LMFDB - Embedded newform 105.3.w.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(17,105)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			17.5
Character	$\chi$	$=$	105.17
Dual form			105.3.w.a.68.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.63032 - 0.704792i) q^{2} +(1.27430 + 2.71591i) q^{3} +(2.95775 + 1.70766i) q^{4} +(-2.97248 - 4.02050i) q^{5} +(-1.43765 - 8.04182i) q^{6} +(6.12741 - 3.38450i) q^{7} +(1.12583 + 1.12583i) q^{8} +(-5.75234 + 6.92175i) q^{9} +(4.98495 + 12.6702i) q^{10} +(5.63427 + 3.25295i) q^{11} +(-0.868794 + 10.2090i) q^{12} +(13.0639 + 13.0639i) q^{13} +(-18.5024 + 4.58376i) q^{14} +(7.13149 - 13.1963i) q^{15} +(-8.99845 - 15.5858i) q^{16} +(30.7094 - 8.22856i) q^{17} +(20.0089 - 14.1522i) q^{18} +(4.50822 + 7.80847i) q^{19} +(-1.92621 - 16.9676i) q^{20} +(17.0001 + 12.3286i) q^{21} +(-12.5273 - 12.5273i) q^{22} +(0.794284 - 2.96431i) q^{23} +(-1.62302 + 4.49231i) q^{24} +(-7.32876 + 23.9017i) q^{25} +(-25.1549 - 43.5695i) q^{26} +(-26.1290 - 6.80247i) q^{27} +(23.9029 + 0.453019i) q^{28} +21.7392 q^{29} +(-28.0587 + 29.6842i) q^{30} +(-15.7113 - 9.07093i) q^{31} +(11.0357 + 41.1859i) q^{32} +(-1.65498 + 19.4474i) q^{33} -86.5750 q^{34} +(-31.8209 - 14.5749i) q^{35} +(-28.8339 + 10.6498i) q^{36} +(5.32041 - 19.8560i) q^{37} +(-6.35472 - 23.7161i) q^{38} +(-18.8331 + 52.1276i) q^{39} +(1.17989 - 7.87293i) q^{40} -60.4331 q^{41} +(-36.0266 - 44.4098i) q^{42} +(16.3358 - 16.3358i) q^{43} +(11.1098 + 19.2428i) q^{44} +(44.9275 + 2.55250i) q^{45} +(-4.17844 + 7.23727i) q^{46} +(-9.02511 + 33.6822i) q^{47} +(30.8629 - 44.2999i) q^{48} +(26.0903 - 41.4764i) q^{49} +(36.1227 - 57.7037i) q^{50} +(61.4809 + 72.9184i) q^{51} +(16.3310 + 60.9483i) q^{52} +(15.7852 - 4.22963i) q^{53} +(63.9334 + 36.3082i) q^{54} +(-3.66928 - 32.3219i) q^{55} +(10.7088 + 3.08807i) q^{56} +(-15.4623 + 22.1942i) q^{57} +(-57.1811 - 15.3216i) q^{58} +(-55.9306 - 32.2915i) q^{59} +(43.6278 - 26.8531i) q^{60} +(52.7606 - 30.4613i) q^{61} +(34.9327 + 34.9327i) q^{62} +(-11.8203 + 61.8812i) q^{63} -44.1224i q^{64} +(13.6912 - 91.3554i) q^{65} +(18.0595 - 49.9865i) q^{66} +(-6.94415 + 1.86068i) q^{67} +(104.882 + 28.1031i) q^{68} +(9.06294 - 1.62020i) q^{69} +(73.4270 + 60.7637i) q^{70} +40.3109i q^{71} +(-14.2689 + 1.31656i) q^{72} +(-85.5456 + 22.9219i) q^{73} +(-27.9887 + 48.4779i) q^{74} +(-74.2538 + 10.5535i) q^{75} +30.7940i q^{76} +(45.5331 + 0.862966i) q^{77} +(86.2761 - 123.839i) q^{78} +(34.2910 - 19.7979i) q^{79} +(-35.9148 + 82.5065i) q^{80} +(-14.8212 - 79.6325i) q^{81} +(158.958 + 42.5928i) q^{82} +(-16.2867 + 16.2867i) q^{83} +(29.2290 + 65.4954i) q^{84} +(-124.366 - 99.0078i) q^{85} +(-54.4817 + 31.4550i) q^{86} +(27.7022 + 59.0418i) q^{87} +(2.68098 + 10.0055i) q^{88} +(5.70943 - 3.29634i) q^{89} +(-116.375 - 38.3785i) q^{90} +(124.262 + 35.8331i) q^{91} +(7.41130 - 7.41130i) q^{92} +(4.61496 - 54.2296i) q^{93} +(47.4778 - 82.2340i) q^{94} +(17.9933 - 41.3358i) q^{95} +(-97.7944 + 82.4551i) q^{96} +(-56.3794 + 56.3794i) q^{97} +(-97.8582 + 90.7080i) q^{98} +(-54.9264 + 20.2870i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.63032	−	0.704792i	−1.31516	−	0.352396i	−0.467997	−	0.883730i	$-0.655024\pi$
$2$	−2.63032	−	0.704792i	−1.31516	−	0.352396i	−0.847162	+	0.531334i	$0.821691\pi$
$3$	1.27430	+	2.71591i	0.424765	+	0.905303i
$3$	1.27430	+	2.71591i	0.424765	+	0.905303i
$4$	2.95775	+	1.70766i	0.739437	+	0.426914i
$5$	−2.97248	−	4.02050i	−0.594495	−	0.804099i
$5$	−2.97248	−	4.02050i	−0.594495	−	0.804099i
$6$	−1.43765	−	8.04182i	−0.239609	−	1.34030i
$7$	6.12741	−	3.38450i	0.875344	−	0.483500i
$7$	6.12741	−	3.38450i	0.875344	−	0.483500i
$8$	1.12583	+	1.12583i	0.140729	+	0.140729i
$9$	−5.75234	+	6.92175i	−0.639149	+	0.769083i
$10$	4.98495	+	12.6702i	0.498495	+	1.26702i
$11$	5.63427	+	3.25295i	0.512207	+	0.295723i	0.733740	−	0.679430i	$-0.237773\pi$
$11$	5.63427	+	3.25295i	0.512207	+	0.295723i	−0.221534	+	0.975153i	$0.571106\pi$
$12$	−0.868794	+	10.2090i	−0.0723995	+	0.850753i
$13$	13.0639	+	13.0639i	1.00491	+	1.00491i	0.999988	+	0.00492615i	$0.00156805\pi$
$13$	13.0639	+	13.0639i	1.00491	+	1.00491i	0.00492615	+	0.999988i	$0.498432\pi$
$14$	−18.5024	+	4.58376i	−1.32160	+	0.327412i
$15$	7.13149	−	13.1963i	0.475432	−	0.879752i
$16$	−8.99845	−	15.5858i	−0.562403	−	0.974110i
$17$	30.7094	−	8.22856i	1.80644	−	0.484033i	0.811483	−	0.584376i	$-0.198661\pi$
$17$	30.7094	−	8.22856i	1.80644	−	0.484033i	0.994953	+	0.100343i	$0.0319939\pi$
$18$	20.0089	−	14.1522i	1.11160	−	0.786234i
$19$	4.50822	+	7.80847i	0.237275	+	0.410972i	0.959931	−	0.280235i	$-0.0904125\pi$
$19$	4.50822	+	7.80847i	0.237275	+	0.410972i	−0.722657	+	0.691207i	$0.757079\pi$
$20$	−1.92621	−	16.9676i	−0.0963106	−	0.848379i
$21$	17.0001	+	12.3286i	0.809530	+	0.587078i
$22$	−12.5273	−	12.5273i	−0.569422	−	0.569422i
$23$	0.794284	−	2.96431i	0.0345341	−	0.128883i	−0.946507	−	0.322684i	$-0.895415\pi$
$23$	0.794284	−	2.96431i	0.0345341	−	0.128883i	0.981041	+	0.193801i	$0.0620816\pi$
$24$	−1.62302	+	4.49231i	−0.0676258	+	0.187180i
$25$	−7.32876	+	23.9017i	−0.293150	+	0.956066i
$26$	−25.1549	−	43.5695i	−0.967495	−	1.67575i
$27$	−26.1290	−	6.80247i	−0.967742	−	0.251943i
$28$	23.9029	+	0.453019i	0.853674	+	0.0161793i
$29$	21.7392			0.749629			0.374814	−	0.927100i	$-0.377706\pi$
$29$	21.7392			0.749629			0.374814	+	0.927100i	$0.377706\pi$
$30$	−28.0587	+	29.6842i	−0.935291	+	0.989474i
$31$	−15.7113	−	9.07093i	−0.506817	−	0.292611i	0.224708	−	0.974426i	$-0.427857\pi$
$31$	−15.7113	−	9.07093i	−0.506817	−	0.292611i	−0.731524	+	0.681816i	$0.761191\pi$
$32$	11.0357	+	41.1859i	0.344867	+	1.28706i
$33$	−1.65498	+	19.4474i	−0.0501510	+	0.589315i
$34$	−86.5750			−2.54632
$35$	−31.8209	−	14.5749i	−0.909170	−	0.416425i
$36$	−28.8339	+	10.6498i	−0.800942	+	0.295827i
$37$	5.32041	−	19.8560i	0.143795	−	0.536650i	−0.856011	−	0.516957i	$-0.827065\pi$
$37$	5.32041	−	19.8560i	0.143795	−	0.536650i	0.999806	−	0.0196925i	$-0.00626871\pi$
$38$	−6.35472	−	23.7161i	−0.167229	−	0.624109i
$39$	−18.8331	+	52.1276i	−0.482899	+	1.33660i
$40$	1.17989	−	7.87293i	0.0294974	−	0.196823i
$41$	−60.4331			−1.47398			−0.736989	−	0.675904i	$-0.763753\pi$
$41$	−60.4331			−1.47398			−0.736989	+	0.675904i	$0.763753\pi$
$42$	−36.0266	−	44.4098i	−0.857777	−	1.05738i
$43$	16.3358	−	16.3358i	0.379902	−	0.379902i	−0.491165	−	0.871067i	$-0.663429\pi$
$43$	16.3358	−	16.3358i	0.379902	−	0.379902i	0.871067	+	0.491165i	$0.163429\pi$
$44$	11.1098	+	19.2428i	0.252496	+	0.437336i
$45$	44.9275	+	2.55250i	0.998390	+	0.0567223i
$46$	−4.17844	+	7.23727i	−0.0908356	+	0.157332i
$47$	−9.02511	+	33.6822i	−0.192024	+	0.716642i	0.800994	+	0.598673i	$0.204305\pi$
$47$	−9.02511	+	33.6822i	−0.192024	+	0.716642i	−0.993017	+	0.117969i	$0.962362\pi$
$48$	30.8629	−	44.2999i	0.642976	−	0.922914i
$49$	26.0903	−	41.4764i	0.532456	−	0.846458i
$50$	36.1227	−	57.7037i	0.722454	−	1.15407i
$51$	61.4809	+	72.9184i	1.20551	+	1.42977i
$52$	16.3310	+	60.9483i	0.314058	+	1.17208i
$53$	15.7852	−	4.22963i	0.297834	−	0.0798044i	−0.106808	−	0.994280i	$-0.534063\pi$
$53$	15.7852	−	4.22963i	0.297834	−	0.0798044i	0.404642	+	0.914475i	$0.367396\pi$
$54$	63.9334	+	36.3082i	1.18395	+	0.672374i
$55$	−3.66928	−	32.3219i	−0.0667142	−	0.587671i
$56$	10.7088	+	3.08807i	0.191229	+	0.0551440i
$57$	−15.4623	+	22.1942i	−0.271268	+	0.389373i
$58$	−57.1811	−	15.3216i	−0.985882	−	0.264166i
$59$	−55.9306	−	32.2915i	−0.947976	−	0.547314i	−0.0555241	−	0.998457i	$-0.517683\pi$
$59$	−55.9306	−	32.2915i	−0.947976	−	0.547314i	−0.892451	+	0.451143i	$0.851016\pi$
$60$	43.6278	−	26.8531i	0.727131	−	0.447552i
$61$	52.7606	−	30.4613i	0.864927	−	0.499366i	−0.000732064	−	1.00000i	$-0.500233\pi$
$61$	52.7606	−	30.4613i	0.864927	−	0.499366i	0.865659	+	0.500634i	$0.166900\pi$
$62$	34.9327	+	34.9327i	0.563430	+	0.563430i
$63$	−11.8203	+	61.8812i	−0.187624	+	0.982241i
$64$		−	44.1224i		−	0.689412i
$65$	13.6912	−	91.3554i	0.210634	−	1.40547i
$66$	18.0595	−	49.9865i	0.273629	−	0.757371i
$67$	−6.94415	+	1.86068i	−0.103644	+	0.0277713i	−0.310268	−	0.950649i	$-0.600419\pi$
$67$	−6.94415	+	1.86068i	−0.103644	+	0.0277713i	0.206624	+	0.978420i	$0.433752\pi$
$68$	104.882	+	28.1031i	1.54239	+	0.413281i
$69$	9.06294	−	1.62020i	0.131347	−	0.0234812i
$70$	73.4270	+	60.7637i	1.04896	+	0.868053i
$71$			40.3109i			0.567759i	0.958860	+	0.283879i	$0.0916215\pi$
$71$			40.3109i			0.567759i	−0.958860	+	0.283879i	$0.908378\pi$
$72$	−14.2689	+	1.31656i	−0.198180	+	0.0182856i
$73$	−85.5456	+	22.9219i	−1.17186	+	0.313998i	−0.791692	−	0.610920i	$-0.790800\pi$
$73$	−85.5456	+	22.9219i	−1.17186	+	0.313998i	−0.380165	+	0.924919i	$0.624133\pi$
$74$	−27.9887	+	48.4779i	−0.378226	+	0.655107i
$75$	−74.2538	+	10.5535i	−0.990050	+	0.140714i
$76$			30.7940i			0.405184i
$77$	45.5331	+	0.862966i	0.591339	+	0.0112074i
$78$	86.2761	−	123.839i	1.10610	−	1.58768i
$79$	34.2910	−	19.7979i	0.434064	−	0.250607i	−0.267013	−	0.963693i	$-0.586037\pi$
$79$	34.2910	−	19.7979i	0.434064	−	0.250607i	0.701076	+	0.713086i	$0.252703\pi$
$80$	−35.9148	+	82.5065i	−0.448935	+	1.03133i
$81$	−14.8212	−	79.6325i	−0.182978	−	0.983117i
$82$	158.958	+	42.5928i	1.93852	+	0.519424i
$83$	−16.2867	+	16.2867i	−0.196226	+	0.196226i	−0.798380	−	0.602154i	$-0.794309\pi$
$83$	−16.2867	+	16.2867i	−0.196226	+	0.196226i	0.602154	+	0.798380i	$0.294309\pi$
$84$	29.2290	+	65.4954i	0.347964	+	0.779707i
$85$	−124.366	−	99.0078i	−1.46313	−	1.16480i
$86$	−54.4817	+	31.4550i	−0.633508	+	0.365756i
$87$	27.7022	+	59.0418i	0.318416	+	0.678642i
$88$	2.68098	+	10.0055i	0.0304657	+	0.113699i
$89$	5.70943	−	3.29634i	0.0641509	−	0.0370376i	−0.467581	−	0.883950i	$-0.654875\pi$
$89$	5.70943	−	3.29634i	0.0641509	−	0.0370376i	0.531732	+	0.846912i	$0.321541\pi$
$90$	−116.375	−	38.3785i	−1.29305	−	0.426427i
$91$	124.262	+	35.8331i	1.36552	+	0.393770i
$92$	7.41130	−	7.41130i	0.0805577	−	0.0805577i
$93$	4.61496	−	54.2296i	0.0496233	−	0.583114i
$94$	47.4778	−	82.2340i	0.505083	−	0.874830i
$95$	17.9933	−	41.3358i	0.189403	−	0.435114i
$96$	−97.7944	+	82.4551i	−1.01869	+	0.858907i
$97$	−56.3794	+	56.3794i	−0.581230	+	0.581230i	−0.935241	−	0.354011i	$-0.884818\pi$
$97$	−56.3794	+	56.3794i	−0.581230	+	0.581230i	0.354011	+	0.935241i	$0.384818\pi$
$98$	−97.8582	+	90.7080i	−0.998553	+	0.925592i
$99$	−54.9264	+	20.2870i	−0.554812	+	0.204919i
$100$	−62.4924	+	58.1800i	−0.624924	+	0.581800i
$101$	−49.1726	+	85.1694i	−0.486857	+	0.843261i	−0.999886	−	0.0151103i	$-0.995190\pi$
$101$	−49.1726	+	85.1694i	−0.486857	+	0.843261i	0.513029	+	0.858371i	$0.328523\pi$
$102$	−110.322	−	235.130i	−1.08159	−	2.30520i
$103$	−19.5269	+	72.8754i	−0.189582	+	0.707528i	0.804022	+	0.594600i	$0.202690\pi$
$103$	−19.5269	+	72.8754i	−0.189582	+	0.707528i	−0.993603	+	0.112928i	$0.963977\pi$
$104$			29.4155i			0.282842i
$105$	−0.965253	−	104.996i	−0.00919289	−	0.999958i
$106$	−44.5011			−0.419822
$107$	98.3911	+	26.3638i	0.919543	+	0.246391i	0.687390	−	0.726288i	$-0.258756\pi$
$107$	98.3911	+	26.3638i	0.919543	+	0.246391i	0.232153	+	0.972679i	$0.425423\pi$
$108$	−65.6668	−	64.7394i	−0.608026	−	0.599439i
$109$	65.6120	+	37.8811i	0.601945	+	0.347533i	0.769806	−	0.638278i	$-0.220353\pi$
$109$	65.6120	+	37.8811i	0.601945	+	0.347533i	−0.167862	+	0.985811i	$0.553686\pi$
$110$	−13.1288	+	87.6030i	−0.119353	+	0.796391i
$111$	60.7070	−	10.8527i	0.546910	−	0.0977723i
$112$	−107.887	−	65.0452i	−0.963279	−	0.580760i
$113$	−10.8560	−	10.8560i	−0.0960709	−	0.0960709i	0.657438	−	0.753509i	$-0.271640\pi$
$113$	−10.8560	−	10.8560i	−0.0960709	−	0.0960709i	−0.753509	+	0.657438i	$0.771640\pi$
$114$	56.3131	−	47.4802i	0.493974	−	0.416493i
$115$	−14.2790	+	5.61792i	−0.124165	+	0.0488515i
$116$	64.2991	+	37.1231i	0.554303	+	0.320027i
$117$	−165.573	+	15.2771i	−1.41515	+	0.130573i
$118$	124.356	+	124.356i	1.05387	+	1.05387i
$119$	160.320	−	154.356i	1.34722	−	1.29711i
$120$	22.8857	−	6.82796i	0.190714	−	0.0568996i
$121$	−39.3366	−	68.1330i	−0.325096	−	0.563083i
$122$	−160.246	+	42.9378i	−1.31349	+	0.351949i
$123$	−77.0097	−	164.131i	−0.626095	−	1.33440i
$124$	−30.9801	−	53.6590i	−0.249839	−	0.432734i
$125$	117.881	−	41.5819i	0.943049	−	0.332655i
$126$	74.7045	−	154.436i	0.592893	−	1.22569i
$127$	88.1969	+	88.1969i	0.694464	+	0.694464i	0.963211	−	0.268747i	$-0.0866095\pi$
$127$	88.1969	+	88.1969i	0.694464	+	0.694464i	−0.268747	+	0.963211i	$0.586609\pi$
$128$	13.0458	−	48.6876i	0.101920	−	0.380372i
$129$	65.1832	+	23.5499i	0.505296	+	0.182557i
$130$	−100.399	+	230.644i	−0.772298	+	1.77419i
$131$	−49.7973	−	86.2514i	−0.380132	−	0.658407i	0.610949	−	0.791670i	$-0.290788\pi$
$131$	−49.7973	−	86.2514i	−0.380132	−	0.658407i	−0.991081	+	0.133262i	$0.957455\pi$
$132$	−38.1045	+	54.6944i	−0.288670	+	0.414351i
$133$	54.0515	+	32.5876i	0.406402	+	0.245020i
$134$	19.5767			0.146095
$135$	50.3187	+	125.272i	0.372731	+	0.927940i
$136$	43.8377	+	25.3097i	0.322336	+	0.186101i
$137$	−10.7816	−	40.2375i	−0.0786979	−	0.293704i	0.915348	−	0.402663i	$-0.131915\pi$
$137$	−10.7816	−	40.2375i	−0.0786979	−	0.293704i	−0.994046	+	0.108958i	$0.965249\pi$
$138$	−24.9803	−	2.12584i	−0.181017	−	0.0154046i
$139$	−231.245			−1.66363			−0.831817	−	0.555051i	$-0.812699\pi$
$139$	−231.245			−1.66363			−0.831817	+	0.555051i	$0.812699\pi$
$140$	−69.2294	−	97.4480i	−0.494496	−	0.696057i
$141$	−102.978	+	18.4097i	−0.730343	+	0.130565i
$142$	28.4108	−	106.030i	0.200076	−	0.746693i
$143$	31.1093	+	116.102i	0.217548	+	0.811900i
$144$	159.643	+	27.3696i	1.10863	+	0.190067i
$145$	−64.6194	−	87.4025i	−0.445651	−	0.602776i
$146$	241.167			1.65183
$147$	145.893	+	18.0057i	0.992470	+	0.122488i
$148$	49.6437	−	49.6437i	0.335430	−	0.335430i
$149$	−12.3181	−	21.3355i	−0.0826715	−	0.143191i	0.821725	−	0.569884i	$-0.193012\pi$
$149$	−12.3181	−	21.3355i	−0.0826715	−	0.143191i	−0.904397	+	0.426693i	$0.859679\pi$
$150$	202.749	+	24.5743i	1.35166	+	0.163829i
$151$	40.7301	−	70.5465i	0.269735	−	0.467196i	−0.699058	−	0.715065i	$-0.746397\pi$
$151$	40.7301	−	70.5465i	0.269735	−	0.467196i	0.968793	+	0.247869i	$0.0797304\pi$
$152$	−3.71553	+	13.8666i	−0.0244443	+	0.0912274i
$153$	−119.695	+	259.896i	−0.782319	+	1.69867i
$154$	−119.158	−	34.3613i	−0.773756	−	0.223125i
$155$	10.2319	+	90.1304i	0.0660122	+	0.581486i
$156$	−144.719	+	122.020i	−0.927689	+	0.782178i
$157$	−47.6860	−	177.967i	−0.303732	−	1.13354i	−0.934031	−	0.357192i	$-0.883734\pi$
$157$	−47.6860	−	177.967i	−0.303732	−	1.13354i	0.630299	−	0.776353i	$-0.282932\pi$
$158$	−104.150	+	27.9068i	−0.659176	+	0.176626i
$159$	31.6023	+	37.4814i	0.198757	+	0.235732i
$160$	132.784	−	166.793i	0.829902	−	1.04246i
$161$	−5.16579	−	20.8518i	−0.0320857	−	0.129514i
$162$	−17.1397	+	219.905i	−0.105801	+	1.35744i
$163$	−173.547	−	46.5018i	−1.06471	−	0.285287i	−0.316390	−	0.948629i	$-0.602471\pi$
$163$	−173.547	−	46.5018i	−1.06471	−	0.285287i	−0.748316	+	0.663342i	$0.769137\pi$
$164$	−178.746	−	103.199i	−1.08991	−	0.629262i
$165$	83.1076	−	51.1531i	0.503682	−	0.310019i
$166$	54.3181	−	31.3605i	0.327217	−	0.188919i
$167$	−64.3049	−	64.3049i	−0.385059	−	0.385059i	0.487862	−	0.872921i	$-0.337777\pi$
$167$	−64.3049	−	64.3049i	−0.385059	−	0.385059i	−0.872921	+	0.487862i	$0.837777\pi$
$168$	5.25932	+	33.0193i	0.0313055	+	0.196544i
$169$			172.330i			1.01970i
$170$	257.342	+	348.074i	1.51378	+	2.04750i
$171$	−79.9811	−	13.7122i	−0.467726	−	0.0801881i
$172$	76.2130	−	20.4212i	0.443099	−	0.118728i
$173$	−221.298	−	59.2966i	−1.27918	−	0.342755i	−0.445638	−	0.895213i	$-0.647023\pi$
$173$	−221.298	−	59.2966i	−1.27918	−	0.342755i	−0.833540	+	0.552459i	$0.813690\pi$
$174$	−31.2535	−	174.823i	−0.179618	−	1.00473i
$175$	35.9888	+	171.259i	0.205650	+	0.978626i
$176$		−	117.086i		−	0.665261i
$177$	16.4288	−	193.051i	0.0928179	−	1.09069i
$178$	−17.3409	+	4.64647i	−0.0974206	+	0.0261038i
$179$	−27.9871	+	48.4751i	−0.156352	+	0.270810i	−0.933551	−	0.358445i	$-0.883307\pi$
$179$	−27.9871	+	48.4751i	−0.156352	+	0.270810i	0.777198	+	0.629256i	$0.216640\pi$
$180$	128.525	+	84.2704i	0.714031	+	0.468169i
$181$		−	59.2423i		−	0.327306i	−0.986518	−	0.163653i	$-0.947672\pi$
$181$		−	59.2423i		−	0.327306i	0.986518	−	0.163653i	$-0.0523277\pi$
$182$	−301.595	−	181.832i	−1.65712	−	0.999075i
$183$	149.963	+	104.476i	0.819469	+	0.570908i
$184$	4.23155	−	2.44309i	0.0229976	−	0.0132776i
$185$	−95.6459	+	37.6309i	−0.517005	+	0.203410i
$186$	−50.3594	+	139.388i	−0.270749	+	0.749401i
$187$	199.792	+	53.5342i	1.06841	+	0.286279i
$188$	−84.2115	+	84.2115i	−0.447934	+	0.447934i
$189$	−183.126	+	46.7521i	−0.968922	+	0.247366i
$190$	−76.4613	+	96.0448i	−0.402428	+	0.505499i
$191$	−178.680	+	103.161i	−0.935496	+	0.540109i	−0.888546	−	0.458788i	$-0.848284\pi$
$191$	−178.680	+	103.161i	−0.935496	+	0.540109i	−0.0469507	+	0.998897i	$0.514950\pi$
$192$	119.832	−	56.2250i	0.624127	−	0.292839i
$193$	−51.2434	−	191.243i	−0.265510	−	0.990897i	−0.961938	−	0.273269i	$-0.911895\pi$
$193$	−51.2434	−	191.243i	−0.265510	−	0.990897i	0.696428	−	0.717627i	$-0.254772\pi$
$194$	188.031	−	108.560i	0.969234	−	0.559588i
$195$	265.560	−	79.2298i	1.36184	−	0.406307i
$196$	147.996	−	78.1235i	0.755082	−	0.398589i
$197$	237.400	−	237.400i	1.20508	−	1.20508i	0.232476	−	0.972602i	$-0.425317\pi$
$197$	237.400	−	237.400i	1.20508	−	1.20508i	0.972602	−	0.232476i	$-0.0746827\pi$
$198$	158.772	−	14.6496i	0.801878	−	0.0739877i
$199$	−51.7490	+	89.6320i	−0.260045	+	0.450412i	−0.966254	−	0.257592i	$-0.917071\pi$
$199$	−51.7490	+	89.6320i	−0.260045	+	0.450412i	0.706208	+	0.708004i	$0.250404\pi$
$200$	−35.1603	+	18.6583i	−0.175801	+	0.0932917i
$201$	−13.9023	−	16.4886i	−0.0691659	−	0.0820330i
$202$	189.366	−	189.366i	0.937456	−	0.937456i
$203$	133.205	−	73.5764i	0.656183	−	0.362445i
$204$	57.3255	+	320.662i	0.281007	+	1.57187i
$205$	179.636	+	242.971i	0.876273	+	1.18522i
$206$	102.724	−	177.923i	0.498660	−	0.863705i
$207$	15.9492	+	22.5495i	0.0770493	+	0.108935i
$208$	86.0560	−	321.165i	0.413731	−	1.54406i
$209$			58.6601i			0.280670i
$210$	−71.4611	+	276.852i	−0.340291	+	1.31834i
$211$	−28.8210			−0.136592			−0.0682962	−	0.997665i	$-0.521756\pi$
$211$	−28.8210			−0.136592			−0.0682962	+	0.997665i	$0.521756\pi$
$212$	53.9114	+	14.4455i	0.254299	+	0.0681392i
$213$	−109.481	+	51.3680i	−0.513994	+	0.241164i
$214$	−240.219	−	138.691i	−1.12252	−	0.648087i
$215$	−114.236	−	17.1202i	−0.531329	−	0.0796288i
$216$	−21.7585	−	37.0754i	−0.100734	−	0.171645i
$217$	−126.970	−	2.40640i	−0.585116	−	0.0110894i
$218$	−145.882	−	145.882i	−0.669184	−	0.669184i
$219$	−171.264	−	203.125i	−0.782028	−	0.927511i
$220$	44.3419	−	101.866i	0.201554	−	0.463026i
$221$	508.681	+	293.687i	2.30172	+	1.32890i
$222$	−167.328	−	14.2397i	−0.753728	−	0.0641427i
$223$	313.729	+	313.729i	1.40686	+	1.40686i	0.775455	+	0.631402i	$0.217520\pi$
$223$	313.729	+	313.729i	1.40686	+	1.40686i	0.631402	+	0.775455i	$0.282480\pi$
$224$	207.014	+	215.013i	0.924170	+	0.959877i
$225$	−123.284	−	188.218i	−0.547928	−	0.836526i
$226$	20.9036	+	36.2060i	0.0924936	+	0.160204i
$227$	134.195	−	35.9575i	0.591169	−	0.158403i	0.0491817	−	0.998790i	$-0.484339\pi$
$227$	134.195	−	35.9575i	0.591169	−	0.158403i	0.541987	+	0.840387i	$0.317672\pi$
$228$	−83.6336	+	39.2406i	−0.366814	+	0.172108i
$229$	−86.9426	−	150.589i	−0.379662	−	0.657594i	0.611351	−	0.791359i	$-0.290626\pi$
$229$	−86.9426	−	150.589i	−0.379662	−	0.657594i	−0.991013	+	0.133766i	$0.957293\pi$
$230$	41.5177	−	4.71322i	0.180512	−	0.0204923i
$231$	55.6790	+	124.764i	0.241034	+	0.540102i
$232$	24.4748	+	24.4748i	0.105495	+	0.105495i
$233$	67.5582	−	252.131i	0.289950	−	1.08211i	−0.655197	−	0.755458i	$-0.727414\pi$
$233$	67.5582	−	252.131i	0.289950	−	1.08211i	0.945146	−	0.326648i	$-0.105919\pi$
$234$	446.276	+	76.5108i	1.90716	+	0.326969i
$235$	162.246	−	63.8341i	0.690408	−	0.271634i
$236$	−110.286	−	191.020i	−0.467312	−	0.809408i
$237$	97.4663	+	67.9029i	0.411250	+	0.286510i
$238$	−530.481	+	293.013i	−2.22891	+	1.23115i
$239$	−267.401			−1.11883			−0.559416	−	0.828887i	$-0.688975\pi$
$239$	−267.401			−1.11883			−0.559416	+	0.828887i	$0.688975\pi$
$240$	−269.847	+	7.59636i	−1.12436	+	0.0316515i
$241$	−92.0246	−	53.1304i	−0.381845	−	0.220458i	0.296776	−	0.954947i	$-0.404089\pi$
$241$	−92.0246	−	53.1304i	−0.381845	−	0.220458i	−0.678621	+	0.734489i	$0.737422\pi$
$242$	55.4483	+	206.936i	0.229125	+	0.855107i
$243$	197.388	−	141.729i	0.812296	−	0.583245i
$244$	208.070			0.852745
$245$	−244.309	+	18.3917i	−0.997178	+	0.0750681i
$246$	86.8820	+	485.993i	0.353179	+	1.97558i
$247$	−43.1140	+	160.904i	−0.174551	+	0.651432i
$248$	−7.47597	−	27.9007i	−0.0301450	−	0.112503i
$249$	−64.9874	−	23.4792i	−0.260994	−	0.0942939i
$250$	−339.371	+	26.2920i	−1.35749	+	0.105168i
$251$	−162.554			−0.647625			−0.323812	−	0.946121i	$-0.604965\pi$
$251$	−162.554			−0.647625			−0.323812	+	0.946121i	$0.604965\pi$
$252$	−140.633	+	162.844i	−0.558068	+	0.646206i
$253$	14.1180	−	14.1180i	0.0558022	−	0.0558022i
$254$	−169.826	−	294.147i	−0.668605	−	1.15806i
$255$	110.417	−	463.932i	0.433009	−	1.81934i
$256$	−156.874	+	271.714i	−0.612789	+	1.06138i
$257$	52.4492	−	195.743i	0.204082	−	0.761646i	−0.785645	−	0.618678i	$-0.787669\pi$
$257$	52.4492	−	195.743i	0.204082	−	0.761646i	0.989727	−	0.142968i	$-0.0456647\pi$
$258$	−154.855	−	107.884i	−0.600212	−	0.418156i
$259$	−34.6024	−	139.673i	−0.133600	−	0.539278i
$260$	196.499	−	246.826i	0.755764	−	0.949331i
$261$	−125.051	+	150.474i	−0.479124	+	0.576527i
$262$	70.1934	+	261.965i	0.267914	+	0.999868i
$263$	−277.759	+	74.4253i	−1.05612	+	0.282986i	−0.744778	−	0.667313i	$-0.767445\pi$
$263$	−277.759	+	74.4253i	−1.05612	+	0.282986i	−0.311340	+	0.950299i	$0.600778\pi$
$264$	−23.7578	+	20.0313i	−0.0899917	+	0.0758762i
$265$	−63.9264	−	50.8918i	−0.241232	−	0.192045i
$266$	−119.205	−	123.811i	−0.448140	−	0.465455i
$267$	16.2281	+	11.3058i	0.0607793	+	0.0423438i
$268$	−23.7164	−	6.35480i	−0.0884942	−	0.0237119i
$269$	154.500	+	89.2008i	0.574351	+	0.331602i	0.758885	−	0.651225i	$-0.225744\pi$
$269$	154.500	+	89.2008i	0.574351	+	0.331602i	−0.184534	+	0.982826i	$0.559078\pi$
$270$	−44.0635	−	364.969i	−0.163198	−	1.35174i
$271$	−408.653	+	235.936i	−1.50794	+	0.870612i	−0.507987	+	0.861364i	$0.669610\pi$
$271$	−408.653	+	235.936i	−1.50794	+	0.870612i	−0.999957	+	0.00924779i	$0.997056\pi$
$272$	−404.586	−	404.586i	−1.48745	−	1.48745i
$273$	61.0278	+	383.148i	0.223545	+	1.40347i
$274$			113.436i			0.414001i
$275$	−119.043	+	110.828i	−0.432884	+	0.403012i
$276$	29.5726	+	10.6842i	0.107147	+	0.0387110i
$277$	−24.9091	+	6.67437i	−0.0899245	+	0.0240952i	−0.303501	−	0.952831i	$-0.598155\pi$
$277$	−24.9091	+	6.67437i	−0.0899245	+	0.0240952i	0.213576	+	0.976926i	$0.431489\pi$
$278$	608.248	+	162.980i	2.18794	+	0.586258i
$279$	153.163	−	56.5707i	0.548973	−	0.202762i
$280$	−19.4162	−	52.2340i	−0.0693436	−	0.186550i
$281$		−	216.505i		−	0.770481i	−0.922816	−	0.385240i	$-0.874119\pi$
$281$		−	216.505i		−	0.770481i	0.922816	−	0.385240i	$-0.125881\pi$
$282$	283.841	+	24.1550i	1.00653	+	0.0856561i
$283$	456.038	−	122.195i	1.61144	−	0.431784i	0.662969	−	0.748647i	$-0.269296\pi$
$283$	456.038	−	122.195i	1.61144	−	0.431784i	0.948471	+	0.316863i	$0.102630\pi$
$284$	−68.8371	+	119.229i	−0.242384	+	0.419822i
$285$	135.193	−	3.80578i	0.474362	−	0.0133536i
$286$		−	327.310i		−	1.14444i
$287$	−370.299	+	204.536i	−1.29024	+	0.712668i
$288$	−348.560	−	160.529i	−1.21028	−	0.557391i
$289$	625.078	−	360.889i	2.16290	−	1.24875i
$290$	108.369	+	275.440i	0.373686	+	0.949792i
$291$	−224.965	−	81.2773i	−0.773077	−	0.279303i
$292$	−292.165	−	78.2853i	−1.00056	−	0.268100i
$293$	106.940	−	106.940i	0.364983	−	0.364983i	−0.500661	−	0.865644i	$-0.666910\pi$
$293$	106.940	−	106.940i	0.364983	−	0.364983i	0.865644	+	0.500661i	$0.166910\pi$
$294$	−371.055	−	150.185i	−1.26209	−	0.510834i
$295$	36.4244	+	320.854i	0.123473	+	1.08764i
$296$	28.3445	−	16.3647i	0.0957585	−	0.0552862i
$297$	−125.090	−	123.323i	−0.421179	−	0.415230i
$298$	17.3633	+	64.8008i	0.0582662	+	0.217452i
$299$	49.1018	−	28.3489i	0.164220	−	0.0948125i
$300$	−237.646	−	95.5852i	−0.792152	−	0.318617i
$301$	44.8076	−	155.385i	0.148863	−	0.516228i
$302$	−156.854	+	156.854i	−0.519383	+	0.519383i
$303$	−293.973	−	25.0172i	−0.970207	−	0.0825651i
$304$	81.1340	−	140.528i	0.266888	−	0.462264i
$305$	−279.299	−	121.578i	−0.915735	−	0.398616i
$306$	498.009	−	599.250i	1.62748	−	1.95833i
$307$	−269.533	+	269.533i	−0.877959	+	0.877959i	−0.993323	−	0.115364i	$-0.963196\pi$
$307$	−269.533	+	269.533i	−0.877959	+	0.877959i	0.115364	+	0.993323i	$0.463196\pi$
$308$	133.202	+	80.3073i	0.432473	+	0.260738i
$309$	−222.806	+	39.8315i	−0.721055	+	0.128905i
$310$	36.6100	−	244.283i	0.118097	−	0.788010i
$311$	−44.2605	+	76.6614i	−0.142317	+	0.246500i	−0.928369	−	0.371661i	$-0.878788\pi$
$311$	−44.2605	+	76.6614i	−0.142317	+	0.246500i	0.786052	+	0.618160i	$0.212122\pi$
$312$	−79.8900	+	37.4841i	−0.256058	+	0.120141i
$313$	−116.641	+	435.312i	−0.372656	+	1.39077i	0.484083	+	0.875022i	$0.339153\pi$
$313$	−116.641	+	435.312i	−0.372656	+	1.39077i	−0.856739	+	0.515750i	$0.827513\pi$
$314$			501.718i			1.59783i
$315$	283.929	−	136.417i	0.901360	−	0.433070i
$316$	135.232			0.427950
$317$	154.877	+	41.4992i	0.488572	+	0.130912i	0.494691	−	0.869069i	$-0.335281\pi$
$317$	154.877	+	41.4992i	0.488572	+	0.130912i	−0.00611946	+	0.999981i	$0.501948\pi$
$318$	−56.7076	−	120.861i	−0.178326	−	0.380066i
$319$	122.485	+	70.7166i	0.383965	+	0.221682i
$320$	−177.394	+	131.153i	−0.554356	+	0.409852i
$321$	53.7777	+	300.817i	0.167532	+	0.937124i
$322$	−1.10849	+	58.4876i	−0.00344250	+	0.181639i
$323$	202.697	+	202.697i	0.627546	+	0.627546i
$324$	92.1474	−	260.842i	0.284406	−	0.805069i
$325$	−407.991	+	216.506i	−1.25536	+	0.666173i
$326$	423.710	+	244.629i	1.29972	+	0.750396i
$327$	−19.2725	+	226.468i	−0.0589374	+	0.692562i
$328$	−68.0377	−	68.0377i	−0.207432	−	0.207432i
$329$	58.6967	+	236.930i	0.178409	+	0.720152i
$330$	−254.652	+	75.9755i	−0.771672	+	0.230229i
$331$	8.64458	+	14.9729i	0.0261166	+	0.0452352i	0.878788	−	0.477212i	$-0.158353\pi$
$331$	8.64458	+	14.9729i	0.0261166	+	0.0452352i	−0.852672	+	0.522447i	$0.825019\pi$
$332$	−75.9841	+	20.3599i	−0.228868	+	0.0613250i
$333$	106.834	+	151.045i	0.320822	+	0.453589i
$334$	123.821	+	214.464i	0.370721	+	0.642108i
$335$	28.1222	+	22.3881i	0.0839468	+	0.0668302i
$336$	39.1766	−	375.899i	0.116597	−	1.11875i
$337$	409.047	+	409.047i	1.21379	+	1.21379i	0.969770	+	0.244020i	$0.0784662\pi$
$337$	409.047	+	409.047i	1.21379	+	1.21379i	0.244020	+	0.969770i	$0.421534\pi$
$338$	121.457	−	453.283i	0.359340	−	1.34107i
$339$	15.6502	−	43.3178i	0.0461657	−	0.127781i
$340$	−198.772	−	505.214i	−0.584622	−	1.48592i
$341$	−59.0146	−	102.216i	−0.173063	−	0.299754i
$342$	200.712	+	92.4374i	0.586876	+	0.270285i
$343$	19.4893	−	342.446i	0.0568200	−	0.998384i
$344$	36.7828			0.106927
$345$	−33.4534	−	31.6215i	−0.0969664	−	0.0916565i
$346$	540.292	+	311.938i	1.56154	+	0.901554i
$347$	96.5884	+	360.473i	0.278353	+	1.03883i	0.953561	+	0.301200i	$0.0973871\pi$
$347$	96.5884	+	360.473i	0.278353	+	1.03883i	−0.675208	+	0.737627i	$0.735946\pi$
$348$	−18.8869	+	221.937i	−0.0542727	+	0.637749i
$349$	−44.3368			−0.127040			−0.0635198	−	0.997981i	$-0.520233\pi$
$349$	−44.3368			−0.127040			−0.0635198	+	0.997981i	$0.520233\pi$
$350$	26.0403	−	475.832i	0.0744007	−	1.35952i
$351$	−252.480	−	430.213i	−0.719316	−	1.22568i
$352$	−71.7974	+	267.951i	−0.203970	+	0.761225i
$353$	−69.3915	−	258.973i	−0.196577	−	0.733634i	−0.991853	−	0.127387i	$-0.959341\pi$
$353$	−69.3915	−	258.973i	−0.196577	−	0.733634i	0.795277	−	0.606247i	$-0.207326\pi$
$354$	−179.274	+	496.208i	−0.506424	+	1.40172i
$355$	162.070	−	119.823i	0.456534	−	0.337530i
$356$	22.5161			0.0632474
$357$	623.511	+	238.719i	1.74653	+	0.668680i
$358$	107.780	−	107.780i	0.301061	−	0.301061i
$359$	257.188	+	445.463i	0.716401	+	1.24084i	0.962417	+	0.271578i	$0.0875454\pi$
$359$	257.188	+	445.463i	0.716401	+	1.24084i	−0.246015	+	0.969266i	$0.579121\pi$
$360$	47.7073	+	53.4547i	0.132520	+	0.148485i
$361$	139.852	−	242.231i	0.387401	−	0.670999i
$362$	−41.7535	+	155.826i	−0.115341	+	0.430459i
$363$	134.917	−	193.656i	0.371671	−	0.533489i
$364$	306.346	+	318.183i	0.841611	+	0.874128i
$365$	346.440	+	275.801i	0.949149	+	0.755619i
$366$	−320.816	−	380.498i	−0.876547	−	1.03961i
$367$	−170.774	−	637.338i	−0.465325	−	1.73662i	−0.655810	−	0.754926i	$-0.727673\pi$
$367$	−170.774	−	637.338i	−0.465325	−	1.73662i	0.190485	−	0.981690i	$-0.438994\pi$
$368$	−53.3483	+	14.2946i	−0.144968	+	0.0388441i
$369$	347.632	−	418.303i	0.942091	−	1.13361i
$370$	278.101	−	31.5709i	0.751625	−	0.0853268i
$371$	82.4072	−	79.3417i	0.222122	−	0.213859i
$372$	106.255	−	152.517i	0.285633	−	0.409991i
$373$	174.593	+	46.7821i	0.468078	+	0.125421i	0.485146	−	0.874433i	$-0.338766\pi$
$373$	174.593	+	46.7821i	0.468078	+	0.125421i	−0.0170677	+	0.999854i	$0.505433\pi$
$374$	−487.787	−	281.624i	−1.30424	−	0.753006i
$375$	263.148	+	267.167i	0.701728	+	0.712445i
$376$	−48.0813	+	27.7598i	−0.127876	+	0.0738292i
$377$	283.999	+	283.999i	0.753313	+	0.753313i
$378$	514.631	+	6.09285i	1.36146	+	0.0161186i
$379$		−	559.197i		−	1.47545i	−0.675100	−	0.737726i	$-0.735899\pi$
$379$		−	559.197i		−	1.47545i	0.675100	−	0.737726i	$-0.264101\pi$
$380$	123.807	−	91.5343i	0.325808	−	0.240880i
$381$	−127.146	+	351.924i	−0.333716	+	0.923685i
$382$	542.692	−	145.414i	1.42066	−	0.380665i
$383$	352.612	+	94.4821i	0.920658	+	0.246689i	0.687866	−	0.725837i	$-0.258547\pi$
$383$	352.612	+	94.4821i	0.920658	+	0.246689i	0.232791	+	0.972527i	$0.425214\pi$
$384$	148.855	−	26.6112i	0.387645	−	0.0693001i
$385$	−131.877	−	185.631i	−0.342537	−	0.482158i
$386$			539.146i			1.39675i
$387$	19.1033	+	207.041i	0.0493625	+	0.534990i
$388$	−263.032	+	70.4793i	−0.677918	+	0.181648i
$389$	338.245	−	585.857i	0.869524	−	1.50606i	0.00703925	−	0.999975i	$-0.497759\pi$
$389$	338.245	−	585.857i	0.869524	−	1.50606i	0.862484	−	0.506084i	$-0.168907\pi$
$390$	−754.347	+	21.2354i	−1.93422	+	0.0544497i
$391$		−	97.5679i		−	0.249534i
$392$	76.0690	−	17.3222i	0.194054	−	0.0441893i
$393$	170.795	−	245.155i	0.434592	−	0.623803i
$394$	−791.757	+	457.121i	−2.00953	+	1.16021i
$395$	−181.527	−	79.0180i	−0.459561	−	0.200046i
$396$	−197.101	−	33.7916i	−0.497731	−	0.0853323i
$397$	−349.363	−	93.6114i	−0.880007	−	0.235797i	−0.209597	−	0.977788i	$-0.567215\pi$
$397$	−349.363	−	93.6114i	−0.880007	−	0.235797i	−0.670410	+	0.741991i	$0.733882\pi$
$398$	199.288	−	199.288i	0.500725	−	0.500725i
$399$	−19.6275	+	188.325i	−0.0491916	+	0.471993i
$400$	438.473	−	100.853i	1.09618	−	0.252134i
$401$	−438.147	+	252.965i	−1.09264	+	0.630834i	−0.934277	−	0.356547i	$-0.883954\pi$
$401$	−438.147	+	252.965i	−1.09264	+	0.630834i	−0.158360	+	0.987381i	$0.550621\pi$
$402$	24.9466	+	53.1686i	0.0620561	+	0.132260i
$403$	−86.7492	−	323.752i	−0.215258	−	0.803356i
$404$	−290.880	+	167.940i	−0.720000	+	0.415692i
$405$	−276.106	+	296.294i	−0.681744	+	0.731591i
$406$	−402.228	+	99.6475i	−0.990710	+	0.245437i
$407$	94.5673	−	94.5673i	0.232352	−	0.232352i
$408$	−12.8767	+	151.311i	−0.0315605	+	0.370861i
$409$	−279.434	+	483.994i	−0.683212	+	1.18336i	0.290783	+	0.956789i	$0.406084\pi$
$409$	−279.434	+	483.994i	−0.683212	+	1.18336i	−0.973995	+	0.226569i	$0.927249\pi$
$410$	−301.256	−	765.697i	−0.734771	−	1.86755i
$411$	95.5425	−	80.5564i	0.232464	−	0.196001i
$412$	−182.202	+	182.202i	−0.442237	+	0.442237i
$413$	−452.000	−	8.56653i	−1.09443	−	0.0207422i
$414$	−26.0588	−	70.5533i	−0.0629439	−	0.170419i
$415$	113.893	+	17.0688i	0.274440	+	0.0411296i
$416$	−393.878	+	682.217i	−0.946823	+	1.63995i
$417$	−294.675	−	628.041i	−0.706654	−	1.50609i
$418$	41.3432	−	154.295i	0.0989071	−	0.369126i
$419$			356.671i			0.851244i	0.904901	+	0.425622i	$0.139945\pi$
$419$			356.671i			0.851244i	−0.904901	+	0.425622i	$0.860055\pi$
$420$	176.441	−	312.199i	0.420098	−	0.743330i
$421$	−73.1717			−0.173805			−0.0869023	−	0.996217i	$-0.527697\pi$
$421$	−73.1717			−0.173805			−0.0869023	+	0.996217i	$0.527697\pi$
$422$	75.8084	+	20.3128i	0.179641	+	0.0481346i
$423$	−181.224	−	256.221i	−0.428426	−	0.605723i
$424$	22.5334	+	13.0097i	0.0531448	+	0.0306832i
$425$	−28.3857	+	794.311i	−0.0667898	+	1.86897i
$426$	324.173	−	57.9531i	0.760969	−	0.136040i
$427$	220.189	−	365.217i	0.515666	−	0.855309i
$428$	245.996	+	245.996i	0.574756	+	0.574756i
$429$	−275.679	+	232.438i	−0.642609	+	0.541814i
$430$	288.410	+	125.544i	0.670721	+	0.291963i
$431$	−263.266	−	151.997i	−0.610826	−	0.352661i	0.162462	−	0.986715i	$-0.448056\pi$
$431$	−263.266	−	151.997i	−0.610826	−	0.352661i	−0.773289	+	0.634054i	$0.781390\pi$
$432$	129.099	+	468.453i	0.298840	+	1.08438i
$433$	−284.409	−	284.409i	−0.656834	−	0.656834i	0.297796	−	0.954630i	$-0.403749\pi$
$433$	−284.409	−	284.409i	−0.656834	−	0.656834i	−0.954630	+	0.297796i	$0.903749\pi$
$434$	332.276	+	95.8172i	0.765613	+	0.220777i
$435$	155.033	−	286.877i	0.356398	−	0.659488i
$436$	129.376	+	224.085i	0.296733	+	0.513957i
$437$	26.7275	−	7.16161i	0.0611613	−	0.0163881i
$438$	307.319	+	654.989i	0.701641	+	1.49541i
$439$	162.341	+	281.183i	0.369797	+	0.640507i	0.989534	−	0.144303i	$-0.0460940\pi$
$439$	162.341	+	281.183i	0.369797	+	0.640507i	−0.619737	+	0.784810i	$0.712761\pi$
$440$	32.2581	−	40.5201i	0.0733139	−	0.0920912i
$441$	137.009	+	419.177i	0.310678	+	0.950515i
$442$	−1131.01	−	1131.01i	−2.55884	−	2.55884i
$443$	−56.1075	+	209.396i	−0.126654	+	0.472678i	−0.999893	−	0.0146134i	$-0.995348\pi$
$443$	−56.1075	+	209.396i	−0.126654	+	0.472678i	0.873240	+	0.487291i	$0.162015\pi$
$444$	198.089	+	71.5670i	0.446145	+	0.161187i
$445$	−30.2241	−	13.1564i	−0.0679193	−	0.0295650i
$446$	−604.094	−	1046.32i	−1.35447	−	2.34601i
$447$	42.2484	−	60.6425i	0.0945155	−	0.135666i
$448$	−149.332	−	270.356i	−0.333331	−	0.603473i
$449$	−180.775			−0.402617			−0.201309	−	0.979528i	$-0.564519\pi$
$449$	−180.775			−0.402617			−0.201309	+	0.979528i	$0.564519\pi$
$450$	191.621	+	581.963i	0.425825	+	1.29325i
$451$	−340.497	−	196.586i	−0.754982	−	0.435889i
$452$	−13.5710	−	50.6477i	−0.0300243	−	0.112052i
$453$	243.500	+	20.7220i	0.537528	+	0.0457439i
$454$	−378.319			−0.833302
$455$	−225.301	−	606.110i	−0.495166	−	1.33211i
$456$	−42.3950	+	7.57905i	−0.0929715	+	0.0166207i
$457$	−53.7265	+	200.510i	−0.117564	+	0.438753i	−0.999466	−	0.0326790i	$-0.989596\pi$
$457$	−53.7265	+	200.510i	−0.117564	+	0.438753i	0.881902	+	0.471432i	$0.156263\pi$
$458$	122.553	+	457.373i	0.267583	+	0.998632i
$459$	−858.382	+	6.10451i	−1.87011	+	0.0132996i
$460$	−51.8270	−	7.76718i	−0.112667	−	0.0168852i
$461$	264.361			0.573452			0.286726	−	0.958013i	$-0.407433\pi$
$461$	264.361			0.573452			0.286726	+	0.958013i	$0.407433\pi$
$462$	−58.5211	−	367.410i	−0.126669	−	0.795260i
$463$	−532.588	+	532.588i	−1.15030	+	1.15030i	−0.163804	+	0.986493i	$0.552377\pi$
$463$	−532.588	+	532.588i	−1.15030	+	1.15030i	−0.986493	+	0.163804i	$0.947623\pi$
$464$	−195.619	−	338.823i	−0.421593	−	0.730221i
$465$	−231.748	+	142.642i	−0.498382	+	0.306756i
$466$	−355.400	+	615.570i	−0.762660	+	1.32097i
$467$	−31.6587	+	118.152i	−0.0677917	+	0.253002i	−0.991502	−	0.130089i	$-0.958474\pi$
$467$	−31.6587	+	118.152i	−0.0677917	+	0.253002i	0.923711	+	0.383091i	$0.125140\pi$
$468$	−515.810	−	237.556i	−1.10216	−	0.507597i
$469$	−36.2522	+	34.9036i	−0.0772968	+	0.0744214i
$470$	−471.748	+	53.5543i	−1.00372	+	0.113945i
$471$	422.575	−	356.293i	0.897187	−	0.756461i
$472$	−26.6136	−	99.3235i	−0.0563848	−	0.210431i
$473$	145.180	−	38.9008i	0.306934	−	0.0822427i
$474$	−208.510	−	247.300i	−0.439895	−	0.521729i
$475$	−219.675	+	50.5276i	−0.462474	+	0.106374i
$476$	737.771	−	182.774i	1.54994	−	0.383980i
$477$	−61.5253	+	133.591i	−0.128984	+	0.280066i
$478$	703.350	+	188.462i	1.47144	+	0.394272i
$479$	−606.632	−	350.239i	−1.26645	−	0.731188i	−0.292139	−	0.956376i	$-0.594367\pi$
$479$	−606.632	−	350.239i	−1.26645	−	0.731188i	−0.974315	+	0.225188i	$0.927700\pi$
$480$	622.202	+	148.086i	1.29625	+	0.308513i
$481$	328.902	−	189.892i	0.683788	−	0.394785i
$482$	204.608	+	204.608i	0.424498	+	0.424498i
$483$	50.0488	−	40.6012i	0.103621	−	0.0840604i
$484$		−	268.694i		−	0.555152i
$485$	394.259	+	59.0866i	0.812906	+	0.121828i
$486$	−619.083	+	233.674i	−1.27383	+	0.480810i
$487$	164.196	−	43.9961i	0.337157	−	0.0903410i	−0.0862682	−	0.996272i	$-0.527494\pi$
$487$	164.196	−	43.9961i	0.337157	−	0.0903410i	0.423426	+	0.905931i	$0.360828\pi$
$488$	93.6941	+	25.1052i	0.191996	+	0.0514452i
$489$	−94.8557	−	530.596i	−0.193979	−	1.08506i
$490$	655.572	+	123.811i	1.33790	+	0.252675i
$491$			246.029i			0.501078i	0.968107	+	0.250539i	$0.0806078\pi$
$491$			246.029i			0.501078i	−0.968107	+	0.250539i	$0.919392\pi$
$492$	52.5039	−	616.964i	0.106715	−	1.25399i
$493$	667.599	−	178.883i	1.35416	−	0.362845i
$494$	226.807	−	392.842i	0.459124	−	0.795227i
$495$	244.831	+	160.529i	0.494608	+	0.324300i
$496$			326.497i			0.658260i
$497$	136.432	+	247.001i	0.274511	+	0.496984i
$498$	154.390	+	107.560i	0.310020	+	0.215985i
$499$	−235.800	+	136.139i	−0.472545	+	0.272824i	−0.717304	−	0.696760i	$-0.754624\pi$
$499$	−235.800	+	136.139i	−0.472545	+	0.272824i	0.244760	+	0.969584i	$0.421291\pi$
$500$	419.670	+	78.3116i	0.839340	+	0.156623i
$501$	92.7028	−	256.590i	0.185036	−	0.512155i
$502$	427.569	+	114.567i	0.851730	+	0.228220i
$503$	−19.6309	+	19.6309i	−0.0390277	+	0.0390277i	−0.726351	−	0.687324i	$-0.758785\pi$
$503$	−19.6309	+	19.6309i	−0.0390277	+	0.0390277i	0.687324	+	0.726351i	$0.258785\pi$
$504$	−82.9757	+	56.3603i	−0.164634	+	0.111826i
$505$	488.587	−	55.4660i	0.967500	−	0.109834i
$506$	−47.0849	+	27.1845i	−0.0930533	+	0.0537243i
$507$	−468.033	+	219.600i	−0.923142	+	0.433135i
$508$	110.254	+	411.474i	0.217036	+	0.809989i
$509$	−107.234	+	61.9115i	−0.210676	+	0.121634i	−0.601625	−	0.798778i	$-0.705480\pi$
$509$	−107.234	+	61.9115i	−0.210676	+	0.121634i	0.390950	+	0.920412i	$0.372147\pi$
$510$	−617.408	+	1142.47i	−1.21060	+	2.24013i
$511$	−446.594	+	429.981i	−0.873961	+	0.841449i
$512$	461.563	−	461.563i	0.901491	−	0.901491i
$513$	−64.6786	−	234.695i	−0.126079	−	0.457495i
$514$	−275.916	+	477.901i	−0.536802	+	0.929768i
$515$	351.038	−	138.113i	0.681628	−	0.268180i
$516$	152.580	+	180.965i	0.295698	+	0.350707i
$517$	−160.416	+	160.416i	−0.310283	+	0.310283i
$518$	−7.42506	+	391.772i	−0.0143341	+	0.756317i
$519$	−120.955	−	676.586i	−0.233054	−	1.30363i
$520$	118.265	−	87.4370i	0.227433	−	0.168148i
$521$	406.692	−	704.411i	0.780598	−	1.35204i	−0.150996	−	0.988534i	$-0.548248\pi$
$521$	406.692	−	704.411i	0.780598	−	1.35204i	0.931594	−	0.363501i	$-0.118419\pi$
$522$	434.978	−	307.658i	0.833291	−	0.589384i
$523$	−55.9284	+	208.728i	−0.106938	+	0.399097i	−0.998558	−	0.0536874i	$-0.982903\pi$
$523$	−55.9284	+	208.728i	−0.106938	+	0.399097i	0.891620	+	0.452784i	$0.149569\pi$
$524$		−	340.146i		−	0.649134i
$525$	−419.265	+	315.978i	−0.798600	+	0.601862i
$526$	783.049			1.48869
$527$	−557.126	−	149.281i	−1.05716	−	0.283267i
$528$	317.995	−	149.202i	0.602263	−	0.282580i
$529$	449.971	+	259.791i	0.850607	+	0.491098i
$530$	132.279	+	178.917i	0.249582	+	0.337578i
$531$	545.245	−	201.386i	1.02683	−	0.379257i
$532$	104.222	+	188.687i	0.195906	+	0.354675i
$533$	−789.491	−	789.491i	−1.48122	−	1.48122i
$534$	−34.7168	−	41.1753i	−0.0650128	−	0.0771072i
$535$	−186.470	−	473.947i	−0.348541	−	0.885882i
$536$	−9.91278	−	5.72315i	−0.0184940	−	0.0106775i
$537$	−167.318	−	14.2388i	−0.311579	−	0.0265155i
$538$	−343.517	−	343.517i	−0.638508	−	0.638508i
$539$	281.921	−	148.819i	0.523044	−	0.276102i
$540$	−65.0913	+	456.449i	−0.120540	+	0.845276i
$541$	−266.695	−	461.929i	−0.492966	−	0.853843i	0.507001	−	0.861946i	$-0.330754\pi$
$541$	−266.695	−	461.929i	−0.492966	−	0.853843i	−0.999967	+	0.00810293i	$0.997421\pi$
$542$	1241.17	−	332.571i	2.28999	−	0.613600i
$543$	160.897	−	75.4923i	0.296311	−	0.139028i
$544$	677.802	+	1173.99i	1.24596	+	2.15806i
$545$	−42.7293	−	376.393i	−0.0784025	−	0.690630i
$546$	109.517	−	1050.81i	0.200580	−	1.92457i
$547$	−447.038	−	447.038i	−0.817255	−	0.817255i	0.168455	−	0.985709i	$-0.446122\pi$
$547$	−447.038	−	447.038i	−0.817255	−	0.817255i	−0.985709	+	0.168455i	$0.946122\pi$
$548$	36.8226	−	137.424i	0.0671944	−	0.250773i
$549$	−92.6509	+	540.419i	−0.168763	+	0.984370i
$550$	391.232	−	207.613i	0.711332	−	0.377479i
$551$	98.0053	+	169.750i	0.177868	+	0.308077i
$552$	12.0275	+	8.37930i	0.0217889	+	0.0151799i
$553$	143.109	−	237.368i	0.258787	−	0.429237i
$554$	70.2229			0.126756
$555$	−224.083	−	211.813i	−0.403754	−	0.381645i
$556$	−683.964	−	394.887i	−1.23015	−	0.710228i
$557$	−2.64549	−	9.87310i	−0.00474953	−	0.0177255i	0.963510	−	0.267671i	$-0.0862540\pi$
$557$	−2.64549	−	9.87310i	−0.00474953	−	0.0177255i	−0.968260	+	0.249945i	$0.919587\pi$
$558$	−442.739	+	40.8507i	−0.793440	+	0.0732091i
$559$	426.818			0.763538
$560$	59.1784	+	627.105i	0.105676	+	1.11983i
$561$	109.201	+	610.837i	0.194654	+	1.08884i
$562$	−152.591	+	569.477i	−0.271514	+	1.01330i
$563$	131.002	+	488.906i	0.232686	+	0.868395i	0.979178	+	0.203001i	$0.0650696\pi$
$563$	131.002	+	488.906i	0.232686	+	0.868395i	−0.746493	+	0.665394i	$0.768264\pi$
$564$	−336.021	−	121.400i	−0.595783	−	0.215249i
$565$	−11.3773	+	75.9158i	−0.0201368	+	0.134364i
$566$	−1285.65			−2.27146
$567$	−360.332	−	437.778i	−0.635506	−	0.772096i
$568$	−45.3834	+	45.3834i	−0.0799003	+	0.0799003i
$569$	367.085	+	635.811i	0.645141	+	1.11742i	0.984269	+	0.176677i	$0.0565348\pi$
$569$	367.085	+	635.811i	0.645141	+	1.11742i	−0.339128	+	0.940740i	$0.610132\pi$
$570$	−358.283	−	85.2726i	−0.628567	−	0.149601i
$571$	382.351	−	662.252i	0.669617	−	1.15981i	−0.308394	−	0.951259i	$-0.599792\pi$
$571$	382.351	−	662.252i	0.669617	−	1.15981i	0.978011	−	0.208552i	$-0.0668751\pi$
$572$	−106.248	+	396.523i	−0.185748	+	0.693223i
$573$	−507.867	−	353.821i	−0.886329	−	0.617488i
$574$	1118.16	−	277.011i	1.94801	−	0.482598i
$575$	65.0307	+	40.7094i	0.113097	+	0.0707989i
$576$	305.404	+	253.807i	0.530216	+	0.440637i
$577$	267.247	+	997.379i	0.463166	+	1.72856i	0.662899	+	0.748709i	$0.269326\pi$
$577$	267.247	+	997.379i	0.463166	+	1.72856i	−0.199733	+	0.979850i	$0.564007\pi$
$578$	−1898.50	+	508.703i	−3.28461	+	0.880109i
$579$	454.100	−	382.873i	0.784283	−	0.661266i
$580$	−41.8744	−	368.862i	−0.0721972	−	0.635969i
$581$	−44.6731	+	154.918i	−0.0768900	+	0.266640i
$582$	534.447	+	372.339i	0.918294	+	0.639757i
$583$	102.697	+	27.5176i	0.176153	+	0.0471999i
$584$	−122.116	−	70.5039i	−0.209103	−	0.120726i
$585$	553.583	+	620.274i	0.946295	+	1.06030i
$586$	−356.657	+	205.916i	−0.608629	+	0.351392i
$587$	−513.474	−	513.474i	−0.874743	−	0.874743i	0.118242	−	0.992985i	$-0.462274\pi$
$587$	−513.474	−	513.474i	−0.874743	−	0.874743i	−0.992985	+	0.118242i	$0.962274\pi$
$588$	400.767	+	302.392i	0.681577	+	0.514271i
$589$		−	163.575i		−	0.277717i
$590$	130.328	−	869.621i	0.220895	−	1.47393i
$591$	947.277	+	342.240i	1.60284	+	0.579086i
$592$	−357.347	+	95.7508i	−0.603627	+	0.161741i
$593$	−594.948	−	159.416i	−1.00329	−	0.268829i	−0.280464	−	0.959865i	$-0.590488\pi$
$593$	−594.948	−	159.416i	−1.00329	−	0.268829i	−0.722821	+	0.691035i	$0.757155\pi$
$594$	242.109	+	412.542i	0.407592	+	0.694516i
$595$	−1097.13	−	185.745i	−1.84392	−	0.312177i
$596$		−	84.1400i		−	0.141174i
$597$	−309.376	−	26.3281i	−0.518218	−	0.0441006i
$598$	−149.133	+	39.9602i	−0.249387	+	0.0668231i
$599$	−224.017	+	388.008i	−0.373985	+	0.647760i	−0.990174	−	0.139837i	$-0.955342\pi$
$599$	−224.017	+	388.008i	−0.373985	+	0.647760i	0.616190	+	0.787598i	$0.288675\pi$
$600$	−95.4790	−	71.7159i	−0.159132	−	0.119527i
$601$			461.606i			0.768063i	0.923320	+	0.384031i	$0.125465\pi$
$601$			461.606i			0.768063i	−0.923320	+	0.384031i	$0.874535\pi$
$602$	−227.372	+	377.131i	−0.377695	+	0.626463i
$603$	27.0659	−	58.7689i	0.0448855	−	0.0974609i
$604$	240.938	−	139.106i	0.398905	−	0.230308i
$605$	−157.001	+	360.677i	−0.259506	+	0.596160i
$606$	755.610	+	272.993i	1.24688	+	0.450483i
$607$	234.564	+	62.8512i	0.386431	+	0.103544i	0.446804	−	0.894632i	$-0.352562\pi$
$607$	234.564	+	62.8512i	0.386431	+	0.103544i	−0.0603725	+	0.998176i	$0.519229\pi$
$608$	−271.847	+	271.847i	−0.447117	+	0.447117i
$609$	369.570	+	268.015i	0.606847	+	0.440091i
$610$	648.959	+	516.637i	1.06387	+	0.846945i
$611$	−557.923	+	322.117i	−0.913131	+	0.527196i
$612$	−797.840	+	564.310i	−1.30366	+	0.922075i
$613$	102.796	+	383.639i	0.167693	+	0.625838i	0.997681	+	0.0680576i	$0.0216801\pi$
$613$	102.796	+	383.639i	0.167693	+	0.625838i	−0.829989	+	0.557780i	$0.811653\pi$
$614$	898.924	−	518.994i	1.46405	−	0.845267i
$615$	−430.978	+	797.493i	−0.700777	+	1.29674i
$616$	50.2912	+	52.2343i	0.0816416	+	0.0847960i
$617$	−382.119	+	382.119i	−0.619317	+	0.619317i	−0.945356	−	0.326039i	$-0.894286\pi$
$617$	−382.119	+	382.119i	−0.619317	+	0.619317i	0.326039	+	0.945356i	$0.394286\pi$
$618$	614.124	+	52.2623i	0.993728	+	0.0845668i
$619$	340.936	−	590.519i	0.550785	−	0.953988i	−0.447433	−	0.894318i	$-0.647662\pi$
$619$	340.936	−	590.519i	0.550785	−	0.953988i	0.998218	−	0.0596706i	$-0.0190050\pi$
$620$	−123.648	+	284.055i	−0.199433	+	0.458154i
$621$	−40.9185	+	72.0514i	−0.0658913	+	0.116025i
$622$	170.449	−	170.449i	0.274034	−	0.274034i
$623$	23.8276	−	39.5216i	0.0382465	−	0.0634376i
$624$	981.917	−	175.539i	1.57358	−	0.281313i
$625$	−517.579	−	350.339i	−0.828126	−	0.560543i
$626$	613.608	−	1062.80i	0.980205	−	1.69777i
$627$	−159.316	+	74.7503i	−0.254092	+	0.119219i
$628$	162.862	−	607.811i	0.259335	−	0.967852i
$629$		−	653.547i		−	1.03902i
$630$	−842.968	+	158.710i	−1.33804	+	0.251920i
$631$	−138.302			−0.219180			−0.109590	−	0.993977i	$-0.534954\pi$
$631$	−138.302			−0.219180			−0.109590	+	0.993977i	$0.534954\pi$
$632$	60.8952	+	16.3168i	0.0963532	+	0.0258178i
$633$	−36.7265	−	78.2752i	−0.0580197	−	0.123658i
$634$	−378.128	−	218.312i	−0.596417	−	0.344341i
$635$	92.4320	−	616.759i	0.145562	−	0.971274i
$636$	29.4664	+	164.826i	0.0463308	+	0.259161i
$637$	882.684	−	201.002i	1.38569	−	0.315545i
$638$	−272.334	−	272.334i	−0.426855	−	0.426855i
$639$	−279.022	−	231.882i	−0.436654	−	0.362882i
$640$	−234.527	+	92.2723i	−0.366448	+	0.144175i
$641$	366.999	+	211.887i	0.572541	+	0.330557i	0.758164	−	0.652064i	$-0.226097\pi$
$641$	366.999	+	211.887i	0.572541	+	0.330557i	−0.185622	+	0.982621i	$0.559430\pi$
$642$	70.5608	−	829.146i	0.109908	−	1.29150i
$643$	−225.887	−	225.887i	−0.351302	−	0.351302i	0.509292	−	0.860594i	$-0.329907\pi$
$643$	−225.887	−	225.887i	−0.351302	−	0.351302i	−0.860594	+	0.509292i	$0.829907\pi$
$644$	20.3286	−	70.4957i	0.0315661	−	0.109465i
$645$	−99.0732	−	332.070i	−0.153602	−	0.514837i
$646$	−390.299	−	676.018i	−0.604178	−	1.04647i
$647$	609.042	−	163.192i	0.941332	−	0.252229i	0.244652	−	0.969611i	$-0.421326\pi$
$647$	609.042	−	163.192i	0.941332	−	0.252229i	0.696680	+	0.717382i	$0.254660\pi$
$648$	72.9667	−	106.339i	0.112603	−	0.164104i
$649$	−210.085	−	363.879i	−0.323706	−	0.560676i
$650$	1225.74	−	281.932i	1.88575	−	0.433742i
$651$	−155.262	−	347.906i	−0.238498	−	0.534418i
$652$	−433.899	−	433.899i	−0.665490	−	0.665490i
$653$	−6.32407	+	23.6018i	−0.00968464	+	0.0361436i	−0.970599	−	0.240702i	$-0.922622\pi$
$653$	−6.32407	+	23.6018i	−0.00968464	+	0.0361436i	0.960914	+	0.276846i	$0.0892890\pi$
$654$	210.306	−	582.100i	0.321568	−	0.890061i
$655$	−198.752	+	456.590i	−0.303438	+	0.697084i
$656$	543.804	+	941.897i	0.828970	+	1.43582i
$657$	333.428	−	723.979i	0.507500	−	1.10195i
$658$	12.5953	−	664.570i	0.0191417	−	1.00999i
$659$	350.045			0.531176			0.265588	−	0.964087i	$-0.414434\pi$
$659$	350.045			0.531176			0.265588	+	0.964087i	$0.414434\pi$
$660$	333.163	−	9.37876i	0.504793	−	0.0142102i
$661$	728.727	+	420.731i	1.10246	+	0.636506i	0.936866	−	0.349688i	$-0.113712\pi$
$661$	728.727	+	420.731i	1.10246	+	0.636506i	0.165595	+	0.986194i	$0.447046\pi$
$662$	−12.1853	−	45.4760i	−0.0184067	−	0.0686949i
$663$	−149.417	+	1755.78i	−0.225366	+	2.64823i
$664$	−36.6723			−0.0552294
$665$	−29.6484	−	314.180i	−0.0445840	−	0.472451i
$666$	−174.551	−	472.593i	−0.262089	−	0.709598i
$667$	17.2671	−	64.4418i	0.0258877	−	0.0966143i
$668$	−80.3869	−	300.008i	−0.120340	−	0.449114i
$669$	−452.276	+	1251.84i	−0.676049	+	1.87122i
$670$	−58.1914	−	78.7081i	−0.0868528	−	0.117475i
$671$	396.357			0.590695
$672$	−320.157	+	836.221i	−0.476425	+	1.24438i
$673$	−814.054	+	814.054i	−1.20959	+	1.20959i	−0.238429	+	0.971160i	$0.576633\pi$
$673$	−814.054	+	814.054i	−1.20959	+	1.20959i	−0.971160	+	0.238429i	$0.923367\pi$
$674$	−787.632	−	1364.22i	−1.16859	−	2.02406i
$675$	354.084	−	574.674i	0.524569	−	0.851368i
$676$	−294.280	+	509.709i	−0.435326	+	0.754007i
$677$	277.070	−	1034.04i	0.409262	−	1.52739i	−0.386796	−	0.922165i	$-0.626418\pi$
$677$	277.070	−	1034.04i	0.409262	−	1.52739i	0.796058	−	0.605220i	$-0.206915\pi$
$678$	−71.6950	+	102.909i	−0.105745	+	0.151784i
$679$	−154.644	+	536.275i	−0.227752	+	0.789802i
$680$	−28.5490	−	251.482i	−0.0419838	−	0.369826i
$681$	268.662	+	318.642i	0.394511	+	0.467903i
$682$	83.1860	+	310.454i	0.121974	+	0.455212i
$683$	793.550	−	212.631i	1.16186	−	0.311319i	0.374151	−	0.927368i	$-0.377934\pi$
$683$	793.550	−	212.631i	1.16186	−	0.311319i	0.787708	+	0.616048i	$0.211267\pi$
$684$	−213.148	−	177.137i	−0.311620	−	0.258973i
$685$	−129.727	+	162.952i	−0.189382	+	0.237887i
$686$	−292.616	+	887.006i	−0.426554	+	1.29301i
$687$	298.195	−	428.023i	0.434054	−	0.623032i
$688$	−401.603	−	107.609i	−0.583725	−	0.156409i
$689$	261.471	+	150.961i	0.379494	+	0.219101i
$690$	65.7066	+	106.752i	0.0952269	+	0.154714i
$691$	347.514	−	200.637i	0.502914	−	0.290357i	−0.227002	−	0.973894i	$-0.572892\pi$
$691$	347.514	−	200.637i	0.502914	−	0.290357i	0.729916	+	0.683537i	$0.239559\pi$
$692$	−553.285	−	553.285i	−0.799544	−	0.799544i
$693$	−267.895	+	310.205i	−0.386573	+	0.447626i
$694$		−	1016.23i		−	1.46431i
$695$	687.370	+	929.719i	0.989022	+	1.33773i
$696$	−35.2832	+	97.6594i	−0.0506942	+	0.140315i
$697$	−1855.87	+	497.278i	−2.66265	+	0.713454i
$698$	116.620	+	31.2482i	0.167077	+	0.0447682i
$699$	770.854	−	137.807i	1.10280	−	0.197149i
$700$	−186.006	+	567.999i	−0.265723	+	0.811426i
$701$		−	243.478i		−	0.347330i	−0.984805	−	0.173665i	$-0.944439\pi$
$701$		−	243.478i		−	0.347330i	0.984805	−	0.173665i	$-0.0555610\pi$
$702$	360.892	+	1309.54i	0.514091	+	1.86545i
$703$	179.031	−	47.9712i	0.254667	−	0.0682378i
$704$	143.528	−	248.598i	0.203875	−	0.353122i
$705$	380.117	+	359.302i	0.539173	+	0.509648i
$706$			730.088i			1.03412i
$707$	−13.0449	+	688.292i	−0.0184510	+	0.973539i
$708$	378.257	−	542.942i	0.534262	−	0.766868i
$709$	110.473	−	63.7815i	0.155815	−	0.0899598i	−0.420065	−	0.907494i	$-0.637993\pi$
$709$	110.473	−	63.7815i	0.155815	−	0.0899598i	0.575880	+	0.817534i	$0.304659\pi$
$710$	−510.745	+	200.948i	−0.719360	+	0.283025i
$711$	−60.2172	+	351.238i	−0.0846937	+	0.494006i
$712$	10.1390	+	2.71674i	0.0142402	+	0.00381565i
$713$	−39.3683	+	39.3683i	−0.0552150	+	0.0552150i
$714$	−1471.79	−	1067.35i	−2.06133	−	1.49489i
$715$	374.314	−	470.184i	0.523517	−	0.657601i
$716$	−165.557	+	95.5846i	−0.231225	+	0.133498i
$717$	−340.748	−	726.237i	−0.475241	−	1.01288i
$718$	−362.528	−	1352.97i	−0.504914	−	1.88436i
$719$	−989.565	+	571.326i	−1.37631	+	0.794611i	−0.991713	−	0.128474i	$-0.958992\pi$
$719$	−989.565	+	571.326i	−1.37631	+	0.794611i	−0.384594	+	0.923086i	$0.625659\pi$
$720$	−364.495	−	723.199i	−0.506244	−	1.00444i
$721$	126.997	+	512.626i	0.176141	+	0.710993i
$722$	−538.577	+	538.577i	−0.745952	+	0.745952i
$723$	27.0308	−	317.634i	0.0373871	−	0.439328i
$724$	101.165	−	175.224i	0.139731	−	0.242022i
$725$	−159.322	+	519.604i	−0.219754	+	0.716695i
$726$	−491.362	+	414.290i	−0.676807	+	0.570648i
$727$	−25.5906	+	25.5906i	−0.0352003	+	0.0352003i	−0.724488	−	0.689288i	$-0.757924\pi$
$727$	−25.5906	+	25.5906i	−0.0352003	+	0.0352003i	0.689288	+	0.724488i	$0.257924\pi$
$728$	99.5569	+	180.241i	0.136754	+	0.247584i
$729$	636.453	+	355.484i	0.873049	+	0.487632i
$730$	−716.864	−	969.612i	−0.982006	−	1.32824i
$731$	367.242	−	636.083i	0.502384	−	0.870154i
$732$	265.143	+	565.099i	0.362217	+	0.771993i
$733$	282.956	−	1056.01i	0.386024	−	1.44066i	−0.450521	−	0.892766i	$-0.648762\pi$
$733$	282.956	−	1056.01i	0.386024	−	1.44066i	0.836546	−	0.547897i	$-0.184572\pi$
$734$			1796.76i			2.44791i
$735$	−361.272	−	640.084i	−0.491526	−	0.870863i
$736$	130.853			0.177790
$737$	−45.1780	−	12.1054i	−0.0612998	−	0.0164252i
$738$	−1209.20	+	855.262i	−1.63848	+	1.15889i
$739$	549.581	+	317.301i	0.743682	+	0.429365i	0.823406	−	0.567452i	$-0.192071\pi$
$739$	549.581	+	317.301i	0.743682	+	0.429365i	−0.0797246	+	0.996817i	$0.525404\pi$
$740$	−347.157	−	52.0275i	−0.469131	−	0.0703074i
$741$	−491.940	+	87.9453i	−0.663887	+	0.118685i
$742$	−272.677	+	150.614i	−0.367489	+	0.202984i
$743$	943.968	+	943.968i	1.27048	+	1.27048i	0.945836	+	0.324645i	$0.105245\pi$
$743$	943.968	+	943.968i	1.27048	+	1.27048i	0.324645	+	0.945836i	$0.394755\pi$
$744$	66.2492	−	55.8578i	0.0890446	−	0.0750777i
$745$	−49.1641	+	112.944i	−0.0659921	+	0.151603i
$746$	−426.264	−	246.104i	−0.571400	−	0.329898i
$747$	−19.0459	−	206.419i	−0.0254965	−	0.276331i
$748$	499.517	+	499.517i	0.667804	+	0.667804i
$749$	692.111	−	171.463i	0.924047	−	0.228922i
$750$	−503.867	−	888.199i	−0.671822	−	1.18426i
$751$	41.5208	+	71.9161i	0.0552873	+	0.0957604i	0.892344	−	0.451355i	$-0.149059\pi$
$751$	41.5208	+	71.9161i	0.0552873	+	0.0957604i	−0.837057	+	0.547115i	$0.815726\pi$
$752$	606.174	−	162.424i	0.806083	−	0.215989i
$753$	−207.142	−	441.482i	−0.275089	−	0.586297i
$754$	−546.848	−	947.168i	−0.725262	−	1.25619i
$755$	−404.701	+	45.9429i	−0.536028	+	0.0608516i
$756$	−621.478	−	174.436i	−0.822060	−	0.230735i
$757$	498.613	+	498.613i	0.658669	+	0.658669i	0.955065	−	0.296396i	$-0.0957848\pi$
$757$	498.613	+	498.613i	0.658669	+	0.658669i	−0.296396	+	0.955065i	$0.595785\pi$
$758$	−394.117	+	1470.87i	−0.519944	+	1.94046i
$759$	56.3336	+	20.3526i	0.0742208	+	0.0268151i
$760$	66.7948	−	26.2797i	0.0878878	−	0.0345786i
$761$	22.8760	+	39.6224i	0.0300605	+	0.0520663i	0.880664	−	0.473741i	$-0.157097\pi$
$761$	22.8760	+	39.6224i	0.0300605	+	0.0520663i	−0.850604	+	0.525807i	$0.823763\pi$
$762$	582.468	−	836.061i	0.764393	−	1.09719i
$763$	530.240	+	10.0494i	0.694941	+	0.0131709i
$764$	−704.653			−0.922320
$765$	1400.70	−	291.303i	1.83098	−	0.380789i
$766$	−860.892	−	497.036i	−1.12388	−	0.648872i
$767$	−308.818	−	1152.52i	−0.402630	−	1.50264i
$768$	−937.855	−	79.8119i	−1.22116	−	0.103922i
$769$	98.8818			0.128585			0.0642925	−	0.997931i	$-0.479521\pi$
$769$	98.8818			0.128585			0.0642925	+	0.997931i	$0.479521\pi$
$770$	216.046	+	581.214i	0.280580	+	0.754823i
$771$	598.456	−	106.987i	0.776208	−	0.138764i
$772$	175.012	−	653.154i	0.226700	−	0.846055i
$773$	86.6476	+	323.373i	0.112093	+	0.418335i	0.999053	−	0.0435102i	$-0.0138541\pi$
$773$	86.6476	+	323.373i	0.112093	+	0.418335i	−0.886960	+	0.461846i	$0.847187\pi$
$774$	95.6732	−	558.048i	0.123609	−	0.720993i
$775$	331.955	−	309.048i	0.428329	−	0.398771i
$776$	−126.948			−0.163592
$777$	335.246	−	271.962i	0.431462	−	0.350015i
$778$	−1302.60	+	1302.60i	−1.67429	+	1.67429i
$779$	−272.446	−	471.890i	−0.349738	−	0.605764i
$780$	920.755	+	219.143i	1.18046	+	0.280952i
$781$	−131.129	+	227.122i	−0.167899	+	0.290810i
$782$	−68.7651	+	256.635i	−0.0879349	+	0.328178i
$783$	−568.025	−	147.881i	−0.725447	−	0.188864i
$784$	−881.215	−	33.4144i	−1.12400	−	0.0426204i
$785$	−573.768	+	720.723i	−0.730915	+	0.918118i
$786$	−622.027	+	524.461i	−0.791383	+	0.667253i
$787$	−112.939	−	421.495i	−0.143506	−	0.535572i	−0.999817	−	0.0191119i	$-0.993916\pi$
$787$	−112.939	−	421.495i	−0.143506	−	0.535572i	0.856311	−	0.516460i	$-0.172751\pi$
$788$	1107.57	−	296.772i	1.40554	−	0.376614i
$789$	−556.080	−	659.529i	−0.704791	−	0.835905i
$790$	421.782	+	335.781i	0.533901	+	0.425039i
$791$	−103.261	−	29.7771i	−0.130545	−	0.0376449i
$792$	−84.6778	−	38.9982i	−0.106916	−	0.0492402i
$793$	1087.20	+	291.315i	1.37100	+	0.367358i
$794$	852.959	+	492.456i	1.07426	+	0.620222i
$795$	56.7565	−	238.470i	0.0713919	−	0.299962i
$796$	−306.121	+	176.739i	−0.384574	+	0.222034i
$797$	65.6167	+	65.6167i	0.0823296	+	0.0823296i	0.747072	−	0.664743i	$-0.231459\pi$
$797$	65.6167	+	65.6167i	0.0823296	+	0.0823296i	−0.664743	+	0.747072i	$0.731459\pi$
$798$	184.357	−	481.522i	0.231023	−	0.603412i
$799$			1108.62i			1.38751i
$800$	−1065.29	−	38.0694i	−1.33161	−	0.0475868i
$801$	−10.0261	+	58.4809i	−0.0125170	+	0.0730099i
$802$	1330.75	−	356.575i	1.65930	−	0.444607i
$803$	−556.551	−	149.127i	−0.693090	−	0.185713i
$804$	−12.9627	−	72.5096i	−0.0161228	−	0.0901861i
$805$	−68.4793	+	82.7505i	−0.0850674	+	0.102796i
$806$			912.712i			1.13240i
$807$	−45.3822	+	533.277i	−0.0562356	+	0.660815i
$808$	−151.247	+	40.5265i	−0.187187	+	0.0501565i
$809$	461.230	−	798.874i	0.570124	−	0.987484i	−0.426429	−	0.904521i	$-0.640228\pi$
$809$	461.230	−	798.874i	0.570124	−	0.987484i	0.996553	−	0.0829625i	$-0.0264382\pi$
$810$	935.073	−	584.751i	1.15441	−	0.721915i
$811$		−	1041.32i		−	1.28400i	−0.766705	−	0.642000i	$-0.778105\pi$
$811$		−	1041.32i		−	1.28400i	0.766705	−	0.642000i	$-0.221895\pi$
$812$	519.630	+	9.84829i	0.639939	+	0.0121284i
$813$	−1161.53	−	809.213i	−1.42869	−	0.995341i
$814$	−315.393	+	182.092i	−0.387460	+	0.223700i
$815$	328.905	+	835.971i	0.403564	+	1.02573i
$816$	583.256	−	1614.38i	0.714775	−	1.97841i
$817$	201.203	+	53.9121i	0.246270	+	0.0659879i
$818$	1076.12	−	1076.12i	1.31554	−	1.31554i
$819$	−962.827	+	653.990i	−1.17561	+	0.798522i
$820$	116.407	+	1025.40i	0.141960	+	1.25049i
$821$	−47.0980	+	27.1920i	−0.0573666	+	0.0331206i	−0.528409	−	0.848990i	$-0.677211\pi$
$821$	−47.0980	+	27.1920i	−0.0573666	+	0.0331206i	0.471042	+	0.882111i	$0.343878\pi$
$822$	−308.083	+	144.551i	−0.374797	+	0.175853i
$823$	328.153	+	1224.68i	0.398727	+	1.48807i	0.815338	+	0.578986i	$0.196551\pi$
$823$	328.153	+	1224.68i	0.398727	+	1.48807i	−0.416610	+	0.909085i	$0.636782\pi$
$824$	−104.030	+	60.0616i	−0.126250	+	0.0728903i
$825$	−452.696	−	182.082i	−0.548723	−	0.220706i
$826$	1182.87	+	341.099i	1.43204	+	0.412953i
$827$	−865.051	+	865.051i	−1.04601	+	1.04601i	−0.0471223	+	0.998889i	$0.515005\pi$
$827$	−865.051	+	865.051i	−1.04601	+	1.04601i	−0.998889	+	0.0471223i	$0.984995\pi$
$828$	8.66687	+	93.9315i	0.0104672	+	0.113444i
$829$	−509.991	+	883.330i	−0.615188	+	1.06554i	0.375164	+	0.926959i	$0.377587\pi$
$829$	−509.991	+	883.330i	−0.615188	+	1.06554i	−0.990352	+	0.138578i	$0.955747\pi$
$830$	−287.544	−	125.167i	−0.346439	−	0.150804i
$831$	−49.8686	−	59.1457i	−0.0600103	−	0.0711742i
$832$	576.410	−	576.410i	0.692800	−	0.692800i
$833$	459.928	−	1488.40i	0.552134	−	1.78680i
$834$	332.451	+	1859.63i	0.398622	+	2.22977i
$835$	−67.3927	+	449.682i	−0.0807098	+	0.538542i
$836$	−100.171	+	173.502i	−0.119822	+	0.207538i
$837$	348.817	+	343.890i	0.416746	+	0.410861i
$838$	251.379	−	938.159i	0.299975	−	1.11952i
$839$		−	574.786i		−	0.685084i	−0.939502	−	0.342542i	$-0.888712\pi$
$839$		−	574.786i		−	0.685084i	0.939502	−	0.342542i	$-0.111288\pi$
$840$	117.121	−	119.294i	0.139430	−	0.142017i
$841$	−368.406			−0.438057
$842$	192.465	+	51.5708i	0.228581	+	0.0612480i
$843$	588.008	−	275.892i	0.697519	−	0.327274i
$844$	−85.2452	−	49.2163i	−0.101001	−	0.0583132i
$845$	692.852	−	512.247i	0.819943	−	0.606210i
$846$	296.095	+	801.667i	0.349994	+	0.947598i
$847$	−471.628	−	284.344i	−0.556822	−	0.335708i
$848$	−207.964	−	207.964i	−0.245241	−	0.245241i
$849$	912.997	+	1082.84i	1.07538	+	1.27544i
$850$	634.487	−	2069.29i	0.746456	−	2.43445i
$851$	−54.6335	−	31.5427i	−0.0641991	−	0.0370654i
$852$	−411.535	−	35.0218i	−0.483022	−	0.0411054i
$853$	516.935	+	516.935i	0.606019	+	0.606019i	0.941903	−	0.335884i	$-0.109035\pi$
$853$	516.935	+	516.935i	0.606019	+	0.606019i	−0.335884	+	0.941903i	$0.609035\pi$
$854$	−836.570	+	805.450i	−0.979590	+	0.943150i
$855$	182.612	+	362.323i	0.213582	+	0.423769i
$856$	81.0908	+	140.453i	0.0947322	+	0.164081i
$857$	−876.518	+	234.862i	−1.02278	+	0.274052i	−0.730958	−	0.682422i	$-0.760927\pi$
$857$	−876.518	+	234.862i	−1.02278	+	0.274052i	−0.291817	+	0.956474i	$0.594260\pi$
$858$	888.945	−	417.090i	1.03607	−	0.486119i
$859$	235.600	+	408.072i	0.274273	+	0.475054i	0.969951	−	0.243299i	$-0.0782295\pi$
$859$	235.600	+	408.072i	0.274273	+	0.475054i	−0.695679	+	0.718353i	$0.744896\pi$
$860$	−308.645	−	245.712i	−0.358889	−	0.285712i
$861$	−1027.37	−	745.058i	−1.19323	−	0.865341i
$862$	585.348	+	585.348i	0.679058	+	0.679058i
$863$	262.256	−	978.754i	0.303889	−	1.13413i	−0.630008	−	0.776589i	$-0.716948\pi$
$863$	262.256	−	978.754i	0.303889	−	1.13413i	0.933897	−	0.357541i	$-0.116385\pi$
$864$	−8.18705	−	1151.22i	−0.00947575	−	1.33243i
$865$	419.401	+	1065.98i	0.484857	+	1.23235i
$866$	547.638	+	948.536i	0.632376	+	1.09531i
$867$	1776.68	+	1237.78i	2.04922	+	1.42765i
$868$	−371.436	−	223.939i	−0.427922	−	0.257994i
$869$	257.607			0.296440
$870$	−609.975	+	645.312i	−0.701121	+	0.741738i
$871$	−115.025	−	66.4099i	−0.132061	−	0.0762456i
$872$	31.2204	+	116.516i	0.0358032	+	0.133619i
$873$	−65.9307	−	714.557i	−0.0755220	−	0.818507i
$874$	−75.3493			−0.0862120
$875$	581.572	−	653.758i	0.664654	−	0.747152i
$876$	−159.689	−	893.252i	−0.182293	−	1.01969i
$877$	410.782	−	1533.06i	0.468395	−	1.74807i	−0.176987	−	0.984213i	$-0.556635\pi$
$877$	410.782	−	1533.06i	0.468395	−	1.74807i	0.645382	−	0.763860i	$-0.276698\pi$
$878$	−228.833	−	854.016i	−0.260630	−	0.972684i
$879$	426.713	+	154.166i	0.485452	+	0.175388i
$880$	−470.744	+	348.035i	−0.534936	+	0.395495i
$881$	821.783			0.932784			0.466392	−	0.884578i	$-0.345554\pi$
$881$	821.783			0.932784			0.466392	+	0.884578i	$0.345554\pi$
$882$	−64.9449	−	1199.13i	−0.0736337	−	1.35956i
$883$	586.983	−	586.983i	0.664760	−	0.664760i	−0.291738	−	0.956498i	$-0.594233\pi$
$883$	586.983	−	586.983i	0.664760	−	0.664760i	0.956498	+	0.291738i	$0.0942335\pi$
$884$	1003.03	+	1737.30i	1.13465	+	1.96528i
$885$	−824.996	+	507.789i	−0.932199	+	0.573773i
$886$	295.161	−	511.235i	0.333139	−	0.577014i
$887$	−345.442	+	1289.21i	−0.389450	+	1.45345i	0.441581	+	0.897222i	$0.354418\pi$
$887$	−345.442	+	1289.21i	−0.389450	+	1.45345i	−0.831031	+	0.556226i	$0.812249\pi$
$888$	80.5644	+	56.1277i	0.0907257	+	0.0632068i
$889$	838.921	+	241.916i	0.943669	+	0.272122i
$890$	70.2265	+	55.9073i	0.0789061	+	0.0628172i
$891$	175.534	−	496.884i	0.197007	−	0.557670i
$892$	392.190	+	1463.67i	0.439675	+	1.64089i
$893$	−303.693	+	81.3744i	−0.340082	+	0.0911247i
$894$	−153.867	+	129.733i	−0.172111	+	0.145115i
$895$	278.085	−	31.5691i	0.310709	−	0.0352727i
$896$	−84.8462	−	342.483i	−0.0946944	−	0.382235i
$897$	139.563	+	97.2311i	0.155589	+	0.108396i
$898$	475.496	+	127.409i	0.529506	+	0.141881i
$899$	−341.552	−	197.195i	−0.379924	−	0.219349i
$900$	−43.2302	−	767.228i	−0.0480336	−	0.852476i
$901$	449.951	−	259.779i	0.499390	−	0.288323i
$902$	757.063	+	757.063i	0.839316	+	0.839316i
$903$	479.109	−	76.3125i	0.530574	−	0.0845099i
$904$		−	24.4442i		−	0.0270400i
$905$	−238.183	+	176.096i	−0.263186	+	0.194582i
$906$	−625.879	−	226.122i	−0.690815	−	0.249583i
$907$	−1178.10	+	315.671i	−1.29890	+	0.348039i	−0.841034	−	0.540983i	$-0.818052\pi$
$907$	−1178.10	+	315.671i	−1.29890	+	0.348039i	−0.457865	+	0.889022i	$0.651386\pi$
$908$	458.319	+	122.806i	0.504757	+	0.135249i
$909$	−306.664	−	830.283i	−0.337364	−	0.913403i
$910$	165.431	+	1753.05i	0.181793	+	1.92643i
$911$		−	880.582i		−	0.966611i	−0.875452	−	0.483305i	$-0.839436\pi$
$911$		−	880.582i		−	0.966611i	0.875452	−	0.483305i	$-0.160564\pi$
$912$	485.051	+	41.2781i	0.531854	+	0.0452610i
$913$	−144.744	+	38.7840i	−0.158537	+	0.0424797i
$914$	282.636	−	489.540i	0.309230	−	0.535602i
$915$	−25.7150	−	913.478i	−0.0281038	−	0.998336i
$916$		−	593.872i		−	0.648332i
$917$	−597.046	−	359.959i	−0.651086	−	0.392540i
$918$	2262.12	+	588.924i	2.46418	+	0.641529i
$919$	−949.330	+	548.096i	−1.03300	+	0.596405i	−0.917844	−	0.396942i	$-0.870071\pi$
$919$	−949.330	+	548.096i	−1.03300	+	0.596405i	−0.115160	+	0.993347i	$0.536738\pi$
$920$	−22.4006	−	9.75091i	−0.0243485	−	0.0105988i
$921$	−1075.49	−	388.563i	−1.16775	−	0.421893i
$922$	−695.354	−	186.320i	−0.754180	−	0.202082i
$923$	−526.616	+	526.616i	−0.570549	+	0.570549i
$924$	−48.3689	+	464.099i	−0.0523473	+	0.502272i
$925$	435.600	+	272.687i	0.470919	+	0.294796i
$926$	1776.24	−	1025.51i	1.91818	−	1.10746i
$927$	−392.100	−	554.364i	−0.422977	−	0.598020i
$928$	239.908	+	895.350i	0.258522	+	0.964817i
$929$	−1019.88	+	588.828i	−1.09783	+	0.633830i	−0.935649	−	0.352932i	$-0.885185\pi$
$929$	−1019.88	+	588.828i	−1.09783	+	0.633830i	−0.162176	+	0.986762i	$0.551851\pi$
$930$	710.103	−	211.859i	0.763551	−	0.227806i
$931$	441.489	+	16.7406i	0.474209	+	0.0179813i
$932$	630.373	−	630.373i	0.676366	−	0.676366i
$933$	−264.606	−	22.5181i	−0.283608	−	0.0241352i
$934$	166.545	−	288.464i	0.178314	−	0.308848i
$935$	−378.644	−	962.393i	−0.404967	−	1.02930i
$936$	−203.607	−	169.208i	−0.217529	−	0.180778i
$937$	323.664	−	323.664i	0.345426	−	0.345426i	−0.512977	−	0.858402i	$-0.671457\pi$
$937$	323.664	−	323.664i	0.345426	−	0.345426i	0.858402	+	0.512977i	$0.171457\pi$
$938$	119.955	−	66.2574i	0.127883	−	0.0706369i
$939$	−1330.90	+	237.929i	−1.41736	+	0.253385i
$940$	588.889	+	88.2552i	0.626477	+	0.0938885i
$941$	−324.061	+	561.290i	−0.344379	+	0.596483i	−0.985241	−	0.171174i	$-0.945244\pi$
$941$	−324.061	+	561.290i	−0.344379	+	0.596483i	0.640861	+	0.767657i	$0.278577\pi$
$942$	−1362.62	+	639.337i	−1.44652	+	0.678702i
$943$	−48.0010	+	179.142i	−0.0509025	+	0.189971i
$944$			1162.29i			1.23124i
$945$	732.305	+	597.289i	0.774926	+	0.632051i
$946$	−409.286			−0.432649
$947$	−942.342	−	252.500i	−0.995081	−	0.266631i	−0.275698	−	0.961244i	$-0.588909\pi$
$947$	−942.342	−	252.500i	−0.995081	−	0.266631i	−0.719383	+	0.694613i	$0.755576\pi$
$948$	172.326	+	367.278i	0.181778	+	0.387425i
$949$	−1417.01	−	818.109i	−1.49316	−	0.862075i
$950$	613.427	+	21.9216i	0.645713	+	0.0230753i
$951$	84.6513	+	473.515i	0.0890129	+	0.497913i
$952$	354.272	+	6.71435i	0.372135	+	0.00705288i
$953$	764.470	+	764.470i	0.802172	+	0.802172i	0.983435	−	0.181262i	$-0.0580183\pi$
$953$	764.470	+	764.470i	0.802172	+	0.802172i	−0.181262	+	0.983435i	$0.558018\pi$
$954$	255.986	−	308.026i	0.268329	−	0.322878i
$955$	945.879	+	411.738i	0.990450	+	0.431139i
$956$	−790.904	−	456.629i	−0.827305	−	0.477645i
$957$	−35.9781	+	422.772i	−0.0375947	+	0.441768i
$958$	1348.79	+	1348.79i	1.40792	+	1.40792i
$959$	−202.247	−	210.061i	−0.210894	−	0.219042i
$960$	−582.252	−	314.658i	−0.606512	−	0.327769i
$961$	−315.936	−	547.218i	−0.328758	−	0.569426i
$962$	−998.952	+	267.668i	−1.03841	+	0.278242i
$963$	−748.463	+	529.385i	−0.777220	+	0.549725i
$964$	−181.457	−	314.292i	−0.188233	−	0.326030i
$965$	−616.572	+	774.489i	−0.638934	+	0.802580i
$966$	−160.260	+	71.5200i	−0.165900	+	0.0740373i
$967$	−108.209	−	108.209i	−0.111901	−	0.111901i	0.648939	−	0.760840i	$-0.275213\pi$
$967$	−108.209	−	108.209i	−0.111901	−	0.111901i	−0.760840	+	0.648939i	$0.775213\pi$
$968$	32.4200	−	120.993i	0.0334917	−	0.124993i
$969$	−292.211	+	808.804i	−0.301560	+	0.834679i
$970$	−995.384	−	433.287i	−1.02617	−	0.446688i
$971$	−527.976	−	914.482i	−0.543745	−	0.941794i	−0.998685	−	0.0512715i	$-0.983673\pi$
$971$	−527.976	−	914.482i	−0.543745	−	0.941794i	0.454940	−	0.890522i	$-0.349661\pi$
$972$	825.847	−	82.1263i	0.849637	−	0.0844920i
$973$	−1416.93	+	782.648i	−1.45625	+	0.804366i
$974$	−462.895			−0.475251
$975$	−1107.91	−	832.172i	−1.13632	−	0.853510i
$976$	−949.526	−	548.209i	−0.972875	−	0.561690i
$977$	−138.822	−	518.091i	−0.142090	−	0.530288i	−0.999868	−	0.0162666i	$-0.994822\pi$
$977$	−138.822	−	518.091i	−0.142090	−	0.530288i	0.857778	−	0.514021i	$-0.171845\pi$
$978$	−124.459	+	1462.49i	−0.127258	+	1.49539i
$979$	42.8914			0.0438114
$980$	−754.010	−	362.797i	−0.769398	−	0.370201i
$981$	−639.626	+	236.245i	−0.652014	+	0.240820i
$982$	173.399	−	647.135i	0.176578	−	0.658997i
$983$	255.618	+	953.980i	0.260039	+	0.970478i	0.965217	+	0.261448i	$0.0842001\pi$
$983$	255.618	+	953.980i	0.260039	+	0.970478i	−0.705179	+	0.709030i	$0.749133\pi$
$984$	98.0841	−	271.484i	0.0996789	−	0.275899i
$985$	−1660.13	−	248.800i	−1.68542	−	0.252589i
$986$	−1882.07			−1.90880
$987$	−568.683	+	461.334i	−0.576174	+	0.467410i
$988$	−402.289	+	402.289i	−0.407175	+	0.407175i
$989$	−35.4490	−	61.3995i	−0.0358433	−	0.0620824i
$990$	−530.844	−	594.796i	−0.536207	−	0.600804i
$991$	423.487	−	733.501i	0.427333	−	0.740163i	−0.569302	−	0.822128i	$-0.692787\pi$
$991$	423.487	−	733.501i	0.427333	−	0.740163i	0.996635	+	0.0819659i	$0.0261198\pi$
$992$	200.209	−	747.189i	0.201823	−	0.753215i
$993$	−29.6492	+	42.5578i	−0.0298582	+	0.0428578i
$994$	−184.775	−	745.848i	−0.185891	−	0.750350i
$995$	514.188	−	58.3722i	0.516772	−	0.0586655i
$996$	−152.122	−	180.422i	−0.152733	−	0.181146i
$997$	−13.0234	−	48.6041i	−0.0130626	−	0.0487504i	0.959087	−	0.283112i	$-0.0913668\pi$
$997$	−13.0234	−	48.6041i	−0.0130626	−	0.0487504i	−0.972150	+	0.234361i	$0.924700\pi$
$998$	716.179	−	191.900i	0.717614	−	0.192284i
$999$	−274.087	+	482.627i	−0.274362	+	0.483110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.5	✓	112
3.2	odd	2	inner	105.3.w.a.17.24	yes	112
5.3	odd	4	inner	105.3.w.a.38.5	yes	112
7.5	odd	6	inner	105.3.w.a.47.24	yes	112
15.8	even	4	inner	105.3.w.a.38.24	yes	112
21.5	even	6	inner	105.3.w.a.47.5	yes	112
35.33	even	12	inner	105.3.w.a.68.24	yes	112
105.68	odd	12	inner	105.3.w.a.68.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.5	✓	112	1.1	even	1	trivial
105.3.w.a.17.24	yes	112	3.2	odd	2	inner
105.3.w.a.38.5	yes	112	5.3	odd	4	inner
105.3.w.a.38.24	yes	112	15.8	even	4	inner
105.3.w.a.47.5	yes	112	21.5	even	6	inner
105.3.w.a.47.24	yes	112	7.5	odd	6	inner
105.3.w.a.68.5	yes	112	105.68	odd	12	inner
105.3.w.a.68.24	yes	112	35.33	even	12	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 $\F_{q}$

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+(-2.63032 - 0.704792i) q^{2} +(1.27430 + 2.71591i) q^{3} +(2.95775 + 1.70766i) q^{4} +(-2.97248 - 4.02050i) q^{5} +(-1.43765 - 8.04182i) q^{6} +(6.12741 - 3.38450i) q^{7} +(1.12583 + 1.12583i) q^{8} +(-5.75234 + 6.92175i) q^{9} +(4.98495 + 12.6702i) q^{10} +(5.63427 + 3.25295i) q^{11} +(-0.868794 + 10.2090i) q^{12} +(13.0639 + 13.0639i) q^{13} +(-18.5024 + 4.58376i) q^{14} +(7.13149 - 13.1963i) q^{15} +(-8.99845 - 15.5858i) q^{16} +(30.7094 - 8.22856i) q^{17} +(20.0089 - 14.1522i) q^{18} +(4.50822 + 7.80847i) q^{19} +(-1.92621 - 16.9676i) q^{20} +(17.0001 + 12.3286i) q^{21} +(-12.5273 - 12.5273i) q^{22} +(0.794284 - 2.96431i) q^{23} +(-1.62302 + 4.49231i) q^{24} +(-7.32876 + 23.9017i) q^{25} +(-25.1549 - 43.5695i) q^{26} +(-26.1290 - 6.80247i) q^{27} +(23.9029 + 0.453019i) q^{28} +21.7392 q^{29} +(-28.0587 + 29.6842i) q^{30} +(-15.7113 - 9.07093i) q^{31} +(11.0357 + 41.1859i) q^{32} +(-1.65498 + 19.4474i) q^{33} -86.5750 q^{34} +(-31.8209 - 14.5749i) q^{35} +(-28.8339 + 10.6498i) q^{36} +(5.32041 - 19.8560i) q^{37} +(-6.35472 - 23.7161i) q^{38} +(-18.8331 + 52.1276i) q^{39} +(1.17989 - 7.87293i) q^{40} -60.4331 q^{41} +(-36.0266 - 44.4098i) q^{42} +(16.3358 - 16.3358i) q^{43} +(11.1098 + 19.2428i) q^{44} +(44.9275 + 2.55250i) q^{45} +(-4.17844 + 7.23727i) q^{46} +(-9.02511 + 33.6822i) q^{47} +(30.8629 - 44.2999i) q^{48} +(26.0903 - 41.4764i) q^{49} +(36.1227 - 57.7037i) q^{50} +(61.4809 + 72.9184i) q^{51} +(16.3310 + 60.9483i) q^{52} +(15.7852 - 4.22963i) q^{53} +(63.9334 + 36.3082i) q^{54} +(-3.66928 - 32.3219i) q^{55} +(10.7088 + 3.08807i) q^{56} +(-15.4623 + 22.1942i) q^{57} +(-57.1811 - 15.3216i) q^{58} +(-55.9306 - 32.2915i) q^{59} +(43.6278 - 26.8531i) q^{60} +(52.7606 - 30.4613i) q^{61} +(34.9327 + 34.9327i) q^{62} +(-11.8203 + 61.8812i) q^{63} -44.1224i q^{64} +(13.6912 - 91.3554i) q^{65} +(18.0595 - 49.9865i) q^{66} +(-6.94415 + 1.86068i) q^{67} +(104.882 + 28.1031i) q^{68} +(9.06294 - 1.62020i) q^{69} +(73.4270 + 60.7637i) q^{70} +40.3109i q^{71} +(-14.2689 + 1.31656i) q^{72} +(-85.5456 + 22.9219i) q^{73} +(-27.9887 + 48.4779i) q^{74} +(-74.2538 + 10.5535i) q^{75} +30.7940i q^{76} +(45.5331 + 0.862966i) q^{77} +(86.2761 - 123.839i) q^{78} +(34.2910 - 19.7979i) q^{79} +(-35.9148 + 82.5065i) q^{80} +(-14.8212 - 79.6325i) q^{81} +(158.958 + 42.5928i) q^{82} +(-16.2867 + 16.2867i) q^{83} +(29.2290 + 65.4954i) q^{84} +(-124.366 - 99.0078i) q^{85} +(-54.4817 + 31.4550i) q^{86} +(27.7022 + 59.0418i) q^{87} +(2.68098 + 10.0055i) q^{88} +(5.70943 - 3.29634i) q^{89} +(-116.375 - 38.3785i) q^{90} +(124.262 + 35.8331i) q^{91} +(7.41130 - 7.41130i) q^{92} +(4.61496 - 54.2296i) q^{93} +(47.4778 - 82.2340i) q^{94} +(17.9933 - 41.3358i) q^{95} +(-97.7944 + 82.4551i) q^{96} +(-56.3794 + 56.3794i) q^{97} +(-97.8582 + 90.7080i) q^{98} +(-54.9264 + 20.2870i) 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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