LMFDB - Embedded newform 230.2.l.a.43.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	230.43
Dual form			230.2.l.a.107.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.800541 + 0.599278i) q^{2} +(-1.19905 + 0.447221i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-1.17492 + 1.90251i) q^{5} +(-1.22790 - 0.360543i) q^{6} +(-4.10116 - 0.892152i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-1.02954 + 0.892104i) q^{9} +(-2.08071 + 0.818938i) q^{10} +(2.30200 + 0.330978i) q^{11} +(-0.766916 - 1.02448i) q^{12} +(-0.202830 - 0.932393i) q^{13} +(-2.74850 - 3.17194i) q^{14} +(0.557939 - 2.80665i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(3.53412 + 6.47225i) q^{17} +(-1.35881 + 0.0971840i) q^{18} +(2.40484 - 0.706126i) q^{19} +(-2.15646 - 0.591327i) q^{20} +(5.31647 - 0.764393i) q^{21} +(1.64450 + 1.64450i) q^{22} +(-4.75448 + 0.628433i) q^{23} -1.27973i q^{24} +(-2.23913 - 4.47061i) q^{25} +(0.396389 - 0.867970i) q^{26} +(2.67544 - 4.89969i) q^{27} +(-0.299416 - 4.18638i) q^{28} +(-1.30732 + 4.45233i) q^{29} +(2.12862 - 1.91248i) q^{30} +(4.15467 + 9.09747i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(-2.90823 + 0.632646i) q^{33} +(-1.04947 + 7.29922i) q^{34} +(6.51587 - 6.75431i) q^{35} +(-1.14602 - 0.736505i) q^{36} +(-0.541530 + 7.57158i) q^{37} +(2.34834 + 0.875887i) q^{38} +(0.660188 + 1.02727i) q^{39} +(-1.37197 - 1.76570i) q^{40} +(5.61379 - 6.47866i) q^{41} +(4.71414 + 2.57411i) q^{42} +(-2.77382 - 7.43689i) q^{43} +(0.330978 + 2.30200i) q^{44} +(-0.487611 - 3.00687i) q^{45} +(-4.18276 - 2.34617i) q^{46} +(7.75527 - 7.75527i) q^{47} +(0.766916 - 1.02448i) q^{48} +(9.65614 + 4.40981i) q^{49} +(0.886622 - 4.92076i) q^{50} +(-7.13210 - 6.18000i) q^{51} +(0.837481 - 0.457299i) q^{52} +(-0.963499 + 4.42914i) q^{53} +(5.07807 - 2.31908i) q^{54} +(-3.33436 + 3.99072i) q^{55} +(2.26911 - 3.53080i) q^{56} +(-2.56773 + 1.92218i) q^{57} +(-3.71475 + 2.78083i) q^{58} +(2.26860 - 3.53001i) q^{59} +(2.85015 - 0.255387i) q^{60} +(-6.04865 + 2.76233i) q^{61} +(-2.12592 + 9.77270i) q^{62} +(5.01821 - 2.74015i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(2.01220 + 0.709601i) q^{65} +(-2.70729 - 1.23638i) q^{66} +(-6.85679 + 9.15961i) q^{67} +(-5.21440 + 5.21440i) q^{68} +(5.41979 - 2.87982i) q^{69} +(9.26392 - 1.50229i) q^{70} +(0.111335 + 0.774350i) q^{71} +(-0.476068 - 1.27639i) q^{72} +(2.62851 + 1.43528i) q^{73} +(-4.97100 + 5.73684i) q^{74} +(4.68416 + 4.35908i) q^{75} +(1.35505 + 2.10849i) q^{76} +(-9.14559 - 3.41113i) q^{77} +(-0.0871138 + 1.21801i) q^{78} +(0.534202 + 0.343311i) q^{79} +(-0.0401714 - 2.23571i) q^{80} +(-0.435106 + 3.02623i) q^{81} +(8.37659 - 1.82222i) q^{82} +(-9.40218 - 0.672457i) q^{83} +(2.23125 + 4.88576i) q^{84} +(-16.4659 - 0.880669i) q^{85} +(2.23621 - 7.61582i) q^{86} +(-0.423637 - 5.92321i) q^{87} +(-1.11458 + 2.04119i) q^{88} +(1.06924 - 2.34132i) q^{89} +(1.41160 - 2.69934i) q^{90} +4.00485i q^{91} +(-1.94247 - 4.38484i) q^{92} +(-9.05023 - 9.05023i) q^{93} +(10.8560 - 1.56085i) q^{94} +(-1.48209 + 5.40489i) q^{95} +(1.22790 - 0.360543i) q^{96} +(-0.460547 + 0.0329390i) q^{97} +(5.08743 + 9.31694i) q^{98} +(-2.66528 + 1.71287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$2$	0.800541	+	0.599278i	0.566068	+	0.423753i
$3$	−1.19905	+	0.447221i	−0.692270	+	0.258203i	−0.670878	−	0.741568i	$-0.734083\pi$
$3$	−1.19905	+	0.447221i	−0.692270	+	0.258203i	−0.0213919	+	0.999771i	$0.506810\pi$
$4$	0.281733	+	0.959493i	0.140866	+	0.479746i
$5$	−1.17492	+	1.90251i	−0.525440	+	0.850830i
$5$	−1.17492	+	1.90251i	−0.525440	+	0.850830i
$6$	−1.22790	−	0.360543i	−0.501286	−	0.147191i
$7$	−4.10116	−	0.892152i	−1.55009	−	0.337202i	−0.645594	−	0.763681i	$-0.723390\pi$
$7$	−4.10116	−	0.892152i	−1.55009	−	0.337202i	−0.904498	+	0.426479i	$0.859754\pi$
$8$	−0.349464	+	0.936950i	−0.123554	+	0.331262i
$9$	−1.02954	+	0.892104i	−0.343181	+	0.297368i
$10$	−2.08071	+	0.818938i	−0.657977	+	0.258971i
$11$	2.30200	+	0.330978i	0.694080	+	0.0997936i	0.480321	−	0.877093i	$-0.340520\pi$
$11$	2.30200	+	0.330978i	0.694080	+	0.0997936i	0.213759	+	0.976886i	$0.431429\pi$
$12$	−0.766916	−	1.02448i	−0.221390	−	0.295742i
$13$	−0.202830	−	0.932393i	−0.0562548	−	0.258599i	0.940427	−	0.339996i	$-0.110426\pi$
$13$	−0.202830	−	0.932393i	−0.0562548	−	0.258599i	−0.996682	+	0.0813964i	$0.974062\pi$
$14$	−2.74850	−	3.17194i	−0.734567	−	0.847736i
$15$	0.557939	−	2.80665i	0.144059	−	0.724675i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	3.53412	+	6.47225i	0.857149	+	1.56975i	0.821373	+	0.570391i	$0.193208\pi$
$17$	3.53412	+	6.47225i	0.857149	+	1.56975i	0.0357758	+	0.999360i	$0.488610\pi$
$18$	−1.35881	+	0.0971840i	−0.320275	+	0.0229065i
$19$	2.40484	−	0.706126i	0.551709	−	0.161996i	0.00601663	−	0.999982i	$-0.498085\pi$
$19$	2.40484	−	0.706126i	0.551709	−	0.161996i	0.545693	+	0.837985i	$0.316267\pi$
$20$	−2.15646	−	0.591327i	−0.482200	−	0.132225i
$21$	5.31647	−	0.764393i	1.16015	−	0.166804i
$22$	1.64450	+	1.64450i	0.350608	+	0.350608i
$23$	−4.75448	+	0.628433i	−0.991377	+	0.131037i
$23$	−4.75448	+	0.628433i	−0.991377	+	0.131037i
$24$		−	1.27973i		−	0.261225i
$25$	−2.23913	−	4.47061i	−0.447825	−	0.894121i
$26$	0.396389	−	0.867970i	0.0777382	−	0.170223i
$27$	2.67544	−	4.89969i	0.514888	−	0.942947i
$28$	−0.299416	−	4.18638i	−0.0565843	−	0.791152i
$29$	−1.30732	+	4.45233i	−0.242764	+	0.826777i	0.744491	+	0.667632i	$0.232692\pi$
$29$	−1.30732	+	4.45233i	−0.242764	+	0.826777i	−0.987255	+	0.159145i	$0.949126\pi$
$30$	2.12862	−	1.91248i	0.388631	−	0.349170i
$31$	4.15467	+	9.09747i	0.746202	+	1.63395i	0.773075	+	0.634315i	$0.218718\pi$
$31$	4.15467	+	9.09747i	0.746202	+	1.63395i	−0.0268732	+	0.999639i	$0.508555\pi$
$32$	−0.997452	−	0.0713392i	−0.176326	−	0.0126111i
$33$	−2.90823	+	0.632646i	−0.506257	+	0.110130i
$34$	−1.04947	+	7.29922i	−0.179982	+	1.25181i
$35$	6.51587	−	6.75431i	1.10138	−	1.14169i
$36$	−1.14602	−	0.736505i	−0.191004	−	0.122751i
$37$	−0.541530	+	7.57158i	−0.0890270	+	1.24476i	0.734944	+	0.678128i	$0.237209\pi$
$37$	−0.541530	+	7.57158i	−0.0890270	+	1.24476i	−0.823971	+	0.566632i	$0.808246\pi$
$38$	2.34834	+	0.875887i	0.380952	+	0.142088i
$39$	0.660188	+	1.02727i	0.105715	+	0.164495i
$40$	−1.37197	−	1.76570i	−0.216927	−	0.279182i
$41$	5.61379	−	6.47866i	0.876727	−	1.01180i	−0.123085	−	0.992396i	$-0.539279\pi$
$41$	5.61379	−	6.47866i	0.876727	−	1.01180i	0.999812	−	0.0194008i	$-0.00617586\pi$
$42$	4.71414	+	2.57411i	0.727407	+	0.397194i
$43$	−2.77382	−	7.43689i	−0.423003	−	1.13411i	−0.957371	−	0.288863i	$-0.906723\pi$
$43$	−2.77382	−	7.43689i	−0.423003	−	1.13411i	0.534368	−	0.845252i	$-0.320550\pi$
$44$	0.330978	+	2.30200i	0.0498968	+	0.347040i
$45$	−0.487611	−	3.00687i	−0.0726887	−	0.448238i
$46$	−4.18276	−	2.34617i	−0.616715	−	0.345923i
$47$	7.75527	−	7.75527i	1.13122	−	1.13122i	0.141248	−	0.989974i	$-0.454888\pi$
$47$	7.75527	−	7.75527i	1.13122	−	1.13122i	0.989974	−	0.141248i	$-0.0451116\pi$
$48$	0.766916	−	1.02448i	0.110695	−	0.147871i
$49$	9.65614	+	4.40981i	1.37945	+	0.629973i
$50$	0.886622	−	4.92076i	0.125387	−	0.695901i
$51$	−7.13210	−	6.18000i	−0.998693	−	0.865372i
$52$	0.837481	−	0.457299i	0.116138	−	0.0634160i
$53$	−0.963499	+	4.42914i	−0.132347	+	0.608389i	0.862418	+	0.506197i	$0.168949\pi$
$53$	−0.963499	+	4.42914i	−0.132347	+	0.608389i	−0.994765	+	0.102192i	$0.967415\pi$
$54$	5.07807	−	2.31908i	0.691038	−	0.315587i
$55$	−3.33436	+	3.99072i	−0.449605	+	0.538108i
$56$	2.26911	−	3.53080i	0.303223	−	0.471823i
$57$	−2.56773	+	1.92218i	−0.340104	+	0.254598i
$58$	−3.71475	+	2.78083i	−0.487770	+	0.365140i
$59$	2.26860	−	3.53001i	0.295347	−	0.459568i	−0.661590	−	0.749866i	$-0.730118\pi$
$59$	2.26860	−	3.53001i	0.295347	−	0.459568i	0.956936	+	0.290298i	$0.0937543\pi$
$60$	2.85015	−	0.255387i	0.367953	−	0.0329703i
$61$	−6.04865	+	2.76233i	−0.774450	+	0.353680i	−0.763121	−	0.646256i	$-0.776334\pi$
$61$	−6.04865	+	2.76233i	−0.774450	+	0.353680i	−0.0113298	+	0.999936i	$0.503606\pi$
$62$	−2.12592	+	9.77270i	−0.269992	+	1.24113i
$63$	5.01821	−	2.74015i	0.632235	−	0.345227i
$64$	−0.755750	−	0.654861i	−0.0944687	−	0.0818576i
$65$	2.01220	+	0.709601i	0.249583	+	0.0880152i
$66$	−2.70729	−	1.23638i	−0.333244	−	0.152187i
$67$	−6.85679	+	9.15961i	−0.837691	+	1.11902i	0.153704	+	0.988117i	$0.450880\pi$
$67$	−6.85679	+	9.15961i	−0.837691	+	1.11902i	−0.991395	+	0.130907i	$0.958211\pi$
$68$	−5.21440	+	5.21440i	−0.632339	+	0.632339i
$69$	5.41979	−	2.87982i	0.652466	−	0.346690i
$70$	9.26392	−	1.50229i	1.10725	−	0.179558i
$71$	0.111335	+	0.774350i	0.0132130	+	0.0918984i	0.995361	−	0.0962122i	$-0.0306727\pi$
$71$	0.111335	+	0.774350i	0.0132130	+	0.0918984i	−0.982148	+	0.188111i	$0.939764\pi$
$72$	−0.476068	−	1.27639i	−0.0561052	−	0.150424i
$73$	2.62851	+	1.43528i	0.307644	+	0.167986i	0.625653	−	0.780101i	$-0.284832\pi$
$73$	2.62851	+	1.43528i	0.307644	+	0.167986i	−0.318009	+	0.948088i	$0.603014\pi$
$74$	−4.97100	+	5.73684i	−0.577867	+	0.666894i
$75$	4.68416	+	4.35908i	0.540881	+	0.503343i
$76$	1.35505	+	2.10849i	0.155434	+	0.241861i
$77$	−9.14559	−	3.41113i	−1.04224	−	0.388734i
$78$	−0.0871138	+	1.21801i	−0.00986370	+	0.137913i
$79$	0.534202	+	0.343311i	0.0601024	+	0.0386255i	0.570347	−	0.821404i	$-0.306809\pi$
$79$	0.534202	+	0.343311i	0.0601024	+	0.0386255i	−0.510245	+	0.860029i	$0.670445\pi$
$80$	−0.0401714	−	2.23571i	−0.00449130	−	0.249960i
$81$	−0.435106	+	3.02623i	−0.0483451	+	0.336247i
$82$	8.37659	−	1.82222i	0.925040	−	0.201230i
$83$	−9.40218	−	0.672457i	−1.03202	−	0.0738118i	−0.454961	−	0.890512i	$-0.650347\pi$
$83$	−9.40218	−	0.672457i	−1.03202	−	0.0738118i	−0.577063	+	0.816700i	$0.695801\pi$
$84$	2.23125	+	4.88576i	0.243449	+	0.533080i
$85$	−16.4659	−	0.880669i	−1.78597	−	0.0955220i
$86$	2.23621	−	7.61582i	0.241136	−	0.821235i
$87$	−0.423637	−	5.92321i	−0.0454186	−	0.635035i
$88$	−1.11458	+	2.04119i	−0.118814	+	0.217592i
$89$	1.06924	−	2.34132i	0.113340	−	0.248179i	−0.844458	−	0.535621i	$-0.820078\pi$
$89$	1.06924	−	2.34132i	0.113340	−	0.248179i	0.957798	+	0.287442i	$0.0928048\pi$
$90$	1.41160	−	2.69934i	0.148796	−	0.284535i
$91$			4.00485i			0.419822i
$92$	−1.94247	−	4.38484i	−0.202516	−	0.457151i
$93$	−9.05023	−	9.05023i	−0.938465	−	0.938465i
$94$	10.8560	−	1.56085i	1.11971	−	0.160990i
$95$	−1.48209	+	5.40489i	−0.152059	+	0.554530i
$96$	1.22790	−	0.360543i	0.125322	−	0.0367977i
$97$	−0.460547	+	0.0329390i	−0.0467614	+	0.00334444i	−0.0947003	−	0.995506i	$-0.530189\pi$
$97$	−0.460547	+	0.0329390i	−0.0467614	+	0.00334444i	0.0479389	+	0.998850i	$0.484735\pi$
$98$	5.08743	+	9.31694i	0.513909	+	0.941153i
$99$	−2.66528	+	1.71287i	−0.267870	+	0.172150i
$100$	3.65868	−	3.40794i	0.365868	−	0.340794i
$101$	1.10510	+	1.27535i	0.109961	+	0.126902i	0.808062	−	0.589097i	$-0.200517\pi$
$101$	1.10510	+	1.27535i	0.109961	+	0.126902i	−0.698101	+	0.716000i	$0.745971\pi$
$102$	−2.00600	−	9.22145i	−0.198624	−	0.913059i
$103$	1.74457	+	2.33048i	0.171898	+	0.229629i	0.878214	−	0.478268i	$-0.158735\pi$
$103$	1.74457	+	2.33048i	0.171898	+	0.229629i	−0.706316	+	0.707897i	$0.749644\pi$
$104$	0.944487	+	0.135797i	0.0926146	+	0.0133160i
$105$	−4.79216	+	11.0128i	−0.467667	+	1.07474i
$106$	−3.42560	+	2.96830i	−0.332724	+	0.288307i
$107$	−0.266339	+	0.714084i	−0.0257480	+	0.0690331i	−0.949188	−	0.314710i	$-0.898093\pi$
$107$	−0.266339	+	0.714084i	−0.0257480	+	0.0690331i	0.923440	+	0.383744i	$0.125365\pi$
$108$	5.45498	+	1.18666i	0.524906	+	0.114186i
$109$	−7.54712	−	2.21603i	−0.722883	−	0.212257i	−0.100463	−	0.994941i	$-0.532032\pi$
$109$	−7.54712	−	2.21603i	−0.722883	−	0.212257i	−0.622420	+	0.782683i	$0.713850\pi$
$110$	−5.06084	+	1.19653i	−0.482532	+	0.114085i
$111$	−2.73685	−	9.32086i	−0.259771	−	0.884697i
$112$	3.93245	−	1.46673i	0.371581	−	0.138593i
$113$	9.05110	+	6.77557i	0.851456	+	0.637392i	0.933238	−	0.359258i	$-0.116970\pi$
$113$	9.05110	+	6.77557i	0.851456	+	0.637392i	−0.0817821	+	0.996650i	$0.526061\pi$
$114$	−3.20749			−0.300409
$115$	4.39053	−	9.78383i	0.409419	−	0.912346i
$116$	−4.64030			−0.430841
$117$	1.04061	+	0.778994i	0.0962048	+	0.0720180i
$118$	3.93156	−	1.46640i	0.361930	−	0.134993i
$119$	−8.71973	−	29.6967i	−0.799337	−	2.72229i
$120$	2.43471	+	1.50359i	0.222258	+	0.137258i
$121$	−5.36476	−	1.57524i	−0.487705	−	0.143203i
$122$	−6.49759	−	1.41347i	−0.588265	−	0.127969i
$123$	−3.83380	+	10.2788i	−0.345682	+	0.926810i
$124$	−7.55845	+	6.54943i	−0.678769	+	0.588157i
$125$	11.1362	+	0.992636i	0.996051	+	0.0887841i
$126$	5.65940	+	0.813699i	0.504179	+	0.0724900i
$127$	−3.45062	−	4.60949i	−0.306193	−	0.409026i	0.620881	−	0.783905i	$-0.286775\pi$
$127$	−3.45062	−	4.60949i	−0.306193	−	0.409026i	−0.927074	+	0.374879i	$0.877684\pi$
$128$	−0.212565	−	0.977147i	−0.0187883	−	0.0863684i
$129$	6.65187	+	7.67666i	0.585664	+	0.675893i
$130$	1.18560	+	1.77393i	0.103984	+	0.155584i
$131$	8.00295	−	5.14318i	0.699221	−	0.449362i	−0.142133	−	0.989848i	$-0.545396\pi$
$131$	8.00295	−	5.14318i	0.699221	−	0.449362i	0.841353	+	0.540486i	$0.181760\pi$
$132$	−1.42636	−	2.61219i	−0.124149	−	0.227362i
$133$	−10.4926	+	0.750447i	−0.909825	+	0.0650720i
$134$	−10.9783	+	3.22352i	−0.948380	+	0.278470i
$135$	6.17832	+	10.8468i	0.531745	+	0.933544i
$136$	−7.29922	+	1.04947i	−0.625903	+	0.0899912i
$137$	12.5073	+	12.5073i	1.06857	+	1.06857i	0.997469	+	0.0711032i	$0.0226520\pi$
$137$	12.5073	+	12.5073i	1.06857	+	1.06857i	0.0711032	+	0.997469i	$0.477348\pi$
$138$	6.06458	+	0.942543i	0.516251	+	0.0802346i
$139$			10.7645i			0.913036i	0.889714	+	0.456518i	$0.150904\pi$
$139$			10.7645i			0.913036i	−0.889714	+	0.456518i	$0.849096\pi$
$140$	8.31644	+	4.34902i	0.702868	+	0.367559i
$141$	−5.83061	+	12.7672i	−0.491026	+	1.07520i
$142$	−0.374922	+	0.686619i	−0.0314628	+	0.0576198i
$143$	−0.158313	−	2.21350i	−0.0132388	−	0.185102i
$144$	0.383799	−	1.30710i	0.0319832	−	0.108925i
$145$	−6.93463	−	7.71833i	−0.575889	−	0.640973i
$146$	1.24410	+	2.72421i	0.102963	+	0.225457i
$147$	−13.5503	−	0.969138i	−1.11761	−	0.0799331i
$148$	−7.41745	+	1.61357i	−0.609710	+	0.132634i
$149$	0.228791	−	1.59128i	0.0187433	−	0.130363i	−0.978301	−	0.207187i	$-0.933569\pi$
$149$	0.228791	−	1.59128i	0.0187433	−	0.130363i	0.997045	+	0.0768246i	$0.0244781\pi$
$150$	1.13757	+	6.29674i	0.0928820	+	0.514127i
$151$	3.55628	+	2.28548i	0.289406	+	0.185990i	0.677286	−	0.735720i	$-0.263156\pi$
$151$	3.55628	+	2.28548i	0.289406	+	0.185990i	−0.387880	+	0.921710i	$0.626792\pi$
$152$	−0.178802	+	2.49998i	−0.0145028	+	0.202775i
$153$	−9.41245	−	3.51066i	−0.760951	−	0.283820i
$154$	−5.27721	−	8.21150i	−0.425250	−	0.661701i
$155$	−22.1895	−	2.78447i	−1.78230	−	0.223654i
$156$	−0.799665	+	0.922862i	−0.0640244	+	0.0738881i
$157$	6.65340	+	3.63303i	0.530999	+	0.289947i	0.722295	−	0.691585i	$-0.243087\pi$
$157$	6.65340	+	3.63303i	0.530999	+	0.289947i	−0.191296	+	0.981532i	$0.561269\pi$
$158$	0.221912	+	0.594970i	0.0176544	+	0.0473333i
$159$	−0.825523	−	5.74164i	−0.0654682	−	0.455341i
$160$	1.30765	−	1.81385i	0.103379	−	0.143397i
$161$	20.0595	+	1.66442i	1.58091	+	0.131175i
$162$	−2.16187	+	2.16187i	−0.169853	+	0.169853i
$163$	3.67376	−	4.90757i	0.287751	−	0.384390i	−0.633252	−	0.773946i	$-0.718280\pi$
$163$	3.67376	−	4.90757i	0.287751	−	0.384390i	0.921003	+	0.389555i	$0.127371\pi$
$164$	7.79782	+	3.56114i	0.608907	+	0.278079i
$165$	2.21332	−	6.27625i	0.172306	−	0.488606i
$166$	−7.12384	−	6.17285i	−0.552917	−	0.479106i
$167$	−15.2079	+	8.30414i	−1.17682	+	0.642593i	−0.944006	−	0.329927i	$-0.892976\pi$
$167$	−15.2079	+	8.30414i	−1.17682	+	0.642593i	−0.232816	+	0.972521i	$0.574794\pi$
$168$	−1.14172	+	5.24839i	−0.0880854	+	0.404922i
$169$	10.9970	−	5.02216i	0.845923	−	0.386320i
$170$	−12.6538	−	10.5726i	−0.970504	−	0.810884i
$171$	−1.84595	+	2.87236i	−0.141164	+	0.219655i
$172$	6.35417	−	4.75667i	0.484501	−	0.362693i
$173$	16.2063	−	12.1319i	1.23215	−	0.922372i	0.233396	−	0.972382i	$-0.425016\pi$
$173$	16.2063	−	12.1319i	1.23215	−	0.922372i	0.998749	+	0.0500095i	$0.0159251\pi$
$174$	3.21051	−	4.99565i	0.243388	−	0.378720i
$175$	5.19454	+	20.3323i	0.392671	+	1.53698i
$176$	−2.11551	+	0.966120i	−0.159462	+	0.0728240i
$177$	−1.14146	+	5.24721i	−0.0857975	+	0.394405i
$178$	2.25907	−	1.23355i	0.169325	−	0.0924582i
$179$	−2.95070	−	2.55680i	−0.220546	−	0.191104i	0.537579	−	0.843213i	$-0.319339\pi$
$179$	−2.95070	−	2.55680i	−0.220546	−	0.191104i	−0.758125	+	0.652109i	$0.773884\pi$
$180$	2.74770	−	1.31499i	0.204801	−	0.0980138i
$181$	0.751070	+	0.343002i	0.0558266	+	0.0254952i	0.443133	−	0.896456i	$-0.353867\pi$
$181$	0.751070	+	0.343002i	0.0558266	+	0.0254952i	−0.387306	+	0.921951i	$0.626594\pi$
$182$	−2.40002	+	3.20604i	−0.177901	+	0.237648i
$183$	6.01724	−	6.01724i	0.444807	−	0.444807i
$184$	1.07271	−	4.67432i	0.0790813	−	0.344596i
$185$	−13.7688	−	9.92628i	−1.01230	−	0.729794i
$186$	−1.82148	−	12.6687i	−0.133557	−	0.928913i
$187$	5.99337	+	16.0688i	0.438278	+	1.17507i
$188$	9.62604	+	5.25622i	0.702051	+	0.383349i
$189$	−15.3437	+	17.7075i	−1.11609	+	1.28803i
$190$	−4.42550	+	3.43866i	−0.321060	+	0.249467i
$191$	1.67203	+	2.60173i	0.120984	+	0.188254i	0.896463	−	0.443119i	$-0.146128\pi$
$191$	1.67203	+	2.60173i	0.120984	+	0.188254i	−0.775479	+	0.631373i	$0.782492\pi$
$192$	1.19905	+	0.447221i	0.0865337	+	0.0322754i
$193$	−0.207894	+	2.90673i	−0.0149645	+	0.209231i	0.984468	+	0.175561i	$0.0561740\pi$
$193$	−0.207894	+	2.90673i	−0.0149645	+	0.209231i	−0.999433	+	0.0336699i	$0.989281\pi$
$194$	−0.388426	−	0.249626i	−0.0278874	−	0.0179221i
$195$	−2.73007	+	0.0490542i	−0.195504	+	0.00351284i
$196$	−1.51073	+	10.5074i	−0.107910	+	0.750527i
$197$	6.89071	−	1.49898i	0.490943	−	0.106798i	0.0397226	−	0.999211i	$-0.487353\pi$
$197$	6.89071	−	1.49898i	0.490943	−	0.106798i	0.451220	+	0.892413i	$0.350989\pi$
$198$	−3.16015	−	0.226018i	−0.224582	−	0.0160624i
$199$	0.216123	+	0.473242i	0.0153205	+	0.0335473i	0.917138	−	0.398571i	$-0.130494\pi$
$199$	0.216123	+	0.473242i	0.0153205	+	0.0335473i	−0.901817	+	0.432118i	$0.857766\pi$
$200$	4.97123	−	0.535631i	0.351519	−	0.0378748i
$201$	4.12525	−	14.0493i	0.290972	−	0.990961i
$202$	0.120387	+	1.68323i	0.00847041	+	0.118432i
$203$	9.33369	−	17.0934i	0.655097	−	1.19972i
$204$	3.92032	−	8.58430i	0.274477	−	0.601021i
$205$	5.72999	+	18.2922i	0.400200	+	1.27759i
$206$			2.91113i			0.202828i
$207$	4.33432	−	4.88849i	0.301256	−	0.339774i
$208$	0.674721	+	0.674721i	0.0467835	+	0.0467835i
$209$	5.76967	−	0.829553i	0.399096	−	0.0573814i
$210$	−10.4360	+	5.94434i	−0.720154	+	0.410198i
$211$	−8.51242	+	2.49947i	−0.586019	+	0.172071i	−0.561284	−	0.827623i	$-0.689692\pi$
$211$	−8.51242	+	2.49947i	−0.586019	+	0.172071i	−0.0247350	+	0.999694i	$0.507874\pi$
$212$	−4.52117	+	0.323361i	−0.310515	+	0.0222085i
$213$	−0.479801	−	0.878690i	−0.0328754	−	0.0602068i
$214$	−0.641150	+	0.412042i	−0.0438281	+	0.0281666i
$215$	17.4078	+	3.46052i	1.18720	+	0.236006i
$216$	3.65580	+	4.21902i	0.248746	+	0.287068i
$217$	−8.92265	−	41.0168i	−0.605709	−	2.78440i
$218$	−4.71376	−	6.29684i	−0.319256	−	0.426476i
$219$	−3.79359	−	0.545436i	−0.256347	−	0.0368572i
$220$	−4.76846	−	2.07498i	−0.321490	−	0.139895i
$221$	5.31786	−	4.60795i	0.357718	−	0.309964i
$222$	3.39482	−	9.10187i	0.227846	−	0.610878i
$223$	20.9975	+	4.56772i	1.40609	+	0.305877i	0.850674	−	0.525693i	$-0.176194\pi$
$223$	20.9975	+	4.56772i	1.40609	+	0.305877i	0.555419	+	0.831570i	$0.312558\pi$
$224$	4.02706	+	1.18245i	0.269069	+	0.0790059i
$225$	6.29352	+	2.60515i	0.419568	+	0.173677i
$226$	3.18533	+	10.8482i	0.211885	+	0.721615i
$227$	9.93587	−	3.70589i	0.659467	−	0.245968i	0.00262466	−	0.999997i	$-0.499165\pi$
$227$	9.93587	−	3.70589i	0.659467	−	0.245968i	0.656842	+	0.754028i	$0.271892\pi$
$228$	−2.56773	−	1.92218i	−0.170052	−	0.127299i
$229$	−1.22852			−0.0811829			−0.0405915	−	0.999176i	$-0.512924\pi$
$229$	−1.22852			−0.0811829			−0.0405915	+	0.999176i	$0.512924\pi$
$230$	9.37803	−	5.20121i	0.618369	−	0.342958i
$231$	12.4915			0.821881
$232$	−3.71475	−	2.78083i	−0.243885	−	0.182570i
$233$	22.5396	−	8.40683i	1.47662	−	0.550750i	0.523148	−	0.852242i	$-0.324757\pi$
$233$	22.5396	−	8.40683i	1.47662	−	0.550750i	0.953469	+	0.301492i	$0.0974847\pi$
$234$	0.366221	+	1.24723i	0.0239406	+	0.0815342i
$235$	5.64269	+	23.8663i	0.368089	+	1.55687i
$236$	4.02616	+	1.18219i	0.262081	+	0.0769538i
$237$	−0.794069	−	0.172739i	−0.0515803	−	0.0112206i
$238$	10.8161	−	28.9990i	0.701101	−	1.87972i
$239$	6.74672	−	5.84607i	0.436409	−	0.378151i	−0.408767	−	0.912639i	$-0.634041\pi$
$239$	6.74672	−	5.84607i	0.436409	−	0.378151i	0.845176	+	0.534488i	$0.179496\pi$
$240$	1.04802	+	2.66275i	0.0676496	+	0.171880i
$241$	9.42581	+	1.35523i	0.607170	+	0.0872979i	0.439041	−	0.898467i	$-0.355318\pi$
$241$	9.42581	+	1.35523i	0.607170	+	0.0872979i	0.168129	+	0.985765i	$0.446227\pi$
$242$	−3.35071	−	4.47602i	−0.215392	−	0.287729i
$243$	2.72829	+	12.5418i	0.175020	+	0.804555i
$244$	−4.35453	−	5.02540i	−0.278770	−	0.321718i
$245$	−19.7349	+	13.1898i	−1.26082	+	0.842663i
$246$	−9.22899	+	5.93111i	−0.588419	+	0.378154i
$247$	−1.14616	−	2.09904i	−0.0729285	−	0.133559i
$248$	−9.97578	+	0.713482i	−0.633463	+	0.0453061i
$249$	11.5744	−	3.39855i	0.733497	−	0.215374i
$250$	8.32011	+	7.46831i	0.526210	+	0.472338i
$251$	−17.2115	+	2.47464i	−1.08638	+	0.156198i	−0.662161	−	0.749361i	$-0.730361\pi$
$251$	−17.2115	+	2.47464i	−1.08638	+	0.156198i	−0.424220	+	0.905559i	$0.639452\pi$
$252$	4.04295	+	4.04295i	0.254682	+	0.254682i
$253$	−11.1528	−	0.126975i	−0.701171	−	0.00798283i
$254$		−	5.75797i		−	0.361287i
$255$	20.1372	−	6.30792i	1.26104	−	0.395017i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	9.65774	−	17.6868i	0.602433	−	1.10327i	−0.381437	−	0.924395i	$-0.624571\pi$
$257$	9.65774	−	17.6868i	0.602433	−	1.10327i	0.983871	−	0.178880i	$-0.0572473\pi$
$258$	0.724641	+	10.1318i	0.0451142	+	0.630778i
$259$	8.97591	−	30.5691i	0.557736	−	1.89947i
$260$	−0.113955	+	2.13061i	−0.00706718	+	0.132135i
$261$	−2.62600	−	5.75014i	−0.162545	−	0.355925i
$262$	9.48888	+	0.678658i	0.586225	+	0.0419276i
$263$	15.1458	−	3.29477i	0.933930	−	0.203164i	0.280243	−	0.959929i	$-0.409585\pi$
$263$	15.1458	−	3.29477i	0.933930	−	0.203164i	0.653687	+	0.756765i	$0.273221\pi$
$264$	0.423564	−	2.94595i	0.0260685	−	0.181311i
$265$	−7.29446	−	7.03695i	−0.448095	−	0.432277i
$266$	−8.84950	−	5.68723i	−0.542598	−	0.348706i
$267$	−0.234986	+	3.28554i	−0.0143809	+	0.201072i
$268$	−10.7204	−	3.99849i	−0.654850	−	0.244246i
$269$	−0.493919	−	0.768553i	−0.0301148	−	0.0468595i	0.825870	−	0.563861i	$-0.190685\pi$
$269$	−0.493919	−	0.768553i	−0.0301148	−	0.0468595i	−0.855985	+	0.517001i	$0.827048\pi$
$270$	−1.55425	+	12.3858i	−0.0945887	+	0.753778i
$271$	−1.03436	+	1.19371i	−0.0628326	+	0.0725127i	−0.786296	−	0.617850i	$-0.788004\pi$
$271$	−1.03436	+	1.19371i	−0.0628326	+	0.0725127i	0.723463	+	0.690363i	$0.242549\pi$
$272$	−6.47225	−	3.53412i	−0.392438	−	0.214287i
$273$	−1.79105	−	4.80200i	−0.108399	−	0.290630i
$274$	2.51727	+	17.5080i	0.152074	+	1.05770i
$275$	−3.67480	−	11.0324i	−0.221599	−	0.665281i
$276$	4.29010	+	4.38891i	0.258234	+	0.264182i
$277$	10.2771	−	10.2771i	0.617490	−	0.617490i	−0.327397	−	0.944887i	$-0.606171\pi$
$277$	10.2771	−	10.2771i	0.617490	−	0.617490i	0.944887	+	0.327397i	$0.106171\pi$
$278$	−6.45094	+	8.61745i	−0.386902	+	0.516840i
$279$	−12.3933	−	5.65984i	−0.741968	−	0.338845i
$280$	4.05138	+	8.46543i	0.242116	+	0.505906i
$281$	−14.5873	−	12.6400i	−0.870206	−	0.754038i	0.100340	−	0.994953i	$-0.468007\pi$
$281$	−14.5873	−	12.6400i	−0.870206	−	0.754038i	−0.970546	+	0.240915i	$0.922552\pi$
$282$	−12.3188	+	6.72656i	−0.733572	+	0.400561i
$283$	−2.79509	+	12.8488i	−0.166151	+	0.763782i	0.816355	+	0.577550i	$0.195991\pi$
$283$	−2.79509	+	12.8488i	−0.166151	+	0.763782i	−0.982506	+	0.186232i	$0.940372\pi$
$284$	−0.711617	+	0.324984i	−0.0422267	+	0.0192843i
$285$	−0.640094	−	7.14354i	−0.0379159	−	0.423147i
$286$	1.19977	−	1.86687i	0.0709437	−	0.110391i
$287$	−28.8030	+	21.5617i	−1.70019	+	1.27274i
$288$	1.09056	−	0.816385i	0.0642620	−	0.0481059i
$289$	−20.2091	+	31.4460i	−1.18877	+	1.84977i
$290$	−0.926029	−	10.3346i	−0.0543783	−	0.606869i
$291$	0.537486	−	0.245462i	0.0315080	−	0.0143892i
$292$	−0.636600	+	2.92640i	−0.0372542	+	0.171255i
$293$	−23.2153	+	12.6765i	−1.35625	+	0.740570i	−0.982377	−	0.186909i	$-0.940153\pi$
$293$	−23.2153	+	12.6765i	−1.35625	+	0.740570i	−0.373875	+	0.927479i	$0.621971\pi$
$294$	−10.2668	−	8.89624i	−0.598772	−	0.518839i
$295$	4.05047	+	8.46353i	0.235828	+	0.492766i
$296$	−6.90495	−	3.15338i	−0.401342	−	0.183287i
$297$	7.78055	−	10.3936i	0.451473	−	0.603098i
$298$	1.13678	−	1.13678i	0.0658516	−	0.0658516i
$299$	1.55030	+	4.30558i	0.0896559	+	0.248998i
$300$	−2.86282	+	5.72252i	−0.165285	+	0.330390i
$301$	4.74102	+	32.9745i	0.273268	+	1.90062i
$302$	1.47731	+	3.96082i	0.0850097	+	0.227920i
$303$	−1.89543	−	1.03498i	−0.108890	−	0.0594582i
$304$	−1.64132	+	1.89419i	−0.0941364	+	0.108639i
$305$	1.85132	−	14.7532i	0.106006	−	0.844763i
$306$	−5.43119	−	8.45110i	−0.310481	−	0.483117i
$307$	−9.93197	−	3.70443i	−0.566847	−	0.211423i	0.0496683	−	0.998766i	$-0.484184\pi$
$307$	−9.93197	−	3.70443i	−0.566847	−	0.211423i	−0.616516	+	0.787343i	$0.711456\pi$
$308$	0.696343	−	9.73615i	0.0396779	−	0.554769i
$309$	−3.13407	−	2.01414i	−0.178291	−	0.114581i
$310$	−16.0949	−	15.5267i	−0.914130	−	0.881860i
$311$	−3.62478	+	25.2109i	−0.205542	+	1.42958i	0.581935	+	0.813235i	$0.302296\pi$
$311$	−3.62478	+	25.2109i	−0.205542	+	1.42958i	−0.787477	+	0.616344i	$0.788613\pi$
$312$	−1.19322	+	0.259568i	−0.0675525	+	0.0146951i
$313$	32.6923	+	2.33820i	1.84788	+	0.132163i	0.950820	−	0.309745i	$-0.100244\pi$
$313$	32.6923	+	2.33820i	1.84788	+	0.132163i	0.897061	+	0.441908i	$0.145698\pi$
$314$	3.14913	+	6.89563i	0.177716	+	0.389143i
$315$	−0.682821	+	12.7667i	−0.0384726	+	0.719321i
$316$	−0.178902	+	0.609285i	−0.0100640	+	0.0342750i
$317$	−0.643460	−	8.99675i	−0.0361403	−	0.505308i	−0.982993	−	0.183641i	$-0.941212\pi$
$317$	−0.643460	−	8.99675i	−0.0361403	−	0.505308i	0.946853	−	0.321667i	$-0.104243\pi$
$318$	2.77997	−	5.09113i	0.155893	−	0.285497i
$319$	−4.48308	+	9.81658i	−0.251004	+	0.549623i
$320$	2.13383	−	0.668416i	0.119285	−	0.0373656i
$321$		−	0.975332i		−	0.0544377i
$322$	15.0610	+	13.3537i	0.839318	+	0.744171i
$323$	13.0692	+	13.0692i	0.727191	+	0.727191i
$324$	−3.02623	+	0.435106i	−0.168124	+	0.0241725i
$325$	−3.71420	+	2.99452i	−0.206027	+	0.166106i
$326$	5.88199	−	1.72711i	0.325773	−	0.0956557i
$327$	10.0404	−	0.718103i	0.555235	−	0.0397112i
$328$	4.10836	+	7.52390i	0.226846	+	0.415438i
$329$	−38.7245	+	24.8867i	−2.13495	+	1.37205i
$330$	5.53307	−	3.69801i	0.304585	−	0.203569i
$331$	−4.08320	−	4.71226i	−0.224433	−	0.259009i	0.632355	−	0.774679i	$-0.282089\pi$
$331$	−4.08320	−	4.71226i	−0.224433	−	0.259009i	−0.856787	+	0.515670i	$0.827543\pi$
$332$	−2.00368	−	9.21078i	−0.109966	−	0.505507i
$333$	−6.19711	−	8.27838i	−0.339600	−	0.453652i
$334$	−17.1510	−	2.46595i	−0.938463	−	0.134931i
$335$	−9.37010	−	23.8070i	−0.511943	−	1.30071i
$336$	−4.05924	+	3.51735i	−0.221449	+	0.191887i
$337$	10.9545	−	29.3702i	0.596730	−	1.59990i	−0.189444	−	0.981891i	$-0.560669\pi$
$337$	10.9545	−	29.3702i	0.596730	−	1.59990i	0.786175	−	0.618004i	$-0.212059\pi$
$338$	11.8132	+	2.56981i	0.642554	+	0.139779i
$339$	−13.8829	−	4.07638i	−0.754014	−	0.221398i
$340$	−3.79397	−	16.0470i	−0.205757	−	0.870270i
$341$	6.55301	+	22.3175i	0.354865	+	1.20856i
$342$	−3.19910	+	1.19320i	−0.172988	+	0.0645211i
$343$	−12.1476	−	9.09358i	−0.655909	−	0.491007i
$344$	7.93734			0.427953
$345$	−0.888917	+	13.6948i	−0.0478577	+	0.737303i
$346$	20.2442			1.08834
$347$	13.2989	+	9.95543i	0.713922	+	0.534435i	0.893364	−	0.449333i	$-0.148338\pi$
$347$	13.2989	+	9.95543i	0.713922	+	0.534435i	−0.179442	+	0.983769i	$0.557429\pi$
$348$	5.56393	−	2.07524i	0.298258	−	0.111244i
$349$	−8.96347	−	30.5268i	−0.479803	−	1.63406i	−0.742981	−	0.669313i	$-0.766589\pi$
$349$	−8.96347	−	30.5268i	−0.479803	−	1.63406i	0.263177	−	0.964748i	$-0.415230\pi$
$350$	−8.02625	+	19.3898i	−0.429021	+	1.03643i
$351$	−5.11110	−	1.50075i	−0.272810	−	0.0801043i
$352$	−2.27252	−	0.494357i	−0.121126	−	0.0263493i
$353$	−11.1947	+	30.0141i	−0.595832	+	1.59749i	0.191863	+	0.981422i	$0.438547\pi$
$353$	−11.1947	+	30.0141i	−0.595832	+	1.59749i	−0.787695	+	0.616065i	$0.788726\pi$
$354$	−4.05832	+	3.51656i	−0.215697	+	0.186903i
$355$	−1.60402	−	0.697983i	−0.0851326	−	0.0370451i
$356$	2.54772	+	0.366307i	0.135029	+	0.0194142i
$357$	23.7364	+	31.7081i	1.25626	+	1.67817i
$358$	−0.829926	−	3.81511i	−0.0438629	−	0.201635i
$359$	2.95583	+	3.41121i	0.156003	+	0.180037i	0.828371	−	0.560180i	$-0.189268\pi$
$359$	2.95583	+	3.41121i	0.156003	+	0.180037i	−0.672368	+	0.740217i	$0.734723\pi$
$360$	2.98769	+	0.593928i	0.157465	+	0.0313027i
$361$	−10.6992	+	6.87593i	−0.563113	+	0.361891i
$362$	0.395709	+	0.724687i	0.0207980	+	0.0380887i
$363$	7.13707	−	0.510453i	0.374599	−	0.0267919i
$364$	−3.84262	+	1.12830i	−0.201408	+	0.0591388i
$365$	−5.81892	+	3.31445i	−0.304576	+	0.173486i
$366$	8.42305	−	1.21105i	0.440280	−	0.0633027i
$367$	−20.0786	−	20.0786i	−1.04809	−	1.04809i	−0.998783	−	0.0493115i	$-0.984297\pi$
$367$	−20.0786	−	20.0786i	−1.04809	−	1.04809i	−0.0493115	−	0.998783i	$-0.515703\pi$
$368$	3.65997	−	3.09914i	0.190789	−	0.161554i
$369$			11.6782i			0.607940i
$370$	−5.07389	−	16.1977i	−0.263779	−	0.842080i
$371$	7.90293	−	17.3050i	0.410300	−	0.898431i
$372$	6.13389	−	11.2334i	0.318027	−	0.582423i
$373$	−1.43915	−	20.1220i	−0.0745166	−	1.04188i	−0.887866	−	0.460102i	$-0.847813\pi$
$373$	−1.43915	−	20.1220i	−0.0745166	−	1.04188i	0.813349	−	0.581775i	$-0.197642\pi$
$374$	−4.83176	+	16.4555i	−0.249844	+	0.850892i
$375$	−13.7967	+	3.79012i	−0.712460	+	0.195721i
$376$	4.55611	+	9.97649i	0.234963	+	0.514498i
$377$	4.41649	+	0.315873i	0.227461	+	0.0162683i
$378$	−22.8950	+	4.98049i	−1.17759	+	0.256169i
$379$	−4.90505	+	34.1154i	−0.251956	+	1.75239i	0.334488	+	0.942400i	$0.391437\pi$
$379$	−4.90505	+	34.1154i	−0.251956	+	1.75239i	−0.586443	+	0.809990i	$0.699472\pi$
$380$	−5.60351	+	0.100684i	−0.287454	+	0.00516500i
$381$	6.19892	+	3.98380i	0.317580	+	0.204096i
$382$	−0.220629	+	3.08480i	−0.0112884	+	0.157832i
$383$	11.2844	+	4.20887i	0.576607	+	0.215063i	0.620812	−	0.783959i	$-0.286803\pi$
$383$	11.2844	+	4.20887i	0.576607	+	0.215063i	−0.0442053	+	0.999022i	$0.514076\pi$
$384$	0.691876	+	1.07658i	0.0353072	+	0.0549390i
$385$	17.2351	−	13.3918i	0.878380	−	0.682510i
$386$	−1.90837	+	2.20237i	−0.0971334	+	0.112098i
$387$	9.49024	+	5.18207i	0.482416	+	0.263419i
$388$	−0.161356	−	0.432611i	−0.00819160	−	0.0219625i
$389$	−1.49097	−	10.3699i	−0.0755953	−	0.525777i	−0.992070	−	0.125685i	$-0.959887\pi$
$389$	−1.49097	−	10.3699i	−0.0755953	−	0.525777i	0.916475	−	0.400092i	$-0.131022\pi$
$390$	−2.21493	−	1.59680i	−0.112157	−	0.0808571i
$391$	−20.8703	−	28.5512i	−1.05545	−	1.44390i
$392$	−7.50624	+	7.50624i	−0.379123	+	0.379123i
$393$	−7.29576	+	9.74600i	−0.368023	+	0.491621i
$394$	6.41460	+	2.92945i	0.323163	+	0.147584i
$395$	−1.28080	+	0.612965i	−0.0644440	+	0.0308416i
$396$	−2.39438	−	2.07474i	−0.120322	−	0.104260i
$397$	−19.8862	+	10.8587i	−0.998062	+	0.544983i	−0.893275	−	0.449511i	$-0.851598\pi$
$397$	−19.8862	+	10.8587i	−0.998062	+	0.544983i	−0.104788	+	0.994495i	$0.533416\pi$
$398$	−0.110589	+	0.508368i	−0.00554331	+	0.0254822i
$399$	12.2455	−	5.59234i	0.613043	−	0.279967i
$400$	4.30066	+	2.55035i	0.215033	+	0.127518i
$401$	−5.67772	+	8.83471i	−0.283532	+	0.441184i	−0.953583	−	0.301131i	$-0.902636\pi$
$401$	−5.67772	+	8.83471i	−0.283532	+	0.441184i	0.670051	+	0.742315i	$0.266272\pi$
$402$	11.7219	−	8.77487i	0.584633	−	0.437651i
$403$	7.63973	−	5.71903i	0.380562	−	0.284885i
$404$	−0.912349	+	1.41964i	−0.0453911	+	0.0706299i
$405$	−5.24623	−	4.38337i	−0.260687	−	0.217811i
$406$	17.7157	−	8.09048i	0.879215	−	0.401524i
$407$	−3.75263	+	17.2506i	−0.186011	+	0.855079i
$408$	8.28276	−	4.52273i	0.410058	−	0.223908i
$409$	6.06057	+	5.25152i	0.299676	+	0.259671i	0.791699	−	0.610912i	$-0.209197\pi$
$409$	6.06057	+	5.25152i	0.299676	+	0.259671i	−0.492023	+	0.870582i	$0.663742\pi$
$410$	−6.37503	+	18.0775i	−0.314840	+	0.892786i
$411$	−20.5904	−	9.40332i	−1.01565	−	0.463831i
$412$	−1.74457	+	2.33048i	−0.0859490	+	0.114814i
$413$	−12.4532	+	12.4532i	−0.612782	+	0.612782i
$414$	6.39936	−	1.31598i	0.314511	−	0.0646769i
$415$	12.3262	−	17.0977i	0.605068	−	0.839293i
$416$	0.135797	+	0.944487i	0.00665798	+	0.0463073i
$417$	−4.81413	−	12.9072i	−0.235749	−	0.632067i
$418$	5.11599	+	2.79354i	0.250231	+	0.136637i
$419$	8.37240	−	9.66226i	0.409018	−	0.472032i	−0.513442	−	0.858124i	$-0.671630\pi$
$419$	8.37240	−	9.66226i	0.409018	−	0.472032i	0.922460	+	0.386092i	$0.126175\pi$
$420$	−11.9168	−	1.49539i	−0.581479	−	0.0729675i
$421$	−16.5885	−	25.8123i	−0.808476	−	1.25801i	−0.962860	−	0.270003i	$-0.912975\pi$
$421$	−16.5885	−	25.8123i	−0.808476	−	1.25801i	0.154383	−	0.988011i	$-0.450661\pi$
$422$	−8.31242	−	3.10037i	−0.404642	−	0.150924i
$423$	−1.06588	+	14.9029i	−0.0518247	+	0.724604i
$424$	−3.81317	−	2.45057i	−0.185184	−	0.119010i
$425$	21.0216	−	30.2918i	1.01969	−	1.46937i
$426$	0.142479	−	0.990962i	0.00690312	−	0.0480122i
$427$	27.2709	−	5.93242i	1.31973	−	0.287090i
$428$	−0.760195	−	0.0543702i	−0.0367454	−	0.00262808i
$429$	1.17975	+	2.58329i	0.0569588	+	0.124722i
$430$	11.8618	+	13.2024i	0.572029	+	0.636676i
$431$	−7.50878	+	25.5726i	−0.361685	+	1.23179i	0.554890	+	0.831924i	$0.312761\pi$
$431$	−7.50878	+	25.5726i	−0.361685	+	1.23179i	−0.916575	+	0.399863i	$0.869058\pi$
$432$	0.398255	+	5.56834i	0.0191611	+	0.267907i
$433$	9.88108	−	18.0958i	0.474854	−	0.869631i	−0.524974	−	0.851118i	$-0.675925\pi$
$433$	9.88108	−	18.0958i	0.474854	−	0.869631i	0.999829	−	0.0185125i	$-0.00589306\pi$
$434$	17.4375	−	38.1828i	0.837026	−	1.83283i
$435$	11.7667	+	6.15333i	0.564172	+	0.295030i
$436$		−	7.86573i		−	0.376700i
$437$	−10.9900	+	4.86854i	−0.525724	+	0.232894i
$438$	−2.71006	−	2.71006i	−0.129492	−	0.129492i
$439$	−2.82670	+	0.406418i	−0.134911	+	0.0193973i	−0.209439	−	0.977822i	$-0.567164\pi$
$439$	−2.82670	+	0.406418i	−0.134911	+	0.0193973i	0.0745285	+	0.997219i	$0.476255\pi$
$440$	−2.57386	−	4.51874i	−0.122704	−	0.215422i
$441$	−13.8754	+	4.07419i	−0.660734	+	0.194009i
$442$	7.01861	−	0.501981i	0.333841	−	0.0238768i
$443$	−4.07331	−	7.45971i	−0.193529	−	0.354422i	0.762838	−	0.646589i	$-0.223805\pi$
$443$	−4.07331	−	7.45971i	−0.193529	−	0.354422i	−0.956367	+	0.292168i	$0.905623\pi$
$444$	8.17224	−	5.25198i	0.387837	−	0.249248i
$445$	3.19811	+	4.78511i	0.151605	+	0.226836i
$446$	14.0720	+	16.2400i	0.666328	+	0.768984i
$447$	0.437322	+	2.01034i	0.0206846	+	0.0950858i
$448$	2.51521	+	3.35993i	0.118833	+	0.158742i
$449$	−31.2043	−	4.48651i	−1.47262	−	0.211731i	−0.641202	−	0.767372i	$-0.721564\pi$
$449$	−31.2043	−	4.48651i	−1.47262	−	0.211731i	−0.831422	+	0.555641i	$0.812473\pi$
$450$	3.47702	+	5.85710i	0.163908	+	0.276106i
$451$	15.0673	−	13.0558i	0.709489	−	0.614776i
$452$	−3.95112	+	10.5934i	−0.185845	+	0.498270i
$453$	−5.28626	−	1.14996i	−0.248370	−	0.0540297i
$454$	10.1749	+	2.98763i	0.477533	+	0.140216i
$455$	−7.61928	−	4.70537i	−0.357197	−	0.220591i
$456$	−0.903653	−	3.07756i	−0.0423175	−	0.144120i
$457$	−26.2513	+	9.79122i	−1.22798	+	0.458014i	−0.877963	−	0.478729i	$-0.841098\pi$
$457$	−26.2513	+	9.79122i	−1.22798	+	0.458014i	−0.350020	+	0.936742i	$0.613825\pi$
$458$	−0.983481	−	0.736225i	−0.0459551	−	0.0344015i
$459$	41.1673			1.92153
$460$	10.6245	+	1.45626i	0.495368	+	0.0678986i
$461$	−4.09221			−0.190593			−0.0952965	−	0.995449i	$-0.530380\pi$
$461$	−4.09221			−0.190593			−0.0952965	+	0.995449i	$0.530380\pi$
$462$	9.99997	+	7.48589i	0.465241	+	0.348275i
$463$	−20.6124	+	7.68804i	−0.957941	+	0.357294i	−0.779321	−	0.626625i	$-0.784436\pi$
$463$	−20.6124	+	7.68804i	−0.957941	+	0.357294i	−0.178620	+	0.983918i	$0.557163\pi$
$464$	−1.30732	−	4.45233i	−0.0606909	−	0.206694i
$465$	27.8515	−	6.58490i	1.29158	−	0.305367i
$466$	23.0819	+	6.77745i	1.06925	+	0.313959i
$467$	−0.168691	−	0.0366965i	−0.00780610	−	0.00169811i	0.208661	−	0.977988i	$-0.433090\pi$
$467$	−0.168691	−	0.0366965i	−0.00780610	−	0.00169811i	−0.216467	+	0.976290i	$0.569453\pi$
$468$	−0.454264	+	1.21793i	−0.0209984	+	0.0562988i
$469$	36.2926	−	31.4477i	1.67583	−	1.45212i
$470$	−9.78536	+	22.4875i	−0.451365	+	1.03727i
$471$	−9.60250	−	1.38063i	−0.442460	−	0.0636161i
$472$	2.51465	+	3.35918i	0.115746	+	0.154619i
$473$	−3.92388	−	18.0378i	−0.180420	−	0.829379i
$474$	−0.532166	−	0.614153i	−0.0244432	−	0.0282090i
$475$	−8.54156	−	9.17001i	−0.391914	−	0.420749i
$476$	26.0371	−	16.7330i	1.19341	−	0.766958i
$477$	−2.95929	−	5.41953i	−0.135496	−	0.248143i
$478$	8.90445	−	0.636859i	0.407280	−	0.0291292i
$479$	15.3082	−	4.49488i	0.699448	−	0.205377i	0.0873725	−	0.996176i	$-0.472153\pi$
$479$	15.3082	−	4.49488i	0.699448	−	0.205377i	0.612076	+	0.790799i	$0.290335\pi$
$480$	−0.756742	+	2.75970i	−0.0345404	+	0.125962i
$481$	7.16953	−	1.03082i	0.326902	−	0.0470015i
$482$	6.73359	+	6.73359i	0.306707	+	0.306707i
$483$	−24.7967	+	6.97533i	−1.12829	+	0.317389i
$484$		−	5.59124i		−	0.254147i
$485$	0.478439	−	0.914898i	0.0217248	−	0.0415434i
$486$	−5.33189	+	11.6752i	−0.241859	+	0.529598i
$487$	3.98656	−	7.30084i	0.180648	−	0.330833i	−0.771626	−	0.636077i	$-0.780556\pi$
$487$	3.98656	−	7.30084i	0.180648	−	0.330833i	0.952274	+	0.305244i	$0.0987380\pi$
$488$	−0.474374	−	6.63262i	−0.0214739	−	0.300244i
$489$	−2.21024	+	7.52739i	−0.0999505	+	0.340400i
$490$	−23.7029	−	1.26774i	−1.07079	−	0.0572708i
$491$	−7.27612	−	15.9325i	−0.328367	−	0.719023i	0.671389	−	0.741105i	$-0.265698\pi$
$491$	−7.27612	−	15.9325i	−0.328367	−	0.719023i	−0.999756	+	0.0220818i	$0.992971\pi$
$492$	−10.9426	−	0.782628i	−0.493329	−	0.0352836i
$493$	−33.4368	+	7.27374i	−1.50592	+	0.327593i
$494$	0.340357	−	2.36723i	0.0153134	−	0.106507i
$495$	−0.127272	−	7.08321i	−0.00572045	−	0.318367i
$496$	−8.41360	−	5.40709i	−0.377782	−	0.242786i
$497$	0.234237	−	3.27506i	0.0105070	−	0.146906i
$498$	11.3024	+	4.21559i	0.506475	+	0.188905i
$499$	2.46768	+	3.83978i	0.110469	+	0.171892i	0.892086	−	0.451866i	$-0.149241\pi$
$499$	2.46768	+	3.83978i	0.110469	+	0.171892i	−0.781617	+	0.623758i	$0.785605\pi$
$500$	2.18500	+	10.9648i	0.0977161	+	0.490359i
$501$	14.5212	−	16.7583i	0.648759	−	0.748707i
$502$	−15.2615	−	8.33342i	−0.681155	−	0.371939i
$503$	11.0316	+	29.5769i	0.491876	+	1.31877i	0.911585	+	0.411112i	$0.134859\pi$
$503$	11.0316	+	29.5769i	0.491876	+	1.31877i	−0.419709	+	0.907659i	$0.637868\pi$
$504$	0.813699	+	5.65940i	0.0362450	+	0.252090i
$505$	−3.72478	+	0.604030i	−0.165751	+	0.0268790i
$506$	−8.85220	−	6.78528i	−0.393528	−	0.301643i
$507$	−10.9399	+	10.9399i	−0.485858	+	0.485858i
$508$	3.45062	−	4.60949i	0.153097	−	0.204513i
$509$	31.9316	+	14.5827i	1.41535	+	0.646367i	0.968675	−	0.248332i	$-0.0798824\pi$
$509$	31.9316	+	14.5827i	1.41535	+	0.646367i	0.446670	+	0.894699i	$0.352610\pi$
$510$	19.9008	+	7.01801i	0.881224	+	0.310763i
$511$	−9.49946	−	8.23133i	−0.420231	−	0.364132i
$512$	0.877679	−	0.479249i	0.0387883	−	0.0211800i
$513$	2.97420	−	13.6722i	0.131314	−	0.603642i
$514$	18.3307	−	8.37137i	0.808535	−	0.369245i
$515$	−6.48351	+	0.580952i	−0.285697	+	0.0255998i
$516$	−5.49166	+	8.54519i	−0.241757	+	0.376181i
$517$	20.4195	−	15.2858i	0.898047	−	0.672270i
$518$	25.5050	−	19.0928i	1.12062	−	0.838889i
$519$	−14.0065	+	21.7945i	−0.614817	+	0.956674i
$520$	−1.36805	+	1.63735i	−0.0599931	+	0.0718026i
$521$	33.6157	−	15.3518i	1.47273	−	0.672573i	0.492478	−	0.870325i	$-0.336091\pi$
$521$	33.6157	−	15.3518i	1.47273	−	0.672573i	0.980252	+	0.197752i	$0.0633639\pi$
$522$	1.34371	−	6.17692i	0.0588125	−	0.270357i
$523$	−7.10799	+	3.88126i	−0.310811	+	0.169715i	−0.627082	−	0.778953i	$-0.715751\pi$
$523$	−7.10799	+	3.88126i	−0.310811	+	0.169715i	0.316271	+	0.948669i	$0.397569\pi$
$524$	7.18954	+	6.22977i	0.314076	+	0.272149i
$525$	−15.3215	−	22.0563i	−0.668687	−	0.962614i
$526$	14.0993	+	6.43894i	0.614760	+	0.280751i
$527$	−44.1980	+	59.0416i	−1.92529	+	2.57189i
$528$	2.10452	−	2.10452i	0.0915876	−	0.0915876i
$529$	22.2101	−	5.97574i	0.965658	−	0.259815i
$530$	−1.62243	−	10.0048i	−0.0704738	−	0.434580i
$531$	0.813516	+	5.65813i	0.0353036	+	0.245542i
$532$	−3.67616	−	9.85617i	−0.159382	−	0.427319i
$533$	−7.17930	−	3.92020i	−0.310970	−	0.169803i
$534$	−2.15706	+	2.48938i	−0.0933453	+	0.107726i
$535$	−1.04563	−	1.34571i	−0.0452064	−	0.0581800i
$536$	−6.18589	−	9.62543i	−0.267190	−	0.415755i
$537$	4.68148	+	1.74610i	0.202021	+	0.0753498i
$538$	0.0651741	−	0.911253i	0.00280986	−	0.0392869i
$539$	20.7689	+	13.3474i	0.894579	+	0.574911i
$540$	−8.66680	+	8.98395i	−0.372960	+	0.386608i
$541$	3.09519	−	21.5275i	0.133073	−	0.925541i	−0.808444	−	0.588574i	$-0.799690\pi$
$541$	3.09519	−	21.5275i	0.133073	−	0.925541i	0.941516	−	0.336967i	$-0.109401\pi$
$542$	−1.54341	+	0.335748i	−0.0662951	+	0.0144216i
$543$	−1.05397	−	0.0753811i	−0.0452300	−	0.00323491i
$544$	−3.06339	−	6.70788i	−0.131342	−	0.287598i
$545$	13.0833	−	11.7548i	0.560427	−	0.503522i
$546$	1.44392	−	4.91753i	0.0617940	−	0.210451i
$547$	1.28496	+	17.9661i	0.0549411	+	0.768177i	0.948007	+	0.318250i	$0.103095\pi$
$547$	1.28496	+	17.9661i	0.0549411	+	0.768177i	−0.893066	+	0.449926i	$0.851450\pi$
$548$	−8.47696	+	15.5244i	−0.362118	+	0.663170i
$549$	3.76306	−	8.23996i	0.160604	−	0.351673i
$550$	3.66967	−	11.0341i	0.156475	−	0.470498i
$551$			11.6303i			0.495467i
$552$	0.804226	+	6.08447i	0.0342302	+	0.258972i
$553$	−1.88456	−	1.88456i	−0.0801397	−	0.0801397i
$554$	14.3861	−	2.06840i	0.611205	−	0.0878780i
$555$	20.9487	+	5.74437i	0.889221	+	0.243835i
$556$	−10.3285	+	3.03272i	−0.438026	+	0.128616i
$557$	3.85261	−	0.275544i	0.163240	−	0.0116752i	0.0105203	−	0.999945i	$-0.496651\pi$
$557$	3.85261	−	0.275544i	0.163240	−	0.0116752i	0.152720	+	0.988269i	$0.451197\pi$
$558$	−6.52954	−	11.9580i	−0.276418	−	0.506221i
$559$	−6.37149	+	4.09471i	−0.269485	+	0.173188i
$560$	−1.82984	+	9.20483i	−0.0773249	+	0.388975i
$561$	−14.3727	−	16.5869i	−0.606814	−	0.700301i
$562$	−4.10289	−	18.8607i	−0.173070	−	0.795590i
$563$	−2.64111	−	3.52811i	−0.111310	−	0.148692i	0.741427	−	0.671034i	$-0.234149\pi$
$563$	−2.64111	−	3.52811i	−0.111310	−	0.148692i	−0.852736	+	0.522342i	$0.825059\pi$
$564$	−13.8928	−	1.99748i	−0.584991	−	0.0841090i
$565$	−23.5249	+	9.25910i	−0.989702	+	0.389533i
$566$	−9.93758	+	8.61097i	−0.417708	+	0.361946i
$567$	4.48429	−	12.0229i	0.188323	−	0.504912i
$568$	−0.764434	−	0.166292i	−0.0320749	−	0.00697748i
$569$	2.83116	+	0.831303i	0.118688	+	0.0348500i	0.340537	−	0.940231i	$-0.389391\pi$
$569$	2.83116	+	0.831303i	0.118688	+	0.0348500i	−0.221849	+	0.975081i	$0.571209\pi$
$570$	3.76854	−	6.10229i	0.157847	−	0.255597i
$571$	−2.24201	−	7.63559i	−0.0938252	−	0.319539i	0.899185	−	0.437569i	$-0.144160\pi$
$571$	−2.24201	−	7.63559i	−0.0938252	−	0.319539i	−0.993010	+	0.118030i	$0.962342\pi$
$572$	2.07924	−	0.775516i	0.0869373	−	0.0324259i
$573$	−3.16839	−	2.37183i	−0.132361	−	0.0990845i
$574$	−35.9794			−1.50175
$575$	13.4553	+	19.8483i	0.561127	+	0.827730i
$576$	1.36228			0.0567617
$577$	−3.56576	−	2.66929i	−0.148444	−	0.111124i	0.522474	−	0.852655i	$-0.325009\pi$
$577$	−3.56576	−	2.66929i	−0.148444	−	0.111124i	−0.670919	+	0.741531i	$0.734100\pi$
$578$	−35.0232	+	13.0630i	−1.45677	+	0.543348i
$579$	−1.05068	−	3.57828i	−0.0436647	−	0.148708i
$580$	5.45198	−	8.82823i	0.226381	−	0.366572i
$581$	37.9599	+	11.1460i	1.57484	+	0.462415i
$582$	0.577379	+	0.125601i	0.0239331	+	0.00520634i
$583$	−3.68392	+	9.87698i	−0.152572	+	0.409063i
$584$	−2.26335	+	1.96121i	−0.0936582	+	0.0811553i
$585$	−2.70469	+	1.06453i	−0.111825	+	0.0440128i
$586$	−26.1816	−	3.76434i	−1.08155	−	0.155503i
$587$	16.1791	+	21.6127i	0.667783	+	0.892053i	0.998667	−	0.0516182i	$-0.0164379\pi$
$587$	16.1791	+	21.6127i	0.667783	+	0.892053i	−0.330884	+	0.943671i	$0.607347\pi$
$588$	−2.88768	−	13.2745i	−0.119086	−	0.547430i
$589$	16.4153	+	18.9443i	0.676381	+	0.780585i
$590$	−1.82943	+	9.20276i	−0.0753165	+	0.378872i
$591$	−7.59190	+	4.87902i	−0.312289	+	0.200696i
$592$	−3.63794	−	6.66239i	−0.149519	−	0.273823i
$593$	25.1905	−	1.80166i	1.03445	−	0.0739854i	0.456227	−	0.889863i	$-0.349200\pi$
$593$	25.1905	−	1.80166i	1.03445	−	0.0739854i	0.578224	+	0.815878i	$0.303746\pi$
$594$	12.4573	−	3.65779i	0.511129	−	0.150081i
$595$	66.7434	+	18.3018i	2.73621	+	0.750301i
$596$	1.59128	−	0.228791i	0.0651814	−	0.00937166i
$597$	−0.470785	−	0.470785i	−0.0192679	−	0.0192679i
$598$	−1.33916	+	4.37585i	−0.0547624	+	0.178942i
$599$		−	5.24778i		−	0.214418i	−0.994236	−	0.107209i	$-0.965809\pi$
$599$		−	5.24778i		−	0.214418i	0.994236	−	0.107209i	$-0.0341915\pi$
$600$	−5.72119	+	2.86548i	−0.233566	+	0.116983i
$601$	−1.57565	+	3.45018i	−0.0642720	+	0.140736i	−0.939042	−	0.343802i	$-0.888285\pi$
$601$	−1.57565	+	3.45018i	−0.0642720	+	0.140736i	0.874770	+	0.484538i	$0.161012\pi$
$602$	−15.9655	+	29.2387i	−0.650706	+	1.19168i
$603$	−1.11196	−	15.5472i	−0.0452824	−	0.633130i
$604$	−1.19099	+	4.05612i	−0.0484605	+	0.165041i
$605$	9.30007	−	8.35576i	0.378102	−	0.339710i
$606$	−0.897127	−	1.96443i	−0.0364433	−	0.0797997i
$607$	25.5649	+	1.82844i	1.03765	+	0.0742141i	0.579753	−	0.814792i	$-0.303149\pi$
$607$	25.5649	+	1.82844i	1.03765	+	0.0742141i	0.457895	+	0.889006i	$0.348604\pi$
$608$	−2.44909	+	0.532767i	−0.0993238	+	0.0216066i
$609$	−3.54701	+	24.6700i	−0.143732	+	0.999678i
$610$	10.3233	−	10.7011i	0.417978	−	0.433273i
$611$	−8.80396	−	5.65796i	−0.356170	−	0.228897i
$612$	0.716662	−	10.0202i	0.0289693	−	0.405044i
$613$	−2.74114	−	1.02239i	−0.110714	−	0.0412941i	0.293497	−	0.955960i	$-0.405181\pi$
$613$	−2.74114	−	1.02239i	−0.110714	−	0.0412941i	−0.404211	+	0.914666i	$0.632454\pi$
$614$	−5.73097	−	8.91756i	−0.231283	−	0.359883i
$615$	−15.0512	−	19.3707i	−0.606923	−	0.781100i
$616$	6.39211	−	7.37689i	0.257546	−	0.297223i
$617$	14.2338	+	7.77224i	0.573031	+	0.312899i	0.739509	−	0.673146i	$-0.235058\pi$
$617$	14.2338	+	7.77224i	0.573031	+	0.312899i	−0.166478	+	0.986045i	$0.553239\pi$
$618$	−1.30192	−	3.49058i	−0.0523708	−	0.140412i
$619$	−4.60667	−	32.0401i	−0.185158	−	1.28780i	−0.844336	−	0.535814i	$-0.820005\pi$
$619$	−4.60667	−	32.0401i	−0.185158	−	1.28780i	0.659179	−	0.751986i	$-0.270904\pi$
$620$	−3.57982	−	22.0751i	−0.143769	−	0.886558i
$621$	−9.64118	+	24.9768i	−0.386887	+	1.00229i
$622$	−18.0101	+	18.0101i	−0.722140	+	0.722140i
$623$	−6.47395	+	8.64818i	−0.259373	+	0.346482i
$624$	−1.11077	−	0.507272i	−0.0444664	−	0.0203071i
$625$	−14.9726	+	20.0205i	−0.598905	+	0.800820i
$626$	24.7703	+	21.4636i	0.990022	+	0.857859i
$627$	−6.54711	+	3.57499i	−0.261466	+	0.142771i
$628$	−1.61139	+	7.40743i	−0.0643014	+	0.295589i
$629$	−50.9190	+	23.2539i	−2.03027	+	0.927195i
$630$	−8.19741	+	9.81106i	−0.326593	+	0.390882i
$631$	−0.184485	+	0.287065i	−0.00734424	+	0.0114279i	−0.844906	−	0.534914i	$-0.820344\pi$
$631$	−0.184485	+	0.287065i	−0.00734424	+	0.0114279i	0.837562	+	0.546342i	$0.183980\pi$
$632$	−0.508349	+	0.380546i	−0.0202211	+	0.0151373i
$633$	9.08896	−	6.80391i	0.361254	−	0.270431i
$634$	4.87643	−	7.58788i	0.193668	−	0.301353i
$635$	12.8238	−	1.14907i	0.508898	−	0.0455996i
$636$	5.27648	−	2.40969i	0.209226	−	0.0955504i
$637$	2.15312	−	9.89776i	0.0853099	−	0.392163i
$638$	−9.47175	+	5.17197i	−0.374990	+	0.204760i
$639$	−0.805425	−	0.697904i	−0.0318621	−	0.0276087i
$640$	2.10878	+	0.743661i	0.0833570	+	0.0293958i
$641$	−13.6502	−	6.23382i	−0.539149	−	0.246221i	0.127179	−	0.991880i	$-0.459408\pi$
$641$	−13.6502	−	6.23382i	−0.539149	−	0.246221i	−0.666328	+	0.745659i	$0.732135\pi$
$642$	0.584495	−	0.780794i	0.0230682	−	0.0308155i
$643$	−12.7991	+	12.7991i	−0.504748	+	0.504748i	−0.912910	−	0.408162i	$-0.866170\pi$
$643$	−12.7991	+	12.7991i	−0.504748	+	0.504748i	0.408162	+	0.912910i	$0.366170\pi$
$644$	4.05442	+	19.7159i	0.159767	+	0.776915i
$645$	−22.4204	+	3.63581i	−0.882802	+	0.143160i
$646$	2.63036	+	18.2945i	0.103490	+	0.719789i
$647$	−13.7972	−	36.9916i	−0.542422	−	1.45429i	−0.862087	−	0.506760i	$-0.830843\pi$
$647$	−13.7972	−	36.9916i	−0.542422	−	1.45429i	0.319665	−	0.947531i	$-0.396430\pi$
$648$	−2.68337	−	1.46523i	−0.105413	−	0.0575597i
$649$	6.39068	−	7.37523i	0.250856	−	0.289503i
$650$	−4.76792	+	0.171396i	−0.187013	+	0.00672271i
$651$	29.0422	+	45.1906i	1.13825	+	1.77116i
$652$	5.74380	+	2.14233i	0.224944	+	0.0838999i
$653$	−1.71310	+	23.9522i	−0.0670386	+	0.937323i	0.846973	+	0.531635i	$0.178422\pi$
$653$	−1.71310	+	23.9522i	−0.0670386	+	0.937323i	−0.914012	+	0.405687i	$0.867032\pi$
$654$	8.46810	+	5.44212i	0.331129	+	0.212804i
$655$	0.382155	+	21.2685i	0.0149320	+	0.831031i
$656$	−1.21999	+	8.48524i	−0.0476328	+	0.331293i
$657$	−3.98658	+	0.867228i	−0.155531	+	0.0338338i
$658$	−45.9146	−	3.28388i	−1.78994	−	0.128019i
$659$	−5.96695	−	13.0658i	−0.232440	−	0.508972i	0.757089	−	0.653312i	$-0.226621\pi$
$659$	−5.96695	−	13.0658i	−0.232440	−	0.508972i	−0.989528	+	0.144341i	$0.953894\pi$
$660$	6.64558	+	0.355436i	0.258679	+	0.0138353i
$661$	11.5842	−	39.4521i	0.450572	−	1.53451i	−0.350863	−	0.936427i	$-0.614112\pi$
$661$	11.5842	−	39.4521i	0.450572	−	1.53451i	0.801436	−	0.598081i	$-0.204070\pi$
$662$	−0.444815	−	6.21933i	−0.0172882	−	0.241721i
$663$	−4.31558	+	7.90340i	−0.167603	+	0.306943i
$664$	3.91578	−	8.57437i	0.151962	−	0.332750i
$665$	10.9003	−	20.8441i	0.422694	−	0.808299i
$666$		−	10.3410i		−	0.400705i
$667$	3.41765	−	21.9901i	0.132332	−	0.851459i
$668$	−12.2523	−	12.2523i	−0.474056	−	0.474056i
$669$	−27.2197	+	3.91360i	−1.05237	+	0.151309i
$670$	6.76583	−	24.6737i	0.261387	−	0.953230i
$671$	−14.8383	+	4.35691i	−0.572825	+	0.168197i
$672$	−5.35745	+	0.383173i	−0.206668	+	0.0147812i
$673$	14.0727	+	25.7723i	0.542463	+	0.993447i	0.994824	+	0.101612i	$0.0324001\pi$
$673$	14.0727	+	25.7723i	0.542463	+	0.993447i	−0.452361	+	0.891835i	$0.649418\pi$
$674$	26.3704	−	16.9472i	1.01575	−	0.652784i
$675$	−27.8952	−	0.989789i	−1.07369	−	0.0380970i
$676$	7.91694	+	9.13664i	0.304498	+	0.351409i
$677$	−1.91228	−	8.79061i	−0.0734949	−	0.337850i	0.925687	−	0.378290i	$-0.123488\pi$
$677$	−1.91228	−	8.79061i	−0.0734949	−	0.337850i	−0.999182	+	0.0404396i	$0.987124\pi$
$678$	−8.67093	−	11.5830i	−0.333005	−	0.444843i
$679$	1.91816	+	0.275790i	0.0736123	+	0.0105838i
$680$	6.57937	−	15.1199i	0.252307	−	0.579822i
$681$	−10.2562	+	8.88706i	−0.393019	+	0.340553i
$682$	−8.12842	+	21.7931i	−0.311253	+	0.834503i
$683$	−23.3721	−	5.08430i	−0.894310	−	0.194545i	−0.258152	−	0.966104i	$-0.583114\pi$
$683$	−23.3721	−	5.08430i	−0.894310	−	0.194545i	−0.636158	+	0.771559i	$0.719477\pi$
$684$	−3.27607	−	0.961942i	−0.125264	−	0.0367808i
$685$	−38.4905	+	9.10026i	−1.47064	+	0.347703i
$686$	−4.27508	−	14.5596i	−0.163223	−	0.555887i
$687$	1.47305	−	0.549420i	0.0562005	−	0.0209617i
$688$	6.35417	+	4.75667i	0.242250	+	0.181346i
$689$	4.32512			0.164774
$690$	−8.91860	+	10.4305i	−0.339525	+	0.397084i
$691$	−30.5887			−1.16365			−0.581825	−	0.813314i	$-0.697661\pi$
$691$	−30.5887			−1.16365			−0.581825	+	0.813314i	$0.697661\pi$
$692$	16.2063	+	12.1319i	0.616073	+	0.461186i
$693$	12.4589	−	4.64692i	0.473273	−	0.176522i
$694$	4.68025	+	15.9395i	0.177660	+	0.605054i
$695$	−20.4797	−	12.6475i	−0.776838	−	0.479746i
$696$	5.69780	+	1.67302i	0.215975	+	0.0634158i
$697$	61.7713	+	13.4375i	2.33976	+	0.508983i
$698$	11.1184	−	29.8095i	0.420837	−	1.12831i
$699$	−23.2663	+	20.1604i	−0.880012	+	0.762535i
$700$	−18.0452	+	10.7124i	−0.682046	+	0.404891i
$701$	42.3952	+	6.09551i	1.60125	+	0.230224i	0.884305	−	0.466910i	$-0.154633\pi$
$701$	42.3952	+	6.09551i	1.60125	+	0.230224i	0.716941	+	0.697134i	$0.245542\pi$
$702$	−3.19228	−	4.26438i	−0.120485	−	0.160949i
$703$	4.04420	+	18.5909i	0.152530	+	0.701168i
$704$	−1.52299	−	1.75763i	−0.0573999	−	0.0662431i
$705$	−17.4394	−	26.0933i	−0.656805	−	0.982731i
$706$	−26.9485	+	17.3188i	−1.01422	+	0.651801i
$707$	−3.39438	−	6.21634i	−0.127659	−	0.233789i
$708$	−5.35625	+	0.383087i	−0.201300	+	0.0143973i
$709$	−38.8250	+	11.4000i	−1.45810	+	0.428137i	−0.912212	−	0.409719i	$-0.865627\pi$
$709$	−38.8250	+	11.4000i	−1.45810	+	0.428137i	−0.545891	+	0.837856i	$0.683809\pi$
$710$	−0.865799	−	1.52002i	−0.0324929	−	0.0570453i
$711$	−0.856253	+	0.123111i	−0.0321120	+	0.00461701i
$712$	1.82003	+	1.82003i	0.0682087	+	0.0682087i
$713$	−25.4705	−	40.6428i	−0.953876	−	1.52208i
$714$			39.6083i			1.48230i
$715$	4.39723	+	2.29950i	0.164447	+	0.0859963i
$716$	1.62192	−	3.55151i	0.0606140	−	0.132726i
$717$	−5.47515	+	10.0270i	−0.204473	+	0.374465i
$718$	0.322002	+	4.50217i	0.0120170	+	0.168020i
$719$	3.16985	−	10.7955i	0.118215	−	0.402605i	−0.879031	−	0.476765i	$-0.841809\pi$
$719$	3.16985	−	10.7955i	0.118215	−	0.402605i	0.997246	+	0.0741600i	$0.0236276\pi$
$720$	2.03584	+	2.26592i	0.0758714	+	0.0844459i
$721$	−5.07563	−	11.1141i	−0.189027	−	0.413910i
$722$	−12.6857	−	0.907299i	−0.472113	−	0.0337662i
$723$	−11.9081	+	2.59044i	−0.442866	+	0.0963396i
$724$	−0.117507	+	0.817282i	−0.00436713	+	0.0303740i
$725$	22.8319	−	4.12480i	0.847955	−	0.153191i
$726$	6.01942	+	3.86845i	0.223402	+	0.143572i
$727$	2.60487	−	36.4208i	0.0966092	−	1.35077i	−0.685700	−	0.727884i	$-0.740504\pi$
$727$	2.60487	−	36.4208i	0.0966092	−	1.35077i	0.782310	−	0.622890i	$-0.214041\pi$
$728$	−3.75234	−	1.39955i	−0.139071	−	0.0518708i
$729$	−13.8391	−	21.5340i	−0.512558	−	0.797556i
$730$	−6.64456	−	0.833800i	−0.245926	−	0.0308603i
$731$	38.3304	−	44.2357i	1.41770	−	1.63611i
$732$	7.46875	+	4.07825i	0.276053	+	0.150736i
$733$	3.67716	+	9.85884i	0.135819	+	0.364144i	0.986998	−	0.160730i	$-0.0513849\pi$
$733$	3.67716	+	9.85884i	0.135819	+	0.364144i	−0.851180	+	0.524875i	$0.824112\pi$
$734$	−4.04109	−	28.1064i	−0.149159	−	1.03743i
$735$	17.7643	−	24.6410i	0.655247	−	0.908898i
$736$	4.78720	−	0.287651i	0.176458	−	0.0106029i
$737$	−18.8160	+	18.8160i	−0.693095	+	0.693095i
$738$	−6.99846	+	9.34884i	−0.257617	+	0.344136i
$739$	−7.50177	−	3.42595i	−0.275957	−	0.126025i	0.272630	−	0.962119i	$-0.412107\pi$
$739$	−7.50177	−	3.42595i	−0.275957	−	0.126025i	−0.548587	+	0.836094i	$0.684834\pi$
$740$	5.64507	−	16.0076i	0.207517	−	0.588452i
$741$	2.31303	+	2.00426i	0.0849714	+	0.0736282i
$742$	16.6971	−	9.11732i	0.612970	−	0.334707i
$743$	2.95731	−	13.5945i	0.108493	−	0.498735i	−0.890545	−	0.454895i	$-0.849677\pi$
$743$	2.95731	−	13.5945i	0.108493	−	0.498735i	0.999039	−	0.0438408i	$-0.0139594\pi$
$744$	11.6423	−	5.31688i	0.426829	−	0.194926i
$745$	2.75862	+	2.30491i	0.101068	+	0.0844452i
$746$	10.9066	−	16.9709i	0.399318	−	0.621350i
$747$	10.2799	−	7.69540i	0.376120	−	0.281560i
$748$	−13.7294	+	10.2777i	−0.501997	+	0.375790i
$749$	1.72937	−	2.69095i	0.0631899	−	0.0983254i
$750$	−13.3162	−	5.23393i	−0.486238	−	0.191116i
$751$	20.5080	−	9.36571i	0.748349	−	0.341760i	−0.00446733	−	0.999990i	$-0.501422\pi$
$751$	20.5080	−	9.36571i	0.748349	−	0.341760i	0.752817	+	0.658230i	$0.228695\pi$
$752$	−2.33133	+	10.7170i	−0.0850150	+	0.390807i
$753$	19.5307	−	10.6646i	0.711738	−	0.388638i
$754$	3.34628	+	2.89957i	0.121864	+	0.105596i
$755$	−8.52651	+	4.08062i	−0.310312	+	0.148509i
$756$	−21.3131	−	9.73335i	−0.775148	−	0.353998i
$757$	−15.2257	+	20.3391i	−0.553386	+	0.739237i	−0.986797	−	0.161959i	$-0.948219\pi$
$757$	−15.2257	+	20.3391i	−0.553386	+	0.739237i	0.433412	+	0.901196i	$0.357310\pi$
$758$	−24.3713	+	24.3713i	−0.885205	+	0.885205i
$759$	13.4295	−	4.83553i	0.487461	−	0.175518i
$760$	−4.54618	−	3.27746i	−0.164907	−	0.118886i
$761$	2.73404	+	19.0157i	0.0991089	+	0.689318i	0.977432	+	0.211250i	$0.0677535\pi$
$761$	2.73404	+	19.0157i	0.0991089	+	0.689318i	−0.878323	+	0.478068i	$0.841337\pi$
$762$	2.57508	+	6.90407i	0.0932855	+	0.250108i
$763$	28.9749	+	15.8215i	1.04896	+	0.572776i
$764$	−2.02528	+	2.33729i	−0.0732719	+	0.0845603i
$765$	17.7380	−	13.7826i	0.641317	−	0.498310i
$766$	6.51136	+	10.1319i	0.235265	+	0.366080i
$767$	−3.75150	−	1.39924i	−0.135459	−	0.0505235i
$768$	−0.0912952	+	1.27647i	−0.00329433	+	0.0460608i
$769$	36.7011	+	23.5864i	1.32348	+	0.850546i	0.995557	−	0.0941597i	$-0.0300164\pi$
$769$	36.7011	+	23.5864i	1.32348	+	0.850546i	0.327919	+	0.944706i	$0.393653\pi$
$770$	21.8228	−	0.392114i	0.786439	−	0.0141308i
$771$	−3.67015	+	25.5265i	−0.132177	+	0.919314i
$772$	−2.84756	+	0.619449i	−0.102486	+	0.0222945i
$773$	−13.0985	−	0.936822i	−0.471120	−	0.0336951i	−0.166239	−	0.986086i	$-0.553162\pi$
$773$	−13.0985	−	0.936822i	−0.471120	−	0.0336951i	−0.304881	+	0.952390i	$0.598617\pi$
$774$	4.49184	+	9.83575i	0.161456	+	0.353539i
$775$	31.3684	−	38.9443i	1.12678	−	1.39892i
$776$	0.130082	−	0.443020i	0.00466969	−	0.0159035i
$777$	2.90863	+	40.6680i	0.104347	+	1.45896i
$778$	5.02089	−	9.19507i	0.180008	−	0.329659i
$779$	8.92555	−	19.5442i	0.319791	−	0.700244i
$780$	−0.816217	−	2.60566i	−0.0292252	−	0.0932977i
$781$			1.81940i			0.0651034i
$782$	0.402613	−	35.3635i	0.0143974	−	1.26460i
$783$	18.3174	+	18.3174i	0.654611	+	0.654611i
$784$	−10.5074	+	1.51073i	−0.375264	+	0.0539548i
$785$	−14.7291	+	8.38967i	−0.525704	+	0.299440i
$786$	−11.6811	+	3.42989i	−0.416652	+	0.122340i
$787$	−32.1360	+	2.29841i	−1.14552	+	0.0819296i	−0.631168	−	0.775646i	$-0.717424\pi$
$787$	−32.1360	+	2.29841i	−1.14552	+	0.0819296i	−0.514357	+	0.857576i	$0.671969\pi$
$788$	3.37960	+	6.18928i	0.120393	+	0.220484i
$789$	−16.6870	+	10.7241i	−0.594074	+	0.381788i
$790$	−1.39267	−	0.276851i	−0.0495489	−	0.00984991i
$791$	−31.0752	−	35.8626i	−1.10491	−	1.27513i
$792$	−0.673454	−	3.09582i	−0.0239301	−	0.110005i
$793$	3.80242	+	5.07944i	0.135028	+	0.180376i
$794$	−22.4271	−	3.22454i	−0.795910	−	0.114435i
$795$	11.8935	+	5.17540i	0.421818	+	0.183552i
$796$	−0.393184	+	0.340696i	−0.0139360	+	0.0120756i
$797$	−13.2540	+	35.5353i	−0.469481	+	1.25873i	0.459361	+	0.888250i	$0.348078\pi$
$797$	−13.2540	+	35.5353i	−0.469481	+	1.25873i	−0.928842	+	0.370477i	$0.879194\pi$
$798$	13.1544	+	2.86157i	0.465661	+	0.101298i
$799$	77.6021	+	22.7860i	2.74536	+	0.806112i
$800$	1.91449	+	4.61895i	0.0676875	+	0.163305i
$801$	0.987866	+	3.36436i	0.0349045	+	0.118874i
$802$	−9.83969	+	3.67002i	−0.347452	+	0.129593i
$803$	5.57579	+	4.17399i	0.196765	+	0.147297i
$804$	14.6424			0.516398
$805$	−26.7349	+	36.2080i	−0.942282	+	1.27616i
$806$	9.54320			0.336145
$807$	0.935945	+	0.700640i	0.0329468	+	0.0246637i
$808$	−1.58113	+	0.589732i	−0.0556241	+	0.0207467i
$809$	9.16373	+	31.2088i	0.322180	+	1.09724i	0.948263	+	0.317487i	$0.102839\pi$
$809$	9.16373	+	31.2088i	0.322180	+	1.09724i	−0.626083	+	0.779756i	$0.715343\pi$
$810$	−1.57297	−	6.65302i	−0.0552684	−	0.233763i
$811$	−29.0961	−	8.54337i	−1.02170	−	0.299998i	−0.272369	−	0.962193i	$-0.587807\pi$
$811$	−29.0961	−	8.54337i	−1.02170	−	0.299998i	−0.749332	+	0.662195i	$0.769625\pi$
$812$	19.0306	+	4.13985i	0.667843	+	0.145280i
$813$	0.706388	−	1.89390i	0.0247741	−	0.0664220i
$814$	−13.3420	+	11.5609i	−0.467637	+	0.405210i
$815$	5.02035	+	12.7554i	0.175855	+	0.446802i
$816$	9.34106	+	1.34304i	0.327002	+	0.0470159i
$817$	−11.9220	−	15.9259i	−0.417097	−	0.557177i
$818$	1.70462	+	7.83602i	0.0596007	+	0.273980i
$819$	−3.57274	−	4.12316i	−0.124842	−	0.144075i
$820$	−15.9369	+	10.6514i	−0.556542	+	0.371963i
$821$	−34.1205	+	21.9279i	−1.19081	+	0.765289i	−0.977343	−	0.211661i	$-0.932113\pi$
$821$	−34.1205	+	21.9279i	−1.19081	+	0.765289i	−0.213469	+	0.976950i	$0.568476\pi$
$822$	−10.8483	−	19.8671i	−0.378376	−	0.692945i
$823$	−42.8343	+	3.06357i	−1.49311	+	0.106789i	−0.793866	−	0.608093i	$-0.791935\pi$
$823$	−42.8343	+	3.06357i	−1.49311	+	0.106789i	−0.699245	+	0.714882i	$0.746480\pi$
$824$	−2.79321	+	0.820160i	−0.0973060	+	0.0285716i
$825$	9.34019	+	11.5850i	0.325184	+	0.403337i
$826$	−17.4322	+	2.50637i	−0.606544	+	0.0872079i
$827$	−10.3293	−	10.3293i	−0.359185	−	0.359185i	0.504327	−	0.863513i	$-0.331741\pi$
$827$	−10.3293	−	10.3293i	−0.359185	−	0.359185i	−0.863513	+	0.504327i	$0.831741\pi$
$828$	5.91159	+	2.78150i	0.205442	+	0.0966637i
$829$		−	4.29279i		−	0.149095i	−0.997217	−	0.0745474i	$-0.976249\pi$
$829$		−	4.29279i		−	0.149095i	0.997217	−	0.0745474i	$-0.0237512\pi$
$830$	20.1139	−	6.30062i	0.698163	−	0.218698i
$831$	−7.72657	+	16.9188i	−0.268032	+	0.586908i
$832$	−0.457299	+	0.837481i	−0.0158540	+	0.0290344i
$833$	5.58451	+	78.0817i	0.193492	+	2.70537i
$834$	3.88107	−	13.2177i	0.134391	−	0.457692i
$835$	2.06932	−	38.6899i	0.0716116	−	1.33892i
$836$	2.42145	+	5.30224i	0.0837477	+	0.183382i
$837$	55.6904	+	3.98306i	1.92494	+	0.137675i
$838$	12.4928	−	2.71765i	0.431557	−	0.0938796i
$839$	−0.954781	+	6.64065i	−0.0329627	+	0.229261i	−0.999643	−	0.0267269i	$-0.991492\pi$
$839$	−0.954781	+	6.64065i	−0.0329627	+	0.229261i	0.966680	+	0.255988i	$0.0824006\pi$
$840$	−8.64371	−	8.33857i	−0.298236	−	0.287708i
$841$	6.28219	+	4.03732i	0.216627	+	0.139218i
$842$	2.18891	−	30.6049i	0.0754348	−	1.05472i
$843$	23.1437	+	8.63217i	0.797112	+	0.297308i
$844$	−4.79645	−	7.46342i	−0.165101	−	0.256902i
$845$	−3.36586	+	26.8226i	−0.115789	+	0.922725i
$846$	−9.78425	+	11.2916i	−0.336390	+	0.388214i
$847$	20.5964	+	11.2465i	0.707700	+	0.386433i
$848$	−1.58402	−	4.24693i	−0.0543956	−	0.145840i
$849$	−2.39482	−	16.6563i	−0.0821900	−	0.571644i
$850$	34.9818	−	11.6521i	1.19987	−	0.399664i
$851$	−2.18353	−	36.3393i	−0.0748506	−	1.24569i
$852$	0.707921	−	0.707921i	0.0242530	−	0.0242530i
$853$	30.4853	−	40.7236i	1.04380	−	1.39435i	0.128437	−	0.991718i	$-0.459004\pi$
$853$	30.4853	−	40.7236i	1.04380	−	1.39435i	0.915361	−	0.402633i	$-0.131905\pi$
$854$	25.3866	+	11.5937i	0.868713	+	0.396728i
$855$	−3.29586	−	6.88675i	−0.112716	−	0.235522i
$856$	−0.575985	−	0.499093i	−0.0196867	−	0.0170587i
$857$	11.6931	−	6.38492i	0.399429	−	0.218105i	−0.266962	−	0.963707i	$-0.586020\pi$
$857$	11.6931	−	6.38492i	0.399429	−	0.218105i	0.666391	+	0.745602i	$0.267838\pi$
$858$	−0.603671	+	2.77503i	−0.0206090	+	0.0947379i
$859$	10.1299	−	4.62618i	0.345628	−	0.157843i	−0.235035	−	0.971987i	$-0.575521\pi$
$859$	10.1299	−	4.62618i	0.345628	−	0.157843i	0.580663	+	0.814144i	$0.302793\pi$
$860$	1.58400	+	17.6776i	0.0540138	+	0.602801i
$861$	24.8933	−	38.7347i	0.848362	−	1.32008i
$862$	−21.3362	+	15.9720i	−0.726712	+	0.544010i
$863$	25.3726	−	18.9937i	0.863694	−	0.646553i	−0.0727579	−	0.997350i	$-0.523180\pi$
$863$	25.3726	−	18.9937i	0.863694	−	0.646553i	0.936452	+	0.350797i	$0.114089\pi$
$864$	−3.01816	+	4.69635i	−0.102680	+	0.159773i
$865$	4.03999	+	45.0868i	0.137364	+	1.53300i
$866$	18.7546	−	8.56496i	0.637309	−	0.291049i
$867$	10.1684	−	46.7432i	0.345336	−	1.58748i
$868$	36.8415	−	20.1170i	1.25048	−	0.682815i
$869$	1.11611	+	0.967111i	0.0378613	+	0.0328070i
$870$	5.73221	+	11.9775i	0.194340	+	0.406077i
$871$	9.93112	+	4.53539i	0.336503	+	0.153676i
$872$	4.71376	−	6.29684i	0.159628	−	0.213238i
$873$	0.444768	−	0.444768i	0.0150531	−	0.0150531i
$874$	−11.7156	−	2.68861i	−0.396285	−	0.0909436i
$875$	−44.7857	−	14.0061i	−1.51403	−	0.473494i
$876$	−0.545436	−	3.79359i	−0.0184286	−	0.128174i
$877$	−7.35276	−	19.7135i	−0.248285	−	0.665678i	−0.999981	−	0.00616811i	$-0.998037\pi$
$877$	−7.35276	−	19.7135i	−0.248285	−	0.665678i	0.751696	−	0.659510i	$-0.229236\pi$
$878$	−2.50644	−	1.36862i	−0.0845884	−	0.0461888i
$879$	22.1670	−	25.5821i	0.747675	−	0.862863i
$880$	0.647495	−	5.15990i	0.0218270	−	0.173940i
$881$	−0.155346	−	0.241723i	−0.00523374	−	0.00814386i	0.838627	−	0.544706i	$-0.183359\pi$
$881$	−0.155346	−	0.241723i	−0.00523374	−	0.00814386i	−0.843861	+	0.536563i	$0.819723\pi$
$882$	−13.5494	−	5.05367i	−0.456233	−	0.170166i
$883$	3.77444	−	52.7736i	0.127020	−	1.77597i	−0.390792	−	0.920479i	$-0.627799\pi$
$883$	3.77444	−	52.7736i	0.127020	−	1.77597i	0.517812	−	0.855494i	$-0.326747\pi$
$884$	5.91951	+	3.80424i	0.199095	+	0.127950i
$885$	−8.64177	−	8.33670i	−0.290490	−	0.280235i
$886$	1.20959	−	8.41285i	0.0406368	−	0.282635i
$887$	16.3664	−	3.56030i	0.549531	−	0.119543i	0.0707768	−	0.997492i	$-0.477452\pi$
$887$	16.3664	−	3.56030i	0.549531	−	0.119543i	0.478754	+	0.877949i	$0.341089\pi$
$888$	9.68961	+	0.693015i	0.325162	+	0.0232561i
$889$	10.0392	+	21.9827i	0.336703	+	0.737277i
$890$	−0.307389	+	5.74724i	−0.0103037	+	0.192648i
$891$	−2.00323	+	6.82237i	−0.0671107	+	0.228558i
$892$	1.53297	+	21.4338i	0.0513278	+	0.717656i
$893$	13.1740	−	24.1264i	0.440852	−	0.807360i
$894$	−0.854656	+	1.87144i	−0.0285840	+	0.0625902i
$895$	8.33118	−	2.60972i	0.278481	−	0.0872333i
$896$			4.19707i			0.140214i
$897$	−3.78442	−	4.46926i	−0.126358	−	0.149224i
$898$	−22.2917	−	22.2917i	−0.743884	−	0.743884i
$899$	−45.9364	+	6.60466i	−1.53207	+	0.220278i
$900$	−0.726532	+	6.77255i	−0.0242177	+	0.225752i
$901$	−32.0716	+	9.41707i	−1.06846	+	0.313728i
$902$	19.8860	−	1.42228i	0.662133	−	0.0473567i
$903$	−20.4316	−	37.4177i	−0.679921	−	1.24518i
$904$	−9.51140	+	6.11261i	−0.316345	+	0.203302i
$905$	−1.53501	+	1.02592i	−0.0510256	+	0.0341028i
$906$	−3.54273	−	4.08853i	−0.117699	−	0.135832i
$907$	11.5239	+	52.9746i	0.382645	+	1.75899i	0.617118	+	0.786870i	$0.288300\pi$
$907$	11.5239	+	52.9746i	0.382645	+	1.75899i	−0.234473	+	0.972123i	$0.575336\pi$
$908$	6.35503	+	8.48933i	0.210899	+	0.281728i
$909$	−2.27549	−	0.327167i	−0.0754734	−	0.0108514i
$910$	−3.27972	−	8.33291i	−0.108722	−	0.276233i
$911$	7.92425	−	6.86640i	0.262542	−	0.227494i	−0.513635	−	0.858009i	$-0.671702\pi$
$911$	7.92425	−	6.86640i	0.262542	−	0.227494i	0.776177	+	0.630515i	$0.217156\pi$
$912$	1.12090	−	3.00525i	0.0371168	−	0.0995139i
$913$	−21.4213	−	4.65991i	−0.708940	−	0.154221i
$914$	−26.8829	−	7.89353i	−0.889207	−	0.261095i
$915$	4.37811	+	18.5177i	0.144736	+	0.612175i
$916$	−0.346114	−	1.17876i	−0.0114359	−	0.0389472i
$917$	−37.4098	+	13.9531i	−1.23538	+	0.460774i
$918$	32.9562	+	24.6707i	1.08772	+	0.814253i
$919$	−36.5354			−1.20519			−0.602596	−	0.798047i	$-0.705867\pi$
$919$	−36.5354			−1.20519			−0.602596	+	0.798047i	$0.705867\pi$
$920$	7.63262	+	7.53280i	0.251640	+	0.248349i
$921$	13.5656			0.447001
$922$	−3.27598	−	2.45237i	−0.107889	−	0.0807645i
$923$	0.699416	−	0.260869i	0.0230216	−	0.00858660i
$924$	3.51927	+	11.9855i	0.115775	+	0.394295i
$925$	35.0621	−	14.5328i	1.15284	−	0.477834i
$926$	−21.1084	−	6.19798i	−0.693664	−	0.203678i
$927$	−3.87515	−	0.842986i	−0.127276	−	0.0276873i
$928$	1.62162	−	4.34772i	0.0532322	−	0.142721i
$929$	−17.3480	+	15.0321i	−0.569169	+	0.493188i	−0.891243	−	0.453527i	$-0.850166\pi$
$929$	−17.3480	+	15.0321i	−0.569169	+	0.493188i	0.322073	+	0.946715i	$0.395620\pi$
$930$	26.2424	+	11.4193i	0.860524	+	0.374453i
$931$	26.3354	+	3.78646i	0.863107	+	0.124096i
$932$	14.4164	+	19.2581i	0.472226	+	0.630820i
$933$	−6.92857	−	31.8501i	−0.226831	−	1.04273i
$934$	−0.113053	−	0.130470i	−0.00369920	−	0.00426911i
$935$	−37.6129	−	7.47713i	−1.23007	−	0.244528i
$936$	−1.09354	+	0.702773i	−0.0357433	+	0.0229708i
$937$	10.4419	+	19.1229i	0.341122	+	0.624719i	0.990776	−	0.135512i	$-0.0432678\pi$
$937$	10.4419	+	19.1229i	0.341122	+	0.624719i	−0.649653	+	0.760230i	$0.725086\pi$
$938$	47.8996	−	3.42585i	1.56398	−	0.111858i
$939$	−40.2453	+	11.8171i	−1.31336	+	0.385636i
$940$	−21.3099	+	12.1380i	−0.695051	+	0.395900i
$941$	−2.81745	+	0.405088i	−0.0918461	+	0.0132055i	−0.188085	−	0.982153i	$-0.560228\pi$
$941$	−2.81745	+	0.405088i	−0.0918461	+	0.0132055i	0.0962385	+	0.995358i	$0.469319\pi$
$942$	−6.85982	−	6.85982i	−0.223505	−	0.223505i
$943$	−22.6193	+	34.3306i	−0.736584	+	1.11796i
$944$			4.19613i			0.136572i
$945$	−15.6613	−	49.9965i	−0.509461	−	1.62639i
$946$	7.66842	−	16.7915i	0.249322	−	0.545939i
$947$	−8.38038	+	15.3475i	−0.272326	+	0.498727i	−0.977672	−	0.210135i	$-0.932610\pi$
$947$	−8.38038	+	15.3475i	−0.272326	+	0.498727i	0.705347	+	0.708862i	$0.250791\pi$
$948$	−0.0579731	−	0.810570i	−0.00188288	−	0.0263261i
$949$	0.805101	−	2.74192i	0.0261347	−	0.0890066i
$950$	−1.34249	−	12.4597i	−0.0435561	−	0.404247i
$951$	4.79507	+	10.4997i	0.155491	+	0.340478i
$952$	30.8715	+	2.20798i	1.00055	+	0.0715609i
$953$	57.1755	−	12.4378i	1.85210	−	0.402899i	0.858209	−	0.513301i	$-0.171578\pi$
$953$	57.1755	−	12.4378i	1.85210	−	0.402899i	0.993887	+	0.110402i	$0.0352140\pi$
$954$	0.878772	−	6.11199i	0.0284513	−	0.197883i
$955$	−6.91433	+	0.124237i	−0.223742	+	0.00402023i
$956$	7.51003	+	4.82640i	0.242892	+	0.156097i
$957$	0.985241	−	13.7755i	0.0318483	−	0.445297i
$958$	14.9485	+	5.57550i	0.482964	+	0.180136i
$959$	−40.1360	−	62.4529i	−1.29606	−	2.01671i
$960$	−2.25963	+	1.75575i	−0.0729292	+	0.0566667i
$961$	−45.2019	+	52.1658i	−1.45813	+	1.68277i
$962$	6.35725	+	3.47132i	0.204966	+	0.111920i
$963$	−0.362829	−	0.972783i	−0.0116920	−	0.0313475i
$964$	1.35523	+	9.42581i	0.0436489	+	0.303585i
$965$	−5.28584	−	3.81070i	−0.170157	−	0.122671i
$966$	−24.0309	−	9.27605i	−0.773182	−	0.298452i
$967$	17.6853	−	17.6853i	0.568722	−	0.568722i	−0.363049	−	0.931770i	$-0.618264\pi$
$967$	17.6853	−	17.6853i	0.568722	−	0.568722i	0.931770	+	0.363049i	$0.118264\pi$
$968$	3.35071	−	4.47602i	0.107696	−	0.143865i
$969$	−21.5154	−	9.82577i	−0.691175	−	0.315649i
$970$	0.931288	−	0.445696i	0.0299019	−	0.0143104i
$971$	33.1374	+	28.7137i	1.06343	+	0.921468i	0.997083	−	0.0763287i	$-0.0243198\pi$
$971$	33.1374	+	28.7137i	1.06343	+	0.921468i	0.0663479	+	0.997797i	$0.478865\pi$
$972$	−11.2651	+	6.15120i	−0.361328	+	0.197300i
$973$	9.60360	−	44.1470i	0.307877	−	1.41529i
$974$	7.56664	−	3.45557i	0.242451	−	0.110724i
$975$	3.11429	−	5.25163i	0.0997370	−	0.168187i
$976$	3.59502	−	5.59396i	0.115074	−	0.179058i
$977$	3.96755	−	2.97007i	0.126933	−	0.0950210i	−0.533925	−	0.845532i	$-0.679283\pi$
$977$	3.96755	−	2.97007i	0.126933	−	0.0950210i	0.660858	+	0.750511i	$0.270193\pi$
$978$	−6.28038	+	4.70144i	−0.200824	+	0.150335i
$979$	3.23632	−	5.03582i	0.103433	−	0.160945i
$980$	−18.2155	−	15.2195i	−0.581871	−	0.486170i
$981$	9.74702	−	4.45131i	0.311198	−	0.142119i
$982$	3.72315	−	17.1150i	0.118810	−	0.546163i
$983$	−29.0885	+	15.8835i	−0.927780	+	0.506606i	−0.870728	−	0.491765i	$-0.836352\pi$
$983$	−29.0885	+	15.8835i	−0.927780	+	0.506606i	−0.0570519	+	0.998371i	$0.518170\pi$
$984$	−8.29096	−	7.18416i	−0.264306	−	0.229023i
$985$	−5.24420	+	14.8709i	−0.167094	+	0.473825i
$986$	−31.1265	−	14.2150i	−0.991271	−	0.452698i
$987$	35.3026	−	47.1587i	1.12369	−	1.50108i
$988$	1.69110	−	1.69110i	0.0538011	−	0.0538011i
$989$	17.8616	+	33.6154i	0.567967	+	1.06891i
$990$	4.14293	−	5.74668i	0.131671	−	0.182641i
$991$	−0.725819	−	5.04818i	−0.0230564	−	0.160361i	0.975040	−	0.222028i	$-0.0712675\pi$
$991$	−0.725819	−	5.04818i	−0.0230564	−	0.160361i	−0.998097	+	0.0616668i	$0.980358\pi$
$992$	−3.49508	−	9.37068i	−0.110969	−	0.297519i
$993$	7.00337	+	3.82413i	0.222245	+	0.121355i
$994$	2.15019	−	2.48145i	0.0681997	−	0.0787067i
$995$	−1.15428	−	0.144846i	−0.0365931	−	0.00459192i
$996$	6.52176	+	10.1481i	0.206650	+	0.321554i
$997$	−21.8868	−	8.16335i	−0.693162	−	0.258536i	−0.0219041	−	0.999760i	$-0.506973\pi$
$997$	−21.8868	−	8.16335i	−0.693162	−	0.258536i	−0.671258	+	0.741224i	$0.734246\pi$
$998$	−0.325618	+	4.55273i	−0.0103073	+	0.144114i
$999$	35.6496	+	22.9106i	1.12790	+	0.724860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.43.8	✓	240
5.2	odd	4	inner	230.2.l.a.227.5	yes	240
23.15	odd	22	inner	230.2.l.a.153.5	yes	240
115.107	even	44	inner	230.2.l.a.107.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.8	✓	240	1.1	even	1	trivial
230.2.l.a.107.8	yes	240	115.107	even	44	inner
230.2.l.a.153.5	yes	240	23.15	odd	22	inner
230.2.l.a.227.5	yes	240	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800541 + 0.599278i) q^{2} +(-1.19905 + 0.447221i) q^{3} +(0.281733 + 0.959493i) q^{4} +(-1.17492 + 1.90251i) q^{5} +(-1.22790 - 0.360543i) q^{6} +(-4.10116 - 0.892152i) q^{7} +(-0.349464 + 0.936950i) q^{8} +(-1.02954 + 0.892104i) q^{9} +(-2.08071 + 0.818938i) q^{10} +(2.30200 + 0.330978i) q^{11} +(-0.766916 - 1.02448i) q^{12} +(-0.202830 - 0.932393i) q^{13} +(-2.74850 - 3.17194i) q^{14} +(0.557939 - 2.80665i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(3.53412 + 6.47225i) q^{17} +(-1.35881 + 0.0971840i) q^{18} +(2.40484 - 0.706126i) q^{19} +(-2.15646 - 0.591327i) q^{20} +(5.31647 - 0.764393i) q^{21} +(1.64450 + 1.64450i) q^{22} +(-4.75448 + 0.628433i) q^{23} -1.27973i q^{24} +(-2.23913 - 4.47061i) q^{25} +(0.396389 - 0.867970i) q^{26} +(2.67544 - 4.89969i) q^{27} +(-0.299416 - 4.18638i) q^{28} +(-1.30732 + 4.45233i) q^{29} +(2.12862 - 1.91248i) q^{30} +(4.15467 + 9.09747i) q^{31} +(-0.997452 - 0.0713392i) q^{32} +(-2.90823 + 0.632646i) q^{33} +(-1.04947 + 7.29922i) q^{34} +(6.51587 - 6.75431i) q^{35} +(-1.14602 - 0.736505i) q^{36} +(-0.541530 + 7.57158i) q^{37} +(2.34834 + 0.875887i) q^{38} +(0.660188 + 1.02727i) q^{39} +(-1.37197 - 1.76570i) q^{40} +(5.61379 - 6.47866i) q^{41} +(4.71414 + 2.57411i) q^{42} +(-2.77382 - 7.43689i) q^{43} +(0.330978 + 2.30200i) q^{44} +(-0.487611 - 3.00687i) q^{45} +(-4.18276 - 2.34617i) q^{46} +(7.75527 - 7.75527i) q^{47} +(0.766916 - 1.02448i) q^{48} +(9.65614 + 4.40981i) q^{49} +(0.886622 - 4.92076i) q^{50} +(-7.13210 - 6.18000i) q^{51} +(0.837481 - 0.457299i) q^{52} +(-0.963499 + 4.42914i) q^{53} +(5.07807 - 2.31908i) q^{54} +(-3.33436 + 3.99072i) q^{55} +(2.26911 - 3.53080i) q^{56} +(-2.56773 + 1.92218i) q^{57} +(-3.71475 + 2.78083i) q^{58} +(2.26860 - 3.53001i) q^{59} +(2.85015 - 0.255387i) q^{60} +(-6.04865 + 2.76233i) q^{61} +(-2.12592 + 9.77270i) q^{62} +(5.01821 - 2.74015i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(2.01220 + 0.709601i) q^{65} +(-2.70729 - 1.23638i) q^{66} +(-6.85679 + 9.15961i) q^{67} +(-5.21440 + 5.21440i) q^{68} +(5.41979 - 2.87982i) q^{69} +(9.26392 - 1.50229i) q^{70} +(0.111335 + 0.774350i) q^{71} +(-0.476068 - 1.27639i) q^{72} +(2.62851 + 1.43528i) q^{73} +(-4.97100 + 5.73684i) q^{74} +(4.68416 + 4.35908i) q^{75} +(1.35505 + 2.10849i) q^{76} +(-9.14559 - 3.41113i) q^{77} +(-0.0871138 + 1.21801i) q^{78} +(0.534202 + 0.343311i) q^{79} +(-0.0401714 - 2.23571i) q^{80} +(-0.435106 + 3.02623i) q^{81} +(8.37659 - 1.82222i) q^{82} +(-9.40218 - 0.672457i) q^{83} +(2.23125 + 4.88576i) q^{84} +(-16.4659 - 0.880669i) q^{85} +(2.23621 - 7.61582i) q^{86} +(-0.423637 - 5.92321i) q^{87} +(-1.11458 + 2.04119i) q^{88} +(1.06924 - 2.34132i) q^{89} +(1.41160 - 2.69934i) q^{90} +4.00485i q^{91} +(-1.94247 - 4.38484i) q^{92} +(-9.05023 - 9.05023i) q^{93} +(10.8560 - 1.56085i) q^{94} +(-1.48209 + 5.40489i) q^{95} +(1.22790 - 0.360543i) q^{96} +(-0.460547 + 0.0329390i) q^{97} +(5.08743 + 9.31694i) q^{98} +(-2.66528 + 1.71287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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