LMFDB - Embedded newform 228.2.c.a.191.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			191.12
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.791500 + 1.17198i) q^{2} +(1.69893 + 0.337110i) q^{3} +(-0.747055 - 1.85524i) q^{4} -0.951020i q^{5} +(-1.73979 + 1.72428i) q^{6} -4.82396i q^{7} +(2.76559 + 0.592892i) q^{8} +(2.77271 + 1.14545i) q^{9} +O(q^{10})$	\(q+(-0.791500 + 1.17198i) q^{2} +(1.69893 + 0.337110i) q^{3} +(-0.747055 - 1.85524i) q^{4} -0.951020i q^{5} +(-1.73979 + 1.72428i) q^{6} -4.82396i q^{7} +(2.76559 + 0.592892i) q^{8} +(2.77271 + 1.14545i) q^{9} +(1.11457 + 0.752732i) q^{10} +3.58981 q^{11} +(-0.643772 - 3.40376i) q^{12} -2.89059 q^{13} +(5.65356 + 3.81816i) q^{14} +(0.320599 - 1.61571i) q^{15} +(-2.88382 + 2.77193i) q^{16} +3.29763i q^{17} +(-3.53705 + 2.34293i) q^{18} -1.00000i q^{19} +(-1.76437 + 0.710464i) q^{20} +(1.62621 - 8.19556i) q^{21} +(-2.84134 + 4.20717i) q^{22} -8.68428 q^{23} +(4.49867 + 1.93959i) q^{24} +4.09556 q^{25} +(2.28790 - 3.38770i) q^{26} +(4.32450 + 2.88075i) q^{27} +(-8.94959 + 3.60376i) q^{28} +5.48837i q^{29} +(1.63982 + 1.65457i) q^{30} +6.59046i q^{31} +(-0.966091 - 5.57375i) q^{32} +(6.09883 + 1.21016i) q^{33} +(-3.86474 - 2.61008i) q^{34} -4.58768 q^{35} +(0.0537190 - 5.99976i) q^{36} +8.68838 q^{37} +(1.17198 + 0.791500i) q^{38} +(-4.91090 - 0.974447i) q^{39} +(0.563852 - 2.63013i) q^{40} -0.964782i q^{41} +(8.31785 + 8.39266i) q^{42} -3.20516i q^{43} +(-2.68179 - 6.65996i) q^{44} +(1.08935 - 2.63690i) q^{45} +(6.87361 - 10.1778i) q^{46} -0.581952 q^{47} +(-5.83385 + 3.73714i) q^{48} -16.2706 q^{49} +(-3.24164 + 4.79990i) q^{50} +(-1.11167 + 5.60244i) q^{51} +(2.15943 + 5.36273i) q^{52} +1.07053i q^{53} +(-6.79901 + 2.78809i) q^{54} -3.41398i q^{55} +(2.86008 - 13.3411i) q^{56} +(0.337110 - 1.69893i) q^{57} +(-6.43224 - 4.34405i) q^{58} -4.73171 q^{59} +(-3.23704 + 0.612240i) q^{60} -5.55370 q^{61} +(-7.72386 - 5.21635i) q^{62} +(5.52561 - 13.3754i) q^{63} +(7.29696 + 3.27939i) q^{64} +2.74901i q^{65} +(-6.24551 + 6.18984i) q^{66} -2.99264i q^{67} +(6.11789 - 2.46351i) q^{68} +(-14.7540 - 2.92756i) q^{69} +(3.63115 - 5.37665i) q^{70} +4.79797 q^{71} +(6.98905 + 4.81177i) q^{72} -1.18991 q^{73} +(-6.87685 + 10.1826i) q^{74} +(6.95806 + 1.38066i) q^{75} +(-1.85524 + 0.747055i) q^{76} -17.3171i q^{77} +(5.02901 - 4.98418i) q^{78} +0.0661975i q^{79} +(2.63616 + 2.74257i) q^{80} +(6.37588 + 6.35202i) q^{81} +(1.13070 + 0.763625i) q^{82} -8.75808 q^{83} +(-16.4196 + 3.10553i) q^{84} +3.13611 q^{85} +(3.75637 + 2.53689i) q^{86} +(-1.85019 + 9.32434i) q^{87} +(9.92794 + 2.12837i) q^{88} +6.42337i q^{89} +(2.22817 + 3.36380i) q^{90} +13.9441i q^{91} +(6.48763 + 16.1114i) q^{92} +(-2.22171 + 11.1967i) q^{93} +(0.460615 - 0.682033i) q^{94} -0.951020 q^{95} +(0.237649 - 9.79508i) q^{96} -0.00303833 q^{97} +(12.8782 - 19.0687i) q^{98} +(9.95352 + 4.11196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.791500	+	1.17198i	−0.559675	+	0.828712i
$2$	−0.791500	+	1.17198i	−0.559675	+	0.828712i
$3$	1.69893	+	0.337110i	0.980877	+	0.194631i
$3$	1.69893	+	0.337110i	0.980877	+	0.194631i
$4$	−0.747055	−	1.85524i	−0.373527	−	0.927619i
$5$		−	0.951020i		−	0.425309i	−0.977127	−	0.212654i	$-0.931789\pi$
$5$		−	0.951020i		−	0.425309i	0.977127	−	0.212654i	$-0.0682109\pi$
$6$	−1.73979	+	1.72428i	−0.710265	+	0.703934i
$7$		−	4.82396i		−	1.82328i	−0.410985	−	0.911642i	$-0.634815\pi$
$7$		−	4.82396i		−	1.82328i	0.410985	−	0.911642i	$-0.365185\pi$
$8$	2.76559	+	0.592892i	0.977783	+	0.209619i
$9$	2.77271	+	1.14545i	0.924238	+	0.381818i
$10$	1.11457	+	0.752732i	0.352459	+	0.238035i
$11$	3.58981			1.08237			0.541184	−	0.840904i	$-0.317976\pi$
$11$	3.58981			1.08237			0.541184	+	0.840904i	$0.317976\pi$
$12$	−0.643772	−	3.40376i	−0.185841	−	0.982580i
$13$	−2.89059			−0.801705			−0.400852	−	0.916143i	$-0.631286\pi$
$13$	−2.89059			−0.801705			−0.400852	+	0.916143i	$0.631286\pi$
$14$	5.65356	+	3.81816i	1.51098	+	1.02045i
$15$	0.320599	−	1.61571i	0.0827782	−	0.417176i
$16$	−2.88382	+	2.77193i	−0.720955	+	0.692982i
$17$			3.29763i			0.799793i	0.916560	+	0.399897i	$0.130954\pi$
$17$			3.29763i			0.799793i	−0.916560	+	0.399897i	$0.869046\pi$
$18$	−3.53705	+	2.34293i	−0.833690	+	0.552233i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.76437	+	0.710464i	−0.394525	+	0.158865i
$21$	1.62621	−	8.19556i	0.354867	−	1.78842i
$22$	−2.84134	+	4.20717i	−0.605775	+	0.896972i
$23$	−8.68428			−1.81080			−0.905399	−	0.424562i	$-0.860428\pi$
$23$	−8.68428			−1.81080			−0.905399	+	0.424562i	$0.860428\pi$
$24$	4.49867	+	1.93959i	0.918286	+	0.395917i
$25$	4.09556			0.819112
$26$	2.28790	−	3.38770i	0.448694	−	0.664382i
$27$	4.32450	+	2.88075i	0.832250	+	0.554401i
$28$	−8.94959	+	3.60376i	−1.69131	+	0.681047i
$29$			5.48837i			1.01916i	0.860422	+	0.509582i	$0.170200\pi$
$29$			5.48837i			1.01916i	−0.860422	+	0.509582i	$0.829800\pi$
$30$	1.63982	+	1.65457i	0.299390	+	0.302082i
$31$			6.59046i			1.18368i	0.806055	+	0.591841i	$0.201599\pi$
$31$			6.59046i			1.18368i	−0.806055	+	0.591841i	$0.798401\pi$
$32$	−0.966091	−	5.57375i	−0.170782	−	0.985309i
$33$	6.09883	+	1.21016i	1.06167	+	0.210662i
$34$	−3.86474	−	2.61008i	−0.662798	−	0.447624i
$35$	−4.58768			−0.775459
$36$	0.0537190	−	5.99976i	0.00895316	−	0.999960i
$37$	8.68838			1.42836			0.714180	−	0.699962i	$-0.246800\pi$
$37$	8.68838			1.42836			0.714180	+	0.699962i	$0.246800\pi$
$38$	1.17198	+	0.791500i	0.190120	+	0.128398i
$39$	−4.91090	−	0.974447i	−0.786374	−	0.156036i
$40$	0.563852	−	2.63013i	0.0891528	−	0.415860i
$41$		−	0.964782i		−	0.150674i	−0.997158	−	0.0753368i	$-0.975997\pi$
$41$		−	0.964782i		−	0.150674i	0.997158	−	0.0753368i	$-0.0240032\pi$
$42$	8.31785	+	8.39266i	1.28347	+	1.29502i
$43$		−	3.20516i		−	0.488783i	−0.969677	−	0.244391i	$-0.921412\pi$
$43$		−	3.20516i		−	0.488783i	0.969677	−	0.244391i	$-0.0785882\pi$
$44$	−2.68179	−	6.65996i	−0.404294	−	1.00403i
$45$	1.08935	−	2.63690i	0.162390	−	0.393087i
$46$	6.87361	−	10.1778i	1.01346	−	1.50063i
$47$	−0.581952			−0.0848864			−0.0424432	−	0.999099i	$-0.513514\pi$
$47$	−0.581952			−0.0848864			−0.0424432	+	0.999099i	$0.513514\pi$
$48$	−5.83385	+	3.73714i	−0.842043	+	0.539410i
$49$	−16.2706			−2.32437
$50$	−3.24164	+	4.79990i	−0.458437	+	0.678808i
$51$	−1.11167	+	5.60244i	−0.155664	+	0.784498i
$52$	2.15943	+	5.36273i	0.299459	+	0.743677i
$53$			1.07053i			0.147049i	0.997293	+	0.0735245i	$0.0234247\pi$
$53$			1.07053i			0.147049i	−0.997293	+	0.0735245i	$0.976575\pi$
$54$	−6.79901	+	2.78809i	−0.925228	+	0.379411i
$55$		−	3.41398i		−	0.460341i
$56$	2.86008	−	13.3411i	0.382195	−	1.78278i
$57$	0.337110	−	1.69893i	0.0446514	−	0.225029i
$58$	−6.43224	−	4.34405i	−0.844594	−	0.570401i
$59$	−4.73171			−0.616016			−0.308008	−	0.951384i	$-0.599662\pi$
$59$	−4.73171			−0.616016			−0.308008	+	0.951384i	$0.599662\pi$
$60$	−3.23704	+	0.612240i	−0.417900	+	0.0790398i
$61$	−5.55370			−0.711079			−0.355540	−	0.934661i	$-0.615703\pi$
$61$	−5.55370			−0.711079			−0.355540	+	0.934661i	$0.615703\pi$
$62$	−7.72386	−	5.21635i	−0.980931	−	0.662477i
$63$	5.52561	−	13.3754i	0.696162	−	1.68515i
$64$	7.29696	+	3.27939i	0.912120	+	0.409923i
$65$			2.74901i			0.340972i
$66$	−6.24551	+	6.18984i	−0.768769	+	0.761916i
$67$		−	2.99264i		−	0.365609i	−0.983149	−	0.182805i	$-0.941482\pi$
$67$		−	2.99264i		−	0.365609i	0.983149	−	0.182805i	$-0.0585176\pi$
$68$	6.11789	−	2.46351i	0.741903	−	0.298745i
$69$	−14.7540	−	2.92756i	−1.77617	−	0.352437i
$70$	3.63115	−	5.37665i	0.434005	−	0.642632i
$71$	4.79797			0.569415			0.284707	−	0.958614i	$-0.408104\pi$
$71$	4.79797			0.569415			0.284707	+	0.958614i	$0.408104\pi$
$72$	6.98905	+	4.81177i	0.823668	+	0.567072i
$73$	−1.18991			−0.139269			−0.0696344	−	0.997573i	$-0.522183\pi$
$73$	−1.18991			−0.139269			−0.0696344	+	0.997573i	$0.522183\pi$
$74$	−6.87685	+	10.1826i	−0.799418	+	1.18370i
$75$	6.95806	+	1.38066i	0.803448	+	0.159424i
$76$	−1.85524	+	0.747055i	−0.212810	+	0.0856931i
$77$		−	17.3171i		−	1.97347i
$78$	5.02901	−	4.98418i	0.569423	−	0.564347i
$79$			0.0661975i			0.00744780i	0.999993	+	0.00372390i	$0.00118536\pi$
$79$			0.0661975i			0.00744780i	−0.999993	+	0.00372390i	$0.998815\pi$
$80$	2.63616	+	2.74257i	0.294732	+	0.306628i
$81$	6.37588	+	6.35202i	0.708431	+	0.705780i
$82$	1.13070	+	0.763625i	0.124865	+	0.0843283i
$83$	−8.75808			−0.961324			−0.480662	−	0.876906i	$-0.659604\pi$
$83$	−8.75808			−0.961324			−0.480662	+	0.876906i	$0.659604\pi$
$84$	−16.4196	+	3.10553i	−1.79152	+	0.338841i
$85$	3.13611			0.340159
$86$	3.75637	+	2.53689i	0.405060	+	0.273560i
$87$	−1.85019	+	9.32434i	−0.198361	+	0.999675i
$88$	9.92794	+	2.12837i	1.05832	+	0.226885i
$89$			6.42337i			0.680876i	0.940267	+	0.340438i	$0.110575\pi$
$89$			6.42337i			0.680876i	−0.940267	+	0.340438i	$0.889425\pi$
$90$	2.22817	+	3.36380i	0.234870	+	0.354576i
$91$			13.9441i			1.46174i
$92$	6.48763	+	16.1114i	0.676382	+	1.67973i
$93$	−2.22171	+	11.1967i	−0.230381	+	1.16105i
$94$	0.460615	−	0.682033i	0.0475088	−	0.0703463i
$95$	−0.951020			−0.0975726
$96$	0.237649	−	9.79508i	0.0242550	−	0.999706i
$97$	−0.00303833			−0.000308495			−0.000154248	−	1.00000i	$-0.500049\pi$
$97$	−0.00303833			−0.000308495			−0.000154248		1.00000i	$0.500049\pi$
$98$	12.8782	−	19.0687i	1.30089	−	1.92623i
$99$	9.95352	+	4.11196i	1.00037	+	0.413267i
$100$	−3.05961	−	7.59824i	−0.305961	−	0.759824i
$101$			8.03074i			0.799089i	0.916714	+	0.399544i	$0.130832\pi$
$101$			8.03074i			0.799089i	−0.916714	+	0.399544i	$0.869168\pi$
$102$	−5.68604	−	5.73718i	−0.563002	−	0.568065i
$103$			10.1386i			0.998989i	0.866317	+	0.499495i	$0.166481\pi$
$103$			10.1386i			0.998989i	−0.866317	+	0.499495i	$0.833519\pi$
$104$	−7.99418	−	1.71381i	−0.783894	−	0.168052i
$105$	−7.79414	−	1.54655i	−0.760630	−	0.150928i
$106$	−1.25464	−	0.847327i	−0.121861	−	0.0822997i
$107$	0.769003			0.0743423			0.0371711	−	0.999309i	$-0.488165\pi$
$107$	0.769003			0.0743423			0.0371711	+	0.999309i	$0.488165\pi$
$108$	2.11385	−	10.1751i	0.203405	−	0.979095i
$109$	2.74345			0.262775			0.131388	−	0.991331i	$-0.458057\pi$
$109$	2.74345			0.262775			0.131388	+	0.991331i	$0.458057\pi$
$110$	4.00110	+	2.70217i	0.381490	+	0.257642i
$111$	14.7609	+	2.92894i	1.40105	+	0.278003i
$112$	13.3717	+	13.9114i	1.26350	+	1.31451i
$113$		−	5.53855i		−	0.521023i	−0.965471	−	0.260512i	$-0.916109\pi$
$113$		−	5.53855i		−	0.521023i	0.965471	−	0.260512i	$-0.0838912\pi$
$114$	1.72428	+	1.73979i	0.161494	+	0.162946i
$115$			8.25892i			0.770148i
$116$	10.1822	−	4.10011i	0.945396	−	0.380686i
$117$	−8.01477	−	3.31103i	−0.740966	−	0.306105i
$118$	3.74515	−	5.54545i	0.344769	−	0.510500i
$119$	15.9076			1.45825
$120$	1.84459	−	4.27832i	0.168387	−	0.390555i
$121$	1.88674			0.171522
$122$	4.39576	−	6.50881i	0.397973	−	0.589280i
$123$	0.325238	−	1.63910i	0.0293257	−	0.147792i
$124$	12.2269	−	4.92343i	1.09801	−	0.442137i
$125$		−	8.65006i		−	0.773685i
$126$	11.3022	+	17.0626i	1.00688	+	1.52005i
$127$		−	10.8027i		−	0.958584i	−0.877655	−	0.479292i	$-0.840893\pi$
$127$		−	10.8027i		−	0.958584i	0.877655	−	0.479292i	$-0.159107\pi$
$128$	−9.61891	+	5.95622i	−0.850199	+	0.526461i
$129$	1.08049	−	5.44534i	0.0951322	−	0.479436i
$130$	−3.22177	−	2.17584i	−0.282568	−	0.190834i
$131$	−0.348602			−0.0304575			−0.0152287	−	0.999884i	$-0.504848\pi$
$131$	−0.348602			−0.0304575			−0.0152287	+	0.999884i	$0.504848\pi$
$132$	−2.31102	−	12.2188i	−0.201149	−	1.06351i
$133$	−4.82396			−0.418290
$134$	3.50730	+	2.36868i	0.302985	+	0.204622i
$135$	2.73965	−	4.11268i	0.235792	−	0.353963i
$136$	−1.95514	+	9.11989i	−0.167652	+	0.782024i
$137$			17.5754i			1.50157i	0.660548	+	0.750784i	$0.270324\pi$
$137$			17.5754i			1.50157i	−0.660548	+	0.750784i	$0.729676\pi$
$138$	15.1088	−	14.9741i	1.28615	−	1.27468i
$139$		−	9.25489i		−	0.784989i	−0.919754	−	0.392495i	$-0.871612\pi$
$139$		−	9.25489i		−	0.784989i	0.919754	−	0.392495i	$-0.128388\pi$
$140$	3.42725	+	8.51124i	0.289655	+	0.719331i
$141$	−0.988694	−	0.196182i	−0.0832630	−	0.0165215i
$142$	−3.79760	+	5.62311i	−0.318687	+	0.471881i
$143$	−10.3767			−0.867740
$144$	−11.1711	+	4.38249i	−0.930926	+	0.365207i
$145$	5.21955			0.433460
$146$	0.941816	−	1.39455i	0.0779452	−	0.115414i
$147$	−27.6425	−	5.48497i	−2.27992	−	0.452393i
$148$	−6.49070	−	16.1190i	−0.533532	−	1.32497i
$149$			0.276738i			0.0226712i	0.999936	+	0.0113356i	$0.00360831\pi$
$149$			0.276738i			0.0226712i	−0.999936	+	0.0113356i	$0.996392\pi$
$150$	−7.12541	+	7.06189i	−0.581787	+	0.576601i
$151$			13.7785i			1.12128i	0.828060	+	0.560640i	$0.189445\pi$
$151$			13.7785i			1.12128i	−0.828060	+	0.560640i	$0.810555\pi$
$152$	0.592892	−	2.76559i	0.0480899	−	0.224319i
$153$	−3.77728	+	9.14339i	−0.305375	+	0.739199i
$154$	20.2952	+	13.7065i	1.63544	+	1.10450i
$155$	6.26766			0.503430
$156$	1.86088	+	9.83886i	0.148990	+	0.787739i
$157$	8.94060			0.713538			0.356769	−	0.934193i	$-0.383878\pi$
$157$	8.94060			0.713538			0.356769	+	0.934193i	$0.383878\pi$
$158$	−0.0775818	−	0.0523953i	−0.00617208	−	0.00416835i
$159$	−0.360888	+	1.81876i	−0.0286203	+	0.144237i
$160$	−5.30074	+	0.918771i	−0.419061	+	0.0726353i
$161$			41.8926i			3.30160i
$162$	−12.4909	+	2.44475i	−0.981380	+	0.192077i
$163$		−	14.0725i		−	1.10224i	−0.834425	−	0.551122i	$-0.814200\pi$
$163$		−	14.0725i		−	1.10224i	0.834425	−	0.551122i	$-0.185800\pi$
$164$	−1.78990	+	0.720745i	−0.139768	+	0.0562807i
$165$	1.15089	−	5.80011i	0.0895965	−	0.451538i
$166$	6.93202	−	10.2643i	0.538029	−	0.796661i
$167$	−5.11581			−0.395873			−0.197937	−	0.980215i	$-0.563424\pi$
$167$	−5.11581			−0.395873			−0.197937	+	0.980215i	$0.563424\pi$
$168$	9.35649	−	21.7014i	0.721869	−	1.67430i
$169$	−4.64450			−0.357269
$170$	−2.48223	+	3.67545i	−0.190379	+	0.281894i
$171$	1.14545	−	2.77271i	0.0875949	−	0.212035i
$172$	−5.94634	+	2.39443i	−0.453404	+	0.182574i
$173$		−	15.6615i		−	1.19073i	−0.803457	−	0.595363i	$-0.797008\pi$
$173$		−	15.6615i		−	1.19073i	0.803457	−	0.595363i	$-0.202992\pi$
$174$	−9.46348	−	9.54859i	−0.717425	−	0.723877i
$175$		−	19.7568i		−	1.49347i
$176$	−10.3524	+	9.95070i	−0.780339	+	0.750062i
$177$	−8.03883	−	1.59511i	−0.604235	−	0.119896i
$178$	−7.52803	−	5.08410i	−0.564250	−	0.381069i
$179$	−14.3431			−1.07205			−0.536026	−	0.844202i	$-0.680075\pi$
$179$	−14.3431			−1.07205			−0.536026	+	0.844202i	$0.680075\pi$
$180$	−5.70589	−	0.0510878i	−0.425292	−	0.00380786i
$181$	3.60378			0.267867			0.133933	−	0.990990i	$-0.457239\pi$
$181$	3.60378			0.267867			0.133933	+	0.990990i	$0.457239\pi$
$182$	−16.3421	−	11.0367i	−1.21136	−	0.818097i
$183$	−9.43535	−	1.87221i	−0.697481	−	0.138398i
$184$	−24.0171	−	5.14884i	−1.77057	−	0.379577i
$185$		−	8.26282i		−	0.607495i
$186$	−11.3638	−	11.4660i	−0.833234	−	0.840728i
$187$			11.8379i			0.865671i
$188$	0.434750	+	1.07966i	0.0317074	+	0.0787422i
$189$	13.8966	−	20.8612i	1.01083	−	1.51743i
$190$	0.752732	−	1.11457i	0.0546089	−	0.0808596i
$191$	12.9210			0.934933			0.467467	−	0.884011i	$-0.345167\pi$
$191$	12.9210			0.934933			0.467467	+	0.884011i	$0.345167\pi$
$192$	11.2915	+	8.03132i	0.814893	+	0.579611i
$193$	−10.4423			−0.751654			−0.375827	−	0.926690i	$-0.622641\pi$
$193$	−10.4423			−0.751654			−0.375827	+	0.926690i	$0.622641\pi$
$194$	0.00240484	−	0.00356085i	0.000172657	−	0.000255654i
$195$	−0.926718	+	4.67036i	−0.0663637	+	0.334452i
$196$	12.1550	+	30.1858i	0.868214	+	2.15613i
$197$		−	17.5579i		−	1.25095i	−0.780244	−	0.625475i	$-0.784905\pi$
$197$		−	17.5579i		−	1.25095i	0.780244	−	0.625475i	$-0.215095\pi$
$198$	−12.6973	+	8.41066i	−0.902360	+	0.597720i
$199$			23.4265i			1.66066i	0.557269	+	0.830332i	$0.311849\pi$
$199$			23.4265i			1.66066i	−0.557269	+	0.830332i	$0.688151\pi$
$200$	11.3266	+	2.42822i	0.800914	+	0.171701i
$201$	1.00885	−	5.08428i	0.0711588	−	0.358618i
$202$	−9.41184	−	6.35633i	−0.662214	−	0.447230i
$203$	26.4757			1.85823
$204$	11.2243	−	2.12292i	0.785860	−	0.148634i
$205$	−0.917527			−0.0640829
$206$	−11.8822	−	8.02473i	−0.827874	−	0.559109i
$207$	−24.0790	−	9.94743i	−1.67361	−	0.691394i
$208$	8.33593	−	8.01250i	0.577993	−	0.555567i
$209$		−	3.58981i		−	0.248312i
$210$	7.98158	−	7.91044i	0.550782	−	0.545872i
$211$		−	10.8969i		−	0.750174i	−0.926990	−	0.375087i	$-0.877613\pi$
$211$		−	10.8969i		−	0.750174i	0.926990	−	0.375087i	$-0.122387\pi$
$212$	1.98609	−	0.799747i	0.136405	−	0.0549268i
$213$	8.15141	+	1.61745i	0.558525	+	0.110826i
$214$	−0.608666	+	0.901253i	−0.0416075	+	0.0616084i
$215$	−3.04817			−0.207884
$216$	10.2518	+	10.5309i	0.697547	+	0.716539i
$217$	31.7921			2.15819
$218$	−2.17144	+	3.21526i	−0.147069	+	0.217765i
$219$	−2.02158	−	0.401132i	−0.136605	−	0.0271060i
$220$	−6.33375	+	2.55043i	−0.427021	+	0.171950i
$221$		−	9.53209i		−	0.641198i
$222$	−15.1159	+	14.9812i	−1.01451	+	1.00547i
$223$			13.9272i			0.932635i	0.884617	+	0.466318i	$0.154420\pi$
$223$			13.9272i			0.932635i	−0.884617	+	0.466318i	$0.845580\pi$
$224$	−26.8875	+	4.66038i	−1.79650	+	0.311385i
$225$	11.3558	+	4.69127i	0.757054	+	0.312751i
$226$	6.49105	+	4.38377i	0.431778	+	0.291604i
$227$	7.19414			0.477492			0.238746	−	0.971082i	$-0.423264\pi$
$227$	7.19414			0.477492			0.238746	+	0.971082i	$0.423264\pi$
$228$	−3.40376	+	0.643772i	−0.225419	+	0.0426349i
$229$	3.92778			0.259555			0.129777	−	0.991543i	$-0.458574\pi$
$229$	3.92778			0.259555			0.129777	+	0.991543i	$0.458574\pi$
$230$	−9.67926	−	6.53694i	−0.638231	−	0.431033i
$231$	5.83777	−	29.4205i	0.384097	−	1.93573i
$232$	−3.25401	+	15.1786i	−0.213636	+	0.996522i
$233$		−	13.7058i		−	0.897898i	−0.893557	−	0.448949i	$-0.851799\pi$
$233$		−	13.7058i		−	0.897898i	0.893557	−	0.448949i	$-0.148201\pi$
$234$	10.2241	−	6.77244i	0.668373	−	0.442728i
$235$			0.553447i			0.0361029i
$236$	3.53484	+	8.77844i	0.230099	+	0.571428i
$237$	−0.0223159	+	0.112465i	−0.00144957	+	0.00730537i
$238$	−12.5909	+	18.6434i	−0.816146	+	1.20847i
$239$	9.08397			0.587593			0.293797	−	0.955868i	$-0.405081\pi$
$239$	9.08397			0.587593			0.293797	+	0.955868i	$0.405081\pi$
$240$	3.55410	+	5.54810i	0.229416	+	0.358129i
$241$	25.2962			1.62947			0.814737	−	0.579831i	$-0.196881\pi$
$241$	25.2962			1.62947			0.814737	+	0.579831i	$0.196881\pi$
$242$	−1.49336	+	2.21122i	−0.0959967	+	0.142142i
$243$	8.69082	+	12.9410i	0.557517	+	0.830166i
$244$	4.14892	+	10.3034i	0.265607	+	0.659611i
$245$			15.4736i			0.988574i
$246$	1.66355	+	1.67852i	0.106064	+	0.107018i
$247$			2.89059i			0.183924i
$248$	−3.90743	+	18.2265i	−0.248122	+	1.15738i
$249$	−14.8793	−	2.95244i	−0.942940	−	0.187103i
$250$	10.1377	+	6.84652i	0.641162	+	0.433012i
$251$	−25.4643			−1.60729			−0.803645	−	0.595109i	$-0.797109\pi$
$251$	−25.4643			−1.60729			−0.803645	+	0.595109i	$0.797109\pi$
$252$	−28.9426	−	0.259138i	−1.82321	−	0.0163242i
$253$	−31.1749			−1.95995
$254$	12.6605	+	8.55034i	0.794390	+	0.536496i
$255$	5.32803	+	1.05722i	0.333654	+	0.0662054i
$256$	0.632818	−	15.9875i	0.0395511	−	0.999218i
$257$			8.31052i			0.518396i	0.965824	+	0.259198i	$0.0834582\pi$
$257$			8.31052i			0.518396i	−0.965824	+	0.259198i	$0.916542\pi$
$258$	5.52660	+	5.57630i	0.344071	+	0.347165i
$259$		−	41.9124i		−	2.60431i
$260$	5.10006	−	2.05366i	0.316292	−	0.127362i
$261$	−6.28667	+	15.2177i	−0.389135	+	0.941950i
$262$	0.275918	−	0.408553i	0.0170463	−	0.0252405i
$263$	−27.9744			−1.72498			−0.862489	−	0.506076i	$-0.831095\pi$
$263$	−27.9744			−1.72498			−0.862489	+	0.506076i	$0.831095\pi$
$264$	16.1494	+	6.96276i	0.993924	+	0.428528i
$265$	1.01810			0.0625412
$266$	3.81816	−	5.65356i	0.234107	−	0.346642i
$267$	−2.16538	+	10.9128i	−0.132519	+	0.667855i
$268$	−5.55206	+	2.23567i	−0.339146	+	0.136565i
$269$		−	23.2667i		−	1.41860i	−0.704908	−	0.709299i	$-0.749012\pi$
$269$		−	23.2667i		−	1.41860i	0.704908	−	0.709299i	$-0.250988\pi$
$270$	2.65153	+	6.46599i	0.161367	+	0.393508i
$271$		−	3.59338i		−	0.218283i	−0.994026	−	0.109141i	$-0.965190\pi$
$271$		−	3.59338i		−	0.218283i	0.994026	−	0.109141i	$-0.0348101\pi$
$272$	−9.14080	−	9.50977i	−0.554242	−	0.576614i
$273$	−4.70069	+	23.6900i	−0.284499	+	1.43378i
$274$	−20.5979	−	13.9109i	−1.24437	−	0.840390i
$275$	14.7023			0.886582
$276$	5.59070	+	29.5592i	0.336520	+	1.77925i
$277$	27.7637			1.66816			0.834078	−	0.551646i	$-0.186000\pi$
$277$	27.7637			1.66816			0.834078	+	0.551646i	$0.186000\pi$
$278$	10.8465	+	7.32525i	0.650530	+	0.439339i
$279$	−7.54906	+	18.2735i	−0.451950	+	1.09400i
$280$	−12.6876	−	2.72000i	−0.758231	−	0.162551i
$281$		−	30.6548i		−	1.82871i	−0.404911	−	0.914356i	$-0.632697\pi$
$281$		−	30.6548i		−	1.82871i	0.404911	−	0.914356i	$-0.367303\pi$
$282$	1.01247	−	1.00345i	0.0602918	−	0.0597544i
$283$		−	15.0302i		−	0.893452i	−0.894671	−	0.446726i	$-0.852590\pi$
$283$		−	15.0302i		−	0.893452i	0.894671	−	0.446726i	$-0.147410\pi$
$284$	−3.58435	−	8.90138i	−0.212692	−	0.528200i
$285$	−1.61571	−	0.320599i	−0.0957066	−	0.0189906i
$286$	8.21313	−	12.1612i	0.485653	−	0.719107i
$287$	−4.65407			−0.274721
$288$	3.70577	−	16.5610i	0.218365	−	0.975867i
$289$	6.12563			0.360331
$290$	−4.13127	+	6.11718i	−0.242597	+	0.359213i
$291$	−0.00516190	−	0.00102425i	−0.000302596	−	6.00427e-5i
$292$	0.888930	+	2.20757i	0.0520207	+	0.129188i
$293$			5.81594i			0.339771i	0.985464	+	0.169885i	$0.0543397\pi$
$293$			5.81594i			0.339771i	−0.985464	+	0.169885i	$0.945660\pi$
$294$	28.3073	−	28.0550i	1.65092	−	1.63620i
$295$			4.49995i			0.261997i
$296$	24.0285	+	5.15127i	1.39663	+	0.299411i
$297$	15.5241	+	10.3414i	0.900801	+	0.600066i
$298$	−0.324330	−	0.219038i	−0.0187879	−	0.0126885i
$299$	25.1027			1.45173
$300$	−2.63661	−	13.9403i	−0.152225	−	0.804843i
$301$	−15.4616			−0.891190
$302$	−16.1481	−	10.9057i	−0.929217	−	0.627552i
$303$	−2.70725	+	13.6437i	−0.155527	+	0.783807i
$304$	2.77193	+	2.88382i	0.158981	+	0.165398i
$305$			5.28168i			0.302428i
$306$	−7.72611	−	11.6639i	−0.441672	−	0.666779i
$307$		−	19.3942i		−	1.10688i	−0.832888	−	0.553442i	$-0.813314\pi$
$307$		−	19.3942i		−	1.10688i	0.832888	−	0.553442i	$-0.186686\pi$
$308$	−32.1273	+	12.9368i	−1.83062	+	0.737144i
$309$	−3.41784	+	17.2248i	−0.194434	+	0.979885i
$310$	−4.96085	+	7.34554i	−0.281757	+	0.417199i
$311$	30.8338			1.74843			0.874213	−	0.485542i	$-0.161378\pi$
$311$	30.8338			1.74843			0.874213	+	0.485542i	$0.161378\pi$
$312$	−13.0038	−	5.60655i	−0.736195	−	0.317408i
$313$	4.21670			0.238342			0.119171	−	0.992874i	$-0.461976\pi$
$313$	4.21670			0.238342			0.119171	+	0.992874i	$0.461976\pi$
$314$	−7.07649	+	10.4782i	−0.399349	+	0.591317i
$315$	−12.7203	−	5.25497i	−0.716709	−	0.296084i
$316$	0.122812	−	0.0494531i	0.00690872	−	0.00278196i
$317$		−	11.1792i		−	0.627885i	−0.949442	−	0.313942i	$-0.898350\pi$
$317$		−	11.1792i		−	0.627885i	0.949442	−	0.313942i	$-0.101650\pi$
$318$	−1.84590	−	1.86250i	−0.103513	−	0.104444i
$319$			19.7022i			1.10311i
$320$	3.11876	−	6.93955i	0.174344	−	0.387933i
$321$	1.30648	+	0.259239i	0.0729206	+	0.0144693i
$322$	−49.0971	−	33.1580i	−2.73607	−	1.84782i
$323$	3.29763			0.183485
$324$	7.02139	−	16.5741i	0.390077	−	0.920782i
$325$	−11.8386			−0.656686
$326$	16.4926	+	11.1384i	0.913443	+	0.616899i
$327$	4.66093	+	0.924846i	0.257750	+	0.0511441i
$328$	0.572011	−	2.66819i	0.0315840	−	0.147326i
$329$			2.80731i			0.154772i
$330$	5.88666	+	5.93960i	0.324050	+	0.326964i
$331$		−	9.21698i		−	0.506611i	−0.967386	−	0.253306i	$-0.918482\pi$
$331$		−	9.21698i		−	0.506611i	0.967386	−	0.253306i	$-0.0815178\pi$
$332$	6.54276	+	16.2483i	0.359081	+	0.891742i
$333$	24.0904	+	9.95213i	1.32015	+	0.545373i
$334$	4.04916	−	5.99560i	0.221560	−	0.328065i
$335$	−2.84606			−0.155497
$336$	18.0278	+	28.1422i	0.983498	+	1.53528i
$337$	−21.7976			−1.18739			−0.593696	−	0.804690i	$-0.702332\pi$
$337$	−21.7976			−1.18739			−0.593696	+	0.804690i	$0.702332\pi$
$338$	3.67612	−	5.44324i	0.199955	−	0.296073i
$339$	1.86710	−	9.40960i	0.101407	−	0.511059i
$340$	−2.34285	−	5.81824i	−0.127059	−	0.315538i
$341$			23.6585i			1.28118i
$342$	2.34293	+	3.53705i	0.126691	+	0.191262i
$343$			44.7208i			2.41470i
$344$	1.90031	−	8.86416i	0.102458	−	0.477924i
$345$	−2.78417	+	14.0313i	−0.149895	+	0.755421i
$346$	18.3550	+	12.3961i	0.986768	+	0.666419i
$347$	−20.9139			−1.12271			−0.561357	−	0.827574i	$-0.689721\pi$
$347$	−20.9139			−1.12271			−0.561357	+	0.827574i	$0.689721\pi$
$348$	18.6811	−	3.53326i	1.00141	−	0.189403i
$349$	−25.3462			−1.35675			−0.678376	−	0.734715i	$-0.737316\pi$
$349$	−25.3462			−1.35675			−0.678376	+	0.734715i	$0.737316\pi$
$350$	23.1545	+	15.6375i	1.23766	+	0.835861i
$351$	−12.5003	−	8.32707i	−0.667219	−	0.444466i
$352$	−3.46808	−	20.0087i	−0.184849	−	1.06647i
$353$		−	11.4825i		−	0.611151i	−0.952168	−	0.305575i	$-0.901151\pi$
$353$		−	11.4825i		−	0.611151i	0.952168	−	0.305575i	$-0.0988488\pi$
$354$	8.23216	−	8.15879i	0.437535	−	0.433635i
$355$		−	4.56297i		−	0.242177i
$356$	11.9169	−	4.79861i	0.631593	−	0.254326i
$357$	27.0259	+	5.36263i	1.43036	+	0.283820i
$358$	11.3525	−	16.8097i	0.600001	−	0.888422i
$359$	18.4842			0.975557			0.487779	−	0.872967i	$-0.337807\pi$
$359$	18.4842			0.975557			0.487779	+	0.872967i	$0.337807\pi$
$360$	4.57609	−	6.64673i	0.241181	−	0.350313i
$361$	−1.00000			−0.0526316
$362$	−2.85239	+	4.22354i	−0.149918	+	0.221984i
$363$	3.20544	+	0.636041i	0.168242	+	0.0333835i
$364$	25.8696	−	10.4170i	1.35593	−	0.545998i
$365$			1.13163i			0.0592322i
$366$	9.66226	−	9.57614i	0.505055	−	0.500553i
$367$		−	10.4391i		−	0.544915i	−0.962168	−	0.272458i	$-0.912164\pi$
$367$		−	10.4391i		−	0.544915i	0.962168	−	0.272458i	$-0.0878364\pi$
$368$	25.0439	−	24.0722i	1.30550	−	1.25485i
$369$	1.10511	−	2.67506i	0.0575298	−	0.139258i
$370$	9.68383	+	6.54002i	0.503438	+	0.340000i
$371$	5.16420			0.268112
$372$	22.4323	−	4.24275i	1.16306	−	0.219977i
$373$	1.43539			0.0743216			0.0371608	−	0.999309i	$-0.488169\pi$
$373$	1.43539			0.0743216			0.0371608	+	0.999309i	$0.488169\pi$
$374$	−13.8737	−	9.36968i	−0.717392	−	0.484495i
$375$	2.91602	−	14.6958i	0.150583	−	0.758889i
$376$	−1.60944	−	0.345034i	−0.0830004	−	0.0177938i
$377$		−	15.8646i		−	0.817069i
$378$	13.4496	+	32.7981i	0.691774	+	1.68695i
$379$			32.2908i			1.65867i	0.558754	+	0.829334i	$0.311280\pi$
$379$			32.2908i			1.65867i	−0.558754	+	0.829334i	$0.688720\pi$
$380$	0.710464	+	1.76437i	0.0364460	+	0.0905102i
$381$	3.64170	−	18.3530i	0.186570	−	0.940253i
$382$	−10.2270	+	15.1431i	−0.523259	+	0.774791i
$383$	−10.1823			−0.520292			−0.260146	−	0.965569i	$-0.583771\pi$
$383$	−10.1823			−0.520292			−0.260146	+	0.965569i	$0.583771\pi$
$384$	−18.3497	+	6.87656i	−0.936406	+	0.350918i
$385$	−16.4689			−0.839333
$386$	8.26509	−	12.2381i	0.420682	−	0.622905i
$387$	3.67136	−	8.88700i	0.186626	−	0.451752i
$388$	0.00226980	+	0.00563682i	0.000115231	+	0.000286166i
$389$		−	28.7081i		−	1.45556i	−0.685812	−	0.727779i	$-0.740553\pi$
$389$		−	28.7081i		−	1.45556i	0.685812	−	0.727779i	$-0.259447\pi$
$390$	−4.74006	−	4.78269i	−0.240022	−	0.242181i
$391$		−	28.6376i		−	1.44826i
$392$	−44.9977	−	9.64668i	−2.27273	−	0.487231i
$393$	−0.592249	−	0.117517i	−0.0298750	−	0.00592796i
$394$	20.5775	+	13.8971i	1.03668	+	0.700125i
$395$	0.0629551			0.00316762
$396$	0.192841	−	21.5380i	0.00969062	−	1.08233i
$397$	−12.3366			−0.619155			−0.309577	−	0.950874i	$-0.600188\pi$
$397$	−12.3366			−0.619155			−0.309577	+	0.950874i	$0.600188\pi$
$398$	−27.4553	−	18.5421i	−1.37621	−	0.929432i
$399$	−8.19556	−	1.62621i	−0.410291	−	0.0814121i
$400$	−11.8109	+	11.3526i	−0.590543	+	0.567630i
$401$			19.0493i			0.951278i	0.879640	+	0.475639i	$0.157783\pi$
$401$			19.0493i			0.951278i	−0.879640	+	0.475639i	$0.842217\pi$
$402$	5.16015	+	5.20656i	0.257365	+	0.259679i
$403$		−	19.0503i		−	0.948963i
$404$	14.8989	−	5.99940i	0.741250	−	0.298481i
$405$	6.04090	−	6.06358i	0.300175	−	0.301302i
$406$	−20.9555	+	31.0288i	−1.04000	+	1.53993i
$407$	31.1896			1.54601
$408$	−6.39605	+	14.8349i	−0.316652	+	0.734439i
$409$	−33.8235			−1.67246			−0.836231	−	0.548377i	$-0.815246\pi$
$409$	−33.8235			−1.67246			−0.836231	+	0.548377i	$0.815246\pi$
$410$	0.726223	−	1.07532i	0.0358656	−	0.0531062i
$411$	−5.92485	+	29.8593i	−0.292251	+	1.47285i
$412$	18.8096	−	7.57411i	0.926681	−	0.373150i
$413$			22.8255i			1.12317i
$414$	30.7167	−	20.3466i	1.50964	−	0.999982i
$415$			8.32910i			0.408860i
$416$	2.79257	+	16.1114i	0.136917	+	0.789927i
$417$	3.11992	−	15.7234i	0.152783	−	0.769978i
$418$	4.20717	+	2.84134i	0.205780	+	0.138974i
$419$	13.9089			0.679496			0.339748	−	0.940516i	$-0.389658\pi$
$419$	13.9089			0.679496			0.339748	+	0.940516i	$0.389658\pi$
$420$	2.95342	+	15.6153i	0.144112	+	0.761951i
$421$	−6.16578			−0.300502			−0.150251	−	0.988648i	$-0.548008\pi$
$421$	−6.16578			−0.300502			−0.150251	+	0.988648i	$0.548008\pi$
$422$	12.7709	+	8.62490i	0.621678	+	0.419854i
$423$	−1.61358	−	0.666598i	−0.0784552	−	0.0324111i
$424$	−0.634710	+	2.96065i	−0.0308242	+	0.143782i
$425$			13.5057i			0.655120i
$426$	−8.34745	+	8.27305i	−0.404435	+	0.400830i
$427$			26.7908i			1.29650i
$428$	−0.574487	−	1.42668i	−0.0277689	−	0.0689613i
$429$	−17.6292	−	3.49808i	−0.851146	−	0.168889i
$430$	2.41263	−	3.57239i	0.116347	−	0.172276i
$431$	−14.8379			−0.714718			−0.357359	−	0.933967i	$-0.616323\pi$
$431$	−14.8379			−0.714718			−0.357359	+	0.933967i	$0.616323\pi$
$432$	−20.4563	+	3.67963i	−0.984204	+	0.177036i
$433$	15.1202			0.726633			0.363316	−	0.931666i	$-0.381644\pi$
$433$	15.1202			0.726633			0.363316	+	0.931666i	$0.381644\pi$
$434$	−25.1634	+	37.2596i	−1.20788	+	1.78852i
$435$	8.86763	+	1.75956i	0.425171	+	0.0843646i
$436$	−2.04951	−	5.08976i	−0.0981537	−	0.243755i
$437$			8.68428i			0.415425i
$438$	2.07019	−	2.05174i	0.0989177	−	0.0980360i
$439$			26.6310i			1.27103i	0.772090	+	0.635514i	$0.219212\pi$
$439$			26.6310i			1.27103i	−0.772090	+	0.635514i	$0.780788\pi$
$440$	2.02412	−	9.44167i	0.0964962	−	0.450114i
$441$	−45.1136	−	18.6372i	−2.14827	−	0.887484i
$442$	11.1714	+	7.54465i	0.531368	+	0.358863i
$443$	−9.37347			−0.445347			−0.222673	−	0.974893i	$-0.571478\pi$
$443$	−9.37347			−0.445347			−0.222673	+	0.974893i	$0.571478\pi$
$444$	−5.59334	−	29.5731i	−0.265448	−	1.40348i
$445$	6.10875			0.289583
$446$	−16.3224	−	11.0234i	−0.772886	−	0.521973i
$447$	−0.0932911	+	0.470157i	−0.00441252	+	0.0222377i
$448$	15.8196	−	35.2002i	0.747407	−	1.66305i
$449$			38.8101i			1.83156i	0.401681	+	0.915780i	$0.368426\pi$
$449$			38.8101i			1.83156i	−0.401681	+	0.915780i	$0.631574\pi$
$450$	−14.4862	+	9.59560i	−0.682885	+	0.452341i
$451$		−	3.46339i		−	0.163084i
$452$	−10.2753	+	4.13760i	−0.483311	+	0.194616i
$453$	−4.64488	+	23.4087i	−0.218235	+	1.09984i
$454$	−5.69417	+	8.43136i	−0.267240	+	0.395703i
$455$	13.2611			0.621689
$456$	1.93959	−	4.49867i	0.0908296	−	0.210669i
$457$	23.2367			1.08697			0.543483	−	0.839420i	$-0.317105\pi$
$457$	23.2367			1.08697			0.543483	+	0.839420i	$0.317105\pi$
$458$	−3.10884	+	4.60326i	−0.145266	+	0.215096i
$459$	−9.49966	+	14.2606i	−0.443406	+	0.665628i
$460$	15.3223	−	6.16987i	0.714404	−	0.287672i
$461$		−	16.9358i		−	0.788778i	−0.918944	−	0.394389i	$-0.870956\pi$
$461$		−	16.9358i		−	0.788778i	0.918944	−	0.394389i	$-0.129044\pi$
$462$	29.8595	+	30.1281i	1.38919	+	1.40168i
$463$		−	20.9617i		−	0.974172i	−0.873354	−	0.487086i	$-0.838060\pi$
$463$		−	20.9617i		−	0.974172i	0.873354	−	0.487086i	$-0.161940\pi$
$464$	−15.2134	−	15.8275i	−0.706263	−	0.734771i
$465$	10.6483	+	2.11289i	0.493803	+	0.0979830i
$466$	16.0629	+	10.8482i	0.744099	+	0.502531i
$467$	−2.88133			−0.133332			−0.0666660	−	0.997775i	$-0.521236\pi$
$467$	−2.88133			−0.133332			−0.0666660	+	0.997775i	$0.521236\pi$
$468$	−0.155279	+	17.3428i	−0.00717779	+	0.801673i
$469$	−14.4364			−0.666610
$470$	−0.648627	−	0.438054i	−0.0299189	−	0.0202059i
$471$	15.1894	+	3.01397i	0.699892	+	0.138876i
$472$	−13.0860	−	2.80539i	−0.602330	−	0.129128i
$473$		−	11.5059i		−	0.529043i
$474$	−0.114143	−	0.115170i	−0.00524276	−	0.00528991i
$475$		−	4.09556i		−	0.187917i
$476$	−11.8839	−	29.5124i	−0.544696	−	1.35270i
$477$	−1.22624	+	2.96828i	−0.0561459	+	0.135908i
$478$	−7.18996	+	10.6462i	−0.328861	+	0.486946i
$479$	6.68550			0.305468			0.152734	−	0.988267i	$-0.451192\pi$
$479$	6.68550			0.305468			0.152734	+	0.988267i	$0.451192\pi$
$480$	−9.31531	−	0.226009i	−0.425184	−	0.0103159i
$481$	−25.1145			−1.14512
$482$	−20.0220	+	29.6466i	−0.911976	+	1.35036i
$483$	−14.1224	+	71.1725i	−0.642593	+	3.23846i
$484$	−1.40950	−	3.50036i	−0.0640682	−	0.159107i
$485$			0.00288951i			0.000131206i
$486$	−22.0453	−	0.0573726i	−0.999997	−	0.00260247i
$487$		−	16.3608i		−	0.741381i	−0.928757	−	0.370690i	$-0.879121\pi$
$487$		−	16.3608i		−	0.741381i	0.928757	−	0.370690i	$-0.120879\pi$
$488$	−15.3593	−	3.29274i	−0.695281	−	0.149056i
$489$	4.74399	−	23.9082i	0.214531	−	1.08117i
$490$	−18.1347	−	12.2474i	−0.819243	−	0.553280i
$491$	5.14652			0.232259			0.116130	−	0.993234i	$-0.462951\pi$
$491$	5.14652			0.232259			0.116130	+	0.993234i	$0.462951\pi$
$492$	−3.28388	+	0.621100i	−0.148049	+	0.0280013i
$493$	−18.0986			−0.815121
$494$	−3.38770	−	2.28790i	−0.152420	−	0.102938i
$495$	3.91055	−	9.46599i	0.175766	−	0.425465i
$496$	−18.2683	−	19.0057i	−0.820270	−	0.853381i
$497$		−	23.1452i		−	1.03820i
$498$	15.2372	−	15.1014i	0.682795	−	0.676709i
$499$			29.0105i			1.29869i	0.760494	+	0.649345i	$0.224957\pi$
$499$			29.0105i			1.29869i	−0.760494	+	0.649345i	$0.775043\pi$
$500$	−16.0479	+	6.46207i	−0.717685	+	0.288992i
$501$	−8.69139	−	1.72459i	−0.388303	−	0.0770491i
$502$	20.1550	−	29.8435i	0.899560	−	1.33198i
$503$	−16.4421			−0.733118			−0.366559	−	0.930395i	$-0.619464\pi$
$503$	−16.4421			−0.733118			−0.366559	+	0.930395i	$0.619464\pi$
$504$	23.2118	−	33.7149i	1.03393	−	1.50178i
$505$	7.63739			0.339860
$506$	24.6750	−	36.5363i	1.09694	−	1.62423i
$507$	−7.89067	−	1.56571i	−0.350437	−	0.0695356i
$508$	−20.0416	+	8.07020i	−0.889201	+	0.358057i
$509$			36.4370i			1.61504i	0.589839	+	0.807521i	$0.299191\pi$
$509$			36.4370i			1.61504i	−0.589839	+	0.807521i	$0.700809\pi$
$510$	−5.45617	+	5.40753i	−0.241603	+	0.239450i
$511$			5.74009i			0.253926i
$512$	18.2361	+	13.3957i	0.805928	+	0.592014i
$513$	2.88075	−	4.32450i	0.127188	−	0.190931i
$514$	−9.73973	−	6.57778i	−0.429601	−	0.290133i
$515$	9.64204			0.424879
$516$	−10.9096	+	2.06339i	−0.480268	+	0.0908359i
$517$	−2.08910			−0.0918783
$518$	49.1203	+	33.1737i	2.15822	+	1.45757i
$519$	5.27967	−	26.6078i	0.231752	−	1.16795i
$520$	−1.62986	+	7.60262i	−0.0714742	+	0.333397i
$521$		−	41.4186i		−	1.81458i	−0.420504	−	0.907291i	$-0.638147\pi$
$521$		−	41.4186i		−	1.81458i	0.420504	−	0.907291i	$-0.361853\pi$
$522$	−12.8588	−	19.4126i	−0.562816	−	0.849667i
$523$		−	24.6573i		−	1.07819i	−0.842245	−	0.539095i	$-0.818766\pi$
$523$		−	24.6573i		−	1.07819i	0.842245	−	0.539095i	$-0.181234\pi$
$524$	0.260425	+	0.646739i	0.0113767	+	0.0282529i
$525$	6.66023	−	33.5654i	0.290676	−	1.46491i
$526$	22.1418	−	32.7854i	0.965427	−	1.42951i
$527$	−21.7329			−0.946700
$528$	−20.9424	+	13.4156i	−0.911401	+	0.583841i
$529$	52.4167			2.27899
$530$	−0.805825	+	1.19319i	−0.0350028	+	0.0518287i
$531$	−13.1197	−	5.41995i	−0.569345	−	0.235206i
$532$	3.60376	+	8.94959i	0.156243	+	0.388014i
$533$			2.78879i			0.120796i
$534$	−11.0757	−	11.1753i	−0.479292	−	0.483602i
$535$		−	0.731337i		−	0.0316184i
$536$	1.77431	−	8.27641i	0.0766386	−	0.357487i
$537$	−24.3678	−	4.83520i	−1.05155	−	0.208654i
$538$	27.2681	+	18.4156i	1.17561	+	0.793954i
$539$	−58.4082			−2.51582
$540$	−9.67667	−	2.01031i	−0.416418	−	0.0865099i
$541$	32.7039			1.40605			0.703026	−	0.711164i	$-0.251832\pi$
$541$	32.7039			1.40605			0.703026	+	0.711164i	$0.251832\pi$
$542$	4.21136	+	2.84416i	0.180893	+	0.122167i
$543$	6.12256	+	1.21487i	0.262744	+	0.0521351i
$544$	18.3802	−	3.18581i	0.788043	−	0.136591i
$545$		−	2.60908i		−	0.111761i
$546$	−24.0435	−	24.2597i	−1.02897	−	1.03822i
$547$			1.87569i			0.0801986i	0.999196	+	0.0400993i	$0.0127674\pi$
$547$			1.87569i			0.0801986i	−0.999196	+	0.0400993i	$0.987233\pi$
$548$	32.6066	−	13.1298i	1.39288	−	0.560877i
$549$	−15.3988	−	6.36151i	−0.657206	−	0.271502i
$550$	−11.6369	+	17.2307i	−0.496198	+	0.734721i
$551$	5.48837			0.233812
$552$	−39.0677	−	16.8439i	−1.66283	−	0.716925i
$553$	0.319334			0.0135795
$554$	−21.9749	+	32.5383i	−0.933626	+	1.38242i
$555$	2.78548	−	14.0379i	0.118237	−	0.595877i
$556$	−17.1700	+	6.91391i	−0.728171	+	0.293215i
$557$		−	1.47483i		−	0.0624906i	−0.999512	−	0.0312453i	$-0.990053\pi$
$557$		−	1.47483i		−	0.0624906i	0.999512	−	0.0312453i	$-0.00994731\pi$
$558$	−15.4410	−	23.3108i	−0.653668	−	0.986823i
$559$			9.26481i			0.391860i
$560$	13.2300	−	12.7167i	0.559071	−	0.537379i
$561$	−3.99067	+	20.1117i	−0.168486	+	0.849116i
$562$	35.9267	+	24.2633i	1.51548	+	1.02349i
$563$	21.3747			0.900836			0.450418	−	0.892818i	$-0.351275\pi$
$563$	21.3747			0.900836			0.450418	+	0.892818i	$0.351275\pi$
$564$	0.374644	+	1.98082i	0.0157754	+	0.0834076i
$565$	−5.26727			−0.221596
$566$	17.6150	+	11.8964i	0.740415	+	0.500043i
$567$	30.6419	−	30.7570i	1.28684	−	1.29167i
$568$	13.2692	+	2.84468i	0.556764	+	0.119360i
$569$		−	0.0254956i		−	0.00106883i	−1.00000		0.000534416i	$-0.999830\pi$
$569$		−	0.0254956i		−	0.00106883i	1.00000		0.000534416i	$-0.000170110\pi$
$570$	1.65457	−	1.63982i	0.0693024	−	0.0686847i
$571$		−	26.7349i		−	1.11882i	−0.828891	−	0.559411i	$-0.811027\pi$
$571$		−	26.7349i		−	1.11882i	0.828891	−	0.559411i	$-0.188973\pi$
$572$	7.75194	+	19.2512i	0.324125	+	0.804933i
$573$	21.9519	+	4.35582i	0.917054	+	0.181967i
$574$	3.68370	−	5.45446i	0.153754	−	0.227665i
$575$	−35.5670			−1.48325
$576$	16.4760	+	17.4511i	0.686500	+	0.727130i
$577$	−2.13654			−0.0889455			−0.0444727	−	0.999011i	$-0.514161\pi$
$577$	−2.13654			−0.0889455			−0.0444727	+	0.999011i	$0.514161\pi$
$578$	−4.84844	+	7.17909i	−0.201668	+	0.298611i
$579$	−17.7407	−	3.52021i	−0.737280	−	0.146295i
$580$	−3.89929	−	9.68350i	−0.161909	−	0.402086i
$581$			42.2486i			1.75277i
$582$	0.00528604	−	0.00523893i	0.000219113	−	0.000217160i
$583$			3.84301i			0.159161i
$584$	−3.29081	−	0.705489i	−0.136175	−	0.0291933i
$585$	−3.14886	+	7.62221i	−0.130189	+	0.315139i
$586$	−6.81614	−	4.60331i	−0.281572	−	0.190161i
$587$	−18.0251			−0.743977			−0.371988	−	0.928237i	$-0.621324\pi$
$587$	−18.0251			−0.743977			−0.371988	+	0.928237i	$0.621324\pi$
$588$	10.4745	+	55.3810i	0.431963	+	2.28387i
$589$	6.59046			0.271555
$590$	−5.27383	−	3.56171i	−0.217120	−	0.146633i
$591$	5.91896	−	29.8296i	0.243473	−	1.22703i
$592$	−25.0557	+	24.0836i	−1.02978	+	0.989829i
$593$			19.2807i			0.791764i	0.918301	+	0.395882i	$0.129561\pi$
$593$			19.2807i			0.791764i	−0.918301	+	0.395882i	$0.870439\pi$
$594$	−24.4072	+	10.0087i	−1.00144	+	0.410663i
$595$		−	15.1285i		−	0.620207i
$596$	0.513414	−	0.206738i	0.0210303	−	0.00846832i
$597$	−7.89733	+	39.8000i	−0.323216	+	1.62891i
$598$	−19.8688	+	29.4197i	−0.812495	+	1.20306i
$599$	−9.53524			−0.389599			−0.194800	−	0.980843i	$-0.562406\pi$
$599$	−9.53524			−0.389599			−0.194800	+	0.980843i	$0.562406\pi$
$600$	18.4246	+	7.94370i	0.752180	+	0.324300i
$601$	−22.8706			−0.932913			−0.466456	−	0.884544i	$-0.654470\pi$
$601$	−22.8706			−0.932913			−0.466456	+	0.884544i	$0.654470\pi$
$602$	12.2378	−	18.1206i	0.498777	−	0.738540i
$603$	3.42793	−	8.29773i	0.139596	−	0.337910i
$604$	25.5624	−	10.2933i	1.04012	−	0.418828i
$605$		−	1.79433i		−	0.0729499i
$606$	−13.8472	−	13.9718i	−0.562506	−	0.567565i
$607$			18.0821i			0.733929i	0.930235	+	0.366964i	$0.119603\pi$
$607$			18.0821i			0.733929i	−0.930235	+	0.366964i	$0.880397\pi$
$608$	−5.57375	+	0.966091i	−0.226045	+	0.0391802i
$609$	44.9802	+	8.92522i	1.82269	+	0.361668i
$610$	−6.19000	−	4.18045i	−0.250626	−	0.169262i
$611$	1.68218			0.0680538
$612$	19.7850	+	0.177145i	0.799761	+	0.00716068i
$613$	7.45343			0.301041			0.150521	−	0.988607i	$-0.451905\pi$
$613$	7.45343			0.301041			0.150521	+	0.988607i	$0.451905\pi$
$614$	22.7295	+	15.3505i	0.917288	+	0.619496i
$615$	−1.55881	−	0.309308i	−0.0628574	−	0.0124725i
$616$	10.2672	−	47.8920i	0.413676	−	1.92962i
$617$		−	28.7715i		−	1.15830i	−0.815222	−	0.579148i	$-0.803385\pi$
$617$		−	28.7715i		−	1.15830i	0.815222	−	0.579148i	$-0.196615\pi$
$618$	−17.4818	−	17.6391i	−0.703223	−	0.709547i
$619$			31.2226i			1.25494i	0.778640	+	0.627471i	$0.215910\pi$
$619$			31.2226i			1.25494i	−0.778640	+	0.627471i	$0.784090\pi$
$620$	−4.68228	−	11.6280i	−0.188045	−	0.466992i
$621$	−37.5551	−	25.0173i	−1.50704	−	1.00391i
$622$	−24.4050	+	36.1365i	−0.978551	+	1.44894i
$623$	30.9861			1.24143
$624$	16.8632	−	10.8025i	0.675070	−	0.432448i
$625$	12.2514			0.490057
$626$	−3.33752	+	4.94188i	−0.133394	+	0.197517i
$627$	1.21016	−	6.09883i	0.0483292	−	0.243564i
$628$	−6.67912	−	16.5869i	−0.266526	−	0.661891i
$629$			28.6511i			1.14239i
$630$	16.2268	−	10.7486i	0.646492	−	0.428234i
$631$			8.36561i			0.333030i	0.986039	+	0.166515i	$0.0532514\pi$
$631$			8.36561i			0.333030i	−0.986039	+	0.166515i	$0.946749\pi$
$632$	−0.0392479	+	0.183075i	−0.00156120	+	0.00728233i
$633$	3.67346	−	18.5131i	0.146007	−	0.735828i
$634$	13.1017	+	8.84832i	0.520336	+	0.351412i
$635$	−10.2736			−0.407694
$636$	3.64383	−	0.689179i	0.144487	−	0.0273277i
$637$	47.0315			1.86346
$638$	−23.0905	−	15.5943i	−0.914162	−	0.617384i
$639$	13.3034	+	5.49585i	0.526274	+	0.217412i
$640$	5.66449	+	9.14777i	0.223908	+	0.361597i
$641$			14.0482i			0.554869i	0.960745	+	0.277434i	$0.0894841\pi$
$641$			14.0482i			0.554869i	−0.960745	+	0.277434i	$0.910516\pi$
$642$	−1.33790	+	1.32598i	−0.0528027	+	0.0523321i
$643$			32.7422i			1.29123i	0.763665	+	0.645613i	$0.223398\pi$
$643$			32.7422i			1.29123i	−0.763665	+	0.645613i	$0.776602\pi$
$644$	77.7207	−	31.2961i	3.06263	−	1.23324i
$645$	−5.17863	−	1.02757i	−0.203908	−	0.0404606i
$646$	−2.61008	+	3.86474i	−0.102692	+	0.152056i
$647$	−38.1801			−1.50101			−0.750507	−	0.660863i	$-0.770190\pi$
$647$	−38.1801			−1.50101			−0.750507	+	0.660863i	$0.770190\pi$
$648$	13.8670	+	21.3473i	0.544747	+	0.838601i
$649$	−16.9859			−0.666756
$650$	9.37024	−	13.8745i	0.367531	−	0.544204i
$651$	54.0125	+	10.7174i	2.11692	+	0.420050i
$652$	−26.1079	+	10.5129i	−1.02246	+	0.411718i
$653$		−	42.6331i		−	1.66836i	−0.551492	−	0.834180i	$-0.685941\pi$
$653$		−	42.6331i		−	1.66836i	0.551492	−	0.834180i	$-0.314059\pi$
$654$	−4.77302	+	4.73048i	−0.186640	+	0.184976i
$655$			0.331527i			0.0129538i
$656$	2.67431	+	2.78226i	0.104414	+	0.108629i
$657$	−3.29929	−	1.36299i	−0.128717	−	0.0531752i
$658$	−3.29010	−	2.22199i	−0.128261	−	0.0866220i
$659$	−2.38481			−0.0928990			−0.0464495	−	0.998921i	$-0.514791\pi$
$659$	−2.38481			−0.0928990			−0.0464495	+	0.998921i	$0.514791\pi$
$660$	−11.6204	+	2.19783i	−0.452322	+	0.0855503i
$661$	50.3186			1.95717			0.978584	−	0.205848i	$-0.0659953\pi$
$661$	50.3186			1.95717			0.978584	+	0.205848i	$0.0659953\pi$
$662$	10.8021	+	7.29524i	0.419835	+	0.283538i
$663$	3.21337	−	16.1943i	0.124797	−	0.628936i
$664$	−24.2212	−	5.19259i	−0.939966	−	0.201512i
$665$			4.58768i			0.177903i
$666$	−30.7312	+	20.3562i	−1.19081	+	0.788788i
$667$		−	47.6625i		−	1.84550i
$668$	3.82179	+	9.49104i	0.147869	+	0.367220i
$669$	−4.69501	+	23.6613i	−0.181520	+	0.914800i
$670$	2.25266	−	3.33551i	0.0870277	−	0.128862i
$671$	−19.9368			−0.769650
$672$	−47.2510	−	1.14641i	−1.82275	−	0.0442237i
$673$	−33.4419			−1.28909			−0.644546	−	0.764566i	$-0.722954\pi$
$673$	−33.4419			−1.28909			−0.644546	+	0.764566i	$0.722954\pi$
$674$	17.2528	−	25.5463i	0.664554	−	0.984006i
$675$	17.7112	+	11.7983i	0.681706	+	0.454117i
$676$	3.46970	+	8.61666i	0.133450	+	0.331410i
$677$			16.8038i			0.645821i	0.946430	+	0.322910i	$0.104661\pi$
$677$			16.8038i			0.645821i	−0.946430	+	0.322910i	$0.895339\pi$
$678$	9.55001	+	9.63590i	0.366766	+	0.370065i
$679$			0.0146568i			0.000562475i
$680$	8.67320	+	1.85937i	0.332602	+	0.0713037i
$681$	12.2223	+	2.42522i	0.468361	+	0.0929347i
$682$	−27.7272	−	18.7257i	−1.06173	−	0.717045i
$683$	37.0755			1.41866			0.709328	−	0.704879i	$-0.248999\pi$
$683$	37.0755			1.41866			0.709328	+	0.704879i	$0.248999\pi$
$684$	−5.99976	−	0.0537190i	−0.229407	−	0.00205400i
$685$	16.7146			0.638630
$686$	−52.4117	−	35.3965i	−2.00109	−	1.35145i
$687$	6.67302	+	1.32410i	0.254591	+	0.0505174i
$688$	8.88448	+	9.24311i	0.338718	+	0.352390i
$689$		−	3.09447i		−	0.117890i
$690$	−14.2407	−	14.3688i	−0.542134	−	0.547010i
$691$			25.6654i			0.976360i	0.872743	+	0.488180i	$0.162339\pi$
$691$			25.6654i			0.976360i	−0.872743	+	0.488180i	$0.837661\pi$
$692$	−29.0559	+	11.7000i	−1.10454	+	0.444768i
$693$	19.8359	−	48.0153i	0.753504	−	1.82395i
$694$	16.5533	−	24.5105i	0.628356	−	0.930407i
$695$	−8.80158			−0.333863
$696$	−10.6452	+	24.6903i	−0.403504	+	0.935885i
$697$	3.18150			0.120508
$698$	20.0615	−	29.7052i	0.759340	−	1.12436i
$699$	4.62037	−	23.2852i	0.174759	−	0.880727i
$700$	−36.6536	+	14.7594i	−1.38538	+	0.557854i
$701$			24.9520i			0.942423i	0.882020	+	0.471212i	$0.156183\pi$
$701$			24.9520i			0.942423i	−0.882020	+	0.471212i	$0.843817\pi$
$702$	19.6531	−	8.05922i	0.741760	−	0.304176i
$703$		−	8.68838i		−	0.327688i
$704$	26.1947	+	11.7724i	0.987250	+	0.443688i
$705$	−0.186573	+	0.940267i	−0.00702674	+	0.0354125i
$706$	13.4572	+	9.08839i	0.506468	+	0.342046i
$707$	38.7400			1.45697
$708$	3.04614	+	16.1056i	0.114481	+	0.605285i
$709$	15.8658			0.595853			0.297927	−	0.954589i	$-0.403705\pi$
$709$	15.8658			0.595853			0.297927	+	0.954589i	$0.403705\pi$
$710$	5.34769	+	3.61159i	0.200695	+	0.135541i
$711$	−0.0758261	+	0.183547i	−0.00284370	+	0.00688354i
$712$	−3.80836	+	17.7644i	−0.142724	+	0.665749i
$713$		−	57.2334i		−	2.14341i
$714$	−27.6759	+	27.4292i	−1.03574	+	1.02651i
$715$			9.86841i			0.369058i
$716$	10.7151	+	26.6098i	0.400441	+	0.994456i
$717$	15.4330	+	3.06230i	0.576356	+	0.114364i
$718$	−14.6302	+	21.6630i	−0.545995	+	0.808456i
$719$	−3.57702			−0.133400			−0.0667001	−	0.997773i	$-0.521247\pi$
$719$	−3.57702			−0.133400			−0.0667001	+	0.997773i	$0.521247\pi$
$720$	4.16783	+	10.6240i	0.155326	+	0.395931i
$721$	48.9083			1.82144
$722$	0.791500	−	1.17198i	0.0294566	−	0.0436164i
$723$	42.9765	+	8.52762i	1.59831	+	0.317146i
$724$	−2.69222	−	6.68587i	−0.100056	−	0.248478i
$725$			22.4780i			0.834810i
$726$	−3.28253	+	3.25327i	−0.121826	+	0.120740i
$727$		−	32.1506i		−	1.19240i	−0.802836	−	0.596199i	$-0.796677\pi$
$727$		−	32.1506i		−	1.19240i	0.802836	−	0.596199i	$-0.203323\pi$
$728$	−8.26732	+	38.5636i	−0.306407	+	1.42926i
$729$	10.4025	+	24.9156i	0.385279	+	0.922800i
$730$	−1.32624	−	0.895686i	−0.0490865	−	0.0331508i
$731$	10.5694			0.390925
$732$	3.57532	+	18.9035i	0.132148	+	0.698692i
$733$	−6.40001			−0.236390			−0.118195	−	0.992990i	$-0.537711\pi$
$733$	−6.40001			−0.236390			−0.118195	+	0.992990i	$0.537711\pi$
$734$	12.2343	+	8.26253i	0.451578	+	0.304975i
$735$	−5.21632	+	26.2886i	−0.192407	+	0.969669i
$736$	8.38980	+	48.4040i	0.309252	+	1.78419i
$737$		−	10.7430i		−	0.395724i
$738$	2.26041	+	3.41248i	0.0832070	+	0.125615i
$739$		−	39.6512i		−	1.45859i	−0.684197	−	0.729297i	$-0.739847\pi$
$739$		−	39.6512i		−	1.45859i	0.684197	−	0.729297i	$-0.260153\pi$
$740$	−15.3295	+	6.17278i	−0.563524	+	0.226916i
$741$	−0.974447	+	4.91090i	−0.0357972	+	0.180406i
$742$	−4.08747	+	6.05232i	−0.150056	+	0.222188i
$743$	22.7258			0.833728			0.416864	−	0.908969i	$-0.363129\pi$
$743$	22.7258			0.833728			0.416864	+	0.908969i	$0.363129\pi$
$744$	−12.7828	+	29.6483i	−0.468639	+	1.08696i
$745$	0.263183			0.00964227
$746$	−1.13611	+	1.68224i	−0.0415960	+	0.0615912i
$747$	−24.2836	−	10.0320i	−0.888492	−	0.367050i
$748$	21.9621	−	8.84354i	0.803013	−	0.323352i
$749$		−	3.70964i		−	0.135547i
$750$	14.9151	+	15.0493i	0.544623	+	0.549521i
$751$		−	18.9665i		−	0.692097i	−0.938217	−	0.346049i	$-0.887523\pi$
$751$		−	18.9665i		−	0.692097i	0.938217	−	0.346049i	$-0.112477\pi$
$752$	1.67824	−	1.61313i	0.0611992	−	0.0588247i
$753$	−43.2619	−	8.58427i	−1.57655	−	0.312828i
$754$	18.5929	+	12.5568i	0.677115	+	0.457293i
$755$	13.1036			0.476890
$756$	−49.0840	−	10.1971i	−1.78517	−	0.370865i
$757$	−24.1900			−0.879202			−0.439601	−	0.898193i	$-0.644880\pi$
$757$	−24.1900			−0.879202			−0.439601	+	0.898193i	$0.644880\pi$
$758$	−37.8440	−	25.5582i	−1.37456	−	0.928315i
$759$	−52.9640	−	10.5094i	−1.92247	−	0.381467i
$760$	−2.63013	−	0.563852i	−0.0954048	−	0.0204530i
$761$			7.33058i			0.265733i	0.991134	+	0.132867i	$0.0424182\pi$
$761$			7.33058i			0.265733i	−0.991134	+	0.132867i	$0.957582\pi$
$762$	18.6269	+	18.7944i	0.674780	+	0.680849i
$763$		−	13.2343i		−	0.479114i
$764$	−9.65272	−	23.9716i	−0.349223	−	0.867262i
$765$	8.69554	+	3.59227i	0.314388	+	0.129879i
$766$	8.05930	−	11.9334i	0.291195	−	0.431172i
$767$	13.6774			0.493863
$768$	6.46466	−	26.9483i	0.233273	−	0.972411i
$769$	−40.7632			−1.46996			−0.734979	−	0.678090i	$-0.762808\pi$
$769$	−40.7632			−1.46996			−0.734979	+	0.678090i	$0.762808\pi$
$770$	13.0351	−	19.3012i	0.469754	−	0.695565i
$771$	−2.80156	+	14.1190i	−0.100896	+	0.508483i
$772$	7.80098	+	19.3730i	0.280763	+	0.697249i
$773$			40.1989i			1.44585i	0.690925	+	0.722927i	$0.257204\pi$
$773$			40.1989i			1.44585i	−0.690925	+	0.722927i	$0.742796\pi$
$774$	7.50946	+	11.3368i	0.269922	+	0.407493i
$775$			26.9916i			0.969568i
$776$	−0.00840276	−	0.00180140i	−0.000301642	−	6.46664e-5i
$777$	14.1291	−	71.2061i	0.506878	−	2.55450i
$778$	33.6452	+	22.7225i	1.20624	+	0.814639i
$779$	−0.964782			−0.0345669
$780$	9.35695	−	1.76973i	0.335032	−	0.0633666i
$781$	17.2238			0.616317
$782$	33.5625	+	22.6666i	1.20019	+	0.810557i
$783$	−15.8106	+	23.7344i	−0.565026	+	0.848199i
$784$	46.9213	−	45.1008i	1.67576	−	1.61074i
$785$		−	8.50269i		−	0.303474i
$786$	0.606493	−	0.601087i	0.0216329	−	0.0214401i
$787$		−	30.1104i		−	1.07332i	−0.843799	−	0.536660i	$-0.819686\pi$
$787$		−	30.1104i		−	1.07332i	0.843799	−	0.536660i	$-0.180314\pi$
$788$	−32.5741	+	13.1167i	−1.16040	+	0.467264i
$789$	−47.5266	−	9.43047i	−1.69199	−	0.335734i
$790$	−0.0498290	+	0.0737819i	−0.00177284	+	0.00262504i
$791$	−26.7177			−0.949973
$792$	25.0894	+	17.2733i	0.891512	+	0.613781i
$793$	16.0535			0.570076
$794$	9.76440	−	14.4582i	0.346526	−	0.513101i
$795$	1.72967	+	0.343211i	0.0613452	+	0.0121725i
$796$	43.4618	−	17.5009i	1.54046	−	0.620303i
$797$			29.1120i			1.03120i	0.856829	+	0.515600i	$0.172431\pi$
$797$			29.1120i			1.03120i	−0.856829	+	0.515600i	$0.827569\pi$
$798$	8.39266	−	8.31785i	0.297097	−	0.294449i
$799$		−	1.91906i		−	0.0678915i
$800$	−3.95668	−	22.8276i	−0.139890	−	0.807079i
$801$	−7.35766	+	17.8102i	−0.259970	+	0.629291i
$802$	−22.3254	−	15.0776i	−0.788336	−	0.532407i
$803$	−4.27156			−0.150740
$804$	−10.1862	+	1.92658i	−0.359240	+	0.0679452i
$805$	39.8407			1.40420
$806$	22.3265	+	15.0783i	0.786417	+	0.531111i
$807$	7.84346	−	39.5285i	0.276103	−	1.39147i
$808$	−4.76136	+	22.2097i	−0.167504	+	0.781336i
$809$			17.5960i			0.618644i	0.950957	+	0.309322i	$0.100102\pi$
$809$			17.5960i			0.618644i	−0.950957	+	0.309322i	$0.899898\pi$
$810$	2.32500	+	11.8791i	0.0816922	+	0.417390i
$811$			12.1077i			0.425159i	0.977144	+	0.212579i	$0.0681864\pi$
$811$			12.1077i			0.425159i	−0.977144	+	0.212579i	$0.931814\pi$
$812$	−19.7788	−	49.1186i	−0.694098	−	1.72373i
$813$	1.21137	−	6.10490i	0.0424845	−	0.214108i
$814$	−24.6866	+	36.5535i	−0.865265	+	1.28120i
$815$	−13.3832			−0.468794
$816$	−12.3237	−	19.2379i	−0.431416	−	0.673460i
$817$	−3.20516			−0.112134
$818$	26.7713	−	39.6403i	0.936036	−	1.38599i
$819$	−15.9723	+	38.6629i	−0.558116	+	1.35099i
$820$	0.685443	+	1.70223i	0.0239367	+	0.0594445i
$821$		−	48.6819i		−	1.69901i	−0.527580	−	0.849506i	$-0.676900\pi$
$821$		−	48.6819i		−	1.69901i	0.527580	−	0.849506i	$-0.323100\pi$
$822$	−30.3049	−	30.5775i	−1.05700	−	1.06651i
$823$			6.40201i			0.223160i	0.993755	+	0.111580i	$0.0355911\pi$
$823$			6.40201i			0.223160i	−0.993755	+	0.111580i	$0.964409\pi$
$824$	−6.01111	+	28.0393i	−0.209407	+	0.976795i
$825$	24.9781	+	4.95630i	0.869627	+	0.172556i
$826$	−26.7510	−	18.0664i	−0.930786	−	0.628611i
$827$	41.1870			1.43221			0.716107	−	0.697991i	$-0.245922\pi$
$827$	41.1870			1.43221			0.716107	+	0.697991i	$0.245922\pi$
$828$	−0.466511	+	52.1036i	−0.0162124	+	1.81072i
$829$	−4.94586			−0.171777			−0.0858883	−	0.996305i	$-0.527373\pi$
$829$	−4.94586			−0.171777			−0.0858883	+	0.996305i	$0.527373\pi$
$830$	−9.76151	−	6.59249i	−0.338827	−	0.228829i
$831$	47.1685	+	9.35942i	1.63626	+	0.324675i
$832$	−21.0925	−	9.47936i	−0.731251	−	0.328638i
$833$		−	53.6543i		−	1.85901i
$834$	15.9580	+	16.1015i	0.552581	+	0.557551i
$835$			4.86523i			0.168368i
$836$	−6.65996	+	2.68179i	−0.230339	+	0.0927515i
$837$	−18.9855	+	28.5004i	−0.656234	+	0.985119i
$838$	−11.0089	+	16.3009i	−0.380297	+	0.563107i
$839$	−47.4963			−1.63975			−0.819877	−	0.572540i	$-0.805958\pi$
$839$	−47.4963			−1.63975			−0.819877	+	0.572540i	$0.805958\pi$
$840$	−20.6384	−	8.89821i	−0.712094	−	0.307017i
$841$	−1.12219			−0.0386962
$842$	4.88021	−	7.22614i	0.168183	−	0.249029i
$843$	10.3341	−	52.0803i	0.355924	−	1.79374i
$844$	−20.2164	+	8.14059i	−0.695876	+	0.280210i
$845$			4.41701i			0.151950i
$846$	2.05839	−	1.36347i	0.0707689	−	0.0468771i
$847$		−	9.10157i		−	0.312734i
$848$	−2.96744	−	3.08722i	−0.101902	−	0.106016i
$849$	5.06684	−	25.5352i	0.173893	−	0.876367i
$850$	−15.8283	−	10.6897i	−0.542906	−	0.366655i
$851$	−75.4523			−2.58647
$852$	−3.08880	−	16.3311i	−0.105821	−	0.559495i
$853$	−37.4489			−1.28222			−0.641112	−	0.767447i	$-0.721527\pi$
$853$	−37.4489			−1.28222			−0.641112	+	0.767447i	$0.721527\pi$
$854$	−31.3982	−	21.2050i	−1.07442	−	0.725618i
$855$	−2.63690	−	1.08935i	−0.0901802	−	0.0372549i
$856$	2.12675	+	0.455935i	0.0726906	+	0.0155835i
$857$			47.8228i			1.63359i	0.576925	+	0.816797i	$0.304253\pi$
$857$			47.8228i			1.63359i	−0.576925	+	0.816797i	$0.695747\pi$
$858$	18.0532	−	17.8923i	0.616326	−	0.610832i
$859$		−	16.5196i		−	0.563643i	−0.959467	−	0.281821i	$-0.909061\pi$
$859$		−	16.5196i		−	0.563643i	0.959467	−	0.281821i	$-0.0909386\pi$
$860$	2.27715	+	5.65509i	0.0776502	+	0.192837i
$861$	−7.90693	−	1.56893i	−0.269467	−	0.0534691i
$862$	11.7442	−	17.3897i	0.400010	−	0.592296i
$863$	11.3696			0.387026			0.193513	−	0.981098i	$-0.438012\pi$
$863$	11.3696			0.387026			0.193513	+	0.981098i	$0.438012\pi$
$864$	11.8787	−	26.8867i	0.404123	−	0.914705i
$865$	−14.8944			−0.506426
$866$	−11.9677	+	17.7206i	−0.406678	+	0.602169i
$867$	10.4070	+	2.06501i	0.353440	+	0.0701315i
$868$	−23.7504	−	58.9819i	−0.806142	−	2.00198i
$869$			0.237636i			0.00806126i
$870$	−9.08090	+	8.99996i	−0.307871	+	0.305127i
$871$			8.65049i			0.293111i
$872$	7.58726	+	1.62657i	0.256937	+	0.0550826i
$873$	−0.00842441	−	0.00348026i	−0.000285123	−	0.000117789i
$874$	−10.1778	−	6.87361i	−0.344268	−	0.232503i
$875$	−41.7275			−1.41065
$876$	0.766033	+	4.05017i	0.0258818	+	0.136843i
$877$	3.22713			0.108973			0.0544863	−	0.998515i	$-0.482648\pi$
$877$	3.22713			0.108973			0.0544863	+	0.998515i	$0.482648\pi$
$878$	−31.2109	−	21.0784i	−1.05332	−	0.711362i
$879$	−1.96061	+	9.88086i	−0.0661298	+	0.333273i
$880$	9.46331	+	9.84530i	0.319008	+	0.331885i
$881$		−	0.717838i		−	0.0241846i	−0.999927	−	0.0120923i	$-0.996151\pi$
$881$		−	0.717838i		−	0.0241846i	0.999927	−	0.0120923i	$-0.00384919\pi$
$882$	57.5497	−	38.1207i	1.93780	−	1.28359i
$883$			16.5693i			0.557601i	0.960349	+	0.278801i	$0.0899369\pi$
$883$			16.5693i			0.557601i	−0.960349	+	0.278801i	$0.910063\pi$
$884$	−17.6843	+	7.12099i	−0.594787	+	0.239505i
$885$	−1.51698	+	7.64509i	−0.0509927	+	0.256987i
$886$	7.41910	−	10.9855i	0.249250	−	0.369064i
$887$	−6.02979			−0.202461			−0.101230	−	0.994863i	$-0.532278\pi$
$887$	−6.02979			−0.202461			−0.101230	+	0.994863i	$0.532278\pi$
$888$	39.0861	+	16.8519i	1.31164	+	0.565512i
$889$	−52.1117			−1.74777
$890$	−4.83508	+	7.15931i	−0.162072	+	0.239981i
$891$	22.8882	+	22.8026i	0.766783	+	0.763915i
$892$	25.8383	−	10.4044i	0.865130	−	0.348365i
$893$			0.581952i			0.0194743i
$894$	−0.477173	−	0.481464i	−0.0159590	−	0.0161026i
$895$			13.6405i			0.455953i
$896$	28.7326	+	46.4012i	0.959888	+	1.55016i
$897$	42.6476	+	8.46237i	1.42396	+	0.282550i
$898$	−45.4844	−	30.7182i	−1.51784	−	1.02508i
$899$	−36.1709			−1.20637
$900$	0.220009	−	24.5724i	0.00733364	−	0.819079i
$901$	−3.53022			−0.117609
$902$	4.05900	+	2.74127i	0.135150	+	0.0912743i
$903$	−26.2681	−	5.21226i	−0.874147	−	0.173453i
$904$	3.28376	−	15.3174i	0.109216	−	0.509448i
$905$		−	3.42726i		−	0.113926i
$906$	−23.7580	−	23.9717i	−0.789307	−	0.796405i
$907$			31.4118i			1.04301i	0.853248	+	0.521506i	$0.174629\pi$
$907$			31.4118i			1.04301i	−0.853248	+	0.521506i	$0.825371\pi$
$908$	−5.37442	−	13.3469i	−0.178356	−	0.442931i
$909$	−9.19883	+	22.2669i	−0.305106	+	0.738548i
$910$	−10.4962	+	15.5417i	−0.347944	+	0.515201i
$911$	−11.8765			−0.393487			−0.196743	−	0.980455i	$-0.563037\pi$
$911$	−11.8765			−0.393487			−0.196743	+	0.980455i	$0.563037\pi$
$912$	3.73714	+	5.83385i	0.123749	+	0.193178i
$913$	−31.4398			−1.04051
$914$	−18.3918	+	27.2328i	−0.608348	+	0.900781i
$915$	−1.78051	+	8.97320i	−0.0588618	+	0.296645i
$916$	−2.93427	−	7.28697i	−0.0969509	−	0.240768i
$917$			1.68164i			0.0555327i
$918$	−9.19409	−	22.4206i	−0.303450	−	0.739991i
$919$		−	3.14393i		−	0.103709i	−0.998655	−	0.0518543i	$-0.983487\pi$
$919$		−	3.14393i		−	0.103709i	0.998655	−	0.0518543i	$-0.0165131\pi$
$920$	−4.89664	+	22.8408i	−0.161438	+	0.753038i
$921$	6.53798	−	32.9493i	0.215434	−	1.08572i
$922$	19.8483	+	13.4047i	0.653669	+	0.441459i
$923$	−13.8690			−0.456502
$924$	−58.9432	+	11.1483i	−1.93909	+	0.366751i
$925$	35.5838			1.16999
$926$	24.5666	+	16.5912i	0.807308	+	0.545220i
$927$	−11.6133	+	28.1115i	−0.381432	+	0.923303i
$928$	30.5908	−	5.30226i	1.00419	−	0.174055i
$929$		−	18.0736i		−	0.592974i	−0.955037	−	0.296487i	$-0.904185\pi$
$929$		−	18.0736i		−	0.592974i	0.955037	−	0.296487i	$-0.0958152\pi$
$930$	−10.9044	+	10.8072i	−0.357569	+	0.354382i
$931$			16.2706i			0.533246i
$932$	−25.4276	+	10.2390i	−0.832907	+	0.335389i
$933$	52.3845	+	10.3944i	1.71499	+	0.340298i
$934$	2.28057	−	3.37685i	0.0746227	−	0.110494i
$935$	11.2581			0.368178
$936$	−20.2025	−	13.9088i	−0.660339	−	0.454625i
$937$	−7.96670			−0.260261			−0.130130	−	0.991497i	$-0.541540\pi$
$937$	−7.96670			−0.260261			−0.130130	+	0.991497i	$0.541540\pi$
$938$	11.4264	−	16.9191i	0.373085	−	0.552427i
$939$	7.16388	+	1.42149i	0.233784	+	0.0463887i
$940$	1.02678	−	0.413455i	0.0334898	−	0.0134854i
$941$		−	15.0985i		−	0.492197i	−0.969245	−	0.246099i	$-0.920851\pi$
$941$		−	15.0985i		−	0.492197i	0.969245	−	0.246099i	$-0.0791487\pi$
$942$	−15.5547	+	15.4161i	−0.506801	+	0.502284i
$943$			8.37844i			0.272840i
$944$	13.6454	−	13.1160i	0.444119	−	0.426888i
$945$	−19.8394	−	13.2160i	−0.645376	−	0.429915i
$946$	13.4847	+	9.10695i	0.438425	+	0.296092i
$947$	−6.70111			−0.217757			−0.108878	−	0.994055i	$-0.534726\pi$
$947$	−6.70111			−0.217757			−0.108878	+	0.994055i	$0.534726\pi$
$948$	0.225320	−	0.0426161i	0.00731806	−	0.00138411i
$949$	3.43955			0.111652
$950$	4.79990	+	3.24164i	0.155729	+	0.105173i
$951$	3.76862	−	18.9926i	0.122206	−	0.615878i
$952$	43.9940	+	9.43150i	1.42585	+	0.305677i
$953$			34.0038i			1.10149i	0.834673	+	0.550746i	$0.185657\pi$
$953$			34.0038i			1.10149i	−0.834673	+	0.550746i	$0.814343\pi$
$954$	−2.50818	−	3.78652i	−0.0812053	−	0.122593i
$955$		−	12.2882i		−	0.397636i
$956$	−6.78622	−	16.8529i	−0.219482	−	0.545063i
$957$	−6.64182	+	33.4726i	−0.214699	+	1.08202i
$958$	−5.29157	+	7.83524i	−0.170963	+	0.253145i
$959$	84.7830			2.73778
$960$	7.63795	−	10.7384i	0.246514	−	0.346581i
$961$	−12.4342			−0.401102
$962$	19.8782	−	29.4336i	0.640897	−	0.948978i
$963$	2.13222	+	0.880856i	0.0687100	+	0.0283852i
$964$	−18.8977	−	46.9305i	−0.608653	−	1.51153i
$965$			9.93084i			0.319685i
$966$	−72.2345	−	72.8842i	−2.32411	−	2.34501i
$967$			15.4605i			0.497177i	0.968609	+	0.248589i	$0.0799667\pi$
$967$			15.4605i			0.497177i	−0.968609	+	0.248589i	$0.920033\pi$
$968$	5.21796	+	1.11863i	0.167711	+	0.0359543i
$969$	5.60244	+	1.11167i	0.179976	+	0.0357118i
$970$	−0.00338643	−	0.00228705i	−0.000108732	−	7.34326e-5i
$971$	−14.5494			−0.466911			−0.233456	−	0.972367i	$-0.575003\pi$
$971$	−14.5494			−0.466911			−0.233456	+	0.972367i	$0.575003\pi$
$972$	17.5161	−	25.7912i	0.561830	−	0.827253i
$973$	−44.6452			−1.43126
$974$	19.1745	+	12.9496i	0.614391	+	0.414932i
$975$	−20.1129	−	3.99091i	−0.644128	−	0.127811i
$976$	16.0159	−	15.3945i	0.512656	−	0.492765i
$977$		−	30.4691i		−	0.974794i	−0.873180	−	0.487397i	$-0.837946\pi$
$977$		−	30.4691i		−	0.974794i	0.873180	−	0.487397i	$-0.162054\pi$
$978$	24.2649	+	24.4832i	0.775907	+	0.782886i
$979$			23.0587i			0.736959i
$980$	28.7073	−	11.5596i	0.917020	−	0.369259i
$981$	7.60681	+	3.14249i	0.242867	+	0.100332i
$982$	−4.07347	+	6.03159i	−0.129990	+	0.192476i
$983$	3.64757			0.116339			0.0581696	−	0.998307i	$-0.481474\pi$
$983$	3.64757			0.116339			0.0581696	+	0.998307i	$0.481474\pi$
$984$	1.87128	−	4.34023i	0.0596542	−	0.138362i
$985$	−16.6979			−0.532040
$986$	14.3251	−	21.2111i	0.456203	−	0.675500i
$987$	−0.946373	+	4.76942i	−0.0301234	+	0.151812i
$988$	5.36273	−	2.15943i	0.170611	−	0.0687005i
$989$			27.8345i			0.885087i
$990$	7.99871	+	12.0754i	0.254216	+	0.383782i
$991$			44.4264i			1.41125i	0.708584	+	0.705626i	$0.249334\pi$
$991$			44.4264i			1.41125i	−0.708584	+	0.705626i	$0.750666\pi$
$992$	36.7336	−	6.36698i	1.16629	−	0.202152i
$993$	3.10714	−	15.6590i	0.0986021	−	0.496923i
$994$	27.1256	+	18.3194i	0.860373	+	0.581057i
$995$	22.2791			0.706295
$996$	5.63821	+	29.8104i	0.178653	+	0.944577i
$997$	−44.7668			−1.41778			−0.708889	−	0.705320i	$-0.750803\pi$
$997$	−44.7668			−1.41778			−0.708889	+	0.705320i	$0.750803\pi$
$998$	−33.9996	−	22.9618i	−1.07624	−	0.726844i
$999$	37.5729	+	25.0291i	1.18875	+	0.791885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.12	yes	36
3.2	odd	2	inner	228.2.c.a.191.25	yes	36
4.3	odd	2	inner	228.2.c.a.191.26	yes	36
12.11	even	2	inner	228.2.c.a.191.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.11	✓	36	12.11	even	2	inner
228.2.c.a.191.12	yes	36	1.1	even	1	trivial
228.2.c.a.191.25	yes	36	3.2	odd	2	inner
228.2.c.a.191.26	yes	36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.791500 + 1.17198i) q^{2} +(1.69893 + 0.337110i) q^{3} +(-0.747055 - 1.85524i) q^{4} -0.951020i q^{5} +(-1.73979 + 1.72428i) q^{6} -4.82396i q^{7} +(2.76559 + 0.592892i) q^{8} +(2.77271 + 1.14545i) q^{9} +O(q^{10})\)	\(q+(-0.791500 + 1.17198i) q^{2} +(1.69893 + 0.337110i) q^{3} +(-0.747055 - 1.85524i) q^{4} -0.951020i q^{5} +(-1.73979 + 1.72428i) q^{6} -4.82396i q^{7} +(2.76559 + 0.592892i) q^{8} +(2.77271 + 1.14545i) q^{9} +(1.11457 + 0.752732i) q^{10} +3.58981 q^{11} +(-0.643772 - 3.40376i) q^{12} -2.89059 q^{13} +(5.65356 + 3.81816i) q^{14} +(0.320599 - 1.61571i) q^{15} +(-2.88382 + 2.77193i) q^{16} +3.29763i q^{17} +(-3.53705 + 2.34293i) q^{18} -1.00000i q^{19} +(-1.76437 + 0.710464i) q^{20} +(1.62621 - 8.19556i) q^{21} +(-2.84134 + 4.20717i) q^{22} -8.68428 q^{23} +(4.49867 + 1.93959i) q^{24} +4.09556 q^{25} +(2.28790 - 3.38770i) q^{26} +(4.32450 + 2.88075i) q^{27} +(-8.94959 + 3.60376i) q^{28} +5.48837i q^{29} +(1.63982 + 1.65457i) q^{30} +6.59046i q^{31} +(-0.966091 - 5.57375i) q^{32} +(6.09883 + 1.21016i) q^{33} +(-3.86474 - 2.61008i) q^{34} -4.58768 q^{35} +(0.0537190 - 5.99976i) q^{36} +8.68838 q^{37} +(1.17198 + 0.791500i) q^{38} +(-4.91090 - 0.974447i) q^{39} +(0.563852 - 2.63013i) q^{40} -0.964782i q^{41} +(8.31785 + 8.39266i) q^{42} -3.20516i q^{43} +(-2.68179 - 6.65996i) q^{44} +(1.08935 - 2.63690i) q^{45} +(6.87361 - 10.1778i) q^{46} -0.581952 q^{47} +(-5.83385 + 3.73714i) q^{48} -16.2706 q^{49} +(-3.24164 + 4.79990i) q^{50} +(-1.11167 + 5.60244i) q^{51} +(2.15943 + 5.36273i) q^{52} +1.07053i q^{53} +(-6.79901 + 2.78809i) q^{54} -3.41398i q^{55} +(2.86008 - 13.3411i) q^{56} +(0.337110 - 1.69893i) q^{57} +(-6.43224 - 4.34405i) q^{58} -4.73171 q^{59} +(-3.23704 + 0.612240i) q^{60} -5.55370 q^{61} +(-7.72386 - 5.21635i) q^{62} +(5.52561 - 13.3754i) q^{63} +(7.29696 + 3.27939i) q^{64} +2.74901i q^{65} +(-6.24551 + 6.18984i) q^{66} -2.99264i q^{67} +(6.11789 - 2.46351i) q^{68} +(-14.7540 - 2.92756i) q^{69} +(3.63115 - 5.37665i) q^{70} +4.79797 q^{71} +(6.98905 + 4.81177i) q^{72} -1.18991 q^{73} +(-6.87685 + 10.1826i) q^{74} +(6.95806 + 1.38066i) q^{75} +(-1.85524 + 0.747055i) q^{76} -17.3171i q^{77} +(5.02901 - 4.98418i) q^{78} +0.0661975i q^{79} +(2.63616 + 2.74257i) q^{80} +(6.37588 + 6.35202i) q^{81} +(1.13070 + 0.763625i) q^{82} -8.75808 q^{83} +(-16.4196 + 3.10553i) q^{84} +3.13611 q^{85} +(3.75637 + 2.53689i) q^{86} +(-1.85019 + 9.32434i) q^{87} +(9.92794 + 2.12837i) q^{88} +6.42337i q^{89} +(2.22817 + 3.36380i) q^{90} +13.9441i q^{91} +(6.48763 + 16.1114i) q^{92} +(-2.22171 + 11.1967i) q^{93} +(0.460615 - 0.682033i) q^{94} -0.951020 q^{95} +(0.237649 - 9.79508i) q^{96} -0.00303833 q^{97} +(12.8782 - 19.0687i) q^{98} +(9.95352 + 4.11196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more