LMFDB - Embedded newform 429.2.bi.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.482212 + 0.946394i) q^{2} +(-1.19043 + 1.25813i) q^{3} +(0.512438 + 0.705310i) q^{4} +(-0.107143 + 0.0545921i) q^{5} +(-0.616644 - 1.73330i) q^{6} +(-1.02889 - 0.162960i) q^{7} +(-3.01277 + 0.477177i) q^{8} +(-0.165763 - 2.99542i) q^{9} +O(q^{10})$	\(q+(-0.482212 + 0.946394i) q^{2} +(-1.19043 + 1.25813i) q^{3} +(0.512438 + 0.705310i) q^{4} +(-0.107143 + 0.0545921i) q^{5} +(-0.616644 - 1.73330i) q^{6} +(-1.02889 - 0.162960i) q^{7} +(-3.01277 + 0.477177i) q^{8} +(-0.165763 - 2.99542i) q^{9} -0.127724i q^{10} +(-3.04439 - 1.31594i) q^{11} +(-1.49739 - 0.194909i) q^{12} +(-2.25836 - 2.81066i) q^{13} +(0.650367 - 0.895153i) q^{14} +(0.0588623 - 0.199787i) q^{15} +(0.462389 - 1.42309i) q^{16} +(-1.66456 + 5.12300i) q^{17} +(2.91478 + 1.28755i) q^{18} +(2.51098 - 0.397700i) q^{19} +(-0.0934084 - 0.0475940i) q^{20} +(1.42984 - 1.10048i) q^{21} +(2.71343 - 2.24663i) q^{22} +2.30860 q^{23} +(2.98614 - 4.35850i) q^{24} +(-2.93043 + 4.03339i) q^{25} +(3.74900 - 0.781970i) q^{26} +(3.96594 + 3.35728i) q^{27} +(-0.412305 - 0.809193i) q^{28} +(-5.82699 - 8.02016i) q^{29} +(0.160693 + 0.152047i) q^{30} +(-3.74371 - 1.90752i) q^{31} +(-3.18999 - 3.18999i) q^{32} +(5.27974 - 2.26370i) q^{33} +(-4.04570 - 4.04570i) q^{34} +(0.119135 - 0.0387092i) q^{35} +(2.02775 - 1.65188i) q^{36} +(2.60691 + 0.412893i) q^{37} +(-0.834443 + 2.56815i) q^{38} +(6.22458 + 0.504576i) q^{39} +(0.296748 - 0.215600i) q^{40} +(-0.591349 - 3.73363i) q^{41} +(0.352001 + 1.88386i) q^{42} +9.22225i q^{43} +(-0.631918 - 2.82157i) q^{44} +(0.181286 + 0.311888i) q^{45} +(-1.11323 + 2.18484i) q^{46} +(10.3667 - 1.64192i) q^{47} +(1.23998 + 2.27583i) q^{48} +(-5.62534 - 1.82778i) q^{49} +(-2.40409 - 4.71828i) q^{50} +(-4.46384 - 8.19279i) q^{51} +(0.825113 - 3.03313i) q^{52} +(-3.47620 + 1.12949i) q^{53} +(-5.08973 + 2.13442i) q^{54} +(0.398025 - 0.0252063i) q^{55} +3.17757 q^{56} +(-2.48878 + 3.63256i) q^{57} +(10.4001 - 1.64721i) q^{58} +(-0.574798 + 3.62913i) q^{59} +(0.171075 - 0.0608624i) q^{60} +(-2.24155 + 6.89877i) q^{61} +(3.61052 - 2.62320i) q^{62} +(-0.317582 + 3.10897i) q^{63} +(7.40341 - 2.40551i) q^{64} +(0.395407 + 0.177853i) q^{65} +(-0.403601 + 6.08829i) q^{66} +(1.29712 - 1.29712i) q^{67} +(-4.46629 + 1.45119i) q^{68} +(-2.74822 + 2.90451i) q^{69} +(-0.0208140 + 0.131414i) q^{70} +(-6.26414 + 3.19174i) q^{71} +(1.92875 + 8.94542i) q^{72} +(-13.3110 - 2.10826i) q^{73} +(-1.64784 + 2.26806i) q^{74} +(-1.58605 - 8.48830i) q^{75} +(1.56722 + 1.56722i) q^{76} +(2.91790 + 1.85007i) q^{77} +(-3.47909 + 5.64759i) q^{78} +(3.68250 + 11.3336i) q^{79} +(0.0281475 + 0.177717i) q^{80} +(-8.94505 + 0.993059i) q^{81} +(3.81864 + 1.24075i) q^{82} +(-8.77797 + 4.47260i) q^{83} +(1.50889 + 0.444555i) q^{84} +(-0.101329 - 0.639765i) q^{85} +(-8.72788 - 4.44708i) q^{86} +(17.0270 + 2.21634i) q^{87} +(9.80000 + 2.51191i) q^{88} +(-2.02639 + 2.02639i) q^{89} +(-0.382588 + 0.0211720i) q^{90} +(1.86558 + 3.25988i) q^{91} +(1.18301 + 1.62828i) q^{92} +(6.85651 - 2.43930i) q^{93} +(-3.44502 + 10.6027i) q^{94} +(-0.247323 + 0.179690i) q^{95} +(7.81085 - 0.215957i) q^{96} +(-8.63655 - 4.40054i) q^{97} +(4.44240 - 4.44240i) q^{98} +(-3.43713 + 9.33735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.482212	+	0.946394i	−0.340975	+	0.669201i	−0.996281	−	0.0861622i	$-0.972540\pi$
$2$	−0.482212	+	0.946394i	−0.340975	+	0.669201i	0.655306	+	0.755363i	$0.272540\pi$
$3$	−1.19043	+	1.25813i	−0.687294	+	0.726379i
$3$	−1.19043	+	1.25813i	−0.687294	+	0.726379i
$4$	0.512438	+	0.705310i	0.256219	+	0.352655i
$5$	−0.107143	+	0.0545921i	−0.0479158	+	0.0244143i	−0.477784	−	0.878477i	$-0.658560\pi$
$5$	−0.107143	+	0.0545921i	−0.0479158	+	0.0244143i	0.429868	+	0.902892i	$0.358560\pi$
$6$	−0.616644	−	1.73330i	−0.251744	−	0.707615i
$7$	−1.02889	−	0.162960i	−0.388884	−	0.0615931i	−0.0410688	−	0.999156i	$-0.513076\pi$
$7$	−1.02889	−	0.162960i	−0.388884	−	0.0615931i	−0.347815	+	0.937563i	$0.613076\pi$
$8$	−3.01277	+	0.477177i	−1.06518	+	0.168707i
$9$	−0.165763	−	2.99542i	−0.0552543	−	0.998472i
$10$		−	0.127724i		−	0.0403900i
$11$	−3.04439	−	1.31594i	−0.917918	−	0.396770i
$11$	−3.04439	−	1.31594i	−0.917918	−	0.396770i
$12$	−1.49739	−	0.194909i	−0.432259	−	0.0562655i
$13$	−2.25836	−	2.81066i	−0.626358	−	0.779536i
$13$	−2.25836	−	2.81066i	−0.626358	−	0.779536i
$14$	0.650367	−	0.895153i	0.173818	−	0.239240i
$15$	0.0588623	−	0.199787i	0.0151982	−	0.0515848i
$16$	0.462389	−	1.42309i	0.115597	−	0.355772i
$17$	−1.66456	+	5.12300i	−0.403716	+	1.24251i	0.518247	+	0.855231i	$0.326585\pi$
$17$	−1.66456	+	5.12300i	−0.403716	+	1.24251i	−0.921963	+	0.387279i	$0.873415\pi$
$18$	2.91478	+	1.28755i	0.687019	+	0.303478i
$19$	2.51098	−	0.397700i	0.576059	−	0.0912387i	0.138394	−	0.990377i	$-0.455806\pi$
$19$	2.51098	−	0.397700i	0.576059	−	0.0912387i	0.437664	+	0.899139i	$0.355806\pi$
$20$	−0.0934084	−	0.0475940i	−0.0208868	−	0.0106423i
$21$	1.42984	−	1.10048i	0.312017	−	0.240145i
$22$	2.71343	−	2.24663i	0.578506	−	0.478983i
$23$	2.30860			0.481376			0.240688	−	0.970602i	$-0.422627\pi$
$23$	2.30860			0.481376			0.240688	+	0.970602i	$0.422627\pi$
$24$	2.98614	−	4.35850i	0.609544	−	0.889674i
$25$	−2.93043	+	4.03339i	−0.586085	+	0.806677i
$26$	3.74900	−	0.781970i	0.735239	−	0.153357i
$27$	3.96594	+	3.35728i	0.763246	+	0.646108i
$28$	−0.412305	−	0.809193i	−0.0779183	−	0.152923i
$29$	−5.82699	−	8.02016i	−1.08204	−	1.48931i	−0.857250	−	0.514900i	$-0.827829\pi$
$29$	−5.82699	−	8.02016i	−1.08204	−	1.48931i	−0.224794	−	0.974406i	$-0.572171\pi$
$30$	0.160693	+	0.152047i	0.0293385	+	0.0277598i
$31$	−3.74371	−	1.90752i	−0.672390	−	0.342600i	0.0842378	−	0.996446i	$-0.473154\pi$
$31$	−3.74371	−	1.90752i	−0.672390	−	0.342600i	−0.756628	+	0.653846i	$0.773154\pi$
$32$	−3.18999	−	3.18999i	−0.563915	−	0.563915i
$33$	5.27974	−	2.26370i	0.919085	−	0.394060i
$34$	−4.04570	−	4.04570i	−0.693832	−	0.693832i
$35$	0.119135	−	0.0387092i	0.0201374	−	0.00654305i
$36$	2.02775	−	1.65188i	0.337959	−	0.275313i
$37$	2.60691	+	0.412893i	0.428573	+	0.0678792i	0.366995	−	0.930223i	$-0.380387\pi$
$37$	2.60691	+	0.412893i	0.428573	+	0.0678792i	0.0615779	+	0.998102i	$0.480387\pi$
$38$	−0.834443	+	2.56815i	−0.135365	+	0.416609i
$39$	6.22458	+	0.504576i	0.996731	+	0.0807969i
$40$	0.296748	−	0.215600i	0.0469199	−	0.0340893i
$41$	−0.591349	−	3.73363i	−0.0923532	−	0.583095i	−0.989855	−	0.142084i	$-0.954620\pi$
$41$	−0.591349	−	3.73363i	−0.0923532	−	0.583095i	0.897501	−	0.441012i	$-0.145380\pi$
$42$	0.352001	+	1.88386i	0.0543149	+	0.290686i
$43$			9.22225i			1.40638i	0.711002	+	0.703190i	$0.248242\pi$
$43$			9.22225i			1.40638i	−0.711002	+	0.703190i	$0.751758\pi$
$44$	−0.631918	−	2.82157i	−0.0952652	−	0.425368i
$45$	0.181286	+	0.311888i	0.0270246	+	0.0464936i
$46$	−1.11323	+	2.18484i	−0.164137	+	0.322138i
$47$	10.3667	−	1.64192i	1.51213	−	0.239498i	0.655409	−	0.755274i	$-0.272496\pi$
$47$	10.3667	−	1.64192i	1.51213	−	0.239498i	0.856724	+	0.515775i	$0.172496\pi$
$48$	1.23998	+	2.27583i	0.178976	+	0.328487i
$49$	−5.62534	−	1.82778i	−0.803620	−	0.261112i
$50$	−2.40409	−	4.71828i	−0.339989	−	0.667266i
$51$	−4.46384	−	8.19279i	−0.625062	−	1.14722i
$52$	0.825113	−	3.03313i	0.114423	−	0.420620i
$53$	−3.47620	+	1.12949i	−0.477493	+	0.155147i	−0.537868	−	0.843029i	$-0.680770\pi$
$53$	−3.47620	+	1.12949i	−0.477493	+	0.155147i	0.0603752	+	0.998176i	$0.480770\pi$
$54$	−5.08973	+	2.13442i	−0.692624	+	0.290458i
$55$	0.398025	−	0.0252063i	0.0536696	−	0.00339881i
$56$	3.17757			0.424621
$57$	−2.48878	+	3.63256i	−0.329648	+	0.481145i
$58$	10.4001	−	1.64721i	1.36560	−	0.216289i
$59$	−0.574798	+	3.62913i	−0.0748323	+	0.472472i	0.921605	+	0.388130i	$0.126879\pi$
$59$	−0.574798	+	3.62913i	−0.0748323	+	0.472472i	−0.996437	+	0.0843423i	$0.973121\pi$
$60$	0.171075	−	0.0608624i	0.0220857	−	0.00785730i
$61$	−2.24155	+	6.89877i	−0.287001	+	0.883297i	0.698791	+	0.715326i	$0.253722\pi$
$61$	−2.24155	+	6.89877i	−0.287001	+	0.883297i	−0.985792	+	0.167971i	$0.946278\pi$
$62$	3.61052	−	2.62320i	0.458536	−	0.333146i
$63$	−0.317582	+	3.10897i	−0.0400115	+	0.391693i
$64$	7.40341	−	2.40551i	0.925426	−	0.300689i
$65$	0.395407	+	0.177853i	0.0490442	+	0.0220600i
$66$	−0.403601	+	6.08829i	−0.0496798	+	0.749417i
$67$	1.29712	−	1.29712i	0.158469	−	0.158469i	−0.623419	−	0.781888i	$-0.714257\pi$
$67$	1.29712	−	1.29712i	0.158469	−	0.158469i	0.781888	+	0.623419i	$0.214257\pi$
$68$	−4.46629	+	1.45119i	−0.541617	+	0.175982i
$69$	−2.74822	+	2.90451i	−0.330847	+	0.349662i
$70$	−0.0208140	+	0.131414i	−0.00248775	+	0.0157070i
$71$	−6.26414	+	3.19174i	−0.743416	+	0.378790i	−0.784306	−	0.620374i	$-0.786981\pi$
$71$	−6.26414	+	3.19174i	−0.743416	+	0.378790i	0.0408897	+	0.999164i	$0.486981\pi$
$72$	1.92875	+	8.94542i	0.227305	+	1.05423i
$73$	−13.3110	−	2.10826i	−1.55794	−	0.246753i	−0.682793	−	0.730612i	$-0.739235\pi$
$73$	−13.3110	−	2.10826i	−1.55794	−	0.246753i	−0.875146	+	0.483859i	$0.839235\pi$
$74$	−1.64784	+	2.26806i	−0.191557	+	0.263656i
$75$	−1.58605	−	8.48830i	−0.183141	−	0.980145i
$76$	1.56722	+	1.56722i	0.179773	+	0.179773i
$77$	2.91790	+	1.85007i	0.332525	+	0.210835i
$78$	−3.47909	+	5.64759i	−0.393930	+	0.639464i
$79$	3.68250	+	11.3336i	0.414314	+	1.27513i	0.912863	+	0.408266i	$0.133866\pi$
$79$	3.68250	+	11.3336i	0.414314	+	1.27513i	−0.498549	+	0.866862i	$0.666134\pi$
$80$	0.0281475	+	0.177717i	0.00314699	+	0.0198693i
$81$	−8.94505	+	0.993059i	−0.993894	+	0.110340i
$82$	3.81864	+	1.24075i	0.421698	+	0.137018i
$83$	−8.77797	+	4.47260i	−0.963508	+	0.490932i	−0.863662	−	0.504071i	$-0.831835\pi$
$83$	−8.77797	+	4.47260i	−0.963508	+	0.490932i	−0.0998457	+	0.995003i	$0.531835\pi$
$84$	1.50889	+	0.444555i	0.164633	+	0.0485049i
$85$	−0.101329	−	0.639765i	−0.0109907	−	0.0693923i
$86$	−8.72788	−	4.44708i	−0.941151	−	0.479541i
$87$	17.0270	+	2.21634i	1.82548	+	0.237616i
$88$	9.80000	+	2.51191i	1.04468	+	0.267770i
$89$	−2.02639	+	2.02639i	−0.214796	+	0.214796i	−0.806301	−	0.591505i	$-0.798534\pi$
$89$	−2.02639	+	2.02639i	−0.214796	+	0.214796i	0.591505	+	0.806301i	$0.298534\pi$
$90$	−0.382588	+	0.0211720i	−0.0403283	+	0.00223172i
$91$	1.86558	+	3.25988i	0.195566	+	0.341728i
$92$	1.18301	+	1.62828i	0.123338	+	0.169760i
$93$	6.85651	−	2.43930i	0.710987	−	0.252944i
$94$	−3.44502	+	10.6027i	−0.355327	+	1.09358i
$95$	−0.247323	+	0.179690i	−0.0253748	+	0.0184358i
$96$	7.81085	−	0.215957i	0.797192	−	0.0220410i
$97$	−8.63655	−	4.40054i	−0.876909	−	0.446807i	−0.0432353	−	0.999065i	$-0.513767\pi$
$97$	−8.63655	−	4.40054i	−0.876909	−	0.446807i	−0.833674	+	0.552257i	$0.813767\pi$
$98$	4.44240	−	4.44240i	0.448751	−	0.448751i
$99$	−3.43713	+	9.33735i	−0.345445	+	0.938439i
$100$	−4.34645			−0.434645
$101$	−3.84668	−	11.8389i	−0.382759	−	1.17801i	−0.938093	−	0.346384i	$-0.887409\pi$
$101$	−3.84668	−	11.8389i	−0.382759	−	1.17801i	0.555334	−	0.831628i	$-0.312591\pi$
$102$	9.90612	−	0.273887i	0.980852	−	0.0271189i
$103$	10.7996	+	14.8644i	1.06412	+	1.46463i	0.875894	+	0.482504i	$0.160273\pi$
$103$	10.7996	+	14.8644i	1.06412	+	1.46463i	0.188222	+	0.982126i	$0.439727\pi$
$104$	8.14512	+	7.39024i	0.798695	+	0.724672i
$105$	−0.0931201	+	0.195967i	−0.00908759	+	0.0191244i
$106$	0.607326	−	3.83451i	0.0589888	−	0.372440i
$107$	−9.59621	+	13.2080i	−0.927700	+	1.27687i	0.0330495	+	0.999454i	$0.489478\pi$
$107$	−9.59621	+	13.2080i	−0.927700	+	1.27687i	−0.960750	+	0.277416i	$0.910522\pi$
$108$	−0.335623	+	4.51761i	−0.0322954	+	0.434708i
$109$	0.287501	−	0.287501i	0.0275376	−	0.0275376i	−0.693204	−	0.720742i	$-0.743801\pi$
$109$	0.287501	−	0.287501i	0.0275376	−	0.0275376i	0.720742	+	0.693204i	$0.243801\pi$
$110$	−0.168077	+	0.388843i	−0.0160255	+	0.0370747i
$111$	−3.62280	+	2.78830i	−0.343861	+	0.264653i
$112$	−0.707654	+	1.38885i	−0.0668670	+	0.131234i
$113$	3.27893	−	4.51306i	0.308456	−	0.424553i	−0.626443	−	0.779467i	$-0.715490\pi$
$113$	3.27893	−	4.51306i	0.308456	−	0.424553i	0.934899	+	0.354914i	$0.115490\pi$
$114$	−2.23771	−	4.10703i	−0.209581	−	0.384659i
$115$	−0.247350	+	0.126031i	−0.0230655	+	0.0117525i
$116$	2.67073	−	8.21967i	0.247971	−	0.763177i
$117$	−8.04473	+	7.23065i	−0.743736	+	0.668473i
$118$	−3.15741	−	2.29399i	−0.290663	−	0.211179i
$119$	2.54750	−	4.99975i	0.233529	−	0.458326i
$120$	−0.0820049	+	0.630002i	−0.00748599	+	0.0575110i
$121$	7.53663	+	8.01245i	0.685148	+	0.728404i
$122$	−5.44805	−	5.44805i	−0.493243	−	0.493243i
$123$	5.40134	+	3.70063i	0.487022	+	0.333674i
$124$	−0.573028	−	3.61796i	−0.0514595	−	0.324902i
$125$	0.187839	−	1.18597i	0.0168009	−	0.106077i
$126$	−2.78916	−	1.79974i	−0.248479	−	0.160333i
$127$	−13.8973	−	4.51552i	−1.23319	−	0.400688i	−0.381321	−	0.924443i	$-0.624531\pi$
$127$	−13.8973	−	4.51552i	−1.23319	−	0.400688i	−0.851869	+	0.523755i	$0.824531\pi$
$128$	0.118006	−	0.745060i	0.0104303	−	0.0658546i
$129$	−11.6028	−	10.9784i	−1.02157	−	0.966596i
$130$	−0.358989	+	0.288448i	−0.0314854	+	0.0252986i
$131$		−	6.62967i		−	0.579237i	−0.957142	−	0.289619i	$-0.906472\pi$
$131$		−	6.62967i		−	0.579237i	0.957142	−	0.289619i	$-0.0935285\pi$
$132$	4.30215	+	2.56385i	0.374454	+	0.223154i
$133$	−2.64833			−0.229640
$134$	0.602102	+	1.85308i	0.0520137	+	0.160082i
$135$	−0.608203	−	0.143200i	−0.0523458	−	0.0123247i
$136$	2.57038	−	16.2287i	0.220408	−	1.39160i
$137$	10.2641	+	20.1444i	0.876918	+	1.72105i	0.669523	+	0.742791i	$0.266498\pi$
$137$	10.2641	+	20.1444i	0.876918	+	1.72105i	0.207395	+	0.978257i	$0.433502\pi$
$138$	−1.42359	−	4.00149i	−0.121184	−	0.340629i
$139$	10.7735	−	7.82742i	0.913798	−	0.663913i	−0.0281745	−	0.999603i	$-0.508969\pi$
$139$	10.7735	−	7.82742i	0.913798	−	0.663913i	0.941973	+	0.335690i	$0.108969\pi$
$140$	0.0883511	+	0.0641908i	0.00746703	+	0.00542511i
$141$	−10.2750	+	14.9972i	−0.865313	+	1.26299i
$142$		−	7.46743i		−	0.626653i
$143$	3.17670	+	11.5286i	0.265649	+	0.964070i
$144$	−4.33939	−	1.14915i	−0.361616	−	0.0957627i
$145$	1.06216	+	0.541196i	0.0882074	+	0.0449439i
$146$	8.41398	−	11.5808i	0.696346	−	0.958438i
$147$	8.99614	−	4.90154i	0.741989	−	0.404272i
$148$	1.04466	+	2.05026i	0.0858705	+	0.168530i
$149$	6.65797	−	3.39240i	0.545442	−	0.277917i	−0.159480	−	0.987201i	$-0.550982\pi$
$149$	6.65797	−	3.39240i	0.545442	−	0.277917i	0.704922	+	0.709285i	$0.250982\pi$
$150$	8.79809	+	2.59213i	0.718361	+	0.211647i
$151$	−1.38975	−	8.77454i	−0.113096	−	0.714062i	−0.977448	−	0.211175i	$-0.932271\pi$
$151$	−1.38975	−	8.77454i	−0.113096	−	0.714062i	0.864352	−	0.502887i	$-0.167729\pi$
$152$	−7.37525	+	2.39636i	−0.598212	+	0.194371i
$153$	15.6214	+	4.13686i	1.26292	+	0.334445i
$154$	−3.15794	+	1.86936i	−0.254474	+	0.150637i
$155$	0.505247			0.0405824
$156$	2.83383	+	4.64882i	0.226888	+	0.372204i
$157$	−17.1918	−	12.4906i	−1.37205	−	0.996855i	−0.997574	−	0.0696199i	$-0.977821\pi$
$157$	−17.1918	−	12.4906i	−1.37205	−	0.996855i	−0.374480	−	0.927235i	$-0.622179\pi$
$158$	−12.5018	−	1.98009i	−0.994588	−	0.157527i
$159$	2.71713	−	5.71808i	0.215483	−	0.453473i
$160$	0.515932	+	0.167637i	0.0407880	+	0.0132528i
$161$	−2.37530	−	0.376210i	−0.187199	−	0.0296495i
$162$	3.37358	−	8.94440i	0.265053	−	0.702738i
$163$	−1.64551	+	3.22950i	−0.128887	+	0.252954i	−0.946427	−	0.322916i	$-0.895337\pi$
$163$	−1.64551	+	3.22950i	−0.128887	+	0.252954i	0.817541	+	0.575870i	$0.195337\pi$
$164$	2.33034	−	2.33034i	0.181969	−	0.181969i
$165$	−0.442107	+	0.530771i	−0.0344180	+	0.0413205i
$166$		−	10.4642i		−	0.812176i
$167$	−8.47701	−	4.31925i	−0.655971	−	0.334234i	0.0941274	−	0.995560i	$-0.469994\pi$
$167$	−8.47701	−	4.31925i	−0.655971	−	0.334234i	−0.750098	+	0.661326i	$0.769994\pi$
$168$	−3.78267	+	3.99779i	−0.291840	+	0.308436i
$169$	−2.79958	+	12.6950i	−0.215352	+	0.976536i
$170$	0.654332	+	0.212605i	0.0501850	+	0.0163061i
$171$	−1.60751	−	7.45551i	−0.122929	−	0.570137i
$172$	−6.50455	+	4.72583i	−0.495967	+	0.360341i
$173$	6.82724	+	4.96028i	0.519065	+	0.377123i	0.816252	−	0.577696i	$-0.196048\pi$
$173$	6.82724	+	4.96028i	0.519065	+	0.377123i	−0.297186	+	0.954820i	$0.596048\pi$
$174$	−10.3081	+	15.0455i	−0.781458	+	1.14060i
$175$	3.67237	−	3.67237i	0.277605	−	0.277605i
$176$	−3.28038	+	3.72396i	−0.247268	+	0.280704i
$177$	−3.88165	−	5.04339i	−0.291763	−	0.379084i
$178$	−0.940611	−	2.89490i	−0.0705018	−	0.216982i
$179$	7.43566	+	5.40232i	0.555767	+	0.403788i	0.829907	−	0.557901i	$-0.188393\pi$
$179$	7.43566	+	5.40232i	0.555767	+	0.403788i	−0.274140	+	0.961690i	$0.588393\pi$
$180$	−0.127080	+	0.287687i	−0.00947199	+	0.0214429i
$181$	−4.53329	−	1.47295i	−0.336957	−	0.109484i	0.135651	−	0.990757i	$-0.456687\pi$
$181$	−4.53329	−	1.47295i	−0.336957	−	0.109484i	−0.472608	+	0.881273i	$0.656687\pi$
$182$	−3.98473	+	0.193624i	−0.295368	+	0.0143524i
$183$	−6.01112	−	11.0326i	−0.444355	−	0.815556i
$184$	−6.95529	+	1.10161i	−0.512751	+	0.0812118i
$185$	−0.301852	+	0.0980777i	−0.0221926	+	0.00721082i
$186$	−0.997752	+	7.66522i	−0.0731587	+	0.562041i
$187$	11.8091	−	13.4060i	0.863569	−	0.980341i
$188$	6.47033	+	6.47033i	0.471897	+	0.471897i
$189$	−3.53341	−	4.10056i	−0.257018	−	0.298272i
$190$	−0.0507960	−	0.320713i	−0.00368513	−	0.0232670i
$191$	2.05458	+	2.82788i	0.148664	+	0.204619i	0.876854	−	0.480757i	$-0.159638\pi$
$191$	2.05458	+	2.82788i	0.148664	+	0.204619i	−0.728190	+	0.685376i	$0.759638\pi$
$192$	−5.78678	+	12.1780i	−0.417625	+	0.878872i
$193$	18.3736	−	9.36182i	1.32256	−	0.673878i	0.357012	−	0.934100i	$-0.383796\pi$
$193$	18.3736	−	9.36182i	1.32256	−	0.673878i	0.965549	+	0.260222i	$0.0837956\pi$
$194$	8.32929	−	6.05158i	0.598008	−	0.434478i
$195$	−0.694466	+	0.285751i	−0.0497317	+	0.0204630i
$196$	−1.59348	−	4.90423i	−0.113820	−	0.350302i
$197$	2.24093	+	2.24093i	0.159659	+	0.159659i	0.782416	−	0.622756i	$-0.213987\pi$
$197$	2.24093	+	2.24093i	0.159659	+	0.159659i	−0.622756	+	0.782416i	$0.713987\pi$
$198$	−7.17939	−	7.75546i	−0.510217	−	0.551156i
$199$			11.8275i			0.838432i	0.907887	+	0.419216i	$0.137695\pi$
$199$			11.8275i			0.838432i	−0.907887	+	0.419216i	$0.862305\pi$
$200$	6.90408	−	13.5500i	0.488192	−	0.958131i
$201$	0.0878132	+	3.17608i	0.00619386	+	0.224023i
$202$	13.0591	+	2.06837i	0.918838	+	0.145530i
$203$	4.68836	+	9.20143i	0.329059	+	0.645814i
$204$	3.49102	−	7.34669i	0.244420	−	0.514371i
$205$	0.267186	+	0.367749i	0.0186611	+	0.0256847i
$206$	−19.2752	+	3.05290i	−1.34297	+	0.212705i
$207$	−0.382680	−	6.91522i	−0.0265981	−	0.480641i
$208$	−5.04405	+	1.91423i	−0.349742	+	0.132728i
$209$	−8.16775	−	2.09353i	−0.564975	−	0.144813i
$210$	−0.140558	−	0.182626i	−0.00969944	−	0.0126024i
$211$	−2.26124	−	6.95939i	−0.155670	−	0.479104i	0.842558	−	0.538606i	$-0.181049\pi$
$211$	−2.26124	−	6.95939i	−0.155670	−	0.479104i	−0.998228	+	0.0595017i	$0.981049\pi$
$212$	−2.57798	−	1.87301i	−0.177056	−	0.128639i
$213$	3.44140	−	11.6806i	0.235801	−	0.800342i
$214$	−7.87261	−	15.4509i	−0.538160	−	1.05620i
$215$	−0.503462	−	0.988099i	−0.0343358	−	0.0673878i
$216$	−13.5505	−	8.22227i	−0.921995	−	0.559454i
$217$	3.54102	+	2.57270i	0.240380	+	0.174646i
$218$	0.133453	+	0.410725i	0.00903856	+	0.0278178i
$219$	18.4983	−	14.2372i	1.25000	−	0.962063i
$220$	0.221741	+	0.267814i	0.0149498	+	0.0180560i
$221$	18.1582	−	6.89109i	1.22145	−	0.463545i
$222$	−0.891867	−	4.77315i	−0.0598582	−	0.320353i
$223$	4.07823	−	0.645929i	0.273099	−	0.0432546i	−0.0183828	−	0.999831i	$-0.505852\pi$
$223$	4.07823	−	0.645929i	0.273099	−	0.0432546i	0.291482	+	0.956576i	$0.405852\pi$
$224$	2.76230	+	3.80199i	0.184564	+	0.254031i
$225$	12.5674	+	8.10926i	0.837829	+	0.540618i
$226$	2.68999	+	5.27941i	0.178936	+	0.351181i
$227$	−2.84054	−	0.449897i	−0.188533	−	0.0298607i	0.0614538	−	0.998110i	$-0.480426\pi$
$227$	−2.84054	−	0.449897i	−0.188533	−	0.0298607i	−0.249987	+	0.968249i	$0.580426\pi$
$228$	−3.83743	+	0.106098i	−0.254140	+	0.00702654i
$229$	4.06440	−	7.97683i	0.268583	−	0.527124i	−0.716842	−	0.697236i	$-0.754413\pi$
$229$	4.06440	−	7.97683i	0.268583	−	0.527124i	0.985425	+	0.170112i	$0.0544130\pi$
$230$		−	0.294864i		−	0.0194428i
$231$	−5.80116	+	1.46871i	−0.381689	+	0.0966341i
$232$	21.3824	+	21.3824i	1.40383	+	1.40383i
$233$	2.31809	+	7.13435i	0.151863	+	0.467387i	0.997830	−	0.0658495i	$-0.0209757\pi$
$233$	2.31809	+	7.13435i	0.151863	+	0.467387i	−0.845966	+	0.533236i	$0.820976\pi$
$234$	−2.96377	−	11.1002i	−0.193748	−	0.725642i
$235$	−1.02108	+	0.741858i	−0.0666079	+	0.0483934i
$236$	−2.85421	+	1.45429i	−0.185793	+	0.0946664i
$237$	−18.6428	−	8.85876i	−1.21098	−	0.575438i
$238$	3.50329	+	4.82187i	0.227085	+	0.312555i
$239$	−0.182552	−	1.15259i	−0.0118083	−	0.0745546i	0.981080	−	0.193600i	$-0.0620165\pi$
$239$	−0.182552	−	1.15259i	−0.0118083	−	0.0745546i	−0.992889	+	0.119046i	$0.962016\pi$
$240$	−0.257097	−	0.176146i	−0.0165956	−	0.0113701i
$241$	−14.8198	−	14.8198i	−0.954629	−	0.954629i	0.0443858	−	0.999014i	$-0.485867\pi$
$241$	−14.8198	−	14.8198i	−0.954629	−	0.954629i	−0.999014	+	0.0443858i	$0.985867\pi$
$242$	−11.2172	+	3.26892i	−0.721067	+	0.210134i
$243$	9.39904	−	12.4362i	0.602949	−	0.797780i
$244$	−6.01443	+	1.95421i	−0.385034	+	0.125105i
$245$	0.702498	−	0.111265i	0.0448809	−	0.00710844i
$246$	−6.10684	+	3.32731i	−0.389358	+	0.212141i
$247$	−6.78851	−	6.15935i	−0.431942	−	0.391910i
$248$	12.1892	+	3.96050i	0.774013	+	0.251492i
$249$	4.82245	−	16.3681i	0.305610	−	1.03729i
$250$	1.03182	+	0.749659i	0.0652579	+	0.0474126i
$251$	−0.582466	−	1.79265i	−0.0367649	−	0.113151i	0.930990	−	0.365045i	$-0.118946\pi$
$251$	−0.582466	−	1.79265i	−0.0367649	−	0.113151i	−0.967755	+	0.251894i	$0.918946\pi$
$252$	−2.35553	+	1.36916i	−0.148384	+	0.0862489i
$253$	−7.02828	−	3.03797i	−0.441864	−	0.190996i
$254$	10.9749	−	10.9749i	0.688628	−	0.688628i
$255$	0.925530	+	0.634110i	0.0579590	+	0.0397095i
$256$	13.2436	+	9.62207i	0.827728	+	0.601379i
$257$	−10.4069	+	7.56106i	−0.649165	+	0.471646i	−0.862987	−	0.505227i	$-0.831409\pi$
$257$	−10.4069	+	7.56106i	−0.649165	+	0.471646i	0.213821	+	0.976873i	$0.431409\pi$
$258$	15.9849	−	5.68685i	0.995176	−	0.354048i
$259$	−2.61493	−	0.849643i	−0.162484	−	0.0527943i
$260$	0.0771800	+	0.370024i	0.00478650	+	0.0229479i
$261$	−23.0578	+	18.7837i	−1.42724	+	1.16268i
$262$	6.27428	+	3.19691i	0.387626	+	0.197505i
$263$			18.2211i			1.12356i	0.827286	+	0.561781i	$0.189884\pi$
$263$			18.2211i			1.12356i	−0.827286	+	0.561781i	$0.810116\pi$
$264$	−14.8265	+	9.33939i	−0.912507	+	0.574800i
$265$	0.310790	−	0.310790i	0.0190917	−	0.0190917i
$266$	1.27706	−	2.50636i	0.0783013	−	0.153675i
$267$	−0.137183	−	4.96171i	−0.00839546	−	0.303652i
$268$	1.57957	+	0.250179i	0.0964876	+	0.0152821i
$269$	13.9821	+	4.54306i	0.852504	+	0.276995i	0.702495	−	0.711689i	$-0.252069\pi$
$269$	13.9821	+	4.54306i	0.852504	+	0.276995i	0.150010	+	0.988685i	$0.452069\pi$
$270$	0.428806	−	0.506547i	0.0260963	−	0.0308275i
$271$	−2.26535	−	0.358797i	−0.137610	−	0.0217954i	0.0872492	−	0.996187i	$-0.472192\pi$
$271$	−2.26535	−	0.358797i	−0.137610	−	0.0217954i	−0.224860	+	0.974391i	$0.572192\pi$
$272$	6.52080	+	4.73764i	0.395382	+	0.287262i
$273$	−6.32218	−	1.53351i	−0.382636	−	0.0928124i
$274$	−24.0139			−1.45074
$275$	14.2290	−	8.42295i	0.858044	−	0.507923i
$276$	−3.45687	−	0.449968i	−0.208079	−	0.0270849i
$277$	−5.08876	+	1.65344i	−0.305754	+	0.0993456i	−0.457876	−	0.889016i	$-0.651390\pi$
$277$	−5.08876	+	1.65344i	−0.305754	+	0.0993456i	0.152121	+	0.988362i	$0.451390\pi$
$278$	2.21270	+	13.9705i	0.132709	+	0.837893i
$279$	−5.09323	+	11.5302i	−0.304924	+	0.690293i
$280$	−0.340455	+	0.173470i	−0.0203461	+	0.0103668i
$281$	11.1385	+	21.8605i	0.664465	+	1.30409i	0.939466	+	0.342642i	$0.111322\pi$
$281$	11.1385	+	21.8605i	0.664465	+	1.30409i	−0.275002	+	0.961444i	$0.588678\pi$
$282$	−9.23848	−	16.9560i	−0.550143	−	1.00972i
$283$	9.07301	−	12.4879i	0.539334	−	0.742330i	−0.449183	−	0.893440i	$-0.648285\pi$
$283$	9.07301	−	12.4879i	0.539334	−	0.742330i	0.988517	+	0.151110i	$0.0482848\pi$
$284$	−5.46115	−	2.78259i	−0.324059	−	0.165117i
$285$	0.0683465	−	0.525072i	0.00404850	−	0.0311026i
$286$	−12.4424	−	2.55282i	−0.735736	−	0.150951i
$287$			3.93786i			0.232445i
$288$	−9.02656	+	10.0841i	−0.531895	+	0.594213i
$289$	−9.72108	−	7.06278i	−0.571828	−	0.415457i
$290$	−1.02437	+	0.744248i	−0.0601531	+	0.0437038i
$291$	15.8176	−	5.62734i	0.927246	−	0.329881i
$292$	−5.33410	−	10.4688i	−0.312155	−	0.612638i
$293$	3.55148	−	22.4232i	0.207480	−	1.30998i	−0.635529	−	0.772077i	$-0.719218\pi$
$293$	3.55148	−	22.4232i	0.207480	−	1.30998i	0.843009	−	0.537899i	$-0.180782\pi$
$294$	0.300743	+	10.8775i	0.0175397	+	0.634387i
$295$	−0.136536	−	0.420215i	−0.00794944	−	0.0244659i
$296$	−8.05104			−0.467957
$297$	−7.65591	−	15.4398i	−0.444241	−	0.895907i
$298$			7.93691i			0.459773i
$299$	−5.21366	−	6.48868i	−0.301514	−	0.375250i
$300$	5.17414	−	5.46838i	0.298729	−	0.315717i
$301$	1.50286	−	9.48868i	0.0866234	−	0.546918i
$302$	8.97432	+	2.91593i	0.516414	+	0.167793i
$303$	19.4740	+	9.25371i	1.11875	+	0.531612i
$304$	0.595088	−	3.75724i	0.0341306	−	0.215492i
$305$	−0.136452	−	0.861525i	−0.00781323	−	0.0493308i
$306$	−11.4479	+	12.7892i	−0.654435	+	0.731110i
$307$	−10.6682	−	10.6682i	−0.608868	−	0.608868i	0.333782	−	0.942650i	$-0.391675\pi$
$307$	−10.6682	−	10.6682i	−0.608868	−	0.608868i	−0.942650	+	0.333782i	$0.891675\pi$
$308$	0.190370	+	3.00607i	0.0108473	+	0.171287i
$309$	−31.5574	−	4.10771i	−1.79524	−	0.233679i
$310$	−0.243636	+	0.478163i	−0.0138376	+	0.0271578i
$311$	17.0839	+	12.4121i	0.968736	+	0.703828i	0.955163	−	0.296080i	$-0.0956794\pi$
$311$	17.0839	+	12.4121i	0.968736	+	0.703828i	0.0135731	+	0.999908i	$0.495679\pi$
$312$	−18.9940	+	1.45005i	−1.07533	+	0.0820929i
$313$	−7.81162	+	24.0417i	−0.441539	+	1.35892i	0.444696	+	0.895681i	$0.353312\pi$
$313$	−7.81162	+	24.0417i	−0.441539	+	1.35892i	−0.886235	+	0.463236i	$0.846688\pi$
$314$	20.1111	−	10.2471i	1.13493	−	0.578277i
$315$	−0.135698	−	0.350441i	−0.00764573	−	0.0197451i
$316$	−6.10664	+	8.40506i	−0.343525	+	0.472822i
$317$	11.9728	−	23.4979i	0.672459	−	1.31977i	−0.262470	−	0.964940i	$-0.584537\pi$
$317$	11.9728	−	23.4979i	0.672459	−	1.31977i	0.934929	−	0.354835i	$-0.115463\pi$
$318$	4.10132	+	5.32880i	0.229990	+	0.298824i
$319$	7.18561	+	32.0844i	0.402317	+	1.79638i
$320$	−0.661901	+	0.661901i	−0.0370014	+	0.0370014i
$321$	−5.19380	−	27.7965i	−0.289889	−	1.55145i
$322$	1.50144	−	2.06655i	0.0836718	−	0.115164i
$323$	−2.14227	+	13.5258i	−0.119199	+	0.752593i
$324$	−5.28419	−	5.80015i	−0.293566	−	0.322231i
$325$	17.9544	−	0.872434i	0.995933	−	0.0483939i
$326$	−2.26289	−	3.11461i	−0.125330	−	0.172502i
$327$	0.0194633	+	0.703961i	0.00107632	+	0.0389292i
$328$	3.56320	+	10.9664i	0.196745	+	0.605519i
$329$	−10.9337			−0.602796
$330$	−0.289130	−	0.674351i	−0.0159161	−	0.0371218i
$331$	23.7833	−	23.7833i	1.30725	−	1.30725i	0.383856	−	0.923393i	$-0.374596\pi$
$331$	23.7833	−	23.7833i	1.30725	−	1.30725i	0.923393	−	0.383856i	$-0.125404\pi$
$332$	−7.65274	−	3.89926i	−0.419998	−	0.214000i
$333$	0.804659	−	7.87721i	0.0440950	−	0.431669i
$334$	8.17543	−	5.93980i	0.447339	−	0.325011i
$335$	−0.0681651	+	0.209790i	−0.00372425	+	0.0114621i
$336$	−0.904936	−	2.54364i	−0.0493683	−	0.138767i
$337$	8.43331	+	11.6075i	0.459391	+	0.632298i	0.974382	−	0.224897i	$-0.0722047\pi$
$337$	8.43331	+	11.6075i	0.459391	+	0.632298i	−0.514991	+	0.857196i	$0.672205\pi$
$338$	−10.6645	−	8.77117i	−0.580070	−	0.477089i
$339$	1.77467	+	9.49778i	0.0963868	+	0.515848i
$340$	0.399308	−	0.399308i	0.0216555	−	0.0216555i
$341$	8.88714	+	10.7337i	0.481266	+	0.581263i
$342$	7.83100	+	2.07380i	0.423452	+	0.112138i
$343$	11.9872	+	6.10779i	0.647249	+	0.329790i
$344$	−4.40064	−	27.7846i	−0.237267	−	1.49804i
$345$	0.135889	−	0.461229i	0.00731604	−	0.0248317i
$346$	−7.98655	+	4.06935i	−0.429360	+	0.218770i
$347$	−12.0704	−	3.92191i	−0.647972	−	0.210539i	−0.0334524	−	0.999440i	$-0.510650\pi$
$347$	−12.0704	−	3.92191i	−0.647972	−	0.210539i	−0.614520	+	0.788901i	$0.710650\pi$
$348$	7.16207	+	13.1450i	0.383927	+	0.704648i
$349$	2.41465	+	15.2455i	0.129253	+	0.816072i	0.964090	+	0.265575i	$0.0855617\pi$
$349$	2.41465	+	15.2455i	0.129253	+	0.816072i	−0.834837	+	0.550497i	$0.814438\pi$
$350$	1.70465	+	5.24636i	0.0911172	+	0.280430i
$351$	0.479611	−	18.7289i	0.0255997	−	0.999672i
$352$	5.51375	+	13.9094i	0.293884	+	0.741373i
$353$	−8.17233	−	8.17233i	−0.434969	−	0.434969i	0.455346	−	0.890315i	$-0.349516\pi$
$353$	−8.17233	−	8.17233i	−0.434969	−	0.434969i	−0.890315	+	0.455346i	$0.849516\pi$
$354$	6.64480	−	1.24159i	0.353167	−	0.0659896i
$355$	0.496915	−	0.683944i	0.0263735	−	0.0363000i
$356$	−2.46763	−	0.390834i	−0.130784	−	0.0207141i
$357$	3.25770	+	9.15691i	0.172416	+	0.484635i
$358$	−8.69828	+	4.43200i	−0.459718	+	0.234238i
$359$	−0.118350	+	0.747232i	−0.00624627	+	0.0394374i	−0.990615	−	0.136685i	$-0.956355\pi$
$359$	−0.118350	+	0.747232i	−0.00624627	+	0.0394374i	0.984368	+	0.176122i	$0.0563553\pi$
$360$	−0.695001	−	0.853144i	−0.0366298	−	0.0449646i
$361$	−11.9232	+	3.87409i	−0.627538	+	0.203899i
$362$	3.58000	−	3.58000i	0.188160	−	0.188160i
$363$	−19.0525	−	0.0562125i	−0.999996	−	0.00295039i
$364$	−1.34323	+	2.98630i	−0.0704044	+	0.156525i
$365$	1.54128	−	0.500791i	0.0806742	−	0.0262126i
$366$	13.3399	−	0.368824i	0.697285	−	0.0192787i
$367$	2.14356	−	1.55738i	0.111893	−	0.0812948i	−0.530432	−	0.847728i	$-0.677970\pi$
$367$	2.14356	−	1.55738i	0.111893	−	0.0812948i	0.642324	+	0.766433i	$0.277970\pi$
$368$	1.06747	−	3.28534i	0.0556458	−	0.171260i
$369$	−11.0858	+	2.39024i	−0.577102	+	0.124431i
$370$	0.0527365	−	0.332965i	0.00274164	−	0.0173100i
$371$	3.76069	−	0.595635i	0.195245	−	0.0309238i
$372$	5.23400	+	3.58598i	0.271370	+	0.185924i
$373$	13.2539			0.686259			0.343130	−	0.939288i	$-0.388513\pi$
$373$	13.2539			0.686259			0.343130	+	0.939288i	$0.388513\pi$
$374$	6.99281	+	17.6406i	0.361590	+	0.912173i
$375$	1.26849	+	1.64814i	0.0655047	+	0.0851095i
$376$	−30.4489	+	9.89346i	−1.57028	+	0.510216i
$377$	−9.38245	+	34.4901i	−0.483221	+	1.77633i
$378$	5.58460	−	1.36666i	0.287241	−	0.0702936i
$379$	11.1180	+	21.8203i	0.571094	+	1.12083i	0.978241	+	0.207472i	$0.0665237\pi$
$379$	11.1180	+	21.8203i	0.571094	+	1.12083i	−0.407147	+	0.913363i	$0.633476\pi$
$380$	−0.253475	−	0.0823590i	−0.0130030	−	0.00422493i
$381$	22.2249	−	12.1092i	1.13862	−	0.620374i
$382$	−3.66703	+	0.580801i	−0.187622	+	0.0297164i
$383$	−13.4186	+	26.3355i	−0.685658	+	1.34568i	0.241277	+	0.970456i	$0.422434\pi$
$383$	−13.4186	+	26.3355i	−0.685658	+	1.34568i	−0.926935	+	0.375223i	$0.877566\pi$
$384$	0.796902	+	1.03541i	0.0406667	+	0.0528379i
$385$	−0.413631	−	0.0389277i	−0.0210806	−	0.00198394i
$386$			21.9030i			1.11483i
$387$	27.6245	−	1.52871i	1.40423	−	0.0777086i
$388$	−1.32195	−	8.34645i	−0.0671117	−	0.423727i
$389$	11.6845	−	8.48929i	0.592428	−	0.430424i	−0.250755	−	0.968051i	$-0.580679\pi$
$389$	11.6845	−	8.48929i	0.592428	−	0.430424i	0.843183	+	0.537626i	$0.180679\pi$
$390$	0.0644467	−	0.795030i	0.00326338	−	0.0402579i
$391$	−3.84281	+	11.8270i	−0.194339	+	0.598115i
$392$	17.8201	+	2.82242i	0.900048	+	0.142554i
$393$	8.34097	+	7.89215i	0.420746	+	0.398106i
$394$	−3.20140	+	1.04020i	−0.161284	+	0.0524044i
$395$	−1.01328	−	1.01328i	−0.0509835	−	0.0509835i
$396$	−8.34704	+	2.36057i	−0.419455	+	0.118623i
$397$	−18.4101	−	18.4101i	−0.923974	−	0.923974i	0.0733331	−	0.997308i	$-0.476636\pi$
$397$	−18.4101	−	18.4101i	−0.923974	−	0.923974i	−0.997308	+	0.0733331i	$0.976636\pi$
$398$	−11.1935	−	5.70338i	−0.561080	−	0.285884i
$399$	3.15265	−	3.33194i	0.157830	−	0.166805i
$400$	4.38486	+	6.03525i	0.219243	+	0.301762i
$401$	8.80979	+	17.2902i	0.439940	+	0.863430i	0.999402	+	0.0345745i	$0.0110076\pi$
$401$	8.80979	+	17.2902i	0.439940	+	0.863430i	−0.559462	+	0.828856i	$0.688992\pi$
$402$	−3.04817	−	1.44844i	−0.152029	−	0.0722414i
$403$	3.09329	+	14.8301i	0.154088	+	0.738742i
$404$	6.37889	−	8.77979i	0.317362	−	0.436811i
$405$	0.904185	−	0.594728i	0.0449293	−	0.0295523i
$406$	−10.9690			−0.544380
$407$	−7.39310	−	4.68753i	−0.366462	−	0.232352i
$408$	17.3580	+	22.5530i	0.859347	+	1.11654i
$409$	26.7450	+	13.6272i	1.32245	+	0.673823i	0.965525	−	0.260309i	$-0.0838243\pi$
$409$	26.7450	+	13.6272i	1.32245	+	0.673823i	0.356928	+	0.934132i	$0.383824\pi$
$410$	−0.476876	+	0.0755297i	−0.0235512	+	0.00373015i
$411$	−37.5628	−	11.0669i	−1.85283	−	0.545891i
$412$	−4.94987	+	15.2341i	−0.243863	+	0.750532i
$413$	1.18281	−	3.64031i	0.0582021	−	0.179128i
$414$	6.72905	+	2.97243i	0.330715	+	0.146087i
$415$	0.696329	−	0.958415i	0.0341815	−	0.0470468i
$416$	−1.76180	+	16.1701i	−0.0863795	+	0.792805i
$417$	−2.97722	+	22.8724i	−0.145795	+	1.12007i
$418$	5.91989	−	6.72038i	0.289551	−	0.328705i
$419$		−	8.41157i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$419$		−	8.41157i		−	0.410932i	0.978664	−	0.205466i	$-0.0658710\pi$
$420$	−0.185936	+	0.0347423i	−0.00907273	+	0.00169525i
$421$	−14.5434	+	2.30345i	−0.708802	+	0.112263i	−0.500418	−	0.865784i	$-0.666820\pi$
$421$	−14.5434	+	2.30345i	−0.708802	+	0.112263i	−0.208384	+	0.978047i	$0.566820\pi$
$422$	7.67672	+	1.21587i	0.373697	+	0.0591878i
$423$	−6.63664	−	30.7803i	−0.322684	−	1.49659i
$424$	9.93405	−	5.06165i	0.482440	−	0.245816i
$425$	−15.7852	−	21.7264i	−0.765693	−	1.05389i
$426$	9.39497	+	8.88944i	0.455188	+	0.430695i
$427$	3.43053	−	6.73279i	0.166015	−	0.325823i
$428$	−14.2332			−0.687989
$429$	−18.2861	−	9.72728i	−0.882859	−	0.469637i
$430$	1.17791			0.0568037
$431$	−3.37297	+	6.61983i	−0.162470	+	0.318866i	−0.957861	−	0.287231i	$-0.907265\pi$
$431$	−3.37297	+	6.61983i	−0.162470	+	0.318866i	0.795391	+	0.606096i	$0.207265\pi$
$432$	6.61151	−	4.09151i	0.318096	−	0.196853i
$433$	9.19037	+	12.6495i	0.441661	+	0.607895i	0.970580	−	0.240778i	$-0.0774025\pi$
$433$	9.19037	+	12.6495i	0.441661	+	0.607895i	−0.528919	+	0.848672i	$0.677402\pi$
$434$	−4.14230	+	2.11061i	−0.198837	+	0.101312i
$435$	−1.94532	+	0.692073i	−0.0932707	+	0.0331824i
$436$	0.350104	+	0.0554510i	0.0167669	+	0.00265562i
$437$	5.79685	−	0.918131i	0.277301	−	0.0439202i
$438$	4.55393	+	24.3720i	0.217595	+	1.16454i
$439$		−	27.4242i		−	1.30889i	−0.756111	−	0.654444i	$-0.772903\pi$
$439$		−	27.4242i		−	1.30889i	0.756111	−	0.654444i	$-0.227097\pi$
$440$	−1.18713	+	0.265869i	−0.0565942	+	0.0126748i
$441$	−4.54250	+	17.1532i	−0.216309	+	0.816819i
$442$	−2.23441	+	20.5078i	−0.106280	+	0.975454i
$443$	16.4950	−	22.7034i	0.783702	−	1.07867i	−0.211162	−	0.977451i	$-0.567725\pi$
$443$	16.4950	−	22.7034i	0.783702	−	1.07867i	0.994864	−	0.101222i	$-0.0322752\pi$
$444$	−3.82308	−	1.12637i	−0.181435	−	0.0534553i
$445$	0.106488	−	0.327737i	0.00504803	−	0.0155362i
$446$	−1.35527	+	4.17109i	−0.0641739	+	0.197507i
$447$	−3.65776	+	12.4150i	−0.173006	+	0.587208i
$448$	−8.00929	+	1.26855i	−0.378403	+	0.0599332i
$449$	−18.9224	−	9.64142i	−0.893001	−	0.455007i	−0.0536270	−	0.998561i	$-0.517078\pi$
$449$	−18.9224	−	9.64142i	−0.893001	−	0.455007i	−0.839374	+	0.543554i	$0.817078\pi$
$450$	−13.7347	+	7.98335i	−0.647461	+	0.376339i
$451$	−3.11292	+	12.1448i	−0.146582	+	0.571877i
$452$	4.86335			0.228753
$453$	12.6939	+	8.69697i	0.596410	+	0.408619i
$454$	1.79552	−	2.47132i	0.0842679	−	0.115985i
$455$	−0.377848	−	0.247427i	−0.0177138	−	0.0115996i
$456$	5.76477	−	12.1317i	0.269960	−	0.568118i
$457$	−1.30336	−	2.55798i	−0.0609684	−	0.119657i	0.858511	−	0.512795i	$-0.171390\pi$
$457$	−1.30336	−	2.55798i	−0.0609684	−	0.119657i	−0.919480	+	0.393137i	$0.871390\pi$
$458$	5.58932	+	7.69304i	0.261172	+	0.359472i
$459$	−23.8009	+	14.7291i	−1.11093	+	0.687496i
$460$	−0.215643	−	0.109875i	−0.0100544	−	0.00512297i
$461$	−7.47374	−	7.47374i	−0.348087	−	0.348087i	0.511310	−	0.859396i	$-0.329160\pi$
$461$	−7.47374	−	7.47374i	−0.348087	−	0.348087i	−0.859396	+	0.511310i	$0.829160\pi$
$462$	1.40741	−	6.19841i	0.0654786	−	0.288376i
$463$	25.2783	+	25.2783i	1.17478	+	1.17478i	0.981055	+	0.193728i	$0.0620580\pi$
$463$	25.2783	+	25.2783i	1.17478	+	1.17478i	0.193728	+	0.981055i	$0.437942\pi$
$464$	−14.1077	+	4.58388i	−0.654935	+	0.212801i
$465$	−0.601460	+	0.635665i	−0.0278921	+	0.0294782i
$466$	−7.86971	−	1.24644i	−0.364557	−	0.0577402i
$467$	−1.10822	+	3.41076i	−0.0512825	+	0.157831i	−0.973418	−	0.229036i	$-0.926443\pi$
$467$	−1.10822	+	3.41076i	−0.0512825	+	0.157831i	0.922136	+	0.386867i	$0.126443\pi$
$468$	−9.22227	−	1.96878i	−0.426300	−	0.0910067i
$469$	−1.54598	+	1.12322i	−0.0713866	+	0.0518654i
$470$	−0.209713	−	1.32408i	−0.00967333	−	0.0610750i
$471$	36.1803	−	6.76032i	1.66710	−	0.311499i
$472$		−	11.2080i		−	0.515891i
$473$	12.1359	−	28.0761i	0.558009	−	1.29094i
$474$	17.3737	−	13.3717i	0.797999	−	0.614181i
$475$	−5.75417	+	11.2932i	−0.264019	+	0.518167i
$476$	4.83181	−	0.765283i	0.221465	−	0.0350767i
$477$	3.95951	+	10.2255i	0.181294	+	0.468191i
$478$	1.17883	+	0.383025i	0.0539184	+	0.0175191i
$479$	0.263065	+	0.516293i	0.0120197	+	0.0235900i	0.896938	−	0.442156i	$-0.145786\pi$
$479$	0.263065	+	0.516293i	0.0120197	+	0.0235900i	−0.884919	+	0.465746i	$0.845786\pi$
$480$	−0.825088	+	0.449549i	−0.0376600	+	0.0205190i
$481$	−4.72684	−	8.25958i	−0.215525	−	0.376604i
$482$	21.1717	−	6.87909i	0.964343	−	0.313334i
$483$	3.30094	−	2.54057i	0.150198	−	0.115600i
$484$	−1.78921	+	9.42154i	−0.0813276	+	0.428252i
$485$	1.16558			0.0529263
$486$	7.23718	+	14.8920i	0.328285	+	0.675517i
$487$	−4.95000	+	0.784003i	−0.224306	+	0.0355266i	−0.267576	−	0.963537i	$-0.586223\pi$
$487$	−4.95000	+	0.784003i	−0.224306	+	0.0355266i	0.0432697	+	0.999063i	$0.486223\pi$
$488$	3.46134	−	21.8541i	0.156688	−	0.989287i
$489$	−2.10426	−	5.91475i	−0.0951577	−	0.267474i
$490$	−0.233452	+	0.718492i	−0.0105463	+	0.0324582i
$491$	−21.0814	+	15.3166i	−0.951392	+	0.691227i	−0.951136	−	0.308773i	$-0.900082\pi$
$491$	−21.0814	+	15.3166i	−0.951392	+	0.691227i	−0.000256452		1.00000i	$0.500082\pi$
$492$	0.157760	+	5.70596i	0.00711237	+	0.257245i
$493$	50.7867	−	16.5016i	2.28732	−	0.743194i
$494$	9.10267	−	3.45449i	0.409548	−	0.155425i
$495$	−0.141481	−	1.18807i	−0.00635910	−	0.0533998i
$496$	−4.44561	+	4.44561i	−0.199614	+	0.199614i
$497$	6.96523	−	2.26314i	0.312433	−	0.101516i
$498$	13.1652	+	12.4568i	0.589948	+	0.558204i
$499$	4.71305	−	29.7570i	0.210985	−	1.33211i	−0.623822	−	0.781566i	$-0.714421\pi$
$499$	4.71305	−	29.7570i	0.210985	−	1.33211i	0.834808	−	0.550542i	$-0.185579\pi$
$500$	0.932734	−	0.475252i	0.0417131	−	0.0212539i
$501$	15.5254	−	5.52339i	0.693625	−	0.246767i
$502$	1.97742	+	0.313192i	0.0882565	+	0.0139785i
$503$	1.49263	−	2.05443i	0.0665531	−	0.0916024i	−0.774443	−	0.632644i	$-0.781970\pi$
$503$	1.49263	−	2.05443i	0.0665531	−	0.0916024i	0.840996	+	0.541041i	$0.181970\pi$
$504$	−0.526724	−	9.51816i	−0.0234622	−	0.423973i
$505$	1.05845	+	1.05845i	0.0471005	+	0.0471005i
$506$	6.26423	−	5.18657i	0.278479	−	0.230571i
$507$	−12.6392	−	18.6347i	−0.561326	−	0.827595i
$508$	−3.93668	−	12.1159i	−0.174662	−	0.537555i
$509$	2.01071	+	12.6951i	0.0891231	+	0.562701i	0.991330	+	0.131397i	$0.0419463\pi$
$509$	2.01071	+	12.6951i	0.0891231	+	0.562701i	−0.902207	+	0.431304i	$0.858054\pi$
$510$	−1.04642	+	0.570141i	−0.0463362	+	0.0252463i
$511$	13.3520	+	4.33834i	0.590659	+	0.191917i
$512$	−14.1482	+	7.20889i	−0.625270	+	0.318591i
$513$	11.2936	+	6.85280i	0.498624	+	0.302559i
$514$	−2.13741	−	13.4951i	−0.0942771	−	0.595242i
$515$	−1.96858	−	1.00304i	−0.0867459	−	0.0441992i
$516$	1.79750	−	13.8093i	0.0791307	−	0.607921i
$517$	−33.7208	−	8.64323i	−1.48304	−	0.380129i
$518$	2.06505	−	2.06505i	0.0907330	−	0.0907330i
$519$	−14.3680	+	2.68467i	−0.630685	+	0.117844i
$520$	−1.27614	−	0.347153i	−0.0559625	−	0.0152237i
$521$	−8.21889	−	11.3123i	−0.360076	−	0.495603i	0.590094	−	0.807335i	$-0.299091\pi$
$521$	−8.21889	−	11.3123i	−0.360076	−	0.495603i	−0.950170	+	0.311732i	$0.899091\pi$
$522$	−6.65802	−	30.8795i	−0.291414	−	1.35156i
$523$	2.03004	−	6.24781i	0.0887672	−	0.273197i	−0.896812	−	0.442412i	$-0.854123\pi$
$523$	2.03004	−	6.24781i	0.0887672	−	0.273197i	0.985579	+	0.169214i	$0.0541230\pi$
$524$	4.67598	−	3.39730i	0.204271	−	0.148412i
$525$	0.248613	+	8.99199i	0.0108504	+	0.392443i
$526$	−17.2443	−	8.78643i	−0.751889	−	0.383107i
$527$	16.0038	−	16.0038i	0.697138	−	0.697138i
$528$	−0.780149	−	8.56024i	−0.0339516	−	0.372537i
$529$	−17.6704			−0.768277
$530$	0.144263	+	0.443996i	0.00626638	+	0.0192859i
$531$	10.9660	+	1.12018i	0.475885	+	0.0486118i
$532$	−1.35711	−	1.86790i	−0.0588380	−	0.0809835i
$533$	−9.15848	+	10.0940i	−0.396698	+	0.437219i
$534$	4.76189	+	2.26277i	0.206067	+	0.0979195i
$535$	0.307111	−	1.93903i	0.0132776	−	0.0838314i
$536$	−3.28899	+	4.52690i	−0.142063	+	0.195532i
$537$	−15.6484	+	2.92392i	−0.675279	+	0.126176i
$538$	−11.0419	+	11.0419i	−0.476049	+	0.476049i
$539$	14.7205	+	12.9671i	0.634056	+	0.558531i
$540$	−0.210666	−	0.502353i	−0.00906563	−	0.0216178i
$541$	−14.8389	+	29.1230i	−0.637976	+	1.25210i	0.315012	+	0.949088i	$0.397991\pi$
$541$	−14.8389	+	29.1230i	−0.637976	+	1.25210i	−0.952987	+	0.303010i	$0.902009\pi$
$542$	1.43194	−	1.97090i	0.0615072	−	0.0846574i
$543$	7.24971	−	3.95000i	0.311115	−	0.169511i
$544$	21.6522	−	11.0324i	0.928332	−	0.473009i
$545$	−0.0151084	+	0.0464990i	−0.000647174	+	0.00199180i
$546$	4.49994	−	5.24379i	0.192579	−	0.224414i
$547$	−1.77215	−	1.28755i	−0.0757718	−	0.0550515i	0.549254	−	0.835655i	$-0.314912\pi$
$547$	−1.77215	−	1.28755i	−0.0757718	−	0.0550515i	−0.625026	+	0.780604i	$0.714912\pi$
$548$	−8.94833	+	17.5621i	−0.382254	+	0.750215i
$549$	21.0363	+	5.57081i	0.897806	+	0.237756i
$550$	1.11002	+	17.5279i	0.0473312	+	0.747393i
$551$	−17.8211	−	17.8211i	−0.759203	−	0.759203i
$552$	6.89381	−	10.0620i	0.293420	−	0.428268i
$553$	−1.94197	−	12.2611i	−0.0825809	−	0.521395i
$554$	0.889056	−	5.61328i	0.0377724	−	0.238485i
$555$	0.235939	−	0.496523i	0.0100151	−	0.0210762i
$556$	11.0415	+	3.58761i	0.468265	+	0.152148i
$557$	−4.99304	+	31.5248i	−0.211562	+	1.33575i	0.621866	+	0.783123i	$0.286375\pi$
$557$	−4.99304	+	31.5248i	−0.211562	+	1.33575i	−0.833429	+	0.552627i	$0.813625\pi$
$558$	−8.45606	−	10.3802i	−0.357973	−	0.439428i
$559$	25.9206	−	20.8272i	1.09632	−	0.880897i
$560$		−	0.187438i		−	0.00792069i
$561$	2.80847	+	30.8162i	0.118574	+	1.30106i
$562$	−26.0597			−1.09926
$563$	−10.5455	−	32.4557i	−0.444440	−	1.36785i	−0.883096	−	0.469191i	$-0.844545\pi$
$563$	−10.5455	−	32.4557i	−0.444440	−	1.36785i	0.438656	−	0.898655i	$-0.355455\pi$
$564$	−15.8430	+	0.438031i	−0.667109	+	0.0184444i
$565$	−0.104937	+	0.662546i	−0.00441473	+	0.0278735i
$566$	7.44338	+	14.6085i	0.312869	+	0.614039i
$567$	9.36530	+	0.435938i	0.393305	+	0.0183077i
$568$	17.3494	−	12.6051i	0.727965	−	0.528898i
$569$	−2.56236	−	1.86166i	−0.107420	−	0.0780450i	0.532779	−	0.846255i	$-0.321148\pi$
$569$	−2.56236	−	1.86166i	−0.107420	−	0.0780450i	−0.640198	+	0.768210i	$0.721148\pi$
$570$	0.463967	+	0.317878i	0.0194334	+	0.0133145i
$571$		−	12.5746i		−	0.526229i	−0.964765	−	0.263114i	$-0.915250\pi$
$571$		−	12.5746i		−	0.526229i	0.964765	−	0.263114i	$-0.0847497\pi$
$572$	−6.50338	+	8.14825i	−0.271920	+	0.340695i
$573$	−6.00366	−	0.781474i	−0.250807	−	0.0326465i
$574$	−3.72677	−	1.89888i	−0.155552	−	0.0792579i
$575$	−6.76518	+	9.31148i	−0.282128	+	0.388315i
$576$	−8.43272	−	21.7775i	−0.351363	−	0.907398i
$577$	−18.9631	−	37.2172i	−0.789444	−	1.54937i	−0.834898	−	0.550405i	$-0.814473\pi$
$577$	−18.9631	−	37.2172i	−0.789444	−	1.54937i	0.0454541	−	0.998966i	$-0.485527\pi$
$578$	11.3718	−	5.79421i	0.473004	−	0.241007i
$579$	−10.0941	+	34.2609i	−0.419496	+	1.42383i
$580$	0.162578	+	1.02648i	0.00675070	+	0.0426223i
$581$	9.76042	−	3.17135i	0.404931	−	0.131570i
$582$	−2.30176	+	17.6833i	−0.0954112	+	0.732995i
$583$	12.0693	+	1.13586i	0.499857	+	0.0470426i
$584$	41.1092			1.70111
$585$	0.467201	−	1.21389i	0.0193164	−	0.0501882i
$586$	19.5086	+	14.1738i	0.805892	+	0.585515i
$587$	−22.6401	−	3.58584i	−0.934456	−	0.148003i	−0.329404	−	0.944189i	$-0.606848\pi$
$587$	−22.6401	−	3.58584i	−0.934456	−	0.148003i	−0.605052	+	0.796186i	$0.706848\pi$
$588$	8.06707	+	3.83333i	0.332680	+	0.158084i
$589$	−10.1590	−	3.30086i	−0.418594	−	0.136010i
$590$	0.463528	+	0.0734156i	0.0190832	+	0.00302247i
$591$	−5.48703	+	0.151707i	−0.225706	+	0.00624039i
$592$	1.79299	−	3.51894i	0.0736913	−	0.144627i
$593$	−19.3554	+	19.3554i	−0.794833	+	0.794833i	−0.982276	−	0.187443i	$-0.939980\pi$
$593$	−19.3554	+	19.3554i	−0.794833	+	0.794833i	0.187443	+	0.982276i	$0.439980\pi$
$594$	18.3039	+	0.199738i	0.751017	+	0.00819535i
$595$			0.674761i			0.0276625i
$596$	5.80449	+	2.95754i	0.237761	+	0.121145i
$597$	−14.8805	−	14.0798i	−0.609020	−	0.576249i
$598$	8.65493	−	1.80526i	0.353927	−	0.0738224i
$599$	−29.1997	−	9.48756i	−1.19307	−	0.387651i	−0.355862	−	0.934539i	$-0.615813\pi$
$599$	−29.1997	−	9.48756i	−1.19307	−	0.387651i	−0.837206	+	0.546887i	$0.815813\pi$
$600$	8.82882	+	24.8165i	0.360435	+	1.01313i
$601$	15.7941	−	11.4751i	0.644254	−	0.468078i	−0.217055	−	0.976159i	$-0.569645\pi$
$601$	15.7941	−	11.4751i	0.644254	−	0.468078i	0.861309	+	0.508082i	$0.169645\pi$
$602$	8.25533	+	5.99785i	0.336462	+	0.244454i
$603$	−4.10044	−	3.67041i	−0.166983	−	0.149471i
$604$	5.47661	−	5.47661i	0.222840	−	0.222840i
$605$	−1.24491	−	0.447037i	−0.0506129	−	0.0181746i
$606$	−18.1482	+	13.9678i	−0.737222	+	0.567404i
$607$	−6.02836	−	18.5534i	−0.244684	−	0.753059i	−0.995688	−	0.0927621i	$-0.970430\pi$
$607$	−6.02836	−	18.5534i	−0.244684	−	0.753059i	0.751005	−	0.660297i	$-0.229570\pi$
$608$	−9.27865	−	6.74134i	−0.376299	−	0.273397i
$609$	−17.1577	−	5.05509i	−0.695266	−	0.204842i
$610$	0.881141	+	0.286300i	0.0356763	+	0.0115919i
$611$	−28.0266	−	25.4291i	−1.13383	−	1.02875i
$612$	5.08725	+	13.1378i	0.205640	+	0.531066i
$613$	−27.1976	+	4.30768i	−1.09850	+	0.173986i	−0.679266	−	0.733892i	$-0.737702\pi$
$613$	−27.1976	+	4.30768i	−1.09850	+	0.173986i	−0.419235	+	0.907878i	$0.637702\pi$
$614$	15.2407	−	4.95200i	0.615064	−	0.199847i
$615$	−0.780740	−	0.101626i	−0.0314825	−	0.00409795i
$616$	−9.67378	−	4.18148i	−0.389768	−	0.168477i
$617$	−15.3123	−	15.3123i	−0.616452	−	0.616452i	0.328168	−	0.944619i	$-0.393569\pi$
$617$	−15.3123	−	15.3123i	−0.616452	−	0.616452i	−0.944619	+	0.328168i	$0.893569\pi$
$618$	19.1049	−	27.8849i	0.768510	−	1.12170i
$619$	−4.45436	−	28.1237i	−0.179036	−	1.13039i	−0.899508	−	0.436904i	$-0.856075\pi$
$619$	−4.45436	−	28.1237i	−0.179036	−	1.13039i	0.720472	−	0.693484i	$-0.243925\pi$
$620$	0.258908	+	0.356356i	0.0103980	+	0.0143116i
$621$	9.15577	+	7.75061i	0.367408	+	0.311021i
$622$	−19.9848	+	10.1828i	−0.801318	+	0.408292i
$623$	2.41515	−	1.75471i	0.0967608	−	0.0703009i
$624$	3.59623	−	8.62481i	0.143965	−	0.345269i
$625$	−7.65846	−	23.5703i	−0.306339	−	0.942813i
$626$	−18.9861	−	18.9861i	−0.758835	−	0.758835i
$627$	12.3571	−	7.78386i	0.493493	−	0.310858i
$628$		−	18.5262i		−	0.739275i
$629$	−6.45461	+	12.6679i	−0.257362	+	0.505102i
$630$	0.397091	+	0.0405629i	0.0158205	+	0.00161606i
$631$	5.75180	+	0.910996i	0.228976	+	0.0362662i	0.269868	−	0.962897i	$-0.413020\pi$
$631$	5.75180	+	0.910996i	0.228976	+	0.0362662i	−0.0408922	+	0.999164i	$0.513020\pi$
$632$	−16.5027	−	32.3883i	−0.656441	−	1.28834i
$633$	11.4476	+	5.43972i	0.455003	+	0.216210i
$634$	16.4649	+	22.6619i	0.653903	+	0.900021i
$635$	1.73551	−	0.274878i	0.0688718	−	0.0109082i
$636$	5.42538	−	1.01374i	0.215130	−	0.0401973i
$637$	7.56679	+	19.9387i	0.299807	+	0.790000i
$638$	−33.8295	−	8.67108i	−1.33932	−	0.343291i
$639$	10.5989	+	18.2346i	0.419288	+	0.721351i
$640$	0.0280309	+	0.0862701i	0.00110802	+	0.00341013i
$641$	−10.6095	−	7.70822i	−0.419048	−	0.304456i	0.358206	−	0.933642i	$-0.383388\pi$
$641$	−10.6095	−	7.70822i	−0.419048	−	0.304456i	−0.777255	+	0.629186i	$0.783388\pi$
$642$	28.8109	+	8.48840i	1.13708	+	0.335011i
$643$	0.306940	+	0.602403i	0.0121045	+	0.0237564i	0.896980	−	0.442072i	$-0.145756\pi$
$643$	0.306940	+	0.602403i	0.0121045	+	0.0237564i	−0.884875	+	0.465828i	$0.845756\pi$
$644$	−0.951846	−	1.86810i	−0.0375080	−	0.0736136i
$645$	1.84249	+	0.542842i	0.0725479	+	0.0213744i
$646$	−11.7677	−	8.54970i	−0.462992	−	0.336384i
$647$	−10.3852	−	31.9625i	−0.408286	−	1.25657i	−0.918120	−	0.396302i	$-0.870293\pi$
$647$	−10.3852	−	31.9625i	−0.408286	−	1.25657i	0.509834	−	0.860273i	$-0.329707\pi$
$648$	26.4755	−	7.26023i	1.04006	−	0.285209i
$649$	6.52561	−	10.2921i	0.256153	−	0.404000i
$650$	−7.83217	+	17.4127i	−0.307203	+	0.682981i
$651$	−7.45210	+	1.39243i	−0.292071	+	0.0545737i
$652$	−3.12102	+	0.494321i	−0.122229	+	0.0193591i
$653$	17.4831	+	24.0635i	0.684168	+	0.941676i	0.999974	−	0.00714726i	$-0.00227506\pi$
$653$	17.4831	+	24.0635i	0.684168	+	0.941676i	−0.315807	+	0.948824i	$0.602275\pi$
$654$	−0.675610	−	0.321038i	−0.0264184	−	0.0125536i
$655$	0.361928	+	0.710323i	0.0141417	+	0.0277546i
$656$	−5.58672	−	0.884849i	−0.218125	−	0.0345476i
$657$	−4.10864	+	40.2216i	−0.160293	+	1.56919i
$658$	5.27237	−	10.3476i	0.205538	−	0.403392i
$659$			24.1061i			0.939042i	0.882921	+	0.469521i	$0.155573\pi$
$659$			24.1061i			0.939042i	−0.882921	+	0.469521i	$0.844427\pi$
$660$	−0.600911	−	0.0398351i	−0.0233904	−	0.00155058i
$661$	−30.4520	−	30.4520i	−1.18445	−	1.18445i	−0.978580	−	0.205867i	$-0.933999\pi$
$661$	−30.4520	−	30.4520i	−1.18445	−	1.18445i	−0.205867	−	0.978580i	$-0.566001\pi$
$662$	11.0398	+	33.9770i	0.429073	+	1.32055i
$663$	−12.9462	+	31.0486i	−0.502787	+	1.20583i
$664$	24.3118	−	17.6636i	0.943482	−	0.685480i
$665$	0.283750	−	0.144578i	0.0110034	−	0.00560649i
$666$	7.06693	+	4.56001i	0.273838	+	0.176697i
$667$	−13.4522	−	18.5153i	−0.520871	−	0.716917i
$668$	−1.29753	−	8.19227i	−0.0502029	−	0.316969i
$669$	−4.04218	+	5.89987i	−0.156280	+	0.228102i
$670$	−0.165674	−	0.165674i	−0.00640056	−	0.00640056i
$671$	15.9025	−	18.0528i	0.613909	−	0.696921i
$672$	−8.07170	−	1.05066i	−0.311373	−	0.0405302i
$673$	4.83146	−	1.56984i	0.186239	−	0.0605128i	−0.214413	−	0.976743i	$-0.568784\pi$
$673$	4.83146	−	1.56984i	0.186239	−	0.0605128i	0.400652	+	0.916230i	$0.368784\pi$
$674$	−15.0519	+	2.38398i	−0.579776	+	0.0918275i
$675$	−25.1631	+	6.15792i	−0.968528	+	0.237018i
$676$	−10.3885	+	4.53081i	−0.399558	+	0.174262i
$677$	4.12699	+	1.34094i	0.158613	+	0.0515365i	0.387247	−	0.921976i	$-0.373426\pi$
$677$	4.12699	+	1.34094i	0.158613	+	0.0515365i	−0.228634	+	0.973512i	$0.573426\pi$
$678$	−9.84440	−	2.90040i	−0.378072	−	0.111389i
$679$	8.16895	+	5.93509i	0.313495	+	0.227768i
$680$	0.610562	+	1.87912i	0.0234140	+	0.0720609i
$681$	3.94748	−	3.03818i	0.151268	−	0.116423i
$682$	−14.4438	+	3.23482i	−0.553081	+	0.123868i
$683$	−12.6656	+	12.6656i	−0.484636	+	0.484636i	−0.906608	−	0.421973i	$-0.861338\pi$
$683$	−12.6656	+	12.6656i	−0.484636	+	0.484636i	0.421973	+	0.906608i	$0.361338\pi$
$684$	4.43470	−	4.95428i	0.169565	−	0.189431i
$685$	−2.19944	−	1.59799i	−0.0840364	−	0.0610560i
$686$	−11.5608	+	8.39938i	−0.441392	+	0.320690i
$687$	5.19749	+	14.6094i	0.198297	+	0.557382i
$688$	13.1241	+	4.26427i	0.500350	+	0.162574i
$689$	11.0251	+	7.21962i	0.420024	+	0.275046i
$690$	0.370977	+	0.351015i	0.0141228	+	0.0133629i
$691$	−10.3065	−	5.25141i	−0.392077	−	0.199773i	0.246827	−	0.969060i	$-0.420612\pi$
$691$	−10.3065	−	5.25141i	−0.392077	−	0.199773i	−0.638904	+	0.769286i	$0.720612\pi$
$692$			7.35716i			0.279677i
$693$	5.05804	−	9.04699i	0.192139	−	0.343667i
$694$	9.53215	−	9.53215i	0.361835	−	0.361835i
$695$	−0.726992	+	1.42680i	−0.0275764	+	0.0541217i
$696$	−52.3561	+	1.44756i	−1.98455	+	0.0548694i
$697$	20.1117	+	3.18539i	0.761787	+	0.120655i
$698$	−15.5926	−	5.06634i	−0.590188	−	0.191764i
$699$	−11.7354	−	5.57648i	−0.443875	−	0.210922i
$700$	4.47202	+	0.708298i	0.169026	+	0.0267712i
$701$	22.1849	+	16.1182i	0.837910	+	0.608777i	0.921786	−	0.387699i	$-0.126730\pi$
$701$	22.1849	+	16.1182i	0.837910	+	0.608777i	−0.0838758	+	0.996476i	$0.526730\pi$
$702$	17.4936	+	9.48517i	0.660253	+	0.357995i
$703$	6.71010			0.253076
$704$	−25.7044	−	2.41909i	−0.968769	−	0.0911728i
$705$	0.282171	−	2.16777i	0.0106272	−	0.0816431i
$706$	11.6750	−	3.79345i	0.439396	−	0.142768i
$707$	2.02855	+	12.8077i	0.0762914	+	0.481685i
$708$	1.56805	−	5.32219i	0.0589308	−	0.200020i
$709$	3.07006	−	1.56427i	0.115299	−	0.0587475i	−0.395390	−	0.918513i	$-0.629391\pi$
$709$	3.07006	−	1.56427i	0.115299	−	0.0587475i	0.510689	+	0.859766i	$0.329391\pi$
$710$	0.407662	+	0.800083i	0.0152993	+	0.0300266i
$711$	33.3384	−	12.9093i	1.25029	−	0.484137i
$712$	5.13810	−	7.07199i	0.192558	−	0.265034i
$713$	−8.64273	−	4.40369i	−0.323673	−	0.164919i
$714$	−10.2369	−	1.33250i	−0.383108	−	0.0498677i
$715$	−0.969731	−	1.06179i	−0.0362659	−	0.0397085i
$716$			8.01280i			0.299452i
$717$	1.66741	+	1.14240i	0.0622707	+	0.0426636i
$718$	−0.650106	−	0.472329i	−0.0242617	−	0.0176272i
$719$	0.763196	−	0.554495i	0.0284624	−	0.0206792i	−0.573463	−	0.819231i	$-0.694400\pi$
$719$	0.763196	−	0.554495i	0.0284624	−	0.0206792i	0.601926	+	0.798552i	$0.294400\pi$
$720$	0.527669	−	0.113772i	0.0196651	−	0.00424005i
$721$	−8.68930	−	17.0537i	−0.323606	−	0.635113i
$722$	2.08310	−	13.1522i	0.0775250	−	0.489474i
$723$	36.2871	−	1.00328i	1.34953	−	0.0373123i
$724$	−1.28414	−	3.95217i	−0.0477246	−	0.146881i
$725$	49.4240			1.83556
$726$	9.24052	−	18.0040i	0.342948	−	0.668192i
$727$			37.6174i			1.39515i	0.716511	+	0.697575i	$0.245738\pi$
$727$			37.6174i			1.39515i	−0.716511	+	0.697575i	$0.754262\pi$
$728$	−7.17612	−	8.93107i	−0.265965	−	0.331007i
$729$	4.45738	+	26.6295i	0.165088	+	0.986279i
$730$	−0.269276	+	1.70014i	−0.00996636	+	0.0629251i
$731$	−47.2456	−	15.3510i	−1.74744	−	0.567778i
$732$	4.70110	−	9.89325i	0.173758	−	0.365665i
$733$	−5.01736	+	31.6784i	−0.185321	+	1.17007i	0.703118	+	0.711073i	$0.251790\pi$
$733$	−5.01736	+	31.6784i	−0.185321	+	1.17007i	−0.888439	+	0.458995i	$0.848210\pi$
$734$	0.440251	+	2.77964i	0.0162500	+	0.102598i
$735$	−0.696288	+	1.01628i	−0.0256830	+	0.0374862i
$736$	−7.36440	−	7.36440i	−0.271455	−	0.271455i
$737$	−5.65589	+	2.24202i	−0.208337	+	0.0825859i
$738$	3.08358	−	11.6441i	0.113508	−	0.428625i
$739$	−7.20749	+	14.1455i	−0.265132	+	0.520351i	−0.984740	−	0.174029i	$-0.944321\pi$
$739$	−7.20749	+	14.1455i	−0.265132	+	0.520351i	0.719609	+	0.694380i	$0.244321\pi$
$740$	−0.223856	−	0.162641i	−0.00822910	−	0.00597879i
$741$	15.8305	−	1.20854i	0.581547	−	0.0443967i
$742$	−1.24974	+	3.84632i	−0.0458795	+	0.141203i
$743$	−29.1179	+	14.8363i	−1.06823	+	0.544292i	−0.897495	−	0.441024i	$-0.854615\pi$
$743$	−29.1179	+	14.8363i	−1.06823	+	0.544292i	−0.170738	+	0.985316i	$0.554615\pi$
$744$	−19.4931	+	10.6208i	−0.714653	+	0.389378i
$745$	−0.528156	+	0.726944i	−0.0193501	+	0.0266332i
$746$	−6.39117	+	12.5434i	−0.233997	+	0.459245i
$747$	14.8524	+	25.5523i	0.543420	+	0.934910i
$748$	15.5068	+	1.45938i	0.566985	+	0.0533601i
$749$	12.0258	−	12.0258i	0.439414	−	0.439414i
$750$	−2.17147	+	0.405741i	−0.0792909	+	0.0148156i
$751$	−8.71572	+	11.9962i	−0.318041	+	0.437746i	−0.937868	−	0.346993i	$-0.887203\pi$
$751$	−8.71572	+	11.9962i	−0.318041	+	0.437746i	0.619827	+	0.784739i	$0.287203\pi$
$752$	2.45684	−	15.5119i	0.0895917	−	0.565660i
$753$	2.94876	+	1.40120i	0.107459	+	0.0510625i
$754$	−28.1169	−	25.5110i	−1.02396	−	0.929057i
$755$	0.627922	+	0.864261i	0.0228524	+	0.0314537i
$756$	1.08151	−	4.59343i	0.0393342	−	0.167062i
$757$	−4.64875	−	14.3074i	−0.168962	−	0.520010i	0.830345	−	0.557250i	$-0.188143\pi$
$757$	−4.64875	−	14.3074i	−0.168962	−	0.520010i	−0.999306	+	0.0372397i	$0.988143\pi$
$758$	−26.0118			−0.944793
$759$	12.1888	−	5.22598i	0.442426	−	0.189691i
$760$	0.659383	−	0.659383i	0.0239183	−	0.0239183i
$761$	22.9993	+	11.7187i	0.833724	+	0.424804i	0.818101	−	0.575074i	$-0.195027\pi$
$761$	22.9993	+	11.7187i	0.833724	+	0.424804i	0.0156231	+	0.999878i	$0.495027\pi$
$762$	0.742984	+	26.8727i	0.0269155	+	0.973495i
$763$	−0.342658	+	0.248956i	−0.0124050	+	0.00901280i
$764$	−0.941692	+	2.89823i	−0.0340692	+	0.104854i
$765$	−1.89957	+	0.409572i	−0.0686790	+	0.0148081i
$766$	−18.4531	−	25.3985i	−0.666738	−	0.917686i
$767$	11.4983	−	6.58034i	0.415181	−	0.237602i
$768$	−27.8714	+	5.20779i	−1.00572	+	0.187920i
$769$	8.58035	−	8.58035i	0.309415	−	0.309415i	−0.535267	−	0.844683i	$-0.679789\pi$
$769$	8.58035	−	8.58035i	0.309415	−	0.309415i	0.844683	+	0.535267i	$0.179789\pi$
$770$	0.236299	−	0.372686i	0.00851561	−	0.0134307i
$771$	2.87591	−	22.0941i	0.103573	−	0.795700i
$772$	16.0183	+	8.16174i	0.576512	+	0.293747i
$773$	−3.37241	−	21.2925i	−0.121297	−	0.765839i	−0.971088	−	0.238720i	$-0.923272\pi$
$773$	−3.37241	−	21.2925i	−0.121297	−	0.765839i	0.849791	−	0.527119i	$-0.176728\pi$
$774$	−11.8741	+	26.8808i	−0.426805	+	0.966210i
$775$	18.6644	−	9.50999i	0.670445	−	0.341609i
$776$	28.1198	+	9.13668i	1.00944	+	0.327988i
$777$	4.18185	−	2.27848i	0.150023	−	0.0817399i
$778$	2.39981	+	15.1518i	0.0860372	+	0.543218i
$779$	−2.96973	−	9.13990i	−0.106402	−	0.327471i
$780$	−0.557414	−	0.343384i	−0.0199586	−	0.0122951i
$781$	23.2706	−	1.47369i	0.832688	−	0.0527328i
$782$	−9.33991	−	9.33991i	−0.333994	−	0.333994i
$783$	3.81641	−	51.3703i	0.136387	−	1.83582i
$784$	−5.20219	+	7.16020i	−0.185792	+	0.255721i
$785$	2.52386	+	0.399741i	0.0900805	+	0.0142674i
$786$	−11.4912	+	4.08815i	−0.409877	+	0.145820i
$787$	−34.6797	+	17.6702i	−1.23620	+	0.629874i	−0.945088	−	0.326815i	$-0.894025\pi$
$787$	−34.6797	+	17.6702i	−1.23620	+	0.629874i	−0.291110	+	0.956690i	$0.594025\pi$
$788$	−0.432213	+	2.72888i	−0.0153969	+	0.0972125i
$789$	−22.9245	−	21.6909i	−0.816132	−	0.772217i
$790$	1.44757	−	0.470345i	0.0515024	−	0.0167341i
$791$	−4.10911	+	4.10911i	−0.146103	+	0.146103i
$792$	5.89973	−	29.7715i	0.209638	−	1.05788i
$793$	24.4523	−	9.27972i	0.868327	−	0.329533i
$794$	26.3007	−	8.54562i	0.933377	−	0.303273i
$795$	0.0210399	+	0.760985i	0.000746210	+	0.0269894i
$796$	−8.34208	+	6.06088i	−0.295677	+	0.214822i
$797$	13.3516	−	41.0920i	0.472939	−	1.45556i	−0.375779	−	0.926709i	$-0.622625\pi$
$797$	13.3516	−	41.0920i	0.472939	−	1.45556i	0.848718	−	0.528846i	$-0.177375\pi$
$798$	1.63308	+	4.59034i	0.0578104	+	0.162496i
$799$	−8.84443	+	55.8415i	−0.312893	+	1.97553i
$800$	22.2145	−	3.51843i	0.785400	−	0.124395i
$801$	6.40577	+	5.73397i	0.226337	+	0.202600i
$802$	−20.6115			−0.727817
$803$	37.7496	+	23.9348i	1.33216	+	0.844642i
$804$	−2.19512	+	1.68948i	−0.0774160	+	0.0595833i
$805$	0.275034	−	0.0893640i	0.00969368	−	0.00314967i
$806$	−15.5268	−	4.22380i	−0.546907	−	0.148777i
$807$	−22.3604	+	12.1831i	−0.787125	+	0.428864i
$808$	17.2384	+	33.8323i	0.606445	+	1.19022i
$809$	−3.87115	−	1.25781i	−0.136102	−	0.0442223i	0.240174	−	0.970730i	$-0.422796\pi$
$809$	−3.87115	−	1.25781i	−0.136102	−	0.0442223i	−0.376276	+	0.926508i	$0.622796\pi$
$810$	0.126838	+	1.14250i	0.00445662	+	0.0401434i
$811$	33.0244	−	5.23056i	1.15964	−	0.183670i	0.453181	−	0.891419i	$-0.350289\pi$
$811$	33.0244	−	5.23056i	1.15964	−	0.183670i	0.706464	+	0.707749i	$0.250289\pi$
$812$	−4.08737	+	8.02191i	−0.143438	+	0.281514i
$813$	3.14815	−	2.42298i	0.110411	−	0.0849776i
$814$	8.00128	−	4.73640i	0.280445	−	0.166011i
$815$		−	0.435850i		−	0.0152672i
$816$	−13.7231	+	2.56417i	−0.480404	+	0.0897640i
$817$	3.66769	+	23.1569i	0.128316	+	0.810157i
$818$	−25.7935	+	18.7400i	−0.901847	+	0.655230i
$819$	9.45545	−	6.12857i	0.330400	−	0.214149i
$820$	−0.122461	+	0.376897i	−0.00427654	+	0.0131618i
$821$	−14.5809	−	2.30939i	−0.508878	−	0.0805983i	−0.103284	−	0.994652i	$-0.532935\pi$
$821$	−14.5809	−	2.30939i	−0.508878	−	0.0805983i	−0.405594	+	0.914054i	$0.632935\pi$
$822$	28.5869	−	30.2126i	0.997081	−	1.05378i
$823$	−2.37926	+	0.773070i	−0.0829360	+	0.0269475i	−0.350191	−	0.936678i	$-0.613883\pi$
$823$	−2.37926	+	0.773070i	−0.0829360	+	0.0269475i	0.267255	+	0.963626i	$0.413883\pi$
$824$	−39.6297	−	39.6297i	−1.38057	−	1.38057i
$825$	−6.34151	+	27.9288i	−0.220783	+	0.972358i
$826$	2.87480	+	2.87480i	0.100027	+	0.100027i
$827$	8.84113	+	4.50478i	0.307436	+	0.156647i	0.600901	−	0.799323i	$-0.294808\pi$
$827$	8.84113	+	4.50478i	0.307436	+	0.156647i	−0.293465	+	0.955970i	$0.594808\pi$
$828$	4.68127	−	3.81353i	0.162686	−	0.132529i
$829$	5.30768	+	7.30540i	0.184343	+	0.253727i	0.891180	−	0.453650i	$-0.149878\pi$
$829$	5.30768	+	7.30540i	0.184343	+	0.253727i	−0.706837	+	0.707377i	$0.749878\pi$
$830$	0.571260	+	1.12116i	0.0198287	+	0.0389161i
$831$	3.97757	−	8.37061i	0.137980	−	0.290373i
$832$	−23.4807	−	15.3759i	−0.814045	−	0.533064i
$833$	18.7275	−	25.7761i	0.648868	−	0.893091i
$834$	−20.2107	−	13.8470i	−0.699838	−	0.479481i
$835$	1.14405			0.0395915
$836$	−2.70887	−	6.83361i	−0.0936884	−	0.236345i
$837$	−8.44327	−	20.1338i	−0.291842	−	0.695925i
$838$	7.96065	+	4.05616i	0.274996	+	0.140118i
$839$	−11.5502	+	1.82937i	−0.398756	+	0.0631567i	−0.352592	−	0.935777i	$-0.614700\pi$
$839$	−11.5502	+	1.82937i	−0.398756	+	0.0631567i	−0.0461639	+	0.998934i	$0.514700\pi$
$840$	0.187039	−	0.634839i	0.00645347	−	0.0219040i
$841$	−21.4077	+	65.8861i	−0.738196	+	2.27194i
$842$	4.83303	−	14.8745i	0.166557	−	0.512610i
$843$	−40.7627	−	12.0097i	−1.40394	−	0.413636i
$844$	3.74978	−	5.16113i	0.129073	−	0.177654i
$845$	−0.393090	−	1.51301i	−0.0135227	−	0.0520492i
$846$	32.3306	+	8.56175i	1.11155	+	0.294359i
$847$	−6.44865	−	9.47209i	−0.221578	−	0.325465i
$848$			5.46920i			0.187813i
$849$	4.91062	+	26.2810i	0.168532	+	0.901960i
$850$	28.1735	−	4.46225i	0.966344	−	0.153054i
$851$	6.01830	+	0.953205i	0.206305	+	0.0326755i
$852$	10.0020	−	3.55833i	0.342661	−	0.121907i
$853$	−9.25969	+	4.71805i	−0.317046	+	0.161543i	−0.605270	−	0.796020i	$-0.706935\pi$
$853$	−9.25969	+	4.71805i	−0.317046	+	0.161543i	0.288225	+	0.957563i	$0.406935\pi$
$854$	4.71763	+	6.49326i	0.161434	+	0.222195i
$855$	0.579245	+	0.711048i	0.0198097	+	0.0243173i
$856$	22.6086	−	44.3720i	0.772747	−	1.51660i
$857$	19.3058			0.659474			0.329737	−	0.944073i	$-0.393040\pi$
$857$	19.3058			0.659474			0.329737	+	0.944073i	$0.393040\pi$
$858$	18.0236	−	12.6152i	0.615315	−	0.430676i
$859$	−20.5897			−0.702510			−0.351255	−	0.936280i	$-0.614245\pi$
$859$	−20.5897			−0.702510			−0.351255	+	0.936280i	$0.614245\pi$
$860$	0.438924	−	0.861436i	0.0149672	−	0.0293747i
$861$	−4.95433	−	4.68774i	−0.168843	−	0.159758i
$862$	−4.63848	−	6.38431i	−0.157987	−	0.217451i
$863$	35.7957	−	18.2388i	1.21850	−	0.620856i	0.277976	−	0.960588i	$-0.410336\pi$
$863$	35.7957	−	18.2388i	1.21850	−	0.620856i	0.940522	+	0.339732i	$0.110336\pi$
$864$	−1.94163	−	23.3610i	−0.0660556	−	0.794756i
$865$	−1.00228	−	0.158746i	−0.0340786	−	0.00539752i
$866$	−16.4031	+	2.59799i	−0.557399	+	0.0882834i
$867$	20.4581	−	3.82262i	0.694794	−	0.129823i
$868$			3.81586i			0.129519i
$869$	3.70329	−	39.3498i	0.125625	−	1.33485i
$870$	0.283080	−	2.17476i	0.00959731	−	0.0737313i
$871$	−6.57515	−	0.716391i	−0.222791	−	0.0242740i
$872$	−0.728987	+	1.00336i	−0.0246866	+	0.0339782i
$873$	−11.7498	+	26.5995i	−0.397672	+	0.900257i
$874$	−1.92640	+	5.92883i	−0.0651613	+	0.200546i
$875$	−0.386532	+	1.18962i	−0.0130672	+	0.0402166i
$876$	19.5209	+	5.75133i	0.659549	+	0.194320i
$877$	20.8674	−	3.30507i	0.704643	−	0.111604i	0.206178	−	0.978514i	$-0.433897\pi$
$877$	20.8674	−	3.30507i	0.704643	−	0.111604i	0.498465	+	0.866910i	$0.333897\pi$
$878$	25.9541	+	13.2243i	0.875909	+	0.446298i
$879$	23.9834	+	31.1614i	0.808940	+	1.05105i
$880$	0.148171	−	0.578079i	0.00499486	−	0.0194870i
$881$	2.41353			0.0813137			0.0406569	−	0.999173i	$-0.487055\pi$
$881$	2.41353			0.0813137			0.0406569	+	0.999173i	$0.487055\pi$
$882$	−14.0432	−	12.5705i	−0.472860	−	0.423270i
$883$	−21.7260	+	29.9032i	−0.731137	+	1.00632i	0.267943	+	0.963435i	$0.413656\pi$
$883$	−21.7260	+	29.9032i	−0.731137	+	1.00632i	−0.999080	+	0.0428887i	$0.986344\pi$
$884$	14.1653	+	9.27590i	0.476430	+	0.311982i
$885$	0.691220	+	0.328456i	0.0232351	+	0.0110409i
$886$	13.5323	+	26.5586i	0.454626	+	0.892255i
$887$	2.52609	+	3.47686i	0.0848177	+	0.116742i	0.849317	−	0.527883i	$-0.177014\pi$
$887$	2.52609	+	3.47686i	0.0848177	+	0.116742i	−0.764500	+	0.644624i	$0.777014\pi$
$888$	9.58419	−	10.1292i	0.321624	−	0.339915i
$889$	13.5630	+	6.91069i	0.454888	+	0.231777i
$890$	0.258819	+	0.258819i	0.00867562	+	0.00867562i
$891$	28.5390	+	8.74785i	0.956093	+	0.293064i
$892$	2.54542	+	2.54542i	0.0852270	+	0.0852270i
$893$	25.3775	−	8.24565i	0.849226	−	0.275930i
$894$	−9.98564	−	9.44832i	−0.333970	−	0.315999i
$895$	−1.09160	−	0.172893i	−0.0364882	−	0.00577917i
$896$	−0.242830	+	0.747355i	−0.00811239	+	0.0249674i
$897$	14.3701	+	1.16486i	0.479803	+	0.0388937i
$898$	18.2492	−	13.2588i	0.608982	−	0.442451i
$899$	6.51597	+	41.1402i	0.217320	+	1.37210i
$900$	0.720481	+	13.0194i	0.0240160	+	0.433981i
$901$		−	19.6887i		−	0.655926i
$902$	−9.99268	−	8.80242i	−0.332720	−	0.293089i
$903$	10.1489	+	13.1864i	0.337735	+	0.438815i
$904$	−7.72515	+	15.1615i	−0.256935	+	0.504263i
$905$	0.566121	−	0.0896648i	0.0188185	−	0.00298056i
$906$	−14.3519	+	7.81962i	−0.476810	+	0.259789i
$907$	−53.1380	−	17.2656i	−1.76442	−	0.573294i	−0.766774	−	0.641917i	$-0.778139\pi$
$907$	−53.1380	−	17.2656i	−1.76442	−	0.573294i	−0.997643	+	0.0686230i	$0.978139\pi$
$908$	−1.13828	−	2.23400i	−0.0377752	−	0.0741380i
$909$	−34.8247	+	13.4849i	−1.15506	+	0.447265i
$910$	0.416366	−	0.238280i	0.0138024	−	0.00789892i
$911$	53.1021	−	17.2539i	1.75935	−	0.571648i	0.762218	−	0.647320i	$-0.224110\pi$
$911$	53.1021	−	17.2539i	1.75935	−	0.571648i	0.997133	+	0.0756725i	$0.0241103\pi$
$912$	4.01867	+	5.22141i	0.133071	+	0.172898i
$913$	32.6092	−	2.06509i	1.07921	−	0.0683446i
$914$	3.04935			0.100864
$915$	1.24634	+	0.853910i	0.0412029	+	0.0282294i
$916$	7.70889	−	1.22097i	0.254709	−	0.0403419i
$917$	−1.08037	+	6.82120i	−0.0356770	+	0.225256i
$918$	−2.46248	−	29.6276i	−0.0812738	−	0.977855i
$919$	−9.15674	+	28.1816i	−0.302053	+	0.929624i	0.678707	+	0.734409i	$0.262540\pi$
$919$	−9.15674	+	28.1816i	−0.302053	+	0.929624i	−0.980760	+	0.195215i	$0.937460\pi$
$920$	0.685071	−	0.497733i	0.0225861	−	0.0164098i
$921$	26.1218	−	0.722222i	0.860741	−	0.0237980i
$922$	10.6770	−	3.46917i	0.351629	−	0.114251i
$923$	23.1176	+	10.3982i	0.760925	+	0.342262i
$924$	−4.00863	−	3.33900i	−0.131874	−	0.109845i
$925$	−9.30470	+	9.30470i	−0.305937	+	0.305937i
$926$	−36.1127	+	11.7337i	−1.18674	+	0.385595i
$927$	42.7348	−	34.8133i	1.40360	−	1.14342i
$928$	−6.99619	+	44.1722i	−0.229661	+	1.45002i
$929$	−6.54140	+	3.33301i	−0.214616	+	0.109353i	−0.557994	−	0.829845i	$-0.688429\pi$
$929$	−6.54140	+	3.33301i	−0.214616	+	0.109353i	0.343378	+	0.939197i	$0.388429\pi$
$930$	−0.311558	−	0.875743i	−0.0102164	−	0.0287167i
$931$	−14.8520	−	2.35233i	−0.486755	−	0.0770945i
$932$	−3.84405	+	5.29088i	−0.125916	+	0.173309i
$933$	−35.9531	+	6.71788i	−1.17705	+	0.219933i
$934$	−2.69352	−	2.69352i	−0.0881348	−	0.0881348i
$935$	−0.533406	+	2.08104i	−0.0174442	+	0.0680572i
$936$	20.7867	−	25.6231i	0.679434	−	0.837516i
$937$	−4.83281	−	14.8739i	−0.157881	−	0.485908i	0.840560	−	0.541718i	$-0.182226\pi$
$937$	−4.83281	−	14.8739i	−0.157881	−	0.485908i	−0.998441	+	0.0558098i	$0.982226\pi$
$938$	−0.317518	−	2.00473i	−0.0103673	−	0.0654568i
$939$	−20.9483	−	38.4479i	−0.683622	−	1.25470i
$940$	−1.04648	−	0.340022i	−0.0341324	−	0.0110903i
$941$	−27.8130	+	14.1714i	−0.906677	+	0.461975i	−0.844174	−	0.536070i	$-0.819908\pi$
$941$	−27.8130	+	14.1714i	−0.906677	+	0.461975i	−0.0625035	+	0.998045i	$0.519908\pi$
$942$	−11.0486	+	37.5007i	−0.359984	+	1.22184i
$943$	−1.36519	−	8.61946i	−0.0444567	−	0.280688i
$944$	4.89879	+	2.49606i	0.159442	+	0.0812397i
$945$	0.602438	+	0.246450i	0.0195973	+	0.00801701i
$946$	20.7190	+	25.0240i	0.673633	+	0.813599i
$947$	−31.9044	+	31.9044i	−1.03675	+	1.03675i	−0.0374567	+	0.999298i	$0.511926\pi$
$947$	−31.9044	+	31.9044i	−1.03675	+	1.03675i	−0.999298	+	0.0374567i	$0.988074\pi$
$948$	−3.30512	−	17.6885i	−0.107345	−	0.574497i
$949$	24.1356	+	42.1740i	0.783474	+	1.36902i
$950$	−7.91307	−	10.8914i	−0.256734	−	0.353364i
$951$	15.3106	+	43.0359i	0.496480	+	1.39553i
$952$	−5.28928	+	16.2787i	−0.171426	+	0.527596i
$953$	−16.3242	+	11.8602i	−0.528793	+	0.384191i	−0.819906	−	0.572498i	$-0.805975\pi$
$953$	−16.3242	+	11.8602i	−0.528793	+	0.384191i	0.291113	+	0.956689i	$0.405975\pi$
$954$	−11.5866	−	1.18358i	−0.375131	−	0.0383197i
$955$	−0.374514	−	0.190824i	−0.0121190	−	0.00617493i
$956$	0.719385	−	0.719385i	0.0232666	−	0.0232666i
$957$	−48.9202	−	29.1538i	−1.58137	−	0.942409i
$958$	−0.615469			−0.0198849
$959$	−7.27786	−	22.3990i	−0.235014	−	0.723300i
$960$	−0.0448096	−	1.62070i	−0.00144622	−	0.0523079i
$961$	−7.84460	−	10.7972i	−0.253052	−	0.348296i
$962$	10.0962	−	0.490588i	0.325513	−	0.0158172i
$963$	41.1543	+	26.5552i	1.32618	+	0.855730i
$964$	2.85833	−	18.0468i	0.0920607	−	0.581249i
$965$	−1.45752	+	2.00611i	−0.0469193	+	0.0645788i
$966$	0.812629	+	4.34908i	0.0261459	+	0.139929i
$967$	−32.6838	+	32.6838i	−1.05104	+	1.05104i	−0.0524161	+	0.998625i	$0.516692\pi$
$967$	−32.6838	+	32.6838i	−1.05104	+	1.05104i	−0.998625	+	0.0524161i	$0.983308\pi$
$968$	−26.5295	−	20.5434i	−0.852691	−	0.660290i
$969$	−14.4669	−	18.7967i	−0.464743	−	0.603836i
$970$	−0.562056	+	1.10310i	−0.0180465	+	0.0354183i
$971$	−15.9476	+	21.9500i	−0.511783	+	0.704409i	−0.984219	−	0.176956i	$-0.943375\pi$
$971$	−15.9476	+	21.9500i	−0.511783	+	0.704409i	0.472436	+	0.881365i	$0.343375\pi$
$972$	13.5878	+	0.256478i	0.435828	+	0.00822654i
$973$	−12.3603	+	6.29790i	−0.396254	+	0.201901i
$974$	1.64497	−	5.06270i	0.0527083	−	0.162219i
$975$	−20.2758	+	23.6275i	−0.649346	+	0.756686i
$976$	8.78109	+	6.37983i	0.281076	+	0.204213i
$977$	8.75005	−	17.1729i	0.279939	−	0.549411i	−0.707633	−	0.706580i	$-0.750237\pi$
$977$	8.75005	−	17.1729i	0.279939	−	0.549411i	0.987572	+	0.157169i	$0.0502369\pi$
$978$	6.61238	+	0.860708i	0.211441	+	0.0275224i
$979$	8.83570	−	3.50251i	0.282390	−	0.111941i
$980$	0.438463	+	0.438463i	0.0140062	+	0.0140062i
$981$	−0.908842	−	0.813528i	−0.0290171	−	0.0259739i
$982$	−4.32978	−	27.3372i	−0.138169	−	0.872364i
$983$	0.970412	−	6.12694i	0.0309513	−	0.195419i	−0.967368	−	0.253377i	$-0.918459\pi$
$983$	0.970412	−	6.12694i	0.0309513	−	0.195419i	0.998319	+	0.0579575i	$0.0184588\pi$
$984$	−18.0389	−	8.57177i	−0.575058	−	0.273258i
$985$	−0.362436	−	0.117763i	−0.0115482	−	0.00375223i
$986$	−8.87293	+	56.0214i	−0.282572	+	1.78409i
$987$	13.0158	−	13.7560i	0.414298	−	0.437858i
$988$	0.865565	−	7.94429i	0.0275373	−	0.252742i
$989$			21.2905i			0.676998i
$990$	1.19261	+	0.439005i	0.0379035	+	0.0139525i
$991$	29.7286			0.944362			0.472181	−	0.881502i	$-0.343467\pi$
$991$	29.7286			0.944362			0.472181	+	0.881502i	$0.343467\pi$
$992$	5.85743	+	18.0273i	0.185974	+	0.572368i
$993$	1.61009	+	58.2347i	0.0510947	+	1.84802i
$994$	−1.21689	+	7.68316i	−0.0385975	+	0.243695i
$995$	−0.645690	−	1.26724i	−0.0204697	−	0.0401741i
$996$	14.0158	−	4.98632i	0.444108	−	0.157997i
$997$	37.2900	−	27.0928i	1.18099	−	0.858037i	0.188704	−	0.982034i	$-0.439571\pi$
$997$	37.2900	−	27.0928i	1.18099	−	0.858037i	0.992283	+	0.123997i	$0.0395713\pi$
$998$	25.8892	+	18.8096i	0.819508	+	0.595407i
$999$	8.95264	+	10.3896i	0.283249	+	0.328713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.18	✓	416
3.2	odd	2	inner	429.2.bi.a.5.35	yes	416
11.9	even	5	inner	429.2.bi.a.317.35	yes	416
13.8	odd	4	inner	429.2.bi.a.203.18	yes	416
33.20	odd	10	inner	429.2.bi.a.317.18	yes	416
39.8	even	4	inner	429.2.bi.a.203.35	yes	416
143.86	odd	20	inner	429.2.bi.a.86.35	yes	416
429.86	even	20	inner	429.2.bi.a.86.18	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.18	✓	416	1.1	even	1	trivial
429.2.bi.a.5.35	yes	416	3.2	odd	2	inner
429.2.bi.a.86.18	yes	416	429.86	even	20	inner
429.2.bi.a.86.35	yes	416	143.86	odd	20	inner
429.2.bi.a.203.18	yes	416	13.8	odd	4	inner
429.2.bi.a.203.35	yes	416	39.8	even	4	inner
429.2.bi.a.317.18	yes	416	33.20	odd	10	inner
429.2.bi.a.317.35	yes	416	11.9	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.482212 + 0.946394i) q^{2} +(-1.19043 + 1.25813i) q^{3} +(0.512438 + 0.705310i) q^{4} +(-0.107143 + 0.0545921i) q^{5} +(-0.616644 - 1.73330i) q^{6} +(-1.02889 - 0.162960i) q^{7} +(-3.01277 + 0.477177i) q^{8} +(-0.165763 - 2.99542i) q^{9} +O(q^{10})\)	\(q+(-0.482212 + 0.946394i) q^{2} +(-1.19043 + 1.25813i) q^{3} +(0.512438 + 0.705310i) q^{4} +(-0.107143 + 0.0545921i) q^{5} +(-0.616644 - 1.73330i) q^{6} +(-1.02889 - 0.162960i) q^{7} +(-3.01277 + 0.477177i) q^{8} +(-0.165763 - 2.99542i) q^{9} -0.127724i q^{10} +(-3.04439 - 1.31594i) q^{11} +(-1.49739 - 0.194909i) q^{12} +(-2.25836 - 2.81066i) q^{13} +(0.650367 - 0.895153i) q^{14} +(0.0588623 - 0.199787i) q^{15} +(0.462389 - 1.42309i) q^{16} +(-1.66456 + 5.12300i) q^{17} +(2.91478 + 1.28755i) q^{18} +(2.51098 - 0.397700i) q^{19} +(-0.0934084 - 0.0475940i) q^{20} +(1.42984 - 1.10048i) q^{21} +(2.71343 - 2.24663i) q^{22} +2.30860 q^{23} +(2.98614 - 4.35850i) q^{24} +(-2.93043 + 4.03339i) q^{25} +(3.74900 - 0.781970i) q^{26} +(3.96594 + 3.35728i) q^{27} +(-0.412305 - 0.809193i) q^{28} +(-5.82699 - 8.02016i) q^{29} +(0.160693 + 0.152047i) q^{30} +(-3.74371 - 1.90752i) q^{31} +(-3.18999 - 3.18999i) q^{32} +(5.27974 - 2.26370i) q^{33} +(-4.04570 - 4.04570i) q^{34} +(0.119135 - 0.0387092i) q^{35} +(2.02775 - 1.65188i) q^{36} +(2.60691 + 0.412893i) q^{37} +(-0.834443 + 2.56815i) q^{38} +(6.22458 + 0.504576i) q^{39} +(0.296748 - 0.215600i) q^{40} +(-0.591349 - 3.73363i) q^{41} +(0.352001 + 1.88386i) q^{42} +9.22225i q^{43} +(-0.631918 - 2.82157i) q^{44} +(0.181286 + 0.311888i) q^{45} +(-1.11323 + 2.18484i) q^{46} +(10.3667 - 1.64192i) q^{47} +(1.23998 + 2.27583i) q^{48} +(-5.62534 - 1.82778i) q^{49} +(-2.40409 - 4.71828i) q^{50} +(-4.46384 - 8.19279i) q^{51} +(0.825113 - 3.03313i) q^{52} +(-3.47620 + 1.12949i) q^{53} +(-5.08973 + 2.13442i) q^{54} +(0.398025 - 0.0252063i) q^{55} +3.17757 q^{56} +(-2.48878 + 3.63256i) q^{57} +(10.4001 - 1.64721i) q^{58} +(-0.574798 + 3.62913i) q^{59} +(0.171075 - 0.0608624i) q^{60} +(-2.24155 + 6.89877i) q^{61} +(3.61052 - 2.62320i) q^{62} +(-0.317582 + 3.10897i) q^{63} +(7.40341 - 2.40551i) q^{64} +(0.395407 + 0.177853i) q^{65} +(-0.403601 + 6.08829i) q^{66} +(1.29712 - 1.29712i) q^{67} +(-4.46629 + 1.45119i) q^{68} +(-2.74822 + 2.90451i) q^{69} +(-0.0208140 + 0.131414i) q^{70} +(-6.26414 + 3.19174i) q^{71} +(1.92875 + 8.94542i) q^{72} +(-13.3110 - 2.10826i) q^{73} +(-1.64784 + 2.26806i) q^{74} +(-1.58605 - 8.48830i) q^{75} +(1.56722 + 1.56722i) q^{76} +(2.91790 + 1.85007i) q^{77} +(-3.47909 + 5.64759i) q^{78} +(3.68250 + 11.3336i) q^{79} +(0.0281475 + 0.177717i) q^{80} +(-8.94505 + 0.993059i) q^{81} +(3.81864 + 1.24075i) q^{82} +(-8.77797 + 4.47260i) q^{83} +(1.50889 + 0.444555i) q^{84} +(-0.101329 - 0.639765i) q^{85} +(-8.72788 - 4.44708i) q^{86} +(17.0270 + 2.21634i) q^{87} +(9.80000 + 2.51191i) q^{88} +(-2.02639 + 2.02639i) q^{89} +(-0.382588 + 0.0211720i) q^{90} +(1.86558 + 3.25988i) q^{91} +(1.18301 + 1.62828i) q^{92} +(6.85651 - 2.43930i) q^{93} +(-3.44502 + 10.6027i) q^{94} +(-0.247323 + 0.179690i) q^{95} +(7.81085 - 0.215957i) q^{96} +(-8.63655 - 4.40054i) q^{97} +(4.44240 - 4.44240i) q^{98} +(-3.43713 + 9.33735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

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