LMFDB - Embedded newform 105.3.w.a.38.10

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			38.10
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.375522 + 1.40147i) q^{2} +(2.60724 - 1.48402i) q^{3} +(1.64101 + 0.947435i) q^{4} +(-1.01169 - 4.89658i) q^{5} +(1.10073 + 4.21124i) q^{6} +(6.33730 - 2.97299i) q^{7} +(-6.04782 + 6.04782i) q^{8} +(4.59537 - 7.73838i) q^{9} +(7.24231 + 0.420920i) q^{10} +(-3.76549 - 2.17401i) q^{11} +(5.68450 + 0.0349040i) 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} +(5.10867 + 19.0658i) q^{17} +(9.11943 + 9.34620i) 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} +(-30.6760 - 8.21961i) q^{23} +(-6.79302 + 24.7432i) q^{24} +(-22.9530 + 9.90766i) q^{25} +(-4.88411 - 8.45952i) q^{26} +(0.497321 - 26.9954i) q^{27} +(13.2163 + 1.12549i) q^{28} +28.8306 q^{29} +(19.5071 - 9.65029i) q^{30} +(-12.3444 - 7.12704i) q^{31} +(-26.2768 + 7.04085i) q^{32} +(-13.0438 - 0.0800915i) q^{33} -28.6386 q^{34} +(-20.9689 - 28.0233i) q^{35} +(14.8726 - 8.34491i) q^{36} +(-49.0654 - 13.1470i) q^{37} +(-35.3027 + 9.45934i) q^{38} +(-5.34718 + 19.4768i) q^{39} +(35.7321 + 23.4951i) q^{40} +1.56196 q^{41} +(19.4956 + 23.4154i) q^{42} +(-46.2033 - 46.2033i) q^{43} +(-4.11946 - 7.13512i) q^{44} +(-42.5407 - 14.6727i) q^{45} +(23.0391 - 39.9048i) q^{46} +(13.2929 + 3.56182i) q^{47} +(-12.5040 - 7.32189i) q^{48} +(31.3227 - 37.6814i) q^{49} +(-5.26592 - 35.8884i) q^{50} +(41.6136 + 42.1278i) q^{51} +(-12.3225 + 3.30181i) q^{52} +(9.04547 + 33.7582i) q^{53} +(37.6465 + 10.8344i) q^{54} +(-6.83568 + 20.6375i) q^{55} +(-20.3468 + 56.3069i) q^{56} +(65.2119 + 38.1859i) q^{57} +(-10.8265 + 40.4052i) q^{58} +(54.4737 + 31.4504i) q^{59} +(-5.58006 - 27.8699i) q^{60} +(9.31520 - 5.37814i) q^{61} +(14.6239 - 14.6239i) q^{62} +(6.11616 - 62.7024i) q^{63} -58.7901i q^{64} +(28.1269 + 18.4944i) q^{65} +(5.01049 - 18.2504i) q^{66} +(30.0473 + 112.138i) q^{67} +(-9.68028 + 36.1273i) q^{68} +(-92.1777 + 24.0933i) q^{69} +(47.1481 - 18.8638i) q^{70} -8.44240i q^{71} +(19.0083 + 74.5923i) q^{72} +(6.96775 + 26.0040i) q^{73} +(36.8503 - 63.8266i) q^{74} +(-45.1407 + 59.8943i) q^{75} +47.7314i q^{76} +(-30.3264 - 2.58258i) q^{77} +(-25.2881 - 14.8079i) q^{78} +(59.9822 - 34.6307i) q^{79} +(-18.0386 + 16.0570i) q^{80} +(-38.7651 - 71.1215i) q^{81} +(-0.586552 + 2.18904i) 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} +(75.1682 - 42.7852i) q^{87} +(35.9210 - 9.62501i) 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} +(-42.7614 - 0.262563i) q^{93} +(-9.98356 + 17.2920i) q^{94} +(94.0768 - 83.7421i) q^{95} +(-58.0611 + 57.3525i) q^{96} +(-124.503 - 124.503i) q^{97} +(41.0469 + 58.0480i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.375522	+	1.40147i	−0.187761	+	0.700734i	0.806261	+	0.591559i	$0.201487\pi$
$2$	−0.375522	+	1.40147i	−0.187761	+	0.700734i	−0.994023	+	0.109175i	$0.965179\pi$
$3$	2.60724	−	1.48402i	0.869079	−	0.494673i
$3$	2.60724	−	1.48402i	0.869079	−	0.494673i
$4$	1.64101	+	0.947435i	0.410251	+	0.236859i
$5$	−1.01169	−	4.89658i	−0.202338	−	0.979316i
$5$	−1.01169	−	4.89658i	−0.202338	−	0.979316i
$6$	1.10073	+	4.21124i	0.183455	+	0.701874i
$7$	6.33730	−	2.97299i	0.905328	−	0.424712i
$7$	6.33730	−	2.97299i	0.905328	−	0.424712i
$8$	−6.04782	+	6.04782i	−0.755977	+	0.755977i
$9$	4.59537	−	7.73838i	0.510597	−	0.859820i
$10$	7.24231	+	0.420920i	0.724231	+	0.0420920i
$11$	−3.76549	−	2.17401i	−0.342318	−	0.197637i	0.318979	−	0.947762i	$-0.396660\pi$
$11$	−3.76549	−	2.17401i	−0.342318	−	0.197637i	−0.661296	+	0.750125i	$0.729993\pi$
$12$	5.68450	+	0.0349040i	0.473709	+	0.00290866i
$13$	−4.76059	+	4.76059i	−0.366199	+	0.366199i	−0.866089	−	0.499890i	$-0.833374\pi$
$13$	−4.76059	+	4.76059i	−0.366199	+	0.366199i	0.499890	+	0.866089i	$0.333374\pi$
$14$	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
$17$	5.10867	+	19.0658i	0.300510	+	1.12152i	0.936742	+	0.350021i	$0.113826\pi$
$17$	5.10867	+	19.0658i	0.300510	+	1.12152i	−0.636231	+	0.771498i	$0.719508\pi$
$18$	9.11943	+	9.34620i	0.506635	+	0.519234i
$19$	12.5949	+	21.8150i	0.662890	+	1.14816i	0.979853	+	0.199721i	$0.0640037\pi$
$19$	12.5949	+	21.8150i	0.662890	+	1.14816i	−0.316963	+	0.948438i	$0.602663\pi$
$20$	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
$23$	−30.6760	−	8.21961i	−1.33374	−	0.357374i	−0.479632	−	0.877470i	$-0.659230\pi$
$23$	−30.6760	−	8.21961i	−1.33374	−	0.357374i	−0.854108	+	0.520095i	$0.825896\pi$
$24$	−6.79302	+	24.7432i	−0.283042	+	1.03097i
$25$	−22.9530	+	9.90766i	−0.918118	+	0.396306i
$26$	−4.88411	−	8.45952i	−0.187850	−	0.325366i
$27$	0.497321	−	26.9954i	0.0184193	−	0.999830i
$28$	13.2163	+	1.12549i	0.472009	+	0.0401962i
$29$	28.8306			0.994158			0.497079	−	0.867705i	$-0.334406\pi$
$29$	28.8306			0.994158			0.497079	+	0.867705i	$0.334406\pi$
$30$	19.5071	−	9.65029i	0.650236	−	0.321676i
$31$	−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	$0.740508\pi$
$32$	−26.2768	+	7.04085i	−0.821151	+	0.220027i
$33$	−13.0438	−	0.0800915i	−0.395267	−	0.00242702i
$34$	−28.6386			−0.842311
$35$	−20.9689	−	28.0233i	−0.599110	−	0.800667i
$36$	14.8726	−	8.34491i	0.413129	−	0.231803i
$37$	−49.0654	−	13.1470i	−1.32609	−	0.355325i	−0.474835	−	0.880075i	$-0.657492\pi$
$37$	−49.0654	−	13.1470i	−1.32609	−	0.355325i	−0.851257	+	0.524750i	$0.824159\pi$
$38$	−35.3027	+	9.45934i	−0.929019	+	0.248930i
$39$	−5.34718	+	19.4768i	−0.137107	+	0.499405i
$40$	35.7321	+	23.4951i	0.893304	+	0.587377i
$41$	1.56196			0.0380967			0.0190483	−	0.999819i	$-0.493936\pi$
$41$	1.56196			0.0380967			0.0190483	+	0.999819i	$0.493936\pi$
$42$	19.4956	+	23.4154i	0.464181	+	0.557511i
$43$	−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
$45$	−42.5407	−	14.6727i	−0.945349	−	0.326061i
$46$	23.0391	−	39.9048i	0.500849	−	0.867496i
$47$	13.2929	+	3.56182i	0.282828	+	0.0757834i	0.397444	−	0.917626i	$-0.369897\pi$
$47$	13.2929	+	3.56182i	0.282828	+	0.0757834i	−0.114616	+	0.993410i	$0.536564\pi$
$48$	−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
$51$	41.6136	+	42.1278i	0.815953	+	0.826035i
$52$	−12.3225	+	3.30181i	−0.236971	+	0.0634963i
$53$	9.04547	+	33.7582i	0.170669	+	0.636946i	0.997249	+	0.0741265i	$0.0236169\pi$
$53$	9.04547	+	33.7582i	0.170669	+	0.636946i	−0.826580	+	0.562820i	$0.809716\pi$
$54$	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
$57$	65.2119	+	38.1859i	1.14407	+	0.669927i
$58$	−10.8265	+	40.4052i	−0.186664	+	0.696641i
$59$	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	$0.487710\pi$
$60$	−5.58006	−	27.8699i	−0.0930010	−	0.464499i
$61$	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
$63$	6.11616	−	62.7024i	0.0970818	−	0.995276i
$64$		−	58.7901i		−	0.918595i
$65$	28.1269	+	18.4944i	0.432721	+	0.284529i
$66$	5.01049	−	18.2504i	0.0759164	−	0.276521i
$67$	30.0473	+	112.138i	0.448467	+	1.67370i	0.706617	+	0.707597i	$0.250221\pi$
$67$	30.0473	+	112.138i	0.448467	+	1.67370i	−0.258150	+	0.966105i	$0.583113\pi$
$68$	−9.68028	+	36.1273i	−0.142357	+	0.531284i
$69$	−92.1777	+	24.0933i	−1.33591	+	0.349178i
$70$	47.1481	−	18.8638i	0.673544	−	0.269483i
$71$		−	8.44240i		−	0.118907i	−0.998231	−	0.0594535i	$-0.981064\pi$
$71$		−	8.44240i		−	0.118907i	0.998231	−	0.0594535i	$-0.0189358\pi$
$72$	19.0083	+	74.5923i	0.264005	+	1.03600i
$73$	6.96775	+	26.0040i	0.0954487	+	0.356219i	0.997087	−	0.0762714i	$-0.0243015\pi$
$73$	6.96775	+	26.0040i	0.0954487	+	0.356219i	−0.901638	+	0.432491i	$0.857635\pi$
$74$	36.8503	−	63.8266i	0.497977	−	0.862521i
$75$	−45.1407	+	59.8943i	−0.601875	+	0.798590i
$76$			47.7314i			0.628045i
$77$	−30.3264	−	2.58258i	−0.393849	−	0.0335401i
$78$	−25.2881	−	14.8079i	−0.324207	−	0.189845i
$79$	59.9822	−	34.6307i	0.759268	−	0.438364i	−0.0697650	−	0.997563i	$-0.522225\pi$
$79$	59.9822	−	34.6307i	0.759268	−	0.438364i	0.829033	+	0.559200i	$0.188892\pi$
$80$	−18.0386	+	16.0570i	−0.225483	+	0.200713i
$81$	−38.7651	−	71.1215i	−0.478581	−	0.878043i
$82$	−0.586552	+	2.18904i	−0.00715307	+	0.0266956i
$83$	−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
$87$	75.1682	−	42.7852i	0.864002	−	0.491783i
$88$	35.9210	−	9.62501i	0.408194	−	0.109375i
$89$	−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
$93$	−42.7614	−	0.262563i	−0.459800	−	0.00282326i
$94$	−9.98356	+	17.2920i	−0.106208	+	0.183958i
$95$	94.0768	−	83.7421i	0.990282	−	0.881495i
$96$	−58.0611	+	57.3525i	−0.604804	+	0.597422i
$97$	−124.503	−	124.503i	−1.28354	−	1.28354i	−0.938639	−	0.344901i	$-0.887913\pi$
$97$	−124.503	−	124.503i	−1.28354	−	1.28354i	−0.344901	−	0.938639i	$-0.612087\pi$
$98$	41.0469	+	58.0480i	0.418846	+	0.592326i
$99$	−34.1272	+	19.1484i	−0.344719	+	0.193419i
$100$	−47.0528	−	5.48791i	−0.470528	−	0.0548791i
$101$	31.5264	−	54.6053i	0.312143	−	0.540647i	−0.666683	−	0.745341i	$-0.732287\pi$
$101$	31.5264	−	54.6053i	0.312143	−	0.540647i	0.978826	+	0.204694i	$0.0656200\pi$
$102$	−74.6676	+	42.5002i	−0.732035	+	0.416669i
$103$	80.5022	+	21.5705i	0.781574	+	0.209422i	0.627479	−	0.778634i	$-0.284087\pi$
$103$	80.5022	+	21.5705i	0.781574	+	0.209422i	0.154096	+	0.988056i	$0.450754\pi$
$104$		−	57.5824i		−	0.553677i
$105$	−96.2579	−	41.9453i	−0.916742	−	0.399479i
$106$	−50.7078			−0.478375
$107$	5.31697	−	19.8432i	0.0496913	−	0.185450i	−0.936619	−	0.350349i	$-0.886063\pi$
$107$	5.31697	−	19.8432i	0.0496913	−	0.185450i	0.986311	+	0.164899i	$0.0527297\pi$
$108$	26.3925	−	43.8285i	0.244375	−	0.405819i
$109$	0.918436	+	0.530259i	0.00842602	+	0.00486476i	0.504207	−	0.863583i	$-0.331785\pi$
$109$	0.918436	+	0.530259i	0.00842602	+	0.00486476i	−0.495781	+	0.868448i	$0.665118\pi$
$110$	−26.3558	−	17.3298i	−0.239598	−	0.157544i
$111$	−147.436	+	38.5366i	−1.32825	+	0.347176i
$112$	−27.7402	−	19.3285i	−0.247680	−	0.172576i
$113$	49.1305	−	49.1305i	0.434783	−	0.434783i	−0.455469	−	0.890252i	$-0.650528\pi$
$113$	49.1305	−	49.1305i	0.434783	−	0.434783i	0.890252	+	0.455469i	$0.150528\pi$
$114$	−78.0048	+	77.0527i	−0.684252	+	0.675901i
$115$	−9.21330	+	158.523i	−0.0801156	+	1.37846i
$116$	47.3112	+	27.3151i	0.407855	+	0.235475i
$117$	14.9626	+	58.7160i	0.127885	+	0.501846i
$118$	−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
$122$	4.03922	+	15.0746i	0.0331084	+	0.123562i
$123$	4.07241	−	2.31798i	0.0331090	−	0.0188454i
$124$	−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	$0.383085\pi$
$128$	−22.7149	−	6.08643i	−0.177460	−	0.0475503i
$129$	−189.029	−	51.8963i	−1.46534	−	0.402297i
$130$	−36.4815	+	32.4739i	−0.280627	+	0.249799i
$131$	48.6464	+	84.2581i	0.371347	+	0.643192i	0.989773	−	0.142651i	$-0.0455627\pi$
$131$	48.6464	+	84.2581i	0.371347	+	0.643192i	−0.618426	+	0.785843i	$0.712229\pi$
$132$	−21.3291	−	12.4896i	−0.161584	−	0.0946181i
$133$	144.673	+	100.804i	1.08777	+	0.757924i
$134$	−168.441			−1.25702
$135$	−132.688	+	24.8759i	−0.982876	+	0.184266i
$136$	−146.203	−	84.4104i	−1.07502	−	0.620664i
$137$	210.719	−	56.4619i	1.53809	−	0.412131i	0.612443	−	0.790514i	$-0.290187\pi$
$137$	210.719	−	56.4619i	1.53809	−	0.412131i	0.925649	+	0.378384i	$0.123520\pi$
$138$	0.848769	−	138.232i	0.00615050	−	1.00168i
$139$	114.866			0.826374			0.413187	−	0.910646i	$-0.364416\pi$
$139$	114.866			0.826374			0.413187	+	0.910646i	$0.364416\pi$
$140$	−7.85972	−	65.8531i	−0.0561408	−	0.470379i
$141$	39.9436	−	10.4404i	0.283288	−	0.0740454i
$142$	11.8318	+	3.17031i	0.0833222	+	0.0223261i
$143$	28.2755	−	7.57641i	0.197731	−	0.0529819i
$144$	−43.4666	−	0.533807i	−0.301851	−	0.00370699i
$145$	−29.1677	−	141.171i	−0.201156	−	0.973595i
$146$	−39.0603			−0.267537
$147$	25.7458	−	144.728i	0.175142	−	0.984543i
$148$	−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	$-0.370144\pi$
$150$	−66.9886	−	85.7548i	−0.446590	−	0.571699i
$151$	−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	$0.214404\pi$
$152$	−208.105	−	55.7616i	−1.36911	−	0.366853i
$153$	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
$156$	−27.2278	+	26.8954i	−0.174537	+	0.172407i
$157$	167.434	−	44.8638i	1.06646	−	0.285757i	0.317422	−	0.948284i	$-0.397183\pi$
$157$	167.434	−	44.8638i	1.06646	−	0.285757i	0.749038	+	0.662528i	$0.230516\pi$
$158$	26.0092	+	97.0677i	0.164615	+	0.614352i
$159$	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
$162$	114.232	−	27.6203i	0.705134	−	0.170496i
$163$	−12.8005	+	47.7722i	−0.0785308	+	0.293081i	−0.994011	−	0.109283i	$-0.965145\pi$
$163$	−12.8005	+	47.7722i	−0.0785308	+	0.293081i	0.915480	+	0.402364i	$0.131811\pi$
$164$	2.56319	+	1.47986i	0.0156292	+	0.00902353i
$165$	12.8041	+	63.9511i	0.0776009	+	0.387582i
$166$	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	$0.253070\pi$
$168$	30.5117	+	177.000i	0.181617	+	1.05357i
$169$			123.674i			0.731796i
$170$	28.9734	+	140.231i	0.170432	+	0.824888i
$171$	226.691	+	2.78396i	1.32568	+	0.0162805i
$172$	−32.0452	−	119.594i	−0.186309	−	0.695316i
$173$	87.0033	−	324.701i	0.502909	−	1.87688i	0.0226723	−	0.999743i	$-0.492783\pi$
$173$	87.0033	−	324.701i	0.502909	−	1.87688i	0.480237	−	0.877139i	$-0.340551\pi$
$174$	31.7347	+	121.413i	0.182383	+	0.697774i
$175$	−116.004	+	131.027i	−0.662882	+	0.748724i
$176$			21.0009i			0.119323i
$177$	188.699	+	1.15865i	1.06610	+	0.00654603i
$178$	−25.3946	−	94.7738i	−0.142666	−	0.532437i
$179$	−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	$0.926063\pi$
$180$	−55.9080	−	64.3826i	−0.310600	−	0.357681i
$181$		−	92.0664i		−	0.508654i	−0.967118	−	0.254327i	$-0.918146\pi$
$181$		−	92.0664i		−	0.508654i	0.967118	−	0.254327i	$-0.0818540\pi$
$182$	−56.1021	−	39.0901i	−0.308253	−	0.214781i
$183$	16.3057	−	27.8460i	0.0891021	−	0.152164i
$184$	235.234	−	135.812i	1.27844	−	0.738110i
$185$	−14.7364	+	253.553i	−0.0796562	+	1.37056i
$186$	16.4258	−	59.8302i	0.0883110	−	0.321668i
$187$	22.2126	−	82.8986i	0.118784	−	0.443308i
$188$	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	−0.392430	−	0.919782i	$-0.628365\pi$
$191$	39.7108	−	22.9270i	0.207910	−	0.120037i	0.600340	+	0.799745i	$0.295032\pi$
$192$	−87.2456	−	153.280i	−0.454404	−	0.798332i
$193$	−261.860	+	70.1653i	−1.35679	+	0.363551i	−0.862637	−	0.505824i	$-0.831188\pi$
$193$	−261.860	+	70.1653i	−1.35679	+	0.363551i	−0.494153	+	0.869375i	$0.664522\pi$
$194$	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	0.507115	−	0.861878i	$-0.330712\pi$
$197$	−69.8883	−	69.8883i	−0.354763	−	0.354763i	−0.861878	+	0.507115i	$0.830712\pi$
$198$	−14.0204	−	55.0188i	−0.0708102	−	0.277873i
$199$	123.211	−	213.408i	0.619153	−	1.07240i	−0.370488	−	0.928837i	$-0.620810\pi$
$199$	123.211	−	213.408i	0.619153	−	1.07240i	0.989641	−	0.143567i	$-0.0458571\pi$
$200$	78.8956	−	198.735i	0.394478	−	0.993675i
$201$	244.755	+	247.780i	1.21769	+	1.23273i
$202$	64.6888	+	64.6888i	0.320241	+	0.320241i
$203$	182.708	−	85.7130i	0.900040	−	0.422231i
$204$	28.3748	+	108.558i	0.139092	+	0.532148i
$205$	−1.58023	−	7.64828i	−0.00770842	−	0.0373087i
$206$	−60.4607	+	104.721i	−0.293499	+	0.508354i
$207$	−204.574	+	199.611i	−0.988281	+	0.964302i
$208$	31.4098	+	8.41624i	0.151009	+	0.0404627i
$209$		−	109.526i		−	0.524047i
$210$	94.9320	−	119.151i	0.452057	−	0.567386i
$211$	149.062			0.706454			0.353227	−	0.935538i	$-0.385084\pi$
$211$	149.062			0.706454			0.353227	+	0.935538i	$0.385084\pi$
$212$	−17.1400	+	63.9673i	−0.0808490	+	0.301733i
$213$	−12.5287	−	22.0113i	−0.0588201	−	0.103340i
$214$	25.8130	+	14.9031i	0.120621	+	0.0696408i
$215$	−179.494	+	272.981i	−0.834858	+	1.26968i
$216$	160.256	+	166.271i	0.741924	+	0.769774i
$217$	−99.4187	−	8.46647i	−0.458151	−	0.0390160i
$218$	−1.08803	+	1.08803i	−0.00499098	+	0.00499098i
$219$	56.7570	+	57.4583i	0.259165	+	0.262367i
$220$	−30.7701	+	27.3898i	−0.139864	+	0.124499i
$221$	−115.085	−	66.4443i	−0.520746	−	0.300653i
$222$	1.35758	−	221.098i	0.00611523	−	0.995935i
$223$	206.164	−	206.164i	0.924500	−	0.924500i	−0.0728430	−	0.997343i	$-0.523207\pi$
$223$	206.164	−	206.164i	0.924500	−	0.924500i	0.997343	+	0.0728430i	$0.0232072\pi$
$224$	−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
$227$	97.4127	+	363.549i	0.429131	+	1.60154i	0.754734	+	0.656031i	$0.227766\pi$
$227$	97.4127	+	363.549i	0.429131	+	1.60154i	−0.325603	+	0.945506i	$0.605567\pi$
$228$	70.8344	+	124.447i	0.310677	+	0.545821i
$229$	−85.7839	−	148.582i	−0.374602	−	0.648830i	0.615665	−	0.788008i	$-0.288887\pi$
$229$	−85.7839	−	148.582i	−0.374602	−	0.648830i	−0.990267	+	0.139178i	$0.955554\pi$
$230$	−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
$233$	−114.379	−	30.6478i	−0.490897	−	0.131535i	0.00487507	−	0.999988i	$-0.498448\pi$
$233$	−114.379	−	30.6478i	−0.490897	−	0.131535i	−0.495772	+	0.868453i	$0.665115\pi$
$234$	−87.9073	−	1.07958i	−0.375672	−	0.00461358i
$235$	3.99242	−	68.6932i	0.0169890	−	0.292311i
$236$	59.5944	+	103.221i	0.252519	+	0.437375i
$237$	104.995	−	179.305i	0.443017	−	0.756562i
$238$	−181.491	+	85.1421i	−0.762568	+	0.357740i
$239$	−283.218			−1.18501			−0.592507	−	0.805566i	$-0.701862\pi$
$239$	−283.218			−1.18501			−0.592507	+	0.805566i	$0.701862\pi$
$240$	−23.2021	+	68.6341i	−0.0966753	+	0.285975i
$241$	−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	$0.721467\pi$
$242$	143.083	−	38.3388i	0.591250	−	0.158425i
$243$	−206.615	−	127.902i	−0.850269	−	0.526348i
$244$	20.3817			0.0835317
$245$	−216.199	−	115.252i	−0.882444	−	0.470417i
$246$	1.71930	+	6.57781i	0.00698903	+	0.0267391i
$247$	−163.812	−	43.8932i	−0.663205	−	0.177705i
$248$	117.760	−	31.5536i	0.474837	−	0.127232i
$249$	−47.3580	−	13.0017i	−0.190193	−	0.0522157i
$250$	−170.403	+	62.0930i	−0.681611	+	0.248372i
$251$	−56.5975			−0.225488			−0.112744	−	0.993624i	$-0.535964\pi$
$251$	−56.5975			−0.225488			−0.112744	+	0.993624i	$0.535964\pi$
$252$	69.4431	−	97.1004i	0.275568	−	0.385319i
$253$	97.6408	+	97.6408i	0.385932	+	0.385932i
$254$	−74.8160	−	129.585i	−0.294551	−	0.510178i
$255$	164.182	−	246.385i	0.643850	−	0.966214i
$256$	134.640	−	233.203i	0.525938	−	0.910951i
$257$	−21.3701	−	5.72610i	−0.0831522	−	0.0222806i	0.217003	−	0.976171i	$-0.430372\pi$
$257$	−21.3701	−	5.72610i	−0.0831522	−	0.0222806i	−0.300155	+	0.953890i	$0.597038\pi$
$258$	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
$261$	132.487	−	223.102i	0.507614	−	0.854797i
$262$	−136.353	+	36.5356i	−0.520431	+	0.139449i
$263$	−50.9027	−	189.972i	−0.193546	−	0.722325i	−0.992638	−	0.121116i	$-0.961353\pi$
$263$	−50.9027	−	189.972i	−0.193546	−	0.722325i	0.799092	−	0.601209i	$-0.205314\pi$
$264$	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
$267$	−102.514	+	175.068i	−0.383947	+	0.655685i
$268$	−56.9357	+	212.487i	−0.212447	+	0.792862i
$269$	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	$0.569170\pi$
$270$	14.9647	−	195.300i	0.0554247	−	0.723333i
$271$	−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
$273$	24.0176	+	139.327i	0.0879764	+	0.510357i
$274$			316.518i			1.15518i
$275$	107.969	+	12.5927i	0.392613	+	0.0457917i
$276$	−174.091	−	47.7951i	−0.630765	−	0.173171i
$277$	8.81335	+	32.8919i	0.0318171	+	0.118743i	0.980008	−	0.198958i	$-0.0637558\pi$
$277$	8.81335	+	32.8919i	0.0318171	+	0.118743i	−0.948191	+	0.317701i	$0.897089\pi$
$278$	−43.1347	+	160.981i	−0.155161	+	0.579068i
$279$	−111.879	+	62.7742i	−0.400999	+	0.224997i
$280$	296.296	+	42.6642i	1.05820	+	0.152372i
$281$		−	454.634i		−	1.61791i	−0.587868	−	0.808957i	$-0.700033\pi$
$281$		−	454.634i		−	1.61791i	0.587868	−	0.808957i	$-0.299967\pi$
$282$	−0.367799	+	59.9002i	−0.00130425	+	0.212412i
$283$	77.1581	+	287.958i	0.272643	+	1.01752i	0.957404	+	0.288751i	$0.0932401\pi$
$283$	77.1581	+	287.958i	0.272643	+	1.01752i	−0.684761	+	0.728768i	$0.740093\pi$
$284$	7.99863	−	13.8540i	0.0281642	−	0.0487818i
$285$	121.006	−	357.947i	0.424582	−	1.25596i
$286$			42.4724i			0.148505i
$287$	9.89863	−	4.64370i	0.0344900	−	0.0161801i
$288$	−66.2670	+	235.695i	−0.230094	+	0.818387i
$289$	−87.1261	+	50.3023i	−0.301474	+	0.174056i
$290$	208.800	+	12.1354i	0.720000	+	0.0418461i
$291$	−509.375	−	139.844i	−1.75043	−	0.480565i
$292$	−13.2030	+	49.2742i	−0.0452157	+	0.168747i
$293$	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
$297$	−60.5609	+	100.570i	−0.203909	+	0.338619i
$298$	249.157	−	66.7615i	0.836099	−	0.224032i
$299$	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
$303$	1.16145	−	189.155i	0.00383316	−	0.624273i
$304$	60.8333	−	105.366i	0.200109	−	0.346600i
$305$	−35.7586	−	40.1716i	−0.117241	−	0.131710i
$306$	−131.605	+	221.616i	−0.430082	+	0.724236i
$307$	311.230	+	311.230i	1.01378	+	1.01378i	0.999904	+	0.0138731i	$0.00441610\pi$
$307$	311.230	+	311.230i	1.01378	+	1.01378i	0.0138731	+	0.999904i	$0.495584\pi$
$308$	−47.3189	−	32.9703i	−0.153633	−	0.107046i
$309$	241.899	−	63.2274i	0.782846	−	0.204619i
$310$	−86.4020	−	56.8122i	−0.278716	−	0.183265i
$311$	63.1444	−	109.369i	0.203037	−	0.351670i	−0.746469	−	0.665421i	$-0.768252\pi$
$311$	63.1444	−	109.369i	0.203037	−	0.351670i	0.949505	+	0.313751i	$0.101586\pi$
$312$	−85.4533	−	150.131i	−0.273889	−	0.481189i
$313$	−23.7393	−	6.36092i	−0.0758443	−	0.0203224i	0.220697	−	0.975342i	$-0.429167\pi$
$313$	−23.7393	−	6.36092i	−0.0758443	−	0.0203224i	−0.296542	+	0.955020i	$0.595833\pi$
$314$			251.501i			0.800958i
$315$	−313.215	+	33.4873i	−0.994333	+	0.106309i
$316$	131.241			0.415321
$317$	−53.9084	+	201.189i	−0.170058	+	0.634666i	0.827283	+	0.561786i	$0.189886\pi$
$317$	−53.9084	+	201.189i	−0.170058	+	0.634666i	−0.997341	+	0.0728796i	$0.976781\pi$
$318$	−132.207	+	75.2513i	−0.415746	+	0.236639i
$319$	−108.561	−	62.6780i	−0.340318	−	0.196483i
$320$	−287.870	+	59.4774i	−0.899594	+	0.185867i
$321$	−15.5851	−	59.6264i	−0.0485517	−	0.185752i
$322$	27.3689	−	321.383i	0.0849967	−	0.998085i
$323$	−351.578	+	351.578i	−1.08848	+	1.08848i
$324$	3.76927	−	153.438i	0.0116336	−	0.473575i
$325$	62.1033	−	156.436i	0.191087	−	0.481341i
$326$	−62.1443	−	35.8790i	−0.190627	−	0.110058i
$327$	3.18149	+	0.0195350i	0.00972934	+	5.97400e-5i
$328$	−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	$0.665614\pi$
$332$	−8.02836	−	29.9622i	−0.0241818	−	0.0902477i
$333$	−327.211	+	319.271i	−0.982614	+	0.958772i
$334$	−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	$0.204390\pi$
$338$	−173.325	−	46.4422i	−0.512795	−	0.137403i
$339$	55.1843	−	201.006i	0.162785	−	0.592937i
$340$	186.694	+	10.8505i	0.549099	+	0.0319134i
$341$	30.9885	+	53.6736i	0.0908753	+	0.157401i
$342$	−89.0293	+	316.655i	−0.260320	+	0.925892i
$343$	86.4751	−	331.920i	0.252114	−	0.967698i
$344$	558.858			1.62459
$345$	211.230	+	426.980i	0.612262	+	1.23762i
$346$	422.386	+	243.865i	1.22077	+	0.704811i
$347$	531.228	−	142.342i	1.53092	−	0.410208i	0.607598	−	0.794244i	$-0.292133\pi$
$347$	531.228	−	142.342i	1.53092	−	0.410208i	0.923318	+	0.384037i	$0.125466\pi$
$348$	163.888	+	1.00630i	0.470941	+	0.00289167i
$349$	82.1461			0.235376			0.117688	−	0.993051i	$-0.462452\pi$
$349$	82.1461			0.235376			0.117688	+	0.993051i	$0.462452\pi$
$350$	−140.067	−	211.780i	−0.400193	−	0.605085i
$351$	126.147	+	130.882i	0.359392	+	0.372882i
$352$	114.252	+	30.6138i	0.324580	+	0.0869709i
$353$	−578.119	+	154.906i	−1.63773	+	0.438828i	−0.956141	−	0.292907i	$-0.905377\pi$
$353$	−578.119	+	154.906i	−1.63773	+	0.438828i	−0.681589	+	0.731735i	$0.738711\pi$
$354$	−72.4844	+	264.020i	−0.204758	+	0.745820i
$355$	−41.3389	+	8.54111i	−0.116448	+	0.0240595i
$356$	−128.140			−0.359944
$357$	388.963	+	143.260i	1.08953	+	0.401288i
$358$	−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	$0.854974\pi$
$360$	346.016	−	168.540i	0.961157	−	0.468167i
$361$	−136.764	+	236.882i	−0.378847	+	0.656182i
$362$	129.028	+	34.5730i	0.356431	+	0.0955055i
$363$	−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
$366$	32.9022	+	33.3087i	0.0898966	+	0.0910074i
$367$	147.378	−	39.4899i	0.401575	−	0.107602i	−0.0523778	−	0.998627i	$-0.516680\pi$
$367$	147.378	−	39.4899i	0.401575	−	0.107602i	0.453953	+	0.891026i	$0.350013\pi$
$368$	39.7006	+	148.165i	0.107882	+	0.402622i
$369$	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
$372$	−69.9230	−	40.9445i	−0.187965	−	0.110066i
$373$	62.2905	−	232.471i	0.166999	−	0.623247i	−0.830778	−	0.556603i	$-0.812104\pi$
$373$	62.2905	−	232.471i	0.166999	−	0.623247i	0.997777	−	0.0666436i	$-0.0212290\pi$
$374$	107.838	+	62.2605i	0.288338	+	0.166472i
$375$	338.945	+	160.440i	0.903854	+	0.427841i
$376$	−101.934	+	58.8518i	−0.271102	+	0.156521i
$377$	−137.251	+	137.251i	−0.364060	+	0.364060i
$378$	270.787	−	43.2618i	0.716368	−	0.114449i
$379$		−	35.3522i		−	0.0932776i	−0.998912	−	0.0466388i	$-0.985149\pi$
$379$		−	35.3522i		−	0.0932776i	0.998912	−	0.0466388i	$-0.0148510\pi$
$380$	233.721	−	48.2895i	0.615055	−	0.127078i
$381$	−81.9095	+	298.350i	−0.214985	+	0.783072i
$382$	17.2192	+	64.2630i	0.0450765	+	0.168228i
$383$	71.0364	−	265.111i	0.185474	−	0.692197i	−0.809055	−	0.587733i	$-0.800021\pi$
$383$	71.0364	−	265.111i	0.185474	−	0.692197i	0.994529	−	0.104464i	$-0.0333127\pi$
$384$	−68.2555	+	17.8405i	−0.177749	+	0.0464597i
$385$	18.0351	+	151.108i	0.0468444	+	0.392489i
$386$		−	393.338i		−	1.01901i
$387$	−569.860	+	145.217i	−1.47251	+	0.375238i
$388$	−86.3519	−	322.270i	−0.222556	−	0.830592i
$389$	−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	$0.960383\pi$
$390$	−46.9241	+	138.806i	−0.120318	+	0.355914i
$391$		−	626.855i		−	1.60321i
$392$	38.4562	+	417.324i	0.0981025	+	1.06460i
$393$	251.873	+	147.489i	0.640899	+	0.375289i
$394$	124.191	−	71.7016i	0.315205	−	0.181984i
$395$	−230.255	−	258.672i	−0.582925	−	0.654865i
$396$	−74.1448	−	0.910561i	−0.187234	−	0.00229940i
$397$	−25.8392	+	96.4334i	−0.0650862	+	0.242905i	−0.990803	−	0.135312i	$-0.956796\pi$
$397$	−25.8392	+	96.4334i	−0.0650862	+	0.242905i	0.925717	+	0.378218i	$0.123463\pi$
$398$	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	−0.0262437	−	0.999656i	$-0.508355\pi$
$401$	331.371	−	191.317i	0.826362	−	0.477100i	0.852605	+	0.522556i	$0.175021\pi$
$402$	−439.166	+	249.970i	−1.09245	+	0.621816i
$403$	92.6955	−	24.8377i	0.230014	−	0.0616320i
$404$	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
$408$	−506.453	−	3.10972i	−1.24131	−	0.00762185i
$409$	−199.716	+	345.918i	−0.488302	+	0.845764i	−0.999909	−	0.0134551i	$-0.995717\pi$
$409$	−199.716	+	345.918i	−0.488302	+	0.845764i	0.511607	+	0.859219i	$0.329050\pi$
$410$	11.3122	+	0.657462i	0.0275908	+	0.00160356i
$411$	465.603	−	459.920i	1.13285	−	1.11903i
$412$	111.668	+	111.668i	0.271039	+	0.271039i
$413$	438.718	+	37.3611i	1.06227	+	0.0904626i
$414$	−202.926	−	361.662i	−0.490158	−	0.873581i
$415$	−44.9691	+	68.3906i	−0.108359	+	0.164797i
$416$	91.5746	−	158.612i	0.220131	−	0.381278i
$417$	299.483	−	170.463i	0.718184	−	0.408785i
$418$	153.497	+	41.1294i	0.367218	+	0.0983956i
$419$		−	186.761i		−	0.445729i	−0.974849	−	0.222865i	$-0.928459\pi$
$419$		−	186.761i		−	0.445729i	0.974849	−	0.222865i	$-0.0715408\pi$
$420$	−118.219	−	160.031i	−0.281475	−	0.381025i
$421$	33.4880			0.0795440			0.0397720	−	0.999209i	$-0.487337\pi$
$421$	33.4880			0.0795440			0.0397720	+	0.999209i	$0.487337\pi$
$422$	−55.9760	+	208.905i	−0.132645	+	0.495036i
$423$	88.6486	−	86.4976i	0.209571	−	0.204486i
$424$	−258.869	−	149.458i	−0.610539	−	0.352495i
$425$	−306.157	−	387.002i	−0.720369	−	0.910594i
$426$	35.5530	−	9.29281i	0.0834577	−	0.0218141i
$427$	43.0441	−	61.7768i	0.100806	−	0.144676i
$428$	27.5253	−	27.5253i	0.0643115	−	0.0643115i
$429$	62.4775	−	61.7149i	0.145635	−	0.143858i
$430$	−315.170	−	354.066i	−0.732955	−	0.823410i
$431$	220.378	+	127.235i	0.511317	+	0.295209i	0.733375	−	0.679824i	$-0.237944\pi$
$431$	220.378	+	127.235i	0.511317	+	0.295209i	−0.222058	+	0.975033i	$0.571277\pi$
$432$	−114.120	+	63.1135i	−0.264166	+	0.146096i
$433$	−510.335	+	510.335i	−1.17860	+	1.17860i	−0.198504	+	0.980100i	$0.563608\pi$
$433$	−510.335	+	510.335i	−1.17860	+	1.17860i	−0.980100	+	0.198504i	$0.936392\pi$
$434$	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
$437$	−207.051	−	772.723i	−0.473800	−	1.76825i
$438$	−101.840	+	57.9663i	−0.232510	+	0.132343i
$439$	231.600	+	401.143i	0.527563	+	0.913766i	0.999484	+	0.0321247i	$0.0102274\pi$
$439$	231.600	+	401.143i	0.527563	+	0.913766i	−0.471921	+	0.881641i	$0.656439\pi$
$440$	−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
$443$	−678.374	−	181.770i	−1.53132	−	0.410315i	−0.607869	−	0.794038i	$-0.707975\pi$
$443$	−678.374	−	181.770i	−1.53132	−	0.410315i	−0.923448	+	0.383722i	$0.874642\pi$
$444$	−278.454	−	76.4469i	−0.627148	−	0.172178i
$445$	224.814	+	252.559i	0.505201	+	0.567548i
$446$	211.513	+	366.351i	0.474244	+	0.821414i
$447$	−460.248	−	269.506i	−1.02964	−	0.602921i
$448$	−174.782	−	372.570i	−0.390138	−	0.831630i
$449$	−452.810			−1.00849			−0.504243	−	0.863562i	$-0.668228\pi$
$449$	−452.810			−1.00849			−0.504243	+	0.863562i	$0.668228\pi$
$450$	−301.917	−	124.171i	−0.670926	−	0.275935i
$451$	−5.88156	−	3.39572i	−0.0130412	−	0.00752932i
$452$	127.171	−	34.0755i	0.281353	−	0.0753882i
$453$	−0.831150	+	135.362i	−0.00183477	+	0.298813i
$454$	−546.083			−1.20283
$455$	233.232	+	33.5835i	0.512597	+	0.0738099i
$456$	−625.331	+	163.448i	−1.37134	+	0.358439i
$457$	226.685	+	60.7402i	0.496029	+	0.132911i	0.498157	−	0.867087i	$-0.334010\pi$
$457$	226.685	+	60.7402i	0.496029	+	0.132911i	−0.00212736	+	0.999998i	$0.500677\pi$
$458$	240.447	−	64.4276i	0.524993	−	0.140672i
$459$	517.231	−	128.429i	1.12686	−	0.279802i
$460$	−165.310	+	251.409i	−0.359369	+	0.546540i
$461$	−315.023			−0.683348			−0.341674	−	0.939819i	$-0.610994\pi$
$461$	−315.023			−0.683348			−0.341674	+	0.939819i	$0.610994\pi$
$462$	−22.5052	−	130.554i	−0.0487127	−	0.282585i
$463$	−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
$465$	41.9757	+	209.650i	0.0902704	+	0.450861i
$466$	85.9037	−	148.790i	0.184343	−	0.319291i
$467$	−755.179	−	202.350i	−1.61709	−	0.433297i	−0.666943	−	0.745109i	$-0.732397\pi$
$467$	−755.179	−	202.350i	−1.61709	−	0.433297i	−0.950144	+	0.311812i	$0.899064\pi$
$468$	−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
$471$	369.962	−	365.446i	0.785481	−	0.775894i
$472$	−519.653	+	139.241i	−1.10096	+	0.295001i
$473$	73.5318	+	274.424i	0.155458	+	0.580178i
$474$	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
$477$	302.801	+	85.1340i	0.634803	+	0.178478i
$478$	106.355	−	396.921i	0.222499	−	0.830379i
$479$	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	$0.561346\pi$
$480$	339.571	+	226.278i	0.707439	+	0.471412i
$481$	296.168	−	170.993i	0.615734	−	0.355494i
$482$	84.7148	−	84.7148i	0.175757	−	0.175757i
$483$	−512.529	+	426.730i	−1.06114	+	0.883498i
$484$		−	193.456i		−	0.399703i
$485$	−483.681	+	735.600i	−0.997281	+	1.51670i
$486$	256.840	−	241.535i	0.528477	−	0.496985i
$487$	−178.892	−	667.636i	−0.367336	−	1.37092i	−0.864227	−	0.503102i	$-0.832192\pi$
$487$	−178.892	−	667.636i	−0.367336	−	1.37092i	0.496891	−	0.867813i	$-0.334475\pi$
$488$	−23.8107	+	88.8626i	−0.0487924	+	0.182096i
$489$	37.5209	+	143.550i	0.0767298	+	0.293558i
$490$	242.710	−	259.716i	0.495326	−	0.530033i
$491$			479.528i			0.976636i	0.872666	+	0.488318i	$0.162389\pi$
$491$			479.528i			0.976636i	−0.872666	+	0.488318i	$0.837611\pi$
$492$	8.87899	+	0.0545187i	0.0180467	+	0.000110810i
$493$	147.286	+	549.679i	0.298755	+	1.11497i
$494$	123.030	−	213.094i	0.249048	−	0.431364i
$495$	128.288	+	147.734i	0.259168	+	0.298452i
$496$			68.8470i			0.138804i
$497$	−25.0991	−	53.5020i	−0.0505013	−	0.107650i
$498$	36.0054	−	61.4882i	0.0723001	−	0.123470i
$499$	−728.049	+	420.340i	−1.45902	+	0.842364i	−0.998963	−	0.0455272i	$-0.985503\pi$
$499$	−728.049	+	420.340i	−1.45902	+	0.842364i	−0.460054	+	0.887891i	$0.652170\pi$
$500$	20.7310	+	235.950i	0.0414619	+	0.471900i
$501$	−2.55825	+	9.31828i	−0.00510629	+	0.0185994i
$502$	21.2536	−	79.3196i	0.0423379	−	0.158007i
$503$	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
$507$	183.534	+	322.446i	0.362000	+	0.635989i
$508$	−188.759	+	50.5779i	−0.371573	+	0.0995628i
$509$	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
$513$	595.170	−	329.156i	1.16017	−	0.641629i
$514$	16.0499	−	27.7992i	0.0312255	−	0.0540841i
$515$	24.1782	−	416.008i	0.0469479	−	0.807782i
$516$	−261.030	−	264.255i	−0.505872	−	0.512123i
$517$	−42.3109	−	42.3109i	−0.0818393	−	0.0818393i
$518$	43.7758	−	514.044i	0.0845093	−	0.992362i
$519$	−255.024	−	975.686i	−0.491375	−	1.87993i
$520$	−281.957	+	58.2556i	−0.542224	+	0.112030i
$521$	−139.064	+	240.867i	−0.266918	+	0.462316i	−0.968064	−	0.250702i	$-0.919339\pi$
$521$	−139.064	+	240.867i	−0.266918	+	0.462316i	0.701146	+	0.713018i	$0.252672\pi$
$522$	262.919	+	269.457i	0.503675	+	0.516200i
$523$	839.729	+	225.005i	1.60560	+	0.430220i	0.946728	−	0.322034i	$-0.104367\pi$
$523$	839.729	+	225.005i	1.60560	+	0.430220i	0.658873	+	0.752254i	$0.271033\pi$
$524$			184.357i			0.351827i
$525$	−108.005	+	513.770i	−0.205724	+	0.978610i
$526$	285.354			0.542498
$527$	72.8194	−	271.766i	0.138177	−	0.515685i
$528$	31.1657	+	54.7542i	0.0590259	+	0.103701i
$529$	415.328	+	239.790i	0.785120	+	0.453289i
$530$	51.3006	+	248.295i	0.0967937	+	0.468480i
$531$	493.702	−	277.012i	0.929759	−	0.521680i
$532$	141.905	+	302.488i	0.266739	+	0.568587i
$533$	−7.43587	+	7.43587i	−0.0139510	+	0.0139510i
$534$	−206.856	−	209.412i	−0.387371	−	0.392157i
$535$	−102.543	−	5.95975i	−0.191669	−	0.0111397i
$536$	−859.911	−	496.470i	−1.60431	−	0.926249i
$537$	−4.52331	+	736.672i	−0.00842329	+	1.37183i
$538$	−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	$0.649516\pi$
$542$	−108.732	−	405.792i	−0.200612	−	0.748694i
$543$	−136.628	−	240.039i	−0.251618	−	0.442061i
$544$	−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	$0.171681\pi$
$548$	399.284	+	106.988i	0.728621	+	0.195233i
$549$	1.18878	−	96.7991i	0.00216535	−	0.176319i
$550$	−58.1929	+	146.586i	−0.105805	+	0.266519i
$551$	363.119	+	628.940i	0.659018	+	1.14145i
$552$	411.762	−	703.186i	0.745946	−	1.27389i
$553$	277.168	−	397.791i	0.501208	−	0.719333i
$554$	−49.4065			−0.0891814
$555$	337.857	+	682.943i	0.608751	+	1.23053i
$556$	188.496	+	108.828i	0.339021	+	0.195734i
$557$	−564.218	+	151.182i	−1.01296	+	0.271421i	−0.726865	−	0.686780i	$-0.759023\pi$
$557$	−564.218	+	151.182i	−1.01296	+	0.271421i	−0.286093	+	0.958202i	$0.592357\pi$
$558$	−45.9631	−	180.368i	−0.0823711	−	0.323240i
$559$	439.910			0.786958
$560$	−66.5789	+	155.387i	−0.118891	+	0.277476i
$561$	−65.1096	−	249.100i	−0.116060	−	0.444029i
$562$	637.154	+	170.725i	1.13373	+	0.303781i
$563$	−130.925	+	35.0813i	−0.232550	+	0.0623115i	−0.373212	−	0.927746i	$-0.621744\pi$
$563$	−130.925	+	35.0813i	−0.232550	+	0.0623115i	0.140662	+	0.990058i	$0.455077\pi$
$564$	75.4392	+	20.7112i	0.133757	+	0.0367219i
$565$	−290.276	−	190.866i	−0.513763	−	0.337817i
$566$	−432.538			−0.764202
$567$	−457.109	−	335.470i	−0.806189	−	0.591658i
$568$	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	$0.913211\pi$
$570$	456.211	+	304.003i	0.800371	+	0.533338i
$571$	−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	$0.285459\pi$
$572$	53.5785	+	14.3563i	0.0936687	+	0.0250984i
$573$	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
$576$	−454.940	−	270.162i	−0.789826	−	0.469032i
$577$	636.928	−	170.664i	1.10386	−	0.295779i	0.339526	−	0.940597i	$-0.389733\pi$
$577$	636.928	−	170.664i	1.10386	−	0.295779i	0.764336	+	0.644818i	$0.223067\pi$
$578$	−37.7792	−	140.994i	−0.0653620	−	0.243934i
$579$	−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
$582$	387.269	−	661.358i	0.665411	−	1.13635i
$583$	39.3299	−	146.781i	0.0674612	−	0.251769i
$584$	−199.407	−	115.128i	−0.341451	−	0.197137i
$585$	272.370	−	132.668i	0.465589	−	0.226783i
$586$	−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	$0.499448\pi$
$588$	179.369	−	213.107i	0.305050	−	0.362426i
$589$		−	359.058i		−	0.609605i
$590$	381.277	+	250.703i	0.646233	+	0.424920i
$591$	−285.931	−	78.4998i	−0.483809	−	0.132825i
$592$	63.5000	+	236.985i	0.107263	+	0.400313i
$593$	104.986	−	391.812i	0.177042	−	0.660728i	−0.819153	−	0.573575i	$-0.805556\pi$
$593$	104.986	−	391.812i	0.177042	−	0.660728i	0.996195	−	0.0871534i	$-0.0277770\pi$
$594$	−118.204	−	122.640i	−0.198996	−	0.206465i
$595$	427.165	−	542.951i	0.717925	−	0.912522i
$596$		−	336.876i		−	0.565228i
$597$	4.53916	−	739.254i	0.00760329	−	1.23828i
$598$	80.2910	+	299.650i	0.134266	+	0.501087i
$599$	−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	$0.817468\pi$
$600$	−89.2271	−	635.232i	−0.148712	−	1.05872i
$601$			601.570i			1.00095i	0.865751	+	0.500474i	$0.166841\pi$
$601$			601.570i			1.00095i	−0.865751	+	0.500474i	$0.833159\pi$
$602$	379.384	−	544.491i	0.630206	−	0.904470i
$603$	1005.85	+	282.799i	1.66807	+	0.468986i
$604$	−74.0448	+	42.7498i	−0.122591	+	0.0707777i
$605$	−381.295	+	339.408i	−0.630239	+	0.561005i
$606$	264.658	+	72.6596i	0.436730	+	0.119900i
$607$	−8.53673	+	31.8595i	−0.0140638	+	0.0524869i	−0.972601	−	0.232480i	$-0.925316\pi$
$607$	−8.53673	+	31.8595i	−0.0140638	+	0.0524869i	0.958537	+	0.284967i	$0.0919826\pi$
$608$	−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
$612$	235.082	+	240.928i	0.384121	+	0.393673i
$613$	425.226	−	113.939i	0.693681	−	0.185871i	0.105282	−	0.994442i	$-0.466425\pi$
$613$	425.226	−	113.939i	0.693681	−	0.185871i	0.588398	+	0.808571i	$0.299759\pi$
$614$	−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	0.752160	−	0.658981i	$-0.229012\pi$
$617$	57.4913	+	57.4913i	0.0931787	+	0.0931787i	−0.658981	+	0.752160i	$0.729012\pi$
$618$	−2.22740	+	362.757i	−0.00360421	+	0.586986i
$619$	−289.165	+	500.848i	−0.467148	+	0.809124i	−0.999296	−	0.0375275i	$-0.988052\pi$
$619$	−289.165	+	500.848i	−0.467148	+	0.809124i	0.532148	+	0.846652i	$0.321385\pi$
$620$	−100.873	+	89.7919i	−0.162699	+	0.144826i
$621$	−237.148	+	824.024i	−0.381880	+	1.32693i
$622$	129.566	+	129.566i	0.208305	+	0.208305i
$623$	−270.618	+	388.391i	−0.434379	+	0.623420i
$624$	94.3827	−	24.6697i	0.151254	−	0.0395347i
$625$	428.677	−	454.820i	0.685883	−	0.727712i
$626$	17.8292	−	30.8812i	0.0284812	−	0.0493309i
$627$	−162.538	−	285.560i	−0.259232	−	0.455438i
$628$	317.266	+	85.0111i	0.505200	+	0.135368i
$629$		−	1002.64i		−	1.59402i
$630$	70.6878	−	451.536i	0.112203	−	0.716724i
$631$	−451.519			−0.715561			−0.357781	−	0.933806i	$-0.616466\pi$
$631$	−451.519			−0.715561			−0.357781	+	0.933806i	$0.616466\pi$
$632$	−153.321	+	572.201i	−0.242596	+	0.905382i
$633$	388.639	−	221.211i	0.613964	−	0.349464i
$634$	−261.716	−	151.102i	−0.412801	−	0.238331i
$635$	430.854	+	283.301i	0.678511	+	0.446144i
$636$	50.2407	+	192.214i	0.0789948	+	0.302223i
$637$	30.2711	+	328.500i	0.0475214	+	0.515699i
$638$	128.608	−	128.608i	0.201581	−	0.201581i
$639$	−65.3305	−	38.7960i	−0.102239	−	0.0607136i
$640$	−6.82223	+	117.383i	−0.0106597	+	0.183411i
$641$	−22.3299	−	12.8922i	−0.0348360	−	0.0201126i	0.482481	−	0.875907i	$-0.339736\pi$
$641$	−22.3299	−	12.8922i	−0.0348360	−	0.0201126i	−0.517317	+	0.855794i	$0.673069\pi$
$642$	89.4171	+	0.549038i	0.139279	+	0.000855199i
$643$	−628.889	+	628.889i	−0.978054	+	0.978054i	−0.999764	−	0.0217104i	$-0.993089\pi$
$643$	−628.889	+	628.889i	−0.978054	+	0.978054i	0.0217104	+	0.999764i	$0.493089\pi$
$644$	−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
$647$	−42.8316	−	159.850i	−0.0662002	−	0.247063i	0.924894	−	0.380225i	$-0.124153\pi$
$647$	−42.8316	−	159.850i	−0.0662002	−	0.247063i	−0.991094	+	0.133162i	$0.957487\pi$
$648$	664.574	+	195.686i	1.02558	+	0.301984i
$649$	−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
$653$	1091.72	+	292.526i	1.67185	+	0.447972i	0.965610	−	0.259996i	$-0.0837212\pi$
$653$	1091.72	+	292.526i	1.67185	+	0.447972i	0.706245	+	0.707968i	$0.250388\pi$
$654$	−1.22210	+	4.45143i	−0.00186865	+	0.00680646i
$655$	363.361	−	323.444i	0.554750	−	0.493808i
$656$	−3.77213	−	6.53352i	−0.00575020	−	0.00995964i
$657$	233.248	+	65.5790i	0.355020	+	0.0998158i
$658$	−11.8598	+	139.266i	−0.0180241	+	0.211650i
$659$	672.256			1.02012			0.510058	−	0.860140i	$-0.329624\pi$
$659$	672.256			1.02012			0.510058	+	0.860140i	$0.329624\pi$
$660$	−39.5778	+	117.075i	−0.0599664	+	0.177387i
$661$	−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	$0.834314\pi$
$662$	−466.541	+	125.009i	−0.704744	+	0.188836i
$663$	−398.658	−	2.44784i	−0.601295	−	0.00369207i
$664$	140.012			0.210861
$665$	347.229	−	810.388i	0.522149	−	1.21863i
$666$	−324.574	−	578.469i	−0.487348	−	0.868572i
$667$	−884.408	−	236.976i	−1.32595	−	0.355287i
$668$	−5.89546	+	1.57968i	−0.00882553	+	0.00236479i
$669$	231.567	−	843.468i	0.346139	−	1.26079i
$670$	170.411	+	824.786i	0.254344	+	1.23102i
$671$	−46.7685			−0.0696996
$672$	−197.443	+	536.075i	−0.293814	+	0.797730i
$673$	−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
$675$	256.046	+	624.552i	0.379328	+	0.925262i
$676$	−117.173	+	202.949i	−0.173332	+	0.300220i
$677$	−166.683	−	44.6627i	−0.246209	−	0.0659714i	0.133604	−	0.991035i	$-0.457345\pi$
$677$	−166.683	−	44.6627i	−0.246209	−	0.0659714i	−0.379813	+	0.925063i	$0.624012\pi$
$678$	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
$681$	793.492	+	803.296i	1.16519	+	1.17958i
$682$	−86.8587	+	23.2737i	−0.127359	+	0.0341257i
$683$	3.48281	+	12.9980i	0.00509928	+	0.0190308i	0.968429	−	0.249291i	$-0.0801976\pi$
$683$	3.48281	+	12.9980i	0.00509928	+	0.0190308i	−0.963329	+	0.268322i	$0.913531\pi$
$684$	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
$687$	−444.158	−	260.084i	−0.646518	−	0.378579i
$688$	−81.6826	+	304.844i	−0.118725	+	0.443087i
$689$	−203.771	−	117.647i	−0.295748	−	0.170750i
$690$	−677.721	+	135.692i	−0.982204	+	0.196655i
$691$	−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
$693$	−159.346	+	222.809i	−0.229936	+	0.321514i
$694$			797.952i			1.14979i
$695$	−116.209	−	562.450i	−0.167207	−	0.809281i
$696$	−195.847	+	713.360i	−0.281389	+	1.02494i
$697$	7.97956	+	29.7801i	0.0114484	+	0.0427262i
$698$	−30.8477	+	115.125i	−0.0441944	+	0.164936i
$699$	−343.695	+	89.8347i	−0.491695	+	0.128519i
$700$	−314.503	+	105.109i	−0.449290	+	0.150155i
$701$			1006.91i			1.43639i	0.695843	+	0.718194i	$0.255031\pi$
$701$			1006.91i			1.43639i	−0.695843	+	0.718194i	$0.744969\pi$
$702$	−230.797	+	127.641i	−0.328771	+	0.181825i
$703$	−331.171	−	1235.95i	−0.471083	−	1.75811i
$704$	−127.810	+	221.374i	−0.181548	+	0.314451i
$705$	−91.5328	−	185.024i	−0.129834	−	0.262446i
$706$		−	868.386i		−	1.23001i
$707$	37.4514	−	439.778i	0.0529722	−	0.622034i
$708$	308.558	+	180.681i	0.435817	+	0.255200i
$709$	422.388	−	243.866i	0.595751	−	0.343957i	−0.171617	−	0.985164i	$-0.554899\pi$
$709$	422.388	−	243.866i	0.595751	−	0.343957i	0.767368	+	0.641207i	$0.221566\pi$
$710$	3.55357	−	61.1425i	0.00500503	−	0.0861162i
$711$	7.65473	−	623.306i	0.0107661	−	0.876661i
$712$	149.698	−	558.680i	0.210250	−	0.784662i
$713$	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
$717$	−738.417	+	420.301i	−1.02987	+	0.586194i
$718$	68.3594	−	18.3168i	0.0952081	−	0.0255109i
$719$	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
$723$	−247.712	−	1.52100i	−0.342617	−	0.00210374i
$724$	87.2269	−	151.081i	0.120479	−	0.208676i
$725$	−661.747	+	285.644i	−0.912755	+	0.393991i
$726$	316.155	−	312.296i	0.435475	−	0.430159i
$727$	654.711	+	654.711i	0.900566	+	0.900566i	0.995485	−	0.0949191i	$-0.0302592\pi$
$727$	654.711	+	654.711i	0.900566	+	0.900566i	−0.0949191	+	0.995485i	$0.530259\pi$
$728$	−171.192	−	364.917i	−0.235153	−	0.501259i
$729$	−728.505	−	26.8508i	−0.999321	−	0.0368324i
$730$	39.5170	+	191.262i	0.0541329	+	0.262003i
$731$	644.866	−	1116.94i	0.882170	−	1.52796i
$732$	53.1400	−	30.2469i	0.0725957	−	0.0413209i
$733$	−392.433	−	105.152i	−0.535379	−	0.143454i	−0.0190079	−	0.999819i	$-0.506051\pi$
$733$	−392.433	−	105.152i	−0.535379	−	0.143454i	−0.516371	+	0.856365i	$0.672717\pi$
$734$			221.375i			0.301601i
$735$	−734.718	+	20.3536i	−0.999617	+	0.0276920i
$736$	863.941			1.17383
$737$	130.646	−	487.578i	0.177267	−	0.661571i
$738$	14.2442	+	14.5984i	0.0193011	+	0.0197811i
$739$	−701.246	−	404.865i	−0.948912	−	0.547855i	−0.0561693	−	0.998421i	$-0.517889\pi$
$739$	−701.246	−	404.865i	−0.948912	−	0.547855i	−0.892743	+	0.450567i	$0.851222\pi$
$740$	−264.408	+	402.121i	−0.357308	+	0.543406i
$741$	−492.234	+	128.660i	−0.664284	+	0.173630i
$742$	−321.350	+	150.753i	−0.433087	+	0.203172i
$743$	−205.338	+	205.338i	−0.276364	+	0.276364i	−0.831656	−	0.555292i	$-0.812607\pi$
$743$	−205.338	+	205.338i	−0.276364	+	0.276364i	0.555292	+	0.831656i	$0.312607\pi$
$744$	260.201	−	257.025i	0.349733	−	0.345464i
$745$	−663.969	+	591.029i	−0.891234	+	0.793328i
$746$	302.409	+	174.596i	0.405375	+	0.234043i
$747$	−142.768	+	36.3816i	−0.191122	+	0.0487036i
$748$	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	$0.929033\pi$
$752$	−17.2036	−	64.2045i	−0.0228771	−	0.0853784i
$753$	−147.563	+	83.9918i	−0.195967	+	0.111543i
$754$	−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	$0.450410\pi$
$758$	49.5450	+	13.2755i	0.0653628	+	0.0175139i
$759$	399.474	+	109.672i	0.526316	+	0.144495i
$760$	−62.5027	+	1075.42i	−0.0822404	+	1.41502i
$761$	−388.123	−	672.248i	−0.510017	−	0.883375i	−0.999933	−	0.0116051i	$-0.996306\pi$
$761$	−388.123	−	672.248i	−0.510017	−	0.883375i	0.489916	−	0.871770i	$-0.337027\pi$
$762$	−387.370	−	226.831i	−0.508359	−	0.297678i
$763$	7.39685	+	0.629914i	0.00969444	+	0.000825575i
$764$	86.8874			0.113727
$765$	62.4216	−	886.032i	0.0815968	−	1.15821i
$766$	344.869	+	199.110i	0.450221	+	0.259935i
$767$	−409.049	+	109.604i	−0.533311	+	0.142900i
$768$	4.96020	−	807.825i	0.00645859	−	1.05186i
$769$	1219.04			1.58522			0.792612	−	0.609727i	$-0.208721\pi$
$769$	1219.04			1.58522			0.792612	+	0.609727i	$0.208721\pi$
$770$	−218.546	−	31.4688i	−0.283826	−	0.0408686i
$771$	−64.2146	+	16.7843i	−0.0832874	+	0.0217696i
$772$	−496.192	−	132.954i	−0.642735	−	0.172220i
$773$	561.179	−	150.367i	0.725975	−	0.194524i	0.123139	−	0.992389i	$-0.460704\pi$
$773$	561.179	−	150.367i	0.725975	−	0.194524i	0.602836	+	0.797865i	$0.294037\pi$
$774$	10.4777	−	853.172i	0.0135371	−	1.10229i
$775$	353.953	+	41.2826i	0.456713	+	0.0532678i
$776$	1505.95			1.94065
$777$	−819.775	+	682.542i	−1.05505	+	0.878432i
$778$	−481.817	−	481.817i	−0.619303	−	0.619303i
$779$	19.6728	+	34.0743i	0.0252539	+	0.0437411i
$780$	159.242	+	106.113i	0.204156	+	0.136042i
$781$	−18.3539	+	31.7898i	−0.0235005	+	0.0407040i
$782$	878.517	+	235.398i	1.12342	+	0.301021i
$783$	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
$786$	−301.285	+	297.607i	−0.383314	+	0.378635i
$787$	860.369	−	230.535i	1.09323	−	0.292929i	0.333222	−	0.942848i	$-0.391864\pi$
$787$	860.369	−	230.535i	1.09323	−	0.292929i	0.760003	+	0.649919i	$0.225197\pi$
$788$	−48.4725	−	180.902i	−0.0615133	−	0.229571i
$789$	−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
$792$	90.5885	−	322.201i	0.114379	−	0.406820i
$793$	−18.7428	+	69.9490i	−0.0236353	+	0.0882080i
$794$	−125.445	−	72.4257i	−0.157991	−	0.0912163i
$795$	290.702	−	436.251i	0.365663	−	0.548743i
$796$	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	$0.261872\pi$
$798$	−265.263	+	720.213i	−0.332410	+	0.902523i
$799$			271.636i			0.339970i
$800$	533.372	−	421.950i	0.666715	−	0.527438i
$801$	−7.47383	+	608.576i	−0.00933063	+	0.759771i
$802$	143.688	+	536.250i	0.179162	+	0.668640i
$803$	30.2959	−	113.066i	0.0377284	−	0.140804i
$804$	166.890	+	638.498i	0.207574	+	0.794151i
$805$	412.900	+	1032.00i	0.512919	+	1.28199i
$806$			139.237i			0.172750i
$807$	486.658	+	2.98817i	0.603045	+	0.00370282i
$808$	139.577	+	520.909i	0.172744	+	0.644689i
$809$	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	$-0.0194762\pi$
$810$	−250.812	−	531.401i	−0.309645	−	0.656051i
$811$			677.071i			0.834859i	0.908709	+	0.417430i	$0.137069\pi$
$811$			677.071i			0.834859i	−0.908709	+	0.417430i	$0.862931\pi$
$812$	381.032	+	32.4486i	0.469252	+	0.0399614i
$813$	−438.933	+	749.587i	−0.539893	+	0.922001i
$814$	−277.519	+	160.226i	−0.340933	+	0.196838i
$815$	246.870	+	14.3480i	0.302909	+	0.0176049i
$816$	75.7194	−	275.803i	0.0927933	−	0.337994i
$817$	425.999	−	1589.85i	0.521419	−	1.94596i
$818$	−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	−0.998845	−	0.0480474i	$-0.984700\pi$
$821$	−1195.92	+	690.462i	−1.45666	+	0.841001i	−0.457812	+	0.889049i	$0.651367\pi$
$822$	469.719	+	825.238i	0.571434	+	1.00394i
$823$	457.896	−	122.693i	0.556374	−	0.149080i	0.0303340	−	0.999540i	$-0.490343\pi$
$823$	457.896	−	122.693i	0.556374	−	0.149080i	0.526040	+	0.850460i	$0.323676\pi$
$824$	−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	0.999879	−	0.0155366i	$-0.00494564\pi$
$827$	814.051	+	814.051i	0.984343	+	0.984343i	−0.0155366	+	0.999879i	$0.504946\pi$
$828$	−524.826	+	133.741i	−0.633847	+	0.161523i
$829$	344.646	−	596.945i	0.415738	−	0.720079i	−0.579768	−	0.814782i	$-0.696857\pi$
$829$	344.646	−	596.945i	0.415738	−	0.720079i	0.995506	+	0.0947031i	$0.0301902\pi$
$830$	−78.9604	−	88.7050i	−0.0951330	−	0.106873i
$831$	71.7906	+	72.6777i	0.0863907	+	0.0874581i
$832$	279.875	+	279.875i	0.336389	+	0.336389i
$833$	878.445	+	404.692i	1.05456	+	0.485824i
$834$	126.436	+	483.728i	0.151602	+	0.580010i
$835$	13.4567	+	8.84825i	0.0161158	+	0.0105967i
$836$	103.769	−	179.732i	0.124125	−	0.214991i
$837$	−198.536	+	329.698i	−0.237200	+	0.393904i
$838$	261.739	+	70.1328i	0.312338	+	0.0836907i
$839$			1583.07i			1.88686i	0.331576	+	0.943429i	$0.392420\pi$
$839$			1583.07i			1.88686i	−0.331576	+	0.943429i	$0.607580\pi$
$840$	835.828	−	328.473i	0.995033	−	0.391039i
$841$	−9.79677			−0.0116490
$842$	−12.5755	+	46.9324i	−0.0149353	+	0.0557392i
$843$	−674.685	−	1185.34i	−0.800338	−	1.40609i
$844$	244.611	+	141.226i	0.289824	+	0.167330i
$845$	605.577	−	125.120i	0.716659	−	0.148070i
$846$	87.9342	+	156.720i	0.103941	+	0.185248i
$847$	−586.364	−	408.560i	−0.692283	−	0.482361i
$848$	119.362	−	119.362i	0.140757	−	0.140757i
$849$	628.505	+	636.271i	0.740288	+	0.749435i
$850$	657.340	−	283.741i	0.773341	−	0.333813i
$851$	1397.07	+	806.597i	1.64168	+	0.947823i
$852$	0.294673	−	47.9909i	0.000345861	−	0.0563273i
$853$	−500.340	+	500.340i	−0.586565	+	0.586565i	−0.936699	−	0.350135i	$-0.886136\pi$
$853$	−500.340	+	500.340i	−0.586565	+	0.586565i	0.350135	+	0.936699i	$0.386136\pi$
$854$	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
$857$	−56.3034	−	210.127i	−0.0656982	−	0.245189i	0.925265	−	0.379321i	$-0.123842\pi$
$857$	−56.3034	−	210.127i	−0.0656982	−	0.245189i	−0.990964	+	0.134131i	$0.957176\pi$
$858$	63.0298	+	110.736i	0.0734613	+	0.129062i
$859$	197.711	+	342.446i	0.230165	+	0.398657i	0.957856	−	0.287247i	$-0.0927402\pi$
$859$	197.711	+	342.446i	0.230165	+	0.398657i	−0.727692	+	0.685904i	$0.759407\pi$
$860$	−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
$863$	−642.646	−	172.197i	−0.744665	−	0.199532i	−0.133515	−	0.991047i	$-0.542626\pi$
$863$	−642.646	−	172.197i	−0.744665	−	0.199532i	−0.611151	+	0.791514i	$0.709293\pi$
$864$	177.003	+	712.855i	0.204864	+	0.825064i
$865$	−1677.94	−	97.5213i	−1.93982	−	0.112741i
$866$	−523.577	−	906.861i	−0.604592	−	1.04718i
$867$	−152.509	+	260.447i	−0.175904	+	0.300400i
$868$	−155.125	−	108.086i	−0.178716	−	0.124523i
$869$	−301.150			−0.346548
$870$	562.401	−	278.224i	0.646438	−	0.319797i
$871$	−676.886	−	390.800i	−0.777137	−	0.448680i
$872$	−8.76144	+	2.34762i	−0.0100475	+	0.00269223i
$873$	−1535.59	+	391.315i	−1.75899	+	0.448242i
$874$	1160.70			1.32803
$875$	758.943	+	435.466i	0.867363	+	0.497676i
$876$	38.7006	+	148.063i	0.0441787	+	0.169022i
$877$	545.589	+	146.190i	0.622109	+	0.166694i	0.556086	−	0.831125i	$-0.312302\pi$
$877$	545.589	+	146.190i	0.622109	+	0.166694i	0.0660226	+	0.997818i	$0.478969\pi$
$878$	−649.160	+	173.942i	−0.739362	+	0.198112i
$879$	508.321	+	139.555i	0.578295	+	0.158766i
$880$	102.832	−	21.2464i	0.116855	−	0.0241436i
$881$	−647.825			−0.735330			−0.367665	−	0.929958i	$-0.619843\pi$
$881$	−647.825			−0.735330			−0.367665	+	0.929958i	$0.619843\pi$
$882$	637.823	−	50.8844i	0.723156	−	0.0576921i
$883$	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
$885$	−185.232	−	925.151i	−0.209301	−	1.04537i
$886$	509.489	−	882.460i	0.575044	−	0.996005i
$887$	620.764	+	166.333i	0.699847	+	0.187523i	0.591162	−	0.806553i	$-0.298669\pi$
$887$	620.764	+	166.333i	0.699847	+	0.187523i	0.108685	+	0.994076i	$0.465336\pi$
$888$	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
$891$	−8.64907	+	352.083i	−0.00970715	+	0.395155i
$892$	533.642	−	142.989i	0.598254	−	0.160302i
$893$	89.7217	+	334.846i	0.100472	+	0.374967i
$894$	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
$897$	324.122	−	553.519i	0.361340	−	0.617078i
$898$	170.040	−	634.599i	0.189354	−	0.706680i
$899$	−355.896	−	205.477i	−0.395880	−	0.228561i
$900$	−258.693	+	338.893i	−0.287436	+	0.376548i
$901$	−597.417	+	344.919i	−0.663060	+	0.382818i
$902$	6.96766	−	6.96766i	0.00772467	−	0.00772467i
$903$	−1352.22	+	233.099i	−1.49748	+	0.258139i
$904$			594.265i			0.657373i
$905$	−450.810	+	93.1429i	−0.498133	+	0.102920i
$906$	−189.394	−	51.9963i	−0.209044	−	0.0573911i
$907$	44.6420	+	166.606i	0.0492194	+	0.183689i	0.986159	−	0.165802i	$-0.0530212\pi$
$907$	44.6420	+	166.606i	0.0492194	+	0.183689i	−0.936940	+	0.349491i	$0.886355\pi$
$908$	−184.584	+	688.878i	−0.203287	+	0.758676i
$909$	−277.681	−	494.895i	−0.305480	−	0.544439i
$910$	−134.650	+	314.255i	−0.147967	+	0.345336i
$911$		−	117.536i		−	0.129019i	−0.997917	−	0.0645093i	$-0.979452\pi$
$911$		−	117.536i		−	0.129019i	0.997917	−	0.0645093i	$-0.0205482\pi$
$912$	2.24113	−	364.993i	0.00245737	−	0.400211i
$913$	18.4221	+	68.7521i	0.0201775	+	0.0753036i
$914$	−170.251	+	294.883i	−0.186270	+	0.322629i
$915$	−152.847	−	51.6705i	−0.167045	−	0.0564705i
$916$		−	325.099i		−	0.354911i
$917$	558.785	+	389.344i	0.609362	+	0.424584i
$918$	−14.2426	+	773.110i	−0.0155148	+	0.842168i
$919$	89.1660	−	51.4800i	0.0970250	−	0.0560174i	−0.450702	−	0.892674i	$-0.648826\pi$
$919$	89.1660	−	51.4800i	0.0970250	−	0.0560174i	0.547727	+	0.836657i	$0.315493\pi$
$920$	−902.999	−	1014.44i	−0.981521	−	1.10265i
$921$	1273.32	+	349.579i	1.38254	+	0.379564i
$922$	118.298	−	441.495i	0.128306	−	0.478845i
$923$	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
$927$	536.858	−	523.832i	0.579135	−	0.565083i
$928$	−757.576	+	202.992i	−0.816354	+	0.218741i
$929$	−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
$933$	2.32627	−	378.859i	0.00249332	−	0.406066i
$934$	567.173	−	982.373i	0.607252	−	1.05179i
$935$	−428.392	−	24.8979i	−0.458173	−	0.0266288i
$936$	−445.594	−	264.612i	−0.476062	−	0.282706i
$937$	−848.278	−	848.278i	−0.905313	−	0.905313i	0.0905767	−	0.995889i	$-0.471129\pi$
$937$	−848.278	−	848.278i	−0.905313	−	0.905313i	−0.995889	+	0.0905767i	$0.971129\pi$
$938$	−1067.46	+	500.773i	−1.13802	+	0.533874i
$939$	−71.3336	+	18.6451i	−0.0759677	+	0.0198563i
$940$	71.6339	−	108.943i	0.0762063	−	0.115897i
$941$	570.470	−	988.083i	0.606238	−	1.05003i	−0.385617	−	0.922659i	$-0.626011\pi$
$941$	570.470	−	988.083i	0.606238	−	1.05003i	0.991855	−	0.127376i	$-0.0406554\pi$
$942$	373.232	+	655.723i	0.396213	+	0.696096i
$943$	−47.9148	−	12.8387i	−0.0508111	−	0.0136148i
$944$		−	303.810i		−	0.321833i
$945$	−766.930	+	552.126i	−0.811566	+	0.584261i
$946$	−412.210			−0.435740
$947$	−145.313	+	542.316i	−0.153446	+	0.572668i	0.845788	+	0.533520i	$0.179131\pi$
$947$	−145.313	+	542.316i	−0.153446	+	0.572668i	−0.999233	+	0.0391479i	$0.987536\pi$
$948$	342.178	−	194.765i	0.360947	−	0.205448i
$949$	−156.965	−	90.6238i	−0.165400	−	0.0954940i
$950$	716.582	−	566.887i	0.754297	−	0.596723i
$951$	158.016	+	604.549i	0.166158	+	0.635698i
$952$	−1177.48	−	100.274i	−1.23685	−	0.105330i
$953$	491.430	−	491.430i	0.515666	−	0.515666i	−0.400591	−	0.916257i	$-0.631195\pi$
$953$	491.430	−	491.430i	0.515666	−	0.515666i	0.916257	+	0.400591i	$0.131195\pi$
$954$	−233.021	+	392.396i	−0.244257	+	0.411317i
$955$	−152.439	−	171.252i	−0.159622	−	0.179321i
$956$	−464.763	−	268.331i	−0.486153	−	0.280681i
$957$	−376.061	−	2.30909i	−0.392958	−	0.00241284i
$958$	−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
$962$	128.423	+	479.281i	0.133496	+	0.498214i
$963$	−129.121	−	132.332i	−0.134082	−	0.137416i
$964$	−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	$0.480719\pi$
$968$	843.453	+	226.003i	0.871336	+	0.233474i
$969$	−394.899	+	1438.40i	−0.407533	+	1.48441i
$970$	−849.286	−	954.098i	−0.875553	−	0.983606i
$971$	−687.381	−	1190.58i	−0.707910	−	1.22614i	−0.965631	−	0.259917i	$-0.916305\pi$
$971$	−687.381	−	1190.58i	−0.707910	−	1.22614i	0.257721	−	0.966219i	$-0.417029\pi$
$972$	−217.878	−	405.643i	−0.224154	−	0.417329i
$973$	727.940	−	341.495i	0.748140	−	0.350971i
$974$	1002.85			1.02962
$975$	−70.2359	−	500.028i	−0.0720368	−	0.512849i
$976$	−44.9923	−	25.9763i	−0.0460987	−	0.0266151i
$977$	590.306	−	158.172i	0.604202	−	0.161896i	0.0562663	−	0.998416i	$-0.482080\pi$
$977$	590.306	−	158.172i	0.604202	−	0.161896i	0.547936	+	0.836520i	$0.315414\pi$
$978$	−215.270	−	1.32180i	−0.220113	−	0.00135153i
$979$	294.033			0.300340
$980$	−245.590	−	393.964i	−0.250602	−	0.402004i
$981$	8.32390	−	4.67047i	0.00848512	−	0.00476092i
$982$	−672.044	−	180.074i	−0.684362	−	0.183374i
$983$	−1087.89	+	291.499i	−1.10670	+	0.296541i	−0.765492	−	0.643445i	$-0.777504\pi$
$983$	−1087.89	+	291.499i	−1.10670	+	0.296541i	−0.341213	+	0.939986i	$0.610838\pi$
$984$	−10.6104	+	38.6479i	−0.0107830	+	0.0392764i
$985$	−271.508	+	412.919i	−0.275643	+	0.419207i
$986$	−825.667			−0.837391
$987$	222.095	−	184.916i	0.225020	−	0.187351i
$988$	−227.230	−	227.230i	−0.229990	−	0.229990i
$989$	1037.56	+	1797.10i	1.04910	+	1.81709i
$990$	−255.219	+	124.314i	−0.257797	+	0.125570i
$991$	−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	$0.209826\pi$
$992$	374.552	+	100.361i	0.377572	+	0.101170i
$993$	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
$996$	−65.3964	−	66.2045i	−0.0656590	−	0.0664703i
$997$	−1022.85	+	274.072i	−1.02593	+	0.274897i	−0.732270	−	0.681014i	$-0.761539\pi$
$997$	−1022.85	+	274.072i	−1.02593	+	0.274897i	−0.293658	+	0.955911i	$0.594873\pi$
$998$	−315.694	−	1178.18i	−0.316326	−	1.18055i
$999$	−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.38.10	yes	112
3.2	odd	2	inner	105.3.w.a.38.19	yes	112
5.2	odd	4	inner	105.3.w.a.17.10	✓	112
7.5	odd	6	inner	105.3.w.a.68.19	yes	112
15.2	even	4	inner	105.3.w.a.17.19	yes	112
21.5	even	6	inner	105.3.w.a.68.10	yes	112
35.12	even	12	inner	105.3.w.a.47.19	yes	112
105.47	odd	12	inner	105.3.w.a.47.10	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.10	✓	112	5.2	odd	4	inner
105.3.w.a.17.19	yes	112	15.2	even	4	inner
105.3.w.a.38.10	yes	112	1.1	even	1	trivial
105.3.w.a.38.19	yes	112	3.2	odd	2	inner
105.3.w.a.47.10	yes	112	105.47	odd	12	inner
105.3.w.a.47.19	yes	112	35.12	even	12	inner
105.3.w.a.68.10	yes	112	21.5	even	6	inner
105.3.w.a.68.19	yes	112	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.375522 + 1.40147i) q^{2} +(2.60724 - 1.48402i) q^{3} +(1.64101 + 0.947435i) q^{4} +(-1.01169 - 4.89658i) q^{5} +(1.10073 + 4.21124i) q^{6} +(6.33730 - 2.97299i) q^{7} +(-6.04782 + 6.04782i) q^{8} +(4.59537 - 7.73838i) q^{9} +(7.24231 + 0.420920i) q^{10} +(-3.76549 - 2.17401i) q^{11} +(5.68450 + 0.0349040i) 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} +(5.10867 + 19.0658i) q^{17} +(9.11943 + 9.34620i) 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} +(-30.6760 - 8.21961i) q^{23} +(-6.79302 + 24.7432i) q^{24} +(-22.9530 + 9.90766i) q^{25} +(-4.88411 - 8.45952i) q^{26} +(0.497321 - 26.9954i) q^{27} +(13.2163 + 1.12549i) q^{28} +28.8306 q^{29} +(19.5071 - 9.65029i) q^{30} +(-12.3444 - 7.12704i) q^{31} +(-26.2768 + 7.04085i) q^{32} +(-13.0438 - 0.0800915i) q^{33} -28.6386 q^{34} +(-20.9689 - 28.0233i) q^{35} +(14.8726 - 8.34491i) q^{36} +(-49.0654 - 13.1470i) q^{37} +(-35.3027 + 9.45934i) q^{38} +(-5.34718 + 19.4768i) q^{39} +(35.7321 + 23.4951i) q^{40} +1.56196 q^{41} +(19.4956 + 23.4154i) q^{42} +(-46.2033 - 46.2033i) q^{43} +(-4.11946 - 7.13512i) q^{44} +(-42.5407 - 14.6727i) q^{45} +(23.0391 - 39.9048i) q^{46} +(13.2929 + 3.56182i) q^{47} +(-12.5040 - 7.32189i) q^{48} +(31.3227 - 37.6814i) q^{49} +(-5.26592 - 35.8884i) q^{50} +(41.6136 + 42.1278i) q^{51} +(-12.3225 + 3.30181i) q^{52} +(9.04547 + 33.7582i) q^{53} +(37.6465 + 10.8344i) q^{54} +(-6.83568 + 20.6375i) q^{55} +(-20.3468 + 56.3069i) q^{56} +(65.2119 + 38.1859i) q^{57} +(-10.8265 + 40.4052i) q^{58} +(54.4737 + 31.4504i) q^{59} +(-5.58006 - 27.8699i) q^{60} +(9.31520 - 5.37814i) q^{61} +(14.6239 - 14.6239i) q^{62} +(6.11616 - 62.7024i) q^{63} -58.7901i q^{64} +(28.1269 + 18.4944i) q^{65} +(5.01049 - 18.2504i) q^{66} +(30.0473 + 112.138i) q^{67} +(-9.68028 + 36.1273i) q^{68} +(-92.1777 + 24.0933i) q^{69} +(47.1481 - 18.8638i) q^{70} -8.44240i q^{71} +(19.0083 + 74.5923i) q^{72} +(6.96775 + 26.0040i) q^{73} +(36.8503 - 63.8266i) q^{74} +(-45.1407 + 59.8943i) q^{75} +47.7314i q^{76} +(-30.3264 - 2.58258i) q^{77} +(-25.2881 - 14.8079i) q^{78} +(59.9822 - 34.6307i) q^{79} +(-18.0386 + 16.0570i) q^{80} +(-38.7651 - 71.1215i) q^{81} +(-0.586552 + 2.18904i) 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} +(75.1682 - 42.7852i) q^{87} +(35.9210 - 9.62501i) 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} +(-42.7614 - 0.262563i) q^{93} +(-9.98356 + 17.2920i) q^{94} +(94.0768 - 83.7421i) q^{95} +(-58.0611 + 57.3525i) q^{96} +(-124.503 - 124.503i) q^{97} +(41.0469 + 58.0480i) 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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