LMFDB - Embedded newform 403.2.l.c.25.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.13
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +O(q^{10})$	\(q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +(1.71425 - 2.96916i) q^{10} +(-0.310190 - 0.179088i) q^{11} +(0.227493 + 0.394029i) q^{12} +(2.94922 + 2.07415i) q^{13} +(1.87818 + 3.25311i) q^{14} +1.46243i q^{15} -0.279074 q^{16} +(-0.359393 - 0.622486i) q^{17} +(-2.24445 - 1.29584i) q^{18} +(-5.27077 + 3.04308i) q^{19} +(3.82854 + 2.21041i) q^{20} +(-1.38762 - 0.801142i) q^{21} +(-0.162885 + 0.282124i) q^{22} +5.38696 q^{23} +(0.969545 - 0.559767i) q^{24} +(4.60478 + 7.97571i) q^{25} +(1.88648 - 2.68238i) q^{26} +2.26936 q^{27} +(-4.19467 + 2.42179i) q^{28} -5.79655 q^{29} +1.33011 q^{30} +(-2.82668 - 4.79686i) q^{31} -5.51758i q^{32} -0.138957i q^{33} +(-0.566165 + 0.326876i) q^{34} -15.5684 q^{35} +(1.67090 - 2.89408i) q^{36} +(5.77708 - 3.33540i) q^{37} +(2.76775 + 4.79389i) q^{38} +(-0.124788 + 1.39323i) q^{39} +(5.43891 - 9.42047i) q^{40} +(-0.227336 - 0.131253i) q^{41} +(-0.728657 + 1.26207i) q^{42} +(-1.36823 - 2.36984i) q^{43} +(-0.363781 - 0.210029i) q^{44} +(9.30224 - 5.37065i) q^{45} -4.89956i q^{46} -3.52717i q^{47} +(-0.0541346 - 0.0937638i) q^{48} +(5.02862 - 8.70982i) q^{49} +(7.25408 - 4.18815i) q^{50} +(0.139429 - 0.241499i) q^{51} +(3.45876 + 2.43250i) q^{52} +(-1.14813 + 1.98862i) q^{53} -2.06403i q^{54} +(-0.675082 - 1.16928i) q^{55} +(5.95904 + 10.3214i) q^{56} +(-2.04484 - 1.18059i) q^{57} +5.27209i q^{58} +(-3.44943 + 1.99153i) q^{59} +1.71510i q^{60} -11.6253 q^{61} +(-4.36285 + 2.57093i) q^{62} +11.7685i q^{63} -5.57651 q^{64} +(5.71852 + 12.3297i) q^{65} -0.126385 q^{66} +(-7.25205 - 4.18697i) q^{67} +(-0.421485 - 0.730033i) q^{68} +(1.04496 + 1.80992i) q^{69} +14.1598i q^{70} +(-8.34100 - 4.81568i) q^{71} +(-7.12114 - 4.11139i) q^{72} +(1.72044 + 0.993294i) q^{73} +(-3.03362 - 5.25439i) q^{74} +(-1.78646 + 3.09424i) q^{75} +(-6.18140 + 3.56883i) q^{76} +1.47928 q^{77} +(1.26717 + 0.113497i) q^{78} +(-3.43571 - 5.95083i) q^{79} +(-0.911045 - 0.525992i) q^{80} +(-3.83402 - 6.64072i) q^{81} +(-0.119377 + 0.206767i) q^{82} +(11.1050 + 6.41147i) q^{83} +(-1.62736 - 0.939555i) q^{84} -2.70950i q^{85} +(-2.15542 + 1.24443i) q^{86} +(-1.12441 - 1.94754i) q^{87} +(-0.516795 + 0.895115i) q^{88} +10.6987i q^{89} +(-4.88473 - 8.46060i) q^{90} +(-14.8317 - 1.32844i) q^{91} +6.31766 q^{92} +(1.06334 - 1.88021i) q^{93} -3.20804 q^{94} -22.9421 q^{95} +(1.85381 - 1.07030i) q^{96} +2.44420i q^{97} +(-7.92177 - 4.57364i) q^{98} +(-0.883881 + 0.510309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.909522i		−	0.643129i	−0.946888	−	0.321565i	$-0.895791\pi$
$2$		−	0.909522i		−	0.643129i	0.946888	−	0.321565i	$-0.104209\pi$
$3$	0.193979	+	0.335982i	0.111994	+	0.193979i	0.916574	−	0.399865i	$-0.130943\pi$
$3$	0.193979	+	0.335982i	0.111994	+	0.193979i	−0.804580	+	0.593844i	$0.797610\pi$
$4$	1.17277			0.586385
$5$	3.26453	+	1.88478i	1.45994	+	0.842898i	0.999008	−	0.0445356i	$-0.0141808\pi$
$5$	3.26453	+	1.88478i	1.45994	+	0.842898i	0.460935	+	0.887434i	$0.347514\pi$
$6$	0.305583	−	0.176429i	0.124754	−	0.0720266i
$7$	−3.57672	+	2.06502i	−1.35187	+	0.780504i	−0.988512	−	0.151144i	$-0.951704\pi$
$7$	−3.57672	+	2.06502i	−1.35187	+	0.780504i	−0.363361	+	0.931648i	$0.618371\pi$
$8$		−	2.88570i		−	1.02025i
$9$	1.42474	−	2.46773i	0.474915	−	0.822576i
$10$	1.71425	−	2.96916i	0.542093	−	0.938932i
$11$	−0.310190	−	0.179088i	−0.0935257	−	0.0539971i	0.452508	−	0.891760i	$-0.350529\pi$
$11$	−0.310190	−	0.179088i	−0.0935257	−	0.0539971i	−0.546033	+	0.837763i	$0.683863\pi$
$12$	0.227493	+	0.394029i	0.0656716	+	0.113746i
$13$	2.94922	+	2.07415i	0.817967	+	0.575265i
$13$	2.94922	+	2.07415i	0.817967	+	0.575265i
$14$	1.87818	+	3.25311i	0.501965	+	0.869429i
$15$			1.46243i			0.377598i
$16$	−0.279074			−0.0697685
$17$	−0.359393	−	0.622486i	−0.0871655	−	0.150975i	0.819146	−	0.573584i	$-0.194448\pi$
$17$	−0.359393	−	0.622486i	−0.0871655	−	0.150975i	−0.906312	+	0.422609i	$0.861114\pi$
$18$	−2.24445	−	1.29584i	−0.529023	−	0.305432i
$19$	−5.27077	+	3.04308i	−1.20920	+	0.698131i	−0.962584	−	0.270983i	$-0.912651\pi$
$19$	−5.27077	+	3.04308i	−1.20920	+	0.698131i	−0.246614	+	0.969114i	$0.579318\pi$
$20$	3.82854	+	2.21041i	0.856088	+	0.494263i
$21$	−1.38762	−	0.801142i	−0.302803	−	0.174824i
$22$	−0.162885	+	0.282124i	−0.0347271	+	0.0601491i
$23$	5.38696			1.12326			0.561630	−	0.827389i	$-0.310175\pi$
$23$	5.38696			1.12326			0.561630	+	0.827389i	$0.310175\pi$
$24$	0.969545	−	0.559767i	0.197908	−	0.114262i
$25$	4.60478	+	7.97571i	0.920955	+	1.59514i
$26$	1.88648	−	2.68238i	0.369970	−	0.526059i
$27$	2.26936			0.436738
$28$	−4.19467	+	2.42179i	−0.792718	+	0.457676i
$29$	−5.79655			−1.07639			−0.538196	−	0.842820i	$-0.680894\pi$
$29$	−5.79655			−1.07639			−0.538196	+	0.842820i	$0.680894\pi$
$30$	1.33011			0.242845
$31$	−2.82668	−	4.79686i	−0.507687	−	0.861541i
$31$	−2.82668	−	4.79686i	−0.507687	−	0.861541i
$32$		−	5.51758i		−	0.975380i
$33$		−	0.138957i		−	0.0241894i
$34$	−0.566165	+	0.326876i	−0.0970965	+	0.0560587i
$35$	−15.5684			−2.63154
$36$	1.67090	−	2.89408i	0.278483	−	0.482346i
$37$	5.77708	−	3.33540i	0.949747	−	0.548336i	0.0567444	−	0.998389i	$-0.481928\pi$
$37$	5.77708	−	3.33540i	0.949747	−	0.548336i	0.893002	+	0.450052i	$0.148595\pi$
$38$	2.76775	+	4.79389i	0.448989	+	0.777671i
$39$	−0.124788	+	1.39323i	−0.0199820	+	0.223095i
$40$	5.43891	−	9.42047i	0.859967	−	1.48951i
$41$	−0.227336	−	0.131253i	−0.0355039	−	0.0204982i	0.482143	−	0.876093i	$-0.339859\pi$
$41$	−0.227336	−	0.131253i	−0.0355039	−	0.0204982i	−0.517647	+	0.855594i	$0.673192\pi$
$42$	−0.728657	+	1.26207i	−0.112434	+	0.194742i
$43$	−1.36823	−	2.36984i	−0.208653	−	0.361397i	0.742638	−	0.669693i	$-0.233574\pi$
$43$	−1.36823	−	2.36984i	−0.208653	−	0.361397i	−0.951290	+	0.308296i	$0.900241\pi$
$44$	−0.363781	−	0.210029i	−0.0548420	−	0.0316630i
$45$	9.30224	−	5.37065i	1.38670	−	0.800610i
$46$		−	4.89956i		−	0.722401i
$47$		−	3.52717i		−	0.514491i	−0.966346	−	0.257245i	$-0.917185\pi$
$47$		−	3.52717i		−	0.514491i	0.966346	−	0.257245i	$-0.0828148\pi$
$48$	−0.0541346	−	0.0937638i	−0.00781365	−	0.0135336i
$49$	5.02862	−	8.70982i	0.718374	−	1.24426i
$50$	7.25408	−	4.18815i	1.02588	−	0.592293i
$51$	0.139429	−	0.241499i	0.0195240	−	0.0338166i
$52$	3.45876	+	2.43250i	0.479643	+	0.337326i
$53$	−1.14813	+	1.98862i	−0.157708	+	0.273158i	−0.934042	−	0.357164i	$-0.883744\pi$
$53$	−1.14813	+	1.98862i	−0.157708	+	0.273158i	0.776334	+	0.630322i	$0.217077\pi$
$54$		−	2.06403i		−	0.280879i
$55$	−0.675082	−	1.16928i	−0.0910281	−	0.157665i
$56$	5.95904	+	10.3214i	0.796310	+	1.37925i
$57$	−2.04484	−	1.18059i	−0.270846	−	0.156373i
$58$			5.27209i			0.692259i
$59$	−3.44943	+	1.99153i	−0.449077	+	0.259275i	−0.707440	−	0.706773i	$-0.750150\pi$
$59$	−3.44943	+	1.99153i	−0.449077	+	0.259275i	0.258363	+	0.966048i	$0.416817\pi$
$60$			1.71510i			0.221418i
$61$	−11.6253			−1.48847			−0.744233	−	0.667920i	$-0.767185\pi$
$61$	−11.6253			−1.48847			−0.744233	+	0.667920i	$0.767185\pi$
$62$	−4.36285	+	2.57093i	−0.554083	+	0.326509i
$63$			11.7685i			1.48269i
$64$	−5.57651			−0.697064
$65$	5.71852	+	12.3297i	0.709296	+	1.52932i
$66$	−0.126385			−0.0155569
$67$	−7.25205	−	4.18697i	−0.885978	−	0.511520i	−0.0133535	−	0.999911i	$-0.504251\pi$
$67$	−7.25205	−	4.18697i	−0.885978	−	0.511520i	−0.872625	+	0.488391i	$0.837584\pi$
$68$	−0.421485	−	0.730033i	−0.0511125	−	0.0885295i
$69$	1.04496	+	1.80992i	0.125798	+	0.217889i
$70$			14.1598i			1.69242i
$71$	−8.34100	−	4.81568i	−0.989894	−	0.571516i	−0.0846515	−	0.996411i	$-0.526978\pi$
$71$	−8.34100	−	4.81568i	−0.989894	−	0.571516i	−0.905243	+	0.424895i	$0.860311\pi$
$72$	−7.12114	−	4.11139i	−0.839234	−	0.484532i
$73$	1.72044	+	0.993294i	0.201362	+	0.116256i	0.597290	−	0.802025i	$-0.296244\pi$
$73$	1.72044	+	0.993294i	0.201362	+	0.116256i	−0.395929	+	0.918281i	$0.629577\pi$
$74$	−3.03362	−	5.25439i	−0.352651	−	0.610810i
$75$	−1.78646	+	3.09424i	−0.206283	+	0.357293i
$76$	−6.18140	+	3.56883i	−0.709055	+	0.409373i
$77$	1.47928			0.168580
$78$	1.26717	+	0.113497i	0.143479	+	0.0128510i
$79$	−3.43571	−	5.95083i	−0.386548	−	0.669521i	0.605435	−	0.795895i	$-0.292999\pi$
$79$	−3.43571	−	5.95083i	−0.386548	−	0.669521i	−0.991983	+	0.126374i	$0.959666\pi$
$80$	−0.911045	−	0.525992i	−0.101858	−	0.0588077i
$81$	−3.83402	−	6.64072i	−0.426003	−	0.737858i
$82$	−0.119377	+	0.206767i	−0.0131830	+	0.0228336i
$83$	11.1050	+	6.41147i	1.21893	+	0.703751i	0.964690	−	0.263390i	$-0.0848405\pi$
$83$	11.1050	+	6.41147i	1.21893	+	0.703751i	0.254243	+	0.967140i	$0.418174\pi$
$84$	−1.62736	−	0.939555i	−0.177559	−	0.102514i
$85$		−	2.70950i		−	0.293887i
$86$	−2.15542	+	1.24443i	−0.232425	+	0.134191i
$87$	−1.12441	−	1.94754i	−0.120549	−	0.208798i
$88$	−0.516795	+	0.895115i	−0.0550905	+	0.0954196i
$89$			10.6987i			1.13406i	0.823697	+	0.567030i	$0.191908\pi$
$89$			10.6987i			1.13406i	−0.823697	+	0.567030i	$0.808092\pi$
$90$	−4.88473	−	8.46060i	−0.514896	−	0.891825i
$91$	−14.8317	−	1.32844i	−1.55478	−	0.139258i
$92$	6.31766			0.658662
$93$	1.06334	−	1.88021i	0.110263	−	0.194968i
$94$	−3.20804			−0.330884
$95$	−22.9421			−2.35381
$96$	1.85381	−	1.07030i	0.189204	−	0.109237i
$97$			2.44420i			0.248171i	0.992272	+	0.124086i	$0.0395997\pi$
$97$			2.44420i			0.248171i	−0.992272	+	0.124086i	$0.960400\pi$
$98$	−7.92177	−	4.57364i	−0.800220	−	0.462007i
$99$	−0.883881	+	0.510309i	−0.0888334	+	0.0512880i
$100$	5.40034	+	9.35366i	0.540034	+	0.935366i
$101$	4.60510			0.458224			0.229112	−	0.973400i	$-0.426418\pi$
$101$	4.60510			0.458224			0.229112	+	0.973400i	$0.426418\pi$
$102$	−0.219649	−	0.126814i	−0.0217485	−	0.0125565i
$103$	−5.42061	+	9.38876i	−0.534108	+	0.925102i	0.465098	+	0.885259i	$0.346019\pi$
$103$	−5.42061	+	9.38876i	−0.534108	+	0.925102i	−0.999206	+	0.0398431i	$0.987314\pi$
$104$	5.98537	−	8.51058i	0.586914	−	0.834531i
$105$	−3.01995	−	5.23071i	−0.294717	−	0.510465i
$106$	1.80869	+	1.04425i	0.175676	+	0.101427i
$107$	1.13520	+	1.96622i	0.109744	+	0.190082i	0.915666	−	0.401939i	$-0.131664\pi$
$107$	1.13520	+	1.96622i	0.109744	+	0.190082i	−0.805923	+	0.592021i	$0.798330\pi$
$108$	2.66144			0.256097
$109$		−	19.6376i		−	1.88094i	−0.339871	−	0.940472i	$-0.610383\pi$
$109$		−	19.6376i		−	1.88094i	0.339871	−	0.940472i	$-0.389617\pi$
$110$	−1.06348	+	0.614002i	−0.101399	+	0.0585428i
$111$	2.24127	+	1.29400i	0.212732	+	0.122821i
$112$	0.998169	−	0.576293i	0.0943181	−	0.0544546i
$113$	−8.81868	+	15.2744i	−0.829592	+	1.43690i	0.0687667	+	0.997633i	$0.478094\pi$
$113$	−8.81868	+	15.2744i	−0.829592	+	1.43690i	−0.898359	+	0.439263i	$0.855240\pi$
$114$	−1.07377	+	1.85983i	−0.100568	+	0.174189i
$115$	17.5859	+	10.1532i	1.63989	+	0.946793i
$116$	−6.79801			−0.631180
$117$	9.32032	−	4.32275i	0.861664	−	0.399639i
$118$	1.81134	+	3.13733i	0.166747	+	0.288815i
$119$	2.57089	+	1.48431i	0.235673	+	0.136066i
$120$	4.22015			0.385245
$121$	−5.43585	−	9.41518i	−0.494169	−	0.855925i
$122$			10.5735i			0.957277i
$123$		−	0.101841i		−	0.00918271i
$124$	−3.31505	−	5.62561i	−0.297700	−	0.505195i
$125$			15.8681i			1.41929i
$126$	10.7037			0.953563
$127$	6.45201	+	11.1752i	0.572523	+	0.991639i	0.996306	+	0.0858754i	$0.0273687\pi$
$127$	6.45201	+	11.1752i	0.572523	+	0.991639i	−0.423783	+	0.905764i	$0.639298\pi$
$128$		−	5.96321i		−	0.527078i
$129$	0.530816	−	0.919400i	0.0467357	−	0.0809486i
$130$	11.2142	−	5.20112i	0.983549	−	0.456169i
$131$	2.03888	+	3.53144i	0.178137	+	0.308543i	0.941243	−	0.337731i	$-0.109660\pi$
$131$	2.03888	+	3.53144i	0.178137	+	0.308543i	−0.763105	+	0.646274i	$0.776326\pi$
$132$		−	0.162965i		−	0.0141843i
$133$	12.5681	−	21.7685i	1.08979	−	1.88757i
$134$	−3.80814	+	6.59590i	−0.328973	+	0.569799i
$135$	7.40840	+	4.27724i	0.637613	+	0.368126i
$136$	−1.79631	+	1.03710i	−0.154032	+	0.0889307i
$137$	8.78186	+	5.07021i	0.750285	+	0.433177i	0.825797	−	0.563968i	$-0.190726\pi$
$137$	8.78186	+	5.07021i	0.750285	+	0.433177i	−0.0755119	+	0.997145i	$0.524059\pi$
$138$	1.64616	−	0.950414i	0.140131	−	0.0809046i
$139$	22.1029			1.87475			0.937373	−	0.348327i	$-0.113250\pi$
$139$	22.1029			1.87475			0.937373	+	0.348327i	$0.113250\pi$
$140$	−18.2582			−1.54310
$141$	1.18507	−	0.684198i	0.0998005	−	0.0576199i
$142$	−4.37996	+	7.58632i	−0.367558	+	0.636630i
$143$	−0.543363	−	1.17155i	−0.0454383	−	0.0979699i
$144$	−0.397609	+	0.688679i	−0.0331341	+	0.0573899i
$145$	−18.9230	−	10.9252i	−1.57147	−	0.907289i
$146$	0.903423	−	1.56477i	0.0747678	−	0.129502i
$147$	3.90179			0.321814
$148$	6.77519	−	3.91166i	0.556917	−	0.321536i
$149$	−7.99387	+	4.61526i	−0.654883	+	0.378097i	−0.790325	−	0.612688i	$-0.790088\pi$
$149$	−7.99387	+	4.61526i	−0.654883	+	0.378097i	0.135441	+	0.990785i	$0.456755\pi$
$150$	2.81428	+	1.62483i	0.229785	+	0.132667i
$151$		−	11.8009i		−	0.960345i	−0.877174	−	0.480173i	$-0.840574\pi$
$151$		−	11.8009i		−	0.960345i	0.877174	−	0.480173i	$-0.159426\pi$
$152$	8.78144	+	15.2099i	0.712269	+	1.23369i
$153$	−2.04817			−0.165585
$154$		−	1.34544i		−	0.108419i
$155$	−0.186784	−	20.9872i	−0.0150028	−	1.68573i
$156$	−0.146347	+	1.63393i	−0.0117172	+	0.130819i
$157$	−14.3208			−1.14292			−0.571461	−	0.820629i	$-0.693623\pi$
$157$	−14.3208			−1.14292			−0.571461	+	0.820629i	$0.693623\pi$
$158$	−5.41241	+	3.12486i	−0.430588	+	0.248600i
$159$	−0.890855			−0.0706494
$160$	10.3994	−	18.0123i	0.822147	−	1.42400i
$161$	−19.2677	+	11.1242i	−1.51850	+	0.876708i
$162$	−6.03989	+	3.48713i	−0.474538	+	0.273975i
$163$		−	11.7697i		−	0.921873i	−0.887433	−	0.460936i	$-0.847514\pi$
$163$		−	11.7697i		−	0.921873i	0.887433	−	0.460936i	$-0.152486\pi$
$164$	−0.266613	−	0.153929i	−0.0208190	−	0.0120198i
$165$	0.261904	−	0.453631i	0.0203892	−	0.0353151i
$166$	5.83138	−	10.1002i	0.452603	−	0.783931i
$167$	−0.00504232	+	0.00291118i	−0.000390186	+	0.000225274i	−0.500195	−	0.865913i	$-0.666738\pi$
$167$	−0.00504232	+	0.00291118i	−0.000390186	+	0.000225274i	0.499805	+	0.866138i	$0.333405\pi$
$168$	−2.31186	+	4.00426i	−0.178364	+	0.308935i
$169$	4.39583	+	12.2342i	0.338141	+	0.941096i
$170$	−2.46435			−0.189007
$171$			17.3425i			1.32621i
$172$	−1.60461	−	2.77927i	−0.122351	−	0.211918i
$173$	1.23700	−	2.14255i	0.0940476	−	0.162895i	−0.815163	−	0.579231i	$-0.803353\pi$
$173$	1.23700	−	2.14255i	0.0940476	−	0.162895i	0.909211	+	0.416336i	$0.136686\pi$
$174$	−1.77133	+	1.02268i	−0.134284	+	0.0775289i
$175$	−32.9400	−	19.0179i	−2.49003	−	1.43762i
$176$	0.0865658	+	0.0499788i	0.00652514	+	0.00376729i
$177$	−1.33824	−	0.772630i	−0.100588	−	0.0580745i
$178$	9.73071			0.729348
$179$	8.40949	+	14.5657i	0.628555	+	1.08869i	0.987842	+	0.155462i	$0.0496867\pi$
$179$	8.40949	+	14.5657i	0.628555	+	1.08869i	−0.359287	+	0.933227i	$0.616980\pi$
$180$	10.9094	−	6.29854i	0.813137	−	0.469465i
$181$	0.575818	−	0.997346i	0.0428002	−	0.0741321i	−0.843832	−	0.536608i	$-0.819705\pi$
$181$	0.575818	−	0.997346i	0.0428002	−	0.0741321i	0.886632	+	0.462476i	$0.153039\pi$
$182$	−1.20824	+	13.4898i	−0.0895610	+	0.999928i
$183$	−2.25507	−	3.90589i	−0.166699	−	0.288732i
$184$		−	15.5452i		−	1.14601i
$185$	25.1460			1.84877
$186$	−1.71009	−	0.967132i	−0.125390	−	0.0709135i
$187$			0.257452i			0.0188267i
$188$		−	4.13656i		−	0.301689i
$189$	−8.11686	+	4.68627i	−0.590415	+	0.340876i
$190$			20.8664i			1.51381i
$191$	−2.91734	+	5.05298i	−0.211091	+	0.365621i	−0.952056	−	0.305923i	$-0.901035\pi$
$191$	−2.91734	+	5.05298i	−0.211091	+	0.365621i	0.740965	+	0.671544i	$0.234368\pi$
$192$	−1.08173	−	1.87361i	−0.0780670	−	0.135216i
$193$	1.84632	−	1.06597i	0.132901	−	0.0767303i	−0.432076	−	0.901837i	$-0.642219\pi$
$193$	1.84632	−	1.06597i	0.132901	−	0.0767303i	0.564976	+	0.825107i	$0.308885\pi$
$194$	2.22306			0.159606
$195$	−3.03330	+	4.31304i	−0.217219	+	0.308863i
$196$	5.89741	−	10.2146i	0.421243	−	0.729615i
$197$	−22.5595	−	13.0247i	−1.60730	−	0.927975i	−0.989971	−	0.141269i	$-0.954882\pi$
$197$	−22.5595	−	13.0247i	−1.60730	−	0.927975i	−0.617328	−	0.786706i	$-0.711785\pi$
$198$	0.464138	+	0.803910i	0.0329848	+	0.0571314i
$199$	−10.1525	+	17.5847i	−0.719694	+	1.24655i	0.241426	+	0.970419i	$0.422385\pi$
$199$	−10.1525	+	17.5847i	−0.719694	+	1.24655i	−0.961121	+	0.276128i	$0.910949\pi$
$200$	23.0155	−	13.2880i	1.62744	−	0.939605i
$201$		−	3.24874i		−	0.229149i
$202$		−	4.18844i		−	0.294697i
$203$	20.7326	−	11.9700i	1.45515	−	0.840129i
$204$	0.163519	−	0.283223i	0.0114486	−	0.0198295i
$205$	−0.494764	−	0.856956i	−0.0345558	−	0.0598524i
$206$	8.53929	+	4.93016i	0.594961	+	0.343501i
$207$	7.67504	−	13.2936i	0.533452	−	0.923966i
$208$	−0.823051	−	0.578840i	−0.0570683	−	0.0401353i
$209$	2.17992			0.150788
$210$	−4.75745	+	2.74671i	−0.328295	+	0.189541i
$211$	−6.70147	−	11.6073i	−0.461348	−	0.799079i	0.537680	−	0.843149i	$-0.319301\pi$
$211$	−6.70147	−	11.6073i	−0.461348	−	0.799079i	−0.999028	+	0.0440701i	$0.985968\pi$
$212$	−1.34649	+	2.33219i	−0.0924775	+	0.160176i
$213$		−	3.73657i		−	0.256025i
$214$	1.78832	−	1.03249i	0.122247	−	0.0705795i
$215$		−	10.3152i		−	0.703492i
$216$		−	6.54870i		−	0.445583i
$217$	20.0159	+	11.3199i	1.35877	+	0.768442i
$218$	−17.8609			−1.20969
$219$			0.770714i			0.0520800i
$220$	−0.791716	−	1.37129i	−0.0533775	−	0.0924525i
$221$	0.231199	−	2.58128i	0.0155521	−	0.173636i
$222$	1.17692	−	2.03848i	0.0789897	−	0.136814i
$223$	6.61419	−	3.81870i	0.442919	−	0.255719i	−0.261916	−	0.965091i	$-0.584354\pi$
$223$	6.61419	−	3.81870i	0.442919	−	0.255719i	0.704835	+	0.709371i	$0.251021\pi$
$224$	11.3939	+	19.7349i	0.761289	+	1.31859i
$225$	26.2425			1.74950
$226$	13.8924	+	8.02079i	0.924110	+	0.533535i
$227$	9.57173	+	5.52624i	0.635298	+	0.366789i	0.782801	−	0.622272i	$-0.213790\pi$
$227$	9.57173	+	5.52624i	0.635298	+	0.366789i	−0.147503	+	0.989062i	$0.547124\pi$
$228$	−2.39813	−	1.38456i	−0.158820	−	0.0916947i
$229$	13.1055	−	7.56649i	0.866038	−	0.500007i	8.59468e−6	−	1.00000i	$-0.499997\pi$
$229$	13.1055	−	7.56649i	0.866038	−	0.500007i	0.866030	+	0.499993i	$0.166664\pi$
$230$	9.23459	−	15.9948i	0.608911	−	1.05466i
$231$	0.286950	+	0.497012i	0.0188799	+	0.0327010i
$232$			16.7271i			1.09819i
$233$	10.6864			0.700088			0.350044	−	0.936733i	$-0.386167\pi$
$233$	10.6864			0.700088			0.350044	+	0.936733i	$0.386167\pi$
$234$	−3.93164	−	8.47704i	−0.257019	−	0.554161i
$235$	6.64793	−	11.5146i	0.433663	−	0.751127i
$236$	−4.04538	+	2.33560i	−0.263332	+	0.152035i
$237$	1.33291	−	2.30868i	0.0865821	−	0.149965i
$238$	1.35001	−	2.33828i	0.0875081	−	0.151568i
$239$	16.0487	+	9.26574i	1.03811	+	0.599351i	0.919296	−	0.393566i	$-0.128759\pi$
$239$	16.0487	+	9.26574i	1.03811	+	0.599351i	0.118810	+	0.992917i	$0.462092\pi$
$240$		−	0.408126i		−	0.0263445i
$241$	−17.3984	+	10.0450i	−1.12073	+	0.647052i	−0.941587	−	0.336771i	$-0.890665\pi$
$241$	−17.3984	+	10.0450i	−1.12073	+	0.647052i	−0.179141	+	0.983823i	$0.557332\pi$
$242$	−8.56331	+	4.94403i	−0.550471	+	0.317814i
$243$	4.89148	−	8.47230i	0.313789	−	0.543498i
$244$	−13.6338			−0.872814
$245$	32.8321	−	18.9556i	2.09757	−	1.21103i
$246$	−0.0926268			−0.00590567
$247$	−21.8565	−	1.95763i	−1.39070	−	0.124561i
$248$	−13.8423	+	8.15697i	−0.878988	+	0.517968i
$249$			4.97477i			0.315264i
$250$	14.4324			0.912787
$251$	−9.87326	−	17.1010i	−0.623195	−	1.07941i	−0.988887	−	0.148669i	$-0.952501\pi$
$251$	−9.87326	−	17.1010i	−0.623195	−	1.07941i	0.365692	−	0.930736i	$-0.380832\pi$
$252$			13.8017i			0.869428i
$253$	−1.67098	−	0.964740i	−0.105054	−	0.0606527i
$254$	10.1641	−	5.86825i	0.637752	−	0.368206i
$255$	0.910344	−	0.525587i	0.0570079	−	0.0329136i
$256$	−16.5767			−1.03604
$257$	−8.11638	+	14.0580i	−0.506286	+	0.876913i	0.493687	+	0.869639i	$0.335649\pi$
$257$	−8.11638	+	14.0580i	−0.506286	+	0.876913i	−0.999974	+	0.00727389i	$0.997685\pi$
$258$	−0.836215	−	0.482789i	−0.0520604	−	0.0300571i
$259$	−13.7753	+	23.8596i	−0.855958	+	1.48256i
$260$	6.70651	+	14.4599i	0.415920	+	0.896768i
$261$	−8.25860	+	14.3043i	−0.511194	+	0.885415i
$262$	3.21192	−	1.85440i	0.198433	−	0.114565i
$263$	8.12284			0.500876			0.250438	−	0.968133i	$-0.419425\pi$
$263$	8.12284			0.500876			0.250438	+	0.968133i	$0.419425\pi$
$264$	−0.400990			−0.0246792
$265$	−7.49622	+	4.32794i	−0.460489	+	0.265863i
$266$	−19.7989	−	11.4309i	−1.21395	−	0.700875i
$267$	−3.59457	+	2.07533i	−0.219984	+	0.127008i
$268$	−8.50498	−	4.91035i	−0.519524	−	0.299947i
$269$	10.6539	−	18.4531i	0.649581	−	1.12511i	−0.333642	−	0.942700i	$-0.608278\pi$
$269$	10.6539	−	18.4531i	0.649581	−	1.12511i	0.983223	−	0.182407i	$-0.0583889\pi$
$270$	3.89024	−	6.73810i	0.236753	−	0.410068i
$271$		−	4.57329i		−	0.277808i	−0.990306	−	0.138904i	$-0.955642\pi$
$271$		−	4.57329i		−	0.277808i	0.990306	−	0.138904i	$-0.0443579\pi$
$272$	0.100297	+	0.173720i	0.00608140	+	0.0105333i
$273$	−2.43071	−	5.24087i	−0.147113	−	0.317192i
$274$	4.61147	−	7.98730i	0.278589	−	0.482530i
$275$		−	3.29864i		−	0.198916i
$276$	1.22550	+	2.12262i	0.0737662	+	0.127767i
$277$	33.1115			1.98948			0.994739	−	0.102446i	$-0.0326668\pi$
$277$	33.1115			1.98948			0.994739	+	0.102446i	$0.0326668\pi$
$278$		−	20.1031i		−	1.20570i
$279$	−15.8646	+	0.141194i	−0.949792	+	0.00845305i
$280$			44.9258i			2.68483i
$281$			19.4695i			1.16145i	0.814099	+	0.580726i	$0.197231\pi$
$281$			19.4695i			1.16145i	−0.814099	+	0.580726i	$0.802769\pi$
$282$	−0.622293	−	1.07784i	−0.0370570	−	0.0641846i
$283$	17.7417			1.05463			0.527317	−	0.849669i	$-0.323198\pi$
$283$	17.7417			1.05463			0.527317	+	0.849669i	$0.323198\pi$
$284$	−9.78206	−	5.64768i	−0.580459	−	0.335128i
$285$	−4.45030	−	7.70815i	−0.263613	−	0.456591i
$286$	−1.06555	+	0.494201i	−0.0630073	+	0.0292227i
$287$	1.08416			0.0639958
$288$	−13.6159	−	7.86115i	−0.802325	−	0.463222i
$289$	8.24167	−	14.2750i	0.484804	−	0.839706i
$290$	−9.93672	+	17.2109i	−0.583504	+	1.01066i
$291$	−0.821208	+	0.474125i	−0.0481401	+	0.0277937i
$292$	2.01767	+	1.16490i	0.118075	+	0.0681709i
$293$	−0.385170	+	0.222378i	−0.0225019	+	0.0129915i	−0.511209	−	0.859457i	$-0.670802\pi$
$293$	−0.385170	+	0.222378i	−0.0225019	+	0.0129915i	0.488707	+	0.872448i	$0.337469\pi$
$294$		−	3.54876i		−	0.206968i
$295$	−15.0143			−0.874169
$296$	−9.62498	−	16.6710i	−0.559441	−	0.968979i
$297$	−0.703932	−	0.406415i	−0.0408463	−	0.0235826i
$298$	4.19768	+	7.27060i	0.243165	+	0.421175i
$299$	15.8873	+	11.1733i	0.918789	+	0.646171i
$300$	−2.09511	+	3.62883i	−0.120961	+	0.209511i
$301$	9.78753	+	5.65083i	0.564144	+	0.325709i
$302$	−10.7332			−0.617626
$303$	0.893294	+	1.54723i	0.0513184	+	0.0888860i
$304$	1.47094	−	0.849245i	0.0843639	−	0.0487075i
$305$	−37.9512	−	21.9111i	−2.17308	−	1.25463i
$306$			1.86286i			0.106492i
$307$	0.0971280	−	0.0560769i	0.00554339	−	0.00320048i	−0.497226	−	0.867621i	$-0.665648\pi$
$307$	0.0971280	−	0.0560769i	0.00554339	−	0.00320048i	0.502769	+	0.864421i	$0.332315\pi$
$308$	1.73486			0.0988526
$309$	−4.20594			−0.239268
$310$	−19.0883	+	0.169884i	−1.08414	+	0.00964876i
$311$	20.5808			1.16703			0.583515	−	0.812102i	$-0.301677\pi$
$311$	20.5808			1.16703			0.583515	+	0.812102i	$0.301677\pi$
$312$	4.02044	+	0.360101i	0.227613	+	0.0203867i
$313$	2.77025	+	4.79821i	0.156584	+	0.271211i	0.933635	−	0.358227i	$-0.116619\pi$
$313$	2.77025	+	4.79821i	0.156584	+	0.271211i	−0.777051	+	0.629438i	$0.783285\pi$
$314$			13.0251i			0.735047i
$315$	−22.1810	+	38.4186i	−1.24976	+	2.16464i
$316$	−4.02930	−	6.97895i	−0.226666	−	0.392597i
$317$	2.08553	−	1.20408i	0.117135	−	0.0676280i	−0.440288	−	0.897857i	$-0.645124\pi$
$317$	2.08553	−	1.20408i	0.117135	−	0.0676280i	0.557423	+	0.830229i	$0.311790\pi$
$318$			0.810252i			0.0454367i
$319$	1.79803	+	1.03809i	0.100670	+	0.0581220i
$320$	−18.2047	−	10.5105i	−1.01767	−	0.587554i
$321$	−0.440410	+	0.762813i	−0.0245813	+	0.0425761i
$322$	10.1177	+	17.5244i	0.563837	+	0.976594i
$323$	3.78856	+	2.18732i	0.210801	+	0.121706i
$324$	−4.49642	−	7.78804i	−0.249801	−	0.432669i
$325$	−2.96228	+	33.0731i	−0.164317	+	1.83457i
$326$	−10.7048			−0.592883
$327$	6.59789	−	3.80930i	0.364864	−	0.210655i
$328$	−0.378756	+	0.656025i	−0.0209133	+	0.0362229i
$329$	7.28368	+	12.6157i	0.401562	+	0.695526i
$330$	−0.412588	−	0.238208i	−0.0227122	−	0.0131129i
$331$	21.4478	+	12.3829i	1.17888	+	0.680626i	0.955755	−	0.294164i	$-0.0950413\pi$
$331$	21.4478	+	12.3829i	1.17888	+	0.680626i	0.223124	+	0.974790i	$0.428375\pi$
$332$	13.0236	+	7.51918i	0.714763	+	0.412669i
$333$		−	19.0084i		−	1.04165i
$334$	0.00264779	+	0.00458610i	0.000144880	+	0.000250940i
$335$	−15.7830	−	27.3370i	−0.862318	−	1.49358i
$336$	0.387248	+	0.223578i	0.0211261	+	0.0121972i
$337$	−0.784988			−0.0427610			−0.0213805	−	0.999771i	$-0.506806\pi$
$337$	−0.784988			−0.0427610			−0.0213805	+	0.999771i	$0.506806\pi$
$338$	11.1273	−	3.99811i	0.605246	−	0.217468i
$339$	−6.84257			−0.371637
$340$		−	3.17762i		−	0.172331i
$341$	0.0177478	+	1.99416i	0.000961099	+	0.107990i
$342$	15.7734			0.852925
$343$			12.6265i			0.681766i
$344$	−6.83866	+	3.94830i	−0.368716	+	0.212878i
$345$			7.87806i			0.424141i
$346$	−1.94870	−	1.12508i	−0.104763	−	0.0604848i
$347$	4.16488	+	7.21378i	0.223582	+	0.387256i	0.955893	−	0.293715i	$-0.0948915\pi$
$347$	4.16488	+	7.21378i	0.223582	+	0.387256i	−0.732311	+	0.680970i	$0.761558\pi$
$348$	−1.31867	−	2.28401i	−0.0706884	−	0.122436i
$349$			24.9286i			1.33440i	0.744880	+	0.667199i	$0.232507\pi$
$349$			24.9286i			1.33440i	−0.744880	+	0.667199i	$0.767493\pi$
$350$	−17.2972	+	29.9597i	−0.924575	+	1.60141i
$351$	6.69285	+	4.70698i	0.357238	+	0.251240i
$352$	−0.988133	+	1.71150i	−0.0526677	+	0.0912231i
$353$	23.1970	−	13.3928i	1.23465	−	0.712825i	0.266654	−	0.963792i	$-0.414082\pi$
$353$	23.1970	−	13.3928i	1.23465	−	0.712825i	0.967996	+	0.250967i	$0.0807486\pi$
$354$	−0.702725	+	1.21715i	−0.0373494	+	0.0646910i
$355$	−18.1530	−	31.4419i	−0.963459	−	1.66876i
$356$			12.5471i			0.664996i
$357$			1.15170i			0.0609544i
$358$	13.2478	−	7.64862i	0.700168	−	0.404242i
$359$	25.9688	+	14.9931i	1.37058	+	0.791305i	0.991001	−	0.133855i	$-0.0427356\pi$
$359$	25.9688	+	14.9931i	1.37058	+	0.791305i	0.379579	+	0.925159i	$0.376069\pi$
$360$	−15.4981	−	26.8435i	−0.816822	−	1.41478i
$361$	9.02071	−	15.6243i	0.474774	−	0.822333i
$362$	−0.907108	−	0.523719i	−0.0476766	−	0.0275261i
$363$	2.10889	−	3.65270i	0.110688	−	0.191717i
$364$	−17.3942	−	1.55795i	−0.911702	−	0.0816588i
$365$	3.74428	+	6.48528i	0.195984	+	0.339455i
$366$	−3.55250	+	2.05103i	−0.185692	+	0.107209i
$367$	−0.537599	+	0.931148i	−0.0280624	+	0.0486055i	−0.879716	−	0.475500i	$-0.842267\pi$
$367$	−0.537599	+	0.931148i	−0.0280624	+	0.0486055i	0.851653	+	0.524106i	$0.175600\pi$
$368$	−1.50336			−0.0783681
$369$	−0.647792	+	0.374003i	−0.0337227	+	0.0194698i
$370$		−	22.8708i		−	1.18900i
$371$		−	9.48365i		−	0.492367i
$372$	1.24705	−	2.20505i	0.0646567	−	0.114326i
$373$	−25.1653			−1.30301			−0.651506	−	0.758643i	$-0.725863\pi$
$373$	−25.1653			−1.30301			−0.651506	+	0.758643i	$0.725863\pi$
$374$	0.234158			0.0121080
$375$	−5.33141	+	3.07809i	−0.275313	+	0.158952i
$376$	−10.1784			−0.524909
$377$	−17.0953	−	12.0229i	−0.880453	−	0.619211i
$378$	4.26227	+	7.38247i	0.219227	+	0.379713i
$379$	−7.17721	+	4.14376i	−0.368668	+	0.212851i	−0.672877	−	0.739755i	$-0.734941\pi$
$379$	−7.17721	+	4.14376i	−0.368668	+	0.212851i	0.304208	+	0.952606i	$0.401608\pi$
$380$	−26.9058			−1.38024
$381$	−2.50311	+	4.33552i	−0.128238	+	0.222115i
$382$	4.59580	+	2.65339i	0.235142	+	0.135759i
$383$	−14.8393	−	8.56747i	−0.758253	−	0.437777i	0.0704154	−	0.997518i	$-0.477568\pi$
$383$	−14.8393	−	8.56747i	−0.758253	−	0.437777i	−0.828668	+	0.559740i	$0.810901\pi$
$384$	2.00353	−	1.15674i	0.102242	−	0.0590296i
$385$	4.82916	+	2.78812i	0.246117	+	0.142096i
$386$	−0.969525	−	1.67927i	−0.0493475	−	0.0854724i
$387$	−7.79750			−0.396369
$388$			2.86648i			0.145524i
$389$	−0.00591396	−	0.0102433i	−0.000299849	−	0.000519354i	0.865875	−	0.500260i	$-0.166762\pi$
$389$	−0.00591396	−	0.0102433i	−0.000299849	−	0.000519354i	−0.866175	+	0.499740i	$0.833429\pi$
$390$	3.92280	+	2.75885i	0.198639	+	0.139700i
$391$	−1.93603	−	3.35331i	−0.0979095	−	0.169584i
$392$	−25.1340	−	14.5111i	−1.26946	−	0.732921i
$393$	−0.790999	+	1.37005i	−0.0399006	+	0.0691099i
$394$	−11.8463	+	20.5184i	−0.596808	+	1.03370i
$395$		−	25.9022i		−	1.30328i
$396$	−1.03659	+	0.598475i	−0.0520906	+	0.0300745i
$397$	−0.778571	+	0.449508i	−0.0390754	+	0.0225602i	−0.519410	−	0.854525i	$-0.673848\pi$
$397$	−0.778571	+	0.449508i	−0.0390754	+	0.0225602i	0.480335	+	0.877085i	$0.340515\pi$
$398$	15.9937	+	9.23396i	0.801691	+	0.462857i
$399$	9.75177			0.488199
$400$	−1.28507	−	2.22581i	−0.0642536	−	0.111291i
$401$			26.1075i			1.30375i	0.758328	+	0.651873i	$0.226017\pi$
$401$			26.1075i			1.30375i	−0.758328	+	0.651873i	$0.773983\pi$
$402$	−2.95480			−0.147372
$403$	1.61287	−	20.0100i	0.0803427	−	0.996767i
$404$	5.40072			0.268696
$405$		−	28.9051i		−	1.43631i
$406$	−10.8870	−	18.8568i	−0.540311	−	0.935847i
$407$	−2.38932			−0.118434
$408$	−0.696895	−	0.402352i	−0.0345014	−	0.0199194i
$409$	20.3475	−	11.7476i	1.00612	−	0.580882i	0.0960643	−	0.995375i	$-0.469375\pi$
$409$	20.3475	−	11.7476i	1.00612	−	0.580882i	0.910052	+	0.414493i	$0.136041\pi$
$410$	−0.779421	+	0.449999i	−0.0384929	+	0.0222239i
$411$			3.93406i			0.194053i
$412$	−6.35712	+	11.0109i	−0.313193	+	0.542466i
$413$	8.22509	−	14.2463i	0.404730	−	0.701013i
$414$	−12.0908	−	6.98062i	−0.594230	−	0.343079i
$415$	24.1684	+	41.8609i	1.18638	+	2.05487i
$416$	11.4443	−	16.2726i	0.561102	−	0.797829i
$417$	4.28751	+	7.42619i	0.209960	+	0.363662i
$418$		−	1.98268i		−	0.0969763i
$419$	−7.93033			−0.387422			−0.193711	−	0.981059i	$-0.562052\pi$
$419$	−7.93033			−0.387422			−0.193711	+	0.981059i	$0.562052\pi$
$420$	−3.54171	−	6.13441i	−0.172818	−	0.299329i
$421$	10.1889	+	5.88256i	0.496577	+	0.286699i	0.727299	−	0.686321i	$-0.240776\pi$
$421$	10.1889	+	5.88256i	0.496577	+	0.286699i	−0.230722	+	0.973020i	$0.574109\pi$
$422$	−10.5571	+	6.09514i	−0.513911	+	0.296707i
$423$	−8.70410	−	5.02531i	−0.423208	−	0.244339i
$424$	5.73857	+	3.31317i	0.278690	+	0.160902i
$425$	3.30985	−	5.73282i	0.160551	−	0.278083i
$426$	−3.39849			−0.164657
$427$	41.5804	−	24.0065i	2.01222	−	1.16175i
$428$	1.33133	+	2.30593i	0.0643521	+	0.111461i
$429$	0.288218	−	0.409817i	0.0139153	−	0.0197861i
$430$	−9.38192			−0.452436
$431$	−21.9290	+	12.6607i	−1.05628	+	0.609844i	−0.924401	−	0.381422i	$-0.875435\pi$
$431$	−21.9290	+	12.6607i	−1.05628	+	0.609844i	−0.131880	+	0.991266i	$0.542101\pi$
$432$	−0.633319			−0.0304706
$433$	4.52861			0.217631			0.108816	−	0.994062i	$-0.465294\pi$
$433$	4.52861			0.217631			0.108816	+	0.994062i	$0.465294\pi$
$434$	10.2957	−	18.2049i	0.494208	−	0.873862i
$435$		−	8.47706i		−	0.406444i
$436$		−	23.0304i		−	1.10296i
$437$	−28.3935	+	16.3930i	−1.35824	+	0.784182i
$438$	0.700981			0.0334942
$439$	−8.50172	+	14.7254i	−0.405765	+	0.702805i	−0.994410	−	0.105586i	$-0.966328\pi$
$439$	−8.50172	+	14.7254i	−0.405765	+	0.702805i	0.588645	+	0.808391i	$0.299662\pi$
$440$	−3.37419	+	1.94809i	−0.160858	+	0.0928714i
$441$	−14.3290	−	24.8185i	−0.682332	−	1.18183i
$442$	−2.34774	−	0.210281i	−0.111670	−	0.0100020i
$443$	−9.59205	+	16.6139i	−0.455732	+	0.789351i	−0.998730	−	0.0503831i	$-0.983956\pi$
$443$	−9.59205	+	16.6139i	−0.455732	+	0.789351i	0.542998	+	0.839734i	$0.317289\pi$
$444$	2.62849	+	1.51756i	0.124743	+	0.0720202i
$445$	−20.1647	+	34.9263i	−0.955898	+	1.65566i
$446$	−3.47319	−	6.01575i	−0.164461	−	0.284854i
$447$	−3.10129	−	1.79053i	−0.146686	−	0.0846892i
$448$	19.9456	−	11.5156i	0.942342	−	0.544062i
$449$		−	37.8768i		−	1.78752i	−0.448550	−	0.893758i	$-0.648060\pi$
$449$		−	37.8768i		−	1.78752i	0.448550	−	0.893758i	$-0.351940\pi$
$450$		−	23.8681i		−	1.12516i
$451$	0.0470115	+	0.0814264i	0.00221369	+	0.00383422i
$452$	−10.3423	+	17.9134i	−0.486460	+	0.842573i
$453$	3.96490	−	2.28913i	0.186287	−	0.107553i
$454$	5.02624	−	8.70570i	0.235893	−	0.408579i
$455$	−45.9147	−	32.2912i	−2.15252	−	1.51383i
$456$	−3.40683	+	5.90081i	−0.159540	+	0.276331i
$457$			24.7668i			1.15854i	0.815134	+	0.579272i	$0.196663\pi$
$457$			24.7668i			1.15854i	−0.815134	+	0.579272i	$0.803337\pi$
$458$	−6.88189	−	11.9198i	−0.321569	−	0.556975i
$459$	−0.815591	−	1.41265i	−0.0380685	−	0.0659366i
$460$	20.6242	+	11.9074i	0.961609	+	0.555185i
$461$			35.5704i			1.65668i	0.560228	+	0.828338i	$0.310713\pi$
$461$			35.5704i			1.65668i	−0.560228	+	0.828338i	$0.689287\pi$
$462$	0.452043	−	0.260987i	0.0210310	−	0.0121422i
$463$			26.4008i			1.22695i	0.789715	+	0.613474i	$0.210229\pi$
$463$			26.4008i			1.22695i	−0.789715	+	0.613474i	$0.789771\pi$
$464$	1.61767			0.0750982
$465$	7.01508	−	4.13383i	0.325317	−	0.191702i
$466$		−	9.71950i		−	0.450247i
$467$	7.08448			0.327831			0.163915	−	0.986474i	$-0.447588\pi$
$467$	7.08448			0.327831			0.163915	+	0.986474i	$0.447588\pi$
$468$	10.9306	−	5.06959i	0.505266	−	0.234342i
$469$	34.5847			1.59697
$470$	−10.4727	−	6.04644i	−0.483072	−	0.278902i
$471$	−2.77794	−	4.81153i	−0.128001	−	0.221703i
$472$	5.74696	+	9.95403i	0.264525	+	0.458171i
$473$			0.980132i			0.0450665i
$474$	−2.09979	−	1.21232i	−0.0964466	−	0.0556835i
$475$	−48.5415	−	28.0254i	−2.22724	−	1.28590i
$476$	3.01506	+	1.74075i	0.138195	+	0.0797871i
$477$	3.27159	+	5.66655i	0.149796	+	0.259454i
$478$	8.42739	−	14.5967i	0.385460	−	0.667636i
$479$	4.07687	−	2.35378i	0.186277	−	0.107547i	−0.403962	−	0.914776i	$-0.632367\pi$
$479$	4.07687	−	2.35378i	0.186277	−	0.107547i	0.590238	+	0.807229i	$0.299034\pi$
$480$	8.06909			0.368302
$481$	23.9560	+	2.14568i	1.09230	+	0.0978346i
$482$	9.13611	+	15.8242i	0.416138	+	0.720773i
$483$	−7.47505	−	4.31572i	−0.340127	−	0.196372i
$484$	−6.37500	−	11.0418i	−0.289773	−	0.501901i
$485$	−4.60678	+	7.97917i	−0.209183	+	0.362316i
$486$	−7.70574	−	4.44891i	−0.349540	−	0.201807i
$487$	17.1608	+	9.90781i	0.777632	+	0.448966i	0.835590	−	0.549353i	$-0.185126\pi$
$487$	17.1608	+	9.90781i	0.777632	+	0.448966i	−0.0579586	+	0.998319i	$0.518459\pi$
$488$			33.5472i			1.51861i
$489$	3.95440	−	2.28308i	0.178824	−	0.103244i
$490$	−17.2406	−	29.8616i	−0.778850	−	1.34901i
$491$	−7.72222	+	13.3753i	−0.348499	+	0.603618i	−0.985983	−	0.166846i	$-0.946642\pi$
$491$	−7.72222	+	13.3753i	−0.348499	+	0.603618i	0.637484	+	0.770464i	$0.279975\pi$
$492$		−	0.119436i		−	0.00538460i
$493$	2.08324	+	3.60827i	0.0938243	+	0.162508i
$494$	−1.78051	+	19.8790i	−0.0801089	+	0.894397i
$495$	−3.84728			−0.172922
$496$	0.788854	+	1.33868i	0.0354206	+	0.0601084i
$497$	39.7779			1.78428
$498$	4.52467			0.202755
$499$	−36.1001	+	20.8424i	−1.61606	+	0.933034i	−0.628137	+	0.778103i	$0.716182\pi$
$499$	−36.1001	+	20.8424i	−1.61606	+	0.933034i	−0.987925	+	0.154931i	$0.950484\pi$
$500$			18.6097i			0.832250i
$501$	−0.00195621	−	0.00112942i	−8.73970e−5	−	5.04587e-5i
$502$	−15.5537	+	8.97995i	−0.694197	+	0.400795i
$503$	−12.5797	−	21.7887i	−0.560902	−	0.971511i	−0.997418	−	0.0718144i	$-0.977121\pi$
$503$	−12.5797	−	21.7887i	−0.560902	−	0.971511i	0.436516	−	0.899697i	$-0.356212\pi$
$504$	33.9604			1.51272
$505$	15.0335	+	8.67959i	0.668981	+	0.386236i
$506$	−0.877453	+	1.51979i	−0.0390075	+	0.0675630i
$507$	−3.25779	+	3.85011i	−0.144683	+	0.170989i
$508$	7.56672	+	13.1059i	0.335719	+	0.581482i
$509$	25.4518	+	14.6946i	1.12813	+	0.651328i	0.943465	−	0.331473i	$-0.107546\pi$
$509$	25.4518	+	14.6946i	1.12813	+	0.651328i	0.184668	+	0.982801i	$0.440879\pi$
$510$	−0.478033	−	0.827978i	−0.0211677	−	0.0366635i
$511$	−8.20469			−0.362954
$512$			3.15046i			0.139232i
$513$	−11.9613	+	6.90585i	−0.528104	+	0.304901i
$514$	12.7861	+	7.38203i	0.563969	+	0.325607i
$515$	−35.3915	+	20.4333i	−1.55953	+	0.900398i
$516$	0.622524	−	1.07824i	0.0274051	−	0.0474670i
$517$	−0.631674	+	1.09409i	−0.0277810	+	0.0481181i
$518$	21.7008	+	12.5290i	0.953479	+	0.550492i
$519$	0.959812			0.0421311
$520$	35.5800	−	16.5020i	1.56029	−	0.723659i
$521$	−11.8267	−	20.4845i	−0.518137	−	0.897440i	−0.999778	−	0.0210715i	$-0.993292\pi$
$521$	−11.8267	−	20.4845i	−0.518137	−	0.897440i	0.481641	−	0.876369i	$-0.340041\pi$
$522$	13.0101	+	7.51138i	0.569436	+	0.328764i
$523$	−19.8878			−0.869634			−0.434817	−	0.900519i	$-0.643187\pi$
$523$	−19.8878			−0.869634			−0.434817	+	0.900519i	$0.643187\pi$
$524$	2.39113	+	4.14156i	0.104457	+	0.180925i
$525$		−	14.7563i		−	0.644019i
$526$		−	7.38790i		−	0.322128i
$527$	−1.97009	+	3.48353i	−0.0858185	+	0.151745i
$528$			0.0387794i			0.00168766i
$529$	6.01935			0.261711
$530$	3.93636	+	6.81798i	0.170985	+	0.296154i
$531$			11.3497i			0.492534i
$532$	14.7394	−	25.5294i	0.639035	−	1.10684i
$533$	−0.398228	−	0.858622i	−0.0172492	−	0.0371910i
$534$	1.88756	+	3.26935i	0.0816826	+	0.141478i
$535$			8.55839i			0.370012i
$536$	−12.0824	+	20.9273i	−0.521878	+	0.903920i
$537$	−3.26254	+	5.65088i	−0.140789	+	0.243853i
$538$	−16.7835	−	9.68998i	−0.723589	−	0.417765i
$539$	−3.11965	+	1.80113i	−0.134373	+	0.0775801i
$540$	8.68834	+	5.01621i	0.373887	+	0.215863i
$541$	24.5522	−	14.1752i	1.05558	−	0.609441i	0.131376	−	0.991333i	$-0.458061\pi$
$541$	24.5522	−	14.1752i	1.05558	−	0.609441i	0.924207	+	0.381892i	$0.124727\pi$
$542$	−4.15951			−0.178666
$543$	0.446787			0.0191735
$544$	−3.43462	+	1.98298i	−0.147258	+	0.0850195i
$545$	37.0126	−	64.1077i	1.58544	−	2.74607i
$546$	−4.76669	+	2.21079i	−0.203996	+	0.0946129i
$547$	12.3886	−	21.4576i	0.529696	−	0.917461i	−0.469704	−	0.882824i	$-0.655639\pi$
$547$	12.3886	−	21.4576i	0.529696	−	0.917461i	0.999400	−	0.0346367i	$-0.0110274\pi$
$548$	10.2991	+	5.94619i	0.439956	+	0.254008i
$549$	−16.5631	+	28.6881i	−0.706895	+	1.22438i
$550$	−3.00019			−0.127928
$551$	30.5523	−	17.6394i	1.30157	−	0.751463i
$552$	5.22290	−	3.01544i	0.222301	−	0.128346i
$553$	24.5772	+	14.1896i	1.04513	+	0.603404i
$554$		−	30.1156i		−	1.27949i
$555$	4.87780	+	8.44859i	0.207051	+	0.358623i
$556$	25.9216			1.09932
$557$		−	27.4248i		−	1.16202i	−0.813895	−	0.581012i	$-0.802657\pi$
$557$		−	27.4248i		−	1.16202i	0.813895	−	0.581012i	$-0.197343\pi$
$558$	0.128419	+	14.4293i	0.00543641	+	0.610839i
$559$	0.880187	−	9.82709i	0.0372280	−	0.415642i
$560$	4.34474			0.183599
$561$	−0.0864991	+	0.0499403i	−0.00365200	+	0.00210848i
$562$	17.7079			0.746964
$563$	1.39229	−	2.41152i	0.0586782	−	0.101634i	−0.835194	−	0.549955i	$-0.814645\pi$
$563$	1.39229	−	2.41152i	0.0586782	−	0.101634i	0.893872	+	0.448322i	$0.147978\pi$
$564$	1.38981	−	0.802406i	0.0585215	−	0.0337874i
$565$	−57.5777	+	33.2425i	−2.42231	+	1.39852i
$566$		−	16.1365i		−	0.678266i
$567$	27.4265	+	15.8347i	1.15180	+	0.664994i
$568$	−13.8966	+	24.0696i	−0.583089	+	1.00994i
$569$	−6.86922	+	11.8978i	−0.287973	+	0.498783i	−0.973326	−	0.229428i	$-0.926315\pi$
$569$	−6.86922	+	11.8978i	−0.287973	+	0.498783i	0.685353	+	0.728211i	$0.259648\pi$
$570$	−7.01073	+	4.04765i	−0.293647	+	0.169537i
$571$	13.1347	−	22.7501i	0.549672	−	0.952060i	−0.448625	−	0.893720i	$-0.648086\pi$
$571$	13.1347	−	22.7501i	0.549672	−	0.952060i	0.998297	−	0.0583397i	$-0.0185807\pi$
$572$	−0.637240	−	1.37396i	−0.0266443	−	0.0574480i
$573$	−2.26362			−0.0945639
$574$		−	0.986065i		−	0.0411576i
$575$	24.8058	+	42.9648i	1.03447	+	1.79176i
$576$	−7.94510	+	13.7613i	−0.331046	+	0.573389i
$577$	10.5431	−	6.08703i	0.438913	−	0.253407i	−0.264223	−	0.964462i	$-0.585116\pi$
$577$	10.5431	−	6.08703i	0.438913	−	0.253407i	0.703136	+	0.711055i	$0.251782\pi$
$578$	−12.9834	−	7.49599i	−0.540039	−	0.311792i
$579$	0.716295	+	0.413553i	0.0297682	+	0.0171867i
$580$	−22.1923	−	12.8127i	−0.921486	−	0.532020i
$581$	−52.9593			−2.19712
$582$	0.431227	+	0.746907i	0.0178749	+	0.0309603i
$583$	0.712276	−	0.411233i	0.0294995	−	0.0170315i
$584$	2.86635	−	4.96467i	0.118610	−	0.205439i
$585$	38.5739	+	3.45497i	1.59483	+	0.142845i
$586$	0.202258	+	0.350321i	0.00835520	+	0.0144716i
$587$		−	29.9359i		−	1.23559i	−0.786340	−	0.617793i	$-0.788027\pi$
$587$		−	29.9359i		−	1.23559i	0.786340	−	0.617793i	$-0.211973\pi$
$588$	4.57590			0.188707
$589$	29.4961	+	16.6813i	1.21536	+	0.687342i
$590$			13.6559i			0.562204i
$591$		−	10.1061i		−	0.415710i
$592$	−1.61223	+	0.930823i	−0.0662624	+	0.0382566i
$593$			13.7440i			0.564397i	0.959356	+	0.282199i	$0.0910637\pi$
$593$			13.7440i			0.564397i	−0.959356	+	0.282199i	$0.908936\pi$
$594$	−0.369644	+	0.640241i	−0.0151667	+	0.0262694i
$595$	5.59517	+	9.69113i	0.229380	+	0.397297i
$596$	−9.37496	+	5.41264i	−0.384013	+	0.221710i
$597$	−7.87753			−0.322406
$598$	10.1624	−	14.4499i	0.415572	−	0.590900i
$599$	20.5094	−	35.5233i	0.837991	−	1.45144i	−0.0535801	−	0.998564i	$-0.517063\pi$
$599$	20.5094	−	35.5233i	0.837991	−	1.45144i	0.891571	−	0.452880i	$-0.149603\pi$
$600$	8.92907	+	5.15520i	0.364528	+	0.210460i
$601$	−14.5900	−	25.2707i	−0.595139	−	1.03081i	−0.993527	−	0.113594i	$-0.963764\pi$
$601$	−14.5900	−	25.2707i	−0.595139	−	1.03081i	0.398388	−	0.917217i	$-0.369570\pi$
$602$	5.13956	−	8.90198i	0.209473	−	0.362818i
$603$	−20.6646	+	11.9307i	−0.841528	+	0.485857i
$604$		−	13.8398i		−	0.563132i
$605$		−	40.9815i		−	1.66614i
$606$	1.40724	−	0.812470i	0.0571652	−	0.0330044i
$607$	−12.6001	+	21.8240i	−0.511421	+	0.885808i	0.488491	+	0.872569i	$0.337547\pi$
$607$	−12.6001	+	21.8240i	−0.511421	+	0.885808i	−0.999912	+	0.0132387i	$0.995786\pi$
$608$	16.7905	+	29.0819i	0.680943	+	1.17943i
$609$	8.04340	+	4.64386i	0.325935	+	0.188179i
$610$	−19.9286	+	34.5174i	−0.806887	+	1.39757i
$611$	7.31587	−	10.4024i	0.295968	−	0.420836i
$612$	−2.40203			−0.0970963
$613$	−24.7990	+	14.3177i	−1.00162	+	0.578287i	−0.908728	−	0.417389i	$-0.862945\pi$
$613$	−24.7990	+	14.3177i	−1.00162	+	0.578287i	−0.0928949	+	0.995676i	$0.529612\pi$
$614$	−0.0510032	−	0.0883401i	−0.00205832	−	0.00356512i
$615$	0.191948	−	0.332464i	0.00774009	−	0.0134062i
$616$		−	4.26877i		−	0.171994i
$617$	19.4862	−	11.2504i	0.784486	−	0.452923i	−0.0535315	−	0.998566i	$-0.517048\pi$
$617$	19.4862	−	11.2504i	0.784486	−	0.452923i	0.838018	+	0.545643i	$0.183714\pi$
$618$			3.82540i			0.153880i
$619$		−	29.1973i		−	1.17354i	−0.809754	−	0.586770i	$-0.800399\pi$
$619$		−	29.1973i		−	1.17354i	0.809754	−	0.586770i	$-0.199601\pi$
$620$	−0.219054	−	24.6131i	−0.00879743	−	0.988486i
$621$	12.2250			0.490570
$622$		−	18.7187i		−	0.750551i
$623$	−22.0930	−	38.2663i	−0.885139	−	1.53311i
$624$	0.0348250	−	0.388813i	0.00139412	−	0.0155650i
$625$	−6.88404	+	11.9235i	−0.275362	+	0.476941i
$626$	4.36408	−	2.51960i	0.174424	−	0.100704i
$627$	0.422859	+	0.732414i	0.0168874	+	0.0292498i
$628$	−16.7950			−0.670192
$629$	−4.15248	−	2.39744i	−0.165570	−	0.0955921i
$630$	34.9426	+	20.1741i	1.39215	+	0.803756i
$631$	−11.7942	−	6.80937i	−0.469519	−	0.271077i	0.246519	−	0.969138i	$-0.420713\pi$
$631$	−11.7942	−	6.80937i	−0.469519	−	0.271077i	−0.716038	+	0.698061i	$0.754046\pi$
$632$	−17.1723	+	9.91445i	−0.683079	+	0.394376i
$633$	2.59989	−	4.50315i	0.103337	−	0.178984i
$634$	−1.09514	−	1.89684i	−0.0434935	−	0.0753330i
$635$			48.6424i			1.93032i
$636$	−1.04477			−0.0414277
$637$	32.8959	−	15.2571i	1.30338	−	0.604509i
$638$	0.944168	−	1.63535i	0.0373800	−	0.0647440i
$639$	−23.7676	+	13.7222i	−0.940230	+	0.542842i
$640$	11.2393	−	19.4671i	0.444273	−	0.769504i
$641$	14.0757	−	24.3799i	0.555958	−	0.962948i	−0.441870	−	0.897079i	$-0.645685\pi$
$641$	14.0757	−	24.3799i	0.555958	−	0.962948i	0.997828	−	0.0658686i	$-0.0209818\pi$
$642$	0.693796	+	0.400563i	0.0273819	+	0.0158090i
$643$			10.7145i			0.422540i	0.977428	+	0.211270i	$0.0677600\pi$
$643$			10.7145i			0.422540i	−0.977428	+	0.211270i	$0.932240\pi$
$644$	−22.5965	+	13.0461i	−0.890427	+	0.514088i
$645$	3.46573	−	2.00094i	0.136463	−	0.0787869i
$646$	1.98942	−	3.44578i	0.0782727	−	0.135572i
$647$	22.4955			0.884388			0.442194	−	0.896919i	$-0.354200\pi$
$647$	22.4955			0.884388			0.442194	+	0.896919i	$0.354200\pi$
$648$	−19.1632	+	11.0639i	−0.752800	+	0.434629i
$649$	1.42663			0.0560003
$650$	30.0807	+	2.69426i	1.17986	+	0.105677i
$651$	0.0793941	+	8.92079i	0.00311170	+	0.349633i
$652$		−	13.8031i		−	0.540572i
$653$	−19.7254			−0.771915			−0.385957	−	0.922517i	$-0.626129\pi$
$653$	−19.7254			−0.771915			−0.385957	+	0.922517i	$0.626129\pi$
$654$	−3.46464	−	6.00093i	−0.135478	−	0.234655i
$655$			15.3713i			0.600607i
$656$	0.0634436	+	0.0366292i	0.00247706	+	0.00143013i
$657$	4.90236	−	2.83038i	0.191259	−	0.110424i
$658$	11.4743	−	6.62466i	0.447313	−	0.258256i
$659$	31.4173			1.22384			0.611922	−	0.790918i	$-0.290397\pi$
$659$	31.4173			1.22384			0.611922	+	0.790918i	$0.290397\pi$
$660$	0.307153	−	0.532005i	0.0119559	−	0.0207082i
$661$	3.40515	+	1.96596i	0.132445	+	0.0764671i	0.564759	−	0.825256i	$-0.308969\pi$
$661$	3.40515	+	1.96596i	0.132445	+	0.0764671i	−0.432314	+	0.901723i	$0.642303\pi$
$662$	11.2625	−	19.5073i	0.437730	−	0.758171i
$663$	0.912113	−	0.423037i	0.0354235	−	0.0164294i
$664$	18.5016	−	32.0457i	0.718002	−	1.24362i
$665$	82.0576	−	47.3760i	3.18206	−	1.83716i
$666$	−17.2885			−0.669917
$667$	−31.2258			−1.20907
$668$	−0.00591347	+	0.00341415i	−0.000228799	+	0.000132097i
$669$	2.56603	+	1.48150i	0.0992085	+	0.0572780i
$670$	−24.8636	+	14.3550i	−0.960565	+	0.554582i
$671$	3.60605	+	2.08195i	0.139210	+	0.0803729i
$672$	−4.42037	+	7.65631i	−0.170520	+	0.295348i
$673$	−9.55937	+	16.5573i	−0.368487	+	0.638238i	−0.989329	−	0.145698i	$-0.953457\pi$
$673$	−9.55937	+	16.5573i	−0.368487	+	0.638238i	0.620842	+	0.783935i	$0.286791\pi$
$674$			0.713964i			0.0275009i
$675$	10.4499	+	18.0997i	0.402217	+	0.696659i
$676$	5.15529	+	14.3479i	0.198281	+	0.551844i
$677$	−18.7512	+	32.4780i	−0.720667	+	1.24823i	0.240066	+	0.970757i	$0.422831\pi$
$677$	−18.7512	+	32.4780i	−0.720667	+	1.24823i	−0.960733	+	0.277475i	$0.910502\pi$
$678$			6.22347i			0.239011i
$679$	−5.04732	−	8.74222i	−0.193699	−	0.335496i
$680$	−7.81882			−0.299838
$681$			4.28791i			0.164313i
$682$	1.81373	−	0.0161420i	0.0694514	−	0.000618111i
$683$			38.4580i			1.47156i	0.677223	+	0.735778i	$0.263183\pi$
$683$			38.4580i			1.47156i	−0.677223	+	0.735778i	$0.736817\pi$
$684$			20.3387i			0.777670i
$685$	19.1124	+	33.1037i	0.730249	+	1.26483i
$686$	11.4841			0.438464
$687$	5.08441	+	2.93548i	0.193982	+	0.111996i
$688$	0.381836	+	0.661360i	0.0145574	+	0.0252141i
$689$	−7.51079	+	3.48349i	−0.286138	+	0.132711i
$690$	7.16527			0.272777
$691$	−25.3906	−	14.6593i	−0.965904	−	0.557665i	−0.0679188	−	0.997691i	$-0.521636\pi$
$691$	−25.3906	−	14.6593i	−0.965904	−	0.557665i	−0.897985	+	0.440026i	$0.854969\pi$
$692$	1.45072	−	2.51272i	0.0551481	−	0.0955193i
$693$	2.10760	−	3.65047i	0.0800610	−	0.138670i
$694$	6.56109	−	3.78805i	0.249056	−	0.143792i
$695$	72.1557	+	41.6591i	2.73702	+	1.58022i
$696$	−5.62001	+	3.24472i	−0.213026	+	0.122991i
$697$			0.188685i			0.00714695i
$698$	22.6731			0.858191
$699$	2.07294	+	3.59043i	0.0784057	+	0.135803i
$700$	−38.6310	−	22.3036i	−1.46011	−	0.842998i
$701$	−21.2663	−	36.8343i	−0.803217	−	1.39121i	−0.917488	−	0.397763i	$-0.869787\pi$
$701$	−21.2663	−	36.8343i	−0.803217	−	1.39121i	0.114271	−	0.993450i	$-0.463547\pi$
$702$	4.28111	−	6.08729i	0.161580	−	0.229750i
$703$	−20.2998	+	35.1603i	−0.765622	+	1.32610i
$704$	1.72978	+	0.998687i	0.0651934	+	0.0376394i
$705$	5.15824			0.194271
$706$	−12.1810	−	21.0982i	−0.458439	−	0.794039i
$707$	−16.4711	+	9.50962i	−0.619461	+	0.357646i
$708$	−1.56944	−	0.906117i	−0.0589832	−	0.0340540i
$709$			12.5966i			0.473075i	0.971622	+	0.236537i	$0.0760126\pi$
$709$			12.5966i			0.473075i	−0.971622	+	0.236537i	$0.923987\pi$
$710$	−28.5971	+	16.5105i	−1.07323	+	0.619629i
$711$	−19.5800			−0.734309
$712$	30.8733			1.15703
$713$	−15.2272	−	25.8405i	−0.570265	−	0.967734i
$714$	1.04750			0.0392015
$715$	0.434284	−	4.84868i	0.0162413	−	0.181330i
$716$	9.86240	+	17.0822i	0.368575	+	0.638391i
$717$			7.18945i			0.268495i
$718$	13.6365	−	23.6192i	0.508911	−	0.881460i
$719$	19.4311	+	33.6557i	0.724658	+	1.25515i	0.959114	+	0.283018i	$0.0913358\pi$
$719$	19.4311	+	33.6557i	0.724658	+	1.25515i	−0.234456	+	0.972127i	$0.575331\pi$
$720$	−2.59601	+	1.49881i	−0.0967477	+	0.0558573i
$721$		−	44.7746i		−	1.66749i
$722$	−14.2107	−	8.20454i	−0.528867	−	0.305341i
$723$	−6.74985	−	3.89703i	−0.251030	−	0.144932i
$724$	0.675302	−	1.16966i	0.0250974	−	0.0434699i
$725$	−26.6918	−	46.2316i	−0.991309	−	1.71700i
$726$	−3.32221	−	1.91808i	−0.123299	−	0.0711866i
$727$	−3.60003	−	6.23544i	−0.133518	−	0.231260i	0.791512	−	0.611153i	$-0.209294\pi$
$727$	−3.60003	−	6.23544i	−0.133518	−	0.231260i	−0.925030	+	0.379893i	$0.875961\pi$
$728$	−3.83348	+	42.7999i	−0.142078	+	1.58627i
$729$	−19.2088			−0.711435
$730$	5.89850	−	3.40550i	0.218313	−	0.126043i
$731$	−0.983462	+	1.70341i	−0.0363746	+	0.0630027i
$732$	−2.64467	−	4.58071i	−0.0977500	−	0.169308i
$733$	13.1856	+	7.61271i	0.487022	+	0.281182i	0.723338	−	0.690494i	$-0.242607\pi$
$733$	13.1856	+	7.61271i	0.487022	+	0.281182i	−0.236316	+	0.971676i	$0.575940\pi$
$734$	0.846900	+	0.488958i	0.0312596	+	0.0180478i
$735$	12.7375	+	7.35401i	0.469830	+	0.271257i
$736$		−	29.7230i		−	1.09560i
$737$	1.49967	+	2.59751i	0.0552411	+	0.0956805i
$738$	0.340164	+	0.589181i	0.0125216	+	0.0216881i
$739$	−40.5581	−	23.4162i	−1.49195	−	0.861380i	−0.491997	−	0.870597i	$-0.663733\pi$
$739$	−40.5581	−	23.4162i	−1.49195	−	0.861380i	−0.999958	+	0.00921712i	$0.997066\pi$
$740$	29.4904			1.08409
$741$	−3.58198	−	7.72313i	−0.131587	−	0.283716i
$742$	−8.62559			−0.316655
$743$			28.0698i			1.02978i	0.857256	+	0.514891i	$0.172168\pi$
$743$			28.0698i			1.02978i	−0.857256	+	0.514891i	$0.827832\pi$
$744$	−5.42572	−	3.06849i	−0.198917	−	0.112496i
$745$	−34.7950			−1.27479
$746$			22.8884i			0.838006i
$747$	31.6436	−	18.2694i	1.15778	−	0.668443i
$748$			0.301931i			0.0110397i
$749$	−8.12058	−	4.68842i	−0.296719	−	0.171311i
$750$	2.79959	+	4.84904i	0.102227	+	0.177062i
$751$	3.14791	+	5.45234i	0.114869	+	0.198959i	0.917727	−	0.397211i	$-0.130022\pi$
$751$	3.14791	+	5.45234i	0.114869	+	0.198959i	−0.802858	+	0.596170i	$0.796689\pi$
$752$			0.984341i			0.0358952i
$753$	3.83042	−	6.63448i	0.139588	−	0.241774i
$754$	−10.9351	+	15.5486i	−0.398232	+	0.566245i
$755$	22.2421	−	38.5245i	0.809473	−	1.40205i
$756$	−9.51921	+	5.49592i	−0.346210	+	0.199885i
$757$	−0.383099	+	0.663547i	−0.0139240	+	0.0241170i	−0.872903	−	0.487893i	$-0.837766\pi$
$757$	−0.383099	+	0.663547i	−0.0139240	+	0.0241170i	0.858979	+	0.512010i	$0.171099\pi$
$758$	3.76884	+	6.52783i	0.136891	+	0.237101i
$759$		−	0.748559i		−	0.0271710i
$760$			66.2042i			2.40148i
$761$	10.5386	−	6.08448i	0.382025	−	0.220562i	−0.296674	−	0.954979i	$-0.595877\pi$
$761$	10.5386	−	6.08448i	0.382025	−	0.220562i	0.678699	+	0.734416i	$0.262544\pi$
$762$	3.94325	+	2.27664i	0.142849	+	0.0824738i
$763$	40.5521	+	70.2383i	1.46809	+	2.54280i
$764$	−3.42137	+	5.92598i	−0.123781	+	0.214395i
$765$	−6.68632	−	3.86035i	−0.241744	−	0.139571i
$766$	−7.79231	+	13.4967i	−0.281547	+	0.487654i
$767$	−14.3038	−	1.28116i	−0.516482	−	0.0462600i
$768$	−3.21554	−	5.56947i	−0.116031	−	0.200971i
$769$	−24.4585	+	14.1211i	−0.881998	+	0.509222i	−0.871317	−	0.490721i	$-0.836733\pi$
$769$	−24.4585	+	14.1211i	−0.881998	+	0.509222i	−0.0106810	+	0.999943i	$0.503400\pi$
$770$	2.53585	−	4.39223i	0.0913858	−	0.158285i
$771$	−6.29764			−0.226804
$772$	2.16530	−	1.25014i	0.0779310	−	0.0449935i
$773$		−	27.8915i		−	1.00319i	−0.865103	−	0.501594i	$-0.832747\pi$
$773$		−	27.8915i		−	1.00319i	0.865103	−	0.501594i	$-0.167253\pi$
$774$			7.09200i			0.254917i
$775$	25.2421	−	44.6333i	0.906723	−	1.60327i
$776$	7.05324			0.253197
$777$	−10.6885			−0.383449
$778$	−0.00931648	+	0.00537887i	−0.000334012	+	0.000192842i
$779$	1.59765			0.0572418
$780$	−3.55736	+	5.05820i	−0.127374	+	0.181113i
$781$	1.72486	+	2.98754i	0.0617203	+	0.106903i
$782$	−3.04991	+	1.76087i	−0.109065	+	0.0629684i
$783$	−13.1545			−0.470102
$784$	−1.40336	+	2.43068i	−0.0501198	+	0.0868101i
$785$	−46.7506	−	26.9915i	−1.66860	−	0.963368i
$786$	1.24609	+	0.719431i	0.0444466	+	0.0256613i
$787$	21.3041	−	12.2999i	0.759409	−	0.438445i	−0.0696746	−	0.997570i	$-0.522196\pi$
$787$	21.3041	−	12.2999i	0.759409	−	0.438445i	0.829083	+	0.559125i	$0.188863\pi$
$788$	−26.4571	−	15.2750i	−0.942495	−	0.544150i
$789$	1.57566	+	2.72913i	0.0560951	+	0.0971595i
$790$	−23.5586			−0.838179
$791$		−	72.8430i		−	2.59000i
$792$	1.47260	+	2.55062i	0.0523266	+	0.0906323i
$793$	−34.2856	−	24.1126i	−1.21752	−	0.856263i
$794$	0.408838	+	0.708128i	0.0145091	+	0.0251305i
$795$	−2.90822	−	1.67906i	−0.103144	−	0.0595502i
$796$	−11.9066	+	20.6228i	−0.422018	+	0.730956i
$797$	21.9092	−	37.9478i	0.776063	−	1.34418i	−0.158132	−	0.987418i	$-0.550547\pi$
$797$	21.9092	−	37.9478i	0.776063	−	1.34418i	0.934195	−	0.356763i	$-0.116120\pi$
$798$		−	8.86945i		−	0.313975i
$799$	−2.19561	+	1.26764i	−0.0776753	+	0.0448458i
$800$	44.0066	−	25.4072i	1.55587	−	0.898282i
$801$	26.4015	+	15.2429i	0.932852	+	0.538582i
$802$	23.7453			0.838477
$803$	−0.355774	−	0.616219i	−0.0125550	−	0.0217459i
$804$		−	3.81003i		−	0.134369i
$805$	−83.8665			−2.95590
$806$	−18.1995	−	1.46694i	−0.641050	−	0.0516708i
$807$	8.26656			0.290997
$808$		−	13.2889i		−	0.467504i
$809$	9.05636	+	15.6861i	0.318405	+	0.551493i	0.980155	−	0.198231i	$-0.0635196\pi$
$809$	9.05636	+	15.6861i	0.318405	+	0.551493i	−0.661751	+	0.749724i	$0.730186\pi$
$810$	−26.2899			−0.923732
$811$	−29.8327	−	17.2239i	−1.04757	−	0.604813i	−0.125600	−	0.992081i	$-0.540086\pi$
$811$	−29.8327	−	17.2239i	−1.04757	−	0.604813i	−0.921967	+	0.387268i	$0.873419\pi$
$812$	24.3146	−	14.0380i	0.853275	−	0.492638i
$813$	1.53654	−	0.887124i	0.0538889	−	0.0311128i
$814$			2.17314i			0.0761685i
$815$	22.1832	−	38.4225i	0.777045	−	1.34588i
$816$	−0.0389111	+	0.0673960i	−0.00136216	+	0.00235933i
$817$	14.4232	+	8.32726i	0.504605	+	0.291334i
$818$	−10.6847	−	18.5065i	−0.373582	−	0.647063i
$819$	−24.4096	+	34.7079i	−0.852940	+	1.21279i
$820$	−0.580244	−	1.00501i	−0.0202630	−	0.0350965i
$821$			19.9966i			0.697887i	0.937144	+	0.348944i	$0.113460\pi$
$821$			19.9966i			0.697887i	−0.937144	+	0.348944i	$0.886540\pi$
$822$	3.57812			0.124801
$823$	−11.2078	−	19.4126i	−0.390681	−	0.676679i	0.601858	−	0.798603i	$-0.294427\pi$
$823$	−11.2078	−	19.4126i	−0.390681	−	0.676679i	−0.992540	+	0.121923i	$0.961094\pi$
$824$	27.0932	+	15.6423i	0.943836	+	0.544924i
$825$	1.10828	−	0.639868i	0.0385855	−	0.0222773i
$826$	−12.9573	−	7.48090i	−0.450842	−	0.260294i
$827$	−24.9689	−	14.4158i	−0.868252	−	0.501286i	−0.00148503	−	0.999999i	$-0.500473\pi$
$827$	−24.9689	−	14.4158i	−0.868252	−	0.501286i	−0.866767	+	0.498713i	$0.833806\pi$
$828$	9.00105	−	15.5903i	0.312808	−	0.541800i
$829$	−32.9374			−1.14396			−0.571981	−	0.820267i	$-0.693825\pi$
$829$	−32.9374			−1.14396			−0.571981	+	0.820267i	$0.693825\pi$
$830$	38.0734	−	21.9817i	1.32155	−	0.762996i
$831$	6.42295	+	11.1249i	0.222810	+	0.385917i
$832$	−16.4464	−	11.5665i	−0.570176	−	0.400997i
$833$	−7.22899			−0.250470
$834$	6.75428	−	3.89959i	0.233882	−	0.135032i
$835$	−0.0219477			−0.000759533
$836$	2.55654			0.0884198
$837$	−6.41476	−	10.8858i	−0.221727	−	0.376268i
$838$			7.21281i			0.249163i
$839$			24.5883i			0.848883i	0.905455	+	0.424441i	$0.139530\pi$
$839$			24.5883i			0.848883i	−0.905455	+	0.424441i	$0.860470\pi$
$840$	−15.0943	+	8.71469i	−0.520802	+	0.300685i
$841$	4.59998			0.158620
$842$	5.35032	−	9.26703i	0.184384	−	0.319363i
$843$	−6.54140	+	3.77668i	−0.225298	+	0.130076i
$844$	−7.85928	−	13.6127i	−0.270528	−	0.468568i
$845$	−8.70851	+	48.2242i	−0.299582	+	1.65896i
$846$	−4.57063	+	7.91657i	−0.157142	+	0.272177i
$847$	38.8851	+	22.4503i	1.33611	+	0.771401i
$848$	0.320413	−	0.554972i	0.0110030	−	0.0190578i
$849$	3.44152	+	5.96089i	0.118113	+	0.204577i
$850$	−5.21413	−	3.01038i	−0.178843	−	0.103255i
$851$	31.1209	−	17.9677i	1.06681	−	0.615924i
$852$		−	4.38213i		−	0.150129i
$853$		−	21.0981i		−	0.722385i	−0.932491	−	0.361192i	$-0.882370\pi$
$853$		−	21.0981i		−	0.722385i	0.932491	−	0.361192i	$-0.117630\pi$
$854$	−21.8344	−	37.8183i	−0.747159	−	1.29412i
$855$	−32.6867	+	56.6150i	−1.11786	+	1.93619i
$856$	5.67394	−	3.27585i	0.193931	−	0.111966i
$857$	−27.1482	+	47.0221i	−0.927365	+	1.60624i	−0.139652	+	0.990201i	$0.544598\pi$
$857$	−27.1482	+	47.0221i	−0.927365	+	1.60624i	−0.787713	+	0.616042i	$0.788735\pi$
$858$	−0.372737	−	0.262141i	−0.0127250	−	0.00894934i
$859$	−7.24856	+	12.5549i	−0.247318	+	0.428367i	−0.962781	−	0.270284i	$-0.912882\pi$
$859$	−7.24856	+	12.5549i	−0.247318	+	0.428367i	0.715463	+	0.698651i	$0.246216\pi$
$860$		−	12.0974i		−	0.412517i
$861$	0.210304	+	0.364257i	0.00716714	+	0.0124139i
$862$	11.5152	+	19.9449i	0.392209	+	0.679325i
$863$	6.02331	+	3.47756i	0.205036	+	0.118377i	0.599002	−	0.800747i	$-0.295564\pi$
$863$	6.02331	+	3.47756i	0.205036	+	0.118377i	−0.393966	+	0.919125i	$0.628897\pi$
$864$		−	12.5214i		−	0.425986i
$865$	8.07647	−	4.66295i	0.274608	−	0.158545i
$866$		−	4.11887i		−	0.139965i
$867$	6.39486			0.217181
$868$	23.4740	+	13.2756i	0.796759	+	0.450603i
$869$			2.46118i			0.0834898i
$870$	−7.71007			−0.261396
$871$	−12.7035	−	27.3901i	−0.430442	−	0.928079i
$872$	−56.6684			−1.91903
$873$	6.03163	+	3.48236i	0.204140	+	0.117860i
$874$	14.9098	+	25.8245i	0.504331	+	0.873526i
$875$	−32.7680	−	56.7559i	−1.10776	−	1.91870i
$876$			0.903869i			0.0305389i
$877$	−4.05976	−	2.34390i	−0.137088	−	0.0791480i	0.429887	−	0.902883i	$-0.358553\pi$
$877$	−4.05976	−	2.34390i	−0.137088	−	0.0791480i	−0.566976	+	0.823735i	$0.691887\pi$
$878$	13.3931	+	7.73250i	0.451995	+	0.260959i
$879$	−0.149430	−	0.0862735i	−0.00504015	−	0.00290993i
$880$	0.188398	+	0.326315i	0.00635089	+	0.0110001i
$881$	−12.8124	+	22.1917i	−0.431660	+	0.747656i	−0.997016	−	0.0771902i	$-0.975405\pi$
$881$	−12.8124	+	22.1917i	−0.431660	+	0.747656i	0.565357	+	0.824846i	$0.308738\pi$
$882$	−22.5730	+	13.0325i	−0.760072	+	0.438828i
$883$	9.22274			0.310370			0.155185	−	0.987885i	$-0.450403\pi$
$883$	9.22274			0.310370			0.155185	+	0.987885i	$0.450403\pi$
$884$	0.271143	−	3.02725i	0.00911953	−	0.101817i
$885$	−2.91247	−	5.04455i	−0.0979017	−	0.169571i
$886$	15.1107	+	8.72418i	0.507655	+	0.293095i
$887$	−4.78177	−	8.28228i	−0.160556	−	0.278092i	0.774512	−	0.632559i	$-0.217995\pi$
$887$	−4.78177	−	8.28228i	−0.160556	−	0.278092i	−0.935068	+	0.354468i	$0.884662\pi$
$888$	3.73409	−	6.46764i	0.125308	−	0.217040i
$889$	−46.1541	−	26.6471i	−1.54796	−	0.893714i
$890$	31.7662	+	18.3402i	1.06481	+	0.614766i
$891$			2.74651i			0.0920116i
$892$	7.75691	−	4.47846i	0.259721	−	0.149950i
$893$	10.7335	+	18.5909i	0.359182	+	0.622121i
$894$	−1.62853	+	2.82069i	−0.0544661	+	0.0943381i
$895$			63.4001i			2.11923i
$896$	12.3141	+	21.3287i	0.411387	+	0.712542i
$897$	−0.672227	+	7.50526i	−0.0224450	+	0.250593i
$898$	−34.4498			−1.14960
$899$	16.3850	+	27.8052i	0.546471	+	0.927356i
$900$	30.7764			1.02588
$901$	1.65052			0.0549868
$902$	0.0740591	−	0.0427580i	0.00246590	−	0.00142369i
$903$			4.38458i			0.145910i
$904$	44.0774	+	25.4481i	1.46599	+	0.846392i
$905$	3.75955	−	2.17058i	0.124972	−	0.0721525i
$906$	−2.08202	−	3.60616i	−0.0691704	−	0.119807i
$907$	−54.1844			−1.79916			−0.899582	−	0.436752i	$-0.856129\pi$
$907$	−54.1844			−1.79916			−0.899582	+	0.436752i	$0.856129\pi$
$908$	11.2254	+	6.48100i	0.372529	+	0.215080i
$909$	6.56108	−	11.3641i	0.217617	−	0.376924i
$910$	−29.3696	+	41.7605i	−0.973591	+	1.38435i
$911$	−26.3790	−	45.6897i	−0.873974	−	1.51377i	−0.857852	−	0.513897i	$-0.828201\pi$
$911$	−26.3790	−	45.6897i	−0.873974	−	1.51377i	−0.0161219	−	0.999870i	$-0.505132\pi$
$912$	0.570662	+	0.329472i	0.0188965	+	0.0109099i
$913$	−2.29644	−	3.97754i	−0.0760010	−	0.131638i
$914$	22.5260			0.745093
$915$		−	17.0012i		−	0.562043i
$916$	15.3698	−	8.87374i	0.507832	−	0.293197i
$917$	−14.5850	−	8.42064i	−0.481638	−	0.278074i
$918$	−1.28483	+	0.741798i	−0.0424058	+	0.0244830i
$919$	4.88900	−	8.46800i	0.161273	−	0.279333i	−0.774052	−	0.633122i	$-0.781773\pi$
$919$	4.88900	−	8.46800i	0.161273	−	0.279333i	0.935326	+	0.353788i	$0.115107\pi$
$920$	29.2992	−	50.7477i	0.965966	−	1.67310i
$921$	0.0376817	+	0.0217555i	0.00124165	+	0.000716869i
$922$	32.3520			1.06546
$923$	−14.6110	−	31.5030i	−0.480928	−	1.03693i
$924$	0.336526	+	0.582880i	0.0110709	+	0.0191754i
$925$	53.2043	+	30.7175i	1.74935	+	1.00999i
$926$	24.0121			0.789086
$927$	15.4460	+	26.7532i	0.507312	+	0.878689i
$928$			31.9830i			1.04989i
$929$		−	0.649852i		−	0.0213209i	−0.999943	−	0.0106605i	$-0.996607\pi$
$929$		−	0.649852i		−	0.0213209i	0.999943	−	0.0106605i	$-0.00339340\pi$
$930$	−3.75981	−	6.38037i	−0.123289	−	0.209221i
$931$			61.2100i			2.00608i
$932$	12.5327			0.410521
$933$	3.99225	+	6.91478i	0.130700	+	0.226380i
$934$		−	6.44349i		−	0.210838i
$935$	−0.485239	+	0.840459i	−0.0158690	+	0.0274859i
$936$	−12.4742	−	26.8957i	−0.407732	−	0.879113i
$937$	22.6947	+	39.3084i	0.741405	+	1.28415i	0.951856	+	0.306546i	$0.0991735\pi$
$937$	22.6947	+	39.3084i	0.741405	+	1.28415i	−0.210451	+	0.977604i	$0.567493\pi$
$938$		−	31.4556i		−	1.02706i
$939$	−1.07474	+	1.86151i	−0.0350729	+	0.0607480i
$940$	7.79649	−	13.5039i	0.254293	−	0.440449i
$941$	−41.2588	−	23.8208i	−1.34500	−	0.776536i	−0.357463	−	0.933927i	$-0.616358\pi$
$941$	−41.2588	−	23.8208i	−1.34500	−	0.776536i	−0.987536	+	0.157391i	$0.949692\pi$
$942$	−4.37619	+	2.52659i	−0.142584	+	0.0823209i
$943$	−1.22465	−	0.707053i	−0.0398801	−	0.0230248i
$944$	0.962645	−	0.555783i	0.0313314	−	0.0180892i
$945$	−35.3303			−1.14930
$946$	0.891452			0.0289836
$947$	−26.9859	+	15.5803i	−0.876924	+	0.506292i	−0.869643	−	0.493681i	$-0.835651\pi$
$947$	−26.9859	+	15.5803i	−0.876924	+	0.506292i	−0.00728105	+	0.999973i	$0.502318\pi$
$948$	1.56320	−	2.70754i	0.0507704	−	0.0879369i
$949$	3.01371	+	6.49788i	0.0978291	+	0.210930i
$950$	−25.4898	+	44.1496i	−0.826997	+	1.43240i
$951$	0.809100	+	0.467134i	0.0262369	+	0.0151479i
$952$	4.28327	−	7.41884i	0.138822	−	0.240446i
$953$	29.7162			0.962602			0.481301	−	0.876555i	$-0.340164\pi$
$953$	29.7162			0.962602			0.481301	+	0.876555i	$0.340164\pi$
$954$	5.15385	−	2.97558i	0.166862	−	0.0963379i
$955$	−19.0475	+	10.9971i	−0.616363	+	0.355857i
$956$	18.8215	+	10.8666i	0.608729	+	0.351450i
$957$			0.805474i			0.0260373i
$958$	−2.14082	−	3.70800i	−0.0691666	−	0.119800i
$959$	−41.8803			−1.35239
$960$		−	8.15527i		−	0.263210i
$961$	−15.0197	+	27.1184i	−0.484507	+	0.874787i
$962$	1.95154	−	21.7885i	0.0629203	−	0.702490i
$963$	6.46947			0.208476
$964$	−20.4043	+	11.7804i	−0.657177	+	0.379422i
$965$	8.03648			0.258703
$966$	−3.92525	+	6.79873i	−0.126293	+	0.218745i
$967$	−20.7111	+	11.9576i	−0.666026	+	0.384530i	−0.794569	−	0.607174i	$-0.792303\pi$
$967$	−20.7111	+	11.9576i	−0.666026	+	0.384530i	0.128543	+	0.991704i	$0.458970\pi$
$968$	−27.1694	+	15.6863i	−0.873258	+	0.504176i
$969$			1.69718i			0.0545213i
$970$	7.25723	+	4.18997i	0.233016	+	0.134532i
$971$	−6.09028	+	10.5487i	−0.195446	+	0.338523i	−0.947047	−	0.321096i	$-0.895949\pi$
$971$	−6.09028	+	10.5487i	−0.195446	+	0.338523i	0.751600	+	0.659619i	$0.229282\pi$
$972$	5.73658	−	9.93605i	0.184001	−	0.318699i
$973$	−79.0560	+	45.6430i	−2.53442	+	1.46325i
$974$	9.01138	−	15.6082i	0.288743	−	0.500118i
$975$	−11.6866	+	5.42023i	−0.374271	+	0.173586i
$976$	3.24432			0.103848
$977$			35.1295i			1.12389i	0.827174	+	0.561947i	$0.189947\pi$
$977$			35.1295i			1.12389i	−0.827174	+	0.561947i	$0.810053\pi$
$978$	−2.07651	−	3.59662i	−0.0663994	−	0.115007i
$979$	1.91601	−	3.31863i	0.0612360	−	0.106064i
$980$	38.5045	−	22.2306i	1.22998	−	0.710131i
$981$	−48.4604	−	27.9786i	−1.54722	−	0.893288i
$982$	12.1651	+	7.02353i	0.388205	+	0.224130i
$983$	−22.4036	−	12.9347i	−0.714564	−	0.412554i	0.0981849	−	0.995168i	$-0.468696\pi$
$983$	−22.4036	−	12.9347i	−0.714564	−	0.412554i	−0.812749	+	0.582615i	$0.802030\pi$
$984$	−0.293884			−0.00936866
$985$	−49.0975	−	85.0394i	−1.56438	−	2.70958i
$986$	3.28180	−	1.89475i	0.104514	−	0.0603411i
$987$	−2.82576	+	4.89437i	−0.0899451	+	0.155789i
$988$	−25.6326	−	2.29585i	−0.815482	−	0.0730407i
$989$	−7.37059	−	12.7662i	−0.234371	−	0.405943i
$990$			3.49918i			0.111211i
$991$	−22.0309			−0.699836			−0.349918	−	0.936780i	$-0.613790\pi$
$991$	−22.0309			−0.699836			−0.349918	+	0.936780i	$0.613790\pi$
$992$	−26.4671	+	15.5965i	−0.840331	+	0.495188i
$993$			9.60811i			0.304904i
$994$		−	36.1789i		−	1.14752i
$995$	−66.2866	+	38.2706i	−2.10143	+	1.21326i
$996$			5.83426i			0.184866i
$997$	26.4675	−	45.8431i	0.838235	−	1.45187i	−0.0531334	−	0.998587i	$-0.516921\pi$
$997$	26.4675	−	45.8431i	0.838235	−	1.45187i	0.891369	−	0.453279i	$-0.149746\pi$
$998$	18.9566	+	32.8338i	0.600062	+	1.03934i
$999$	13.1103	−	7.56922i	0.414791	−	0.239480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.13	✓	68
13.12	even	2	inner	403.2.l.c.25.22	yes	68
31.5	even	3	inner	403.2.l.c.129.13	yes	68
403.129	even	6	inner	403.2.l.c.129.22	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.13	✓	68	1.1	even	1	trivial
403.2.l.c.25.22	yes	68	13.12	even	2	inner
403.2.l.c.129.13	yes	68	31.5	even	3	inner
403.2.l.c.129.22	yes	68	403.129	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +O(q^{10})\)	\(q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +(1.71425 - 2.96916i) q^{10} +(-0.310190 - 0.179088i) q^{11} +(0.227493 + 0.394029i) q^{12} +(2.94922 + 2.07415i) q^{13} +(1.87818 + 3.25311i) q^{14} +1.46243i q^{15} -0.279074 q^{16} +(-0.359393 - 0.622486i) q^{17} +(-2.24445 - 1.29584i) q^{18} +(-5.27077 + 3.04308i) q^{19} +(3.82854 + 2.21041i) q^{20} +(-1.38762 - 0.801142i) q^{21} +(-0.162885 + 0.282124i) q^{22} +5.38696 q^{23} +(0.969545 - 0.559767i) q^{24} +(4.60478 + 7.97571i) q^{25} +(1.88648 - 2.68238i) q^{26} +2.26936 q^{27} +(-4.19467 + 2.42179i) q^{28} -5.79655 q^{29} +1.33011 q^{30} +(-2.82668 - 4.79686i) q^{31} -5.51758i q^{32} -0.138957i q^{33} +(-0.566165 + 0.326876i) q^{34} -15.5684 q^{35} +(1.67090 - 2.89408i) q^{36} +(5.77708 - 3.33540i) q^{37} +(2.76775 + 4.79389i) q^{38} +(-0.124788 + 1.39323i) q^{39} +(5.43891 - 9.42047i) q^{40} +(-0.227336 - 0.131253i) q^{41} +(-0.728657 + 1.26207i) q^{42} +(-1.36823 - 2.36984i) q^{43} +(-0.363781 - 0.210029i) q^{44} +(9.30224 - 5.37065i) q^{45} -4.89956i q^{46} -3.52717i q^{47} +(-0.0541346 - 0.0937638i) q^{48} +(5.02862 - 8.70982i) q^{49} +(7.25408 - 4.18815i) q^{50} +(0.139429 - 0.241499i) q^{51} +(3.45876 + 2.43250i) q^{52} +(-1.14813 + 1.98862i) q^{53} -2.06403i q^{54} +(-0.675082 - 1.16928i) q^{55} +(5.95904 + 10.3214i) q^{56} +(-2.04484 - 1.18059i) q^{57} +5.27209i q^{58} +(-3.44943 + 1.99153i) q^{59} +1.71510i q^{60} -11.6253 q^{61} +(-4.36285 + 2.57093i) q^{62} +11.7685i q^{63} -5.57651 q^{64} +(5.71852 + 12.3297i) q^{65} -0.126385 q^{66} +(-7.25205 - 4.18697i) q^{67} +(-0.421485 - 0.730033i) q^{68} +(1.04496 + 1.80992i) q^{69} +14.1598i q^{70} +(-8.34100 - 4.81568i) q^{71} +(-7.12114 - 4.11139i) q^{72} +(1.72044 + 0.993294i) q^{73} +(-3.03362 - 5.25439i) q^{74} +(-1.78646 + 3.09424i) q^{75} +(-6.18140 + 3.56883i) q^{76} +1.47928 q^{77} +(1.26717 + 0.113497i) q^{78} +(-3.43571 - 5.95083i) q^{79} +(-0.911045 - 0.525992i) q^{80} +(-3.83402 - 6.64072i) q^{81} +(-0.119377 + 0.206767i) q^{82} +(11.1050 + 6.41147i) q^{83} +(-1.62736 - 0.939555i) q^{84} -2.70950i q^{85} +(-2.15542 + 1.24443i) q^{86} +(-1.12441 - 1.94754i) q^{87} +(-0.516795 + 0.895115i) q^{88} +10.6987i q^{89} +(-4.88473 - 8.46060i) q^{90} +(-14.8317 - 1.32844i) q^{91} +6.31766 q^{92} +(1.06334 - 1.88021i) q^{93} -3.20804 q^{94} -22.9421 q^{95} +(1.85381 - 1.07030i) q^{96} +2.44420i q^{97} +(-7.92177 - 4.57364i) q^{98} +(-0.883881 + 0.510309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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