LMFDB - Embedded newform 322.2.g.a.229.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("322.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (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:	$2.57118294509$
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} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 $ x^16 + 18x^14 + 226x^12 + 1434x^10 + 6585x^8 + 14406x^6 + 22423x^4 + 8085*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.5
Root			$-0.306090 + 0.530164i$ of defining polynomial
Character	$\chi$	$=$	322.229
Dual form			322.2.g.a.45.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.05590 - 0.609623i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23610 + 2.14099i) q^{5} +1.21925i q^{6} +(1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 + 1.31067i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.05590 - 0.609623i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23610 + 2.14099i) q^{5} +1.21925i q^{6} +(1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 + 1.31067i) q^{9} +(-1.23610 - 2.14099i) q^{10} +(-1.09791 + 0.633878i) q^{11} +(-1.05590 - 0.609623i) q^{12} -3.39445i q^{13} +(-2.63288 + 0.260678i) q^{14} +3.01423i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.14715 + 3.71897i) q^{17} +(-0.756718 - 1.31067i) q^{18} +(-1.23610 + 2.14099i) q^{19} +2.47221 q^{20} +(2.93897 + 1.32981i) q^{21} -1.26776i q^{22} +(-3.41053 + 3.37169i) q^{23} +(1.05590 - 0.609623i) q^{24} +(-0.555899 - 0.962845i) q^{25} +(2.93968 + 1.69722i) q^{26} +5.50299i q^{27} +(1.09069 - 2.41048i) q^{28} +8.99116 q^{29} +(-2.61040 - 1.50711i) q^{30} +(3.32605 - 1.92030i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.772854 + 1.33862i) q^{33} -4.29430 q^{34} +(-6.50901 + 0.644450i) q^{35} +1.51344 q^{36} +(-1.24062 - 0.716272i) q^{37} +(-1.23610 - 2.14099i) q^{38} +(-2.06934 - 3.58419i) q^{39} +(-1.23610 + 2.14099i) q^{40} -3.39445i q^{41} +(-2.62114 + 1.88031i) q^{42} -12.9877i q^{43} +(1.09791 + 0.633878i) q^{44} +(-1.87076 - 3.24026i) q^{45} +(-1.21471 - 4.63945i) q^{46} +(-1.43968 - 0.831199i) q^{47} +1.21925i q^{48} +(-2.24328 + 6.63081i) q^{49} +1.11180 q^{50} +(4.53435 + 2.61791i) q^{51} +(-2.93968 + 1.69722i) q^{52} +(-7.14474 + 4.12502i) q^{53} +(-4.76573 - 2.75150i) q^{54} -3.13415i q^{55} +(1.54219 + 2.14980i) q^{56} +3.01423i q^{57} +(-4.49558 + 7.78657i) q^{58} +(8.43785 - 4.87160i) q^{59} +(2.61040 - 1.50711i) q^{60} +(4.61935 - 8.00096i) q^{61} +3.84060i q^{62} +(-3.98469 + 0.394520i) q^{63} +1.00000 q^{64} +(7.26749 + 4.19589i) q^{65} +(-0.772854 - 1.33862i) q^{66} +(9.87789 - 5.70300i) q^{67} +(2.14715 - 3.71897i) q^{68} +(-1.54571 + 5.63930i) q^{69} +(2.69640 - 5.95920i) q^{70} -10.1030 q^{71} +(-0.756718 + 1.31067i) q^{72} +(3.32605 - 1.92030i) q^{73} +(1.24062 - 0.716272i) q^{74} +(-1.17395 - 0.677778i) q^{75} +2.47221 q^{76} +(-3.05590 - 1.38272i) q^{77} +4.13867 q^{78} +(-6.44145 - 3.71897i) q^{79} +(-1.23610 - 2.14099i) q^{80} +(1.08460 + 1.87858i) q^{81} +(2.93968 + 1.69722i) q^{82} +5.21176 q^{83} +(-0.317831 - 3.21013i) q^{84} -10.6164 q^{85} +(11.2477 + 6.49384i) q^{86} +(9.49375 - 5.48122i) q^{87} +(-1.09791 + 0.633878i) q^{88} +(3.43192 - 5.94426i) q^{89} +3.74153 q^{90} +(7.29739 - 5.23489i) q^{91} +(4.62523 + 1.26776i) q^{92} +(2.34132 - 4.05528i) q^{93} +(1.43968 - 0.831199i) q^{94} +(-3.05590 - 5.29297i) q^{95} +(-1.05590 - 0.609623i) q^{96} +6.49915 q^{97} +(-4.62081 - 5.25815i) q^{98} -1.91867i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.05590	−	0.609623i	0.609623	−	0.351966i	−0.163195	−	0.986594i	$-0.552180\pi$
$3$	1.05590	−	0.609623i	0.609623	−	0.351966i	0.772818	+	0.634628i	$0.218847\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.23610	+	2.14099i	−0.552802	+	0.957481i	0.445269	+	0.895397i	$0.353108\pi$
$5$	−1.23610	+	2.14099i	−0.552802	+	0.957481i	−0.998071	+	0.0620841i	$0.980225\pi$
$6$			1.21925i			0.497755i
$7$	1.54219	+	2.14980i	0.582894	+	0.812548i
$7$	1.54219	+	2.14980i	0.582894	+	0.812548i
$8$	1.00000			0.353553
$9$	−0.756718	+	1.31067i	−0.252239	+	0.436892i
$10$	−1.23610	−	2.14099i	−0.390890	−	0.677041i
$11$	−1.09791	+	0.633878i	−0.331032	+	0.191121i	−0.656299	−	0.754501i	$-0.727879\pi$
$11$	−1.09791	+	0.633878i	−0.331032	+	0.191121i	0.325267	+	0.945622i	$0.394546\pi$
$12$	−1.05590	−	0.609623i	−0.304812	−	0.175983i
$13$		−	3.39445i		−	0.941451i	−0.882280	−	0.470725i	$-0.843992\pi$
$13$		−	3.39445i		−	0.941451i	0.882280	−	0.470725i	$-0.156008\pi$
$14$	−2.63288	+	0.260678i	−0.703666	+	0.0696692i
$15$			3.01423i			0.778270i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.14715	+	3.71897i	0.520760	+	0.901983i	0.999709	+	0.0241402i	$0.00768482\pi$
$17$	2.14715	+	3.71897i	0.520760	+	0.901983i	−0.478948	+	0.877843i	$0.658982\pi$
$18$	−0.756718	−	1.31067i	−0.178360	−	0.308929i
$19$	−1.23610	+	2.14099i	−0.283581	+	0.491177i	−0.972264	−	0.233885i	$-0.924856\pi$
$19$	−1.23610	+	2.14099i	−0.283581	+	0.491177i	0.688683	+	0.725063i	$0.258189\pi$
$20$	2.47221			0.552802
$21$	2.93897	+	1.32981i	0.641336	+	0.290189i
$22$		−	1.26776i		−	0.270287i
$23$	−3.41053	+	3.37169i	−0.711144	+	0.703046i
$23$	−3.41053	+	3.37169i	−0.711144	+	0.703046i
$24$	1.05590	−	0.609623i	0.215534	−	0.124439i
$25$	−0.555899	−	0.962845i	−0.111180	−	0.192569i
$26$	2.93968	+	1.69722i	0.576518	+	0.332853i
$27$			5.50299i			1.05905i
$28$	1.09069	−	2.41048i	0.206120	−	0.455538i
$29$	8.99116			1.66962			0.834808	−	0.550541i	$-0.185579\pi$
$29$	8.99116			1.66962			0.834808	+	0.550541i	$0.185579\pi$
$30$	−2.61040	−	1.50711i	−0.476591	−	0.275160i
$31$	3.32605	−	1.92030i	0.597377	−	0.344896i	−0.170632	−	0.985335i	$-0.554581\pi$
$31$	3.32605	−	1.92030i	0.597377	−	0.344896i	0.768009	+	0.640439i	$0.221248\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.772854	+	1.33862i	−0.134537	+	0.233024i
$34$	−4.29430			−0.736466
$35$	−6.50901	+	0.644450i	−1.10022	+	0.108932i
$36$	1.51344			0.252239
$37$	−1.24062	−	0.716272i	−0.203957	−	0.117754i	0.394543	−	0.918877i	$-0.370903\pi$
$37$	−1.24062	−	0.716272i	−0.203957	−	0.117754i	−0.598500	+	0.801123i	$0.704236\pi$
$38$	−1.23610	−	2.14099i	−0.200522	−	0.347315i
$39$	−2.06934	−	3.58419i	−0.331359	−	0.573930i
$40$	−1.23610	+	2.14099i	−0.195445	+	0.338521i
$41$		−	3.39445i		−	0.530124i	−0.964231	−	0.265062i	$-0.914608\pi$
$41$		−	3.39445i		−	0.530124i	0.964231	−	0.265062i	$-0.0853924\pi$
$42$	−2.62114	+	1.88031i	−0.404450	+	0.290139i
$43$		−	12.9877i		−	1.98060i	−0.138933	−	0.990302i	$-0.544367\pi$
$43$		−	12.9877i		−	1.98060i	0.138933	−	0.990302i	$-0.455633\pi$
$44$	1.09791	+	0.633878i	0.165516	+	0.0955607i
$45$	−1.87076	−	3.24026i	−0.278877	−	0.483029i
$46$	−1.21471	−	4.63945i	−0.179099	−	0.684049i
$47$	−1.43968	−	0.831199i	−0.209999	−	0.121243i	0.391312	−	0.920258i	$-0.372021\pi$
$47$	−1.43968	−	0.831199i	−0.209999	−	0.121243i	−0.601311	+	0.799015i	$0.705355\pi$
$48$			1.21925i			0.175983i
$49$	−2.24328	+	6.63081i	−0.320469	+	0.947259i
$50$	1.11180			0.157232
$51$	4.53435	+	2.61791i	0.634935	+	0.366580i
$52$	−2.93968	+	1.69722i	−0.407660	+	0.235363i
$53$	−7.14474	+	4.12502i	−0.981406	+	0.566615i	−0.902694	−	0.430282i	$-0.858414\pi$
$53$	−7.14474	+	4.12502i	−0.981406	+	0.566615i	−0.0787118	+	0.996897i	$0.525081\pi$
$54$	−4.76573	−	2.75150i	−0.648534	−	0.374431i
$55$		−	3.13415i		−	0.422609i
$56$	1.54219	+	2.14980i	0.206084	+	0.287279i
$57$			3.01423i			0.399244i
$58$	−4.49558	+	7.78657i	−0.590298	+	1.02243i
$59$	8.43785	−	4.87160i	1.09851	−	0.634228i	0.162684	−	0.986678i	$-0.447985\pi$
$59$	8.43785	−	4.87160i	1.09851	−	0.634228i	0.935830	+	0.352450i	$0.114651\pi$
$60$	2.61040	−	1.50711i	0.337001	−	0.194568i
$61$	4.61935	−	8.00096i	0.591448	−	1.02442i	−0.402590	−	0.915380i	$-0.631890\pi$
$61$	4.61935	−	8.00096i	0.591448	−	1.02442i	0.994038	−	0.109037i	$-0.0347768\pi$
$62$			3.84060i			0.487756i
$63$	−3.98469	+	0.394520i	−0.502024	+	0.0497048i
$64$	1.00000			0.125000
$65$	7.26749	+	4.19589i	0.901421	+	0.520436i
$66$	−0.772854	−	1.33862i	−0.0951317	−	0.164773i
$67$	9.87789	−	5.70300i	1.20678	−	0.696732i	0.244722	−	0.969593i	$-0.421303\pi$
$67$	9.87789	−	5.70300i	1.20678	−	0.696732i	0.962054	+	0.272861i	$0.0879698\pi$
$68$	2.14715	−	3.71897i	0.260380	−	0.450992i
$69$	−1.54571	+	5.63930i	−0.186081	+	0.678892i
$70$	2.69640	−	5.95920i	0.322281	−	0.712260i
$71$	−10.1030			−1.19900			−0.599500	−	0.800375i	$-0.704634\pi$
$71$	−10.1030			−1.19900			−0.599500	+	0.800375i	$0.704634\pi$
$72$	−0.756718	+	1.31067i	−0.0891801	+	0.154464i
$73$	3.32605	−	1.92030i	0.389285	−	0.224754i	−0.292565	−	0.956246i	$-0.594509\pi$
$73$	3.32605	−	1.92030i	0.389285	−	0.224754i	0.681850	+	0.731492i	$0.261176\pi$
$74$	1.24062	−	0.716272i	0.144219	−	0.0832649i
$75$	−1.17395	−	0.677778i	−0.135556	−	0.0782631i
$76$	2.47221			0.283581
$77$	−3.05590	−	1.38272i	−0.348252	−	0.157576i
$78$	4.13867			0.468612
$79$	−6.44145	−	3.71897i	−0.724720	−	0.418417i	0.0917676	−	0.995780i	$-0.470748\pi$
$79$	−6.44145	−	3.71897i	−0.724720	−	0.418417i	−0.816487	+	0.577363i	$0.804082\pi$
$80$	−1.23610	−	2.14099i	−0.138200	−	0.239370i
$81$	1.08460	+	1.87858i	0.120511	+	0.208731i
$82$	2.93968	+	1.69722i	0.324633	+	0.187427i
$83$	5.21176			0.572065			0.286033	−	0.958220i	$-0.407663\pi$
$83$	5.21176			0.572065			0.286033	+	0.958220i	$0.407663\pi$
$84$	−0.317831	−	3.21013i	−0.0346782	−	0.350254i
$85$	−10.6164			−1.15151
$86$	11.2477	+	6.49384i	1.21287	+	0.700249i
$87$	9.49375	−	5.48122i	1.01784	−	0.587648i
$88$	−1.09791	+	0.633878i	−0.117037	+	0.0675716i
$89$	3.43192	−	5.94426i	0.363783	−	0.630090i	−0.624797	−	0.780787i	$-0.714818\pi$
$89$	3.43192	−	5.94426i	0.363783	−	0.630090i	0.988580	+	0.150697i	$0.0481517\pi$
$90$	3.74153			0.394391
$91$	7.29739	−	5.23489i	0.764974	−	0.548766i
$92$	4.62523	+	1.26776i	0.482214	+	0.132173i
$93$	2.34132	−	4.05528i	0.242783	−	0.420513i
$94$	1.43968	−	0.831199i	0.148492	−	0.0857316i
$95$	−3.05590	−	5.29297i	−0.313529	−	0.543047i
$96$	−1.05590	−	0.609623i	−0.107767	−	0.0622194i
$97$	6.49915			0.659889			0.329944	−	0.944000i	$-0.392970\pi$
$97$	6.49915			0.659889			0.329944	+	0.944000i	$0.392970\pi$
$98$	−4.62081	−	5.25815i	−0.466773	−	0.531153i
$99$		−	1.91867i		−	0.192833i
$100$	−0.555899	+	0.962845i	−0.0555899	+	0.0962845i
$101$	6.16770	−	3.56092i	0.613709	−	0.354325i	−0.160707	−	0.987002i	$-0.551377\pi$
$101$	6.16770	−	3.56092i	0.613709	−	0.354325i	0.774416	+	0.632677i	$0.218044\pi$
$102$	−4.53435	+	2.61791i	−0.448967	+	0.259211i
$103$	6.95337	−	12.0436i	0.685136	−	1.18669i	−0.288259	−	0.957553i	$-0.593076\pi$
$103$	6.95337	−	12.0436i	0.685136	−	1.18669i	0.973394	−	0.229137i	$-0.0735904\pi$
$104$		−	3.39445i		−	0.332853i
$105$	−6.47999	+	4.64852i	−0.632382	+	0.453649i
$106$		−	8.25004i		−	0.801315i
$107$	5.07809	+	2.93183i	0.490917	+	0.283431i	0.724955	−	0.688796i	$-0.241861\pi$
$107$	5.07809	+	2.93183i	0.490917	+	0.283431i	−0.234038	+	0.972228i	$0.575194\pi$
$108$	4.76573	−	2.75150i	0.458583	−	0.264763i
$109$	−12.3456	+	7.12772i	−1.18249	+	0.682712i	−0.956590	−	0.291438i	$-0.905866\pi$
$109$	−12.3456	+	7.12772i	−1.18249	+	0.682712i	−0.225902	+	0.974150i	$0.572533\pi$
$110$	2.71426	+	1.56708i	0.258794	+	0.149415i
$111$	−1.74662			−0.165782
$112$	−2.63288	+	0.260678i	−0.248784	+	0.0246318i
$113$			15.6954i			1.47650i	0.674528	+	0.738249i	$0.264347\pi$
$113$			15.6954i			1.47650i	−0.674528	+	0.738249i	$0.735653\pi$
$114$	−2.61040	−	1.50711i	−0.244486	−	0.141154i
$115$	−3.00301	−	11.4697i	−0.280032	−	1.06955i
$116$	−4.49558	−	7.78657i	−0.417404	−	0.722965i
$117$	4.44902	+	2.56864i	0.411312	+	0.237471i
$118$			9.74319i			0.896934i
$119$	−4.68373	+	10.3513i	−0.429357	+	0.948904i
$120$			3.01423i			0.275160i
$121$	−4.69640	+	8.13440i	−0.426945	+	0.739491i
$122$	4.61935	+	8.00096i	0.418217	+	0.724373i
$123$	−2.06934	−	3.58419i	−0.186586	−	0.323176i
$124$	−3.32605	−	1.92030i	−0.298688	−	0.172448i
$125$	−9.61243			−0.859762
$126$	1.65068	−	3.64811i	0.147055	−	0.324999i
$127$	1.99116			0.176686			0.0883432	−	0.996090i	$-0.471843\pi$
$127$	1.99116			0.176686			0.0883432	+	0.996090i	$0.471843\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−7.91760	−	13.7137i	−0.697106	−	1.20742i
$130$	−7.26749	+	4.19589i	−0.637401	+	0.368004i
$131$	9.81980	+	5.66947i	0.857960	+	0.495344i	0.863329	−	0.504642i	$-0.168375\pi$
$131$	9.81980	+	5.66947i	0.857960	+	0.495344i	−0.00536840	+	0.999986i	$0.501709\pi$
$132$	1.54571			0.134537
$133$	−6.50901	+	0.644450i	−0.564403	+	0.0558809i
$134$			11.4060i			0.985328i
$135$	−11.7819	−	6.80226i	−1.01402	−	0.585446i
$136$	2.14715	+	3.71897i	0.184117	+	0.318899i
$137$	−1.36978	+	0.790842i	−0.117028	+	0.0675662i	−0.557371	−	0.830263i	$-0.688190\pi$
$137$	−1.36978	+	0.790842i	−0.117028	+	0.0675662i	0.440343	+	0.897829i	$0.354857\pi$
$138$	−4.11093	−	4.15827i	−0.349945	−	0.353976i
$139$			14.1603i			1.20106i	0.799603	+	0.600528i	$0.205043\pi$
$139$			14.1603i			1.20106i	−0.799603	+	0.600528i	$0.794957\pi$
$140$	3.81262	+	5.31475i	0.322225	+	0.449178i
$141$	−2.02687			−0.170694
$142$	5.05148	−	8.74941i	0.423910	−	0.734235i
$143$	2.15167	+	3.72680i	0.179931	+	0.311650i
$144$	−0.756718	−	1.31067i	−0.0630599	−	0.109223i
$145$	−11.1140	+	19.2500i	−0.922967	+	1.59863i
$146$			3.84060i			0.317850i
$147$	1.67362	+	8.36903i	0.138038	+	0.690266i
$148$			1.43254i			0.117754i
$149$	−2.19582	−	1.26776i	−0.179888	−	0.103859i	0.407352	−	0.913271i	$-0.366452\pi$
$149$	−2.19582	−	1.26776i	−0.179888	−	0.103859i	−0.587240	+	0.809413i	$0.699786\pi$
$150$	1.17395	−	0.677778i	0.0958523	−	0.0553403i
$151$	−4.01344	−	6.95148i	−0.326609	−	0.565703i	0.655228	−	0.755431i	$-0.272573\pi$
$151$	−4.01344	−	6.95148i	−0.326609	−	0.565703i	−0.981837	+	0.189728i	$0.939239\pi$
$152$	−1.23610	+	2.14099i	−0.100261	+	0.173657i
$153$	−6.49915			−0.525425
$154$	2.72542	−	1.95512i	0.219621	−	0.157548i
$155$			9.49474i			0.762636i
$156$	−2.06934	+	3.58419i	−0.165679	+	0.286965i
$157$	9.60150	+	16.6303i	0.766283	+	1.32724i	0.939566	+	0.342369i	$0.111229\pi$
$157$	9.60150	+	16.6303i	0.766283	+	1.32724i	−0.173282	+	0.984872i	$0.555437\pi$
$158$	6.44145	−	3.71897i	0.512454	−	0.295866i
$159$	−5.02942	+	8.71121i	−0.398859	+	0.690844i
$160$	2.47221			0.195445
$161$	−12.5082	−	2.13215i	−0.985781	−	0.168037i
$162$	−2.16920			−0.170428
$163$	1.24328	−	2.15343i	0.0973813	−	0.168669i	−0.813219	−	0.581958i	$-0.802287\pi$
$163$	1.24328	−	2.15343i	0.0973813	−	0.168669i	0.910600	+	0.413289i	$0.135620\pi$
$164$	−2.93968	+	1.69722i	−0.229550	+	0.132531i
$165$	−1.91065	−	3.30935i	−0.148744	−	0.257632i
$166$	−2.60588	+	4.51352i	−0.202256	+	0.350317i
$167$		−	8.20178i		−	0.634673i	−0.948313	−	0.317337i	$-0.897212\pi$
$167$		−	8.20178i		−	0.634673i	0.948313	−	0.317337i	$-0.102788\pi$
$168$	2.93897	+	1.32981i	0.226746	+	0.102597i
$169$	1.47772			0.113671
$170$	5.30819	−	9.19406i	0.407120	−	0.705152i
$171$	−1.87076	−	3.24026i	−0.143061	−	0.247789i
$172$	−11.2477	+	6.49384i	−0.857627	+	0.495151i
$173$	15.2173	+	8.78574i	1.15695	+	0.667967i	0.950572	−	0.310504i	$-0.100498\pi$
$173$	15.2173	+	8.78574i	1.15695	+	0.667967i	0.206381	+	0.978472i	$0.433831\pi$
$174$			10.9624i			0.831060i
$175$	1.21262	−	2.67996i	0.0916655	−	0.202586i
$176$		−	1.26776i		−	0.0955607i
$177$	5.93968	−	10.2878i	0.446454	−	0.773280i
$178$	3.43192	+	5.94426i	0.257233	+	0.445541i
$179$	−3.25672	−	5.64080i	−0.243419	−	0.421613i	0.718267	−	0.695767i	$-0.244936\pi$
$179$	−3.25672	−	5.64080i	−0.243419	−	0.421613i	−0.961686	+	0.274154i	$0.911602\pi$
$180$	−1.87076	+	3.24026i	−0.139438	+	0.241514i
$181$	−10.2407			−0.761184			−0.380592	−	0.924743i	$-0.624280\pi$
$181$	−10.2407			−0.761184			−0.380592	+	0.924743i	$0.624280\pi$
$182$	0.884859	+	8.93717i	0.0655901	+	0.662467i
$183$		−	11.2643i		−	0.832679i
$184$	−3.41053	+	3.37169i	−0.251427	+	0.248564i
$185$	3.06707	−	1.77077i	0.225495	−	0.130190i
$186$	2.34132	+	4.05528i	0.171674	+	0.297348i
$187$	−4.71475	−	2.72206i	−0.344777	−	0.199057i
$188$			1.66240i			0.121243i
$189$	−11.8303	+	8.48668i	−0.860530	+	0.617315i
$190$	6.11180			0.443396
$191$	−8.51452	−	4.91586i	−0.616089	−	0.355699i	0.159256	−	0.987237i	$-0.449091\pi$
$191$	−8.51452	−	4.91586i	−0.616089	−	0.355699i	−0.775345	+	0.631538i	$0.782424\pi$
$192$	1.05590	−	0.609623i	0.0762029	−	0.0439958i
$193$	3.94227	+	6.82822i	0.283771	+	0.491506i	0.972310	−	0.233693i	$-0.0750811\pi$
$193$	3.94227	+	6.82822i	0.283771	+	0.491506i	−0.688539	+	0.725199i	$0.741748\pi$
$194$	−3.24958	+	5.62843i	−0.233306	+	0.404098i
$195$	10.2316			0.732703
$196$	6.86409	−	1.37267i	0.490292	−	0.0980477i
$197$	−5.96063			−0.424677			−0.212339	−	0.977196i	$-0.568108\pi$
$197$	−5.96063			−0.424677			−0.212339	+	0.977196i	$0.568108\pi$
$198$	1.66162	+	0.959334i	0.118086	+	0.0681769i
$199$	−11.6259	−	20.1367i	−0.824139	−	1.42745i	−0.902576	−	0.430531i	$-0.858326\pi$
$199$	−11.6259	−	20.1367i	−0.824139	−	1.42745i	0.0784372	−	0.996919i	$-0.475007\pi$
$200$	−0.555899	−	0.962845i	−0.0393080	−	0.0680834i
$201$	6.95337	−	12.0436i	0.490453	−	0.849489i
$202$			7.12184i			0.501091i
$203$	13.8661	+	19.3292i	0.973209	+	1.35664i
$204$		−	5.23581i		−	0.366580i
$205$	7.26749	+	4.19589i	0.507583	+	0.293053i
$206$	6.95337	+	12.0436i	0.484464	+	0.839116i
$207$	−1.83838	−	7.02151i	−0.127777	−	0.488029i
$208$	2.93968	+	1.69722i	0.203830	+	0.117681i
$209$		−	3.13415i		−	0.216794i
$210$	−0.785744	−	7.93610i	−0.0542215	−	0.547643i
$211$	−7.62889			−0.525194			−0.262597	−	0.964906i	$-0.584579\pi$
$211$	−7.62889			−0.525194			−0.262597	+	0.964906i	$0.584579\pi$
$212$	7.14474	+	4.12502i	0.490703	+	0.283308i
$213$	−10.6677	+	6.15900i	−0.730939	+	0.422008i
$214$	−5.07809	+	2.93183i	−0.347131	+	0.200416i
$215$	27.8065	+	16.0541i	1.89639	+	1.09488i
$216$			5.50299i			0.374431i
$217$	9.25767	+	4.18888i	0.628452	+	0.284360i
$218$		−	14.2554i		−	0.965500i
$219$	2.34132	−	4.05528i	0.158212	−	0.274031i
$220$	−2.71426	+	1.56708i	−0.182995	+	0.105652i
$221$	12.6239	−	7.28839i	0.849173	−	0.490270i
$222$	0.873312	−	1.51262i	0.0586129	−	0.101520i
$223$			8.38464i			0.561477i	0.959784	+	0.280738i	$0.0905794\pi$
$223$			8.38464i			0.561477i	−0.959784	+	0.280738i	$0.909421\pi$
$224$	1.09069	−	2.41048i	0.0728745	−	0.161057i
$225$	1.68264			0.112176
$226$	−13.5926	−	7.84770i	−0.904167	−	0.522021i
$227$	−6.49463	−	11.2490i	−0.431064	−	0.746625i	0.565901	−	0.824473i	$-0.308528\pi$
$227$	−6.49463	−	11.2490i	−0.431064	−	0.746625i	−0.996965	+	0.0778483i	$0.975195\pi$
$228$	2.61040	−	1.50711i	0.172878	−	0.0998111i
$229$	1.55022	−	2.68507i	0.102442	−	0.177434i	−0.810248	−	0.586087i	$-0.800668\pi$
$229$	1.55022	−	2.68507i	0.102442	−	0.177434i	0.912690	+	0.408652i	$0.134001\pi$
$230$	11.4345	+	3.13415i	0.753970	+	0.206660i
$231$	−4.06966	+	0.402932i	−0.267764	+	0.0265110i
$232$	8.99116			0.590298
$233$	12.4182	−	21.5089i	0.813541	−	1.40909i	−0.0968297	−	0.995301i	$-0.530870\pi$
$233$	12.4182	−	21.5089i	0.813541	−	1.40909i	0.910371	−	0.413794i	$-0.135796\pi$
$234$	−4.44902	+	2.56864i	−0.290841	+	0.167917i
$235$	3.55918	−	2.05489i	0.232175	−	0.134047i
$236$	−8.43785	−	4.87160i	−0.549257	−	0.317114i
$237$	−9.06869			−0.589075
$238$	−6.62264	−	9.23189i	−0.429282	−	0.598414i
$239$	−24.6701			−1.59578			−0.797889	−	0.602804i	$-0.794050\pi$
$239$	−24.6701			−1.59578			−0.797889	+	0.602804i	$0.794050\pi$
$240$	−2.61040	−	1.50711i	−0.168500	−	0.0972838i
$241$	10.0757	+	17.4516i	0.649032	+	1.12416i	0.983355	+	0.181697i	$0.0581591\pi$
$241$	10.0757	+	17.4516i	0.649032	+	1.12416i	−0.334323	+	0.942459i	$0.608508\pi$
$242$	−4.69640	−	8.13440i	−0.301896	−	0.522899i
$243$	−12.0067	−	6.93210i	−0.770233	−	0.444694i
$244$	−9.23871			−0.591448
$245$	−11.4236	−	12.9992i	−0.729827	−	0.830489i
$246$	4.13867			0.263872
$247$	7.26749	+	4.19589i	0.462419	+	0.266978i
$248$	3.32605	−	1.92030i	0.211205	−	0.121939i
$249$	5.50310	−	3.17721i	0.348744	−	0.201348i
$250$	4.80622	−	8.32461i	0.303972	−	0.526495i
$251$	29.3772			1.85427			0.927137	−	0.374721i	$-0.122262\pi$
$251$	29.3772			1.85427			0.927137	+	0.374721i	$0.122262\pi$
$252$	2.33401	+	3.25359i	0.147029	+	0.204957i
$253$	1.60721	−	5.86367i	0.101044	−	0.368646i
$254$	−0.995578	+	1.72439i	−0.0624681	+	0.108198i
$255$	−11.2098	+	6.47200i	−0.701987	+	0.405292i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.93918	+	2.27429i	0.245720	+	0.141866i	0.617803	−	0.786333i	$-0.288023\pi$
$257$	3.93918	+	2.27429i	0.245720	+	0.141866i	−0.372083	+	0.928199i	$0.621356\pi$
$258$	15.8352			0.985856
$259$	−0.373433	−	3.77171i	−0.0232040	−	0.234363i
$260$		−	8.39177i		−	0.520436i
$261$	−6.80377	+	11.7845i	−0.421143	+	0.729441i
$262$	−9.81980	+	5.66947i	−0.606670	+	0.350261i
$263$	4.94893	−	2.85726i	0.305164	−	0.176186i	−0.339596	−	0.940571i	$-0.610290\pi$
$263$	4.94893	−	2.85726i	0.305164	−	0.176186i	0.644760	+	0.764385i	$0.276957\pi$
$264$	−0.772854	+	1.33862i	−0.0475659	+	0.0823865i
$265$		−	20.3958i		−	1.25290i
$266$	2.69640	−	5.95920i	0.165327	−	0.365382i
$267$		−	8.36872i		−	0.512157i
$268$	−9.87789	−	5.70300i	−0.603388	−	0.348366i
$269$	−7.17395	+	4.14188i	−0.437403	+	0.252535i	−0.702496	−	0.711688i	$-0.747931\pi$
$269$	−7.17395	+	4.14188i	−0.437403	+	0.252535i	0.265092	+	0.964223i	$0.414598\pi$
$270$	11.7819	−	6.80226i	0.717022	−	0.413973i
$271$	0.343470	+	0.198302i	0.0208643	+	0.0120460i	0.510396	−	0.859940i	$-0.329499\pi$
$271$	0.343470	+	0.198302i	0.0208643	+	0.0120460i	−0.489532	+	0.871986i	$0.662832\pi$
$272$	−4.29430			−0.260380
$273$	4.51399	−	9.97618i	0.273199	−	0.603786i
$274$		−	1.58168i		−	0.0955531i
$275$	1.22065	+	0.704744i	0.0736081	+	0.0424977i
$276$	5.65663	−	1.48103i	0.340489	−	0.0891475i
$277$	8.75948	+	15.1719i	0.526306	+	0.911589i	0.999530	+	0.0306472i	$0.00975682\pi$
$277$	8.75948	+	15.1719i	0.526306	+	0.911589i	−0.473224	+	0.880942i	$0.656910\pi$
$278$	−12.2631	−	7.08013i	−0.735494	−	0.424638i
$279$			5.81250i			0.347985i
$280$	−6.50901	+	0.644450i	−0.388988	+	0.0385133i
$281$			20.4451i			1.21965i	0.792536	+	0.609826i	$0.208761\pi$
$281$			20.4451i			1.21965i	−0.792536	+	0.609826i	$0.791239\pi$
$282$	1.01344	−	1.75532i	0.0603493	−	0.104528i
$283$	7.00655	+	12.1357i	0.416496	+	0.721393i	0.995584	−	0.0938724i	$-0.0299246\pi$
$283$	7.00655	+	12.1357i	0.416496	+	0.721393i	−0.579088	+	0.815265i	$0.696591\pi$
$284$	5.05148	+	8.74941i	0.299750	+	0.519182i
$285$	−6.45344	−	3.72590i	−0.382269	−	0.220703i
$286$	−4.30333			−0.254461
$287$	7.29739	−	5.23489i	0.430751	−	0.309006i
$288$	1.51344			0.0891801
$289$	−0.720506	+	1.24795i	−0.0423827	+	0.0734090i
$290$	−11.1140	−	19.2500i	−0.652636	−	1.13040i
$291$	6.86245	−	3.96204i	0.402284	−	0.232259i
$292$	−3.32605	−	1.92030i	−0.194643	−	0.112377i
$293$	−4.28527			−0.250348			−0.125174	−	0.992135i	$-0.539949\pi$
$293$	−4.28527			−0.250348			−0.125174	+	0.992135i	$0.539949\pi$
$294$	−8.08460	−	2.73511i	−0.471503	−	0.159515i
$295$			24.0872i			1.40241i
$296$	−1.24062	−	0.716272i	−0.0721095	−	0.0416325i
$297$	−3.48823	−	6.04179i	−0.202407	−	0.350580i
$298$	2.19582	−	1.26776i	0.127200	−	0.0734391i
$299$	11.4450	+	11.5769i	0.661884	+	0.669507i
$300$			1.35556i			0.0782631i
$301$	27.9209	−	20.0295i	1.60934	−	1.15448i
$302$	8.02687			0.461895
$303$	4.34164	−	7.51995i	0.249421	−	0.432010i
$304$	−1.23610	−	2.14099i	−0.0708953	−	0.122794i
$305$	11.4200	+	19.7800i	0.653907	+	1.13260i
$306$	3.24958	−	5.62843i	0.185766	−	0.321756i
$307$		−	29.9300i		−	1.70820i	−0.520111	−	0.854098i	$-0.674110\pi$
$307$		−	29.9300i		−	1.70820i	0.520111	−	0.854098i	$-0.325890\pi$
$308$	0.330476	+	3.33785i	0.0188306	+	0.190192i
$309$		−	16.9557i		−	0.964578i
$310$	−8.22269	−	4.74737i	−0.467017	−	0.269633i
$311$	4.83673	−	2.79248i	0.274266	−	0.158347i	−0.356559	−	0.934273i	$-0.616050\pi$
$311$	4.83673	−	2.79248i	0.274266	−	0.158347i	0.630825	+	0.775926i	$0.282717\pi$
$312$	−2.06934	−	3.58419i	−0.117153	−	0.202915i
$313$	4.42798	−	7.66948i	0.250284	−	0.433505i	−0.713320	−	0.700839i	$-0.752809\pi$
$313$	4.42798	−	7.66948i	0.250284	−	0.433505i	0.963604	+	0.267334i	$0.0861427\pi$
$314$	−19.2030			−1.08369
$315$	4.08083	−	9.01887i	0.229929	−	0.508156i
$316$			7.43795i			0.418417i
$317$	−9.52428	+	16.4965i	−0.534937	+	0.926538i	0.464230	+	0.885715i	$0.346331\pi$
$317$	−9.52428	+	16.4965i	−0.534937	+	0.926538i	−0.999166	+	0.0408228i	$0.987002\pi$
$318$	−5.02942	−	8.71121i	−0.282036	−	0.488500i
$319$	−9.87147	+	5.69930i	−0.552696	+	0.319099i
$320$	−1.23610	+	2.14099i	−0.0691002	+	0.119685i
$321$	7.14926			0.399033
$322$	8.10057	−	9.76631i	0.451427	−	0.544255i
$323$	−10.6164			−0.590712
$324$	1.08460	−	1.87858i	0.0602555	−	0.104366i
$325$	−3.26833	+	1.88697i	−0.181294	+	0.104670i
$326$	1.24328	+	2.15343i	0.0688590	+	0.119267i
$327$	−8.69045	+	15.0523i	−0.480583	+	0.832394i
$328$		−	3.39445i		−	0.187427i
$329$	−0.433351	−	4.37689i	−0.0238914	−	0.241306i
$330$	3.82131			0.210356
$331$	−1.30101	+	2.25341i	−0.0715098	+	0.123859i	−0.899563	−	0.436791i	$-0.856115\pi$
$331$	−1.30101	+	2.25341i	−0.0715098	+	0.123859i	0.828053	+	0.560649i	$0.189448\pi$
$332$	−2.60588	−	4.51352i	−0.143016	−	0.247712i
$333$	1.87760	−	1.08403i	0.102892	−	0.0594046i
$334$	7.10295	+	4.10089i	0.388656	+	0.224391i
$335$			28.1980i			1.54062i
$336$	−2.62114	+	1.88031i	−0.142995	+	0.102580i
$337$		−	5.37754i		−	0.292934i	−0.989216	−	0.146467i	$-0.953210\pi$
$337$		−	5.37754i		−	0.292934i	0.989216	−	0.146467i	$-0.0467901\pi$
$338$	−0.738859	+	1.27974i	−0.0401886	+	0.0696088i
$339$	9.56828	+	16.5728i	0.519678	+	0.900108i
$340$	5.30819	+	9.19406i	0.287877	+	0.498618i
$341$	−2.43447	+	4.21663i	−0.131834	+	0.228343i
$342$	3.74153			0.202319
$343$	−17.7145	+	5.40339i	−0.956493	+	0.291755i
$344$		−	12.9877i		−	0.700249i
$345$	−10.1631	−	10.2801i	−0.547160	−	0.553462i
$346$	−15.2173	+	8.78574i	−0.818090	+	0.472324i
$347$	−6.84623	−	11.8580i	−0.367525	−	0.636572i	0.621653	−	0.783293i	$-0.286461\pi$
$347$	−6.84623	−	11.8580i	−0.367525	−	0.636572i	−0.989178	+	0.146721i	$0.953128\pi$
$348$	−9.49375	−	5.48122i	−0.508918	−	0.293824i
$349$		−	23.2774i		−	1.24601i	−0.782217	−	0.623006i	$-0.785911\pi$
$349$		−	23.2774i		−	1.24601i	0.782217	−	0.623006i	$-0.214089\pi$
$350$	1.71461	+	2.39014i	0.0916496	+	0.127759i
$351$	18.6796			0.997045
$352$	1.09791	+	0.633878i	0.0585187	+	0.0337858i
$353$	−27.4228	+	15.8325i	−1.45957	+	0.842681i	−0.998990	−	0.0449392i	$-0.985691\pi$
$353$	−27.4228	+	15.8325i	−1.45957	+	0.842681i	−0.460576	+	0.887620i	$0.652357\pi$
$354$	5.93968	+	10.2878i	0.315690	+	0.546792i
$355$	12.4883	−	21.6303i	0.662809	−	1.14802i
$356$	−6.86384			−0.363783
$357$	1.36486	+	13.7853i	0.0722362	+	0.729593i
$358$	6.51344			0.344246
$359$	−30.4661	−	17.5896i	−1.60794	−	0.928345i	−0.989830	−	0.142253i	$-0.954565\pi$
$359$	−30.4661	−	17.5896i	−1.60794	−	0.928345i	−0.618110	−	0.786092i	$-0.712101\pi$
$360$	−1.87076	−	3.24026i	−0.0985979	−	0.170777i
$361$	6.44410	+	11.1615i	0.339163	+	0.587448i
$362$	5.12034	−	8.86869i	0.269119	−	0.466128i
$363$			11.4521i			0.601081i
$364$	−8.18225	−	3.70227i	−0.428866	−	0.194052i
$365$			9.49474i			0.496977i
$366$	9.75514	+	5.63213i	0.509910	+	0.294396i
$367$	6.62379	+	11.4727i	0.345759	+	0.598873i	0.985491	−	0.169725i	$-0.0542880\pi$
$367$	6.62379	+	11.4727i	0.345759	+	0.598873i	−0.639732	+	0.768598i	$0.720955\pi$
$368$	−1.21471	−	4.63945i	−0.0633210	−	0.241848i
$369$	4.44902	+	2.56864i	0.231607	+	0.133718i
$370$			3.54154i			0.184116i
$371$	−19.8865	−	8.99820i	−1.03246	−	0.467163i
$372$	−4.68264			−0.242783
$373$	31.6868	+	18.2944i	1.64068	+	0.947246i	0.980593	+	0.196056i	$0.0628135\pi$
$373$	31.6868	+	18.2944i	1.64068	+	0.947246i	0.660086	+	0.751190i	$0.270520\pi$
$374$	4.71475	−	2.72206i	0.243794	−	0.140755i
$375$	−10.1498	+	5.85997i	−0.524131	+	0.302607i
$376$	−1.43968	−	0.831199i	−0.0742458	−	0.0428658i
$377$		−	30.5200i		−	1.57186i
$378$	−1.43451	−	14.4887i	−0.0737833	−	0.745219i
$379$		−	1.29081i		−	0.0663045i	−0.999450	−	0.0331523i	$-0.989445\pi$
$379$		−	1.29081i		−	0.0663045i	0.999450	−	0.0331523i	$-0.0105546\pi$
$380$	−3.05590	+	5.29297i	−0.156764	+	0.271524i
$381$	2.10246	−	1.21386i	0.107712	−	0.0621877i
$382$	8.51452	−	4.91586i	0.435641	−	0.251517i
$383$	−2.42354	+	4.19769i	−0.123837	+	0.214492i	−0.921278	−	0.388905i	$-0.872853\pi$
$383$	−2.42354	+	4.19769i	−0.123837	+	0.214492i	0.797441	+	0.603397i	$0.206187\pi$
$384$			1.21925i			0.0622194i
$385$	6.73780	−	4.83347i	0.343390	−	0.246336i
$386$	−7.88455			−0.401313
$387$	17.0226	+	9.82802i	0.865309	+	0.499586i
$388$	−3.24958	−	5.62843i	−0.164972	−	0.285740i
$389$	12.3624	−	7.13745i	0.626800	−	0.361883i	−0.152712	−	0.988271i	$-0.548801\pi$
$389$	12.3624	−	7.13745i	0.626800	−	0.361883i	0.779512	+	0.626388i	$0.215467\pi$
$390$	−5.11582	+	8.86086i	−0.259050	+	0.448687i
$391$	−19.8621	−	5.44413i	−1.00447	−	0.275321i
$392$	−2.24328	+	6.63081i	−0.113303	+	0.334907i
$393$	13.8250			0.697377
$394$	2.98031	−	5.16206i	0.150146	−	0.260061i
$395$	15.9246	−	9.19406i	0.801253	−	0.462604i
$396$	−1.66162	+	0.959334i	−0.0834993	+	0.0482084i
$397$	−27.4857	−	15.8689i	−1.37947	−	0.796435i	−0.387371	−	0.921924i	$-0.626617\pi$
$397$	−27.4857	−	15.8689i	−1.37947	−	0.796435i	−0.992095	+	0.125488i	$0.959950\pi$
$398$	23.2518			1.16551
$399$	−6.47999	+	4.64852i	−0.324405	+	0.232717i
$400$	1.11180			0.0555899
$401$	3.68834	+	2.12946i	0.184187	+	0.106340i	0.589258	−	0.807945i	$-0.299420\pi$
$401$	3.68834	+	2.12946i	0.184187	+	0.106340i	−0.405071	+	0.914285i	$0.632753\pi$
$402$	6.95337	+	12.0436i	0.346802	+	0.600679i
$403$	−6.51835	−	11.2901i	−0.324702	−	0.562401i
$404$	−6.16770	−	3.56092i	−0.306854	−	0.177162i
$405$	−5.36270			−0.266475
$406$	−23.6726	+	2.34380i	−1.17485	+	0.116321i
$407$	1.81612			0.0900215
$408$	4.53435	+	2.61791i	0.224484	+	0.129606i
$409$	−6.42276	+	3.70818i	−0.317585	+	0.183358i	−0.650316	−	0.759664i	$-0.725363\pi$
$409$	−6.42276	+	3.70818i	−0.317585	+	0.183358i	0.332731	+	0.943022i	$0.392030\pi$
$410$	−7.26749	+	4.19589i	−0.358916	+	0.207220i
$411$	−0.964232	+	1.67010i	−0.0475621	+	0.0823799i
$412$	−13.9067			−0.685136
$413$	23.4858	+	10.6268i	1.15566	+	0.522908i
$414$	7.00000	+	1.91867i	0.344031	+	0.0942974i
$415$	−6.44227	+	11.1583i	−0.316239	+	0.547742i
$416$	−2.93968	+	1.69722i	−0.144130	+	0.0832133i
$417$	8.63242	+	14.9518i	0.422732	+	0.732192i
$418$	2.71426	+	1.56708i	0.132759	+	0.0766482i
$419$	−33.1406			−1.61903			−0.809513	−	0.587102i	$-0.800269\pi$
$419$	−33.1406			−1.61903			−0.809513	+	0.587102i	$0.800269\pi$
$420$	7.26573	+	3.28757i	0.354531	+	0.160417i
$421$		−	28.6831i		−	1.39793i	−0.715157	−	0.698964i	$-0.753645\pi$
$421$		−	28.6831i		−	1.39793i	0.715157	−	0.698964i	$-0.246355\pi$
$422$	3.81444	−	6.60681i	0.185684	−	0.321615i
$423$	2.17886	−	1.25797i	0.105940	−	0.0611644i
$424$	−7.14474	+	4.12502i	−0.346979	+	0.200329i
$425$	2.38720	−	4.13475i	0.115796	−	0.200565i
$426$		−	12.3180i		−	0.596809i
$427$	24.3244	−	2.40833i	1.17714	−	0.116547i
$428$		−	5.86367i		−	0.283431i
$429$	4.54388	+	2.62341i	0.219381	+	0.126660i
$430$	−27.8065	+	16.0541i	−1.34095	+	0.774198i
$431$	−21.2811	+	12.2866i	−1.02507	+	0.591827i	−0.915570	−	0.402159i	$-0.868260\pi$
$431$	−21.2811	+	12.2866i	−1.02507	+	0.591827i	−0.109505	+	0.993986i	$0.534926\pi$
$432$	−4.76573	−	2.75150i	−0.229291	−	0.132381i
$433$	24.3265			1.16906			0.584528	−	0.811374i	$-0.301280\pi$
$433$	24.3265			1.16906			0.584528	+	0.811374i	$0.301280\pi$
$434$	−8.25651	+	5.92294i	−0.396325	+	0.284310i
$435$			27.1014i			1.29941i
$436$	12.3456	+	7.12772i	0.591246	+	0.341356i
$437$	−3.00301	−	11.4697i	−0.143653	−	0.548669i
$438$	2.34132	+	4.05528i	0.111872	+	0.193769i
$439$	3.93526	+	2.27202i	0.187820	+	0.108438i	0.590961	−	0.806700i	$-0.298749\pi$
$439$	3.93526	+	2.27202i	0.187820	+	0.108438i	−0.403142	+	0.915138i	$0.632082\pi$
$440$		−	3.13415i		−	0.149415i
$441$	−6.99331	−	7.95787i	−0.333015	−	0.378946i
$442$			14.5768i			0.693347i
$443$	10.2326	−	17.7234i	0.486166	−	0.842064i	−0.513708	−	0.857965i	$-0.671728\pi$
$443$	10.2326	−	17.7234i	0.486166	−	0.842064i	0.999874	+	0.0159012i	$0.00506171\pi$
$444$	0.873312	+	1.51262i	0.0414456	+	0.0717858i
$445$	8.48441	+	14.6954i	0.402200	+	0.696630i
$446$	−7.26131	−	4.19232i	−0.343833	−	0.198512i
$447$	−3.09142			−0.146219
$448$	1.54219	+	2.14980i	0.0728618	+	0.101569i
$449$	−31.4921			−1.48620			−0.743102	−	0.669178i	$-0.766646\pi$
$449$	−31.4921			−1.48620			−0.743102	+	0.669178i	$0.766646\pi$
$450$	−0.841318	+	1.45721i	−0.0396601	+	0.0686933i
$451$	2.15167	+	3.72680i	0.101318	+	0.175488i
$452$	13.5926	−	7.84770i	0.639343	−	0.369125i
$453$	−8.47557	−	4.89337i	−0.398217	−	0.229911i
$454$	12.9893			0.609617
$455$	2.18755	+	22.0945i	0.102554	+	1.03581i
$456$			3.01423i			0.141154i
$457$	−9.36053	−	5.40430i	−0.437867	−	0.252803i	0.264825	−	0.964296i	$-0.414686\pi$
$457$	−9.36053	−	5.40430i	−0.437867	−	0.252803i	−0.702692	+	0.711494i	$0.748019\pi$
$458$	1.55022	+	2.68507i	0.0724372	+	0.125465i
$459$	−20.4655	+	11.8158i	−0.955247	+	0.551512i
$460$	−8.43152	+	8.33552i	−0.393122	+	0.388645i
$461$		−	36.3796i		−	1.69437i	−0.531299	−	0.847185i	$-0.678296\pi$
$461$		−	36.3796i		−	1.69437i	0.531299	−	0.847185i	$-0.321704\pi$
$462$	1.68588	−	3.72590i	0.0784343	−	0.173344i
$463$	25.6344			1.19133			0.595666	−	0.803232i	$-0.296888\pi$
$463$	25.6344			1.19133			0.595666	+	0.803232i	$0.296888\pi$
$464$	−4.49558	+	7.78657i	−0.208702	+	0.361482i
$465$	5.78822	+	10.0255i	0.268422	+	0.464921i
$466$	12.4182	+	21.5089i	0.575260	+	0.996380i
$467$	18.2010	−	31.5251i	0.842243	−	1.45881i	−0.0457505	−	0.998953i	$-0.514568\pi$
$467$	18.2010	−	31.5251i	0.842243	−	1.45881i	0.887994	−	0.459855i	$-0.152099\pi$
$468$		−	5.13728i		−	0.237471i
$469$	27.4939	+	12.4404i	1.26955	+	0.574442i
$470$			4.10979i			0.189570i
$471$	20.2764	+	11.7066i	0.934288	+	0.539412i
$472$	8.43785	−	4.87160i	0.388384	−	0.224233i
$473$	8.23261	+	14.2593i	0.378536	+	0.655643i
$474$	4.53435	−	7.85372i	0.208269	−	0.360733i
$475$	2.74859			0.126114
$476$	11.3064	−	1.11943i	0.518227	−	0.0513090i
$477$		−	12.4859i		−	0.571691i
$478$	12.3351	−	21.3650i	0.564193	−	0.977211i
$479$	1.95577	+	3.38750i	0.0893615	+	0.154779i	0.907241	−	0.420610i	$-0.138184\pi$
$479$	1.95577	+	3.38750i	0.0893615	+	0.154779i	−0.817880	+	0.575389i	$0.804851\pi$
$480$	2.61040	−	1.50711i	0.119148	−	0.0687900i
$481$	−2.43135	+	4.21122i	−0.110860	+	0.192015i
$482$	−20.1514			−0.917869
$483$	−14.5072	+	5.37393i	−0.660098	+	0.244522i
$484$	9.39279			0.426945
$485$	−8.03362	+	13.9146i	−0.364788	+	0.631831i
$486$	12.0067	−	6.93210i	0.544637	−	0.314446i
$487$	15.1951	+	26.3186i	0.688554	+	1.19261i	0.972306	+	0.233713i	$0.0750876\pi$
$487$	15.1951	+	26.3186i	0.688554	+	1.19261i	−0.283752	+	0.958898i	$0.591579\pi$
$488$	4.61935	−	8.00096i	0.209108	−	0.362186i
$489$		−	3.03173i		−	0.137100i
$490$	16.9694	−	3.39352i	0.766601	−	0.153303i
$491$	−20.2990			−0.916082			−0.458041	−	0.888931i	$-0.651449\pi$
$491$	−20.2990			−0.916082			−0.458041	+	0.888931i	$0.651449\pi$
$492$	−2.06934	+	3.58419i	−0.0932929	+	0.161588i
$493$	19.3054	+	33.4379i	0.869470	+	1.50597i
$494$	−7.26749	+	4.19589i	−0.326980	+	0.188782i
$495$	4.10786	+	2.37167i	0.184634	+	0.106599i
$496$			3.84060i			0.172448i
$497$	−15.5807	−	21.7193i	−0.698890	−	0.974245i
$498$			6.35443i			0.284749i
$499$	−3.40473	+	5.89716i	−0.152417	+	0.263993i	−0.932115	−	0.362162i	$-0.882039\pi$
$499$	−3.40473	+	5.89716i	−0.152417	+	0.263993i	0.779699	+	0.626155i	$0.215372\pi$
$500$	4.80622	+	8.32461i	0.214941	+	0.372288i
$501$	−5.00000	−	8.66025i	−0.223384	−	0.386912i
$502$	−14.6886	+	25.4414i	−0.655585	+	1.13551i
$503$	−3.19779			−0.142582			−0.0712911	−	0.997456i	$-0.522712\pi$
$503$	−3.19779			−0.142582			−0.0712911	+	0.997456i	$0.522712\pi$
$504$	−3.98469	+	0.394520i	−0.177492	+	0.0175733i
$505$			17.6067i			0.783486i
$506$	4.27448	+	4.32372i	0.190024	+	0.192213i
$507$	1.56032	−	0.900852i	0.0692963	−	0.0400082i
$508$	−0.995578	−	1.72439i	−0.0441716	−	0.0765075i
$509$	7.04396	+	4.06683i	0.312218	+	0.180259i	0.647919	−	0.761710i	$-0.275640\pi$
$509$	7.04396	+	4.06683i	0.312218	+	0.180259i	−0.335700	+	0.941969i	$0.608973\pi$
$510$		−	12.9440i		−	0.573170i
$511$	9.25767	+	4.18888i	0.409535	+	0.185305i
$512$	1.00000			0.0441942
$513$	−11.7819	−	6.80226i	−0.520182	−	0.300327i
$514$	−3.93918	+	2.27429i	−0.173750	+	0.100315i
$515$	17.1901	+	29.7742i	0.757488	+	1.31201i
$516$	−7.91760	+	13.7137i	−0.348553	+	0.603711i
$517$	2.10752			0.0926884
$518$	3.45312	+	1.56245i	0.151721	+	0.0686503i
$519$	21.4240			0.940408
$520$	7.26749	+	4.19589i	0.318700	+	0.184002i
$521$	−19.8849	−	34.4417i	−0.871175	−	1.50892i	−0.860782	−	0.508973i	$-0.830025\pi$
$521$	−19.8849	−	34.4417i	−0.871175	−	1.50892i	−0.0103923	−	0.999946i	$-0.503308\pi$
$522$	−6.80377	−	11.7845i	−0.297793	−	0.515793i
$523$	−16.2253	+	28.1030i	−0.709483	+	1.22886i	0.255567	+	0.966791i	$0.417738\pi$
$523$	−16.2253	+	28.1030i	−0.709483	+	1.22886i	−0.965049	+	0.262068i	$0.915595\pi$
$524$		−	11.3389i		−	0.495344i
$525$	−0.353364	−	3.56901i	−0.0154221	−	0.155765i
$526$			5.71453i			0.249165i
$527$	14.2831	+	8.24634i	0.622180	+	0.359216i
$528$	−0.772854	−	1.33862i	−0.0336342	−	0.0582561i
$529$	0.263379	−	22.9985i	0.0114513	−	0.999934i
$530$	17.6633	+	10.1979i	0.767244	+	0.442968i
$531$			14.7457i			0.639909i
$532$	3.81262	+	5.31475i	0.165298	+	0.230423i
$533$	−11.5223			−0.499085
$534$	7.24752	+	4.18436i	0.313631	+	0.181075i
$535$	−12.5541	+	7.24810i	−0.542760	+	0.313363i
$536$	9.87789	−	5.70300i	0.426660	−	0.246332i
$537$	−6.87753	−	3.97074i	−0.296787	−	0.171350i
$538$		−	8.28376i		−	0.357138i
$539$	−1.74021	−	8.70200i	−0.0749561	−	0.374822i
$540$			13.6045i			0.585446i
$541$	−11.1614	+	19.3322i	−0.479868	+	0.831156i	−0.999733	−	0.0230924i	$-0.992649\pi$
$541$	−11.1614	+	19.3322i	−0.479868	+	0.831156i	0.519865	+	0.854248i	$0.325982\pi$
$542$	−0.343470	+	0.198302i	−0.0147533	+	0.00851781i
$543$	−10.8131	+	6.24296i	−0.464035	+	0.267911i
$544$	2.14715	−	3.71897i	0.0920583	−	0.159450i
$545$		−	35.2424i		−	1.50962i
$546$	6.38263	+	8.89732i	0.273151	+	0.380770i
$547$	−12.9010			−0.551609			−0.275804	−	0.961214i	$-0.588944\pi$
$547$	−12.9010			−0.551609			−0.275804	+	0.961214i	$0.588944\pi$
$548$	1.36978	+	0.790842i	0.0585141	+	0.0337831i
$549$	6.99110	+	12.1089i	0.298373	+	0.516797i
$550$	−1.22065	+	0.704744i	−0.0520488	+	0.0300504i
$551$	−11.1140	+	19.2500i	−0.473472	+	0.820077i
$552$	−1.54571	+	5.63930i	−0.0657897	+	0.240025i
$553$	−1.93891	−	19.5832i	−0.0824509	−	0.832763i
$554$	−17.5190			−0.744310
$555$	2.15901	−	3.73951i	0.0916447	−	0.158733i
$556$	12.2631	−	7.08013i	0.520073	−	0.300264i
$557$	−1.60885	+	0.928870i	−0.0681692	+	0.0393575i	−0.533697	−	0.845676i	$-0.679198\pi$
$557$	−1.60885	+	0.928870i	−0.0681692	+	0.0393575i	0.465528	+	0.885033i	$0.345864\pi$
$558$	−5.03377	−	2.90625i	−0.213097	−	0.123031i
$559$	−44.0860			−1.86464
$560$	2.69640	−	5.95920i	0.113944	−	0.251822i
$561$	−6.63773			−0.280245
$562$	−17.7060	−	10.2225i	−0.746881	−	0.431212i
$563$	2.88227	+	4.99224i	0.121473	+	0.210398i	0.920349	−	0.391099i	$-0.127905\pi$
$563$	2.88227	+	4.99224i	0.121473	+	0.210398i	−0.798876	+	0.601496i	$0.794572\pi$
$564$	1.01344	+	1.75532i	0.0426734	+	0.0739125i
$565$	−33.6037	−	19.4011i	−1.41372	−	0.816211i
$566$	−14.0131			−0.589015
$567$	−2.36591	+	5.22881i	−0.0993590	+	0.219589i
$568$	−10.1030			−0.423910
$569$	−23.8451	−	13.7670i	−0.999641	−	0.577143i	−0.0914986	−	0.995805i	$-0.529166\pi$
$569$	−23.8451	−	13.7670i	−0.999641	−	0.577143i	−0.908142	+	0.418662i	$0.862499\pi$
$570$	6.45344	−	3.72590i	0.270305	−	0.156061i
$571$	26.7378	−	15.4371i	1.11894	−	0.646023i	0.177813	−	0.984064i	$-0.443098\pi$
$571$	26.7378	−	15.4371i	1.11894	−	0.646023i	0.941131	+	0.338042i	$0.109765\pi$
$572$	2.15167	−	3.72680i	0.0899657	−	0.155825i
$573$	−11.9873			−0.500777
$574$	0.884859	+	8.93717i	0.0369333	+	0.373030i
$575$	5.14233	+	1.40949i	0.214450	+	0.0587797i
$576$	−0.756718	+	1.31067i	−0.0315299	+	0.0546114i
$577$	−35.7439	+	20.6367i	−1.48804	+	0.859119i	−0.999907	−	0.0136513i	$-0.995655\pi$
$577$	−35.7439	+	20.6367i	−1.48804	+	0.859119i	−0.488131	+	0.872770i	$0.662321\pi$
$578$	−0.720506	−	1.24795i	−0.0299691	−	0.0519080i
$579$	8.32529	+	4.80661i	0.345987	+	0.199756i
$580$	22.2280			0.922967
$581$	8.03755	+	11.2043i	0.333454	+	0.464831i
$582$			7.92407i			0.328463i
$583$	5.22952	−	9.05779i	0.216585	−	0.375136i
$584$	3.32605	−	1.92030i	0.137633	−	0.0794625i
$585$	−10.9989	+	6.35021i	−0.454748	+	0.262549i
$586$	2.14263	−	3.71115i	0.0885114	−	0.153306i
$587$		−	13.5868i		−	0.560787i	−0.959885	−	0.280393i	$-0.909535\pi$
$587$		−	13.5868i		−	0.560787i	0.959885	−	0.280393i	$-0.0904649\pi$
$588$	6.41098	−	5.63391i	0.264384	−	0.232339i
$589$			9.49474i			0.391224i
$590$	−20.8601	−	12.0436i	−0.858797	−	0.495827i
$591$	−6.29382	+	3.63374i	−0.258893	+	0.149472i
$592$	1.24062	−	0.716272i	0.0509891	−	0.0294386i
$593$	12.3664	+	7.13972i	0.507826	+	0.293193i	0.731939	−	0.681370i	$-0.238615\pi$
$593$	12.3664	+	7.13972i	0.507826	+	0.293193i	−0.224114	+	0.974563i	$0.571949\pi$
$594$	6.97645			0.286247
$595$	−16.3725	−	22.8231i	−0.671208	−	0.935657i
$596$			2.53551i			0.103859i
$597$	−24.5516	−	14.1749i	−1.00483	−	0.580138i
$598$	−15.7484	+	4.12326i	−0.643999	+	0.168613i
$599$	−11.6674	−	20.2085i	−0.476716	−	0.825696i	0.522928	−	0.852377i	$-0.324840\pi$
$599$	−11.6674	−	20.2085i	−0.476716	−	0.825696i	−0.999644	+	0.0266806i	$0.991506\pi$
$600$	−1.17395	−	0.677778i	−0.0479261	−	0.0276702i
$601$			41.8019i			1.70513i	0.522618	+	0.852567i	$0.324955\pi$
$601$			41.8019i			1.70513i	−0.522618	+	0.852567i	$0.675045\pi$
$602$	3.38561	+	34.1950i	0.137987	+	1.39368i
$603$			17.2623i			0.702974i
$604$	−4.01344	+	6.95148i	−0.163304	+	0.282852i
$605$	−11.6105	−	20.1099i	−0.472032	−	0.817584i
$606$	4.34164	+	7.51995i	0.176367	+	0.305477i
$607$	−6.12191	−	3.53448i	−0.248480	−	0.143460i	0.370588	−	0.928797i	$-0.379156\pi$
$607$	−6.12191	−	3.53448i	−0.248480	−	0.143460i	−0.619068	+	0.785337i	$0.712490\pi$
$608$	2.47221			0.100261
$609$	26.4247	+	11.9566i	1.07078	+	0.484505i
$610$	−22.8400			−0.924764
$611$	−2.82146	+	4.88692i	−0.114144	+	0.197703i
$612$	3.24958	+	5.62843i	0.131356	+	0.227516i
$613$	36.2475	−	20.9275i	1.46402	−	0.845254i	0.464829	−	0.885401i	$-0.346116\pi$
$613$	36.2475	−	20.9275i	1.46402	−	0.845254i	0.999194	+	0.0401467i	$0.0127825\pi$
$614$	25.9202	+	14.9650i	1.04605	+	0.603939i
$615$	10.2316			0.412580
$616$	−3.05590	−	1.38272i	−0.123126	−	0.0557115i
$617$		−	44.8424i		−	1.80529i	−0.430390	−	0.902643i	$-0.641624\pi$
$617$		−	44.8424i		−	1.80529i	0.430390	−	0.902643i	$-0.358376\pi$
$618$	14.6841	+	8.47787i	0.590681	+	0.341030i
$619$	−2.13812	−	3.70333i	−0.0859382	−	0.148849i	0.819852	−	0.572575i	$-0.194055\pi$
$619$	−2.13812	−	3.70333i	−0.0859382	−	0.148849i	−0.905791	+	0.423726i	$0.860722\pi$
$620$	8.22269	−	4.74737i	0.330231	−	0.190659i
$621$	−18.5544	−	18.7681i	−0.744563	−	0.753138i
$622$			5.58497i			0.223937i
$623$	18.0717	−	1.78925i	0.724026	−	0.0716849i
$624$	4.13867			0.165679
$625$	14.6614	−	25.3944i	0.586458	−	1.01577i
$626$	4.42798	+	7.66948i	0.176978	+	0.306534i
$627$	−1.91065	−	3.30935i	−0.0763041	−	0.132163i
$628$	9.60150	−	16.6303i	0.383142	−	0.663621i
$629$		−	6.15177i		−	0.245287i
$630$	5.77016	+	8.04353i	0.229888	+	0.320462i
$631$		−	34.7236i		−	1.38232i	−0.722700	−	0.691162i	$-0.757099\pi$
$631$		−	34.7236i		−	1.38232i	0.722700	−	0.691162i	$-0.242901\pi$
$632$	−6.44145	−	3.71897i	−0.256227	−	0.147933i
$633$	−8.05533	+	4.65075i	−0.320171	+	0.184851i
$634$	−9.52428	−	16.4965i	−0.378257	−	0.655161i
$635$	−2.46127	+	4.26305i	−0.0976726	+	0.169174i
$636$	10.0588			0.398859
$637$	22.5080	+	7.61470i	0.891798	+	0.301706i
$638$		−	11.3986i		−	0.451275i
$639$	7.64509	−	13.2417i	0.302435	−	0.523833i
$640$	−1.23610	−	2.14099i	−0.0488612	−	0.0846302i
$641$	−6.73329	+	3.88746i	−0.265949	+	0.153546i	−0.627045	−	0.778983i	$-0.715736\pi$
$641$	−6.73329	+	3.88746i	−0.265949	+	0.153546i	0.361096	+	0.932529i	$0.382403\pi$
$642$	−3.57463	+	6.19144i	−0.141079	+	0.244357i
$643$	29.0738			1.14656			0.573278	−	0.819361i	$-0.305671\pi$
$643$	29.0738			1.14656			0.573278	+	0.819361i	$0.305671\pi$
$644$	4.40758	+	11.8985i	0.173683	+	0.468865i
$645$	39.1479			1.54145
$646$	5.30819	−	9.19406i	0.208848	−	0.361736i
$647$	0.980757	−	0.566241i	0.0385576	−	0.0222612i	−0.480597	−	0.876941i	$-0.659580\pi$
$647$	0.980757	−	0.566241i	0.0385576	−	0.0222612i	0.519155	+	0.854680i	$0.326247\pi$
$648$	1.08460	+	1.87858i	0.0426071	+	0.0737976i
$649$	−6.17600	+	10.6971i	−0.242429	+	0.419899i
$650$		−	3.77394i		−	0.148026i
$651$	12.3288	−	1.22066i	0.483204	−	0.0478415i
$652$	−2.48656			−0.0973813
$653$	11.5471	−	20.0001i	0.451871	−	0.782664i	−0.546631	−	0.837374i	$-0.684090\pi$
$653$	11.5471	−	20.0001i	0.451871	−	0.782664i	0.998502	+	0.0547097i	$0.0174233\pi$
$654$	−8.69045	−	15.0523i	−0.339824	−	0.588592i
$655$	−24.2766	+	14.0161i	−0.948564	+	0.547654i
$656$	2.93968	+	1.69722i	0.114775	+	0.0662655i
$657$			5.81250i			0.226767i
$658$	4.00717	+	1.81315i	0.156216	+	0.0706840i
$659$		−	4.27458i		−	0.166514i	−0.996528	−	0.0832569i	$-0.973468\pi$
$659$		−	4.27458i		−	0.166514i	0.996528	−	0.0832569i	$-0.0265322\pi$
$660$	−1.91065	+	3.30935i	−0.0743721	+	0.128816i
$661$	−18.4774	−	32.0038i	−0.718688	−	1.24480i	−0.961520	−	0.274736i	$-0.911409\pi$
$661$	−18.4774	−	32.0038i	−0.718688	−	1.24480i	0.242831	−	0.970069i	$-0.421924\pi$
$662$	−1.30101	−	2.25341i	−0.0505651	−	0.0875813i
$663$	8.88635	−	15.3916i	0.345117	−	0.597760i
$664$	5.21176			0.202256
$665$	6.66605	−	14.7324i	0.258498	−	0.571296i
$666$			2.16806i			0.0840108i
$667$	−30.6646	+	30.3154i	−1.18734	+	1.17382i
$668$	−7.10295	+	4.10089i	−0.274822	+	0.158668i
$669$	5.11147	+	8.85333i	0.197621	+	0.342290i
$670$	−24.4202	−	14.0990i	−0.943433	−	0.544691i
$671$			11.7124i			0.452153i
$672$	−0.317831	−	3.21013i	−0.0122606	−	0.123833i
$673$	16.0507			0.618711			0.309355	−	0.950947i	$-0.399887\pi$
$673$	16.0507			0.618711			0.309355	+	0.950947i	$0.399887\pi$
$674$	4.65709	+	2.68877i	0.179384	+	0.103568i
$675$	5.29853	−	3.05911i	0.203941	−	0.117745i
$676$	−0.738859	−	1.27974i	−0.0284177	−	0.0492208i
$677$	2.01347	−	3.48744i	0.0773841	−	0.134033i	−0.824736	−	0.565517i	$-0.808677\pi$
$677$	2.01347	−	3.48744i	0.0773841	−	0.134033i	0.902121	+	0.431484i	$0.142010\pi$
$678$	−19.1366			−0.734935
$679$	10.0229	+	13.9719i	0.384645	+	0.536191i
$680$	−10.6164			−0.407120
$681$	−13.7154	−	7.91856i	−0.525574	−	0.303440i
$682$	−2.43447	−	4.21663i	−0.0932207	−	0.161463i
$683$	11.6692	+	20.2116i	0.446509	+	0.773377i	0.998156	−	0.0607009i	$-0.0193336\pi$
$683$	11.6692	+	20.2116i	0.446509	+	0.773377i	−0.551647	+	0.834078i	$0.686000\pi$
$684$	−1.87076	+	3.24026i	−0.0715304	+	0.123894i
$685$		−	3.91025i		−	0.149403i
$686$	4.17778	−	18.0429i	0.159508	−	0.688881i
$687$		−	3.78021i		−	0.144224i
$688$	11.2477	+	6.49384i	0.428813	+	0.247575i
$689$	14.0022	+	24.2525i	0.533440	+	0.923946i
$690$	13.9844	−	3.66141i	0.532375	−	0.139387i
$691$	−32.7506	−	18.9086i	−1.24589	−	0.719317i	−0.275605	−	0.961271i	$-0.588878\pi$
$691$	−32.7506	−	18.9086i	−1.24589	−	0.719317i	−0.970288	+	0.241954i	$0.922212\pi$
$692$		−	17.5715i		−	0.667967i
$693$	4.12475	−	2.95896i	0.156686	−	0.112402i
$694$	13.6925			0.519759
$695$	−30.3170	−	17.5035i	−1.14999	−	0.663946i
$696$	9.49375	−	5.48122i	0.359860	−	0.207765i
$697$	12.6239	−	7.28839i	0.478163	−	0.276067i
$698$	20.1589	+	11.6387i	0.763024	+	0.440532i
$699$		−	30.2816i		−	1.14536i
$700$	−2.92723	+	0.289821i	−0.110639	+	0.0109542i
$701$		−	26.4771i		−	1.00003i	−0.866017	−	0.500014i	$-0.833328\pi$
$701$		−	26.4771i		−	1.00003i	0.866017	−	0.500014i	$-0.166672\pi$
$702$	−9.33982	+	16.1770i	−0.352509	+	0.610563i
$703$	3.06707	−	1.77077i	0.115677	−	0.0667859i
$704$	−1.09791	+	0.633878i	−0.0413790	+	0.0238902i
$705$	2.50542	−	4.33952i	0.0943597	−	0.163436i
$706$		−	31.6651i		−	1.19173i
$707$	17.1670	+	7.76769i	0.645633	+	0.292134i
$708$	−11.8794			−0.446454
$709$	14.1532	+	8.17135i	0.531534	+	0.306882i	0.741641	−	0.670797i	$-0.234048\pi$
$709$	14.1532	+	8.17135i	0.531534	+	0.306882i	−0.210107	+	0.977678i	$0.567381\pi$
$710$	12.4883	+	21.6303i	0.468677	+	0.811772i
$711$	9.74873	−	5.62843i	0.365606	−	0.211083i
$712$	3.43192	−	5.94426i	0.128617	−	0.222771i
$713$	−4.86894	+	17.7637i	−0.182343	+	0.665254i
$714$	−12.6208	−	5.71062i	−0.472322	−	0.213715i
$715$	−10.6387			−0.397866
$716$	−3.25672	+	5.64080i	−0.121709	+	0.210807i
$717$	−26.0492	+	15.0395i	−0.972824	+	0.561660i
$718$	30.4661	−	17.5896i	1.13699	−	0.656439i
$719$	−37.3661	−	21.5733i	−1.39352	−	0.804549i	−0.399817	−	0.916595i	$-0.630926\pi$
$719$	−37.3661	−	21.5733i	−1.39352	−	0.804549i	−0.993703	+	0.112046i	$0.964260\pi$
$720$	3.74153			0.139438
$721$	36.6147	−	3.62518i	1.36360	−	0.135009i
$722$	−12.8882			−0.479649
$723$	21.2778	+	12.2847i	0.791330	+	0.456875i
$724$	5.12034	+	8.86869i	0.190296	+	0.329602i
$725$	−4.99817	−	8.65709i	−0.185627	−	0.321516i
$726$	−9.91784	−	5.72607i	−0.368086	−	0.212514i
$727$	13.4385			0.498405			0.249203	−	0.968451i	$-0.419832\pi$
$727$	13.4385			0.498405			0.249203	+	0.968451i	$0.419832\pi$
$728$	7.29739	−	5.23489i	0.270459	−	0.194018i
$729$	−23.4115			−0.867092
$730$	−8.22269	−	4.74737i	−0.304335	−	0.175708i
$731$	48.3009	−	27.8865i	1.78647	−	1.03142i
$732$	−9.75514	+	5.63213i	−0.360560	+	0.208170i
$733$	−15.4206	+	26.7093i	−0.569573	+	0.986530i	0.427035	+	0.904235i	$0.359558\pi$
$733$	−15.4206	+	26.7093i	−0.569573	+	0.986530i	−0.996608	+	0.0822949i	$0.973775\pi$
$734$	−13.2476			−0.488977
$735$	−19.9868	−	6.76176i	−0.737224	−	0.249411i
$736$	4.62523	+	1.26776i	0.170488	+	0.0467301i
$737$	−7.23001	+	12.5228i	−0.266321	+	0.461282i
$738$	−4.44902	+	2.56864i	−0.163771	+	0.0945530i
$739$	−0.993256	−	1.72037i	−0.0365375	−	0.0632848i	0.847178	−	0.531309i	$-0.178300\pi$
$739$	−0.993256	−	1.72037i	−0.0365375	−	0.0632848i	−0.883716	+	0.468024i	$0.844966\pi$
$740$	−3.06707	−	1.77077i	−0.112748	−	0.0650948i
$741$	10.2316			0.375869
$742$	17.7359	−	12.7232i	0.651107	−	0.467082i
$743$		−	1.57808i		−	0.0578941i	−0.999581	−	0.0289471i	$-0.990785\pi$
$743$		−	1.57808i		−	0.0578941i	0.999581	−	0.0289471i	$-0.00921543\pi$
$744$	2.34132	−	4.05528i	0.0858369	−	0.148674i
$745$	5.42851	−	3.13415i	0.198885	−	0.114826i
$746$	−31.6868	+	18.2944i	−1.16014	+	0.669804i
$747$	−3.94384	+	6.83093i	−0.144297	+	0.249931i
$748$			5.44413i			0.199057i
$749$	1.52853	+	15.4383i	0.0558513	+	0.564104i
$750$		−	11.7199i		−	0.427951i
$751$	14.9992	+	8.65979i	0.547329	+	0.316000i	0.748044	−	0.663649i	$-0.230993\pi$
$751$	14.9992	+	8.65979i	0.547329	+	0.316000i	−0.200715	+	0.979650i	$0.564327\pi$
$752$	1.43968	−	0.831199i	0.0524997	−	0.0303107i
$753$	31.0194	−	17.9091i	1.13041	−	0.652642i
$754$	26.4311	+	15.2600i	0.962564	+	0.555737i
$755$	19.8441			0.722200
$756$	13.2648	+	6.00203i	0.482438	+	0.218292i
$757$			29.1470i			1.05937i	0.848196	+	0.529683i	$0.177689\pi$
$757$			29.1470i			1.05937i	−0.848196	+	0.529683i	$0.822311\pi$
$758$	1.11788	+	0.645406i	0.0406031	+	0.0234422i
$759$	−1.87758	−	7.17123i	−0.0681520	−	0.260299i
$760$	−3.05590	−	5.29297i	−0.110849	−	0.191996i
$761$	−16.6464	−	9.61082i	−0.603432	−	0.348392i	0.166958	−	0.985964i	$-0.446605\pi$
$761$	−16.6464	−	9.61082i	−0.603432	−	0.348392i	−0.770391	+	0.637572i	$0.779939\pi$
$762$			2.42771i			0.0879467i
$763$	−34.3624	−	15.5482i	−1.24400	−	0.562883i
$764$			9.83173i			0.355699i
$765$	8.03362	−	13.9146i	0.290456	−	0.503085i
$766$	−2.42354	−	4.19769i	−0.0875659	−	0.151669i
$767$	−16.5364	−	28.6419i	−0.597094	−	1.03420i
$768$	−1.05590	−	0.609623i	−0.0381015	−	0.0219979i
$769$	32.3533			1.16669			0.583344	−	0.812225i	$-0.301744\pi$
$769$	32.3533			1.16669			0.583344	+	0.812225i	$0.301744\pi$
$770$	0.817005	+	8.25184i	0.0294428	+	0.297376i
$771$	5.54584			0.199729
$772$	3.94227	−	6.82822i	0.141886	−	0.245753i
$773$	−18.0142	−	31.2015i	−0.647925	−	1.12224i	−0.983618	−	0.180267i	$-0.942304\pi$
$773$	−18.0142	−	31.2015i	−0.647925	−	1.12224i	0.335693	−	0.941971i	$-0.391030\pi$
$774$	−17.0226	+	9.82802i	−0.611866	+	0.353261i
$775$	−3.69790	−	2.13498i	−0.132832	−	0.0766909i
$776$	6.49915			0.233306
$777$	−2.69363	−	3.75489i	−0.0966335	−	0.134706i
$778$			14.2749i			0.511780i
$779$	7.26749	+	4.19589i	0.260385	+	0.150333i
$780$	−5.11582	−	8.86086i	−0.183176	−	0.317270i
$781$	11.0921	−	6.40404i	0.396907	−	0.229155i
$782$	14.6458	−	14.4791i	0.523734	−	0.517770i
$783$			49.4783i			1.76821i
$784$	−4.62081	−	5.25815i	−0.165029	−	0.187791i
$785$	−47.4738			−1.69441
$786$	−6.91248	+	11.9728i	−0.246560	+	0.427054i
$787$	−14.6732	−	25.4147i	−0.523042	−	0.905935i	−0.999640	−	0.0268143i	$-0.991464\pi$
$787$	−14.6732	−	25.4147i	−0.523042	−	0.905935i	0.476598	−	0.879121i	$-0.341870\pi$
$788$	2.98031	+	5.16206i	0.106169	+	0.183891i
$789$	3.48371	−	6.03396i	0.124023	−	0.214815i
$790$			18.3881i			0.654220i
$791$	−33.7420	+	24.2053i	−1.19973	+	0.860642i
$792$		−	1.91867i		−	0.0681769i
$793$	−27.1588	−	15.6802i	−0.964439	−	0.556819i
$794$	27.4857	−	15.8689i	0.975430	−	0.563165i
$795$	−12.4338	−	21.5359i	−0.440980	−	0.763799i
$796$	−11.6259	+	20.1367i	−0.412069	+	0.713725i
$797$	23.8046			0.843202			0.421601	−	0.906782i	$-0.361468\pi$
$797$	23.8046			0.843202			0.421601	+	0.906782i	$0.361468\pi$
$798$	−0.785744	−	7.93610i	−0.0278150	−	0.280935i
$799$		−	7.13883i		−	0.252554i
$800$	−0.555899	+	0.962845i	−0.0196540	+	0.0340417i
$801$	5.19399	+	8.99626i	0.183521	+	0.317867i
$802$	−3.68834	+	2.12946i	−0.130240	+	0.0751940i
$803$	−2.43447	+	4.21663i	−0.0859106	+	0.148801i
$804$	−13.9067			−0.490453
$805$	20.0263	−	24.1443i	0.705834	−	0.850975i
$806$	13.0367			0.459198
$807$	−5.04997	+	8.74681i	−0.177768	+	0.307902i
$808$	6.16770	−	3.56092i	0.216979	−	0.125273i
$809$	25.5237	+	44.2084i	0.897366	+	1.55428i	0.830849	+	0.556498i	$0.187855\pi$
$809$	25.5237	+	44.2084i	0.897366	+	1.55428i	0.0665172	+	0.997785i	$0.478811\pi$
$810$	2.68135	−	4.64424i	0.0942131	−	0.163182i
$811$			48.7844i			1.71305i	0.516104	+	0.856526i	$0.327382\pi$
$811$			48.7844i			1.71305i	−0.516104	+	0.856526i	$0.672618\pi$
$812$	9.80652	−	21.6730i	0.344141	−	0.760573i
$813$	0.483559			0.0169591
$814$	−0.908058	+	1.57280i	−0.0318274	+	0.0551267i
$815$	3.07365	+	5.32371i	0.107665	+	0.186482i
$816$	−4.53435	+	2.61791i	−0.158734	+	0.0916450i
$817$	27.8065	+	16.0541i	0.972828	+	0.561662i
$818$		−	7.41636i		−	0.259307i
$819$	1.33918	+	13.5258i	0.0467947	+	0.472631i
$820$		−	8.39177i		−	0.293053i
$821$	−0.368516	+	0.638289i	−0.0128613	+	0.0222764i	−0.872384	−	0.488820i	$-0.837427\pi$
$821$	−0.368516	+	0.638289i	−0.0128613	+	0.0222764i	0.859523	+	0.511097i	$0.170761\pi$
$822$	−0.964232	−	1.67010i	−0.0336315	−	0.0582514i
$823$	−25.2931	−	43.8089i	−0.881662	−	1.52708i	−0.849492	−	0.527601i	$-0.823092\pi$
$823$	−25.2931	−	43.8089i	−0.881662	−	1.52708i	−0.0321698	−	0.999482i	$-0.510242\pi$
$824$	6.95337	−	12.0436i	0.242232	−	0.419558i
$825$	1.71851			0.0598310
$826$	−20.9459	+	15.0259i	−0.728802	+	0.522817i
$827$			18.2125i			0.633310i	0.948541	+	0.316655i	$0.102560\pi$
$827$			18.2125i			0.633310i	−0.948541	+	0.316655i	$0.897440\pi$
$828$	−5.16162	+	5.10284i	−0.179379	+	0.177336i
$829$	21.2080	−	12.2444i	0.736585	−	0.425267i	−0.0842416	−	0.996445i	$-0.526847\pi$
$829$	21.2080	−	12.2444i	0.736585	−	0.425267i	0.820826	+	0.571178i	$0.193513\pi$
$830$	−6.44227	−	11.1583i	−0.223615	−	0.387312i
$831$	18.4983	+	10.6800i	0.641697	+	0.370484i
$832$		−	3.39445i		−	0.117681i
$833$	−29.4765	+	5.89465i	−1.02130	+	0.204237i
$834$	−17.2648			−0.597833
$835$	17.5600	+	10.1382i	0.607687	+	0.350848i
$836$	−2.71426	+	1.56708i	−0.0938745	+	0.0541985i
$837$	10.5674	+	18.3033i	0.365262	+	0.632653i
$838$	16.5703	−	28.7006i	0.572412	−	0.991447i
$839$	−20.0986			−0.693881			−0.346940	−	0.937887i	$-0.612779\pi$
$839$	−20.0986			−0.693881			−0.346940	+	0.937887i	$0.612779\pi$
$840$	−6.47999	+	4.64852i	−0.223581	+	0.160389i
$841$	51.8409			1.78762
$842$	24.8403	+	14.3415i	0.856052	+	0.494242i
$843$	12.4638	+	21.5879i	0.429276	+	0.743528i
$844$	3.81444	+	6.60681i	0.131299	+	0.227416i
$845$	−1.82661	+	3.16378i	−0.0628373	+	0.108837i
$846$			2.51593i			0.0864996i
$847$	−24.7301	+	2.44850i	−0.849736	+	0.0841313i
$848$		−	8.25004i		−	0.283308i
$849$	14.7964	+	8.54272i	0.507812	+	0.293185i
$850$	2.38720	+	4.13475i	0.0818802	+	0.141821i
$851$	6.64621	−	1.74012i	0.227829	−	0.0596506i
$852$	10.6677	+	6.15900i	0.365469	+	0.211004i
$853$			28.1854i			0.965050i	0.875882	+	0.482525i	$0.160280\pi$
$853$			28.1854i			0.965050i	−0.875882	+	0.482525i	$0.839720\pi$
$854$	−10.0765	+	22.2697i	−0.344812	+	0.762054i
$855$	9.24982			0.316337
$856$	5.07809	+	2.93183i	0.173565	+	0.100208i
$857$	−45.4805	+	26.2582i	−1.55358	+	0.896962i	−0.555738	+	0.831357i	$0.687564\pi$
$857$	−45.4805	+	26.2582i	−1.55358	+	0.896962i	−0.997846	+	0.0656045i	$0.979102\pi$
$858$	−4.54388	+	2.62341i	−0.155126	+	0.0895618i
$859$	−8.57908	−	4.95314i	−0.292715	−	0.168999i	0.346451	−	0.938068i	$-0.387387\pi$
$859$	−8.57908	−	4.95314i	−0.292715	−	0.168999i	−0.639165	+	0.769069i	$0.720720\pi$
$860$		−	32.1082i		−	1.09488i
$861$	4.51399	−	9.97618i	0.153836	−	0.339987i
$862$		−	24.5733i		−	0.836970i
$863$	−3.48933	+	6.04369i	−0.118778	+	0.205730i	−0.919284	−	0.393596i	$-0.871231\pi$
$863$	−3.48933	+	6.04369i	−0.118778	+	0.205730i	0.800506	+	0.599325i	$0.204564\pi$
$864$	4.76573	−	2.75150i	0.162134	−	0.0936078i
$865$	−37.6204	+	21.7201i	−1.27913	+	0.738507i
$866$	−12.1632	+	21.0673i	−0.413323	+	0.715897i
$867$			1.75695i			0.0596691i
$868$	−1.00116	−	10.1118i	−0.0339816	−	0.343218i
$869$	9.42950			0.319874
$870$	−23.4705	−	13.5507i	−0.795724	−	0.459412i
$871$	−19.3585	−	33.5300i	−0.655939	−	1.13612i
$872$	−12.3456	+	7.12772i	−0.418074	+	0.241375i
$873$	−4.91803	+	8.51827i	−0.166450	+	0.288300i
$874$	11.4345	+	3.13415i	0.386779	+	0.106014i
$875$	−14.8242	−	20.6648i	−0.501150	−	0.698598i
$876$	−4.68264			−0.158212
$877$	19.5669	−	33.8909i	0.660728	−	1.14441i	−0.319697	−	0.947520i	$-0.603581\pi$
$877$	19.5669	−	33.8909i	0.660728	−	1.14441i	0.980425	−	0.196894i	$-0.0630855\pi$
$878$	−3.93526	+	2.27202i	−0.132808	+	0.0766770i
$879$	−4.52481	+	2.61240i	−0.152618	+	0.0881140i
$880$	2.71426	+	1.56708i	0.0914976	+	0.0528261i
$881$	−16.1961			−0.545660			−0.272830	−	0.962062i	$-0.587960\pi$
$881$	−16.1961			−0.545660			−0.272830	+	0.962062i	$0.587960\pi$
$882$	10.3884	−	2.07745i	0.349795	−	0.0699512i
$883$	3.29018			0.110723			0.0553617	−	0.998466i	$-0.482369\pi$
$883$	3.29018			0.110723			0.0553617	+	0.998466i	$0.482369\pi$
$884$	−12.6239	−	7.28839i	−0.424586	−	0.245135i
$885$	14.6841	+	25.4336i	0.493601	+	0.854942i
$886$	10.2326	+	17.7234i	0.343771	+	0.595429i
$887$	−11.9436	−	6.89564i	−0.401027	−	0.231533i	0.285900	−	0.958259i	$-0.407707\pi$
$887$	−11.9436	−	6.89564i	−0.401027	−	0.231533i	−0.686927	+	0.726726i	$0.741041\pi$
$888$	−1.74662			−0.0586129
$889$	3.07075	+	4.28059i	0.102990	+	0.143566i
$890$	−16.9688			−0.568796
$891$	−2.38158	−	1.37501i	−0.0797860	−	0.0460645i
$892$	7.26131	−	4.19232i	0.243127	−	0.140369i
$893$	3.55918	−	2.05489i	0.119103	−	0.0687644i
$894$	1.54571	−	2.67724i	0.0516962	−	0.0895405i
$895$	16.1026			0.538249
$896$	−2.63288	+	0.260678i	−0.0879583	+	0.00870865i
$897$	19.1423	+	5.24683i	0.639144	+	0.175186i
$898$	15.7460	−	27.2730i	0.525452	−	0.910110i
$899$	29.9051	−	17.2657i	0.997390	−	0.575843i
$900$	−0.841318	−	1.45721i	−0.0280439	−	0.0485735i
$901$	−30.6817	−	17.7141i	−1.02215	−	0.590141i
$902$	−4.30333			−0.143285
$903$	17.2712	−	38.1704i	0.574750	−	1.27023i
$904$			15.6954i			0.522021i
$905$	12.6585	−	21.9252i	0.420784	−	0.728819i
$906$	8.47557	−	4.89337i	0.281582	−	0.162571i
$907$	10.0175	−	5.78359i	0.332625	−	0.192041i	−0.324381	−	0.945926i	$-0.605156\pi$
$907$	10.0175	−	5.78359i	0.332625	−	0.192041i	0.657006	+	0.753885i	$0.271823\pi$
$908$	−6.49463	+	11.2490i	−0.215532	+	0.373312i
$909$			10.7785i			0.357499i
$910$	−20.2282	−	9.15278i	−0.670558	−	0.303412i
$911$			52.9276i			1.75357i	0.480882	+	0.876785i	$0.340317\pi$
$911$			52.9276i			1.75357i	−0.480882	+	0.876785i	$0.659683\pi$
$912$	−2.61040	−	1.50711i	−0.0864389	−	0.0499055i
$913$	−5.72204	+	3.30362i	−0.189372	+	0.109334i
$914$	9.36053	−	5.40430i	0.309619	−	0.178758i
$915$	24.1167	+	13.9238i	0.797274	+	0.460306i
$916$	−3.10045			−0.102442
$917$	2.95581	+	29.8540i	0.0976095	+	0.985867i
$918$		−	23.6315i		−	0.779956i
$919$	1.20381	+	0.695019i	0.0397100	+	0.0229266i	0.519724	−	0.854334i	$-0.326035\pi$
$919$	1.20381	+	0.695019i	0.0397100	+	0.0229266i	−0.480014	+	0.877261i	$0.659368\pi$
$920$	−3.00301	−	11.4697i	−0.0990062	−	0.378144i
$921$	−18.2460	−	31.6031i	−0.601228	−	1.04136i
$922$	31.5057	+	18.1898i	1.03758	+	0.599050i
$923$			34.2940i			1.12880i
$924$	2.38378	+	3.32296i	0.0784206	+	0.109317i
$925$			1.59270i			0.0523676i
$926$	−12.8172	+	22.2001i	−0.421200	+	0.729539i
$927$	10.5235	+	18.2272i	0.345636	+	0.598660i
$928$	−4.49558	−	7.78657i	−0.147575	−	0.255607i
$929$	14.2728	+	8.24038i	0.468274	+	0.270358i	0.715517	−	0.698596i	$-0.246191\pi$
$929$	14.2728	+	8.24038i	0.468274	+	0.270358i	−0.247243	+	0.968953i	$0.579525\pi$
$930$	−11.5764			−0.379606
$931$	−11.4236	−	12.9992i	−0.374393	−	0.426032i
$932$	−24.8363			−0.813541
$933$	3.40473	−	5.89716i	0.111466	−	0.193064i
$934$	18.2010	+	31.5251i	0.595556	+	1.03153i
$935$	11.6558	−	6.72950i	0.381186	−	0.220078i
$936$	4.44902	+	2.56864i	0.145421	+	0.0839587i
$937$	−41.9928			−1.37184			−0.685922	−	0.727675i	$-0.740601\pi$
$937$	−41.9928			−1.37184			−0.685922	+	0.727675i	$0.740601\pi$
$938$	−24.5206	+	17.5903i	−0.800627	+	0.574342i
$939$		−	10.7976i		−	0.352366i
$940$	−3.55918	−	2.05489i	−0.116088	−	0.0670233i
$941$	16.7249	+	28.9683i	0.545216	+	0.944341i	0.998593	+	0.0530227i	$0.0168856\pi$
$941$	16.7249	+	28.9683i	0.545216	+	0.944341i	−0.453378	+	0.891319i	$0.649781\pi$
$942$	−20.2764	+	11.7066i	−0.660642	+	0.381422i
$943$	11.4450	+	11.5769i	0.372702	+	0.376994i
$944$			9.74319i			0.317114i
$945$	−3.54640	−	35.8191i	−0.115365	−	1.16519i
$946$	−16.4652			−0.535330
$947$	5.02687	−	8.70680i	0.163351	−	0.282933i	−0.772717	−	0.634750i	$-0.781103\pi$
$947$	5.02687	−	8.70680i	0.163351	−	0.282933i	0.936069	+	0.351817i	$0.114436\pi$
$948$	4.53435	+	7.85372i	0.147269	+	0.255077i
$949$	−6.51835	−	11.2901i	−0.211595	−	0.366493i
$950$	−1.37430	+	2.38035i	−0.0445880	+	0.0772288i
$951$			23.2249i			0.753119i
$952$	−4.68373	+	10.3513i	−0.151801	+	0.335488i
$953$			19.7821i			0.640806i	0.947281	+	0.320403i	$0.103818\pi$
$953$			19.7821i			0.640806i	−0.947281	+	0.320403i	$0.896182\pi$
$954$	10.8131	+	6.24296i	0.350088	+	0.202123i
$955$	21.0496	−	12.1530i	0.681151	−	0.393263i
$956$	12.3351	+	21.3650i	0.398945	+	0.690992i
$957$	−6.94885	+	12.0358i	−0.224624	+	0.389061i
$958$	−3.91154			−0.126376
$959$	−3.81262	−	1.72512i	−0.123116	−	0.0557070i
$960$			3.01423i			0.0972838i
$961$	−8.12491	+	14.0728i	−0.262094	+	0.453960i
$962$	−2.43135	−	4.21122i	−0.0783898	−	0.135775i
$963$	−7.68536	+	4.43715i	−0.247657	+	0.142985i
$964$	10.0757	−	17.4516i	0.324516	−	0.562078i
$965$	−19.4922			−0.627477
$966$	2.59962	−	15.2505i	0.0836413	−	0.490678i
$967$	39.6200			1.27409			0.637047	−	0.770825i	$-0.280156\pi$
$967$	39.6200			1.27409			0.637047	+	0.770825i	$0.280156\pi$
$968$	−4.69640	+	8.13440i	−0.150948	+	0.261449i
$969$	−11.2098	+	6.47200i	−0.360112	+	0.207911i
$970$	−8.03362	−	13.9146i	−0.257944	−	0.446772i
$971$	23.8065	−	41.2340i	0.763987	−	1.32326i	−0.176794	−	0.984248i	$-0.556573\pi$
$971$	23.8065	−	41.2340i	0.763987	−	1.32326i	0.940781	−	0.339016i	$-0.110094\pi$
$972$			13.8642i			0.444694i
$973$	−30.4417	+	21.8378i	−0.975916	+	0.700089i
$974$	−30.3901			−0.973763
$975$	−2.30068	+	3.98490i	−0.0736808	+	0.127619i
$976$	4.61935	+	8.00096i	0.147862	+	0.256104i
$977$	−0.251904	+	0.145437i	−0.00805912	+	0.00465293i	−0.504024	−	0.863690i	$-0.668148\pi$
$977$	−0.251904	+	0.145437i	−0.00805912	+	0.00465293i	0.495965	+	0.868342i	$0.334814\pi$
$978$	2.62556	+	1.51587i	0.0839561	+	0.0484721i
$979$			8.70168i			0.278107i
$980$	−5.54585	+	16.3927i	−0.177156	+	0.523647i
$981$		−	21.5747i		−	0.688828i
$982$	10.1495	−	17.5795i	0.323884	−	0.560983i
$983$	15.7179	+	27.2242i	0.501323	+	0.868317i	0.999999	+	0.00152833i	$0.000486483\pi$
$983$	15.7179	+	27.2242i	0.501323	+	0.868317i	−0.498676	+	0.866789i	$0.666180\pi$
$984$	−2.06934	−	3.58419i	−0.0659680	−	0.114260i
$985$	7.36795	−	12.7617i	0.234762	−	0.406620i
$986$	−38.6107			−1.22962
$987$	−3.12583	−	4.35737i	−0.0994963	−	0.138697i
$988$		−	8.39177i		−	0.266978i
$989$	43.7905	+	44.2948i	1.39246	+	1.40849i
$990$	−4.10786	+	2.37167i	−0.130556	+	0.0753767i
$991$	6.83645	+	11.8411i	0.217167	+	0.376144i	0.953941	−	0.299995i	$-0.0969850\pi$
$991$	6.83645	+	11.8411i	0.217167	+	0.376144i	−0.736774	+	0.676139i	$0.763652\pi$
$992$	−3.32605	−	1.92030i	−0.105602	−	0.0609695i
$993$			3.17250i			0.100676i
$994$	26.5998	−	2.63362i	0.843696	−	0.0835333i
$995$	57.4832			1.82234
$996$	−5.50310	−	3.17721i	−0.174372	−	0.100674i
$997$	−8.61882	+	4.97608i	−0.272961	+	0.157594i	−0.630232	−	0.776407i	$-0.717040\pi$
$997$	−8.61882	+	4.97608i	−0.272961	+	0.157594i	0.357272	+	0.934001i	$0.383707\pi$
$998$	−3.40473	−	5.89716i	−0.107775	−	0.186671i
$999$	3.94164	−	6.82712i	0.124708	−	0.216001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.a.229.5	yes	16
7.2	even	3		2254.2.c.c.2253.12		16
7.3	odd	6	inner	322.2.g.a.45.6	yes	16
7.5	odd	6		2254.2.c.c.2253.5		16
23.22	odd	2	inner	322.2.g.a.229.6	yes	16
161.45	even	6	inner	322.2.g.a.45.5	✓	16
161.68	even	6		2254.2.c.c.2253.6		16
161.114	odd	6		2254.2.c.c.2253.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.a.45.5	✓	16	161.45	even	6	inner
322.2.g.a.45.6	yes	16	7.3	odd	6	inner
322.2.g.a.229.5	yes	16	1.1	even	1	trivial
322.2.g.a.229.6	yes	16	23.22	odd	2	inner
2254.2.c.c.2253.5		16	7.5	odd	6
2254.2.c.c.2253.6		16	161.68	even	6
2254.2.c.c.2253.11		16	161.114	odd	6
2254.2.c.c.2253.12		16	7.2	even	3

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.05590 - 0.609623i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23610 + 2.14099i) q^{5} +1.21925i q^{6} +(1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 + 1.31067i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.05590 - 0.609623i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23610 + 2.14099i) q^{5} +1.21925i q^{6} +(1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 + 1.31067i) q^{9} +(-1.23610 - 2.14099i) q^{10} +(-1.09791 + 0.633878i) q^{11} +(-1.05590 - 0.609623i) q^{12} -3.39445i q^{13} +(-2.63288 + 0.260678i) q^{14} +3.01423i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.14715 + 3.71897i) q^{17} +(-0.756718 - 1.31067i) q^{18} +(-1.23610 + 2.14099i) q^{19} +2.47221 q^{20} +(2.93897 + 1.32981i) q^{21} -1.26776i q^{22} +(-3.41053 + 3.37169i) q^{23} +(1.05590 - 0.609623i) q^{24} +(-0.555899 - 0.962845i) q^{25} +(2.93968 + 1.69722i) q^{26} +5.50299i q^{27} +(1.09069 - 2.41048i) q^{28} +8.99116 q^{29} +(-2.61040 - 1.50711i) q^{30} +(3.32605 - 1.92030i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.772854 + 1.33862i) q^{33} -4.29430 q^{34} +(-6.50901 + 0.644450i) q^{35} +1.51344 q^{36} +(-1.24062 - 0.716272i) q^{37} +(-1.23610 - 2.14099i) q^{38} +(-2.06934 - 3.58419i) q^{39} +(-1.23610 + 2.14099i) q^{40} -3.39445i q^{41} +(-2.62114 + 1.88031i) q^{42} -12.9877i q^{43} +(1.09791 + 0.633878i) q^{44} +(-1.87076 - 3.24026i) q^{45} +(-1.21471 - 4.63945i) q^{46} +(-1.43968 - 0.831199i) q^{47} +1.21925i q^{48} +(-2.24328 + 6.63081i) q^{49} +1.11180 q^{50} +(4.53435 + 2.61791i) q^{51} +(-2.93968 + 1.69722i) q^{52} +(-7.14474 + 4.12502i) q^{53} +(-4.76573 - 2.75150i) q^{54} -3.13415i q^{55} +(1.54219 + 2.14980i) q^{56} +3.01423i q^{57} +(-4.49558 + 7.78657i) q^{58} +(8.43785 - 4.87160i) q^{59} +(2.61040 - 1.50711i) q^{60} +(4.61935 - 8.00096i) q^{61} +3.84060i q^{62} +(-3.98469 + 0.394520i) q^{63} +1.00000 q^{64} +(7.26749 + 4.19589i) q^{65} +(-0.772854 - 1.33862i) q^{66} +(9.87789 - 5.70300i) q^{67} +(2.14715 - 3.71897i) q^{68} +(-1.54571 + 5.63930i) q^{69} +(2.69640 - 5.95920i) q^{70} -10.1030 q^{71} +(-0.756718 + 1.31067i) q^{72} +(3.32605 - 1.92030i) q^{73} +(1.24062 - 0.716272i) q^{74} +(-1.17395 - 0.677778i) q^{75} +2.47221 q^{76} +(-3.05590 - 1.38272i) q^{77} +4.13867 q^{78} +(-6.44145 - 3.71897i) q^{79} +(-1.23610 - 2.14099i) q^{80} +(1.08460 + 1.87858i) q^{81} +(2.93968 + 1.69722i) q^{82} +5.21176 q^{83} +(-0.317831 - 3.21013i) q^{84} -10.6164 q^{85} +(11.2477 + 6.49384i) q^{86} +(9.49375 - 5.48122i) q^{87} +(-1.09791 + 0.633878i) q^{88} +(3.43192 - 5.94426i) q^{89} +3.74153 q^{90} +(7.29739 - 5.23489i) q^{91} +(4.62523 + 1.26776i) q^{92} +(2.34132 - 4.05528i) q^{93} +(1.43968 - 0.831199i) q^{94} +(-3.05590 - 5.29297i) q^{95} +(-1.05590 - 0.609623i) q^{96} +6.49915 q^{97} +(-4.62081 - 5.25815i) q^{98} -1.91867i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

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