LMFDB - Embedded newform 153.3.i.a.101.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.i (of order $6$, degree $2$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.31
Character	$\chi$	$=$	153.101
Dual form			153.3.i.a.50.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.92590 + 1.68927i) q^{2} +(-2.55367 - 1.57441i) q^{3} +(3.70725 + 6.42114i) q^{4} +(1.55065 + 2.68581i) q^{5} +(-4.81216 - 8.92040i) q^{6} +(5.43225 + 3.13631i) q^{7} +11.5360i q^{8} +(4.04244 + 8.04106i) q^{9} +10.4779i q^{10} +(-1.87833 + 3.25336i) q^{11} +(0.642462 - 22.2342i) q^{12} +(1.73808 + 3.01044i) q^{13} +(10.5961 + 18.3530i) q^{14} +(0.268726 - 9.30002i) q^{15} +(-4.65840 + 8.06858i) q^{16} +(0.217614 - 16.9986i) q^{17} +(-1.75576 + 30.3561i) q^{18} -18.1729 q^{19} +(-11.4973 + 19.9139i) q^{20} +(-8.93431 - 16.5617i) q^{21} +(-10.9916 + 6.34600i) q^{22} +(-0.563797 - 0.976526i) q^{23} +(18.1625 - 29.4591i) q^{24} +(7.69097 - 13.3211i) q^{25} +11.7443i q^{26} +(2.33693 - 26.8987i) q^{27} +46.5083i q^{28} +(22.3389 - 38.6921i) q^{29} +(16.4965 - 26.7570i) q^{30} +(-13.2930 + 7.67472i) q^{31} +(12.7019 - 7.33345i) q^{32} +(9.91876 - 5.35073i) q^{33} +(29.3519 - 49.3686i) q^{34} +19.4533i q^{35} +(-36.6465 + 55.7673i) q^{36} +18.6072i q^{37} +(-53.1720 - 30.6989i) q^{38} +(0.301207 - 10.4241i) q^{39} +(-30.9835 + 17.8883i) q^{40} +(-29.8151 - 51.6413i) q^{41} +(1.83630 - 63.5503i) q^{42} +(-16.0790 + 27.8497i) q^{43} -27.8537 q^{44} +(-15.3283 + 23.3261i) q^{45} -3.80962i q^{46} +(-38.0772 - 21.9839i) q^{47} +(24.5993 - 13.2702i) q^{48} +(-4.82711 - 8.36080i) q^{49} +(45.0059 - 25.9842i) q^{50} +(-27.3186 + 43.0662i) q^{51} +(-12.8870 + 22.3209i) q^{52} +89.1367i q^{53} +(52.2767 - 74.7551i) q^{54} -11.6505 q^{55} +(-36.1805 + 62.6664i) q^{56} +(46.4075 + 28.6116i) q^{57} +(130.723 - 75.4728i) q^{58} +(48.3462 - 27.9127i) q^{59} +(60.7130 - 32.7520i) q^{60} +(84.9883 + 49.0680i) q^{61} -51.8586 q^{62} +(-3.25975 + 56.3594i) q^{63} +86.8198 q^{64} +(-5.39030 + 9.33627i) q^{65} +(38.0601 + 1.09975i) q^{66} +(17.8439 + 30.9065i) q^{67} +(109.957 - 61.6207i) q^{68} +(-0.0977055 + 3.38137i) q^{69} +(-32.8618 + 56.9183i) q^{70} -121.996 q^{71} +(-92.7617 + 46.6336i) q^{72} -34.4286i q^{73} +(-31.4325 + 54.4427i) q^{74} +(-40.6132 + 21.9090i) q^{75} +(-67.3714 - 116.691i) q^{76} +(-20.4071 + 11.7820i) q^{77} +(18.4904 - 29.9911i) q^{78} +(91.8612 + 53.0361i) q^{79} -28.8942 q^{80} +(-48.3174 + 65.0110i) q^{81} -201.463i q^{82} +(-85.2416 - 49.2143i) q^{83} +(73.2234 - 118.767i) q^{84} +(45.9924 - 25.7744i) q^{85} +(-94.0911 + 54.3235i) q^{86} +(-117.964 + 63.6361i) q^{87} +(-37.5308 - 21.6684i) q^{88} +59.2783i q^{89} +(-84.2531 + 42.3561i) q^{90} +21.8046i q^{91} +(4.18027 - 7.24045i) q^{92} +(46.0291 + 1.33002i) q^{93} +(-74.2733 - 128.645i) q^{94} +(-28.1798 - 48.8088i) q^{95} +(-43.9823 - 1.27088i) q^{96} +(-8.23298 - 4.75331i) q^{97} -32.6171i q^{98} +(-33.7535 - 1.95226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.92590	+	1.68927i	1.46295	+	0.844634i	0.999147	−	0.0413052i	$-0.0131516\pi$
$2$	2.92590	+	1.68927i	1.46295	+	0.844634i	0.463802	+	0.885939i	$0.346485\pi$
$3$	−2.55367	−	1.57441i	−0.851223	−	0.524805i
$3$	−2.55367	−	1.57441i	−0.851223	−	0.524805i
$4$	3.70725	+	6.42114i	0.926812	+	1.60529i
$5$	1.55065	+	2.68581i	0.310130	+	0.537161i	0.978390	−	0.206767i	$-0.0662940\pi$
$5$	1.55065	+	2.68581i	0.310130	+	0.537161i	−0.668260	+	0.743928i	$0.732961\pi$
$6$	−4.81216	−	8.92040i	−0.802027	−	1.48673i
$7$	5.43225	+	3.13631i	0.776036	+	0.448044i	0.835023	−	0.550214i	$-0.185454\pi$
$7$	5.43225	+	3.13631i	0.776036	+	0.448044i	−0.0589878	+	0.998259i	$0.518787\pi$
$8$			11.5360i			1.44200i
$9$	4.04244	+	8.04106i	0.449160	+	0.893452i
$10$			10.4779i			1.04779i
$11$	−1.87833	+	3.25336i	−0.170757	+	0.295760i	−0.938685	−	0.344777i	$-0.887955\pi$
$11$	−1.87833	+	3.25336i	−0.170757	+	0.295760i	0.767928	+	0.640537i	$0.221288\pi$
$12$	0.642462	−	22.2342i	0.0535385	−	1.85285i
$13$	1.73808	+	3.01044i	0.133698	+	0.231572i	0.925099	−	0.379725i	$-0.123981\pi$
$13$	1.73808	+	3.01044i	0.133698	+	0.231572i	−0.791401	+	0.611297i	$0.790648\pi$
$14$	10.5961	+	18.3530i	0.756867	+	1.31093i
$15$	0.268726	−	9.30002i	0.0179151	−	0.620001i
$16$	−4.65840	+	8.06858i	−0.291150	+	0.504286i
$17$	0.217614	−	16.9986i	0.0128008	−	0.999918i
$17$	0.217614	−	16.9986i	0.0128008	−	0.999918i
$18$	−1.75576	+	30.3561i	−0.0975420	+	1.68645i
$19$	−18.1729			−0.956467			−0.478234	−	0.878233i	$-0.658723\pi$
$19$	−18.1729			−0.956467			−0.478234	+	0.878233i	$0.658723\pi$
$20$	−11.4973	+	19.9139i	−0.574865	+	0.995695i
$21$	−8.93431	−	16.5617i	−0.425443	−	0.788653i
$22$	−10.9916	+	6.34600i	−0.499618	+	0.288454i
$23$	−0.563797	−	0.976526i	−0.0245129	−	0.0424576i	0.853509	−	0.521079i	$-0.174470\pi$
$23$	−0.563797	−	0.976526i	−0.0245129	−	0.0424576i	−0.878022	+	0.478621i	$0.841137\pi$
$24$	18.1625	−	29.4591i	0.756769	−	1.22746i
$25$	7.69097	−	13.3211i	0.307639	−	0.532846i
$26$			11.7443i			0.451704i
$27$	2.33693	−	26.8987i	0.0865531	−	0.996247i
$28$			46.5083i			1.66101i
$29$	22.3389	−	38.6921i	0.770307	−	1.33421i	−0.167087	−	0.985942i	$-0.553436\pi$
$29$	22.3389	−	38.6921i	0.770307	−	1.33421i	0.937394	−	0.348269i	$-0.113231\pi$
$30$	16.4965	−	26.7570i	0.549883	−	0.891899i
$31$	−13.2930	+	7.67472i	−0.428807	+	0.247572i	−0.698838	−	0.715280i	$-0.746299\pi$
$31$	−13.2930	+	7.67472i	−0.428807	+	0.247572i	0.270031	+	0.962852i	$0.412966\pi$
$32$	12.7019	−	7.33345i	0.396934	−	0.229170i
$33$	9.91876	−	5.35073i	0.300569	−	0.162143i
$34$	29.3519	−	49.3686i	0.863292	−	1.45202i
$35$			19.4533i			0.555808i
$36$	−36.6465	+	55.7673i	−1.01796	+	1.54909i
$37$			18.6072i			0.502897i	0.967871	+	0.251448i	$0.0809069\pi$
$37$			18.6072i			0.502897i	−0.967871	+	0.251448i	$0.919093\pi$
$38$	−53.1720	−	30.6989i	−1.39926	−	0.807865i
$39$	0.301207	−	10.4241i	0.00772325	−	0.267285i
$40$	−30.9835	+	17.8883i	−0.774586	+	0.447208i
$41$	−29.8151	−	51.6413i	−0.727198	−	1.25954i	−0.958063	−	0.286558i	$-0.907489\pi$
$41$	−29.8151	−	51.6413i	−0.727198	−	1.25954i	0.230865	−	0.972986i	$-0.425844\pi$
$42$	1.83630	−	63.5503i	0.0437214	−	1.51310i
$43$	−16.0790	+	27.8497i	−0.373931	+	0.647667i	−0.990166	−	0.139895i	$-0.955324\pi$
$43$	−16.0790	+	27.8497i	−0.373931	+	0.647667i	0.616236	+	0.787562i	$0.288657\pi$
$44$	−27.8537			−0.633039
$45$	−15.3283	+	23.3261i	−0.340630	+	0.518357i
$46$		−	3.80962i		−	0.0828178i
$47$	−38.0772	−	21.9839i	−0.810153	−	0.467742i	0.0368561	−	0.999321i	$-0.488266\pi$
$47$	−38.0772	−	21.9839i	−0.810153	−	0.467742i	−0.847009	+	0.531579i	$0.821599\pi$
$48$	24.5993	−	13.2702i	0.512485	−	0.276463i
$49$	−4.82711	−	8.36080i	−0.0985125	−	0.170629i
$50$	45.0059	−	25.9842i	0.900119	−	0.519684i
$51$	−27.3186	+	43.0662i	−0.535658	+	0.844435i
$52$	−12.8870	+	22.3209i	−0.247826	+	0.429248i
$53$			89.1367i			1.68183i	0.541171	+	0.840913i	$0.317981\pi$
$53$			89.1367i			1.68183i	−0.541171	+	0.840913i	$0.682019\pi$
$54$	52.2767	−	74.7551i	0.968087	−	1.38435i
$55$	−11.6505			−0.211828
$56$	−36.1805	+	62.6664i	−0.646080	+	1.11904i
$57$	46.4075	+	28.6116i	0.814166	+	0.501959i
$58$	130.723	−	75.4728i	2.25384	−	1.30126i
$59$	48.3462	−	27.9127i	0.819427	−	0.473097i	−0.0307916	−	0.999526i	$-0.509803\pi$
$59$	48.3462	−	27.9127i	0.819427	−	0.473097i	0.850219	+	0.526429i	$0.176469\pi$
$60$	60.7130	−	32.7520i	1.01188	−	0.545866i
$61$	84.9883	+	49.0680i	1.39325	+	0.804394i	0.993674	−	0.112306i	$-0.0358236\pi$
$61$	84.9883	+	49.0680i	1.39325	+	0.804394i	0.399577	+	0.916699i	$0.369157\pi$
$62$	−51.8586			−0.836429
$63$	−3.25975	+	56.3594i	−0.0517421	+	0.894594i
$64$	86.8198			1.35656
$65$	−5.39030	+	9.33627i	−0.0829277	+	0.143635i
$66$	38.0601	+	1.09975i	0.576668	+	0.0166629i
$67$	17.8439	+	30.9065i	0.266326	+	0.461291i	0.967910	−	0.251296i	$-0.0808567\pi$
$67$	17.8439	+	30.9065i	0.266326	+	0.461291i	−0.701584	+	0.712587i	$0.747523\pi$
$68$	109.957	−	61.6207i	1.61702	−	0.906187i
$69$	−0.0977055	+	3.38137i	−0.00141602	+	0.0490054i
$70$	−32.8618	+	56.9183i	−0.469454	+	0.813119i
$71$	−121.996			−1.71825			−0.859124	−	0.511767i	$-0.828991\pi$
$71$	−121.996			−1.71825			−0.859124	+	0.511767i	$0.828991\pi$
$72$	−92.7617	+	46.6336i	−1.28836	+	0.647688i
$73$		−	34.4286i		−	0.471625i	−0.971799	−	0.235812i	$-0.924225\pi$
$73$		−	34.4286i		−	0.471625i	0.971799	−	0.235812i	$-0.0757751\pi$
$74$	−31.4325	+	54.4427i	−0.424764	+	0.735712i
$75$	−40.6132	+	21.9090i	−0.541509	+	0.292120i
$76$	−67.3714	−	116.691i	−0.886466	−	1.53540i
$77$	−20.4071	+	11.7820i	−0.265027	+	0.153014i
$78$	18.4904	−	29.9911i	0.237057	−	0.384501i
$79$	91.8612	+	53.0361i	1.16280	+	0.671343i	0.951974	−	0.306180i	$-0.0990510\pi$
$79$	91.8612	+	53.0361i	1.16280	+	0.671343i	0.210827	+	0.977523i	$0.432384\pi$
$80$	−28.8942			−0.361177
$81$	−48.3174	+	65.0110i	−0.596511	+	0.802605i
$82$		−	201.463i		−	2.45686i
$83$	−85.2416	−	49.2143i	−1.02701	−	0.592943i	−0.110881	−	0.993834i	$-0.535367\pi$
$83$	−85.2416	−	49.2143i	−1.02701	−	0.592943i	−0.916126	+	0.400891i	$0.868701\pi$
$84$	73.2234	−	118.767i	0.871707	−	1.41389i
$85$	45.9924	−	25.7744i	0.541087	−	0.303229i
$86$	−94.0911	+	54.3235i	−1.09408	+	0.631669i
$87$	−117.964	+	63.6361i	−1.35590	+	0.731450i
$88$	−37.5308	−	21.6684i	−0.426486	−	0.246232i
$89$			59.2783i			0.666048i	0.942918	+	0.333024i	$0.108069\pi$
$89$			59.2783i			0.666048i	−0.942918	+	0.333024i	$0.891931\pi$
$90$	−84.2531	+	42.3561i	−0.936146	+	0.470623i
$91$			21.8046i			0.239611i
$92$	4.18027	−	7.24045i	0.0454378	−	0.0787005i
$93$	46.0291	+	1.33002i	0.494937	+	0.0143013i
$94$	−74.2733	−	128.645i	−0.790141	−	1.36856i
$95$	−28.1798	−	48.8088i	−0.296629	−	0.513777i
$96$	−43.9823	−	1.27088i	−0.458149	−	0.0132383i
$97$	−8.23298	−	4.75331i	−0.0848761	−	0.0490032i	0.456961	−	0.889487i	$-0.348938\pi$
$97$	−8.23298	−	4.75331i	−0.0848761	−	0.0490032i	−0.541837	+	0.840483i	$0.682271\pi$
$98$		−	32.6171i		−	0.332828i
$99$	−33.7535	−	1.95226i	−0.340944	−	0.0197198i
$100$	114.049			1.14049
$101$	40.1218	+	23.1644i	0.397246	+	0.229350i	0.685295	−	0.728266i	$-0.259673\pi$
$101$	40.1218	+	23.1644i	0.397246	+	0.229350i	−0.288049	+	0.957616i	$0.593007\pi$
$102$	−152.682	+	79.8588i	−1.49688	+	0.782930i
$103$	−24.2875	−	42.0672i	−0.235801	−	0.408419i	0.723704	−	0.690110i	$-0.242438\pi$
$103$	−24.2875	−	42.0672i	−0.235801	−	0.408419i	−0.959505	+	0.281691i	$0.909105\pi$
$104$	−34.7284	+	20.0505i	−0.333927	+	0.192793i
$105$	30.6275	−	49.6772i	0.291691	−	0.473116i
$106$	−150.576	+	260.805i	−1.42053	+	2.46042i
$107$	35.7990			0.334570			0.167285	−	0.985909i	$-0.446500\pi$
$107$	35.7990			0.334570			0.167285	+	0.985909i	$0.446500\pi$
$108$	181.384	−	84.7143i	1.67948	−	0.784392i
$109$			127.370i			1.16853i	0.811561	+	0.584267i	$0.198618\pi$
$109$			127.370i			1.16853i	−0.811561	+	0.584267i	$0.801382\pi$
$110$	−34.0882	−	19.6808i	−0.309893	−	0.178917i
$111$	29.2954	−	47.5166i	0.263923	−	0.428077i
$112$	−50.6112	+	29.2204i	−0.451885	+	0.260896i
$113$	−94.1325	−	163.042i	−0.833031	−	1.44285i	−0.895623	−	0.444814i	$-0.853270\pi$
$113$	−94.1325	−	163.042i	−0.833031	−	1.44285i	0.0625918	−	0.998039i	$-0.480063\pi$
$114$	87.4508	+	162.109i	0.767112	+	1.42201i
$115$	1.74851	−	3.02850i	0.0152044	−	0.0263348i
$116$	331.264			2.85572
$117$	−17.1811	+	26.1455i	−0.146847	+	0.223466i
$118$	188.608			1.59837
$119$	54.4950	−	91.6582i	0.457942	−	0.770237i
$120$	107.285	+	3.10002i	0.894042	+	0.0258335i
$121$	53.4438	+	92.5673i	0.441684	+	0.765019i
$122$	165.778	+	287.136i	1.35884	+	2.35357i
$123$	−5.16693	+	178.816i	−0.0420075	+	1.45379i
$124$	−98.5610	−	56.9042i	−0.794847	−	0.458905i
$125$	125.237			1.00189
$126$	−104.744	+	159.395i	−0.831300	+	1.26504i
$127$	−64.3461			−0.506662			−0.253331	−	0.967380i	$-0.581526\pi$
$127$	−64.3461			−0.506662			−0.253331	+	0.967380i	$0.581526\pi$
$128$	203.218	+	117.328i	1.58764	+	0.916626i
$129$	84.9074	−	45.8038i	0.658197	−	0.355068i
$130$	−31.5429	+	18.2113i	−0.242638	+	0.140087i
$131$	−108.920	−	188.655i	−0.831452	−	1.44012i	−0.896887	−	0.442260i	$-0.854177\pi$
$131$	−108.920	−	188.655i	−0.831452	−	1.44012i	0.0654350	−	0.997857i	$-0.479157\pi$
$132$	71.1292	+	43.8533i	0.538857	+	0.332222i
$133$	−98.7196	−	56.9958i	−0.742253	−	0.428540i
$134$			120.572i			0.899793i
$135$	75.8684	−	35.4339i	0.561988	−	0.262473i
$136$	196.096	+	2.51040i	1.44188	+	0.0184588i
$137$	26.0269	+	15.0267i	0.189978	+	0.109684i	0.591972	−	0.805958i	$-0.298350\pi$
$137$	26.0269	+	15.0267i	0.189978	+	0.109684i	−0.401995	+	0.915642i	$0.631683\pi$
$138$	−5.99792	+	9.72850i	−0.0434632	+	0.0704964i
$139$	−162.976	+	94.0945i	−1.17249	+	0.676939i	−0.954266	−	0.298959i	$-0.903361\pi$
$139$	−162.976	+	94.0945i	−1.17249	+	0.676939i	−0.218227	+	0.975898i	$0.570027\pi$
$140$	−124.912	+	72.1182i	−0.892231	+	0.515130i
$141$	62.6247	+	116.089i	0.444147	+	0.823325i
$142$	−356.947	−	206.083i	−2.51371	−	1.45129i
$143$	−13.0587			−0.0913197
$144$	−83.7112	−	4.84175i	−0.581328	−	0.0336233i
$145$	138.559			0.955582
$146$	58.1591	−	100.735i	0.398350	−	0.689963i
$147$	−0.836533	+	28.9506i	−0.00569070	+	0.196943i
$148$	−119.479	+	68.9815i	−0.807293	+	0.466091i
$149$	132.226	−	76.3405i	0.887420	−	0.512352i	0.0143224	−	0.999897i	$-0.495441\pi$
$149$	132.226	−	76.3405i	0.887420	−	0.512352i	0.873098	+	0.487545i	$0.162108\pi$
$150$	−155.840	−	4.50303i	−1.03893	−	0.0300202i
$151$	−81.9727	+	141.981i	−0.542866	+	0.940271i	0.455872	+	0.890045i	$0.349327\pi$
$151$	−81.9727	+	141.981i	−0.542866	+	0.940271i	−0.998738	+	0.0502257i	$0.984006\pi$
$152$		−	209.642i		−	1.37923i
$153$	137.567	−	66.9659i	0.899128	−	0.437686i
$154$	−79.6121			−0.516962
$155$	−41.2256	−	23.8016i	−0.265972	−	0.153559i
$156$	68.0514	−	36.7107i	0.436227	−	0.235325i
$157$	−67.7624	−	117.368i	−0.431608	−	0.747567i	0.565404	−	0.824814i	$-0.308720\pi$
$157$	−67.7624	−	117.368i	−0.431608	−	0.747567i	−0.997012	+	0.0772472i	$0.975387\pi$
$158$	179.184	+	310.356i	1.13408	+	1.96428i
$159$	140.338	−	227.626i	0.882630	−	1.43161i
$160$	39.3924	+	22.7432i	0.246203	+	0.142145i
$161$		−	7.07297i		−	0.0439315i
$162$	−251.193	+	108.594i	−1.55057	+	0.670336i
$163$		−	27.3494i		−	0.167788i	−0.996475	−	0.0838939i	$-0.973264\pi$
$163$		−	27.3494i		−	0.167788i	0.996475	−	0.0838939i	$-0.0267357\pi$
$164$	221.064	−	382.894i	1.34795	−	2.33472i
$165$	29.7516	+	18.3428i	0.180312	+	0.111168i
$166$	−166.272	−	287.992i	−1.00164	−	1.73489i
$167$	129.894	+	224.983i	0.777810	+	1.34721i	0.933202	+	0.359353i	$0.117003\pi$
$167$	129.894	+	224.983i	0.777810	+	1.34721i	−0.155392	+	0.987853i	$0.549664\pi$
$168$	191.056	−	103.066i	1.13724	−	0.613489i
$169$	78.4582	−	135.894i	0.464250	−	0.804104i
$170$	178.109	+	2.28013i	1.04770	+	0.0134125i
$171$	−73.4627	−	146.129i	−0.429606	−	0.854557i
$172$	−238.436			−1.38625
$173$	−36.9180	+	63.9438i	−0.213399	+	0.369617i	−0.952776	−	0.303674i	$-0.901787\pi$
$173$	−36.9180	+	63.9438i	−0.213399	+	0.369617i	0.739377	+	0.673291i	$0.235120\pi$
$174$	−452.648	−	13.0794i	−2.60142	−	0.0751687i
$175$	83.5585	−	48.2425i	0.477477	−	0.275672i
$176$	−17.5000	−	30.3109i	−0.0994318	−	0.172221i
$177$	−167.406	−	4.83724i	−0.945798	−	0.0273290i
$178$	−100.137	+	173.442i	−0.562567	+	0.974394i
$179$		−	45.6082i		−	0.254795i	−0.991852	−	0.127397i	$-0.959338\pi$
$179$		−	45.6082i		−	0.254795i	0.991852	−	0.127397i	$-0.0406623\pi$
$180$	−206.606	−	11.9498i	−1.14781	−	0.0663879i
$181$			160.242i			0.885315i	0.896691	+	0.442657i	$0.145964\pi$
$181$			160.242i			0.885315i	−0.896691	+	0.442657i	$0.854036\pi$
$182$	−36.8338	+	63.7980i	−0.202383	+	0.350538i
$183$	−139.778	−	259.110i	−0.763817	−	1.41590i
$184$	11.2652	−	6.50397i	0.0612239	−	0.0353476i
$185$	−49.9753	+	28.8532i	−0.270137	+	0.155963i
$186$	132.430	+	81.6470i	0.711988	+	0.438962i
$187$	54.8938	+	32.6369i	0.293550	+	0.174529i
$188$		−	325.999i		−	1.73404i
$189$	97.0574	−	138.791i	0.513531	−	0.734344i
$190$		−	190.413i		−	1.00217i
$191$	−198.771	−	114.761i	−1.04069	−	0.600842i	−0.120660	−	0.992694i	$-0.538501\pi$
$191$	−198.771	−	114.761i	−1.04069	−	0.600842i	−0.920028	+	0.391852i	$0.871834\pi$
$192$	−221.709	−	136.690i	−1.15473	−	0.711929i
$193$	−195.454	+	112.845i	−1.01271	+	0.584690i	−0.911985	−	0.410224i	$-0.865450\pi$
$193$	−195.454	+	112.845i	−1.01271	+	0.584690i	−0.100728	+	0.994914i	$0.532117\pi$
$194$	−16.0592	−	27.8154i	−0.0827796	−	0.143378i
$195$	28.4642	−	15.3552i	0.145970	−	0.0787445i
$196$	35.7906	−	61.9911i	0.182605	−	0.316281i
$197$	21.3390			0.108320			0.0541598	−	0.998532i	$-0.482752\pi$
$197$	21.3390			0.108320			0.0541598	+	0.998532i	$0.482752\pi$
$198$	−95.4614	−	62.7308i	−0.482128	−	0.316822i
$199$			226.404i			1.13771i	0.822438	+	0.568855i	$0.192613\pi$
$199$			226.404i			1.13771i	−0.822438	+	0.568855i	$0.807387\pi$
$200$	153.673	+	88.7230i	0.768364	+	0.443615i
$201$	3.09232	−	107.019i	0.0153847	−	0.532431i
$202$	78.2616	+	135.553i	0.387434	+	0.671055i
$203$	242.701	−	140.124i	1.19557	−	0.690264i
$204$	−377.811	−	15.7594i	−1.85201	−	0.0772522i
$205$	92.4656	−	160.155i	0.451052	−	0.781245i
$206$		−	164.112i		−	0.796662i
$207$	5.57319	−	8.48107i	0.0269236	−	0.0409714i
$208$	−32.3866			−0.155705
$209$	34.1346	−	59.1229i	0.163324	−	0.282885i
$210$	173.531	−	93.6123i	0.826339	−	0.445773i
$211$	278.389	−	160.728i	1.31938	−	0.761744i	0.335751	−	0.941951i	$-0.391010\pi$
$211$	278.389	−	160.728i	1.31938	−	0.761744i	0.983629	+	0.180206i	$0.0576766\pi$
$212$	−572.360	+	330.452i	−2.69981	+	1.55874i
$213$	311.536	+	192.072i	1.46261	+	0.901745i
$214$	104.744	+	60.4740i	0.489458	+	0.282589i
$215$	−99.7317			−0.463869
$216$	310.303	+	26.9589i	1.43659	+	0.124810i
$217$	−96.2812			−0.443692
$218$	−215.162	+	372.672i	−0.986983	+	1.70951i
$219$	−54.2049	+	87.9192i	−0.247511	+	0.401458i
$220$	−43.1914	−	74.8097i	−0.196325	−	0.340044i
$221$	51.5515	−	28.8898i	0.233265	−	0.130723i
$222$	165.984	−	89.5408i	0.747674	−	0.403337i
$223$	214.036	−	370.721i	0.959803	−	1.66243i	0.236831	−	0.971551i	$-0.423891\pi$
$223$	214.036	−	370.721i	0.959803	−	1.66243i	0.722973	−	0.690877i	$-0.242775\pi$
$224$	91.9999			0.410714
$225$	138.206	+	7.99368i	0.614251	+	0.0355275i
$226$		−	636.060i		−	2.81443i
$227$	−97.0001	+	168.009i	−0.427313	+	0.740128i	−0.996633	−	0.0819880i	$-0.973873\pi$
$227$	−97.0001	+	168.009i	−0.427313	+	0.740128i	0.569320	+	0.822116i	$0.307206\pi$
$228$	−11.6754	+	404.060i	−0.0512078	+	1.77219i
$229$	190.008	+	329.103i	0.829728	+	1.43713i	0.898251	+	0.439482i	$0.144838\pi$
$229$	190.008	+	329.103i	0.829728	+	1.43713i	−0.0685233	+	0.997650i	$0.521829\pi$
$230$	10.2319	−	5.90739i	0.0444865	−	0.0256843i
$231$	70.6628	+	2.04181i	0.305899	+	0.00883903i
$232$	446.353	+	257.702i	1.92393	+	1.11078i
$233$	−320.365			−1.37496			−0.687478	−	0.726205i	$-0.741282\pi$
$233$	−320.365			−1.37496			−0.687478	+	0.726205i	$0.741282\pi$
$234$	−94.4367	+	47.4756i	−0.403576	+	0.202887i
$235$		−	136.357i		−	0.580243i
$236$	358.463	+	206.959i	1.51891	+	0.876944i
$237$	−151.082	−	280.064i	−0.637478	−	1.18171i
$238$	314.282	−	176.126i	1.32051	−	0.740024i
$239$	−274.338	+	158.389i	−1.14786	+	0.662716i	−0.948364	−	0.317183i	$-0.897263\pi$
$239$	−274.338	+	158.389i	−1.14786	+	0.662716i	−0.199494	+	0.979899i	$0.563930\pi$
$240$	73.7861	+	45.4914i	0.307442	+	0.189548i
$241$	−343.500	−	198.320i	−1.42531	−	0.822903i	−0.428564	−	0.903511i	$-0.640980\pi$
$241$	−343.500	−	198.320i	−1.42531	−	0.822903i	−0.996746	+	0.0806081i	$0.974314\pi$
$242$			361.123i			1.49224i
$243$	225.741	−	89.9447i	0.928975	−	0.370143i
$244$			727.630i			2.98209i
$245$	14.9703	−	25.9294i	0.0611034	−	0.105834i
$246$	−317.186	+	514.469i	−1.28937	+	2.09134i
$247$	−31.5859	−	54.7083i	−0.127878	−	0.221491i
$248$	−88.5356	−	153.348i	−0.356998	−	0.618339i
$249$	140.195	+	259.882i	0.563032	+	1.04370i
$250$	366.429	+	211.558i	1.46572	+	0.846232i
$251$			34.8071i			0.138674i	0.997593	+	0.0693369i	$0.0220883\pi$
$251$			34.8071i			0.138674i	−0.997593	+	0.0693369i	$0.977912\pi$
$252$	−373.977	+	188.007i	−1.48403	+	0.746059i
$253$	4.23599			0.0167430
$254$	−188.270	−	108.698i	−0.741221	−	0.427944i
$255$	−158.029	−	6.59179i	−0.619721	−	0.0258501i
$256$	222.757	+	385.827i	0.870146	+	1.50714i
$257$	186.465	−	107.655i	0.725544	−	0.418893i	−0.0912460	−	0.995828i	$-0.529085\pi$
$257$	186.465	−	107.655i	0.725544	−	0.418893i	0.816790	+	0.576936i	$0.195752\pi$
$258$	325.805	+	9.41421i	1.26281	+	0.0364892i
$259$	−58.3579	+	101.079i	−0.225320	+	0.390266i
$260$	−79.9327			−0.307434
$261$	401.430	+	23.2182i	1.53804	+	0.0889585i
$262$		−	735.981i		−	2.80909i
$263$	93.8398	+	54.1785i	0.356806	+	0.206002i	0.667679	−	0.744450i	$-0.267288\pi$
$263$	93.8398	+	54.1785i	0.356806	+	0.206002i	−0.310873	+	0.950451i	$0.600621\pi$
$264$	61.7261	+	114.423i	0.233811	+	0.433420i
$265$	−239.404	+	138.220i	−0.903411	+	0.521585i
$266$	−192.562	−	333.528i	−0.723918	−	1.25386i
$267$	93.3286	−	151.377i	0.349545	−	0.566955i
$268$	−132.303	+	229.156i	−0.493669	+	0.855060i
$269$	16.9331			0.0629482			0.0314741	−	0.999505i	$-0.489980\pi$
$269$	16.9331			0.0629482			0.0314741	+	0.999505i	$0.489980\pi$
$270$	281.840	+	24.4860i	1.04385	+	0.0906890i
$271$	99.3182			0.366488			0.183244	−	0.983067i	$-0.441340\pi$
$271$	99.3182			0.366488			0.183244	+	0.983067i	$0.441340\pi$
$272$	136.141	+	80.9421i	0.500518	+	0.297581i
$273$	34.3295	−	55.6817i	0.125749	−	0.203962i
$274$	50.7681	+	87.9329i	0.185285	+	0.320923i
$275$	28.8923	+	50.0430i	0.105063	+	0.181974i
$276$	−22.0745	+	11.9082i	−0.0799801	+	0.0431457i
$277$	−113.792	−	65.6978i	−0.410801	−	0.237176i	0.280333	−	0.959903i	$-0.409555\pi$
$277$	−113.792	−	65.6978i	−0.410801	−	0.237176i	−0.691134	+	0.722727i	$0.742888\pi$
$278$	−635.803			−2.28706
$279$	−115.449	−	75.8654i	−0.413796	−	0.271919i
$280$	−224.413			−0.801476
$281$	225.418	+	130.145i	0.802201	+	0.463151i	0.844240	−	0.535965i	$-0.180052\pi$
$281$	225.418	+	130.145i	0.802201	+	0.463151i	−0.0420394	+	0.999116i	$0.513386\pi$
$282$	−12.8715	+	445.454i	−0.0456435	+	1.57962i
$283$	−133.186	+	76.8948i	−0.470621	+	0.271713i	−0.716500	−	0.697588i	$-0.754257\pi$
$283$	−133.186	+	76.8948i	−0.470621	+	0.271713i	0.245879	+	0.969301i	$0.420923\pi$
$284$	−452.268	−	783.352i	−1.59249	−	2.75828i
$285$	−4.88353	+	169.008i	−0.0171352	+	0.593011i
$286$	−38.2085	−	22.0597i	−0.133596	−	0.0771317i
$287$		−	374.038i		−	1.30327i
$288$	110.315	+	72.4918i	0.383039	+	0.251708i
$289$	−288.905	−	7.39828i	−0.999672	−	0.0255996i
$290$	405.411	+	234.064i	1.39797	+	0.807117i
$291$	13.5406	+	25.1005i	0.0465313	+	0.0862561i
$292$	221.071	−	127.635i	0.757093	−	0.437108i
$293$	82.2824	−	47.5058i	0.280827	−	0.162136i	−0.352971	−	0.935634i	$-0.614828\pi$
$293$	82.2824	−	47.5058i	0.280827	−	0.162136i	0.633798	+	0.773499i	$0.281495\pi$
$294$	−51.3529	+	83.2933i	−0.174670	+	0.283311i
$295$	149.936	+	86.5657i	0.508258	+	0.293443i
$296$	−214.653			−0.725177
$297$	83.1215	+	58.1274i	0.279871	+	0.195715i
$298$	515.838			1.73100
$299$	1.95985	−	3.39455i	0.00655467	−	0.0113530i
$300$	−291.244	−	179.561i	−0.970813	−	0.598536i
$301$	−174.690	+	100.858i	−0.580367	+	0.335075i
$302$	−479.687	+	276.948i	−1.58837	+	0.917045i
$303$	−65.9875	−	122.322i	−0.217781	−	0.403704i
$304$	84.6565	−	146.629i	0.278475	−	0.482333i
$305$			304.349i			0.997867i
$306$	515.629	+	36.4513i	1.68506	+	0.119122i
$307$	−471.076			−1.53445			−0.767224	−	0.641379i	$-0.778363\pi$
$307$	−471.076			−1.53445			−0.767224	+	0.641379i	$0.778363\pi$
$308$	−151.308	−	87.3579i	−0.491261	−	0.283630i
$309$	−4.20900	+	145.664i	−0.0136213	+	0.471405i
$310$	−80.4146	−	139.282i	−0.259402	−	0.449297i
$311$	190.810	+	330.493i	0.613539	+	1.06268i	0.990639	+	0.136508i	$0.0435878\pi$
$311$	190.810	+	330.493i	0.613539	+	1.06268i	−0.377101	+	0.926172i	$0.623079\pi$
$312$	120.253	+	3.47472i	0.385425	+	0.0111369i
$313$	−10.4278	−	6.02047i	−0.0333155	−	0.0192347i	0.483250	−	0.875483i	$-0.339456\pi$
$313$	−10.4278	−	6.02047i	−0.0333155	−	0.0192347i	−0.516565	+	0.856248i	$0.672790\pi$
$314$		−	457.876i		−	1.45820i
$315$	−156.425	+	78.6387i	−0.496588	+	0.249647i
$316$			786.472i			2.48884i
$317$	137.067	−	237.407i	0.432388	−	0.748919i	−0.564690	−	0.825303i	$-0.691004\pi$
$317$	137.067	−	237.407i	0.432388	−	0.748919i	0.997078	+	0.0763844i	$0.0243376\pi$
$318$	795.136	−	428.940i	2.50043	−	1.34887i
$319$	83.9196	+	145.353i	0.263071	+	0.455652i
$320$	134.627	+	233.181i	0.420710	+	0.728691i
$321$	−91.4187	−	56.3624i	−0.284793	−	0.175584i
$322$	11.9481	−	20.6948i	0.0371060	−	0.0642695i
$323$	−3.95468	+	308.914i	−0.0122436	+	0.956389i
$324$	−596.570	−	69.2413i	−1.84126	−	0.213708i
$325$	53.4700			0.164523
$326$	46.2005	−	80.0216i	0.141719	−	0.245465i
$327$	200.534	−	325.261i	0.613252	−	0.994683i
$328$	595.734	−	343.947i	1.81626	−	1.04862i
$329$	−137.897	−	238.844i	−0.419138	−	0.725969i
$330$	56.0642	+	103.927i	0.169891	+	0.314931i
$331$	57.1777	−	99.0347i	0.172742	−	0.299199i	−0.766635	−	0.642083i	$-0.778071\pi$
$331$	57.1777	−	99.0347i	0.172742	−	0.299199i	0.939378	+	0.342884i	$0.111404\pi$
$332$		−	729.798i		−	2.19819i
$333$	−149.622	+	75.2184i	−0.449314	+	0.225881i
$334$			877.704i			2.62786i
$335$	−55.3392	+	95.8503i	−0.165192	+	0.286120i
$336$	175.249	+	5.06386i	0.521574	+	0.0150710i
$337$	242.067	−	139.758i	0.718301	−	0.414711i	−0.0958260	−	0.995398i	$-0.530549\pi$
$337$	242.067	−	139.758i	0.718301	−	0.414711i	0.814127	+	0.580687i	$0.197216\pi$
$338$	459.121	−	265.074i	1.35835	−	0.784242i
$339$	−16.3131	+	564.560i	−0.0481211	+	1.66537i
$340$	336.007	+	199.772i	0.988255	+	0.587563i
$341$		−	57.6626i		−	0.169098i
$342$	31.9071	−	551.657i	0.0932958	−	1.61303i
$343$		−	367.916i		−	1.07264i
$344$	−321.274	−	185.488i	−0.933936	−	0.539208i
$345$	−9.23322	+	4.98091i	−0.0267629	+	0.0144374i
$346$	−216.036	+	124.729i	−0.624383	+	0.360488i
$347$	162.231	+	280.992i	0.467523	+	0.809774i	0.999311	−	0.0371034i	$-0.0118131\pi$
$347$	162.231	+	280.992i	0.467523	+	0.809774i	−0.531788	+	0.846877i	$0.678480\pi$
$348$	−845.937	−	521.547i	−2.43085	−	1.49870i
$349$	−139.028	+	240.803i	−0.398360	+	0.689980i	−0.993524	−	0.113625i	$-0.963754\pi$
$349$	−139.028	+	240.803i	−0.398360	+	0.689980i	0.595164	+	0.803604i	$0.297087\pi$
$350$	325.978			0.931366
$351$	85.0385	−	39.7168i	0.242275	−	0.113153i
$352$			55.0985i			0.156530i
$353$	−410.603	−	237.062i	−1.16318	−	0.671563i	−0.211117	−	0.977461i	$-0.567710\pi$
$353$	−410.603	−	237.062i	−1.16318	−	0.671563i	−0.952065	+	0.305897i	$0.901044\pi$
$354$	−481.642	−	296.947i	−1.36057	−	0.838834i
$355$	−189.173	−	327.657i	−0.532881	−	0.922976i
$356$	−380.635	+	219.759i	−1.06920	+	0.617302i
$357$	−283.470	+	148.267i	−0.794034	+	0.415313i
$358$	77.0445	−	133.445i	0.215208	−	0.372751i
$359$			486.308i			1.35462i	0.735699	+	0.677309i	$0.236854\pi$
$359$			486.308i			1.35462i	−0.735699	+	0.677309i	$0.763146\pi$
$360$	−269.090	−	176.828i	−0.747471	−	0.491188i
$361$	−30.7465			−0.0851704
$362$	−270.692	+	468.851i	−0.747767	+	1.29517i
$363$	9.26175	−	320.529i	0.0255145	−	0.882999i
$364$	−140.010	+	80.8351i	−0.384644	+	0.222074i
$365$	92.4686	−	53.3868i	0.253339	−	0.146265i
$366$	28.7292	−	994.253i	0.0784950	−	2.71654i
$367$	−282.323	−	162.999i	−0.769271	−	0.444139i	0.0633433	−	0.997992i	$-0.479824\pi$
$367$	−282.323	−	162.999i	−0.769271	−	0.444139i	−0.832615	+	0.553853i	$0.813157\pi$
$368$	10.5056			0.0285477
$369$	294.725	−	448.502i	0.798713	−	1.21545i
$370$	−194.963			−0.526928
$371$	−279.560	+	484.213i	−0.753532	+	1.30516i
$372$	162.101	+	300.490i	0.435756	+	0.807770i
$373$	167.244	+	289.676i	0.448377	+	0.776611i	0.998281	−	0.0586169i	$-0.0186690\pi$
$373$	167.244	+	289.676i	0.448377	+	0.776611i	−0.549904	+	0.835228i	$0.685336\pi$
$374$	105.481	+	188.223i	0.282035	+	0.503269i
$375$	−319.812	−	197.174i	−0.852833	−	0.525798i
$376$	253.606	−	439.259i	0.674484	−	1.16824i
$377$	155.307			0.411955
$378$	518.435	−	242.132i	1.37152	−	0.640561i
$379$			56.3312i			0.148631i	0.997235	+	0.0743155i	$0.0236772\pi$
$379$			56.3312i			0.148631i	−0.997235	+	0.0743155i	$0.976323\pi$
$380$	208.939	−	361.893i	0.549839	−	0.952350i
$381$	164.319	+	101.307i	0.431282	+	0.265899i
$382$	−387.723	−	671.556i	−1.01498	−	1.75800i
$383$	−41.7301	+	24.0929i	−0.108956	+	0.0629057i	−0.553488	−	0.832857i	$-0.686703\pi$
$383$	−41.7301	+	24.0929i	−0.108956	+	0.0629057i	0.444532	+	0.895763i	$0.353370\pi$
$384$	−334.229	−	619.567i	−0.870387	−	1.61345i
$385$	−63.2885	−	36.5397i	−0.164386	−	0.0949082i
$386$	−762.502			−1.97539
$387$	−288.939	−	16.7119i	−0.746613	−	0.0431832i
$388$		−	70.4869i		−	0.181667i
$389$	−30.8371	−	17.8038i	−0.0792728	−	0.0457682i	0.459840	−	0.888002i	$-0.347907\pi$
$389$	−30.8371	−	17.8038i	−0.0792728	−	0.0457682i	−0.539112	+	0.842234i	$0.681240\pi$
$390$	109.222	+	3.15600i	0.280057	+	0.00809231i
$391$	−16.7223	+	9.37126i	−0.0427679	+	0.0239674i
$392$	96.4502	−	55.6856i	0.246046	−	0.142055i
$393$	−18.8758	+	653.249i	−0.0480299	+	1.66221i
$394$	62.4356	+	36.0472i	0.158466	+	0.0914904i
$395$			328.962i			0.832815i
$396$	−112.597	−	223.974i	−0.284336	−	0.565590i
$397$			151.892i			0.382601i	0.981532	+	0.191300i	$0.0612704\pi$
$397$			151.892i			0.382601i	−0.981532	+	0.191300i	$0.938730\pi$
$398$	−382.457	+	662.435i	−0.960948	+	1.66441i
$399$	162.362	+	300.974i	0.406922	+	0.754321i
$400$	71.6551	+	124.110i	0.179138	+	0.310276i
$401$	132.184	+	228.950i	0.329636	+	0.570947i	0.982440	−	0.186580i	$-0.0597405\pi$
$401$	132.184	+	228.950i	0.329636	+	0.570947i	−0.652803	+	0.757527i	$0.726407\pi$
$402$	189.831	−	307.902i	0.472216	−	0.765924i
$403$	−46.2085	−	26.6785i	−0.114661	−	0.0661998i
$404$			343.504i			0.850258i
$405$	−249.530	−	28.9619i	−0.616124	−	0.0715109i
$406$	946.825			2.33208
$407$	−60.5359	−	34.9504i	−0.148737	−	0.0858732i
$408$	−496.812	−	315.147i	−1.21768	−	0.772419i
$409$	17.3829	+	30.1081i	0.0425011	+	0.0736140i	0.886493	−	0.462741i	$-0.153134\pi$
$409$	17.3829	+	30.1081i	0.0425011	+	0.0736140i	−0.843992	+	0.536355i	$0.819801\pi$
$410$	541.090	−	312.398i	1.31973	−	0.761947i
$411$	−42.8059	−	79.3502i	−0.104151	−	0.193066i
$412$	180.080	−	311.907i	0.437086	−	0.757056i
$413$	350.172			0.847873
$414$	30.6334	−	15.4001i	0.0739937	−	0.0371984i
$415$		−	305.256i		−	0.735558i
$416$	44.1538	+	25.4922i	0.106139	+	0.0612793i
$417$	564.331	+	16.3065i	1.35331	+	0.0391043i
$418$	199.749	−	115.325i	0.477868	−	0.275897i
$419$	45.5169	+	78.8375i	0.108632	+	0.188156i	0.915216	−	0.402963i	$-0.132020\pi$
$419$	45.5169	+	78.8375i	0.108632	+	0.188156i	−0.806584	+	0.591119i	$0.798686\pi$
$420$	432.529	+	12.4980i	1.02983	+	0.0297571i
$421$	−270.867	+	469.156i	−0.643390	+	1.11438i	0.341281	+	0.939961i	$0.389139\pi$
$421$	−270.867	+	469.156i	−0.643390	+	1.11438i	−0.984671	+	0.174423i	$0.944194\pi$
$422$	1086.05			2.57358
$423$	22.8492	−	395.049i	0.0540169	−	0.933923i
$424$	−1028.28			−2.42519
$425$	−224.767	−	133.635i	−0.528864	−	0.314434i
$426$	587.063	+	1088.25i	1.37808	+	2.55458i
$427$	307.785	+	533.100i	0.720808	+	1.24848i
$428$	132.716	+	229.870i	0.310083	+	0.537080i
$429$	33.3476	+	20.5598i	0.0777334	+	0.0479250i
$430$	−291.805	−	168.474i	−0.678616	−	0.391799i
$431$	−16.8736			−0.0391498			−0.0195749	−	0.999808i	$-0.506231\pi$
$431$	−16.8736			−0.0391498			−0.0195749	+	0.999808i	$0.506231\pi$
$432$	206.148	+	144.160i	0.477194	+	0.333705i
$433$	254.232			0.587141			0.293571	−	0.955937i	$-0.405156\pi$
$433$	254.232			0.587141			0.293571	+	0.955937i	$0.405156\pi$
$434$	−281.709	−	162.645i	−0.649099	−	0.374758i
$435$	−353.835	−	218.150i	−0.813413	−	0.501494i
$436$	−817.863	+	472.193i	−1.87583	+	1.08301i
$437$	10.2458	+	17.7463i	0.0234458	+	0.0406093i
$438$	−307.117	+	165.676i	−0.701181	+	0.378256i
$439$	628.864	+	363.075i	1.43249	+	0.827049i	0.997310	−	0.0732936i	$-0.0233510\pi$
$439$	628.864	+	363.075i	1.43249	+	0.827049i	0.435181	+	0.900343i	$0.356684\pi$
$440$		−	134.400i		−	0.305456i
$441$	47.7165	−	72.6131i	0.108201	−	0.164656i
$442$	199.637	+	2.55573i	0.451667	+	0.00578220i
$443$	−288.481	−	166.555i	−0.651199	−	0.375970i	0.137716	−	0.990472i	$-0.456024\pi$
$443$	−288.481	−	166.555i	−0.651199	−	0.375970i	−0.788916	+	0.614502i	$0.789357\pi$
$444$	413.716	+	11.9544i	0.931793	+	0.0269244i
$445$	−159.210	+	91.9199i	−0.357775	+	0.206562i
$446$	1252.50	−	723.128i	2.80829	−	1.62136i
$447$	−457.852	−	13.2297i	−1.02428	−	0.0295967i
$448$	471.627	+	272.294i	1.05274	+	0.607799i
$449$	229.219			0.510509			0.255254	−	0.966874i	$-0.417841\pi$
$449$	229.219			0.510509			0.255254	+	0.966874i	$0.417841\pi$
$450$	390.874	+	256.856i	0.868609	+	0.570792i
$451$	224.010			0.496697
$452$	697.946	−	1208.88i	1.54413	−	2.67451i
$453$	432.868	−	233.513i	0.955558	−	0.515481i
$454$	−567.624	+	327.718i	−1.25027	+	0.721846i
$455$	−58.5629	+	33.8113i	−0.128710	+	0.0743106i
$456$	−330.064	+	535.357i	−0.723825	+	1.17403i
$457$	284.894	−	493.451i	0.623401	−	1.07976i	−0.365447	−	0.930832i	$-0.619084\pi$
$457$	284.894	−	493.451i	0.623401	−	1.07976i	0.988848	−	0.148930i	$-0.0475828\pi$
$458$			1283.90i			2.80327i
$459$	−456.731	−	45.5781i	−0.995058	−	0.0992988i
$460$	25.9286			0.0563665
$461$	53.8225	+	31.0745i	0.116752	+	0.0674066i	0.557239	−	0.830352i	$-0.311861\pi$
$461$	53.8225	+	31.0745i	0.116752	+	0.0674066i	−0.440487	+	0.897759i	$0.645194\pi$
$462$	203.303	+	125.342i	0.440049	+	0.271304i
$463$	−217.615	−	376.921i	−0.470011	−	0.814084i	0.529400	−	0.848372i	$-0.322417\pi$
$463$	−217.615	−	376.921i	−0.470011	−	0.814084i	−0.999412	+	0.0342882i	$0.989084\pi$
$464$	208.127	+	360.487i	0.448550	+	0.776911i
$465$	67.8029	+	125.688i	0.145813	+	0.270296i
$466$	−937.354	−	541.182i	−2.01149	−	1.16133i
$467$		−	63.8071i		−	0.136632i	−0.997664	−	0.0683159i	$-0.978237\pi$
$467$		−	63.8071i		−	0.136632i	0.997664	−	0.0683159i	$-0.0217626\pi$
$468$	−231.578	−	13.3942i	−0.494826	−	0.0286201i
$469$			223.856i			0.477304i
$470$	230.344	−	398.967i	0.490093	−	0.848866i
$471$	−11.7432	+	406.405i	−0.0249324	+	0.862856i
$472$	322.001	+	557.722i	0.682205	+	1.18161i
$473$	−60.4033	−	104.622i	−0.127703	−	0.221187i
$474$	31.0525	−	1074.66i	0.0655115	−	2.26721i
$475$	−139.767	+	242.084i	−0.294246	+	0.509650i
$476$	790.577	+	10.1209i	1.66088	+	0.0212624i
$477$	−716.754	+	360.330i	−1.50263	+	0.755408i
$478$	−1070.25			−2.23901
$479$	320.143	−	554.503i	0.668356	−	1.15763i	−0.310007	−	0.950734i	$-0.600331\pi$
$479$	320.143	−	554.503i	0.668356	−	1.15763i	0.978364	−	0.206893i	$-0.0663352\pi$
$480$	−64.7879	−	120.099i	−0.134975	−	0.250206i
$481$	−56.0158	+	32.3407i	−0.116457	+	0.0672364i
$482$	−670.030	−	1160.53i	−1.39010	−	2.40773i
$483$	−11.1358	+	18.0620i	−0.0230555	+	0.0373955i
$484$	−396.259	+	686.340i	−0.818716	+	1.41806i
$485$		−	29.4829i		−	0.0607895i
$486$	812.435	+	118.168i	1.67168	+	0.243143i
$487$		−	140.676i		−	0.288863i	−0.989515	−	0.144432i	$-0.953865\pi$
$487$		−	140.676i		−	0.288863i	0.989515	−	0.144432i	$-0.0461354\pi$
$488$	−566.049	+	980.425i	−1.15994	+	2.00907i
$489$	−43.0593	+	69.8413i	−0.0880559	+	0.142825i
$490$	87.6033	−	50.5778i	0.178782	−	0.103220i
$491$	−145.858	+	84.2113i	−0.297064	+	0.171510i	−0.641123	−	0.767438i	$-0.721531\pi$
$491$	−145.858	+	84.2113i	−0.297064	+	0.171510i	0.344059	+	0.938948i	$0.388198\pi$
$492$	−1167.36	+	629.738i	−2.37268	+	1.27996i
$493$	−652.851	−	388.150i	−1.32424	−	0.787323i
$494$		−	213.428i		−	0.432040i
$495$	−47.0965	−	93.6826i	−0.0951444	−	0.189258i
$496$		−	143.008i		−	0.288322i
$497$	−662.711	−	382.616i	−1.33342	−	0.769852i
$498$	−28.8148	+	997.216i	−0.0578610	+	2.00244i
$499$	−101.189	+	58.4214i	−0.202783	+	0.117077i	−0.597953	−	0.801531i	$-0.704019\pi$
$499$	−101.189	+	58.4214i	−0.202783	+	0.117077i	0.395170	+	0.918608i	$0.370686\pi$
$500$	464.283	+	804.162i	0.928566	+	1.60832i
$501$	22.5105	−	779.040i	0.0449312	−	1.55497i
$502$	−58.7986	+	101.842i	−0.117129	+	0.202873i
$503$	−572.958			−1.13908			−0.569541	−	0.821963i	$-0.692879\pi$
$503$	−572.958			−1.13908			−0.569541	+	0.821963i	$0.692879\pi$
$504$	−650.162	−	37.6045i	−1.29000	−	0.0746122i
$505$			143.679i			0.284513i
$506$	12.3941	+	7.15571i	0.0244942	+	0.0141417i
$507$	−414.309	+	223.501i	−0.817177	+	0.440831i
$508$	−238.547	−	413.176i	−0.469581	−	0.813338i
$509$	385.460	−	222.546i	0.757290	−	0.437221i	−0.0710321	−	0.997474i	$-0.522629\pi$
$509$	385.460	−	222.546i	0.757290	−	0.437221i	0.828322	+	0.560253i	$0.189296\pi$
$510$	−451.241	−	286.240i	−0.884786	−	0.561255i
$511$	107.979	−	187.025i	0.211309	−	0.365998i
$512$			566.563i			1.10657i
$513$	−42.4688	+	488.826i	−0.0827852	+	0.952878i
$514$	727.435			1.41524
$515$	75.3228	−	130.463i	0.146258	−	0.253326i
$516$	608.885	+	375.397i	1.18001	+	0.727513i
$517$	143.043	−	82.5859i	0.276679	−	0.159741i
$518$	−341.498	+	197.164i	−0.659263	+	0.380626i
$519$	194.950	−	105.167i	0.375627	−	0.202634i
$520$	−107.703	−	62.1825i	−0.207122	−	0.119582i
$521$	353.566			0.678630			0.339315	−	0.940673i	$-0.389805\pi$
$521$	353.566			0.678630			0.339315	+	0.940673i	$0.389805\pi$
$522$	1135.32	+	746.056i	2.17494	+	1.42923i
$523$	−606.215			−1.15911			−0.579556	−	0.814933i	$-0.696774\pi$
$523$	−606.215			−1.15911			−0.579556	+	0.814933i	$0.696774\pi$
$524$	807.589	−	1398.78i	1.54120	−	2.66944i
$525$	−289.334	−	8.36038i	−0.551113	−	0.0159245i
$526$	183.044	+	317.041i	0.347992	+	0.602740i
$527$	127.567	+	227.633i	0.242062	+	0.431941i
$528$	−3.03273	+	104.956i	−0.00574381	+	0.198781i
$529$	263.864	−	457.026i	0.498798	−	0.863944i
$530$	−933.962			−1.76219
$531$	419.884	+	275.920i	0.790743	+	0.519623i
$532$		−	845.190i		−	1.58870i
$533$	103.642	−	179.513i	0.194450	−	0.336797i
$534$	528.786	−	285.257i	0.990237	−	0.534189i
$535$	55.5117	+	96.1491i	0.103760	+	0.179718i
$536$	−356.537	+	205.847i	−0.665182	+	0.384043i
$537$	−71.8063	+	116.468i	−0.133717	+	0.216887i
$538$	49.5444	+	28.6045i	0.0920899	+	0.0531682i
$539$	36.2676			0.0672868
$540$	508.789	+	355.799i	0.942202	+	0.658888i
$541$		−	973.359i		−	1.79918i	−0.436731	−	0.899592i	$-0.643864\pi$
$541$		−	973.359i		−	1.79918i	0.436731	−	0.899592i	$-0.356136\pi$
$542$	290.595	+	167.775i	0.536153	+	0.309548i
$543$	252.287	−	409.205i	0.464618	−	0.753600i
$544$	−121.894	−	217.511i	−0.224070	−	0.399836i
$545$	−342.092	+	197.507i	−0.627691	+	0.362398i
$546$	194.506	−	104.927i	0.356238	−	0.192174i
$547$	939.697	+	542.534i	1.71791	+	0.991836i	0.922714	+	0.385485i	$0.125966\pi$
$547$	939.697	+	542.534i	1.71791	+	0.991836i	0.795197	+	0.606351i	$0.207368\pi$
$548$			222.830i			0.406624i
$549$	−50.9993	+	881.751i	−0.0928949	+	1.60610i
$550$			195.227i			0.354959i
$551$	−405.962	+	703.147i	−0.736774	+	1.27613i
$552$	−39.0075	−	1.12713i	−0.0706658	−	0.00204190i
$553$	332.675	+	576.211i	0.601583	+	1.04197i
$554$	−221.962	−	384.450i	−0.400654	−	0.693953i
$555$	173.047	+	5.00023i	0.311797	+	0.00900943i
$556$	−1208.39	−	697.663i	−2.17336	−	1.25479i
$557$		−	266.109i		−	0.477755i	−0.971050	−	0.238877i	$-0.923221\pi$
$557$		−	266.109i		−	0.477755i	0.971050	−	0.238877i	$-0.0767794\pi$
$558$	−209.635	−	416.999i	−0.375690	−	0.747309i
$559$	−111.786			−0.199975
$560$	−156.960	−	90.6211i	−0.280286	−	0.161823i
$561$	−88.7965	−	169.770i	−0.158283	−	0.302620i
$562$	439.701	+	761.584i	0.782386	+	1.35513i
$563$	95.8869	−	55.3603i	0.170314	−	0.0983310i	−0.412420	−	0.910994i	$-0.635316\pi$
$563$	95.8869	−	55.3603i	0.170314	−	0.0983310i	0.582734	+	0.812663i	$0.301983\pi$
$564$	−513.257	+	832.493i	−0.910031	+	1.47605i
$565$	291.933	−	505.643i	0.516696	−	0.894944i
$566$	−519.583			−0.917992
$567$	−466.367	+	201.617i	−0.822517	+	0.355586i
$568$		−	1407.34i		−	2.47771i
$569$	820.458	+	473.692i	1.44193	+	0.832499i	0.997979	−	0.0635520i	$-0.0202429\pi$
$569$	820.458	+	473.692i	1.44193	+	0.832499i	0.443952	+	0.896051i	$0.353576\pi$
$570$	−299.789	+	486.251i	−0.525945	+	0.853072i
$571$	781.546	−	451.226i	1.36873	−	0.790238i	0.377966	−	0.925819i	$-0.376624\pi$
$571$	781.546	−	451.226i	1.36873	−	0.790238i	0.990766	+	0.135582i	$0.0432903\pi$
$572$	−48.4119	−	83.8519i	−0.0846362	−	0.146594i
$573$	326.915	+	606.009i	0.570532	+	1.05761i
$574$	631.850	−	1094.40i	1.10078	−	1.90661i
$575$	−17.3446			−0.0301645
$576$	350.963	+	698.124i	0.609312	+	1.21202i
$577$	−770.496			−1.33535			−0.667674	−	0.744453i	$-0.732710\pi$
$577$	−770.496			−1.33535			−0.667674	+	0.744453i	$0.732710\pi$
$578$	−832.809	−	509.685i	−1.44085	−	0.881808i
$579$	676.788	+	19.5559i	1.16889	+	0.0337754i
$580$	513.674	+	889.710i	0.885645	+	1.53398i
$581$	−308.702	−	534.688i	−0.531329	−	0.920290i
$582$	−2.78305	+	96.3152i	−0.00478187	+	0.165490i
$583$	−289.994	−	167.428i	−0.497417	−	0.287184i
$584$	397.169			0.680083
$585$	−96.8635	−	5.60246i	−0.165579	−	0.00957685i
$586$	321.000			0.547781
$587$	749.343	+	432.633i	1.27656	+	0.737024i	0.976215	−	0.216805i	$-0.0695636\pi$
$587$	749.343	+	432.633i	1.27656	+	0.737024i	0.300349	+	0.953829i	$0.402897\pi$
$588$	−188.997	+	101.956i	−0.321424	+	0.173394i
$589$	241.572	−	139.472i	0.410140	−	0.236794i
$590$	292.465	+	506.565i	0.495704	+	0.858584i
$591$	−54.4926	−	33.5964i	−0.0922041	−	0.0568467i
$592$	−150.134	−	86.6797i	−0.253604	−	0.146418i
$593$		−	197.080i		−	0.332344i	−0.986097	−	0.166172i	$-0.946859\pi$
$593$		−	197.080i		−	0.332344i	0.986097	−	0.166172i	$-0.0531406\pi$
$594$	145.012	+	310.489i	0.244128	+	0.522709i
$595$	330.679	+	4.23332i	0.555763	+	0.00711482i
$596$	980.387	+	566.026i	1.64494	+	0.949709i
$597$	356.454	−	578.161i	0.597075	−	0.968444i
$598$	11.4686	−	6.62141i	0.0191783	−	0.0110726i
$599$	498.466	−	287.789i	0.832164	−	0.480450i	−0.0224293	−	0.999748i	$-0.507140\pi$
$599$	498.466	−	287.789i	0.832164	−	0.480450i	0.854593	+	0.519299i	$0.173807\pi$
$600$	−252.742	−	468.514i	−0.421237	−	0.780856i
$601$	603.473	+	348.416i	1.00412	+	0.579726i	0.909463	−	0.415784i	$-0.136493\pi$
$601$	603.473	+	348.416i	1.00412	+	0.579726i	0.0946521	+	0.995510i	$0.469826\pi$
$602$	−681.502			−1.13206
$603$	−176.388	+	268.421i	−0.292518	+	0.445143i
$604$	−1215.57			−2.01254
$605$	−165.745	+	287.079i	−0.273959	+	0.474511i
$606$	13.5626	−	469.374i	0.0223806	−	0.774544i
$607$	383.777	−	221.574i	0.632252	−	0.365031i	−0.149372	−	0.988781i	$-0.547725\pi$
$607$	383.777	−	221.574i	0.632252	−	0.365031i	0.781624	+	0.623750i	$0.214392\pi$
$608$	−230.830	+	133.270i	−0.379655	+	0.219194i
$609$	−840.391	−	24.2833i	−1.37995	−	0.0398740i
$610$	−514.128	+	890.495i	−0.842832	+	1.45983i
$611$		−	152.839i		−	0.250145i
$612$	939.991	+	635.075i	1.53593	+	1.03770i
$613$	−718.550			−1.17219			−0.586093	−	0.810244i	$-0.699335\pi$
$613$	−718.550			−1.17219			−0.586093	+	0.810244i	$0.699335\pi$
$614$	−1378.32	−	795.773i	−2.24482	−	1.29605i
$615$	−488.277	+	263.404i	−0.793947	+	0.428299i
$616$	−135.918	−	235.416i	−0.220646	−	0.382169i
$617$	−382.705	−	662.864i	−0.620267	−	1.07433i	−0.989436	−	0.144971i	$-0.953691\pi$
$617$	−382.705	−	662.864i	−0.620267	−	1.07433i	0.369169	−	0.929362i	$-0.379642\pi$
$618$	−258.381	+	419.088i	−0.418092	+	0.678136i
$619$	74.0367	+	42.7451i	0.119607	+	0.0690551i	0.558610	−	0.829430i	$-0.311335\pi$
$619$	74.0367	+	42.7451i	0.119607	+	0.0690551i	−0.439003	+	0.898486i	$0.644668\pi$
$620$		−	352.954i		−	0.569281i
$621$	−27.5848	+	12.8833i	−0.0444200	+	0.0207461i
$622$			1289.32i			2.07286i
$623$	−185.915	+	322.015i	−0.298419	+	0.516877i
$624$	82.7046	+	50.9900i	0.132539	+	0.0817147i
$625$	1.92394	+	3.33236i	0.00307830	+	0.00533177i
$626$	−20.3404	−	35.2305i	−0.0324926	−	0.0562788i
$627$	−180.252	+	97.2382i	−0.287484	+	0.155085i
$628$	502.425	−	870.225i	0.800039	−	1.38571i
$629$	316.296	+	4.04919i	0.502856	+	0.00643751i
$630$	−590.526	−	34.1552i	−0.937342	−	0.0542147i
$631$	151.653			0.240338			0.120169	−	0.992753i	$-0.461656\pi$
$631$	151.653			0.240338			0.120169	+	0.992753i	$0.461656\pi$
$632$	−611.825	+	1059.71i	−0.968077	+	1.67676i
$633$	−963.966	−	27.8540i	−1.52285	−	0.0440032i
$634$	802.089	−	463.086i	1.26512	−	0.730420i
$635$	−99.7783	−	172.821i	−0.157131	−	0.272159i
$636$	1981.89	+	57.2670i	3.11617	+	0.0900424i
$637$	16.7798	−	29.0634i	0.0263419	−	0.0456255i
$638$			567.051i			0.888794i
$639$	−493.160	−	980.975i	−0.771768	−	1.53517i
$640$			727.739i			1.13709i
$641$	367.170	−	635.958i	0.572809	−	0.992134i	−0.423467	−	0.905911i	$-0.639187\pi$
$641$	367.170	−	635.958i	0.572809	−	0.992134i	0.996276	−	0.0862224i	$-0.0274796\pi$
$642$	−172.270	−	319.341i	−0.268334	−	0.497416i
$643$	1094.69	−	632.019i	1.70247	−	0.982922i	0.759225	−	0.650828i	$-0.225578\pi$
$643$	1094.69	−	632.019i	1.70247	−	0.982922i	0.943246	−	0.332094i	$-0.107755\pi$
$644$	45.4166	−	26.2213i	0.0705226	−	0.0407163i
$645$	254.682	+	157.019i	0.394855	+	0.243441i
$646$	−533.409	+	897.169i	−0.825710	+	1.38881i
$647$		−	654.568i		−	1.01170i	−0.862622	−	0.505849i	$-0.831179\pi$
$647$		−	654.568i		−	1.01170i	0.862622	−	0.505849i	$-0.168821\pi$
$648$	−749.967	−	557.390i	−1.15736	−	0.860170i
$649$			209.717i			0.323138i
$650$	156.448	+	90.3251i	0.240689	+	0.138962i
$651$	245.870	+	151.587i	0.377681	+	0.232852i
$652$	175.615	−	101.391i	0.269348	−	0.155508i
$653$	351.643	+	609.064i	0.538504	+	0.932716i	0.998985	+	0.0450465i	$0.0143436\pi$
$653$	351.643	+	609.064i	0.538504	+	0.932716i	−0.460481	+	0.887670i	$0.652323\pi$
$654$	1136.19	−	612.926i	1.73730	−	0.937196i
$655$	337.794	−	585.077i	0.515717	−	0.893247i
$656$	555.562			0.846894
$657$	276.843	−	139.175i	0.421374	−	0.211835i
$658$		−	931.776i		−	1.41607i
$659$	394.144	+	227.559i	0.598094	+	0.345310i	0.768292	−	0.640100i	$-0.221107\pi$
$659$	394.144	+	227.559i	0.598094	+	0.345310i	−0.170197	+	0.985410i	$0.554440\pi$
$660$	−7.48502	+	259.040i	−0.0113409	+	0.392485i
$661$	−134.035	−	232.155i	−0.202776	−	0.351218i	0.746646	−	0.665222i	$-0.231663\pi$
$661$	−134.035	−	232.155i	−0.202776	−	0.351218i	−0.949422	+	0.314004i	$0.898330\pi$
$662$	334.592	−	193.177i	0.505426	−	0.291808i
$663$	−177.130	−	7.38853i	−0.267164	−	0.0111441i
$664$	567.736	−	983.347i	0.855024	−	1.48094i
$665$		−	353.522i		−	0.531612i
$666$	−564.841	−	32.6697i	−0.848110	−	0.0490536i
$667$	−50.3785			−0.0755300
$668$	−963.100	+	1668.14i	−1.44177	+	2.49721i
$669$	−1130.25	+	609.718i	−1.68946	+	0.911387i
$670$	−323.834	+	186.965i	−0.483334	+	0.279053i
$671$	−319.272	+	184.332i	−0.475815	+	0.274712i
$672$	−234.937	−	144.846i	−0.349609	−	0.215545i
$673$	572.251	+	330.389i	0.850299	+	0.490920i	0.860752	−	0.509025i	$-0.169994\pi$
$673$	572.251	+	330.389i	0.850299	+	0.490920i	−0.0104531	+	0.999945i	$0.503327\pi$
$674$	944.353			1.40112
$675$	−340.348	−	238.007i	−0.504219	−	0.352604i
$676$	1163.46			1.72109
$677$	367.380	−	636.321i	0.542659	−	0.939913i	−0.456091	−	0.889933i	$-0.650751\pi$
$677$	367.380	−	636.321i	0.542659	−	0.939913i	0.998750	−	0.0499797i	$-0.0159157\pi$
$678$	−1001.42	+	1624.29i	−1.47702	+	2.39570i
$679$	−29.8157	−	51.6424i	−0.0439113	−	0.0760565i
$680$	297.334	+	530.568i	0.437256	+	0.780248i
$681$	512.222	−	276.321i	0.752161	−	0.405758i
$682$	97.4075	−	168.715i	0.142826	−	0.247382i
$683$	−290.069			−0.424699			−0.212349	−	0.977194i	$-0.568111\pi$
$683$	−290.069			−0.424699			−0.212349	+	0.977194i	$0.568111\pi$
$684$	665.973	−	1013.45i	0.973644	−	1.48166i
$685$			93.2043i			0.136065i
$686$	621.508	−	1076.48i	0.905988	−	1.56922i
$687$	32.9281	−	1139.57i	0.0479303	−	1.65876i
$688$	−149.805	−	259.470i	−0.217740	−	0.377136i
$689$	−268.341	+	154.926i	−0.389464	+	0.224857i
$690$	−35.4295	−	1.02374i	−0.0513471	−	0.00148369i
$691$	−141.683	−	81.8008i	−0.205041	−	0.118380i	0.393964	−	0.919126i	$-0.371104\pi$
$691$	−141.683	−	81.8008i	−0.205041	−	0.118380i	−0.599004	+	0.800746i	$0.704437\pi$
$692$	−547.457			−0.791122
$693$	−177.235	−	116.467i	−0.255750	−	0.168061i
$694$			1096.20i			1.57954i
$695$	−505.439	−	291.815i	−0.727250	−	0.419878i
$696$	−734.107	−	1360.83i	−1.05475	−	1.95521i
$697$	−884.318	+	495.577i	−1.26875	+	0.711015i
$698$	−813.561	+	469.710i	−1.16556	+	0.672936i
$699$	818.105	+	504.387i	1.17039	+	0.721583i
$700$	619.544	+	357.694i	0.885063	+	0.510992i
$701$			447.750i			0.638730i	0.947632	+	0.319365i	$0.103470\pi$
$701$			447.750i			0.638730i	−0.947632	+	0.319365i	$0.896530\pi$
$702$	315.906	+	27.4457i	0.450009	+	0.0390964i
$703$		−	338.146i		−	0.481004i
$704$	−163.076	+	282.456i	−0.231642	+	0.401216i
$705$	−214.683	+	348.211i	−0.304515	+	0.493916i
$706$	−800.922	−	1387.24i	−1.13445	−	1.96493i
$707$	145.301	+	251.669i	0.205518	+	0.355968i
$708$	−589.556	−	1092.87i	−0.832707	−	1.54361i
$709$	−1029.74	−	594.519i	−1.45238	−	0.838532i	−0.453763	−	0.891122i	$-0.649919\pi$
$709$	−1029.74	−	594.519i	−1.45238	−	0.838532i	−0.998616	+	0.0525907i	$0.983252\pi$
$710$		−	1278.25i		−	1.80036i
$711$	−55.1236	+	953.057i	−0.0775297	+	1.34045i
$712$	−683.835			−0.960442
$713$	14.9891	+	8.65397i	0.0210226	+	0.0121374i
$714$	−1079.87	−	45.0440i	−1.51242	−	0.0630868i
$715$	−20.2495	−	35.0732i	−0.0283210	−	0.0490534i
$716$	292.857	−	169.081i	0.409018	−	0.236147i
$717$	949.939	+	27.4487i	1.32488	+	0.0382827i
$718$	−821.504	+	1422.89i	−1.14416	+	1.98174i
$719$	746.256			1.03791			0.518954	−	0.854802i	$-0.326322\pi$
$719$	746.256			1.03791			0.518954	+	0.854802i	$0.326322\pi$
$720$	−116.803	−	232.340i	−0.162226	−	0.322694i
$721$		−	304.692i		−	0.422597i
$722$	−89.9611	−	51.9391i	−0.124600	−	0.0719378i
$723$	564.947	+	1047.25i	0.781392	+	1.44848i
$724$	−1028.94	+	594.057i	−1.42118	+	0.820521i
$725$	−343.616	−	595.160i	−0.473953	−	0.820910i
$726$	568.558	−	922.189i	0.783137	−	1.27023i
$727$	195.358	−	338.371i	0.268719	−	0.465434i	−0.699813	−	0.714327i	$-0.746733\pi$
$727$	195.358	−	338.371i	0.268719	−	0.465434i	0.968531	+	0.248892i	$0.0800665\pi$
$728$	−251.538			−0.345519
$729$	−718.077	−	125.721i	−0.985017	−	0.172457i
$730$	360.738			0.494162
$731$	469.907	+	279.381i	0.642827	+	0.382191i
$732$	1145.59	−	1858.12i	1.56501	−	2.53842i
$733$	−4.87965	−	8.45179i	−0.00665709	−	0.0115304i	0.862678	−	0.505754i	$-0.168786\pi$
$733$	−4.87965	−	8.45179i	−0.00665709	−	0.0115304i	−0.869335	+	0.494224i	$0.835452\pi$
$734$	−550.698	−	953.837i	−0.750270	−	1.29951i
$735$	−79.0528	+	42.6455i	−0.107555	+	0.0580210i
$736$	−14.3226	−	8.26916i	−0.0194601	−	0.0112353i
$737$	−134.067			−0.181909
$738$	1619.97	−	814.400i	2.19509	−	1.10352i
$739$	1168.07			1.58060			0.790302	−	0.612717i	$-0.209924\pi$
$739$	1168.07			1.58060			0.790302	+	0.612717i	$0.209924\pi$
$740$	−370.542	−	213.932i	−0.500732	−	0.289098i
$741$	−5.47379	+	189.436i	−0.00738704	+	0.255649i
$742$	−1635.93	+	944.505i	−2.20476	+	1.27292i
$743$	113.536	+	196.649i	0.152807	+	0.264670i	0.932258	−	0.361793i	$-0.117835\pi$
$743$	113.536	+	196.649i	0.152807	+	0.264670i	−0.779451	+	0.626463i	$0.784502\pi$
$744$	−15.3431	+	530.992i	−0.0206225	+	0.713699i
$745$	410.071	+	236.755i	0.550431	+	0.317792i
$746$			1130.08i			1.51486i
$747$	51.1513	−	884.379i	0.0684757	−	1.18391i
$748$	−6.06137	+	473.475i	−0.00810344	+	0.632987i
$749$	194.469	+	112.277i	0.259638	+	0.149902i
$750$	−602.658	−	1117.16i	−0.803544	−	1.48955i
$751$	123.140	−	71.0950i	0.163968	−	0.0946670i	−0.415770	−	0.909470i	$-0.636488\pi$
$751$	123.140	−	71.0950i	0.163968	−	0.0946670i	0.579739	+	0.814803i	$0.303155\pi$
$752$	354.757	−	204.819i	0.471752	−	0.272366i
$753$	54.8009	−	88.8858i	0.0727767	−	0.118042i
$754$	454.412	+	262.355i	0.602669	+	0.347951i
$755$	−508.444			−0.673436
$756$	1251.01	+	108.687i	1.65478	+	0.143766i
$757$	−479.636			−0.633601			−0.316800	−	0.948492i	$-0.602609\pi$
$757$	−479.636			−0.633601			−0.316800	+	0.948492i	$0.602609\pi$
$758$	−95.1584	+	164.819i	−0.125539	+	0.217440i
$759$	−10.8173	−	6.66920i	−0.0142520	−	0.00878682i
$760$	563.059	−	325.082i	0.740867	−	0.427740i
$761$	−37.8559	+	21.8561i	−0.0497449	+	0.0287202i	−0.524666	−	0.851308i	$-0.675810\pi$
$761$	−37.8559	+	21.8561i	−0.0497449	+	0.0287202i	0.474921	+	0.880028i	$0.342477\pi$
$762$	309.644	+	573.993i	0.406357	+	0.753272i
$763$	−399.473	+	691.907i	−0.523555	+	0.906824i
$764$		−	1701.79i		−	2.22747i
$765$	393.175	+	265.636i	0.513954	+	0.347237i
$766$	−162.797			−0.212529
$767$	168.059	+	97.0288i	0.219112	+	0.126504i
$768$	38.6036	−	1335.99i	0.0502651	−	1.73957i
$769$	475.251	+	823.159i	0.618012	+	1.07043i	0.989848	+	0.142129i	$0.0453949\pi$
$769$	475.251	+	823.159i	0.618012	+	1.07043i	−0.371836	+	0.928298i	$0.621272\pi$
$770$	−123.451	−	213.823i	−0.160325	−	0.277692i
$771$	−645.663	−	18.6566i	−0.837436	−	0.0241979i
$772$	−1449.19	−	836.690i	−1.87719	−	1.08380i
$773$			416.660i			0.539017i	0.962998	+	0.269509i	$0.0868613\pi$
$773$			416.660i			0.539017i	−0.962998	+	0.269509i	$0.913139\pi$
$774$	−817.176	−	536.993i	−1.05578	−	0.693790i
$775$			236.104i			0.304650i
$776$	54.8342	−	94.9757i	0.0706627	−	0.122391i
$777$	308.167	−	166.242i	0.396611	−	0.213954i
$778$	−60.1508	−	104.184i	−0.0773147	−	0.133913i
$779$	541.826	+	938.471i	0.695541	+	1.20471i
$780$	204.122	+	125.847i	0.261694	+	0.161343i
$781$	229.148	−	396.896i	0.293403	−	0.508189i
$782$	−64.7582	−	0.829028i	−0.0828110	−	0.00106014i
$783$	−988.563	−	691.308i	−1.26253	−	0.882897i
$784$	89.9464			0.114728
$785$	210.152	−	363.993i	0.267709	−	0.463686i
$786$	−1158.74	+	1879.45i	−1.47422	+	2.39116i
$787$	−783.381	+	452.285i	−0.995401	+	0.574695i	−0.906884	−	0.421380i	$-0.861546\pi$
$787$	−783.381	+	452.285i	−0.995401	+	0.574695i	−0.0885166	+	0.996075i	$0.528213\pi$
$788$	79.1088	+	137.021i	0.100392	+	0.173884i
$789$	−154.336	−	286.097i	−0.195610	−	0.362607i
$790$	−555.705	+	962.509i	−0.703424	+	1.21837i
$791$		−	1180.92i		−	1.49294i
$792$	22.5213	−	389.380i	0.0284359	−	0.491642i
$793$			341.136i			0.430184i
$794$	−256.587	+	444.422i	−0.323157	+	0.559725i
$795$	828.973	+	23.9534i	1.04273	+	0.0301300i
$796$	−1453.77	+	839.337i	−1.82635	+	1.05444i
$797$	−1150.83	+	664.429i	−1.44395	+	0.833663i	−0.998110	−	0.0614514i	$-0.980427\pi$
$797$	−1150.83	+	664.429i	−1.44395	+	0.833663i	−0.445837	+	0.895114i	$0.647094\pi$
$798$	−33.3708	+	1154.89i	−0.0418181	+	1.44723i
$799$	−381.981	+	642.475i	−0.478074	+	0.804099i
$800$		−	225.605i		−	0.282006i
$801$	−476.661	+	239.629i	−0.595082	+	0.299162i
$802$			893.178i			1.11369i
$803$	112.009	+	64.6682i	0.139488	+	0.0805333i
$804$	698.646	−	376.888i	0.868962	−	0.468766i
$805$	18.9966	−	10.9677i	0.0235983	−	0.0136245i
$806$	−90.1343	−	156.117i	−0.111829	−	0.193694i
$807$	−43.2414	−	26.6597i	−0.0535829	−	0.0330355i
$808$	−267.224	+	462.846i	−0.330723	+	0.572829i
$809$	807.379			0.997996			0.498998	−	0.866603i	$-0.333701\pi$
$809$	807.379			0.997996			0.498998	+	0.866603i	$0.333701\pi$
$810$	−681.175	−	506.263i	−0.840957	−	0.625016i
$811$			108.693i			0.134024i	0.997752	+	0.0670118i	$0.0213465\pi$
$811$			108.693i			0.134024i	−0.997752	+	0.0670118i	$0.978654\pi$
$812$	1799.51	+	1038.95i	2.21614	+	1.27949i
$813$	−253.626	−	156.368i	−0.311963	−	0.192335i
$814$	−118.081	−	204.523i	−0.145063	−	0.251256i
$815$	73.4552	−	42.4094i	0.0901291	−	0.0520361i
$816$	−220.222	−	421.041i	−0.269880	−	0.515982i
$817$	292.202	−	506.109i	0.357652	−	0.619472i
$818$			117.458i			0.143591i
$819$	−175.332	+	88.1437i	−0.214081	+	0.107624i
$820$	1371.17			1.67216
$821$	465.360	−	806.027i	0.566821	−	0.981762i	−0.430057	−	0.902802i	$-0.641507\pi$
$821$	465.360	−	806.027i	0.566821	−	0.981762i	0.996878	−	0.0789605i	$-0.0251601\pi$
$822$	8.79805	−	304.481i	0.0107032	−	0.370415i
$823$	804.670	−	464.576i	0.977727	−	0.564491i	0.0761441	−	0.997097i	$-0.475739\pi$
$823$	804.670	−	464.576i	0.977727	−	0.564491i	0.901583	+	0.432606i	$0.142406\pi$
$824$	485.287	−	280.181i	0.588940	−	0.340025i
$825$	5.00701	−	173.282i	0.00606910	−	0.210038i
$826$	1024.57	+	591.533i	1.24039	+	0.716142i
$827$	309.018			0.373661			0.186830	−	0.982392i	$-0.440179\pi$
$827$	309.018			0.373661			0.186830	+	0.982392i	$0.440179\pi$
$828$	75.1194	+	4.34481i	0.0907239	+	0.00524735i
$829$	−356.784			−0.430378			−0.215189	−	0.976572i	$-0.569037\pi$
$829$	−356.784			−0.430378			−0.215189	+	0.976572i	$0.569037\pi$
$830$	515.660	−	893.149i	0.621277	−	1.07608i
$831$	187.151	+	346.926i	0.225212	+	0.417480i
$832$	150.899	+	261.366i	0.181370	+	0.314141i
$833$	−143.172	+	80.2347i	−0.171876	+	0.0963202i
$834$	1623.63	+	1001.02i	1.94680	+	1.20026i
$835$	−402.841	+	697.741i	−0.482444	+	0.835618i
$836$	506.182			0.605481
$837$	175.375	+	375.500i	0.209528	+	0.448626i
$838$			307.561i			0.367017i
$839$	−201.748	+	349.438i	−0.240462	+	0.416493i	−0.960846	−	0.277083i	$-0.910632\pi$
$839$	−201.748	+	349.438i	−0.240462	+	0.416493i	0.720384	+	0.693576i	$0.243966\pi$
$840$	573.077	+	353.319i	0.682234	+	0.420618i
$841$	−577.554	−	1000.35i	−0.686747	−	1.18948i
$842$	−1585.06	+	915.134i	−1.88249	+	1.08686i
$843$	−370.741	−	687.250i	−0.439787	−	0.815243i
$844$	2064.12	+	1191.72i	2.44563	+	1.41199i
$845$	486.645			0.575911
$846$	734.199	−	1117.28i	0.867847	−	1.32066i
$847$			670.465i			0.791576i
$848$	−719.207	−	415.234i	−0.848121	−	0.489663i
$849$	461.176	+	13.3258i	0.543199	+	0.0156959i
$850$	−431.901	−	770.693i	−0.508119	−	0.906698i
$851$	18.1704	−	10.4907i	0.0213518	−	0.0123275i
$852$	−78.3776	+	2712.48i	−0.0919925	+	3.18366i
$853$	−159.462	−	92.0654i	−0.186943	−	0.107931i	0.403608	−	0.914932i	$-0.367756\pi$
$853$	−159.462	−	92.0654i	−0.186943	−	0.107931i	−0.590550	+	0.807001i	$0.701089\pi$
$854$			2079.73i			2.43528i
$855$	278.560	−	423.902i	0.325801	−	0.495792i
$856$			412.977i			0.482450i
$857$	−488.567	+	846.222i	−0.570090	+	0.987424i	0.426467	+	0.904503i	$0.359758\pi$
$857$	−488.567	+	846.222i	−0.570090	+	0.987424i	−0.996556	+	0.0829208i	$0.973575\pi$
$858$	62.8406	+	116.489i	0.0732408	+	0.135768i
$859$	598.778	+	1037.11i	0.697064	+	1.20735i	0.969480	+	0.245171i	$0.0788440\pi$
$859$	598.778	+	1037.11i	0.697064	+	1.20735i	−0.272416	+	0.962180i	$0.587823\pi$
$860$	−369.730	−	640.392i	−0.429919	−	0.744642i
$861$	−588.891	+	955.168i	−0.683961	+	1.10937i
$862$	−49.3703	−	28.5039i	−0.0572741	−	0.0330672i
$863$			20.1789i			0.0233823i	0.999932	+	0.0116912i	$0.00372149\pi$
$863$			20.1789i			0.0233823i	−0.999932	+	0.0116912i	$0.996279\pi$
$864$	−167.577	−	358.802i	−0.193954	−	0.415280i
$865$	−228.988			−0.264725
$866$	743.857	+	429.466i	0.858958	+	0.495919i
$867$	726.120	+	473.750i	0.837509	+	0.546424i
$868$	−356.939	−	618.236i	−0.411220	−	0.712253i
$869$	−345.091	+	199.238i	−0.397113	+	0.229273i
$870$	−666.770	−	1236.01i	−0.766402	−	1.42070i
$871$	−62.0280	+	107.436i	−0.0712147	+	0.123348i
$872$	−1469.34			−1.68503
$873$	4.94040	−	85.4169i	0.00565911	−	0.0978430i
$874$			69.2317i			0.0792125i
$875$	680.316	+	392.781i	0.777504	+	0.448892i
$876$	−765.493	−	22.1191i	−0.873851	−	0.0252501i
$877$	−600.576	+	346.742i	−0.684807	+	0.395373i	−0.801664	−	0.597775i	$-0.796051\pi$
$877$	−600.576	+	346.742i	−0.684807	+	0.395373i	0.116857	+	0.993149i	$0.462718\pi$
$878$	1226.66	+	2124.64i	1.39711	+	2.41986i
$879$	−284.916	−	8.23270i	−0.324136	−	0.00936599i
$880$	54.2728	−	94.0032i	0.0616736	−	0.106822i
$881$	−1461.79			−1.65925			−0.829623	−	0.558325i	$-0.811444\pi$
$881$	−1461.79			−1.65925			−0.829623	+	0.558325i	$0.811444\pi$
$882$	262.276	−	131.853i	0.297366	−	0.149493i
$883$	1331.57			1.50801			0.754006	−	0.656868i	$-0.228119\pi$
$883$	1331.57			1.50801			0.754006	+	0.656868i	$0.228119\pi$
$884$	376.620	+	223.918i	0.426040	+	0.253301i
$885$	−246.597	−	457.122i	−0.278640	−	0.516522i
$886$	−562.711	−	974.644i	−0.635114	−	1.10005i
$887$	−159.590	−	276.418i	−0.179921	−	0.311632i	0.761932	−	0.647657i	$-0.224251\pi$
$887$	−159.590	−	276.418i	−0.179921	−	0.311632i	−0.941853	+	0.336025i	$0.890917\pi$
$888$	548.151	+	337.952i	0.617287	+	0.380577i
$889$	−349.544	−	201.809i	−0.393188	−	0.227007i
$890$	−621.109			−0.697876
$891$	−120.748	−	279.306i	−0.135520	−	0.313475i
$892$	3173.94			3.55823
$893$	691.972	+	399.510i	0.774885	+	0.447380i
$894$	−1317.28	−	812.143i	−1.47347	−	0.908437i
$895$	122.495	−	70.7224i	0.136866	−	0.0790194i
$896$	735.955	+	1274.71i	0.821378	+	1.42267i
$897$	−10.3492	+	5.58295i	−0.0115376	+	0.00622402i
$898$	670.670	+	387.211i	0.746848	+	0.431193i
$899$			685.780i			0.762825i
$900$	461.037	+	917.078i	0.512263	+	1.01898i
$901$	1515.20	+	19.3974i	1.68169	+	0.0215288i
$902$	655.431	+	378.413i	0.726642	+	0.419527i
$903$	604.893	+	17.4785i	0.669870	+	0.0193560i
$904$	1880.86	−	1085.91i	2.08059	−	1.20123i
$905$	−430.379	+	248.479i	−0.475557	+	0.274563i
$906$	1660.99	+	47.9947i	1.83333	+	0.0529743i
$907$	−97.7878	−	56.4578i	−0.107815	−	0.0622468i	0.445123	−	0.895469i	$-0.353160\pi$
$907$	−97.7878	−	56.4578i	−0.107815	−	0.0622468i	−0.552938	+	0.833223i	$0.686493\pi$
$908$	−1438.41			−1.58416
$909$	−24.0761	+	416.263i	−0.0264863	+	0.457935i
$910$	−228.465			−0.251061
$911$	−0.456798	+	0.791197i	−0.000501424	+	0.000868493i	−0.866276	−	0.499566i	$-0.833493\pi$
$911$	−0.456798	+	0.791197i	−0.000501424	+	0.000868493i	0.865775	+	0.500434i	$0.166826\pi$
$912$	−447.040	+	241.158i	−0.490175	+	0.264428i
$913$	320.223	−	184.881i	0.350738	−	0.202498i
$914$	1667.14	−	962.525i	1.82401	−	1.05309i
$915$	479.172	−	777.207i	0.523686	−	0.849407i
$916$	−1408.81	+	2440.13i	−1.53800	+	2.66390i
$917$		−	1366.43i		−	1.49011i
$918$	−1259.36	−	904.899i	−1.37185	−	0.985728i
$919$	−211.594			−0.230244			−0.115122	−	0.993351i	$-0.536726\pi$
$919$	−211.594			−0.230244			−0.115122	+	0.993351i	$0.536726\pi$
$920$	34.9368	+	20.1708i	0.0379748	+	0.0219247i
$921$	1202.97	+	741.669i	1.30616	+	0.805286i
$922$	104.986	+	181.841i	0.113868	+	0.197225i
$923$	−212.038	−	367.260i	−0.229727	−	0.397898i
$924$	248.854	+	461.305i	0.269322	+	0.499248i
$925$	247.869	+	143.107i	0.267966	+	0.154711i
$926$		−	1470.44i		−	1.58795i
$927$	240.084	−	365.351i	0.258990	−	0.394122i
$928$		−	655.285i		−	0.706126i
$929$	−205.464	+	355.873i	−0.221166	+	0.383071i	−0.955162	−	0.296082i	$-0.904320\pi$
$929$	−205.464	+	355.873i	−0.221166	+	0.383071i	0.733996	+	0.679154i	$0.237653\pi$
$930$	−13.9358	+	482.286i	−0.0149847	+	0.518587i
$931$	87.7225	+	151.940i	0.0942239	+	0.163201i
$932$	−1187.67	−	2057.11i	−1.27433	−	2.20720i
$933$	33.0672	−	1144.39i	0.0354419	−	1.22657i
$934$	107.787	−	186.693i	0.115404	−	0.199885i
$935$	−2.53532	+	198.043i	−0.00271157	+	0.211810i
$936$	−301.614	−	198.201i	−0.322238	−	0.211753i
$937$	−1139.43			−1.21604			−0.608018	−	0.793923i	$-0.708035\pi$
$937$	−1139.43			−1.21604			−0.608018	+	0.793923i	$0.708035\pi$
$938$	−378.152	+	654.979i	−0.403147	+	0.698272i
$939$	17.1503	+	31.7919i	0.0182644	+	0.0338572i
$940$	875.569	−	505.510i	0.931457	−	0.537777i
$941$	201.972	+	349.826i	0.214636	+	0.371760i	0.953160	−	0.302467i	$-0.0978102\pi$
$941$	201.972	+	349.826i	0.214636	+	0.371760i	−0.738524	+	0.674227i	$0.764477\pi$
$942$	−720.886	+	1169.26i	−0.765272	+	1.24125i
$943$	−33.6194	+	58.2304i	−0.0356515	+	0.0617502i
$944$			520.114i			0.550968i
$945$	523.268	+	45.4610i	0.553722	+	0.0481069i
$946$		−	408.150i		−	0.431448i
$947$	−869.969	+	1506.83i	−0.918658	+	1.59116i	−0.117201	+	0.993108i	$0.537392\pi$
$947$	−869.969	+	1506.83i	−0.918658	+	1.59116i	−0.801456	+	0.598054i	$0.795941\pi$
$948$	1238.23	−	2008.39i	1.30615	−	2.11855i
$949$	103.645	−	59.8396i	0.109215	−	0.0630554i
$950$	−817.888	+	472.208i	−0.860934	+	0.497061i
$951$	−723.801	+	390.459i	−0.761095	+	0.410577i
$952$	1057.37	+	628.655i	1.11068	+	0.660352i
$953$		−	1741.50i		−	1.82739i	−0.406406	−	0.913693i	$-0.633218\pi$
$953$		−	1741.50i		−	1.82739i	0.406406	−	0.913693i	$-0.366782\pi$
$954$	−2705.84	−	156.502i	−2.83631	−	0.164049i
$955$		−	711.815i		−	0.745356i
$956$	−2034.08	−	1174.38i	−2.12770	−	1.22843i
$957$	14.5432	−	503.308i	0.0151966	−	0.525922i
$958$	1873.41	−	1081.61i	1.95554	−	1.12903i
$959$	94.2565	+	163.257i	0.0982862	+	0.170237i
$960$	23.3307	−	807.426i	0.0243029	−	0.841069i
$961$	−362.697	+	628.210i	−0.377417	+	0.653705i
$962$	−218.528			−0.227161
$963$	144.715	+	287.862i	0.150275	+	0.298922i
$964$		−	2940.88i		−	3.05071i
$965$	−606.160	−	349.967i	−0.628145	−	0.362660i
$966$	−63.0938	+	34.0363i	−0.0653145	+	0.0352343i
$967$	−914.968	−	1584.77i	−0.946192	−	1.63885i	−0.753347	−	0.657623i	$-0.771562\pi$
$967$	−914.968	−	1584.77i	−0.946192	−	1.63885i	−0.192845	−	0.981229i	$-0.561771\pi$
$968$	−1067.86	+	616.527i	−1.10316	+	0.636908i
$969$	496.457	−	782.636i	0.512340	−	0.807674i
$970$	49.8045	−	86.2640i	0.0513449	−	0.0889319i
$971$			799.025i			0.822889i	0.911435	+	0.411445i	$0.134976\pi$
$971$			799.025i			0.822889i	−0.911435	+	0.411445i	$0.865024\pi$
$972$	1414.43	+	1116.07i	1.45517	+	1.14822i
$973$	−1180.44			−1.21319
$974$	237.640	−	411.605i	0.243984	−	0.422592i
$975$	−136.544	−	84.1839i	−0.140046	−	0.0863425i
$976$	−791.819	+	457.157i	−0.811290	+	0.468398i
$977$	51.3985	−	29.6749i	0.0526085	−	0.0303735i	−0.473465	−	0.880813i	$-0.656997\pi$
$977$	51.3985	−	29.6749i	0.0526085	−	0.0303735i	0.526074	+	0.850439i	$0.323664\pi$
$978$	−243.968	+	131.610i	−0.249456	+	0.134570i
$979$	−192.854	−	111.344i	−0.196990	−	0.113732i
$980$	221.995			0.226525
$981$	−1024.19	+	514.886i	−1.04403	+	0.524858i
$982$	−569.022			−0.579452
$983$	−586.501	+	1015.85i	−0.596644	+	1.03342i	0.396668	+	0.917962i	$0.370166\pi$
$983$	−586.501	+	1015.85i	−0.596644	+	1.03342i	−0.993313	+	0.115456i	$0.963167\pi$
$984$	−2062.82	−	59.6057i	−2.09636	−	0.0605749i
$985$	33.0893	+	57.3123i	0.0335932	+	0.0581851i
$986$	−1254.49	−	2238.53i	−1.27230	−	2.27031i
$987$	−23.8973	+	827.034i	−0.0242121	+	0.837927i
$988$	234.193	−	405.635i	0.237038	−	0.410561i
$989$	36.2612			0.0366645
$990$	20.4555	−	353.664i	0.0206621	−	0.357237i
$991$		−	46.3789i		−	0.0468001i	−0.999726	−	0.0234000i	$-0.992551\pi$
$991$		−	46.3789i		−	0.0468001i	0.999726	−	0.0234000i	$-0.00744914\pi$
$992$	−112.564	+	194.967i	−0.113472	+	0.196539i
$993$	−301.935	+	162.880i	−0.304063	+	0.164029i
$994$	−1292.68	−	2238.99i	−1.30049	−	2.25251i
$995$	−608.078	+	351.074i	−0.611133	+	0.352838i
$996$	−1149.00	+	1863.66i	−1.15362	+	1.87115i
$997$	−1421.66	−	820.797i	−1.42594	−	0.823267i	−0.429142	−	0.903237i	$-0.641184\pi$
$997$	−1421.66	−	820.797i	−1.42594	−	0.823267i	−0.996797	+	0.0799703i	$0.974517\pi$
$998$	−394.758			−0.395549
$999$	500.509	+	43.4837i	0.501010	+	0.0435273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.101.31	yes	68
3.2	odd	2		459.3.i.a.305.4		68
9.4	even	3		459.3.i.a.152.3		68
9.5	odd	6	inner	153.3.i.a.50.32	yes	68
17.16	even	2	inner	153.3.i.a.101.32	yes	68
51.50	odd	2		459.3.i.a.305.3		68
153.50	odd	6	inner	153.3.i.a.50.31	✓	68
153.67	even	6		459.3.i.a.152.4		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.31	✓	68	153.50	odd	6	inner
153.3.i.a.50.32	yes	68	9.5	odd	6	inner
153.3.i.a.101.31	yes	68	1.1	even	1	trivial
153.3.i.a.101.32	yes	68	17.16	even	2	inner
459.3.i.a.152.3		68	9.4	even	3
459.3.i.a.152.4		68	153.67	even	6
459.3.i.a.305.3		68	51.50	odd	2
459.3.i.a.305.4		68	3.2	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.92590 + 1.68927i) q^{2} +(-2.55367 - 1.57441i) q^{3} +(3.70725 + 6.42114i) q^{4} +(1.55065 + 2.68581i) q^{5} +(-4.81216 - 8.92040i) q^{6} +(5.43225 + 3.13631i) q^{7} +11.5360i q^{8} +(4.04244 + 8.04106i) q^{9} +10.4779i q^{10} +(-1.87833 + 3.25336i) q^{11} +(0.642462 - 22.2342i) q^{12} +(1.73808 + 3.01044i) q^{13} +(10.5961 + 18.3530i) q^{14} +(0.268726 - 9.30002i) q^{15} +(-4.65840 + 8.06858i) q^{16} +(0.217614 - 16.9986i) q^{17} +(-1.75576 + 30.3561i) q^{18} -18.1729 q^{19} +(-11.4973 + 19.9139i) q^{20} +(-8.93431 - 16.5617i) q^{21} +(-10.9916 + 6.34600i) q^{22} +(-0.563797 - 0.976526i) q^{23} +(18.1625 - 29.4591i) q^{24} +(7.69097 - 13.3211i) q^{25} +11.7443i q^{26} +(2.33693 - 26.8987i) q^{27} +46.5083i q^{28} +(22.3389 - 38.6921i) q^{29} +(16.4965 - 26.7570i) q^{30} +(-13.2930 + 7.67472i) q^{31} +(12.7019 - 7.33345i) q^{32} +(9.91876 - 5.35073i) q^{33} +(29.3519 - 49.3686i) q^{34} +19.4533i q^{35} +(-36.6465 + 55.7673i) q^{36} +18.6072i q^{37} +(-53.1720 - 30.6989i) q^{38} +(0.301207 - 10.4241i) q^{39} +(-30.9835 + 17.8883i) q^{40} +(-29.8151 - 51.6413i) q^{41} +(1.83630 - 63.5503i) q^{42} +(-16.0790 + 27.8497i) q^{43} -27.8537 q^{44} +(-15.3283 + 23.3261i) q^{45} -3.80962i q^{46} +(-38.0772 - 21.9839i) q^{47} +(24.5993 - 13.2702i) q^{48} +(-4.82711 - 8.36080i) q^{49} +(45.0059 - 25.9842i) q^{50} +(-27.3186 + 43.0662i) q^{51} +(-12.8870 + 22.3209i) q^{52} +89.1367i q^{53} +(52.2767 - 74.7551i) q^{54} -11.6505 q^{55} +(-36.1805 + 62.6664i) q^{56} +(46.4075 + 28.6116i) q^{57} +(130.723 - 75.4728i) q^{58} +(48.3462 - 27.9127i) q^{59} +(60.7130 - 32.7520i) q^{60} +(84.9883 + 49.0680i) q^{61} -51.8586 q^{62} +(-3.25975 + 56.3594i) q^{63} +86.8198 q^{64} +(-5.39030 + 9.33627i) q^{65} +(38.0601 + 1.09975i) q^{66} +(17.8439 + 30.9065i) q^{67} +(109.957 - 61.6207i) q^{68} +(-0.0977055 + 3.38137i) q^{69} +(-32.8618 + 56.9183i) q^{70} -121.996 q^{71} +(-92.7617 + 46.6336i) q^{72} -34.4286i q^{73} +(-31.4325 + 54.4427i) q^{74} +(-40.6132 + 21.9090i) q^{75} +(-67.3714 - 116.691i) q^{76} +(-20.4071 + 11.7820i) q^{77} +(18.4904 - 29.9911i) q^{78} +(91.8612 + 53.0361i) q^{79} -28.8942 q^{80} +(-48.3174 + 65.0110i) q^{81} -201.463i q^{82} +(-85.2416 - 49.2143i) q^{83} +(73.2234 - 118.767i) q^{84} +(45.9924 - 25.7744i) q^{85} +(-94.0911 + 54.3235i) q^{86} +(-117.964 + 63.6361i) q^{87} +(-37.5308 - 21.6684i) q^{88} +59.2783i q^{89} +(-84.2531 + 42.3561i) q^{90} +21.8046i q^{91} +(4.18027 - 7.24045i) q^{92} +(46.0291 + 1.33002i) q^{93} +(-74.2733 - 128.645i) q^{94} +(-28.1798 - 48.8088i) q^{95} +(-43.9823 - 1.27088i) q^{96} +(-8.23298 - 4.75331i) q^{97} -32.6171i q^{98} +(-33.7535 - 1.95226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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