LMFDB - Embedded newform 675.2.u.e.124.21

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			124.21
Character	$\chi$	$=$	675.124
Dual form			675.2.u.e.49.21

$q$-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	$-0.452169\pi$
$2$	1.55198	−	1.84958i	1.09742	−	1.30785i	0.947715	−	0.319118i	$-0.103387\pi$
$3$	−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	0.235833	−	0.971794i	$-0.424218\pi$
$7$	0.330906	+	0.0583477i	0.125071	+	0.0220534i	−0.110762	+	0.993847i	$0.535329\pi$
$8$	−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	$-0.900054\pi$
$13$	−3.93046	−	4.68414i	−1.09011	−	1.29915i	−0.139005	−	0.990292i	$-0.544390\pi$
$14$	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	−0.145231	−	0.989398i	$-0.546393\pi$
$17$	2.63465	−	1.52112i	0.638996	−	0.368925i	0.784228	+	0.620473i	$0.213059\pi$
$18$	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	−0.194335	−	0.980935i	$-0.562255\pi$
$23$	−0.198788	+	0.0350517i	−0.0414501	+	0.00730878i	0.152885	+	0.988244i	$0.451144\pi$
$24$	−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	0.0135239	−	0.999909i	$-0.495695\pi$
$37$	5.39074	−	3.11234i	0.886232	−	0.511666i	0.872708	+	0.488242i	$0.162362\pi$
$38$	−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	$0.0622303\pi$
$43$	2.32373	+	6.38441i	0.354366	+	0.973613i	−0.626584	+	0.779354i	$0.715548\pi$
$44$	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	0.955649	−	0.294508i	$-0.0951559\pi$
$47$	12.0175	+	2.11902i	1.75294	+	0.309090i	0.797288	+	0.603598i	$0.206267\pi$
$48$	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	$-0.939547\pi$
$53$		−	2.74867i		−	0.377558i	0.982020	−	0.188779i	$-0.0604530\pi$
$54$	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	0.499562	−	0.866278i	$-0.333494\pi$
$67$	−3.60403	−	4.29512i	−0.440303	−	0.524732i	−0.939865	+	0.341545i	$0.889050\pi$
$68$	−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	0.424048	−	0.905640i	$-0.360609\pi$
$73$	−1.26652	−	0.731226i	−0.148235	−	0.0855835i	−0.572283	+	0.820056i	$0.693942\pi$
$74$	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	−0.792031	−	0.610481i	$-0.790976\pi$
$83$	−0.485499	+	0.578595i	−0.0532905	+	0.0635091i	0.738741	+	0.673990i	$0.235421\pi$
$84$	−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	$-0.929123\pi$
$97$	−3.64534	−	10.0155i	−0.370128	−	1.01692i	0.605184	−	0.796086i	$-0.293099\pi$
$98$	−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	−0.975561	−	0.219730i	$-0.929482\pi$
$103$	−0.882932	+	2.42584i	−0.0869979	+	0.239025i	0.888563	+	0.458755i	$0.151704\pi$
$104$	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	$0.0833913\pi$
$107$			5.35813i			0.517990i	−0.965879	+	0.258995i	$0.916609\pi$
$108$	−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	$-0.599848\pi$
$113$	5.73211	−	15.7488i	0.539232	−	1.48153i	0.847796	−	0.530323i	$-0.177929\pi$
$114$	−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	0.159768	−	0.987155i	$-0.448925\pi$
$127$	−6.93350	−	4.00306i	−0.615249	−	0.355214i	−0.775017	+	0.631940i	$0.782259\pi$
$128$	−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	−0.272318	−	0.962207i	$-0.587790\pi$
$137$	8.45733	−	10.0791i	0.722559	−	0.861112i	0.994877	+	0.101095i	$0.0322347\pi$
$138$	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	−0.864171	−	0.503199i	$-0.832156\pi$
$157$	1.51954	−	4.17491i	0.121273	−	0.333194i	0.985443	+	0.170005i	$0.0543785\pi$
$158$	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	$-0.775042\pi$
$163$		−	16.5806i		−	1.29869i	0.760492	−	0.649347i	$-0.224958\pi$
$164$	−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	$0.393938\pi$
$167$	−6.86091	+	18.8502i	−0.530913	+	1.45867i	−0.857986	+	0.513673i	$0.828284\pi$
$168$	−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	0.975585	−	0.219623i	$-0.0704827\pi$
$173$	1.14526	+	3.14658i	0.0870725	+	0.239230i	−0.888512	+	0.458853i	$0.848261\pi$
$174$	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	0.463477	−	0.886109i	$-0.346602\pi$
$193$	16.6997	−	2.94460i	1.20207	−	0.211957i	0.738593	+	0.674152i	$0.235491\pi$
$194$	−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	0.274370	−	0.961624i	$-0.411531\pi$
$197$	−5.91232	−	3.41348i	−0.421236	−	0.243200i	−0.695606	+	0.718424i	$0.744864\pi$
$198$	−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	0.275444	−	0.961317i	$-0.411175\pi$
$223$	3.06856	+	0.541070i	0.205486	+	0.0362328i	−0.0699575	+	0.997550i	$0.522286\pi$
$224$	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	0.993349	−	0.115143i	$-0.0367325\pi$
$227$	2.38634	+	6.55642i	0.158387	+	0.435165i	−0.834962	+	0.550308i	$0.814510\pi$
$228$	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	−0.783442	−	0.621465i	$-0.786538\pi$
$233$	−9.72275	+	5.61343i	−0.636959	+	0.367748i	0.146483	+	0.989213i	$0.453205\pi$
$234$	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	$0.0465847\pi$
$257$	15.4081	+	18.3627i	0.961131	+	1.14543i	−0.0281791	+	0.999603i	$0.508971\pi$
$258$	−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	−0.0817395	−	0.996654i	$-0.526048\pi$
$263$	−8.09931	−	1.42813i	−0.499425	−	0.0880621i	−0.417686	+	0.908592i	$0.637159\pi$
$264$	−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	0.209152	−	0.977883i	$-0.432930\pi$
$277$	1.18559	+	0.209051i	0.0712350	+	0.0125607i	−0.137917	+	0.990444i	$0.544041\pi$
$278$	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	$0.0132925\pi$
$283$	14.5809	+	17.3768i	0.866745	+	1.03295i	−0.132383	+	0.991199i	$0.542263\pi$
$284$	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	0.328606	−	0.944467i	$-0.393421\pi$
$293$	16.4398	−	2.89878i	0.960422	−	0.169348i	0.631816	+	0.775119i	$0.282310\pi$
$294$	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	−0.334766	−	0.942301i	$-0.608657\pi$
$307$	5.50011	−	3.17549i	0.313908	−	0.181235i	0.648674	+	0.761066i	$0.275324\pi$
$308$	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	$-0.959833\pi$
$313$	−5.53741	−	15.2139i	−0.312993	−	0.859942i	0.679056	−	0.734087i	$-0.262390\pi$
$314$	−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	−0.0646113	−	0.997911i	$-0.520581\pi$
$317$	−8.30814	−	1.46495i	−0.466631	−	0.0822797i	−0.402020	+	0.915631i	$0.631692\pi$
$318$	−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	0.259468	−	0.965752i	$-0.416453\pi$
$337$	−13.5234	−	16.1166i	−0.736667	−	0.877926i	−0.996136	+	0.0878255i	$0.972008\pi$
$338$	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	−0.460553	−	0.887632i	$-0.652349\pi$
$347$	−10.9857	+	1.93708i	−0.589744	+	0.103988i	−0.129190	+	0.991620i	$0.541238\pi$
$348$	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	−0.577208	−	0.816597i	$-0.695858\pi$
$353$	6.14780	−	7.32667i	0.327214	−	0.389959i	0.904422	+	0.426638i	$0.140302\pi$
$354$	−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	$-0.863775\pi$
$367$	−9.18829	−	25.2446i	−0.479625	−	1.31776i	0.430188	−	0.902740i	$-0.358447\pi$
$368$	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	$-0.662793\pi$
$373$	8.61440	−	23.6679i	0.446037	−	1.22548i	0.935461	−	0.353430i	$-0.114985\pi$
$374$	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	−0.995630	−	0.0933808i	$-0.970233\pi$
$383$	−3.38390	+	9.29719i	−0.172909	+	0.475064i	0.822721	+	0.568445i	$0.192455\pi$
$384$	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	0.104540	−	0.994521i	$-0.466663\pi$
$397$	−14.0365	−	8.10396i	−0.704470	−	0.406726i	−0.809010	+	0.587795i	$0.799996\pi$
$398$	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	$-0.914701\pi$
$433$		−	11.0194i		−	0.529557i	0.964309	−	0.264778i	$-0.0852988\pi$
$434$	−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	$-0.937039\pi$
$443$	−7.48678	−	20.5698i	−0.355708	−	0.977299i	0.624794	−	0.780789i	$-0.285183\pi$
$444$	−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	−0.614251	−	0.789111i	$-0.710542\pi$
$457$	5.76201	−	6.86690i	0.269536	−	0.321220i	0.883786	+	0.467891i	$0.154986\pi$
$458$		−	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	−0.479318	−	0.877642i	$-0.659116\pi$
$463$	−13.5465	+	2.38861i	−0.629558	+	0.111008i	−0.150240	+	0.988650i	$0.548005\pi$
$464$	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	0.581599	−	0.813476i	$-0.302427\pi$
$467$	3.62851	+	2.09492i	0.167907	+	0.0969414i	−0.413691	+	0.910417i	$0.635761\pi$
$468$	−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	$0.104390\pi$
$487$			14.2164i			0.644205i	−0.946705	+	0.322102i	$0.895610\pi$
$488$	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	0.407790	−	0.913076i	$-0.366300\pi$
$503$	31.4533	−	18.1596i	1.40243	−	0.809694i	0.994642	+	0.103381i	$0.0329662\pi$
$504$	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	−0.174686	−	0.984624i	$-0.555891\pi$
$523$	13.5084	−	7.79908i	0.590681	−	0.341030i	0.765367	+	0.643594i	$0.222558\pi$
$524$	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	0.425968	−	0.904738i	$-0.359934\pi$
$547$	12.0871	+	2.13129i	0.516808	+	0.0911273i	0.0908404	+	0.995865i	$0.471045\pi$
$548$	−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	−0.792249	−	0.610198i	$-0.791090\pi$
$557$	−15.5748	+	8.99212i	−0.659926	+	0.381008i	0.132323	+	0.991207i	$0.457756\pi$
$558$	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	0.0250923	−	0.999685i	$-0.492012\pi$
$563$	9.26763	−	1.63413i	0.390584	−	0.0688705i	0.365492	+	0.930815i	$0.380901\pi$
$564$	−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	−0.185622	−	0.982621i	$-0.559430\pi$
$577$	13.7529	−	7.94027i	0.572543	−	0.330558i	0.758164	+	0.652064i	$0.226096\pi$
$578$	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	0.562270	−	0.826953i	$-0.309928\pi$
$587$	19.5714	+	3.45096i	0.807797	+	0.142436i	0.245527	+	0.969390i	$0.421039\pi$
$588$	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	$0.344802\pi$
$593$			43.0280i			1.76695i	−0.468480	+	0.883474i	$0.655198\pi$
$594$	−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	0.777032	−	0.629461i	$-0.216724\pi$
$607$	0.547047	+	0.651945i	0.0222040	+	0.0264616i	−0.754828	+	0.655923i	$0.772280\pi$
$608$	−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	0.497060	−	0.867716i	$-0.334413\pi$
$613$	−0.145420	−	0.0839581i	−0.00587345	−	0.00339104i	−0.502934	+	0.864325i	$0.667746\pi$
$614$	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	0.166322	−	0.986071i	$-0.446811\pi$
$617$	16.3908	−	2.89015i	0.659871	−	0.116353i	0.493548	+	0.869718i	$0.335700\pi$
$618$	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	$0.298386\pi$
$643$	−9.62646	+	26.4485i	−0.379631	+	1.04303i	−0.971510	+	0.237000i	$0.923836\pi$
$644$	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	$-0.969449\pi$
$647$		−	4.87520i		−	0.191664i	0.995398	−	0.0958319i	$-0.0305511\pi$
$648$	−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	−0.913920	−	0.405895i	$-0.866960\pi$
$653$	1.20328	−	3.30599i	0.0470880	−	0.129373i	0.961008	+	0.276522i	$0.0891819\pi$
$654$	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	$0.516400\pi$
$673$	−26.6182	+	31.7224i	−1.02606	+	1.22281i	−0.974558	+	0.224134i	$0.928045\pi$
$674$	−50.7970			−1.95663
$675$		0			0
$676$	93.4024			3.59240
$677$	19.9896	−	23.8227i	0.768264	−	0.915581i	−0.230077	−	0.973173i	$-0.573898\pi$
$677$	19.9896	−	23.8227i	0.768264	−	0.915581i	0.998340	+	0.0575915i	$0.0183421\pi$
$678$	−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	0.699651	−	0.714485i	$-0.253339\pi$
$683$	11.2564	+	6.49887i	0.430713	+	0.248673i	−0.268937	+	0.963158i	$0.586672\pi$
$684$	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	−0.338459	−	0.940981i	$-0.609906\pi$
$727$	17.4450	−	20.7902i	0.647000	−	0.771064i	0.985458	+	0.169917i	$0.0543500\pi$
$728$			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	0.103911	−	0.994587i	$-0.466864\pi$
$733$	14.6666	−	2.58612i	0.541724	−	0.0955205i	0.437813	+	0.899066i	$0.355753\pi$
$734$	−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	0.533842	−	0.845584i	$-0.320748\pi$
$743$	−10.6742	−	12.7210i	−0.391597	−	0.466687i	−0.925439	+	0.378897i	$0.876303\pi$
$744$	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	$0.291306\pi$
$757$			43.6180i			1.58532i	−0.609661	+	0.792662i	$0.708694\pi$
$758$	−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	−0.929257	−	0.369435i	$-0.879551\pi$
$773$	−29.8587	+	17.2390i	−1.07394	+	0.620042i	−0.144688	+	0.989477i	$0.546218\pi$
$774$	−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	0.510604	−	0.859816i	$-0.329422\pi$
$787$	36.0345	−	6.35385i	1.28449	−	0.226490i	0.773886	+	0.633325i	$0.218311\pi$
$788$	−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	$-0.856089\pi$
$797$	−33.1308	−	39.4838i	−1.17355	−	1.39859i	−0.274027	−	0.961722i	$-0.588356\pi$
$798$	−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	0.989955	−	0.141381i	$-0.0451542\pi$
$823$	19.4739	+	23.2081i	0.678818	+	0.808984i	−0.311137	+	0.950365i	$0.600710\pi$
$824$	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	−0.744637	−	0.667470i	$-0.767377\pi$
$827$	−15.4977	+	8.94761i	−0.538909	+	0.311139i	0.205728	+	0.978609i	$0.434044\pi$
$828$	−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	$0.0405468\pi$
$853$	9.16250	+	25.1738i	0.313718	+	0.861933i	−0.678180	+	0.734896i	$0.737231\pi$
$854$	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	−0.0838474	−	0.996479i	$-0.526721\pi$
$857$	−14.7384	−	2.59878i	−0.503454	−	0.0887725i	−0.419607	+	0.907706i	$0.637832\pi$
$858$	−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	$0.310052\pi$
$863$			48.5994i			1.65434i	−0.561949	+	0.827172i	$0.689948\pi$
$864$	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	0.483697	−	0.875236i	$-0.339294\pi$
$877$	−13.6887	−	16.3136i	−0.462235	−	0.550870i	−0.945932	+	0.324365i	$0.894849\pi$
$878$	−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	−0.482790	−	0.875736i	$-0.660377\pi$
$883$	−44.0558	−	25.4356i	−1.48259	−	0.855976i	−0.999805	+	0.0197597i	$0.993710\pi$
$884$	−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	−0.899461	−	0.437002i	$-0.856040\pi$
$887$	−47.5095	+	8.37721i	−1.59521	+	0.281279i	−0.695753	+	0.718281i	$0.744929\pi$
$888$	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	0.998600	−	0.0528898i	$-0.0168432\pi$
$907$	6.01218	+	16.5183i	0.199631	+	0.548482i	−0.798969	+	0.601372i	$0.794621\pi$
$908$	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	0.720572	−	0.693380i	$-0.243879\pi$
$937$	14.7044	+	8.48960i	0.480373	+	0.277343i	−0.240199	+	0.970724i	$0.577213\pi$
$938$	−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	−0.767013	−	0.641631i	$-0.778258\pi$
$947$	−0.0596897	+	0.0711354i	−0.00193966	+	0.00231159i	0.765074	+	0.643943i	$0.222702\pi$
$948$	−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	−0.396320	−	0.918113i	$-0.629713\pi$
$953$	−42.8976	−	24.7669i	−1.38959	−	0.802279i	−0.993269	+	0.115833i	$0.963046\pi$
$954$	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	$0.235909\pi$
$967$	−8.12772	+	22.3307i	−0.261370	+	0.718107i	−0.999076	+	0.0429853i	$0.986313\pi$
$968$	−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	$0.265579\pi$
$977$	−9.97323	+	27.4012i	−0.319072	+	0.876643i	−0.990738	+	0.135789i	$0.956643\pi$
$978$	−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	$0.0815242\pi$
$983$	12.2012	+	33.5226i	0.389158	+	1.06920i	−0.578223	+	0.815879i	$0.696254\pi$
$984$	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	$0.528013\pi$
$997$	−33.2686	+	39.6480i	−1.05363	+	1.25566i	−0.965734	+	0.259533i	$0.916431\pi$
$998$			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.124.21		132
5.2	odd	4		675.2.l.g.151.11	yes	66
5.3	odd	4		675.2.l.f.151.1	yes	66
5.4	even	2	inner	675.2.u.e.124.2		132
27.22	even	9	inner	675.2.u.e.49.2		132
135.22	odd	36		675.2.l.g.76.11	yes	66
135.49	even	18	inner	675.2.u.e.49.21		132
135.103	odd	36		675.2.l.f.76.1	✓	66

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

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

Fields

Representations

Groups

Database

Properties

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