LMFDB - Embedded newform 429.2.bd.a.76.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.2
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.a.175.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52014 - 0.675270i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(4.16307 + 2.40355i) q^{4} +(0.961072 + 0.961072i) q^{5} +(0.675270 + 2.52014i) q^{6} +(1.60148 - 0.429116i) q^{7} +(-5.17874 - 5.17874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.52014 - 0.675270i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(4.16307 + 2.40355i) q^{4} +(0.961072 + 0.961072i) q^{5} +(0.675270 + 2.52014i) q^{6} +(1.60148 - 0.429116i) q^{7} +(-5.17874 - 5.17874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.77305 - 3.07102i) q^{10} +(2.06845 - 2.59259i) q^{11} -4.80710i q^{12} +(1.63725 + 3.21239i) q^{13} -4.32573 q^{14} +(0.351777 - 1.31285i) q^{15} +(4.74702 + 8.22207i) q^{16} +(-2.72976 + 4.72807i) q^{17} +(1.84487 - 1.84487i) q^{18} +(1.35133 + 5.04322i) q^{19} +(1.69103 + 6.31100i) q^{20} +(-1.17237 - 1.17237i) q^{21} +(-6.96348 + 5.13693i) q^{22} +(-2.95274 + 1.70476i) q^{23} +(-1.89555 + 7.07430i) q^{24} -3.15268i q^{25} +(-1.95687 - 9.20125i) q^{26} +1.00000 q^{27} +(7.69849 + 2.06280i) q^{28} +(0.554187 - 0.319960i) q^{29} +(-1.77305 + 3.07102i) q^{30} +(4.70021 + 4.70021i) q^{31} +(-2.61993 - 9.77771i) q^{32} +(-3.27947 - 0.495035i) q^{33} +(10.0721 - 10.0721i) q^{34} +(1.95155 + 1.12673i) q^{35} +(-4.16307 + 2.40355i) q^{36} +(-2.76558 - 0.741034i) q^{37} -13.6221i q^{38} +(1.96338 - 3.02409i) q^{39} -9.95429i q^{40} +(9.83418 + 2.63506i) q^{41} +(2.16286 + 3.74619i) q^{42} +(4.82451 - 8.35629i) q^{43} +(14.8425 - 5.82151i) q^{44} +(-1.31285 + 0.351777i) q^{45} +(8.59250 - 2.30235i) q^{46} +(4.28943 - 4.28943i) q^{47} +(4.74702 - 8.22207i) q^{48} +(-3.68158 + 2.12556i) q^{49} +(-2.12891 + 7.94520i) q^{50} +5.45951 q^{51} +(-0.905155 + 17.3086i) q^{52} -1.56234 q^{53} +(-2.52014 - 0.675270i) q^{54} +(4.47959 - 0.503736i) q^{55} +(-10.5159 - 6.07138i) q^{56} +(3.69190 - 3.69190i) q^{57} +(-1.61269 + 0.432119i) q^{58} +(2.79457 + 10.4295i) q^{59} +(4.61997 - 4.61997i) q^{60} +(-0.0110680 - 0.00639011i) q^{61} +(-8.67128 - 15.0191i) q^{62} +(-0.429116 + 1.60148i) q^{63} +7.42231i q^{64} +(-1.51382 + 4.66085i) q^{65} +(7.93045 + 3.46209i) q^{66} +(2.45326 - 9.15568i) q^{67} +(-22.7283 + 13.1222i) q^{68} +(2.95274 + 1.70476i) q^{69} +(-4.15734 - 4.15734i) q^{70} +(11.8334 - 3.17074i) q^{71} +(7.07430 - 1.89555i) q^{72} +(-2.12085 - 2.12085i) q^{73} +(6.46924 + 3.73502i) q^{74} +(-2.73030 + 1.57634i) q^{75} +(-6.49597 + 24.2433i) q^{76} +(2.20006 - 5.03959i) q^{77} +(-6.99008 + 6.29532i) q^{78} -3.06758i q^{79} +(-3.33978 + 12.4642i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-23.0041 - 13.2814i) q^{82} +(1.12056 - 1.12056i) q^{83} +(-2.06280 - 7.69849i) q^{84} +(-7.16751 + 1.92053i) q^{85} +(-17.8012 + 17.8012i) q^{86} +(-0.554187 - 0.319960i) q^{87} +(-24.1383 + 2.71438i) q^{88} +(8.68479 + 2.32708i) q^{89} +3.54611 q^{90} +(4.00051 + 4.44201i) q^{91} -16.3900 q^{92} +(1.72039 - 6.42060i) q^{93} +(-13.7065 + 7.91344i) q^{94} +(-3.54818 + 6.14563i) q^{95} +(-7.15778 + 7.15778i) q^{96} +(-10.8124 + 2.89718i) q^{97} +(10.7134 - 2.87065i) q^{98} +(1.21102 + 3.08762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.52014	−	0.675270i	−1.78201	−	0.477488i	−0.791062	−	0.611737i	$-0.790471\pi$
$2$	−2.52014	−	0.675270i	−1.78201	−	0.477488i	−0.990948	+	0.134249i	$0.957138\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	4.16307	+	2.40355i	2.08154	+	1.20178i
$5$	0.961072	+	0.961072i	0.429805	+	0.429805i	0.888562	−	0.458757i	$-0.151705\pi$
$5$	0.961072	+	0.961072i	0.429805	+	0.429805i	−0.458757	+	0.888562i	$0.651705\pi$
$6$	0.675270	+	2.52014i	0.275678	+	1.02884i
$7$	1.60148	−	0.429116i	0.605303	−	0.162190i	0.0568653	−	0.998382i	$-0.481889\pi$
$7$	1.60148	−	0.429116i	0.605303	−	0.162190i	0.548438	+	0.836191i	$0.315223\pi$
$8$	−5.17874	−	5.17874i	−1.83096	−	1.83096i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.77305	−	3.07102i	−0.560689	−	0.971142i
$11$	2.06845	−	2.59259i	0.623661	−	0.781695i
$11$	2.06845	−	2.59259i	0.623661	−	0.781695i
$12$		−	4.80710i		−	1.38769i
$13$	1.63725	+	3.21239i	0.454091	+	0.890955i
$13$	1.63725	+	3.21239i	0.454091	+	0.890955i
$14$	−4.32573			−1.15610
$15$	0.351777	−	1.31285i	0.0908284	−	0.338976i
$16$	4.74702	+	8.22207i	1.18675	+	2.05552i
$17$	−2.72976	+	4.72807i	−0.662063	+	1.14673i	0.318010	+	0.948087i	$0.396985\pi$
$17$	−2.72976	+	4.72807i	−0.662063	+	1.14673i	−0.980073	+	0.198639i	$0.936348\pi$
$18$	1.84487	−	1.84487i	0.434840	−	0.434840i
$19$	1.35133	+	5.04322i	0.310016	+	1.15699i	0.928541	+	0.371230i	$0.121064\pi$
$19$	1.35133	+	5.04322i	0.310016	+	1.15699i	−0.618525	+	0.785765i	$0.712270\pi$
$20$	1.69103	+	6.31100i	0.378125	+	1.41118i
$21$	−1.17237	−	1.17237i	−0.255831	−	0.255831i
$22$	−6.96348	+	5.13693i	−1.48462	+	1.09520i
$23$	−2.95274	+	1.70476i	−0.615689	+	0.355468i	−0.775189	−	0.631730i	$-0.782345\pi$
$23$	−2.95274	+	1.70476i	−0.615689	+	0.355468i	0.159500	+	0.987198i	$0.449012\pi$
$24$	−1.89555	+	7.07430i	−0.386928	+	1.44403i
$25$		−	3.15268i		−	0.630536i
$26$	−1.95687	−	9.20125i	−0.383773	−	1.80451i
$27$	1.00000			0.192450
$28$	7.69849	+	2.06280i	1.45488	+	0.389833i
$29$	0.554187	−	0.319960i	0.102910	−	0.0594151i	−0.447662	−	0.894203i	$-0.647743\pi$
$29$	0.554187	−	0.319960i	0.102910	−	0.0594151i	0.550572	+	0.834788i	$0.314410\pi$
$30$	−1.77305	+	3.07102i	−0.323714	+	0.560689i
$31$	4.70021	+	4.70021i	0.844182	+	0.844182i	0.989400	−	0.145218i	$-0.0463883\pi$
$31$	4.70021	+	4.70021i	0.844182	+	0.844182i	−0.145218	+	0.989400i	$0.546388\pi$
$32$	−2.61993	−	9.77771i	−0.463143	−	1.72847i
$33$	−3.27947	−	0.495035i	−0.570883	−	0.0861746i
$34$	10.0721	−	10.0721i	1.72735	−	1.72735i
$35$	1.95155	+	1.12673i	0.329872	+	0.190452i
$36$	−4.16307	+	2.40355i	−0.693846	+	0.400592i
$37$	−2.76558	−	0.741034i	−0.454658	−	0.121825i	0.0242202	−	0.999707i	$-0.492290\pi$
$37$	−2.76558	−	0.741034i	−0.454658	−	0.121825i	−0.478878	+	0.877881i	$0.658956\pi$
$38$		−	13.6221i		−	2.20980i
$39$	1.96338	−	3.02409i	0.314393	−	0.484242i
$40$		−	9.95429i		−	1.57391i
$41$	9.83418	+	2.63506i	1.53584	+	0.411527i	0.924919	−	0.380164i	$-0.124133\pi$
$41$	9.83418	+	2.63506i	1.53584	+	0.411527i	0.610921	+	0.791691i	$0.290799\pi$
$42$	2.16286	+	3.74619i	0.333737	+	0.578050i
$43$	4.82451	−	8.35629i	0.735730	−	1.27432i	−0.218672	−	0.975799i	$-0.570172\pi$
$43$	4.82451	−	8.35629i	0.735730	−	1.27432i	0.954402	−	0.298524i	$-0.0964943\pi$
$44$	14.8425	−	5.82151i	2.23760	−	0.877626i
$45$	−1.31285	+	0.351777i	−0.195708	+	0.0524398i
$46$	8.59250	−	2.30235i	1.26689	−	0.339463i
$47$	4.28943	−	4.28943i	0.625677	−	0.625677i	−0.321300	−	0.946977i	$-0.604120\pi$
$47$	4.28943	−	4.28943i	0.625677	−	0.625677i	0.946977	+	0.321300i	$0.104120\pi$
$48$	4.74702	−	8.22207i	0.685173	−	1.18675i
$49$	−3.68158	+	2.12556i	−0.525939	+	0.303651i
$50$	−2.12891	+	7.94520i	−0.301073	+	1.12362i
$51$	5.45951			0.764484
$52$	−0.905155	+	17.3086i	−0.125522	+	2.40027i
$53$	−1.56234			−0.214603			−0.107302	−	0.994227i	$-0.534221\pi$
$53$	−1.56234			−0.214603			−0.107302	+	0.994227i	$0.534221\pi$
$54$	−2.52014	−	0.675270i	−0.342948	−	0.0918926i
$55$	4.47959	−	0.503736i	0.604028	−	0.0679237i
$56$	−10.5159	−	6.07138i	−1.40525	−	0.811323i
$57$	3.69190	−	3.69190i	0.489004	−	0.489004i
$58$	−1.61269	+	0.432119i	−0.211757	+	0.0567400i
$59$	2.79457	+	10.4295i	0.363822	+	1.35780i	0.869010	+	0.494794i	$0.164757\pi$
$59$	2.79457	+	10.4295i	0.363822	+	1.35780i	−0.505188	+	0.863009i	$0.668577\pi$
$60$	4.61997	−	4.61997i	0.596436	−	0.596436i
$61$	−0.0110680	−	0.00639011i	−0.00141711	−	0.000818169i	0.499291	−	0.866434i	$-0.333594\pi$
$61$	−0.0110680	−	0.00639011i	−0.00141711	−	0.000818169i	−0.500708	+	0.865616i	$0.666927\pi$
$62$	−8.67128	−	15.0191i	−1.10125	−	1.90743i
$63$	−0.429116	+	1.60148i	−0.0540635	+	0.201768i
$64$			7.42231i			0.927789i
$65$	−1.51382	+	4.66085i	−0.187766	+	0.578107i
$66$	7.93045	+	3.46209i	0.976171	+	0.426154i
$67$	2.45326	−	9.15568i	0.299713	−	1.11854i	−0.637689	−	0.770294i	$-0.720109\pi$
$67$	2.45326	−	9.15568i	0.299713	−	1.11854i	0.937402	−	0.348250i	$-0.113224\pi$
$68$	−22.7283	+	13.1222i	−2.75622	+	1.59130i
$69$	2.95274	+	1.70476i	0.355468	+	0.205230i
$70$	−4.15734	−	4.15734i	−0.496897	−	0.496897i
$71$	11.8334	−	3.17074i	1.40436	−	0.376298i	0.524454	−	0.851439i	$-0.324270\pi$
$71$	11.8334	−	3.17074i	1.40436	−	0.376298i	0.879910	+	0.475141i	$0.157603\pi$
$72$	7.07430	−	1.89555i	0.833714	−	0.223393i
$73$	−2.12085	−	2.12085i	−0.248227	−	0.248227i	0.572016	−	0.820243i	$-0.306162\pi$
$73$	−2.12085	−	2.12085i	−0.248227	−	0.248227i	−0.820243	+	0.572016i	$0.806162\pi$
$74$	6.46924	+	3.73502i	0.752034	+	0.434187i
$75$	−2.73030	+	1.57634i	−0.315268	+	0.182020i
$76$	−6.49597	+	24.2433i	−0.745139	+	2.78090i
$77$	2.20006	−	5.03959i	0.250720	−	0.574314i
$78$	−6.99008	+	6.29532i	−0.791471	+	0.712805i
$79$		−	3.06758i		−	0.345130i	−0.984998	−	0.172565i	$-0.944795\pi$
$79$		−	3.06758i		−	0.345130i	0.984998	−	0.172565i	$-0.0552055\pi$
$80$	−3.33978	+	12.4642i	−0.373399	+	1.39354i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−23.0041	−	13.2814i	−2.54038	−	1.46669i
$83$	1.12056	−	1.12056i	0.122997	−	0.122997i	−0.642929	−	0.765926i	$-0.722281\pi$
$83$	1.12056	−	1.12056i	0.122997	−	0.122997i	0.765926	+	0.642929i	$0.222281\pi$
$84$	−2.06280	−	7.69849i	−0.225070	−	0.839974i
$85$	−7.16751	+	1.92053i	−0.777426	+	0.208311i
$86$	−17.8012	+	17.8012i	−1.91955	+	1.91955i
$87$	−0.554187	−	0.319960i	−0.0594151	−	0.0343033i
$88$	−24.1383	+	2.71438i	−2.57315	+	0.289354i
$89$	8.68479	+	2.32708i	0.920585	+	0.246670i	0.687836	−	0.725866i	$-0.258561\pi$
$89$	8.68479	+	2.32708i	0.920585	+	0.246670i	0.232750	+	0.972537i	$0.425228\pi$
$90$	3.54611			0.373793
$91$	4.00051	+	4.44201i	0.419367	+	0.465649i
$92$	−16.3900			−1.70877
$93$	1.72039	−	6.42060i	0.178397	−	0.665785i
$94$	−13.7065	+	7.91344i	−1.41372	+	0.816209i
$95$	−3.54818	+	6.14563i	−0.364035	+	0.630528i
$96$	−7.15778	+	7.15778i	−0.730538	+	0.730538i
$97$	−10.8124	+	2.89718i	−1.09784	+	0.294164i	−0.761883	−	0.647715i	$-0.775725\pi$
$97$	−10.8124	+	2.89718i	−1.09784	+	0.294164i	−0.335953	+	0.941879i	$0.609058\pi$
$98$	10.7134	−	2.87065i	1.08222	−	0.289980i
$99$	1.21102	+	3.08762i	0.121712	+	0.310318i
$100$	7.57763	−	13.1248i	0.757763	−	1.31248i
$101$	2.70271	+	4.68123i	0.268929	+	0.465799i	0.968586	−	0.248680i	$-0.0799969\pi$
$101$	2.70271	+	4.68123i	0.268929	+	0.465799i	−0.699656	+	0.714480i	$0.746664\pi$
$102$	−13.7587	−	3.68664i	−1.36232	−	0.365032i
$103$			19.4249i			1.91399i	0.290104	+	0.956995i	$0.406310\pi$
$103$			19.4249i			1.91399i	−0.290104	+	0.956995i	$0.593690\pi$
$104$	8.15724	−	25.1150i	0.799883	−	2.46273i
$105$		−	2.25346i		−	0.219915i
$106$	3.93731	+	1.05500i	0.382425	+	0.102471i
$107$	−5.86935	+	3.38867i	−0.567412	+	0.327595i	−0.756115	−	0.654439i	$-0.772905\pi$
$107$	−5.86935	+	3.38867i	−0.567412	+	0.327595i	0.188703	+	0.982034i	$0.439572\pi$
$108$	4.16307	+	2.40355i	0.400592	+	0.231282i
$109$	4.46615	−	4.46615i	0.427780	−	0.427780i	−0.460092	−	0.887871i	$-0.652184\pi$
$109$	4.46615	−	4.46615i	0.427780	−	0.427780i	0.887871	+	0.460092i	$0.152184\pi$
$110$	−11.6294	−	1.75545i	−1.10882	−	0.167376i
$111$	0.741034	+	2.76558i	0.0703358	+	0.262497i
$112$	11.1305	+	11.1305i	1.05173	+	1.05173i
$113$	0.497831	−	0.862268i	0.0468320	−	0.0811154i	−0.841659	−	0.540009i	$-0.818421\pi$
$113$	0.497831	−	0.862268i	0.0468320	−	0.0811154i	0.888491	+	0.458894i	$0.151754\pi$
$114$	−11.7971	+	6.81107i	−1.10490	+	0.637916i
$115$	−4.47620	−	1.19939i	−0.417407	−	0.111844i
$116$	3.07616			0.285615
$117$	−3.60063	−	0.188295i	−0.332878	−	0.0174079i
$118$		−	28.1709i		−	2.59334i
$119$	−2.34276	+	8.74330i	−0.214761	+	0.801497i
$120$	−8.62067	+	4.97715i	−0.786956	+	0.454349i
$121$	−2.44303	−	10.7253i	−0.222094	−	0.975025i
$122$	0.0235779	+	0.0235779i	0.00213464	+	0.00213464i
$123$	−2.63506	−	9.83418i	−0.237595	−	0.886718i
$124$	8.27011	+	30.8645i	0.742678	+	2.77171i
$125$	7.83531	−	7.83531i	0.700812	−	0.700812i
$126$	2.16286	−	3.74619i	0.192683	−	0.333737i
$127$	6.59346	+	11.4202i	0.585075	+	1.01338i	0.994866	+	0.101201i	$0.0322684\pi$
$127$	6.59346	+	11.4202i	0.585075	+	1.01338i	−0.409791	+	0.912180i	$0.634398\pi$
$128$	−0.227796	+	0.850144i	−0.0201345	+	0.0751429i
$129$	−9.64901			−0.849548
$130$	6.96237	−	10.7238i	0.610641	−	0.940536i
$131$		−	3.02964i		−	0.264701i	−0.991203	−	0.132351i	$-0.957748\pi$
$131$		−	3.02964i		−	0.264701i	0.991203	−	0.132351i	$-0.0422524\pi$
$132$	−12.4628	−	9.94325i	−1.08475	−	0.865449i
$133$	4.32825	+	7.49675i	0.375307	+	0.650051i
$134$	−12.3651	+	21.4170i	−1.06818	+	1.85015i
$135$	0.961072	+	0.961072i	0.0827159	+	0.0827159i
$136$	38.6222	−	10.3488i	3.31183	−	0.887401i
$137$	−4.99234	−	18.6317i	−0.426524	−	1.59181i	−0.760572	−	0.649254i	$-0.775081\pi$
$137$	−4.99234	−	18.6317i	−0.426524	−	1.59181i	0.334048	−	0.942556i	$-0.391585\pi$
$138$	−6.29014	−	6.29014i	−0.535453	−	0.535453i
$139$	−12.8592	−	7.42426i	−1.09070	−	0.629718i	−0.156940	−	0.987608i	$-0.550163\pi$
$139$	−12.8592	−	7.42426i	−1.09070	−	0.629718i	−0.933764	+	0.357890i	$0.883496\pi$
$140$	5.41630	+	9.38130i	0.457761	+	0.792865i
$141$	−5.85947	−	1.57004i	−0.493456	−	0.132221i
$142$	−31.9629			−2.68227
$143$	11.7150	+	2.39995i	0.979654	+	0.200694i
$144$	−9.49403			−0.791169
$145$	0.840119	+	0.225109i	0.0697681	+	0.0186943i
$146$	3.91270	+	6.77700i	0.323818	+	0.560869i
$147$	3.68158	+	2.12556i	0.303651	+	0.175313i
$148$	−9.73218	−	9.73218i	−0.799980	−	0.799980i
$149$	−0.563509	−	2.10304i	−0.0461644	−	0.172288i	0.938995	−	0.343932i	$-0.111759\pi$
$149$	−0.563509	−	2.10304i	−0.0461644	−	0.172288i	−0.985159	+	0.171644i	$0.945092\pi$
$150$	7.94520	−	2.12891i	0.648723	−	0.173825i
$151$	−14.9809	−	14.9809i	−1.21913	−	1.21913i	−0.967938	−	0.251189i	$-0.919178\pi$
$151$	−14.9809	−	14.9809i	−1.21913	−	1.21913i	−0.251189	−	0.967938i	$-0.580822\pi$
$152$	19.1194	−	33.1157i	1.55079	−	2.68604i
$153$	−2.72976	−	4.72807i	−0.220688	−	0.382242i
$154$	−8.94755	+	11.2148i	−0.721014	+	0.903717i
$155$			9.03447i			0.725666i
$156$	15.4423	−	7.87042i	1.23637	−	0.630138i
$157$	10.7407			0.857200			0.428600	−	0.903494i	$-0.359007\pi$
$157$	10.7407			0.857200			0.428600	+	0.903494i	$0.359007\pi$
$158$	−2.07145	+	7.73074i	−0.164795	+	0.615025i
$159$	0.781168	+	1.35302i	0.0619507	+	0.107302i
$160$	6.87914	−	11.9150i	0.543844	−	0.941966i
$161$	−3.99721	+	3.99721i	−0.315025	+	0.315025i
$162$	0.675270	+	2.52014i	0.0530542	+	0.198001i
$163$	4.16614	+	15.5483i	0.326317	+	1.21783i	0.912981	+	0.408002i	$0.133775\pi$
$163$	4.16614	+	15.5483i	0.326317	+	1.21783i	−0.586663	+	0.809831i	$0.699559\pi$
$164$	34.6069	+	34.6069i	2.70234	+	2.70234i
$165$	−2.67604	−	3.62757i	−0.208330	−	0.282406i
$166$	−3.58064	+	2.06729i	−0.277912	+	0.160453i
$167$	−2.55031	+	9.51789i	−0.197349	+	0.736516i	0.794297	+	0.607529i	$0.207839\pi$
$167$	−2.55031	+	9.51789i	−0.197349	+	0.736516i	−0.991646	+	0.128987i	$0.958827\pi$
$168$			12.1428i			0.936835i
$169$	−7.63884	+	10.5189i	−0.587603	+	0.809149i
$170$	19.3600			1.48485
$171$	−5.04322	−	1.35133i	−0.385665	−	0.103339i
$172$	40.1696	−	23.1919i	3.06290	−	1.76837i
$173$	0.216407	−	0.374828i	0.0164531	−	0.0284977i	−0.857682	−	0.514181i	$-0.828096\pi$
$173$	0.216407	−	0.374828i	0.0164531	−	0.0284977i	0.874135	+	0.485683i	$0.161429\pi$
$174$	1.18057	+	1.18057i	0.0894988	+	0.0894988i
$175$	−1.35286	−	5.04896i	−0.102267	−	0.381665i
$176$	31.1354	+	4.69988i	2.34692	+	0.354267i
$177$	7.63492	−	7.63492i	0.573875	−	0.573875i
$178$	−20.3155	−	11.7291i	−1.52271	−	0.879137i
$179$	−6.24988	+	3.60837i	−0.467138	+	0.269702i	−0.715041	−	0.699083i	$-0.753592\pi$
$179$	−6.24988	+	3.60837i	−0.467138	+	0.269702i	0.247903	+	0.968785i	$0.420259\pi$
$180$	−6.31100	−	1.69103i	−0.470394	−	0.126042i
$181$		−	9.08846i		−	0.675540i	−0.941229	−	0.337770i	$-0.890327\pi$
$181$		−	9.08846i		−	0.675540i	0.941229	−	0.337770i	$-0.109673\pi$
$182$	−7.08229	−	13.8959i	−0.524974	−	1.03003i
$183$			0.0127802i			0.000944741i
$184$	24.1200	+	6.46294i	1.77815	+	0.476454i
$185$	−1.94573	−	3.37010i	−0.143053	−	0.247775i
$186$	−8.67128	+	15.0191i	−0.635809	+	1.10125i
$187$	6.61159	+	16.8569i	0.483488	+	1.23270i
$188$	28.1671	−	7.54734i	2.05429	−	0.550446i
$189$	1.60148	−	0.429116i	0.116491	−	0.0312136i
$190$	13.0919	−	13.0919i	0.949784	−	0.949784i
$191$	−4.77206	+	8.26545i	−0.345294	+	0.598067i	−0.985407	−	0.170214i	$-0.945554\pi$
$191$	−4.77206	+	8.26545i	−0.345294	+	0.598067i	0.640113	+	0.768281i	$0.278887\pi$
$192$	6.42791	−	3.71116i	0.463895	−	0.267830i
$193$	5.46017	−	20.3776i	0.393032	−	1.46682i	−0.432074	−	0.901838i	$-0.642218\pi$
$193$	5.46017	−	20.3776i	0.393032	−	1.46682i	0.825106	−	0.564977i	$-0.191115\pi$
$194$	29.2052			2.09681
$195$	4.79332	−	1.01942i	0.343257	−	0.0730018i
$196$	−20.4356			−1.45968
$197$	−17.8592	−	4.78535i	−1.27241	−	0.340942i	−0.441458	−	0.897282i	$-0.645539\pi$
$197$	−17.8592	−	4.78535i	−1.27241	−	0.340942i	−0.830955	+	0.556340i	$0.812205\pi$
$198$	−0.966970	−	8.59902i	−0.0687195	−	0.611106i
$199$	−5.22232	−	3.01511i	−0.370201	−	0.213735i	0.303345	−	0.952881i	$-0.401896\pi$
$199$	−5.22232	−	3.01511i	−0.370201	−	0.213735i	−0.673546	+	0.739145i	$0.735230\pi$
$200$	−16.3269	+	16.3269i	−1.15449	+	1.15449i
$201$	−9.15568	+	2.45326i	−0.645792	+	0.173039i
$202$	−3.65011	−	13.6224i	−0.256821	−	0.958469i
$203$	0.750221	−	0.750221i	0.0526552	−	0.0526552i
$204$	22.7283	+	13.1222i	1.59130	+	0.918739i
$205$	6.91887	+	11.9838i	0.483235	+	0.836987i
$206$	13.1170	−	48.9535i	0.913907	−	3.41075i
$207$		−	3.40953i		−	0.236979i
$208$	−18.6404	+	28.7108i	−1.29248	+	1.99074i
$209$	15.8702	+	6.92822i	1.09776	+	0.479235i
$210$	−1.52169	+	5.67903i	−0.105007	+	0.391890i
$211$	14.6977	−	8.48570i	1.01183	−	0.584180i	0.100102	−	0.994977i	$-0.468083\pi$
$211$	14.6977	−	8.48570i	1.01183	−	0.584180i	0.911727	+	0.410797i	$0.134750\pi$
$212$	−6.50412	−	3.75515i	−0.446705	−	0.257905i
$213$	−8.66263	−	8.66263i	−0.593554	−	0.593554i
$214$	17.0799	−	4.57654i	1.16756	−	0.312846i
$215$	12.6677	−	3.39430i	0.863930	−	0.231489i
$216$	−5.17874	−	5.17874i	−0.352369	−	0.352369i
$217$	9.54422	+	5.51036i	0.647904	+	0.374068i
$218$	−14.2712	+	8.23947i	−0.966567	+	0.558047i
$219$	−0.776286	+	2.89714i	−0.0524566	+	0.195771i
$220$	19.8596	+	8.66985i	1.33894	+	0.584521i
$221$	−19.6577	−	1.02800i	−1.32232	−	0.0691508i
$222$		−	7.47004i		−	0.501356i
$223$	6.26475	−	23.3804i	0.419519	−	1.56567i	−0.356090	−	0.934452i	$-0.615890\pi$
$223$	6.26475	−	23.3804i	0.419519	−	1.56567i	0.775609	−	0.631214i	$-0.217443\pi$
$224$	−8.39154	−	14.5346i	−0.560683	−	0.971132i
$225$	2.73030	+	1.57634i	0.182020	+	0.105089i
$226$	−1.83687	+	1.83687i	−0.122187	+	0.122187i
$227$	1.80089	+	6.72102i	0.119529	+	0.446090i	0.999586	−	0.0287794i	$-0.00916202\pi$
$227$	1.80089	+	6.72102i	0.119529	+	0.446090i	−0.880056	+	0.474869i	$0.842495\pi$
$228$	24.2433	−	6.49597i	1.60555	−	0.430206i
$229$	−9.22717	+	9.22717i	−0.609749	+	0.609749i	−0.942880	−	0.333132i	$-0.891895\pi$
$229$	−9.22717	+	9.22717i	−0.609749	+	0.609749i	0.333132	+	0.942880i	$0.391895\pi$
$230$	10.4707	+	6.04528i	0.690420	+	0.398614i
$231$	−5.46444	+	0.614483i	−0.359534	+	0.0404300i
$232$	−4.52699	−	1.21300i	−0.297211	−	0.0796375i
$233$	−23.5216			−1.54095			−0.770474	−	0.637471i	$-0.779980\pi$
$233$	−23.5216			−1.54095			−0.770474	+	0.637471i	$0.779980\pi$
$234$	8.94695	+	2.90593i	0.584880	+	0.189966i
$235$	8.24490			0.537838
$236$	−13.4338	+	50.1356i	−0.874466	+	3.26355i
$237$	−2.65660	+	1.53379i	−0.172565	+	0.0996305i
$238$	11.8082	−	20.4524i	0.765411	−	1.32573i
$239$	−0.178037	+	0.178037i	−0.0115163	+	0.0115163i	−0.712841	−	0.701325i	$-0.752592\pi$
$239$	−0.178037	+	0.178037i	−0.0115163	+	0.0115163i	0.701325	+	0.712841i	$0.252592\pi$
$240$	12.4642	−	3.33978i	0.804563	−	0.215582i
$241$	−16.2126	+	4.34416i	−1.04435	+	0.279832i	−0.739914	−	0.672701i	$-0.765134\pi$
$241$	−16.2126	+	4.34416i	−1.04435	+	0.279832i	−0.304434	+	0.952533i	$0.598467\pi$
$242$	−1.08567	+	28.6789i	−0.0697894	+	1.84355i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.0307179	−	0.0532050i	−0.00196651	−	0.00340610i
$245$	−5.58107	−	1.49544i	−0.356562	−	0.0955404i
$246$			26.5629i			1.69359i
$247$	−13.9883	+	12.5980i	−0.890056	+	0.801591i
$248$		−	48.6823i		−	3.09133i
$249$	−1.53071	−	0.410153i	−0.0970049	−	0.0259924i
$250$	−25.0371	+	14.4551i	−1.58348	+	0.914224i
$251$	−20.5509	−	11.8651i	−1.29716	−	0.748917i	−0.317249	−	0.948342i	$-0.602759\pi$
$251$	−20.5509	−	11.8651i	−1.29716	−	0.748917i	−0.979913	+	0.199425i	$0.936092\pi$
$252$	−5.63568	+	5.63568i	−0.355015	+	0.355015i
$253$	−1.68784	+	11.1815i	−0.106113	+	0.702972i
$254$	−8.90474	−	33.2329i	−0.558733	−	2.08522i
$255$	5.24698	+	5.24698i	0.328579	+	0.328579i
$256$	8.57047	−	14.8445i	0.535654	−	0.927780i
$257$	−2.95376	+	1.70536i	−0.184251	+	0.106377i	−0.589288	−	0.807923i	$-0.700592\pi$
$257$	−2.95376	+	1.70536i	−0.184251	+	0.106377i	0.405038	+	0.914300i	$0.367258\pi$
$258$	24.3169	+	6.51569i	1.51390	+	0.405649i
$259$	−4.74701			−0.294965
$260$	−17.5047	+	15.7649i	−1.08560	+	0.977697i
$261$			0.639920i			0.0396101i
$262$	−2.04583	+	7.63513i	−0.126392	+	0.471700i
$263$	18.0171	−	10.4022i	1.11098	−	0.641425i	0.171897	−	0.985115i	$-0.445010\pi$
$263$	18.0171	−	10.4022i	1.11098	−	0.641425i	0.939083	+	0.343690i	$0.111677\pi$
$264$	14.4199	+	19.5472i	0.887483	+	1.20305i
$265$	−1.50152	−	1.50152i	−0.0922375	−	0.0922375i
$266$	−5.84548	−	21.8156i	−0.358409	−	1.33760i
$267$	−2.32708	−	8.68479i	−0.142415	−	0.531500i
$268$	32.2192	−	32.2192i	1.96810	−	1.96810i
$269$	−8.24353	+	14.2782i	−0.502617	+	0.870558i	0.497378	+	0.867534i	$0.334296\pi$
$269$	−8.24353	+	14.2782i	−0.502617	+	0.870558i	−0.999995	+	0.00302452i	$0.999037\pi$
$270$	−1.77305	−	3.07102i	−0.107905	−	0.186896i
$271$	2.10359	−	7.85071i	0.127784	−	0.476897i	−0.872139	−	0.489257i	$-0.837268\pi$
$271$	2.10359	−	7.85071i	0.127784	−	0.476897i	0.999924	+	0.0123605i	$0.00393457\pi$
$272$	−51.8328			−3.14282
$273$	1.84664	−	5.68554i	0.111764	−	0.344105i
$274$			50.3256i			3.04028i
$275$	−8.17361	−	6.52116i	−0.492887	−	0.393241i
$276$	8.19498	+	14.1941i	0.493280	+	0.854386i
$277$	2.71102	−	4.69562i	0.162889	−	0.282133i	−0.773014	−	0.634388i	$-0.781252\pi$
$277$	2.71102	−	4.69562i	0.162889	−	0.282133i	0.935904	+	0.352256i	$0.114585\pi$
$278$	27.3936	+	27.3936i	1.64296	+	1.64296i
$279$	−6.42060	+	1.72039i	−0.384391	+	0.102997i
$280$	−4.27154	−	15.9416i	−0.255274	−	0.952694i
$281$	−15.5601	−	15.5601i	−0.928236	−	0.928236i	0.0693561	−	0.997592i	$-0.477906\pi$
$281$	−15.5601	−	15.5601i	−0.928236	−	0.928236i	−0.997592	+	0.0693561i	$0.977906\pi$
$282$	13.7065	+	7.91344i	0.816209	+	0.471239i
$283$	5.18525	+	8.98112i	0.308231	+	0.533872i	0.977976	−	0.208719i	$-0.0669296\pi$
$283$	5.18525	+	8.98112i	0.308231	+	0.533872i	−0.669744	+	0.742592i	$0.733596\pi$
$284$	56.8843	+	15.2421i	3.37546	+	0.904452i
$285$	7.09636			0.420352
$286$	−27.9027	−	13.9590i	−1.64992	−	0.825411i
$287$	16.8800			0.996395
$288$	9.77771	+	2.61993i	0.576157	+	0.154381i
$289$	−6.40312	−	11.0905i	−0.376654	−	0.652385i
$290$	−1.96521	−	1.13461i	−0.115401	−	0.0666268i
$291$	7.91525	+	7.91525i	0.464000	+	0.464000i
$292$	−3.73169	−	13.9268i	−0.218381	−	0.815007i
$293$	−20.7879	+	5.57010i	−1.21444	+	0.325409i	−0.808504	−	0.588491i	$-0.799722\pi$
$293$	−20.7879	+	5.57010i	−1.21444	+	0.325409i	−0.405939	+	0.913900i	$0.633055\pi$
$294$	−7.84277	−	7.84277i	−0.457399	−	0.457399i
$295$	−7.33770	+	12.7093i	−0.427218	+	0.739963i
$296$	10.4846	+	18.1598i	0.609404	+	1.05552i
$297$	2.06845	−	2.59259i	0.120024	−	0.150437i
$298$			5.68049i			0.329062i
$299$	−10.3107	−	6.69422i	−0.596285	−	0.387136i
$300$	−15.1553			−0.874989
$301$	4.14054	−	15.4527i	0.238657	−	0.890680i
$302$	27.6378	+	47.8701i	1.59038	+	2.75461i
$303$	2.70271	−	4.68123i	0.155266	−	0.268929i
$304$	−35.0510	+	35.0510i	−2.01031	+	2.01031i
$305$	−0.00449578	−	0.0167785i	−0.000257428	−	0.000960733i
$306$	3.68664	+	13.7587i	0.210751	+	0.786535i
$307$	22.6181	+	22.6181i	1.29088	+	1.29088i	0.934241	+	0.356643i	$0.116079\pi$
$307$	22.6181	+	22.6181i	1.29088	+	1.29088i	0.356643	+	0.934241i	$0.383921\pi$
$308$	21.2719	−	15.6922i	1.21208	−	0.894146i
$309$	16.8224	−	9.71244i	0.956995	−	0.552521i
$310$	6.10071	−	22.7682i	0.346497	−	1.29314i
$311$		−	32.0604i		−	1.81798i	−0.416820	−	0.908989i	$-0.636856\pi$
$311$		−	32.0604i		−	1.81798i	0.416820	−	0.908989i	$-0.363144\pi$
$312$	−25.8289	+	5.49313i	−1.46227	+	0.310987i
$313$	−23.4905			−1.32776			−0.663880	−	0.747839i	$-0.731091\pi$
$313$	−23.4905			−1.32776			−0.663880	+	0.747839i	$0.731091\pi$
$314$	−27.0680	−	7.25286i	−1.52754	−	0.409303i
$315$	−1.95155	+	1.12673i	−0.109957	+	0.0634839i
$316$	7.37309	−	12.7706i	0.414769	−	0.718401i
$317$	18.8484	+	18.8484i	1.05863	+	1.05863i	0.998171	+	0.0604588i	$0.0192564\pi$
$317$	18.8484	+	18.8484i	1.05863	+	1.05863i	0.0604588	+	0.998171i	$0.480744\pi$
$318$	−1.05500	−	3.93731i	−0.0591614	−	0.220793i
$319$	0.316783	−	2.09860i	0.0177365	−	0.117499i
$320$	−7.13338	+	7.13338i	−0.398768	+	0.398768i
$321$	5.86935	+	3.38867i	0.327595	+	0.189137i
$322$	12.7727	−	7.37435i	0.711797	−	0.410956i
$323$	−27.5335	−	7.37759i	−1.53201	−	0.410500i
$324$		−	4.80710i		−	0.267061i
$325$	10.1276	−	5.16172i	0.561780	−	0.286321i
$326$		−	41.9971i		−	2.32600i
$327$	−6.10087	−	1.63472i	−0.337379	−	0.0904004i
$328$	−37.2824	−	64.5750i	−2.05858	−	3.56556i
$329$	5.02878	−	8.71010i	0.277245	−	0.480203i
$330$	4.29442	+	10.9491i	0.236400	+	0.602726i
$331$	−17.1632	+	4.59887i	−0.943376	+	0.252777i	−0.697549	−	0.716537i	$-0.745726\pi$
$331$	−17.1632	+	4.59887i	−0.943376	+	0.252777i	−0.245827	+	0.969314i	$0.579060\pi$
$332$	7.35829	−	1.97165i	0.403838	−	0.108208i
$333$	2.02454	−	2.02454i	0.110944	−	0.110944i
$334$	12.8543	−	22.2643i	0.703355	−	1.21825i
$335$	11.1570	−	6.44151i	0.609573	−	0.351937i
$336$	4.07404	−	15.2045i	0.222257	−	0.829474i
$337$	−17.9628			−0.978495			−0.489247	−	0.872145i	$-0.662729\pi$
$337$	−17.9628			−0.978495			−0.489247	+	0.872145i	$0.662729\pi$
$338$	26.3541	−	21.3509i	1.43347	−	1.16134i
$339$	−0.995662			−0.0540769
$340$	−34.4550	−	9.23218i	−1.86858	−	0.500685i
$341$	21.9078	−	2.46356i	1.18638	−	0.133409i
$342$	11.7971	+	6.81107i	0.637916	+	0.368301i
$343$	−13.1904	+	13.1904i	−0.712216	+	0.712216i
$344$	−68.2600	+	18.2902i	−3.68033	+	0.986142i
$345$	1.19939	+	4.47620i	0.0645732	+	0.240990i
$346$	−0.798487	+	0.798487i	−0.0429269	+	0.0429269i
$347$	16.3710	+	9.45179i	0.878840	+	0.507398i	0.870276	−	0.492565i	$-0.163941\pi$
$347$	16.3710	+	9.45179i	0.878840	+	0.507398i	0.00856421	+	0.999963i	$0.497274\pi$
$348$	−1.53808	−	2.66403i	−0.0824498	−	0.142807i
$349$	−5.34954	+	19.9647i	−0.286354	+	1.06869i	0.661490	+	0.749954i	$0.269924\pi$
$349$	−5.34954	+	19.9647i	−0.286354	+	1.06869i	−0.947844	+	0.318734i	$0.896742\pi$
$350$			13.6376i			0.728963i
$351$	1.63725	+	3.21239i	0.0873898	+	0.171464i
$352$	−30.7688	−	13.4323i	−1.63998	−	0.715944i
$353$	6.42598	−	23.9821i	0.342021	−	1.27644i	−0.554034	−	0.832494i	$-0.686912\pi$
$353$	6.42598	−	23.9821i	0.342021	−	1.27644i	0.896054	−	0.443944i	$-0.146421\pi$
$354$	−24.3967	+	14.0854i	−1.29667	+	0.748633i
$355$	14.4200	+	8.32541i	0.765336	+	0.441867i
$356$	30.5621	+	30.5621i	1.61979	+	1.61979i
$357$	8.74330	−	2.34276i	0.462745	−	0.123992i
$358$	18.1872	−	4.87325i	0.961223	−	0.257559i
$359$	5.72888	+	5.72888i	0.302359	+	0.302359i	0.841936	−	0.539577i	$-0.181416\pi$
$359$	5.72888	+	5.72888i	0.302359	+	0.302359i	−0.539577	+	0.841936i	$0.681416\pi$
$360$	8.62067	+	4.97715i	0.454349	+	0.262319i
$361$	−7.15354	+	4.13010i	−0.376502	+	0.217374i
$362$	−6.13716	+	22.9042i	−0.322562	+	1.20382i
$363$	−8.06685	+	7.47837i	−0.423400	+	0.392513i
$364$	5.97780	+	28.1078i	0.313322	+	1.47325i
$365$		−	4.07659i		−	0.213378i
$366$	0.00863009	−	0.0322079i	0.000451102	−	0.00168354i
$367$	−1.45193	−	2.51482i	−0.0757902	−	0.131272i	0.825639	−	0.564198i	$-0.190815\pi$
$367$	−1.45193	−	2.51482i	−0.0757902	−	0.131272i	−0.901430	+	0.432926i	$0.857481\pi$
$368$	−28.0334	−	16.1851i	−1.46134	−	0.843706i
$369$	−7.19912	+	7.19912i	−0.374771	+	0.374771i
$370$	2.62779	+	9.80703i	0.136612	+	0.509843i
$371$	−2.50205	+	0.670423i	−0.129900	+	0.0348066i
$372$	22.5944	−	22.5944i	1.17146	−	1.17146i
$373$	1.62956	+	0.940827i	0.0843754	+	0.0487142i	0.541594	−	0.840640i	$-0.317821\pi$
$373$	1.62956	+	0.940827i	0.0843754	+	0.0487142i	−0.457219	+	0.889354i	$0.651154\pi$
$374$	−5.27918	−	46.9464i	−0.272980	−	2.42754i
$375$	−10.7032	−	2.86792i	−0.552713	−	0.148099i
$376$	−44.4277			−2.29118
$377$	1.93518	+	1.25641i	0.0996667	+	0.0647084i
$378$	−4.32573			−0.222491
$379$	−2.87501	+	10.7297i	−0.147679	+	0.551147i	0.851942	+	0.523636i	$0.175425\pi$
$379$	−2.87501	+	10.7297i	−0.147679	+	0.551147i	−0.999622	+	0.0275109i	$0.991242\pi$
$380$	−29.5427	+	17.0565i	−1.51551	+	0.874978i
$381$	6.59346	−	11.4202i	0.337793	−	0.585075i
$382$	17.6077	−	17.6077i	0.900887	−	0.900887i
$383$	−22.2044	+	5.94965i	−1.13459	+	0.304013i	−0.776775	−	0.629779i	$-0.783146\pi$
$383$	−22.2044	+	5.94965i	−1.13459	+	0.304013i	−0.357817	+	0.933792i	$0.616479\pi$
$384$	0.850144	−	0.227796i	0.0433838	−	0.0116246i
$385$	6.95783	−	2.72899i	0.354604	−	0.139082i
$386$	−27.5208	+	47.6675i	−1.40077	+	2.42621i
$387$	4.82451	+	8.35629i	0.245243	+	0.424774i
$388$	−51.9765	−	13.9271i	−2.63871	−	0.707039i
$389$		−	20.5510i		−	1.04197i	−0.853564	−	0.520987i	$-0.825564\pi$
$389$		−	20.5510i		−	1.04197i	0.853564	−	0.520987i	$-0.174436\pi$
$390$	−12.7682	−	0.667716i	−0.646545	−	0.0338111i
$391$		−	18.6144i		−	0.941369i
$392$	30.0737	+	8.05821i	1.51895	+	0.407001i
$393$	−2.62375	+	1.51482i	−0.132351	+	0.0764126i
$394$	41.7762	+	24.1195i	2.10466	+	1.21512i
$395$	2.94817	−	2.94817i	0.148338	−	0.148338i
$396$	−2.37969	+	15.7648i	−0.119584	+	0.792209i
$397$	−0.592709	−	2.21202i	−0.0297472	−	0.111018i	0.949456	−	0.313900i	$-0.101636\pi$
$397$	−0.592709	−	2.21202i	−0.0297472	−	0.111018i	−0.979203	+	0.202882i	$0.934969\pi$
$398$	11.1250	+	11.1250i	0.557645	+	0.557645i
$399$	4.32825	−	7.49675i	0.216684	−	0.375307i
$400$	25.9216	−	14.9658i	1.29608	−	0.748291i
$401$	−12.0017	−	3.21585i	−0.599338	−	0.160592i	−0.0536205	−	0.998561i	$-0.517076\pi$
$401$	−12.0017	−	3.21585i	−0.599338	−	0.160592i	−0.545717	+	0.837969i	$0.683743\pi$
$402$	24.7302			1.23343
$403$	−7.40348	+	22.7943i	−0.368793	+	1.13546i
$404$			25.9844i			1.29277i
$405$	0.351777	−	1.31285i	0.0174799	−	0.0652360i
$406$	−2.39726	+	1.38406i	−0.118974	+	0.0686898i
$407$	−7.64165	+	5.63721i	−0.378782	+	0.279426i
$408$	−28.2734	−	28.2734i	−1.39974	−	1.39974i
$409$	8.20444	+	30.6194i	0.405684	+	1.51403i	0.802792	+	0.596260i	$0.203347\pi$
$409$	8.20444	+	30.6194i	0.405684	+	1.51403i	−0.397108	+	0.917772i	$0.629986\pi$
$410$	−9.34421	−	34.8731i	−0.461478	−	1.72226i
$411$	−13.6393	+	13.6393i	−0.672778	+	0.672778i
$412$	−46.6887	+	80.8672i	−2.30019	+	3.98404i
$413$	8.95091	+	15.5034i	0.440446	+	0.762874i
$414$	−2.30235	+	8.59250i	−0.113154	+	0.422298i
$415$	2.15387			0.105730
$416$	27.1203	−	24.4248i	1.32968	−	1.19752i
$417$			14.8485i			0.727136i
$418$	−35.3166	−	28.1767i	−1.72739	−	1.37817i
$419$	11.8108	+	20.4570i	0.576997	+	0.999388i	0.995822	+	0.0913206i	$0.0291088\pi$
$419$	11.8108	+	20.4570i	0.576997	+	0.999388i	−0.418825	+	0.908067i	$0.637558\pi$
$420$	5.41630	−	9.38130i	0.264288	−	0.457761i
$421$	19.0951	+	19.0951i	0.930638	+	0.930638i	0.997746	−	0.0671078i	$-0.0213772\pi$
$421$	19.0951	+	19.0951i	0.930638	+	0.930638i	−0.0671078	+	0.997746i	$0.521377\pi$
$422$	−42.7703	+	11.4603i	−2.08203	+	0.557878i
$423$	1.57004	+	5.85947i	0.0763379	+	0.284897i
$424$	8.09094	+	8.09094i	0.392931	+	0.392931i
$425$	14.9061	+	8.60605i	0.723053	+	0.417455i
$426$	15.9814	+	27.6807i	0.774304	+	1.34113i
$427$	−0.0204673	−	0.00548419i	−0.000990481	−	0.000265399i
$428$	−32.5794			−1.57478
$429$	−3.77906	−	11.3454i	−0.182455	−	0.547762i
$430$	−34.2165			−1.65006
$431$	14.5108	+	3.88814i	0.698958	+	0.187285i	0.590764	−	0.806844i	$-0.298826\pi$
$431$	14.5108	+	3.88814i	0.698958	+	0.187285i	0.108194	+	0.994130i	$0.465493\pi$
$432$	4.74702	+	8.22207i	0.228391	+	0.395585i
$433$	−0.355494	−	0.205245i	−0.0170840	−	0.00986344i	0.491434	−	0.870915i	$-0.336473\pi$
$433$	−0.355494	−	0.205245i	−0.0170840	−	0.00986344i	−0.508518	+	0.861052i	$0.669806\pi$
$434$	−20.3318	−	20.3318i	−0.975958	−	0.975958i
$435$	−0.225109	−	0.840119i	−0.0107932	−	0.0402806i
$436$	29.3275	−	7.85829i	1.40453	−	0.376344i
$437$	−12.5876	−	12.5876i	−0.602148	−	0.602148i
$438$	3.91270	−	6.77700i	0.186956	−	0.323818i
$439$	−1.06660	−	1.84741i	−0.0509062	−	0.0881721i	0.839449	−	0.543438i	$-0.182878\pi$
$439$	−1.06660	−	1.84741i	−0.0509062	−	0.0881721i	−0.890356	+	0.455266i	$0.849544\pi$
$440$	−25.8074	−	20.5900i	−1.23032	−	0.981588i
$441$		−	4.25112i		−	0.202434i
$442$	48.8460	+	15.8649i	2.32337	+	0.754619i
$443$	6.81953			0.324006			0.162003	−	0.986790i	$-0.448205\pi$
$443$	6.81953			0.324006			0.162003	+	0.986790i	$0.448205\pi$
$444$	−3.56223	+	13.2944i	−0.169056	+	0.630925i
$445$	6.11021	+	10.5832i	0.289652	+	0.501692i
$446$	−31.5761	+	54.6915i	−1.49517	+	2.58972i
$447$	−1.53953	+	1.53953i	−0.0728175	+	0.0728175i
$448$	3.18503	+	11.8867i	0.150479	+	0.561594i
$449$	−6.83466	−	25.5073i	−0.322548	−	1.20376i	−0.916754	−	0.399452i	$-0.869200\pi$
$449$	−6.83466	−	25.5073i	−0.322548	−	1.20376i	0.594206	−	0.804313i	$-0.297466\pi$
$450$	−5.81629	−	5.81629i	−0.274183	−	0.274183i
$451$	27.1731	−	20.0455i	1.27953	−	0.943905i
$452$	4.14501	−	2.39312i	0.194965	−	0.112563i
$453$	−5.48338	+	20.4643i	−0.257632	+	0.961495i
$454$		−	18.1540i		−	0.852010i
$455$	−0.424315	+	8.11386i	−0.0198922	+	0.380384i
$456$	−38.2388			−1.79069
$457$	7.56462	+	2.02693i	0.353858	+	0.0948160i	0.431369	−	0.902176i	$-0.358031\pi$
$457$	7.56462	+	2.02693i	0.353858	+	0.0948160i	−0.0775112	+	0.996991i	$0.524697\pi$
$458$	29.4846	−	17.0229i	1.37773	−	0.795430i
$459$	−2.72976	+	4.72807i	−0.127414	+	0.220688i
$460$	−15.7519	−	15.7519i	−0.734438	−	0.734438i
$461$	−1.25798	−	4.69484i	−0.0585899	−	0.218660i	0.930424	−	0.366486i	$-0.119439\pi$
$461$	−1.25798	−	4.69484i	−0.0585899	−	0.218660i	−0.989013	+	0.147826i	$0.952773\pi$
$462$	14.1861	+	2.14139i	0.659997	+	0.0996264i
$463$	15.8516	−	15.8516i	0.736687	−	0.736687i	−0.235248	−	0.971935i	$-0.575590\pi$
$463$	15.8516	−	15.8516i	0.736687	−	0.736687i	0.971935	+	0.235248i	$0.0755903\pi$
$464$	5.26147	+	3.03771i	0.244258	+	0.141022i
$465$	7.82408	−	4.51724i	0.362833	−	0.209482i
$466$	59.2776	+	15.8834i	2.74598	+	0.735784i
$467$			4.83455i			0.223716i	0.993724	+	0.111858i	$0.0356802\pi$
$467$			4.83455i			0.223716i	−0.993724	+	0.111858i	$0.964320\pi$
$468$	−14.5371	−	9.43819i	−0.671978	−	0.436280i
$469$		−	15.7154i		−	0.725669i
$470$	−20.7783	−	5.56753i	−0.958432	−	0.256811i
$471$	−5.37034	−	9.30170i	−0.247452	−	0.428600i
$472$	39.5393	−	68.4840i	1.81994	−	3.15223i
$473$	−11.6852	−	29.7925i	−0.537285	−	1.36986i
$474$	7.73074	−	2.07145i	0.355085	−	0.0951447i
$475$	15.8997	−	4.26031i	0.729527	−	0.195476i
$476$	−30.7681	+	30.7681i	−1.41025	+	1.41025i
$477$	0.781168	−	1.35302i	0.0357672	−	0.0619507i
$478$	0.568901	−	0.328455i	0.0260209	−	0.0150232i
$479$	6.96084	−	25.9782i	0.318049	−	1.18697i	−0.603069	−	0.797689i	$-0.706055\pi$
$479$	6.96084	−	25.9782i	0.318049	−	1.18697i	0.921117	−	0.389285i	$-0.127278\pi$
$480$	−13.7583			−0.627977
$481$	−2.14744	−	10.0974i	−0.0979150	−	0.460400i
$482$	43.7916			1.99465
$483$	5.46030	+	1.46308i	0.248452	+	0.0665725i
$484$	15.6082	−	50.5221i	0.709465	−	2.29646i
$485$	−13.1759	−	7.60712i	−0.598288	−	0.345422i
$486$	1.84487	−	1.84487i	0.0836851	−	0.0836851i
$487$	23.1126	−	6.19300i	1.04733	−	0.280632i	0.306183	−	0.951973i	$-0.400948\pi$
$487$	23.1126	−	6.19300i	1.04733	−	0.280632i	0.741149	+	0.671341i	$0.234281\pi$
$488$	0.0242256	+	0.0904110i	0.00109664	+	0.00409271i
$489$	11.3821	−	11.3821i	0.514717	−	0.514717i
$490$	13.0553	+	7.53746i	0.589777	+	0.340508i
$491$	−7.95974	−	13.7867i	−0.359218	−	0.622184i	0.628612	−	0.777719i	$-0.283623\pi$
$491$	−7.95974	−	13.7867i	−0.359218	−	0.622184i	−0.987830	+	0.155535i	$0.950290\pi$
$492$	12.6670	−	47.2739i	0.571073	−	2.13127i
$493$			3.49365i			0.157346i
$494$	43.7596	−	22.3028i	1.96884	−	1.00345i
$495$	−1.80355	+	4.13131i	−0.0810635	+	0.185689i
$496$	−16.3335	+	60.9574i	−0.733395	+	2.73707i
$497$	17.5903	−	10.1558i	0.789034	−	0.455549i
$498$	3.58064	+	2.06729i	0.160453	+	0.0926373i
$499$	−4.39259	−	4.39259i	−0.196639	−	0.196639i	0.601918	−	0.798558i	$-0.294403\pi$
$499$	−4.39259	−	4.39259i	−0.196639	−	0.196639i	−0.798558	+	0.601918i	$0.794403\pi$
$500$	51.4516	−	13.7864i	2.30098	−	0.616547i
$501$	9.51789	−	2.55031i	0.425228	−	0.113939i
$502$	43.7791	+	43.7791i	1.95396	+	1.95396i
$503$	−8.54618	−	4.93414i	−0.381055	−	0.220002i	0.297222	−	0.954808i	$-0.403940\pi$
$503$	−8.54618	−	4.93414i	−0.381055	−	0.220002i	−0.678277	+	0.734806i	$0.737273\pi$
$504$	10.5159	−	6.07138i	0.468417	−	0.270441i
$505$	−1.90150	+	7.09649i	−0.0846156	+	0.315790i
$506$	11.8041	−	27.0391i	0.524756	−	1.20203i
$507$	12.9291	+	1.35596i	0.574201	+	0.0602205i
$508$			63.3909i			2.81252i
$509$	9.72909	−	36.3094i	0.431234	−	1.60939i	−0.318687	−	0.947860i	$-0.603242\pi$
$509$	9.72909	−	36.3094i	0.431234	−	1.60939i	0.749921	−	0.661528i	$-0.230092\pi$
$510$	−9.68001	−	16.7663i	−0.428638	−	0.742423i
$511$	−4.30660	−	2.48642i	−0.190513	−	0.109993i
$512$	−30.3781	+	30.3781i	−1.34254	+	1.34254i
$513$	1.35133	+	5.04322i	0.0596626	+	0.222664i
$514$	8.59548	−	2.30315i	0.379130	−	0.101588i
$515$	−18.6687	+	18.6687i	−0.822642	+	0.822642i
$516$	−40.1696	−	23.1919i	−1.76837	−	1.02097i
$517$	−2.24826	−	19.9932i	−0.0988782	−	0.879299i
$518$	11.9631	+	3.20551i	0.525630	+	0.140842i
$519$	−0.432815			−0.0189985
$520$	31.9770	−	16.2976i	1.40229	−	0.714699i
$521$	5.86126			0.256786			0.128393	−	0.991723i	$-0.459018\pi$
$521$	5.86126			0.256786			0.128393	+	0.991723i	$0.459018\pi$
$522$	0.432119	−	1.61269i	0.0189133	−	0.0705855i
$523$	6.64905	−	3.83883i	0.290743	−	0.167860i	−0.347534	−	0.937667i	$-0.612981\pi$
$523$	6.64905	−	3.83883i	0.290743	−	0.167860i	0.638277	+	0.769807i	$0.279648\pi$
$524$	7.28190	−	12.6126i	0.318111	−	0.550985i
$525$	−3.69609	+	3.69609i	−0.161311	+	0.161311i
$526$	−52.4298	+	14.0485i	−2.28605	+	0.612545i
$527$	−35.0533	+	9.39251i	−1.52695	+	0.409144i
$528$	−11.4975	−	29.3140i	−0.500364	−	1.27573i
$529$	−5.68756	+	9.85114i	−0.247285	+	0.428310i
$530$	2.77011	+	4.79797i	0.120326	+	0.208410i
$531$	−10.4295	−	2.79457i	−0.452601	−	0.121274i
$532$			41.6127i			1.80414i
$533$	7.63615	+	35.9054i	0.330758	+	1.55524i
$534$			23.4583i			1.01514i
$535$	−8.89763	−	2.38411i	−0.384678	−	0.103074i
$536$	−60.1197	+	34.7101i	−2.59678	+	1.49925i
$537$	6.24988	+	3.60837i	0.269702	+	0.155713i
$538$	30.4165	−	30.4165i	1.31135	−	1.31135i
$539$	−2.10445	+	13.9414i	−0.0906452	+	0.600500i
$540$	1.69103	+	6.31100i	0.0727702	+	0.271582i
$541$	−1.85907	−	1.85907i	−0.0799277	−	0.0799277i	0.666013	−	0.745940i	$-0.268000\pi$
$541$	−1.85907	−	1.85907i	−0.0799277	−	0.0799277i	−0.745940	+	0.666013i	$0.768000\pi$
$542$	−10.6027	+	18.3644i	−0.455425	+	0.788819i
$543$	−7.87084	+	4.54423i	−0.337770	+	0.195012i
$544$	53.3815	+	14.3035i	2.28871	+	0.613259i
$545$	8.58458			0.367723
$546$	−8.49307	+	13.0814i	−0.363470	+	0.559832i
$547$		−	2.32182i		−	0.0992737i	−0.998767	−	0.0496368i	$-0.984194\pi$
$547$		−	2.32182i		−	0.0992737i	0.998767	−	0.0496368i	$-0.0158064\pi$
$548$	23.9987	−	89.5643i	1.02517	−	3.82600i
$549$	0.0110680	−	0.00639011i	0.000472370	−	0.000272723i
$550$	16.1951	+	21.9536i	0.690561	+	0.936106i
$551$	2.36252	+	2.36252i	0.100647	+	0.100647i
$552$	−6.46294	−	24.1200i	−0.275081	−	1.02662i
$553$	−1.31635	−	4.91268i	−0.0559768	−	0.208908i
$554$	−10.0030	+	10.0030i	−0.424985	+	0.424985i
$555$	−1.94573	+	3.37010i	−0.0825917	+	0.143053i
$556$	−35.6892	−	61.8155i	−1.51356	−	2.62156i
$557$	−1.62681	+	6.07133i	−0.0689300	+	0.257250i	−0.991789	−	0.127889i	$-0.959180\pi$
$557$	−1.62681	+	6.07133i	−0.0689300	+	0.257250i	0.922858	+	0.385139i	$0.125847\pi$
$558$	17.3426			0.734169
$559$	34.7425	+	1.81686i	1.46945	+	0.0768452i
$560$			21.3944i			0.904078i
$561$	11.2927	−	14.1543i	0.476779	−	0.597594i
$562$	28.7063	+	49.7208i	1.21090	+	2.09735i
$563$	20.6813	−	35.8210i	0.871611	−	1.50968i	0.0112820	−	0.999936i	$-0.496409\pi$
$563$	20.6813	−	35.8210i	0.871611	−	1.50968i	0.860329	−	0.509739i	$-0.170258\pi$
$564$	−20.6197	−	20.6197i	−0.868247	−	0.868247i
$565$	1.30715	−	0.350251i	0.0549924	−	0.0147352i
$566$	−7.00289	−	26.1352i	−0.294354	−	1.09854i
$567$	−1.17237	−	1.17237i	−0.0492347	−	0.0492347i
$568$	−77.7025	−	44.8616i	−3.26032	−	1.88235i
$569$	14.3615	+	24.8749i	0.602066	+	1.04281i	0.992508	+	0.122181i	$0.0389890\pi$
$569$	14.3615	+	24.8749i	0.602066	+	1.04281i	−0.390442	+	0.920628i	$0.627678\pi$
$570$	−17.8838	−	4.79196i	−0.749071	−	0.200713i
$571$	13.9719			0.584704			0.292352	−	0.956311i	$-0.405562\pi$
$571$	13.9719			0.584704			0.292352	+	0.956311i	$0.405562\pi$
$572$	43.0018	+	38.1487i	1.79800	+	1.59508i
$573$	9.54412			0.398711
$574$	−42.5400	−	11.3986i	−1.77558	−	0.475766i
$575$	5.37458	+	9.30904i	0.224135	+	0.388214i
$576$	−6.42791	−	3.71116i	−0.267830	−	0.154632i
$577$	−21.9466	−	21.9466i	−0.913649	−	0.913649i	0.0829085	−	0.996557i	$-0.473579\pi$
$577$	−21.9466	−	21.9466i	−0.913649	−	0.913649i	−0.996557	+	0.0829085i	$0.973579\pi$
$578$	8.64767	+	32.2736i	0.359696	+	1.34240i
$579$	−20.3776	+	5.46017i	−0.846866	+	0.226917i
$580$	2.95641	+	2.95641i	0.122758	+	0.122758i
$581$	1.31370	−	2.27540i	0.0545016	−	0.0943996i
$582$	−14.6026	−	25.2925i	−0.605298	−	1.04841i
$583$	−3.23161	+	4.05049i	−0.133840	+	0.167754i
$584$			21.9667i			0.908989i
$585$	−3.27950	−	3.64143i	−0.135591	−	0.150555i
$586$	56.1498			2.31953
$587$	−8.09028	+	30.1933i	−0.333922	+	1.24621i	0.571112	+	0.820872i	$0.306512\pi$
$587$	−8.09028	+	30.1933i	−0.333922	+	1.24621i	−0.905034	+	0.425340i	$0.860154\pi$
$588$	10.2178	+	17.6977i	0.421374	+	0.729841i
$589$	−17.3527	+	30.0557i	−0.715004	+	1.23842i
$590$	27.0742	−	27.0742i	1.11463	−	1.11463i
$591$	4.78535	+	17.8592i	0.196843	+	0.734628i
$592$	−7.03540	−	26.2565i	−0.289153	−	1.07913i
$593$	−7.31362	−	7.31362i	−0.300334	−	0.300334i	0.540810	−	0.841145i	$-0.318118\pi$
$593$	−7.31362	−	7.31362i	−0.300334	−	0.300334i	−0.841145	+	0.540810i	$0.818118\pi$
$594$	−6.96348	+	5.13693i	−0.285715	+	0.210771i
$595$	−10.6545	+	6.15138i	−0.436792	+	0.252182i
$596$	2.70884	−	10.1095i	0.110959	−	0.414103i
$597$			6.03022i			0.246800i
$598$	21.4641	+	23.8329i	0.877732	+	0.974599i
$599$	16.0666			0.656461			0.328231	−	0.944598i	$-0.393548\pi$
$599$	16.0666			0.656461			0.328231	+	0.944598i	$0.393548\pi$
$600$	22.3030	+	5.97607i	0.910516	+	0.243972i
$601$	−14.1583	+	8.17432i	−0.577531	+	0.333438i	−0.760151	−	0.649746i	$-0.774875\pi$
$601$	−14.1583	+	8.17432i	−0.577531	+	0.333438i	0.182621	+	0.983183i	$0.441542\pi$
$602$	−20.8695	+	36.1470i	−0.850578	+	1.47324i
$603$	6.70242	+	6.70242i	0.272944	+	0.272944i
$604$	−26.3592	−	98.3738i	−1.07254	−	4.00277i
$605$	7.95983	−	12.6557i	0.323613	−	0.514527i
$606$	−9.97229	+	9.97229i	−0.405097	+	0.405097i
$607$	−38.6839	−	22.3342i	−1.57013	−	0.906515i	−0.996152	−	0.0876455i	$-0.972066\pi$
$607$	−38.6839	−	22.3342i	−1.57013	−	0.906515i	−0.573979	−	0.818870i	$-0.694601\pi$
$608$	45.7708	−	26.4258i	1.85625	−	1.07171i
$609$	−1.02482	−	0.274600i	−0.0415278	−	0.0111273i
$610$			0.0453200i			0.00183495i
$611$	20.8021	+	6.75644i	0.841565	+	0.273336i
$612$		−	26.2444i		−	1.06087i
$613$	30.8700	+	8.27158i	1.24683	+	0.334086i	0.821109	−	0.570771i	$-0.193356\pi$
$613$	30.8700	+	8.27158i	1.24683	+	0.334086i	0.425716	+	0.904857i	$0.360022\pi$
$614$	−41.7275	−	72.2742i	−1.68399	−	2.91675i
$615$	6.91887	−	11.9838i	0.278996	−	0.483235i
$616$	−37.4923	+	14.7052i	−1.51061	+	0.592488i
$617$	40.2381	−	10.7818i	1.61993	−	0.434058i	0.668947	−	0.743310i	$-0.266745\pi$
$617$	40.2381	−	10.7818i	1.61993	−	0.434058i	0.950980	+	0.309252i	$0.100079\pi$
$618$	−48.9535	+	13.1170i	−1.96920	+	0.527645i
$619$	−23.2879	+	23.2879i	−0.936021	+	0.936021i	−0.998073	−	0.0620515i	$-0.980236\pi$
$619$	−23.2879	+	23.2879i	−0.936021	+	0.936021i	0.0620515	+	0.998073i	$0.480236\pi$
$620$	−21.7148	+	37.6112i	−0.872088	+	1.51050i
$621$	−2.95274	+	1.70476i	−0.118489	+	0.0684098i
$622$	−21.6494	+	80.7967i	−0.868062	+	3.23965i
$623$	14.9071			0.597241
$624$	34.1845	+	1.78768i	1.36848	+	0.0715645i
$625$	−0.702801			−0.0281120
$626$	59.1993	+	15.8624i	2.36608	+	0.633989i
$627$	−1.93507	−	17.2081i	−0.0772792	−	0.687224i
$628$	44.7142	+	25.8158i	1.78429	+	1.03016i
$629$	11.0530	−	11.0530i	0.440712	−	0.440712i
$630$	5.67903	−	1.52169i	0.226258	−	0.0606256i
$631$	−7.90829	−	29.5141i	−0.314824	−	1.17494i	−0.924153	−	0.382022i	$-0.875228\pi$
$631$	−7.90829	−	29.5141i	−0.314824	−	1.17494i	0.609329	−	0.792917i	$-0.291439\pi$
$632$	−15.8862	+	15.8862i	−0.631920	+	0.631920i
$633$	−14.6977	−	8.48570i	−0.584180	−	0.337276i
$634$	−34.7728	−	60.2283i	−1.38100	−	2.39197i
$635$	−4.63886	+	17.3124i	−0.184087	+	0.687023i
$636$			7.51031i			0.297803i
$637$	−12.8558	−	8.34658i	−0.509364	−	0.330703i
$638$	−2.21546	+	5.07486i	−0.0877109	+	0.200916i
$639$	−3.17074	+	11.8334i	−0.125433	+	0.468121i
$640$	−1.03598	+	0.598122i	−0.0409506	+	0.0236429i
$641$	−2.85461	−	1.64811i	−0.112750	−	0.0650964i	0.442564	−	0.896737i	$-0.354069\pi$
$641$	−2.85461	−	1.64811i	−0.112750	−	0.0650964i	−0.555315	+	0.831640i	$0.687402\pi$
$642$	−12.5033	−	12.5033i	−0.493467	−	0.493467i
$643$	−19.3151	+	5.17547i	−0.761713	+	0.204100i	−0.618708	−	0.785621i	$-0.712343\pi$
$643$	−19.3151	+	5.17547i	−0.761713	+	0.204100i	−0.143006	+	0.989722i	$0.545677\pi$
$644$	−26.2482	+	7.03319i	−1.03432	+	0.277146i
$645$	−9.27340	−	9.27340i	−0.365140	−	0.365140i
$646$	64.4065	+	37.1851i	2.53404	+	1.46303i
$647$	−5.08836	+	2.93776i	−0.200044	+	0.115495i	−0.596676	−	0.802482i	$-0.703512\pi$
$647$	−5.08836	+	2.93776i	−0.200044	+	0.115495i	0.396632	+	0.917978i	$0.370179\pi$
$648$	−1.89555	+	7.07430i	−0.0744643	+	0.277905i
$649$	32.8198	+	14.3277i	1.28829	+	0.562411i
$650$	−29.0086	+	6.16938i	−1.13781	+	0.241983i
$651$		−	11.0207i		−	0.431936i
$652$	−20.0271	+	74.7421i	−0.784321	+	2.92712i
$653$	20.4294	+	35.3848i	0.799465	+	1.38471i	0.919965	+	0.392001i	$0.128217\pi$
$653$	20.4294	+	35.3848i	0.799465	+	1.38471i	−0.120500	+	0.992713i	$0.538450\pi$
$654$	14.2712	+	8.23947i	0.558047	+	0.322189i
$655$	2.91170	−	2.91170i	0.113770	−	0.113770i
$656$	25.0173	+	93.3660i	0.976763	+	3.64533i
$657$	2.89714	−	0.776286i	0.113028	−	0.0302858i
$658$	−18.5549	+	18.5549i	−0.723345	+	0.723345i
$659$	−29.7560	−	17.1796i	−1.15913	−	0.669224i	−0.208035	−	0.978121i	$-0.566707\pi$
$659$	−29.7560	−	17.1796i	−1.15913	−	0.669224i	−0.951095	+	0.308898i	$0.900040\pi$
$660$	−2.42151	−	21.5339i	−0.0942571	−	0.838205i
$661$	−25.9552	−	6.95468i	−1.00954	−	0.270506i	−0.284104	−	0.958794i	$-0.591696\pi$
$661$	−25.9552	−	6.95468i	−1.00954	−	0.270506i	−0.725438	+	0.688288i	$0.758363\pi$
$662$	46.3592			1.80180
$663$	8.93857	+	17.5381i	0.347145	+	0.681122i
$664$	−11.6062			−0.450407
$665$	−3.04516	+	11.3647i	−0.118086	+	0.440703i
$666$	−6.46924	+	3.73502i	−0.250678	+	0.144729i
$667$	−1.09091	+	1.88952i	−0.0422403	+	0.0731624i
$668$	−33.4939	+	33.4939i	−1.29592	+	1.29592i
$669$	−23.3804	+	6.26475i	−0.903938	+	0.242209i
$670$	−32.4670	+	8.69952i	−1.25431	+	0.336092i
$671$	−0.0394605	+	0.0154771i	−0.00152336	+	0.000597488i
$672$	−8.39154	+	14.5346i	−0.323711	+	0.560683i
$673$	−2.85773	−	4.94974i	−0.110157	−	0.190798i	0.805676	−	0.592356i	$-0.201802\pi$
$673$	−2.85773	−	4.94974i	−0.110157	−	0.190798i	−0.915834	+	0.401558i	$0.868469\pi$
$674$	45.2687	+	12.1297i	1.74369	+	0.467220i
$675$		−	3.15268i		−	0.121347i
$676$	−57.0839	+	25.4308i	−2.19553	+	0.978106i
$677$		−	24.8367i		−	0.954551i	−0.878754	−	0.477276i	$-0.841624\pi$
$677$		−	24.8367i		−	0.954551i	0.878754	−	0.477276i	$-0.158376\pi$
$678$	2.50921	+	0.672340i	0.0963656	+	0.0258211i
$679$	−16.0727	+	9.27957i	−0.616813	+	0.356117i
$680$	47.0646	+	27.1728i	1.80485	+	1.04203i
$681$	4.92013	−	4.92013i	0.188540	−	0.188540i
$682$	−56.8744	−	8.58518i	−2.17783	−	0.328743i
$683$	−5.60653	−	20.9238i	−0.214528	−	0.800629i	−0.986332	−	0.164769i	$-0.947312\pi$
$683$	−5.60653	−	20.9238i	−0.214528	−	0.800629i	0.771804	−	0.635860i	$-0.219354\pi$
$684$	−17.7473	−	17.7473i	−0.678586	−	0.678586i
$685$	13.1084	−	22.7044i	0.500845	−	0.867489i
$686$	42.1488	−	24.3346i	1.60925	−	0.929101i
$687$	12.6046	+	3.37738i	0.480894	+	0.128855i
$688$	91.6081			3.49252
$689$	−2.55793	−	5.01883i	−0.0974494	−	0.191202i
$690$		−	12.0906i		−	0.460280i
$691$	12.7484	−	47.5777i	0.484972	−	1.80994i	−0.0952123	−	0.995457i	$-0.530353\pi$
$691$	12.7484	−	47.5777i	0.484972	−	1.80994i	0.580185	−	0.814485i	$-0.302980\pi$
$692$	1.80184	−	1.04029i	0.0684956	−	0.0395460i
$693$	3.26438	+	4.42510i	0.124003	+	0.168096i
$694$	−34.8747	−	34.8747i	−1.32382	−	1.32382i
$695$	−5.22337	−	19.4939i	−0.198134	−	0.739445i
$696$	1.21300	+	4.52699i	0.0459787	+	0.171595i
$697$	−39.3036	+	39.3036i	−1.48873	+	1.48873i
$698$	26.9632	−	46.7016i	1.02057	−	1.76768i
$699$	11.7608	+	20.3703i	0.444833	+	0.770474i
$700$	6.50336	−	24.2709i	0.245804	−	0.917353i
$701$	−37.9633			−1.43385			−0.716926	−	0.697149i	$-0.754452\pi$
$701$	−37.9633			−1.43385			−0.716926	+	0.697149i	$0.754452\pi$
$702$	−1.95687	−	9.20125i	−0.0738572	−	0.347279i
$703$		−	14.9488i		−	0.563805i
$704$	19.2430	+	15.3527i	0.725248	+	0.578626i
$705$	−4.12245	−	7.14029i	−0.155260	−	0.268919i
$706$	−32.3888	+	56.0990i	−1.21897	+	2.11131i
$707$	6.33712	+	6.33712i	0.238332	+	0.238332i
$708$	50.1356	−	13.4338i	1.88421	−	0.504873i
$709$	1.74788	+	6.52317i	0.0656429	+	0.244983i	0.990949	−	0.134238i	$-0.0428587\pi$
$709$	1.74788	+	6.52317i	0.0656429	+	0.244983i	−0.925306	+	0.379221i	$0.876192\pi$
$710$	−30.7186	−	30.7186i	−1.15285	−	1.15285i
$711$	2.65660	+	1.53379i	0.0996305	+	0.0575217i
$712$	−32.9249	−	57.0276i	−1.23391	−	2.13720i
$713$	−21.8912	−	5.86574i	−0.819833	−	0.219674i
$714$	−23.6164			−0.883820
$715$	8.95240	+	13.5654i	0.334801	+	0.507319i
$716$	−34.6916			−1.29649
$717$	0.243203	+	0.0651660i	0.00908258	+	0.00243367i
$718$	−10.5691	−	18.3061i	−0.394434	−	0.683179i
$719$	−37.9175	−	21.8917i	−1.41408	−	0.816421i	−0.418312	−	0.908303i	$-0.637378\pi$
$719$	−37.9175	−	21.8917i	−1.41408	−	0.816421i	−0.995770	+	0.0918824i	$0.970712\pi$
$720$	−9.12445	−	9.12445i	−0.340048	−	0.340048i
$721$	8.33552	+	31.1086i	0.310431	+	1.15854i
$722$	20.8169	−	5.57786i	0.774723	−	0.207586i
$723$	11.8685	+	11.8685i	0.441393	+	0.441393i
$724$	21.8446	−	37.8359i	0.811847	−	1.40616i
$725$	−1.00873	−	1.74718i	−0.0374634	−	0.0648885i
$726$	25.3795	−	13.3992i	0.941922	−	0.497293i
$727$		−	36.3948i		−	1.34981i	−0.737906	−	0.674904i	$-0.764185\pi$
$727$		−	36.3948i		−	1.34981i	0.737906	−	0.674904i	$-0.235815\pi$
$728$	2.28643	−	43.7216i	0.0847406	−	1.62043i
$729$	1.00000			0.0370370
$730$	−2.75280	+	10.2736i	−0.101886	+	0.380242i
$731$	26.3394	+	45.6213i	0.974200	+	1.68736i
$732$	−0.0307179	+	0.0532050i	−0.00113537	+	0.00196651i
$733$	−31.0571	+	31.0571i	−1.14712	+	1.14712i	−0.160002	+	0.987117i	$0.551150\pi$
$733$	−31.0571	+	31.0571i	−1.14712	+	1.14712i	−0.987117	+	0.160002i	$0.948850\pi$
$734$	1.96089	+	7.31814i	0.0723778	+	0.270118i
$735$	1.49544	+	5.58107i	0.0551603	+	0.205861i
$736$	24.4047	+	24.4047i	0.899568	+	0.899568i
$737$	−18.6625	−	25.2983i	−0.687441	−	0.931876i
$738$	23.0041	−	13.2814i	0.846794	−	0.488897i
$739$	0.995601	−	3.71563i	0.0366238	−	0.136682i	−0.945193	−	0.326511i	$-0.894127\pi$
$739$	0.995601	−	3.71563i	0.0366238	−	0.136682i	0.981817	+	0.189830i	$0.0607935\pi$
$740$		−	18.7067i		−	0.687670i
$741$	17.9043	+	5.81525i	0.657732	+	0.213628i
$742$	6.75824			0.248103
$743$	7.18897	+	1.92628i	0.263738	+	0.0706683i	0.388265	−	0.921548i	$-0.373075\pi$
$743$	7.18897	+	1.92628i	0.263738	+	0.0706683i	−0.124527	+	0.992216i	$0.539741\pi$
$744$	−42.1601	+	24.3412i	−1.54567	+	0.892390i
$745$	1.47960	−	2.56275i	0.0542085	−	0.0938918i
$746$	−3.47141	−	3.47141i	−0.127097	−	0.127097i
$747$	0.410153	+	1.53071i	0.0150067	+	0.0560058i
$748$	−12.9919	+	86.0679i	−0.475032	+	3.14695i
$749$	−7.94552	+	7.94552i	−0.290323	+	0.290323i
$750$	25.0371	+	14.4551i	0.914224	+	0.527827i
$751$	6.95937	−	4.01799i	0.253951	−	0.146619i	−0.367621	−	0.929976i	$-0.619828\pi$
$751$	6.95937	−	4.01799i	0.253951	−	0.146619i	0.621572	+	0.783357i	$0.286494\pi$
$752$	55.6300	+	14.9060i	2.02862	+	0.543566i
$753$			23.7301i			0.864775i
$754$	−4.02850	−	4.47310i	−0.146709	−	0.162901i
$755$		−	28.7954i		−	1.04797i
$756$	7.69849	+	2.06280i	0.279991	+	0.0750234i
$757$	4.43348	+	7.67900i	0.161137	+	0.279098i	0.935277	−	0.353917i	$-0.115150\pi$
$757$	4.43348	+	7.67900i	0.161137	+	0.279098i	−0.774139	+	0.633015i	$0.781817\pi$
$758$	14.4909	−	25.0989i	0.526332	−	0.911634i
$759$	10.5273	−	4.12902i	0.382118	−	0.149874i
$760$	50.2017	−	13.4515i	1.82101	−	0.487938i
$761$	−25.2074	+	6.75430i	−0.913767	+	0.244843i	−0.684919	−	0.728619i	$-0.740163\pi$
$761$	−25.2074	+	6.75430i	−0.913767	+	0.244843i	−0.228848	+	0.973462i	$0.573496\pi$
$762$	−24.3282	+	24.3282i	−0.881317	+	0.881317i
$763$	5.23596	−	9.06895i	0.189554	−	0.328318i
$764$	−39.7329	+	22.9398i	−1.43748	+	0.829932i
$765$	1.92053	−	7.16751i	0.0694369	−	0.259142i
$766$	59.9758			2.16702
$767$	−28.9281	+	26.0529i	−1.04453	+	0.940716i
$768$	−17.1409			−0.618520
$769$	10.2746	+	2.75307i	0.370512	+	0.0992783i	0.439270	−	0.898355i	$-0.355237\pi$
$769$	10.2746	+	2.75307i	0.370512	+	0.0992783i	−0.0687584	+	0.997633i	$0.521904\pi$
$770$	−19.3775	+	2.17902i	−0.698317	+	0.0785266i
$771$	2.95376	+	1.70536i	0.106377	+	0.0614169i
$772$	71.7098	−	71.7098i	2.58089	−	2.58089i
$773$	−11.8490	+	3.17493i	−0.426179	+	0.114194i	−0.465532	−	0.885031i	$-0.654137\pi$
$773$	−11.8490	+	3.17493i	−0.426179	+	0.114194i	0.0393530	+	0.999225i	$0.487470\pi$
$774$	−6.51569	−	24.3169i	−0.234202	−	0.874052i
$775$	14.8182	−	14.8182i	0.532287	−	0.532287i
$776$	70.9986	+	40.9910i	2.54870	+	1.47149i
$777$	2.37350	+	4.11103i	0.0851490	+	0.147482i
$778$	−13.8774	+	51.7913i	−0.497530	+	1.85681i
$779$			53.1568i			1.90454i
$780$	22.4052	+	7.27710i	0.802234	+	0.260562i
$781$	16.2563	−	37.2376i	0.581696	−	1.33247i
$782$	−12.5697	+	46.9108i	−0.449492	+	1.67753i
$783$	0.554187	−	0.319960i	0.0198050	−	0.0114344i
$784$	−34.9530	−	20.1801i	−1.24832	−	0.720719i
$785$	10.3226	+	10.3226i	0.368428	+	0.368428i
$786$	7.63513	−	2.04583i	0.272336	−	0.0729722i
$787$	6.57583	−	1.76199i	0.234403	−	0.0628081i	−0.139705	−	0.990193i	$-0.544616\pi$
$787$	6.57583	−	1.76199i	0.234403	−	0.0628081i	0.374108	+	0.927385i	$0.377949\pi$
$788$	−62.8472	−	62.8472i	−2.23884	−	2.23884i
$789$	−18.0171	−	10.4022i	−0.641425	−	0.370327i
$790$	−9.42061	+	5.43899i	−0.335170	+	0.193511i
$791$	0.427254	−	1.59453i	0.0151914	−	0.0566951i
$792$	9.71844	−	22.2616i	0.345330	−	0.791031i
$793$	0.00240645	−	0.0460168i	8.54557e−5	−	0.00163411i
$794$			5.97485i			0.212039i
$795$	−0.549594	+	2.05111i	−0.0194921	+	0.0727454i
$796$	−14.4939	−	25.1042i	−0.513724	−	0.889796i
$797$	−19.5131	−	11.2659i	−0.691191	−	0.399059i	0.112867	−	0.993610i	$-0.463997\pi$
$797$	−19.5131	−	11.2659i	−0.691191	−	0.399059i	−0.804058	+	0.594551i	$0.797330\pi$
$798$	−15.9701	+	15.9701i	−0.565337	+	0.565337i
$799$	8.57164	+	31.9898i	0.303243	+	1.13172i
$800$	−30.8260	+	8.25980i	−1.08986	+	0.292028i
$801$	−6.35770	+	6.35770i	−0.224638	+	0.224638i
$802$	28.0745	+	16.2088i	0.991345	+	0.572353i
$803$	−9.88538	+	1.11162i	−0.348847	+	0.0392283i
$804$	−44.0123	−	11.7931i	−1.55219	−	0.415909i
$805$	−7.68322			−0.270798
$806$	34.0501	−	52.4454i	1.19936	−	1.84731i
$807$	16.4871			0.580372
$808$	10.2462	−	38.2395i	0.360462	−	1.34526i
$809$	−1.76308	+	1.01792i	−0.0619866	+	0.0357880i	−0.530673	−	0.847577i	$-0.678061\pi$
$809$	−1.76308	+	1.01792i	−0.0619866	+	0.0357880i	0.468686	+	0.883365i	$0.344727\pi$
$810$	−1.77305	+	3.07102i	−0.0622988	+	0.107905i
$811$	31.7724	−	31.7724i	1.11568	−	1.11568i	0.123314	−	0.992368i	$-0.460648\pi$
$811$	31.7724	−	31.7724i	1.11568	−	1.11568i	0.992368	−	0.123314i	$-0.0393522\pi$
$812$	4.92642	−	1.32003i	0.172883	−	0.0463240i
$813$	−7.85071	+	2.10359i	−0.275336	+	0.0737762i
$814$	23.0647	−	9.04639i	0.808416	−	0.317076i
$815$	−10.9390	+	18.9470i	−0.383178	+	0.663683i
$816$	25.9164	+	44.8885i	0.907255	+	1.57141i
$817$	48.6621	+	13.0390i	1.70247	+	0.456176i
$818$		−	82.7054i		−	2.89173i
$819$	−5.84714	+	1.24354i	−0.204316	+	0.0434527i
$820$			66.5194i			2.32296i
$821$	7.97290	+	2.13633i	0.278256	+	0.0745585i	0.395248	−	0.918574i	$-0.370659\pi$
$821$	7.97290	+	2.13633i	0.278256	+	0.0745585i	−0.116992	+	0.993133i	$0.537325\pi$
$822$	43.5832	−	25.1628i	1.52014	−	0.877653i
$823$	40.9489	+	23.6419i	1.42739	+	0.824104i	0.996914	−	0.0784980i	$-0.0250124\pi$
$823$	40.9489	+	23.6419i	1.42739	+	0.824104i	0.430476	+	0.902602i	$0.358346\pi$
$824$	100.597	−	100.597i	3.50445	−	3.50445i
$825$	−1.56069	+	10.3391i	−0.0543362	+	0.359962i
$826$	−12.0886	−	45.1151i	−0.420615	−	1.56976i
$827$	32.8124	+	32.8124i	1.14100	+	1.14100i	0.988268	+	0.152731i	$0.0488069\pi$
$827$	32.8124	+	32.8124i	1.14100	+	1.14100i	0.152731	+	0.988268i	$0.451193\pi$
$828$	8.19498	−	14.1941i	0.284795	−	0.493280i
$829$	−27.5748	+	15.9203i	−0.957713	+	0.552936i	−0.895468	−	0.445125i	$-0.853159\pi$
$829$	−27.5748	+	15.9203i	−0.957713	+	0.552936i	−0.0622448	+	0.998061i	$0.519826\pi$
$830$	−5.42807	−	1.45445i	−0.188411	−	0.0504846i
$831$	−5.42204			−0.188088
$832$	−23.8433	+	12.1522i	−0.826619	+	0.421300i
$833$		−	23.2090i		−	0.804145i
$834$	10.0268	−	37.4204i	0.347198	−	1.29576i
$835$	−11.5984	+	6.69634i	−0.401379	+	0.231737i
$836$	49.4163	+	66.9874i	1.70910	+	2.31681i
$837$	4.70021	+	4.70021i	0.162463	+	0.162463i
$838$	−15.9510	−	59.5299i	−0.551018	−	2.05643i
$839$	−0.782013	−	2.91851i	−0.0269981	−	0.100758i	0.951112	−	0.308846i	$-0.0999427\pi$
$839$	−0.782013	−	2.91851i	−0.0269981	−	0.100758i	−0.978110	+	0.208088i	$0.933276\pi$
$840$	−11.6701	+	11.6701i	−0.402656	+	0.402656i
$841$	−14.2953	+	24.7601i	−0.492940	+	0.853797i
$842$	−35.2280	−	61.0167i	−1.21404	−	2.10277i
$843$	−5.69538	+	21.2554i	−0.196159	+	0.732077i
$844$	81.5833			2.80821
$845$	−17.4509	+	2.76798i	−0.600331	+	0.0952213i
$846$		−	15.8269i		−	0.544139i
$847$	−8.51486	−	16.1280i	−0.292574	−	0.554164i
$848$	−7.41643	−	12.8456i	−0.254681	−	0.441121i
$849$	5.18525	−	8.98112i	0.177957	−	0.308231i
$850$	−31.7541	−	31.7541i	−1.08916	−	1.08916i
$851$	9.42931	−	2.52658i	0.323233	−	0.0866099i
$852$	−15.2421	−	56.8843i	−0.522185	−	1.94882i
$853$	−21.3389	−	21.3389i	−0.730630	−	0.730630i	0.240115	−	0.970745i	$-0.422815\pi$
$853$	−21.3389	−	21.3389i	−0.730630	−	0.730630i	−0.970745	+	0.240115i	$0.922815\pi$
$854$	0.0478771	+	0.0276419i	0.00163832	+	0.000945885i
$855$	−3.54818	−	6.14563i	−0.121345	−	0.210176i
$856$	47.9449	+	12.8468i	1.63872	+	0.439095i
$857$	−49.5292			−1.69189			−0.845943	−	0.533274i	$-0.820962\pi$
$857$	−49.5292			−1.69189			−0.845943	+	0.533274i	$0.820962\pi$
$858$	1.86255	+	31.1440i	0.0635863	+	1.06324i
$859$	17.7017			0.603974			0.301987	−	0.953312i	$-0.402350\pi$
$859$	17.7017			0.603974			0.301987	+	0.953312i	$0.402350\pi$
$860$	60.8949	+	16.3167i	2.07650	+	0.556396i
$861$	−8.44000	−	14.6185i	−0.287634	−	0.498197i
$862$	−33.9436	−	19.5973i	−1.15612	−	0.667488i
$863$	−33.7200	−	33.7200i	−1.14784	−	1.14784i	−0.986977	−	0.160864i	$-0.948572\pi$
$863$	−33.7200	−	33.7200i	−1.14784	−	1.14784i	−0.160864	−	0.986977i	$-0.551428\pi$
$864$	−2.61993	−	9.77771i	−0.0891318	−	0.332644i
$865$	0.568220	−	0.152254i	0.0193201	−	0.00517680i
$866$	0.757301	+	0.757301i	0.0257341	+	0.0257341i
$867$	−6.40312	+	11.0905i	−0.217462	+	0.376654i
$868$	26.4889	+	45.8801i	0.899091	+	1.55727i
$869$	−7.95298	−	6.34514i	−0.269786	−	0.215244i
$870$			2.26923i			0.0769340i
$871$	33.4282	−	7.10930i	1.13267	−	0.240889i
$872$	−46.2581			−1.56650
$873$	2.89718	−	10.8124i	0.0980548	−	0.365945i
$874$	23.2226	+	40.2226i	0.785515	+	1.36055i
$875$	9.18585	−	15.9104i	0.310539	−	0.537868i
$876$	−10.1952	+	10.1952i	−0.344463	+	0.344463i
$877$	−9.26099	−	34.5625i	−0.312721	−	1.16709i	−0.926092	−	0.377297i	$-0.876854\pi$
$877$	−9.26099	−	34.5625i	−0.312721	−	1.16709i	0.613371	−	0.789795i	$-0.289813\pi$
$878$	1.44049	+	5.37598i	0.0486142	+	0.181430i
$879$	15.2178	+	15.2178i	0.513284	+	0.513284i
$880$	25.4065	+	34.4403i	0.856451	+	1.16098i
$881$	19.0380	−	10.9916i	0.641405	−	0.370316i	−0.143750	−	0.989614i	$-0.545916\pi$
$881$	19.0380	−	10.9916i	0.641405	−	0.370316i	0.785156	+	0.619298i	$0.212583\pi$
$882$	−2.87065	+	10.7134i	−0.0966599	+	0.360740i
$883$			19.6602i			0.661618i	0.943698	+	0.330809i	$0.107322\pi$
$883$			19.6602i			0.661618i	−0.943698	+	0.330809i	$0.892678\pi$
$884$	−79.3655	−	51.5279i	−2.66935	−	1.73307i
$885$	14.6754			0.493308
$886$	−17.1862	−	4.60502i	−0.577381	−	0.154709i
$887$	−10.8039	+	6.23761i	−0.362758	+	0.209438i	−0.670290	−	0.742099i	$-0.733830\pi$
$887$	−10.8039	+	6.23761i	−0.362758	+	0.209438i	0.307532	+	0.951538i	$0.400497\pi$
$888$	10.4846	−	18.1598i	0.351840	−	0.609404i
$889$	15.4599	+	15.4599i	0.518508	+	0.518508i
$890$	−8.25209	−	30.7972i	−0.276611	−	1.03232i
$891$	−3.27947	−	0.495035i	−0.109866	−	0.0165843i
$892$	82.2766	−	82.2766i	2.75482	−	2.75482i
$893$	27.4290	+	15.8361i	0.917875	+	0.529935i
$894$	4.91945	−	2.84024i	0.164531	−	0.0949919i
$895$	−9.47449	−	2.53868i	−0.316697	−	0.0848587i
$896$			1.45924i			0.0487498i
$897$	−0.641998	+	12.2765i	−0.0214357	+	0.409899i
$898$			68.8973i			2.29913i
$899$	4.10867	+	1.10092i	0.137032	+	0.0367176i
$900$	7.57763	+	13.1248i	0.252588	+	0.437495i
$901$	4.26479	−	7.38684i	0.142081	−	0.246091i
$902$	−82.0162	+	32.1683i	−2.73084	+	1.07109i
$903$	−15.4527	+	4.14054i	−0.514234	+	0.137789i
$904$	−7.04361	+	1.88733i	−0.234267	+	0.0627716i
$905$	8.73466	−	8.73466i	0.290350	−	0.290350i
$906$	27.6378	−	47.8701i	0.918205	−	1.59038i
$907$	−6.75356	+	3.89917i	−0.224248	+	0.129470i	−0.607916	−	0.794002i	$-0.707994\pi$
$907$	−6.75356	+	3.89917i	−0.224248	+	0.129470i	0.383668	+	0.923471i	$0.374661\pi$
$908$	−8.65707	+	32.3086i	−0.287295	+	1.07220i
$909$	−5.40541			−0.179286
$910$	6.54838	−	20.1616i	0.217077	−	0.668349i
$911$	−6.71165			−0.222367			−0.111183	−	0.993800i	$-0.535464\pi$
$911$	−6.71165			−0.222367			−0.111183	+	0.993800i	$0.535464\pi$
$912$	47.8805	+	12.8295i	1.58548	+	0.424829i
$913$	−0.587329	−	5.22297i	−0.0194377	−	0.172855i
$914$	−17.6952	−	10.2163i	−0.585305	−	0.337926i
$915$	−0.0122827	+	0.0122827i	−0.000406054	+	0.000406054i
$916$	−60.5914	+	16.2354i	−2.00200	+	0.536433i
$917$	−1.30007	−	4.85191i	−0.0429320	−	0.160224i
$918$	10.0721	−	10.0721i	0.332429	−	0.332429i
$919$	−29.2830	−	16.9065i	−0.965956	−	0.557695i	−0.0679550	−	0.997688i	$-0.521647\pi$
$919$	−29.2830	−	16.9065i	−0.965956	−	0.557695i	−0.898001	+	0.439993i	$0.854981\pi$
$920$	16.9697	+	29.3924i	0.559475	+	0.969040i
$921$	8.27880	−	30.8969i	0.272796	−	1.01809i
$922$			12.6811i			0.417631i
$923$	29.5598	+	32.8221i	0.972973	+	1.08035i
$924$	−24.2258	−	10.5759i	−0.796971	−	0.347923i
$925$	−2.33624	+	8.71898i	−0.0768152	+	0.286678i
$926$	−50.6524	+	29.2442i	−1.66454	+	0.961024i
$927$	−16.8224	−	9.71244i	−0.552521	−	0.318998i
$928$	−4.58041	−	4.58041i	−0.150359	−	0.150359i
$929$	51.5903	−	13.8236i	1.69262	−	0.453537i	0.721558	−	0.692354i	$-0.243426\pi$
$929$	51.5903	−	13.8236i	1.69262	−	0.453537i	0.971065	+	0.238817i	$0.0767597\pi$
$930$	−22.7682	+	6.10071i	−0.746597	+	0.200050i
$931$	−15.6947	−	15.6947i	−0.514372	−	0.514372i
$932$	−97.9220	−	56.5353i	−3.20754	−	1.85187i
$933$	−27.7651	+	16.0302i	−0.908989	+	0.524805i
$934$	3.26463	−	12.1838i	0.106822	−	0.398665i
$935$	−9.84649	+	22.5549i	−0.322015	+	0.737625i
$936$	17.6716	+	19.6219i	0.577615	+	0.641361i
$937$			58.6447i			1.91584i	0.287037	+	0.957919i	$0.407330\pi$
$937$			58.6447i			1.91584i	−0.287037	+	0.957919i	$0.592670\pi$
$938$	−10.6121	+	39.6050i	−0.346498	+	1.29315i
$939$	11.7452	+	20.3433i	0.383291	+	0.663880i
$940$	34.3241	+	19.8170i	1.11953	+	0.646360i
$941$	19.6140	−	19.6140i	0.639397	−	0.639397i	−0.311010	−	0.950407i	$-0.600667\pi$
$941$	19.6140	−	19.6140i	0.639397	−	0.639397i	0.950407	+	0.311010i	$0.100667\pi$
$942$	7.25286	+	27.0680i	0.236311	+	0.881924i
$943$	−33.5299	+	8.98431i	−1.09188	+	0.292569i
$944$	−72.4861	+	72.4861i	−2.35922	+	2.35922i
$945$	1.95155	+	1.12673i	0.0634839	+	0.0366525i
$946$	9.33031	+	82.9720i	0.303354	+	2.69765i
$947$	35.4560	+	9.50041i	1.15217	+	0.308722i	0.783833	−	0.620972i	$-0.213262\pi$
$947$	35.4560	+	9.50041i	1.15217	+	0.308722i	0.368333	+	0.929694i	$0.379929\pi$
$948$	−14.7462			−0.478934
$949$	3.34064	−	10.2854i	0.108442	−	0.333877i
$950$	−42.9463			−1.39336
$951$	6.89898	−	25.7473i	0.223715	−	0.834915i
$952$	57.4119	−	33.1468i	1.86073	−	1.07429i
$953$	11.2702	−	19.5206i	0.365079	−	0.632335i	−0.623710	−	0.781656i	$-0.714375\pi$
$953$	11.2702	−	19.5206i	0.365079	−	0.632335i	0.988789	+	0.149321i	$0.0477087\pi$
$954$	−2.88231	+	2.88231i	−0.0933182	+	0.0933182i
$955$	−12.5300	+	3.35740i	−0.405461	+	0.108643i
$956$	−1.16910	+	0.313260i	−0.0378115	+	0.0101315i
$957$	−1.97583	+	0.774958i	−0.0638696	+	0.0250508i
$958$	−35.0846	+	60.7683i	−1.13353	+	1.96333i
$959$	−15.9903	−	27.6960i	−0.516353	−	0.894349i
$960$	9.74437	+	2.61100i	0.314498	+	0.0842696i
$961$			13.1839i			0.425286i
$962$	−1.40657	+	26.8969i	−0.0453497	+	0.867189i
$963$		−	6.77734i		−	0.218397i
$964$	−77.9358	−	20.8828i	−2.51014	−	0.672591i
$965$	24.8320	−	14.3368i	0.799371	−	0.461517i
$966$	−12.7727	−	7.37435i	−0.410956	−	0.237266i
$967$	−7.19901	+	7.19901i	−0.231505	+	0.231505i	−0.813320	−	0.581816i	$-0.802342\pi$
$967$	−7.19901	+	7.19901i	−0.231505	+	0.231505i	0.581816	+	0.813320i	$0.302342\pi$
$968$	−42.8916	+	68.1953i	−1.37859	+	2.19188i
$969$	7.37759	+	27.5335i	0.237002	+	0.884504i
$970$	28.0683	+	28.0683i	0.901220	+	0.901220i
$971$	−25.5673	+	44.2838i	−0.820493	+	1.42113i	0.0848233	+	0.996396i	$0.472967\pi$
$971$	−25.5673	+	44.2838i	−0.820493	+	1.42113i	−0.905316	+	0.424739i	$0.860366\pi$
$972$	−4.16307	+	2.40355i	−0.133531	+	0.0770939i
$973$	−23.7796	−	6.37174i	−0.762340	−	0.204268i
$974$	−62.4290			−2.00035
$975$	−9.53399	−	6.18992i	−0.305332	−	0.198236i
$976$		−	0.121336i		−	0.00388386i
$977$	−1.55179	+	5.79134i	−0.0496460	+	0.185282i	−0.986296	−	0.164985i	$-0.947242\pi$
$977$	−1.55179	+	5.79134i	−0.0496460	+	0.185282i	0.936650	+	0.350267i	$0.113909\pi$
$978$	−36.3705	+	20.9985i	−1.16300	+	0.671459i
$979$	23.9972	−	17.7026i	0.766954	−	0.565778i
$980$	−19.6400	−	19.6400i	−0.627378	−	0.627378i
$981$	1.63472	+	6.10087i	0.0521927	+	0.194786i
$982$	10.7499	+	40.1194i	0.343045	+	1.28026i
$983$	31.8795	−	31.8795i	1.01680	−	1.01680i	0.0169429	−	0.999856i	$-0.494607\pi$
$983$	31.8795	−	31.8795i	1.01680	−	1.01680i	0.999856	−	0.0169429i	$-0.00539335\pi$
$984$	−37.2824	+	64.5750i	−1.18852	+	2.05858i
$985$	−12.5649	−	21.7630i	−0.400350	−	0.693427i
$986$	2.35916	−	8.80450i	0.0751309	−	0.280392i
$987$	−10.0576			−0.320135
$988$	−88.5143	+	18.8247i	−2.81602	+	0.598893i
$989$			32.8986i			1.04611i
$990$	7.33495	−	9.19360i	0.233120	−	0.292192i
$991$	−13.7483	−	23.8127i	−0.436729	−	0.756436i	0.560706	−	0.828015i	$-0.310530\pi$
$991$	−13.7483	−	23.8127i	−0.436729	−	0.756436i	−0.997435	+	0.0715785i	$0.977196\pi$
$992$	33.6430	−	58.2715i	1.06817	−	1.85012i
$993$	12.5644	+	12.5644i	0.398718	+	0.398718i
$994$	−51.1880	+	13.7158i	−1.62358	+	0.435038i
$995$	−2.12129	−	7.91677i	−0.0672495	−	0.250978i
$996$	−5.38664	−	5.38664i	−0.170682	−	0.170682i
$997$	22.2695	+	12.8573i	0.705283	+	0.407196i	0.809312	−	0.587379i	$-0.199840\pi$
$997$	22.2695	+	12.8573i	0.705283	+	0.407196i	−0.104029	+	0.994574i	$0.533173\pi$
$998$	8.10376	+	14.0361i	0.256520	+	0.444306i
$999$	−2.76558	−	0.741034i	−0.0874989	−	0.0234453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.76.2	✓	56
11.10	odd	2	inner	429.2.bd.a.76.13	yes	56
13.6	odd	12	inner	429.2.bd.a.175.13	yes	56
143.32	even	12	inner	429.2.bd.a.175.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.2	✓	56	1.1	even	1	trivial
429.2.bd.a.76.13	yes	56	11.10	odd	2	inner
429.2.bd.a.175.2	yes	56	143.32	even	12	inner
429.2.bd.a.175.13	yes	56	13.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52014 - 0.675270i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(4.16307 + 2.40355i) q^{4} +(0.961072 + 0.961072i) q^{5} +(0.675270 + 2.52014i) q^{6} +(1.60148 - 0.429116i) q^{7} +(-5.17874 - 5.17874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.52014 - 0.675270i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(4.16307 + 2.40355i) q^{4} +(0.961072 + 0.961072i) q^{5} +(0.675270 + 2.52014i) q^{6} +(1.60148 - 0.429116i) q^{7} +(-5.17874 - 5.17874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.77305 - 3.07102i) q^{10} +(2.06845 - 2.59259i) q^{11} -4.80710i q^{12} +(1.63725 + 3.21239i) q^{13} -4.32573 q^{14} +(0.351777 - 1.31285i) q^{15} +(4.74702 + 8.22207i) q^{16} +(-2.72976 + 4.72807i) q^{17} +(1.84487 - 1.84487i) q^{18} +(1.35133 + 5.04322i) q^{19} +(1.69103 + 6.31100i) q^{20} +(-1.17237 - 1.17237i) q^{21} +(-6.96348 + 5.13693i) q^{22} +(-2.95274 + 1.70476i) q^{23} +(-1.89555 + 7.07430i) q^{24} -3.15268i q^{25} +(-1.95687 - 9.20125i) q^{26} +1.00000 q^{27} +(7.69849 + 2.06280i) q^{28} +(0.554187 - 0.319960i) q^{29} +(-1.77305 + 3.07102i) q^{30} +(4.70021 + 4.70021i) q^{31} +(-2.61993 - 9.77771i) q^{32} +(-3.27947 - 0.495035i) q^{33} +(10.0721 - 10.0721i) q^{34} +(1.95155 + 1.12673i) q^{35} +(-4.16307 + 2.40355i) q^{36} +(-2.76558 - 0.741034i) q^{37} -13.6221i q^{38} +(1.96338 - 3.02409i) q^{39} -9.95429i q^{40} +(9.83418 + 2.63506i) q^{41} +(2.16286 + 3.74619i) q^{42} +(4.82451 - 8.35629i) q^{43} +(14.8425 - 5.82151i) q^{44} +(-1.31285 + 0.351777i) q^{45} +(8.59250 - 2.30235i) q^{46} +(4.28943 - 4.28943i) q^{47} +(4.74702 - 8.22207i) q^{48} +(-3.68158 + 2.12556i) q^{49} +(-2.12891 + 7.94520i) q^{50} +5.45951 q^{51} +(-0.905155 + 17.3086i) q^{52} -1.56234 q^{53} +(-2.52014 - 0.675270i) q^{54} +(4.47959 - 0.503736i) q^{55} +(-10.5159 - 6.07138i) q^{56} +(3.69190 - 3.69190i) q^{57} +(-1.61269 + 0.432119i) q^{58} +(2.79457 + 10.4295i) q^{59} +(4.61997 - 4.61997i) q^{60} +(-0.0110680 - 0.00639011i) q^{61} +(-8.67128 - 15.0191i) q^{62} +(-0.429116 + 1.60148i) q^{63} +7.42231i q^{64} +(-1.51382 + 4.66085i) q^{65} +(7.93045 + 3.46209i) q^{66} +(2.45326 - 9.15568i) q^{67} +(-22.7283 + 13.1222i) q^{68} +(2.95274 + 1.70476i) q^{69} +(-4.15734 - 4.15734i) q^{70} +(11.8334 - 3.17074i) q^{71} +(7.07430 - 1.89555i) q^{72} +(-2.12085 - 2.12085i) q^{73} +(6.46924 + 3.73502i) q^{74} +(-2.73030 + 1.57634i) q^{75} +(-6.49597 + 24.2433i) q^{76} +(2.20006 - 5.03959i) q^{77} +(-6.99008 + 6.29532i) q^{78} -3.06758i q^{79} +(-3.33978 + 12.4642i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-23.0041 - 13.2814i) q^{82} +(1.12056 - 1.12056i) q^{83} +(-2.06280 - 7.69849i) q^{84} +(-7.16751 + 1.92053i) q^{85} +(-17.8012 + 17.8012i) q^{86} +(-0.554187 - 0.319960i) q^{87} +(-24.1383 + 2.71438i) q^{88} +(8.68479 + 2.32708i) q^{89} +3.54611 q^{90} +(4.00051 + 4.44201i) q^{91} -16.3900 q^{92} +(1.72039 - 6.42060i) q^{93} +(-13.7065 + 7.91344i) q^{94} +(-3.54818 + 6.14563i) q^{95} +(-7.15778 + 7.15778i) q^{96} +(-10.8124 + 2.89718i) q^{97} +(10.7134 - 2.87065i) q^{98} +(1.21102 + 3.08762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

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