LMFDB - Embedded newform 105.3.w.a.17.19

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			17.19
Character	$\chi$	$=$	105.17
Dual form			105.3.w.a.68.19

$q$-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} +(0.0184202 + 2.99994i) 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} +(-8.99932 + 0.110519i) q^{9} +(3.98568 + 6.06157i) q^{10} +(3.76549 + 2.17401i) q^{11} +(2.81202 - 4.94038i) q^{12} +(4.76059 + 4.76059i) q^{13} +(1.78675 + 9.99794i) q^{14} +(-9.90434 + 11.2652i) q^{15} +(-2.41499 - 4.18289i) q^{16} +(19.0658 - 5.10867i) q^{17} +(-12.6538 - 3.22456i) q^{18} +(-12.5949 - 21.8150i) q^{19} +(-2.97900 - 8.99383i) q^{20} +(-18.9568 + 9.03552i) q^{21} +(4.46083 + 4.46083i) q^{22} +(8.21961 - 30.6760i) q^{23} +(18.0317 - 18.2545i) q^{24} +(2.89619 + 24.8317i) q^{25} +(4.88411 + 8.45952i) q^{26} +(-0.497321 - 26.9954i) q^{27} +(1.12549 - 13.2163i) q^{28} +28.8306 q^{29} +(-18.1109 + 12.0685i) q^{30} +(-12.3444 - 7.12704i) q^{31} +(7.04085 + 26.2768i) q^{32} +(-6.45254 + 11.3363i) 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} +(-14.1938 + 14.3692i) q^{39} +(-2.48127 - 42.6925i) q^{40} -1.56196 q^{41} +(-29.9604 + 5.54431i) q^{42} +(-46.2033 + 46.2033i) q^{43} +(-4.11946 - 7.13512i) q^{44} +(-33.9773 - 29.5049i) q^{45} +(23.0391 - 39.9048i) q^{46} +(3.56182 - 13.2929i) q^{47} +(12.5040 - 7.32189i) q^{48} +(-31.3227 + 37.6814i) q^{49} +(-5.26592 + 35.8884i) q^{50} +(15.6769 + 57.1023i) q^{51} +(-3.30181 - 12.3225i) q^{52} +(-33.7582 + 9.04547i) q^{53} +(9.44040 - 38.0200i) q^{54} +(6.83568 + 20.6375i) q^{55} +(20.3468 - 56.3069i) q^{56} +(65.2119 - 38.1859i) q^{57} +(40.4052 + 10.8265i) q^{58} +(54.4737 + 31.4504i) q^{59} +(26.9261 - 9.10249i) q^{60} +(9.31520 - 5.37814i) q^{61} +(-14.6239 - 14.6239i) q^{62} +(-27.4552 - 56.7028i) q^{63} +58.7901i q^{64} +(1.95315 + 33.6057i) q^{65} +(-13.3001 + 13.4644i) 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} +(55.0947 + 53.7579i) q^{72} +(26.0040 - 6.96775i) q^{73} +(36.8503 - 63.8266i) q^{74} +(-74.4403 + 9.14583i) q^{75} +47.7314i q^{76} +(-2.58258 + 30.3264i) q^{77} +(-25.2881 + 14.8079i) q^{78} +(-59.9822 + 34.6307i) q^{79} +(4.88646 - 23.6504i) q^{80} +(80.9756 - 1.98920i) q^{81} +(-2.18904 - 0.586552i) q^{82} +(11.5754 - 11.5754i) q^{83} +(39.6687 + 3.13297i) q^{84} +(88.1889 + 44.3038i) q^{85} +(-82.1027 + 47.4020i) q^{86} +(0.531066 + 86.4902i) q^{87} +(-9.62501 - 35.9210i) q^{88} +(-58.5647 + 33.8123i) q^{89} +(-36.5384 - 54.1095i) q^{90} +(-16.0161 + 44.3225i) q^{91} +(-42.5520 + 42.5520i) q^{92} +(21.1533 - 37.1638i) q^{93} +(9.98356 - 17.2920i) q^{94} +(25.4843 - 123.344i) q^{95} +(-78.6993 + 21.6062i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.40147	+	0.375522i	0.700734	+	0.187761i	0.591559	−	0.806261i	$-0.298513\pi$
$2$	1.40147	+	0.375522i	0.700734	+	0.187761i	0.109175	+	0.994023i	$0.465179\pi$
$3$	0.0184202	+	2.99994i	0.00614008	+	0.999981i
$3$	0.0184202	+	2.99994i	0.00614008	+	0.999981i
$4$	−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
$9$	−8.99932	+	0.110519i	−0.999925	+	0.0122799i
$10$	3.98568	+	6.06157i	0.398568	+	0.606157i
$11$	3.76549	+	2.17401i	0.342318	+	0.197637i	0.661296	−	0.750125i	$-0.270007\pi$
$11$	3.76549	+	2.17401i	0.342318	+	0.197637i	−0.318979	+	0.947762i	$0.603340\pi$
$12$	2.81202	−	4.94038i	0.234335	−	0.411698i
$13$	4.76059	+	4.76059i	0.366199	+	0.366199i	0.866089	−	0.499890i	$-0.166626\pi$
$13$	4.76059	+	4.76059i	0.366199	+	0.366199i	−0.499890	+	0.866089i	$0.666626\pi$
$14$	1.78675	+	9.99794i	0.127625	+	0.714139i
$15$	−9.90434	+	11.2652i	−0.660289	+	0.751011i
$16$	−2.41499	−	4.18289i	−0.150937	−	0.261431i
$17$	19.0658	−	5.10867i	1.12152	−	0.300510i	0.350021	−	0.936742i	$-0.386174\pi$
$17$	19.0658	−	5.10867i	1.12152	−	0.300510i	0.771498	+	0.636231i	$0.219508\pi$
$18$	−12.6538	−	3.22456i	−0.702987	−	0.179142i
$19$	−12.5949	−	21.8150i	−0.662890	−	1.14816i	−0.979853	−	0.199721i	$-0.935996\pi$
$19$	−12.5949	−	21.8150i	−0.662890	−	1.14816i	0.316963	−	0.948438i	$-0.397337\pi$
$20$	−2.97900	−	8.99383i	−0.148950	−	0.449691i
$21$	−18.9568	+	9.03552i	−0.902704	+	0.430263i
$22$	4.46083	+	4.46083i	0.202765	+	0.202765i
$23$	8.21961	−	30.6760i	0.357374	−	1.33374i	−0.520095	−	0.854108i	$-0.674104\pi$
$23$	8.21961	−	30.6760i	0.357374	−	1.33374i	0.877470	−	0.479632i	$-0.159230\pi$
$24$	18.0317	−	18.2545i	0.751321	−	0.760605i
$25$	2.89619	+	24.8317i	0.115848	+	0.993267i
$26$	4.88411	+	8.45952i	0.187850	+	0.325366i
$27$	−0.497321	−	26.9954i	−0.0184193	−	0.999830i
$28$	1.12549	−	13.2163i	0.0401962	−	0.472009i
$29$	28.8306			0.994158			0.497079	−	0.867705i	$-0.334406\pi$
$29$	28.8306			0.994158			0.497079	+	0.867705i	$0.334406\pi$
$30$	−18.1109	+	12.0685i	−0.603698	+	0.402283i
$31$	−12.3444	−	7.12704i	−0.398206	−	0.229904i	0.287504	−	0.957780i	$-0.407175\pi$
$31$	−12.3444	−	7.12704i	−0.398206	−	0.229904i	−0.685710	+	0.727875i	$0.740508\pi$
$32$	7.04085	+	26.2768i	0.220027	+	0.821151i
$33$	−6.45254	+	11.3363i	−0.195532	+	0.343525i
$34$	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	−0.524750	−	0.851257i	$-0.675841\pi$
$37$	13.1470	−	49.0654i	0.355325	−	1.32609i	0.880075	−	0.474835i	$-0.157492\pi$
$38$	−9.45934	−	35.3027i	−0.248930	−	0.929019i
$39$	−14.1938	+	14.3692i	−0.363944	+	0.368441i
$40$	−2.48127	−	42.6925i	−0.0620317	−	1.06731i
$41$	−1.56196			−0.0380967			−0.0190483	−	0.999819i	$-0.506064\pi$
$41$	−1.56196			−0.0380967			−0.0190483	+	0.999819i	$0.506064\pi$
$42$	−29.9604	+	5.54431i	−0.713342	+	0.132007i
$43$	−46.2033	+	46.2033i	−1.07449	+	1.07449i	−0.0775021	+	0.996992i	$0.524694\pi$
$43$	−46.2033	+	46.2033i	−1.07449	+	1.07449i	−0.996992	+	0.0775021i	$0.975306\pi$
$44$	−4.11946	−	7.13512i	−0.0936242	−	0.162162i
$45$	−33.9773	−	29.5049i	−0.755051	−	0.655666i
$46$	23.0391	−	39.9048i	0.500849	−	0.867496i
$47$	3.56182	−	13.2929i	0.0757834	−	0.282828i	−0.917626	−	0.397444i	$-0.869897\pi$
$47$	3.56182	−	13.2929i	0.0757834	−	0.282828i	0.993410	+	0.114616i	$0.0365639\pi$
$48$	12.5040	−	7.32189i	0.260499	−	0.152539i
$49$	−31.3227	+	37.6814i	−0.639239	+	0.769008i
$50$	−5.26592	+	35.8884i	−0.105318	+	0.717768i
$51$	15.6769	+	57.1023i	0.307391	+	1.11965i
$52$	−3.30181	−	12.3225i	−0.0634963	−	0.236971i
$53$	−33.7582	+	9.04547i	−0.636946	+	0.170669i	−0.562820	−	0.826580i	$-0.690284\pi$
$53$	−33.7582	+	9.04547i	−0.636946	+	0.170669i	−0.0741265	+	0.997249i	$0.523617\pi$
$54$	9.44040	−	38.0200i	0.174822	−	0.704074i
$55$	6.83568	+	20.6375i	0.124285	+	0.375227i
$56$	20.3468	−	56.3069i	0.363335	−	1.00548i
$57$	65.2119	−	38.1859i	1.14407	−	0.669927i
$58$	40.4052	+	10.8265i	0.696641	+	0.186664i
$59$	54.4737	+	31.4504i	0.923283	+	0.533058i	0.884681	−	0.466197i	$-0.154376\pi$
$59$	54.4737	+	31.4504i	0.923283	+	0.533058i	0.0386020	+	0.999255i	$0.487710\pi$
$60$	26.9261	−	9.10249i	0.448768	−	0.151708i
$61$	9.31520	−	5.37814i	0.152708	−	0.0881662i	−0.421699	−	0.906736i	$-0.638566\pi$
$61$	9.31520	−	5.37814i	0.152708	−	0.0881662i	0.574407	+	0.818570i	$0.305233\pi$
$62$	−14.6239	−	14.6239i	−0.235869	−	0.235869i
$63$	−27.4552	−	56.7028i	−0.435798	−	0.900045i
$64$			58.7901i			0.918595i
$65$	1.95315	+	33.6057i	0.0300485	+	0.517012i
$66$	−13.3001	+	13.4644i	−0.201516	+	0.204006i
$67$	−112.138	+	30.0473i	−1.67370	+	0.448467i	−0.966105	−	0.258150i	$-0.916887\pi$
$67$	−112.138	+	30.0473i	−1.67370	+	0.448467i	−0.707597	+	0.706617i	$0.750221\pi$
$68$	−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	$0.981064\pi$
$72$	55.0947	+	53.7579i	0.765204	+	0.746637i
$73$	26.0040	−	6.96775i	0.356219	−	0.0954487i	−0.0762714	−	0.997087i	$-0.524302\pi$
$73$	26.0040	−	6.96775i	0.356219	−	0.0954487i	0.432491	+	0.901638i	$0.357635\pi$
$74$	36.8503	−	63.8266i	0.497977	−	0.862521i
$75$	−74.4403	+	9.14583i	−0.992537	+	0.121944i
$76$			47.7314i			0.628045i
$77$	−2.58258	+	30.3264i	−0.0335401	+	0.393849i
$78$	−25.2881	+	14.8079i	−0.324207	+	0.189845i
$79$	−59.9822	+	34.6307i	−0.759268	+	0.438364i	−0.829033	−	0.559200i	$-0.811108\pi$
$79$	−59.9822	+	34.6307i	−0.759268	+	0.438364i	0.0697650	+	0.997563i	$0.477775\pi$
$80$	4.88646	−	23.6504i	0.0610807	−	0.295630i
$81$	80.9756	−	1.98920i	0.999698	−	0.0245580i
$82$	−2.18904	−	0.586552i	−0.0266956	−	0.00715307i
$83$	11.5754	−	11.5754i	0.139463	−	0.139463i	−0.633929	−	0.773391i	$-0.718559\pi$
$83$	11.5754	−	11.5754i	0.139463	−	0.139463i	0.773391	+	0.633929i	$0.218559\pi$
$84$	39.6687	+	3.13297i	0.472247	+	0.0372972i
$85$	88.1889	+	44.3038i	1.03752	+	0.521221i
$86$	−82.1027	+	47.4020i	−0.954683	+	0.551186i
$87$	0.531066	+	86.4902i	0.00610421	+	0.994140i
$88$	−9.62501	−	35.9210i	−0.109375	−	0.408194i
$89$	−58.5647	+	33.8123i	−0.658030	+	0.379914i	−0.791526	−	0.611135i	$-0.790713\pi$
$89$	−58.5647	+	33.8123i	−0.658030	+	0.379914i	0.133496	+	0.991049i	$0.457380\pi$
$90$	−36.5384	−	54.1095i	−0.405982	−	0.601216i
$91$	−16.0161	+	44.3225i	−0.176001	+	0.487060i
$92$	−42.5520	+	42.5520i	−0.462521	+	0.462521i
$93$	21.1533	−	37.1638i	0.227455	−	0.399610i
$94$	9.98356	−	17.2920i	0.106208	−	0.183958i
$95$	25.4843	−	123.344i	0.268256	−	1.29836i
$96$	−78.6993	+	21.6062i	−0.819784	+	0.225064i
$97$	124.503	−	124.503i	1.28354	−	1.28354i	0.344901	−	0.938639i	$-0.387913\pi$
$97$	124.503	−	124.503i	1.28354	−	1.28354i	0.938639	−	0.344901i	$-0.112087\pi$
$98$	−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	$-0.934380\pi$
$101$	−31.5264	+	54.6053i	−0.312143	+	0.540647i	0.666683	+	0.745341i	$0.267713\pi$
$102$	0.527529	+	85.9141i	0.00517186	+	0.842295i
$103$	21.5705	−	80.5022i	0.209422	−	0.781574i	−0.778634	−	0.627479i	$-0.784087\pi$
$103$	21.5705	−	80.5022i	0.209422	−	0.781574i	0.988056	−	0.154096i	$-0.0492464\pi$
$104$		−	57.5824i		−	0.553677i
$105$	−100.836	−	29.2756i	−0.960345	−	0.278815i
$106$	−50.7078			−0.478375
$107$	−19.8432	−	5.31697i	−0.185450	−	0.0496913i	0.164899	−	0.986311i	$-0.447270\pi$
$107$	−19.8432	−	5.31697i	−0.185450	−	0.0496913i	−0.350349	+	0.936619i	$0.613937\pi$
$108$	−24.7603	+	44.7708i	−0.229262	+	0.414545i
$109$	−0.918436	−	0.530259i	−0.00842602	−	0.00486476i	0.495781	−	0.868448i	$-0.334882\pi$
$109$	−0.918436	−	0.530259i	−0.00842602	−	0.00486476i	−0.504207	+	0.863583i	$0.668215\pi$
$110$	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	$-0.150528\pi$
$113$	49.1305	+	49.1305i	0.434783	+	0.434783i	−0.455469	+	0.890252i	$0.650528\pi$
$114$	105.732	−	29.0278i	0.927473	−	0.254630i
$115$	132.678	−	87.2406i	1.15373	−	0.758614i
$116$	−47.3112	−	27.3151i	−0.407855	−	0.235475i
$117$	−43.3682	−	42.3159i	−0.370669	−	0.361675i
$118$	64.5328	+	64.5328i	0.546888	+	0.546888i
$119$	89.0576	+	105.638i	0.748384	+	0.887713i
$120$	128.029	−	8.23007i	1.06691	−	0.0685839i
$121$	−51.0474	−	88.4166i	−0.421879	−	0.730716i
$122$	15.0746	−	4.03922i	0.123562	−	0.0331084i
$123$	−0.0287717	−	4.68580i	−0.000233917	−	0.0380960i
$124$	13.5048	+	23.3910i	0.108910	+	0.188637i
$125$	−71.7350	+	102.367i	−0.573880	+	0.818940i
$126$	−17.1845	−	89.7772i	−0.136385	−	0.712518i
$127$	−72.9239	−	72.9239i	−0.574204	−	0.574204i	0.359096	−	0.933300i	$-0.383085\pi$
$127$	−72.9239	−	72.9239i	−0.574204	−	0.574204i	−0.933300	+	0.359096i	$0.883085\pi$
$128$	6.08643	−	22.7149i	0.0475503	−	0.177460i
$129$	−139.458	−	137.756i	−1.08107	−	1.06788i
$130$	−9.88243	+	47.8308i	−0.0760187	+	0.367930i
$131$	−48.6464	−	84.2581i	−0.371347	−	0.643192i	0.618426	−	0.785843i	$-0.287771\pi$
$131$	−48.6464	−	84.2581i	−0.371347	−	0.643192i	−0.989773	+	0.142651i	$0.954437\pi$
$132$	21.3291	−	12.4896i	0.161584	−	0.0946181i
$133$	100.804	−	144.673i	0.757924	−	1.08777i
$134$	−168.441			−1.25702
$135$	87.8873	−	102.474i	0.651017	−	0.759063i
$136$	−146.203	−	84.4104i	−1.07502	−	0.620664i
$137$	−56.4619	−	210.719i	−0.412131	−	1.53809i	−0.790514	−	0.612443i	$-0.790187\pi$
$137$	−56.4619	−	210.719i	−0.412131	−	1.53809i	0.378384	−	0.925649i	$-0.376480\pi$
$138$	120.137	+	68.3808i	0.870555	+	0.495513i
$139$	−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
$144$	22.1956	+	37.3763i	0.154136	+	0.259557i
$145$	107.674	+	95.8456i	0.742580	+	0.661004i
$146$	39.0603			0.267537
$147$	−113.619	−	93.2723i	−0.772919	−	0.634505i
$148$	−68.0606	+	68.0606i	−0.459869	+	0.459869i
$149$	−88.8916	−	153.965i	−0.596588	−	1.03332i	−0.993321	−	0.115386i	$-0.963189\pi$
$149$	−88.8916	−	153.965i	−0.596588	−	1.03332i	0.396733	−	0.917934i	$-0.370144\pi$
$150$	−107.760	−	15.1364i	−0.718401	−	0.100909i
$151$	−22.5608	+	39.0764i	−0.149409	+	0.258784i	−0.931009	−	0.364996i	$-0.881070\pi$
$151$	−22.5608	+	39.0764i	−0.149409	+	0.258784i	0.781600	+	0.623780i	$0.214404\pi$
$152$	−55.7616	+	208.105i	−0.366853	+	1.36911i
$153$	−171.015	+	48.0817i	−1.11774	+	0.314260i
$154$	−15.0076	+	41.5316i	−0.0974521	+	0.269686i
$155$	−22.4094	−	67.6556i	−0.144577	−	0.436488i
$156$	36.9060	−	10.1322i	0.236577	−	0.0649501i
$157$	44.8638	+	167.434i	0.285757	+	1.06646i	0.948284	+	0.317422i	$0.102817\pi$
$157$	44.8638	+	167.434i	0.285757	+	1.06646i	−0.662528	+	0.749038i	$0.730516\pi$
$158$	−97.0677	+	26.0092i	−0.614352	+	0.164615i
$159$	−27.7577	−	101.106i	−0.174577	−	0.635886i
$160$	−61.0601	+	121.543i	−0.381626	+	0.759646i
$161$	218.840	−	39.1092i	1.35925	−	0.242914i
$162$	114.232	+	27.6203i	0.705134	+	0.170496i
$163$	47.7722	+	12.8005i	0.293081	+	0.0785308i	0.402364	−	0.915480i	$-0.368189\pi$
$163$	47.7722	+	12.8005i	0.293081	+	0.0785308i	−0.109283	+	0.994011i	$0.534855\pi$
$164$	2.56319	+	1.47986i	0.0156292	+	0.00902353i
$165$	−61.7853	+	20.8868i	−0.374456	+	0.126587i
$166$	20.5694	−	11.8757i	0.123912	−	0.0715406i
$167$	2.27761	+	2.27761i	0.0136384	+	0.0136384i	0.713893	−	0.700255i	$-0.246930\pi$
$167$	2.27761	+	2.27761i	0.0136384	+	0.0136384i	−0.700255	+	0.713893i	$0.746930\pi$
$168$	169.292	+	60.0019i	1.00769	+	0.357154i
$169$		−	123.674i		−	0.731796i
$170$	106.957	+	95.2072i	0.629158	+	0.560043i
$171$	115.757	+	194.928i	0.676939	+	1.13993i
$172$	119.594	−	32.0452i	0.695316	−	0.186309i
$173$	324.701	+	87.0033i	1.87688	+	0.502909i	0.999743	+	0.0226723i	$0.00721745\pi$
$173$	324.701	+	87.0033i	1.87688	+	0.502909i	0.877139	+	0.480237i	$0.159449\pi$
$174$	−31.7347	+	121.413i	−0.182383	+	0.697774i
$175$	−148.755	+	92.1783i	−0.850031	+	0.526733i
$176$		−	21.0009i		−	0.119323i
$177$	−93.3460	+	163.997i	−0.527379	+	0.926538i
$178$	−94.7738	+	25.3946i	−0.532437	+	0.142666i
$179$	−122.781	+	212.663i	−0.685927	+	1.18806i	0.287217	+	0.957865i	$0.407270\pi$
$179$	−122.781	+	212.663i	−0.685927	+	1.18806i	−0.973144	+	0.230195i	$0.926063\pi$
$180$	27.8029	+	80.6091i	0.154461	+	0.447828i
$181$		−	92.0664i		−	0.508654i	−0.967118	−	0.254327i	$-0.918146\pi$
$181$		−	92.0664i		−	0.508654i	0.967118	−	0.254327i	$-0.0818540\pi$
$182$	−39.0901	+	56.1021i	−0.214781	+	0.308253i
$183$	16.3057	+	27.8460i	0.0891021	+	0.152164i
$184$	−235.234	+	135.812i	−1.27844	+	0.738110i
$185$	212.215	−	139.539i	1.14711	−	0.754264i
$186$	43.6015	−	44.1403i	0.234417	−	0.237313i
$187$	82.8986	+	22.2126i	0.443308	+	0.118784i
$188$	−18.4391	+	18.4391i	−0.0980805	+	0.0980805i
$189$	169.600	−	83.4087i	0.897352	−	0.441316i
$190$	82.0339	−	163.293i	0.431757	−	0.859435i
$191$	−39.7108	+	22.9270i	−0.207910	+	0.120037i	−0.600340	−	0.799745i	$-0.704968\pi$
$191$	−39.7108	+	22.9270i	−0.207910	+	0.120037i	0.392430	+	0.919782i	$0.371635\pi$
$192$	−176.367	+	1.08293i	−0.918577	+	0.00564024i
$193$	70.1653	+	261.860i	0.363551	+	1.35679i	0.869375	+	0.494153i	$0.164522\pi$
$193$	70.1653	+	261.860i	0.363551	+	1.35679i	−0.505824	+	0.862637i	$0.668812\pi$
$194$	221.241	−	127.734i	1.14042	−	0.658421i
$195$	−100.779	+	6.47837i	−0.516817	+	0.0332224i
$196$	87.1014	−	32.1592i	0.444395	−	0.164077i
$197$	−69.8883	+	69.8883i	−0.354763	+	0.354763i	−0.861878	−	0.507115i	$-0.830712\pi$
$197$	−69.8883	+	69.8883i	−0.354763	+	0.354763i	0.507115	+	0.861878i	$0.330712\pi$
$198$	−40.6375	−	39.6514i	−0.205240	−	0.200260i
$199$	−123.211	+	213.408i	−0.619153	+	1.07240i	0.370488	+	0.928837i	$0.379190\pi$
$199$	−123.211	+	213.408i	−0.619153	+	1.07240i	−0.989641	+	0.143567i	$0.954143\pi$
$200$	132.662	−	167.693i	0.663309	−	0.838465i
$201$	−92.2058	−	335.854i	−0.458735	−	1.67092i
$202$	−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
$207$	−70.5807	+	276.972i	−0.340969	+	1.33803i
$208$	8.41624	−	31.4098i	0.0404627	−	0.151009i
$209$		−	109.526i		−	0.524047i
$210$	−130.325	−	78.8950i	−0.620596	−	0.375690i
$211$	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
$213$	−25.3267	+	0.155511i	−0.118905	+	0.000730099i
$214$	−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
$219$	21.3819	+	77.8822i	0.0976341	+	0.355626i
$220$	8.33526	−	40.3426i	0.0378875	−	0.183375i
$221$	115.085	+	66.4443i	0.520746	+	0.300653i
$222$	192.155	+	109.373i	0.865563	+	0.492672i
$223$	−206.164	−	206.164i	−0.924500	−	0.924500i	0.0728430	−	0.997343i	$-0.476793\pi$
$223$	−206.164	−	206.164i	−0.924500	−	0.924500i	−0.997343	+	0.0728430i	$0.976793\pi$
$224$	−145.592	+	122.741i	−0.649963	+	0.547949i
$225$	−28.8082	−	223.148i	−0.128036	−	0.991769i
$226$	50.4052	+	87.3045i	0.223032	+	0.386303i
$227$	363.549	−	97.4127i	1.60154	−	0.429131i	0.656031	−	0.754734i	$-0.272234\pi$
$227$	363.549	−	97.4127i	1.60154	−	0.429131i	0.945506	+	0.325603i	$0.105567\pi$
$228$	−143.192	+	0.879224i	−0.628034	+	0.00385625i
$229$	85.7839	+	148.582i	0.374602	+	0.648830i	0.990267	−	0.139178i	$-0.0444459\pi$
$229$	85.7839	+	148.582i	0.374602	+	0.648830i	−0.615665	+	0.788008i	$0.711113\pi$
$230$	218.705	−	72.4411i	0.950893	−	0.314961i
$231$	−91.0249	−	7.18899i	−0.394047	−	0.0311212i
$232$	−174.362	−	174.362i	−0.751561	−	0.751561i
$233$	30.6478	−	114.379i	0.131535	−	0.490897i	−0.868453	−	0.495772i	$-0.834885\pi$
$233$	30.6478	−	114.379i	0.131535	−	0.490897i	0.999988	+	0.00487507i	$0.00155179\pi$
$234$	−44.8886	−	75.5902i	−0.191832	−	0.323035i
$235$	57.4938	−	37.8041i	0.244655	−	0.160869i
$236$	−59.5944	−	103.221i	−0.252519	−	0.437375i
$237$	−104.995	−	179.305i	−0.443017	−	0.756562i
$238$	85.1421	+	181.491i	0.357740	+	0.762568i
$239$	−283.218			−1.18501			−0.592507	−	0.805566i	$-0.701862\pi$
$239$	−283.218			−1.18501			−0.592507	+	0.805566i	$0.701862\pi$
$240$	71.0399	+	14.2235i	0.296000	+	0.0592644i
$241$	−71.5098	−	41.2862i	−0.296721	−	0.171312i	0.344248	−	0.938879i	$-0.388134\pi$
$241$	−71.5098	−	41.2862i	−0.296721	−	0.171312i	−0.640969	+	0.767567i	$0.721467\pi$
$242$	−38.3388	−	143.083i	−0.158425	−	0.591250i
$243$	7.45907	+	242.885i	0.0306958	+	0.999529i
$244$	−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
$249$	34.9388	+	34.5123i	0.140316	+	0.138604i
$250$	−138.976	+	116.527i	−0.555902	+	0.466107i
$251$	56.5975			0.225488			0.112744	−	0.993624i	$-0.464036\pi$
$251$	56.5975			0.225488			0.112744	+	0.993624i	$0.464036\pi$
$252$	−8.66802	+	119.062i	−0.0343969	+	0.472467i
$253$	97.6408	−	97.6408i	0.385932	−	0.385932i
$254$	−74.8160	−	129.585i	−0.294551	−	0.510178i
$255$	−131.284	+	265.378i	−0.514841	+	1.04070i
$256$	134.640	−	233.203i	0.525938	−	0.910951i
$257$	−5.72610	+	21.3701i	−0.0222806	+	0.0831522i	−0.976171	−	0.217003i	$-0.930372\pi$
$257$	−5.72610	+	21.3701i	−0.0222806	+	0.0831522i	0.953890	+	0.300155i	$0.0970385\pi$
$258$	−143.716	−	245.430i	−0.557038	−	0.951281i
$259$	350.028	−	62.5541i	1.35146	−	0.241521i
$260$	28.6341	−	56.9977i	0.110131	−	0.219222i
$261$	−259.456	+	3.18634i	−0.994084	+	0.0122082i
$262$	−36.5356	−	136.353i	−0.139449	−	0.520431i
$263$	189.972	−	50.9027i	0.722325	−	0.193546i	0.121116	−	0.992638i	$-0.461353\pi$
$263$	189.972	−	50.9027i	0.722325	−	0.193546i	0.601209	+	0.799092i	$0.294686\pi$
$264$	107.584	−	29.5362i	0.407514	−	0.111879i
$265$	−156.148	−	78.4447i	−0.589239	−	0.296018i
$266$	195.602	−	164.901i	0.735344	−	0.619929i
$267$	−102.514	−	175.068i	−0.383947	−	0.655685i
$268$	212.487	+	56.9357i	0.792862	+	0.212447i
$269$	140.489	+	81.1111i	0.522263	+	0.301528i	0.737860	−	0.674954i	$-0.235837\pi$
$269$	140.489	+	81.1111i	0.522263	+	0.301528i	−0.215597	+	0.976482i	$0.569170\pi$
$270$	161.652	−	110.610i	0.598712	−	0.409666i
$271$	−250.756	+	144.774i	−0.925299	+	0.534221i	−0.885322	−	0.464979i	$-0.846062\pi$
$271$	−250.756	+	144.774i	−0.925299	+	0.534221i	−0.0399771	+	0.999201i	$0.512728\pi$
$272$	−67.4129	−	67.4129i	−0.247841	−	0.247841i
$273$	−133.260	−	47.2310i	−0.488131	−	0.173007i
$274$		−	316.518i		−	1.15518i
$275$	−43.0787	+	99.7999i	−0.156650	+	0.362909i
$276$	−128.437	−	126.870i	−0.465353	−	0.459673i
$277$	−32.8919	+	8.81335i	−0.118743	+	0.0318171i	−0.317701	−	0.948191i	$-0.602911\pi$
$277$	−32.8919	+	8.81335i	−0.118743	+	0.0318171i	0.198958	+	0.980008i	$0.436244\pi$
$278$	−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	$0.700033\pi$
$282$	52.0590	+	29.6316i	0.184606	+	0.105077i
$283$	287.958	−	77.1581i	1.01752	−	0.272643i	0.288751	−	0.957404i	$-0.406760\pi$
$283$	287.958	−	77.1581i	1.01752	−	0.272643i	0.728768	+	0.684761i	$0.240093\pi$
$284$	7.99863	−	13.8540i	0.0281642	−	0.0487818i
$285$	370.494	+	74.1796i	1.29998	+	0.260279i
$286$			42.4724i			0.148505i
$287$	−4.64370	−	9.89863i	−0.0161801	−	0.0344900i
$288$	−66.2670	−	235.695i	−0.230094	−	0.818387i
$289$	87.1261	−	50.3023i	0.301474	−	0.174056i
$290$	114.910	+	174.759i	0.396240	+	0.602616i
$291$	375.796	+	371.210i	1.29140	+	1.27563i
$292$	−49.2742	−	13.2030i	−0.168747	−	0.0452157i
$293$	−124.246	+	124.246i	−0.424047	+	0.424047i	−0.886594	−	0.462548i	$-0.846935\pi$
$293$	−124.246	+	124.246i	−0.424047	+	0.424047i	0.462548	+	0.886594i	$0.346935\pi$
$294$	−124.208	−	173.385i	−0.422475	−	0.589743i
$295$	98.8887	+	298.553i	0.335216	+	1.01204i
$296$	−376.249	+	217.228i	−1.27111	+	0.733877i
$297$	56.8156	−	102.732i	0.191298	−	0.345900i
$298$	−66.7615	−	249.157i	−0.224032	−	0.836099i
$299$	185.166	−	106.906i	0.619285	−	0.357544i
$300$	130.822	+	55.5190i	0.436073	+	0.185063i
$301$	−430.165	−	155.442i	−1.42912	−	0.516419i
$302$	−46.2923	+	46.2923i	−0.153286	+	0.153286i
$303$	−164.394	−	93.5716i	−0.542553	−	0.308817i
$304$	−60.8333	+	105.366i	−0.200109	+	0.346600i
$305$	52.6689	+	10.8820i	0.172685	+	0.0356788i
$306$	−257.728	+	3.16512i	−0.842248	+	0.0103435i
$307$	−311.230	+	311.230i	−1.01378	+	1.01378i	−0.0138731	+	0.999904i	$0.504416\pi$
$307$	−311.230	+	311.230i	−1.01378	+	1.01378i	−0.999904	+	0.0138731i	$0.995584\pi$
$308$	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	$-0.898414\pi$
$311$	−63.1444	+	109.369i	−0.203037	+	0.351670i	0.746469	+	0.665421i	$0.231748\pi$
$312$	172.744	−	1.06068i	0.553666	−	0.00339962i
$313$	−6.36092	+	23.7393i	−0.0203224	+	0.0758443i	−0.975342	−	0.220697i	$-0.929167\pi$
$313$	−6.36092	+	23.7393i	−0.0203224	+	0.0758443i	0.955020	+	0.296542i	$0.0958334\pi$
$314$			251.501i			0.800958i
$315$	85.9676	−	303.042i	0.272913	−	0.962039i
$316$	131.241			0.415321
$317$	201.189	+	53.9084i	0.634666	+	0.170058i	0.561786	−	0.827283i	$-0.310114\pi$
$317$	201.189	+	53.9084i	0.634666	+	0.170058i	0.0728796	+	0.997341i	$0.476781\pi$
$318$	−0.934049	−	152.120i	−0.00293726	−	0.478366i
$319$	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
$324$	−134.766	−	73.4548i	−0.415944	−	0.226712i
$325$	−104.426	+	132.001i	−0.321310	+	0.406157i
$326$	62.1443	+	35.8790i	0.190627	+	0.110058i
$327$	1.57383	−	2.76502i	0.00481293	−	0.00845573i
$328$	9.44647	+	9.44647i	0.0288002	+	0.0288002i
$329$	94.8303	−	16.9473i	0.288238	−	0.0515115i
$330$	−94.4336	+	6.07045i	−0.286162	+	0.0183953i
$331$	166.447	+	288.295i	0.502861	+	0.870981i	0.999995	+	0.00330721i	$0.00105272\pi$
$331$	166.447	+	288.295i	0.502861	+	0.870981i	−0.497133	+	0.867674i	$0.665614\pi$
$332$	−29.9622	+	8.02836i	−0.0902477	+	0.0241818i
$333$	−112.892	+	443.008i	−0.339014	+	1.33036i
$334$	2.33670	+	4.04729i	0.00699612	+	0.0121176i
$335$	−518.694	−	260.578i	−1.54834	−	0.777845i
$336$	83.5751	+	57.4734i	0.248735	+	0.171052i
$337$	68.0561	+	68.0561i	0.201947	+	0.201947i	0.800834	−	0.598887i	$-0.204390\pi$
$337$	68.0561	+	68.0561i	0.201947	+	0.201947i	−0.598887	+	0.800834i	$0.704390\pi$
$338$	46.4422	−	173.325i	0.137403	−	0.512795i
$339$	−146.484	+	148.294i	−0.432106	+	0.437445i
$340$	−102.744	−	156.256i	−0.302187	−	0.459577i
$341$	−30.9885	−	53.6736i	−0.0908753	−	0.157401i
$342$	89.0293	+	316.655i	0.260320	+	0.925892i
$343$	−331.920	−	86.4751i	−0.967698	−	0.252114i
$344$	558.858			1.62459
$345$	264.161	+	396.421i	0.765683	+	1.14905i
$346$	422.386	+	243.865i	1.22077	+	0.704811i
$347$	−142.342	−	531.228i	−0.410208	−	1.53092i	−0.794244	−	0.607598i	$-0.792133\pi$
$347$	−142.342	−	531.228i	−0.410208	−	1.53092i	0.384037	−	0.923318i	$-0.374534\pi$
$348$	81.0723	−	142.434i	0.232966	−	0.409293i
$349$	−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	−0.731735	−	0.681589i	$-0.761289\pi$
$353$	−154.906	−	578.119i	−0.438828	−	1.63773i	0.292907	−	0.956141i	$-0.405377\pi$
$354$	−192.406	+	194.784i	−0.543520	+	0.550236i
$355$	−28.0663	+	31.5300i	−0.0790599	+	0.0888168i
$356$	128.140			0.359944
$357$	−315.267	+	269.114i	−0.883101	+	0.753820i
$358$	−251.933	+	251.933i	−0.703724	+	0.703724i
$359$	−24.3885	−	42.2421i	−0.0679345	−	0.117666i	0.830057	−	0.557678i	$-0.188308\pi$
$359$	−24.3885	−	42.2421i	−0.0679345	−	0.117666i	−0.897992	+	0.440012i	$0.854974\pi$
$360$	27.0481	+	383.929i	0.0751335	+	1.06647i
$361$	−136.764	+	236.882i	−0.378847	+	0.656182i
$362$	34.5730	−	129.028i	0.0955055	−	0.356431i
$363$	264.305	−	154.768i	0.728112	−	0.426358i
$364$	68.2752	−	57.5592i	0.187569	−	0.158130i
$365$	120.281	+	60.4262i	0.329538	+	0.165551i
$366$	12.3951	+	45.1485i	0.0338664	+	0.123356i
$367$	39.4899	+	147.378i	0.107602	+	0.401575i	0.998627	−	0.0523778i	$-0.0166800\pi$
$367$	39.4899	+	147.378i	0.107602	+	0.401575i	−0.891026	+	0.453953i	$0.850013\pi$
$368$	−148.165	+	39.7006i	−0.402622	+	0.107882i
$369$	14.0566	−	0.172627i	0.0380938	−	0.000467824i
$370$	349.813	−	115.868i	0.945441	−	0.313155i
$371$	−157.686	−	187.043i	−0.425031	−	0.504160i
$372$	−69.9230	+	40.9445i	−0.187965	+	0.110066i
$373$	−232.471	−	62.2905i	−0.623247	−	0.166999i	−0.0666436	−	0.997777i	$-0.521229\pi$
$373$	−232.471	−	62.2905i	−0.623247	−	0.166999i	−0.556603	+	0.830778i	$0.687896\pi$
$374$	107.838	+	62.2605i	0.288338	+	0.166472i
$375$	−308.418	−	213.315i	−0.822448	−	0.568840i
$376$	−101.934	+	58.8518i	−0.271102	+	0.156521i
$377$	137.251	+	137.251i	0.364060	+	0.364060i
$378$	269.010	−	53.2062i	0.711667	−	0.140757i
$379$			35.3522i			0.0932776i	0.998912	+	0.0466388i	$0.0148510\pi$
$379$			35.3522i			0.0932776i	−0.998912	+	0.0466388i	$0.985149\pi$
$380$	−158.680	+	178.263i	−0.417580	+	0.469114i
$381$	217.424	−	220.111i	0.570668	−	0.577719i
$382$	−64.2630	+	17.2192i	−0.168228	+	0.0450765i
$383$	265.111	+	71.0364i	0.692197	+	0.185474i	0.587733	−	0.809055i	$-0.300021\pi$
$383$	265.111	+	71.0364i	0.692197	+	0.185474i	0.104464	+	0.994529i	$0.466687\pi$
$384$	68.2555	+	17.8405i	0.177749	+	0.0464597i
$385$	−110.463	+	104.675i	−0.286918	+	0.271882i
$386$			393.338i			1.01901i
$387$	410.692	−	420.904i	1.06122	−	1.08761i
$388$	−322.270	+	86.3519i	−0.830592	+	0.222556i
$389$	−234.816	+	406.714i	−0.603641	+	1.04554i	0.388624	+	0.921396i	$0.372950\pi$
$389$	−234.816	+	406.714i	−0.603641	+	1.04554i	−0.992265	+	0.124140i	$0.960383\pi$
$390$	−143.672	−	28.7657i	−0.368389	−	0.0737581i
$391$		−	626.855i		−	1.60321i
$392$	417.324	−	38.4562i	1.06460	−	0.0981025i
$393$	251.873	−	147.489i	0.640899	−	0.375289i
$394$	−124.191	+	71.7016i	−0.315205	+	0.181984i
$395$	−339.144	−	70.0712i	−0.858592	−	0.177396i
$396$	37.8610	+	63.7560i	0.0956085	+	0.161000i
$397$	−96.4334	−	25.8392i	−0.242905	−	0.0650862i	0.135312	−	0.990803i	$-0.456796\pi$
$397$	−96.4334	−	25.8392i	−0.242905	−	0.0650862i	−0.378218	+	0.925717i	$0.623463\pi$
$398$	−252.816	+	252.816i	−0.635217	+	0.635217i
$399$	435.869	+	299.741i	1.09240	+	0.751230i
$400$	96.8739	−	72.0828i	0.242185	−	0.180207i
$401$	−331.371	+	191.317i	−0.826362	+	0.477100i	−0.852605	−	0.522556i	$-0.824979\pi$
$401$	−331.371	+	191.317i	−0.826362	+	0.477100i	0.0262437	+	0.999656i	$0.491645\pi$
$402$	−3.10273	−	505.314i	−0.00771823	−	1.25700i
$403$	−24.8377	−	92.6955i	−0.0616320	−	0.230014i
$404$	103.470	−	59.7384i	0.256114	−	0.147867i
$405$	309.034	+	261.769i	0.763046	+	0.646344i
$406$	51.5130	+	288.247i	0.126879	+	0.709967i
$407$	156.174	−	156.174i	0.383719	−	0.383719i
$408$	250.533	−	440.156i	0.614052	−	1.07881i
$409$	199.716	−	345.918i	0.488302	−	0.845764i	−0.511607	−	0.859219i	$-0.670950\pi$
$409$	199.716	−	345.918i	0.488302	−	0.845764i	0.999909	+	0.0134551i	$0.00428304\pi$
$410$	−6.22549	−	9.46795i	−0.0151841	−	0.0230925i
$411$	631.104	−	173.264i	1.53553	−	0.421567i
$412$	−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
$417$	−2.11586	−	344.591i	−0.00507400	−	0.826358i
$418$	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	$-0.0715408\pi$
$420$	137.736	+	143.577i	0.327943	+	0.341850i
$421$	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
$423$	−30.5849	+	120.021i	−0.0723046	+	0.283737i
$424$	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
$429$	−84.6855	+	23.2496i	−0.197402	+	0.0541950i
$430$	−464.216	−	95.9125i	−1.07957	−	0.223052i
$431$	−220.378	−	127.235i	−0.511317	−	0.295209i	0.222058	−	0.975033i	$-0.428723\pi$
$431$	−220.378	−	127.235i	−0.511317	−	0.295209i	−0.733375	+	0.679824i	$0.762056\pi$
$432$	−111.718	+	67.2740i	−0.258606	+	0.155727i
$433$	510.335	+	510.335i	1.17860	+	1.17860i	0.980100	+	0.198504i	$0.0636082\pi$
$433$	510.335	+	510.335i	1.17860	+	1.17860i	0.198504	+	0.980100i	$0.436392\pi$
$434$	49.1994	−	136.153i	0.113363	−	0.313716i
$435$	−285.548	+	324.782i	−0.656432	+	0.746624i
$436$	1.00477	+	1.74032i	0.00230452	+	0.00399155i
$437$	−772.723	+	207.051i	−1.76825	+	0.473800i
$438$	0.719500	+	117.179i	0.00164270	+	0.267531i
$439$	−231.600	−	401.143i	−0.527563	−	0.913766i	−0.999484	−	0.0321247i	$-0.989773\pi$
$439$	−231.600	−	401.143i	−0.527563	−	0.913766i	0.471921	−	0.881641i	$-0.343561\pi$
$440$	83.4706	−	166.153i	0.189706	−	0.377620i
$441$	277.719	−	342.569i	0.629747	−	0.776800i
$442$	136.337	+	136.337i	0.308454	+	0.308454i
$443$	181.770	−	678.374i	0.410315	−	1.53132i	−0.383722	−	0.923448i	$-0.625358\pi$
$443$	181.770	−	678.374i	0.410315	−	1.53132i	0.794038	−	0.607869i	$-0.207975\pi$
$444$	−205.432	−	202.924i	−0.462684	−	0.457037i
$445$	−331.130	−	68.4154i	−0.744111	−	0.153742i
$446$	−211.513	−	366.351i	−0.474244	−	0.821414i
$447$	460.248	−	269.506i	1.02964	−	0.602921i
$448$	−372.570	+	174.782i	−0.831630	+	0.390138i
$449$	−452.810			−1.00849			−0.504243	−	0.863562i	$-0.668228\pi$
$449$	−452.810			−1.00849			−0.504243	+	0.863562i	$0.668228\pi$
$450$	43.4234	−	323.553i	0.0964964	−	0.719007i
$451$	−5.88156	−	3.39572i	−0.0130412	−	0.00752932i
$452$	−34.0755	−	127.171i	−0.0753882	−	0.281353i
$453$	−117.643	−	66.9613i	−0.259697	−	0.147817i
$454$	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	−0.999998	−	0.00212736i	$-0.999323\pi$
$457$	−60.7402	+	226.685i	−0.132911	+	0.496029i	0.867087	+	0.498157i	$0.165990\pi$
$458$	64.4276	+	240.447i	0.140672	+	0.524993i
$459$	−147.393	−	512.150i	−0.321117	−	1.11579i
$460$	−300.381	+	17.4580i	−0.653002	+	0.0379522i
$461$	315.023			0.683348			0.341674	−	0.939819i	$-0.389006\pi$
$461$	315.023			0.683348			0.341674	+	0.939819i	$0.389006\pi$
$462$	−124.869	−	44.2570i	−0.270279	−	0.0957944i
$463$	−295.471	+	295.471i	−0.638167	+	0.638167i	−0.950103	−	0.311936i	$-0.899022\pi$
$463$	−295.471	+	295.471i	−0.638167	+	0.638167i	0.311936	+	0.950103i	$0.399022\pi$
$464$	−69.6257	−	120.595i	−0.150055	−	0.259904i
$465$	202.550	−	68.4731i	0.435592	−	0.147254i
$466$	85.9037	−	148.790i	0.184343	−	0.319291i
$467$	−202.350	+	755.179i	−0.433297	+	1.61709i	0.311812	+	0.950144i	$0.399064\pi$
$467$	−202.350	+	755.179i	−0.433297	+	1.61709i	−0.745109	+	0.666943i	$0.767603\pi$
$468$	31.0759	+	110.529i	0.0664015	+	0.236174i
$469$	−523.803	−	621.322i	−1.11685	−	1.32478i
$470$	94.7721	−	31.3911i	0.201643	−	0.0667895i
$471$	−501.466	+	137.673i	−1.06468	+	0.292300i
$472$	−139.241	−	519.653i	−0.295001	−	1.10096i
$473$	−274.424	+	73.5318i	−0.580178	+	0.155458i
$474$	−79.8142	−	290.718i	−0.168384	−	0.613330i
$475$	505.226	−	375.933i	1.06363	−	0.791439i
$476$	−46.0591	−	257.729i	−0.0967628	−	0.541447i
$477$	302.801	−	85.1340i	0.634803	−	0.178478i
$478$	−396.921	−	106.355i	−0.830379	−	0.222499i
$479$	269.530	+	155.613i	0.562693	+	0.324871i	0.754226	−	0.656615i	$-0.228012\pi$
$479$	269.530	+	155.613i	0.562693	+	0.324871i	−0.191533	+	0.981486i	$0.561346\pi$
$480$	−365.748	−	180.938i	−0.761975	−	0.376954i
$481$	296.168	−	170.993i	0.615734	−	0.355494i
$482$	−84.7148	−	84.7148i	−0.175757	−	0.175757i
$483$	121.357	+	655.787i	0.251256	+	1.35774i
$484$			193.456i			0.399703i
$485$	878.889	−	51.0806i	1.81214	−	0.105321i
$486$	−80.7553	+	343.197i	−0.166163	+	0.706167i
$487$	667.636	−	178.892i	1.37092	−	0.367336i	0.503102	−	0.864227i	$-0.332192\pi$
$487$	667.636	−	178.892i	1.37092	−	0.367336i	0.867813	+	0.496891i	$0.165525\pi$
$488$	−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	$-0.162389\pi$
$492$	−4.39228	+	7.71669i	−0.00892740	+	0.0156843i
$493$	549.679	−	147.286i	1.11497	−	0.298755i
$494$	123.030	−	213.094i	0.249048	−	0.431364i
$495$	−63.7974	−	184.968i	−0.128884	−	0.373672i
$496$			68.8470i			0.138804i
$497$	−53.5020	+	25.0991i	−0.107650	+	0.0505013i
$498$	36.0054	+	61.4882i	0.0723001	+	0.123470i
$499$	728.049	−	420.340i	1.45902	−	0.842364i	0.460054	−	0.887891i	$-0.347830\pi$
$499$	728.049	−	420.340i	1.45902	−	0.842364i	0.998963	+	0.0455272i	$0.0144968\pi$
$500$	214.704	−	100.021i	0.429408	−	0.200043i
$501$	−6.79075	+	6.87465i	−0.0135544	+	0.0137219i
$502$	79.3196	+	21.2536i	0.158007	+	0.0423379i
$503$	−108.595	+	108.595i	−0.215895	+	0.215895i	−0.806766	−	0.590871i	$-0.798784\pi$
$503$	−108.595	+	108.595i	−0.215895	+	0.215895i	0.590871	+	0.806766i	$0.298784\pi$
$504$	−176.884	+	508.973i	−0.350960	+	1.00987i
$505$	−299.274	+	99.1277i	−0.592622	+	0.196292i
$506$	173.507	−	100.174i	0.342899	−	0.197973i
$507$	371.014	−	2.27810i	0.731782	−	0.00449329i
$508$	50.5779	+	188.759i	0.0995628	+	0.371573i
$509$	376.708	−	217.493i	0.740095	−	0.427294i	−0.0820092	−	0.996632i	$-0.526134\pi$
$509$	376.708	−	217.493i	0.740095	−	0.427294i	0.822104	+	0.569338i	$0.192800\pi$
$510$	−283.646	+	322.618i	−0.556169	+	0.632585i
$511$	121.466	+	144.080i	0.237703	+	0.281957i
$512$	209.753	−	209.753i	0.409674	−	0.409674i
$513$	−582.642	+	350.854i	−1.13575	+	0.683926i
$514$	−16.0499	+	27.7992i	−0.0312255	+	0.0540841i
$515$	348.184	−	228.943i	0.676086	−	0.444549i
$516$	98.3368	+	358.186i	0.190575	+	0.694159i
$517$	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	$-0.747328\pi$
$521$	139.064	−	240.867i	0.266918	−	0.462316i	0.968064	+	0.250702i	$0.0806613\pi$
$522$	−364.816	−	92.9659i	−0.698880	−	0.178096i
$523$	225.005	−	839.729i	0.430220	−	1.60560i	−0.322034	−	0.946728i	$-0.604367\pi$
$523$	225.005	−	839.729i	0.430220	−	1.60560i	0.752254	−	0.658873i	$-0.228967\pi$
$524$			184.357i			0.351827i
$525$	−279.270	−	444.560i	−0.531942	−	0.846781i
$526$	285.354			0.542498
$527$	−271.766	−	72.8194i	−0.515685	−	0.138177i
$528$	63.0014	−	0.386841i	0.119321	−	0.000732653i
$529$	−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
$534$	−77.9280	−	283.848i	−0.145933	−	0.531551i
$535$	−56.4327	−	85.8249i	−0.105482	−	0.160420i
$536$	859.911	+	496.470i	1.60431	+	0.926249i
$537$	−640.238	−	364.419i	−1.19225	−	0.678619i
$538$	166.431	+	166.431i	0.309352	+	0.309352i
$539$	−199.865	+	73.7932i	−0.370807	+	0.136908i
$540$	−241.311	+	84.8921i	−0.446871	+	0.157208i
$541$	295.339	+	511.543i	0.545914	+	0.945550i	0.998549	+	0.0538543i	$0.0171506\pi$
$541$	295.339	+	511.543i	0.545914	+	0.945550i	−0.452635	+	0.891696i	$0.649516\pi$
$542$	−405.792	+	108.732i	−0.748694	+	0.200612i
$543$	276.194	−	1.69588i	0.508645	−	0.00312318i
$544$	268.479	+	465.020i	0.493528	+	0.854816i
$545$	−1.66728	−	5.03365i	−0.00305923	−	0.00923606i
$546$	−169.023	−	116.235i	−0.309566	−	0.212884i
$547$	188.420	+	188.420i	0.344460	+	0.344460i	0.858041	−	0.513581i	$-0.171681\pi$
$547$	188.420	+	188.420i	0.344460	+	0.344460i	−0.513581	+	0.858041i	$0.671681\pi$
$548$	−106.988	+	399.284i	−0.195233	+	0.728621i
$549$	−83.2361	+	49.4291i	−0.151614	+	0.0900348i
$550$	−97.8505	+	123.689i	−0.177910	+	0.224890i
$551$	−363.119	−	628.940i	−0.659018	−	1.14145i
$552$	−411.762	−	703.186i	−0.745946	−	1.27389i
$553$	−397.791	−	277.168i	−0.719333	−	0.501208i
$554$	−49.4065			−0.0891814
$555$	422.517	+	634.064i	0.761293	+	1.14246i
$556$	188.496	+	108.828i	0.339021	+	0.195734i
$557$	151.182	+	564.218i	0.271421	+	1.01296i	0.958202	+	0.286093i	$0.0923567\pi$
$557$	151.182	+	564.218i	0.271421	+	1.01296i	−0.686780	+	0.726865i	$0.740977\pi$
$558$	133.221	+	129.989i	0.238748	+	0.232955i
$559$	−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	$-0.121744\pi$
$563$	−35.0813	−	130.925i	−0.0623115	−	0.232550i	−0.990058	+	0.140662i	$0.955077\pi$
$564$	−55.6560	−	54.9767i	−0.0986809	−	0.0974764i
$565$	20.1570	+	346.820i	0.0356761	+	0.613841i
$566$	432.538			0.764202
$567$	253.345	+	507.253i	0.446817	+	0.894625i
$568$	51.0581	−	51.0581i	0.0898910	−	0.0898910i
$569$	−141.292	−	244.725i	−0.248316	−	0.430096i	0.714742	−	0.699388i	$-0.246544\pi$
$569$	−141.292	−	244.725i	−0.248316	−	0.430096i	−0.963059	+	0.269291i	$0.913211\pi$
$570$	491.380	+	243.089i	0.862070	+	0.426472i
$571$	−208.184	+	360.585i	−0.364595	+	0.631498i	−0.988711	−	0.149834i	$-0.952126\pi$
$571$	−208.184	+	360.585i	−0.364595	+	0.631498i	0.624116	+	0.781332i	$0.285459\pi$
$572$	14.3563	−	53.5785i	0.0250984	−	0.0936687i
$573$	−69.5112	−	118.708i	−0.121311	−	0.207169i
$574$	−2.79084	−	15.6164i	−0.00486208	−	0.0272063i
$575$	785.542	+	115.263i	1.36616	+	0.200457i
$576$	−6.49744	−	529.071i	−0.0112803	−	0.918525i
$577$	170.664	+	636.928i	0.295779	+	1.10386i	0.940597	+	0.339526i	$0.110267\pi$
$577$	170.664	+	636.928i	0.295779	+	1.10386i	−0.644818	+	0.764336i	$0.723067\pi$
$578$	140.994	−	37.7792i	0.243934	−	0.0653620i
$579$	−784.274	+	215.315i	−1.35453	+	0.371875i
$580$	−85.8863	−	259.297i	−0.148080	−	0.447064i
$581$	107.770	+	38.9433i	0.185491	+	0.0670280i
$582$	387.269	+	661.358i	0.665411	+	1.13635i
$583$	−146.781	−	39.3299i	−0.251769	−	0.0674612i
$584$	−199.407	−	115.128i	−0.341451	−	0.197137i
$585$	−21.2911	−	302.213i	−0.0363951	−	0.516604i
$586$	−220.784	+	127.469i	−0.376764	+	0.217525i
$587$	585.980	+	585.980i	0.998263	+	0.998263i	0.999998	−	0.00173550i	$-0.000552427\pi$
$587$	585.980	+	585.980i	0.998263	+	0.998263i	−0.00173550	+	0.999998i	$0.500552\pi$
$588$	98.0801	+	260.707i	0.166803	+	0.443379i
$589$			359.058i			0.609605i
$590$	26.4762	+	455.547i	0.0448749	+	0.772114i
$591$	−210.948	−	208.374i	−0.356935	−	0.352578i
$592$	−236.985	+	63.5000i	−0.400313	+	0.107263i
$593$	391.812	+	104.986i	0.660728	+	0.177042i	0.573575	−	0.819153i	$-0.305556\pi$
$593$	391.812	+	104.986i	0.660728	+	0.177042i	0.0871534	+	0.996195i	$0.472223\pi$
$594$	118.204	−	122.640i	0.198996	−	0.206465i
$595$	−18.5818	+	690.594i	−0.0312299	+	1.16066i
$596$			336.876i			0.565228i
$597$	−642.483	−	365.696i	−1.07619	−	0.612556i
$598$	299.650	−	80.2910i	0.501087	−	0.134266i
$599$	−533.026	+	923.228i	−0.889860	+	1.54128i	−0.0498203	+	0.998758i	$0.515865\pi$
$599$	−533.026	+	923.228i	−0.889860	+	1.54128i	−0.840040	+	0.542525i	$0.817468\pi$
$600$	505.513	+	394.889i	0.842522	+	0.658148i
$601$			601.570i			1.00095i	0.865751	+	0.500474i	$0.166841\pi$
$601$			601.570i			1.00095i	−0.865751	+	0.500474i	$0.833159\pi$
$602$	−544.491	−	379.384i	−0.904470	−	0.630206i
$603$	1005.85	−	282.799i	1.66807	−	0.468986i
$604$	74.0448	−	42.7498i	0.122591	−	0.0707777i
$605$	103.288	−	499.915i	0.170725	−	0.826306i
$606$	−195.254	−	192.871i	−0.322202	−	0.318269i
$607$	−31.8595	−	8.53673i	−0.0524869	−	0.0140638i	0.232480	−	0.972601i	$-0.425316\pi$
$607$	−31.8595	−	8.53673i	−0.0524869	−	0.0140638i	−0.284967	+	0.958537i	$0.591983\pi$
$608$	484.551	−	484.551i	0.796958	−	0.796958i
$609$	−546.535	+	260.500i	−0.897430	+	0.427750i
$610$	69.7274	+	35.0292i	0.114307	+	0.0574249i
$611$	80.2384	−	46.3257i	0.131323	−	0.0758194i
$612$	326.191	+	83.1231i	0.532992	+	0.135822i
$613$	−113.939	−	425.226i	−0.185871	−	0.693681i	−0.994442	−	0.105282i	$-0.966425\pi$
$613$	−113.939	−	425.226i	−0.185871	−	0.693681i	0.808571	−	0.588398i	$-0.200241\pi$
$614$	−553.052	+	319.305i	−0.900736	+	0.520040i
$615$	15.4702	−	17.5958i	0.0251548	−	0.0286110i
$616$	199.027	−	167.789i	0.323096	−	0.272385i
$617$	57.4913	−	57.4913i	0.0931787	−	0.0931787i	−0.658981	−	0.752160i	$-0.729012\pi$
$617$	57.4913	−	57.4913i	0.0931787	−	0.0931787i	0.752160	+	0.658981i	$0.229012\pi$
$618$	315.271	+	179.450i	0.510147	+	0.290372i
$619$	289.165	−	500.848i	0.467148	−	0.809124i	−0.532148	−	0.846652i	$-0.678615\pi$
$619$	289.165	−	500.848i	0.467148	−	0.809124i	0.999296	+	0.0375275i	$0.0119482\pi$
$620$	−27.3254	+	132.255i	−0.0440733	+	0.213314i
$621$	−832.200	−	206.636i	−1.34010	−	0.332747i
$622$	−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
$627$	328.571	−	2.01749i	0.524037	−	0.00321769i
$628$	85.0111	−	317.266i	0.135368	−	0.505200i
$629$		−	1002.64i		−	1.59402i
$630$	234.280	−	392.421i	0.371873	−	0.622891i
$631$	−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
$633$	2.74575	+	447.177i	0.00433768	+	0.706440i
$634$	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
$639$	−0.933048	−	75.9759i	−0.00146017	−	0.118898i
$640$	98.2453	−	64.5996i	0.153508	−	0.100937i
$641$	22.3299	+	12.8922i	0.0348360	+	0.0201126i	0.517317	−	0.855794i	$-0.326931\pi$
$641$	22.3299	+	12.8922i	0.0348360	+	0.0201126i	−0.482481	+	0.875907i	$0.660264\pi$
$642$	44.2330	−	77.7120i	0.0688988	−	0.121047i
$643$	628.889	+	628.889i	0.978054	+	0.978054i	0.999764	−	0.0217104i	$-0.00691118\pi$
$643$	628.889	+	628.889i	0.978054	+	0.978054i	−0.0217104	+	0.999764i	$0.506911\pi$
$644$	−396.171	−	143.158i	−0.615172	−	0.222295i
$645$	−62.8749	−	978.100i	−0.0974805	−	1.51643i
$646$	−360.700	−	624.751i	−0.558360	−	0.967107i
$647$	−159.850	+	42.8316i	−0.247063	+	0.0662002i	−0.380225	−	0.924894i	$-0.624153\pi$
$647$	−159.850	+	42.8316i	−0.247063	+	0.0662002i	0.133162	+	0.991094i	$0.457487\pi$
$648$	−501.756	−	477.695i	−0.774314	−	0.737184i
$649$	136.747	+	236.853i	0.210704	+	0.364950i
$650$	−195.919	+	145.781i	−0.301414	+	0.224278i
$651$	298.406	+	23.5676i	0.458381	+	0.0362022i
$652$	−66.2668	−	66.2668i	−0.101636	−	0.101636i
$653$	−292.526	+	1091.72i	−0.447972	+	1.67185i	0.259996	+	0.965610i	$0.416279\pi$
$653$	−292.526	+	1091.72i	−0.447972	+	1.67185i	−0.707968	+	0.706245i	$0.750388\pi$
$654$	3.24400	−	3.28408i	0.00496024	−	0.00502153i
$655$	98.4304	−	476.402i	0.150275	−	0.727332i
$656$	3.77213	+	6.53352i	0.00575020	+	0.00995964i
$657$	−233.248	+	65.5790i	−0.355020	+	0.0998158i
$658$	139.266	+	11.8598i	0.211650	+	0.0180241i
$659$	672.256			1.02012			0.510058	−	0.860140i	$-0.329624\pi$
$659$	672.256			1.02012			0.510058	+	0.860140i	$0.329624\pi$
$660$	121.179	+	24.2622i	0.183604	+	0.0367609i
$661$	−575.495	−	332.262i	−0.870642	−	0.502666i	−0.00308073	−	0.999995i	$-0.500981\pi$
$661$	−575.495	−	332.262i	−0.870642	−	0.502666i	−0.867562	+	0.497330i	$0.834314\pi$
$662$	125.009	+	466.541i	0.188836	+	0.704744i
$663$	−197.209	+	346.472i	−0.297450	+	0.522583i
$664$	−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
$669$	614.682	−	622.277i	0.918806	−	0.930159i
$670$	−629.080	−	559.973i	−0.938926	−	0.835780i
$671$	46.7685			0.0696996
$672$	−370.897	−	434.506i	−0.551930	−	0.646586i
$673$	−106.959	+	106.959i	−0.158929	+	0.158929i	−0.782092	−	0.623163i	$-0.785847\pi$
$673$	−106.959	+	106.959i	−0.158929	+	0.158929i	0.623163	+	0.782092i	$0.285847\pi$
$674$	69.8218	+	120.935i	0.103593	+	0.179429i
$675$	668.901	−	90.5333i	0.990965	−	0.134123i
$676$	−117.173	+	202.949i	−0.173332	+	0.300220i
$677$	−44.6627	+	166.683i	−0.0659714	+	0.246209i	−0.991035	−	0.133604i	$-0.957345\pi$
$677$	−44.6627	+	166.683i	−0.0659714	+	0.246209i	0.925063	+	0.379813i	$0.124012\pi$
$678$	−260.980	+	152.821i	−0.384926	+	0.225400i
$679$	1159.16	+	418.868i	1.70716	+	0.616890i
$680$	−265.409	−	801.292i	−0.390308	−	1.17837i
$681$	298.929	+	1088.83i	0.438956	+	1.59887i
$682$	−23.2737	−	86.8587i	−0.0341257	−	0.127359i
$683$	−12.9980	+	3.48281i	−0.0190308	+	0.00509928i	−0.268322	−	0.963329i	$-0.586469\pi$
$683$	−12.9980	+	3.48281i	−0.0190308	+	0.00509928i	0.249291	+	0.968429i	$0.419802\pi$
$684$	−5.27525	−	429.551i	−0.00771235	−	0.627998i
$685$	489.652	−	974.678i	0.714821	−	1.42289i
$686$	−432.702	−	245.836i	−0.630761	−	0.358361i
$687$	−444.158	+	260.084i	−0.646518	+	0.378579i
$688$	304.844	+	81.6826i	0.443087	+	0.118725i
$689$	−203.771	−	117.647i	−0.295748	−	0.170750i
$690$	221.348	+	654.770i	0.320794	+	0.948941i
$691$	−407.010	+	234.987i	−0.589016	+	0.340069i	−0.764708	−	0.644376i	$-0.777117\pi$
$691$	−407.010	+	234.987i	−0.589016	+	0.340069i	0.175692	+	0.984445i	$0.443784\pi$
$692$	−450.406	−	450.406i	−0.650875	−	0.650875i
$693$	19.8899	−	273.202i	0.0287011	−	0.394231i
$694$		−	797.952i		−	1.14979i
$695$	−428.992	−	381.865i	−0.617254	−	0.549446i
$696$	519.865	−	526.288i	0.746932	−	0.756162i
$697$	−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	$-0.255031\pi$
$702$	225.939	−	136.056i	0.321851	−	0.193811i
$703$	−1235.95	+	331.171i	−1.75811	+	0.471083i
$704$	−127.810	+	221.374i	−0.181548	+	0.314451i
$705$	114.469	+	171.782i	0.162368	+	0.243662i
$706$		−	868.386i		−	1.23001i
$707$	−439.778	−	37.4514i	−0.622034	−	0.0529722i
$708$	308.558	−	180.681i	0.435817	−	0.255200i
$709$	−422.388	+	243.866i	−0.595751	+	0.343957i	−0.767368	−	0.641207i	$-0.778434\pi$
$709$	−422.388	+	243.866i	−0.595751	+	0.343957i	0.171617	+	0.985164i	$0.445101\pi$
$710$	−51.1742	+	33.6487i	−0.0720763	+	0.0473926i
$711$	535.971	−	318.282i	0.753828	−	0.447654i
$712$	558.680	+	149.698i	0.784662	+	0.210250i
$713$	−320.095	+	320.095i	−0.448941	+	0.448941i
$714$	−542.895	+	258.765i	−0.760357	+	0.362415i
$715$	−65.7046	+	130.788i	−0.0918946	+	0.182921i
$716$	402.969	−	232.654i	0.562805	−	0.324936i
$717$	−5.21694	−	849.638i	−0.00727607	−	1.18499i
$718$	−18.3168	−	68.3594i	−0.0255109	−	0.0952081i
$719$	999.752	−	577.207i	1.39048	−	0.802792i	0.397108	−	0.917772i	$-0.370014\pi$
$719$	999.752	−	577.207i	1.39048	−	0.802792i	0.993368	+	0.114980i	$0.0366805\pi$
$720$	−41.3610	+	213.378i	−0.0574458	+	0.296358i
$721$	574.295	−	102.633i	0.796526	−	0.142348i
$722$	−280.624	+	280.624i	−0.388676	+	0.388676i
$723$	122.539	−	215.286i	0.169487	−	0.297767i
$724$	−87.2269	+	151.081i	−0.120479	+	0.208676i
$725$	83.4990	+	715.912i	0.115171	+	0.987465i
$726$	428.533	−	117.650i	0.590266	−	0.162052i
$727$	−654.711	+	654.711i	−0.900566	+	0.900566i	−0.995485	−	0.0949191i	$-0.969741\pi$
$727$	−654.711	+	654.711i	−0.900566	+	0.900566i	0.0949191	+	0.995485i	$0.469741\pi$
$728$	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
$732$	−0.375436	−	61.1441i	−0.000512891	−	0.0835301i
$733$	−105.152	+	392.433i	−0.143454	+	0.535379i	0.856365	+	0.516371i	$0.172717\pi$
$733$	−105.152	+	392.433i	−0.143454	+	0.535379i	−0.999819	+	0.0190079i	$0.993949\pi$
$734$			221.375i			0.301601i
$735$	−114.257	−	726.065i	−0.155451	−	0.987844i
$736$	863.941			1.17383
$737$	−487.578	−	130.646i	−0.661571	−	0.177267i
$738$	19.7647	+	5.03664i	0.0267815	+	0.00682471i
$739$	701.246	+	404.865i	0.948912	+	0.547855i	0.892743	−	0.450567i	$-0.148778\pi$
$739$	701.246	+	404.865i	0.948912	+	0.547855i	0.0561693	+	0.998421i	$0.482111\pi$
$740$	−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	$-0.312607\pi$
$743$	−205.338	−	205.338i	−0.276364	−	0.276364i	−0.831656	+	0.555292i	$0.812607\pi$
$744$	−352.691	+	96.8282i	−0.474047	+	0.130145i
$745$	179.862	−	870.529i	0.241425	−	1.16850i
$746$	−302.409	−	174.596i	−0.405375	−	0.234043i
$747$	−102.891	+	105.450i	−0.137740	+	0.141165i
$748$	−114.992	−	114.992i	−0.153733	−	0.153733i
$749$	−25.2983	−	141.560i	−0.0337761	−	0.188998i
$750$	−352.133	−	414.772i	−0.469511	−	0.553030i
$751$	−222.402	−	385.211i	−0.296141	−	0.512931i	0.679109	−	0.734038i	$-0.262366\pi$
$751$	−222.402	−	385.211i	−0.296141	−	0.512931i	−0.975250	+	0.221107i	$0.929033\pi$
$752$	−64.2045	+	17.2036i	−0.0853784	+	0.0228771i
$753$	1.04254	+	169.789i	0.00138451	+	0.225484i
$754$	140.812	+	243.893i	0.186753	+	0.323466i
$755$	−214.165	+	70.9373i	−0.283663	+	0.0939567i
$756$	−357.338	−	23.8104i	−0.472669	−	0.0314953i
$757$	−630.375	−	630.375i	−0.832728	−	0.832728i	0.155161	−	0.987889i	$-0.450410\pi$
$757$	−630.375	−	630.375i	−0.832728	−	0.832728i	−0.987889	+	0.155161i	$0.950410\pi$
$758$	−13.2755	+	49.5450i	−0.0175139	+	0.0653628i
$759$	294.716	+	291.118i	0.388295	+	0.383555i
$760$	−900.086	+	591.837i	−1.18432	+	0.778733i
$761$	388.123	+	672.248i	0.510017	+	0.883375i	0.999933	+	0.0116051i	$0.00369410\pi$
$761$	388.123	+	672.248i	0.510017	+	0.883375i	−0.489916	+	0.871770i	$0.662973\pi$
$762$	387.370	−	226.831i	0.508359	−	0.297678i
$763$	0.629914	−	7.39685i	0.000825575	−	0.00969444i
$764$	86.8874			0.113727
$765$	−798.537	−	388.957i	−1.04384	−	0.508441i
$766$	344.869	+	199.110i	0.450221	+	0.259935i
$767$	109.604	+	409.049i	0.142900	+	0.533311i
$768$	702.077	+	399.617i	0.914163	+	0.520334i
$769$	−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	0.992389	+	0.123139i	$0.0392961\pi$
$773$	150.367	+	561.179i	0.194524	+	0.725975i	−0.797865	+	0.602836i	$0.794037\pi$
$774$	733.630	−	435.660i	0.947843	−	0.562868i
$775$	141.225	−	327.173i	0.182225	−	0.422159i
$776$	−1505.95			−1.94065
$777$	194.106	+	1048.91i	0.249815	+	1.34995i
$778$	−481.817	+	481.817i	−0.619303	+	0.619303i
$779$	19.6728	+	34.0743i	0.0252539	+	0.0437411i
$780$	171.517	+	84.8509i	0.219894	+	0.108783i
$781$	−18.3539	+	31.7898i	−0.0235005	+	0.0407040i
$782$	235.398	−	878.517i	0.301021	−	1.12342i
$783$	−14.3381	−	778.294i	−0.0183117	−	0.993990i
$784$	233.261	+	40.0192i	0.297527	+	0.0510448i
$785$	−389.071	+	774.466i	−0.495632	+	0.986581i
$786$	408.378	−	112.117i	0.519565	−	0.142642i
$787$	230.535	+	860.369i	0.292929	+	1.09323i	0.942848	+	0.333222i	$0.108136\pi$
$787$	230.535	+	860.369i	0.292929	+	1.09323i	−0.649919	+	0.760003i	$0.725197\pi$
$788$	180.902	−	48.4725i	0.229571	−	0.0615133i
$789$	156.205	+	568.966i	0.197978	+	0.721123i
$790$	−448.986	−	225.559i	−0.568337	−	0.285517i
$791$	−165.290	+	457.419i	−0.208964	+	0.578279i
$792$	90.5885	+	322.201i	0.114379	+	0.406820i
$793$	69.9490	+	18.7428i	0.0882080	+	0.0236353i
$794$	−125.445	−	72.4257i	−0.157991	−	0.0912163i
$795$	232.453	−	469.881i	0.292394	−	0.591045i
$796$	404.381	−	233.470i	0.508016	−	0.293303i
$797$	42.0291	+	42.0291i	0.0527341	+	0.0527341i	0.732982	−	0.680248i	$-0.238128\pi$
$797$	42.0291	+	42.0291i	0.0527341	+	0.0527341i	−0.680248	+	0.732982i	$0.738128\pi$
$798$	498.297	+	583.756i	0.624433	+	0.731524i
$799$		−	271.636i		−	0.339970i
$800$	−632.106	+	250.939i	−0.790132	+	0.313674i
$801$	523.306	−	310.761i	0.653315	−	0.387966i
$802$	−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
$807$	−240.741	+	422.952i	−0.298316	+	0.524104i
$808$	520.909	−	139.577i	0.644689	−	0.172744i
$809$	446.584	−	773.507i	0.552020	−	0.956127i	−0.446109	−	0.894979i	$-0.647191\pi$
$809$	446.584	−	773.507i	0.552020	−	0.956127i	0.998129	−	0.0611480i	$-0.0194762\pi$
$810$	334.801	+	482.910i	0.413334	+	0.596186i
$811$			677.071i			0.834859i	0.908709	+	0.417430i	$0.137069\pi$
$811$			677.071i			0.834859i	−0.908709	+	0.417430i	$0.862931\pi$
$812$	32.4486	−	381.032i	0.0399614	−	0.469252i
$813$	−438.933	−	749.587i	−0.539893	−	0.922001i
$814$	277.519	−	160.226i	0.340933	−	0.196838i
$815$	135.861	+	206.622i	0.166701	+	0.253524i
$816$	200.993	−	203.477i	0.246315	−	0.249359i
$817$	1589.85	+	425.999i	1.94596	+	0.521419i
$818$	409.795	−	409.795i	0.500972	−	0.500972i
$819$	139.236	−	400.642i	0.170007	−	0.489184i
$820$	4.65309	+	14.0480i	0.00567450	+	0.0171317i
$821$	1195.92	−	690.462i	1.45666	−	0.841001i	0.457812	−	0.889049i	$-0.348633\pi$
$821$	1195.92	−	690.462i	1.45666	−	0.841001i	0.998845	+	0.0480474i	$0.0152999\pi$
$822$	949.536	−	5.83034i	1.15515	−	0.00709287i
$823$	−122.693	−	457.896i	−0.149080	−	0.556374i	−0.999540	−	0.0303340i	$-0.990343\pi$
$823$	−122.693	−	457.896i	−0.149080	−	0.556374i	0.850460	−	0.526040i	$-0.176324\pi$
$824$	−617.317	+	356.408i	−0.749171	+	0.432534i
$825$	−300.187	−	127.395i	−0.363864	−	0.154418i
$826$	−217.109	+	600.819i	−0.262843	+	0.727384i
$827$	814.051	−	814.051i	0.984343	−	0.984343i	−0.0155366	−	0.999879i	$-0.504946\pi$
$827$	814.051	−	814.051i	0.984343	−	0.984343i	0.999879	+	0.0155366i	$0.00494564\pi$
$828$	378.236	−	387.642i	0.456807	−	0.468166i
$829$	−344.646	+	596.945i	−0.415738	+	0.720079i	−0.995506	−	0.0947031i	$-0.969810\pi$
$829$	−344.646	+	596.945i	−0.415738	+	0.720079i	0.579768	+	0.814782i	$0.303143\pi$
$830$	116.301	+	24.0292i	0.140122	+	0.0289508i
$831$	−27.0454	−	98.5114i	−0.0325456	−	0.118546i
$832$	−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
$837$	−186.258	+	336.786i	−0.222531	+	0.402373i
$838$	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	$0.607580\pi$
$840$	432.786	+	786.892i	0.515221	+	0.936776i
$841$	−9.79677			−0.0116490
$842$	46.9324	+	12.5755i	0.0557392	+	0.0149353i
$843$	−1363.88	+	8.37446i	−1.61788	+	0.00993411i
$844$	−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
$849$	236.774	+	862.436i	0.278886	+	1.01583i
$850$	82.9429	+	711.144i	0.0975799	+	0.836640i
$851$	−1397.07	−	806.597i	−1.64168	−	0.947823i
$852$	41.7086	+	23.7402i	0.0489538	+	0.0278641i
$853$	500.340	+	500.340i	0.586565	+	0.586565i	0.936699	−	0.350135i	$-0.113864\pi$
$853$	500.340	+	500.340i	0.586565	+	0.586565i	−0.350135	+	0.936699i	$0.613864\pi$
$854$	70.4142	+	83.5235i	0.0824523	+	0.0978027i
$855$	−215.710	+	1112.83i	−0.252292	+	1.30155i
$856$	87.8520	+	152.164i	0.102631	+	0.177762i
$857$	−210.127	+	56.3034i	−0.245189	+	0.0656982i	−0.379321	−	0.925265i	$-0.623842\pi$
$857$	−210.127	+	56.3034i	−0.245189	+	0.0656982i	0.134131	+	0.990964i	$0.457176\pi$
$858$	−127.415	+	0.782351i	−0.148502	+	0.000911831i
$859$	−197.711	−	342.446i	−0.230165	−	0.398657i	0.727692	−	0.685904i	$-0.240593\pi$
$859$	−197.711	−	342.446i	−0.230165	−	0.398657i	−0.957856	+	0.287247i	$0.907260\pi$
$860$	553.183	+	277.905i	0.643237	+	0.323145i
$861$	29.6098	−	14.1132i	0.0343900	−	0.0163916i
$862$	−261.073	−	261.073i	−0.302868	−	0.302868i
$863$	172.197	−	642.646i	0.199532	−	0.744665i	−0.791514	−	0.611151i	$-0.790707\pi$
$863$	172.197	−	642.646i	0.199532	−	0.744665i	0.991047	−	0.133515i	$-0.0426264\pi$
$864$	705.852	−	203.139i	0.816959	−	0.235114i
$865$	923.427	+	1404.38i	1.06755	+	1.62356i
$866$	523.577	+	906.861i	0.604592	+	1.04718i
$867$	152.509	+	260.447i	0.175904	+	0.300400i
$868$	−108.086	+	155.125i	−0.124523	+	0.178716i
$869$	−301.150			−0.346548
$870$	−522.149	+	347.941i	−0.600171	+	0.399933i
$871$	−676.886	−	390.800i	−0.777137	−	0.448680i
$872$	2.34762	+	8.76144i	0.00269223	+	0.0100475i
$873$	−1106.69	+	1134.21i	−1.26768	+	1.29920i
$874$	−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	0.831125	+	0.556086i	$0.187698\pi$
$877$	−146.190	+	545.589i	−0.166694	+	0.622109i	−0.997818	+	0.0660226i	$0.978969\pi$
$878$	−173.942	−	649.160i	−0.198112	−	0.739362i
$879$	−375.019	−	370.442i	−0.426643	−	0.421435i
$880$	69.8161	−	78.4322i	0.0793365	−	0.0891276i
$881$	647.825			0.735330			0.367665	−	0.929958i	$-0.380157\pi$
$881$	647.825			0.735330			0.367665	+	0.929958i	$0.380157\pi$
$882$	517.856	−	375.810i	0.587138	−	0.426088i
$883$	687.897	−	687.897i	0.779046	−	0.779046i	−0.200623	−	0.979669i	$-0.564297\pi$
$883$	687.897	−	687.897i	0.779046	−	0.779046i	0.979669	+	0.200623i	$0.0642966\pi$
$884$	−125.903	−	218.071i	−0.142425	−	0.246687i
$885$	−893.820	+	302.160i	−1.00997	+	0.341424i
$886$	509.489	−	882.460i	0.575044	−	0.996005i
$887$	166.333	−	620.764i	0.187523	−	0.699847i	−0.806553	−	0.591162i	$-0.798669\pi$
$887$	166.333	−	620.764i	0.187523	−	0.699847i	0.994076	−	0.108685i	$-0.0346639\pi$
$888$	−658.601	−	1124.73i	−0.741668	−	1.26658i
$889$	245.339	−	678.942i	0.275972	−	0.763715i
$890$	−438.376	−	220.228i	−0.492557	−	0.247448i
$891$	309.238	+	168.551i	0.347068	+	0.189171i
$892$	142.989	+	533.642i	0.160302	+	0.598254i
$893$	−334.846	+	89.7217i	−0.374967	+	0.100472i
$894$	746.228	−	204.870i	0.834707	−	0.229161i
$895$	−1165.54	+	386.057i	−1.30228	+	0.431349i
$896$	162.046	−	28.9595i	0.180855	−	0.0323208i
$897$	324.122	+	553.519i	0.361340	+	0.617078i
$898$	−634.599	−	170.040i	−0.706680	−	0.189354i
$899$	−355.896	−	205.477i	−0.395880	−	0.228561i
$900$	−164.144	+	393.481i	−0.182382	+	0.437201i
$901$	−597.417	+	344.919i	−0.663060	+	0.382818i
$902$	−6.96766	−	6.96766i	−0.00772467	−	0.00772467i
$903$	458.394	−	1293.34i	0.507635	−	1.43227i
$904$		−	594.265i		−	0.657373i
$905$	306.069	−	343.842i	0.338198	−	0.379936i
$906$	−139.727	−	138.022i	−0.154224	−	0.152342i
$907$	−166.606	+	44.6420i	−0.183689	+	0.0492194i	−0.349491	−	0.936940i	$-0.613645\pi$
$907$	−166.606	+	44.6420i	−0.183689	+	0.0492194i	0.165802	+	0.986159i	$0.446979\pi$
$908$	−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	$0.979452\pi$
$912$	−317.213	−	180.555i	−0.347822	−	0.197977i
$913$	68.7521	−	18.4221i	0.0753036	−	0.0201775i
$914$	−170.251	+	294.883i	−0.186270	+	0.322629i
$915$	−31.6753	+	158.204i	−0.0346178	+	0.172901i
$916$		−	325.099i		−	0.354911i
$917$	389.344	−	558.785i	0.424584	−	0.609362i
$918$	−14.2426	−	773.110i	−0.0155148	−	0.842168i
$919$	−89.1660	+	51.4800i	−0.0970250	+	0.0560174i	−0.547727	−	0.836657i	$-0.684507\pi$
$919$	−89.1660	+	51.4800i	−0.0970250	+	0.0560174i	0.450702	+	0.892674i	$0.351174\pi$
$920$	−1330.03	−	274.800i	−1.44569	−	0.298696i
$921$	−939.404	−	927.938i	−1.01998	−	1.00753i
$922$	441.495	+	118.298i	0.478845	+	0.128306i
$923$	−40.1908	+	40.1908i	−0.0435437	+	0.0435437i
$924$	142.561	+	98.0374i	0.154287	+	0.106101i
$925$	1256.45	+	184.360i	1.35833	+	0.199308i
$926$	−525.049	+	303.137i	−0.567008	+	0.327362i
$927$	−185.223	+	726.849i	−0.199809	+	0.784087i
$928$	202.992	+	757.576i	0.218741	+	0.816354i
$929$	−339.509	+	196.016i	−0.365457	+	0.210997i	−0.671472	−	0.741030i	$-0.734338\pi$
$929$	−339.509	+	196.016i	−0.365457	+	0.210997i	0.306015	+	0.952027i	$0.401004\pi$
$930$	309.581	−	19.9007i	0.332883	−	0.0213986i
$931$	1216.53	+	208.712i	1.30669	+	0.224180i
$932$	−158.660	+	158.660i	−0.170236	+	0.170236i
$933$	−329.265	−	187.415i	−0.352910	−	0.200874i
$934$	−567.173	+	982.373i	−0.607252	+	1.05179i
$935$	235.758	+	358.549i	0.252148	+	0.383475i
$936$	6.36396	+	518.202i	0.00679911	+	0.553635i
$937$	848.278	−	848.278i	0.905313	−	0.905313i	−0.0905767	−	0.995889i	$-0.528871\pi$
$937$	848.278	−	848.278i	0.905313	−	0.905313i	0.995889	+	0.0905767i	$0.0288710\pi$
$938$	−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	0.385617	+	0.922659i	$0.373989\pi$
$941$	−570.470	+	988.083i	−0.606238	+	1.05003i	−0.991855	+	0.127376i	$0.959345\pi$
$942$	−754.489	+	4.63271i	−0.800943	+	0.00491795i
$943$	−12.8387	+	47.9148i	−0.0136148	+	0.0508111i
$944$		−	303.810i		−	0.321833i
$945$	910.693	+	252.316i	0.963696	+	0.267001i
$946$	−412.210			−0.435740
$947$	542.316	+	145.313i	0.572668	+	0.153446i	0.533520	−	0.845788i	$-0.320869\pi$
$947$	542.316	+	145.313i	0.572668	+	0.153446i	0.0391479	+	0.999233i	$0.487536\pi$
$948$	2.41750	+	393.717i	0.00255010	+	0.415313i
$949$	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	$-0.131195\pi$
$953$	491.430	+	491.430i	0.515666	+	0.515666i	−0.400591	+	0.916257i	$0.631195\pi$
$954$	456.335	−	5.60419i	0.478339	−	0.00587441i
$955$	−224.528	−	46.3902i	−0.235108	−	0.0485761i
$956$	464.763	+	268.331i	0.486153	+	0.280681i
$957$	−186.031	+	326.833i	−0.194389	+	0.341518i
$958$	319.302	+	319.302i	0.333300	+	0.333300i
$959$	1167.53	−	984.279i	1.21744	−	1.02636i
$960$	−662.280	−	582.277i	−0.689875	−	0.606538i
$961$	−378.911	−	656.293i	−0.394288	−	0.682927i
$962$	479.281	−	128.423i	0.498214	−	0.133496i
$963$	179.163	+	45.6561i	0.186047	+	0.0474102i
$964$	78.2320	+	135.502i	0.0811535	+	0.140562i
$965$	−608.492	+	1211.23i	−0.630562	+	1.25517i
$966$	−76.1853	+	964.636i	−0.0788667	+	0.998588i
$967$	−906.688	−	906.688i	−0.937630	−	0.937630i	0.0605361	−	0.998166i	$-0.480719\pi$
$967$	−906.688	−	906.688i	−0.937630	−	0.937630i	−0.998166	+	0.0605361i	$0.980719\pi$
$968$	−226.003	+	843.453i	−0.233474	+	0.871336i
$969$	1048.24	−	1061.19i	1.08177	−	1.09514i
$970$	1250.92	+	258.454i	1.28960	+	0.266448i
$971$	687.381	+	1190.58i	0.707910	+	1.22614i	0.965631	+	0.259917i	$0.0836952\pi$
$971$	687.381	+	1190.58i	0.707910	+	1.22614i	−0.257721	+	0.966219i	$0.582971\pi$
$972$	217.878	−	405.643i	0.224154	−	0.417329i
$973$	−341.495	−	727.940i	−0.350971	−	0.748140i
$974$	1002.85			1.02962
$975$	−397.919	−	310.840i	−0.408122	−	0.318810i
$976$	−44.9923	−	25.9763i	−0.0460987	−	0.0266151i
$977$	−158.172	−	590.306i	−0.161896	−	0.604202i	−0.998416	−	0.0562663i	$-0.982080\pi$
$977$	−158.172	−	590.306i	−0.161896	−	0.604202i	0.836520	−	0.547936i	$-0.184586\pi$
$978$	−106.490	+	187.090i	−0.108886	+	0.191299i
$979$	−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	−0.939986	−	0.341213i	$-0.889162\pi$
$983$	−291.499	−	1087.89i	−0.296541	−	1.10670i	0.643445	−	0.765492i	$-0.277504\pi$
$984$	−28.1649	+	28.5129i	−0.0286228	+	0.0289765i
$985$	−493.353	+	28.6734i	−0.500866	+	0.0291101i
$986$	825.667			0.837391
$987$	52.5877	+	284.173i	0.0532803	+	0.287916i
$988$	−227.230	+	227.230i	−0.229990	+	0.229990i
$989$	1037.56	+	1797.10i	1.04910	+	1.81709i
$990$	−19.9505	−	283.184i	−0.0201520	−	0.286044i
$991$	−133.957	+	232.021i	−0.135174	+	0.234128i	−0.925664	−	0.378347i	$-0.876493\pi$
$991$	−133.957	+	232.021i	−0.135174	+	0.234128i	0.790490	+	0.612475i	$0.209826\pi$
$992$	100.361	−	374.552i	0.101170	−	0.377572i
$993$	−861.802	+	504.642i	−0.867877	+	0.508200i
$994$	−84.4067	+	15.0844i	−0.0849162	+	0.0151755i
$995$	−1169.62	+	387.411i	−1.17550	+	0.389357i
$996$	−24.6365	−	89.7372i	−0.0247355	−	0.0900976i
$997$	−274.072	−	1022.85i	−0.274897	−	1.02593i	−0.955911	−	0.293658i	$-0.905127\pi$
$997$	−274.072	−	1022.85i	−0.274897	−	1.02593i	0.681014	−	0.732270i	$-0.261539\pi$
$998$	1178.18	−	315.694i	1.18055	−	0.316326i
$999$	−1331.08	−	330.508i	−1.33241	−	0.330839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.19	yes	112
3.2	odd	2	inner	105.3.w.a.17.10	✓	112
5.3	odd	4	inner	105.3.w.a.38.19	yes	112
7.5	odd	6	inner	105.3.w.a.47.10	yes	112
15.8	even	4	inner	105.3.w.a.38.10	yes	112
21.5	even	6	inner	105.3.w.a.47.19	yes	112
35.33	even	12	inner	105.3.w.a.68.10	yes	112
105.68	odd	12	inner	105.3.w.a.68.19	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.10	✓	112	3.2	odd	2	inner
105.3.w.a.17.19	yes	112	1.1	even	1	trivial
105.3.w.a.38.10	yes	112	15.8	even	4	inner
105.3.w.a.38.19	yes	112	5.3	odd	4	inner
105.3.w.a.47.10	yes	112	7.5	odd	6	inner
105.3.w.a.47.19	yes	112	21.5	even	6	inner
105.3.w.a.68.10	yes	112	35.33	even	12	inner
105.3.w.a.68.19	yes	112	105.68	odd	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 $\F_{q}$
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} +(0.0184202 + 2.99994i) 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} +(-8.99932 + 0.110519i) q^{9} +(3.98568 + 6.06157i) q^{10} +(3.76549 + 2.17401i) q^{11} +(2.81202 - 4.94038i) q^{12} +(4.76059 + 4.76059i) q^{13} +(1.78675 + 9.99794i) q^{14} +(-9.90434 + 11.2652i) q^{15} +(-2.41499 - 4.18289i) q^{16} +(19.0658 - 5.10867i) q^{17} +(-12.6538 - 3.22456i) q^{18} +(-12.5949 - 21.8150i) q^{19} +(-2.97900 - 8.99383i) q^{20} +(-18.9568 + 9.03552i) q^{21} +(4.46083 + 4.46083i) q^{22} +(8.21961 - 30.6760i) q^{23} +(18.0317 - 18.2545i) q^{24} +(2.89619 + 24.8317i) q^{25} +(4.88411 + 8.45952i) q^{26} +(-0.497321 - 26.9954i) q^{27} +(1.12549 - 13.2163i) q^{28} +28.8306 q^{29} +(-18.1109 + 12.0685i) q^{30} +(-12.3444 - 7.12704i) q^{31} +(7.04085 + 26.2768i) q^{32} +(-6.45254 + 11.3363i) 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} +(-14.1938 + 14.3692i) q^{39} +(-2.48127 - 42.6925i) q^{40} -1.56196 q^{41} +(-29.9604 + 5.54431i) q^{42} +(-46.2033 + 46.2033i) q^{43} +(-4.11946 - 7.13512i) q^{44} +(-33.9773 - 29.5049i) q^{45} +(23.0391 - 39.9048i) q^{46} +(3.56182 - 13.2929i) q^{47} +(12.5040 - 7.32189i) q^{48} +(-31.3227 + 37.6814i) q^{49} +(-5.26592 + 35.8884i) q^{50} +(15.6769 + 57.1023i) q^{51} +(-3.30181 - 12.3225i) q^{52} +(-33.7582 + 9.04547i) q^{53} +(9.44040 - 38.0200i) q^{54} +(6.83568 + 20.6375i) q^{55} +(20.3468 - 56.3069i) q^{56} +(65.2119 - 38.1859i) q^{57} +(40.4052 + 10.8265i) q^{58} +(54.4737 + 31.4504i) q^{59} +(26.9261 - 9.10249i) q^{60} +(9.31520 - 5.37814i) q^{61} +(-14.6239 - 14.6239i) q^{62} +(-27.4552 - 56.7028i) q^{63} +58.7901i q^{64} +(1.95315 + 33.6057i) q^{65} +(-13.3001 + 13.4644i) 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} +(55.0947 + 53.7579i) q^{72} +(26.0040 - 6.96775i) q^{73} +(36.8503 - 63.8266i) q^{74} +(-74.4403 + 9.14583i) q^{75} +47.7314i q^{76} +(-2.58258 + 30.3264i) q^{77} +(-25.2881 + 14.8079i) q^{78} +(-59.9822 + 34.6307i) q^{79} +(4.88646 - 23.6504i) q^{80} +(80.9756 - 1.98920i) q^{81} +(-2.18904 - 0.586552i) q^{82} +(11.5754 - 11.5754i) q^{83} +(39.6687 + 3.13297i) q^{84} +(88.1889 + 44.3038i) q^{85} +(-82.1027 + 47.4020i) q^{86} +(0.531066 + 86.4902i) q^{87} +(-9.62501 - 35.9210i) q^{88} +(-58.5647 + 33.8123i) q^{89} +(-36.5384 - 54.1095i) q^{90} +(-16.0161 + 44.3225i) q^{91} +(-42.5520 + 42.5520i) q^{92} +(21.1533 - 37.1638i) q^{93} +(9.98356 - 17.2920i) q^{94} +(25.4843 - 123.344i) q^{95} +(-78.6993 + 21.6062i) 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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