LMFDB - Embedded newform 675.2.l.g.151.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.11
Character	$\chi$	$=$	675.151
Dual form			675.2.l.g.76.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84958 + 1.55198i) q^{2} +(-1.53931 + 0.794060i) q^{3} +(0.665000 + 3.77140i) q^{4} +(-4.07944 - 0.920299i) q^{6} +(-0.0583477 + 0.330906i) q^{7} +(-2.20872 + 3.82562i) q^{8} +(1.73894 - 2.44461i) q^{9} +(-4.97408 + 1.81042i) q^{11} +(-4.01836 - 5.27730i) q^{12} +(-4.68414 + 3.93046i) q^{13} +(-0.621479 + 0.521483i) q^{14} +(-2.82523 + 1.02830i) q^{16} +(1.52112 + 2.63465i) q^{17} +(7.01028 - 1.82269i) q^{18} +(-0.260295 + 0.450843i) q^{19} +(-0.172944 - 0.555698i) q^{21} +(-12.0097 - 4.37117i) q^{22} +(0.0350517 + 0.198788i) q^{23} +(0.362131 - 7.64266i) q^{24} -14.7637 q^{26} +(-0.735594 + 5.14382i) q^{27} -1.28678 q^{28} +(1.41738 + 1.18933i) q^{29} +(-1.58422 - 8.98458i) q^{31} +(1.48070 + 0.538930i) q^{32} +(6.21906 - 6.73651i) q^{33} +(-1.27550 + 7.23373i) q^{34} +(10.3760 + 4.93257i) q^{36} +(3.11234 + 5.39074i) q^{37} +(-1.18114 + 0.429898i) q^{38} +(4.08931 - 9.76968i) q^{39} +(6.96293 - 5.84259i) q^{41} +(0.542558 - 1.29621i) q^{42} +(6.38441 - 2.32373i) q^{43} +(-10.1356 - 17.5553i) q^{44} +(-0.243684 + 0.422073i) q^{46} +(-2.11902 + 12.0175i) q^{47} +(3.53236 - 3.82627i) q^{48} +(6.47175 + 2.35553i) q^{49} +(-4.43354 - 2.84768i) q^{51} +(-17.9383 - 15.0520i) q^{52} -2.74867 q^{53} +(-9.34365 + 8.37227i) q^{54} +(-1.13705 - 0.954096i) q^{56} +(0.0426766 - 0.900676i) q^{57} +(0.775751 + 4.39950i) q^{58} +(-6.56519 - 2.38954i) q^{59} +(-2.16727 + 12.2912i) q^{61} +(11.0137 - 19.0764i) q^{62} +(0.707472 + 0.718062i) q^{63} +(4.90880 + 8.50230i) q^{64} +(21.9576 - 2.80784i) q^{66} +(4.29512 - 3.60403i) q^{67} +(-8.92479 + 7.48879i) q^{68} +(-0.211805 - 0.278163i) q^{69} +(1.58699 + 2.74874i) q^{71} +(5.51130 + 12.0520i) q^{72} +(-0.731226 + 1.26652i) q^{73} +(-2.60980 + 14.8009i) q^{74} +(-1.87341 - 0.681865i) q^{76} +(-0.308852 - 1.75159i) q^{77} +(22.7259 - 11.7233i) q^{78} +(-2.18198 - 1.83090i) q^{79} +(-2.95220 - 8.50203i) q^{81} +21.9461 q^{82} +(0.578595 + 0.485499i) q^{83} +(1.98075 - 1.02178i) q^{84} +(15.4149 + 5.61055i) q^{86} +(-3.12618 - 0.705250i) q^{87} +(4.06039 - 23.0276i) q^{88} +(-3.18070 + 5.50914i) q^{89} +(-1.02731 - 1.77934i) q^{91} +(-0.726400 + 0.264388i) q^{92} +(9.57291 + 12.5721i) q^{93} +(-22.5703 + 18.9387i) q^{94} +(-2.70719 + 0.346184i) q^{96} +(10.0155 - 3.64534i) q^{97} +(8.31429 + 14.4008i) q^{98} +(-4.22385 + 15.3079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.84958	+	1.55198i	1.30785	+	1.09742i	0.988731	+	0.149701i	$0.0478311\pi$
$2$	1.84958	+	1.55198i	1.30785	+	1.09742i	0.319118	+	0.947715i	$0.396613\pi$
$3$	−1.53931	+	0.794060i	−0.888720	+	0.458451i
$3$	−1.53931	+	0.794060i	−0.888720	+	0.458451i
$4$	0.665000	+	3.77140i	0.332500	+	1.88570i
$5$		0			0
$5$		0			0
$6$	−4.07944	−	0.920299i	−1.66542	−	0.375710i
$7$	−0.0583477	+	0.330906i	−0.0220534	+	0.125071i	−0.993847	−	0.110762i	$-0.964671\pi$
$7$	−0.0583477	+	0.330906i	−0.0220534	+	0.125071i	0.971794	+	0.235833i	$0.0757819\pi$
$8$	−2.20872	+	3.82562i	−0.780901	+	1.35256i
$9$	1.73894	−	2.44461i	0.579646	−	0.814869i
$10$		0			0
$11$	−4.97408	+	1.81042i	−1.49974	+	0.545861i	−0.955994	−	0.293387i	$-0.905217\pi$
$11$	−4.97408	+	1.81042i	−1.49974	+	0.545861i	−0.543748	+	0.839249i	$0.682995\pi$
$12$	−4.01836	−	5.27730i	−1.16000	−	1.52343i
$13$	−4.68414	+	3.93046i	−1.29915	+	1.09011i	−0.308855	+	0.951109i	$0.599946\pi$
$13$	−4.68414	+	3.93046i	−1.29915	+	1.09011i	−0.990292	+	0.139005i	$0.955610\pi$
$14$	−0.621479	+	0.521483i	−0.166097	+	0.139372i
$15$		0			0
$16$	−2.82523	+	1.02830i	−0.706307	+	0.257075i
$17$	1.52112	+	2.63465i	0.368925	+	0.638996i	0.989398	−	0.145231i	$-0.0463927\pi$
$17$	1.52112	+	2.63465i	0.368925	+	0.638996i	−0.620473	+	0.784228i	$0.713059\pi$
$18$	7.01028	−	1.82269i	1.65234	−	0.429613i
$19$	−0.260295	+	0.450843i	−0.0597157	+	0.103431i	−0.894338	−	0.447392i	$-0.852353\pi$
$19$	−0.260295	+	0.450843i	−0.0597157	+	0.103431i	0.834622	+	0.550823i	$0.185686\pi$
$20$		0			0
$21$	−0.172944	−	0.555698i	−0.0377396	−	0.121263i
$22$	−12.0097	−	4.37117i	−2.56047	−	0.931936i
$23$	0.0350517	+	0.198788i	0.00730878	+	0.0414501i	0.988244	−	0.152885i	$-0.0488563\pi$
$23$	0.0350517	+	0.198788i	0.00730878	+	0.0414501i	−0.980935	+	0.194335i	$0.937745\pi$
$24$	0.362131	−	7.64266i	0.0739197	−	1.56005i
$25$		0			0
$26$	−14.7637			−2.89540
$27$	−0.735594	+	5.14382i	−0.141565	+	0.989929i
$28$	−1.28678			−0.243179
$29$	1.41738	+	1.18933i	0.263201	+	0.220852i	0.764832	−	0.644230i	$-0.222822\pi$
$29$	1.41738	+	1.18933i	0.263201	+	0.220852i	−0.501631	+	0.865082i	$0.667266\pi$
$30$		0			0
$31$	−1.58422	−	8.98458i	−0.284535	−	1.61368i	−0.706942	−	0.707272i	$-0.749926\pi$
$31$	−1.58422	−	8.98458i	−0.284535	−	1.61368i	0.422407	−	0.906406i	$-0.361185\pi$
$32$	1.48070	+	0.538930i	0.261753	+	0.0952703i
$33$	6.21906	−	6.73651i	1.08260	−	1.17268i
$34$	−1.27550	+	7.23373i	−0.218747	+	1.24058i
$35$		0			0
$36$	10.3760	+	4.93257i	1.72933	+	0.822095i
$37$	3.11234	+	5.39074i	0.511666	+	0.886232i	0.999909	+	0.0135239i	$0.00430493\pi$
$37$	3.11234	+	5.39074i	0.511666	+	0.886232i	−0.488242	+	0.872708i	$0.662362\pi$
$38$	−1.18114	+	0.429898i	−0.191605	+	0.0697387i
$39$	4.08931	−	9.76968i	0.654814	−	1.56440i
$40$		0			0
$41$	6.96293	−	5.84259i	1.08743	−	0.912459i	0.0909107	−	0.995859i	$-0.471022\pi$
$41$	6.96293	−	5.84259i	1.08743	−	0.912459i	0.996516	+	0.0833996i	$0.0265778\pi$
$42$	0.542558	−	1.29621i	0.0837186	−	0.200010i
$43$	6.38441	−	2.32373i	0.973613	−	0.354366i	0.194259	−	0.980950i	$-0.437770\pi$
$43$	6.38441	−	2.32373i	0.973613	−	0.354366i	0.779354	+	0.626584i	$0.215548\pi$
$44$	−10.1356	−	17.5553i	−1.52800	−	2.64657i
$45$		0			0
$46$	−0.243684	+	0.422073i	−0.0359293	+	0.0622313i
$47$	−2.11902	+	12.0175i	−0.309090	+	1.75294i	0.294508	+	0.955649i	$0.404844\pi$
$47$	−2.11902	+	12.0175i	−0.309090	+	1.75294i	−0.603598	+	0.797288i	$0.706267\pi$
$48$	3.53236	−	3.82627i	0.509853	−	0.552275i
$49$	6.47175	+	2.35553i	0.924536	+	0.336504i
$50$		0			0
$51$	−4.43354	−	2.84768i	−0.620819	−	0.398755i
$52$	−17.9383	−	15.0520i	−2.48760	−	2.08734i
$53$	−2.74867			−0.377558			−0.188779	−	0.982020i	$-0.560453\pi$
$53$	−2.74867			−0.377558			−0.188779	+	0.982020i	$0.560453\pi$
$54$	−9.34365	+	8.37227i	−1.27151	+	1.13932i
$55$		0			0
$56$	−1.13705	−	0.954096i	−0.151944	−	0.127496i
$57$	0.0426766	−	0.900676i	0.00565265	−	0.119297i
$58$	0.775751	+	4.39950i	0.101861	+	0.577683i
$59$	−6.56519	−	2.38954i	−0.854716	−	0.311091i	−0.122754	−	0.992437i	$-0.539173\pi$
$59$	−6.56519	−	2.38954i	−0.854716	−	0.311091i	−0.731961	+	0.681346i	$0.761395\pi$
$60$		0			0
$61$	−2.16727	+	12.2912i	−0.277491	+	1.57373i	0.453447	+	0.891283i	$0.350194\pi$
$61$	−2.16727	+	12.2912i	−0.277491	+	1.57373i	−0.730938	+	0.682444i	$0.760917\pi$
$62$	11.0137	−	19.0764i	1.39875	−	2.42270i
$63$	0.707472	+	0.718062i	0.0891332	+	0.0904673i
$64$	4.90880	+	8.50230i	0.613601	+	1.06279i
$65$		0			0
$66$	21.9576	−	2.80784i	2.70279	−	0.345621i
$67$	4.29512	−	3.60403i	0.524732	−	0.440303i	−0.341545	−	0.939865i	$-0.610950\pi$
$67$	4.29512	−	3.60403i	0.524732	−	0.440303i	0.866278	+	0.499562i	$0.166506\pi$
$68$	−8.92479	+	7.48879i	−1.08229	+	0.908149i
$69$	−0.211805	−	0.278163i	−0.0254983	−	0.0334868i
$70$		0			0
$71$	1.58699	+	2.74874i	0.188341	+	0.326216i	0.944697	−	0.327944i	$-0.106356\pi$
$71$	1.58699	+	2.74874i	0.188341	+	0.326216i	−0.756356	+	0.654160i	$0.773022\pi$
$72$	5.51130	+	12.0520i	0.649513	+	1.42034i
$73$	−0.731226	+	1.26652i	−0.0855835	+	0.148235i	−0.905640	−	0.424048i	$-0.860609\pi$
$73$	−0.731226	+	1.26652i	−0.0855835	+	0.148235i	0.820056	+	0.572283i	$0.193942\pi$
$74$	−2.60980	+	14.8009i	−0.303383	+	1.72057i
$75$		0			0
$76$	−1.87341	−	0.681865i	−0.214895	−	0.0782153i
$77$	−0.308852	−	1.75159i	−0.0351970	−	0.199612i
$78$	22.7259	−	11.7233i	2.57320	−	1.32740i
$79$	−2.18198	−	1.83090i	−0.245491	−	0.205992i	0.511737	−	0.859142i	$-0.329002\pi$
$79$	−2.18198	−	1.83090i	−0.245491	−	0.205992i	−0.757228	+	0.653151i	$0.773447\pi$
$80$		0			0
$81$	−2.95220	−	8.50203i	−0.328022	−	0.944670i
$82$	21.9461			2.42354
$83$	0.578595	+	0.485499i	0.0635091	+	0.0532905i	0.673990	−	0.738741i	$-0.264579\pi$
$83$	0.578595	+	0.485499i	0.0635091	+	0.0532905i	−0.610481	+	0.792031i	$0.709024\pi$
$84$	1.98075	−	1.02178i	0.216118	−	0.111486i
$85$		0			0
$86$	15.4149	+	5.61055i	1.66223	+	0.605001i
$87$	−3.12618	−	0.705250i	−0.335162	−	0.0756108i
$88$	4.06039	−	23.0276i	0.432840	−	2.45476i
$89$	−3.18070	+	5.50914i	−0.337154	+	0.583968i	−0.983896	−	0.178741i	$-0.942798\pi$
$89$	−3.18070	+	5.50914i	−0.337154	+	0.583968i	0.646742	+	0.762709i	$0.276131\pi$
$90$		0			0
$91$	−1.02731	−	1.77934i	−0.107691	−	0.186526i
$92$	−0.726400	+	0.264388i	−0.0757325	+	0.0275644i
$93$	9.57291	+	12.5721i	0.992664	+	1.30366i
$94$	−22.5703	+	18.9387i	−2.32794	+	1.95338i
$95$		0			0
$96$	−2.70719	+	0.346184i	−0.276302	+	0.0353323i
$97$	10.0155	−	3.64534i	1.01692	−	0.370128i	0.220832	−	0.975312i	$-0.429123\pi$
$97$	10.0155	−	3.64534i	1.01692	−	0.370128i	0.796086	+	0.605184i	$0.206901\pi$
$98$	8.31429	+	14.4008i	0.839870	+	1.45470i
$99$	−4.22385	+	15.3079i	−0.424513	+	1.53850i
$100$		0			0
$101$	−2.11146	+	11.9747i	−0.210098	+	1.19152i	0.679116	+	0.734031i	$0.262363\pi$
$101$	−2.11146	+	11.9747i	−0.210098	+	1.19152i	−0.889213	+	0.457493i	$0.848748\pi$
$102$	−3.78063	−	12.1478i	−0.374338	−	1.20281i
$103$	2.42584	+	0.882932i	0.239025	+	0.0869979i	0.458755	−	0.888563i	$-0.348296\pi$
$103$	2.42584	+	0.882932i	0.239025	+	0.0869979i	−0.219730	+	0.975561i	$0.570518\pi$
$104$	−4.69048	−	26.6010i	−0.459939	−	2.60845i
$105$		0			0
$106$	−5.08387	−	4.26588i	−0.493790	−	0.414339i
$107$	−5.35813			−0.517990			−0.258995	−	0.965879i	$-0.583391\pi$
$107$	−5.35813			−0.517990			−0.258995	+	0.965879i	$0.583391\pi$
$108$	−19.8886	+	0.646421i	−1.91378	+	0.0622019i
$109$	17.4957			1.67579			0.837893	−	0.545834i	$-0.183787\pi$
$109$	17.4957			1.67579			0.837893	+	0.545834i	$0.183787\pi$
$110$		0			0
$111$	−9.07143	−	5.82662i	−0.861022	−	0.553038i
$112$	−0.175425	−	0.994885i	−0.0165761	−	0.0940078i
$113$	−15.7488	−	5.73211i	−1.48153	−	0.539232i	−0.530323	−	0.847796i	$-0.677929\pi$
$113$	−15.7488	−	5.73211i	−1.48153	−	0.539232i	−0.951204	+	0.308564i	$0.900152\pi$
$114$	1.47677	−	1.59964i	0.138312	−	0.149820i
$115$		0			0
$116$	−3.54287	+	6.13642i	−0.328947	+	0.569753i
$117$	1.46300	+	18.2857i	0.135255	+	1.69051i
$118$	−8.43433	−	14.6087i	−0.776443	−	1.34484i
$119$	−0.960576	+	0.349621i	−0.0880558	+	0.0320497i
$120$		0			0
$121$	13.0374	−	10.9397i	1.18522	−	0.994514i
$122$	−23.0842	+	19.3700i	−2.08995	+	1.75368i
$123$	−6.07872	+	14.5225i	−0.548100	+	1.30945i
$124$	32.8310	−	11.9495i	2.94831	−	1.07310i
$125$		0			0
$126$	0.194107	+	2.42610i	0.0172925	+	0.216134i
$127$	4.00306	−	6.93350i	0.355214	−	0.615249i	−0.631940	−	0.775017i	$-0.717741\pi$
$127$	4.00306	−	6.93350i	0.355214	−	0.615249i	0.987155	+	0.159768i	$0.0510746\pi$
$128$	−3.56894	+	20.2405i	−0.315453	+	1.78902i
$129$	−7.98238	+	8.64655i	−0.702810	+	0.761286i
$130$		0			0
$131$	1.87834	+	10.6526i	0.164111	+	0.930721i	0.949976	+	0.312323i	$0.101107\pi$
$131$	1.87834	+	10.6526i	0.164111	+	0.930721i	−0.785865	+	0.618398i	$0.787782\pi$
$132$	29.5418	+	18.9748i	2.57128	+	1.65154i
$133$	−0.133999	−	0.112439i	−0.0116192	−	0.00974968i
$134$	13.5376			1.16947
$135$		0			0
$136$	−13.4389			−1.15238
$137$	10.0791	+	8.45733i	0.861112	+	0.722559i	0.962207	−	0.272318i	$-0.0877903\pi$
$137$	10.0791	+	8.45733i	0.861112	+	0.722559i	−0.101095	+	0.994877i	$0.532235\pi$
$138$	0.0399532	−	0.843201i	0.00340105	−	0.0717780i
$139$	−1.27373	−	7.22368i	−0.108036	−	0.612705i	−0.989964	−	0.141320i	$-0.954865\pi$
$139$	−1.27373	−	7.22368i	−0.108036	−	0.612705i	0.881928	−	0.471385i	$-0.156246\pi$
$140$		0			0
$141$	−6.28083	−	20.1813i	−0.528941	−	1.69957i
$142$	−1.33074	+	7.54699i	−0.111673	+	0.633329i
$143$	16.1835	−	28.0307i	1.35333	−	2.34404i
$144$	−2.39911	+	8.69472i	−0.199926	+	0.724560i
$145$		0			0
$146$	−3.31807	+	1.20768i	−0.274606	+	0.0999483i
$147$	−11.8325	+	1.51308i	−0.975924	+	0.124797i
$148$	−18.2609	+	15.3228i	−1.50104	+	1.25952i
$149$	10.1927	−	8.55268i	0.835017	−	0.700663i	−0.121420	−	0.992601i	$-0.538745\pi$
$149$	10.1927	−	8.55268i	0.835017	−	0.700663i	0.956437	+	0.291939i	$0.0943003\pi$
$150$		0			0
$151$	8.57654	−	3.12160i	0.697949	−	0.254033i	0.0314139	−	0.999506i	$-0.489999\pi$
$151$	8.57654	−	3.12160i	0.697949	−	0.254033i	0.666535	+	0.745474i	$0.267777\pi$
$152$	−1.14984	−	1.99158i	−0.0932641	−	0.161538i
$153$	9.08581	+	0.862960i	0.734544	+	0.0697662i
$154$	2.14718	−	3.71903i	0.173025	−	0.299688i
$155$		0			0
$156$	39.5648	+	8.92561i	3.16772	+	0.714620i
$157$	4.17491	+	1.51954i	0.333194	+	0.121273i	0.503199	−	0.864171i	$-0.332156\pi$
$157$	4.17491	+	1.51954i	0.333194	+	0.121273i	−0.170005	+	0.985443i	$0.554378\pi$
$158$	−1.19422	−	6.77277i	−0.0950072	−	0.538813i
$159$	4.23104	−	2.18261i	0.335544	−	0.173092i
$160$		0			0
$161$	−0.0678253			−0.00534539
$162$	7.73466	−	20.3069i	0.607693	−	1.59546i
$163$	−16.5806			−1.29869			−0.649347	−	0.760492i	$-0.724958\pi$
$163$	−16.5806			−1.29869			−0.649347	+	0.760492i	$0.724958\pi$
$164$	26.6651	+	22.3747i	2.08220	+	1.74717i
$165$		0			0
$166$	0.316672	+	1.79594i	0.0245785	+	0.139392i
$167$	−18.8502	−	6.86091i	−1.45867	−	0.530913i	−0.513673	−	0.857986i	$-0.671716\pi$
$167$	−18.8502	−	6.86091i	−1.45867	−	0.530913i	−0.944999	+	0.327073i	$0.893938\pi$
$168$	2.50788	+	0.565763i	0.193487	+	0.0436496i
$169$	4.23523	−	24.0192i	0.325787	−	1.84763i
$170$		0			0
$171$	0.649499	+	1.42031i	0.0496684	+	0.108613i
$172$	13.0094	+	22.5329i	0.991955	+	1.71812i
$173$	3.14658	−	1.14526i	0.239230	−	0.0870725i	−0.219623	−	0.975585i	$-0.570483\pi$
$173$	3.14658	−	1.14526i	0.239230	−	0.0870725i	0.458853	+	0.888512i	$0.348261\pi$
$174$	−4.68759	−	6.15619i	−0.355365	−	0.466700i
$175$		0			0
$176$	12.1913	−	10.2297i	0.918951	−	0.771091i
$177$	12.0033	−	1.53493i	0.902223	−	0.115372i
$178$	−14.4330	+	5.25320i	−1.08180	+	0.393744i
$179$	−6.19883	−	10.7367i	−0.463323	−	0.802498i	0.535802	−	0.844344i	$-0.320010\pi$
$179$	−6.19883	−	10.7367i	−0.463323	−	0.802498i	−0.999124	+	0.0418458i	$0.986676\pi$
$180$		0			0
$181$	2.32049	−	4.01921i	0.172481	−	0.298746i	−0.766806	−	0.641879i	$-0.778155\pi$
$181$	2.32049	−	4.01921i	0.172481	−	0.298746i	0.939287	+	0.343134i	$0.111488\pi$
$182$	0.861427	−	4.88540i	0.0638532	−	0.362130i
$183$	−6.42386	−	20.6409i	−0.474865	−	1.52582i
$184$	−0.837906	−	0.304973i	−0.0617713	−	0.0224829i
$185$		0			0
$186$	−1.80576	+	38.1100i	−0.132405	+	2.79436i
$187$	−12.3360	−	10.3511i	−0.902095	−	0.756948i
$188$	−46.7321			−3.40829
$189$	−1.65920	−	0.543543i	−0.120689	−	0.0395369i
$190$		0			0
$191$	10.8645	+	9.11641i	0.786129	+	0.659641i	0.944784	−	0.327694i	$-0.106271\pi$
$191$	10.8645	+	9.11641i	0.786129	+	0.659641i	−0.158655	+	0.987334i	$0.550716\pi$
$192$	−14.3075	−	9.18977i	−1.03255	−	0.663214i
$193$	−2.94460	−	16.6997i	−0.211957	−	1.20207i	−0.886109	−	0.463477i	$-0.846602\pi$
$193$	−2.94460	−	16.6997i	−0.211957	−	1.20207i	0.674152	−	0.738593i	$-0.264509\pi$
$194$	24.1819	+	8.80149i	1.73616	+	0.631910i
$195$		0			0
$196$	−4.57992	+	25.9740i	−0.327137	+	1.85529i
$197$	3.41348	−	5.91232i	0.243200	−	0.421236i	−0.718424	−	0.695606i	$-0.755136\pi$
$197$	3.41348	−	5.91232i	0.243200	−	0.421236i	0.961624	+	0.274370i	$0.0884694\pi$
$198$	−31.5699	+	21.7578i	−2.24357	+	1.54626i
$199$	−7.72021	−	13.3718i	−0.547271	−	0.947901i	−0.998460	−	0.0554726i	$-0.982333\pi$
$199$	−7.72021	−	13.3718i	−0.547271	−	0.947901i	0.451189	−	0.892428i	$-0.351000\pi$
$200$		0			0
$201$	−3.74969	+	8.95830i	−0.264483	+	0.631870i
$202$	−22.4898	+	18.8711i	−1.58237	+	1.32777i
$203$	−0.476256	+	0.399626i	−0.0334266	+	0.0280483i
$204$	7.79145	−	18.6144i	0.545510	−	1.30327i
$205$		0			0
$206$	3.11648	+	5.39790i	0.217135	+	0.376090i
$207$	0.546911	+	0.259992i	0.0380129	+	0.0180707i
$208$	9.19208	−	15.9211i	0.637356	−	1.10393i
$209$	0.478511	−	2.71377i	0.0330993	−	0.187716i
$210$		0			0
$211$	17.3343	+	6.30917i	1.19334	+	0.434341i	0.860896	−	0.508781i	$-0.169904\pi$
$211$	17.3343	+	6.30917i	1.19334	+	0.434341i	0.332447	+	0.943122i	$0.392126\pi$
$212$	−1.82786	−	10.3663i	−0.125538	−	0.711963i
$213$	−4.62553	−	2.97100i	−0.316936	−	0.203569i
$214$	−9.91028	−	8.31571i	−0.677453	−	0.568450i
$215$		0			0
$216$	−18.0536	−	14.1754i	−1.22839	−	0.964512i
$217$	3.06549			0.208099
$218$	32.3597	+	27.1530i	2.19168	+	1.83904i
$219$	0.119888	−	2.53020i	0.00810129	−	0.170975i
$220$		0			0
$221$	−17.4805	−	6.36239i	−1.17587	−	0.427980i
$222$	−7.73552	−	24.8555i	−0.519174	−	1.66819i
$223$	0.541070	−	3.06856i	0.0362328	−	0.205486i	−0.961317	−	0.275444i	$-0.911175\pi$
$223$	0.541070	−	3.06856i	0.0362328	−	0.205486i	0.997550	+	0.0699575i	$0.0222864\pi$
$224$	−0.264731	+	0.458527i	−0.0176881	+	0.0306366i
$225$		0			0
$226$	−20.2326	−	35.0439i	−1.34585	−	2.33108i
$227$	−6.55642	+	2.38634i	−0.435165	+	0.158387i	−0.550308	−	0.834962i	$-0.685490\pi$
$227$	−6.55642	+	2.38634i	−0.435165	+	0.158387i	0.115143	+	0.993349i	$0.463267\pi$
$228$	3.42519	−	0.437999i	0.226839	−	0.0290072i
$229$	−7.76380	+	6.51460i	−0.513046	+	0.430497i	−0.862200	−	0.506569i	$-0.830914\pi$
$229$	−7.76380	+	6.51460i	−0.513046	+	0.430497i	0.349153	+	0.937066i	$0.386469\pi$
$230$		0			0
$231$	1.86628	+	2.45099i	0.122793	+	0.161263i
$232$	−7.68051	+	2.79548i	−0.504250	+	0.183532i
$233$	5.61343	+	9.72275i	0.367748	+	0.636959i	0.989213	−	0.146483i	$-0.0467955\pi$
$233$	5.61343	+	9.72275i	0.367748	+	0.636959i	−0.621465	+	0.783442i	$0.713462\pi$
$234$	−25.6731	+	36.0914i	−1.67830	+	2.35937i
$235$		0			0
$236$	4.64605	−	26.3490i	0.302432	−	1.71518i
$237$	4.81257	+	1.08569i	0.312610	+	0.0705232i
$238$	−2.31926	−	0.844143i	−0.150336	−	0.0547177i
$239$	2.49115	+	14.1280i	0.161139	+	0.913864i	0.952957	+	0.303106i	$0.0980238\pi$
$239$	2.49115	+	14.1280i	0.161139	+	0.913864i	−0.791818	+	0.610757i	$0.790865\pi$
$240$		0			0
$241$	−7.78696	−	6.53404i	−0.501602	−	0.420894i	0.356560	−	0.934272i	$-0.383949\pi$
$241$	−7.78696	−	6.53404i	−0.501602	−	0.420894i	−0.858163	+	0.513378i	$0.828394\pi$
$242$	41.0918			2.64148
$243$	11.2955	+	10.7430i	0.724605	+	0.689165i
$244$	−47.7963			−3.05985
$245$		0			0
$246$	−33.7818	+	17.4265i	−2.15385	+	1.11107i
$247$	−0.552766	−	3.13489i	−0.0351717	−	0.199468i
$248$	37.8707	+	13.7838i	2.40479	+	0.875273i
$249$	−1.27615	−	0.287893i	−0.0808728	−	0.0182445i
$250$		0			0
$251$	0.766397	−	1.32744i	0.0483745	−	0.0837872i	−0.840824	−	0.541308i	$-0.817929\pi$
$251$	0.766397	−	1.32744i	0.0483745	−	0.0837872i	0.889199	+	0.457521i	$0.151263\pi$
$252$	−2.23763	+	3.14568i	−0.140958	+	0.198159i
$253$	−0.534239	−	0.925329i	−0.0335873	−	0.0581749i
$254$	18.1646	−	6.61139i	1.13975	−	0.414835i
$255$		0			0
$256$	−22.9724	+	19.2761i	−1.43577	+	1.20476i
$257$	−18.3627	+	15.4081i	−1.14543	+	0.961131i	−0.999603	−	0.0281791i	$-0.991029\pi$
$257$	−18.3627	+	15.4081i	−1.14543	+	0.961131i	−0.145828	+	0.989310i	$0.546585\pi$
$258$	−28.1833	+	3.60396i	−1.75462	+	0.224373i
$259$	−1.96543	+	0.715357i	−0.122126	+	0.0444501i
$260$		0			0
$261$	5.37217	−	1.39678i	0.332529	−	0.0864586i
$262$	−13.0585	+	22.6179i	−0.806755	+	1.39734i
$263$	−1.42813	+	8.09931i	−0.0880621	+	0.499425i	0.908592	+	0.417686i	$0.137159\pi$
$263$	−1.42813	+	8.09931i	−0.0880621	+	0.499425i	−0.996654	+	0.0817395i	$0.973952\pi$
$264$	12.0351	+	38.6708i	0.740712	+	2.38002i
$265$		0			0
$266$	−0.0733394	−	0.415929i	−0.00449673	−	0.0255022i
$267$	0.521493	−	11.0059i	0.0319148	−	0.673552i
$268$	16.4485	+	13.8019i	1.00475	+	0.843088i
$269$	2.05741			0.125442			0.0627211	−	0.998031i	$-0.480022\pi$
$269$	2.05741			0.125442			0.0627211	+	0.998031i	$0.480022\pi$
$270$		0			0
$271$	−15.4436			−0.938131			−0.469066	−	0.883163i	$-0.655409\pi$
$271$	−15.4436			−0.938131			−0.469066	+	0.883163i	$0.655409\pi$
$272$	−7.00671	−	5.87933i	−0.424844	−	0.356486i
$273$	2.99425	+	1.92322i	0.181220	+	0.116398i
$274$	5.51639	+	31.2850i	0.333257	+	1.89000i
$275$		0			0
$276$	0.908213	−	0.983780i	0.0546680	−	0.0592166i
$277$	−0.209051	+	1.18559i	−0.0125607	+	0.0712350i	−0.990444	−	0.137917i	$-0.955959\pi$
$277$	−0.209051	+	1.18559i	−0.0125607	+	0.0712350i	0.977883	+	0.209152i	$0.0670704\pi$
$278$	8.85515	−	15.3376i	0.531097	−	0.919887i
$279$	−24.7186	−	11.7508i	−1.47987	−	0.703503i
$280$		0			0
$281$	26.1069	−	9.50212i	1.55740	−	0.566849i	0.587265	−	0.809395i	$-0.300205\pi$
$281$	26.1069	−	9.50212i	1.55740	−	0.566849i	0.970140	+	0.242546i	$0.0779825\pi$
$282$	19.7041	−	47.0746i	1.17336	−	2.80325i
$283$	17.3768	−	14.5809i	1.03295	−	0.866745i	0.0417476	−	0.999128i	$-0.486707\pi$
$283$	17.3768	−	14.5809i	1.03295	−	0.866745i	0.991199	+	0.132383i	$0.0422630\pi$
$284$	−9.31127	+	7.81309i	−0.552522	+	0.463621i
$285$		0			0
$286$	73.4357	−	26.7284i	4.34235	−	1.58048i
$287$	1.52708	+	2.64498i	0.0901406	+	0.156128i
$288$	3.89231	−	2.68256i	0.229357	−	0.158071i
$289$	3.87241	−	6.70722i	0.227789	−	0.394542i
$290$		0			0
$291$	−12.5223	+	13.5642i	−0.734069	+	0.795147i
$292$	−5.26282	−	1.91551i	−0.307983	−	0.112097i
$293$	−2.89878	−	16.4398i	−0.169348	−	0.960422i	−0.944467	−	0.328606i	$-0.893421\pi$
$293$	−2.89878	−	16.4398i	−0.169348	−	0.960422i	0.775119	−	0.631816i	$-0.217690\pi$
$294$	−24.2333	−	15.5652i	−1.41332	−	0.907779i
$295$		0			0
$296$	−27.4972			−1.59824
$297$	−5.65356	−	26.9175i	−0.328053	−	1.56191i
$298$	32.1258			1.86100
$299$	−0.945515	−	0.793381i	−0.0546806	−	0.0458824i
$300$		0			0
$301$	0.396423	+	2.24822i	0.0228494	+	0.129586i
$302$	20.7076	+	7.53697i	1.19159	+	0.433704i
$303$	−6.25842	−	20.1093i	−0.359537	−	1.15525i
$304$	0.271790	−	1.54140i	0.0155882	−	0.0884051i
$305$		0			0
$306$	15.4656	+	15.6971i	0.884110	+	0.897344i
$307$	3.17549	+	5.50011i	0.181235	+	0.313908i	0.942301	−	0.334766i	$-0.108657\pi$
$307$	3.17549	+	5.50011i	0.181235	+	0.313908i	−0.761066	+	0.648674i	$0.775324\pi$
$308$	6.40056	−	2.32961i	0.364706	−	0.132742i
$309$	−4.43521	+	0.567156i	−0.252310	+	0.0322644i
$310$		0			0
$311$	−0.398806	+	0.334638i	−0.0226142	+	0.0189756i	−0.654025	−	0.756473i	$-0.726921\pi$
$311$	−0.398806	+	0.334638i	−0.0226142	+	0.0189756i	0.631410	+	0.775449i	$0.282476\pi$
$312$	28.3429	+	37.2227i	1.60460	+	2.10732i
$313$	−15.2139	+	5.53741i	−0.859942	+	0.312993i	−0.734087	−	0.679056i	$-0.762390\pi$
$313$	−15.2139	+	5.53741i	−0.859942	+	0.312993i	−0.125855	+	0.992049i	$0.540167\pi$
$314$	5.36352	+	9.28988i	0.302681	+	0.524258i
$315$		0			0
$316$	5.45403	−	9.44666i	0.306813	−	0.531416i
$317$	1.46495	−	8.30814i	0.0822797	−	0.466631i	−0.915631	−	0.402020i	$-0.868308\pi$
$317$	1.46495	−	8.30814i	0.0822797	−	0.466631i	0.997911	−	0.0646113i	$-0.0205807\pi$
$318$	11.2130	+	2.52960i	0.628794	+	0.141853i
$319$	−9.20335	−	3.34975i	−0.515289	−	0.187550i
$320$		0			0
$321$	8.24781	−	4.25468i	0.460348	−	0.237473i
$322$	−0.125448	−	0.105264i	−0.00699096	−	0.00586611i
$323$	−1.58375			−0.0881223
$324$	30.1014	−	16.7878i	1.67230	−	0.932655i
$325$		0			0
$326$	−30.6672	−	25.7328i	−1.69850	−	1.42521i
$327$	−26.9313	+	13.8927i	−1.48930	+	0.768266i
$328$	6.97235	+	39.5422i	0.384984	+	2.18335i
$329$	−3.85304	−	1.40239i	−0.212425	−	0.0773163i
$330$		0			0
$331$	−1.19110	+	6.75507i	−0.0654688	+	0.371292i	0.934417	+	0.356181i	$0.115921\pi$
$331$	−1.19110	+	6.75507i	−0.0654688	+	0.371292i	−0.999886	+	0.0151112i	$0.995190\pi$
$332$	−1.44625	+	2.50497i	−0.0793731	+	0.137478i
$333$	18.5904	+	1.76570i	1.01875	+	0.0967596i
$334$	−24.2169	−	41.9449i	−1.32509	−	2.29513i
$335$		0			0
$336$	1.06003	+	1.39214i	0.0578295	+	0.0759472i
$337$	16.1166	−	13.5234i	0.877926	−	0.736667i	−0.0878255	−	0.996136i	$-0.527992\pi$
$337$	16.1166	−	13.5234i	0.877926	−	0.736667i	0.965752	+	0.259468i	$0.0835474\pi$
$338$	45.1107	−	37.8523i	2.45370	−	2.05890i
$339$	28.7940	−	3.68205i	1.56387	−	0.199981i
$340$		0			0
$341$	24.1459	+	41.8219i	1.30757	+	2.26478i
$342$	−1.00299	+	3.63498i	−0.0542354	+	0.196557i
$343$	−2.33311	+	4.04106i	−0.125976	+	0.218197i
$344$	−5.21166	+	29.5568i	−0.280994	+	1.59360i
$345$		0			0
$346$	7.59726	+	2.76518i	0.408431	+	0.148657i
$347$	−1.93708	−	10.9857i	−0.103988	−	0.589744i	−0.991620	−	0.129190i	$-0.958762\pi$
$347$	−1.93708	−	10.9857i	−0.103988	−	0.589744i	0.887632	−	0.460553i	$-0.152349\pi$
$348$	0.580871	−	12.2591i	0.0311379	−	0.657156i
$349$	−6.90169	−	5.79120i	−0.369439	−	0.309996i	0.439101	−	0.898438i	$-0.355297\pi$
$349$	−6.90169	−	5.79120i	−0.369439	−	0.309996i	−0.808540	+	0.588442i	$0.799742\pi$
$350$		0			0
$351$	−16.7720	−	26.9856i	−0.895221	−	1.44039i
$352$	−8.34080			−0.444566
$353$	−7.32667	−	6.14780i	−0.389959	−	0.327214i	0.426638	−	0.904422i	$-0.359698\pi$
$353$	−7.32667	−	6.14780i	−0.389959	−	0.327214i	−0.816597	+	0.577208i	$0.804142\pi$
$354$	24.5832	+	15.7899i	1.30658	+	0.839224i
$355$		0			0
$356$	−22.8924	−	8.33214i	−1.21329	−	0.441603i
$357$	1.20100	−	1.30093i	0.0635637	−	0.0688525i
$358$	5.19791	−	29.4788i	0.274718	−	1.55800i
$359$	−12.6845	+	21.9702i	−0.669463	+	1.15954i	0.308591	+	0.951195i	$0.400143\pi$
$359$	−12.6845	+	21.9702i	−0.669463	+	1.15954i	−0.978054	+	0.208350i	$0.933191\pi$
$360$		0			0
$361$	9.36449	+	16.2198i	0.492868	+	0.853673i
$362$	10.5297	−	3.83249i	0.553427	−	0.201431i
$363$	−11.3818	+	27.1919i	−0.597389	+	1.42721i
$364$	6.02747	−	5.05765i	0.315925	−	0.265093i
$365$		0			0
$366$	20.1528	−	48.1466i	1.05341	−	2.51667i
$367$	25.2446	−	9.18829i	1.31776	−	0.479625i	0.415019	−	0.909813i	$-0.363775\pi$
$367$	25.2446	−	9.18829i	1.31776	−	0.479625i	0.902740	+	0.430188i	$0.141553\pi$
$368$	−0.303442	−	0.525578i	−0.0158180	−	0.0273976i
$369$	−2.17474	−	27.1815i	−0.113213	−	1.41501i
$370$		0			0
$371$	0.160378	−	0.909551i	0.00832643	−	0.0472215i
$372$	−41.0484	+	44.4637i	−2.12826	+	2.30534i
$373$	−23.6679	−	8.61440i	−1.22548	−	0.446037i	−0.353430	−	0.935461i	$-0.614985\pi$
$373$	−23.6679	−	8.61440i	−1.22548	−	0.446037i	−0.872046	+	0.489424i	$0.837207\pi$
$374$	−6.75162	−	38.2904i	−0.349118	−	1.97995i
$375$		0			0
$376$	−41.2942	−	34.6499i	−2.12959	−	1.78693i
$377$	−11.3138			−0.582691
$378$	−2.22526	−	3.58037i	−0.114455	−	0.184155i
$379$	25.4242			1.30595			0.652976	−	0.757379i	$-0.273520\pi$
$379$	25.4242			1.30595			0.652976	+	0.757379i	$0.273520\pi$
$380$		0			0
$381$	−0.656322	+	13.8515i	−0.0336244	+	0.709632i
$382$	5.94628	+	33.7230i	0.304238	+	1.72542i
$383$	9.29719	+	3.38390i	0.475064	+	0.172909i	0.568445	−	0.822721i	$-0.307545\pi$
$383$	9.29719	+	3.38390i	0.475064	+	0.172909i	−0.0933808	+	0.995630i	$0.529767\pi$
$384$	−10.5784	−	33.9903i	−0.539829	−	1.73456i
$385$		0			0
$386$	20.4713	−	35.4573i	1.04196	−	1.80473i
$387$	5.42146	−	19.6482i	0.275589	−	0.998773i
$388$	20.4083	+	35.3483i	1.03608	+	1.79454i
$389$	−4.09700	+	1.49119i	−0.207726	+	0.0756061i	−0.443788	−	0.896132i	$-0.646366\pi$
$389$	−4.09700	+	1.49119i	−0.207726	+	0.0756061i	0.236061	+	0.971738i	$0.424143\pi$
$390$		0			0
$391$	−0.470419	+	0.394728i	−0.0237901	+	0.0199623i
$392$	−23.3057	+	19.5558i	−1.17711	+	0.987715i
$393$	−11.3501	−	14.9061i	−0.572539	−	0.751913i
$394$	15.4893	−	5.63765i	0.780340	−	0.284021i
$395$		0			0
$396$	−60.5410	−	5.75012i	−3.04230	−	0.288954i
$397$	8.10396	−	14.0365i	0.406726	−	0.704470i	−0.587795	−	0.809010i	$-0.700004\pi$
$397$	8.10396	−	14.0365i	0.406726	−	0.704470i	0.994521	+	0.104540i	$0.0333371\pi$
$398$	6.47363	−	36.7138i	0.324494	−	1.84030i
$399$	0.295549	+	0.0666743i	0.0147960	+	0.00333789i
$400$		0			0
$401$	−0.111264	−	0.631007i	−0.00555624	−	0.0315110i	0.981904	−	0.189381i	$-0.0606483\pi$
$401$	−0.111264	−	0.631007i	−0.00555624	−	0.0315110i	−0.987460	+	0.157870i	$0.949537\pi$
$402$	−20.8385	+	10.7496i	−1.03933	+	0.536143i
$403$	42.7343	+	35.8583i	2.12875	+	1.78623i
$404$	−46.5654			−2.31672
$405$		0			0
$406$	−1.50109			−0.0744976
$407$	−25.2405	−	21.1793i	−1.25113	−	1.04982i
$408$	20.6866	−	10.6713i	1.02414	−	0.528308i
$409$	4.23533	+	24.0197i	0.209423	+	1.18770i	0.890326	+	0.455325i	$0.150477\pi$
$409$	4.23533	+	24.0197i	0.209423	+	1.18770i	−0.680902	+	0.732374i	$0.738412\pi$
$410$		0			0
$411$	−22.2304	−	5.01506i	−1.09654	−	0.247375i
$412$	−1.71671	+	9.73596i	−0.0845763	+	0.479656i
$413$	1.17378	−	2.03304i	0.0577577	−	0.100039i
$414$	0.608052	+	1.32967i	0.0298841	+	0.0653497i
$415$		0			0
$416$	−9.05405	+	3.29540i	−0.443911	+	0.161570i
$417$	7.69670	+	10.1081i	0.376909	+	0.494994i
$418$	5.09677	−	4.27669i	0.249291	−	0.209180i
$419$	−13.1999	+	11.0760i	−0.644855	+	0.541098i	−0.905505	−	0.424336i	$-0.860508\pi$
$419$	−13.1999	+	11.0760i	−0.644855	+	0.541098i	0.260650	+	0.965433i	$0.416063\pi$
$420$		0			0
$421$	21.2230	−	7.72454i	1.03435	−	0.376471i	0.231612	−	0.972808i	$-0.425600\pi$
$421$	21.2230	−	7.72454i	1.03435	−	0.376471i	0.802734	+	0.596337i	$0.203378\pi$
$422$	22.2694	+	38.5718i	1.08406	+	1.87765i
$423$	25.6933	+	26.0779i	1.24925	+	1.26795i
$424$	6.07104	−	10.5154i	0.294836	−	0.510671i
$425$		0			0
$426$	−3.94435	−	12.6738i	−0.191104	−	0.614049i
$427$	−3.94078	−	1.43433i	−0.190708	−	0.0694119i
$428$	−3.56316	−	20.2077i	−0.172232	−	0.976775i
$429$	−2.65337	+	55.9985i	−0.128106	+	2.70363i
$430$		0			0
$431$	−10.3129			−0.496754			−0.248377	−	0.968663i	$-0.579897\pi$
$431$	−10.3129			−0.496754			−0.248377	+	0.968663i	$0.579897\pi$
$432$	−3.21117	−	15.2889i	−0.154497	−	0.735587i
$433$	−11.0194			−0.529557			−0.264778	−	0.964309i	$-0.585299\pi$
$433$	−11.0194			−0.529557			−0.264778	+	0.964309i	$0.585299\pi$
$434$	5.66986	+	4.75758i	0.272162	+	0.228371i
$435$		0			0
$436$	11.6347	+	65.9835i	0.557199	+	3.16003i
$437$	−0.0987460	−	0.0359406i	−0.00472366	−	0.00171927i
$438$	4.14856	−	4.49374i	0.198226	−	0.214719i
$439$	−4.27981	+	24.2720i	−0.204264	+	1.15844i	0.694329	+	0.719658i	$0.255701\pi$
$439$	−4.27981	+	24.2720i	−0.204264	+	1.15844i	−0.898593	+	0.438783i	$0.855410\pi$
$440$		0			0
$441$	17.0123	−	11.7248i	0.810110	−	0.558323i
$442$	−22.4573	−	38.8971i	−1.06818	−	1.85015i
$443$	−20.5698	+	7.48678i	−0.977299	+	0.355708i	−0.780789	−	0.624794i	$-0.785183\pi$
$443$	−20.5698	+	7.48678i	−0.977299	+	0.355708i	−0.196509	+	0.980502i	$0.562961\pi$
$444$	15.9420	−	38.0867i	0.756575	−	1.80752i
$445$		0			0
$446$	5.76310	−	4.83582i	0.272891	−	0.228983i
$447$	−8.89834	+	21.2588i	−0.420877	+	1.00551i
$448$	−3.09988	+	1.12826i	−0.146456	+	0.0533055i
$449$	−0.0863524	−	0.149567i	−0.00407522	−	0.00705849i	0.863981	−	0.503525i	$-0.167964\pi$
$449$	−0.0863524	−	0.149567i	−0.00407522	−	0.00705849i	−0.868056	+	0.496467i	$0.834631\pi$
$450$		0			0
$451$	−24.0566	+	41.6673i	−1.13278	+	1.96204i
$452$	11.1451	−	63.2071i	0.524222	−	2.97301i
$453$	−10.7232	+	11.6154i	−0.503819	+	0.545739i
$454$	−15.8302	−	5.76171i	−0.742947	−	0.270411i
$455$		0			0
$456$	3.35138	+	2.15261i	0.156943	+	0.100805i
$457$	6.86690	+	5.76201i	0.321220	+	0.269536i	0.789111	−	0.614251i	$-0.210542\pi$
$457$	6.86690	+	5.76201i	0.321220	+	0.269536i	−0.467891	+	0.883786i	$0.654986\pi$
$458$	−24.4703			−1.14342
$459$	−14.6711	+	5.88632i	−0.684788	+	0.274750i
$460$		0			0
$461$	12.4655	+	10.4598i	0.580576	+	0.487161i	0.885136	−	0.465332i	$-0.154065\pi$
$461$	12.4655	+	10.4598i	0.580576	+	0.487161i	−0.304560	+	0.952493i	$0.598510\pi$
$462$	−0.352042	+	7.42973i	−0.0163785	+	0.345662i
$463$	2.38861	+	13.5465i	0.111008	+	0.629558i	0.988650	+	0.150240i	$0.0480047\pi$
$463$	2.38861	+	13.5465i	0.111008	+	0.629558i	−0.877642	+	0.479318i	$0.840884\pi$
$464$	−5.22741	−	1.90262i	−0.242677	−	0.0883270i
$465$		0			0
$466$	−4.70704	+	26.6949i	−0.218049	+	1.23662i
$467$	−2.09492	+	3.62851i	−0.0969414	+	0.167907i	−0.910417	−	0.413691i	$-0.864239\pi$
$467$	−2.09492	+	3.62851i	−0.0969414	+	0.167907i	0.813476	+	0.581599i	$0.197573\pi$
$468$	−67.9899	+	17.6776i	−3.14283	+	0.817146i
$469$	0.941987	+	1.63157i	0.0434969	+	0.0753389i
$470$		0			0
$471$	−7.63307	+	0.976085i	−0.351713	+	0.0449756i
$472$	23.6421	−	19.8381i	1.08822	−	0.913123i
$473$	−27.5496	+	23.1169i	−1.26673	+	1.06292i
$474$	7.21626	+	9.47709i	0.331454	+	0.435297i
$475$		0			0
$476$	−1.95734	−	3.39022i	−0.0897148	−	0.155391i
$477$	−4.77976	+	6.71941i	−0.218850	+	0.307661i
$478$	−17.3188	+	29.9970i	−0.792143	+	1.37203i
$479$	4.29952	−	24.3838i	0.196450	−	1.11412i	−0.713888	−	0.700259i	$-0.753068\pi$
$479$	4.29952	−	24.3838i	0.196450	−	1.11412i	0.910339	−	0.413864i	$-0.135821\pi$
$480$		0			0
$481$	−35.7668	−	13.0180i	−1.63082	−	0.593571i
$482$	−4.26190	−	24.1704i	−0.194124	−	1.10093i
$483$	0.104404	−	0.0538574i	0.00475055	−	0.00245060i
$484$	49.9277	+	41.8943i	2.26944	+	1.90429i
$485$		0			0
$486$	4.21890	+	37.4004i	0.191373	+	1.69652i
$487$	−14.2164			−0.644205			−0.322102	−	0.946705i	$-0.604390\pi$
$487$	−14.2164			−0.644205			−0.322102	+	0.946705i	$0.604390\pi$
$488$	−42.2346	−	35.4390i	−1.91187	−	1.60425i
$489$	25.5227	−	13.1660i	1.15418	−	0.595388i
$490$		0			0
$491$	−10.7333	−	3.90659i	−0.484385	−	0.176302i	0.0882726	−	0.996096i	$-0.471865\pi$
$491$	−10.7333	−	3.90659i	−0.484385	−	0.176302i	−0.572658	+	0.819795i	$0.694088\pi$
$492$	−58.8127	−	13.2678i	−2.65148	−	0.598160i
$493$	−0.977453	+	5.54341i	−0.0440222	+	0.249663i
$494$	3.84291	−	6.65611i	0.172901	−	0.299473i
$495$		0			0
$496$	13.7146	+	23.7544i	0.615805	+	1.06661i
$497$	−1.00217	+	0.364761i	−0.0449536	+	0.0163618i
$498$	−1.91354	−	2.51304i	−0.0857477	−	0.112612i
$499$	29.0144	−	24.3459i	1.29886	−	1.08987i	0.308520	−	0.951218i	$-0.400166\pi$
$499$	29.0144	−	24.3459i	1.29886	−	1.08987i	0.990341	−	0.138656i	$-0.0442781\pi$
$500$		0			0
$501$	34.4642	−	4.40714i	1.53975	−	0.196897i
$502$	3.47767	−	1.26577i	0.155216	−	0.0564940i
$503$	−18.1596	−	31.4533i	−0.809694	−	1.40243i	−0.913076	−	0.407790i	$-0.866300\pi$
$503$	−18.1596	−	31.4533i	−0.809694	−	1.40243i	0.103381	−	0.994642i	$-0.467034\pi$
$504$	−4.30964	+	1.12052i	−0.191967	+	0.0499120i
$505$		0			0
$506$	0.447976	−	2.54060i	0.0199149	−	0.112943i
$507$	12.5533	+	40.3359i	0.557514	+	1.79138i
$508$	28.8111	+	10.4864i	1.27828	+	0.465258i
$509$	−1.95163	−	11.0682i	−0.0865043	−	0.490590i	−0.997022	−	0.0771197i	$-0.975428\pi$
$509$	−1.95163	−	11.0682i	−0.0865043	−	0.490590i	0.910518	−	0.413470i	$-0.135683\pi$
$510$		0			0
$511$	−0.376434	−	0.315866i	−0.0166525	−	0.0139731i
$512$	−31.3000			−1.38328
$513$	−2.12759	−	1.67055i	−0.0939352	−	0.0737564i
$514$	−57.8762			−2.55281
$515$		0			0
$516$	−37.9179	−	24.3548i	−1.66924	−	1.07216i
$517$	−11.2166	−	63.6125i	−0.493305	−	2.79767i
$518$	−4.74543	−	1.72720i	−0.208502	−	0.0758886i
$519$	−3.93414	+	4.26148i	−0.172690	+	0.187058i
$520$		0			0
$521$	2.20153	−	3.81316i	0.0964507	−	0.167057i	−0.813762	−	0.581198i	$-0.802584\pi$
$521$	2.20153	−	3.81316i	0.0964507	−	0.167057i	0.910213	+	0.414140i	$0.135918\pi$
$522$	12.1040	+	5.75405i	0.529779	+	0.251848i
$523$	−7.79908	−	13.5084i	−0.341030	−	0.590681i	0.643594	−	0.765367i	$-0.277442\pi$
$523$	−7.79908	−	13.5084i	−0.341030	−	0.590681i	−0.984624	+	0.174686i	$0.944109\pi$
$524$	−38.9261	+	14.1679i	−1.70050	+	0.618930i
$525$		0			0
$526$	−15.2114	+	12.7639i	−0.663249	+	0.556532i
$527$	21.2614	−	17.8405i	0.926163	−	0.777143i
$528$	−10.6431	+	25.4272i	−0.463182	+	1.10658i
$529$	21.5746	−	7.85253i	0.938028	−	0.341414i
$530$		0			0
$531$	−17.2579	+	11.8941i	−0.748930	+	0.516158i
$532$	0.334942	−	0.580137i	0.0145216	−	0.0251521i
$533$	−9.65127	+	54.7350i	−0.418043	+	2.37084i
$534$	18.0455	−	19.5470i	0.780907	−	0.845881i
$535$		0			0
$536$	4.30093	+	24.3918i	0.185772	+	1.05357i
$537$	18.0675	+	11.6048i	0.779670	+	0.500785i
$538$	3.80533	+	3.19305i	0.164060	+	0.137662i
$539$	−36.4555			−1.57025
$540$		0			0
$541$	−1.52861			−0.0657202			−0.0328601	−	0.999460i	$-0.510462\pi$
$541$	−1.52861			−0.0657202			−0.0328601	+	0.999460i	$0.510462\pi$
$542$	−28.5641	−	23.9681i	−1.22693	−	1.02952i
$543$	−0.380456	+	8.02941i	−0.0163269	+	0.344575i
$544$	0.832422	+	4.72090i	0.0356898	+	0.202407i
$545$		0			0
$546$	2.55330	+	8.20415i	0.109271	+	0.351105i
$547$	−2.13129	+	12.0871i	−0.0911273	+	0.516808i	0.904738	+	0.425968i	$0.140066\pi$
$547$	−2.13129	+	12.0871i	−0.0911273	+	0.516808i	−0.995865	+	0.0908404i	$0.971045\pi$
$548$	−25.1934	+	43.6363i	−1.07621	+	1.86405i
$549$	26.2784	+	26.6717i	1.12154	+	1.13832i
$550$		0			0
$551$	−0.905136	+	0.329443i	−0.0385601	+	0.0140347i
$552$	1.53196	−	0.195901i	0.0652047	−	0.00833809i
$553$	0.733168	−	0.615201i	0.0311775	−	0.0261610i
$554$	−2.22666	+	1.86839i	−0.0946019	+	0.0793804i
$555$		0			0
$556$	26.3964	−	9.60751i	1.11946	−	0.407449i
$557$	−8.99212	−	15.5748i	−0.381008	−	0.659926i	0.610198	−	0.792249i	$-0.291090\pi$
$557$	−8.99212	−	15.5748i	−0.381008	−	0.659926i	−0.991207	+	0.132323i	$0.957756\pi$
$558$	−27.4820	−	60.0969i	−1.16341	−	2.54410i
$559$	−20.7721	+	35.9784i	−0.878567	+	1.52172i
$560$		0			0
$561$	27.2082	+	6.13804i	1.14873	+	0.259148i
$562$	63.0338	+	22.9424i	2.65892	+	0.967768i
$563$	−1.63413	−	9.26763i	−0.0688705	−	0.390584i	−0.999685	−	0.0250923i	$-0.992012\pi$
$563$	−1.63413	−	9.26763i	−0.0688705	−	0.390584i	0.930815	−	0.365492i	$-0.119099\pi$
$564$	71.9351	−	37.1081i	3.02901	−	1.56253i
$565$		0			0
$566$	54.7691			2.30212
$567$	2.98563	−	0.480827i	0.125385	−	0.0201928i
$568$	−14.0209			−0.588302
$569$	−25.8778	−	21.7141i	−1.08485	−	0.910301i	−0.0885394	−	0.996073i	$-0.528220\pi$
$569$	−25.8778	−	21.7141i	−1.08485	−	0.910301i	−0.996315	+	0.0857719i	$0.972664\pi$
$570$		0			0
$571$	−0.978955	−	5.55193i	−0.0409680	−	0.232341i	0.957448	−	0.288606i	$-0.0931919\pi$
$571$	−0.978955	−	5.55193i	−0.0409680	−	0.232341i	−0.998416	+	0.0562653i	$0.982081\pi$
$572$	116.477	+	42.3942i	4.87015	+	1.77259i
$573$	−23.9628	−	5.40588i	−1.00106	−	0.225834i
$574$	−1.28050	+	7.26209i	−0.0534472	+	0.303114i
$575$		0			0
$576$	29.3209	+	2.78486i	1.22170	+	0.116036i
$577$	7.94027	+	13.7529i	0.330558	+	0.572543i	0.982621	−	0.185622i	$-0.0594298\pi$
$577$	7.94027	+	13.7529i	0.330558	+	0.572543i	−0.652064	+	0.758164i	$0.726096\pi$
$578$	17.5718	−	6.39561i	0.730891	−	0.266022i
$579$	17.7932	+	23.3678i	0.739460	+	0.971131i
$580$		0			0
$581$	−0.194414	+	0.163133i	−0.00806567	+	0.00676790i
$582$	−44.2123	+	5.65368i	−1.83266	+	0.234353i
$583$	13.6721	−	4.97623i	0.566240	−	0.206094i
$584$	−3.23015	−	5.59478i	−0.133664	−	0.231514i
$585$		0			0
$586$	20.1527	−	34.9055i	0.832500	−	1.44193i
$587$	−3.45096	+	19.5714i	−0.142436	+	0.807797i	0.826953	+	0.562270i	$0.190072\pi$
$587$	−3.45096	+	19.5714i	−0.142436	+	0.807797i	−0.969390	+	0.245527i	$0.921039\pi$
$588$	−13.5750	−	43.6187i	−0.559825	−	1.79881i
$589$	4.46300	+	1.62440i	0.183895	+	0.0669323i
$590$		0			0
$591$	−0.559657	+	11.8114i	−0.0230212	+	0.485856i
$592$	−14.3364	−	12.0296i	−0.589221	−	0.494416i
$593$	43.0280			1.76695			0.883474	−	0.468480i	$-0.155198\pi$
$593$	43.0280			1.76695			0.883474	+	0.468480i	$0.155198\pi$
$594$	31.3188	−	58.5603i	1.28502	−	2.40276i
$595$		0			0
$596$	39.0337	+	32.7532i	1.59888	+	1.34162i
$597$	22.5018	+	14.4530i	0.920936	+	0.591521i
$598$	−0.517492	−	2.93484i	−0.0211618	−	0.120015i
$599$	36.3045	+	13.2138i	1.48336	+	0.539900i	0.951693	−	0.307051i	$-0.0993422\pi$
$599$	36.3045	+	13.2138i	1.48336	+	0.539900i	0.531671	+	0.846951i	$0.321564\pi$
$600$		0			0
$601$	−1.31942	+	7.48281i	−0.0538203	+	0.305230i	−0.999821	−	0.0189352i	$-0.993972\pi$
$601$	−1.31942	+	7.48281i	−0.0538203	+	0.305230i	0.946000	+	0.324166i	$0.105083\pi$
$602$	−2.75599	+	4.77351i	−0.112326	+	0.194554i
$603$	−1.34150	−	16.7671i	−0.0546302	−	0.682808i
$604$	17.4762	+	30.2697i	0.711098	+	1.23166i
$605$		0			0
$606$	19.6338	−	46.9067i	0.797570	−	1.90546i
$607$	−0.651945	+	0.547047i	−0.0264616	+	0.0222040i	−0.655923	−	0.754828i	$-0.727720\pi$
$607$	−0.651945	+	0.547047i	−0.0264616	+	0.0222040i	0.629461	+	0.777032i	$0.283276\pi$
$608$	−0.628391	+	0.527283i	−0.0254846	+	0.0213841i
$609$	0.415777	−	0.993324i	0.0168482	−	0.0402515i
$610$		0			0
$611$	−37.3087	−	64.6205i	−1.50935	−	2.61427i
$612$	2.78749	+	34.8401i	0.112678	+	1.40833i
$613$	−0.0839581	+	0.145420i	−0.00339104	+	0.00587345i	−0.867716	−	0.497060i	$-0.834413\pi$
$613$	−0.0839581	+	0.145420i	−0.00339104	+	0.00587345i	0.864325	+	0.502934i	$0.167746\pi$
$614$	−2.66275	+	15.1012i	−0.107460	+	0.609434i
$615$		0			0
$616$	7.38308	+	2.68722i	0.297473	+	0.108271i
$617$	2.89015	+	16.3908i	0.116353	+	0.659871i	0.986071	+	0.166322i	$0.0531892\pi$
$617$	2.89015	+	16.3908i	0.116353	+	0.659871i	−0.869718	+	0.493548i	$0.835700\pi$
$618$	−9.08348	−	5.83436i	−0.365391	−	0.234692i
$619$	−33.6283	−	28.2175i	−1.35163	−	1.13416i	−0.978470	−	0.206391i	$-0.933828\pi$
$619$	−33.6283	−	28.2175i	−1.35163	−	1.13416i	−0.373165	−	0.927765i	$-0.621728\pi$
$620$		0			0
$621$	−1.04831	+	0.0340724i	−0.0420674	+	0.00136728i
$622$	−1.25698			−0.0504001
$623$	−1.63742	−	1.37396i	−0.0656020	−	0.0550466i
$624$	−1.50709	+	31.8066i	−0.0603318	+	1.27328i
$625$		0			0
$626$	−36.7333	−	13.3698i	−1.46816	−	0.534366i
$627$	1.41832	+	4.55730i	0.0566423	+	0.182001i
$628$	−2.95449	+	16.7558i	−0.117897	+	0.668627i
$629$	−9.46847	+	16.3999i	−0.377533	+	0.653906i
$630$		0			0
$631$	6.62243	+	11.4704i	0.263635	+	0.456629i	0.967205	−	0.253997i	$-0.0817453\pi$
$631$	6.62243	+	11.4704i	0.263635	+	0.456629i	−0.703570	+	0.710626i	$0.748412\pi$
$632$	11.8237	−	4.30347i	0.470321	−	0.171183i
$633$	−31.6927	+	4.05273i	−1.25967	+	0.161081i
$634$	15.6036	−	13.0930i	0.619698	−	0.519989i
$635$		0			0
$636$	11.0451	+	14.5055i	0.437968	+	0.575182i
$637$	−39.5729	+	14.4034i	−1.56794	+	0.570682i
$638$	−11.8236	−	20.4790i	−0.468100	−	0.810773i
$639$	9.47927	+	0.900331i	0.374994	+	0.0356165i
$640$		0			0
$641$	−7.29257	+	41.3582i	−0.288039	+	1.63355i	0.406183	+	0.913792i	$0.366859\pi$
$641$	−7.29257	+	41.3582i	−0.288039	+	1.63355i	−0.694223	+	0.719760i	$0.744252\pi$
$642$	21.8581	+	4.93108i	0.862672	+	0.194614i
$643$	26.4485	+	9.62646i	1.04303	+	0.379631i	0.806027	−	0.591879i	$-0.201614\pi$
$643$	26.4485	+	9.62646i	1.04303	+	0.379631i	0.237000	+	0.971510i	$0.423836\pi$
$644$	−0.0451039	−	0.255797i	−0.00177734	−	0.0100798i
$645$		0			0
$646$	−2.92927	−	2.45795i	−0.115251	−	0.0967069i
$647$	4.87520			0.191664			0.0958319	−	0.995398i	$-0.469449\pi$
$647$	4.87520			0.191664			0.0958319	+	0.995398i	$0.469449\pi$
$648$	39.0461	+	7.48464i	1.53388	+	0.294024i
$649$	36.9819			1.45166
$650$		0			0
$651$	−4.71873	+	2.43418i	−0.184942	+	0.0954032i
$652$	−11.0261	−	62.5322i	−0.431816	−	2.44895i
$653$	−3.30599	−	1.20328i	−0.129373	−	0.0470880i	0.276522	−	0.961008i	$-0.410818\pi$
$653$	−3.30599	−	1.20328i	−0.129373	−	0.0470880i	−0.405895	+	0.913920i	$0.633040\pi$
$654$	−71.3727	−	16.1013i	−2.79089	−	0.629611i
$655$		0			0
$656$	−13.6639	+	23.6666i	−0.533487	+	0.924027i
$657$	1.82459	+	3.98996i	0.0711839	+	0.155663i
$658$	−4.95001	−	8.57367i	−0.192972	−	0.334236i
$659$	−3.85106	+	1.40167i	−0.150016	+	0.0546013i	−0.415937	−	0.909394i	$-0.636546\pi$
$659$	−3.85106	+	1.40167i	−0.150016	+	0.0546013i	0.265921	+	0.963995i	$0.414324\pi$
$660$		0			0
$661$	10.8180	−	9.07740i	0.420773	−	0.353070i	−0.407684	−	0.913123i	$-0.633664\pi$
$661$	10.8180	−	9.07740i	0.420773	−	0.353070i	0.828457	+	0.560053i	$0.189219\pi$
$662$	−12.6868	+	10.6455i	−0.493085	+	0.413748i
$663$	31.9600	−	4.08691i	1.24122	−	0.158722i
$664$	−3.13529	+	1.14115i	−0.121673	+	0.0442853i
$665$		0			0
$666$	31.6441	+	32.1177i	1.22618	+	1.24454i
$667$	−0.186742	+	0.323446i	−0.00723067	+	0.0125239i
$668$	13.3399	−	75.6542i	0.516136	−	2.92715i
$669$	1.60375	+	5.15311i	0.0620046	+	0.199231i
$670$		0			0
$671$	−11.4720	−	65.0611i	−0.442873	−	2.51166i
$672$	0.0434039	−	0.916026i	0.00167434	−	0.0353365i
$673$	31.7224	+	26.6182i	1.22281	+	1.02606i	0.998673	+	0.0514985i	$0.0163997\pi$
$673$	31.7224	+	26.6182i	1.22281	+	1.02606i	0.224134	+	0.974558i	$0.428045\pi$
$674$	50.7970			1.95663
$675$		0			0
$676$	93.4024			3.59240
$677$	23.8227	+	19.9896i	0.915581	+	0.768264i	0.973173	−	0.230077i	$-0.0738977\pi$
$677$	23.8227	+	19.9896i	0.915581	+	0.768264i	−0.0575915	+	0.998340i	$0.518342\pi$
$678$	58.9711	+	37.8774i	2.26477	+	1.45467i
$679$	0.621884	+	3.52688i	0.0238657	+	0.135349i
$680$		0			0
$681$	8.19745	−	8.87951i	0.314127	−	0.340264i
$682$	−20.2471	+	114.827i	−0.775301	+	4.39695i
$683$	6.49887	−	11.2564i	0.248673	−	0.430713i	−0.714485	−	0.699651i	$-0.753339\pi$
$683$	6.49887	−	11.2564i	0.248673	−	0.430713i	0.963158	+	0.268937i	$0.0866724\pi$
$684$	−4.92463	+	3.39403i	−0.188298	+	0.129774i
$685$		0			0
$686$	−10.5869	+	3.85332i	−0.404210	+	0.147121i
$687$	6.77789	−	16.1929i	0.258593	−	0.617798i
$688$	−15.6479	+	13.1302i	−0.596571	+	0.500583i
$689$	12.8751	−	10.8035i	0.490504	−	0.411582i
$690$		0			0
$691$	−44.3322	+	16.1356i	−1.68648	+	0.613827i	−0.994175	−	0.107782i	$-0.965625\pi$
$691$	−44.3322	+	16.1356i	−1.68648	+	0.613827i	−0.692301	+	0.721609i	$0.743403\pi$
$692$	6.41171	+	11.1054i	0.243737	+	0.422164i
$693$	−4.81902	−	2.29088i	−0.183059	−	0.0870233i
$694$	13.4668	−	23.3252i	0.511194	−	0.885413i
$695$		0			0
$696$	9.60289	−	10.4019i	0.363997	−	0.394283i
$697$	25.9846	+	9.45762i	0.984237	+	0.358233i
$698$	−3.77738	−	21.4226i	−0.142976	−	0.810856i
$699$	−16.3613	−	10.5089i	−0.618839	−	0.397483i
$700$		0			0
$701$	8.98862			0.339496			0.169748	−	0.985488i	$-0.445705\pi$
$701$	8.98862			0.339496			0.169748	+	0.985488i	$0.445705\pi$
$702$	10.8601	−	75.9418i	0.409887	−	2.86624i
$703$	−3.24051			−0.122218
$704$	−39.8095	−	33.4041i	−1.50038	−	1.25897i
$705$		0			0
$706$	−4.00997	−	22.7417i	−0.150917	−	0.855895i
$707$	−3.83929	−	1.39739i	−0.144391	−	0.0525542i
$708$	13.7710	+	44.2485i	0.517547	+	1.66296i
$709$	−6.01200	+	34.0958i	−0.225785	+	1.28049i	0.635392	+	0.772189i	$0.280838\pi$
$709$	−6.01200	+	34.0958i	−0.225785	+	1.28049i	−0.861178	+	0.508304i	$0.830273\pi$
$710$		0			0
$711$	−8.27014	+	2.15026i	−0.310154	+	0.0806411i
$712$	−14.0506	−	24.3363i	−0.526568	−	0.912043i
$713$	1.73050	−	0.629849i	0.0648076	−	0.0235880i
$714$	4.24036	−	0.542240i	0.158692	−	0.0202928i
$715$		0			0
$716$	36.3702	−	30.5182i	1.35922	−	1.14052i
$717$	−15.0531	−	19.7692i	−0.562169	−	0.738294i
$718$	−57.5584	+	20.9495i	−2.14806	+	0.781830i
$719$	11.7846	+	20.4116i	0.439493	+	0.761224i	0.997650	−	0.0685110i	$-0.0218248\pi$
$719$	11.7846	+	20.4116i	0.439493	+	0.761224i	−0.558157	+	0.829735i	$0.688491\pi$
$720$		0			0
$721$	−0.433710	+	0.751207i	−0.0161522	+	0.0279764i
$722$	−7.85242	+	44.5333i	−0.292237	+	1.65736i
$723$	17.1750	+	3.87458i	0.638743	+	0.144097i
$724$	16.7012	+	6.07874i	0.620695	+	0.225915i
$725$		0			0
$726$	−63.2529	+	32.6293i	−2.34753	+	1.21099i
$727$	20.7902	+	17.4450i	0.771064	+	0.647000i	0.940981	−	0.338459i	$-0.109906\pi$
$727$	20.7902	+	17.4450i	0.771064	+	0.647000i	−0.169917	+	0.985458i	$0.554350\pi$
$728$	9.07613			0.336384
$729$	−25.9178	−	7.56753i	−0.959919	−	0.280279i
$730$		0			0
$731$	15.8336	+	13.2860i	0.585629	+	0.491401i
$732$	73.5733	−	37.9532i	2.71935	−	1.40279i
$733$	−2.58612	−	14.6666i	−0.0955205	−	0.541724i	−0.994587	−	0.103911i	$-0.966864\pi$
$733$	−2.58612	−	14.6666i	−0.0955205	−	0.541724i	0.899066	−	0.437813i	$-0.144247\pi$
$734$	60.9520	+	22.1847i	2.24978	+	0.818852i
$735$		0			0
$736$	−0.0552319	+	0.313235i	−0.00203587	+	0.0115460i
$737$	−14.8395	+	25.7027i	−0.546619	+	0.946771i
$738$	38.1628	−	53.6495i	1.40479	−	1.97487i
$739$	−5.36887	−	9.29916i	−0.197497	−	0.342075i	0.750219	−	0.661189i	$-0.229948\pi$
$739$	−5.36887	−	9.29916i	−0.197497	−	0.342075i	−0.947716	+	0.319114i	$0.896615\pi$
$740$		0			0
$741$	3.34017	+	4.38663i	0.122704	+	0.161147i
$742$	1.70824	−	1.43338i	0.0627114	−	0.0526211i
$743$	−12.7210	+	10.6742i	−0.466687	+	0.391597i	−0.845584	−	0.533842i	$-0.820748\pi$
$743$	−12.7210	+	10.6742i	−0.466687	+	0.391597i	0.378897	+	0.925439i	$0.376303\pi$
$744$	−69.2398	+	8.85410i	−2.53846	+	0.324607i
$745$		0			0
$746$	−30.4062	−	52.6651i	−1.11325	−	1.92821i
$747$	2.19300	−	0.570186i	0.0802375	−	0.0208620i
$748$	30.8348	−	53.4074i	1.12743	−	1.95277i
$749$	0.312635	−	1.77304i	0.0114234	−	0.0647854i
$750$		0			0
$751$	−4.89963	−	1.78332i	−0.178790	−	0.0650743i	0.251074	−	0.967968i	$-0.419216\pi$
$751$	−4.89963	−	1.78332i	−0.178790	−	0.0650743i	−0.429864	+	0.902894i	$0.641439\pi$
$752$	−6.37092	−	36.1313i	−0.232323	−	1.31757i
$753$	−0.125655	+	2.65190i	−0.00457911	+	0.0966407i
$754$	−20.9258	−	17.5588i	−0.762072	−	0.639455i
$755$		0			0
$756$	0.946549	−	6.61898i	0.0344257	−	0.240730i
$757$	−43.6180			−1.58532			−0.792662	−	0.609661i	$-0.791306\pi$
$757$	−43.6180			−1.58532			−0.792662	+	0.609661i	$0.791306\pi$
$758$	47.0240	+	39.4578i	1.70799	+	1.43317i
$759$	1.55712	+	1.00015i	0.0565200	+	0.0363031i
$760$		0			0
$761$	11.6568	+	4.24273i	0.422559	+	0.153799i	0.544542	−	0.838733i	$-0.316703\pi$
$761$	11.6568	+	4.24273i	0.422559	+	0.153799i	−0.121984	+	0.992532i	$0.538926\pi$
$762$	−22.7111	+	24.6008i	−0.822737	+	0.891192i
$763$	−1.02084	+	5.78945i	−0.0369567	+	0.209592i
$764$	−27.1568	+	47.0369i	−0.982497	+	1.70174i
$765$		0			0
$766$	11.9441	+	20.6878i	0.431559	+	0.747482i
$767$	40.1443	−	14.6113i	1.44953	−	0.527584i
$768$	20.0552	−	47.9133i	0.723679	−	1.72892i
$769$	−30.8699	+	25.9030i	−1.11320	+	0.934085i	−0.998241	−	0.0592857i	$-0.981118\pi$
$769$	−30.8699	+	25.9030i	−1.11320	+	0.934085i	−0.114958	+	0.993370i	$0.536673\pi$
$770$		0			0
$771$	16.0308	−	38.2989i	0.577336	−	1.37930i
$772$	61.0231	−	22.2106i	2.19627	−	0.799376i
$773$	17.2390	+	29.8587i	0.620042	+	1.07394i	0.989477	+	0.144688i	$0.0462179\pi$
$773$	17.2390	+	29.8587i	0.620042	+	1.07394i	−0.369435	+	0.929257i	$0.620449\pi$
$774$	40.5210	−	27.9269i	1.45650	−	1.00381i
$775$		0			0
$776$	−8.17574	+	46.3669i	−0.293492	+	1.66448i
$777$	2.45736	−	2.66182i	0.0881573	−	0.0954923i
$778$	−9.89201	−	3.60040i	−0.354646	−	0.129081i
$779$	0.821681	+	4.65998i	0.0294398	+	0.166961i
$780$		0			0
$781$	−12.8702	−	10.7994i	−0.460531	−	0.386431i
$782$	−1.48269			−0.0530208
$783$	−7.16030	+	6.41590i	−0.255888	+	0.229286i
$784$	−20.7064			−0.739513
$785$		0			0
$786$	2.14100	−	45.1852i	0.0763670	−	1.61170i
$787$	6.35385	+	36.0345i	0.226490	+	1.28449i	0.859816	+	0.510604i	$0.170578\pi$
$787$	6.35385	+	36.0345i	0.226490	+	1.28449i	−0.633325	+	0.773886i	$0.718311\pi$
$788$	24.5677	+	8.94192i	0.875189	+	0.318543i
$789$	−4.23302	−	13.6014i	−0.150699	−	0.484221i
$790$		0			0
$791$	2.81570	−	4.87693i	0.100115	−	0.173404i
$792$	−49.2328	−	49.9697i	−1.74941	−	1.77560i
$793$	−38.1583	−	66.0921i	−1.35504	−	2.34700i
$794$	36.7732	−	13.3844i	1.30503	−	0.474993i
$795$		0			0
$796$	45.2965	−	38.0083i	1.60549	−	1.34717i
$797$	39.4838	−	33.1308i	1.39859	−	1.17355i	0.436866	−	0.899527i	$-0.356089\pi$
$797$	39.4838	−	33.1308i	1.39859	−	1.17355i	0.961722	−	0.274027i	$-0.0883559\pi$
$798$	0.443164	+	0.582006i	0.0156878	+	0.0206028i
$799$	−34.8853	+	12.6972i	−1.23415	+	0.449195i
$800$		0			0
$801$	7.93664	+	17.3556i	0.280427	+	0.613231i
$802$	0.773520	−	1.33978i	0.0273140	−	0.0473092i
$803$	1.34425	−	7.62359i	0.0474374	−	0.269031i
$804$	−36.2789	−	8.18433i	−1.27946	−	0.288639i
$805$		0			0
$806$	23.3890	+	132.646i	0.823842	+	4.67224i
$807$	−3.16698	+	1.63370i	−0.111483	+	0.0575091i
$808$	−41.1469	−	34.5263i	−1.44754	−	1.21463i
$809$	−18.5065			−0.650654			−0.325327	−	0.945602i	$-0.605474\pi$
$809$	−18.5065			−0.650654			−0.325327	+	0.945602i	$0.605474\pi$
$810$		0			0
$811$	36.6261			1.28611			0.643057	−	0.765818i	$-0.277666\pi$
$811$	36.6261			1.28611			0.643057	+	0.765818i	$0.277666\pi$
$812$	−1.82386	−	1.53040i	−0.0640050	−	0.0537066i
$813$	23.7724	−	12.2631i	0.833736	−	0.430087i
$814$	−13.8145	−	78.3456i	−0.484196	−	2.74601i
$815$		0			0
$816$	15.4540	+	3.48634i	0.540999	+	0.122046i
$817$	−0.614186	+	3.48322i	−0.0214877	+	0.121863i
$818$	−29.4446	+	50.9995i	−1.02951	+	1.78316i
$819$	−6.13622	−	0.582811i	−0.214417	−	0.0203651i
$820$		0			0
$821$	20.6784	−	7.52630i	0.721679	−	0.262670i	0.0450409	−	0.998985i	$-0.485658\pi$
$821$	20.6784	−	7.52630i	0.721679	−	0.262670i	0.676639	+	0.736315i	$0.263436\pi$
$822$	−33.3336	−	43.7769i	−1.16264	−	1.52689i
$823$	23.2081	−	19.4739i	0.808984	−	0.678818i	−0.141381	−	0.989955i	$-0.545154\pi$
$823$	23.2081	−	19.4739i	0.808984	−	0.678818i	0.950365	+	0.311137i	$0.100710\pi$
$824$	−8.73576	+	7.33017i	−0.304325	+	0.255359i
$825$		0			0
$826$	5.32623	−	1.93859i	0.185323	−	0.0674521i
$827$	−8.94761	−	15.4977i	−0.311139	−	0.538909i	0.667470	−	0.744637i	$-0.267377\pi$
$827$	−8.94761	−	15.4977i	−0.311139	−	0.538909i	−0.978609	+	0.205728i	$0.934044\pi$
$828$	−0.616839	+	2.23552i	−0.0214366	+	0.0776896i
$829$	−12.0856	+	20.9328i	−0.419749	+	0.727026i	−0.995914	−	0.0903070i	$-0.971215\pi$
$829$	−12.0856	+	20.9328i	−0.419749	+	0.727026i	0.576165	+	0.817333i	$0.304549\pi$
$830$		0			0
$831$	−0.619634	−	1.99098i	−0.0214949	−	0.0690664i
$832$	−56.4115	−	20.5321i	−1.95572	−	0.711823i
$833$	3.63830	+	20.6338i	0.126060	+	0.714920i
$834$	−1.45185	+	30.6408i	−0.0502734	+	1.06100i
$835$		0			0
$836$	10.5529			0.364981
$837$	47.3804	−	1.53996i	1.63771	−	0.0532289i
$838$	−41.6039			−1.43718
$839$	41.0703	+	34.4621i	1.41790	+	1.18976i	0.952452	+	0.304690i	$0.0985528\pi$
$839$	41.0703	+	34.4621i	1.41790	+	1.18976i	0.465452	+	0.885073i	$0.345892\pi$
$840$		0			0
$841$	−4.44132	−	25.1880i	−0.153149	−	0.868551i
$842$	51.2420	+	18.6505i	1.76591	+	0.642740i
$843$	−32.6412	+	35.3571i	−1.12422	+	1.21776i
$844$	−12.2671	+	69.5703i	−0.422252	+	2.39471i
$845$		0			0
$846$	7.04940	+	88.1086i	0.242364	+	3.02924i
$847$	2.85930	+	4.95245i	0.0982467	+	0.170168i
$848$	7.76561	−	2.82645i	0.266672	−	0.0970607i
$849$	−15.1702	+	36.2428i	−0.520640	+	1.24385i
$850$		0			0
$851$	−0.962521	+	0.807651i	−0.0329948	+	0.0276859i
$852$	8.12885	−	19.4205i	0.278490	−	0.665334i
$853$	25.1738	−	9.16250i	0.861933	−	0.313718i	0.127037	−	0.991898i	$-0.459453\pi$
$853$	25.1738	−	9.16250i	0.861933	−	0.313718i	0.734896	+	0.678180i	$0.237231\pi$
$854$	−5.06274	−	8.76892i	−0.173243	−	0.300066i
$855$		0			0
$856$	11.8346	−	20.4982i	0.404499	−	0.700613i
$857$	2.59878	−	14.7384i	0.0887725	−	0.503454i	−0.907706	−	0.419607i	$-0.862168\pi$
$857$	2.59878	−	14.7384i	0.0887725	−	0.503454i	0.996479	−	0.0838474i	$-0.0267208\pi$
$858$	−91.8162	+	99.4557i	−3.13455	+	3.39536i
$859$	0.649627	+	0.236445i	0.0221650	+	0.00806740i	0.353079	−	0.935594i	$-0.385135\pi$
$859$	0.649627	+	0.236445i	0.0221650	+	0.00806740i	−0.330914	+	0.943661i	$0.607357\pi$
$860$		0			0
$861$	−4.45092	−	2.85884i	−0.151687	−	0.0974291i
$862$	−19.0745	−	16.0054i	−0.649679	−	0.545146i
$863$	48.5994			1.65434			0.827172	−	0.561949i	$-0.189948\pi$
$863$	48.5994			1.65434			0.827172	+	0.561949i	$0.189948\pi$
$864$	−3.86135	+	7.22002i	−0.131366	+	0.245630i
$865$		0			0
$866$	−20.3812	−	17.1018i	−0.692581	−	0.581144i
$867$	−0.634902	+	13.3994i	−0.0215624	+	0.455067i
$868$	2.03855	+	11.5612i	0.0691929	+	0.392413i
$869$	14.1680	+	5.15673i	0.480617	+	0.174930i
$870$		0			0
$871$	−5.95343	+	33.7636i	−0.201724	+	1.14404i
$872$	−38.6432	+	66.9320i	−1.30862	+	2.26660i
$873$	8.50487	−	30.8229i	0.287846	−	1.04320i
$874$	−0.126859	−	0.219727i	−0.00429108	−	0.00743237i
$875$		0			0
$876$	9.62214	−	1.23044i	0.325102	−	0.0415726i
$877$	16.3136	−	13.6887i	0.550870	−	0.462235i	−0.324365	−	0.945932i	$-0.605151\pi$
$877$	16.3136	−	13.6887i	0.550870	−	0.462235i	0.875236	+	0.483697i	$0.160706\pi$
$878$	−45.5856	+	38.2508i	−1.53844	+	1.29090i
$879$	17.5163	+	23.0041i	0.590810	+	0.775908i
$880$		0			0
$881$	−21.0931	−	36.5344i	−0.710646	−	1.23087i	−0.964615	−	0.263662i	$-0.915070\pi$
$881$	−21.0931	−	36.5344i	−0.710646	−	1.23087i	0.253969	−	0.967212i	$-0.418264\pi$
$882$	49.6622	+	4.71686i	1.67221	+	0.158825i
$883$	−25.4356	+	44.0558i	−0.855976	+	1.48259i	0.0197597	+	0.999805i	$0.493710\pi$
$883$	−25.4356	+	44.0558i	−0.855976	+	1.48259i	−0.875736	+	0.482790i	$0.839623\pi$
$884$	12.3706	−	70.1571i	0.416068	−	2.35964i
$885$		0			0
$886$	−49.6647	−	18.0765i	−1.66852	−	0.607291i
$887$	−8.37721	−	47.5095i	−0.281279	−	1.59521i	−0.718281	−	0.695753i	$-0.755071\pi$
$887$	−8.37721	−	47.5095i	−0.281279	−	1.59521i	0.437002	−	0.899461i	$-0.356040\pi$
$888$	42.3267	−	21.8345i	1.42039	−	0.732716i
$889$	2.06077	+	1.72919i	0.0691160	+	0.0579952i
$890$		0			0
$891$	30.0767	+	36.9451i	1.00761	+	1.23771i
$892$	11.9326			0.399533
$893$	−4.86646	−	4.08344i	−0.162850	−	0.136647i
$894$	−49.4514	+	25.5098i	−1.65390	+	0.853175i
$895$		0			0
$896$	−6.48946	−	2.36197i	−0.216797	−	0.0789078i
$897$	2.08543	+	0.470462i	0.0696305	+	0.0157083i
$898$	0.0724092	−	0.410653i	0.00241633	−	0.0137037i
$899$	8.44014	−	14.6187i	0.281494	−	0.487563i
$900$		0			0
$901$	−4.18104	−	7.24177i	−0.139291	−	0.241258i
$902$	−109.162	+	39.7315i	−3.63468	+	1.32292i
$903$	−2.39544	−	3.14593i	−0.0797153	−	0.104690i
$904$	56.7137	−	47.5884i	1.88627	−	1.58277i
$905$		0			0
$906$	−37.8602	+	4.84141i	−1.25782	+	0.160845i
$907$	−16.5183	+	6.01218i	−0.548482	+	0.199631i	−0.601372	−	0.798969i	$-0.705379\pi$
$907$	−16.5183	+	6.01218i	−0.548482	+	0.199631i	0.0528898	+	0.998600i	$0.483157\pi$
$908$	−13.3599	−	23.1400i	−0.443364	−	0.767928i
$909$	25.6017	+	25.9849i	0.849153	+	0.861864i
$910$		0			0
$911$	−0.694543	+	3.93895i	−0.0230112	+	0.130503i	−0.994149	−	0.108015i	$-0.965551\pi$
$911$	−0.694543	+	3.93895i	−0.0230112	+	0.130503i	0.971138	+	0.238518i	$0.0766617\pi$
$912$	0.805593	+	2.58850i	0.0266759	+	0.0857138i
$913$	−3.75694	−	1.36741i	−0.124336	−	0.0452548i
$914$	3.75834	+	21.3146i	0.124315	+	0.705024i
$915$		0			0
$916$	−29.7321	−	24.9482i	−0.982377	−	0.824312i
$917$	−3.63460			−0.120025
$918$	−36.2708	−	11.8820i	−1.19711	−	0.392166i
$919$	5.86587			0.193497			0.0967486	−	0.995309i	$-0.469156\pi$
$919$	5.86587			0.193497			0.0967486	+	0.995309i	$0.469156\pi$
$920$		0			0
$921$	−9.25548	−	5.94483i	−0.304978	−	0.195889i
$922$	6.82251	+	38.6924i	0.224688	+	1.27427i
$923$	−18.2375	−	6.63791i	−0.600295	−	0.218489i
$924$	−8.00258	+	8.66842i	−0.263265	+	0.285170i
$925$		0			0
$926$	−16.6059	+	28.7623i	−0.545705	+	0.945189i
$927$	6.37679	−	4.39485i	0.209441	−	0.144346i
$928$	1.45775	+	2.52490i	0.0478531	+	0.0828840i
$929$	30.1086	−	10.9586i	0.987832	−	0.359541i	0.202951	−	0.979189i	$-0.434947\pi$
$929$	30.1086	−	10.9586i	0.987832	−	0.359541i	0.784880	+	0.619647i	$0.212724\pi$
$930$		0			0
$931$	−2.74654	+	2.30462i	−0.0900141	+	0.0755308i
$932$	−32.9355	+	27.6362i	−1.07884	+	0.905253i
$933$	0.348163	−	0.831787i	0.0113983	−	0.0272315i
$934$	−9.50610	+	3.45994i	−0.311049	+	0.113213i
$935$		0			0
$936$	−73.1855	−	34.7911i	−2.39214	−	1.13718i
$937$	−8.48960	+	14.7044i	−0.277343	+	0.480373i	−0.970724	−	0.240199i	$-0.922787\pi$
$937$	−8.48960	+	14.7044i	−0.277343	+	0.480373i	0.693380	+	0.720572i	$0.256121\pi$
$938$	−0.789885	+	4.47966i	−0.0257907	+	0.146266i
$939$	19.0219	−	20.6046i	0.620755	−	0.672404i
$940$		0			0
$941$	−5.92567	−	33.6061i	−0.193171	−	1.09553i	−0.914999	−	0.403456i	$-0.867809\pi$
$941$	−5.92567	−	33.6061i	−0.193171	−	1.09553i	0.721828	−	0.692073i	$-0.243302\pi$
$942$	−15.6328	−	10.0410i	−0.509345	−	0.327155i
$943$	1.40550	+	1.17935i	0.0457693	+	0.0384050i
$944$	21.0053			0.683665
$945$		0			0
$946$	−86.8321			−2.82316
$947$	−0.0711354	−	0.0596897i	−0.00231159	−	0.00193966i	0.641631	−	0.767013i	$-0.278258\pi$
$947$	−0.0711354	−	0.0596897i	−0.00231159	−	0.00193966i	−0.643943	+	0.765074i	$0.722702\pi$
$948$	−0.894216	+	18.8721i	−0.0290428	+	0.612939i
$949$	−1.55284	−	8.80661i	−0.0504074	−	0.285875i
$950$		0			0
$951$	4.34215	+	13.9520i	0.140804	+	0.452426i
$952$	0.784128	−	4.44701i	0.0254137	−	0.144129i
$953$	−24.7669	+	42.8976i	−0.802279	+	1.38959i	0.115833	+	0.993269i	$0.463046\pi$
$953$	−24.7669	+	42.8976i	−0.802279	+	1.38959i	−0.918113	+	0.396320i	$0.870287\pi$
$954$	−19.2689	+	5.00998i	−0.623854	+	0.162204i
$955$		0			0
$956$	−51.6257	+	18.7902i	−1.66970	+	0.607720i
$957$	16.8267	−	2.15173i	0.543930	−	0.0695554i
$958$	45.7955	−	38.4270i	1.47958	−	1.24152i
$959$	−3.38667	+	2.84176i	−0.109361	+	0.0917651i
$960$		0			0
$961$	−49.0825	+	17.8646i	−1.58331	+	0.576276i
$962$	−45.9497	−	79.5872i	−1.48148	−	2.56599i
$963$	−9.31745	+	13.0985i	−0.300251	+	0.422094i
$964$	19.4642	−	33.7129i	0.626898	−	1.08582i
$965$		0			0
$966$	0.276689	+	0.0624196i	0.00890233	+	0.00200832i
$967$	−22.3307	−	8.12772i	−0.718107	−	0.261370i	−0.0429853	−	0.999076i	$-0.513687\pi$
$967$	−22.3307	−	8.12772i	−0.718107	−	0.261370i	−0.675122	+	0.737706i	$0.735909\pi$
$968$	13.0550	+	74.0387i	0.419604	+	2.37969i
$969$	2.43788	−	1.25759i	0.0783161	−	0.0403998i
$970$		0			0
$971$	34.5957			1.11023			0.555115	−	0.831774i	$-0.312674\pi$
$971$	34.5957			1.11023			0.555115	+	0.831774i	$0.312674\pi$
$972$	−33.0048	+	49.7439i	−1.05863	+	1.59554i
$973$	2.46468			0.0790141
$974$	−26.2943	−	22.0635i	−0.842523	−	0.706961i
$975$		0			0
$976$	−6.51600	−	36.9541i	−0.208572	−	1.18287i
$977$	−27.4012	−	9.97323i	−0.876643	−	0.319072i	−0.135789	−	0.990738i	$-0.543357\pi$
$977$	−27.4012	−	9.97323i	−0.876643	−	0.319072i	−0.740854	+	0.671666i	$0.765579\pi$
$978$	67.6396	+	15.2591i	2.16288	+	0.487933i
$979$	5.84723	−	33.1613i	0.186878	−	1.05984i
$980$		0			0
$981$	30.4240	−	42.7702i	0.971362	−	1.36555i
$982$	−13.7891	−	23.8833i	−0.440026	−	0.762148i
$983$	33.5226	−	12.2012i	1.06920	−	0.389158i	0.253325	−	0.967381i	$-0.418476\pi$
$983$	33.5226	−	12.2012i	1.06920	−	0.389158i	0.815879	+	0.578223i	$0.196254\pi$
$984$	−42.1315	−	55.3311i	−1.34310	−	1.76389i
$985$		0			0
$986$	−10.4111	+	8.73598i	−0.331558	+	0.278210i
$987$	7.04459	−	0.900833i	0.224232	−	0.0286738i
$988$	11.4554	−	4.16941i	0.364443	−	0.132647i
$989$	0.685714	+	1.18769i	0.0218044	+	0.0377664i
$990$		0			0
$991$	−14.8225	+	25.6734i	−0.470853	+	0.815541i	−0.999444	−	0.0333351i	$-0.989387\pi$
$991$	−14.8225	+	25.6734i	−0.470853	+	0.815541i	0.528591	+	0.848877i	$0.322720\pi$
$992$	2.49630	−	14.1572i	0.0792577	−	0.449493i
$993$	−3.53046	−	11.3439i	−0.112036	−	0.359989i
$994$	−2.41970	−	0.880699i	−0.0767482	−	0.0279341i
$995$		0			0
$996$	0.237120	−	5.00433i	0.00751342	−	0.158568i
$997$	−39.6480	−	33.2686i	−1.25566	−	1.05363i	−0.996130	−	0.0878926i	$-0.971987\pi$
$997$	−39.6480	−	33.2686i	−1.25566	−	1.05363i	−0.259533	−	0.965734i	$-0.583569\pi$
$998$	91.4487			2.89476
$999$	−30.0184	+	12.0440i	−0.949741	+	0.381054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.g.151.11	yes	66
5.2	odd	4		675.2.u.e.124.2		132
5.3	odd	4		675.2.u.e.124.21		132
5.4	even	2		675.2.l.f.151.1	yes	66
27.22	even	9	inner	675.2.l.g.76.11	yes	66
135.22	odd	36		675.2.u.e.49.21		132
135.49	even	18		675.2.l.f.76.1	✓	66
135.103	odd	36		675.2.u.e.49.2		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.1	✓	66	135.49	even	18
675.2.l.f.151.1	yes	66	5.4	even	2
675.2.l.g.76.11	yes	66	27.22	even	9	inner
675.2.l.g.151.11	yes	66	1.1	even	1	trivial
675.2.u.e.49.2		132	135.103	odd	36
675.2.u.e.49.21		132	135.22	odd	36
675.2.u.e.124.2		132	5.2	odd	4
675.2.u.e.124.21		132	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84958 + 1.55198i) q^{2} +(-1.53931 + 0.794060i) q^{3} +(0.665000 + 3.77140i) q^{4} +(-4.07944 - 0.920299i) q^{6} +(-0.0583477 + 0.330906i) q^{7} +(-2.20872 + 3.82562i) q^{8} +(1.73894 - 2.44461i) q^{9} +(-4.97408 + 1.81042i) q^{11} +(-4.01836 - 5.27730i) q^{12} +(-4.68414 + 3.93046i) q^{13} +(-0.621479 + 0.521483i) q^{14} +(-2.82523 + 1.02830i) q^{16} +(1.52112 + 2.63465i) q^{17} +(7.01028 - 1.82269i) q^{18} +(-0.260295 + 0.450843i) q^{19} +(-0.172944 - 0.555698i) q^{21} +(-12.0097 - 4.37117i) q^{22} +(0.0350517 + 0.198788i) q^{23} +(0.362131 - 7.64266i) q^{24} -14.7637 q^{26} +(-0.735594 + 5.14382i) q^{27} -1.28678 q^{28} +(1.41738 + 1.18933i) q^{29} +(-1.58422 - 8.98458i) q^{31} +(1.48070 + 0.538930i) q^{32} +(6.21906 - 6.73651i) q^{33} +(-1.27550 + 7.23373i) q^{34} +(10.3760 + 4.93257i) q^{36} +(3.11234 + 5.39074i) q^{37} +(-1.18114 + 0.429898i) q^{38} +(4.08931 - 9.76968i) q^{39} +(6.96293 - 5.84259i) q^{41} +(0.542558 - 1.29621i) q^{42} +(6.38441 - 2.32373i) q^{43} +(-10.1356 - 17.5553i) q^{44} +(-0.243684 + 0.422073i) q^{46} +(-2.11902 + 12.0175i) q^{47} +(3.53236 - 3.82627i) q^{48} +(6.47175 + 2.35553i) q^{49} +(-4.43354 - 2.84768i) q^{51} +(-17.9383 - 15.0520i) q^{52} -2.74867 q^{53} +(-9.34365 + 8.37227i) q^{54} +(-1.13705 - 0.954096i) q^{56} +(0.0426766 - 0.900676i) q^{57} +(0.775751 + 4.39950i) q^{58} +(-6.56519 - 2.38954i) q^{59} +(-2.16727 + 12.2912i) q^{61} +(11.0137 - 19.0764i) q^{62} +(0.707472 + 0.718062i) q^{63} +(4.90880 + 8.50230i) q^{64} +(21.9576 - 2.80784i) q^{66} +(4.29512 - 3.60403i) q^{67} +(-8.92479 + 7.48879i) q^{68} +(-0.211805 - 0.278163i) q^{69} +(1.58699 + 2.74874i) q^{71} +(5.51130 + 12.0520i) q^{72} +(-0.731226 + 1.26652i) q^{73} +(-2.60980 + 14.8009i) q^{74} +(-1.87341 - 0.681865i) q^{76} +(-0.308852 - 1.75159i) q^{77} +(22.7259 - 11.7233i) q^{78} +(-2.18198 - 1.83090i) q^{79} +(-2.95220 - 8.50203i) q^{81} +21.9461 q^{82} +(0.578595 + 0.485499i) q^{83} +(1.98075 - 1.02178i) q^{84} +(15.4149 + 5.61055i) q^{86} +(-3.12618 - 0.705250i) q^{87} +(4.06039 - 23.0276i) q^{88} +(-3.18070 + 5.50914i) q^{89} +(-1.02731 - 1.77934i) q^{91} +(-0.726400 + 0.264388i) q^{92} +(9.57291 + 12.5721i) q^{93} +(-22.5703 + 18.9387i) q^{94} +(-2.70719 + 0.346184i) q^{96} +(10.0155 - 3.64534i) q^{97} +(8.31429 + 14.4008i) q^{98} +(-4.22385 + 15.3079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Introduction

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