LMFDB - Embedded newform 153.3.i.a.50.32

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			50.32
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.32

$q$-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} +(28.0785 + 50.1038i) 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} +(26.2071 + 43.7514i) 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} +(108.344 + 64.4154i) 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} +(-45.3175 - 26.9434i) 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	−0.978390	−	0.206767i	$-0.933706\pi$
$5$	−1.55065	+	2.68581i	−0.310130	+	0.537161i	0.668260	+	0.743928i	$0.267039\pi$
$6$	4.81216	−	8.92040i	0.802027	−	1.48673i
$7$	−5.43225	+	3.13631i	−0.776036	+	0.448044i	−0.835023	−	0.550214i	$-0.814546\pi$
$7$	−5.43225	+	3.13631i	−0.776036	+	0.448044i	0.0589878	+	0.998259i	$0.481213\pi$
$8$		−	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	$-0.112045\pi$
$11$	1.87833	+	3.25336i	0.170757	+	0.295760i	−0.767928	+	0.640537i	$0.778712\pi$
$12$	−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	−0.853509	−	0.521079i	$-0.825530\pi$
$23$	0.563797	−	0.976526i	0.0245129	−	0.0424576i	0.878022	+	0.478621i	$0.158863\pi$
$24$	−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	$-0.886769\pi$
$29$	−22.3389	−	38.6921i	−0.770307	−	1.33421i	0.167087	−	0.985942i	$-0.446564\pi$
$30$	16.4965	+	26.7570i	0.549883	+	0.891899i
$31$	13.2930	+	7.67472i	0.428807	+	0.247572i	0.698838	−	0.715280i	$-0.253701\pi$
$31$	13.2930	+	7.67472i	0.428807	+	0.247572i	−0.270031	+	0.962852i	$0.587034\pi$
$32$	12.7019	+	7.33345i	0.396934	+	0.229170i
$33$	9.91876	+	5.35073i	0.300569	+	0.162143i
$34$	28.0785	+	50.1038i	0.825838	+	1.47364i
$35$		−	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	−0.230865	−	0.972986i	$-0.574156\pi$
$41$	29.8151	−	51.6413i	0.727198	−	1.25954i	0.958063	−	0.286558i	$-0.0925110\pi$
$42$	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
$51$	26.2071	+	43.7514i	0.513866	+	0.857871i
$52$	−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	−0.993674	−	0.112306i	$-0.964176\pi$
$61$	−84.9883	+	49.0680i	−1.39325	+	0.804394i	−0.399577	+	0.916699i	$0.630843\pi$
$62$	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	$0.0808567\pi$
$68$	108.344	+	64.4154i	1.59329	+	0.947285i
$69$	−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	$-0.171009\pi$
$71$	121.996			1.71825			0.859124	+	0.511767i	$0.171009\pi$
$72$	−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	$-0.900949\pi$
$79$	−91.8612	+	53.0361i	−1.16280	+	0.671343i	−0.210827	+	0.977523i	$0.567616\pi$
$80$	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
$85$	−45.3175	−	26.9434i	−0.533147	−	0.316981i
$86$	−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	−0.456961	−	0.889487i	$-0.651062\pi$
$97$	8.23298	−	4.75331i	0.0848761	−	0.0490032i	0.541837	+	0.840483i	$0.317729\pi$
$98$			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	$0.259673\pi$
$102$	150.587	+	83.7412i	1.47635	+	0.820993i
$103$	−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	$-0.553500\pi$
$107$	−35.7990			−0.334570			−0.167285	+	0.985909i	$0.553500\pi$
$108$	−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	−0.0625918	−	0.998039i	$-0.519937\pi$
$113$	94.1325	−	163.042i	0.833031	−	1.44285i	0.895623	−	0.444814i	$-0.146730\pi$
$114$	−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
$119$	−52.1308	−	93.0232i	−0.438074	−	0.781707i
$120$	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	$-0.520843\pi$
$131$	108.920	−	188.655i	0.831452	−	1.44012i	0.896887	−	0.442260i	$-0.145823\pi$
$132$	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	0.954266	−	0.298959i	$-0.0966395\pi$
$139$	162.976	+	94.0945i	1.17249	+	0.676939i	0.218227	+	0.975898i	$0.429973\pi$
$140$	−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
$153$	135.807	+	70.4656i	0.887629	+	0.460560i
$154$	−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	$-0.973264\pi$
$163$		−	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	0.155392	+	0.987853i	$0.450336\pi$
$167$	−129.894	+	224.983i	−0.777810	+	1.34721i	−0.933202	+	0.359353i	$0.882997\pi$
$168$	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	$-0.0982133\pi$
$173$	36.9180	+	63.9438i	0.213399	+	0.369617i	−0.739377	+	0.673291i	$0.764880\pi$
$174$	−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	$0.145964\pi$
$181$			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
$187$	−55.7113	+	31.2210i	−0.297922	+	0.166957i
$188$			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	0.911985	−	0.410224i	$-0.134550\pi$
$193$	195.454	+	112.845i	1.01271	+	0.584690i	0.100728	+	0.994914i	$0.467883\pi$
$194$	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	$-0.517248\pi$
$197$	−21.3390			−0.108320			−0.0541598	+	0.998532i	$0.517248\pi$
$198$	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
$204$	378.091	−	6.08248i	1.85338	−	0.0298161i
$205$	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	$-0.608990\pi$
$211$	−278.389	−	160.728i	−1.31938	−	0.761744i	−0.983629	+	0.180206i	$0.942323\pi$
$212$	−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
$221$	50.7950	+	30.2000i	0.229842	+	0.136652i
$222$	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	0.996633	−	0.0819880i	$-0.0261269\pi$
$227$	97.0001	+	168.009i	0.427313	+	0.740128i	−0.569320	+	0.822116i	$0.692794\pi$
$228$	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	$-0.258718\pi$
$233$	320.365			1.37496			0.687478	+	0.726205i	$0.258718\pi$
$234$	−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
$238$	−309.670	−	184.113i	−1.30114	−	0.773586i
$239$	−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	0.428564	−	0.903511i	$-0.359020\pi$
$241$	343.500	−	198.320i	1.42531	−	0.822903i	0.996746	+	0.0806081i	$0.0256862\pi$
$242$		−	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
$255$	−158.146	+	2.54415i	−0.620180	+	0.00997706i
$256$	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	$-0.510020\pi$
$269$	−16.9331			−0.0629482			−0.0314741	+	0.999505i	$0.510020\pi$
$270$	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	$0.441340\pi$
$272$	138.168	−	77.4304i	0.507972	−	0.284671i
$273$	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	$-0.590445\pi$
$277$	113.792	−	65.6978i	0.410801	−	0.237176i	0.691134	+	0.722727i	$0.257112\pi$
$278$	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	0.716500	−	0.697588i	$-0.245743\pi$
$283$	133.186	+	76.8948i	0.470621	+	0.271713i	−0.245879	+	0.969301i	$0.579077\pi$
$284$	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
$306$	516.393	−	23.2395i	1.68756	−	0.0759461i
$307$	−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	$0.376921\pi$
$311$	−190.810	+	330.493i	−0.613539	+	1.06268i	−0.990639	+	0.136508i	$0.956412\pi$
$312$	−120.253	+	3.47472i	−0.385425	+	0.0111369i
$313$	10.4278	−	6.02047i	0.0333155	−	0.0192347i	−0.483250	−	0.875483i	$-0.660544\pi$
$313$	10.4278	−	6.02047i	0.0333155	−	0.0192347i	0.516565	+	0.856248i	$0.327210\pi$
$314$			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	$-0.308996\pi$
$317$	−137.067	−	237.407i	−0.432388	−	0.748919i	−0.997078	+	0.0763844i	$0.975662\pi$
$318$	−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	0.0958260	−	0.995398i	$-0.469451\pi$
$337$	−242.067	−	139.758i	−0.718301	−	0.414711i	−0.814127	+	0.580687i	$0.802784\pi$
$338$	459.121	+	265.074i	1.35835	+	0.784242i
$339$	−16.3131	−	564.560i	−0.0481211	−	1.66537i
$340$	−341.011	+	191.104i	−1.00297	+	0.562072i
$341$			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	$-0.988187\pi$
$347$	−162.231	+	280.992i	−0.467523	+	0.809774i	0.531788	+	0.846877i	$0.321520\pi$
$348$	−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
$357$	−279.582	−	155.475i	−0.783142	−	0.435504i
$358$	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	−0.0633433	−	0.997992i	$-0.520176\pi$
$367$	282.323	−	162.999i	0.769271	−	0.444139i	0.832615	+	0.553853i	$0.186843\pi$
$368$	−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	$0.0186690\pi$
$374$	−110.265	+	185.461i	−0.294826	+	0.495884i
$375$	−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	0.444532	−	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
$391$	16.4769	+	9.79627i	0.0421404	+	0.0250544i
$392$	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	$-0.940259\pi$
$401$	−132.184	+	228.950i	−0.329636	+	0.570947i	0.652803	+	0.757527i	$0.273593\pi$
$402$	−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
$408$	504.716	−	302.326i	1.23705	−	0.740994i
$409$	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	−0.915216	−	0.402963i	$-0.867980\pi$
$419$	−45.5169	+	78.8375i	−0.108632	+	0.188156i	0.806584	+	0.591119i	$0.201314\pi$
$420$	−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
$425$	−228.115	+	127.837i	−0.536740	+	0.300793i
$426$	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	$-0.493769\pi$
$431$	16.8736			0.0391498			0.0195749	+	0.999808i	$0.493769\pi$
$432$	−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	$-0.976649\pi$
$439$	−628.864	+	363.075i	−1.43249	+	0.827049i	−0.435181	+	0.900343i	$0.643316\pi$
$440$			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	$-0.582159\pi$
$449$	−229.219			−0.510509			−0.255254	+	0.966874i	$0.582159\pi$
$450$	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
$459$	457.749	−	33.8711i	0.997274	−	0.0737932i
$460$	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	$-0.933665\pi$
$479$	−320.143	−	554.503i	−0.668356	−	1.15763i	0.310007	−	0.950734i	$-0.399669\pi$
$480$	−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	0.344059	−	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
$493$	662.574	−	371.310i	1.34396	−	0.753165i
$494$			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	$-0.295981\pi$
$499$	101.189	+	58.4214i	0.202783	+	0.117077i	−0.395170	+	0.918608i	$0.629314\pi$
$500$	−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	$-0.307121\pi$
$503$	572.958			1.13908			0.569541	+	0.821963i	$0.307121\pi$
$504$	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	$0.522629\pi$
$510$	−458.421	+	274.595i	−0.898864	+	0.538421i
$511$	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	$-0.610195\pi$
$521$	−353.566			−0.678630			−0.339315	+	0.940673i	$0.610195\pi$
$522$	−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
$527$	−133.352	+	224.292i	−0.253040	+	0.425602i
$528$	−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
$544$	−127.423	+	214.319i	−0.234233	+	0.393968i
$545$	−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	$0.792632\pi$
$547$	−939.697	+	542.534i	−1.71791	+	0.991836i	−0.922714	+	0.385485i	$0.874034\pi$
$548$		−	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
$561$	−93.1135	+	167.441i	−0.165978	+	0.298468i
$562$	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	−0.377966	−	0.925819i	$-0.623376\pi$
$571$	−781.546	−	451.226i	−1.36873	−	0.790238i	−0.990766	+	0.135582i	$0.956710\pi$
$572$	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	$0.732710\pi$
$578$	−857.805	+	466.392i	−1.48409	+	0.806906i
$579$	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	−0.909463	−	0.415784i	$-0.863507\pi$
$601$	−603.473	+	348.416i	−1.00412	+	0.579726i	−0.0946521	+	0.995510i	$0.530174\pi$
$602$	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	$-0.452275\pi$
$607$	−383.777	−	221.574i	−0.632252	−	0.365031i	−0.781624	+	0.623750i	$0.785608\pi$
$608$	−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
$612$	955.941	−	610.804i	1.56200	−	0.998046i
$613$	−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	$-0.620358\pi$
$617$	382.705	−	662.864i	0.620267	−	1.07433i	0.989436	−	0.144971i	$-0.0463090\pi$
$618$	258.381	+	419.088i	0.418092	+	0.678136i
$619$	−74.0367	+	42.7451i	−0.119607	+	0.0690551i	−0.558610	−	0.829430i	$-0.688665\pi$
$619$	−74.0367	+	42.7451i	−0.119607	+	0.0690551i	0.439003	+	0.898486i	$0.355332\pi$
$620$			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	$-0.972520\pi$
$641$	−367.170	−	635.958i	−0.572809	−	0.992134i	0.423467	−	0.905911i	$-0.360813\pi$
$642$	−172.270	+	319.341i	−0.268334	+	0.497416i
$643$	−1094.69	−	632.019i	−1.70247	−	0.982922i	−0.943246	−	0.332094i	$-0.892245\pi$
$643$	−1094.69	−	632.019i	−1.70247	−	0.982922i	−0.759225	−	0.650828i	$-0.774422\pi$
$644$	45.4166	+	26.2213i	0.0705226	+	0.0407163i
$645$	254.682	−	157.019i	0.394855	−	0.243441i
$646$	−510.267	−	910.530i	−0.789887	−	1.40949i
$647$			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	$0.347677\pi$
$653$	−351.643	+	609.064i	−0.538504	+	0.932716i	−0.998985	+	0.0450465i	$0.985656\pi$
$654$	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
$663$	177.261	−	2.85166i	0.267362	−	0.00430115i
$664$	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	$-0.830006\pi$
$673$	−572.251	+	330.389i	−0.850299	+	0.490920i	0.0104531	+	0.999945i	$0.496673\pi$
$674$	−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	$-0.984084\pi$
$677$	−367.380	−	636.321i	−0.542659	−	0.939913i	0.456091	−	0.889933i	$-0.349249\pi$
$678$	−1001.42	−	1624.29i	−1.47702	−	2.39570i
$679$	−29.8157	+	51.6424i	−0.0439113	+	0.0760565i
$680$	−310.819	+	522.783i	−0.457086	+	0.768798i
$681$	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	$-0.431889\pi$
$683$	290.069			0.424699			0.212349	+	0.977194i	$0.431889\pi$
$684$	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	$-0.628896\pi$
$691$	141.683	−	81.8008i	0.205041	−	0.118380i	0.599004	+	0.800746i	$0.295563\pi$
$692$	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
$697$	871.342	+	518.053i	1.25013	+	0.743261i
$698$	−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	0.453763	−	0.891122i	$-0.350081\pi$
$709$	1029.74	−	594.519i	1.45238	−	0.838532i	0.998616	+	0.0525907i	$0.0167479\pi$
$710$			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
$714$	−1080.67	+	17.3851i	−1.51354	+	0.0243488i
$715$	−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	$-0.673678\pi$
$719$	−746.256			−1.03791			−0.518954	+	0.854802i	$0.673678\pi$
$720$	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
$731$	476.905	−	267.260i	0.652400	−	0.365609i
$732$	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	−0.932258	−	0.361793i	$-0.882165\pi$
$743$	−113.536	+	196.649i	−0.152807	+	0.264670i	0.779451	+	0.626463i	$0.215498\pi$
$744$	−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	$-0.363512\pi$
$751$	−123.140	−	71.0950i	−0.163968	−	0.0946670i	−0.579739	+	0.814803i	$0.696845\pi$
$752$	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
$765$	−399.846	+	255.484i	−0.522675	+	0.333966i
$766$	−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	0.906884	−	0.421380i	$-0.138454\pi$
$787$	783.381	+	452.285i	0.995401	+	0.574695i	0.0885166	+	0.996075i	$0.471787\pi$
$788$	−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
$799$	−365.409	−	652.043i	−0.457333	−	0.816074i
$800$			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	$-0.666299\pi$
$809$	−807.379			−0.997996			−0.498998	+	0.866603i	$0.666299\pi$
$810$	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
$816$	230.928	−	415.266i	0.283001	−	0.508904i
$817$	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	$-0.974840\pi$
$821$	−465.360	−	806.027i	−0.566821	−	0.981762i	0.430057	−	0.902802i	$-0.358493\pi$
$822$	−8.79805	−	304.481i	−0.0107032	−	0.370415i
$823$	−804.670	−	464.576i	−0.977727	−	0.564491i	−0.0761441	−	0.997097i	$-0.524261\pi$
$823$	−804.670	−	464.576i	−0.977727	−	0.564491i	−0.901583	+	0.432606i	$0.857594\pi$
$824$	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	$-0.559821\pi$
$827$	−309.018			−0.373661			−0.186830	+	0.982392i	$0.559821\pi$
$828$	−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
$833$	−141.072	−	83.8736i	−0.169354	−	0.100689i
$834$	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	$-0.0893676\pi$
$839$	201.748	+	349.438i	0.240462	+	0.416493i	−0.720384	+	0.693576i	$0.756034\pi$
$840$	−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
$850$	−451.489	+	759.384i	−0.531164	+	0.893393i
$851$	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	$-0.632244\pi$
$853$	159.462	−	92.0654i	0.186943	−	0.107931i	0.590550	+	0.807001i	$0.298911\pi$
$854$		−	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	$0.0264249\pi$
$857$	488.567	+	846.222i	0.570090	+	0.987424i	−0.426467	+	0.904503i	$0.640242\pi$
$858$	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
$867$	−749.416	+	435.964i	−0.864378	+	0.502842i
$868$	−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	$-0.203949\pi$
$877$	600.576	+	346.742i	0.684807	+	0.395373i	−0.116857	+	0.993149i	$0.537282\pi$
$878$	−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	$-0.188556\pi$
$881$	1461.79			1.65925			0.829623	+	0.558325i	$0.188556\pi$
$882$	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	$0.228119\pi$
$884$	382.228	−	214.203i	0.432385	−	0.242311i
$885$	−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	$-0.775749\pi$
$887$	159.590	−	276.418i	0.179921	−	0.311632i	0.941853	+	0.336025i	$0.109083\pi$
$888$	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	$-0.646840\pi$
$907$	97.7878	−	56.4578i	0.107815	−	0.0622468i	0.552938	+	0.833223i	$0.313507\pi$
$908$	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	$-0.166507\pi$
$911$	0.456798	+	0.791197i	0.000501424	+	0.000868493i	−0.865775	+	0.500434i	$0.833174\pi$
$912$	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
$918$	1282.11	−	872.363i	1.39663	−	0.950287i
$919$	−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	$-0.0956803\pi$
$929$	205.464	+	355.873i	0.221166	+	0.383071i	−0.733996	+	0.679154i	$0.762347\pi$
$930$	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	$-0.902190\pi$
$941$	−201.972	+	349.826i	−0.214636	+	0.371760i	0.738524	+	0.674227i	$0.235523\pi$
$942$	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	$0.204059\pi$
$947$	869.969	+	1506.83i	0.918658	+	1.59116i	0.117201	+	0.993108i	$0.462608\pi$
$948$	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
$952$	−1073.12	+	601.381i	−1.12722	+	0.631703i
$953$			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
$969$	−476.259	−	795.089i	−0.491496	−	0.820525i
$970$	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	$0.0368330\pi$
$983$	586.501	+	1015.85i	0.596644	+	1.03342i	−0.396668	+	0.917962i	$0.629834\pi$
$984$	−2062.82	+	59.6057i	−2.09636	+	0.0605749i
$985$	33.0893	−	57.3123i	0.0335932	−	0.0581851i
$986$	1311.38	−	2205.68i	1.33000	−	2.23700i
$987$	−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	$-0.358816\pi$
$997$	1421.66	−	820.797i	1.42594	−	0.823267i	0.996797	+	0.0799703i	$0.0254825\pi$
$998$	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.50.32	yes	68
3.2	odd	2		459.3.i.a.152.3		68
9.2	odd	6	inner	153.3.i.a.101.31	yes	68
9.7	even	3		459.3.i.a.305.4		68
17.16	even	2	inner	153.3.i.a.50.31	✓	68
51.50	odd	2		459.3.i.a.152.4		68
153.16	even	6		459.3.i.a.305.3		68
153.101	odd	6	inner	153.3.i.a.101.32	yes	68

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

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} +(28.0785 + 50.1038i) 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} +(26.2071 + 43.7514i) 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} +(108.344 + 64.4154i) 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} +(-45.3175 - 26.9434i) 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