LMFDB - Embedded newform 117.3.u.a.68.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(68,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.6
Character	$\chi$	$=$	117.68
Dual form			117.3.u.a.74.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.23352 - 1.28952i) q^{2} +(-0.951185 + 2.84521i) q^{3} +(1.32573 + 2.29623i) q^{4} +(-0.817198 - 0.471810i) q^{5} +(5.79345 - 5.12826i) q^{6} +5.04701 q^{7} +3.47795i q^{8} +(-7.19049 - 5.41265i) q^{9} +(1.21682 + 2.10759i) q^{10} +(-13.8424 - 7.99194i) q^{11} +(-7.79428 + 1.58784i) q^{12} +(-1.19389 - 12.9451i) q^{13} +(-11.2726 - 6.50822i) q^{14} +(2.11971 - 1.87633i) q^{15} +(9.78780 - 16.9530i) q^{16} +(-21.5804 - 12.4595i) q^{17} +(9.08035 + 21.3615i) q^{18} +(-17.4215 + 30.1749i) q^{19} -2.50197i q^{20} +(-4.80064 + 14.3598i) q^{21} +(20.6116 + 35.7003i) q^{22} -20.5334i q^{23} +(-9.89551 - 3.30817i) q^{24} +(-12.0548 - 20.8795i) q^{25} +(-14.0264 + 30.4525i) q^{26} +(22.2396 - 15.3101i) q^{27} +(6.69097 + 11.5891i) q^{28} +(15.4628 + 8.92748i) q^{29} +(-7.15396 + 1.45740i) q^{30} +(10.2399 - 17.7361i) q^{31} +(-31.6745 + 18.2873i) q^{32} +(35.9055 - 31.7829i) q^{33} +(32.1335 + 55.6568i) q^{34} +(-4.12441 - 2.38123i) q^{35} +(2.89605 - 23.6867i) q^{36} +(1.09928 + 1.90401i) q^{37} +(77.8224 - 44.9308i) q^{38} +(37.9671 + 8.91629i) q^{39} +(1.64093 - 2.84217i) q^{40} +5.87340i q^{41} +(29.2396 - 25.8824i) q^{42} +1.87960 q^{43} -42.3806i q^{44} +(3.32232 + 7.81575i) q^{45} +(-26.4783 + 45.8617i) q^{46} +(-6.18058 + 3.56836i) q^{47} +(38.9248 + 43.9738i) q^{48} -23.5277 q^{49} +62.1796i q^{50} +(55.9768 - 49.5497i) q^{51} +(28.1421 - 19.9031i) q^{52} +34.1353i q^{53} +(-69.4153 + 5.51678i) q^{54} +(7.54135 + 13.0620i) q^{55} +17.5532i q^{56} +(-69.2831 - 78.2699i) q^{57} +(-23.0243 - 39.8793i) q^{58} +(-28.2515 + 16.3110i) q^{59} +(7.11863 + 2.37983i) q^{60} +13.3637 q^{61} +(-45.7421 + 26.4092i) q^{62} +(-36.2905 - 27.3177i) q^{63} +16.0248 q^{64} +(-5.13196 + 11.1420i) q^{65} +(-121.180 + 24.6867i) q^{66} -78.5770 q^{67} -66.0715i q^{68} +(58.4220 + 19.5311i) q^{69} +(6.14128 + 10.6370i) q^{70} +(121.405 + 70.0932i) q^{71} +(18.8249 - 25.0082i) q^{72} -89.5686 q^{73} -5.67018i q^{74} +(70.8730 - 14.4382i) q^{75} -92.3848 q^{76} +(-69.8630 - 40.3354i) q^{77} +(-73.3023 - 68.8740i) q^{78} +(28.9076 + 50.0695i) q^{79} +(-15.9971 + 9.23596i) q^{80} +(22.4064 + 77.8393i) q^{81} +(7.57387 - 13.1183i) q^{82} +(38.2595 - 22.0891i) q^{83} +(-39.3378 + 8.01386i) q^{84} +(11.7570 + 20.3637i) q^{85} +(-4.19812 - 2.42379i) q^{86} +(-40.1086 + 35.5034i) q^{87} +(27.7956 - 48.1433i) q^{88} +(-48.6143 + 28.0675i) q^{89} +(2.65813 - 21.7408i) q^{90} +(-6.02555 - 65.3338i) q^{91} +(47.1494 - 27.2217i) q^{92} +(40.7229 + 46.0051i) q^{93} +18.4059 q^{94} +(28.4736 - 16.4393i) q^{95} +(-21.9029 - 107.515i) q^{96} -156.758 q^{97} +(52.5495 + 30.3395i) q^{98} +(56.2764 + 132.390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.23352	−	1.28952i	−1.11676	−	0.644761i	−0.176187	−	0.984357i	$-0.556376\pi$
$2$	−2.23352	−	1.28952i	−1.11676	−	0.644761i	−0.940571	+	0.339596i	$0.889710\pi$
$3$	−0.951185	+	2.84521i	−0.317062	+	0.948405i
$3$	−0.951185	+	2.84521i	−0.317062	+	0.948405i
$4$	1.32573	+	2.29623i	0.331432	+	0.574057i
$5$	−0.817198	−	0.471810i	−0.163440	−	0.0943619i	0.416049	−	0.909342i	$-0.363414\pi$
$5$	−0.817198	−	0.471810i	−0.163440	−	0.0943619i	−0.579489	+	0.814980i	$0.696748\pi$
$6$	5.79345	−	5.12826i	0.965575	−	0.854710i
$7$	5.04701			0.721001			0.360501	−	0.932759i	$-0.382606\pi$
$7$	5.04701			0.721001			0.360501	+	0.932759i	$0.382606\pi$
$8$			3.47795i			0.434743i
$9$	−7.19049	−	5.41265i	−0.798944	−	0.601406i
$10$	1.21682	+	2.10759i	0.121682	+	0.210759i
$11$	−13.8424	−	7.99194i	−1.25840	−	0.726540i	−0.285640	−	0.958337i	$-0.592206\pi$
$11$	−13.8424	−	7.99194i	−1.25840	−	0.726540i	−0.972764	+	0.231797i	$0.925540\pi$
$12$	−7.79428	+	1.58784i	−0.649523	+	0.132320i
$13$	−1.19389	−	12.9451i	−0.0918373	−	0.995774i
$13$	−1.19389	−	12.9451i	−0.0918373	−	0.995774i
$14$	−11.2726	−	6.50822i	−0.805184	−	0.464873i
$15$	2.11971	−	1.87633i	0.141314	−	0.125088i
$16$	9.78780	−	16.9530i	0.611738	−	1.05956i
$17$	−21.5804	−	12.4595i	−1.26944	−	0.732909i	−0.294555	−	0.955635i	$-0.595171\pi$
$17$	−21.5804	−	12.4595i	−1.26944	−	0.732909i	−0.974881	+	0.222725i	$0.928505\pi$
$18$	9.08035	+	21.3615i	0.504464	+	1.18675i
$19$	−17.4215	+	30.1749i	−0.916921	+	1.58815i	−0.112858	+	0.993611i	$0.536000\pi$
$19$	−17.4215	+	30.1749i	−0.916921	+	1.58815i	−0.804064	+	0.594543i	$0.797333\pi$
$20$		−	2.50197i		−	0.125098i
$21$	−4.80064	+	14.3598i	−0.228602	+	0.683801i
$22$	20.6116	+	35.7003i	0.936889	+	1.62274i
$23$		−	20.5334i		−	0.892757i	−0.894844	−	0.446379i	$-0.852713\pi$
$23$		−	20.5334i		−	0.892757i	0.894844	−	0.446379i	$-0.147287\pi$
$24$	−9.89551	−	3.30817i	−0.412313	−	0.137840i
$25$	−12.0548	−	20.8795i	−0.482192	−	0.835180i
$26$	−14.0264	+	30.4525i	−0.539476	+	1.17125i
$27$	22.2396	−	15.3101i	0.823691	−	0.567039i
$28$	6.69097	+	11.5891i	0.238963	+	0.413896i
$29$	15.4628	+	8.92748i	0.533202	+	0.307844i	0.742319	−	0.670046i	$-0.233726\pi$
$29$	15.4628	+	8.92748i	0.533202	+	0.307844i	−0.209118	+	0.977890i	$0.567059\pi$
$30$	−7.15396	+	1.45740i	−0.238465	+	0.0485799i
$31$	10.2399	−	17.7361i	0.330321	−	0.572132i	−0.652254	−	0.758001i	$-0.726176\pi$
$31$	10.2399	−	17.7361i	0.330321	−	0.572132i	0.982575	+	0.185868i	$0.0595098\pi$
$32$	−31.6745	+	18.2873i	−0.989827	+	0.571477i
$33$	35.9055	−	31.7829i	1.08805	−	0.963119i
$34$	32.1335	+	55.6568i	0.945102	+	1.63696i
$35$	−4.12441	−	2.38123i	−0.117840	−	0.0680351i
$36$	2.89605	−	23.6867i	0.0804458	−	0.657965i
$37$	1.09928	+	1.90401i	0.0297103	+	0.0514597i	0.880498	−	0.474049i	$-0.157208\pi$
$37$	1.09928	+	1.90401i	0.0297103	+	0.0514597i	−0.850788	+	0.525509i	$0.823875\pi$
$38$	77.8224	−	44.9308i	2.04796	−	1.18239i
$39$	37.9671	+	8.91629i	0.973515	+	0.228623i
$40$	1.64093	−	2.84217i	0.0410232	−	0.0710543i
$41$			5.87340i			0.143254i	0.997431	+	0.0716268i	$0.0228191\pi$
$41$			5.87340i			0.143254i	−0.997431	+	0.0716268i	$0.977181\pi$
$42$	29.2396	−	25.8824i	0.696181	−	0.616247i
$43$	1.87960			0.0437117			0.0218559	−	0.999761i	$-0.493043\pi$
$43$	1.87960			0.0437117			0.0218559	+	0.999761i	$0.493043\pi$
$44$		−	42.3806i		−	0.963195i
$45$	3.32232	+	7.81575i	0.0738293	+	0.173683i
$46$	−26.4783	+	45.8617i	−0.575615	+	0.996994i
$47$	−6.18058	+	3.56836i	−0.131502	+	0.0759225i	−0.564308	−	0.825565i	$-0.690857\pi$
$47$	−6.18058	+	3.56836i	−0.131502	+	0.0759225i	0.432806	+	0.901487i	$0.357523\pi$
$48$	38.9248	+	43.9738i	0.810934	+	0.916121i
$49$	−23.5277			−0.480157
$50$			62.1796i			1.24359i
$51$	55.9768	−	49.5497i	1.09758	−	0.971562i
$52$	28.1421	−	19.9031i	0.541194	−	0.382751i
$53$			34.1353i			0.644062i	0.946729	+	0.322031i	$0.104366\pi$
$53$			34.1353i			0.644062i	−0.946729	+	0.322031i	$0.895634\pi$
$54$	−69.4153	+	5.51678i	−1.28547	+	0.102163i
$55$	7.54135	+	13.0620i	0.137115	+	0.237491i
$56$			17.5532i			0.313451i
$57$	−69.2831	−	78.2699i	−1.21549	−	1.37316i
$58$	−23.0243	−	39.8793i	−0.396971	−	0.687575i
$59$	−28.2515	+	16.3110i	−0.478839	+	0.276458i	−0.719933	−	0.694044i	$-0.755827\pi$
$59$	−28.2515	+	16.3110i	−0.478839	+	0.276458i	0.241093	+	0.970502i	$0.422494\pi$
$60$	7.11863	+	2.37983i	0.118644	+	0.0396639i
$61$	13.3637			0.219076			0.109538	−	0.993983i	$-0.465063\pi$
$61$	13.3637			0.219076			0.109538	+	0.993983i	$0.465063\pi$
$62$	−45.7421	+	26.4092i	−0.737777	+	0.425956i
$63$	−36.2905	−	27.3177i	−0.576039	−	0.433614i
$64$	16.0248			0.250387
$65$	−5.13196	+	11.1420i	−0.0789533	+	0.171415i
$66$	−121.180	+	24.6867i	−1.83607	+	0.374042i
$67$	−78.5770			−1.17279			−0.586396	−	0.810025i	$-0.699454\pi$
$67$	−78.5770			−1.17279			−0.586396	+	0.810025i	$0.699454\pi$
$68$		−	66.0715i		−	0.971639i
$69$	58.4220	+	19.5311i	0.846695	+	0.283059i
$70$	6.14128	+	10.6370i	0.0877326	+	0.151957i
$71$	121.405	+	70.0932i	1.70993	+	0.987228i	0.934622	+	0.355643i	$0.115738\pi$
$71$	121.405	+	70.0932i	1.70993	+	0.987228i	0.775307	+	0.631585i	$0.217595\pi$
$72$	18.8249	−	25.0082i	0.261457	−	0.347336i
$73$	−89.5686			−1.22697			−0.613483	−	0.789708i	$-0.710232\pi$
$73$	−89.5686			−1.22697			−0.613483	+	0.789708i	$0.710232\pi$
$74$		−	5.67018i		−	0.0766240i
$75$	70.8730	−	14.4382i	0.944974	−	0.192509i
$76$	−92.3848			−1.21559
$77$	−69.8630	−	40.3354i	−0.907311	−	0.523836i
$78$	−73.3023	−	68.8740i	−0.939774	−	0.883000i
$79$	28.9076	+	50.0695i	0.365920	+	0.633791i	0.988923	−	0.148428i	$-0.0474212\pi$
$79$	28.9076	+	50.0695i	0.365920	+	0.633791i	−0.623004	+	0.782219i	$0.714088\pi$
$80$	−15.9971	+	9.23596i	−0.199964	+	0.115449i
$81$	22.4064	+	77.8393i	0.276622	+	0.960979i
$82$	7.57387	−	13.1183i	0.0923643	−	0.159980i
$83$	38.2595	−	22.0891i	0.460958	−	0.266134i	−0.251489	−	0.967860i	$-0.580920\pi$
$83$	38.2595	−	22.0891i	0.460958	−	0.266134i	0.712447	+	0.701726i	$0.247587\pi$
$84$	−39.3378	+	8.01386i	−0.468307	+	0.0954031i
$85$	11.7570	+	20.3637i	0.138317	+	0.239573i
$86$	−4.19812	−	2.42379i	−0.0488154	−	0.0281836i
$87$	−40.1086	+	35.5034i	−0.461019	+	0.408085i
$88$	27.7956	−	48.1433i	0.315859	−	0.547083i
$89$	−48.6143	+	28.0675i	−0.546228	+	0.315365i	−0.747599	−	0.664150i	$-0.768794\pi$
$89$	−48.6143	+	28.0675i	−0.546228	+	0.315365i	0.201371	+	0.979515i	$0.435460\pi$
$90$	2.65813	−	21.7408i	0.0295348	−	0.241564i
$91$	−6.02555	−	65.3338i	−0.0662148	−	0.717954i
$92$	47.1494	−	27.2217i	0.512494	−	0.295888i
$93$	40.7229	+	46.0051i	0.437881	+	0.494679i
$94$	18.4059			0.195807
$95$	28.4736	−	16.4393i	0.299723	−	0.173045i
$96$	−21.9029	−	107.515i	−0.228155	−	1.11995i
$97$	−156.758			−1.61606			−0.808032	−	0.589139i	$-0.799467\pi$
$97$	−156.758			−1.61606			−0.808032	+	0.589139i	$0.799467\pi$
$98$	52.5495	+	30.3395i	0.536219	+	0.309586i
$99$	56.2764	+	132.390i	0.568449	+	1.33728i
$100$	31.9628	−	55.3611i	0.319628	−	0.553611i
$101$	−96.8462	−	55.9142i	−0.958873	−	0.553606i	−0.0630472	−	0.998011i	$-0.520082\pi$
$101$	−96.8462	−	55.9142i	−0.958873	−	0.553606i	−0.895826	+	0.444405i	$0.853415\pi$
$102$	−188.920	+	38.4867i	−1.85216	+	0.377321i
$103$	79.5352	−	137.759i	0.772187	−	1.33747i	−0.164176	−	0.986431i	$-0.552496\pi$
$103$	79.5352	−	137.759i	0.772187	−	1.33747i	0.936362	−	0.351035i	$-0.114170\pi$
$104$	45.0222	−	4.15227i	0.432906	−	0.0399257i
$105$	10.6982	−	9.46983i	0.101887	−	0.0901889i
$106$	44.0182	−	76.2417i	0.415266	−	0.719262i
$107$	172.079	−	99.3501i	1.60822	−	0.928505i	0.618450	−	0.785824i	$-0.287761\pi$
$107$	172.079	−	99.3501i	1.60822	−	0.928505i	0.989769	−	0.142681i	$-0.0455724\pi$
$108$	64.6392	+	30.7703i	0.598511	+	0.284911i
$109$	99.6164			0.913912			0.456956	−	0.889489i	$-0.348940\pi$
$109$	99.6164			0.913912			0.456956	+	0.889489i	$0.348940\pi$
$110$		−	38.8989i		−	0.353626i
$111$	−6.46293	+	1.31662i	−0.0582246	+	0.0118615i
$112$	49.3991	−	85.5618i	0.441064	−	0.763945i
$113$	19.4882	−	11.2515i	0.172462	−	0.0995708i	−0.411284	−	0.911507i	$-0.634920\pi$
$113$	19.4882	−	11.2515i	0.172462	−	0.0995708i	0.583746	+	0.811936i	$0.301586\pi$
$114$	53.8142	+	264.159i	0.472055	+	2.31718i
$115$	−9.68786	+	16.7799i	−0.0842423	+	0.145912i
$116$			47.3417i			0.408118i
$117$	−61.4825	+	99.5435i	−0.525491	+	0.850799i
$118$	84.1336			0.712996
$119$	−108.917	−	62.8830i	−0.915265	−	0.528429i
$120$	6.52576	+	7.37223i	0.0543813	+	0.0614352i
$121$	67.2423	+	116.467i	0.555721	+	0.962537i
$122$	−29.8480	−	17.2327i	−0.244655	−	0.141252i
$123$	−16.7111	−	5.58669i	−0.135863	−	0.0454203i
$124$	54.3015			0.437916
$125$			46.3407i			0.370726i
$126$	45.8286	+	107.812i	0.363719	+	0.855650i
$127$	−58.8631	−	101.954i	−0.463489	−	0.802786i	0.535643	−	0.844444i	$-0.320069\pi$
$127$	−58.8631	−	101.954i	−0.463489	−	0.802786i	−0.999132	+	0.0416583i	$0.986736\pi$
$128$	90.9062	+	52.4847i	0.710205	+	0.410037i
$129$	−1.78785	+	5.34788i	−0.0138593	+	0.0414564i
$130$	25.8301	−	18.2680i	0.198693	−	0.140523i
$131$	−77.7495	−	44.8887i	−0.593507	−	0.342662i	0.172976	−	0.984926i	$-0.444662\pi$
$131$	−77.7495	−	44.8887i	−0.593507	−	0.342662i	−0.766483	+	0.642264i	$0.777995\pi$
$132$	120.582	+	40.3118i	0.913499	+	0.305392i
$133$	−87.9265	+	152.293i	−0.661101	+	1.14506i
$134$	175.503	+	101.327i	1.30972	+	0.756170i
$135$	−25.3976	+	2.01848i	−0.188131	+	0.0149517i
$136$	43.3333	−	75.0556i	0.318628	−	0.551879i
$137$		−	9.13731i		−	0.0666957i	−0.999444	−	0.0333478i	$-0.989383\pi$
$137$		−	9.13731i		−	0.0666957i	0.999444	−	0.0333478i	$-0.0106169\pi$
$138$	−105.301	−	118.959i	−0.763048	−	0.862024i
$139$	74.3522	+	128.782i	0.534908	+	0.926488i	0.999168	+	0.0407890i	$0.0129871\pi$
$139$	74.3522	+	128.782i	0.534908	+	0.926488i	−0.464260	+	0.885699i	$0.653680\pi$
$140$		−	12.6274i		−	0.0901960i
$141$	−4.27387	−	20.9792i	−0.0303111	−	0.148789i
$142$	−180.773	−	313.108i	−1.27305	−	2.20499i
$143$	−86.9299	+	188.733i	−0.607901	+	1.31981i
$144$	−162.140	+	68.9223i	−1.12597	+	0.478627i
$145$	−8.42414	−	14.5910i	−0.0580975	−	0.100628i
$146$	200.053	+	115.501i	1.37022	+	0.791100i
$147$	22.3792	−	66.9414i	0.152239	−	0.455383i
$148$	−2.91469	+	5.04840i	−0.0196939	+	0.0341108i
$149$	28.5068	−	16.4584i	0.191321	−	0.110459i	−0.401280	−	0.915956i	$-0.631434\pi$
$149$	28.5068	−	16.4584i	0.191321	−	0.110459i	0.592601	+	0.805496i	$0.298101\pi$
$150$	−176.914	−	59.1443i	−1.17943	−	0.394296i
$151$	53.6782	+	92.9733i	0.355485	+	0.615717i	0.987201	−	0.159482i	$-0.0509825\pi$
$151$	53.6782	+	92.9733i	0.355485	+	0.615717i	−0.631716	+	0.775200i	$0.717649\pi$
$152$	−104.947	−	60.5911i	−0.690440	−	0.398626i
$153$	87.7351	+	206.397i	0.573432	+	1.34900i
$154$	104.027	+	180.180i	0.675498	+	1.17000i
$155$	−16.7361	+	9.66260i	−0.107975	+	0.0623394i
$156$	29.8602	+	99.0017i	0.191412	+	0.634627i
$157$	−2.21063	+	3.82892i	−0.0140804	+	0.0243880i	−0.872980	−	0.487756i	$-0.837815\pi$
$157$	−2.21063	+	3.82892i	−0.0140804	+	0.0243880i	0.858899	+	0.512144i	$0.171149\pi$
$158$		−	149.108i		−	0.943722i
$159$	−97.1223	−	32.4690i	−0.610832	−	0.204207i
$160$	34.5124			0.215703
$161$		−	103.632i		−	0.643679i
$162$	50.3303	−	202.749i	0.310681	−	1.25154i
$163$	47.2209	−	81.7891i	0.289699	−	0.501774i	−0.684039	−	0.729446i	$-0.739778\pi$
$163$	47.2209	−	81.7891i	0.289699	−	0.501774i	0.973738	+	0.227672i	$0.0731114\pi$
$164$	−13.4867	+	7.78654i	−0.0822358	+	0.0474789i
$165$	−44.3374	+	9.03238i	−0.268712	+	0.0547417i
$166$	−113.938			−0.686371
$167$		−	164.333i		−	0.984030i	−0.870587	−	0.492015i	$-0.836261\pi$
$167$		−	164.333i		−	0.984030i	0.870587	−	0.492015i	$-0.163739\pi$
$168$	−49.9427	−	16.6964i	−0.297278	−	0.0993832i
$169$	−166.149	+	30.9098i	−0.983132	+	0.182898i
$170$		−	60.6435i		−	0.356727i
$171$	288.596	−	122.676i	1.68769	−	0.717404i
$172$	2.49184	+	4.31600i	0.0144875	+	0.0250930i
$173$			101.216i			0.585062i	0.956256	+	0.292531i	$0.0944974\pi$
$173$			101.216i			0.585062i	−0.956256	+	0.292531i	$0.905503\pi$
$174$	135.366	−	27.5766i	0.777963	−	0.158486i
$175$	−60.8406	−	105.379i	−0.347661	−	0.602166i
$176$	−270.974	+	156.447i	−1.53963	+	0.888904i
$177$	−19.5359	−	95.8964i	−0.110372	−	0.541788i
$178$	144.774			0.813339
$179$	−176.959	+	102.167i	−0.988595	+	0.570766i	−0.904854	−	0.425722i	$-0.860020\pi$
$179$	−176.959	+	102.167i	−0.988595	+	0.570766i	−0.0837411	+	0.996488i	$0.526687\pi$
$180$	−13.5423	+	17.9904i	−0.0752348	+	0.0999465i
$181$	−121.248			−0.669879			−0.334939	−	0.942240i	$-0.608716\pi$
$181$	−121.248			−0.669879			−0.334939	+	0.942240i	$0.608716\pi$
$182$	−70.7912	+	153.694i	−0.388963	+	0.844474i
$183$	−12.7113	+	38.0225i	−0.0694608	+	0.207773i
$184$	71.4141			0.388120
$185$		−	2.07460i		−	0.0112141i
$186$	−31.6307	−	155.266i	−0.170058	−	0.834765i
$187$	199.151	+	344.939i	1.06498	+	1.84459i
$188$	−16.3875	−	9.46135i	−0.0871677	−	0.0503263i
$189$	112.244	−	77.2700i	0.593882	−	0.408836i
$190$	−84.7951			−0.446290
$191$		−	181.312i		−	0.949279i	−0.880180	−	0.474640i	$-0.842578\pi$
$191$		−	181.312i		−	0.949279i	0.880180	−	0.474640i	$-0.157422\pi$
$192$	−15.2425	+	45.5940i	−0.0793883	+	0.237469i
$193$	−2.45422			−0.0127162			−0.00635808	−	0.999980i	$-0.502024\pi$
$193$	−2.45422			−0.0127162			−0.00635808	+	0.999980i	$0.502024\pi$
$194$	350.122	+	202.143i	1.80475	+	1.04197i
$195$	−26.8198	−	25.1996i	−0.137538	−	0.129229i
$196$	−31.1913	−	54.0250i	−0.159140	−	0.275638i
$197$	300.863	−	173.703i	1.52722	−	0.881743i	0.527748	−	0.849401i	$-0.323037\pi$
$197$	300.863	−	173.703i	1.52722	−	0.881743i	0.999477	−	0.0323423i	$-0.0102967\pi$
$198$	45.0258	−	368.266i	0.227403	−	1.85993i
$199$	88.3111	−	152.959i	0.443774	−	0.768640i	−0.554192	−	0.832389i	$-0.686973\pi$
$199$	88.3111	−	152.959i	0.443774	−	0.768640i	0.997966	+	0.0637495i	$0.0203059\pi$
$200$	72.6178	−	41.9259i	0.363089	−	0.209630i
$201$	74.7413	−	223.569i	0.371847	−	1.11228i
$202$	144.205	+	249.770i	0.713886	+	1.23649i
$203$	78.0411	+	45.0571i	0.384439	+	0.221956i
$204$	187.987	+	62.8462i	0.921507	+	0.308070i
$205$	2.77113	−	4.79973i	0.0135177	−	0.0234133i
$206$	−355.286	+	205.125i	−1.72469	+	0.995751i
$207$	−111.140	+	147.645i	−0.536909	+	0.713263i
$208$	−231.143	−	106.464i	−1.11126	−	0.511845i
$209$	482.313	−	278.463i	2.30772	−	1.33236i
$210$	−36.1061	+	7.35550i	−0.171934	+	0.0350262i
$211$	−272.761			−1.29270			−0.646352	−	0.763039i	$-0.723706\pi$
$211$	−272.761			−1.29270			−0.646352	+	0.763039i	$0.723706\pi$
$212$	−78.3825	+	45.2542i	−0.369729	+	0.213463i
$213$	−314.909	+	278.752i	−1.47844	+	1.30869i
$214$	−512.456			−2.39465
$215$	−1.53601	−	0.886815i	−0.00714423	−	0.00412472i
$216$	53.2476	+	77.3483i	0.246517	+	0.358094i
$217$	51.6811	−	89.5143i	0.238162	−	0.412508i
$218$	−222.495	−	128.457i	−1.02062	−	0.589254i
$219$	85.1963	−	254.842i	0.389024	−	1.16366i
$220$	−19.9956	+	34.6333i	−0.0908889	+	0.157424i
$221$	−135.524	+	294.235i	−0.613230	+	1.33138i
$222$	16.1329	+	5.39339i	0.0726706	+	0.0242946i
$223$	18.6902	−	32.3723i	0.0838124	−	0.145167i	−0.821072	−	0.570824i	$-0.806624\pi$
$223$	18.6902	−	32.3723i	0.0838124	−	0.145167i	0.904885	+	0.425657i	$0.139957\pi$
$224$	−159.861	+	92.2960i	−0.713666	+	0.412036i
$225$	−26.3336	+	215.382i	−0.117038	+	0.957255i
$226$	−58.0362			−0.256797
$227$			198.854i			0.876011i	0.898972	+	0.438005i	$0.144315\pi$
$227$			198.854i			0.876011i	−0.898972	+	0.438005i	$0.855685\pi$
$228$	87.8750	−	262.855i	0.385417	−	1.15287i
$229$	−138.042	+	239.095i	−0.602802	+	1.04408i	0.389593	+	0.920987i	$0.372616\pi$
$229$	−138.042	+	239.095i	−0.602802	+	1.04408i	−0.992395	+	0.123096i	$0.960718\pi$
$230$	43.2760	−	24.9854i	0.188156	−	0.108632i
$231$	181.216	−	160.409i	0.784483	−	0.694410i
$232$	−31.0493	+	53.7790i	−0.133833	+	0.231806i
$233$		−	106.047i		−	0.455137i	−0.973762	−	0.227568i	$-0.926922\pi$
$233$		−	106.047i		−	0.455137i	0.973762	−	0.227568i	$-0.0730775\pi$
$234$	265.686	−	143.049i	1.13541	−	0.611320i
$235$	6.73434			0.0286568
$236$	−74.9077	−	43.2480i	−0.317405	−	0.183254i
$237$	−169.955	+	34.6231i	−0.717110	+	0.146089i
$238$	162.178	+	280.900i	0.681420	+	1.18025i
$239$	−331.745	−	191.533i	−1.38805	−	0.801393i	−0.394957	−	0.918700i	$-0.629241\pi$
$239$	−331.745	−	191.533i	−1.38805	−	0.801393i	−0.993096	+	0.117307i	$0.962574\pi$
$240$	−11.0620	−	54.3004i	−0.0460918	−	0.226252i
$241$	−46.9860			−0.194963			−0.0974813	−	0.995237i	$-0.531079\pi$
$241$	−46.9860			−0.194963			−0.0974813	+	0.995237i	$0.531079\pi$
$242$		−	346.841i		−	1.43323i
$243$	−242.782	−	10.2885i	−0.999103	−	0.0423397i
$244$	17.7166	+	30.6860i	0.0726090	+	0.125762i
$245$	19.2268	+	11.1006i	0.0784767	+	0.0453085i
$246$	30.1203	+	34.0273i	0.122440	+	0.138322i
$247$	411.416	+	189.497i	1.66565	+	0.767195i
$248$	61.6852	+	35.6140i	0.248731	+	0.143605i
$249$	26.4565	+	129.867i	0.106251	+	0.521556i
$250$	59.7574	−	103.503i	0.239029	−	0.414011i
$251$	−40.4117	−	23.3317i	−0.161003	−	0.0929549i	0.417334	−	0.908753i	$-0.362965\pi$
$251$	−40.4117	−	23.3317i	−0.161003	−	0.0929549i	−0.578336	+	0.815798i	$0.696298\pi$
$252$	14.6164	−	119.547i	0.0580015	−	0.474394i
$253$	−164.102	+	284.233i	−0.648624	+	1.12345i
$254$			303.621i			1.19536i
$255$	−69.1221	+	14.0815i	−0.271067	+	0.0552216i
$256$	−167.410	−	289.962i	−0.653945	−	1.13267i
$257$		−	119.957i		−	0.466757i	−0.972386	−	0.233379i	$-0.925022\pi$
$257$		−	119.957i		−	0.466757i	0.972386	−	0.233379i	$-0.0749782\pi$
$258$	10.8894	−	9.63910i	0.0422069	−	0.0373608i
$259$	5.54808	+	9.60955i	0.0214211	+	0.0371025i
$260$	−32.3881	+	2.98706i	−0.124570	+	0.0114887i
$261$	−62.8642	−	147.888i	−0.240859	−	0.566621i
$262$	115.770	+	200.519i	0.441869	+	0.765340i
$263$	−293.463	−	169.431i	−1.11583	−	0.644225i	−0.175497	−	0.984480i	$-0.556153\pi$
$263$	−293.463	−	169.431i	−1.11583	−	0.644225i	−0.940333	+	0.340255i	$0.889487\pi$
$264$	110.539	+	124.878i	0.418710	+	0.473021i
$265$	16.1054	−	27.8953i	0.0607749	−	0.105265i
$266$	392.770	−	226.766i	1.47658	−	0.852504i
$267$	−33.6168	−	165.015i	−0.125906	−	0.618035i
$268$	−104.172	−	180.431i	−0.388701	−	0.673250i
$269$	−194.820	−	112.479i	−0.724236	−	0.418138i	0.0920735	−	0.995752i	$-0.470651\pi$
$269$	−194.820	−	112.479i	−0.724236	−	0.418138i	−0.816310	+	0.577614i	$0.803984\pi$
$270$	59.3289	+	28.2425i	0.219737	+	0.104602i
$271$	2.75897	+	4.77868i	0.0101807	+	0.0176335i	0.871071	−	0.491157i	$-0.163426\pi$
$271$	2.75897	+	4.77868i	0.0101807	+	0.0176335i	−0.860890	+	0.508791i	$0.830093\pi$
$272$	−422.450	+	243.901i	−1.55312	+	0.896696i
$273$	191.620	+	45.0006i	0.701906	+	0.164837i
$274$	−11.7828	+	20.4083i	−0.0430027	+	0.0744829i
$275$			385.365i			1.40133i
$276$	32.6039	+	160.043i	0.118130	+	0.579867i
$277$	232.341			0.838775			0.419387	−	0.907807i	$-0.362245\pi$
$277$	232.341			0.838775			0.419387	+	0.907807i	$0.362245\pi$
$278$		−	383.515i		−	1.37955i
$279$	−169.630	+	72.1061i	−0.607991	+	0.258445i
$280$	8.28178	−	14.3445i	0.0295778	−	0.0512302i
$281$	108.117	−	62.4211i	0.384757	−	0.222139i	−0.295129	−	0.955457i	$-0.595363\pi$
$281$	108.117	−	62.4211i	0.384757	−	0.222139i	0.679886	+	0.733318i	$0.262029\pi$
$282$	−17.5074	+	52.3687i	−0.0620830	+	0.185705i
$283$	428.800			1.51519			0.757597	−	0.652722i	$-0.226373\pi$
$283$	428.800			1.51519			0.757597	+	0.652722i	$0.226373\pi$
$284$			371.698i			1.30880i
$285$	19.6895	+	96.6504i	0.0690861	+	0.339124i
$286$	437.534	−	309.440i	1.52984	−	1.08196i
$287$			29.6431i			0.103286i
$288$	326.738	+	39.9484i	1.13451	+	0.138710i
$289$	165.976	+	287.479i	0.574312	+	0.994738i
$290$			43.4524i			0.149836i
$291$	149.106	−	446.011i	0.512392	−	1.53268i
$292$	−118.744	−	205.670i	−0.406656	−	0.704349i
$293$	−132.057	+	76.2431i	−0.450706	+	0.260215i	−0.708128	−	0.706084i	$-0.750460\pi$
$293$	−132.057	+	76.2431i	−0.450706	+	0.260215i	0.257422	+	0.966299i	$0.417127\pi$
$294$	−136.307	+	120.656i	−0.463628	+	0.410395i
$295$	30.7828			0.104348
$296$	−6.62204	+	3.82324i	−0.0223718	+	0.0129163i
$297$	−430.208	+	34.1908i	−1.44851	+	0.115121i
$298$	−84.8940			−0.284879
$299$	−265.806	+	24.5145i	−0.888984	+	0.0819884i
$300$	127.112	+	143.600i	0.423706	+	0.478665i
$301$	9.48638			0.0315162
$302$		−	276.877i		−	0.916810i
$303$	251.207	−	222.363i	0.829064	−	0.733873i
$304$	341.036	+	590.692i	1.12183	+	1.94307i
$305$	−10.9208	−	6.30510i	−0.0358058	−	0.0206725i
$306$	70.1954	−	574.127i	0.229397	−	1.87623i
$307$	559.739			1.82325			0.911627	−	0.411019i	$-0.134827\pi$
$307$	559.739			1.82325			0.911627	+	0.411019i	$0.134827\pi$
$308$		−	213.895i		−	0.694465i
$309$	316.301	+	357.329i	1.02363	+	1.15641i
$310$	49.8405			0.160776
$311$	278.602	+	160.851i	0.895827	+	0.517206i	0.875844	−	0.482594i	$-0.160305\pi$
$311$	278.602	+	160.851i	0.895827	+	0.517206i	0.0199832	+	0.999800i	$0.493639\pi$
$312$	−31.0104	+	132.048i	−0.0993923	+	0.423229i
$313$	−174.107	−	301.562i	−0.556252	−	0.963456i	−0.997805	−	0.0662213i	$-0.978906\pi$
$313$	−174.107	−	301.562i	−0.556252	−	0.963456i	0.441553	−	0.897235i	$-0.354428\pi$
$314$	9.87494	−	5.70130i	0.0314488	−	0.0181570i
$315$	16.7678	+	39.4462i	0.0532310	+	0.125226i
$316$	−76.6474	+	132.757i	−0.242555	+	0.420118i
$317$	−74.3159	+	42.9063i	−0.234435	+	0.135351i	−0.612616	−	0.790380i	$-0.709883\pi$
$317$	−74.3159	+	42.9063i	−0.234435	+	0.135351i	0.378181	+	0.925732i	$0.376550\pi$
$318$	175.055	+	197.761i	0.550486	+	0.621891i
$319$	−142.696	−	247.156i	−0.447322	−	0.774785i
$320$	−13.0954	−	7.56065i	−0.0409232	−	0.0236270i
$321$	118.993	+	584.103i	0.370695	+	1.81964i
$322$	−133.636	+	231.464i	−0.415019	+	0.718834i
$323$	751.927	−	434.125i	2.32795	−	1.34404i
$324$	−149.032	+	154.644i	−0.459975	+	0.477296i
$325$	−255.895	+	180.978i	−0.787368	+	0.556855i
$326$	−210.937	+	121.785i	−0.647047	+	0.373573i
$327$	−94.7536	+	283.430i	−0.289766	+	0.866758i
$328$	−20.4274			−0.0622786
$329$	−31.1934	+	18.0095i	−0.0948128	+	0.0547402i
$330$	110.676	+	37.0001i	0.335381	+	0.112121i
$331$	6.04410			0.0182601			0.00913006	−	0.999958i	$-0.497094\pi$
$331$	6.04410			0.0182601			0.00913006	+	0.999958i	$0.497094\pi$
$332$	101.443	+	58.5684i	0.305553	+	0.176411i
$333$	2.40137	−	19.6408i	0.00721132	−	0.0589813i
$334$	−211.911	+	367.040i	−0.634464	+	1.09892i
$335$	64.2130	+	37.0734i	0.191681	+	0.110667i
$336$	196.454	+	221.936i	0.584684	+	0.660524i
$337$	201.907	−	349.714i	0.599132	−	1.03773i	−0.393818	−	0.919189i	$-0.628846\pi$
$337$	201.907	−	349.714i	0.599132	−	1.03773i	0.992950	−	0.118538i	$-0.0378208\pi$
$338$	410.956	+	145.215i	1.21585	+	0.429631i
$339$	13.4761	+	66.1503i	0.0397524	+	0.195134i
$340$	−31.1731	+	53.9935i	−0.0916857	+	0.158804i
$341$	−283.492	+	163.674i	−0.831354	+	0.479983i
$342$	−802.776	−	98.1511i	−2.34730	−	0.286991i
$343$	−366.048			−1.06720
$344$			6.53716i			0.0190034i
$345$	−38.5274	−	43.5248i	−0.111674	−	0.126159i
$346$	130.520	−	226.067i	0.377225	−	0.653372i
$347$	254.992	−	147.220i	0.734847	−	0.424264i	−0.0853458	−	0.996351i	$-0.527199\pi$
$347$	254.992	−	147.220i	0.734847	−	0.424264i	0.820193	+	0.572087i	$0.193866\pi$
$348$	−134.697	−	45.0307i	−0.387061	−	0.129398i
$349$	255.135	−	441.906i	0.731045	−	1.26621i	−0.225393	−	0.974268i	$-0.572366\pi$
$349$	255.135	−	441.906i	0.731045	−	1.26621i	0.956437	−	0.291938i	$-0.0943002\pi$
$350$			313.821i			0.896632i
$351$	−224.741	−	269.615i	−0.640289	−	0.768134i
$352$	584.603			1.66080
$353$	−434.981	−	251.137i	−1.23224	−	0.711435i	−0.264745	−	0.964318i	$-0.585288\pi$
$353$	−434.981	−	251.137i	−1.23224	−	0.711435i	−0.967497	+	0.252883i	$0.918621\pi$
$354$	−80.0266	+	239.378i	−0.226064	+	0.676209i
$355$	−66.1413	−	114.560i	−0.186313	−	0.322704i
$356$	−128.899	−	74.4197i	−0.362075	−	0.209044i
$357$	282.515	−	250.078i	0.791360	−	0.700498i
$358$	526.986			1.47203
$359$			258.046i			0.718791i	0.933185	+	0.359395i	$0.117017\pi$
$359$			258.046i			0.718791i	−0.933185	+	0.359395i	$0.882983\pi$
$360$	−27.1828	+	11.5548i	−0.0755077	+	0.0320968i
$361$	−426.518	−	738.750i	−1.18149	−	2.04640i
$362$	270.809	+	156.352i	0.748092	+	0.431911i
$363$	−395.334	+	80.5370i	−1.08907	+	0.221865i
$364$	142.033	−	100.451i	0.390201	−	0.275964i
$365$	73.1953	+	42.2593i	0.200535	+	0.115779i
$366$	77.4217	−	68.5323i	0.211535	−	0.187247i
$367$	58.6436	−	101.574i	0.159792	−	0.276768i	−0.775002	−	0.631959i	$-0.782251\pi$
$367$	58.6436	−	101.574i	0.159792	−	0.276768i	0.934794	+	0.355192i	$0.115584\pi$
$368$	−348.102	−	200.977i	−0.945930	−	0.546133i
$369$	31.7907	−	42.2327i	0.0861536	−	0.114452i
$370$	−2.67524	+	4.63366i	−0.00723039	+	0.0125234i
$371$			172.281i			0.464370i
$372$	−51.6508	+	154.500i	−0.138846	+	0.415321i
$373$	−351.544	−	608.892i	−0.942476	−	1.63242i	−0.760727	−	0.649072i	$-0.775157\pi$
$373$	−351.544	−	608.892i	−0.942476	−	1.63242i	−0.181750	−	0.983345i	$-0.558176\pi$
$374$		−	1027.24i		−	2.74662i
$375$	−131.849	−	44.0786i	−0.351598	−	0.117543i
$376$	−12.4106	−	21.4957i	−0.0330068	−	0.0571695i
$377$	97.1059	−	210.826i	0.257575	−	0.559220i
$378$	−350.339	+	27.8432i	−0.926824	+	0.0736594i
$379$	166.355	+	288.136i	0.438932	+	0.760252i	0.997607	−	0.0691341i	$-0.0220236\pi$
$379$	166.355	+	288.136i	0.438932	+	0.760252i	−0.558676	+	0.829386i	$0.688690\pi$
$380$	75.4967	+	43.5880i	0.198675	+	0.114705i
$381$	346.070	−	70.5011i	0.908321	−	0.185042i
$382$	−233.806	+	404.964i	−0.612058	+	1.06012i
$383$	−288.687	+	166.673i	−0.753751	+	0.435179i	−0.827048	−	0.562132i	$-0.809981\pi$
$383$	−288.687	+	166.673i	−0.753751	+	0.435179i	0.0732964	+	0.997310i	$0.476648\pi$
$384$	−235.799	+	208.725i	−0.614060	+	0.543555i
$385$	38.0613	+	65.9240i	0.0988604	+	0.171231i
$386$	5.48154	+	3.16477i	0.0142009	+	0.00819888i
$387$	−13.5153	−	10.1736i	−0.0349232	−	0.0262885i
$388$	−207.819	−	359.953i	−0.535615	−	0.927713i
$389$	505.351	−	291.765i	1.29910	−	0.750038i	0.318855	−	0.947804i	$-0.396702\pi$
$389$	505.351	−	291.765i	1.29910	−	0.750038i	0.980249	+	0.197766i	$0.0633685\pi$
$390$	27.4071	+	90.8685i	0.0702746	+	0.232996i
$391$	−255.835	+	443.120i	−0.654310	+	1.13330i
$392$		−	81.8281i		−	0.208745i
$393$	201.672	−	178.516i	0.513160	−	0.454240i
$394$	−895.977			−2.27405
$395$		−	54.5556i		−	0.138115i
$396$	−229.391	+	304.737i	−0.579271	+	0.769539i
$397$	−107.622	+	186.406i	−0.271088	+	0.469538i	−0.969141	−	0.246508i	$-0.920717\pi$
$397$	−107.622	+	186.406i	−0.271088	+	0.469538i	0.698053	+	0.716046i	$0.254050\pi$
$398$	−394.488	+	227.758i	−0.991177	+	0.572256i
$399$	−349.672	−	395.029i	−0.876372	−	0.990047i
$400$	−471.960			−1.17990
$401$		−	131.881i		−	0.328880i	−0.986387	−	0.164440i	$-0.947418\pi$
$401$		−	131.881i		−	0.328880i	0.986387	−	0.164440i	$-0.0525817\pi$
$402$	−455.232	+	402.963i	−1.13242	+	1.00240i
$403$	−241.820	−	111.382i	−0.600050	−	0.276382i
$404$		−	296.508i		−	0.733931i
$405$	18.4148	−	74.1817i	0.0454688	−	0.183165i
$406$	−116.204	−	201.271i	−0.286217	−	0.495742i
$407$		−	35.1415i		−	0.0863428i
$408$	172.331	+	194.684i	0.422380	+	0.477168i
$409$	29.9756	+	51.9192i	0.0732899	+	0.126942i	0.900341	−	0.435184i	$-0.143317\pi$
$409$	29.9756	+	51.9192i	0.0732899	+	0.126942i	−0.827051	+	0.562126i	$0.809983\pi$
$410$	−12.3787	+	7.14685i	−0.0301920	+	0.0174313i
$411$	25.9976	+	8.69127i	0.0632545	+	0.0211467i
$412$	421.769			1.02371
$413$	−142.586	+	82.3218i	−0.345244	+	0.199326i
$414$	438.625	−	186.451i	1.05948	−	0.450364i
$415$	−41.6875			−0.100452
$416$	274.545	+	388.195i	0.659965	+	0.933161i
$417$	−437.135	+	89.0527i	−1.04828	+	0.213556i
$418$	−1436.34			−3.43621
$419$			415.938i			0.992691i	0.868125	+	0.496346i	$0.165325\pi$
$419$			415.938i			0.992691i	−0.868125	+	0.496346i	$0.834675\pi$
$420$	35.9278	+	12.0110i	0.0855424	+	0.0285977i
$421$	−3.52056	−	6.09779i	−0.00836237	−	0.0144841i	0.861814	−	0.507225i	$-0.169329\pi$
$421$	−3.52056	−	6.09779i	−0.00836237	−	0.0144841i	−0.870176	+	0.492740i	$0.835995\pi$
$422$	609.215	+	351.731i	1.44364	+	0.833485i
$423$	63.7557	+	7.79506i	0.150723	+	0.0184280i
$424$	−118.721			−0.280002
$425$			600.785i			1.41361i
$426$	1062.81	−	216.515i	2.49486	−	0.508250i
$427$	67.4465			0.157954
$428$	456.261	+	263.423i	1.06603	+	0.615473i
$429$	−454.299	−	426.854i	−1.05897	−	0.994998i
$430$	2.28713	+	3.96143i	0.00531891	+	0.00921263i
$431$	28.5577	−	16.4878i	0.0662592	−	0.0382548i	−0.466504	−	0.884519i	$-0.654487\pi$
$431$	28.5577	−	16.4878i	0.0662592	−	0.0382548i	0.532764	+	0.846264i	$0.321153\pi$
$432$	−41.8738	−	526.880i	−0.0969301	−	1.21963i
$433$	169.487	−	293.559i	0.391424	−	0.677966i	−0.601214	−	0.799088i	$-0.705316\pi$
$433$	169.487	−	293.559i	0.391424	−	0.677966i	0.992638	+	0.121122i	$0.0386492\pi$
$434$	−230.861	+	133.288i	−0.531938	+	0.307114i
$435$	49.5275	−	10.0897i	0.113856	−	0.0231947i
$436$	132.064	+	228.742i	0.302900	+	0.524638i
$437$	619.594	+	357.723i	1.41784	+	0.818588i
$438$	−518.911	+	459.331i	−1.18473	+	1.04870i
$439$	−245.419	+	425.079i	−0.559042	+	0.968289i	0.438535	+	0.898714i	$0.355498\pi$
$439$	−245.419	+	425.079i	−0.559042	+	0.968289i	−0.997577	+	0.0695749i	$0.977836\pi$
$440$	−45.4289	+	26.2284i	−0.103248	+	0.0596100i
$441$	169.176	+	127.347i	0.383619	+	0.288769i
$442$	682.117	−	482.418i	1.54325	−	1.09144i
$443$	−182.064	+	105.115i	−0.410980	+	0.237279i	−0.691211	−	0.722653i	$-0.742922\pi$
$443$	−182.064	+	105.115i	−0.410980	+	0.237279i	0.280231	+	0.959933i	$0.409589\pi$
$444$	−11.5914	−	13.0949i	−0.0261067	−	0.0294930i
$445$	52.9700			0.119034
$446$	−83.4896	+	48.2027i	−0.187196	+	0.108078i
$447$	19.7125	+	96.7631i	0.0440995	+	0.216472i
$448$	80.8773			0.180530
$449$	−70.3212	−	40.6000i	−0.156617	−	0.0904231i	0.419643	−	0.907689i	$-0.362155\pi$
$449$	−70.3212	−	40.6000i	−0.156617	−	0.0904231i	−0.576260	+	0.817266i	$0.695489\pi$
$450$	336.557	−	447.102i	0.747904	−	0.993560i
$451$	46.9399	−	81.3023i	0.104080	−	0.180271i
$452$	51.6720	+	29.8329i	0.114319	+	0.0660019i
$453$	−315.587	+	64.2911i	−0.696660	+	0.141923i
$454$	256.427	−	444.145i	0.564817	−	0.978292i
$455$	−25.9011	+	56.2336i	−0.0569254	+	0.123590i
$456$	272.218	−	240.963i	0.596970	−	0.528427i
$457$	−10.9124	+	18.9008i	−0.0238782	+	0.0413583i	−0.877718	−	0.479178i	$-0.840935\pi$
$457$	−10.9124	+	18.9008i	−0.0238782	+	0.0413583i	0.853839	+	0.520537i	$0.174268\pi$
$458$	616.636	−	356.015i	1.34637	−	0.777326i
$459$	−670.696	+	53.3036i	−1.46121	+	0.116130i
$460$	−51.3739			−0.111682
$461$		−	466.479i		−	1.01188i	−0.862567	−	0.505942i	$-0.831145\pi$
$461$		−	466.479i		−	1.01188i	0.862567	−	0.505942i	$-0.168855\pi$
$462$	−611.598	+	124.594i	−1.32381	+	0.269684i
$463$	132.919	−	230.222i	0.287081	−	0.497239i	−0.686031	−	0.727573i	$-0.740648\pi$
$463$	132.919	−	230.222i	0.287081	−	0.497239i	0.973112	+	0.230333i	$0.0739817\pi$
$464$	302.694	−	174.761i	0.652359	−	0.376640i
$465$	−11.5730	−	56.8088i	−0.0248882	−	0.122169i
$466$	−136.750	+	236.857i	−0.293454	+	0.508278i
$467$			534.686i			1.14494i	0.819926	+	0.572469i	$0.194014\pi$
$467$			534.686i			1.14494i	−0.819926	+	0.572469i	$0.805986\pi$
$468$	−310.084	−	9.21027i	−0.662572	−	0.0196801i
$469$	−396.579			−0.845584
$470$	−15.0413	−	8.68407i	−0.0320027	−	0.0184767i
$471$	−8.79137	−	9.93171i	−0.0186653	−	0.0210864i
$472$	−56.7289	−	98.2573i	−0.120188	−	0.208172i
$473$	−26.0183	−	15.0217i	−0.0550070	−	0.0317583i
$474$	424.244	+	141.829i	0.895030	+	0.299218i
$475$	840.050			1.76853
$476$		−	333.463i		−	0.700553i
$477$	184.763	−	245.450i	0.387343	−	0.514570i
$478$	493.971	+	855.583i	1.03341	+	1.78992i
$479$	137.211	+	79.2191i	0.286454	+	0.165384i	0.636342	−	0.771407i	$-0.280447\pi$
$479$	137.211	+	79.2191i	0.286454	+	0.165384i	−0.349888	+	0.936792i	$0.613780\pi$
$480$	−32.8277	+	98.1952i	−0.0683910	+	0.204573i
$481$	23.3351	−	16.5034i	0.0485137	−	0.0343106i
$482$	104.944	+	60.5894i	0.217726	+	0.125704i
$483$	294.856	+	98.5735i	0.610468	+	0.204086i
$484$	−178.290	+	308.807i	−0.368368	+	0.638032i
$485$	128.102	+	73.9600i	0.264129	+	0.152495i
$486$	528.990	+	336.052i	1.08846	+	0.691466i
$487$	280.748	−	486.271i	0.576486	−	0.998502i	−0.419393	−	0.907805i	$-0.637757\pi$
$487$	280.748	−	486.271i	0.576486	−	0.998502i	0.995878	−	0.0906974i	$-0.0289096\pi$
$488$			46.4781i			0.0952420i
$489$	187.792	+	212.150i	0.384032	+	0.433845i
$490$	−28.6289	−	49.5867i	−0.0584263	−	0.101197i
$491$			462.966i			0.942904i	0.881892	+	0.471452i	$0.156270\pi$
$491$			462.966i			0.942904i	−0.881892	+	0.471452i	$0.843730\pi$
$492$	−9.32604	−	45.7789i	−0.0189554	−	0.0930466i
$493$	−222.463	−	385.317i	−0.451244	−	0.781577i
$494$	−674.543	−	953.774i	−1.36547	−	1.93072i
$495$	16.4740	−	134.741i	0.0332809	−	0.272204i
$496$	−200.453	−	347.195i	−0.404139	−	0.699990i
$497$	612.732	+	353.761i	1.23286	+	0.711793i
$498$	108.376	−	324.177i	0.217622	−	0.650958i
$499$	161.354	−	279.473i	0.323354	−	0.560065i	−0.657824	−	0.753172i	$-0.728523\pi$
$499$	161.354	−	279.473i	0.323354	−	0.560065i	0.981178	+	0.193106i	$0.0618563\pi$
$500$	−106.409	+	61.4353i	−0.212818	+	0.122871i
$501$	467.563	+	156.311i	0.933259	+	0.311998i
$502$	60.1734	+	104.223i	0.119867	+	0.207616i
$503$	278.116	+	160.570i	0.552915	+	0.319225i	0.750297	−	0.661101i	$-0.229911\pi$
$503$	278.116	+	160.570i	0.552915	+	0.319225i	−0.197382	+	0.980327i	$0.563244\pi$
$504$	95.0095	−	126.216i	0.188511	−	0.250429i
$505$	52.7617	+	91.3859i	0.104479	+	0.180962i
$506$	733.048	−	423.226i	1.44871	−	0.836414i
$507$	70.0936	−	502.131i	0.138252	−	0.990397i
$508$	156.073	−	270.326i	0.307230	−	0.532138i
$509$		−	728.101i		−	1.43045i	−0.698893	−	0.715226i	$-0.746324\pi$
$509$		−	728.101i		−	1.43045i	0.698893	−	0.715226i	$-0.253676\pi$
$510$	172.544	+	57.6832i	0.338321	+	0.113104i
$511$	−452.053			−0.884645
$512$			443.636i			0.866477i
$513$	74.5320	+	937.804i	0.145287	+	1.82808i
$514$	−154.687	+	267.925i	−0.300947	+	0.521255i
$515$	−129.992	+	75.0509i	−0.252412	+	0.145730i
$516$	−14.6502	+	2.98452i	−0.0283918	+	0.00578395i
$517$	114.072			0.220643
$518$		−	28.6174i		−	0.0552460i
$519$	−287.980	−	96.2748i	−0.554875	−	0.185501i
$520$	−38.7512	−	17.8487i	−0.0745215	−	0.0343244i
$521$			819.761i			1.57344i	0.617311	+	0.786719i	$0.288222\pi$
$521$			819.761i			1.57344i	−0.617311	+	0.786719i	$0.711778\pi$
$522$	−50.2965	+	411.375i	−0.0963535	+	0.788074i
$523$	485.658	+	841.184i	0.928601	+	1.60838i	0.785666	+	0.618651i	$0.212321\pi$
$523$	485.658	+	841.184i	0.928601	+	1.60838i	0.142935	+	0.989732i	$0.454346\pi$
$524$		−	238.041i		−	0.454276i
$525$	357.697	−	72.8697i	0.681327	−	0.138799i
$526$	436.970	+	756.854i	0.830741	+	1.43889i
$527$	−441.964	+	255.168i	−0.838642	+	0.484190i
$528$	−187.379	−	919.790i	−0.354884	−	1.74203i
$529$	107.379			0.202985
$530$	−71.9432	+	41.5364i	−0.135742	+	0.0783706i
$531$	291.428	+	35.6313i	0.548829	+	0.0671023i
$532$	−466.267			−0.876441
$533$	76.0315	−	7.01217i	0.142648	−	0.0131560i
$534$	−137.707	+	411.914i	−0.257879	+	0.771375i
$535$	−187.497			−0.350462
$536$		−	273.287i		−	0.509863i
$537$	−122.367	−	600.665i	−0.227871	−	1.11856i
$538$	290.088	+	502.448i	0.539198	+	0.933918i
$539$	325.681	+	188.032i	0.604232	+	0.348853i
$540$	−38.3053	−	55.6428i	−0.0709357	−	0.103042i
$541$	−850.073			−1.57130			−0.785650	−	0.618672i	$-0.787671\pi$
$541$	−850.073			−1.57130			−0.785650	+	0.618672i	$0.787671\pi$
$542$		−	14.2310i		−	0.0262565i
$543$	115.329	−	344.977i	0.212393	−	0.635316i
$544$	911.397			1.67536
$545$	−81.4063	−	46.9999i	−0.149369	−	0.0862384i
$546$	−369.958	−	347.608i	−0.677578	−	0.636644i
$547$	−290.185	−	502.616i	−0.530503	−	0.918859i	−0.999367	−	0.0355881i	$-0.988670\pi$
$547$	−290.185	−	502.616i	−0.530503	−	0.918859i	0.468863	−	0.883271i	$-0.344664\pi$
$548$	20.9814	−	12.1136i	0.0382872	−	0.0221051i
$549$	−96.0913	−	72.3329i	−0.175030	−	0.131754i
$550$	496.936	−	860.718i	0.903520	−	1.56494i
$551$	−538.772	+	311.060i	−0.977808	+	0.564538i
$552$	−67.9281	+	203.189i	−0.123058	+	0.368095i
$553$	145.897	+	252.701i	0.263828	+	0.456964i
$554$	−518.936	−	299.608i	−0.936708	−	0.540809i
$555$	5.90269	+	1.97333i	0.0106355	+	0.00355555i
$556$	−197.142	+	341.460i	−0.354572	+	0.614136i
$557$	−76.5165	+	44.1768i	−0.137373	+	0.0793121i	−0.567111	−	0.823641i	$-0.691939\pi$
$557$	−76.5165	+	44.1768i	−0.137373	+	0.0793121i	0.429739	+	0.902953i	$0.358606\pi$
$558$	471.853	+	57.6908i	0.845614	+	0.103389i
$559$	−2.24403	−	24.3316i	−0.00401437	−	0.0435270i
$560$	−80.7377	+	46.6140i	−0.144175	+	0.0832392i
$561$	−1170.85	+	238.525i	−2.08708	+	0.425179i
$562$	−321.974			−0.572907
$563$	−736.014	+	424.938i	−1.30731	+	0.754774i	−0.981646	−	0.190712i	$-0.938920\pi$
$563$	−736.014	+	424.938i	−1.30731	+	0.754774i	−0.325662	+	0.945486i	$0.605587\pi$
$564$	42.5071	−	37.6266i	0.0753673	−	0.0667138i
$565$	−21.2343			−0.0375828
$566$	−957.732	−	552.947i	−1.69211	−	0.976937i
$567$	113.085	+	392.856i	0.199445	+	0.692867i
$568$	−243.780	+	422.240i	−0.429191	+	0.743380i
$569$	264.713	+	152.832i	0.465225	+	0.268598i	0.714239	−	0.699902i	$-0.246773\pi$
$569$	264.713	+	152.832i	0.465225	+	0.268598i	−0.249014	+	0.968500i	$0.580106\pi$
$570$	80.6558	−	241.260i	0.141501	−	0.423264i
$571$	−76.3088	+	132.171i	−0.133641	+	0.231472i	−0.925077	−	0.379779i	$-0.876000\pi$
$571$	−76.3088	+	132.171i	−0.133641	+	0.231472i	0.791437	+	0.611251i	$0.209333\pi$
$572$	−548.619	+	50.5976i	−0.959125	+	0.0884573i
$573$	515.873	+	172.462i	0.900301	+	0.300980i
$574$	38.2254	−	66.2084i	0.0665948	−	0.115346i
$575$	−428.728	+	247.526i	−0.745613	+	0.430480i
$576$	−115.226	−	86.7366i	−0.200045	−	0.150584i
$577$	−357.654			−0.619851			−0.309926	−	0.950761i	$-0.600304\pi$
$577$	−357.654			−0.619851			−0.309926	+	0.950761i	$0.600304\pi$
$578$		−	856.120i		−	1.48118i
$579$	2.33442	−	6.98278i	0.00403181	−	0.0120601i
$580$	22.3362	−	38.6875i	0.0385108	−	0.0667026i
$581$	193.096	−	111.484i	0.332351	−	0.191883i
$582$	−908.171	+	803.896i	−1.56043	+	1.38127i
$583$	272.807	−	472.516i	0.467937	−	0.810491i
$584$		−	311.515i		−	0.533416i
$585$	97.2089	−	52.3387i	0.166169	−	0.0894679i
$586$	393.268			0.671106
$587$	−699.202	−	403.685i	−1.19115	−	0.687708i	−0.232579	−	0.972577i	$-0.574716\pi$
$587$	−699.202	−	403.685i	−1.19115	−	0.687708i	−0.958566	+	0.284869i	$0.908050\pi$
$588$	183.381	−	37.3583i	0.311873	−	0.0635345i
$589$	356.790	+	617.979i	0.605756	+	1.04920i
$590$	−68.7538	−	39.6950i	−0.116532	−	0.0672797i
$591$	208.047	+	1021.24i	0.352025	+	1.72799i
$592$	43.0381			0.0726996
$593$		−	246.824i		−	0.416230i	−0.978104	−	0.208115i	$-0.933267\pi$
$593$		−	246.824i		−	0.416230i	0.978104	−	0.208115i	$-0.0667328\pi$
$594$	1004.97	+	478.397i	1.69186	+	0.805382i
$595$	59.3376	+	102.776i	0.0997271	+	0.172732i
$596$	75.5847	+	43.6388i	0.126820	+	0.0732195i
$597$	351.202	+	396.757i	0.588278	+	0.664584i
$598$	625.295	+	288.009i	1.04564	+	0.481621i
$599$	120.864	+	69.7811i	0.201777	+	0.116496i	0.597484	−	0.801881i	$-0.296167\pi$
$599$	120.864	+	69.7811i	0.201777	+	0.116496i	−0.395707	+	0.918377i	$0.629500\pi$
$600$	50.2153	+	246.493i	0.0836921	+	0.410821i
$601$	484.572	−	839.304i	0.806277	−	1.39651i	−0.109149	−	0.994025i	$-0.534812\pi$
$601$	484.572	−	839.304i	0.806277	−	1.39651i	0.915426	−	0.402487i	$-0.131854\pi$
$602$	−21.1880	−	12.2329i	−0.0351960	−	0.0203204i
$603$	565.008	+	425.310i	0.936994	+	0.705324i
$604$	−142.325	+	246.515i	−0.235638	+	0.408137i
$605$		−	126.902i		−	0.209756i
$606$	−847.816	+	172.716i	−1.39904	+	0.285010i
$607$	301.520	+	522.248i	0.496738	+	0.860376i	0.999993	−	0.00376245i	$-0.00119763\pi$
$607$	301.520	+	522.248i	0.496738	+	0.860376i	−0.503255	+	0.864138i	$0.667864\pi$
$608$		−	1274.37i		−	2.09600i
$609$	−202.429	+	179.186i	−0.332395	+	0.294230i
$610$	16.2611	+	28.1651i	0.0266576	+	0.0461723i
$611$	53.5715	+	75.7477i	0.0876784	+	0.123973i
$612$	−357.622	+	475.086i	−0.584349	+	0.776285i
$613$	520.011	+	900.685i	0.848305	+	1.46931i	0.882720	+	0.469900i	$0.155710\pi$
$613$	520.011	+	900.685i	0.848305	+	1.46931i	−0.0344149	+	0.999408i	$0.510957\pi$
$614$	−1250.19	−	721.795i	−2.03613	−	1.17556i
$615$	11.0204	+	12.4499i	0.0179194	+	0.0202437i
$616$	140.284	−	242.980i	0.227734	−	0.394448i
$617$	164.067	−	94.7239i	0.265910	−	0.153523i	−0.361117	−	0.932520i	$-0.617605\pi$
$617$	164.067	−	94.7239i	0.265910	−	0.153523i	0.627028	+	0.778997i	$0.284271\pi$
$618$	−245.681	−	1205.98i	−0.397542	−	1.95142i
$619$	−378.224	−	655.103i	−0.611024	−	1.05832i	−0.991068	−	0.133356i	$-0.957425\pi$
$619$	−378.224	−	655.103i	−0.611024	−	1.05832i	0.380044	−	0.924968i	$-0.375909\pi$
$620$	−44.3751	−	25.6200i	−0.0715728	−	0.0413226i
$621$	−314.368	−	456.656i	−0.506229	−	0.735356i
$622$	−414.842	−	718.527i	−0.666948	−	1.15519i
$623$	−245.357	+	141.657i	−0.393831	+	0.227378i
$624$	522.772	−	556.384i	0.837776	−	0.891641i
$625$	−279.506	+	484.118i	−0.447209	+	0.774589i
$626$			898.058i			1.43460i
$627$	333.519	+	1637.15i	0.531929	+	2.61109i
$628$	−11.7228			−0.0186668
$629$		−	54.7857i		−	0.0870998i
$630$	13.4156	−	109.726i	0.0212946	−	0.174168i
$631$	363.821	−	630.156i	0.576578	−	0.998662i	−0.419290	−	0.907852i	$-0.637721\pi$
$631$	363.821	−	630.156i	0.576578	−	0.998662i	0.995868	−	0.0908100i	$-0.0289456\pi$
$632$	−174.139	+	100.539i	−0.275537	+	0.159081i
$633$	259.446	−	776.063i	0.409867	−	1.22601i
$634$	221.314			0.349076
$635$			111.089i			0.174943i
$636$	−54.2015	−	266.060i	−0.0852225	−	0.418333i
$637$	28.0894	+	304.568i	0.0440963	+	0.478128i
$638$			736.037i			1.15366i
$639$	−493.571	−	1161.13i	−0.772412	−	1.81710i
$640$	−49.5256	−	85.7808i	−0.0773837	−	0.134033i
$641$		−	877.528i		−	1.36900i	−0.729014	−	0.684499i	$-0.760021\pi$
$641$		−	877.528i		−	1.36900i	0.729014	−	0.684499i	$-0.239979\pi$
$642$	487.441	−	1458.05i	0.759253	−	2.27110i
$643$	207.759	+	359.849i	0.323108	+	0.559640i	0.981128	−	0.193361i	$-0.0619389\pi$
$643$	207.759	+	359.849i	0.323108	+	0.559640i	−0.658019	+	0.753001i	$0.728606\pi$
$644$	237.964	−	137.388i	0.369509	−	0.213336i
$645$	3.98421	−	3.52675i	0.00617707	−	0.00546783i
$646$	−2239.25			−3.46634
$647$	327.840	−	189.279i	0.506708	−	0.292548i	−0.224772	−	0.974411i	$-0.572164\pi$
$647$	327.840	−	189.279i	0.506708	−	0.292548i	0.731479	+	0.681864i	$0.238830\pi$
$648$	−270.721	+	77.9283i	−0.417779	+	0.120260i
$649$	521.427			0.803431
$650$	804.919	−	74.2353i	1.23834	−	0.114208i
$651$	205.529	+	232.188i	0.315713	+	0.356664i
$652$	250.409			0.384062
$653$			302.192i			0.462775i	0.972862	+	0.231387i	$0.0743265\pi$
$653$			302.192i			0.462775i	−0.972862	+	0.231387i	$0.925674\pi$
$654$	577.123	−	510.859i	0.882450	−	0.781129i
$655$	42.3578	+	73.3659i	0.0646684	+	0.112009i
$656$	99.5716	+	57.4877i	0.151786	+	0.0876337i
$657$	644.042	+	484.803i	0.980277	+	0.737905i
$658$	92.8947			0.141177
$659$			7.34584i			0.0111469i	0.999984	+	0.00557347i	$0.00177410\pi$
$659$			7.34584i			0.0111469i	−0.999984	+	0.00557347i	$0.998226\pi$
$660$	−79.5198	−	89.8344i	−0.120485	−	0.136113i
$661$	631.994			0.956118			0.478059	−	0.878328i	$-0.341341\pi$
$661$	631.994			0.956118			0.478059	+	0.878328i	$0.341341\pi$
$662$	−13.4996	−	7.79399i	−0.0203921	−	0.0117734i
$663$	−708.253	−	665.467i	−1.06826	−	1.00372i
$664$	76.8248	+	133.065i	0.115700	+	0.200398i
$665$	143.707	−	82.9691i	0.216100	−	0.124766i
$666$	−30.6907	+	40.7714i	−0.0460821	+	0.0612183i
$667$	183.312	−	317.505i	0.274830	−	0.476019i
$668$	377.346	−	217.861i	0.564890	−	0.326139i
$669$	74.3284	+	83.9696i	0.111104	+	0.125515i
$670$	−95.6138	−	165.608i	−0.142707	−	0.247176i
$671$	−184.986	−	106.802i	−0.275687	−	0.159168i
$672$	−110.544	−	542.630i	−0.164500	−	0.807485i
$673$	−505.494	+	875.541i	−0.751105	+	1.30095i	0.196182	+	0.980567i	$0.437146\pi$
$673$	−505.494	+	875.541i	−0.751105	+	1.30095i	−0.947287	+	0.320385i	$0.896188\pi$
$674$	−901.927	+	520.728i	−1.33817	+	0.772593i
$675$	−587.761	−	279.793i	−0.870757	−	0.414509i
$676$	−291.245	−	340.539i	−0.430836	−	0.503756i
$677$	453.715	−	261.952i	0.670185	−	0.386931i	−0.125962	−	0.992035i	$-0.540202\pi$
$677$	453.715	−	261.952i	0.670185	−	0.386931i	0.796147	+	0.605104i	$0.206868\pi$
$678$	55.2031	−	165.125i	0.0814206	−	0.243548i
$679$	−791.160			−1.16518
$680$	−70.8238	+	40.8902i	−0.104153	+	0.0601326i
$681$	−565.784	−	189.147i	−0.830813	−	0.277750i
$682$	844.244			1.23790
$683$	−733.152	−	423.286i	−1.07343	−	0.619745i	−0.144313	−	0.989532i	$-0.546097\pi$
$683$	−733.152	−	423.286i	−1.07343	−	0.619745i	−0.929116	+	0.369787i	$0.879431\pi$
$684$	664.292	+	500.047i	0.971187	+	0.731062i
$685$	−4.31107	+	7.46699i	−0.00629353	+	0.0109007i
$686$	817.574	+	472.027i	1.19180	+	0.688085i
$687$	−548.974	−	620.182i	−0.799089	−	0.902739i
$688$	18.3972	−	31.8649i	0.0267401	−	0.0463152i
$689$	441.884	−	40.7536i	0.641341	−	0.0591490i
$690$	29.9254	+	146.895i	0.0433701	+	0.212892i
$691$	−340.658	+	590.037i	−0.492993	+	0.853888i	−0.999967	−	0.00807270i	$-0.997430\pi$
$691$	−340.658	+	590.037i	−0.492993	+	0.853888i	0.506975	+	0.861961i	$0.330764\pi$
$692$	−232.414	+	134.185i	−0.335859	+	0.193908i
$693$	284.028	+	668.175i	0.409852	+	0.964178i
$694$	−759.371			−1.09419
$695$		−	140.320i		−	0.201900i
$696$	−123.479	−	139.496i	−0.177412	−	0.200425i
$697$	73.1794	−	126.750i	0.104992	−	0.181851i
$698$	−1139.69	+	658.003i	−1.63280	+	0.942697i
$699$	301.726	+	100.870i	0.431654	+	0.144306i
$700$	161.316	−	279.408i	0.230452	−	0.399155i
$701$		−	253.593i		−	0.361759i	−0.983505	−	0.180880i	$-0.942106\pi$
$701$		−	253.593i		−	0.361759i	0.983505	−	0.180880i	$-0.0578945\pi$
$702$	154.289	+	891.998i	0.219785	+	1.27065i
$703$	−76.6045			−0.108968
$704$	−221.822	−	128.069i	−0.315089	−	0.181917i
$705$	−6.40560	+	19.1606i	−0.00908596	+	0.0271782i
$706$	647.692	+	1121.84i	0.917410	+	1.58900i
$707$	−488.784	−	282.199i	−0.691349	−	0.399150i
$708$	194.301	−	171.992i	0.274436	−	0.242926i
$709$	254.782			0.359354			0.179677	−	0.983726i	$-0.442495\pi$
$709$	254.782			0.359354			0.179677	+	0.983726i	$0.442495\pi$
$710$			341.162i			0.480510i
$711$	63.1486	−	516.491i	0.0888166	−	0.726430i
$712$	−97.6172	−	169.078i	−0.137103	−	0.237469i
$713$	−364.183	−	210.261i	−0.510775	−	0.294896i
$714$	−953.483	+	194.243i	−1.33541	+	0.272049i
$715$	160.085	−	113.218i	0.223895	−	0.158346i
$716$	−469.198	−	270.892i	−0.655305	−	0.378340i
$717$	860.503	−	761.701i	1.20014	−	1.06235i
$718$	332.756	−	576.350i	0.463448	−	0.802716i
$719$	129.197	+	74.5922i	0.179690	+	0.103744i	0.587147	−	0.809480i	$-0.300251\pi$
$719$	129.197	+	74.5922i	0.179690	+	0.103744i	−0.407457	+	0.913224i	$0.633584\pi$
$720$	165.018	+	20.1759i	0.229192	+	0.0280221i
$721$	401.415	−	695.271i	0.556748	−	0.964315i
$722$			2200.01i			3.04711i
$723$	44.6924	−	133.685i	0.0618152	−	0.184904i
$724$	−160.742	−	278.413i	−0.222019	−	0.384549i
$725$		−	430.475i		−	0.593759i
$726$	986.838	+	329.910i	1.35928	+	0.454422i
$727$	495.936	+	858.987i	0.682168	+	1.18155i	0.974318	+	0.225178i	$0.0722962\pi$
$727$	495.936	+	858.987i	0.682168	+	1.18155i	−0.292149	+	0.956373i	$0.594370\pi$
$728$	227.228	−	20.9565i	0.312126	−	0.0287865i
$729$	260.204	−	680.981i	0.356933	−	0.934130i
$730$	−108.989	−	188.774i	−0.149299	−	0.258594i
$731$	−40.5626	−	23.4188i	−0.0554892	−	0.0320367i
$732$	−104.160	+	21.2194i	−0.142295	+	0.0289883i
$733$	−48.4482	+	83.9147i	−0.0660958	+	0.114481i	−0.897180	−	0.441666i	$-0.854388\pi$
$733$	−48.4482	+	83.9147i	−0.0660958	+	0.114481i	0.831084	+	0.556147i	$0.187721\pi$
$734$	−261.963	+	151.244i	−0.356898	+	0.206055i
$735$	−49.8718	+	44.1456i	−0.0678528	+	0.0600621i
$736$	375.500	+	650.385i	0.510190	+	0.883675i
$737$	1087.70	+	627.983i	1.47585	+	0.852080i
$738$	−125.465	+	53.3326i	−0.170007	+	0.0722663i
$739$	508.944	+	881.516i	0.688692	+	1.19285i	0.972261	+	0.233898i	$0.0751483\pi$
$739$	508.944	+	881.516i	0.688692	+	1.19285i	−0.283569	+	0.958952i	$0.591518\pi$
$740$	4.76377	−	2.75036i	0.00643752	−	0.00371670i
$741$	−930.492	+	990.319i	−1.25573	+	1.33646i
$742$	222.160	−	384.793i	0.299407	−	0.518589i
$743$		−	1.69538i		−	0.00228180i	−0.999999	−	0.00114090i	$-0.999637\pi$
$743$		−	1.69538i		−	0.00228180i	0.999999	−	0.00114090i	$-0.000363160\pi$
$744$	−160.003	+	141.632i	−0.215058	+	0.190366i
$745$	−31.0610			−0.0416926
$746$			1813.29i			2.43069i
$747$	−394.665	−	48.2536i	−0.528334	−	0.0645965i
$748$	−528.039	+	914.591i	−0.705935	+	1.22271i
$749$	868.486	−	501.421i	1.15953	−	0.669454i
$750$	237.647	+	268.473i	0.316863	+	0.357964i
$751$	−1393.46			−1.85547			−0.927734	−	0.373242i	$-0.878246\pi$
$751$	−1393.46			−1.85547			−0.927734	+	0.373242i	$0.878246\pi$
$752$			139.705i			0.185779i
$753$	104.823	−	92.7871i	0.139207	−	0.123223i
$754$	−488.752	+	345.663i	−0.648212	+	0.458439i
$755$		−	101.303i		−	0.134177i
$756$	326.234	+	155.298i	0.431527	+	0.205421i
$757$	−89.1160	−	154.353i	−0.117723	−	0.203901i	0.801142	−	0.598474i	$-0.204226\pi$
$757$	−89.1160	−	154.353i	−0.117723	−	0.203901i	−0.918865	+	0.394573i	$0.870893\pi$
$758$		−	858.074i		−	1.13202i
$759$	−652.612	−	737.263i	−0.859831	−	0.971361i
$760$	57.1749	+	99.0298i	0.0752301	+	0.130302i
$761$	−71.7101	+	41.4019i	−0.0942315	+	0.0544046i	−0.546375	−	0.837541i	$-0.683993\pi$
$761$	−71.7101	+	41.4019i	−0.0942315	+	0.0544046i	0.452144	+	0.891945i	$0.350659\pi$
$762$	−863.866	−	288.799i	−1.13368	−	0.379002i
$763$	502.765			0.658931
$764$	416.335	−	240.371i	0.544941	−	0.314622i
$765$	25.6831	−	210.061i	0.0335726	−	0.274590i
$766$	859.715			1.12234
$767$	244.876	+	346.244i	0.319265	+	0.451426i
$768$	984.243	−	200.509i	1.28157	−	0.261080i
$769$	−585.402			−0.761251			−0.380625	−	0.924729i	$-0.624291\pi$
$769$	−585.402			−0.761251			−0.380625	+	0.924729i	$0.624291\pi$
$770$		−	196.323i		−	0.254965i
$771$	341.302	+	114.101i	0.442675	+	0.147991i
$772$	−3.25363	−	5.63545i	−0.00421454	−	0.00729980i
$773$	−1324.82	−	764.883i	−1.71386	−	0.989499i	−0.929200	−	0.369576i	$-0.879503\pi$
$773$	−1324.82	−	764.883i	−1.71386	−	0.989499i	−0.784663	−	0.619923i	$-0.787164\pi$
$774$	17.0675	+	40.1512i	0.0220510	+	0.0518750i
$775$	−493.761			−0.637112
$776$		−	545.196i		−	0.702573i
$777$	−32.6185	+	6.64501i	−0.0419800	+	0.00855213i
$778$	−1504.95			−1.93438
$779$	−177.229	−	102.323i	−0.227509	−	0.131352i
$780$	22.3083	−	94.9924i	0.0286003	−	0.121785i
$781$	−1120.36	−	1940.52i	−1.43452	−	2.48466i
$782$	1142.82	−	659.810i	1.46141	−	0.843747i
$783$	480.568	−	38.1932i	0.613753	−	0.0487780i
$784$	−230.284	+	398.864i	−0.293730	+	0.508756i
$785$	3.61304	−	2.08599i	0.00460260	−	0.00265731i
$786$	−680.638	+	138.659i	−0.865952	+	0.176411i
$787$	−20.0530	−	34.7329i	−0.0254804	−	0.0441333i	0.853004	−	0.521904i	$-0.174778\pi$
$787$	−20.0530	−	34.7329i	−0.0254804	−	0.0441333i	−0.878484	+	0.477771i	$0.841445\pi$
$788$	797.726	+	460.567i	1.01234	+	0.584476i
$789$	761.206	−	673.806i	0.964773	−	0.854000i
$790$	−70.3506	+	121.851i	−0.0890514	+	0.154242i
$791$	98.3570	−	56.7864i	0.124345	−	0.0717907i
$792$	−460.447	+	195.727i	−0.581372	+	0.247129i
$793$	−15.9547	−	172.993i	−0.0201194	−	0.218151i
$794$	480.750	−	277.561i	0.605479	−	0.349573i
$795$	64.0489	+	72.3568i	0.0805647	+	0.0910148i
$796$	468.306			0.588324
$797$	−1083.60	+	625.614i	−1.35959	+	0.784961i	−0.989569	−	0.144061i	$-0.953984\pi$
$797$	−1083.60	+	625.614i	−1.35959	+	0.784961i	−0.370024	+	0.929022i	$0.620650\pi$
$798$	271.601	+	1333.21i	0.340352	+	1.67069i
$799$	177.839			0.222577
$800$	763.658	+	440.898i	0.954572	+	0.551123i
$801$	501.480	+	61.3132i	0.626068	+	0.0765459i
$802$	−170.063	+	294.558i	−0.212049	+	0.367279i
$803$	1239.85	+	715.827i	1.54402	+	0.891441i
$804$	612.451	−	124.768i	0.761755	−	0.155184i
$805$	−48.8947	+	84.6881i	−0.0607388	+	0.105203i
$806$	396.480	+	560.605i	0.491911	+	0.695540i
$807$	505.337	−	447.315i	0.626192	−	0.554294i
$808$	194.467	−	336.826i	0.240676	−	0.416864i
$809$	−121.940	+	70.4022i	−0.150730	+	0.0870238i	−0.573468	−	0.819228i	$-0.694402\pi$
$809$	−121.940	+	70.4022i	−0.150730	+	0.0870238i	0.422738	+	0.906252i	$0.361069\pi$
$810$	−136.789	+	141.940i	−0.168875	+	0.175234i
$811$	110.823			0.136650			0.0683250	−	0.997663i	$-0.478235\pi$
$811$	110.823			0.136650			0.0683250	+	0.997663i	$0.478235\pi$
$812$			238.934i			0.294253i
$813$	−16.2207	+	3.30446i	−0.0199516	+	0.00406453i
$814$	−45.3157	+	78.4892i	−0.0556704	+	0.0964240i
$815$	−77.1777	+	44.5586i	−0.0946966	+	0.0546731i
$816$	−292.124	−	1433.96i	−0.357995	−	1.75730i
$817$	−32.7455	+	56.7169i	−0.0400802	+	0.0694210i
$818$		−	154.617i		−	0.189018i
$819$	−310.303	+	502.397i	−0.378880	+	0.613427i
$820$	14.6950			0.0179208
$821$	568.499	+	328.223i	0.692447	+	0.399785i	0.804528	−	0.593915i	$-0.202418\pi$
$821$	568.499	+	328.223i	0.692447	+	0.399785i	−0.112081	+	0.993699i	$0.535752\pi$
$822$	−46.8585	−	52.9366i	−0.0570055	−	0.0643997i
$823$	−517.709	−	896.698i	−0.629051	−	1.08955i	−0.987743	−	0.156092i	$-0.950110\pi$
$823$	−517.709	−	896.698i	−0.629051	−	1.08955i	0.358692	−	0.933456i	$-0.383223\pi$
$824$	479.119	+	276.619i	0.581455	+	0.335703i
$825$	−1096.45	−	366.553i	−1.32902	−	0.444307i
$826$	424.623			0.514071
$827$		−	1102.24i		−	1.33281i	−0.745588	−	0.666407i	$-0.767831\pi$
$827$		−	1102.24i		−	1.33281i	0.745588	−	0.666407i	$-0.232169\pi$
$828$	−486.370	−	59.4657i	−0.587403	−	0.0718185i
$829$	145.685	+	252.334i	0.175736	+	0.304384i	0.940416	−	0.340027i	$-0.110436\pi$
$829$	145.685	+	252.334i	0.175736	+	0.304384i	−0.764680	+	0.644411i	$0.777103\pi$
$830$	93.1096	+	53.7568i	0.112180	+	0.0647673i
$831$	−220.999	+	661.059i	−0.265943	+	0.795498i
$832$	−19.1318	−	207.442i	−0.0229949	−	0.249329i
$833$	507.738	+	293.142i	0.609529	+	0.351912i
$834$	1091.18	+	364.794i	1.30837	+	0.437403i
$835$	−77.5339	+	134.293i	−0.0928549	+	0.160829i
$836$	1278.83	+	738.334i	1.52970	+	0.883174i
$837$	−43.8081	−	551.219i	−0.0523395	−	0.658565i
$838$	536.360	−	929.004i	0.640048	−	1.10860i
$839$		−	1335.97i		−	1.59234i	−0.605073	−	0.796170i	$-0.706856\pi$
$839$		−	1335.97i		−	1.59234i	0.605073	−	0.796170i	$-0.293144\pi$
$840$	32.9356	+	37.2077i	0.0392090	+	0.0442949i
$841$	−261.100	−	452.239i	−0.310464	−	0.537740i
$842$			18.1593i			0.0215669i
$843$	74.7627	+	366.989i	0.0886864	+	0.435337i
$844$	−361.607	−	626.321i	−0.428444	−	0.742087i
$845$	150.360	+	53.1314i	0.177941	+	0.0628773i
$846$	−132.347	−	99.6247i	−0.156439	−	0.117760i
$847$	339.372	+	587.810i	0.400676	+	0.693991i
$848$	578.695	+	334.110i	0.682423	+	0.393997i
$849$	−407.868	+	1220.03i	−0.480410	+	1.43702i
$850$	774.725	−	1341.86i	0.911441	−	1.57866i
$851$	39.0958	−	22.5720i	0.0459410	−	0.0265241i
$852$	−1057.56	−	353.554i	−1.24127	−	0.414969i
$853$	821.791	+	1423.38i	0.963412	+	1.66868i	0.713822	+	0.700327i	$0.246963\pi$
$853$	821.791	+	1423.38i	0.963412	+	1.66868i	0.249590	+	0.968352i	$0.419704\pi$
$854$	−150.643	−	86.9737i	−0.176397	−	0.101843i
$855$	−293.720	−	35.9115i	−0.343532	−	0.0420017i
$856$	345.534	+	598.483i	0.403662	+	0.699162i
$857$	425.718	−	245.788i	0.496754	−	0.286801i	−0.230618	−	0.973044i	$-0.574075\pi$
$857$	425.718	−	245.788i	0.496754	−	0.286801i	0.727372	+	0.686243i	$0.240741\pi$
$858$	464.247	+	1539.21i	0.541080	+	1.79396i
$859$	−121.372	+	210.222i	−0.141294	+	0.244728i	−0.927984	−	0.372620i	$-0.878460\pi$
$859$	−121.372	+	210.222i	−0.141294	+	0.244728i	0.786690	+	0.617348i	$0.211793\pi$
$860$		−	4.70270i		−	0.00546826i
$861$	−84.3410	−	28.1961i	−0.0979570	−	0.0327481i
$862$	−85.0455			−0.0986607
$863$			1159.09i			1.34309i	0.740963	+	0.671546i	$0.234369\pi$
$863$			1159.09i			1.34309i	−0.740963	+	0.671546i	$0.765631\pi$
$864$	−424.450	+	891.640i	−0.491261	+	1.03199i
$865$	47.7545	−	82.7132i	0.0552075	−	0.0956222i
$866$	−757.102	+	437.113i	−0.874252	+	0.504750i
$867$	−975.815	+	198.792i	−1.12551	+	0.229287i
$868$	274.060			0.315738
$869$		−	924.113i		−	1.06342i
$870$	−123.631	−	41.3313i	−0.142105	−	0.0475072i
$871$	93.8120	+	1017.18i	0.107706	+	1.16784i
$872$			346.460i			0.397317i
$873$	1127.17	+	848.477i	1.29114	+	0.971910i
$874$	−922.583	−	1597.96i	−1.05559	−	1.82833i
$875$			233.882i			0.267294i
$876$	698.122	−	142.221i	0.796943	−	0.162353i
$877$	−694.324	−	1202.60i	−0.791703	−	1.37127i	−0.924912	−	0.380182i	$-0.875861\pi$
$877$	−694.324	−	1202.60i	−0.791703	−	1.37127i	0.133208	−	0.991088i	$-0.457472\pi$
$878$	1096.30	−	632.947i	1.24863	−	0.720896i
$879$	−91.3174	−	448.252i	−0.103888	−	0.509956i
$880$	295.253			0.335515
$881$	−34.1161	+	19.6969i	−0.0387243	+	0.0223575i	−0.519237	−	0.854630i	$-0.673784\pi$
$881$	−34.1161	+	19.6969i	−0.0387243	+	0.0223575i	0.480513	+	0.876988i	$0.340451\pi$
$882$	−213.640	−	502.588i	−0.242222	−	0.569827i
$883$	−665.708			−0.753916			−0.376958	−	0.926230i	$-0.623030\pi$
$883$	−665.708			−0.753916			−0.376958	+	0.926230i	$0.623030\pi$
$884$	−855.299	+	78.8817i	−0.967533	+	0.0892327i
$885$	−29.2801	+	87.5836i	−0.0330849	+	0.0989645i
$886$	542.191			0.611954
$887$		−	983.416i		−	1.10870i	−0.832284	−	0.554350i	$-0.812967\pi$
$887$		−	983.416i		−	1.10870i	0.832284	−	0.554350i	$-0.187033\pi$
$888$	−4.57915	−	22.4777i	−0.00515670	−	0.0253128i
$889$	−297.082	−	514.562i	−0.334176	−	0.578810i
$890$	−118.309	−	68.3059i	−0.132932	−	0.0767482i
$891$	311.928	−	1256.56i	0.350087	−	1.41028i
$892$	99.1124			0.111113
$893$		−	248.665i		−	0.278460i
$894$	80.7499	−	241.542i	0.0903243	−	0.270181i
$895$	192.814			0.215434
$896$	458.804	+	264.891i	0.512059	+	0.295637i
$897$	183.082	−	779.594i	0.204105	−	0.869113i
$898$	104.709	+	181.361i	0.116602	+	0.201961i
$899$	316.677	−	182.834i	0.352255	−	0.203375i
$900$	−529.479	+	225.071i	−0.588310	+	0.250078i
$901$	425.307	−	736.654i	0.472039	−	0.817596i
$902$	−209.682	+	121.060i	−0.232463	+	0.134213i
$903$	−9.02330	+	26.9908i	−0.00999258	+	0.0298901i
$904$	39.1321	+	67.7788i	0.0432877	+	0.0749766i
$905$	99.0836	+	57.2060i	0.109485	+	0.0632110i
$906$	787.773	+	263.361i	0.869507	+	0.290685i
$907$	249.749	−	432.578i	0.275357	−	0.476932i	−0.694868	−	0.719137i	$-0.744537\pi$
$907$	249.749	−	432.578i	0.275357	−	0.476932i	0.970225	+	0.242205i	$0.0778706\pi$
$908$	−456.616	+	263.627i	−0.502881	+	0.290338i
$909$	393.728	+	926.245i	0.433144	+	1.01897i
$910$	130.365	−	92.1987i	0.143258	−	0.101317i
$911$	−1056.33	+	609.875i	−1.15953	+	0.669456i	−0.951192	−	0.308600i	$-0.900140\pi$
$911$	−1056.33	+	609.875i	−1.15953	+	0.669456i	−0.208340	+	0.978056i	$0.566806\pi$
$912$	−2005.04	+	408.464i	−2.19850	+	0.447877i
$913$	−706.140			−0.773429
$914$	48.7459	−	28.1434i	0.0533324	−	0.0307915i
$915$	28.3270	−	25.0746i	0.0309585	−	0.0274039i
$916$	−732.023			−0.799152
$917$	−392.402	−	226.554i	−0.427920	−	0.247059i
$918$	1566.75	+	745.822i	1.70670	+	0.812442i
$919$	−243.309	+	421.423i	−0.264754	+	0.458567i	−0.967499	−	0.252874i	$-0.918624\pi$
$919$	−243.309	+	421.423i	−0.264754	+	0.458567i	0.702745	+	0.711442i	$0.251957\pi$
$920$	−58.3595	−	33.6939i	−0.0634342	−	0.0366238i
$921$	−532.415	+	1592.58i	−0.578084	+	1.72918i
$922$	−601.534	+	1041.89i	−0.652423	+	1.13003i
$923$	762.417	−	1655.28i	0.826021	−	1.79337i
$924$	608.578	+	203.454i	0.658634	+	0.220188i
$925$	26.5032	−	45.9049i	0.0286521	−	0.0496269i
$926$	−593.752	+	342.803i	−0.641201	+	0.370197i
$927$	−1317.54	+	560.059i	−1.42129	+	0.604163i
$928$	−653.036			−0.703703
$929$		−	527.781i		−	0.568118i	−0.958807	−	0.284059i	$-0.908319\pi$
$929$		−	527.781i		−	0.568118i	0.958807	−	0.284059i	$-0.0916811\pi$
$930$	−47.4076	+	141.807i	−0.0509759	+	0.152481i
$931$	409.888	−	709.947i	0.440266	−	0.762564i
$932$	243.508	−	140.589i	0.261275	−	0.150847i
$933$	−722.658	+	639.684i	−0.774553	+	0.685621i
$934$	689.489	−	1194.23i	0.738211	−	1.27862i
$935$		−	375.844i		−	0.401973i
$936$	−346.207	−	213.833i	−0.369879	−	0.228454i
$937$	0.208716			0.000222750			0.000111375	−	1.00000i	$-0.499965\pi$
$937$	0.208716			0.000222750			0.000111375		1.00000i	$0.499965\pi$
$938$	885.766	+	511.397i	0.944313	+	0.545199i
$939$	1023.62	−	208.530i	1.09011	−	0.222077i
$940$	8.92791	+	15.4636i	0.00949777	+	0.0164506i
$941$	−1349.91	−	779.372i	−1.43455	−	0.828238i	−0.437088	−	0.899419i	$-0.643990\pi$
$941$	−1349.91	−	779.372i	−1.43455	−	0.828238i	−0.997463	+	0.0711805i	$0.977323\pi$
$942$	6.82852	+	33.5193i	0.00724896	+	0.0355831i
$943$	120.601			0.127891
$944$			638.596i			0.676479i
$945$	−128.182	+	10.1873i	−0.135642	+	0.0107802i
$946$	38.7416	+	67.1023i	0.0409530	+	0.0709327i
$947$	−794.732	−	458.838i	−0.839210	−	0.484518i	0.0177859	−	0.999842i	$-0.494338\pi$
$947$	−794.732	−	458.838i	−0.839210	−	0.484518i	−0.856995	+	0.515324i	$0.827672\pi$
$948$	−304.817	−	344.355i	−0.321537	−	0.363244i
$949$	106.935	+	1159.47i	0.112681	+	1.22178i
$950$	−1876.27	−	1083.26i	−1.97502	−	1.14028i
$951$	−51.3895	−	252.257i	−0.0540373	−	0.265254i
$952$	218.704	−	378.806i	0.229731	−	0.397906i
$953$	1137.28	+	656.609i	1.19337	+	0.688991i	0.959069	−	0.283173i	$-0.0913872\pi$
$953$	1137.28	+	656.609i	1.19337	+	0.688991i	0.234299	+	0.972165i	$0.424721\pi$
$954$	−729.183	+	309.961i	−0.764342	+	0.324906i
$955$	−85.5449	+	148.168i	−0.0895758	+	0.155150i
$956$		−	1015.68i		−	1.06243i
$957$	838.943	−	170.909i	0.876638	−	0.178588i
$958$	−204.309	−	353.874i	−0.213267	−	0.369388i
$959$		−	46.1161i		−	0.0480877i
$960$	33.9679	−	30.0677i	0.0353832	−	0.0313206i
$961$	270.787	+	469.017i	0.281776	+	0.488051i
$962$	−73.4008	+	6.76954i	−0.0763002	+	0.00703695i
$963$	−1775.08	−	217.030i	−1.84328	−	0.225368i
$964$	−62.2907	−	107.891i	−0.0646169	−	0.111920i
$965$	2.00558	+	1.15792i	0.00207832	+	0.00119992i
$966$	−531.453	−	600.389i	−0.550159	−	0.621521i
$967$	675.676	−	1170.31i	0.698735	−	1.21024i	−0.270171	−	0.962812i	$-0.587080\pi$
$967$	675.676	−	1170.31i	0.698735	−	1.21024i	0.968905	−	0.247431i	$-0.0795865\pi$
$968$	−405.066	+	233.865i	−0.418457	+	0.241596i
$969$	519.958	+	2552.33i	0.536592	+	2.63398i
$970$	−190.746	−	330.382i	−0.196645	−	0.340600i
$971$	759.567	+	438.536i	0.782252	+	0.451634i	0.837228	−	0.546854i	$-0.184175\pi$
$971$	759.567	+	438.536i	0.782252	+	0.451634i	−0.0549755	+	0.998488i	$0.517508\pi$
$972$	−298.238	−	571.123i	−0.306830	−	0.587575i
$973$	375.256	+	649.963i	0.385670	+	0.667999i
$974$	−1254.11	+	724.062i	−1.28759	+	0.743390i
$975$	−271.518	−	900.218i	−0.278480	−	0.923301i
$976$	130.801	−	226.554i	0.134017	−	0.232125i
$977$		−	327.759i		−	0.335475i	−0.985832	−	0.167737i	$-0.946354\pi$
$977$		−	327.759i		−	0.335475i	0.985832	−	0.167737i	$-0.0536460\pi$
$978$	−145.863	−	716.002i	−0.149145	−	0.732109i
$979$	897.254			0.916501
$980$			58.8655i			0.0600668i
$981$	−716.291	−	539.189i	−0.730164	−	0.549632i
$982$	597.004	−	1034.04i	0.607947	−	1.05300i
$983$	−1226.87	+	708.331i	−1.24808	+	0.720581i	−0.970727	−	0.240187i	$-0.922791\pi$
$983$	−1226.87	+	708.331i	−1.24808	+	0.720581i	−0.277356	+	0.960767i	$0.589458\pi$
$984$	19.4302	−	58.1203i	0.0197462	−	0.0590653i
$985$	−327.820			−0.332812
$986$			1147.48i			1.16378i
$987$	−21.5703	−	105.882i	−0.0218544	−	0.107277i
$988$	110.297	+	1195.93i	0.111636	+	1.21045i
$989$		−	38.5947i		−	0.0390239i
$990$	−210.546	+	279.702i	−0.212673	+	0.282528i
$991$	565.364	+	979.240i	0.570499	+	0.988133i	0.996515	+	0.0834174i	$0.0265835\pi$
$991$	565.364	+	979.240i	0.570499	+	0.988133i	−0.426016	+	0.904716i	$0.640083\pi$
$992$			749.042i			0.755082i
$993$	−5.74906	+	17.1968i	−0.00578958	+	0.0173180i
$994$	−912.364	−	1580.26i	−0.917871	−	1.58980i
$995$	−144.335	+	83.3320i	−0.145061	+	0.0837508i
$996$	−263.131	+	232.919i	−0.264188	+	0.233854i
$997$	1061.77			1.06497			0.532485	−	0.846440i	$-0.321258\pi$
$997$	1061.77			1.06497			0.532485	+	0.846440i	$0.321258\pi$
$998$	−720.772	+	416.138i	−0.722216	+	0.416972i
$999$	53.5981	+	25.5144i	0.0536518	+	0.0255400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.u.a.68.6	yes	52
3.2	odd	2		351.3.u.a.341.21		52
9.2	odd	6		117.3.k.a.29.6	✓	52
9.7	even	3		351.3.k.a.224.21		52
13.9	even	3		117.3.k.a.113.21	yes	52
39.35	odd	6		351.3.k.a.152.6		52
117.61	even	3		351.3.u.a.35.21		52
117.74	odd	6	inner	117.3.u.a.74.6	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.6	✓	52	9.2	odd	6
117.3.k.a.113.21	yes	52	13.9	even	3
117.3.u.a.68.6	yes	52	1.1	even	1	trivial
117.3.u.a.74.6	yes	52	117.74	odd	6	inner
351.3.k.a.152.6		52	39.35	odd	6
351.3.k.a.224.21		52	9.7	even	3
351.3.u.a.35.21		52	117.61	even	3
351.3.u.a.341.21		52	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23352 - 1.28952i) q^{2} +(-0.951185 + 2.84521i) q^{3} +(1.32573 + 2.29623i) q^{4} +(-0.817198 - 0.471810i) q^{5} +(5.79345 - 5.12826i) q^{6} +5.04701 q^{7} +3.47795i q^{8} +(-7.19049 - 5.41265i) q^{9} +(1.21682 + 2.10759i) q^{10} +(-13.8424 - 7.99194i) q^{11} +(-7.79428 + 1.58784i) q^{12} +(-1.19389 - 12.9451i) q^{13} +(-11.2726 - 6.50822i) q^{14} +(2.11971 - 1.87633i) q^{15} +(9.78780 - 16.9530i) q^{16} +(-21.5804 - 12.4595i) q^{17} +(9.08035 + 21.3615i) q^{18} +(-17.4215 + 30.1749i) q^{19} -2.50197i q^{20} +(-4.80064 + 14.3598i) q^{21} +(20.6116 + 35.7003i) q^{22} -20.5334i q^{23} +(-9.89551 - 3.30817i) q^{24} +(-12.0548 - 20.8795i) q^{25} +(-14.0264 + 30.4525i) q^{26} +(22.2396 - 15.3101i) q^{27} +(6.69097 + 11.5891i) q^{28} +(15.4628 + 8.92748i) q^{29} +(-7.15396 + 1.45740i) q^{30} +(10.2399 - 17.7361i) q^{31} +(-31.6745 + 18.2873i) q^{32} +(35.9055 - 31.7829i) q^{33} +(32.1335 + 55.6568i) q^{34} +(-4.12441 - 2.38123i) q^{35} +(2.89605 - 23.6867i) q^{36} +(1.09928 + 1.90401i) q^{37} +(77.8224 - 44.9308i) q^{38} +(37.9671 + 8.91629i) q^{39} +(1.64093 - 2.84217i) q^{40} +5.87340i q^{41} +(29.2396 - 25.8824i) q^{42} +1.87960 q^{43} -42.3806i q^{44} +(3.32232 + 7.81575i) q^{45} +(-26.4783 + 45.8617i) q^{46} +(-6.18058 + 3.56836i) q^{47} +(38.9248 + 43.9738i) q^{48} -23.5277 q^{49} +62.1796i q^{50} +(55.9768 - 49.5497i) q^{51} +(28.1421 - 19.9031i) q^{52} +34.1353i q^{53} +(-69.4153 + 5.51678i) q^{54} +(7.54135 + 13.0620i) q^{55} +17.5532i q^{56} +(-69.2831 - 78.2699i) q^{57} +(-23.0243 - 39.8793i) q^{58} +(-28.2515 + 16.3110i) q^{59} +(7.11863 + 2.37983i) q^{60} +13.3637 q^{61} +(-45.7421 + 26.4092i) q^{62} +(-36.2905 - 27.3177i) q^{63} +16.0248 q^{64} +(-5.13196 + 11.1420i) q^{65} +(-121.180 + 24.6867i) q^{66} -78.5770 q^{67} -66.0715i q^{68} +(58.4220 + 19.5311i) q^{69} +(6.14128 + 10.6370i) q^{70} +(121.405 + 70.0932i) q^{71} +(18.8249 - 25.0082i) q^{72} -89.5686 q^{73} -5.67018i q^{74} +(70.8730 - 14.4382i) q^{75} -92.3848 q^{76} +(-69.8630 - 40.3354i) q^{77} +(-73.3023 - 68.8740i) q^{78} +(28.9076 + 50.0695i) q^{79} +(-15.9971 + 9.23596i) q^{80} +(22.4064 + 77.8393i) q^{81} +(7.57387 - 13.1183i) q^{82} +(38.2595 - 22.0891i) q^{83} +(-39.3378 + 8.01386i) q^{84} +(11.7570 + 20.3637i) q^{85} +(-4.19812 - 2.42379i) q^{86} +(-40.1086 + 35.5034i) q^{87} +(27.7956 - 48.1433i) q^{88} +(-48.6143 + 28.0675i) q^{89} +(2.65813 - 21.7408i) q^{90} +(-6.02555 - 65.3338i) q^{91} +(47.1494 - 27.2217i) q^{92} +(40.7229 + 46.0051i) q^{93} +18.4059 q^{94} +(28.4736 - 16.4393i) q^{95} +(-21.9029 - 107.515i) q^{96} -156.758 q^{97} +(52.5495 + 30.3395i) q^{98} +(56.2764 + 132.390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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