LMFDB - Embedded newform 431.3.f.a.101.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,3,Mod(47,431)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(86))

chi = DirichletCharacter(H, H._module([63]))

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

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

chi := DirichletCharacter("431.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	431.f (of order $86$, degree $42$, 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:	$11.7438993939$
Analytic rank:	$0$
Dimension:	$2982$
Relative dimension:	$71$ over $\Q(\zeta_{86})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{86}]$

Embedding invariants

Embedding label			101.34
Character	$\chi$	$=$	431.101
Dual form			431.3.f.a.367.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.192896 + 0.375186i) q^{2} +(0.272798 + 2.47928i) q^{3} +(2.22388 + 3.10842i) q^{4} +(1.03997 + 0.487516i) q^{5} +(-0.982812 - 0.375894i) q^{6} +(1.86059 + 8.35245i) q^{7} +(-3.26470 + 0.480465i) q^{8} +(2.71228 - 0.604186i) q^{9} +(-0.383515 + 0.296141i) q^{10} +(12.6832 - 7.11816i) q^{11} +(-7.09996 + 6.36159i) q^{12} +(18.0714 - 9.29113i) q^{13} +(-3.49262 - 0.913090i) q^{14} +(-0.924988 + 2.71136i) q^{15} +(-4.48674 + 13.1517i) q^{16} +(14.2297 + 25.3547i) q^{17} +(-0.296507 + 1.13415i) q^{18} +(-3.45876 + 1.62140i) q^{19} +(0.797358 + 4.31683i) q^{20} +(-20.2005 + 6.89144i) q^{21} +(0.224089 + 6.13163i) q^{22} +(-13.2107 - 13.7023i) q^{23} +(-2.08181 - 7.96304i) q^{24} +(-15.1480 - 18.2022i) q^{25} +8.57234i q^{26} +(9.48593 + 27.8055i) q^{27} +(-21.8251 + 24.3583i) q^{28} +(3.39464 - 4.74483i) q^{29} +(-0.838837 - 0.870054i) q^{30} +(-20.4017 - 53.3424i) q^{31} +(-13.2303 - 13.7226i) q^{32} +(21.1079 + 29.5034i) q^{33} +(-12.2576 + 0.447971i) q^{34} +(-2.13701 + 9.59333i) q^{35} +(7.90985 + 7.08726i) q^{36} +(-55.7993 - 14.5878i) q^{37} +(0.0588559 - 1.61044i) q^{38} +(27.9651 + 42.2693i) q^{39} +(-3.62942 - 1.09193i) q^{40} +(5.96657 - 17.4894i) q^{41} +(1.31102 - 8.90826i) q^{42} +(38.5993 - 49.9877i) q^{43} +(50.3322 + 23.5947i) q^{44} +(3.11523 + 0.693948i) q^{45} +(7.68918 - 2.31333i) q^{46} +(-3.70211 + 50.5817i) q^{47} +(-33.8308 - 7.53612i) q^{48} +(-21.9346 + 10.2825i) q^{49} +(9.75118 - 2.17217i) q^{50} +(-58.9795 + 42.1962i) q^{51} +(69.0692 + 35.5109i) q^{52} +(-59.7078 + 4.37005i) q^{53} +(-12.2620 - 1.80460i) q^{54} +(16.6603 - 1.21938i) q^{55} +(-10.0873 - 26.3743i) q^{56} +(-4.96345 - 8.13292i) q^{57} +(1.12538 + 2.18888i) q^{58} +(-35.6853 + 69.4084i) q^{59} +(-10.4851 + 3.15449i) q^{60} +(-38.1833 - 89.8529i) q^{61} +(23.9487 + 2.63511i) q^{62} +(10.0929 + 21.5300i) q^{63} +(-45.5266 + 13.6969i) q^{64} +(23.3232 - 0.852379i) q^{65} +(-15.1409 + 2.22828i) q^{66} +(-66.3189 - 17.3380i) q^{67} +(-47.1677 + 100.618i) q^{68} +(30.3679 - 36.4908i) q^{69} +(-3.18706 - 2.65229i) q^{70} +(5.28094 - 72.1532i) q^{71} +(-8.56451 + 3.27565i) q^{72} +(13.3047 + 20.1101i) q^{73} +(16.2366 - 18.1212i) q^{74} +(40.9959 - 42.5215i) q^{75} +(-12.7319 - 7.14547i) q^{76} +(83.0523 + 92.6919i) q^{77} +(-21.2532 + 2.33852i) q^{78} +(-24.3213 + 80.8406i) q^{79} +(-11.0777 + 11.4900i) q^{80} +(-43.7057 + 20.4884i) q^{81} +(5.41086 + 5.61222i) q^{82} +(52.9872 - 5.83025i) q^{83} +(-66.3449 - 47.4657i) q^{84} +(2.43763 + 33.3053i) q^{85} +(11.3090 + 24.1244i) q^{86} +(12.6898 + 7.12187i) q^{87} +(-37.9869 + 29.3325i) q^{88} +(114.223 - 21.0981i) q^{89} +(-0.861276 + 1.03493i) q^{90} +(111.227 + 133.653i) q^{91} +(13.2134 - 71.5364i) q^{92} +(126.685 - 65.1333i) q^{93} +(-18.2634 - 11.1460i) q^{94} -4.38746 q^{95} +(30.4130 - 36.5451i) q^{96} +(82.6959 - 24.8795i) q^{97} +(0.373249 - 10.2130i) q^{98} +(30.0997 - 26.9695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) $ 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/431\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{37}{86}\right)$

Coefficient data

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

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

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

$2$	−0.192896	+	0.375186i	−0.0964482	+	0.187593i	−0.932606	−	0.360896i	$-0.882471\pi$
$2$	−0.192896	+	0.375186i	−0.0964482	+	0.187593i	0.836158	+	0.548489i	$0.184797\pi$
$3$	0.272798	+	2.47928i	0.0909327	+	0.826426i	0.949509	+	0.313740i	$0.101582\pi$
$3$	0.272798	+	2.47928i	0.0909327	+	0.826426i	−0.858576	+	0.512686i	$0.828651\pi$
$4$	2.22388	+	3.10842i	0.555970	+	0.777104i
$5$	1.03997	+	0.487516i	0.207993	+	0.0975033i	0.525644	−	0.850704i	$-0.323824\pi$
$5$	1.03997	+	0.487516i	0.207993	+	0.0975033i	−0.317651	+	0.948208i	$0.602894\pi$
$6$	−0.982812	−	0.375894i	−0.163802	−	0.0626489i
$7$	1.86059	+	8.35245i	0.265798	+	1.19321i	0.905420	+	0.424517i	$0.139556\pi$
$7$	1.86059	+	8.35245i	0.265798	+	1.19321i	−0.639622	+	0.768690i	$0.720909\pi$
$8$	−3.26470	+	0.480465i	−0.408088	+	0.0600581i
$9$	2.71228	−	0.604186i	0.301365	−	0.0671318i
$10$	−0.383515	+	0.296141i	−0.0383515	+	0.0296141i
$11$	12.6832	−	7.11816i	1.15302	−	0.647106i	0.209300	−	0.977852i	$-0.432882\pi$
$11$	12.6832	−	7.11816i	1.15302	−	0.647106i	0.943720	+	0.330746i	$0.107300\pi$
$12$	−7.09996	+	6.36159i	−0.591663	+	0.530132i
$13$	18.0714	−	9.29113i	1.39010	−	0.714702i	0.409797	−	0.912177i	$-0.365600\pi$
$13$	18.0714	−	9.29113i	1.39010	−	0.714702i	0.980308	+	0.197475i	$0.0632741\pi$
$14$	−3.49262	−	0.913090i	−0.249473	−	0.0652207i
$15$	−0.924988	+	2.71136i	−0.0616658	+	0.180757i
$16$	−4.48674	+	13.1517i	−0.280422	+	0.821983i
$17$	14.2297	+	25.3547i	0.837044	+	1.49145i	0.870586	+	0.492016i	$0.163740\pi$
$17$	14.2297	+	25.3547i	0.837044	+	1.49145i	−0.0335421	+	0.999437i	$0.510679\pi$
$18$	−0.296507	+	1.13415i	−0.0164726	+	0.0630086i
$19$	−3.45876	+	1.62140i	−0.182040	+	0.0853370i	−0.513327	−	0.858193i	$-0.671587\pi$
$19$	−3.45876	+	1.62140i	−0.182040	+	0.0853370i	0.331287	+	0.943530i	$0.392517\pi$
$20$	0.797358	+	4.31683i	0.0398679	+	0.215841i
$21$	−20.2005	+	6.89144i	−0.961927	+	0.328164i
$22$	0.224089	+	6.13163i	0.0101859	+	0.278710i
$23$	−13.2107	−	13.7023i	−0.574376	−	0.595751i	0.368198	−	0.929747i	$-0.379975\pi$
$23$	−13.2107	−	13.7023i	−0.574376	−	0.595751i	−0.942574	+	0.333996i	$0.891603\pi$
$24$	−2.08181	−	7.96304i	−0.0867421	−	0.331793i
$25$	−15.1480	−	18.2022i	−0.605919	−	0.728087i
$26$			8.57234i			0.329705i
$27$	9.48593	+	27.8055i	0.351331	+	1.02983i
$28$	−21.8251	+	24.3583i	−0.779469	+	0.869940i
$29$	3.39464	−	4.74483i	0.117056	−	0.163615i	−0.750637	−	0.660715i	$-0.770253\pi$
$29$	3.39464	−	4.74483i	0.117056	−	0.163615i	0.867693	+	0.497100i	$0.165602\pi$
$30$	−0.838837	−	0.870054i	−0.0279612	−	0.0290018i
$31$	−20.4017	−	53.3424i	−0.658120	−	1.72072i	−0.692606	−	0.721316i	$-0.743537\pi$
$31$	−20.4017	−	53.3424i	−0.658120	−	1.72072i	0.0344855	−	0.999405i	$-0.489021\pi$
$32$	−13.2303	−	13.7226i	−0.413446	−	0.428832i
$33$	21.1079	+	29.5034i	0.639632	+	0.894042i
$34$	−12.2576	+	0.447971i	−0.360517	+	0.0131756i
$35$	−2.13701	+	9.59333i	−0.0610573	+	0.274095i
$36$	7.90985	+	7.08726i	0.219718	+	0.196868i
$37$	−55.7993	−	14.5878i	−1.50809	−	0.394266i	−0.595571	−	0.803303i	$-0.703074\pi$
$37$	−55.7993	−	14.5878i	−1.50809	−	0.394266i	−0.912518	+	0.409037i	$0.865865\pi$
$38$	0.0588559	−	1.61044i	0.00154884	−	0.0423800i
$39$	27.9651	+	42.2693i	0.717054	+	1.08383i
$40$	−3.62942	−	1.09193i	−0.0907354	−	0.0272982i
$41$	5.96657	−	17.4894i	0.145526	−	0.426572i	−0.849331	−	0.527861i	$-0.822994\pi$
$41$	5.96657	−	17.4894i	0.145526	−	0.426572i	0.994857	+	0.101289i	$0.0322967\pi$
$42$	1.31102	−	8.90826i	0.0312149	−	0.212102i
$43$	38.5993	−	49.9877i	0.897658	−	1.16251i	−0.0883972	−	0.996085i	$-0.528174\pi$
$43$	38.5993	−	49.9877i	0.897658	−	1.16251i	0.986055	−	0.166420i	$-0.0532209\pi$
$44$	50.3322	+	23.5947i	1.14391	+	0.536244i
$45$	3.11523	+	0.693948i	0.0692274	+	0.0154211i
$46$	7.68918	−	2.31333i	0.167156	−	0.0502898i
$47$	−3.70211	+	50.5817i	−0.0787682	+	1.07621i	0.800328	+	0.599562i	$0.204659\pi$
$47$	−3.70211	+	50.5817i	−0.0787682	+	1.07621i	−0.879096	+	0.476644i	$0.841853\pi$
$48$	−33.8308	−	7.53612i	−0.704807	−	0.157003i
$49$	−21.9346	+	10.2825i	−0.447645	+	0.209847i
$50$	9.75118	−	2.17217i	0.195024	−	0.0434434i
$51$	−58.9795	+	42.1962i	−1.15646	+	0.827377i
$52$	69.0692	+	35.5109i	1.32825	+	0.682903i
$53$	−59.7078	+	4.37005i	−1.12656	+	0.0824538i	−0.623520	−	0.781808i	$-0.714298\pi$
$53$	−59.7078	+	4.37005i	−1.12656	+	0.0824538i	−0.503043	+	0.864261i	$0.667786\pi$
$54$	−12.2620	−	1.80460i	−0.227075	−	0.0334185i
$55$	16.6603	−	1.21938i	0.302915	−	0.0221705i
$56$	−10.0873	−	26.3743i	−0.180131	−	0.470970i
$57$	−4.96345	−	8.13292i	−0.0870781	−	0.142683i
$58$	1.12538	+	2.18888i	0.0194031	+	0.0377393i
$59$	−35.6853	+	69.4084i	−0.604836	+	1.17641i	0.364622	+	0.931156i	$0.381198\pi$
$59$	−35.6853	+	69.4084i	−0.604836	+	1.17641i	−0.969458	+	0.245258i	$0.921127\pi$
$60$	−10.4851	+	3.15449i	−0.174752	+	0.0525749i
$61$	−38.1833	−	89.8529i	−0.625956	−	1.47300i	−0.864890	−	0.501962i	$-0.832612\pi$
$61$	−38.1833	−	89.8529i	−0.625956	−	1.47300i	0.238934	−	0.971036i	$-0.423202\pi$
$62$	23.9487	+	2.63511i	0.386270	+	0.0425017i
$63$	10.0929	+	21.5300i	0.160204	+	0.341747i
$64$	−45.5266	+	13.6969i	−0.711354	+	0.214014i
$65$	23.3232	−	0.852379i	0.358818	−	0.0131135i
$66$	−15.1409	+	2.22828i	−0.229407	+	0.0337618i
$67$	−66.3189	−	17.3380i	−0.989835	−	0.258777i	−0.277584	−	0.960701i	$-0.589534\pi$
$67$	−66.3189	−	17.3380i	−0.989835	−	0.258777i	−0.712251	+	0.701925i	$0.752324\pi$
$68$	−47.1677	+	100.618i	−0.693642	+	1.47967i
$69$	30.3679	−	36.4908i	0.440115	−	0.528853i
$70$	−3.18706	−	2.65229i	−0.0455294	−	0.0378899i
$71$	5.28094	−	72.1532i	0.0743794	−	1.01624i	−0.820997	−	0.570933i	$-0.806582\pi$
$71$	5.28094	−	72.1532i	0.0743794	−	1.01624i	0.895376	−	0.445310i	$-0.146907\pi$
$72$	−8.56451	+	3.27565i	−0.118951	+	0.0454951i
$73$	13.3047	+	20.1101i	0.182256	+	0.275480i	0.913673	−	0.406450i	$-0.133234\pi$
$73$	13.3047	+	20.1101i	0.182256	+	0.275480i	−0.731417	+	0.681931i	$0.761141\pi$
$74$	16.2366	−	18.1212i	0.219414	−	0.244880i
$75$	40.9959	−	42.5215i	0.546612	−	0.566954i
$76$	−12.7319	−	7.14547i	−0.167525	−	0.0940194i
$77$	83.0523	+	92.6919i	1.07860	+	1.20379i
$78$	−21.2532	+	2.33852i	−0.272477	+	0.0299810i
$79$	−24.3213	+	80.8406i	−0.307865	+	1.02330i	0.655520	+	0.755178i	$0.272449\pi$
$79$	−24.3213	+	80.8406i	−0.307865	+	1.02330i	−0.963385	+	0.268121i	$0.913597\pi$
$80$	−11.0777	+	11.4900i	−0.138472	+	0.143625i
$81$	−43.7057	+	20.4884i	−0.539576	+	0.252943i
$82$	5.41086	+	5.61222i	0.0659861	+	0.0684417i
$83$	52.9872	−	5.83025i	0.638400	−	0.0702440i	0.215621	−	0.976477i	$-0.430822\pi$
$83$	52.9872	−	5.83025i	0.638400	−	0.0702440i	0.422778	+	0.906233i	$0.361055\pi$
$84$	−66.3449	−	47.4657i	−0.789820	−	0.565068i
$85$	2.43763	+	33.3053i	0.0286780	+	0.391827i
$86$	11.3090	+	24.1244i	0.131500	+	0.280516i
$87$	12.6898	+	7.12187i	0.145860	+	0.0818606i
$88$	−37.9869	+	29.3325i	−0.431669	+	0.333324i
$89$	114.223	−	21.0981i	1.28341	−	0.237057i	0.504069	−	0.863663i	$-0.331836\pi$
$89$	114.223	−	21.0981i	1.28341	−	0.237057i	0.779336	+	0.626606i	$0.215557\pi$
$90$	−0.861276	+	1.03493i	−0.00956973	+	0.0114992i
$91$	111.227	+	133.653i	1.22227	+	1.46872i
$92$	13.2134	−	71.5364i	0.143624	−	0.777570i
$93$	126.685	−	65.1333i	1.36220	−	0.700358i
$94$	−18.2634	−	11.1460i	−0.194292	−	0.118575i
$95$	−4.38746			−0.0461838
$96$	30.4130	−	36.5451i	0.316802	−	0.380678i
$97$	82.6959	−	24.8795i	0.852535	−	0.256490i	0.168286	−	0.985738i	$-0.446177\pi$
$97$	82.6959	−	24.8795i	0.852535	−	0.256490i	0.684249	+	0.729248i	$0.260130\pi$
$98$	0.373249	−	10.2130i	0.00380866	−	0.104214i
$99$	30.0997	−	26.9695i	0.304038	−	0.272419i
$100$	22.8927	−	87.5656i	0.228927	−	0.875656i
$101$	23.4320	−	77.8847i	0.232000	−	0.771135i	−0.760548	−	0.649282i	$-0.775070\pi$
$101$	23.4320	−	77.8847i	0.232000	−	0.771135i	0.992548	−	0.121854i	$-0.0388838\pi$
$102$	−4.45449	−	30.2678i	−0.0436715	−	0.296743i
$103$	−71.2503	−	13.1606i	−0.691751	−	0.127773i	−0.175844	−	0.984418i	$-0.556266\pi$
$103$	−71.2503	−	13.1606i	−0.691751	−	0.127773i	−0.515906	+	0.856645i	$0.672545\pi$
$104$	−54.5336	+	39.0154i	−0.524361	+	0.375148i
$105$	−24.3675	−	2.68119i	−0.232071	−	0.0255351i
$106$	9.87784	−	23.2445i	0.0931872	−	0.219288i
$107$	−50.0796	+	89.2323i	−0.468034	+	0.833947i	−0.999917	−	0.0128705i	$-0.995903\pi$
$107$	−50.0796	+	89.2323i	−0.468034	+	0.833947i	0.531883	+	0.846818i	$0.321484\pi$
$108$	−65.3355	+	91.3223i	−0.604959	+	0.845577i
$109$	91.0418	−	51.0952i	0.835246	−	0.468763i	−0.0120222	−	0.999928i	$-0.503827\pi$
$109$	91.0418	−	51.0952i	0.835246	−	0.468763i	0.847269	+	0.531165i	$0.178245\pi$
$110$	−2.75622	+	6.48594i	−0.0250566	+	0.0589631i
$111$	20.9454	−	142.321i	0.188697	−	1.28218i
$112$	−118.197	−	13.0054i	−1.05533	−	0.116119i
$113$	8.78209	−	29.1904i	0.0777176	−	0.258322i	−0.909991	−	0.414628i	$-0.863912\pi$
$113$	8.78209	−	29.1904i	0.0777176	−	0.258322i	0.987709	+	0.156305i	$0.0499584\pi$
$114$	4.00879	−	0.293406i	0.0351648	−	0.00257373i
$115$	−7.05855	−	20.6903i	−0.0613787	−	0.179916i
$116$	22.2982			0.192226
$117$	43.4010	−	36.1186i	0.370949	−	0.308706i
$118$	−19.1575	−	26.7773i	−0.162352	−	0.226926i
$119$	−185.298	+	166.028i	−1.55713	+	1.39519i
$120$	1.71710	−	9.29621i	0.0143091	−	0.0774684i
$121$	47.1619	−	77.2777i	0.389768	−	0.638658i
$122$	41.0769	+	3.00644i	0.336696	+	0.0246430i
$123$	44.9888	+	10.0217i	0.365763	+	0.0814772i
$124$	120.439	−	182.044i	0.971284	−	1.46810i
$125$	−14.1423	−	54.0950i	−0.113138	−	0.432760i
$126$	−10.0246	−	0.366365i	−0.0795606	−	0.00290766i
$127$	201.849	−	22.2097i	1.58936	−	0.174879i	0.728982	−	0.684533i	$-0.239994\pi$
$127$	201.849	−	22.2097i	1.58936	−	0.174879i	0.860380	+	0.509654i	$0.170226\pi$
$128$	17.4923	−	94.7018i	0.136659	−	0.739858i
$129$	134.463	+	82.0618i	1.04235	+	0.636138i
$130$	−4.17916	+	8.91495i	−0.0321474	+	0.0685765i
$131$	−7.29170	+	49.5463i	−0.0556619	+	0.378216i	0.943271	+	0.332025i	$0.107732\pi$
$131$	−7.29170	+	49.5463i	−0.0556619	+	0.378216i	−0.998933	+	0.0461915i	$0.985292\pi$
$132$	−44.7674	+	131.224i	−0.339147	+	0.994121i
$133$	−19.9780	−	25.8724i	−0.150211	−	0.194529i
$134$	19.2977	−	21.5375i	0.144012	−	0.160727i
$135$	−3.69060	+	33.5414i	−0.0273378	+	0.248454i
$136$	−58.6380	−	75.9387i	−0.431162	−	0.558373i
$137$	7.85173	+	107.278i	0.0573119	+	0.783050i	0.945923	+	0.324390i	$0.105159\pi$
$137$	7.85173	+	107.278i	0.0573119	+	0.783050i	−0.888612	+	0.458660i	$0.848329\pi$
$138$	7.83299	+	18.4326i	0.0567608	+	0.133569i
$139$	−116.784	−	44.6662i	−0.840175	−	0.321340i	−0.101028	−	0.994884i	$-0.532213\pi$
$139$	−116.784	−	44.6662i	−0.840175	−	0.321340i	−0.739147	+	0.673544i	$0.764771\pi$
$140$	−34.5725	+	14.6917i	−0.246946	+	0.104941i
$141$	−126.416	+	4.62005i	−0.896568	+	0.0327663i
$142$	26.0522	+	15.8994i	0.183466	+	0.111968i
$143$	163.067	−	246.476i	1.14033	−	1.72361i
$144$	−4.22322	+	38.3820i	−0.0293279	+	0.266542i
$145$	5.84349	−	3.27953i	0.0402999	−	0.0226174i
$146$	−10.1114	+	1.11257i	−0.0692564	+	0.00762037i
$147$	−31.4769	−	51.5769i	−0.214129	−	0.350863i
$148$	−78.7459	−	205.889i	−0.532067	−	1.39114i
$149$	−145.866	−	68.3792i	−0.978967	−	0.458921i	−0.132396	−	0.991197i	$-0.542267\pi$
$149$	−145.866	−	68.3792i	−0.978967	−	0.458921i	−0.846571	+	0.532276i	$0.821337\pi$
$150$	8.04552	+	23.5833i	0.0536368	+	0.157222i
$151$	−71.5440	−	5.23634i	−0.473801	−	0.0346778i	−0.165994	−	0.986127i	$-0.553083\pi$
$151$	−71.5440	−	5.23634i	−0.473801	−	0.0346778i	−0.307807	+	0.951449i	$0.599595\pi$
$152$	10.5128	−	6.95521i	0.0691633	−	0.0457580i
$153$	53.9140	+	60.1717i	0.352379	+	0.393279i
$154$	−50.7972	+	13.2801i	−0.329852	+	0.0862345i
$155$	4.78816	−	65.4205i	0.0308914	−	0.422067i
$156$	−69.1995	+	180.929i	−0.443587	+	1.15980i
$157$	38.6918	−	91.0493i	0.246444	−	0.579932i	−0.750252	−	0.661152i	$-0.770068\pi$
$157$	38.6918	−	91.0493i	0.246444	−	0.579932i	0.996696	+	0.0812203i	$0.0258817\pi$
$158$	−25.6388	−	24.7189i	−0.162271	−	0.156449i
$159$	−27.1228	−	146.840i	−0.170583	−	0.923523i
$160$	−7.06904	−	20.7211i	−0.0441815	−	0.129507i
$161$	89.8679	−	135.836i	0.558186	−	0.843699i
$162$	0.743715	−	20.3499i	0.00459083	−	0.125617i
$163$	−39.8721	+	15.2498i	−0.244614	+	0.0935569i	−0.476462	−	0.879195i	$-0.658081\pi$
$163$	−39.8721	+	15.2498i	−0.244614	+	0.0935569i	0.231848	+	0.972752i	$0.425523\pi$
$164$	67.6333	−	20.3478i	0.412398	−	0.124072i
$165$	7.56809	+	40.9730i	0.0458672	+	0.248321i
$166$	−8.03361	+	21.0047i	−0.0483952	+	0.126534i
$167$	−117.684	+	113.462i	−0.704697	+	0.679413i	−0.957607	−	0.288077i	$-0.906984\pi$
$167$	−117.684	+	113.462i	−0.704697	+	0.679413i	0.252911	+	0.967490i	$0.418612\pi$
$168$	62.6375	−	32.2041i	0.372842	−	0.191691i
$169$	141.915	−	198.361i	0.839733	−	1.17373i
$170$	−12.9659	−	5.50990i	−0.0762699	−	0.0324112i
$171$	−8.40151	+	6.48744i	−0.0491317	+	0.0379382i
$172$	241.223	+	8.81583i	1.40246	+	0.0512548i
$173$	−108.097	−	177.124i	−0.624838	−	1.02384i	−0.995472	−	0.0950571i	$-0.969697\pi$
$173$	−108.097	−	177.124i	−0.624838	−	1.02384i	0.370634	−	0.928779i	$-0.379141\pi$
$174$	−5.11984	+	3.38726i	−0.0294244	+	0.0194670i
$175$	123.849	−	160.389i	0.707706	−	0.916510i
$176$	36.7098	+	198.743i	0.208578	+	1.12922i
$177$	−181.818	−	69.5394i	−1.02722	−	0.392878i
$178$	−14.1175	+	46.9246i	−0.0793119	+	0.263621i
$179$	−55.6595	−	31.2376i	−0.310947	−	0.174512i	0.326103	−	0.945334i	$-0.394264\pi$
$179$	−55.6595	−	31.2376i	−0.310947	−	0.174512i	−0.637050	+	0.770822i	$0.719846\pi$
$180$	4.77083	+	11.2267i	0.0265046	+	0.0623705i
$181$	−48.7263	+	218.740i	−0.269206	+	1.20851i	0.631949	+	0.775010i	$0.282255\pi$
$181$	−48.7263	+	218.740i	−0.269206	+	1.20851i	−0.901155	+	0.433496i	$0.857280\pi$
$182$	−71.6000	+	15.9496i	−0.393407	+	0.0876351i
$183$	212.354	−	119.179i	1.16040	−	0.651250i
$184$	49.7123	+	38.3866i	0.270176	+	0.208623i
$185$	−50.9176	−	42.3739i	−0.275230	−	0.229048i
$186$			60.0944i			0.323088i
$187$	360.958	+	220.289i	1.93026	+	1.17802i
$188$	−165.462	+	100.980i	−0.880117	+	0.537128i
$189$	−214.595	+	130.965i	−1.13542	+	0.692938i
$190$	0.846325	−	1.64611i	0.00445434	−	0.00866375i
$191$	−94.5109	+	122.396i	−0.494821	+	0.640815i	−0.971155	−	0.238449i	$-0.923361\pi$
$191$	−94.5109	+	122.396i	−0.494821	+	0.640815i	0.476333	+	0.879265i	$0.341966\pi$
$192$	−46.3781	−	109.137i	−0.241552	−	0.568420i
$193$	−33.6226	+	8.79010i	−0.174210	+	0.0455446i	−0.339011	−	0.940782i	$-0.610093\pi$
$193$	−33.6226	+	8.79010i	−0.174210	+	0.0455446i	0.164801	+	0.986327i	$0.447302\pi$
$194$	−6.61731	+	35.8255i	−0.0341098	+	0.184668i
$195$	8.47581	+	57.5921i	0.0434657	+	0.295344i
$196$	−80.7422	−	45.3147i	−0.411950	−	0.231198i
$197$	253.461	−	56.4608i	1.28660	−	0.286603i	0.479776	−	0.877391i	$-0.340718\pi$
$197$	253.461	−	56.4608i	1.28660	−	0.286603i	0.806827	+	0.590788i	$0.201183\pi$
$198$	4.31244	+	16.4953i	0.0217800	+	0.0833097i
$199$	10.3275	+	5.30975i	0.0518971	+	0.0266822i	0.482996	−	0.875622i	$-0.339548\pi$
$199$	10.3275	+	5.30975i	0.0518971	+	0.0266822i	−0.431099	+	0.902305i	$0.641874\pi$
$200$	58.1991	+	52.1467i	0.290996	+	0.260733i
$201$	24.8941	−	169.153i	0.123851	−	0.841556i
$202$	24.7013	+	23.8150i	0.122284	+	0.117896i
$203$	45.9470	+	19.5253i	0.226340	+	0.0961840i
$204$	−262.327	−	89.4935i	−1.28592	−	0.438693i
$205$	14.7314	−	15.2796i	0.0718605	−	0.0745348i
$206$	18.6816	−	24.1935i	0.0906873	−	0.117444i
$207$	−44.1097	−	29.1827i	−0.213090	−	0.140979i
$208$	41.1127	+	279.356i	0.197657	+	1.34306i
$209$	−32.3268	+	45.1846i	−0.154674	+	0.216194i
$210$	5.70635	−	8.62515i	0.0271731	−	0.0410721i
$211$	−231.004	+	192.243i	−1.09481	+	0.911105i	−0.996462	−	0.0840477i	$-0.973215\pi$
$211$	−231.004	+	192.243i	−1.09481	+	0.911105i	−0.0983445	+	0.995152i	$0.531355\pi$
$212$	−146.367	−	175.878i	−0.690410	−	0.829614i
$213$	180.329	−	6.59036i	0.846613	−	0.0309407i
$214$	−23.8185	−	36.0017i	−0.111302	−	0.168232i
$215$	64.5118	−	33.1678i	0.300055	−	0.154269i
$216$	−44.3283	−	86.2191i	−0.205224	−	0.399163i
$217$	407.580	−	269.652i	1.87825	−	1.24264i
$218$	1.60854	+	44.0137i	0.00737863	+	0.201898i
$219$	−46.2289	+	38.4720i	−0.211091	+	0.175671i
$220$	40.8409	+	49.0755i	0.185641	+	0.223070i
$221$	492.725	+	325.984i	2.22952	+	1.47504i
$222$	49.3567	+	35.3117i	0.222328	+	0.159062i
$223$	352.128	−	51.8225i	1.57905	−	0.232388i	0.701783	−	0.712391i	$-0.252388\pi$
$223$	352.128	−	51.8225i	1.57905	−	0.232388i	0.877267	+	0.480003i	$0.159365\pi$
$224$	90.0014	−	136.037i	0.401792	−	0.607310i
$225$	−52.0831	−	40.2172i	−0.231480	−	0.178743i
$226$	9.25780	+	8.92564i	0.0409637	+	0.0394940i
$227$	−113.297	+	332.101i	−0.499106	+	1.46300i	0.350994	+	0.936378i	$0.385844\pi$
$227$	−113.297	+	332.101i	−0.499106	+	1.46300i	−0.850100	+	0.526622i	$0.823458\pi$
$228$	14.2424	−	33.5151i	0.0624666	−	0.146996i
$229$	−96.9623	+	100.571i	−0.423416	+	0.439173i	−0.897305	−	0.441412i	$-0.854478\pi$
$229$	−96.9623	+	100.571i	−0.423416	+	0.439173i	0.473889	+	0.880585i	$0.342850\pi$
$230$	9.12428	+	1.34282i	0.0396708	+	0.00583833i
$231$	−207.152	+	231.196i	−0.896764	+	1.00085i
$232$	−8.80276	+	17.1215i	−0.0379429	+	0.0737995i
$233$	−79.9349	+	20.8977i	−0.343068	+	0.0896898i	−0.420460	−	0.907311i	$-0.638131\pi$
$233$	−79.9349	+	20.8977i	−0.343068	+	0.0896898i	0.0773920	+	0.997001i	$0.475341\pi$
$234$	5.17929	+	23.2506i	0.0221337	+	0.0993615i
$235$	−28.5095	+	50.7985i	−0.121317	+	0.216164i
$236$	−295.110	+	43.4312i	−1.25047	+	0.184031i
$237$	−207.061	−	38.2461i	−0.873676	−	0.161376i
$238$	−26.5480	−	101.547i	−0.111546	−	0.426670i
$239$	181.111	−	76.9640i	0.757788	−	0.322025i	0.0224704	−	0.999748i	$-0.492847\pi$
$239$	181.111	−	76.9640i	0.757788	−	0.322025i	0.735318	+	0.677722i	$0.237033\pi$
$240$	−31.5089	−	24.3304i	−0.131287	−	0.101376i
$241$	−169.524	−	87.1582i	−0.703419	−	0.361652i	0.0682579	−	0.997668i	$-0.478256\pi$
$241$	−169.524	−	87.1582i	−0.703419	−	0.361652i	−0.771676	+	0.636015i	$0.780582\pi$
$242$	19.8961	+	32.6010i	0.0822154	+	0.134715i
$243$	75.0235	+	122.931i	0.308739	+	0.505887i
$244$	194.385	−	318.512i	0.796659	−	1.30538i
$245$	−27.8241			−0.113568
$246$	−12.4382	+	14.9460i	−0.0505617	+	0.0607562i
$247$	−47.4399	+	61.4368i	−0.192064	+	0.248732i
$248$	92.2347	+	164.345i	0.371914	+	0.662680i
$249$	28.9096	+	129.780i	0.116103	+	0.521203i
$250$	23.0237	+	5.12874i	0.0920947	+	0.0205150i
$251$	51.7862	−	22.0067i	0.206320	−	0.0876763i	−0.285480	−	0.958385i	$-0.592153\pi$
$251$	51.7862	−	22.0067i	0.206320	−	0.0876763i	0.491800	+	0.870708i	$0.336339\pi$
$252$	−44.4790	+	79.2530i	−0.176504	+	0.314496i
$253$	−265.089	−	79.7533i	−1.04778	−	0.315230i
$254$	−30.6031	+	80.0150i	−0.120485	+	0.315020i
$255$	−81.9081	+	15.1292i	−0.321208	+	0.0593302i
$256$	−118.362	−	91.3962i	−0.462352	−	0.357016i
$257$	−184.921	−	279.509i	−0.719538	−	1.08758i	−0.992101	−	0.125445i	$-0.959964\pi$
$257$	−184.921	−	279.509i	−0.719538	−	1.08758i	0.272562	−	0.962138i	$-0.412129\pi$
$258$	−56.7259	+	34.6193i	−0.219868	+	0.134183i
$259$	18.0248	−	493.202i	0.0695937	−	1.90426i
$260$	54.5175	+	70.6026i	0.209683	+	0.271548i
$261$	6.34045	−	14.9203i	0.0242929	−	0.0571660i
$262$	−17.1825	−	12.2930i	−0.0655822	−	0.0469200i
$263$	205.363	+	399.433i	0.780846	+	1.51876i	0.853321	+	0.521386i	$0.174585\pi$
$263$	205.363	+	399.433i	0.780846	+	1.51876i	−0.0724744	+	0.997370i	$0.523090\pi$
$264$	−83.0863	−	86.1783i	−0.314721	−	0.326433i
$265$	−64.2246	−	24.5638i	−0.242357	−	0.0926937i
$266$	13.5606	−	2.50478i	0.0509798	−	0.00941645i
$267$	83.4678	+	277.435i	0.312614	+	1.03908i
$268$	−93.5915	−	244.704i	−0.349222	−	0.913076i
$269$	−346.554	−	12.6653i	−1.28830	−	0.0470829i	−0.616230	−	0.787566i	$-0.711341\pi$
$269$	−346.554	−	12.6653i	−1.28830	−	0.0470829i	−0.672075	+	0.740483i	$0.734597\pi$
$270$	−11.8723	−	7.85466i	−0.0439716	−	0.0290913i
$271$	−165.240	+	56.3719i	−0.609740	+	0.208014i	−0.610540	−	0.791985i	$-0.709048\pi$
$271$	−165.240	+	56.3719i	−0.609740	+	0.208014i	0.000800058		1.00000i	$0.499745\pi$
$272$	−397.303	+	73.3856i	−1.46067	+	0.269800i
$273$	−301.021	+	312.223i	−1.10264	+	1.14367i
$274$	−41.7637	−	17.7477i	−0.152422	−	0.0647725i
$275$	−321.691	−	123.036i	−1.16979	−	0.447405i
$276$	180.963	+	13.2448i	0.655664	+	0.0479884i
$277$	89.3605	+	341.809i	0.322601	+	1.23397i	0.906523	+	0.422157i	$0.138727\pi$
$277$	89.3605	+	341.809i	0.322601	+	1.23397i	−0.583922	+	0.811810i	$0.698483\pi$
$278$	39.2854	−	35.1999i	0.141314	−	0.126618i
$279$	−87.5640	−	132.353i	−0.313849	−	0.474384i
$280$	2.36743	−	32.3461i	0.00845512	−	0.115522i
$281$	351.887	−	120.047i	1.25227	−	0.427214i	0.384010	−	0.923329i	$-0.374543\pi$
$281$	351.887	−	120.047i	1.25227	−	0.427214i	0.868257	+	0.496115i	$0.165241\pi$
$282$	22.6518	−	48.3207i	0.0803256	−	0.171350i
$283$	385.165	−	147.313i	1.36101	−	0.520541i	0.435814	−	0.900037i	$-0.356461\pi$
$283$	385.165	−	147.313i	1.36101	−	0.520541i	0.925194	+	0.379496i	$0.123902\pi$
$284$	236.026	−	144.045i	0.831079	−	0.507200i
$285$	−1.19689	−	10.8777i	−0.00419962	−	0.0381675i
$286$	61.0193	+	108.725i	0.213354	+	0.380157i
$287$	157.181	+	17.2948i	0.547668	+	0.0602607i
$288$	−44.1753	−	29.2261i	−0.153386	−	0.101479i
$289$	−289.823	+	474.894i	−1.00285	+	1.64323i
$290$	0.103244	+	2.82500i	0.000356013	+	0.00974139i
$291$	84.2425	+	198.239i	0.289493	+	0.681234i
$292$	−32.9224	+	86.0789i	−0.112748	+	0.294791i
$293$	−149.416	+	63.4949i	−0.509952	+	0.216706i	−0.630772	−	0.775968i	$-0.717262\pi$
$293$	−149.416	+	63.4949i	−0.509952	+	0.216706i	0.120820	+	0.992674i	$0.461448\pi$
$294$	25.4227	−	1.86070i	0.0864718	−	0.00632892i
$295$	−70.9493	+	54.7853i	−0.240506	+	0.185713i
$296$	189.177	+	20.8154i	0.639112	+	0.0703223i
$297$	318.236	+	285.141i	1.07150	+	0.960071i
$298$	53.7919	−	41.5368i	0.180510	−	0.139385i
$299$	−366.044	−	124.877i	−1.22423	−	0.417648i
$300$	223.345	+	32.8695i	0.744482	+	0.109565i
$301$	489.337	+	229.392i	1.62571	+	0.762099i
$302$	15.7652	−	25.8322i	0.0522025	−	0.0855371i
$303$	199.490	+	36.8477i	0.658383	+	0.121609i
$304$	−5.80564	−	52.7635i	−0.0190975	−	0.173564i
$305$	4.09535	−	112.059i	0.0134274	−	0.367406i
$306$	−32.9754	+	8.62089i	−0.107763	+	0.0281729i
$307$	−372.100	−	246.179i	−1.21205	−	0.801886i	−0.226958	−	0.973905i	$-0.572878\pi$
$307$	−372.100	−	246.179i	−1.21205	−	0.801886i	−0.985094	+	0.172019i	$0.944971\pi$
$308$	−103.426	+	464.297i	−0.335800	+	1.50746i
$309$	13.1918	−	180.240i	0.0426920	−	0.583299i
$310$	23.6212	+	14.4158i	0.0761974	+	0.0465026i
$311$	460.874	+	85.1277i	1.48191	+	0.273723i	0.860374	−	0.509663i	$-0.170230\pi$
$311$	460.874	+	85.1277i	1.48191	+	0.273723i	0.621536	+	0.783386i	$0.286509\pi$
$312$	−111.607	−	124.561i	−0.357714	−	0.399233i
$313$	278.337	−	199.133i	0.889256	−	0.636208i	−0.0425777	−	0.999093i	$-0.513557\pi$
$313$	278.337	−	199.133i	0.889256	−	0.636208i	0.931834	+	0.362885i	$0.118208\pi$
$314$	26.6969	+	32.0797i	0.0850220	+	0.102165i
$315$			27.3110i			0.0867015i
$316$	−305.374	+	104.179i	−0.966373	+	0.329681i
$317$	18.3042	+	250.089i	0.0577418	+	0.788924i	0.944879	+	0.327419i	$0.106179\pi$
$317$	18.3042	+	250.089i	0.0577418	+	0.788924i	−0.887137	+	0.461505i	$0.847310\pi$
$318$	60.3242	+	18.1489i	0.189699	+	0.0570719i
$319$	9.28040	−	84.3433i	0.0290922	−	0.264399i
$320$	−54.0237	−	7.95064i	−0.168824	−	0.0248457i
$321$	−234.893	−	99.8189i	−0.731755	−	0.310962i
$322$	33.6284	+	59.9193i	0.104436	+	0.186085i
$323$	−90.3275	−	64.6238i	−0.279652	−	0.200074i
$324$	−160.883	−	90.2917i	−0.496551	−	0.278678i
$325$	−442.863	−	188.196i	−1.36266	−	0.579066i
$326$	1.96968	−	17.9011i	0.00604195	−	0.0549112i
$327$	151.515	+	211.779i	0.463349	+	0.647643i
$328$	−11.0760	+	59.9645i	−0.0337683	+	0.182819i
$329$	−429.369	+	63.1900i	−1.30507	+	0.192067i
$330$	−16.8323	−	5.06409i	−0.0510071	−	0.0153457i
$331$	181.928	+	47.5621i	0.549630	+	0.143692i	0.517330	−	0.855786i	$-0.326926\pi$
$331$	181.928	+	47.5621i	0.549630	+	0.143692i	0.0323004	+	0.999478i	$0.489717\pi$
$332$	135.960	+	151.740i	0.409518	+	0.457049i
$333$	−160.157	−	5.85317i	−0.480952	−	0.0175771i
$334$	−19.8684	−	66.0399i	−0.0594864	−	0.197724i
$335$	−60.5169	−	50.3625i	−0.180647	−	0.150336i
$336$		−	296.591i		−	0.882712i
$337$	−105.893	+	173.512i	−0.314222	+	0.514872i	−0.970958	−	0.239248i	$-0.923099\pi$
$337$	−105.893	+	173.512i	−0.314222	+	0.514872i	0.656737	+	0.754120i	$0.271936\pi$
$338$	47.0472	+	91.5074i	0.139193	+	0.270732i
$339$	74.7669	+	13.8101i	0.220551	+	0.0407379i
$340$	−98.1056	+	81.6441i	−0.288546	+	0.240130i
$341$	−638.459	−	531.330i	−1.87231	−	1.55815i
$342$	−0.813373	−	4.40353i	−0.00237828	−	0.0128758i
$343$	129.571	+	167.799i	0.377757	+	0.489211i
$344$	−101.998	+	181.741i	−0.296505	+	0.528316i
$345$	49.3715	−	23.1444i	0.143106	−	0.0670852i
$346$	87.3058	−	6.38996i	0.252329	−	0.0184681i
$347$	−69.7978	+	97.5595i	−0.201146	+	0.281151i	−0.901622	−	0.432525i	$-0.857623\pi$
$347$	−69.7978	+	97.5595i	−0.201146	+	0.281151i	0.700475	+	0.713677i	$0.252971\pi$
$348$	6.08290	+	55.2834i	0.0174796	+	0.158860i
$349$	207.973	−	200.511i	0.595912	−	0.574531i	−0.333881	−	0.942615i	$-0.608358\pi$
$349$	207.973	−	200.511i	0.595912	−	0.574531i	0.929792	+	0.368084i	$0.119986\pi$
$350$	36.2858	+	77.4047i	0.103674	+	0.221156i
$351$	429.768	+	414.349i	1.22441	+	1.18048i
$352$	−265.482	−	79.8718i	−0.754211	−	0.226908i
$353$	−5.62802	−	51.1492i	−0.0159434	−	0.144899i	0.983385	−	0.181530i	$-0.0581048\pi$
$353$	−5.62802	−	51.1492i	−0.0159434	−	0.144899i	−0.999329	+	0.0366310i	$0.988337\pi$
$354$	61.1621	−	54.8015i	0.172774	−	0.154807i
$355$	40.6679	−	72.4624i	0.114557	−	0.204120i
$356$	319.600	+	308.133i	0.897753	+	0.865542i
$357$	−462.178	−	414.113i	−1.29462	−	1.15998i
$358$	22.4564	−	14.8570i	0.0627274	−	0.0415001i
$359$	222.715	+	582.311i	0.620376	+	1.62204i	0.773477	+	0.633825i	$0.218516\pi$
$359$	222.715	+	582.311i	0.620376	+	1.62204i	−0.153101	+	0.988211i	$0.548926\pi$
$360$	−10.5037	−	0.768774i	−0.0291770	−	0.00213548i
$361$	−221.588	+	266.266i	−0.613817	+	0.737578i
$362$	−72.6689	−	60.4755i	−0.200743	−	0.167059i
$363$	204.458	+	95.8462i	0.563247	+	0.264039i
$364$	−168.094	+	642.968i	−0.461796	+	1.76640i
$365$	4.03245	+	27.4000i	0.0110478	+	0.0750686i
$366$	3.75190	+	102.661i	0.0102511	+	0.280495i
$367$	−71.9202	−	239.053i	−0.195968	−	0.651370i	−0.998500	−	0.0547601i	$-0.982561\pi$
$367$	−71.9202	−	239.053i	−0.195968	−	0.651370i	0.802532	−	0.596610i	$-0.203486\pi$
$368$	239.481	−	112.264i	0.650764	−	0.305066i
$369$	5.61613	−	51.0412i	0.0152199	−	0.138323i
$370$	25.7199	−	10.9298i	0.0695133	−	0.0295399i
$371$	−147.592	−	490.576i	−0.397823	−	1.32231i
$372$	484.194	+	248.941i	1.30160	+	0.669196i
$373$	169.227	−	87.0057i	0.453692	−	0.233259i	−0.215272	−	0.976554i	$-0.569064\pi$
$373$	169.227	−	87.0057i	0.453692	−	0.233259i	0.668964	+	0.743295i	$0.266738\pi$
$374$	−152.277	+	92.9333i	−0.407158	+	0.248485i
$375$	130.259	−	49.8197i	0.347356	−	0.132852i
$376$	−12.2165	−	166.913i	−0.0324906	−	0.443918i
$377$	17.2609	−	117.286i	0.0457848	−	0.311102i
$378$	−7.74178	−	105.776i	−0.0204809	−	0.279830i
$379$	−217.517	+	423.072i	−0.573922	+	1.11629i	0.405430	+	0.914126i	$0.367122\pi$
$379$	−217.517	+	423.072i	−0.573922	+	1.11629i	−0.979352	+	0.202160i	$0.935204\pi$
$380$	−9.75718	−	13.6380i	−0.0256768	−	0.0358896i
$381$	110.128	+	494.381i	0.289050	+	1.29759i
$382$	−27.6903	−	59.0688i	−0.0724878	−	0.154630i
$383$	−93.0503	+	417.716i	−0.242951	+	1.09064i	0.688060	+	0.725654i	$0.258462\pi$
$383$	−93.0503	+	417.716i	−0.242951	+	1.09064i	−0.931011	+	0.364990i	$0.881072\pi$
$384$	239.564	+	17.5338i	0.623864	+	0.0456610i
$385$	41.1828	+	136.886i	0.106968	+	0.355548i
$386$	3.18775	−	14.3103i	0.00825843	−	0.0370733i
$387$	74.4902	−	158.902i	0.192481	−	0.410599i
$388$	261.242	+	201.724i	0.673303	+	0.519908i
$389$	204.750	+	30.1330i	0.526350	+	0.0774627i	0.403530	−	0.914966i	$-0.367783\pi$
$389$	204.750	+	30.1330i	0.526350	+	0.0774627i	0.122820	+	0.992429i	$0.460806\pi$
$390$	−23.2427	−	7.92931i	−0.0595967	−	0.0203316i
$391$	159.433	−	529.932i	0.407757	−	1.35533i
$392$	66.6696	−	44.1082i	0.170075	−	0.112521i
$393$	−124.828	−	4.56202i	−0.317629	−	0.0116082i
$394$	−27.7083	+	105.986i	−0.0703258	+	0.269000i
$395$	−64.7045	+	72.2145i	−0.163809	+	0.182822i
$396$	150.771	+	33.5856i	0.380734	+	0.0848121i
$397$	−22.9095	−	626.860i	−0.0577065	−	1.57899i	−0.641521	−	0.767105i	$-0.721696\pi$
$397$	−22.9095	−	626.860i	−0.0577065	−	1.57899i	0.583815	−	0.811887i	$-0.301559\pi$
$398$	−3.98428	+	2.85051i	−0.0100108	+	0.00716209i
$399$	58.6949	−	56.5890i	0.147105	−	0.141827i
$400$	307.355	−	117.553i	0.768388	−	0.293883i
$401$	294.945	−	284.362i	0.735523	−	0.709133i	−0.228914	−	0.973447i	$-0.573517\pi$
$401$	294.945	−	284.362i	0.735523	−	0.709133i	0.964437	+	0.264313i	$0.0851454\pi$
$402$	58.6618	+	41.9689i	0.145925	+	0.104400i
$403$	−864.298	−	774.414i	−2.14466	−	1.92162i
$404$	294.208	−	100.370i	0.728237	−	0.248440i
$405$	−55.4408			−0.136891
$406$	−16.1886	+	13.4723i	−0.0398735	+	0.0331830i
$407$	−811.553	+	212.168i	−1.99399	+	0.521297i
$408$	172.277	−	166.096i	0.422247	−	0.407097i
$409$	−468.803	+	17.1331i	−1.14622	+	0.0418901i	−0.603028	−	0.797720i	$-0.706039\pi$
$409$	−468.803	+	17.1331i	−1.14622	+	0.0418901i	−0.543189	+	0.839610i	$0.682783\pi$
$410$	2.89106	+	8.47440i	0.00705137	+	0.0206693i
$411$	−263.830	+	48.7318i	−0.641922	+	0.118569i
$412$	−117.544	−	250.743i	−0.285300	−	0.608600i
$413$	−646.126	−	168.919i	−1.56447	−	0.409006i
$414$	19.4575	−	10.9201i	0.0469989	−	0.0263771i
$415$	57.9473	+	19.7689i	0.139632	+	0.0476358i
$416$	−366.588	−	125.062i	−0.881221	−	0.300631i
$417$	78.8814	−	301.726i	0.189164	−	0.723563i
$418$	−10.7169	−	20.8445i	−0.0256385	−	0.0498673i
$419$	254.794	+	284.367i	0.608100	+	0.678680i	0.967024	−	0.254687i	$-0.0819724\pi$
$419$	254.794	+	284.367i	0.608100	+	0.678680i	−0.358924	+	0.933367i	$0.616856\pi$
$420$	−45.8562	−	81.7070i	−0.109181	−	0.194540i
$421$	−59.6215	−	77.2124i	−0.141619	−	0.183402i	0.715357	−	0.698759i	$-0.246264\pi$
$421$	−59.6215	−	77.2124i	−0.141619	−	0.183402i	−0.856976	+	0.515357i	$0.827659\pi$
$422$	−27.5670	−	123.752i	−0.0653247	−	0.293252i
$423$	20.5196	+	139.429i	0.0485098	+	0.329618i
$424$	192.829	−	42.9544i	0.454785	−	0.101308i
$425$	245.959	−	643.085i	0.578727	−	1.51314i
$426$	−32.3121	+	68.9280i	−0.0758500	+	0.161803i
$427$	679.448	−	486.103i	1.59121	−	1.13841i
$428$	−388.742	+	42.7738i	−0.908276	+	0.0999388i
$429$	655.568	+	337.051i	1.52813	+	0.785666i
$430$			30.6019i			0.0711671i
$431$	372.236	−	217.260i	0.863656	−	0.504082i
$431$	372.236	−	217.260i	0.863656	−	0.504082i
$432$	−408.251			−0.945026
$433$	−48.1669	+	93.6852i	−0.111240	+	0.216363i	−0.938358	−	0.345665i	$-0.887653\pi$
$433$	−48.1669	+	93.6852i	−0.111240	+	0.216363i	0.827118	+	0.562028i	$0.189979\pi$
$434$	22.5491	+	204.933i	0.0519564	+	0.472196i
$435$	9.72495	+	13.5930i	0.0223562	+	0.0312483i
$436$	361.291	+	169.366i	0.828649	+	0.388455i
$437$	67.9094	+	25.9732i	0.155399	+	0.0594351i
$438$	−5.51676	−	24.7656i	−0.0125953	−	0.0565424i
$439$	−97.0963	+	14.2896i	−0.221176	+	0.0325504i	−0.255277	−	0.966868i	$-0.582167\pi$
$439$	−97.0963	+	14.2896i	−0.221176	+	0.0325504i	0.0341007	+	0.999418i	$0.489143\pi$
$440$	−53.8052	+	11.9856i	−0.122285	+	0.0272401i
$441$	−53.2802	+	41.1417i	−0.120817	+	0.0932917i
$442$	−217.349	+	121.982i	−0.491740	+	0.275978i
$443$	−148.257	+	132.839i	−0.334667	+	0.299863i	−0.817591	−	0.575799i	$-0.804691\pi$
$443$	−148.257	+	132.839i	−0.334667	+	0.299863i	0.482924	+	0.875662i	$0.339575\pi$
$444$	488.974	−	251.399i	1.10129	−	0.566214i
$445$	129.074	+	33.7443i	0.290054	+	0.0758299i
$446$	−48.4811	+	142.110i	−0.108702	+	0.318632i
$447$	129.739	−	380.296i	0.290244	−	0.850775i
$448$	−199.109	−	354.774i	−0.444440	−	0.791907i
$449$	−24.3497	+	93.1388i	−0.0542309	+	0.207436i	−0.989024	−	0.147758i	$-0.952794\pi$
$449$	−24.3497	+	93.1388i	−0.0542309	+	0.207436i	0.934793	+	0.355194i	$0.115585\pi$
$450$	25.1356	−	11.7831i	0.0558568	−	0.0261846i
$451$	−48.8174	−	264.293i	−0.108243	−	0.586016i
$452$	110.266	−	37.6176i	0.243952	−	0.0832248i
$453$	−6.53471	−	178.806i	−0.0144254	−	0.394715i
$454$	−102.745	−	106.568i	−0.226310	−	0.234732i
$455$	50.5142	+	193.220i	0.111020	+	0.424659i
$456$	20.1118	+	24.1668i	0.0441048	+	0.0529974i
$457$			552.999i			1.21006i	0.796202	+	0.605031i	$0.206839\pi$
$457$			552.999i			1.21006i	−0.796202	+	0.605031i	$0.793161\pi$
$458$	−19.0290	−	55.7786i	−0.0415481	−	0.121787i
$459$	−570.018	+	636.178i	−1.24187	+	1.38601i
$460$	48.6167	−	67.9537i	0.105688	−	0.147725i
$461$	144.069	+	149.430i	0.312514	+	0.324144i	0.857680	−	0.514184i	$-0.171905\pi$
$461$	144.069	+	149.430i	0.312514	+	0.324144i	−0.545166	+	0.838328i	$0.683533\pi$
$462$	−46.7825	−	122.318i	−0.101261	−	0.264756i
$463$	186.215	+	193.145i	0.402193	+	0.417160i	0.890121	−	0.455724i	$-0.150619\pi$
$463$	186.215	+	193.145i	0.402193	+	0.417160i	−0.487929	+	0.872884i	$0.662247\pi$
$464$	47.1719	+	65.9342i	0.101663	+	0.142100i
$465$	163.502	−	5.97540i	0.351617	−	0.0128503i
$466$	7.57862	−	34.0215i	0.0162631	−	0.0730076i
$467$	449.789	+	403.013i	0.963146	+	0.862982i	0.990621	−	0.136640i	$-0.0436304\pi$
$467$	449.789	+	403.013i	0.963146	+	0.862982i	−0.0274750	+	0.999622i	$0.508747\pi$
$468$	208.790	+	54.5850i	0.446133	+	0.116635i
$469$	21.4229	−	586.184i	0.0456779	−	1.24986i
$470$	−13.5595	−	20.4952i	−0.0288500	−	0.0436068i
$471$	236.292	+	71.0895i	0.501681	+	0.150933i
$472$	83.1537	−	243.743i	0.176173	−	0.516406i
$473$	133.742	−	908.761i	0.282753	−	1.92127i
$474$	54.2907	−	70.3089i	0.114537	−	0.148331i
$475$	81.9063	+	38.3961i	0.172434	+	0.0808339i
$476$	−928.164	−	206.757i	−1.94992	−	0.434364i
$477$	−159.304	+	47.9275i	−0.333971	+	0.100477i
$478$	−6.05992	+	82.7965i	−0.0126777	+	0.173214i
$479$	−219.939	−	48.9936i	−0.459164	−	0.102283i	−0.0182516	−	0.999833i	$-0.505810\pi$
$479$	−219.939	−	48.9936i	−0.459164	−	0.102283i	−0.440912	+	0.897550i	$0.645345\pi$
$480$	49.4448	−	23.1788i	0.103010	−	0.0482891i
$481$	−1143.91	+	254.816i	−2.37818	+	0.529763i
$482$	65.4011	−	46.7904i	0.135687	−	0.0970756i
$483$	361.290	+	185.752i	0.748012	+	0.384580i
$484$	345.093	−	25.2576i	0.713003	−	0.0521851i
$485$	98.1302	+	14.4418i	0.202330	+	0.0297768i
$486$	−60.5936	+	4.43488i	−0.124678	+	0.00912526i
$487$	−173.489	−	453.605i	−0.356240	−	0.931427i	−0.987748	−	0.156057i	$-0.950122\pi$
$487$	−173.489	−	453.605i	−0.356240	−	0.931427i	0.631508	−	0.775370i	$-0.282436\pi$
$488$	167.828	+	274.997i	0.343911	+	0.563519i
$489$	−48.6855	−	94.6939i	−0.0995613	−	0.193648i
$490$	5.36717	−	10.4392i	0.0109534	−	0.0213045i
$491$	−197.489	+	59.4156i	−0.402218	+	0.121009i	−0.482783	−	0.875740i	$-0.660374\pi$
$491$	−197.489	+	59.4156i	−0.402218	+	0.121009i	0.0805652	+	0.996749i	$0.474327\pi$
$492$	68.8982	+	162.131i	0.140037	+	0.329535i
$493$	168.609	+	18.5522i	0.342005	+	0.0376313i
$494$	−13.8992	−	29.6497i	−0.0281361	−	0.0600196i
$495$	44.4508	−	13.3733i	0.0897996	−	0.0270167i
$496$	793.081	−	28.9843i	1.59895	−	0.0584360i
$497$	612.482	−	90.1386i	1.23236	−	0.181365i
$498$	−54.2680	−	14.1875i	−0.108972	−	0.0284890i
$499$	264.472	−	564.170i	0.530004	−	1.13060i	−0.442297	−	0.896869i	$-0.645836\pi$
$499$	264.472	−	564.170i	0.530004	−	1.13060i	0.972301	−	0.233733i	$-0.0750941\pi$
$500$	136.699	−	164.261i	0.273398	−	0.328522i
$501$	−313.408	−	260.820i	−0.625565	−	0.520599i
$502$	−1.73275	+	23.6745i	−0.00345169	+	0.0471603i
$503$	−687.840	+	263.076i	−1.36747	+	0.523015i	−0.927105	−	0.374802i	$-0.877711\pi$
$503$	−687.840	+	263.076i	−1.36747	+	0.523015i	−0.440370	+	0.897816i	$0.645153\pi$
$504$	−43.2947	−	65.4399i	−0.0859021	−	0.129841i
$505$	62.3385	−	69.5740i	0.123443	−	0.137770i
$506$	81.0569	−	84.0733i	0.160191	−	0.166153i
$507$	530.505	+	297.734i	1.04636	+	0.587246i
$508$	517.925	+	578.039i	1.01954	+	1.13787i
$509$	123.748	−	13.6162i	0.243121	−	0.0267509i	0.0130101	−	0.999915i	$-0.495859\pi$
$509$	123.748	−	13.6162i	0.243121	−	0.0267509i	0.230111	+	0.973164i	$0.426091\pi$
$510$	10.1235	−	33.6491i	0.0198500	−	0.0659786i
$511$	−143.214	+	148.543i	−0.280262	+	0.290691i
$512$	405.914	−	190.285i	0.792801	−	0.371650i
$513$	−77.8935	−	80.7922i	−0.151839	−	0.157490i
$514$	140.538	−	15.4636i	0.273421	−	0.0300849i
$515$	−67.6819	−	48.4223i	−0.131421	−	0.0940238i
$516$	43.9483	+	600.463i	0.0851711	+	1.16369i
$517$	313.094	+	667.891i	0.605599	+	1.29186i
$518$	181.566	+	101.900i	0.350513	+	0.196717i
$519$	409.650	−	316.322i	0.789307	−	0.609483i
$520$	−75.7338	+	13.9887i	−0.145642	+	0.0269014i
$521$	−500.273	+	601.141i	−0.960217	+	1.15382i	0.0278208	+	0.999613i	$0.491143\pi$
$521$	−500.273	+	601.141i	−0.960217	+	1.15382i	−0.988038	+	0.154208i	$0.950717\pi$
$522$	4.37484	+	5.25692i	0.00838092	+	0.0100707i
$523$	76.7245	−	415.380i	0.146701	−	0.794225i	−0.826266	−	0.563280i	$-0.809539\pi$
$523$	76.7245	−	415.380i	0.146701	−	0.794225i	0.972967	−	0.230945i	$-0.0741817\pi$
$524$	−170.226	+	87.5194i	−0.324859	+	0.167022i
$525$	431.435	+	263.301i	0.821782	+	0.501526i
$526$	−189.475			−0.360219
$527$	1062.17	−	1276.33i	2.01550	−	2.42188i
$528$	−482.726	+	145.231i	−0.914254	+	0.275058i
$529$	6.08918	−	166.615i	0.0115107	−	0.314962i
$530$	21.6047	−	19.3579i	0.0407636	−	0.0365243i
$531$	−54.8530	+	209.816i	−0.103301	+	0.395133i
$532$	35.9934	−	119.637i	0.0676568	−	0.224882i
$533$	−54.6726	−	371.494i	−0.102575	−	0.696987i
$534$	−120.190	−	22.2003i	−0.225076	−	0.0415736i
$535$	−95.5834	+	68.3840i	−0.178660	+	0.127821i
$536$	224.842	+	24.7397i	0.419481	+	0.0461561i
$537$	62.2629	−	146.517i	0.115946	−	0.272843i
$538$	71.6008	−	127.579i	0.133087	−	0.237136i
$539$	−205.009	+	286.549i	−0.380350	+	0.531632i
$540$	−112.468	+	63.1200i	−0.208274	+	0.116889i
$541$	80.6369	−	189.754i	0.149052	−	0.350747i	−0.828957	−	0.559312i	$-0.811065\pi$
$541$	80.6369	−	189.754i	0.149052	−	0.350747i	0.978009	+	0.208565i	$0.0668792\pi$
$542$	10.7242	−	72.8695i	0.0197863	−	0.134446i
$543$	−555.609	−	61.1344i	−1.02322	−	0.112586i
$544$	159.670	−	530.719i	0.293510	−	0.975587i
$545$	119.590	−	8.75287i	0.219432	−	0.0160603i
$546$	−59.0758	−	173.165i	−0.108197	−	0.317153i
$547$	−310.199			−0.567091			−0.283545	−	0.958959i	$-0.591511\pi$
$547$	−310.199			−0.567091			−0.283545	+	0.958959i	$0.591511\pi$
$548$	−316.003	+	262.980i	−0.576648	+	0.479890i
$549$	−157.852	−	220.636i	−0.287526	−	0.401888i
$550$	108.215	−	96.9606i	0.196754	−	0.176292i
$551$	−4.04797	+	21.9153i	−0.00734658	+	0.0397737i
$552$	−81.6097	+	133.722i	−0.147844	+	0.242251i
$553$	−720.469	−	52.7315i	−1.30284	−	0.0953554i
$554$	−145.479	−	32.4069i	−0.262598	−	0.0584961i
$555$	91.1665	−	137.798i	0.164264	−	0.248285i
$556$	−120.873	−	462.346i	−0.217398	−	0.831558i
$557$	888.609	+	32.4755i	1.59535	+	0.0583043i	0.819675	−	0.572829i	$-0.194154\pi$
$557$	888.609	+	32.4755i	1.59535	+	0.0583043i	0.775674	+	0.631134i	$0.217410\pi$
$558$	66.5477	−	7.32233i	0.119261	−	0.0131225i
$559$	233.099	−	1261.98i	0.416993	−	2.25756i
$560$	−116.581	−	71.1481i	−0.208180	−	0.127050i
$561$	−447.690	+	955.010i	−0.798022	+	1.70233i
$562$	−22.8377	+	155.180i	−0.0406365	+	0.276120i
$563$	−43.4876	+	127.473i	−0.0772427	+	0.226417i	−0.978266	−	0.207354i	$-0.933515\pi$
$563$	−43.4876	+	127.473i	−0.0772427	+	0.226417i	0.901023	+	0.433771i	$0.142817\pi$
$564$	−295.495	−	382.679i	−0.523928	−	0.678509i
$565$	23.3639	−	26.0756i	0.0413520	−	0.0461516i
$566$	−19.0271	+	172.925i	−0.0336168	+	0.305521i
$567$	−252.446	−	326.929i	−0.445231	−	0.576594i
$568$	17.4264	+	238.096i	0.0306803	+	0.419184i
$569$	−284.699	−	669.952i	−0.500349	−	1.17742i	−0.957605	−	0.288085i	$-0.906982\pi$
$569$	−284.699	−	669.952i	−0.500349	−	1.17742i	0.457256	−	0.889335i	$-0.348832\pi$
$570$	4.31205	+	1.64922i	0.00756499	+	0.00289336i
$571$	−61.3485	+	26.0703i	−0.107441	+	0.0456573i	−0.444158	−	0.895948i	$-0.646497\pi$
$571$	−61.3485	+	26.0703i	−0.107441	+	0.0456573i	0.336718	+	0.941606i	$0.390683\pi$
$572$	1128.79	−	41.2533i	1.97341	−	0.0721212i
$573$	−329.235	−	200.929i	−0.574582	−	0.350662i
$574$	−36.8084	+	55.6359i	−0.0641261	+	0.0969267i
$575$	−49.2967	+	448.024i	−0.0857334	+	0.779173i
$576$	−115.206	+	64.6565i	−0.200010	+	0.112251i
$577$	1040.15	−	114.449i	1.80269	−	0.198353i	0.855236	−	0.518238i	$-0.173412\pi$
$577$	1040.15	−	114.449i	1.80269	−	0.198353i	0.947456	+	0.319886i	$0.103645\pi$
$578$	−122.268	−	200.343i	−0.211535	−	0.346614i
$579$	−30.9653	−	80.9619i	−0.0534806	−	0.139830i
$580$	23.1894	+	10.8707i	0.0399817	+	0.0187426i
$581$	147.284	+	431.725i	0.253501	+	0.743072i
$582$	−90.6266	−	6.63301i	−0.155716	−	0.0113969i
$583$	−726.181	+	480.436i	−1.24559	+	0.824076i
$584$	−53.0981	−	59.2610i	−0.0909213	−	0.101474i
$585$	62.7440	−	16.4034i	0.107255	−	0.0280401i
$586$	4.99940	−	68.3066i	0.00853140	−	0.116564i
$587$	−267.473	+	699.335i	−0.455661	+	1.19137i	0.491575	+	0.870835i	$0.336421\pi$
$587$	−267.473	+	699.335i	−0.455661	+	1.19137i	−0.947236	+	0.320536i	$0.896137\pi$
$588$	90.3215	−	212.544i	0.153608	−	0.361470i
$589$	157.054	+	151.419i	0.266645	+	0.257079i
$590$	−6.86879	−	37.1870i	−0.0116420	−	0.0630289i
$591$	209.126	+	612.997i	0.353850	+	1.03722i
$592$	442.212	−	668.405i	0.746980	−	1.12906i
$593$	−17.2227	+	471.256i	−0.0290434	+	0.794699i	0.902419	+	0.430860i	$0.141790\pi$
$593$	−17.2227	+	471.256i	−0.0290434	+	0.794699i	−0.931462	+	0.363838i	$0.881466\pi$
$594$	−168.367	+	64.3951i	−0.283447	+	0.108409i
$595$	−273.645	+	82.3275i	−0.459908	+	0.138366i
$596$	−111.838	−	605.480i	−0.187647	−	1.01591i
$597$	−10.3470	+	27.0533i	−0.0173317	+	0.0453154i
$598$	117.461	−	113.246i	0.196422	−	0.189375i
$599$	−733.708	+	377.225i	−1.22489	+	0.629758i	−0.943988	−	0.329979i	$-0.892958\pi$
$599$	−733.708	+	377.225i	−1.22489	+	0.629758i	−0.280899	+	0.959737i	$0.590633\pi$
$600$	−113.409	+	158.517i	−0.189016	+	0.264196i
$601$	−588.060	−	249.899i	−0.978470	−	0.415805i	−0.157965	−	0.987445i	$-0.550493\pi$
$601$	−588.060	−	249.899i	−0.978470	−	0.415805i	−0.820504	+	0.571640i	$0.806307\pi$
$602$	−180.456	+	139.344i	−0.299761	+	0.231468i
$603$	−190.351	−	6.95664i	−0.315673	−	0.0115367i
$604$	−142.828	−	234.033i	−0.236471	−	0.387472i
$605$	86.7209	−	57.3740i	0.143340	−	0.0948331i
$606$	−52.3056	+	67.7380i	−0.0863129	+	0.111779i
$607$	−48.6828	−	263.564i	−0.0802023	−	0.434208i	−0.999202	−	0.0399492i	$-0.987280\pi$
$607$	−48.6828	−	263.564i	−0.0802023	−	0.434208i	0.918999	−	0.394259i	$-0.128999\pi$
$608$	68.0103	+	26.0117i	0.111859	+	0.0427825i
$609$	−35.8745	+	119.242i	−0.0589073	+	0.195799i
$610$	41.2529	+	23.1523i	0.0676278	+	0.0379546i
$611$	403.059	+	948.477i	0.659671	+	1.55234i
$612$	−67.1401	+	301.402i	−0.109706	+	0.492487i
$613$	−590.972	+	131.645i	−0.964066	+	0.214755i	−0.671099	−	0.741368i	$-0.734177\pi$
$613$	−590.972	+	131.645i	−0.964066	+	0.214755i	−0.292967	+	0.956123i	$0.594643\pi$
$614$	164.140	−	92.1196i	0.267328	−	0.150032i
$615$	41.9011	+	32.3550i	0.0681320	+	0.0526098i
$616$	−315.676	−	262.708i	−0.512462	−	0.426474i
$617$			289.013i			0.468416i	0.972186	+	0.234208i	$0.0752498\pi$
$617$			289.013i			0.468416i	−0.972186	+	0.234208i	$0.924750\pi$
$618$	65.0787	+	39.7169i	0.105305	+	0.0642669i
$619$	558.485	−	340.838i	0.902237	−	0.550627i	0.00887286	−	0.999961i	$-0.497176\pi$
$619$	558.485	−	340.838i	0.902237	−	0.550627i	0.893364	+	0.449333i	$0.148338\pi$
$620$	214.002	−	130.604i	0.345165	−	0.210651i
$621$	255.684	−	497.308i	0.411729	−	0.800818i
$622$	−120.840	+	156.493i	−0.194276	+	0.251596i
$623$	388.742	+	914.787i	0.623984	+	1.46836i
$624$	−681.387	+	178.138i	−1.09197	+	0.285477i
$625$	−95.8679	+	519.021i	−0.153389	+	0.830433i
$626$	21.0217	+	142.840i	0.0335810	+	0.228179i
$627$	−120.844	−	67.8209i	−0.192734	−	0.108167i
$628$	369.065	−	82.2127i	0.587683	−	0.130912i
$629$	−424.139	−	1622.36i	−0.674307	−	2.57926i
$630$	−10.2467	−	5.26818i	−0.0162646	−	0.00836219i
$631$	−402.827	−	360.934i	−0.638394	−	0.572004i	0.283727	−	0.958905i	$-0.408429\pi$
$631$	−402.827	−	360.934i	−0.638394	−	0.572004i	−0.922121	+	0.386901i	$0.873545\pi$
$632$	40.5608	−	275.606i	0.0641785	−	0.436086i
$633$	−539.642	−	520.280i	−0.852514	−	0.821927i
$634$	−97.3606	−	41.3738i	−0.153566	−	0.0652583i
$635$	220.744	+	75.3073i	0.347628	+	0.118594i
$636$	396.122	−	410.864i	0.622834	−	0.646012i
$637$	−300.852	+	389.616i	−0.472295	+	0.611642i
$638$	29.8543	+	19.7514i	0.0467935	+	0.0309583i
$639$	−29.2706	−	198.891i	−0.0458069	−	0.311253i
$640$	64.3601	−	89.9589i	0.100563	−	0.140561i
$641$	580.948	−	878.104i	0.906315	−	1.36990i	−0.0226557	−	0.999743i	$-0.507212\pi$
$641$	580.948	−	878.104i	0.906315	−	1.36990i	0.928971	−	0.370153i	$-0.120695\pi$
$642$	82.7607	−	68.8740i	0.128911	−	0.107280i
$643$	−240.648	−	289.169i	−0.374258	−	0.449718i	0.547892	−	0.836549i	$-0.315430\pi$
$643$	−240.648	−	289.169i	−0.374258	−	0.449718i	−0.922151	+	0.386831i	$0.873570\pi$
$644$	622.089	−	22.7351i	0.965976	−	0.0353030i
$645$	99.8309	+	150.895i	0.154777	+	0.233945i
$646$	41.6698	−	21.4239i	0.0645043	−	0.0331639i
$647$	−68.4615	−	133.158i	−0.105814	−	0.205809i	0.830462	−	0.557076i	$-0.188077\pi$
$647$	−68.4615	−	133.158i	−0.105814	−	0.205809i	−0.936275	+	0.351267i	$0.885751\pi$
$648$	132.842	−	87.8875i	0.205003	−	0.135629i
$649$	41.4559	+	1134.34i	0.0638766	+	1.74782i
$650$	156.035	−	129.854i	0.240054	−	0.199775i
$651$	779.730	+	936.944i	1.19774	+	1.43924i
$652$	−136.073	−	90.0253i	−0.208701	−	0.138076i
$653$	−281.636	−	201.493i	−0.431296	−	0.308566i	0.345384	−	0.938461i	$-0.387749\pi$
$653$	−281.636	−	201.493i	−0.431296	−	0.308566i	−0.776680	+	0.629896i	$0.783098\pi$
$654$	−108.683	+	15.9949i	−0.166182	+	0.0244570i
$655$	−31.7378	+	47.9717i	−0.0484546	+	0.0732392i
$656$	203.246	+	156.941i	0.309826	+	0.239240i
$657$	48.2363	+	46.5056i	0.0734190	+	0.0707848i
$658$	59.1157	−	173.282i	0.0898415	−	0.263347i
$659$	−146.000	+	343.567i	−0.221548	+	0.521346i	−0.993433	−	0.114416i	$-0.963500\pi$
$659$	−146.000	+	343.567i	−0.221548	+	0.521346i	0.771885	+	0.635763i	$0.219314\pi$
$660$	−110.530	+	114.644i	−0.167470	+	0.173703i
$661$	−458.366	−	67.4575i	−0.693443	−	0.102054i	−0.210355	−	0.977625i	$-0.567462\pi$
$661$	−458.366	−	67.4575i	−0.693443	−	0.102054i	−0.483089	+	0.875571i	$0.660485\pi$
$662$	−52.9378	+	59.0821i	−0.0799665	+	0.0892479i
$663$	−673.790	+	1310.53i	−1.01627	+	1.97667i
$664$	−170.186	+	44.4925i	−0.256305	+	0.0670068i
$665$	−8.16325	−	36.6460i	−0.0122756	−	0.0551068i
$666$	33.0897	−	58.9596i	0.0496843	−	0.0885280i
$667$	−109.860	+	16.1681i	−0.164708	+	0.0242400i
$668$	−614.403	−	113.486i	−0.919765	−	0.169889i
$669$	224.542	+	858.886i	0.335639	+	1.28384i
$670$	30.5688	−	12.9903i	0.0456251	−	0.0193885i
$671$	−1123.87	−	867.828i	−1.67493	−	1.29334i
$672$	361.827	+	186.028i	0.538432	+	0.276827i
$673$	409.068	+	670.283i	0.607828	+	0.995963i	0.997193	+	0.0748799i	$0.0238573\pi$
$673$	409.068	+	670.283i	0.607828	+	0.995963i	−0.389365	+	0.921084i	$0.627305\pi$
$674$	−44.6728	−	73.1992i	−0.0662802	−	0.108604i
$675$	362.429	−	593.862i	0.536931	−	0.879795i
$676$	932.189			1.37898
$677$	419.221	−	503.746i	0.619233	−	0.744086i	−0.362992	−	0.931792i	$-0.618245\pi$
$677$	419.221	−	503.746i	0.619233	−	0.744086i	0.982225	+	0.187706i	$0.0601053\pi$
$678$	−19.6036	+	25.3876i	−0.0289139	+	0.0374448i
$679$	361.668	+	644.423i	0.532647	+	0.949076i
$680$	−23.9602	−	107.561i	−0.0352355	−	0.158177i
$681$	−854.278	−	190.298i	−1.25445	−	0.279440i
$682$	322.504	−	137.049i	0.472880	−	0.200952i
$683$	575.899	−	1026.14i	0.843191	−	1.50241i	−0.0213094	−	0.999773i	$-0.506784\pi$
$683$	575.899	−	1026.14i	0.843191	−	1.50241i	0.864500	−	0.502633i	$-0.167635\pi$
$684$	−38.8496	−	11.6881i	−0.0567977	−	0.0170879i
$685$	−44.1342	+	115.393i	−0.0644295	+	0.168457i
$686$	−87.9496	+	16.2451i	−0.128206	+	0.0236809i
$687$	−275.794	−	212.961i	−0.401447	−	0.309987i
$688$	484.240	+	731.929i	0.703837	+	1.06385i
$689$	−1038.40	+	633.726i	−1.50711	+	0.919776i
$690$	−0.840127	+	22.9879i	−0.00121758	+	0.0333159i
$691$	114.937	+	148.848i	0.166334	+	0.215409i	0.867301	−	0.497784i	$-0.165853\pi$
$691$	114.937	+	148.848i	0.166334	+	0.215409i	−0.700967	+	0.713193i	$0.747248\pi$
$692$	310.179	−	729.912i	0.448236	−	1.05479i
$693$	281.264	+	201.227i	0.405865	+	0.290371i
$694$	−23.1392	−	45.0060i	−0.0333418	−	0.0648502i
$695$	−99.6763	−	103.386i	−0.143419	−	0.148756i
$696$	−44.8503	−	17.1538i	−0.0644401	−	0.0246462i
$697$	528.342	−	97.5897i	0.758023	−	0.140014i
$698$	35.1117	+	116.706i	0.0503034	+	0.167201i
$699$	−73.6174	−	192.480i	−0.105318	−	0.275365i
$700$	773.981	+	28.2862i	1.10569	+	0.0404089i
$701$	103.432	+	68.4297i	0.147549	+	0.0976172i	0.623379	−	0.781920i	$-0.285759\pi$
$701$	103.432	+	68.4297i	0.147549	+	0.0976172i	−0.475830	+	0.879537i	$0.657852\pi$
$702$	−238.358	+	81.3166i	−0.339542	+	0.115836i
$703$	216.649	−	40.0172i	0.308178	−	0.0569234i
$704$	−479.927	+	497.787i	−0.681715	+	0.707084i
$705$	−133.721	−	56.8252i	−0.189675	−	0.0806031i
$706$	20.2761	+	7.75495i	0.0287197	+	0.0109843i
$707$	694.125	+	50.8034i	0.981789	+	0.0718577i
$708$	−188.184	−	719.812i	−0.265796	−	1.01668i
$709$	−619.867	+	555.403i	−0.874283	+	0.783361i	−0.977420	−	0.211306i	$-0.932228\pi$
$709$	−619.867	+	555.403i	−0.874283	+	0.783361i	0.103137	+	0.994667i	$0.467112\pi$
$710$	19.3422	+	29.2357i	0.0272425	+	0.0411771i
$711$	−17.1235	+	233.957i	−0.0240836	+	0.329054i
$712$	−362.768	+	123.759i	−0.509505	+	0.173819i
$713$	−461.392	+	984.238i	−0.647113	+	1.38042i
$714$	244.522	−	93.5217i	0.342468	−	0.130983i
$715$	289.746	−	176.829i	0.405239	−	0.247314i
$716$	−26.6806	−	242.481i	−0.0372633	−	0.338661i
$717$	240.222	+	428.030i	0.335038	+	0.596973i
$718$	−261.436	−	28.7661i	−0.364116	−	0.0400642i
$719$	798.021	+	527.966i	1.10990	+	0.734305i	0.966834	−	0.255407i	$-0.0822095\pi$
$719$	798.021	+	527.966i	1.10990	+	0.734305i	0.143070	+	0.989713i	$0.454303\pi$
$720$	−23.1039	+	37.8571i	−0.0320887	+	0.0525793i
$721$	−22.6442	−	619.601i	−0.0314066	−	0.859363i
$722$	−57.1556	−	134.498i	−0.0791628	−	0.186286i
$723$	169.844	−	444.073i	0.234915	−	0.614209i
$724$	−788.295	+	334.989i	−1.08881	+	0.462692i
$725$	−137.788	+	10.0848i	−0.190053	+	0.0139101i
$726$	−75.3994	+	58.2215i	−0.103856	+	0.0801950i
$727$	−171.382	−	18.8574i	−0.235739	−	0.0259386i	−0.00926975	−	0.999957i	$-0.502951\pi$
$727$	−171.382	−	18.8574i	−0.235739	−	0.0259386i	−0.226469	+	0.974018i	$0.572718\pi$
$728$	−427.339	−	382.897i	−0.587004	−	0.525958i
$729$	−628.160	+	485.050i	−0.861674	+	0.665363i
$730$	−11.0580	−	3.77245i	−0.0151479	−	0.00516774i
$731$	1816.68	+	267.360i	2.48520	+	0.365746i
$732$	842.707	+	395.045i	1.15124	+	0.539679i
$733$	−102.691	+	168.266i	−0.140097	+	0.229558i	−0.915890	−	0.401430i	$-0.868513\pi$
$733$	−102.691	+	168.266i	−0.140097	+	0.229558i	0.775792	+	0.630988i	$0.217350\pi$
$734$	103.562	+	19.1289i	0.141093	+	0.0260612i
$735$	−7.59037	−	68.9838i	−0.0103270	−	0.0938555i
$736$	−13.2506	+	362.570i	−0.0180036	+	0.492622i
$737$	−964.552	+	252.167i	−1.30875	+	0.342153i
$738$	18.0666	+	11.9527i	0.0244805	+	0.0161961i
$739$	13.3100	−	59.7507i	0.0180109	−	0.0808534i	−0.966233	−	0.257670i	$-0.917045\pi$
$739$	13.3100	−	59.7507i	0.0180109	−	0.0808534i	0.984244	+	0.176817i	$0.0565800\pi$
$740$	18.4812	−	252.508i	0.0249746	−	0.341226i
$741$	−165.260	−	100.857i	−0.223023	−	0.136109i
$742$	212.527	+	39.2557i	0.286424	+	0.0529053i
$743$	124.888	+	139.384i	0.168087	+	0.187596i	0.822885	−	0.568207i	$-0.192363\pi$
$743$	124.888	+	139.384i	0.168087	+	0.187596i	−0.654799	+	0.755803i	$0.727247\pi$
$744$	−382.295	+	273.509i	−0.513837	+	0.367619i
$745$	−118.360	−	142.224i	−0.158872	−	0.190905i
$746$			80.2747i			0.107607i
$747$	140.194	−	47.8274i	0.187676	−	0.0640260i
$748$	117.976	+	1611.90i	0.157722	+	2.15495i
$749$	−838.486	−	252.263i	−1.11947	−	0.336799i
$750$	−6.43476	+	58.4812i	−0.00857968	+	0.0779749i
$751$	−474.126	−	69.7768i	−0.631326	−	0.0929119i	−0.177672	−	0.984090i	$-0.556857\pi$
$751$	−474.126	−	69.7768i	−0.631326	−	0.0929119i	−0.453654	+	0.891178i	$0.649880\pi$
$752$	−648.626	−	275.636i	−0.862535	−	0.366538i
$753$	68.6880	+	122.389i	0.0912192	+	0.162535i
$754$	40.6743	+	29.1000i	0.0539447	+	0.0385941i
$755$	−71.8505	−	40.3245i	−0.0951663	−	0.0534099i
$756$	−884.327	−	375.798i	−1.16975	−	0.497088i
$757$	−26.8105	+	243.662i	−0.0354168	+	0.321879i	0.963177	+	0.268868i	$0.0866494\pi$
$757$	−26.8105	+	243.662i	−0.0354168	+	0.321879i	−0.998594	+	0.0530114i	$0.983118\pi$
$758$	−116.773	−	163.218i	−0.154054	−	0.215327i
$759$	125.415	−	678.985i	0.165237	−	0.894578i
$760$	14.3238	−	2.10802i	0.0188470	−	0.00277371i
$761$	−446.868	−	134.443i	−0.587212	−	0.176666i	−0.0193826	−	0.999812i	$-0.506170\pi$
$761$	−446.868	−	134.443i	−0.587212	−	0.176666i	−0.567829	+	0.823146i	$0.692217\pi$
$762$	−206.728	−	54.0458i	−0.271297	−	0.0709262i
$763$	596.161	+	665.355i	0.781338	+	0.872025i
$764$	−590.638	−	21.5857i	−0.773086	−	0.0282535i
$765$	26.7341	+	88.8605i	0.0349466	+	0.116158i
$766$	−138.772	−	115.487i	−0.181165	−	0.150766i
$767$			1585.86i			2.06762i
$768$	194.308	−	318.385i	0.253005	−	0.414564i
$769$	−222.637	−	433.031i	−0.289514	−	0.563109i	0.698840	−	0.715278i	$-0.253700\pi$
$769$	−222.637	−	433.031i	−0.289514	−	0.563109i	−0.988355	+	0.152169i	$0.951374\pi$
$770$	−59.3016	−	10.9536i	−0.0770151	−	0.0142254i
$771$	642.534	−	534.721i	0.833378	−	0.693542i
$772$	−102.096	−	84.9649i	−0.132249	−	0.110058i
$773$	79.8374	+	432.233i	0.103283	+	0.559163i	0.994426	+	0.105440i	$0.0336252\pi$
$773$	79.8374	+	432.233i	0.103283	+	0.559163i	−0.891143	+	0.453722i	$0.850096\pi$
$774$	45.2489	+	58.5993i	0.0584611	+	0.0757096i
$775$	−661.903	+	1179.38i	−0.854068	+	1.52179i
$776$	−258.024	+	120.957i	−0.332505	+	0.155872i
$777$	1227.70	−	89.8563i	1.58006	−	0.115645i
$778$	−50.8010	+	71.0068i	−0.0652970	+	0.0912684i
$779$	7.72046	+	70.1660i	0.00991073	+	0.0900719i
$780$	−160.171	+	154.424i	−0.205348	+	0.197980i
$781$	−446.619	−	952.726i	−0.571856	−	1.21988i
$782$	168.069	+	162.039i	0.214922	+	0.207211i
$783$	164.134	+	49.3805i	0.209622	+	0.0630658i
$784$	−36.8179	−	334.613i	−0.0469616	−	0.426802i
$785$	84.6261	−	75.8254i	0.107804	−	0.0965928i
$786$	25.7905	−	45.9538i	0.0328124	−	0.0584654i
$787$	999.360	+	963.504i	1.26983	+	1.22427i	0.962067	+	0.272813i	$0.0879541\pi$
$787$	999.360	+	963.504i	1.26983	+	1.22427i	0.307768	+	0.951461i	$0.400418\pi$
$788$	739.170	+	662.299i	0.938033	+	0.840481i
$789$	−934.283	+	618.116i	−1.18414	+	0.783417i
$790$	−14.6126	−	38.2061i	−0.0184970	−	0.0483622i
$791$	260.151	+	19.0406i	0.328889	+	0.0240716i
$792$	−85.3089	+	102.509i	−0.107713	+	0.129431i
$793$	−1524.86	−	1269.00i	−1.92290	−	1.60025i
$794$	239.608	+	112.324i	0.301773	+	0.141466i
$795$	43.3802	−	165.932i	0.0545663	−	0.208719i
$796$	6.46229	+	43.9105i	0.00811845	+	0.0551639i
$797$	−47.0435	−	1287.23i	−0.0590258	−	1.61509i	−0.618187	−	0.786031i	$-0.712132\pi$
$797$	−47.0435	−	1287.23i	−0.0590258	−	1.61509i	0.559161	−	0.829059i	$-0.311123\pi$
$798$	9.90935	+	32.9373i	0.0124177	+	0.0412748i
$799$	−1335.16	+	625.900i	−1.67104	+	0.783354i
$800$	−49.3699	+	448.690i	−0.0617124	+	0.560862i
$801$	297.058	−	126.236i	0.370859	−	0.157598i
$802$	49.7950	+	165.511i	0.0620885	+	0.206373i
$803$	311.893	+	160.355i	0.388410	+	0.199695i
$804$	581.159	−	298.794i	0.722834	−	0.371635i
$805$	159.682	−	97.4523i	0.198362	−	0.121059i
$806$	457.269	−	174.891i	0.567331	−	0.216986i
$807$	−63.1385	−	862.659i	−0.0782385	−	1.06897i
$808$	−39.0777	+	265.529i	−0.0483635	+	0.328625i
$809$	36.6219	+	500.363i	0.0452681	+	0.618496i	0.970810	+	0.239851i	$0.0770985\pi$
$809$	36.6219	+	500.363i	0.0452681	+	0.618496i	−0.925542	+	0.378646i	$0.876390\pi$
$810$	10.6943	−	20.8006i	0.0132029	−	0.0256798i
$811$	290.573	+	406.147i	0.358290	+	0.500798i	0.952928	−	0.303196i	$-0.0980536\pi$
$811$	290.573	+	406.147i	0.358290	+	0.500798i	−0.594638	+	0.803993i	$0.702705\pi$
$812$	41.4877	+	186.244i	0.0510932	+	0.229365i
$813$	−184.839	−	394.297i	−0.227354	−	0.484990i
$814$	76.9432	−	345.410i	0.0945249	−	0.424336i
$815$	−48.9001	−	3.57903i	−0.0600002	−	0.00439145i
$816$	−290.327	−	965.006i	−0.355793	−	1.18261i
$817$	−52.4556	+	235.481i	−0.0642051	+	0.288226i
$818$	84.0022	−	179.193i	0.102692	−	0.219062i
$819$	382.430	+	295.303i	0.466948	+	0.360565i
$820$	80.2563	+	11.8113i	0.0978736	+	0.0144040i
$821$	141.479	+	48.2661i	0.172326	+	0.0587894i	0.407702	−	0.913115i	$-0.366330\pi$
$821$	141.479	+	48.2661i	0.172326	+	0.0587894i	−0.235377	+	0.971904i	$0.575632\pi$
$822$	32.6083	−	108.385i	0.0396695	−	0.131856i
$823$	970.010	−	641.753i	1.17863	−	0.779772i	0.198883	−	0.980023i	$-0.436269\pi$
$823$	970.010	−	641.753i	1.17863	−	0.779772i	0.979745	+	0.200251i	$0.0641757\pi$
$824$	238.934	+	8.73219i	0.289969	+	0.0105973i
$825$	217.285	−	831.126i	0.263375	−	1.00743i
$826$	188.011	−	209.833i	0.227617	−	0.254035i
$827$	395.444	+	88.0889i	0.478167	+	0.106516i	0.449890	−	0.893084i	$-0.351463\pi$
$827$	395.444	+	88.0889i	0.478167	+	0.106516i	0.0282766	+	0.999600i	$0.490998\pi$
$828$	−7.38275	−	202.010i	−0.00891636	−	0.243974i
$829$	−292.310	+	209.130i	−0.352605	+	0.252267i	−0.744325	−	0.667817i	$-0.767229\pi$
$829$	−292.310	+	209.130i	−0.352605	+	0.252267i	0.391720	+	0.920084i	$0.371880\pi$
$830$	−18.5948	+	17.9276i	−0.0224034	+	0.0215996i
$831$	−823.062	+	314.794i	−0.990447	+	0.378814i
$832$	−695.468	+	670.516i	−0.835900	+	0.805908i
$833$	−572.834	−	409.828i	−0.687676	−	0.491990i
$834$	97.9872	+	87.7969i	0.117491	+	0.105272i
$835$	−177.702	+	60.6236i	−0.212817	+	0.0726031i
$836$	−212.344			−0.254000
$837$	1289.68	−	1073.28i	1.54084	−	1.28230i
$838$	−155.839	+	40.7417i	−0.185966	+	0.0486178i
$839$	743.419	−	716.746i	0.886077	−	0.854286i	−0.104034	−	0.994574i	$-0.533175\pi$
$839$	743.419	−	716.746i	0.886077	−	0.854286i	0.990111	+	0.140288i	$0.0448029\pi$
$840$	80.8409	−	2.95444i	0.0962392	−	0.00351720i
$841$	260.553	+	763.742i	0.309813	+	0.908135i
$842$	40.4698	−	7.47515i	0.0480639	−	0.00887784i
$843$	393.624	+	839.677i	0.466933	+	0.996058i
$844$	−1111.30	−	290.531i	−1.31670	−	0.344231i
$845$	244.291	−	137.103i	0.289101	−	0.162252i
$846$	−56.2698	−	19.1966i	−0.0665128	−	0.0226910i
$847$	733.206	+	250.135i	0.865651	+	0.295319i
$848$	210.420	−	804.868i	0.248137	−	0.949137i
$849$	470.303	+	914.745i	0.553949	+	1.07744i
$850$	193.832	+	216.329i	0.228037	+	0.254505i
$851$	537.258	+	957.292i	0.631326	+	1.12490i
$852$	421.515	+	545.880i	0.494736	+	0.640704i
$853$	−166.533	−	747.590i	−0.195232	−	0.876424i	−0.969794	−	0.243926i	$-0.921565\pi$
$853$	−166.533	−	747.590i	−0.195232	−	0.876424i	0.774562	−	0.632498i	$-0.217970\pi$
$854$	51.3160	+	348.687i	0.0600890	+	0.408298i
$855$	−11.9000	+	2.65084i	−0.0139182	+	0.00310040i
$856$	120.622	−	315.379i	0.140914	−	0.368433i
$857$	−279.588	+	596.416i	−0.326241	+	0.695934i	−0.999036	−	0.0438940i	$-0.986024\pi$
$857$	−279.588	+	596.416i	−0.326241	+	0.695934i	0.672796	+	0.739828i	$0.265093\pi$
$858$	−252.913	+	180.944i	−0.294771	+	0.210890i
$859$	−795.231	+	87.5003i	−0.925764	+	0.101863i	−0.559671	−	0.828715i	$-0.689072\pi$
$859$	−795.231	+	87.5003i	−0.925764	+	0.101863i	−0.366093	+	0.930578i	$0.619305\pi$
$860$	246.566	+	126.768i	0.286704	+	0.147405i
$861$			394.413i			0.458087i
$862$	9.70981	+	181.566i	0.0112643	+	0.210633i
$863$	148.154			0.171673			0.0858365	−	0.996309i	$-0.472644\pi$
$863$	148.154			0.171673			0.0858365	+	0.996309i	$0.472644\pi$
$864$	256.063	−	498.047i	0.296370	−	0.576443i
$865$	−26.0666	−	236.902i	−0.0301348	−	0.273875i
$866$	−25.8581	−	36.1431i	−0.0298593	−	0.0417356i
$867$	−1256.46	−	589.003i	−1.44920	−	0.679357i
$868$	1744.60	+	667.253i	2.00991	+	0.768725i
$869$	266.964	+	1198.44i	0.307209	+	1.37910i
$870$	−6.97581	+	1.02663i	−0.00801817	+	0.00118003i
$871$	−1359.56	+	302.856i	−1.56092	+	0.347710i
$872$	−272.675	+	210.553i	−0.312701	+	0.241460i
$873$	209.263	−	117.444i	0.239705	−	0.134529i
$874$	−22.8442	+	20.4685i	−0.0261376	+	0.0234194i
$875$	425.513	−	218.771i	0.486300	−	0.250024i
$876$	−222.395	−	58.1416i	−0.253875	−	0.0663717i
$877$	343.544	−	1007.01i	0.391726	−	1.14824i	−0.556555	−	0.830811i	$-0.687877\pi$
$877$	343.544	−	1007.01i	0.391726	−	1.14824i	0.948281	−	0.317432i	$-0.102821\pi$
$878$	13.3683	−	39.1856i	0.0152258	−	0.0446305i
$879$	−198.182	−	353.122i	−0.225463	−	0.401732i
$880$	−58.7137	+	224.583i	−0.0667202	+	0.255208i
$881$	−16.1303	+	7.56156i	−0.0183091	+	0.00858293i	−0.433590	−	0.901110i	$-0.642753\pi$
$881$	−16.1303	+	7.56156i	−0.0183091	+	0.00858293i	0.415280	+	0.909693i	$0.363683\pi$
$882$	−5.15820	−	27.9261i	−0.00584830	−	0.0316622i
$883$	480.598	−	163.957i	0.544278	−	0.185682i	−0.0371056	−	0.999311i	$-0.511814\pi$
$883$	480.598	−	163.957i	0.544278	−	0.185682i	0.581384	+	0.813629i	$0.302511\pi$
$884$	82.4685	+	2256.54i	0.0932901	+	2.55265i
$885$	−155.183	−	160.958i	−0.175348	−	0.181873i
$886$	−21.2411	−	81.2483i	−0.0239741	−	0.0917023i
$887$	−45.4890	−	54.6607i	−0.0512841	−	0.0616242i	0.742387	−	0.669971i	$-0.233693\pi$
$887$	−45.4890	−	54.6607i	−0.0512841	−	0.0616242i	−0.793671	+	0.608347i	$0.791833\pi$
$888$			474.701i			0.534573i
$889$	561.063	+	1644.61i	0.631117	+	1.84995i
$890$	−37.5582	+	41.9175i	−0.0422003	+	0.0470983i
$891$	−408.489	+	570.963i	−0.458461	+	0.640811i
$892$	944.176	+	979.313i	1.05849	+	1.09788i
$893$	−69.2086	−	180.953i	−0.0775012	−	0.202635i
$894$	117.656	+	122.034i	0.131606	+	0.136503i
$895$	−42.6552	−	59.6210i	−0.0476594	−	0.0666156i
$896$	823.537	−	30.0973i	0.919127	−	0.0335908i
$897$	209.748	−	941.591i	0.233833	−	1.04971i
$898$	−30.2474	−	27.1018i	−0.0336831	−	0.0301801i
$899$	−322.357	−	84.2752i	−0.358573	−	0.0937433i
$900$	9.18536	−	251.334i	0.0102060	−	0.279260i
$901$	−960.429	−	1451.69i	−1.06596	−	1.61120i
$902$	108.576	+	32.6656i	0.120372	+	0.0362146i
$903$	−435.236	+	1275.78i	−0.481989	+	1.41282i
$904$	−14.6460	+	99.5176i	−0.0162013	+	0.110086i
$905$	−157.313	+	203.727i	−0.173826	+	0.225113i
$906$	68.3459	+	32.0393i	0.0754370	+	0.0353634i
$907$	723.504	+	161.167i	0.797689	+	0.177693i	0.597294	−	0.802022i	$-0.296243\pi$
$907$	723.504	+	161.167i	0.797689	+	0.177693i	0.200395	+	0.979715i	$0.435777\pi$
$908$	−1284.27	+	386.378i	−1.41439	+	0.425527i
$909$	16.4973	−	225.402i	0.0181489	−	0.247967i
$910$	−82.2373	−	18.3191i	−0.0903707	−	0.0201309i
$911$	−1029.37	+	482.551i	−1.12994	+	0.529693i	−0.896661	−	0.442717i	$-0.854015\pi$
$911$	−1029.37	+	482.551i	−1.12994	+	0.529693i	−0.233277	+	0.972410i	$0.574945\pi$
$912$	129.232	−	28.7876i	0.141701	−	0.0315653i
$913$	630.547	−	451.118i	0.690632	−	0.494105i
$914$	−207.477	−	106.671i	−0.226999	−	0.116708i
$915$	278.943	−	20.4160i	0.304855	−	0.0223125i
$916$	−528.248	−	77.7420i	−0.576690	−	0.0848711i
$917$	−427.400	+	31.2816i	−0.466085	+	0.0341130i
$918$	−128.731	−	336.579i	−0.140229	−	0.366644i
$919$	−145.918	−	239.096i	−0.158779	−	0.260169i	0.764233	−	0.644940i	$-0.223118\pi$
$919$	−145.918	−	239.096i	−0.158779	−	0.260169i	−0.923012	+	0.384771i	$0.874281\pi$
$920$	32.9851	+	64.1564i	0.0358533	+	0.0697352i
$921$	508.838	−	989.696i	0.552484	−	1.07459i
$922$	−83.8545	+	25.2281i	−0.0909485	+	0.0273623i
$923$	−574.951	−	1352.97i	−0.622916	−	1.46584i
$924$	−1179.34	−	129.764i	−1.27634	−	0.140437i
$925$	579.715	+	1236.64i	0.626719	+	1.33691i
$926$	−108.385	+	32.6083i	−0.117047	+	0.0352142i
$927$	−201.202	+	7.35322i	−0.217047	+	0.00793228i
$928$	−110.024	+	16.1921i	−0.118560	+	0.0174484i
$929$	−287.219	−	75.0889i	−0.309170	−	0.0808277i	0.0950987	−	0.995468i	$-0.469683\pi$
$929$	−287.219	−	75.0889i	−0.309170	−	0.0808277i	−0.404269	+	0.914640i	$0.632474\pi$
$930$	−29.2970	+	62.4961i	−0.0315021	+	0.0672002i
$931$	59.1945	−	71.1296i	0.0635816	−	0.0764013i
$932$	−242.725	−	201.997i	−0.260434	−	0.216735i
$933$	−85.3298	+	1165.86i	−0.0914574	+	1.24958i
$934$	−237.967	+	91.0148i	−0.254783	+	0.0974462i
$935$	267.989	+	405.067i	0.286620	+	0.433226i
$936$	−124.338	+	138.769i	−0.132840	+	0.148258i
$937$	118.781	−	123.201i	0.126767	−	0.131484i	−0.653512	−	0.756916i	$-0.726705\pi$
$937$	118.781	−	123.201i	0.126767	−	0.131484i	0.780279	+	0.625432i	$0.215077\pi$
$938$	215.796	+	121.110i	0.230059	+	0.129115i
$939$	569.636	+	635.752i	0.606642	+	0.677052i
$940$	−221.304	+	24.3504i	−0.235430	+	0.0259047i
$941$	236.753	−	786.932i	0.251597	−	0.836272i	−0.735689	−	0.677319i	$-0.763142\pi$
$941$	236.753	−	786.932i	0.251597	−	0.836272i	0.987286	−	0.158953i	$-0.0508119\pi$
$942$	−72.2515	+	74.9403i	−0.0767002	+	0.0795545i
$943$	−318.467	+	149.291i	−0.337717	+	0.158315i
$944$	−752.729	−	780.741i	−0.797383	−	0.827056i
$945$	−287.019	+	31.5811i	−0.303724	+	0.0334191i
$946$	315.156	+	225.475i	0.333146	+	0.238345i
$947$	−6.97908	−	95.3549i	−0.00736967	−	0.100692i	0.992376	−	0.123248i	$-0.0393311\pi$
$947$	−6.97908	−	95.3549i	−0.00736967	−	0.100692i	−0.999746	+	0.0225565i	$0.992819\pi$
$948$	−341.594	−	728.687i	−0.360332	−	0.768657i
$949$	427.279	+	239.801i	0.450241	+	0.252688i
$950$	−30.2051	+	23.3236i	−0.0317948	+	0.0245512i
$951$	−615.047	+	113.605i	−0.646737	+	0.119458i
$952$	525.173	−	631.061i	0.551652	−	0.662879i
$953$	−94.5730	−	113.641i	−0.0992372	−	0.119246i	0.716713	−	0.697369i	$-0.245646\pi$
$953$	−94.5730	−	113.641i	−0.0992372	−	0.119246i	−0.815950	+	0.578123i	$0.803785\pi$
$954$	12.7475	−	69.0137i	0.0133621	−	0.0723414i
$955$	−157.958	+	81.2118i	−0.165401	+	0.0850386i
$956$	642.006	+	391.811i	0.671554	+	0.409844i
$957$	211.642			0.221152
$958$	60.8072	−	73.0674i	0.0634730	−	0.0762708i
$959$	−881.424	+	265.181i	−0.919107	+	0.276518i
$960$	4.97428	−	136.109i	0.00518154	−	0.141780i
$961$	−1713.45	+	1535.26i	−1.78299	+	1.59756i
$962$	125.052	−	478.330i	0.129992	−	0.497225i
$963$	−81.9170	+	272.281i	−0.0850644	+	0.282742i
$964$	−106.077	−	720.780i	−0.110038	−	0.747697i
$965$	−39.2517	−	7.25016i	−0.0406753	−	0.00751311i
$966$	−139.383	+	99.7199i	−0.144289	+	0.103230i
$967$	−672.914	−	74.0416i	−0.695878	−	0.0765683i	−0.245487	−	0.969400i	$-0.578948\pi$
$967$	−672.914	−	74.0416i	−0.695878	−	0.0765683i	−0.450391	+	0.892832i	$0.648715\pi$
$968$	−116.840	+	274.948i	−0.120703	+	0.284038i
$969$	135.579	−	241.576i	0.139917	−	0.249305i
$970$	−24.3473	+	34.0313i	−0.0251003	+	0.0350838i
$971$	1053.67	−	591.348i	1.08514	−	0.609009i	0.159416	−	0.987212i	$-0.449039\pi$
$971$	1053.67	−	591.348i	1.08514	−	0.609009i	0.925723	+	0.378202i	$0.123458\pi$
$972$	−215.276	+	506.587i	−0.221478	+	0.521180i
$973$	155.785	−	1058.54i	0.160108	−	1.08791i
$974$	203.651	+	22.4080i	0.209088	+	0.0230062i
$975$	345.779	−	1149.32i	0.354645	−	1.17879i
$976$	1353.04	−	99.0297i	1.38631	−	0.101465i
$977$	−290.100	−	850.353i	−0.296929	−	0.870371i	−0.988918	−	0.148463i	$-0.952567\pi$
$977$	−290.100	−	850.353i	−0.296929	−	0.870371i	0.691989	−	0.721908i	$-0.256735\pi$
$978$	44.9190			0.0459295
$979$	1298.54	−	1080.65i	1.32639	−	1.10383i
$980$	−61.8776	−	86.4890i	−0.0631404	−	0.0882541i
$981$	216.060	−	193.591i	0.220245	−	0.197340i
$982$	15.8030	−	85.5561i	0.0160927	−	0.0871243i
$983$	−596.853	+	977.980i	−0.607174	+	0.994893i	0.390076	+	0.920783i	$0.372449\pi$
$983$	−596.853	+	977.980i	−0.607174	+	0.994893i	−0.997250	+	0.0741102i	$0.976388\pi$
$984$	−151.690	−	11.1023i	−0.154157	−	0.0112828i
$985$	291.116	+	64.8489i	0.295549	+	0.0658364i
$986$	−39.4845	+	59.6809i	−0.0400452	+	0.0605283i
$987$	−273.797	−	1047.29i	−0.277403	−	1.06108i
$988$	−296.472	−	10.8350i	−0.300073	−	0.0109666i
$989$	−1194.87	+	131.473i	−1.20816	+	0.132935i
$990$	−3.55694	+	19.2570i	−0.00359287	+	0.0194515i
$991$	−443.437	−	270.626i	−0.447464	−	0.273084i	0.278996	−	0.960292i	$-0.409999\pi$
$991$	−443.437	−	270.626i	−0.447464	−	0.273084i	−0.726460	+	0.687209i	$0.758836\pi$
$992$	−462.077	+	985.700i	−0.465804	+	0.993649i
$993$	−68.2902	+	464.024i	−0.0687716	+	0.467295i
$994$	−84.3267	+	247.182i	−0.0848357	+	0.248674i
$995$	8.15170	+	10.5568i	0.00819266	+	0.0106099i
$996$	−339.117	+	378.477i	−0.340479	+	0.379997i
$997$	197.465	−	1794.63i	0.198060	−	1.80003i	−0.322883	−	0.946439i	$-0.604652\pi$
$997$	197.465	−	1794.63i	0.198060	−	1.80003i	0.520943	−	0.853592i	$-0.325581\pi$
$998$	160.653	+	208.053i	0.160975	+	0.208469i
$999$	−123.685	−	1689.91i	−0.123809	−	1.69160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.3.f.a.101.34	✓	2982
431.367	odd	86	inner	431.3.f.a.367.34	yes	2982

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.3.f.a.101.34	✓	2982	1.1	even	1	trivial
431.3.f.a.367.34	yes	2982	431.367	odd	86	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	431.f (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.192896 + 0.375186i) q^{2} +(0.272798 + 2.47928i) q^{3} +(2.22388 + 3.10842i) q^{4} +(1.03997 + 0.487516i) q^{5} +(-0.982812 - 0.375894i) q^{6} +(1.86059 + 8.35245i) q^{7} +(-3.26470 + 0.480465i) q^{8} +(2.71228 - 0.604186i) q^{9} +(-0.383515 + 0.296141i) q^{10} +(12.6832 - 7.11816i) q^{11} +(-7.09996 + 6.36159i) q^{12} +(18.0714 - 9.29113i) q^{13} +(-3.49262 - 0.913090i) q^{14} +(-0.924988 + 2.71136i) q^{15} +(-4.48674 + 13.1517i) q^{16} +(14.2297 + 25.3547i) q^{17} +(-0.296507 + 1.13415i) q^{18} +(-3.45876 + 1.62140i) q^{19} +(0.797358 + 4.31683i) q^{20} +(-20.2005 + 6.89144i) q^{21} +(0.224089 + 6.13163i) q^{22} +(-13.2107 - 13.7023i) q^{23} +(-2.08181 - 7.96304i) q^{24} +(-15.1480 - 18.2022i) q^{25} +8.57234i q^{26} +(9.48593 + 27.8055i) q^{27} +(-21.8251 + 24.3583i) q^{28} +(3.39464 - 4.74483i) q^{29} +(-0.838837 - 0.870054i) q^{30} +(-20.4017 - 53.3424i) q^{31} +(-13.2303 - 13.7226i) q^{32} +(21.1079 + 29.5034i) q^{33} +(-12.2576 + 0.447971i) q^{34} +(-2.13701 + 9.59333i) q^{35} +(7.90985 + 7.08726i) q^{36} +(-55.7993 - 14.5878i) q^{37} +(0.0588559 - 1.61044i) q^{38} +(27.9651 + 42.2693i) q^{39} +(-3.62942 - 1.09193i) q^{40} +(5.96657 - 17.4894i) q^{41} +(1.31102 - 8.90826i) q^{42} +(38.5993 - 49.9877i) q^{43} +(50.3322 + 23.5947i) q^{44} +(3.11523 + 0.693948i) q^{45} +(7.68918 - 2.31333i) q^{46} +(-3.70211 + 50.5817i) q^{47} +(-33.8308 - 7.53612i) q^{48} +(-21.9346 + 10.2825i) q^{49} +(9.75118 - 2.17217i) q^{50} +(-58.9795 + 42.1962i) q^{51} +(69.0692 + 35.5109i) q^{52} +(-59.7078 + 4.37005i) q^{53} +(-12.2620 - 1.80460i) q^{54} +(16.6603 - 1.21938i) q^{55} +(-10.0873 - 26.3743i) q^{56} +(-4.96345 - 8.13292i) q^{57} +(1.12538 + 2.18888i) q^{58} +(-35.6853 + 69.4084i) q^{59} +(-10.4851 + 3.15449i) q^{60} +(-38.1833 - 89.8529i) q^{61} +(23.9487 + 2.63511i) q^{62} +(10.0929 + 21.5300i) q^{63} +(-45.5266 + 13.6969i) q^{64} +(23.3232 - 0.852379i) q^{65} +(-15.1409 + 2.22828i) q^{66} +(-66.3189 - 17.3380i) q^{67} +(-47.1677 + 100.618i) q^{68} +(30.3679 - 36.4908i) q^{69} +(-3.18706 - 2.65229i) q^{70} +(5.28094 - 72.1532i) q^{71} +(-8.56451 + 3.27565i) q^{72} +(13.3047 + 20.1101i) q^{73} +(16.2366 - 18.1212i) q^{74} +(40.9959 - 42.5215i) q^{75} +(-12.7319 - 7.14547i) q^{76} +(83.0523 + 92.6919i) q^{77} +(-21.2532 + 2.33852i) q^{78} +(-24.3213 + 80.8406i) q^{79} +(-11.0777 + 11.4900i) q^{80} +(-43.7057 + 20.4884i) q^{81} +(5.41086 + 5.61222i) q^{82} +(52.9872 - 5.83025i) q^{83} +(-66.3449 - 47.4657i) q^{84} +(2.43763 + 33.3053i) q^{85} +(11.3090 + 24.1244i) q^{86} +(12.6898 + 7.12187i) q^{87} +(-37.9869 + 29.3325i) q^{88} +(114.223 - 21.0981i) q^{89} +(-0.861276 + 1.03493i) q^{90} +(111.227 + 133.653i) q^{91} +(13.2134 - 71.5364i) q^{92} +(126.685 - 65.1333i) q^{93} +(-18.2634 - 11.1460i) q^{94} -4.38746 q^{95} +(30.4130 - 36.5451i) q^{96} +(82.6959 - 24.8795i) q^{97} +(0.373249 - 10.2130i) q^{98} +(30.0997 - 26.9695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) \) 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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