LMFDB - Embedded newform 273.2.bd.b.43.8

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			43.8
Root			$1.31463 + 1.12772i$ of defining polynomial
Character	$\chi$	$=$	273.43
Dual form			273.2.bd.b.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.35660 + 1.36058i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.70236 + 4.68063i) q^{4} -1.58278i q^{5} +(2.35660 - 1.36058i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.26480i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(2.35660 + 1.36058i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.70236 + 4.68063i) q^{4} -1.58278i q^{5} +(2.35660 - 1.36058i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.26480i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.15350 - 3.72996i) q^{10} +(-4.79969 - 2.77110i) q^{11} +5.40472 q^{12} +(-1.34211 - 3.34645i) q^{13} -2.72116 q^{14} +(-1.37073 - 0.791388i) q^{15} +(-7.20078 + 12.4721i) q^{16} +(2.40288 + 4.16192i) q^{17} -2.72116i q^{18} +(0.772957 - 0.446267i) q^{19} +(7.40839 - 4.27723i) q^{20} +1.00000i q^{21} +(-7.54062 - 13.0607i) q^{22} +(-2.31507 + 4.00983i) q^{23} +(8.02355 + 4.63240i) q^{24} +2.49482 q^{25} +(1.39030 - 9.71228i) q^{26} -1.00000 q^{27} +(-4.68063 - 2.70236i) q^{28} +(0.941087 - 1.63001i) q^{29} +(-2.15350 - 3.72996i) q^{30} +1.47545i q^{31} +(-17.8916 + 10.3297i) q^{32} +(-4.79969 + 2.77110i) q^{33} +13.0773i q^{34} +(0.791388 + 1.37073i) q^{35} +(2.70236 - 4.68063i) q^{36} +(4.32400 + 2.49646i) q^{37} +2.42873 q^{38} +(-3.56917 - 0.510922i) q^{39} +14.6641 q^{40} +(-8.45175 - 4.87962i) q^{41} +(-1.36058 + 2.35660i) q^{42} +(0.506349 + 0.877022i) q^{43} -29.9541i q^{44} +(-1.37073 + 0.791388i) q^{45} +(-10.9114 + 6.29969i) q^{46} -12.5703i q^{47} +(7.20078 + 12.4721i) q^{48} +(0.500000 - 0.866025i) q^{49} +(5.87927 + 3.39440i) q^{50} +4.80577 q^{51} +(12.0366 - 15.3252i) q^{52} +6.25784 q^{53} +(-2.35660 - 1.36058i) q^{54} +(-4.38604 + 7.59684i) q^{55} +(-4.63240 - 8.02355i) q^{56} -0.892533i q^{57} +(4.43552 - 2.56085i) q^{58} +(2.98511 - 1.72345i) q^{59} -8.55447i q^{60} +(1.79275 + 3.10513i) q^{61} +(-2.00746 + 3.47703i) q^{62} +(0.866025 + 0.500000i) q^{63} -27.4144 q^{64} +(-5.29669 + 2.12426i) q^{65} -15.0812 q^{66} +(12.7653 + 7.37003i) q^{67} +(-12.9869 + 22.4940i) q^{68} +(2.31507 + 4.00983i) q^{69} +4.30699i q^{70} +(-11.3794 + 6.56988i) q^{71} +(8.02355 - 4.63240i) q^{72} +5.33654i q^{73} +(6.79328 + 11.7663i) q^{74} +(1.24741 - 2.16058i) q^{75} +(4.17762 + 2.41195i) q^{76} +5.54221 q^{77} +(-7.71593 - 6.06018i) q^{78} +0.779028 q^{79} +(19.7406 + 11.3972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.2782 - 22.9986i) q^{82} +1.47136i q^{83} +(-4.68063 + 2.70236i) q^{84} +(6.58738 - 3.80323i) q^{85} +2.75571i q^{86} +(-0.941087 - 1.63001i) q^{87} +(25.6737 - 44.4682i) q^{88} +(6.63332 + 3.82975i) q^{89} -4.30699 q^{90} +(2.83553 + 2.22706i) q^{91} -25.0247 q^{92} +(1.27777 + 0.737723i) q^{93} +(17.1029 - 29.6231i) q^{94} +(-0.706341 - 1.22342i) q^{95} +20.6594i q^{96} +(-0.657035 + 0.379340i) q^{97} +(2.35660 - 1.36058i) q^{98} +5.54221i 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 $

$2$	2.35660	+	1.36058i	1.66636	+	0.962076i	0.969573	+	0.244802i	$0.0787230\pi$
$2$	2.35660	+	1.36058i	1.66636	+	0.962076i	0.696791	+	0.717274i	$0.254610\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	2.70236	+	4.68063i	1.35118	+	2.34031i
$5$		−	1.58278i		−	0.707839i	−0.935276	−	0.353920i	$-0.884849\pi$
$5$		−	1.58278i		−	0.707839i	0.935276	−	0.353920i	$-0.115151\pi$
$6$	2.35660	−	1.36058i	0.962076	−	0.555455i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			9.26480i			3.27560i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.15350	−	3.72996i	0.680995	−	1.17952i
$11$	−4.79969	−	2.77110i	−1.44716	−	0.835519i	−0.448850	−	0.893607i	$-0.648166\pi$
$11$	−4.79969	−	2.77110i	−1.44716	−	0.835519i	−0.998311	+	0.0580877i	$0.981500\pi$
$12$	5.40472			1.56021
$13$	−1.34211	−	3.34645i	−0.372235	−	0.928139i
$13$	−1.34211	−	3.34645i	−0.372235	−	0.928139i
$14$	−2.72116			−0.727261
$15$	−1.37073	−	0.791388i	−0.353920	−	0.204336i
$16$	−7.20078	+	12.4721i	−1.80020	+	3.11803i
$17$	2.40288	+	4.16192i	0.582785	+	1.00941i	0.995148	+	0.0983932i	$0.0313703\pi$
$17$	2.40288	+	4.16192i	0.582785	+	1.00941i	−0.412363	+	0.911020i	$0.635296\pi$
$18$		−	2.72116i		−	0.641384i
$19$	0.772957	−	0.446267i	0.177328	−	0.102381i	−0.408708	−	0.912665i	$-0.634021\pi$
$19$	0.772957	−	0.446267i	0.177328	−	0.102381i	0.586037	+	0.810284i	$0.300687\pi$
$20$	7.40839	−	4.27723i	1.65657	−	0.956419i
$21$			1.00000i			0.218218i
$22$	−7.54062	−	13.0607i	−1.60767	−	2.78456i
$23$	−2.31507	+	4.00983i	−0.482726	+	0.836107i	−0.999803	−	0.0198323i	$-0.993687\pi$
$23$	−2.31507	+	4.00983i	−0.482726	+	0.836107i	0.517077	+	0.855939i	$0.327020\pi$
$24$	8.02355	+	4.63240i	1.63780	+	0.945584i
$25$	2.49482			0.498963
$26$	1.39030	−	9.71228i	0.272661	−	1.90474i
$27$	−1.00000			−0.192450
$28$	−4.68063	−	2.70236i	−0.884555	−	0.510698i
$29$	0.941087	−	1.63001i	0.174755	−	0.302685i	−0.765321	−	0.643649i	$-0.777420\pi$
$29$	0.941087	−	1.63001i	0.174755	−	0.302685i	0.940077	+	0.340963i	$0.110753\pi$
$30$	−2.15350	−	3.72996i	−0.393173	−	0.680995i
$31$			1.47545i			0.264998i	0.991183	+	0.132499i	$0.0423001\pi$
$31$			1.47545i			0.264998i	−0.991183	+	0.132499i	$0.957700\pi$
$32$	−17.8916	+	10.3297i	−3.16281	+	1.82605i
$33$	−4.79969	+	2.77110i	−0.835519	+	0.482387i
$34$			13.0773i			2.24273i
$35$	0.791388	+	1.37073i	0.133769	+	0.231695i
$36$	2.70236	−	4.68063i	0.450393	−	0.780104i
$37$	4.32400	+	2.49646i	0.710862	+	0.410416i	0.811380	−	0.584519i	$-0.198717\pi$
$37$	4.32400	+	2.49646i	0.710862	+	0.410416i	−0.100518	+	0.994935i	$0.532050\pi$
$38$	2.42873			0.393992
$39$	−3.56917	−	0.510922i	−0.571524	−	0.0818130i
$40$	14.6641			2.31860
$41$	−8.45175	−	4.87962i	−1.31994	−	0.762069i	−0.336223	−	0.941782i	$-0.609150\pi$
$41$	−8.45175	−	4.87962i	−1.31994	−	0.762069i	−0.983719	+	0.179713i	$0.942483\pi$
$42$	−1.36058	+	2.35660i	−0.209942	+	0.363631i
$43$	0.506349	+	0.877022i	0.0772174	+	0.133745i	0.902048	−	0.431635i	$-0.142063\pi$
$43$	0.506349	+	0.877022i	0.0772174	+	0.133745i	−0.824831	+	0.565379i	$0.808730\pi$
$44$		−	29.9541i		−	4.51575i
$45$	−1.37073	+	0.791388i	−0.204336	+	0.117973i
$46$	−10.9114	+	6.29969i	−1.60880	+	0.928839i
$47$		−	12.5703i		−	1.83357i	−0.399385	−	0.916783i	$-0.630776\pi$
$47$		−	12.5703i		−	1.83357i	0.399385	−	0.916783i	$-0.369224\pi$
$48$	7.20078	+	12.4721i	1.03934	+	1.80020i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	5.87927	+	3.39440i	0.831455	+	0.480041i
$51$	4.80577			0.672942
$52$	12.0366	−	15.3252i	1.66918	−	2.12523i
$53$	6.25784			0.859581			0.429790	−	0.902929i	$-0.358587\pi$
$53$	6.25784			0.859581			0.429790	+	0.902929i	$0.358587\pi$
$54$	−2.35660	−	1.36058i	−0.320692	−	0.185152i
$55$	−4.38604	+	7.59684i	−0.591413	+	1.02436i
$56$	−4.63240	−	8.02355i	−0.619030	−	1.07219i
$57$		−	0.892533i		−	0.118219i
$58$	4.43552	−	2.56085i	0.582413	−	0.336256i
$59$	2.98511	−	1.72345i	0.388628	−	0.224374i	−0.292938	−	0.956132i	$-0.594633\pi$
$59$	2.98511	−	1.72345i	0.388628	−	0.224374i	0.681565	+	0.731757i	$0.261300\pi$
$60$		−	8.55447i		−	1.10438i
$61$	1.79275	+	3.10513i	0.229538	+	0.397571i	0.957671	−	0.287864i	$-0.0929453\pi$
$61$	1.79275	+	3.10513i	0.229538	+	0.397571i	−0.728134	+	0.685435i	$0.759612\pi$
$62$	−2.00746	+	3.47703i	−0.254948	+	0.441583i
$63$	0.866025	+	0.500000i	0.109109	+	0.0629941i
$64$	−27.4144			−3.42681
$65$	−5.29669	+	2.12426i	−0.656973	+	0.263483i
$66$	−15.0812			−1.85637
$67$	12.7653	+	7.37003i	1.55953	+	0.900392i	0.997302	+	0.0734069i	$0.0233872\pi$
$67$	12.7653	+	7.37003i	1.55953	+	0.900392i	0.562223	+	0.826986i	$0.309946\pi$
$68$	−12.9869	+	22.4940i	−1.57489	+	2.72780i
$69$	2.31507	+	4.00983i	0.278702	+	0.482726i
$70$			4.30699i			0.514784i
$71$	−11.3794	+	6.56988i	−1.35048	+	0.779702i	−0.988317	−	0.152412i	$-0.951296\pi$
$71$	−11.3794	+	6.56988i	−1.35048	+	0.779702i	−0.362166	+	0.932114i	$0.617963\pi$
$72$	8.02355	−	4.63240i	0.945584	−	0.545933i
$73$			5.33654i			0.624595i	0.949984	+	0.312298i	$0.101099\pi$
$73$			5.33654i			0.624595i	−0.949984	+	0.312298i	$0.898901\pi$
$74$	6.79328	+	11.7663i	0.789703	+	1.36781i
$75$	1.24741	−	2.16058i	0.144038	−	0.249482i
$76$	4.17762	+	2.41195i	0.479205	+	0.276669i
$77$	5.54221			0.631593
$78$	−7.71593	−	6.06018i	−0.873657	−	0.686180i
$79$	0.779028			0.0876475			0.0438237	−	0.999039i	$-0.486046\pi$
$79$	0.779028			0.0876475			0.0438237	+	0.999039i	$0.486046\pi$
$80$	19.7406	+	11.3972i	2.20707	+	1.27425i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−13.2782	−	22.9986i	−1.46634	−	2.53977i
$83$			1.47136i			0.161503i	0.996734	+	0.0807513i	$0.0257320\pi$
$83$			1.47136i			0.161503i	−0.996734	+	0.0807513i	$0.974268\pi$
$84$	−4.68063	+	2.70236i	−0.510698	+	0.294852i
$85$	6.58738	−	3.80323i	0.714502	−	0.412518i
$86$			2.75571i			0.297156i
$87$	−0.941087	−	1.63001i	−0.100895	−	0.174755i
$88$	25.6737	−	44.4682i	2.73683	−	4.74032i
$89$	6.63332	+	3.82975i	0.703130	+	0.405953i	0.808512	−	0.588479i	$-0.200273\pi$
$89$	6.63332	+	3.82975i	0.703130	+	0.405953i	−0.105382	+	0.994432i	$0.533606\pi$
$90$	−4.30699			−0.453997
$91$	2.83553	+	2.22706i	0.297244	+	0.233459i
$92$	−25.0247			−2.60900
$93$	1.27777	+	0.737723i	0.132499	+	0.0764983i
$94$	17.1029	−	29.6231i	1.76403	−	3.05539i
$95$	−0.706341	−	1.22342i	−0.0724690	−	0.125520i
$96$			20.6594i			2.10854i
$97$	−0.657035	+	0.379340i	−0.0667118	+	0.0385161i	−0.532985	−	0.846125i	$-0.678930\pi$
$97$	−0.657035	+	0.379340i	−0.0667118	+	0.0385161i	0.466273	+	0.884641i	$0.345596\pi$
$98$	2.35660	−	1.36058i	0.238052	−	0.137439i
$99$			5.54221i			0.557013i
$100$	6.74190	+	11.6773i	0.674190	+	1.16773i
$101$	−5.88701	+	10.1966i	−0.585779	+	1.01460i	0.408998	+	0.912535i	$0.365878\pi$
$101$	−5.88701	+	10.1966i	−0.585779	+	1.01460i	−0.994778	+	0.102064i	$0.967455\pi$
$102$	11.3252	+	6.53863i	1.12137	+	0.647421i
$103$	−9.61981			−0.947868			−0.473934	−	0.880560i	$-0.657167\pi$
$103$	−9.61981			−0.947868			−0.473934	+	0.880560i	$0.657167\pi$
$104$	31.0042	−	12.4344i	3.04021	−	1.21929i
$105$	1.58278			0.154463
$106$	14.7472	+	8.51430i	1.43237	+	0.826982i
$107$	−1.84459	+	3.19493i	−0.178323	+	0.308865i	−0.941306	−	0.337553i	$-0.890401\pi$
$107$	−1.84459	+	3.19493i	−0.178323	+	0.308865i	0.762983	+	0.646419i	$0.223734\pi$
$108$	−2.70236	−	4.68063i	−0.260035	−	0.450393i
$109$		−	8.92215i		−	0.854587i	−0.904113	−	0.427293i	$-0.859467\pi$
$109$		−	8.92215i		−	0.854587i	0.904113	−	0.427293i	$-0.140533\pi$
$110$	−20.6722	+	11.9351i	−1.97102	+	1.13797i
$111$	4.32400	−	2.49646i	0.410416	−	0.236954i
$112$		−	14.4016i		−	1.36082i
$113$	−8.06766	−	13.9736i	−0.758941	−	1.31452i	−0.943391	−	0.331683i	$-0.892384\pi$
$113$	−8.06766	−	13.9736i	−0.758941	−	1.31452i	0.184450	−	0.982842i	$-0.440950\pi$
$114$	1.21436	−	2.10334i	0.113736	−	0.196996i
$115$	6.34666	+	3.66425i	0.591829	+	0.341693i
$116$	10.1726			0.944504
$117$	−2.22706	+	2.83553i	−0.205891	+	0.262145i
$118$	9.37958			0.863460
$119$	−4.16192	−	2.40288i	−0.381522	−	0.220272i
$120$	7.33205	−	12.6995i	0.669322	−	1.15930i
$121$	9.85803	+	17.0746i	0.896185	+	1.55224i
$122$			9.75670i			0.883330i
$123$	−8.45175	+	4.87962i	−0.762069	+	0.439981i
$124$	−6.90601	+	3.98719i	−0.620178	+	0.358060i
$125$		−	11.8626i		−	1.06103i
$126$	1.36058	+	2.35660i	0.121210	+	0.209942i
$127$	−2.31228	+	4.00499i	−0.205182	+	0.355386i	−0.950191	−	0.311669i	$-0.899112\pi$
$127$	−2.31228	+	4.00499i	−0.205182	+	0.355386i	0.745009	+	0.667055i	$0.232445\pi$
$128$	−28.8216	−	16.6402i	−2.54749	−	1.47080i
$129$	1.01270			0.0891630
$130$	−15.3724	−	2.20054i	−1.34825	−	0.193000i
$131$	−7.78183			−0.679902			−0.339951	−	0.940443i	$-0.610410\pi$
$131$	−7.78183			−0.679902			−0.339951	+	0.940443i	$0.610410\pi$
$132$	−25.9410	−	14.9770i	−2.25787	−	1.30358i
$133$	−0.446267	+	0.772957i	−0.0386962	+	0.0670238i
$134$	20.0550	+	34.7364i	1.73249	+	3.00076i
$135$			1.58278i			0.136224i
$136$	−38.5593	+	22.2622i	−3.30643	+	1.90897i
$137$	0.239328	−	0.138176i	0.0204472	−	0.0118052i	−0.489742	−	0.871868i	$-0.662909\pi$
$137$	0.239328	−	0.138176i	0.0204472	−	0.0118052i	0.510189	+	0.860062i	$0.329576\pi$
$138$			12.5994i			1.07253i
$139$	−1.98032	−	3.43002i	−0.167969	−	0.290931i	0.769737	−	0.638362i	$-0.220387\pi$
$139$	−1.98032	−	3.43002i	−0.167969	−	0.290931i	−0.937706	+	0.347431i	$0.887054\pi$
$140$	−4.27723	+	7.40839i	−0.361492	+	0.626123i
$141$	−10.8862	−	6.28515i	−0.916783	−	0.529305i
$142$	−35.7554			−3.00053
$143$	−2.83164	+	19.7811i	−0.236793	+	1.65418i
$144$	14.4016			1.20013
$145$	−2.57994	−	1.48953i	−0.214253	−	0.123699i
$146$	−7.26080	+	12.5761i	−0.600908	+	1.04080i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$			26.9854i			2.21818i
$149$	18.7838	−	10.8449i	1.53883	−	0.888446i	0.539925	−	0.841713i	$-0.318452\pi$
$149$	18.7838	−	10.8449i	1.53883	−	0.888446i	0.998907	−	0.0467327i	$-0.0148809\pi$
$150$	5.87927	−	3.39440i	0.480041	−	0.277152i
$151$		−	5.66673i		−	0.461152i	−0.973054	−	0.230576i	$-0.925939\pi$
$151$		−	5.66673i		−	0.461152i	0.973054	−	0.230576i	$-0.0740610\pi$
$152$	4.13457	+	7.16129i	0.335358	+	0.580857i
$153$	2.40288	−	4.16192i	0.194262	−	0.336471i
$154$	13.0607	+	7.54062i	1.05246	+	0.607641i
$155$	2.33530			0.187576
$156$	−7.25374	−	18.0866i	−0.580764	−	1.44809i
$157$	1.06406			0.0849216			0.0424608	−	0.999098i	$-0.486480\pi$
$157$	1.06406			0.0849216			0.0424608	+	0.999098i	$0.486480\pi$
$158$	1.83585	+	1.05993i	0.146053	+	0.0843235i
$159$	3.12892	−	5.41945i	0.248140	−	0.429790i
$160$	16.3496	+	28.3184i	1.29255	+	2.23876i
$161$		−	4.63015i		−	0.364907i
$162$	−2.35660	+	1.36058i	−0.185152	+	0.106897i
$163$	−6.24073	+	3.60309i	−0.488812	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$163$	−6.24073	+	3.60309i	−0.488812	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$164$		−	52.7460i		−	4.11877i
$165$	4.38604	+	7.59684i	0.341453	+	0.591413i
$166$	−2.00190	+	3.46740i	−0.155378	+	0.269122i
$167$	−0.405731	−	0.234249i	−0.0313964	−	0.0181267i	0.484220	−	0.874946i	$-0.339104\pi$
$167$	−0.405731	−	0.234249i	−0.0313964	−	0.0181267i	−0.515616	+	0.856820i	$0.672437\pi$
$168$	−9.26480			−0.714795
$169$	−9.39747	+	8.98263i	−0.722882	+	0.690971i
$170$	20.6984			1.58749
$171$	−0.772957	−	0.446267i	−0.0591095	−	0.0341269i
$172$	−2.73667	+	4.74006i	−0.208669	+	0.361426i
$173$	−5.30504	−	9.18861i	−0.403335	−	0.698597i	0.590791	−	0.806825i	$-0.298816\pi$
$173$	−5.30504	−	9.18861i	−0.403335	−	0.698597i	−0.994126	+	0.108228i	$0.965482\pi$
$174$		−	5.12170i		−	0.388275i
$175$	−2.16058	+	1.24741i	−0.163324	+	0.0942952i
$176$	69.1231	−	39.9082i	5.21035	−	3.00820i
$177$		−	3.44690i		−	0.259085i
$178$	10.4214	+	18.0503i	0.781114	+	1.35293i
$179$	−9.68369	+	16.7726i	−0.723793	+	1.25365i	0.235676	+	0.971832i	$0.424270\pi$
$179$	−9.68369	+	16.7726i	−0.723793	+	1.25365i	−0.959469	+	0.281814i	$0.909064\pi$
$180$	−7.40839	−	4.27723i	−0.552189	−	0.318806i
$181$	16.0004			1.18930			0.594649	−	0.803986i	$-0.297291\pi$
$181$	16.0004			1.18930			0.594649	+	0.803986i	$0.297291\pi$
$182$	3.65210	+	9.10623i	0.270712	+	0.674999i
$183$	3.58549			0.265047
$184$	−37.1502	−	21.4487i	−2.73875	−	1.58122i
$185$	3.95134	−	6.84393i	0.290509	−	0.503176i
$186$	2.00746	+	3.47703i	0.147194	+	0.254948i
$187$		−	26.6346i		−	1.94771i
$188$	58.8369	−	33.9695i	4.29112	−	2.47748i
$189$	0.866025	−	0.500000i	0.0629941	−	0.0363696i
$190$		−	3.84413i		−	0.278883i
$191$	−1.57415	−	2.72651i	−0.113902	−	0.197284i	0.803438	−	0.595388i	$-0.203002\pi$
$191$	−1.57415	−	2.72651i	−0.113902	−	0.197284i	−0.917340	+	0.398104i	$0.869668\pi$
$192$	−13.7072	+	23.7416i	−0.989234	+	1.71340i
$193$	20.1629	+	11.6411i	1.45136	+	0.837942i	0.998559	−	0.0536700i	$-0.0170919\pi$
$193$	20.1629	+	11.6411i	1.45136	+	0.837942i	0.452800	+	0.891612i	$0.350425\pi$
$194$	−2.06449			−0.148222
$195$	−0.808676	+	5.64920i	−0.0579105	+	0.404547i
$196$	5.40472			0.386052
$197$	−15.2788	−	8.82123i	−1.08857	−	0.628487i	−0.155376	−	0.987855i	$-0.549659\pi$
$197$	−15.2788	−	8.82123i	−1.08857	−	0.628487i	−0.933196	+	0.359369i	$0.882992\pi$
$198$	−7.54062	+	13.0607i	−0.535889	+	0.928186i
$199$	5.96255	+	10.3274i	0.422674	+	0.732093i	0.996200	−	0.0870944i	$-0.0277582\pi$
$199$	5.96255	+	10.3274i	0.422674	+	0.732093i	−0.573526	+	0.819187i	$0.694425\pi$
$200$			23.1140i			1.63440i
$201$	12.7653	−	7.37003i	0.900392	−	0.519842i
$202$	−27.7466	+	16.0195i	−1.95224	+	1.12713i
$203$			1.88217i			0.132103i
$204$	12.9869	+	22.4940i	0.909266	+	1.57489i
$205$	−7.72335	+	13.3772i	−0.539422	+	0.934307i
$206$	−22.6700	−	13.0885i	−1.57949	−	0.911921i
$207$	4.63015			0.321818
$208$	51.4016	+	7.35808i	3.56406	+	0.510191i
$209$	−4.94661			−0.342164
$210$	3.72996	+	2.15350i	0.257392	+	0.148605i
$211$	7.56510	−	13.1031i	0.520803	−	0.902057i	−0.478904	−	0.877867i	$-0.658966\pi$
$211$	7.56510	−	13.1031i	0.520803	−	0.902057i	0.999707	−	0.0241902i	$-0.00770074\pi$
$212$	16.9109	+	29.2906i	1.16145	+	2.01169i
$213$			13.1398i			0.900322i
$214$	−8.69391	+	5.01943i	−0.594304	+	0.343121i
$215$	1.38813	−	0.801437i	0.0946696	−	0.0546575i
$216$		−	9.26480i		−	0.630390i
$217$	−0.737723	−	1.27777i	−0.0500799	−	0.0867409i
$218$	12.1393	−	21.0259i	0.822177	−	1.42405i
$219$	4.62158	+	2.66827i	0.312298	+	0.180305i
$220$	−47.4106			−3.19642
$221$	10.7027	−	13.6269i	0.719942	−	0.916644i
$222$	13.5866			0.911870
$223$	−16.5898	−	9.57812i	−1.11093	−	0.641398i	−0.171863	−	0.985121i	$-0.554979\pi$
$223$	−16.5898	−	9.57812i	−1.11093	−	0.641398i	−0.939071	+	0.343723i	$0.888312\pi$
$224$	10.3297	−	17.8916i	0.690182	−	1.19543i
$225$	−1.24741	−	2.16058i	−0.0831606	−	0.144038i
$226$		−	43.9068i		−	2.92064i
$227$	−15.1052	+	8.72097i	−1.00257	+	0.578831i	−0.909006	−	0.416782i	$-0.863158\pi$
$227$	−15.1052	+	8.72097i	−1.00257	+	0.578831i	−0.0935590	+	0.995614i	$0.529824\pi$
$228$	4.17762	−	2.41195i	0.276669	−	0.159735i
$229$			10.5075i			0.694354i	0.937800	+	0.347177i	$0.112860\pi$
$229$			10.5075i			0.694354i	−0.937800	+	0.347177i	$0.887140\pi$
$230$	9.97101	+	17.2703i	0.657469	+	1.13877i
$231$	2.77110	−	4.79969i	0.182325	−	0.315797i
$232$	15.1017	+	8.71898i	0.991476	+	0.572429i
$233$	9.69049			0.634845			0.317422	−	0.948284i	$-0.397183\pi$
$233$	9.69049			0.634845			0.317422	+	0.948284i	$0.397183\pi$
$234$	−9.10623	+	3.65210i	−0.595293	+	0.238746i
$235$	−19.8960			−1.29787
$236$	16.1337	+	9.31478i	1.05021	+	0.606340i
$237$	0.389514	−	0.674658i	0.0253017	−	0.0438237i
$238$	−6.53863	−	11.3252i	−0.423837	−	0.734107i
$239$		−	18.4302i		−	1.19215i	−0.802929	−	0.596074i	$-0.796726\pi$
$239$		−	18.4302i		−	1.19215i	0.802929	−	0.596074i	$-0.203274\pi$
$240$	19.7406	−	11.3972i	1.27425	−	0.735688i
$241$	13.2961	−	7.67652i	0.856479	−	0.494488i	−0.00635271	−	0.999980i	$-0.502022\pi$
$241$	13.2961	−	7.67652i	0.856479	−	0.494488i	0.862832	+	0.505492i	$0.168689\pi$
$242$			53.6506i			3.44879i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−9.68929	+	16.7823i	−0.620293	+	1.07438i
$245$	−1.37073	−	0.791388i	−0.0875724	−	0.0505600i
$246$	−26.5565			−1.69318
$247$	−2.53080	−	1.98772i	−0.161031	−	0.126476i
$248$	−13.6697			−0.868027
$249$	1.27423	+	0.735679i	0.0807513	+	0.0466218i
$250$	16.1401	−	27.9554i	1.02079	−	1.76805i
$251$	4.31450	+	7.47294i	0.272329	+	0.471688i	0.969458	−	0.245258i	$-0.0788728\pi$
$251$	4.31450	+	7.47294i	0.272329	+	0.471688i	−0.697129	+	0.716946i	$0.745539\pi$
$252$			5.40472i			0.340465i
$253$	22.2233	−	12.8306i	1.39717	−	0.806654i
$254$	−10.8982	+	6.29210i	−0.683816	+	0.394801i
$255$		−	7.60646i		−	0.476335i
$256$	−17.8661	−	30.9450i	−1.11663	−	1.93407i
$257$	1.36475	−	2.36381i	0.0851305	−	0.147450i	−0.820316	−	0.571910i	$-0.806203\pi$
$257$	1.36475	−	2.36381i	0.0851305	−	0.147450i	0.905447	+	0.424460i	$0.139536\pi$
$258$	2.38652	+	1.37786i	0.148578	+	0.0857816i
$259$	−4.99293			−0.310245
$260$	−24.2564	−	19.0513i	−1.50432	−	1.18151i
$261$	−1.88217			−0.116504
$262$	−18.3386	−	10.5878i	−1.13296	−	0.654117i
$263$	2.80709	−	4.86203i	0.173093	−	0.299806i	−0.766407	−	0.642356i	$-0.777957\pi$
$263$	2.80709	−	4.86203i	0.173093	−	0.299806i	0.939500	+	0.342550i	$0.111291\pi$
$264$	−25.6737	−	44.4682i	−1.58011	−	2.73683i
$265$		−	9.90477i		−	0.608445i
$266$	−2.10334	+	1.21436i	−0.128964	+	0.0744574i
$267$	6.63332	−	3.82975i	0.405953	−	0.234377i
$268$			79.6659i			4.86637i
$269$	0.0911180	+	0.157821i	0.00555556	+	0.00962252i	0.868790	−	0.495181i	$-0.164898\pi$
$269$	0.0911180	+	0.157821i	0.00555556	+	0.00962252i	−0.863234	+	0.504804i	$0.831565\pi$
$270$	−2.15350	+	3.72996i	−0.131058	+	0.226998i
$271$	−25.4028	−	14.6663i	−1.54311	−	0.890914i	−0.998640	−	0.0521319i	$-0.983398\pi$
$271$	−25.4028	−	14.6663i	−1.54311	−	0.890914i	−0.544468	−	0.838782i	$-0.683268\pi$
$272$	−69.2106			−4.19651
$273$	3.34645	−	1.34211i	0.202536	−	0.0812283i
$274$	0.752000			0.0454300
$275$	−11.9744	−	6.91340i	−0.722081	−	0.416894i
$276$	−12.5123	+	21.6720i	−0.753154	+	1.30450i
$277$	−8.08739	−	14.0078i	−0.485924	−	0.841646i	0.513945	−	0.857823i	$-0.328184\pi$
$277$	−8.08739	−	14.0078i	−0.485924	−	0.841646i	−0.999869	+	0.0161776i	$0.994850\pi$
$278$		−	10.7776i		−	0.646395i
$279$	1.27777	−	0.737723i	0.0764983	−	0.0441663i
$280$	−12.6995	+	7.33205i	−0.758940	+	0.438174i
$281$		−	3.71644i		−	0.221704i	−0.993837	−	0.110852i	$-0.964642\pi$
$281$		−	3.71644i		−	0.221704i	0.993837	−	0.110852i	$-0.0353580\pi$
$282$	−17.1029	−	29.6231i	−1.01846	−	1.76403i
$283$	1.88685	−	3.26812i	0.112162	−	0.194270i	−0.804480	−	0.593980i	$-0.797556\pi$
$283$	1.88685	−	3.26812i	0.112162	−	0.194270i	0.916642	+	0.399710i	$0.130889\pi$
$284$	−61.5023	−	35.5084i	−3.64949	−	2.10703i
$285$	−1.41268			−0.0836800
$286$	−33.5868	+	42.7633i	−1.98603	+	2.52865i
$287$	9.75924			0.576070
$288$	17.8916	+	10.3297i	1.05427	+	0.608684i
$289$	−3.04770	+	5.27877i	−0.179276	+	0.310516i
$290$	−4.05325	−	7.02044i	−0.238015	−	0.412254i
$291$			0.758679i			0.0444746i
$292$	−24.9784	+	14.4213i	−1.46175	+	0.843941i
$293$	13.3509	−	7.70816i	0.779970	−	0.450316i	−0.0564499	−	0.998405i	$-0.517978\pi$
$293$	13.3509	−	7.70816i	0.779970	−	0.450316i	0.836419	+	0.548090i	$0.184645\pi$
$294$		−	2.72116i		−	0.158701i
$295$	−2.72784	−	4.72476i	−0.158821	−	0.275086i
$296$	−23.1292	+	40.0610i	−1.34436	+	2.32850i
$297$	4.79969	+	2.77110i	0.278506	+	0.160796i
$298$	59.0212			3.41901
$299$	16.5258	+	2.36565i	0.955710	+	0.136809i
$300$	13.4838			0.778487
$301$	−0.877022	−	0.506349i	−0.0505507	−	0.0291854i
$302$	7.71004	−	13.3542i	0.443663	−	0.768447i
$303$	5.88701	+	10.1966i	0.338200	+	0.585779i
$304$			12.8539i			0.737221i
$305$	4.91472	−	2.83752i	0.281416	−	0.162476i
$306$	11.3252	−	6.53863i	0.647421	−	0.373789i
$307$		−	33.2617i		−	1.89834i	−0.314758	−	0.949172i	$-0.601923\pi$
$307$		−	33.2617i		−	1.89834i	0.314758	−	0.949172i	$-0.398077\pi$
$308$	14.9770	+	25.9410i	0.853396	+	1.47813i
$309$	−4.80991	+	8.33100i	−0.273626	+	0.473934i
$310$	5.50336	+	3.17737i	0.312570	+	0.180462i
$311$	5.28263			0.299551			0.149775	−	0.988720i	$-0.452145\pi$
$311$	5.28263			0.299551			0.149775	+	0.988720i	$0.452145\pi$
$312$	4.73359	−	33.0676i	0.267987	−	1.87209i
$313$	−17.4853			−0.988329			−0.494165	−	0.869368i	$-0.664526\pi$
$313$	−17.4853			−0.988329			−0.494165	+	0.869368i	$0.664526\pi$
$314$	2.50757	+	1.44775i	0.141510	+	0.0817010i
$315$	0.791388	−	1.37073i	0.0445897	−	0.0772316i
$316$	2.10521	+	3.64634i	0.118428	+	0.205123i
$317$		−	6.89451i		−	0.387234i	−0.981077	−	0.193617i	$-0.937978\pi$
$317$		−	6.89451i		−	0.387234i	0.981077	−	0.193617i	$-0.0620219\pi$
$318$	14.7472	−	8.51430i	0.826982	−	0.477458i
$319$	−9.03386	+	5.21570i	−0.505799	+	0.292023i
$320$			43.3909i			2.42563i
$321$	1.84459	+	3.19493i	0.102955	+	0.178323i
$322$	6.29969	−	10.9114i	0.351068	−	0.608068i
$323$	3.71465	+	2.14465i	0.206689	+	0.119332i
$324$	−5.40472			−0.300262
$325$	−3.34832	−	8.34878i	−0.185732	−	0.463107i
$326$	−19.6092			−1.08605
$327$	−7.72680	−	4.46107i	−0.427293	−	0.246698i
$328$	45.2087	−	78.3038i	2.49623	−	4.32360i
$329$	6.28515	+	10.8862i	0.346512	+	0.600176i
$330$			23.8702i			1.31401i
$331$	−2.60340	+	1.50307i	−0.143096	+	0.0826163i	−0.569839	−	0.821757i	$-0.692994\pi$
$331$	−2.60340	+	1.50307i	−0.143096	+	0.0826163i	0.426743	+	0.904373i	$0.359661\pi$
$332$	−6.88688	+	3.97614i	−0.377967	+	0.218219i
$333$		−	4.99293i		−	0.273611i
$334$	−0.637429	−	1.10406i	−0.0348785	−	0.0604114i
$335$	11.6651	−	20.2046i	0.637333	−	1.10389i
$336$	−12.4721	−	7.20078i	−0.680410	−	0.392835i
$337$	7.21913			0.393251			0.196626	−	0.980479i	$-0.437002\pi$
$337$	7.21913			0.393251			0.196626	+	0.980479i	$0.437002\pi$
$338$	−34.3676	+	8.38240i	−1.86935	+	0.455942i
$339$	−16.1353			−0.876350
$340$	35.6030	+	20.5554i	1.93084	+	1.11477i
$341$	4.08861	−	7.08169i	0.221411	−	0.383495i
$342$	−1.21436	−	2.10334i	−0.0656653	−	0.113736i
$343$			1.00000i			0.0539949i
$344$	−8.12543	+	4.69122i	−0.438094	+	0.252933i
$345$	6.34666	−	3.66425i	0.341693	−	0.197276i
$346$		−	28.8718i		−	1.55216i
$347$	−0.962380	−	1.66689i	−0.0516633	−	0.0894834i	0.839037	−	0.544074i	$-0.183119\pi$
$347$	−0.962380	−	1.66689i	−0.0516633	−	0.0894834i	−0.890701	+	0.454591i	$0.849786\pi$
$348$	5.08631	−	8.80975i	0.272655	−	0.472252i
$349$	2.82299	+	1.62985i	0.151111	+	0.0872441i	0.573649	−	0.819101i	$-0.305527\pi$
$349$	2.82299	+	1.62985i	0.151111	+	0.0872441i	−0.422538	+	0.906345i	$0.638861\pi$
$350$	−6.78880			−0.362877
$351$	1.34211	+	3.34645i	0.0716367	+	0.178620i
$352$	114.499			6.10280
$353$	7.71876	+	4.45643i	0.410828	+	0.237192i	0.691145	−	0.722716i	$-0.257106\pi$
$353$	7.71876	+	4.45643i	0.410828	+	0.237192i	−0.280317	+	0.959907i	$0.590440\pi$
$354$	4.68979	−	8.12296i	0.249260	−	0.431730i
$355$	10.3987	+	18.0110i	0.551903	+	0.955925i
$356$			41.3974i			2.19406i
$357$	−4.16192	+	2.40288i	−0.220272	+	0.127174i
$358$	−45.6411	+	26.3509i	−2.41221	+	1.39269i
$359$			20.1320i			1.06253i	0.847207	+	0.531263i	$0.178282\pi$
$359$			20.1320i			1.06253i	−0.847207	+	0.531263i	$0.821718\pi$
$360$	−7.33205	−	12.6995i	−0.386433	−	0.669322i
$361$	−9.10169	+	15.7646i	−0.479036	+	0.829715i
$362$	37.7064	+	21.7698i	1.98180	+	1.14419i
$363$	19.7161			1.03483
$364$	−2.76139	+	19.2904i	−0.144736	+	1.01109i
$365$	8.44656			0.442113
$366$	8.44955	+	4.87835i	0.441665	+	0.254996i
$367$	15.6709	−	27.1428i	0.818013	−	1.41684i	−0.0891309	−	0.996020i	$-0.528409\pi$
$367$	15.6709	−	27.1428i	0.818013	−	1.41684i	0.907144	−	0.420820i	$-0.138258\pi$
$368$	−33.3407	−	57.7478i	−1.73800	−	3.01031i
$369$			9.75924i			0.508046i
$370$	18.6234	−	10.7522i	0.968187	−	0.558983i
$371$	−5.41945	+	3.12892i	−0.281364	+	0.162446i
$372$			7.97437i			0.413452i
$373$	−8.97172	−	15.5395i	−0.464538	−	0.804604i	0.534642	−	0.845078i	$-0.320446\pi$
$373$	−8.97172	−	15.5395i	−0.464538	−	0.804604i	−0.999181	+	0.0404746i	$0.987113\pi$
$374$	36.2385	−	62.7669i	1.87385	−	3.24560i
$375$	−10.2733	−	5.93131i	−0.530513	−	0.306292i
$376$	116.461			6.00603
$377$	−6.71779	−	0.961644i	−0.345984	−	0.0495272i
$378$	2.72116			0.139961
$379$	17.4484	+	10.0738i	0.896263	+	0.517458i	0.875986	−	0.482337i	$-0.160212\pi$
$379$	17.4484	+	10.0738i	0.896263	+	0.517458i	0.0202771	+	0.999794i	$0.493545\pi$
$380$	3.81757	−	6.61223i	0.195837	−	0.339200i
$381$	2.31228	+	4.00499i	0.118462	+	0.205182i
$382$		−	8.56705i		−	0.438329i
$383$	−32.4871	+	18.7565i	−1.66002	+	0.958410i	−0.687311	+	0.726363i	$0.741209\pi$
$383$	−32.4871	+	18.7565i	−1.66002	+	0.958410i	−0.972705	+	0.232047i	$0.925458\pi$
$384$	−28.8216	+	16.6402i	−1.47080	+	0.849165i
$385$		−	8.77208i		−	0.447067i
$386$	31.6772	+	54.8666i	1.61233	+	2.79263i
$387$	0.506349	−	0.877022i	0.0257391	−	0.0445815i
$388$	−3.55109	−	2.05022i	−0.180279	−	0.104084i
$389$	23.1946			1.17601			0.588006	−	0.808857i	$-0.299913\pi$
$389$	23.1946			1.17601			0.588006	+	0.808857i	$0.299913\pi$
$390$	−9.59191	+	12.2126i	−0.485705	+	0.618409i
$391$	−22.2514			−1.12530
$392$	8.02355	+	4.63240i	0.405250	+	0.233971i
$393$	−3.89091	+	6.73926i	−0.196271	+	0.339951i
$394$	−24.0040	−	41.5762i	−1.20930	−	2.09458i
$395$		−	1.23303i		−	0.0620403i
$396$	−25.9410	+	14.9770i	−1.30358	+	0.752625i
$397$	−33.0480	+	19.0803i	−1.65863	+	0.957612i	−0.685286	+	0.728274i	$0.740323\pi$
$397$	−33.0480	+	19.0803i	−1.65863	+	0.957612i	−0.973347	+	0.229339i	$0.926344\pi$
$398$			32.4501i			1.62658i
$399$	0.446267	+	0.772957i	0.0223413	+	0.0386962i
$400$	−17.9646	+	31.1157i	−0.898232	+	1.55578i
$401$	7.17772	+	4.14406i	0.358438	+	0.206944i	0.668395	−	0.743806i	$-0.266981\pi$
$401$	7.17772	+	4.14406i	0.358438	+	0.206944i	−0.309957	+	0.950750i	$0.600315\pi$
$402$	40.1101			2.00051
$403$	4.93751	−	1.98021i	0.245955	−	0.0986415i
$404$	−63.6353			−3.16597
$405$	1.37073	+	0.791388i	0.0681119	+	0.0393244i
$406$	−2.56085	+	4.43552i	−0.127093	+	0.220131i
$407$	−13.8359	−	23.9645i	−0.685821	−	1.18788i
$408$			44.5245i			2.20429i
$409$	−33.8724	+	19.5562i	−1.67488	+	0.966994i	−0.710041	+	0.704160i	$0.751324\pi$
$409$	−33.8724	+	19.5562i	−1.67488	+	0.966994i	−0.964841	+	0.262834i	$0.915343\pi$
$410$	−36.4016	+	21.0165i	−1.79775	+	1.03793i
$411$		−	0.276352i		−	0.0136315i
$412$	−25.9962	−	45.0267i	−1.28074	−	2.21831i
$413$	−1.72345	+	2.98511i	−0.0848055	+	0.146887i
$414$	10.9114	+	6.29969i	0.536265	+	0.309613i
$415$	2.32883			0.114318
$416$	58.5803	+	46.0096i	2.87214	+	2.25581i
$417$	−3.96065			−0.193954
$418$	−11.6571	−	6.73026i	−0.570170	−	0.329188i
$419$	−13.7733	+	23.8560i	−0.672869	+	1.16544i	0.304218	+	0.952602i	$0.401605\pi$
$419$	−13.7733	+	23.8560i	−0.672869	+	1.16544i	−0.977087	+	0.212841i	$0.931728\pi$
$420$	4.27723	+	7.40839i	0.208708	+	0.361492i
$421$		−	34.1236i		−	1.66308i	−0.555465	−	0.831540i	$-0.687460\pi$
$421$		−	34.1236i		−	1.66308i	0.555465	−	0.831540i	$-0.312540\pi$
$422$	35.6558	−	20.5859i	1.73570	−	1.00210i
$423$	−10.8862	+	6.28515i	−0.529305	+	0.305594i
$424$			57.9776i			2.81564i
$425$	5.99476	+	10.3832i	0.290788	+	0.503660i
$426$	−17.8777	+	30.9651i	−0.866178	+	1.50026i
$427$	−3.10513	−	1.79275i	−0.150268	−	0.0867571i
$428$	−19.9390			−0.963788
$429$	15.7151	+	12.3428i	0.758732	+	0.595916i
$430$	4.36168			0.210339
$431$	−4.33090	−	2.50044i	−0.208612	−	0.120442i	0.392054	−	0.919942i	$-0.371765\pi$
$431$	−4.33090	−	2.50044i	−0.208612	−	0.120442i	−0.600666	+	0.799500i	$0.705098\pi$
$432$	7.20078	−	12.4721i	0.346448	−	0.600065i
$433$	7.45679	+	12.9155i	0.358351	+	0.620681i	0.987685	−	0.156453i	$-0.0500059\pi$
$433$	7.45679	+	12.9155i	0.358351	+	0.620681i	−0.629335	+	0.777134i	$0.716673\pi$
$434$		−	4.01493i		−	0.192723i
$435$	−2.57994	+	1.48953i	−0.123699	+	0.0714175i
$436$	41.7612	−	24.1109i	2.00000	−	1.15470i
$437$			4.13256i			0.197687i
$438$	7.26080	+	12.5761i	0.346934	+	0.600908i
$439$	−3.55138	+	6.15117i	−0.169498	+	0.293579i	−0.938244	−	0.345976i	$-0.887548\pi$
$439$	−3.55138	+	6.15117i	−0.169498	+	0.293579i	0.768745	+	0.639555i	$0.220881\pi$
$440$	−70.3832	−	40.6358i	−3.35539	−	1.93723i
$441$	−1.00000			−0.0476190
$442$	43.7624	−	17.5512i	2.08157	−	0.834824i
$443$	−4.63166			−0.220057			−0.110028	−	0.993928i	$-0.535094\pi$
$443$	−4.63166			−0.220057			−0.110028	+	0.993928i	$0.535094\pi$
$444$	23.3700	+	13.4927i	1.10909	+	0.640335i
$445$	6.06164	−	10.4991i	0.287349	−	0.497703i
$446$	−26.0636	−	45.1435i	−1.23415	−	2.13761i
$447$		−	21.6897i		−	1.02589i
$448$	23.7416	−	13.7072i	1.12169	−	0.647605i
$449$	−19.5486	+	11.2864i	−0.922558	+	0.532639i	−0.884450	−	0.466635i	$-0.845466\pi$
$449$	−19.5486	+	11.2864i	−0.922558	+	0.532639i	−0.0381076	+	0.999274i	$0.512133\pi$
$450$		−	6.78880i		−	0.320027i
$451$	27.0439	+	46.8414i	1.27345	+	2.20567i
$452$	43.6034	−	75.5234i	2.05093	−	3.55232i
$453$	−4.90753	−	2.83336i	−0.230576	−	0.133123i
$454$	−47.4624			−2.22752
$455$	3.52493	−	4.48801i	0.165251	−	0.210401i
$456$	8.26914			0.387238
$457$	25.8184	+	14.9063i	1.20773	+	0.697286i	0.962264	−	0.272118i	$-0.0877241\pi$
$457$	25.8184	+	14.9063i	1.20773	+	0.697286i	0.245471	+	0.969404i	$0.421057\pi$
$458$	−14.2963	+	24.7619i	−0.668022	+	1.15705i
$459$	−2.40288	−	4.16192i	−0.112157	−	0.194262i
$460$			39.6085i			1.84675i
$461$	−13.2819	+	7.66832i	−0.618601	+	0.357149i	−0.776324	−	0.630334i	$-0.782918\pi$
$461$	−13.2819	+	7.66832i	−0.618601	+	0.357149i	0.157723	+	0.987483i	$0.449585\pi$
$462$	13.0607	−	7.54062i	0.607641	−	0.350821i
$463$		−	13.7066i		−	0.636998i	−0.947923	−	0.318499i	$-0.896821\pi$
$463$		−	13.7066i		−	0.636998i	0.947923	−	0.318499i	$-0.103179\pi$
$464$	13.5531	+	23.4747i	0.629188	+	1.08979i
$465$	1.16765	−	2.02243i	0.0541485	−	0.0937880i
$466$	22.8366	+	13.1847i	1.05788	+	0.610769i
$467$	41.2833			1.91036			0.955182	−	0.296020i	$-0.0956594\pi$
$467$	41.2833			1.91036			0.955182	+	0.296020i	$0.0956594\pi$
$468$	−19.2904	−	2.76139i	−0.891697	−	0.127645i
$469$	−14.7401			−0.680633
$470$	−46.8868	−	27.0701i	−2.16273	−	1.24865i
$471$	0.532032	−	0.921507i	0.0245147	−	0.0424608i
$472$	15.9674	+	27.6564i	0.734961	+	1.27299i
$473$		−	5.61258i		−	0.258067i
$474$	1.83585	−	1.05993i	0.0843235	−	0.0486842i
$475$	1.92839	−	1.11335i	0.0884804	−	0.0510842i
$476$		−	25.9738i		−	1.19051i
$477$	−3.12892	−	5.41945i	−0.143263	−	0.248140i
$478$	25.0757	−	43.4324i	1.14694	−	1.98655i
$479$	−2.65614	−	1.53352i	−0.121362	−	0.0700685i	0.438090	−	0.898931i	$-0.355655\pi$
$479$	−2.65614	−	1.53352i	−0.121362	−	0.0700685i	−0.559452	+	0.828863i	$0.688988\pi$
$480$	32.6992			1.49251
$481$	2.55100	−	17.8206i	0.116315	−	0.812549i
$482$	41.7781			1.90294
$483$	−4.00983	−	2.31507i	−0.182453	−	0.105340i
$484$	−53.2799	+	92.2835i	−2.42181	+	4.19471i
$485$	0.600410	+	1.03994i	0.0272632	+	0.0472213i
$486$			2.72116i			0.123434i
$487$	7.17045	−	4.13986i	0.324924	−	0.187595i	−0.328661	−	0.944448i	$-0.606597\pi$
$487$	7.17045	−	4.13986i	0.324924	−	0.187595i	0.653585	+	0.756853i	$0.273264\pi$
$488$	−28.7684	+	16.6094i	−1.30228	+	0.751874i
$489$			7.20618i			0.325875i
$490$	−2.15350	−	3.72996i	−0.0972850	−	0.168503i
$491$	−2.48977	+	4.31241i	−0.112362	+	0.194616i	−0.916722	−	0.399526i	$-0.869175\pi$
$491$	−2.48977	+	4.31241i	−0.112362	+	0.194616i	0.804360	+	0.594142i	$0.202508\pi$
$492$	−45.6794	−	26.3730i	−2.05939	−	1.18899i
$493$	9.04529			0.407379
$494$	−3.25963	−	8.12762i	−0.146657	−	0.365679i
$495$	8.77208			0.394276
$496$	−18.4019	−	10.6244i	−0.826272	−	0.477048i
$497$	6.56988	−	11.3794i	0.294699	−	0.510434i
$498$	2.00190	+	3.46740i	0.0897074	+	0.155378i
$499$		−	0.00121934i		−	5.45852e-5i	−1.00000		2.72926e-5i	$-0.999991\pi$
$499$		−	0.00121934i		−	5.45852e-5i	1.00000		2.72926e-5i	$-8.68751e-6\pi$
$500$	55.5245	−	32.0571i	2.48313	−	1.43364i
$501$	−0.405731	+	0.234249i	−0.0181267	+	0.0104655i
$502$			23.4809i			1.04800i
$503$	6.65968	+	11.5349i	0.296941	+	0.514316i	0.975434	−	0.220290i	$-0.0707004\pi$
$503$	6.65968	+	11.5349i	0.296941	+	0.514316i	−0.678494	+	0.734606i	$0.737367\pi$
$504$	−4.63240	+	8.02355i	−0.206343	+	0.357397i
$505$	16.1389	+	9.31782i	0.718173	+	0.414638i
$506$	69.8284			3.10425
$507$	3.08045	+	12.6298i	0.136807	+	0.560907i
$508$	−24.9945			−1.10895
$509$	21.6361	+	12.4916i	0.959005	+	0.553682i	0.895867	−	0.444323i	$-0.146556\pi$
$509$	21.6361	+	12.4916i	0.959005	+	0.553682i	0.0631380	+	0.998005i	$0.479889\pi$
$510$	10.3492	−	17.9253i	0.458270	−	0.793747i
$511$	−2.66827	−	4.62158i	−0.118037	−	0.204447i
$512$		−	30.6726i		−	1.35555i
$513$	−0.772957	+	0.446267i	−0.0341269	+	0.0197032i
$514$	6.43230	−	3.71369i	0.283717	−	0.163804i
$515$			15.2260i			0.670939i
$516$	2.73667	+	4.74006i	0.120475	+	0.208669i
$517$	−34.8336	+	60.3336i	−1.53198	+	2.65347i
$518$	−11.7663	−	6.79328i	−0.516982	−	0.298480i
$519$	−10.6101			−0.465731
$520$	−19.6809	−	49.0727i	−0.863064	−	2.15198i
$521$	29.3265			1.28482			0.642409	−	0.766362i	$-0.277935\pi$
$521$	29.3265			1.28482			0.642409	+	0.766362i	$0.277935\pi$
$522$	−4.43552	−	2.56085i	−0.194138	−	0.112085i
$523$	−5.72560	+	9.91702i	−0.250363	+	0.433641i	−0.963626	−	0.267255i	$-0.913883\pi$
$523$	−5.72560	+	9.91702i	−0.250363	+	0.433641i	0.713263	+	0.700897i	$0.247217\pi$
$524$	−21.0293	−	36.4238i	−0.918670	−	1.59118i
$525$			2.49482i			0.108883i
$526$	13.2304	−	7.63856i	0.576872	−	0.333057i
$527$	−6.14068	+	3.54532i	−0.267492	+	0.154437i
$528$		−	79.8165i		−	3.47357i
$529$	0.780861	+	1.35249i	0.0339505	+	0.0588040i
$530$	13.4762	−	23.3415i	0.585370	−	1.01389i
$531$	−2.98511	−	1.72345i	−0.129543	−	0.0747914i
$532$	−4.82389			−0.209142
$533$	−4.98621	+	34.8324i	−0.215977	+	1.50876i
$534$	20.8427			0.901953
$535$	5.05686	+	2.91958i	0.218627	+	0.126224i
$536$	−68.2818	+	118.268i	−2.94933	+	5.10838i
$537$	9.68369	+	16.7726i	0.417882	+	0.723793i
$538$			0.495894i			0.0213795i
$539$	−4.79969	+	2.77110i	−0.206737	+	0.119360i
$540$	−7.40839	+	4.27723i	−0.318806	+	0.184063i
$541$		−	7.24411i		−	0.311449i	−0.987801	−	0.155724i	$-0.950229\pi$
$541$		−	7.24411i		−	0.311449i	0.987801	−	0.155724i	$-0.0497712\pi$
$542$	−39.9094	−	69.1250i	−1.71425	−	2.96917i
$543$	8.00018	−	13.8567i	0.343321	−	0.594649i
$544$	−85.9827	−	49.6421i	−3.68648	−	2.12839i
$545$	−14.1218			−0.604910
$546$	9.71228	+	1.39030i	0.415647	+	0.0594994i
$547$	24.3579			1.04147			0.520735	−	0.853718i	$-0.325658\pi$
$547$	24.3579			1.04147			0.520735	+	0.853718i	$0.325658\pi$
$548$	1.29350	+	0.746804i	0.0552557	+	0.0319019i
$549$	1.79275	−	3.10513i	0.0765125	−	0.132524i
$550$	−18.8125	−	32.5842i	−0.802167	−	1.38939i
$551$		−	1.67990i		−	0.0715663i
$552$	−37.1502	+	21.4487i	−1.58122	+	0.912917i
$553$	−0.674658	+	0.389514i	−0.0286894	+	0.0165638i
$554$		−	44.0142i		−	1.86998i
$555$	−3.95134	−	6.84393i	−0.167725	−	0.290509i
$556$	10.7031	−	18.5383i	0.453913	−	0.786200i
$557$	3.59179	+	2.07372i	0.152189	+	0.0878664i	0.574161	−	0.818743i	$-0.305328\pi$
$557$	3.59179	+	2.07372i	0.152189	+	0.0878664i	−0.421972	+	0.906609i	$0.638662\pi$
$558$	4.01493			0.169965
$559$	2.25533	−	2.87153i	0.0953904	−	0.121453i
$560$	−22.7945			−0.963242
$561$	−23.0662	−	13.3173i	−0.973856	−	0.562256i
$562$	5.05652	−	8.75814i	0.213296	−	0.369440i
$563$	−0.483932	−	0.838195i	−0.0203953	−	0.0353257i	0.855648	−	0.517559i	$-0.173159\pi$
$563$	−0.483932	−	0.838195i	−0.0203953	−	0.0353257i	−0.876043	+	0.482233i	$0.839826\pi$
$564$		−	67.9390i		−	2.86075i
$565$	−22.1171	+	12.7693i	−0.930472	+	0.537209i
$566$	8.89308	−	5.13442i	0.373804	−	0.215816i
$567$		−	1.00000i		−	0.0419961i
$568$	−60.8686	−	105.428i	−2.55399	−	4.42364i
$569$	−6.08730	+	10.5435i	−0.255193	+	0.442007i	−0.964948	−	0.262442i	$-0.915472\pi$
$569$	−6.08730	+	10.5435i	−0.255193	+	0.442007i	0.709755	+	0.704449i	$0.248806\pi$
$570$	−3.32912	−	1.92207i	−0.139441	−	0.0805065i
$571$	−28.8995			−1.20941			−0.604703	−	0.796451i	$-0.706708\pi$
$571$	−28.8995			−1.20941			−0.604703	+	0.796451i	$0.706708\pi$
$572$	−100.240	+	40.2017i	−4.19124	+	1.68092i
$573$	−3.14831			−0.131522
$574$	22.9986	+	13.2782i	0.959943	+	0.554223i
$575$	−5.77569	+	10.0038i	−0.240863	+	0.417187i
$576$	13.7072	+	23.7416i	0.571134	+	0.989234i
$577$		−	14.5003i		−	0.603657i	−0.953362	−	0.301828i	$-0.902403\pi$
$577$		−	14.5003i		−	0.603657i	0.953362	−	0.301828i	$-0.0975970\pi$
$578$	−14.3644	+	8.29328i	−0.597479	+	0.344955i
$579$	20.1629	−	11.6411i	0.837942	−	0.483786i
$580$		−	16.1010i		−	0.668557i
$581$	−0.735679	−	1.27423i	−0.0305211	−	0.0528641i
$582$	−1.03224	+	1.78790i	−0.0427879	+	0.0741108i
$583$	−30.0357	−	17.3411i	−1.24395	−	0.718196i
$584$	−49.4420			−2.04592
$585$	4.48801	+	3.52493i	0.185556	+	0.145738i
$586$	41.9503			1.73295
$587$	24.0493	+	13.8849i	0.992621	+	0.573090i	0.906057	−	0.423157i	$-0.139078\pi$
$587$	24.0493	+	13.8849i	0.992621	+	0.573090i	0.0865640	+	0.996246i	$0.472411\pi$
$588$	2.70236	−	4.68063i	0.111443	−	0.193026i
$589$	0.658442	+	1.14046i	0.0271306	+	0.0469917i
$590$		−	14.8458i		−	0.611191i
$591$	−15.2788	+	8.82123i	−0.628487	+	0.362857i
$592$	−62.2724	+	35.9530i	−2.55938	+	1.47766i
$593$			8.09800i			0.332545i	0.986080	+	0.166273i	$0.0531731\pi$
$593$			8.09800i			0.332545i	−0.986080	+	0.166273i	$0.946827\pi$
$594$	7.54062	+	13.0607i	0.309395	+	0.535889i
$595$	−3.80323	+	6.58738i	−0.155917	+	0.270056i
$596$	101.521	+	58.6134i	4.15848	+	2.40090i
$597$	11.9251			0.488062
$598$	35.7259	+	28.0595i	1.46094	+	1.14744i
$599$	12.8054			0.523216			0.261608	−	0.965174i	$-0.415747\pi$
$599$	12.8054			0.523216			0.261608	+	0.965174i	$0.415747\pi$
$600$	20.0173	+	11.5570i	0.817202	+	0.471812i
$601$	8.90245	−	15.4195i	0.363138	−	0.628974i	−0.625337	−	0.780355i	$-0.715039\pi$
$601$	8.90245	−	15.4195i	0.363138	−	0.628974i	0.988476	+	0.151381i	$0.0483719\pi$
$602$	−1.37786	−	2.38652i	−0.0561572	−	0.0972672i
$603$		−	14.7401i		−	0.600262i
$604$	26.5238	−	15.3135i	1.07924	−	0.623099i
$605$	27.0253	−	15.6031i	1.09873	−	0.634355i
$606$			32.0390i			1.30150i
$607$	−3.05078	−	5.28410i	−0.123827	−	0.214475i	0.797447	−	0.603389i	$-0.206184\pi$
$607$	−3.05078	−	5.28410i	−0.123827	−	0.214475i	−0.921274	+	0.388914i	$0.872850\pi$
$608$	−9.21960	+	15.9688i	−0.373904	+	0.647621i
$609$	1.63001	+	0.941087i	0.0660513	+	0.0381348i
$610$	15.4427			0.625256
$611$	−42.0659	+	16.8708i	−1.70180	+	0.682518i
$612$	25.9738			1.04993
$613$	−14.7559	−	8.51931i	−0.595984	−	0.344092i	0.171476	−	0.985188i	$-0.445146\pi$
$613$	−14.7559	−	8.51931i	−0.595984	−	0.344092i	−0.767460	+	0.641097i	$0.778480\pi$
$614$	45.2552	−	78.3843i	1.82635	−	3.16333i
$615$	7.72335	+	13.3772i	0.311436	+	0.539422i
$616$			51.3474i			2.06885i
$617$	−21.9462	+	12.6707i	−0.883523	+	0.510102i	−0.871818	−	0.489830i	$-0.837059\pi$
$617$	−21.9462	+	12.6707i	−0.883523	+	0.510102i	−0.0117043	+	0.999932i	$0.503726\pi$
$618$	−22.6700	+	13.0885i	−0.911921	+	0.526498i
$619$			45.5457i			1.83064i	0.402731	+	0.915319i	$0.368061\pi$
$619$			45.5457i			1.83064i	−0.402731	+	0.915319i	$0.631939\pi$
$620$	6.31083	+	10.9307i	0.253449	+	0.438986i
$621$	2.31507	−	4.00983i	0.0929007	−	0.160909i
$622$	12.4490	+	7.18745i	0.499161	+	0.288191i
$623$	−7.65950			−0.306871
$624$	32.0731	−	40.8361i	1.28395	−	1.63475i
$625$	−6.30180			−0.252072
$626$	−41.2059	−	23.7902i	−1.64692	−	0.950848i
$627$	−2.47330	+	4.28389i	−0.0987742	+	0.171082i
$628$	2.87549	+	4.98049i	0.114744	+	0.198743i
$629$			23.9948i			0.956737i
$630$	3.72996	−	2.15350i	0.148605	−	0.0857973i
$631$	1.72180	−	0.994084i	0.0685440	−	0.0395739i	−0.465336	−	0.885134i	$-0.654067\pi$
$631$	1.72180	−	0.994084i	0.0685440	−	0.0395739i	0.533880	+	0.845560i	$0.320733\pi$
$632$			7.21754i			0.287098i
$633$	−7.56510	−	13.1031i	−0.300686	−	0.520803i
$634$	9.38054	−	16.2476i	0.372549	−	0.645273i
$635$	6.33901	+	3.65983i	0.251556	+	0.145236i
$636$	33.8219			1.34113
$637$	−3.56917	−	0.510922i	−0.141416	−	0.0202435i
$638$	−28.3855			−1.12379
$639$	11.3794	+	6.56988i	0.450161	+	0.259901i
$640$	−26.3377	+	45.6182i	−1.04109	+	1.80322i
$641$	−6.84746	−	11.8602i	−0.270459	−	0.468448i	0.698521	−	0.715590i	$-0.253842\pi$
$641$	−6.84746	−	11.8602i	−0.270459	−	0.468448i	−0.968979	+	0.247142i	$0.920509\pi$
$642$			10.0389i			0.396202i
$643$	16.7590	−	9.67580i	0.660909	−	0.381576i	−0.131714	−	0.991288i	$-0.542048\pi$
$643$	16.7590	−	9.67580i	0.660909	−	0.381576i	0.792623	+	0.609711i	$0.208715\pi$
$644$	21.6720	−	12.5123i	0.853996	−	0.493055i
$645$		−	1.60287i		−	0.0631131i
$646$	5.83595	+	10.1082i	0.229612	+	0.397700i
$647$	−18.3354	+	31.7578i	−0.720839	+	1.24853i	0.239825	+	0.970816i	$0.422910\pi$
$647$	−18.3354	+	31.7578i	−0.720839	+	1.24853i	−0.960664	+	0.277713i	$0.910423\pi$
$648$	−8.02355	−	4.63240i	−0.315195	−	0.181978i
$649$	−19.1035			−0.749876
$650$	3.46855	−	24.2304i	0.136048	−	0.950393i
$651$	−1.47545			−0.0578273
$652$	−33.7294	−	19.4737i	−1.32095	−	0.762649i
$653$	7.79808	−	13.5067i	0.305163	−	0.528557i	−0.672135	−	0.740429i	$-0.734623\pi$
$653$	7.79808	−	13.5067i	0.305163	−	0.528557i	0.977298	+	0.211872i	$0.0679559\pi$
$654$	−12.1393	−	21.0259i	−0.474684	−	0.822177i
$655$			12.3169i			0.481261i
$656$	121.719	−	70.2742i	4.75231	−	2.74375i
$657$	4.62158	−	2.66827i	0.180305	−	0.104099i
$658$			34.2058i			1.33348i
$659$	13.7314	+	23.7835i	0.534900	+	0.926474i	0.999168	+	0.0407792i	$0.0129840\pi$
$659$	13.7314	+	23.7835i	0.534900	+	0.926474i	−0.464268	+	0.885695i	$0.653683\pi$
$660$	−23.7053	+	41.0588i	−0.922728	+	1.59821i
$661$	−13.2412	−	7.64481i	−0.515023	−	0.297348i	0.219873	−	0.975528i	$-0.429436\pi$
$661$	−13.2412	−	7.64481i	−0.515023	−	0.297348i	−0.734896	+	0.678180i	$0.762769\pi$
$662$	−8.18021			−0.317933
$663$	−6.44988	−	16.0823i	−0.250493	−	0.624583i
$664$	−13.6318			−0.529018
$665$	1.22342	+	0.706341i	0.0474421	+	0.0273907i
$666$	6.79328	−	11.7663i	0.263234	−	0.455935i
$667$	4.35737	+	7.54719i	0.168718	+	0.292228i
$668$		−	2.53210i		−	0.0979698i
$669$	−16.5898	+	9.57812i	−0.641398	+	0.370311i
$670$	54.9799	−	31.7427i	2.12406	−	1.22633i
$671$		−	19.8715i		−	0.767132i
$672$	−10.3297	−	17.8916i	−0.398477	−	0.690182i
$673$	−12.4288	+	21.5273i	−0.479094	+	0.829815i	−0.999713	−	0.0239740i	$-0.992368\pi$
$673$	−12.4288	+	21.5273i	−0.479094	+	0.829815i	0.520618	+	0.853789i	$0.325701\pi$
$674$	17.0126	+	9.82222i	0.655300	+	0.378338i
$675$	−2.49482			−0.0960256
$676$	−67.4397	−	19.7117i	−2.59383	−	0.758144i
$677$	−4.31671			−0.165905			−0.0829523	−	0.996554i	$-0.526435\pi$
$677$	−4.31671			−0.165905			−0.0829523	+	0.996554i	$0.526435\pi$
$678$	−38.0244	−	21.9534i	−1.46032	−	0.843115i
$679$	0.379340	−	0.657035i	0.0145577	−	0.0252147i
$680$	35.2361	+	61.0308i	1.35124	+	2.34042i
$681$			17.4419i			0.668377i
$682$	19.2704	−	11.1258i	0.737902	−	0.426028i
$683$	32.6030	−	18.8233i	1.24752	−	0.720255i	0.276904	−	0.960897i	$-0.410691\pi$
$683$	32.6030	−	18.8233i	1.24752	−	0.720255i	0.970614	+	0.240642i	$0.0773581\pi$
$684$		−	4.82389i		−	0.184446i
$685$	−0.218702	−	0.378803i	−0.00835618	−	0.0144733i
$686$	−1.36058	+	2.35660i	−0.0519472	+	0.0899752i
$687$	9.09975	+	5.25374i	0.347177	+	0.200443i
$688$	−14.5844			−0.556026
$689$	−8.39873	−	20.9416i	−0.319966	−	0.797810i
$690$	19.9420			0.759179
$691$	43.5579	+	25.1482i	1.65702	+	0.956682i	0.974078	+	0.226210i	$0.0726337\pi$
$691$	43.5579	+	25.1482i	1.65702	+	0.956682i	0.682943	+	0.730472i	$0.260700\pi$
$692$	28.6723	−	49.6618i	1.08996	−	1.88786i
$693$	−2.77110	−	4.79969i	−0.105266	−	0.182325i
$694$		−	5.23758i		−	0.198816i
$695$	−5.42896	+	3.13441i	−0.205932	+	0.118895i
$696$	15.1017	−	8.71898i	0.572429	−	0.330492i
$697$		−	46.9007i		−	1.77649i
$698$	4.43510	+	7.68182i	0.167871	+	0.290761i
$699$	4.84524	−	8.39221i	0.183264	−	0.317422i
$700$	−11.6773	−	6.74190i	−0.441361	−	0.254820i
$701$	12.0336			0.454504			0.227252	−	0.973836i	$-0.427026\pi$
$701$	12.0336			0.454504			0.227252	+	0.973836i	$0.427026\pi$
$702$	−1.39030	+	9.71228i	−0.0524736	+	0.366566i
$703$	4.45635			0.168075
$704$	131.581	+	75.9683i	4.95914	+	2.86316i
$705$	−9.94799	+	17.2304i	−0.374663	+	0.648935i
$706$	12.1267	+	21.0040i	0.456393	+	0.790495i
$707$		−	11.7740i		−	0.442808i
$708$	16.1337	−	9.31478i	0.606340	−	0.350071i
$709$	−37.4205	+	21.6047i	−1.40536	+	0.811383i	−0.994936	−	0.100513i	$-0.967951\pi$
$709$	−37.4205	+	21.6047i	−1.40536	+	0.811383i	−0.410421	+	0.911896i	$0.634618\pi$
$710$			56.5929i			2.12389i
$711$	−0.389514	−	0.674658i	−0.0146079	−	0.0253017i
$712$	−35.4818	+	61.4564i	−1.32974	+	2.30317i
$713$	−5.91628	−	3.41577i	−0.221567	−	0.127921i
$714$	−13.0773			−0.489404
$715$	31.3090	+	4.48185i	1.17089	+	0.167612i
$716$	−104.675			−3.91190
$717$	−15.9610	−	9.21508i	−0.596074	−	0.344143i
$718$	−27.3912	+	47.4429i	−1.02223	+	1.77055i
$719$	20.4763	+	35.4661i	0.763639	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$719$	20.4763	+	35.4661i	0.763639	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$720$		−	22.7945i		−	0.849500i
$721$	8.33100	−	4.80991i	0.310263	−	0.179130i
$722$	−42.8980	+	24.7672i	−1.59650	+	0.921739i
$723$		−	15.3530i		−	0.570986i
$724$	43.2387	+	74.8917i	1.60695	+	2.78333i
$725$	2.34784	−	4.06658i	0.0871966	−	0.151029i
$726$	46.4628	+	26.8253i	1.72440	+	0.995580i
$727$	24.7078			0.916360			0.458180	−	0.888859i	$-0.348501\pi$
$727$	24.7078			0.916360			0.458180	+	0.888859i	$0.348501\pi$
$728$	−20.6332	+	26.2706i	−0.764718	+	0.973653i
$729$	1.00000			0.0370370
$730$	19.9051	+	11.4922i	0.736722	+	0.425346i
$731$	−2.43339	+	4.21476i	−0.0900023	+	0.155889i
$732$	9.68929	+	16.7823i	0.358127	+	0.620293i
$733$		−	8.10694i		−	0.299437i	−0.988729	−	0.149718i	$-0.952163\pi$
$733$		−	8.10694i		−	0.299437i	0.988729	−	0.149718i	$-0.0478367\pi$
$734$	73.8598	−	42.6430i	2.72622	−	1.57398i
$735$	−1.37073	+	0.791388i	−0.0505600	+	0.0291908i
$736$		−	95.6561i		−	3.52593i
$737$	−40.8462	−	70.7477i	−1.50459	−	2.60603i
$738$	−13.2782	+	22.9986i	−0.488779	+	0.846590i
$739$	−31.9300	−	18.4348i	−1.17456	−	0.678135i	−0.219813	−	0.975542i	$-0.570545\pi$
$739$	−31.9300	−	18.4348i	−1.17456	−	0.678135i	−0.954751	+	0.297408i	$0.903878\pi$
$740$	42.7118			1.57012
$741$	−2.98682	+	1.19788i	−0.109724	+	0.0440052i
$742$	−17.0286			−0.625140
$743$	−6.60077	−	3.81096i	−0.242159	−	0.139810i	0.374010	−	0.927425i	$-0.377983\pi$
$743$	−6.60077	−	3.81096i	−0.242159	−	0.139810i	−0.616169	+	0.787614i	$0.711316\pi$
$744$	−6.83485	+	11.8383i	−0.250578	+	0.434014i
$745$	−17.1650	−	29.7306i	−0.628877	−	1.08925i
$746$		−	48.8270i		−	1.78768i
$747$	1.27423	−	0.735679i	0.0466218	−	0.0269171i
$748$	124.666	−	71.9762i	4.55825	−	2.63171i
$749$		−	3.68918i		−	0.134800i
$750$	−16.1401	−	27.9554i	−0.589352	−	1.02079i
$751$	10.3356	−	17.9017i	0.377150	−	0.653243i	−0.613496	−	0.789698i	$-0.710237\pi$
$751$	10.3356	−	17.9017i	0.377150	−	0.653243i	0.990646	+	0.136455i	$0.0435708\pi$
$752$	156.778	+	90.5160i	5.71712	+	3.30078i
$753$	8.62900			0.314458
$754$	−14.5227	−	11.4063i	−0.528886	−	0.415393i
$755$	−8.96916			−0.326421
$756$	4.68063	+	2.70236i	0.170233	+	0.0982839i
$757$	1.09408	−	1.89500i	0.0397650	−	0.0688749i	−0.845458	−	0.534042i	$-0.820672\pi$
$757$	1.09408	−	1.89500i	0.0397650	−	0.0688749i	0.885223	+	0.465167i	$0.154006\pi$
$758$	27.4125	+	47.4799i	0.995667	+	1.72455i
$759$		−	25.6612i		−	0.931444i
$760$	11.3347	−	6.54410i	0.411153	−	0.237380i
$761$	27.1726	−	15.6881i	0.985006	−	0.568694i	0.0812283	−	0.996696i	$-0.474116\pi$
$761$	27.1726	−	15.6881i	0.985006	−	0.568694i	0.903778	+	0.428002i	$0.140782\pi$
$762$			12.5842i			0.455877i
$763$	4.46107	+	7.72680i	0.161502	+	0.279729i
$764$	8.50786	−	14.7360i	0.307804	−	0.533132i
$765$	−6.58738	−	3.80323i	−0.238167	−	0.137506i
$766$	−102.079			−3.68825
$767$	−9.77379	−	7.67645i	−0.352911	−	0.277180i
$768$	−35.7323			−1.28938
$769$	7.71490	+	4.45420i	0.278207	+	0.160623i	0.632611	−	0.774470i	$-0.281983\pi$
$769$	7.71490	+	4.45420i	0.278207	+	0.160623i	−0.354405	+	0.935092i	$0.615316\pi$
$770$	11.9351	−	20.6722i	0.430112	−	0.744976i
$771$	−1.36475	−	2.36381i	−0.0491501	−	0.0851305i
$772$			125.833i			4.52884i
$773$	3.06396	−	1.76898i	0.110203	−	0.0636258i	−0.443885	−	0.896084i	$-0.646400\pi$
$773$	3.06396	−	1.76898i	0.110203	−	0.0636258i	0.554088	+	0.832458i	$0.313067\pi$
$774$	2.38652	−	1.37786i	0.0857816	−	0.0495260i
$775$			3.68097i			0.132224i
$776$	−3.51450	−	6.08730i	−0.126163	−	0.218521i
$777$	−2.49646	+	4.32400i	−0.0895601	+	0.155123i
$778$	54.6602	+	31.5581i	1.95966	+	1.13141i
$779$	−8.71045			−0.312084
$780$	−28.6271	+	11.4811i	−1.02501	+	0.411088i
$781$	72.8233			2.60582
$782$	−52.4376	−	30.2749i	−1.87516	−	1.08263i
$783$	−0.941087	+	1.63001i	−0.0336317	+	0.0582518i
$784$	7.20078	+	12.4721i	0.257171	+	0.445433i
$785$		−	1.68418i		−	0.0601108i
$786$	−18.3386	+	10.5878i	−0.654117	+	0.377655i
$787$	−17.7715	+	10.2604i	−0.633484	+	0.365742i	−0.782100	−	0.623153i	$-0.785852\pi$
$787$	−17.7715	+	10.2604i	−0.633484	+	0.365742i	0.148616	+	0.988895i	$0.452518\pi$
$788$		−	95.3526i		−	3.39680i
$789$	−2.80709	−	4.86203i	−0.0999352	−	0.173093i
$790$	1.67763	−	2.90575i	0.0596875	−	0.103382i
$791$	13.9736	+	8.06766i	0.496844	+	0.286853i
$792$	−51.3474			−1.82455
$793$	7.98509	−	10.1668i	0.283559	−	0.361032i
$794$	−103.841			−3.68518
$795$	−8.57778	−	4.95238i	−0.304223	−	0.175643i
$796$	−32.2259	+	55.8170i	−1.14222	+	1.97838i
$797$	−19.9325	−	34.5241i	−0.706045	−	1.22291i	−0.966313	−	0.257369i	$-0.917144\pi$
$797$	−19.9325	−	34.5241i	−0.706045	−	1.22291i	0.260269	−	0.965536i	$-0.416189\pi$
$798$			2.42873i			0.0859760i
$799$	52.3165	−	30.2050i	1.85083	−	1.06857i
$800$	−44.6362	+	25.7707i	−1.57813	+	0.911133i
$801$		−	7.65950i		−	0.270635i
$802$	11.2767	+	19.5317i	0.398192	+	0.689690i
$803$	14.7881	−	25.6138i	0.521861	−	0.903890i
$804$	68.9927	+	39.8330i	2.43318	+	1.40480i
$805$	−7.32849			−0.258295
$806$	14.3299	+	2.05132i	0.504751	+	0.0722545i
$807$	0.182236			0.00641501
$808$	−94.4694	−	54.5419i	−3.32342	−	1.91878i
$809$	−20.8347	+	36.0868i	−0.732509	+	1.26874i	0.223299	+	0.974750i	$0.428317\pi$
$809$	−20.8347	+	36.0868i	−0.732509	+	1.26874i	−0.955808	+	0.293993i	$0.905016\pi$
$810$	2.15350	+	3.72996i	0.0756661	+	0.131058i
$811$			20.6446i			0.724931i	0.931997	+	0.362465i	$0.118065\pi$
$811$			20.6446i			0.724931i	−0.931997	+	0.362465i	$0.881935\pi$
$812$	−8.80975	+	5.08631i	−0.309162	+	0.178495i
$813$	−25.4028	+	14.6663i	−0.890914	+	0.514369i
$814$		−	75.2995i		−	2.63925i
$815$	5.70289	+	9.87769i	0.199763	+	0.346000i
$816$	−34.6053	+	59.9381i	−1.21143	+	2.09825i
$817$	0.782771	+	0.451933i	0.0273857	+	0.0158111i
$818$	−106.431			−3.72129
$819$	0.510922	−	3.56917i	0.0178531	−	0.124717i
$820$	−83.4851			−2.91543
$821$	−12.2424	−	7.06813i	−0.427261	−	0.246679i	0.270918	−	0.962602i	$-0.412673\pi$
$821$	−12.2424	−	7.06813i	−0.427261	−	0.246679i	−0.698179	+	0.715923i	$0.746006\pi$
$822$	0.376000	−	0.651251i	0.0131145	−	0.0227150i
$823$	0.822984	+	1.42545i	0.0286874	+	0.0496881i	0.880013	−	0.474950i	$-0.157534\pi$
$823$	0.822984	+	1.42545i	0.0286874	+	0.0496881i	−0.851325	+	0.524638i	$0.824201\pi$
$824$		−	89.1256i		−	3.10484i
$825$	−11.9744	+	6.91340i	−0.416894	+	0.240694i
$826$	−8.12296	+	4.68979i	−0.282634	+	0.163179i
$827$		−	10.1980i		−	0.354620i	−0.984155	−	0.177310i	$-0.943260\pi$
$827$		−	10.1980i		−	0.354620i	0.984155	−	0.177310i	$-0.0567396\pi$
$828$	12.5123	+	21.6720i	0.434834	+	0.753154i
$829$	−0.838869	+	1.45296i	−0.0291351	+	0.0504635i	−0.880225	−	0.474556i	$-0.842609\pi$
$829$	−0.838869	+	1.45296i	−0.0291351	+	0.0504635i	0.851090	+	0.525020i	$0.175942\pi$
$830$	5.48812	+	3.16856i	0.190495	+	0.109982i
$831$	−16.1748			−0.561097
$832$	36.7933	+	91.7411i	1.27558	+	3.18055i
$833$	4.80577			0.166510
$834$	−9.33365	−	5.38878i	−0.323198	−	0.186598i
$835$	−0.370763	+	0.642181i	−0.0128308	+	0.0222236i
$836$	−13.3675	−	23.1532i	−0.462325	−	0.800771i
$837$		−	1.47545i		−	0.0509989i
$838$	−64.9161	+	37.4793i	−2.24249	+	1.29470i
$839$	−9.28491	+	5.36065i	−0.320551	+	0.185070i	−0.651638	−	0.758530i	$-0.725918\pi$
$839$	−9.28491	+	5.36065i	−0.320551	+	0.185070i	0.331087	+	0.943600i	$0.392585\pi$
$840$			14.6641i			0.505960i
$841$	12.7287	+	22.0468i	0.438921	+	0.760234i
$842$	46.4279	−	80.4154i	1.60001	−	2.77130i
$843$	−3.21853	−	1.85822i	−0.110852	−	0.0640005i
$844$	81.7745			2.81480
$845$	14.2175	+	14.8741i	0.489097	+	0.511685i
$846$	−34.2058			−1.17602
$847$	−17.0746	−	9.85803i	−0.586691	−	0.338726i
$848$	−45.0614	+	78.0486i	−1.54741	+	2.68020i
$849$	−1.88685	−	3.26812i	−0.0647565	−	0.112162i
$850$			32.6254i			1.11904i
$851$	−20.0208	+	11.5590i	−0.686303	+	0.396237i
$852$	−61.5023	+	35.5084i	−2.10703	+	1.21650i
$853$		−	5.01741i		−	0.171793i	−0.996304	−	0.0858964i	$-0.972625\pi$
$853$		−	5.01741i		−	0.171793i	0.996304	−	0.0858964i	$-0.0273754\pi$
$854$	−4.87835	−	8.44955i	−0.166934	−	0.289138i
$855$	−0.706341	+	1.22342i	−0.0241563	+	0.0418400i
$856$	−29.6004	−	17.0898i	−1.01172	−	0.584116i
$857$	−25.0009			−0.854015			−0.427008	−	0.904248i	$-0.640432\pi$
$857$	−25.0009			−0.854015			−0.427008	+	0.904248i	$0.640432\pi$
$858$	20.2407	+	50.4686i	0.691007	+	1.72297i
$859$	17.9200			0.611424			0.305712	−	0.952124i	$-0.401106\pi$
$859$	17.9200			0.611424			0.305712	+	0.952124i	$0.401106\pi$
$860$	7.50245	+	4.33154i	0.255832	+	0.147704i
$861$	4.87962	−	8.45175i	0.166297	−	0.288035i
$862$	−6.80411	−	11.7851i	−0.231749	−	0.401401i
$863$		−	7.10038i		−	0.241700i	−0.992671	−	0.120850i	$-0.961438\pi$
$863$		−	7.10038i		−	0.241700i	0.992671	−	0.120850i	$-0.0385620\pi$
$864$	17.8916	−	10.3297i	0.608684	−	0.351424i
$865$	−14.5435	+	8.39670i	−0.494494	+	0.285496i
$866$			40.5823i			1.37904i
$867$	3.04770	+	5.27877i	0.103505	+	0.179276i
$868$	3.98719	−	6.90601i	0.135334	−	0.234405i
$869$	−3.73909	−	2.15877i	−0.126840	−	0.0732312i
$870$	−8.10651			−0.274836
$871$	7.53102	−	52.6097i	0.255179	−	1.78261i
$872$	82.6619			2.79928
$873$	0.657035	+	0.379340i	0.0222373	+	0.0128387i
$874$	−5.62269	+	9.73878i	−0.190190	+	0.329419i
$875$	5.93131	+	10.2733i	0.200515	+	0.347302i
$876$			28.8425i			0.974499i
$877$	23.1653	−	13.3745i	0.782236	−	0.451624i	−0.0549864	−	0.998487i	$-0.517512\pi$
$877$	23.1653	−	13.3745i	0.782236	−	0.451624i	0.837222	+	0.546863i	$0.184178\pi$
$878$	−16.7383	+	9.66388i	−0.564891	+	0.326140i
$879$		−	15.4163i		−	0.519980i
$880$	−63.1658	−	109.406i	−2.12932	−	3.68809i
$881$	5.01467	−	8.68567i	0.168949	−	0.292628i	−0.769102	−	0.639126i	$-0.779296\pi$
$881$	5.01467	−	8.68567i	0.168949	−	0.292628i	0.938050	+	0.346499i	$0.112629\pi$
$882$	−2.35660	−	1.36058i	−0.0793507	−	0.0458131i
$883$	1.88319			0.0633743			0.0316871	−	0.999498i	$-0.489912\pi$
$883$	1.88319			0.0633743			0.0316871	+	0.999498i	$0.489912\pi$
$884$	92.7050	+	13.2706i	3.11801	+	0.446339i
$885$	−5.45568			−0.183391
$886$	−10.9149	−	6.30174i	−0.366695	−	0.211711i
$887$	19.2887	−	33.4090i	0.647652	−	1.12177i	−0.336030	−	0.941851i	$-0.609084\pi$
$887$	19.2887	−	33.4090i	0.647652	−	1.12177i	0.983682	−	0.179915i	$-0.0575822\pi$
$888$	23.1292	+	40.0610i	0.776166	+	1.34436i
$889$		−	4.62457i		−	0.155103i
$890$	28.5697	−	16.4947i	0.957657	−	0.552903i
$891$	4.79969	−	2.77110i	0.160796	−	0.0928355i
$892$		−	103.534i		−	3.46658i
$893$	−5.60971	−	9.71630i	−0.187722	−	0.325143i
$894$	29.5106	−	51.1139i	0.986983	−	1.70950i
$895$	26.5473	+	15.3271i	0.887380	+	0.512329i
$896$	33.2803			1.11182
$897$	10.3116	−	13.1289i	0.344294	−	0.438362i
$898$	−61.4243			−2.04976
$899$	2.40499	+	1.38852i	0.0802110	+	0.0463098i
$900$	6.74190	−	11.6773i	0.224730	−	0.389244i
$901$	15.0369	+	26.0446i	0.500951	+	0.867672i
$902$			147.182i			4.90061i
$903$	−0.877022	+	0.506349i	−0.0291854	+	0.0168502i
$904$	129.462	−	74.7452i	4.30586	−	2.48599i
$905$		−	25.3250i		−	0.841831i
$906$	−7.71004	−	13.3542i	−0.256149	−	0.443663i
$907$	18.1585	−	31.4515i	0.602944	−	1.04433i	−0.389429	−	0.921056i	$-0.627328\pi$
$907$	18.1585	−	31.4515i	0.602944	−	1.04433i	0.992373	−	0.123273i	$-0.0393390\pi$
$908$	−81.6392	−	47.1344i	−2.70929	−	1.56421i
$909$	11.7740			0.390520
$910$	14.4131	−	5.78047i	0.477791	−	0.191621i
$911$	5.42183			0.179633			0.0898167	−	0.995958i	$-0.471372\pi$
$911$	5.42183			0.179633			0.0898167	+	0.995958i	$0.471372\pi$
$912$	11.1318	+	6.42694i	0.368610	+	0.212817i
$913$	4.07729	−	7.06207i	0.134939	−	0.233720i
$914$	40.5624	+	70.2561i	1.34168	+	2.32387i
$915$		−	5.67503i		−	0.187611i
$916$	−49.1816	+	28.3950i	−1.62501	+	0.938198i
$917$	6.73926	−	3.89091i	0.222550	−	0.128489i
$918$		−	13.0773i		−	0.431614i
$919$	−7.91774	−	13.7139i	−0.261182	−	0.452381i	0.705374	−	0.708835i	$-0.250779\pi$
$919$	−7.91774	−	13.7139i	−0.261182	−	0.452381i	−0.966556	+	0.256454i	$0.917446\pi$
$920$	−33.9485	+	58.8005i	−1.11925	+	1.93860i
$921$	−28.8054	−	16.6308i	−0.949172	−	0.548005i
$922$	−41.7335			−1.37442
$923$	37.2582	+	29.2630i	1.22637	+	0.963203i
$924$	29.9541			0.985417
$925$	10.7876	+	6.22822i	0.354694	+	0.204783i
$926$	18.6489	−	32.3008i	0.612841	−	1.06147i
$927$	4.80991	+	8.33100i	0.157978	+	0.273626i
$928$			38.8846i			1.27645i
$929$	−19.9419	+	11.5135i	−0.654272	+	0.377744i	−0.790091	−	0.612990i	$-0.789967\pi$
$929$	−19.9419	+	11.5135i	−0.654272	+	0.377744i	0.135819	+	0.990734i	$0.456633\pi$
$930$	5.50336	−	3.17737i	0.180462	−	0.104190i
$931$		−	0.892533i		−	0.0292516i
$932$	26.1872	+	45.3575i	0.857790	+	1.48574i
$933$	2.64132	−	4.57490i	0.0864728	−	0.149775i
$934$	97.2880	+	56.1693i	3.18336	+	1.83792i
$935$	−42.1566			−1.37867
$936$	−26.2706	−	20.6332i	−0.858681	−	0.674418i
$937$	−48.9751			−1.59995			−0.799974	−	0.600035i	$-0.795153\pi$
$937$	−48.9751			−1.59995			−0.799974	+	0.600035i	$0.795153\pi$
$938$	−34.7364	−	20.0550i	−1.13418	−	0.654820i
$939$	−8.74267	+	15.1427i	−0.285306	+	0.494165i
$940$	−53.7661	−	93.1256i	−1.75366	−	3.03742i
$941$			31.1637i			1.01591i	0.861384	+	0.507954i	$0.169598\pi$
$941$			31.1637i			1.01591i	−0.861384	+	0.507954i	$0.830402\pi$
$942$	2.50757	−	1.44775i	0.0817010	−	0.0471701i
$943$	39.1329	−	22.5934i	1.27434	−	0.735742i
$944$			49.6408i			1.61567i
$945$	−0.791388	−	1.37073i	−0.0257439	−	0.0445897i
$946$	7.63637	−	13.2266i	0.248280	−	0.430033i
$947$	39.0165	+	22.5262i	1.26787	+	0.732003i	0.974584	−	0.224023i	$-0.0719192\pi$
$947$	39.0165	+	22.5262i	1.26787	+	0.732003i	0.293282	+	0.956026i	$0.405253\pi$
$948$	4.21043			0.136748
$949$	17.8585	−	7.16224i	0.579711	−	0.232496i
$950$	6.05923			0.196587
$951$	−5.97082	−	3.44725i	−0.193617	−	0.111785i
$952$	22.2622	−	38.5593i	0.721523	−	1.24971i
$953$	4.36983	+	7.56877i	0.141553	+	0.245176i	0.928081	−	0.372377i	$-0.121457\pi$
$953$	4.36983	+	7.56877i	0.141553	+	0.245176i	−0.786529	+	0.617554i	$0.788124\pi$
$954$		−	17.0286i		−	0.551321i
$955$	−4.31546	+	2.49153i	−0.139645	+	0.0806242i
$956$	86.2647	−	49.8049i	2.79000	−	1.61081i
$957$			10.4314i			0.337199i
$958$	−4.17297	−	7.22779i	−0.134822	−	0.233519i
$959$	−0.138176	+	0.239328i	−0.00446194	+	0.00772831i
$960$	37.5777	+	21.6955i	1.21281	+	0.700218i
$961$	28.8231			0.929776
$962$	30.2580	−	38.5251i	0.975558	−	1.24210i
$963$	3.68918			0.118882
$964$	71.8619	+	41.4895i	2.31451	+	1.33629i
$965$	18.4252	−	31.9134i	0.593128	−	1.02733i
$966$	−6.29969	−	10.9114i	−0.202689	−	0.351068i
$967$			5.92797i			0.190631i	0.995447	+	0.0953154i	$0.0303860\pi$
$967$			5.92797i			0.190631i	−0.995447	+	0.0953154i	$0.969614\pi$
$968$	−158.193	+	91.3327i	−5.08451	+	2.93554i
$969$	3.71465	−	2.14465i	0.119332	−	0.0688962i
$970$			3.26762i			0.104917i
$971$	15.7086	+	27.2081i	0.504114	+	0.873151i	0.999989	+	0.00475668i	$0.00151410\pi$
$971$	15.7086	+	27.2081i	0.504114	+	0.873151i	−0.495875	+	0.868394i	$0.665153\pi$
$972$	−2.70236	+	4.68063i	−0.0866783	+	0.150131i
$973$	3.43002	+	1.98032i	0.109961	+	0.0634863i
$974$	22.5305			0.721923
$975$	−8.90442	−	1.27466i	−0.285170	−	0.0408217i
$976$	−51.6367			−1.65285
$977$	−33.1515	−	19.1400i	−1.06061	−	0.612344i	−0.135010	−	0.990844i	$-0.543107\pi$
$977$	−33.1515	−	19.1400i	−1.06061	−	0.612344i	−0.925601	+	0.378500i	$0.876440\pi$
$978$	−9.80459	+	16.9820i	−0.313516	+	0.543026i
$979$	−21.2253	−	36.7632i	−0.678362	−	1.17496i
$980$		−	8.55447i		−	0.273262i
$981$	−7.72680	+	4.46107i	−0.246698	+	0.142431i
$982$	−11.7348	+	6.77507i	−0.374471	+	0.216201i
$983$		−	30.9632i		−	0.987572i	−0.869583	−	0.493786i	$-0.835613\pi$
$983$		−	30.9632i		−	0.987572i	0.869583	−	0.493786i	$-0.164387\pi$
$984$	−45.2087	−	78.3038i	−1.44120	−	2.49623i
$985$	−13.9620	+	24.1830i	−0.444868	+	0.770534i
$986$	21.3161	+	12.3068i	0.678842	+	0.391930i
$987$	12.5703			0.400117
$988$	2.46463	−	17.2173i	0.0784105	−	0.547755i
$989$	−4.68894			−0.149100
$990$	20.6722	+	11.9351i	0.657007	+	0.379323i
$991$	5.56474	−	9.63842i	0.176770	−	0.306174i	−0.764002	−	0.645213i	$-0.776768\pi$
$991$	5.56474	−	9.63842i	0.176770	−	0.306174i	0.940772	+	0.339039i	$0.110102\pi$
$992$	−15.2409	−	26.3980i	−0.483900	−	0.838139i
$993$			3.00614i			0.0953971i
$994$	30.9651	−	17.8777i	0.982153	−	0.567047i
$995$	16.3460	−	9.43739i	0.518204	−	0.299185i
$996$			7.95228i			0.251978i
$997$	−7.14902	−	12.3825i	−0.226412	−	0.392156i	0.730330	−	0.683094i	$-0.239366\pi$
$997$	−7.14902	−	12.3825i	−0.226412	−	0.392156i	−0.956742	+	0.290938i	$0.906033\pi$
$998$	0.00165901	−	0.00287349i	5.25151e−5	−	9.09588e-5i
$999$	−4.32400	−	2.49646i	−0.136805	−	0.0789846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.43.8	✓	16
3.2	odd	2		819.2.ct.c.316.1		16
13.6	odd	12		3549.2.a.ba.1.1		8
13.7	odd	12		3549.2.a.bc.1.8		8
13.10	even	6	inner	273.2.bd.b.127.8	yes	16
39.23	odd	6		819.2.ct.c.127.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.8	✓	16	1.1	even	1	trivial
273.2.bd.b.127.8	yes	16	13.10	even	6	inner
819.2.ct.c.127.1		16	39.23	odd	6
819.2.ct.c.316.1		16	3.2	odd	2
3549.2.a.ba.1.1		8	13.6	odd	12
3549.2.a.bc.1.8		8	13.7	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)

\(f(q)\)	\(=\)	\(q+(2.35660 + 1.36058i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.70236 + 4.68063i) q^{4} -1.58278i q^{5} +(2.35660 - 1.36058i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.26480i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.35660 + 1.36058i) q^{2} +(0.500000 - 0.866025i) q^{3} +(2.70236 + 4.68063i) q^{4} -1.58278i q^{5} +(2.35660 - 1.36058i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.26480i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.15350 - 3.72996i) q^{10} +(-4.79969 - 2.77110i) q^{11} +5.40472 q^{12} +(-1.34211 - 3.34645i) q^{13} -2.72116 q^{14} +(-1.37073 - 0.791388i) q^{15} +(-7.20078 + 12.4721i) q^{16} +(2.40288 + 4.16192i) q^{17} -2.72116i q^{18} +(0.772957 - 0.446267i) q^{19} +(7.40839 - 4.27723i) q^{20} +1.00000i q^{21} +(-7.54062 - 13.0607i) q^{22} +(-2.31507 + 4.00983i) q^{23} +(8.02355 + 4.63240i) q^{24} +2.49482 q^{25} +(1.39030 - 9.71228i) q^{26} -1.00000 q^{27} +(-4.68063 - 2.70236i) q^{28} +(0.941087 - 1.63001i) q^{29} +(-2.15350 - 3.72996i) q^{30} +1.47545i q^{31} +(-17.8916 + 10.3297i) q^{32} +(-4.79969 + 2.77110i) q^{33} +13.0773i q^{34} +(0.791388 + 1.37073i) q^{35} +(2.70236 - 4.68063i) q^{36} +(4.32400 + 2.49646i) q^{37} +2.42873 q^{38} +(-3.56917 - 0.510922i) q^{39} +14.6641 q^{40} +(-8.45175 - 4.87962i) q^{41} +(-1.36058 + 2.35660i) q^{42} +(0.506349 + 0.877022i) q^{43} -29.9541i q^{44} +(-1.37073 + 0.791388i) q^{45} +(-10.9114 + 6.29969i) q^{46} -12.5703i q^{47} +(7.20078 + 12.4721i) q^{48} +(0.500000 - 0.866025i) q^{49} +(5.87927 + 3.39440i) q^{50} +4.80577 q^{51} +(12.0366 - 15.3252i) q^{52} +6.25784 q^{53} +(-2.35660 - 1.36058i) q^{54} +(-4.38604 + 7.59684i) q^{55} +(-4.63240 - 8.02355i) q^{56} -0.892533i q^{57} +(4.43552 - 2.56085i) q^{58} +(2.98511 - 1.72345i) q^{59} -8.55447i q^{60} +(1.79275 + 3.10513i) q^{61} +(-2.00746 + 3.47703i) q^{62} +(0.866025 + 0.500000i) q^{63} -27.4144 q^{64} +(-5.29669 + 2.12426i) q^{65} -15.0812 q^{66} +(12.7653 + 7.37003i) q^{67} +(-12.9869 + 22.4940i) q^{68} +(2.31507 + 4.00983i) q^{69} +4.30699i q^{70} +(-11.3794 + 6.56988i) q^{71} +(8.02355 - 4.63240i) q^{72} +5.33654i q^{73} +(6.79328 + 11.7663i) q^{74} +(1.24741 - 2.16058i) q^{75} +(4.17762 + 2.41195i) q^{76} +5.54221 q^{77} +(-7.71593 - 6.06018i) q^{78} +0.779028 q^{79} +(19.7406 + 11.3972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.2782 - 22.9986i) q^{82} +1.47136i q^{83} +(-4.68063 + 2.70236i) q^{84} +(6.58738 - 3.80323i) q^{85} +2.75571i q^{86} +(-0.941087 - 1.63001i) q^{87} +(25.6737 - 44.4682i) q^{88} +(6.63332 + 3.82975i) q^{89} -4.30699 q^{90} +(2.83553 + 2.22706i) q^{91} -25.0247 q^{92} +(1.27777 + 0.737723i) q^{93} +(17.1029 - 29.6231i) q^{94} +(-0.706341 - 1.22342i) q^{95} +20.6594i q^{96} +(-0.657035 + 0.379340i) q^{97} +(2.35660 - 1.36058i) q^{98} +5.54221i 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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