LMFDB - Embedded newform 273.2.bd.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.7
Root			$0.590887 - 1.62814i$ of defining polynomial
Character	$\chi$	$=$	273.43
Dual form			273.2.bd.b.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85837 + 1.07293i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.30235 + 2.25573i) q^{4} +1.91954i q^{5} +(1.85837 - 1.07293i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.29759i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.85837 + 1.07293i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.30235 + 2.25573i) q^{4} +1.91954i q^{5} +(1.85837 - 1.07293i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.29759i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.05953 + 3.56721i) q^{10} +(-1.23117 - 0.710818i) q^{11} +2.60470 q^{12} +(1.05481 + 3.44781i) q^{13} +2.14586 q^{14} +(1.66237 + 0.959770i) q^{15} +(1.21247 - 2.10007i) q^{16} +(-3.23553 - 5.60411i) q^{17} -2.14586i q^{18} +(-4.97497 + 2.87230i) q^{19} +(-4.32997 + 2.49991i) q^{20} -1.00000i q^{21} +(-1.52531 - 2.64192i) q^{22} +(-1.07136 + 1.85564i) q^{23} +(1.12375 + 0.648797i) q^{24} +1.31537 q^{25} +(-1.73903 + 7.53902i) q^{26} -1.00000 q^{27} +(2.25573 + 1.30235i) q^{28} +(3.81988 - 6.61623i) q^{29} +(2.05953 + 3.56721i) q^{30} +2.50499i q^{31} +(6.75393 - 3.89939i) q^{32} +(-1.23117 + 0.710818i) q^{33} -13.8860i q^{34} +(0.959770 + 1.66237i) q^{35} +(1.30235 - 2.25573i) q^{36} +(-6.77537 - 3.91176i) q^{37} -12.3271 q^{38} +(3.51329 + 0.810413i) q^{39} -2.49078 q^{40} +(-7.52965 - 4.34725i) q^{41} +(1.07293 - 1.85837i) q^{42} +(3.53722 + 6.12665i) q^{43} -3.70293i q^{44} +(1.66237 - 0.959770i) q^{45} +(-3.98194 + 2.29897i) q^{46} -0.362849i q^{47} +(-1.21247 - 2.10007i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.44443 + 1.41129i) q^{50} -6.47107 q^{51} +(-6.40361 + 6.86962i) q^{52} +0.524776 q^{53} +(-1.85837 - 1.07293i) q^{54} +(1.36444 - 2.36328i) q^{55} +(0.648797 + 1.12375i) q^{56} +5.74461i q^{57} +(14.1975 - 8.19691i) q^{58} +(-7.80101 + 4.50392i) q^{59} +4.99982i q^{60} +(3.95123 + 6.84374i) q^{61} +(-2.68767 + 4.65518i) q^{62} +(-0.866025 - 0.500000i) q^{63} +11.8851 q^{64} +(-6.61820 + 2.02475i) q^{65} -3.05062 q^{66} +(-0.351053 - 0.202681i) q^{67} +(8.42759 - 14.5970i) q^{68} +(1.07136 + 1.85564i) q^{69} +4.11906i q^{70} +(0.210713 - 0.121655i) q^{71} +(1.12375 - 0.648797i) q^{72} +0.330581i q^{73} +(-8.39408 - 14.5390i) q^{74} +(0.657684 - 1.13914i) q^{75} +(-12.9583 - 7.48148i) q^{76} -1.42164 q^{77} +(5.65947 + 5.27555i) q^{78} +8.64577 q^{79} +(4.03116 + 2.32739i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.32857 - 16.1576i) q^{82} +11.4277i q^{83} +(2.25573 - 1.30235i) q^{84} +(10.7573 - 6.21074i) q^{85} +15.1807i q^{86} +(-3.81988 - 6.61623i) q^{87} +(0.922352 - 1.59756i) q^{88} +(10.9755 + 6.33670i) q^{89} +4.11906 q^{90} +(2.63739 + 2.45848i) q^{91} -5.58111 q^{92} +(2.16938 + 1.25249i) q^{93} +(0.389311 - 0.674306i) q^{94} +(-5.51350 - 9.54966i) q^{95} -7.79877i q^{96} +(14.8509 - 8.57418i) q^{97} +(1.85837 - 1.07293i) q^{98} +1.42164i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.85837	+	1.07293i	1.31406	+	0.758675i	0.982766	−	0.184852i	$-0.0591806\pi$
$2$	1.85837	+	1.07293i	1.31406	+	0.758675i	0.331297	+	0.943527i	$0.392514\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.30235	+	2.25573i	0.651174	+	1.12787i
$5$			1.91954i			0.858444i	0.903199	+	0.429222i	$0.141212\pi$
$5$			1.91954i			0.858444i	−0.903199	+	0.429222i	$0.858788\pi$
$6$	1.85837	−	1.07293i	0.758675	−	0.438021i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			1.29759i			0.458768i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.05953	+	3.56721i	−0.651280	+	1.12805i
$11$	−1.23117	−	0.710818i	−0.371212	−	0.214320i	0.302776	−	0.953062i	$-0.402087\pi$
$11$	−1.23117	−	0.710818i	−0.371212	−	0.214320i	−0.673988	+	0.738742i	$0.735420\pi$
$12$	2.60470			0.751911
$13$	1.05481	+	3.44781i	0.292551	+	0.956250i
$13$	1.05481	+	3.44781i	0.292551	+	0.956250i
$14$	2.14586			0.573504
$15$	1.66237	+	0.959770i	0.429222	+	0.247811i
$16$	1.21247	−	2.10007i	0.303118	−	0.525016i
$17$	−3.23553	−	5.60411i	−0.784732	−	1.35920i	−0.929159	−	0.369681i	$-0.879467\pi$
$17$	−3.23553	−	5.60411i	−0.784732	−	1.35920i	0.144426	−	0.989516i	$-0.453866\pi$
$18$		−	2.14586i		−	0.505783i
$19$	−4.97497	+	2.87230i	−1.14134	+	0.658952i	−0.946761	−	0.321936i	$-0.895666\pi$
$19$	−4.97497	+	2.87230i	−1.14134	+	0.658952i	−0.194576	+	0.980887i	$0.562333\pi$
$20$	−4.32997	+	2.49991i	−0.968211	+	0.558997i
$21$		−	1.00000i		−	0.218218i
$22$	−1.52531	−	2.64192i	−0.325198	−	0.563259i
$23$	−1.07136	+	1.85564i	−0.223393	+	0.386928i	−0.955836	−	0.293900i	$-0.905047\pi$
$23$	−1.07136	+	1.85564i	−0.223393	+	0.386928i	0.732443	+	0.680828i	$0.238380\pi$
$24$	1.12375	+	0.648797i	0.229384	+	0.132435i
$25$	1.31537			0.263074
$26$	−1.73903	+	7.53902i	−0.341052	+	1.47852i
$27$	−1.00000			−0.192450
$28$	2.25573	+	1.30235i	0.426294	+	0.246121i
$29$	3.81988	−	6.61623i	0.709334	−	1.22860i	−0.255770	−	0.966738i	$-0.582329\pi$
$29$	3.81988	−	6.61623i	0.709334	−	1.22860i	0.965104	−	0.261865i	$-0.0843376\pi$
$30$	2.05953	+	3.56721i	0.376017	+	0.651280i
$31$			2.50499i			0.449909i	0.974369	+	0.224954i	$0.0722233\pi$
$31$			2.50499i			0.449909i	−0.974369	+	0.224954i	$0.927777\pi$
$32$	6.75393	−	3.89939i	1.19394	−	0.689321i
$33$	−1.23117	+	0.710818i	−0.214320	+	0.123737i
$34$		−	13.8860i		−	2.38143i
$35$	0.959770	+	1.66237i	0.162231	+	0.280992i
$36$	1.30235	−	2.25573i	0.217058	−	0.375956i
$37$	−6.77537	−	3.91176i	−1.11386	−	0.643090i	−0.174037	−	0.984739i	$-0.555681\pi$
$37$	−6.77537	−	3.91176i	−1.11386	−	0.643090i	−0.939827	+	0.341649i	$0.889014\pi$
$38$	−12.3271			−1.99972
$39$	3.51329	+	0.810413i	0.562577	+	0.129770i
$40$	−2.49078			−0.393827
$41$	−7.52965	−	4.34725i	−1.17593	−	0.678926i	−0.220864	−	0.975305i	$-0.570888\pi$
$41$	−7.52965	−	4.34725i	−1.17593	−	0.678926i	−0.955071	+	0.296379i	$0.904221\pi$
$42$	1.07293	−	1.85837i	0.165556	−	0.286752i
$43$	3.53722	+	6.12665i	0.539422	+	0.934306i	0.998935	+	0.0461349i	$0.0146904\pi$
$43$	3.53722	+	6.12665i	0.539422	+	0.934306i	−0.459514	+	0.888171i	$0.651976\pi$
$44$		−	3.70293i		−	0.558238i
$45$	1.66237	−	0.959770i	0.247811	−	0.143074i
$46$	−3.98194	+	2.29897i	−0.587105	+	0.338965i
$47$		−	0.362849i		−	0.0529270i	−0.999650	−	0.0264635i	$-0.991575\pi$
$47$		−	0.362849i		−	0.0529270i	0.999650	−	0.0264635i	$-0.00842457\pi$
$48$	−1.21247	−	2.10007i	−0.175005	−	0.303118i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	2.44443	+	1.41129i	0.345695	+	0.199587i
$51$	−6.47107			−0.906131
$52$	−6.40361	+	6.86962i	−0.888021	+	0.952644i
$53$	0.524776			0.0720835			0.0360417	−	0.999350i	$-0.488525\pi$
$53$	0.524776			0.0720835			0.0360417	+	0.999350i	$0.488525\pi$
$54$	−1.85837	−	1.07293i	−0.252892	−	0.146007i
$55$	1.36444	−	2.36328i	0.183981	−	0.318665i
$56$	0.648797	+	1.12375i	0.0866991	+	0.150167i
$57$			5.74461i			0.760892i
$58$	14.1975	−	8.19691i	1.86422	−	1.07631i
$59$	−7.80101	+	4.50392i	−1.01560	+	0.586360i	−0.912828	−	0.408345i	$-0.866106\pi$
$59$	−7.80101	+	4.50392i	−1.01560	+	0.586360i	−0.102777	+	0.994704i	$0.532773\pi$
$60$			4.99982i			0.645474i
$61$	3.95123	+	6.84374i	0.505904	+	0.876251i	0.999977	+	0.00683058i	$0.00217426\pi$
$61$	3.95123	+	6.84374i	0.505904	+	0.876251i	−0.494073	+	0.869420i	$0.664492\pi$
$62$	−2.68767	+	4.65518i	−0.341334	+	0.591208i
$63$	−0.866025	−	0.500000i	−0.109109	−	0.0629941i
$64$	11.8851			1.48564
$65$	−6.61820	+	2.02475i	−0.820887	+	0.251139i
$66$	−3.05062			−0.375506
$67$	−0.351053	−	0.202681i	−0.0428879	−	0.0247614i	0.478403	−	0.878141i	$-0.341216\pi$
$67$	−0.351053	−	0.202681i	−0.0428879	−	0.0247614i	−0.521291	+	0.853379i	$0.674549\pi$
$68$	8.42759	−	14.5970i	1.02200	−	1.77015i
$69$	1.07136	+	1.85564i	0.128976	+	0.223393i
$70$			4.11906i			0.492321i
$71$	0.210713	−	0.121655i	0.0250071	−	0.0144378i	−0.487444	−	0.873154i	$-0.662071\pi$
$71$	0.210713	−	0.121655i	0.0250071	−	0.0144378i	0.512451	+	0.858716i	$0.328737\pi$
$72$	1.12375	−	0.648797i	0.132435	−	0.0764614i
$73$			0.330581i			0.0386916i	0.999813	+	0.0193458i	$0.00615835\pi$
$73$			0.330581i			0.0386916i	−0.999813	+	0.0193458i	$0.993842\pi$
$74$	−8.39408	−	14.5390i	−0.975792	−	1.69012i
$75$	0.657684	−	1.13914i	0.0759428	−	0.131537i
$76$	−12.9583	−	7.48148i	−1.48642	−	0.858185i
$77$	−1.42164			−0.162010
$78$	5.65947	+	5.27555i	0.640809	+	0.597339i
$79$	8.64577			0.972725			0.486363	−	0.873757i	$-0.338323\pi$
$79$	8.64577			0.972725			0.486363	+	0.873757i	$0.338323\pi$
$80$	4.03116	+	2.32739i	0.450697	+	0.260210i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−9.32857	−	16.1576i	−1.03017	−	1.78430i
$83$			11.4277i			1.25435i	0.778877	+	0.627177i	$0.215790\pi$
$83$			11.4277i			1.25435i	−0.778877	+	0.627177i	$0.784210\pi$
$84$	2.25573	−	1.30235i	0.246121	−	0.142098i
$85$	10.7573	−	6.21074i	1.16679	−	0.673649i
$86$			15.1807i			1.63698i
$87$	−3.81988	−	6.61623i	−0.409534	−	0.709334i
$88$	0.922352	−	1.59756i	0.0983231	−	0.170301i
$89$	10.9755	+	6.33670i	1.16340	+	0.671689i	0.952117	−	0.305735i	$-0.0989023\pi$
$89$	10.9755	+	6.33670i	1.16340	+	0.671689i	0.211284	+	0.977425i	$0.432236\pi$
$90$	4.11906			0.434187
$91$	2.63739	+	2.45848i	0.276474	+	0.257719i
$92$	−5.58111			−0.581871
$93$	2.16938	+	1.25249i	0.224954	+	0.129877i
$94$	0.389311	−	0.674306i	0.0401543	−	0.0695494i
$95$	−5.51350	−	9.54966i	−0.565673	−	0.979775i
$96$		−	7.79877i		−	0.795959i
$97$	14.8509	−	8.57418i	1.50788	−	0.870576i	0.507923	−	0.861402i	$-0.330413\pi$
$97$	14.8509	−	8.57418i	1.50788	−	0.870576i	0.999958	−	0.00917340i	$-0.00292002\pi$
$98$	1.85837	−	1.07293i	0.187723	−	0.108382i
$99$			1.42164i			0.142880i
$100$	1.71307	+	2.96712i	0.171307	+	0.296712i
$101$	4.00285	−	6.93315i	0.398299	−	0.689874i	−0.595217	−	0.803565i	$-0.702934\pi$
$101$	4.00285	−	6.93315i	0.398299	−	0.689874i	0.993516	+	0.113691i	$0.0362674\pi$
$102$	−12.0256	−	6.94299i	−1.19071	−	0.687459i
$103$	14.4716			1.42593			0.712965	−	0.701199i	$-0.247352\pi$
$103$	14.4716			1.42593			0.712965	+	0.701199i	$0.247352\pi$
$104$	−4.47385	+	1.36871i	−0.438697	+	0.134213i
$105$	1.91954			0.187328
$106$	0.975225	+	0.563046i	0.0947222	+	0.0546879i
$107$	−7.32426	+	12.6860i	−0.708063	+	1.22640i	0.257511	+	0.966275i	$0.417097\pi$
$107$	−7.32426	+	12.6860i	−0.708063	+	1.22640i	−0.965575	+	0.260126i	$0.916236\pi$
$108$	−1.30235	−	2.25573i	−0.125319	−	0.217058i
$109$			13.6710i			1.30944i	0.755871	+	0.654720i	$0.227214\pi$
$109$			13.6710i			1.30944i	−0.755871	+	0.654720i	$0.772786\pi$
$110$	5.07127	−	2.92790i	0.483526	−	0.279164i
$111$	−6.77537	+	3.91176i	−0.643090	+	0.371288i
$112$		−	2.42495i		−	0.229136i
$113$	0.733062	+	1.26970i	0.0689607	+	0.119443i	0.898444	−	0.439088i	$-0.144698\pi$
$113$	0.733062	+	1.26970i	0.0689607	+	0.119443i	−0.829483	+	0.558531i	$0.811365\pi$
$114$	−6.16355	+	10.6756i	−0.577269	+	0.999860i
$115$	−3.56198	−	2.05651i	−0.332156	−	0.191771i
$116$	19.8993			1.84760
$117$	2.45848	−	2.63739i	0.227287	−	0.243827i
$118$	−19.3295			−1.77943
$119$	−5.60411	−	3.23553i	−0.513728	−	0.296601i
$120$	−1.24539	+	2.15708i	−0.113688	+	0.196914i
$121$	−4.48948	−	7.77600i	−0.408134	−	0.706909i
$122$			16.9576i			1.53527i
$123$	−7.52965	+	4.34725i	−0.678926	+	0.391978i
$124$	−5.65058	+	3.26236i	−0.507437	+	0.292969i
$125$			12.1226i			1.08428i
$126$	−1.07293	−	1.85837i	−0.0955840	−	0.165556i
$127$	−4.48636	+	7.77061i	−0.398101	+	0.689530i	−0.993492	−	0.113906i	$-0.963664\pi$
$127$	−4.48636	+	7.77061i	−0.398101	+	0.689530i	0.595391	+	0.803436i	$0.296997\pi$
$128$	8.57908	+	4.95313i	0.758291	+	0.437799i
$129$	7.07445			0.622870
$130$	−14.4715	−	3.33814i	−1.26923	−	0.292774i
$131$	−1.49838			−0.130914			−0.0654569	−	0.997855i	$-0.520850\pi$
$131$	−1.49838			−0.130914			−0.0654569	+	0.997855i	$0.520850\pi$
$132$	−3.20683	−	1.85146i	−0.279119	−	0.161149i
$133$	−2.87230	+	4.97497i	−0.249060	+	0.431385i
$134$	−0.434923	−	0.753309i	−0.0375716	−	0.0650760i
$135$		−	1.91954i		−	0.165208i
$136$	7.27186	−	4.19841i	0.623556	−	0.360010i
$137$	−11.7519	+	6.78499i	−1.00404	+	0.579681i	−0.909440	−	0.415835i	$-0.863489\pi$
$137$	−11.7519	+	6.78499i	−1.00404	+	0.579681i	−0.0945964	+	0.995516i	$0.530156\pi$
$138$			4.59795i			0.391403i
$139$	−3.16710	−	5.48558i	−0.268630	−	0.465281i	0.699878	−	0.714262i	$-0.253238\pi$
$139$	−3.16710	−	5.48558i	−0.268630	−	0.465281i	−0.968508	+	0.248981i	$0.919904\pi$
$140$	−2.49991	+	4.32997i	−0.211281	+	0.365949i
$141$	−0.314236	−	0.181424i	−0.0264635	−	0.0152787i
$142$	0.522110			0.0438145
$143$	1.15211	−	4.99462i	0.0963444	−	0.417671i
$144$	−2.42495			−0.202079
$145$	12.7001	+	7.33241i	1.05469	+	0.608924i
$146$	−0.354690	+	0.614341i	−0.0293544	+	0.0508432i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		−	20.3779i		−	1.67505i
$149$	14.7387	−	8.50938i	1.20744	−	0.697115i	0.245240	−	0.969462i	$-0.421133\pi$
$149$	14.7387	−	8.50938i	1.20744	−	0.697115i	0.962199	+	0.272347i	$0.0877998\pi$
$150$	2.44443	−	1.41129i	0.199587	−	0.115232i
$151$			6.81585i			0.554666i	0.960774	+	0.277333i	$0.0894505\pi$
$151$			6.81585i			0.554666i	−0.960774	+	0.277333i	$0.910550\pi$
$152$	−3.72708	−	6.45549i	−0.302306	−	0.523610i
$153$	−3.23553	+	5.60411i	−0.261577	+	0.453065i
$154$	−2.64192	−	1.52531i	−0.212892	−	0.122913i
$155$	−4.80842			−0.386222
$156$	2.74746	+	8.98050i	0.219973	+	0.719015i
$157$	−11.7919			−0.941096			−0.470548	−	0.882374i	$-0.655944\pi$
$157$	−11.7919			−0.941096			−0.470548	+	0.882374i	$0.655944\pi$
$158$	16.0670	+	9.27629i	1.27822	+	0.737982i
$159$	0.262388	−	0.454469i	0.0208087	−	0.0360417i
$160$	7.48503	+	12.9644i	0.591743	+	1.02493i
$161$			2.14271i			0.168869i
$162$	−1.85837	+	1.07293i	−0.146007	+	0.0842972i
$163$	7.70873	−	4.45064i	0.603794	−	0.348601i	−0.166739	−	0.986001i	$-0.553324\pi$
$163$	7.70873	−	4.45064i	0.603794	−	0.348601i	0.770533	+	0.637400i	$0.219990\pi$
$164$		−	22.6465i		−	1.76840i
$165$	−1.36444	−	2.36328i	−0.106222	−	0.183981i
$166$	−12.2611	+	21.2369i	−0.951647	+	1.64830i
$167$	−9.56796	−	5.52407i	−0.740391	−	0.427465i	0.0818203	−	0.996647i	$-0.473927\pi$
$167$	−9.56796	−	5.52407i	−0.740391	−	0.427465i	−0.822212	+	0.569182i	$0.807260\pi$
$168$	1.29759			0.100111
$169$	−10.7748	+	7.27355i	−0.828827	+	0.559504i
$170$	26.6547			2.04432
$171$	4.97497	+	2.87230i	0.380446	+	0.219651i
$172$	−9.21340	+	15.9581i	−0.702515	+	1.21679i
$173$	−6.38590	−	11.0607i	−0.485511	−	0.840929i	0.514351	−	0.857580i	$-0.328033\pi$
$173$	−6.38590	−	11.0607i	−0.485511	−	0.840929i	−0.999861	+	0.0166506i	$0.994700\pi$
$174$		−	16.3938i		−	1.24281i
$175$	1.13914	−	0.657684i	0.0861110	−	0.0497162i
$176$	−2.98553	+	1.72369i	−0.225043	+	0.129928i
$177$			9.00783i			0.677070i
$178$	13.5977	+	23.5518i	1.01919	+	1.76528i
$179$	10.4293	−	18.0641i	0.779524	−	1.35018i	−0.152692	−	0.988274i	$-0.548794\pi$
$179$	10.4293	−	18.0641i	0.779524	−	1.35018i	0.932216	−	0.361902i	$-0.117872\pi$
$180$	4.32997	+	2.49991i	0.322737	+	0.186332i
$181$	−0.377072			−0.0280275			−0.0140138	−	0.999902i	$-0.504461\pi$
$181$	−0.377072			−0.0280275			−0.0140138	+	0.999902i	$0.504461\pi$
$182$	2.26347	+	7.39850i	0.167779	+	0.548413i
$183$	7.90247			0.584167
$184$	−2.40787	−	1.39018i	−0.177510	−	0.102486i
$185$	7.50878	−	13.0056i	0.552057	−	0.956190i
$186$	2.68767	+	4.65518i	0.197069	+	0.341334i
$187$			9.19950i			0.672734i
$188$	0.818491	−	0.472556i	0.0596946	−	0.0344647i
$189$	−0.866025	+	0.500000i	−0.0629941	+	0.0363696i
$190$		−	23.6623i		−	1.71665i
$191$	−8.70506	−	15.0776i	−0.629876	−	1.09098i	−0.987576	−	0.157140i	$-0.949772\pi$
$191$	−8.70506	−	15.0776i	−0.629876	−	1.09098i	0.357700	−	0.933836i	$-0.383561\pi$
$192$	5.94257	−	10.2928i	0.428868	−	0.742822i
$193$	−9.65866	−	5.57643i	−0.695245	−	0.401400i	0.110329	−	0.993895i	$-0.464810\pi$
$193$	−9.65866	−	5.57643i	−0.695245	−	0.401400i	−0.805574	+	0.592495i	$0.798143\pi$
$194$	36.7979			2.64193
$195$	−1.55562	+	6.74391i	−0.111400	+	0.482941i
$196$	2.60470			0.186050
$197$	7.19522	+	4.15416i	0.512638	+	0.295972i	0.733917	−	0.679239i	$-0.237690\pi$
$197$	7.19522	+	4.15416i	0.512638	+	0.295972i	−0.221279	+	0.975210i	$0.571023\pi$
$198$	−1.52531	+	2.64192i	−0.108399	+	0.187753i
$199$	−4.66548	−	8.08084i	−0.330727	−	0.572836i	0.651928	−	0.758281i	$-0.273961\pi$
$199$	−4.66548	−	8.08084i	−0.330727	−	0.572836i	−0.982655	+	0.185445i	$0.940627\pi$
$200$			1.70681i			0.120690i
$201$	−0.351053	+	0.202681i	−0.0247614	+	0.0142960i
$202$	14.8775	−	8.58955i	1.04678	−	0.604358i
$203$		−	7.63976i		−	0.536206i
$204$	−8.42759	−	14.5970i	−0.590049	−	1.02200i
$205$	8.34471	−	14.4535i	0.582820	−	1.00947i
$206$	26.8936	+	15.5270i	1.87376	+	1.08182i
$207$	2.14271			0.148929
$208$	8.51955	+	1.96521i	0.590724	+	0.136263i
$209$	8.16673			0.564905
$210$	3.56721	+	2.05953i	0.246161	+	0.142121i
$211$	−13.7629	+	23.8381i	−0.947478	+	1.64108i	−0.196767	+	0.980450i	$0.563044\pi$
$211$	−13.7629	+	23.8381i	−0.947478	+	1.64108i	−0.750711	+	0.660630i	$0.770289\pi$
$212$	0.683441	+	1.18375i	0.0469389	+	0.0813006i
$213$		−	0.243311i		−	0.0166714i
$214$	−27.2223	+	15.7168i	−1.86088	+	1.07438i
$215$	−11.7604	+	6.78984i	−0.802049	+	0.463063i
$216$		−	1.29759i		−	0.0882900i
$217$	1.25249	+	2.16938i	0.0850248	+	0.147267i
$218$	−14.6680	+	25.4056i	−0.993439	+	1.72069i
$219$	0.286292	+	0.165291i	0.0193458	+	0.0111693i
$220$	7.10792			0.479216
$221$	15.9090	−	17.0668i	1.07016	−	1.14803i
$222$	−16.7882			−1.12675
$223$	−7.52662	−	4.34550i	−0.504020	−	0.290996i	0.226352	−	0.974046i	$-0.427320\pi$
$223$	−7.52662	−	4.34550i	−0.504020	−	0.290996i	−0.730372	+	0.683050i	$0.760653\pi$
$224$	3.89939	−	6.75393i	0.260539	−	0.451266i
$225$	−0.657684	−	1.13914i	−0.0438456	−	0.0759428i
$226$			3.14609i			0.209275i
$227$	2.60436	−	1.50363i	0.172857	−	0.0997993i	−0.411075	−	0.911601i	$-0.634847\pi$
$227$	2.60436	−	1.50363i	0.172857	−	0.0997993i	0.583932	+	0.811802i	$0.301513\pi$
$228$	−12.9583	+	7.48148i	−0.858185	+	0.495473i
$229$			11.8292i			0.781696i	0.920455	+	0.390848i	$0.127818\pi$
$229$			11.8292i			0.781696i	−0.920455	+	0.390848i	$0.872182\pi$
$230$	−4.41297	−	7.64349i	−0.290983	−	0.503997i
$231$	−0.710818	+	1.23117i	−0.0467684	+	0.0810052i
$232$	8.58517	+	4.95665i	0.563644	+	0.325420i
$233$	14.8027			0.969755			0.484877	−	0.874582i	$-0.338864\pi$
$233$	14.8027			0.969755			0.484877	+	0.874582i	$0.338864\pi$
$234$	7.39850	−	2.26347i	0.483655	−	0.147967i
$235$	0.696503			0.0454348
$236$	−20.3193	−	11.7313i	−1.32267	−	0.763645i
$237$	4.32289	−	7.48746i	0.280802	−	0.486363i
$238$	−6.94299	−	12.0256i	−0.450047	−	0.779505i
$239$			8.41715i			0.544460i	0.962232	+	0.272230i	$0.0877612\pi$
$239$			8.41715i			0.544460i	−0.962232	+	0.272230i	$0.912239\pi$
$240$	4.03116	−	2.32739i	0.260210	−	0.150232i
$241$	15.5226	−	8.96200i	0.999901	−	0.577293i	0.0916822	−	0.995788i	$-0.470776\pi$
$241$	15.5226	−	8.96200i	0.999901	−	0.577293i	0.908219	+	0.418495i	$0.137442\pi$
$242$		−	19.2675i		−	1.23856i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−10.2918	+	17.8259i	−0.658863	+	1.14118i
$245$	1.66237	+	0.959770i	0.106205	+	0.0613174i
$246$	−18.6571			−1.18954
$247$	−15.1508	−	14.1230i	−0.964022	−	0.898627i
$248$	−3.25045			−0.206404
$249$	9.89669	+	5.71385i	0.627177	+	0.362101i
$250$	−13.0067	+	22.5282i	−0.822614	+	1.42481i
$251$	2.32656	+	4.02972i	0.146851	+	0.254354i	0.930062	−	0.367403i	$-0.119753\pi$
$251$	2.32656	+	4.02972i	0.146851	+	0.254354i	−0.783211	+	0.621756i	$0.786420\pi$
$252$		−	2.60470i		−	0.164081i
$253$	2.63805	−	1.52308i	0.165853	−	0.0957550i
$254$	−16.6746	+	9.62709i	−1.04626	+	0.604057i
$255$		−	12.4215i		−	0.777863i
$256$	−1.25644	−	2.17621i	−0.0785272	−	0.136013i
$257$	13.5100	−	23.4000i	0.842729	−	1.45965i	−0.0448506	−	0.998994i	$-0.514281\pi$
$257$	13.5100	−	23.4000i	0.842729	−	1.45965i	0.887579	−	0.460655i	$-0.152385\pi$
$258$	13.1469	+	7.59037i	0.818491	+	0.472556i
$259$	−7.82352			−0.486130
$260$	−13.1865	−	12.2920i	−0.817792	−	0.762316i
$261$	−7.63976			−0.472889
$262$	−2.78453	−	1.60765i	−0.172029	−	0.0993210i
$263$	−5.86983	+	10.1668i	−0.361949	+	0.626914i	−0.988282	−	0.152642i	$-0.951222\pi$
$263$	−5.86983	+	10.1668i	−0.361949	+	0.626914i	0.626333	+	0.779556i	$0.284555\pi$
$264$	−0.922352	−	1.59756i	−0.0567668	−	0.0983231i
$265$			1.00733i			0.0618796i
$266$	−10.6756	+	6.16355i	−0.654562	+	0.377911i
$267$	10.9755	−	6.33670i	0.671689	−	0.387800i
$268$		−	1.05584i		−	0.0644959i
$269$	−1.76092	−	3.05001i	−0.107365	−	0.185962i	0.807337	−	0.590091i	$-0.200908\pi$
$269$	−1.76092	−	3.05001i	−0.107365	−	0.185962i	−0.914702	+	0.404129i	$0.867575\pi$
$270$	2.05953	−	3.56721i	0.125339	−	0.217093i
$271$	−18.6097	−	10.7443i	−1.13046	−	0.652671i	−0.186409	−	0.982472i	$-0.559685\pi$
$271$	−18.6097	−	10.7443i	−1.13046	−	0.652671i	−0.944050	+	0.329801i	$0.893018\pi$
$272$	−15.6920			−0.951467
$273$	3.44781	−	1.05481i	0.208671	−	0.0638399i
$274$	−29.1192			−1.75916
$275$	−1.61944	−	0.934986i	−0.0976562	−	0.0563818i
$276$	−2.79056	+	4.83339i	−0.167972	+	0.290936i
$277$	−12.7082	−	22.0113i	−0.763565	−	1.32253i	−0.941002	−	0.338401i	$-0.890114\pi$
$277$	−12.7082	−	22.0113i	−0.763565	−	1.32253i	0.177437	−	0.984132i	$-0.443219\pi$
$278$		−	13.5923i		−	0.815211i
$279$	2.16938	−	1.25249i	0.129877	−	0.0749848i
$280$	−2.15708	+	1.24539i	−0.128910	+	0.0744263i
$281$			2.42268i			0.144525i	0.997386	+	0.0722624i	$0.0230219\pi$
$281$			2.42268i			0.144525i	−0.997386	+	0.0722624i	$0.976978\pi$
$282$	−0.389311	−	0.674306i	−0.0231831	−	0.0401543i
$283$	14.3940	−	24.9311i	0.855632	−	1.48200i	−0.0204246	−	0.999791i	$-0.506502\pi$
$283$	14.3940	−	24.9311i	0.855632	−	1.48200i	0.876057	−	0.482207i	$-0.160165\pi$
$284$	0.548845	+	0.316876i	0.0325679	+	0.0188031i
$285$	−11.0270			−0.653183
$286$	7.49991	−	8.04570i	0.443479	−	0.475752i
$287$	−8.69450			−0.513220
$288$	−6.75393	−	3.89939i	−0.397979	−	0.229774i
$289$	−12.4374	+	21.5422i	−0.731610	+	1.26719i
$290$	15.7343	+	27.2526i	0.923950	+	1.60033i
$291$		−	17.1484i		−	1.00525i
$292$	−0.745704	+	0.430532i	−0.0436390	+	0.0251950i
$293$	−11.4206	+	6.59369i	−0.667199	+	0.385207i	−0.795014	−	0.606591i	$-0.792537\pi$
$293$	−11.4206	+	6.59369i	−0.667199	+	0.385207i	0.127816	+	0.991798i	$0.459203\pi$
$294$		−	2.14586i		−	0.125149i
$295$	−8.64544	−	14.9743i	−0.503357	−	0.871840i
$296$	5.07588	−	8.79167i	0.295029	−	0.511006i
$297$	1.23117	+	0.710818i	0.0714399	+	0.0412458i
$298$	36.5198			2.11554
$299$	−7.52797	−	1.73648i	−0.435354	−	0.100423i
$300$	3.42613			0.197808
$301$	6.12665	+	3.53722i	0.353134	+	0.203882i
$302$	−7.31291	+	12.6663i	−0.420811	+	0.728866i
$303$	−4.00285	−	6.93315i	−0.229958	−	0.398299i
$304$			13.9304i			0.798961i
$305$	−13.1368	+	7.58455i	−0.752213	+	0.434290i
$306$	−12.0256	+	6.94299i	−0.687459	+	0.396904i
$307$		−	6.41459i		−	0.366100i	−0.983104	−	0.183050i	$-0.941403\pi$
$307$		−	6.41459i		−	0.366100i	0.983104	−	0.183050i	$-0.0585970\pi$
$308$	−1.85146	−	3.20683i	−0.105497	−	0.182726i
$309$	7.23581	−	12.5328i	0.411631	−	0.712965i
$310$	−8.93580	−	5.15909i	−0.507519	−	0.293016i
$311$	−26.4924			−1.50225			−0.751124	−	0.660161i	$-0.770488\pi$
$311$	−26.4924			−1.50225			−0.751124	+	0.660161i	$0.770488\pi$
$312$	−1.05159	+	4.55883i	−0.0595343	+	0.258093i
$313$	5.44885			0.307987			0.153994	−	0.988072i	$-0.450786\pi$
$313$	5.44885			0.307987			0.153994	+	0.988072i	$0.450786\pi$
$314$	−21.9137	−	12.6519i	−1.23666	−	0.713986i
$315$	0.959770	−	1.66237i	0.0540769	−	0.0936639i
$316$	11.2598	+	19.5026i	0.633414	+	1.09710i
$317$		−	26.2903i		−	1.47661i	−0.674467	−	0.738305i	$-0.735626\pi$
$317$		−	26.2903i		−	1.47661i	0.674467	−	0.738305i	$-0.264374\pi$
$318$	0.975225	−	0.563046i	0.0546879	−	0.0315741i
$319$	−9.40586	+	5.43048i	−0.526627	+	0.304048i
$320$			22.8140i			1.27534i
$321$	7.32426	+	12.6860i	0.408800	+	0.708063i
$322$	−2.29897	+	3.98194i	−0.128117	+	0.221905i
$323$	32.1934	+	18.5869i	1.79129	+	1.03420i
$324$	−2.60470			−0.144705
$325$	1.38746	+	4.53513i	0.0769625	+	0.251564i
$326$	19.1009			1.05790
$327$	11.8394	+	6.83548i	0.654720	+	0.378003i
$328$	5.64096	−	9.77043i	0.311470	−	0.539482i
$329$	−0.181424	−	0.314236i	−0.0100023	−	0.0173244i
$330$		−	5.85579i		−	0.322351i
$331$	31.2553	−	18.0453i	1.71795	−	0.991858i	0.795299	−	0.606218i	$-0.207314\pi$
$331$	31.2553	−	18.0453i	1.71795	−	0.991858i	0.922649	−	0.385640i	$-0.126019\pi$
$332$	−25.7779	+	14.8829i	−1.41474	+	0.816803i
$333$			7.82352i			0.428726i
$334$	−11.8539	−	20.5315i	−0.648614	−	1.12343i
$335$	0.389053	−	0.673860i	0.0212563	−	0.0368169i
$336$	−2.10007	−	1.21247i	−0.114568	−	0.0661458i
$337$	−13.7825			−0.750781			−0.375390	−	0.926867i	$-0.622491\pi$
$337$	−13.7825			−0.750781			−0.375390	+	0.926867i	$0.622491\pi$
$338$	−27.8274	+	1.95639i	−1.51361	+	0.106413i
$339$	1.46612			0.0796290
$340$	28.0195	+	16.1771i	1.51957	+	0.877326i
$341$	1.78059	−	3.08407i	0.0964242	−	0.167012i
$342$	6.16355	+	10.6756i	0.333287	+	0.577269i
$343$		−	1.00000i		−	0.0539949i
$344$	−7.94990	+	4.58988i	−0.428630	+	0.247470i
$345$	−3.56198	+	2.05651i	−0.191771	+	0.110719i
$346$		−	27.4064i		−	1.47338i
$347$	8.92096	+	15.4516i	0.478902	+	0.829483i	0.999707	−	0.0241927i	$-0.00770153\pi$
$347$	8.92096	+	15.4516i	0.478902	+	0.829483i	−0.520805	+	0.853676i	$0.674368\pi$
$348$	9.94963	−	17.2333i	0.533356	−	0.923800i
$349$	19.7513	+	11.4034i	1.05726	+	0.610411i	0.924674	−	0.380760i	$-0.124338\pi$
$349$	19.7513	+	11.4034i	1.05726	+	0.610411i	0.132589	+	0.991171i	$0.457671\pi$
$350$	2.82259			0.150874
$351$	−1.05481	−	3.44781i	−0.0563015	−	0.184030i
$352$	−11.0870			−0.590940
$353$	−2.92799	−	1.69048i	−0.155841	−	0.0899750i	0.420051	−	0.907500i	$-0.362012\pi$
$353$	−2.92799	−	1.69048i	−0.155841	−	0.0899750i	−0.575893	+	0.817525i	$0.695345\pi$
$354$	−9.66475	+	16.7398i	−0.513676	+	0.889713i
$355$	0.233522	+	0.404473i	0.0123941	+	0.0214672i
$356$			33.0104i			1.74955i
$357$	−5.60411	+	3.23553i	−0.296601	+	0.171243i
$358$	38.7630	−	22.3798i	2.04869	−	1.18281i
$359$		−	11.4402i		−	0.603789i	−0.953341	−	0.301894i	$-0.902381\pi$
$359$		−	11.4402i		−	0.603789i	0.953341	−	0.301894i	$-0.0976190\pi$
$360$	1.24539	+	2.15708i	0.0656379	+	0.113688i
$361$	7.00025	−	12.1248i	0.368434	−	0.638147i
$362$	−0.700738	−	0.404571i	−0.0368300	−	0.0212638i
$363$	−8.97895			−0.471273
$364$	−2.11088	+	9.15107i	−0.110640	+	0.479646i
$365$	−0.634564			−0.0332146
$366$	14.6857	+	8.47878i	0.767633	+	0.443193i
$367$	4.68792	−	8.11971i	0.244707	−	0.423846i	−0.717342	−	0.696721i	$-0.754641\pi$
$367$	4.68792	−	8.11971i	0.244707	−	0.423846i	0.962049	+	0.272876i	$0.0879748\pi$
$368$	2.59798	+	4.49983i	0.135429	+	0.234570i
$369$			8.69450i			0.452617i
$370$	27.9081	−	16.1128i	1.45087	−	0.837663i
$371$	0.454469	−	0.262388i	0.0235949	−	0.0136225i
$372$			6.52473i			0.338291i
$373$	2.12650	+	3.68320i	0.110106	+	0.190709i	0.915813	−	0.401605i	$-0.131548\pi$
$373$	2.12650	+	3.68320i	0.110106	+	0.190709i	−0.805707	+	0.592314i	$0.798214\pi$
$374$	−9.87040	+	17.0960i	−0.510386	+	0.884015i
$375$	10.4985	+	6.06130i	0.542139	+	0.313004i
$376$	0.470830			0.0242812
$377$	26.8407	+	6.19136i	1.38237	+	0.318871i
$378$	−2.14586			−0.110371
$379$	−19.0987	−	11.0266i	−0.981033	−	0.566400i	−0.0784512	−	0.996918i	$-0.524997\pi$
$379$	−19.0987	−	11.0266i	−0.981033	−	0.566400i	−0.902582	+	0.430518i	$0.858331\pi$
$380$	14.3610	−	24.8740i	0.736704	−	1.27601i
$381$	4.48636	+	7.77061i	0.229843	+	0.398101i
$382$		−	37.3596i		−	1.91148i
$383$	−12.1449	+	7.01187i	−0.620576	+	0.358290i	−0.777093	−	0.629385i	$-0.783307\pi$
$383$	−12.1449	+	7.01187i	−0.620576	+	0.358290i	0.156517	+	0.987675i	$0.449973\pi$
$384$	8.57908	−	4.95313i	0.437799	−	0.252764i
$385$		−	2.72888i		−	0.139077i
$386$	−11.9662	−	20.7261i	−0.609064	−	1.05493i
$387$	3.53722	−	6.12665i	0.179807	−	0.311435i
$388$	38.6821	+	22.3331i	1.96379	+	1.13379i
$389$	−9.60683			−0.487086			−0.243543	−	0.969890i	$-0.578310\pi$
$389$	−9.60683			−0.487086			−0.243543	+	0.969890i	$0.578310\pi$
$390$	−10.1266	+	10.8636i	−0.512782	+	0.550099i
$391$	13.8656			0.701215
$392$	1.12375	+	0.648797i	0.0567579	+	0.0327692i
$393$	−0.749189	+	1.29763i	−0.0377916	+	0.0654569i
$394$	8.91423	+	15.4399i	0.449093	+	0.777851i
$395$			16.5959i			0.835030i
$396$	−3.20683	+	1.85146i	−0.161149	+	0.0930396i
$397$	34.0184	−	19.6406i	1.70734	−	0.985731i	0.769505	−	0.638641i	$-0.220503\pi$
$397$	34.0184	−	19.6406i	1.70734	−	0.985731i	0.937832	−	0.347090i	$-0.112830\pi$
$398$		−	20.0229i		−	1.00366i
$399$	2.87230	+	4.97497i	0.143795	+	0.249060i
$400$	1.59485	−	2.76236i	0.0797424	−	0.138118i
$401$	1.79678	+	1.03737i	0.0897270	+	0.0518039i	0.544192	−	0.838961i	$-0.316836\pi$
$401$	1.79678	+	1.03737i	0.0897270	+	0.0518039i	−0.454465	+	0.890765i	$0.650170\pi$
$402$	−0.869846			−0.0433840
$403$	−8.63671	+	2.64228i	−0.430225	+	0.131621i
$404$	20.8524			1.03745
$405$	−1.66237	−	0.959770i	−0.0826038	−	0.0476913i
$406$	8.19691	−	14.1975i	0.406806	−	0.704609i
$407$	5.56110	+	9.63211i	0.275653	+	0.477446i
$408$		−	8.39682i		−	0.415704i
$409$	−32.3179	+	18.6587i	−1.59802	+	0.922615i	−0.606146	+	0.795353i	$0.707285\pi$
$409$	−32.3179	+	18.6587i	−1.59802	+	0.922615i	−0.991869	+	0.127261i	$0.959381\pi$
$410$	31.0151	−	17.9066i	1.53172	−	0.884342i
$411$			13.5700i			0.669358i
$412$	18.8471	+	32.6441i	0.928529	+	1.60826i
$413$	−4.50392	+	7.80101i	−0.221623	+	0.383863i
$414$	3.98194	+	2.29897i	0.195702	+	0.112988i
$415$	−21.9359			−1.07679
$416$	20.5684	+	19.1732i	1.00845	+	0.940042i
$417$	−6.33420			−0.310187
$418$	15.1768	+	8.76232i	0.742320	+	0.428579i
$419$	−7.02427	+	12.1664i	−0.343158	+	0.594367i	−0.985017	−	0.172455i	$-0.944830\pi$
$419$	−7.02427	+	12.1664i	−0.343158	+	0.594367i	0.641859	+	0.766822i	$0.278163\pi$
$420$	2.49991	+	4.32997i	0.121983	+	0.211281i
$421$			20.3637i			0.992467i	0.868189	+	0.496233i	$0.165284\pi$
$421$			20.3637i			0.992467i	−0.868189	+	0.496233i	$0.834716\pi$
$422$	−51.1531	+	29.5332i	−2.49009	+	1.43766i
$423$	−0.314236	+	0.181424i	−0.0152787	+	0.00882116i
$424$			0.680945i			0.0330696i
$425$	−4.25592	−	7.37147i	−0.206442	−	0.357569i
$426$	0.261055	−	0.452161i	0.0126482	−	0.0219073i
$427$	6.84374	+	3.95123i	0.331192	+	0.191214i
$428$	−38.1550			−1.84429
$429$	−3.74941	−	3.49507i	−0.181023	−	0.168743i
$430$	−29.1400			−1.40526
$431$	32.6736	+	18.8641i	1.57383	+	0.908653i	0.995693	+	0.0927159i	$0.0295548\pi$
$431$	32.6736	+	18.8641i	1.57383	+	0.908653i	0.578141	+	0.815937i	$0.303778\pi$
$432$	−1.21247	+	2.10007i	−0.0583352	+	0.101039i
$433$	14.7861	+	25.6104i	0.710577	+	1.23076i	0.964641	+	0.263568i	$0.0848993\pi$
$433$	14.7861	+	25.6104i	0.710577	+	1.23076i	−0.254064	+	0.967187i	$0.581767\pi$
$434$			5.37534i			0.258024i
$435$	12.7001	−	7.33241i	0.608924	−	0.351562i
$436$	−30.8380	+	17.8044i	−1.47687	+	0.852674i
$437$		−	12.3090i		−	0.588821i
$438$	0.354690	+	0.614341i	0.0169477	+	0.0293544i
$439$	−5.11420	+	8.85805i	−0.244087	+	0.422772i	−0.961875	−	0.273491i	$-0.911822\pi$
$439$	−5.11420	+	8.85805i	−0.244087	+	0.422772i	0.717787	+	0.696263i	$0.245155\pi$
$440$	3.06658	+	1.77049i	0.146194	+	0.0844049i
$441$	−1.00000			−0.0476190
$442$	47.8762	−	14.6471i	2.27724	−	0.696689i
$443$	−0.256887			−0.0122051			−0.00610253	−	0.999981i	$-0.501943\pi$
$443$	−0.256887			−0.0122051			−0.00610253	+	0.999981i	$0.501943\pi$
$444$	−17.6478	−	10.1890i	−0.837527	−	0.483546i
$445$	−12.1636	+	21.0679i	−0.576608	+	0.998714i
$446$	−9.32481	−	16.1510i	−0.441542	−	0.764774i
$447$		−	17.0188i		−	0.804960i
$448$	10.2928	−	5.94257i	0.486291	−	0.280760i
$449$	7.69432	−	4.44232i	0.363118	−	0.209646i	−0.307330	−	0.951603i	$-0.599435\pi$
$449$	7.69432	−	4.44232i	0.363118	−	0.209646i	0.670447	+	0.741957i	$0.266102\pi$
$450$		−	2.82259i		−	0.133058i
$451$	6.18020	+	10.7044i	0.291014	+	0.504051i
$452$	−1.90941	+	3.30719i	−0.0898109	+	0.155557i
$453$	5.90270	+	3.40792i	0.277333	+	0.160118i
$454$	6.45314			0.302861
$455$	−4.71916	+	5.06258i	−0.221238	+	0.237338i
$456$	−7.45416			−0.349073
$457$	−23.5402	−	13.5909i	−1.10116	−	0.635758i	−0.164638	−	0.986354i	$-0.552646\pi$
$457$	−23.5402	−	13.5909i	−1.10116	−	0.635758i	−0.936527	+	0.350596i	$0.885979\pi$
$458$	−12.6919	+	21.9830i	−0.593053	+	1.02720i
$459$	3.23553	+	5.60411i	0.151022	+	0.261577i
$460$		−	10.7132i		−	0.499504i
$461$	31.3117	−	18.0778i	1.45833	−	0.841969i	0.459403	−	0.888228i	$-0.348063\pi$
$461$	31.3117	−	18.0778i	1.45833	−	0.841969i	0.998929	+	0.0462592i	$0.0147300\pi$
$462$	−2.64192	+	1.52531i	−0.122913	+	0.0709639i
$463$		−	13.0662i		−	0.607240i	−0.952793	−	0.303620i	$-0.901805\pi$
$463$		−	13.0662i		−	0.607240i	0.952793	−	0.303620i	$-0.0981953\pi$
$464$	−9.26301	−	16.0440i	−0.430024	−	0.744824i
$465$	−2.40421	+	4.16421i	−0.111493	+	0.193111i
$466$	27.5088	+	15.8822i	1.27432	+	0.735728i
$467$	−14.7172			−0.681029			−0.340514	−	0.940239i	$-0.610601\pi$
$467$	−14.7172			−0.681029			−0.340514	+	0.940239i	$0.610601\pi$
$468$	9.15107	+	2.11088i	0.423008	+	0.0975755i
$469$	−0.405361			−0.0187178
$470$	1.29436	+	0.747297i	0.0597042	+	0.0344703i
$471$	−5.89595	+	10.2121i	−0.271671	+	0.470548i
$472$	−5.84425	−	10.1225i	−0.269003	−	0.465928i
$473$		−	10.0573i		−	0.462434i
$474$	16.0670	−	9.27629i	0.737982	−	0.426074i
$475$	−6.54392	+	3.77813i	−0.300256	+	0.173353i
$476$		−	16.8552i		−	0.772556i
$477$	−0.262388	−	0.454469i	−0.0120139	−	0.0208087i
$478$	−9.03099	+	15.6421i	−0.413068	+	0.715455i
$479$	1.92721	+	1.11267i	0.0880563	+	0.0508393i	0.543382	−	0.839486i	$-0.317144\pi$
$479$	1.92721	+	1.11267i	0.0880563	+	0.0508393i	−0.455325	+	0.890325i	$0.650477\pi$
$480$	14.9701			0.683286
$481$	6.34028	−	27.4863i	0.289092	−	1.25327i
$482$	38.4623			1.75191
$483$	1.85564	+	1.07136i	0.0844347	+	0.0487484i
$484$	11.6937	−	20.2541i	0.531533	−	0.920642i
$485$	16.4585	+	28.5069i	0.747341	+	1.29443i
$486$			2.14586i			0.0973380i
$487$	12.2071	−	7.04777i	0.553157	−	0.319365i	−0.197238	−	0.980356i	$-0.563197\pi$
$487$	12.2071	−	7.04777i	0.553157	−	0.319365i	0.750394	+	0.660991i	$0.229864\pi$
$488$	−8.88039	+	5.12710i	−0.401996	+	0.232093i
$489$		−	8.90127i		−	0.402530i
$490$	2.05953	+	3.56721i	0.0930400	+	0.161150i
$491$	−16.0714	+	27.8364i	−0.725291	+	1.25624i	0.233563	+	0.972342i	$0.424961\pi$
$491$	−16.0714	+	27.8364i	−0.725291	+	1.25624i	−0.958854	+	0.283899i	$0.908372\pi$
$492$	−19.6125	−	11.3233i	−0.884198	−	0.510492i
$493$	−49.4374			−2.22655
$494$	−13.0027	−	42.5015i	−0.585020	−	1.91223i
$495$	−2.72888			−0.122654
$496$	5.26063	+	3.03723i	0.236209	+	0.136376i
$497$	0.121655	−	0.210713i	0.00545699	−	0.00945179i
$498$	12.2611	+	21.2369i	0.549433	+	0.951647i
$499$			38.9893i			1.74540i	0.488255	+	0.872701i	$0.337633\pi$
$499$			38.9893i			1.74540i	−0.488255	+	0.872701i	$0.662367\pi$
$500$	−27.3454	+	15.7878i	−1.22292	+	0.706054i
$501$	−9.56796	+	5.52407i	−0.427465	+	0.246797i
$502$			9.98492i			0.445649i
$503$	−12.5768	−	21.7837i	−0.560772	−	0.971286i	−0.997429	−	0.0716578i	$-0.977171\pi$
$503$	−12.5768	−	21.7837i	−0.560772	−	0.971286i	0.436657	−	0.899628i	$-0.356162\pi$
$504$	0.648797	−	1.12375i	0.0288997	−	0.0500557i
$505$	13.3084	+	7.68364i	0.592218	+	0.341917i
$506$	6.53661			0.290588
$507$	0.911705	+	12.9680i	0.0404902	+	0.575929i
$508$	−23.3712			−1.03693
$509$	−9.25827	−	5.34527i	−0.410366	−	0.236925i	0.280581	−	0.959830i	$-0.409473\pi$
$509$	−9.25827	−	5.34527i	−0.410366	−	0.236925i	−0.690947	+	0.722906i	$0.742806\pi$
$510$	13.3273	−	23.0836i	0.590145	−	1.02216i
$511$	0.165291	+	0.286292i	0.00731203	+	0.0126648i
$512$		−	25.2048i		−	1.11391i
$513$	4.97497	−	2.87230i	0.219651	−	0.126815i
$514$	50.2129	−	28.9904i	2.21480	−	1.27871i
$515$			27.7788i			1.22408i
$516$	9.21340	+	15.9581i	0.405597	+	0.702515i
$517$	−0.257919	+	0.446730i	−0.0113433	+	0.0196471i
$518$	−14.5390	−	8.39408i	−0.638806	−	0.368815i
$519$	−12.7718			−0.560620
$520$	−2.62730	−	8.58774i	−0.115215	−	0.376597i
$521$	−25.5518			−1.11944			−0.559722	−	0.828680i	$-0.689092\pi$
$521$	−25.5518			−1.11944			−0.559722	+	0.828680i	$0.689092\pi$
$522$	−14.1975	−	8.19691i	−0.621406	−	0.358769i
$523$	4.78539	−	8.28854i	0.209251	−	0.362432i	−0.742228	−	0.670147i	$-0.766231\pi$
$523$	4.78539	−	8.28854i	0.209251	−	0.362432i	0.951479	+	0.307715i	$0.0995643\pi$
$524$	−1.95141	−	3.37994i	−0.0852477	−	0.147653i
$525$		−	1.31537i		−	0.0574074i
$526$	−21.8166	+	12.5958i	−0.951247	+	0.549203i
$527$	14.0382	−	8.10497i	0.611514	−	0.353058i
$528$			3.44739i			0.150028i
$529$	9.20439	+	15.9425i	0.400191	+	0.693151i
$530$	−1.08079	+	1.87198i	−0.0469465	+	0.0813137i
$531$	7.80101	+	4.50392i	0.338535	+	0.195453i
$532$	−14.9630			−0.648727
$533$	7.04613	−	30.5463i	0.305202	−	1.32311i
$534$	27.1953			1.17686
$535$	−24.3513	−	14.0592i	−1.05280	−	0.607833i
$536$	0.262997	−	0.455524i	0.0113597	−	0.0196756i
$537$	−10.4293	−	18.0641i	−0.450058	−	0.779524i
$538$		−	7.55738i		−	0.325822i
$539$	−1.23117	+	0.710818i	−0.0530303	+	0.0306171i
$540$	4.32997	−	2.49991i	0.186332	−	0.107579i
$541$			36.9121i			1.58697i	0.608587	+	0.793487i	$0.291737\pi$
$541$			36.9121i			1.58697i	−0.608587	+	0.793487i	$0.708263\pi$
$542$	−23.0558	−	39.9338i	−0.990330	−	1.71530i
$543$	−0.188536	+	0.326554i	−0.00809085	+	0.0140138i
$544$	−43.7052	−	25.2332i	−1.87384	−	1.08186i
$545$	−26.2419			−1.12408
$546$	7.53902	+	1.73903i	0.322640	+	0.0744236i
$547$	−11.8055			−0.504767			−0.252383	−	0.967627i	$-0.581214\pi$
$547$	−11.8055			−0.504767			−0.252383	+	0.967627i	$0.581214\pi$
$548$	−30.6103	−	17.6728i	−1.30761	−	0.754946i
$549$	3.95123	−	6.84374i	0.168635	−	0.292084i
$550$	−2.00635	−	3.47509i	−0.0855509	−	0.148178i
$551$			43.8874i			1.86967i
$552$	−2.40787	+	1.39018i	−0.102486	+	0.0591701i
$553$	7.48746	−	4.32289i	0.318399	−	0.183828i
$554$		−	54.5401i		−	2.31719i
$555$	−7.50878	−	13.0056i	−0.318730	−	0.552057i
$556$	8.24934	−	14.2883i	0.349850	−	0.605958i
$557$	−25.6132	−	14.7878i	−1.08526	−	0.626578i	−0.152953	−	0.988233i	$-0.548878\pi$
$557$	−25.6132	−	14.7878i	−1.08526	−	0.626578i	−0.932312	+	0.361656i	$0.882212\pi$
$558$	5.37534			0.227556
$559$	−17.3924	+	18.6581i	−0.735621	+	0.789154i
$560$	4.65478			0.196700
$561$	7.96700	+	4.59975i	0.336367	+	0.194202i
$562$	−2.59936	+	4.50222i	−0.109647	+	0.189915i
$563$	−6.38047	−	11.0513i	−0.268905	−	0.465756i	0.699675	−	0.714462i	$-0.253328\pi$
$563$	−6.38047	−	11.0513i	−0.268905	−	0.465756i	−0.968579	+	0.248705i	$0.919995\pi$
$564$		−	0.945112i		−	0.0397964i
$565$	−2.43724	+	1.40714i	−0.102536	+	0.0591989i
$566$	53.4985	−	30.8874i	2.24871	−	1.29829i
$567$			1.00000i			0.0419961i
$568$	0.157859	+	0.273420i	0.00662363	+	0.0114725i
$569$	−17.2939	+	29.9539i	−0.724998	+	1.25573i	0.233977	+	0.972242i	$0.424826\pi$
$569$	−17.2939	+	29.9539i	−0.724998	+	1.25573i	−0.958975	+	0.283491i	$0.908507\pi$
$570$	−20.4922	−	11.8312i	−0.858324	−	0.495553i
$571$	39.8897			1.66933			0.834666	−	0.550757i	$-0.185661\pi$
$571$	39.8897			1.66933			0.834666	+	0.550757i	$0.185661\pi$
$572$	12.7670	−	3.90588i	0.533815	−	0.163313i
$573$	−17.4101			−0.727318
$574$	−16.1576	−	9.32857i	−0.674403	−	0.389367i
$575$	−1.40923	+	2.44085i	−0.0587688	+	0.101791i
$576$	−5.94257	−	10.2928i	−0.247607	−	0.428868i
$577$		−	21.8823i		−	0.910972i	−0.890243	−	0.455486i	$-0.849465\pi$
$577$		−	21.8823i		−	0.910972i	0.890243	−	0.455486i	$-0.150535\pi$
$578$	−46.2264	+	26.6888i	−1.92276	+	1.11011i
$579$	−9.65866	+	5.57643i	−0.401400	+	0.231748i
$580$			38.1974i			1.58606i
$581$	5.71385	+	9.89669i	0.237051	+	0.410584i
$582$	18.3989	−	31.8679i	0.762661	−	1.32097i
$583$	−0.646089	−	0.373020i	−0.0267583	−	0.0154489i
$584$	−0.428960			−0.0177505
$585$	5.06258	+	4.71916i	0.209312	+	0.195113i
$586$	−28.2982			−1.16899
$587$	36.5972	+	21.1294i	1.51053	+	0.872103i	0.999925	+	0.0122866i	$0.00391104\pi$
$587$	36.5972	+	21.1294i	1.51053	+	0.872103i	0.510603	+	0.859817i	$0.329422\pi$
$588$	1.30235	−	2.25573i	0.0537080	−	0.0930249i
$589$	−7.19508	−	12.4622i	−0.296468	−	0.513498i
$590$		−	37.1038i		−	1.52754i
$591$	7.19522	−	4.15416i	0.295972	−	0.170879i
$592$	−16.4299	+	9.48581i	−0.675265	+	0.389865i
$593$			8.62045i			0.353999i	0.984211	+	0.177000i	$0.0566391\pi$
$593$			8.62045i			0.353999i	−0.984211	+	0.177000i	$0.943361\pi$
$594$	1.52531	+	2.64192i	0.0625843	+	0.108399i
$595$	6.21074	−	10.7573i	0.254615	−	0.441007i
$596$	38.3898	+	22.1644i	1.57251	+	0.907887i
$597$	−9.33095			−0.381890
$598$	−12.1266	−	11.3040i	−0.495894	−	0.462254i
$599$	45.0330			1.84000			0.919999	−	0.391921i	$-0.128189\pi$
$599$	45.0330			1.84000			0.919999	+	0.391921i	$0.128189\pi$
$600$	1.47814	+	0.853406i	0.0603449	+	0.0348402i
$601$	20.9576	−	36.2996i	0.854878	−	1.48069i	−0.0218807	−	0.999761i	$-0.506965\pi$
$601$	20.9576	−	36.2996i	0.854878	−	1.48069i	0.876758	−	0.480931i	$-0.159701\pi$
$602$	7.59037	+	13.1469i	0.309360	+	0.535828i
$603$			0.405361i			0.0165076i
$604$	−15.3747	+	8.87661i	−0.625589	+	0.361184i
$605$	14.9263	−	8.61773i	0.606842	−	0.350360i
$606$		−	17.1791i		−	0.697853i
$607$	−4.05732	−	7.02748i	−0.164681	−	0.285236i	0.771861	−	0.635792i	$-0.219326\pi$
$607$	−4.05732	−	7.02748i	−0.164681	−	0.285236i	−0.936542	+	0.350555i	$0.885993\pi$
$608$	−22.4004	+	38.7987i	−0.908458	+	1.57349i
$609$	−6.61623	−	3.81988i	−0.268103	−	0.154789i
$610$	−32.5507			−1.31794
$611$	1.25103	−	0.382736i	0.0506114	−	0.0154838i
$612$	−16.8552			−0.681330
$613$	−2.66161	−	1.53668i	−0.107501	−	0.0620659i	0.445285	−	0.895389i	$-0.353102\pi$
$613$	−2.66161	−	1.53668i	−0.107501	−	0.0620659i	−0.552787	+	0.833323i	$0.686436\pi$
$614$	6.88239	−	11.9206i	0.277751	−	0.481078i
$615$	−8.34471	−	14.4535i	−0.336491	−	0.582820i
$616$		−	1.84470i		−	0.0743252i
$617$	5.84446	−	3.37430i	0.235289	−	0.135844i	−0.377721	−	0.925920i	$-0.623292\pi$
$617$	5.84446	−	3.37430i	0.235289	−	0.135844i	0.613010	+	0.790075i	$0.289959\pi$
$618$	26.8936	−	15.5270i	1.08182	−	0.624588i
$619$		−	1.73712i		−	0.0698208i	−0.999390	−	0.0349104i	$-0.988885\pi$
$619$		−	1.73712i		−	0.0698208i	0.999390	−	0.0349104i	$-0.0111146\pi$
$620$	−6.26224	−	10.8465i	−0.251498	−	0.435606i
$621$	1.07136	−	1.85564i	0.0429920	−	0.0744644i
$622$	−49.2327	−	28.4245i	−1.97405	−	1.13972i
$623$	12.6734			0.507749
$624$	5.96169	−	6.39554i	0.238659	−	0.256027i
$625$	−16.6930			−0.667719
$626$	10.1260	+	5.84622i	0.404715	+	0.233662i
$627$	4.08337	−	7.07260i	0.163074	−	0.282452i
$628$	−15.3572	−	26.5994i	−0.612818	−	1.06143i
$629$			50.6266i			2.01861i
$630$	3.56721	−	2.05953i	0.142121	−	0.0820535i
$631$	−36.4153	+	21.0244i	−1.44967	+	0.836968i	−0.998461	−	0.0554494i	$-0.982341\pi$
$631$	−36.4153	+	21.0244i	−1.44967	+	0.836968i	−0.451210	+	0.892418i	$0.649008\pi$
$632$			11.2187i			0.446256i
$633$	13.7629	+	23.8381i	0.547027	+	0.947478i
$634$	28.2076	−	48.8570i	1.12027	−	1.94036i
$635$	−14.9160	−	8.61176i	−0.591923	−	0.341747i
$636$	1.36688			0.0542004
$637$	3.51329	+	0.810413i	0.139202	+	0.0321097i
$638$	−23.3060			−0.922695
$639$	−0.210713	−	0.121655i	−0.00833569	−	0.00481261i
$640$	−9.50774	+	16.4679i	−0.375826	+	0.650950i
$641$	1.25436	+	2.17262i	0.0495444	+	0.0858133i	0.889734	−	0.456479i	$-0.150890\pi$
$641$	1.25436	+	2.17262i	0.0495444	+	0.0858133i	−0.840190	+	0.542293i	$0.817556\pi$
$642$			31.4336i			1.24059i
$643$	−26.7441	+	15.4407i	−1.05468	+	0.608923i	−0.923957	−	0.382496i	$-0.875065\pi$
$643$	−26.7441	+	15.4407i	−1.05468	+	0.608923i	−0.130728	+	0.991418i	$0.541731\pi$
$644$	−4.83339	+	2.79056i	−0.190462	+	0.109963i
$645$			13.5797i			0.534699i
$646$	39.8847	+	69.0824i	1.56924	+	2.71801i
$647$	−5.02947	+	8.71130i	−0.197729	+	0.342477i	−0.947792	−	0.318890i	$-0.896690\pi$
$647$	−5.02947	+	8.71130i	−0.197729	+	0.342477i	0.750063	+	0.661367i	$0.230023\pi$
$648$	−1.12375	−	0.648797i	−0.0441450	−	0.0254871i
$649$	12.8058			0.502674
$650$	−2.28746	+	9.91658i	−0.0897217	+	0.388960i
$651$	2.50499			0.0981781
$652$	20.0789	+	11.5926i	0.786351	+	0.454000i
$653$	12.2239	−	21.1724i	0.478358	−	0.828540i	−0.521334	−	0.853353i	$-0.674566\pi$
$653$	12.2239	−	21.1724i	0.478358	−	0.828540i	0.999692	+	0.0248125i	$0.00789889\pi$
$654$	14.6680	+	25.4056i	0.573562	+	0.993439i
$655$		−	2.87620i		−	0.112382i
$656$	−18.2590	+	10.5418i	−0.712895	+	0.411590i
$657$	0.286292	−	0.165291i	0.0111693	−	0.00644860i
$658$		−	0.778622i		−	0.0303538i
$659$	23.7648	+	41.1619i	0.925746	+	1.60344i	0.790357	+	0.612647i	$0.209895\pi$
$659$	23.7648	+	41.1619i	0.925746	+	1.60344i	0.135389	+	0.990792i	$0.456771\pi$
$660$	3.55396	−	6.15564i	0.138338	−	0.239608i
$661$	25.7024	+	14.8393i	0.999708	+	0.577182i	0.908162	−	0.418619i	$-0.137486\pi$
$661$	25.7024	+	14.8393i	0.999708	+	0.577182i	0.0915463	+	0.995801i	$0.470819\pi$
$662$	77.4451			3.00999
$663$	−6.82574	−	22.3110i	−0.265090	−	0.866488i
$664$	−14.8285			−0.575458
$665$	−9.54966	−	5.51350i	−0.370320	−	0.213804i
$666$	−8.39408	+	14.5390i	−0.325264	+	0.563374i
$667$	8.18490	+	14.1767i	0.316921	+	0.548923i
$668$		−	28.7770i		−	1.11342i
$669$	−7.52662	+	4.34550i	−0.290996	+	0.168007i
$670$	1.44601	−	0.834852i	0.0558641	−	0.0322532i
$671$		−	11.2344i		−	0.433700i
$672$	−3.89939	−	6.75393i	−0.150422	−	0.260539i
$673$	0.610338	−	1.05714i	0.0235268	−	0.0407496i	−0.854022	−	0.520236i	$-0.825844\pi$
$673$	0.610338	−	1.05714i	0.0235268	−	0.0407496i	0.877549	+	0.479487i	$0.159177\pi$
$674$	−25.6129	−	14.7876i	−0.986573	−	0.569598i
$675$	−1.31537			−0.0506285
$676$	−30.4397	−	14.8323i	−1.17076	−	0.570472i
$677$	6.05760			0.232812			0.116406	−	0.993202i	$-0.462863\pi$
$677$	6.05760			0.232812			0.116406	+	0.993202i	$0.462863\pi$
$678$	2.72460	+	1.57305i	0.104637	+	0.0604125i
$679$	8.57418	−	14.8509i	0.329047	−	0.569926i
$680$	8.05901	+	13.9586i	0.309049	+	0.535288i
$681$		−	3.00725i		−	0.115238i
$682$	6.61797	−	3.82088i	0.253415	−	0.146309i
$683$	−25.0316	+	14.4520i	−0.957808	+	0.552991i	−0.895498	−	0.445066i	$-0.853180\pi$
$683$	−25.0316	+	14.4520i	−0.957808	+	0.552991i	−0.0623106	+	0.998057i	$0.519847\pi$
$684$			14.9630i			0.572123i
$685$	−13.0241	−	22.5583i	−0.497624	−	0.861909i
$686$	1.07293	−	1.85837i	0.0409646	−	0.0709527i
$687$	10.2444	+	5.91461i	0.390848	+	0.225656i
$688$	17.1552			0.654034
$689$	0.553538	+	1.80933i	0.0210881	+	0.0689298i
$690$	−8.82595			−0.335998
$691$	−9.91022	−	5.72167i	−0.377003	−	0.217663i	0.299511	−	0.954093i	$-0.403177\pi$
$691$	−9.91022	−	5.72167i	−0.377003	−	0.217663i	−0.676513	+	0.736430i	$0.736510\pi$
$692$	16.6333	−	28.8098i	0.632304	−	1.09518i
$693$	0.710818	+	1.23117i	0.0270017	+	0.0467684i
$694$			38.2862i			1.45332i
$695$	10.5298	−	6.07938i	0.399418	−	0.230604i
$696$	8.58517	−	4.95665i	0.325420	−	0.187881i
$697$			56.2627i			2.13110i
$698$	24.4701	+	42.3835i	0.926207	+	1.60424i
$699$	7.40133	−	12.8195i	0.279944	−	0.484877i
$700$	2.96712	+	1.71307i	0.112147	+	0.0647479i
$701$	10.1839			0.384640			0.192320	−	0.981332i	$-0.438399\pi$
$701$	10.1839			0.384640			0.192320	+	0.981332i	$0.438399\pi$
$702$	1.73903	−	7.53902i	0.0656354	−	0.284542i
$703$	44.9431			1.69506
$704$	−14.6327	−	8.44817i	−0.551489	−	0.318402i
$705$	0.348251	−	0.603189i	0.0131159	−	0.0227174i
$706$	−3.62752	−	6.28305i	−0.136523	−	0.236466i
$707$		−	8.00571i		−	0.301086i
$708$	−20.3193	+	11.7313i	−0.763645	+	0.440891i
$709$	−1.76115	+	1.01680i	−0.0661415	+	0.0381868i	−0.532706	−	0.846300i	$-0.678825\pi$
$709$	−1.76115	+	1.01680i	−0.0661415	+	0.0381868i	0.466565	+	0.884487i	$0.345492\pi$
$710$			1.00221i			0.0376123i
$711$	−4.32289	−	7.48746i	−0.162121	−	0.280802i
$712$	−8.22246	+	14.2417i	−0.308150	+	0.533731i
$713$	−4.64836	−	2.68373i	−0.174082	−	0.100506i
$714$	−13.8860			−0.519670
$715$	9.58737	+	2.21152i	0.358547	+	0.0827063i
$716$	54.3304			2.03042
$717$	7.28947	+	4.20857i	0.272230	+	0.157172i
$718$	12.2745	−	21.2600i	0.458079	−	0.793416i
$719$	−3.87410	−	6.71014i	−0.144480	−	0.250246i	0.784699	−	0.619877i	$-0.212817\pi$
$719$	−3.87410	−	6.71014i	−0.144480	−	0.250246i	−0.929179	+	0.369631i	$0.879484\pi$
$720$		−	4.65478i		−	0.173473i
$721$	12.5328	−	7.23581i	0.466745	−	0.269476i
$722$	26.0180	−	15.0215i	0.968291	−	0.559043i
$723$		−	17.9240i		−	0.666601i
$724$	−0.491079	−	0.850574i	−0.0182508	−	0.0316113i
$725$	5.02455	−	8.70277i	0.186607	−	0.323213i
$726$	−16.6862	−	9.63377i	−0.619282	−	0.357543i
$727$	13.8427			0.513399			0.256699	−	0.966491i	$-0.417365\pi$
$727$	13.8427			0.513399			0.256699	+	0.966491i	$0.417365\pi$
$728$	−3.19011	+	3.42227i	−0.118233	+	0.126838i
$729$	1.00000			0.0370370
$730$	−1.17925	−	0.680842i	−0.0436461	−	0.0251991i
$731$	22.8896	−	39.6460i	0.846603	−	1.46636i
$732$	10.2918	+	17.8259i	0.380395	+	0.658863i
$733$		−	35.7612i		−	1.32087i	−0.750883	−	0.660435i	$-0.770372\pi$
$733$		−	35.7612i		−	1.32087i	0.750883	−	0.660435i	$-0.229628\pi$
$734$	17.4237	−	10.0596i	0.643122	−	0.371307i
$735$	1.66237	−	0.959770i	0.0613174	−	0.0354016i
$736$			16.7105i			0.615958i
$737$	0.288138	+	0.499069i	0.0106137	+	0.0183835i
$738$	−9.32857	+	16.1576i	−0.343389	+	0.594768i
$739$	9.87496	+	5.70131i	0.363256	+	0.209726i	0.670508	−	0.741902i	$-0.266076\pi$
$739$	9.87496	+	5.70131i	0.363256	+	0.209726i	−0.307252	+	0.951628i	$0.599409\pi$
$740$	39.1162			1.43794
$741$	−19.8063	+	6.05946i	−0.727603	+	0.222600i
$742$	1.12609			0.0413402
$743$	−29.8150	−	17.2137i	−1.09381	−	0.631510i	−0.159219	−	0.987243i	$-0.550898\pi$
$743$	−29.8150	−	17.2137i	−1.09381	−	0.631510i	−0.934587	+	0.355734i	$0.884231\pi$
$744$	−1.62523	+	2.81497i	−0.0595837	+	0.103202i
$745$	16.3341	+	28.2915i	0.598435	+	1.03652i
$746$			9.12632i			0.334138i
$747$	9.89669	−	5.71385i	0.362101	−	0.209059i
$748$	−20.7516	+	11.9810i	−0.758755	+	0.438067i
$749$			14.6485i			0.535245i
$750$	13.0067	+	22.5282i	0.474937	+	0.822614i
$751$	23.2990	−	40.3550i	0.850192	−	1.47258i	−0.0308432	−	0.999524i	$-0.509819\pi$
$751$	23.2990	−	40.3550i	0.850192	−	1.47258i	0.881035	−	0.473051i	$-0.156847\pi$
$752$	−0.762007	−	0.439945i	−0.0277875	−	0.0160431i
$753$	4.65312			0.169569
$754$	43.2370	+	40.3040i	1.57460	+	1.46778i
$755$	−13.0833			−0.476150
$756$	−2.25573	−	1.30235i	−0.0820403	−	0.0473660i
$757$	−26.0499	+	45.1197i	−0.946799	+	1.63990i	−0.194690	+	0.980865i	$0.562370\pi$
$757$	−26.0499	+	45.1197i	−0.946799	+	1.63990i	−0.752109	+	0.659039i	$0.770963\pi$
$758$	−23.6615	−	40.9830i	−0.859426	−	1.48857i
$759$		−	3.04615i		−	0.110568i
$760$	12.3916	−	7.15428i	0.449490	−	0.259513i
$761$	−35.9488	+	20.7550i	−1.30314	+	0.752370i	−0.980942	−	0.194302i	$-0.937756\pi$
$761$	−35.9488	+	20.7550i	−1.30314	+	0.752370i	−0.322201	+	0.946671i	$0.604423\pi$
$762$			19.2542i			0.697506i
$763$	6.83548	+	11.8394i	0.247461	+	0.428615i
$764$	22.6740	−	39.2726i	0.820318	−	1.42083i
$765$	−10.7573	−	6.21074i	−0.388931	−	0.224550i
$766$	−30.0929			−1.08730
$767$	−23.7572	−	22.1456i	−0.857823	−	0.799632i
$768$	−2.51287			−0.0906754
$769$	−13.3409	−	7.70236i	−0.481085	−	0.277754i	0.239784	−	0.970826i	$-0.422923\pi$
$769$	−13.3409	−	7.70236i	−0.481085	−	0.277754i	−0.720868	+	0.693072i	$0.756257\pi$
$770$	2.92790	−	5.07127i	0.105514	−	0.182756i
$771$	−13.5100	−	23.4000i	−0.486550	−	0.842729i
$772$		−	29.0498i		−	1.04553i
$773$	4.49904	−	2.59752i	0.161819	−	0.0934264i	−0.416903	−	0.908951i	$-0.636885\pi$
$773$	4.49904	−	2.59752i	0.161819	−	0.0934264i	0.578723	+	0.815524i	$0.303551\pi$
$774$	13.1469	−	7.59037i	0.472556	−	0.272830i
$775$			3.29498i			0.118359i
$776$	11.1258	+	19.2704i	0.399393	+	0.691768i
$777$	−3.91176	+	6.77537i	−0.140334	+	0.243065i
$778$	−17.8530	−	10.3074i	−0.640061	−	0.369540i
$779$	49.9465			1.78952
$780$	−17.2384	+	5.27385i	−0.617234	+	0.188834i
$781$	−0.345899			−0.0123773
$782$	25.7674	+	14.8768i	0.921441	+	0.531994i
$783$	−3.81988	+	6.61623i	−0.136511	+	0.236445i
$784$	−1.21247	−	2.10007i	−0.0433026	−	0.0750023i
$785$		−	22.6350i		−	0.807878i
$786$	−2.78453	+	1.60765i	−0.0993210	+	0.0573430i
$787$	−5.83647	+	3.36969i	−0.208048	+	0.120116i	−0.600404	−	0.799697i	$-0.704993\pi$
$787$	−5.83647	+	3.36969i	−0.208048	+	0.120116i	0.392356	+	0.919813i	$0.371660\pi$
$788$			21.6407i			0.770917i
$789$	5.86983	+	10.1668i	0.208971	+	0.361949i
$790$	−17.8062	+	30.8412i	−0.633516	+	1.09728i
$791$	1.26970	+	0.733062i	0.0451454	+	0.0260647i
$792$	−1.84470			−0.0655487
$793$	−19.4281	+	20.8419i	−0.689912	+	0.740119i
$794$	84.2916			2.99140
$795$	0.872371	+	0.503664i	0.0309398	+	0.0178631i
$796$	12.1522	−	21.0481i	0.430722	−	0.746032i
$797$	−18.5168	−	32.0720i	−0.655898	−	1.13605i	−0.981668	−	0.190600i	$-0.938957\pi$
$797$	−18.5168	−	32.0720i	−0.655898	−	1.13605i	0.325769	−	0.945449i	$-0.394377\pi$
$798$			12.3271i			0.436374i
$799$	−2.03345	+	1.17401i	−0.0719381	+	0.0415335i
$800$	8.88391	−	5.12913i	0.314094	−	0.181342i
$801$		−	12.6734i		−	0.447793i
$802$	2.22605	+	3.85563i	0.0786046	+	0.136147i
$803$	0.234983	−	0.407003i	0.00829237	−	0.0143628i
$804$	−0.914387	−	0.527921i	−0.0322479	−	0.0186184i
$805$	−4.11302			−0.144965
$806$	−18.8851	−	4.35624i	−0.665201	−	0.153442i
$807$	−3.52185			−0.123975
$808$	8.99640	+	5.19408i	0.316492	+	0.182727i
$809$	−27.6600	+	47.9085i	−0.972474	+	1.68437i	−0.284444	+	0.958693i	$0.591809\pi$
$809$	−27.6600	+	47.9085i	−0.972474	+	1.68437i	−0.688031	+	0.725682i	$0.741525\pi$
$810$	−2.05953	−	3.56721i	−0.0723644	−	0.125339i
$811$		−	5.37007i		−	0.188569i	−0.995545	−	0.0942843i	$-0.969944\pi$
$811$		−	5.37007i		−	0.188569i	0.995545	−	0.0942843i	$-0.0300563\pi$
$812$	17.2333	−	9.94963i	0.604769	−	0.349164i
$813$	−18.6097	+	10.7443i	−0.652671	+	0.376820i
$814$			23.8666i			0.836525i
$815$	8.54317	+	14.7972i	0.299254	+	0.518324i
$816$	−7.84600	+	13.5897i	−0.274665	+	0.475734i
$817$	−35.1952	−	20.3200i	−1.23132	−	0.710905i
$818$	−80.0779			−2.79986
$819$	0.810413	−	3.51329i	0.0283181	−	0.122764i
$820$	43.4709			1.51807
$821$	31.9676	+	18.4565i	1.11568	+	0.644137i	0.940294	−	0.340363i	$-0.110550\pi$
$821$	31.9676	+	18.4565i	1.11568	+	0.644137i	0.175384	+	0.984500i	$0.443883\pi$
$822$	−14.5596	+	25.2180i	−0.507825	+	0.879578i
$823$	−17.2446	−	29.8686i	−0.601110	−	1.04115i	−0.992653	−	0.120993i	$-0.961392\pi$
$823$	−17.2446	−	29.8686i	−0.601110	−	1.04115i	0.391543	−	0.920160i	$-0.371941\pi$
$824$			18.7783i			0.654172i
$825$	−1.61944	+	0.934986i	−0.0563818	+	0.0325521i
$826$	−16.7398	+	9.66475i	−0.582454	+	0.336280i
$827$		−	35.2495i		−	1.22575i	−0.790181	−	0.612873i	$-0.790014\pi$
$827$		−	35.2495i		−	1.22575i	0.790181	−	0.612873i	$-0.209986\pi$
$828$	2.79056	+	4.83339i	0.0969786	+	0.167972i
$829$	−2.71022	+	4.69424i	−0.0941299	+	0.163038i	−0.909245	−	0.416261i	$-0.863340\pi$
$829$	−2.71022	+	4.69424i	−0.0941299	+	0.163038i	0.815115	+	0.579299i	$0.196674\pi$
$830$	−40.7650	−	23.5357i	−1.41497	−	0.816936i
$831$	−25.4165			−0.881689
$832$	12.5366	+	40.9777i	0.434627	+	1.42065i
$833$	−6.47107			−0.224209
$834$	−11.7713	−	6.79614i	−0.407606	−	0.235331i
$835$	10.6037	−	18.3661i	0.366955	−	0.635585i
$836$	10.6359	+	18.4220i	0.367851	+	0.637137i
$837$		−	2.50499i		−	0.0865850i
$838$	−26.1073	+	15.0731i	−0.901863	+	0.520691i
$839$	−2.89459	+	1.67119i	−0.0999323	+	0.0576959i	−0.549133	−	0.835735i	$-0.685042\pi$
$839$	−2.89459	+	1.67119i	−0.0999323	+	0.0576959i	0.449201	+	0.893431i	$0.351709\pi$
$840$			2.49078i			0.0859401i
$841$	−14.6830	−	25.4317i	−0.506310	−	0.876954i
$842$	−21.8488	+	37.8432i	−0.752959	+	1.30416i
$843$	2.09810	+	1.21134i	0.0722624	+	0.0417207i
$844$	−71.6965			−2.46789
$845$	−13.9619	−	20.6826i	−0.480303	−	0.711502i
$846$	−0.778622			−0.0267696
$847$	−7.77600	−	4.48948i	−0.267187	−	0.154260i
$848$	0.636276	−	1.10206i	0.0218498	−	0.0378450i
$849$	−14.3940	−	24.9311i	−0.494000	−	0.855632i
$850$		−	18.2652i		−	0.626490i
$851$	14.5177	−	8.38178i	0.497659	−	0.287324i
$852$	0.548845	−	0.316876i	0.0188031	−	0.0108560i
$853$		−	30.6155i		−	1.04826i	−0.851640	−	0.524128i	$-0.824391\pi$
$853$		−	30.6155i		−	1.04826i	0.851640	−	0.524128i	$-0.175609\pi$
$854$	8.47878	+	14.6857i	0.290138	+	0.502534i
$855$	−5.51350	+	9.54966i	−0.188558	+	0.326592i
$856$	−16.4613	−	9.50391i	−0.562634	−	0.324837i
$857$	−14.5325			−0.496422			−0.248211	−	0.968706i	$-0.579843\pi$
$857$	−14.5325			−0.496422			−0.248211	+	0.968706i	$0.579843\pi$
$858$	−3.21782	−	10.5180i	−0.109855	−	0.359077i
$859$	54.9295			1.87417			0.937085	−	0.349102i	$-0.113513\pi$
$859$	54.9295			1.87417			0.937085	+	0.349102i	$0.113513\pi$
$860$	−30.6322	−	17.6855i	−1.04455	−	0.603070i
$861$	−4.34725	+	7.52965i	−0.148154	+	0.256610i
$862$	40.4797	+	70.1129i	1.37874	+	2.38805i
$863$			31.6403i			1.07705i	0.842610	+	0.538525i	$0.181018\pi$
$863$			31.6403i			1.07705i	−0.842610	+	0.538525i	$0.818982\pi$
$864$	−6.75393	+	3.89939i	−0.229774	+	0.132660i
$865$	21.2315	−	12.2580i	0.721891	−	0.416784i
$866$			63.4579i			2.15639i
$867$	12.4374	+	21.5422i	0.422395	+	0.731610i
$868$	−3.26236	+	5.65058i	−0.110732	+	0.191793i
$869$	−10.6444	−	6.14557i	−0.361088	−	0.208474i
$870$	31.4686			1.06689
$871$	0.328510	−	1.42415i	0.0111311	−	0.0482556i
$872$	−17.7393			−0.600730
$873$	−14.8509	−	8.57418i	−0.502627	−	0.290192i
$874$	13.2067	−	22.8747i	0.446723	−	0.773748i
$875$	6.06130	+	10.4985i	0.204909	+	0.354913i
$876$			0.861065i			0.0290927i
$877$	4.05349	−	2.34028i	0.136877	−	0.0790258i	−0.429998	−	0.902830i	$-0.641486\pi$
$877$	4.05349	−	2.34028i	0.136877	−	0.0790258i	0.566875	+	0.823804i	$0.308152\pi$
$878$	−19.0081	+	10.9743i	−0.641492	+	0.370366i
$879$			13.1874i			0.444799i
$880$	−3.30870	−	5.73084i	−0.111536	−	0.193186i
$881$	13.5013	−	23.3849i	0.454870	−	0.787859i	−0.543810	−	0.839208i	$-0.683019\pi$
$881$	13.5013	−	23.3849i	0.454870	−	0.787859i	0.998681	+	0.0513495i	$0.0163523\pi$
$882$	−1.85837	−	1.07293i	−0.0625744	−	0.0361274i
$883$	−3.28945			−0.110699			−0.0553495	−	0.998467i	$-0.517627\pi$
$883$	−3.28945			−0.110699			−0.0553495	+	0.998467i	$0.517627\pi$
$884$	59.2172	+	13.6597i	1.99169	+	0.459424i
$885$	−17.2909			−0.581227
$886$	−0.477389	−	0.275621i	−0.0160382	−	0.00925967i
$887$	19.4200	−	33.6364i	0.652060	−	1.12940i	−0.330562	−	0.943784i	$-0.607238\pi$
$887$	19.4200	−	33.6364i	0.652060	−	1.12940i	0.982622	−	0.185617i	$-0.0594283\pi$
$888$	−5.07588	−	8.79167i	−0.170335	−	0.295029i
$889$			8.97273i			0.300936i
$890$	−45.2087	+	26.1012i	−1.51540	+	0.874915i
$891$	1.23117	−	0.710818i	0.0412458	−	0.0238133i
$892$		−	22.6374i		−	0.757956i
$893$	1.04221	+	1.80516i	0.0348763	+	0.0604075i
$894$	18.2599	−	31.6271i	0.610702	−	1.05777i
$895$	34.6748	+	20.0195i	1.15905	+	0.669178i
$896$	9.90627			0.330945
$897$	−5.26782	+	5.65118i	−0.175887	+	0.188687i
$898$	19.0652			0.636213
$899$	16.5736	+	9.56875i	0.552759	+	0.319136i
$900$	1.71307	−	2.96712i	0.0571022	−	0.0989040i
$901$	−1.69793	−	2.94090i	−0.0565662	−	0.0979756i
$902$			26.5236i			0.883141i
$903$	6.12665	−	3.53722i	0.203882	−	0.117711i
$904$	−1.64756	+	0.951217i	−0.0547969	+	0.0316370i
$905$		−	0.723805i		−	0.0240601i
$906$	7.31291	+	12.6663i	0.242955	+	0.420811i
$907$	21.4577	−	37.1659i	0.712493	−	1.23407i	−0.251426	−	0.967877i	$-0.580899\pi$
$907$	21.4577	−	37.1659i	0.712493	−	1.23407i	0.963919	−	0.266197i	$-0.0857672\pi$
$908$	6.78357	+	3.91649i	0.225121	+	0.129973i
$909$	−8.00571			−0.265533
$910$	−14.2017	+	4.34482i	−0.470782	+	0.144029i
$911$	−10.9906			−0.364133			−0.182067	−	0.983286i	$-0.558279\pi$
$911$	−10.9906			−0.364133			−0.182067	+	0.983286i	$0.558279\pi$
$912$	12.0640	+	6.96518i	0.399481	+	0.230640i
$913$	8.12302	−	14.0695i	0.268833	−	0.465632i
$914$	−29.1642	−	50.5139i	−0.964666	−	1.67085i
$915$			15.1691i			0.501475i
$916$	−26.6836	+	15.4058i	−0.881649	+	0.509021i
$917$	−1.29763	+	0.749189i	−0.0428516	+	0.0247404i
$918$			13.8860i			0.458306i
$919$	−13.5962	−	23.5493i	−0.448497	−	0.776820i	0.549791	−	0.835302i	$-0.314707\pi$
$919$	−13.5962	−	23.5493i	−0.448497	−	0.776820i	−0.998288	+	0.0584821i	$0.981374\pi$
$920$	2.66851	−	4.62200i	0.0879783	−	0.152383i
$921$	−5.55519	−	3.20729i	−0.183050	−	0.105684i
$922$	77.5849			2.55512
$923$	0.641707	+	0.598176i	0.0211220	+	0.0196892i
$924$	−3.70293			−0.121817
$925$	−8.91210	−	5.14541i	−0.293028	−	0.169180i
$926$	14.0191	−	24.2819i	0.460697	−	0.797951i
$927$	−7.23581	−	12.5328i	−0.237655	−	0.411631i
$928$		−	59.5808i		−	1.95583i
$929$	15.1593	−	8.75224i	0.497361	−	0.287152i	−0.230262	−	0.973129i	$-0.573958\pi$
$929$	15.1593	−	8.75224i	0.497361	−	0.287152i	0.727623	+	0.685977i	$0.240625\pi$
$930$	−8.93580	+	5.15909i	−0.293016	+	0.169173i
$931$			5.74461i			0.188272i
$932$	19.2782	+	33.3909i	0.631479	+	1.09375i
$933$	−13.2462	+	22.9431i	−0.433662	+	0.751124i
$934$	−27.3499	−	15.7905i	−0.894915	−	0.516679i
$935$	−17.6588			−0.577505
$936$	3.42227	+	3.19011i	0.111860	+	0.104272i
$937$	−10.8883			−0.355705			−0.177853	−	0.984057i	$-0.556915\pi$
$937$	−10.8883			−0.355705			−0.177853	+	0.984057i	$0.556915\pi$
$938$	−0.753309	−	0.434923i	−0.0245964	−	0.0142007i
$939$	2.72442	−	4.71884i	0.0889082	−	0.153994i
$940$	0.907090	+	1.57113i	0.0295860	+	0.0512445i
$941$		−	19.7105i		−	0.642542i	−0.946987	−	0.321271i	$-0.895890\pi$
$941$		−	19.7105i		−	0.642542i	0.946987	−	0.321271i	$-0.104110\pi$
$942$	−21.9137	+	12.6519i	−0.713986	+	0.412220i
$943$	16.1339	−	9.31490i	0.525391	−	0.303335i
$944$			21.8435i			0.710946i
$945$	−0.959770	−	1.66237i	−0.0312213	−	0.0540769i
$946$	10.7907	−	18.6901i	0.350837	−	0.607668i
$947$	7.94534	+	4.58724i	0.258189	+	0.149065i	0.623508	−	0.781817i	$-0.285707\pi$
$947$	7.94534	+	4.58724i	0.258189	+	0.149065i	−0.365319	+	0.930882i	$0.619040\pi$
$948$	22.5196			0.731403
$949$	−1.13978	+	0.348700i	−0.0369989	+	0.0113193i
$950$	−16.2147			−0.526073
$951$	−22.7681	−	13.1452i	−0.738305	−	0.426261i
$952$	4.19841	−	7.27186i	0.136071	−	0.235682i
$953$	3.05014	+	5.28300i	0.0988038	+	0.171133i	0.911190	−	0.411987i	$-0.135165\pi$
$953$	3.05014	+	5.28300i	0.0988038	+	0.171133i	−0.812386	+	0.583120i	$0.801832\pi$
$954$		−	1.12609i		−	0.0364586i
$955$	28.9421	−	16.7097i	0.936543	−	0.540713i
$956$	−18.9869	+	10.9621i	−0.614079	+	0.354538i
$957$			10.8610i			0.351085i
$958$	2.38764	+	4.13551i	0.0771410	+	0.133612i
$959$	−6.78499	+	11.7519i	−0.219099	+	0.379490i
$960$	19.7575	+	11.4070i	0.637671	+	0.368160i
$961$	24.7250			0.797582
$962$	41.2734	−	44.2770i	1.33071	−	1.42755i
$963$	14.6485			0.472042
$964$	40.4318	+	23.3433i	1.30222	+	0.751837i
$965$	10.7042	−	18.5402i	0.344580	−	0.596829i
$966$	2.29897	+	3.98194i	0.0739683	+	0.128117i
$967$		−	27.5349i		−	0.885463i	−0.896654	−	0.442731i	$-0.854010\pi$
$967$		−	27.5349i		−	0.885463i	0.896654	−	0.442731i	$-0.145990\pi$
$968$	10.0901	−	5.82551i	0.324308	−	0.187239i
$969$	32.1934	−	18.5869i	1.03420	−	0.597096i
$970$			70.6350i			2.26795i
$971$	6.19999	+	10.7387i	0.198967	+	0.344621i	0.948194	−	0.317692i	$-0.102908\pi$
$971$	6.19999	+	10.7387i	0.198967	+	0.344621i	−0.749227	+	0.662314i	$0.769575\pi$
$972$	−1.30235	+	2.25573i	−0.0417729	+	0.0723527i
$973$	−5.48558	−	3.16710i	−0.175860	−	0.101533i
$974$	30.2470			0.969177
$975$	4.62127	+	1.06599i	0.147999	+	0.0341390i
$976$	19.1631			0.613395
$977$	3.47915	+	2.00869i	0.111308	+	0.0642636i	0.554620	−	0.832104i	$-0.312864\pi$
$977$	3.47915	+	2.00869i	0.111308	+	0.0642636i	−0.443313	+	0.896367i	$0.646197\pi$
$978$	9.55043	−	16.5418i	0.305389	−	0.528949i
$979$	−9.00848	−	15.6031i	−0.287912	−	0.498679i
$980$			4.99982i			0.159713i
$981$	11.8394	−	6.83548i	0.378003	−	0.218240i
$982$	−59.7330	+	34.4868i	−1.90616	+	1.10052i
$983$			34.4710i			1.09945i	0.835345	+	0.549727i	$0.185268\pi$
$983$			34.4710i			1.09945i	−0.835345	+	0.549727i	$0.814732\pi$
$984$	−5.64096	−	9.77043i	−0.179827	−	0.311470i
$985$	−7.97408	+	13.8115i	−0.254075	+	0.440071i
$986$	−91.8728	−	53.0428i	−2.92583	−	1.68923i
$987$	−0.362849			−0.0115496
$988$	12.1262	−	52.5693i	0.385785	−	1.67245i
$989$	−15.1585			−0.482012
$990$	−5.07127	−	2.92790i	−0.161175	−	0.0930547i
$991$	−8.19055	+	14.1864i	−0.260181	+	0.450647i	−0.966290	−	0.257456i	$-0.917116\pi$
$991$	−8.19055	+	14.1864i	−0.260181	+	0.450647i	0.706109	+	0.708103i	$0.250449\pi$
$992$	9.76791	+	16.9185i	0.310131	+	0.537163i
$993$		−	36.0905i		−	1.14530i
$994$	0.452161	−	0.261055i	0.0143417	−	0.00828016i
$995$	15.5115	−	8.95557i	0.491748	−	0.283911i
$996$			29.7657i			0.943163i
$997$	8.06889	+	13.9757i	0.255544	+	0.442616i	0.965043	−	0.262091i	$-0.0844120\pi$
$997$	8.06889	+	13.9757i	0.255544	+	0.442616i	−0.709499	+	0.704707i	$0.751079\pi$
$998$	−41.8327	+	72.4564i	−1.32419	+	2.29357i
$999$	6.77537	+	3.91176i	0.214363	+	0.123763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.43.7	✓	16
3.2	odd	2		819.2.ct.c.316.2		16
13.6	odd	12		3549.2.a.bc.1.2		8
13.7	odd	12		3549.2.a.ba.1.7		8
13.10	even	6	inner	273.2.bd.b.127.7	yes	16
39.23	odd	6		819.2.ct.c.127.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.7	✓	16	1.1	even	1	trivial
273.2.bd.b.127.7	yes	16	13.10	even	6	inner
819.2.ct.c.127.2		16	39.23	odd	6
819.2.ct.c.316.2		16	3.2	odd	2
3549.2.a.ba.1.7		8	13.7	odd	12
3549.2.a.bc.1.2		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85837 + 1.07293i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.30235 + 2.25573i) q^{4} +1.91954i q^{5} +(1.85837 - 1.07293i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.29759i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.85837 + 1.07293i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.30235 + 2.25573i) q^{4} +1.91954i q^{5} +(1.85837 - 1.07293i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.29759i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.05953 + 3.56721i) q^{10} +(-1.23117 - 0.710818i) q^{11} +2.60470 q^{12} +(1.05481 + 3.44781i) q^{13} +2.14586 q^{14} +(1.66237 + 0.959770i) q^{15} +(1.21247 - 2.10007i) q^{16} +(-3.23553 - 5.60411i) q^{17} -2.14586i q^{18} +(-4.97497 + 2.87230i) q^{19} +(-4.32997 + 2.49991i) q^{20} -1.00000i q^{21} +(-1.52531 - 2.64192i) q^{22} +(-1.07136 + 1.85564i) q^{23} +(1.12375 + 0.648797i) q^{24} +1.31537 q^{25} +(-1.73903 + 7.53902i) q^{26} -1.00000 q^{27} +(2.25573 + 1.30235i) q^{28} +(3.81988 - 6.61623i) q^{29} +(2.05953 + 3.56721i) q^{30} +2.50499i q^{31} +(6.75393 - 3.89939i) q^{32} +(-1.23117 + 0.710818i) q^{33} -13.8860i q^{34} +(0.959770 + 1.66237i) q^{35} +(1.30235 - 2.25573i) q^{36} +(-6.77537 - 3.91176i) q^{37} -12.3271 q^{38} +(3.51329 + 0.810413i) q^{39} -2.49078 q^{40} +(-7.52965 - 4.34725i) q^{41} +(1.07293 - 1.85837i) q^{42} +(3.53722 + 6.12665i) q^{43} -3.70293i q^{44} +(1.66237 - 0.959770i) q^{45} +(-3.98194 + 2.29897i) q^{46} -0.362849i q^{47} +(-1.21247 - 2.10007i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.44443 + 1.41129i) q^{50} -6.47107 q^{51} +(-6.40361 + 6.86962i) q^{52} +0.524776 q^{53} +(-1.85837 - 1.07293i) q^{54} +(1.36444 - 2.36328i) q^{55} +(0.648797 + 1.12375i) q^{56} +5.74461i q^{57} +(14.1975 - 8.19691i) q^{58} +(-7.80101 + 4.50392i) q^{59} +4.99982i q^{60} +(3.95123 + 6.84374i) q^{61} +(-2.68767 + 4.65518i) q^{62} +(-0.866025 - 0.500000i) q^{63} +11.8851 q^{64} +(-6.61820 + 2.02475i) q^{65} -3.05062 q^{66} +(-0.351053 - 0.202681i) q^{67} +(8.42759 - 14.5970i) q^{68} +(1.07136 + 1.85564i) q^{69} +4.11906i q^{70} +(0.210713 - 0.121655i) q^{71} +(1.12375 - 0.648797i) q^{72} +0.330581i q^{73} +(-8.39408 - 14.5390i) q^{74} +(0.657684 - 1.13914i) q^{75} +(-12.9583 - 7.48148i) q^{76} -1.42164 q^{77} +(5.65947 + 5.27555i) q^{78} +8.64577 q^{79} +(4.03116 + 2.32739i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.32857 - 16.1576i) q^{82} +11.4277i q^{83} +(2.25573 - 1.30235i) q^{84} +(10.7573 - 6.21074i) q^{85} +15.1807i q^{86} +(-3.81988 - 6.61623i) q^{87} +(0.922352 - 1.59756i) q^{88} +(10.9755 + 6.33670i) q^{89} +4.11906 q^{90} +(2.63739 + 2.45848i) q^{91} -5.58111 q^{92} +(2.16938 + 1.25249i) q^{93} +(0.389311 - 0.674306i) q^{94} +(-5.51350 - 9.54966i) q^{95} -7.79877i q^{96} +(14.8509 - 8.57418i) q^{97} +(1.85837 - 1.07293i) q^{98} +1.42164i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

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