LMFDB - Embedded newform 58.2.d.b.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(7,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			23.1
Root			$0.760453 + 3.33176i$ of defining polynomial
Character	$\chi$	$=$	58.23
Dual form			58.2.d.b.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.623490 - 0.781831i) q^{2} +(-0.760453 + 3.33176i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.00725 - 1.26305i) q^{5} +(2.13074 + 2.67187i) q^{6} +(0.338433 - 1.48277i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-7.81944 - 3.76565i) q^{9} +(-0.359484 - 1.57500i) q^{10} +(-1.70872 + 0.822877i) q^{11} +3.41744 q^{12} +(2.87014 - 1.38219i) q^{13} +(-0.948269 - 1.18909i) q^{14} +(3.44223 + 4.31642i) q^{15} +(-0.900969 + 0.433884i) q^{16} -1.69929 q^{17} +(-7.81944 + 3.76565i) q^{18} +(0.818639 + 3.58669i) q^{19} +(-1.45552 - 0.700942i) q^{20} +(4.68289 + 2.25516i) q^{21} +(-0.422020 + 1.84899i) q^{22} +(-1.67782 - 2.10392i) q^{23} +(2.13074 - 2.67187i) q^{24} +(0.531856 + 2.33021i) q^{25} +(0.708867 - 3.10575i) q^{26} +(12.1003 - 15.1733i) q^{27} -1.52091 q^{28} +(-4.31703 + 3.21920i) q^{29} +5.52091 q^{30} +(-1.11130 + 1.39353i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-1.44223 - 6.31882i) q^{33} +(-1.05949 + 1.32856i) q^{34} +(-1.53194 - 1.92099i) q^{35} +(-1.93124 + 8.46133i) q^{36} +(6.37006 + 3.06766i) q^{37} +(3.31460 + 1.59623i) q^{38} +(2.42251 + 10.6137i) q^{39} +(-1.45552 + 0.700942i) q^{40} -5.03259 q^{41} +(4.68289 - 2.25516i) q^{42} +(-1.18247 - 1.48277i) q^{43} +(1.18247 + 1.48277i) q^{44} +(-12.6324 + 6.08343i) q^{45} -2.69101 q^{46} +(-2.31606 + 1.11536i) q^{47} +(-0.760453 - 3.33176i) q^{48} +(4.22270 + 2.03355i) q^{49} +(2.15344 + 1.03704i) q^{50} +(1.29223 - 5.66162i) q^{51} +(-1.98620 - 2.49062i) q^{52} +(5.14319 - 6.44936i) q^{53} +(-4.31856 - 18.9208i) q^{54} +(-0.681776 + 2.98705i) q^{55} +(-0.948269 + 1.18909i) q^{56} -12.5725 q^{57} +(-0.174748 + 5.38233i) q^{58} +2.95027 q^{59} +(3.44223 - 4.31642i) q^{60} +(1.72363 - 7.55173i) q^{61} +(0.396619 + 1.73770i) q^{62} +(-8.22996 + 10.3200i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.14518 - 5.01736i) q^{65} +(-5.83946 - 2.81214i) q^{66} +(-2.23359 - 1.07564i) q^{67} +(0.378127 + 1.65668i) q^{68} +(8.28565 - 3.99016i) q^{69} -2.45703 q^{70} +(-5.46771 + 2.63311i) q^{71} +(5.41122 + 6.78546i) q^{72} +(2.33692 + 2.93041i) q^{73} +(6.37006 - 3.06766i) q^{74} -8.16816 q^{75} +(3.31460 - 1.59623i) q^{76} +(0.641852 + 2.81214i) q^{77} +(9.80856 + 4.72355i) q^{78} +(-8.30753 - 4.00069i) q^{79} +(-0.359484 + 1.57500i) q^{80} +(25.1185 + 31.4977i) q^{81} +(-3.13777 + 3.93464i) q^{82} +(1.22901 + 5.38465i) q^{83} +(1.15658 - 5.06730i) q^{84} +(-1.71161 + 2.14629i) q^{85} -1.89654 q^{86} +(-7.44272 - 16.8314i) q^{87} +1.89654 q^{88} +(9.95740 - 12.4862i) q^{89} +(-3.11994 + 13.6693i) q^{90} +(-1.07812 - 4.72355i) q^{91} +(-1.67782 + 2.10392i) q^{92} +(-3.79781 - 4.76231i) q^{93} +(-0.572020 + 2.50618i) q^{94} +(5.35476 + 2.57872i) q^{95} +(-3.07901 - 1.48277i) q^{96} +(-3.31730 - 14.5341i) q^{97} +(4.22270 - 2.03355i) q^{98} +16.4599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

Coefficient data

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

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

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

$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$3$	−0.760453	+	3.33176i	−0.439048	+	1.92359i	−0.0600525	+	0.998195i	$0.519127\pi$
$3$	−0.760453	+	3.33176i	−0.439048	+	1.92359i	−0.378995	+	0.925399i	$0.623730\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	1.00725	−	1.26305i	0.450457	−	0.564855i	−0.503809	−	0.863815i	$-0.668068\pi$
$5$	1.00725	−	1.26305i	0.450457	−	0.564855i	0.954266	+	0.298960i	$0.0966398\pi$
$6$	2.13074	+	2.67187i	0.869872	+	1.09078i
$7$	0.338433	−	1.48277i	0.127916	−	0.560436i	−0.869831	−	0.493349i	$-0.835772\pi$
$7$	0.338433	−	1.48277i	0.127916	−	0.560436i	0.997747	−	0.0670866i	$-0.0213704\pi$
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	−7.81944	−	3.76565i	−2.60648	−	1.25522i
$10$	−0.359484	−	1.57500i	−0.113679	−	0.498060i
$11$	−1.70872	+	0.822877i	−0.515199	+	0.248107i	−0.673371	−	0.739305i	$-0.735154\pi$
$11$	−1.70872	+	0.822877i	−0.515199	+	0.248107i	0.158172	+	0.987412i	$0.449440\pi$
$12$	3.41744			0.986531
$13$	2.87014	−	1.38219i	0.796035	−	0.383350i	0.00876713	−	0.999962i	$-0.497209\pi$
$13$	2.87014	−	1.38219i	0.796035	−	0.383350i	0.787268	+	0.616611i	$0.211495\pi$
$14$	−0.948269	−	1.18909i	−0.253436	−	0.317798i
$15$	3.44223	+	4.31642i	0.888780	+	1.11449i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.69929			−0.412138			−0.206069	−	0.978537i	$-0.566067\pi$
$17$	−1.69929			−0.412138			−0.206069	+	0.978537i	$0.566067\pi$
$18$	−7.81944	+	3.76565i	−1.84306	+	0.887571i
$19$	0.818639	+	3.58669i	0.187809	+	0.822843i	0.977769	+	0.209685i	$0.0672439\pi$
$19$	0.818639	+	3.58669i	0.187809	+	0.822843i	−0.789960	+	0.613158i	$0.789899\pi$
$20$	−1.45552	−	0.700942i	−0.325465	−	0.156735i
$21$	4.68289	+	2.25516i	1.02189	+	0.492116i
$22$	−0.422020	+	1.84899i	−0.0899749	+	0.394206i
$23$	−1.67782	−	2.10392i	−0.349849	−	0.438697i	0.575506	−	0.817797i	$-0.304805\pi$
$23$	−1.67782	−	2.10392i	−0.349849	−	0.438697i	−0.925356	+	0.379100i	$0.876234\pi$
$24$	2.13074	−	2.67187i	0.434936	−	0.545392i
$25$	0.531856	+	2.33021i	0.106371	+	0.466042i
$26$	0.708867	−	3.10575i	0.139020	−	0.609088i
$27$	12.1003	−	15.1733i	2.32871	−	2.92011i
$28$	−1.52091			−0.287424
$29$	−4.31703	+	3.21920i	−0.801652	+	0.597791i
$29$	−4.31703	+	3.21920i	−0.801652	+	0.597791i
$30$	5.52091			1.00797
$31$	−1.11130	+	1.39353i	−0.199596	+	0.250285i	−0.871549	−	0.490308i	$-0.836884\pi$
$31$	−1.11130	+	1.39353i	−0.199596	+	0.250285i	0.671953	+	0.740594i	$0.265456\pi$
$32$	−0.222521	+	0.974928i	−0.0393365	+	0.172345i
$33$	−1.44223	−	6.31882i	−0.251060	−	1.09996i
$34$	−1.05949	+	1.32856i	−0.181701	+	0.227846i
$35$	−1.53194	−	1.92099i	−0.258944	−	0.324706i
$36$	−1.93124	+	8.46133i	−0.321874	+	1.41022i
$37$	6.37006	+	3.06766i	1.04723	+	0.504320i	0.876703	−	0.481032i	$-0.159738\pi$
$37$	6.37006	+	3.06766i	1.04723	+	0.504320i	0.170529	+	0.985353i	$0.445452\pi$
$38$	3.31460	+	1.59623i	0.537699	+	0.258942i
$39$	2.42251	+	10.6137i	0.387913	+	1.69956i
$40$	−1.45552	+	0.700942i	−0.230138	+	0.110829i
$41$	−5.03259			−0.785959			−0.392979	−	0.919547i	$-0.628556\pi$
$41$	−5.03259			−0.785959			−0.392979	+	0.919547i	$0.628556\pi$
$42$	4.68289	−	2.25516i	0.722585	−	0.347979i
$43$	−1.18247	−	1.48277i	−0.180325	−	0.226121i	0.683451	−	0.729997i	$-0.260478\pi$
$43$	−1.18247	−	1.48277i	−0.180325	−	0.226121i	−0.863776	+	0.503876i	$0.831907\pi$
$44$	1.18247	+	1.48277i	0.178264	+	0.223537i
$45$	−12.6324	+	6.08343i	−1.88312	+	0.906864i
$46$	−2.69101			−0.396768
$47$	−2.31606	+	1.11536i	−0.337832	+	0.162691i	−0.595106	−	0.803647i	$-0.702890\pi$
$47$	−2.31606	+	1.11536i	−0.337832	+	0.162691i	0.257274	+	0.966339i	$0.417176\pi$
$48$	−0.760453	−	3.33176i	−0.109762	−	0.480898i
$49$	4.22270	+	2.03355i	0.603243	+	0.290507i
$50$	2.15344	+	1.03704i	0.304542	+	0.146660i
$51$	1.29223	−	5.66162i	0.180948	−	0.792786i
$52$	−1.98620	−	2.49062i	−0.275437	−	0.345387i
$53$	5.14319	−	6.44936i	0.706472	−	0.885888i	−0.291016	−	0.956718i	$-0.593993\pi$
$53$	5.14319	−	6.44936i	0.706472	−	0.885888i	0.997488	+	0.0708303i	$0.0225649\pi$
$54$	−4.31856	−	18.9208i	−0.587681	−	2.57480i
$55$	−0.681776	+	2.98705i	−0.0919306	+	0.402774i
$56$	−0.948269	+	1.18909i	−0.126718	+	0.158899i
$57$	−12.5725			−1.66527
$58$	−0.174748	+	5.38233i	−0.0229456	+	0.706734i
$59$	2.95027			0.384093			0.192046	−	0.981386i	$-0.438488\pi$
$59$	2.95027			0.384093			0.192046	+	0.981386i	$0.438488\pi$
$60$	3.44223	−	4.31642i	0.444390	−	0.557247i
$61$	1.72363	−	7.55173i	0.220688	−	0.966899i	−0.736273	−	0.676685i	$-0.763416\pi$
$61$	1.72363	−	7.55173i	0.220688	−	0.966899i	0.956962	−	0.290215i	$-0.0937268\pi$
$62$	0.396619	+	1.73770i	0.0503707	+	0.220688i
$63$	−8.22996	+	10.3200i	−1.03688	+	1.30020i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	1.14518	−	5.01736i	0.142042	−	0.622327i
$66$	−5.83946	−	2.81214i	−0.718788	−	0.346150i
$67$	−2.23359	−	1.07564i	−0.272876	−	0.131410i	0.292442	−	0.956283i	$-0.405532\pi$
$67$	−2.23359	−	1.07564i	−0.272876	−	0.131410i	−0.565318	+	0.824873i	$0.691246\pi$
$68$	0.378127	+	1.65668i	0.0458546	+	0.200902i
$69$	8.28565	−	3.99016i	0.997475	−	0.480359i
$70$	−2.45703			−0.293672
$71$	−5.46771	+	2.63311i	−0.648898	+	0.312493i	−0.729223	−	0.684276i	$-0.760118\pi$
$71$	−5.46771	+	2.63311i	−0.648898	+	0.312493i	0.0803250	+	0.996769i	$0.474404\pi$
$72$	5.41122	+	6.78546i	0.637719	+	0.799674i
$73$	2.33692	+	2.93041i	0.273516	+	0.342978i	0.899550	−	0.436817i	$-0.143894\pi$
$73$	2.33692	+	2.93041i	0.273516	+	0.342978i	−0.626034	+	0.779796i	$0.715323\pi$
$74$	6.37006	−	3.06766i	0.740505	−	0.356608i
$75$	−8.16816			−0.943178
$76$	3.31460	−	1.59623i	0.380211	−	0.183100i
$77$	0.641852	+	2.81214i	0.0731458	+	0.320473i
$78$	9.80856	+	4.72355i	1.11060	+	0.534837i
$79$	−8.30753	−	4.00069i	−0.934670	−	0.450113i	−0.0963841	−	0.995344i	$-0.530728\pi$
$79$	−8.30753	−	4.00069i	−0.934670	−	0.450113i	−0.838286	+	0.545231i	$0.816442\pi$
$80$	−0.359484	+	1.57500i	−0.0401915	+	0.176091i
$81$	25.1185	+	31.4977i	2.79095	+	3.49974i
$82$	−3.13777	+	3.93464i	−0.346509	+	0.434508i
$83$	1.22901	+	5.38465i	0.134902	+	0.591042i	0.996510	+	0.0834694i	$0.0266001\pi$
$83$	1.22901	+	5.38465i	0.134902	+	0.591042i	−0.861609	+	0.507573i	$0.830543\pi$
$84$	1.15658	−	5.06730i	0.126193	−	0.552887i
$85$	−1.71161	+	2.14629i	−0.185650	+	0.232798i
$86$	−1.89654			−0.204509
$87$	−7.44272	−	16.8314i	−0.797944	−	1.80451i
$88$	1.89654			0.202172
$89$	9.95740	−	12.4862i	1.05548	−	1.32353i	0.111417	−	0.993774i	$-0.464461\pi$
$89$	9.95740	−	12.4862i	1.05548	−	1.32353i	0.944065	−	0.329759i	$-0.106968\pi$
$90$	−3.11994	+	13.6693i	−0.328870	+	1.44087i
$91$	−1.07812	−	4.72355i	−0.113018	−	0.495163i
$92$	−1.67782	+	2.10392i	−0.174925	+	0.219348i
$93$	−3.79781	−	4.76231i	−0.393815	−	0.493828i
$94$	−0.572020	+	2.50618i	−0.0589994	+	0.258493i
$95$	5.35476	+	2.57872i	0.549387	+	0.264571i
$96$	−3.07901	−	1.48277i	−0.314250	−	0.151335i
$97$	−3.31730	−	14.5341i	−0.336821	−	1.47571i	−0.805635	−	0.592412i	$-0.798176\pi$
$97$	−3.31730	−	14.5341i	−0.336821	−	1.47571i	0.468814	−	0.883297i	$-0.344682\pi$
$98$	4.22270	−	2.03355i	0.426557	−	0.205419i
$99$	16.4599			1.65428
$100$	2.15344	−	1.03704i	0.215344	−	0.103704i
$101$	0.114672	+	0.143794i	0.0114102	+	0.0143080i	0.787504	−	0.616310i	$-0.211373\pi$
$101$	0.114672	+	0.143794i	0.0114102	+	0.0143080i	−0.776094	+	0.630618i	$0.782802\pi$
$102$	−3.62074	−	4.54027i	−0.358507	−	0.449554i
$103$	13.5567	−	6.52856i	1.33578	−	0.643279i	0.376681	−	0.926343i	$-0.377065\pi$
$103$	13.5567	−	6.52856i	1.33578	−	0.643279i	0.959101	+	0.283065i	$0.0913511\pi$
$104$	−3.18562			−0.312376
$105$	7.56524	−	3.64323i	0.738291	−	0.355542i
$106$	−1.83558	−	8.04222i	−0.178288	−	0.781130i
$107$	0.273899	+	0.131903i	0.0264789	+	0.0127515i	0.447076	−	0.894496i	$-0.352465\pi$
$107$	0.273899	+	0.131903i	0.0264789	+	0.0127515i	−0.420597	+	0.907247i	$0.638180\pi$
$108$	−17.4855	−	8.42057i	−1.68254	−	0.810269i
$109$	−2.00800	+	8.79762i	−0.192332	+	0.842660i	0.783019	+	0.621998i	$0.213679\pi$
$109$	−2.00800	+	8.79762i	−0.192332	+	0.842660i	−0.975350	+	0.220662i	$0.929178\pi$
$110$	1.91029	+	2.39543i	0.182139	+	0.228395i
$111$	−15.0649	+	18.8907i	−1.42989	+	1.79303i
$112$	0.338433	+	1.48277i	0.0319790	+	0.140109i
$113$	−1.80183	+	7.89435i	−0.169502	+	0.742638i	0.816696	+	0.577069i	$0.195803\pi$
$113$	−1.80183	+	7.89435i	−0.169502	+	0.742638i	−0.986198	+	0.165570i	$0.947054\pi$
$114$	−7.83885	+	9.82960i	−0.734175	+	0.920627i
$115$	−4.34735			−0.405392
$116$	4.09912	+	3.49245i	0.380594	+	0.324266i
$117$	−27.6478			−2.55604
$118$	1.83946	−	2.30662i	0.169336	−	0.212341i
$119$	−0.575096	+	2.51966i	−0.0527189	+	0.230977i
$120$	−1.22852	−	5.38249i	−0.112148	−	0.491351i
$121$	−4.61578	+	5.78801i	−0.419617	+	0.526183i
$122$	−4.82951	−	6.05601i	−0.437243	−	0.548286i
$123$	3.82705	−	16.7674i	0.345073	−	1.51187i
$124$	1.60588	+	0.773350i	0.144212	+	0.0694489i
$125$	10.7565	+	5.18006i	0.962091	+	0.463319i
$126$	2.93724	+	12.8689i	0.261670	+	1.14645i
$127$	8.57262	−	4.12836i	0.760697	−	0.366332i	−0.0129773	−	0.999916i	$-0.504131\pi$
$127$	8.57262	−	4.12836i	0.760697	−	0.366332i	0.773674	+	0.633583i	$0.218417\pi$
$128$	1.00000			0.0883883
$129$	5.83946	−	2.81214i	0.514136	−	0.247595i
$130$	−3.20872	−	4.02361i	−0.281424	−	0.352894i
$131$	8.88757	+	11.1447i	0.776511	+	0.973714i	1.00000		0.000992917i	$-0.000316055\pi$
$131$	8.88757	+	11.1447i	0.776511	+	0.973714i	−0.223489	+	0.974706i	$0.571745\pi$
$132$	−5.83946	+	2.81214i	−0.508260	+	0.244765i
$133$	5.59530			0.485174
$134$	−2.23359	+	1.07564i	−0.192952	+	0.0929210i
$135$	−6.97666	−	30.5668i	−0.600455	−	2.63077i
$136$	1.53101	+	0.737293i	0.131283	+	0.0632224i
$137$	−5.82435	−	2.80486i	−0.497608	−	0.239635i	0.168208	−	0.985752i	$-0.446202\pi$
$137$	−5.82435	−	2.80486i	−0.497608	−	0.239635i	−0.665816	+	0.746116i	$0.731916\pi$
$138$	2.04639	−	8.96581i	0.174200	−	0.763220i
$139$	−8.88930	−	11.1468i	−0.753980	−	0.945462i	0.245734	−	0.969337i	$-0.420971\pi$
$139$	−8.88930	−	11.1468i	−0.753980	−	0.945462i	−0.999715	+	0.0238756i	$0.992399\pi$
$140$	−1.53194	+	1.92099i	−0.129472	+	0.162353i
$141$	−1.95485	−	8.56474i	−0.164628	−	0.721281i
$142$	−1.35041	+	5.91655i	−0.113324	+	0.496506i
$143$	−3.76691	+	4.72355i	−0.315005	+	0.395003i
$144$	8.67893			0.723244
$145$	−0.282307	+	8.69519i	−0.0234443	+	0.722096i
$146$	3.74813			0.310198
$147$	−9.98646	+	12.5226i	−0.823669	+	1.03285i
$148$	1.57328	−	6.89297i	0.129322	−	0.566599i
$149$	1.83339	+	8.03260i	0.150197	+	0.658056i	0.992827	+	0.119563i	$0.0381492\pi$
$149$	1.83339	+	8.03260i	0.150197	+	0.658056i	−0.842630	+	0.538493i	$0.818994\pi$
$150$	−5.09277	+	6.38613i	−0.415823	+	0.521425i
$151$	−13.7186	−	17.2026i	−1.11640	−	1.39992i	−0.906502	−	0.422201i	$-0.861258\pi$
$151$	−13.7186	−	17.2026i	−1.11640	−	1.39992i	−0.209900	−	0.977723i	$-0.567314\pi$
$152$	0.818639	−	3.58669i	0.0664004	−	0.290919i
$153$	13.2875	+	6.39891i	1.07423	+	0.517322i
$154$	2.59881	+	1.25152i	0.209418	+	0.100850i
$155$	0.640741	+	2.80727i	0.0514655	+	0.225485i
$156$	9.80856	−	4.72355i	0.785313	−	0.378187i
$157$	0.135585			0.0108208			0.00541041	−	0.999985i	$-0.498278\pi$
$157$	0.135585			0.0108208			0.00541041	+	0.999985i	$0.498278\pi$
$158$	−8.30753	+	4.00069i	−0.660911	+	0.318278i
$159$	17.5766	+	22.0403i	1.39391	+	1.74791i
$160$	1.00725	+	1.26305i	0.0796303	+	0.0998532i
$161$	−3.68746	+	1.77579i	−0.290613	+	0.139952i
$162$	40.2870			3.16525
$163$	−9.23815	+	4.44886i	−0.723587	+	0.348461i	−0.759158	−	0.650906i	$-0.774389\pi$
$163$	−9.23815	+	4.44886i	−0.723587	+	0.348461i	0.0355711	+	0.999367i	$0.488675\pi$
$164$	1.11986	+	4.90641i	0.0874461	+	0.383127i
$165$	−9.43370	−	4.54303i	−0.734412	−	0.353674i
$166$	4.97617	+	2.39640i	0.386225	+	0.185996i
$167$	−3.73573	+	16.3673i	−0.289079	+	1.26654i	0.596712	+	0.802456i	$0.296474\pi$
$167$	−3.73573	+	16.3673i	−0.289079	+	1.26654i	−0.885791	+	0.464084i	$0.846384\pi$
$168$	−3.24066	−	4.06366i	−0.250022	−	0.313518i
$169$	−1.77808	+	2.22965i	−0.136776	+	0.171511i
$170$	0.610867	+	2.67638i	0.0468513	+	0.205269i
$171$	7.10491	−	31.1286i	0.543326	−	2.38047i
$172$	−1.18247	+	1.48277i	−0.0901627	+	0.113060i
$173$	4.15473			0.315878			0.157939	−	0.987449i	$-0.449515\pi$
$173$	4.15473			0.315878			0.157939	+	0.987449i	$0.449515\pi$
$174$	−17.7998	−	4.67523i	−1.34940	−	0.354428i
$175$	3.63517			0.274793
$176$	1.18247	−	1.48277i	0.0891322	−	0.111768i
$177$	−2.24354	+	9.82960i	−0.168635	+	0.738838i
$178$	−3.55376	−	15.5700i	−0.266365	−	1.16702i
$179$	6.60922	−	8.28770i	0.493996	−	0.619452i	−0.470867	−	0.882204i	$-0.656059\pi$
$179$	6.60922	−	8.28770i	0.493996	−	0.619452i	0.964863	+	0.262753i	$0.0846303\pi$
$180$	8.74187	+	10.9620i	0.651580	+	0.817056i
$181$	−4.84352	+	21.2209i	−0.360016	+	1.57733i	0.393131	+	0.919483i	$0.371392\pi$
$181$	−4.84352	+	21.2209i	−0.360016	+	1.57733i	−0.753147	+	0.657852i	$0.771465\pi$
$182$	−4.36522	−	2.10218i	−0.323572	−	0.155824i
$183$	23.8498	+	11.4855i	1.76303	+	0.849030i
$184$	0.598806	+	2.62354i	0.0441446	+	0.193410i
$185$	10.2909	−	4.95583i	0.756601	−	0.364360i
$186$	−6.09122			−0.446630
$187$	2.90361	−	1.39831i	0.212333	−	0.102254i
$188$	1.60276	+	2.00980i	0.116894	+	0.146580i
$189$	−18.4035	−	23.0772i	−1.33866	−	1.67862i
$190$	5.35476	−	2.57872i	0.388475	−	0.187080i
$191$	−14.5209			−1.05069			−0.525346	−	0.850888i	$-0.676064\pi$
$191$	−14.5209			−1.05069			−0.525346	+	0.850888i	$0.676064\pi$
$192$	−3.07901	+	1.48277i	−0.222209	+	0.107010i
$193$	1.06926	+	4.68476i	0.0769674	+	0.337216i	0.998721	−	0.0505599i	$-0.0161006\pi$
$193$	1.06926	+	4.68476i	0.0769674	+	0.337216i	−0.921754	+	0.387776i	$0.873243\pi$
$194$	−13.4315	−	6.46826i	−0.964324	−	0.464394i
$195$	15.8458	+	7.63093i	1.13474	+	0.546462i
$196$	1.04292	−	4.56934i	0.0744944	−	0.326381i
$197$	−9.49108	−	11.9014i	−0.676212	−	0.847943i	0.318787	−	0.947826i	$-0.396724\pi$
$197$	−9.49108	−	11.9014i	−0.676212	−	0.847943i	−0.994999	+	0.0998835i	$0.968153\pi$
$198$	10.2626	−	12.8689i	0.729331	−	0.914552i
$199$	2.71330	+	11.8877i	0.192341	+	0.842699i	0.975345	+	0.220683i	$0.0708288\pi$
$199$	2.71330	+	11.8877i	0.192341	+	0.842699i	−0.783005	+	0.622015i	$0.786314\pi$
$200$	0.531856	−	2.33021i	0.0376079	−	0.164771i
$201$	5.28231	−	6.62381i	0.372585	−	0.467207i
$202$	0.183919			0.0129405
$203$	3.31232	+	7.49066i	0.232480	+	0.525741i
$204$	−5.80722			−0.406587
$205$	−5.06909	+	6.35644i	−0.354040	+	0.443953i
$206$	3.34823	−	14.6696i	0.233282	−	1.02208i
$207$	5.19700	+	22.7695i	0.361216	+	1.58259i
$208$	−1.98620	+	2.49062i	−0.137718	+	0.172693i
$209$	−4.35023	−	5.45502i	−0.300912	−	0.377332i
$210$	1.86846	−	8.18625i	0.128936	−	0.564905i
$211$	−12.9606	−	6.24151i	−0.892246	−	0.429683i	−0.0691638	−	0.997605i	$-0.522033\pi$
$211$	−12.9606	−	6.24151i	−0.892246	−	0.429683i	−0.823082	+	0.567922i	$0.807747\pi$
$212$	−7.43213	−	3.57912i	−0.510441	−	0.245815i
$213$	−4.61496	−	20.2195i	−0.316212	−	1.38542i
$214$	0.273899	−	0.131903i	0.0187234	−	0.00901670i
$215$	−3.06387			−0.208954
$216$	−17.4855	+	8.42057i	−1.18974	+	0.572947i
$217$	1.69019	+	2.11943i	0.114737	+	0.143876i
$218$	5.62629	+	7.05515i	0.381061	+	0.477835i
$219$	−11.5405	+	5.55763i	−0.779838	+	0.375550i
$220$	3.06387			0.206566
$221$	−4.87720	+	2.34874i	−0.328076	+	0.157993i
$222$	5.37658	+	23.5564i	0.360853	+	1.58100i
$223$	11.5189	+	5.54720i	0.771362	+	0.371468i	0.777801	−	0.628511i	$-0.216335\pi$
$223$	11.5189	+	5.54720i	0.771362	+	0.371468i	−0.00643891	+	0.999979i	$0.502050\pi$
$224$	1.37029	+	0.659896i	0.0915563	+	0.0440912i
$225$	4.61594	−	20.2237i	0.307729	−	1.34825i
$226$	5.04863	+	6.33078i	0.335830	+	0.421117i
$227$	16.4768	−	20.6612i	1.09360	−	1.37133i	0.171141	−	0.985246i	$-0.445255\pi$
$227$	16.4768	−	20.6612i	1.09360	−	1.37133i	0.922462	−	0.386088i	$-0.126174\pi$
$228$	2.79765	+	12.2573i	0.185279	+	0.811761i
$229$	−4.27284	+	18.7206i	−0.282358	+	1.23709i	0.612404	+	0.790545i	$0.290203\pi$
$229$	−4.27284	+	18.7206i	−0.282358	+	1.23709i	−0.894762	+	0.446544i	$0.852655\pi$
$230$	−2.71053	+	3.39889i	−0.178727	+	0.224116i
$231$	−9.85747			−0.648574
$232$	5.28627	−	1.02731i	0.347060	−	0.0674464i
$233$	−8.12368			−0.532200			−0.266100	−	0.963945i	$-0.585735\pi$
$233$	−8.12368			−0.532200			−0.266100	+	0.963945i	$0.585735\pi$
$234$	−17.2381	+	21.6159i	−1.12689	+	1.41308i
$235$	−0.924102	+	4.04876i	−0.0602818	+	0.264112i
$236$	−0.656497	−	2.87630i	−0.0427343	−	0.187231i
$237$	19.6468	−	24.6364i	1.27620	−	1.60030i
$238$	1.61138	+	2.02061i	0.104450	+	0.130977i
$239$	6.74549	−	29.5539i	0.436329	−	1.91168i	0.0261983	−	0.999657i	$-0.491660\pi$
$239$	6.74549	−	29.5539i	0.436329	−	1.91168i	0.410131	−	0.912027i	$-0.365483\pi$
$240$	−4.97416	−	2.39543i	−0.321081	−	0.154624i
$241$	−4.12092	−	1.98453i	−0.265452	−	0.127835i	0.296424	−	0.955056i	$-0.404206\pi$
$241$	−4.12092	−	1.98453i	−0.265452	−	0.127835i	−0.561876	+	0.827222i	$0.689920\pi$
$242$	1.64735	+	7.21753i	0.105896	+	0.463960i
$243$	−71.5877	+	34.4748i	−4.59235	+	2.21156i
$244$	−7.74593			−0.495883
$245$	6.82180	−	3.28521i	0.435829	−	0.209884i
$246$	−10.7232	−	13.4464i	−0.683683	−	0.857312i
$247$	7.30709	+	9.16281i	0.464939	+	0.583015i
$248$	1.60588	−	0.773350i	0.101973	−	0.0491078i
$249$	−18.8750			−1.19615
$250$	10.7565	−	5.18006i	0.680301	−	0.327616i
$251$	2.96313	+	12.9823i	0.187031	+	0.819438i	0.978171	+	0.207802i	$0.0666311\pi$
$251$	2.96313	+	12.9823i	0.187031	+	0.819438i	−0.791139	+	0.611636i	$0.790512\pi$
$252$	11.8926	+	5.72719i	0.749166	+	0.360779i
$253$	4.59819	+	2.21437i	0.289086	+	0.139216i
$254$	2.11726	−	9.27633i	0.132849	−	0.582049i
$255$	−5.84934	−	7.33484i	−0.366300	−	0.459325i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−4.33421	−	18.9894i	−0.270360	−	1.18453i	−0.909589	−	0.415510i	$-0.863603\pi$
$257$	−4.33421	−	18.9894i	−0.270360	−	1.18453i	0.639228	−	0.769017i	$-0.279254\pi$
$258$	1.44223	−	6.31882i	0.0897892	−	0.393392i
$259$	6.70449	−	8.40716i	0.416597	−	0.522396i
$260$	−5.14639			−0.319166
$261$	45.8791	−	8.91598i	2.83985	−	0.551885i
$262$	14.2546			0.880649
$263$	6.26071	−	7.85069i	0.386052	−	0.484094i	−0.550394	−	0.834905i	$-0.685523\pi$
$263$	6.26071	−	7.85069i	0.386052	−	0.484094i	0.936446	+	0.350811i	$0.114094\pi$
$264$	−1.44223	+	6.31882i	−0.0887630	+	0.388896i
$265$	−2.96540	−	12.9923i	−0.182163	−	0.798108i
$266$	3.48862	−	4.37459i	0.213901	−	0.268223i
$267$	34.0289	+	42.6709i	2.08253	+	2.61141i
$268$	−0.551650	+	2.41694i	−0.0336974	+	0.147638i
$269$	5.34815	+	2.57553i	0.326083	+	0.157033i	0.589762	−	0.807577i	$-0.299222\pi$
$269$	5.34815	+	2.57553i	0.326083	+	0.157033i	−0.263679	+	0.964610i	$0.584936\pi$
$270$	−28.2479	−	13.6035i	−1.71911	−	0.827882i
$271$	−4.22317	−	18.5029i	−0.256540	−	1.12397i	−0.924922	−	0.380156i	$-0.875870\pi$
$271$	−4.22317	−	18.5029i	−0.256540	−	1.12397i	0.668383	−	0.743817i	$-0.266987\pi$
$272$	1.53101	−	0.737293i	0.0928308	−	0.0447050i
$273$	16.5576			1.00211
$274$	−5.82435	+	2.80486i	−0.351862	+	0.169448i
$275$	−2.82627	−	3.54403i	−0.170431	−	0.213713i
$276$	−5.73385	−	7.19002i	−0.345137	−	0.432788i
$277$	23.2546	−	11.1988i	1.39723	−	0.672872i	0.424634	−	0.905365i	$-0.360403\pi$
$277$	23.2546	−	11.1988i	1.39723	−	0.672872i	0.972598	+	0.232494i	$0.0746884\pi$
$278$	−14.2573			−0.855098
$279$	13.9373	−	6.71185i	0.834404	−	0.401828i
$280$	0.546742	+	2.39543i	0.0326741	+	0.143154i
$281$	−22.7311	−	10.9467i	−1.35602	−	0.653027i	−0.392278	−	0.919847i	$-0.628313\pi$
$281$	−22.7311	−	10.9467i	−1.35602	−	0.653027i	−0.963747	+	0.266820i	$0.914027\pi$
$282$	−7.91501	−	3.81167i	−0.471332	−	0.226982i
$283$	−2.74754	+	12.0378i	−0.163324	+	0.715571i	0.825241	+	0.564780i	$0.191039\pi$
$283$	−2.74754	+	12.0378i	−0.163324	+	0.715571i	−0.988566	+	0.150791i	$0.951818\pi$
$284$	3.78378	+	4.74470i	0.224526	+	0.281546i
$285$	−12.6637	+	15.8798i	−0.750134	+	0.940638i
$286$	1.34439	+	5.89017i	0.0794957	+	0.348293i
$287$	−1.70320	+	7.46219i	−0.100537	+	0.440479i
$288$	5.41122	−	6.78546i	0.318859	−	0.399837i
$289$	−14.1124			−0.830142
$290$	6.62216	+	5.64208i	0.388866	+	0.331314i
$291$	50.9467			2.98655
$292$	2.33692	−	2.93041i	0.136758	−	0.171489i
$293$	−2.74795	+	12.0396i	−0.160537	+	0.703359i	0.829020	+	0.559219i	$0.188899\pi$
$293$	−2.74795	+	12.0396i	−0.160537	+	0.703359i	−0.989557	+	0.144140i	$0.953958\pi$
$294$	3.56413	+	15.6155i	0.207864	+	0.910712i
$295$	2.97167	−	3.72635i	0.173017	−	0.216957i
$296$	−4.40822	−	5.52773i	−0.256223	−	0.321293i
$297$	−8.19031	+	35.8841i	−0.475250	+	2.08221i
$298$	7.42324	+	3.57484i	0.430016	+	0.207085i
$299$	−7.72359	−	3.71948i	−0.446667	−	0.215103i
$300$	1.81759	+	7.96337i	0.104938	+	0.459765i
$301$	−2.59881	+	1.25152i	−0.149793	+	0.0721364i
$302$	−22.0029			−1.26612
$303$	−0.566288	+	0.272710i	−0.0325324	+	0.0156668i
$304$	−2.29377	−	2.87630i	−0.131557	−	0.164967i
$305$	−7.80211	−	9.78353i	−0.446747	−	0.560203i
$306$	13.2875	−	6.39891i	0.759595	−	0.365802i
$307$	11.8371			0.675579			0.337790	−	0.941222i	$-0.390321\pi$
$307$	11.8371			0.675579			0.337790	+	0.941222i	$0.390321\pi$
$308$	2.59881	−	1.25152i	0.148081	−	0.0713119i
$309$	11.4424	+	50.1324i	0.650935	+	2.85193i
$310$	2.59431	+	1.24935i	0.147347	+	0.0709584i
$311$	9.16959	+	4.41584i	0.519960	+	0.250400i	0.675408	−	0.737445i	$-0.263968\pi$
$311$	9.16959	+	4.41584i	0.519960	+	0.250400i	−0.155448	+	0.987844i	$0.549682\pi$
$312$	2.42251	−	10.6137i	0.137148	−	0.600884i
$313$	−8.31868	−	10.4313i	−0.470200	−	0.589612i	0.489020	−	0.872272i	$-0.337354\pi$
$313$	−8.31868	−	10.4313i	−0.470200	−	0.589612i	−0.959220	+	0.282661i	$0.908783\pi$
$314$	0.0845356	−	0.106004i	0.00477062	−	0.00598217i
$315$	4.74513	+	20.7898i	0.267358	+	1.17137i
$316$	−2.05179	+	8.98948i	−0.115422	+	0.505698i
$317$	−7.46575	+	9.36176i	−0.419318	+	0.525809i	−0.945962	−	0.324278i	$-0.894879\pi$
$317$	−7.46575	+	9.36176i	−0.419318	+	0.525809i	0.526644	+	0.850086i	$0.323450\pi$
$318$	28.1906			1.58085
$319$	4.72759	−	9.05311i	0.264694	−	0.506877i
$320$	1.61551			0.0903096
$321$	−0.647757	+	0.812262i	−0.0361543	+	0.0453360i
$322$	−0.910728	+	3.99016i	−0.0507529	+	0.222363i
$323$	−1.39110	−	6.09482i	−0.0774030	−	0.339125i
$324$	25.1185	−	31.4977i	1.39547	−	1.74987i
$325$	4.74729	+	5.95292i	0.263332	+	0.330208i
$326$	−2.28163	+	9.99649i	−0.126368	+	0.553654i
$327$	−27.7846	−	13.3804i	−1.53649	−	0.739936i
$328$	4.53421	+	2.18356i	0.250360	+	0.120567i
$329$	0.869989	+	3.81167i	0.0479640	+	0.210144i
$330$	−9.43370	+	4.54303i	−0.519308	+	0.250085i
$331$	−23.3952			−1.28592			−0.642958	−	0.765902i	$-0.722293\pi$
$331$	−23.3952			−1.28592			−0.642958	+	0.765902i	$0.722293\pi$
$332$	4.97617	−	2.39640i	0.273103	−	0.131519i
$333$	−38.2586	−	47.9748i	−2.09656	−	2.62900i
$334$	10.4673	+	13.1256i	0.572744	+	0.718198i
$335$	−3.60837	+	1.73770i	−0.197147	+	0.0949408i
$336$	−5.19761			−0.283553
$337$	−20.5917	+	9.91642i	−1.12170	+	0.540182i	−0.900417	−	0.435028i	$-0.856738\pi$
$337$	−20.5917	+	9.91642i	−1.12170	+	0.540182i	−0.221282	+	0.975210i	$0.571024\pi$
$338$	0.634591	+	2.78033i	0.0345172	+	0.151230i
$339$	−24.9319	−	12.0066i	−1.35412	−	0.652107i
$340$	2.47335	+	1.19110i	0.134136	+	0.0645966i
$341$	0.752203	−	3.29562i	0.0407341	−	0.178468i
$342$	−19.9075	−	24.9632i	−1.07647	−	1.34986i
$343$	11.0823	−	13.8967i	0.598387	−	0.750353i
$344$	0.422020	+	1.84899i	0.0227538	+	0.0996908i
$345$	3.30595	−	14.4843i	0.177986	−	0.779810i
$346$	2.59043	−	3.24830i	0.139262	−	0.174630i
$347$	6.48177			0.347960			0.173980	−	0.984749i	$-0.444337\pi$
$347$	6.48177			0.347960			0.173980	+	0.984749i	$0.444337\pi$
$348$	−14.7532	+	11.0014i	−0.790855	+	0.589740i
$349$	−11.7835			−0.630754			−0.315377	−	0.948966i	$-0.602131\pi$
$349$	−11.7835			−0.630754			−0.315377	+	0.948966i	$0.602131\pi$
$350$	2.26649	−	2.84209i	0.121149	−	0.151916i
$351$	13.7573	−	60.2746i	0.734310	−	3.21722i
$352$	−0.422020	−	1.84899i	−0.0224937	−	0.0985514i
$353$	−11.9204	+	14.9477i	−0.634457	+	0.795584i	−0.990298	−	0.138963i	$-0.955623\pi$
$353$	−11.9204	+	14.9477i	−0.634457	+	0.795584i	0.355841	+	0.934547i	$0.384195\pi$
$354$	6.28627	+	7.88273i	0.334111	+	0.418962i
$355$	−2.18160	+	9.55823i	−0.115787	+	0.507298i
$356$	−14.3889	−	6.92931i	−0.762608	−	0.367253i
$357$	−7.95757	−	3.83216i	−0.421159	−	0.202820i
$358$	−2.35880	−	10.3346i	−0.124667	−	0.546200i
$359$	7.46972	−	3.59723i	0.394237	−	0.189854i	−0.226254	−	0.974068i	$-0.572648\pi$
$359$	7.46972	−	3.59723i	0.394237	−	0.189854i	0.620490	+	0.784214i	$0.286934\pi$
$360$	14.0209			0.738965
$361$	4.92423	−	2.37138i	0.259170	−	0.124810i
$362$	13.5713	+	17.0178i	0.713289	+	0.894437i
$363$	−15.7742	−	19.7802i	−0.827930	−	1.03819i
$364$	−4.36522	+	2.10218i	−0.228800	+	0.110184i
$365$	6.05514			0.316940
$366$	23.8498	−	11.4855i	1.24665	−	0.600355i
$367$	−6.42229	−	28.1379i	−0.335241	−	1.46879i	−0.808831	−	0.588041i	$-0.799899\pi$
$367$	−6.42229	−	28.1379i	−0.335241	−	1.46879i	0.473590	−	0.880746i	$-0.342958\pi$
$368$	2.42452	+	1.16759i	0.126387	+	0.0608646i
$369$	39.3521	+	18.9510i	2.04859	+	0.986547i
$370$	2.54164	−	11.1356i	0.132133	−	0.578915i
$371$	−7.82231	−	9.80887i	−0.406114	−	0.509251i
$372$	−3.79781	+	4.76231i	−0.196907	+	0.246914i
$373$	4.97759	+	21.8082i	0.257730	+	1.12919i	0.923672	+	0.383185i	$0.125173\pi$
$373$	4.97759	+	21.8082i	0.257730	+	1.12919i	−0.665942	+	0.746004i	$0.731970\pi$
$374$	0.717133	−	3.14196i	0.0370820	−	0.162467i
$375$	−25.4385	+	31.8989i	−1.31364	+	1.64725i
$376$	2.57063			0.132570
$377$	−7.94095	+	15.2065i	−0.408980	+	0.783176i
$378$	−29.5169			−1.51818
$379$	−9.28671	+	11.6452i	−0.477026	+	0.598172i	−0.960876	−	0.276979i	$-0.910667\pi$
$379$	−9.28671	+	11.6452i	−0.477026	+	0.598172i	0.483850	+	0.875151i	$0.339238\pi$
$380$	1.32252	−	5.79432i	0.0678437	−	0.297243i
$381$	7.23563	+	31.7014i	0.370692	+	1.62411i
$382$	−9.05361	+	11.3529i	−0.463223	+	0.580863i
$383$	6.81614	+	8.54717i	0.348289	+	0.436740i	0.924861	−	0.380306i	$-0.124181\pi$
$383$	6.81614	+	8.54717i	0.348289	+	0.436740i	−0.576572	+	0.817046i	$0.695610\pi$
$384$	−0.760453	+	3.33176i	−0.0388067	+	0.170023i
$385$	4.19839	+	2.02184i	0.213970	+	0.103042i
$386$	4.32937	+	2.08491i	0.220359	+	0.106119i
$387$	3.66268	+	16.0472i	0.186184	+	0.815727i
$388$	−13.4315	+	6.46826i	−0.681880	+	0.328376i
$389$	15.6282			0.792380			0.396190	−	0.918169i	$-0.370332\pi$
$389$	15.6282			0.792380			0.396190	+	0.918169i	$0.370332\pi$
$390$	15.8458	−	7.63093i	0.802383	−	0.386407i
$391$	2.85109	+	3.57516i	0.144186	+	0.180804i
$392$	−2.92220	−	3.66432i	−0.147593	−	0.185076i
$393$	−43.8899	+	21.1363i	−2.21395	+	1.06618i
$394$	−15.2225			−0.766899
$395$	−13.4209	+	6.46315i	−0.675277	+	0.325196i
$396$	−3.66268	−	16.0472i	−0.184056	−	0.806404i
$397$	6.90371	+	3.32465i	0.346487	+	0.166859i	0.599031	−	0.800726i	$-0.295553\pi$
$397$	6.90371	+	3.32465i	0.346487	+	0.166859i	−0.252543	+	0.967586i	$0.581267\pi$
$398$	10.9859	+	5.29054i	0.550674	+	0.265191i
$399$	−4.25497	+	18.6422i	−0.213015	+	0.933279i
$400$	−1.49023	−	1.86868i	−0.0745113	−	0.0934342i
$401$	2.93903	−	3.68543i	0.146768	−	0.184042i	−0.703013	−	0.711177i	$-0.748162\pi$
$401$	2.93903	−	3.68543i	0.146768	−	0.184042i	0.849781	+	0.527135i	$0.176734\pi$
$402$	−1.88523	−	8.25975i	−0.0940269	−	0.411959i
$403$	−1.26348	+	5.53566i	−0.0629383	+	0.275751i
$404$	0.114672	−	0.143794i	0.00570512	−	0.00715400i
$405$	65.0840			3.23405
$406$	7.92163	+	2.08067i	0.393144	+	0.103262i
$407$	−13.4090			−0.664658
$408$	−3.62074	+	4.54027i	−0.179253	+	0.224777i
$409$	1.71367	−	7.50807i	0.0847354	−	0.371250i	−0.914726	−	0.404075i	$-0.867593\pi$
$409$	1.71367	−	7.50807i	0.0847354	−	0.371250i	0.999461	+	0.0328253i	$0.0104505\pi$
$410$	1.80914	+	7.92635i	0.0893469	+	0.391454i
$411$	13.7743	−	17.2724i	0.679434	−	0.851984i
$412$	−9.38153	−	11.7641i	−0.462195	−	0.579574i
$413$	0.998471	−	4.37459i	0.0491315	−	0.215259i
$414$	21.0422	+	10.1334i	1.03417	+	0.498029i
$415$	8.03903	+	3.87139i	0.394621	+	0.190039i
$416$	0.708867	+	3.10575i	0.0347551	+	0.152272i
$417$	43.8985	−	21.1404i	2.14972	−	1.03525i
$418$	−6.97723			−0.341268
$419$	23.2064	−	11.1756i	1.13370	−	0.545963i	0.229605	−	0.973284i	$-0.426257\pi$
$419$	23.2064	−	11.1756i	1.13370	−	0.545963i	0.904100	+	0.427321i	$0.140542\pi$
$420$	−5.23531	−	6.56487i	−0.255457	−	0.320333i
$421$	3.59860	+	4.51250i	0.175385	+	0.219926i	0.861752	−	0.507329i	$-0.169367\pi$
$421$	3.59860	+	4.51250i	0.175385	+	0.219926i	−0.686367	+	0.727255i	$0.740796\pi$
$422$	−12.9606	+	6.24151i	−0.630913	+	0.303832i
$423$	22.3104			1.08477
$424$	−7.43213	+	3.57912i	−0.360936	+	0.173818i
$425$	−0.903775	−	3.95970i	−0.0438395	−	0.192074i
$426$	−18.6856	−	8.99852i	−0.905321	−	0.435980i
$427$	−10.6142	−	5.11151i	−0.513655	−	0.247363i
$428$	0.0676476	−	0.296383i	0.00326987	−	0.0143262i
$429$	−12.8732	−	16.1425i	−0.621524	−	0.779366i
$430$	−1.91029	+	2.39543i	−0.0921225	+	0.115518i
$431$	3.64058	+	15.9504i	0.175361	+	0.768305i	0.983733	+	0.179634i	$0.0574914\pi$
$431$	3.64058	+	15.9504i	0.175361	+	0.768305i	−0.808373	+	0.588671i	$0.799651\pi$
$432$	−4.31856	+	18.9208i	−0.207777	+	0.910329i
$433$	15.7575	−	19.7592i	0.757255	−	0.949568i	−0.242533	−	0.970143i	$-0.577978\pi$
$433$	15.7575	−	19.7592i	0.757255	−	0.949568i	0.999788	+	0.0205753i	$0.00654978\pi$
$434$	2.71085			0.130125
$435$	−28.7556	−	7.55286i	−1.37873	−	0.362132i
$436$	9.02387			0.432165
$437$	6.17257	−	7.74016i	0.295274	−	0.370262i
$438$	−2.85028	+	12.4879i	−0.136192	+	0.596694i
$439$	−1.44144	−	6.31536i	−0.0687961	−	0.301415i	0.928811	−	0.370554i	$-0.120832\pi$
$439$	−1.44144	−	6.31536i	−0.0687961	−	0.301415i	−0.997607	+	0.0691384i	$0.977975\pi$
$440$	1.91029	−	2.39543i	0.0910696	−	0.114198i
$441$	−25.3616	−	31.8024i	−1.20769	−	1.51440i
$442$	−1.20457	+	5.27756i	−0.0572955	+	0.251028i
$443$	23.3182	+	11.2295i	1.10788	+	0.533528i	0.896128	−	0.443795i	$-0.146368\pi$
$443$	23.3182	+	11.2295i	1.10788	+	0.533528i	0.211754	+	0.977323i	$0.432082\pi$
$444$	21.7693	+	10.4836i	1.03313	+	0.497528i
$445$	−5.74112	−	25.1535i	−0.272155	−	1.19239i
$446$	11.5189	−	5.54720i	0.545435	−	0.262668i
$447$	−28.1569			−1.33178
$448$	1.37029	−	0.659896i	0.0647401	−	0.0311772i
$449$	5.52744	+	6.93120i	0.260856	+	0.327103i	0.894962	−	0.446143i	$-0.147203\pi$
$449$	5.52744	+	6.93120i	0.260856	+	0.327103i	−0.634105	+	0.773247i	$0.718631\pi$
$450$	−12.9336	−	16.2182i	−0.609694	−	0.764532i
$451$	8.59930	−	4.14120i	0.404925	−	0.195002i
$452$	8.09737			0.380868
$453$	67.7471	−	32.6253i	3.18304	−	1.53287i
$454$	−5.88050	−	25.7641i	−0.275985	−	1.20917i
$455$	−7.05204	−	3.39608i	−0.330605	−	0.159211i
$456$	11.3275	+	5.45502i	0.530457	+	0.255455i
$457$	−4.93294	+	21.6126i	−0.230753	+	1.01100i	0.718263	+	0.695771i	$0.244937\pi$
$457$	−4.93294	+	21.6126i	−0.230753	+	1.01100i	−0.949017	+	0.315225i	$0.897920\pi$
$458$	11.9722	+	15.0127i	0.559426	+	0.701498i
$459$	−20.5619	+	25.7839i	−0.959749	+	1.20349i
$460$	0.967375	+	4.23835i	0.0451041	+	0.197614i
$461$	−8.58503	+	37.6135i	−0.399845	+	1.75183i	0.228159	+	0.973624i	$0.426730\pi$
$461$	−8.58503	+	37.6135i	−0.399845	+	1.75183i	−0.628003	+	0.778211i	$0.716128\pi$
$462$	−6.14603	+	7.70688i	−0.285939	+	0.358557i
$463$	30.1073			1.39921			0.699603	−	0.714531i	$-0.253360\pi$
$463$	30.1073			1.39921			0.699603	+	0.714531i	$0.253360\pi$
$464$	2.49275	−	4.77349i	0.115723	−	0.221604i
$465$	−9.84041			−0.456338
$466$	−5.06503	+	6.35135i	−0.234633	+	0.294220i
$467$	−1.25558	+	5.50105i	−0.0581012	+	0.254558i	−0.995635	−	0.0933375i	$-0.970246\pi$
$467$	−1.25558	+	5.50105i	−0.0581012	+	0.254558i	0.937533	+	0.347895i	$0.113104\pi$
$468$	6.15221	+	26.9546i	0.284386	+	1.24598i
$469$	−2.35085	+	2.94787i	−0.108552	+	0.136120i
$470$	2.58928	+	3.24685i	0.119434	+	0.149766i
$471$	−0.103106	+	0.451736i	−0.00475086	+	0.0208149i
$472$	−2.65810	−	1.28007i	−0.122349	−	0.0589202i
$473$	3.24066	+	1.56062i	0.149006	+	0.0717573i
$474$	−7.01188	−	30.7211i	−0.322066	−	1.41106i
$475$	−7.92235	+	3.81520i	−0.363502	+	0.175053i
$476$	2.58446			0.118458
$477$	−64.5029	+	31.0630i	−2.95339	+	1.42228i
$478$	−18.9004	−	23.7004i	−0.864486	−	1.08403i
$479$	−13.3395	−	16.7271i	−0.609495	−	0.764283i	0.377329	−	0.926079i	$-0.376843\pi$
$479$	−13.3395	−	16.7271i	−0.609495	−	0.764283i	−0.986824	+	0.161797i	$0.948271\pi$
$480$	−4.97416	+	2.39543i	−0.227039	+	0.109336i
$481$	22.5231			1.02696
$482$	−4.12092	+	1.98453i	−0.187703	+	0.0903928i
$483$	−3.11236	−	13.6361i	−0.141617	−	0.620466i
$484$	6.67000	+	3.21210i	0.303182	+	0.146005i
$485$	−21.6987	−	10.4495i	−0.985285	−	0.474488i
$486$	−17.6807	+	77.4642i	−0.802013	+	3.51385i
$487$	7.91124	+	9.92038i	0.358492	+	0.449535i	0.928072	−	0.372401i	$-0.121465\pi$
$487$	7.91124	+	9.92038i	0.358492	+	0.449535i	−0.569580	+	0.821936i	$0.692894\pi$
$488$	−4.82951	+	6.05601i	−0.218622	+	0.274143i
$489$	−7.79736	−	34.1624i	−0.352609	−	1.54488i
$490$	1.68485	−	7.38179i	0.0761136	−	0.333475i
$491$	−7.68443	+	9.63597i	−0.346794	+	0.434865i	−0.924385	−	0.381460i	$-0.875421\pi$
$491$	−7.68443	+	9.63597i	−0.346794	+	0.434865i	0.577592	+	0.816326i	$0.303993\pi$
$492$	−17.1986			−0.775373
$493$	7.33587	−	5.47035i	0.330391	−	0.246372i
$494$	11.7197			0.527293
$495$	16.5793	−	20.7898i	0.745184	−	0.934431i
$496$	0.396619	−	1.73770i	0.0178087	−	0.0780251i
$497$	2.05385	+	8.99852i	0.0921279	+	0.403639i
$498$	−11.7684	+	14.7571i	−0.527353	+	0.661280i
$499$	−2.40764	−	3.01909i	−0.107781	−	0.135153i	0.725015	−	0.688733i	$-0.241833\pi$
$499$	−2.40764	−	3.01909i	−0.107781	−	0.135153i	−0.832796	+	0.553580i	$0.813261\pi$
$500$	2.65664	−	11.6395i	0.118808	−	0.520534i
$501$	−51.6911	−	24.8931i	−2.30939	−	1.11214i
$502$	11.9975	+	5.77769i	0.535474	+	0.257871i
$503$	8.65503	+	37.9202i	0.385909	+	1.69078i	0.678550	+	0.734554i	$0.262609\pi$
$503$	8.65503	+	37.9202i	0.385909	+	1.69078i	−0.292642	+	0.956222i	$0.594534\pi$
$504$	11.8926	−	5.72719i	0.529740	−	0.255109i
$505$	0.297122			0.0132218
$506$	4.59819	−	2.21437i	0.204414	−	0.0984408i
$507$	−6.07651	−	7.61970i	−0.269867	−	0.338403i
$508$	−5.93244	−	7.43904i	−0.263209	−	0.330054i
$509$	29.1230	−	14.0249i	1.29085	−	0.621642i	0.342697	−	0.939446i	$-0.388660\pi$
$509$	29.1230	−	14.0249i	1.29085	−	0.621642i	0.948156	+	0.317804i	$0.102945\pi$
$510$	−9.38161			−0.415425
$511$	5.13603	−	2.47338i	0.227204	−	0.109416i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	64.3279	+	30.9787i	2.84014	+	1.36774i
$514$	−17.5489	−	8.45108i	−0.774047	−	0.372761i
$515$	5.40909	−	23.6988i	0.238353	−	1.04429i
$516$	−4.04103	−	5.06730i	−0.177897	−	0.223075i
$517$	3.03970	−	3.81167i	0.133686	−	0.167637i
$518$	−2.39280	−	10.4836i	−0.105134	−	0.460621i
$519$	−3.15948	+	13.8426i	−0.138686	+	0.607621i
$520$	−3.20872	+	4.02361i	−0.140712	+	0.176447i
$521$	7.79081			0.341321			0.170661	−	0.985330i	$-0.445410\pi$
$521$	7.79081			0.341321			0.170661	+	0.985330i	$0.445410\pi$
$522$	21.6344	−	41.4288i	0.946911	−	1.81329i
$523$	−34.8524			−1.52399			−0.761995	−	0.647582i	$-0.775780\pi$
$523$	−34.8524			−1.52399			−0.761995	+	0.647582i	$0.775780\pi$
$524$	8.88757	−	11.1447i	0.388255	−	0.486857i
$525$	−2.76438	+	12.1115i	−0.120647	+	0.528591i
$526$	−2.23442	−	9.78965i	−0.0974255	−	0.426849i
$527$	1.88842	−	2.36801i	0.0822609	−	0.103152i
$528$	4.04103	+	5.06730i	0.175863	+	0.220526i
$529$	3.50659	−	15.3634i	0.152460	−	0.667972i
$530$	−12.0067	−	5.78210i	−0.521536	−	0.251158i
$531$	−23.0695	−	11.1097i	−1.00113	−	0.482119i
$532$	−1.24507	−	5.45502i	−0.0539807	−	0.236505i
$533$	−14.4443	+	6.95599i	−0.625650	+	0.301297i
$534$	54.5781			2.36182
$535$	0.442486	−	0.213090i	0.0191304	−	0.00921269i
$536$	1.54569	+	1.93823i	0.0667636	+	0.0837189i
$537$	22.5866	+	28.3228i	0.974686	+	1.22222i
$538$	5.34815	−	2.57553i	0.230575	−	0.111039i
$539$	−8.88878			−0.382867
$540$	−28.2479	+	13.6035i	−1.21560	+	0.585401i
$541$	−2.73274	−	11.9729i	−0.117490	−	0.514757i	−0.999086	−	0.0427517i	$-0.986388\pi$
$541$	−2.73274	−	11.9729i	−0.117490	−	0.514757i	0.881596	−	0.472005i	$-0.156470\pi$
$542$	−17.0993	−	8.23458i	−0.734477	−	0.353705i
$543$	−67.0196	−	32.2749i	−2.87609	−	1.38505i
$544$	0.378127	−	1.65668i	0.0162121	−	0.0710297i
$545$	9.08931	+	11.3976i	0.389343	+	0.488221i
$546$	10.3235	−	12.9453i	0.441805	−	0.554006i
$547$	−0.742753	−	3.25421i	−0.0317578	−	0.139140i	0.956564	−	0.291524i	$-0.0941622\pi$
$547$	−0.742753	−	3.25421i	−0.0317578	−	0.139140i	−0.988321	+	0.152384i	$0.951305\pi$
$548$	−1.43850	+	6.30246i	−0.0614495	+	0.269228i
$549$	−41.9150	+	52.5597i	−1.78889	+	2.24319i
$550$	−4.53299			−0.193287
$551$	−15.0804	−	12.8485i	−0.642445	−	0.547364i
$552$	−9.19638			−0.391424
$553$	−8.74367	+	10.9642i	−0.371819	+	0.466246i
$554$	5.74341	−	25.1635i	0.244014	−	1.06909i
$555$	8.68591	+	38.0555i	0.368696	+	1.61536i
$556$	−8.88930	+	11.1468i	−0.376990	+	0.472731i
$557$	5.15315	+	6.46185i	0.218346	+	0.273797i	0.878926	−	0.476959i	$-0.158261\pi$
$557$	5.15315	+	6.46185i	0.218346	+	0.273797i	−0.660580	+	0.750756i	$0.729689\pi$
$558$	3.44223	−	15.0814i	0.145721	−	0.638446i
$559$	−5.44334	−	2.62137i	−0.230229	−	0.110872i
$560$	2.21371	+	1.06607i	0.0935464	+	0.0450496i
$561$	2.45076	+	10.7375i	0.103471	+	0.453337i
$562$	−22.7311	+	10.9467i	−0.958854	+	0.461760i
$563$	16.4004			0.691193			0.345596	−	0.938383i	$-0.387677\pi$
$563$	16.4004			0.691193			0.345596	+	0.938383i	$0.387677\pi$
$564$	−7.91501	+	3.81167i	−0.333282	+	0.160500i
$565$	8.15610	+	10.2274i	0.343130	+	0.430271i
$566$	7.69844	+	9.65354i	0.323590	+	0.405769i
$567$	55.2049	−	26.5853i	2.31839	−	1.11648i
$568$	6.06870			0.254637
$569$	16.8135	−	8.09698i	0.704861	−	0.339443i	−0.0468812	−	0.998900i	$-0.514928\pi$
$569$	16.8135	−	8.09698i	0.704861	−	0.339443i	0.751742	+	0.659457i	$0.229214\pi$
$570$	4.51963	+	19.8018i	0.189306	+	0.829405i
$571$	35.3010	+	17.0001i	1.47730	+	0.711430i	0.987089	−	0.160174i	$-0.0512055\pi$
$571$	35.3010	+	17.0001i	1.47730	+	0.711430i	0.490211	+	0.871604i	$0.336920\pi$
$572$	5.44334	+	2.62137i	0.227597	+	0.109605i
$573$	11.0424	−	48.3801i	0.461304	−	2.02111i
$574$	4.77225	+	5.98421i	0.199190	+	0.249776i
$575$	4.01021	−	5.02865i	0.167237	−	0.209709i
$576$	−1.93124	−	8.46133i	−0.0804685	−	0.352555i
$577$	−1.73944	+	7.62100i	−0.0724140	+	0.317266i	−0.998143	−	0.0609223i	$-0.980596\pi$
$577$	−1.73944	+	7.62100i	−0.0724140	+	0.317266i	0.925729	+	0.378189i	$0.123453\pi$
$578$	−8.79895	+	11.0335i	−0.365988	+	0.458935i
$579$	−16.4216			−0.682459
$580$	8.54000	−	1.65963i	0.354604	−	0.0689125i
$581$	8.40016			0.348497
$582$	31.7647	−	39.8317i	1.31669	−	1.65108i
$583$	−3.48126	+	15.2524i	−0.144179	+	0.631689i
$584$	−0.834038	−	3.65416i	−0.0345127	−	0.151210i
$585$	−27.8483	+	34.9206i	−1.15138	+	1.44379i
$586$	7.69959	+	9.65498i	0.318067	+	0.398844i
$587$	1.70127	−	7.45375i	0.0702189	−	0.307649i	−0.927607	−	0.373558i	$-0.878138\pi$
$587$	1.70127	−	7.45375i	0.0702189	−	0.307649i	0.997826	+	0.0659091i	$0.0209947\pi$
$588$	14.4308	+	6.94953i	0.595118	+	0.286594i
$589$	−5.90791	−	2.84510i	−0.243431	−	0.117230i
$590$	−1.06058	−	4.64669i	−0.0436632	−	0.191301i
$591$	46.8703	−	22.5715i	1.92799	−	0.928469i
$592$	−7.07024			−0.290585
$593$	−8.78740	+	4.23179i	−0.360855	+	0.173779i	−0.605522	−	0.795828i	$-0.707036\pi$
$593$	−8.78740	+	4.23179i	−0.360855	+	0.173779i	0.244667	+	0.969607i	$0.421321\pi$
$594$	22.9487	+	28.7768i	0.941599	+	1.18073i
$595$	2.60320	+	3.26431i	0.106721	+	0.133824i
$596$	7.42324	−	3.57484i	0.304068	−	0.146431i
$597$	−41.6704			−1.70546
$598$	−7.72359	+	3.71948i	−0.315841	+	0.152101i
$599$	4.77068	+	20.9017i	0.194925	+	0.854022i	0.973902	+	0.226969i	$0.0728817\pi$
$599$	4.77068	+	20.9017i	0.194925	+	0.854022i	−0.778977	+	0.627052i	$0.784261\pi$
$600$	7.35926	+	3.54403i	0.300440	+	0.144685i
$601$	−24.6258	−	11.8592i	−1.00451	−	0.483745i	−0.142041	−	0.989861i	$-0.545367\pi$
$601$	−24.6258	−	11.8592i	−1.00451	−	0.483745i	−0.862465	+	0.506116i	$0.831081\pi$
$602$	−0.641852	+	2.81214i	−0.0261599	+	0.114614i
$603$	13.4149	+	16.8218i	0.546298	+	0.685036i
$604$	−13.7186	+	17.2026i	−0.558201	+	0.699962i
$605$	2.66131	+	11.6600i	0.108198	+	0.474045i
$606$	−0.139862	+	0.612774i	−0.00568149	+	0.0248922i
$607$	20.7591	−	26.0310i	0.842584	−	1.05657i	−0.155056	−	0.987906i	$-0.549556\pi$
$607$	20.7591	−	26.0310i	0.842584	−	1.05657i	0.997640	−	0.0686611i	$-0.0218727\pi$
$608$	−3.67893			−0.149200
$609$	−27.4760	+	5.33958i	−1.11338	+	0.216371i
$610$	−12.5136			−0.506661
$611$	−5.10580	+	6.40247i	−0.206558	+	0.259016i
$612$	3.28174	−	14.3782i	0.132656	−	0.581206i
$613$	−6.67444	−	29.2426i	−0.269578	−	1.18110i	−0.910506	−	0.413497i	$-0.864307\pi$
$613$	−6.67444	−	29.2426i	−0.269578	−	1.18110i	0.640928	−	0.767601i	$-0.278550\pi$
$614$	7.38031	−	9.25462i	0.297845	−	0.373486i
$615$	−17.3233	−	21.7228i	−0.698544	−	0.875946i
$616$	0.641852	−	2.81214i	0.0258610	−	0.113304i
$617$	17.1426	+	8.25544i	0.690135	+	0.332352i	0.745868	−	0.666094i	$-0.232035\pi$
$617$	17.1426	+	8.25544i	0.690135	+	0.332352i	−0.0557324	+	0.998446i	$0.517749\pi$
$618$	46.3293	+	22.3110i	1.86364	+	0.897480i
$619$	9.12639	+	39.9853i	0.366820	+	1.60715i	0.735457	+	0.677572i	$0.236968\pi$
$619$	9.12639	+	39.9853i	0.366820	+	1.60715i	−0.368636	+	0.929574i	$0.620175\pi$
$620$	2.59431	−	1.24935i	0.104190	−	0.0501752i
$621$	−52.2256			−2.09574
$622$	9.16959	−	4.41584i	0.367667	−	0.177059i
$623$	−15.1443	−	18.9903i	−0.606742	−	0.760831i
$624$	−6.78773	−	8.51155i	−0.271727	−	0.340735i
$625$	6.61001	−	3.18321i	0.264400	−	0.127329i
$626$	−13.3421			−0.533259
$627$	21.4830	−	10.3457i	0.857947	−	0.413166i
$628$	−0.0301704	−	0.132185i	−0.00120393	−	0.00527476i
$629$	−10.8246	−	5.21284i	−0.431604	−	0.207849i
$630$	19.2126	+	9.25232i	0.765450	+	0.368621i
$631$	−6.01242	+	26.3421i	−0.239350	+	1.04866i	0.702250	+	0.711931i	$0.252179\pi$
$631$	−6.01242	+	26.3421i	−0.239350	+	1.04866i	−0.941600	+	0.336732i	$0.890678\pi$
$632$	5.74899	+	7.20900i	0.228682	+	0.286759i
$633$	30.6512	−	38.4353i	1.21827	−	1.52767i
$634$	2.66450	+	11.6739i	0.105821	+	0.463631i
$635$	3.42045	−	14.9860i	0.135737	−	0.594701i
$636$	17.5766	−	22.0403i	0.696957	−	0.873956i
$637$	14.9305			0.591568
$638$	−4.13040	−	9.34070i	−0.163524	−	0.369802i
$639$	52.6699			2.08359
$640$	1.00725	−	1.26305i	0.0398151	−	0.0499266i
$641$	−6.88451	+	30.1630i	−0.271922	+	1.19137i	0.635820	+	0.771837i	$0.280662\pi$
$641$	−6.88451	+	30.1630i	−0.271922	+	1.19137i	−0.907742	+	0.419529i	$0.862195\pi$
$642$	0.231182	+	1.01287i	0.00912402	+	0.0399749i
$643$	−1.31321	+	1.64672i	−0.0517881	+	0.0649403i	−0.807051	−	0.590482i	$-0.798938\pi$
$643$	−1.31321	+	1.64672i	−0.0517881	+	0.0649403i	0.755263	+	0.655422i	$0.227509\pi$
$644$	2.55180	+	3.19986i	0.100555	+	0.126092i
$645$	2.32993	−	10.2081i	0.0917409	−	0.401943i
$646$	−5.63246	−	2.71245i	−0.221606	−	0.106720i
$647$	14.0227	+	6.75299i	0.551291	+	0.265488i	0.688724	−	0.725023i	$-0.258171\pi$
$647$	14.0227	+	6.75299i	0.551291	+	0.265488i	−0.137434	+	0.990511i	$0.543885\pi$
$648$	−8.96470	−	39.2769i	−0.352167	−	1.54294i
$649$	−5.04120	+	2.42771i	−0.197884	+	0.0952960i
$650$	7.61407			0.298648
$651$	−8.34673	+	4.01957i	−0.327134	+	0.157540i
$652$	6.39299	+	8.01656i	0.250369	+	0.313953i
$653$	−28.0153	−	35.1301i	−1.09633	−	1.37475i	−0.920691	−	0.390293i	$-0.872374\pi$
$653$	−28.0153	−	35.1301i	−1.09633	−	1.37475i	−0.175634	−	0.984455i	$-0.556198\pi$
$654$	−27.7846	+	13.3804i	−1.08646	+	0.523213i
$655$	23.0283			0.899792
$656$	4.53421	−	2.18356i	0.177031	−	0.0852537i
$657$	−7.23856	−	31.7142i	−0.282403	−	1.23729i
$658$	3.52251	+	1.69635i	0.137322	+	0.0661307i
$659$	−7.73847	−	3.72665i	−0.301448	−	0.145170i	0.277045	−	0.960857i	$-0.410645\pi$
$659$	−7.73847	−	3.72665i	−0.301448	−	0.145170i	−0.578493	+	0.815687i	$0.696359\pi$
$660$	−2.32993	+	10.2081i	−0.0906924	+	0.397349i
$661$	−1.97142	−	2.47208i	−0.0766794	−	0.0961529i	0.742012	−	0.670386i	$-0.233872\pi$
$661$	−1.97142	−	2.47208i	−0.0766794	−	0.0961529i	−0.818692	+	0.574233i	$0.805300\pi$
$662$	−14.5867	+	18.2911i	−0.566927	+	0.710903i
$663$	−4.11655	−	18.0358i	−0.159873	−	0.700451i
$664$	1.22901	−	5.38465i	0.0476949	−	0.208965i
$665$	5.63588	−	7.06717i	0.218550	−	0.274053i
$666$	−61.3621			−2.37773
$667$	14.0161	+	3.68143i	0.542706	+	0.142546i
$668$	16.7882			0.649555
$669$	−27.2415	+	34.1598i	−1.05322	+	1.32069i
$670$	−0.891195	+	3.90458i	−0.0344299	+	0.150847i
$671$	3.26894	+	14.3221i	0.126196	+	0.552900i
$672$	−3.24066	+	4.06366i	−0.125011	+	0.156759i
$673$	10.9959	+	13.7885i	0.423862	+	0.531506i	0.947210	−	0.320613i	$-0.103889\pi$
$673$	10.9959	+	13.7885i	0.423862	+	0.531506i	−0.523349	+	0.852119i	$0.675317\pi$
$674$	−5.08572	+	22.2820i	−0.195895	+	0.858270i
$675$	41.7927	+	20.1263i	1.60860	+	0.774662i
$676$	2.56941	+	1.23736i	0.0988233	+	0.0475908i
$677$	0.959235	+	4.20268i	0.0368664	+	0.161522i	0.990010	−	0.140995i	$-0.0450302\pi$
$677$	0.959235	+	4.20268i	0.0368664	+	0.161522i	−0.953144	+	0.302517i	$0.902173\pi$
$678$	−24.9319	+	12.0066i	−0.957504	+	0.461110i
$679$	−22.6734			−0.870125
$680$	2.47335	−	1.19110i	0.0948486	−	0.0456767i
$681$	56.3085	+	70.6087i	2.15775	+	2.70573i
$682$	−2.10763	−	2.64288i	−0.0807052	−	0.101201i
$683$	−35.8251	+	17.2525i	−1.37081	+	0.660148i	−0.967019	−	0.254703i	$-0.918022\pi$
$683$	−35.8251	+	17.2525i	−1.37081	+	0.660148i	−0.403791	+	0.914851i	$0.632308\pi$
$684$	−31.9292			−1.22084
$685$	−9.40928	+	4.53127i	−0.359510	+	0.173131i
$686$	−3.95522	−	17.3289i	−0.151011	−	0.661622i
$687$	−59.1231	−	28.4722i	−2.25569	−	1.08628i
$688$	1.70872	+	0.822877i	0.0651444	+	0.0313719i
$689$	5.84747	−	25.6195i	0.222771	−	0.976024i
$690$	−9.26307	−	11.6155i	−0.352639	−	0.442195i
$691$	−11.5115	+	14.4349i	−0.437916	+	0.549130i	−0.950993	−	0.309213i	$-0.899934\pi$
$691$	−11.5115	+	14.4349i	−0.437916	+	0.549130i	0.513076	+	0.858343i	$0.328506\pi$
$692$	−0.924514	−	4.05056i	−0.0351448	−	0.153979i
$693$	5.57059	−	24.4063i	0.211609	−	0.927120i
$694$	4.04132	−	5.06765i	0.153406	−	0.192365i
$695$	−23.0328			−0.873684
$696$	−0.597193	+	18.3938i	−0.0226365	+	0.697216i
$697$	8.55182			0.323923
$698$	−7.34687	+	9.21268i	−0.278083	+	0.348705i
$699$	6.17767	−	27.0662i	0.233661	−	1.02374i
$700$	−0.808902	−	3.54403i	−0.0305736	−	0.133952i
$701$	12.1339	−	15.2154i	0.458291	−	0.574679i	−0.497970	−	0.867195i	$-0.665921\pi$
$701$	12.1339	−	15.2154i	0.458291	−	0.574679i	0.956261	+	0.292515i	$0.0944923\pi$
$702$	−38.5471	−	48.3365i	−1.45486	−	1.82434i
$703$	−5.78797	+	25.3588i	−0.218297	+	0.956423i
$704$	−1.70872	−	0.822877i	−0.0643999	−	0.0310134i
$705$	−12.7868	−	6.15778i	−0.481577	−	0.231915i
$706$	4.25433	+	18.6394i	0.160114	+	0.701504i
$707$	0.252022	−	0.121367i	0.00947826	−	0.00456449i
$708$	10.0824			0.378919
$709$	−5.96289	+	2.87158i	−0.223941	+	0.107844i	−0.542491	−	0.840062i	$-0.682519\pi$
$709$	−5.96289	+	2.87158i	−0.223941	+	0.107844i	0.318549	+	0.947906i	$0.396804\pi$
$710$	6.11272	+	7.66510i	0.229406	+	0.287666i
$711$	49.8951	+	62.5664i	1.87121	+	2.34642i
$712$	−14.3889	+	6.92931i	−0.539245	+	0.259687i
$713$	4.79643			0.179628
$714$	−7.95757	+	3.83216i	−0.297805	+	0.143415i
$715$	2.17188	+	9.51562i	0.0812236	+	0.355864i
$716$	−9.55060	−	4.59933i	−0.356923	−	0.171885i
$717$	93.3370	+	44.9487i	3.48573	+	1.67864i
$718$	1.84487	−	8.08289i	0.0688498	−	0.301651i
$719$	−11.3027	−	14.1732i	−0.421521	−	0.528571i	0.525047	−	0.851073i	$-0.324048\pi$
$719$	−11.3027	−	14.1732i	−0.421521	−	0.528571i	−0.946569	+	0.322502i	$0.895476\pi$
$720$	8.74187	−	10.9620i	0.325790	−	0.408528i
$721$	−5.09234	−	22.3110i	−0.189649	−	0.830905i
$722$	1.21618	−	5.32845i	0.0452617	−	0.198304i
$723$	9.74574	−	12.2208i	0.362448	−	0.454496i
$724$	21.7666			0.808949
$725$	−9.79746	−	8.34744i	−0.363868	−	0.310016i
$726$	−25.2998			−0.938965
$727$	−8.87894	+	11.1338i	−0.329302	+	0.412931i	−0.918728	−	0.394891i	$-0.870782\pi$
$727$	−8.87894	+	11.1338i	−0.329302	+	0.412931i	0.589426	+	0.807822i	$0.299354\pi$
$728$	−1.07812	+	4.72355i	−0.0399578	+	0.175067i
$729$	−33.5287	−	146.899i	−1.24180	−	5.44070i
$730$	3.77532	−	4.73410i	0.139731	−	0.175217i
$731$	2.00936	+	2.51966i	0.0743189	+	0.0931929i
$732$	5.89042	−	25.8076i	0.217716	−	0.953877i
$733$	−17.0908	−	8.23048i	−0.631262	−	0.304000i	0.0907571	−	0.995873i	$-0.471071\pi$
$733$	−17.0908	−	8.23048i	−0.631262	−	0.304000i	−0.722019	+	0.691873i	$0.756786\pi$
$734$	−26.0033	−	12.5225i	−0.959801	−	0.462216i
$735$	5.75787	+	25.2269i	0.212382	+	0.930507i
$736$	2.42452	−	1.16759i	0.0893689	−	0.0430378i
$737$	4.70170			0.173189
$738$	39.3521	−	18.9510i	1.44857	−	0.697594i
$739$	−27.5316	−	34.5236i	−1.01277	−	1.26997i	−0.962514	−	0.271233i	$-0.912569\pi$
$739$	−27.5316	−	34.5236i	−1.01277	−	1.26997i	−0.0502534	−	0.998737i	$-0.516003\pi$
$740$	−7.12151	−	8.93009i	−0.261792	−	0.328277i
$741$	−36.0850	+	17.3776i	−1.32562	+	0.638383i
$742$	−12.5460			−0.460579
$743$	−29.1694	+	14.0473i	−1.07012	+	0.515344i	−0.884146	−	0.467210i	$-0.845259\pi$
$743$	−29.1694	+	14.0473i	−1.07012	+	0.515344i	−0.185977	+	0.982554i	$0.559545\pi$
$744$	1.35542	+	5.93850i	0.0496922	+	0.217716i
$745$	11.9923	+	5.77518i	0.439363	+	0.211586i
$746$	20.1538	+	9.70558i	0.737885	+	0.355347i
$747$	10.6665	−	46.7330i	0.390267	−	1.70987i
$748$	−2.00936	−	2.51966i	−0.0734695	−	0.0921278i
$749$	0.288279	−	0.361490i	0.0105335	−	0.0132086i
$750$	9.07891	+	39.7773i	0.331515	+	1.45246i
$751$	6.02269	−	26.3871i	0.219771	−	0.962881i	−0.737876	−	0.674936i	$-0.764171\pi$
$751$	6.02269	−	26.3871i	0.219771	−	0.962881i	0.957647	−	0.287944i	$-0.0929718\pi$
$752$	1.60276	−	2.00980i	0.0584468	−	0.0732900i
$753$	−45.5074			−1.65838
$754$	6.93784	+	15.6896i	0.252661	+	0.571381i
$755$	−35.5458			−1.29364
$756$	−18.4035	+	23.0772i	−0.669328	+	0.839310i
$757$	11.1140	−	48.6936i	0.403945	−	1.76980i	−0.207217	−	0.978295i	$-0.566441\pi$
$757$	11.1140	−	48.6936i	0.403945	−	1.76980i	0.611162	−	0.791505i	$-0.290702\pi$
$758$	3.31439	+	14.5213i	0.120384	+	0.527437i
$759$	−10.8745	+	13.6361i	−0.394718	+	0.494961i
$760$	−3.70561	−	4.64669i	−0.134417	−	0.168553i
$761$	1.94753	−	8.53268i	0.0705979	−	0.309309i	−0.927284	−	0.374358i	$-0.877863\pi$
$761$	1.94753	−	8.53268i	0.0705979	−	0.309309i	0.997882	+	0.0650486i	$0.0207202\pi$
$762$	29.2965	+	14.1084i	1.06130	+	0.511094i
$763$	12.3653	+	5.95482i	0.447654	+	0.215579i
$764$	3.23120	+	14.1568i	0.116901	+	0.512175i
$765$	21.4660	−	10.3375i	0.776106	−	0.373753i
$766$	10.9322			0.394998
$767$	8.46771	−	4.07783i	0.305751	−	0.147242i
$768$	2.13074	+	2.67187i	0.0768865	+	0.0964127i
$769$	13.7625	+	17.2576i	0.496287	+	0.622325i	0.965387	−	0.260820i	$-0.0839931\pi$
$769$	13.7625	+	17.2576i	0.496287	+	0.622325i	−0.469100	+	0.883145i	$0.655422\pi$
$770$	4.19839	−	2.02184i	0.151299	−	0.0728620i
$771$	66.5642			2.39725
$772$	4.32937	−	2.08491i	0.155817	−	0.0750376i
$773$	−2.56666	−	11.2453i	−0.0923162	−	0.404464i	0.907564	−	0.419913i	$-0.137939\pi$
$773$	−2.56666	−	11.2453i	−0.0923162	−	0.404464i	−0.999881	+	0.0154490i	$0.995082\pi$
$774$	14.8299	+	7.14169i	0.533049	+	0.256703i
$775$	−3.83827	−	1.84841i	−0.137875	−	0.0663969i
$776$	−3.31730	+	14.5341i	−0.119084	+	0.521742i
$777$	22.9122	+	28.7310i	0.821971	+	1.03072i
$778$	9.74401	−	12.2186i	0.349340	−	0.438058i
$779$	−4.11987	−	18.0503i	−0.147610	−	0.646721i
$780$	3.91359	−	17.1466i	0.140129	−	0.613945i
$781$	7.17608	−	8.99852i	0.256780	−	0.321992i
$782$	4.57280			0.163523
$783$	−3.39142	+	104.457i	−0.121199	+	3.73299i
$784$	−4.68684			−0.167387
$785$	0.136568	−	0.171251i	0.00487432	−	0.00611220i
$786$	−10.8399	+	47.4928i	−0.386647	+	1.69401i
$787$	−1.09728	−	4.80749i	−0.0391137	−	0.171368i	0.951598	−	0.307344i	$-0.0994402\pi$
$787$	−1.09728	−	4.80749i	−0.0391137	−	0.171368i	−0.990712	+	0.135976i	$0.956583\pi$
$788$	−9.49108	+	11.9014i	−0.338106	+	0.423971i
$789$	21.3956	+	26.8293i	0.761705	+	0.955148i
$790$	−3.31468	+	14.5226i	−0.117931	+	0.516690i
$791$	11.0957	+	5.34343i	0.394519	+	0.189990i
$792$	−14.8299	−	7.14169i	−0.526957	−	0.253769i
$793$	−5.49084	−	24.0569i	−0.194985	−	0.854287i
$794$	6.90371	−	3.32465i	0.245003	−	0.117987i
$795$	45.5422			1.61521
$796$	10.9859	−	5.29054i	0.389385	−	0.187518i
$797$	14.5094	+	18.1942i	0.513950	+	0.644473i	0.969312	−	0.245833i	$-0.0790616\pi$
$797$	14.5094	+	18.1942i	0.513950	+	0.644473i	−0.455362	+	0.890306i	$0.650490\pi$
$798$	11.9222	+	14.9499i	0.422040	+	0.529221i
$799$	3.93565	−	1.89531i	0.139233	−	0.0670513i
$800$	−2.39014			−0.0845041
$801$	−124.880	+	60.1390i	−4.41241	+	2.12491i
$802$	−1.04893	−	4.59566i	−0.0370389	−	0.162278i
$803$	−6.40452	−	3.08425i	−0.226011	−	0.108841i
$804$	−7.63316	−	3.67594i	−0.269201	−	0.129640i
$805$	−1.47129	+	6.44613i	−0.0518561	+	0.227196i
$806$	3.54019	+	4.43925i	0.124698	+	0.156366i
$807$	−12.6481	+	15.8602i	−0.445234	+	0.558305i
$808$	−0.0409258	−	0.179308i	−0.00143976	−	0.00630802i
$809$	7.86490	−	34.4584i	0.276515	−	1.21149i	−0.625651	−	0.780103i	$-0.715167\pi$
$809$	7.86490	−	34.4584i	0.276515	−	1.21149i	0.902166	−	0.431389i	$-0.141976\pi$
$810$	40.5792	−	50.8847i	1.42581	−	1.78791i
$811$	−9.47070			−0.332561			−0.166281	−	0.986078i	$-0.553176\pi$
$811$	−9.47070			−0.332561			−0.166281	+	0.986078i	$0.553176\pi$
$812$	6.56579	−	4.89611i	0.230414	−	0.171820i
$813$	64.8589			2.27470
$814$	−8.36036	+	10.4836i	−0.293031	+	0.367449i
$815$	−3.68599	+	16.1494i	−0.129115	+	0.565689i
$816$	1.29223	+	5.66162i	0.0452370	+	0.198196i
$817$	4.35023	−	5.45502i	0.152195	−	0.190847i
$818$	−4.80159	−	6.02100i	−0.167884	−	0.210519i
$819$	−9.35693	+	40.9954i	−0.326958	+	1.43249i
$820$	7.32504	+	3.52756i	0.255802	+	0.123188i
$821$	−26.5108	−	12.7669i	−0.925234	−	0.445569i	−0.0902971	−	0.995915i	$-0.528782\pi$
$821$	−26.5108	−	12.7669i	−0.925234	−	0.445569i	−0.834937	+	0.550346i	$0.814496\pi$
$822$	−4.91598	−	21.5383i	−0.171464	−	0.751235i
$823$	−26.5320	+	12.7772i	−0.924849	+	0.445384i	−0.834800	−	0.550553i	$-0.814417\pi$
$823$	−26.5320	+	12.7772i	−0.924849	+	0.445384i	−0.0900492	+	0.995937i	$0.528702\pi$
$824$	−15.0468			−0.524180
$825$	13.9571	−	6.72139i	0.485925	−	0.234009i
$826$	−2.79765	−	3.50815i	−0.0973428	−	0.122064i
$827$	−9.42602	−	11.8199i	−0.327775	−	0.411017i	0.590451	−	0.807073i	$-0.298950\pi$
$827$	−9.42602	−	11.8199i	−0.327775	−	0.411017i	−0.918226	+	0.396057i	$0.870378\pi$
$828$	21.0422	−	10.1334i	0.731267	−	0.352160i
$829$	44.2208			1.53585			0.767925	−	0.640539i	$-0.221289\pi$
$829$	44.2208			1.53585			0.767925	+	0.640539i	$0.221289\pi$
$830$	8.03903	−	3.87139i	0.279039	−	0.134378i
$831$	19.6278	+	85.9949i	0.680880	+	2.98313i
$832$	2.87014	+	1.38219i	0.0995043	+	0.0479188i
$833$	−7.17558	−	3.45558i	−0.248619	−	0.119729i
$834$	10.8420	−	47.5020i	0.375429	−	1.64486i
$835$	16.9100	+	21.2044i	0.585193	+	0.733809i
$836$	−4.35023	+	5.45502i	−0.150456	+	0.188666i
$837$	7.69735	+	33.7243i	0.266060	+	1.16568i
$838$	5.73150	−	25.1113i	0.197991	−	0.867456i
$839$	2.97931	−	3.73593i	0.102857	−	0.128979i	−0.727739	−	0.685854i	$-0.759429\pi$
$839$	2.97931	−	3.73593i	0.102857	−	0.128979i	0.830596	+	0.556876i	$0.188000\pi$
$840$	−8.39678			−0.289716
$841$	8.27346	−	27.7948i	0.285292	−	0.958441i
$842$	5.77170			0.198906
$843$	53.7578	−	67.4102i	1.85152	−	2.32173i
$844$	−3.20101	+	14.0245i	−0.110183	+	0.482744i
$845$	1.02519	+	4.49164i	0.0352675	+	0.154517i
$846$	13.9103	−	17.4429i	0.478245	−	0.599700i
$847$	7.02017	+	8.80302i	0.241216	+	0.302475i
$848$	−1.83558	+	8.04222i	−0.0630342	+	0.276171i
$849$	−38.0176	−	18.3083i	−1.30476	−	0.628340i
$850$	−3.65931	−	1.76223i	−0.125513	−	0.0604441i
$851$	−4.23370	−	18.5491i	−0.145129	−	0.635854i
$852$	−18.6856	+	8.99852i	−0.640158	+	0.308284i
$853$	7.44372			0.254868			0.127434	−	0.991847i	$-0.459326\pi$
$853$	7.44372			0.254868			0.127434	+	0.991847i	$0.459326\pi$
$854$	−10.6142	+	5.11151i	−0.363209	+	0.174912i
$855$	−32.1607	−	40.3283i	−1.09987	−	1.37920i
$856$	−0.189544	−	0.237681i	−0.00647849	−	0.00812377i
$857$	−11.4490	+	5.51356i	−0.391092	+	0.188340i	−0.619087	−	0.785322i	$-0.712497\pi$
$857$	−11.4490	+	5.51356i	−0.391092	+	0.188340i	0.227995	+	0.973662i	$0.426783\pi$
$858$	−20.6470			−0.704877
$859$	−15.5600	+	7.49332i	−0.530902	+	0.255669i	−0.680075	−	0.733142i	$-0.738053\pi$
$859$	−15.5600	+	7.49332i	−0.530902	+	0.255669i	0.149174	+	0.988811i	$0.452339\pi$
$860$	0.681776	+	2.98705i	0.0232484	+	0.101858i
$861$	−23.5671	−	11.3493i	−0.803163	−	0.386783i
$862$	14.7404	+	7.09861i	0.502060	+	0.241780i
$863$	8.10854	−	35.5258i	0.276018	−	1.20931i	−0.626762	−	0.779211i	$-0.715620\pi$
$863$	8.10854	−	35.5258i	0.276018	−	1.20931i	0.902780	−	0.430103i	$-0.141523\pi$
$864$	12.1003	+	15.1733i	0.411662	+	0.516207i
$865$	4.18486	−	5.24765i	0.142290	−	0.178425i
$866$	−5.62377	−	24.6394i	−0.191104	−	0.837279i
$867$	10.7318	−	47.0192i	0.364472	−	1.59686i
$868$	1.69019	−	2.11943i	0.0573686	−	0.0719380i
$869$	17.4873			0.593217
$870$	−23.8339	+	17.7729i	−0.808045	+	0.602558i
$871$	−7.89745			−0.267595
$872$	5.62629	−	7.05515i	0.190530	−	0.238917i
$873$	−28.7906	+	126.140i	−0.974415	+	4.26919i
$874$	−2.20296	−	9.65182i	−0.0745164	−	0.326478i
$875$	11.3212	−	14.1964i	0.382727	−	0.479924i
$876$	7.98630	+	10.0145i	0.269832	+	0.338359i
$877$	−1.92576	+	8.43729i	−0.0650282	+	0.284907i	−0.996978	−	0.0776791i	$-0.975249\pi$
$877$	−1.92576	+	8.43729i	−0.0650282	+	0.284907i	0.931950	+	0.362586i	$0.118106\pi$
$878$	−5.83627	−	2.81060i	−0.196964	−	0.0948531i
$879$	−38.0233	−	18.3110i	−1.28249	−	0.617616i
$880$	−0.681776	−	2.98705i	−0.0229827	−	0.100694i
$881$	−6.87863	+	3.31257i	−0.231747	+	0.111603i	−0.546154	−	0.837685i	$-0.683909\pi$
$881$	−6.87863	+	3.31257i	−0.231747	+	0.111603i	0.314407	+	0.949288i	$0.398194\pi$
$882$	−40.6768			−1.36966
$883$	0.556272	−	0.267887i	0.0187201	−	0.00901510i	−0.424500	−	0.905428i	$-0.639550\pi$
$883$	0.556272	−	0.267887i	0.0187201	−	0.00901510i	0.443220	+	0.896413i	$0.353836\pi$
$884$	3.37513	+	4.23228i	0.113518	+	0.142347i
$885$	10.1555	+	12.7346i	0.341374	+	0.428069i
$886$	23.3182	−	11.2295i	0.783391	−	0.377261i
$887$	−20.0952			−0.674732			−0.337366	−	0.941374i	$-0.609536\pi$
$887$	−20.0952			−0.674732			−0.337366	+	0.941374i	$0.609536\pi$
$888$	21.7693	−	10.4836i	0.730531	−	0.351805i
$889$	−3.22016	−	14.1084i	−0.108001	−	0.473182i
$890$	−23.2453	−	11.1944i	−0.779185	−	0.375235i
$891$	−68.8393	−	33.1513i	−2.30620	−	1.11061i
$892$	2.84493	−	12.4645i	0.0952553	−	0.417341i
$893$	−5.89646	−	7.39392i	−0.197317	−	0.247428i
$894$	−17.5555	+	22.0140i	−0.587145	+	0.736257i
$895$	−3.81066	−	16.6956i	−0.127376	−	0.558073i
$896$	0.338433	−	1.48277i	0.0113063	−	0.0495360i
$897$	18.2659	−	22.9047i	0.609879	−	0.764765i
$898$	8.86533			0.295840
$899$	0.311470	−	9.59341i	0.0103881	−	0.319958i
$900$	−20.7438			−0.691461
$901$	−8.73976	+	10.9593i	−0.291164	+	0.365108i
$902$	2.12385	−	9.30520i	0.0707165	−	0.309829i
$903$	−2.19349	−	9.61033i	−0.0729949	−	0.319812i
$904$	5.04863	−	6.33078i	0.167915	−	0.210559i
$905$	21.9245	+	27.4924i	0.728794	+	0.913878i
$906$	16.7322	−	73.3084i	0.555889	−	2.43551i
$907$	−0.161465	−	0.0777573i	−0.00536135	−	0.00258189i	0.431201	−	0.902256i	$-0.358090\pi$
$907$	−0.161465	−	0.0777573i	−0.00536135	−	0.00258189i	−0.436562	+	0.899674i	$0.643804\pi$
$908$	−23.8097	−	11.4661i	−0.790151	−	0.380517i
$909$	−0.355192	−	1.55620i	−0.0117810	−	0.0516158i
$910$	−7.05204	+	3.39608i	−0.233773	+	0.112579i
$911$	43.3911			1.43761			0.718806	−	0.695211i	$-0.244689\pi$
$911$	43.3911			1.43761			0.718806	+	0.695211i	$0.244689\pi$
$912$	11.3275	−	5.45502i	0.375090	−	0.180634i
$913$	−6.53095	−	8.18955i	−0.216143	−	0.271035i
$914$	13.8218	+	17.3320i	0.457185	+	0.573291i
$915$	38.5295	−	18.5548i	1.27375	−	0.613404i
$916$	19.2020			0.634452
$917$	19.5329	−	9.40653i	0.645032	−	0.310631i
$918$	7.33847	+	32.1519i	0.242206	+	1.06117i
$919$	16.9880	+	8.18100i	0.560383	+	0.269866i	0.692561	−	0.721360i	$-0.256483\pi$
$919$	16.9880	+	8.18100i	0.560383	+	0.269866i	−0.132177	+	0.991226i	$0.542197\pi$
$920$	3.91682	+	1.88624i	0.129134	+	0.0621876i
$921$	−9.00156	+	39.4384i	−0.296611	+	1.29954i
$922$	24.0547	+	30.1637i	0.792200	+	0.993388i
$923$	−12.0537	+	15.1148i	−0.396751	+	0.497511i
$924$	2.19349	+	9.61033i	0.0721607	+	0.316157i
$925$	−3.76034	+	16.4751i	−0.123639	+	0.541700i
$926$	18.7716	−	23.5389i	0.616874	−	0.773535i
$927$	−130.590			−4.28914
$928$	−2.17786	−	4.92513i	−0.0714918	−	0.161675i
$929$	44.1780			1.44943			0.724717	−	0.689047i	$-0.241970\pi$
$929$	44.1780			1.44943			0.724717	+	0.689047i	$0.241970\pi$
$930$	−6.13539	+	7.69354i	−0.201187	+	0.252281i
$931$	−3.83683	+	16.8103i	−0.125747	+	0.550934i
$932$	1.80769	+	7.92000i	0.0592128	+	0.259428i
$933$	−21.6856	+	27.1929i	−0.709954	+	0.890254i
$934$	3.51805	+	4.41150i	0.115114	+	0.144349i
$935$	1.15853	−	5.07586i	0.0378881	−	0.165998i
$936$	24.9098	+	11.9959i	0.814202	+	0.392099i
$937$	−47.4638	−	22.8573i	−1.55057	−	0.746717i	−0.554247	−	0.832352i	$-0.686994\pi$
$937$	−47.4638	−	22.8573i	−1.55057	−	0.746717i	−0.996327	+	0.0856358i	$0.972708\pi$
$938$	0.839008	+	3.67594i	0.0273946	+	0.120024i
$939$	41.0806	−	19.7834i	1.34061	−	0.645606i
$940$	4.15288			0.135452
$941$	−19.7537	+	9.51288i	−0.643952	+	0.310111i	−0.727208	−	0.686417i	$-0.759182\pi$
$941$	−19.7537	+	9.51288i	−0.643952	+	0.310111i	0.0832559	+	0.996528i	$0.473468\pi$
$942$	0.288896	+	0.362264i	0.00941273	+	0.0118032i
$943$	8.44377	+	10.5882i	0.274967	+	0.344798i
$944$	−2.65810	+	1.28007i	−0.0865139	+	0.0416629i
$945$	−47.6847			−1.55118
$946$	3.24066	−	1.56062i	0.105363	−	0.0507401i
$947$	−1.47868	−	6.47853i	−0.0480507	−	0.210524i	0.945203	−	0.326482i	$-0.105863\pi$
$947$	−1.47868	−	6.47853i	−0.0480507	−	0.210524i	−0.993254	+	0.115958i	$0.963006\pi$
$948$	−28.3905	−	13.6722i	−0.922081	−	0.444051i
$949$	10.7577	+	5.18063i	0.349209	+	0.168170i
$950$	−1.95666	+	8.57268i	−0.0634824	+	0.278135i
$951$	−25.5138	−	31.9933i	−0.827341	−	1.03745i
$952$	1.61138	−	2.02061i	0.0522252	−	0.0654883i
$953$	−0.663211	−	2.90572i	−0.0214835	−	0.0941255i	0.963050	−	0.269324i	$-0.0868003\pi$
$953$	−0.663211	−	2.90572i	−0.0214835	−	0.0941255i	−0.984533	+	0.175199i	$0.943943\pi$
$954$	−15.9309	+	69.7979i	−0.515782	+	2.25979i
$955$	−14.6262	+	18.3406i	−0.473292	+	0.593489i
$956$	−30.3139			−0.980423
$957$	26.5677	+	22.6357i	0.858812	+	0.731708i
$958$	−21.3948			−0.691235
$959$	−6.13013	+	7.68693i	−0.197952	+	0.248224i
$960$	−1.22852	+	5.38249i	−0.0396502	+	0.173719i
$961$	6.19122	+	27.1255i	0.199717	+	0.875016i
$962$	14.0429	−	17.6093i	0.452762	−	0.567745i
$963$	−1.64504	−	2.06282i	−0.0530107	−	0.0664733i
$964$	−1.01778	+	4.45920i	−0.0327806	+	0.143621i
$965$	6.99412	+	3.36819i	0.225149	+	0.108426i
$966$	−12.6017	−	6.06866i	−0.405453	−	0.195256i
$967$	−1.40773	−	6.16768i	−0.0452696	−	0.198339i	0.947236	−	0.320536i	$-0.103863\pi$
$967$	−1.40773	−	6.16768i	−0.0452696	−	0.198339i	−0.992506	+	0.122197i	$0.961006\pi$
$968$	6.67000	−	3.21210i	0.214382	−	0.103241i
$969$	21.3644			0.686322
$970$	−21.6987	+	10.4495i	−0.696702	+	0.335514i
$971$	12.5515	+	15.7391i	0.402797	+	0.505092i	0.941318	−	0.337520i	$-0.109588\pi$
$971$	12.5515	+	15.7391i	0.402797	+	0.505092i	−0.538521	+	0.842612i	$0.681017\pi$
$972$	49.5402	+	62.1215i	1.58900	+	1.99255i
$973$	−19.5367	+	9.40836i	−0.626317	+	0.301618i
$974$	12.6886			0.406570
$975$	−23.4438	+	11.2899i	−0.750803	+	0.361567i
$976$	1.72363	+	7.55173i	0.0551721	+	0.241725i
$977$	24.9341	+	12.0076i	0.797713	+	0.384158i	0.787907	−	0.615794i	$-0.211165\pi$
$977$	24.9341	+	12.0076i	0.797713	+	0.384158i	0.00980533	+	0.999952i	$0.496879\pi$
$978$	−31.5709	−	15.2037i	−1.00952	−	0.486161i
$979$	−6.73984	+	29.5291i	−0.215406	+	0.943756i
$980$	−4.72083	−	5.91974i	−0.150802	−	0.189099i
$981$	48.8302	−	61.2311i	1.55903	−	1.95496i
$982$	2.74254	+	12.0159i	0.0875180	+	0.383442i
$983$	1.31895	−	5.77869i	0.0420679	−	0.184312i	−0.949529	−	0.313680i	$-0.898438\pi$
$983$	1.31895	−	5.77869i	0.0420679	−	0.184312i	0.991597	+	0.129369i	$0.0412951\pi$
$984$	−10.7232	+	13.4464i	−0.341842	+	0.428656i
$985$	−24.5921			−0.783569
$986$	0.296948	−	9.14612i	0.00945675	−	0.291272i
$987$	−13.3612			−0.425290
$988$	7.30709	−	9.16281i	0.232470	−	0.291508i
$989$	−1.13566	+	4.97565i	−0.0361119	+	0.158216i
$990$	−5.91708	−	25.9244i	−0.188057	−	0.823932i
$991$	38.4258	−	48.1844i	1.22064	−	1.53063i	0.450461	−	0.892796i	$-0.351259\pi$
$991$	38.4258	−	48.1844i	1.22064	−	1.53063i	0.770175	−	0.637833i	$-0.220169\pi$
$992$	−1.11130	−	1.39353i	−0.0352839	−	0.0442446i
$993$	17.7909	−	77.9472i	0.564578	−	2.47358i
$994$	8.31588	+	4.00472i	0.263764	+	0.127022i
$995$	17.7478	+	8.54690i	0.562644	+	0.270955i
$996$	4.20008	+	18.4018i	0.133085	+	0.583082i
$997$	−43.8638	+	21.1237i	−1.38918	+	0.668994i	−0.970936	−	0.239340i	$-0.923069\pi$
$997$	−43.8638	+	21.1237i	−1.38918	+	0.668994i	−0.418245	+	0.908334i	$0.637355\pi$
$998$	−3.86155			−0.122235
$999$	123.627	−	59.5354i	3.91137	−	1.88362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.d.b.23.1	✓	12
3.2	odd	2		522.2.k.h.487.1		12
4.3	odd	2		464.2.u.h.81.2		12
29.11	odd	28		1682.2.b.i.1681.1		12
29.13	even	14		1682.2.a.q.1.1		6
29.16	even	7		1682.2.a.t.1.6		6
29.18	odd	28		1682.2.b.i.1681.12		12
29.24	even	7	inner	58.2.d.b.53.1	yes	12
87.53	odd	14		522.2.k.h.343.1		12
116.111	odd	14		464.2.u.h.401.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.23.1	✓	12	1.1	even	1	trivial
58.2.d.b.53.1	yes	12	29.24	even	7	inner
464.2.u.h.81.2		12	4.3	odd	2
464.2.u.h.401.2		12	116.111	odd	14
522.2.k.h.343.1		12	87.53	odd	14
522.2.k.h.487.1		12	3.2	odd	2
1682.2.a.q.1.1		6	29.13	even	14
1682.2.a.t.1.6		6	29.16	even	7
1682.2.b.i.1681.1		12	29.11	odd	28
1682.2.b.i.1681.12		12	29.18	odd	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.760453 + 3.33176i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(1.00725 - 1.26305i) q^{5} +(2.13074 + 2.67187i) q^{6} +(0.338433 - 1.48277i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-7.81944 - 3.76565i) q^{9} +(-0.359484 - 1.57500i) q^{10} +(-1.70872 + 0.822877i) q^{11} +3.41744 q^{12} +(2.87014 - 1.38219i) q^{13} +(-0.948269 - 1.18909i) q^{14} +(3.44223 + 4.31642i) q^{15} +(-0.900969 + 0.433884i) q^{16} -1.69929 q^{17} +(-7.81944 + 3.76565i) q^{18} +(0.818639 + 3.58669i) q^{19} +(-1.45552 - 0.700942i) q^{20} +(4.68289 + 2.25516i) q^{21} +(-0.422020 + 1.84899i) q^{22} +(-1.67782 - 2.10392i) q^{23} +(2.13074 - 2.67187i) q^{24} +(0.531856 + 2.33021i) q^{25} +(0.708867 - 3.10575i) q^{26} +(12.1003 - 15.1733i) q^{27} -1.52091 q^{28} +(-4.31703 + 3.21920i) q^{29} +5.52091 q^{30} +(-1.11130 + 1.39353i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-1.44223 - 6.31882i) q^{33} +(-1.05949 + 1.32856i) q^{34} +(-1.53194 - 1.92099i) q^{35} +(-1.93124 + 8.46133i) q^{36} +(6.37006 + 3.06766i) q^{37} +(3.31460 + 1.59623i) q^{38} +(2.42251 + 10.6137i) q^{39} +(-1.45552 + 0.700942i) q^{40} -5.03259 q^{41} +(4.68289 - 2.25516i) q^{42} +(-1.18247 - 1.48277i) q^{43} +(1.18247 + 1.48277i) q^{44} +(-12.6324 + 6.08343i) q^{45} -2.69101 q^{46} +(-2.31606 + 1.11536i) q^{47} +(-0.760453 - 3.33176i) q^{48} +(4.22270 + 2.03355i) q^{49} +(2.15344 + 1.03704i) q^{50} +(1.29223 - 5.66162i) q^{51} +(-1.98620 - 2.49062i) q^{52} +(5.14319 - 6.44936i) q^{53} +(-4.31856 - 18.9208i) q^{54} +(-0.681776 + 2.98705i) q^{55} +(-0.948269 + 1.18909i) q^{56} -12.5725 q^{57} +(-0.174748 + 5.38233i) q^{58} +2.95027 q^{59} +(3.44223 - 4.31642i) q^{60} +(1.72363 - 7.55173i) q^{61} +(0.396619 + 1.73770i) q^{62} +(-8.22996 + 10.3200i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.14518 - 5.01736i) q^{65} +(-5.83946 - 2.81214i) q^{66} +(-2.23359 - 1.07564i) q^{67} +(0.378127 + 1.65668i) q^{68} +(8.28565 - 3.99016i) q^{69} -2.45703 q^{70} +(-5.46771 + 2.63311i) q^{71} +(5.41122 + 6.78546i) q^{72} +(2.33692 + 2.93041i) q^{73} +(6.37006 - 3.06766i) q^{74} -8.16816 q^{75} +(3.31460 - 1.59623i) q^{76} +(0.641852 + 2.81214i) q^{77} +(9.80856 + 4.72355i) q^{78} +(-8.30753 - 4.00069i) q^{79} +(-0.359484 + 1.57500i) q^{80} +(25.1185 + 31.4977i) q^{81} +(-3.13777 + 3.93464i) q^{82} +(1.22901 + 5.38465i) q^{83} +(1.15658 - 5.06730i) q^{84} +(-1.71161 + 2.14629i) q^{85} -1.89654 q^{86} +(-7.44272 - 16.8314i) q^{87} +1.89654 q^{88} +(9.95740 - 12.4862i) q^{89} +(-3.11994 + 13.6693i) q^{90} +(-1.07812 - 4.72355i) q^{91} +(-1.67782 + 2.10392i) q^{92} +(-3.79781 - 4.76231i) q^{93} +(-0.572020 + 2.50618i) q^{94} +(5.35476 + 2.57872i) q^{95} +(-3.07901 - 1.48277i) q^{96} +(-3.31730 - 14.5341i) q^{97} +(4.22270 - 2.03355i) q^{98} +16.4599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

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