LMFDB - Embedded newform 222.3.l.d.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,3,Mod(97,222)] 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("222.97"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	222.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,8,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.04906186880$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 318 x^{13} + 8876 x^{12} - 14732 x^{11} + 38482 x^{10} + 1520688 x^{9} + \cdots + 4 $ x^16 - 4x^15 + 8x^14 + 318x^13 + 8876x^12 - 14732x^11 + 38482x^10 + 1520688x^9 + 22685392x^8 + 15961410x^7 + 5199688x^6 - 6131200x^5 + 2764889x^4 - 258648x^3 + 12800x^2 - 320*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$-5.45996 + 5.45996i$ of defining polynomial
Character	$\chi$	$=$	222.97
Dual form			222.3.l.d.103.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-2.36451 + 8.82447i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-4.27169 - 7.39879i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +12.9199 q^{10} +8.88099i q^{11} +(-1.73205 + 3.00000i) q^{12} +(-4.38313 + 16.3581i) q^{13} +(-8.54338 + 8.54338i) q^{14} +(4.09545 + 15.2844i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-10.2285 + 2.74071i) q^{17} +(-4.09808 - 1.09808i) q^{18} +(-7.84483 + 29.2773i) q^{19} +(-4.72902 - 17.6489i) q^{20} +(-12.8151 - 7.39879i) q^{21} +(12.1317 - 3.25067i) q^{22} +(26.9493 + 26.9493i) q^{23} +(4.73205 + 1.26795i) q^{24} +(-50.6298 - 29.2311i) q^{25} +23.9499 q^{26} -5.19615i q^{27} +(14.7976 + 8.54338i) q^{28} +(35.0886 - 35.0886i) q^{29} +(19.3799 - 11.1890i) q^{30} +(8.07977 - 8.07977i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(7.69117 + 13.3215i) q^{33} +(7.48776 + 12.9692i) q^{34} +(75.3908 - 20.2009i) q^{35} +6.00000i q^{36} +(-36.9831 - 1.11766i) q^{37} +42.8650 q^{38} +(7.59180 + 28.3330i) q^{39} +(-22.3780 + 12.9199i) q^{40} +(-33.8332 + 19.5336i) q^{41} +(-5.41629 + 20.2139i) q^{42} +(-6.81615 - 6.81615i) q^{43} +(-8.88099 - 15.3823i) q^{44} +(19.3799 + 19.3799i) q^{45} +(26.9493 - 46.6775i) q^{46} -46.2282 q^{47} -6.92820i q^{48} +(-11.9947 + 20.7754i) q^{49} +(-21.3987 + 79.8609i) q^{50} +(-12.9692 + 12.9692i) q^{51} +(-8.76626 - 32.7161i) q^{52} +(24.3949 - 42.2532i) q^{53} +(-7.09808 + 1.90192i) q^{54} +(-78.3701 - 20.9992i) q^{55} +(6.25419 - 23.3410i) q^{56} +(13.5877 + 50.7098i) q^{57} +(-60.7752 - 35.0886i) q^{58} +(29.2966 - 7.85000i) q^{59} +(-22.3780 - 22.3780i) q^{60} +(32.7891 + 8.78582i) q^{61} +(-13.9946 - 8.07977i) q^{62} -25.6301 q^{63} +8.00000i q^{64} +(-133.987 - 77.3576i) q^{65} +(15.3823 - 15.3823i) q^{66} +(30.6840 - 17.7154i) q^{67} +(14.9755 - 14.9755i) q^{68} +(63.7626 + 17.0851i) q^{69} +(-55.1899 - 95.5918i) q^{70} +(41.7426 + 72.3003i) q^{71} +(8.19615 - 2.19615i) q^{72} +55.4373i q^{73} +(12.0100 + 50.9290i) q^{74} -101.260 q^{75} +(-15.6897 - 58.5546i) q^{76} +(65.7086 - 37.9369i) q^{77} +(35.9248 - 20.7412i) q^{78} +(24.2914 - 90.6567i) q^{79} +(25.8399 + 25.8399i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(39.0672 + 39.0672i) q^{82} +(-32.5526 + 56.3828i) q^{83} +29.5951 q^{84} -96.7412i q^{85} +(-6.81615 + 11.8059i) q^{86} +(22.2453 - 83.0205i) q^{87} +(-17.7620 + 17.7620i) q^{88} +(18.4963 + 69.0290i) q^{89} +(19.3799 - 33.5670i) q^{90} +(139.753 - 37.4467i) q^{91} +(-73.6267 - 19.7282i) q^{92} +(5.12237 - 19.1169i) q^{93} +(16.9207 + 63.1489i) q^{94} +(-239.808 - 138.453i) q^{95} +(-9.46410 + 2.53590i) q^{96} +(-104.978 - 104.978i) q^{97} +(32.7701 + 8.78072i) q^{98} +(23.0735 + 13.3215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−2.36451	+	8.82447i	−0.472902	+	1.76489i	0.156359	+	0.987700i	$0.450024\pi$
$5$	−2.36451	+	8.82447i	−0.472902	+	1.76489i	−0.629261	+	0.777194i	$0.716642\pi$
$6$	−1.73205	−	1.73205i	−0.288675	−	0.288675i
$7$	−4.27169	−	7.39879i	−0.610242	−	1.05697i	−0.991199	−	0.132377i	$-0.957739\pi$
$7$	−4.27169	−	7.39879i	−0.610242	−	1.05697i	0.380958	−	0.924592i	$-0.375594\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	12.9199			1.29199
$11$			8.88099i			0.807363i	0.914900	+	0.403682i	$0.132270\pi$
$11$			8.88099i			0.807363i	−0.914900	+	0.403682i	$0.867730\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	−4.38313	+	16.3581i	−0.337164	+	1.25831i	0.564340	+	0.825542i	$0.309131\pi$
$13$	−4.38313	+	16.3581i	−0.337164	+	1.25831i	−0.901504	+	0.432770i	$0.857536\pi$
$14$	−8.54338	+	8.54338i	−0.610242	+	0.610242i
$15$	4.09545	+	15.2844i	0.273030	+	1.01896i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−10.2285	+	2.74071i	−0.601674	+	0.161218i	−0.546783	−	0.837274i	$-0.684148\pi$
$17$	−10.2285	+	2.74071i	−0.601674	+	0.161218i	−0.0548911	+	0.998492i	$0.517481\pi$
$18$	−4.09808	−	1.09808i	−0.227671	−	0.0610042i
$19$	−7.84483	+	29.2773i	−0.412886	+	1.54091i	0.376147	+	0.926560i	$0.377249\pi$
$19$	−7.84483	+	29.2773i	−0.412886	+	1.54091i	−0.789033	+	0.614351i	$0.789418\pi$
$20$	−4.72902	−	17.6489i	−0.236451	−	0.882447i
$21$	−12.8151	−	7.39879i	−0.610242	−	0.352323i
$22$	12.1317	−	3.25067i	0.551439	−	0.147758i
$23$	26.9493	+	26.9493i	1.17171	+	1.17171i	0.981803	+	0.189904i	$0.0608178\pi$
$23$	26.9493	+	26.9493i	1.17171	+	1.17171i	0.189904	+	0.981803i	$0.439182\pi$
$24$	4.73205	+	1.26795i	0.197169	+	0.0528312i
$25$	−50.6298	−	29.2311i	−2.02519	−	1.16924i
$26$	23.9499			0.921149
$27$		−	5.19615i		−	0.192450i
$28$	14.7976	+	8.54338i	0.528485	+	0.305121i
$29$	35.0886	−	35.0886i	1.20995	−	1.20995i	0.238910	−	0.971042i	$-0.423210\pi$
$29$	35.0886	−	35.0886i	1.20995	−	1.20995i	0.971042	−	0.238910i	$-0.0767901\pi$
$30$	19.3799	−	11.1890i	0.645996	−	0.372966i
$31$	8.07977	−	8.07977i	0.260638	−	0.260638i	−0.564675	−	0.825313i	$-0.690999\pi$
$31$	8.07977	−	8.07977i	0.260638	−	0.260638i	0.825313	+	0.564675i	$0.190999\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	7.69117	+	13.3215i	0.233066	+	0.403682i
$34$	7.48776	+	12.9692i	0.220228	+	0.381446i
$35$	75.3908	−	20.2009i	2.15402	−	0.577169i
$36$			6.00000i			0.166667i
$37$	−36.9831	−	1.11766i	−0.999544	−	0.0302071i
$37$	−36.9831	−	1.11766i	−0.999544	−	0.0302071i
$38$	42.8650			1.12803
$39$	7.59180	+	28.3330i	0.194662	+	0.726487i
$40$	−22.3780	+	12.9199i	−0.559449	+	0.322998i
$41$	−33.8332	+	19.5336i	−0.825200	+	0.476429i	−0.852206	−	0.523206i	$-0.824736\pi$
$41$	−33.8332	+	19.5336i	−0.825200	+	0.476429i	0.0270063	+	0.999635i	$0.491403\pi$
$42$	−5.41629	+	20.2139i	−0.128959	+	0.481282i
$43$	−6.81615	−	6.81615i	−0.158515	−	0.158515i	0.623393	−	0.781908i	$-0.285754\pi$
$43$	−6.81615	−	6.81615i	−0.158515	−	0.158515i	−0.781908	+	0.623393i	$0.785754\pi$
$44$	−8.88099	−	15.3823i	−0.201841	−	0.349598i
$45$	19.3799	+	19.3799i	0.430664	+	0.430664i
$46$	26.9493	−	46.6775i	0.585853	−	1.01473i
$47$	−46.2282			−0.983579			−0.491790	−	0.870714i	$-0.663657\pi$
$47$	−46.2282			−0.983579			−0.491790	+	0.870714i	$0.663657\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−11.9947	+	20.7754i	−0.244789	+	0.423988i
$50$	−21.3987	+	79.8609i	−0.427973	+	1.59722i
$51$	−12.9692	+	12.9692i	−0.254298	+	0.254298i
$52$	−8.76626	−	32.7161i	−0.168582	−	0.629156i
$53$	24.3949	−	42.2532i	0.460281	−	0.797231i	−0.538693	−	0.842502i	$-0.681082\pi$
$53$	24.3949	−	42.2532i	0.460281	−	0.797231i	0.998975	+	0.0452712i	$0.0144152\pi$
$54$	−7.09808	+	1.90192i	−0.131446	+	0.0352208i
$55$	−78.3701	−	20.9992i	−1.42491	−	0.381804i
$56$	6.25419	−	23.3410i	0.111682	−	0.416803i
$57$	13.5877	+	50.7098i	0.238380	+	0.889646i
$58$	−60.7752	−	35.0886i	−1.04785	−	0.604976i
$59$	29.2966	−	7.85000i	0.496553	−	0.133051i	−0.00184699	−	0.999998i	$-0.500588\pi$
$59$	29.2966	−	7.85000i	0.496553	−	0.133051i	0.498400	+	0.866947i	$0.333921\pi$
$60$	−22.3780	−	22.3780i	−0.372966	−	0.372966i
$61$	32.7891	+	8.78582i	0.537527	+	0.144030i	0.517362	−	0.855767i	$-0.326914\pi$
$61$	32.7891	+	8.78582i	0.537527	+	0.144030i	0.0201650	+	0.999797i	$0.493581\pi$
$62$	−13.9946	−	8.07977i	−0.225719	−	0.130319i
$63$	−25.6301			−0.406828
$64$			8.00000i			0.125000i
$65$	−133.987	−	77.3576i	−2.06134	−	1.19012i
$66$	15.3823	−	15.3823i	0.233066	−	0.233066i
$67$	30.6840	−	17.7154i	0.457969	−	0.264409i	−0.253221	−	0.967409i	$-0.581490\pi$
$67$	30.6840	−	17.7154i	0.457969	−	0.264409i	0.711190	+	0.703000i	$0.248157\pi$
$68$	14.9755	−	14.9755i	0.220228	−	0.220228i
$69$	63.7626	+	17.0851i	0.924096	+	0.247611i
$70$	−55.1899	−	95.5918i	−0.788428	−	1.36560i
$71$	41.7426	+	72.3003i	0.587924	+	1.01831i	0.994504	+	0.104699i	$0.0333878\pi$
$71$	41.7426	+	72.3003i	0.587924	+	1.01831i	−0.406580	+	0.913615i	$0.633279\pi$
$72$	8.19615	−	2.19615i	0.113835	−	0.0305021i
$73$			55.4373i			0.759415i	0.925107	+	0.379708i	$0.123975\pi$
$73$			55.4373i			0.759415i	−0.925107	+	0.379708i	$0.876025\pi$
$74$	12.0100	+	50.9290i	0.162297	+	0.688229i
$75$	−101.260			−1.35013
$76$	−15.6897	−	58.5546i	−0.206443	−	0.770456i
$77$	65.7086	−	37.9369i	0.853358	−	0.492687i
$78$	35.9248	−	20.7412i	0.460574	−	0.265913i
$79$	24.2914	−	90.6567i	0.307486	−	1.14755i	−0.623298	−	0.781984i	$-0.714208\pi$
$79$	24.2914	−	90.6567i	0.307486	−	1.14755i	0.930784	−	0.365569i	$-0.119126\pi$
$80$	25.8399	+	25.8399i	0.322998	+	0.322998i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	39.0672	+	39.0672i	0.476429	+	0.476429i
$83$	−32.5526	+	56.3828i	−0.392200	+	0.679311i	−0.992739	−	0.120284i	$-0.961619\pi$
$83$	−32.5526	+	56.3828i	−0.392200	+	0.679311i	0.600539	+	0.799595i	$0.294953\pi$
$84$	29.5951			0.352323
$85$		−	96.7412i		−	1.13813i
$86$	−6.81615	+	11.8059i	−0.0792576	+	0.137278i
$87$	22.2453	−	83.0205i	0.255693	−	0.954259i
$88$	−17.7620	+	17.7620i	−0.201841	+	0.201841i
$89$	18.4963	+	69.0290i	0.207823	+	0.775607i	0.988570	+	0.150760i	$0.0481721\pi$
$89$	18.4963	+	69.0290i	0.207823	+	0.775607i	−0.780747	+	0.624847i	$0.785161\pi$
$90$	19.3799	−	33.5670i	0.215332	−	0.372966i
$91$	139.753	−	37.4467i	1.53575	−	0.411503i
$92$	−73.6267	−	19.7282i	−0.800291	−	0.214437i
$93$	5.12237	−	19.1169i	0.0550792	−	0.205558i
$94$	16.9207	+	63.1489i	0.180008	+	0.671797i
$95$	−239.808	−	138.453i	−2.52429	−	1.45740i
$96$	−9.46410	+	2.53590i	−0.0985844	+	0.0264156i
$97$	−104.978	−	104.978i	−1.08225	−	1.08225i	−0.996300	−	0.0859490i	$-0.972608\pi$
$97$	−104.978	−	104.978i	−1.08225	−	1.08225i	−0.0859490	−	0.996300i	$-0.527392\pi$
$98$	32.7701	+	8.78072i	0.334389	+	0.0895992i
$99$	23.0735	+	13.3215i	0.233066	+	0.134561i
$100$	116.924			1.16924
$101$		−	123.465i		−	1.22243i	−0.791466	−	0.611214i	$-0.790682\pi$
$101$		−	123.465i		−	1.22243i	0.791466	−	0.611214i	$-0.209318\pi$
$102$	22.4633	+	12.9692i	0.220228	+	0.127149i
$103$	−25.7922	+	25.7922i	−0.250410	+	0.250410i	−0.821139	−	0.570729i	$-0.806661\pi$
$103$	−25.7922	+	25.7922i	−0.250410	+	0.250410i	0.570729	+	0.821139i	$0.306661\pi$
$104$	−41.4824	+	23.9499i	−0.398869	+	0.230287i
$105$	95.5918	−	95.5918i	0.910398	−	0.910398i
$106$	−66.6481	−	17.8583i	−0.628756	−	0.168475i
$107$	37.0450	+	64.1639i	0.346215	+	0.599663i	0.985574	−	0.169246i	$-0.0541333\pi$
$107$	37.0450	+	64.1639i	0.346215	+	0.599663i	−0.639358	+	0.768909i	$0.720800\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	−66.1580	+	17.7270i	−0.606954	+	0.162633i	−0.549190	−	0.835697i	$-0.685064\pi$
$109$	−66.1580	+	17.7270i	−0.606954	+	0.162633i	−0.0577641	+	0.998330i	$0.518397\pi$
$110$			114.742i			1.04311i
$111$	−56.4426	+	30.3518i	−0.508492	+	0.273440i
$112$	−34.1735			−0.305121
$113$	53.7327	+	200.533i	0.475511	+	1.77463i	0.619442	+	0.785043i	$0.287359\pi$
$113$	53.7327	+	200.533i	0.475511	+	1.77463i	−0.143931	+	0.989588i	$0.545974\pi$
$114$	64.2975	−	37.1222i	0.564013	−	0.325633i
$115$	−301.535	+	174.091i	−2.62204	+	1.51384i
$116$	−25.6866	+	95.8638i	−0.221437	+	0.826412i
$117$	35.9248	+	35.9248i	0.307050	+	0.307050i
$118$	−21.4466	−	37.1466i	−0.181751	−	0.314802i
$119$	63.9708	+	63.9708i	0.537569	+	0.537569i
$120$	−22.3780	+	38.7598i	−0.186483	+	0.322998i
$121$	42.1279			0.348165
$122$		−	48.0066i		−	0.393497i
$123$	−33.8332	+	58.6008i	−0.275067	+	0.476429i
$124$	−5.91480	+	22.0743i	−0.0477000	+	0.178019i
$125$	216.165	−	216.165i	1.72932	−	1.72932i
$126$	9.38128	+	35.0114i	0.0744546	+	0.277868i
$127$	42.0200	−	72.7807i	0.330866	−	0.573077i	−0.651816	−	0.758377i	$-0.725993\pi$
$127$	42.0200	−	72.7807i	0.330866	−	0.573077i	0.982682	+	0.185301i	$0.0593259\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	−16.1272	−	4.32127i	−0.125017	−	0.0334982i
$130$	−56.6297	+	211.345i	−0.435613	+	1.62573i
$131$	6.40060	+	23.8874i	0.0488595	+	0.182346i	0.986043	−	0.166490i	$-0.0532435\pi$
$131$	6.40060	+	23.8874i	0.0488595	+	0.182346i	−0.937184	+	0.348837i	$0.886577\pi$
$132$	−26.6430	−	15.3823i	−0.201841	−	0.116533i
$133$	250.127	−	67.0214i	1.88066	−	0.503920i
$134$	−35.4308	−	35.4308i	−0.264409	−	0.264409i
$135$	45.8533	+	12.2864i	0.339654	+	0.0910101i
$136$	−25.9383	−	14.9755i	−0.190723	−	0.110114i
$137$	−4.85457			−0.0354348			−0.0177174	−	0.999843i	$-0.505640\pi$
$137$	−4.85457			−0.0354348			−0.0177174	+	0.999843i	$0.505640\pi$
$138$		−	93.3550i		−	0.676485i
$139$	170.807	+	98.6153i	1.22883	+	0.709463i	0.966784	−	0.255594i	$-0.0822710\pi$
$139$	170.807	+	98.6153i	1.22883	+	0.709463i	0.262041	+	0.965057i	$0.415604\pi$
$140$	−110.380	+	110.380i	−0.788428	+	0.788428i
$141$	−69.3424	+	40.0348i	−0.491790	+	0.283935i
$142$	83.4852	−	83.4852i	0.587924	−	0.587924i
$143$	−145.276	−	38.9265i	−1.01592	−	0.272214i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	226.671	+	392.606i	1.56325	+	2.70763i
$146$	75.7288	−	20.2915i	0.518690	−	0.138983i
$147$			41.5508i			0.282659i
$148$	65.1743	−	35.0473i	0.440367	−	0.236806i
$149$	218.459			1.46617			0.733084	−	0.680139i	$-0.238080\pi$
$149$	218.459			1.46617			0.733084	+	0.680139i	$0.238080\pi$
$150$	37.0636	+	138.323i	0.247091	+	0.922154i
$151$	164.220	−	94.8127i	1.08755	−	0.627899i	0.154629	−	0.987973i	$-0.450582\pi$
$151$	164.220	−	94.8127i	1.08755	−	0.627899i	0.932924	+	0.360074i	$0.117249\pi$
$152$	−74.2443	+	42.8650i	−0.488449	+	0.282006i
$153$	−8.22213	+	30.6854i	−0.0537394	+	0.200558i
$154$	−75.8737	−	75.8737i	−0.492687	−	0.492687i
$155$	52.1950	+	90.4044i	0.336742	+	0.583254i
$156$	−41.4824	−	41.4824i	−0.265913	−	0.265913i
$157$	−54.4613	+	94.3298i	−0.346887	+	0.600827i	−0.985695	−	0.168540i	$-0.946095\pi$
$157$	−54.4613	+	94.3298i	−0.346887	+	0.600827i	0.638807	+	0.769367i	$0.279428\pi$
$158$	−132.731			−0.840067
$159$		−	84.5064i		−	0.531487i
$160$	25.8399	−	44.7559i	0.161499	−	0.279725i
$161$	84.2729	−	314.511i	0.523434	−	1.95348i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−7.12012	−	26.5727i	−0.0436817	−	0.163022i	0.940640	−	0.339407i	$-0.110226\pi$
$163$	−7.12012	−	26.5727i	−0.0436817	−	0.163022i	−0.984321	+	0.176385i	$0.943560\pi$
$164$	39.0672	−	67.6664i	0.238215	−	0.412600i
$165$	−135.741	+	36.3717i	−0.822673	+	0.220434i
$166$	88.9354	+	23.8302i	0.535756	+	0.143555i
$167$	−19.5004	+	72.7764i	−0.116769	+	0.435787i	−0.999413	−	0.0342543i	$-0.989094\pi$
$167$	−19.5004	+	72.7764i	−0.116769	+	0.435787i	0.882644	+	0.470041i	$0.155761\pi$
$168$	−10.8326	−	40.4277i	−0.0644796	−	0.240641i
$169$	−102.016	−	58.8990i	−0.603645	−	0.348515i
$170$	−132.151	+	35.4098i	−0.777359	+	0.208293i
$171$	64.2975	+	64.2975i	0.376009	+	0.376009i
$172$	18.6221	+	4.98977i	0.108268	+	0.0290103i
$173$	121.970	+	70.4192i	0.705027	+	0.407047i	0.809217	−	0.587510i	$-0.199892\pi$
$173$	121.970	+	70.4192i	0.705027	+	0.407047i	−0.104190	+	0.994557i	$0.533225\pi$
$174$	−121.550			−0.698566
$175$			499.465i			2.85409i
$176$	30.7647	+	17.7620i	0.174799	+	0.100920i
$177$	37.1466	−	37.1466i	0.209868	−	0.209868i
$178$	87.5253	−	50.5328i	0.491715	−	0.283892i
$179$	−55.4856	+	55.4856i	−0.309976	+	0.309976i	−0.844900	−	0.534924i	$-0.820340\pi$
$179$	−55.4856	+	55.4856i	−0.309976	+	0.309976i	0.534924	+	0.844900i	$0.320340\pi$
$180$	−52.9468	−	14.1871i	−0.294149	−	0.0788170i
$181$	−80.8368	−	140.013i	−0.446612	−	0.773555i	0.551551	−	0.834141i	$-0.314036\pi$
$181$	−80.8368	−	140.013i	−0.446612	−	0.773555i	−0.998163	+	0.0605863i	$0.980703\pi$
$182$	−102.306	−	177.200i	−0.562123	−	0.973626i
$183$	56.7924	−	15.2175i	0.310341	−	0.0831557i
$184$			107.797i			0.585853i
$185$	97.3097	−	323.714i	0.525999	−	1.74980i
$186$	−27.9891			−0.150479
$187$	−24.3402	−	90.8389i	−0.130162	−	0.485770i
$188$	80.0696	−	46.2282i	0.425902	−	0.245895i
$189$	−38.4452	+	22.1964i	−0.203414	+	0.117441i
$190$	−101.355	+	378.261i	−0.533446	+	1.99085i
$191$	140.367	+	140.367i	0.734908	+	0.734908i	0.971588	−	0.236679i	$-0.0760591\pi$
$191$	140.367	+	140.367i	0.734908	+	0.734908i	−0.236679	+	0.971588i	$0.576059\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	−102.777	−	102.777i	−0.532523	−	0.532523i	0.388800	−	0.921322i	$-0.372890\pi$
$193$	−102.777	−	102.777i	−0.532523	−	0.532523i	−0.921322	+	0.388800i	$0.872890\pi$
$194$	−104.978	+	181.827i	−0.541124	+	0.937255i
$195$	−267.975			−1.37423
$196$		−	47.9787i		−	0.244789i
$197$	−24.0872	+	41.7203i	−0.122270	+	0.211778i	−0.920663	−	0.390359i	$-0.872351\pi$
$197$	−24.0872	+	41.7203i	−0.122270	+	0.211778i	0.798392	+	0.602137i	$0.205684\pi$
$198$	9.75201	−	36.3950i	0.0492526	−	0.183813i
$199$	−179.315	+	179.315i	−0.901079	+	0.901079i	−0.995530	−	0.0944509i	$-0.969890\pi$
$199$	−179.315	+	179.315i	−0.901079	+	0.901079i	0.0944509	+	0.995530i	$0.469890\pi$
$200$	−42.7973	−	159.722i	−0.213987	−	0.798609i
$201$	30.6840	−	53.1462i	0.152656	−	0.264409i
$202$	−168.657	+	45.1914i	−0.834933	+	0.223720i
$203$	−409.501	−	109.725i	−2.01724	−	0.540519i
$204$	9.49409	−	35.4324i	0.0465397	−	0.173688i
$205$	−92.3749	−	344.748i	−0.450609	−	1.68170i
$206$	44.6735	+	25.7922i	0.216862	+	0.125205i
$207$	110.440	−	29.5923i	0.533527	−	0.142958i
$208$	47.8997	+	47.8997i	0.230287	+	0.230287i
$209$	−260.012	−	69.6699i	−1.24408	−	0.333349i
$210$	−165.570	−	95.5918i	−0.788428	−	0.455199i
$211$	364.495			1.72746			0.863732	−	0.503952i	$-0.168121\pi$
$211$	364.495			1.72746			0.863732	+	0.503952i	$0.168121\pi$
$212$			97.5796i			0.460281i
$213$	125.228	+	72.3003i	0.587924	+	0.339438i
$214$	74.0901	−	74.0901i	0.346215	−	0.346215i
$215$	76.2658	−	44.0321i	0.354725	−	0.204800i
$216$	10.3923	−	10.3923i	0.0481125	−	0.0481125i
$217$	−94.2947	−	25.2662i	−0.434538	−	0.116434i
$218$	48.4310	+	83.8850i	0.222161	+	0.384794i
$219$	48.0101	+	83.1560i	0.219224	+	0.379708i
$220$	156.740	−	41.9984i	0.712455	−	0.190902i
$221$		−	179.331i		−	0.811451i
$222$	62.1208	+	65.9925i	0.279823	+	0.297263i
$223$	44.3869			0.199044			0.0995222	−	0.995035i	$-0.468269\pi$
$223$	44.3869			0.199044			0.0995222	+	0.995035i	$0.468269\pi$
$224$	12.5084	+	46.6819i	0.0558410	+	0.208401i
$225$	−151.889	+	87.6934i	−0.675064	+	0.389748i
$226$	254.266	−	146.801i	1.12507	−	0.649560i
$227$	−80.7851	+	301.494i	−0.355881	+	1.32817i	0.523491	+	0.852032i	$0.324630\pi$
$227$	−80.7851	+	301.494i	−0.355881	+	1.32817i	−0.879372	+	0.476136i	$0.842037\pi$
$228$	−74.2443	−	74.2443i	−0.325633	−	0.325633i
$229$	20.2733	+	35.1144i	0.0885297	+	0.153338i	0.906890	−	0.421368i	$-0.138450\pi$
$229$	20.2733	+	35.1144i	0.0885297	+	0.153338i	−0.818360	+	0.574706i	$0.805117\pi$
$230$	348.182	+	348.182i	1.51384	+	1.51384i
$231$	65.7086	−	113.811i	0.284453	−	0.492687i
$232$	140.354			0.604976
$233$		−	76.0503i		−	0.326396i	−0.986593	−	0.163198i	$-0.947819\pi$
$233$		−	76.0503i		−	0.326396i	0.986593	−	0.163198i	$-0.0521810\pi$
$234$	35.9248	−	62.2236i	0.153525	−	0.265913i
$235$	109.307	−	407.940i	0.465137	−	1.73591i
$236$	−42.8932	+	42.8932i	−0.181751	+	0.181751i
$237$	−42.0739	−	157.022i	−0.177527	−	0.662540i
$238$	63.9708	−	110.801i	0.268785	−	0.465549i
$239$	370.520	−	99.2807i	1.55029	−	0.415400i	0.620720	−	0.784033i	$-0.286841\pi$
$239$	370.520	−	99.2807i	1.55029	−	0.415400i	0.929575	+	0.368632i	$0.120174\pi$
$240$	61.1377	+	16.3818i	0.254741	+	0.0682575i
$241$	−50.4560	+	188.304i	−0.209361	+	0.781346i	0.778715	+	0.627378i	$0.215872\pi$
$241$	−50.4560	+	188.304i	−0.209361	+	0.781346i	−0.988076	+	0.153968i	$0.950795\pi$
$242$	−15.4199	−	57.5478i	−0.0637186	−	0.237801i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$	−65.5783	+	17.5716i	−0.268763	+	0.0720149i
$245$	−154.970	−	154.970i	−0.632532	−	0.632532i
$246$	92.4340	+	24.7676i	0.375748	+	0.100681i
$247$	−444.535	−	256.653i	−1.79974	−	1.03908i
$248$	32.3191			0.130319
$249$			112.766i			0.452874i
$250$	−374.409	−	216.165i	−1.49763	−	0.864659i
$251$	−95.5131	+	95.5131i	−0.380530	+	0.380530i	−0.871293	−	0.490763i	$-0.836718\pi$
$251$	−95.5131	+	95.5131i	−0.380530	+	0.380530i	0.490763	+	0.871293i	$0.336718\pi$
$252$	44.3927	−	25.6301i	0.176162	−	0.101707i
$253$	−239.336	+	239.336i	−0.945993	+	0.945993i
$254$	−114.801	−	30.7608i	−0.451971	−	0.121105i
$255$	−83.7804	−	145.112i	−0.328550	−	0.569066i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−167.277	+	44.8217i	−0.650882	+	0.174403i	−0.569128	−	0.822249i	$-0.692719\pi$
$257$	−167.277	+	44.8217i	−0.650882	+	0.174403i	−0.0817545	+	0.996653i	$0.526052\pi$
$258$			23.6118i			0.0915188i
$259$	149.711	+	278.404i	0.578035	+	1.07492i
$260$	309.430			1.19012
$261$	−38.5300	−	143.796i	−0.147624	−	0.550942i
$262$	30.2880	−	17.4868i	0.115603	−	0.0667434i
$263$	−25.9264	+	14.9686i	−0.0985795	+	0.0569149i	−0.548479	−	0.836164i	$-0.684793\pi$
$263$	−25.9264	+	14.9686i	−0.0985795	+	0.0569149i	0.449900	+	0.893079i	$0.351460\pi$
$264$	−11.2606	+	42.0253i	−0.0426540	+	0.159187i
$265$	315.180	+	315.180i	1.18936	+	1.18936i
$266$	−183.106	−	317.149i	−0.688368	−	1.19229i
$267$	87.5253	+	87.5253i	0.327810	+	0.327810i
$268$	−35.4308	+	61.3679i	−0.132204	+	0.228985i
$269$	−108.575			−0.403626			−0.201813	−	0.979424i	$-0.564683\pi$
$269$	−108.575			−0.403626			−0.201813	+	0.979424i	$0.564683\pi$
$270$		−	67.1339i		−	0.248644i
$271$	−26.1772	+	45.3402i	−0.0965947	+	0.167307i	−0.910273	−	0.414008i	$-0.864128\pi$
$271$	−26.1772	+	45.3402i	−0.0965947	+	0.167307i	0.813678	+	0.581315i	$0.197462\pi$
$272$	−10.9628	+	40.9139i	−0.0403045	+	0.150419i
$273$	177.200	−	177.200i	0.649084	−	0.649084i
$274$	1.77690	+	6.63147i	0.00648502	+	0.0242024i
$275$	259.601	−	449.643i	0.944005	−	1.63506i
$276$	−127.525	+	34.1703i	−0.462048	+	0.123805i
$277$	334.172	+	89.5411i	1.20640	+	0.323253i	0.805347	−	0.592803i	$-0.201979\pi$
$277$	334.172	+	89.5411i	1.20640	+	0.323253i	0.401050	+	0.916056i	$0.368645\pi$
$278$	72.1914	−	269.422i	0.259681	−	0.969144i
$279$	−8.87220	−	33.1115i	−0.0318000	−	0.118679i
$280$	191.184	+	110.380i	0.682798	+	0.394214i
$281$	−76.3197	+	20.4498i	−0.271600	+	0.0727751i	−0.392049	−	0.919945i	$-0.628233\pi$
$281$	−76.3197	+	20.4498i	−0.271600	+	0.0727751i	0.120448	+	0.992720i	$0.461567\pi$
$282$	80.0696	+	80.0696i	0.283935	+	0.283935i
$283$	−58.0432	−	15.5526i	−0.205100	−	0.0549563i	0.154806	−	0.987945i	$-0.450525\pi$
$283$	−58.0432	−	15.5526i	−0.205100	−	0.0549563i	−0.359906	+	0.932989i	$0.617191\pi$
$284$	−144.601	−	83.4852i	−0.509157	−	0.293962i
$285$	−479.615			−1.68286
$286$			212.699i			0.743701i
$287$	289.050	+	166.883i	1.00714	+	0.581474i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$	−153.171	+	88.4335i	−0.530005	+	0.305998i
$290$	453.342	−	453.342i	1.56325	−	1.56325i
$291$	−248.381	−	66.5535i	−0.853543	−	0.228706i
$292$	−55.4373	−	96.0202i	−0.189854	−	0.328836i
$293$	−117.327	−	203.216i	−0.400433	−	0.693570i	0.593345	−	0.804948i	$-0.297807\pi$
$293$	−117.327	−	203.216i	−0.400433	−	0.693570i	−0.993778	+	0.111378i	$0.964474\pi$
$294$	56.7595	−	15.2086i	0.193059	−	0.0517301i
$295$			277.089i			0.939283i
$296$	−71.7309	−	76.2016i	−0.242334	−	0.257438i
$297$	46.1470			0.155377
$298$	−79.9615	−	298.420i	−0.268327	−	1.00141i
$299$	−558.960	+	322.716i	−1.86943	+	1.07932i
$300$	175.387	−	101.260i	0.584622	−	0.337532i
$301$	−21.3147	+	79.5477i	−0.0708131	+	0.264278i
$302$	−189.625	−	189.625i	−0.627899	−	0.627899i
$303$	−106.924	−	185.198i	−0.352884	−	0.611214i
$304$	85.7299	+	85.7299i	0.282006	+	0.282006i
$305$	−155.061	+	268.573i	−0.508395	+	0.880566i
$306$	44.9265			0.146819
$307$		−	278.858i		−	0.908333i	−0.890917	−	0.454166i	$-0.849937\pi$
$307$		−	278.858i		−	0.908333i	0.890917	−	0.454166i	$-0.150063\pi$
$308$	−75.8737	+	131.417i	−0.246343	+	0.426679i
$309$	−16.3516	+	61.0251i	−0.0529179	+	0.197492i
$310$	104.390	−	104.390i	0.336742	−	0.336742i
$311$	6.28916	+	23.4715i	0.0202224	+	0.0754710i	0.975300	−	0.220886i	$-0.0708949\pi$
$311$	6.28916	+	23.4715i	0.0202224	+	0.0754710i	−0.955077	+	0.296357i	$0.904228\pi$
$312$	−41.4824	+	71.8496i	−0.132956	+	0.230287i
$313$	429.076	−	114.970i	1.37085	−	0.367318i	0.503060	−	0.864252i	$-0.332208\pi$
$313$	429.076	−	114.970i	1.37085	−	0.367318i	0.867788	+	0.496934i	$0.165541\pi$
$314$	148.791	+	39.8685i	0.473857	+	0.126970i
$315$	60.6027	−	226.173i	0.192390	−	0.718008i
$316$	48.5828	+	181.313i	0.153743	+	0.573776i
$317$	−73.4076	−	42.3819i	−0.231570	−	0.133697i	0.379726	−	0.925099i	$-0.376018\pi$
$317$	−73.4076	−	42.3819i	−0.231570	−	0.133697i	−0.611296	+	0.791402i	$0.709351\pi$
$318$	−115.438	+	30.9315i	−0.363012	+	0.0972689i
$319$	311.622	+	311.622i	0.976870	+	0.976870i
$320$	−70.5958	−	18.9161i	−0.220612	−	0.0591128i
$321$	111.135	+	64.1639i	0.346215	+	0.199888i
$322$	−460.476			−1.43005
$323$		−	320.962i		−	0.993692i
$324$	15.5885	+	9.00000i	0.0481125	+	0.0277778i
$325$	700.081	−	700.081i	2.15410	−	2.15410i
$326$	−33.6928	+	19.4525i	−0.103352	+	0.0596704i
$327$	−83.8850	+	83.8850i	−0.256529	+	0.256529i
$328$	−106.734	−	28.5992i	−0.325407	−	0.0871926i
$329$	197.473	+	342.033i	0.600221	+	1.03961i
$330$	99.3693	+	172.113i	0.301119	+	0.521554i
$331$	−411.046	+	110.139i	−1.24183	+	0.332748i	−0.819176	−	0.573543i	$-0.805569\pi$
$331$	−411.046	+	110.139i	−1.24183	+	0.332748i	−0.422656	+	0.906290i	$0.638902\pi$
$332$		−	130.211i		−	0.392200i
$333$	−58.3784	+	94.4085i	−0.175311	+	0.283509i
$334$	106.552			0.319018
$335$	83.7764	+	312.658i	0.250079	+	0.933307i
$336$	−51.2603	+	29.5951i	−0.152560	+	0.0880808i
$337$	344.088	−	198.659i	1.02103	−	0.589494i	0.106630	−	0.994299i	$-0.465994\pi$
$337$	344.088	−	198.659i	1.02103	−	0.589494i	0.914403	+	0.404805i	$0.132661\pi$
$338$	−43.1171	+	160.915i	−0.127565	+	0.476080i
$339$	254.266	+	254.266i	0.750047	+	0.750047i
$340$	96.7412	+	167.561i	0.284533	+	0.492826i
$341$	71.7564	+	71.7564i	0.210429	+	0.210429i
$342$	64.2975	−	111.366i	0.188004	−	0.325633i
$343$	−213.675			−0.622960
$344$		−	27.2646i		−	0.0792576i
$345$	−301.535	+	522.274i	−0.874014	+	1.51384i
$346$	51.5504	−	192.389i	0.148990	−	0.556037i
$347$	−40.1976	+	40.1976i	−0.115843	+	0.115843i	−0.762652	−	0.646809i	$-0.776103\pi$
$347$	−40.1976	+	40.1976i	−0.115843	+	0.115843i	0.646809	+	0.762652i	$0.276103\pi$
$348$	44.4906	+	166.041i	0.127846	+	0.477129i
$349$	29.2656	−	50.6896i	0.0838557	−	0.145242i	−0.821047	−	0.570860i	$-0.806610\pi$
$349$	29.2656	−	50.6896i	0.0838557	−	0.145242i	0.904903	+	0.425618i	$0.139943\pi$
$350$	682.282	−	182.817i	1.94938	−	0.522334i
$351$	84.9990	+	22.7754i	0.242162	+	0.0648872i
$352$	13.0027	−	48.5267i	0.0369394	−	0.137860i
$353$	−123.026	−	459.138i	−0.348514	−	1.30067i	−0.888452	−	0.458969i	$-0.848219\pi$
$353$	−123.026	−	459.138i	−0.348514	−	1.30067i	0.539938	−	0.841705i	$-0.318448\pi$
$354$	−64.3398	−	37.1466i	−0.181751	−	0.104934i
$355$	−736.713	+	197.402i	−2.07525	+	0.556061i
$356$	−101.066	−	101.066i	−0.283892	−	0.283892i
$357$	151.356	+	40.5558i	0.423968	+	0.113602i
$358$	96.1039	+	55.4856i	0.268447	+	0.154988i
$359$	127.254			0.354469			0.177234	−	0.984169i	$-0.443285\pi$
$359$	127.254			0.354469			0.177234	+	0.984169i	$0.443285\pi$
$360$			77.5196i			0.215332i
$361$	−482.985	−	278.851i	−1.33791	−	0.772442i
$362$	−161.674	+	161.674i	−0.446612	+	0.446612i
$363$	63.1919	−	36.4839i	0.174082	−	0.100507i
$364$	−204.613	+	204.613i	−0.562123	+	0.562123i
$365$	−489.205	−	131.082i	−1.34029	−	0.359129i
$366$	−41.5750	−	72.0099i	−0.113593	−	0.196748i
$367$	−62.2315	−	107.788i	−0.169568	−	0.293701i	0.768700	−	0.639610i	$-0.220904\pi$
$367$	−62.2315	−	107.788i	−0.169568	−	0.293701i	−0.938268	+	0.345909i	$0.887571\pi$
$368$	147.253	−	39.4565i	0.400145	−	0.107219i
$369$			117.202i			0.317620i
$370$	−477.819	−	14.4401i	−1.29140	−	0.0390273i
$371$	−416.830			−1.12353
$372$	10.2447	+	38.2339i	0.0275396	+	0.102779i
$373$	154.529	−	89.2171i	0.414286	−	0.239188i	−0.278344	−	0.960482i	$-0.589785\pi$
$373$	154.529	−	89.2171i	0.414286	−	0.239188i	0.692630	+	0.721294i	$0.256452\pi$
$374$	−115.179	+	66.4987i	−0.307966	+	0.177804i
$375$	137.043	−	511.452i	0.365448	−	1.36387i
$376$	−92.4565	−	92.4565i	−0.245895	−	0.245895i
$377$	420.184	+	727.779i	1.11455	+	1.93045i
$378$	44.3927	+	44.3927i	0.117441	+	0.117441i
$379$	163.974	−	284.011i	0.432648	−	0.749368i	−0.564452	−	0.825466i	$-0.690913\pi$
$379$	163.974	−	284.011i	0.432648	−	0.749368i	0.997100	+	0.0760974i	$0.0242460\pi$
$380$	553.812			1.45740
$381$		−	145.561i		−	0.382051i
$382$	140.367	−	243.124i	0.367454	−	0.636449i
$383$	101.757	−	379.763i	0.265684	−	0.991548i	−0.696146	−	0.717901i	$-0.745103\pi$
$383$	101.757	−	379.763i	0.265684	−	0.991548i	0.961830	−	0.273647i	$-0.0882301\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	179.404	+	669.546i	0.465985	+	1.73908i
$386$	−102.777	+	178.015i	−0.266261	+	0.461178i
$387$	−27.9331	+	7.48465i	−0.0721786	+	0.0193402i
$388$	286.806	+	76.8493i	0.739190	+	0.198065i
$389$	−139.165	+	519.371i	−0.357751	+	1.33514i	0.519237	+	0.854631i	$0.326216\pi$
$389$	−139.165	+	519.371i	−0.357751	+	1.33514i	−0.876987	+	0.480513i	$0.840450\pi$
$390$	98.0855	+	366.060i	0.251501	+	0.938616i
$391$	−349.510	−	201.789i	−0.893886	−	0.516086i
$392$	−65.5402	+	17.5614i	−0.167194	+	0.0447996i
$393$	30.2880	+	30.2880i	0.0770686	+	0.0770686i
$394$	65.8075	+	17.6331i	0.167024	+	0.0447540i
$395$	742.560	+	428.717i	1.87990	+	1.08536i
$396$	−53.2860			−0.134561
$397$			638.499i			1.60831i	0.594420	+	0.804154i	$0.297382\pi$
$397$			638.499i			1.60831i	−0.594420	+	0.804154i	$0.702618\pi$
$398$	310.582	+	179.315i	0.780357	+	0.450539i
$399$	317.149	−	317.149i	0.794859	−	0.794859i
$400$	−202.519	+	116.924i	−0.506298	+	0.292311i
$401$	−408.409	+	408.409i	−1.01848	+	1.01848i	−0.0186490	+	0.999826i	$0.505937\pi$
$401$	−408.409	+	408.409i	−1.01848	+	1.01848i	−0.999826	+	0.0186490i	$0.994063\pi$
$402$	−83.8301	−	22.4622i	−0.208533	−	0.0558761i
$403$	96.7547	+	167.584i	0.240086	+	0.415841i
$404$	123.465	+	213.848i	0.305607	+	0.529327i
$405$	79.4203	−	21.2806i	0.196099	−	0.0525447i
$406$			599.551i			1.47673i
$407$	9.92595	−	328.447i	0.0243881	−	0.806995i
$408$	−51.8767			−0.127149
$409$	−29.5448	−	110.263i	−0.0722368	−	0.269591i	0.920356	−	0.391082i	$-0.127899\pi$
$409$	−29.5448	−	110.263i	−0.0722368	−	0.269591i	−0.992593	+	0.121491i	$0.961233\pi$
$410$	−437.122	+	252.373i	−1.06615	+	0.615543i
$411$	−7.28185	+	4.20418i	−0.0177174	+	0.0102292i
$412$	18.8812	−	70.4657i	0.0458282	−	0.171033i
$413$	−183.227	−	183.227i	−0.443648	−	0.443648i
$414$	−80.8478	−	140.032i	−0.195284	−	0.338243i
$415$	−420.578	−	420.578i	−1.01344	−	1.01344i
$416$	47.8997	−	82.9648i	0.115144	−	0.199435i
$417$	341.614			0.819217
$418$			380.684i			0.910726i
$419$	−395.505	+	685.034i	−0.943925	+	1.63493i	−0.186037	+	0.982543i	$0.559564\pi$
$419$	−395.505	+	685.034i	−0.943925	+	1.63493i	−0.757889	+	0.652384i	$0.773769\pi$
$420$	−69.9780	+	261.162i	−0.166614	+	0.621813i
$421$	52.6344	−	52.6344i	0.125022	−	0.125022i	−0.641827	−	0.766849i	$-0.721823\pi$
$421$	52.6344	−	52.6344i	0.125022	−	0.125022i	0.766849	+	0.641827i	$0.221823\pi$
$422$	−133.414	−	497.909i	−0.316148	−	1.17988i
$423$	−69.3424	+	120.104i	−0.163930	+	0.283935i
$424$	133.296	−	35.7166i	0.314378	−	0.0842373i
$425$	597.979	+	160.228i	1.40701	+	0.377007i
$426$	52.9275	−	197.528i	0.124243	−	0.463681i
$427$	−75.0606	−	280.130i	−0.175786	−	0.656042i
$428$	−128.328	−	74.0901i	−0.299831	−	0.173108i
$429$	−251.625	+	67.4228i	−0.586539	+	0.157163i
$430$	−88.0642	−	88.0642i	−0.204800	−	0.204800i
$431$	274.083	+	73.4403i	0.635923	+	0.170395i	0.562356	−	0.826895i	$-0.309895\pi$
$431$	274.083	+	73.4403i	0.635923	+	0.170395i	0.0735669	+	0.997290i	$0.476562\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$	−494.881			−1.14291			−0.571456	−	0.820632i	$-0.693621\pi$
$433$	−494.881			−1.14291			−0.571456	+	0.820632i	$0.693621\pi$
$434$			138.057i			0.318104i
$435$	680.013	+	392.606i	1.56325	+	0.902542i
$436$	96.8621	−	96.8621i	0.222161	−	0.222161i
$437$	−1000.41	+	577.590i	−2.28928	+	1.32172i
$438$	96.0202	−	96.0202i	0.219224	−	0.219224i
$439$	210.586	+	56.4265i	0.479696	+	0.128534i	0.490561	−	0.871407i	$-0.336792\pi$
$439$	210.586	+	56.4265i	0.479696	+	0.128534i	−0.0108651	+	0.999941i	$0.503459\pi$
$440$	−114.742	−	198.739i	−0.260777	−	0.451679i
$441$	35.9841	+	62.3262i	0.0815965	+	0.141329i
$442$	−244.970	+	65.6396i	−0.554232	+	0.148506i
$443$			427.408i			0.964804i	0.875950	+	0.482402i	$0.160236\pi$
$443$			427.408i			0.964804i	−0.875950	+	0.482402i	$0.839764\pi$
$444$	67.4096	−	109.013i	0.151823	−	0.245526i
$445$	−652.880			−1.46715
$446$	−16.2467	−	60.6336i	−0.0364276	−	0.135950i
$447$	327.688	−	189.191i	0.733084	−	0.423246i
$448$	59.1903	−	34.1735i	0.132121	−	0.0762802i
$449$	92.2152	−	344.152i	0.205379	−	0.766485i	−0.783955	−	0.620818i	$-0.786801\pi$
$449$	92.2152	−	344.152i	0.205379	−	0.766485i	0.989334	−	0.145667i	$-0.0465328\pi$
$450$	175.387	+	175.387i	0.389748	+	0.389748i
$451$	−173.478	−	300.472i	−0.384652	−	0.666236i
$452$	−293.601	−	293.601i	−0.649560	−	0.649560i
$453$	164.220	−	284.438i	0.362517	−	0.627899i
$454$	441.418			0.972286
$455$			1321.79i			2.90504i
$456$	−74.2443	+	128.595i	−0.162816	+	0.282006i
$457$	24.6718	−	92.0764i	0.0539864	−	0.201480i	−0.933665	−	0.358148i	$-0.883408\pi$
$457$	24.6718	−	92.0764i	0.0539864	−	0.201480i	0.987651	+	0.156668i	$0.0500751\pi$
$458$	40.5466	−	40.5466i	0.0885297	−	0.0885297i
$459$	14.2411	+	53.1487i	0.0310264	+	0.115792i
$460$	348.182	−	603.070i	0.756918	−	1.31102i
$461$	762.975	−	204.438i	1.65504	−	0.443467i	0.694024	−	0.719952i	$-0.255836\pi$
$461$	762.975	−	204.438i	1.65504	−	0.443467i	0.961018	+	0.276484i	$0.0891694\pi$
$462$	−179.519	−	48.1020i	−0.388570	−	0.104117i
$463$	−62.7375	+	234.140i	−0.135502	+	0.505701i	0.864493	+	0.502645i	$0.167640\pi$
$463$	−62.7375	+	234.140i	−0.135502	+	0.505701i	−0.999995	+	0.00305638i	$0.999027\pi$
$464$	−51.3733	−	191.728i	−0.110718	−	0.413206i
$465$	156.585	+	90.4044i	0.336742	+	0.194418i
$466$	−103.887	+	27.8363i	−0.222933	+	0.0597346i
$467$	−73.8392	−	73.8392i	−0.158114	−	0.158114i	0.623616	−	0.781730i	$-0.285663\pi$
$467$	−73.8392	−	73.8392i	−0.158114	−	0.158114i	−0.781730	+	0.623616i	$0.785663\pi$
$468$	−98.1484	−	26.2988i	−0.209719	−	0.0561940i
$469$	−262.145	−	151.349i	−0.558944	−	0.322706i
$470$	−597.265			−1.27078
$471$			188.660i			0.400551i
$472$	74.2932	+	42.8932i	0.157401	+	0.0908754i
$473$	60.5342	−	60.5342i	0.127979	−	0.127979i
$474$	−199.096	+	114.948i	−0.420033	+	0.242506i
$475$	1252.99	−	1252.99i	2.63788	−	2.63788i
$476$	−174.771	−	46.8298i	−0.367167	−	0.0983820i
$477$	−73.1847	−	126.760i	−0.153427	−	0.265744i
$478$	−271.240	−	469.801i	−0.567447	−	0.982848i
$479$	−35.6019	+	9.53951i	−0.0743255	+	0.0199155i	−0.295790	−	0.955253i	$-0.595583\pi$
$479$	−35.6019	+	9.53951i	−0.0743255	+	0.0199155i	0.221465	+	0.975168i	$0.428916\pi$
$480$		−	89.5119i		−	0.186483i
$481$	180.385	−	600.073i	0.375020	−	1.24755i
$482$	275.697			0.571985
$483$	−145.965	−	544.748i	−0.302205	−	1.12784i
$484$	−72.9677	+	42.1279i	−0.150760	+	0.0870412i
$485$	1174.60	−	678.155i	2.42185	−	1.39826i
$486$	−5.70577	+	21.2942i	−0.0117403	+	0.0438153i
$487$	−429.852	−	429.852i	−0.882652	−	0.882652i	0.111151	−	0.993803i	$-0.464546\pi$
$487$	−429.852	−	429.852i	−0.882652	−	0.882652i	−0.993803	+	0.111151i	$0.964546\pi$
$488$	48.0066	+	83.1499i	0.0983742	+	0.170389i
$489$	−33.6928	−	33.6928i	−0.0689014	−	0.0689014i
$490$	−154.970	+	268.417i	−0.316266	+	0.547789i
$491$	52.0824			0.106074			0.0530371	−	0.998593i	$-0.483110\pi$
$491$	52.0824			0.106074			0.0530371	+	0.998593i	$0.483110\pi$
$492$		−	135.333i		−	0.275067i
$493$	−262.735	+	455.070i	−0.532931	+	0.923063i
$494$	−187.883	+	701.188i	−0.380329	+	1.41941i
$495$	−172.113	+	172.113i	−0.347702	+	0.347702i
$496$	−11.8296	−	44.1487i	−0.0238500	−	0.0890094i
$497$	356.623	−	617.689i	0.717551	−	1.24283i
$498$	154.041	−	41.2751i	0.309319	−	0.0828817i
$499$	325.923	+	87.3309i	0.653153	+	0.175012i	0.570154	−	0.821538i	$-0.306883\pi$
$499$	325.923	+	87.3309i	0.653153	+	0.175012i	0.0829991	+	0.996550i	$0.473550\pi$
$500$	−158.244	+	590.573i	−0.316487	+	1.18115i
$501$	33.7757	+	126.053i	0.0674165	+	0.251602i
$502$	165.434	+	95.5131i	0.329549	+	0.190265i
$503$	389.979	−	104.495i	0.775306	−	0.207743i	0.150592	−	0.988596i	$-0.451882\pi$
$503$	389.979	−	104.495i	0.775306	−	0.207743i	0.624714	+	0.780853i	$0.285215\pi$
$504$	−51.2603	−	51.2603i	−0.101707	−	0.101707i
$505$	1089.52	+	291.935i	2.15746	+	0.578089i
$506$	414.542	+	239.336i	0.819254	+	0.472996i
$507$	−204.032			−0.402430
$508$			168.080i			0.330866i
$509$	−594.800	−	343.408i	−1.16857	−	0.674671i	−0.215223	−	0.976565i	$-0.569048\pi$
$509$	−594.800	−	343.408i	−1.16857	−	0.674671i	−0.953342	+	0.301893i	$0.902381\pi$
$510$	−167.561	+	167.561i	−0.328550	+	0.328550i
$511$	410.169	−	236.811i	0.802679	−	0.463427i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	152.129	+	40.7630i	0.296549	+	0.0794599i
$514$	122.455	+	212.098i	0.238239	+	0.412643i
$515$	−166.617	−	288.589i	−0.323528	−	0.560367i
$516$	32.2544	−	8.64253i	0.0625085	−	0.0167491i
$517$		−	410.553i		−	0.794106i
$518$	325.509	−	306.412i	0.628397	−	0.591529i
$519$	243.939			0.470018
$520$	−113.259	−	422.690i	−0.217807	−	0.812865i
$521$	−562.332	+	324.663i	−1.07933	+	0.623153i	−0.930716	−	0.365742i	$-0.880815\pi$
$521$	−562.332	+	324.663i	−1.07933	+	0.623153i	−0.148616	+	0.988895i	$0.547482\pi$
$522$	−182.326	+	105.266i	−0.349283	+	0.201659i
$523$	261.533	−	976.053i	0.500063	−	1.86626i	0.000467747	−	1.00000i	$-0.499851\pi$
$523$	261.533	−	976.053i	0.500063	−	1.86626i	0.499595	−	0.866259i	$-0.333482\pi$
$524$	−34.9735	−	34.9735i	−0.0667434	−	0.0667434i
$525$	432.550	+	749.198i	0.823904	+	1.42704i
$526$	29.9372	+	29.9372i	0.0569149	+	0.0569149i
$527$	−60.4993	+	104.788i	−0.114799	+	0.198839i
$528$	61.5293			0.116533
$529$			923.525i			1.74579i
$530$	315.180	−	545.909i	0.594680	−	1.03002i
$531$	23.5500	−	87.8898i	0.0443503	−	0.165518i
$532$	−366.212	+	366.212i	−0.688368	+	0.688368i
$533$	−171.237	−	639.064i	−0.321270	−	1.19899i
$534$	87.5253	−	151.598i	0.163905	−	0.283892i
$535$	−653.806	+	175.187i	−1.22207	+	0.327452i
$536$	96.7987	+	25.9371i	0.180595	+	0.0483902i
$537$	−35.1765	+	131.280i	−0.0655055	+	0.244470i
$538$	39.7413	+	148.317i	0.0738686	+	0.275681i
$539$	−184.506	−	106.525i	−0.342312	−	0.197634i
$540$	−91.7066	+	24.5727i	−0.169827	+	0.0455050i
$541$	36.4564	+	36.4564i	0.0673871	+	0.0673871i	0.739997	−	0.672610i	$-0.234827\pi$
$541$	36.4564	+	36.4564i	0.0673871	+	0.0673871i	−0.672610	+	0.739997i	$0.734827\pi$
$542$	71.5174	+	19.1630i	0.131951	+	0.0353561i
$543$	−242.510	−	140.013i	−0.446612	−	0.257852i
$544$	59.9020			0.110114
$545$		−	625.726i		−	1.14812i
$546$	−306.919	−	177.200i	−0.562123	−	0.324542i
$547$	67.1790	−	67.1790i	0.122814	−	0.122814i	−0.643029	−	0.765842i	$-0.722322\pi$
$547$	67.1790	−	67.1790i	0.122814	−	0.122814i	0.765842	+	0.643029i	$0.222322\pi$
$548$	8.40836	−	4.85457i	0.0153437	−	0.00885870i
$549$	72.0099	−	72.0099i	0.131166	−	0.131166i
$550$	−709.244	−	190.041i	−1.28954	−	0.345530i
$551$	752.036	+	1302.56i	1.36486	+	2.36400i
$552$	93.3550	+	161.696i	0.169121	+	0.292927i
$553$	−774.515	+	207.531i	−1.40057	+	0.375281i
$554$		−	489.262i		−	0.883144i
$555$	−134.380	−	569.843i	−0.242126	−	1.02674i
$556$	−394.461			−0.709463
$557$	−50.5633	−	188.705i	−0.0907780	−	0.338788i	0.905568	−	0.424202i	$-0.139445\pi$
$557$	−50.5633	−	188.705i	−0.0907780	−	0.338788i	−0.996346	+	0.0854140i	$0.972779\pi$
$558$	−41.9837	+	24.2393i	−0.0752396	+	0.0434396i
$559$	141.375	−	81.6229i	0.252907	−	0.146016i
$560$	80.8037	−	301.563i	0.144292	−	0.538506i
$561$	−115.179	−	115.179i	−0.205310	−	0.205310i
$562$	55.8699	+	96.7695i	0.0994126	+	0.172188i
$563$	216.680	+	216.680i	0.384866	+	0.384866i	0.872852	−	0.487985i	$-0.162268\pi$
$563$	216.680	+	216.680i	0.384866	+	0.384866i	−0.487985	+	0.872852i	$0.662268\pi$
$564$	80.0696	−	138.685i	0.141967	−	0.245895i
$565$	−1896.65			−3.35691
$566$			84.9811i			0.150143i
$567$	−38.4452	+	66.5891i	−0.0678046	+	0.117441i
$568$	−61.1154	+	228.086i	−0.107598	+	0.401559i
$569$	−494.372	+	494.372i	−0.868843	+	0.868843i	−0.992344	−	0.123501i	$-0.960588\pi$
$569$	−494.372	+	494.372i	−0.868843	+	0.868843i	0.123501	+	0.992344i	$0.460588\pi$
$570$	175.551	+	655.167i	0.307985	+	1.14942i
$571$	98.4049	−	170.442i	0.172338	−	0.298498i	−0.766899	−	0.641768i	$-0.778201\pi$
$571$	98.4049	−	170.442i	0.172338	−	0.298498i	0.939237	+	0.343270i	$0.111535\pi$
$572$	290.552	−	77.8531i	0.507958	−	0.136107i
$573$	332.113	+	88.9894i	0.579604	+	0.155304i
$574$	122.167	−	455.933i	0.212834	−	0.794308i
$575$	−576.678	−	2152.19i	−1.00292	−	3.74294i
$576$	20.7846	+	12.0000i	0.0360844	+	0.0208333i
$577$	108.913	−	29.1832i	0.188758	−	0.0505775i	−0.163202	−	0.986593i	$-0.552182\pi$
$577$	108.913	−	29.1832i	0.188758	−	0.0505775i	0.351959	+	0.936015i	$0.385515\pi$
$578$	176.867	+	176.867i	0.305998	+	0.305998i
$579$	−243.173	−	65.1579i	−0.419987	−	0.112535i
$580$	−785.212	−	453.342i	−1.35381	−	0.781624i
$581$	556.219			0.957348
$582$			363.655i			0.624836i
$583$	375.251	+	216.651i	0.643655	+	0.371614i
$584$	−110.875	+	110.875i	−0.189854	+	0.189854i
$585$	−401.962	+	232.073i	−0.687114	+	0.396706i
$586$	−234.654	+	234.654i	−0.400433	+	0.400433i
$587$	221.005	+	59.2180i	0.376499	+	0.100882i	0.442105	−	0.896963i	$-0.354232\pi$
$587$	221.005	+	59.2180i	0.376499	+	0.100882i	−0.0656069	+	0.997846i	$0.520898\pi$
$588$	−41.5508	−	71.9681i	−0.0706646	−	0.122395i
$589$	173.170	+	299.938i	0.294006	+	0.509233i
$590$	378.510	−	101.421i	0.641542	−	0.171901i
$591$			83.4405i			0.141185i
$592$	−77.8379	+	125.878i	−0.131483	+	0.212632i
$593$	−669.803			−1.12952			−0.564758	−	0.825257i	$-0.691030\pi$
$593$	−669.803			−1.12952			−0.564758	+	0.825257i	$0.691030\pi$
$594$	−16.8910	−	63.0380i	−0.0284360	−	0.106125i
$595$	−715.768	+	413.249i	−1.20297	+	0.694536i
$596$	−378.382	+	218.459i	−0.634869	+	0.366542i
$597$	−113.681	+	424.263i	−0.190420	+	0.710658i
$598$	645.431	+	645.431i	1.07932	+	1.07932i
$599$	−192.911	−	334.132i	−0.322055	−	0.557816i	0.658857	−	0.752268i	$-0.271040\pi$
$599$	−192.911	−	334.132i	−0.322055	−	0.557816i	−0.980912	+	0.194453i	$0.937707\pi$
$600$	−202.519	−	202.519i	−0.337532	−	0.337532i
$601$	322.435	−	558.473i	0.536497	−	0.929240i	−0.462592	−	0.886571i	$-0.653081\pi$
$601$	322.435	−	558.473i	0.536497	−	0.929240i	0.999089	−	0.0426688i	$-0.0135860\pi$
$602$	116.466			0.193465
$603$		−	106.292i		−	0.176273i
$604$	−189.625	+	328.441i	−0.313949	+	0.543776i
$605$	−99.6120	+	371.757i	−0.164648	+	0.614474i
$606$	−213.848	+	213.848i	−0.352884	+	0.352884i
$607$	−303.608	−	1133.08i	−0.500178	−	1.86669i	−0.498843	−	0.866692i	$-0.666242\pi$
$607$	−303.608	−	1133.08i	−0.500178	−	1.86669i	−0.00133517	−	0.999999i	$-0.500425\pi$
$608$	85.7299	−	148.489i	0.141003	−	0.244225i
$609$	−709.276	+	190.050i	−1.16466	+	0.312069i
$610$	423.633	+	113.512i	0.694481	+	0.186086i
$611$	202.624	−	756.204i	0.331627	−	1.23765i
$612$	−16.4443	−	61.3708i	−0.0268697	−	0.100279i
$613$	−363.563	−	209.903i	−0.593087	−	0.342419i	0.173230	−	0.984881i	$-0.444580\pi$
$613$	−363.563	−	209.903i	−0.593087	−	0.342419i	−0.766317	+	0.642462i	$0.777913\pi$
$614$	−380.927	+	102.069i	−0.620403	+	0.166236i
$615$	−437.122	−	437.122i	−0.710768	−	0.710768i
$616$	207.291	+	55.5434i	0.336511	+	0.0901679i
$617$	−26.2019	−	15.1277i	−0.0424666	−	0.0245181i	0.478616	−	0.878024i	$-0.341138\pi$
$617$	−26.2019	−	15.1277i	−0.0424666	−	0.0245181i	−0.521083	+	0.853506i	$0.674472\pi$
$618$	89.3470			0.144574
$619$			1017.69i			1.64409i	0.569420	+	0.822046i	$0.307168\pi$
$619$			1017.69i			1.64409i	−0.569420	+	0.822046i	$0.692832\pi$
$620$	−180.809	−	104.390i	−0.291627	−	0.168371i
$621$	140.032	−	140.032i	0.225495	−	0.225495i
$622$	29.7606	−	17.1823i	0.0478467	−	0.0276243i
$623$	431.721	−	431.721i	0.692971	−	0.692971i
$624$	113.332	+	30.3672i	0.181622	+	0.0486654i
$625$	665.639	+	1152.92i	1.06502	+	1.84467i
$626$	−314.105	−	544.046i	−0.501765	−	0.869083i
$627$	−450.353	+	120.672i	−0.718267	+	0.192459i
$628$		−	217.845i		−	0.346887i
$629$	381.344	−	89.9280i	0.606270	−	0.142970i
$630$	−331.140			−0.525618
$631$	143.608	+	535.952i	0.227588	+	0.849369i	0.981351	+	0.192223i	$0.0615697\pi$
$631$	143.608	+	535.952i	0.227588	+	0.849369i	−0.753764	+	0.657146i	$0.771764\pi$
$632$	229.896	−	132.731i	0.363760	−	0.210017i
$633$	546.742	−	315.662i	0.863732	−	0.498676i
$634$	−31.0257	+	115.789i	−0.0489364	+	0.182633i
$635$	542.895	+	542.895i	0.854953	+	0.854953i
$636$	84.5064	+	146.369i	0.132872	+	0.230141i
$637$	−287.271	−	287.271i	−0.450975	−	0.450975i
$638$	311.622	−	539.745i	0.488435	−	0.845995i
$639$	250.456			0.391949
$640$			103.359i			0.161499i
$641$	562.003	−	973.417i	0.876759	−	1.51859i	0.0218828	−	0.999761i	$-0.493034\pi$
$641$	562.003	−	973.417i	0.876759	−	1.51859i	0.854877	−	0.518831i	$-0.173633\pi$
$642$	46.9712	−	175.299i	0.0731639	−	0.273051i
$643$	465.705	−	465.705i	0.724269	−	0.724269i	−0.245203	−	0.969472i	$-0.578854\pi$
$643$	465.705	−	465.705i	0.724269	−	0.724269i	0.969472	+	0.245203i	$0.0788545\pi$
$644$	168.546	+	629.021i	0.261717	+	0.976741i
$645$	76.2658	−	132.096i	0.118242	−	0.204800i
$646$	−438.443	+	117.480i	−0.678704	+	0.181858i
$647$	−351.920	−	94.2968i	−0.543926	−	0.145745i	−0.0236148	−	0.999721i	$-0.507518\pi$
$647$	−351.920	−	94.2968i	−0.543926	−	0.145745i	−0.520312	+	0.853976i	$0.674184\pi$
$648$	6.58846	−	24.5885i	0.0101674	−	0.0379452i
$649$	69.7158	+	260.183i	0.107420	+	0.400898i
$650$	−1212.58	−	700.081i	−1.86550	−	1.07705i
$651$	−163.323	+	43.7623i	−0.250881	+	0.0672233i
$652$	38.9051	+	38.9051i	0.0596704	+	0.0596704i
$653$	−590.305	−	158.172i	−0.903989	−	0.242223i	−0.223261	−	0.974759i	$-0.571670\pi$
$653$	−590.305	−	158.172i	−0.903989	−	0.242223i	−0.680729	+	0.732536i	$0.738337\pi$
$654$	145.293	+	83.8850i	0.222161	+	0.128265i
$655$	−225.928			−0.344928
$656$			156.269i			0.238215i
$657$	144.030	+	83.1560i	0.219224	+	0.126569i
$658$	394.945	−	394.945i	0.600221	−	0.600221i
$659$	571.145	−	329.751i	0.866685	−	0.500381i	0.000439553	−	1.00000i	$-0.499860\pi$
$659$	571.145	−	329.751i	0.866685	−	0.500381i	0.866245	+	0.499619i	$0.166527\pi$
$660$	198.739	−	198.739i	0.301119	−	0.301119i
$661$	71.5635	+	19.1754i	0.108266	+	0.0290097i	0.312545	−	0.949903i	$-0.398818\pi$
$661$	71.5635	+	19.1754i	0.108266	+	0.0290097i	−0.204280	+	0.978913i	$0.565485\pi$
$662$	300.907	+	521.186i	0.454542	+	0.787289i
$663$	−155.305	−	268.996i	−0.234246	−	0.405726i
$664$	−177.871	+	47.6604i	−0.267878	+	0.0717776i
$665$			2365.71i			3.55747i
$666$	150.332	+	45.1905i	0.225724	+	0.0678537i
$667$	1891.22			2.83542
$668$	−39.0008	−	145.553i	−0.0583844	−	0.217894i
$669$	66.5803	−	38.4402i	0.0995222	−	0.0574592i
$670$	396.434	−	228.881i	0.591693	−	0.341614i
$671$	−78.0268	+	291.200i	−0.116284	+	0.433979i
$672$	59.1903	+	59.1903i	0.0880808	+	0.0880808i
$673$	235.551	+	407.986i	0.350001	+	0.606220i	0.986249	−	0.165264i	$-0.0528478\pi$
$673$	235.551	+	407.986i	0.350001	+	0.606220i	−0.636248	+	0.771485i	$0.719514\pi$
$674$	−397.319	−	397.319i	−0.589494	−	0.589494i
$675$	−151.889	+	263.080i	−0.225021	+	0.389748i
$676$	235.596			0.348515
$677$		−	1264.81i		−	1.86825i	−0.356945	−	0.934125i	$-0.616182\pi$
$677$		−	1264.81i		−	1.86825i	0.356945	−	0.934125i	$-0.383818\pi$
$678$	254.266	−	440.402i	0.375024	−	0.649560i
$679$	−328.276	+	1225.14i	−0.483471	+	1.80434i
$680$	193.482	−	193.482i	0.284533	−	0.284533i
$681$	139.924	+	522.203i	0.205468	+	0.766818i
$682$	71.7564	−	124.286i	0.105215	−	0.182237i
$683$	899.080	−	240.908i	1.31637	−	0.352720i	0.468753	−	0.883329i	$-0.344703\pi$
$683$	899.080	−	240.908i	1.31637	−	0.352720i	0.847617	+	0.530609i	$0.178037\pi$
$684$	−175.664	−	47.0690i	−0.256819	−	0.0688143i
$685$	11.4787	−	42.8390i	0.0167572	−	0.0625387i
$686$	78.2106	+	291.886i	0.114010	+	0.425490i
$687$	60.8199	+	35.1144i	0.0885297	+	0.0511126i
$688$	−37.2441	+	9.97954i	−0.0541339	+	0.0145051i
$689$	584.255	+	584.255i	0.847975	+	0.847975i
$690$	823.808	+	220.739i	1.19393	+	0.319911i
$691$	−688.307	−	397.394i	−0.996102	−	0.575100i	−0.0890097	−	0.996031i	$-0.528370\pi$
$691$	−688.307	−	397.394i	−0.996102	−	0.575100i	−0.907093	+	0.420931i	$0.861704\pi$
$692$	−281.677			−0.407047
$693$		−	227.621i		−	0.328458i
$694$	69.6242	+	40.1976i	0.100323	+	0.0579216i
$695$	−1274.10	+	1274.10i	−1.83324	+	1.83324i
$696$	210.532	−	121.550i	0.302488	−	0.174641i
$697$	292.526	−	292.526i	0.419693	−	0.419693i
$698$	−79.9552	−	21.4239i	−0.114549	−	0.0306933i
$699$	−65.8615	−	114.075i	−0.0942224	−	0.163198i
$700$	−499.465	−	865.099i	−0.713522	−	1.23586i
$701$	779.484	−	208.862i	1.11196	−	0.297949i	0.344334	−	0.938847i	$-0.388105\pi$
$701$	779.484	−	208.862i	1.11196	−	0.297949i	0.767626	+	0.640898i	$0.221438\pi$
$702$		−	124.447i		−	0.177275i
$703$	322.849	−	1074.00i	0.459244	−	1.52774i
$704$	−71.0480			−0.100920
$705$	−189.326	−	706.572i	−0.268547	−	1.00223i
$706$	−582.163	+	336.112i	−0.824594	+	0.476080i
$707$	−913.492	+	527.405i	−1.29207	+	0.745976i
$708$	−27.1932	+	101.486i	−0.0384085	+	0.143342i
$709$	−749.019	−	749.019i	−1.05644	−	1.05644i	−0.998309	−	0.0581363i	$-0.981484\pi$
$709$	−749.019	−	749.019i	−1.05644	−	1.05644i	−0.0581363	−	0.998309i	$-0.518516\pi$
$710$	539.311	+	934.114i	0.759593	+	1.31565i
$711$	−199.096	−	199.096i	−0.280022	−	0.280022i
$712$	−101.066	+	175.051i	−0.141946	+	0.245858i
$713$	435.488			0.610782
$714$		−	221.601i		−	0.310366i
$715$	687.013	−	1189.94i	0.960857	−	1.66425i
$716$	40.6183	−	151.590i	0.0567295	−	0.211717i
$717$	469.801	−	469.801i	0.655232	−	0.655232i
$718$	−46.5783	−	173.833i	−0.0648723	−	0.242107i
$719$	144.216	−	249.789i	0.200578	−	0.347412i	−0.748136	−	0.663545i	$-0.769051\pi$
$719$	144.216	−	249.789i	0.200578	−	0.347412i	0.948715	+	0.316133i	$0.102384\pi$
$720$	105.894	−	28.3741i	0.147075	−	0.0394085i
$721$	301.008	+	80.6548i	0.417487	+	0.111865i
$722$	−204.133	+	761.836i	−0.282733	+	1.05517i
$723$	87.3923	+	326.153i	0.120875	+	0.451110i
$724$	280.027	+	161.674i	0.386778	+	0.223306i
$725$	−2802.21	+	750.849i	−3.86511	+	1.03565i
$726$	−72.9677	−	72.9677i	−0.100507	−	0.100507i
$727$	1296.88	+	347.498i	1.78388	+	0.477989i	0.991282	−	0.131755i	$-0.0420611\pi$
$727$	1296.88	+	347.498i	1.78388	+	0.477989i	0.792598	+	0.609744i	$0.208728\pi$
$728$	354.400	+	204.613i	0.486813	+	0.281062i
$729$	−27.0000			−0.0370370
$730$			716.246i			0.981159i
$731$	88.3998	+	51.0377i	0.120930	+	0.0698190i
$732$	−83.1499	+	83.1499i	−0.113593	+	0.113593i
$733$	309.756	−	178.838i	0.422586	−	0.243980i	−0.273597	−	0.961844i	$-0.588213\pi$
$733$	309.756	−	178.838i	0.422586	−	0.243980i	0.696183	+	0.717864i	$0.254880\pi$
$734$	−124.463	+	124.463i	−0.169568	+	0.169568i
$735$	−366.664	−	98.2473i	−0.498863	−	0.133670i
$736$	−107.797	−	186.710i	−0.146463	−	0.253682i
$737$	157.330	+	272.504i	0.213474	+	0.369748i
$738$	160.100	−	42.8988i	0.216938	−	0.0581284i
$739$			1149.98i			1.55613i	0.628181	+	0.778067i	$0.283800\pi$
$739$			1149.98i			1.55613i	−0.628181	+	0.778067i	$0.716200\pi$
$740$	155.168	+	657.998i	0.209687	+	0.889187i
$741$	−889.071			−1.19983
$742$	152.570	+	569.400i	0.205620	+	0.767386i
$743$	−694.973	+	401.243i	−0.935361	+	0.540031i	−0.888503	−	0.458871i	$-0.848254\pi$
$743$	−694.973	+	401.243i	−0.935361	+	0.540031i	−0.0468578	+	0.998902i	$0.514921\pi$
$744$	48.4786	−	27.9891i	0.0651594	−	0.0376198i
$745$	−516.548	+	1927.78i	−0.693354	+	2.58763i
$746$	−178.434	−	178.434i	−0.239188	−	0.239188i
$747$	97.6579	+	169.148i	0.130733	+	0.226437i
$748$	132.997	+	132.997i	0.177804	+	0.177804i
$749$	316.490	−	548.177i	0.422550	−	0.731878i
$750$	−748.817			−0.998423
$751$			289.206i			0.385095i	0.981288	+	0.192547i	$0.0616749\pi$
$751$			289.206i			0.385095i	−0.981288	+	0.192547i	$0.938325\pi$
$752$	−92.4565	+	160.139i	−0.122947	+	0.212951i
$753$	−60.5529	+	225.986i	−0.0804155	+	0.300115i
$754$	840.367	−	840.367i	1.11455	−	1.11455i
$755$	448.371	+	1673.34i	0.593869	+	2.21635i
$756$	44.3927	−	76.8904i	0.0587205	−	0.101707i
$757$	400.517	−	107.318i	0.529085	−	0.141768i	0.0156190	−	0.999878i	$-0.495028\pi$
$757$	400.517	−	107.318i	0.529085	−	0.141768i	0.513465	+	0.858110i	$0.328361\pi$
$758$	−447.984	−	120.037i	−0.591008	−	0.158360i
$759$	−151.733	+	566.276i	−0.199912	+	0.746081i
$760$	−202.709	−	756.522i	−0.266723	−	0.995423i
$761$	−97.0558	−	56.0352i	−0.127537	−	0.0736336i	0.434874	−	0.900491i	$-0.356793\pi$
$761$	−97.0558	−	56.0352i	−0.127537	−	0.0736336i	−0.562411	+	0.826858i	$0.690126\pi$
$762$	−198.841	+	53.2792i	−0.260946	+	0.0699202i
$763$	413.765	+	413.765i	0.542287	+	0.542287i
$764$	−383.491	−	102.756i	−0.501952	−	0.134498i
$765$	−251.341	−	145.112i	−0.328550	−	0.189689i
$766$	−556.011			−0.725863
$767$			513.643i			0.669678i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$	−303.708	+	303.708i	−0.394939	+	0.394939i	−0.876444	−	0.481505i	$-0.840090\pi$
$769$	−303.708	+	303.708i	−0.394939	+	0.394939i	0.481505	+	0.876444i	$0.340090\pi$
$770$	848.950	−	490.141i	1.10253	−	0.636547i
$771$	−212.098	+	212.098i	−0.275095	+	0.275095i
$772$	280.792	+	75.2379i	0.363720	+	0.0974584i
$773$	82.7843	+	143.387i	0.107095	+	0.185494i	0.914592	−	0.404378i	$-0.132512\pi$
$773$	82.7843	+	143.387i	0.107095	+	0.185494i	−0.807497	+	0.589871i	$0.799179\pi$
$774$	20.4485	+	35.4178i	0.0264192	+	0.0457594i
$775$	−645.258	+	172.896i	−0.832591	+	0.223092i
$776$		−	419.912i		−	0.541124i
$777$	465.672	+	287.953i	0.599320	+	0.370596i
$778$	760.412			0.977393
$779$	−306.476	−	1143.78i	−0.393422	−	1.46827i
$780$	464.146	−	267.975i	0.595059	−	0.343557i
$781$	−642.098	+	370.716i	−0.822149	+	0.474668i
$782$	−147.720	+	551.299i	−0.188900	+	0.704986i
$783$	−182.326	−	182.326i	−0.232855	−	0.232855i
$784$	47.9787	+	83.1016i	0.0611974	+	0.105997i
$785$	−703.636	−	703.636i	−0.896352	−	0.896352i
$786$	30.2880	−	52.4603i	0.0385343	−	0.0667434i
$787$	−345.812			−0.439405			−0.219703	−	0.975567i	$-0.570509\pi$
$787$	−345.812			−0.439405			−0.219703	+	0.975567i	$0.570509\pi$
$788$		−	96.3488i		−	0.122270i
$789$	−25.9264	+	44.9059i	−0.0328598	+	0.0569149i
$790$	313.843	−	1171.28i	0.397269	−	1.48263i
$791$	1254.17	−	1254.17i	1.58555	−	1.58555i
$792$	19.5040	+	72.7900i	0.0246263	+	0.0919065i
$793$	−287.438	+	497.857i	−0.362469	+	0.627815i
$794$	872.205	−	233.707i	1.09850	−	0.294341i
$795$	745.725	+	199.816i	0.938019	+	0.251341i
$796$	131.267	−	489.897i	0.164909	−	0.615448i
$797$	324.739	+	1211.94i	0.407451	+	1.52063i	0.799490	+	0.600680i	$0.205103\pi$
$797$	324.739	+	1211.94i	0.407451	+	1.52063i	−0.392039	+	0.919949i	$0.628230\pi$
$798$	−549.318	−	317.149i	−0.688368	−	0.397429i
$799$	472.844	−	126.698i	0.591795	−	0.158571i
$800$	233.849	+	233.849i	0.292311	+	0.292311i
$801$	207.087	+	55.4888i	0.258536	+	0.0692744i
$802$	707.384	+	408.409i	0.882025	+	0.509238i
$803$	−492.338			−0.613124
$804$			122.736i			0.152656i
$805$	2576.13	+	1487.33i	3.20016	+	1.84761i
$806$	193.509	−	193.509i	0.240086	−	0.240086i
$807$	−162.863	+	94.0290i	−0.201813	+	0.116517i
$808$	246.930	−	246.930i	0.305607	−	0.305607i
$809$	−743.195	−	199.138i	−0.918658	−	0.246154i	−0.231647	−	0.972800i	$-0.574411\pi$
$809$	−743.195	−	199.138i	−0.918658	−	0.246154i	−0.687012	+	0.726646i	$0.741078\pi$
$810$	−58.1397	−	100.701i	−0.0717774	−	0.124322i
$811$	634.104	+	1098.30i	0.781879	+	1.35425i	0.930846	+	0.365411i	$0.119072\pi$
$811$	634.104	+	1098.30i	0.781879	+	1.35425i	−0.148967	+	0.988842i	$0.547595\pi$
$812$	819.001	−	219.451i	1.00862	−	0.270260i
$813$			90.6804i			0.111538i
$814$	−452.300	+	106.661i	−0.555651	+	0.131033i
$815$	251.325			0.308375
$816$	18.9882	+	70.8649i	0.0232698	+	0.0868442i
$817$	253.030	−	146.087i	0.309706	−	0.178809i
$818$	−139.808	+	80.7180i	−0.170914	+	0.0986773i
$819$	112.340	−	419.259i	0.137168	−	0.511916i
$820$	504.746	+	504.746i	0.615543	+	0.615543i
$821$	9.69377	+	16.7901i	0.0118073	+	0.0204508i	0.871869	−	0.489740i	$-0.162908\pi$
$821$	9.69377	+	16.7901i	0.0118073	+	0.0204508i	−0.860061	+	0.510191i	$0.829575\pi$
$822$	8.40836	+	8.40836i	0.0102292	+	0.0102292i
$823$	−79.0872	+	136.983i	−0.0960962	+	0.166444i	−0.910066	−	0.414464i	$-0.863969\pi$
$823$	−79.0872	+	136.983i	−0.0960962	+	0.166444i	0.813969	+	0.580908i	$0.197302\pi$
$824$	−103.169			−0.125205
$825$		−	899.286i		−	1.09004i
$826$	−183.227	+	317.358i	−0.221824	+	0.384210i
$827$	59.4239	−	221.773i	0.0718547	−	0.268165i	−0.920647	−	0.390396i	$-0.872338\pi$
$827$	59.4239	−	221.773i	0.0718547	−	0.268165i	0.992502	+	0.122231i	$0.0390047\pi$
$828$	−161.696	+	161.696i	−0.195284	+	0.195284i
$829$	−14.4001	−	53.7420i	−0.0173705	−	0.0648275i	0.956697	−	0.291087i	$-0.0940169\pi$
$829$	−14.4001	−	53.7420i	−0.0173705	−	0.0648275i	−0.974067	+	0.226260i	$0.927350\pi$
$830$	−420.578	+	728.462i	−0.506720	+	0.877665i
$831$	578.803	−	155.090i	0.696514	−	0.186630i
$832$	−130.864	−	35.0650i	−0.157289	−	0.0421455i
$833$	65.7479	−	245.374i	0.0789290	−	0.294567i
$834$	−125.039	−	466.653i	−0.149927	−	0.559536i
$835$	−596.105	−	344.161i	−0.713898	−	0.412169i
$836$	520.023	−	139.340i	0.622038	−	0.166674i
$837$	−41.9837	−	41.9837i	−0.0501597	−	0.0501597i
$838$	1080.54	+	289.530i	1.28943	+	0.345501i
$839$	−402.163	−	232.189i	−0.479336	−	0.276744i	0.240804	−	0.970574i	$-0.422589\pi$
$839$	−402.163	−	232.189i	−0.479336	−	0.276744i	−0.720140	+	0.693829i	$0.755922\pi$
$840$	382.367			0.455199
$841$		−	1621.42i		−	1.92797i
$842$	−91.1655	−	52.6344i	−0.108273	−	0.0625112i
$843$	−96.7695	+	96.7695i	−0.114792	+	0.114792i
$844$	−631.323	+	364.495i	−0.748013	+	0.431866i
$845$	760.971	−	760.971i	0.900557	−	0.900557i
$846$	189.447	+	50.7621i	0.223932	+	0.0600025i
$847$	−179.958	−	311.696i	−0.212465	−	0.367999i
$848$	−97.5796	−	169.013i	−0.115070	−	0.199308i
$849$	−100.534	+	26.9379i	−0.118414	+	0.0317290i
$850$		−	875.502i		−	1.03000i
$851$	−966.547	−	1026.79i	−1.13578	−	1.20657i
$852$	−289.201			−0.339438
$853$	−50.9442	−	190.126i	−0.0597236	−	0.222891i	0.929613	−	0.368536i	$-0.120141\pi$
$853$	−50.9442	−	190.126i	−0.0597236	−	0.222891i	−0.989337	+	0.145645i	$0.953474\pi$
$854$	−355.191	+	205.069i	−0.415914	+	0.240128i
$855$	−719.423	+	415.359i	−0.841431	+	0.485800i
$856$	−54.2377	+	202.418i	−0.0633618	+	0.236469i
$857$	−734.782	−	734.782i	−0.857388	−	0.857388i	0.133642	−	0.991030i	$-0.457333\pi$
$857$	−734.782	−	734.782i	−0.857388	−	0.857388i	−0.991030	+	0.133642i	$0.957333\pi$
$858$	184.202	+	319.048i	0.214688	+	0.371851i
$859$	−188.861	−	188.861i	−0.219862	−	0.219862i	0.588578	−	0.808440i	$-0.299688\pi$
$859$	−188.861	−	188.861i	−0.219862	−	0.219862i	−0.808440	+	0.588578i	$0.799688\pi$
$860$	−88.0642	+	152.532i	−0.102400	+	0.177362i
$861$	578.100			0.671428
$862$		−	401.285i		−	0.465528i
$863$	−697.425	+	1207.98i	−0.808140	+	1.39974i	0.106010	+	0.994365i	$0.466192\pi$
$863$	−697.425	+	1207.98i	−0.808140	+	1.39974i	−0.914150	+	0.405375i	$0.867141\pi$
$864$	−7.60770	+	28.3923i	−0.00880520	+	0.0328615i
$865$	−909.811	+	909.811i	−1.05180	+	1.05180i
$866$	181.139	+	676.020i	0.209168	+	0.780624i
$867$	−153.171	+	265.301i	−0.176668	+	0.305998i
$868$	188.589	−	50.5324i	0.217269	−	0.0582171i
$869$	805.121	+	215.732i	0.926492	+	0.248253i
$870$	287.407	−	1072.62i	0.330353	−	1.23290i
$871$	155.298	+	579.579i	0.178298	+	0.665418i
$872$	−167.770	−	96.8621i	−0.192397	−	0.111080i
$873$	−430.208	+	115.274i	−0.492793	+	0.132043i
$874$	1155.18	+	1155.18i	1.32172	+	1.32172i
$875$	−2522.75	−	675.968i	−2.88314	−	0.772535i
$876$	−166.312	−	96.0202i	−0.189854	−	0.109612i
$877$	−1361.48			−1.55243			−0.776214	−	0.630470i	$-0.782862\pi$
$877$	−1361.48			−1.55243			−0.776214	+	0.630470i	$0.782862\pi$
$878$		−	308.320i		−	0.351162i
$879$	−351.981	−	203.216i	−0.400433	−	0.231190i
$880$	−229.484	+	229.484i	−0.260777	+	0.260777i
$881$	−770.928	+	445.096i	−0.875061	+	0.505217i	−0.869027	−	0.494765i	$-0.835254\pi$
$881$	−770.928	+	445.096i	−0.875061	+	0.505217i	−0.00603404	+	0.999982i	$0.501921\pi$
$882$	71.9681	−	71.9681i	0.0815965	−	0.0815965i
$883$	181.386	+	48.6022i	0.205420	+	0.0550421i	0.360062	−	0.932929i	$-0.382756\pi$
$883$	181.386	+	48.6022i	0.205420	+	0.0550421i	−0.154642	+	0.987971i	$0.549422\pi$
$884$	179.331	+	310.610i	0.202863	+	0.351369i
$885$	239.966	+	415.633i	0.271148	+	0.469642i
$886$	583.851	−	156.442i	0.658973	−	0.176571i
$887$			217.677i			0.245408i	0.992443	+	0.122704i	$0.0391566\pi$
$887$			217.677i			0.245408i	−0.992443	+	0.122704i	$0.960843\pi$
$888$	−173.589	−	52.1815i	−0.195483	−	0.0587630i
$889$	−717.985			−0.807633
$890$	238.971	+	891.850i	0.268506	+	1.00208i
$891$	69.2205	−	39.9645i	0.0776886	−	0.0448535i
$892$	−76.8804	+	44.3869i	−0.0861887	+	0.0497611i
$893$	362.653	−	1353.44i	0.406106	−	1.51561i
$894$	−378.382	−	378.382i	−0.423246	−	0.423246i
$895$	−358.435	−	620.828i	−0.400486	−	0.693662i
$896$	−68.3471	−	68.3471i	−0.0762802	−	0.0762802i
$897$	−558.960	+	968.147i	−0.623144	+	1.07932i
$898$	−503.873			−0.561106
$899$		−	567.016i		−	0.630718i
$900$	175.387	−	303.779i	0.194874	−	0.337532i
$901$	−133.719	+	499.045i	−0.148411	+	0.553879i
$902$	−346.956	+	346.956i	−0.384652	+	0.384652i
$903$	36.9182	+	137.781i	0.0408840	+	0.152581i
$904$	−293.601	+	508.532i	−0.324780	+	0.562535i
$905$	1426.68	−	382.279i	1.57645	−	0.422408i
$906$	−448.658	−	120.218i	−0.495208	−	0.132691i
$907$	−24.3713	+	90.9549i	−0.0268702	+	0.100281i	−0.978059	−	0.208330i	$-0.933197\pi$
$907$	−24.3713	+	90.9549i	−0.0268702	+	0.100281i	0.951188	+	0.308611i	$0.0998640\pi$
$908$	−161.570	−	602.988i	−0.177941	−	0.664084i
$909$	−320.772	−	185.198i	−0.352884	−	0.203738i
$910$	1805.60	−	483.809i	1.98418	−	0.531658i
$911$	106.207	+	106.207i	0.116583	+	0.116583i	0.762992	−	0.646408i	$-0.223730\pi$
$911$	106.207	+	106.207i	0.116583	+	0.116583i	−0.646408	+	0.762992i	$0.723730\pi$
$912$	202.839	+	54.3506i	0.222411	+	0.0595950i
$913$	−500.735	−	289.100i	−0.548451	−	0.316648i
$914$	−134.809			−0.147494
$915$			537.145i			0.587044i
$916$	−70.2288	−	40.5466i	−0.0766689	−	0.0442648i
$917$	149.396	−	149.396i	0.162918	−	0.162918i
$918$	67.3898	−	38.9075i	0.0734094	−	0.0423829i
$919$	222.228	−	222.228i	0.241815	−	0.241815i	−0.575786	−	0.817601i	$-0.695304\pi$
$919$	222.228	−	222.228i	0.241815	−	0.241815i	0.817601	+	0.575786i	$0.195304\pi$
$920$	−951.252	−	254.887i	−1.03397	−	0.277051i
$921$	−241.498	−	418.287i	−0.262213	−	0.454166i
$922$	−558.536	−	967.413i	−0.605788	−	1.04926i
$923$	−1365.66	+	365.926i	−1.47958	+	0.396453i
$924$			262.834i			0.284453i
$925$	1839.78	+	1137.64i	1.98895	+	1.22989i
$926$	342.804			0.370199
$927$	28.3219	+	105.699i	0.0305522	+	0.114022i
$928$	−243.101	+	140.354i	−0.261962	+	0.151244i
$929$	823.257	−	475.308i	0.886176	−	0.511634i	0.0134861	−	0.999909i	$-0.495707\pi$
$929$	823.257	−	475.308i	0.886176	−	0.511634i	0.872690	+	0.488275i	$0.162374\pi$
$930$	66.1806	−	246.989i	0.0711620	−	0.265580i
$931$	−514.152	−	514.152i	−0.552258	−	0.552258i
$932$	76.0503	+	131.723i	0.0815990	+	0.141334i
$933$	29.7606	+	29.7606i	0.0318978	+	0.0318978i
$934$	−73.8392	+	127.893i	−0.0790570	+	0.136931i
$935$	859.158			0.918886
$936$			143.699i			0.153525i
$937$	204.011	−	353.358i	0.217728	−	0.377116i	−0.736385	−	0.676563i	$-0.763469\pi$
$937$	204.011	−	353.358i	0.217728	−	0.377116i	0.954113	+	0.299447i	$0.0968021\pi$
$938$	−110.795	+	413.494i	−0.118119	+	0.440825i
$939$	544.046	−	544.046i	0.579389	−	0.579389i
$940$	218.614	+	815.880i	0.232568	+	0.867957i
$941$	793.453	−	1374.30i	0.843202	−	1.46047i	−0.0439719	−	0.999033i	$-0.514001\pi$
$941$	793.453	−	1374.30i	0.843202	−	1.46047i	0.887174	−	0.461436i	$-0.152665\pi$
$942$	257.714	−	69.0542i	0.273581	−	0.0733059i
$943$	−1438.20	−	385.363i	−1.52513	−	0.408657i
$944$	31.4000	−	117.186i	0.0332627	−	0.124138i
$945$	−104.967	−	391.742i	−0.111076	−	0.414542i
$946$	−104.848	−	60.5342i	−0.110833	−	0.0639896i
$947$	1400.43	−	375.243i	1.47880	−	0.396244i	0.572863	−	0.819651i	$-0.305833\pi$
$947$	1400.43	−	375.243i	1.47880	−	0.396244i	0.905940	+	0.423407i	$0.139166\pi$
$948$	229.896	+	229.896i	0.242506	+	0.242506i
$949$	−906.847	−	242.989i	−0.955582	−	0.256047i
$950$	−2170.24	−	1252.99i	−2.28447	−	1.31894i
$951$	−146.815			−0.154380
$952$			255.883i			0.268785i
$953$	−956.250	−	552.091i	−1.00341	−	0.579319i	−0.0941548	−	0.995558i	$-0.530015\pi$
$953$	−956.250	−	552.091i	−1.00341	−	0.579319i	−0.909256	+	0.416238i	$0.863348\pi$
$954$	−146.369	+	146.369i	−0.153427	+	0.153427i
$955$	−1570.57	+	906.769i	−1.64458	+	0.949496i
$956$	−542.480	+	542.480i	−0.567447	+	0.567447i
$957$	737.305	+	197.560i	0.770433	+	0.206437i
$958$	26.0624	+	45.1414i	0.0272050	+	0.0471205i
$959$	20.7372	+	35.9179i	0.0216238	+	0.0374535i
$960$	−122.275	+	32.7636i	−0.127370	+	0.0341288i
$961$			830.435i			0.864136i
$962$	−885.741	−	26.7679i	−0.920728	−	0.0278252i
$963$	222.270			0.230810
$964$	−100.912	−	376.609i	−0.104680	−	0.390673i
$965$	1149.97	−	663.935i	1.19168	−	0.688016i
$966$	−690.713	+	398.784i	−0.715024	+	0.412819i
$967$	−351.109	+	1310.36i	−0.363091	+	1.35507i	0.506899	+	0.862005i	$0.330792\pi$
$967$	−351.109	+	1310.36i	−0.363091	+	1.35507i	−0.869990	+	0.493069i	$0.835875\pi$
$968$	84.2559	+	84.2559i	0.0870412	+	0.0870412i
$969$	−277.962	−	481.444i	−0.286854	−	0.496846i
$970$	−1356.31	−	1356.31i	−1.39826	−	1.39826i
$971$	277.225	−	480.168i	0.285505	−	0.494509i	−0.687227	−	0.726443i	$-0.741172\pi$
$971$	277.225	−	480.168i	0.285505	−	0.494509i	0.972731	+	0.231934i	$0.0745055\pi$
$972$	31.1769			0.0320750
$973$		−	1685.02i		−	1.73177i
$974$	−429.852	+	744.525i	−0.441326	+	0.764399i
$975$	443.834	−	1656.41i	0.455214	−	1.69888i
$976$	96.0133	−	96.0133i	0.0983742	−	0.0983742i
$977$	447.541	+	1670.25i	0.458077	+	1.70957i	0.678881	+	0.734249i	$0.262465\pi$
$977$	447.541	+	1670.25i	0.458077	+	1.70957i	−0.220803	+	0.975318i	$0.570868\pi$
$978$	−33.6928	+	58.3576i	−0.0344507	+	0.0596704i
$979$	−613.047	+	164.265i	−0.626197	+	0.167789i
$980$	423.387	+	113.446i	0.432028	+	0.115761i
$981$	−53.1810	+	198.474i	−0.0542110	+	0.202318i
$982$	−19.0635	−	71.1459i	−0.0194129	−	0.0724500i
$983$	968.728	+	559.295i	0.985481	+	0.568968i	0.903920	−	0.427701i	$-0.140676\pi$
$983$	968.728	+	559.295i	0.985481	+	0.568968i	0.0815605	+	0.996668i	$0.474010\pi$
$984$	−184.868	+	49.5352i	−0.187874	+	0.0503407i
$985$	−311.205	−	311.205i	−0.315944	−	0.315944i
$986$	717.805	+	192.335i	0.727997	+	0.195066i
$987$	592.418	+	342.033i	0.600221	+	0.346538i
$988$	1026.61			1.03908
$989$		−	367.380i		−	0.371467i
$990$	298.108	+	172.113i	0.301119	+	0.173851i
$991$	−1048.23	+	1048.23i	−1.05775	+	1.05775i	−0.0595241	+	0.998227i	$0.518958\pi$
$991$	−1048.23	+	1048.23i	−1.05775	+	1.05775i	−0.998227	+	0.0595241i	$0.981042\pi$
$992$	−55.9783	+	32.3191i	−0.0564297	+	0.0325797i
$993$	−521.186	+	521.186i	−0.524860	+	0.524860i
$994$	−974.312	−	261.066i	−0.980193	−	0.262642i
$995$	−1158.37	−	2006.35i	−1.16419	−	2.01643i
$996$	−112.766	−	195.316i	−0.113218	−	0.196100i
$997$	979.275	−	262.396i	0.982222	−	0.263185i	0.268242	−	0.963352i	$-0.413557\pi$
$997$	979.275	−	262.396i	0.982222	−	0.263185i	0.713980	+	0.700166i	$0.246891\pi$
$998$		−	477.185i		−	0.478141i
$999$	−5.80754	+	192.170i	−0.00581336	+	0.192362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.3.l.d.97.1	✓	16
37.29	odd	12	inner	222.3.l.d.103.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.3.l.d.97.1	✓	16	1.1	even	1	trivial
222.3.l.d.103.1	yes	16	37.29	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	222.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-2.36451 + 8.82447i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-4.27169 - 7.39879i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +12.9199 q^{10} +8.88099i q^{11} +(-1.73205 + 3.00000i) q^{12} +(-4.38313 + 16.3581i) q^{13} +(-8.54338 + 8.54338i) q^{14} +(4.09545 + 15.2844i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-10.2285 + 2.74071i) q^{17} +(-4.09808 - 1.09808i) q^{18} +(-7.84483 + 29.2773i) q^{19} +(-4.72902 - 17.6489i) q^{20} +(-12.8151 - 7.39879i) q^{21} +(12.1317 - 3.25067i) q^{22} +(26.9493 + 26.9493i) q^{23} +(4.73205 + 1.26795i) q^{24} +(-50.6298 - 29.2311i) q^{25} +23.9499 q^{26} -5.19615i q^{27} +(14.7976 + 8.54338i) q^{28} +(35.0886 - 35.0886i) q^{29} +(19.3799 - 11.1890i) q^{30} +(8.07977 - 8.07977i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(7.69117 + 13.3215i) q^{33} +(7.48776 + 12.9692i) q^{34} +(75.3908 - 20.2009i) q^{35} +6.00000i q^{36} +(-36.9831 - 1.11766i) q^{37} +42.8650 q^{38} +(7.59180 + 28.3330i) q^{39} +(-22.3780 + 12.9199i) q^{40} +(-33.8332 + 19.5336i) q^{41} +(-5.41629 + 20.2139i) q^{42} +(-6.81615 - 6.81615i) q^{43} +(-8.88099 - 15.3823i) q^{44} +(19.3799 + 19.3799i) q^{45} +(26.9493 - 46.6775i) q^{46} -46.2282 q^{47} -6.92820i q^{48} +(-11.9947 + 20.7754i) q^{49} +(-21.3987 + 79.8609i) q^{50} +(-12.9692 + 12.9692i) q^{51} +(-8.76626 - 32.7161i) q^{52} +(24.3949 - 42.2532i) q^{53} +(-7.09808 + 1.90192i) q^{54} +(-78.3701 - 20.9992i) q^{55} +(6.25419 - 23.3410i) q^{56} +(13.5877 + 50.7098i) q^{57} +(-60.7752 - 35.0886i) q^{58} +(29.2966 - 7.85000i) q^{59} +(-22.3780 - 22.3780i) q^{60} +(32.7891 + 8.78582i) q^{61} +(-13.9946 - 8.07977i) q^{62} -25.6301 q^{63} +8.00000i q^{64} +(-133.987 - 77.3576i) q^{65} +(15.3823 - 15.3823i) q^{66} +(30.6840 - 17.7154i) q^{67} +(14.9755 - 14.9755i) q^{68} +(63.7626 + 17.0851i) q^{69} +(-55.1899 - 95.5918i) q^{70} +(41.7426 + 72.3003i) q^{71} +(8.19615 - 2.19615i) q^{72} +55.4373i q^{73} +(12.0100 + 50.9290i) q^{74} -101.260 q^{75} +(-15.6897 - 58.5546i) q^{76} +(65.7086 - 37.9369i) q^{77} +(35.9248 - 20.7412i) q^{78} +(24.2914 - 90.6567i) q^{79} +(25.8399 + 25.8399i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(39.0672 + 39.0672i) q^{82} +(-32.5526 + 56.3828i) q^{83} +29.5951 q^{84} -96.7412i q^{85} +(-6.81615 + 11.8059i) q^{86} +(22.2453 - 83.0205i) q^{87} +(-17.7620 + 17.7620i) q^{88} +(18.4963 + 69.0290i) q^{89} +(19.3799 - 33.5670i) q^{90} +(139.753 - 37.4467i) q^{91} +(-73.6267 - 19.7282i) q^{92} +(5.12237 - 19.1169i) q^{93} +(16.9207 + 63.1489i) q^{94} +(-239.808 - 138.453i) q^{95} +(-9.46410 + 2.53590i) q^{96} +(-104.978 - 104.978i) q^{97} +(32.7701 + 8.78072i) q^{98} +(23.0735 + 13.3215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Introduction

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