LMFDB - Embedded newform 798.2.bq.d.499.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(25,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 12, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			499.6
Character	$\chi$	$=$	798.499
Dual form			798.2.bq.d.403.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.87086 - 1.04491i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.51108 + 2.17178i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.530514 - 3.00870i) q^{10} +1.13991 q^{11} +1.00000 q^{12} +(0.231152 + 1.31093i) q^{13} +(2.40118 - 1.11100i) q^{14} +(-2.34035 + 1.96379i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.82042 + 3.20571i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.90717 + 1.93236i) q^{19} -3.05511 q^{20} +(-2.16275 - 1.52399i) q^{21} +(0.197943 - 1.12259i) q^{22} +(0.525841 + 2.98219i) q^{23} +(0.173648 - 0.984808i) q^{24} +(3.31981 - 2.78565i) q^{25} +1.33115 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.677160 - 2.55763i) q^{28} +(0.824151 + 0.299966i) q^{29} +(1.52756 + 2.64580i) q^{30} +(-0.283629 + 0.491259i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-1.07116 + 0.389871i) q^{33} +(3.82042 - 3.20571i) q^{34} +(6.60742 + 4.65594i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.25484 - 7.36959i) q^{37} +(1.22453 + 4.18336i) q^{38} +(-0.665576 - 1.15281i) q^{39} +(-0.530514 + 3.00870i) q^{40} +(1.24536 - 7.06280i) q^{41} +(-1.87639 + 1.86525i) q^{42} +(5.69144 + 4.77568i) q^{43} +(-1.07116 - 0.389871i) q^{44} +(1.52756 - 2.64580i) q^{45} +3.02820 q^{46} +(1.52167 - 1.27683i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-2.43326 + 6.56348i) q^{49} +(-2.16685 - 3.75309i) q^{50} +(-4.68644 - 1.70572i) q^{51} +(0.231152 - 1.31093i) q^{52} +(-0.922847 - 0.335889i) q^{53} +(0.766044 + 0.642788i) q^{54} +(3.27251 - 1.19110i) q^{55} +(-2.63636 + 0.222745i) q^{56} +(3.01063 - 3.15215i) q^{57} +(0.438521 - 0.759541i) q^{58} +(1.62000 + 1.35934i) q^{59} +(2.87086 - 1.04491i) q^{60} +(-1.18911 - 6.74378i) q^{61} +(0.434544 + 0.364626i) q^{62} +(2.55355 + 0.692376i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.03341 + 3.52197i) q^{65} +(0.197943 + 1.12259i) q^{66} +(-2.63143 - 14.9236i) q^{67} +(-2.49360 - 4.31905i) q^{68} +(-1.51410 - 2.62250i) q^{69} +(5.73258 - 5.69855i) q^{70} +(5.79268 + 4.86064i) q^{71} +(0.173648 + 0.984808i) q^{72} +(0.723140 - 0.263201i) q^{73} +(-6.51879 - 5.46991i) q^{74} +(-2.16685 + 3.75309i) q^{75} +(4.33245 - 0.479492i) q^{76} +(1.72249 + 2.47562i) q^{77} +(-1.25087 + 0.455281i) q^{78} +(-11.4520 - 9.60935i) q^{79} +(2.87086 + 1.04491i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-6.73924 - 2.45288i) q^{82} +(-1.28689 - 2.22896i) q^{83} +(1.51108 + 2.17178i) q^{84} +(14.3176 + 5.21118i) q^{85} +(5.69144 - 4.77568i) q^{86} -0.877043 q^{87} +(-0.569953 + 0.987187i) q^{88} +(5.94428 + 2.16354i) q^{89} +(-2.34035 - 1.96379i) q^{90} +(-2.49776 + 2.48293i) q^{91} +(0.525841 - 2.98219i) q^{92} +(0.0985032 - 0.558639i) q^{93} +(-0.993199 - 1.72027i) q^{94} +(-9.19782 + 9.63018i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(16.3405 - 5.94744i) q^{97} +(6.04123 + 3.53603i) q^{98} +(0.873218 - 0.732717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} - 18 q^{8} - 6 q^{10} - 6 q^{11} + 36 q^{12} + 27 q^{13} + 3 q^{15} - 3 q^{17} - 18 q^{18} + 6 q^{19} - 6 q^{20} - 3 q^{22} - 18 q^{23} - 21 q^{25} - 18 q^{26} - 18 q^{27} + 12 q^{28} + 9 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 - 18 * q^8 - 6 * q^10 - 6 * q^11 + 36 * q^12 + 27 * q^13 + 3 * q^15 - 3 * q^17 - 18 * q^18 + 6 * q^19 - 6 * q^20 - 3 * q^22 - 18 * q^23 - 21 * q^25 - 18 * q^26 - 18 * q^27 + 12 * q^28 + 9 * q^29 + 3 * q^30 - 3 * q^31 - 3 * q^33 - 3 * q^34 + 12 * q^35 + 21 * q^37 + 9 * q^38 + 9 * q^39 - 6 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 - 3 * q^44 + 3 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 27 * q^52 - 15 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 33 * q^59 + 3 * q^60 + 21 * q^61 - 24 * q^62 + 3 * q^63 - 18 * q^64 + 42 * q^65 - 3 * q^66 - 3 * q^67 + 18 * q^68 + 6 * q^69 - 33 * q^70 + 6 * q^71 - 42 * q^73 - 3 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 - 24 * q^79 + 3 * q^80 + 27 * q^82 + 30 * q^83 + 36 * q^85 + 51 * q^86 - 36 * q^87 + 3 * q^88 - 42 * q^89 + 3 * q^90 + 24 * q^91 - 18 * q^92 + 21 * q^93 + 18 * q^94 - 39 * q^95 - 18 * q^96 + 45 * q^97 + 3 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.87086	−	1.04491i	1.28389	−	0.467298i	0.392173	−	0.919892i	$-0.371724\pi$
$5$	2.87086	−	1.04491i	1.28389	−	0.467298i	0.891717	+	0.452594i	$0.149501\pi$
$6$	0.173648	+	0.984808i	0.0708916	+	0.402046i
$7$	1.51108	+	2.17178i	0.571135	+	0.820856i
$7$	1.51108	+	2.17178i	0.571135	+	0.820856i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−0.530514	−	3.00870i	−0.167763	−	0.951433i
$11$	1.13991			0.343694			0.171847	−	0.985124i	$-0.445026\pi$
$11$	1.13991			0.343694			0.171847	+	0.985124i	$0.445026\pi$
$12$	1.00000			0.288675
$13$	0.231152	+	1.31093i	0.0641101	+	0.363586i	0.999938	+	0.0111292i	$0.00354261\pi$
$13$	0.231152	+	1.31093i	0.0641101	+	0.363586i	−0.935828	+	0.352457i	$0.885346\pi$
$14$	2.40118	−	1.11100i	0.641743	−	0.296927i
$15$	−2.34035	+	1.96379i	−0.604276	+	0.507048i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.82042	+	3.20571i	0.926588	+	0.777500i	0.975202	−	0.221318i	$-0.0710359\pi$
$17$	3.82042	+	3.20571i	0.926588	+	0.777500i	−0.0486136	+	0.998818i	$0.515480\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−3.90717	+	1.93236i	−0.896367	+	0.443314i
$19$	−3.90717	+	1.93236i	−0.896367	+	0.443314i
$20$	−3.05511			−0.683143
$21$	−2.16275	−	1.52399i	−0.471950	−	0.332561i
$22$	0.197943	−	1.12259i	0.0422015	−	0.239337i
$23$	0.525841	+	2.98219i	0.109645	+	0.621830i	0.989263	+	0.146148i	$0.0466876\pi$
$23$	0.525841	+	2.98219i	0.109645	+	0.621830i	−0.879617	+	0.475682i	$0.842201\pi$
$24$	0.173648	−	0.984808i	0.0354458	−	0.201023i
$25$	3.31981	−	2.78565i	0.663961	−	0.557129i
$26$	1.33115			0.261060
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−0.677160	−	2.55763i	−0.127971	−	0.483346i
$29$	0.824151	+	0.299966i	0.153041	+	0.0557024i	0.417405	−	0.908721i	$-0.362940\pi$
$29$	0.824151	+	0.299966i	0.153041	+	0.0557024i	−0.264364	+	0.964423i	$0.585162\pi$
$30$	1.52756	+	2.64580i	0.278892	+	0.483055i
$31$	−0.283629	+	0.491259i	−0.0509412	+	0.0882328i	−0.890372	−	0.455234i	$-0.849555\pi$
$31$	−0.283629	+	0.491259i	−0.0509412	+	0.0882328i	0.839430	+	0.543467i	$0.182889\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−1.07116	+	0.389871i	−0.186465	+	0.0678678i
$34$	3.82042	−	3.20571i	0.655197	−	0.549775i
$35$	6.60742	+	4.65594i	1.11686	+	0.786998i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	4.25484	−	7.36959i	0.699491	−	1.21155i	−0.269153	−	0.963098i	$-0.586744\pi$
$37$	4.25484	−	7.36959i	0.699491	−	1.21155i	0.968643	−	0.248456i	$-0.0799231\pi$
$38$	1.22453	+	4.18336i	0.198645	+	0.678631i
$39$	−0.665576	−	1.15281i	−0.106577	−	0.184598i
$40$	−0.530514	+	3.00870i	−0.0838817	+	0.475717i
$41$	1.24536	−	7.06280i	0.194493	−	1.10302i	−0.718646	−	0.695376i	$-0.755238\pi$
$41$	1.24536	−	7.06280i	0.194493	−	1.10302i	0.913139	−	0.407648i	$-0.133651\pi$
$42$	−1.87639	+	1.86525i	−0.289533	+	0.287814i
$43$	5.69144	+	4.77568i	0.867936	+	0.728285i	0.963662	−	0.267123i	$-0.0860730\pi$
$43$	5.69144	+	4.77568i	0.867936	+	0.728285i	−0.0957266	+	0.995408i	$0.530517\pi$
$44$	−1.07116	−	0.389871i	−0.161484	−	0.0587752i
$45$	1.52756	−	2.64580i	0.227714	−	0.394413i
$46$	3.02820			0.446483
$47$	1.52167	−	1.27683i	0.221958	−	0.186245i	−0.525027	−	0.851085i	$-0.675945\pi$
$47$	1.52167	−	1.27683i	0.221958	−	0.186245i	0.746986	+	0.664840i	$0.231500\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−2.43326	+	6.56348i	−0.347609	+	0.937640i
$50$	−2.16685	−	3.75309i	−0.306439	−	0.530767i
$51$	−4.68644	−	1.70572i	−0.656233	−	0.238849i
$52$	0.231152	−	1.31093i	0.0320550	−	0.181793i
$53$	−0.922847	−	0.335889i	−0.126763	−	0.0461379i	0.277860	−	0.960622i	$-0.410375\pi$
$53$	−0.922847	−	0.335889i	−0.126763	−	0.0461379i	−0.404623	+	0.914484i	$0.632597\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	3.27251	−	1.19110i	0.441266	−	0.160608i
$56$	−2.63636	+	0.222745i	−0.352298	+	0.0297655i
$57$	3.01063	−	3.15215i	0.398768	−	0.417513i
$58$	0.438521	−	0.759541i	0.0575807	−	0.0997327i
$59$	1.62000	+	1.35934i	0.210906	+	0.176971i	0.742121	−	0.670266i	$-0.233820\pi$
$59$	1.62000	+	1.35934i	0.210906	+	0.176971i	−0.531215	+	0.847237i	$0.678264\pi$
$60$	2.87086	−	1.04491i	0.370627	−	0.134897i
$61$	−1.18911	−	6.74378i	−0.152250	−	0.863453i	−0.961257	−	0.275654i	$-0.911106\pi$
$61$	−1.18911	−	6.74378i	−0.152250	−	0.863453i	0.809007	−	0.587799i	$-0.200005\pi$
$62$	0.434544	+	0.364626i	0.0551872	+	0.0463076i
$63$	2.55355	+	0.692376i	0.321717	+	0.0872312i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.03341	+	3.52197i	0.252213	+	0.436846i
$66$	0.197943	+	1.12259i	0.0243650	+	0.138181i
$67$	−2.63143	−	14.9236i	−0.321480	−	1.82320i	−0.533338	−	0.845902i	$-0.679063\pi$
$67$	−2.63143	−	14.9236i	−0.321480	−	1.82320i	0.211859	−	0.977300i	$-0.432048\pi$
$68$	−2.49360	−	4.31905i	−0.302394	−	0.523761i
$69$	−1.51410	−	2.62250i	−0.182276	−	0.315711i
$70$	5.73258	−	5.69855i	0.685174	−	0.681107i
$71$	5.79268	+	4.86064i	0.687465	+	0.576851i	0.918177	−	0.396171i	$-0.129661\pi$
$71$	5.79268	+	4.86064i	0.687465	+	0.576851i	−0.230712	+	0.973022i	$0.574106\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	0.723140	−	0.263201i	0.0846371	−	0.0308054i	−0.299355	−	0.954142i	$-0.596771\pi$
$73$	0.723140	−	0.263201i	0.0846371	−	0.0308054i	0.383992	+	0.923337i	$0.374549\pi$
$74$	−6.51879	−	5.46991i	−0.757793	−	0.635864i
$75$	−2.16685	+	3.75309i	−0.250206	+	0.433370i
$76$	4.33245	−	0.479492i	0.496966	−	0.0550016i
$77$	1.72249	+	2.47562i	0.196296	+	0.282124i
$78$	−1.25087	+	0.455281i	−0.141634	+	0.0515504i
$79$	−11.4520	−	9.60935i	−1.28845	−	1.08114i	−0.992020	−	0.126080i	$-0.959760\pi$
$79$	−11.4520	−	9.60935i	−1.28845	−	1.08114i	−0.296428	−	0.955055i	$-0.595795\pi$
$80$	2.87086	+	1.04491i	0.320972	+	0.116824i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−6.73924	−	2.45288i	−0.744225	−	0.270876i
$83$	−1.28689	−	2.22896i	−0.141254	−	0.244660i	0.786715	−	0.617316i	$-0.211780\pi$
$83$	−1.28689	−	2.22896i	−0.141254	−	0.244660i	−0.927969	+	0.372657i	$0.878447\pi$
$84$	1.51108	+	2.17178i	0.164873	+	0.236961i
$85$	14.3176	+	5.21118i	1.55296	+	0.565231i
$86$	5.69144	−	4.77568i	0.613723	−	0.514975i
$87$	−0.877043			−0.0940289
$88$	−0.569953	+	0.987187i	−0.0607572	+	0.105235i
$89$	5.94428	+	2.16354i	0.630093	+	0.229335i	0.637272	−	0.770639i	$-0.280063\pi$
$89$	5.94428	+	2.16354i	0.630093	+	0.229335i	−0.00717882	+	0.999974i	$0.502285\pi$
$90$	−2.34035	−	1.96379i	−0.246695	−	0.207001i
$91$	−2.49776	+	2.48293i	−0.261836	+	0.260282i
$92$	0.525841	−	2.98219i	0.0548227	−	0.310915i
$93$	0.0985032	−	0.558639i	0.0102143	−	0.0579282i
$94$	−0.993199	−	1.72027i	−0.102441	−	0.177432i
$95$	−9.19782	+	9.63018i	−0.943676	+	0.988036i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	16.3405	−	5.94744i	1.65912	−	0.603871i	0.668898	−	0.743355i	$-0.266766\pi$
$97$	16.3405	−	5.94744i	1.65912	−	0.603871i	0.990224	+	0.139484i	$0.0445443\pi$
$98$	6.04123	+	3.53603i	0.610257	+	0.357193i
$99$	0.873218	−	0.732717i	0.0877617	−	0.0736408i
$100$	−4.07234	+	1.48221i	−0.407234	+	0.148221i
$101$	−4.76787	+	4.00071i	−0.474420	+	0.398086i	−0.848404	−	0.529349i	$-0.822436\pi$
$101$	−4.76787	+	4.00071i	−0.474420	+	0.398086i	0.373984	+	0.927435i	$0.377992\pi$
$102$	−2.49360	+	4.31905i	−0.246903	+	0.427649i
$103$	9.37938	+	16.2456i	0.924178	+	1.60072i	0.792878	+	0.609380i	$0.208582\pi$
$103$	9.37938	+	16.2456i	0.924178	+	1.60072i	0.131299	+	0.991343i	$0.458085\pi$
$104$	−1.25087	−	0.455281i	−0.122658	−	0.0446439i
$105$	−7.80138	−	2.11528i	−0.761336	−	0.206431i
$106$	−0.491036	+	0.850500i	−0.0476937	+	0.0826079i
$107$	−15.7969			−1.52714			−0.763572	−	0.645723i	$-0.776556\pi$
$107$	−15.7969			−1.52714			−0.763572	+	0.645723i	$0.776556\pi$
$108$	0.766044	−	0.642788i	0.0737127	−	0.0618523i
$109$	0.335171	−	1.90085i	0.0321035	−	0.182068i	−0.964539	−	0.263939i	$-0.914978\pi$
$109$	0.335171	−	1.90085i	0.0321035	−	0.182068i	0.996643	+	0.0818706i	$0.0260894\pi$
$110$	−0.604736	−	3.42963i	−0.0576593	−	0.327002i
$111$	−1.47769	+	8.38039i	−0.140256	+	0.795431i
$112$	−0.238438	+	2.63499i	−0.0225303	+	0.248983i
$113$	−14.5684			−1.37048			−0.685238	−	0.728319i	$-0.740302\pi$
$113$	−14.5684			−1.37048			−0.685238	+	0.728319i	$0.740302\pi$
$114$	−2.58148	−	3.51226i	−0.241777	−	0.328953i
$115$	4.62574	+	8.01201i	0.431352	+	0.747124i
$116$	−0.671854	−	0.563752i	−0.0623801	−	0.0523431i
$117$	1.01972	+	0.855648i	0.0942733	+	0.0791047i
$118$	1.62000	−	1.35934i	0.149133	−	0.125137i
$119$	−1.18914	+	13.1412i	−0.109008	+	1.20465i
$120$	−0.530514	−	3.00870i	−0.0484291	−	0.274655i
$121$	−9.70062			−0.881874
$122$	−6.84782			−0.619972
$123$	1.24536	+	7.06280i	0.112290	+	0.636831i
$124$	0.434544	−	0.364626i	0.0390232	−	0.0327444i
$125$	−1.01781	+	1.76290i	−0.0910360	+	0.157679i
$126$	1.12528	−	2.39453i	0.100248	−	0.213321i
$127$	−0.383628	−	2.17566i	−0.0340415	−	0.193059i	0.963045	−	0.269341i	$-0.0868060\pi$
$127$	−0.383628	−	2.17566i	−0.0340415	−	0.193059i	−0.997086	+	0.0762825i	$0.975695\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−6.98158	−	2.54109i	−0.614694	−	0.223730i
$130$	3.82156	−	1.39093i	0.335173	−	0.121993i
$131$	−3.07504	+	17.4394i	−0.268667	+	1.52369i	0.489718	+	0.871881i	$0.337100\pi$
$131$	−3.07504	+	17.4394i	−0.268667	+	1.52369i	−0.758385	+	0.651806i	$0.774011\pi$
$132$	1.13991			0.0992160
$133$	−10.1007	−	5.56557i	−0.875843	−	0.482596i
$134$	−15.1538			−1.30909
$135$	−0.530514	+	3.00870i	−0.0456594	+	0.258947i
$136$	−4.68644	+	1.70572i	−0.401859	+	0.146265i
$137$	−4.89979	−	1.78338i	−0.418617	−	0.152364i	0.124119	−	0.992267i	$-0.460389\pi$
$137$	−4.89979	−	1.78338i	−0.418617	−	0.152364i	−0.542736	+	0.839903i	$0.682612\pi$
$138$	−2.84557	+	1.03570i	−0.242231	+	0.0881650i
$139$	−1.15971	−	6.57706i	−0.0983655	−	0.557859i	−0.993664	−	0.112392i	$-0.964149\pi$
$139$	−1.15971	−	6.57706i	−0.0983655	−	0.557859i	0.895298	−	0.445467i	$-0.146962\pi$
$140$	−4.61652	−	6.63503i	−0.390167	−	0.560762i
$141$	−0.993199	+	1.72027i	−0.0836425	+	0.144873i
$142$	5.79268	−	4.86064i	0.486111	−	0.407895i
$143$	0.263492	+	1.49433i	0.0220343	+	0.124963i
$144$	1.00000			0.0833333
$145$	2.67946			0.222517
$146$	−0.133631	−	0.757858i	−0.0110594	−	0.0627208i
$147$	0.0416783	−	6.99988i	0.00343757	−	0.577340i
$148$	−6.51879	+	5.46991i	−0.535841	+	0.449624i
$149$	1.06050	+	0.889863i	0.0868794	+	0.0729004i	0.685193	−	0.728362i	$-0.259718\pi$
$149$	1.06050	+	0.889863i	0.0868794	+	0.0729004i	−0.598314	+	0.801262i	$0.704162\pi$
$150$	3.31981	+	2.78565i	0.271061	+	0.227447i
$151$	−3.18936	−	5.52413i	−0.259546	−	0.449548i	0.706574	−	0.707639i	$-0.250240\pi$
$151$	−3.18936	−	5.52413i	−0.259546	−	0.449548i	−0.966120	+	0.258092i	$0.916906\pi$
$152$	0.280113	−	4.34989i	0.0227202	−	0.352823i
$153$	4.98720			0.403192
$154$	2.73712	−	1.26643i	0.220564	−	0.102052i
$155$	−0.300938	+	1.70671i	−0.0241719	+	0.137086i
$156$	0.231152	+	1.31093i	0.0185070	+	0.104958i
$157$	0.252795	−	1.43367i	0.0201752	−	0.114419i	−0.973057	−	0.230565i	$-0.925943\pi$
$157$	0.252795	−	1.43367i	0.0201752	−	0.114419i	0.993232	+	0.116145i	$0.0370538\pi$
$158$	−11.4520	+	9.60935i	−0.911070	+	0.764478i
$159$	0.982073			0.0778834
$160$	1.52756	−	2.64580i	0.120764	−	0.209169i
$161$	−5.68208	+	5.64835i	−0.447810	+	0.445152i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	−8.47695	−	14.6825i	−0.663966	−	1.15002i	−0.979564	−	0.201130i	$-0.935538\pi$
$163$	−8.47695	−	14.6825i	−0.663966	−	1.15002i	0.315598	−	0.948893i	$-0.397795\pi$
$164$	−3.58588	+	6.21092i	−0.280010	+	0.484991i
$165$	−2.66778	+	2.23853i	−0.207686	+	0.174269i
$166$	−2.41856	+	0.880283i	−0.187717	+	0.0683232i
$167$	−5.82947	+	4.89151i	−0.451098	+	0.378516i	−0.839843	−	0.542829i	$-0.817353\pi$
$167$	−5.82947	+	4.89151i	−0.451098	+	0.378516i	0.388745	+	0.921345i	$0.372909\pi$
$168$	2.40118	−	1.11100i	0.185255	−	0.0857155i
$169$	10.5509	−	3.84021i	0.811608	−	0.295401i
$170$	7.61823	−	13.1952i	0.584292	−	1.01202i
$171$	−1.75097	+	3.99175i	−0.133900	+	0.305257i
$172$	−3.71482	−	6.43426i	−0.283252	−	0.490608i
$173$	−0.467885	+	2.65351i	−0.0355726	+	0.201742i	−0.997414	−	0.0718637i	$-0.977105\pi$
$173$	−0.467885	+	2.65351i	−0.0355726	+	0.201742i	0.961842	+	0.273606i	$0.0882165\pi$
$174$	−0.152297	+	0.863719i	−0.0115456	+	0.0654783i
$175$	11.0663	+	3.00055i	0.836535	+	0.226820i
$176$	0.873218	+	0.732717i	0.0658213	+	0.0552306i
$177$	−1.98722	−	0.723290i	−0.149369	−	0.0543658i
$178$	3.16289	−	5.47828i	0.237068	−	0.410615i
$179$	−9.75495			−0.729119			−0.364560	−	0.931180i	$-0.618780\pi$
$179$	−9.75495			−0.729119			−0.364560	+	0.931180i	$0.618780\pi$
$180$	−2.34035	+	1.96379i	−0.174439	+	0.146372i
$181$	−6.90082	−	2.51169i	−0.512934	−	0.186693i	0.0725684	−	0.997363i	$-0.476880\pi$
$181$	−6.90082	−	2.51169i	−0.512934	−	0.186693i	−0.585502	+	0.810671i	$0.699103\pi$
$182$	2.01148	+	2.89097i	0.149101	+	0.214293i
$183$	3.42391	+	5.93038i	0.253103	+	0.438387i
$184$	−2.84557	−	1.03570i	−0.209778	−	0.0763531i
$185$	4.51450	−	25.6030i	0.331913	−	1.88237i
$186$	−0.533048	−	0.194013i	−0.0390849	−	0.0142258i
$187$	4.35492	+	3.65421i	0.318463	+	0.267222i
$188$	−1.86660	+	0.679388i	−0.136136	+	0.0495495i
$189$	−2.63636	+	0.222745i	−0.191767	+	0.0162023i
$190$	7.88669	+	10.7303i	0.572161	+	0.778461i
$191$	−9.73152	+	16.8555i	−0.704148	+	1.21962i	0.262850	+	0.964837i	$0.415337\pi$
$191$	−9.73152	+	16.8555i	−0.704148	+	1.21962i	−0.966998	+	0.254783i	$0.917996\pi$
$192$	0.766044	+	0.642788i	0.0552845	+	0.0463892i
$193$	−22.8404	+	8.31321i	−1.64409	+	0.598398i	−0.987746	−	0.156068i	$-0.950118\pi$
$193$	−22.8404	+	8.31321i	−1.64409	+	0.598398i	−0.656339	+	0.754466i	$0.727896\pi$
$194$	−3.01959	−	17.1250i	−0.216794	−	1.22950i
$195$	−3.11536	−	2.61410i	−0.223096	−	0.187199i
$196$	4.53136	−	5.33543i	0.323669	−	0.381102i
$197$	−6.81901	−	11.8109i	−0.485834	−	0.841489i	0.514033	−	0.857770i	$-0.328151\pi$
$197$	−6.81901	−	11.8109i	−0.485834	−	0.841489i	−0.999867	+	0.0162808i	$0.994817\pi$
$198$	−0.569953	−	0.987187i	−0.0405048	−	0.0701563i
$199$	3.94757	+	22.3878i	0.279836	+	1.58703i	0.723170	+	0.690670i	$0.242684\pi$
$199$	3.94757	+	22.3878i	0.279836	+	1.58703i	−0.443334	+	0.896356i	$0.646204\pi$
$200$	0.752539	+	4.26786i	0.0532125	+	0.301783i
$201$	7.57689	+	13.1236i	0.534432	+	0.925664i
$202$	3.11200	+	5.39015i	0.218960	+	0.379249i
$203$	0.593898	+	2.24315i	0.0416835	+	0.157438i
$204$	3.82042	+	3.20571i	0.267483	+	0.224445i
$205$	−3.80472	−	21.5776i	−0.265733	−	1.50705i
$206$	17.6275	−	6.41587i	1.22816	−	0.447015i
$207$	2.31973	+	1.94649i	0.161233	+	0.135290i
$208$	−0.665576	+	1.15281i	−0.0461494	+	0.0799331i
$209$	−4.45381	+	2.20271i	−0.308076	+	0.152364i
$210$	−3.43784	+	7.31554i	−0.237234	+	0.504820i
$211$	6.59222	−	2.39937i	0.453827	−	0.165180i	−0.104985	−	0.994474i	$-0.533479\pi$
$211$	6.59222	−	2.39937i	0.453827	−	0.165180i	0.558812	+	0.829294i	$0.311257\pi$
$212$	0.752311	+	0.631264i	0.0516690	+	0.0433554i
$213$	−7.10577	−	2.58629i	−0.486880	−	0.177210i
$214$	−2.74310	+	15.5569i	−0.187515	+	1.06345i
$215$	21.3295	+	7.76330i	1.45466	+	0.529453i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−1.49549	+	0.126354i	−0.101521	+	0.00857745i
$218$	−1.81377	−	0.660157i	−0.122844	−	0.0447115i
$219$	−0.589509	+	0.494657i	−0.0398353	+	0.0334258i
$220$	−3.48254			−0.234793
$221$	−3.31936	+	5.74931i	−0.223285	+	0.386740i
$222$	7.99647	+	2.91048i	0.536688	+	0.195339i
$223$	−11.6772	−	9.79833i	−0.781963	−	0.656145i	0.161779	−	0.986827i	$-0.448277\pi$
$223$	−11.6772	−	9.79833i	−0.781963	−	0.656145i	−0.943742	+	0.330682i	$0.892721\pi$
$224$	2.55355	+	0.692376i	0.170616	+	0.0462613i
$225$	0.752539	−	4.26786i	0.0501692	−	0.284524i
$226$	−2.52977	+	14.3470i	−0.168278	+	0.954350i
$227$	11.0079	+	19.0662i	0.730619	+	1.26547i	0.956619	+	0.291342i	$0.0941018\pi$
$227$	11.0079	+	19.0662i	0.730619	+	1.26547i	−0.226000	+	0.974127i	$0.572565\pi$
$228$	−3.90717	+	1.93236i	−0.258759	+	0.127974i
$229$	2.47139	−	4.28058i	0.163314	−	0.282868i	−0.772741	−	0.634721i	$-0.781115\pi$
$229$	2.47139	−	4.28058i	0.163314	−	0.282868i	0.936055	+	0.351853i	$0.114448\pi$
$230$	8.69354	−	3.16419i	0.573235	−	0.208641i
$231$	−2.46533	−	1.73720i	−0.162206	−	0.114299i
$232$	−0.671854	+	0.563752i	−0.0441094	+	0.0370122i
$233$	17.6564	−	6.42640i	1.15671	−	0.421007i	0.308788	−	0.951131i	$-0.400077\pi$
$233$	17.6564	−	6.42640i	1.15671	−	0.421007i	0.847920	+	0.530123i	$0.177854\pi$
$234$	1.01972	−	0.855648i	0.0666613	−	0.0559355i
$235$	3.03433	−	5.25562i	0.197938	−	0.342839i
$236$	−1.05738	−	1.83143i	−0.0688295	−	0.119216i
$237$	14.0479	+	5.11303i	0.912511	+	0.332127i
$238$	12.7351	+	3.45302i	0.825492	+	0.223826i
$239$	7.33540	−	12.7053i	0.474487	−	0.821836i	−0.525086	−	0.851049i	$-0.675967\pi$
$239$	7.33540	−	12.7053i	0.474487	−	0.821836i	0.999573	+	0.0292129i	$0.00930009\pi$
$240$	−3.05511			−0.197207
$241$	6.15507	−	5.16472i	0.396483	−	0.332689i	−0.422649	−	0.906293i	$-0.638900\pi$
$241$	6.15507	−	5.16472i	0.396483	−	0.332689i	0.819132	+	0.573605i	$0.194455\pi$
$242$	−1.68449	+	9.55324i	−0.108283	+	0.614106i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−1.18911	+	6.74378i	−0.0761250	+	0.431727i
$245$	−0.127332	+	21.3854i	−0.00813493	+	1.36626i
$246$	7.17175			0.457254
$247$	−3.43634	−	4.67535i	−0.218649	−	0.297486i
$248$	−0.283629	−	0.491259i	−0.0180104	−	0.0311950i
$249$	1.97163	+	1.65439i	0.124947	+	0.104843i
$250$	1.55938	+	1.30848i	0.0986239	+	0.0827553i
$251$	18.6257	−	15.6288i	1.17564	−	0.986481i	0.175644	−	0.984454i	$-0.443799\pi$
$251$	18.6257	−	15.6288i	1.17564	−	0.986481i	0.999998	−	0.00202683i	$-0.000645160\pi$
$252$	−2.16275	−	1.52399i	−0.136240	−	0.0960021i
$253$	0.599409	+	3.39942i	0.0376845	+	0.213719i
$254$	−2.20923			−0.138619
$255$	−15.2365			−0.954144
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	13.1346	−	11.0212i	0.819314	−	0.687486i	−0.133497	−	0.991049i	$-0.542621\pi$
$257$	13.1346	−	11.0212i	0.819314	−	0.687486i	0.952811	+	0.303563i	$0.0981762\pi$
$258$	−3.71482	+	6.43426i	−0.231275	+	0.400579i
$259$	22.4345	−	1.89549i	1.39401	−	0.117780i
$260$	−0.706195	−	4.00503i	−0.0437964	−	0.248382i
$261$	0.824151	−	0.299966i	0.0510136	−	0.0185675i
$262$	16.6405	+	6.05664i	1.02805	+	0.374180i
$263$	3.67497	−	1.33758i	0.226609	−	0.0824788i	−0.226220	−	0.974076i	$-0.572637\pi$
$263$	3.67497	−	1.33758i	0.226609	−	0.0824788i	0.452829	+	0.891597i	$0.350415\pi$
$264$	0.197943	−	1.12259i	0.0121825	−	0.0690905i
$265$	−3.00034			−0.184309
$266$	−7.23498	+	8.98081i	−0.443605	+	0.550649i
$267$	−6.32578			−0.387131
$268$	−2.63143	+	14.9236i	−0.160740	+	0.911601i
$269$	−10.1943	+	3.71043i	−0.621558	+	0.226229i	−0.633553	−	0.773699i	$-0.718404\pi$
$269$	−10.1943	+	3.71043i	−0.621558	+	0.226229i	0.0119945	+	0.999928i	$0.496182\pi$
$270$	2.87086	+	1.04491i	0.174715	+	0.0635911i
$271$	−24.2955	+	8.84283i	−1.47585	+	0.537164i	−0.949681	−	0.313219i	$-0.898593\pi$
$271$	−24.2955	+	8.84283i	−1.47585	+	0.537164i	−0.526164	+	0.850383i	$0.676370\pi$
$272$	0.866019	+	4.91144i	0.0525101	+	0.297800i
$273$	1.49791	−	3.18748i	0.0906579	−	0.192915i
$274$	−2.60712	+	4.51567i	−0.157502	+	0.272802i
$275$	3.78426	−	3.17537i	0.228200	−	0.191482i
$276$	0.525841	+	2.98219i	0.0316519	+	0.179507i
$277$	−23.7161			−1.42496			−0.712482	−	0.701690i	$-0.752429\pi$
$277$	−23.7161			−1.42496			−0.712482	+	0.701690i	$0.752429\pi$
$278$	−6.67852			−0.400551
$279$	0.0985032	+	0.558639i	0.00589723	+	0.0334449i
$280$	−7.33588	+	3.39423i	−0.438403	+	0.202844i
$281$	−11.6037	+	9.73666i	−0.692218	+	0.580840i	−0.919548	−	0.392978i	$-0.871445\pi$
$281$	−11.6037	+	9.73666i	−0.692218	+	0.580840i	0.227330	+	0.973818i	$0.427001\pi$
$282$	1.52167	+	1.27683i	0.0906141	+	0.0760343i
$283$	−8.29548	−	6.96073i	−0.493115	−	0.413773i	0.362026	−	0.932168i	$-0.382085\pi$
$283$	−8.29548	−	6.96073i	−0.493115	−	0.413773i	−0.855141	+	0.518395i	$0.826530\pi$
$284$	−3.78090	−	6.54872i	−0.224355	−	0.388595i
$285$	5.34941	−	12.1952i	0.316872	−	0.722384i
$286$	1.51739			0.0897250
$287$	17.2207	−	7.96781i	1.01651	−	0.470325i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	1.36700	+	7.75262i	0.0804115	+	0.456036i
$290$	0.465284	−	2.63876i	0.0273224	−	0.154953i
$291$	−13.3209	+	11.1775i	−0.780883	+	0.655238i
$292$	−0.769549			−0.0450345
$293$	2.36141	−	4.09008i	0.137955	−	0.238945i	−0.788767	−	0.614692i	$-0.789280\pi$
$293$	2.36141	−	4.09008i	0.137955	−	0.238945i	0.926722	+	0.375747i	$0.122614\pi$
$294$	−6.88629	−	1.25656i	−0.401617	−	0.0732841i
$295$	6.07118	+	2.20973i	0.353478	+	0.128655i
$296$	4.25484	+	7.36959i	0.247307	+	0.428349i
$297$	−0.569953	+	0.987187i	−0.0330720	+	0.0572824i
$298$	1.06050	−	0.889863i	0.0614330	−	0.0515484i
$299$	−3.78789	+	1.37868i	−0.219059	+	0.0797311i
$300$	3.31981	−	2.78565i	0.191669	−	0.160829i
$301$	−1.77151	+	19.5770i	−0.102108	+	1.12840i
$302$	−5.99404	+	2.18165i	−0.344918	+	0.125540i
$303$	3.11200	−	5.39015i	0.178780	−	0.309656i
$304$	−4.23516	−	1.03121i	−0.242903	−	0.0591439i
$305$	−10.4604	−	18.1180i	−0.598962	−	1.03743i
$306$	0.866019	−	4.91144i	0.0495070	−	0.280768i
$307$	4.80028	−	27.2237i	0.273966	−	1.55374i	−0.468259	−	0.883591i	$-0.655119\pi$
$307$	4.80028	−	27.2237i	0.273966	−	1.55374i	0.742226	−	0.670150i	$-0.233770\pi$
$308$	−0.771898	−	2.91545i	−0.0439830	−	0.166123i
$309$	−14.3700	−	12.0579i	−0.817483	−	0.685950i
$310$	1.62852	+	0.592732i	0.0924937	+	0.0336649i
$311$	12.4914	−	21.6358i	0.708325	−	1.22685i	−0.257154	−	0.966371i	$-0.582785\pi$
$311$	12.4914	−	21.6358i	0.708325	−	1.22685i	0.965478	−	0.260484i	$-0.0838821\pi$
$312$	1.33115			0.0753616
$313$	5.32736	−	4.47019i	0.301120	−	0.252670i	−0.479690	−	0.877438i	$-0.659251\pi$
$313$	5.32736	−	4.47019i	0.301120	−	0.252670i	0.780810	+	0.624768i	$0.214806\pi$
$314$	−1.36799	−	0.497908i	−0.0772002	−	0.0280986i
$315$	8.05436	−	0.680510i	0.453812	−	0.0383424i
$316$	7.47474	+	12.9466i	0.420487	+	0.728305i
$317$	18.2333	+	6.63636i	1.02408	+	0.372735i	0.798825	−	0.601564i	$-0.205456\pi$
$317$	18.2333	+	6.63636i	1.02408	+	0.372735i	0.225257	+	0.974299i	$0.427678\pi$
$318$	0.170535	−	0.967153i	0.00956314	−	0.0542352i
$319$	0.939454	+	0.341933i	0.0525993	+	0.0191446i
$320$	−2.34035	−	1.96379i	−0.130830	−	0.109779i
$321$	14.8442	−	5.40286i	0.828524	−	0.301558i
$322$	4.57585	+	6.57658i	0.255002	+	0.366498i
$323$	−21.1216	−	5.14285i	−1.17524	−	0.286156i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	4.41916	+	3.70812i	0.245131	+	0.205689i
$326$	−15.9315	+	5.79858i	−0.882362	+	0.321154i
$327$	0.335171	+	1.90085i	0.0185350	+	0.105117i
$328$	5.49388	+	4.60991i	0.303349	+	0.254540i
$329$	5.07237	+	1.37533i	0.279649	+	0.0758246i
$330$	1.74127	+	3.01597i	0.0958537	+	0.166023i
$331$	11.4805	+	19.8849i	0.631027	+	1.09297i	0.987342	+	0.158605i	$0.0506997\pi$
$331$	11.4805	+	19.8849i	0.631027	+	1.09297i	−0.356315	+	0.934366i	$0.615967\pi$
$332$	0.446932	+	2.53467i	0.0245286	+	0.139108i
$333$	−1.47769	−	8.38039i	−0.0809768	−	0.459243i
$334$	3.80492	+	6.59031i	0.208196	+	0.360606i
$335$	−23.1482	−	40.0939i	−1.26472	−	2.19056i
$336$	−0.677160	−	2.55763i	−0.0369421	−	0.139530i
$337$	−20.2363	−	16.9803i	−1.10234	−	0.924974i	−0.104761	−	0.994497i	$-0.533408\pi$
$337$	−20.2363	−	16.9803i	−1.10234	−	0.924974i	−0.997580	+	0.0695234i	$0.977852\pi$
$338$	−1.94973	−	11.0575i	−0.106051	−	0.601446i
$339$	13.6898	−	4.98267i	0.743527	−	0.270622i
$340$	−11.6718	−	9.79381i	−0.632993	−	0.531144i
$341$	−0.323310	+	0.559989i	−0.0175082	+	0.0303251i
$342$	3.62706	+	2.41753i	0.196129	+	0.130725i
$343$	−17.9313	+	4.63344i	−0.968199	+	0.250182i
$344$	−6.98158	+	2.54109i	−0.376422	+	0.137006i
$345$	−7.08704	−	5.94673i	−0.381553	−	0.320161i
$346$	2.53195	+	0.921553i	0.136118	+	0.0495430i
$347$	0.782123	−	4.43564i	0.0419866	−	0.238118i	−0.956591	−	0.291433i	$-0.905868\pi$
$347$	0.782123	−	4.43564i	0.0419866	−	0.238118i	0.998578	+	0.0533157i	$0.0169790\pi$
$348$	0.824151	+	0.299966i	0.0441791	+	0.0160799i
$349$	−4.87036	−	8.43570i	−0.260704	−	0.451553i	0.705725	−	0.708486i	$-0.250621\pi$
$349$	−4.87036	−	8.43570i	−0.260704	−	0.451553i	−0.966429	+	0.256933i	$0.917288\pi$
$350$	4.87661	−	10.3772i	0.260666	−	0.554682i
$351$	−1.25087	−	0.455281i	−0.0667667	−	0.0243011i
$352$	0.873218	−	0.732717i	0.0465427	−	0.0390540i
$353$	5.16859			0.275096			0.137548	−	0.990495i	$-0.456078\pi$
$353$	5.16859			0.275096			0.137548	+	0.990495i	$0.456078\pi$
$354$	−1.05738	+	1.83143i	−0.0561990	+	0.0973396i
$355$	21.7089	+	7.90140i	1.15219	+	0.419363i
$356$	−4.84583	−	4.06613i	−0.256828	−	0.215504i
$357$	−3.37713	−	12.7554i	−0.178737	−	0.675088i
$358$	−1.69393	+	9.60675i	−0.0895269	+	0.507733i
$359$	4.57405	−	25.9407i	0.241409	−	1.36910i	−0.587277	−	0.809386i	$-0.699800\pi$
$359$	4.57405	−	25.9407i	0.241409	−	1.36910i	0.828686	−	0.559714i	$-0.189089\pi$
$360$	1.52756	+	2.64580i	0.0805092	+	0.139446i
$361$	11.5320	−	15.1001i	0.606946	−	0.794743i
$362$	−3.67185	+	6.35983i	−0.192988	+	0.334265i
$363$	9.11560	−	3.31781i	0.478445	−	0.174140i
$364$	3.19634	−	1.47891i	0.167534	−	0.0775159i
$365$	1.80101	−	1.51123i	0.0942694	−	0.0791014i
$366$	6.43484	−	2.34209i	0.336355	−	0.122423i
$367$	−4.86471	+	4.08198i	−0.253936	+	0.213078i	−0.760865	−	0.648910i	$-0.775225\pi$
$367$	−4.86471	+	4.08198i	−0.253936	+	0.213078i	0.506929	+	0.861988i	$0.330781\pi$
$368$	−1.51410	+	2.62250i	−0.0789278	+	0.136707i
$369$	−3.58588	−	6.21092i	−0.186673	−	0.323328i
$370$	−24.4301	−	8.89183i	−1.27006	−	0.462264i
$371$	−0.665020	−	2.51178i	−0.0345261	−	0.130405i
$372$	−0.283629	+	0.491259i	−0.0147055	+	0.0254706i
$373$	−6.29361			−0.325871			−0.162935	−	0.986637i	$-0.552096\pi$
$373$	−6.29361			−0.325871			−0.162935	+	0.986637i	$0.552096\pi$
$374$	4.35492	−	3.65421i	0.225187	−	0.188955i
$375$	0.353483	−	2.00470i	0.0182538	−	0.103522i
$376$	0.344934	+	1.95622i	0.0177886	+	0.100884i
$377$	−0.202730	+	1.14974i	−0.0104411	+	0.0592147i
$378$	−0.238438	+	2.63499i	−0.0122639	+	0.135529i
$379$	−1.27897			−0.0656965			−0.0328482	−	0.999460i	$-0.510458\pi$
$379$	−1.27897			−0.0656965			−0.0328482	+	0.999460i	$0.510458\pi$
$380$	11.9368	−	5.90357i	0.612347	−	0.302847i
$381$	1.10461	+	1.91325i	0.0565911	+	0.0980186i
$382$	14.9096	+	12.5106i	0.762839	+	0.640098i
$383$	12.1519	+	10.1967i	0.620933	+	0.521025i	0.898097	−	0.439798i	$-0.144950\pi$
$383$	12.1519	+	10.1967i	0.620933	+	0.521025i	−0.277164	+	0.960823i	$0.589394\pi$
$384$	0.766044	−	0.642788i	0.0390920	−	0.0328021i
$385$	7.53184	+	5.30734i	0.383858	+	0.270487i
$386$	4.22073	+	23.9369i	0.214829	+	1.21836i
$387$	7.42964			0.377670
$388$	−17.3892			−0.882800
$389$	2.13037	+	12.0819i	0.108014	+	0.612577i	0.989974	+	0.141252i	$0.0451129\pi$
$389$	2.13037	+	12.0819i	0.108014	+	0.612577i	−0.881960	+	0.471325i	$0.843776\pi$
$390$	−3.11536	+	2.61410i	−0.157752	+	0.132370i
$391$	−7.55112	+	13.0789i	−0.381876	+	0.661429i
$392$	−4.46751	−	5.38901i	−0.225643	−	0.272186i
$393$	−3.07504	−	17.4394i	−0.155115	−	0.879701i
$394$	−12.8155	+	4.66448i	−0.645638	+	0.234993i
$395$	−42.9180	−	15.6209i	−2.15944	−	0.785971i
$396$	−1.07116	+	0.389871i	−0.0538279	+	0.0195917i
$397$	0.996746	−	5.65283i	0.0500253	−	0.283707i	−0.949525	−	0.313691i	$-0.898434\pi$
$397$	0.996746	−	5.65283i	0.0500253	−	0.283707i	0.999550	+	0.0299836i	$0.00954552\pi$
$398$	22.7331			1.13951
$399$	11.3951	+	1.77527i	0.570469	+	0.0888748i
$400$	4.33370			0.216685
$401$	−2.61930	+	14.8548i	−0.130801	+	0.741812i	0.846890	+	0.531767i	$0.178472\pi$
$401$	−2.61930	+	14.8548i	−0.130801	+	0.741812i	−0.977692	+	0.210044i	$0.932639\pi$
$402$	14.2399	−	5.18290i	0.710221	−	0.258499i
$403$	−0.709567	−	0.258261i	−0.0353461	−	0.0128649i
$404$	5.84865	−	2.12874i	0.290981	−	0.105909i
$405$	−0.530514	−	3.00870i	−0.0263615	−	0.149503i
$406$	2.31220	−	0.195357i	0.114753	−	0.00969540i
$407$	4.85011	−	8.40064i	0.240411	−	0.416404i
$408$	3.82042	−	3.20571i	0.189139	−	0.158706i
$409$	0.433836	+	2.46041i	0.0214518	+	0.121659i	0.993653	−	0.112487i	$-0.0358816\pi$
$409$	0.433836	+	2.46041i	0.0214518	+	0.121659i	−0.972201	+	0.234146i	$0.924771\pi$
$410$	−21.9105			−1.08208
$411$	5.21425			0.257200
$412$	−3.25742	−	18.4738i	−0.160482	−	0.910137i
$413$	−0.504238	+	5.57236i	−0.0248120	+	0.274198i
$414$	2.31973	−	1.94649i	0.114009	−	0.0956646i
$415$	−6.02354	−	5.05435i	−0.295684	−	0.248108i
$416$	1.01972	+	0.855648i	0.0499960	+	0.0419516i
$417$	3.33926	+	5.78377i	0.163524	+	0.283232i
$418$	1.39585	+	4.76864i	0.0682731	+	0.233242i
$419$	10.5302			0.514432			0.257216	−	0.966354i	$-0.417195\pi$
$419$	10.5302			0.514432			0.257216	+	0.966354i	$0.417195\pi$
$420$	6.60742	+	4.65594i	0.322409	+	0.227187i
$421$	−2.16891	+	12.3005i	−0.105706	+	0.599490i	0.885230	+	0.465154i	$0.154001\pi$
$421$	−2.16891	+	12.3005i	−0.105706	+	0.599490i	−0.990936	+	0.134336i	$0.957110\pi$
$422$	−1.21819	−	6.90872i	−0.0593007	−	0.336311i
$423$	0.344934	−	1.95622i	0.0167713	−	0.0951147i
$424$	0.752311	−	0.631264i	0.0365355	−	0.0306569i
$425$	21.6130			1.04839
$426$	−3.78090	+	6.54872i	−0.183185	+	0.317286i
$427$	12.8492	−	12.7729i	0.621815	−	0.618124i
$428$	14.8442	+	5.40286i	0.717523	+	0.261157i
$429$	−0.758694	−	1.31410i	−0.0366301	−	0.0634452i
$430$	11.3492	−	19.6574i	0.547306	−	0.947962i
$431$	−0.196250	+	0.164673i	−0.00945301	+	0.00793202i	−0.647502	−	0.762064i	$-0.724186\pi$
$431$	−0.196250	+	0.164673i	−0.00945301	+	0.00793202i	0.638049	+	0.769996i	$0.279742\pi$
$432$	−0.939693	+	0.342020i	−0.0452110	+	0.0164555i
$433$	−18.6222	+	15.6259i	−0.894928	+	0.750934i	−0.969192	−	0.246305i	$-0.920784\pi$
$433$	−18.6222	+	15.6259i	−0.894928	+	0.750934i	0.0742645	+	0.997239i	$0.476339\pi$
$434$	−0.135256	+	1.49471i	−0.00649248	+	0.0717486i
$435$	−2.51787	+	0.916430i	−0.120723	+	0.0439395i
$436$	−0.965086	+	1.67158i	−0.0462192	+	0.0800540i
$437$	−7.81722	−	10.6358i	−0.373948	−	0.508780i
$438$	0.384775	+	0.666449i	0.0183852	+	0.0318442i
$439$	−6.01275	+	34.1000i	−0.286973	+	1.62750i	0.411179	+	0.911555i	$0.365117\pi$
$439$	−6.01275	+	34.1000i	−0.286973	+	1.62750i	−0.698152	+	0.715950i	$0.745994\pi$
$440$	−0.604736	+	3.42963i	−0.0288297	+	0.163501i
$441$	2.35493	+	6.59199i	0.112140	+	0.313904i
$442$	5.08556	+	4.26729i	0.241895	+	0.202974i
$443$	−8.97381	−	3.26620i	−0.426359	−	0.155182i	0.119923	−	0.992783i	$-0.461735\pi$
$443$	−8.97381	−	3.26620i	−0.426359	−	0.155182i	−0.546282	+	0.837601i	$0.683957\pi$
$444$	4.25484	−	7.36959i	0.201926	−	0.349745i
$445$	19.3259			0.916137
$446$	−11.6772	+	9.79833i	−0.552931	+	0.463964i
$447$	−1.30089	−	0.473486i	−0.0615301	−	0.0223951i
$448$	1.12528	−	2.39453i	0.0531643	−	0.113131i
$449$	−5.58726	−	9.67742i	−0.263679	−	0.456706i	0.703538	−	0.710658i	$-0.251603\pi$
$449$	−5.58726	−	9.67742i	−0.263679	−	0.456706i	−0.967217	+	0.253952i	$0.918269\pi$
$450$	−4.07234	−	1.48221i	−0.191972	−	0.0698721i
$451$	1.41959	−	8.05092i	0.0668461	−	0.379103i
$452$	13.6898	+	4.98267i	0.643913	+	0.234365i
$453$	4.88638	+	4.10016i	0.229582	+	0.192642i
$454$	20.6881	−	7.52984i	0.970939	−	0.353393i
$455$	−4.57629	+	9.73809i	−0.214540	+	0.456529i
$456$	1.22453	+	4.18336i	0.0573438	+	0.195904i
$457$	−1.38749	+	2.40320i	−0.0649039	+	0.112417i	−0.896651	−	0.442737i	$-0.854007\pi$
$457$	−1.38749	+	2.40320i	−0.0649039	+	0.112417i	0.831747	+	0.555154i	$0.187341\pi$
$458$	−3.78639	−	3.17716i	−0.176926	−	0.148459i
$459$	−4.68644	+	1.70572i	−0.218744	+	0.0796164i
$460$	−1.60650	−	9.11092i	−0.0749035	−	0.424799i
$461$	22.3914	+	18.7886i	1.04287	+	0.875072i	0.992326	−	0.123649i	$-0.0394598\pi$
$461$	22.3914	+	18.7886i	1.04287	+	0.875072i	0.0505446	+	0.998722i	$0.483904\pi$
$462$	−2.13891	+	2.12621i	−0.0995110	+	0.0989202i
$463$	−0.132687	−	0.229820i	−0.00616648	−	0.0106807i	0.862926	−	0.505331i	$-0.168630\pi$
$463$	−0.132687	−	0.229820i	−0.00616648	−	0.0106807i	−0.869092	+	0.494650i	$0.835296\pi$
$464$	0.438521	+	0.759541i	0.0203578	+	0.0352608i
$465$	−0.300938	−	1.70671i	−0.0139557	−	0.0791466i
$466$	−3.26277	−	18.5041i	−0.151145	−	0.857185i
$467$	−8.49826	−	14.7194i	−0.393252	−	0.681133i	0.599624	−	0.800282i	$-0.295317\pi$
$467$	−8.49826	−	14.7194i	−0.393252	−	0.681133i	−0.992876	+	0.119149i	$0.961983\pi$
$468$	−0.665576	−	1.15281i	−0.0307663	−	0.0532887i
$469$	28.4344	−	28.2656i	1.31298	−	1.30518i
$470$	−4.64887	−	3.90086i	−0.214436	−	0.179933i
$471$	0.252795	+	1.43367i	0.0116482	+	0.0660600i
$472$	−1.98722	+	0.723290i	−0.0914693	+	0.0332921i
$473$	6.48770	+	5.44383i	0.298305	+	0.250307i
$474$	7.47474	−	12.9466i	0.343326	−	0.594659i
$475$	−7.58818	+	17.2991i	−0.348169	+	0.793735i
$476$	5.61198	−	11.9420i	0.257225	−	0.547360i
$477$	−0.922847	+	0.335889i	−0.0422542	+	0.0153793i
$478$	−11.2385	−	9.43021i	−0.514036	−	0.431328i
$479$	17.7819	+	6.47209i	0.812477	+	0.295717i	0.714647	−	0.699486i	$-0.246588\pi$
$479$	17.7819	+	6.47209i	0.812477	+	0.295717i	0.0978303	+	0.995203i	$0.468810\pi$
$480$	−0.530514	+	3.00870i	−0.0242146	+	0.137328i
$481$	10.6445	+	3.87429i	0.485348	+	0.176652i
$482$	−4.01744	−	6.95841i	−0.182989	−	0.316947i
$483$	3.40756	−	7.25109i	0.155049	−	0.329936i
$484$	9.11560	+	3.31781i	0.414345	+	0.150809i
$485$	40.6967	−	34.1486i	1.84794	−	1.55061i
$486$	1.00000			0.0453609
$487$	18.4282	−	31.9185i	0.835059	−	1.44637i	−0.0589227	−	0.998263i	$-0.518767\pi$
$487$	18.4282	−	31.9185i	0.835059	−	1.44637i	0.893982	−	0.448103i	$-0.147900\pi$
$488$	6.43484	+	2.34209i	0.291292	+	0.106022i
$489$	12.9874	+	10.8978i	0.587313	+	0.492814i
$490$	21.0384	+	3.83893i	0.950418	+	0.173425i
$491$	−1.55290	+	8.80693i	−0.0700813	+	0.397451i	0.929508	+	0.368802i	$0.120232\pi$
$491$	−1.55290	+	8.80693i	−0.0700813	+	0.397451i	−0.999590	+	0.0286495i	$0.990879\pi$
$492$	1.24536	−	7.06280i	0.0561452	−	0.318415i
$493$	2.18700	+	3.78799i	0.0984974	+	0.170602i
$494$	−5.20104	+	2.57226i	−0.234006	+	0.115732i
$495$	1.74127	−	3.01597i	0.0782642	−	0.135558i
$496$	−0.533048	+	0.194013i	−0.0239345	+	0.00871146i
$497$	−1.80302	+	19.9252i	−0.0808766	+	0.893769i
$498$	1.97163	−	1.65439i	0.0883507	−	0.0741350i
$499$	13.4514	−	4.89590i	0.602166	−	0.219170i	−0.0229062	−	0.999738i	$-0.507292\pi$
$499$	13.4514	−	4.89590i	0.602166	−	0.219170i	0.625072	+	0.780567i	$0.285070\pi$
$500$	1.55938	−	1.30848i	0.0697376	−	0.0585168i
$501$	3.80492	−	6.59031i	0.169991	−	0.294433i
$502$	−12.1570	−	21.0566i	−0.542595	−	0.939803i
$503$	−37.0484	−	13.4845i	−1.65191	−	0.601244i	−0.662845	−	0.748757i	$-0.730651\pi$
$503$	−37.0484	−	13.4845i	−1.65191	−	0.601244i	−0.989060	+	0.147512i	$0.952873\pi$
$504$	−1.87639	+	1.86525i	−0.0835811	+	0.0830849i
$505$	−9.50751	+	16.4675i	−0.423079	+	0.732794i
$506$	3.45186			0.153454
$507$	−8.60117	+	7.21724i	−0.381992	+	0.320529i
$508$	−0.383628	+	2.17566i	−0.0170207	+	0.0965295i
$509$	0.225847	+	1.28084i	0.0100105	+	0.0567723i	0.989404	−	0.145190i	$-0.0463793\pi$
$509$	0.225847	+	1.28084i	0.0100105	+	0.0567723i	−0.979393	+	0.201962i	$0.935268\pi$
$510$	−2.64578	+	15.0050i	−0.117157	+	0.664432i
$511$	1.66434	+	1.17278i	0.0736260	+	0.0518808i
$512$	1.00000			0.0441942
$513$	0.280113	−	4.34989i	0.0123673	−	0.192052i
$514$	−8.57301	−	14.8489i	−0.378139	−	0.654956i
$515$	43.9021	+	36.8382i	1.93456	+	1.62329i
$516$	5.69144	+	4.77568i	0.250551	+	0.210238i
$517$	1.73456	−	1.45547i	0.0762858	−	0.0640114i
$518$	2.02903	−	22.4229i	0.0891504	−	0.985204i
$519$	−0.467885	−	2.65351i	−0.0205379	−	0.116476i
$520$	−4.06682			−0.178342
$521$	−19.8765			−0.870806			−0.435403	−	0.900236i	$-0.643394\pi$
$521$	−19.8765			−0.870806			−0.435403	+	0.900236i	$0.643394\pi$
$522$	−0.152297	−	0.863719i	−0.00666585	−	0.0378039i
$523$	−30.8625	+	25.8967i	−1.34952	+	1.13238i	−0.370453	+	0.928851i	$0.620797\pi$
$523$	−30.8625	+	25.8967i	−1.34952	+	1.13238i	−0.979068	+	0.203531i	$0.934758\pi$
$524$	8.85421	−	15.3359i	0.386798	−	0.669954i
$525$	−11.4252	+	0.965309i	−0.498636	+	0.0421295i
$526$	−0.679108	−	3.85141i	−0.0296105	−	0.167930i
$527$	−2.65842	+	0.967585i	−0.115802	+	0.0421487i
$528$	−1.07116	−	0.389871i	−0.0466163	−	0.0169669i
$529$	12.9960	−	4.73015i	0.565042	−	0.205659i
$530$	−0.521004	+	2.95476i	−0.0226310	+	0.128347i
$531$	2.11476			0.0917727
$532$	7.58803	+	8.68457i	0.328983	+	0.376524i
$533$	9.54669			0.413513
$534$	−1.09846	+	6.22967i	−0.0475350	+	0.269584i
$535$	−45.3507	+	16.5063i	−1.96068	+	0.713630i
$536$	14.2399	+	5.18290i	0.615070	+	0.223867i
$537$	9.16665	−	3.33639i	0.395570	−	0.143976i
$538$	1.88383	+	10.6838i	0.0812178	+	0.460609i
$539$	−2.77369	+	7.48174i	−0.119471	+	0.322262i
$540$	1.52756	−	2.64580i	0.0657355	−	0.113857i
$541$	12.7116	−	10.6663i	0.546514	−	0.458580i	−0.327244	−	0.944940i	$-0.606120\pi$
$541$	12.7116	−	10.6663i	0.546514	−	0.458580i	0.873759	+	0.486360i	$0.161676\pi$
$542$	4.48962	+	25.4619i	0.192846	+	1.09368i
$543$	7.34370			0.315148
$544$	4.98720			0.213825
$545$	−1.02398	−	5.80730i	−0.0438626	−	0.248757i
$546$	−2.87894	−	2.02866i	−0.123207	−	0.0868185i
$547$	8.54886	−	7.17335i	0.365523	−	0.306710i	−0.441465	−	0.897279i	$-0.645541\pi$
$547$	8.54886	−	7.17335i	0.365523	−	0.306710i	0.806987	+	0.590569i	$0.201096\pi$
$548$	3.99434	+	3.35165i	0.170630	+	0.143175i
$549$	−5.24573	−	4.40169i	−0.223882	−	0.187860i
$550$	−2.47000	−	4.27817i	−0.105321	−	0.182422i
$551$	−3.79974	+	0.420535i	−0.161874	+	0.0179154i
$552$	3.02820			0.128889
$553$	3.56452	−	39.3917i	0.151579	−	1.67510i
$554$	−4.11826	+	23.3558i	−0.174968	+	0.992294i
$555$	4.51450	+	25.6030i	0.191630	+	1.08679i
$556$	−1.15971	+	6.57706i	−0.0491828	+	0.278929i
$557$	−10.2967	+	8.63992i	−0.436284	+	0.366085i	−0.834316	−	0.551286i	$-0.814137\pi$
$557$	−10.2967	+	8.63992i	−0.436284	+	0.366085i	0.398033	+	0.917371i	$0.369693\pi$
$558$	0.567257			0.0240139
$559$	−4.94499	+	8.56497i	−0.209151	+	0.362260i
$560$	2.06880	+	7.81383i	0.0874226	+	0.330195i
$561$	−5.34210	−	1.94436i	−0.225544	−	0.0820911i
$562$	7.57377	+	13.1182i	0.319480	+	0.553356i
$563$	7.36581	−	12.7580i	0.310432	−	0.537684i	−0.668024	−	0.744140i	$-0.732860\pi$
$563$	7.36581	−	12.7580i	0.310432	−	0.537684i	0.978456	+	0.206456i	$0.0661930\pi$
$564$	1.52167	−	1.27683i	0.0640738	−	0.0537643i
$565$	−41.8238	+	15.2226i	−1.75954	+	0.640420i
$566$	−8.29548	+	6.96073i	−0.348685	+	0.292581i
$567$	2.40118	−	1.11100i	0.100840	−	0.0466576i
$568$	−7.10577	+	2.58629i	−0.298152	+	0.108518i
$569$	−16.4089	+	28.4211i	−0.687899	+	1.19148i	0.284618	+	0.958641i	$0.408133\pi$
$569$	−16.4089	+	28.4211i	−0.687899	+	1.19148i	−0.972516	+	0.232834i	$0.925200\pi$
$570$	−11.0811	−	7.38582i	−0.464135	−	0.309358i
$571$	−16.8473	−	29.1804i	−0.705038	−	1.22116i	−0.966678	−	0.255996i	$-0.917597\pi$
$571$	−16.8473	−	29.1804i	−0.705038	−	1.22116i	0.261640	−	0.965165i	$-0.415737\pi$
$572$	0.263492	−	1.49433i	0.0110171	−	0.0624813i
$573$	3.37972	−	19.1673i	0.141190	−	0.800727i
$574$	−4.85642	−	18.3427i	−0.202703	−	0.765608i
$575$	10.0530	+	8.43549i	0.419240	+	0.351784i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	−12.7596	+	22.1004i	−0.531191	+	0.920050i	0.468146	+	0.883651i	$0.344922\pi$
$577$	−12.7596	+	22.1004i	−0.531191	+	0.920050i	−0.999337	+	0.0363989i	$0.988411\pi$
$578$	7.87221			0.327441
$579$	18.6196	−	15.6237i	0.773806	−	0.649300i
$580$	−2.51787	−	0.916430i	−0.104549	−	0.0380527i
$581$	2.89621	−	6.16297i	0.120155	−	0.255683i
$582$	8.69458	+	15.0594i	0.360402	+	0.624234i
$583$	−1.05196	−	0.382881i	−0.0435676	−	0.0158573i
$584$	−0.133631	+	0.757858i	−0.00552968	+	0.0313604i
$585$	3.82156	+	1.39093i	0.158002	+	0.0575080i
$586$	−3.61789	−	3.03577i	−0.149454	−	0.125407i
$587$	15.9499	−	5.80527i	0.658321	−	0.239609i	0.00880969	−	0.999961i	$-0.497196\pi$
$587$	15.9499	−	5.80527i	0.658321	−	0.239609i	0.649511	+	0.760352i	$0.274974\pi$
$588$	−2.43326	+	6.56348i	−0.100346	+	0.270673i
$589$	0.158896	−	2.46751i	0.00654721	−	0.101672i
$590$	3.23041	−	5.59523i	0.132994	−	0.230352i
$591$	10.4473	+	8.76635i	0.429746	+	0.360599i
$592$	7.99647	−	2.91048i	0.328653	−	0.119620i
$593$	3.79237	+	21.5076i	0.155734	+	0.883211i	0.958112	+	0.286395i	$0.0924568\pi$
$593$	3.79237	+	21.5076i	0.155734	+	0.883211i	−0.802378	+	0.596816i	$0.796432\pi$
$594$	0.873218	+	0.732717i	0.0358286	+	0.0300637i
$595$	10.3175	+	38.9692i	0.422977	+	1.59758i
$596$	−0.692191	−	1.19891i	−0.0283532	−	0.0491093i
$597$	−11.3666	−	19.6875i	−0.465203	−	0.805755i
$598$	0.699974	+	3.96975i	0.0286241	+	0.162335i
$599$	5.34687	+	30.3236i	0.218467	+	1.23899i	0.874788	+	0.484507i	$0.161001\pi$
$599$	5.34687	+	30.3236i	0.218467	+	1.23899i	−0.656320	+	0.754482i	$0.727888\pi$
$600$	−2.16685	−	3.75309i	−0.0884612	−	0.153219i
$601$	−8.69549	−	15.0610i	−0.354696	−	0.614352i	0.632370	−	0.774667i	$-0.282082\pi$
$601$	−8.69549	−	15.0610i	−0.354696	−	0.614352i	−0.987066	+	0.160315i	$0.948749\pi$
$602$	18.9720	+	5.14410i	0.773239	+	0.209658i
$603$	−11.6085	−	9.74066i	−0.472733	−	0.396670i
$604$	1.10765	+	6.28181i	0.0450698	+	0.255603i
$605$	−27.8492	+	10.1363i	−1.13223	+	0.412098i
$606$	−4.76787	−	4.00071i	−0.193681	−	0.162518i
$607$	−8.85273	+	15.3334i	−0.359321	+	0.622362i	−0.987848	−	0.155426i	$-0.950325\pi$
$607$	−8.85273	+	15.3334i	−0.359321	+	0.622362i	0.628526	+	0.777788i	$0.283658\pi$
$608$	−1.75097	+	3.99175i	−0.0710112	+	0.161887i
$609$	−1.32528	−	1.90474i	−0.0537032	−	0.0771842i
$610$	−19.6592	+	7.15535i	−0.795976	+	0.289712i
$611$	2.02557	+	1.69966i	0.0819459	+	0.0687608i
$612$	−4.68644	−	1.70572i	−0.189438	−	0.0689498i
$613$	7.74045	−	43.8983i	0.312634	−	1.77303i	−0.272558	−	0.962139i	$-0.587870\pi$
$613$	7.74045	−	43.8983i	0.312634	−	1.77303i	0.585192	−	0.810895i	$-0.301019\pi$
$614$	−25.9766	−	9.45471i	−1.04833	−	0.381561i
$615$	10.9552	+	18.9750i	0.441758	+	0.765147i
$616$	−3.00520	+	0.253908i	−0.121083	+	0.0102302i
$617$	41.3761	+	15.0597i	1.66574	+	0.606279i	0.991249	−	0.132007i	$-0.0421420\pi$
$617$	41.3761	+	15.0597i	1.66574	+	0.606279i	0.674488	+	0.738285i	$0.264364\pi$
$618$	−14.3700	+	12.0579i	−0.578048	+	0.485040i
$619$	−9.53188			−0.383119			−0.191559	−	0.981481i	$-0.561354\pi$
$619$	−9.53188			−0.383119			−0.191559	+	0.981481i	$0.561354\pi$
$620$	0.866517	−	1.50085i	0.0348002	−	0.0602756i
$621$	−2.84557	−	1.03570i	−0.114189	−	0.0415614i
$622$	−19.1380	−	16.0587i	−0.767364	−	0.643895i
$623$	4.28356	+	16.1790i	0.171617	+	0.648197i
$624$	0.231152	−	1.31093i	0.00925349	−	0.0524791i
$625$	−4.84262	+	27.4639i	−0.193705	+	1.09856i
$626$	−3.47719	−	6.02267i	−0.138976	−	0.240714i
$627$	3.43184	−	3.59316i	0.137054	−	0.143497i
$628$	−0.727893	+	1.26075i	−0.0290461	+	0.0503093i
$629$	39.8801	−	14.5152i	1.59012	−	0.578757i
$630$	0.728454	−	8.05017i	0.0290223	−	0.320726i
$631$	−17.9128	+	15.0306i	−0.713098	+	0.598360i	−0.925467	−	0.378829i	$-0.876327\pi$
$631$	−17.9128	+	15.0306i	−0.713098	+	0.598360i	0.212368	+	0.977190i	$0.431882\pi$
$632$	14.0479	−	5.11303i	0.558796	−	0.203385i
$633$	−5.37403	+	4.50935i	−0.213599	+	0.179230i
$634$	9.70172	−	16.8039i	0.385304	−	0.667367i
$635$	−3.37472	−	5.84518i	−0.133921	−	0.231959i
$636$	−0.922847	−	0.335889i	−0.0365932	−	0.0133189i
$637$	−9.16670	−	1.67267i	−0.363198	−	0.0662737i
$638$	0.499873	−	0.865805i	0.0197902	−	0.0342776i
$639$	7.56181			0.299140
$640$	−2.34035	+	1.96379i	−0.0925105	+	0.0776255i
$641$	−2.27609	+	12.9083i	−0.0899001	+	0.509849i	0.906291	+	0.422654i	$0.138901\pi$
$641$	−2.27609	+	12.9083i	−0.0899001	+	0.509849i	−0.996191	+	0.0871950i	$0.972210\pi$
$642$	−2.74310	−	15.5569i	−0.108262	−	0.613982i
$643$	1.78053	−	10.0979i	0.0702174	−	0.398223i	−0.929361	−	0.369173i	$-0.879641\pi$
$643$	1.78053	−	10.0979i	0.0702174	−	0.398223i	0.999578	−	0.0290493i	$-0.00924798\pi$
$644$	7.27125	−	3.36432i	0.286528	−	0.132573i
$645$	−22.6984			−0.893748
$646$	−8.73245	+	19.9077i	−0.343574	+	0.783258i
$647$	−13.1501	−	22.7767i	−0.516985	−	0.895445i	−0.999805	−	0.0197254i	$-0.993721\pi$
$647$	−13.1501	−	22.7767i	−0.516985	−	0.895445i	0.482820	−	0.875720i	$-0.339613\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	1.84665	+	1.54952i	0.0724872	+	0.0608239i
$650$	4.41916	−	3.70812i	0.173334	−	0.145444i
$651$	1.36209	−	0.630223i	0.0533845	−	0.0247004i
$652$	2.94402	+	16.6963i	0.115297	+	0.653879i
$653$	−7.46023			−0.291941			−0.145971	−	0.989289i	$-0.546631\pi$
$653$	−7.46023			−0.291941			−0.145971	+	0.989289i	$0.546631\pi$
$654$	1.93017			0.0754757
$655$	9.39457	+	53.2793i	0.367076	+	2.08179i
$656$	5.49388	−	4.60991i	0.214500	−	0.179987i
$657$	0.384775	−	0.666449i	0.0150115	−	0.0260007i
$658$	2.23525	−	4.75648i	0.0871390	−	0.185427i
$659$	−7.61162	−	43.1676i	−0.296506	−	1.68157i	−0.661016	−	0.750372i	$-0.729874\pi$
$659$	−7.61162	−	43.1676i	−0.296506	−	1.68157i	0.364509	−	0.931200i	$-0.381237\pi$
$660$	3.27251	−	1.19110i	0.127382	−	0.0463634i
$661$	−6.16769	−	2.24485i	−0.239895	−	0.0873147i	0.219275	−	0.975663i	$-0.429631\pi$
$661$	−6.16769	−	2.24485i	−0.239895	−	0.0873147i	−0.459170	+	0.888348i	$0.651853\pi$
$662$	21.5763	−	7.85315i	0.838589	−	0.305221i
$663$	1.15280	−	6.53787i	0.0447712	−	0.253910i
$664$	2.57378			0.0998819
$665$	−34.8133	−	5.42366i	−1.35000	−	0.210320i
$666$	−8.50967			−0.329743
$667$	−0.461185	+	2.61551i	−0.0178572	+	0.101273i
$668$	7.15090	−	2.60272i	0.276677	−	0.100702i
$669$	14.3242	+	5.21358i	0.553806	+	0.201569i
$670$	−43.5044	+	15.8343i	−1.68072	+	0.611733i
$671$	−1.35547	−	7.68728i	−0.0523275	−	0.296764i
$672$	−2.63636	+	0.222745i	−0.101700	+	0.00859257i
$673$	−22.1546	+	38.3729i	−0.853998	+	1.47917i	0.0235733	+	0.999722i	$0.492496\pi$
$673$	−22.1546	+	38.3729i	−0.853998	+	1.47917i	−0.877571	+	0.479446i	$0.840838\pi$
$674$	−20.2363	+	16.9803i	−0.779473	+	0.654055i
$675$	0.752539	+	4.26786i	0.0289652	+	0.164270i
$676$	−11.2280			−0.431847
$677$	8.60860			0.330855			0.165428	−	0.986222i	$-0.447100\pi$
$677$	8.60860			0.330855			0.165428	+	0.986222i	$0.447100\pi$
$678$	−2.52977	−	14.3470i	−0.0971552	−	0.550994i
$679$	37.6083	+	26.5008i	1.44327	+	1.01701i
$680$	−11.6718	+	9.79381i	−0.447593	+	0.375575i
$681$	−16.8651	−	14.1515i	−0.646271	−	0.542285i
$682$	0.495340	+	0.415639i	0.0189675	+	0.0159156i
$683$	−5.40581	−	9.36314i	−0.206848	−	0.358271i	0.743872	−	0.668322i	$-0.232987\pi$
$683$	−5.40581	−	9.36314i	−0.206848	−	0.358271i	−0.950720	+	0.310051i	$0.899654\pi$
$684$	3.01063	−	3.15215i	0.115114	−	0.120526i
$685$	−15.9301			−0.608658
$686$	1.44931	+	18.4635i	0.0553348	+	0.704938i
$687$	−0.858305	+	4.86769i	−0.0327464	+	0.185714i
$688$	1.29014	+	7.31677i	0.0491863	+	0.278949i
$689$	0.227008	−	1.28743i	0.00864832	−	0.0490471i
$690$	−7.08704	+	5.94673i	−0.269799	+	0.226388i
$691$	38.4134			1.46131			0.730657	−	0.682745i	$-0.239214\pi$
$691$	38.4134			1.46131			0.730657	+	0.682745i	$0.239214\pi$
$692$	1.34722	−	2.33346i	0.0512137	−	0.0887047i
$693$	2.91081	+	0.789243i	0.110572	+	0.0299809i
$694$	−4.23244	−	1.54048i	−0.160661	−	0.0584759i
$695$	−10.2018	−	17.6700i	−0.386977	−	0.670263i
$696$	0.438521	−	0.759541i	0.0166221	−	0.0287903i
$697$	27.3991	−	22.9906i	1.03782	−	0.870830i
$698$	−9.15327	+	3.33152i	−0.346457	+	0.126100i
$699$	−14.3936	+	12.0777i	−0.544417	+	0.456820i
$700$	−9.37268	−	6.60449i	−0.354254	−	0.249626i
$701$	38.4371	−	13.9900i	1.45175	−	0.528393i	0.508670	−	0.860962i	$-0.330137\pi$
$701$	38.4371	−	13.9900i	1.45175	−	0.528393i	0.943079	+	0.332568i	$0.107915\pi$
$702$	−0.665576	+	1.15281i	−0.0251205	+	0.0435101i
$703$	−2.38367	+	37.0161i	−0.0899020	+	1.39609i
$704$	−0.569953	−	0.987187i	−0.0214809	−	0.0372060i
$705$	−1.05381	+	5.97647i	−0.0396889	+	0.225087i
$706$	0.897516	−	5.09007i	0.0337785	−	0.191567i
$707$	−15.8933	−	4.30935i	−0.597729	−	0.162070i
$708$	1.62000	+	1.35934i	0.0608833	+	0.0510871i
$709$	1.90480	+	0.693291i	0.0715363	+	0.0260371i	0.377540	−	0.925993i	$-0.376770\pi$
$709$	1.90480	+	0.693291i	0.0715363	+	0.0260371i	−0.306004	+	0.952030i	$0.598992\pi$
$710$	11.5511	−	20.0070i	0.433504	−	0.750851i
$711$	−14.9495			−0.560650
$712$	−4.84583	+	4.06613i	−0.181605	+	0.152385i
$713$	−1.61417	−	0.587511i	−0.0604512	−	0.0220025i
$714$	−13.1481	+	1.11087i	−0.492054	+	0.0415734i
$715$	2.31789	+	4.01471i	0.0866843	+	0.150142i
$716$	9.16665	+	3.33639i	0.342574	+	0.124687i
$717$	−2.54756	+	14.4479i	−0.0951403	+	0.539567i
$718$	−24.7524	−	9.00913i	−0.923750	−	0.336218i
$719$	−27.0482	−	22.6962i	−1.00873	−	0.846424i	−0.0205589	−	0.999789i	$-0.506545\pi$
$719$	−27.0482	−	22.6962i	−1.00873	−	0.846424i	−0.988170	+	0.153365i	$0.950989\pi$
$720$	2.87086	−	1.04491i	0.106991	−	0.0389415i
$721$	−21.1088	+	44.9183i	−0.786132	+	1.67285i
$722$	−12.8682	−	13.9789i	−0.478905	−	0.520240i
$723$	−4.01744	+	6.95841i	−0.149410	+	0.258786i
$724$	5.62560	+	4.72044i	0.209074	+	0.175434i
$725$	3.57162	−	1.29996i	0.132647	−	0.0482794i
$726$	−1.68449	−	9.55324i	−0.0625174	−	0.354554i
$727$	11.4180	+	9.58083i	0.423470	+	0.355333i	0.829481	−	0.558535i	$-0.188636\pi$
$727$	11.4180	+	9.58083i	0.423470	+	0.355333i	−0.406011	+	0.913868i	$0.633081\pi$
$728$	−0.901402	−	3.40459i	−0.0334082	−	0.126182i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−1.17553	−	2.03608i	−0.0435083	−	0.0753585i
$731$	6.43421	+	36.4902i	0.237978	+	1.34964i
$732$	−1.18911	−	6.74378i	−0.0439508	−	0.249257i
$733$	−20.3313	−	35.2148i	−0.750954	−	1.30069i	−0.947361	−	0.320168i	$-0.896261\pi$
$733$	−20.3313	−	35.2148i	−0.750954	−	1.30069i	0.196407	−	0.980522i	$-0.437073\pi$
$734$	3.17522	+	5.49964i	0.117199	+	0.202995i
$735$	−7.19458	−	20.1392i	−0.265376	−	0.742847i
$736$	2.31973	+	1.94649i	0.0855065	+	0.0717485i
$737$	−2.99958	−	17.0114i	−0.110491	−	0.626624i
$738$	−6.73924	+	2.45288i	−0.248075	+	0.0902919i
$739$	−29.8667	−	25.0612i	−1.09867	−	0.921890i	−0.101331	−	0.994853i	$-0.532310\pi$
$739$	−29.8667	−	25.0612i	−1.09867	−	0.921890i	−0.997335	+	0.0729631i	$0.976754\pi$
$740$	−12.9990	+	22.5149i	−0.477852	+	0.827665i
$741$	4.82816	+	3.21810i	0.177367	+	0.118220i
$742$	−2.58910	+	0.218752i	−0.0950487	+	0.00803063i
$743$	38.1353	−	13.8801i	1.39905	−	0.509212i	0.471152	−	0.882052i	$-0.343838\pi$
$743$	38.1353	−	13.8801i	1.39905	−	0.509212i	0.927895	+	0.372841i	$0.121616\pi$
$744$	0.434544	+	0.364626i	0.0159312	+	0.0133678i
$745$	3.97437	+	1.44655i	0.145610	+	0.0529976i
$746$	−1.09287	+	6.19799i	−0.0400129	+	0.226925i
$747$	−2.41856	−	0.880283i	−0.0884904	−	0.0322079i
$748$	−2.84247	−	4.92330i	−0.103931	−	0.180014i
$749$	−23.8704	−	34.3074i	−0.872205	−	1.25356i
$750$	−1.91286	−	0.696225i	−0.0698479	−	0.0254226i
$751$	−28.2643	+	23.7166i	−1.03138	+	0.865430i	−0.991014	−	0.133755i	$-0.957297\pi$
$751$	−28.2643	+	23.7166i	−1.03138	+	0.865430i	−0.0403651	+	0.999185i	$0.512852\pi$
$752$	1.98640			0.0724365
$753$	−12.1570	+	21.0566i	−0.443027	+	0.767346i
$754$	1.09707	+	0.399301i	0.0399529	+	0.0145417i
$755$	−14.9284	−	12.5264i	−0.543301	−	0.455884i
$756$	2.55355	+	0.692376i	0.0928717	+	0.0251815i
$757$	6.09996	−	34.5946i	0.221707	−	1.25736i	−0.647175	−	0.762342i	$-0.724050\pi$
$757$	6.09996	−	34.5946i	0.221707	−	1.25736i	0.868881	−	0.495020i	$-0.164839\pi$
$758$	−0.222092	+	1.25954i	−0.00806673	+	0.0457487i
$759$	−1.72593	−	2.98940i	−0.0626473	−	0.108508i
$760$	−3.74107	−	12.7806i	−0.135703	−	0.463602i
$761$	−19.0246	+	32.9515i	−0.689640	+	1.19449i	0.282314	+	0.959322i	$0.408898\pi$
$761$	−19.0246	+	32.9515i	−0.689640	+	1.19449i	−0.971954	+	0.235170i	$0.924435\pi$
$762$	2.07599	−	0.755600i	0.0752053	−	0.0273725i
$763$	4.63469	−	2.14442i	0.167787	−	0.0776332i
$764$	14.9096	−	12.5106i	0.539409	−	0.452618i
$765$	14.3176	−	5.21118i	0.517654	−	0.188410i
$766$	12.1519	−	10.1967i	0.439066	−	0.368420i
$767$	−1.40753	+	2.43792i	−0.0508230	+	0.0880281i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	28.3739	+	10.3273i	1.02319	+	0.372411i	0.798484	−	0.602016i	$-0.205636\pi$
$769$	28.3739	+	10.3273i	1.02319	+	0.372411i	0.224706	+	0.974427i	$0.427858\pi$
$770$	6.53460	−	6.49581i	0.235491	−	0.234093i
$771$	−8.57301	+	14.8489i	−0.308749	+	0.534770i
$772$	24.3062			0.874800
$773$	7.83016	−	6.57028i	0.281631	−	0.236317i	−0.491019	−	0.871149i	$-0.663375\pi$
$773$	7.83016	−	6.57028i	0.281631	−	0.236317i	0.772650	+	0.634832i	$0.218931\pi$
$774$	1.29014	−	7.31677i	0.0463733	−	0.262996i
$775$	0.426883	+	2.42097i	0.0153341	+	0.0869640i
$776$	−3.01959	+	17.1250i	−0.108397	+	0.614751i
$777$	−20.4333	+	9.45424i	−0.733040	+	0.339169i
$778$	12.2683			0.439839
$779$	8.78202	+	30.0020i	0.314648	+	1.07493i
$780$	2.03341	+	3.52197i	0.0728077	+	0.126107i
$781$	6.60311	+	5.54066i	0.236278	+	0.198261i
$782$	11.5690	+	9.70753i	0.413706	+	0.347141i
$783$	−0.671854	+	0.563752i	−0.0240101	+	0.0201469i
$784$	−6.08291	+	3.46384i	−0.217247	+	0.123709i
$785$	−0.772315	−	4.38002i	−0.0275651	−	0.156330i
$786$	−17.7084			−0.631639
$787$	−8.97490			−0.319920			−0.159960	−	0.987123i	$-0.551137\pi$
$787$	−8.97490			−0.319920			−0.159960	+	0.987123i	$0.551137\pi$
$788$	2.36822	+	13.4308i	0.0843642	+	0.478453i
$789$	−2.99587	+	2.51383i	−0.106656	+	0.0894947i
$790$	−22.8362	+	39.5534i	−0.812474	+	1.40725i
$791$	−22.0140	−	31.6393i	−0.782727	−	1.12496i
$792$	0.197943	+	1.12259i	0.00703358	+	0.0398894i
$793$	8.56575	−	3.11768i	0.304179	−	0.110712i
$794$	−5.39387	−	1.96321i	−0.191421	−	0.0696716i
$795$	2.81940	−	1.02618i	0.0999937	−	0.0363947i
$796$	3.94757	−	22.3878i	0.139918	−	0.793513i
$797$	50.6851			1.79536			0.897678	−	0.440651i	$-0.145252\pi$
$797$	50.6851			1.79536			0.897678	+	0.440651i	$0.145252\pi$
$798$	3.72704	−	10.9137i	0.131936	−	0.386341i
$799$	9.90658			0.350469
$800$	0.752539	−	4.26786i	0.0266063	−	0.150892i
$801$	5.94428	−	2.16354i	0.210031	−	0.0764450i
$802$	14.1743	+	5.15901i	0.500510	+	0.182171i
$803$	0.824311	−	0.300025i	0.0290893	−	0.0105876i
$804$	−2.63143	−	14.9236i	−0.0928032	−	0.526313i
$805$	−10.4105	+	22.1529i	−0.366921	+	0.780787i
$806$	−0.377553	+	0.653941i	−0.0132987	+	0.0230341i
$807$	8.31048	−	6.97332i	0.292543	−	0.245473i
$808$	−1.08079	−	6.12945i	−0.0380220	−	0.215633i
$809$	−11.4145			−0.401311			−0.200656	−	0.979662i	$-0.564307\pi$
$809$	−11.4145			−0.401311			−0.200656	+	0.979662i	$0.564307\pi$
$810$	−3.05511			−0.107346
$811$	−0.685364	−	3.88689i	−0.0240664	−	0.136487i	0.970407	−	0.241474i	$-0.0776310\pi$
$811$	−0.685364	−	3.88689i	−0.0240664	−	0.136487i	−0.994474	+	0.104987i	$0.966520\pi$
$812$	0.209120	−	2.31100i	0.00733868	−	0.0811000i
$813$	19.8059	−	16.6191i	0.694622	−	0.582857i
$814$	−7.43080	−	6.23518i	−0.260449	−	0.218543i
$815$	−39.6781	−	33.2939i	−1.38986	−	1.16623i
$816$	−2.49360	−	4.31905i	−0.0872935	−	0.151197i
$817$	−31.4657	−	7.66151i	−1.10085	−	0.268042i
$818$	2.49836			0.0873532
$819$	−0.317397	+	3.50757i	−0.0110908	+	0.122564i
$820$	−3.80472	+	21.5776i	−0.132866	+	0.753523i
$821$	8.41388	+	47.7175i	0.293647	+	1.66535i	0.672653	+	0.739958i	$0.265155\pi$
$821$	8.41388	+	47.7175i	0.293647	+	1.66535i	−0.379006	+	0.925394i	$0.623734\pi$
$822$	0.905444	−	5.13503i	0.0315810	−	0.179105i
$823$	−2.65666	+	2.22920i	−0.0926053	+	0.0777051i	−0.687915	−	0.725791i	$-0.741474\pi$
$823$	−2.65666	+	2.22920i	−0.0926053	+	0.0777051i	0.595310	+	0.803496i	$0.297029\pi$
$824$	−18.7588			−0.653492
$825$	−2.47000	+	4.27817i	−0.0859945	+	0.148947i
$826$	5.40014	+	1.46421i	0.187895	+	0.0509463i
$827$	18.1299	+	6.59875i	0.630439	+	0.229461i	0.637422	−	0.770514i	$-0.280001\pi$
$827$	18.1299	+	6.59875i	0.630439	+	0.229461i	−0.00698321	+	0.999976i	$0.502223\pi$
$828$	−1.51410	−	2.62250i	−0.0526186	−	0.0911380i
$829$	−4.72648	+	8.18651i	−0.164158	+	0.284329i	−0.936356	−	0.351052i	$-0.885824\pi$
$829$	−4.72648	+	8.18651i	−0.164158	+	0.284329i	0.772198	+	0.635382i	$0.219157\pi$
$830$	−6.02354	+	5.05435i	−0.209080	+	0.175439i
$831$	22.2859	−	8.11139i	0.773088	−	0.281381i
$832$	1.01972	−	0.855648i	0.0353525	−	0.0296643i
$833$	−30.3367	+	17.2749i	−1.05110	+	0.598540i
$834$	6.27575	−	2.28419i	0.217312	−	0.0790950i
$835$	−11.6244	+	20.1341i	−0.402280	+	0.696770i
$836$	4.93858	−	0.546576i	0.170804	−	0.0189037i
$837$	−0.283629	−	0.491259i	−0.00980364	−	0.0169804i
$838$	1.82854	−	10.3702i	0.0631660	−	0.358232i
$839$	1.47288	−	8.35309i	0.0508493	−	0.288381i	−0.948770	−	0.315967i	$-0.897671\pi$
$839$	1.47288	−	8.35309i	0.0508493	−	0.288381i	0.999619	+	0.0275864i	$0.00878215\pi$
$840$	5.73258	−	5.69855i	0.197793	−	0.196619i
$841$	−21.6260	−	18.1464i	−0.745726	−	0.625738i
$842$	11.7370	+	4.27192i	0.404484	+	0.147220i
$843$	7.57377	−	13.1182i	0.260855	−	0.451813i
$844$	−7.01530			−0.241477
$845$	26.2775	−	22.0495i	0.903975	−	0.758525i
$846$	−1.86660	−	0.679388i	−0.0641752	−	0.0233579i
$847$	−14.6584	−	21.0676i	−0.503669	−	0.723892i
$848$	−0.491036	−	0.850500i	−0.0168623	−	0.0292063i
$849$	10.1759	+	3.70373i	0.349236	+	0.127112i
$850$	3.75306	−	21.2847i	0.128729	−	0.730059i
$851$	24.2149	+	8.81350i	0.830076	+	0.302123i
$852$	5.79268	+	4.86064i	0.198454	+	0.166523i
$853$	46.9448	−	17.0865i	1.60736	−	0.585031i	0.626444	−	0.779467i	$-0.284510\pi$
$853$	46.9448	−	17.0865i	1.60736	−	0.585031i	0.980915	+	0.194436i	$0.0622876\pi$
$854$	−10.3476	−	14.8720i	−0.354088	−	0.508908i
$855$	−0.855778	+	13.2894i	−0.0292670	+	0.454488i
$856$	7.89845	−	13.6805i	0.269963	−	0.467590i
$857$	7.55707	+	6.34114i	0.258145	+	0.216609i	0.762670	−	0.646788i	$-0.223888\pi$
$857$	7.55707	+	6.34114i	0.258145	+	0.216609i	−0.504525	+	0.863397i	$0.668332\pi$
$858$	−1.42588	+	0.518977i	−0.0486787	+	0.0177176i
$859$	2.51361	+	14.2554i	0.0857632	+	0.486387i	0.997189	+	0.0749233i	$0.0238712\pi$
$859$	2.51361	+	14.2554i	0.0857632	+	0.486387i	−0.911426	+	0.411464i	$0.865018\pi$
$860$	−17.3880	−	14.5902i	−0.592925	−	0.497523i
$861$	−13.4570	+	13.3771i	−0.458613	+	0.455891i
$862$	0.128093	+	0.221863i	0.00436286	+	0.00755669i
$863$	−12.1096	−	20.9745i	−0.412216	−	0.713979i	0.582916	−	0.812533i	$-0.301912\pi$
$863$	−12.1096	−	20.9745i	−0.412216	−	0.713979i	−0.995132	+	0.0985534i	$0.968578\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	1.42944	+	8.10676i	0.0486024	+	0.275638i
$866$	12.1548	+	21.0527i	0.413037	+	0.715401i
$867$	−3.93611	−	6.81754i	−0.133677	−	0.231536i
$868$	1.44852	+	0.392755i	0.0491660	+	0.0133310i
$869$	−13.0542	−	10.9537i	−0.442832	−	0.371580i
$870$	0.465284	+	2.63876i	0.0157746	+	0.0894622i
$871$	18.9555	−	6.89922i	0.642281	−	0.233771i
$872$	1.47860	+	1.24069i	0.0500716	+	0.0420151i
$873$	8.69458	−	15.0594i	0.294267	−	0.509685i
$874$	−11.8317	+	5.85156i	−0.400213	+	0.197932i
$875$	−5.36664	+	0.453425i	−0.181426	+	0.0153286i
$876$	0.723140	−	0.263201i	0.0244326	−	0.00889275i
$877$	−37.2181	−	31.2297i	−1.25677	−	1.05455i	−0.996019	−	0.0891464i	$-0.971586\pi$
$877$	−37.2181	−	31.2297i	−1.25677	−	1.05455i	−0.260749	−	0.965407i	$-0.583969\pi$
$878$	32.5378	+	11.8428i	1.09810	+	0.399675i
$879$	−0.820110	+	4.65107i	−0.0276616	+	0.156877i
$880$	3.27251	+	1.19110i	0.110316	+	0.0401519i
$881$	27.2890	+	47.2659i	0.919389	+	1.59243i	0.800346	+	0.599539i	$0.204649\pi$
$881$	27.2890	+	47.2659i	0.919389	+	1.59243i	0.119043	+	0.992889i	$0.462017\pi$
$882$	6.90077	−	1.17447i	0.232361	−	0.0395465i
$883$	−7.08753	−	2.57965i	−0.238514	−	0.0868122i	0.219997	−	0.975500i	$-0.429395\pi$
$883$	−7.08753	−	2.57965i	−0.238514	−	0.0868122i	−0.458512	+	0.888688i	$0.651617\pi$
$884$	5.08556	−	4.26729i	0.171046	−	0.143525i
$885$	−6.46082			−0.217178
$886$	−4.77487	+	8.27031i	−0.160415	+	0.277847i
$887$	−26.5624	−	9.66791i	−0.891877	−	0.324617i	−0.144884	−	0.989449i	$-0.546281\pi$
$887$	−26.5624	−	9.66791i	−0.891877	−	0.324617i	−0.746993	+	0.664832i	$0.768503\pi$
$888$	−6.51879	−	5.46991i	−0.218756	−	0.183558i
$889$	4.14537	−	4.12076i	0.139031	−	0.138206i
$890$	3.35591	−	19.0323i	0.112491	−	0.637965i
$891$	0.197943	−	1.12259i	0.00663132	−	0.0376081i
$892$	7.62175	+	13.2013i	0.255195	+	0.442011i
$893$	−3.47812	+	7.92921i	−0.116391	+	0.265341i
$894$	−0.692191	+	1.19891i	−0.0231503	+	0.0400975i
$895$	−28.0051	+	10.1930i	−0.936109	+	0.340716i
$896$	−2.16275	−	1.52399i	−0.0722522	−	0.0509128i
$897$	3.08792	−	2.59107i	0.103103	−	0.0865133i
$898$	−10.5006	+	3.82191i	−0.350410	+	0.127539i
$899$	−0.381114	+	0.319793i	−0.0127109	+	0.0106657i
$900$	−2.16685	+	3.75309i	−0.0722283	+	0.125103i
$901$	−2.44890	−	4.24162i	−0.0815847	−	0.141309i
$902$	−7.68210	−	2.79606i	−0.255786	−	0.0930985i
$903$	−5.03105	−	19.0023i	−0.167423	−	0.632355i
$904$	7.28418	−	12.6166i	0.242268	−	0.419621i
$905$	−22.4358			−0.745791
$906$	4.88638	−	4.10016i	0.162339	−	0.136219i
$907$	−0.124708	+	0.707256i	−0.00414087	+	0.0234841i	−0.986808	−	0.161894i	$-0.948240\pi$
$907$	−0.124708	+	0.707256i	−0.00414087	+	0.0234841i	0.982667	+	0.185378i	$0.0593509\pi$
$908$	−3.82300	−	21.6813i	−0.126871	−	0.719519i
$909$	−1.08079	+	6.12945i	−0.0358475	+	0.203301i
$910$	8.79549	+	6.19777i	0.291568	+	0.205454i
$911$	−46.2601			−1.53267			−0.766333	−	0.642444i	$-0.777921\pi$
$911$	−46.2601			−1.53267			−0.766333	+	0.642444i	$0.777921\pi$
$912$	4.33245	−	0.479492i	0.143462	−	0.0158776i
$913$	−1.46693	−	2.54080i	−0.0485483	−	0.0840882i
$914$	2.12575	+	1.78372i	0.0703137	+	0.0590002i
$915$	16.0263	+	13.4477i	0.529813	+	0.444566i
$916$	−3.78639	+	3.17716i	−0.125106	+	0.104976i
$917$	−42.5212	+	19.6741i	−1.40417	+	0.649694i
$918$	0.866019	+	4.91144i	0.0285829	+	0.162102i
$919$	−10.1594			−0.335128			−0.167564	−	0.985861i	$-0.553590\pi$
$919$	−10.1594			−0.335128			−0.167564	+	0.985861i	$0.553590\pi$
$920$	−9.25147			−0.305012
$921$	4.80028	+	27.2237i	0.158175	+	0.897053i
$922$	22.3914	−	18.7886i	0.737421	−	0.618770i
$923$	−5.03296	+	8.71734i	−0.165662	+	0.286935i
$924$	1.72249	+	2.47562i	0.0566658	+	0.0814421i
$925$	−6.40386	−	36.3181i	−0.210558	−	1.19413i
$926$	−0.249370	+	0.0907631i	−0.00819479	+	0.00298266i
$927$	17.6275	+	6.41587i	0.578962	+	0.210725i
$928$	0.824151	−	0.299966i	0.0270541	−	0.00984688i
$929$	−8.51447	+	48.2880i	−0.279351	+	1.58428i	0.445443	+	0.895311i	$0.353046\pi$
$929$	−8.51447	+	48.2880i	−0.279351	+	1.58428i	−0.724793	+	0.688966i	$0.758065\pi$
$930$	−1.73303			−0.0568284
$931$	−3.17582	−	30.3466i	−0.104083	−	0.994569i
$932$	−18.7895			−0.615472
$933$	−4.33823	+	24.6033i	−0.142027	+	0.805477i
$934$	−15.9715	+	5.81315i	−0.522603	+	0.190212i
$935$	16.3207	+	5.94025i	0.533744	+	0.194267i
$936$	−1.25087	+	0.455281i	−0.0408861	+	0.0148813i
$937$	−1.69138	−	9.59230i	−0.0552550	−	0.313367i	0.944636	−	0.328120i	$-0.106415\pi$
$937$	−1.69138	−	9.59230i	−0.0552550	−	0.313367i	−0.999891	+	0.0147529i	$0.995304\pi$
$938$	−22.8986	−	32.9107i	−0.747666	−	1.07457i
$939$	−3.47719	+	6.02267i	−0.113474	+	0.196542i
$940$	−4.64887	+	3.90086i	−0.151629	+	0.127232i
$941$	−8.55419	−	48.5132i	−0.278859	−	1.58149i	−0.726431	−	0.687239i	$-0.758822\pi$
$941$	−8.55419	−	48.5132i	−0.278859	−	1.58149i	0.447573	−	0.894248i	$-0.352289\pi$
$942$	1.45579			0.0474321
$943$	21.7175			0.707218
$944$	0.367224	+	2.08263i	0.0119521	+	0.0677838i
$945$	−7.33588	+	3.39423i	−0.238636	+	0.110414i
$946$	6.48770	−	5.44383i	0.210933	−	0.176994i
$947$	−3.52719	−	2.95966i	−0.114618	−	0.0961762i	0.583677	−	0.811986i	$-0.301613\pi$
$947$	−3.52719	−	2.95966i	−0.114618	−	0.0961762i	−0.698295	+	0.715810i	$0.746058\pi$
$948$	−11.4520	−	9.60935i	−0.371943	−	0.312097i
$949$	0.512193	+	0.887145i	0.0166265	+	0.0287979i
$950$	15.7186	+	10.4768i	0.509978	+	0.339914i
$951$	−19.4034			−0.629199
$952$	−10.7861	−	7.60043i	−0.349578	−	0.246331i
$953$	−5.89542	+	33.4346i	−0.190972	+	1.08305i	0.727068	+	0.686565i	$0.240882\pi$
$953$	−5.89542	+	33.4346i	−0.190972	+	1.08305i	−0.918040	+	0.396488i	$0.870229\pi$
$954$	0.170535	+	0.967153i	0.00552128	+	0.0313127i
$955$	−10.3254	+	58.5584i	−0.334123	+	1.89490i
$956$	−11.2385	+	9.43021i	−0.363478	+	0.304995i
$957$	−0.999746			−0.0323172
$958$	9.46157	−	16.3879i	0.305689	−	0.529469i
$959$	−3.53088	−	13.3361i	−0.114018	−	0.430645i
$960$	2.87086	+	1.04491i	0.0926568	+	0.0337243i
$961$	15.3391	+	26.5681i	0.494810	+	0.857036i
$962$	5.66383	−	9.81004i	0.182609	−	0.316289i
$963$	−12.1011	+	10.1540i	−0.389953	+	0.327210i
$964$	−7.55031	+	2.74809i	−0.243179	+	0.0885100i
$965$	−56.8850	+	47.7322i	−1.83119	+	1.53655i
$966$	−6.54922	−	4.61493i	−0.210718	−	0.148483i
$967$	34.0587	−	12.3963i	1.09525	−	0.398640i	0.269689	−	0.962948i	$-0.413079\pi$
$967$	34.0587	−	12.3963i	1.09525	−	0.398640i	0.825564	+	0.564308i	$0.190857\pi$
$968$	4.85031	−	8.40098i	0.155895	−	0.270018i
$969$	21.6068	−	2.39133i	0.694110	−	0.0768205i
$970$	−26.5629	−	46.0083i	−0.852883	−	1.47724i
$971$	5.71940	−	32.4363i	0.183544	−	1.04093i	−0.744267	−	0.667882i	$-0.767201\pi$
$971$	5.71940	−	32.4363i	0.183544	−	1.04093i	0.927811	−	0.373050i	$-0.121688\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	12.5315	−	12.4571i	0.401742	−	0.399357i
$974$	−28.2336	−	23.6908i	−0.904662	−	0.759101i
$975$	−5.42091	−	1.97305i	−0.173608	−	0.0631881i
$976$	3.42391	−	5.93038i	0.109597	−	0.189827i
$977$	−10.8180			−0.346099			−0.173050	−	0.984913i	$-0.555362\pi$
$977$	−10.8180			−0.346099			−0.173050	+	0.984913i	$0.555362\pi$
$978$	12.9874	−	10.8978i	0.415293	−	0.348472i
$979$	6.77592	+	2.46623i	0.216559	+	0.0788212i
$980$	7.43389	−	20.0521i	0.237467	−	0.640542i
$981$	−0.965086	−	1.67158i	−0.0308128	−	0.0533694i
$982$	8.40347	+	3.05861i	0.268166	+	0.0976043i
$983$	8.85006	−	50.1912i	0.282273	−	1.60085i	−0.432594	−	0.901589i	$-0.642402\pi$
$983$	8.85006	−	50.1912i	0.282273	−	1.60085i	0.714867	−	0.699261i	$-0.246487\pi$
$984$	−6.73924	−	2.45288i	−0.214839	−	0.0781951i
$985$	−31.9177	−	26.7822i	−1.01698	−	0.853350i
$986$	4.11021	−	1.49599i	0.130896	−	0.0476421i
$987$	−5.23686	+	0.442460i	−0.166691	+	0.0140837i
$988$	1.63003	+	5.56869i	0.0518583	+	0.177164i
$989$	−11.2492	+	19.4842i	−0.357704	+	0.619561i
$990$	−2.66778	−	2.23853i	−0.0847876	−	0.0711452i
$991$	30.8613	−	11.2326i	0.980341	−	0.356815i	0.198368	−	0.980128i	$-0.436436\pi$
$991$	30.8613	−	11.2326i	0.980341	−	0.356815i	0.781973	+	0.623313i	$0.214214\pi$
$992$	0.0985032	+	0.558639i	0.00312748	+	0.0177368i
$993$	−17.5892	−	14.7591i	−0.558176	−	0.468366i
$994$	19.3094	+	5.23561i	0.612458	+	0.166064i
$995$	34.7261	+	60.1474i	1.10089	+	1.90680i
$996$	−1.28689	−	2.22896i	−0.0407766	−	0.0706272i
$997$	6.90380	+	39.1534i	0.218646	+	1.24000i	0.874467	+	0.485085i	$0.161211\pi$
$997$	6.90380	+	39.1534i	0.218646	+	1.24000i	−0.655822	+	0.754916i	$0.727678\pi$
$998$	−2.48571	−	14.0972i	−0.0786838	−	0.446238i
$999$	4.25484	+	7.36959i	0.134617	+	0.233164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bq.d.499.6	yes	36
7.4	even	3		798.2.bp.d.613.1	yes	36
19.4	even	9		798.2.bp.d.289.1	✓	36
133.4	even	9	inner	798.2.bq.d.403.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.d.289.1	✓	36	19.4	even	9
798.2.bp.d.613.1	yes	36	7.4	even	3
798.2.bq.d.403.6	yes	36	133.4	even	9	inner
798.2.bq.d.499.6	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.87086 - 1.04491i) q^{5} +(0.173648 + 0.984808i) q^{6} +(1.51108 + 2.17178i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.530514 - 3.00870i) q^{10} +1.13991 q^{11} +1.00000 q^{12} +(0.231152 + 1.31093i) q^{13} +(2.40118 - 1.11100i) q^{14} +(-2.34035 + 1.96379i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.82042 + 3.20571i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.90717 + 1.93236i) q^{19} -3.05511 q^{20} +(-2.16275 - 1.52399i) q^{21} +(0.197943 - 1.12259i) q^{22} +(0.525841 + 2.98219i) q^{23} +(0.173648 - 0.984808i) q^{24} +(3.31981 - 2.78565i) q^{25} +1.33115 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.677160 - 2.55763i) q^{28} +(0.824151 + 0.299966i) q^{29} +(1.52756 + 2.64580i) q^{30} +(-0.283629 + 0.491259i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-1.07116 + 0.389871i) q^{33} +(3.82042 - 3.20571i) q^{34} +(6.60742 + 4.65594i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(4.25484 - 7.36959i) q^{37} +(1.22453 + 4.18336i) q^{38} +(-0.665576 - 1.15281i) q^{39} +(-0.530514 + 3.00870i) q^{40} +(1.24536 - 7.06280i) q^{41} +(-1.87639 + 1.86525i) q^{42} +(5.69144 + 4.77568i) q^{43} +(-1.07116 - 0.389871i) q^{44} +(1.52756 - 2.64580i) q^{45} +3.02820 q^{46} +(1.52167 - 1.27683i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-2.43326 + 6.56348i) q^{49} +(-2.16685 - 3.75309i) q^{50} +(-4.68644 - 1.70572i) q^{51} +(0.231152 - 1.31093i) q^{52} +(-0.922847 - 0.335889i) q^{53} +(0.766044 + 0.642788i) q^{54} +(3.27251 - 1.19110i) q^{55} +(-2.63636 + 0.222745i) q^{56} +(3.01063 - 3.15215i) q^{57} +(0.438521 - 0.759541i) q^{58} +(1.62000 + 1.35934i) q^{59} +(2.87086 - 1.04491i) q^{60} +(-1.18911 - 6.74378i) q^{61} +(0.434544 + 0.364626i) q^{62} +(2.55355 + 0.692376i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.03341 + 3.52197i) q^{65} +(0.197943 + 1.12259i) q^{66} +(-2.63143 - 14.9236i) q^{67} +(-2.49360 - 4.31905i) q^{68} +(-1.51410 - 2.62250i) q^{69} +(5.73258 - 5.69855i) q^{70} +(5.79268 + 4.86064i) q^{71} +(0.173648 + 0.984808i) q^{72} +(0.723140 - 0.263201i) q^{73} +(-6.51879 - 5.46991i) q^{74} +(-2.16685 + 3.75309i) q^{75} +(4.33245 - 0.479492i) q^{76} +(1.72249 + 2.47562i) q^{77} +(-1.25087 + 0.455281i) q^{78} +(-11.4520 - 9.60935i) q^{79} +(2.87086 + 1.04491i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-6.73924 - 2.45288i) q^{82} +(-1.28689 - 2.22896i) q^{83} +(1.51108 + 2.17178i) q^{84} +(14.3176 + 5.21118i) q^{85} +(5.69144 - 4.77568i) q^{86} -0.877043 q^{87} +(-0.569953 + 0.987187i) q^{88} +(5.94428 + 2.16354i) q^{89} +(-2.34035 - 1.96379i) q^{90} +(-2.49776 + 2.48293i) q^{91} +(0.525841 - 2.98219i) q^{92} +(0.0985032 - 0.558639i) q^{93} +(-0.993199 - 1.72027i) q^{94} +(-9.19782 + 9.63018i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(16.3405 - 5.94744i) q^{97} +(6.04123 + 3.53603i) q^{98} +(0.873218 - 0.732717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} - 18 q^{8} - 6 q^{10} - 6 q^{11} + 36 q^{12} + 27 q^{13} + 3 q^{15} - 3 q^{17} - 18 q^{18} + 6 q^{19} - 6 q^{20} - 3 q^{22} - 18 q^{23} - 21 q^{25} - 18 q^{26} - 18 q^{27} + 12 q^{28} + 9 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 - 18 * q^8 - 6 * q^10 - 6 * q^11 + 36 * q^12 + 27 * q^13 + 3 * q^15 - 3 * q^17 - 18 * q^18 + 6 * q^19 - 6 * q^20 - 3 * q^22 - 18 * q^23 - 21 * q^25 - 18 * q^26 - 18 * q^27 + 12 * q^28 + 9 * q^29 + 3 * q^30 - 3 * q^31 - 3 * q^33 - 3 * q^34 + 12 * q^35 + 21 * q^37 + 9 * q^38 + 9 * q^39 - 6 * q^40 - 9 * q^41 - 15 * q^42 + 51 * q^43 - 3 * q^44 + 3 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 27 * q^52 - 15 * q^53 + 27 * q^55 - 9 * q^57 + 18 * q^58 + 33 * q^59 + 3 * q^60 + 21 * q^61 - 24 * q^62 + 3 * q^63 - 18 * q^64 + 42 * q^65 - 3 * q^66 - 3 * q^67 + 18 * q^68 + 6 * q^69 - 33 * q^70 + 6 * q^71 - 42 * q^73 - 3 * q^74 - 9 * q^75 - 6 * q^76 + 9 * q^77 - 27 * q^78 - 24 * q^79 + 3 * q^80 + 27 * q^82 + 30 * q^83 + 36 * q^85 + 51 * q^86 - 36 * q^87 + 3 * q^88 - 42 * q^89 + 3 * q^90 + 24 * q^91 - 18 * q^92 + 21 * q^93 + 18 * q^94 - 39 * q^95 - 18 * q^96 + 45 * q^97 + 3 * q^98 + 6 * q^99

Introduction

L-functions

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