LMFDB - Embedded newform 228.2.m.a.11.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(11,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.32
Character	$\chi$	$=$	228.11
Dual form			228.2.m.a.83.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33479 - 0.467269i) q^{2} +(-1.73065 + 0.0695904i) q^{3} +(1.56332 - 1.24741i) q^{4} +(-0.0574154 - 0.0331488i) q^{5} +(-2.27754 + 0.901568i) q^{6} -3.60595i q^{7} +(1.50383 - 2.39552i) q^{8} +(2.99031 - 0.240874i) q^{9} +(-0.0921267 - 0.0174182i) q^{10} +1.08432 q^{11} +(-2.61876 + 2.26762i) q^{12} +(0.113579 + 0.196724i) q^{13} +(-1.68495 - 4.81318i) q^{14} +(0.101673 + 0.0533734i) q^{15} +(0.887940 - 3.90020i) q^{16} +(2.43120 + 1.40366i) q^{17} +(3.87888 - 1.71880i) q^{18} +(-4.35886 - 0.0194115i) q^{19} +(-0.131109 + 0.0197983i) q^{20} +(0.250939 + 6.24065i) q^{21} +(1.44733 - 0.506666i) q^{22} +(4.30600 + 7.45822i) q^{23} +(-2.43590 + 4.25046i) q^{24} +(-2.49780 - 4.32632i) q^{25} +(0.243527 + 0.209513i) q^{26} +(-5.15843 + 0.624965i) q^{27} +(-4.49810 - 5.63725i) q^{28} +(-4.65184 + 2.68574i) q^{29} +(0.160651 + 0.0237337i) q^{30} +6.89036i q^{31} +(-0.637229 - 5.62085i) q^{32} +(-1.87657 + 0.0754579i) q^{33} +(3.90103 + 0.737559i) q^{34} +(-0.119533 + 0.207037i) q^{35} +(4.37435 - 4.10671i) q^{36} +1.80655 q^{37} +(-5.82722 + 2.01085i) q^{38} +(-0.210255 - 0.332557i) q^{39} +(-0.165751 + 0.0876895i) q^{40} +(2.63274 + 1.52002i) q^{41} +(3.25101 + 8.21268i) q^{42} +(5.11992 + 2.95599i) q^{43} +(1.69513 - 1.35259i) q^{44} +(-0.179675 - 0.0852954i) q^{45} +(9.23260 + 7.94308i) q^{46} +(-0.205933 - 0.356687i) q^{47} +(-1.26530 + 6.81168i) q^{48} -6.00287 q^{49} +(-5.35559 - 4.60758i) q^{50} +(-4.30525 - 2.26005i) q^{51} +(0.422956 + 0.165864i) q^{52} +(-0.727053 + 0.419764i) q^{53} +(-6.59339 + 3.24457i) q^{54} +(-0.0622564 - 0.0359437i) q^{55} +(-8.63812 - 5.42272i) q^{56} +(7.54501 - 0.269740i) q^{57} +(-4.95426 + 5.75856i) q^{58} +(-4.44625 + 7.70114i) q^{59} +(0.225526 - 0.0433879i) q^{60} +(4.67311 + 8.09407i) q^{61} +(3.21965 + 9.19718i) q^{62} +(-0.868578 - 10.7829i) q^{63} +(-3.47701 - 7.20489i) q^{64} -0.0150600i q^{65} +(-2.46957 + 0.977584i) q^{66} +(5.00700 - 2.89079i) q^{67} +(5.55168 - 0.838342i) q^{68} +(-7.97122 - 12.6079i) q^{69} +(-0.0628092 + 0.332204i) q^{70} +(5.70164 - 9.87552i) q^{71} +(3.91990 - 7.52558i) q^{72} +(7.27491 - 12.6005i) q^{73} +(2.41136 - 0.844143i) q^{74} +(4.62390 + 7.31353i) q^{75} +(-6.83850 + 5.40693i) q^{76} -3.90999i q^{77} +(-0.436040 - 0.345648i) q^{78} +(-3.33564 - 1.92583i) q^{79} +(-0.180268 + 0.194497i) q^{80} +(8.88396 - 1.44058i) q^{81} +(4.22441 + 0.798701i) q^{82} -9.87713 q^{83} +(8.17694 + 9.44310i) q^{84} +(-0.0930590 - 0.161183i) q^{85} +(8.21525 + 1.55324i) q^{86} +(7.86382 - 4.97181i) q^{87} +(1.63062 - 2.59750i) q^{88} +(-13.7070 + 7.91375i) q^{89} +(-0.279683 - 0.0298950i) q^{90} +(0.709378 - 0.409559i) q^{91} +(16.0351 + 6.28823i) q^{92} +(-0.479503 - 11.9248i) q^{93} +(-0.441546 - 0.379876i) q^{94} +(0.249622 + 0.145605i) q^{95} +(1.49398 + 9.68339i) q^{96} +(4.49303 - 7.78215i) q^{97} +(-8.01257 + 2.80495i) q^{98} +(3.24244 - 0.261183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) $ 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.33479	−	0.467269i	0.943838	−	0.330409i
$2$	1.33479	−	0.467269i	0.943838	−	0.330409i
$3$	−1.73065	+	0.0695904i	−0.999193	+	0.0401780i
$3$	−1.73065	+	0.0695904i	−0.999193	+	0.0401780i
$4$	1.56332	−	1.24741i	0.781660	−	0.623705i
$5$	−0.0574154	−	0.0331488i	−0.0256769	−	0.0148246i	0.487107	−	0.873343i	$-0.338052\pi$
$5$	−0.0574154	−	0.0331488i	−0.0256769	−	0.0148246i	−0.512784	+	0.858518i	$0.671386\pi$
$6$	−2.27754	+	0.901568i	−0.929801	+	0.368064i
$7$		−	3.60595i		−	1.36292i	−0.731855	−	0.681460i	$-0.761345\pi$
$7$		−	3.60595i		−	1.36292i	0.731855	−	0.681460i	$-0.238655\pi$
$8$	1.50383	−	2.39552i	0.531683	−	0.846943i
$9$	2.99031	−	0.240874i	0.996771	−	0.0802912i
$10$	−0.0921267	−	0.0174182i	−0.0291330	−	0.00550812i
$11$	1.08432			0.326933			0.163467	−	0.986549i	$-0.447732\pi$
$11$	1.08432			0.326933			0.163467	+	0.986549i	$0.447732\pi$
$12$	−2.61876	+	2.26762i	−0.755970	+	0.654607i
$13$	0.113579	+	0.196724i	0.0315011	+	0.0545615i	0.881346	−	0.472471i	$-0.156638\pi$
$13$	0.113579	+	0.196724i	0.0315011	+	0.0545615i	−0.849845	+	0.527033i	$0.823305\pi$
$14$	−1.68495	−	4.81318i	−0.450321	−	1.28638i
$15$	0.101673	+	0.0533734i	0.0262518	+	0.0137810i
$16$	0.887940	−	3.90020i	0.221985	−	0.975050i
$17$	2.43120	+	1.40366i	0.589654	+	0.340437i	0.764961	−	0.644077i	$-0.222758\pi$
$17$	2.43120	+	1.40366i	0.589654	+	0.340437i	−0.175307	+	0.984514i	$0.556092\pi$
$18$	3.87888	−	1.71880i	0.914262	−	0.405124i
$19$	−4.35886	−	0.0194115i	−0.999990	−	0.00445331i
$19$	−4.35886	−	0.0194115i	−0.999990	−	0.00445331i
$20$	−0.131109	+	0.0197983i	−0.0293168	+	0.00442704i
$21$	0.250939	+	6.24065i	0.0547595	+	1.36182i
$22$	1.44733	−	0.506666i	0.308572	−	0.108022i
$23$	4.30600	+	7.45822i	0.897864	+	1.55515i	0.830220	+	0.557436i	$0.188215\pi$
$23$	4.30600	+	7.45822i	0.897864	+	1.55515i	0.0676443	+	0.997710i	$0.478452\pi$
$24$	−2.43590	+	4.25046i	−0.497225	+	0.867622i
$25$	−2.49780	−	4.32632i	−0.499560	−	0.865264i
$26$	0.243527	+	0.209513i	0.0477595	+	0.0410890i
$27$	−5.15843	+	0.624965i	−0.992741	+	0.120275i
$28$	−4.49810	−	5.63725i	−0.850060	−	1.06534i
$29$	−4.65184	+	2.68574i	−0.863825	+	0.498730i	−0.865291	−	0.501269i	$-0.832867\pi$
$29$	−4.65184	+	2.68574i	−0.863825	+	0.498730i	0.00146616	+	0.999999i	$0.499533\pi$
$30$	0.160651	+	0.0237337i	0.0293308	+	0.00433316i
$31$			6.89036i			1.23755i	0.785570	+	0.618773i	$0.212370\pi$
$31$			6.89036i			1.23755i	−0.785570	+	0.618773i	$0.787630\pi$
$32$	−0.637229	−	5.62085i	−0.112647	−	0.993635i
$33$	−1.87657	+	0.0754579i	−0.326669	+	0.0131355i
$34$	3.90103	+	0.737559i	0.669021	+	0.126490i
$35$	−0.119533	+	0.207037i	−0.0202047	+	0.0349956i
$36$	4.37435	−	4.10671i	0.729058	−	0.684451i
$37$	1.80655			0.296995			0.148497	−	0.988913i	$-0.452556\pi$
$37$	1.80655			0.296995			0.148497	+	0.988913i	$0.452556\pi$
$38$	−5.82722	+	2.01085i	−0.945300	+	0.326202i
$39$	−0.210255	−	0.332557i	−0.0336678	−	0.0532518i
$40$	−0.165751	+	0.0876895i	−0.0262076	+	0.0138649i
$41$	2.63274	+	1.52002i	0.411166	+	0.237387i	0.691290	−	0.722577i	$-0.257043\pi$
$41$	2.63274	+	1.52002i	0.411166	+	0.237387i	−0.280125	+	0.959964i	$0.590376\pi$
$42$	3.25101	+	8.21268i	0.501641	+	1.26724i
$43$	5.11992	+	2.95599i	0.780780	+	0.450784i	0.836707	−	0.547651i	$-0.184478\pi$
$43$	5.11992	+	2.95599i	0.780780	+	0.450784i	−0.0559266	+	0.998435i	$0.517811\pi$
$44$	1.69513	−	1.35259i	0.255551	−	0.203910i
$45$	−0.179675	−	0.0852954i	−0.0267843	−	0.0127151i
$46$	9.23260	+	7.94308i	1.36127	+	1.17114i
$47$	−0.205933	−	0.356687i	−0.0300385	−	0.0520282i	0.850615	−	0.525788i	$-0.176230\pi$
$47$	−0.205933	−	0.356687i	−0.0300385	−	0.0520282i	−0.880654	+	0.473760i	$0.842896\pi$
$48$	−1.26530	+	6.81168i	−0.182630	+	0.983182i
$49$	−6.00287			−0.857553
$50$	−5.35559	−	4.60758i	−0.757395	−	0.651610i
$51$	−4.30525	−	2.26005i	−0.602856	−	0.316471i
$52$	0.422956	+	0.165864i	0.0586534	+	0.0230012i
$53$	−0.727053	+	0.419764i	−0.0998684	+	0.0576590i	−0.549102	−	0.835755i	$-0.685030\pi$
$53$	−0.727053	+	0.419764i	−0.0998684	+	0.0576590i	0.449234	+	0.893414i	$0.351697\pi$
$54$	−6.59339	+	3.24457i	−0.897246	+	0.441530i
$55$	−0.0622564	−	0.0359437i	−0.00839464	−	0.00484665i
$56$	−8.63812	−	5.42272i	−1.15432	−	0.724642i
$57$	7.54501	−	0.269740i	0.999362	−	0.0357279i
$58$	−4.95426	+	5.75856i	−0.650526	+	0.756135i
$59$	−4.44625	+	7.70114i	−0.578853	+	1.00260i	0.416758	+	0.909017i	$0.363166\pi$
$59$	−4.44625	+	7.70114i	−0.578853	+	1.00260i	−0.995611	+	0.0935854i	$0.970167\pi$
$60$	0.225526	−	0.0433879i	0.0291152	−	0.00560135i
$61$	4.67311	+	8.09407i	0.598331	+	1.03634i	0.993068	+	0.117545i	$0.0375025\pi$
$61$	4.67311	+	8.09407i	0.598331	+	1.03634i	−0.394737	+	0.918794i	$0.629164\pi$
$62$	3.21965	+	9.19718i	0.408896	+	1.16804i
$63$	−0.868578	−	10.7829i	−0.109431	−	1.35852i
$64$	−3.47701	−	7.20489i	−0.434626	−	0.900611i
$65$		−	0.0150600i		−	0.00186796i
$66$	−2.46957	+	0.977584i	−0.303983	+	0.120332i
$67$	5.00700	−	2.89079i	0.611703	−	0.353167i	−0.161929	−	0.986802i	$-0.551771\pi$
$67$	5.00700	−	2.89079i	0.611703	−	0.353167i	0.773632	+	0.633636i	$0.218438\pi$
$68$	5.55168	−	0.838342i	0.673241	−	0.101664i
$69$	−7.97122	−	12.6079i	−0.959622	−	1.51782i
$70$	−0.0628092	+	0.332204i	−0.00750713	+	0.0397060i
$71$	5.70164	−	9.87552i	0.676660	−	1.17201i	−0.299321	−	0.954152i	$-0.596760\pi$
$71$	5.70164	−	9.87552i	0.676660	−	1.17201i	0.975981	−	0.217856i	$-0.0699065\pi$
$72$	3.91990	−	7.52558i	0.461964	−	0.886899i
$73$	7.27491	−	12.6005i	0.851464	−	1.47478i	−0.0284230	−	0.999596i	$-0.509049\pi$
$73$	7.27491	−	12.6005i	0.851464	−	1.47478i	0.879887	−	0.475183i	$-0.157618\pi$
$74$	2.41136	−	0.844143i	0.280315	−	0.0981297i
$75$	4.62390	+	7.31353i	0.533922	+	0.844494i
$76$	−6.83850	+	5.40693i	−0.784430	+	0.620217i
$77$		−	3.90999i		−	0.445584i
$78$	−0.436040	−	0.345648i	−0.0493718	−	0.0391369i
$79$	−3.33564	−	1.92583i	−0.375289	−	0.216673i	0.300478	−	0.953789i	$-0.402854\pi$
$79$	−3.33564	−	1.92583i	−0.375289	−	0.216673i	−0.675767	+	0.737116i	$0.736187\pi$
$80$	−0.180268	+	0.194497i	−0.0201546	+	0.0217455i
$81$	8.88396	−	1.44058i	0.987107	−	0.160064i
$82$	4.22441	+	0.798701i	0.466508	+	0.0882017i
$83$	−9.87713			−1.08416			−0.542078	−	0.840328i	$-0.682362\pi$
$83$	−9.87713			−1.08416			−0.542078	+	0.840328i	$0.682362\pi$
$84$	8.17694	+	9.44310i	0.892177	+	1.03033i
$85$	−0.0930590	−	0.161183i	−0.0100937	−	0.0174827i
$86$	8.21525	+	1.55324i	0.885873	+	0.167490i
$87$	7.86382	−	4.97181i	0.843090	−	0.533034i
$88$	1.63062	−	2.59750i	0.173825	−	0.276894i
$89$	−13.7070	+	7.91375i	−1.45294	+	0.838856i	−0.998647	−	0.0519957i	$-0.983442\pi$
$89$	−13.7070	+	7.91375i	−1.45294	+	0.838856i	−0.454294	+	0.890852i	$0.650108\pi$
$90$	−0.279683	−	0.0298950i	−0.0294812	−	0.00315121i
$91$	0.709378	−	0.409559i	0.0743630	−	0.0429335i
$92$	16.0351	+	6.28823i	1.67178	+	0.655594i
$93$	−0.479503	−	11.9248i	−0.0497222	−	1.23655i
$94$	−0.441546	−	0.379876i	−0.0455420	−	0.0391812i
$95$	0.249622	+	0.145605i	0.0256107	+	0.0149388i
$96$	1.49398	+	9.68339i	0.152479	+	0.988307i
$97$	4.49303	−	7.78215i	0.456198	−	0.790158i	−0.542558	−	0.840018i	$-0.682544\pi$
$97$	4.49303	−	7.78215i	0.456198	−	0.790158i	0.998756	+	0.0498604i	$0.0158776\pi$
$98$	−8.01257	+	2.80495i	−0.809392	+	0.283343i
$99$	3.24244	−	0.261183i	0.325878	−	0.0262499i
$100$	−9.30156	−	3.64764i	−0.930156	−	0.364764i
$101$	−14.1683	+	8.18009i	−1.40980	+	0.813949i	−0.995369	−	0.0961309i	$-0.969353\pi$
$101$	−14.1683	+	8.18009i	−1.40980	+	0.813949i	−0.414433	+	0.910080i	$0.636020\pi$
$102$	−6.80265	−	1.00498i	−0.673563	−	0.0995082i
$103$		−	9.27449i		−	0.913843i	−0.889507	−	0.456921i	$-0.848952\pi$
$103$		−	9.27449i		−	0.913843i	0.889507	−	0.456921i	$-0.151048\pi$
$104$	0.642059	+	0.0237591i	0.0629591	+	0.00232977i
$105$	0.192462	−	0.366627i	0.0187824	−	0.0357792i
$106$	−0.774319	+	0.900025i	−0.0752085	+	0.0874182i
$107$	10.7650			1.04069			0.520346	−	0.853955i	$-0.325803\pi$
$107$	10.7650			1.04069			0.520346	+	0.853955i	$0.325803\pi$
$108$	−7.28469	+	7.41170i	−0.700970	+	0.713191i
$109$	−5.77711	+	10.0062i	−0.553347	+	0.958425i	0.444683	+	0.895688i	$0.353316\pi$
$109$	−5.77711	+	10.0062i	−0.553347	+	0.958425i	−0.998030	+	0.0627368i	$0.980017\pi$
$110$	−0.0998944	−	0.0188868i	−0.00952456	−	0.00180079i
$111$	−3.12651	+	0.125718i	−0.296755	+	0.0119327i
$112$	−14.0639	−	3.20187i	−1.32892	−	0.302548i
$113$		−	0.563097i		−	0.0529717i	−0.999649	−	0.0264858i	$-0.991568\pi$
$113$		−	0.563097i		−	0.0529717i	0.999649	−	0.0264858i	$-0.00843169\pi$
$114$	9.94496	−	3.88559i	0.931431	−	0.363919i
$115$		−	0.570955i		−	0.0532418i
$116$	−3.92210	+	10.0014i	−0.364158	+	0.928609i
$117$	0.387022	+	0.560909i	0.0357802	+	0.0518561i
$118$	−2.33631	+	12.3570i	−0.215075	+	1.13755i
$119$	5.06151	−	8.76680i	0.463988	−	0.803651i
$120$	0.280755	−	0.163295i	0.0256293	−	0.0149067i
$121$	−9.82426			−0.893115
$122$	10.0197	+	8.62027i	0.907143	+	0.780443i
$123$	−4.66214	−	2.44741i	−0.420371	−	0.220675i
$124$	8.59511	+	10.7718i	0.771863	+	0.967340i
$125$			0.662684i			0.0592723i
$126$	−6.19789	−	13.9871i	−0.552152	−	1.24607i
$127$	−3.96530	+	2.28937i	−0.351864	+	0.203149i	−0.665506	−	0.746393i	$-0.731784\pi$
$127$	−3.96530	+	2.28937i	−0.351864	+	0.203149i	0.313642	+	0.949541i	$0.398451\pi$
$128$	−8.00769	−	7.99230i	−0.707787	−	0.706426i
$129$	−9.06650	−	4.75949i	−0.798261	−	0.419049i
$130$	−0.00703706	−	0.0201019i	−0.000617191	−	0.00176305i
$131$	5.09359	−	8.82236i	0.445029	−	0.770813i	−0.553025	−	0.833165i	$-0.686527\pi$
$131$	5.09359	−	8.82236i	0.445029	−	0.770813i	0.998054	+	0.0623514i	$0.0198600\pi$
$132$	−2.83956	+	2.45882i	−0.247152	+	0.214013i
$133$	−0.0699971	+	15.7178i	−0.00606951	+	1.36291i
$134$	5.33251	−	6.19821i	0.460659	−	0.535444i
$135$	0.316890	+	0.135113i	0.0272736	+	0.0116287i
$136$	7.01859	−	3.71314i	0.601839	−	0.318399i
$137$	0.500698	−	0.289078i	0.0427775	−	0.0246976i	−0.478459	−	0.878110i	$-0.658804\pi$
$137$	0.500698	−	0.289078i	0.0427775	−	0.0246976i	0.521236	+	0.853412i	$0.325471\pi$
$138$	−16.5312	−	13.1042i	−1.40723	−	1.11550i
$139$	11.8727	−	6.85472i	1.00703	−	0.581410i	0.0967105	−	0.995313i	$-0.469168\pi$
$139$	11.8727	−	6.85472i	1.00703	−	0.581410i	0.910321	+	0.413903i	$0.135835\pi$
$140$	0.0713917	+	0.472771i	0.00603370	+	0.0399565i
$141$	0.381221	+	0.602971i	0.0321046	+	0.0507793i
$142$	2.99596	−	15.8459i	0.251415	−	1.32976i
$143$	0.123155	+	0.213311i	0.0102988	+	0.0178380i
$144$	1.71576	−	11.8767i	0.142980	−	0.989726i
$145$	0.356116			0.0295738
$146$	3.82264	−	20.2184i	0.316364	−	1.67328i
$147$	10.3889	−	0.417742i	0.856861	−	0.0344548i
$148$	2.82421	−	2.25351i	0.232149	−	0.185237i
$149$	7.60188	+	4.38895i	0.622771	+	0.359557i	0.777947	−	0.628330i	$-0.216261\pi$
$149$	7.60188	+	4.38895i	0.622771	+	0.359557i	−0.155176	+	0.987887i	$0.549595\pi$
$150$	9.58931	+	7.60142i	0.782964	+	0.620653i
$151$			16.1081i			1.31086i	0.755257	+	0.655429i	$0.227512\pi$
$151$			16.1081i			1.31086i	−0.755257	+	0.655429i	$0.772488\pi$
$152$	−6.60146	+	10.4125i	−0.535449	+	0.844567i
$153$	7.60817	+	3.61176i	0.615084	+	0.291994i
$154$	−1.82701	−	5.21901i	−0.147225	−	0.420559i
$155$	0.228407	−	0.395613i	0.0183461	−	0.0317764i
$156$	−0.743532	−	0.257619i	−0.0595302	−	0.0206260i
$157$	−2.73796	+	4.74229i	−0.218513	+	0.378476i	−0.954354	−	0.298679i	$-0.903454\pi$
$157$	−2.73796	+	4.74229i	−0.218513	+	0.378476i	0.735840	+	0.677155i	$0.236787\pi$
$158$	−5.35226	−	1.01194i	−0.425803	−	0.0805056i
$159$	1.22906	−	0.777062i	0.0974711	−	0.0616250i
$160$	−0.149737	+	0.343846i	−0.0118378	+	0.0271834i
$161$	26.8940	−	15.5272i	2.11954	−	1.22372i
$162$	11.1851	−	6.07406i	0.878782	−	0.477223i
$163$		−	2.54802i		−	0.199576i	−0.995009	−	0.0997880i	$-0.968184\pi$
$163$		−	2.54802i		−	0.199576i	0.995009	−	0.0997880i	$-0.0318165\pi$
$164$	6.01191	−	0.907839i	0.469451	−	0.0708903i
$165$	0.110245	+	0.0578736i	0.00858260	+	0.00450546i
$166$	−13.1839	+	4.61527i	−1.02327	+	0.358214i
$167$	6.52564	+	11.3027i	0.504969	+	0.874633i	0.999983	+	0.00574771i	$0.00182956\pi$
$167$	6.52564	+	11.3027i	0.504969	+	0.874633i	−0.495014	+	0.868885i	$0.664837\pi$
$168$	15.3269	+	8.78372i	1.18250	+	0.677679i
$169$	6.47420	−	11.2136i	0.498015	−	0.862588i
$170$	−0.199530	−	0.171661i	−0.0153032	−	0.0131658i
$171$	−13.0390	+	0.991886i	−0.997119	+	0.0758514i
$172$	11.6914	−	1.76548i	0.891460	−	0.134617i
$173$	−10.4328	−	6.02338i	−0.793192	−	0.457949i	0.0478933	−	0.998852i	$-0.484749\pi$
$173$	−10.4328	−	6.02338i	−0.793192	−	0.457949i	−0.841085	+	0.540903i	$0.818083\pi$
$174$	8.17336	−	10.3108i	0.619621	−	0.781662i
$175$	−15.6005	+	9.00695i	−1.17929	+	0.680861i
$176$	0.962807	−	4.22905i	0.0725743	−	0.318776i
$177$	7.15899	−	13.6374i	0.538103	−	1.02505i
$178$	−14.5981	+	16.9680i	−1.09418	+	1.27181i
$179$	−4.43830			−0.331734			−0.165867	−	0.986148i	$-0.553042\pi$
$179$	−4.43830			−0.331734			−0.165867	+	0.986148i	$0.553042\pi$
$180$	−0.387287	+	0.0907838i	−0.0288667	+	0.00676662i
$181$	−0.959000	−	1.66104i	−0.0712819	−	0.123464i	0.828181	−	0.560460i	$-0.189376\pi$
$181$	−0.959000	−	1.66104i	−0.0712819	−	0.123464i	−0.899463	+	0.436996i	$0.856042\pi$
$182$	0.755495	−	0.878145i	0.0560010	−	0.0650924i
$183$	−8.65081	−	13.6828i	−0.639486	−	1.01146i
$184$	24.3418	+	0.900756i	1.79450	+	0.0664046i
$185$	−0.103724	−	0.0598849i	−0.00762591	−	0.00440282i
$186$	−6.21213	−	15.6931i	−0.455496	−	1.15067i
$187$	2.63619	+	1.52201i	0.192777	+	0.111300i
$188$	−0.766875	−	0.300733i	−0.0559301	−	0.0219332i
$189$	2.25359	+	18.6010i	0.163925	+	1.35303i
$190$	0.401229	+	0.0777118i	0.0291082	+	0.00563780i
$191$	−20.8595			−1.50934			−0.754669	−	0.656105i	$-0.772203\pi$
$191$	−20.8595			−1.50934			−0.754669	+	0.656105i	$0.772203\pi$
$192$	6.51889	+	12.2272i	0.470460	+	0.882421i
$193$	−11.1740	+	19.3539i	−0.804319	+	1.39312i	0.112431	+	0.993660i	$0.464136\pi$
$193$	−11.1740	+	19.3539i	−0.804319	+	1.39312i	−0.916750	+	0.399462i	$0.869197\pi$
$194$	2.36089	−	12.4870i	0.169502	−	0.896513i
$195$	0.00104803	+	0.0260636i	7.50510e−5	+	0.00186645i
$196$	−9.38441	+	7.48804i	−0.670315	+	0.534860i
$197$		−	21.2443i		−	1.51359i	−0.653651	−	0.756796i	$-0.726763\pi$
$197$		−	21.2443i		−	1.51359i	0.653651	−	0.756796i	$-0.273237\pi$
$198$	4.20593	−	1.86372i	0.298903	−	0.132449i
$199$	1.22792	−	0.708941i	0.0870451	−	0.0502555i	−0.455846	−	0.890059i	$-0.650663\pi$
$199$	1.22792	−	0.708941i	0.0870451	−	0.0502555i	0.542891	+	0.839803i	$0.317330\pi$
$200$	−14.1200	−	0.522505i	−0.998438	−	0.0369467i
$201$	−8.46421	+	5.35140i	−0.597019	+	0.377459i
$202$	−15.0894	+	17.5391i	−1.06169	+	1.23405i
$203$	9.68465	+	16.7743i	0.679729	+	1.17733i
$204$	−9.54969	+	1.83722i	−0.668612	+	0.128631i
$205$	−0.100773	−	0.174545i	−0.00703831	−	0.0121907i
$206$	−4.33368	−	12.3795i	−0.301942	−	0.862520i
$207$	14.6728	+	21.2652i	1.01983	+	1.47803i
$208$	0.868115	−	0.268301i	0.0601929	−	0.0186033i
$209$	−4.72637	−	0.0210482i	−0.326930	−	0.00145594i
$210$	0.0855826	−	0.579301i	0.00590576	−	0.0399756i
$211$	−13.7991	−	7.96692i	−0.949970	−	0.548466i	−0.0568985	−	0.998380i	$-0.518121\pi$
$211$	−13.7991	−	7.96692i	−0.949970	−	0.548466i	−0.893072	+	0.449914i	$0.851454\pi$
$212$	−0.612999	+	1.56316i	−0.0421009	+	0.107358i
$213$	−9.18031	+	17.4879i	−0.629024	+	1.19825i
$214$	14.3690	−	5.03015i	0.982245	−	0.343854i
$215$	−0.195975	−	0.339438i	−0.0133654	−	0.0231495i
$216$	−6.26027	+	13.2970i	−0.425957	+	0.904743i
$217$	24.8463			1.68668
$218$	−3.03561	+	16.0557i	−0.205598	+	1.08743i
$219$	−11.7135	+	22.3134i	−0.791523	+	1.50780i
$220$	−0.142163	+	0.0214676i	−0.00958464	+	0.00144735i
$221$			0.637702i			0.0428965i
$222$	−4.11448	+	1.62873i	−0.276146	+	0.109313i
$223$	0.981114	+	0.566446i	0.0657002	+	0.0379320i	0.532490	−	0.846436i	$-0.321256\pi$
$223$	0.981114	+	0.566446i	0.0657002	+	0.0379320i	−0.466790	+	0.884368i	$0.654590\pi$
$224$	−20.2685	+	2.29782i	−1.35425	+	0.153529i
$225$	−8.51131	−	12.3354i	−0.567421	−	0.822360i
$226$	−0.263117	−	0.751615i	−0.0175023	−	0.0499967i
$227$	9.94899			0.660338			0.330169	−	0.943922i	$-0.392894\pi$
$227$	9.94899			0.660338			0.330169	+	0.943922i	$0.392894\pi$
$228$	11.4588	−	9.83341i	0.758877	−	0.651234i
$229$	−12.3392			−0.815397			−0.407698	−	0.913117i	$-0.633669\pi$
$229$	−12.3392			−0.815397			−0.407698	+	0.913117i	$0.633669\pi$
$230$	−0.266789	−	0.762104i	−0.0175916	−	0.0502517i
$231$	0.272098	+	6.76683i	0.0179027	+	0.445225i
$232$	−0.561820	+	15.1825i	−0.0368853	+	0.996777i
$233$	24.9320	+	14.3945i	1.63335	+	0.943016i	0.983049	+	0.183341i	$0.0586914\pi$
$233$	24.9320	+	14.3945i	1.63335	+	0.943016i	0.650303	+	0.759675i	$0.274642\pi$
$234$	0.778687	+	0.567852i	0.0509044	+	0.0371216i
$235$			0.0273058i			0.00178123i
$236$	2.65555	+	17.5856i	0.172862	+	1.14473i
$237$	5.90685	+	3.10082i	0.383691	+	0.201420i
$238$	2.65960	−	14.0669i	0.172396	−	0.911822i
$239$	−18.7292			−1.21149			−0.605746	−	0.795658i	$-0.707125\pi$
$239$	−18.7292			−1.21149			−0.605746	+	0.795658i	$0.707125\pi$
$240$	0.298446	−	0.349152i	0.0192646	−	0.0225377i
$241$	−0.171030	−	0.296232i	−0.0110170	−	0.0190820i	0.860464	−	0.509511i	$-0.170174\pi$
$241$	−0.171030	−	0.296232i	−0.0110170	−	0.0190820i	−0.871481	+	0.490429i	$0.836840\pi$
$242$	−13.1133	+	4.59057i	−0.842955	+	0.295093i
$243$	−15.2748	+	3.11137i	−0.979879	+	0.199595i
$244$	17.4022	+	6.82434i	1.11406	+	0.436884i
$245$	0.344657	+	0.198988i	0.0220193	+	0.0127129i
$246$	−7.36657	−	1.08829i	−0.469675	−	0.0693871i
$247$	−0.491255	−	0.859697i	−0.0312578	−	0.0547012i
$248$	16.5060	+	10.3619i	1.04813	+	0.657982i
$249$	17.0939	−	0.687353i	1.08328	−	0.0435592i
$250$	0.309651	+	0.884543i	0.0195841	+	0.0559434i
$251$	−10.5008	−	18.1880i	−0.662806	−	1.14801i	−0.979875	−	0.199612i	$-0.936032\pi$
$251$	−10.5008	−	18.1880i	−0.662806	−	1.14801i	0.317069	−	0.948403i	$-0.397301\pi$
$252$	−14.8086	−	15.7737i	−0.932853	−	0.993649i
$253$	4.66907	+	8.08706i	0.293542	+	0.508429i
$254$	−4.22309	+	4.90868i	−0.264980	+	0.307998i
$255$	0.172269	+	0.272475i	0.0107879	+	0.0170631i
$256$	−14.4231	−	6.92629i	−0.901445	−	0.432893i
$257$	−13.5869	+	7.84438i	−0.847526	+	0.489319i	−0.859815	−	0.510605i	$-0.829421\pi$
$257$	−13.5869	+	7.84438i	−0.847526	+	0.489319i	0.0122895	+	0.999924i	$0.496088\pi$
$258$	−14.3258	−	2.11641i	−0.891887	−	0.131762i
$259$		−	6.51432i		−	0.404780i
$260$	−0.0187860	−	0.0235436i	−0.00116506	−	0.00146011i
$261$	−13.2635	+	9.15172i	−0.820993	+	0.566477i
$262$	2.67646	−	14.1561i	0.165352	−	0.874564i
$263$	−14.0127	+	24.2707i	−0.864059	+	1.49659i	0.00391948	+	0.999992i	$0.498752\pi$
$263$	−14.0127	+	24.2707i	−0.864059	+	1.49659i	−0.867978	+	0.496602i	$0.834581\pi$
$264$	−2.64128	+	4.60884i	−0.162559	+	0.283654i
$265$	0.0556587			0.00341908
$266$	7.25101	+	21.0127i	0.444588	+	1.28837i
$267$	23.1714	−	14.6498i	1.41806	−	0.896555i
$268$	4.22155	−	10.7650i	0.257872	−	0.657578i
$269$	19.4875	+	11.2511i	1.18817	+	0.685991i	0.957891	−	0.287133i	$-0.0927021\pi$
$269$	19.4875	+	11.2511i	1.18817	+	0.685991i	0.230281	+	0.973124i	$0.426035\pi$
$270$	0.486115	+	0.0322746i	0.0295840	+	0.00196417i
$271$	12.9598	+	7.48235i	0.787252	+	0.454520i	0.838994	−	0.544140i	$-0.183144\pi$
$271$	12.9598	+	7.48235i	0.787252	+	0.454520i	−0.0517422	+	0.998660i	$0.516477\pi$
$272$	7.63330	−	8.23582i	0.462837	−	0.499370i
$273$	−1.19918	+	0.758171i	−0.0725779	+	0.0458866i
$274$	0.533249	−	0.619819i	0.0322148	−	0.0374446i
$275$	−2.70841	−	4.69110i	−0.163323	−	0.282884i
$276$	−28.1888	−	9.76685i	−1.69677	−	0.587896i
$277$	−10.1303			−0.608668			−0.304334	−	0.952565i	$-0.598434\pi$
$277$	−10.1303			−0.608668			−0.304334	+	0.952565i	$0.598434\pi$
$278$	12.6446	−	14.6974i	0.758372	−	0.881489i
$279$	1.65971	+	20.6044i	0.0993640	+	1.23355i
$280$	0.316204	+	0.597691i	0.0188968	+	0.0357188i
$281$	18.4562	−	10.6557i	1.10100	−	0.635665i	0.164520	−	0.986374i	$-0.447393\pi$
$281$	18.4562	−	10.6557i	1.10100	−	0.635665i	0.936485	+	0.350709i	$0.114059\pi$
$282$	0.790599	+	0.626705i	0.0470795	+	0.0373198i
$283$	−4.84844	−	2.79925i	−0.288210	−	0.166398i	0.348924	−	0.937151i	$-0.386547\pi$
$283$	−4.84844	−	2.79925i	−0.288210	−	0.166398i	−0.637134	+	0.770753i	$0.719880\pi$
$284$	−3.40534	−	22.5509i	−0.202070	−	1.33815i
$285$	−0.442141	−	0.234621i	−0.0261902	−	0.0138977i
$286$	0.264060	+	0.227179i	0.0156142	+	0.0134334i
$287$	5.48110	−	9.49355i	0.323539	−	0.560386i
$288$	−3.25943	−	16.6546i	−0.192064	−	0.981382i
$289$	−4.55950	−	7.89728i	−0.268206	−	0.464546i
$290$	0.475340	−	0.166402i	0.0279129	−	0.00977145i
$291$	−7.23430	+	13.7809i	−0.424082	+	0.807849i
$292$	−4.34499	−	28.7734i	−0.254271	−	1.68384i
$293$		−	24.2140i		−	1.41460i	−0.706915	−	0.707299i	$-0.749914\pi$
$293$		−	24.2140i		−	1.41460i	0.706915	−	0.707299i	$-0.250086\pi$
$294$	13.6718	−	5.41200i	0.797354	−	0.315634i
$295$	0.510566	−	0.294776i	0.0297263	−	0.0171625i
$296$	2.71674	−	4.32762i	0.157907	−	0.251538i
$297$	−5.59337	+	0.677660i	−0.324560	+	0.0393218i
$298$	12.1977	+	2.30620i	0.706595	+	0.133594i
$299$	−0.978141	+	1.69419i	−0.0565674	+	0.0979776i
$300$	16.3516	+	5.66550i	0.944060	+	0.327098i
$301$	10.6591	−	18.4622i	0.614382	−	1.06414i
$302$	7.52681	+	21.5009i	0.433119	+	1.23724i
$303$	23.9512	−	15.1429i	1.37596	−	0.869935i
$304$	−3.94611	+	16.9832i	−0.226325	+	0.974052i
$305$		−	0.619632i		−	0.0354800i
$306$	11.8430	+	1.26588i	0.677017	+	0.0723655i
$307$	11.2463	+	6.49305i	0.641860	+	0.370578i	0.785331	−	0.619077i	$-0.212493\pi$
$307$	11.2463	+	6.49305i	0.641860	+	0.370578i	−0.143471	+	0.989655i	$0.545826\pi$
$308$	−4.87735	−	6.11256i	−0.277913	−	0.348296i
$309$	0.645416	+	16.0509i	0.0367164	+	0.913105i
$310$	0.120018	−	0.634787i	0.00681655	−	0.0360535i
$311$	−7.00672			−0.397315			−0.198657	−	0.980069i	$-0.563658\pi$
$311$	−7.00672			−0.397315			−0.198657	+	0.980069i	$0.563658\pi$
$312$	−1.11283	+	0.00356241i	−0.0630018	+	0.000201682i
$313$	−8.22035	−	14.2381i	−0.464641	−	0.804783i	0.534544	−	0.845141i	$-0.320483\pi$
$313$	−8.22035	−	14.2381i	−0.464641	−	0.804783i	−0.999185	+	0.0403582i	$0.987150\pi$
$314$	−1.43868	+	7.60932i	−0.0811893	+	0.429419i
$315$	−0.307571	+	0.647898i	−0.0173297	+	0.0365049i
$316$	−7.61698	+	1.15022i	−0.428488	+	0.0647047i
$317$	−12.2361	+	7.06454i	−0.687250	+	0.396784i	−0.802581	−	0.596543i	$-0.796540\pi$
$317$	−12.2361	+	7.06454i	−0.687250	+	0.396784i	0.115331	+	0.993327i	$0.463207\pi$
$318$	1.27744	−	1.61152i	0.0716355	−	0.0903693i
$319$	−5.04406	+	2.91219i	−0.282413	+	0.163051i
$320$	−0.0391993	+	0.528930i	−0.00219131	+	0.0295681i
$321$	−18.6305	+	0.749141i	−1.03985	+	0.0418130i
$322$	28.6424	−	33.2923i	1.59618	−	1.85531i
$323$	−10.5700	−	6.16553i	−0.588132	−	0.343059i
$324$	12.0915	−	13.3340i	0.671749	−	0.740779i
$325$	0.567395	−	0.982756i	0.0314734	−	0.0545135i
$326$	−1.19061	−	3.40106i	−0.0659417	−	0.188367i
$327$	9.30183	−	17.7194i	0.514392	−	0.979883i
$328$	7.60042	−	4.02095i	0.419663	−	0.222020i
$329$	−1.28620	+	0.742586i	−0.0709103	+	0.0409401i
$330$	0.174197	+	0.0257348i	0.00958922	+	0.00141666i
$331$		−	26.0553i		−	1.43213i	−0.698034	−	0.716065i	$-0.745941\pi$
$331$		−	26.0553i		−	1.43213i	0.698034	−	0.716065i	$-0.254059\pi$
$332$	−15.4411	+	12.3208i	−0.847441	+	0.676193i
$333$	5.40215	−	0.435150i	0.296036	−	0.0238461i
$334$	13.9918	+	12.0375i	0.765596	+	0.658665i
$335$	−0.383305			−0.0209422
$336$	24.5626	+	4.56260i	1.34000	+	0.248910i
$337$	−4.66024	+	8.07177i	−0.253859	+	0.439697i	−0.964585	−	0.263772i	$-0.915033\pi$
$337$	−4.66024	+	8.07177i	−0.253859	+	0.439697i	0.710726	+	0.703469i	$0.248367\pi$
$338$	3.40190	−	17.9930i	0.185039	−	0.978692i
$339$	0.0391861	+	0.974524i	0.00212830	+	0.0529289i
$340$	−0.346542	−	0.135898i	−0.0187939	−	0.00737009i
$341$			7.47133i			0.404595i
$342$	−16.9409	+	7.41668i	−0.916057	+	0.401048i
$343$		−	3.59558i		−	0.194143i
$344$	14.7806	−	7.81956i	0.796916	−	0.421603i
$345$	0.0397330	+	0.988124i	0.00213915	+	0.0531988i
$346$	−16.7401	−	3.16502i	−0.899955	−	0.170153i
$347$	11.7069	−	20.2769i	0.628459	−	1.08852i	−0.359402	−	0.933183i	$-0.617019\pi$
$347$	11.7069	−	20.2769i	0.628459	−	1.08852i	0.987861	−	0.155340i	$-0.0496473\pi$
$348$	6.09178	−	17.5819i	0.326554	−	0.942490i
$349$	19.3123			1.03376			0.516881	−	0.856057i	$-0.327093\pi$
$349$	19.3123			1.03376			0.516881	+	0.856057i	$0.327093\pi$
$350$	−16.6147	+	19.3120i	−0.888093	+	1.03227i
$351$	−0.708834	−	0.943806i	−0.0378348	−	0.0503766i
$352$	−0.690957	−	6.09477i	−0.0368281	−	0.324852i
$353$		−	0.804702i		−	0.0428300i	−0.999771	−	0.0214150i	$-0.993183\pi$
$353$		−	0.804702i		−	0.0428300i	0.999771	−	0.0214150i	$-0.00681712\pi$
$354$	3.18341	−	21.5482i	0.169196	−	1.14528i
$355$	−0.654723	+	0.378004i	−0.0347491	+	0.0200624i
$356$	−11.5568	+	29.4700i	−0.612508	+	1.56191i
$357$	−8.14964	+	15.5245i	−0.431324	+	0.821644i
$358$	−5.92419	+	2.07388i	−0.313103	+	0.109608i
$359$	−2.14236	+	3.71068i	−0.113070	+	0.195842i	−0.917006	−	0.398872i	$-0.869402\pi$
$359$	−2.14236	+	3.71068i	−0.113070	+	0.195842i	0.803937	+	0.594715i	$0.202735\pi$
$360$	−0.474526	+	0.302144i	−0.0250097	+	0.0159244i
$361$	18.9992	+	0.169224i	0.999960	+	0.00890654i
$362$	−2.05621	−	1.76902i	−0.108072	−	0.0929777i
$363$	17.0024	−	0.683674i	0.892393	−	0.0358836i
$364$	0.598096	−	1.52516i	0.0313488	−	0.0799399i
$365$	−0.835383	+	0.482309i	−0.0437260	+	0.0252452i
$366$	−17.9405	−	14.2214i	−0.937767	−	0.743365i
$367$	−19.9401	+	11.5124i	−1.04086	+	0.600943i	−0.920078	−	0.391735i	$-0.871875\pi$
$367$	−19.9401	+	11.5124i	−1.04086	+	0.600943i	−0.120786	+	0.992679i	$0.538542\pi$
$368$	32.9120	−	10.1718i	1.71566	−	0.530243i
$369$	8.23887	+	3.91117i	0.428898	+	0.203607i
$370$	−0.166431	−	0.0314668i	−0.00865236	−	0.00163588i
$371$	1.51365	+	2.62172i	0.0785847	+	0.136113i
$372$	−15.6248	−	18.0442i	−0.810106	−	0.935547i
$373$	−32.6423			−1.69015			−0.845076	−	0.534646i	$-0.820445\pi$
$373$	−32.6423			−1.69015			−0.845076	+	0.534646i	$0.820445\pi$
$374$	4.22994	+	0.799747i	0.218725	+	0.0413539i
$375$	−0.0461164	−	1.14688i	−0.00238144	−	0.0592244i
$376$	−1.16414	−	0.0430784i	−0.0600359	−	0.00222160i
$377$	−1.05670	−	0.610086i	−0.0544229	−	0.0314211i
$378$	11.6998	+	23.7754i	0.601770	+	1.22288i
$379$		−	9.50252i		−	0.488112i	−0.969761	−	0.244056i	$-0.921522\pi$
$379$		−	9.50252i		−	0.488112i	0.969761	−	0.244056i	$-0.0784780\pi$
$380$	0.571868	−	0.0837529i	0.0293362	−	0.00429644i
$381$	6.70324	−	4.23805i	0.343418	−	0.217122i
$382$	−27.8430	+	9.74698i	−1.42457	+	0.498699i
$383$	18.2486	−	31.6075i	0.932460	−	1.61507i	0.153359	−	0.988171i	$-0.450991\pi$
$383$	18.2486	−	31.6075i	0.932460	−	1.61507i	0.779101	−	0.626898i	$-0.215676\pi$
$384$	14.4147	+	13.2746i	0.735598	+	0.677418i
$385$	−0.129611	+	0.224493i	−0.00660560	+	0.0114412i
$386$	−5.87142	+	31.0546i	−0.298847	+	1.58064i
$387$	16.0222	+	7.60607i	0.814453	+	0.386638i
$388$	−2.68349	−	17.7706i	−0.136233	−	0.902167i
$389$	4.61960	−	2.66713i	0.234223	−	0.135229i	−0.378296	−	0.925685i	$-0.623490\pi$
$389$	4.61960	−	2.66713i	0.234223	−	0.135229i	0.612519	+	0.790456i	$0.290156\pi$
$390$	0.0135776	+	0.0342997i	0.000687528	+	0.00173683i
$391$			24.1766i			1.22266i
$392$	−9.02728	+	14.3800i	−0.455947	+	0.726299i
$393$	−8.20128	+	15.6229i	−0.413700	+	0.788071i
$394$	−9.92679	−	28.3566i	−0.500104	−	1.42859i
$395$	0.127678	+	0.221145i	0.00642418	+	0.0111270i
$396$	4.74318	−	4.45297i	0.238354	−	0.223770i
$397$	4.78790	−	8.29289i	0.240298	−	0.416208i	−0.720501	−	0.693454i	$-0.756088\pi$
$397$	4.78790	−	8.29289i	0.240298	−	0.416208i	0.960799	+	0.277246i	$0.0894216\pi$
$398$	1.30775	−	1.52006i	0.0655516	−	0.0761935i
$399$	−0.972668	−	27.2069i	−0.0486943	−	1.36205i
$400$	−19.0914	+	5.90042i	−0.954571	+	0.295021i
$401$	−23.8972	−	13.7970i	−1.19337	−	0.688991i	−0.234299	−	0.972165i	$-0.575279\pi$
$401$	−23.8972	−	13.7970i	−1.19337	−	0.688991i	−0.959069	+	0.283174i	$0.908613\pi$
$402$	−8.79739	+	11.0980i	−0.438774	+	0.553520i
$403$	−1.35550	+	0.782599i	−0.0675223	+	0.0389840i
$404$	−11.9457	+	30.4618i	−0.594322	+	1.51553i
$405$	−0.557829	−	0.211781i	−0.0277187	−	0.0105235i
$406$	20.7651	+	17.8648i	1.03055	+	0.886616i
$407$	1.95887			0.0970975
$408$	−11.8883	+	6.91458i	−0.588561	+	0.342323i
$409$	0.247829	+	0.429253i	0.0122544	+	0.0212252i	0.872088	−	0.489350i	$-0.162766\pi$
$409$	0.247829	+	0.429253i	0.0122544	+	0.0212252i	−0.859833	+	0.510575i	$0.829433\pi$
$410$	−0.216070	−	0.185892i	−0.0106709	−	0.00918054i
$411$	−0.846418	+	0.535138i	−0.0417507	+	0.0263964i
$412$	−11.5691	−	14.4990i	−0.569968	−	0.714314i
$413$	27.7699	+	16.0330i	1.36647	+	0.788931i
$414$	29.5216	+	21.5284i	1.45091	+	1.05806i
$415$	0.567099	+	0.327415i	0.0278378	+	0.0160722i
$416$	1.03338	−	0.763767i	0.0506657	−	0.0374468i
$417$	−20.0705	+	12.6894i	−0.982859	+	0.621401i
$418$	−6.31854	+	2.18039i	−0.309050	+	0.106646i
$419$	−26.4145			−1.29043			−0.645216	−	0.764000i	$-0.723233\pi$
$419$	−26.4145			−1.29043			−0.645216	+	0.764000i	$0.723233\pi$
$420$	−0.156455	−	0.813234i	−0.00763420	−	0.0396818i
$421$	13.5509	−	23.4708i	0.660430	−	1.14390i	−0.320073	−	0.947393i	$-0.603708\pi$
$421$	13.5509	−	23.4708i	0.660430	−	1.14390i	0.980503	−	0.196505i	$-0.0629591\pi$
$422$	−22.1416	−	4.18626i	−1.07784	−	0.203784i
$423$	−0.701722	−	1.01700i	−0.0341189	−	0.0494484i
$424$	−0.0878088	+	2.37292i	−0.00426437	+	0.115239i
$425$		−	14.0242i		−	0.680275i
$426$	−4.08223	+	27.6323i	−0.197785	+	1.33879i
$427$	29.1868	−	16.8510i	1.41245	−	0.815478i
$428$	16.8292	−	13.4284i	0.813468	−	0.649085i
$429$	−0.227983	−	0.360597i	−0.0110071	−	0.0174098i
$430$	−0.420193	−	0.361505i	−0.0202635	−	0.0174333i
$431$	0.166246	+	0.287947i	0.00800780	+	0.0138699i	0.870002	−	0.493049i	$-0.164118\pi$
$431$	0.166246	+	0.287947i	0.00800780	+	0.0138699i	−0.861994	+	0.506919i	$0.830784\pi$
$432$	−2.14289	+	20.6738i	−0.103100	+	0.994671i
$433$	−9.53952	−	16.5229i	−0.458440	−	0.794041i	0.540439	−	0.841383i	$-0.318258\pi$
$433$	−9.53952	−	16.5229i	−0.458440	−	0.794041i	−0.998879	+	0.0473421i	$0.984925\pi$
$434$	33.1646	−	11.6099i	1.59195	−	0.557293i
$435$	−0.616313	+	0.0247823i	−0.0295500	+	0.00118822i
$436$	3.45041	+	22.8494i	0.165245	+	1.09429i
$437$	−18.6245	−	32.5929i	−0.890929	−	1.55913i
$438$	−5.20866	+	35.2570i	−0.248879	+	1.68464i
$439$	13.6352	+	7.87227i	0.650772	+	0.375723i	0.788752	−	0.614712i	$-0.210728\pi$
$439$	13.6352	+	7.87227i	0.650772	+	0.375723i	−0.137980	+	0.990435i	$0.544061\pi$
$440$	−0.179727	+	0.0950831i	−0.00856813	+	0.00453291i
$441$	−17.9505	+	1.44593i	−0.854785	+	0.0688540i
$442$	0.297978	+	0.851198i	0.0141734	+	0.0404873i
$443$	8.64486	+	14.9733i	0.410730	+	0.711405i	0.994970	−	0.100176i	$-0.0319407\pi$
$443$	8.64486	+	14.9733i	0.410730	+	0.711405i	−0.584240	+	0.811581i	$0.698607\pi$
$444$	−4.73091	+	4.09657i	−0.224519	+	0.194415i
$445$	1.04932			0.0497428
$446$	1.57426	+	0.297642i	0.0745435	+	0.0140938i
$447$	−13.4616	−	7.06673i	−0.636714	−	0.334245i
$448$	−25.9805	+	12.5379i	−1.22746	+	0.592362i
$449$			14.4783i			0.683275i	0.939832	+	0.341637i	$0.110981\pi$
$449$			14.4783i			0.683275i	−0.939832	+	0.341637i	$0.889019\pi$
$450$	−17.1247	−	12.4881i	−0.807268	−	0.588694i
$451$	2.85473	+	1.64818i	0.134424	+	0.0776096i
$452$	−0.702412	−	0.880300i	−0.0330387	−	0.0414058i
$453$	−1.12097	−	27.8775i	−0.0526677	−	1.30980i
$454$	13.2798	−	4.64885i	0.623252	−	0.218181i
$455$	−0.0543056			−0.00254588
$456$	10.7002	−	18.4799i	0.501084	−	0.865399i
$457$	33.7644			1.57943			0.789716	−	0.613472i	$-0.210228\pi$
$457$	33.7644			1.57943			0.789716	+	0.613472i	$0.210228\pi$
$458$	−16.4702	+	5.76572i	−0.769603	+	0.269414i
$459$	−13.4184	−	5.72125i	−0.626319	−	0.267045i
$460$	−0.712215	−	0.892585i	−0.0332072	−	0.0416170i
$461$	1.31774	+	0.760795i	0.0613731	+	0.0354338i	0.530373	−	0.847765i	$-0.322052\pi$
$461$	1.31774	+	0.760795i	0.0613731	+	0.0354338i	−0.468999	+	0.883198i	$0.655385\pi$
$462$	3.52512	+	8.90514i	0.164003	+	0.414305i
$463$		−	18.2142i		−	0.846488i	−0.906016	−	0.423244i	$-0.860891\pi$
$463$		−	18.2142i		−	0.846488i	0.906016	−	0.423244i	$-0.139109\pi$
$464$	6.34438	+	20.5279i	0.294530	+	0.952983i
$465$	−0.367762	+	0.700563i	−0.0170546	+	0.0324878i
$466$	40.0051	+	7.56368i	1.85320	+	0.350381i
$467$	29.4320			1.36195			0.680975	−	0.732306i	$-0.261556\pi$
$467$	29.4320			1.36195			0.680975	+	0.732306i	$0.261556\pi$
$468$	1.30472	+	0.394106i	0.0603108	+	0.0182175i
$469$	−10.4241	−	18.0550i	−0.481338	−	0.833703i
$470$	0.0127591	+	0.0364474i	0.000588535	+	0.00168119i
$471$	4.40844	−	8.39779i	0.203130	−	0.386950i
$472$	11.7618	+	22.2323i	0.541382	+	1.02332i
$473$	5.55160	+	3.20522i	0.255263	+	0.147376i
$474$	9.33332	+	1.37885i	0.428693	+	0.0633327i
$475$	10.8036	+	18.9063i	0.495702	+	0.867480i
$476$	−3.02302	−	20.0191i	−0.138560	−	0.917574i
$477$	−2.07301	+	1.43035i	−0.0949164	+	0.0654914i
$478$	−24.9995	+	8.75156i	−1.14345	+	0.400287i
$479$	4.06914	+	7.04796i	0.185924	+	0.322029i	0.943887	−	0.330267i	$-0.107139\pi$
$479$	4.06914	+	7.04796i	0.185924	+	0.322029i	−0.757964	+	0.652297i	$0.773806\pi$
$480$	0.235215	−	0.605499i	0.0107361	−	0.0276371i
$481$	0.205186	+	0.355392i	0.00935566	+	0.0162045i
$482$	−0.366708	−	0.315490i	−0.0167031	−	0.0143702i
$483$	−45.4635	+	28.7438i	−2.06866	+	1.30789i
$484$	−15.3585	+	12.2549i	−0.698112	+	0.557040i
$485$	−0.515937	+	0.297877i	−0.0234275	+	0.0135259i
$486$	−18.9348	+	11.2905i	−0.858899	+	0.512145i
$487$			27.5866i			1.25007i	0.780598	+	0.625033i	$0.214915\pi$
$487$			27.5866i			1.25007i	−0.780598	+	0.625033i	$0.785085\pi$
$488$	26.4170	+	0.977550i	1.19584	+	0.0442516i
$489$	0.177317	+	4.40973i	0.00801857	+	0.199415i
$490$	0.553025	+	0.104559i	0.0249831	+	0.00472351i
$491$	1.88290	−	3.26127i	0.0849740	−	0.147179i	−0.820406	−	0.571781i	$-0.806253\pi$
$491$	1.88290	−	3.26127i	0.0849740	−	0.147179i	0.905380	+	0.424602i	$0.139586\pi$
$492$	−10.3413	+	1.98952i	−0.466224	+	0.0896947i
$493$	−15.0794			−0.679144
$494$	−1.05743	−	0.917966i	−0.0475761	−	0.0413012i
$495$	−0.194824	−	0.0924871i	−0.00875669	−	0.00415699i
$496$	26.8738	+	6.11823i	1.20667	+	0.274717i
$497$	−35.6106	−	20.5598i	−1.59736	−	0.922234i
$498$	22.4955	−	8.90490i	1.00805	−	0.399038i
$499$	14.6121	+	8.43629i	0.654127	+	0.377660i	0.790035	−	0.613061i	$-0.210062\pi$
$499$	14.6121	+	8.43629i	0.654127	+	0.377660i	−0.135909	+	0.990721i	$0.543395\pi$
$500$	0.826638	+	1.03599i	0.0369684	+	0.0463308i
$501$	−12.0802	−	19.1070i	−0.539703	−	0.853638i
$502$	−22.5151	−	19.3704i	−1.00490	−	0.864543i
$503$	−11.9622	−	20.7191i	−0.533366	−	0.923818i	−0.999241	−	0.0389668i	$-0.987593\pi$
$503$	−11.9622	−	20.7191i	−0.533366	−	0.923818i	0.465874	−	0.884851i	$-0.345740\pi$
$504$	−27.1369	−	14.1350i	−1.20877	−	0.629621i
$505$	1.08464			0.0482658
$506$	10.0110	+	8.61281i	0.445045	+	0.382886i
$507$	−10.4242	+	19.8575i	−0.462956	+	0.881901i
$508$	−3.34326	+	8.52537i	−0.148333	+	0.378252i
$509$	−22.1517	+	12.7893i	−0.981858	+	0.566876i	−0.902830	−	0.429997i	$-0.858515\pi$
$509$	−22.1517	+	12.7893i	−0.981858	+	0.566876i	−0.0790271	+	0.996872i	$0.525181\pi$
$510$	0.357263	+	0.283201i	0.0158199	+	0.0125403i
$511$	−45.4368	−	26.2330i	−2.01001	−	1.16048i
$512$	−22.4883	−	2.50566i	−0.993850	−	0.110735i
$513$	22.4970	−	2.62400i	0.993266	−	0.115852i
$514$	−14.4702	+	16.8193i	−0.638252	+	0.741868i
$515$	−0.307438	+	0.532498i	−0.0135473	+	0.0234647i
$516$	−20.1109	+	3.86904i	−0.885332	+	0.170325i
$517$	−0.223297	−	0.386761i	−0.00982058	−	0.0170098i
$518$	−3.04394	−	8.69525i	−0.133743	−	0.382047i
$519$	18.4747	+	9.69836i	0.810951	+	0.425711i
$520$	−0.0360765	−	0.0226476i	−0.00158206	−	0.000993163i
$521$		−	0.00191766i		−	8.40143e-5i	−1.00000		4.20072e-5i	$-0.999987\pi$
$521$		−	0.00191766i		−	8.40143e-5i	1.00000		4.20072e-5i	$-1.33713e-5\pi$
$522$	−13.4277	+	18.4132i	−0.587715	+	0.805926i
$523$	15.9634	−	9.21644i	0.698029	−	0.403007i	−0.108584	−	0.994087i	$-0.534632\pi$
$523$	15.9634	−	9.21644i	0.698029	−	0.403007i	0.806613	+	0.591080i	$0.201298\pi$
$524$	−3.04218	−	20.1460i	−0.132898	−	0.880081i
$525$	26.3722	−	16.6735i	1.15098	−	0.727693i
$526$	−7.36304	+	38.9439i	−0.321044	+	1.69803i
$527$	−9.67170	+	16.7519i	−0.421306	+	0.729723i
$528$	−1.37198	+	7.38601i	−0.0597079	+	0.321435i
$529$	−25.5833	+	44.3116i	−1.11232	+	1.92659i
$530$	0.0742925	−	0.0260075i	0.00322706	−	0.00112970i
$531$	−11.4407	+	24.0998i	−0.496484	+	1.04584i
$532$	19.4971	+	24.6593i	0.845307	+	1.06912i
$533$			0.690566i			0.0299117i
$534$	24.0835	−	30.3817i	1.04219	−	1.31474i
$535$	−0.618077	−	0.356847i	−0.0267218	−	0.0154278i
$536$	0.604714	−	16.3416i	0.0261197	−	0.705850i
$537$	7.68115	−	0.308863i	0.331466	−	0.0133284i
$538$	31.2689	+	5.91195i	1.34810	+	0.254882i
$539$	−6.50901			−0.280363
$540$	0.663942	−	0.184067i	0.0285715	−	0.00792097i
$541$	18.6544	+	32.3104i	0.802017	+	1.38913i	0.918287	+	0.395916i	$0.129573\pi$
$541$	18.6544	+	32.3104i	0.802017	+	1.38913i	−0.116270	+	0.993218i	$0.537094\pi$
$542$	20.7949	+	3.93164i	0.893216	+	0.168878i
$543$	1.77529	+	2.80794i	0.0761849	+	0.120500i
$544$	6.34051	−	14.5599i	0.271847	−	0.624250i
$545$	0.663390	−	0.383008i	0.0284165	−	0.0164063i
$546$	−1.24639	+	1.57234i	−0.0533405	+	0.0672899i
$547$	12.2611	−	7.07894i	0.524246	−	0.302674i	−0.214424	−	0.976741i	$-0.568787\pi$
$547$	12.2611	−	7.07894i	0.524246	−	0.302674i	0.738670	+	0.674067i	$0.235454\pi$
$548$	0.422153	−	1.07650i	0.0180335	−	0.0459857i
$549$	15.9237	+	23.0782i	0.679608	+	0.984953i
$550$	−5.80715	−	4.99607i	−0.247618	−	0.213033i
$551$	20.3288	−	11.6165i	0.866038	−	0.494878i
$552$	−42.1898	+	0.135058i	−1.79572	+	0.00574847i
$553$	−6.94446	+	12.0282i	−0.295308	+	0.511489i
$554$	−13.5217	+	4.73355i	−0.574484	+	0.201109i
$555$	0.183677	+	0.0964217i	0.00779665	+	0.00409287i
$556$	10.0102	−	25.5263i	0.424528	−	1.08256i
$557$	11.1884	−	6.45965i	0.474069	−	0.273704i	−0.243872	−	0.969807i	$-0.578418\pi$
$557$	11.1884	−	6.45965i	0.474069	−	0.273704i	0.717942	+	0.696103i	$0.245084\pi$
$558$	11.8431	+	26.7269i	0.501359	+	1.13144i
$559$			1.34295i			0.0568007i
$560$	0.701347	+	0.650038i	0.0296373	+	0.0274691i
$561$	−4.66825	−	2.45061i	−0.197094	−	0.103465i
$562$	19.6560	−	22.8471i	0.829140	−	0.963746i
$563$	−21.0550			−0.887364			−0.443682	−	0.896184i	$-0.646328\pi$
$563$	−21.0550			−0.887364			−0.443682	+	0.896184i	$0.646328\pi$
$564$	1.34812	+	0.467097i	0.0567662	+	0.0196683i
$565$	−0.0186660	+	0.0323304i	−0.000785283	+	0.00136015i
$566$	−7.77964	−	1.47088i	−0.327003	−	0.0618257i
$567$	−5.19464	−	32.0351i	−0.218154	−	1.34535i
$568$	−15.0827	−	28.5094i	−0.632857	−	1.19623i
$569$			20.4572i			0.857609i	0.903397	+	0.428805i	$0.141065\pi$
$569$			20.4572i			0.857609i	−0.903397	+	0.428805i	$0.858935\pi$
$570$	−0.699796	−	0.106570i	−0.0293112	−	0.00446374i
$571$			30.1475i			1.26163i	0.775932	+	0.630816i	$0.217280\pi$
$571$			30.1475i			1.26163i	−0.775932	+	0.630816i	$0.782720\pi$
$572$	0.458617	+	0.179849i	0.0191758	+	0.00751985i
$573$	36.1005	−	1.45162i	1.50812	−	0.0606423i
$574$	2.88007	−	15.2330i	0.120212	−	0.635814i
$575$	21.5111	−	37.2583i	0.897075	−	1.55378i
$576$	−12.1328	−	20.7074i	−0.505534	−	0.862806i
$577$	8.53496			0.355315			0.177658	−	0.984092i	$-0.443148\pi$
$577$	8.53496			0.355315			0.177658	+	0.984092i	$0.443148\pi$
$578$	−9.77612	−	8.41069i	−0.406633	−	0.349839i
$579$	17.9914	−	34.2724i	0.747697	−	1.42431i
$580$	0.556724	−	0.444223i	0.0231167	−	0.0184453i
$581$			35.6164i			1.47762i
$582$	−3.21690	+	21.7749i	−0.133345	+	0.902599i
$583$	−0.788354	+	0.455157i	−0.0326503	+	0.0188507i
$584$	−19.2446	−	36.3762i	−0.796345	−	1.50526i
$585$	−0.00362755	−	0.0450341i	−0.000149981	−	0.00186193i
$586$	−11.3144	−	32.3206i	−0.467395	−	1.33515i
$587$	−17.1850	+	29.7654i	−0.709303	+	1.22855i	0.255813	+	0.966726i	$0.417657\pi$
$587$	−17.1850	+	29.7654i	−0.709303	+	1.22855i	−0.965116	+	0.261822i	$0.915677\pi$
$588$	15.7201	−	13.6123i	0.648284	−	0.561360i
$589$	0.133753	−	30.0341i	0.00551118	−	1.23753i
$590$	0.543759	−	0.632035i	0.0223862	−	0.0260205i
$591$	1.47840	+	36.7665i	0.0608132	+	1.51237i
$592$	1.60411	−	7.04590i	0.0659284	−	0.289585i
$593$	24.7534	−	14.2914i	1.01650	−	0.586877i	0.103413	−	0.994639i	$-0.467024\pi$
$593$	24.7534	−	14.2914i	1.01650	−	0.586877i	0.913089	+	0.407761i	$0.133690\pi$
$594$	−7.14931	+	3.51814i	−0.293340	+	0.144351i
$595$	−0.581217	+	0.335566i	−0.0238276	+	0.0137569i
$596$	17.3590	−	2.62133i	0.711052	−	0.107374i
$597$	−2.07577	+	1.31238i	−0.0849556	+	0.0537122i
$598$	−0.513970	+	2.71844i	−0.0210178	+	0.111165i
$599$	1.33281	+	2.30849i	0.0544571	+	0.0943224i	0.891969	−	0.452097i	$-0.149324\pi$
$599$	1.33281	+	2.30849i	0.0544571	+	0.0943224i	−0.837512	+	0.546419i	$0.815991\pi$
$600$	24.4732	−	0.0783439i	0.999116	−	0.00319838i
$601$	8.37653			0.341686			0.170843	−	0.985298i	$-0.445351\pi$
$601$	8.37653			0.341686			0.170843	+	0.985298i	$0.445351\pi$
$602$	5.60090	−	29.6238i	0.228276	−	1.20737i
$603$	14.2762	−	9.85044i	0.581372	−	0.401141i
$604$	20.0934	+	25.1821i	0.817588	+	1.02465i
$605$	0.564063	+	0.325662i	0.0229324	+	0.0132400i
$606$	24.8940	−	31.4042i	1.01125	−	1.27571i
$607$			1.64216i			0.0666533i	0.999445	+	0.0333267i	$0.0106102\pi$
$607$			1.64216i			0.0666533i	−0.999445	+	0.0333267i	$0.989390\pi$
$608$	2.66848	+	24.5128i	0.108221	+	0.994127i
$609$	−17.9281	−	28.3565i	−0.726483	−	1.14906i
$610$	−0.289535	−	0.827078i	−0.0117229	−	0.0334874i
$611$	0.0467793	−	0.0810242i	0.00189249	−	0.00327789i
$612$	16.3993	−	3.84416i	0.662904	−	0.155391i
$613$	−15.2963	+	26.4940i	−0.617812	+	1.07008i	0.372072	+	0.928204i	$0.378647\pi$
$613$	−15.2963	+	26.4940i	−0.617812	+	1.07008i	−0.989884	+	0.141878i	$0.954686\pi$
$614$	18.0454	+	3.41181i	0.728254	+	0.137689i
$615$	0.186550	+	0.295063i	0.00752243	+	0.0118981i
$616$	−9.36644	−	5.87994i	−0.377385	−	0.236910i
$617$	−6.15678	+	3.55462i	−0.247863	+	0.143104i	−0.618785	−	0.785560i	$-0.712375\pi$
$617$	−6.15678	+	3.55462i	−0.247863	+	0.143104i	0.370922	+	0.928664i	$0.379042\pi$
$618$	8.36158	+	21.1230i	0.336352	+	0.849692i
$619$		−	4.26335i		−	0.171359i	−0.996323	−	0.0856793i	$-0.972694\pi$
$619$		−	4.26335i		−	0.171359i	0.996323	−	0.0856793i	$-0.0273061\pi$
$620$	−0.136418	−	0.903387i	−0.00547866	−	0.0362809i
$621$	−26.8734	−	35.7816i	−1.07839	−	1.43587i
$622$	−9.35249	+	3.27402i	−0.375001	+	0.131276i
$623$	28.5366	+	49.4268i	1.14329	+	1.98024i
$624$	−1.48373	+	0.524748i	−0.0593969	+	0.0210067i
$625$	−12.4670	+	21.5936i	−0.498682	+	0.863742i
$626$	−17.6254	−	15.1637i	−0.704453	−	0.606063i
$627$	8.18118	−	0.292483i	0.326725	−	0.0116806i
$628$	1.63527	+	10.8291i	0.0652542	+	0.432127i
$629$	4.39209	+	2.53577i	0.175124	+	0.101108i
$630$	−0.107800	+	1.00852i	−0.00429485	+	0.0401806i
$631$	−12.5246	+	7.23110i	−0.498598	+	0.287865i	−0.728134	−	0.685435i	$-0.759612\pi$
$631$	−12.5246	+	7.23110i	−0.498598	+	0.287865i	0.229537	+	0.973300i	$0.426279\pi$
$632$	−9.62959	+	5.09447i	−0.383045	+	0.202647i
$633$	24.4359	+	12.8277i	0.971239	+	0.509855i
$634$	−13.0316	+	15.1472i	−0.517552	+	0.601573i
$635$	0.303559			0.0120464
$636$	0.952107	−	2.74794i	0.0377535	−	0.108963i
$637$	−0.681799	−	1.18091i	−0.0270139	−	0.0467894i
$638$	−5.37198	+	6.24409i	−0.212679	+	0.247206i
$639$	14.6709	−	30.9043i	0.580373	−	1.22255i
$640$	0.194830	+	0.724326i	0.00770131	+	0.0286315i
$641$	11.8782	+	6.85786i	0.469159	+	0.270869i	0.715888	−	0.698215i	$-0.246022\pi$
$641$	11.8782	+	6.85786i	0.469159	+	0.270869i	−0.246728	+	0.969085i	$0.579356\pi$
$642$	−24.5177	+	9.70539i	−0.967637	+	0.383041i
$643$	−15.8960	−	9.17754i	−0.626876	−	0.361927i	0.152665	−	0.988278i	$-0.451214\pi$
$643$	−15.8960	−	9.17754i	−0.626876	−	0.361927i	−0.779541	+	0.626351i	$0.784548\pi$
$644$	22.6751	−	57.8218i	0.893522	−	2.27850i
$645$	0.362785	+	0.573811i	0.0142847	+	0.0225938i
$646$	−16.9897	−	3.29064i	−0.668451	−	0.129468i
$647$	10.7256			0.421667			0.210833	−	0.977522i	$-0.432382\pi$
$647$	10.7256			0.421667			0.210833	+	0.977522i	$0.432382\pi$
$648$	9.90901	−	23.4481i	0.389263	−	0.921127i
$649$	−4.82114	+	8.35046i	−0.189246	+	0.327784i
$650$	0.298141	−	1.57690i	0.0116940	−	0.0618510i
$651$	−43.0003	+	1.72906i	−1.68532	+	0.0677674i
$652$	−3.17842	−	3.98337i	−0.124477	−	0.156001i
$653$			34.5202i			1.35088i	0.737416	+	0.675439i	$0.236046\pi$
$653$			34.5202i			1.35088i	−0.737416	+	0.675439i	$0.763954\pi$
$654$	4.13627	−	27.9981i	0.161741	−	1.09481i
$655$	−0.584901	+	0.337693i	−0.0228540	+	0.0131947i
$656$	8.26609	−	8.91855i	0.322736	−	0.348211i
$657$	18.7191	−	39.4318i	0.730303	−	1.53838i
$658$	−1.36981	+	1.59219i	−0.0534009	+	0.0620702i
$659$	−1.94679	−	3.37194i	−0.0758361	−	0.131352i	0.825613	−	0.564236i	$-0.190829\pi$
$659$	−1.94679	−	3.37194i	−0.0758361	−	0.131352i	−0.901450	+	0.432884i	$0.857496\pi$
$660$	0.244541	−	0.0470462i	0.00951875	−	0.00183127i
$661$	−1.71778	−	2.97528i	−0.0668139	−	0.115725i	0.830683	−	0.556745i	$-0.187950\pi$
$661$	−1.71778	−	2.97528i	−0.0668139	−	0.115725i	−0.897497	+	0.441020i	$0.854617\pi$
$662$	−12.1748	−	34.7783i	−0.473188	−	1.35170i
$663$	−0.0443779	−	1.10364i	−0.00172350	−	0.0428619i
$664$	−14.8535	+	23.6608i	−0.576427	+	0.918218i
$665$	0.525045	−	0.900124i	0.0203604	−	0.0349053i
$666$	7.00739	−	3.10509i	0.271531	−	0.120320i
$667$	−40.0617	−	23.1296i	−1.55120	−	0.895583i
$668$	24.3008	+	9.52966i	0.940227	+	0.368714i
$669$	−1.73739	−	0.912045i	−0.0671712	−	0.0352617i
$670$	−0.511631	+	0.179106i	−0.0197660	+	0.00691949i
$671$	5.06713	+	8.77653i	0.195614	+	0.338814i
$672$	34.9178	−	5.38721i	1.34698	−	0.207816i
$673$	−10.8539			−0.418388			−0.209194	−	0.977874i	$-0.567084\pi$
$673$	−10.8539			−0.418388			−0.209194	+	0.977874i	$0.567084\pi$
$674$	−2.44875	+	12.9517i	−0.0943223	+	0.498880i
$675$	15.5885	+	20.7560i	0.600003	+	0.798898i
$676$	−3.86676	−	25.6065i	−0.148721	−	0.984865i
$677$		−	6.67800i		−	0.256657i	−0.991732	−	0.128328i	$-0.959039\pi$
$677$		−	6.67800i		−	0.256657i	0.991732	−	0.128328i	$-0.0409611\pi$
$678$	0.507670	+	1.28247i	0.0194969	+	0.0492531i
$679$	−28.0620	−	16.2016i	−1.07692	−	0.621761i
$680$	−0.526061	−	0.0194666i	−0.0201735	−	0.000746511i
$681$	−17.2182	+	0.692354i	−0.659804	+	0.0265311i
$682$	3.49112	+	9.97264i	0.133682	+	0.381872i
$683$	−12.2326			−0.468068			−0.234034	−	0.972228i	$-0.575193\pi$
$683$	−12.2326			−0.468068			−0.234034	+	0.972228i	$0.575193\pi$
$684$	−19.1469	+	17.8156i	−0.732099	+	0.681198i
$685$	−0.0383304			−0.00146453
$686$	−1.68010	−	4.79934i	−0.0641467	−	0.183240i
$687$	21.3549	−	0.858689i	0.814738	−	0.0327610i
$688$	16.0751	−	17.3440i	0.612858	−	0.661232i
$689$	−0.165156	−	0.0953526i	−0.00629192	−	0.00363264i
$690$	0.514755	+	1.30037i	0.0195964	+	0.0495043i
$691$		−	9.10551i		−	0.346390i	−0.984888	−	0.173195i	$-0.944591\pi$
$691$		−	9.10551i		−	0.346390i	0.984888	−	0.173195i	$-0.0554091\pi$
$692$	−23.8234	+	3.59750i	−0.905631	+	0.136757i
$693$	−0.941812	−	11.6921i	−0.0357765	−	0.444146i
$694$	6.15145	−	32.5357i	0.233506	−	1.23504i
$695$	−0.908903			−0.0344766
$696$	−0.0842386	−	26.3147i	−0.00319306	−	0.997454i
$697$	4.26716	+	7.39094i	0.161630	+	0.279952i
$698$	25.7778	−	9.02401i	0.975704	−	0.341564i
$699$	−44.1504	−	23.1769i	−1.66992	−	0.876630i
$700$	−13.1532	+	33.5409i	−0.497145	+	1.26773i
$701$	2.44982	+	1.41441i	0.0925286	+	0.0534214i	0.545550	−	0.838078i	$-0.316321\pi$
$701$	2.44982	+	1.41441i	0.0925286	+	0.0534214i	−0.453022	+	0.891499i	$0.649654\pi$
$702$	−1.38715	−	0.928565i	−0.0523548	−	0.0350464i
$703$	−7.87449	−	0.0350679i	−0.296992	−	0.00132261i
$704$	−3.77018	−	7.81237i	−0.142094	−	0.294440i
$705$	−0.00190022	−	0.0472568i	−7.15664e−5	−	0.00177979i
$706$	−0.376012	−	1.07411i	−0.0141514	−	0.0404246i
$707$	29.4970	+	51.0903i	1.10935	+	1.92145i
$708$	−5.81963	−	30.2498i	−0.218715	−	1.13686i
$709$	6.24505	+	10.8167i	0.234538	+	0.406232i	0.959138	−	0.282938i	$-0.0913090\pi$
$709$	6.24505	+	10.8167i	0.234538	+	0.406232i	−0.724600	+	0.689169i	$0.757976\pi$
$710$	−0.697287	+	0.810487i	−0.0261687	+	0.0304170i
$711$	−10.4385	−	4.95538i	−0.391474	−	0.185841i
$712$	−1.65545	+	44.7363i	−0.0620405	+	1.67656i
$713$	−51.3898	+	29.6699i	−1.92456	+	1.11115i
$714$	−3.62392	+	24.5300i	−0.135622	+	0.918013i
$715$		−	0.0163298i		−	0.000610699i
$716$	−6.93848	+	5.53637i	−0.259303	+	0.206904i
$717$	32.4137	−	1.30337i	1.21051	−	0.0486753i
$718$	−1.12572	+	5.95404i	−0.0420114	+	0.222203i
$719$	−9.48282	+	16.4247i	−0.353649	+	0.612539i	−0.986886	−	0.161420i	$-0.948393\pi$
$719$	−9.48282	+	16.4247i	−0.353649	+	0.612539i	0.633236	+	0.773958i	$0.281726\pi$
$720$	−0.492209	+	0.625030i	−0.0183436	+	0.0232935i
$721$	−33.4434			−1.24550
$722$	25.4390	−	8.65187i	0.946743	−	0.321989i
$723$	0.316608	+	0.500772i	0.0117748	+	0.0186239i
$724$	−3.57122	−	1.40047i	−0.132723	−	0.0520479i
$725$	23.2388	+	13.4169i	0.863066	+	0.498291i
$726$	22.3751	−	8.85724i	0.830418	−	0.328723i
$727$	18.1204	+	10.4618i	0.672049	+	0.388007i	0.796852	−	0.604174i	$-0.206497\pi$
$727$	18.1204	+	10.4618i	0.672049	+	0.388007i	−0.124804	+	0.992181i	$0.539830\pi$
$728$	0.0856741	−	2.31523i	0.00317529	−	0.0858082i
$729$	26.2188	−	6.44768i	0.971068	−	0.238803i
$730$	−0.889692	+	1.03413i	−0.0329290	+	0.0382748i
$731$	8.29838	+	14.3732i	0.306927	+	0.531612i
$732$	−30.5921	−	10.5995i	−1.13071	−	0.391770i
$733$	39.5695			1.46153			0.730766	−	0.682628i	$-0.239163\pi$
$733$	39.5695			1.46153			0.730766	+	0.682628i	$0.239163\pi$
$734$	−21.2364	+	24.6840i	−0.783850	+	0.911104i
$735$	−0.610329	−	0.320394i	−0.0225123	−	0.0118179i
$736$	39.1776	−	28.9560i	1.44411	−	1.06733i
$737$	5.42917	−	3.13453i	0.199986	−	0.115462i
$738$	12.8247	+	1.37082i	0.472084	+	0.0504605i
$739$	−30.9794	−	17.8859i	−1.13959	−	0.657945i	−0.193264	−	0.981147i	$-0.561907\pi$
$739$	−30.9794	−	17.8859i	−1.13959	−	0.657945i	−0.946330	+	0.323202i	$0.895241\pi$
$740$	−0.236854	+	0.0357666i	−0.00870693	+	0.00131481i
$741$	0.910018	+	1.45365i	0.0334303	+	0.0534012i
$742$	3.24545	+	2.79216i	0.119144	+	0.102503i
$743$	−4.68614	+	8.11663i	−0.171918	+	0.297770i	−0.939090	−	0.343670i	$-0.888330\pi$
$743$	−4.68614	+	8.11663i	−0.171918	+	0.297770i	0.767173	+	0.641441i	$0.221663\pi$
$744$	−29.2872	−	16.7842i	−1.07372	−	0.615339i
$745$	−0.290977	−	0.503986i	−0.0106606	−	0.0184646i
$746$	−43.5705	+	15.2527i	−1.59523	+	0.558441i
$747$	−29.5357	+	2.37914i	−1.08066	+	0.0870481i
$748$	6.01978	−	0.909027i	0.220105	−	0.0332373i
$749$		−	38.8181i		−	1.41838i
$750$	−0.597455	−	1.50929i	−0.0218160	−	0.0551114i
$751$	8.07650	−	4.66297i	0.294716	−	0.170154i	−0.345351	−	0.938474i	$-0.612240\pi$
$751$	8.07650	−	4.66297i	0.294716	−	0.170154i	0.640067	+	0.768319i	$0.278907\pi$
$752$	−1.57401	+	0.486465i	−0.0573982	+	0.0177396i
$753$	19.4390	+	30.7463i	0.708396	+	1.12046i
$754$	−1.69555	−	0.320573i	−0.0617482	−	0.0116746i
$755$	0.533964	−	0.924852i	0.0194329	−	0.0336588i
$756$	26.7262	+	26.2682i	0.972023	+	0.955367i
$757$	6.55774	−	11.3583i	0.238345	−	0.412826i	−0.721895	−	0.692003i	$-0.756728\pi$
$757$	6.55774	−	11.3583i	0.238345	−	0.412826i	0.960240	+	0.279177i	$0.0900618\pi$
$758$	−4.44023	−	12.6839i	−0.161276	−	0.460698i
$759$	−8.64331	−	13.6710i	−0.313732	−	0.496225i
$760$	0.724188	−	0.379008i	0.0262691	−	0.0137481i
$761$			9.12600i			0.330817i	0.986225	+	0.165409i	$0.0528943\pi$
$761$			9.12600i			0.330817i	−0.986225	+	0.165409i	$0.947106\pi$
$762$	6.96710	−	8.78911i	0.252392	−	0.318396i
$763$	36.0820	+	20.8320i	1.30626	+	0.754168i
$764$	−32.6100	+	26.0203i	−1.17979	+	0.941382i
$765$	−0.317100	−	0.459572i	−0.0114648	−	0.0166159i
$766$	9.58883	−	50.7164i	0.346459	−	1.83246i
$767$	−2.02000			−0.0729380
$768$	25.4434	+	10.9833i	0.918110	+	0.396325i
$769$	13.0400	+	22.5859i	0.470233	+	0.814467i	0.999421	−	0.0340376i	$-0.0108366\pi$
$769$	13.0400	+	22.5859i	0.470233	+	0.814467i	−0.529188	+	0.848505i	$0.677503\pi$
$770$	−0.0681050	+	0.360214i	−0.00245433	+	0.0129812i
$771$	22.9683	−	14.5214i	0.827181	−	0.522976i
$772$	6.67372	+	44.1948i	0.240192	+	1.59061i
$773$	2.68879	−	1.55237i	0.0967090	−	0.0558350i	−0.450866	−	0.892592i	$-0.648885\pi$
$773$	2.68879	−	1.55237i	0.0967090	−	0.0558350i	0.547575	+	0.836757i	$0.315551\pi$
$774$	24.9403	+	2.66584i	0.896461	+	0.0958215i
$775$	29.8099	−	17.2108i	1.07080	−	0.618229i
$776$	−11.8855	−	22.4661i	−0.426666	−	0.806487i
$777$	0.453334	+	11.2740i	0.0162633	+	0.404454i
$778$	4.91992	−	5.71864i	0.176388	−	0.205023i
$779$	−11.4462	−	6.67664i	−0.410104	−	0.239215i
$780$	0.0341504	+	0.0394384i	0.00122278	+	0.00141212i
$781$	6.18237	−	10.7082i	0.221223	−	0.383169i
$782$	11.2970	+	32.2706i	0.403979	+	1.15400i
$783$	22.3177	−	16.7615i	0.797570	−	0.599006i
$784$	−5.33019	+	23.4124i	−0.190364	+	0.836158i
$785$	0.314402	−	0.181520i	0.0112215	−	0.00647873i
$786$	−3.64689	+	24.6855i	−0.130080	+	0.880502i
$787$		−	9.79232i		−	0.349058i	−0.984652	−	0.174529i	$-0.944160\pi$
$787$		−	9.79232i		−	0.349058i	0.984652	−	0.174529i	$-0.0558404\pi$
$788$	−26.5003	−	33.2116i	−0.944035	−	1.18311i
$789$	22.5621	−	42.9793i	0.803231	−	1.53010i
$790$	0.273757	+	0.235522i	0.00973984	+	0.00837948i
$791$	−2.03050			−0.0721962
$792$	4.25040	−	8.16011i	0.151032	−	0.289957i
$793$	−1.06153	+	1.83863i	−0.0376961	+	0.0652916i
$794$	2.51583	−	13.3065i	0.0892834	−	0.472229i
$795$	−0.0963258	+	0.00387331i	−0.00341632	+	0.000137372i
$796$	1.03530	−	2.64002i	0.0366951	−	0.0935731i
$797$			5.59036i			0.198021i	0.995086	+	0.0990104i	$0.0315677\pi$
$797$			5.59036i			0.198021i	−0.995086	+	0.0990104i	$0.968432\pi$
$798$	−14.0113	−	35.8610i	−0.495993	−	1.26947i
$799$		−	1.15624i		−	0.0409048i
$800$	−22.7259	+	16.7966i	−0.803483	+	0.593850i
$801$	−39.0821	+	26.9663i	−1.38090	+	0.952806i
$802$	−38.3446	−	7.24973i	−1.35399	−	0.255997i
$803$	7.88830	−	13.6629i	0.278372	−	0.482154i
$804$	−6.55688	+	18.9243i	−0.231244	+	0.667408i
$805$	−2.05883			−0.0725644
$806$	−1.44362	+	1.67799i	−0.0508495	+	0.0591046i
$807$	−34.5090	−	18.1156i	−1.21477	−	0.637699i
$808$	−1.71116	+	46.2419i	−0.0601984	+	1.62678i
$809$			8.57218i			0.301382i	0.988581	+	0.150691i	$0.0481498\pi$
$809$			8.57218i			0.301382i	−0.988581	+	0.150691i	$0.951850\pi$
$810$	−0.843542	−	0.0220272i	−0.0296391	−	0.000773955i
$811$	7.74988	−	4.47439i	0.272135	−	0.157117i	−0.357722	−	0.933828i	$-0.616447\pi$
$811$	7.74988	−	4.47439i	0.272135	−	0.157117i	0.629857	+	0.776711i	$0.283113\pi$
$812$	36.0646	+	14.1429i	1.26562	+	0.496318i
$813$	−22.9496	−	12.0475i	−0.804878	−	0.422523i
$814$	2.61468	−	0.915318i	0.0916443	−	0.0320819i
$815$	−0.0844636	+	0.146295i	−0.00295863	+	0.00512450i
$816$	−12.6375	+	14.7845i	−0.442400	+	0.517563i
$817$	−22.2596	−	12.9841i	−0.778765	−	0.454256i
$818$	0.531376	+	0.457159i	0.0185791	+	0.0159842i
$819$	2.02261	−	1.39558i	0.0706757	−	0.0487656i
$820$	−0.375269	−	0.147163i	−0.0131050	−	0.00513917i
$821$	22.5728	−	13.0324i	0.787794	−	0.454833i	−0.0513910	−	0.998679i	$-0.516365\pi$
$821$	22.5728	−	13.0324i	0.787794	−	0.454833i	0.839186	+	0.543845i	$0.183032\pi$
$822$	−0.879735	+	1.10980i	−0.0306843	+	0.0387087i
$823$	−15.5961	+	9.00439i	−0.543645	+	0.313873i	−0.746555	−	0.665324i	$-0.768293\pi$
$823$	−15.5961	+	9.00439i	−0.543645	+	0.313873i	0.202910	+	0.979197i	$0.434960\pi$
$824$	−22.2172	−	13.9472i	−0.773973	−	0.485875i
$825$	5.01376	+	7.93018i	0.174557	+	0.276093i
$826$	44.5587	+	8.42461i	1.55039	+	0.293130i
$827$	−13.4740	−	23.3377i	−0.468538	−	0.811531i	0.530816	−	0.847487i	$-0.321886\pi$
$827$	−13.4740	−	23.3377i	−0.468538	−	0.811531i	−0.999353	+	0.0359561i	$0.988552\pi$
$828$	49.4647	+	14.9414i	1.71902	+	0.519248i
$829$	23.0503			0.800569			0.400284	−	0.916391i	$-0.368911\pi$
$829$	23.0503			0.800569			0.400284	+	0.916391i	$0.368911\pi$
$830$	0.909947	+	0.172042i	0.0315847	+	0.00597166i
$831$	17.5319	−	0.704968i	0.608176	−	0.0244551i
$832$	1.02246	−	1.50233i	0.0354475	−	0.0520841i
$833$	−14.5942	−	8.42597i	−0.505660	−	0.291943i
$834$	−20.8606	+	26.3160i	−0.722343	+	0.911247i
$835$		−	0.865268i		−	0.0299438i
$836$	−7.41509	+	5.86282i	−0.256456	+	0.202770i
$837$	−4.30624	−	35.5435i	−0.148845	−	1.22856i
$838$	−35.2578	+	12.3427i	−1.21796	+	0.426370i
$839$	−16.8082	+	29.1127i	−0.580284	+	1.00508i	0.415162	+	0.909748i	$0.363725\pi$
$839$	−16.8082	+	29.1127i	−0.580284	+	1.00508i	−0.995445	+	0.0953334i	$0.969608\pi$
$840$	−0.588833	−	1.01239i	−0.0203167	−	0.0349308i
$841$	−0.0735821	+	0.127448i	−0.00253731	+	0.00439476i
$842$	7.12039	−	37.6605i	0.245385	−	1.29787i
$843$	−31.1997	+	19.7257i	−1.07458	+	0.679388i
$844$	−31.5104	+	4.75829i	−1.08463	+	0.163787i
$845$	−0.743437	+	0.429224i	−0.0255750	+	0.0147657i
$846$	−1.41186	−	1.02959i	−0.0485409	−	0.0353981i
$847$			35.4258i			1.21724i
$848$	0.991585	+	3.20838i	0.0340512	+	0.110176i
$849$	8.58577	+	4.50712i	0.294663	+	0.154684i
$850$	−6.55308	−	18.7194i	−0.224769	−	0.642069i
$851$	7.77901	+	13.4736i	0.266661	+	0.461870i
$852$	7.46278	+	38.7907i	0.255671	+	1.32895i
$853$	−4.35531	+	7.54363i	−0.149123	+	0.258289i	−0.930904	−	0.365265i	$-0.880978\pi$
$853$	−4.35531	+	7.54363i	−0.149123	+	0.258289i	0.781780	+	0.623554i	$0.214312\pi$
$854$	31.0843	−	36.1306i	1.06368	−	1.23636i
$855$	0.781520	+	0.375278i	0.0267274	+	0.0128342i
$856$	16.1887	−	25.7878i	0.553319	−	0.881408i
$857$	13.2683	+	7.66045i	0.453236	+	0.261676i	0.709196	−	0.705011i	$-0.249058\pi$
$857$	13.2683	+	7.66045i	0.453236	+	0.261676i	−0.255960	+	0.966687i	$0.582391\pi$
$858$	−0.472805	−	0.374791i	−0.0161413	−	0.0127952i
$859$	13.0828	−	7.55337i	0.446380	−	0.257718i	−0.259920	−	0.965630i	$-0.583696\pi$
$859$	13.0828	−	7.55337i	0.446380	−	0.257718i	0.706300	+	0.707913i	$0.250363\pi$
$860$	−0.729789	−	0.286190i	−0.0248856	−	0.00975899i
$861$	−8.82522	+	16.8115i	−0.300763	+	0.572933i
$862$	0.356452	+	0.306667i	0.0121408	+	0.0104451i
$863$	16.8019			0.571945			0.285973	−	0.958238i	$-0.407683\pi$
$863$	16.8019			0.571945			0.285973	+	0.958238i	$0.407683\pi$
$864$	6.79994	+	28.5965i	0.231339	+	0.972873i
$865$	0.399336	+	0.691669i	0.0135778	+	0.0235175i
$866$	−20.4539	−	17.5971i	−0.695051	−	0.597974i
$867$	8.44048	+	13.3502i	0.286654	+	0.453395i
$868$	38.8427	−	30.9935i	1.31841	−	1.05199i
$869$	−3.61689	−	2.08821i	−0.122694	−	0.0708377i
$870$	−0.811068	+	0.321063i	−0.0274978	+	0.0108851i
$871$	1.13738	+	0.656666i	0.0385386	+	0.0222503i
$872$	15.2824	+	28.8868i	0.517526	+	0.978231i
$873$	11.5610	−	24.3533i	0.391282	−	0.824235i
$874$	−40.0894	−	34.8020i	−1.35604	−	1.17719i
$875$	2.38961			0.0807834
$876$	9.52201	+	49.4944i	0.321719	+	1.67226i
$877$	12.0992	−	20.9565i	0.408562	−	0.707650i	−0.586167	−	0.810190i	$-0.699364\pi$
$877$	12.0992	−	20.9565i	0.408562	−	0.707650i	0.994729	+	0.102540i	$0.0326971\pi$
$878$	21.8785	+	4.13653i	0.738365	+	0.139601i
$879$	1.68506	+	41.9060i	0.0568357	+	1.41345i
$880$	−0.195468	+	0.210896i	−0.00658921	+	0.00710932i
$881$			51.7294i			1.74281i	0.490565	+	0.871405i	$0.336790\pi$
$881$			51.7294i			1.74281i	−0.490565	+	0.871405i	$0.663210\pi$
$882$	−23.2845	+	10.3177i	−0.784028	+	0.347415i
$883$	−21.8823	+	12.6337i	−0.736397	+	0.425159i	−0.820758	−	0.571276i	$-0.806448\pi$
$883$	−21.8823	+	12.6337i	−0.736397	+	0.425159i	0.0843609	+	0.996435i	$0.473115\pi$
$884$	0.795476	+	0.996933i	0.0267547	+	0.0335305i
$885$	−0.863099	+	0.545685i	−0.0290128	+	0.0183430i
$886$	18.5356	+	15.9468i	0.622717	+	0.535742i
$887$	−14.7061	−	25.4718i	−0.493784	−	0.855258i	0.506191	−	0.862422i	$-0.331053\pi$
$887$	−14.7061	−	25.4718i	−0.493784	−	0.855258i	−0.999974	+	0.00716328i	$0.997720\pi$
$888$	−4.40056	+	7.67866i	−0.147673	+	0.257679i
$889$	8.25535	+	14.2987i	0.276876	+	0.479562i
$890$	1.40063	−	0.490316i	0.0469491	−	0.0164354i
$891$	9.63301	−	1.56204i	0.322718	−	0.0523302i
$892$	2.24039	−	0.338314i	0.0750136	−	0.0113276i
$893$	0.890710	+	1.55875i	0.0298065	+	0.0521614i
$894$	−21.2705	−	3.14238i	−0.711392	−	0.105097i
$895$	0.254826	+	0.147124i	0.00851791	+	0.00491782i
$896$	−28.8198	+	28.8753i	−0.962803	+	0.964657i
$897$	1.57492	−	3.00012i	0.0525851	−	0.100171i
$898$	6.76527	+	19.3255i	0.225760	+	0.644901i
$899$	−18.5057	−	32.0529i	−0.617201	−	1.06902i
$900$	−28.6932	−	8.66710i	−0.956440	−	0.288903i
$901$	−2.35682			−0.0785170
$902$	4.58060	+	0.866044i	0.152517	+	0.0288361i
$903$	−17.1625	+	32.6934i	−0.571131	+	1.08797i
$904$	−1.34891	−	0.846800i	−0.0448640	−	0.0281641i
$905$			0.127159i			0.00422690i
$906$	−14.5225	−	36.6868i	−0.482479	−	1.21884i
$907$	19.1736	+	11.0699i	0.636649	+	0.367570i	0.783323	−	0.621615i	$-0.213523\pi$
$907$	19.1736	+	11.0699i	0.636649	+	0.367570i	−0.146673	+	0.989185i	$0.546857\pi$
$908$	15.5535	−	12.4105i	0.516159	−	0.411856i
$909$	−40.3974	+	27.8738i	−1.33990	+	0.924516i
$910$	−0.0724864	+	0.0253753i	−0.00240290	+	0.000841182i
$911$	8.98945			0.297834			0.148917	−	0.988850i	$-0.452421\pi$
$911$	8.98945			0.297834			0.148917	+	0.988850i	$0.452421\pi$
$912$	5.64748	−	29.6666i	0.187007	−	0.982359i
$913$	−10.7099			−0.354447
$914$	45.0683	−	15.7770i	1.49073	−	0.521858i
$915$	0.0431204	+	1.07237i	0.00142552	+	0.0354514i
$916$	−19.2901	+	15.3920i	−0.637363	+	0.508567i
$917$	−31.8130	−	18.3672i	−1.05056	−	0.606540i
$918$	−20.5841	−	1.36664i	−0.679378	−	0.0451058i
$919$			0.380683i			0.0125576i	0.999980	+	0.00627879i	$0.00199862\pi$
$919$			0.380683i			0.0125576i	−0.999980	+	0.00627879i	$0.998001\pi$
$920$	−1.36773	−	0.858617i	−0.0450928	−	0.0283078i
$921$	−19.9153	−	10.4546i	−0.656231	−	0.344490i
$922$	2.11439	+	0.399764i	0.0696339	+	0.0131655i
$923$	2.59034			0.0852620
$924$	8.86638	+	10.2393i	0.291682	+	0.336848i
$925$	−4.51240	−	7.81571i	−0.148367	−	0.256979i
$926$	−8.51094	−	24.3122i	−0.279687	−	0.798947i
$927$	−2.23398	−	27.7336i	−0.0733735	−	0.910892i
$928$	18.0604	+	24.4359i	0.592863	+	0.802147i
$929$	−46.4956	−	26.8443i	−1.52547	−	0.880732i	−0.999544	−	0.0302029i	$-0.990385\pi$
$929$	−46.4956	−	26.8443i	−1.52547	−	0.880732i	−0.525928	−	0.850529i	$-0.676282\pi$
$930$	−0.163534	+	1.10695i	−0.00536249	+	0.0362982i
$931$	26.1657	+	0.116525i	0.857545	+	0.00381895i
$932$	56.9326	−	8.59722i	1.86489	−	0.281611i
$933$	12.1262	−	0.487601i	0.396994	−	0.0159633i
$934$	39.2855	−	13.7526i	1.28546	−	0.450000i
$935$	−0.100905	−	0.174773i	−0.00329995	−	0.00571569i
$936$	1.92568	−	0.0836079i	0.0629429	−	0.00273281i
$937$	−17.4603	−	30.2422i	−0.570404	−	0.987969i	−0.996524	−	0.0833024i	$-0.973453\pi$
$937$	−17.4603	−	30.2422i	−0.570404	−	0.987969i	0.426120	−	0.904667i	$-0.359880\pi$
$938$	−22.3505	−	19.2288i	−0.729768	−	0.627842i
$939$	15.2174	+	24.0691i	0.496601	+	0.785464i
$940$	0.0340615	+	0.0426877i	0.00111096	+	0.00139232i
$941$	27.2658	−	15.7419i	0.888839	−	0.513171i	0.0152764	−	0.999883i	$-0.495137\pi$
$941$	27.2658	−	15.7419i	0.888839	−	0.513171i	0.873563	+	0.486712i	$0.161804\pi$
$942$	1.96032	−	13.2692i	0.0638705	−	0.432334i
$943$			26.1808i			0.852563i
$944$	26.0880	+	24.1794i	0.849091	+	0.786973i
$945$	0.487211	−	1.14269i	0.0158490	−	0.0371717i
$946$	8.90792	+	1.68420i	0.289621	+	0.0547581i
$947$	−10.1473	+	17.5756i	−0.329743	+	0.571131i	−0.982461	−	0.186470i	$-0.940295\pi$
$947$	−10.1473	+	17.5756i	−0.329743	+	0.571131i	0.652718	+	0.757601i	$0.273629\pi$
$948$	13.1023	−	2.52069i	0.425543	−	0.0818683i
$949$	3.30510			0.107288
$950$	23.2548	+	20.1877i	0.754486	+	0.654976i
$951$	20.6849	−	13.0778i	0.670753	−	0.424076i
$952$	−13.3894	−	25.3087i	−0.433953	−	0.820259i
$953$	−38.6657	−	22.3237i	−1.25251	−	0.723135i	−0.280900	−	0.959737i	$-0.590633\pi$
$953$	−38.6657	−	22.3237i	−1.25251	−	0.723135i	−0.971607	+	0.236602i	$0.923966\pi$
$954$	−2.09866	+	2.87787i	−0.0679468	+	0.0931745i
$955$	1.19765	+	0.691466i	0.0387552	+	0.0223753i
$956$	−29.2797	+	23.3630i	−0.946974	+	0.755613i
$957$	8.52686	−	5.39101i	0.275634	−	0.174267i
$958$	8.72473	+	7.50615i	0.281883	+	0.242513i
$959$	−1.04240	−	1.80549i	−0.0336609	−	0.0583024i
$960$	0.0310319	−	0.918121i	0.00100155	−	0.0296322i
$961$	−16.4771			−0.531520
$962$	0.439943	+	0.378496i	0.0141843	+	0.0122032i
$963$	32.1908	−	2.59301i	1.03733	−	0.0835585i
$964$	−0.636896	−	0.249761i	−0.0205131	−	0.00804427i
$965$	1.28311	−	0.740806i	0.0413049	−	0.0238474i
$966$	−47.2531	+	59.6106i	−1.52034	+	1.91794i
$967$	42.3551	+	24.4537i	1.36205	+	0.786379i	0.989896	−	0.141793i	$-0.0452868\pi$
$967$	42.3551	+	24.4537i	1.36205	+	0.786379i	0.372152	+	0.928172i	$0.378620\pi$
$968$	−14.7740	+	23.5342i	−0.474854	+	0.756418i
$969$	18.7221	+	9.93481i	0.601440	+	0.319152i
$970$	−0.549479	+	0.638684i	−0.0176427	+	0.0205069i
$971$	28.7069	−	49.7218i	0.921249	−	1.59565i	0.123764	−	0.992312i	$-0.460504\pi$
$971$	28.7069	−	49.7218i	0.921249	−	1.59565i	0.797485	−	0.603338i	$-0.206163\pi$
$972$	−19.9982	+	23.9180i	−0.641444	+	0.767170i
$973$	−24.7178	−	42.8125i	−0.792416	−	1.37250i
$974$	12.8903	+	36.8222i	0.413033	+	1.17986i
$975$	−0.913572	+	1.74029i	−0.0292577	+	0.0557340i
$976$	35.7179	−	11.0390i	1.14330	−	0.353351i
$977$		−	31.8377i		−	1.01858i	−0.860595	−	0.509289i	$-0.829908\pi$
$977$		−	31.8377i		−	1.01858i	0.860595	−	0.509289i	$-0.170092\pi$
$978$	2.29721	+	5.80320i	0.0734567	+	0.185566i
$979$	−14.8627	+	8.58100i	−0.475015	+	0.274250i
$980$	0.787029	−	0.118847i	0.0251407	−	0.00379642i
$981$	−14.8651	+	31.3134i	−0.474607	+	0.999759i
$982$	0.989379	−	5.23293i	0.0315724	−	0.166990i
$983$	22.2451	−	38.5296i	0.709508	−	1.22890i	−0.255532	−	0.966801i	$-0.582251\pi$
$983$	22.2451	−	38.5296i	0.709508	−	1.22890i	0.965040	−	0.262103i	$-0.0844160\pi$
$984$	−12.8739	+	7.48778i	−0.410404	+	0.238702i
$985$	−0.704222	+	1.21975i	−0.0224384	+	0.0388644i
$986$	−20.1279	+	7.04615i	−0.641001	+	0.224395i
$987$	2.17428	−	1.37466i	0.0692082	−	0.0437561i
$988$	−1.84038	−	0.731186i	−0.0585504	−	0.0232621i
$989$			50.9139i			1.61897i
$990$	−0.303265	−	0.0324156i	−0.00963840	−	0.00103024i
$991$	−5.66131	−	3.26856i	−0.179837	−	0.103829i	0.407379	−	0.913259i	$-0.366443\pi$
$991$	−5.66131	−	3.26856i	−0.179837	−	0.103829i	−0.587216	+	0.809430i	$0.699776\pi$
$992$	38.7297	−	4.39074i	1.22967	−	0.139406i
$993$	1.81320	+	45.0927i	0.0575402	+	1.43097i
$994$	−57.1396	−	10.8033i	−1.81236	−	0.342659i
$995$	−0.0940021			−0.00298007
$996$	25.8658	−	22.3976i	0.819589	−	0.709695i
$997$	−9.26164	−	16.0416i	−0.293319	−	0.508044i	0.681273	−	0.732029i	$-0.261427\pi$
$997$	−9.26164	−	16.0416i	−0.293319	−	0.508044i	−0.974592	+	0.223985i	$0.928093\pi$
$998$	23.4461	+	4.43290i	0.742172	+	0.140321i
$999$	−9.31896	+	1.12903i	−0.294839	+	0.0357209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.m.a.11.32	yes	72
3.2	odd	2	inner	228.2.m.a.11.5	✓	72
4.3	odd	2	inner	228.2.m.a.11.20	yes	72
12.11	even	2	inner	228.2.m.a.11.17	yes	72
19.7	even	3	inner	228.2.m.a.83.17	yes	72
57.26	odd	6	inner	228.2.m.a.83.20	yes	72
76.7	odd	6	inner	228.2.m.a.83.5	yes	72
228.83	even	6	inner	228.2.m.a.83.32	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.5	✓	72	3.2	odd	2	inner
228.2.m.a.11.17	yes	72	12.11	even	2	inner
228.2.m.a.11.20	yes	72	4.3	odd	2	inner
228.2.m.a.11.32	yes	72	1.1	even	1	trivial
228.2.m.a.83.5	yes	72	76.7	odd	6	inner
228.2.m.a.83.17	yes	72	19.7	even	3	inner
228.2.m.a.83.20	yes	72	57.26	odd	6	inner
228.2.m.a.83.32	yes	72	228.83	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33479 - 0.467269i) q^{2} +(-1.73065 + 0.0695904i) q^{3} +(1.56332 - 1.24741i) q^{4} +(-0.0574154 - 0.0331488i) q^{5} +(-2.27754 + 0.901568i) q^{6} -3.60595i q^{7} +(1.50383 - 2.39552i) q^{8} +(2.99031 - 0.240874i) q^{9} +(-0.0921267 - 0.0174182i) q^{10} +1.08432 q^{11} +(-2.61876 + 2.26762i) q^{12} +(0.113579 + 0.196724i) q^{13} +(-1.68495 - 4.81318i) q^{14} +(0.101673 + 0.0533734i) q^{15} +(0.887940 - 3.90020i) q^{16} +(2.43120 + 1.40366i) q^{17} +(3.87888 - 1.71880i) q^{18} +(-4.35886 - 0.0194115i) q^{19} +(-0.131109 + 0.0197983i) q^{20} +(0.250939 + 6.24065i) q^{21} +(1.44733 - 0.506666i) q^{22} +(4.30600 + 7.45822i) q^{23} +(-2.43590 + 4.25046i) q^{24} +(-2.49780 - 4.32632i) q^{25} +(0.243527 + 0.209513i) q^{26} +(-5.15843 + 0.624965i) q^{27} +(-4.49810 - 5.63725i) q^{28} +(-4.65184 + 2.68574i) q^{29} +(0.160651 + 0.0237337i) q^{30} +6.89036i q^{31} +(-0.637229 - 5.62085i) q^{32} +(-1.87657 + 0.0754579i) q^{33} +(3.90103 + 0.737559i) q^{34} +(-0.119533 + 0.207037i) q^{35} +(4.37435 - 4.10671i) q^{36} +1.80655 q^{37} +(-5.82722 + 2.01085i) q^{38} +(-0.210255 - 0.332557i) q^{39} +(-0.165751 + 0.0876895i) q^{40} +(2.63274 + 1.52002i) q^{41} +(3.25101 + 8.21268i) q^{42} +(5.11992 + 2.95599i) q^{43} +(1.69513 - 1.35259i) q^{44} +(-0.179675 - 0.0852954i) q^{45} +(9.23260 + 7.94308i) q^{46} +(-0.205933 - 0.356687i) q^{47} +(-1.26530 + 6.81168i) q^{48} -6.00287 q^{49} +(-5.35559 - 4.60758i) q^{50} +(-4.30525 - 2.26005i) q^{51} +(0.422956 + 0.165864i) q^{52} +(-0.727053 + 0.419764i) q^{53} +(-6.59339 + 3.24457i) q^{54} +(-0.0622564 - 0.0359437i) q^{55} +(-8.63812 - 5.42272i) q^{56} +(7.54501 - 0.269740i) q^{57} +(-4.95426 + 5.75856i) q^{58} +(-4.44625 + 7.70114i) q^{59} +(0.225526 - 0.0433879i) q^{60} +(4.67311 + 8.09407i) q^{61} +(3.21965 + 9.19718i) q^{62} +(-0.868578 - 10.7829i) q^{63} +(-3.47701 - 7.20489i) q^{64} -0.0150600i q^{65} +(-2.46957 + 0.977584i) q^{66} +(5.00700 - 2.89079i) q^{67} +(5.55168 - 0.838342i) q^{68} +(-7.97122 - 12.6079i) q^{69} +(-0.0628092 + 0.332204i) q^{70} +(5.70164 - 9.87552i) q^{71} +(3.91990 - 7.52558i) q^{72} +(7.27491 - 12.6005i) q^{73} +(2.41136 - 0.844143i) q^{74} +(4.62390 + 7.31353i) q^{75} +(-6.83850 + 5.40693i) q^{76} -3.90999i q^{77} +(-0.436040 - 0.345648i) q^{78} +(-3.33564 - 1.92583i) q^{79} +(-0.180268 + 0.194497i) q^{80} +(8.88396 - 1.44058i) q^{81} +(4.22441 + 0.798701i) q^{82} -9.87713 q^{83} +(8.17694 + 9.44310i) q^{84} +(-0.0930590 - 0.161183i) q^{85} +(8.21525 + 1.55324i) q^{86} +(7.86382 - 4.97181i) q^{87} +(1.63062 - 2.59750i) q^{88} +(-13.7070 + 7.91375i) q^{89} +(-0.279683 - 0.0298950i) q^{90} +(0.709378 - 0.409559i) q^{91} +(16.0351 + 6.28823i) q^{92} +(-0.479503 - 11.9248i) q^{93} +(-0.441546 - 0.379876i) q^{94} +(0.249622 + 0.145605i) q^{95} +(1.49398 + 9.68339i) q^{96} +(4.49303 - 7.78215i) q^{97} +(-8.01257 + 2.80495i) q^{98} +(3.24244 - 0.261183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) \) 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more