LMFDB - Embedded newform 105.3.w.a.38.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			38.28
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.998723 - 3.72728i) q^{2} +(2.89768 + 0.776828i) q^{3} +(-9.43110 - 5.44505i) q^{4} +(1.07764 - 4.88249i) q^{5} +(5.78944 - 10.0246i) q^{6} +(3.36385 + 6.13877i) q^{7} +(-18.8000 + 18.8000i) q^{8} +(7.79308 + 4.50199i) q^{9} +(-17.1222 - 8.89293i) q^{10} +(-2.12166 - 1.22494i) q^{11} +(-23.0984 - 23.1043i) q^{12} +(-2.54324 + 2.54324i) q^{13} +(26.2405 - 6.40708i) q^{14} +(6.91551 - 13.3107i) q^{15} +(29.5169 + 51.1248i) q^{16} +(-0.720080 - 2.68738i) q^{17} +(24.5633 - 24.5508i) q^{18} +(-0.652966 - 1.13097i) q^{19} +(-36.7487 + 40.1794i) q^{20} +(4.97858 + 20.4013i) q^{21} +(-6.68464 + 6.68464i) q^{22} +(21.4692 + 5.75265i) q^{23} +(-69.0809 + 39.8721i) q^{24} +(-22.6774 - 10.5231i) q^{25} +(6.93938 + 12.0194i) q^{26} +(19.0846 + 19.0992i) q^{27} +(1.70114 - 76.2117i) q^{28} +14.4234 q^{29} +(-42.7062 - 39.0698i) q^{30} +(5.76876 + 3.33060i) q^{31} +(117.310 - 31.4332i) q^{32} +(-5.19631 - 5.19764i) q^{33} -10.7358 q^{34} +(33.5975 - 9.80855i) q^{35} +(-48.9837 - 84.8924i) q^{36} +(-32.5475 - 8.72107i) q^{37} +(-4.86758 + 1.30426i) q^{38} +(-9.34515 + 5.39383i) q^{39} +(71.5313 + 112.051i) q^{40} -9.57556 q^{41} +(81.0137 + 1.81870i) q^{42} +(27.5904 + 27.5904i) q^{43} +(13.3397 + 23.1050i) q^{44} +(30.3791 - 33.1981i) q^{45} +(42.8835 - 74.2765i) q^{46} +(-23.2584 - 6.23208i) q^{47} +(45.8153 + 171.073i) q^{48} +(-26.3691 + 41.2998i) q^{49} +(-61.8712 + 74.0153i) q^{50} +(0.00106809 - 8.34653i) q^{51} +(37.8336 - 10.1375i) q^{52} +(-14.2328 - 53.1174i) q^{53} +(90.2484 - 52.0587i) q^{54} +(-8.26714 + 9.03892i) q^{55} +(-178.650 - 52.1687i) q^{56} +(-1.01352 - 3.78443i) q^{57} +(14.4050 - 53.7600i) q^{58} +(-66.1564 - 38.1954i) q^{59} +(-137.698 + 87.8796i) q^{60} +(-77.6638 + 44.8392i) q^{61} +(18.1755 - 18.1755i) q^{62} +(-1.42200 + 62.9839i) q^{63} -232.507i q^{64} +(9.67663 + 15.1580i) q^{65} +(-24.5628 + 14.1771i) q^{66} +(-1.30554 - 4.87233i) q^{67} +(-7.84174 + 29.2658i) q^{68} +(57.7420 + 33.3472i) q^{69} +(-3.00464 - 135.023i) q^{70} +120.663i q^{71} +(-231.148 + 61.8725i) q^{72} +(26.5743 + 99.1765i) q^{73} +(-65.0118 + 112.604i) q^{74} +(-57.5371 - 48.1091i) q^{75} +14.2217i q^{76} +(0.382694 - 17.1449i) q^{77} +(10.7711 + 40.2190i) q^{78} +(9.38512 - 5.41850i) q^{79} +(281.425 - 89.0217i) q^{80} +(40.4641 + 70.1688i) q^{81} +(-9.56333 + 35.6908i) q^{82} +(-53.8586 - 53.8586i) q^{83} +(64.1327 - 219.515i) q^{84} +(-13.8971 + 0.619755i) q^{85} +(130.393 - 75.2822i) q^{86} +(41.7943 + 11.2045i) q^{87} +(62.9162 - 16.8583i) q^{88} +(54.6094 - 31.5288i) q^{89} +(-93.3984 - 146.387i) q^{90} +(-24.1674 - 7.05730i) q^{91} +(-171.155 - 171.155i) q^{92} +(14.1287 + 14.1323i) q^{93} +(-46.4575 + 80.4667i) q^{94} +(-6.22562 + 1.96932i) q^{95} +(364.346 + 0.0466246i) q^{96} +(-79.9577 - 79.9577i) q^{97} +(127.601 + 139.532i) q^{98} +(-11.0196 - 19.0977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.998723	−	3.72728i	0.499361	−	1.86364i	−0.00472484	−	0.999989i	$-0.501504\pi$
$2$	0.998723	−	3.72728i	0.499361	−	1.86364i	0.504086	−	0.863653i	$-0.331829\pi$
$3$	2.89768	+	0.776828i	0.965893	+	0.258943i
$3$	2.89768	+	0.776828i	0.965893	+	0.258943i
$4$	−9.43110	−	5.44505i	−2.35777	−	1.36126i
$5$	1.07764	−	4.88249i	0.215528	−	0.976498i
$5$	1.07764	−	4.88249i	0.215528	−	0.976498i
$6$	5.78944	−	10.0246i	0.964906	−	1.67077i
$7$	3.36385	+	6.13877i	0.480550	+	0.876968i
$7$	3.36385	+	6.13877i	0.480550	+	0.876968i
$8$	−18.8000	+	18.8000i	−2.35001	+	2.35001i
$9$	7.79308	+	4.50199i	0.865897	+	0.500222i
$10$	−17.1222	−	8.89293i	−1.71222	−	0.889293i
$11$	−2.12166	−	1.22494i	−0.192878	−	0.111358i	0.400451	−	0.916318i	$-0.368853\pi$
$11$	−2.12166	−	1.22494i	−0.192878	−	0.111358i	−0.593329	+	0.804960i	$0.702187\pi$
$12$	−23.0984	−	23.1043i	−1.92487	−	1.92536i
$13$	−2.54324	+	2.54324i	−0.195634	+	0.195634i	−0.798125	−	0.602492i	$-0.794175\pi$
$13$	−2.54324	+	2.54324i	−0.195634	+	0.195634i	0.602492	+	0.798125i	$0.294175\pi$
$14$	26.2405	−	6.40708i	1.87432	−	0.457649i
$15$	6.91551	−	13.3107i	0.461034	−	0.887382i
$16$	29.5169	+	51.1248i	1.84481	+	3.19530i
$17$	−0.720080	−	2.68738i	−0.0423577	−	0.158081i	0.941508	−	0.336992i	$-0.109409\pi$
$17$	−0.720080	−	2.68738i	−0.0423577	−	0.158081i	−0.983865	+	0.178911i	$0.942743\pi$
$18$	24.5633	−	24.5508i	1.36463	−	1.36393i
$19$	−0.652966	−	1.13097i	−0.0343667	−	0.0595248i	0.848331	−	0.529467i	$-0.177608\pi$
$19$	−0.652966	−	1.13097i	−0.0343667	−	0.0595248i	−0.882697	+	0.469942i	$0.844275\pi$
$20$	−36.7487	+	40.1794i	−1.83744	+	2.00897i
$21$	4.97858	+	20.4013i	0.237075	+	0.971491i
$22$	−6.68464	+	6.68464i	−0.303847	+	0.303847i
$23$	21.4692	+	5.75265i	0.933443	+	0.250115i	0.693322	−	0.720628i	$-0.256146\pi$
$23$	21.4692	+	5.75265i	0.933443	+	0.250115i	0.240121	+	0.970743i	$0.422813\pi$
$24$	−69.0809	+	39.8721i	−2.87837	+	1.66134i
$25$	−22.6774	−	10.5231i	−0.907095	−	0.420926i
$26$	6.93938	+	12.0194i	0.266899	+	0.462283i
$27$	19.0846	+	19.0992i	0.706835	+	0.707378i
$28$	1.70114	−	76.2117i	0.0607548	−	2.72185i
$29$	14.4234			0.497358			0.248679	−	0.968586i	$-0.420004\pi$
$29$	14.4234			0.497358			0.248679	+	0.968586i	$0.420004\pi$
$30$	−42.7062	−	39.0698i	−1.42354	−	1.30233i
$31$	5.76876	+	3.33060i	0.186089	+	0.107439i	0.590150	−	0.807293i	$-0.299068\pi$
$31$	5.76876	+	3.33060i	0.186089	+	0.107439i	−0.404061	+	0.914732i	$0.632402\pi$
$32$	117.310	−	31.4332i	3.66595	−	0.982288i
$33$	−5.19631	−	5.19764i	−0.157464	−	0.157504i
$34$	−10.7358			−0.315758
$35$	33.5975	−	9.80855i	0.959929	−	0.280244i
$36$	−48.9837	−	84.8924i	−1.36066	−	2.35812i
$37$	−32.5475	−	8.72107i	−0.879661	−	0.235704i	−0.209400	−	0.977830i	$-0.567151\pi$
$37$	−32.5475	−	8.72107i	−0.879661	−	0.235704i	−0.670261	+	0.742126i	$0.733818\pi$
$38$	−4.86758	+	1.30426i	−0.128094	+	0.0343228i
$39$	−9.34515	+	5.39383i	−0.239619	+	0.138303i
$40$	71.5313	+	112.051i	1.78828	+	2.80127i
$41$	−9.57556			−0.233550			−0.116775	−	0.993158i	$-0.537256\pi$
$41$	−9.57556			−0.233550			−0.116775	+	0.993158i	$0.537256\pi$
$42$	81.0137	+	1.81870i	1.92890	+	0.0433023i
$43$	27.5904	+	27.5904i	0.641638	+	0.641638i	0.950958	−	0.309320i	$-0.100101\pi$
$43$	27.5904	+	27.5904i	0.641638	+	0.641638i	−0.309320	+	0.950958i	$0.600101\pi$
$44$	13.3397	+	23.1050i	0.303175	+	0.525115i
$45$	30.3791	−	33.1981i	0.675091	−	0.737735i
$46$	42.8835	−	74.2765i	0.932251	−	1.61471i
$47$	−23.2584	−	6.23208i	−0.494860	−	0.132597i	0.00275330	−	0.999996i	$-0.499124\pi$
$47$	−23.2584	−	6.23208i	−0.494860	−	0.132597i	−0.497614	+	0.867399i	$0.665790\pi$
$48$	45.8153	+	171.073i	0.954486	+	3.56401i
$49$	−26.3691	+	41.2998i	−0.538144	+	0.842853i
$50$	−61.8712	+	74.0153i	−1.23742	+	1.48031i
$51$	0.00106809	−	8.34653i	2.09429e−5	−	0.163657i
$52$	37.8336	−	10.1375i	0.727569	−	0.194952i
$53$	−14.2328	−	53.1174i	−0.268543	−	1.00221i	−0.960046	−	0.279842i	$-0.909718\pi$
$53$	−14.2328	−	53.1174i	−0.268543	−	1.00221i	0.691503	−	0.722373i	$-0.256949\pi$
$54$	90.2484	−	52.0587i	1.67127	−	0.964051i
$55$	−8.26714	+	9.03892i	−0.150312	+	0.164344i
$56$	−178.650	−	52.1687i	−3.19017	−	0.931585i
$57$	−1.01352	−	3.78443i	−0.0177810	−	0.0663935i
$58$	14.4050	−	53.7600i	0.248361	−	0.926897i
$59$	−66.1564	−	38.1954i	−1.12129	−	0.647379i	−0.179563	−	0.983746i	$-0.557468\pi$
$59$	−66.1564	−	38.1954i	−1.12129	−	0.647379i	−0.941731	+	0.336367i	$0.890802\pi$
$60$	−137.698	+	87.8796i	−2.29497	+	1.46466i
$61$	−77.6638	+	44.8392i	−1.27318	+	0.735069i	−0.975584	−	0.219625i	$-0.929517\pi$
$61$	−77.6638	+	44.8392i	−1.27318	+	0.735069i	−0.297592	+	0.954693i	$0.596183\pi$
$62$	18.1755	−	18.1755i	0.293153	−	0.293153i
$63$	−1.42200	+	62.9839i	−0.0225715	+	0.999745i
$64$		−	232.507i		−	3.63292i
$65$	9.67663	+	15.1580i	0.148871	+	0.233201i
$66$	−24.5628	+	14.1771i	−0.372163	+	0.214805i
$67$	−1.30554	−	4.87233i	−0.0194856	−	0.0727213i	0.955498	−	0.294996i	$-0.0953184\pi$
$67$	−1.30554	−	4.87233i	−0.0194856	−	0.0727213i	−0.974984	+	0.222275i	$0.928652\pi$
$68$	−7.84174	+	29.2658i	−0.115320	+	0.430379i
$69$	57.7420	+	33.3472i	0.836840	+	0.483293i
$70$	−3.00464	−	135.023i	−0.0429235	−	1.92891i
$71$			120.663i			1.69948i	0.527205	+	0.849738i	$0.323240\pi$
$71$			120.663i			1.69948i	−0.527205	+	0.849738i	$0.676760\pi$
$72$	−231.148	+	61.8725i	−3.21039	+	0.859340i
$73$	26.5743	+	99.1765i	0.364031	+	1.35858i	0.868729	+	0.495287i	$0.164937\pi$
$73$	26.5743	+	99.1765i	0.364031	+	1.35858i	−0.504698	+	0.863296i	$0.668396\pi$
$74$	−65.0118	+	112.604i	−0.878538	+	1.52167i
$75$	−57.5371	−	48.1091i	−0.767161	−	0.641455i
$76$			14.2217i			0.187128i
$77$	0.382694	−	17.1449i	0.00497005	−	0.222661i
$78$	10.7711	+	40.2190i	0.138091	+	0.515628i
$79$	9.38512	−	5.41850i	0.118799	−	0.0685886i	−0.439423	−	0.898280i	$-0.644817\pi$
$79$	9.38512	−	5.41850i	0.118799	−	0.0685886i	0.558222	+	0.829692i	$0.311484\pi$
$80$	281.425	−	89.0217i	3.51781	−	1.11277i
$81$	40.4641	+	70.1688i	0.499557	+	0.866281i
$82$	−9.56333	+	35.6908i	−0.116626	+	0.435254i
$83$	−53.8586	−	53.8586i	−0.648899	−	0.648899i	0.303828	−	0.952727i	$-0.401735\pi$
$83$	−53.8586	−	53.8586i	−0.648899	−	0.648899i	−0.952727	+	0.303828i	$0.901735\pi$
$84$	64.1327	−	219.515i	0.763485	−	2.61328i
$85$	−13.8971	+	0.619755i	−0.163495	+	0.00729123i
$86$	130.393	−	75.2822i	1.51619	−	0.875375i
$87$	41.7943	+	11.2045i	0.480394	+	0.128787i
$88$	62.9162	−	16.8583i	0.714956	−	0.191572i
$89$	54.6094	−	31.5288i	0.613589	−	0.354256i	−0.160780	−	0.986990i	$-0.551401\pi$
$89$	54.6094	−	31.5288i	0.613589	−	0.354256i	0.774369	+	0.632735i	$0.218068\pi$
$90$	−93.3984	−	146.387i	−1.03776	−	1.62652i
$91$	−24.1674	−	7.05730i	−0.265576	−	0.0775527i
$92$	−171.155	−	171.155i	−1.86038	−	1.86038i
$93$	14.1287	+	14.1323i	0.151922	+	0.151961i
$94$	−46.4575	+	80.4667i	−0.494228	+	0.856029i
$95$	−6.22562	+	1.96932i	−0.0655328	+	0.0207297i
$96$	364.346	+	0.0466246i	3.79527	+	0.000485672i
$97$	−79.9577	−	79.9577i	−0.824306	−	0.824306i	0.162416	−	0.986722i	$-0.448071\pi$
$97$	−79.9577	−	79.9577i	−0.824306	−	0.824306i	−0.986722	+	0.162416i	$0.948071\pi$
$98$	127.601	+	139.532i	1.30205	+	1.42380i
$99$	−11.0196	−	19.0977i	−0.111309	−	0.192906i
$100$	156.574	+	222.724i	1.56574	+	2.22724i
$101$	−67.0901	+	116.203i	−0.664259	+	1.15053i	0.315227	+	0.949016i	$0.397919\pi$
$101$	−67.0901	+	116.203i	−0.664259	+	1.15053i	−0.979486	+	0.201513i	$0.935414\pi$
$102$	−31.1088	−	8.33985i	−0.304988	−	0.0817632i
$103$	4.67983	+	1.25396i	0.0454353	+	0.0121743i	0.281465	−	0.959571i	$-0.409180\pi$
$103$	4.67983	+	1.25396i	0.0454353	+	0.0121743i	−0.236030	+	0.971746i	$0.575846\pi$
$104$		−	95.6260i		−	0.919481i
$105$	104.974	−	2.32253i	0.999755	−	0.0221193i
$106$	−212.198			−2.00187
$107$	37.1306	−	138.573i	0.347015	−	1.29508i	−0.543226	−	0.839586i	$-0.682797\pi$
$107$	37.1306	−	138.573i	0.347015	−	1.29508i	0.890241	−	0.455490i	$-0.150536\pi$
$108$	−75.9922	−	284.043i	−0.703631	−	2.63003i
$109$	68.2088	+	39.3803i	0.625768	+	0.361288i	0.779111	−	0.626885i	$-0.215671\pi$
$109$	68.2088	+	39.3803i	0.625768	+	0.361288i	−0.153343	+	0.988173i	$0.549004\pi$
$110$	25.4340	+	39.8413i	0.231219	+	0.362194i
$111$	−87.5373	−	50.5546i	−0.788624	−	0.455447i
$112$	−214.553	+	353.173i	−1.91565	+	3.15333i
$113$	91.5753	−	91.5753i	0.810401	−	0.810401i	−0.174293	−	0.984694i	$-0.555764\pi$
$113$	91.5753	−	91.5753i	0.810401	−	0.810401i	0.984694	+	0.174293i	$0.0557639\pi$
$114$	−15.1179	−	0.00193460i	−0.132613	−	1.69702e-5i
$115$	51.2234	−	98.6238i	0.445420	−	0.857598i
$116$	−136.028	−	78.5360i	−1.17266	−	0.677034i
$117$	−31.2693	+	8.37001i	−0.267259	+	0.0715385i
$118$	−208.437	+	208.437i	−1.76641	+	1.76641i
$119$	14.0750	−	13.4603i	0.118277	−	0.113112i
$120$	120.231	+	380.254i	1.00192	+	3.16879i
$121$	−57.4990	−	99.5913i	−0.475199	−	0.823068i
$122$	89.5638	+	334.257i	0.734130	+	2.73981i
$123$	−27.7469	−	7.43856i	−0.225584	−	0.0604761i
$124$	−36.2705	−	62.8224i	−0.292504	−	0.506632i
$125$	−75.8172	+	99.3818i	−0.606538	+	0.795055i
$126$	233.339	+	68.2037i	1.85190	+	0.541299i
$127$	134.984	−	134.984i	1.06286	−	1.06286i	0.0649759	−	0.997887i	$-0.479303\pi$
$127$	134.984	−	134.984i	1.06286	−	1.06286i	0.997887	−	0.0649759i	$-0.0206971\pi$
$128$	−397.378	−	106.477i	−3.10452	−	0.831853i
$129$	58.5152	+	101.381i	0.453606	+	0.785901i
$130$	66.1626	−	20.9289i	0.508943	−	0.160991i
$131$	−114.473	−	198.272i	−0.873837	−	1.51353i	−0.857997	−	0.513655i	$-0.828291\pi$
$131$	−114.473	−	198.272i	−0.873837	−	1.51353i	−0.0158402	−	0.999875i	$-0.505042\pi$
$132$	20.7055	+	77.3136i	0.156860	+	0.585709i
$133$	4.74629	−	7.81283i	0.0356864	−	0.0587430i
$134$	−19.4644			−0.145257
$135$	113.818	−	72.5980i	0.843096	−	0.537763i
$136$	64.0603	+	36.9853i	0.471032	+	0.271950i
$137$	43.5915	−	11.6803i	0.318186	−	0.0852577i	−0.0961913	−	0.995363i	$-0.530666\pi$
$137$	43.5915	−	11.6803i	0.318186	−	0.0852577i	0.414377	+	0.910105i	$0.363999\pi$
$138$	181.963	−	181.916i	1.31857	−	1.31823i
$139$	55.1047			0.396436			0.198218	−	0.980158i	$-0.436485\pi$
$139$	55.1047			0.396436			0.198218	+	0.980158i	$0.436485\pi$
$140$	−370.269	−	90.4347i	−2.64478	−	0.645962i
$141$	−62.5542	−	36.1264i	−0.443647	−	0.256215i
$142$	449.745	+	120.509i	3.16722	+	0.848653i
$143$	8.51119	−	2.28057i	0.0595188	−	0.0159480i
$144$	−0.135980	+	531.304i	−0.000944303	+	3.68961i
$145$	15.5432	−	70.4220i	0.107195	−	0.485669i
$146$	396.199			2.71369
$147$	−108.492	+	99.1893i	−0.738040	+	0.674757i
$148$	259.472	+	259.472i	1.75319	+	1.75319i
$149$	50.8418	+	88.0605i	0.341220	+	0.591010i	0.984660	−	0.174487i	$-0.0558266\pi$
$149$	50.8418	+	88.0605i	0.341220	+	0.591010i	−0.643440	+	0.765497i	$0.722493\pi$
$150$	−236.780	+	166.409i	−1.57853	+	1.10940i
$151$	−92.1891	+	159.676i	−0.610524	+	1.05746i	0.380629	+	0.924728i	$0.375708\pi$
$151$	−92.1891	+	159.676i	−0.610524	+	1.05746i	−0.991152	+	0.132730i	$0.957626\pi$
$152$	33.5381	+	8.98651i	0.220645	+	0.0591218i
$153$	6.48691	−	24.1847i	0.0423981	−	0.158070i
$154$	−63.5216	−	18.5494i	−0.412478	−	0.120451i
$155$	22.4783	−	24.5767i	0.145021	−	0.158560i
$156$	117.505	+	0.0150368i	0.753235	+	9.63899e-5i
$157$	−78.1455	+	20.9390i	−0.497742	+	0.133370i	−0.498952	−	0.866630i	$-0.666282\pi$
$157$	−78.1455	+	20.9390i	−0.497742	+	0.133370i	0.00120996	+	0.999999i	$0.499615\pi$
$158$	−10.8232	−	40.3926i	−0.0685010	−	0.255649i
$159$	0.0211113	−	164.974i	0.000132775	−	1.03757i
$160$	−27.0538	−	606.640i	−0.169086	−	3.79150i
$161$	36.9049	+	151.146i	0.229223	+	0.938792i
$162$	301.951	−	80.7420i	1.86390	−	0.498407i
$163$	61.5557	−	229.729i	0.377642	−	1.40938i	−0.471803	−	0.881704i	$-0.656397\pi$
$163$	61.5557	−	229.729i	0.377642	−	1.40938i	0.849445	−	0.527677i	$-0.176937\pi$
$164$	90.3080	+	52.1394i	0.550659	+	0.317923i
$165$	−30.9772	+	19.7697i	−0.187740	+	0.119817i
$166$	−254.536	+	146.956i	−1.53335	+	0.885280i
$167$	63.1204	−	63.1204i	0.377967	−	0.377967i	−0.492402	−	0.870368i	$-0.663881\pi$
$167$	63.1204	−	63.1204i	0.377967	−	0.377967i	0.870368	+	0.492402i	$0.163881\pi$
$168$	−477.143	−	289.948i	−2.84014	−	1.72588i
$169$			156.064i			0.923455i
$170$	−11.5693	+	52.4173i	−0.0680548	+	0.308337i
$171$	0.00300811	−	11.7534i	1.75913e−5	−	0.0687333i
$172$	−109.977	−	410.440i	−0.639401	−	2.38628i
$173$	30.9387	−	115.465i	0.178837	−	0.667428i	−0.817030	−	0.576596i	$-0.804381\pi$
$173$	30.9387	−	115.465i	0.178837	−	0.667428i	0.995866	−	0.0908318i	$-0.0289526\pi$
$174$	83.5032	−	144.589i	0.479904	−	0.830972i
$175$	−11.6840	−	174.610i	−0.0667659	−	0.997769i
$176$		−	144.626i		−	0.821736i
$177$	−162.029	−	162.070i	−0.915416	−	0.915650i
$178$	−62.9770	−	235.033i	−0.353803	−	1.32041i
$179$	30.3894	−	52.6360i	0.169773	−	0.294056i	−0.768567	−	0.639770i	$-0.779030\pi$
$179$	30.3894	−	52.6360i	0.169773	−	0.294056i	0.938340	+	0.345714i	$0.112363\pi$
$180$	−467.273	+	147.679i	−2.59596	+	0.820437i
$181$		−	6.33738i		−	0.0350131i	−0.999847	−	0.0175066i	$-0.994427\pi$
$181$		−	6.33738i		−	0.0350131i	0.999847	−	0.0175066i	$-0.00557280\pi$
$182$	−50.4411	+	83.0306i	−0.277149	+	0.456212i
$183$	−259.877	+	69.5982i	−1.42009	+	0.380318i
$184$	−511.772	+	295.472i	−2.78137	+	1.60582i
$185$	−77.6550	+	149.514i	−0.419757	+	0.808186i
$186$	66.7859	−	38.5475i	0.359064	−	0.207244i
$187$	−1.76411	+	6.58374i	−0.00943374	+	0.0352072i
$188$	185.419	+	185.419i	0.986270	+	0.986270i
$189$	−53.0482	+	181.403i	−0.280678	+	0.959802i
$190$	1.12255	+	25.1714i	0.00590815	+	0.132481i
$191$	26.6831	−	15.4055i	0.139702	−	0.0806570i	−0.428520	−	0.903532i	$-0.640965\pi$
$191$	26.6831	−	15.4055i	0.139702	−	0.0806570i	0.568222	+	0.822875i	$0.307631\pi$
$192$	180.618	−	673.730i	0.940718	−	3.50901i
$193$	183.046	−	49.0471i	0.948426	−	0.254130i	0.248732	−	0.968572i	$-0.419986\pi$
$193$	183.046	−	49.0471i	0.948426	−	0.254130i	0.699694	+	0.714442i	$0.253320\pi$
$194$	−377.881	+	218.169i	−1.94784	+	1.12458i
$195$	16.2646	+	51.4402i	0.0834081	+	0.263796i
$196$	473.569	−	245.922i	2.41617	−	1.25470i
$197$	−111.387	−	111.387i	−0.565418	−	0.565418i	0.365423	−	0.930841i	$-0.380924\pi$
$197$	−111.387	−	111.387i	−0.565418	−	0.565418i	−0.930841	+	0.365423i	$0.880924\pi$
$198$	−82.1882	+	21.9997i	−0.415092	+	0.111110i
$199$	133.135	−	230.596i	0.669019	−	1.15877i	−0.309160	−	0.951010i	$-0.600048\pi$
$199$	133.135	−	230.596i	0.669019	−	1.15877i	0.978179	−	0.207764i	$-0.0666188\pi$
$200$	624.171	−	228.500i	3.12086	−	1.14250i
$201$	0.00193649	−	15.1326i	9.63427e−6	−	0.0752867i
$202$	366.119	+	366.119i	1.81247	+	1.81247i
$203$	48.5180	+	88.5419i	0.239005	+	0.436167i
$204$	−45.4573	+	78.7111i	−0.222830	+	0.385839i
$205$	−10.3190	+	46.7525i	−0.0503367	+	0.228061i
$206$	9.34771	−	16.1907i	0.0453772	−	0.0785957i
$207$	141.413	+	141.485i	0.683153	+	0.683503i
$208$	−205.091	−	54.9540i	−0.986015	−	0.264202i
$209$			3.19938i			0.0153080i
$210$	96.1835	−	393.589i	0.458017	−	1.87423i
$211$	363.838			1.72435			0.862176	−	0.506608i	$-0.169101\pi$
$211$	363.838			1.72435			0.862176	+	0.506608i	$0.169101\pi$
$212$	−154.996	+	578.453i	−0.731114	+	2.72855i
$213$	−93.7342	+	349.642i	−0.440067	+	1.64151i
$214$	−479.419	−	276.792i	−2.24027	−	1.29342i
$215$	164.443	−	104.977i	0.764849	−	0.488267i
$216$	−717.857	−	0.275588i	−3.32341	−	0.00127587i
$217$	−1.04054	+	46.6167i	−0.00479512	+	0.214824i
$218$	214.903	−	214.903i	0.985795	−	0.985795i
$219$	−0.0394173	+	308.025i	−0.000179988	+	1.40651i
$220$	127.186	−	40.2320i	0.578116	−	0.182873i
$221$	8.66598	+	5.00330i	0.0392126	+	0.0226394i
$222$	−275.857	+	275.786i	−1.24260	+	1.24228i
$223$	−185.409	+	185.409i	−0.831429	+	0.831429i	−0.987712	−	0.156284i	$-0.950049\pi$
$223$	−185.409	+	185.409i	−0.831429	+	0.831429i	0.156284	+	0.987712i	$0.450049\pi$
$224$	587.576	+	614.405i	2.62311	+	2.74288i
$225$	−129.351	−	184.101i	−0.574895	−	0.818227i
$226$	−249.869	−	432.786i	−1.10561	−	1.91498i
$227$	−72.7298	−	271.431i	−0.320396	−	1.19573i	−0.918860	−	0.394584i	$-0.870889\pi$
$227$	−72.7298	−	271.431i	−0.320396	−	1.19573i	0.598464	−	0.801150i	$-0.295778\pi$
$228$	−11.0478	+	41.2100i	−0.0484554	+	0.180746i
$229$	48.1860	+	83.4605i	0.210419	+	0.364456i	0.951846	−	0.306577i	$-0.0991838\pi$
$229$	48.1860	+	83.4605i	0.210419	+	0.364456i	−0.741427	+	0.671034i	$0.765851\pi$
$230$	−316.441	−	289.422i	−1.37583	−	1.25836i
$231$	14.4275	−	49.3830i	0.0624569	−	0.213779i
$232$	−271.160	+	271.160i	−1.16879	+	1.16879i
$233$	−177.088	−	47.4507i	−0.760035	−	0.203651i	−0.142071	−	0.989857i	$-0.545376\pi$
$233$	−177.088	−	47.4507i	−0.760035	−	0.203651i	−0.617965	+	0.786206i	$0.712043\pi$
$234$	−0.0319686	+	124.909i	−0.000136618	+	0.533799i
$235$	−55.4923	+	106.843i	−0.236138	+	0.454651i
$236$	415.951	+	720.449i	1.76251	+	3.05275i
$237$	31.4043	−	8.41045i	0.132508	−	0.0354871i
$238$	−36.1135	−	65.9045i	−0.151737	−	0.276910i
$239$	−215.563			−0.901937			−0.450968	−	0.892540i	$-0.648921\pi$
$239$	−215.563			−0.901937			−0.450968	+	0.892540i	$0.648921\pi$
$240$	884.633	−	39.3377i	3.68597	−	0.163907i
$241$	332.441	+	191.935i	1.37943	+	0.796411i	0.992090	−	0.125528i	$-0.0400624\pi$
$241$	332.441	+	191.935i	1.37943	+	0.796411i	0.387335	+	0.921939i	$0.373396\pi$
$242$	−428.631	+	114.851i	−1.77120	+	0.474592i
$243$	62.7428	+	234.760i	0.258201	+	0.966091i
$244$	976.606			4.00248
$245$	173.229	+	173.253i	0.707058	+	0.707155i
$246$	−55.4371	+	95.9915i	−0.225354	+	0.390209i
$247$	4.53698	+	1.21568i	0.0183683	+	0.00492178i
$248$	−171.068	+	45.8376i	−0.689792	+	0.184829i
$249$	−114.226	−	197.904i	−0.458739	−	0.794794i
$250$	294.704	+	381.847i	1.17882	+	1.52739i
$251$	−210.985			−0.840578			−0.420289	−	0.907390i	$-0.638071\pi$
$251$	−210.985			−0.840578			−0.420289	+	0.907390i	$0.638071\pi$
$252$	356.362	−	586.265i	1.41413	−	2.32645i
$253$	−38.5036	−	38.5036i	−0.152188	−	0.152188i
$254$	−368.311	−	637.933i	−1.45004	−	2.51155i
$255$	−40.7507	−	8.99978i	−0.159807	−	0.0352933i
$256$	−328.727	+	569.372i	−1.28409	+	2.22411i
$257$	−201.340	−	53.9490i	−0.783425	−	0.209918i	−0.155131	−	0.987894i	$-0.549580\pi$
$257$	−201.340	−	53.9490i	−0.783425	−	0.209918i	−0.628294	+	0.777976i	$0.716247\pi$
$258$	436.317	−	116.851i	1.69115	−	0.452911i
$259$	−55.9480	−	229.138i	−0.216016	−	0.884702i
$260$	−8.72508	−	195.647i	−0.0335580	−	0.752487i
$261$	112.403	+	64.9340i	0.430661	+	0.248789i
$262$	−853.344	+	228.653i	−3.25704	+	0.872721i
$263$	48.6819	+	181.683i	0.185102	+	0.690811i	0.994609	+	0.103700i	$0.0330681\pi$
$263$	48.6819	+	181.683i	0.185102	+	0.690811i	−0.809507	+	0.587111i	$0.800265\pi$
$264$	195.407	+	0.0250058i	0.740177	+	9.47189e-5i
$265$	−274.683	+	12.2498i	−1.03654	+	0.0462256i
$266$	−24.3804	−	25.4936i	−0.0916556	−	0.0958407i
$267$	182.733	−	48.9381i	0.684393	−	0.183289i
$268$	−14.2174	+	53.0601i	−0.0530501	+	0.197986i
$269$	−114.316	−	66.0005i	−0.424967	−	0.245355i	0.272233	−	0.962231i	$-0.412238\pi$
$269$	−114.316	−	66.0005i	−0.424967	−	0.245355i	−0.697200	+	0.716876i	$0.745571\pi$
$270$	−156.921	−	496.737i	−0.581188	−	1.83977i
$271$	29.8453	−	17.2312i	0.110130	−	0.0635838i	−0.443923	−	0.896065i	$-0.646414\pi$
$271$	29.8453	−	17.2312i	0.110130	−	0.0635838i	0.554053	+	0.832481i	$0.313080\pi$
$272$	116.137	−	116.137i	0.426974	−	0.426974i
$273$	−64.5471	−	39.2237i	−0.236436	−	0.143677i
$274$		−	174.143i		−	0.635559i
$275$	35.2234	+	50.1049i	0.128085	+	0.182200i
$276$	−362.993	−	628.909i	−1.31519	−	2.27865i
$277$	133.597	+	498.589i	0.482298	+	1.79996i	0.591930	+	0.805990i	$0.298366\pi$
$277$	133.597	+	498.589i	0.482298	+	1.79996i	−0.109631	+	0.993972i	$0.534967\pi$
$278$	55.0343	−	205.391i	0.197965	−	0.738816i
$279$	29.9621	+	51.9265i	0.107391	+	0.186117i
$280$	−447.234	+	816.036i	−1.59726	+	2.91441i
$281$			339.109i			1.20679i	0.797441	+	0.603397i	$0.206187\pi$
$281$			339.109i			1.20679i	−0.797441	+	0.603397i	$0.793813\pi$
$282$	−197.128	+	197.077i	−0.699034	+	0.698855i
$283$	8.19840	+	30.5969i	0.0289696	+	0.108116i	0.978897	−	0.204355i	$-0.0655098\pi$
$283$	8.19840	+	30.5969i	0.0289696	+	0.108116i	−0.949927	+	0.312471i	$0.898843\pi$
$284$	657.015	−	1137.98i	2.31343	−	4.00698i
$285$	−19.5697	+	0.870221i	−0.0686654	+	0.00305341i
$286$		−	34.0013i		−	0.118886i
$287$	−32.2107	−	58.7822i	−0.112232	−	0.204816i
$288$	1055.72	+	283.169i	3.66570	+	0.983226i
$289$	243.578	−	140.630i	0.842830	−	0.486608i
$290$	−246.959	−	128.266i	−0.851584	−	0.442297i
$291$	−169.578	−	293.805i	−0.582743	−	1.00964i
$292$	289.396	−	1080.04i	0.991083	−	3.69877i
$293$	137.824	+	137.824i	0.470390	+	0.470390i	0.902041	−	0.431651i	$-0.142069\pi$
$293$	137.824	+	137.824i	0.470390	+	0.470390i	−0.431651	+	0.902041i	$0.642069\pi$
$294$	261.353	+	503.443i	0.888957	+	1.71239i
$295$	−257.781	+	281.847i	−0.873835	+	0.955412i
$296$	775.850	−	447.937i	2.62112	−	1.51330i
$297$	−17.0955	−	63.8994i	−0.0575606	−	0.215149i
$298$	379.003	−	101.554i	1.27182	−	0.340784i
$299$	−69.2317	+	39.9709i	−0.231544	+	0.133682i
$300$	280.681	+	767.014i	0.935605	+	2.55671i
$301$	−76.5614	+	262.182i	−0.254357	+	0.871035i
$302$	503.087	+	503.087i	1.66585	+	1.66585i
$303$	−284.676	+	284.603i	−0.939524	+	0.939283i
$304$	38.5471	−	66.7655i	0.126800	−	0.219623i
$305$	135.233	+	427.513i	0.443387	+	1.40168i
$306$	−83.6647	−	48.3324i	−0.273414	−	0.157949i
$307$	−234.301	−	234.301i	−0.763197	−	0.763197i	0.213702	−	0.976899i	$-0.431448\pi$
$307$	−234.301	−	234.301i	−0.763197	−	0.763197i	−0.976899	+	0.213702i	$0.931448\pi$
$308$	−96.9639	+	159.611i	−0.314818	+	0.518218i
$309$	12.5865	+	7.26899i	0.0407331	+	0.0235242i
$310$	−69.1549	−	108.328i	−0.223080	−	0.349446i
$311$	190.372	−	329.734i	0.612129	−	1.06024i	−0.378752	−	0.925498i	$-0.623647\pi$
$311$	190.372	−	329.734i	0.612129	−	1.06024i	0.990881	−	0.134740i	$-0.0430200\pi$
$312$	74.2850	−	277.094i	0.238093	−	0.888120i
$313$	−317.171	−	84.9856i	−1.01332	−	0.271519i	−0.286307	−	0.958138i	$-0.592428\pi$
$313$	−317.171	−	84.9856i	−1.01332	−	0.271519i	−0.727018	+	0.686619i	$0.759094\pi$
$314$			312.183i			0.994212i
$315$	305.986	+	74.8170i	0.971384	+	0.237514i
$316$	−118.016			−0.373468
$317$	−54.9044	+	204.906i	−0.173200	+	0.646392i	0.823651	+	0.567097i	$0.191933\pi$
$317$	−54.9044	+	204.906i	−0.173200	+	0.646392i	−0.996851	+	0.0792948i	$0.974733\pi$
$318$	−614.882	−	164.841i	−1.93359	−	0.518369i
$319$	−30.6015	−	17.6678i	−0.0959293	−	0.0553848i
$320$	−1135.21	−	250.559i	−3.54754	−	0.782998i
$321$	215.240	−	372.696i	0.670530	−	1.16105i
$322$	600.220	+	13.3976i	1.86404	+	0.0416075i
$323$	−2.56916	+	2.56916i	−0.00795404	+	0.00795404i
$324$	0.451520	−	882.098i	0.00139358	−	2.72252i
$325$	84.4369	−	30.9111i	0.259806	−	0.0951111i
$326$	−794.788	−	458.871i	−2.43800	−	1.40758i
$327$	167.055	+	167.098i	0.510872	+	0.511003i
$328$	180.021	−	180.021i	0.548844	−	0.548844i
$329$	−39.9805	−	163.742i	−0.121521	−	0.497696i
$330$	42.7498	+	135.205i	0.129545	+	0.409713i
$331$	129.187	+	223.759i	0.390293	+	0.676008i	0.992488	−	0.122341i	$-0.0390403\pi$
$331$	129.187	+	223.759i	0.390293	+	0.676008i	−0.602195	+	0.798349i	$0.705707\pi$
$332$	214.683	+	801.208i	0.646636	+	2.41328i
$333$	−214.383	−	214.492i	−0.643792	−	0.644121i
$334$	−172.228	−	298.308i	−0.515653	−	0.893136i
$335$	−25.1960	+	1.12364i	−0.0752119	+	0.00335416i
$336$	−896.061	+	856.712i	−2.66685	+	2.54974i
$337$	−62.9036	+	62.9036i	−0.186658	+	0.186658i	−0.794249	−	0.607592i	$-0.792136\pi$
$337$	−62.9036	+	62.9036i	−0.186658	+	0.186658i	0.607592	+	0.794249i	$0.292136\pi$
$338$	581.694	+	155.865i	1.72099	+	0.461138i
$339$	336.494	−	194.218i	0.992608	−	0.572913i
$340$	134.439	+	69.8252i	0.395410	+	0.205368i
$341$	−8.15956	−	14.1328i	−0.0239283	−	0.0414451i
$342$	−43.8052	−	11.7496i	−0.128085	−	0.0343555i
$343$	−342.232	−	22.9475i	−0.997760	−	0.0669024i
$344$	−1037.40			−3.01571
$345$	225.042	−	245.988i	0.652297	−	0.713009i
$346$	−399.472	−	230.635i	−1.15454	−	0.666575i
$347$	278.507	−	74.6257i	0.802614	−	0.215060i	0.165882	−	0.986146i	$-0.446953\pi$
$347$	278.507	−	74.6257i	0.802614	−	0.215060i	0.636731	+	0.771086i	$0.280286\pi$
$348$	−333.157	−	333.243i	−0.957349	−	0.957594i
$349$	−412.563			−1.18213			−0.591065	−	0.806624i	$-0.701292\pi$
$349$	−412.563			−1.18213			−0.591065	+	0.806624i	$0.701292\pi$
$350$	−662.488	−	130.837i	−1.89282	−	0.373819i
$351$	−97.1104	−	0.0372810i	−0.276668	−	0.000106214i
$352$	−287.396	−	77.0076i	−0.816466	−	0.218771i
$353$	649.418	−	174.011i	1.83971	−	0.492949i	0.840877	−	0.541226i	$-0.182040\pi$
$353$	649.418	−	174.011i	1.83971	−	0.492949i	0.998834	+	0.0482767i	$0.0153729\pi$
$354$	−765.903	+	442.063i	−2.16357	+	1.24877i
$355$	589.135	+	130.031i	1.65953	+	0.366285i
$356$	−686.703			−1.92894
$357$	51.2410	−	28.0699i	0.143532	−	0.0786271i
$358$	−165.839	−	165.839i	−0.463237	−	0.463237i
$359$	117.727	+	203.909i	0.327930	+	0.567992i	0.982101	−	0.188355i	$-0.0603156\pi$
$359$	117.727	+	203.909i	0.327930	+	0.567992i	−0.654171	+	0.756347i	$0.726982\pi$
$360$	52.9971	+	1195.25i	0.147214	+	3.32015i
$361$	179.647	−	311.158i	0.497638	−	0.861934i
$362$	−23.6212	−	6.32928i	−0.0652519	−	0.0174842i
$363$	−89.2484	−	333.250i	−0.245863	−	0.918045i
$364$	189.498	+	198.151i	0.520599	+	0.544371i
$365$	512.866	−	22.8718i	1.40511	−	0.0626625i
$366$	−0.132849	+	1038.14i	−0.000362976	+	2.83646i
$367$	−284.747	+	76.2977i	−0.775878	+	0.207896i	−0.624967	−	0.780652i	$-0.714887\pi$
$367$	−284.747	+	76.2977i	−0.775878	+	0.207896i	−0.150911	+	0.988547i	$0.548221\pi$
$368$	339.601	+	1267.41i	0.922829	+	3.44404i
$369$	−74.6231	−	43.1091i	−0.202231	−	0.116827i
$370$	479.727	+	438.766i	1.29656	+	1.18585i
$371$	278.199	−	266.050i	0.749862	−	0.717117i
$372$	−56.2981	−	210.215i	−0.151339	−	0.565094i
$373$	140.170	−	523.121i	0.375791	−	1.40247i	−0.476396	−	0.879231i	$-0.658057\pi$
$373$	140.170	−	523.121i	0.375791	−	1.40247i	0.852186	−	0.523238i	$-0.175276\pi$
$374$	22.7776	+	13.1507i	0.0609028	+	0.0351622i
$375$	−296.896	+	229.080i	−0.791724	+	0.610879i
$376$	554.423	−	320.096i	1.47453	−	0.851320i
$377$	−36.6821	+	36.6821i	−0.0973000	+	0.0973000i
$378$	623.158	+	378.897i	1.64857	+	1.00237i
$379$			459.859i			1.21335i	0.794950	+	0.606675i	$0.207497\pi$
$379$			459.859i			1.21335i	−0.794950	+	0.606675i	$0.792503\pi$
$380$	69.4374	+	15.3259i	0.182730	+	0.0403314i
$381$	495.998	−	286.280i	1.30183	−	0.751391i
$382$	−30.7716	−	114.841i	−0.0805540	−	0.300632i
$383$	−114.402	+	426.954i	−0.298700	+	1.11476i	0.639535	+	0.768762i	$0.279127\pi$
$383$	−114.402	+	426.954i	−0.298700	+	1.11476i	−0.938234	+	0.346000i	$0.887540\pi$
$384$	−1068.76	−	617.231i	−2.78323	−	1.60737i
$385$	−83.2972	−	20.3445i	−0.216356	−	0.0528429i
$386$		−	731.250i		−	1.89443i
$387$	90.8024	+	339.226i	0.234632	+	0.876554i
$388$	318.715	+	1189.46i	0.821432	+	3.06562i
$389$	−147.618	+	255.681i	−0.379480	+	0.657278i	−0.990987	−	0.133961i	$-0.957230\pi$
$389$	−147.618	+	255.681i	−0.379480	+	0.657278i	0.611507	+	0.791239i	$0.290564\pi$
$390$	207.976	−	9.24825i	0.533272	−	0.0237135i
$391$		−	61.8382i		−	0.158154i
$392$	−280.698	−	1272.18i	−0.716067	−	3.24535i
$393$	−177.681	−	663.455i	−0.452115	−	1.68818i
$394$	−526.417	+	303.927i	−1.33608	+	0.771389i
$395$	−16.3420	−	51.6619i	−0.0413721	−	0.130790i
$396$	−0.0614539	+	240.115i	−0.000155187	+	0.606350i
$397$	74.7001	−	278.785i	0.188162	−	0.702229i	−0.805770	−	0.592229i	$-0.798248\pi$
$397$	74.7001	−	278.785i	0.188162	−	0.702229i	0.993932	−	0.110000i	$-0.0350851\pi$
$398$	−726.533	−	726.533i	−1.82546	−	1.82546i
$399$	19.8225	−	18.9520i	0.0496803	−	0.0474987i
$400$	−131.373	−	1469.99i	−0.328431	−	3.67497i
$401$	−424.590	+	245.137i	−1.05883	+	0.611315i	−0.925108	−	0.379705i	$-0.876026\pi$
$401$	−424.590	+	245.137i	−1.05883	+	0.611315i	−0.133720	+	0.991019i	$0.542692\pi$
$402$	−56.4016	−	15.1205i	−0.140303	−	0.0376132i
$403$	−23.1419	+	6.20084i	−0.0574239	+	0.0153867i
$404$	1265.47	−	730.618i	3.13234	−	1.80846i
$405$	386.204	−	121.949i	0.953590	−	0.301108i
$406$	378.477	−	92.4118i	0.932209	−	0.227615i
$407$	58.3718	+	58.3718i	0.143420	+	0.143420i
$408$	156.895	+	156.935i	0.384547	+	0.384645i
$409$	291.419	−	504.753i	0.712516	−	1.23411i	−0.251394	−	0.967885i	$-0.580889\pi$
$409$	291.419	−	504.753i	0.712516	−	1.23411i	0.963910	−	0.266229i	$-0.0857777\pi$
$410$	163.954	+	85.1548i	0.399888	+	0.207695i
$411$	135.388	+	0.0173253i	0.329410	+	4.21539e-5i
$412$	−37.3081	−	37.3081i	−0.0905537	−	0.0905537i
$413$	11.9330	−	534.602i	0.0288934	−	1.29444i
$414$	668.587	−	385.781i	1.61494	−	0.931838i
$415$	−321.004	+	204.924i	−0.773504	+	0.493792i
$416$	−218.406	+	378.291i	−0.525015	+	0.909352i
$417$	159.676	+	42.8068i	0.382915	+	0.102654i
$418$	11.9250	+	3.19529i	0.0285287	+	0.00764423i
$419$		−	35.2066i		−	0.0840252i	−0.999117	−	0.0420126i	$-0.986623\pi$
$419$		−	35.2066i		−	0.0840252i	0.999117	−	0.0420126i	$-0.0133770\pi$
$420$	−1002.67	−	549.686i	−2.38731	−	1.30878i
$421$	−219.332			−0.520979			−0.260490	−	0.965477i	$-0.583884\pi$
$421$	−219.332			−0.520979			−0.260490	+	0.965477i	$0.583884\pi$
$422$	363.374	−	1356.13i	0.861075	−	3.21358i
$423$	−153.198	−	153.276i	−0.362170	−	0.362356i
$424$	1266.19	+	731.033i	2.98629	+	1.72413i
$425$	−11.9501	+	68.5201i	−0.0281179	+	0.161224i
$426$	1209.60	+	698.570i	2.83944	+	1.63983i
$427$	−536.507	−	325.928i	−1.25646	−	0.763297i
$428$	−1104.72	+	1104.72i	−2.58112	+	2.58112i
$429$	26.4343	+	0.00338274i	0.0616184	+	7.88518e-6i
$430$	−227.048	−	717.768i	−0.528019	−	1.66923i
$431$	98.9389	+	57.1224i	0.229557	+	0.132535i	0.610368	−	0.792118i	$-0.291022\pi$
$431$	98.9389	+	57.1224i	0.229557	+	0.132535i	−0.380811	+	0.924653i	$0.624355\pi$
$432$	−413.126	+	1539.44i	−0.956310	+	3.56353i
$433$	−19.7022	+	19.7022i	−0.0455017	+	0.0455017i	−0.729492	−	0.683990i	$-0.760243\pi$
$433$	−19.7022	+	19.7022i	−0.0455017	+	0.0455017i	0.683990	+	0.729492i	$0.260243\pi$
$434$	172.715	+	50.4356i	0.397960	+	0.116211i
$435$	99.7450	−	191.986i	0.229299	−	0.441347i
$436$	−428.856	−	742.800i	−0.983614	−	1.70367i
$437$	−7.51258	−	28.0373i	−0.0171913	−	0.0641586i
$438$	1148.06	+	307.779i	2.62114	+	0.702691i
$439$	67.2260	+	116.439i	0.153134	+	0.265237i	0.932378	−	0.361484i	$-0.117730\pi$
$439$	67.2260	+	116.439i	0.153134	+	0.265237i	−0.779244	+	0.626721i	$0.784397\pi$
$440$	−14.5095	−	325.355i	−0.0329762	−	0.739442i
$441$	−391.428	+	203.139i	−0.887591	+	0.460633i
$442$	27.3036	−	27.3036i	0.0617730	−	0.0617730i
$443$	−332.092	−	88.9837i	−0.749643	−	0.200866i	−0.136283	−	0.990670i	$-0.543516\pi$
$443$	−332.092	−	88.9837i	−0.749643	−	0.200866i	−0.613360	+	0.789804i	$0.710182\pi$
$444$	550.301	+	953.430i	1.23942	+	2.14737i
$445$	−95.0894	−	300.607i	−0.213684	−	0.675520i
$446$	505.899	+	876.242i	1.13430	+	1.96467i
$447$	78.9152	+	294.666i	0.176544	+	0.659209i
$448$	1427.31	−	782.118i	3.18595	−	1.74580i
$449$	−439.282			−0.978357			−0.489178	−	0.872184i	$-0.662703\pi$
$449$	−439.282			−0.978357			−0.489178	+	0.872184i	$0.662703\pi$
$450$	−815.383	+	298.263i	−1.81196	+	0.662808i
$451$	20.3160	+	11.7295i	0.0450467	+	0.0260077i
$452$	−1362.29	+	365.024i	−3.01391	+	0.807575i
$453$	−391.175	+	391.075i	−0.863521	+	0.863300i
$454$	−1084.34			−2.38841
$455$	−60.5010	+	110.392i	−0.132969	+	0.242620i
$456$	90.2017	+	52.0934i	0.197811	+	0.114240i
$457$	69.7512	+	18.6898i	0.152628	+	0.0408966i	0.334324	−	0.942458i	$-0.391492\pi$
$457$	69.7512	+	18.6898i	0.152628	+	0.0408966i	−0.181696	+	0.983355i	$0.558159\pi$
$458$	359.205	−	96.2488i	0.784291	−	0.210150i
$459$	37.5844	−	65.0403i	0.0818831	−	0.141700i
$460$	−1020.10	+	651.217i	−2.21762	+	1.41569i
$461$	83.9387			0.182080			0.0910399	−	0.995847i	$-0.470981\pi$
$461$	83.9387			0.182080			0.0910399	+	0.995847i	$0.470981\pi$
$462$	−169.656	−	103.096i	−0.367220	−	0.223150i
$463$	227.307	+	227.307i	0.490944	+	0.490944i	0.908604	−	0.417659i	$-0.137149\pi$
$463$	227.307	+	227.307i	0.490944	+	0.490944i	−0.417659	+	0.908604i	$0.637149\pi$
$464$	425.733	+	737.392i	0.917529	+	1.58921i
$465$	84.2267	−	53.7537i	0.181133	−	0.115599i
$466$	−353.724	+	612.668i	−0.759065	+	1.31474i
$467$	420.786	+	112.749i	0.901040	+	0.241433i	0.679463	−	0.733710i	$-0.262213\pi$
$467$	420.786	+	112.749i	0.901040	+	0.241433i	0.221577	+	0.975143i	$0.428879\pi$
$468$	340.479	+	91.3245i	0.727519	+	0.195138i
$469$	25.5185	−	24.4042i	0.0544104	−	0.0520345i
$470$	342.813	+	313.542i	0.729390	+	0.667111i
$471$	−242.706	−	0.0310586i	−0.515300	−	6.59419e-5i
$472$	1961.82	−	525.668i	4.15639	−	1.11370i
$473$	−24.7408	−	92.3341i	−0.0523062	−	0.195209i
$474$	0.0160539	−	125.452i	3.38689e−5	−	0.264668i
$475$	2.90619	+	32.5187i	0.00611830	+	0.0684604i
$476$	−206.034	+	50.3069i	−0.432845	+	0.105687i
$477$	128.217	−	478.024i	0.268799	−	1.00215i
$478$	−215.288	+	803.464i	−0.450392	+	1.68089i
$479$	−138.709	−	80.0837i	−0.289580	−	0.167189i	0.348172	−	0.937431i	$-0.386802\pi$
$479$	−138.709	−	80.0837i	−0.289580	−	0.167189i	−0.637753	+	0.770241i	$0.720136\pi$
$480$	392.862	−	1778.86i	0.818462	−	3.70597i
$481$	104.956	−	60.5962i	0.218203	−	0.125980i
$482$	1047.41	−	1047.41i	2.17306	−	2.17306i
$483$	−10.4757	+	466.640i	−0.0216888	+	0.966128i
$484$			1252.34i			2.58748i
$485$	−476.558	+	304.227i	−0.982594	+	0.627272i
$486$	937.681	+	0.599965i	1.92938	+	0.00123450i
$487$	129.753	+	484.246i	0.266434	+	0.994345i	0.961367	+	0.275270i	$0.0887674\pi$
$487$	129.753	+	484.246i	0.266434	+	0.994345i	−0.694933	+	0.719075i	$0.744566\pi$
$488$	617.103	−	2303.06i	1.26456	−	4.71939i
$489$	356.829	−	617.863i	0.729711	−	1.26352i
$490$	818.771	−	472.643i	1.67096	−	0.964578i
$491$		−	47.0322i		−	0.0957886i	−0.998852	−	0.0478943i	$-0.984749\pi$
$491$		−	47.0322i		−	0.0957886i	0.998852	−	0.0478943i	$-0.0152511\pi$
$492$	221.180	+	221.237i	0.449553	+	0.449669i
$493$	−10.3860	−	38.7610i	−0.0210669	−	0.0786228i
$494$	9.06237	−	15.6965i	0.0183449	−	0.0317743i
$495$	−105.120	+	33.2224i	−0.212363	+	0.0671159i
$496$			393.236i			0.792814i
$497$	−740.722	+	405.891i	−1.49039	+	0.816682i
$498$	−851.724	+	228.102i	−1.71029	+	0.458036i
$499$	−208.153	+	120.177i	−0.417141	+	0.240837i	−0.693853	−	0.720116i	$-0.744088\pi$
$499$	−208.153	+	120.177i	−0.417141	+	0.240837i	0.276712	+	0.960953i	$0.410755\pi$
$500$	1256.18	−	524.452i	2.51236	−	1.04890i
$501$	231.936	−	133.869i	0.462947	−	0.267204i
$502$	−210.716	+	786.401i	−0.419752	+	1.56654i
$503$	428.825	+	428.825i	0.852535	+	0.852535i	0.990445	−	0.137910i	$-0.0440385\pi$
$503$	428.825	+	428.825i	0.852535	+	0.852535i	−0.137910	+	0.990445i	$0.544038\pi$
$504$	−1157.37	−	1210.84i	−2.29636	−	2.40245i
$505$	495.063	+	452.792i	0.980323	+	0.896619i
$506$	−181.968	+	105.059i	−0.359621	+	0.207627i
$507$	−121.235	+	452.223i	−0.239122	+	0.891958i
$508$	−2008.04	+	538.051i	−3.95283	+	1.05916i
$509$	−505.629	+	291.925i	−0.993377	+	0.573527i	−0.906282	−	0.422673i	$-0.861092\pi$
$509$	−505.629	+	291.925i	−0.993377	+	0.573527i	−0.0870951	+	0.996200i	$0.527758\pi$
$510$	−74.2434	+	142.901i	−0.145575	+	0.280198i
$511$	−519.430	+	496.748i	−1.01650	+	0.972110i
$512$	630.301	+	630.301i	1.23106	+	1.23106i
$513$	9.13908	−	34.0552i	0.0178150	−	0.0663844i
$514$	−402.166	+	696.573i	−0.782425	+	1.35520i
$515$	11.1656	−	21.4979i	0.0216808	−	0.0417435i
$516$	0.163128	−	1274.75i	0.000316139	−	2.47045i
$517$	41.7125	+	41.7125i	0.0806818	+	0.0806818i
$518$	−909.938	−	20.3109i	−1.75664	−	0.0392102i
$519$	179.347	−	310.546i	0.345563	−	0.598355i
$520$	−466.893	−	103.051i	−0.897871	−	0.198174i
$521$	−251.052	+	434.835i	−0.481866	+	0.834616i	−0.999783	−	0.0208143i	$-0.993374\pi$
$521$	−251.052	+	434.835i	−0.481866	+	0.834616i	0.517917	+	0.855431i	$0.326707\pi$
$522$	354.286	−	354.105i	0.678709	−	0.678362i
$523$	727.663	+	194.977i	1.39133	+	0.372805i	0.875222	−	0.483721i	$-0.160715\pi$
$523$	727.663	+	194.977i	1.39133	+	0.372805i	0.516104	+	0.856526i	$0.327382\pi$
$524$			2493.24i			4.75808i
$525$	101.785	−	515.039i	0.193876	−	0.981026i
$526$	725.804			1.37986
$527$	4.79659	−	17.9011i	0.00910170	−	0.0339680i
$528$	112.349	−	419.078i	0.212783	−	0.793709i
$529$	−30.2942	−	17.4904i	−0.0572670	−	0.0330631i
$530$	−228.674	+	1036.06i	−0.431460	+	1.95482i
$531$	−343.606	−	595.495i	−0.647092	−	1.12146i
$532$	−87.3040	+	47.8397i	−0.164105	+	0.0899243i
$533$	24.3529	−	24.3529i	0.0456903	−	0.0456903i
$534$	0.0934131	−	729.973i	0.000174931	−	1.36699i
$535$	−636.569	−	330.622i	−1.18985	−	0.617985i
$536$	116.144	+	67.0559i	0.216687	+	0.125104i
$537$	128.948	−	128.915i	0.240126	−	0.240065i
$538$	−360.173	+	360.173i	−0.669466	+	0.669466i
$539$	106.536	−	55.3235i	0.197655	−	0.102641i
$540$	−1468.73	+	64.9346i	−2.71987	+	0.120249i
$541$	−235.346	−	407.630i	−0.435019	−	0.753476i	0.562278	−	0.826948i	$-0.309925\pi$
$541$	−235.346	−	407.630i	−0.435019	−	0.753476i	−0.997297	+	0.0734727i	$0.976592\pi$
$542$	−34.4184	−	128.451i	−0.0635026	−	0.236995i
$543$	4.92305	−	18.3637i	0.00906639	−	0.0338189i
$544$	−168.946	−	292.623i	−0.310562	−	0.537909i
$545$	265.779	−	290.591i	0.487667	−	0.533194i
$546$	−210.663	+	201.412i	−0.385829	+	0.368886i
$547$	372.080	−	372.080i	0.680219	−	0.680219i	−0.279831	−	0.960049i	$-0.590278\pi$
$547$	372.080	−	372.080i	0.680219	−	0.680219i	0.960049	+	0.279831i	$0.0902783\pi$
$548$	−474.716	−	127.200i	−0.866269	−	0.232116i
$549$	−807.105	−	0.206567i	−1.47014	−	0.000376261i
$550$	221.934	−	81.2467i	0.403516	−	0.147721i
$551$	−9.41798	−	16.3124i	−0.0170925	−	0.0296051i
$552$	−1712.48	+	458.623i	−3.10232	+	0.830839i
$553$	64.8331	+	39.3861i	0.117239	+	0.0712226i
$554$	1991.81			3.59533
$555$	−341.166	+	372.920i	−0.614714	+	0.671928i
$556$	−519.697	−	300.047i	−0.934708	−	0.539654i
$557$	347.233	−	93.0408i	0.623399	−	0.167039i	0.0667262	−	0.997771i	$-0.478745\pi$
$557$	347.233	−	93.0408i	0.623399	−	0.167039i	0.556672	+	0.830732i	$0.312078\pi$
$558$	223.469	−	59.8170i	0.400482	−	0.107199i
$559$	−140.338			−0.251052
$560$	1493.15	+	1428.15i	2.66635	+	2.55026i
$561$	−10.2263	+	17.7072i	−0.0182286	+	0.0315636i
$562$	1263.96	+	338.676i	2.24903	+	0.602626i
$563$	201.049	−	53.8708i	0.357102	−	0.0956853i	−0.0758076	−	0.997122i	$-0.524153\pi$
$563$	201.049	−	53.8708i	0.357102	−	0.0956853i	0.432910	+	0.901437i	$0.357487\pi$
$564$	393.245	+	681.322i	0.697243	+	1.20802i
$565$	−348.430	−	545.801i	−0.616690	−	0.966019i
$566$	122.231			0.215956
$567$	−294.635	+	484.437i	−0.519639	+	0.854386i
$568$	−2268.47	−	2268.47i	−3.99378	−	3.99378i
$569$	−217.518	−	376.753i	−0.382282	−	0.662132i	0.609106	−	0.793089i	$-0.291528\pi$
$569$	−217.518	−	376.753i	−0.382282	−	0.662132i	−0.991388	+	0.130957i	$0.958195\pi$
$570$	−16.3011	+	73.8108i	−0.0285984	+	0.129493i
$571$	318.278	−	551.273i	0.557404	−	0.965452i	−0.440308	−	0.897847i	$-0.645131\pi$
$571$	318.278	−	551.273i	0.557404	−	0.965452i	0.997712	−	0.0676055i	$-0.0215359\pi$
$572$	−92.6877	−	24.8356i	−0.162041	−	0.0434189i
$573$	89.2865	−	23.9120i	0.155823	−	0.0417312i
$574$	−251.267	+	61.3514i	−0.437748	+	0.106884i
$575$	−426.329	−	356.378i	−0.741442	−	0.619789i
$576$	1046.75	−	1811.94i	1.81727	−	3.14574i
$577$	−454.755	+	121.851i	−0.788136	+	0.211181i	−0.630369	−	0.776296i	$-0.717096\pi$
$577$	−454.755	+	121.851i	−0.788136	+	0.211181i	−0.157768	+	0.987476i	$0.550430\pi$
$578$	−280.900	−	1048.33i	−0.485987	−	1.81373i
$579$	568.510	+	0.0727510i	0.981883	+	0.000125649i
$580$	−530.041	+	579.523i	−0.913863	+	0.999178i
$581$	149.454	−	511.798i	0.257235	−	0.880891i
$582$	−1264.46	+	338.637i	−2.17261	+	0.581850i
$583$	−34.8685	+	130.131i	−0.0598088	+	0.223209i
$584$	−2364.12	−	1364.93i	−4.04815	−	2.33720i
$585$	7.16936	+	161.692i	0.0122553	+	0.276396i
$586$	651.359	−	376.062i	1.11153	−	0.641744i
$587$	134.856	−	134.856i	0.229738	−	0.229738i	−0.582845	−	0.812583i	$-0.698061\pi$
$587$	134.856	−	134.856i	0.229738	−	0.229738i	0.812583	+	0.582845i	$0.198061\pi$
$588$	1563.29	−	344.720i	2.65865	−	0.586259i
$589$		−	8.69907i		−	0.0147692i
$590$	793.070	+	1242.31i	1.34419	+	2.10561i
$591$	−236.236	−	409.293i	−0.399722	−	0.692544i
$592$	−514.838	−	1921.40i	−0.869658	−	3.24561i
$593$	−54.6296	+	203.880i	−0.0921241	+	0.343812i	−0.996568	−	0.0827813i	$-0.973620\pi$
$593$	−54.6296	+	203.880i	−0.0921241	+	0.343812i	0.904444	+	0.426593i	$0.140286\pi$
$594$	−255.245	−	0.0979894i	−0.429705	−	0.000164965i
$595$	−50.5522	−	83.2262i	−0.0849616	−	0.139876i
$596$		−	1107.34i		−	1.85796i
$597$	564.915	−	564.771i	0.946256	−	0.946014i
$598$	79.8397	+	297.966i	0.133511	+	0.498271i
$599$	33.2136	−	57.5277i	0.0554484	−	0.0960395i	−0.836969	−	0.547251i	$-0.815674\pi$
$599$	33.2136	−	57.5277i	0.0554484	−	0.0960395i	0.892417	+	0.451211i	$0.149008\pi$
$600$	1986.15	−	177.246i	3.31026	−	0.295410i
$601$			1104.49i			1.83776i	0.394539	+	0.918879i	$0.370904\pi$
$601$			1104.49i			1.83776i	−0.394539	+	0.918879i	$0.629096\pi$
$602$	900.761	+	547.213i	1.49628	+	0.908992i
$603$	11.7611	−	43.8480i	0.0195042	−	0.0727163i
$604$	1738.89	−	1003.95i	2.87895	−	1.66217i
$605$	−548.217	+	173.415i	−0.906143	+	0.286636i
$606$	776.484	+	1345.31i	1.28133	+	2.21998i
$607$	38.6680	−	144.311i	0.0637035	−	0.237745i	−0.926732	−	0.375724i	$-0.877394\pi$
$607$	38.6680	−	144.311i	0.0637035	−	0.237745i	0.990435	+	0.137979i	$0.0440608\pi$
$608$	−112.150	−	112.150i	−0.184457	−	0.184457i
$609$	71.8079	+	294.256i	0.117911	+	0.483179i
$610$	1728.52	−	77.0853i	2.83364	−	0.126369i
$611$	75.0014	−	43.3021i	0.122752	−	0.0708709i
$612$	−192.866	+	192.767i	−0.315140	+	0.314979i
$613$	635.521	−	170.287i	1.03674	−	0.277793i	0.299978	−	0.953946i	$-0.403021\pi$
$613$	635.521	−	170.287i	1.03674	−	0.277793i	0.736761	+	0.676153i	$0.236354\pi$
$614$	−1107.31	+	639.306i	−1.80344	+	1.04121i
$615$	−66.2199	+	127.458i	−0.107675	+	0.207248i
$616$	315.130	+	329.519i	0.511574	+	0.534934i
$617$	−382.686	−	382.686i	−0.620237	−	0.620237i	0.325355	−	0.945592i	$-0.394516\pi$
$617$	−382.686	−	382.686i	−0.620237	−	0.620237i	−0.945592	+	0.325355i	$0.894516\pi$
$618$	39.6641	−	39.6539i	0.0641813	−	0.0641649i
$619$	−24.7022	+	42.7855i	−0.0399067	+	0.0691204i	−0.885289	−	0.465042i	$-0.846039\pi$
$619$	−24.7022	+	42.7855i	−0.0399067	+	0.0691204i	0.845382	+	0.534162i	$0.179373\pi$
$620$	−345.816	+	109.390i	−0.557768	+	0.176436i
$621$	299.859	+	519.831i	0.482864	+	0.837088i
$622$	−1038.88	−	1038.88i	−1.67023	−	1.67023i
$623$	377.246	+	229.177i	0.605531	+	0.367860i
$624$	−551.598	−	318.559i	−0.883971	−	0.510512i
$625$	403.527	+	477.275i	0.645643	+	0.763639i
$626$	−633.531	+	1097.31i	−1.01203	+	1.75289i
$627$	−2.48536	+	9.27076i	−0.00396390	+	0.0147859i
$628$	851.012	+	228.028i	1.35511	+	0.363102i
$629$			93.7471i			0.149042i
$630$	584.460	−	1065.78i	0.927714	−	1.69171i
$631$	−961.487			−1.52375			−0.761875	−	0.647724i	$-0.775721\pi$
$631$	−961.487			−1.52375			−0.761875	+	0.647724i	$0.775721\pi$
$632$	−74.5726	+	278.309i	−0.117995	+	0.440362i
$633$	1054.29	+	282.640i	1.66554	+	0.446509i
$634$	708.909	+	409.289i	1.11815	+	0.645566i
$635$	−513.592	−	804.520i	−0.808806	−	1.26696i
$636$	−898.488	+	1555.77i	−1.41272	+	2.44617i
$637$	−37.9724	−	172.098i	−0.0596113	−	0.270170i
$638$	−96.4151	+	96.4151i	−0.151121	+	0.151121i
$639$	−543.223	+	940.334i	−0.850115	+	1.47157i
$640$	−948.105	+	1825.45i	−1.48141	+	2.85227i
$641$	383.389	+	221.349i	0.598110	+	0.345319i	0.768298	−	0.640093i	$-0.221104\pi$
$641$	383.389	+	221.349i	0.598110	+	0.345319i	−0.170188	+	0.985412i	$0.554437\pi$
$642$	−1174.18	−	1174.48i	−1.82894	−	1.82941i
$643$	810.278	−	810.278i	1.26015	−	1.26015i	0.309134	−	0.951019i	$-0.399961\pi$
$643$	810.278	−	810.278i	1.26015	−	1.26015i	0.951019	−	0.309134i	$-0.100039\pi$
$644$	474.941	−	1626.42i	0.737487	−	2.52549i
$645$	558.051	−	176.447i	0.865196	−	0.273561i
$646$	7.01010	+	12.1418i	0.0108515	+	0.0187954i
$647$	196.946	+	735.012i	0.304399	+	1.13603i	0.933462	+	0.358677i	$0.116772\pi$
$647$	196.946	+	735.012i	0.304399	+	1.13603i	−0.629063	+	0.777354i	$0.716561\pi$
$648$	−2079.90	−	558.450i	−3.20973	−	0.861805i
$649$	93.5740	+	162.075i	0.144182	+	0.249730i
$650$	−30.8855	−	345.592i	−0.0475162	−	0.531680i
$651$	−39.2283	+	134.272i	−0.0602586	+	0.206255i
$652$	−1831.42	+	1831.42i	−2.80893	+	2.80893i
$653$	−540.019	−	144.698i	−0.826982	−	0.221589i	−0.179585	−	0.983742i	$-0.557476\pi$
$653$	−540.019	−	144.698i	−0.826982	−	0.221589i	−0.647396	+	0.762153i	$0.724142\pi$
$654$	789.664	−	455.778i	1.20744	−	0.696908i
$655$	−1091.42	+	345.245i	−1.66629	+	0.527091i
$656$	−282.641	−	489.548i	−0.430855	−	0.746263i
$657$	−239.397	+	892.528i	−0.364379	+	1.35849i
$658$	−650.243	−	14.5142i	−0.988211	−	0.0220580i
$659$	680.452			1.03255			0.516276	−	0.856422i	$-0.327318\pi$
$659$	680.452			1.03255			0.516276	+	0.856422i	$0.327318\pi$
$660$	399.796	−	17.7781i	0.605752	−	0.0269365i
$661$	226.750	+	130.914i	0.343040	+	0.198054i	0.661616	−	0.749843i	$-0.269871\pi$
$661$	226.750	+	130.914i	0.343040	+	0.198054i	−0.318575	+	0.947898i	$0.603204\pi$
$662$	963.034	−	258.044i	1.45473	−	0.389795i
$663$	21.2245	+	21.2299i	0.0320128	+	0.0320210i
$664$	2025.09			3.04983
$665$	−33.0312	−	31.5932i	−0.0496710	−	0.0475085i
$666$	−1013.58	+	584.847i	−1.52190	+	0.878148i
$667$	309.658	+	82.9727i	0.464255	+	0.124397i
$668$	−938.989	+	251.601i	−1.40567	+	0.376649i
$669$	−681.285	+	393.224i	−1.01836	+	0.587778i
$670$	−20.9757	+	95.0348i	−0.0313070	+	0.141843i
$671$	219.701			0.327423
$672$	1225.32	+	2236.79i	1.82339	+	3.32856i
$673$	−96.6114	−	96.6114i	−0.143553	−	0.143553i	0.631678	−	0.775231i	$-0.282367\pi$
$673$	−96.6114	−	96.6114i	−0.143553	−	0.143553i	−0.775231	+	0.631678i	$0.782367\pi$
$674$	171.636	+	297.283i	0.254653	+	0.441072i
$675$	−231.804	−	633.950i	−0.343413	−	0.939184i
$676$	849.775	−	1471.85i	1.25706	−	2.17730i
$677$	396.695	+	106.294i	0.585961	+	0.157008i	0.539607	−	0.841917i	$-0.318573\pi$
$677$	396.695	+	106.294i	0.585961	+	0.157008i	0.0463543	+	0.998925i	$0.485240\pi$
$678$	−387.840	−	1448.18i	−0.572035	−	2.13596i
$679$	221.877	−	759.807i	0.326770	−	1.11901i
$680$	249.614	−	272.917i	0.367080	−	0.401349i
$681$	0.107879	−	843.020i	0.000158413	−	1.23791i
$682$	−60.8260	+	16.2983i	−0.0891877	+	0.0238978i
$683$	−81.1849	−	302.986i	−0.118865	−	0.443611i	0.880682	−	0.473708i	$-0.157085\pi$
$683$	−81.1849	−	302.986i	−0.118865	−	0.443611i	−0.999547	+	0.0300976i	$0.990418\pi$
$684$	−64.0262	+	110.831i	−0.0936055	+	0.162034i
$685$	−10.0529	−	225.422i	−0.0146758	−	0.329083i
$686$	−427.326	+	1252.68i	−0.622925	+	1.82606i
$687$	74.7929	+	279.274i	0.108869	+	0.406512i
$688$	−596.171	+	2224.94i	−0.866527	+	3.23392i
$689$	171.288	+	98.8929i	0.248603	+	0.143531i
$690$	−692.113	−	1084.47i	−1.00306	−	1.57170i
$691$	−289.130	+	166.930i	−0.418423	+	0.241577i	−0.694402	−	0.719587i	$-0.744331\pi$
$691$	−289.130	+	166.930i	−0.418423	+	0.241577i	0.275979	+	0.961164i	$0.410998\pi$
$692$	−920.499	+	920.499i	−1.33020	+	1.33020i
$693$	80.1685	−	131.888i	0.115683	−	0.190315i
$694$		−	1112.60i		−	1.60318i
$695$	59.3831	−	269.048i	0.0854433	−	0.387119i
$696$	−996.380	+	575.090i	−1.43158	+	0.826279i
$697$	6.89517	+	25.7331i	0.00989264	+	0.0369198i
$698$	−412.036	+	1537.74i	−0.590310	+	2.20307i
$699$	−476.284	−	275.064i	−0.681379	−	0.393511i
$700$	−840.564	+	1710.38i	−1.20081	+	2.44340i
$701$			396.476i			0.565586i	0.959181	+	0.282793i	$0.0912609\pi$
$701$			396.476i			0.565586i	−0.959181	+	0.282793i	$0.908739\pi$
$702$	−97.1254	+	361.921i	−0.138355	+	0.515557i
$703$	11.3891	+	42.5048i	0.0162007	+	0.0604620i
$704$	−284.807	+	493.300i	−0.404555	+	0.700710i
$705$	−243.798	+	266.489i	−0.345812	+	0.377998i
$706$		−	2594.35i		−	3.67472i
$707$	−939.028	−	20.9602i	−1.32819	−	0.0296467i
$708$	645.628	+	2410.75i	0.911905	+	3.40502i
$709$	669.988	−	386.818i	0.944977	−	0.545582i	0.0534597	−	0.998570i	$-0.482975\pi$
$709$	669.988	−	386.818i	0.944977	−	0.545582i	0.891517	+	0.452988i	$0.149642\pi$
$710$	1073.05	−	2066.01i	1.51133	−	2.90987i
$711$	97.5330	+	0.0249622i	0.137177	+	3.51085e-5i
$712$	−433.918	+	1619.40i	−0.609435	+	2.27444i
$713$	104.691	+	104.691i	0.146832	+	0.146832i
$714$	−53.4489	−	219.024i	−0.0748584	−	0.306756i
$715$	−1.96283	−	44.0134i	−0.00274521	−	0.0615573i
$716$	−573.211	+	330.944i	−0.800574	+	0.462212i
$717$	−624.632	−	167.455i	−0.871174	−	0.233550i
$718$	877.604	−	235.153i	1.22229	−	0.327511i
$719$	1103.74	−	637.243i	1.53510	−	0.886290i	0.535985	−	0.844228i	$-0.319940\pi$
$719$	1103.74	−	637.243i	1.53510	−	0.886290i	0.999115	−	0.0420625i	$-0.0133929\pi$
$720$	2593.94	+	573.219i	3.60269	+	0.796138i
$721$	8.04448	+	32.9466i	0.0111574	+	0.0456956i
$722$	−980.357	−	980.357i	−1.35784	−	1.35784i
$723$	814.208	+	814.416i	1.12615	+	1.12644i
$724$	−34.5073	+	59.7684i	−0.0476620	+	0.0825531i
$725$	−327.084	−	151.779i	−0.451151	−	0.209351i
$726$	−1331.25	−	0.170358i	−1.83368	−	0.000234652i
$727$	846.968	+	846.968i	1.16502	+	1.16502i	0.983362	+	0.181656i	$0.0581457\pi$
$727$	846.968	+	846.968i	1.16502	+	1.16502i	0.181656	+	0.983362i	$0.441854\pi$
$728$	587.027	−	321.671i	0.806355	−	0.441856i
$729$	−0.559731	+	729.000i	−0.000767807	+	1.00000i
$730$	426.961	−	1934.44i	0.584878	−	2.64992i
$731$	54.2786	−	94.0132i	0.0742525	−	0.128609i
$732$	2829.89	+	758.655i	3.86597	+	1.03641i
$733$	−907.256	−	243.099i	−1.23773	−	0.331649i	−0.420145	−	0.907457i	$-0.638021\pi$
$733$	−907.256	−	243.099i	−1.23773	−	0.331649i	−0.817585	+	0.575808i	$0.804688\pi$
$734$			1137.53i			1.54977i
$735$	367.375	+	636.601i	0.499830	+	0.866124i
$736$	2699.38			3.66764
$737$	−3.19841	+	11.9366i	−0.00433976	+	0.0161962i
$738$	−235.208	+	235.087i	−0.318710	+	0.318546i
$739$	115.539	+	66.7062i	0.156344	+	0.0902655i	0.576131	−	0.817357i	$-0.304562\pi$
$739$	115.539	+	66.7062i	0.156344	+	0.0902655i	−0.419787	+	0.907623i	$0.637895\pi$
$740$	1546.49	−	987.250i	2.08984	−	1.33412i
$741$	12.2023	+	7.04710i	0.0164674	+	0.00951026i
$742$	−713.802	−	1302.64i	−0.961998	−	1.75557i
$743$	36.7081	−	36.7081i	0.0494053	−	0.0494053i	−0.681973	−	0.731378i	$-0.738878\pi$
$743$	36.7081	−	36.7081i	0.0494053	−	0.0494053i	0.731378	+	0.681973i	$0.238878\pi$
$744$	−531.309	−	0.0679905i	−0.714125	−	9.13851e-5i
$745$	484.744	−	153.337i	0.650663	−	0.205821i
$746$	−1809.83	−	1044.91i	−2.42605	−	1.40068i
$747$	−177.253	−	662.195i	−0.237287	−	0.886473i
$748$	52.4863	−	52.4863i	0.0701688	−	0.0701688i
$749$	975.571	−	238.203i	1.30250	−	0.318028i
$750$	557.328	+	1335.40i	0.743104	+	1.78054i
$751$	359.128	+	622.028i	0.478200	+	0.828266i	0.999688	−	0.0249923i	$-0.00795613\pi$
$751$	359.128	+	622.028i	0.478200	+	0.828266i	−0.521488	+	0.853259i	$0.674623\pi$
$752$	−367.903	−	1373.03i	−0.489233	−	1.82584i
$753$	−611.367	−	163.899i	−0.811908	−	0.217662i
$754$	100.089	+	173.360i	0.132745	+	0.229920i
$755$	680.270	+	622.186i	0.901020	+	0.824087i
$756$	1488.05	−	1421.98i	1.96832	−	1.88092i
$757$	539.096	−	539.096i	0.712148	−	0.712148i	−0.254837	−	0.966984i	$-0.582022\pi$
$757$	539.096	−	539.096i	0.712148	−	0.712148i	0.966984	+	0.254837i	$0.0820217\pi$
$758$	1714.03	+	459.272i	2.26125	+	0.605900i
$759$	−81.6604	−	141.482i	−0.107589	−	0.186405i
$760$	80.0186	−	154.065i	0.105288	−	0.202717i
$761$	−273.235	−	473.257i	−0.359047	−	0.621888i	0.628755	−	0.777604i	$-0.283565\pi$
$761$	−273.235	−	473.257i	−0.359047	−	0.621888i	−0.987802	+	0.155716i	$0.950232\pi$
$762$	−571.682	−	2134.64i	−0.750239	−	2.80136i
$763$	−12.3032	+	551.188i	−0.0161247	+	0.722395i
$764$	−335.535			−0.439181
$765$	−111.091	−	57.7347i	−0.145217	−	0.0754702i
$766$	1477.12	+	852.817i	1.92836	+	1.11334i
$767$	265.391	−	71.1114i	0.346012	−	0.0927137i
$768$	−1394.85	+	1394.49i	−1.81621	+	1.81575i
$769$	−457.090			−0.594396			−0.297198	−	0.954816i	$-0.596052\pi$
$769$	−457.090			−0.594396			−0.297198	+	0.954816i	$0.596052\pi$
$770$	−159.021	+	290.154i	−0.206520	+	0.376823i
$771$	−541.510	−	312.734i	−0.702348	−	0.405621i
$772$	−1993.39	−	534.127i	−2.58211	−	0.691875i
$773$	719.311	−	192.739i	0.930544	−	0.249339i	0.238457	−	0.971153i	$-0.423358\pi$
$773$	719.311	−	192.739i	0.930544	−	0.249339i	0.692087	+	0.721814i	$0.256692\pi$
$774$	1355.08	+	0.346813i	1.75075	+	0.000448079i
$775$	−95.7721	−	136.235i	−0.123577	−	0.175787i
$776$	3006.42			3.87425
$777$	15.8812	−	707.430i	0.0204392	−	0.910463i
$778$	805.568	+	805.568i	1.03543	+	1.03543i
$779$	6.25252	+	10.8297i	0.00802634	+	0.0139020i
$780$	126.701	−	573.699i	0.162438	−	0.735512i
$781$	147.805	−	256.005i	0.189250	−	0.327791i
$782$	−230.488	−	61.7592i	−0.294742	−	0.0789759i
$783$	275.264	+	275.475i	0.351550	+	0.351820i
$784$	−2889.78	−	129.071i	−3.68594	−	0.164631i
$785$	18.0217	+	404.109i	0.0229576	+	0.514789i
$786$	−2650.34	−	0.339158i	−3.37193	−	0.000431499i
$787$	569.075	−	152.483i	0.723094	−	0.193752i	0.121542	−	0.992586i	$-0.461216\pi$
$787$	569.075	−	152.483i	0.723094	−	0.193752i	0.601552	+	0.798834i	$0.294549\pi$
$788$	443.996	+	1657.01i	0.563446	+	2.10281i
$789$	−0.0722093	+	564.277i	−9.15200e−5	+	0.715180i
$790$	−208.880	+	9.31522i	−0.264405	+	0.0117914i
$791$	870.205	+	254.115i	1.10013	+	0.321258i
$792$	566.207	+	151.870i	0.714907	+	0.191755i
$793$	83.4807	−	311.554i	0.105272	−	0.392881i
$794$	−964.505	−	556.857i	−1.21474	−	0.701332i
$795$	−805.458	−	177.885i	−1.01316	−	0.223755i
$796$	−2511.21	+	1449.85i	−3.15479	+	1.82142i
$797$	−517.339	+	517.339i	−0.649108	+	0.649108i	−0.952778	−	0.303669i	$-0.901788\pi$
$797$	−517.339	+	517.339i	−0.649108	+	0.649108i	0.303669	+	0.952778i	$0.401788\pi$
$798$	−50.8424	−	92.8117i	−0.0637122	−	0.116305i
$799$			66.9918i			0.0838445i
$800$	−2991.07	−	521.651i	−3.73883	−	0.652064i
$801$	567.518	+	0.145248i	0.708512	+	0.000181333i
$802$	489.648	+	1827.39i	0.610534	+	2.27854i
$803$	65.1037	−	242.970i	0.0810756	−	0.302578i
$804$	−82.4161	+	142.707i	−0.102508	+	0.177496i
$805$	777.736	−	17.3068i	0.966132	−	0.0214991i
$806$			92.4492i			0.114701i
$807$	−279.981	−	280.052i	−0.346940	−	0.347029i
$808$	−923.334	−	3445.93i	−1.14274	−	4.26476i
$809$	−201.098	+	348.312i	−0.248576	+	0.430547i	−0.963131	−	0.269033i	$-0.913296\pi$
$809$	−201.098	+	348.312i	−0.248576	+	0.430547i	0.714555	+	0.699580i	$0.246629\pi$
$810$	−68.8265	−	1561.29i	−0.0849709	−	1.92751i
$811$			671.468i			0.827950i	0.910288	+	0.413975i	$0.135860\pi$
$811$			671.468i			0.827950i	−0.910288	+	0.413975i	$0.864140\pi$
$812$	24.5361	−	1099.23i	0.0302169	−	1.35373i
$813$	99.8678	−	26.7458i	0.122839	−	0.0328977i
$814$	275.865	−	159.271i	0.338901	−	0.195665i
$815$	−1055.31	−	548.111i	−1.29486	−	0.672528i
$816$	426.746	−	246.309i	0.522973	−	0.301849i
$817$	13.1884	−	49.2196i	0.0161424	−	0.0602443i
$818$	−1590.31	−	1590.31i	−1.94414	−	1.94414i
$819$	−156.567	−	163.800i	−0.191168	−	0.200000i
$820$	351.890	−	384.740i	0.429134	−	0.469196i
$821$	804.438	−	464.443i	0.979828	−	0.565704i	0.0776095	−	0.996984i	$-0.475271\pi$
$821$	804.438	−	464.443i	0.979828	−	0.565704i	0.902218	+	0.431280i	$0.141938\pi$
$822$	135.279	−	504.611i	0.164573	−	0.613882i
$823$	744.166	−	199.399i	0.904211	−	0.242283i	0.223387	−	0.974730i	$-0.428289\pi$
$823$	744.166	−	199.399i	0.904211	−	0.242283i	0.680824	+	0.732447i	$0.261622\pi$
$824$	−111.556	+	64.4066i	−0.135383	+	0.0781634i
$825$	63.1432	+	172.550i	0.0765372	+	0.209152i
$826$	−1980.70	−	578.397i	−2.39794	−	0.700239i
$827$	587.764	+	587.764i	0.710718	+	0.710718i	0.966685	−	0.255967i	$-0.0823939\pi$
$827$	587.764	+	587.764i	0.710718	+	0.710718i	−0.255967	+	0.966685i	$0.582394\pi$
$828$	−563.284	−	2104.36i	−0.680295	−	2.54150i
$829$	−286.905	+	496.935i	−0.346086	+	0.599439i	−0.985550	−	0.169382i	$-0.945823\pi$
$829$	−286.905	+	496.935i	−0.346086	+	0.599439i	0.639464	+	0.768821i	$0.279156\pi$
$830$	443.215	+	1401.14i	0.533993	+	1.68812i
$831$	−0.198162	+	1548.53i	−0.000238463	+	1.86346i
$832$	591.321	+	591.321i	0.710722	+	0.710722i
$833$	129.976	+	41.1244i	0.156033	+	0.0493691i
$834$	319.025	−	552.404i	0.382524	−	0.662355i
$835$	−240.164	−	376.206i	−0.287621	−	0.450546i
$836$	17.4208	−	30.1736i	0.0208382	−	0.0360929i
$837$	46.4825	+	173.742i	0.0555346	+	0.207577i
$838$	−131.225	−	35.1616i	−0.156593	−	0.0419589i
$839$		−	996.548i		−	1.18778i	−0.804546	−	0.593891i	$-0.797591\pi$
$839$		−	996.548i		−	1.18778i	0.804546	−	0.593891i	$-0.202409\pi$
$840$	−1929.86	+	2017.19i	−2.29745	+	2.40141i
$841$	−632.966			−0.752635
$842$	−219.052	+	817.513i	−0.260157	+	0.970918i
$843$	−263.429	+	982.629i	−0.312491	+	1.16563i
$844$	−3431.40	−	1981.12i	−4.06564	−	2.34730i
$845$	761.980	+	168.181i	0.901751	+	0.199031i
$846$	−724.307	+	417.932i	−0.856155	+	0.494009i
$847$	417.950	−	687.983i	0.493448	−	0.812259i
$848$	2295.51	−	2295.51i	2.70697	−	2.70697i
$849$	−0.0121606	+	95.0286i	−1.43234e−5	+	0.111930i
$850$	243.459	+	112.974i	0.286423	+	0.132911i
$851$	−648.598	−	374.468i	−0.762160	−	0.440033i
$852$	2787.83	−	2787.12i	3.27211	−	3.27127i
$853$	−459.861	+	459.861i	−0.539111	+	0.539111i	−0.923268	−	0.384157i	$-0.874492\pi$
$853$	−459.861	+	459.861i	−0.539111	+	0.539111i	0.384157	+	0.923268i	$0.374492\pi$
$854$	−1750.65	+	1674.20i	−2.04994	+	1.96042i
$855$	−57.3826	−	12.6806i	−0.0671141	−	0.0148312i
$856$	1907.13	+	3303.24i	2.22795	+	3.85893i
$857$	241.166	+	900.042i	0.281407	+	1.05022i	0.951425	+	0.307880i	$0.0996195\pi$
$857$	241.166	+	900.042i	0.281407	+	1.05022i	−0.670019	+	0.742344i	$0.733714\pi$
$858$	26.4132	−	98.5248i	0.0307846	−	0.114831i
$859$	843.166	+	1460.41i	0.981567	+	1.70012i	0.656296	+	0.754503i	$0.272122\pi$
$859$	843.166	+	1460.41i	0.981567	+	1.70012i	0.325271	+	0.945621i	$0.394544\pi$
$860$	−2122.48	+	94.6544i	−2.46800	+	0.110063i
$861$	−47.6726	−	195.354i	−0.0553689	−	0.226892i
$862$	311.724	−	311.724i	0.361629	−	0.361629i
$863$	−1162.27	−	311.431i	−1.34678	−	0.360870i	−0.487838	−	0.872934i	$-0.662214\pi$
$863$	−1162.27	−	311.431i	−1.34678	−	0.360870i	−0.858947	+	0.512065i	$0.828881\pi$
$864$	2839.17	+	1640.65i	3.28607	+	1.89890i
$865$	−530.415	−	275.488i	−0.613197	−	0.318483i
$866$	53.7587	+	93.1129i	0.0620771	+	0.107521i
$867$	815.055	−	218.282i	0.940087	−	0.251767i
$868$	263.644	−	433.981i	0.303737	−	0.499979i
$869$	−26.5493			−0.0305516
$870$	−615.968	−	563.519i	−0.708009	−	0.647723i
$871$	15.7118	+	9.07121i	0.0180388	+	0.0104147i
$872$	−2022.68	+	541.976i	−2.31959	+	0.621532i
$873$	−263.147	−	983.085i	−0.301429	−	1.12610i
$874$	−112.006			−0.128153
$875$	−865.120	−	131.119i	−0.988709	−	0.149851i
$876$	1677.58	−	2904.80i	1.91505	−	3.31598i
$877$	−219.033	−	58.6896i	−0.249752	−	0.0669209i	0.131771	−	0.991280i	$-0.457934\pi$
$877$	−219.033	−	58.6896i	−0.249752	−	0.0669209i	−0.381523	+	0.924359i	$0.624600\pi$
$878$	501.141	−	134.280i	0.570776	−	0.152939i
$879$	292.305	+	506.436i	0.332542	+	0.576150i
$880$	−706.133	−	155.855i	−0.802424	−	0.177107i
$881$	−754.788			−0.856740			−0.428370	−	0.903604i	$-0.640912\pi$
$881$	−754.788			−0.856740			−0.428370	+	0.903604i	$0.640912\pi$
$882$	366.229	+	1661.84i	0.415226	+	1.88417i
$883$	−446.257	−	446.257i	−0.505387	−	0.505387i	0.407720	−	0.913107i	$-0.366324\pi$
$883$	−446.257	−	446.257i	−0.505387	−	0.505387i	−0.913107	+	0.407720i	$0.866324\pi$
$884$	−54.4865	−	94.3733i	−0.0616363	−	0.106757i
$885$	−965.914	+	616.449i	−1.09143	+	0.696553i
$886$	−663.335	+	1148.93i	−0.748685	+	1.29676i
$887$	−439.047	−	117.642i	−0.494980	−	0.132630i	0.00268920	−	0.999996i	$-0.499144\pi$
$887$	−439.047	−	117.642i	−0.494980	−	0.132630i	−0.497669	+	0.867367i	$0.665811\pi$
$888$	2596.13	−	695.276i	2.92358	−	0.782969i
$889$	1282.70	+	374.569i	1.44285	+	0.421338i
$890$	−1215.41	+	54.2027i	−1.36563	+	0.0609019i
$891$	0.101576	−	198.440i	0.000114002	−	0.222716i
$892$	2758.17	−	739.048i	3.09211	−	0.828529i
$893$	8.13868	+	30.3740i	0.00911386	+	0.0340134i
$894$	1177.12	+	0.150633i	1.31669	+	0.000168494i
$895$	−224.246	−	205.099i	−0.250554	−	0.229161i
$896$	−683.080	−	2797.59i	−0.762366	−	3.12231i
$897$	−231.662	+	62.0418i	−0.258263	+	0.0691658i
$898$	−438.721	+	1637.33i	−0.488554	+	1.82331i
$899$	83.2051	+	48.0385i	0.0925529	+	0.0534354i
$900$	217.487	+	2440.60i	0.241652	+	2.71178i
$901$	−132.498	+	76.4976i	−0.147056	+	0.0849030i
$902$	64.0092	−	64.0092i	0.0709636	−	0.0709636i
$903$	−425.520	+	700.243i	−0.471230	+	0.775462i
$904$			3443.24i			3.80889i
$905$	−30.9422	−	6.82942i	−0.0341902	−	0.00754632i
$906$	1066.97	+	1848.60i	1.17767	+	2.04039i
$907$	−232.618	−	868.142i	−0.256470	−	0.957158i	−0.967267	−	0.253761i	$-0.918332\pi$
$907$	−232.618	−	868.142i	−0.256470	−	0.957158i	0.710797	−	0.703397i	$-0.248334\pi$
$908$	−792.035	+	2955.91i	−0.872285	+	3.25541i
$909$	−1045.99	+	603.543i	−1.15070	+	0.663964i
$910$	351.039	+	335.755i	0.385757	+	0.368962i
$911$			865.000i			0.949506i	0.880119	+	0.474753i	$0.157463\pi$
$911$			865.000i			0.949506i	−0.880119	+	0.474753i	$0.842537\pi$
$912$	163.562	−	163.521i	0.179345	−	0.179299i
$913$	48.2959	+	180.243i	0.0528981	+	0.197418i
$914$	139.324	−	241.317i	0.152433	−	0.264022i
$915$	59.7580	+	1343.85i	0.0653093	+	1.46869i
$916$		−	1049.50i		−	1.14574i
$917$	832.081	−	1369.68i	0.907395	−	1.49365i
$918$	−204.887	−	205.045i	−0.223189	−	0.223360i
$919$	−846.227	+	488.569i	−0.920813	+	0.531632i	−0.883894	−	0.467687i	$-0.845088\pi$
$919$	−846.227	+	488.569i	−0.920813	+	0.531632i	−0.0369185	+	0.999318i	$0.511754\pi$
$920$	891.130	+	2817.13i	0.968620	+	3.06210i
$921$	−496.918	−	860.942i	−0.539542	−	0.934791i
$922$	83.8315	−	312.864i	0.0909236	−	0.339331i
$923$	−306.874	−	306.874i	−0.332475	−	0.332475i
$924$	−404.961	+	387.178i	−0.438269	+	0.419024i
$925$	646.318	+	540.273i	0.698722	+	0.584078i
$926$	1074.26	−	620.222i	1.16010	−	0.669786i
$927$	30.8250	+	30.8408i	0.0332524	+	0.0332694i
$928$	1692.01	−	453.373i	1.82329	−	0.488549i
$929$	−1273.67	+	735.355i	−1.37101	+	0.791555i	−0.991056	−	0.133449i	$-0.957395\pi$
$929$	−1273.67	+	735.355i	−1.37101	+	0.791555i	−0.379958	+	0.925004i	$0.624062\pi$
$930$	−116.236	−	367.622i	−0.124985	−	0.395292i
$931$	63.9270	+	2.85527i	0.0686648	+	0.00306689i
$932$	1411.77	+	1411.77i	1.51477	+	1.51477i
$933$	807.784	−	807.577i	0.865792	−	0.865570i
$934$	840.497	−	1455.78i	0.899889	−	1.55865i
$935$	30.2440	+	15.7082i	0.0323465	+	0.0168002i
$936$	430.508	−	745.221i	0.459944	−	0.796176i
$937$	250.386	+	250.386i	0.267221	+	0.267221i	0.827979	−	0.560758i	$-0.189490\pi$
$937$	250.386	+	250.386i	0.267221	+	0.267221i	−0.560758	+	0.827979i	$0.689490\pi$
$938$	−65.4754	−	119.488i	−0.0698032	−	0.127386i
$939$	−853.039	−	492.648i	−0.908455	−	0.524652i
$940$	1105.12	−	705.490i	1.17566	−	0.750521i
$941$	108.981	−	188.761i	0.115814	−	0.200596i	−0.802291	−	0.596934i	$-0.796386\pi$
$941$	108.981	−	188.761i	0.115814	−	0.200596i	0.918105	+	0.396337i	$0.129719\pi$
$942$	−242.512	+	904.605i	−0.257444	+	0.960302i
$943$	−205.580	−	55.0849i	−0.218006	−	0.0584145i
$944$		−	4509.64i		−	4.77716i
$945$	828.529	+	454.494i	0.876750	+	0.480946i
$946$	−368.865			−0.389920
$947$	−137.101	+	511.668i	−0.144774	+	0.540304i	0.854991	+	0.518642i	$0.173562\pi$
$947$	−137.101	+	511.668i	−0.144774	+	0.540304i	−0.999765	+	0.0216619i	$0.993104\pi$
$948$	−341.972	−	91.6781i	−0.360730	−	0.0967069i
$949$	−319.814	−	184.645i	−0.337001	−	0.194568i
$950$	124.109	+	21.6450i	0.130641	+	0.0227842i
$951$	−318.272	+	551.101i	−0.334671	+	0.579496i
$952$	−11.5549	+	517.665i	−0.0121375	+	0.543765i
$953$	−710.730	+	710.730i	−0.745782	+	0.745782i	−0.973684	−	0.227902i	$-0.926813\pi$
$953$	−710.730	+	710.730i	−0.745782	+	0.745782i	0.227902	+	0.973684i	$0.426813\pi$
$954$	−1653.68	−	955.315i	−1.73341	−	1.00138i
$955$	−46.4623	−	146.882i	−0.0486516	−	0.153803i
$956$	2032.99	+	1173.75i	2.12656	+	1.22777i
$957$	−74.9484	−	74.9676i	−0.0783160	−	0.0783360i
$958$	−437.026	+	437.026i	−0.456186	+	0.456186i
$959$	218.338	+	228.308i	0.227672	+	0.238068i
$960$	−3094.84	−	1607.90i	−3.22379	−	1.67490i
$961$	−458.314	−	793.824i	−0.476914	−	0.826039i
$962$	−121.038	−	451.719i	−0.125819	−	0.469562i
$963$	913.217	−	912.750i	0.948305	−	0.947819i
$964$	−2090.19	−	3620.32i	−2.16825	−	3.75552i
$965$	−42.2136	−	946.576i	−0.0437447	−	0.980908i
$966$	1728.84	+	505.090i	1.78969	+	0.522867i
$967$	236.165	−	236.165i	0.244224	−	0.244224i	−0.574371	−	0.818595i	$-0.694753\pi$
$967$	236.165	−	236.165i	0.244224	−	0.244224i	0.818595	+	0.574371i	$0.194753\pi$
$968$	2953.31	+	791.336i	3.05094	+	0.817496i
$969$	−9.44038	+	5.44879i	−0.00974239	+	0.00562311i
$970$	657.990	+	2080.11i	0.678340	+	2.14444i
$971$	−731.438	−	1266.89i	−0.753283	−	1.30472i	−0.946224	−	0.323514i	$-0.895136\pi$
$971$	−731.438	−	1266.89i	−0.753283	−	1.30472i	0.192941	−	0.981210i	$-0.438197\pi$
$972$	686.546	−	2555.68i	0.706324	−	2.62930i
$973$	185.364	+	338.275i	0.190507	+	0.347662i
$974$	1934.51			1.98615
$975$	268.683	−	23.9776i	0.275573	−	0.0245924i
$976$	−4584.79	−	2647.03i	−4.69753	−	2.71212i
$977$	−141.942	+	38.0332i	−0.145283	+	0.0389286i	−0.330728	−	0.943726i	$-0.607294\pi$
$977$	−141.942	+	38.0332i	−0.145283	+	0.0389286i	0.185444	+	0.982655i	$0.440628\pi$
$978$	−1946.58	−	1947.08i	−1.99037	−	1.99087i
$979$	−154.483			−0.157797
$980$	−690.372	−	2577.21i	−0.704461	−	2.62980i
$981$	354.266	+	613.969i	0.361127	+	0.625861i
$982$	−175.302	−	46.9721i	−0.178516	−	0.0478331i
$983$	−1527.87	+	409.391i	−1.55429	+	0.416471i	−0.930850	−	0.365401i	$-0.880932\pi$
$983$	−1527.87	+	409.391i	−1.55429	+	0.416471i	−0.623439	+	0.781872i	$0.714265\pi$
$984$	661.488	−	381.798i	0.672244	−	0.388006i
$985$	−663.883	+	423.812i	−0.673993	+	0.430266i
$986$	−154.846			−0.157045
$987$	11.3487	−	505.530i	0.0114982	−	0.512188i
$988$	−36.1693	−	36.1693i	−0.0366086	−	0.0366086i
$989$	433.626	+	751.063i	0.438449	+	0.759416i
$990$	18.8439	+	424.991i	0.0190343	+	0.429283i
$991$	198.059	−	343.048i	0.199858	−	0.346164i	−0.748624	−	0.662994i	$-0.769285\pi$
$991$	198.059	−	343.048i	0.199858	−	0.346164i	0.948482	+	0.316831i	$0.102619\pi$
$992$	781.427	+	209.383i	0.787729	+	0.211071i
$993$	200.521	+	748.736i	0.201934	+	0.754015i
$994$	773.096	+	3166.25i	0.777763	+	3.18536i
$995$	−982.411	−	898.529i	−0.987348	−	0.903044i
$996$	−0.318437	+	2488.42i	−0.000319716	+	2.49841i
$997$	−1616.02	+	433.012i	−1.62089	+	0.434315i	−0.951262	−	0.308385i	$-0.900211\pi$
$997$	−1616.02	+	433.012i	−1.62089	+	0.434315i	−0.669624	+	0.742700i	$0.733545\pi$
$998$	240.048	+	895.871i	0.240529	+	0.897666i
$999$	−454.588	−	788.068i	−0.455043	−	0.788857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.38.28	yes	112
3.2	odd	2	inner	105.3.w.a.38.1	yes	112
5.2	odd	4	inner	105.3.w.a.17.28	yes	112
7.5	odd	6	inner	105.3.w.a.68.1	yes	112
15.2	even	4	inner	105.3.w.a.17.1	✓	112
21.5	even	6	inner	105.3.w.a.68.28	yes	112
35.12	even	12	inner	105.3.w.a.47.1	yes	112
105.47	odd	12	inner	105.3.w.a.47.28	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.1	✓	112	15.2	even	4	inner
105.3.w.a.17.28	yes	112	5.2	odd	4	inner
105.3.w.a.38.1	yes	112	3.2	odd	2	inner
105.3.w.a.38.28	yes	112	1.1	even	1	trivial
105.3.w.a.47.1	yes	112	35.12	even	12	inner
105.3.w.a.47.28	yes	112	105.47	odd	12	inner
105.3.w.a.68.1	yes	112	7.5	odd	6	inner
105.3.w.a.68.28	yes	112	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998723 - 3.72728i) q^{2} +(2.89768 + 0.776828i) q^{3} +(-9.43110 - 5.44505i) q^{4} +(1.07764 - 4.88249i) q^{5} +(5.78944 - 10.0246i) q^{6} +(3.36385 + 6.13877i) q^{7} +(-18.8000 + 18.8000i) q^{8} +(7.79308 + 4.50199i) q^{9} +(-17.1222 - 8.89293i) q^{10} +(-2.12166 - 1.22494i) q^{11} +(-23.0984 - 23.1043i) q^{12} +(-2.54324 + 2.54324i) q^{13} +(26.2405 - 6.40708i) q^{14} +(6.91551 - 13.3107i) q^{15} +(29.5169 + 51.1248i) q^{16} +(-0.720080 - 2.68738i) q^{17} +(24.5633 - 24.5508i) q^{18} +(-0.652966 - 1.13097i) q^{19} +(-36.7487 + 40.1794i) q^{20} +(4.97858 + 20.4013i) q^{21} +(-6.68464 + 6.68464i) q^{22} +(21.4692 + 5.75265i) q^{23} +(-69.0809 + 39.8721i) q^{24} +(-22.6774 - 10.5231i) q^{25} +(6.93938 + 12.0194i) q^{26} +(19.0846 + 19.0992i) q^{27} +(1.70114 - 76.2117i) q^{28} +14.4234 q^{29} +(-42.7062 - 39.0698i) q^{30} +(5.76876 + 3.33060i) q^{31} +(117.310 - 31.4332i) q^{32} +(-5.19631 - 5.19764i) q^{33} -10.7358 q^{34} +(33.5975 - 9.80855i) q^{35} +(-48.9837 - 84.8924i) q^{36} +(-32.5475 - 8.72107i) q^{37} +(-4.86758 + 1.30426i) q^{38} +(-9.34515 + 5.39383i) q^{39} +(71.5313 + 112.051i) q^{40} -9.57556 q^{41} +(81.0137 + 1.81870i) q^{42} +(27.5904 + 27.5904i) q^{43} +(13.3397 + 23.1050i) q^{44} +(30.3791 - 33.1981i) q^{45} +(42.8835 - 74.2765i) q^{46} +(-23.2584 - 6.23208i) q^{47} +(45.8153 + 171.073i) q^{48} +(-26.3691 + 41.2998i) q^{49} +(-61.8712 + 74.0153i) q^{50} +(0.00106809 - 8.34653i) q^{51} +(37.8336 - 10.1375i) q^{52} +(-14.2328 - 53.1174i) q^{53} +(90.2484 - 52.0587i) q^{54} +(-8.26714 + 9.03892i) q^{55} +(-178.650 - 52.1687i) q^{56} +(-1.01352 - 3.78443i) q^{57} +(14.4050 - 53.7600i) q^{58} +(-66.1564 - 38.1954i) q^{59} +(-137.698 + 87.8796i) q^{60} +(-77.6638 + 44.8392i) q^{61} +(18.1755 - 18.1755i) q^{62} +(-1.42200 + 62.9839i) q^{63} -232.507i q^{64} +(9.67663 + 15.1580i) q^{65} +(-24.5628 + 14.1771i) q^{66} +(-1.30554 - 4.87233i) q^{67} +(-7.84174 + 29.2658i) q^{68} +(57.7420 + 33.3472i) q^{69} +(-3.00464 - 135.023i) q^{70} +120.663i q^{71} +(-231.148 + 61.8725i) q^{72} +(26.5743 + 99.1765i) q^{73} +(-65.0118 + 112.604i) q^{74} +(-57.5371 - 48.1091i) q^{75} +14.2217i q^{76} +(0.382694 - 17.1449i) q^{77} +(10.7711 + 40.2190i) q^{78} +(9.38512 - 5.41850i) q^{79} +(281.425 - 89.0217i) q^{80} +(40.4641 + 70.1688i) q^{81} +(-9.56333 + 35.6908i) q^{82} +(-53.8586 - 53.8586i) q^{83} +(64.1327 - 219.515i) q^{84} +(-13.8971 + 0.619755i) q^{85} +(130.393 - 75.2822i) q^{86} +(41.7943 + 11.2045i) q^{87} +(62.9162 - 16.8583i) q^{88} +(54.6094 - 31.5288i) q^{89} +(-93.3984 - 146.387i) q^{90} +(-24.1674 - 7.05730i) q^{91} +(-171.155 - 171.155i) q^{92} +(14.1287 + 14.1323i) q^{93} +(-46.4575 + 80.4667i) q^{94} +(-6.22562 + 1.96932i) q^{95} +(364.346 + 0.0466246i) q^{96} +(-79.9577 - 79.9577i) q^{97} +(127.601 + 139.532i) q^{98} +(-11.0196 - 19.0977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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