LMFDB - Embedded newform 105.3.w.a.68.10

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			68.10
Character	$\chi$	$=$	105.68
Dual form			105.3.w.a.17.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40147 + 0.375522i) q^{2} +(-1.48402 + 2.60724i) q^{3} +(-1.64101 + 0.947435i) q^{4} +(-3.73472 + 3.32444i) q^{5} +(1.10073 - 4.21124i) q^{6} +(2.97299 - 6.33730i) q^{7} +(6.04782 - 6.04782i) q^{8} +(-4.59537 - 7.73838i) q^{9} +(3.98568 - 6.06157i) q^{10} +(-3.76549 + 2.17401i) q^{11} +(-0.0349040 - 5.68450i) q^{12} +(4.76059 - 4.76059i) q^{13} +(-1.78675 + 9.99794i) q^{14} +(-3.12522 - 14.6708i) q^{15} +(-2.41499 + 4.18289i) q^{16} +(-19.0658 - 5.10867i) q^{17} +(9.34620 + 9.11943i) q^{18} +(-12.5949 + 21.8150i) q^{19} +(2.97900 - 8.99383i) q^{20} +(12.1109 + 17.1560i) q^{21} +(4.46083 - 4.46083i) q^{22} +(-8.21961 - 30.6760i) q^{23} +(6.79302 + 24.7432i) q^{24} +(2.89619 - 24.8317i) q^{25} +(-4.88411 + 8.45952i) q^{26} +(26.9954 - 0.497321i) q^{27} +(1.12549 + 13.2163i) q^{28} -28.8306 q^{29} +(9.88911 + 19.3871i) q^{30} +(-12.3444 + 7.12704i) q^{31} +(-7.04085 + 26.2768i) q^{32} +(-0.0800915 - 13.0438i) q^{33} +28.6386 q^{34} +(9.96472 + 33.5515i) q^{35} +(14.8726 + 8.34491i) q^{36} +(13.1470 + 49.0654i) q^{37} +(9.45934 - 35.3027i) q^{38} +(5.34718 + 19.4768i) q^{39} +(-2.48127 + 42.6925i) q^{40} +1.56196 q^{41} +(-23.4154 - 19.4956i) q^{42} +(-46.2033 - 46.2033i) q^{43} +(4.11946 - 7.13512i) q^{44} +(42.8882 + 13.6236i) q^{45} +(23.0391 + 39.9048i) q^{46} +(-3.56182 - 13.2929i) q^{47} +(-7.32189 - 12.5040i) q^{48} +(-31.3227 - 37.6814i) q^{49} +(5.26592 + 35.8884i) q^{50} +(41.6136 - 42.1278i) q^{51} +(-3.30181 + 12.3225i) q^{52} +(33.7582 + 9.04547i) q^{53} +(-37.6465 + 10.8344i) q^{54} +(6.83568 - 20.6375i) q^{55} +(-20.3468 - 56.3069i) q^{56} +(-38.1859 - 65.2119i) q^{57} +(40.4052 - 10.8265i) q^{58} +(-54.4737 + 31.4504i) q^{59} +(19.0281 + 21.1140i) q^{60} +(9.31520 + 5.37814i) q^{61} +(14.6239 - 14.6239i) q^{62} +(-62.7024 + 6.11616i) q^{63} -58.7901i q^{64} +(-1.95315 + 33.6057i) q^{65} +(5.01049 + 18.2504i) q^{66} +(-112.138 - 30.0473i) q^{67} +(36.1273 - 9.68028i) q^{68} +(92.1777 + 24.0933i) q^{69} +(-26.5646 - 43.2794i) q^{70} +8.44240i q^{71} +(-74.5923 - 19.0083i) q^{72} +(26.0040 + 6.96775i) q^{73} +(-36.8503 - 63.8266i) q^{74} +(60.4441 + 44.4018i) q^{75} -47.7314i q^{76} +(2.58258 + 30.3264i) q^{77} +(-14.8079 - 25.2881i) q^{78} +(-59.9822 - 34.6307i) q^{79} +(-4.88646 - 23.6504i) q^{80} +(-38.7651 + 71.1215i) q^{81} +(-2.18904 + 0.586552i) q^{82} +(-11.5754 - 11.5754i) q^{83} +(-36.1282 - 16.6788i) q^{84} +(88.1889 - 44.3038i) q^{85} +(82.1027 + 47.4020i) q^{86} +(42.7852 - 75.1682i) q^{87} +(-9.62501 + 35.9210i) q^{88} +(58.5647 + 33.8123i) q^{89} +(-65.2224 - 2.98758i) q^{90} +(-16.0161 - 44.3225i) q^{91} +(42.5520 + 42.5520i) q^{92} +(-0.262563 - 42.7614i) q^{93} +(9.98356 + 17.2920i) q^{94} +(-25.4843 - 123.344i) q^{95} +(-58.0611 - 57.3525i) q^{96} +(124.503 + 124.503i) q^{97} +(58.0480 + 41.0469i) q^{98} +(34.1272 + 19.1484i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.40147	+	0.375522i	−0.700734	+	0.187761i	−0.591559	−	0.806261i	$-0.701487\pi$
$2$	−1.40147	+	0.375522i	−0.700734	+	0.187761i	−0.109175	+	0.994023i	$0.534821\pi$
$3$	−1.48402	+	2.60724i	−0.494673	+	0.869079i
$3$	−1.48402	+	2.60724i	−0.494673	+	0.869079i
$4$	−1.64101	+	0.947435i	−0.410251	+	0.236859i
$5$	−3.73472	+	3.32444i	−0.746943	+	0.664888i
$5$	−3.73472	+	3.32444i	−0.746943	+	0.664888i
$6$	1.10073	−	4.21124i	0.183455	−	0.701874i
$7$	2.97299	−	6.33730i	0.424712	−	0.905328i
$7$	2.97299	−	6.33730i	0.424712	−	0.905328i
$8$	6.04782	−	6.04782i	0.755977	−	0.755977i
$9$	−4.59537	−	7.73838i	−0.510597	−	0.859820i
$10$	3.98568	−	6.06157i	0.398568	−	0.606157i
$11$	−3.76549	+	2.17401i	−0.342318	+	0.197637i	−0.661296	−	0.750125i	$-0.729993\pi$
$11$	−3.76549	+	2.17401i	−0.342318	+	0.197637i	0.318979	+	0.947762i	$0.396660\pi$
$12$	−0.0349040	−	5.68450i	−0.00290866	−	0.473709i
$13$	4.76059	−	4.76059i	0.366199	−	0.366199i	−0.499890	−	0.866089i	$-0.666626\pi$
$13$	4.76059	−	4.76059i	0.366199	−	0.366199i	0.866089	+	0.499890i	$0.166626\pi$
$14$	−1.78675	+	9.99794i	−0.127625	+	0.714139i
$15$	−3.12522	−	14.6708i	−0.208348	−	0.978055i
$16$	−2.41499	+	4.18289i	−0.150937	+	0.261431i
$17$	−19.0658	−	5.10867i	−1.12152	−	0.300510i	−0.350021	−	0.936742i	$-0.613826\pi$
$17$	−19.0658	−	5.10867i	−1.12152	−	0.300510i	−0.771498	+	0.636231i	$0.780492\pi$
$18$	9.34620	+	9.11943i	0.519234	+	0.506635i
$19$	−12.5949	+	21.8150i	−0.662890	+	1.14816i	0.316963	+	0.948438i	$0.397337\pi$
$19$	−12.5949	+	21.8150i	−0.662890	+	1.14816i	−0.979853	+	0.199721i	$0.935996\pi$
$20$	2.97900	−	8.99383i	0.148950	−	0.449691i
$21$	12.1109	+	17.1560i	0.576708	+	0.816950i
$22$	4.46083	−	4.46083i	0.202765	−	0.202765i
$23$	−8.21961	−	30.6760i	−0.357374	−	1.33374i	−0.877470	−	0.479632i	$-0.840770\pi$
$23$	−8.21961	−	30.6760i	−0.357374	−	1.33374i	0.520095	−	0.854108i	$-0.325896\pi$
$24$	6.79302	+	24.7432i	0.283042	+	1.03097i
$25$	2.89619	−	24.8317i	0.115848	−	0.993267i
$26$	−4.88411	+	8.45952i	−0.187850	+	0.325366i
$27$	26.9954	−	0.497321i	0.999830	−	0.0184193i
$28$	1.12549	+	13.2163i	0.0401962	+	0.472009i
$29$	−28.8306			−0.994158			−0.497079	−	0.867705i	$-0.665594\pi$
$29$	−28.8306			−0.994158			−0.497079	+	0.867705i	$0.665594\pi$
$30$	9.88911	+	19.3871i	0.329637	+	0.646237i
$31$	−12.3444	+	7.12704i	−0.398206	+	0.229904i	−0.685710	−	0.727875i	$-0.740508\pi$
$31$	−12.3444	+	7.12704i	−0.398206	+	0.229904i	0.287504	+	0.957780i	$0.407175\pi$
$32$	−7.04085	+	26.2768i	−0.220027	+	0.821151i
$33$	−0.0800915	−	13.0438i	−0.00242702	−	0.395267i
$34$	28.6386			0.842311
$35$	9.96472	+	33.5515i	0.284706	+	0.958615i
$36$	14.8726	+	8.34491i	0.413129	+	0.231803i
$37$	13.1470	+	49.0654i	0.355325	+	1.32609i	0.880075	+	0.474835i	$0.157492\pi$
$37$	13.1470	+	49.0654i	0.355325	+	1.32609i	−0.524750	+	0.851257i	$0.675841\pi$
$38$	9.45934	−	35.3027i	0.248930	−	0.929019i
$39$	5.34718	+	19.4768i	0.137107	+	0.499405i
$40$	−2.48127	+	42.6925i	−0.0620317	+	1.06731i
$41$	1.56196			0.0380967			0.0190483	−	0.999819i	$-0.493936\pi$
$41$	1.56196			0.0380967			0.0190483	+	0.999819i	$0.493936\pi$
$42$	−23.4154	−	19.4956i	−0.557511	−	0.464181i
$43$	−46.2033	−	46.2033i	−1.07449	−	1.07449i	−0.996992	−	0.0775021i	$-0.975306\pi$
$43$	−46.2033	−	46.2033i	−1.07449	−	1.07449i	−0.0775021	−	0.996992i	$-0.524694\pi$
$44$	4.11946	−	7.13512i	0.0936242	−	0.162162i
$45$	42.8882	+	13.6236i	0.953071	+	0.302747i
$46$	23.0391	+	39.9048i	0.500849	+	0.867496i
$47$	−3.56182	−	13.2929i	−0.0757834	−	0.282828i	0.917626	−	0.397444i	$-0.130103\pi$
$47$	−3.56182	−	13.2929i	−0.0757834	−	0.282828i	−0.993410	+	0.114616i	$0.963436\pi$
$48$	−7.32189	−	12.5040i	−0.152539	−	0.260499i
$49$	−31.3227	−	37.6814i	−0.639239	−	0.769008i
$50$	5.26592	+	35.8884i	0.105318	+	0.717768i
$51$	41.6136	−	42.1278i	0.815953	−	0.826035i
$52$	−3.30181	+	12.3225i	−0.0634963	+	0.236971i
$53$	33.7582	+	9.04547i	0.636946	+	0.170669i	0.562820	−	0.826580i	$-0.309716\pi$
$53$	33.7582	+	9.04547i	0.636946	+	0.170669i	0.0741265	+	0.997249i	$0.476383\pi$
$54$	−37.6465	+	10.8344i	−0.697157	+	0.200636i
$55$	6.83568	−	20.6375i	0.124285	−	0.375227i
$56$	−20.3468	−	56.3069i	−0.363335	−	1.00548i
$57$	−38.1859	−	65.2119i	−0.669927	−	1.14407i
$58$	40.4052	−	10.8265i	0.696641	−	0.186664i
$59$	−54.4737	+	31.4504i	−0.923283	+	0.533058i	−0.884681	−	0.466197i	$-0.845624\pi$
$59$	−54.4737	+	31.4504i	−0.923283	+	0.533058i	−0.0386020	+	0.999255i	$0.512290\pi$
$60$	19.0281	+	21.1140i	0.317136	+	0.351899i
$61$	9.31520	+	5.37814i	0.152708	+	0.0881662i	0.574407	−	0.818570i	$-0.305233\pi$
$61$	9.31520	+	5.37814i	0.152708	+	0.0881662i	−0.421699	+	0.906736i	$0.638566\pi$
$62$	14.6239	−	14.6239i	0.235869	−	0.235869i
$63$	−62.7024	+	6.11616i	−0.995276	+	0.0970818i
$64$		−	58.7901i		−	0.918595i
$65$	−1.95315	+	33.6057i	−0.0300485	+	0.517012i
$66$	5.01049	+	18.2504i	0.0759164	+	0.276521i
$67$	−112.138	−	30.0473i	−1.67370	−	0.448467i	−0.707597	−	0.706617i	$-0.750221\pi$
$67$	−112.138	−	30.0473i	−1.67370	−	0.448467i	−0.966105	+	0.258150i	$0.916887\pi$
$68$	36.1273	−	9.68028i	0.531284	−	0.142357i
$69$	92.1777	+	24.0933i	1.33591	+	0.349178i
$70$	−26.5646	−	43.2794i	−0.379494	−	0.618277i
$71$			8.44240i			0.118907i	0.998231	+	0.0594535i	$0.0189358\pi$
$71$			8.44240i			0.118907i	−0.998231	+	0.0594535i	$0.981064\pi$
$72$	−74.5923	−	19.0083i	−1.03600	−	0.264005i
$73$	26.0040	+	6.96775i	0.356219	+	0.0954487i	0.432491	−	0.901638i	$-0.357635\pi$
$73$	26.0040	+	6.96775i	0.356219	+	0.0954487i	−0.0762714	+	0.997087i	$0.524302\pi$
$74$	−36.8503	−	63.8266i	−0.497977	−	0.862521i
$75$	60.4441	+	44.4018i	0.805921	+	0.592023i
$76$		−	47.7314i		−	0.628045i
$77$	2.58258	+	30.3264i	0.0335401	+	0.393849i
$78$	−14.8079	−	25.2881i	−0.189845	−	0.324207i
$79$	−59.9822	−	34.6307i	−0.759268	−	0.438364i	0.0697650	−	0.997563i	$-0.477775\pi$
$79$	−59.9822	−	34.6307i	−0.759268	−	0.438364i	−0.829033	+	0.559200i	$0.811108\pi$
$80$	−4.88646	−	23.6504i	−0.0610807	−	0.295630i
$81$	−38.7651	+	71.1215i	−0.478581	+	0.878043i
$82$	−2.18904	+	0.586552i	−0.0266956	+	0.00715307i
$83$	−11.5754	−	11.5754i	−0.139463	−	0.139463i	0.633929	−	0.773391i	$-0.281441\pi$
$83$	−11.5754	−	11.5754i	−0.139463	−	0.139463i	−0.773391	+	0.633929i	$0.781441\pi$
$84$	−36.1282	−	16.6788i	−0.430097	−	0.198557i
$85$	88.1889	−	44.3038i	1.03752	−	0.521221i
$86$	82.1027	+	47.4020i	0.954683	+	0.551186i
$87$	42.7852	−	75.1682i	0.491783	−	0.864002i
$88$	−9.62501	+	35.9210i	−0.109375	+	0.408194i
$89$	58.5647	+	33.8123i	0.658030	+	0.379914i	0.791526	−	0.611135i	$-0.209287\pi$
$89$	58.5647	+	33.8123i	0.658030	+	0.379914i	−0.133496	+	0.991049i	$0.542620\pi$
$90$	−65.2224	−	2.98758i	−0.724693	−	0.0331953i
$91$	−16.0161	−	44.3225i	−0.176001	−	0.487060i
$92$	42.5520	+	42.5520i	0.462521	+	0.462521i
$93$	−0.262563	−	42.7614i	−0.00282326	−	0.459800i
$94$	9.98356	+	17.2920i	0.106208	+	0.183958i
$95$	−25.4843	−	123.344i	−0.268256	−	1.29836i
$96$	−58.0611	−	57.3525i	−0.604804	−	0.597422i
$97$	124.503	+	124.503i	1.28354	+	1.28354i	0.938639	+	0.344901i	$0.112087\pi$
$97$	124.503	+	124.503i	1.28354	+	1.28354i	0.344901	+	0.938639i	$0.387913\pi$
$98$	58.0480	+	41.0469i	0.592326	+	0.418846i
$99$	34.1272	+	19.1484i	0.344719	+	0.193419i
$100$	18.7737	+	43.4929i	0.187737	+	0.434929i
$101$	31.5264	+	54.6053i	0.312143	+	0.540647i	0.978826	−	0.204694i	$-0.0656200\pi$
$101$	31.5264	+	54.6053i	0.312143	+	0.540647i	−0.666683	+	0.745341i	$0.732287\pi$
$102$	−42.5002	+	74.6676i	−0.416669	+	0.732035i
$103$	21.5705	+	80.5022i	0.209422	+	0.781574i	0.988056	+	0.154096i	$0.0492464\pi$
$103$	21.5705	+	80.5022i	0.209422	+	0.781574i	−0.778634	+	0.627479i	$0.784087\pi$
$104$		−	57.5824i		−	0.553677i
$105$	−102.265	−	23.8107i	−0.973949	−	0.226769i
$106$	−50.7078			−0.478375
$107$	19.8432	−	5.31697i	0.185450	−	0.0496913i	−0.164899	−	0.986311i	$-0.552730\pi$
$107$	19.8432	−	5.31697i	0.185450	−	0.0496913i	0.350349	+	0.936619i	$0.386063\pi$
$108$	−43.8285	+	26.3925i	−0.405819	+	0.244375i
$109$	−0.918436	+	0.530259i	−0.00842602	+	0.00486476i	−0.504207	−	0.863583i	$-0.668215\pi$
$109$	−0.918436	+	0.530259i	−0.00842602	+	0.00486476i	0.495781	+	0.868448i	$0.334882\pi$
$110$	−1.83017	+	31.4897i	−0.0166379	+	0.286270i
$111$	−147.436	−	38.5366i	−1.32825	−	0.347176i
$112$	19.3285	+	27.7402i	0.172576	+	0.247680i
$113$	−49.1305	+	49.1305i	−0.434783	+	0.434783i	−0.890252	−	0.455469i	$-0.849472\pi$
$113$	−49.1305	+	49.1305i	−0.434783	+	0.434783i	0.455469	+	0.890252i	$0.349472\pi$
$114$	78.0048	+	77.0527i	0.684252	+	0.675901i
$115$	132.678	+	87.2406i	1.15373	+	0.758614i
$116$	47.3112	−	27.3151i	0.407855	−	0.235475i
$117$	−58.7160	−	14.9626i	−0.501846	−	0.127885i
$118$	64.5328	−	64.5328i	0.546888	−	0.546888i
$119$	−89.0576	+	105.638i	−0.748384	+	0.887713i
$120$	−107.627	−	69.8257i	−0.896893	−	0.581881i
$121$	−51.0474	+	88.4166i	−0.421879	+	0.730716i
$122$	−15.0746	−	4.03922i	−0.123562	−	0.0331084i
$123$	−2.31798	+	4.07241i	−0.0188454	+	0.0331090i
$124$	13.5048	−	23.3910i	0.108910	−	0.188637i
$125$	71.7350	+	102.367i	0.573880	+	0.818940i
$126$	85.5787	−	32.1177i	0.679196	−	0.254903i
$127$	−72.9239	+	72.9239i	−0.574204	+	0.574204i	−0.933300	−	0.359096i	$-0.883085\pi$
$127$	−72.9239	+	72.9239i	−0.574204	+	0.574204i	0.359096	+	0.933300i	$0.383085\pi$
$128$	−6.08643	−	22.7149i	−0.0475503	−	0.177460i
$129$	189.029	−	51.8963i	1.46534	−	0.402297i
$130$	−9.88243	−	47.8308i	−0.0760187	−	0.367930i
$131$	48.6464	−	84.2581i	0.371347	−	0.643192i	−0.618426	−	0.785843i	$-0.712229\pi$
$131$	48.6464	−	84.2581i	0.371347	−	0.643192i	0.989773	+	0.142651i	$0.0455627\pi$
$132$	12.4896	+	21.3291i	0.0946181	+	0.161584i
$133$	100.804	+	144.673i	0.757924	+	1.08777i
$134$	168.441			1.25702
$135$	−99.1669	+	91.6020i	−0.734570	+	0.678533i
$136$	−146.203	+	84.4104i	−1.07502	+	0.620664i
$137$	56.4619	−	210.719i	0.412131	−	1.53809i	−0.378384	−	0.925649i	$-0.623520\pi$
$137$	56.4619	−	210.719i	0.412131	−	1.53809i	0.790514	−	0.612443i	$-0.209813\pi$
$138$	−138.232	+	0.848769i	−1.00168	+	0.00615050i
$139$	−114.866			−0.826374			−0.413187	−	0.910646i	$-0.635584\pi$
$139$	−114.866			−0.826374			−0.413187	+	0.910646i	$0.635584\pi$
$140$	−48.1400	−	45.6173i	−0.343857	−	0.325838i
$141$	39.9436	+	10.4404i	0.283288	+	0.0740454i
$142$	−3.17031	−	11.8318i	−0.0223261	−	0.0833222i
$143$	−7.57641	+	28.2755i	−0.0529819	+	0.197731i
$144$	43.4666	−	0.533807i	0.301851	−	0.00370699i
$145$	107.674	−	95.8456i	0.742580	−	0.661004i
$146$	−39.0603			−0.267537
$147$	144.728	−	25.7458i	0.984543	−	0.175142i
$148$	−68.0606	−	68.0606i	−0.459869	−	0.459869i
$149$	88.8916	−	153.965i	0.596588	−	1.03332i	−0.396733	−	0.917934i	$-0.629856\pi$
$149$	88.8916	−	153.965i	0.596588	−	1.03332i	0.993321	−	0.115386i	$-0.0368106\pi$
$150$	−101.384	−	39.5295i	−0.675895	−	0.263530i
$151$	−22.5608	−	39.0764i	−0.149409	−	0.258784i	0.781600	−	0.623780i	$-0.214404\pi$
$151$	−22.5608	−	39.0764i	−0.149409	−	0.258784i	−0.931009	+	0.364996i	$0.881070\pi$
$152$	55.7616	+	208.105i	0.366853	+	1.36911i
$153$	48.0817	+	171.015i	0.314260	+	1.11774i
$154$	−15.0076	−	41.5316i	−0.0974521	−	0.269686i
$155$	22.4094	−	67.6556i	0.144577	−	0.436488i
$156$	−27.2278	−	26.8954i	−0.174537	−	0.172407i
$157$	44.8638	−	167.434i	0.285757	−	1.06646i	−0.662528	−	0.749038i	$-0.730516\pi$
$157$	44.8638	−	167.434i	0.285757	−	1.06646i	0.948284	−	0.317422i	$-0.102817\pi$
$158$	97.0677	+	26.0092i	0.614352	+	0.164615i
$159$	−73.6815	+	74.5919i	−0.463405	+	0.469131i
$160$	−61.0601	−	121.543i	−0.381626	−	0.759646i
$161$	−218.840	−	39.1092i	−1.35925	−	0.242914i
$162$	27.6203	−	114.232i	0.170496	−	0.705134i
$163$	47.7722	−	12.8005i	0.293081	−	0.0785308i	−0.109283	−	0.994011i	$-0.534855\pi$
$163$	47.7722	−	12.8005i	0.293081	−	0.0785308i	0.402364	+	0.915480i	$0.368189\pi$
$164$	−2.56319	+	1.47986i	−0.0156292	+	0.00902353i
$165$	43.6625	+	48.4486i	0.264621	+	0.293628i
$166$	20.5694	+	11.8757i	0.123912	+	0.0715406i
$167$	−2.27761	+	2.27761i	−0.0136384	+	0.0136384i	−0.713893	−	0.700255i	$-0.753070\pi$
$167$	−2.27761	+	2.27761i	−0.0136384	+	0.0136384i	0.700255	+	0.713893i	$0.253070\pi$
$168$	177.000	+	30.5117i	1.05357	+	0.181617i
$169$			123.674i			0.731796i
$170$	−106.957	+	95.2072i	−0.629158	+	0.560043i
$171$	226.691	−	2.78396i	1.32568	−	0.0162805i
$172$	119.594	+	32.0452i	0.695316	+	0.186309i
$173$	−324.701	+	87.0033i	−1.87688	+	0.502909i	−0.877139	+	0.480237i	$0.840551\pi$
$173$	−324.701	+	87.0033i	−1.87688	+	0.502909i	−0.999743	+	0.0226723i	$0.992783\pi$
$174$	−31.7347	+	121.413i	−0.182383	+	0.697774i
$175$	−148.755	−	92.1783i	−0.850031	−	0.526733i
$176$		−	21.0009i		−	0.119323i
$177$	−1.15865	−	188.699i	−0.00654603	−	1.06610i
$178$	−94.7738	−	25.3946i	−0.532437	−	0.142666i
$179$	122.781	+	212.663i	0.685927	+	1.18806i	0.973144	+	0.230195i	$0.0739365\pi$
$179$	122.781	+	212.663i	0.685927	+	1.18806i	−0.287217	+	0.957865i	$0.592730\pi$
$180$	−83.2873	+	18.2774i	−0.462707	+	0.101541i
$181$			92.0664i			0.508654i	0.967118	+	0.254327i	$0.0818540\pi$
$181$			92.0664i			0.508654i	−0.967118	+	0.254327i	$0.918146\pi$
$182$	39.0901	+	56.1021i	0.214781	+	0.308253i
$183$	−27.8460	+	16.3057i	−0.152164	+	0.0891021i
$184$	−235.234	−	135.812i	−1.27844	−	0.738110i
$185$	−212.215	−	139.539i	−1.14711	−	0.754264i
$186$	16.4258	+	59.8302i	0.0883110	+	0.321668i
$187$	82.8986	−	22.2126i	0.443308	−	0.118784i
$188$	18.4391	+	18.4391i	0.0980805	+	0.0980805i
$189$	77.1053	−	172.557i	0.407965	−	0.912998i
$190$	82.0339	+	163.293i	0.431757	+	0.859435i
$191$	39.7108	+	22.9270i	0.207910	+	0.120037i	0.600340	−	0.799745i	$-0.295032\pi$
$191$	39.7108	+	22.9270i	0.207910	+	0.120037i	−0.392430	+	0.919782i	$0.628365\pi$
$192$	153.280	+	87.2456i	0.798332	+	0.454404i
$193$	70.1653	−	261.860i	0.363551	−	1.35679i	−0.505824	−	0.862637i	$-0.668812\pi$
$193$	70.1653	−	261.860i	0.363551	−	1.35679i	0.869375	−	0.494153i	$-0.164522\pi$
$194$	−221.241	−	127.734i	−1.14042	−	0.658421i
$195$	−84.7196	−	54.9639i	−0.434460	−	0.281866i
$196$	87.1014	+	32.1592i	0.444395	+	0.164077i
$197$	69.8883	+	69.8883i	0.354763	+	0.354763i	0.861878	−	0.507115i	$-0.169288\pi$
$197$	69.8883	+	69.8883i	0.354763	+	0.354763i	−0.507115	+	0.861878i	$0.669288\pi$
$198$	−55.0188	−	14.0204i	−0.277873	−	0.0708102i
$199$	−123.211	−	213.408i	−0.619153	−	1.07240i	−0.989641	−	0.143567i	$-0.954143\pi$
$199$	−123.211	−	213.408i	−0.619153	−	1.07240i	0.370488	−	0.928837i	$-0.379190\pi$
$200$	−132.662	−	167.693i	−0.663309	−	0.838465i
$201$	244.755	−	247.780i	1.21769	−	1.23273i
$202$	−64.6888	−	64.6888i	−0.320241	−	0.320241i
$203$	−85.7130	+	182.708i	−0.422231	+	0.900040i
$204$	−28.3748	+	108.558i	−0.139092	+	0.532148i
$205$	−5.83349	+	5.19265i	−0.0284560	+	0.0253300i
$206$	−60.4607	−	104.721i	−0.293499	−	0.508354i
$207$	−199.611	+	204.574i	−0.964302	+	0.988281i
$208$	8.41624	+	31.4098i	0.0404627	+	0.151009i
$209$		−	109.526i		−	0.524047i
$210$	152.262	−	5.03266i	0.725057	−	0.0239651i
$211$	149.062			0.706454			0.353227	−	0.935538i	$-0.385084\pi$
$211$	149.062			0.706454			0.353227	+	0.935538i	$0.385084\pi$
$212$	−63.9673	+	17.1400i	−0.301733	+	0.0808490i
$213$	−22.0113	−	12.5287i	−0.103340	−	0.0588201i
$214$	−25.8130	+	14.9031i	−0.120621	+	0.0696408i
$215$	326.156	+	18.9560i	1.51700	+	0.0881676i
$216$	160.256	−	166.271i	0.741924	−	0.769774i
$217$	8.46647	+	99.4187i	0.0390160	+	0.458151i
$218$	1.08803	−	1.08803i	0.00499098	−	0.00499098i
$219$	−56.7570	+	57.4583i	−0.259165	+	0.262367i
$220$	8.33526	+	40.3426i	0.0378875	+	0.183375i
$221$	−115.085	+	66.4443i	−0.520746	+	0.300653i
$222$	221.098	−	1.35758i	0.995935	−	0.00611523i
$223$	−206.164	+	206.164i	−0.924500	+	0.924500i	−0.997343	−	0.0728430i	$-0.976793\pi$
$223$	−206.164	+	206.164i	−0.924500	+	0.924500i	0.0728430	+	0.997343i	$0.476793\pi$
$224$	145.592	+	122.741i	0.649963	+	0.547949i
$225$	−205.466	+	91.6990i	−0.913182	+	0.407551i
$226$	50.4052	−	87.3045i	0.223032	−	0.386303i
$227$	−363.549	−	97.4127i	−1.60154	−	0.429131i	−0.656031	−	0.754734i	$-0.727766\pi$
$227$	−363.549	−	97.4127i	−1.60154	−	0.429131i	−0.945506	+	0.325603i	$0.894433\pi$
$228$	124.447	+	70.8344i	0.545821	+	0.310677i
$229$	85.7839	−	148.582i	0.374602	−	0.648830i	−0.615665	−	0.788008i	$-0.711113\pi$
$229$	85.7839	−	148.582i	0.374602	−	0.648830i	0.990267	+	0.139178i	$0.0444459\pi$
$230$	−218.705	−	72.4411i	−0.950893	−	0.314961i
$231$	−82.9006	−	38.2715i	−0.358877	−	0.165677i
$232$	−174.362	+	174.362i	−0.751561	+	0.751561i
$233$	−30.6478	−	114.379i	−0.131535	−	0.490897i	0.868453	−	0.495772i	$-0.165115\pi$
$233$	−30.6478	−	114.379i	−0.131535	−	0.490897i	−0.999988	+	0.00487507i	$0.998448\pi$
$234$	87.9073	−	1.07958i	0.375672	−	0.00461358i
$235$	57.4938	+	37.8041i	0.244655	+	0.160869i
$236$	59.5944	−	103.221i	0.252519	−	0.437375i
$237$	179.305	−	104.995i	0.756562	−	0.443017i
$238$	85.1421	−	181.491i	0.357740	−	0.762568i
$239$	283.218			1.18501			0.592507	−	0.805566i	$-0.298138\pi$
$239$	283.218			1.18501			0.592507	+	0.805566i	$0.298138\pi$
$240$	68.9138	+	22.3575i	0.287141	+	0.0931563i
$241$	−71.5098	+	41.2862i	−0.296721	+	0.171312i	−0.640969	−	0.767567i	$-0.721467\pi$
$241$	−71.5098	+	41.2862i	−0.296721	+	0.171312i	0.344248	+	0.938879i	$0.388134\pi$
$242$	38.3388	−	143.083i	0.158425	−	0.591250i
$243$	−127.902	−	206.615i	−0.526348	−	0.850269i
$244$	−20.3817			−0.0835317
$245$	242.251	+	36.5988i	0.988779	+	0.149383i
$246$	1.71930	−	6.57781i	0.00698903	−	0.0267391i
$247$	43.8932	+	163.812i	0.177705	+	0.663205i
$248$	−31.5536	+	117.760i	−0.127232	+	0.474837i
$249$	47.3580	−	13.0017i	0.190193	−	0.0522157i
$250$	−138.976	−	116.527i	−0.555902	−	0.466107i
$251$	−56.5975			−0.225488			−0.112744	−	0.993624i	$-0.535964\pi$
$251$	−56.5975			−0.225488			−0.112744	+	0.993624i	$0.535964\pi$
$252$	97.1004	−	69.4431i	0.385319	−	0.275568i
$253$	97.6408	+	97.6408i	0.385932	+	0.385932i
$254$	74.8160	−	129.585i	0.294551	−	0.510178i
$255$	−15.3636	+	295.677i	−0.0602495	+	1.15952i
$256$	134.640	+	233.203i	0.525938	+	0.910951i
$257$	5.72610	+	21.3701i	0.0222806	+	0.0831522i	0.976171	−	0.217003i	$-0.0696282\pi$
$257$	5.72610	+	21.3701i	0.0222806	+	0.0831522i	−0.953890	+	0.300155i	$0.902962\pi$
$258$	−245.430	+	143.716i	−0.951281	+	0.557038i
$259$	350.028	+	62.5541i	1.35146	+	0.241521i
$260$	−28.6341	−	56.9977i	−0.110131	−	0.219222i
$261$	132.487	+	223.102i	0.507614	+	0.854797i
$262$	−36.5356	+	136.353i	−0.139449	+	0.520431i
$263$	−189.972	−	50.9027i	−0.722325	−	0.193546i	−0.121116	−	0.992638i	$-0.538647\pi$
$263$	−189.972	−	50.9027i	−0.722325	−	0.193546i	−0.601209	+	0.799092i	$0.705314\pi$
$264$	−79.3709	−	78.4022i	−0.300648	−	0.296978i
$265$	−156.148	+	78.4447i	−0.589239	+	0.296018i
$266$	−195.602	−	164.901i	−0.735344	−	0.619929i
$267$	−175.068	+	102.514i	−0.655685	+	0.383947i
$268$	212.487	−	56.9357i	0.792862	−	0.212447i
$269$	−140.489	+	81.1111i	−0.522263	+	0.301528i	−0.737860	−	0.674954i	$-0.764163\pi$
$269$	−140.489	+	81.1111i	−0.522263	+	0.301528i	0.215597	+	0.976482i	$0.430830\pi$
$270$	104.581	−	165.617i	0.387336	−	0.613395i
$271$	−250.756	−	144.774i	−0.925299	−	0.534221i	−0.0399771	−	0.999201i	$-0.512728\pi$
$271$	−250.756	−	144.774i	−0.925299	−	0.534221i	−0.885322	+	0.464979i	$0.846062\pi$
$272$	67.4129	−	67.4129i	0.247841	−	0.247841i
$273$	139.327	+	24.0176i	0.510357	+	0.0879764i
$274$			316.518i			1.15518i
$275$	43.0787	+	99.7999i	0.156650	+	0.362909i
$276$	−174.091	+	47.7951i	−0.630765	+	0.173171i
$277$	−32.8919	−	8.81335i	−0.118743	−	0.0318171i	0.198958	−	0.980008i	$-0.436244\pi$
$277$	−32.8919	−	8.81335i	−0.118743	−	0.0318171i	−0.317701	+	0.948191i	$0.602911\pi$
$278$	160.981	−	43.1347i	0.579068	−	0.155161i
$279$	111.879	+	62.7742i	0.400999	+	0.224997i
$280$	263.178	+	142.649i	0.939922	+	0.509460i
$281$			454.634i			1.61791i	0.587868	+	0.808957i	$0.299967\pi$
$281$			454.634i			1.61791i	−0.587868	+	0.808957i	$0.700033\pi$
$282$	−59.9002	+	0.367799i	−0.212412	+	0.00130425i
$283$	287.958	+	77.1581i	1.01752	+	0.272643i	0.728768	−	0.684761i	$-0.240093\pi$
$283$	287.958	+	77.1581i	1.01752	+	0.272643i	0.288751	+	0.957404i	$0.406760\pi$
$284$	−7.99863	−	13.8540i	−0.0281642	−	0.0487818i
$285$	359.406	+	116.601i	1.26107	+	0.409127i
$286$		−	42.4724i		−	0.148505i
$287$	4.64370	−	9.89863i	0.0161801	−	0.0344900i
$288$	235.695	−	66.2670i	0.818387	−	0.230094i
$289$	87.1261	+	50.3023i	0.301474	+	0.174056i
$290$	−114.910	+	174.759i	−0.396240	+	0.602616i
$291$	−509.375	+	139.844i	−1.75043	+	0.480565i
$292$	−49.2742	+	13.2030i	−0.168747	+	0.0452157i
$293$	124.246	+	124.246i	0.424047	+	0.424047i	0.886594	−	0.462548i	$-0.153065\pi$
$293$	124.246	+	124.246i	0.424047	+	0.424047i	−0.462548	+	0.886594i	$0.653065\pi$
$294$	−193.163	+	90.4305i	−0.657018	+	0.307587i
$295$	98.8887	−	298.553i	0.335216	−	1.01204i
$296$	376.249	+	217.228i	1.27111	+	0.733877i
$297$	−100.570	+	60.5609i	−0.338619	+	0.203909i
$298$	−66.7615	+	249.157i	−0.224032	+	0.836099i
$299$	−185.166	−	106.906i	−0.619285	−	0.357544i
$300$	−141.257	−	15.5967i	−0.470856	−	0.0519890i
$301$	−430.165	+	155.442i	−1.42912	+	0.516419i
$302$	46.2923	+	46.2923i	0.153286	+	0.153286i
$303$	−189.155	+	1.16145i	−0.624273	+	0.00383316i
$304$	−60.8333	−	105.366i	−0.200109	−	0.346600i
$305$	−52.6689	+	10.8820i	−0.172685	+	0.0356788i
$306$	−131.605	−	221.616i	−0.430082	−	0.724236i
$307$	−311.230	−	311.230i	−1.01378	−	1.01378i	−0.999904	−	0.0138731i	$-0.995584\pi$
$307$	−311.230	−	311.230i	−1.01378	−	1.01378i	−0.0138731	−	0.999904i	$-0.504416\pi$
$308$	−32.9703	−	47.3189i	−0.107046	−	0.153633i
$309$	−241.899	−	63.2274i	−0.782846	−	0.204619i
$310$	−5.99982	+	103.232i	−0.0193543	+	0.333008i
$311$	63.1444	+	109.369i	0.203037	+	0.351670i	0.949505	−	0.313751i	$-0.101586\pi$
$311$	63.1444	+	109.369i	0.203037	+	0.351670i	−0.746469	+	0.665421i	$0.768252\pi$
$312$	150.131	+	85.4533i	0.481189	+	0.273889i
$313$	−6.36092	−	23.7393i	−0.0203224	−	0.0758443i	0.955020	−	0.296542i	$-0.0958334\pi$
$313$	−6.36092	−	23.7393i	−0.0203224	−	0.0758443i	−0.975342	+	0.220697i	$0.929167\pi$
$314$			251.501i			0.800958i
$315$	213.843	−	231.293i	0.678866	−	0.734262i
$316$	131.241			0.415321
$317$	−201.189	+	53.9084i	−0.634666	+	0.170058i	−0.561786	−	0.827283i	$-0.689886\pi$
$317$	−201.189	+	53.9084i	−0.634666	+	0.170058i	−0.0728796	+	0.997341i	$0.523219\pi$
$318$	75.2513	−	132.207i	0.236639	−	0.415746i
$319$	108.561	−	62.6780i	0.340318	−	0.196483i
$320$	195.444	+	219.564i	0.610763	+	0.686138i
$321$	−15.5851	+	59.6264i	−0.0485517	+	0.185752i
$322$	321.383	−	27.3689i	0.998085	−	0.0849967i
$323$	351.578	−	351.578i	1.08848	−	1.08848i
$324$	−3.76927	−	153.438i	−0.0116336	−	0.473575i
$325$	−104.426	−	132.001i	−0.321310	−	0.406157i
$326$	−62.1443	+	35.8790i	−0.190627	+	0.110058i
$327$	−0.0195350	−	3.18149i	−5.97400e−5	−	0.00972934i
$328$	9.44647	−	9.44647i	0.0288002	−	0.0288002i
$329$	−94.8303	−	16.9473i	−0.288238	−	0.0515115i
$330$	−79.3851	−	51.5030i	−0.240561	−	0.156070i
$331$	166.447	−	288.295i	0.502861	−	0.870981i	−0.497133	−	0.867674i	$-0.665614\pi$
$331$	166.447	−	288.295i	0.502861	−	0.870981i	0.999995	−	0.00330721i	$-0.00105272\pi$
$332$	29.9622	+	8.02836i	0.0902477	+	0.0241818i
$333$	319.271	−	327.211i	0.958772	−	0.982614i
$334$	2.33670	−	4.04729i	0.00699612	−	0.0121176i
$335$	518.694	−	260.578i	1.54834	−	0.777845i
$336$	−101.009	+	9.22695i	−0.300622	+	0.0274612i
$337$	68.0561	−	68.0561i	0.201947	−	0.201947i	−0.598887	−	0.800834i	$-0.704390\pi$
$337$	68.0561	−	68.0561i	0.201947	−	0.201947i	0.800834	+	0.598887i	$0.204390\pi$
$338$	−46.4422	−	173.325i	−0.137403	−	0.512795i
$339$	−55.1843	−	201.006i	−0.162785	−	0.592937i
$340$	−102.744	+	156.256i	−0.302187	+	0.459577i
$341$	30.9885	−	53.6736i	0.0908753	−	0.157401i
$342$	−316.655	+	89.0293i	−0.925892	+	0.260320i
$343$	−331.920	+	86.4751i	−0.967698	+	0.252114i
$344$	−558.858			−1.62459
$345$	−424.354	+	216.458i	−1.23001	+	0.627413i
$346$	422.386	−	243.865i	1.22077	−	0.704811i
$347$	142.342	−	531.228i	0.410208	−	1.53092i	−0.384037	−	0.923318i	$-0.625466\pi$
$347$	142.342	−	531.228i	0.410208	−	1.53092i	0.794244	−	0.607598i	$-0.207867\pi$
$348$	1.00630	+	163.888i	0.00289167	+	0.470941i
$349$	−82.1461			−0.235376			−0.117688	−	0.993051i	$-0.537548\pi$
$349$	−82.1461			−0.235376			−0.117688	+	0.993051i	$0.537548\pi$
$350$	243.091	+	73.3239i	0.694546	+	0.209497i
$351$	126.147	−	130.882i	0.359392	−	0.372882i
$352$	−30.6138	−	114.252i	−0.0869709	−	0.324580i
$353$	154.906	−	578.119i	0.438828	−	1.63773i	−0.292907	−	0.956141i	$-0.594623\pi$
$353$	154.906	−	578.119i	0.438828	−	1.63773i	0.731735	−	0.681589i	$-0.238711\pi$
$354$	72.4844	+	264.020i	0.204758	+	0.745820i
$355$	−28.0663	−	31.5300i	−0.0790599	−	0.0888168i
$356$	−128.140			−0.359944
$357$	−143.260	−	388.963i	−0.401288	−	1.08953i
$358$	−251.933	−	251.933i	−0.703724	−	0.703724i
$359$	24.3885	−	42.2421i	0.0679345	−	0.117666i	−0.830057	−	0.557678i	$-0.811692\pi$
$359$	24.3885	−	42.2421i	0.0679345	−	0.117666i	0.897992	+	0.440012i	$0.145026\pi$
$360$	341.773	−	176.987i	0.949370	−	0.491630i
$361$	−136.764	−	236.882i	−0.378847	−	0.656182i
$362$	−34.5730	−	129.028i	−0.0955055	−	0.356431i
$363$	−154.768	−	264.305i	−0.426358	−	0.728112i
$364$	68.2752	+	57.5592i	0.187569	+	0.158130i
$365$	−120.281	+	60.4262i	−0.329538	+	0.165551i
$366$	32.9022	−	33.3087i	0.0898966	−	0.0910074i
$367$	39.4899	−	147.378i	0.107602	−	0.401575i	−0.891026	−	0.453953i	$-0.850013\pi$
$367$	39.4899	−	147.378i	0.107602	−	0.401575i	0.998627	+	0.0523778i	$0.0166800\pi$
$368$	148.165	+	39.7006i	0.402622	+	0.107882i
$369$	−7.17781	−	12.0871i	−0.0194520	−	0.0327563i
$370$	349.813	+	115.868i	0.945441	+	0.313155i
$371$	157.686	−	187.043i	0.425031	−	0.504160i
$372$	40.9445	+	69.9230i	0.110066	+	0.187965i
$373$	−232.471	+	62.2905i	−0.623247	+	0.166999i	−0.556603	−	0.830778i	$-0.687896\pi$
$373$	−232.471	+	62.2905i	−0.623247	+	0.166999i	−0.0666436	+	0.997777i	$0.521229\pi$
$374$	−107.838	+	62.2605i	−0.288338	+	0.166472i
$375$	−373.352	+	35.1148i	−0.995606	+	0.0936394i
$376$	−101.934	−	58.8518i	−0.271102	−	0.156521i
$377$	−137.251	+	137.251i	−0.364060	+	0.364060i
$378$	−43.2618	+	270.787i	−0.114449	+	0.716368i
$379$		−	35.3522i		−	0.0932776i	−0.998912	−	0.0466388i	$-0.985149\pi$
$379$		−	35.3522i		−	0.0932776i	0.998912	−	0.0466388i	$-0.0148510\pi$
$380$	158.680	+	178.263i	0.417580	+	0.469114i
$381$	−81.9095	−	298.350i	−0.214985	−	0.783072i
$382$	−64.2630	−	17.2192i	−0.168228	−	0.0450765i
$383$	−265.111	+	71.0364i	−0.692197	+	0.185474i	−0.587733	−	0.809055i	$-0.699979\pi$
$383$	−265.111	+	71.0364i	−0.692197	+	0.185474i	−0.104464	+	0.994529i	$0.533313\pi$
$384$	68.2555	+	17.8405i	0.177749	+	0.0464597i
$385$	−110.463	−	104.675i	−0.286918	−	0.271882i
$386$			393.338i			1.01901i
$387$	−145.217	+	569.860i	−0.375238	+	1.47251i
$388$	−322.270	−	86.3519i	−0.830592	−	0.222556i
$389$	234.816	+	406.714i	0.603641	+	1.04554i	0.992265	+	0.124140i	$0.0396171\pi$
$389$	234.816	+	406.714i	0.603641	+	1.04554i	−0.388624	+	0.921396i	$0.627050\pi$
$390$	139.372	+	45.2161i	0.357364	+	0.115939i
$391$			626.855i			1.60321i
$392$	−417.324	−	38.4562i	−1.06460	−	0.0981025i
$393$	147.489	+	251.873i	0.375289	+	0.640899i
$394$	−124.191	−	71.7016i	−0.315205	−	0.181984i
$395$	339.144	−	70.0712i	0.858592	−	0.177396i
$396$	−74.1448	+	0.910561i	−0.187234	+	0.00229940i
$397$	−96.4334	+	25.8392i	−0.242905	+	0.0650862i	−0.378218	−	0.925717i	$-0.623463\pi$
$397$	−96.4334	+	25.8392i	−0.242905	+	0.0650862i	0.135312	+	0.990803i	$0.456796\pi$
$398$	252.816	+	252.816i	0.635217	+	0.635217i
$399$	−526.793	+	48.1213i	−1.32028	+	0.120605i
$400$	96.8739	+	72.0828i	0.242185	+	0.180207i
$401$	331.371	+	191.317i	0.826362	+	0.477100i	0.852605	−	0.522556i	$-0.175021\pi$
$401$	331.371	+	191.317i	0.826362	+	0.477100i	−0.0262437	+	0.999656i	$0.508355\pi$
$402$	−249.970	+	439.166i	−0.621816	+	1.09245i
$403$	−24.8377	+	92.6955i	−0.0616320	+	0.230014i
$404$	−103.470	−	59.7384i	−0.256114	−	0.147867i
$405$	−91.6626	−	394.491i	−0.226327	−	0.974051i
$406$	51.5130	−	288.247i	0.126879	−	0.709967i
$407$	−156.174	−	156.174i	−0.383719	−	0.383719i
$408$	−3.10972	−	506.453i	−0.00762185	−	1.24131i
$409$	199.716	+	345.918i	0.488302	+	0.845764i	0.999909	−	0.0134551i	$-0.00428304\pi$
$409$	199.716	+	345.918i	0.488302	+	0.845764i	−0.511607	+	0.859219i	$0.670950\pi$
$410$	6.22549	−	9.46795i	0.0151841	−	0.0230925i
$411$	465.603	+	459.920i	1.13285	+	1.11903i
$412$	−111.668	−	111.668i	−0.271039	−	0.271039i
$413$	37.3611	+	438.718i	0.0904626	+	1.06227i
$414$	202.926	−	361.662i	0.490158	−	0.873581i
$415$	81.7126	+	4.74910i	0.196898	+	0.0114436i
$416$	91.5746	+	158.612i	0.220131	+	0.381278i
$417$	170.463	−	299.483i	0.408785	−	0.718184i
$418$	41.1294	+	153.497i	0.0983956	+	0.367218i
$419$		−	186.761i		−	0.445729i	−0.974849	−	0.222865i	$-0.928459\pi$
$419$		−	186.761i		−	0.445729i	0.974849	−	0.222865i	$-0.0715408\pi$
$420$	190.376	−	57.8155i	0.453276	−	0.137656i
$421$	33.4880			0.0795440			0.0397720	−	0.999209i	$-0.487337\pi$
$421$	33.4880			0.0795440			0.0397720	+	0.999209i	$0.487337\pi$
$422$	−208.905	+	55.9760i	−0.495036	+	0.132645i
$423$	−86.4976	+	88.6486i	−0.204486	+	0.209571i
$424$	258.869	−	149.458i	0.610539	−	0.352495i
$425$	−182.075	+	458.641i	−0.428412	+	1.07915i
$426$	35.5530	+	9.29281i	0.0834577	+	0.0218141i
$427$	61.7768	−	43.0441i	0.144676	−	0.100806i
$428$	−27.5253	+	27.5253i	−0.0643115	+	0.0643115i
$429$	−62.4775	−	61.7149i	−0.145635	−	0.143858i
$430$	−464.216	+	95.9125i	−1.07957	+	0.223052i
$431$	220.378	−	127.235i	0.511317	−	0.295209i	−0.222058	−	0.975033i	$-0.571277\pi$
$431$	220.378	−	127.235i	0.511317	−	0.295209i	0.733375	+	0.679824i	$0.237944\pi$
$432$	−63.1135	+	114.120i	−0.146096	+	0.264166i
$433$	510.335	−	510.335i	1.17860	−	1.17860i	0.198504	−	0.980100i	$-0.436392\pi$
$433$	510.335	−	510.335i	1.17860	−	1.17860i	0.980100	−	0.198504i	$-0.0636082\pi$
$434$	−49.1994	−	136.153i	−0.113363	−	0.313716i
$435$	90.1018	+	422.969i	0.207131	+	0.972341i
$436$	1.00477	−	1.74032i	0.00230452	−	0.00399155i
$437$	772.723	+	207.051i	1.76825	+	0.473800i
$438$	57.9663	−	101.840i	0.132343	−	0.232510i
$439$	−231.600	+	401.143i	−0.527563	+	0.913766i	0.471921	+	0.881641i	$0.343561\pi$
$439$	−231.600	+	401.143i	−0.527563	+	0.913766i	−0.999484	+	0.0321247i	$0.989773\pi$
$440$	−83.4706	−	166.153i	−0.189706	−	0.377620i
$441$	−147.653	+	415.547i	−0.334815	+	0.942284i
$442$	136.337	−	136.337i	0.308454	−	0.308454i
$443$	−181.770	−	678.374i	−0.410315	−	1.53132i	−0.794038	−	0.607869i	$-0.792025\pi$
$443$	−181.770	−	678.374i	−0.410315	−	1.53132i	0.383722	−	0.923448i	$-0.374642\pi$
$444$	278.454	−	76.4469i	0.627148	−	0.172178i
$445$	−331.130	+	68.4154i	−0.744111	+	0.153742i
$446$	211.513	−	366.351i	0.474244	−	0.821414i
$447$	269.506	+	460.248i	0.602921	+	1.02964i
$448$	−372.570	−	174.782i	−0.831630	−	0.390138i
$449$	452.810			1.00849			0.504243	−	0.863562i	$-0.331772\pi$
$449$	452.810			1.00849			0.504243	+	0.863562i	$0.331772\pi$
$450$	253.519	−	205.670i	0.563376	−	0.457045i
$451$	−5.88156	+	3.39572i	−0.0130412	+	0.00752932i
$452$	34.0755	−	127.171i	0.0753882	−	0.281353i
$453$	135.362	−	0.831150i	0.298813	−	0.00183477i
$454$	546.083			1.20283
$455$	207.163	+	112.287i	0.455303	+	0.246785i
$456$	−625.331	−	163.448i	−1.37134	−	0.358439i
$457$	−60.7402	−	226.685i	−0.132911	−	0.496029i	0.867087	−	0.498157i	$-0.165990\pi$
$457$	−60.7402	−	226.685i	−0.132911	−	0.496029i	−0.999998	+	0.00212736i	$0.999323\pi$
$458$	−64.4276	+	240.447i	−0.140672	+	0.524993i
$459$	−517.231	−	128.429i	−1.12686	−	0.279802i
$460$	−300.381	−	17.4580i	−0.653002	−	0.0379522i
$461$	−315.023			−0.683348			−0.341674	−	0.939819i	$-0.610994\pi$
$461$	−315.023			−0.683348			−0.341674	+	0.939819i	$0.610994\pi$
$462$	130.554	+	22.5052i	0.282585	+	0.0487127i
$463$	−295.471	−	295.471i	−0.638167	−	0.638167i	0.311936	−	0.950103i	$-0.399022\pi$
$463$	−295.471	−	295.471i	−0.638167	−	0.638167i	−0.950103	+	0.311936i	$0.899022\pi$
$464$	69.6257	−	120.595i	0.150055	−	0.259904i
$465$	143.138	+	158.829i	0.307824	+	0.341567i
$466$	85.9037	+	148.790i	0.184343	+	0.319291i
$467$	202.350	+	755.179i	0.433297	+	1.61709i	0.745109	+	0.666943i	$0.232397\pi$
$467$	202.350	+	755.179i	0.433297	+	1.61709i	−0.311812	+	0.950144i	$0.600936\pi$
$468$	110.529	−	31.0759i	0.236174	−	0.0664015i
$469$	−523.803	+	621.322i	−1.11685	+	1.32478i
$470$	−94.7721	−	31.3911i	−0.201643	−	0.0667895i
$471$	369.962	+	365.446i	0.785481	+	0.775894i
$472$	−139.241	+	519.653i	−0.295001	+	1.10096i
$473$	274.424	+	73.5318i	0.580178	+	0.155458i
$474$	−211.863	+	214.480i	−0.446967	+	0.452490i
$475$	505.226	+	375.933i	1.06363	+	0.791439i
$476$	46.0591	−	257.729i	0.0967628	−	0.541447i
$477$	−85.1340	−	302.801i	−0.178478	−	0.634803i
$478$	−396.921	+	106.355i	−0.830379	+	0.222499i
$479$	−269.530	+	155.613i	−0.562693	+	0.324871i	−0.754226	−	0.656615i	$-0.771988\pi$
$479$	−269.530	+	155.613i	−0.562693	+	0.324871i	0.191533	+	0.981486i	$0.438654\pi$
$480$	407.507	+	21.1744i	0.848972	+	0.0441133i
$481$	296.168	+	170.993i	0.615734	+	0.355494i
$482$	84.7148	−	84.7148i	0.175757	−	0.175757i
$483$	426.730	−	512.529i	0.883498	−	1.06114i
$484$		−	193.456i		−	0.399703i
$485$	−878.889	−	51.0806i	−1.81214	−	0.105321i
$486$	256.840	+	241.535i	0.528477	+	0.496985i
$487$	667.636	+	178.892i	1.37092	+	0.367336i	0.867813	−	0.496891i	$-0.165525\pi$
$487$	667.636	+	178.892i	1.37092	+	0.367336i	0.503102	+	0.864227i	$0.332192\pi$
$488$	88.8626	−	23.8107i	0.182096	−	0.0487924i
$489$	−37.5209	+	143.550i	−0.0767298	+	0.293558i
$490$	−353.251	+	39.6786i	−0.720920	+	0.0809766i
$491$		−	479.528i		−	0.976636i	−0.872666	−	0.488318i	$-0.837611\pi$
$491$		−	479.528i		−	0.976636i	0.872666	−	0.488318i	$-0.162389\pi$
$492$	−0.0545187	−	8.87899i	−0.000110810	−	0.0180467i
$493$	549.679	+	147.286i	1.11497	+	0.298755i
$494$	−123.030	−	213.094i	−0.249048	−	0.431364i
$495$	−191.113	+	41.9397i	−0.386087	+	0.0847267i
$496$		−	68.8470i		−	0.138804i
$497$	53.5020	+	25.0991i	0.107650	+	0.0505013i
$498$	−61.4882	+	36.0054i	−0.123470	+	0.0723001i
$499$	728.049	+	420.340i	1.45902	+	0.842364i	0.998963	−	0.0455272i	$-0.0144968\pi$
$499$	728.049	+	420.340i	1.45902	+	0.842364i	0.460054	+	0.887891i	$0.347830\pi$
$500$	−214.704	−	100.021i	−0.429408	−	0.200043i
$501$	−2.55825	−	9.31828i	−0.00510629	−	0.0185994i
$502$	79.3196	−	21.2536i	0.158007	−	0.0423379i
$503$	108.595	+	108.595i	0.215895	+	0.215895i	0.806766	−	0.590871i	$-0.201216\pi$
$503$	108.595	+	108.595i	0.215895	+	0.215895i	−0.590871	+	0.806766i	$0.701216\pi$
$504$	−342.223	+	416.202i	−0.679015	+	0.825798i
$505$	−299.274	−	99.1277i	−0.592622	−	0.196292i
$506$	−173.507	−	100.174i	−0.342899	−	0.197973i
$507$	−322.446	−	183.534i	−0.635989	−	0.362000i
$508$	50.5779	−	188.759i	0.0995628	−	0.371573i
$509$	−376.708	−	217.493i	−0.740095	−	0.427294i	0.0820092	−	0.996632i	$-0.473866\pi$
$509$	−376.708	−	217.493i	−0.740095	−	0.427294i	−0.822104	+	0.569338i	$0.807200\pi$
$510$	−89.5017	−	420.151i	−0.175494	−	0.823826i
$511$	121.466	−	144.080i	0.237703	−	0.281957i
$512$	−209.753	−	209.753i	−0.409674	−	0.409674i
$513$	−329.156	+	595.170i	−0.641629	+	1.16017i
$514$	−16.0499	−	27.7992i	−0.0312255	−	0.0540841i
$515$	−348.184	−	228.943i	−0.676086	−	0.444549i
$516$	−261.030	+	264.255i	−0.505872	+	0.512123i
$517$	42.3109	+	42.3109i	0.0818393	+	0.0818393i
$518$	−514.044	+	43.7758i	−0.992362	+	0.0845093i
$519$	255.024	−	975.686i	0.491375	−	1.87993i
$520$	191.429	+	215.054i	0.368133	+	0.413565i
$521$	−139.064	−	240.867i	−0.266918	−	0.462316i	0.701146	−	0.713018i	$-0.252672\pi$
$521$	−139.064	−	240.867i	−0.266918	−	0.462316i	−0.968064	+	0.250702i	$0.919339\pi$
$522$	−269.457	−	262.919i	−0.516200	−	0.503675i
$523$	225.005	+	839.729i	0.430220	+	1.60560i	0.752254	+	0.658873i	$0.228967\pi$
$523$	225.005	+	839.729i	0.430220	+	1.60560i	−0.322034	+	0.946728i	$0.604367\pi$
$524$			184.357i			0.351827i
$525$	461.086	−	251.046i	0.878260	−	0.478183i
$526$	285.354			0.542498
$527$	271.766	−	72.8194i	0.515685	−	0.138177i
$528$	54.7542	+	31.1657i	0.103701	+	0.0590259i
$529$	−415.328	+	239.790i	−0.785120	+	0.453289i
$530$	189.379	−	168.575i	0.357319	−	0.318066i
$531$	493.702	+	277.012i	0.929759	+	0.521680i
$532$	−302.488	−	141.905i	−0.568587	−	0.266739i
$533$	7.43587	−	7.43587i	0.0139510	−	0.0139510i
$534$	206.856	−	209.412i	0.387371	−	0.392157i
$535$	−56.4327	+	85.8249i	−0.105482	+	0.160420i
$536$	−859.911	+	496.470i	−1.60431	+	0.926249i
$537$	−736.672	+	4.52331i	−1.37183	+	0.00842329i
$538$	166.431	−	166.431i	0.309352	−	0.309352i
$539$	199.865	+	73.7932i	0.370807	+	0.136908i
$540$	75.9465	−	244.274i	0.140642	−	0.452359i
$541$	295.339	−	511.543i	0.545914	−	0.945550i	−0.452635	−	0.891696i	$-0.649516\pi$
$541$	295.339	−	511.543i	0.545914	−	0.945550i	0.998549	−	0.0538543i	$-0.0171506\pi$
$542$	405.792	+	108.732i	0.748694	+	0.200612i
$543$	−240.039	−	136.628i	−0.442061	−	0.251618i
$544$	268.479	−	465.020i	0.493528	−	0.854816i
$545$	1.66728	−	5.03365i	0.00305923	−	0.00923606i
$546$	−204.282	+	18.6607i	−0.374143	+	0.0341771i
$547$	188.420	−	188.420i	0.344460	−	0.344460i	−0.513581	−	0.858041i	$-0.671681\pi$
$547$	188.420	−	188.420i	0.344460	−	0.344460i	0.858041	+	0.513581i	$0.171681\pi$
$548$	106.988	+	399.284i	0.195233	+	0.728621i
$549$	−1.18878	−	96.7991i	−0.00216535	−	0.176319i
$550$	−97.8505	−	123.689i	−0.177910	−	0.224890i
$551$	363.119	−	628.940i	0.659018	−	1.14145i
$552$	703.186	−	411.762i	1.27389	−	0.745946i
$553$	−397.791	+	277.168i	−0.719333	+	0.501208i
$554$	49.4065			0.0891814
$555$	678.742	−	346.218i	1.22296	−	0.623816i
$556$	188.496	−	108.828i	0.339021	−	0.195734i
$557$	−151.182	+	564.218i	−0.271421	+	1.01296i	0.686780	+	0.726865i	$0.259023\pi$
$557$	−151.182	+	564.218i	−0.271421	+	1.01296i	−0.958202	+	0.286093i	$0.907643\pi$
$558$	−180.368	−	45.9631i	−0.323240	−	0.0823711i
$559$	−439.910			−0.786958
$560$	−164.407	−	39.3454i	−0.293584	−	0.0702596i
$561$	−65.1096	+	249.100i	−0.116060	+	0.444029i
$562$	−170.725	−	637.154i	−0.303781	−	1.13373i
$563$	35.0813	−	130.925i	0.0623115	−	0.232550i	−0.927746	−	0.373212i	$-0.878256\pi$
$563$	35.0813	−	130.925i	0.0623115	−	0.232550i	0.990058	+	0.140662i	$0.0449232\pi$
$564$	−75.4392	+	20.7112i	−0.133757	+	0.0367219i
$565$	20.1570	−	346.820i	0.0356761	−	0.613841i
$566$	−432.538			−0.764202
$567$	335.470	+	457.109i	0.591658	+	0.806189i
$568$	51.0581	+	51.0581i	0.0898910	+	0.0898910i
$569$	141.292	−	244.725i	0.248316	−	0.430096i	−0.714742	−	0.699388i	$-0.753456\pi$
$569$	141.292	−	244.725i	0.248316	−	0.430096i	0.963059	+	0.269291i	$0.0867894\pi$
$570$	−547.483	−	28.4476i	−0.960496	−	0.0499082i
$571$	−208.184	−	360.585i	−0.364595	−	0.631498i	0.624116	−	0.781332i	$-0.285459\pi$
$571$	−208.184	−	360.585i	−0.364595	−	0.631498i	−0.988711	+	0.149834i	$0.952126\pi$
$572$	−14.3563	−	53.5785i	−0.0250984	−	0.0936687i
$573$	−118.708	+	69.5112i	−0.207169	+	0.121311i
$574$	−2.79084	+	15.6164i	−0.00486208	+	0.0272063i
$575$	−785.542	+	115.263i	−1.36616	+	0.200457i
$576$	−454.940	+	270.162i	−0.789826	+	0.469032i
$577$	170.664	−	636.928i	0.295779	−	1.10386i	−0.644818	−	0.764336i	$-0.723067\pi$
$577$	170.664	−	636.928i	0.295779	−	1.10386i	0.940597	−	0.339526i	$-0.110267\pi$
$578$	−140.994	−	37.7792i	−0.243934	−	0.0653620i
$579$	578.606	+	571.543i	0.999319	+	0.987122i
$580$	−85.8863	+	259.297i	−0.148080	+	0.447064i
$581$	−107.770	+	38.9433i	−0.185491	+	0.0670280i
$582$	661.358	−	387.269i	1.13635	−	0.665411i
$583$	−146.781	+	39.3299i	−0.251769	+	0.0674612i
$584$	199.407	−	115.128i	0.341451	−	0.197137i
$585$	269.030	−	139.317i	0.459880	−	0.238148i
$586$	−220.784	−	127.469i	−0.376764	−	0.217525i
$587$	−585.980	+	585.980i	−0.998263	+	0.998263i	−0.999998	−	0.00173550i	$-0.999448\pi$
$587$	−585.980	+	585.980i	−0.998263	+	0.998263i	0.00173550	+	0.999998i	$0.499448\pi$
$588$	−213.107	+	179.369i	−0.362426	+	0.305050i
$589$		−	359.058i		−	0.609605i
$590$	−26.4762	+	455.547i	−0.0448749	+	0.772114i
$591$	−285.931	+	78.4998i	−0.483809	+	0.132825i
$592$	−236.985	−	63.5000i	−0.400313	−	0.107263i
$593$	−391.812	+	104.986i	−0.660728	+	0.177042i	−0.573575	−	0.819153i	$-0.694444\pi$
$593$	−391.812	+	104.986i	−0.660728	+	0.177042i	−0.0871534	+	0.996195i	$0.527777\pi$
$594$	118.204	−	122.640i	0.198996	−	0.206465i
$595$	−18.5818	−	690.594i	−0.0312299	−	1.16066i
$596$			336.876i			0.565228i
$597$	739.254	−	4.53916i	1.23828	−	0.00760329i
$598$	299.650	+	80.2910i	0.501087	+	0.134266i
$599$	533.026	+	923.228i	0.889860	+	1.54128i	0.840040	+	0.542525i	$0.182532\pi$
$599$	533.026	+	923.228i	0.889860	+	1.54128i	0.0498203	+	0.998758i	$0.484135\pi$
$600$	634.088	−	97.0210i	1.05681	−	0.161702i
$601$		−	601.570i		−	1.00095i	−0.865751	−	0.500474i	$-0.833159\pi$
$601$		−	601.570i		−	1.00095i	0.865751	−	0.500474i	$-0.166841\pi$
$602$	544.491	−	379.384i	0.904470	−	0.630206i
$603$	282.799	+	1005.85i	0.468986	+	1.66807i
$604$	74.0448	+	42.7498i	0.122591	+	0.0707777i
$605$	−103.288	−	499.915i	−0.170725	−	0.826306i
$606$	264.658	−	72.6596i	0.436730	−	0.119900i
$607$	−31.8595	+	8.53673i	−0.0524869	+	0.0140638i	−0.284967	−	0.958537i	$-0.591983\pi$
$607$	−31.8595	+	8.53673i	−0.0524869	+	0.0140638i	0.232480	+	0.972601i	$0.425316\pi$
$608$	−484.551	−	484.551i	−0.796958	−	0.796958i
$609$	−349.164	−	494.616i	−0.573339	−	0.812178i
$610$	69.7274	−	35.0292i	0.114307	−	0.0574249i
$611$	−80.2384	−	46.3257i	−0.131323	−	0.0758194i
$612$	−240.928	−	235.082i	−0.393673	−	0.384121i
$613$	−113.939	+	425.226i	−0.185871	+	0.693681i	0.808571	+	0.588398i	$0.200241\pi$
$613$	−113.939	+	425.226i	−0.185871	+	0.693681i	−0.994442	+	0.105282i	$0.966425\pi$
$614$	553.052	+	319.305i	0.900736	+	0.520040i
$615$	−4.88147	−	22.9153i	−0.00793735	−	0.0372606i
$616$	199.027	+	167.789i	0.323096	+	0.272385i
$617$	−57.4913	−	57.4913i	−0.0931787	−	0.0931787i	0.658981	−	0.752160i	$-0.270988\pi$
$617$	−57.4913	−	57.4913i	−0.0931787	−	0.0931787i	−0.752160	+	0.658981i	$0.770988\pi$
$618$	362.757	−	2.22740i	0.586986	−	0.00360421i
$619$	289.165	+	500.848i	0.467148	+	0.809124i	0.999296	−	0.0375275i	$-0.0119482\pi$
$619$	289.165	+	500.848i	0.467148	+	0.809124i	−0.532148	+	0.846652i	$0.678615\pi$
$620$	27.3254	+	132.255i	0.0440733	+	0.213314i
$621$	−237.148	−	824.024i	−0.381880	−	1.32693i
$622$	−129.566	−	129.566i	−0.208305	−	0.208305i
$623$	388.391	−	270.618i	0.623420	−	0.434379i
$624$	−94.3827	−	24.6697i	−0.151254	−	0.0395347i
$625$	−608.224	−	143.835i	−0.973159	−	0.230136i
$626$	17.8292	+	30.8812i	0.0284812	+	0.0493309i
$627$	285.560	+	162.538i	0.455438	+	0.259232i
$628$	85.0111	+	317.266i	0.135368	+	0.505200i
$629$		−	1002.64i		−	1.59402i
$630$	−212.838	+	404.452i	−0.337839	+	0.641987i
$631$	−451.519			−0.715561			−0.357781	−	0.933806i	$-0.616466\pi$
$631$	−451.519			−0.715561			−0.357781	+	0.933806i	$0.616466\pi$
$632$	−572.201	+	153.321i	−0.905382	+	0.242596i
$633$	−221.211	+	388.639i	−0.349464	+	0.613964i
$634$	261.716	−	151.102i	0.412801	−	0.238331i
$635$	29.9189	−	514.781i	0.0471163	−	0.810679i
$636$	50.2407	−	192.214i	0.0789948	−	0.302223i
$637$	−328.500	−	30.2711i	−0.515699	−	0.0475214i
$638$	−128.608	+	128.608i	−0.201581	+	0.201581i
$639$	65.3305	−	38.7960i	0.102239	−	0.0607136i
$640$	98.2453	+	64.5996i	0.153508	+	0.100937i
$641$	−22.3299	+	12.8922i	−0.0348360	+	0.0201126i	−0.517317	−	0.855794i	$-0.673069\pi$
$641$	−22.3299	+	12.8922i	−0.0348360	+	0.0201126i	0.482481	+	0.875907i	$0.339736\pi$
$642$	−0.549038	−	89.4171i	−0.000855199	−	0.139279i
$643$	628.889	−	628.889i	0.978054	−	0.978054i	−0.0217104	−	0.999764i	$-0.506911\pi$
$643$	628.889	−	628.889i	0.978054	−	0.978054i	0.999764	+	0.0217104i	$0.00691118\pi$
$644$	396.171	−	143.158i	0.615172	−	0.222295i
$645$	−533.445	+	822.235i	−0.827046	+	1.27478i
$646$	−360.700	+	624.751i	−0.558360	+	0.967107i
$647$	159.850	+	42.8316i	0.247063	+	0.0662002i	0.380225	−	0.924894i	$-0.375847\pi$
$647$	159.850	+	42.8316i	0.247063	+	0.0662002i	−0.133162	+	0.991094i	$0.542513\pi$
$648$	195.686	+	664.574i	0.301984	+	1.02558i
$649$	136.747	−	236.853i	0.210704	−	0.364950i
$650$	195.919	+	145.781i	0.301414	+	0.224278i
$651$	−271.772	−	125.465i	−0.417469	−	0.192727i
$652$	−66.2668	+	66.2668i	−0.101636	+	0.101636i
$653$	292.526	+	1091.72i	0.447972	+	1.67185i	0.707968	+	0.706245i	$0.249612\pi$
$653$	292.526	+	1091.72i	0.447972	+	1.67185i	−0.259996	+	0.965610i	$0.583721\pi$
$654$	1.22210	+	4.45143i	0.00186865	+	0.00680646i
$655$	98.4304	+	476.402i	0.150275	+	0.727332i
$656$	−3.77213	+	6.53352i	−0.00575020	+	0.00995964i
$657$	−65.5790	−	233.248i	−0.0998158	−	0.355020i
$658$	139.266	−	11.8598i	0.211650	−	0.0180241i
$659$	−672.256			−1.02012			−0.510058	−	0.860140i	$-0.670376\pi$
$659$	−672.256			−1.02012			−0.510058	+	0.860140i	$0.670376\pi$
$660$	−117.552	−	38.1371i	−0.178110	−	0.0577835i
$661$	−575.495	+	332.262i	−0.870642	+	0.502666i	−0.867562	−	0.497330i	$-0.834314\pi$
$661$	−575.495	+	332.262i	−0.870642	+	0.502666i	−0.00308073	+	0.999995i	$0.500981\pi$
$662$	−125.009	+	466.541i	−0.188836	+	0.704744i
$663$	−2.44784	−	398.658i	−0.00369207	−	0.601295i
$664$	−140.012			−0.210861
$665$	−857.432	−	205.198i	−1.28937	−	0.308568i
$666$	−324.574	+	578.469i	−0.487348	+	0.868572i
$667$	236.976	+	884.408i	0.355287	+	1.32595i
$668$	1.57968	−	5.89546i	0.00236479	−	0.00882553i
$669$	−231.567	−	843.468i	−0.346139	−	1.26079i
$670$	−629.080	+	559.973i	−0.938926	+	0.835780i
$671$	−46.7685			−0.0696996
$672$	−536.075	+	197.443i	−0.797730	+	0.293814i
$673$	−106.959	−	106.959i	−0.158929	−	0.158929i	0.623163	−	0.782092i	$-0.285847\pi$
$673$	−106.959	−	106.959i	−0.158929	−	0.158929i	−0.782092	+	0.623163i	$0.785847\pi$
$674$	−69.8218	+	120.935i	−0.103593	+	0.179429i
$675$	65.8347	−	671.782i	0.0975328	−	0.995232i
$676$	−117.173	−	202.949i	−0.173332	−	0.300220i
$677$	44.6627	+	166.683i	0.0659714	+	0.246209i	0.991035	−	0.133604i	$-0.0426550\pi$
$677$	44.6627	+	166.683i	0.0659714	+	0.246209i	−0.925063	+	0.379813i	$0.875988\pi$
$678$	152.821	+	260.980i	0.225400	+	0.384926i
$679$	1159.16	−	418.868i	1.70716	−	0.616890i
$680$	265.409	−	801.292i	0.390308	−	1.17837i
$681$	793.492	−	803.296i	1.16519	−	1.17958i
$682$	−23.2737	+	86.8587i	−0.0341257	+	0.127359i
$683$	12.9980	+	3.48281i	0.0190308	+	0.00509928i	0.268322	−	0.963329i	$-0.413531\pi$
$683$	12.9980	+	3.48281i	0.0190308	+	0.00509928i	−0.249291	+	0.968429i	$0.580198\pi$
$684$	−369.364	+	219.344i	−0.540006	+	0.320678i
$685$	489.652	+	974.678i	0.714821	+	1.42289i
$686$	432.702	−	245.836i	0.630761	−	0.358361i
$687$	260.084	+	444.158i	0.378579	+	0.646518i
$688$	304.844	−	81.6826i	0.443087	−	0.118725i
$689$	203.771	−	117.647i	0.295748	−	0.170750i
$690$	513.434	−	462.713i	0.744108	−	0.670598i
$691$	−407.010	−	234.987i	−0.589016	−	0.340069i	0.175692	−	0.984445i	$-0.443784\pi$
$691$	−407.010	−	234.987i	−0.589016	−	0.340069i	−0.764708	+	0.644376i	$0.777117\pi$
$692$	450.406	−	450.406i	0.650875	−	0.650875i
$693$	222.809	−	159.346i	0.321514	−	0.229936i
$694$			797.952i			1.14979i
$695$	428.992	−	381.865i	0.617254	−	0.549446i
$696$	−195.847	−	713.360i	−0.281389	−	1.02494i
$697$	−29.7801	−	7.97956i	−0.0427262	−	0.0114484i
$698$	115.125	−	30.8477i	0.164936	−	0.0441944i
$699$	343.695	+	89.8347i	0.491695	+	0.128519i
$700$	331.441	+	10.3290i	0.473488	+	0.0147557i
$701$		−	1006.91i		−	1.43639i	−0.695843	−	0.718194i	$-0.744969\pi$
$701$		−	1006.91i		−	1.43639i	0.695843	−	0.718194i	$-0.255031\pi$
$702$	−127.641	+	230.797i	−0.181825	+	0.328771i
$703$	−1235.95	−	331.171i	−1.75811	−	0.471083i
$704$	127.810	+	221.374i	0.181548	+	0.314451i
$705$	−183.886	+	93.7980i	−0.260832	+	0.133047i
$706$			868.386i			1.23001i
$707$	439.778	−	37.4514i	0.622034	−	0.0529722i
$708$	180.681	+	308.558i	0.255200	+	0.435817i
$709$	−422.388	−	243.866i	−0.595751	−	0.343957i	0.171617	−	0.985164i	$-0.445101\pi$
$709$	−422.388	−	243.866i	−0.595751	−	0.343957i	−0.767368	+	0.641207i	$0.778434\pi$
$710$	51.1742	+	33.6487i	0.0720763	+	0.0473926i
$711$	7.65473	+	623.306i	0.0107661	+	0.876661i
$712$	558.680	−	149.698i	0.784662	−	0.210250i
$713$	320.095	+	320.095i	0.448941	+	0.448941i
$714$	346.838	+	491.322i	0.485768	+	0.688126i
$715$	−65.7046	−	130.788i	−0.0918946	−	0.182921i
$716$	−402.969	−	232.654i	−0.562805	−	0.324936i
$717$	−420.301	+	738.417i	−0.586194	+	1.02987i
$718$	−18.3168	+	68.3594i	−0.0255109	+	0.0952081i
$719$	−999.752	−	577.207i	−1.39048	−	0.802792i	−0.397108	−	0.917772i	$-0.629986\pi$
$719$	−999.752	−	577.207i	−1.39048	−	0.802792i	−0.993368	+	0.114980i	$0.963320\pi$
$720$	−160.561	+	146.496i	−0.223001	+	0.203466i
$721$	574.295	+	102.633i	0.796526	+	0.142348i
$722$	280.624	+	280.624i	0.388676	+	0.388676i
$723$	−1.52100	−	247.712i	−0.00210374	−	0.342617i
$724$	−87.2269	−	151.081i	−0.120479	−	0.208676i
$725$	−83.4990	+	715.912i	−0.115171	+	0.987465i
$726$	316.155	+	312.296i	0.435475	+	0.430159i
$727$	−654.711	−	654.711i	−0.900566	−	0.900566i	0.0949191	−	0.995485i	$-0.469741\pi$
$727$	−654.711	−	654.711i	−0.900566	−	0.900566i	−0.995485	+	0.0949191i	$0.969741\pi$
$728$	−364.917	−	171.192i	−0.501259	−	0.235153i
$729$	728.505	−	26.8508i	0.999321	−	0.0368324i
$730$	145.879	−	129.854i	0.199835	−	0.177882i
$731$	644.866	+	1116.94i	0.882170	+	1.52796i
$732$	30.2469	−	53.1400i	0.0413209	−	0.0725957i
$733$	−105.152	−	392.433i	−0.143454	−	0.535379i	−0.999819	−	0.0190079i	$-0.993949\pi$
$733$	−105.152	−	392.433i	−0.143454	−	0.535379i	0.856365	−	0.516371i	$-0.172717\pi$
$734$			221.375i			0.301601i
$735$	−454.927	+	577.292i	−0.618948	+	0.785432i
$736$	863.941			1.17383
$737$	487.578	−	130.646i	0.661571	−	0.177267i
$738$	14.5984	+	14.2442i	0.0197811	+	0.0193011i
$739$	701.246	−	404.865i	0.948912	−	0.547855i	0.0561693	−	0.998421i	$-0.482111\pi$
$739$	701.246	−	404.865i	0.948912	−	0.547855i	0.892743	+	0.450567i	$0.148778\pi$
$740$	480.451	+	27.9236i	0.649258	+	0.0377346i
$741$	−492.234	−	128.660i	−0.664284	−	0.173630i
$742$	−150.753	+	321.350i	−0.203172	+	0.433087i
$743$	205.338	−	205.338i	0.276364	−	0.276364i	−0.555292	−	0.831656i	$-0.687393\pi$
$743$	205.338	−	205.338i	0.276364	−	0.276364i	0.831656	+	0.555292i	$0.187393\pi$
$744$	−260.201	−	257.025i	−0.349733	−	0.345464i
$745$	179.862	+	870.529i	0.241425	+	1.16850i
$746$	302.409	−	174.596i	0.405375	−	0.234043i
$747$	−36.3816	+	142.768i	−0.0487036	+	0.191122i
$748$	−114.992	+	114.992i	−0.153733	+	0.153733i
$749$	25.2983	−	141.560i	0.0337761	−	0.188998i
$750$	510.055	−	189.414i	0.680073	−	0.252552i
$751$	−222.402	+	385.211i	−0.296141	+	0.512931i	−0.975250	−	0.221107i	$-0.929033\pi$
$751$	−222.402	+	385.211i	−0.296141	+	0.512931i	0.679109	+	0.734038i	$0.262366\pi$
$752$	64.2045	+	17.2036i	0.0853784	+	0.0228771i
$753$	83.9918	−	147.563i	0.111543	−	0.195967i
$754$	140.812	−	243.893i	0.186753	−	0.323466i
$755$	214.165	+	70.9373i	0.283663	+	0.0939567i
$756$	36.9559	+	356.219i	0.0488834	+	0.471189i
$757$	−630.375	+	630.375i	−0.832728	+	0.832728i	−0.987889	−	0.155161i	$-0.950410\pi$
$757$	−630.375	+	630.375i	−0.832728	+	0.832728i	0.155161	+	0.987889i	$0.450410\pi$
$758$	13.2755	+	49.5450i	0.0175139	+	0.0653628i
$759$	−399.474	+	109.672i	−0.526316	+	0.144495i
$760$	−900.086	−	591.837i	−1.18432	−	0.778733i
$761$	−388.123	+	672.248i	−0.510017	+	0.883375i	0.489916	+	0.871770i	$0.337027\pi$
$761$	−388.123	+	672.248i	−0.510017	+	0.883375i	−0.999933	+	0.0116051i	$0.996306\pi$
$762$	226.831	+	387.370i	0.297678	+	0.508359i
$763$	0.629914	+	7.39685i	0.000825575	+	0.00969444i
$764$	−86.8874			−0.113727
$765$	−748.101	−	478.847i	−0.977909	−	0.625944i
$766$	344.869	−	199.110i	0.450221	−	0.259935i
$767$	−109.604	+	409.049i	−0.142900	+	0.533311i
$768$	−807.825	+	4.96020i	−1.05186	+	0.00645859i
$769$	−1219.04			−1.58522			−0.792612	−	0.609727i	$-0.791279\pi$
$769$	−1219.04			−1.58522			−0.792612	+	0.609727i	$0.791279\pi$
$770$	194.119	+	105.217i	0.252102	+	0.136645i
$771$	−64.2146	−	16.7843i	−0.0832874	−	0.0217696i
$772$	132.954	+	496.192i	0.172220	+	0.642735i
$773$	−150.367	+	561.179i	−0.194524	+	0.725975i	0.797865	+	0.602836i	$0.205963\pi$
$773$	−150.367	+	561.179i	−0.194524	+	0.725975i	−0.992389	+	0.123139i	$0.960704\pi$
$774$	−10.4777	−	853.172i	−0.0135371	−	1.10229i
$775$	141.225	+	327.173i	0.182225	+	0.422159i
$776$	1505.95			1.94065
$777$	−682.542	+	819.775i	−0.878432	+	1.05505i
$778$	−481.817	−	481.817i	−0.619303	−	0.619303i
$779$	−19.6728	+	34.0743i	−0.0252539	+	0.0437411i
$780$	191.100	+	9.92972i	0.245000	+	0.0127304i
$781$	−18.3539	−	31.7898i	−0.0235005	−	0.0407040i
$782$	−235.398	−	878.517i	−0.301021	−	1.12342i
$783$	−778.294	+	14.3381i	−0.993990	+	0.0183117i
$784$	233.261	−	40.0192i	0.297527	−	0.0510448i
$785$	389.071	+	774.466i	0.495632	+	0.986581i
$786$	−301.285	−	297.607i	−0.383314	−	0.378635i
$787$	230.535	−	860.369i	0.292929	−	1.09323i	−0.649919	−	0.760003i	$-0.725197\pi$
$787$	230.535	−	860.369i	0.292929	−	1.09323i	0.942848	−	0.333222i	$-0.108136\pi$
$788$	−180.902	−	48.4725i	−0.229571	−	0.0615133i
$789$	414.637	−	419.760i	0.525522	−	0.532015i
$790$	−448.986	+	225.559i	−0.568337	+	0.285517i
$791$	165.290	+	457.419i	0.208964	+	0.578279i
$792$	322.201	−	90.5885i	0.406820	−	0.114379i
$793$	69.9490	−	18.7428i	0.0882080	−	0.0236353i
$794$	125.445	−	72.4257i	0.157991	−	0.0912163i
$795$	27.2030	−	523.529i	0.0342176	−	0.658527i
$796$	404.381	+	233.470i	0.508016	+	0.293303i
$797$	−42.0291	+	42.0291i	−0.0527341	+	0.0527341i	−0.732982	−	0.680248i	$-0.761872\pi$
$797$	−42.0291	+	42.0291i	−0.0527341	+	0.0527341i	0.680248	+	0.732982i	$0.261872\pi$
$798$	720.213	−	265.263i	0.902523	−	0.332410i
$799$			271.636i			0.339970i
$800$	632.106	+	250.939i	0.790132	+	0.313674i
$801$	−7.47383	−	608.576i	−0.00933063	−	0.759771i
$802$	−536.250	−	143.688i	−0.668640	−	0.179162i
$803$	−113.066	+	30.2959i	−0.140804	+	0.0377284i
$804$	−166.890	+	638.498i	−0.207574	+	0.794151i
$805$	947.321	−	581.458i	1.17680	−	0.722308i
$806$		−	139.237i		−	0.172750i
$807$	−2.98817	−	486.658i	−0.00370282	−	0.603045i
$808$	520.909	+	139.577i	0.644689	+	0.172744i
$809$	−446.584	−	773.507i	−0.552020	−	0.956127i	−0.998129	−	0.0611480i	$-0.980524\pi$
$809$	−446.584	−	773.507i	−0.552020	−	0.956127i	0.446109	−	0.894979i	$-0.352809\pi$
$810$	276.602	+	518.445i	0.341484	+	0.640055i
$811$		−	677.071i		−	0.834859i	−0.908709	−	0.417430i	$-0.862931\pi$
$811$		−	677.071i		−	0.834859i	0.908709	−	0.417430i	$-0.137069\pi$
$812$	−32.4486	−	381.032i	−0.0399614	−	0.469252i
$813$	749.587	−	438.933i	0.922001	−	0.539893i
$814$	277.519	+	160.226i	0.340933	+	0.196838i
$815$	−135.861	+	206.622i	−0.166701	+	0.253524i
$816$	75.7194	+	275.803i	0.0927933	+	0.337994i
$817$	1589.85	−	425.999i	1.94596	−	0.521419i
$818$	−409.795	−	409.795i	−0.500972	−	0.500972i
$819$	−269.384	+	327.617i	−0.328918	+	0.400021i
$820$	4.65309	−	14.0480i	0.00567450	−	0.0171317i
$821$	−1195.92	−	690.462i	−1.45666	−	0.841001i	−0.457812	−	0.889049i	$-0.651367\pi$
$821$	−1195.92	−	690.462i	−1.45666	−	0.841001i	−0.998845	+	0.0480474i	$0.984700\pi$
$822$	−825.238	−	469.719i	−1.00394	−	0.571434i
$823$	−122.693	+	457.896i	−0.149080	+	0.556374i	0.850460	+	0.526040i	$0.176324\pi$
$823$	−122.693	+	457.896i	−0.149080	+	0.556374i	−0.999540	+	0.0303340i	$0.990343\pi$
$824$	617.317	+	356.408i	0.749171	+	0.432534i
$825$	−324.132	−	35.7886i	−0.392887	−	0.0433801i
$826$	−217.109	−	600.819i	−0.262843	−	0.727384i
$827$	−814.051	−	814.051i	−0.984343	−	0.984343i	0.0155366	−	0.999879i	$-0.495054\pi$
$827$	−814.051	−	814.051i	−0.984343	−	0.984343i	−0.999879	+	0.0155366i	$0.995054\pi$
$828$	133.741	−	524.826i	0.161523	−	0.633847i
$829$	−344.646	−	596.945i	−0.415738	−	0.720079i	0.579768	−	0.814782i	$-0.303143\pi$
$829$	−344.646	−	596.945i	−0.415738	−	0.720079i	−0.995506	+	0.0947031i	$0.969810\pi$
$830$	−116.301	+	24.0292i	−0.140122	+	0.0289508i
$831$	71.7906	−	72.6777i	0.0863907	−	0.0874581i
$832$	−279.875	−	279.875i	−0.336389	−	0.336389i
$833$	404.692	+	878.445i	0.485824	+	1.05456i
$834$	−126.436	+	483.728i	−0.151602	+	0.580010i
$835$	0.934446	−	16.0780i	0.00111910	−	0.0192551i
$836$	103.769	+	179.732i	0.124125	+	0.214991i
$837$	−329.698	+	198.536i	−0.393904	+	0.237200i
$838$	70.1328	+	261.739i	0.0836907	+	0.312338i
$839$			1583.07i			1.88686i	0.331576	+	0.943429i	$0.392420\pi$
$839$			1583.07i			1.88686i	−0.331576	+	0.943429i	$0.607580\pi$
$840$	−762.481	+	474.475i	−0.907715	+	0.564851i
$841$	−9.79677			−0.0116490
$842$	−46.9324	+	12.5755i	−0.0557392	+	0.0149353i
$843$	−1185.34	−	674.685i	−1.40609	−	0.800338i
$844$	−244.611	+	141.226i	−0.289824	+	0.167330i
$845$	−411.145	−	461.886i	−0.486563	−	0.546610i
$846$	87.9342	−	156.720i	0.103941	−	0.185248i
$847$	408.560	+	586.364i	0.482361	+	0.692283i
$848$	−119.362	+	119.362i	−0.140757	+	0.140757i
$849$	−628.505	+	636.271i	−0.740288	+	0.749435i
$850$	82.9429	−	711.144i	0.0975799	−	0.836640i
$851$	1397.07	−	806.597i	1.64168	−	0.947823i
$852$	47.9909	−	0.294673i	0.0563273	−	0.000345861i
$853$	500.340	−	500.340i	0.586565	−	0.586565i	−0.350135	−	0.936699i	$-0.613864\pi$
$853$	500.340	−	500.340i	0.586565	−	0.586565i	0.936699	+	0.350135i	$0.113864\pi$
$854$	−70.4142	+	83.5235i	−0.0824523	+	0.0978027i
$855$	−837.372	+	764.019i	−0.979383	+	0.893590i
$856$	87.8520	−	152.164i	0.102631	−	0.177762i
$857$	210.127	+	56.3034i	0.245189	+	0.0656982i	0.379321	−	0.925265i	$-0.376158\pi$
$857$	210.127	+	56.3034i	0.245189	+	0.0656982i	−0.134131	+	0.990964i	$0.542824\pi$
$858$	110.736	+	63.0298i	0.129062	+	0.0734613i
$859$	−197.711	+	342.446i	−0.230165	+	0.398657i	−0.957856	−	0.287247i	$-0.907260\pi$
$859$	−197.711	+	342.446i	−0.230165	+	0.398657i	0.727692	+	0.685904i	$0.240593\pi$
$860$	−553.183	+	277.905i	−0.643237	+	0.323145i
$861$	18.9167	+	26.7970i	0.0219707	+	0.0311231i
$862$	−261.073	+	261.073i	−0.302868	+	0.302868i
$863$	−172.197	−	642.646i	−0.199532	−	0.744665i	−0.991047	−	0.133515i	$-0.957374\pi$
$863$	−172.197	−	642.646i	−0.199532	−	0.744665i	0.791514	−	0.611151i	$-0.209293\pi$
$864$	−177.003	+	712.855i	−0.204864	+	0.825064i
$865$	923.427	−	1404.38i	1.06755	−	1.62356i
$866$	−523.577	+	906.861i	−0.604592	+	1.04718i
$867$	−260.447	+	152.509i	−0.300400	+	0.175904i
$868$	−108.086	−	155.125i	−0.124523	−	0.178716i
$869$	301.150			0.346548
$870$	−285.109	−	558.942i	−0.327711	−	0.642462i
$871$	−676.886	+	390.800i	−0.777137	+	0.448680i
$872$	−2.34762	+	8.76144i	−0.00269223	+	0.0100475i
$873$	391.315	−	1535.59i	0.448242	−	1.75899i
$874$	−1160.70			−1.32803
$875$	862.000	−	150.269i	0.985143	−	0.171736i
$876$	38.7006	−	148.063i	0.0441787	−	0.169022i
$877$	−146.190	−	545.589i	−0.166694	−	0.622109i	−0.997818	−	0.0660226i	$-0.978969\pi$
$877$	−146.190	−	545.589i	−0.166694	−	0.622109i	0.831125	−	0.556086i	$-0.187698\pi$
$878$	173.942	−	649.160i	0.198112	−	0.739362i
$879$	−508.321	+	139.555i	−0.578295	+	0.158766i
$880$	69.8161	+	78.4322i	0.0793365	+	0.0891276i
$881$	−647.825			−0.735330			−0.367665	−	0.929958i	$-0.619843\pi$
$881$	−647.825			−0.735330			−0.367665	+	0.929958i	$0.619843\pi$
$882$	50.8844	−	637.823i	0.0576921	−	0.723156i
$883$	687.897	+	687.897i	0.779046	+	0.779046i	0.979669	−	0.200623i	$-0.0642966\pi$
$883$	687.897	+	687.897i	0.779046	+	0.779046i	−0.200623	+	0.979669i	$0.564297\pi$
$884$	125.903	−	218.071i	0.142425	−	0.246687i
$885$	631.645	+	700.885i	0.713723	+	0.791960i
$886$	509.489	+	882.460i	0.575044	+	0.996005i
$887$	−166.333	−	620.764i	−0.187523	−	0.699847i	−0.994076	−	0.108685i	$-0.965336\pi$
$887$	−166.333	−	620.764i	−0.187523	−	0.699847i	0.806553	−	0.591162i	$-0.201331\pi$
$888$	−1124.73	+	658.601i	−1.26658	+	0.741668i
$889$	245.339	+	678.942i	0.275972	+	0.763715i
$890$	438.376	−	220.228i	0.492557	−	0.247448i
$891$	−8.64907	−	352.083i	−0.00970715	−	0.395155i
$892$	142.989	−	533.642i	0.160302	−	0.598254i
$893$	334.846	+	89.7217i	0.374967	+	0.100472i
$894$	−550.537	−	543.818i	−0.615813	−	0.608297i
$895$	−1165.54	−	386.057i	−1.30228	−	0.431349i
$896$	−162.046	−	28.9595i	−0.180855	−	0.0323208i
$897$	553.519	−	324.122i	0.617078	−	0.361340i
$898$	−634.599	+	170.040i	−0.706680	+	0.189354i
$899$	355.896	−	205.477i	0.395880	−	0.228561i
$900$	250.292	−	345.144i	0.278102	−	0.383494i
$901$	−597.417	−	344.919i	−0.663060	−	0.382818i
$902$	6.96766	−	6.96766i	0.00772467	−	0.00772467i
$903$	233.099	−	1352.22i	0.258139	−	1.49748i
$904$			594.265i			0.657373i
$905$	−306.069	−	343.842i	−0.338198	−	0.379936i
$906$	−189.394	+	51.9963i	−0.209044	+	0.0573911i
$907$	−166.606	−	44.6420i	−0.183689	−	0.0492194i	0.165802	−	0.986159i	$-0.446979\pi$
$907$	−166.606	−	44.6420i	−0.183689	−	0.0492194i	−0.349491	+	0.936940i	$0.613645\pi$
$908$	688.878	−	184.584i	0.758676	−	0.203287i
$909$	277.681	−	494.895i	0.305480	−	0.544439i
$910$	−332.499	−	79.5725i	−0.365383	−	0.0874423i
$911$			117.536i			0.129019i	0.997917	+	0.0645093i	$0.0205482\pi$
$911$			117.536i			0.129019i	−0.997917	+	0.0645093i	$0.979452\pi$
$912$	364.993	−	2.24113i	0.400211	−	0.00245737i
$913$	68.7521	+	18.4221i	0.0753036	+	0.0201775i
$914$	170.251	+	294.883i	0.186270	+	0.322629i
$915$	49.7897	−	153.470i	0.0544149	−	0.167726i
$916$			325.099i			0.354911i
$917$	−389.344	−	558.785i	−0.424584	−	0.609362i
$918$	773.110	−	14.2426i	0.842168	−	0.0155148i
$919$	−89.1660	−	51.4800i	−0.0970250	−	0.0560174i	0.450702	−	0.892674i	$-0.351174\pi$
$919$	−89.1660	−	51.4800i	−0.0970250	−	0.0560174i	−0.547727	+	0.836657i	$0.684507\pi$
$920$	1330.03	−	274.800i	1.44569	−	0.298696i
$921$	1273.32	−	349.579i	1.38254	−	0.379564i
$922$	441.495	−	118.298i	0.478845	−	0.128306i
$923$	40.1908	+	40.1908i	0.0435437	+	0.0435437i
$924$	172.300	−	15.7392i	0.186472	−	0.0170338i
$925$	1256.45	−	184.360i	1.35833	−	0.199308i
$926$	525.049	+	303.137i	0.567008	+	0.327362i
$927$	523.832	−	536.858i	0.565083	−	0.579135i
$928$	202.992	−	757.576i	0.218741	−	0.816354i
$929$	339.509	+	196.016i	0.365457	+	0.210997i	0.671472	−	0.741030i	$-0.265662\pi$
$929$	339.509	+	196.016i	0.365457	+	0.210997i	−0.306015	+	0.952027i	$0.598996\pi$
$930$	−260.248	−	168.842i	−0.279836	−	0.181550i
$931$	1216.53	−	208.712i	1.30669	−	0.224180i
$932$	158.660	+	158.660i	0.170236	+	0.170236i
$933$	−378.859	+	2.32627i	−0.406066	+	0.00249332i
$934$	−567.173	−	982.373i	−0.607252	−	1.05179i
$935$	−235.758	+	358.549i	−0.252148	+	0.383475i
$936$	−445.594	+	264.612i	−0.476062	+	0.282706i
$937$	848.278	+	848.278i	0.905313	+	0.905313i	0.995889	−	0.0905767i	$-0.0288710\pi$
$937$	848.278	+	848.278i	0.905313	+	0.905313i	−0.0905767	+	0.995889i	$0.528871\pi$
$938$	500.773	−	1067.46i	0.533874	−	1.13802i
$939$	71.3336	+	18.6451i	0.0759677	+	0.0198563i
$940$	−130.165	−	7.56511i	−0.138473	−	0.00804799i
$941$	570.470	+	988.083i	0.606238	+	1.05003i	0.991855	+	0.127376i	$0.0406554\pi$
$941$	570.470	+	988.083i	0.606238	+	1.05003i	−0.385617	+	0.922659i	$0.626011\pi$
$942$	−655.723	−	373.232i	−0.696096	−	0.396213i
$943$	−12.8387	−	47.9148i	−0.0136148	−	0.0508111i
$944$		−	303.810i		−	0.321833i
$945$	285.688	+	900.782i	0.302315	+	0.953208i
$946$	−412.210			−0.435740
$947$	−542.316	+	145.313i	−0.572668	+	0.153446i	−0.533520	−	0.845788i	$-0.679131\pi$
$947$	−542.316	+	145.313i	−0.572668	+	0.153446i	−0.0391479	+	0.999233i	$0.512464\pi$
$948$	−194.765	+	342.178i	−0.205448	+	0.360947i
$949$	156.965	−	90.6238i	0.165400	−	0.0954940i
$950$	−849.230	−	337.135i	−0.893926	−	0.354879i
$951$	158.016	−	604.549i	0.166158	−	0.635698i
$952$	100.274	+	1177.48i	0.105330	+	1.23685i
$953$	−491.430	+	491.430i	−0.515666	+	0.515666i	−0.916257	−	0.400591i	$-0.868805\pi$
$953$	−491.430	+	491.430i	−0.515666	+	0.515666i	0.400591	+	0.916257i	$0.368805\pi$
$954$	233.021	+	392.396i	0.244257	+	0.411317i
$955$	−224.528	+	46.3902i	−0.235108	+	0.0485761i
$956$	−464.763	+	268.331i	−0.486153	+	0.280681i
$957$	2.30909	+	376.061i	0.00241284	+	0.392958i
$958$	319.302	−	319.302i	0.333300	−	0.333300i
$959$	−1167.53	−	984.279i	−1.21744	−	1.02636i
$960$	−862.499	+	183.732i	−0.898436	+	0.191387i
$961$	−378.911	+	656.293i	−0.394288	+	0.682927i
$962$	−479.281	−	128.423i	−0.498214	−	0.133496i
$963$	−132.332	−	129.121i	−0.137416	−	0.134082i
$964$	78.2320	−	135.502i	0.0811535	−	0.140562i
$965$	608.492	+	1211.23i	0.630562	+	1.25517i
$966$	−405.582	+	878.539i	−0.419857	+	0.909461i
$967$	−906.688	+	906.688i	−0.937630	+	0.937630i	−0.998166	−	0.0605361i	$-0.980719\pi$
$967$	−906.688	+	906.688i	−0.937630	+	0.937630i	0.0605361	+	0.998166i	$0.480719\pi$
$968$	226.003	+	843.453i	0.233474	+	0.871336i
$969$	394.899	+	1438.40i	0.407533	+	1.48441i
$970$	1250.92	−	258.454i	1.28960	−	0.266448i
$971$	−687.381	+	1190.58i	−0.707910	+	1.22614i	0.257721	+	0.966219i	$0.417029\pi$
$971$	−687.381	+	1190.58i	−0.707910	+	1.22614i	−0.965631	+	0.259917i	$0.916305\pi$
$972$	405.643	+	217.878i	0.417329	+	0.224154i
$973$	−341.495	+	727.940i	−0.350971	+	0.748140i
$974$	−1002.85			−1.02962
$975$	499.128	−	76.3709i	0.511926	−	0.0783291i
$976$	−44.9923	+	25.9763i	−0.0460987	+	0.0266151i
$977$	158.172	−	590.306i	0.161896	−	0.604202i	−0.836520	−	0.547936i	$-0.815414\pi$
$977$	158.172	−	590.306i	0.161896	−	0.604202i	0.998416	−	0.0562663i	$-0.0179196\pi$
$978$	−1.32180	−	215.270i	−0.00135153	−	0.220113i
$979$	−294.033			−0.300340
$980$	−432.210	+	169.458i	−0.441031	+	0.172917i
$981$	8.32390	+	4.67047i	0.00848512	+	0.00476092i
$982$	180.074	+	672.044i	0.183374	+	0.684362i
$983$	291.499	−	1087.89i	0.296541	−	1.10670i	−0.643445	−	0.765492i	$-0.722496\pi$
$983$	291.499	−	1087.89i	0.296541	−	1.10670i	0.939986	−	0.341213i	$-0.110838\pi$
$984$	10.6104	+	38.6479i	0.0107830	+	0.0392764i
$985$	−493.353	−	28.6734i	−0.500866	−	0.0291101i
$986$	−825.667			−0.837391
$987$	184.916	−	222.095i	0.187351	−	0.225020i
$988$	−227.230	−	227.230i	−0.229990	−	0.229990i
$989$	−1037.56	+	1797.10i	−1.04910	+	1.81709i
$990$	252.090	−	130.544i	0.254636	−	0.131863i
$991$	−133.957	−	232.021i	−0.135174	−	0.234128i	0.790490	−	0.612475i	$-0.209826\pi$
$991$	−133.957	−	232.021i	−0.135174	−	0.234128i	−0.925664	+	0.378347i	$0.876493\pi$
$992$	−100.361	−	374.552i	−0.101170	−	0.377572i
$993$	504.642	+	861.802i	0.508200	+	0.867877i
$994$	−84.4067	−	15.0844i	−0.0849162	−	0.0151755i
$995$	1169.62	+	387.411i	1.17550	+	0.389357i
$996$	−65.3964	+	66.2045i	−0.0656590	+	0.0664703i
$997$	−274.072	+	1022.85i	−0.274897	+	1.02593i	0.681014	+	0.732270i	$0.261539\pi$
$997$	−274.072	+	1022.85i	−0.274897	+	1.02593i	−0.955911	+	0.293658i	$0.905127\pi$
$998$	−1178.18	−	315.694i	−1.18055	−	0.316326i
$999$	379.311	+	1318.00i	0.379691	+	1.31932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.68.10	yes	112
3.2	odd	2	inner	105.3.w.a.68.19	yes	112
5.2	odd	4	inner	105.3.w.a.47.10	yes	112
7.3	odd	6	inner	105.3.w.a.38.19	yes	112
15.2	even	4	inner	105.3.w.a.47.19	yes	112
21.17	even	6	inner	105.3.w.a.38.10	yes	112
35.17	even	12	inner	105.3.w.a.17.19	yes	112
105.17	odd	12	inner	105.3.w.a.17.10	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.10	✓	112	105.17	odd	12	inner
105.3.w.a.17.19	yes	112	35.17	even	12	inner
105.3.w.a.38.10	yes	112	21.17	even	6	inner
105.3.w.a.38.19	yes	112	7.3	odd	6	inner
105.3.w.a.47.10	yes	112	5.2	odd	4	inner
105.3.w.a.47.19	yes	112	15.2	even	4	inner
105.3.w.a.68.10	yes	112	1.1	even	1	trivial
105.3.w.a.68.19	yes	112	3.2	odd	2	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+(-1.40147 + 0.375522i) q^{2} +(-1.48402 + 2.60724i) q^{3} +(-1.64101 + 0.947435i) q^{4} +(-3.73472 + 3.32444i) q^{5} +(1.10073 - 4.21124i) q^{6} +(2.97299 - 6.33730i) q^{7} +(6.04782 - 6.04782i) q^{8} +(-4.59537 - 7.73838i) q^{9} +(3.98568 - 6.06157i) q^{10} +(-3.76549 + 2.17401i) q^{11} +(-0.0349040 - 5.68450i) q^{12} +(4.76059 - 4.76059i) q^{13} +(-1.78675 + 9.99794i) q^{14} +(-3.12522 - 14.6708i) q^{15} +(-2.41499 + 4.18289i) q^{16} +(-19.0658 - 5.10867i) q^{17} +(9.34620 + 9.11943i) q^{18} +(-12.5949 + 21.8150i) q^{19} +(2.97900 - 8.99383i) q^{20} +(12.1109 + 17.1560i) q^{21} +(4.46083 - 4.46083i) q^{22} +(-8.21961 - 30.6760i) q^{23} +(6.79302 + 24.7432i) q^{24} +(2.89619 - 24.8317i) q^{25} +(-4.88411 + 8.45952i) q^{26} +(26.9954 - 0.497321i) q^{27} +(1.12549 + 13.2163i) q^{28} -28.8306 q^{29} +(9.88911 + 19.3871i) q^{30} +(-12.3444 + 7.12704i) q^{31} +(-7.04085 + 26.2768i) q^{32} +(-0.0800915 - 13.0438i) q^{33} +28.6386 q^{34} +(9.96472 + 33.5515i) q^{35} +(14.8726 + 8.34491i) q^{36} +(13.1470 + 49.0654i) q^{37} +(9.45934 - 35.3027i) q^{38} +(5.34718 + 19.4768i) q^{39} +(-2.48127 + 42.6925i) q^{40} +1.56196 q^{41} +(-23.4154 - 19.4956i) q^{42} +(-46.2033 - 46.2033i) q^{43} +(4.11946 - 7.13512i) q^{44} +(42.8882 + 13.6236i) q^{45} +(23.0391 + 39.9048i) q^{46} +(-3.56182 - 13.2929i) q^{47} +(-7.32189 - 12.5040i) q^{48} +(-31.3227 - 37.6814i) q^{49} +(5.26592 + 35.8884i) q^{50} +(41.6136 - 42.1278i) q^{51} +(-3.30181 + 12.3225i) q^{52} +(33.7582 + 9.04547i) q^{53} +(-37.6465 + 10.8344i) q^{54} +(6.83568 - 20.6375i) q^{55} +(-20.3468 - 56.3069i) q^{56} +(-38.1859 - 65.2119i) q^{57} +(40.4052 - 10.8265i) q^{58} +(-54.4737 + 31.4504i) q^{59} +(19.0281 + 21.1140i) q^{60} +(9.31520 + 5.37814i) q^{61} +(14.6239 - 14.6239i) q^{62} +(-62.7024 + 6.11616i) q^{63} -58.7901i q^{64} +(-1.95315 + 33.6057i) q^{65} +(5.01049 + 18.2504i) q^{66} +(-112.138 - 30.0473i) q^{67} +(36.1273 - 9.68028i) q^{68} +(92.1777 + 24.0933i) q^{69} +(-26.5646 - 43.2794i) q^{70} +8.44240i q^{71} +(-74.5923 - 19.0083i) q^{72} +(26.0040 + 6.96775i) q^{73} +(-36.8503 - 63.8266i) q^{74} +(60.4441 + 44.4018i) q^{75} -47.7314i q^{76} +(2.58258 + 30.3264i) q^{77} +(-14.8079 - 25.2881i) q^{78} +(-59.9822 - 34.6307i) q^{79} +(-4.88646 - 23.6504i) q^{80} +(-38.7651 + 71.1215i) q^{81} +(-2.18904 + 0.586552i) q^{82} +(-11.5754 - 11.5754i) q^{83} +(-36.1282 - 16.6788i) q^{84} +(88.1889 - 44.3038i) q^{85} +(82.1027 + 47.4020i) q^{86} +(42.7852 - 75.1682i) q^{87} +(-9.62501 + 35.9210i) q^{88} +(58.5647 + 33.8123i) q^{89} +(-65.2224 - 2.98758i) q^{90} +(-16.0161 - 44.3225i) q^{91} +(42.5520 + 42.5520i) q^{92} +(-0.262563 - 42.7614i) q^{93} +(9.98356 + 17.2920i) q^{94} +(-25.4843 - 123.344i) q^{95} +(-58.0611 - 57.3525i) q^{96} +(124.503 + 124.503i) q^{97} +(58.0480 + 41.0469i) q^{98} +(34.1272 + 19.1484i) 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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