LMFDB - Embedded newform 261.3.s.a.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	261.55
Dual form			261.3.s.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488049 + 0.776726i) q^{2} +(1.37042 + 2.84571i) q^{4} +(1.98497 - 0.453055i) q^{5} +(9.56374 + 4.60566i) q^{7} +(-6.52543 - 0.735239i) q^{8} +O(q^{10})$	\(q+(-0.488049 + 0.776726i) q^{2} +(1.37042 + 2.84571i) q^{4} +(1.98497 - 0.453055i) q^{5} +(9.56374 + 4.60566i) q^{7} +(-6.52543 - 0.735239i) q^{8} +(-0.616861 + 1.76289i) q^{10} +(11.6332 - 1.31075i) q^{11} +(-11.0274 - 8.79408i) q^{13} +(-8.24491 + 5.18062i) q^{14} +(-4.12137 + 5.16804i) q^{16} +(-0.154761 - 0.154761i) q^{17} +(20.3603 + 7.12436i) q^{19} +(4.00951 + 5.02777i) q^{20} +(-4.65948 + 9.67551i) q^{22} +(-1.51251 + 6.62676i) q^{23} +(-18.7894 + 9.04850i) q^{25} +(12.2125 - 4.27334i) q^{26} +33.5274i q^{28} +(15.7913 + 24.3235i) q^{29} +(-0.406230 + 0.646512i) q^{31} +(-10.6781 - 30.5163i) q^{32} +(0.195737 - 0.0446758i) q^{34} +(21.0703 + 4.80916i) q^{35} +(-6.96097 - 0.784313i) q^{37} +(-15.4705 + 12.3373i) q^{38} +(-13.2858 + 1.49696i) q^{40} +(-35.8917 + 35.8917i) q^{41} +(18.2000 - 11.4358i) q^{43} +(19.6724 + 31.3084i) q^{44} +(-4.40899 - 4.40899i) q^{46} +(2.57409 + 22.8457i) q^{47} +(39.7021 + 49.7849i) q^{49} +(2.14195 - 19.0103i) q^{50} +(9.91319 - 43.4325i) q^{52} +(-12.7427 - 55.8292i) q^{53} +(22.4976 - 7.87226i) q^{55} +(-59.0212 - 37.0855i) q^{56} +(-26.5997 + 0.394450i) q^{58} +48.4185 q^{59} +(-24.4350 - 69.8312i) q^{61} +(-0.303902 - 0.631059i) q^{62} +(3.13649 + 0.715883i) q^{64} +(-25.8733 - 12.4599i) q^{65} +(33.7392 - 26.9061i) q^{67} +(0.228317 - 0.652492i) q^{68} +(-14.0188 + 14.0188i) q^{70} +(-78.3788 - 62.5050i) q^{71} +(5.59603 + 8.90604i) q^{73} +(4.00650 - 5.02399i) q^{74} +(7.62828 + 67.7029i) q^{76} +(117.294 + 41.0428i) q^{77} +(4.65001 - 41.2700i) q^{79} +(-5.83937 + 12.1256i) q^{80} +(-10.3611 - 45.3949i) q^{82} +(-85.5238 + 41.1861i) q^{83} +(-0.377310 - 0.237079i) q^{85} +19.7176i q^{86} -76.8752 q^{88} +(89.2455 - 142.033i) q^{89} +(-64.9610 - 134.893i) q^{91} +(-20.9306 + 4.77728i) q^{92} +(-19.0011 - 9.15045i) q^{94} +(43.6421 + 4.91729i) q^{95} +(20.2947 - 57.9990i) q^{97} +(-58.0458 + 6.54019i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{19}{28}\right)$	$1$

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 $

$2$	−0.488049	+	0.776726i	−0.244025	+	0.388363i	−0.946170	−	0.323671i	$-0.895083\pi$
$2$	−0.488049	+	0.776726i	−0.244025	+	0.388363i	0.702145	+	0.712034i	$0.252226\pi$
$3$		0			0
$3$		0			0
$4$	1.37042	+	2.84571i	0.342606	+	0.711429i
$5$	1.98497	−	0.453055i	0.396993	−	0.0906111i	−0.0193635	−	0.999813i	$-0.506164\pi$
$5$	1.98497	−	0.453055i	0.396993	−	0.0906111i	0.416356	+	0.909201i	$0.363307\pi$
$6$		0			0
$7$	9.56374	+	4.60566i	1.36625	+	0.657951i	0.966021	−	0.258465i	$-0.0832165\pi$
$7$	9.56374	+	4.60566i	1.36625	+	0.657951i	0.400228	+	0.916415i	$0.368931\pi$
$8$	−6.52543	−	0.735239i	−0.815678	−	0.0919049i
$9$		0			0
$10$	−0.616861	+	1.76289i	−0.0616861	+	0.176289i
$11$	11.6332	−	1.31075i	1.05756	−	0.119159i	0.433985	−	0.900920i	$-0.357107\pi$
$11$	11.6332	−	1.31075i	1.05756	−	0.119159i	0.623577	+	0.781762i	$0.285679\pi$
$12$		0			0
$13$	−11.0274	−	8.79408i	−0.848264	−	0.676468i	0.0996406	−	0.995023i	$-0.468231\pi$
$13$	−11.0274	−	8.79408i	−0.848264	−	0.676468i	−0.947904	+	0.318556i	$0.896802\pi$
$14$	−8.24491	+	5.18062i	−0.588922	+	0.370044i
$15$		0			0
$16$	−4.12137	+	5.16804i	−0.257586	+	0.323002i
$17$	−0.154761	−	0.154761i	−0.00910357	−	0.00910357i	0.702540	−	0.711644i	$-0.252049\pi$
$17$	−0.154761	−	0.154761i	−0.00910357	−	0.00910357i	−0.711644	+	0.702540i	$0.752049\pi$
$18$		0			0
$19$	20.3603	+	7.12436i	1.07159	+	0.374966i	0.807705	−	0.589587i	$-0.200710\pi$
$19$	20.3603	+	7.12436i	1.07159	+	0.374966i	0.263888	+	0.964553i	$0.414995\pi$
$20$	4.00951	+	5.02777i	0.200475	+	0.251388i
$21$		0			0
$22$	−4.65948	+	9.67551i	−0.211794	+	0.439796i
$23$	−1.51251	+	6.62676i	−0.0657615	+	0.288120i	−0.997106	−	0.0760183i	$-0.975779\pi$
$23$	−1.51251	+	6.62676i	−0.0657615	+	0.288120i	0.931345	+	0.364138i	$0.118636\pi$
$24$		0			0
$25$	−18.7894	+	9.04850i	−0.751576	+	0.361940i
$26$	12.2125	−	4.27334i	0.469712	−	0.164359i
$27$		0			0
$28$			33.5274i			1.19741i
$29$	15.7913	+	24.3235i	0.544528	+	0.838742i
$29$	15.7913	+	24.3235i	0.544528	+	0.838742i
$30$		0			0
$31$	−0.406230	+	0.646512i	−0.0131042	+	0.0208552i	−0.853212	−	0.521564i	$-0.825349\pi$
$31$	−0.406230	+	0.646512i	−0.0131042	+	0.0208552i	0.840108	+	0.542419i	$0.182492\pi$
$32$	−10.6781	−	30.5163i	−0.333691	−	0.953634i
$33$		0			0
$34$	0.195737	−	0.0446758i	0.00575698	−	0.00131399i
$35$	21.0703	+	4.80916i	0.602009	+	0.137405i
$36$		0			0
$37$	−6.96097	−	0.784313i	−0.188134	−	0.0211977i	0.0173945	−	0.999849i	$-0.494463\pi$
$37$	−6.96097	−	0.784313i	−0.188134	−	0.0211977i	−0.205529	+	0.978651i	$0.565891\pi$
$38$	−15.4705	+	12.3373i	−0.407118	+	0.324666i
$39$		0			0
$40$	−13.2858	+	1.49696i	−0.332146	+	0.0374239i
$41$	−35.8917	+	35.8917i	−0.875407	+	0.875407i	−0.993055	−	0.117648i	$-0.962464\pi$
$41$	−35.8917	+	35.8917i	−0.875407	+	0.875407i	0.117648	+	0.993055i	$0.462464\pi$
$42$		0			0
$43$	18.2000	−	11.4358i	0.423256	−	0.265949i	−0.303519	−	0.952825i	$-0.598161\pi$
$43$	18.2000	−	11.4358i	0.423256	−	0.265949i	0.726774	+	0.686876i	$0.241019\pi$
$44$	19.6724	+	31.3084i	0.447100	+	0.711556i
$45$		0			0
$46$	−4.40899	−	4.40899i	−0.0958477	−	0.0958477i
$47$	2.57409	+	22.8457i	0.0547678	+	0.486078i	0.990917	+	0.134475i	$0.0429347\pi$
$47$	2.57409	+	22.8457i	0.0547678	+	0.486078i	−0.936149	+	0.351603i	$0.885637\pi$
$48$		0			0
$49$	39.7021	+	49.7849i	0.810247	+	1.01602i
$50$	2.14195	−	19.0103i	0.0428390	−	0.380206i
$51$		0			0
$52$	9.91319	−	43.4325i	0.190638	−	0.835241i
$53$	−12.7427	−	55.8292i	−0.240427	−	1.05338i	−0.940629	−	0.339436i	$-0.889764\pi$
$53$	−12.7427	−	55.8292i	−0.240427	−	1.05338i	0.700202	−	0.713945i	$-0.253093\pi$
$54$		0			0
$55$	22.4976	−	7.87226i	0.409048	−	0.143132i
$56$	−59.0212	−	37.0855i	−1.05395	−	0.662241i
$57$		0			0
$58$	−26.5997	+	0.394450i	−0.458615	+	0.00680085i
$59$	48.4185			0.820652			0.410326	−	0.911939i	$-0.365415\pi$
$59$	48.4185			0.820652			0.410326	+	0.911939i	$0.365415\pi$
$60$		0			0
$61$	−24.4350	−	69.8312i	−0.400574	−	1.14477i	−0.950813	−	0.309766i	$-0.899749\pi$
$61$	−24.4350	−	69.8312i	−0.400574	−	1.14477i	0.550239	−	0.835007i	$-0.314537\pi$
$62$	−0.303902	−	0.631059i	−0.00490165	−	0.0101784i
$63$		0			0
$64$	3.13649	+	0.715883i	0.0490076	+	0.0111857i
$65$	−25.8733	−	12.4599i	−0.398050	−	0.191691i
$66$		0			0
$67$	33.7392	−	26.9061i	0.503570	−	0.401584i	−0.338488	−	0.940971i	$-0.609915\pi$
$67$	33.7392	−	26.9061i	0.503570	−	0.401584i	0.842058	+	0.539387i	$0.181344\pi$
$68$	0.228317	−	0.652492i	0.00335760	−	0.00959548i
$69$		0			0
$70$	−14.0188	+	14.0188i	−0.200268	+	0.200268i
$71$	−78.3788	−	62.5050i	−1.10393	−	0.880352i	−0.110393	−	0.993888i	$-0.535211\pi$
$71$	−78.3788	−	62.5050i	−1.10393	−	0.880352i	−0.993534	+	0.113536i	$0.963782\pi$
$72$		0			0
$73$	5.59603	+	8.90604i	0.0766580	+	0.122001i	0.882853	−	0.469649i	$-0.155620\pi$
$73$	5.59603	+	8.90604i	0.0766580	+	0.122001i	−0.806195	+	0.591650i	$0.798477\pi$
$74$	4.00650	−	5.02399i	0.0541418	−	0.0678917i
$75$		0			0
$76$	7.62828	+	67.7029i	0.100372	+	0.890827i
$77$	117.294	+	41.0428i	1.52329	+	0.533024i
$78$		0			0
$79$	4.65001	−	41.2700i	0.0588609	−	0.522405i	−0.929338	−	0.369230i	$-0.879622\pi$
$79$	4.65001	−	41.2700i	0.0588609	−	0.522405i	0.988199	−	0.153175i	$-0.0489499\pi$
$80$	−5.83937	+	12.1256i	−0.0729922	+	0.151570i
$81$		0			0
$82$	−10.3611	−	45.3949i	−0.126355	−	0.553597i
$83$	−85.5238	+	41.1861i	−1.03041	+	0.496218i	−0.871149	−	0.491019i	$-0.836625\pi$
$83$	−85.5238	+	41.1861i	−1.03041	+	0.496218i	−0.159259	+	0.987237i	$0.550910\pi$
$84$		0			0
$85$	−0.377310	−	0.237079i	−0.00443894	−	0.00278917i
$86$			19.7176i			0.229275i
$87$		0			0
$88$	−76.8752			−0.873582
$89$	89.2455	−	142.033i	1.00276	−	1.59588i	0.218126	−	0.975921i	$-0.430006\pi$
$89$	89.2455	−	142.033i	1.00276	−	1.59588i	0.784633	−	0.619961i	$-0.212852\pi$
$90$		0			0
$91$	−64.9610	−	134.893i	−0.713857	−	1.48234i
$92$	−20.9306	+	4.77728i	−0.227507	+	0.0519270i
$93$		0			0
$94$	−19.0011	−	9.15045i	−0.202139	−	0.0973452i
$95$	43.6421	+	4.91729i	0.459391	+	0.0517609i
$96$		0			0
$97$	20.2947	−	57.9990i	0.209224	−	0.597928i	−0.790673	−	0.612238i	$-0.790269\pi$
$97$	20.2947	−	57.9990i	0.209224	−	0.597928i	0.999898	+	0.0143099i	$0.00455513\pi$
$98$	−58.0458	+	6.54019i	−0.592304	+	0.0667367i
$99$		0			0
$100$	−51.4989	−	41.0690i	−0.514989	−	0.410690i
$101$	119.742	−	75.2390i	1.18557	−	0.744941i	0.212883	−	0.977078i	$-0.431715\pi$
$101$	119.742	−	75.2390i	1.18557	−	0.744941i	0.972683	+	0.232137i	$0.0745717\pi$
$102$		0			0
$103$	61.1848	−	76.7234i	0.594028	−	0.744887i	−0.390406	−	0.920643i	$-0.627665\pi$
$103$	61.1848	−	76.7234i	0.594028	−	0.744887i	0.984434	+	0.175756i	$0.0562368\pi$
$104$	65.4929	+	65.4929i	0.629739	+	0.629739i
$105$		0			0
$106$	49.5831	+	17.3499i	0.467765	+	0.163678i
$107$	−91.2780	−	114.459i	−0.853066	−	1.06971i	−0.996787	−	0.0800922i	$-0.974479\pi$
$107$	−91.2780	−	114.459i	−0.853066	−	1.06971i	0.143722	−	0.989618i	$-0.454093\pi$
$108$		0			0
$109$	−8.55158	+	17.7575i	−0.0784549	+	0.162913i	−0.936507	−	0.350650i	$-0.885961\pi$
$109$	−8.55158	+	17.7575i	−0.0784549	+	0.162913i	0.858052	+	0.513563i	$0.171675\pi$
$110$	−4.86536	+	21.3165i	−0.0442306	+	0.193787i
$111$		0			0
$112$	−63.2180	+	30.4442i	−0.564446	+	0.271823i
$113$	36.2240	−	12.6753i	0.320566	−	0.112171i	−0.165199	−	0.986260i	$-0.552827\pi$
$113$	36.2240	−	12.6753i	0.320566	−	0.112171i	0.485765	+	0.874089i	$0.338541\pi$
$114$		0			0
$115$			13.8391i			0.120340i
$116$	−47.5770	+	78.2711i	−0.410147	+	0.674751i
$117$		0			0
$118$	−23.6306	+	37.6079i	−0.200259	+	0.318711i
$119$	−0.767317	−	2.19287i	−0.00644804	−	0.0184274i
$120$		0			0
$121$	15.6466	−	3.57125i	0.129311	−	0.0295144i
$122$	66.1652	+	15.1018i	0.542337	+	0.123785i
$123$		0			0
$124$	−2.39650	−	0.270020i	−0.0193266	−	0.00217758i
$125$	−72.9923	+	58.2094i	−0.583938	+	0.465675i
$126$		0			0
$127$	53.9964	−	6.08394i	0.425169	−	0.0479050i	0.103212	−	0.994659i	$-0.467088\pi$
$127$	53.9964	−	6.08394i	0.425169	−	0.0479050i	0.321957	+	0.946754i	$0.395659\pi$
$128$	89.3579	−	89.3579i	0.698108	−	0.698108i
$129$		0			0
$130$	22.3054	−	14.0154i	0.171580	−	0.107811i
$131$	37.0804	+	59.0132i	0.283057	+	0.450482i	0.957744	−	0.287621i	$-0.0928644\pi$
$131$	37.0804	+	59.0132i	0.283057	+	0.450482i	−0.674687	+	0.738104i	$0.735722\pi$
$132$		0			0
$133$	161.908	+	161.908i	1.21735	+	1.21735i
$134$	4.43229	+	39.3376i	0.0330768	+	0.293565i
$135$		0			0
$136$	0.896093	+	1.12367i	0.00658892	+	0.00826224i
$137$	−10.8849	+	96.6061i	−0.0794518	+	0.705154i	0.889335	+	0.457257i	$0.151168\pi$
$137$	−10.8849	+	96.6061i	−0.0794518	+	0.705154i	−0.968786	+	0.247897i	$0.920260\pi$
$138$		0			0
$139$	−43.7002	+	191.463i	−0.314390	+	1.37743i	0.532845	+	0.846213i	$0.321123\pi$
$139$	−43.7002	+	191.463i	−0.314390	+	1.37743i	−0.847235	+	0.531219i	$0.821734\pi$
$140$	15.1898	+	66.5507i	0.108498	+	0.475362i
$141$		0			0
$142$	86.8020	−	30.3733i	0.611282	−	0.213897i
$143$	−139.811	−	87.8490i	−0.977698	−	0.614329i
$144$		0			0
$145$	42.3651	+	41.1270i	0.292173	+	0.283635i
$146$	−9.64869			−0.0660869
$147$		0			0
$148$	−7.30755	−	20.8838i	−0.0493754	−	0.141107i
$149$	−14.9818	−	31.1100i	−0.100549	−	0.208792i	0.844626	−	0.535357i	$-0.179823\pi$
$149$	−14.9818	−	31.1100i	−0.100549	−	0.208792i	−0.945175	+	0.326565i	$0.894109\pi$
$150$		0			0
$151$	−84.5495	−	19.2979i	−0.559931	−	0.127801i	−0.0668168	−	0.997765i	$-0.521284\pi$
$151$	−84.5495	−	19.2979i	−0.559931	−	0.127801i	−0.493114	+	0.869965i	$0.664141\pi$
$152$	−127.621	−	61.4591i	−0.839613	−	0.404336i
$153$		0			0
$154$	−89.1241	+	71.0741i	−0.578728	+	0.461520i
$155$	−0.513447	+	1.46735i	−0.00331256	+	0.00946676i
$156$		0			0
$157$	−31.5274	+	31.5274i	−0.200812	+	0.200812i	−0.800348	−	0.599536i	$-0.795352\pi$
$157$	−31.5274	+	31.5274i	−0.200812	+	0.200812i	0.599536	+	0.800348i	$0.295352\pi$
$158$	29.7860	+	23.7536i	0.188519	+	0.150339i
$159$		0			0
$160$	−35.0212	−	55.7360i	−0.218883	−	0.348350i
$161$	−44.9859	+	56.4105i	−0.279415	+	0.350376i
$162$		0			0
$163$	−10.5971	−	94.0522i	−0.0650131	−	0.577008i	−0.983416	−	0.181362i	$-0.941949\pi$
$163$	−10.5971	−	94.0522i	−0.0650131	−	0.577008i	0.918403	−	0.395646i	$-0.129479\pi$
$164$	−151.324	−	52.9507i	−0.922709	−	0.322870i
$165$		0			0
$166$	9.74953	−	86.5295i	0.0587321	−	0.521262i
$167$	−9.33539	+	19.3851i	−0.0559006	+	0.116079i	−0.927048	−	0.374943i	$-0.877662\pi$
$167$	−9.33539	+	19.3851i	−0.0559006	+	0.116079i	0.871147	+	0.491022i	$0.163376\pi$
$168$		0			0
$169$	6.66226	+	29.1893i	0.0394217	+	0.172718i
$170$	0.368291	−	0.177360i	0.00216642	−	0.00104329i
$171$		0			0
$172$	57.4848	+	36.1201i	0.334214	+	0.210000i
$173$			76.1743i			0.440314i	0.975464	+	0.220157i	$0.0706569\pi$
$173$			76.1743i			0.440314i	−0.975464	+	0.220157i	$0.929343\pi$
$174$		0			0
$175$	−221.371			−1.26498
$176$	−41.1707	+	65.5228i	−0.233924	+	0.372289i
$177$		0			0
$178$	66.7649	+	138.639i	0.375083	+	0.778869i
$179$	−107.104	+	24.4459i	−0.598349	+	0.136569i	−0.510959	−	0.859605i	$-0.670710\pi$
$179$	−107.104	+	24.4459i	−0.598349	+	0.136569i	−0.0873895	+	0.996174i	$0.527852\pi$
$180$		0			0
$181$	267.619	+	128.879i	1.47856	+	0.712036i	0.987284	−	0.158968i	$-0.0508167\pi$
$181$	267.619	+	128.879i	1.47856	+	0.712036i	0.491275	+	0.871005i	$0.336531\pi$
$182$	136.479	+	15.3775i	0.749884	+	0.0844917i
$183$		0			0
$184$	14.7420	−	42.1304i	0.0801198	−	0.228969i
$185$	−14.1726	+	1.59687i	−0.0766088	+	0.00863174i
$186$		0			0
$187$	−2.00321	−	1.59751i	−0.0107124	−	0.00854282i
$188$	−61.4846	+	38.6333i	−0.327046	+	0.205497i
$189$		0			0
$190$	−25.1189	+	31.4981i	−0.132205	+	0.165779i
$191$	131.587	+	131.587i	0.688937	+	0.688937i	0.961997	−	0.273060i	$-0.0880357\pi$
$191$	131.587	+	131.587i	0.688937	+	0.688937i	−0.273060	+	0.961997i	$0.588036\pi$
$192$		0			0
$193$	10.5516	+	3.69218i	0.0546717	+	0.0191304i	0.357476	−	0.933922i	$-0.383637\pi$
$193$	10.5516	+	3.69218i	0.0546717	+	0.0191304i	−0.302805	+	0.953053i	$0.597923\pi$
$194$	35.1445	+	44.0698i	0.181157	+	0.227164i
$195$		0			0
$196$	−87.2648	+	181.207i	−0.445229	+	0.924527i
$197$	43.6695	−	191.329i	0.221673	−	0.971211i	−0.734546	−	0.678559i	$-0.762605\pi$
$197$	43.6695	−	191.329i	0.221673	−	0.971211i	0.956219	−	0.292652i	$-0.0945379\pi$
$198$		0			0
$199$	−191.282	+	92.1164i	−0.961214	+	0.462896i	−0.847604	−	0.530629i	$-0.821956\pi$
$199$	−191.282	+	92.1164i	−0.961214	+	0.462896i	−0.113610	+	0.993525i	$0.536241\pi$
$200$	129.262	−	45.2306i	0.646308	−	0.226153i
$201$		0			0
$202$			129.727i			0.642214i
$203$	38.9983	+	305.353i	0.192110	+	1.50420i
$204$		0			0
$205$	−54.9828	+	87.5047i	−0.268209	+	0.426852i
$206$	29.7318	+	84.9687i	0.144329	+	0.412469i
$207$		0			0
$208$	90.8963	−	20.7465i	0.437001	−	0.0997427i
$209$	246.193	+	56.1919i	1.17796	+	0.268861i
$210$		0			0
$211$	347.213	+	39.1215i	1.64556	+	0.185410i	0.885564	−	0.464517i	$-0.153772\pi$
$211$	347.213	+	39.1215i	1.64556	+	0.185410i	0.759996	+	0.649927i	$0.225201\pi$
$212$	141.411	−	112.772i	0.667034	−	0.531942i
$213$		0			0
$214$	133.451	−	15.0364i	0.623605	−	0.0702634i
$215$	30.9453	−	30.9453i	0.143932	−	0.143932i
$216$		0			0
$217$	−6.86269	+	4.31212i	−0.0316253	+	0.0198715i
$218$	−9.61915	−	15.3088i	−0.0441246	−	0.0702238i
$219$		0			0
$220$	53.2335	+	53.2335i	0.241970	+	0.241970i
$221$	0.345634	+	3.06759i	0.00156396	+	0.0138805i
$222$		0			0
$223$	−223.712	−	280.525i	−1.00319	−	1.25796i	−0.965970	−	0.258654i	$-0.916721\pi$
$223$	−223.712	−	280.525i	−1.00319	−	1.25796i	−0.0372207	−	0.999307i	$-0.511850\pi$
$224$	38.4248	−	341.030i	0.171539	−	1.52245i
$225$		0			0
$226$	−7.83384	+	34.3223i	−0.0346630	+	0.151869i
$227$	−22.9453	−	100.530i	−0.101080	−	0.442862i	−0.999989	−	0.00472574i	$-0.998496\pi$
$227$	−22.9453	−	100.530i	−0.101080	−	0.442862i	0.898908	−	0.438137i	$-0.144361\pi$
$228$		0			0
$229$	−143.168	+	50.0967i	−0.625189	+	0.218763i	−0.624235	−	0.781237i	$-0.714589\pi$
$229$	−143.168	+	50.0967i	−0.625189	+	0.218763i	−0.000953694		1.00000i	$0.500304\pi$
$230$	−10.7492	−	6.75418i	−0.0467357	−	0.0293660i
$231$		0			0
$232$	−85.1615	−	170.332i	−0.367075	−	0.734189i
$233$	−317.385			−1.36217			−0.681083	−	0.732206i	$-0.738491\pi$
$233$	−317.385			−1.36217			−0.681083	+	0.732206i	$0.738491\pi$
$234$		0			0
$235$	15.4598	+	44.1816i	0.0657865	+	0.188007i
$236$	66.3538	+	137.785i	0.281160	+	0.583835i
$237$		0			0
$238$	2.07774	+	0.474232i	0.00873002	+	0.00199257i
$239$	−26.5371	−	12.7796i	−0.111034	−	0.0534711i	0.377542	−	0.925992i	$-0.376769\pi$
$239$	−26.5371	−	12.7796i	−0.111034	−	0.0534711i	−0.488576	+	0.872521i	$0.662484\pi$
$240$		0			0
$241$	114.945	−	91.6659i	0.476952	−	0.380356i	−0.355302	−	0.934752i	$-0.615622\pi$
$241$	114.945	−	91.6659i	0.476952	−	0.380356i	0.832253	+	0.554395i	$0.187050\pi$
$242$	−4.86246	+	13.8961i	−0.0200928	+	0.0574219i
$243$		0			0
$244$	165.233	−	165.233i	0.677186	−	0.677186i
$245$	101.363	+	80.8340i	0.413725	+	0.329935i
$246$		0			0
$247$	−161.869	−	257.613i	−0.655340	−	1.04297i
$248$	3.12617	−	3.92009i	0.0126055	−	0.0158068i
$249$		0			0
$250$	−9.58893	−	85.1041i	−0.0383557	−	0.340416i
$251$	−77.7163	−	27.1941i	−0.309627	−	0.108343i	0.170993	−	0.985272i	$-0.445302\pi$
$251$	−77.7163	−	27.1941i	−0.309627	−	0.108343i	−0.480620	+	0.876929i	$0.659588\pi$
$252$		0			0
$253$	−8.90937	+	79.0728i	−0.0352149	+	0.312541i
$254$	−21.6274	+	44.9097i	−0.0851471	+	0.176810i
$255$		0			0
$256$	28.6591	+	125.564i	0.111949	+	0.490483i
$257$	137.519	−	66.2259i	0.535095	−	0.257688i	−0.146764	−	0.989171i	$-0.546886\pi$
$257$	137.519	−	66.2259i	0.535095	−	0.257688i	0.681859	+	0.731483i	$0.261172\pi$
$258$		0			0
$259$	−62.9607	−	39.5608i	−0.243091	−	0.152745i
$260$		−	90.7033i		−	0.348859i
$261$		0			0
$262$	−63.9342			−0.244024
$263$	163.041	−	259.478i	0.619928	−	0.986609i	−0.378217	−	0.925717i	$-0.623463\pi$
$263$	163.041	−	259.478i	0.619928	−	0.986609i	0.998144	−	0.0608922i	$-0.0193946\pi$
$264$		0			0
$265$	−50.5875	−	105.046i	−0.190896	−	0.396400i
$266$	−204.777	+	46.7390i	−0.769839	+	0.175711i
$267$		0			0
$268$	122.804	+	59.1394i	0.458225	+	0.220669i
$269$	289.980	+	32.6729i	1.07799	+	0.121461i	0.633060	−	0.774103i	$-0.281799\pi$
$269$	289.980	+	32.6729i	1.07799	+	0.121461i	0.444934	+	0.895563i	$0.353227\pi$
$270$		0			0
$271$	−51.9021	+	148.328i	−0.191521	+	0.547335i	−0.999100	−	0.0424247i	$-0.986492\pi$
$271$	−51.9021	+	148.328i	−0.191521	+	0.547335i	0.807579	+	0.589759i	$0.200777\pi$
$272$	1.43764	−	0.161983i	0.00528542	−	0.000595524i
$273$		0			0
$274$	−69.7241	−	55.6031i	−0.254468	−	0.202931i
$275$	−206.720	+	129.891i	−0.751710	+	0.472331i
$276$		0			0
$277$	−83.4157	+	104.600i	−0.301140	+	0.377617i	−0.909261	−	0.416227i	$-0.863352\pi$
$277$	−83.4157	+	104.600i	−0.301140	+	0.377617i	0.608121	+	0.793844i	$0.291924\pi$
$278$	−127.386	−	127.386i	−0.458225	−	0.458225i
$279$		0			0
$280$	−133.957	−	46.8735i	−0.478417	−	0.167405i
$281$	−233.501	−	292.801i	−0.830965	−	1.04200i	−0.998424	−	0.0561179i	$-0.982128\pi$
$281$	−233.501	−	292.801i	−0.830965	−	1.04200i	0.167459	−	0.985879i	$-0.446444\pi$
$282$		0			0
$283$	61.5039	−	127.714i	0.217328	−	0.451287i	−0.763591	−	0.645700i	$-0.776566\pi$
$283$	61.5039	−	127.714i	0.217328	−	0.451287i	0.980920	+	0.194413i	$0.0622801\pi$
$284$	70.4592	−	308.702i	0.248096	−	1.08698i
$285$		0			0
$286$	136.469	−	65.7201i	0.477165	−	0.229791i
$287$	−508.564	+	177.954i	−1.77200	+	0.620049i
$288$		0			0
$289$		−	288.952i		−	0.999834i
$290$	−52.6207	+	12.8341i	−0.181451	+	0.0442555i
$291$		0			0
$292$	−17.6751	+	28.1298i	−0.0605312	+	0.0963348i
$293$	129.389	+	369.772i	0.441600	+	1.26202i	0.922756	+	0.385385i	$0.125931\pi$
$293$	129.389	+	369.772i	0.441600	+	1.26202i	−0.481156	+	0.876635i	$0.659783\pi$
$294$		0			0
$295$	96.1090	−	21.9362i	0.325793	−	0.0743601i
$296$	44.8467	+	10.2360i	0.151509	+	0.0345809i
$297$		0			0
$298$	31.4757	+	3.54647i	0.105623	+	0.0119009i
$299$	74.9554	−	59.7749i	0.250687	−	0.199916i
$300$		0			0
$301$	226.729	−	25.5463i	0.753254	−	0.0848713i
$302$	56.2535	−	56.2535i	0.186270	−	0.186270i
$303$		0			0
$304$	−120.731	+	75.8604i	−0.397142	+	0.249541i
$305$	−80.1400	−	127.542i	−0.262754	−	0.418171i
$306$		0			0
$307$	−364.784	−	364.784i	−1.18822	−	1.18822i	−0.977559	−	0.210663i	$-0.932438\pi$
$307$	−364.784	−	364.784i	−1.18822	−	1.18822i	−0.210663	−	0.977559i	$-0.567562\pi$
$308$	43.9459	+	390.030i	0.142681	+	1.26633i
$309$		0			0
$310$	−0.889140	−	1.11495i	−0.00286819	−	0.00359660i
$311$	−1.60736	+	14.2657i	−0.00516836	+	0.0458705i	−0.996032	−	0.0889994i	$-0.971633\pi$
$311$	−1.60736	+	14.2657i	−0.00516836	+	0.0458705i	0.990863	+	0.134870i	$0.0430616\pi$
$312$		0			0
$313$	3.75343	−	16.4449i	0.0119918	−	0.0525395i	−0.968578	−	0.248710i	$-0.919993\pi$
$313$	3.75343	−	16.4449i	0.0119918	−	0.0525395i	0.980570	+	0.196170i	$0.0628506\pi$
$314$	−9.10123	−	39.8751i	−0.0289848	−	0.126991i
$315$		0			0
$316$	123.815	−	43.3248i	0.391820	−	0.137104i
$317$	−45.2757	−	28.4486i	−0.142825	−	0.0897432i	0.458724	−	0.888579i	$-0.348307\pi$
$317$	−45.2757	−	28.4486i	−0.142825	−	0.0897432i	−0.601549	+	0.798836i	$0.705450\pi$
$318$		0			0
$319$	215.585	+	262.262i	0.675816	+	0.822137i
$320$	6.55015			0.0204692
$321$		0			0
$322$	−21.8602	−	62.4728i	−0.0678887	−	0.194015i
$323$	−2.04840	−	4.25354i	−0.00634178	−	0.0131688i
$324$		0			0
$325$	286.772	+	65.4538i	0.882375	+	0.201396i
$326$	78.2248	+	37.6711i	0.239953	+	0.115555i
$327$		0			0
$328$	260.597	−	207.820i	0.794505	−	0.633596i
$329$	−80.6013	+	230.345i	−0.244989	+	0.700138i
$330$		0			0
$331$	−397.745	+	397.745i	−1.20165	+	1.20165i	−0.227980	+	0.973666i	$0.573212\pi$
$331$	−397.745	+	397.745i	−1.20165	+	1.20165i	−0.973666	+	0.227980i	$0.926788\pi$
$332$	−234.408	−	186.934i	−0.706048	−	0.563054i
$333$		0			0
$334$	−10.5008	−	16.7119i	−0.0314396	−	0.0500358i
$335$	54.7812	−	68.6935i	0.163526	−	0.205055i
$336$		0			0
$337$	−42.6588	−	378.607i	−0.126584	−	1.12346i	−0.883000	−	0.469373i	$-0.844480\pi$
$337$	−42.6588	−	378.607i	−0.126584	−	1.12346i	0.756416	−	0.654091i	$-0.226949\pi$
$338$	−25.9236	−	9.07105i	−0.0766970	−	0.0268374i
$339$		0			0
$340$	0.157586	−	1.39861i	0.000463488	−	0.00411357i
$341$	−3.87834	+	8.05346i	−0.0113734	+	0.0236172i
$342$		0			0
$343$	34.6684	+	151.892i	0.101074	+	0.442834i
$344$	−127.171	+	61.2422i	−0.369682	+	0.178030i
$345$		0			0
$346$	−59.1666	−	37.1768i	−0.171002	−	0.107447i
$347$		−	274.022i		−	0.789689i	−0.918748	−	0.394845i	$-0.870798\pi$
$347$		−	274.022i		−	0.789689i	0.918748	−	0.394845i	$-0.129202\pi$
$348$		0			0
$349$	−156.235			−0.447666			−0.223833	−	0.974628i	$-0.571857\pi$
$349$	−156.235			−0.447666			−0.223833	+	0.974628i	$0.571857\pi$
$350$	108.040	−	171.945i	0.308686	−	0.491271i
$351$		0			0
$352$	−164.220	−	341.005i	−0.466533	−	0.968765i
$353$	−339.627	+	77.5177i	−0.962117	+	0.219597i	−0.674604	−	0.738180i	$-0.735686\pi$
$353$	−339.627	+	77.5177i	−0.962117	+	0.219597i	−0.287513	+	0.957777i	$0.592828\pi$
$354$		0			0
$355$	−183.897	−	88.5603i	−0.518021	−	0.249466i
$356$	526.491	+	59.3213i	1.47891	+	0.166633i
$357$		0			0
$358$	33.2845	−	95.1216i	0.0929734	−	0.265703i
$359$	291.435	−	32.8368i	0.811796	−	0.0914674i	0.303700	−	0.952768i	$-0.401778\pi$
$359$	291.435	−	32.8368i	0.811796	−	0.0914674i	0.508096	+	0.861300i	$0.330349\pi$
$360$		0			0
$361$	81.5423	+	65.0278i	0.225879	+	0.180132i
$362$	−230.715	+	144.968i	−0.637333	+	0.400463i
$363$		0			0
$364$	294.842	−	369.721i	0.810007	−	1.01572i
$365$	15.1429	+	15.1429i	0.0414873	+	0.0414873i
$366$		0			0
$367$	94.9299	+	33.2174i	0.258665	+	0.0905107i	0.456496	−	0.889725i	$-0.349104\pi$
$367$	94.9299	+	33.2174i	0.258665	+	0.0905107i	−0.197832	+	0.980236i	$0.563390\pi$
$368$	−28.0137	−	35.1281i	−0.0761242	−	0.0954567i
$369$		0			0
$370$	5.67661	−	11.7876i	0.0153422	−	0.0318584i
$371$	135.263	−	592.625i	0.364589	−	1.59737i
$372$		0			0
$373$	−579.925	+	279.277i	−1.55476	+	0.748732i	−0.996708	−	0.0810749i	$-0.974165\pi$
$373$	−579.925	+	279.277i	−1.55476	+	0.748732i	−0.558050	+	0.829807i	$0.688450\pi$
$374$	2.21849	−	0.776284i	0.00593180	−	0.00207563i
$375$		0			0
$376$		−	150.970i		−	0.401516i
$377$	39.7654	−	407.096i	0.105478	−	1.07983i
$378$		0			0
$379$	−311.876	+	496.348i	−0.822893	+	1.30963i	0.125361	+	0.992111i	$0.459991\pi$
$379$	−311.876	+	496.348i	−0.822893	+	1.30963i	−0.948253	+	0.317515i	$0.897152\pi$
$380$	45.8150	+	130.932i	0.120566	+	0.344557i
$381$		0			0
$382$	−166.428	+	37.9861i	−0.435675	+	0.0994401i
$383$	588.492	+	134.319i	1.53653	+	0.350704i	0.905260	−	0.424858i	$-0.139676\pi$
$383$	588.492	+	134.319i	1.53653	+	0.350704i	0.631272	+	0.775561i	$0.282533\pi$
$384$		0			0
$385$	251.418	+	28.3281i	0.653035	+	0.0735794i
$386$	−8.01753	+	6.39376i	−0.0207708	+	0.0165642i
$387$		0			0
$388$	192.861	−	21.7302i	0.497065	−	0.0560057i
$389$	−458.331	+	458.331i	−1.17823	+	1.17823i	−0.198033	+	0.980195i	$0.563455\pi$
$389$	−458.331	+	458.331i	−1.17823	+	1.17823i	−0.980195	+	0.198033i	$0.936545\pi$
$390$		0			0
$391$	1.25964	−	0.791484i	0.00322158	−	0.00202426i
$392$	−222.469	−	354.058i	−0.567524	−	0.903209i
$393$		0			0
$394$	127.297	+	127.297i	0.323089	+	0.323089i
$395$	−9.46748	−	84.0262i	−0.0239683	−	0.212725i
$396$		0			0
$397$	−105.509	−	132.305i	−0.265767	−	0.333261i	0.630985	−	0.775795i	$-0.282651\pi$
$397$	−105.509	−	132.305i	−0.265767	−	0.333261i	−0.896752	+	0.442534i	$0.854080\pi$
$398$	21.8057	−	193.531i	0.0547881	−	0.486258i
$399$		0			0
$400$	30.6751	−	134.397i	0.0766878	−	0.335991i
$401$	127.467	+	558.467i	0.317872	+	1.39269i	0.841278	+	0.540603i	$0.181804\pi$
$401$	127.467	+	558.467i	0.317872	+	1.39269i	−0.523406	+	0.852084i	$0.675339\pi$
$402$		0			0
$403$	10.1652	−	3.55694i	0.0252237	−	0.00882615i
$404$	378.206	+	237.643i	0.936154	+	0.588225i
$405$		0			0
$406$	−256.209	−	118.736i	−0.631057	−	0.292454i
$407$	−82.0063			−0.201490
$408$		0			0
$409$	198.692	+	567.828i	0.485799	+	1.38833i	0.882468	+	0.470372i	$0.155880\pi$
$409$	198.692	+	567.828i	0.485799	+	1.38833i	−0.396670	+	0.917961i	$0.629834\pi$
$410$	−41.1328	−	85.4132i	−0.100324	−	0.208325i
$411$		0			0
$412$	302.182	+	68.9711i	0.733451	+	0.167405i
$413$	463.062	+	222.999i	1.12121	+	0.539949i
$414$		0			0
$415$	−151.102	+	120.500i	−0.364102	+	0.290362i
$416$	−150.611	+	430.420i	−0.362045	+	1.03466i
$417$		0			0
$418$	−163.800	+	163.800i	−0.391866	+	0.391866i
$419$	447.663	+	356.999i	1.06841	+	0.852026i	0.989453	−	0.144852i	$-0.0462706\pi$
$419$	447.663	+	356.999i	1.06841	+	0.852026i	0.0789538	+	0.996878i	$0.474842\pi$
$420$		0			0
$421$	−11.6235	−	18.4986i	−0.0276092	−	0.0439398i	0.832635	−	0.553823i	$-0.186832\pi$
$421$	−11.6235	−	18.4986i	−0.0276092	−	0.0439398i	−0.860244	+	0.509883i	$0.829689\pi$
$422$	−199.844	+	250.596i	−0.473564	+	0.593830i
$423$		0			0
$424$	42.1034	+	373.678i	0.0993005	+	0.881317i
$425$	4.30821	+	1.50751i	0.0101370	+	0.00354708i
$426$		0			0
$427$	87.9284	−	780.387i	0.205921	−	1.82760i
$428$	200.628	−	416.608i	0.468757	−	0.973384i
$429$		0			0
$430$	8.93318	+	39.1388i	0.0207748	+	0.0910206i
$431$	−493.089	+	237.459i	−1.14406	+	0.550949i	−0.907243	−	0.420606i	$-0.861817\pi$
$431$	−493.089	+	237.459i	−1.14406	+	0.550949i	−0.236814	+	0.971555i	$0.576103\pi$
$432$		0			0
$433$	694.921	+	436.648i	1.60490	+	1.00842i	0.972238	+	0.233993i	$0.0751794\pi$
$433$	694.921	+	436.648i	1.60490	+	1.00842i	0.632659	+	0.774430i	$0.281963\pi$
$434$		−	7.43496i		−	0.0171312i
$435$		0			0
$436$	−62.2522			−0.142780
$437$	−78.0066	+	124.147i	−0.178505	+	0.284089i
$438$		0			0
$439$	36.2784	+	75.3329i	0.0826387	+	0.171601i	0.938193	−	0.346111i	$-0.112498\pi$
$439$	36.2784	+	75.3329i	0.0826387	+	0.171601i	−0.855555	+	0.517712i	$0.826784\pi$
$440$	−152.595	+	34.8287i	−0.346806	+	0.0791562i
$441$		0			0
$442$	−2.55136	−	1.22867i	−0.00577231	−	0.00277980i
$443$	−596.083	−	67.1625i	−1.34556	−	0.151608i	−0.590380	−	0.807125i	$-0.701022\pi$
$443$	−596.083	−	67.1625i	−1.34556	−	0.151608i	−0.755180	+	0.655517i	$0.772451\pi$
$444$		0			0
$445$	112.800	−	322.365i	0.253484	−	0.724415i
$446$	327.074	−	36.8523i	0.733349	−	0.0826286i
$447$		0			0
$448$	26.6994	+	21.2921i	0.0595970	+	0.0475270i
$449$	143.331	−	90.0608i	0.319223	−	0.200581i	−0.362883	−	0.931835i	$-0.618207\pi$
$449$	143.331	−	90.0608i	0.319223	−	0.200581i	0.682105	+	0.731254i	$0.261065\pi$
$450$		0			0
$451$	−370.490	+	464.579i	−0.821485	+	1.03011i
$452$	85.7126	+	85.7126i	0.189630	+	0.189630i
$453$		0			0
$454$	89.2825	+	31.2413i	0.196657	+	0.0688134i
$455$	−190.059	−	238.327i	−0.417712	−	0.523795i
$456$		0			0
$457$	−307.067	+	637.632i	−0.671919	+	1.39526i	0.234181	+	0.972193i	$0.424759\pi$
$457$	−307.067	+	637.632i	−0.671919	+	1.39526i	−0.906101	+	0.423062i	$0.860955\pi$
$458$	30.9617	−	135.652i	0.0676020	−	0.296184i
$459$		0			0
$460$	−39.3822	+	18.9655i	−0.0856135	+	0.0412293i
$461$	189.621	−	66.3513i	0.411326	−	0.143929i	−0.116681	−	0.993169i	$-0.537225\pi$
$461$	189.621	−	66.3513i	0.411326	−	0.143929i	0.528006	+	0.849240i	$0.322940\pi$
$462$		0			0
$463$			545.754i			1.17873i	0.807865	+	0.589367i	$0.200623\pi$
$463$			545.754i			1.17873i	−0.807865	+	0.589367i	$0.799377\pi$
$464$	−190.787	−	18.6362i	−0.411179	−	0.0401642i
$465$		0			0
$466$	154.899	−	246.521i	0.332402	−	0.529015i
$467$	8.31232	+	23.7552i	0.0177994	+	0.0508677i	0.952440	−	0.304725i	$-0.0985646\pi$
$467$	8.31232	+	23.7552i	0.0177994	+	0.0508677i	−0.934641	+	0.355593i	$0.884279\pi$
$468$		0			0
$469$	446.594	−	101.932i	0.952225	−	0.217339i
$470$	−41.8622	−	9.55477i	−0.0890685	−	0.0203293i
$471$		0			0
$472$	−315.951	−	35.5991i	−0.669388	−	0.0754219i
$473$	196.734	−	156.890i	0.415929	−	0.331692i
$474$		0			0
$475$	−447.022	+	50.3672i	−0.941098	+	0.106036i
$476$	5.18872	−	5.18872i	0.0109007	−	0.0109007i
$477$		0			0
$478$	22.8776	−	14.3750i	0.0478612	−	0.0300732i
$479$	−125.217	−	199.282i	−0.261414	−	0.416038i	0.690067	−	0.723746i	$-0.257581\pi$
$479$	−125.217	−	199.282i	−0.261414	−	0.416038i	−0.951481	+	0.307707i	$0.900438\pi$
$480$		0			0
$481$	69.8643	+	69.8643i	0.145248	+	0.145248i
$482$	15.1003	+	134.019i	0.0313283	+	0.278047i
$483$		0			0
$484$	31.6053	+	39.6318i	0.0653002	+	0.0818838i
$485$	14.0076	−	124.321i	0.0288816	−	0.256331i
$486$		0			0
$487$	205.721	−	901.323i	0.422425	−	1.85077i	−0.0956278	−	0.995417i	$-0.530486\pi$
$487$	205.721	−	901.323i	0.422425	−	1.85077i	0.518053	−	0.855348i	$-0.326657\pi$
$488$	108.106	+	473.644i	0.221529	+	0.970581i
$489$		0			0
$490$	−112.256	+	39.2800i	−0.229094	+	0.0801633i
$491$	−413.153	−	259.601i	−0.841452	−	0.528720i	0.0409794	−	0.999160i	$-0.486952\pi$
$491$	−413.153	−	259.601i	−0.841452	−	0.528720i	−0.882432	+	0.470440i	$0.844095\pi$
$492$		0			0
$493$	1.32045	−	6.20820i	0.00267840	−	0.0125927i
$494$	279.095			0.564969
$495$		0			0
$496$	−1.66697	−	4.76393i	−0.00336083	−	0.00960470i
$497$	−461.718	−	958.768i	−0.929010	−	1.92911i
$498$		0			0
$499$	464.245	+	105.961i	0.930351	+	0.212347i	0.660733	−	0.750621i	$-0.270245\pi$
$499$	464.245	+	105.961i	0.930351	+	0.212347i	0.269618	+	0.962967i	$0.413103\pi$
$500$	−265.678	−	127.944i	−0.531355	−	0.255887i
$501$		0			0
$502$	59.0518	−	47.0922i	0.117633	−	0.0938092i
$503$	16.5430	−	47.2773i	0.0328887	−	0.0939906i	−0.926268	−	0.376865i	$-0.877002\pi$
$503$	16.5430	−	47.2773i	0.0328887	−	0.0939906i	0.959157	+	0.282874i	$0.0912879\pi$
$504$		0			0
$505$	203.597	−	203.597i	0.403162	−	0.403162i
$506$	−57.0697	−	45.5116i	−0.112786	−	0.0899438i
$507$		0			0
$508$	91.3111	+	145.321i	0.179746	+	0.286065i
$509$	−484.514	+	607.562i	−0.951895	+	1.19364i	0.0290946	+	0.999577i	$0.490738\pi$
$509$	−484.514	+	607.562i	−0.951895	+	1.19364i	−0.980989	+	0.194062i	$0.937834\pi$
$510$		0			0
$511$	12.5009	+	110.948i	0.0244636	+	0.217120i
$512$	365.603	+	127.930i	0.714068	+	0.249863i
$513$		0			0
$514$	−15.6769	+	139.136i	−0.0304998	+	0.270693i
$515$	86.6899	−	180.013i	0.168330	−	0.349540i
$516$		0			0
$517$	59.8897	+	262.394i	0.115841	+	0.507531i
$518$	61.4558	−	29.5956i	0.118641	−	0.0571343i
$519$		0			0
$520$	159.673	+	100.329i	0.307063	+	0.192941i
$521$			368.806i			0.707881i	0.935268	+	0.353940i	$0.115158\pi$
$521$			368.806i			0.707881i	−0.935268	+	0.353940i	$0.884842\pi$
$522$		0			0
$523$	384.561			0.735299			0.367649	−	0.929964i	$-0.380163\pi$
$523$	384.561			0.735299			0.367649	+	0.929964i	$0.380163\pi$
$524$	−117.119	+	186.393i	−0.223509	+	0.355713i
$525$		0			0
$526$	121.971	+	253.276i	0.231885	+	0.481514i
$527$	0.162923	−	0.0371861i	0.000309152	−	7.05619e-5i
$528$		0			0
$529$	434.986	+	209.478i	0.822280	+	0.395989i
$530$	106.281	+	11.9750i	0.200530	+	0.0225943i
$531$		0			0
$532$	−238.861	+	682.626i	−0.448987	+	1.28313i
$533$	711.427	−	80.1586i	1.33476	−	0.150391i
$534$		0			0
$535$	−233.040	−	185.843i	−0.435589	−	0.347370i
$536$	−239.945	+	150.768i	−0.447659	+	0.281283i
$537$		0			0
$538$	−166.903	+	209.289i	−0.310228	+	0.389014i
$539$	527.117	+	527.117i	0.977954	+	0.977954i
$540$		0			0
$541$	−216.745	−	75.8424i	−0.400638	−	0.140189i	0.122436	−	0.992476i	$-0.460929\pi$
$541$	−216.745	−	75.8424i	−0.400638	−	0.140189i	−0.523074	+	0.852287i	$0.675215\pi$
$542$	−89.8792	−	112.705i	−0.165829	−	0.207943i
$543$		0			0
$544$	−3.07017	+	6.37527i	−0.00564369	+	0.0117193i
$545$	−8.92944	+	39.1224i	−0.0163843	+	0.0717843i
$546$		0			0
$547$	−20.9942	+	10.1103i	−0.0383807	+	0.0184832i	−0.452976	−	0.891523i	$-0.649638\pi$
$547$	−20.9942	+	10.1103i	−0.0383807	+	0.0184832i	0.414595	+	0.910006i	$0.363923\pi$
$548$	−289.830	+	101.416i	−0.528888	+	0.185066i
$549$		0			0
$550$		−	223.958i		−	0.407197i
$551$	148.226	+	607.736i	0.269012	+	1.10297i
$552$		0			0
$553$	234.547	−	373.279i	0.424136	−	0.675008i
$554$	−40.5346	−	115.841i	−0.0731671	−	0.209099i
$555$		0			0
$556$	−604.737	+	138.027i	−1.08766	+	0.248250i
$557$	1081.10	+	246.754i	1.94093	+	0.443005i	0.991733	+	0.128322i	$0.0409592\pi$
$557$	1081.10	+	246.754i	1.94093	+	0.443005i	0.949197	+	0.314682i	$0.101898\pi$
$558$		0			0
$559$	−301.266	−	33.9446i	−0.538938	−	0.0607238i
$560$	−111.693	+	89.0718i	−0.199451	+	0.159057i
$561$		0			0
$562$	341.386	−	38.4650i	0.607449	−	0.0684431i
$563$	−160.111	+	160.111i	−0.284390	+	0.284390i	−0.834857	−	0.550467i	$-0.814450\pi$
$563$	−160.111	+	160.111i	−0.284390	+	0.284390i	0.550467	+	0.834857i	$0.314450\pi$
$564$		0			0
$565$	66.1608	−	41.5716i	0.117099	−	0.0735780i
$566$	69.1820	+	110.103i	0.122230	+	0.194527i
$567$		0			0
$568$	465.499	+	465.499i	0.819540	+	0.819540i
$569$	56.4577	+	501.076i	0.0992226	+	0.880625i	0.940447	+	0.339939i	$0.110407\pi$
$569$	56.4577	+	501.076i	0.0992226	+	0.880625i	−0.841225	+	0.540686i	$0.818165\pi$
$570$		0			0
$571$	−35.8730	−	44.9834i	−0.0628249	−	0.0787800i	0.749426	−	0.662088i	$-0.230329\pi$
$571$	−35.8730	−	44.9834i	−0.0628249	−	0.0787800i	−0.812251	+	0.583308i	$0.801758\pi$
$572$	58.3930	−	518.252i	0.102086	−	0.906035i
$573$		0			0
$574$	109.983	−	481.865i	0.191607	−	0.839486i
$575$	−31.5430	−	138.199i	−0.0548573	−	0.240346i
$576$		0			0
$577$	−699.675	+	244.827i	−1.21261	+	0.424310i	−0.859434	−	0.511247i	$-0.829184\pi$
$577$	−699.675	+	244.827i	−1.21261	+	0.424310i	−0.353175	+	0.935557i	$0.614898\pi$
$578$	224.437	+	141.023i	0.388299	+	0.243984i
$579$		0			0
$580$	−58.9776	+	176.920i	−0.101685	+	0.305035i
$581$	−1007.62			−1.73428
$582$		0			0
$583$	−221.416	−	632.769i	−0.379787	−	1.08537i
$584$	−29.9684	−	62.2301i	−0.0513158	−	0.106558i
$585$		0			0
$586$	−350.359	−	79.9672i	−0.597883	−	0.136463i
$587$	381.756	+	183.844i	0.650351	+	0.313192i	0.729814	−	0.683645i	$-0.239607\pi$
$587$	381.756	+	183.844i	0.650351	+	0.313192i	−0.0794637	+	0.996838i	$0.525321\pi$
$588$		0			0
$589$	−12.8769	+	10.2690i	−0.0218624	+	0.0174347i
$590$	−29.8675	+	85.3563i	−0.0506228	+	0.144672i
$591$		0			0
$592$	32.7421	−	32.7421i	0.0553077	−	0.0553077i
$593$	−491.712	−	392.127i	−0.829194	−	0.661260i	0.114008	−	0.993480i	$-0.463631\pi$
$593$	−491.712	−	392.127i	−0.829194	−	0.661260i	−0.943202	+	0.332220i	$0.892202\pi$
$594$		0			0
$595$	−2.51659	−	4.00512i	−0.00422956	−	0.00673130i
$596$	67.9987	−	85.2676i	0.114092	−	0.143067i
$597$		0			0
$598$	9.84681	+	87.3929i	0.0164662	+	0.146142i
$599$	−1029.67	−	360.297i	−1.71898	−	0.601498i	−0.722983	−	0.690866i	$-0.757229\pi$
$599$	−1029.67	−	360.297i	−1.71898	−	0.601498i	−0.995999	+	0.0893686i	$0.971515\pi$
$600$		0			0
$601$	2.18327	−	19.3770i	0.00363272	−	0.0322413i	−0.991765	−	0.128070i	$-0.959122\pi$
$601$	2.18327	−	19.3770i	0.00363272	−	0.0322413i	0.995398	+	0.0958291i	$0.0305502\pi$
$602$	−90.8127	+	188.575i	−0.150852	+	0.313247i
$603$		0			0
$604$	−60.9524	−	267.050i	−0.100915	−	0.442136i
$605$	29.4401	−	14.1776i	0.0486613	−	0.0234340i
$606$		0			0
$607$	−678.738	−	426.479i	−1.11818	−	0.702602i	−0.159535	−	0.987192i	$-0.551000\pi$
$607$	−678.738	−	426.479i	−1.11818	−	0.702602i	−0.958649	+	0.284591i	$0.908142\pi$
$608$		−	697.394i		−	1.14703i
$609$		0			0
$610$	138.177			0.226520
$611$	172.521	−	274.566i	0.282358	−	0.449371i
$612$		0			0
$613$	−376.980	−	782.807i	−0.614975	−	1.27701i	−0.943142	−	0.332390i	$-0.892145\pi$
$613$	−376.980	−	782.807i	−0.614975	−	1.27701i	0.328167	−	0.944620i	$-0.393569\pi$
$614$	461.370	−	105.305i	0.751417	−	0.171506i
$615$		0			0
$616$	−735.215	−	354.061i	−1.19353	−	0.574774i
$617$	−80.6908	−	9.09167i	−0.130779	−	0.0147353i	0.0463322	−	0.998926i	$-0.485247\pi$
$617$	−80.6908	−	9.09167i	−0.130779	−	0.0147353i	−0.177111	+	0.984191i	$0.556675\pi$
$618$		0			0
$619$	−330.849	+	945.513i	−0.534490	+	1.52748i	0.287384	+	0.957815i	$0.407214\pi$
$619$	−330.849	+	945.513i	−0.534490	+	1.52748i	−0.821874	+	0.569669i	$0.807071\pi$
$620$	−4.87929	+	0.549765i	−0.00786983	+	0.000886717i
$621$		0			0
$622$	−10.2961	−	8.21085i	−0.0165532	−	0.0132007i
$623$	1507.68	−	947.337i	2.42003	−	1.52061i
$624$		0			0
$625$	206.552	−	259.007i	0.330482	−	0.414412i
$626$	10.9413	+	10.9413i	0.0174781	+	0.0174781i
$627$		0			0
$628$	−132.924	−	46.5121i	−0.211662	−	0.0740639i
$629$	0.955904	+	1.19867i	0.00151972	+	0.00190567i
$630$		0			0
$631$	335.980	−	697.669i	0.532456	−	1.10566i	−0.445197	−	0.895433i	$-0.646866\pi$
$631$	335.980	−	697.669i	0.532456	−	1.10566i	0.977653	−	0.210224i	$-0.0674193\pi$
$632$	−60.6866	+	265.885i	−0.0960231	+	0.420705i
$633$		0			0
$634$	44.1935	−	21.2825i	0.0697059	−	0.0335686i
$635$	104.425	−	36.5398i	0.164448	−	0.0575430i
$636$		0			0
$637$		−	898.143i		−	1.40996i
$638$	−308.922	+	39.4541i	−0.484203	+	0.0618403i
$639$		0			0
$640$	136.888	−	217.856i	0.213888	−	0.340400i
$641$	−26.7029	−	76.3125i	−0.0416582	−	0.119052i	0.921175	−	0.389148i	$-0.127230\pi$
$641$	−26.7029	−	76.3125i	−0.0416582	−	0.119052i	−0.962834	+	0.270095i	$0.912945\pi$
$642$		0			0
$643$	−682.001	+	155.662i	−1.06066	+	0.242088i	−0.717047	−	0.697025i	$-0.754507\pi$
$643$	−682.001	+	155.662i	−1.06066	+	0.242088i	−0.343609	+	0.939113i	$0.611649\pi$
$644$	−222.178	−	50.7106i	−0.344997	−	0.0787432i
$645$		0			0
$646$	4.30355	+	0.484894i	0.00666184	+	0.000750610i
$647$	−854.959	+	681.807i	−1.32142	+	1.05380i	−0.327368	+	0.944897i	$0.606162\pi$
$647$	−854.959	+	681.807i	−1.32142	+	1.05380i	−0.994053	+	0.108901i	$0.965267\pi$
$648$		0			0
$649$	563.261	−	63.4643i	0.867890	−	0.0977878i
$650$	−190.798	+	190.798i	−0.293536	+	0.293536i
$651$		0			0
$652$	253.123	−	159.048i	0.388226	−	0.243938i
$653$	−272.229	−	433.250i	−0.416889	−	0.663476i	0.570588	−	0.821236i	$-0.306715\pi$
$653$	−272.229	−	433.250i	−0.416889	−	0.663476i	−0.987477	+	0.157761i	$0.949572\pi$
$654$		0			0
$655$	100.340	+	100.340i	0.153190	+	0.153190i
$656$	−37.5666	−	333.413i	−0.0572661	−	0.508251i
$657$		0			0
$658$	−139.578	−	175.025i	−0.212124	−	0.265996i
$659$	105.681	−	937.943i	0.160365	−	1.42328i	−0.613381	−	0.789787i	$-0.710191\pi$
$659$	105.681	−	937.943i	0.160365	−	1.42328i	0.773746	−	0.633495i	$-0.218380\pi$
$660$		0			0
$661$	−116.346	+	509.745i	−0.176015	+	0.771173i	0.807429	+	0.589964i	$0.200858\pi$
$661$	−116.346	+	509.745i	−0.176015	+	0.771173i	−0.983445	+	0.181209i	$0.941999\pi$
$662$	−114.820	−	503.058i	−0.173444	−	0.759906i
$663$		0			0
$664$	588.361	−	205.876i	0.886086	−	0.310055i
$665$	394.735	+	248.028i	0.593586	+	0.372975i
$666$		0			0
$667$	−185.071	+	67.8556i	−0.277467	+	0.101733i
$668$	−67.9580			−0.101734
$669$		0			0
$670$	26.6201	+	76.0758i	0.0397314	+	0.113546i
$671$	−375.788	−	780.331i	−0.560041	−	1.16294i
$672$		0			0
$673$	734.243	+	167.586i	1.09100	+	0.249014i	0.729928	−	0.683524i	$-0.239554\pi$
$673$	734.243	+	167.586i	1.09100	+	0.249014i	0.361072	+	0.932538i	$0.382411\pi$
$674$	314.894	+	151.645i	0.467201	+	0.224992i
$675$		0			0
$676$	−73.9342	+	58.9606i	−0.109370	+	0.0872198i
$677$	−84.8727	+	242.552i	−0.125366	+	0.358275i	−0.989411	−	0.145139i	$-0.953637\pi$
$677$	−84.8727	+	242.552i	−0.125366	+	0.358275i	0.864045	+	0.503414i	$0.167923\pi$
$678$		0			0
$679$	461.217	−	461.217i	0.679260	−	0.679260i
$680$	2.28780	+	1.82446i	0.00336441	+	0.00268302i
$681$		0			0
$682$	−4.36251	−	6.94289i	−0.00639664	−	0.0101802i
$683$	−765.006	+	959.287i	−1.12007	+	1.40452i	−0.216390	+	0.976307i	$0.569428\pi$
$683$	−765.006	+	959.287i	−1.12007	+	1.40452i	−0.903678	+	0.428213i	$0.859143\pi$
$684$		0			0
$685$	22.1618	+	196.691i	0.0323530	+	0.287141i
$686$	−134.899	−	47.2030i	−0.196645	−	0.0688091i
$687$		0			0
$688$	−15.9082	+	141.189i	−0.0231224	+	0.205217i
$689$	−350.448	+	727.712i	−0.508633	+	1.05619i
$690$		0			0
$691$	−36.0165	−	157.799i	−0.0521223	−	0.228363i	0.942157	−	0.335171i	$-0.108794\pi$
$691$	−36.0165	−	157.799i	−0.0521223	−	0.228363i	−0.994280	+	0.106808i	$0.965937\pi$
$692$	−216.770	+	104.391i	−0.313252	+	0.150854i
$693$		0			0
$694$	212.840	+	133.736i	0.306686	+	0.192704i
$695$			399.846i			0.575318i
$696$		0			0
$697$	11.1092			0.0159387
$698$	76.2506	−	121.352i	0.109241	−	0.173857i
$699$		0			0
$700$	−303.372	−	629.959i	−0.433389	−	0.899942i
$701$	956.674	−	218.355i	1.36473	−	0.311490i	0.523433	−	0.852067i	$-0.324651\pi$
$701$	956.674	−	218.355i	1.36473	−	0.311490i	0.841295	+	0.540577i	$0.181794\pi$
$702$		0			0
$703$	−136.139	−	65.5613i	−0.193655	−	0.0932593i
$704$	37.4257	+	4.21686i	0.0531615	+	0.00598986i
$705$		0			0
$706$	105.545	−	301.630i	0.149497	−	0.427238i
$707$	1491.71	−	168.075i	2.10991	−	0.237730i
$708$		0			0
$709$	−46.3533	−	36.9655i	−0.0653784	−	0.0521375i	0.590255	−	0.807217i	$-0.299027\pi$
$709$	−46.3533	−	36.9655i	−0.0653784	−	0.0521375i	−0.655634	+	0.755079i	$0.727598\pi$
$710$	158.538	−	99.6161i	0.223293	−	0.140304i
$711$		0			0
$712$	−686.794	+	861.212i	−0.964598	+	1.20957i
$713$	−3.66985	−	3.66985i	−0.00514705	−	0.00514705i
$714$		0			0
$715$	−317.320	−	111.035i	−0.443804	−	0.155294i
$716$	−216.344	−	271.287i	−0.302157	−	0.378893i
$717$		0			0
$718$	−116.729	+	242.391i	−0.162576	+	0.337592i
$719$	13.6399	−	59.7604i	0.0189707	−	0.0831160i	−0.964556	−	0.263877i	$-0.914999\pi$
$719$	13.6399	−	59.7604i	0.0189707	−	0.0831160i	0.983527	+	0.180761i	$0.0578559\pi$
$720$		0			0
$721$	938.518	−	451.966i	1.30169	−	0.626860i
$722$	−90.3055	+	31.5992i	−0.125077	+	0.0437663i
$723$		0			0
$724$			938.186i			1.29584i
$725$	−516.801	−	314.137i	−0.712829	−	0.433292i
$726$		0			0
$727$	495.191	−	788.091i	0.681142	−	1.08403i	−0.309937	−	0.950757i	$-0.600308\pi$
$727$	495.191	−	788.091i	0.681142	−	1.08403i	0.991079	−	0.133275i	$-0.0425493\pi$
$728$	324.719	+	927.995i	0.446043	+	1.27472i
$729$		0			0
$730$	−19.1523	+	4.37139i	−0.0262361	+	0.00598821i
$731$	−4.58646	−	1.04683i	−0.00627422	−	0.00143205i
$732$		0			0
$733$	905.749	+	102.053i	1.23567	+	0.139227i	0.705530	−	0.708680i	$-0.250709\pi$
$733$	905.749	+	102.053i	1.23567	+	0.139227i	0.530144	+	0.847907i	$0.322138\pi$
$734$	−72.1313	+	57.5228i	−0.0982716	+	0.0783690i
$735$		0			0
$736$	218.375	−	24.6049i	0.296705	−	0.0334306i
$737$	357.227	−	357.227i	0.484705	−	0.484705i
$738$		0			0
$739$	725.917	−	456.124i	0.982297	−	0.617218i	0.0577679	−	0.998330i	$-0.481602\pi$
$739$	725.917	−	456.124i	0.982297	−	0.617218i	0.924529	+	0.381112i	$0.124459\pi$
$740$	−23.9667	−	38.1429i	−0.0323875	−	0.0515444i
$741$		0			0
$742$	394.292	+	394.292i	0.531391	+	0.531391i
$743$	28.5464	+	253.356i	0.0384204	+	0.340991i	0.998187	+	0.0601911i	$0.0191710\pi$
$743$	28.5464	+	253.356i	0.0384204	+	0.340991i	−0.959766	+	0.280799i	$0.909400\pi$
$744$		0			0
$745$	−43.8328	−	54.9646i	−0.0588360	−	0.0737780i
$746$	66.1101	−	586.744i	0.0886195	−	0.786520i
$747$		0			0
$748$	1.80080	−	7.88983i	0.00240749	−	0.0105479i
$749$	−345.801	−	1515.05i	−0.461683	−	2.02277i
$750$		0			0
$751$	322.155	−	112.727i	0.428968	−	0.150103i	−0.107155	−	0.994242i	$-0.534174\pi$
$751$	322.155	−	112.727i	0.428968	−	0.150103i	0.536123	+	0.844140i	$0.319888\pi$
$752$	−128.676	−	80.8525i	−0.171112	−	0.107517i
$753$		0			0
$754$	296.795	+	229.570i	0.393627	+	0.304469i
$755$	−176.571			−0.233869
$756$		0			0
$757$	−182.836	−	522.514i	−0.241527	−	0.690244i	−0.999289	−	0.0377125i	$-0.987993\pi$
$757$	−182.836	−	522.514i	−0.241527	−	0.690244i	0.757762	−	0.652531i	$-0.226293\pi$
$758$	−233.316	−	484.485i	−0.307804	−	0.639162i
$759$		0			0
$760$	−281.168	−	64.1748i	−0.369958	−	0.0844405i
$761$	449.183	+	216.315i	0.590253	+	0.284251i	0.705072	−	0.709135i	$-0.250915\pi$
$761$	449.183	+	216.315i	0.590253	+	0.284251i	−0.114819	+	0.993386i	$0.536629\pi$
$762$		0			0
$763$	−163.570	+	130.443i	−0.214378	+	0.170961i
$764$	−194.129	+	554.789i	−0.254096	+	0.726164i
$765$		0			0
$766$	−391.542	+	391.542i	−0.511152	+	0.511152i
$767$	−533.931	−	425.796i	−0.696129	−	0.555144i
$768$		0			0
$769$	−44.7471	−	71.2146i	−0.0581887	−	0.0926068i	0.816363	−	0.577539i	$-0.195987\pi$
$769$	−44.7471	−	71.2146i	−0.0581887	−	0.0926068i	−0.874552	+	0.484933i	$0.838844\pi$
$770$	−144.708	+	181.458i	−0.187932	+	0.235659i
$771$		0			0
$772$	3.95333	+	35.0868i	0.00512089	+	0.0454492i
$773$	657.345	+	230.015i	0.850381	+	0.297561i	0.720061	−	0.693911i	$-0.244114\pi$
$773$	657.345	+	230.015i	0.850381	+	0.297561i	0.130320	+	0.991472i	$0.458399\pi$
$774$		0			0
$775$	1.78286	−	15.8233i	0.00230047	−	0.0204172i
$776$	−175.075	+	363.547i	−0.225612	+	0.468488i
$777$		0			0
$778$	−132.309	−	579.686i	−0.170064	−	0.745097i
$779$	−986.469	+	475.059i	−1.26633	+	0.609831i
$780$		0			0
$781$	−993.723	−	624.398i	−1.27237	−	0.799485i
$782$			1.36468i			0.00174511i
$783$		0			0
$784$	−420.917			−0.536884
$785$	−48.2972	+	76.8645i	−0.0615251	+	0.0979166i
$786$		0			0
$787$	380.344	+	789.793i	0.483284	+	1.00355i	0.989951	+	0.141408i	$0.0451629\pi$
$787$	380.344	+	789.793i	0.483284	+	1.00355i	−0.506668	+	0.862141i	$0.669123\pi$
$788$	604.312	−	137.930i	0.766894	−	0.175038i
$789$		0			0
$790$	69.8860	+	33.6553i	0.0884632	+	0.0426016i
$791$	404.815	+	45.6117i	0.511777	+	0.0576634i
$792$		0			0
$793$	−344.646	+	984.941i	−0.434610	+	1.24204i
$794$	154.258	−	17.3807i	0.194280	−	0.0218901i
$795$		0			0
$796$	−524.274	−	418.094i	−0.658635	−	0.525244i
$797$	248.165	−	155.932i	0.311373	−	0.195649i	−0.367275	−	0.930113i	$-0.619709\pi$
$797$	248.165	−	155.932i	0.311373	−	0.195649i	0.678648	+	0.734464i	$0.262566\pi$
$798$		0			0
$799$	3.13724	−	3.93398i	0.00392646	−	0.00492363i
$800$	476.762	+	476.762i	0.595952	+	0.595952i
$801$		0			0
$802$	−495.986	−	173.553i	−0.618437	−	0.216400i
$803$	76.7732	+	96.2706i	0.0956080	+	0.119889i
$804$		0			0
$805$	−63.7383	+	132.354i	−0.0791780	+	0.164415i
$806$	−2.19833	+	9.63150i	−0.00272745	+	0.0119498i
$807$		0			0
$808$	−836.687	+	402.927i	−1.03550	+	0.498673i
$809$	651.558	−	227.990i	0.805387	−	0.281817i	0.103981	−	0.994579i	$-0.466842\pi$
$809$	651.558	−	227.990i	0.805387	−	0.281817i	0.701406	+	0.712762i	$0.252556\pi$
$810$		0			0
$811$		−	334.956i		−	0.413016i	−0.978445	−	0.206508i	$-0.933790\pi$
$811$		−	334.956i		−	0.413016i	0.978445	−	0.206508i	$-0.0662100\pi$
$812$	−815.504	+	529.442i	−1.00432	+	0.652022i
$813$		0			0
$814$	40.0231	−	63.6965i	0.0491685	−	0.0782512i
$815$	−63.6458	−	181.889i	−0.0780930	−	0.223177i
$816$		0			0
$817$	452.029	−	103.173i	0.553279	−	0.126282i
$818$	−538.018	−	122.799i	−0.657724	−	0.150121i
$819$		0			0
$820$	−324.363	−	36.5469i	−0.395565	−	0.0445694i
$821$	537.270	−	428.458i	0.654409	−	0.521874i	−0.239056	−	0.971006i	$-0.576838\pi$
$821$	537.270	−	428.458i	0.654409	−	0.521874i	0.893465	+	0.449132i	$0.148267\pi$
$822$		0			0
$823$	202.923	−	22.8639i	0.246565	−	0.0277812i	0.0121831	−	0.999926i	$-0.496122\pi$
$823$	202.923	−	22.8639i	0.246565	−	0.0277812i	0.234382	+	0.972145i	$0.424693\pi$
$824$	−455.667	+	455.667i	−0.552994	+	0.552994i
$825$		0			0
$826$	−399.206	+	250.838i	−0.483300	+	0.303678i
$827$	245.883	+	391.321i	0.297319	+	0.473181i	0.961658	−	0.274250i	$-0.0884297\pi$
$827$	245.883	+	391.321i	0.297319	+	0.473181i	−0.664339	+	0.747431i	$0.731287\pi$
$828$		0			0
$829$	−21.6446	−	21.6446i	−0.0261092	−	0.0261092i	0.693932	−	0.720041i	$-0.255877\pi$
$829$	−21.6446	−	21.6446i	−0.0261092	−	0.0261092i	−0.720041	+	0.693932i	$0.755877\pi$
$830$	−19.8502	−	176.175i	−0.0239159	−	0.212259i
$831$		0			0
$832$	−28.2918	−	35.4769i	−0.0340046	−	0.0426404i
$833$	1.56042	−	13.8491i	0.00187325	−	0.0166255i
$834$		0			0
$835$	−9.74789	+	42.7083i	−0.0116741	+	0.0511476i
$836$	177.482	+	777.601i	0.212300	+	0.930145i
$837$		0			0
$838$	−495.772	+	173.478i	−0.591613	+	0.207014i
$839$	36.4943	+	22.9309i	0.0434974	+	0.0273312i	0.553605	−	0.832779i	$-0.313252\pi$
$839$	36.4943	+	22.9309i	0.0434974	+	0.0273312i	−0.510108	+	0.860110i	$0.670395\pi$
$840$		0			0
$841$	−342.268	+	768.201i	−0.406978	+	0.913438i
$842$	20.0412			0.0238019
$843$		0			0
$844$	364.501	+	1041.68i	0.431873	+	1.23422i
$845$	26.4487	+	54.9213i	0.0313002	+	0.0649956i
$846$		0			0
$847$	166.088	+	37.9086i	0.196090	+	0.0447563i
$848$	341.045	+	164.239i	0.402175	+	0.193677i
$849$		0			0
$850$	−3.27354	+	2.61056i	−0.00385122	+	0.00307125i
$851$	15.7260	−	44.9424i	0.0184795	−	0.0528113i
$852$		0			0
$853$	461.282	−	461.282i	0.540776	−	0.540776i	−0.382981	−	0.923756i	$-0.625102\pi$
$853$	461.282	−	461.282i	0.540776	−	0.540776i	0.923756	+	0.382981i	$0.125102\pi$
$854$	563.233	+	449.163i	0.659524	+	0.525953i
$855$		0			0
$856$	511.473	+	814.005i	0.597515	+	0.950940i
$857$	−840.141	+	1053.50i	−0.980328	+	1.22929i	−0.00697618	+	0.999976i	$0.502221\pi$
$857$	−840.141	+	1053.50i	−0.980328	+	1.22929i	−0.973352	+	0.229317i	$0.926351\pi$
$858$		0			0
$859$	186.858	+	1658.41i	0.217530	+	1.93063i	0.344626	+	0.938740i	$0.388006\pi$
$859$	186.858	+	1658.41i	0.217530	+	1.93063i	−0.127096	+	0.991890i	$0.540566\pi$
$860$	130.470	+	45.6533i	0.151709	+	0.0530852i
$861$		0			0
$862$	56.2110	−	498.886i	0.0652100	−	0.578755i
$863$	74.4614	−	154.621i	0.0862821	−	0.179167i	−0.853363	−	0.521317i	$-0.825441\pi$
$863$	74.4614	−	154.621i	0.0862821	−	0.179167i	0.939645	+	0.342150i	$0.111155\pi$
$864$		0			0
$865$	34.5112	+	151.203i	0.0398973	+	0.174802i
$866$	−678.311	+	326.657i	−0.783269	+	0.377202i
$867$		0			0
$868$	−21.6759	−	13.6198i	−0.0249722	−	0.0156911i
$869$		−	486.197i		−	0.559490i
$870$		0			0
$871$	−608.671			−0.698819
$872$	68.8587	−	109.588i	0.0789665	−	0.125674i
$873$		0			0
$874$	−58.3570	−	121.180i	−0.0667700	−	0.138649i
$875$	−966.172	+	220.522i	−1.10420	+	0.252026i
$876$		0			0
$877$	−482.080	−	232.158i	−0.549693	−	0.264718i	0.138356	−	0.990383i	$-0.455818\pi$
$877$	−482.080	−	232.158i	−0.549693	−	0.264718i	−0.688049	+	0.725665i	$0.741532\pi$
$878$	−76.2186	−	8.58778i	−0.0868094	−	0.00978107i
$879$		0			0
$880$	−52.0370	+	148.713i	−0.0591329	+	0.168992i
$881$	559.545	−	63.0456i	0.635125	−	0.0715614i	0.211469	−	0.977385i	$-0.432175\pi$
$881$	559.545	−	63.0456i	0.635125	−	0.0715614i	0.423656	+	0.905823i	$0.360747\pi$
$882$		0			0
$883$	1277.65	+	1018.89i	1.44694	+	1.15389i	0.959840	+	0.280547i	$0.0905160\pi$
$883$	1277.65	+	1018.89i	1.44694	+	1.15389i	0.487098	+	0.873347i	$0.338055\pi$
$884$	−8.25582	+	5.18747i	−0.00933916	+	0.00586818i
$885$		0			0
$886$	343.085	−	430.215i	0.387229	−	0.485570i
$887$	−131.492	−	131.492i	−0.148244	−	0.148244i	0.629089	−	0.777333i	$-0.283428\pi$
$887$	−131.492	−	131.492i	−0.148244	−	0.148244i	−0.777333	+	0.629089i	$0.783428\pi$
$888$		0			0
$889$	544.429	+	190.504i	0.612406	+	0.214290i
$890$	195.337	+	244.945i	0.219480	+	0.275219i
$891$		0			0
$892$	491.715	−	1021.06i	0.551251	−	1.14468i
$893$	−110.352	+	483.482i	−0.123574	+	0.541413i
$894$		0			0
$895$	−201.523	+	97.0484i	−0.225166	+	0.108434i
$896$	1266.15	−	443.044i	1.41311	−	0.494469i
$897$		0			0
$898$			155.283i			0.172921i
$899$	−22.1404	+	0.328322i	−0.0246278	+	0.000365208i
$900$		0			0
$901$	−6.66811	+	10.6122i	−0.00740078	+	0.0117783i
$902$	−180.034	−	514.507i	−0.199594	−	0.570407i
$903$		0			0
$904$	−245.696	+	56.0786i	−0.271788	+	0.0620339i
$905$	589.604	+	134.573i	0.651496	+	0.148700i
$906$		0			0
$907$	−231.412	−	26.0738i	−0.255140	−	0.0287473i	−0.0165319	−	0.999863i	$-0.505262\pi$
$907$	−231.412	−	26.0738i	−0.255140	−	0.0287473i	−0.238608	+	0.971116i	$0.576691\pi$
$908$	254.634	−	203.064i	0.280434	−	0.223639i
$909$		0			0
$910$	277.873	−	31.3087i	0.305355	−	0.0344052i
$911$	231.694	−	231.694i	0.254330	−	0.254330i	−0.568413	−	0.822743i	$-0.692443\pi$
$911$	231.694	−	231.694i	0.254330	−	0.254330i	0.822743	+	0.568413i	$0.192443\pi$
$912$		0			0
$913$	−940.930	+	591.226i	−1.03059	+	0.647564i
$914$	−345.401	−	549.703i	−0.377901	−	0.601425i
$915$		0			0
$916$	−338.762	−	338.762i	−0.369828	−	0.369828i
$917$	82.8334	+	735.167i	0.0903309	+	0.801709i
$918$		0			0
$919$	−117.240	−	147.015i	−0.127574	−	0.159973i	0.713942	−	0.700205i	$-0.246908\pi$
$919$	−117.240	−	147.015i	−0.127574	−	0.159973i	−0.841516	+	0.540232i	$0.818336\pi$
$920$	10.1751	−	90.3062i	0.0110599	−	0.0981590i
$921$		0			0
$922$	−41.0077	+	179.666i	−0.0444769	+	0.194866i
$923$	314.642	+	1378.54i	0.340891	+	1.49354i
$924$		0			0
$925$	137.889	−	48.2496i	0.149070	−	0.0521617i
$926$	−423.902	−	266.355i	−0.457777	−	0.287640i
$927$		0			0
$928$	573.642	−	741.622i	0.618149	−	0.799162i
$929$	76.1717			0.0819932			0.0409966	−	0.999159i	$-0.486947\pi$
$929$	76.1717			0.0819932			0.0409966	+	0.999159i	$0.486947\pi$
$930$		0			0
$931$	453.660	+	1296.49i	0.487282	+	1.39257i
$932$	−434.952	−	903.187i	−0.466686	−	0.969084i
$933$		0			0
$934$	−22.5081	−	5.13733i	−0.0240986	−	0.00550036i
$935$	−4.70006	−	2.26343i	−0.00502681	−	0.00242078i
$936$		0			0
$937$	−919.598	+	733.355i	−0.981428	+	0.782662i	−0.976100	−	0.217323i	$-0.930267\pi$
$937$	−919.598	+	733.355i	−0.981428	+	0.782662i	−0.00532804	+	0.999986i	$0.501696\pi$
$938$	−138.786	+	396.629i	−0.147960	+	0.422845i
$939$		0			0
$940$	−104.542	+	104.542i	−0.111215	+	0.111215i
$941$	−895.245	−	713.934i	−0.951377	−	0.758697i	0.0191189	−	0.999817i	$-0.493914\pi$
$941$	−895.245	−	713.934i	−0.951377	−	0.758697i	−0.970495	+	0.241120i	$0.922485\pi$
$942$		0			0
$943$	−183.559	−	292.132i	−0.194654	−	0.309790i
$944$	−199.551	+	250.228i	−0.211388	+	0.265073i
$945$		0			0
$946$	25.8448	+	229.379i	0.0273201	+	0.242473i
$947$	−420.871	−	147.269i	−0.444426	−	0.155511i	0.0987829	−	0.995109i	$-0.468505\pi$
$947$	−420.871	−	147.269i	−0.444426	−	0.155511i	−0.543209	+	0.839598i	$0.682791\pi$
$948$		0			0
$949$	16.6105	−	147.423i	0.0175032	−	0.155345i
$950$	179.047	−	371.795i	0.188471	−	0.391363i
$951$		0			0
$952$	3.39479	+	14.8735i	0.00356595	+	0.0156235i
$953$	−456.945	+	220.053i	−0.479481	+	0.230906i	−0.657982	−	0.753034i	$-0.728590\pi$
$953$	−456.945	+	220.053i	−0.479481	+	0.230906i	0.178501	+	0.983940i	$0.442875\pi$
$954$		0			0
$955$	320.812	+	201.579i	0.335929	+	0.211078i
$956$		−	93.0304i		−	0.0973122i
$957$		0			0
$958$	215.900			0.225365
$959$	−549.035	+	873.784i	−0.572508	+	0.911141i
$960$		0			0
$961$	416.709	+	865.306i	0.433621	+	0.900422i
$962$	−88.3627	+	20.1682i	−0.0918531	+	0.0209649i
$963$		0			0
$964$	418.379	+	201.481i	0.434003	+	0.209005i
$965$	22.6174	+	2.54837i	0.0234377	+	0.00264080i
$966$		0			0
$967$	323.141	−	923.483i	0.334168	−	0.954998i	−0.647109	−	0.762397i	$-0.724022\pi$
$967$	323.141	−	923.483i	0.334168	−	0.954998i	0.981277	−	0.192600i	$-0.0616920\pi$
$968$	−104.727	+	11.7999i	−0.108189	+	0.0121899i
$969$		0			0
$970$	89.7267	+	71.5547i	0.0925018	+	0.0737677i
$971$	−445.089	+	279.668i	−0.458382	+	0.288021i	−0.741362	−	0.671105i	$-0.765820\pi$
$971$	−445.089	+	279.668i	−0.458382	+	0.288021i	0.282980	+	0.959126i	$0.408677\pi$
$972$		0			0
$973$	−1299.75	+	1629.84i	−1.33582	+	1.67506i
$974$	599.679	+	599.679i	0.615687	+	0.615687i
$975$		0			0
$976$	461.596	+	161.519i	0.472947	+	0.165491i
$977$	394.310	+	494.449i	0.403593	+	0.506089i	0.941546	−	0.336886i	$-0.109374\pi$
$977$	394.310	+	494.449i	0.403593	+	0.506089i	−0.537953	+	0.842975i	$0.680802\pi$
$978$		0			0
$979$	852.040	−	1769.28i	0.870317	−	1.80723i
$980$	−91.1207	+	399.226i	−0.0929803	+	0.407373i
$981$		0			0
$982$	403.278	−	194.209i	0.410670	−	0.197768i
$983$	1062.58	−	371.814i	1.08096	−	0.378245i	0.269709	−	0.962942i	$-0.413072\pi$
$983$	1062.58	−	371.814i	1.08096	−	0.378245i	0.811252	+	0.584697i	$0.198787\pi$
$984$		0			0
$985$		−	399.565i		−	0.405650i
$986$	4.17763	+	4.05554i	0.00423694	+	0.00411312i
$987$		0			0
$988$	511.264	−	813.672i	0.517474	−	0.823555i
$989$	48.2546	+	137.904i	0.0487913	+	0.139438i
$990$		0			0
$991$	590.647	−	134.811i	0.596011	−	0.136036i	0.0861349	−	0.996283i	$-0.472548\pi$
$991$	590.647	−	134.811i	0.596011	−	0.136036i	0.509876	+	0.860248i	$0.329691\pi$
$992$	24.0669	+	5.49312i	0.0242610	+	0.00553742i
$993$		0			0
$994$	970.041	+	109.297i	0.975896	+	0.109957i
$995$	−337.954	+	269.509i	−0.339652	+	0.270863i
$996$		0			0
$997$	−1562.89	+	176.095i	−1.56759	+	0.176625i	−0.852620	−	0.522532i	$-0.824988\pi$
$997$	−1562.89	+	176.095i	−1.56759	+	0.176625i	−0.714969	+	0.699157i	$0.753559\pi$
$998$	−308.877	+	308.877i	−0.309496	+	0.309496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.55.2		48
3.2	odd	2		29.3.f.a.26.3	yes	48
29.19	odd	28	inner	261.3.s.a.19.2		48
87.77	even	28		29.3.f.a.19.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.19.3	✓	48	87.77	even	28
29.3.f.a.26.3	yes	48	3.2	odd	2
261.3.s.a.19.2		48	29.19	odd	28	inner
261.3.s.a.55.2		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.488049 + 0.776726i) q^{2} +(1.37042 + 2.84571i) q^{4} +(1.98497 - 0.453055i) q^{5} +(9.56374 + 4.60566i) q^{7} +(-6.52543 - 0.735239i) q^{8} +O(q^{10})\)	\(q+(-0.488049 + 0.776726i) q^{2} +(1.37042 + 2.84571i) q^{4} +(1.98497 - 0.453055i) q^{5} +(9.56374 + 4.60566i) q^{7} +(-6.52543 - 0.735239i) q^{8} +(-0.616861 + 1.76289i) q^{10} +(11.6332 - 1.31075i) q^{11} +(-11.0274 - 8.79408i) q^{13} +(-8.24491 + 5.18062i) q^{14} +(-4.12137 + 5.16804i) q^{16} +(-0.154761 - 0.154761i) q^{17} +(20.3603 + 7.12436i) q^{19} +(4.00951 + 5.02777i) q^{20} +(-4.65948 + 9.67551i) q^{22} +(-1.51251 + 6.62676i) q^{23} +(-18.7894 + 9.04850i) q^{25} +(12.2125 - 4.27334i) q^{26} +33.5274i q^{28} +(15.7913 + 24.3235i) q^{29} +(-0.406230 + 0.646512i) q^{31} +(-10.6781 - 30.5163i) q^{32} +(0.195737 - 0.0446758i) q^{34} +(21.0703 + 4.80916i) q^{35} +(-6.96097 - 0.784313i) q^{37} +(-15.4705 + 12.3373i) q^{38} +(-13.2858 + 1.49696i) q^{40} +(-35.8917 + 35.8917i) q^{41} +(18.2000 - 11.4358i) q^{43} +(19.6724 + 31.3084i) q^{44} +(-4.40899 - 4.40899i) q^{46} +(2.57409 + 22.8457i) q^{47} +(39.7021 + 49.7849i) q^{49} +(2.14195 - 19.0103i) q^{50} +(9.91319 - 43.4325i) q^{52} +(-12.7427 - 55.8292i) q^{53} +(22.4976 - 7.87226i) q^{55} +(-59.0212 - 37.0855i) q^{56} +(-26.5997 + 0.394450i) q^{58} +48.4185 q^{59} +(-24.4350 - 69.8312i) q^{61} +(-0.303902 - 0.631059i) q^{62} +(3.13649 + 0.715883i) q^{64} +(-25.8733 - 12.4599i) q^{65} +(33.7392 - 26.9061i) q^{67} +(0.228317 - 0.652492i) q^{68} +(-14.0188 + 14.0188i) q^{70} +(-78.3788 - 62.5050i) q^{71} +(5.59603 + 8.90604i) q^{73} +(4.00650 - 5.02399i) q^{74} +(7.62828 + 67.7029i) q^{76} +(117.294 + 41.0428i) q^{77} +(4.65001 - 41.2700i) q^{79} +(-5.83937 + 12.1256i) q^{80} +(-10.3611 - 45.3949i) q^{82} +(-85.5238 + 41.1861i) q^{83} +(-0.377310 - 0.237079i) q^{85} +19.7176i q^{86} -76.8752 q^{88} +(89.2455 - 142.033i) q^{89} +(-64.9610 - 134.893i) q^{91} +(-20.9306 + 4.77728i) q^{92} +(-19.0011 - 9.15045i) q^{94} +(43.6421 + 4.91729i) q^{95} +(20.2947 - 57.9990i) q^{97} +(-58.0458 + 6.54019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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