LMFDB - Embedded newform 72.3.j.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95473 + 0.423142i) q^{2} +(2.84278 - 0.958433i) q^{3} +(3.64190 - 1.65425i) q^{4} +(-3.64648 - 6.31589i) q^{5} +(-5.15130 + 3.07637i) q^{6} +(-0.487126 + 0.843726i) q^{7} +(-6.41894 + 4.77465i) q^{8} +(7.16281 - 5.44923i) q^{9} +O(q^{10})$	\(q+(-1.95473 + 0.423142i) q^{2} +(2.84278 - 0.958433i) q^{3} +(3.64190 - 1.65425i) q^{4} +(-3.64648 - 6.31589i) q^{5} +(-5.15130 + 3.07637i) q^{6} +(-0.487126 + 0.843726i) q^{7} +(-6.41894 + 4.77465i) q^{8} +(7.16281 - 5.44923i) q^{9} +(9.80039 + 10.8029i) q^{10} +(7.19410 - 12.4606i) q^{11} +(8.76764 - 8.19319i) q^{12} +(5.50333 - 3.17735i) q^{13} +(0.595181 - 1.85538i) q^{14} +(-16.4195 - 14.4598i) q^{15} +(10.5269 - 12.0492i) q^{16} +27.9331i q^{17} +(-11.6955 + 13.6826i) q^{18} +9.44492i q^{19} +(-23.7282 - 16.9697i) q^{20} +(-0.576137 + 2.86541i) q^{21} +(-8.78992 + 27.4011i) q^{22} +(5.15167 - 2.97432i) q^{23} +(-13.6715 + 19.7254i) q^{24} +(-14.0937 + 24.4110i) q^{25} +(-9.41303 + 8.53953i) q^{26} +(15.1396 - 22.3560i) q^{27} +(-0.378329 + 3.87860i) q^{28} +(-24.9939 + 43.2907i) q^{29} +(38.2142 + 21.3172i) q^{30} +(-11.0551 - 19.1481i) q^{31} +(-15.4787 + 28.0073i) q^{32} +(8.50866 - 42.3177i) q^{33} +(-11.8196 - 54.6015i) q^{34} +7.10518 q^{35} +(17.0719 - 31.6947i) q^{36} +20.4275i q^{37} +(-3.99654 - 18.4622i) q^{38} +(12.5995 - 14.3071i) q^{39} +(53.5627 + 23.1307i) q^{40} +(16.9300 - 9.77457i) q^{41} +(-0.0862836 - 5.84487i) q^{42} +(-19.6424 - 11.3405i) q^{43} +(5.58734 - 57.2810i) q^{44} +(-60.5358 - 25.3690i) q^{45} +(-8.81154 + 7.99386i) q^{46} +(71.3325 + 41.1838i) q^{47} +(18.3773 - 44.3427i) q^{48} +(24.0254 + 41.6132i) q^{49} +(17.2200 - 53.6803i) q^{50} +(26.7720 + 79.4076i) q^{51} +(14.7865 - 20.6755i) q^{52} +53.3204 q^{53} +(-20.1340 + 50.1061i) q^{54} -104.933 q^{55} +(-0.901666 - 7.74168i) q^{56} +(9.05232 + 26.8499i) q^{57} +(30.5381 - 95.1974i) q^{58} +(-29.5218 - 51.1333i) q^{59} +(-83.7184 - 25.4992i) q^{60} +(-9.09207 - 5.24931i) q^{61} +(29.7121 + 32.7513i) q^{62} +(1.10847 + 8.69791i) q^{63} +(18.4055 - 61.2963i) q^{64} +(-40.1356 - 23.1723i) q^{65} +(1.27428 + 86.3198i) q^{66} +(-44.8003 + 25.8655i) q^{67} +(46.2083 + 101.730i) q^{68} +(11.7944 - 13.3929i) q^{69} +(-13.8887 + 3.00650i) q^{70} +11.6970i q^{71} +(-19.9595 + 69.1782i) q^{72} -39.1030 q^{73} +(-8.64373 - 39.9302i) q^{74} +(-16.6690 + 82.9029i) q^{75} +(15.6243 + 34.3975i) q^{76} +(7.00886 + 12.1397i) q^{77} +(-18.5746 + 33.2978i) q^{78} +(49.7902 - 86.2392i) q^{79} +(-114.488 - 22.5495i) q^{80} +(21.6118 - 78.0636i) q^{81} +(-28.9576 + 26.2704i) q^{82} +(3.61441 - 6.26034i) q^{83} +(2.64187 + 11.3886i) q^{84} +(176.422 - 101.857i) q^{85} +(43.1941 + 13.8561i) q^{86} +(-29.5610 + 147.021i) q^{87} +(13.3162 + 114.333i) q^{88} -97.4870i q^{89} +(129.066 + 23.9743i) q^{90} +6.19107i q^{91} +(13.8416 - 19.3543i) q^{92} +(-49.7795 - 43.8382i) q^{93} +(-156.862 - 50.3194i) q^{94} +(59.6531 - 34.4408i) q^{95} +(-17.1594 + 94.4540i) q^{96} +(-2.40597 + 4.16727i) q^{97} +(-64.5714 - 71.1763i) q^{98} +(-16.3704 - 128.455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.95473	+	0.423142i	−0.977363	+	0.211571i
$2$	−1.95473	+	0.423142i	−0.977363	+	0.211571i
$3$	2.84278	−	0.958433i	0.947594	−	0.319478i
$3$	2.84278	−	0.958433i	0.947594	−	0.319478i
$4$	3.64190	−	1.65425i	0.910476	−	0.413563i
$5$	−3.64648	−	6.31589i	−0.729297	−	1.26318i	−0.957181	−	0.289490i	$-0.906514\pi$
$5$	−3.64648	−	6.31589i	−0.729297	−	1.26318i	0.227884	−	0.973688i	$-0.426819\pi$
$6$	−5.15130	+	3.07637i	−0.858551	+	0.512729i
$7$	−0.487126	+	0.843726i	−0.0695894	+	0.120532i	−0.898721	−	0.438522i	$-0.855502\pi$
$7$	−0.487126	+	0.843726i	−0.0695894	+	0.120532i	0.829131	+	0.559054i	$0.188836\pi$
$8$	−6.41894	+	4.77465i	−0.802367	+	0.596831i
$9$	7.16281	−	5.44923i	0.795868	−	0.605470i
$10$	9.80039	+	10.8029i	0.980039	+	1.08029i
$11$	7.19410	−	12.4606i	0.654009	−	1.13278i	−0.328132	−	0.944632i	$-0.606419\pi$
$11$	7.19410	−	12.4606i	0.654009	−	1.13278i	0.982141	−	0.188146i	$-0.0602477\pi$
$12$	8.76764	−	8.19319i	0.730637	−	0.682766i
$13$	5.50333	−	3.17735i	0.423333	−	0.244411i	−0.273169	−	0.961966i	$-0.588072\pi$
$13$	5.50333	−	3.17735i	0.423333	−	0.244411i	0.696502	+	0.717554i	$0.254739\pi$
$14$	0.595181	−	1.85538i	0.0425129	−	0.132527i
$15$	−16.4195	−	14.4598i	−1.09463	−	0.963986i
$16$	10.5269	−	12.0492i	0.657932	−	0.753078i
$17$			27.9331i			1.64312i	0.570120	+	0.821561i	$0.306897\pi$
$17$			27.9331i			1.64312i	−0.570120	+	0.821561i	$0.693103\pi$
$18$	−11.6955	+	13.6826i	−0.649752	+	0.760146i
$19$			9.44492i			0.497101i	0.968619	+	0.248551i	$0.0799542\pi$
$19$			9.44492i			0.497101i	−0.968619	+	0.248551i	$0.920046\pi$
$20$	−23.7282	−	16.9697i	−1.18641	−	0.848483i
$21$	−0.576137	+	2.86541i	−0.0274351	+	0.136448i
$22$	−8.78992	+	27.4011i	−0.399542	+	1.24550i
$23$	5.15167	−	2.97432i	0.223986	−	0.129318i	−0.383809	−	0.923413i	$-0.625388\pi$
$23$	5.15167	−	2.97432i	0.223986	−	0.129318i	0.607794	+	0.794094i	$0.292054\pi$
$24$	−13.6715	+	19.7254i	−0.569644	+	0.821892i
$25$	−14.0937	+	24.4110i	−0.563747	+	0.976438i
$26$	−9.41303	+	8.53953i	−0.362040	+	0.328444i
$27$	15.1396	−	22.3560i	0.560726	−	0.828002i
$28$	−0.378329	+	3.87860i	−0.0135117	+	0.138521i
$29$	−24.9939	+	43.2907i	−0.861858	+	1.49278i	0.00827466	+	0.999966i	$0.497366\pi$
$29$	−24.9939	+	43.2907i	−0.861858	+	1.49278i	−0.870133	+	0.492817i	$0.835967\pi$
$30$	38.2142	+	21.3172i	1.27381	+	0.710572i
$31$	−11.0551	−	19.1481i	−0.356617	−	0.617679i	0.630776	−	0.775965i	$-0.282737\pi$
$31$	−11.0551	−	19.1481i	−0.356617	−	0.617679i	−0.987393	+	0.158286i	$0.949403\pi$
$32$	−15.4787	+	28.0073i	−0.483709	+	0.875229i
$33$	8.50866	−	42.3177i	0.257838	−	1.28235i
$34$	−11.8196	−	54.6015i	−0.347637	−	1.60593i
$35$	7.10518			0.203005
$36$	17.0719	−	31.6947i	0.474219	−	0.880407i
$37$			20.4275i			0.552095i	0.961144	+	0.276048i	$0.0890247\pi$
$37$			20.4275i			0.552095i	−0.961144	+	0.276048i	$0.910975\pi$
$38$	−3.99654	−	18.4622i	−0.105172	−	0.485848i
$39$	12.5995	−	14.3071i	0.323064	−	0.366848i
$40$	53.5627	+	23.1307i	1.33907	+	0.578266i
$41$	16.9300	−	9.77457i	0.412928	−	0.238404i	−0.279119	−	0.960257i	$-0.590042\pi$
$41$	16.9300	−	9.77457i	0.412928	−	0.238404i	0.692047	+	0.721852i	$0.256709\pi$
$42$	−0.0862836	−	5.84487i	−0.00205437	−	0.139164i
$43$	−19.6424	−	11.3405i	−0.456800	−	0.263733i	0.253898	−	0.967231i	$-0.418287\pi$
$43$	−19.6424	−	11.3405i	−0.456800	−	0.263733i	−0.710698	+	0.703498i	$0.751621\pi$
$44$	5.58734	−	57.2810i	0.126985	−	1.30184i
$45$	−60.5358	−	25.3690i	−1.34524	−	0.563756i
$46$	−8.81154	+	7.99386i	−0.191555	+	0.173780i
$47$	71.3325	+	41.1838i	1.51771	+	0.876252i	0.999783	+	0.0208290i	$0.00663055\pi$
$47$	71.3325	+	41.1838i	1.51771	+	0.876252i	0.517930	+	0.855423i	$0.326703\pi$
$48$	18.3773	−	44.3427i	0.382861	−	0.923806i
$49$	24.0254	+	41.6132i	0.490315	+	0.849250i
$50$	17.2200	−	53.6803i	0.344399	−	1.07361i
$51$	26.7720	+	79.4076i	0.524941	+	1.55701i
$52$	14.7865	−	20.6755i	0.284355	−	0.397606i
$53$	53.3204			1.00605			0.503023	−	0.864273i	$-0.332221\pi$
$53$	53.3204			1.00605			0.503023	+	0.864273i	$0.332221\pi$
$54$	−20.1340	+	50.1061i	−0.372851	+	0.927891i
$55$	−104.933			−1.90787
$56$	−0.901666	−	7.74168i	−0.0161012	−	0.138244i
$57$	9.05232	+	26.8499i	0.158813	+	0.471050i
$58$	30.5381	−	95.1974i	0.526519	−	1.64133i
$59$	−29.5218	−	51.1333i	−0.500370	−	0.866667i	−1.00000		0.000427657i	$-0.999864\pi$
$59$	−29.5218	−	51.1333i	−0.500370	−	0.866667i	0.499630	−	0.866239i	$-0.333469\pi$
$60$	−83.7184	−	25.4992i	−1.39531	−	0.424986i
$61$	−9.09207	−	5.24931i	−0.149050	−	0.0860543i	0.423620	−	0.905840i	$-0.360759\pi$
$61$	−9.09207	−	5.24931i	−0.149050	−	0.0860543i	−0.572670	+	0.819786i	$0.694093\pi$
$62$	29.7121	+	32.7513i	0.479227	+	0.528247i
$63$	1.10847	+	8.69791i	0.0175947	+	0.138062i
$64$	18.4055	−	61.2963i	0.287586	−	0.957755i
$65$	−40.1356	−	23.1723i	−0.617471	−	0.356497i
$66$	1.27428	+	86.3198i	0.0193072	+	1.30788i
$67$	−44.8003	+	25.8655i	−0.668662	+	0.386052i	−0.795569	−	0.605862i	$-0.792828\pi$
$67$	−44.8003	+	25.8655i	−0.668662	+	0.386052i	0.126908	+	0.991915i	$0.459495\pi$
$68$	46.2083	+	101.730i	0.679534	+	1.49602i
$69$	11.7944	−	13.3929i	0.170933	−	0.194099i
$70$	−13.8887	+	3.00650i	−0.198410	+	0.0429500i
$71$			11.6970i			0.164746i	0.996602	+	0.0823731i	$0.0262499\pi$
$71$			11.6970i			0.164746i	−0.996602	+	0.0823731i	$0.973750\pi$
$72$	−19.9595	+	69.1782i	−0.277215	+	0.960808i
$73$	−39.1030			−0.535658			−0.267829	−	0.963466i	$-0.586306\pi$
$73$	−39.1030			−0.535658			−0.267829	+	0.963466i	$0.586306\pi$
$74$	−8.64373	−	39.9302i	−0.116807	−	0.539597i
$75$	−16.6690	+	82.9029i	−0.222253	+	1.10537i
$76$	15.6243	+	34.3975i	0.205583	+	0.452599i
$77$	7.00886	+	12.1397i	0.0910242	+	0.157659i
$78$	−18.5746	+	33.2978i	−0.238136	+	0.426895i
$79$	49.7902	−	86.2392i	0.630256	−	1.09163i	−0.357244	−	0.934011i	$-0.616283\pi$
$79$	49.7902	−	86.2392i	0.630256	−	1.09163i	0.987499	−	0.157624i	$-0.0503833\pi$
$80$	−114.488	−	22.5495i	−1.43110	−	0.281868i
$81$	21.6118	−	78.0636i	0.266812	−	0.963749i
$82$	−28.9576	+	26.2704i	−0.353141	+	0.320371i
$83$	3.61441	−	6.26034i	0.0435471	−	0.0754258i	−0.843430	−	0.537239i	$-0.819467\pi$
$83$	3.61441	−	6.26034i	0.0435471	−	0.0754258i	0.886977	+	0.461813i	$0.152801\pi$
$84$	2.64187	+	11.3886i	0.0314508	+	0.135579i
$85$	176.422	−	101.857i	2.07556	−	1.19832i
$86$	43.1941	+	13.8561i	0.502257	+	0.161118i
$87$	−29.5610	+	147.021i	−0.339781	+	1.68990i
$88$	13.3162	+	114.333i	0.151321	+	1.29924i
$89$		−	97.4870i		−	1.09536i	−0.836688	−	0.547680i	$-0.815511\pi$
$89$		−	97.4870i		−	1.09536i	0.836688	−	0.547680i	$-0.184489\pi$
$90$	129.066	+	23.9743i	1.43406	+	0.266381i
$91$			6.19107i			0.0680338i
$92$	13.8416	−	19.3543i	0.150452	−	0.210373i
$93$	−49.7795	−	43.8382i	−0.535263	−	0.471378i
$94$	−156.862	−	50.3194i	−1.66875	−	0.535312i
$95$	59.6531	−	34.4408i	0.627928	−	0.362534i
$96$	−17.1594	+	94.4540i	−0.178743	+	0.983896i
$97$	−2.40597	+	4.16727i	−0.0248038	+	0.0429615i	−0.878161	−	0.478365i	$-0.841229\pi$
$97$	−2.40597	+	4.16727i	−0.0248038	+	0.0429615i	0.853357	+	0.521327i	$0.174563\pi$
$98$	−64.5714	−	71.1763i	−0.658892	−	0.726289i
$99$	−16.3704	−	128.455i	−0.165358	−	1.29752i
$100$	−10.9459	+	112.217i	−0.109459	+	1.12217i
$101$	−43.9528	+	76.1284i	−0.435176	+	0.753747i	−0.997310	−	0.0732995i	$-0.976647\pi$
$101$	−43.9528	+	76.1284i	−0.435176	+	0.753747i	0.562134	+	0.827046i	$0.309980\pi$
$102$	−85.9325	−	143.892i	−0.842476	−	1.41070i
$103$	45.3603	+	78.5664i	0.440392	+	0.762781i	0.997718	−	0.0675126i	$-0.0215063\pi$
$103$	45.3603	+	78.5664i	0.440392	+	0.762781i	−0.557327	+	0.830293i	$0.688173\pi$
$104$	−20.1548	+	46.6717i	−0.193796	+	0.448766i
$105$	20.1985	−	6.80984i	0.192366	−	0.0648556i
$106$	−104.227	+	22.5621i	−0.983272	+	0.212850i
$107$	89.7751			0.839019			0.419510	−	0.907751i	$-0.362202\pi$
$107$	89.7751			0.839019			0.419510	+	0.907751i	$0.362202\pi$
$108$	18.1544	−	106.463i	0.168096	−	0.985771i
$109$		−	23.2258i		−	0.213081i	−0.994308	−	0.106541i	$-0.966023\pi$
$109$		−	23.2258i		−	0.213081i	0.994308	−	0.106541i	$-0.0339774\pi$
$110$	205.115	−	44.4014i	1.86468	−	0.403649i
$111$	19.5784	+	58.0710i	0.176382	+	0.523162i
$112$	5.03834	+	14.7513i	0.0449851	+	0.131708i
$113$	−176.078	+	101.659i	−1.55821	+	0.899636i	−0.560787	+	0.827960i	$0.689501\pi$
$113$	−176.078	+	101.659i	−1.55821	+	0.899636i	−0.997428	+	0.0716756i	$0.977165\pi$
$114$	−29.0561	−	48.6537i	−0.254878	−	0.426787i
$115$	−37.5709	−	21.6916i	−0.326704	−	0.188623i
$116$	−19.4117	+	199.007i	−0.167342	+	1.71557i
$117$	22.1052	−	52.7477i	0.188934	−	0.450835i
$118$	79.3437	+	87.4597i	0.672405	+	0.741184i
$119$	−23.5679	−	13.6069i	−0.198049	−	0.114344i
$120$	174.436	+	14.4191i	1.45364	+	0.120160i
$121$	−43.0102	−	74.4959i	−0.355457	−	0.615669i
$122$	19.9937	+	6.41373i	0.163883	+	0.0525715i
$123$	38.7602	−	44.0133i	0.315123	−	0.357831i
$124$	−71.9374	−	51.4474i	−0.580141	−	0.414898i
$125$	23.2452			0.185962
$126$	−5.84720	−	16.5330i	−0.0464064	−	0.131214i
$127$	136.231			1.07268			0.536341	−	0.844001i	$-0.319806\pi$
$127$	136.231			1.07268			0.536341	+	0.844001i	$0.319806\pi$
$128$	−10.0407	+	127.606i	−0.0784428	+	0.996919i
$129$	−66.7081	−	13.4128i	−0.517117	−	0.103975i
$130$	88.2592	+	28.3124i	0.678917	+	0.217788i
$131$	−64.6178	−	111.921i	−0.493265	−	0.854361i	0.506705	−	0.862120i	$-0.330863\pi$
$131$	−64.6178	−	111.921i	−0.493265	−	0.854361i	−0.999970	+	0.00775919i	$0.997530\pi$
$132$	−39.0164	−	168.192i	−0.295579	−	1.27418i
$133$	−7.96893	−	4.60086i	−0.0599168	−	0.0345930i
$134$	76.6276	−	69.5168i	0.571848	−	0.518782i
$135$	−196.405	−	14.0991i	−1.45485	−	0.104438i
$136$	−133.371	−	179.301i	−0.980666	−	1.31839i
$137$	−49.8871	−	28.8023i	−0.364139	−	0.210236i	0.306756	−	0.951788i	$-0.400757\pi$
$137$	−49.8871	−	28.8023i	−0.364139	−	0.210236i	−0.670895	+	0.741552i	$0.734090\pi$
$138$	−17.3877	+	31.1701i	−0.125998	+	0.225870i
$139$	−177.605	+	102.541i	−1.27774	+	0.737702i	−0.976432	−	0.215826i	$-0.930756\pi$
$139$	−177.605	+	102.541i	−1.27774	+	0.737702i	−0.301305	+	0.953528i	$0.597422\pi$
$140$	25.8764	−	11.7538i	0.184831	−	0.0839554i
$141$	242.255	+	48.7093i	1.71812	+	0.345456i
$142$	−4.94948	−	22.8644i	−0.0348555	−	0.161017i
$143$		−	91.4327i		−	0.639390i
$144$	9.74318	−	143.670i	0.0676610	−	0.997708i
$145$	364.559			2.51420
$146$	76.4357	−	16.5461i	0.523532	−	0.113330i
$147$	108.183	+	95.2706i	0.735935	+	0.648099i
$148$	33.7922	+	74.3950i	0.228326	+	0.502669i
$149$	−56.1503	−	97.2551i	−0.376847	−	0.652719i	0.613754	−	0.789497i	$-0.289659\pi$
$149$	−56.1503	−	97.2551i	−0.376847	−	0.652719i	−0.990602	+	0.136778i	$0.956325\pi$
$150$	−2.49638	−	169.106i	−0.0166426	−	1.12737i
$151$	56.2835	−	97.4858i	0.372738	−	0.645602i	−0.617247	−	0.786769i	$-0.711752\pi$
$151$	56.2835	−	97.4858i	0.372738	−	0.645602i	0.989986	+	0.141167i	$0.0450856\pi$
$152$	−45.0962	−	60.6264i	−0.296685	−	0.398858i
$153$	152.214	+	200.079i	0.994861	+	1.30771i
$154$	−18.8372	−	20.7641i	−0.122320	−	0.134832i
$155$	−80.6248	+	139.646i	−0.520160	+	0.900943i
$156$	22.2186	−	72.9477i	0.142427	−	0.467614i
$157$	−136.615	+	78.8748i	−0.870160	+	0.502387i	−0.867402	−	0.497609i	$-0.834212\pi$
$157$	−136.615	+	78.8748i	−0.870160	+	0.502387i	−0.00275886	+	0.999996i	$0.500878\pi$
$158$	−60.8348	+	189.642i	−0.385030	+	1.20027i
$159$	151.578	−	51.1040i	0.953323	−	0.321409i
$160$	233.334	−	4.36656i	1.45834	−	0.0272910i
$161$			5.79546i			0.0359967i
$162$	−9.21314	+	161.738i	−0.0568712	+	0.998382i
$163$		−	65.7610i		−	0.403442i	−0.979443	−	0.201721i	$-0.935347\pi$
$163$		−	65.7610i		−	0.403442i	0.979443	−	0.201721i	$-0.0646534\pi$
$164$	45.4880	−	63.6046i	0.277366	−	0.387833i
$165$	−298.301	+	100.571i	−1.80788	+	0.609521i
$166$	−4.41617	+	13.7667i	−0.0266034	+	0.0829317i
$167$	−182.106	+	105.139i	−1.09046	+	0.629576i	−0.933698	−	0.358061i	$-0.883438\pi$
$167$	−182.106	+	105.139i	−1.09046	+	0.629576i	−0.156759	+	0.987637i	$0.550105\pi$
$168$	−9.98312	−	21.1437i	−0.0594233	−	0.125855i
$169$	−64.3089	+	111.386i	−0.380526	+	0.659090i
$170$	−301.757	+	273.755i	−1.77504	+	1.61032i
$171$	51.4676	+	67.6522i	0.300980	+	0.395627i
$172$	−90.2957	−	8.80769i	−0.524975	−	0.0512075i
$173$	−23.7597	+	41.1530i	−0.137339	+	0.237878i	−0.926489	−	0.376323i	$-0.877188\pi$
$173$	−23.7597	+	41.1530i	−0.137339	+	0.237878i	0.789149	+	0.614201i	$0.210522\pi$
$174$	−4.42712	−	299.894i	−0.0254432	−	1.72353i
$175$	−13.7308	−	23.7824i	−0.0784616	−	0.135899i
$176$	−74.4085	−	217.855i	−0.422776	−	1.23781i
$177$	−132.932	−	117.066i	−0.751028	−	0.661391i
$178$	41.2508	+	190.560i	0.231746	+	1.07056i
$179$	70.1002			0.391621			0.195811	−	0.980642i	$-0.437266\pi$
$179$	70.1002			0.391621			0.195811	+	0.980642i	$0.437266\pi$
$180$	−262.432	+	7.74988i	−1.45796	+	0.0430549i
$181$			203.289i			1.12314i	0.827428	+	0.561572i	$0.189803\pi$
$181$			203.289i			1.12314i	−0.827428	+	0.561572i	$0.810197\pi$
$182$	−2.61970	−	12.1018i	−0.0143940	−	0.0664937i
$183$	−30.8779	−	6.20850i	−0.168732	−	0.0339262i
$184$	−18.8669	+	43.6894i	−0.102538	+	0.237442i
$185$	129.018	−	74.4886i	0.697395	−	0.402641i
$186$	115.855	+	64.6278i	0.622876	+	0.347461i
$187$	348.062	+	200.953i	1.86129	+	1.07462i
$188$	327.914	+	31.9857i	1.74423	+	0.170137i
$189$	11.4875	+	23.6639i	0.0607804	+	0.125206i
$190$	−102.032	+	92.5639i	−0.537011	+	0.487179i
$191$	−213.002	−	122.977i	−1.11519	−	0.643858i	−0.175024	−	0.984564i	$-0.556000\pi$
$191$	−213.002	−	122.977i	−1.11519	−	0.643858i	−0.940170	+	0.340706i	$0.889334\pi$
$192$	−6.42558	−	191.892i	−0.0334665	−	0.999440i
$193$	−38.1192	−	66.0245i	−0.197509	−	0.342096i	0.750211	−	0.661198i	$-0.229952\pi$
$193$	−38.1192	−	66.0245i	−0.197509	−	0.342096i	−0.947720	+	0.319103i	$0.896619\pi$
$194$	2.93967	−	9.16393i	0.0151529	−	0.0472367i
$195$	−136.306	−	27.4065i	−0.699004	−	0.140546i
$196$	156.337	+	111.807i	0.797638	+	0.570445i
$197$	−111.573			−0.566362			−0.283181	−	0.959066i	$-0.591390\pi$
$197$	−111.573			−0.566362			−0.283181	+	0.959066i	$0.591390\pi$
$198$	86.3543	+	244.167i	0.436133	+	1.23317i
$199$	−167.601			−0.842215			−0.421107	−	0.907011i	$-0.638358\pi$
$199$	−167.601			−0.842215			−0.421107	+	0.907011i	$0.638358\pi$
$200$	−26.0873	−	223.985i	−0.130436	−	1.11992i
$201$	−102.567	+	116.468i	−0.510285	+	0.579443i
$202$	53.7025	−	167.408i	0.265854	−	0.828754i
$203$	−24.3503	−	42.1760i	−0.119952	−	0.207764i
$204$	228.861	+	244.907i	1.12187	+	1.20053i
$205$	−123.470	−	71.2856i	−0.602294	−	0.347735i
$206$	−121.912	−	134.382i	−0.591804	−	0.652339i
$207$	20.6927	−	49.3771i	0.0999647	−	0.238537i
$208$	19.6484	−	99.7586i	0.0944635	−	0.479609i
$209$	117.689	+	67.9478i	0.563105	+	0.325109i
$210$	−36.6009	+	21.8582i	−0.174290	+	0.104087i
$211$	214.255	−	123.700i	1.01543	−	0.586258i	0.102652	−	0.994717i	$-0.467267\pi$
$211$	214.255	−	123.700i	1.01543	−	0.586258i	0.912777	+	0.408459i	$0.133934\pi$
$212$	194.188	−	88.2054i	0.915980	−	0.416063i
$213$	11.2108	+	33.2519i	0.0526327	+	0.156112i
$214$	−175.486	+	37.9876i	−0.820026	+	0.177512i
$215$			165.412i			0.769359i
$216$	9.56213	+	215.788i	0.0442691	+	0.999020i
$217$	21.5410			0.0992671
$218$	9.82782	+	45.4001i	0.0450817	+	0.208258i
$219$	−111.161	+	37.4776i	−0.507586	+	0.171131i
$220$	−382.155	+	173.585i	−1.73707	+	0.789023i
$221$	88.7532	+	153.725i	0.401598	+	0.695588i
$222$	−62.8427	−	105.228i	−0.283075	−	0.474002i
$223$	−12.4529	+	21.5690i	−0.0558425	+	0.0967220i	−0.892595	−	0.450859i	$-0.851118\pi$
$223$	−12.4529	+	21.5690i	−0.0558425	+	0.0967220i	0.836753	+	0.547581i	$0.184451\pi$
$224$	−16.0905	−	26.7029i	−0.0718324	−	0.119209i
$225$	32.0706	+	251.651i	0.142536	+	1.11845i
$226$	301.169	−	273.221i	1.33260	−	1.20894i
$227$	−35.0772	+	60.7555i	−0.154525	+	0.267645i	−0.932886	−	0.360172i	$-0.882718\pi$
$227$	−35.0772	+	60.7555i	−0.154525	+	0.267645i	0.778361	+	0.627817i	$0.216051\pi$
$228$	77.3841	+	82.8097i	0.339404	+	0.363201i
$229$	−39.4105	+	22.7537i	−0.172098	+	0.0993610i	−0.583575	−	0.812059i	$-0.698347\pi$
$229$	−39.4105	+	22.7537i	−0.172098	+	0.0993610i	0.411477	+	0.911420i	$0.365013\pi$
$230$	82.6195	+	26.5033i	0.359215	+	0.115232i
$231$	31.5598	+	27.7930i	0.136622	+	0.120316i
$232$	−46.2635	−	397.217i	−0.199412	−	1.71214i
$233$			61.2376i			0.262823i	0.991328	+	0.131411i	$0.0419508\pi$
$233$			61.2376i			0.262823i	−0.991328	+	0.131411i	$0.958049\pi$
$234$	−20.8899	+	112.461i	−0.0892731	+	0.480602i
$235$		−	600.705i		−	2.55619i
$236$	−192.103	−	137.386i	−0.813996	−	0.582144i
$237$	58.8882	−	292.880i	0.248474	−	1.23578i
$238$	51.8264	+	16.6252i	0.217758	+	0.0698540i
$239$	333.772	−	192.703i	1.39654	−	0.806290i	0.402508	−	0.915417i	$-0.368139\pi$
$239$	333.772	−	192.703i	1.39654	−	0.806290i	0.994028	+	0.109126i	$0.0348053\pi$
$240$	−347.076	+	45.6257i	−1.44615	+	0.190107i
$241$	−74.7946	+	129.548i	−0.310351	+	0.537544i	−0.978438	−	0.206539i	$-0.933780\pi$
$241$	−74.7946	+	129.548i	−0.310351	+	0.537544i	0.668087	+	0.744083i	$0.267113\pi$
$242$	115.596	+	127.420i	0.477668	+	0.526528i
$243$	−13.3812	−	242.631i	−0.0550665	−	0.998483i
$244$	−41.7961	−	4.07691i	−0.171296	−	0.0167086i
$245$	175.217	−	303.484i	0.715170	−	1.23871i
$246$	−57.1416	+	102.435i	−0.232283	+	0.416402i
$247$	30.0098	+	51.9785i	0.121497	+	0.210439i
$248$	162.387	+	70.1258i	0.654788	+	0.282765i
$249$	4.27486	−	21.2610i	0.0171681	−	0.0853854i
$250$	−45.4380	+	9.83600i	−0.181752	+	0.0393440i
$251$	45.3870			0.180825			0.0904124	−	0.995904i	$-0.471181\pi$
$251$	45.3870			0.180825			0.0904124	+	0.995904i	$0.471181\pi$
$252$	18.4255	+	29.8433i	0.0731169	+	0.118426i
$253$		−	85.5902i		−	0.338301i
$254$	−266.294	+	57.6449i	−1.04840	+	0.226948i
$255$	403.907	−	458.648i	1.58395	−	1.79862i
$256$	−34.3684	−	253.682i	−0.134252	−	0.990947i
$257$	222.508	−	128.465i	0.865792	−	0.499865i	−0.000155813	−	1.00000i	$-0.500050\pi$
$257$	222.508	−	128.465i	0.865792	−	0.499865i	0.865947	+	0.500135i	$0.166716\pi$
$258$	136.072	−	2.00873i	0.527409	−	0.00778576i
$259$	−17.2352	−	9.95077i	−0.0665453	−	0.0384200i
$260$	−184.503	−	17.9969i	−0.709626	−	0.0692188i
$261$	56.8744	+	446.281i	0.217909	+	1.70989i
$262$	173.668	+	191.433i	0.662857	+	0.730660i
$263$	−32.8570	−	18.9700i	−0.124932	−	0.0721293i	0.436232	−	0.899834i	$-0.356313\pi$
$263$	−32.8570	−	18.9700i	−0.124932	−	0.0721293i	−0.561163	+	0.827705i	$0.689646\pi$
$264$	147.435	+	312.260i	0.558468	+	1.18280i
$265$	−194.432	−	336.766i	−0.733706	−	1.27082i
$266$	17.5239	+	5.62144i	0.0658793	+	0.0211332i
$267$	−93.4348	−	277.134i	−0.349943	−	1.03796i
$268$	−120.370	+	168.311i	−0.449144	+	0.628025i
$269$	263.974			0.981317			0.490658	−	0.871352i	$-0.336756\pi$
$269$	263.974			0.981317			0.490658	+	0.871352i	$0.336756\pi$
$270$	389.883	−	55.5471i	1.44401	−	0.205730i
$271$	−168.684			−0.622452			−0.311226	−	0.950336i	$-0.600740\pi$
$271$	−168.684			−0.622452			−0.311226	+	0.950336i	$0.600740\pi$
$272$	336.572	+	294.049i	1.23740	+	1.08106i
$273$	5.93373	+	17.5999i	0.0217353	+	0.0644684i
$274$	109.703	+	35.1913i	0.400376	+	0.128436i
$275$	202.783	+	351.230i	0.737392	+	1.27720i
$276$	20.7988	−	68.2864i	0.0753581	−	0.247414i
$277$	−133.553	−	77.1069i	−0.482141	−	0.278364i	0.239167	−	0.970978i	$-0.423126\pi$
$277$	−133.553	−	77.1069i	−0.482141	−	0.278364i	−0.721308	+	0.692614i	$0.756459\pi$
$278$	303.781	−	275.591i	1.09274	−	0.991334i
$279$	−183.528	−	76.9120i	−0.657807	−	0.275670i
$280$	−45.6077	+	33.9247i	−0.162885	+	0.121160i
$281$	315.098	+	181.922i	1.12135	+	0.647409i	0.941744	−	0.336330i	$-0.109186\pi$
$281$	315.098	+	181.922i	1.12135	+	0.647409i	0.179602	+	0.983739i	$0.442519\pi$
$282$	−494.152	+	7.29481i	−1.75231	+	0.0258681i
$283$	−196.214	+	113.284i	−0.693336	+	0.400298i	−0.804861	−	0.593464i	$-0.797760\pi$
$283$	−196.214	+	113.284i	−0.693336	+	0.400298i	0.111525	+	0.993762i	$0.464427\pi$
$284$	19.3497	+	42.5992i	0.0681329	+	0.149997i
$285$	136.572	−	155.081i	0.479199	−	0.544144i
$286$	38.6890	+	178.726i	0.135276	+	0.624916i
$287$			19.0458i			0.0663616i
$288$	41.7475	+	284.958i	0.144957	+	0.989438i
$289$	−491.257			−1.69985
$290$	−712.613	+	154.260i	−2.45729	+	0.531932i
$291$	−2.84561	+	14.1526i	−0.00977872	+	0.0486343i
$292$	−142.409	+	64.6862i	−0.487703	+	0.221528i
$293$	−239.739	−	415.240i	−0.818223	−	1.41720i	−0.906991	−	0.421151i	$-0.861626\pi$
$293$	−239.739	−	415.240i	−0.818223	−	1.41720i	0.0887681	−	0.996052i	$-0.471707\pi$
$294$	−251.780	−	140.451i	−0.856395	−	0.477726i
$295$	−215.302	+	372.914i	−0.729837	+	1.26411i
$296$	−97.5342	−	131.123i	−0.329507	−	0.442983i
$297$	−169.653	−	349.479i	−0.571222	−	1.17670i
$298$	150.911	+	166.348i	0.506413	+	0.558213i
$299$	18.9009	−	32.7373i	0.0632137	−	0.109489i
$300$	76.4354	+	329.499i	0.254785	+	1.09833i
$301$	19.1366	−	11.0485i	0.0635768	−	0.0367061i
$302$	−68.7684	+	214.374i	−0.227710	+	0.709847i
$303$	−51.9841	+	258.542i	−0.171565	+	0.853275i
$304$	113.804	+	99.4258i	0.374356	+	0.327059i
$305$			76.5661i			0.251036i
$306$	−382.198	−	326.692i	−1.24901	−	1.06762i
$307$			499.062i			1.62561i	0.582537	+	0.812804i	$0.302060\pi$
$307$			499.062i			1.62561i	−0.582537	+	0.812804i	$0.697940\pi$
$308$	45.6077	+	32.6172i	0.148077	+	0.105900i
$309$	204.250	+	179.872i	0.661004	+	0.582111i
$310$	98.5092	−	307.086i	0.317771	−	0.990599i
$311$	−328.817	+	189.843i	−1.05729	+	0.610426i	−0.924681	−	0.380742i	$-0.875668\pi$
$311$	−328.817	+	189.843i	−1.05729	+	0.610426i	−0.132608	+	0.991169i	$0.542335\pi$
$312$	−12.5641	+	151.994i	−0.0402695	+	0.487161i
$313$	5.44519	−	9.43134i	0.0173968	−	0.0301321i	−0.857196	−	0.514990i	$-0.827795\pi$
$313$	5.44519	−	9.43134i	0.0173968	−	0.0301321i	0.874593	+	0.484858i	$0.161129\pi$
$314$	233.670	−	211.986i	0.744172	−	0.675115i
$315$	50.8931	−	38.7178i	0.161565	−	0.122914i
$316$	38.6698	−	396.440i	0.122373	−	1.25456i
$317$	4.28748	−	7.42613i	0.0135252	−	0.0234263i	−0.859184	−	0.511667i	$-0.829028\pi$
$317$	4.28748	−	7.42613i	0.0135252	−	0.0234263i	0.872709	+	0.488241i	$0.162361\pi$
$318$	−274.670	+	164.033i	−0.863741	+	0.515829i
$319$	359.617	+	622.875i	1.12733	+	1.95259i
$320$	−454.256	+	107.269i	−1.41955	+	0.335215i
$321$	255.211	−	86.0434i	0.795049	−	0.268048i
$322$	−2.45230	−	11.3285i	−0.00761584	−	0.0351818i
$323$	−263.826			−0.816798
$324$	−50.4288	−	320.051i	−0.155645	−	0.987813i
$325$			179.122i			0.551145i
$326$	27.8262	+	128.545i	0.0853565	+	0.394309i
$327$	−22.2604	−	66.0260i	−0.0680746	−	0.201914i
$328$	−62.0028	+	143.577i	−0.189033	+	0.437736i
$329$	−69.4958	+	40.1234i	−0.211233	+	0.121956i
$330$	540.540	−	322.812i	1.63800	−	0.978218i
$331$	223.655	+	129.127i	0.675696	+	0.390113i	0.798231	−	0.602351i	$-0.205769\pi$
$331$	223.655	+	129.127i	0.675696	+	0.390113i	−0.122535	+	0.992464i	$0.539103\pi$
$332$	2.80715	−	28.7787i	0.00845528	−	0.0866828i
$333$	111.314	+	146.319i	0.334277	+	0.439395i
$334$	311.479	−	282.575i	0.932573	−	0.846033i
$335$	326.727	+	188.636i	0.975306	+	0.563093i
$336$	28.4610	+	37.1059i	0.0847055	+	0.110434i
$337$	−232.942	−	403.468i	−0.691223	−	1.19723i	−0.971437	−	0.237296i	$-0.923739\pi$
$337$	−232.942	−	403.468i	−0.691223	−	1.19723i	0.280214	−	0.959937i	$-0.409594\pi$
$338$	78.5741	−	244.941i	0.232468	−	0.724679i
$339$	−403.119	+	457.753i	−1.18914	+	1.35030i
$340$	474.015	−	662.802i	1.39416	−	1.94942i
$341$	−318.127			−0.932925
$342$	−129.231	−	110.463i	−0.377870	−	0.322993i
$343$	−94.5519			−0.275661
$344$	180.230	−	20.9913i	0.523925	−	0.0610211i
$345$	−127.596	−	25.6552i	−0.369843	−	0.0743630i
$346$	29.0301	−	90.4965i	0.0839021	−	0.261551i
$347$	164.749	+	285.353i	0.474781	+	0.822344i	0.999583	−	0.0288800i	$-0.00919406\pi$
$347$	164.749	+	285.353i	0.474781	+	0.822344i	−0.524802	+	0.851224i	$0.675861\pi$
$348$	135.551	+	584.337i	0.389516	+	1.67913i
$349$	−228.379	−	131.855i	−0.654382	−	0.377808i	0.135751	−	0.990743i	$-0.456655\pi$
$349$	−228.379	−	131.855i	−0.654382	−	0.377808i	−0.790133	+	0.612935i	$0.789989\pi$
$350$	36.9032	+	40.6780i	0.105438	+	0.116223i
$351$	12.2852	−	171.136i	0.0350006	−	0.487568i
$352$	237.632	+	394.361i	0.675090	+	1.12034i
$353$	35.4468	+	20.4652i	0.100416	+	0.0579752i	0.549367	−	0.835581i	$-0.314869\pi$
$353$	35.4468	+	20.4652i	0.100416	+	0.0579752i	−0.448951	+	0.893556i	$0.648202\pi$
$354$	309.381	+	172.583i	0.873958	+	0.487523i
$355$	73.8768	−	42.6528i	0.208104	−	0.120149i
$356$	−161.268	−	355.038i	−0.453000	−	0.997298i
$357$	−80.0396	−	16.0933i	−0.224201	−	0.0450792i
$358$	−137.027	+	29.6623i	−0.382756	+	0.0828556i
$359$		−	289.090i		−	0.805265i	−0.915362	−	0.402632i	$-0.868095\pi$
$359$		−	289.090i		−	0.805265i	0.915362	−	0.402632i	$-0.131905\pi$
$360$	509.704	−	126.195i	1.41584	−	0.350541i
$361$	271.793			0.752890
$362$	−86.0201	−	397.374i	−0.237625	−	1.09772i
$363$	−193.668	−	170.553i	−0.533521	−	0.469844i
$364$	10.2416	+	22.5473i	0.0281362	+	0.0619431i
$365$	142.588	+	246.971i	0.390653	+	0.676632i
$366$	62.9849	−	0.929800i	0.172090	−	0.00254044i
$367$	322.584	−	558.732i	0.878976	−	1.52243i	0.0265099	−	0.999649i	$-0.491561\pi$
$367$	322.584	−	558.732i	0.878976	−	1.52243i	0.852466	−	0.522783i	$-0.175106\pi$
$368$	18.3929	−	93.3841i	0.0499806	−	0.253761i
$369$	68.0029	−	162.269i	0.184290	−	0.439754i
$370$	−220.676	+	200.198i	−0.596421	+	0.541075i
$371$	−25.9737	+	44.9878i	−0.0700101	+	0.121261i
$372$	−253.811	−	77.3065i	−0.682288	−	0.207813i
$373$	314.478	−	181.564i	0.843105	−	0.486767i	−0.0152134	−	0.999884i	$-0.504843\pi$
$373$	314.478	−	181.564i	0.843105	−	0.486767i	0.858318	+	0.513117i	$0.171509\pi$
$374$	−765.397	−	245.530i	−2.04651	−	0.656496i
$375$	66.0810	−	22.2790i	0.176216	−	0.0594105i
$376$	−654.517	+	76.2310i	−1.74074	+	0.202742i
$377$			317.657i			0.842592i
$378$	−32.4681	−	41.3955i	−0.0858944	−	0.109512i
$379$		−	75.5395i		−	0.199313i	−0.995022	−	0.0996563i	$-0.968226\pi$
$379$		−	75.5395i		−	0.199313i	0.995022	−	0.0996563i	$-0.0317743\pi$
$380$	160.277	−	224.111i	0.421782	−	0.589766i
$381$	387.274	−	130.568i	1.01647	−	0.342698i
$382$	468.397	+	150.256i	1.22617	+	0.393340i
$383$	−354.219	+	204.508i	−0.924853	+	0.533964i	−0.885180	−	0.465249i	$-0.845965\pi$
$383$	−354.219	+	204.508i	−0.924853	+	0.533964i	−0.0396729	+	0.999213i	$0.512632\pi$
$384$	93.7579	+	372.378i	0.244161	+	0.969735i
$385$	51.1154	−	88.5345i	0.132767	−	0.229960i
$386$	102.450	+	112.930i	0.265415	+	0.292564i
$387$	−202.492	+	25.8057i	−0.523235	+	0.0666815i
$388$	−1.86861	+	19.1569i	−0.00481601	+	0.0493734i
$389$	190.096	−	329.255i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$389$	190.096	−	329.255i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414603\pi$
$390$	278.037	−	4.10446i	0.712916	−	0.0105243i
$391$	83.0818	+	143.902i	0.212486	+	0.368036i
$392$	−352.906	−	152.400i	−0.900271	−	0.388775i
$393$	−290.963	−	256.236i	−0.740364	−	0.652000i
$394$	218.095	−	47.2113i	0.553541	−	0.119826i
$395$	−726.236			−1.83857
$396$	−272.116	−	440.740i	−0.687162	−	1.11298i
$397$			360.629i			0.908385i	0.890903	+	0.454193i	$0.150072\pi$
$397$			360.629i			0.908385i	−0.890903	+	0.454193i	$0.849928\pi$
$398$	327.613	−	70.9188i	0.823149	−	0.178188i
$399$	−27.0635	−	5.44157i	−0.0678284	−	0.0136380i
$400$	145.771	+	426.790i	0.364427	+	1.06697i
$401$	252.357	−	145.699i	0.629320	−	0.363338i	−0.151169	−	0.988508i	$-0.548304\pi$
$401$	252.357	−	145.699i	0.629320	−	0.363338i	0.780489	+	0.625170i	$0.214970\pi$
$402$	151.208	−	271.064i	0.376140	−	0.674287i
$403$	−121.680	−	70.2521i	−0.301936	−	0.174323i
$404$	−34.1362	+	349.961i	−0.0844954	+	0.866240i
$405$	−571.849	+	148.160i	−1.41197	+	0.365827i
$406$	65.4446	+	72.1389i	0.161194	+	0.177682i
$407$	254.538	+	146.958i	0.625401	+	0.361075i
$408$	−550.991	−	381.886i	−1.35047	−	0.935995i
$409$	355.574	+	615.872i	0.869374	+	1.50580i	0.862637	+	0.505823i	$0.168811\pi$
$409$	355.574	+	615.872i	0.869374	+	1.50580i	0.00673737	+	0.999977i	$0.497855\pi$
$410$	271.514	+	87.0983i	0.662230	+	0.212435i
$411$	−169.423	−	34.0653i	−0.412222	−	0.0828839i
$412$	295.166	+	211.094i	0.716423	+	0.512364i
$413$	57.5234			0.139282
$414$	−19.5550	+	105.275i	−0.0472344	+	0.254287i
$415$	−52.7195			−0.127035
$416$	3.80479	+	203.315i	0.00914613	+	0.488737i
$417$	−406.615	+	461.723i	−0.975096	+	1.10725i
$418$	−258.801	−	83.0201i	−0.619141	−	0.198613i
$419$	−45.5135	−	78.8317i	−0.108624	−	0.188143i	0.806589	−	0.591113i	$-0.201311\pi$
$419$	−45.5135	−	78.8317i	−0.108624	−	0.188143i	−0.915213	+	0.402970i	$0.867978\pi$
$420$	62.2957	−	58.2141i	0.148323	−	0.138605i
$421$	522.383	+	301.598i	1.24081	+	0.716384i	0.969260	−	0.246039i	$-0.0791291\pi$
$421$	522.383	+	301.598i	1.24081	+	0.716384i	0.271554	+	0.962423i	$0.412462\pi$
$422$	−366.468	+	332.461i	−0.868407	+	0.787822i
$423$	735.362	−	93.7151i	1.73844	−	0.221549i
$424$	−342.260	+	254.586i	−0.807218	+	0.600439i
$425$	−681.873	−	393.680i	−1.60441	−	0.926305i
$426$	−35.9842	−	60.2547i	−0.0844701	−	0.141443i
$427$	8.85796	−	5.11415i	0.0207446	−	0.0119769i
$428$	326.952	−	148.510i	0.763907	−	0.346987i
$429$	−87.6321	−	259.923i	−0.204271	−	0.605882i
$430$	−69.9928	−	323.336i	−0.162774	−	0.751943i
$431$			359.559i			0.834243i	0.908851	+	0.417121i	$0.136961\pi$
$431$			359.559i			0.834243i	−0.908851	+	0.417121i	$0.863039\pi$
$432$	−110.000	−	417.761i	−0.254630	−	0.967038i
$433$	116.165			0.268280			0.134140	−	0.990962i	$-0.457173\pi$
$433$	116.165			0.268280			0.134140	+	0.990962i	$0.457173\pi$
$434$	−42.1067	+	9.11488i	−0.0970200	+	0.0210020i
$435$	1036.36	−	349.406i	2.38244	−	0.803231i
$436$	−38.4214	−	84.5863i	−0.0881224	−	0.194005i
$437$	28.0922	+	48.6571i	0.0642842	+	0.111344i
$438$	201.432	−	120.295i	0.459889	−	0.274647i
$439$	−36.5695	+	63.3402i	−0.0833018	+	0.144283i	−0.904666	−	0.426121i	$-0.859880\pi$
$439$	−36.5695	+	63.3402i	−0.0833018	+	0.144283i	0.821364	+	0.570404i	$0.193213\pi$
$440$	673.556	−	501.017i	1.53081	−	1.13867i
$441$	398.850	+	167.148i	0.904421	+	0.379020i
$442$	−238.535	−	262.935i	−0.539673	−	0.594875i
$443$	339.905	−	588.732i	0.767279	−	1.32897i	−0.171754	−	0.985140i	$-0.554944\pi$
$443$	339.905	−	588.732i	0.767279	−	1.32897i	0.939033	−	0.343826i	$-0.111723\pi$
$444$	167.367	+	179.101i	0.376952	+	0.403381i
$445$	−615.718	+	355.485i	−1.38363	+	0.798842i
$446$	15.2152	−	47.4308i	0.0341148	−	0.106347i
$447$	−252.835	−	222.659i	−0.565627	−	0.498118i
$448$	42.7515	+	45.3882i	0.0954275	+	0.101313i
$449$		−	441.902i		−	0.984193i	−0.870541	−	0.492096i	$-0.836231\pi$
$449$		−	441.902i		−	0.984193i	0.870541	−	0.492096i	$-0.163769\pi$
$450$	−169.173	−	478.338i	−0.375940	−	1.06297i
$451$		−	281.277i		−	0.623674i
$452$	−473.091	+	661.509i	−1.04666	+	1.46352i
$453$	66.5680	−	331.075i	0.146949	−	0.730850i
$454$	42.8581	−	133.603i	0.0944011	−	0.294279i
$455$	39.1022	−	22.5756i	0.0859388	−	0.0496168i
$456$	−186.305	−	129.126i	−0.408563	−	0.283171i
$457$	95.9222	−	166.142i	0.209895	−	0.363550i	−0.741786	−	0.670637i	$-0.766021\pi$
$457$	95.9222	−	166.142i	0.209895	−	0.363550i	0.951681	+	0.307087i	$0.0993543\pi$
$458$	67.4087	−	61.1534i	0.147181	−	0.133523i
$459$	624.473	+	422.895i	1.36051	+	0.921341i
$460$	−172.713	−	16.8469i	−0.375463	−	0.0366237i
$461$	−196.690	+	340.678i	−0.426660	+	0.738997i	−0.996574	−	0.0827075i	$-0.973643\pi$
$461$	−196.690	+	340.678i	−0.426660	+	0.738997i	0.569914	+	0.821705i	$0.306977\pi$
$462$	−73.4510	−	40.9735i	−0.158985	−	0.0886871i
$463$	−373.830	−	647.493i	−0.807409	−	1.39847i	−0.914653	−	0.404240i	$-0.867536\pi$
$463$	−373.830	−	647.493i	−0.807409	−	1.39847i	0.107244	−	0.994233i	$-0.465797\pi$
$464$	258.512	+	756.875i	0.557137	+	1.63120i
$465$	−95.3571	+	474.257i	−0.205069	+	1.01991i
$466$	−25.9122	−	119.703i	−0.0556056	−	0.256873i
$467$	31.9600			0.0684367			0.0342184	−	0.999414i	$-0.489106\pi$
$467$	31.9600			0.0684367			0.0342184	+	0.999414i	$0.489106\pi$
$468$	−6.75283	−	228.669i	−0.0144291	−	0.488610i
$469$		−	50.3990i		−	0.107460i
$470$	254.183	+	1174.21i	0.540815	+	2.49832i
$471$	−312.771	+	355.160i	−0.664057	+	0.754056i
$472$	433.643	+	187.265i	0.918734	+	0.396749i
$473$	−282.619	+	163.170i	−0.597502	+	0.344968i
$474$	8.81924	+	597.417i	0.0186060	+	1.26037i
$475$	−230.560	−	133.114i	−0.485389	−	0.280239i
$476$	−108.341	−	10.5679i	−0.227607	−	0.0222015i
$477$	381.924	−	290.555i	0.800680	−	0.609131i
$478$	−570.892	+	517.915i	−1.19433	+	1.08350i
$479$	−599.414	−	346.072i	−1.25139	−	0.722489i	−0.280002	−	0.959999i	$-0.590335\pi$
$479$	−599.414	−	346.072i	−1.25139	−	0.722489i	−0.971385	+	0.237511i	$0.923668\pi$
$480$	659.133	−	236.048i	1.37319	−	0.491767i
$481$	64.9054	+	112.419i	0.134938	+	0.233720i
$482$	91.3858	−	284.880i	0.189597	−	0.591037i
$483$	5.55456	+	16.4752i	0.0115001	+	0.0341102i
$484$	−279.874	−	200.157i	−0.578252	−	0.413548i
$485$	35.0933			0.0723574
$486$	128.824	+	468.615i	0.265070	+	0.964229i
$487$	386.943			0.794545			0.397273	−	0.917701i	$-0.369957\pi$
$487$	386.943			0.794545			0.397273	+	0.917701i	$0.369957\pi$
$488$	83.4250	−	9.71644i	0.170953	−	0.0199107i
$489$	−63.0275	−	186.944i	−0.128891	−	0.382299i
$490$	−214.084	+	667.369i	−0.436905	+	1.36198i
$491$	167.006	+	289.263i	0.340134	+	0.589130i	0.984457	−	0.175623i	$-0.0561941\pi$
$491$	167.006	+	289.263i	0.340134	+	0.589130i	−0.644323	+	0.764754i	$0.722861\pi$
$492$	68.3517	−	224.411i	0.138926	−	0.456120i
$493$	−1209.24	−	698.156i	−2.45282	−	1.41614i
$494$	−80.6552	−	88.9054i	−0.163270	−	0.179970i
$495$	−751.613	+	571.802i	−1.51841	+	1.15516i
$496$	−347.096	−	68.3638i	−0.699790	−	0.137830i
$497$	−9.86904	−	5.69790i	−0.0198572	−	0.0114646i
$498$	0.640213	+	43.3682i	0.00128557	+	0.0870847i
$499$	225.775	−	130.351i	0.452456	−	0.261225i	−0.256411	−	0.966568i	$-0.582540\pi$
$499$	225.775	−	130.351i	0.452456	−	0.261225i	0.708867	+	0.705342i	$0.249207\pi$
$500$	84.6567	−	38.4534i	0.169313	−	0.0769068i
$501$	−416.920	+	473.425i	−0.832176	+	0.944959i
$502$	−88.7191	+	19.2051i	−0.176731	+	0.0382572i
$503$		−	659.956i		−	1.31204i	−0.754743	−	0.656020i	$-0.772239\pi$
$503$		−	659.956i		−	1.31204i	0.754743	−	0.656020i	$-0.227761\pi$
$504$	−48.6447	−	50.5388i	−0.0965172	−	0.100275i
$505$	641.092			1.26949
$506$	36.2168	+	167.305i	0.0715746	+	0.330643i
$507$	−76.0599	+	378.283i	−0.150020	+	0.746120i
$508$	496.139	−	225.360i	0.976651	−	0.443621i
$509$	321.378	+	556.642i	0.631390	+	1.09360i	0.987268	+	0.159067i	$0.0508486\pi$
$509$	321.378	+	556.642i	0.631390	+	1.09360i	−0.355878	+	0.934533i	$0.615818\pi$
$510$	−595.454	+	1067.44i	−1.16756	+	2.09302i
$511$	19.0481	−	32.9922i	0.0372761	−	0.0645641i
$512$	174.524	+	481.337i	0.340868	+	0.940111i
$513$	211.151	+	142.992i	0.411601	+	0.278737i
$514$	−380.584	+	345.267i	−0.740436	+	0.671726i
$515$	330.811	−	572.982i	0.642352	−	1.11259i
$516$	−265.133	+	61.5041i	−0.513823	+	0.119194i
$517$	1026.35	−	592.562i	1.98520	−	1.14615i
$518$	37.9007	+	12.1581i	0.0731675	+	0.0234712i
$519$	−28.1012	+	139.761i	−0.0541449	+	0.269289i
$520$	368.267	−	42.8918i	0.708207	−	0.0824842i
$521$			33.8228i			0.0649190i	0.999473	+	0.0324595i	$0.0103340\pi$
$521$			33.8228i			0.0649190i	−0.999473	+	0.0324595i	$0.989666\pi$
$522$	−300.014	−	848.290i	−0.574739	−	1.62508i
$523$			384.438i			0.735062i	0.930011	+	0.367531i	$0.119797\pi$
$523$			384.438i			0.735062i	−0.930011	+	0.367531i	$0.880203\pi$
$524$	−420.477	−	300.712i	−0.802438	−	0.573878i
$525$	−61.8274	−	54.4481i	−0.117767	−	0.103711i
$526$	72.2535	+	23.1780i	0.137364	+	0.0440646i
$527$	534.864	−	308.804i	1.01492	−	0.585966i
$528$	−420.326	−	547.997i	−0.796072	−	1.03787i
$529$	−246.807	+	427.482i	−0.466554	+	0.808095i
$530$	522.561	+	576.013i	0.985964	+	1.08682i
$531$	−490.097	−	205.387i	−0.922970	−	0.386793i
$532$	−36.6331	−	3.57329i	−0.0688591	−	0.00671671i
$533$	62.1144	−	107.585i	0.116537	−	0.201849i
$534$	299.906	+	502.185i	0.561622	+	0.940422i
$535$	−327.363	−	567.010i	−0.611894	−	1.05983i
$536$	164.072	−	379.935i	0.306105	−	0.708834i
$537$	199.280	−	67.1864i	0.371098	−	0.125114i
$538$	−515.997	+	111.698i	−0.959102	+	0.207618i
$539$	691.365			1.28268
$540$	−738.610	+	273.555i	−1.36780	+	0.506583i
$541$		−	339.351i		−	0.627266i	−0.949544	−	0.313633i	$-0.898454\pi$
$541$		−	339.351i		−	0.627266i	0.949544	−	0.313633i	$-0.101546\pi$
$542$	329.732	−	71.3774i	0.608361	−	0.131693i
$543$	194.839	+	577.907i	0.358819	+	1.06428i
$544$	−782.331	−	432.367i	−1.43811	−	0.794793i
$545$	−146.692	+	84.6926i	−0.269160	+	0.155399i
$546$	−19.0460	−	31.8921i	−0.0348829	−	0.0584104i
$547$	−309.896	−	178.918i	−0.566537	−	0.327090i	0.189228	−	0.981933i	$-0.439401\pi$
$547$	−309.896	−	178.918i	−0.566537	−	0.327090i	−0.755765	+	0.654843i	$0.772735\pi$
$548$	−229.330	−	22.3695i	−0.418486	−	0.0408203i
$549$	−93.7295	+	11.9450i	−0.170728	+	0.0217577i
$550$	−545.004	−	600.752i	−0.990917	−	1.09228i
$551$	−408.877	−	236.065i	−0.742064	−	0.428431i
$552$	−11.7612	+	142.282i	−0.0213066	+	0.257757i
$553$	48.5082	+	84.0186i	0.0877182	+	0.151932i
$554$	293.687	+	94.2109i	0.530120	+	0.170056i
$555$	295.378	−	335.410i	0.532212	−	0.604342i
$556$	−477.194	+	667.247i	−0.858262	+	1.20008i
$557$	−791.740			−1.42144			−0.710718	−	0.703477i	$-0.751630\pi$
$557$	−791.740			−1.42144			−0.710718	+	0.703477i	$0.751630\pi$
$558$	391.292	+	72.6835i	0.701240	+	0.130257i
$559$	−144.131			−0.257838
$560$	74.7956	−	85.6120i	0.133564	−	0.152879i
$561$	1182.06	+	237.673i	2.10706	+	0.423660i
$562$	−692.909	−	222.276i	−1.23293	−	0.395510i
$563$	−238.818	−	413.646i	−0.424189	−	0.734717i	0.572155	−	0.820145i	$-0.306107\pi$
$563$	−238.818	−	413.646i	−0.424189	−	0.734717i	−0.996344	+	0.0854283i	$0.972774\pi$
$564$	962.845	−	223.356i	1.70717	−	0.396021i
$565$	1284.13	+	741.394i	2.27280	+	1.31220i
$566$	335.609	−	304.466i	0.592949	−	0.537926i
$567$	55.3367	+	56.2612i	0.0975956	+	0.0992261i
$568$	−55.8489	−	75.0821i	−0.0983256	−	0.132187i
$569$	413.668	+	238.831i	0.727008	+	0.419739i	0.817327	−	0.576174i	$-0.195455\pi$
$569$	413.668	+	238.831i	0.727008	+	0.419739i	−0.0903183	+	0.995913i	$0.528788\pi$
$570$	−201.339	+	360.930i	−0.353226	+	0.633211i
$571$	−175.986	+	101.605i	−0.308206	+	0.177943i	−0.646123	−	0.763233i	$-0.723611\pi$
$571$	−175.986	+	101.605i	−0.308206	+	0.177943i	0.337917	+	0.941176i	$0.390278\pi$
$572$	−151.253	−	332.989i	−0.264428	−	0.582149i
$573$	−723.383	−	145.448i	−1.26245	−	0.253836i
$574$	−8.05905	−	37.2292i	−0.0140402	−	0.0648593i
$575$			167.676i			0.291611i
$576$	−202.183	−	539.350i	−0.351011	−	0.936371i
$577$	−342.508			−0.593602			−0.296801	−	0.954939i	$-0.595920\pi$
$577$	−342.508			−0.593602			−0.296801	+	0.954939i	$0.595920\pi$
$578$	960.272	−	207.871i	1.66137	−	0.359639i
$579$	−171.645	−	151.158i	−0.296450	−	0.261068i
$580$	1327.69	−	603.072i	2.28912	−	1.03978i
$581$	3.52134	+	6.09915i	0.00606083	+	0.0104977i
$582$	−0.426165	−	28.8685i	−0.000732242	−	0.0496023i
$583$	383.593	−	664.402i	0.657963	−	1.13963i
$584$	251.000	−	186.703i	0.429794	−	0.319697i
$585$	−413.755	+	52.7293i	−0.707273	+	0.0901355i
$586$	644.330	+	710.237i	1.09954	+	1.21201i
$587$	−371.350	+	643.197i	−0.632623	+	1.09574i	0.354390	+	0.935098i	$0.384688\pi$
$587$	−371.350	+	643.197i	−0.632623	+	1.09574i	−0.987013	+	0.160638i	$0.948645\pi$
$588$	551.592	+	168.005i	0.938081	+	0.285723i
$589$	180.852	−	104.415i	0.307049	−	0.177275i
$590$	263.061	−	820.047i	0.445866	−	1.38991i
$591$	−317.179	+	106.936i	−0.536681	+	0.180940i
$592$	246.136	+	215.039i	0.415771	+	0.363241i
$593$		−	380.547i		−	0.641732i	−0.947125	−	0.320866i	$-0.896026\pi$
$593$		−	380.547i		−	0.641732i	0.947125	−	0.320866i	$-0.103974\pi$
$594$	479.504	+	611.349i	0.807246	+	1.02921i
$595$			198.470i			0.333562i
$596$	−365.378	−	261.307i	−0.613051	−	0.438435i
$597$	−476.452	+	160.634i	−0.798077	+	0.269069i
$598$	−23.0935	+	71.9902i	−0.0386180	+	0.120385i
$599$	890.398	−	514.072i	1.48647	−	0.858217i	0.486593	−	0.873629i	$-0.338239\pi$
$599$	890.398	−	514.072i	1.48647	−	0.858217i	0.999881	+	0.0154120i	$0.00490599\pi$
$600$	−288.835	−	611.737i	−0.481391	−	1.01956i
$601$	213.705	−	370.147i	0.355582	−	0.615885i	−0.631636	−	0.775265i	$-0.717616\pi$
$601$	213.705	−	370.147i	0.355582	−	0.615885i	0.987217	+	0.159380i	$0.0509495\pi$
$602$	−32.7317	+	29.6943i	−0.0543717	+	0.0493261i
$603$	−179.949	+	429.397i	−0.298424	+	0.712101i
$604$	43.7129	−	448.141i	0.0723723	−	0.741955i
$605$	−313.672	+	543.296i	−0.518466	+	0.898010i
$606$	−7.78526	−	527.376i	−0.0128470	−	0.870257i
$607$	187.149	+	324.151i	0.308318	+	0.534022i	0.977994	−	0.208631i	$-0.0669007\pi$
$607$	187.149	+	324.151i	0.308318	+	0.534022i	−0.669677	+	0.742653i	$0.733567\pi$
$608$	−264.527	−	146.195i	−0.435077	−	0.240452i
$609$	−109.646	−	96.5590i	−0.180042	−	0.158553i
$610$	−32.3983	−	149.666i	−0.0531120	−	0.245354i
$611$	523.422			0.856664
$612$	885.329	+	476.870i	1.44662	+	0.779199i
$613$		−	695.896i		−	1.13523i	−0.823294	−	0.567615i	$-0.807866\pi$
$613$		−	695.896i		−	1.13523i	0.823294	−	0.567615i	$-0.192134\pi$
$614$	−211.174	−	975.529i	−0.343931	−	1.58881i
$615$	−419.321	−	84.3114i	−0.681823	−	0.137092i
$616$	−102.952	−	44.4592i	−0.167130	−	0.0721740i
$617$	−808.252	+	466.645i	−1.30997	+	0.756312i	−0.982091	−	0.188407i	$-0.939668\pi$
$617$	−808.252	+	466.645i	−1.30997	+	0.756312i	−0.327880	+	0.944719i	$0.606334\pi$
$618$	−475.364	−	265.174i	−0.769198	−	0.429084i
$619$	120.480	+	69.5590i	0.194636	+	0.112373i	0.594151	−	0.804354i	$-0.297488\pi$
$619$	120.480	+	69.5590i	0.194636	+	0.112373i	−0.399515	+	0.916727i	$0.630821\pi$
$620$	−62.6177	+	641.951i	−0.100996	+	1.03541i
$621$	11.5002	−	160.201i	0.0185188	−	0.257972i
$622$	562.417	−	510.226i	0.904207	−	0.820299i
$623$	82.2524	+	47.4884i	0.132026	+	0.0762254i
$624$	−39.7558	−	302.424i	−0.0637113	−	0.484653i
$625$	267.579	+	463.460i	0.428126	+	0.741536i
$626$	−6.65305	+	20.7398i	−0.0106279	+	0.0331306i
$627$	399.687	+	80.3637i	0.637460	+	0.128172i
$628$	−367.060	+	513.250i	−0.584491	+	0.817277i
$629$	−570.604			−0.907160
$630$	−83.0989	+	97.2176i	−0.131903	+	0.154314i
$631$	133.491			0.211554			0.105777	−	0.994390i	$-0.466267\pi$
$631$	133.491			0.211554			0.105777	+	0.994390i	$0.466267\pi$
$632$	92.1613	+	791.294i	0.145825	+	1.25205i
$633$	490.523	−	557.003i	0.774918	−	0.879941i
$634$	−5.23854	+	16.3303i	−0.00826268	+	0.0257575i
$635$	−496.763	−	860.418i	−0.782304	−	1.35499i
$636$	467.495	−	436.865i	0.735054	−	0.686894i
$637$	264.440	+	152.674i	0.415133	+	0.239677i
$638$	−966.518	−	1065.38i	−1.51492	−	1.66988i
$639$	63.7395	+	83.7832i	0.0997488	+	0.131116i
$640$	842.556	−	401.896i	1.31649	−	0.627962i
$641$	−765.055	−	441.704i	−1.19353	−	0.689086i	−0.234427	−	0.972134i	$-0.575321\pi$
$641$	−765.055	−	441.704i	−1.19353	−	0.689086i	−0.959106	+	0.283047i	$0.908655\pi$
$642$	−462.459	+	276.181i	−0.720341	+	0.430189i
$643$	−377.850	+	218.152i	−0.587636	+	0.339272i	−0.764162	−	0.645024i	$-0.776847\pi$
$643$	−377.850	+	218.152i	−0.587636	+	0.339272i	0.176526	+	0.984296i	$0.443514\pi$
$644$	9.58715	+	21.1065i	0.0148869	+	0.0327741i
$645$	158.537	+	470.231i	0.245793	+	0.729040i
$646$	515.707	−	111.636i	0.798308	−	0.172811i
$647$			688.668i			1.06440i	0.846618	+	0.532201i	$0.178635\pi$
$647$			688.668i			1.06440i	−0.846618	+	0.532201i	$0.821365\pi$
$648$	234.002	+	604.274i	0.361114	+	0.932522i
$649$	−849.533			−1.30899
$650$	−75.7940	−	350.134i	−0.116606	−	0.538668i
$651$	61.2363	−	20.6456i	0.0940649	−	0.0317136i
$652$	−108.785	−	239.495i	−0.166849	−	0.367324i
$653$	646.149	+	1119.16i	0.989508	+	1.71388i	0.619876	+	0.784700i	$0.287183\pi$
$653$	646.149	+	1119.16i	0.989508	+	1.71388i	0.369632	+	0.929178i	$0.379484\pi$
$654$	71.4513	+	119.643i	0.109253	+	0.182941i
$655$	−471.255	+	816.238i	−0.719473	+	1.24616i
$656$	60.4449	−	306.890i	0.0921416	−	0.467820i
$657$	−280.088	+	213.081i	−0.426313	+	0.324325i
$658$	118.867	−	107.837i	0.180649	−	0.163886i
$659$	−194.969	+	337.696i	−0.295856	+	0.512437i	−0.975184	−	0.221398i	$-0.928938\pi$
$659$	−194.969	+	337.696i	−0.295856	+	0.512437i	0.679328	+	0.733835i	$0.262271\pi$
$660$	−920.013	+	859.734i	−1.39396	+	1.30263i
$661$	−855.234	+	493.769i	−1.29385	+	0.747004i	−0.979334	−	0.202249i	$-0.935175\pi$
$661$	−855.234	+	493.769i	−1.29385	+	0.747004i	−0.314514	+	0.949253i	$0.601842\pi$
$662$	−491.824	−	157.771i	−0.742937	−	0.238325i
$663$	399.641	+	351.943i	0.602777	+	0.530833i
$664$	6.69025	+	57.4423i	0.0100757	+	0.0865094i
$665$			67.1079i			0.100914i
$666$	−279.502	−	238.911i	−0.419673	−	0.358725i
$667$			297.359i			0.445816i
$668$	−489.287	+	684.156i	−0.732466	+	1.02419i
$669$	−14.7283	+	73.2512i	−0.0220155	+	0.109494i
$670$	−718.482	−	230.480i	−1.07236	−	0.344000i
$671$	−130.819	+	75.5282i	−0.194961	+	0.112561i
$672$	−71.3346	−	60.4888i	−0.106153	−	0.0900130i
$673$	291.228	−	504.422i	0.432731	−	0.749512i	−0.564376	−	0.825518i	$-0.690883\pi$
$673$	291.228	−	504.422i	0.432731	−	0.749512i	0.997107	+	0.0760054i	$0.0242166\pi$
$674$	626.062	+	690.101i	0.928875	+	1.02389i
$675$	332.360	+	684.651i	0.492385	+	1.01430i
$676$	−49.9459	+	512.041i	−0.0738844	+	0.757457i
$677$	269.345	−	466.519i	0.397850	−	0.689097i	−0.595610	−	0.803274i	$-0.703090\pi$
$677$	269.345	−	466.519i	0.397850	−	0.689097i	0.993460	+	0.114177i	$0.0364230\pi$
$678$	594.292	−	1065.36i	0.876537	−	1.57132i
$679$	−2.34402	−	4.05996i	−0.00345217	−	0.00597933i
$680$	−646.110	+	1496.17i	−0.950162	+	2.20025i
$681$	−41.4867	+	206.334i	−0.0609203	+	0.302986i
$682$	621.851	−	134.613i	0.911806	−	0.197380i
$683$	−82.2620			−0.120442			−0.0602211	−	0.998185i	$-0.519181\pi$
$683$	−82.2620			−0.120442			−0.0602211	+	0.998185i	$0.519181\pi$
$684$	299.354	+	161.243i	0.437651	+	0.235735i
$685$			420.109i			0.613298i
$686$	184.823	−	40.0088i	0.269421	−	0.0583219i
$687$	−90.2277	+	102.456i	−0.131336	+	0.149135i
$688$	−343.418	+	117.295i	−0.499155	+	0.170487i
$689$	293.440	−	169.418i	0.425893	−	0.245889i
$690$	260.271	−	3.84219i	0.377204	−	0.00556839i
$691$	−839.455	−	484.660i	−1.21484	−	0.701389i	−0.251031	−	0.967979i	$-0.580770\pi$
$691$	−839.455	−	484.660i	−1.21484	−	0.701389i	−0.963810	+	0.266590i	$0.914103\pi$
$692$	−18.4531	+	189.180i	−0.0266663	+	0.273381i
$693$	116.355	+	48.7615i	0.167901	+	0.0703630i
$694$	−442.784	−	488.076i	−0.638017	−	0.703279i
$695$	1295.27	+	747.825i	1.86370	+	1.07601i
$696$	−512.223	−	1084.86i	−0.735953	−	1.55871i
$697$	273.034	+	472.908i	0.391727	+	0.678491i
$698$	502.212	+	161.103i	0.719501	+	0.230807i
$699$	58.6922	+	174.085i	0.0839659	+	0.249049i
$700$	−89.3482	−	63.8990i	−0.127640	−	0.0912843i
$701$	982.538			1.40162			0.700812	−	0.713346i	$-0.252821\pi$
$701$	982.538			1.40162			0.700812	+	0.713346i	$0.252821\pi$
$702$	48.4007	+	339.723i	0.0689469	+	0.483936i
$703$	−192.936			−0.274447
$704$	−631.375	−	670.315i	−0.896839	−	0.952152i
$705$	−575.735	−	1707.67i	−0.816646	−	2.42223i
$706$	−77.9485	−	25.0049i	−0.110409	−	0.0354177i
$707$	−42.8210	−	74.1682i	−0.0605672	−	0.104906i
$708$	−677.782	−	206.441i	−0.957320	−	0.291583i
$709$	382.227	+	220.679i	0.539108	+	0.311254i	0.744717	−	0.667380i	$-0.232584\pi$
$709$	382.227	+	220.679i	0.539108	+	0.311254i	−0.205610	+	0.978634i	$0.565918\pi$
$710$	−126.361	+	114.635i	−0.177973	+	0.161458i
$711$	−113.299	−	889.033i	−0.159352	−	1.25040i
$712$	465.466	+	625.763i	0.653744	+	0.878881i
$713$	−113.905	−	65.7630i	−0.159754	−	0.0922342i
$714$	163.265	−	2.41017i	0.228663	−	0.00337558i
$715$	−577.479	+	333.408i	−0.807663	+	0.466305i
$716$	255.298	−	115.963i	0.356562	−	0.161960i
$717$	764.148	−	867.712i	1.06576	−	1.21020i
$718$	122.326	+	565.092i	0.170370	+	0.787036i
$719$			641.416i			0.892095i	0.895009	+	0.446048i	$0.147169\pi$
$719$			641.416i			0.892095i	−0.895009	+	0.446048i	$0.852831\pi$
$720$	−942.933	+	462.353i	−1.30963	+	0.642157i
$721$	−88.3847			−0.122586
$722$	−531.281	+	115.007i	−0.735847	+	0.159290i
$723$	−88.4616	+	439.963i	−0.122354	+	0.608524i
$724$	336.291	+	740.359i	0.464491	+	1.02260i
$725$	−704.511	−	1220.25i	−0.971740	−	1.68310i
$726$	450.736	+	251.436i	0.620849	+	0.346330i
$727$	243.186	−	421.211i	0.334506	−	0.579382i	−0.648883	−	0.760888i	$-0.724764\pi$
$727$	243.186	−	421.211i	0.334506	−	0.579382i	0.983390	+	0.181506i	$0.0580971\pi$
$728$	−29.5602	−	39.7401i	−0.0406046	−	0.0545881i
$729$	−270.586	−	676.923i	−0.371174	−	0.928564i
$730$	−383.225	−	422.424i	−0.524966	−	0.578664i
$731$	316.776	−	548.672i	0.433346	−	0.750578i
$732$	−122.725	+	28.4690i	−0.167657	+	0.0388921i
$733$	−124.277	+	71.7514i	−0.169546	+	0.0978873i	−0.582372	−	0.812923i	$-0.697875\pi$
$733$	−124.277	+	71.7514i	−0.169546	+	0.0978873i	0.412826	+	0.910810i	$0.364542\pi$
$734$	−394.141	+	1228.67i	−0.536976	+	1.67393i
$735$	207.233	−	1030.67i	0.281950	−	1.40227i
$736$	3.56166	+	190.323i	0.00483922	+	0.258591i
$737$			744.316i			1.00993i
$738$	−64.2642	+	345.966i	−0.0870788	+	0.468789i
$739$			934.347i			1.26434i	0.774830	+	0.632170i	$0.217836\pi$
$739$			934.347i			1.26434i	−0.774830	+	0.632170i	$0.782164\pi$
$740$	346.648	−	484.708i	0.468444	−	0.655011i
$741$	135.129	+	119.001i	0.182361	+	0.160595i
$742$	31.7353	−	98.9295i	0.0427700	−	0.133328i
$743$	−619.702	+	357.785i	−0.834053	+	0.481541i	−0.855239	−	0.518235i	$-0.826589\pi$
$743$	−619.702	+	357.785i	−0.834053	+	0.481541i	0.0211850	+	0.999776i	$0.493256\pi$
$744$	528.843	+	43.7149i	0.710811	+	0.0587566i
$745$	−409.502	+	709.278i	−0.549667	+	0.952051i
$746$	−537.891	+	487.977i	−0.721034	+	0.654124i
$747$	−8.22470	−	64.5374i	−0.0110103	−	0.0863955i
$748$	1600.03	+	156.072i	2.13908	+	0.208652i
$749$	−43.7317	+	75.7456i	−0.0583868	+	0.101129i
$750$	−119.743	+	71.5108i	−0.159657	+	0.0953478i
$751$	−513.275	−	889.018i	−0.683455	−	1.18378i	−0.973920	−	0.226893i	$-0.927143\pi$
$751$	−513.275	−	889.018i	−0.683455	−	1.18378i	0.290465	−	0.956886i	$-0.406190\pi$
$752$	1247.14	−	425.964i	1.65844	−	0.566442i
$753$	129.025	−	43.5004i	0.171348	−	0.0577694i
$754$	−134.414	−	620.933i	−0.178268	−	0.823518i
$755$	−820.947			−1.08735
$756$	80.9823	+	67.1783i	0.107119	+	0.0888602i
$757$		−	693.047i		−	0.915518i	−0.889076	−	0.457759i	$-0.848652\pi$
$757$		−	693.047i		−	0.915518i	0.889076	−	0.457759i	$-0.151348\pi$
$758$	31.9639	+	147.659i	0.0421687	+	0.194801i
$759$	−82.0324	−	243.314i	−0.108080	−	0.320572i
$760$	−218.467	+	505.896i	−0.287457	+	0.665652i
$761$	802.542	−	463.348i	1.05459	−	0.608867i	0.130658	−	0.991428i	$-0.458291\pi$
$761$	802.542	−	463.348i	1.05459	−	0.608867i	0.923930	+	0.382561i	$0.124958\pi$
$762$	−701.766	+	419.096i	−0.920952	+	0.549995i
$763$	19.5963	+	11.3139i	0.0256832	+	0.0148282i
$764$	−979.167	−	95.5106i	−1.28163	−	0.125014i
$765$	708.635	−	1690.95i	0.926321	−	2.21039i
$766$	605.864	−	549.642i	0.790946	−	0.717548i
$767$	−324.937	−	187.602i	−0.423647	−	0.244593i
$768$	−340.840	−	688.224i	−0.443802	−	0.896125i
$769$	220.097	+	381.219i	0.286212	+	0.495733i	0.972902	−	0.231217i	$-0.0742706\pi$
$769$	220.097	+	381.219i	0.286212	+	0.495733i	−0.686691	+	0.726950i	$0.740937\pi$
$770$	−62.4540	+	194.690i	−0.0811090	+	0.252844i
$771$	509.418	−	578.458i	0.660723	−	0.750270i
$772$	−248.048	−	177.396i	−0.321305	−	0.229787i
$773$	547.513			0.708296			0.354148	−	0.935189i	$-0.384771\pi$
$773$	547.513			0.708296			0.354148	+	0.935189i	$0.384771\pi$
$774$	384.897	−	136.126i	0.497282	−	0.175873i
$775$	623.230			0.804168
$776$	−4.45344	−	38.2371i	−0.00573897	−	0.0492746i
$777$	−58.5332	−	11.7690i	−0.0753322	−	0.0151468i
$778$	−232.263	+	724.041i	−0.298539	+	0.930644i
$779$	92.3200	+	159.903i	0.118511	+	0.205267i
$780$	−541.750	+	125.672i	−0.694551	+	0.161118i
$781$	145.751	+	84.1492i	0.186621	+	0.107746i
$782$	−223.293	−	246.133i	−0.285541	−	0.314749i
$783$	589.411	+	1214.17i	0.752760	+	1.55066i
$784$	754.321	+	148.571i	0.962145	+	0.189503i
$785$	996.330	+	575.231i	1.26921	+	0.732779i
$786$	677.177	+	377.752i	0.861548	+	0.480601i
$787$	780.893	−	450.849i	0.992241	−	0.572870i	0.0862974	−	0.996269i	$-0.472496\pi$
$787$	780.893	−	450.849i	0.992241	−	0.572870i	0.905943	+	0.423399i	$0.139163\pi$
$788$	−406.339	+	184.570i	−0.515659	+	0.234226i
$789$	−111.587	−	22.4363i	−0.141428	−	0.0284364i
$790$	1419.59	−	307.301i	1.79695	−	0.388988i
$791$		−	198.082i		−	0.250420i
$792$	718.407	+	746.381i	0.907080	+	0.942401i
$793$	−66.7156			−0.0841306
$794$	−152.597	−	704.931i	−0.192188	−	0.887822i
$795$	−875.495	−	771.003i	−1.10125	−	0.969814i
$796$	−610.385	+	277.254i	−0.766816	+	0.348309i
$797$	−56.6006	−	98.0352i	−0.0710171	−	0.123005i	0.828330	−	0.560240i	$-0.189291\pi$
$797$	−56.6006	−	98.0352i	−0.0710171	−	0.123005i	−0.899347	+	0.437235i	$0.855958\pi$
$798$	55.2044	−	0.814942i	0.0691784	−	0.00102123i
$799$	−1150.39	+	1992.54i	−1.43979	+	2.49379i
$800$	−465.534	−	772.575i	−0.581918	−	0.965719i
$801$	−531.229	−	698.281i	−0.663207	−	0.871762i
$802$	−431.638	+	391.583i	−0.538202	+	0.488259i
$803$	−281.311	+	487.245i	−0.350325	+	0.606781i
$804$	−180.873	+	593.837i	−0.224966	+	0.738604i
$805$	36.6035	−	21.1331i	0.0454702	−	0.0262522i
$806$	267.578	+	85.8356i	0.331983	+	0.106496i
$807$	750.421	−	253.002i	0.929890	−	0.313509i
$808$	−81.3563	−	698.522i	−0.100688	−	0.864508i
$809$		−	1119.41i		−	1.38370i	−0.722041	−	0.691851i	$-0.756796\pi$
$809$		−	1119.41i		−	1.38370i	0.722041	−	0.691851i	$-0.243204\pi$
$810$	1055.11	−	531.585i	1.30261	−	0.656278i
$811$		−	1428.00i		−	1.76079i	−0.474238	−	0.880397i	$-0.657276\pi$
$811$		−	1428.00i		−	1.76079i	0.474238	−	0.880397i	$-0.342724\pi$
$812$	−158.451	−	113.319i	−0.195137	−	0.139556i
$813$	−479.533	+	161.673i	−0.589831	+	0.198859i
$814$	−559.736	−	179.556i	−0.687637	−	0.220585i
$815$	−415.340	+	239.796i	−0.509619	+	0.294229i
$816$	1238.63	+	513.335i	1.51793	+	0.629087i
$817$	107.110	−	185.521i	0.131102	−	0.227076i
$818$	−955.651	−	1053.40i	−1.16828	−	1.28778i
$819$	33.7366	+	44.3455i	0.0411924	+	0.0541459i
$820$	−567.591	−	55.3643i	−0.692184	−	0.0675175i
$821$	−158.760	+	274.981i	−0.193374	+	0.334934i	−0.946366	−	0.323095i	$-0.895277\pi$
$821$	−158.760	+	274.981i	−0.193374	+	0.334934i	0.752992	+	0.658030i	$0.228610\pi$
$822$	345.590	−	5.10170i	0.420426	−	0.00620645i
$823$	−57.5756	−	99.7238i	−0.0699582	−	0.121171i	0.828924	−	0.559361i	$-0.188953\pi$
$823$	−57.5756	−	99.7238i	−0.0699582	−	0.121171i	−0.898883	+	0.438189i	$0.855620\pi$
$824$	−666.292	−	287.733i	−0.808607	−	0.349191i
$825$	913.097	+	804.116i	1.10678	+	0.974686i
$826$	−112.442	+	24.3405i	−0.136129	+	0.0294680i
$827$	−83.4266			−0.100879			−0.0504393	−	0.998727i	$-0.516062\pi$
$827$	−83.4266			−0.100879			−0.0504393	+	0.998727i	$0.516062\pi$
$828$	−6.32133	−	214.058i	−0.00763445	−	0.258524i
$829$		−	1243.37i		−	1.49984i	−0.661530	−	0.749919i	$-0.730093\pi$
$829$		−	1243.37i		−	1.49984i	0.661530	−	0.749919i	$-0.269907\pi$
$830$	103.052	−	22.3078i	0.124159	−	0.0268769i
$831$	−453.564	−	91.1964i	−0.545805	−	0.109743i
$832$	−93.4682	−	395.815i	−0.112342	−	0.475739i
$833$	−1162.39	+	671.104i	−1.39542	+	0.805647i
$834$	599.447	−	1074.60i	0.718761	−	1.28849i
$835$	1328.10	+	766.777i	1.59053	+	0.918295i
$836$	541.014	+	52.7720i	0.647146	+	0.0631244i
$837$	−595.445	−	42.7447i	−0.711404	−	0.0510689i
$838$	122.323	+	134.836i	0.145971	+	0.160902i
$839$	1361.07	+	785.816i	1.62226	+	0.936610i	0.986315	+	0.164872i	$0.0527212\pi$
$839$	1361.07	+	785.816i	1.62226	+	0.936610i	0.635941	+	0.771738i	$0.280612\pi$
$840$	−97.1382	+	140.152i	−0.115641	+	0.166848i
$841$	−828.890	−	1435.68i	−0.985600	−	1.70711i
$842$	−1148.73	−	368.499i	−1.36429	−	0.437647i
$843$	1070.12	+	215.164i	1.26941	+	0.255236i
$844$	575.666	−	804.937i	0.682069	−	0.953717i
$845$	938.005			1.11007
$846$	−1397.78	+	494.349i	−1.65222	+	0.584337i
$847$	83.8056			0.0989440
$848$	561.299	−	642.471i	0.661909	−	0.757631i
$849$	−449.218	+	510.100i	−0.529115	+	0.600825i
$850$	1499.46	+	481.007i	1.76407	+	0.565890i
$851$	60.7579	+	105.236i	0.0713959	+	0.123661i
$852$	95.8356	+	102.555i	0.112483	+	0.120370i
$853$	558.722	+	322.578i	0.655008	+	0.378169i	0.790372	−	0.612627i	$-0.209887\pi$
$853$	558.722	+	322.578i	0.655008	+	0.378169i	−0.135364	+	0.990796i	$0.543220\pi$
$854$	−15.1509	+	13.7449i	−0.0177411	+	0.0160948i
$855$	239.609	−	571.756i	0.280244	−	0.668721i
$856$	−576.260	+	428.644i	−0.673201	+	0.500753i
$857$	208.924	+	120.622i	0.243785	+	0.140749i	0.616915	−	0.787030i	$-0.288382\pi$
$857$	208.924	+	120.622i	0.243785	+	0.140749i	−0.373130	+	0.927779i	$0.621716\pi$
$858$	281.281	+	470.998i	0.327833	+	0.548948i
$859$	842.735	−	486.553i	0.981065	−	0.566418i	0.0784738	−	0.996916i	$-0.474995\pi$
$859$	842.735	−	486.553i	0.981065	−	0.566418i	0.902592	+	0.430498i	$0.141662\pi$
$860$	273.633	+	602.415i	0.318178	+	0.700483i
$861$	18.2541	+	54.1430i	0.0212010	+	0.0628838i
$862$	−152.144	−	702.838i	−0.176501	−	0.815358i
$863$			130.532i			0.151254i	0.997136	+	0.0756270i	$0.0240958\pi$
$863$			130.532i			0.151254i	−0.997136	+	0.0756270i	$0.975904\pi$
$864$	391.792	+	770.062i	0.453463	+	0.891275i
$865$	346.557			0.400644
$866$	−227.071	+	49.1543i	−0.262207	+	0.0567601i
$867$	−1396.54	+	470.837i	−1.61077	+	0.543064i
$868$	78.4501	−	35.6342i	0.0903803	−	0.0410532i
$869$	−716.392	−	1240.83i	−0.824386	−	1.42788i
$870$	−1877.96	+	1121.52i	−2.15857	+	1.28910i
$871$	−164.367	+	284.693i	−0.188711	+	0.326857i
$872$	110.895	+	149.085i	0.127173	+	0.170969i
$873$	5.47486	+	42.9600i	0.00627132	+	0.0492097i
$874$	−75.5014	−	83.2243i	−0.0863860	−	0.0952223i
$875$	−11.3233	+	19.6126i	−0.0129409	+	0.0224144i
$876$	−342.841	+	320.379i	−0.391371	+	0.365729i
$877$	−778.864	+	449.677i	−0.888100	+	0.512745i	−0.873321	−	0.487146i	$-0.838038\pi$
$877$	−778.864	+	449.677i	−0.888100	+	0.512745i	−0.0147795	+	0.999891i	$0.504705\pi$
$878$	44.6814	−	139.287i	0.0508900	−	0.158641i
$879$	−1079.51	−	950.664i	−1.22811	−	1.08153i
$880$	−1104.62	+	1264.36i	−1.25525	+	1.43677i
$881$			444.924i			0.505021i	0.967594	+	0.252511i	$0.0812563\pi$
$881$			444.924i			0.505021i	−0.967594	+	0.252511i	$0.918744\pi$
$882$	−850.369	−	157.958i	−0.964137	−	0.179091i
$883$		−	168.849i		−	0.191222i	−0.995419	−	0.0956108i	$-0.969520\pi$
$883$		−	168.849i		−	0.191222i	0.995419	−	0.0956108i	$-0.0304804\pi$
$884$	577.530	+	413.031i	0.653314	+	0.467230i
$885$	−254.643	+	1266.46i	−0.287733	+	1.43103i
$886$	−415.303	+	1294.64i	−0.468739	+	1.46122i
$887$	−4.52391	+	2.61188i	−0.00510024	+	0.00294463i	−0.502548	−	0.864549i	$-0.667604\pi$
$887$	−4.52391	+	2.61188i	−0.00510024	+	0.00294463i	0.497448	+	0.867494i	$0.334271\pi$
$888$	−402.941	−	279.274i	−0.453762	−	0.314498i
$889$	−66.3614	+	114.941i	−0.0746473	+	0.129293i
$890$	1053.14	−	955.411i	1.18330	−	1.07350i
$891$	−817.239	−	830.893i	−0.917215	−	0.932539i
$892$	−9.67159	+	99.1524i	−0.0108426	+	0.111157i
$893$	−388.978	+	673.730i	−0.435586	+	0.754457i
$894$	588.440	+	328.252i	0.658210	+	0.367172i
$895$	−255.619	−	442.746i	−0.285608	−	0.494688i
$896$	−102.773	−	70.6315i	−0.114702	−	0.0788298i
$897$	22.3546	−	111.180i	0.0249215	−	0.123947i
$898$	186.987	+	863.798i	0.208226	+	0.961913i
$899$	1105.24			1.22941
$900$	533.091	+	863.435i	0.592324	+	0.959372i
$901$			1489.40i			1.65306i
$902$	119.020	+	549.819i	0.131951	+	0.609556i
$903$	43.8119	−	49.7497i	0.0485182	−	0.0550938i
$904$	644.850	−	1493.25i	0.713330	−	1.65183i
$905$	1283.95	−	741.290i	1.41873	−	0.819105i
$906$	9.96938	+	675.328i	0.0110037	+	0.745395i
$907$	−613.512	−	354.211i	−0.676419	−	0.390531i	0.122085	−	0.992520i	$-0.461042\pi$
$907$	−613.512	−	354.211i	−0.676419	−	0.390531i	−0.798505	+	0.601989i	$0.794375\pi$
$908$	−27.2429	+	279.292i	−0.0300032	+	0.307590i
$909$	100.016	+	784.802i	0.110028	+	0.863369i
$910$	−66.8813	+	60.6749i	−0.0734959	+	0.0666757i
$911$	−867.967	−	501.121i	−0.952762	−	0.550078i	−0.0588245	−	0.998268i	$-0.518735\pi$
$911$	−867.967	−	501.121i	−0.952762	−	0.550078i	−0.893938	+	0.448191i	$0.852069\pi$
$912$	418.813	+	173.572i	0.459225	+	0.190320i
$913$	−52.0049	−	90.0751i	−0.0569604	−	0.0986584i
$914$	−117.200	+	365.351i	−0.128227	+	0.399727i
$915$	73.3834	+	217.661i	0.0802005	+	0.237880i
$916$	−105.889	+	148.062i	−0.115599	+	0.161639i
$917$	125.908			0.137304
$918$	−1399.62	−	562.404i	−1.52464	−	0.612640i
$919$	744.434			0.810048			0.405024	−	0.914306i	$-0.367263\pi$
$919$	744.434			0.810048			0.405024	+	0.914306i	$0.367263\pi$
$920$	344.735	−	40.1510i	0.374712	−	0.0436424i
$921$	478.317	+	1418.72i	0.519346	+	1.54042i
$922$	240.321	−	749.159i	0.260652	−	0.812537i
$923$	37.1654	+	64.3723i	0.0402658	+	0.0697425i
$924$	160.914	+	49.0117i	0.174150	+	0.0530429i
$925$	−498.655	−	287.899i	−0.539087	−	0.311242i
$926$	1004.72	+	1107.49i	1.08501	+	1.19599i
$927$	753.034	+	315.578i	0.812334	+	0.340429i
$928$	−825.584	−	1370.09i	−0.889638	−	1.47640i
$929$	270.245	+	156.026i	0.290899	+	0.167951i	0.638347	−	0.769749i	$-0.279618\pi$
$929$	270.245	+	156.026i	0.290899	+	0.167951i	−0.347448	+	0.937699i	$0.612952\pi$
$930$	−14.2809	−	967.392i	−0.0153558	−	1.04021i
$931$	−393.034	+	226.918i	−0.422163	+	0.243736i
$932$	101.302	+	223.022i	0.108694	+	0.239294i
$933$	−752.803	+	854.830i	−0.806863	+	0.916216i
$934$	−62.4729	+	13.5236i	−0.0668875	+	0.0144792i
$935$		−	2931.09i		−	3.13486i
$936$	109.959	+	444.129i	0.117478	+	0.474496i
$937$	−1674.63			−1.78723			−0.893614	−	0.448837i	$-0.851838\pi$
$937$	−1674.63			−1.78723			−0.893614	+	0.448837i	$0.851838\pi$
$938$	21.3259	+	98.5162i	0.0227355	+	0.105028i
$939$	6.44017	−	32.0301i	0.00685854	−	0.0341108i
$940$	−993.716	−	2187.71i	−1.05715	−	2.32735i
$941$	−383.379	−	664.032i	−0.407416	−	0.705666i	0.587183	−	0.809454i	$-0.300237\pi$
$941$	−383.379	−	664.032i	−0.407416	−	0.705666i	−0.994599	+	0.103788i	$0.966904\pi$
$942$	461.098	−	826.587i	0.489488	−	0.877481i
$943$	58.1453	−	100.711i	0.0616599	−	0.106798i
$944$	−926.892	−	182.560i	−0.981877	−	0.193390i
$945$	107.570	−	158.844i	0.113830	−	0.168089i
$946$	483.398	−	438.540i	0.510991	−	0.463573i
$947$	−164.388	+	284.728i	−0.173588	+	0.300663i	−0.939672	−	0.342078i	$-0.888869\pi$
$947$	−164.388	+	284.728i	−0.173588	+	0.300663i	0.766084	+	0.642741i	$0.222203\pi$
$948$	−270.031	−	1164.05i	−0.284843	−	1.22791i
$949$	−215.197	+	124.244i	−0.226762	+	0.130921i
$950$	507.007	+	162.641i	0.533691	+	0.171201i
$951$	5.07092	−	25.2201i	0.00533220	−	0.0265196i
$952$	216.249	−	25.1863i	0.227152	−	0.0264562i
$953$			1207.43i			1.26697i	0.773754	+	0.633487i	$0.218377\pi$
$953$			1207.43i			1.26697i	−0.773754	+	0.633487i	$0.781623\pi$
$954$	−623.611	+	729.564i	−0.653680	+	0.764742i
$955$			1793.73i			1.87825i
$956$	896.785	−	1253.95i	0.938060	−	1.31166i
$957$	1619.30	+	1426.03i	1.69206	+	1.49010i
$958$	1318.13	+	422.839i	1.37592	+	0.441376i
$959$	48.6026	−	28.0607i	0.0506805	−	0.0292604i
$960$	−1188.54	+	740.316i	−1.23806	+	0.771162i
$961$	236.068	−	408.881i	0.245648	−	0.425475i
$962$	−174.442	−	192.285i	−0.181332	−	0.199880i
$963$	643.042	−	489.205i	0.667749	−	0.508001i
$964$	−58.0897	+	595.531i	−0.0602590	+	0.617770i
$965$	−278.002	+	481.514i	−0.288085	+	0.498978i
$966$	−17.8290	−	29.8542i	−0.0184565	−	0.0309050i
$967$	39.9030	+	69.1140i	0.0412647	+	0.0714726i	0.885920	−	0.463838i	$-0.153528\pi$
$967$	39.9030	+	69.1140i	0.0412647	+	0.0714726i	−0.844655	+	0.535310i	$0.820195\pi$
$968$	631.772	+	272.826i	0.652657	+	0.281845i
$969$	−749.999	+	252.859i	−0.773993	+	0.260949i
$970$	−68.5979	+	14.8495i	−0.0707194	+	0.0153087i
$971$	493.841			0.508590			0.254295	−	0.967127i	$-0.418157\pi$
$971$	493.841			0.508590			0.254295	+	0.967127i	$0.418157\pi$
$972$	−450.106	−	861.504i	−0.463072	−	0.886321i
$973$		−	199.800i		−	0.205345i
$974$	−756.368	+	163.732i	−0.776559	+	0.168103i
$975$	171.676	+	509.205i	0.176078	+	0.522261i
$976$	−158.962	+	54.2936i	−0.162871	+	0.0556287i
$977$	89.1874	−	51.4923i	0.0912870	−	0.0527046i	−0.453662	−	0.891174i	$-0.649883\pi$
$977$	89.1874	−	51.4923i	0.0912870	−	0.0527046i	0.544949	+	0.838469i	$0.316549\pi$
$978$	202.305	+	338.755i	0.206856	+	0.346375i
$979$	−1214.74	−	701.332i	−1.24080	−	0.716376i
$980$	136.083	−	1395.11i	0.138860	−	1.42358i
$981$	−126.563	−	166.362i	−0.129014	−	0.169584i
$982$	−448.850	−	494.762i	−0.457077	−	0.503831i
$983$	−1067.85	−	616.521i	−1.08631	−	0.627183i	−0.153720	−	0.988114i	$-0.549126\pi$
$983$	−1067.85	−	616.521i	−1.08631	−	0.627183i	−0.932592	+	0.360931i	$0.882459\pi$
$984$	−38.6512	+	467.584i	−0.0392797	+	0.475187i
$985$	406.850	+	704.686i	0.413046	+	0.715417i
$986$	2659.16	+	853.023i	2.69691	+	0.865135i
$987$	−159.106	+	180.669i	−0.161201	+	0.183049i
$988$	195.278	+	139.657i	0.197650	+	0.141353i
$989$	−134.921			−0.136422
$990$	1227.24	−	1435.76i	1.23964	−	1.45026i
$991$	738.473			0.745180			0.372590	−	0.927996i	$-0.378470\pi$
$991$	738.473			0.745180			0.372590	+	0.927996i	$0.378470\pi$
$992$	707.405	−	13.2382i	0.713110	−	0.0133450i
$993$	759.563	+	152.723i	0.764918	+	0.153799i
$994$	21.7023	+	6.96182i	0.0218333	+	0.00700384i
$995$	611.153	+	1058.55i	0.614224	+	1.06387i
$996$	−19.6023	−	84.5020i	−0.0196811	−	0.0848414i
$997$	−424.123	−	244.867i	−0.425399	−	0.245604i	0.271986	−	0.962301i	$-0.412320\pi$
$997$	−424.123	−	244.867i	−0.425399	−	0.245604i	−0.697385	+	0.716697i	$0.745653\pi$
$998$	−386.172	+	350.336i	−0.386946	+	0.351038i
$999$	456.679	+	309.264i	0.457136	+	0.309574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.1	yes	44
3.2	odd	2		216.3.j.a.197.22		44
4.3	odd	2		288.3.n.a.209.3		44
8.3	odd	2		288.3.n.a.209.20		44
8.5	even	2	inner	72.3.j.a.29.9	yes	44
9.2	odd	6		648.3.h.a.485.11		44
9.4	even	3		216.3.j.a.125.14		44
9.5	odd	6	inner	72.3.j.a.5.9	yes	44
9.7	even	3		648.3.h.a.485.34		44
12.11	even	2		864.3.n.a.305.20		44
24.5	odd	2		216.3.j.a.197.14		44
24.11	even	2		864.3.n.a.305.3		44
36.7	odd	6		2592.3.h.a.1457.40		44
36.11	even	6		2592.3.h.a.1457.5		44
36.23	even	6		288.3.n.a.113.20		44
36.31	odd	6		864.3.n.a.17.3		44
72.5	odd	6	inner	72.3.j.a.5.1	✓	44
72.11	even	6		2592.3.h.a.1457.39		44
72.13	even	6		216.3.j.a.125.22		44
72.29	odd	6		648.3.h.a.485.33		44
72.43	odd	6		2592.3.h.a.1457.6		44
72.59	even	6		288.3.n.a.113.3		44
72.61	even	6		648.3.h.a.485.12		44
72.67	odd	6		864.3.n.a.17.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.1	✓	44	72.5	odd	6	inner
72.3.j.a.5.9	yes	44	9.5	odd	6	inner
72.3.j.a.29.1	yes	44	1.1	even	1	trivial
72.3.j.a.29.9	yes	44	8.5	even	2	inner
216.3.j.a.125.14		44	9.4	even	3
216.3.j.a.125.22		44	72.13	even	6
216.3.j.a.197.14		44	24.5	odd	2
216.3.j.a.197.22		44	3.2	odd	2
288.3.n.a.113.3		44	72.59	even	6
288.3.n.a.113.20		44	36.23	even	6
288.3.n.a.209.3		44	4.3	odd	2
288.3.n.a.209.20		44	8.3	odd	2
648.3.h.a.485.11		44	9.2	odd	6
648.3.h.a.485.12		44	72.61	even	6
648.3.h.a.485.33		44	72.29	odd	6
648.3.h.a.485.34		44	9.7	even	3
864.3.n.a.17.3		44	36.31	odd	6
864.3.n.a.17.20		44	72.67	odd	6
864.3.n.a.305.3		44	24.11	even	2
864.3.n.a.305.20		44	12.11	even	2
2592.3.h.a.1457.5		44	36.11	even	6
2592.3.h.a.1457.6		44	72.43	odd	6
2592.3.h.a.1457.39		44	72.11	even	6
2592.3.h.a.1457.40		44	36.7	odd	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95473 + 0.423142i) q^{2} +(2.84278 - 0.958433i) q^{3} +(3.64190 - 1.65425i) q^{4} +(-3.64648 - 6.31589i) q^{5} +(-5.15130 + 3.07637i) q^{6} +(-0.487126 + 0.843726i) q^{7} +(-6.41894 + 4.77465i) q^{8} +(7.16281 - 5.44923i) q^{9} +O(q^{10})\)	\(q+(-1.95473 + 0.423142i) q^{2} +(2.84278 - 0.958433i) q^{3} +(3.64190 - 1.65425i) q^{4} +(-3.64648 - 6.31589i) q^{5} +(-5.15130 + 3.07637i) q^{6} +(-0.487126 + 0.843726i) q^{7} +(-6.41894 + 4.77465i) q^{8} +(7.16281 - 5.44923i) q^{9} +(9.80039 + 10.8029i) q^{10} +(7.19410 - 12.4606i) q^{11} +(8.76764 - 8.19319i) q^{12} +(5.50333 - 3.17735i) q^{13} +(0.595181 - 1.85538i) q^{14} +(-16.4195 - 14.4598i) q^{15} +(10.5269 - 12.0492i) q^{16} +27.9331i q^{17} +(-11.6955 + 13.6826i) q^{18} +9.44492i q^{19} +(-23.7282 - 16.9697i) q^{20} +(-0.576137 + 2.86541i) q^{21} +(-8.78992 + 27.4011i) q^{22} +(5.15167 - 2.97432i) q^{23} +(-13.6715 + 19.7254i) q^{24} +(-14.0937 + 24.4110i) q^{25} +(-9.41303 + 8.53953i) q^{26} +(15.1396 - 22.3560i) q^{27} +(-0.378329 + 3.87860i) q^{28} +(-24.9939 + 43.2907i) q^{29} +(38.2142 + 21.3172i) q^{30} +(-11.0551 - 19.1481i) q^{31} +(-15.4787 + 28.0073i) q^{32} +(8.50866 - 42.3177i) q^{33} +(-11.8196 - 54.6015i) q^{34} +7.10518 q^{35} +(17.0719 - 31.6947i) q^{36} +20.4275i q^{37} +(-3.99654 - 18.4622i) q^{38} +(12.5995 - 14.3071i) q^{39} +(53.5627 + 23.1307i) q^{40} +(16.9300 - 9.77457i) q^{41} +(-0.0862836 - 5.84487i) q^{42} +(-19.6424 - 11.3405i) q^{43} +(5.58734 - 57.2810i) q^{44} +(-60.5358 - 25.3690i) q^{45} +(-8.81154 + 7.99386i) q^{46} +(71.3325 + 41.1838i) q^{47} +(18.3773 - 44.3427i) q^{48} +(24.0254 + 41.6132i) q^{49} +(17.2200 - 53.6803i) q^{50} +(26.7720 + 79.4076i) q^{51} +(14.7865 - 20.6755i) q^{52} +53.3204 q^{53} +(-20.1340 + 50.1061i) q^{54} -104.933 q^{55} +(-0.901666 - 7.74168i) q^{56} +(9.05232 + 26.8499i) q^{57} +(30.5381 - 95.1974i) q^{58} +(-29.5218 - 51.1333i) q^{59} +(-83.7184 - 25.4992i) q^{60} +(-9.09207 - 5.24931i) q^{61} +(29.7121 + 32.7513i) q^{62} +(1.10847 + 8.69791i) q^{63} +(18.4055 - 61.2963i) q^{64} +(-40.1356 - 23.1723i) q^{65} +(1.27428 + 86.3198i) q^{66} +(-44.8003 + 25.8655i) q^{67} +(46.2083 + 101.730i) q^{68} +(11.7944 - 13.3929i) q^{69} +(-13.8887 + 3.00650i) q^{70} +11.6970i q^{71} +(-19.9595 + 69.1782i) q^{72} -39.1030 q^{73} +(-8.64373 - 39.9302i) q^{74} +(-16.6690 + 82.9029i) q^{75} +(15.6243 + 34.3975i) q^{76} +(7.00886 + 12.1397i) q^{77} +(-18.5746 + 33.2978i) q^{78} +(49.7902 - 86.2392i) q^{79} +(-114.488 - 22.5495i) q^{80} +(21.6118 - 78.0636i) q^{81} +(-28.9576 + 26.2704i) q^{82} +(3.61441 - 6.26034i) q^{83} +(2.64187 + 11.3886i) q^{84} +(176.422 - 101.857i) q^{85} +(43.1941 + 13.8561i) q^{86} +(-29.5610 + 147.021i) q^{87} +(13.3162 + 114.333i) q^{88} -97.4870i q^{89} +(129.066 + 23.9743i) q^{90} +6.19107i q^{91} +(13.8416 - 19.3543i) q^{92} +(-49.7795 - 43.8382i) q^{93} +(-156.862 - 50.3194i) q^{94} +(59.6531 - 34.4408i) q^{95} +(-17.1594 + 94.4540i) q^{96} +(-2.40597 + 4.16727i) q^{97} +(-64.5714 - 71.1763i) q^{98} +(-16.3704 - 128.455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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