LMFDB - Embedded newform 171.3.p.d.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$1.56632 + 2.71294i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.d.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.90671 - 1.67819i) q^{2} +(3.63264 - 6.29191i) q^{4} +(-3.47303 - 6.01546i) q^{5} -1.22892 q^{7} -10.9595i q^{8} +O(q^{10})$	\(q+(2.90671 - 1.67819i) q^{2} +(3.63264 - 6.29191i) q^{4} +(-3.47303 - 6.01546i) q^{5} -1.22892 q^{7} -10.9595i q^{8} +(-20.1902 - 11.6568i) q^{10} +0.0363521 q^{11} +(14.6268 + 8.44481i) q^{13} +(-3.57212 + 2.06236i) q^{14} +(-3.86156 - 6.68842i) q^{16} +(4.59329 + 7.95581i) q^{17} +(12.7864 - 14.0537i) q^{19} -50.4650 q^{20} +(0.105665 - 0.0610058i) q^{22} +(4.87974 - 8.45195i) q^{23} +(-11.6238 + 20.1331i) q^{25} +56.6879 q^{26} +(-4.46423 + 7.73228i) q^{28} +(-4.50339 - 2.60003i) q^{29} +44.3727i q^{31} +(15.5160 + 8.95814i) q^{32} +(26.7027 + 15.4168i) q^{34} +(4.26808 + 7.39254i) q^{35} -45.5661i q^{37} +(13.5817 - 62.3081i) q^{38} +(-65.9264 + 38.0626i) q^{40} +(-50.0829 + 28.9153i) q^{41} +(15.1574 + 26.2534i) q^{43} +(0.132054 - 0.228724i) q^{44} -32.7565i q^{46} +(-25.5066 + 44.1787i) q^{47} -47.4897 q^{49} +78.0280i q^{50} +(106.268 - 61.3538i) q^{52} +(-10.0847 - 5.82239i) q^{53} +(-0.126252 - 0.218675i) q^{55} +13.4684i q^{56} -17.4534 q^{58} +(17.7409 - 10.2427i) q^{59} +(-8.23849 + 14.2695i) q^{61} +(74.4658 + 128.978i) q^{62} +91.0263 q^{64} -117.316i q^{65} +(-1.83276 - 1.05814i) q^{67} +66.7430 q^{68} +(24.8121 + 14.3253i) q^{70} +(33.7958 - 19.5120i) q^{71} +(-28.1064 - 48.6818i) q^{73} +(-76.4686 - 132.447i) q^{74} +(-41.9762 - 131.503i) q^{76} -0.0446740 q^{77} +(39.8385 - 23.0008i) q^{79} +(-26.8226 + 46.4581i) q^{80} +(-97.0508 + 168.097i) q^{82} -65.3332 q^{83} +(31.9053 - 55.2615i) q^{85} +(88.1162 + 50.8739i) q^{86} -0.398401i q^{88} +(134.435 + 77.6163i) q^{89} +(-17.9753 - 10.3780i) q^{91} +(-35.4526 - 61.4058i) q^{92} +171.219i q^{94} +(-128.947 - 28.1074i) q^{95} +(-98.8107 + 57.0484i) q^{97} +(-138.039 + 79.6968i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.90671	−	1.67819i	1.45335	−	0.839095i	0.454684	−	0.890653i	$-0.349752\pi$
$2$	2.90671	−	1.67819i	1.45335	−	0.839095i	0.998670	+	0.0515581i	$0.0164187\pi$
$3$		0			0
$3$		0			0
$4$	3.63264	−	6.29191i	0.908159	−	1.57298i
$5$	−3.47303	−	6.01546i	−0.694606	−	1.20309i	−0.970313	−	0.241851i	$-0.922246\pi$
$5$	−3.47303	−	6.01546i	−0.694606	−	1.20309i	0.275708	−	0.961241i	$-0.411088\pi$
$6$		0			0
$7$	−1.22892			−0.175560			−0.0877802	−	0.996140i	$-0.527977\pi$
$7$	−1.22892			−0.175560			−0.0877802	+	0.996140i	$0.527977\pi$
$8$		−	10.9595i		−	1.36994i
$9$		0			0
$10$	−20.1902	−	11.6568i	−2.01902	−	1.16568i
$11$	0.0363521			0.00330474			0.00165237	−	0.999999i	$-0.499474\pi$
$11$	0.0363521			0.00330474			0.00165237	+	0.999999i	$0.499474\pi$
$12$		0			0
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.942708	−	0.333618i	$-0.108269\pi$
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.182433	+	0.983218i	$0.441603\pi$
$14$	−3.57212	+	2.06236i	−0.255151	+	0.147312i
$15$		0			0
$16$	−3.86156	−	6.68842i	−0.241348	−	0.418026i
$17$	4.59329	+	7.95581i	0.270194	+	0.467989i	0.968911	−	0.247408i	$-0.0795790\pi$
$17$	4.59329	+	7.95581i	0.270194	+	0.467989i	−0.698718	+	0.715398i	$0.746246\pi$
$18$		0			0
$19$	12.7864	−	14.0537i	0.672971	−	0.739669i
$19$	12.7864	−	14.0537i	0.672971	−	0.739669i
$20$	−50.4650			−2.52325
$21$		0			0
$22$	0.105665	−	0.0610058i	0.00480296	−	0.00277299i
$23$	4.87974	−	8.45195i	0.212162	−	0.367476i	−0.740229	−	0.672355i	$-0.765283\pi$
$23$	4.87974	−	8.45195i	0.212162	−	0.367476i	0.952391	+	0.304879i	$0.0986161\pi$
$24$		0			0
$25$	−11.6238	+	20.1331i	−0.464954	+	0.805323i
$26$	56.6879			2.18031
$27$		0			0
$28$	−4.46423	+	7.73228i	−0.159437	+	0.276153i
$29$	−4.50339	−	2.60003i	−0.155289	−	0.0896564i	0.420342	−	0.907366i	$-0.361910\pi$
$29$	−4.50339	−	2.60003i	−0.155289	−	0.0896564i	−0.575631	+	0.817710i	$0.695244\pi$
$30$		0			0
$31$			44.3727i			1.43138i	0.698420	+	0.715689i	$0.253887\pi$
$31$			44.3727i			1.43138i	−0.698420	+	0.715689i	$0.746113\pi$
$32$	15.5160	+	8.95814i	0.484873	+	0.279942i
$33$		0			0
$34$	26.7027	+	15.4168i	0.785374	+	0.453436i
$35$	4.26808	+	7.39254i	0.121945	+	0.211215i
$36$		0			0
$37$		−	45.5661i		−	1.23152i	−0.787935	−	0.615758i	$-0.788850\pi$
$37$		−	45.5661i		−	1.23152i	0.787935	−	0.615758i	$-0.211150\pi$
$38$	13.5817	−	62.3081i	0.357413	−	1.63969i
$39$		0			0
$40$	−65.9264	+	38.0626i	−1.64816	+	0.951566i
$41$	−50.0829	+	28.9153i	−1.22153	+	0.705252i	−0.965245	−	0.261348i	$-0.915833\pi$
$41$	−50.0829	+	28.9153i	−1.22153	+	0.705252i	−0.256288	+	0.966600i	$0.582500\pi$
$42$		0			0
$43$	15.1574	+	26.2534i	0.352497	+	0.610543i	0.986686	−	0.162635i	$-0.0519992\pi$
$43$	15.1574	+	26.2534i	0.352497	+	0.610543i	−0.634189	+	0.773178i	$0.718666\pi$
$44$	0.132054	−	0.228724i	0.00300123	−	0.00519828i
$45$		0			0
$46$		−	32.7565i		−	0.712097i
$47$	−25.5066	+	44.1787i	−0.542693	+	0.939972i	0.456055	+	0.889951i	$0.349262\pi$
$47$	−25.5066	+	44.1787i	−0.542693	+	0.939972i	−0.998748	+	0.0500204i	$0.984071\pi$
$48$		0			0
$49$	−47.4897			−0.969179
$50$			78.0280i			1.56056i
$51$		0			0
$52$	106.268	−	61.3538i	2.04362	−	1.17988i
$53$	−10.0847	−	5.82239i	−0.190277	−	0.109856i	0.401835	−	0.915712i	$-0.368372\pi$
$53$	−10.0847	−	5.82239i	−0.190277	−	0.109856i	−0.592112	+	0.805856i	$0.701706\pi$
$54$		0			0
$55$	−0.126252	−	0.218675i	−0.00229549	−	0.00397591i
$56$			13.4684i			0.240507i
$57$		0			0
$58$	−17.4534			−0.300921
$59$	17.7409	−	10.2427i	0.300694	−	0.173606i	−0.342061	−	0.939678i	$-0.611125\pi$
$59$	17.7409	−	10.2427i	0.300694	−	0.173606i	0.642754	+	0.766072i	$0.277792\pi$
$60$		0			0
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	−0.925619	−	0.378456i	$-0.876455\pi$
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	0.790562	+	0.612382i	$0.209788\pi$
$62$	74.4658	+	128.978i	1.20106	+	2.08030i
$63$		0			0
$64$	91.0263			1.42229
$65$		−	117.316i		−	1.80486i
$66$		0			0
$67$	−1.83276	−	1.05814i	−0.0273546	−	0.0157932i	0.486260	−	0.873814i	$-0.338361\pi$
$67$	−1.83276	−	1.05814i	−0.0273546	−	0.0157932i	−0.513615	+	0.858021i	$0.671694\pi$
$68$	66.7430			0.981515
$69$		0			0
$70$	24.8121	+	14.3253i	0.354459	+	0.204647i
$71$	33.7958	−	19.5120i	0.475998	−	0.274817i	−0.242749	−	0.970089i	$-0.578049\pi$
$71$	33.7958	−	19.5120i	0.475998	−	0.274817i	0.718747	+	0.695272i	$0.244716\pi$
$72$		0			0
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	0.606752	−	0.794891i	$-0.292472\pi$
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	−0.991772	+	0.128017i	$0.959139\pi$
$74$	−76.4686	−	132.447i	−1.03336	−	1.78983i
$75$		0			0
$76$	−41.9762	−	131.503i	−0.552319	−	1.73031i
$77$	−0.0446740			−0.000580181
$78$		0			0
$79$	39.8385	−	23.0008i	0.504285	−	0.291149i	−0.226196	−	0.974082i	$-0.572629\pi$
$79$	39.8385	−	23.0008i	0.504285	−	0.291149i	0.730481	+	0.682933i	$0.239296\pi$
$80$	−26.8226	+	46.4581i	−0.335283	+	0.580727i
$81$		0			0
$82$	−97.0508	+	168.097i	−1.18355	+	2.04996i
$83$	−65.3332			−0.787146			−0.393573	−	0.919293i	$-0.628761\pi$
$83$	−65.3332			−0.787146			−0.393573	+	0.919293i	$0.628761\pi$
$84$		0			0
$85$	31.9053	−	55.2615i	0.375356	−	0.650136i
$86$	88.1162	+	50.8739i	1.02461	+	0.591557i
$87$		0			0
$88$		−	0.398401i		−	0.00452729i
$89$	134.435	+	77.6163i	1.51051	+	0.872093i	0.999925	+	0.0122654i	$0.00390430\pi$
$89$	134.435	+	77.6163i	1.51051	+	0.872093i	0.510585	+	0.859828i	$0.329429\pi$
$90$		0			0
$91$	−17.9753	−	10.3780i	−0.197530	−	0.114044i
$92$	−35.4526	−	61.4058i	−0.385355	−	0.667454i
$93$		0			0
$94$			171.219i			1.82148i
$95$	−128.947	−	28.1074i	−1.35734	−	0.295868i
$96$		0			0
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.913718	−	0.406350i	$-0.866801\pi$
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.104949	+	0.994478i	$0.533468\pi$
$98$	−138.039	+	79.6968i	−1.40856	+	0.813232i
$99$		0			0
$100$	84.4504	+	146.272i	0.844504	+	1.46272i
$101$	−85.7095	+	148.453i	−0.848609	+	1.46983i	0.0338413	+	0.999427i	$0.489226\pi$
$101$	−85.7095	+	148.453i	−0.848609	+	1.46983i	−0.882450	+	0.470406i	$0.844107\pi$
$102$		0			0
$103$		−	121.297i		−	1.17764i	−0.808264	−	0.588820i	$-0.799593\pi$
$103$		−	121.297i		−	1.17764i	0.808264	−	0.588820i	$-0.200407\pi$
$104$	92.5508	−	160.303i	0.889912	−	1.54137i
$105$		0			0
$106$	−39.0843			−0.368720
$107$		−	56.0566i		−	0.523893i	−0.965082	−	0.261947i	$-0.915636\pi$
$107$		−	56.0566i		−	0.523893i	0.965082	−	0.261947i	$-0.0843644\pi$
$108$		0			0
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	−0.696109	−	0.717936i	$-0.745087\pi$
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	0.273696	+	0.961816i	$0.411754\pi$
$110$	−0.733955	−	0.423749i	−0.00667232	−	0.00385227i
$111$		0			0
$112$	4.74556	+	8.21955i	0.0423711	+	0.0733888i
$113$		−	136.946i		−	1.21191i	−0.795497	−	0.605957i	$-0.792790\pi$
$113$		−	136.946i		−	1.21191i	0.795497	−	0.605957i	$-0.207210\pi$
$114$		0			0
$115$	−67.7898			−0.589477
$116$	−32.7184	+	18.8900i	−0.282055	+	0.162845i
$117$		0			0
$118$	34.3785	−	59.5453i	0.291343	−	0.504621i
$119$	−5.64480	−	9.77708i	−0.0474353	−	0.0821603i
$120$		0			0
$121$	−120.999			−0.999989
$122$			55.3030i			0.453303i
$123$		0			0
$124$	279.189	+	161.190i	2.25153	+	1.29992i
$125$	−12.1717			−0.0973736
$126$		0			0
$127$	136.758	+	78.9573i	1.07684	+	0.621711i	0.930041	−	0.367456i	$-0.119771\pi$
$127$	136.758	+	78.9573i	1.07684	+	0.621711i	0.146794	+	0.989167i	$0.453104\pi$
$128$	202.523	−	116.927i	1.58221	−	0.913490i
$129$		0			0
$130$	−196.879	−	341.004i	−1.51445	−	2.62311i
$131$	−38.5396	−	66.7525i	−0.294195	−	0.509561i	0.680602	−	0.732653i	$-0.261718\pi$
$131$	−38.5396	−	66.7525i	−0.294195	−	0.509561i	−0.974797	+	0.223092i	$0.928385\pi$
$132$		0			0
$133$	−15.7136	+	17.2709i	−0.118147	+	0.129857i
$134$	−7.10307			−0.0530080
$135$		0			0
$136$	87.1917	−	50.3402i	0.641116	−	0.370148i
$137$	−45.3969	+	78.6298i	−0.331364	+	0.573940i	−0.982780	−	0.184781i	$-0.940842\pi$
$137$	−45.3969	+	78.6298i	−0.331364	+	0.573940i	0.651415	+	0.758721i	$0.274176\pi$
$138$		0			0
$139$	45.7773	−	79.2886i	0.329333	−	0.570421i	−0.653047	−	0.757318i	$-0.726509\pi$
$139$	45.7773	−	79.2886i	0.329333	−	0.570421i	0.982380	+	0.186896i	$0.0598428\pi$
$140$	62.0176			0.442983
$141$		0			0
$142$	65.4897	−	113.432i	0.461195	−	0.798814i
$143$	0.531717	+	0.306987i	0.00371830	+	0.00214676i
$144$		0			0
$145$			36.1200i			0.249103i
$146$	−163.394	−	94.3358i	−1.11914	−	0.646136i
$147$		0			0
$148$	−286.698	−	165.525i	−1.93715	−	1.11841i
$149$	12.0587	+	20.8863i	0.0809308	+	0.140176i	0.903650	−	0.428272i	$-0.140877\pi$
$149$	12.0587	+	20.8863i	0.0809308	+	0.140176i	−0.822719	+	0.568448i	$0.807544\pi$
$150$		0			0
$151$		−	251.451i		−	1.66524i	−0.553848	−	0.832618i	$-0.686841\pi$
$151$		−	251.451i		−	1.66524i	0.553848	−	0.832618i	$-0.313159\pi$
$152$	−154.022	−	140.133i	−1.01330	−	0.921928i
$153$		0			0
$154$	−0.129854	+	0.0749714i	−0.000843209	+	0.000486827i
$155$	266.922	−	154.108i	1.72208	−	0.994242i
$156$		0			0
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	0.971474	−	0.237144i	$-0.0762113\pi$
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	−0.691110	+	0.722750i	$0.742878\pi$
$158$	77.1994	−	133.713i	0.488604	−	0.846286i
$159$		0			0
$160$		−	124.447i		−	0.777797i
$161$	−5.99682	+	10.3868i	−0.0372473	+	0.0645143i
$162$		0			0
$163$	−28.3608			−0.173992			−0.0869962	−	0.996209i	$-0.527727\pi$
$163$	−28.3608			−0.173992			−0.0869962	+	0.996209i	$0.527727\pi$
$164$			420.156i			2.56193i
$165$		0			0
$166$	−189.904	+	109.641i	−1.14400	+	0.660490i
$167$	52.1162	+	30.0893i	0.312073	+	0.180176i	0.647854	−	0.761765i	$-0.275667\pi$
$167$	52.1162	+	30.0893i	0.312073	+	0.180176i	−0.335781	+	0.941940i	$0.609000\pi$
$168$		0			0
$169$	58.1295	+	100.683i	0.343962	+	0.595759i
$170$		−	214.172i		−	1.25984i
$171$		0			0
$172$	220.245			1.28050
$173$	−152.888	+	88.2699i	−0.883745	+	0.510230i	−0.871891	−	0.489699i	$-0.837107\pi$
$173$	−152.888	+	88.2699i	−0.883745	+	0.510230i	−0.0118536	+	0.999930i	$0.503773\pi$
$174$		0			0
$175$	14.2848	−	24.7420i	0.0816275	−	0.141383i
$176$	−0.140376	−	0.243138i	−0.000797591	−	0.00138147i
$177$		0			0
$178$	521.019			2.92707
$179$		−	0.226943i		−	0.00126784i	−1.00000		0.000633920i	$-0.999798\pi$
$179$		−	0.226943i		−	0.00126784i	1.00000		0.000633920i	$-0.000201783\pi$
$180$		0			0
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	0.812899	−	0.582405i	$-0.197888\pi$
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	−0.0979279	+	0.995194i	$0.531221\pi$
$182$	−69.6651			−0.382775
$183$		0			0
$184$	−92.6291	−	53.4795i	−0.503419	−	0.290649i
$185$	−274.101	+	158.252i	−1.48163	+	0.855418i
$186$		0			0
$187$	0.166976	+	0.289211i	0.000892919	+	0.00154658i
$188$	185.312	+	320.970i	0.985703	+	1.70729i
$189$		0			0
$190$	−421.982	+	134.698i	−2.22096	+	0.708935i
$191$	251.306			1.31574			0.657870	−	0.753132i	$-0.271458\pi$
$191$	251.306			1.31574			0.657870	+	0.753132i	$0.271458\pi$
$192$		0			0
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	−0.756703	−	0.653758i	$-0.773191\pi$
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	0.187820	+	0.982204i	$0.439858\pi$
$194$	−191.476	+	331.646i	−0.986989	+	1.70952i
$195$		0			0
$196$	−172.513	+	298.801i	−0.880169	+	1.52450i
$197$	285.803			1.45077			0.725387	−	0.688341i	$-0.241661\pi$
$197$	285.803			1.45077			0.725387	+	0.688341i	$0.241661\pi$
$198$		0			0
$199$	−77.0371	+	133.432i	−0.387121	+	0.670514i	−0.992061	−	0.125757i	$-0.959864\pi$
$199$	−77.0371	+	133.432i	−0.387121	+	0.670514i	0.604940	+	0.796271i	$0.293197\pi$
$200$	220.648	+	127.391i	1.10324	+	0.636957i
$201$		0			0
$202$			575.347i			2.84825i
$203$	5.53432	+	3.19524i	0.0272627	+	0.0157401i
$204$		0			0
$205$	347.878	+	200.848i	1.69697	+	0.979744i
$206$	−203.559	−	352.575i	−0.988151	−	1.71153i
$207$		0			0
$208$		−	130.441i		−	0.627118i
$209$	0.464815	−	0.510882i	0.00222399	−	0.00244441i
$210$		0			0
$211$	−138.091	+	79.7266i	−0.654458	+	0.377851i	−0.790162	−	0.612898i	$-0.790004\pi$
$211$	−138.091	+	79.7266i	−0.654458	+	0.377851i	0.135704	+	0.990749i	$0.456670\pi$
$212$	−73.2680	+	42.3013i	−0.345604	+	0.199534i
$213$		0			0
$214$	−94.0735	−	162.940i	−0.439596	−	0.761402i
$215$	105.284	−	182.357i	0.489693	−	0.848173i
$216$		0			0
$217$		−	54.5306i		−	0.251293i
$218$	−89.2226	+	154.538i	−0.409278	+	0.708890i
$219$		0			0
$220$	−1.83451			−0.00833868
$221$			155.158i			0.702072i
$222$		0			0
$223$	−161.907	+	93.4771i	−0.726041	+	0.419180i	−0.816972	−	0.576677i	$-0.804349\pi$
$223$	−161.907	+	93.4771i	−0.726041	+	0.419180i	0.0909314	+	0.995857i	$0.471016\pi$
$224$	−19.0679	−	11.0089i	−0.0851246	−	0.0491467i
$225$		0			0
$226$	−229.822	−	398.063i	−1.01691	−	1.76134i
$227$			8.87518i			0.0390977i	0.999809	+	0.0195489i	$0.00622299\pi$
$227$			8.87518i			0.0390977i	−0.999809	+	0.0195489i	$0.993777\pi$
$228$		0			0
$229$	265.920			1.16122			0.580611	−	0.814181i	$-0.302814\pi$
$229$	265.920			1.16122			0.580611	+	0.814181i	$0.302814\pi$
$230$	−197.045	+	113.764i	−0.856719	+	0.494627i
$231$		0			0
$232$	−28.4951	+	49.3549i	−0.122824	+	0.212737i
$233$	−4.52199	−	7.83232i	−0.0194077	−	0.0336151i	0.856158	−	0.516713i	$-0.172845\pi$
$233$	−4.52199	−	7.83232i	−0.0194077	−	0.0336151i	−0.875566	+	0.483098i	$0.839511\pi$
$234$		0			0
$235$	354.340			1.50783
$236$		−	148.832i		−	0.630646i
$237$		0			0
$238$	−32.8156	−	18.9461i	−0.137881	−	0.0796054i
$239$	48.3793			0.202424			0.101212	−	0.994865i	$-0.467728\pi$
$239$	48.3793			0.202424			0.101212	+	0.994865i	$0.467728\pi$
$240$		0			0
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	0.228883	−	0.973454i	$-0.426493\pi$
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	−0.728594	+	0.684945i	$0.759826\pi$
$242$	−351.708	+	203.059i	−1.45334	+	0.839085i
$243$		0			0
$244$	59.8549	+	103.672i	0.245307	+	0.424884i
$245$	164.933	+	285.673i	0.673197	+	1.16601i
$246$		0			0
$247$	305.706	−	97.5823i	1.23768	−	0.395070i
$248$	486.302			1.96090
$249$		0			0
$250$	−35.3796	+	20.4264i	−0.141518	+	0.0817056i
$251$	109.025	−	188.837i	0.434363	−	0.752340i	−0.562880	−	0.826539i	$-0.690307\pi$
$251$	109.025	−	188.837i	0.434363	−	0.752340i	0.997243	+	0.0741991i	$0.0236400\pi$
$252$		0			0
$253$	0.177389	−	0.307246i	0.000701142	−	0.00121441i
$254$	530.021			2.08670
$255$		0			0
$256$	210.398	−	364.420i	0.821867	−	1.42352i
$257$	−192.080	−	110.898i	−0.747394	−	0.431508i	0.0773578	−	0.997003i	$-0.475352\pi$
$257$	−192.080	−	110.898i	−0.747394	−	0.431508i	−0.824751	+	0.565495i	$0.808685\pi$
$258$		0			0
$259$			55.9973i			0.216206i
$260$	−738.143	−	426.167i	−2.83901	−	1.63910i
$261$		0			0
$262$	−224.047	−	129.353i	−0.855139	−	0.493715i
$263$	160.691	+	278.326i	0.610994	+	1.05827i	0.991073	+	0.133319i	$0.0425634\pi$
$263$	160.691	+	278.326i	0.610994	+	1.05827i	−0.380079	+	0.924954i	$0.624103\pi$
$264$		0			0
$265$			80.8853i			0.305228i
$266$	−16.6908	+	76.5719i	−0.0627475	+	0.287864i
$267$		0			0
$268$	−13.3155	+	7.68771i	−0.0496847	+	0.0286855i
$269$	137.447	−	79.3552i	0.510956	−	0.295001i	−0.222270	−	0.974985i	$-0.571347\pi$
$269$	137.447	−	79.3552i	0.510956	−	0.295001i	0.733227	+	0.679984i	$0.238013\pi$
$270$		0			0
$271$	−244.649	−	423.745i	−0.902765	−	1.56364i	−0.823889	−	0.566751i	$-0.808200\pi$
$271$	−244.649	−	423.745i	−0.902765	−	1.56364i	−0.0788765	−	0.996884i	$-0.525133\pi$
$272$	35.4745	−	61.4437i	0.130421	−	0.225896i
$273$		0			0
$274$			304.739i			1.11218i
$275$	−0.422551	+	0.731881i	−0.00153655	+	0.00266138i
$276$		0			0
$277$	−183.051			−0.660835			−0.330417	−	0.943835i	$-0.607189\pi$
$277$	−183.051			−0.660835			−0.330417	+	0.943835i	$0.607189\pi$
$278$		−	307.292i		−	1.10537i
$279$		0			0
$280$	81.0185	−	46.7760i	0.289352	−	0.167057i
$281$	−230.908	−	133.315i	−0.821736	−	0.474430i	0.0292787	−	0.999571i	$-0.490679\pi$
$281$	−230.908	−	133.315i	−0.821736	−	0.474430i	−0.851015	+	0.525142i	$0.824012\pi$
$282$		0			0
$283$	178.014	+	308.329i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498789\pi$
$283$	178.014	+	308.329i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$284$		−	283.521i		−	0.998312i
$285$		0			0
$286$	2.06073			0.00720534
$287$	61.5480	−	35.5347i	0.214453	−	0.123814i
$288$		0			0
$289$	102.303	−	177.195i	0.353991	−	0.613130i
$290$	60.6161	+	104.990i	0.209021	+	0.362035i
$291$		0			0
$292$	−408.402			−1.39864
$293$			357.755i			1.22101i	0.792014	+	0.610503i	$0.209033\pi$
$293$			357.755i			1.22101i	−0.792014	+	0.610503i	$0.790967\pi$
$294$		0			0
$295$	−123.229	−	71.1465i	−0.417727	−	0.241175i
$296$	−499.382			−1.68710
$297$		0			0
$298$	70.1022	+	40.4735i	0.235242	+	0.135817i
$299$	142.750	−	82.4169i	0.477425	−	0.275642i
$300$		0			0
$301$	−18.6273	−	32.2634i	−0.0618846	−	0.107187i
$302$	−421.982	−	730.894i	−1.39729	−	2.42018i
$303$		0			0
$304$	−143.373	−	31.2518i	−0.471621	−	0.102802i
$305$	114.450			0.375246
$306$		0			0
$307$	125.866	−	72.6688i	0.409987	−	0.236706i	−0.280797	−	0.959767i	$-0.590599\pi$
$307$	125.866	−	72.6688i	0.409987	−	0.236706i	0.690784	+	0.723061i	$0.257265\pi$
$308$	−0.162284	+	0.281085i	−0.000526897	+	0.000912613i
$309$		0			0
$310$	517.243	−	895.892i	1.66853	−	2.88997i
$311$	191.291			0.615084			0.307542	−	0.951534i	$-0.400494\pi$
$311$	191.291			0.615084			0.307542	+	0.951534i	$0.400494\pi$
$312$		0			0
$313$	156.376	−	270.851i	0.499603	−	0.865337i	−0.500397	−	0.865796i	$-0.666813\pi$
$313$	156.376	−	270.851i	0.499603	−	0.865337i	1.00000		0.000458751i	$0.000146025\pi$
$314$	255.890	+	147.738i	0.814938	+	0.470505i
$315$		0			0
$316$		−	334.214i		−	1.05764i
$317$	−78.3676	−	45.2456i	−0.247217	−	0.142731i	0.371273	−	0.928524i	$-0.378922\pi$
$317$	−78.3676	−	45.2456i	−0.247217	−	0.142731i	−0.618489	+	0.785793i	$0.712255\pi$
$318$		0			0
$319$	−0.163708	−	0.0945168i	−0.000513191	−	0.000296291i
$320$	−316.137	−	547.565i	−0.987928	−	1.71114i
$321$		0			0
$322$			40.2552i			0.125016i
$323$	170.541	+	37.1738i	0.527989	+	0.115089i
$324$		0			0
$325$	−340.040	+	196.322i	−1.04628	+	0.604068i
$326$	−82.4365	+	47.5947i	−0.252873	+	0.145996i
$327$		0			0
$328$	316.898	+	548.883i	0.966152	+	1.67342i
$329$	31.3456	−	54.2922i	0.0952754	−	0.165022i
$330$		0			0
$331$			251.295i			0.759199i	0.925151	+	0.379599i	$0.123938\pi$
$331$			251.295i			0.759199i	−0.925151	+	0.379599i	$0.876062\pi$
$332$	−237.332	+	411.071i	−0.714854	+	1.23816i
$333$		0			0
$334$	201.982			0.604737
$335$			14.6999i			0.0438802i
$336$		0			0
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	−0.796031	−	0.605256i	$-0.793071\pi$
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	0.126152	+	0.992011i	$0.459737\pi$
$338$	337.931	+	195.105i	0.999797	+	0.577233i
$339$		0			0
$340$	−231.800	−	401.490i	−0.681766	−	1.18085i
$341$			1.61304i			0.00473033i
$342$		0			0
$343$	118.578			0.345710
$344$	287.724	−	166.117i	0.836406	−	0.482899i
$345$		0			0
$346$	−296.267	+	513.150i	−0.856263	+	1.48309i
$347$	−169.713	−	293.952i	−0.489088	−	0.847125i	0.510833	−	0.859680i	$-0.329337\pi$
$347$	−169.713	−	293.952i	−0.489088	−	0.847125i	−0.999921	+	0.0125549i	$0.996004\pi$
$348$		0			0
$349$	−76.4095			−0.218938			−0.109469	−	0.993990i	$-0.534915\pi$
$349$	−76.4095			−0.218938			−0.109469	+	0.993990i	$0.534915\pi$
$350$		−	95.8904i		−	0.273973i
$351$		0			0
$352$	0.564038	+	0.325647i	0.00160238	+	0.000925135i
$353$	−635.437			−1.80010			−0.900052	−	0.435783i	$-0.856472\pi$
$353$	−635.437			−1.80010			−0.900052	+	0.435783i	$0.856472\pi$
$354$		0			0
$355$	−234.748	−	135.532i	−0.661261	−	0.381779i
$356$	976.710	−	563.904i	2.74357	−	1.58400i
$357$		0			0
$358$	−0.380854	−	0.659658i	−0.00106384	−	0.00184262i
$359$	2.43138	+	4.21127i	0.00677264	+	0.0117306i	0.869392	−	0.494123i	$-0.164511\pi$
$359$	2.43138	+	4.21127i	0.00677264	+	0.0117306i	−0.862619	+	0.505854i	$0.831178\pi$
$360$		0			0
$361$	−34.0136	−	359.394i	−0.0942206	−	0.995551i
$362$	501.542			1.38548
$363$		0			0
$364$	−130.595	+	75.3991i	−0.358778	+	0.207141i
$365$	−195.229	+	338.146i	−0.534874	+	0.926428i
$366$		0			0
$367$	−149.568	+	259.060i	−0.407542	+	0.705884i	−0.994614	−	0.103651i	$-0.966948\pi$
$367$	−149.568	+	259.060i	−0.407542	+	0.705884i	0.587071	+	0.809535i	$0.300281\pi$
$368$	−75.3736			−0.204820
$369$		0			0
$370$	−531.155	+	919.987i	−1.43555	+	2.48645i
$371$	12.3933	+	7.15527i	0.0334051	+	0.0192864i
$372$		0			0
$373$			286.394i			0.767813i	0.923372	+	0.383907i	$0.125422\pi$
$373$			286.394i			0.767813i	−0.923372	+	0.383907i	$0.874578\pi$
$374$	0.970701	+	0.560434i	0.00259546	+	0.00149849i
$375$		0			0
$376$	484.176	+	279.539i	1.28770	+	0.743455i
$377$	−43.9136	−	76.0605i	−0.116482	−	0.201752i
$378$		0			0
$379$		−	638.486i		−	1.68466i	−0.538962	−	0.842330i	$-0.681183\pi$
$379$		−	638.486i		−	1.68466i	0.538962	−	0.842330i	$-0.318817\pi$
$380$	−645.268	+	709.221i	−1.69807	+	1.86637i
$381$		0			0
$382$	730.474	−	421.739i	1.91224	−	1.10403i
$383$	−297.246	+	171.615i	−0.776100	+	0.448082i	−0.835046	−	0.550180i	$-0.814559\pi$
$383$	−297.246	+	171.615i	−0.776100	+	0.448082i	0.0589464	+	0.998261i	$0.481226\pi$
$384$		0			0
$385$	0.155154	+	0.268734i	0.000402997	+	0.000698012i
$386$	−212.761	+	368.512i	−0.551193	+	0.954694i
$387$		0			0
$388$			828.944i			2.13645i
$389$	176.043	−	304.915i	0.452552	−	0.783843i	−0.545992	−	0.837791i	$-0.683847\pi$
$389$	176.043	−	304.915i	0.452552	−	0.783843i	0.998544	+	0.0539474i	$0.0171803\pi$
$390$		0			0
$391$	89.6562			0.229300
$392$			520.464i			1.32771i
$393$		0			0
$394$	830.745	−	479.631i	2.10849	−	1.21734i
$395$	−276.721	−	159.765i	−0.700559	−	0.404468i
$396$		0			0
$397$	205.686	+	356.259i	0.518101	+	0.897378i	0.999779	+	0.0210293i	$0.00669432\pi$
$397$	205.686	+	356.259i	0.518101	+	0.897378i	−0.481678	+	0.876349i	$0.659972\pi$
$398$			517.132i			1.29933i
$399$		0			0
$400$	179.545			0.448862
$401$	26.8409	−	15.4966i	0.0669349	−	0.0386449i	−0.466159	−	0.884701i	$-0.654363\pi$
$401$	26.8409	−	15.4966i	0.0669349	−	0.0386449i	0.533094	+	0.846056i	$0.321029\pi$
$402$		0			0
$403$	−374.719	+	649.032i	−0.929823	+	1.61050i
$404$	622.703	+	1078.55i	1.54134	+	2.66969i
$405$		0			0
$406$	21.4489			0.0528297
$407$		−	1.65643i		−	0.00406984i
$408$		0			0
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	0.0279377	−	0.999610i	$-0.491106\pi$
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	−0.851719	+	0.524000i	$0.824439\pi$
$410$	1348.24			3.28839
$411$		0			0
$412$	−763.190	−	440.628i	−1.85240	−	1.06948i
$413$	−21.8022	+	12.5875i	−0.0527899	+	0.0304783i
$414$		0			0
$415$	226.904	+	393.009i	0.546756	+	0.947010i
$416$	151.300	+	262.058i	0.363701	+	0.629948i
$417$		0			0
$418$	0.493723	−	2.26503i	0.00118116	−	0.00541874i
$419$	−455.941			−1.08817			−0.544083	−	0.839032i	$-0.683122\pi$
$419$	−455.941			−1.08817			−0.544083	+	0.839032i	$0.683122\pi$
$420$		0			0
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	−0.694754	−	0.719248i	$-0.744487\pi$
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	0.275510	+	0.961298i	$0.411153\pi$
$422$	−267.593	+	463.484i	−0.634106	+	1.09830i
$423$		0			0
$424$	−63.8105	+	110.523i	−0.150496	+	0.260668i
$425$	−213.567			−0.502510
$426$		0			0
$427$	10.1245	−	17.5361i	0.0237107	−	0.0410681i
$428$	−352.703	−	203.633i	−0.824072	−	0.475778i
$429$		0			0
$430$		−	706.746i		−	1.64360i
$431$	−609.299	−	351.779i	−1.41369	−	0.816193i	−0.417954	−	0.908468i	$-0.637253\pi$
$431$	−609.299	−	351.779i	−1.41369	−	0.816193i	−0.995734	+	0.0922756i	$0.970586\pi$
$432$		0			0
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	0.297295	−	0.954786i	$-0.403916\pi$
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	−0.678221	+	0.734858i	$0.737249\pi$
$434$	−91.5127	−	158.505i	−0.210859	−	0.365218i
$435$		0			0
$436$			386.265i			0.885930i
$437$	−56.3868	−	176.649i	−0.129032	−	0.404231i
$438$		0			0
$439$	415.097	−	239.656i	0.945551	−	0.545914i	0.0538552	−	0.998549i	$-0.482849\pi$
$439$	415.097	−	239.656i	0.945551	−	0.545914i	0.891696	+	0.452634i	$0.149516\pi$
$440$	−2.39657	+	1.38366i	−0.00544674	+	0.00314468i
$441$		0			0
$442$	260.384	+	450.999i	0.589105	+	1.02036i
$443$	383.888	−	664.914i	0.866565	−	1.50094i	0.00108097	−	0.999999i	$-0.499656\pi$
$443$	383.888	−	664.914i	0.866565	−	1.50094i	0.865484	−	0.500936i	$-0.167011\pi$
$444$		0			0
$445$		−	1078.25i		−	2.42304i
$446$	−313.744	+	543.421i	−0.703463	+	1.21843i
$447$		0			0
$448$	−111.864			−0.249697
$449$			392.421i			0.873988i	0.899464	+	0.436994i	$0.143957\pi$
$449$			392.421i			0.873988i	−0.899464	+	0.436994i	$0.856043\pi$
$450$		0			0
$451$	−1.82062	+	1.05113i	−0.00403685	+	0.00233068i
$452$	−861.654	−	497.476i	−1.90631	−	1.10061i
$453$		0			0
$454$	14.8942	+	25.7976i	0.0328067	+	0.0568228i
$455$			144.173i			0.316863i
$456$		0			0
$457$	−695.090			−1.52099			−0.760493	−	0.649347i	$-0.775042\pi$
$457$	−695.090			−1.52099			−0.760493	+	0.649347i	$0.775042\pi$
$458$	772.952	−	446.264i	1.68767	−	0.974376i
$459$		0			0
$460$	−246.256	+	426.528i	−0.535339	+	0.927234i
$461$	−351.150	−	608.210i	−0.761714	−	1.31933i	−0.941967	−	0.335707i	$-0.891025\pi$
$461$	−351.150	−	608.210i	−0.761714	−	1.31933i	0.180253	−	0.983620i	$-0.442308\pi$
$462$		0			0
$463$	−14.4955			−0.0313077			−0.0156538	−	0.999877i	$-0.504983\pi$
$463$	−14.4955			−0.0313077			−0.0156538	+	0.999877i	$0.504983\pi$
$464$			40.1608i			0.0865534i
$465$		0			0
$466$	−26.2882	−	15.1775i	−0.0564125	−	0.0325698i
$467$	863.890			1.84987			0.924935	−	0.380124i	$-0.124119\pi$
$467$	863.890			1.84987			0.924935	+	0.380124i	$0.124119\pi$
$468$		0			0
$469$	2.25232	+	1.30038i	0.00480239	+	0.00277266i
$470$	1029.96	−	594.650i	2.19141	−	1.26521i
$471$		0			0
$472$	−112.255	−	194.432i	−0.237829	−	0.411931i
$473$	0.551003	+	0.954366i	0.00116491	+	0.00201769i
$474$		0			0
$475$	134.317	+	420.789i	0.282773	+	0.885871i
$476$	−82.0221			−0.172315
$477$		0			0
$478$	140.625	−	81.1897i	0.294194	−	0.169853i
$479$	198.015	−	342.972i	0.413393	−	0.716017i	−0.581866	−	0.813285i	$-0.697677\pi$
$479$	198.015	−	342.972i	0.413393	−	0.716017i	0.995258	+	0.0972678i	$0.0310103\pi$
$480$		0			0
$481$	384.797	−	666.488i	0.799994	−	1.38563i
$482$	−466.742			−0.968344
$483$		0			0
$484$	−439.544	+	761.313i	−0.908149	+	1.57296i
$485$	686.345	+	396.261i	1.41514	+	0.817033i
$486$		0			0
$487$		−	872.905i		−	1.79241i	−0.443636	−	0.896207i	$-0.646312\pi$
$487$		−	872.905i		−	1.79241i	0.443636	−	0.896207i	$-0.353688\pi$
$488$	156.386	+	90.2897i	0.320464	+	0.185020i
$489$		0			0
$490$	958.826	+	553.578i	1.95679	+	1.12975i
$491$	350.193	+	606.552i	0.713224	+	1.23534i	0.963641	+	0.267201i	$0.0860989\pi$
$491$	350.193	+	606.552i	0.713224	+	1.23534i	−0.250417	+	0.968138i	$0.580568\pi$
$492$		0			0
$493$		−	47.7709i		−	0.0968983i
$494$	724.837	−	796.676i	1.46728	−	1.61270i
$495$		0			0
$496$	296.783	−	171.348i	0.598353	−	0.345459i
$497$	−41.5325	+	23.9788i	−0.0835663	+	0.0482470i
$498$		0			0
$499$	−76.5488	−	132.586i	−0.153404	−	0.265704i	0.779073	−	0.626934i	$-0.215690\pi$
$499$	−76.5488	−	132.586i	−0.153404	−	0.265704i	−0.932477	+	0.361230i	$0.882357\pi$
$500$	−44.2154	+	76.5832i	−0.0884307	+	0.153166i
$501$		0			0
$502$		−	731.860i		−	1.45789i
$503$	−203.824	+	353.033i	−0.405216	+	0.701855i	−0.994347	−	0.106183i	$-0.966137\pi$
$503$	−203.824	+	353.033i	−0.405216	+	0.701855i	0.589130	+	0.808038i	$0.299470\pi$
$504$		0			0
$505$	1190.69			2.35779
$506$		−	1.19077i		−	0.00235330i
$507$		0			0
$508$	993.585	−	573.647i	1.95588	−	1.12923i
$509$	171.070	+	98.7673i	0.336090	+	0.194042i	0.658542	−	0.752544i	$-0.271174\pi$
$509$	171.070	+	98.7673i	0.336090	+	0.194042i	−0.322452	+	0.946586i	$0.604507\pi$
$510$		0			0
$511$	34.5406	+	59.8261i	0.0675942	+	0.117077i
$512$		−	476.936i		−	0.931515i
$513$		0			0
$514$	−744.428			−1.44830
$515$	−729.657	+	421.268i	−1.41681	+	0.817995i
$516$		0			0
$517$	−0.927218	+	1.60599i	−0.00179346	+	0.00310636i
$518$	93.9740	+	162.768i	0.181417	+	0.314223i
$519$		0			0
$520$	−1285.73			−2.47255
$521$		−	698.844i		−	1.34135i	−0.741751	−	0.670676i	$-0.766004\pi$
$521$		−	698.844i		−	1.34135i	0.741751	−	0.670676i	$-0.233996\pi$
$522$		0			0
$523$	−381.571	−	220.300i	−0.729582	−	0.421224i	0.0886874	−	0.996060i	$-0.471733\pi$
$523$	−381.571	−	220.300i	−0.729582	−	0.421224i	−0.818269	+	0.574835i	$0.805066\pi$
$524$	−560.001			−1.06870
$525$		0			0
$526$	934.166	+	539.341i	1.77598	+	1.02536i
$527$	−353.021	+	203.817i	−0.669869	+	0.386749i
$528$		0			0
$529$	216.876	+	375.641i	0.409974	+	0.710096i
$530$	135.741	+	235.110i	0.256115	+	0.443604i
$531$		0			0
$532$	51.5855	+	161.607i	0.0969653	+	0.303773i
$533$	−976.738			−1.83253
$534$		0			0
$535$	−337.206	+	194.686i	−0.630292	+	0.363899i
$536$	−11.5967	+	20.0861i	−0.0216357	+	0.0374741i
$537$		0			0
$538$	266.346	−	461.325i	0.495067	−	0.857481i
$539$	−1.72635			−0.00320288
$540$		0			0
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	0.0886479	+	0.996063i	$0.471745\pi$
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	−0.906940	+	0.421260i	$0.861588\pi$
$542$	−1422.25	−	821.136i	−2.62408	−	1.51501i
$543$		0			0
$544$			164.589i			0.302554i
$545$	319.818	+	184.647i	0.586822	+	0.338802i
$546$		0			0
$547$	−801.617	−	462.814i	−1.46548	−	0.846095i	−0.466223	−	0.884667i	$-0.654386\pi$
$547$	−801.617	−	462.814i	−1.46548	−	0.846095i	−0.999256	+	0.0385725i	$0.987719\pi$
$548$	329.821	+	571.267i	0.601863	+	1.04246i
$549$		0			0
$550$			2.83648i			0.00515725i
$551$	−94.1225	+	30.0442i	−0.170821	+	0.0545266i
$552$		0			0
$553$	−48.9585	+	28.2662i	−0.0885325	+	0.0511143i
$554$	−532.077	+	307.195i	−0.960427	+	0.554503i
$555$		0			0
$556$	−332.585	−	576.053i	−0.598174	−	1.03607i
$557$	−176.665	+	305.992i	−0.317172	+	0.549358i	−0.979897	−	0.199505i	$-0.936067\pi$
$557$	−176.665	+	305.992i	−0.317172	+	0.549358i	0.662725	+	0.748863i	$0.269400\pi$
$558$		0			0
$559$			512.005i			0.915930i
$560$	32.9629	−	57.0935i	0.0588624	−	0.101953i
$561$		0			0
$562$	−894.909			−1.59236
$563$			21.4065i			0.0380221i	0.999819	+	0.0190111i	$0.00605177\pi$
$563$			21.4065i			0.0380221i	−0.999819	+	0.0190111i	$0.993948\pi$
$564$		0			0
$565$	−823.795	+	475.618i	−1.45804	+	0.841802i
$566$	1034.87	+	597.482i	1.82839	+	1.05562i
$567$		0			0
$568$	−213.842	−	370.385i	−0.376482	−	0.652087i
$569$		−	378.852i		−	0.665821i	−0.942958	−	0.332911i	$-0.891969\pi$
$569$		−	378.852i		−	0.665821i	0.942958	−	0.332911i	$-0.108031\pi$
$570$		0			0
$571$	−38.5842			−0.0675730			−0.0337865	−	0.999429i	$-0.510757\pi$
$571$	−38.5842			−0.0675730			−0.0337865	+	0.999429i	$0.510757\pi$
$572$	3.86307	−	2.23034i	0.00675362	−	0.00389920i
$573$		0			0
$574$	119.268	−	206.578i	0.207784	−	0.359892i
$575$	113.443	+	196.488i	0.197291	+	0.341719i
$576$		0			0
$577$	399.348			0.692112			0.346056	−	0.938214i	$-0.387521\pi$
$577$	399.348			0.692112			0.346056	+	0.938214i	$0.387521\pi$
$578$		−	686.737i		−	1.18813i
$579$		0			0
$580$	227.264	+	131.211i	0.391834	+	0.226225i
$581$	80.2894			0.138192
$582$		0			0
$583$	−0.366600	−	0.211656i	−0.000628816	−	0.000363047i
$584$	−533.528	+	308.032i	−0.913575	+	0.527453i
$585$		0			0
$586$	600.380	+	1039.89i	1.02454	+	1.77455i
$587$	247.769	+	429.148i	0.422093	+	0.731087i	0.996144	−	0.0877330i	$-0.0279622\pi$
$587$	247.769	+	429.148i	0.422093	+	0.731087i	−0.574051	+	0.818820i	$0.694629\pi$
$588$		0			0
$589$	623.601	+	567.369i	1.05875	+	0.963275i
$590$	−477.589			−0.809474
$591$		0			0
$592$	−304.765	+	175.956i	−0.514806	+	0.297224i
$593$	114.717	−	198.696i	0.193452	−	0.335069i	−0.752940	−	0.658089i	$-0.771365\pi$
$593$	114.717	−	198.696i	0.193452	−	0.335069i	0.946392	+	0.323020i	$0.104698\pi$
$594$		0			0
$595$	−39.2091	+	67.9121i	−0.0658976	+	0.114138i
$596$	175.219			0.293992
$597$		0			0
$598$	276.622	−	479.124i	0.462579	−	0.801210i
$599$	26.4546	+	15.2736i	0.0441646	+	0.0254984i	0.521920	−	0.852995i	$-0.325216\pi$
$599$	26.4546	+	15.2736i	0.0441646	+	0.0254984i	−0.477755	+	0.878493i	$0.658549\pi$
$600$		0			0
$601$			962.490i			1.60148i	0.599012	+	0.800740i	$0.295560\pi$
$601$			962.490i			1.60148i	−0.599012	+	0.800740i	$0.704440\pi$
$602$	−108.288	−	62.5201i	−0.179880	−	0.103854i
$603$		0			0
$604$	−1582.10	−	913.429i	−2.61938	−	1.51230i
$605$	420.232	+	727.863i	0.694598	+	1.20308i
$606$		0			0
$607$			249.770i			0.411483i	0.978606	+	0.205741i	$0.0659606\pi$
$607$			249.770i			0.411483i	−0.978606	+	0.205741i	$0.934039\pi$
$608$	324.289	−	103.514i	0.533370	−	0.170253i
$609$		0			0
$610$	332.673	−	192.069i	0.545365	−	0.314867i
$611$	−746.161	+	430.796i	−1.22121	+	0.705067i
$612$		0			0
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	0.669655	−	0.742672i	$-0.266442\pi$
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	−0.978000	+	0.208603i	$0.933108\pi$
$614$	243.904	−	422.454i	0.397238	−	0.688036i
$615$		0			0
$616$			0.489604i			0.000794812i
$617$	259.371	−	449.243i	0.420374	−	0.728109i	−0.575602	−	0.817730i	$-0.695232\pi$
$617$	259.371	−	449.243i	0.420374	−	0.728109i	0.995976	+	0.0896208i	$0.0285655\pi$
$618$		0			0
$619$	1035.34			1.67261			0.836303	−	0.548267i	$-0.184712\pi$
$619$	1035.34			1.67261			0.836303	+	0.548267i	$0.184712\pi$
$620$		−	2239.27i		−	3.61172i
$621$		0			0
$622$	556.028	−	321.023i	0.893935	−	0.516114i
$623$	−165.211	−	95.3844i	−0.265186	−	0.153105i
$624$		0			0
$625$	332.869	+	576.545i	0.532590	+	0.922473i
$626$		−	1049.71i		−	1.67686i
$627$		0			0
$628$	639.594			1.01846
$629$	362.516	−	209.298i	0.576336	−	0.332748i
$630$		0			0
$631$	528.945	−	916.160i	0.838265	−	1.45192i	−0.0530794	−	0.998590i	$-0.516904\pi$
$631$	528.945	−	916.160i	0.838265	−	1.45192i	0.891344	−	0.453327i	$-0.149763\pi$
$632$	−252.077	−	436.610i	−0.398856	−	0.690839i
$633$		0			0
$634$	−303.723			−0.479058
$635$		−	1096.88i		−	1.72738i
$636$		0			0
$637$	−694.625	−	401.042i	−1.09046	−	0.629579i
$638$	−0.634468			−0.000994464
$639$		0			0
$640$	−1406.74	−	812.180i	−2.19803	−	1.26903i
$641$	560.504	−	323.607i	0.874421	−	0.504847i	0.00560636	−	0.999984i	$-0.498215\pi$
$641$	560.504	−	323.607i	0.874421	−	0.504847i	0.868815	+	0.495137i	$0.164882\pi$
$642$		0			0
$643$	157.333	+	272.508i	0.244685	+	0.423807i	0.962043	−	0.272898i	$-0.0879820\pi$
$643$	157.333	+	272.508i	0.244685	+	0.423807i	−0.717358	+	0.696705i	$0.754649\pi$
$644$	43.5685	+	75.4629i	0.0676530	+	0.117178i
$645$		0			0
$646$	558.096	−	178.146i	0.863926	−	0.275768i
$647$	320.116			0.494769			0.247384	−	0.968917i	$-0.420429\pi$
$647$	320.116			0.494769			0.247384	+	0.968917i	$0.420429\pi$
$648$		0			0
$649$	0.644920	−	0.372345i	0.000993714	−	0.000573721i
$650$	−658.932	+	1141.30i	−1.01374	+	1.75585i
$651$		0			0
$652$	−103.024	+	178.443i	−0.158013	+	0.273686i
$653$	−131.969			−0.202097			−0.101049	−	0.994881i	$-0.532220\pi$
$653$	−131.969			−0.202097			−0.101049	+	0.994881i	$0.532220\pi$
$654$		0			0
$655$	−267.698	+	463.666i	−0.408699	+	0.707888i
$656$	386.796	+	223.317i	0.589628	+	0.340422i
$657$		0			0
$658$		−	210.415i		−	0.319780i
$659$	635.205	+	366.736i	0.963892	+	0.556503i	0.897369	−	0.441281i	$-0.145476\pi$
$659$	635.205	+	366.736i	0.963892	+	0.556503i	0.0665235	+	0.997785i	$0.478809\pi$
$660$		0			0
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.874807	−	0.484472i	$-0.160988\pi$
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.0178378	+	0.999841i	$0.494322\pi$
$662$	421.720	+	730.441i	0.637040	+	1.10338i
$663$		0			0
$664$			716.019i			1.07834i
$665$	158.466	+	34.5419i	0.238295	+	0.0519426i
$666$		0			0
$667$	−43.9507	+	25.3750i	−0.0658931	+	0.0380434i
$668$	378.639	−	218.607i	0.566824	−	0.327256i
$669$		0			0
$670$	24.6692	+	42.7282i	0.0368196	+	0.0637735i
$671$	−0.299487	+	0.518726i	−0.000446329	+	0.000773064i
$672$		0			0
$673$		−	710.831i		−	1.05621i	−0.849178	−	0.528107i	$-0.822902\pi$
$673$		−	710.831i		−	1.05621i	0.849178	−	0.528107i	$-0.177098\pi$
$674$	−437.458	+	757.700i	−0.649048	+	1.12418i
$675$		0			0
$676$	844.654			1.24949
$677$			493.970i			0.729645i	0.931077	+	0.364823i	$0.118870\pi$
$677$			493.970i			0.729645i	−0.931077	+	0.364823i	$0.881130\pi$
$678$		0			0
$679$	121.431	−	70.1081i	0.178838	−	0.103252i
$680$	−605.639	−	349.666i	−0.890645	−	0.514214i
$681$		0			0
$682$	2.70699	+	4.68864i	0.00396919	+	0.00687484i
$683$		−	442.962i		−	0.648553i	−0.945962	−	0.324276i	$-0.894879\pi$
$683$		−	442.962i		−	0.648553i	0.945962	−	0.324276i	$-0.105121\pi$
$684$		0			0
$685$	630.659			0.920670
$686$	344.673	−	198.997i	0.502439	−	0.290083i
$687$		0			0
$688$	117.062	−	202.758i	0.170149	−	0.294706i
$689$	−98.3380	−	170.326i	−0.142726	−	0.247208i
$690$		0			0
$691$	924.711			1.33822			0.669110	−	0.743163i	$-0.266675\pi$
$691$	924.711			1.33822			0.669110	+	0.743163i	$0.266675\pi$
$692$			1282.61i			1.85348i
$693$		0			0
$694$	−986.615	−	569.622i	−1.42164	−	0.820782i
$695$	−635.943			−0.915026
$696$		0			0
$697$	−460.090	−	265.633i	−0.660101	−	0.381109i
$698$	−222.100	+	128.230i	−0.318195	+	0.183710i
$699$		0			0
$700$	−103.783	−	179.757i	−0.148261	−	0.256796i
$701$	277.112	+	479.973i	0.395310	+	0.684697i	0.993141	−	0.116925i	$-0.0373038\pi$
$701$	277.112	+	479.973i	0.395310	+	0.684697i	−0.597831	+	0.801622i	$0.703970\pi$
$702$		0			0
$703$	−640.373	−	582.629i	−0.910915	−	0.828775i
$704$	3.30900			0.00470028
$705$		0			0
$706$	−1847.03	+	1066.38i	−2.61619	+	1.51046i
$707$	105.330	−	182.437i	0.148982	−	0.258045i
$708$		0			0
$709$	249.802	−	432.670i	0.352331	−	0.610254i	−0.634327	−	0.773065i	$-0.718723\pi$
$709$	249.802	−	432.670i	0.352331	−	0.610254i	0.986657	+	0.162811i	$0.0520560\pi$
$710$	−909.791			−1.28140
$711$		0			0
$712$	850.635	−	1473.34i	1.19471	−	2.06930i
$713$	375.036	+	216.527i	0.525997	+	0.303684i
$714$		0			0
$715$		−	4.26469i		−	0.00596461i
$716$	−1.42791	−	0.824403i	−0.00199428	−	0.00115140i
$717$		0			0
$718$	14.1346	+	8.16063i	0.0196861	+	0.0113658i
$719$	−174.396	−	302.062i	−0.242553	−	0.420114i	0.718888	−	0.695126i	$-0.244652\pi$
$719$	−174.396	−	302.062i	−0.242553	−	0.420114i	−0.961441	+	0.275012i	$0.911318\pi$
$720$		0			0
$721$			149.065i			0.206747i
$722$	−701.999	−	987.573i	−0.972298	−	1.36783i
$723$		0			0
$724$	940.198	−	542.823i	1.29862	−	0.749756i
$725$	104.693	−	60.4448i	0.144405	−	0.0833721i
$726$		0			0
$727$	41.3116	+	71.5538i	0.0568247	+	0.0984233i	0.893038	−	0.449980i	$-0.148569\pi$
$727$	41.3116	+	71.5538i	0.0568247	+	0.0984233i	−0.836214	+	0.548404i	$0.815236\pi$
$728$	−113.738	+	197.000i	−0.156233	+	0.270604i
$729$		0			0
$730$			1310.52i			1.79524i
$731$	−139.245	+	241.179i	−0.190485	+	0.329930i
$732$		0			0
$733$	−981.828			−1.33947			−0.669733	−	0.742602i	$-0.733591\pi$
$733$	−981.828			−1.33947			−0.669733	+	0.742602i	$0.733591\pi$
$734$			1004.01i			1.36787i
$735$		0			0
$736$	151.428	−	87.4267i	0.205744	−	0.118786i
$737$	−0.0666248	−	0.0384658i	−9.03999e−5	−	5.21924e-5i
$738$		0			0
$739$	−64.8765	−	112.369i	−0.0877895	−	0.152056i	0.818787	−	0.574097i	$-0.194647\pi$
$739$	−64.8765	−	112.369i	−0.0877895	−	0.152056i	−0.906576	+	0.422042i	$0.861314\pi$
$740$			2299.49i			3.10743i
$741$		0			0
$742$	48.0316			0.0647326
$743$	450.862	−	260.306i	0.606814	−	0.350344i	−0.164904	−	0.986310i	$-0.552731\pi$
$743$	450.862	−	260.306i	0.606814	−	0.350344i	0.771717	+	0.635966i	$0.219398\pi$
$744$		0			0
$745$	83.7603	−	145.077i	0.112430	−	0.194734i
$746$	480.624	+	832.465i	0.644268	+	1.11590i
$747$		0			0
$748$	2.42625			0.00324365
$749$			68.8892i			0.0919749i
$750$		0			0
$751$	880.913	+	508.595i	1.17299	+	0.677224i	0.954382	−	0.298590i	$-0.0965161\pi$
$751$	880.913	+	508.595i	1.17299	+	0.677224i	0.218605	+	0.975813i	$0.429849\pi$
$752$	393.981			0.523910
$753$		0			0
$754$	−255.288	−	147.391i	−0.338578	−	0.195478i
$755$	−1512.59	+	873.295i	−2.00343	+	1.15668i
$756$		0			0
$757$	155.490	+	269.317i	0.205403	+	0.355768i	0.950261	−	0.311455i	$-0.100816\pi$
$757$	155.490	+	269.317i	0.205403	+	0.355768i	−0.744858	+	0.667223i	$0.767483\pi$
$758$	−1071.50	−	1855.89i	−1.41359	−	2.44841i
$759$		0			0
$760$	−308.043	+	1413.20i	−0.405320	+	1.85947i
$761$	1402.51			1.84298			0.921489	−	0.388404i	$-0.126973\pi$
$761$	1402.51			1.84298			0.921489	+	0.388404i	$0.126973\pi$
$762$		0			0
$763$	56.5834	−	32.6684i	0.0741591	−	0.0428158i
$764$	912.904	−	1581.20i	1.19490	−	2.06963i
$765$		0			0
$766$	−576.006	+	997.671i	−0.751966	+	1.30244i
$767$	345.991			0.451097
$768$		0			0
$769$	196.711	−	340.714i	0.255802	−	0.443061i	−0.709311	−	0.704895i	$-0.750994\pi$
$769$	196.711	−	340.714i	0.255802	−	0.443061i	0.965113	+	0.261834i	$0.0843273\pi$
$770$	0.901975	+	0.520755i	0.00117140	+	0.000676306i
$771$		0			0
$772$			921.090i			1.19312i
$773$	−201.825	−	116.524i	−0.261093	−	0.150742i	0.363740	−	0.931501i	$-0.381500\pi$
$773$	−201.825	−	116.524i	−0.261093	−	0.150742i	−0.624833	+	0.780758i	$0.714833\pi$
$774$		0			0
$775$	−893.359	−	515.781i	−1.15272	−	0.665524i
$776$	625.222	+	1082.92i	0.805698	+	1.39551i
$777$		0			0
$778$		−	1181.73i		−	1.51894i
$779$	−234.014	+	1073.57i	−0.300403	+	1.37814i
$780$		0			0
$781$	1.22855	−	0.709304i	0.00157305	−	0.000908200i
$782$	260.604	−	150.460i	0.333254	−	0.192404i
$783$		0			0
$784$	183.385	+	317.631i	0.233909	+	0.405142i
$785$	305.746	−	529.568i	0.389485	−	0.674609i
$786$		0			0
$787$		−	193.205i		−	0.245495i	−0.992438	−	0.122748i	$-0.960829\pi$
$787$		−	193.205i		−	0.245495i	0.992438	−	0.122748i	$-0.0391706\pi$
$788$	1038.22	−	1798.25i	1.31753	−	2.28204i
$789$		0			0
$790$	−1072.46			−1.35755
$791$			168.296i			0.212764i
$792$		0			0
$793$	−241.006	+	139.145i	−0.303917	+	0.175466i
$794$	1195.74	+	690.361i	1.50597	+	0.869472i
$795$		0			0
$796$	559.696	+	969.422i	0.703136	+	1.21787i
$797$		−	255.622i		−	0.320730i	−0.987058	−	0.160365i	$-0.948733\pi$
$797$		−	255.622i		−	0.320730i	0.987058	−	0.160365i	$-0.0512672\pi$
$798$		0			0
$799$	−468.636			−0.586529
$800$	−360.710	+	208.256i	−0.450887	+	0.260320i
$801$		0			0
$802$	52.0124	−	90.0882i	0.0648534	−	0.112329i
$803$	−1.02173	−	1.76969i	−0.00127239	−	0.00220384i
$804$		0			0
$805$	83.3085			0.103489
$806$			2515.40i			3.12084i
$807$		0			0
$808$	1626.97	+	939.333i	2.01358	+	1.16254i
$809$	−478.346			−0.591281			−0.295641	−	0.955299i	$-0.595533\pi$
$809$	−478.346			−0.591281			−0.295641	+	0.955299i	$0.595533\pi$
$810$		0			0
$811$	810.296	+	467.825i	0.999132	+	0.576849i	0.907991	−	0.418989i	$-0.137615\pi$
$811$	810.296	+	467.825i	0.999132	+	0.576849i	0.0911409	+	0.995838i	$0.470949\pi$
$812$	40.2084	−	23.2143i	0.0495177	−	0.0285890i
$813$		0			0
$814$	−2.77980	−	4.81475i	−0.00341498	−	0.00591492i
$815$	98.4977	+	170.603i	0.120856	+	0.209329i
$816$		0			0
$817$	562.766	+	122.670i	0.688820	+	0.150146i
$818$	−1305.80			−1.59633
$819$		0			0
$820$	2527.43	−	1459.21i	3.08223	−	1.77953i
$821$	−207.851	+	360.008i	−0.253168	+	0.438500i	−0.964396	−	0.264461i	$-0.914806\pi$
$821$	−207.851	+	360.008i	−0.253168	+	0.438500i	0.711228	+	0.702961i	$0.248139\pi$
$822$		0			0
$823$	−571.455	+	989.790i	−0.694356	+	1.20266i	0.276041	+	0.961146i	$0.410978\pi$
$823$	−571.455	+	989.790i	−0.694356	+	1.20266i	−0.970397	+	0.241515i	$0.922356\pi$
$824$	−1329.35			−1.61329
$825$		0			0
$826$	−42.2485	+	73.1765i	−0.0511483	+	0.0885914i
$827$	−943.619	−	544.799i	−1.14101	−	0.658765i	−0.194333	−	0.980936i	$-0.562254\pi$
$827$	−943.619	−	544.799i	−1.14101	−	0.658765i	−0.946682	+	0.322170i	$0.895588\pi$
$828$		0			0
$829$		−	242.265i		−	0.292237i	−0.989267	−	0.146119i	$-0.953322\pi$
$829$		−	242.265i		−	0.292237i	0.989267	−	0.146119i	$-0.0466781\pi$
$830$	1319.09	+	761.575i	1.58926	+	0.917560i
$831$		0			0
$832$	1331.43	+	768.699i	1.60027	+	0.923918i
$833$	−218.134	−	377.820i	−0.261866	−	0.453565i
$834$		0			0
$835$		−	418.004i		−	0.500604i
$836$	−1.52592	−	4.78042i	−0.00182527	−	0.00571821i
$837$		0			0
$838$	−1325.29	+	765.156i	−1.58149	+	0.913074i
$839$	1272.95	−	734.939i	1.51723	−	0.875971i	0.517431	−	0.855725i	$-0.326888\pi$
$839$	1272.95	−	734.939i	1.51723	−	0.875971i	0.999795	−	0.0202457i	$-0.00644485\pi$
$840$		0			0
$841$	−406.980	−	704.909i	−0.483923	−	0.838180i
$842$	−342.026	+	592.407i	−0.406207	+	0.703571i
$843$		0			0
$844$			1158.47i			1.37260i
$845$	403.771	−	699.352i	0.477836	−	0.827635i
$846$		0			0
$847$	148.698			0.175558
$848$			89.9341i			0.106054i
$849$		0			0
$850$	−620.776	+	358.405i	−0.730325	+	0.421653i
$851$	−385.123	−	222.351i	−0.452553	−	0.261282i
$852$		0			0
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	−0.995619	−	0.0935062i	$-0.970192\pi$
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	0.416831	−	0.908984i	$-0.363141\pi$
$854$		−	67.9631i		−	0.0795821i
$855$		0			0
$856$	−614.352			−0.717701
$857$	1279.05	−	738.461i	1.49248	−	0.861681i	0.492513	−	0.870305i	$-0.336078\pi$
$857$	1279.05	−	738.461i	1.49248	−	0.861681i	0.999963	+	0.00862354i	$0.00274499\pi$
$858$		0			0
$859$	466.025	−	807.179i	0.542520	−	0.939673i	−0.456238	−	0.889858i	$-0.650803\pi$
$859$	466.025	−	807.179i	0.542520	−	0.939673i	0.998758	−	0.0498150i	$-0.0158632\pi$
$860$	−764.917	−	1324.88i	−0.889439	−	1.54055i
$861$		0			0
$862$	−2361.41			−2.73945
$863$			1088.87i			1.26172i	0.775896	+	0.630861i	$0.217298\pi$
$863$			1088.87i			1.26172i	−0.775896	+	0.630861i	$0.782702\pi$
$864$		0			0
$865$	1061.97	+	613.127i	1.22771	+	0.708818i
$866$	−639.248			−0.738162
$867$		0			0
$868$	−343.102	−	198.090i	−0.395279	−	0.228214i
$869$	1.44822	−	0.836128i	0.00166653	−	0.000962172i
$870$		0			0
$871$	−17.8717	−	30.9546i	−0.0205185	−	0.0355392i
$872$	291.336	+	504.609i	0.334101	+	0.578680i
$873$		0			0
$874$	−460.350	−	418.839i	−0.526716	−	0.479221i
$875$	14.9581			0.0170949
$876$		0			0
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	−0.610881	−	0.791723i	$-0.709184\pi$
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	0.380212	+	0.924899i	$0.375851\pi$
$878$	804.378	−	1393.22i	0.916148	−	1.58681i
$879$		0			0
$880$	−0.975059	+	1.68885i	−0.00110802	+	0.00191915i
$881$	−488.267			−0.554220			−0.277110	−	0.960838i	$-0.589377\pi$
$881$	−488.267			−0.554220			−0.277110	+	0.960838i	$0.589377\pi$
$882$		0			0
$883$	−833.774	+	1444.14i	−0.944252	+	1.63549i	−0.187009	+	0.982358i	$0.559879\pi$
$883$	−833.774	+	1444.14i	−0.944252	+	1.63549i	−0.757243	+	0.653134i	$0.773454\pi$
$884$	976.240	+	563.632i	1.10434	+	0.637593i
$885$		0			0
$886$		−	2576.95i		−	2.90852i
$887$	−544.718	−	314.493i	−0.614113	−	0.354558i	0.160460	−	0.987042i	$-0.448702\pi$
$887$	−544.718	−	314.493i	−0.614113	−	0.354558i	−0.774573	+	0.632484i	$0.782035\pi$
$888$		0			0
$889$	−168.065	−	97.0325i	−0.189050	−	0.109148i
$890$	−1809.51	−	3134.17i	−2.03316	−	3.52154i
$891$		0			0
$892$			1358.27i			1.52273i
$893$	294.736	+	923.350i	0.330052	+	1.03399i
$894$		0			0
$895$	−1.36517	+	0.788180i	−0.00152533	+	0.000880648i
$896$	−248.885	+	143.694i	−0.277774	+	0.160373i
$897$		0			0
$898$	658.556	+	1140.65i	0.733359	+	1.27021i
$899$	115.371	−	199.828i	0.128332	−	0.222278i
$900$		0			0
$901$		−	106.976i		−	0.118730i
$902$	−3.52801	+	6.11068i	−0.00391131	+	0.00677460i
$903$		0			0
$904$	−1500.86			−1.66025
$905$		−	1037.95i		−	1.14690i
$906$		0			0
$907$	−1402.39	+	809.670i	−1.54619	+	0.892690i	−0.547757	+	0.836637i	$0.684518\pi$
$907$	−1402.39	+	809.670i	−1.54619	+	0.892690i	−0.998428	+	0.0560533i	$0.982148\pi$
$908$	55.8419	+	32.2403i	0.0614999	+	0.0355070i
$909$		0			0
$910$	241.949	+	419.068i	0.265878	+	0.460514i
$911$			895.922i			0.983449i	0.870751	+	0.491725i	$0.163633\pi$
$911$			895.922i			0.983449i	−0.870751	+	0.491725i	$0.836367\pi$
$912$		0			0
$913$	−2.37500			−0.00260131
$914$	−2020.42	+	1166.49i	−2.21053	+	1.27625i
$915$		0			0
$916$	965.991	−	1673.15i	1.05458	−	1.82658i
$917$	47.3621	+	82.0336i	0.0516490	+	0.0894587i
$918$		0			0
$919$	741.588			0.806951			0.403476	−	0.914990i	$-0.367802\pi$
$919$	741.588			0.806951			0.403476	+	0.914990i	$0.367802\pi$
$920$			742.943i			0.807546i
$921$		0			0
$922$	−2041.38	−	1178.59i	−2.21408	−	1.27830i
$923$	659.101			0.714086
$924$		0			0
$925$	917.387	+	529.653i	0.991769	+	0.572598i
$926$	−42.1341	+	24.3261i	−0.0455012	+	0.0262701i
$927$		0			0
$928$	−46.5829	−	80.6840i	−0.0501971	−	0.0869440i
$929$	−657.059	−	1138.06i	−0.707275	−	1.22504i	−0.965864	−	0.259049i	$-0.916591\pi$
$929$	−657.059	−	1138.06i	−0.707275	−	1.22504i	0.258589	−	0.965988i	$-0.416743\pi$
$930$		0			0
$931$	−607.225	+	667.407i	−0.652229	+	0.716871i
$932$	−65.7070			−0.0705011
$933$		0			0
$934$	2511.08	−	1449.77i	2.68852	−	1.55222i
$935$	1.15982	−	2.00887i	0.00124045	−	0.00214853i
$936$		0			0
$937$	392.873	−	680.475i	0.419288	−	0.726228i	−0.576580	−	0.817041i	$-0.695613\pi$
$937$	392.873	−	680.475i	0.419288	−	0.726228i	0.995868	+	0.0908128i	$0.0289465\pi$
$938$	8.72912			0.00930610
$939$		0			0
$940$	1287.19	−	2229.48i	1.36935	−	2.37178i
$941$	224.279	+	129.487i	0.238341	+	0.137606i	0.614414	−	0.788984i	$-0.289392\pi$
$941$	224.279	+	129.487i	0.238341	+	0.137606i	−0.376073	+	0.926590i	$0.622726\pi$
$942$		0			0
$943$			564.397i			0.598512i
$944$	−137.015	−	79.1058i	−0.145143	−	0.0837985i
$945$		0			0
$946$	3.20321	+	1.84938i	0.00338606	+	0.00195494i
$947$	211.830	+	366.901i	0.223686	+	0.387435i	0.955924	−	0.293613i	$-0.0948577\pi$
$947$	211.830	+	366.901i	0.223686	+	0.387435i	−0.732239	+	0.681048i	$0.761524\pi$
$948$		0			0
$949$		−	949.414i		−	1.00044i
$950$	1096.58	+	997.701i	1.15430	+	1.05021i
$951$		0			0
$952$	−107.152	+	61.8642i	−0.112555	+	0.0649834i
$953$	−1077.21	+	621.927i	−1.13034	+	0.652599i	−0.944019	−	0.329891i	$-0.892988\pi$
$953$	−1077.21	+	621.927i	−1.13034	+	0.652599i	−0.186316	+	0.982490i	$0.559655\pi$
$954$		0			0
$955$	−872.794	−	1511.72i	−0.913920	−	1.58296i
$956$	175.745	−	304.398i	0.183833	−	0.318408i
$957$		0			0
$958$		−	1329.23i		−	1.38750i
$959$	55.7893	−	96.6299i	0.0581745	−	0.100761i
$960$		0			0
$961$	−1007.94			−1.04884
$962$		−	2583.05i		−	2.68508i
$963$		0			0
$964$	−874.961	+	505.159i	−0.907636	+	0.524024i
$965$	762.639	+	440.310i	0.790300	+	0.456280i
$966$		0			0
$967$	120.498	+	208.709i	0.124610	+	0.215832i	0.921581	−	0.388187i	$-0.126899\pi$
$967$	120.498	+	208.709i	0.124610	+	0.215832i	−0.796970	+	0.604019i	$0.793565\pi$
$968$			1326.08i			1.36992i
$969$		0			0
$970$	2660.00			2.74227
$971$	−94.1758	+	54.3724i	−0.0969885	+	0.0559963i	−0.547710	−	0.836668i	$-0.684500\pi$
$971$	−94.1758	+	54.3724i	−0.0969885	+	0.0559963i	0.450721	+	0.892665i	$0.351167\pi$
$972$		0			0
$973$	−56.2567	+	97.4395i	−0.0578178	+	0.100143i
$974$	−1464.90	−	2537.28i	−1.50400	−	2.60501i
$975$		0			0
$976$	127.254			0.130383
$977$		−	1730.59i		−	1.77133i	−0.464323	−	0.885666i	$-0.653702\pi$
$977$		−	1730.59i		−	1.77133i	0.464323	−	0.885666i	$-0.346298\pi$
$978$		0			0
$979$	4.88701	+	2.82152i	0.00499184	+	0.00288204i
$980$	2396.57			2.44548
$981$		0			0
$982$	2035.82	+	1175.38i	2.07313	+	1.19692i
$983$	−1505.59	+	869.256i	−1.53163	+	0.884288i	−0.532346	+	0.846527i	$0.678689\pi$
$983$	−1505.59	+	869.256i	−1.53163	+	0.884288i	−0.999287	+	0.0377615i	$0.987977\pi$
$984$		0			0
$985$	−992.600	−	1719.23i	−1.00772	−	1.74542i
$986$	−80.1685	−	138.856i	−0.0813068	−	0.140828i
$987$		0			0
$988$	496.540	−	2277.96i	0.502571	−	2.30562i
$989$	295.856			0.299147
$990$		0			0
$991$	−273.421	+	157.860i	−0.275904	+	0.159293i	−0.631568	−	0.775321i	$-0.717588\pi$
$991$	−273.421	+	157.860i	−0.275904	+	0.159293i	0.355663	+	0.934614i	$0.384255\pi$
$992$	−397.497	+	688.485i	−0.400702	+	0.694037i
$993$		0			0
$994$	−80.4818	+	139.399i	−0.0809677	+	0.140240i
$995$	1070.21			1.07559
$996$		0			0
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	−0.345731	−	0.938334i	$-0.612369\pi$
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	0.985486	−	0.169755i	$-0.0542976\pi$
$998$	−445.010	−	256.927i	−0.445902	−	0.257442i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.d.145.3		6
3.2	odd	2		19.3.d.a.12.1	yes	6
12.11	even	2		304.3.r.b.145.2		6
19.8	odd	6	inner	171.3.p.d.46.3		6
57.2	even	18		361.3.f.h.333.1		18
57.5	odd	18		361.3.f.i.262.1		18
57.8	even	6		19.3.d.a.8.1	✓	6
57.11	odd	6		361.3.d.c.293.3		6
57.14	even	18		361.3.f.h.262.3		18
57.17	odd	18		361.3.f.i.333.3		18
57.23	odd	18		361.3.f.h.116.1		18
57.26	odd	6		361.3.b.b.360.1		6
57.29	even	18		361.3.f.i.307.1		18
57.32	even	18		361.3.f.i.299.1		18
57.35	odd	18		361.3.f.i.127.1		18
57.41	even	18		361.3.f.h.127.3		18
57.44	odd	18		361.3.f.h.299.3		18
57.47	odd	18		361.3.f.h.307.3		18
57.50	even	6		361.3.b.b.360.6		6
57.53	even	18		361.3.f.i.116.3		18
57.56	even	2		361.3.d.c.69.3		6
228.179	odd	6		304.3.r.b.65.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.1	✓	6	57.8	even	6
19.3.d.a.12.1	yes	6	3.2	odd	2
171.3.p.d.46.3		6	19.8	odd	6	inner
171.3.p.d.145.3		6	1.1	even	1	trivial
304.3.r.b.65.2		6	228.179	odd	6
304.3.r.b.145.2		6	12.11	even	2
361.3.b.b.360.1		6	57.26	odd	6
361.3.b.b.360.6		6	57.50	even	6
361.3.d.c.69.3		6	57.56	even	2
361.3.d.c.293.3		6	57.11	odd	6
361.3.f.h.116.1		18	57.23	odd	18
361.3.f.h.127.3		18	57.41	even	18
361.3.f.h.262.3		18	57.14	even	18
361.3.f.h.299.3		18	57.44	odd	18
361.3.f.h.307.3		18	57.47	odd	18
361.3.f.h.333.1		18	57.2	even	18
361.3.f.i.116.3		18	57.53	even	18
361.3.f.i.127.1		18	57.35	odd	18
361.3.f.i.262.1		18	57.5	odd	18
361.3.f.i.299.1		18	57.32	even	18
361.3.f.i.307.1		18	57.29	even	18
361.3.f.i.333.3		18	57.17	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.90671 - 1.67819i) q^{2} +(3.63264 - 6.29191i) q^{4} +(-3.47303 - 6.01546i) q^{5} -1.22892 q^{7} -10.9595i q^{8} +O(q^{10})\)	\(q+(2.90671 - 1.67819i) q^{2} +(3.63264 - 6.29191i) q^{4} +(-3.47303 - 6.01546i) q^{5} -1.22892 q^{7} -10.9595i q^{8} +(-20.1902 - 11.6568i) q^{10} +0.0363521 q^{11} +(14.6268 + 8.44481i) q^{13} +(-3.57212 + 2.06236i) q^{14} +(-3.86156 - 6.68842i) q^{16} +(4.59329 + 7.95581i) q^{17} +(12.7864 - 14.0537i) q^{19} -50.4650 q^{20} +(0.105665 - 0.0610058i) q^{22} +(4.87974 - 8.45195i) q^{23} +(-11.6238 + 20.1331i) q^{25} +56.6879 q^{26} +(-4.46423 + 7.73228i) q^{28} +(-4.50339 - 2.60003i) q^{29} +44.3727i q^{31} +(15.5160 + 8.95814i) q^{32} +(26.7027 + 15.4168i) q^{34} +(4.26808 + 7.39254i) q^{35} -45.5661i q^{37} +(13.5817 - 62.3081i) q^{38} +(-65.9264 + 38.0626i) q^{40} +(-50.0829 + 28.9153i) q^{41} +(15.1574 + 26.2534i) q^{43} +(0.132054 - 0.228724i) q^{44} -32.7565i q^{46} +(-25.5066 + 44.1787i) q^{47} -47.4897 q^{49} +78.0280i q^{50} +(106.268 - 61.3538i) q^{52} +(-10.0847 - 5.82239i) q^{53} +(-0.126252 - 0.218675i) q^{55} +13.4684i q^{56} -17.4534 q^{58} +(17.7409 - 10.2427i) q^{59} +(-8.23849 + 14.2695i) q^{61} +(74.4658 + 128.978i) q^{62} +91.0263 q^{64} -117.316i q^{65} +(-1.83276 - 1.05814i) q^{67} +66.7430 q^{68} +(24.8121 + 14.3253i) q^{70} +(33.7958 - 19.5120i) q^{71} +(-28.1064 - 48.6818i) q^{73} +(-76.4686 - 132.447i) q^{74} +(-41.9762 - 131.503i) q^{76} -0.0446740 q^{77} +(39.8385 - 23.0008i) q^{79} +(-26.8226 + 46.4581i) q^{80} +(-97.0508 + 168.097i) q^{82} -65.3332 q^{83} +(31.9053 - 55.2615i) q^{85} +(88.1162 + 50.8739i) q^{86} -0.398401i q^{88} +(134.435 + 77.6163i) q^{89} +(-17.9753 - 10.3780i) q^{91} +(-35.4526 - 61.4058i) q^{92} +171.219i q^{94} +(-128.947 - 28.1074i) q^{95} +(-98.8107 + 57.0484i) q^{97} +(-138.039 + 79.6968i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

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