3.16014	−	0.116351i	−0.999323	−	0.0367935i
$11$			4.64044i			1.39915i	0.714561	+	0.699573i	$0.246627\pi$
$11$			4.64044i			1.39915i	−0.714561	+	0.699573i	$0.753373\pi$
$12$		0			0
$13$	−4.85741			−1.34720			−0.673602	−	0.739094i	$-0.735254\pi$
$13$	−4.85741			−1.34720			−0.673602	+	0.739094i	$0.735254\pi$
$14$	1.46728	−	0.940350i	0.392148	−	0.251319i
$15$		0			0
$16$	−2.60414	−	3.03619i	−0.651035	−	0.759047i
$17$		−	0.206211i		−	0.0500136i	−0.999687	−	0.0250068i	$-0.992039\pi$
$17$		−	0.206211i		−	0.0500136i	0.999687	−	0.0250068i	$-0.00796075\pi$
$18$		0			0
$19$			7.40698i			1.69928i	0.527366	+	0.849638i	$0.323180\pi$
$19$			7.40698i			1.69928i	−0.527366	+	0.849638i	$0.676820\pi$
$20$	2.27290	+	3.85149i	0.508235	+	0.861218i
$21$		0			0
$22$	5.52527	−	3.54102i	1.17799	−	0.754949i
$23$		−	1.04676i		−	0.218264i	−0.994027	−	0.109132i	$-0.965193\pi$
$23$		−	1.04676i		−	0.218264i	0.994027	−	0.109132i	$-0.0348071\pi$
$24$		0			0
$25$	−1.74883	−	4.68419i	−0.349765	−	0.936837i
$26$	3.70659	+	5.78361i	0.726922	+	1.13426i
$27$		0			0
$28$	−2.23930	−	1.02950i	−0.423189	−	0.194557i
$29$			6.52114i			1.21095i	0.795866	+	0.605473i	$0.207016\pi$
$29$			6.52114i			1.21095i	−0.795866	+	0.605473i	$0.792984\pi$
$30$		0			0
$31$	−6.41781			−1.15267			−0.576337	−	0.817212i	$-0.695518\pi$
$31$	−6.41781			−1.15267			−0.576337	+	0.817212i	$0.695518\pi$
$32$	−1.62795	+	5.41754i	−0.287784	+	0.957695i
$33$		0			0
$34$	−0.245531	+	0.157356i	−0.0421082	+	0.0269863i
$35$	2.26370	+	1.57118i	0.382635	+	0.265577i
$36$		0			0
$37$	−8.11597			−1.33426			−0.667129	−	0.744942i	$-0.732477\pi$
$37$	−8.11597			−1.33426			−0.667129	+	0.744942i	$0.732477\pi$
$38$	8.81931	−	5.65211i	1.43068	−	0.916893i
$39$		0			0
$40$	2.85147	−	5.64527i	0.450858	−	0.892596i
$41$	−10.6717			−1.66665			−0.833323	−	0.552787i	$-0.813564\pi$
$41$	−10.6717			−1.66665			−0.833323	+	0.552787i	$0.813564\pi$
$42$		0			0
$43$	2.55576			0.389750			0.194875	−	0.980828i	$-0.437570\pi$
$43$	2.55576			0.389750			0.194875	+	0.980828i	$0.437570\pi$
$44$	−8.43243	−	3.87673i	−1.27124	−	0.584439i
$45$		0			0
$46$	−1.24635	+	0.798757i	−0.183764	+	0.117770i
$47$		−	4.41816i		−	0.644455i	−0.946662	−	0.322227i	$-0.895568\pi$
$47$		−	4.41816i		−	0.644455i	0.946662	−	0.322227i	$-0.104432\pi$
$48$		0			0
$49$	5.48141			0.783059
$50$	−4.24286	+	5.65669i	−0.600031	+	0.799977i
$51$		0			0
$52$	4.05799	−	8.82669i	0.562741	−	1.22404i
$53$	3.80300			0.522382			0.261191	−	0.965287i	$-0.415885\pi$
$53$	3.80300			0.522382			0.261191	+	0.965287i	$0.415885\pi$
$54$		0			0
$55$	8.52430	+	5.91650i	1.14942	+	0.797780i
$56$	0.482966	+	3.45188i	0.0645391	+	0.461276i
$57$		0			0
$58$	7.76457	−	4.97615i	1.01954	−	0.653400i
$59$			5.04607i			0.656942i	0.944514	+	0.328471i	$0.106533\pi$
$59$			5.04607i			0.656942i	−0.944514	+	0.328471i	$0.893467\pi$
$60$		0			0
$61$			7.09226i			0.908071i	0.890983	+	0.454036i	$0.150016\pi$
$61$			7.09226i			0.908071i	−0.890983	+	0.454036i	$0.849984\pi$
$62$	4.89730	+	7.64154i	0.621957	+	0.970477i
$63$		0			0
$64$	7.69280	−	2.19565i	0.961600	−	0.274456i
$65$	−6.19313	+	8.92286i	−0.768163	+	1.10674i
$66$		0			0
$67$	−13.9851			−1.70855			−0.854276	−	0.519819i	$-0.825999\pi$
$67$	−13.9851			−1.70855			−0.854276	+	0.519819i	$0.825999\pi$
$68$	0.374719	+	0.172273i	0.0454414	+	0.0208912i
$69$		0			0
$70$	0.143381	−	3.89427i	0.0171373	−	0.465454i
$71$	9.12769			1.08326			0.541629	−	0.840618i	$-0.317808\pi$
$71$	9.12769			1.08326			0.541629	+	0.840618i	$0.317808\pi$
$72$		0			0
$73$			8.71998i			1.02060i	0.859997	+	0.510298i	$0.170465\pi$
$73$			8.71998i			1.02060i	−0.859997	+	0.510298i	$0.829535\pi$
$74$	6.19313	+	9.66350i	0.719936	+	1.12336i
$75$		0			0
$76$	−13.4597	−	6.18795i	−1.54393	−	0.709806i
$77$	−5.71847			−0.651680
$78$		0			0
$79$	6.11122			0.687566			0.343783	−	0.939049i	$-0.388291\pi$
$79$	6.11122			0.687566			0.343783	+	0.939049i	$0.388291\pi$
$80$	−8.89759	+	0.912603i	−0.994781	+	0.102032i
$81$		0			0
$82$	8.14338	+	12.7066i	0.899285	+	1.40321i
$83$	17.3731			1.90694			0.953471	−	0.301485i	$-0.0974823\pi$
$83$	17.3731			1.90694			0.953471	+	0.301485i	$0.0974823\pi$
$84$		0			0
$85$	−0.378802	−	0.262916i	−0.0410868	−	0.0285173i
$86$	−1.95025	−	3.04309i	−0.210301	−	0.328145i
$87$		0			0
$88$	1.81868	+	12.9985i	0.193872	+	1.38565i
$89$	7.15906			0.758859			0.379429	−	0.925221i	$-0.376120\pi$
$89$	7.15906			0.758859			0.379429	+	0.925221i	$0.376120\pi$
$90$		0			0
$91$		−	5.98584i		−	0.627486i
$92$	1.90212	+	0.874482i	0.198310	+	0.0911711i
$93$		0			0
$94$	−5.26060	+	3.37140i	−0.542589	+	0.347734i
$95$	13.6063	+	9.44378i	1.39598	+	0.968912i
$96$		0			0
$97$			5.82040i			0.590972i	0.955347	+	0.295486i	$0.0954815\pi$
$97$			5.82040i			0.590972i	−0.955347	+	0.295486i	$0.904518\pi$
$98$	−4.18275	−	6.52659i	−0.422521	−	0.659285i
$99$		0			0
$100$	9.97292	+	0.735371i	0.997292	+	0.0735371i
$101$		−	7.22189i		−	0.718605i	−0.933221	−	0.359303i	$-0.883015\pi$
$101$		−	7.22189i		−	0.718605i	0.933221	−	0.359303i	$-0.116985\pi$
$102$		0			0
$103$		−	3.54798i		−	0.349593i	−0.984605	−	0.174796i	$-0.944073\pi$
$103$		−	3.54798i		−	0.349593i	0.984605	−	0.174796i	$-0.0559267\pi$
$104$	−13.6063	+	1.90371i	−1.33421	+	0.186675i
$105$		0			0
$106$	−2.90199	−	4.52814i	−0.281866	−	0.439812i
$107$	−0.281533			−0.0272168			−0.0136084	−	0.999907i	$-0.504332\pi$
$107$	−0.281533			−0.0272168			−0.0136084	+	0.999907i	$0.504332\pi$
$108$		0			0
$109$			6.33529i			0.606811i	0.952862	+	0.303406i	$0.0981237\pi$
$109$			6.33529i			0.606811i	−0.952862	+	0.303406i	$0.901876\pi$
$110$	0.539921	−	14.6644i	0.0514794	−	1.39820i
$111$		0			0
$112$	3.74153	−	3.20911i	0.353541	−	0.303232i
$113$			2.85048i			0.268151i	0.990971	+	0.134075i	$0.0428064\pi$
$113$			2.85048i			0.268151i	−0.990971	+	0.134075i	$0.957194\pi$
$114$		0			0
$115$	−1.92285	−	1.33460i	−0.179306	−	0.124452i
$116$	−11.8500	−	5.44790i	−1.10024	−	0.505825i
$117$		0			0
$118$	6.00824	−	3.85055i	0.553103	−	0.354472i
$119$	0.254116			0.0232948
$120$		0			0
$121$	−10.5337			−0.957612
$122$	8.44459	−	5.41196i	0.764538	−	0.489976i
$123$		0			0
$124$	5.36158	−	11.6622i	0.481484	−	1.04730i
$125$	−10.8344	−	2.75975i	−0.969056	−	0.246839i
$126$		0			0
$127$			10.8083i			0.959084i	0.877519	+	0.479542i	$0.159197\pi$
$127$			10.8083i			0.959084i	−0.877519	+	0.479542i	$0.840803\pi$
$128$	−8.48451	−	7.48418i	−0.749932	−	0.661515i
$129$		0			0
$130$	15.3501	+	0.565165i	1.34629	+	0.0495683i
$131$			3.99206i			0.348787i	0.984676	+	0.174394i	$0.0557966\pi$
$131$			3.99206i			0.348787i	−0.984676	+	0.174394i	$0.944203\pi$
$132$		0			0
$133$	−9.12769			−0.791471
$134$	10.6717	+	16.6517i	0.921898	+	1.43849i
$135$		0			0
$136$	−0.0808183	−	0.577628i	−0.00693011	−	0.0495312i
$137$			5.42687i			0.463649i	0.972758	+	0.231825i	$0.0744695\pi$
$137$			5.42687i			0.463649i	−0.972758	+	0.231825i	$0.925530\pi$
$138$		0			0
$139$			11.6189i			0.985504i	0.870170	+	0.492752i	$0.164009\pi$
$139$			11.6189i			0.985504i	−0.870170	+	0.492752i	$0.835991\pi$
$140$	−4.74622	+	2.80091i	−0.401129	+	0.236720i
$141$		0			0
$142$	−6.96515	−	10.8681i	−0.584502	−	0.912033i
$143$		−	22.5405i		−	1.88494i
$144$		0			0
$145$	11.9791	+	8.31436i	0.994807	+	0.690470i
$146$	10.3827	−	6.65403i	0.859277	−	0.550692i
$147$		0			0
$148$	6.78026	−	14.7480i	0.557334	−	1.21228i
$149$		−	20.2872i		−	1.66199i	−0.556278	−	0.830996i	$-0.687771\pi$
$149$		−	20.2872i		−	1.66199i	0.556278	−	0.830996i	$-0.312229\pi$
$150$		0			0
$151$	−2.74572			−0.223444			−0.111722	−	0.993740i	$-0.535637\pi$
$151$	−2.74572			−0.223444			−0.111722	+	0.993740i	$0.535637\pi$
$152$	2.90294	+	20.7480i	0.235459	+	1.68288i
$153$		0			0
$154$	4.36364	+	6.80885i	0.351632	+	0.548672i
$155$	−8.18261	+	11.7893i	−0.657243	+	0.946935i
$156$		0			0
$157$	22.3552			1.78414			0.892069	−	0.451899i	$-0.149253\pi$
$157$	22.3552			1.78414			0.892069	+	0.451899i	$0.149253\pi$
$158$	−4.66334	−	7.27649i	−0.370996	−	0.578886i
$159$		0			0
$160$	7.87618	+	9.89777i	0.622667	+	0.782487i
$161$	1.28993			0.101661
$162$		0			0
$163$	−8.11597			−0.635692			−0.317846	−	0.948142i	$-0.602959\pi$
$163$	−8.11597			−0.635692			−0.317846	+	0.948142i	$0.602959\pi$
$164$	8.91540	−	19.3923i	0.696176	−	1.51428i
$165$		0			0
$166$	−13.2570	−	20.6857i	−1.02894	−	1.60552i
$167$		−	21.2171i		−	1.64183i	−0.571050	−	0.820915i	$-0.693464\pi$
$167$		−	21.2171i		−	1.64183i	0.571050	−	0.820915i	$-0.306536\pi$
$168$		0			0
$169$	10.5944			0.814957
$170$	−0.0239929	+	0.651656i	−0.00184017	+	0.0499798i
$171$		0			0
$172$	−2.13514	+	4.64423i	−0.162803	+	0.354119i
$173$	3.15570			0.239923			0.119962	−	0.992779i	$-0.461723\pi$
$173$	3.15570			0.239923			0.119962	+	0.992779i	$0.461723\pi$
$174$		0			0
$175$	5.77237	−	2.15510i	0.436350	−	0.162910i
$176$	14.0893	−	12.0844i	1.06202	−	0.910894i
$177$		0			0
$178$	−5.46293	−	8.52412i	−0.409464	−	0.638910i
$179$		−	9.89993i		−	0.739956i	−0.929041	−	0.369978i	$-0.879365\pi$
$179$		−	9.89993i		−	0.739956i	0.929041	−	0.369978i	$-0.120635\pi$
$180$		0			0
$181$		−	5.53279i		−	0.411249i	−0.978631	−	0.205625i	$-0.934077\pi$
$181$		−	5.53279i		−	0.411249i	0.978631	−	0.205625i	$-0.0659226\pi$
$182$	−7.12720	+	4.56767i	−0.528303	+	0.338578i
$183$		0			0
$184$	−0.410244	−	2.93211i	−0.0302436	−	0.216158i
$185$	−10.3477	+	14.9087i	−0.760781	+	1.09611i
$186$		0			0
$187$	0.956913			0.0699764
$188$	8.02850	+	3.69103i	0.585539	+	0.269196i
$189$		0			0
$190$	0.861810	−	23.4071i	0.0625223	−	1.69813i
$191$	3.51268			0.254168			0.127084	−	0.991892i	$-0.459438\pi$
$191$	3.51268			0.254168			0.127084	+	0.991892i	$0.459438\pi$
$192$		0			0
$193$			1.41061i			0.101538i	0.998710	+	0.0507689i	$0.0161672\pi$
$193$			1.41061i			0.101538i	−0.998710	+	0.0507689i	$0.983833\pi$
$194$	6.93021	−	4.44142i	0.497560	−	0.318875i
$195$		0			0
$196$	−4.57929	+	9.96060i	−0.327092	+	0.711472i
$197$	−15.2744			−1.08825			−0.544127	−	0.839003i	$-0.683139\pi$
$197$	−15.2744			−1.08825			−0.544127	+	0.839003i	$0.683139\pi$
$198$		0			0
$199$	−2.52491			−0.178986			−0.0894931	−	0.995987i	$-0.528525\pi$
$199$	−2.52491			−0.178986			−0.0894931	+	0.995987i	$0.528525\pi$
$200$	−6.73454	−	12.4357i	−0.476204	−	0.879335i
$201$		0			0
$202$	−8.59894	+	5.51087i	−0.605019	+	0.387744i
$203$	−8.03607			−0.564022
$204$		0			0
$205$	−13.6063	+	19.6035i	−0.950305	+	1.36917i
$206$	−4.22449	+	2.70739i	−0.294334	+	0.188633i
$207$		0			0
$208$	12.6494	+	14.7480i	0.877077	+	1.02259i
$209$	−34.3717			−2.37754
$210$		0			0
$211$			13.2892i			0.914868i	0.889244	+	0.457434i	$0.151231\pi$
$211$			13.2892i			0.914868i	−0.889244	+	0.457434i	$0.848769\pi$
$212$	−3.17711	+	6.91066i	−0.218205	+	0.474626i
$213$		0			0
$214$	0.214832	+	0.335215i	0.0146856	+	0.0229148i
$215$	3.25856	−	4.69483i	0.222232	−	0.320185i
$216$		0			0
$217$		−	7.90874i		−	0.536880i
$218$	7.54329	−	4.83433i	0.510896	−	0.327422i
$219$		0			0
$220$	−17.8726	+	10.5473i	−1.20497	+	0.711096i
$221$			1.00165i			0.0673785i
$222$		0			0
$223$			3.54798i			0.237590i	0.992919	+	0.118795i	$0.0379032\pi$
$223$			3.54798i			0.237590i	−0.992919	+	0.118795i	$0.962097\pi$
$224$	−6.67609	−	2.00614i	−0.446065	−	0.134041i
$225$		0			0
$226$	3.39400	−	2.17514i	0.225766	−	0.144688i
$227$	−8.12871			−0.539522			−0.269761	−	0.962927i	$-0.586945\pi$
$227$	−8.12871			−0.539522			−0.269761	+	0.962927i	$0.586945\pi$
$228$		0			0
$229$		−	20.6234i		−	1.36283i	−0.731896	−	0.681417i	$-0.761364\pi$
$229$		−	20.6234i		−	1.36283i	0.731896	−	0.681417i	$-0.238636\pi$
$230$	−0.121791	+	3.30789i	−0.00803067	+	0.218116i
$231$		0			0
$232$	2.55576	+	18.2667i	0.167794	+	1.19926i
$233$			8.83632i			0.578886i	0.957195	+	0.289443i	$0.0934701\pi$
$233$			8.83632i			0.578886i	−0.957195	+	0.289443i	$0.906530\pi$
$234$		0			0
$235$	−8.11597	−	5.63309i	−0.529428	−	0.367462i
$236$	−9.16951	−	4.21559i	−0.596885	−	0.274412i
$237$		0			0
$238$	−0.193911	−	0.302571i	−0.0125694	−	0.0196127i
$239$	12.3863			0.801200			0.400600	−	0.916253i	$-0.368802\pi$
$239$	12.3863			0.801200			0.400600	+	0.916253i	$0.368802\pi$
$240$		0			0
$241$	−27.7157			−1.78533			−0.892664	−	0.450724i	$-0.851166\pi$
$241$	−27.7157			−1.78533			−0.892664	+	0.450724i	$0.851166\pi$
$242$	8.03806	+	12.5423i	0.516706	+	0.806247i
$243$		0			0
$244$	−12.8878	−	5.92503i	−0.825056	−	0.379311i
$245$	6.98872	−	10.0691i	0.446493	−	0.643293i
$246$		0			0
$247$		−	35.9787i		−	2.28927i
$248$	−17.9772	+	2.51527i	−1.14155	+	0.159720i
$249$		0			0
$250$	4.98152	+	15.0061i	0.315059	+	0.949072i
$251$			0.765217i			0.0483001i	0.999708	+	0.0241500i	$0.00768794\pi$
$251$			0.765217i			0.0483001i	−0.999708	+	0.0241500i	$0.992312\pi$
$252$		0			0
$253$	4.85741			0.305383
$254$	12.8692	−	8.24760i	0.807487	−	0.517501i
$255$		0			0
$256$	−2.43689	+	15.8133i	−0.152306	+	0.988333i
$257$		−	19.8507i		−	1.23826i	−0.785290	−	0.619128i	$-0.787486\pi$
$257$		−	19.8507i		−	1.23826i	0.785290	−	0.619128i	$-0.212514\pi$
$258$		0			0
$259$		−	10.0014i		−	0.621456i
$260$	−11.0404	−	18.7083i	−0.684696	−	1.16024i
$261$		0			0
$262$	4.75325	−	3.04625i	0.293657	−	0.188198i
$263$			24.4072i			1.50501i	0.658584	+	0.752507i	$0.271156\pi$
$263$			24.4072i			1.50501i	−0.658584	+	0.752507i	$0.728844\pi$
$264$		0			0
$265$	4.84877	−	6.98595i	0.297857	−	0.429143i
$266$	6.96515	+	10.8681i	0.427061	+	0.666368i
$267$		0			0
$268$	11.6835	−	25.4132i	0.713681	−	1.55236i
$269$		−	5.51949i		−	0.336529i	−0.985742	−	0.168265i	$-0.946184\pi$
$269$		−	5.51949i		−	0.336529i	0.985742	−	0.168265i	$-0.0538163\pi$
$270$		0			0
$271$	−4.10588			−0.249414			−0.124707	−	0.992194i	$-0.539799\pi$
$271$	−4.10588			−0.249414			−0.124707	+	0.992194i	$0.539799\pi$
$272$	−0.626097	+	0.537004i	−0.0379627	+	0.0325606i
$273$		0			0
$274$	6.46165	−	4.14113i	0.390363	−	0.250175i
$275$	21.7367	−	8.11534i	1.31077	−	0.489373i
$276$		0			0
$277$	−8.37009			−0.502910			−0.251455	−	0.967869i	$-0.580909\pi$
$277$	−8.37009			−0.502910			−0.251455	+	0.967869i	$0.580909\pi$
$278$	13.8344	−	8.86615i	0.829731	−	0.531757i
$279$		0			0
$280$	6.95673	+	3.51390i	0.415744	+	0.209996i
$281$	−19.5453			−1.16598			−0.582988	−	0.812481i	$-0.698116\pi$
$281$	−19.5453			−1.16598			−0.582988	+	0.812481i	$0.698116\pi$
$282$		0			0
$283$	−15.7833			−0.938218			−0.469109	−	0.883140i	$-0.655425\pi$
$283$	−15.7833			−0.938218			−0.469109	+	0.883140i	$0.655425\pi$
$284$	−7.62547	+	16.5865i	−0.452488	+	0.984226i
$285$		0			0
$286$	−26.8385	+	17.2002i	−1.58699	+	1.01707i
$287$		−	13.1509i		−	0.776272i
$288$		0			0
$289$	16.9575			0.997499
$290$	0.758743	−	20.6077i	0.0445549	−	1.21013i
$291$		0			0
$292$	−15.8456	−	7.28486i	−0.927294	−	0.426314i
$293$	−16.0562			−0.938011			−0.469006	−	0.883195i	$-0.655388\pi$
$293$	−16.0562			−0.938011			−0.469006	+	0.883195i	$0.655388\pi$
$294$		0			0
$295$	9.26941	+	6.43366i	0.539686	+	0.374582i
$296$	−22.7340	+	3.18081i	−1.32139	+	0.184881i
$297$		0			0
$298$	−24.1555	+	15.4807i	−1.39929	+	0.896775i
$299$			5.08452i			0.294046i
$300$		0			0
$301$			3.14949i			0.181534i
$302$	2.09520	+	3.26927i	0.120565	+	0.188125i
$303$		0			0
$304$	22.4890	−	19.2888i	1.28983	−	1.10629i
$305$	13.0282	+	9.04253i	0.745992	+	0.517774i
$306$		0			0
$307$	22.1011			1.26137			0.630687	−	0.776037i	$-0.282773\pi$
$307$	22.1011			1.26137			0.630687	+	0.776037i	$0.282773\pi$
$308$	4.77733	−	10.3914i	0.272214	−	0.592103i
$309$		0			0
$310$	20.2812	+	0.746720i	1.15189	+	0.0424108i
$311$	12.2158			0.692693			0.346347	−	0.938107i	$-0.387422\pi$
$311$	12.2158			0.692693			0.346347	+	0.938107i	$0.387422\pi$
$312$		0			0
$313$		−	24.7003i		−	1.39614i	−0.716027	−	0.698072i	$-0.754041\pi$
$313$		−	24.7003i		−	1.39614i	0.716027	−	0.698072i	$-0.245959\pi$
$314$	−17.0588	−	26.6178i	−0.962682	−	1.50213i
$315$		0			0
$316$	−5.10545	+	11.1051i	−0.287204	+	0.624709i
$317$	−21.2309			−1.19244			−0.596222	−	0.802819i	$-0.703332\pi$
$317$	−21.2309			−1.19244			−0.596222	+	0.802819i	$0.703332\pi$
$318$		0			0
$319$	−30.2610			−1.69429
$320$	5.77489	−	16.9308i	0.322826	−	0.946458i
$321$		0			0
$322$	−0.984316	−	1.53589i	−0.0548538	−	0.0855916i
$323$	1.52740			0.0849870
$324$		0			0
$325$	8.49477	+	22.7530i	0.471205	+	1.26211i
$326$	6.19313	+	9.66350i	0.343006	+	0.535212i
$327$		0			0
$328$	−29.8931	+	4.18246i	−1.65057	+	0.230938i
$329$	5.44454			0.300167
$330$		0			0
$331$		−	11.6189i		−	0.638634i	−0.947648	−	0.319317i	$-0.896547\pi$
$331$		−	11.6189i		−	0.638634i	0.947648	−	0.319317i	$-0.103453\pi$
$332$	−14.5138	+	31.5696i	−0.796550	+	1.73261i
$333$		0			0
$334$	−25.2627	+	16.1903i	−1.38232	+	0.885896i
$335$	−17.8308	+	25.6900i	−0.974200	+	1.40360i
$336$		0			0
$337$			26.0264i			1.41775i	0.705334	+	0.708875i	$0.250797\pi$
$337$			26.0264i			1.41775i	−0.705334	+	0.708875i	$0.749203\pi$
$338$	−8.08440	−	12.6146i	−0.439733	−	0.686142i
$339$		0			0
$340$	0.794220	−	0.468697i	0.0430727	−	0.0254187i
$341$		−	29.7815i		−	1.61276i
$342$		0			0
$343$			15.3810i			0.830494i
$344$	7.15906	−	1.00165i	0.385991	−	0.0540056i
$345$		0			0
$346$	−2.40805	−	3.75742i	−0.129457	−	0.202000i
$347$	−2.44534			−0.131273			−0.0656363	−	0.997844i	$-0.520908\pi$
$347$	−2.44534			−0.131273			−0.0656363	+	0.997844i	$0.520908\pi$
$348$		0			0
$349$		−	36.1943i		−	1.93744i	−0.248159	−	0.968719i	$-0.579826\pi$
$349$		−	36.1943i		−	1.93744i	0.248159	−	0.968719i	$-0.420174\pi$
$350$	−6.97080	−	5.22852i	−0.372605	−	0.279476i
$351$		0			0
$352$	−25.1398	−	7.55443i	−1.33996	−	0.402652i
$353$			20.9811i			1.11671i	0.829602	+	0.558355i	$0.188567\pi$
$353$			20.9811i			1.11671i	−0.829602	+	0.558355i	$0.811433\pi$
$354$		0			0
$355$	11.6377	−	16.7672i	0.617663	−	0.889910i
$356$	−5.98083	+	13.0092i	−0.316983	+	0.689484i
$357$		0			0
$358$	−11.7876	+	7.55443i	−0.622995	+	0.399264i
$359$	30.2170			1.59479			0.797397	−	0.603455i	$-0.206210\pi$
$359$	30.2170			1.59479			0.797397	+	0.603455i	$0.206210\pi$
$360$		0			0
$361$	−35.8633			−1.88754
$362$	−6.58776	+	4.22196i	−0.346245	+	0.221901i
$363$		0			0
$364$	10.8772	+	5.00070i	0.570122	+	0.262108i
$365$	16.0182	+	11.1178i	0.838433	+	0.581935i
$366$		0			0
$367$			15.1830i			0.792546i	0.918133	+	0.396273i	$0.129697\pi$
$367$			15.1830i			0.792546i	−0.918133	+	0.396273i	$0.870303\pi$
$368$	−3.17815	+	2.72590i	−0.165672	+	0.142097i
$369$		0			0
$370$	25.6476	+	0.944303i	1.33335	+	0.0490920i
$371$			4.68647i			0.243310i
$372$		0			0
$373$	31.4829			1.63012			0.815061	−	0.579375i	$-0.196703\pi$
$373$	31.4829			1.63012			0.815061	+	0.579375i	$0.196703\pi$
$374$	−0.730200	−	1.13937i	−0.0377577	−	0.0589156i
$375$		0			0
$376$	−1.73156	−	12.3759i	−0.0892985	−	0.638238i
$377$		−	31.6759i		−	1.63139i
$378$		0			0
$379$			25.0117i			1.28477i	0.766383	+	0.642383i	$0.222054\pi$
$379$			25.0117i			1.28477i	−0.766383	+	0.642383i	$0.777946\pi$
$380$	−28.5279	+	16.8353i	−1.46345	+	0.863632i
$381$		0			0
$382$	−2.68045	−	4.18246i	−0.137144	−	0.213993i
$383$		−	6.78343i		−	0.346617i	−0.984868	−	0.173309i	$-0.944554\pi$
$383$		−	6.78343i		−	0.346617i	0.984868	−	0.173309i	$-0.0554458\pi$
$384$		0			0
$385$	−7.29096	+	10.5046i	−0.371582	+	0.535363i
$386$	1.67958	−	1.07640i	0.0854882	−	0.0547876i
$387$		0			0
$388$	−10.5766	−	4.86248i	−0.536945	−	0.246855i
$389$		−	0.654718i		−	0.0331955i	−0.999862	−	0.0165978i	$-0.994717\pi$
$389$		−	0.654718i		−	0.0331955i	0.999862	−	0.0165978i	$-0.00528348\pi$
$390$		0			0
$391$	−0.215853			−0.0109162
$392$	15.3542	−	2.14827i	0.775505	−	0.108504i
$393$		0			0
$394$	11.6556	+	18.1868i	0.587198	+	0.916240i
$395$	7.79172	−	11.2261i	0.392044	−	0.564844i
$396$		0			0
$397$	−14.2392			−0.714646			−0.357323	−	0.933981i	$-0.616310\pi$
$397$	−14.2392			−0.714646			−0.357323	+	0.933981i	$0.616310\pi$
$398$	1.92671	+	3.00635i	0.0965771	+	0.150695i
$399$		0			0
$400$	−9.66788	+	17.5081i	−0.483394	+	0.875403i
$401$	23.6999			1.18352			0.591759	−	0.806115i	$-0.298434\pi$
$401$	23.6999			1.18352			0.591759	+	0.806115i	$0.298434\pi$
$402$		0			0
$403$	31.1740			1.55289
$404$	13.1233	+	6.03332i	0.652910	+	0.300169i
$405$		0			0
$406$	6.13216	+	9.56836i	0.304334	+	0.474870i
$407$		−	37.6617i		−	1.86682i
$408$		0			0
$409$	5.25525			0.259856			0.129928	−	0.991523i	$-0.458525\pi$
$409$	5.25525			0.259856			0.129928	+	0.991523i	$0.458525\pi$
$410$	33.7241	+	1.24167i	1.66552	+	0.0613216i
$411$		0			0
$412$	6.44724	+	2.96406i	0.317633	+	0.146029i
$413$	−6.21832			−0.305984
$414$		0			0
$415$	22.1504	−	31.9136i	1.08732	−	1.56658i
$416$	7.90764	−	26.3152i	0.387704	−	1.29021i
$417$		0			0
$418$	26.2283	+	40.9255i	1.28287	+	2.00173i
$419$			31.9343i			1.56009i	0.625721	+	0.780047i	$0.284805\pi$
$419$			31.9343i			1.56009i	−0.625721	+	0.780047i	$0.715195\pi$
$420$		0			0
$421$			17.1972i			0.838143i	0.907953	+	0.419071i	$0.137644\pi$
$421$			17.1972i			0.838143i	−0.907953	+	0.419071i	$0.862356\pi$
$422$	15.8232	−	10.1407i	0.770260	−	0.493643i
$423$		0			0
$424$	10.6527	−	1.49047i	0.517343	−	0.0723836i
$425$	−0.965933	+	0.360628i	−0.0468546	+	0.0174930i
$426$		0			0
$427$	−8.73987			−0.422952
$428$	0.235199	−	0.511590i	0.0113688	−	0.0247286i
$429$		0			0
$430$	−8.07656	−	0.297366i	−0.389486	−	0.0143403i
$431$	20.4414			0.984626			0.492313	−	0.870418i	$-0.336152\pi$
$431$	20.4414			0.984626			0.492313	+	0.870418i	$0.336152\pi$
$432$		0			0
$433$		−	14.4605i		−	0.694926i	−0.937694	−	0.347463i	$-0.887043\pi$
$433$		−	14.4605i		−	0.694926i	0.937694	−	0.347463i	$-0.112957\pi$
$434$	−9.41675	+	6.03499i	−0.452018	+	0.289689i
$435$		0			0
$436$	−11.5122	−	5.29264i	−0.551337	−	0.253472i
$437$	7.75329			0.370890
$438$		0			0
$439$	2.49792			0.119219			0.0596097	−	0.998222i	$-0.481014\pi$
$439$	2.49792			0.119219			0.0596097	+	0.998222i	$0.481014\pi$
$440$	26.1966	+	13.2321i	1.24887	+	0.630816i
$441$		0			0
$442$	1.19265	−	0.764341i	0.0567284	−	0.0363560i
$443$	17.0800			0.811494			0.405747	−	0.913985i	$-0.367011\pi$
$443$	17.0800			0.811494			0.405747	+	0.913985i	$0.367011\pi$
$444$		0			0
$445$	9.12769	−	13.1509i	0.432694	−	0.623412i
$446$	4.22449	−	2.70739i	0.200036	−	0.128198i
$447$		0			0
$448$	2.70572	+	9.47991i	0.127833	+	0.447884i
$449$	−16.1163			−0.760574			−0.380287	−	0.924868i	$-0.624175\pi$
$449$	−16.1163			−0.760574			−0.380287	+	0.924868i	$0.624175\pi$
$450$		0			0
$451$		−	49.5216i		−	2.33188i
$452$	−5.17978	−	2.38135i	−0.243636	−	0.112009i
$453$		0			0
$454$	6.20285	+	9.67867i	0.291114	+	0.454242i
$455$	−10.9957	−	7.63185i	−0.515488	−	0.357787i
$456$		0			0
$457$		−	39.8891i		−	1.86593i	−0.359964	−	0.932966i	$-0.617211\pi$
$457$		−	39.8891i		−	1.86593i	0.359964	−	0.932966i	$-0.382789\pi$
$458$	−24.5558	+	15.7373i	−1.14742	+	0.735355i
$459$		0			0
$460$	4.03156	−	2.37917i	0.187973	−	0.110929i
$461$			20.2642i			0.943797i	0.881653	+	0.471899i	$0.156431\pi$
$461$			20.2642i			0.943797i	−0.881653	+	0.471899i	$0.843569\pi$
$462$		0			0
$463$		−	4.31020i		−	0.200312i	−0.994972	−	0.100156i	$-0.968066\pi$
$463$		−	4.31020i		−	0.200312i	0.994972	−	0.100156i	$-0.0319341\pi$
$464$	19.7994	−	16.9820i	0.919165	−	0.788369i
$465$		0			0
$466$	10.5212	−	6.74281i	0.487385	−	0.312355i
$467$	−25.7806			−1.19298			−0.596491	−	0.802620i	$-0.703439\pi$
$467$	−25.7806			−1.19298			−0.596491	+	0.802620i	$0.703439\pi$
$468$		0			0
$469$		−	17.2340i		−	0.795791i
$470$	−0.514058	+	13.9620i	−0.0237117	+	0.644018i
$471$		0			0
$472$	1.97765	+	14.1348i	0.0910289	+	0.650605i
$473$			11.8599i			0.545318i
$474$		0			0
$475$	34.6957	−	12.9535i	1.59195	−	0.594348i
$476$	−0.212294	+	0.461770i	−0.00973050	+	0.0211652i
$477$		0			0
$478$	−9.45169	−	14.7480i	−0.432310	−	0.674559i
$479$	−3.25856			−0.148887			−0.0744437	−	0.997225i	$-0.523718\pi$
$479$	−3.25856			−0.148887			−0.0744437	+	0.997225i	$0.523718\pi$
$480$		0			0
$481$	39.4226			1.79752
$482$	21.1493	+	33.0005i	0.963324	+	1.50313i
$483$		0			0
$484$	8.80010	−	19.1415i	0.400005	−	0.870067i
$485$	10.6918	+	7.42092i	0.485491	+	0.336966i
$486$		0			0
$487$			0.683514i			0.0309730i	0.999880	+	0.0154865i	$0.00492970\pi$
$487$			0.683514i			0.0309730i	−0.999880	+	0.0154865i	$0.995070\pi$
$488$	2.77960	+	19.8664i	0.125826	+	0.899312i
$489$		0			0
$490$	−17.3220	−	0.637768i	−0.782529	−	0.0288114i
$491$		−	26.2565i		−	1.18494i	−0.805592	−	0.592471i	$-0.798153\pi$
$491$		−	26.2565i		−	1.18494i	0.805592	−	0.592471i	$-0.201847\pi$
$492$		0			0
$493$	1.34473			0.0605638
$494$	−42.8390	+	27.4546i	−1.92742	+	1.23524i
$495$		0			0
$496$	16.7129	+	19.4857i	0.750431	+	0.874934i
$497$			11.2481i			0.504548i
$498$		0			0
$499$			28.4834i			1.27509i	0.770412	+	0.637547i	$0.220051\pi$
$499$			28.4834i			1.27509i	−0.770412	+	0.637547i	$0.779949\pi$
$500$	14.0662	−	17.3823i	0.629058	−	0.777358i
$501$		0			0
$502$	0.911126	−	0.583921i	0.0406655	−	0.0260617i
$503$			34.8617i			1.55441i	0.629250	+	0.777203i	$0.283362\pi$
$503$			34.8617i			1.55441i	−0.629250	+	0.777203i	$0.716638\pi$
$504$		0			0
$505$	−13.2663	−	9.20780i	−0.590343	−	0.409742i
$506$	−3.70659	−	5.78361i	−0.164778	−	0.257113i
$507$		0			0
$508$	−19.6405	−	9.02951i	−0.871404	−	0.400620i
$509$			13.7661i			0.610170i	0.952325	+	0.305085i	$0.0986848\pi$
$509$			13.7661i			0.610170i	−0.952325	+	0.305085i	$0.901315\pi$
$510$		0			0
$511$	−10.7457			−0.475363
$512$	20.6881	−	9.16527i	0.914294	−	0.405052i
$513$		0			0
$514$	−23.6358	+	15.1477i	−1.04253	+	0.668136i
$515$	−6.51748	−	4.52362i	−0.287195	−	0.199334i
$516$		0			0
$517$	20.5022			0.901687
$518$	−11.9084	+	7.63185i	−0.523226	+	0.335324i
$519$		0			0
$520$	−13.8508	+	27.4214i	−0.607397	+	1.20251i
$521$	−4.15462			−0.182017			−0.0910085	−	0.995850i	$-0.529009\pi$
$521$	−4.15462			−0.182017			−0.0910085	+	0.995850i	$0.529009\pi$
$522$		0			0
$523$	26.9037			1.17642			0.588208	−	0.808710i	$-0.299834\pi$
$523$	26.9037			1.17642			0.588208	+	0.808710i	$0.299834\pi$
$524$	−7.25420	−	3.33505i	−0.316901	−	0.145692i
$525$		0			0
$526$	29.0611	−	18.6246i	1.26713	−	0.812073i
$527$			1.32343i			0.0576494i
$528$		0			0
$529$	21.9043			0.952361
$530$	−12.0180	−	0.442483i	−0.522028	−	0.0192202i
$531$		0			0
$532$	7.62547	−	16.5865i	0.330606	−	0.719115i
$533$	51.8370			2.24531
$534$		0			0
$535$	−0.358950	+	0.517164i	−0.0155188	+	0.0223589i
$536$	−39.1743	+	5.48104i	−1.69207	+	0.236745i
$537$		0			0
$538$	−6.57193	+	4.21181i	−0.283336	+	0.181584i
$539$			25.4362i			1.09561i
$540$		0			0
$541$		−	29.1201i		−	1.25197i	−0.779835	−	0.625985i	$-0.784697\pi$
$541$		−	29.1201i		−	1.25197i	0.779835	−	0.625985i	$-0.215303\pi$
$542$	3.13311	+	4.88877i	0.134578	+	0.209991i
$543$		0			0
$544$	1.11716	+	0.335703i	0.0478978	+	0.0143931i
$545$	11.6377	+	8.07741i	0.498503	+	0.345998i
$546$		0			0
$547$	32.1248			1.37356			0.686779	−	0.726866i	$-0.259024\pi$
$547$	32.1248			1.37356			0.686779	+	0.726866i	$0.259024\pi$
$548$	−9.86150	−	4.53373i	−0.421262	−	0.193671i
$549$		0			0
$550$	−26.2496	−	19.6887i	−1.11929	−	0.839531i
$551$	−48.3020			−2.05773
$552$		0			0
$553$			7.53092i			0.320247i
$554$	6.38704	+	9.96607i	0.271359	+	0.423418i
$555$		0			0
$556$	−21.1134	−	9.70670i	−0.895410	−	0.411656i
$557$	28.8413			1.22204			0.611022	−	0.791613i	$-0.290759\pi$
$557$	28.8413			1.22204			0.611022	+	0.791613i	$0.290759\pi$
$558$		0			0
$559$	−12.4144			−0.525073
$560$	−1.12461	−	10.9646i	−0.0475235	−	0.463339i
$561$		0			0
$562$	14.9146	+	23.2721i	0.629135	+	0.981676i
$563$	−22.0549			−0.929504			−0.464752	−	0.885441i	$-0.653857\pi$
$563$	−22.0549			−0.929504			−0.464752	+	0.885441i	$0.653857\pi$
$564$		0			0
$565$	5.23621	+	3.63432i	0.220289	+	0.152897i
$566$	12.0439	+	18.7928i	0.506242	+	0.789919i
$567$		0			0
$568$	25.5680	−	3.57732i	1.07281	−	0.150101i
$569$	21.9854			0.921676			0.460838	−	0.887484i	$-0.347549\pi$
$569$	21.9854			0.921676			0.460838	+	0.887484i	$0.347549\pi$
$570$		0			0
$571$			13.6420i			0.570899i	0.958394	+	0.285449i	$0.0921429\pi$
$571$			13.6420i			0.570899i	−0.958394	+	0.285449i	$0.907857\pi$
$572$	40.9598	+	18.8309i	1.71261	+	0.787358i
$573$		0			0
$574$	−15.6585	+	10.0352i	−0.653571	+	0.418860i
$575$	−4.90320	+	1.83059i	−0.204478	+	0.0763411i
$576$		0			0
$577$			1.21841i			0.0507229i	0.999678	+	0.0253614i	$0.00807367\pi$
$577$			1.21841i			0.0507229i	−0.999678	+	0.0253614i	$0.991926\pi$
$578$	−12.9399	−	20.1909i	−0.538229	−	0.839830i
$579$		0			0
$580$	−25.1161	+	14.8219i	−1.04289	+	0.615445i
$581$			21.4090i			0.888195i
$582$		0			0
$583$			17.6476i			0.730889i
$584$	3.41753	+	24.4259i	0.141418	+	1.01075i
$585$		0			0
$586$	12.2521	+	19.1177i	0.506131	+	0.789745i
$587$	29.2109			1.20566			0.602831	−	0.797869i	$-0.294039\pi$
$587$	29.2109			1.20566			0.602831	+	0.797869i	$0.294039\pi$
$588$		0			0
$589$		−	47.5366i		−	1.95871i
$590$	0.587116	−	15.9463i	0.0241712	−	0.656497i
$591$		0			0
$592$	21.1351	+	24.6416i	0.868649	+	1.01276i
$593$		−	2.64427i		−	0.108587i	−0.998525	−	0.0542936i	$-0.982709\pi$
$593$		−	2.64427i		−	0.108587i	0.998525	−	0.0542936i	$-0.0172907\pi$
$594$		0			0
$595$	0.323995	−	0.466801i	0.0132825	−	0.0191370i
$596$	36.8651	+	16.9484i	1.51005	+	0.694232i
$597$		0			0
$598$	6.05402	−	3.87989i	0.247567	−	0.158661i
$599$	−24.6020			−1.00521			−0.502606	−	0.864516i	$-0.667625\pi$
$599$	−24.6020			−1.00521			−0.502606	+	0.864516i	$0.667625\pi$
$600$		0			0
$601$	2.29243			0.0935101			0.0467551	−	0.998906i	$-0.485112\pi$
$601$	2.29243			0.0935101			0.0467551	+	0.998906i	$0.485112\pi$
$602$	3.75003	−	2.40331i	0.152840	−	0.0979517i
$603$		0			0
$604$	2.29384	−	4.98942i	0.0933349	−	0.203017i
$605$	−13.4303	+	19.3500i	−0.546021	+	0.786690i
$606$		0			0
$607$			38.3002i			1.55456i	0.629157	+	0.777278i	$0.283400\pi$
$607$			38.3002i			1.55456i	−0.629157	+	0.777278i	$0.716600\pi$
$608$	−40.1276	−	12.0582i	−1.62739	−	0.489025i
$609$		0			0
$610$	0.825193	−	22.4125i	0.0334111	−	0.907457i
$611$			21.4608i			0.868212i
$612$		0			0
$613$	−5.11153			−0.206453			−0.103226	−	0.994658i	$-0.532917\pi$
$613$	−5.11153			−0.206453			−0.103226	+	0.994658i	$0.532917\pi$
$614$	−16.8649	−	26.3152i	−0.680610	−	1.06200i
$615$		0			0
$616$	−16.0182	+	2.24118i	−0.645393	+	0.0902997i
$617$		−	25.5019i		−	1.02667i	−0.858189	−	0.513333i	$-0.828411\pi$
$617$		−	25.5019i		−	1.02667i	0.858189	−	0.513333i	$-0.171589\pi$
$618$		0			0
$619$			1.61753i			0.0650140i	0.999472	+	0.0325070i	$0.0103491\pi$
$619$			1.61753i			0.0650140i	−0.999472	+	0.0325070i	$0.989651\pi$
$620$	−14.5870	−	24.7181i	−0.585829	−	0.992703i
$621$		0			0
$622$	−9.32160	−	14.5450i	−0.373762	−	0.583203i
$623$			8.82218i			0.353453i
$624$		0			0
$625$	−18.8832	+	16.3837i	−0.755328	+	0.655347i
$626$	−29.4101	+	18.8483i	−1.17546	+	0.753329i
$627$		0			0
$628$	−18.6760	+	40.6230i	−0.745254	+	1.62103i
$629$			1.67361i			0.0667311i
$630$		0			0
$631$	−29.1604			−1.16086			−0.580428	−	0.814312i	$-0.697115\pi$
$631$	−29.1604			−1.16086			−0.580428	+	0.814312i	$0.697115\pi$
$632$	17.1184	−	2.39511i	0.680934	−	0.0952723i
$633$		0			0
$634$	16.2008	+	25.2791i	0.643417	+	1.00396i
$635$	19.8544	+	13.7804i	0.787899	+	0.546860i
$636$		0			0
$637$	−26.6255			−1.05494
$638$	23.0915	+	36.0311i	0.914203	+	1.42648i
$639$		0			0
$640$	−24.5658	+	6.04347i	−0.971047	+	0.238889i
$641$	5.86913			0.231817			0.115908	−	0.993260i	$-0.463022\pi$
$641$	5.86913			0.231817			0.115908	+	0.993260i	$0.463022\pi$
$642$		0			0
$643$	−22.7250			−0.896185			−0.448093	−	0.893987i	$-0.647897\pi$
$643$	−22.7250			−0.896185			−0.448093	+	0.893987i	$0.647897\pi$
$644$	−1.07763	+	2.34401i	−0.0424647	+	0.0923667i
$645$		0			0
$646$	−1.16553	−	1.81864i	−0.0458571	−	0.0715536i
$647$		−	3.20814i		−	0.126125i	−0.998010	−	0.0630626i	$-0.979913\pi$
$647$		−	3.20814i		−	0.126125i	0.998010	−	0.0630626i	$-0.0200868\pi$
$648$		0			0
$649$	−23.4160			−0.919158
$650$	20.6093	−	27.4769i	0.808364	−	1.07773i
$651$		0			0
$652$	6.78026	−	14.7480i	0.265535	−	0.577577i
$653$	−44.7124			−1.74973			−0.874866	−	0.484365i	$-0.839051\pi$
$653$	−44.7124			−1.74973			−0.874866	+	0.484365i	$0.839051\pi$
$654$		0			0
$655$	7.33324	+	5.08981i	0.286533	+	0.198875i
$656$	27.7907	+	32.4014i	1.08505	+	1.26506i
$657$		0			0
$658$	−4.15462	−	6.48269i	−0.161964	−	0.252722i
$659$		−	14.4529i		−	0.563005i	−0.959561	−	0.281502i	$-0.909167\pi$
$659$		−	14.4529i		−	0.563005i	0.959561	−	0.281502i	$-0.0908328\pi$
$660$		0			0
$661$			19.1187i			0.743631i	0.928307	+	0.371816i	$0.121265\pi$
$661$			19.1187i			0.743631i	−0.928307	+	0.371816i	$0.878735\pi$
$662$	−13.8344	+	8.86615i	−0.537688	+	0.344593i
$663$		0			0
$664$	48.6644	−	6.80885i	1.88855	−	0.264234i
$665$	−11.6377	+	16.7672i	−0.451289	+	0.650204i
$666$		0			0
$667$	6.82604			0.264305
$668$	38.5549	+	17.7252i	1.49173	+	0.685810i
$669$		0			0
$670$	44.1948	+	1.62718i	1.70740	+	0.0628635i
$671$	−32.9113			−1.27053
$672$		0			0
$673$			28.2402i			1.08858i	0.838898	+	0.544289i	$0.183201\pi$
$673$			28.2402i			1.08858i	−0.838898	+	0.544289i	$0.816799\pi$
$674$	30.9891	−	19.8602i	1.19365	−	0.764987i
$675$		0			0
$676$	−8.85083	+	19.2518i	−0.340416	+	0.740454i
$677$	−36.2679			−1.39389			−0.696944	−	0.717125i	$-0.745458\pi$
$677$	−36.2679			−1.39389			−0.696944	+	0.717125i	$0.745458\pi$
$678$		0			0
$679$	−7.17253			−0.275257
$680$	−1.16412	−	0.588007i	−0.0446420	−	0.0225490i
$681$		0			0
$682$	−35.4601	+	22.7256i	−1.35784	+	0.870210i
$683$	20.3380			0.778211			0.389105	−	0.921193i	$-0.372784\pi$
$683$	20.3380			0.778211			0.389105	+	0.921193i	$0.372784\pi$
$684$		0			0
$685$	9.96894	+	6.91918i	0.380894	+	0.264368i
$686$	18.3138	−	11.7369i	0.699223	−	0.448117i
$687$		0			0
$688$	−6.65557	−	7.75978i	−0.253741	−	0.295839i
$689$	−18.4727			−0.703755
$690$		0			0
$691$		−	13.6695i		−	0.520012i	−0.965607	−	0.260006i	$-0.916276\pi$
$691$		−	13.6695i		−	0.520012i	0.965607	−	0.260006i	$-0.0837245\pi$
$692$	−2.63634	+	5.73441i	−0.100219	+	0.217990i
$693$		0			0
$694$	1.86599	+	2.91161i	0.0708319	+	0.110523i
$695$	21.3435	+	14.8140i	0.809604	+	0.561925i
$696$		0			0
$697$			2.20063i			0.0833550i
$698$	−43.0957	+	27.6191i	−1.63120	+	1.04540i
$699$		0			0
$700$	−0.906205	+	12.2897i	−0.0342513	+	0.464508i
$701$			34.2993i			1.29547i	0.761866	+	0.647734i	$0.224283\pi$
$701$			34.2993i			1.29547i	−0.761866	+	0.647734i	$0.775717\pi$
$702$		0			0
$703$		−	60.1148i		−	2.26727i
$704$	10.1888	+	35.6980i	0.384004	+	1.34542i
$705$		0			0
$706$	24.9817	−	16.0102i	0.940198	−	0.602552i
$707$	8.89961			0.334704
$708$		0			0
$709$			17.1484i			0.644022i	0.946736	+	0.322011i	$0.104359\pi$
$709$			17.1484i			0.644022i	−0.946736	+	0.322011i	$0.895641\pi$
$710$	−28.8448	−	1.06202i	−1.08252	−	0.0398568i
$711$		0			0
$712$	20.0535	−	2.80578i	0.751538	−	0.105151i
$713$			6.71788i			0.251587i
$714$		0			0
$715$	−41.4060	−	28.7389i	−1.54850	−	1.07477i
$716$	17.9898	+	8.27062i	0.672309	+	0.309088i
$717$		0			0
$718$	−23.0580	−	35.9787i	−0.860516	−	1.34271i
$719$	−18.2554			−0.680811			−0.340405	−	0.940279i	$-0.610564\pi$
$719$	−18.2554			−0.680811			−0.340405	+	0.940279i	$0.610564\pi$
$720$		0			0
$721$	4.37221			0.162830
$722$	27.3665	+	42.7016i	1.01848	+	1.58919i
$723$		0			0
$724$	10.0540	+	4.62221i	0.373653	+	0.171783i
$725$	30.5463	−	11.4044i	1.13446	−	0.423547i
$726$		0			0
$727$		−	30.1151i		−	1.11691i	−0.829536	−	0.558453i	$-0.811395\pi$
$727$		−	30.1151i		−	1.11691i	0.829536	−	0.558453i	$-0.188605\pi$
$728$	−2.34597	−	16.7672i	−0.0869473	−	0.621433i
$729$		0			0
$730$	1.01458	−	27.5563i	0.0375513	−	1.01991i
$731$		−	0.527028i		−	0.0194928i
$732$		0			0
$733$	13.2275			0.488569			0.244284	−	0.969704i	$-0.421447\pi$
$733$	13.2275			0.488569			0.244284	+	0.969704i	$0.421447\pi$
$734$	18.0780	−	11.5858i	0.667272	−	0.427640i
$735$		0			0
$736$	5.67084	+	1.70407i	0.209030	+	0.0628129i
$737$		−	64.8971i		−	2.39052i
$738$		0			0
$739$			43.7322i			1.60871i	0.594147	+	0.804357i	$0.297490\pi$
$739$			43.7322i			1.60871i	−0.594147	+	0.804357i	$0.702510\pi$
$740$	−18.4468	−	31.2585i	−0.678117	−	1.14909i
$741$		0			0
$742$	5.58008	−	3.57615i	0.204851	−	0.131285i
$743$			23.8234i			0.873994i	0.899463	+	0.436997i	$0.143958\pi$
$743$			23.8234i			0.873994i	−0.899463	+	0.436997i	$0.856042\pi$
$744$		0			0
$745$	−37.2667	−	25.8659i	−1.36535	−	0.947652i
$746$	−24.0239	−	37.4859i	−0.879578	−	1.37246i
$747$		0			0
$748$	−0.799426	+	1.73886i	−0.0292299	+	0.0635792i
$749$		−	0.346936i		−	0.0126768i
$750$		0			0
$751$	27.5406			1.00497			0.502486	−	0.864585i	$-0.332419\pi$
$751$	27.5406			1.00497			0.502486	+	0.864585i	$0.332419\pi$
$752$	−13.4144	+	11.5055i	−0.489172	+	0.419563i
$753$		0			0
$754$	−37.7157	+	24.1712i	−1.37353	+	0.880263i
$755$	−3.50076	+	5.04378i	−0.127406	+	0.183562i
$756$		0			0
$757$	28.7018			1.04319			0.521593	−	0.853194i	$-0.325338\pi$
$757$	28.7018			1.04319			0.521593	+	0.853194i	$0.325338\pi$
$758$	29.7809	−	19.0859i	1.08169	−	0.693232i
$759$		0			0
$760$	41.8144	+	21.1208i	1.51677	+	0.766132i
$761$	32.4398			1.17594			0.587971	−	0.808882i	$-0.299927\pi$
$761$	32.4398			1.17594			0.587971	+	0.808882i	$0.299927\pi$
$762$		0			0
$763$	−7.80705			−0.282634
$764$	−2.93457	+	6.38310i	−0.106169	+	0.230932i
$765$		0			0
$766$	−8.07687	+	5.17629i	−0.291829	+	0.187027i
$767$		−	24.5108i		−	0.885035i
$768$		0			0
$769$	41.4133			1.49340			0.746700	−	0.665161i	$-0.231637\pi$
$769$	41.4133			1.49340			0.746700	+	0.665161i	$0.231637\pi$
$770$	18.0711	+	0.665350i	0.651239	+	0.0239776i
$771$		0			0
$772$	−2.56330	−	1.17845i	−0.0922552	−	0.0424134i
$773$	−9.75003			−0.350684			−0.175342	−	0.984508i	$-0.556103\pi$
$773$	−9.75003			−0.350684			−0.175342	+	0.984508i	$0.556103\pi$
$774$		0			0
$775$	11.2236	+	30.0622i	0.403165	+	1.07987i
$776$	2.28113	+	16.3038i	0.0818877	+	0.585271i
$777$		0			0
$778$	−0.779558	+	0.499602i	−0.0279485	+	0.0179116i
$779$		−	79.0453i		−	2.83209i
$780$		0			0
$781$			42.3565i			1.51564i
$782$	0.164713	+	0.257011i	0.00589012	+	0.00919070i
$783$		0			0
$784$	−14.2744	−	16.6426i	−0.509799	−	0.594379i
$785$	28.5025	−	41.0655i	1.01730	−	1.46569i
$786$		0			0
$787$	−39.0586			−1.39229			−0.696144	−	0.717902i	$-0.745103\pi$
$787$	−39.0586			−1.39229			−0.696144	+	0.717902i	$0.745103\pi$
$788$	12.7605	−	27.7560i	0.454575	−	0.988766i
$789$		0			0
$790$	−19.3123	−	0.711048i	−0.687101	−	0.0252979i
$791$	−3.51268			−0.124896
$792$		0			0
$793$		−	34.4500i		−	1.22336i
$794$	10.8656	+	16.9543i	0.385607	+	0.601686i
$795$		0			0
$796$	2.10937	−	4.58817i	0.0747645	−	0.162623i
$797$	29.8658			1.05790			0.528950	−	0.848653i	$-0.322586\pi$
$797$	29.8658			1.05790			0.528950	+	0.848653i	$0.322586\pi$
$798$		0			0
$799$	−0.911075			−0.0322315
$800$	28.2238	−	1.84871i	0.997862	−	0.0653616i
$801$		0			0
$802$	−18.0849	−	28.2189i	−0.638600	−	0.996446i
$803$	−40.4646			−1.42796
$804$		0			0
$805$	1.64464	−	2.36954i	0.0579659	−	0.0835154i
$806$	−23.7882	−	37.1181i	−0.837903	−	1.30743i
$807$		0			0
$808$	−2.83040	−	20.2295i	−0.0995732	−	0.711673i
$809$	31.3672			1.10281			0.551406	−	0.834237i	$-0.314091\pi$
$809$	31.3672			1.10281			0.551406	+	0.834237i	$0.314091\pi$
$810$		0			0
$811$		−	37.9027i		−	1.33094i	−0.746423	−	0.665471i	$-0.768231\pi$
$811$		−	37.9027i		−	1.33094i	0.746423	−	0.665471i	$-0.231769\pi$
$812$	6.71351	−	14.6028i	0.235598	−	0.512459i
$813$		0			0
$814$	−44.8429	+	28.7389i	−1.57174	+	1.00730i
$815$	−10.3477	+	14.9087i	−0.362466	+	0.522229i
$816$		0			0
$817$			18.9305i			0.662294i
$818$	−4.01017	−	6.25731i	−0.140212	−	0.218782i
$819$		0			0
$820$	−24.2558	−	41.1020i	−0.847048	−	1.43535i
$821$			14.7417i			0.514489i	0.966346	+	0.257244i	$0.0828145\pi$
$821$			14.7417i			0.514489i	−0.966346	+	0.257244i	$0.917185\pi$
$822$		0			0
$823$		−	27.8484i		−	0.970736i	−0.874310	−	0.485368i	$-0.838686\pi$
$823$		−	27.8484i		−	0.970736i	0.874310	−	0.485368i	$-0.161314\pi$
$824$	−1.39052	−	9.93839i	−0.0484411	−	0.346220i
$825$		0			0
$826$	4.74507	+	7.40401i	0.165102	+	0.257618i
$827$	−44.3212			−1.54120			−0.770599	−	0.637320i	$-0.780043\pi$
$827$	−44.3212			−1.54120			−0.770599	+	0.637320i	$0.780043\pi$
$828$		0			0
$829$			29.1201i			1.01138i	0.862714	+	0.505691i	$0.168763\pi$
$829$			29.1201i			1.01138i	−0.862714	+	0.505691i	$0.831237\pi$
$830$	−54.9013	−	2.02138i	−1.90565	−	0.0701630i
$831$		0			0
$832$	−37.3671	+	10.6652i	−1.29547	+	0.369748i
$833$		−	1.13033i		−	0.0391636i
$834$		0			0
$835$	−38.9750	−	27.0515i	−1.34878	−	0.936156i
$836$	28.7148	−	62.4588i	0.993123	−	2.16018i
$837$		0			0
$838$	38.0234	−	24.3684i	1.31350	−	0.841792i
$839$	−6.37736			−0.220171			−0.110086	−	0.993922i	$-0.535112\pi$
$839$	−6.37736			−0.220171			−0.110086	+	0.993922i	$0.535112\pi$
$840$		0			0
$841$	−13.5253			−0.466390
$842$	20.4764	−	13.1229i	0.705662	−	0.452243i
$843$		0			0
$844$	−24.1486	−	11.1021i	−0.831231	−	0.382150i
$845$	13.5078	−	19.4616i	0.464681	−	0.669498i
$846$		0			0
$847$		−	12.9808i		−	0.446026i
$848$	−9.90355	−	11.5466i	−0.340089	−	0.396513i
$849$		0			0
$850$	1.16647	+	0.874926i	0.0400097	+	0.0300097i
$851$			8.49544i			0.291220i
$852$		0			0
$853$	−26.4550			−0.905802			−0.452901	−	0.891561i	$-0.649611\pi$
$853$	−26.4550			−0.905802			−0.452901	+	0.891561i	$0.649611\pi$
$854$	6.66921	+	10.4064i	0.228216	+	0.356098i
$855$		0			0
$856$	−0.788614	+	0.110338i	−0.0269543	+	0.00377128i
$857$		−	12.2474i		−	0.418362i	−0.977877	−	0.209181i	$-0.932920\pi$
$857$		−	12.2474i		−	0.418362i	0.977877	−	0.209181i	$-0.0670799\pi$
$858$		0			0
$859$			28.1307i			0.959807i	0.877321	+	0.479903i	$0.159328\pi$
$859$			28.1307i			0.959807i	−0.877321	+	0.479903i	$0.840672\pi$
$860$	5.80899	+	9.84349i	0.198085	+	0.335660i
$861$		0			0
$862$	−15.5984	−	24.3391i	−0.531283	−	0.828992i
$863$			21.8108i			0.742449i	0.928543	+	0.371225i	$0.121062\pi$
$863$			21.8108i			0.742449i	−0.928543	+	0.371225i	$0.878938\pi$
$864$		0			0
$865$	4.02347	−	5.79689i	0.136802	−	0.197100i
$866$	−17.2177	+	11.0345i	−0.585083	+	0.374967i
$867$		0			0
$868$	14.3714	+	6.60713i	0.487798	+	0.224261i
$869$			28.3588i			0.962006i
$870$		0			0
$871$	67.9314			2.30177
$872$	2.48293	+	17.7461i	0.0840825	+	0.600958i
$873$		0			0
$874$	−5.91637	−	9.23167i	−0.200124	−	0.312266i
$875$	3.40086	−	13.3513i	0.114970	−	0.451357i
$876$		0			0
$877$	−7.86186			−0.265476			−0.132738	−	0.991151i	$-0.542377\pi$
$877$	−7.86186			−0.265476			−0.132738	+	0.991151i	$0.542377\pi$
$878$	−1.90611	−	2.97422i	−0.0643282	−	0.100375i
$879$		0			0
$880$	−4.23488	−	41.2888i	−0.142758	−	1.39184i
$881$	−10.1635			−0.342417			−0.171209	−	0.985235i	$-0.554767\pi$
$881$	−10.1635			−0.342417			−0.171209	+	0.985235i	$0.554767\pi$
$882$		0			0
$883$	−15.2750			−0.514046			−0.257023	−	0.966405i	$-0.582742\pi$
$883$	−15.2750			−0.514046			−0.257023	+	0.966405i	$0.582742\pi$
$884$	−1.82017	−	0.836803i	−0.0612188	−	0.0281447i
$885$		0			0
$886$	−13.0334	−	20.3367i	−0.437865	−	0.683226i
$887$			18.9961i			0.637825i	0.947784	+	0.318913i	$0.103318\pi$
$887$			18.9961i			0.637825i	−0.947784	+	0.318913i	$0.896682\pi$
$888$		0			0
$889$	−13.3192			−0.446712
$890$	−22.6236	−	0.832965i	−0.758345	−	0.0279210i
$891$		0			0
$892$	−6.44724	−	2.96406i	−0.215870	−	0.0992439i
$893$	32.7252			1.09511
$894$		0			0
$895$	−18.1858	−	12.6223i	−0.607883	−	0.421916i
$896$	9.22284	−	10.4556i	0.308113	−	0.349296i
$897$		0			0
$898$	12.2980	+	19.1893i	0.410389	+	0.640354i
$899$		−	41.8515i		−	1.39583i
$900$		0			0
$901$		−	0.784222i		−	0.0261262i
$902$	−58.9642	+	37.7889i	−1.96329	+	1.25823i
$903$		0			0
$904$	1.11716	+	7.98460i	0.0371562	+	0.265564i
$905$	−10.1635	−	7.05422i	−0.337846	−	0.234490i
$906$		0			0
$907$	2.33841			0.0776458			0.0388229	−	0.999246i	$-0.487639\pi$
$907$	2.33841			0.0776458			0.0388229	+	0.999246i	$0.487639\pi$
$908$	6.79090	−	14.7712i	0.225364	−	0.490198i
$909$		0			0
$910$	−0.696459	+	18.9161i	−0.0230874	+	0.627061i
$911$	23.0212			0.762727			0.381364	−	0.924425i	$-0.375455\pi$
$911$	23.0212			0.762727			0.381364	+	0.924425i	$0.375455\pi$
$912$		0			0
$913$			80.6188i			2.66809i
$914$	−47.4950	+	30.4385i	−1.57099	+	1.00682i
$915$		0			0
$916$	37.4760	+	17.2292i	1.23824	+	0.569270i
$917$	−4.91945			−0.162455
$918$		0			0
$919$	−56.6304			−1.86806			−0.934032	−	0.357190i	$-0.883735\pi$
$919$	−56.6304			−1.86806			−0.934032	+	0.357190i	$0.883735\pi$
$920$	−5.90922	−	2.98480i	−0.194821	−	0.0984058i
$921$		0			0
$922$	24.1281	−	15.4632i	0.794616	−	0.509252i
$923$	−44.3370			−1.45937
$924$		0			0
$925$	14.1934	+	38.0167i	0.466677	+	1.24998i
$926$	−5.13205	+	3.28902i	−0.168650	+	0.108084i
$927$		0			0
$928$	−35.3286	−	10.6161i	−1.15972	−	0.348491i
$929$	53.7833			1.76457			0.882286	−	0.470714i	$-0.156004\pi$
$929$	53.7833			1.76457			0.882286	+	0.470714i	$0.156004\pi$
$930$		0			0
$931$			40.6007i			1.33063i
$932$	−16.0570	−	7.38205i	−0.525965	−	0.241807i
$933$		0			0
$934$	19.6726	+	30.6963i	0.643707	+	1.00441i
$935$	1.22005	−	1.75781i	0.0398999	−	0.0574865i
$936$		0			0
$937$		−	27.3784i		−	0.894412i	−0.894431	−	0.447206i	$-0.852419\pi$
$937$		−	27.3784i		−	0.894412i	0.894431	−	0.447206i	$-0.147581\pi$
$938$	−20.5201	+	13.1509i	−0.670005	+	0.429392i
$939$		0			0
$940$	17.0165	−	10.0420i	0.555016	−	0.327535i
$941$		−	54.0147i		−	1.76083i	−0.474204	−	0.880415i	$-0.657264\pi$
$941$		−	54.0147i		−	1.76083i	0.474204	−	0.880415i	$-0.342736\pi$
$942$		0			0
$943$			11.1707i			0.363768i
$944$	15.3208	−	13.1407i	0.498650	−	0.427693i
$945$		0			0
$946$	14.1213	−	9.05002i	0.459123	−	0.294242i
$947$	−22.8802			−0.743506			−0.371753	−	0.928332i	$-0.621243\pi$
$947$	−22.8802			−0.743506			−0.371753	+	0.928332i	$0.621243\pi$
$948$		0			0
$949$		−	42.3565i		−	1.37495i
$950$	−41.8990	−	31.4267i	−1.35938	−	1.01962i
$951$		0			0
$952$	0.711816	−	0.0995932i	0.0230701	−	0.00322783i
$953$			10.9797i			0.355667i	0.984061	+	0.177833i	$0.0569088\pi$
$953$			10.9797i			0.355667i	−0.984061	+	0.177833i	$0.943091\pi$
$954$		0			0
$955$	4.47861	−	6.45264i	0.144924	−	0.208802i
$956$	−10.3477	+	22.5078i	−0.334670	+	0.727954i
$957$		0			0
$958$	2.48654	+	3.87989i	0.0803364	+	0.125354i
$959$	−6.68759			−0.215954
$960$		0			0
$961$	10.1883			0.328656
$962$	−30.0826	−	46.9396i	−0.969901	−	1.51339i
$963$		0			0
$964$	23.1543	−	50.3639i	0.745750	−	1.62211i
$965$	2.59123	+	1.79850i	0.0834145	+	0.0578959i
$966$		0			0
$967$		−	12.4308i		−	0.399748i	−0.979822	−	0.199874i	$-0.935947\pi$
$967$		−	12.4308i		−	0.399748i	0.979822	−	0.199874i	$-0.0640533\pi$
$968$	−29.5065	+	4.12837i	−0.948374	+	0.132691i
$969$		0			0
$970$	0.677210	−	18.3932i	0.0217439	−	0.590572i
$971$		−	45.3777i		−	1.45624i	−0.685450	−	0.728120i	$-0.740394\pi$
$971$		−	45.3777i		−	1.45624i	0.685450	−	0.728120i	$-0.259606\pi$
$972$		0			0
$973$	−14.3181			−0.459018
$974$	0.813844	−	0.521575i	0.0260772	−	0.0167123i
$975$		0			0
$976$	21.5335	−	18.4693i	0.689269	−	0.591187i
$977$			33.1258i			1.05979i	0.848063	+	0.529895i	$0.177769\pi$
$977$			33.1258i			1.05979i	−0.848063	+	0.529895i	$0.822231\pi$
$978$		0			0
$979$			33.2212i			1.06175i
$980$	12.4587	+	21.1116i	0.397978	+	0.674385i
$981$		0			0
$982$	−31.2631	+	20.0358i	−0.997644	+	0.639368i
$983$			4.89355i			0.156080i	0.996950	+	0.0780400i	$0.0248662\pi$
$983$			4.89355i			0.156080i	−0.996950	+	0.0780400i	$0.975134\pi$
$984$		0			0
$985$	−19.4746	+	28.0584i	−0.620512	+	0.894014i
$986$	−1.02614	−	1.60114i	−0.0326789	−	0.0509908i
$987$		0			0
$988$	65.3791	+	30.0574i	2.07999	+	0.956253i
$989$		−	2.67526i		−	0.0850683i
$990$		0			0
$991$	47.7631			1.51724			0.758622	−	0.651531i	$-0.225873\pi$
$991$	47.7631			1.51724			0.758622	+	0.651531i	$0.225873\pi$
$992$	10.4479	−	34.7688i	0.331721	−	1.10391i
$993$		0			0
$994$	13.3929	−	8.58322i	0.424797	−	0.272243i
$995$	−3.21922	+	4.63816i	−0.102056	+	0.147039i
$996$		0			0
$997$	−1.76932			−0.0560350			−0.0280175	−	0.999607i	$-0.508919\pi$
$997$	−1.76932			−0.0560350			−0.0280175	+	0.999607i	$0.508919\pi$
$998$	33.9146	−	21.7351i	1.07355	−	0.688013i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.g.109.5	✓	16
3.2	odd	2		1080.2.d.h.109.12	yes	16
4.3	odd	2		4320.2.d.g.3889.13		16
5.4	even	2		1080.2.d.h.109.11	yes	16
8.3	odd	2		4320.2.d.h.3889.4		16
8.5	even	2		1080.2.d.h.109.10	yes	16
12.11	even	2		4320.2.d.h.3889.3		16
15.14	odd	2	inner	1080.2.d.g.109.6	yes	16
20.19	odd	2		4320.2.d.h.3889.2		16
24.5	odd	2	inner	1080.2.d.g.109.7	yes	16
24.11	even	2		4320.2.d.g.3889.14		16
40.19	odd	2		4320.2.d.g.3889.15		16
40.29	even	2	inner	1080.2.d.g.109.8	yes	16
60.59	even	2		4320.2.d.g.3889.16		16
120.29	odd	2		1080.2.d.h.109.9	yes	16
120.59	even	2		4320.2.d.h.3889.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.g.109.5	✓	16	1.1	even	1	trivial
1080.2.d.g.109.6	yes	16	15.14	odd	2	inner
1080.2.d.g.109.7	yes	16	24.5	odd	2	inner
1080.2.d.g.109.8	yes	16	40.29	even	2	inner
1080.2.d.h.109.9	yes	16	120.29	odd	2
1080.2.d.h.109.10	yes	16	8.5	even	2
1080.2.d.h.109.11	yes	16	5.4	even	2
1080.2.d.h.109.12	yes	16	3.2	odd	2
4320.2.d.g.3889.13		16	4.3	odd	2
4320.2.d.g.3889.14		16	24.11	even	2
4320.2.d.g.3889.15		16	40.19	odd	2
4320.2.d.g.3889.16		16	60.59	even	2
4320.2.d.h.3889.1		16	120.59	even	2
4320.2.d.h.3889.2		16	20.19	odd	2
4320.2.d.h.3889.3		16	12.11	even	2
4320.2.d.h.3889.4		16	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.763079 - 1.19068i) q^{2} +(-0.835421 + 1.81716i) q^{4} +(1.27498 - 1.83696i) q^{5} +1.23231i q^{7} +(2.80114 - 0.391920i) q^{8} +O(q^{10})\)	\(q+(-0.763079 - 1.19068i) q^{2} +(-0.835421 + 1.81716i) q^{4} +(1.27498 - 1.83696i) q^{5} +1.23231i q^{7} +(2.80114 - 0.391920i) q^{8} +(-3.16014 - 0.116351i) q^{10} +4.64044i q^{11} -4.85741 q^{13} +(1.46728 - 0.940350i) q^{14} +(-2.60414 - 3.03619i) q^{16} -0.206211i q^{17} +7.40698i q^{19} +(2.27290 + 3.85149i) q^{20} +(5.52527 - 3.54102i) q^{22} -1.04676i q^{23} +(-1.74883 - 4.68419i) q^{25} +(3.70659 + 5.78361i) q^{26} +(-2.23930 - 1.02950i) q^{28} +6.52114i q^{29} -6.41781 q^{31} +(-1.62795 + 5.41754i) q^{32} +(-0.245531 + 0.157356i) q^{34} +(2.26370 + 1.57118i) q^{35} -8.11597 q^{37} +(8.81931 - 5.65211i) q^{38} +(2.85147 - 5.64527i) q^{40} -10.6717 q^{41} +2.55576 q^{43} +(-8.43243 - 3.87673i) q^{44} +(-1.24635 + 0.798757i) q^{46} -4.41816i q^{47} +5.48141 q^{49} +(-4.24286 + 5.65669i) q^{50} +(4.05799 - 8.82669i) q^{52} +3.80300 q^{53} +(8.52430 + 5.91650i) q^{55} +(0.482966 + 3.45188i) q^{56} +(7.76457 - 4.97615i) q^{58} +5.04607i q^{59} +7.09226i q^{61} +(4.89730 + 7.64154i) q^{62} +(7.69280 - 2.19565i) q^{64} +(-6.19313 + 8.92286i) q^{65} -13.9851 q^{67} +(0.374719 + 0.172273i) q^{68} +(0.143381 - 3.89427i) q^{70} +9.12769 q^{71} +8.71998i q^{73} +(6.19313 + 9.66350i) q^{74} +(-13.4597 - 6.18795i) q^{76} -5.71847 q^{77} +6.11122 q^{79} +(-8.89759 + 0.912603i) q^{80} +(8.14338 + 12.7066i) q^{82} +17.3731 q^{83} +(-0.378802 - 0.262916i) q^{85} +(-1.95025 - 3.04309i) q^{86} +(1.81868 + 12.9985i) q^{88} +7.15906 q^{89} -5.98584i q^{91} +(1.90212 + 0.874482i) q^{92} +(-5.26060 + 3.37140i) q^{94} +(13.6063 + 9.44378i) q^{95} +5.82040i q^{97} +(-4.18275 - 6.52659i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more