LMFDB - Embedded newform 153.3.i.a.50.31

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			50.31
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.31

$q$-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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.463802	−	0.885939i	$-0.346485\pi$
$2$	2.92590	−	1.68927i	1.46295	−	0.844634i	0.999147	+	0.0413052i	$0.0131516\pi$
$3$	−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	−0.668260	−	0.743928i	$-0.732961\pi$
$5$	1.55065	−	2.68581i	0.310130	−	0.537161i	0.978390	+	0.206767i	$0.0662940\pi$
$6$	−4.81216	+	8.92040i	−0.802027	+	1.48673i
$7$	5.43225	−	3.13631i	0.776036	−	0.448044i	−0.0589878	−	0.998259i	$-0.518787\pi$
$7$	5.43225	−	3.13631i	0.776036	−	0.448044i	0.835023	+	0.550214i	$0.185454\pi$
$8$		−	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	0.767928	−	0.640537i	$-0.221288\pi$
$11$	−1.87833	−	3.25336i	−0.170757	−	0.295760i	−0.938685	+	0.344777i	$0.887955\pi$
$12$	0.642462	+	22.2342i	0.0535385	+	1.85285i
$13$	1.73808	−	3.01044i	0.133698	−	0.231572i	−0.791401	−	0.611297i	$-0.790648\pi$
$13$	1.73808	−	3.01044i	0.133698	−	0.231572i	0.925099	+	0.379725i	$0.123981\pi$
$14$	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	−0.878022	−	0.478621i	$-0.841137\pi$
$23$	−0.563797	+	0.976526i	−0.0245129	+	0.0424576i	0.853509	+	0.521079i	$0.174470\pi$
$24$	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	0.937394	+	0.348269i	$0.113231\pi$
$29$	22.3389	+	38.6921i	0.770307	+	1.33421i	−0.167087	+	0.985942i	$0.553436\pi$
$30$	16.4965	+	26.7570i	0.549883	+	0.891899i
$31$	−13.2930	−	7.67472i	−0.428807	−	0.247572i	0.270031	−	0.962852i	$-0.412966\pi$
$31$	−13.2930	−	7.67472i	−0.428807	−	0.247572i	−0.698838	+	0.715280i	$0.746299\pi$
$32$	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	$-0.919093\pi$
$37$		−	18.6072i		−	0.502897i	0.967871	−	0.251448i	$-0.0809069\pi$
$38$	−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	0.230865	+	0.972986i	$0.425844\pi$
$41$	−29.8151	+	51.6413i	−0.727198	+	1.25954i	−0.958063	+	0.286558i	$0.907489\pi$
$42$	1.83630	+	63.5503i	0.0437214	+	1.51310i
$43$	−16.0790	−	27.8497i	−0.373931	−	0.647667i	0.616236	−	0.787562i	$-0.288657\pi$
$43$	−16.0790	−	27.8497i	−0.373931	−	0.647667i	−0.990166	+	0.139895i	$0.955324\pi$
$44$	−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	−0.847009	−	0.531579i	$-0.821599\pi$
$47$	−38.0772	+	21.9839i	−0.810153	+	0.467742i	0.0368561	+	0.999321i	$0.488266\pi$
$48$	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	$-0.682019\pi$
$53$		−	89.1367i		−	1.68183i	0.541171	−	0.840913i	$-0.317981\pi$
$54$	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	0.850219	−	0.526429i	$-0.176469\pi$
$59$	48.3462	+	27.9127i	0.819427	+	0.473097i	−0.0307916	+	0.999526i	$0.509803\pi$
$60$	60.7130	+	32.7520i	1.01188	+	0.545866i
$61$	84.9883	−	49.0680i	1.39325	−	0.804394i	0.399577	−	0.916699i	$-0.369157\pi$
$61$	84.9883	−	49.0680i	1.39325	−	0.804394i	0.993674	+	0.112306i	$0.0358236\pi$
$62$	−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	−0.701584	−	0.712587i	$-0.747523\pi$
$67$	17.8439	−	30.9065i	0.266326	−	0.461291i	0.967910	+	0.251296i	$0.0808567\pi$
$68$	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	$0.0757751\pi$
$73$			34.4286i			0.471625i	−0.971799	+	0.235812i	$0.924225\pi$
$74$	−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	0.210827	−	0.977523i	$-0.432384\pi$
$79$	91.8612	−	53.0361i	1.16280	−	0.671343i	0.951974	+	0.306180i	$0.0990510\pi$
$80$	−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	−0.916126	−	0.400891i	$-0.868701\pi$
$83$	−85.2416	+	49.2143i	−1.02701	+	0.592943i	−0.110881	+	0.993834i	$0.535367\pi$
$84$	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	$-0.891931\pi$
$89$		−	59.2783i		−	0.666048i	0.942918	−	0.333024i	$-0.108069\pi$
$90$	−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	−0.541837	−	0.840483i	$-0.682271\pi$
$97$	−8.23298	+	4.75331i	−0.0848761	+	0.0490032i	0.456961	+	0.889487i	$0.348938\pi$
$98$			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	−0.288049	−	0.957616i	$-0.593007\pi$
$101$	40.1218	−	23.1644i	0.397246	−	0.229350i	0.685295	+	0.728266i	$0.259673\pi$
$102$	−152.682	−	79.8588i	−1.49688	−	0.782930i
$103$	−24.2875	+	42.0672i	−0.235801	+	0.408419i	−0.959505	−	0.281691i	$-0.909105\pi$
$103$	−24.2875	+	42.0672i	−0.235801	+	0.408419i	0.723704	+	0.690110i	$0.242438\pi$
$104$	−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	$-0.801382\pi$
$109$		−	127.370i		−	1.16853i	0.811561	−	0.584267i	$-0.198618\pi$
$110$	−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	0.0625918	+	0.998039i	$0.480063\pi$
$113$	−94.1325	+	163.042i	−0.833031	+	1.44285i	−0.895623	+	0.444814i	$0.853270\pi$
$114$	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	0.0654350	+	0.997857i	$0.479157\pi$
$131$	−108.920	+	188.655i	−0.831452	+	1.44012i	−0.896887	+	0.442260i	$0.854177\pi$
$132$	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	−0.401995	−	0.915642i	$-0.631683\pi$
$137$	26.0269	−	15.0267i	0.189978	−	0.109684i	0.591972	+	0.805958i	$0.298350\pi$
$138$	−5.99792	−	9.72850i	−0.0434632	−	0.0704964i
$139$	−162.976	−	94.0945i	−1.17249	−	0.676939i	−0.218227	−	0.975898i	$-0.570027\pi$
$139$	−162.976	−	94.0945i	−1.17249	−	0.676939i	−0.954266	+	0.298959i	$0.903361\pi$
$140$	−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	0.873098	−	0.487545i	$-0.162108\pi$
$149$	132.226	+	76.3405i	0.887420	+	0.512352i	0.0143224	+	0.999897i	$0.495441\pi$
$150$	−155.840	+	4.50303i	−1.03893	+	0.0300202i
$151$	−81.9727	−	141.981i	−0.542866	−	0.940271i	−0.998738	−	0.0502257i	$-0.984006\pi$
$151$	−81.9727	−	141.981i	−0.542866	−	0.940271i	0.455872	−	0.890045i	$-0.349327\pi$
$152$			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	−0.997012	−	0.0772472i	$-0.975387\pi$
$157$	−67.7624	+	117.368i	−0.431608	+	0.747567i	0.565404	+	0.824814i	$0.308720\pi$
$158$	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	$0.0267357\pi$
$163$			27.3494i			0.167788i	−0.996475	+	0.0838939i	$0.973264\pi$
$164$	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	−0.155392	−	0.987853i	$-0.549664\pi$
$167$	129.894	−	224.983i	0.777810	−	1.34721i	0.933202	−	0.359353i	$-0.117003\pi$
$168$	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	0.739377	−	0.673291i	$-0.235120\pi$
$173$	−36.9180	−	63.9438i	−0.213399	−	0.369617i	−0.952776	+	0.303674i	$0.901787\pi$
$174$	−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	$0.0406623\pi$
$179$			45.6082i			0.254795i	−0.991852	+	0.127397i	$0.959338\pi$
$180$	−206.606	+	11.9498i	−1.14781	+	0.0663879i
$181$		−	160.242i		−	0.885315i	−0.896691	−	0.442657i	$-0.854036\pi$
$181$		−	160.242i		−	0.885315i	0.896691	−	0.442657i	$-0.145964\pi$
$182$	−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	−0.920028	−	0.391852i	$-0.871834\pi$
$191$	−198.771	+	114.761i	−1.04069	+	0.600842i	−0.120660	+	0.992694i	$0.538501\pi$
$192$	−221.709	+	136.690i	−1.15473	+	0.711929i
$193$	−195.454	−	112.845i	−1.01271	−	0.584690i	−0.100728	−	0.994914i	$-0.532117\pi$
$193$	−195.454	−	112.845i	−1.01271	−	0.584690i	−0.911985	+	0.410224i	$0.865450\pi$
$194$	−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	$-0.807387\pi$
$199$		−	226.404i		−	1.13771i	0.822438	−	0.568855i	$-0.192613\pi$
$200$	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	0.983629	−	0.180206i	$-0.0576766\pi$
$211$	278.389	+	160.728i	1.31938	+	0.761744i	0.335751	+	0.941951i	$0.391010\pi$
$212$	−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	0.722973	+	0.690877i	$0.242775\pi$
$223$	214.036	+	370.721i	0.959803	+	1.66243i	0.236831	+	0.971551i	$0.423891\pi$
$224$	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	0.569320	−	0.822116i	$-0.307206\pi$
$227$	−97.0001	−	168.009i	−0.427313	−	0.740128i	−0.996633	+	0.0819880i	$0.973873\pi$
$228$	−11.6754	−	404.060i	−0.0512078	−	1.77219i
$229$	190.008	−	329.103i	0.829728	−	1.43713i	−0.0685233	−	0.997650i	$-0.521829\pi$
$229$	190.008	−	329.103i	0.829728	−	1.43713i	0.898251	−	0.439482i	$-0.144838\pi$
$230$	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	−0.199494	−	0.979899i	$-0.563930\pi$
$239$	−274.338	−	158.389i	−1.14786	−	0.662716i	−0.948364	+	0.317183i	$0.897263\pi$
$240$	73.7861	−	45.4914i	0.307442	−	0.189548i
$241$	−343.500	+	198.320i	−1.42531	+	0.822903i	−0.996746	−	0.0806081i	$-0.974314\pi$
$241$	−343.500	+	198.320i	−1.42531	+	0.822903i	−0.428564	+	0.903511i	$0.640980\pi$
$242$		−	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	$-0.977912\pi$
$251$		−	34.8071i		−	0.138674i	0.997593	−	0.0693369i	$-0.0220883\pi$
$252$	−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	0.816790	−	0.576936i	$-0.195752\pi$
$257$	186.465	+	107.655i	0.725544	+	0.418893i	−0.0912460	+	0.995828i	$0.529085\pi$
$258$	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	−0.310873	−	0.950451i	$-0.600621\pi$
$263$	93.8398	−	54.1785i	0.356806	−	0.206002i	0.667679	+	0.744450i	$0.267288\pi$
$264$	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	−0.691134	−	0.722727i	$-0.742888\pi$
$277$	−113.792	+	65.6978i	−0.410801	+	0.237176i	0.280333	+	0.959903i	$0.409555\pi$
$278$	−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	−0.0420394	−	0.999116i	$-0.513386\pi$
$281$	225.418	−	130.145i	0.802201	−	0.463151i	0.844240	+	0.535965i	$0.180052\pi$
$282$	−12.8715	−	445.454i	−0.0456435	−	1.57962i
$283$	−133.186	−	76.8948i	−0.470621	−	0.271713i	0.245879	−	0.969301i	$-0.420923\pi$
$283$	−133.186	−	76.8948i	−0.470621	−	0.271713i	−0.716500	+	0.697588i	$0.754257\pi$
$284$	−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	0.633798	−	0.773499i	$-0.281495\pi$
$293$	82.2824	+	47.5058i	0.280827	+	0.162136i	−0.352971	+	0.935634i	$0.614828\pi$
$294$	−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	−0.377101	−	0.926172i	$-0.623079\pi$
$311$	190.810	−	330.493i	0.613539	−	1.06268i	0.990639	−	0.136508i	$-0.0435878\pi$
$312$	120.253	−	3.47472i	0.385425	−	0.0111369i
$313$	−10.4278	+	6.02047i	−0.0333155	+	0.0192347i	−0.516565	−	0.856248i	$-0.672790\pi$
$313$	−10.4278	+	6.02047i	−0.0333155	+	0.0192347i	0.483250	+	0.875483i	$0.339456\pi$
$314$			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	0.997078	−	0.0763844i	$-0.0243376\pi$
$317$	137.067	+	237.407i	0.432388	+	0.748919i	−0.564690	+	0.825303i	$0.691004\pi$
$318$	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	0.939378	−	0.342884i	$-0.111404\pi$
$331$	57.1777	+	99.0347i	0.172742	+	0.299199i	−0.766635	+	0.642083i	$0.778071\pi$
$332$			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	0.814127	−	0.580687i	$-0.197216\pi$
$337$	242.067	+	139.758i	0.718301	+	0.414711i	−0.0958260	+	0.995398i	$0.530549\pi$
$338$	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	−0.531788	−	0.846877i	$-0.678480\pi$
$347$	162.231	−	280.992i	0.467523	−	0.809774i	0.999311	+	0.0371034i	$0.0118131\pi$
$348$	−845.937	+	521.547i	−2.43085	+	1.49870i
$349$	−139.028	−	240.803i	−0.398360	−	0.689980i	0.595164	−	0.803604i	$-0.297087\pi$
$349$	−139.028	−	240.803i	−0.398360	−	0.689980i	−0.993524	+	0.113625i	$0.963754\pi$
$350$	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	−0.952065	−	0.305897i	$-0.901044\pi$
$353$	−410.603	+	237.062i	−1.16318	+	0.671563i	−0.211117	+	0.977461i	$0.567710\pi$
$354$	−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	$-0.763146\pi$
$359$		−	486.308i		−	1.35462i	0.735699	−	0.677309i	$-0.236854\pi$
$360$	−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	−0.832615	−	0.553853i	$-0.813157\pi$
$367$	−282.323	+	162.999i	−0.769271	+	0.444139i	0.0633433	+	0.997992i	$0.479824\pi$
$368$	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	−0.549904	−	0.835228i	$-0.685336\pi$
$373$	167.244	−	289.676i	0.448377	−	0.776611i	0.998281	+	0.0586169i	$0.0186690\pi$
$374$	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	$-0.976323\pi$
$379$		−	56.3312i		−	0.148631i	0.997235	−	0.0743155i	$-0.0236772\pi$
$380$	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	0.444532	−	0.895763i	$-0.353370\pi$
$383$	−41.7301	−	24.0929i	−0.108956	−	0.0629057i	−0.553488	+	0.832857i	$0.686703\pi$
$384$	−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	−0.539112	−	0.842234i	$-0.681240\pi$
$389$	−30.8371	+	17.8038i	−0.0792728	+	0.0457682i	0.459840	+	0.888002i	$0.347907\pi$
$390$	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	$-0.938730\pi$
$397$		−	151.892i		−	0.382601i	0.981532	−	0.191300i	$-0.0612704\pi$
$398$	−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	−0.652803	−	0.757527i	$-0.726407\pi$
$401$	132.184	−	228.950i	0.329636	−	0.570947i	0.982440	+	0.186580i	$0.0597405\pi$
$402$	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	−0.843992	−	0.536355i	$-0.819801\pi$
$409$	17.3829	−	30.1081i	0.0425011	−	0.0736140i	0.886493	+	0.462741i	$0.153134\pi$
$410$	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	−0.806584	−	0.591119i	$-0.798686\pi$
$419$	45.5169	−	78.8375i	0.108632	−	0.188156i	0.915216	+	0.402963i	$0.132020\pi$
$420$	432.529	−	12.4980i	1.02983	−	0.0297571i
$421$	−270.867	−	469.156i	−0.643390	−	1.11438i	−0.984671	−	0.174423i	$-0.944194\pi$
$421$	−270.867	−	469.156i	−0.643390	−	1.11438i	0.341281	−	0.939961i	$-0.389139\pi$
$422$	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	0.435181	−	0.900343i	$-0.356684\pi$
$439$	628.864	−	363.075i	1.43249	−	0.827049i	0.997310	+	0.0732936i	$0.0233510\pi$
$440$			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	−0.788916	−	0.614502i	$-0.789357\pi$
$443$	−288.481	+	166.555i	−0.651199	+	0.375970i	0.137716	+	0.990472i	$0.456024\pi$
$444$	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	0.988848	+	0.148930i	$0.0475828\pi$
$457$	284.894	+	493.451i	0.623401	+	1.07976i	−0.365447	+	0.930832i	$0.619084\pi$
$458$		−	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	−0.440487	−	0.897759i	$-0.645194\pi$
$461$	53.8225	−	31.0745i	0.116752	−	0.0674066i	0.557239	+	0.830352i	$0.311861\pi$
$462$	203.303	−	125.342i	0.440049	−	0.271304i
$463$	−217.615	+	376.921i	−0.470011	+	0.814084i	−0.999412	−	0.0342882i	$-0.989084\pi$
$463$	−217.615	+	376.921i	−0.470011	+	0.814084i	0.529400	+	0.848372i	$0.322417\pi$
$464$	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	$0.0217626\pi$
$467$			63.8071i			0.136632i	−0.997664	+	0.0683159i	$0.978237\pi$
$468$	−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	0.978364	+	0.206893i	$0.0663352\pi$
$479$	320.143	+	554.503i	0.668356	+	1.15763i	−0.310007	+	0.950734i	$0.600331\pi$
$480$	−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	$0.0461354\pi$
$487$			140.676i			0.288863i	−0.989515	+	0.144432i	$0.953865\pi$
$488$	−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	0.344059	−	0.938948i	$-0.388198\pi$
$491$	−145.858	−	84.2113i	−0.297064	−	0.171510i	−0.641123	+	0.767438i	$0.721531\pi$
$492$	−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	0.395170	−	0.918608i	$-0.370686\pi$
$499$	−101.189	−	58.4214i	−0.202783	−	0.117077i	−0.597953	+	0.801531i	$0.704019\pi$
$500$	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	0.828322	−	0.560253i	$-0.189296\pi$
$509$	385.460	+	222.546i	0.757290	+	0.437221i	−0.0710321	+	0.997474i	$0.522629\pi$
$510$	−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	$0.356136\pi$
$541$			973.359i			1.79918i	−0.436731	+	0.899592i	$0.643864\pi$
$542$	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	0.795197	−	0.606351i	$-0.207368\pi$
$547$	939.697	−	542.534i	1.71791	−	0.991836i	0.922714	−	0.385485i	$-0.125966\pi$
$548$		−	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	$0.0767794\pi$
$557$			266.109i			0.477755i	−0.971050	+	0.238877i	$0.923221\pi$
$558$	−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	0.582734	−	0.812663i	$-0.301983\pi$
$563$	95.8869	+	55.3603i	0.170314	+	0.0983310i	−0.412420	+	0.910994i	$0.635316\pi$
$564$	−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	0.443952	−	0.896051i	$-0.353576\pi$
$569$	820.458	−	473.692i	1.44193	−	0.832499i	0.997979	+	0.0635520i	$0.0202429\pi$
$570$	−299.789	−	486.251i	−0.525945	−	0.853072i
$571$	781.546	+	451.226i	1.36873	+	0.790238i	0.990766	−	0.135582i	$-0.0432903\pi$
$571$	781.546	+	451.226i	1.36873	+	0.790238i	0.377966	+	0.925819i	$0.376624\pi$
$572$	−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	0.300349	−	0.953829i	$-0.402897\pi$
$587$	749.343	−	432.633i	1.27656	−	0.737024i	0.976215	+	0.216805i	$0.0695636\pi$
$588$	−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	$0.0531406\pi$
$593$			197.080i			0.332344i	−0.986097	+	0.166172i	$0.946859\pi$
$594$	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	0.854593	−	0.519299i	$-0.173807\pi$
$599$	498.466	+	287.789i	0.832164	+	0.480450i	−0.0224293	+	0.999748i	$0.507140\pi$
$600$	−252.742	+	468.514i	−0.421237	+	0.780856i
$601$	603.473	−	348.416i	1.00412	−	0.579726i	0.0946521	−	0.995510i	$-0.469826\pi$
$601$	603.473	−	348.416i	1.00412	−	0.579726i	0.909463	+	0.415784i	$0.136493\pi$
$602$	−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	0.781624	−	0.623750i	$-0.214392\pi$
$607$	383.777	+	221.574i	0.632252	+	0.365031i	−0.149372	+	0.988781i	$0.547725\pi$
$608$	−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	0.369169	+	0.929362i	$0.379642\pi$
$617$	−382.705	+	662.864i	−0.620267	+	1.07433i	−0.989436	+	0.144971i	$0.953691\pi$
$618$	−258.381	−	419.088i	−0.418092	−	0.678136i
$619$	74.0367	−	42.7451i	0.119607	−	0.0690551i	−0.439003	−	0.898486i	$-0.644668\pi$
$619$	74.0367	−	42.7451i	0.119607	−	0.0690551i	0.558610	+	0.829430i	$0.311335\pi$
$620$			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	0.996276	+	0.0862224i	$0.0274796\pi$
$641$	367.170	+	635.958i	0.572809	+	0.992134i	−0.423467	+	0.905911i	$0.639187\pi$
$642$	−172.270	+	319.341i	−0.268334	+	0.497416i
$643$	1094.69	+	632.019i	1.70247	+	0.982922i	0.943246	+	0.332094i	$0.107755\pi$
$643$	1094.69	+	632.019i	1.70247	+	0.982922i	0.759225	+	0.650828i	$0.225578\pi$
$644$	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	$0.168821\pi$
$647$			654.568i			1.01170i	−0.862622	+	0.505849i	$0.831179\pi$
$648$	−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	−0.460481	−	0.887670i	$-0.652323\pi$
$653$	351.643	−	609.064i	0.538504	−	0.932716i	0.998985	−	0.0450465i	$-0.0143436\pi$
$654$	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	−0.170197	−	0.985410i	$-0.554440\pi$
$659$	394.144	−	227.559i	0.598094	−	0.345310i	0.768292	+	0.640100i	$0.221107\pi$
$660$	−7.48502	−	259.040i	−0.0113409	−	0.392485i
$661$	−134.035	+	232.155i	−0.202776	+	0.351218i	−0.949422	−	0.314004i	$-0.898330\pi$
$661$	−134.035	+	232.155i	−0.202776	+	0.351218i	0.746646	+	0.665222i	$0.231663\pi$
$662$	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	−0.0104531	−	0.999945i	$-0.503327\pi$
$673$	572.251	−	330.389i	0.850299	−	0.490920i	0.860752	+	0.509025i	$0.169994\pi$
$674$	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	0.998750	+	0.0499797i	$0.0159157\pi$
$677$	367.380	+	636.321i	0.542659	+	0.939913i	−0.456091	+	0.889933i	$0.650751\pi$
$678$	−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	−0.599004	−	0.800746i	$-0.704437\pi$
$691$	−141.683	+	81.8008i	−0.205041	+	0.118380i	0.393964	+	0.919126i	$0.371104\pi$
$692$	−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	$-0.896530\pi$
$701$		−	447.750i		−	0.638730i	0.947632	−	0.319365i	$-0.103470\pi$
$702$	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	−0.998616	−	0.0525907i	$-0.983252\pi$
$709$	−1029.74	+	594.519i	−1.45238	+	0.838532i	−0.453763	+	0.891122i	$0.649919\pi$
$710$			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	0.968531	−	0.248892i	$-0.0800665\pi$
$727$	195.358	+	338.371i	0.268719	+	0.465434i	−0.699813	+	0.714327i	$0.746733\pi$
$728$	−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	−0.869335	−	0.494224i	$-0.835452\pi$
$733$	−4.87965	+	8.45179i	−0.00665709	+	0.0115304i	0.862678	+	0.505754i	$0.168786\pi$
$734$	−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	−0.779451	−	0.626463i	$-0.784502\pi$
$743$	113.536	−	196.649i	0.152807	−	0.264670i	0.932258	+	0.361793i	$0.117835\pi$
$744$	−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	0.579739	−	0.814803i	$-0.303155\pi$
$751$	123.140	+	71.0950i	0.163968	+	0.0946670i	−0.415770	+	0.909470i	$0.636488\pi$
$752$	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	0.474921	−	0.880028i	$-0.342477\pi$
$761$	−37.8559	−	21.8561i	−0.0497449	−	0.0287202i	−0.524666	+	0.851308i	$0.675810\pi$
$762$	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	−0.371836	−	0.928298i	$-0.621272\pi$
$769$	475.251	−	823.159i	0.618012	−	1.07043i	0.989848	−	0.142129i	$-0.0453949\pi$
$770$	−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	$-0.913139\pi$
$773$		−	416.660i		−	0.539017i	0.962998	−	0.269509i	$-0.0868613\pi$
$774$	−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	−0.0885166	−	0.996075i	$-0.528213\pi$
$787$	−783.381	−	452.285i	−0.995401	−	0.574695i	−0.906884	+	0.421380i	$0.861546\pi$
$788$	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	−0.445837	−	0.895114i	$-0.647094\pi$
$797$	−1150.83	−	664.429i	−1.44395	−	0.833663i	−0.998110	+	0.0614514i	$0.980427\pi$
$798$	−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	$-0.978654\pi$
$811$		−	108.693i		−	0.134024i	0.997752	−	0.0670118i	$-0.0213465\pi$
$812$	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	0.996878	+	0.0789605i	$0.0251601\pi$
$821$	465.360	+	806.027i	0.566821	+	0.981762i	−0.430057	+	0.902802i	$0.641507\pi$
$822$	8.79805	+	304.481i	0.0107032	+	0.370415i
$823$	804.670	+	464.576i	0.977727	+	0.564491i	0.901583	−	0.432606i	$-0.142406\pi$
$823$	804.670	+	464.576i	0.977727	+	0.564491i	0.0761441	+	0.997097i	$0.475739\pi$
$824$	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	0.720384	−	0.693576i	$-0.243966\pi$
$839$	−201.748	−	349.438i	−0.240462	−	0.416493i	−0.960846	+	0.277083i	$0.910632\pi$
$840$	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	−0.590550	−	0.807001i	$-0.701089\pi$
$853$	−159.462	+	92.0654i	−0.186943	+	0.107931i	0.403608	+	0.914932i	$0.367756\pi$
$854$		−	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	−0.996556	−	0.0829208i	$-0.973575\pi$
$857$	−488.567	−	846.222i	−0.570090	−	0.987424i	0.426467	−	0.904503i	$-0.359758\pi$
$858$	62.8406	−	116.489i	0.0732408	−	0.135768i
$859$	598.778	−	1037.11i	0.697064	−	1.20735i	−0.272416	−	0.962180i	$-0.587823\pi$
$859$	598.778	−	1037.11i	0.697064	−	1.20735i	0.969480	−	0.245171i	$-0.0788440\pi$
$860$	−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	$-0.996279\pi$
$863$		−	20.1789i		−	0.0233823i	0.999932	−	0.0116912i	$-0.00372149\pi$
$864$	−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	0.116857	−	0.993149i	$-0.462718\pi$
$877$	−600.576	−	346.742i	−0.684807	−	0.395373i	−0.801664	+	0.597775i	$0.796051\pi$
$878$	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	−0.941853	−	0.336025i	$-0.890917\pi$
$887$	−159.590	+	276.418i	−0.179921	+	0.311632i	0.761932	+	0.647657i	$0.224251\pi$
$888$	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	−0.552938	−	0.833223i	$-0.686493\pi$
$907$	−97.7878	+	56.4578i	−0.107815	+	0.0622468i	0.445123	+	0.895469i	$0.353160\pi$
$908$	−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	0.865775	−	0.500434i	$-0.166826\pi$
$911$	−0.456798	−	0.791197i	−0.000501424	−	0.000868493i	−0.866276	+	0.499566i	$0.833493\pi$
$912$	−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	0.733996	−	0.679154i	$-0.237653\pi$
$929$	−205.464	−	355.873i	−0.221166	−	0.383071i	−0.955162	+	0.296082i	$0.904320\pi$
$930$	−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	−0.738524	−	0.674227i	$-0.764477\pi$
$941$	201.972	−	349.826i	0.214636	−	0.371760i	0.953160	+	0.302467i	$0.0978102\pi$
$942$	−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	−0.801456	−	0.598054i	$-0.795941\pi$
$947$	−869.969	−	1506.83i	−0.918658	−	1.59116i	−0.117201	−	0.993108i	$-0.537392\pi$
$948$	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	$0.366782\pi$
$953$			1741.50i			1.82739i	−0.406406	+	0.913693i	$0.633218\pi$
$954$	−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	−0.192845	+	0.981229i	$0.561771\pi$
$967$	−914.968	+	1584.77i	−0.946192	+	1.63885i	−0.753347	+	0.657623i	$0.771562\pi$
$968$	−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	$-0.865024\pi$
$971$		−	799.025i		−	0.822889i	0.911435	−	0.411445i	$-0.134976\pi$
$972$	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	0.526074	−	0.850439i	$-0.323664\pi$
$977$	51.3985	+	29.6749i	0.0526085	+	0.0303735i	−0.473465	+	0.880813i	$0.656997\pi$
$978$	−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	−0.993313	−	0.115456i	$-0.963167\pi$
$983$	−586.501	−	1015.85i	−0.596644	−	1.03342i	0.396668	−	0.917962i	$-0.370166\pi$
$984$	−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	$0.00744914\pi$
$991$			46.3789i			0.0468001i	−0.999726	+	0.0234000i	$0.992551\pi$
$992$	−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	−0.996797	−	0.0799703i	$-0.974517\pi$
$997$	−1421.66	+	820.797i	−1.42594	+	0.823267i	−0.429142	+	0.903237i	$0.641184\pi$
$998$	−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.50.31	✓	68
3.2	odd	2		459.3.i.a.152.4		68
9.2	odd	6	inner	153.3.i.a.101.32	yes	68
9.7	even	3		459.3.i.a.305.3		68
17.16	even	2	inner	153.3.i.a.50.32	yes	68
51.50	odd	2		459.3.i.a.152.3		68
153.16	even	6		459.3.i.a.305.4		68
153.101	odd	6	inner	153.3.i.a.101.31	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.31	✓	68	1.1	even	1	trivial
153.3.i.a.50.32	yes	68	17.16	even	2	inner
153.3.i.a.101.31	yes	68	153.101	odd	6	inner
153.3.i.a.101.32	yes	68	9.2	odd	6	inner
459.3.i.a.152.3		68	51.50	odd	2
459.3.i.a.152.4		68	3.2	odd	2
459.3.i.a.305.3		68	9.7	even	3
459.3.i.a.305.4		68	153.16	even	6

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

Related objects

Downloads

Learn more