LMFDB - Embedded newform 153.3.q.a.128.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(2,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 21])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.q (of order $24$, degree $8$, 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:	$272$
Relative dimension:	$34$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			128.20
Character	$\chi$	$=$	153.128
Dual form			153.3.q.a.104.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.289257 - 0.0775060i) q^{2} +(-1.27816 - 2.71409i) q^{3} +(-3.38644 + 1.95516i) q^{4} +(-0.482534 - 3.66521i) q^{5} +(-0.580075 - 0.686004i) q^{6} +(4.81280 + 0.633617i) q^{7} +(-1.67501 + 1.67501i) q^{8} +(-5.73260 + 6.93810i) q^{9} +(-0.423652 - 1.02279i) q^{10} +(-13.9733 - 1.83962i) q^{11} +(9.63491 + 6.69210i) q^{12} +(-17.7309 + 10.2370i) q^{13} +(1.44124 - 0.189743i) q^{14} +(-9.33096 + 5.99437i) q^{15} +(7.46596 - 12.9314i) q^{16} +(-16.5975 + 3.67736i) q^{17} +(-1.12045 + 2.45120i) q^{18} +(-10.6134 + 10.6134i) q^{19} +(8.80015 + 11.4686i) q^{20} +(-4.43184 - 13.8723i) q^{21} +(-4.18445 + 0.550893i) q^{22} +(11.9276 - 15.5444i) q^{23} +(6.68709 + 2.40521i) q^{24} +(10.9472 - 2.93330i) q^{25} +(-4.33536 + 4.33536i) q^{26} +(26.1579 + 6.69080i) q^{27} +(-17.5371 + 7.26410i) q^{28} +(31.2711 - 23.9952i) q^{29} +(-2.23444 + 2.45712i) q^{30} +(-0.963434 - 7.31801i) q^{31} +(3.60971 - 13.4716i) q^{32} +(12.8672 + 40.2762i) q^{33} +(-4.51592 + 2.35011i) q^{34} -17.9457i q^{35} +(5.84800 - 34.7036i) q^{36} +(-43.8166 - 18.1494i) q^{37} +(-2.24740 + 3.89261i) q^{38} +(50.4471 + 35.0389i) q^{39} +(6.94753 + 5.33103i) q^{40} +(-10.2327 - 7.85182i) q^{41} +(-2.35712 - 3.66915i) q^{42} +(-70.5703 + 18.9093i) q^{43} +(50.9165 - 21.0903i) q^{44} +(28.1958 + 17.6633i) q^{45} +(2.24536 - 5.42077i) q^{46} +(33.1317 - 57.3857i) q^{47} +(-44.6398 - 3.73486i) q^{48} +(-24.5688 - 6.58318i) q^{49} +(2.93921 - 1.69695i) q^{50} +(31.1950 + 40.3469i) q^{51} +(40.0298 - 69.3337i) q^{52} +(-27.5694 - 27.5694i) q^{53} +(8.08491 - 0.0920336i) q^{54} +52.1028i q^{55} +(-9.12283 + 7.00019i) q^{56} +(42.3716 + 15.2402i) q^{57} +(7.18560 - 9.36446i) q^{58} +(-20.7499 - 5.55991i) q^{59} +(19.8788 - 38.5431i) q^{60} +(59.9261 + 7.88942i) q^{61} +(-0.845869 - 2.04211i) q^{62} +(-31.9860 + 29.7594i) q^{63} +55.5512i q^{64} +(46.0764 + 60.0479i) q^{65} +(6.84358 + 10.6529i) q^{66} +(45.0944 + 78.1058i) q^{67} +(49.0166 - 44.9039i) q^{68} +(-57.4343 - 12.5044i) q^{69} +(-1.39090 - 5.19090i) q^{70} +(-27.6841 + 66.8352i) q^{71} +(-2.01923 - 21.2236i) q^{72} +(9.76419 - 23.5728i) q^{73} +(-14.0809 - 1.85379i) q^{74} +(-21.9536 - 25.9626i) q^{75} +(15.1908 - 56.6928i) q^{76} +(-66.0851 - 17.7075i) q^{77} +(17.3079 + 6.22528i) q^{78} +(-1.49620 + 11.3647i) q^{79} +(-50.9990 - 21.1245i) q^{80} +(-15.2745 - 79.5468i) q^{81} +(-3.56844 - 1.47810i) q^{82} +(1.31090 - 0.351254i) q^{83} +(42.1307 + 38.3126i) q^{84} +(21.4871 + 59.0589i) q^{85} +(-18.9473 + 10.9393i) q^{86} +(-105.095 - 54.2030i) q^{87} +(26.4869 - 20.3241i) q^{88} +117.164 q^{89} +(9.52482 + 2.92389i) q^{90} +(-91.8218 + 38.0338i) q^{91} +(-10.0004 + 75.9604i) q^{92} +(-18.6303 + 11.9684i) q^{93} +(5.13581 - 19.1671i) q^{94} +(44.0219 + 33.7792i) q^{95} +(-41.1770 + 7.42182i) q^{96} +(-111.896 - 145.826i) q^{97} -7.61692 q^{98} +(92.8669 - 86.4024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) $ 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

Character values

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

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.289257	−	0.0775060i	0.144628	−	0.0387530i	−0.185779	−	0.982592i	$-0.559481\pi$
$2$	0.289257	−	0.0775060i	0.144628	−	0.0387530i	0.330407	+	0.943839i	$0.392814\pi$
$3$	−1.27816	−	2.71409i	−0.426054	−	0.904698i
$3$	−1.27816	−	2.71409i	−0.426054	−	0.904698i
$4$	−3.38644	+	1.95516i	−0.846610	+	0.488790i
$5$	−0.482534	−	3.66521i	−0.0965068	−	0.733042i	−0.969462	−	0.245242i	$-0.921133\pi$
$5$	−0.482534	−	3.66521i	−0.0965068	−	0.733042i	0.872955	−	0.487800i	$-0.162201\pi$
$6$	−0.580075	−	0.686004i	−0.0966792	−	0.114334i
$7$	4.81280	+	0.633617i	0.687543	+	0.0905168i	0.466200	−	0.884679i	$-0.345623\pi$
$7$	4.81280	+	0.633617i	0.687543	+	0.0905168i	0.221343	+	0.975196i	$0.428956\pi$
$8$	−1.67501	+	1.67501i	−0.209377	+	0.209377i
$9$	−5.73260	+	6.93810i	−0.636956	+	0.770900i
$10$	−0.423652	−	1.02279i	−0.0423652	−	0.102279i
$11$	−13.9733	−	1.83962i	−1.27030	−	0.167238i	−0.534926	−	0.844899i	$-0.679660\pi$
$11$	−13.9733	−	1.83962i	−1.27030	−	0.167238i	−0.735374	+	0.677661i	$0.762994\pi$
$12$	9.63491	+	6.69210i	0.802909	+	0.557675i
$13$	−17.7309	+	10.2370i	−1.36392	+	0.787458i	−0.990143	−	0.140061i	$-0.955270\pi$
$13$	−17.7309	+	10.2370i	−1.36392	+	0.787458i	−0.373775	+	0.927519i	$0.621937\pi$
$14$	1.44124	−	0.189743i	0.102946	−	0.0135531i
$15$	−9.33096	+	5.99437i	−0.622064	+	0.399625i
$16$	7.46596	−	12.9314i	0.466623	−	0.808214i
$17$	−16.5975	+	3.67736i	−0.976324	+	0.216315i
$17$	−16.5975	+	3.67736i	−0.976324	+	0.216315i
$18$	−1.12045	+	2.45120i	−0.0622471	+	0.136178i
$19$	−10.6134	+	10.6134i	−0.558602	+	0.558602i	−0.928909	−	0.370307i	$-0.879252\pi$
$19$	−10.6134	+	10.6134i	−0.558602	+	0.558602i	0.370307	+	0.928909i	$0.379252\pi$
$20$	8.80015	+	11.4686i	0.440007	+	0.573429i
$21$	−4.43184	−	13.8723i	−0.211040	−	0.660584i
$22$	−4.18445	+	0.550893i	−0.190202	+	0.0250406i
$23$	11.9276	−	15.5444i	0.518592	−	0.675842i	−0.458492	−	0.888699i	$-0.651610\pi$
$23$	11.9276	−	15.5444i	0.518592	−	0.675842i	0.977083	+	0.212857i	$0.0682768\pi$
$24$	6.68709	+	2.40521i	0.278629	+	0.100217i
$25$	10.9472	−	2.93330i	0.437889	−	0.117332i
$26$	−4.33536	+	4.33536i	−0.166745	+	0.166745i
$27$	26.1579	+	6.69080i	0.968809	+	0.247807i
$28$	−17.5371	+	7.26410i	−0.626324	+	0.259432i
$29$	31.2711	−	23.9952i	1.07831	−	0.827419i	0.0925758	−	0.995706i	$-0.470490\pi$
$29$	31.2711	−	23.9952i	1.07831	−	0.827419i	0.985738	+	0.168286i	$0.0538233\pi$
$30$	−2.23444	+	2.45712i	−0.0744814	+	0.0819039i
$31$	−0.963434	−	7.31801i	−0.0310785	−	0.236065i	0.968855	−	0.247630i	$-0.0796518\pi$
$31$	−0.963434	−	7.31801i	−0.0310785	−	0.236065i	−0.999933	+	0.0115655i	$0.996318\pi$
$32$	3.60971	−	13.4716i	0.112803	−	0.420988i
$33$	12.8672	+	40.2762i	0.389916	+	1.22049i
$34$	−4.51592	+	2.35011i	−0.132821	+	0.0691208i
$35$		−	17.9457i		−	0.512733i
$36$	5.84800	−	34.7036i	0.162445	−	0.963990i
$37$	−43.8166	−	18.1494i	−1.18423	−	0.490525i	−0.298359	−	0.954454i	$-0.596439\pi$
$37$	−43.8166	−	18.1494i	−1.18423	−	0.490525i	−0.885873	+	0.463929i	$0.846439\pi$
$38$	−2.24740	+	3.89261i	−0.0591422	+	0.102437i
$39$	50.4471	+	35.0389i	1.29351	+	0.898434i
$40$	6.94753	+	5.33103i	0.173688	+	0.133276i
$41$	−10.2327	−	7.85182i	−0.249578	−	0.191508i	0.476395	−	0.879232i	$-0.341943\pi$
$41$	−10.2327	−	7.85182i	−0.249578	−	0.191508i	−0.725973	+	0.687724i	$0.758610\pi$
$42$	−2.35712	−	3.66915i	−0.0561220	−	0.0873606i
$43$	−70.5703	+	18.9093i	−1.64117	+	0.439750i	−0.957122	−	0.289686i	$-0.906449\pi$
$43$	−70.5703	+	18.9093i	−1.64117	+	0.439750i	−0.684049	+	0.729436i	$0.739782\pi$
$44$	50.9165	−	21.0903i	1.15719	−	0.479325i
$45$	28.1958	+	17.6633i	0.626573	+	0.392518i
$46$	2.24536	−	5.42077i	0.0488121	−	0.117843i
$47$	33.1317	−	57.3857i	0.704929	−	1.22097i	−0.261788	−	0.965125i	$-0.584312\pi$
$47$	33.1317	−	57.3857i	0.704929	−	1.22097i	0.966717	−	0.255848i	$-0.0823545\pi$
$48$	−44.6398	−	3.73486i	−0.929996	−	0.0778096i
$49$	−24.5688	−	6.58318i	−0.501404	−	0.134351i
$50$	2.93921	−	1.69695i	0.0587841	−	0.0339390i
$51$	31.1950	+	40.3469i	0.611666	+	0.791116i
$52$	40.0298	−	69.3337i	0.769804	−	1.33334i
$53$	−27.5694	−	27.5694i	−0.520178	−	0.520178i	0.397447	−	0.917625i	$-0.369896\pi$
$53$	−27.5694	−	27.5694i	−0.520178	−	0.520178i	−0.917625	+	0.397447i	$0.869896\pi$
$54$	8.08491	−	0.0920336i	0.149720	−	0.00170433i
$55$			52.1028i			0.947323i
$56$	−9.12283	+	7.00019i	−0.162908	+	0.125003i
$57$	42.3716	+	15.2402i	0.743361	+	0.267372i
$58$	7.18560	−	9.36446i	0.123890	−	0.161456i
$59$	−20.7499	−	5.55991i	−0.351693	−	0.0942358i	0.0786476	−	0.996902i	$-0.474940\pi$
$59$	−20.7499	−	5.55991i	−0.351693	−	0.0942358i	−0.430340	+	0.902667i	$0.641606\pi$
$60$	19.8788	−	38.5431i	0.331313	−	0.642385i
$61$	59.9261	+	7.88942i	0.982395	+	0.129335i	0.604578	−	0.796546i	$-0.293342\pi$
$61$	59.9261	+	7.88942i	0.982395	+	0.129335i	0.377816	+	0.925881i	$0.376675\pi$
$62$	−0.845869	−	2.04211i	−0.0136431	−	0.0329372i
$63$	−31.9860	+	29.7594i	−0.507714	+	0.472372i
$64$			55.5512i			0.867987i
$65$	46.0764	+	60.0479i	0.708867	+	0.923814i
$66$	6.84358	+	10.6529i	0.103691	+	0.161407i
$67$	45.0944	+	78.1058i	0.673050	+	1.16576i	0.977035	+	0.213080i	$0.0683496\pi$
$67$	45.0944	+	78.1058i	0.673050	+	1.16576i	−0.303984	+	0.952677i	$0.598317\pi$
$68$	49.0166	−	44.9039i	0.720832	−	0.660352i
$69$	−57.4343	−	12.5044i	−0.832381	−	0.181224i
$70$	−1.39090	−	5.19090i	−0.0198700	−	0.0741557i
$71$	−27.6841	+	66.8352i	−0.389916	+	0.941341i	0.600040	+	0.799970i	$0.295151\pi$
$71$	−27.6841	+	66.8352i	−0.389916	+	0.941341i	−0.989957	+	0.141372i	$0.954849\pi$
$72$	−2.01923	−	21.2236i	−0.0280448	−	0.294772i
$73$	9.76419	−	23.5728i	0.133756	−	0.322916i	−0.842784	−	0.538252i	$-0.819085\pi$
$73$	9.76419	−	23.5728i	0.133756	−	0.322916i	0.976540	+	0.215337i	$0.0690848\pi$
$74$	−14.0809	−	1.85379i	−0.190283	−	0.0250512i
$75$	−21.9536	−	25.9626i	−0.292714	−	0.346167i
$76$	15.1908	−	56.6928i	0.199879	−	0.745958i
$77$	−66.0851	−	17.7075i	−0.858248	−	0.229967i
$78$	17.3079	+	6.22528i	0.221896	+	0.0798113i
$79$	−1.49620	+	11.3647i	−0.0189392	+	0.143857i	−0.998302	−	0.0582535i	$-0.981447\pi$
$79$	−1.49620	+	11.3647i	−0.0189392	+	0.143857i	0.979363	+	0.202111i	$0.0647802\pi$
$80$	−50.9990	−	21.1245i	−0.637487	−	0.264056i
$81$	−15.2745	−	79.5468i	−0.188574	−	0.982059i
$82$	−3.56844	−	1.47810i	−0.0435175	−	0.0180256i
$83$	1.31090	−	0.351254i	0.0157939	−	0.00423197i	−0.250913	−	0.968010i	$-0.580731\pi$
$83$	1.31090	−	0.351254i	0.0157939	−	0.00423197i	0.266707	+	0.963778i	$0.414064\pi$
$84$	42.1307	+	38.3126i	0.501556	+	0.456102i
$85$	21.4871	+	59.0589i	0.252790	+	0.694810i
$86$	−18.9473	+	10.9393i	−0.220318	+	0.127201i
$87$	−105.095	−	54.2030i	−1.20798	−	0.623023i
$88$	26.4869	−	20.3241i	0.300987	−	0.230956i
$89$	117.164			1.31645			0.658226	−	0.752821i	$-0.271307\pi$
$89$	117.164			1.31645			0.658226	+	0.752821i	$0.271307\pi$
$90$	9.52482	+	2.92389i	0.105831	+	0.0324876i
$91$	−91.8218	+	38.0338i	−1.00903	+	0.417954i
$92$	−10.0004	+	75.9604i	−0.108700	+	0.825657i
$93$	−18.6303	+	11.9684i	−0.200326	+	0.128693i
$94$	5.13581	−	19.1671i	0.0546363	−	0.203905i
$95$	44.0219	+	33.7792i	0.463388	+	0.355570i
$96$	−41.1770	+	7.42182i	−0.428927	+	0.0773106i
$97$	−111.896	−	145.826i	−1.15357	−	1.50336i	−0.830532	−	0.556970i	$-0.811964\pi$
$97$	−111.896	−	145.826i	−1.15357	−	1.50336i	−0.323035	−	0.946387i	$-0.604703\pi$
$98$	−7.61692			−0.0777236
$99$	92.8669	−	86.4024i	0.938049	−	0.872751i
$100$	−31.3370	+	31.3370i	−0.313370	+	0.313370i
$101$	−87.6938	−	50.6300i	−0.868255	−	0.501287i	−0.00148706	−	0.999999i	$-0.500473\pi$
$101$	−87.6938	−	50.6300i	−0.868255	−	0.501287i	−0.866768	+	0.498712i	$0.833807\pi$
$102$	12.1505	+	9.25280i	0.119122	+	0.0907138i
$103$	13.3629	+	23.1452i	0.129737	+	0.224711i	0.923575	−	0.383419i	$-0.125253\pi$
$103$	13.3629	+	23.1452i	0.129737	+	0.224711i	−0.793838	+	0.608130i	$0.791920\pi$
$104$	12.5525	−	46.8466i	0.120697	−	0.450448i
$105$	−48.7062	+	22.9375i	−0.463869	+	0.218452i
$106$	−10.1114	−	5.83784i	−0.0953908	−	0.0550739i
$107$	−42.8540	−	17.7507i	−0.400505	−	0.165894i	0.173334	−	0.984863i	$-0.444546\pi$
$107$	−42.8540	−	17.7507i	−0.400505	−	0.165894i	−0.573838	+	0.818969i	$0.694546\pi$
$108$	−101.664	+	28.4848i	−0.941329	+	0.263748i
$109$	−1.60841	−	3.88305i	−0.0147561	−	0.0356243i	0.916330	−	0.400424i	$-0.131137\pi$
$109$	−1.60841	−	3.88305i	−0.0147561	−	0.0356243i	−0.931086	+	0.364800i	$0.881137\pi$
$110$	4.03828	+	15.0711i	0.0367116	+	0.137010i
$111$	6.74547	+	142.120i	0.0607700	+	1.28036i
$112$	44.1258	−	57.5058i	0.393980	−	0.513445i
$113$	−80.6072	+	105.049i	−0.713338	+	0.929640i	−0.999593	−	0.0285133i	$-0.990923\pi$
$113$	−80.6072	+	105.049i	−0.713338	+	0.929640i	0.286256	+	0.958153i	$0.407589\pi$
$114$	13.4375	+	1.12427i	0.117872	+	0.00986199i
$115$	−62.7288	−	36.2165i	−0.545468	−	0.314926i
$116$	−58.9833	+	142.398i	−0.508477	+	1.22757i
$117$	30.6193	−	181.703i	0.261704	−	1.55302i
$118$	−6.43296			−0.0545167
$119$	−82.2105	+	7.18193i	−0.690845	+	0.0603523i
$120$	5.58884	−	25.6702i	0.0465736	−	0.213918i
$121$	74.9919	+	20.0940i	0.619768	+	0.166066i
$122$	17.9455	−	2.36257i	0.147094	−	0.0193653i
$123$	−8.23154	+	37.8084i	−0.0669231	+	0.307385i
$124$	17.5705	+	22.8983i	0.141698	+	0.184664i
$125$	−51.4015	−	124.094i	−0.411212	−	0.992754i
$126$	−6.94562	+	11.0872i	−0.0551240	+	0.0879938i
$127$	106.818	+	106.818i	0.841089	+	0.841089i	0.989001	−	0.147911i	$-0.0472551\pi$
$127$	106.818	+	106.818i	0.841089	+	0.841089i	−0.147911	+	0.989001i	$0.547255\pi$
$128$	18.7444	+	69.9550i	0.146440	+	0.546523i
$129$	141.522	+	167.365i	1.09707	+	1.29741i
$130$	17.9820	+	13.7980i	0.138323	+	0.106139i
$131$	26.7423	+	203.128i	0.204139	+	1.55059i	0.720033	+	0.693940i	$0.244127\pi$
$131$	26.7423	+	203.128i	0.204139	+	1.55059i	−0.515894	+	0.856653i	$0.672540\pi$
$132$	−122.321	−	111.235i	−0.926671	−	0.842692i
$133$	−57.8053	+	44.3555i	−0.434626	+	0.333500i
$134$	19.0975	+	19.0975i	0.142519	+	0.142519i
$135$	11.9011	−	99.1025i	0.0881566	−	0.734093i
$136$	21.6414	−	33.9607i	0.159128	−	0.249711i
$137$	43.2321	+	24.9601i	0.315563	+	0.182190i	0.649413	−	0.760436i	$-0.275015\pi$
$137$	43.2321	+	24.9601i	0.315563	+	0.182190i	−0.333850	+	0.942626i	$0.608348\pi$
$138$	−17.5824	+	0.834516i	−0.127409	+	0.00604722i
$139$	9.72393	+	73.8606i	0.0699564	+	0.531371i	0.990161	+	0.139933i	$0.0446889\pi$
$139$	9.72393	+	73.8606i	0.0699564	+	0.531371i	−0.920205	+	0.391438i	$0.871978\pi$
$140$	35.0867	+	60.7719i	0.250619	+	0.434085i
$141$	−198.098	−	16.5742i	−1.40495	−	0.117547i
$142$	−2.82766	+	21.4782i	−0.0199131	+	0.151255i
$143$	266.592	−	110.426i	1.86428	−	0.772209i
$144$	46.9201	+	125.930i	0.325834	+	0.874516i
$145$	−103.037	−	103.037i	−0.710598	−	0.710598i
$146$	0.997318	−	7.57538i	0.00683094	−	0.0518862i
$147$	13.5355	+	75.0963i	0.0920783	+	0.510859i
$148$	183.867	−	24.2066i	1.24235	−	0.163558i
$149$	−77.6639	−	134.518i	−0.521234	−	0.902804i	−0.999695	−	0.0246953i	$-0.992138\pi$
$149$	−77.6639	−	134.518i	−0.521234	−	0.902804i	0.478461	−	0.878109i	$-0.341195\pi$
$150$	−8.36247	−	5.80830i	−0.0557498	−	0.0387220i
$151$	12.5993	+	47.0212i	0.0834391	+	0.311399i	0.995014	−	0.0997350i	$-0.0317995\pi$
$151$	12.5993	+	47.0212i	0.0834391	+	0.311399i	−0.911575	+	0.411134i	$0.865133\pi$
$152$		−	35.5554i		−	0.233917i
$153$	69.6330	−	136.236i	0.455118	−	0.890431i
$154$	−20.4880			−0.133039
$155$	−26.3571	+	7.06237i	−0.170046	+	0.0455637i
$156$	−239.343	−	20.0250i	−1.53425	−	0.128365i
$157$	116.928	−	67.5085i	0.744766	−	0.429991i	−0.0790338	−	0.996872i	$-0.525184\pi$
$157$	116.928	−	67.5085i	0.744766	−	0.429991i	0.823800	+	0.566881i	$0.191850\pi$
$158$	0.448051	+	3.40329i	0.00283577	+	0.0215398i
$159$	−39.5878	+	110.064i	−0.248980	+	0.692227i
$160$	−51.1181	−	6.72982i	−0.319488	−	0.0420614i
$161$	67.2544	−	67.2544i	0.417729	−	0.417729i
$162$	−10.5836	−	21.8256i	−0.0653309	−	0.134726i
$163$	−28.0428	−	67.7012i	−0.172042	−	0.415345i	0.814216	−	0.580563i	$-0.197167\pi$
$163$	−28.0428	−	67.7012i	−0.172042	−	0.415345i	−0.986257	+	0.165218i	$0.947167\pi$
$164$	50.0040	+	6.58315i	0.304902	+	0.0401412i
$165$	141.412	−	66.5958i	0.857041	−	0.403611i
$166$	0.351961	−	0.203205i	0.00212025	−	0.00122412i
$167$	85.8226	−	11.2988i	0.513908	−	0.0676572i	0.130888	−	0.991397i	$-0.458217\pi$
$167$	85.8226	−	11.2988i	0.513908	−	0.0676572i	0.383020	+	0.923740i	$0.374884\pi$
$168$	30.6596	+	15.8128i	0.182498	+	0.0941240i
$169$	125.091	−	216.663i	0.740181	−	1.28203i
$170$	10.7927	+	15.4178i	0.0634866	+	0.0906928i
$171$	−12.7945	−	134.480i	−0.0748216	−	0.786432i
$172$	202.011	−	202.011i	1.17449	−	1.17449i
$173$	−188.849	−	246.113i	−1.09161	−	1.42262i	−0.897159	−	0.441708i	$-0.854373\pi$
$173$	−188.849	−	246.113i	−1.09161	−	1.42262i	−0.194456	−	0.980911i	$-0.562294\pi$
$174$	−34.6004	−	7.53310i	−0.198853	−	0.0432937i
$175$	54.5454	−	7.18104i	0.311688	−	0.0410345i
$176$	−128.113	+	166.960i	−0.727915	+	0.948637i
$177$	11.4316	+	63.4236i	0.0645852	+	0.358325i
$178$	33.8905	−	9.08093i	0.190396	−	0.0510165i
$179$	−115.575	+	115.575i	−0.645671	+	0.645671i	−0.951944	−	0.306273i	$-0.900918\pi$
$179$	−115.575	+	115.575i	−0.645671	+	0.645671i	0.306273	+	0.951944i	$0.400918\pi$
$180$	−130.018	−	4.68848i	−0.722322	−	0.0260471i
$181$	−120.420	+	49.8794i	−0.665301	+	0.275577i	−0.689667	−	0.724126i	$-0.742243\pi$
$181$	−120.420	+	49.8794i	−0.665301	+	0.275577i	0.0243661	+	0.999703i	$0.492243\pi$
$182$	−23.6122	+	18.1183i	−0.129737	+	0.0995510i
$183$	−55.1826	−	172.729i	−0.301544	−	0.943874i
$184$	6.05812	+	46.0160i	0.0329245	+	0.250087i
$185$	−45.3785	+	169.355i	−0.245289	+	0.915431i
$186$	−4.46132	+	4.90591i	−0.0239856	+	0.0263759i
$187$	238.687	−	20.8517i	1.27640	−	0.111507i
$188$			259.111i			1.37825i
$189$	121.653	+	48.7756i	0.643667	+	0.258072i
$190$	15.3517	+	6.35888i	0.0807984	+	0.0334678i
$191$	−15.9352	+	27.6005i	−0.0834301	+	0.144505i	−0.904721	−	0.426004i	$-0.859921\pi$
$191$	−15.9352	+	27.6005i	−0.0834301	+	0.144505i	0.821291	+	0.570509i	$0.193254\pi$
$192$	150.771	−	71.0034i	0.785266	−	0.369809i
$193$	283.412	+	217.470i	1.46846	+	1.12679i	0.964834	+	0.262861i	$0.0846660\pi$
$193$	283.412	+	217.470i	1.46846	+	1.12679i	0.503621	+	0.863924i	$0.332001\pi$
$194$	−43.6690	−	33.5084i	−0.225098	−	0.172724i
$195$	104.083	−	201.807i	0.533757	−	1.03491i
$196$	96.0719	−	25.7424i	0.490163	−	0.131339i
$197$	−127.660	+	52.8785i	−0.648020	+	0.268419i	−0.682387	−	0.730991i	$-0.739058\pi$
$197$	−127.660	+	52.8785i	−0.648020	+	0.268419i	0.0343677	+	0.999409i	$0.489058\pi$
$198$	20.1656	−	32.1902i	0.101847	−	0.162577i
$199$	75.5702	−	182.443i	0.379750	−	0.916797i	−0.612262	−	0.790655i	$-0.709740\pi$
$199$	75.5702	−	182.443i	0.379750	−	0.916797i	0.992012	−	0.126143i	$-0.0402597\pi$
$200$	−13.4234	+	23.2501i	−0.0671172	+	0.116250i
$201$	154.348	−	222.222i	0.767902	−	1.10558i
$202$	−29.2901	−	7.84826i	−0.145001	−	0.0388528i
$203$	165.705	−	95.6700i	0.816283	−	0.471281i
$204$	−184.525	−	75.6411i	−0.904533	−	0.370790i
$205$	−23.8410	+	41.2937i	−0.116297	+	0.201433i
$206$	5.65920	+	5.65920i	0.0274718	+	0.0274718i
$207$	39.4721	+	171.865i	0.190687	+	0.830264i
$208$			305.715i			1.46978i
$209$	167.830	−	128.780i	0.803012	−	0.616173i
$210$	−12.3108	+	10.4098i	−0.0586228	+	0.0495707i
$211$	−167.017	+	217.660i	−0.791548	+	1.03157i	0.207034	+	0.978334i	$0.433619\pi$
$211$	−167.017	+	217.660i	−0.791548	+	1.03157i	−0.998582	+	0.0532319i	$0.983048\pi$
$212$	147.265	+	39.4595i	0.694645	+	0.186130i
$213$	216.782	−	10.2891i	1.01775	−	0.0483058i
$214$	−13.7716	−	1.81306i	−0.0643532	−	0.00847226i
$215$	103.359	+	249.531i	0.480739	+	1.16061i
$216$	−55.0220	+	32.6076i	−0.254731	+	0.150961i
$217$		−	35.8306i		−	0.165118i
$218$	−0.766203	−	0.998535i	−0.00351469	−	0.00458043i
$219$	−76.4591	+	3.62899i	−0.349128	+	0.0165707i
$220$	−101.869	−	176.443i	−0.463042	−	0.802013i
$221$	256.644	−	235.111i	1.16129	−	1.06385i
$222$	12.9663	+	40.5864i	0.0584070	+	0.182822i
$223$	−23.0426	−	85.9961i	−0.103330	−	0.385633i	0.894820	−	0.446426i	$-0.147304\pi$
$223$	−23.0426	−	85.9961i	−0.103330	−	0.385633i	−0.998150	+	0.0607935i	$0.980637\pi$
$224$	25.9086	−	62.5490i	0.115664	−	0.279237i
$225$	−42.4046	+	92.7684i	−0.188465	+	0.412304i
$226$	−15.1742	+	36.6337i	−0.0671424	+	0.162096i
$227$	−75.1787	−	9.89746i	−0.331184	−	0.0436012i	−0.0368991	−	0.999319i	$-0.511748\pi$
$227$	−75.1787	−	9.89746i	−0.331184	−	0.0436012i	−0.294285	+	0.955718i	$0.595081\pi$
$228$	−173.286	+	31.2334i	−0.760026	+	0.136988i
$229$	−51.0116	+	190.378i	−0.222758	+	0.831345i	0.760532	+	0.649300i	$0.224938\pi$
$229$	−51.0116	+	190.378i	−0.222758	+	0.831345i	−0.983290	+	0.182044i	$0.941729\pi$
$230$	−20.9517	−	5.61400i	−0.0910944	−	0.0244087i
$231$	36.4078	+	201.994i	0.157610	+	0.874433i
$232$	−12.1873	+	92.5718i	−0.0525315	+	0.399016i
$233$	−254.160	−	105.277i	−1.09082	−	0.451831i	−0.236525	−	0.971625i	$-0.576009\pi$
$233$	−254.160	−	105.277i	−1.09082	−	0.451831i	−0.854291	+	0.519794i	$0.826009\pi$
$234$	−5.22627	−	54.9321i	−0.0223345	−	0.234753i
$235$	−226.318	−	93.7439i	−0.963055	−	0.398910i
$236$	81.1387	−	21.7411i	0.343808	−	0.0921231i
$237$	32.7573	−	10.4652i	0.138217	−	0.0441568i
$238$	−23.2233	+	8.44923i	−0.0975768	+	0.0355010i
$239$	−288.853	+	166.769i	−1.20859	+	0.697779i	−0.962451	−	0.271456i	$-0.912495\pi$
$239$	−288.853	+	166.769i	−1.20859	+	0.697779i	−0.246137	+	0.969235i	$0.579161\pi$
$240$	7.85118	+	165.416i	0.0327132	+	0.689235i
$241$	−83.1519	+	63.8047i	−0.345029	+	0.264750i	−0.766709	−	0.641995i	$-0.778107\pi$
$241$	−83.1519	+	63.8047i	−0.345029	+	0.264750i	0.421680	+	0.906745i	$0.361440\pi$
$242$	23.2493			0.0960715
$243$	−196.374	+	143.130i	−0.808124	+	0.589013i
$244$	−218.361	+	90.4481i	−0.894923	+	0.370689i
$245$	−12.2735	+	93.2263i	−0.0500958	+	0.380516i
$246$	0.549353	+	11.5743i	0.00223314	+	0.0470501i
$247$	79.5369	−	296.836i	0.322012	−	1.20176i
$248$	13.8715	+	10.6440i	0.0559336	+	0.0429194i
$249$	−2.62887	−	3.10894i	−0.0105577	−	0.0124857i
$250$	−24.4863	−	31.9111i	−0.0979451	−	0.127645i
$251$	121.642			0.484628			0.242314	−	0.970198i	$-0.422094\pi$
$251$	121.642			0.484628			0.242314	+	0.970198i	$0.422094\pi$
$252$	50.1341	−	163.316i	0.198945	−	0.648080i
$253$	−195.264	+	195.264i	−0.771794	+	0.771794i
$254$	39.1770	+	22.6188i	0.154240	+	0.0890505i
$255$	132.827	−	133.805i	0.520891	−	0.524725i
$256$	−100.258	−	173.653i	−0.391635	−	0.678331i
$257$	73.2198	−	273.260i	0.284902	−	1.06327i	−0.664009	−	0.747725i	$-0.731146\pi$
$257$	73.2198	−	273.260i	0.284902	−	1.06327i	0.948911	−	0.315544i	$-0.102187\pi$
$258$	53.9079	+	37.4427i	0.208945	+	0.145127i
$259$	−199.381	−	115.113i	−0.769810	−	0.444450i
$260$	−273.438	−	113.262i	−1.05169	−	0.435622i
$261$	−12.7840	+	354.517i	−0.0489807	+	1.35830i
$262$	23.4790	+	56.6833i	0.0896145	+	0.216348i
$263$	4.03575	+	15.0616i	0.0153451	+	0.0572686i	0.973174	−	0.230071i	$-0.0738958\pi$
$263$	4.03575	+	15.0616i	0.0153451	+	0.0572686i	−0.957829	+	0.287340i	$0.907229\pi$
$264$	−89.0160	−	45.9104i	−0.337182	−	0.173903i
$265$	−87.7445	+	114.351i	−0.331111	+	0.431513i
$266$	−13.2827	+	17.3104i	−0.0499351	+	0.0650766i
$267$	−149.755	−	317.995i	−0.560879	−	1.19099i
$268$	−305.419	−	176.334i	−1.13962	−	0.657961i
$269$	82.1655	−	198.365i	0.305448	−	0.737416i	−0.694393	−	0.719596i	$-0.744327\pi$
$269$	82.1655	−	198.365i	0.305448	−	0.737416i	0.999841	−	0.0178207i	$-0.00567282\pi$
$270$	−4.23856	−	29.5885i	−0.0156984	−	0.109587i
$271$	215.939			0.796823			0.398412	−	0.917207i	$-0.369562\pi$
$271$	215.939			0.796823			0.398412	+	0.917207i	$0.369562\pi$
$272$	−76.3628	+	242.084i	−0.280746	+	0.890016i
$273$	220.590	+	200.599i	0.808024	+	0.734797i
$274$	14.4397	+	3.86912i	0.0526998	+	0.0141209i
$275$	−158.365	+	20.8491i	−0.575873	+	0.0758151i
$276$	218.946	−	69.9478i	0.793282	−	0.253434i
$277$	236.208	+	307.833i	0.852738	+	1.11131i	0.992635	+	0.121144i	$0.0386562\pi$
$277$	236.208	+	307.833i	0.852738	+	1.11131i	−0.139897	+	0.990166i	$0.544677\pi$
$278$	8.53736	+	20.6110i	0.0307099	+	0.0741403i
$279$	56.2961	+	35.2668i	0.201778	+	0.126404i
$280$	30.0593	+	30.0593i	0.107354	+	0.107354i
$281$	−63.5134	−	237.035i	−0.226026	−	0.843542i	−0.981991	−	0.188929i	$-0.939498\pi$
$281$	−63.5134	−	237.035i	−0.226026	−	0.843542i	0.755964	−	0.654613i	$-0.227168\pi$
$282$	−58.5857	+	10.5596i	−0.207751	+	0.0374454i
$283$	−368.948	−	283.103i	−1.30370	−	1.00037i	−0.998849	−	0.0479657i	$-0.984726\pi$
$283$	−368.948	−	283.103i	−1.30370	−	1.00037i	−0.304852	−	0.952400i	$-0.598607\pi$
$284$	−36.9233	−	280.460i	−0.130012	−	0.987536i
$285$	35.4127	−	162.655i	0.124255	−	0.570718i
$286$	68.5547	−	52.6039i	0.239702	−	0.183930i
$287$	−44.2729	−	44.2729i	−0.154261	−	0.154261i
$288$	72.7744	+	102.272i	0.252689	+	0.355111i
$289$	261.954	−	122.070i	0.906416	−	0.422387i
$290$	−37.7900	−	21.8181i	−0.130310	−	0.0752347i
$291$	−252.763	+	490.085i	−0.868602	+	1.68414i
$292$	13.0229	+	98.9185i	0.0445989	+	0.338762i
$293$	12.0454	+	20.8632i	0.0411104	+	0.0712054i	0.885848	−	0.463975i	$-0.153577\pi$
$293$	12.0454	+	20.8632i	0.0411104	+	0.0712054i	−0.844738	+	0.535180i	$0.820244\pi$
$294$	9.73565	+	20.6730i	0.0331145	+	0.0703164i
$295$	−10.3657	+	78.7355i	−0.0351381	+	0.266900i
$296$	103.794	−	42.9929i	0.350655	−	0.145246i
$297$	−353.203	−	141.613i	−1.18924	−	0.476812i
$298$	−32.8907	−	32.8907i	−0.110372	−	0.110372i
$299$	−52.3606	+	397.719i	−0.175119	+	1.33016i
$300$	125.105	+	44.9978i	0.417018	+	0.149993i
$301$	−351.622	+	46.2919i	−1.16818	+	0.153794i
$302$	7.28886	+	12.6247i	0.0241353	+	0.0418036i
$303$	−25.3277	+	302.722i	−0.0835899	+	0.999084i
$304$	58.0074	+	216.487i	0.190814	+	0.712127i
$305$		−	223.449i		−	0.732618i
$306$	9.58269	−	44.8041i	0.0313160	−	0.146419i
$307$	31.0770			0.101228			0.0506140	−	0.998718i	$-0.483882\pi$
$307$	31.0770			0.101228			0.0506140	+	0.998718i	$0.483882\pi$
$308$	258.414	−	69.2419i	0.839007	−	0.224811i
$309$	45.7383	−	65.8515i	0.148021	−	0.213112i
$310$	−7.07660	+	4.08568i	−0.0228277	+	0.0131796i
$311$	−27.3280	−	207.577i	−0.0878713	−	0.667449i	−0.977526	−	0.210815i	$-0.932388\pi$
$311$	−27.3280	−	207.577i	−0.0878713	−	0.667449i	0.889655	−	0.456634i	$-0.150945\pi$
$312$	−143.190	+	25.8089i	−0.458943	+	0.0827208i
$313$	171.441	+	22.5707i	0.547735	+	0.0721107i	0.399315	−	0.916814i	$-0.369248\pi$
$313$	171.441	+	22.5707i	0.547735	+	0.0721107i	0.148420	+	0.988924i	$0.452581\pi$
$314$	28.5899	−	28.5899i	0.0910507	−	0.0910507i
$315$	124.509	+	102.875i	0.395266	+	0.326589i
$316$	−17.1531	−	41.4113i	−0.0542820	−	0.131048i
$317$	158.386	+	20.8519i	0.499640	+	0.0657789i	0.376135	−	0.926565i	$-0.377253\pi$
$317$	158.386	+	20.8519i	0.499640	+	0.0657789i	0.123506	+	0.992344i	$0.460586\pi$
$318$	−2.92039	+	34.9051i	−0.00918361	+	0.109764i
$319$	−481.103	+	277.765i	−1.50816	+	0.870736i
$320$	203.607	−	26.8053i	0.636271	−	0.0837666i
$321$	6.59728	+	138.998i	0.0205523	+	0.433016i
$322$	14.2411	−	24.6664i	0.0442272	−	0.0766037i
$323$	137.127	−	215.186i	0.424543	−	0.666211i
$324$	207.253	+	239.516i	0.639670	+	0.739248i
$325$	−164.076	+	164.076i	−0.504851	+	0.504851i
$326$	−13.3588	−	17.4095i	−0.0409779	−	0.0534035i
$327$	−8.48314	+	9.32854i	−0.0259423	+	0.0285276i
$328$	30.2918	−	3.98800i	0.0923532	−	0.0121585i
$329$	195.817	−	255.193i	0.595188	−	0.775664i
$330$	35.7427	−	30.2235i	0.108311	−	0.0915864i
$331$	−72.4644	+	19.4168i	−0.218926	+	0.0586610i	−0.366615	−	0.930373i	$-0.619483\pi$
$331$	−72.4644	+	19.4168i	−0.218926	+	0.0586610i	0.147689	+	0.989034i	$0.452817\pi$
$332$	−3.75251	+	3.75251i	−0.0113027	+	0.0113027i
$333$	377.106	−	199.960i	1.13245	−	0.600482i
$334$	23.9490	−	9.92001i	0.0717036	−	0.0297006i
$335$	264.514	−	202.969i	0.789595	−	0.605878i
$336$	−212.476	−	46.2597i	−0.632369	−	0.137678i
$337$	16.7678	+	127.364i	0.0497560	+	0.377934i	0.998148	+	0.0608338i	$0.0193760\pi$
$337$	16.7678	+	127.364i	0.0497560	+	0.377934i	−0.948392	+	0.317101i	$0.897291\pi$
$338$	19.3906	−	72.3666i	0.0573685	−	0.214102i
$339$	388.143	+	84.5053i	1.14496	+	0.249278i
$340$	−188.235	−	157.988i	−0.553631	−	0.464672i
$341$			104.029i			0.305071i
$342$	−14.1239	−	37.9075i	−0.0412979	−	0.110841i
$343$	−333.829	−	138.277i	−0.973264	−	0.403139i
$344$	86.5330	−	149.880i	0.251550	−	0.435697i
$345$	−18.1174	+	216.542i	−0.0525141	+	0.627659i
$346$	−73.7011	−	56.5529i	−0.213009	−	0.163448i
$347$	111.754	+	85.7521i	0.322059	+	0.247124i	0.757119	−	0.653277i	$-0.226606\pi$
$347$	111.754	+	85.7521i	0.322059	+	0.247124i	−0.435060	+	0.900401i	$0.643273\pi$
$348$	461.872	−	21.9219i	1.32722	−	0.0629940i
$349$	−20.5975	+	5.51909i	−0.0590187	+	0.0158140i	−0.288208	−	0.957568i	$-0.593059\pi$
$349$	−20.5975	+	5.51909i	−0.0590187	+	0.0158140i	0.229189	+	0.973382i	$0.426393\pi$
$350$	15.2210	−	6.30476i	0.0434887	−	0.0180136i
$351$	−532.297	+	149.143i	−1.51651	+	0.424908i
$352$	−75.2221	+	181.602i	−0.213699	+	0.515916i
$353$	21.3992	−	37.0646i	0.0606211	−	0.104999i	−0.834122	−	0.551580i	$-0.814025\pi$
$353$	21.3992	−	37.0646i	0.0606211	−	0.104999i	0.894743	+	0.446581i	$0.147359\pi$
$354$	8.22237	+	17.4597i	0.0232270	+	0.0493211i
$355$	258.324	+	69.2176i	0.727672	+	0.194979i
$356$	−396.769	+	229.075i	−1.11452	+	0.643469i
$357$	124.571	+	213.947i	0.348938	+	0.599292i
$358$	−24.4731	+	42.3886i	−0.0683605	+	0.118404i
$359$	−89.1192	−	89.1192i	−0.248243	−	0.248243i	0.572006	−	0.820249i	$-0.306165\pi$
$359$	−89.1192	−	89.1192i	−0.248243	−	0.248243i	−0.820249	+	0.572006i	$0.806165\pi$
$360$	−76.8147	+	17.6420i	−0.213374	+	0.0490056i
$361$			135.710i			0.375927i
$362$	−30.9662	+	23.7612i	−0.0855419	+	0.0656386i
$363$	−41.3148	−	229.218i	−0.113815	−	0.631456i
$364$	236.587	−	308.326i	0.649963	−	0.847049i
$365$	−91.1109	−	24.4131i	−0.249619	−	0.0668852i
$366$	−29.3495	−	45.6860i	−0.0801898	−	0.124825i
$367$	375.825	+	49.4783i	1.02405	+	0.134818i	0.623796	−	0.781588i	$-0.285590\pi$
$367$	375.825	+	49.4783i	1.02405	+	0.134818i	0.400250	+	0.916406i	$0.368923\pi$
$368$	−111.960	−	270.295i	−0.304238	−	0.734496i
$369$	113.137	−	25.9841i	0.306604	−	0.0704176i
$370$			52.5040i			0.141903i
$371$	−115.218	−	150.155i	−0.310560	−	0.404729i
$372$	39.6902	−	76.9557i	0.106694	−	0.206870i
$373$	−201.186	−	348.464i	−0.539372	−	0.934220i	−0.998938	−	0.0460759i	$-0.985328\pi$
$373$	−201.186	−	348.464i	−0.539372	−	0.934220i	0.459566	−	0.888144i	$-0.348005\pi$
$374$	67.4256	−	24.5312i	0.180282	−	0.0655914i
$375$	−271.104	+	298.121i	−0.722944	+	0.794989i
$376$	40.6259	+	151.618i	0.108048	+	0.403239i
$377$	−308.828	+	745.578i	−0.819173	+	1.97766i
$378$	38.9694	+	4.67980i	0.103094	+	0.0123804i
$379$	185.848	−	448.676i	0.490364	−	1.18384i	−0.464172	−	0.885745i	$-0.653648\pi$
$379$	185.848	−	448.676i	0.490364	−	1.18384i	0.954535	−	0.298097i	$-0.0963520\pi$
$380$	−215.121	−	28.3212i	−0.566108	−	0.0745295i
$381$	153.384	−	426.446i	0.402582	−	1.11928i
$382$	−2.47014	+	9.21870i	−0.00646634	+	0.0241327i
$383$	−418.981	−	112.266i	−1.09394	−	0.293121i	−0.333648	−	0.942698i	$-0.608280\pi$
$383$	−418.981	−	112.266i	−1.09394	−	0.293121i	−0.760296	+	0.649576i	$0.774946\pi$
$384$	165.906	−	140.288i	0.432047	−	0.365333i
$385$	−33.0132	+	250.760i	−0.0857486	+	0.651325i
$386$	98.8339	+	40.9384i	0.256046	+	0.106058i
$387$	273.357	−	598.023i	0.706350	−	1.54528i
$388$	664.042	+	275.055i	1.71145	+	0.708905i
$389$	316.446	−	84.7915i	0.813486	−	0.217973i	0.171990	−	0.985099i	$-0.444980\pi$
$389$	316.446	−	84.7915i	0.813486	−	0.217973i	0.641497	+	0.767126i	$0.278314\pi$
$390$	14.4653	−	66.4409i	0.0370906	−	0.170361i
$391$	−140.806	+	301.860i	−0.360118	+	0.772020i
$392$	52.1800	−	30.1261i	0.133112	−	0.0768524i
$393$	517.126	−	332.211i	1.31584	−	0.845321i
$394$	−32.8281	+	25.1898i	−0.0833199	+	0.0639336i
$395$	42.3761			0.107281
$396$	−145.557	+	474.166i	−0.367569	+	1.19739i
$397$	408.401	−	169.165i	1.02872	−	0.426109i	0.196469	−	0.980510i	$-0.437052\pi$
$397$	408.401	−	169.165i	1.02872	−	0.426109i	0.832250	+	0.554401i	$0.187052\pi$
$398$	7.71877	−	58.6299i	0.0193939	−	0.147311i
$399$	194.270	+	100.195i	0.486891	+	0.251116i
$400$	43.7998	−	163.463i	0.109500	−	0.408658i
$401$	−127.765	−	98.0374i	−0.318615	−	0.244482i	0.437054	−	0.899435i	$-0.356022\pi$
$401$	−127.765	−	98.0374i	−0.318615	−	0.244482i	−0.755670	+	0.654953i	$0.772688\pi$
$402$	27.4227	−	76.2421i	0.0682157	−	0.189657i
$403$	91.9967	+	119.892i	0.228280	+	0.297500i
$404$	395.959			0.980098
$405$	−284.185	+	94.3683i	−0.701692	+	0.233008i
$406$	40.5163	−	40.5163i	0.0997940	−	0.0997940i
$407$	578.874	+	334.213i	1.42230	+	0.821163i
$408$	−119.834	−	15.3296i	−0.293710	−	0.0375725i
$409$	−353.106	−	611.597i	−0.863339	−	1.49535i	−0.868687	−	0.495361i	$-0.835036\pi$
$409$	−353.106	−	611.597i	−0.863339	−	1.49535i	0.00534802	−	0.999986i	$-0.498298\pi$
$410$	−3.69564	+	13.7923i	−0.00901375	+	0.0336398i
$411$	12.4863	−	149.239i	0.0303803	−	0.363112i
$412$	−90.5053	−	52.2533i	−0.219673	−	0.126828i
$413$	−96.3422	−	39.9062i	−0.233274	−	0.0966253i
$414$	24.7381	+	46.6536i	0.0597539	+	0.112690i
$415$	−1.91997	−	4.63522i	−0.00462643	−	0.0111692i
$416$	73.9048	+	275.817i	0.177656	+	0.663021i
$417$	188.036	−	120.798i	0.450925	−	0.289682i
$418$	38.5646	−	50.2583i	0.0922597	−	0.120235i
$419$	−46.1087	+	60.0900i	−0.110045	+	0.143413i	−0.845128	−	0.534563i	$-0.820476\pi$
$419$	−46.1087	+	60.0900i	−0.110045	+	0.143413i	0.735084	+	0.677976i	$0.237143\pi$
$420$	120.094	−	172.905i	0.285939	−	0.411678i
$421$	−125.977	−	72.7329i	−0.299233	−	0.172762i	0.342865	−	0.939385i	$-0.388603\pi$
$421$	−125.977	−	72.7329i	−0.299233	−	0.172762i	−0.642098	+	0.766622i	$0.721936\pi$
$422$	−31.4407	+	75.9045i	−0.0745039	+	0.179868i
$423$	208.217	+	558.841i	0.492240	+	1.32114i
$424$	92.3583			0.217826
$425$	−170.910	+	88.9423i	−0.402141	+	0.209276i
$426$	61.9081	−	19.7781i	0.145324	−	0.0464275i
$427$	283.413	+	75.9404i	0.663732	+	0.177846i
$428$	179.828	−	23.6748i	0.420159	−	0.0553150i
$429$	−640.454	−	582.413i	−1.49290	−	1.35761i
$430$	49.2374	+	64.1674i	0.114506	+	0.149227i
$431$	149.910	+	361.916i	0.347820	+	0.839711i	0.996877	+	0.0789715i	$0.0251636\pi$
$431$	149.910	+	361.916i	0.347820	+	0.839711i	−0.649057	+	0.760740i	$0.724836\pi$
$432$	281.815	−	288.305i	0.652350	−	0.667373i
$433$	−317.168	−	317.168i	−0.732489	−	0.732489i	0.238623	−	0.971112i	$-0.423304\pi$
$433$	−317.168	−	317.168i	−0.732489	−	0.732489i	−0.971112	+	0.238623i	$0.923304\pi$
$434$	−2.77709	−	10.3642i	−0.00639881	−	0.0238807i
$435$	−147.954	+	411.349i	−0.340123	+	0.945629i
$436$	13.0388	+	10.0050i	0.0299054	+	0.0229472i
$437$	38.3862	+	291.572i	0.0878403	+	0.667214i
$438$	−21.8350	+	6.97575i	−0.0498516	+	0.0159264i
$439$	−114.638	+	87.9649i	−0.261135	+	0.200376i	−0.731028	−	0.682348i	$-0.760959\pi$
$439$	−114.638	+	87.9649i	−0.261135	+	0.200376i	0.469893	+	0.882723i	$0.344292\pi$
$440$	−87.2729	−	87.2729i	−0.198347	−	0.198347i
$441$	186.518	−	132.722i	0.422943	−	0.300957i
$442$	56.0135	−	87.8988i	0.126727	−	0.198866i
$443$	−547.612	−	316.164i	−1.23614	−	0.713688i	−0.267840	−	0.963463i	$-0.586310\pi$
$443$	−547.612	−	316.164i	−1.23614	−	0.713688i	−0.968304	+	0.249775i	$0.919643\pi$
$444$	−300.711	−	468.093i	−0.677277	−	1.05426i
$445$	−56.5357	−	429.431i	−0.127047	−	0.965014i
$446$	−13.3304	−	23.0890i	−0.0298889	−	0.0517691i
$447$	−265.827	+	382.723i	−0.594691	+	0.856203i
$448$	−35.1982	+	267.357i	−0.0785674	+	0.596778i
$449$	−294.020	+	121.787i	−0.654832	+	0.271240i	−0.685262	−	0.728297i	$-0.740312\pi$
$449$	−294.020	+	121.787i	−0.654832	+	0.271240i	0.0304299	+	0.999537i	$0.490312\pi$
$450$	−5.07568	+	30.1205i	−0.0112793	+	0.0669344i
$451$	128.540	+	128.540i	0.285011	+	0.285011i
$452$	67.5829	−	513.343i	0.149520	−	1.13572i
$453$	111.516	−	94.2964i	0.246172	−	0.208160i
$454$	−22.5130	+	2.96390i	−0.0495882	+	0.00652841i
$455$	183.709	+	318.193i	0.403756	+	0.699326i
$456$	−96.5005	+	45.4455i	−0.211624	+	0.0996612i
$457$	−22.7642	−	84.9570i	−0.0498122	−	0.185901i	0.936537	−	0.350569i	$-0.114012\pi$
$457$	−22.7642	−	84.9570i	−0.0498122	−	0.185901i	−0.986349	+	0.164667i	$0.947345\pi$
$458$			59.0218i			0.128868i
$459$	−458.759	−	14.8588i	−0.999476	−	0.0323722i
$460$	283.236			0.615731
$461$	−721.822	+	193.412i	−1.56578	+	0.419548i	−0.934486	−	0.356000i	$-0.884140\pi$
$461$	−721.822	+	193.412i	−1.56578	+	0.419548i	−0.631289	+	0.775548i	$0.717474\pi$
$462$	26.1870	+	55.6063i	0.0566817	+	0.120360i
$463$	−109.502	+	63.2210i	−0.236505	+	0.136546i	−0.613569	−	0.789641i	$-0.710267\pi$
$463$	−109.502	+	63.2210i	−0.236505	+	0.136546i	0.377064	+	0.926187i	$0.376934\pi$
$464$	−76.8228	−	583.527i	−0.165566	−	1.25760i
$465$	52.8566	+	62.5089i	0.113670	+	0.134428i
$466$	−81.6771	−	10.7530i	−0.175273	−	0.0230751i
$467$	486.008	−	486.008i	1.04070	−	1.04070i	0.0415673	−	0.999136i	$-0.486765\pi$
$467$	486.008	−	486.008i	1.04070	−	1.04070i	0.999136	−	0.0415673i	$-0.0132351\pi$
$468$	251.569	+	675.194i	0.537541	+	1.44272i
$469$	167.541	+	404.480i	0.357231	+	0.862431i
$470$	−72.7296	−	9.57504i	−0.154744	−	0.0203724i
$471$	−332.678	−	231.067i	−0.706322	−	0.490589i
$472$	44.0693	−	25.4434i	0.0933671	−	0.0539055i
$473$	1020.89	−	134.402i	2.15832	−	0.284148i
$474$	8.66416	−	5.56601i	0.0182788	−	0.0117426i
$475$	−85.0554	+	147.320i	−0.179064	+	0.310148i
$476$	264.359	−	185.056i	0.555376	−	0.388773i
$477$	349.324	−	33.2349i	0.732335	−	0.0696748i
$478$	−70.6269	+	70.6269i	−0.147755	+	0.147755i
$479$	148.168	+	193.096i	0.309327	+	0.403123i	0.921985	−	0.387225i	$-0.126566\pi$
$479$	148.168	+	193.096i	0.309327	+	0.403123i	−0.612658	+	0.790348i	$0.709900\pi$
$480$	47.0718	+	147.341i	0.0980663	+	0.306960i
$481$	962.704	−	126.742i	2.00146	−	0.263498i
$482$	−19.1070	+	24.9007i	−0.0396410	+	0.0516612i
$483$	−268.497	−	96.5727i	−0.555894	−	0.199943i
$484$	−293.243	+	78.5741i	−0.605873	+	0.162343i
$485$	−480.488	+	480.488i	−0.990697	+	0.990697i
$486$	−45.7090	+	56.6215i	−0.0940515	+	0.116505i
$487$	403.701	−	167.218i	0.828955	−	0.343364i	0.0724659	−	0.997371i	$-0.476913\pi$
$487$	403.701	−	167.218i	0.828955	−	0.343364i	0.756489	+	0.654007i	$0.226913\pi$
$488$	−113.592	+	87.1622i	−0.232770	+	0.178611i
$489$	−147.904	+	162.644i	−0.302463	+	0.332605i
$490$	3.67542	+	27.9176i	0.00750086	+	0.0569747i
$491$	−217.102	+	810.235i	−0.442162	+	1.65017i	0.281159	+	0.959661i	$0.409281\pi$
$491$	−217.102	+	810.235i	−0.442162	+	1.65017i	−0.723321	+	0.690512i	$0.757385\pi$
$492$	−46.0459	−	144.130i	−0.0935893	−	0.292947i
$493$	−430.783	+	513.255i	−0.873800	+	1.04108i
$494$		−	92.0263i		−	0.186288i
$495$	−361.494	−	298.684i	−0.730291	−	0.603403i
$496$	−101.825	−	42.1774i	−0.205293	−	0.0850351i
$497$	−175.586	+	304.124i	−0.353291	+	0.611919i
$498$	−1.00138	−	0.695526i	−0.00201080	−	0.00139664i
$499$	3.56537	+	2.73581i	0.00714504	+	0.00548258i	0.612328	−	0.790604i	$-0.290233\pi$
$499$	3.56537	+	2.73581i	0.00714504	+	0.00548258i	−0.605183	+	0.796087i	$0.706900\pi$
$500$	416.692	+	319.739i	0.833385	+	0.639479i
$501$	−140.361	−	218.489i	−0.280162	−	0.436105i
$502$	35.1856	−	9.42796i	0.0700909	−	0.0187808i
$503$	70.1498	−	29.0570i	0.139463	−	0.0577674i	−0.311860	−	0.950128i	$-0.600952\pi$
$503$	70.1498	−	29.0570i	0.139463	−	0.0577674i	0.451323	+	0.892361i	$0.350952\pi$
$504$	3.72951	−	103.424i	0.00739983	−	0.205207i
$505$	−143.254	+	345.847i	−0.283672	+	0.684845i
$506$	−41.3472	+	71.6154i	−0.0817138	+	0.141532i
$507$	−747.931	−	62.5768i	−1.47521	−	0.123426i
$508$	−570.581	−	152.887i	−1.12319	−	0.300958i
$509$	−821.706	+	474.412i	−1.61435	+	0.932048i	−0.626009	+	0.779816i	$0.715313\pi$
$509$	−821.706	+	474.412i	−1.61435	+	0.932048i	−0.988345	+	0.152232i	$0.951354\pi$
$510$	28.0504	−	48.9989i	0.0550009	−	0.0960762i
$511$	61.9293	−	107.265i	0.121192	−	0.209911i
$512$	−247.302	−	247.302i	−0.483012	−	0.483012i
$513$	−348.637	+	206.612i	−0.679605	+	0.402753i
$514$		−	84.7172i		−	0.164820i
$515$	78.3840	−	60.1462i	0.152202	−	0.116789i
$516$	−806.481	−	290.075i	−1.56295	−	0.562160i
$517$	−568.527	+	740.918i	−1.09966	+	1.43311i
$518$	−66.5941	−	17.8438i	−0.128560	−	0.0344476i
$519$	−426.594	+	827.127i	−0.821954	+	1.59369i
$520$	−177.760	−	23.4025i	−0.341846	−	0.0450048i
$521$	−121.919	−	294.339i	−0.234010	−	0.564950i	0.762632	−	0.646832i	$-0.223907\pi$
$521$	−121.919	−	294.339i	−0.234010	−	0.564950i	−0.996642	+	0.0818827i	$0.973907\pi$
$522$	23.7794	+	103.537i	0.0455543	+	0.198347i
$523$		−	636.286i		−	1.21661i	−0.793704	−	0.608304i	$-0.791850\pi$
$523$		−	636.286i		−	1.21661i	0.793704	−	0.608304i	$-0.208150\pi$
$524$	−487.708	−	635.594i	−0.930741	−	1.21297i
$525$	−89.2079	−	138.863i	−0.169920	−	0.264501i
$526$	2.33473	+	4.04388i	0.00443866	+	0.00768798i
$527$	42.9015	+	117.918i	0.0814071	+	0.223753i
$528$	616.895	+	134.309i	1.16836	+	0.254372i
$529$	37.5559	+	140.161i	0.0709942	+	0.264954i
$530$	−16.5178	+	39.8775i	−0.0311656	+	0.0752405i
$531$	157.526	−	112.092i	0.296659	−	0.211096i
$532$	109.032	−	263.226i	0.204947	−	0.494786i
$533$	261.814	+	34.4685i	0.491208	+	0.0646688i
$534$	−67.9640	−	80.3751i	−0.127274	−	0.150515i
$535$	−44.3815	+	165.634i	−0.0829562	+	0.309597i
$536$	−206.362	−	55.2945i	−0.385004	−	0.103161i
$537$	461.405	+	165.958i	0.859228	+	0.309046i
$538$	8.39241	−	63.7467i	0.0155993	−	0.118488i
$539$	331.196	+	137.186i	0.614465	+	0.254520i
$540$	153.459	+	358.873i	0.284183	+	0.664580i
$541$	184.646	+	76.4830i	0.341306	+	0.141373i	0.546751	−	0.837295i	$-0.315864\pi$
$541$	184.646	+	76.4830i	0.341306	+	0.141373i	−0.205446	+	0.978669i	$0.565864\pi$
$542$	62.4618	−	16.7366i	0.115243	−	0.0308793i
$543$	289.293	+	263.076i	0.532768	+	0.484486i
$544$	−10.3722	+	236.869i	−0.0190665	+	0.435421i
$545$	−13.4561	+	7.76886i	−0.0246900	+	0.0142548i
$546$	79.3549	+	40.9276i	0.145339	+	0.0749590i
$547$	705.424	−	541.291i	1.28962	−	0.989563i	0.290154	−	0.956980i	$-0.406293\pi$
$547$	705.424	−	541.291i	1.28962	−	0.989563i	0.999469	−	0.0325826i	$-0.0103732\pi$
$548$	−195.204			−0.356212
$549$	−398.270	+	370.546i	−0.725446	+	0.674948i
$550$	−44.1922	+	18.3050i	−0.0803494	+	0.0332818i
$551$	−77.2228	+	586.566i	−0.140150	+	1.06455i
$552$	117.148	−	75.2581i	0.212225	−	0.136337i
$553$	−14.4018	+	53.7482i	−0.0260430	+	0.0971939i
$554$	92.1837	+	70.7351i	0.166397	+	0.127681i
$555$	517.645	−	93.3014i	0.932694	−	0.168111i
$556$	−177.339	−	231.113i	−0.318955	−	0.415670i
$557$	511.810			0.918868			0.459434	−	0.888212i	$-0.348052\pi$
$557$	511.810			0.918868			0.459434	+	0.888212i	$0.348052\pi$
$558$	19.0174	+	5.83787i	0.0340814	+	0.0104621i
$559$	1057.70	−	1057.70i	1.89214	−	1.89214i
$560$	−232.063	−	133.982i	−0.414398	−	0.239253i
$561$	−361.674	−	621.166i	−0.644695	−	1.10725i
$562$	−36.7433	−	63.6413i	−0.0653796	−	0.113241i
$563$	150.404	−	561.314i	0.267147	−	0.997005i	−0.693777	−	0.720190i	$-0.744055\pi$
$563$	150.404	−	561.314i	0.267147	−	0.997005i	0.960923	−	0.276815i	$-0.0892788\pi$
$564$	703.252	−	331.186i	1.24690	−	0.587209i
$565$	423.923	+	244.752i	0.750307	+	0.433190i
$566$	−128.663	−	53.2938i	−0.227319	−	0.0941587i
$567$	−23.1110	−	392.521i	−0.0407601	−	0.692277i
$568$	−65.5788	−	158.321i	−0.115456	−	0.278735i
$569$	183.339	+	684.230i	0.322213	+	1.20251i	0.917084	+	0.398693i	$0.130536\pi$
$569$	183.339	+	684.230i	0.322213	+	1.20251i	−0.594872	+	0.803821i	$0.702797\pi$
$570$	−2.36336	−	49.7936i	−0.00414625	−	0.0873572i
$571$	467.565	−	609.343i	0.818854	−	1.06715i	−0.177691	−	0.984086i	$-0.556863\pi$
$571$	467.565	−	609.343i	0.818854	−	1.06715i	0.996544	−	0.0830645i	$-0.0264707\pi$
$572$	−686.896	+	895.181i	−1.20087	+	1.56500i
$573$	95.2780	+	7.97159i	0.166279	+	0.0139120i
$574$	−16.2376	−	9.37480i	−0.0282886	−	0.0163324i
$575$	84.9779	−	205.155i	0.147788	−	0.356791i
$576$	−385.420	−	318.453i	−0.669131	−	0.552870i
$577$	−615.561			−1.06683			−0.533415	−	0.845853i	$-0.679092\pi$
$577$	−615.561			−1.06683			−0.533415	+	0.845853i	$0.679092\pi$
$578$	66.3108	−	55.6125i	0.114725	−	0.0962155i
$579$	227.986	−	1047.17i	0.393759	−	1.80858i
$580$	550.381	+	147.474i	0.948932	+	0.254266i
$581$	6.53164	−	0.859907i	0.0112421	−	0.00148005i
$582$	−35.1289	+	161.351i	−0.0603589	+	0.277235i
$583$	334.518	+	435.953i	0.573788	+	0.747775i
$584$	23.1297	+	55.8400i	0.0396056	+	0.0956164i
$585$	−680.756	−	24.5482i	−1.16369	−	0.0419628i
$586$	5.10122	+	5.10122i	0.00870516	+	0.00870516i
$587$	−158.679	−	592.196i	−0.270321	−	1.00885i	−0.958912	−	0.283702i	$-0.908437\pi$
$587$	−158.679	−	592.196i	−0.270321	−	1.00885i	0.688591	−	0.725150i	$-0.258229\pi$
$588$	−192.663	−	227.845i	−0.327658	−	0.387492i
$589$	87.8946	+	67.4439i	0.149227	+	0.114506i
$590$	3.10412	+	23.5782i	0.00526123	+	0.0399630i
$591$	306.687	+	278.894i	0.518929	+	0.471901i
$592$	−561.831	+	431.108i	−0.949039	+	0.728223i
$593$	−764.340	−	764.340i	−1.28894	−	1.28894i	−0.935433	−	0.353505i	$-0.884990\pi$
$593$	−764.340	−	764.340i	−1.28894	−	1.28894i	−0.353505	−	0.935433i	$-0.615010\pi$
$594$	−113.142	−	13.5871i	−0.190475	−	0.0228740i
$595$	65.9926	+	297.853i	0.110912	+	0.500594i
$596$	526.008	+	303.691i	0.882564	+	0.509549i
$597$	−591.757	+	28.0867i	−0.991218	+	0.0470463i
$598$	15.6799	+	119.101i	0.0262206	+	0.199165i
$599$	326.880	+	566.173i	0.545710	+	0.945197i	0.998562	+	0.0536112i	$0.0170732\pi$
$599$	326.880	+	566.173i	0.545710	+	0.945197i	−0.452852	+	0.891586i	$0.649594\pi$
$600$	80.2602	+	6.71510i	0.133767	+	0.0111918i
$601$	6.81500	−	51.7651i	0.0113394	−	0.0861316i	−0.984839	−	0.173469i	$-0.944502\pi$
$601$	6.81500	−	51.7651i	0.0113394	−	0.0861316i	0.996179	+	0.0873372i	$0.0278358\pi$
$602$	−98.1211	+	40.6431i	−0.162992	+	0.0675134i
$603$	−800.414	−	134.880i	−1.32739	−	0.223682i
$604$	−134.601	−	134.601i	−0.222849	−	0.222849i
$605$	37.4627	−	284.557i	0.0619217	−	0.470342i
$606$	16.1366	+	89.5275i	0.0266281	+	0.147735i
$607$	−416.355	+	54.8142i	−0.685922	+	0.0903034i	−0.465429	−	0.885085i	$-0.654100\pi$
$607$	−416.355	+	54.8142i	−0.685922	+	0.0903034i	−0.220493	+	0.975389i	$0.570767\pi$
$608$	104.669	+	181.292i	0.172153	+	0.298177i
$609$	−471.456	−	327.458i	−0.774147	−	0.537698i
$610$	−17.3186	−	64.6339i	−0.0283912	−	0.105957i
$611$			1356.67i			2.22041i
$612$	30.5554	+	597.499i	0.0499271	+	0.976305i
$613$	−1015.02			−1.65583			−0.827914	−	0.560855i	$-0.810472\pi$
$613$	−1015.02			−1.65583			−0.827914	+	0.560855i	$0.810472\pi$
$614$	8.98923	−	2.40866i	0.0146404	−	0.00392289i
$615$	142.548	+	11.9265i	0.231785	+	0.0193926i
$616$	140.354	−	81.0333i	0.227847	−	0.131548i
$617$	−104.337	−	792.520i	−0.169104	−	1.28447i	−0.839863	−	0.542798i	$-0.817365\pi$
$617$	−104.337	−	792.520i	−0.169104	−	1.28447i	0.670759	−	0.741675i	$-0.265968\pi$
$618$	8.12622	−	22.5930i	0.0131492	−	0.0365582i
$619$	712.350	+	93.7826i	1.15081	+	0.151507i	0.681698	−	0.731634i	$-0.261242\pi$
$619$	712.350	+	93.7826i	1.15081	+	0.151507i	0.469109	+	0.883140i	$0.344575\pi$
$620$	75.4488	−	75.4488i	0.121692	−	0.121692i
$621$	416.005	−	326.802i	0.669895	−	0.526251i
$622$	−23.9932	−	57.9248i	−0.0385743	−	0.0931267i
$623$	563.888	+	74.2373i	0.905117	+	0.119161i
$624$	829.739	−	390.753i	1.32971	−	0.626207i
$625$	−184.653	+	106.610i	−0.295445	+	0.170575i
$626$	51.3398	−	6.75902i	0.0820125	−	0.0107972i
$627$	−564.035	−	290.903i	−0.899577	−	0.463960i
$628$	−263.980	+	457.227i	−0.420351	+	0.728069i
$629$	793.988	+	140.106i	1.26230	+	0.222744i
$630$	43.9885	+	20.1072i	0.0698230	+	0.0319162i
$631$	94.3715	−	94.3715i	0.149559	−	0.149559i	−0.628362	−	0.777921i	$-0.716274\pi$
$631$	94.3715	−	94.3715i	0.149559	−	0.149559i	0.777921	+	0.628362i	$0.216274\pi$
$632$	−16.5300	−	21.5423i	−0.0261550	−	0.0340858i
$633$	804.225	+	175.094i	1.27050	+	0.276609i
$634$	47.4303	−	6.24432i	0.0748112	−	0.00984909i
$635$	339.968	−	443.055i	0.535383	−	0.697724i
$636$	−81.1316	−	450.126i	−0.127565	−	0.707745i
$637$	503.019	−	134.784i	0.789669	−	0.211591i
$638$	−117.634	+	117.634i	−0.184379	+	0.184379i
$639$	−305.008	−	575.215i	−0.477321	−	0.900180i
$640$	247.355	−	102.458i	0.386492	−	0.160090i
$641$	−443.616	+	340.399i	−0.692069	+	0.531043i	−0.893838	−	0.448390i	$-0.851998\pi$
$641$	−443.616	+	340.399i	−0.692069	+	0.531043i	0.201769	+	0.979433i	$0.435331\pi$
$642$	12.6815	+	39.6948i	0.0197531	+	0.0618298i
$643$	59.2783	+	450.264i	0.0921902	+	0.700254i	0.973659	+	0.228011i	$0.0732223\pi$
$643$	59.2783	+	450.264i	0.0921902	+	0.700254i	−0.881468	+	0.472243i	$0.843444\pi$
$644$	−96.2597	+	359.246i	−0.149472	+	0.557836i
$645$	545.140	−	599.467i	0.845178	−	0.929406i
$646$	22.9867	−	72.8722i	0.0355832	−	0.112805i
$647$			1012.77i			1.56533i	0.622441	+	0.782666i	$0.286141\pi$
$647$			1012.77i			1.56533i	−0.622441	+	0.782666i	$0.713859\pi$
$648$	158.827	+	107.657i	0.245103	+	0.166137i
$649$	279.716	+	115.862i	0.430996	+	0.178524i
$650$	−34.7433	+	60.1771i	−0.0534512	+	0.0925801i
$651$	−97.2475	+	45.7973i	−0.149382	+	0.0703491i
$652$	227.332	+	174.438i	0.348669	+	0.267543i
$653$	−306.286	−	235.022i	−0.469045	−	0.359911i	0.347033	−	0.937853i	$-0.387189\pi$
$653$	−306.286	−	235.022i	−0.469045	−	0.359911i	−0.816078	+	0.577942i	$0.803856\pi$
$654$	−1.73079	+	3.35583i	−0.00264646	+	0.00513125i
$655$	731.601	−	196.032i	1.11695	−	0.299285i
$656$	−177.932	+	73.7019i	−0.271238	+	0.112351i
$657$	107.577	+	202.879i	0.163739	+	0.308796i
$658$	36.8622	−	88.9933i	0.0560216	−	0.135248i
$659$	−372.958	+	645.982i	−0.565945	+	0.980246i	0.431016	+	0.902344i	$0.358155\pi$
$659$	−372.958	+	645.982i	−0.565945	+	0.980246i	−0.996961	+	0.0779013i	$0.975178\pi$
$660$	−348.677	+	502.005i	−0.528298	+	0.760614i
$661$	139.826	+	37.4662i	0.211537	+	0.0566812i	0.363031	−	0.931777i	$-0.381742\pi$
$661$	139.826	+	37.4662i	0.211537	+	0.0566812i	−0.151494	+	0.988458i	$0.548409\pi$
$662$	−19.4559	+	11.2329i	−0.0293895	+	0.0169681i
$663$	−966.146	−	396.046i	−1.45723	−	0.597355i
$664$	−1.60742	+	2.78412i	−0.00242081	+	0.00419296i
$665$	190.465	+	190.465i	0.286414	+	0.286414i
$666$	93.5821	−	87.0678i	0.140514	−	0.130732i
$667$		−	772.294i		−	1.15786i
$668$	−268.542	+	206.060i	−0.402009	+	0.308472i
$669$	−203.949	+	172.457i	−0.304857	+	0.257783i
$670$	60.7812	−	79.2116i	0.0907182	−	0.118226i
$671$	−822.851	−	220.482i	−1.22631	−	0.328588i
$672$	−202.879	+	9.62928i	−0.301904	+	0.0143293i
$673$	143.458	+	18.8866i	0.213162	+	0.0280633i	0.236351	−	0.971668i	$-0.424049\pi$
$673$	143.458	+	18.8866i	0.213162	+	0.0280633i	−0.0231887	+	0.999731i	$0.507382\pi$
$674$	14.7217	+	35.5412i	0.0218422	+	0.0527318i
$675$	305.982	−	3.48311i	0.453307	−	0.00516016i
$676$			978.290i			1.44717i
$677$	15.1454	+	19.7379i	0.0223714	+	0.0291549i	0.804405	−	0.594081i	$-0.202484\pi$
$677$	15.1454	+	19.7379i	0.0223714	+	0.0291549i	−0.782034	+	0.623236i	$0.785818\pi$
$678$	118.822	−	5.63969i	0.175254	−	0.00831812i
$679$	−446.135	−	772.729i	−0.657048	−	1.13804i
$680$	−134.916	−	62.9332i	−0.198406	−	0.0925488i
$681$	69.2279	+	216.693i	0.101656	+	0.318198i
$682$	8.06288	+	30.0911i	0.0118224	+	0.0441218i
$683$	440.862	−	1064.33i	0.645478	−	1.55832i	−0.173709	−	0.984797i	$-0.555575\pi$
$683$	440.862	−	1064.33i	0.645478	−	1.55832i	0.819187	−	0.573526i	$-0.194425\pi$
$684$	306.258	+	430.393i	0.447745	+	0.629229i
$685$	70.6230	−	170.499i	0.103099	−	0.248904i
$686$	−107.280	−	14.1236i	−0.156384	−	0.0205884i
$687$	581.905	−	104.884i	0.847023	−	0.152669i
$688$	−282.352	+	1053.75i	−0.410395	+	1.53161i
$689$	771.058	+	206.604i	1.11910	+	0.299861i
$690$	11.5428	+	64.0405i	0.0167287	+	0.0928123i
$691$	109.550	−	832.116i	0.158539	−	1.20422i	−0.708402	−	0.705809i	$-0.750584\pi$
$691$	109.550	−	832.116i	0.158539	−	1.20422i	0.866941	−	0.498411i	$-0.166083\pi$
$692$	1120.72	+	464.217i	1.61953	+	0.670833i
$693$	501.696	−	356.995i	0.723948	−	0.515145i
$694$	38.9720	+	16.1427i	0.0561556	+	0.0232604i
$695$	266.023	−	71.2805i	0.382766	−	0.102562i
$696$	266.826	−	85.2443i	0.383370	−	0.122477i
$697$	198.711	+	92.6914i	0.285095	+	0.132986i
$698$	−5.53021	+	3.19287i	−0.00792293	+	0.00457431i
$699$	39.1274	+	824.375i	0.0559763	+	1.17936i
$700$	−170.675	+	130.963i	−0.243821	+	0.187090i
$701$	−277.761			−0.396236			−0.198118	−	0.980178i	$-0.563483\pi$
$701$	−277.761			−0.396236			−0.198118	+	0.980178i	$0.563483\pi$
$702$	−142.411	+	84.3967i	−0.202864	+	0.120223i
$703$	657.673	−	272.417i	0.935523	−	0.387506i
$704$	102.193	−	776.233i	0.145161	−	1.10260i
$705$	34.8411	+	734.068i	0.0494201	+	1.04123i
$706$	3.31714	−	12.3797i	0.00469850	−	0.0175350i
$707$	−389.973	−	299.236i	−0.551588	−	0.423248i
$708$	−162.716	−	192.430i	−0.229824	−	0.271793i
$709$	386.219	+	503.330i	0.544737	+	0.709916i	0.981886	−	0.189474i	$-0.0606782\pi$
$709$	386.219	+	503.330i	0.544737	+	0.709916i	−0.437148	+	0.899389i	$0.644012\pi$
$710$	80.0866			0.112798
$711$	−70.2726	−	75.5303i	−0.0988363	−	0.106231i
$712$	−196.252	+	196.252i	−0.275634	+	0.275634i
$713$	−125.245	−	72.3104i	−0.175659	−	0.101417i
$714$	52.6151	+	52.2307i	0.0736906	+	0.0731522i
$715$	−533.374	−	923.830i	−0.745977	−	1.29207i
$716$	165.420	−	617.356i	0.231034	−	0.862229i
$717$	821.827	+	570.815i	1.14620	+	0.796116i
$718$	−32.6856	−	18.8710i	−0.0455231	−	0.0262828i
$719$	−837.800	−	347.028i	−1.16523	−	0.482654i	−0.285616	−	0.958344i	$-0.592198\pi$
$719$	−837.800	−	347.028i	−1.16523	−	0.482654i	−0.879613	+	0.475690i	$0.842198\pi$
$720$	438.921	−	232.738i	0.609612	−	0.323247i
$721$	49.6478	+	119.860i	0.0688596	+	0.166242i
$722$	10.5183	+	39.2549i	0.0145683	+	0.0543696i
$723$	279.453	+	144.129i	0.386519	+	0.199349i
$724$	310.271	−	404.353i	0.428551	−	0.558499i
$725$	271.947	−	354.408i	0.375099	−	0.488839i
$726$	−29.7164	−	63.1008i	−0.0409316	−	0.0869157i
$727$	−1066.98	−	616.023i	−1.46765	−	0.847349i	−0.468308	−	0.883566i	$-0.655136\pi$
$727$	−1066.98	−	616.023i	−1.46765	−	0.847349i	−0.999344	+	0.0362166i	$0.988469\pi$
$728$	90.0956	−	217.510i	0.123758	−	0.298778i
$729$	639.466	+	350.034i	0.877183	+	0.480156i
$730$	−28.2466			−0.0386940
$731$	1101.76	−	573.359i	1.50719	−	0.784349i
$732$	524.586	+	477.045i	0.716647	+	0.651701i
$733$	570.609	+	152.894i	0.778456	+	0.208587i	0.626104	−	0.779739i	$-0.284648\pi$
$733$	570.609	+	152.894i	0.778456	+	0.208587i	0.152352	+	0.988326i	$0.451315\pi$
$734$	112.545	−	14.8168i	0.153331	−	0.0201864i
$735$	268.712	−	85.8470i	0.365595	−	0.116799i
$736$	−166.352	−	216.795i	−0.226022	−	0.294558i
$737$	−486.432	−	1174.35i	−0.660017	−	1.59342i
$738$	30.7116	−	16.2849i	0.0416147	−	0.0220662i
$739$	−83.5804	−	83.5804i	−0.113099	−	0.113099i	0.648292	−	0.761392i	$-0.275483\pi$
$739$	−83.5804	−	83.5804i	−0.113099	−	0.113099i	−0.761392	+	0.648292i	$0.775483\pi$
$740$	−177.444	−	662.232i	−0.239790	−	0.894908i
$741$	−907.301	+	163.534i	−1.22443	+	0.220693i
$742$	−44.9653	−	34.5031i	−0.0606002	−	0.0465002i
$743$	79.9472	+	607.259i	0.107601	+	0.817307i	0.957108	+	0.289731i	$0.0935658\pi$
$743$	79.9472	+	607.259i	0.107601	+	0.817307i	−0.849508	+	0.527576i	$0.823101\pi$
$744$	11.1587	−	51.2534i	0.0149983	−	0.0688890i
$745$	−455.561	+	349.564i	−0.611491	+	0.469213i
$746$	−85.2023	−	85.2023i	−0.114212	−	0.114212i
$747$	−5.07781	+	11.1087i	−0.00679761	+	0.0148711i
$748$	−767.530	+	537.284i	−1.02611	+	0.718295i
$749$	−195.001	−	112.584i	−0.260348	−	0.150312i
$750$	−55.3124	+	107.246i	−0.0737498	+	0.142994i
$751$	26.0715	+	198.033i	0.0347157	+	0.263692i	0.999997	+	0.00247903i	$0.000789099\pi$
$751$	26.0715	+	198.033i	0.0347157	+	0.263692i	−0.965281	+	0.261213i	$0.915878\pi$
$752$	−494.720	−	856.879i	−0.657872	−	1.13947i
$753$	−155.478	−	330.147i	−0.206478	−	0.438442i
$754$	−31.5438	+	239.599i	−0.0418353	+	0.317771i
$755$	166.263	−	68.8684i	0.220216	−	0.0912165i
$756$	−507.335	+	72.6760i	−0.671078	+	0.0961323i
$757$	−47.6215	−	47.6215i	−0.0629081	−	0.0629081i	0.674953	−	0.737861i	$-0.264164\pi$
$757$	−47.6215	−	47.6215i	−0.0629081	−	0.0629081i	−0.737861	+	0.674953i	$0.764164\pi$
$758$	18.9826	−	144.187i	0.0250430	−	0.190220i
$759$	779.543	+	280.385i	1.02707	+	0.369414i
$760$	−130.318	+	17.1567i	−0.171471	+	0.0225746i
$761$	534.984	+	926.619i	0.703001	+	1.21763i	0.967408	+	0.253222i	$0.0814903\pi$
$761$	534.984	+	926.619i	0.703001	+	1.21763i	−0.264408	+	0.964411i	$0.585176\pi$
$762$	11.3151	−	135.240i	0.0148492	−	0.177481i
$763$	−5.28059	−	19.7074i	−0.00692083	−	0.0258289i
$764$		−	124.623i		−	0.163119i
$765$	−532.934	−	189.481i	−0.696645	−	0.247688i
$766$	−129.894			−0.169575
$767$	424.831	−	113.833i	0.553887	−	0.148414i
$768$	−343.163	+	494.067i	−0.446827	+	0.643317i
$769$	−72.4576	+	41.8334i	−0.0942231	+	0.0543997i	−0.546371	−	0.837543i	$-0.683991\pi$
$769$	−72.4576	+	41.8334i	−0.0942231	+	0.0543997i	0.452148	+	0.891943i	$0.350658\pi$
$770$	9.88615	+	75.0927i	0.0128392	+	0.0975230i
$771$	−835.240	+	150.545i	−1.08332	+	0.195260i
$772$	−1384.95	−	182.331i	−1.79397	−	0.236181i
$773$	843.735	−	843.735i	1.09151	−	1.09151i	0.0961392	−	0.995368i	$-0.469351\pi$
$773$	843.735	−	843.735i	1.09151	−	1.09151i	0.995368	−	0.0961392i	$-0.0306494\pi$
$774$	32.7200	−	194.169i	0.0422738	−	0.250864i
$775$	−32.0128	−	77.2858i	−0.0413069	−	0.0997236i
$776$	431.688	+	56.8327i	0.556298	+	0.0732381i
$777$	−57.5852	+	688.270i	−0.0741123	+	0.885805i
$778$	84.9623	−	49.0530i	0.109206	−	0.0630501i
$779$	191.939	−	25.2693i	0.246392	−	0.0324381i
$780$	42.0952	+	886.904i	0.0539682	+	1.13706i
$781$	509.789	−	882.981i	0.652739	−	1.13058i
$782$	−17.3332	+	98.2282i	−0.0221652	+	0.125612i
$783$	978.532	−	418.433i	1.24972	−	0.534397i
$784$	−268.560	+	268.560i	−0.342550	+	0.342550i
$785$	−303.855	−	395.991i	−0.387076	−	0.504447i
$786$	123.834	−	136.175i	0.157549	−	0.173250i
$787$	−180.220	+	23.7265i	−0.228997	+	0.0301480i	−0.244151	−	0.969737i	$-0.578509\pi$
$787$	−180.220	+	23.7265i	−0.228997	+	0.0301480i	0.0151545	+	0.999885i	$0.495176\pi$
$788$	328.927	−	428.665i	0.417419	−	0.543992i
$789$	35.7203	−	30.2046i	0.0452729	−	0.0382821i
$790$	12.2576	−	3.28440i	0.0155159	−	0.00415747i
$791$	−454.507	+	454.507i	−0.574599	+	0.574599i
$792$	−10.8281	+	300.279i	−0.0136719	+	0.379140i
$793$	−1143.31	+	473.574i	−1.44175	+	0.597193i
$794$	105.021	−	80.5858i	0.132269	−	0.101493i
$795$	422.511	+	91.9878i	0.531460	+	0.115708i
$796$	100.791	+	765.583i	0.126622	+	0.961788i
$797$	264.997	−	988.980i	0.332493	−	1.24088i	−0.574070	−	0.818806i	$-0.694636\pi$
$797$	264.997	−	988.980i	0.332493	−	1.24088i	0.906562	−	0.422072i	$-0.138697\pi$
$798$	63.9595	+	13.9251i	0.0801497	+	0.0174500i
$799$	−338.875	+	1074.30i	−0.424124	+	1.34455i
$800$		−	158.065i		−	0.197581i
$801$	−671.656	+	812.897i	−0.838522	+	1.01485i
$802$	−44.5553	−	18.4554i	−0.0555552	−	0.0230117i
$803$	−179.803	+	311.428i	−0.223914	+	0.387831i
$804$	−88.2112	+	1054.32i	−0.109715	+	1.31134i
$805$	−278.954	−	214.049i	−0.346527	−	0.265899i
$806$	35.9030	+	27.5494i	0.0445447	+	0.0341804i
$807$	−643.402	+	30.5379i	−0.797276	+	0.0378412i
$808$	231.694	−	62.0823i	0.286750	−	0.0768345i
$809$	−1135.92	+	470.515i	−1.40411	+	0.581601i	−0.950815	−	0.309761i	$-0.899751\pi$
$809$	−1135.92	+	470.515i	−1.40411	+	0.581601i	−0.453293	+	0.891361i	$0.649751\pi$
$810$	−74.8883	+	49.3227i	−0.0924547	+	0.0608922i
$811$	−391.773	+	945.824i	−0.483074	+	1.16624i	0.475068	+	0.879949i	$0.342424\pi$
$811$	−391.773	+	945.824i	−0.483074	+	1.16624i	−0.958142	+	0.286295i	$0.907576\pi$
$812$	−374.101	+	647.962i	−0.460715	+	0.797982i
$813$	−276.005	−	586.079i	−0.339490	−	0.720884i
$814$	193.347	+	51.8071i	0.237527	+	0.0636451i
$815$	−234.608	+	135.451i	−0.287862	+	0.166197i
$816$	754.644	−	102.167i	0.924808	−	0.125205i
$817$	548.302	−	949.687i	0.671116	−	1.16241i
$818$	−149.541	−	149.541i	−0.182812	−	0.182812i
$819$	262.495	−	855.102i	0.320507	−	1.04408i
$820$		−	186.452i		−	0.227380i
$821$	−154.895	+	118.855i	−0.188666	+	0.144769i	−0.698776	−	0.715341i	$-0.746272\pi$
$821$	−154.895	+	118.855i	−0.188666	+	0.144769i	0.510110	+	0.860109i	$0.329605\pi$
$822$	−7.95518	−	44.1361i	−0.00967784	−	0.0536936i
$823$	−771.088	+	1004.90i	−0.936923	+	1.22102i	0.0381803	+	0.999271i	$0.487844\pi$
$823$	−771.088	+	1004.90i	−0.936923	+	1.22102i	−0.975103	+	0.221751i	$0.928823\pi$
$824$	−61.1516	−	16.3855i	−0.0742132	−	0.0198854i
$825$	259.003	+	403.169i	0.313943	+	0.488689i
$826$	−30.9606	−	4.07604i	−0.0374825	−	0.00493467i
$827$	59.4069	+	143.421i	0.0718342	+	0.173423i	0.955718	−	0.294283i	$-0.0950807\pi$
$827$	59.4069	+	143.421i	0.0718342	+	0.173423i	−0.883884	+	0.467706i	$0.845081\pi$
$828$	−469.693	−	504.835i	−0.567262	−	0.609704i
$829$			1294.44i			1.56145i	0.624877	+	0.780723i	$0.285149\pi$
$829$			1294.44i			1.56145i	−0.624877	+	0.780723i	$0.714851\pi$
$830$	−0.914621	−	1.19196i	−0.00110195	−	0.00143609i
$831$	533.574	−	1034.55i	0.642087	−	1.24495i
$832$	−568.675	−	984.974i	−0.683504	−	1.18386i
$833$	431.989	+	18.9162i	0.518594	+	0.0227086i
$834$	45.0281	−	49.5154i	0.0539905	−	0.0593710i
$835$	−82.8246	−	309.106i	−0.0991912	−	0.370186i
$836$	−316.559	+	764.240i	−0.378659	+	0.914163i
$837$	23.7620	−	197.869i	0.0283895	−	0.236403i
$838$	−8.67990	+	20.9551i	−0.0103579	+	0.0250061i
$839$	1340.78	+	176.516i	1.59806	+	0.210389i	0.876305	−	0.481756i	$-0.160001\pi$
$839$	1340.78	+	176.516i	1.59806	+	0.210389i	0.721758	+	0.692145i	$0.243334\pi$
$840$	43.1630	−	120.004i	0.0513845	−	0.142862i
$841$	184.447	−	688.367i	0.219319	−	0.818510i
$842$	−42.0769	−	11.2745i	−0.0499726	−	0.0133901i
$843$	−562.155	+	475.351i	−0.666851	+	0.563880i
$844$	140.031	−	1063.64i	0.165913	−	1.26023i
$845$	−854.477	−	353.936i	−1.01122	−	0.418859i
$846$	103.542	+	145.510i	0.122390	+	0.171998i
$847$	348.189	+	144.225i	0.411085	+	0.170277i
$848$	−562.344	+	150.680i	−0.663142	+	0.177688i
$849$	−296.794	+	1363.21i	−0.349581	+	1.60567i
$850$	−42.5432	+	38.9737i	−0.0500508	+	0.0458514i
$851$	−804.748	+	464.622i	−0.945650	+	0.545971i
$852$	−714.001	+	458.687i	−0.838030	+	0.538365i
$853$	409.096	−	313.911i	0.479597	−	0.368008i	−0.340488	−	0.940249i	$-0.610592\pi$
$853$	409.096	−	313.911i	0.479597	−	0.368008i	0.820086	+	0.572241i	$0.193926\pi$
$854$	87.8650			0.102886
$855$	−486.723	+	111.786i	−0.569267	+	0.130743i
$856$	101.514	−	42.0484i	0.118591	−	0.0491219i
$857$	−5.68096	+	43.1512i	−0.00662890	+	0.0503515i	−0.994440	−	0.105308i	$-0.966417\pi$
$857$	−5.68096	+	43.1512i	−0.00662890	+	0.0503515i	0.987811	+	0.155660i	$0.0497504\pi$
$858$	−230.396	−	118.828i	−0.268527	−	0.138494i
$859$	250.168	−	933.639i	0.291231	−	1.08689i	−0.652933	−	0.757416i	$-0.726462\pi$
$859$	250.168	−	933.639i	0.291231	−	1.08689i	0.944164	−	0.329475i	$-0.106872\pi$
$860$	−837.892	−	642.937i	−0.974293	−	0.747601i
$861$	−63.5728	+	176.749i	−0.0738360	+	0.205283i
$862$	71.4132	+	93.0675i	0.0828459	+	0.107967i
$863$	128.812			0.149261			0.0746304	−	0.997211i	$-0.476222\pi$
$863$	128.812			0.149261			0.0746304	+	0.997211i	$0.476222\pi$
$864$	184.558	−	328.236i	0.213609	−	0.379903i
$865$	−810.930	+	810.930i	−0.937492	+	0.937492i
$866$	−116.325	−	67.1604i	−0.134325	−	0.0775524i
$867$	−666.129	−	554.943i	−0.768315	−	0.640072i
$868$	70.0545	+	121.338i	0.0807080	+	0.139790i
$869$	41.8136	−	156.050i	0.0481169	−	0.179575i
$870$	−10.9145	+	130.453i	−0.0125454	+	0.149945i
$871$	−1599.13	−	923.259i	−1.83597	−	1.06000i
$872$	9.19827	+	3.81005i	0.0105485	+	0.00436932i
$873$	1653.21	+	59.6151i	1.89371	+	0.0682877i
$874$	33.7021	+	81.3640i	0.0385607	+	0.0930938i
$875$	−168.757	−	629.810i	−0.192865	−	0.719783i
$876$	251.829	−	161.779i	0.287476	−	0.184679i
$877$	−790.651	+	1030.40i	−0.901541	+	1.17491i	0.0824329	+	0.996597i	$0.473731\pi$
$877$	−790.651	+	1030.40i	−0.901541	+	1.17491i	−0.983974	+	0.178314i	$0.942936\pi$
$878$	−26.3420	+	34.3296i	−0.0300023	+	0.0390997i
$879$	41.2287	−	59.3588i	0.0469041	−	0.0675299i
$880$	673.763	+	388.997i	0.765640	+	0.442042i
$881$	56.1817	−	135.635i	0.0637703	−	0.153955i	−0.888782	−	0.458330i	$-0.848448\pi$
$881$	56.1817	−	135.635i	0.0637703	−	0.153955i	0.952552	+	0.304375i	$0.0984477\pi$
$882$	43.6648	−	52.8469i	0.0495065	−	0.0599172i
$883$	−1041.43			−1.17943			−0.589714	−	0.807612i	$-0.700760\pi$
$883$	−1041.43			−1.17943			−0.589714	+	0.807612i	$0.700760\pi$
$884$	−409.430	+	1297.97i	−0.463156	+	1.46829i
$885$	226.945	−	72.5032i	0.256435	−	0.0819245i
$886$	−182.905	−	49.0092i	−0.206439	−	0.0553151i
$887$	806.927	−	106.234i	0.909726	−	0.119768i	0.338885	−	0.940828i	$-0.389950\pi$
$887$	806.927	−	106.234i	0.909726	−	0.119768i	0.570842	+	0.821060i	$0.306617\pi$
$888$	−249.352	−	226.755i	−0.280802	−	0.255354i
$889$	446.413	+	581.777i	0.502152	+	0.654418i
$890$	−49.6368	−	119.834i	−0.0557717	−	0.134645i
$891$	67.0995	+	1139.63i	0.0753081	+	1.27905i
$892$	246.169	+	246.169i	0.275974	+	0.275974i
$893$	257.419	+	960.702i	0.288263	+	1.07581i
$894$	−47.2288	+	131.308i	−0.0528287	+	0.146877i
$895$	479.376	+	367.838i	0.535615	+	0.410992i
$896$	45.8883	+	348.556i	0.0512146	+	0.389014i
$897$	1146.37	−	366.237i	1.27800	−	0.408291i
$898$	−75.6079	+	58.0160i	−0.0841958	+	0.0646057i
$899$	−205.724	−	205.724i	−0.228837	−	0.228837i
$900$	−37.7767	−	397.062i	−0.0419742	−	0.441180i
$901$	558.966	+	356.201i	0.620384	+	0.395339i
$902$	47.1437	+	27.2184i	0.0522658	+	0.0301757i
$903$	575.071	+	895.167i	0.636845	+	0.991325i
$904$	−40.9409	−	310.977i	−0.0452887	−	0.344002i
$905$	240.925	+	417.294i	0.266215	+	0.461099i
$906$	24.9482	−	35.9190i	0.0275366	−	0.0396457i
$907$	16.2433	−	123.380i	0.0179088	−	0.136031i	−0.980155	−	0.198234i	$-0.936479\pi$
$907$	16.2433	−	123.380i	0.0179088	−	0.136031i	0.998064	+	0.0622032i	$0.0198127\pi$
$908$	273.939	−	113.469i	0.301695	−	0.124966i
$909$	853.990	−	318.186i	0.939483	−	0.350040i
$910$	77.8010	+	77.8010i	0.0854956	+	0.0854956i
$911$	2.52148	−	19.1526i	0.00276782	−	0.0210237i	−0.990005	−	0.141031i	$-0.954958\pi$
$911$	2.52148	−	19.1526i	0.00276782	−	0.0210237i	0.992773	+	0.120007i	$0.0382917\pi$
$912$	513.422	−	434.142i	0.562963	−	0.476033i
$913$	−18.9637	+	2.49662i	−0.0207708	+	0.00273452i
$914$	−13.1694	−	22.8100i	−0.0144085	−	0.0249562i
$915$	−606.460	+	285.603i	−0.662798	+	0.312135i
$916$	−199.472	−	744.439i	−0.217764	−	0.812707i
$917$			994.557i			1.08458i
$918$	−133.851	+	31.2586i	−0.145807	+	0.0340508i
$919$	−152.878			−0.166353			−0.0831764	−	0.996535i	$-0.526506\pi$
$919$	−152.878			−0.166353			−0.0831764	+	0.996535i	$0.526506\pi$
$920$	165.735	−	44.4085i	0.180147	−	0.0482701i
$921$	−39.7215	−	84.3459i	−0.0431286	−	0.0915808i
$922$	−193.801	+	111.891i	−0.210197	+	0.121357i
$923$	−193.325	−	1468.45i	−0.209453	−	1.59096i
$924$	−518.224	−	612.858i	−0.560848	−	0.663266i
$925$	−532.908	−	70.1586i	−0.576116	−	0.0758472i
$926$	−26.7741	+	26.7741i	−0.0289138	+	0.0289138i
$927$	−237.188	−	39.9692i	−0.255866	−	0.0431167i
$928$	−210.374	−	507.887i	−0.226696	−	0.547293i
$929$	−829.215	−	109.168i	−0.892589	−	0.117512i	−0.329740	−	0.944072i	$-0.606961\pi$
$929$	−829.215	−	109.168i	−0.892589	−	0.117512i	−0.562848	+	0.826560i	$0.690294\pi$
$930$	20.1339	+	13.9844i	0.0216494	+	0.0150370i
$931$	330.630	−	190.889i	0.355134	−	0.205037i
$932$	1066.53	−	140.412i	1.14435	−	0.150656i
$933$	−528.452	+	339.487i	−0.566401	+	0.363866i
$934$	102.912	−	178.250i	0.110185	−	0.190845i
$935$	−191.600	−	864.775i	−0.204920	−	0.924894i
$936$	253.068	+	355.644i	0.270372	+	0.379961i
$937$	−584.743	+	584.743i	−0.624059	+	0.624059i	−0.946567	−	0.322508i	$-0.895474\pi$
$937$	−584.743	+	584.743i	−0.624059	+	0.624059i	0.322508	+	0.946567i	$0.395474\pi$
$938$	79.8120	+	104.013i	0.0850874	+	0.110888i
$939$	−157.871	−	494.156i	−0.168126	−	0.526258i
$940$	949.696	−	125.030i	1.01032	−	0.133011i
$941$	130.966	−	170.679i	0.139178	−	0.181380i	−0.718564	−	0.695461i	$-0.755200\pi$
$941$	130.966	−	170.679i	0.139178	−	0.181380i	0.857742	+	0.514081i	$0.171867\pi$
$942$	−114.138	−	41.0532i	−0.121166	−	0.0435809i
$943$	−244.103	+	65.4073i	−0.258858	+	0.0693608i
$944$	−226.815	+	226.815i	−0.240271	+	0.240271i
$945$	120.071	−	469.420i	0.127059	−	0.496741i
$946$	284.881	−	118.002i	0.301143	−	0.124737i
$947$	230.152	−	176.602i	0.243033	−	0.186486i	−0.480062	−	0.877235i	$-0.659386\pi$
$947$	230.152	−	176.602i	0.243033	−	0.186486i	0.723095	+	0.690749i	$0.242719\pi$
$948$	−90.4697	+	99.4855i	−0.0954321	+	0.104943i
$949$	68.1860	+	517.924i	0.0718504	+	0.545758i
$950$	−13.1846	+	49.2056i	−0.0138785	+	0.0517954i
$951$	−145.849	−	456.526i	−0.153364	−	0.480049i
$952$	125.674	−	149.734i	0.132010	−	0.157283i
$953$			317.999i			0.333682i	0.985984	+	0.166841i	$0.0533566\pi$
$953$			317.999i			0.333682i	−0.985984	+	0.166841i	$0.946643\pi$
$954$	98.4683	−	36.6881i	0.103216	−	0.0384572i
$955$	108.851	+	45.0875i	0.113980	+	0.0472121i
$956$	652.121	−	1129.51i	0.682135	−	1.18149i
$957$	1368.81	+	950.729i	1.43031	+	0.993447i
$958$	57.8246	+	44.3704i	0.0603597	+	0.0463156i
$959$	192.253	+	147.521i	0.200472	+	0.153827i
$960$	−332.994	−	518.346i	−0.346869	−	0.539944i
$961$	875.630	−	234.624i	0.911165	−	0.244146i
$962$	268.645	−	111.276i	0.279257	−	0.115672i
$963$	368.821	−	195.568i	0.382992	−	0.203082i
$964$	156.840	−	378.646i	0.162697	−	0.392786i
$965$	660.316	−	1143.70i	0.684265	−	1.18518i
$966$	−85.1494	−	7.12416i	−0.0881464	−	0.00737490i
$967$	996.917	+	267.123i	1.03094	+	0.276239i	0.734353	−	0.678768i	$-0.237486\pi$
$967$	996.917	+	267.123i	1.03094	+	0.276239i	0.296585	+	0.955007i	$0.404152\pi$
$968$	−159.270	+	91.9548i	−0.164535	+	0.0949946i
$969$	−759.306	−	97.1334i	−0.783598	−	0.100241i
$970$	−101.744	+	176.225i	−0.104890	+	0.181675i
$971$	1276.33	+	1276.33i	1.31445	+	1.31445i	0.918096	+	0.396357i	$0.129726\pi$
$971$	1276.33	+	1276.33i	1.31445	+	1.31445i	0.396357	+	0.918096i	$0.370274\pi$
$972$	385.166	−	868.645i	0.396262	−	0.893667i
$973$			361.638i			0.371673i
$974$	103.813	−	79.6583i	0.106584	−	0.0817847i
$975$	655.035	+	235.602i	0.671831	+	0.241644i
$976$	549.427	−	716.027i	0.562938	−	0.733635i
$977$	−1472.64	−	394.591i	−1.50730	−	0.403881i	−0.591765	−	0.806111i	$-0.701569\pi$
$977$	−1472.64	−	394.591i	−1.50730	−	0.403881i	−0.915539	+	0.402230i	$0.868235\pi$
$978$	−30.1764	+	58.5093i	−0.0308552	+	0.0598254i
$979$	−1637.17	−	215.538i	−1.67229	−	0.220161i
$980$	−140.709	−	339.702i	−0.143581	−	0.346635i
$981$	36.1613	+	11.1006i	0.0368617	+	0.0113156i
$982$			251.192i			0.255797i
$983$	−634.320	−	826.662i	−0.645290	−	0.840958i	0.350116	−	0.936707i	$-0.386142\pi$
$983$	−634.320	−	826.662i	−0.645290	−	0.840958i	−0.995406	+	0.0957482i	$0.969476\pi$
$984$	−49.5417	−	77.1176i	−0.0503472	−	0.0783715i
$985$	255.411	+	442.385i	0.259300	+	0.449121i
$986$	−84.8266	+	181.851i	−0.0860310	+	0.184433i
$987$	−942.904	−	205.286i	−0.955323	−	0.207990i
$988$	311.015	+	1160.72i	0.314792	+	1.17482i
$989$	−547.803	+	1322.51i	−0.553896	+	1.33722i
$990$	−127.714	−	58.3784i	−0.129004	−	0.0589681i
$991$	234.150	−	565.288i	0.236276	−	0.570422i	−0.760616	−	0.649203i	$-0.775103\pi$
$991$	234.150	−	565.288i	0.236276	−	0.570422i	0.996892	+	0.0787808i	$0.0251027\pi$
$992$	−102.063	−	13.4369i	−0.102886	−	0.0135452i
$993$	145.320	+	171.857i	0.146345	+	0.173069i
$994$	−27.2179	+	101.579i	−0.0273822	+	0.102192i
$995$	−705.156	−	188.946i	−0.708699	−	0.189895i
$996$	14.9810	+	5.38835i	0.0150412	+	0.00540999i
$997$	53.1509	−	403.721i	0.0533109	−	0.404936i	−0.943896	−	0.330244i	$-0.892869\pi$
$997$	53.1509	−	403.721i	0.0533109	−	0.404936i	0.997207	−	0.0746926i	$-0.0237976\pi$
$998$	1.24335	+	0.515012i	0.00124584	+	0.000516044i
$999$	−1024.71	−	767.918i	−1.02574	−	0.768687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.q.a.128.20	yes	272
9.5	odd	6	inner	153.3.q.a.77.20	yes	272
17.2	even	8	inner	153.3.q.a.2.20	✓	272
153.104	odd	24	inner	153.3.q.a.104.20	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.q.a.2.20	✓	272	17.2	even	8	inner
153.3.q.a.77.20	yes	272	9.5	odd	6	inner
153.3.q.a.104.20	yes	272	153.104	odd	24	inner
153.3.q.a.128.20	yes	272	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.q (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.289257 - 0.0775060i) q^{2} +(-1.27816 - 2.71409i) q^{3} +(-3.38644 + 1.95516i) q^{4} +(-0.482534 - 3.66521i) q^{5} +(-0.580075 - 0.686004i) q^{6} +(4.81280 + 0.633617i) q^{7} +(-1.67501 + 1.67501i) q^{8} +(-5.73260 + 6.93810i) q^{9} +(-0.423652 - 1.02279i) q^{10} +(-13.9733 - 1.83962i) q^{11} +(9.63491 + 6.69210i) q^{12} +(-17.7309 + 10.2370i) q^{13} +(1.44124 - 0.189743i) q^{14} +(-9.33096 + 5.99437i) q^{15} +(7.46596 - 12.9314i) q^{16} +(-16.5975 + 3.67736i) q^{17} +(-1.12045 + 2.45120i) q^{18} +(-10.6134 + 10.6134i) q^{19} +(8.80015 + 11.4686i) q^{20} +(-4.43184 - 13.8723i) q^{21} +(-4.18445 + 0.550893i) q^{22} +(11.9276 - 15.5444i) q^{23} +(6.68709 + 2.40521i) q^{24} +(10.9472 - 2.93330i) q^{25} +(-4.33536 + 4.33536i) q^{26} +(26.1579 + 6.69080i) q^{27} +(-17.5371 + 7.26410i) q^{28} +(31.2711 - 23.9952i) q^{29} +(-2.23444 + 2.45712i) q^{30} +(-0.963434 - 7.31801i) q^{31} +(3.60971 - 13.4716i) q^{32} +(12.8672 + 40.2762i) q^{33} +(-4.51592 + 2.35011i) q^{34} -17.9457i q^{35} +(5.84800 - 34.7036i) q^{36} +(-43.8166 - 18.1494i) q^{37} +(-2.24740 + 3.89261i) q^{38} +(50.4471 + 35.0389i) q^{39} +(6.94753 + 5.33103i) q^{40} +(-10.2327 - 7.85182i) q^{41} +(-2.35712 - 3.66915i) q^{42} +(-70.5703 + 18.9093i) q^{43} +(50.9165 - 21.0903i) q^{44} +(28.1958 + 17.6633i) q^{45} +(2.24536 - 5.42077i) q^{46} +(33.1317 - 57.3857i) q^{47} +(-44.6398 - 3.73486i) q^{48} +(-24.5688 - 6.58318i) q^{49} +(2.93921 - 1.69695i) q^{50} +(31.1950 + 40.3469i) q^{51} +(40.0298 - 69.3337i) q^{52} +(-27.5694 - 27.5694i) q^{53} +(8.08491 - 0.0920336i) q^{54} +52.1028i q^{55} +(-9.12283 + 7.00019i) q^{56} +(42.3716 + 15.2402i) q^{57} +(7.18560 - 9.36446i) q^{58} +(-20.7499 - 5.55991i) q^{59} +(19.8788 - 38.5431i) q^{60} +(59.9261 + 7.88942i) q^{61} +(-0.845869 - 2.04211i) q^{62} +(-31.9860 + 29.7594i) q^{63} +55.5512i q^{64} +(46.0764 + 60.0479i) q^{65} +(6.84358 + 10.6529i) q^{66} +(45.0944 + 78.1058i) q^{67} +(49.0166 - 44.9039i) q^{68} +(-57.4343 - 12.5044i) q^{69} +(-1.39090 - 5.19090i) q^{70} +(-27.6841 + 66.8352i) q^{71} +(-2.01923 - 21.2236i) q^{72} +(9.76419 - 23.5728i) q^{73} +(-14.0809 - 1.85379i) q^{74} +(-21.9536 - 25.9626i) q^{75} +(15.1908 - 56.6928i) q^{76} +(-66.0851 - 17.7075i) q^{77} +(17.3079 + 6.22528i) q^{78} +(-1.49620 + 11.3647i) q^{79} +(-50.9990 - 21.1245i) q^{80} +(-15.2745 - 79.5468i) q^{81} +(-3.56844 - 1.47810i) q^{82} +(1.31090 - 0.351254i) q^{83} +(42.1307 + 38.3126i) q^{84} +(21.4871 + 59.0589i) q^{85} +(-18.9473 + 10.9393i) q^{86} +(-105.095 - 54.2030i) q^{87} +(26.4869 - 20.3241i) q^{88} +117.164 q^{89} +(9.52482 + 2.92389i) q^{90} +(-91.8218 + 38.0338i) q^{91} +(-10.0004 + 75.9604i) q^{92} +(-18.6303 + 11.9684i) q^{93} +(5.13581 - 19.1671i) q^{94} +(44.0219 + 33.7792i) q^{95} +(-41.1770 + 7.42182i) q^{96} +(-111.896 - 145.826i) q^{97} -7.61692 q^{98} +(92.8669 - 86.4024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 12 q^{2} - 8 q^{3} - 12 q^{5} - 8 q^{6} - 4 q^{7} + 16 q^{9} - 16 q^{10} - 84 q^{11} - 140 q^{12} - 12 q^{14} + 44 q^{15} + 440 q^{16} - 48 q^{18} - 16 q^{19} - 12 q^{20} - 4 q^{22} - 120 q^{23}+ \cdots - 832 q^{99}+O(q^{100}) \) 272 * q - 12 * q^2 - 8 * q^3 - 12 * q^5 - 8 * q^6 - 4 * q^7 + 16 * q^9 - 16 * q^10 - 84 * q^11 - 140 * q^12 - 12 * q^14 + 44 * q^15 + 440 * q^16 - 48 * q^18 - 16 * q^19 - 12 * q^20 - 4 * q^22 - 120 * q^23 + 112 * q^24 - 4 * q^25 + 40 * q^27 - 144 * q^28 - 12 * q^29 - 4 * q^31 - 204 * q^32 + 112 * q^33 - 28 * q^34 - 200 * q^36 - 16 * q^37 - 148 * q^39 + 60 * q^40 - 12 * q^41 - 624 * q^42 + 116 * q^43 + 44 * q^45 - 352 * q^46 - 168 * q^48 - 4 * q^49 - 24 * q^50 - 256 * q^51 - 264 * q^52 - 20 * q^54 + 708 * q^56 + 76 * q^57 - 4 * q^58 + 492 * q^59 - 656 * q^60 - 4 * q^61 + 708 * q^63 + 348 * q^65 - 508 * q^66 - 8 * q^67 - 204 * q^68 + 176 * q^69 + 12 * q^70 - 16 * q^73 + 492 * q^74 - 868 * q^75 + 92 * q^76 + 528 * q^77 + 864 * q^78 - 4 * q^79 + 176 * q^82 + 1428 * q^83 - 440 * q^84 + 188 * q^85 - 1824 * q^86 - 796 * q^87 + 156 * q^88 - 1000 * q^90 - 744 * q^91 - 12 * q^92 + 44 * q^93 + 28 * q^94 - 12 * q^95 - 1452 * q^96 - 364 * q^97 - 832 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more