LMFDB - Embedded newform 675.2.u.e.124.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); 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, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.2
Character	$\chi$	$=$	675.124
Dual form			675.2.u.e.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55198 + 1.84958i) q^{2} +(0.794060 + 1.53931i) q^{3} +(-0.665000 - 3.77140i) q^{4} +(-4.07944 - 0.920299i) q^{6} +(-0.330906 - 0.0583477i) q^{7} +(3.82562 + 2.20872i) q^{8} +(-1.73894 + 2.44461i) q^{9} +(-4.97408 + 1.81042i) q^{11} +(5.27730 - 4.01836i) q^{12} +(3.93046 + 4.68414i) q^{13} +(0.621479 - 0.521483i) q^{14} +(-2.82523 + 1.02830i) q^{16} +(-2.63465 + 1.52112i) q^{17} +(-1.82269 - 7.01028i) q^{18} +(0.260295 - 0.450843i) q^{19} +(-0.172944 - 0.555698i) q^{21} +(4.37117 - 12.0097i) q^{22} +(0.198788 - 0.0350517i) q^{23} +(-0.362131 + 7.64266i) q^{24} -14.7637 q^{26} +(-5.14382 - 0.735594i) q^{27} +1.28678i q^{28} +(-1.41738 - 1.18933i) q^{29} +(-1.58422 - 8.98458i) q^{31} +(-0.538930 + 1.48070i) q^{32} +(-6.73651 - 6.21906i) q^{33} +(1.27550 - 7.23373i) q^{34} +(10.3760 + 4.93257i) q^{36} +(-5.39074 + 3.11234i) q^{37} +(0.429898 + 1.18114i) q^{38} +(-4.08931 + 9.76968i) q^{39} +(6.96293 - 5.84259i) q^{41} +(1.29621 + 0.542558i) q^{42} +(-2.32373 - 6.38441i) q^{43} +(10.1356 + 17.5553i) q^{44} +(-0.243684 + 0.422073i) q^{46} +(-12.0175 - 2.11902i) q^{47} +(-3.82627 - 3.53236i) q^{48} +(-6.47175 - 2.35553i) q^{49} +(-4.43354 - 2.84768i) q^{51} +(15.0520 - 17.9383i) q^{52} +2.74867i q^{53} +(9.34365 - 8.37227i) q^{54} +(-1.13705 - 0.954096i) q^{56} +(0.900676 + 0.0426766i) q^{57} +(4.39950 - 0.775751i) q^{58} +(6.56519 + 2.38954i) q^{59} +(-2.16727 + 12.2912i) q^{61} +(19.0764 + 11.0137i) q^{62} +(0.718062 - 0.707472i) q^{63} +(-4.90880 - 8.50230i) q^{64} +(21.9576 - 2.80784i) q^{66} +(3.60403 + 4.29512i) q^{67} +(7.48879 + 8.92479i) q^{68} +(0.211805 + 0.278163i) q^{69} +(1.58699 + 2.74874i) q^{71} +(-12.0520 + 5.51130i) q^{72} +(1.26652 + 0.731226i) q^{73} +(2.60980 - 14.8009i) q^{74} +(-1.87341 - 0.681865i) q^{76} +(1.75159 - 0.308852i) q^{77} +(-11.7233 - 22.7259i) q^{78} +(2.18198 + 1.83090i) q^{79} +(-2.95220 - 8.50203i) q^{81} +21.9461i q^{82} +(0.485499 - 0.578595i) q^{83} +(-1.98075 + 1.02178i) q^{84} +(15.4149 + 5.61055i) q^{86} +(0.705250 - 3.12618i) q^{87} +(-23.0276 - 4.06039i) q^{88} +(3.18070 - 5.50914i) q^{89} +(-1.02731 - 1.77934i) q^{91} +(-0.264388 - 0.726400i) q^{92} +(12.5721 - 9.57291i) q^{93} +(22.5703 - 18.9387i) q^{94} +(-2.70719 + 0.346184i) q^{96} +(3.64534 + 10.0155i) q^{97} +(14.4008 - 8.31429i) q^{98} +(4.22385 - 15.3079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * 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 $

$2$	−1.55198	+	1.84958i	−1.09742	+	1.30785i	−0.149701	+	0.988731i	$0.547831\pi$
$2$	−1.55198	+	1.84958i	−1.09742	+	1.30785i	−0.947715	+	0.319118i	$0.896613\pi$
$3$	0.794060	+	1.53931i	0.458451	+	0.888720i
$3$	0.794060	+	1.53931i	0.458451	+	0.888720i
$4$	−0.665000	−	3.77140i	−0.332500	−	1.88570i
$5$		0			0
$5$		0			0
$6$	−4.07944	−	0.920299i	−1.66542	−	0.375710i
$7$	−0.330906	−	0.0583477i	−0.125071	−	0.0220534i	0.110762	−	0.993847i	$-0.464671\pi$
$7$	−0.330906	−	0.0583477i	−0.125071	−	0.0220534i	−0.235833	+	0.971794i	$0.575782\pi$
$8$	3.82562	+	2.20872i	1.35256	+	0.780901i
$9$	−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	$0.682995\pi$
$12$	5.27730	−	4.01836i	1.52343	−	1.16000i
$13$	3.93046	+	4.68414i	1.09011	+	1.29915i	0.951109	+	0.308855i	$0.0999459\pi$
$13$	3.93046	+	4.68414i	1.09011	+	1.29915i	0.139005	+	0.990292i	$0.455610\pi$
$14$	0.621479	−	0.521483i	0.166097	−	0.139372i
$15$		0			0
$16$	−2.82523	+	1.02830i	−0.706307	+	0.257075i
$17$	−2.63465	+	1.52112i	−0.638996	+	0.368925i	−0.784228	−	0.620473i	$-0.786941\pi$
$17$	−2.63465	+	1.52112i	−0.638996	+	0.368925i	0.145231	+	0.989398i	$0.453607\pi$
$18$	−1.82269	−	7.01028i	−0.429613	−	1.65234i
$19$	0.260295	−	0.450843i	0.0597157	−	0.103431i	−0.834622	−	0.550823i	$-0.814314\pi$
$19$	0.260295	−	0.450843i	0.0597157	−	0.103431i	0.894338	+	0.447392i	$0.147647\pi$
$20$		0			0
$21$	−0.172944	−	0.555698i	−0.0377396	−	0.121263i
$22$	4.37117	−	12.0097i	0.931936	−	2.56047i
$23$	0.198788	−	0.0350517i	0.0414501	−	0.00730878i	−0.152885	−	0.988244i	$-0.548856\pi$
$23$	0.198788	−	0.0350517i	0.0414501	−	0.00730878i	0.194335	+	0.980935i	$0.437745\pi$
$24$	−0.362131	+	7.64266i	−0.0739197	+	1.56005i
$25$		0			0
$26$	−14.7637			−2.89540
$27$	−5.14382	−	0.735594i	−0.989929	−	0.141565i
$28$			1.28678i			0.243179i
$29$	−1.41738	−	1.18933i	−0.263201	−	0.220852i	0.501631	−	0.865082i	$-0.332734\pi$
$29$	−1.41738	−	1.18933i	−0.263201	−	0.220852i	−0.764832	+	0.644230i	$0.777178\pi$
$30$		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	$-0.361185\pi$
$32$	−0.538930	+	1.48070i	−0.0952703	+	0.261753i
$33$	−6.73651	−	6.21906i	−1.17268	−	1.08260i
$34$	1.27550	−	7.23373i	0.218747	−	1.24058i
$35$		0			0
$36$	10.3760	+	4.93257i	1.72933	+	0.822095i
$37$	−5.39074	+	3.11234i	−0.886232	+	0.511666i	−0.872708	−	0.488242i	$-0.837638\pi$
$37$	−5.39074	+	3.11234i	−0.886232	+	0.511666i	−0.0135239	+	0.999909i	$0.504305\pi$
$38$	0.429898	+	1.18114i	0.0697387	+	0.191605i
$39$	−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	$0.0265778\pi$
$42$	1.29621	+	0.542558i	0.200010	+	0.0837186i
$43$	−2.32373	−	6.38441i	−0.354366	−	0.973613i	−0.980950	−	0.194259i	$-0.937770\pi$
$43$	−2.32373	−	6.38441i	−0.354366	−	0.973613i	0.626584	−	0.779354i	$-0.284452\pi$
$44$	10.1356	+	17.5553i	1.52800	+	2.64657i
$45$		0			0
$46$	−0.243684	+	0.422073i	−0.0359293	+	0.0622313i
$47$	−12.0175	−	2.11902i	−1.75294	−	0.309090i	−0.797288	−	0.603598i	$-0.793733\pi$
$47$	−12.0175	−	2.11902i	−1.75294	−	0.309090i	−0.955649	+	0.294508i	$0.904844\pi$
$48$	−3.82627	−	3.53236i	−0.552275	−	0.509853i
$49$	−6.47175	−	2.35553i	−0.924536	−	0.336504i
$50$		0			0
$51$	−4.43354	−	2.84768i	−0.620819	−	0.398755i
$52$	15.0520	−	17.9383i	2.08734	−	2.48760i
$53$			2.74867i			0.377558i	0.982020	+	0.188779i	$0.0604530\pi$
$53$			2.74867i			0.377558i	−0.982020	+	0.188779i	$0.939547\pi$
$54$	9.34365	−	8.37227i	1.27151	−	1.13932i
$55$		0			0
$56$	−1.13705	−	0.954096i	−0.151944	−	0.127496i
$57$	0.900676	+	0.0426766i	0.119297	+	0.00565265i
$58$	4.39950	−	0.775751i	0.577683	−	0.101861i
$59$	6.56519	+	2.38954i	0.854716	+	0.311091i	0.731961	−	0.681346i	$-0.238605\pi$
$59$	6.56519	+	2.38954i	0.854716	+	0.311091i	0.122754	+	0.992437i	$0.460827\pi$
$60$		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	$0.760917\pi$
$62$	19.0764	+	11.0137i	2.42270	+	1.39875i
$63$	0.718062	−	0.707472i	0.0904673	−	0.0891332i
$64$	−4.90880	−	8.50230i	−0.613601	−	1.06279i
$65$		0			0
$66$	21.9576	−	2.80784i	2.70279	−	0.345621i
$67$	3.60403	+	4.29512i	0.440303	+	0.524732i	0.939865	−	0.341545i	$-0.110950\pi$
$67$	3.60403	+	4.29512i	0.440303	+	0.524732i	−0.499562	+	0.866278i	$0.666506\pi$
$68$	7.48879	+	8.92479i	0.908149	+	1.08229i
$69$	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	$0.773022\pi$
$72$	−12.0520	+	5.51130i	−1.42034	+	0.649513i
$73$	1.26652	+	0.731226i	0.148235	+	0.0855835i	0.572283	−	0.820056i	$-0.306058\pi$
$73$	1.26652	+	0.731226i	0.148235	+	0.0855835i	−0.424048	+	0.905640i	$0.639391\pi$
$74$	2.60980	−	14.8009i	0.303383	−	1.72057i
$75$		0			0
$76$	−1.87341	−	0.681865i	−0.214895	−	0.0782153i
$77$	1.75159	−	0.308852i	0.199612	−	0.0351970i
$78$	−11.7233	−	22.7259i	−1.32740	−	2.57320i
$79$	2.18198	+	1.83090i	0.245491	+	0.205992i	0.757228	−	0.653151i	$-0.226553\pi$
$79$	2.18198	+	1.83090i	0.245491	+	0.205992i	−0.511737	+	0.859142i	$0.670998\pi$
$80$		0			0
$81$	−2.95220	−	8.50203i	−0.328022	−	0.944670i
$82$			21.9461i			2.42354i
$83$	0.485499	−	0.578595i	0.0532905	−	0.0635091i	−0.738741	−	0.673990i	$-0.764579\pi$
$83$	0.485499	−	0.578595i	0.0532905	−	0.0635091i	0.792031	+	0.610481i	$0.209024\pi$
$84$	−1.98075	+	1.02178i	−0.216118	+	0.111486i
$85$		0			0
$86$	15.4149	+	5.61055i	1.66223	+	0.605001i
$87$	0.705250	−	3.12618i	0.0756108	−	0.335162i
$88$	−23.0276	−	4.06039i	−2.45476	−	0.432840i
$89$	3.18070	−	5.50914i	0.337154	−	0.583968i	−0.646742	−	0.762709i	$-0.723869\pi$
$89$	3.18070	−	5.50914i	0.337154	−	0.583968i	0.983896	+	0.178741i	$0.0572024\pi$
$90$		0			0
$91$	−1.02731	−	1.77934i	−0.107691	−	0.186526i
$92$	−0.264388	−	0.726400i	−0.0275644	−	0.0757325i
$93$	12.5721	−	9.57291i	1.30366	−	0.992664i
$94$	22.5703	−	18.9387i	2.32794	−	1.95338i
$95$		0			0
$96$	−2.70719	+	0.346184i	−0.276302	+	0.0353323i
$97$	3.64534	+	10.0155i	0.370128	+	1.01692i	0.975312	+	0.220832i	$0.0708773\pi$
$97$	3.64534	+	10.0155i	0.370128	+	1.01692i	−0.605184	+	0.796086i	$0.706901\pi$
$98$	14.4008	−	8.31429i	1.45470	−	0.839870i
$99$	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	$0.848748\pi$
$102$	12.1478	−	3.78063i	1.20281	−	0.374338i
$103$	0.882932	−	2.42584i	0.0869979	−	0.239025i	−0.888563	−	0.458755i	$-0.848296\pi$
$103$	0.882932	−	2.42584i	0.0869979	−	0.239025i	0.975561	+	0.219730i	$0.0705178\pi$
$104$	4.69048	+	26.6010i	0.459939	+	2.60845i
$105$		0			0
$106$	−5.08387	−	4.26588i	−0.493790	−	0.414339i
$107$		−	5.35813i		−	0.517990i	−0.965879	−	0.258995i	$-0.916609\pi$
$107$		−	5.35813i		−	0.517990i	0.965879	−	0.258995i	$-0.0833913\pi$
$108$	0.646421	+	19.8886i	0.0622019	+	1.91378i
$109$	−17.4957			−1.67579			−0.837893	−	0.545834i	$-0.816213\pi$
$109$	−17.4957			−1.67579			−0.837893	+	0.545834i	$0.816213\pi$
$110$		0			0
$111$	−9.07143	−	5.82662i	−0.861022	−	0.553038i
$112$	0.994885	−	0.175425i	0.0940078	−	0.0165761i
$113$	−5.73211	+	15.7488i	−0.539232	+	1.48153i	0.308564	+	0.951204i	$0.400152\pi$
$113$	−5.73211	+	15.7488i	−0.539232	+	1.48153i	−0.847796	+	0.530323i	$0.822071\pi$
$114$	−1.47677	+	1.59964i	−0.138312	+	0.149820i
$115$		0			0
$116$	−3.54287	+	6.13642i	−0.328947	+	0.569753i
$117$	−18.2857	+	1.46300i	−1.69051	+	0.135255i
$118$	−14.6087	+	8.43433i	−1.34484	+	0.776443i
$119$	0.960576	−	0.349621i	0.0880558	−	0.0320497i
$120$		0			0
$121$	13.0374	−	10.9397i	1.18522	−	0.994514i
$122$	−19.3700	−	23.0842i	−1.75368	−	2.08995i
$123$	14.5225	+	6.07872i	1.30945	+	0.548100i
$124$	−32.8310	+	11.9495i	−2.94831	+	1.07310i
$125$		0			0
$126$	0.194107	+	2.42610i	0.0172925	+	0.216134i
$127$	6.93350	+	4.00306i	0.615249	+	0.355214i	0.775017	−	0.631940i	$-0.217741\pi$
$127$	6.93350	+	4.00306i	0.615249	+	0.355214i	−0.159768	+	0.987155i	$0.551075\pi$
$128$	20.2405	+	3.56894i	1.78902	+	0.315453i
$129$	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	$0.787782\pi$
$132$	−18.9748	+	29.5418i	−1.65154	+	2.57128i
$133$	−0.112439	+	0.133999i	−0.00974968	+	0.0116192i
$134$	−13.5376			−1.16947
$135$		0			0
$136$	−13.4389			−1.15238
$137$	−8.45733	+	10.0791i	−0.722559	+	0.861112i	−0.994877	−	0.101095i	$-0.967765\pi$
$137$	−8.45733	+	10.0791i	−0.722559	+	0.861112i	0.272318	+	0.962207i	$0.412210\pi$
$138$	−0.843201	−	0.0399532i	−0.0717780	−	0.00340105i
$139$	1.27373	+	7.22368i	0.108036	+	0.612705i	0.989964	+	0.141320i	$0.0451346\pi$
$139$	1.27373	+	7.22368i	0.108036	+	0.612705i	−0.881928	+	0.471385i	$0.843754\pi$
$140$		0			0
$141$	−6.28083	−	20.1813i	−0.528941	−	1.69957i
$142$	−7.54699	−	1.33074i	−0.633329	−	0.111673i
$143$	−28.0307	−	16.1835i	−2.34404	−	1.35333i
$144$	2.39911	−	8.69472i	0.199926	−	0.724560i
$145$		0			0
$146$	−3.31807	+	1.20768i	−0.274606	+	0.0999483i
$147$	−1.51308	−	11.8325i	−0.124797	−	0.975924i
$148$	15.3228	+	18.2609i	1.25952	+	1.50104i
$149$	−10.1927	+	8.55268i	−0.835017	+	0.700663i	−0.956437	−	0.291939i	$-0.905700\pi$
$149$	−10.1927	+	8.55268i	−0.835017	+	0.700663i	0.121420	+	0.992601i	$0.461255\pi$
$150$		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	$0.267777\pi$
$152$	1.99158	−	1.14984i	0.161538	−	0.0932641i
$153$	0.862960	−	9.08581i	0.0697662	−	0.734544i
$154$	−2.14718	+	3.71903i	−0.173025	+	0.299688i
$155$		0			0
$156$	39.5648	+	8.92561i	3.16772	+	0.714620i
$157$	−1.51954	+	4.17491i	−0.121273	+	0.333194i	−0.985443	−	0.170005i	$-0.945622\pi$
$157$	−1.51954	+	4.17491i	−0.121273	+	0.333194i	0.864171	+	0.503199i	$0.167844\pi$
$158$	−6.77277	+	1.19422i	−0.538813	+	0.0950072i
$159$	−4.23104	+	2.18261i	−0.335544	+	0.173092i
$160$		0			0
$161$	−0.0678253			−0.00534539
$162$	20.3069	+	7.73466i	1.59546	+	0.607693i
$163$			16.5806i			1.29869i	0.760492	+	0.649347i	$0.224958\pi$
$163$			16.5806i			1.29869i	−0.760492	+	0.649347i	$0.775042\pi$
$164$	−26.6651	−	22.3747i	−2.08220	−	1.74717i
$165$		0			0
$166$	0.316672	+	1.79594i	0.0245785	+	0.139392i
$167$	6.86091	−	18.8502i	0.530913	−	1.45867i	−0.327073	−	0.944999i	$-0.606062\pi$
$167$	6.86091	−	18.8502i	0.530913	−	1.45867i	0.857986	−	0.513673i	$-0.171716\pi$
$168$	0.565763	−	2.50788i	0.0436496	−	0.193487i
$169$	−4.23523	+	24.0192i	−0.325787	+	1.84763i
$170$		0			0
$171$	0.649499	+	1.42031i	0.0496684	+	0.108613i
$172$	−22.5329	+	13.0094i	−1.71812	+	0.991955i
$173$	−1.14526	−	3.14658i	−0.0870725	−	0.239230i	0.888512	−	0.458853i	$-0.151739\pi$
$173$	−1.14526	−	3.14658i	−0.0870725	−	0.239230i	−0.975585	+	0.219623i	$0.929517\pi$
$174$	4.68759	+	6.15619i	0.355365	+	0.466700i
$175$		0			0
$176$	12.1913	−	10.2297i	0.918951	−	0.771091i
$177$	1.53493	+	12.0033i	0.115372	+	0.902223i
$178$	5.25320	+	14.4330i	0.393744	+	1.08180i
$179$	6.19883	+	10.7367i	0.463323	+	0.802498i	0.999124	−	0.0418458i	$-0.0133238\pi$
$179$	6.19883	+	10.7367i	0.463323	+	0.802498i	−0.535802	+	0.844344i	$0.679990\pi$
$180$		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	$0.111488\pi$
$182$	4.88540	+	0.861427i	0.362130	+	0.0638532i
$183$	−20.6409	+	6.42386i	−1.52582	+	0.474865i
$184$	0.837906	+	0.304973i	0.0617713	+	0.0224829i
$185$		0			0
$186$	−1.80576	+	38.1100i	−0.132405	+	2.79436i
$187$	10.3511	−	12.3360i	0.756948	−	0.902095i
$188$			46.7321i			3.40829i
$189$	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	$0.550716\pi$
$192$	9.18977	−	14.3075i	0.663214	−	1.03255i
$193$	−16.6997	+	2.94460i	−1.20207	+	0.211957i	−0.738593	−	0.674152i	$-0.764509\pi$
$193$	−16.6997	+	2.94460i	−1.20207	+	0.211957i	−0.463477	+	0.886109i	$0.653398\pi$
$194$	−24.1819	−	8.80149i	−1.73616	−	0.631910i
$195$		0			0
$196$	−4.57992	+	25.9740i	−0.327137	+	1.85529i
$197$	5.91232	+	3.41348i	0.421236	+	0.243200i	0.695606	−	0.718424i	$-0.255136\pi$
$197$	5.91232	+	3.41348i	0.421236	+	0.243200i	−0.274370	+	0.961624i	$0.588469\pi$
$198$	21.7578	+	31.5699i	1.54626	+	2.24357i
$199$	7.72021	+	13.3718i	0.547271	+	0.947901i	0.998460	+	0.0554726i	$0.0176666\pi$
$199$	7.72021	+	13.3718i	0.547271	+	0.947901i	−0.451189	+	0.892428i	$0.649000\pi$
$200$		0			0
$201$	−3.74969	+	8.95830i	−0.264483	+	0.631870i
$202$	−18.8711	−	22.4898i	−1.32777	−	1.58237i
$203$	0.399626	+	0.476256i	0.0280483	+	0.0334266i
$204$	−7.79145	+	18.6144i	−0.545510	+	1.30327i
$205$		0			0
$206$	3.11648	+	5.39790i	0.217135	+	0.376090i
$207$	−0.259992	+	0.546911i	−0.0180707	+	0.0380129i
$208$	−15.9211	−	9.19208i	−1.10393	−	0.637356i
$209$	−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	$0.392126\pi$
$212$	10.3663	−	1.82786i	0.711963	−	0.125538i
$213$	−2.97100	+	4.62553i	−0.203569	+	0.316936i
$214$	9.91028	+	8.31571i	0.677453	+	0.568450i
$215$		0			0
$216$	−18.0536	−	14.1754i	−1.22839	−	0.964512i
$217$			3.06549i			0.208099i
$218$	27.1530	−	32.3597i	1.83904	−	2.19168i
$219$	−0.119888	+	2.53020i	−0.00810129	+	0.170975i
$220$		0			0
$221$	−17.4805	−	6.36239i	−1.17587	−	0.427980i
$222$	24.8555	−	7.73552i	1.66819	−	0.519174i
$223$	−3.06856	−	0.541070i	−0.205486	−	0.0362328i	0.0699575	−	0.997550i	$-0.477714\pi$
$223$	−3.06856	−	0.541070i	−0.205486	−	0.0362328i	−0.275444	+	0.961317i	$0.588825\pi$
$224$	0.264731	−	0.458527i	0.0176881	−	0.0306366i
$225$		0			0
$226$	−20.2326	−	35.0439i	−1.34585	−	2.33108i
$227$	−2.38634	−	6.55642i	−0.158387	−	0.435165i	0.834962	−	0.550308i	$-0.185490\pi$
$227$	−2.38634	−	6.55642i	−0.158387	−	0.435165i	−0.993349	+	0.115143i	$0.963267\pi$
$228$	−0.437999	−	3.42519i	−0.0290072	−	0.226839i
$229$	7.76380	−	6.51460i	0.513046	−	0.430497i	−0.349153	−	0.937066i	$-0.613531\pi$
$229$	7.76380	−	6.51460i	0.513046	−	0.430497i	0.862200	+	0.506569i	$0.169086\pi$
$230$		0			0
$231$	1.86628	+	2.45099i	0.122793	+	0.161263i
$232$	−2.79548	−	7.68051i	−0.183532	−	0.504250i
$233$	9.72275	−	5.61343i	0.636959	−	0.367748i	−0.146483	−	0.989213i	$-0.546795\pi$
$233$	9.72275	−	5.61343i	0.636959	−	0.367748i	0.783442	+	0.621465i	$0.213462\pi$
$234$	25.6731	−	36.0914i	1.67830	−	2.35937i
$235$		0			0
$236$	4.64605	−	26.3490i	0.302432	−	1.71518i
$237$	−1.08569	+	4.81257i	−0.0705232	+	0.312610i
$238$	−0.844143	+	2.31926i	−0.0547177	+	0.150336i
$239$	−2.49115	−	14.1280i	−0.161139	−	0.913864i	−0.952957	−	0.303106i	$-0.901976\pi$
$239$	−2.49115	−	14.1280i	−0.161139	−	0.913864i	0.791818	−	0.610757i	$-0.209135\pi$
$240$		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	$0.828394\pi$
$242$			41.0918i			2.64148i
$243$	10.7430	−	11.2955i	0.689165	−	0.724605i
$244$	47.7963			3.05985
$245$		0			0
$246$	−33.7818	+	17.4265i	−2.15385	+	1.11107i
$247$	3.13489	−	0.552766i	0.199468	−	0.0351717i
$248$	13.7838	−	37.8707i	0.875273	−	2.40479i
$249$	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	$0.151263\pi$
$252$	−3.14568	−	2.23763i	−0.198159	−	0.140958i
$253$	−0.925329	+	0.534239i	−0.0581749	+	0.0335873i
$254$	−18.1646	+	6.61139i	−1.13975	+	0.414835i
$255$		0			0
$256$	−22.9724	+	19.2761i	−1.43577	+	1.20476i
$257$	−15.4081	−	18.3627i	−0.961131	−	1.14543i	−0.989310	−	0.145828i	$-0.953415\pi$
$257$	−15.4081	−	18.3627i	−0.961131	−	1.14543i	0.0281791	−	0.999603i	$-0.491029\pi$
$258$	3.60396	+	28.1833i	0.224373	+	1.75462i
$259$	1.96543	−	0.715357i	0.122126	−	0.0444501i
$260$		0			0
$261$	5.37217	−	1.39678i	0.332529	−	0.0864586i
$262$	−22.6179	−	13.0585i	−1.39734	−	0.806755i
$263$	8.09931	+	1.42813i	0.499425	+	0.0880621i	0.417686	−	0.908592i	$-0.362841\pi$
$263$	8.09931	+	1.42813i	0.499425	+	0.0880621i	0.0817395	+	0.996654i	$0.473952\pi$
$264$	−12.0351	−	38.6708i	−0.740712	−	2.38002i
$265$		0			0
$266$	−0.0733394	−	0.415929i	−0.00449673	−	0.0255022i
$267$	11.0059	+	0.521493i	0.673552	+	0.0319148i
$268$	13.8019	−	16.4485i	0.843088	−	1.00475i
$269$	−2.05741			−0.125442			−0.0627211	−	0.998031i	$-0.519978\pi$
$269$	−2.05741			−0.125442			−0.0627211	+	0.998031i	$0.519978\pi$
$270$		0			0
$271$	−15.4436			−0.938131			−0.469066	−	0.883163i	$-0.655409\pi$
$271$	−15.4436			−0.938131			−0.469066	+	0.883163i	$0.655409\pi$
$272$	5.87933	−	7.00671i	0.356486	−	0.424844i
$273$	1.92322	−	2.99425i	0.116398	−	0.181220i
$274$	−5.51639	−	31.2850i	−0.333257	−	1.89000i
$275$		0			0
$276$	0.908213	−	0.983780i	0.0546680	−	0.0592166i
$277$	−1.18559	−	0.209051i	−0.0712350	−	0.0125607i	0.137917	−	0.990444i	$-0.455959\pi$
$277$	−1.18559	−	0.209051i	−0.0712350	−	0.0125607i	−0.209152	+	0.977883i	$0.567070\pi$
$278$	−15.3376	−	8.85515i	−0.919887	−	0.531097i
$279$	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	$0.0779825\pi$
$282$	47.0746	+	19.7041i	2.80325	+	1.17336i
$283$	−14.5809	−	17.3768i	−0.866745	−	1.03295i	−0.999128	−	0.0417476i	$-0.986707\pi$
$283$	−14.5809	−	17.3768i	−0.866745	−	1.03295i	0.132383	−	0.991199i	$-0.457737\pi$
$284$	9.31127	−	7.81309i	0.552522	−	0.463621i
$285$		0			0
$286$	73.4357	−	26.7284i	4.34235	−	1.58048i
$287$	−2.64498	+	1.52708i	−0.156128	+	0.0901406i
$288$	−2.68256	−	3.89231i	−0.158071	−	0.229357i
$289$	−3.87241	+	6.70722i	−0.227789	+	0.394542i
$290$		0			0
$291$	−12.5223	+	13.5642i	−0.734069	+	0.795147i
$292$	1.91551	−	5.26282i	0.112097	−	0.307983i
$293$	−16.4398	+	2.89878i	−0.960422	+	0.169348i	−0.631816	−	0.775119i	$-0.717690\pi$
$293$	−16.4398	+	2.89878i	−0.960422	+	0.169348i	−0.328606	+	0.944467i	$0.606579\pi$
$294$	24.2333	+	15.5652i	1.41332	+	0.907779i
$295$		0			0
$296$	−27.4972			−1.59824
$297$	26.9175	−	5.65356i	1.56191	−	0.328053i
$298$		−	32.1258i		−	1.86100i
$299$	0.945515	+	0.793381i	0.0546806	+	0.0458824i
$300$		0			0
$301$	0.396423	+	2.24822i	0.0228494	+	0.129586i
$302$	−7.53697	+	20.7076i	−0.433704	+	1.19159i
$303$	−20.1093	+	6.25842i	−1.15525	+	0.359537i
$304$	−0.271790	+	1.54140i	−0.0155882	+	0.0884051i
$305$		0			0
$306$	15.4656	+	15.6971i	0.884110	+	0.897344i
$307$	−5.50011	+	3.17549i	−0.313908	+	0.181235i	−0.648674	−	0.761066i	$-0.724676\pi$
$307$	−5.50011	+	3.17549i	−0.313908	+	0.181235i	0.334766	+	0.942301i	$0.391343\pi$
$308$	−2.32961	−	6.40056i	−0.132742	−	0.364706i
$309$	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	$0.282476\pi$
$312$	−37.2227	+	28.3429i	−2.10732	+	1.60460i
$313$	5.53741	+	15.2139i	0.312993	+	0.859942i	0.992049	+	0.125855i	$0.0401673\pi$
$313$	5.53741	+	15.2139i	0.312993	+	0.859942i	−0.679056	+	0.734087i	$0.737610\pi$
$314$	−5.36352	−	9.28988i	−0.302681	−	0.524258i
$315$		0			0
$316$	5.45403	−	9.44666i	0.306813	−	0.531416i
$317$	8.30814	+	1.46495i	0.466631	+	0.0822797i	0.402020	−	0.915631i	$-0.368308\pi$
$317$	8.30814	+	1.46495i	0.466631	+	0.0822797i	0.0646113	+	0.997911i	$0.479419\pi$
$318$	2.52960	−	11.2130i	0.141853	−	0.628794i
$319$	9.20335	+	3.34975i	0.515289	+	0.187550i
$320$		0			0
$321$	8.24781	−	4.25468i	0.460348	−	0.237473i
$322$	0.105264	−	0.125448i	0.00586611	−	0.00699096i
$323$			1.58375i			0.0881223i
$324$	−30.1014	+	16.7878i	−1.67230	+	0.932655i
$325$		0			0
$326$	−30.6672	−	25.7328i	−1.69850	−	1.42521i
$327$	−13.8927	−	26.9313i	−0.768266	−	1.48930i
$328$	39.5422	−	6.97235i	2.18335	−	0.384984i
$329$	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	$0.995190\pi$
$332$	−2.50497	−	1.44625i	−0.137478	−	0.0793731i
$333$	1.76570	−	18.5904i	0.0967596	−	1.01875i
$334$	24.2169	+	41.9449i	1.32509	+	2.29513i
$335$		0			0
$336$	1.06003	+	1.39214i	0.0578295	+	0.0759472i
$337$	13.5234	+	16.1166i	0.736667	+	0.877926i	0.996136	−	0.0878255i	$-0.0279918\pi$
$337$	13.5234	+	16.1166i	0.736667	+	0.877926i	−0.259468	+	0.965752i	$0.583547\pi$
$338$	−37.8523	−	45.1107i	−2.05890	−	2.45370i
$339$	−28.7940	+	3.68205i	−1.56387	+	0.199981i
$340$		0			0
$341$	24.1459	+	41.8219i	1.30757	+	2.26478i
$342$	−3.63498	−	1.00299i	−0.196557	−	0.0542354i
$343$	4.04106	+	2.33311i	0.218197	+	0.125976i
$344$	5.21166	−	29.5568i	0.280994	−	1.59360i
$345$		0			0
$346$	7.59726	+	2.76518i	0.408431	+	0.148657i
$347$	10.9857	−	1.93708i	0.589744	−	0.103988i	0.129190	−	0.991620i	$-0.458762\pi$
$347$	10.9857	−	1.93708i	0.589744	−	0.103988i	0.460553	+	0.887632i	$0.347651\pi$
$348$	−12.2591	−	0.580871i	−0.657156	−	0.0311379i
$349$	6.90169	+	5.79120i	0.369439	+	0.309996i	0.808540	−	0.588442i	$-0.200258\pi$
$349$	6.90169	+	5.79120i	0.369439	+	0.309996i	−0.439101	+	0.898438i	$0.644703\pi$
$350$		0			0
$351$	−16.7720	−	26.9856i	−0.895221	−	1.44039i
$352$		−	8.34080i		−	0.444566i
$353$	−6.14780	+	7.32667i	−0.327214	+	0.389959i	−0.904422	−	0.426638i	$-0.859698\pi$
$353$	−6.14780	+	7.32667i	−0.327214	+	0.389959i	0.577208	+	0.816597i	$0.304142\pi$
$354$	−24.5832	−	15.7899i	−1.30658	−	0.839224i
$355$		0			0
$356$	−22.8924	−	8.33214i	−1.21329	−	0.441603i
$357$	1.30093	+	1.20100i	0.0688525	+	0.0635637i
$358$	−29.4788	−	5.19791i	−1.55800	−	0.274718i
$359$	12.6845	−	21.9702i	0.669463	−	1.15954i	−0.308591	−	0.951195i	$-0.599857\pi$
$359$	12.6845	−	21.9702i	0.669463	−	1.15954i	0.978054	−	0.208350i	$-0.0668092\pi$
$360$		0			0
$361$	9.36449	+	16.2198i	0.492868	+	0.853673i
$362$	3.83249	+	10.5297i	0.201431	+	0.553427i
$363$	27.1919	+	11.3818i	1.42721	+	0.597389i
$364$	−6.02747	+	5.05765i	−0.315925	+	0.265093i
$365$		0			0
$366$	20.1528	−	48.1466i	1.05341	−	2.51667i
$367$	9.18829	+	25.2446i	0.479625	+	1.31776i	0.909813	+	0.415019i	$0.136225\pi$
$367$	9.18829	+	25.2446i	0.479625	+	1.31776i	−0.430188	+	0.902740i	$0.641553\pi$
$368$	−0.525578	+	0.303442i	−0.0273976	+	0.0158180i
$369$	2.17474	+	27.1815i	0.113213	+	1.41501i
$370$		0			0
$371$	0.160378	−	0.909551i	0.00832643	−	0.0472215i
$372$	−44.4637	−	41.0484i	−2.30534	−	2.12826i
$373$	−8.61440	+	23.6679i	−0.446037	+	1.22548i	0.489424	+	0.872046i	$0.337207\pi$
$373$	−8.61440	+	23.6679i	−0.446037	+	1.22548i	−0.935461	+	0.353430i	$0.885015\pi$
$374$	6.75162	+	38.2904i	0.349118	+	1.97995i
$375$		0			0
$376$	−41.2942	−	34.6499i	−2.12959	−	1.78693i
$377$		−	11.3138i		−	0.582691i
$378$	−3.58037	+	2.22526i	−0.184155	+	0.114455i
$379$	−25.4242			−1.30595			−0.652976	−	0.757379i	$-0.726480\pi$
$379$	−25.4242			−1.30595			−0.652976	+	0.757379i	$0.726480\pi$
$380$		0			0
$381$	−0.656322	+	13.8515i	−0.0336244	+	0.709632i
$382$	−33.7230	+	5.94628i	−1.72542	+	0.304238i
$383$	3.38390	−	9.29719i	0.172909	−	0.475064i	−0.822721	−	0.568445i	$-0.807545\pi$
$383$	3.38390	−	9.29719i	0.172909	−	0.475064i	0.995630	+	0.0933808i	$0.0297674\pi$
$384$	10.5784	+	33.9903i	0.539829	+	1.73456i
$385$		0			0
$386$	20.4713	−	35.4573i	1.04196	−	1.80473i
$387$	19.6482	+	5.42146i	0.998773	+	0.275589i
$388$	35.3483	−	20.4083i	1.79454	−	1.03608i
$389$	4.09700	−	1.49119i	0.207726	−	0.0756061i	−0.236061	−	0.971738i	$-0.575857\pi$
$389$	4.09700	−	1.49119i	0.207726	−	0.0756061i	0.443788	+	0.896132i	$0.353634\pi$
$390$		0			0
$391$	−0.470419	+	0.394728i	−0.0237901	+	0.0199623i
$392$	−19.5558	−	23.3057i	−0.987715	−	1.17711i
$393$	−14.9061	+	11.3501i	−0.751913	+	0.572539i
$394$	−15.4893	+	5.63765i	−0.780340	+	0.284021i
$395$		0			0
$396$	−60.5410	−	5.75012i	−3.04230	−	0.288954i
$397$	14.0365	+	8.10396i	0.704470	+	0.406726i	0.809010	−	0.587795i	$-0.200004\pi$
$397$	14.0365	+	8.10396i	0.704470	+	0.406726i	−0.104540	+	0.994521i	$0.533337\pi$
$398$	−36.7138	−	6.47363i	−1.84030	−	0.324494i
$399$	−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	$0.949537\pi$
$402$	−10.7496	−	20.8385i	−0.536143	−	1.03933i
$403$	35.8583	−	42.7343i	1.78623	−	2.12875i
$404$	46.5654			2.31672
$405$		0			0
$406$	−1.50109			−0.0744976
$407$	21.1793	−	25.2405i	1.04982	−	1.25113i
$408$	−10.6713	−	20.6866i	−0.528308	−	1.02414i
$409$	−4.23533	−	24.0197i	−0.209423	−	1.18770i	−0.890326	−	0.455325i	$-0.849523\pi$
$409$	−4.23533	−	24.0197i	−0.209423	−	1.18770i	0.680902	−	0.732374i	$-0.261588\pi$
$410$		0			0
$411$	−22.2304	−	5.01506i	−1.09654	−	0.247375i
$412$	−9.73596	−	1.71671i	−0.479656	−	0.0845763i
$413$	−2.03304	−	1.17378i	−0.100039	−	0.0577577i
$414$	−0.608052	−	1.32967i	−0.0298841	−	0.0653497i
$415$		0			0
$416$	−9.05405	+	3.29540i	−0.443911	+	0.161570i
$417$	−10.1081	+	7.69670i	−0.494994	+	0.376909i
$418$	−4.27669	−	5.09677i	−0.209180	−	0.249291i
$419$	13.1999	−	11.0760i	0.644855	−	0.541098i	−0.260650	−	0.965433i	$-0.583937\pi$
$419$	13.1999	−	11.0760i	0.644855	−	0.541098i	0.905505	+	0.424336i	$0.139492\pi$
$420$		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	$0.203378\pi$
$422$	−38.5718	+	22.2694i	−1.87765	+	1.08406i
$423$	26.0779	−	25.6933i	1.26795	−	1.24925i
$424$	−6.07104	+	10.5154i	−0.294836	+	0.510671i
$425$		0			0
$426$	−3.94435	−	12.6738i	−0.191104	−	0.614049i
$427$	1.43433	−	3.94078i	0.0694119	−	0.190708i
$428$	−20.2077	+	3.56316i	−0.976775	+	0.172232i
$429$	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	$0.579897\pi$
$432$	15.2889	−	3.21117i	0.735587	−	0.154497i
$433$			11.0194i			0.529557i	0.964309	+	0.264778i	$0.0852988\pi$
$433$			11.0194i			0.529557i	−0.964309	+	0.264778i	$0.914701\pi$
$434$	−5.66986	−	4.75758i	−0.272162	−	0.228371i
$435$		0			0
$436$	11.6347	+	65.9835i	0.557199	+	3.16003i
$437$	0.0359406	−	0.0987460i	0.00171927	−	0.00472366i
$438$	−4.49374	−	4.14856i	−0.214719	−	0.198226i
$439$	4.27981	−	24.2720i	0.204264	−	1.15844i	−0.694329	−	0.719658i	$-0.744299\pi$
$439$	4.27981	−	24.2720i	0.204264	−	1.15844i	0.898593	−	0.438783i	$-0.144590\pi$
$440$		0			0
$441$	17.0123	−	11.7248i	0.810110	−	0.558323i
$442$	38.8971	−	22.4573i	1.85015	−	1.06818i
$443$	7.48678	+	20.5698i	0.355708	+	0.977299i	0.980502	+	0.196509i	$0.0629606\pi$
$443$	7.48678	+	20.5698i	0.355708	+	0.977299i	−0.624794	+	0.780789i	$0.714817\pi$
$444$	−15.9420	+	38.0867i	−0.756575	+	1.80752i
$445$		0			0
$446$	5.76310	−	4.83582i	0.272891	−	0.228983i
$447$	−21.2588	−	8.89834i	−1.00551	−	0.420877i
$448$	1.12826	+	3.09988i	0.0533055	+	0.146456i
$449$	0.0863524	+	0.149567i	0.00407522	+	0.00705849i	0.868056	−	0.496467i	$-0.165369\pi$
$449$	0.0863524	+	0.149567i	0.00407522	+	0.00705849i	−0.863981	+	0.503525i	$0.832036\pi$
$450$		0			0
$451$	−24.0566	+	41.6673i	−1.13278	+	1.96204i
$452$	63.2071	+	11.1451i	2.97301	+	0.524222i
$453$	11.6154	+	10.7232i	0.545739	+	0.503819i
$454$	15.8302	+	5.76171i	0.742947	+	0.270411i
$455$		0			0
$456$	3.35138	+	2.15261i	0.156943	+	0.100805i
$457$	−5.76201	+	6.86690i	−0.269536	+	0.321220i	−0.883786	−	0.467891i	$-0.845014\pi$
$457$	−5.76201	+	6.86690i	−0.269536	+	0.321220i	0.614251	+	0.789111i	$0.289458\pi$
$458$			24.4703i			1.14342i
$459$	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	$0.598510\pi$
$462$	−7.42973	−	0.352042i	−0.345662	−	0.0163785i
$463$	13.5465	−	2.38861i	0.629558	−	0.111008i	0.150240	−	0.988650i	$-0.451995\pi$
$463$	13.5465	−	2.38861i	0.629558	−	0.111008i	0.479318	+	0.877642i	$0.340884\pi$
$464$	5.22741	+	1.90262i	0.242677	+	0.0883270i
$465$		0			0
$466$	−4.70704	+	26.6949i	−0.218049	+	1.23662i
$467$	−3.62851	−	2.09492i	−0.167907	−	0.0969414i	0.413691	−	0.910417i	$-0.364239\pi$
$467$	−3.62851	−	2.09492i	−0.167907	−	0.0969414i	−0.581599	+	0.813476i	$0.697573\pi$
$468$	17.6776	+	67.9899i	0.817146	+	3.14283i
$469$	−0.941987	−	1.63157i	−0.0434969	−	0.0753389i
$470$		0			0
$471$	−7.63307	+	0.976085i	−0.351713	+	0.0449756i
$472$	19.8381	+	23.6421i	0.913123	+	1.08822i
$473$	23.1169	+	27.5496i	1.06292	+	1.26673i
$474$	−7.21626	−	9.47709i	−0.331454	−	0.435297i
$475$		0			0
$476$	−1.95734	−	3.39022i	−0.0897148	−	0.155391i
$477$	−6.71941	−	4.77976i	−0.307661	−	0.218850i
$478$	29.9970	+	17.3188i	1.37203	+	0.792143i
$479$	−4.29952	+	24.3838i	−0.196450	+	1.11412i	0.713888	+	0.700259i	$0.246932\pi$
$479$	−4.29952	+	24.3838i	−0.196450	+	1.11412i	−0.910339	+	0.413864i	$0.864179\pi$
$480$		0			0
$481$	−35.7668	−	13.0180i	−1.63082	−	0.593571i
$482$	24.1704	−	4.26190i	1.10093	−	0.194124i
$483$	−0.0538574	−	0.104404i	−0.00245060	−	0.00475055i
$484$	−49.9277	−	41.8943i	−2.26944	−	1.90429i
$485$		0			0
$486$	4.21890	+	37.4004i	0.191373	+	1.69652i
$487$		−	14.2164i		−	0.644205i	−0.946705	−	0.322102i	$-0.895610\pi$
$487$		−	14.2164i		−	0.644205i	0.946705	−	0.322102i	$-0.104390\pi$
$488$	−35.4390	+	42.2346i	−1.60425	+	1.91187i
$489$	−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	$0.694088\pi$
$492$	13.2678	−	58.8127i	0.598160	−	2.65148i
$493$	5.54341	+	0.977453i	0.249663	+	0.0440222i
$494$	−3.84291	+	6.65611i	−0.172901	+	0.299473i
$495$		0			0
$496$	13.7146	+	23.7544i	0.615805	+	1.06661i
$497$	−0.364761	−	1.00217i	−0.0163618	−	0.0449536i
$498$	−2.51304	+	1.91354i	−0.112612	+	0.0857477i
$499$	−29.0144	+	24.3459i	−1.29886	+	1.08987i	−0.308520	+	0.951218i	$0.599834\pi$
$499$	−29.0144	+	24.3459i	−1.29886	+	1.08987i	−0.990341	+	0.138656i	$0.955722\pi$
$500$		0			0
$501$	34.4642	−	4.40714i	1.53975	−	0.196897i
$502$	1.26577	+	3.47767i	0.0564940	+	0.155216i
$503$	−31.4533	+	18.1596i	−1.40243	+	0.809694i	−0.994642	−	0.103381i	$-0.967034\pi$
$503$	−31.4533	+	18.1596i	−1.40243	+	0.809694i	−0.407790	+	0.913076i	$0.633700\pi$
$504$	4.30964	−	1.12052i	0.191967	−	0.0499120i
$505$		0			0
$506$	0.447976	−	2.54060i	0.0199149	−	0.112943i
$507$	−40.3359	+	12.5533i	−1.79138	+	0.557514i
$508$	10.4864	−	28.8111i	0.465258	−	1.27828i
$509$	1.95163	+	11.0682i	0.0865043	+	0.490590i	0.997022	+	0.0771197i	$0.0245724\pi$
$509$	1.95163	+	11.0682i	0.0865043	+	0.490590i	−0.910518	+	0.413470i	$0.864317\pi$
$510$		0			0
$511$	−0.376434	−	0.315866i	−0.0166525	−	0.0139731i
$512$		−	31.3000i		−	1.38328i
$513$	−1.67055	+	2.12759i	−0.0737564	+	0.0939352i
$514$	57.8762			2.55281
$515$		0			0
$516$	−37.9179	−	24.3548i	−1.66924	−	1.07216i
$517$	63.6125	−	11.2166i	2.79767	−	0.493305i
$518$	−1.72720	+	4.74543i	−0.0758886	+	0.208502i
$519$	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	$0.135918\pi$
$522$	−5.75405	+	12.1040i	−0.251848	+	0.529779i
$523$	−13.5084	+	7.79908i	−0.590681	+	0.341030i	−0.765367	−	0.643594i	$-0.777442\pi$
$523$	−13.5084	+	7.79908i	−0.590681	+	0.341030i	0.174686	+	0.984624i	$0.444109\pi$
$524$	38.9261	−	14.1679i	1.70050	−	0.618930i
$525$		0			0
$526$	−15.2114	+	12.7639i	−0.663249	+	0.556532i
$527$	17.8405	+	21.2614i	0.777143	+	0.926163i
$528$	25.4272	+	10.6431i	1.10658	+	0.463182i
$529$	−21.5746	+	7.85253i	−0.938028	+	0.341414i
$530$		0			0
$531$	−17.2579	+	11.8941i	−0.748930	+	0.516158i
$532$	0.580137	+	0.334942i	0.0251521	+	0.0145216i
$533$	54.7350	+	9.65127i	2.37084	+	0.418043i
$534$	−18.0455	+	19.5470i	−0.780907	+	0.845881i
$535$		0			0
$536$	4.30093	+	24.3918i	0.185772	+	1.05357i
$537$	−11.6048	+	18.0675i	−0.500785	+	0.779670i
$538$	3.19305	−	3.80533i	0.137662	−	0.164060i
$539$	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	$0.510462\pi$
$542$	23.9681	−	28.5641i	1.02952	−	1.22693i
$543$	8.02941	+	0.380456i	0.344575	+	0.0163269i
$544$	−0.832422	−	4.72090i	−0.0356898	−	0.202407i
$545$		0			0
$546$	2.55330	+	8.20415i	0.109271	+	0.351105i
$547$	−12.0871	−	2.13129i	−0.516808	−	0.0911273i	−0.0908404	−	0.995865i	$-0.528955\pi$
$547$	−12.0871	−	2.13129i	−0.516808	−	0.0911273i	−0.425968	+	0.904738i	$0.640066\pi$
$548$	43.6363	+	25.1934i	1.86405	+	1.07621i
$549$	−26.2784	−	26.6717i	−1.12154	−	1.13832i
$550$		0			0
$551$	−0.905136	+	0.329443i	−0.0385601	+	0.0140347i
$552$	0.195901	+	1.53196i	0.00833809	+	0.0652047i
$553$	−0.615201	−	0.733168i	−0.0261610	−	0.0311775i
$554$	2.22666	−	1.86839i	0.0946019	−	0.0793804i
$555$		0			0
$556$	26.3964	−	9.60751i	1.11946	−	0.407449i
$557$	15.5748	−	8.99212i	0.659926	−	0.381008i	−0.132323	−	0.991207i	$-0.542244\pi$
$557$	15.5748	−	8.99212i	0.659926	−	0.381008i	0.792249	+	0.610198i	$0.208910\pi$
$558$	−60.0969	+	27.4820i	−2.54410	+	1.16341i
$559$	20.7721	−	35.9784i	0.878567	−	1.52172i
$560$		0			0
$561$	27.2082	+	6.13804i	1.14873	+	0.259148i
$562$	−22.9424	+	63.0338i	−0.967768	+	2.65892i
$563$	−9.26763	+	1.63413i	−0.390584	+	0.0688705i	−0.365492	−	0.930815i	$-0.619099\pi$
$563$	−9.26763	+	1.63413i	−0.390584	+	0.0688705i	−0.0250923	+	0.999685i	$0.507988\pi$
$564$	−71.9351	+	37.1081i	−3.02901	+	1.56253i
$565$		0			0
$566$	54.7691			2.30212
$567$	0.480827	+	2.98563i	0.0201928	+	0.125385i
$568$			14.0209i			0.588302i
$569$	25.8778	+	21.7141i	1.08485	+	0.910301i	0.996315	−	0.0857719i	$-0.0273356\pi$
$569$	25.8778	+	21.7141i	1.08485	+	0.910301i	0.0885394	+	0.996073i	$0.471780\pi$
$570$		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	$0.982081\pi$
$572$	−42.3942	+	116.477i	−1.77259	+	4.87015i
$573$	−5.40588	+	23.9628i	−0.225834	+	1.00106i
$574$	1.28050	−	7.26209i	0.0534472	−	0.303114i
$575$		0			0
$576$	29.3209	+	2.78486i	1.22170	+	0.116036i
$577$	−13.7529	+	7.94027i	−0.572543	+	0.330558i	−0.758164	−	0.652064i	$-0.773904\pi$
$577$	−13.7529	+	7.94027i	−0.572543	+	0.330558i	0.185622	+	0.982621i	$0.440570\pi$
$578$	−6.39561	−	17.5718i	−0.266022	−	0.730891i
$579$	−17.7932	−	23.3678i	−0.739460	−	0.971131i
$580$		0			0
$581$	−0.194414	+	0.163133i	−0.00806567	+	0.00676790i
$582$	−5.65368	−	44.2123i	−0.234353	−	1.83266i
$583$	−4.97623	−	13.6721i	−0.206094	−	0.566240i
$584$	3.23015	+	5.59478i	0.133664	+	0.231514i
$585$		0			0
$586$	20.1527	−	34.9055i	0.832500	−	1.44193i
$587$	−19.5714	−	3.45096i	−0.807797	−	0.142436i	−0.245527	−	0.969390i	$-0.578961\pi$
$587$	−19.5714	−	3.45096i	−0.807797	−	0.142436i	−0.562270	+	0.826953i	$0.690072\pi$
$588$	−43.6187	+	13.5750i	−1.79881	+	0.559825i
$589$	−4.46300	−	1.62440i	−0.183895	−	0.0669323i
$590$		0			0
$591$	−0.559657	+	11.8114i	−0.0230212	+	0.485856i
$592$	12.0296	−	14.3364i	0.494416	−	0.589221i
$593$		−	43.0280i		−	1.76695i	−0.468480	−	0.883474i	$-0.655198\pi$
$593$		−	43.0280i		−	1.76695i	0.468480	−	0.883474i	$-0.344802\pi$
$594$	−31.3188	+	58.5603i	−1.28502	+	2.40276i
$595$		0			0
$596$	39.0337	+	32.7532i	1.59888	+	1.34162i
$597$	−14.4530	+	22.5018i	−0.591521	+	0.920936i
$598$	−2.93484	+	0.517492i	−0.120015	+	0.0211618i
$599$	−36.3045	−	13.2138i	−1.48336	−	0.539900i	−0.531671	−	0.846951i	$-0.678436\pi$
$599$	−36.3045	−	13.2138i	−1.48336	−	0.539900i	−0.951693	+	0.307051i	$0.900658\pi$
$600$		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	$0.105083\pi$
$602$	−4.77351	−	2.75599i	−0.194554	−	0.112326i
$603$	−16.7671	+	1.34150i	−0.682808	+	0.0546302i
$604$	−17.4762	−	30.2697i	−0.711098	−	1.23166i
$605$		0			0
$606$	19.6338	−	46.9067i	0.797570	−	1.90546i
$607$	−0.547047	−	0.651945i	−0.0222040	−	0.0264616i	0.754828	−	0.655923i	$-0.227720\pi$
$607$	−0.547047	−	0.651945i	−0.0222040	−	0.0264616i	−0.777032	+	0.629461i	$0.783276\pi$
$608$	0.527283	+	0.628391i	0.0213841	+	0.0254846i
$609$	−0.415777	+	0.993324i	−0.0168482	+	0.0402515i
$610$		0			0
$611$	−37.3087	−	64.6205i	−1.50935	−	2.61427i
$612$	−34.8401	+	2.78749i	−1.40833	+	0.112678i
$613$	0.145420	+	0.0839581i	0.00587345	+	0.00339104i	0.502934	−	0.864325i	$-0.332254\pi$
$613$	0.145420	+	0.0839581i	0.00587345	+	0.00339104i	−0.497060	+	0.867716i	$0.665587\pi$
$614$	2.66275	−	15.1012i	0.107460	−	0.609434i
$615$		0			0
$616$	7.38308	+	2.68722i	0.297473	+	0.108271i
$617$	−16.3908	+	2.89015i	−0.659871	+	0.116353i	−0.493548	−	0.869718i	$-0.664300\pi$
$617$	−16.3908	+	2.89015i	−0.659871	+	0.116353i	−0.166322	+	0.986071i	$0.553189\pi$
$618$	−5.83436	+	9.08348i	−0.234692	+	0.365391i
$619$	33.6283	+	28.2175i	1.35163	+	1.13416i	0.978470	+	0.206391i	$0.0661720\pi$
$619$	33.6283	+	28.2175i	1.35163	+	1.13416i	0.373165	+	0.927765i	$0.378272\pi$
$620$		0			0
$621$	−1.04831	+	0.0340724i	−0.0420674	+	0.00136728i
$622$		−	1.25698i		−	0.0504001i
$623$	−1.37396	+	1.63742i	−0.0550466	+	0.0656020i
$624$	1.50709	−	31.8066i	0.0603318	−	1.27328i
$625$		0			0
$626$	−36.7333	−	13.3698i	−1.46816	−	0.534366i
$627$	−4.55730	+	1.41832i	−0.182001	+	0.0566423i
$628$	16.7558	+	2.95449i	0.668627	+	0.117897i
$629$	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	$0.748412\pi$
$632$	4.30347	+	11.8237i	0.171183	+	0.470321i
$633$	4.05273	+	31.6927i	0.161081	+	1.25967i
$634$	−15.6036	+	13.0930i	−0.619698	+	0.519989i
$635$		0			0
$636$	11.0451	+	14.5055i	0.437968	+	0.575182i
$637$	−14.4034	−	39.5729i	−0.570682	−	1.56794i
$638$	−20.4790	+	11.8236i	−0.810773	+	0.468100i
$639$	−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	$0.744252\pi$
$642$	−4.93108	+	21.8581i	−0.194614	+	0.862672i
$643$	9.62646	−	26.4485i	0.379631	−	1.04303i	−0.591879	−	0.806027i	$-0.701614\pi$
$643$	9.62646	−	26.4485i	0.379631	−	1.04303i	0.971510	−	0.237000i	$-0.0761640\pi$
$644$	0.0451039	+	0.255797i	0.00177734	+	0.0100798i
$645$		0			0
$646$	−2.92927	−	2.45795i	−0.115251	−	0.0967069i
$647$			4.87520i			0.191664i	0.995398	+	0.0958319i	$0.0305511\pi$
$647$			4.87520i			0.191664i	−0.995398	+	0.0958319i	$0.969449\pi$
$648$	7.48464	−	39.0461i	0.294024	−	1.53388i
$649$	−36.9819			−1.45166
$650$		0			0
$651$	−4.71873	+	2.43418i	−0.184942	+	0.0954032i
$652$	62.5322	−	11.0261i	2.44895	−	0.431816i
$653$	−1.20328	+	3.30599i	−0.0470880	+	0.129373i	−0.961008	−	0.276522i	$-0.910818\pi$
$653$	−1.20328	+	3.30599i	−0.0470880	+	0.129373i	0.913920	+	0.405895i	$0.133040\pi$
$654$	71.3727	+	16.1013i	2.79089	+	0.629611i
$655$		0			0
$656$	−13.6639	+	23.6666i	−0.533487	+	0.924027i
$657$	−3.98996	+	1.82459i	−0.155663	+	0.0711839i
$658$	−8.57367	+	4.95001i	−0.334236	+	0.192972i
$659$	3.85106	−	1.40167i	0.150016	−	0.0546013i	−0.265921	−	0.963995i	$-0.585676\pi$
$659$	3.85106	−	1.40167i	0.150016	−	0.0546013i	0.415937	+	0.909394i	$0.363454\pi$
$660$		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	$0.189219\pi$
$662$	−10.6455	−	12.6868i	−0.413748	−	0.493085i
$663$	−4.08691	−	31.9600i	−0.158722	−	1.24122i
$664$	3.13529	−	1.14115i	0.121673	−	0.0442853i
$665$		0			0
$666$	31.6441	+	32.1177i	1.22618	+	1.24454i
$667$	−0.323446	−	0.186742i	−0.0125239	−	0.00723067i
$668$	−75.6542	−	13.3399i	−2.92715	−	0.516136i
$669$	−1.60375	−	5.15311i	−0.0620046	−	0.199231i
$670$		0			0
$671$	−11.4720	−	65.0611i	−0.442873	−	2.51166i
$672$	0.916026	+	0.0434039i	0.0353365	+	0.00167434i
$673$	26.6182	−	31.7224i	1.02606	−	1.22281i	0.0514985	−	0.998673i	$-0.483600\pi$
$673$	26.6182	−	31.7224i	1.02606	−	1.22281i	0.974558	−	0.224134i	$-0.0719553\pi$
$674$	−50.7970			−1.95663
$675$		0			0
$676$	93.4024			3.59240
$677$	−19.9896	+	23.8227i	−0.768264	+	0.915581i	−0.998340	−	0.0575915i	$-0.981658\pi$
$677$	−19.9896	+	23.8227i	−0.768264	+	0.915581i	0.230077	+	0.973173i	$0.426102\pi$
$678$	37.8774	−	58.9711i	1.45467	−	2.26477i
$679$	−0.621884	−	3.52688i	−0.0238657	−	0.135349i
$680$		0			0
$681$	8.19745	−	8.87951i	0.314127	−	0.340264i
$682$	−114.827	−	20.2471i	−4.39695	−	0.775301i
$683$	−11.2564	−	6.49887i	−0.430713	−	0.248673i	0.268937	−	0.963158i	$-0.413328\pi$
$683$	−11.2564	−	6.49887i	−0.430713	−	0.248673i	−0.699651	+	0.714485i	$0.746661\pi$
$684$	4.92463	−	3.39403i	0.188298	−	0.129774i
$685$		0			0
$686$	−10.5869	+	3.85332i	−0.404210	+	0.147121i
$687$	16.1929	+	6.77789i	0.617798	+	0.258593i
$688$	13.1302	+	15.6479i	0.500583	+	0.596571i
$689$	−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	$0.743403\pi$
$692$	−11.1054	+	6.41171i	−0.422164	+	0.243737i
$693$	−2.29088	+	4.81902i	−0.0870233	+	0.183059i
$694$	−13.4668	+	23.3252i	−0.511194	+	0.885413i
$695$		0			0
$696$	9.60289	−	10.4019i	0.363997	−	0.394283i
$697$	−9.45762	+	25.9846i	−0.358233	+	0.984237i
$698$	−21.4226	+	3.77738i	−0.810856	+	0.142976i
$699$	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	$0.445705\pi$
$702$	75.9418	+	10.8601i	2.86624	+	0.409887i
$703$			3.24051i			0.122218i
$704$	39.8095	+	33.4041i	1.50038	+	1.25897i
$705$		0			0
$706$	−4.00997	−	22.7417i	−0.150917	−	0.855895i
$707$	1.39739	−	3.83929i	0.0525542	−	0.144391i
$708$	44.2485	−	13.7710i	1.66296	−	0.517547i
$709$	6.01200	−	34.0958i	0.225785	−	1.28049i	−0.635392	−	0.772189i	$-0.719162\pi$
$709$	6.01200	−	34.0958i	0.225785	−	1.28049i	0.861178	−	0.508304i	$-0.169727\pi$
$710$		0			0
$711$	−8.27014	+	2.15026i	−0.310154	+	0.0806411i
$712$	24.3363	−	14.0506i	0.912043	−	0.526568i
$713$	−0.629849	−	1.73050i	−0.0235880	−	0.0648076i
$714$	−4.24036	+	0.542240i	−0.158692	+	0.0202928i
$715$		0			0
$716$	36.3702	−	30.5182i	1.35922	−	1.14052i
$717$	19.7692	−	15.0531i	0.738294	−	0.562169i
$718$	20.9495	+	57.5584i	0.781830	+	2.14806i
$719$	−11.7846	−	20.4116i	−0.439493	−	0.761224i	0.558157	−	0.829735i	$-0.311509\pi$
$719$	−11.7846	−	20.4116i	−0.439493	−	0.761224i	−0.997650	+	0.0685110i	$0.978175\pi$
$720$		0			0
$721$	−0.433710	+	0.751207i	−0.0161522	+	0.0279764i
$722$	−44.5333	−	7.85242i	−1.65736	−	0.292237i
$723$	3.87458	−	17.1750i	0.144097	−	0.638743i
$724$	−16.7012	−	6.07874i	−0.620695	−	0.225915i
$725$		0			0
$726$	−63.2529	+	32.6293i	−2.34753	+	1.21099i
$727$	−17.4450	+	20.7902i	−0.647000	+	0.771064i	−0.985458	−	0.169917i	$-0.945650\pi$
$727$	−17.4450	+	20.7902i	−0.647000	+	0.771064i	0.338459	+	0.940981i	$0.390094\pi$
$728$		−	9.07613i		−	0.336384i
$729$	25.9178	+	7.56753i	0.959919	+	0.280279i
$730$		0			0
$731$	15.8336	+	13.2860i	0.585629	+	0.491401i
$732$	37.9532	+	73.5733i	1.40279	+	2.71935i
$733$	−14.6666	+	2.58612i	−0.541724	+	0.0955205i	−0.437813	−	0.899066i	$-0.644247\pi$
$733$	−14.6666	+	2.58612i	−0.541724	+	0.0955205i	−0.103911	+	0.994587i	$0.533136\pi$
$734$	−60.9520	−	22.1847i	−2.24978	−	0.818852i
$735$		0			0
$736$	−0.0552319	+	0.313235i	−0.00203587	+	0.0115460i
$737$	−25.7027	−	14.8395i	−0.946771	−	0.546619i
$738$	−53.6495	−	38.1628i	−1.97487	−	1.40479i
$739$	5.36887	+	9.29916i	0.197497	+	0.342075i	0.947716	−	0.319114i	$-0.103385\pi$
$739$	5.36887	+	9.29916i	0.197497	+	0.342075i	−0.750219	+	0.661189i	$0.770052\pi$
$740$		0			0
$741$	3.34017	+	4.38663i	0.122704	+	0.161147i
$742$	1.43338	+	1.70824i	0.0526211	+	0.0627114i
$743$	10.6742	+	12.7210i	0.391597	+	0.466687i	0.925439	−	0.378897i	$-0.123697\pi$
$743$	10.6742	+	12.7210i	0.391597	+	0.466687i	−0.533842	+	0.845584i	$0.679252\pi$
$744$	69.2398	−	8.85410i	2.53846	−	0.324607i
$745$		0			0
$746$	−30.4062	−	52.6651i	−1.11325	−	1.92821i
$747$	0.570186	+	2.19300i	0.0208620	+	0.0802375i
$748$	−53.4074	−	30.8348i	−1.95277	−	1.12743i
$749$	−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	$0.641439\pi$
$752$	36.1313	−	6.37092i	1.31757	−	0.232323i
$753$	2.65190	+	0.125655i	0.0966407	+	0.00457911i
$754$	20.9258	+	17.5588i	0.762072	+	0.639455i
$755$		0			0
$756$	0.946549	−	6.61898i	0.0344257	−	0.240730i
$757$		−	43.6180i		−	1.58532i	−0.609661	−	0.792662i	$-0.708694\pi$
$757$		−	43.6180i		−	1.58532i	0.609661	−	0.792662i	$-0.291306\pi$
$758$	39.4578	−	47.0240i	1.43317	−	1.70799i
$759$	−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	$0.538926\pi$
$762$	−24.6008	−	22.7111i	−0.891192	−	0.822737i
$763$	5.78945	+	1.02084i	0.209592	+	0.0369567i
$764$	27.1568	−	47.0369i	0.982497	−	1.70174i
$765$		0			0
$766$	11.9441	+	20.6878i	0.431559	+	0.747482i
$767$	14.6113	+	40.1443i	0.527584	+	1.44953i
$768$	−47.9133	−	20.0552i	−1.72892	−	0.723679i
$769$	30.8699	−	25.9030i	1.11320	−	0.934085i	0.114958	−	0.993370i	$-0.463327\pi$
$769$	30.8699	−	25.9030i	1.11320	−	0.934085i	0.998241	+	0.0592857i	$0.0188823\pi$
$770$		0			0
$771$	16.0308	−	38.2989i	0.577336	−	1.37930i
$772$	22.2106	+	61.0231i	0.799376	+	2.19627i
$773$	29.8587	−	17.2390i	1.07394	−	0.620042i	0.144688	−	0.989477i	$-0.453782\pi$
$773$	29.8587	−	17.2390i	1.07394	−	0.620042i	0.929257	+	0.369435i	$0.120449\pi$
$774$	−40.5210	+	27.9269i	−1.45650	+	1.00381i
$775$		0			0
$776$	−8.17574	+	46.3669i	−0.293492	+	1.66448i
$777$	2.66182	+	2.45736i	0.0954923	+	0.0881573i
$778$	−3.60040	+	9.89201i	−0.129081	+	0.354646i
$779$	−0.821681	−	4.65998i	−0.0294398	−	0.166961i
$780$		0			0
$781$	−12.8702	−	10.7994i	−0.460531	−	0.386431i
$782$		−	1.48269i		−	0.0530208i
$783$	6.41590	+	7.16030i	0.229286	+	0.255888i
$784$	20.7064			0.739513
$785$		0			0
$786$	2.14100	−	45.1852i	0.0763670	−	1.61170i
$787$	−36.0345	+	6.35385i	−1.28449	+	0.226490i	−0.773886	−	0.633325i	$-0.781689\pi$
$787$	−36.0345	+	6.35385i	−1.28449	+	0.226490i	−0.510604	+	0.859816i	$0.670578\pi$
$788$	8.94192	−	24.5677i	0.318543	−	0.875189i
$789$	4.23302	+	13.6014i	0.150699	+	0.484221i
$790$		0			0
$791$	2.81570	−	4.87693i	0.100115	−	0.173404i
$792$	49.9697	−	49.2328i	1.77560	−	1.74941i
$793$	−66.0921	+	38.1583i	−2.34700	+	1.35504i
$794$	−36.7732	+	13.3844i	−1.30503	+	0.474993i
$795$		0			0
$796$	45.2965	−	38.0083i	1.60549	−	1.34717i
$797$	33.1308	+	39.4838i	1.17355	+	1.39859i	0.899527	+	0.436866i	$0.143911\pi$
$797$	33.1308	+	39.4838i	1.17355	+	1.39859i	0.274027	+	0.961722i	$0.411644\pi$
$798$	0.582006	−	0.443164i	0.0206028	−	0.0156878i
$799$	34.8853	−	12.6972i	1.23415	−	0.449195i
$800$		0			0
$801$	7.93664	+	17.3556i	0.280427	+	0.613231i
$802$	1.33978	+	0.773520i	0.0473092	+	0.0273140i
$803$	−7.62359	−	1.34425i	−0.269031	−	0.0474374i
$804$	36.2789	+	8.18433i	1.27946	+	0.288639i
$805$		0			0
$806$	23.3890	+	132.646i	0.823842	+	4.67224i
$807$	−1.63370	−	3.16698i	−0.0575091	−	0.111483i
$808$	−34.5263	+	41.1469i	−1.21463	+	1.44754i
$809$	18.5065			0.650654			0.325327	−	0.945602i	$-0.394526\pi$
$809$	18.5065			0.650654			0.325327	+	0.945602i	$0.394526\pi$
$810$		0			0
$811$	36.6261			1.28611			0.643057	−	0.765818i	$-0.277666\pi$
$811$	36.6261			1.28611			0.643057	+	0.765818i	$0.277666\pi$
$812$	1.53040	−	1.82386i	0.0537066	−	0.0640050i
$813$	−12.2631	−	23.7724i	−0.430087	−	0.833736i
$814$	13.8145	+	78.3456i	0.484196	+	2.74601i
$815$		0			0
$816$	15.4540	+	3.48634i	0.540999	+	0.122046i
$817$	−3.48322	−	0.614186i	−0.121863	−	0.0214877i
$818$	50.9995	+	29.4446i	1.78316	+	1.02951i
$819$	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	$0.263436\pi$
$822$	43.7769	−	33.3336i	1.52689	−	1.16264i
$823$	−19.4739	−	23.2081i	−0.678818	−	0.808984i	0.311137	−	0.950365i	$-0.399290\pi$
$823$	−19.4739	−	23.2081i	−0.678818	−	0.808984i	−0.989955	+	0.141381i	$0.954846\pi$
$824$	8.73576	−	7.33017i	0.304325	−	0.255359i
$825$		0			0
$826$	5.32623	−	1.93859i	0.185323	−	0.0674521i
$827$	15.4977	−	8.94761i	0.538909	−	0.311139i	−0.205728	−	0.978609i	$-0.565956\pi$
$827$	15.4977	−	8.94761i	0.538909	−	0.311139i	0.744637	+	0.667470i	$0.232623\pi$
$828$	2.23552	+	0.616839i	0.0776896	+	0.0214366i
$829$	12.0856	−	20.9328i	0.419749	−	0.727026i	−0.576165	−	0.817333i	$-0.695451\pi$
$829$	12.0856	−	20.9328i	0.419749	−	0.727026i	0.995914	+	0.0903070i	$0.0287848\pi$
$830$		0			0
$831$	−0.619634	−	1.99098i	−0.0214949	−	0.0690664i
$832$	20.5321	−	56.4115i	0.711823	−	1.95572i
$833$	20.6338	−	3.63830i	0.714920	−	0.126060i
$834$	1.45185	−	30.6408i	0.0502734	−	1.06100i
$835$		0			0
$836$	10.5529			0.364981
$837$	1.53996	+	47.3804i	0.0532289	+	1.63771i
$838$			41.6039i			1.43718i
$839$	−41.0703	−	34.4621i	−1.41790	−	1.18976i	−0.952452	−	0.304690i	$-0.901447\pi$
$839$	−41.0703	−	34.4621i	−1.41790	−	1.18976i	−0.465452	−	0.885073i	$-0.654108\pi$
$840$		0			0
$841$	−4.44132	−	25.1880i	−0.153149	−	0.868551i
$842$	−18.6505	+	51.2420i	−0.642740	+	1.76591i
$843$	35.3571	+	32.6412i	1.21776	+	1.12422i
$844$	12.2671	−	69.5703i	0.422252	−	2.39471i
$845$		0			0
$846$	7.04940	+	88.1086i	0.242364	+	3.02924i
$847$	−4.95245	+	2.85930i	−0.170168	+	0.0982467i
$848$	−2.82645	−	7.76561i	−0.0970607	−	0.266672i
$849$	15.1702	−	36.2428i	0.520640	−	1.24385i
$850$		0			0
$851$	−0.962521	+	0.807651i	−0.0329948	+	0.0276859i
$852$	19.4205	+	8.12885i	0.665334	+	0.278490i
$853$	−9.16250	−	25.1738i	−0.313718	−	0.861933i	−0.991898	−	0.127037i	$-0.959453\pi$
$853$	−9.16250	−	25.1738i	−0.313718	−	0.861933i	0.678180	−	0.734896i	$-0.262769\pi$
$854$	5.06274	+	8.76892i	0.173243	+	0.300066i
$855$		0			0
$856$	11.8346	−	20.4982i	0.404499	−	0.700613i
$857$	14.7384	+	2.59878i	0.503454	+	0.0887725i	0.419607	−	0.907706i	$-0.362168\pi$
$857$	14.7384	+	2.59878i	0.503454	+	0.0887725i	0.0838474	+	0.996479i	$0.473279\pi$
$858$	99.4557	+	91.8162i	3.39536	+	3.13455i
$859$	−0.649627	−	0.236445i	−0.0221650	−	0.00806740i	0.330914	−	0.943661i	$-0.392643\pi$
$859$	−0.649627	−	0.236445i	−0.0221650	−	0.00806740i	−0.353079	+	0.935594i	$0.614865\pi$
$860$		0			0
$861$	−4.45092	−	2.85884i	−0.151687	−	0.0974291i
$862$	16.0054	−	19.0745i	0.545146	−	0.649679i
$863$		−	48.5994i		−	1.65434i	−0.561949	−	0.827172i	$-0.689948\pi$
$863$		−	48.5994i		−	1.65434i	0.561949	−	0.827172i	$-0.310052\pi$
$864$	3.86135	−	7.22002i	0.131366	−	0.245630i
$865$		0			0
$866$	−20.3812	−	17.1018i	−0.692581	−	0.581144i
$867$	−13.3994	−	0.634902i	−0.455067	−	0.0215624i
$868$	11.5612	−	2.03855i	0.392413	−	0.0691929i
$869$	−14.1680	−	5.15673i	−0.480617	−	0.174930i
$870$		0			0
$871$	−5.95343	+	33.7636i	−0.201724	+	1.14404i
$872$	−66.9320	−	38.6432i	−2.26660	−	1.30862i
$873$	−30.8229	−	8.50487i	−1.04320	−	0.287846i
$874$	0.126859	+	0.219727i	0.00429108	+	0.00743237i
$875$		0			0
$876$	9.62214	−	1.23044i	0.325102	−	0.0415726i
$877$	13.6887	+	16.3136i	0.462235	+	0.550870i	0.945932	−	0.324365i	$-0.105151\pi$
$877$	13.6887	+	16.3136i	0.462235	+	0.550870i	−0.483697	+	0.875236i	$0.660706\pi$
$878$	38.2508	+	45.5856i	1.29090	+	1.53844i
$879$	−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	$-0.418264\pi$
$882$	−4.71686	+	49.6622i	−0.158825	+	1.67221i
$883$	44.0558	+	25.4356i	1.48259	+	0.855976i	0.999805	−	0.0197597i	$-0.00629013\pi$
$883$	44.0558	+	25.4356i	1.48259	+	0.855976i	0.482790	+	0.875736i	$0.339623\pi$
$884$	−12.3706	+	70.1571i	−0.416068	+	2.35964i
$885$		0			0
$886$	−49.6647	−	18.0765i	−1.66852	−	0.607291i
$887$	47.5095	−	8.37721i	1.59521	−	0.281279i	0.695753	−	0.718281i	$-0.255071\pi$
$887$	47.5095	−	8.37721i	1.59521	−	0.281279i	0.899461	+	0.437002i	$0.143960\pi$
$888$	−21.8345	−	42.3267i	−0.732716	−	1.42039i
$889$	−2.06077	−	1.72919i	−0.0691160	−	0.0579952i
$890$		0			0
$891$	30.0767	+	36.9451i	1.00761	+	1.23771i
$892$			11.9326i			0.399533i
$893$	−4.08344	+	4.86646i	−0.136647	+	0.162850i
$894$	49.4514	−	25.5098i	1.65390	−	0.853175i
$895$		0			0
$896$	−6.48946	−	2.36197i	−0.216797	−	0.0789078i
$897$	−0.470462	+	2.08543i	−0.0157083	+	0.0696305i
$898$	−0.410653	−	0.0724092i	−0.0137037	−	0.00241633i
$899$	−8.44014	+	14.6187i	−0.281494	+	0.487563i
$900$		0			0
$901$	−4.18104	−	7.24177i	−0.139291	−	0.241258i
$902$	−39.7315	−	109.162i	−1.32292	−	3.63468i
$903$	−3.14593	+	2.39544i	−0.104690	+	0.0797153i
$904$	−56.7137	+	47.5884i	−1.88627	+	1.58277i
$905$		0			0
$906$	−37.8602	+	4.84141i	−1.25782	+	0.160845i
$907$	−6.01218	−	16.5183i	−0.199631	−	0.548482i	0.798969	−	0.601372i	$-0.205379\pi$
$907$	−6.01218	−	16.5183i	−0.199631	−	0.548482i	−0.998600	+	0.0528898i	$0.983157\pi$
$908$	−23.1400	+	13.3599i	−0.767928	+	0.443364i
$909$	−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	$0.0766617\pi$
$912$	−2.58850	+	0.805593i	−0.0857138	+	0.0266759i
$913$	−1.36741	+	3.75694i	−0.0452548	+	0.124336i
$914$	−3.75834	−	21.3146i	−0.124315	−	0.705024i
$915$		0			0
$916$	−29.7321	−	24.9482i	−0.982377	−	0.824312i
$917$		−	3.63460i		−	0.120025i
$918$	−11.8820	+	36.2708i	−0.392166	+	1.19711i
$919$	−5.86587			−0.193497			−0.0967486	−	0.995309i	$-0.530844\pi$
$919$	−5.86587			−0.193497			−0.0967486	+	0.995309i	$0.530844\pi$
$920$		0			0
$921$	−9.25548	−	5.94483i	−0.304978	−	0.195889i
$922$	−38.6924	+	6.82251i	−1.27427	+	0.224688i
$923$	−6.63791	+	18.2375i	−0.218489	+	0.600295i
$924$	8.00258	−	8.66842i	0.263265	−	0.285170i
$925$		0			0
$926$	−16.6059	+	28.7623i	−0.545705	+	0.945189i
$927$	4.39485	+	6.37679i	0.144346	+	0.209441i
$928$	2.52490	−	1.45775i	0.0828840	−	0.0478531i
$929$	−30.1086	+	10.9586i	−0.987832	+	0.359541i	−0.784880	−	0.619647i	$-0.787276\pi$
$929$	−30.1086	+	10.9586i	−0.987832	+	0.359541i	−0.202951	+	0.979189i	$0.565053\pi$
$930$		0			0
$931$	−2.74654	+	2.30462i	−0.0900141	+	0.0755308i
$932$	−27.6362	−	32.9355i	−0.905253	−	1.07884i
$933$	−0.831787	−	0.348163i	−0.0272315	−	0.0113983i
$934$	9.50610	−	3.45994i	0.311049	−	0.113213i
$935$		0			0
$936$	−73.1855	−	34.7911i	−2.39214	−	1.13718i
$937$	−14.7044	−	8.48960i	−0.480373	−	0.277343i	0.240199	−	0.970724i	$-0.422787\pi$
$937$	−14.7044	−	8.48960i	−0.480373	−	0.277343i	−0.720572	+	0.693380i	$0.756121\pi$
$938$	4.47966	+	0.789885i	0.146266	+	0.0257907i
$939$	−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	$-0.243302\pi$
$942$	10.0410	−	15.6328i	0.327155	−	0.509345i
$943$	1.17935	−	1.40550i	0.0384050	−	0.0457693i
$944$	−21.0053			−0.683665
$945$		0			0
$946$	−86.8321			−2.82316
$947$	0.0596897	−	0.0711354i	0.00193966	−	0.00231159i	−0.765074	−	0.643943i	$-0.777298\pi$
$947$	0.0596897	−	0.0711354i	0.00193966	−	0.00231159i	0.767013	+	0.641631i	$0.221742\pi$
$948$	18.8721	+	0.894216i	0.612939	+	0.0290428i
$949$	1.55284	+	8.80661i	0.0504074	+	0.285875i
$950$		0			0
$951$	4.34215	+	13.9520i	0.140804	+	0.452426i
$952$	4.44701	+	0.784128i	0.144129	+	0.0254137i
$953$	42.8976	+	24.7669i	1.38959	+	0.802279i	0.993269	−	0.115833i	$-0.0369538\pi$
$953$	42.8976	+	24.7669i	1.38959	+	0.802279i	0.396320	+	0.918113i	$0.370287\pi$
$954$	19.2689	−	5.00998i	0.623854	−	0.162204i
$955$		0			0
$956$	−51.6257	+	18.7902i	−1.66970	+	0.607720i
$957$	2.15173	+	16.8267i	0.0695554	+	0.543930i
$958$	−38.4270	−	45.7955i	−1.24152	−	1.47958i
$959$	3.38667	−	2.84176i	0.109361	−	0.0917651i
$960$		0			0
$961$	−49.0825	+	17.8646i	−1.58331	+	0.576276i
$962$	79.5872	−	45.9497i	2.56599	−	1.48148i
$963$	13.0985	+	9.31745i	0.422094	+	0.300251i
$964$	−19.4642	+	33.7129i	−0.626898	+	1.08582i
$965$		0			0
$966$	0.276689	+	0.0624196i	0.00890233	+	0.00200832i
$967$	8.12772	−	22.3307i	0.261370	−	0.718107i	−0.737706	−	0.675122i	$-0.764091\pi$
$967$	8.12772	−	22.3307i	0.261370	−	0.718107i	0.999076	−	0.0429853i	$-0.0136869\pi$
$968$	74.0387	−	13.0550i	2.37969	−	0.419604i
$969$	−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	$0.312674\pi$
$972$	−49.7439	−	33.0048i	−1.59554	−	1.05863i
$973$		−	2.46468i		−	0.0790141i
$974$	26.2943	+	22.0635i	0.842523	+	0.706961i
$975$		0			0
$976$	−6.51600	−	36.9541i	−0.208572	−	1.18287i
$977$	9.97323	−	27.4012i	0.319072	−	0.876643i	−0.671666	−	0.740854i	$-0.734421\pi$
$977$	9.97323	−	27.4012i	0.319072	−	0.876643i	0.990738	−	0.135789i	$-0.0433568\pi$
$978$	15.2591	−	67.6396i	0.487933	−	2.16288i
$979$	−5.84723	+	33.1613i	−0.186878	+	1.05984i
$980$		0			0
$981$	30.4240	−	42.7702i	0.971362	−	1.36555i
$982$	23.8833	−	13.7891i	0.762148	−	0.440026i
$983$	−12.2012	−	33.5226i	−0.389158	−	1.06920i	−0.967381	−	0.253325i	$-0.918476\pi$
$983$	−12.2012	−	33.5226i	−0.389158	−	1.06920i	0.578223	−	0.815879i	$-0.303746\pi$
$984$	42.1315	+	55.3311i	1.34310	+	1.76389i
$985$		0			0
$986$	−10.4111	+	8.73598i	−0.331558	+	0.278210i
$987$	0.900833	+	7.04459i	0.0286738	+	0.224232i
$988$	−4.16941	−	11.4554i	−0.132647	−	0.364443i
$989$	−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	$0.322720\pi$
$992$	14.1572	+	2.49630i	0.449493	+	0.0792577i
$993$	−11.3439	+	3.53046i	−0.359989	+	0.112036i
$994$	2.41970	+	0.880699i	0.0767482	+	0.0279341i
$995$		0			0
$996$	0.237120	−	5.00433i	0.00751342	−	0.158568i
$997$	33.2686	−	39.6480i	1.05363	−	1.25566i	0.0878926	−	0.996130i	$-0.471987\pi$
$997$	33.2686	−	39.6480i	1.05363	−	1.25566i	0.965734	−	0.259533i	$-0.0835688\pi$
$998$		−	91.4487i		−	2.89476i
$999$	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.u.e.124.2		132
5.2	odd	4		675.2.l.f.151.1	yes	66
5.3	odd	4		675.2.l.g.151.11	yes	66
5.4	even	2	inner	675.2.u.e.124.21		132
27.22	even	9	inner	675.2.u.e.49.21		132
135.22	odd	36		675.2.l.f.76.1	✓	66
135.49	even	18	inner	675.2.u.e.49.2		132
135.103	odd	36		675.2.l.g.76.11	yes	66

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.55198 + 1.84958i) q^{2} +(0.794060 + 1.53931i) q^{3} +(-0.665000 - 3.77140i) q^{4} +(-4.07944 - 0.920299i) q^{6} +(-0.330906 - 0.0583477i) q^{7} +(3.82562 + 2.20872i) q^{8} +(-1.73894 + 2.44461i) q^{9} +(-4.97408 + 1.81042i) q^{11} +(5.27730 - 4.01836i) q^{12} +(3.93046 + 4.68414i) q^{13} +(0.621479 - 0.521483i) q^{14} +(-2.82523 + 1.02830i) q^{16} +(-2.63465 + 1.52112i) q^{17} +(-1.82269 - 7.01028i) q^{18} +(0.260295 - 0.450843i) q^{19} +(-0.172944 - 0.555698i) q^{21} +(4.37117 - 12.0097i) q^{22} +(0.198788 - 0.0350517i) q^{23} +(-0.362131 + 7.64266i) q^{24} -14.7637 q^{26} +(-5.14382 - 0.735594i) q^{27} +1.28678i q^{28} +(-1.41738 - 1.18933i) q^{29} +(-1.58422 - 8.98458i) q^{31} +(-0.538930 + 1.48070i) q^{32} +(-6.73651 - 6.21906i) q^{33} +(1.27550 - 7.23373i) q^{34} +(10.3760 + 4.93257i) q^{36} +(-5.39074 + 3.11234i) q^{37} +(0.429898 + 1.18114i) q^{38} +(-4.08931 + 9.76968i) q^{39} +(6.96293 - 5.84259i) q^{41} +(1.29621 + 0.542558i) q^{42} +(-2.32373 - 6.38441i) q^{43} +(10.1356 + 17.5553i) q^{44} +(-0.243684 + 0.422073i) q^{46} +(-12.0175 - 2.11902i) q^{47} +(-3.82627 - 3.53236i) q^{48} +(-6.47175 - 2.35553i) q^{49} +(-4.43354 - 2.84768i) q^{51} +(15.0520 - 17.9383i) q^{52} +2.74867i q^{53} +(9.34365 - 8.37227i) q^{54} +(-1.13705 - 0.954096i) q^{56} +(0.900676 + 0.0426766i) q^{57} +(4.39950 - 0.775751i) q^{58} +(6.56519 + 2.38954i) q^{59} +(-2.16727 + 12.2912i) q^{61} +(19.0764 + 11.0137i) q^{62} +(0.718062 - 0.707472i) q^{63} +(-4.90880 - 8.50230i) q^{64} +(21.9576 - 2.80784i) q^{66} +(3.60403 + 4.29512i) q^{67} +(7.48879 + 8.92479i) q^{68} +(0.211805 + 0.278163i) q^{69} +(1.58699 + 2.74874i) q^{71} +(-12.0520 + 5.51130i) q^{72} +(1.26652 + 0.731226i) q^{73} +(2.60980 - 14.8009i) q^{74} +(-1.87341 - 0.681865i) q^{76} +(1.75159 - 0.308852i) q^{77} +(-11.7233 - 22.7259i) q^{78} +(2.18198 + 1.83090i) q^{79} +(-2.95220 - 8.50203i) q^{81} +21.9461i q^{82} +(0.485499 - 0.578595i) q^{83} +(-1.98075 + 1.02178i) q^{84} +(15.4149 + 5.61055i) q^{86} +(0.705250 - 3.12618i) q^{87} +(-23.0276 - 4.06039i) q^{88} +(3.18070 - 5.50914i) q^{89} +(-1.02731 - 1.77934i) q^{91} +(-0.264388 - 0.726400i) q^{92} +(12.5721 - 9.57291i) q^{93} +(22.5703 - 18.9387i) q^{94} +(-2.70719 + 0.346184i) q^{96} +(3.64534 + 10.0155i) q^{97} +(14.4008 - 8.31429i) q^{98} +(4.22385 - 15.3079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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