LMFDB - Embedded newform 216.3.h.d.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.121670000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} - 6x^{3} + 16x^{2} - 16x + 64 $ x^6 - x^5 + 4x^4 - 6x^3 + 16x^2 - 16x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.5
Root			$1.63177 - 1.15643i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.d.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63177 - 1.15643i) q^{2} +(1.32536 - 3.77405i) q^{4} +2.38717 q^{5} +2.13992 q^{7} +(-2.20173 - 7.69106i) q^{8} +O(q^{10})$	\(q+(1.63177 - 1.15643i) q^{2} +(1.32536 - 3.77405i) q^{4} +2.38717 q^{5} +2.13992 q^{7} +(-2.20173 - 7.69106i) q^{8} +(3.89531 - 2.76059i) q^{10} +8.30142 q^{11} -12.4597i q^{13} +(3.49185 - 2.47466i) q^{14} +(-12.4869 - 10.0039i) q^{16} +7.26216i q^{17} -13.6788i q^{19} +(3.16385 - 9.00929i) q^{20} +(13.5460 - 9.59999i) q^{22} +33.4007i q^{23} -19.3014 q^{25} +(-14.4088 - 20.3314i) q^{26} +(2.83615 - 8.07615i) q^{28} -6.69858 q^{29} +42.3240 q^{31} +(-31.9445 - 1.88396i) q^{32} +(8.39816 + 11.8502i) q^{34} +5.10834 q^{35} -45.4869i q^{37} +(-15.8185 - 22.3207i) q^{38} +(-5.25590 - 18.3599i) q^{40} +78.0420i q^{41} +57.9466i q^{43} +(11.0023 - 31.3300i) q^{44} +(38.6254 + 54.5023i) q^{46} +33.0272i q^{47} -44.4208 q^{49} +(-31.4955 + 22.3207i) q^{50} +(-47.0236 - 16.5136i) q^{52} +51.6254 q^{53} +19.8169 q^{55} +(-4.71152 - 16.4582i) q^{56} +(-10.9305 + 7.74641i) q^{58} -30.6248 q^{59} +29.7957i q^{61} +(69.0631 - 48.9446i) q^{62} +(-54.3048 + 33.8673i) q^{64} -29.7435i q^{65} +107.786i q^{67} +(27.4078 + 9.62495i) q^{68} +(8.33565 - 5.90742i) q^{70} -37.3792i q^{71} -118.435 q^{73} +(-52.6022 - 74.2242i) q^{74} +(-51.6244 - 18.1293i) q^{76} +17.7644 q^{77} +92.2725 q^{79} +(-29.8083 - 23.8810i) q^{80} +(90.2499 + 127.347i) q^{82} +93.6374 q^{83} +17.3360i q^{85} +(67.0110 + 94.5556i) q^{86} +(-18.2775 - 63.8467i) q^{88} -48.2986i q^{89} -26.6628i q^{91} +(126.056 + 44.2678i) q^{92} +(38.1935 + 53.8928i) q^{94} -32.6536i q^{95} +7.17272 q^{97} +(-72.4845 + 51.3693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 7 q^{4} + 2 q^{5} - 10 q^{7} + 7 q^{8}+O(q^{10}) $ 6 * q + q^2 - 7 * q^4 + 2 * q^5 - 10 * q^7 + 7 * q^8	$ 6 q + q^{2} - 7 q^{4} + 2 q^{5} - 10 q^{7} + 7 q^{8} - 3 q^{10} - 10 q^{11} + 35 q^{14} - 23 q^{16} + 41 q^{20} + 25 q^{22} - 56 q^{25} - 60 q^{26} - 5 q^{28} - 100 q^{29} + 6 q^{31} - 29 q^{32} - 4 q^{34} - 110 q^{35} + 132 q^{38} + 59 q^{40} + 125 q^{44} - 76 q^{46} - 24 q^{49} - 36 q^{50} + 80 q^{52} + 2 q^{53} + 170 q^{55} - 175 q^{56} + 10 q^{58} + 20 q^{59} + 191 q^{62} - 151 q^{64} + 312 q^{68} + 115 q^{70} + 130 q^{73} - 300 q^{74} - 176 q^{76} - 50 q^{77} - 76 q^{79} - 331 q^{80} + 100 q^{82} + 38 q^{83} + 360 q^{86} - 5 q^{88} + 408 q^{92} + 240 q^{94} - 70 q^{97} - 324 q^{98}+O(q^{100}) $ 6 * q + q^2 - 7 * q^4 + 2 * q^5 - 10 * q^7 + 7 * q^8 - 3 * q^10 - 10 * q^11 + 35 * q^14 - 23 * q^16 + 41 * q^20 + 25 * q^22 - 56 * q^25 - 60 * q^26 - 5 * q^28 - 100 * q^29 + 6 * q^31 - 29 * q^32 - 4 * q^34 - 110 * q^35 + 132 * q^38 + 59 * q^40 + 125 * q^44 - 76 * q^46 - 24 * q^49 - 36 * q^50 + 80 * q^52 + 2 * q^53 + 170 * q^55 - 175 * q^56 + 10 * q^58 + 20 * q^59 + 191 * q^62 - 151 * q^64 + 312 * q^68 + 115 * q^70 + 130 * q^73 - 300 * q^74 - 176 * q^76 - 50 * q^77 - 76 * q^79 - 331 * q^80 + 100 * q^82 + 38 * q^83 + 360 * q^86 - 5 * q^88 + 408 * q^92 + 240 * q^94 - 70 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.63177	−	1.15643i	0.815886	−	0.578213i
$2$	1.63177	−	1.15643i	0.815886	−	0.578213i
$3$		0			0
$3$		0			0
$4$	1.32536	−	3.77405i	0.331339	−	0.943512i
$5$	2.38717			0.477434			0.238717	−	0.971089i	$-0.423273\pi$
$5$	2.38717			0.477434			0.238717	+	0.971089i	$0.423273\pi$
$6$		0			0
$7$	2.13992			0.305702			0.152851	−	0.988249i	$-0.451154\pi$
$7$	2.13992			0.305702			0.152851	+	0.988249i	$0.451154\pi$
$8$	−2.20173	−	7.69106i	−0.275216	−	0.961382i
$9$		0			0
$10$	3.89531	−	2.76059i	0.389531	−	0.276059i
$11$	8.30142			0.754675			0.377337	−	0.926076i	$-0.376840\pi$
$11$	8.30142			0.754675			0.377337	+	0.926076i	$0.376840\pi$
$12$		0			0
$13$		−	12.4597i		−	0.958441i	−0.877695	−	0.479220i	$-0.840919\pi$
$13$		−	12.4597i		−	0.958441i	0.877695	−	0.479220i	$-0.159081\pi$
$14$	3.49185	−	2.47466i	0.249418	−	0.176761i
$15$		0			0
$16$	−12.4869	−	10.0039i	−0.780429	−	0.625244i
$17$			7.26216i			0.427186i	0.976923	+	0.213593i	$0.0685167\pi$
$17$			7.26216i			0.427186i	−0.976923	+	0.213593i	$0.931483\pi$
$18$		0			0
$19$		−	13.6788i		−	0.719937i	−0.932964	−	0.359968i	$-0.882787\pi$
$19$		−	13.6788i		−	0.719937i	0.932964	−	0.359968i	$-0.117213\pi$
$20$	3.16385	−	9.00929i	0.158192	−	0.450464i
$21$		0			0
$22$	13.5460	−	9.59999i	0.615728	−	0.436363i
$23$			33.4007i			1.45220i	0.687587	+	0.726102i	$0.258670\pi$
$23$			33.4007i			1.45220i	−0.687587	+	0.726102i	$0.741330\pi$
$24$		0			0
$25$	−19.3014			−0.772057
$26$	−14.4088	−	20.3314i	−0.554183	−	0.781978i
$27$		0			0
$28$	2.83615	−	8.07615i	0.101291	−	0.288434i
$29$	−6.69858			−0.230985			−0.115493	−	0.993308i	$-0.536845\pi$
$29$	−6.69858			−0.230985			−0.115493	+	0.993308i	$0.536845\pi$
$30$		0			0
$31$	42.3240			1.36529			0.682646	−	0.730750i	$-0.260829\pi$
$31$	42.3240			1.36529			0.682646	+	0.730750i	$0.260829\pi$
$32$	−31.9445	−	1.88396i	−0.998265	−	0.0588737i
$33$		0			0
$34$	8.39816	+	11.8502i	0.247005	+	0.348535i
$35$	5.10834			0.145953
$36$		0			0
$37$		−	45.4869i		−	1.22938i	−0.788771	−	0.614688i	$-0.789282\pi$
$37$		−	45.4869i		−	1.22938i	0.788771	−	0.614688i	$-0.210718\pi$
$38$	−15.8185	−	22.3207i	−0.416277	−	0.587386i
$39$		0			0
$40$	−5.25590	−	18.3599i	−0.131398	−	0.458996i
$41$			78.0420i			1.90346i	0.306929	+	0.951732i	$0.400698\pi$
$41$			78.0420i			1.90346i	−0.306929	+	0.951732i	$0.599302\pi$
$42$		0			0
$43$			57.9466i			1.34760i	0.738916	+	0.673798i	$0.235338\pi$
$43$			57.9466i			1.34760i	−0.738916	+	0.673798i	$0.764662\pi$
$44$	11.0023	−	31.3300i	0.250053	−	0.712045i
$45$		0			0
$46$	38.6254	+	54.5023i	0.839684	+	1.18483i
$47$			33.0272i			0.702705i	0.936243	+	0.351353i	$0.114278\pi$
$47$			33.0272i			0.702705i	−0.936243	+	0.351353i	$0.885722\pi$
$48$		0			0
$49$	−44.4208			−0.906546
$50$	−31.4955	+	22.3207i	−0.629910	+	0.446414i
$51$		0			0
$52$	−47.0236	−	16.5136i	−0.904300	−	0.317569i
$53$	51.6254			0.974065			0.487033	−	0.873384i	$-0.338079\pi$
$53$	51.6254			0.974065			0.487033	+	0.873384i	$0.338079\pi$
$54$		0			0
$55$	19.8169			0.360307
$56$	−4.71152	−	16.4582i	−0.0841343	−	0.293897i
$57$		0			0
$58$	−10.9305	+	7.74641i	−0.188458	+	0.133559i
$59$	−30.6248			−0.519065			−0.259532	−	0.965734i	$-0.583568\pi$
$59$	−30.6248			−0.519065			−0.259532	+	0.965734i	$0.583568\pi$
$60$		0			0
$61$			29.7957i			0.488455i	0.969718	+	0.244227i	$0.0785343\pi$
$61$			29.7957i			0.488455i	−0.969718	+	0.244227i	$0.921466\pi$
$62$	69.0631	−	48.9446i	1.11392	−	0.789429i
$63$		0			0
$64$	−54.3048	+	33.8673i	−0.848512	+	0.529176i
$65$		−	29.7435i		−	0.457592i
$66$		0			0
$67$			107.786i			1.60874i	0.594129	+	0.804370i	$0.297497\pi$
$67$			107.786i			1.60874i	−0.594129	+	0.804370i	$0.702503\pi$
$68$	27.4078	+	9.62495i	0.403055	+	0.141543i
$69$		0			0
$70$	8.33565	−	5.90742i	0.119081	−	0.0843917i
$71$		−	37.3792i		−	0.526467i	−0.964732	−	0.263234i	$-0.915211\pi$
$71$		−	37.3792i		−	0.526467i	0.964732	−	0.263234i	$-0.0847890\pi$
$72$		0			0
$73$	−118.435			−1.62240			−0.811199	−	0.584771i	$-0.801184\pi$
$73$	−118.435			−1.62240			−0.811199	+	0.584771i	$0.801184\pi$
$74$	−52.6022	−	74.2242i	−0.710841	−	1.00303i
$75$		0			0
$76$	−51.6244	−	18.1293i	−0.679269	−	0.238543i
$77$	17.7644			0.230706
$78$		0			0
$79$	92.2725			1.16801			0.584003	−	0.811751i	$-0.301486\pi$
$79$	92.2725			1.16801			0.584003	+	0.811751i	$0.301486\pi$
$80$	−29.8083	−	23.8810i	−0.372603	−	0.298513i
$81$		0			0
$82$	90.2499	+	127.347i	1.10061	+	1.55301i
$83$	93.6374			1.12816			0.564081	−	0.825719i	$-0.309231\pi$
$83$	93.6374			1.12816			0.564081	+	0.825719i	$0.309231\pi$
$84$		0			0
$85$			17.3360i			0.203953i
$86$	67.0110	+	94.5556i	0.779198	+	1.09948i
$87$		0			0
$88$	−18.2775	−	63.8467i	−0.207699	−	0.725531i
$89$		−	48.2986i		−	0.542681i	−0.962483	−	0.271340i	$-0.912533\pi$
$89$		−	48.2986i		−	0.542681i	0.962483	−	0.271340i	$-0.0874669\pi$
$90$		0			0
$91$		−	26.6628i		−	0.292998i
$92$	126.056	+	44.2678i	1.37017	+	0.481172i
$93$		0			0
$94$	38.1935	+	53.8928i	0.406314	+	0.573327i
$95$		−	32.6536i		−	0.343722i
$96$		0			0
$97$	7.17272			0.0739456			0.0369728	−	0.999316i	$-0.488229\pi$
$97$	7.17272			0.0739456			0.0369728	+	0.999316i	$0.488229\pi$
$98$	−72.4845	+	51.3693i	−0.739638	+	0.524177i
$99$		0			0
$100$	−25.5813	+	72.8445i	−0.255813	+	0.728445i
$101$	−97.3277			−0.963640			−0.481820	−	0.876270i	$-0.660024\pi$
$101$	−97.3277			−0.963640			−0.481820	+	0.876270i	$0.660024\pi$
$102$		0			0
$103$	37.0236			0.359452			0.179726	−	0.983717i	$-0.442479\pi$
$103$	37.0236			0.359452			0.179726	+	0.983717i	$0.442479\pi$
$104$	−95.8285	+	27.4330i	−0.921428	+	0.263778i
$105$		0			0
$106$	84.2409	−	59.7010i	0.794726	−	0.563217i
$107$	−55.9279			−0.522690			−0.261345	−	0.965245i	$-0.584166\pi$
$107$	−55.9279			−0.522690			−0.261345	+	0.965245i	$0.584166\pi$
$108$		0			0
$109$		−	191.176i		−	1.75391i	−0.480575	−	0.876953i	$-0.659572\pi$
$109$		−	191.176i		−	1.75391i	0.480575	−	0.876953i	$-0.340428\pi$
$110$	32.3367	−	22.9168i	0.293970	−	0.208334i
$111$		0			0
$112$	−26.7208	−	21.4075i	−0.238579	−	0.191139i
$113$		−	18.5551i		−	0.164204i	−0.996624	−	0.0821022i	$-0.973837\pi$
$113$		−	18.5551i		−	0.164204i	0.996624	−	0.0821022i	$-0.0261634\pi$
$114$		0			0
$115$			79.7331i			0.693331i
$116$	−8.87800	+	25.2807i	−0.0765345	+	0.217937i
$117$		0			0
$118$	−49.9727	+	35.4154i	−0.423498	+	0.300130i
$119$			15.5404i			0.130592i
$120$		0			0
$121$	−52.0864			−0.430466
$122$	34.4566	+	48.6198i	0.282431	+	0.398523i
$123$		0			0
$124$	56.0944	−	159.733i	0.452374	−	1.28817i
$125$	−105.755			−0.846040
$126$		0			0
$127$	−7.15214			−0.0563161			−0.0281580	−	0.999603i	$-0.508964\pi$
$127$	−7.15214			−0.0563161			−0.0281580	+	0.999603i	$0.508964\pi$
$128$	−49.4480	+	118.063i	−0.386312	+	0.922368i
$129$		0			0
$130$	−34.3961	−	48.5346i	−0.264586	−	0.373343i
$131$	−154.209			−1.17717			−0.588584	−	0.808436i	$-0.700314\pi$
$131$	−154.209			−1.17717			−0.588584	+	0.808436i	$0.700314\pi$
$132$		0			0
$133$		−	29.2715i		−	0.220086i
$134$	124.646	+	175.881i	0.930194	+	1.31255i
$135$		0			0
$136$	55.8537	−	15.9893i	0.410689	−	0.117569i
$137$		−	196.321i		−	1.43300i	−0.697587	−	0.716501i	$-0.745743\pi$
$137$		−	196.321i		−	1.43300i	0.697587	−	0.716501i	$-0.254257\pi$
$138$		0			0
$139$		−	33.6235i		−	0.241896i	−0.992659	−	0.120948i	$-0.961407\pi$
$139$		−	33.6235i		−	0.241896i	0.992659	−	0.120948i	$-0.0385934\pi$
$140$	6.77037	−	19.2791i	0.0483598	−	0.137708i
$141$		0			0
$142$	−43.2263	−	60.9943i	−0.304410	−	0.429537i
$143$		−	103.433i		−	0.723311i
$144$		0			0
$145$	−15.9906			−0.110280
$146$	−193.259	+	136.961i	−1.32369	+	0.938091i
$147$		0			0
$148$	−171.670	−	60.2863i	−1.15993	−	0.407340i
$149$	165.496			1.11071			0.555355	−	0.831613i	$-0.312582\pi$
$149$	165.496			1.11071			0.555355	+	0.831613i	$0.312582\pi$
$150$		0			0
$151$	124.735			0.826062			0.413031	−	0.910717i	$-0.364470\pi$
$151$	124.735			0.826062			0.413031	+	0.910717i	$0.364470\pi$
$152$	−105.204	+	30.1170i	−0.692135	+	0.198138i
$153$		0			0
$154$	28.9874	−	20.5432i	0.188230	−	0.133397i
$155$	101.035			0.651836
$156$		0			0
$157$			24.9195i			0.158723i	0.996846	+	0.0793613i	$0.0252881\pi$
$157$			24.9195i			0.158723i	−0.996846	+	0.0793613i	$0.974712\pi$
$158$	150.568	−	106.706i	0.952959	−	0.675357i
$159$		0			0
$160$	−76.2569	−	4.49733i	−0.476606	−	0.0281083i
$161$			71.4747i			0.443942i
$162$		0			0
$163$		−	242.234i		−	1.48610i	−0.669237	−	0.743049i	$-0.733379\pi$
$163$		−	242.234i		−	1.48610i	0.669237	−	0.743049i	$-0.266621\pi$
$164$	294.534	+	103.433i	1.79594	+	0.630692i
$165$		0			0
$166$	152.795	−	108.285i	0.920451	−	0.652318i
$167$		−	286.351i		−	1.71468i	−0.514754	−	0.857338i	$-0.672117\pi$
$167$		−	286.351i		−	1.71468i	0.514754	−	0.857338i	$-0.327883\pi$
$168$		0			0
$169$	13.7552			0.0813914
$170$	20.0478	+	28.2884i	0.117928	+	0.166402i
$171$		0			0
$172$	218.693	+	76.7999i	1.27147	+	0.446511i
$173$	−291.447			−1.68467			−0.842333	−	0.538957i	$-0.818819\pi$
$173$	−291.447			−1.68467			−0.842333	+	0.538957i	$0.818819\pi$
$174$		0			0
$175$	−41.3034			−0.236020
$176$	−103.659	−	83.0467i	−0.588970	−	0.471856i
$177$		0			0
$178$	−55.8537	−	78.8122i	−0.313785	−	0.442765i
$179$	−45.9499			−0.256703			−0.128352	−	0.991729i	$-0.540969\pi$
$179$	−45.9499			−0.256703			−0.128352	+	0.991729i	$0.540969\pi$
$180$		0			0
$181$		−	54.7152i		−	0.302294i	−0.988511	−	0.151147i	$-0.951703\pi$
$181$		−	54.7152i		−	0.302294i	0.988511	−	0.151147i	$-0.0482967\pi$
$182$	−30.8335	−	43.5076i	−0.169415	−	0.239053i
$183$		0			0
$184$	256.887	−	73.5393i	1.39612	−	0.399670i
$185$		−	108.585i		−	0.586945i
$186$		0			0
$187$			60.2863i			0.322387i
$188$	124.646	+	43.7727i	0.663011	+	0.232834i
$189$		0			0
$190$	−37.7615	−	53.2832i	−0.198745	−	0.280438i
$191$			147.649i			0.773032i	0.922283	+	0.386516i	$0.126322\pi$
$191$			147.649i			0.773032i	−0.922283	+	0.386516i	$0.873678\pi$
$192$		0			0
$193$	250.933			1.30017			0.650085	−	0.759862i	$-0.274733\pi$
$193$	250.933			1.30017			0.650085	+	0.759862i	$0.274733\pi$
$194$	11.7042	−	8.29473i	0.0603312	−	0.0427563i
$195$		0			0
$196$	−58.8733	+	167.646i	−0.300374	+	0.855337i
$197$	326.156			1.65561			0.827807	−	0.561014i	$-0.189588\pi$
$197$	326.156			1.65561			0.827807	+	0.561014i	$0.189588\pi$
$198$		0			0
$199$	−100.185			−0.503443			−0.251721	−	0.967800i	$-0.580997\pi$
$199$	−100.185			−0.503443			−0.251721	+	0.967800i	$0.580997\pi$
$200$	42.4965	+	148.448i	0.212483	+	0.742242i
$201$		0			0
$202$	−158.816	+	112.552i	−0.786220	+	0.557189i
$203$	−14.3344			−0.0706128
$204$		0			0
$205$			186.300i			0.908778i
$206$	60.4141	−	42.8151i	0.293272	−	0.207840i
$207$		0			0
$208$	−124.646	+	155.583i	−0.599260	+	0.747995i
$209$		−	113.554i		−	0.543318i
$210$		0			0
$211$		−	52.3755i		−	0.248225i	−0.992268	−	0.124113i	$-0.960392\pi$
$211$		−	52.3755i		−	0.248225i	0.992268	−	0.124113i	$-0.0396084\pi$
$212$	68.4221	−	194.837i	0.322746	−	0.919042i
$213$		0			0
$214$	−91.2615	+	64.6765i	−0.426456	+	0.302227i
$215$			138.328i			0.643388i
$216$		0			0
$217$	90.5699			0.417373
$218$	−221.081	−	311.955i	−1.01413	−	1.43099i
$219$		0			0
$220$	26.2644	−	74.7899i	0.119384	−	0.339954i
$221$	90.4846			0.409433
$222$		0			0
$223$	−409.655			−1.83702			−0.918509	−	0.395401i	$-0.870606\pi$
$223$	−409.655			−1.83702			−0.918509	+	0.395401i	$0.870606\pi$
$224$	−68.3586	−	4.03152i	−0.305172	−	0.0179978i
$225$		0			0
$226$	−21.4576	−	30.2777i	−0.0949451	−	0.133972i
$227$	234.137			1.03144			0.515720	−	0.856757i	$-0.327525\pi$
$227$	234.137			1.03144			0.515720	+	0.856757i	$0.327525\pi$
$228$		0			0
$229$			127.829i			0.558204i	0.960261	+	0.279102i	$0.0900367\pi$
$229$			127.829i			0.558204i	−0.960261	+	0.279102i	$0.909963\pi$
$230$	92.2055	+	130.106i	0.400893	+	0.565679i
$231$		0			0
$232$	14.7485	+	51.5191i	0.0635709	+	0.222065i
$233$			270.437i			1.16067i	0.814377	+	0.580337i	$0.197079\pi$
$233$			270.437i			1.16067i	−0.814377	+	0.580337i	$0.802921\pi$
$234$		0			0
$235$			78.8414i			0.335495i
$236$	−40.5888	+	115.580i	−0.171986	+	0.489744i
$237$		0			0
$238$	17.9714	+	25.3584i	0.0755099	+	0.106548i
$239$		−	219.923i		−	0.920180i	−0.887872	−	0.460090i	$-0.847817\pi$
$239$		−	219.923i		−	0.920180i	0.887872	−	0.460090i	$-0.152183\pi$
$240$		0			0
$241$	−4.32503			−0.0179462			−0.00897309	−	0.999960i	$-0.502856\pi$
$241$	−4.32503			−0.0179462			−0.00897309	+	0.999960i	$0.502856\pi$
$242$	−84.9930	+	60.2340i	−0.351211	+	0.248901i
$243$		0			0
$244$	112.451	+	39.4900i	0.460863	+	0.161844i
$245$	−106.040			−0.432816
$246$		0			0
$247$	−170.434			−0.690017
$248$	−93.1861	−	325.517i	−0.375750	−	1.31257i
$249$		0			0
$250$	−172.568	+	122.298i	−0.690272	+	0.489191i
$251$	−255.378			−1.01744			−0.508722	−	0.860931i	$-0.669882\pi$
$251$	−255.378			−1.01744			−0.508722	+	0.860931i	$0.669882\pi$
$252$		0			0
$253$			277.273i			1.09594i
$254$	−11.6707	+	8.27092i	−0.0459475	+	0.0325627i
$255$		0			0
$256$	55.8435	+	249.835i	0.218139	+	0.975918i
$257$			280.931i			1.09311i	0.837422	+	0.546557i	$0.184062\pi$
$257$			280.931i			1.09311i	−0.837422	+	0.546557i	$0.815938\pi$
$258$		0			0
$259$		−	97.3381i		−	0.375823i
$260$	−112.253	−	39.4207i	−0.431743	−	0.151618i
$261$		0			0
$262$	−251.634	+	178.331i	−0.960434	+	0.680654i
$263$			439.925i			1.67272i	0.548182	+	0.836359i	$0.315320\pi$
$263$			439.925i			1.67272i	−0.548182	+	0.836359i	$0.684680\pi$
$264$		0			0
$265$	123.239			0.465052
$266$	−33.8503	−	47.7644i	−0.127257	−	0.179565i
$267$		0			0
$268$	406.788	+	142.854i	1.51786	+	0.533038i
$269$	−222.894			−0.828602			−0.414301	−	0.910140i	$-0.635974\pi$
$269$	−222.894			−0.828602			−0.414301	+	0.910140i	$0.635974\pi$
$270$		0			0
$271$	−35.2726			−0.130157			−0.0650787	−	0.997880i	$-0.520730\pi$
$271$	−35.2726			−0.130157			−0.0650787	+	0.997880i	$0.520730\pi$
$272$	72.6501	−	90.6817i	0.267096	−	0.333388i
$273$		0			0
$274$	−227.031	−	320.351i	−0.828580	−	1.16917i
$275$	−160.229			−0.582652
$276$		0			0
$277$			274.114i			0.989581i	0.869012	+	0.494791i	$0.164755\pi$
$277$			274.114i			0.989581i	−0.869012	+	0.494791i	$0.835245\pi$
$278$	−38.8831	−	54.8659i	−0.139867	−	0.197359i
$279$		0			0
$280$	−11.2472	−	39.2886i	−0.0401685	−	0.140316i
$281$			163.451i			0.581675i	0.956772	+	0.290838i	$0.0939340\pi$
$281$			163.451i			0.581675i	−0.956772	+	0.290838i	$0.906066\pi$
$282$		0			0
$283$		−	163.392i		−	0.577358i	−0.957426	−	0.288679i	$-0.906784\pi$
$283$		−	163.392i		−	0.577358i	0.957426	−	0.288679i	$-0.0932161\pi$
$284$	−141.071	−	49.5407i	−0.496728	−	0.174439i
$285$		0			0
$286$	−119.613	−	168.780i	−0.418228	−	0.590139i
$287$			167.003i			0.581894i
$288$		0			0
$289$	236.261			0.817512
$290$	−26.0931	+	18.4920i	−0.0899761	+	0.0637655i
$291$		0			0
$292$	−156.969	+	446.979i	−0.537563	+	1.53075i
$293$	375.244			1.28069			0.640347	−	0.768085i	$-0.278790\pi$
$293$	375.244			1.28069			0.640347	+	0.768085i	$0.278790\pi$
$294$		0			0
$295$	−73.1066			−0.247819
$296$	−349.842	+	100.150i	−1.18190	+	0.338344i
$297$		0			0
$298$	270.051	−	191.384i	0.906213	−	0.642228i
$299$	416.164			1.39185
$300$		0			0
$301$			124.001i			0.411963i
$302$	203.540	−	144.247i	0.673972	−	0.477640i
$303$		0			0
$304$	−136.842	+	170.805i	−0.450137	+	0.561860i
$305$			71.1275i			0.233205i
$306$		0			0
$307$			229.505i			0.747574i	0.927515	+	0.373787i	$0.121941\pi$
$307$			229.505i			0.747574i	−0.927515	+	0.373787i	$0.878059\pi$
$308$	23.5441	−	67.0435i	0.0764419	−	0.217674i
$309$		0			0
$310$	164.865	−	116.839i	0.531824	−	0.376900i
$311$			272.305i			0.875578i	0.899078	+	0.437789i	$0.144238\pi$
$311$			272.305i			0.875578i	−0.899078	+	0.437789i	$0.855762\pi$
$312$		0			0
$313$	346.204			1.10608			0.553042	−	0.833153i	$-0.313467\pi$
$313$	346.204			1.10608			0.553042	+	0.833153i	$0.313467\pi$
$314$	28.8175	+	40.6629i	0.0917755	+	0.129500i
$315$		0			0
$316$	122.294	−	348.241i	0.387006	−	1.10203i
$317$	−315.386			−0.994907			−0.497454	−	0.867491i	$-0.665732\pi$
$317$	−315.386			−0.994907			−0.497454	+	0.867491i	$0.665732\pi$
$318$		0			0
$319$	−55.6077			−0.174319
$320$	−129.635	+	80.8469i	−0.405108	+	0.252647i
$321$		0			0
$322$	82.6552	+	116.630i	0.256693	+	0.362206i
$323$	99.3377			0.307547
$324$		0			0
$325$			240.491i			0.739971i
$326$	−280.126	−	395.270i	−0.859281	−	1.21249i
$327$		0			0
$328$	600.226	−	171.827i	1.82996	−	0.523864i
$329$			70.6754i			0.214819i
$330$		0			0
$331$		−	410.306i		−	1.23959i	−0.784762	−	0.619797i	$-0.787215\pi$
$331$		−	410.306i		−	1.23959i	0.784762	−	0.619797i	$-0.212785\pi$
$332$	124.103	−	353.392i	0.373804	−	1.06443i
$333$		0			0
$334$	−331.144	−	467.259i	−0.991448	−	1.39898i
$335$			257.302i			0.768066i
$336$		0			0
$337$	−225.321			−0.668607			−0.334303	−	0.942465i	$-0.608501\pi$
$337$	−225.321			−0.668607			−0.334303	+	0.942465i	$0.608501\pi$
$338$	22.4453	−	15.9068i	0.0664061	−	0.0470616i
$339$		0			0
$340$	65.4269	+	22.9764i	0.192432	+	0.0675776i
$341$	351.350			1.03035
$342$		0			0
$343$	−199.913			−0.582836
$344$	445.671	−	127.583i	1.29555	−	0.370880i
$345$		0			0
$346$	−475.576	+	337.037i	−1.37450	+	0.974097i
$347$	94.0081			0.270917			0.135458	−	0.990783i	$-0.456749\pi$
$347$	94.0081			0.270917			0.135458	+	0.990783i	$0.456749\pi$
$348$		0			0
$349$		−	580.645i		−	1.66374i	−0.554971	−	0.831870i	$-0.687271\pi$
$349$		−	580.645i		−	1.66374i	0.554971	−	0.831870i	$-0.312729\pi$
$350$	−67.3978	+	47.7644i	−0.192565	+	0.136470i
$351$		0			0
$352$	−265.185	−	15.6395i	−0.753366	−	0.0444305i
$353$		−	280.478i		−	0.794556i	−0.917698	−	0.397278i	$-0.869955\pi$
$353$		−	280.478i		−	0.794556i	0.917698	−	0.397278i	$-0.130045\pi$
$354$		0			0
$355$		−	89.2304i		−	0.251353i
$356$	−182.281	−	64.0128i	−0.512025	−	0.179811i
$357$		0			0
$358$	−74.9797	+	53.1376i	−0.209440	+	0.148429i
$359$		−	419.954i		−	1.16979i	−0.811110	−	0.584894i	$-0.801136\pi$
$359$		−	419.954i		−	1.16979i	0.811110	−	0.584894i	$-0.198864\pi$
$360$		0			0
$361$	173.890			0.481691
$362$	−63.2741	−	89.2827i	−0.174790	−	0.246637i
$363$		0			0
$364$	−100.627	−	35.3377i	−0.276447	−	0.0970815i
$365$	−282.724			−0.774587
$366$		0			0
$367$	−34.1680			−0.0931009			−0.0465504	−	0.998916i	$-0.514823\pi$
$367$	−34.1680			−0.0931009			−0.0465504	+	0.998916i	$0.514823\pi$
$368$	334.138	−	417.070i	0.907983	−	1.13334i
$369$		0			0
$370$	−125.570	−	177.186i	−0.339380	−	0.478880i
$371$	110.474			0.297774
$372$		0			0
$373$		−	435.552i		−	1.16770i	−0.811861	−	0.583851i	$-0.801545\pi$
$373$		−	435.552i		−	1.16770i	0.811861	−	0.583851i	$-0.198455\pi$
$374$	69.7167	+	98.3735i	0.186408	+	0.263031i
$375$		0			0
$376$	254.014	−	72.7169i	0.675569	−	0.193396i
$377$			83.4624i			0.221386i
$378$		0			0
$379$		−	199.159i		−	0.525485i	−0.964866	−	0.262742i	$-0.915373\pi$
$379$		−	199.159i		−	0.525485i	0.964866	−	0.262742i	$-0.0846270\pi$
$380$	−123.236	−	43.2777i	−0.324306	−	0.113889i
$381$		0			0
$382$	170.745	+	240.929i	0.446977	+	0.630705i
$383$			118.062i			0.308257i	0.988051	+	0.154128i	$0.0492569\pi$
$383$			118.062i			0.308257i	−0.988051	+	0.154128i	$0.950743\pi$
$384$		0			0
$385$	42.4065			0.110147
$386$	409.465	−	290.185i	1.06079	−	0.751775i
$387$		0			0
$388$	9.50641	−	27.0702i	0.0245011	−	0.0697686i
$389$	309.791			0.796378			0.398189	−	0.917303i	$-0.369639\pi$
$389$	309.791			0.796378			0.398189	+	0.917303i	$0.369639\pi$
$390$		0			0
$391$	−242.561			−0.620362
$392$	97.8025	+	341.643i	0.249496	+	0.871537i
$393$		0			0
$394$	532.212	−	377.175i	1.35079	−	0.957297i
$395$	220.270			0.557646
$396$		0			0
$397$			509.118i			1.28241i	0.767368	+	0.641207i	$0.221566\pi$
$397$			509.118i			1.28241i	−0.767368	+	0.641207i	$0.778434\pi$
$398$	−163.479	+	115.857i	−0.410752	+	0.291097i
$399$		0			0
$400$	241.014	+	193.090i	0.602536	+	0.482724i
$401$			186.627i			0.465404i	0.972548	+	0.232702i	$0.0747566\pi$
$401$			186.627i			0.465404i	−0.972548	+	0.232702i	$0.925243\pi$
$402$		0			0
$403$		−	527.346i		−	1.30855i
$404$	−128.994	+	367.319i	−0.319292	+	0.909206i
$405$		0			0
$406$	−23.3905	+	16.5767i	−0.0576120	+	0.0408292i
$407$		−	377.606i		−	0.927779i
$408$		0			0
$409$	91.8228			0.224506			0.112253	−	0.993680i	$-0.464193\pi$
$409$	91.8228			0.224506			0.112253	+	0.993680i	$0.464193\pi$
$410$	215.442	+	303.998i	0.525468	+	0.741459i
$411$		0			0
$412$	49.0695	−	139.729i	0.119101	−	0.339148i
$413$	−65.5346			−0.158679
$414$		0			0
$415$	223.528			0.538623
$416$	−23.4736	+	398.020i	−0.0564270	+	0.956778i
$417$		0			0
$418$	−131.316	−	185.293i	−0.314154	−	0.443286i
$419$	−626.046			−1.49414			−0.747072	−	0.664743i	$-0.768541\pi$
$419$	−626.046			−1.49414			−0.747072	+	0.664743i	$0.768541\pi$
$420$		0			0
$421$		−	360.212i		−	0.855609i	−0.903871	−	0.427805i	$-0.859287\pi$
$421$		−	360.212i		−	0.855609i	0.903871	−	0.427805i	$-0.140713\pi$
$422$	−60.5684	−	85.4649i	−0.143527	−	0.202523i
$423$		0			0
$424$	−113.665	−	397.054i	−0.268078	−	0.936449i
$425$		−	140.170i		−	0.329812i
$426$		0			0
$427$			63.7604i			0.149322i
$428$	−74.1243	+	211.074i	−0.173188	+	0.493165i
$429$		0			0
$430$	159.967	+	225.720i	0.372015	+	0.524931i
$431$		−	50.4353i		−	0.117019i	−0.998287	−	0.0585096i	$-0.981365\pi$
$431$		−	50.4353i		−	0.117019i	0.998287	−	0.0585096i	$-0.0186348\pi$
$432$		0			0
$433$	217.525			0.502366			0.251183	−	0.967940i	$-0.419180\pi$
$433$	217.525			0.502366			0.251183	+	0.967940i	$0.419180\pi$
$434$	147.789	−	104.737i	0.340528	−	0.241330i
$435$		0			0
$436$	−721.507	−	253.376i	−1.65483	−	0.581138i
$437$	456.881			1.04550
$438$		0			0
$439$	297.599			0.677902			0.338951	−	0.940804i	$-0.389928\pi$
$439$	297.599			0.677902			0.338951	+	0.940804i	$0.389928\pi$
$440$	−43.6315	−	152.413i	−0.0991624	−	0.346393i
$441$		0			0
$442$	147.650	−	104.639i	0.334050	−	0.236739i
$443$	−473.512			−1.06888			−0.534438	−	0.845208i	$-0.679477\pi$
$443$	−473.512			−1.06888			−0.534438	+	0.845208i	$0.679477\pi$
$444$		0			0
$445$		−	115.297i		−	0.259094i
$446$	−668.463	+	473.736i	−1.49880	+	1.06219i
$447$		0			0
$448$	−116.208	+	72.4731i	−0.259392	+	0.161770i
$449$		−	601.508i		−	1.33966i	−0.742514	−	0.669831i	$-0.766367\pi$
$449$		−	601.508i		−	1.33966i	0.742514	−	0.669831i	$-0.233633\pi$
$450$		0			0
$451$			647.860i			1.43650i
$452$	−70.0278	−	24.5921i	−0.154929	−	0.0544073i
$453$		0			0
$454$	382.058	−	270.762i	0.841537	−	0.596392i
$455$		−	63.6486i		−	0.139887i
$456$		0			0
$457$	−316.434			−0.692415			−0.346208	−	0.938158i	$-0.612531\pi$
$457$	−316.434			−0.692415			−0.346208	+	0.938158i	$0.612531\pi$
$458$	147.824	+	208.587i	0.322761	+	0.455431i
$459$		0			0
$460$	300.916	+	105.675i	0.654166	+	0.229728i
$461$	−664.063			−1.44048			−0.720242	−	0.693723i	$-0.755969\pi$
$461$	−664.063			−1.44048			−0.720242	+	0.693723i	$0.755969\pi$
$462$		0			0
$463$	568.056			1.22690			0.613451	−	0.789733i	$-0.289781\pi$
$463$	568.056			1.22690			0.613451	+	0.789733i	$0.289781\pi$
$464$	83.6442	+	67.0120i	0.180268	+	0.144422i
$465$		0			0
$466$	312.740	+	441.291i	0.671117	+	0.946977i
$467$	−95.6187			−0.204751			−0.102375	−	0.994746i	$-0.532644\pi$
$467$	−95.6187			−0.204751			−0.102375	+	0.994746i	$0.532644\pi$
$468$		0			0
$469$			230.652i			0.491795i
$470$	91.1743	+	128.651i	0.193988	+	0.273726i
$471$		0			0
$472$	67.4276	+	235.537i	0.142855	+	0.499020i
$473$			481.039i			1.01700i
$474$		0			0
$475$			264.020i			0.555832i
$476$	58.6503	+	20.5966i	0.123215	+	0.0432702i
$477$		0			0
$478$	−254.325	−	358.864i	−0.532060	−	0.750762i
$479$		−	631.251i		−	1.31785i	−0.752208	−	0.658926i	$-0.771011\pi$
$479$		−	631.251i		−	1.31785i	0.752208	−	0.658926i	$-0.228989\pi$
$480$		0			0
$481$	−566.754			−1.17828
$482$	−7.05746	+	5.00158i	−0.0146420	+	0.0103767i
$483$		0			0
$484$	−69.0330	+	196.576i	−0.142630	+	0.406150i
$485$	17.1225			0.0353041
$486$		0			0
$487$	38.8713			0.0798179			0.0399089	−	0.999203i	$-0.487293\pi$
$487$	38.8713			0.0798179			0.0399089	+	0.999203i	$0.487293\pi$
$488$	229.161	−	65.6022i	0.469592	−	0.134431i
$489$		0			0
$490$	−173.033	+	122.627i	−0.353128	+	0.250260i
$491$	142.692			0.290615			0.145308	−	0.989387i	$-0.453583\pi$
$491$	142.692			0.290615			0.145308	+	0.989387i	$0.453583\pi$
$492$		0			0
$493$		−	48.6462i		−	0.0986738i
$494$	−278.110	+	197.095i	−0.562975	+	0.398977i
$495$		0			0
$496$	−528.494	−	423.406i	−1.06551	−	0.853641i
$497$		−	79.9883i		−	0.160942i
$498$		0			0
$499$		−	244.377i		−	0.489733i	−0.969557	−	0.244866i	$-0.921256\pi$
$499$		−	244.377i		−	0.489733i	0.969557	−	0.244866i	$-0.0787441\pi$
$500$	−140.163	+	399.124i	−0.280326	+	0.798249i
$501$		0			0
$502$	−416.719	+	295.326i	−0.830118	+	0.588299i
$503$		−	63.9435i		−	0.127124i	−0.997978	−	0.0635622i	$-0.979754\pi$
$503$		−	63.9435i		−	0.127124i	0.997978	−	0.0635622i	$-0.0202461\pi$
$504$		0			0
$505$	−232.338			−0.460074
$506$	320.646	+	452.447i	0.633688	+	0.894163i
$507$		0			0
$508$	−9.47913	+	26.9925i	−0.0186597	+	0.0531349i
$509$	−980.687			−1.92669			−0.963347	−	0.268258i	$-0.913552\pi$
$509$	−980.687			−1.92669			−0.963347	+	0.268258i	$0.913552\pi$
$510$		0			0
$511$	−253.441			−0.495971
$512$	380.040	+	343.095i	0.742265	+	0.670107i
$513$		0			0
$514$	324.875	+	458.414i	0.632053	+	0.891857i
$515$	88.3816			0.171615
$516$		0			0
$517$			274.172i			0.530314i
$518$	−112.564	−	158.834i	−0.217306	−	0.306629i
$519$		0			0
$520$	−228.759	+	65.4871i	−0.439921	+	0.125937i
$521$		−	649.111i		−	1.24589i	−0.782264	−	0.622947i	$-0.785935\pi$
$521$		−	649.111i		−	1.24589i	0.782264	−	0.622947i	$-0.214065\pi$
$522$		0			0
$523$			697.757i			1.33414i	0.744993	+	0.667072i	$0.232453\pi$
$523$			697.757i			1.33414i	−0.744993	+	0.667072i	$0.767547\pi$
$524$	−204.382	+	581.992i	−0.390041	+	1.11067i
$525$		0			0
$526$	508.741	+	717.857i	0.967187	+	1.36475i
$527$			307.364i			0.583233i
$528$		0			0
$529$	−586.606			−1.10890
$530$	201.097	−	142.516i	0.379429	−	0.268899i
$531$		0			0
$532$	−110.472	−	38.7951i	−0.207654	−	0.0729232i
$533$	972.383			1.82436
$534$		0			0
$535$	−133.509			−0.249550
$536$	828.985	−	237.315i	1.54661	−	0.442751i
$537$		0			0
$538$	−363.712	+	257.761i	−0.676045	+	0.479109i
$539$	−368.756			−0.684148
$540$		0			0
$541$		−	529.627i		−	0.978978i	−0.872009	−	0.489489i	$-0.837183\pi$
$541$		−	529.627i		−	0.978978i	0.872009	−	0.489489i	$-0.162817\pi$
$542$	−57.5569	+	40.7902i	−0.106194	+	0.0752587i
$543$		0			0
$544$	13.6816	−	231.986i	0.0251500	−	0.426445i
$545$		−	456.369i		−	0.837374i
$546$		0			0
$547$			636.266i			1.16319i	0.813478	+	0.581596i	$0.197571\pi$
$547$			636.266i			1.16319i	−0.813478	+	0.581596i	$0.802429\pi$
$548$	−740.925	−	260.195i	−1.35205	−	0.474809i
$549$		0			0
$550$	−261.458	+	185.293i	−0.475377	+	0.336897i
$551$			91.6285i			0.166295i
$552$		0			0
$553$	197.455			0.357062
$554$	316.993	+	447.291i	0.572189	+	0.807385i
$555$		0			0
$556$	−126.897	−	44.5631i	−0.228232	−	0.0801495i
$557$	−545.994			−0.980241			−0.490120	−	0.871655i	$-0.663047\pi$
$557$	−545.994			−0.980241			−0.490120	+	0.871655i	$0.663047\pi$
$558$		0			0
$559$	721.999			1.29159
$560$	−63.7872	−	51.1034i	−0.113906	−	0.0912561i
$561$		0			0
$562$	189.019	+	266.714i	0.336332	+	0.474581i
$563$	747.743			1.32814			0.664070	−	0.747670i	$-0.268828\pi$
$563$	747.743			1.32814			0.664070	+	0.747670i	$0.268828\pi$
$564$		0			0
$565$		−	44.2941i		−	0.0783967i
$566$	−188.951	−	266.619i	−0.333836	−	0.471059i
$567$		0			0
$568$	−287.486	+	82.2989i	−0.506136	+	0.144892i
$569$		−	654.879i		−	1.15093i	−0.817826	−	0.575465i	$-0.804821\pi$
$569$		−	654.879i		−	1.15093i	0.817826	−	0.575465i	$-0.195179\pi$
$570$		0			0
$571$			833.039i			1.45891i	0.684027	+	0.729456i	$0.260227\pi$
$571$			833.039i			1.45891i	−0.684027	+	0.729456i	$0.739773\pi$
$572$	−390.363	−	137.086i	−0.682453	−	0.239661i
$573$		0			0
$574$	193.127	+	272.511i	0.336459	+	0.474759i
$575$		−	644.681i		−	1.12118i
$576$		0			0
$577$	−737.547			−1.27824			−0.639122	−	0.769105i	$-0.720702\pi$
$577$	−737.547			−1.27824			−0.639122	+	0.769105i	$0.720702\pi$
$578$	385.524	−	273.218i	0.666996	−	0.472696i
$579$		0			0
$580$	−21.1933	+	60.3494i	−0.0365401	+	0.104051i
$581$	200.376			0.344882
$582$		0			0
$583$	428.565			0.735102
$584$	260.762	+	910.891i	0.446510	+	1.55974i
$585$		0			0
$586$	612.312	−	433.942i	1.04490	−	0.740515i
$587$	−196.742			−0.335164			−0.167582	−	0.985858i	$-0.553596\pi$
$587$	−196.742			−0.335164			−0.167582	+	0.985858i	$0.553596\pi$
$588$		0			0
$589$		−	578.942i		−	0.982923i
$590$	−119.293	+	84.5425i	−0.202192	+	0.143292i
$591$		0			0
$592$	−455.047	+	567.988i	−0.768660	+	0.959440i
$593$			589.277i			0.993722i	0.867830	+	0.496861i	$0.165514\pi$
$593$			589.277i			0.993722i	−0.867830	+	0.496861i	$0.834486\pi$
$594$		0			0
$595$			37.0976i			0.0623490i
$596$	219.341	−	624.589i	0.368022	−	1.04797i
$597$		0			0
$598$	679.084	−	481.263i	1.13559	−	0.804787i
$599$		−	503.416i		−	0.840428i	−0.907425	−	0.420214i	$-0.861955\pi$
$599$		−	503.416i		−	0.840428i	0.907425	−	0.420214i	$-0.138045\pi$
$600$		0			0
$601$	−402.529			−0.669766			−0.334883	−	0.942260i	$-0.608697\pi$
$601$	−402.529			−0.669766			−0.334883	+	0.942260i	$0.608697\pi$
$602$	143.398	+	202.341i	0.238203	+	0.336115i
$603$		0			0
$604$	165.319	−	470.757i	0.273707	−	0.779400i
$605$	−124.339			−0.205519
$606$		0			0
$607$	243.551			0.401237			0.200618	−	0.979669i	$-0.435705\pi$
$607$	243.551			0.401237			0.200618	+	0.979669i	$0.435705\pi$
$608$	−25.7703	+	436.962i	−0.0423854	+	0.718688i
$609$		0			0
$610$	82.2537	+	116.064i	0.134842	+	0.190269i
$611$	411.509			0.673501
$612$		0			0
$613$			8.10769i			0.0132263i	0.999978	+	0.00661313i	$0.00210504\pi$
$613$			8.10769i			0.0132263i	−0.999978	+	0.00661313i	$0.997895\pi$
$614$	265.406	+	374.500i	0.432257	+	0.609935i
$615$		0			0
$616$	−39.1123	−	136.627i	−0.0634940	−	0.221797i
$617$		−	665.164i		−	1.07806i	−0.842286	−	0.539031i	$-0.818791\pi$
$617$		−	665.164i		−	1.07806i	0.842286	−	0.539031i	$-0.181209\pi$
$618$		0			0
$619$		−	183.153i		−	0.295885i	−0.988996	−	0.147943i	$-0.952735\pi$
$619$		−	183.153i		−	0.295885i	0.988996	−	0.147943i	$-0.0472651\pi$
$620$	133.907	−	381.309i	0.215979	−	0.615015i
$621$		0			0
$622$	314.900	+	444.339i	0.506271	+	0.714371i
$623$		−	103.355i		−	0.165899i
$624$		0			0
$625$	230.081			0.368129
$626$	564.926	−	400.360i	0.902438	−	0.639553i
$627$		0			0
$628$	94.0472	+	33.0272i	0.149757	+	0.0525910i
$629$	330.333			0.525172
$630$		0			0
$631$	870.949			1.38027			0.690134	−	0.723681i	$-0.257551\pi$
$631$	870.949			1.38027			0.690134	+	0.723681i	$0.257551\pi$
$632$	−203.159	−	709.673i	−0.321454	−	1.12290i
$633$		0			0
$634$	−514.637	+	364.720i	−0.811730	+	0.575268i
$635$	−17.0734			−0.0268872
$636$		0			0
$637$			553.471i			0.868871i
$638$	−90.7391	+	64.3062i	−0.142224	+	0.100793i
$639$		0			0
$640$	−118.041	+	281.837i	−0.184439	+	0.440370i
$641$			1235.09i			1.92681i	0.268047	+	0.963406i	$0.413622\pi$
$641$			1235.09i			1.92681i	−0.268047	+	0.963406i	$0.586378\pi$
$642$		0			0
$643$		−	667.608i		−	1.03827i	−0.854692	−	0.519135i	$-0.826254\pi$
$643$		−	667.608i		−	1.03827i	0.854692	−	0.519135i	$-0.173746\pi$
$644$	269.749	+	94.7294i	0.418865	+	0.147095i
$645$		0			0
$646$	162.096	−	114.877i	0.250923	−	0.177828i
$647$			873.230i			1.34966i	0.737974	+	0.674830i	$0.235783\pi$
$647$			873.230i			1.34966i	−0.737974	+	0.674830i	$0.764217\pi$
$648$		0			0
$649$	−254.230			−0.391725
$650$	278.110	+	392.426i	0.427861	+	0.603732i
$651$		0			0
$652$	−914.202	−	321.046i	−1.40215	−	0.492402i
$653$	−225.426			−0.345215			−0.172608	−	0.984991i	$-0.555219\pi$
$653$	−225.426			−0.345215			−0.172608	+	0.984991i	$0.555219\pi$
$654$		0			0
$655$	−368.123			−0.562020
$656$	780.726	−	974.500i	1.19013	−	1.48552i
$657$		0			0
$658$	81.7308	+	115.326i	0.124211	+	0.175268i
$659$	−533.112			−0.808971			−0.404486	−	0.914544i	$-0.632549\pi$
$659$	−533.112			−0.808971			−0.404486	+	0.914544i	$0.632549\pi$
$660$		0			0
$661$		−	318.946i		−	0.482521i	−0.970460	−	0.241260i	$-0.922439\pi$
$661$		−	318.946i		−	0.482521i	0.970460	−	0.241260i	$-0.0775608\pi$
$662$	−474.488	−	669.525i	−0.716750	−	1.01137i
$663$		0			0
$664$	−206.164	−	720.171i	−0.310488	−	1.08459i
$665$		−	69.8760i		−	0.105077i
$666$		0			0
$667$		−	223.737i		−	0.335438i
$668$	−1080.70	−	379.517i	−1.61782	−	0.568139i
$669$		0			0
$670$	297.551	+	419.859i	0.444106	+	0.626654i
$671$			247.347i			0.368625i
$672$		0			0
$673$	−51.6517			−0.0767485			−0.0383743	−	0.999263i	$-0.512218\pi$
$673$	−51.6517			−0.0767485			−0.0383743	+	0.999263i	$0.512218\pi$
$674$	−367.672	+	260.567i	−0.545507	+	0.386597i
$675$		0			0
$676$	18.2305	−	51.9126i	0.0269682	−	0.0767938i
$677$	703.643			1.03935			0.519677	−	0.854363i	$-0.326052\pi$
$677$	703.643			1.03935			0.519677	+	0.854363i	$0.326052\pi$
$678$		0			0
$679$	15.3490			0.0226054
$680$	133.332	−	38.1692i	0.196077	−	0.0561312i
$681$		0			0
$682$	573.322	−	406.310i	0.840649	−	0.595762i
$683$	314.352			0.460252			0.230126	−	0.973161i	$-0.426086\pi$
$683$	314.352			0.460252			0.230126	+	0.973161i	$0.426086\pi$
$684$		0			0
$685$		−	468.652i		−	0.684163i
$686$	−326.212	+	231.184i	−0.475527	+	0.337003i
$687$		0			0
$688$	579.693	−	723.571i	0.842577	−	1.05170i
$689$		−	643.239i		−	0.933584i
$690$		0			0
$691$			803.400i			1.16266i	0.813667	+	0.581331i	$0.197468\pi$
$691$			803.400i			1.16266i	−0.813667	+	0.581331i	$0.802532\pi$
$692$	−386.272	+	1099.94i	−0.558196	+	1.58950i
$693$		0			0
$694$	153.400	−	108.713i	0.221037	−	0.156648i
$695$		−	80.2650i		−	0.115489i
$696$		0			0
$697$	−566.754			−0.813134
$698$	−671.473	−	947.480i	−0.961996	−	1.35742i
$699$		0			0
$700$	−54.7418	+	155.881i	−0.0782025	+	0.222687i
$701$	−338.315			−0.482618			−0.241309	−	0.970448i	$-0.577577\pi$
$701$	−338.315			−0.482618			−0.241309	+	0.970448i	$0.577577\pi$
$702$		0			0
$703$	−622.206			−0.885073
$704$	−450.807	+	281.147i	−0.640351	+	0.399356i
$705$		0			0
$706$	−324.353	−	457.677i	−0.459423	−	0.648267i
$707$	−208.273			−0.294587
$708$		0			0
$709$		−	912.778i		−	1.28742i	−0.765271	−	0.643708i	$-0.777395\pi$
$709$		−	912.778i		−	1.28742i	0.765271	−	0.643708i	$-0.222605\pi$
$710$	−103.188	−	145.604i	−0.145336	−	0.205076i
$711$		0			0
$712$	−371.467	+	106.340i	−0.521723	+	0.149354i
$713$			1413.65i			1.98268i
$714$		0			0
$715$		−	246.913i		−	0.345333i
$716$	−60.8999	+	173.417i	−0.0850557	+	0.242202i
$717$		0			0
$718$	−485.646	−	685.268i	−0.676387	−	0.954413i
$719$			774.391i			1.07704i	0.842613	+	0.538520i	$0.181016\pi$
$719$			774.391i			1.07704i	−0.842613	+	0.538520i	$0.818984\pi$
$720$		0			0
$721$	79.2274			0.109885
$722$	283.749	−	201.091i	0.393005	−	0.278520i
$723$		0			0
$724$	−206.498	−	72.5171i	−0.285218	−	0.100162i
$725$	129.292			0.178334
$726$		0			0
$727$	1056.26			1.45291			0.726453	−	0.687216i	$-0.241167\pi$
$727$	1056.26			1.45291			0.726453	+	0.687216i	$0.241167\pi$
$728$	−205.065	+	58.7042i	−0.281683	+	0.0806377i
$729$		0			0
$730$	−461.342	+	326.950i	−0.631975	+	0.447877i
$731$	−420.818			−0.575674
$732$		0			0
$733$			707.223i			0.964833i	0.875942	+	0.482417i	$0.160241\pi$
$733$			707.223i			0.964833i	−0.875942	+	0.482417i	$0.839759\pi$
$734$	−55.7544	+	39.5128i	−0.0759597	+	0.0538321i
$735$		0			0
$736$	62.9255	−	1066.97i	0.0854967	−	1.44969i
$737$			894.773i			1.21408i
$738$		0			0
$739$		−	280.734i		−	0.379883i	−0.981795	−	0.189942i	$-0.939170\pi$
$739$		−	280.734i		−	0.379883i	0.981795	−	0.189942i	$-0.0608299\pi$
$740$	−409.804	−	143.914i	−0.553790	−	0.194478i
$741$		0			0
$742$	180.269	−	127.755i	0.242950	−	0.172177i
$743$			869.278i			1.16996i	0.811049	+	0.584978i	$0.198897\pi$
$743$			869.278i			1.16996i	−0.811049	+	0.584978i	$0.801103\pi$
$744$		0			0
$745$	395.067			0.530291
$746$	−503.684	−	710.722i	−0.675180	−	0.952711i
$747$		0			0
$748$	227.523	+	79.9008i	0.304176	+	0.106819i
$749$	−119.681			−0.159788
$750$		0			0
$751$	667.106			0.888290			0.444145	−	0.895955i	$-0.353507\pi$
$751$	667.106			0.888290			0.444145	+	0.895955i	$0.353507\pi$
$752$	330.401	−	412.406i	0.439363	−	0.548412i
$753$		0			0
$754$	96.5182	+	136.192i	0.128008	+	0.180626i
$755$	297.765			0.394390
$756$		0			0
$757$		−	1058.12i		−	1.39778i	−0.715229	−	0.698890i	$-0.753678\pi$
$757$		−	1058.12i		−	1.39778i	0.715229	−	0.698890i	$-0.246322\pi$
$758$	−230.312	−	324.982i	−0.303842	−	0.428736i
$759$		0			0
$760$	−251.141	+	71.8944i	−0.330448	+	0.0945979i
$761$			158.378i			0.208118i	0.994571	+	0.104059i	$0.0331831\pi$
$761$			158.378i			0.208118i	−0.994571	+	0.104059i	$0.966817\pi$
$762$		0			0
$763$		−	409.100i		−	0.536173i
$764$	557.234	+	195.688i	0.729364	+	0.256136i
$765$		0			0
$766$	136.530	+	192.651i	0.178238	+	0.251502i
$767$			381.577i			0.497493i
$768$		0			0
$769$	426.768			0.554965			0.277482	−	0.960731i	$-0.410500\pi$
$769$	426.768			0.554965			0.277482	+	0.960731i	$0.410500\pi$
$770$	69.1977	−	49.0400i	0.0898672	−	0.0636883i
$771$		0			0
$772$	332.575	−	947.032i	0.430797	−	1.22673i
$773$	−20.8165			−0.0269295			−0.0134648	−	0.999909i	$-0.504286\pi$
$773$	−20.8165			−0.0269295			−0.0134648	+	0.999909i	$0.504286\pi$
$774$		0			0
$775$	−816.914			−1.05408
$776$	−15.7924	−	55.1658i	−0.0203510	−	0.0710900i
$777$		0			0
$778$	505.508	−	358.250i	0.649753	−	0.460476i
$779$	1067.52			1.37037
$780$		0			0
$781$		−	310.300i		−	0.397312i
$782$	−395.805	+	280.504i	−0.506144	+	0.358701i
$783$		0			0
$784$	554.676	+	444.381i	0.707495	+	0.566813i
$785$			59.4870i			0.0757796i
$786$		0			0
$787$			1189.19i			1.51104i	0.655128	+	0.755518i	$0.272615\pi$
$787$			1189.19i			1.51104i	−0.655128	+	0.755518i	$0.727385\pi$
$788$	432.273	−	1230.93i	0.548569	−	1.56209i
$789$		0			0
$790$	359.430	−	254.726i	0.454975	−	0.322438i
$791$		−	39.7063i		−	0.0501976i
$792$		0			0
$793$	371.247			0.468155
$794$	588.758	+	830.764i	0.741508	+	1.04630i
$795$		0			0
$796$	−132.781	+	378.103i	−0.166810	+	0.475004i
$797$	−857.988			−1.07652			−0.538261	−	0.842778i	$-0.680918\pi$
$797$	−857.988			−1.07652			−0.538261	+	0.842778i	$0.680918\pi$
$798$		0			0
$799$	−239.849			−0.300186
$800$	616.574	+	36.3631i	0.770718	+	0.0454539i
$801$		0			0
$802$	215.820	+	304.532i	0.269103	+	0.379716i
$803$	−983.179			−1.22438
$804$		0			0
$805$			170.622i			0.211953i
$806$	−609.837	−	860.508i	−0.756621	−	1.06763i
$807$		0			0
$808$	214.289	+	748.553i	0.265209	+	0.926427i
$809$			386.041i			0.477183i	0.971120	+	0.238591i	$0.0766857\pi$
$809$			386.041i			0.477183i	−0.971120	+	0.238591i	$0.923314\pi$
$810$		0			0
$811$		−	1343.34i		−	1.65639i	−0.560437	−	0.828197i	$-0.689367\pi$
$811$		−	1343.34i		−	1.65639i	0.560437	−	0.828197i	$-0.310633\pi$
$812$	−18.9982	+	54.0987i	−0.0233968	+	0.0666240i
$813$		0			0
$814$	−436.673	−	616.166i	−0.536454	−	0.756961i
$815$		−	578.253i		−	0.709513i
$816$		0			0
$817$	792.640			0.970184
$818$	149.834	−	106.186i	0.183171	−	0.129812i
$819$		0			0
$820$	703.103	+	246.913i	0.857443	+	0.301114i
$821$	1563.88			1.90484			0.952422	−	0.304782i	$-0.0985836\pi$
$821$	1563.88			1.90484			0.952422	+	0.304782i	$0.0985836\pi$
$822$		0			0
$823$	−748.077			−0.908964			−0.454482	−	0.890756i	$-0.650176\pi$
$823$	−748.077			−0.908964			−0.454482	+	0.890756i	$0.650176\pi$
$824$	−81.5160	−	284.751i	−0.0989271	−	0.345571i
$825$		0			0
$826$	−106.937	+	75.7859i	−0.129464	+	0.0917505i
$827$	−261.110			−0.315731			−0.157866	−	0.987461i	$-0.550461\pi$
$827$	−261.110			−0.315731			−0.157866	+	0.987461i	$0.550461\pi$
$828$		0			0
$829$			108.978i			0.131458i	0.997838	+	0.0657288i	$0.0209372\pi$
$829$			108.978i			0.131458i	−0.997838	+	0.0657288i	$0.979063\pi$
$830$	364.747	−	258.494i	0.439455	−	0.311439i
$831$		0			0
$832$	421.977	+	676.623i	0.507184	+	0.813248i
$833$		−	322.591i		−	0.387264i
$834$		0			0
$835$		−	683.568i		−	0.818644i
$836$	−428.556	−	150.499i	−0.512627	−	0.180023i
$837$		0			0
$838$	−1021.56	+	723.976i	−1.21905	+	0.863934i
$839$		−	758.470i		−	0.904017i	−0.892014	−	0.452008i	$-0.850708\pi$
$839$		−	758.470i		−	0.904017i	0.892014	−	0.452008i	$-0.149292\pi$
$840$		0			0
$841$	−796.129			−0.946646
$842$	−416.558	−	587.783i	−0.494725	−	0.698079i
$843$		0			0
$844$	−197.668	−	69.4162i	−0.234203	−	0.0822467i
$845$	32.8359			0.0388590
$846$		0			0
$847$	−111.460			−0.131594
$848$	−644.640	−	516.456i	−0.760189	−	0.609029i
$849$		0			0
$850$	−162.096	−	228.726i	−0.190702	−	0.269089i
$851$	1519.29			1.78530
$852$		0			0
$853$			1581.97i			1.85459i	0.374329	+	0.927296i	$0.377873\pi$
$853$			1581.97i			1.85459i	−0.374329	+	0.927296i	$0.622127\pi$
$854$	73.7342	+	104.042i	0.0863398	+	0.121830i
$855$		0			0
$856$	123.138	+	430.145i	0.143853	+	0.502505i
$857$			583.334i			0.680670i	0.940304	+	0.340335i	$0.110540\pi$
$857$			583.334i			0.680670i	−0.940304	+	0.340335i	$0.889460\pi$
$858$		0			0
$859$		−	88.9294i		−	0.103527i	−0.998659	−	0.0517633i	$-0.983516\pi$
$859$		−	88.9294i		−	0.103527i	0.998659	−	0.0517633i	$-0.0164841\pi$
$860$	522.058	+	183.334i	0.607044	+	0.213179i
$861$		0			0
$862$	−58.3247	−	82.2989i	−0.0676621	−	0.0954743i
$863$			1185.55i			1.37376i	0.726771	+	0.686880i	$0.241020\pi$
$863$			1185.55i			1.37376i	−0.726771	+	0.686880i	$0.758980\pi$
$864$		0			0
$865$	−695.734			−0.804317
$866$	354.950	−	251.551i	0.409873	−	0.290475i
$867$		0			0
$868$	120.037	−	341.815i	0.138292	−	0.393796i
$869$	765.993			0.881465
$870$		0			0
$871$	1342.98			1.54188
$872$	−1470.34	+	420.918i	−1.68618	+	0.482704i
$873$		0			0
$874$	745.526	−	528.350i	0.853005	−	0.604519i
$875$	−226.307			−0.258636
$876$		0			0
$877$		−	149.575i		−	0.170553i	−0.996357	−	0.0852766i	$-0.972823\pi$
$877$		−	149.575i		−	0.170553i	0.996357	−	0.0852766i	$-0.0271774\pi$
$878$	485.614	−	344.151i	0.553091	−	0.391972i
$879$		0			0
$880$	−247.451	−	198.247i	−0.281194	−	0.225280i
$881$		−	929.138i		−	1.05464i	−0.849667	−	0.527320i	$-0.823197\pi$
$881$		−	929.138i		−	1.05464i	0.849667	−	0.527320i	$-0.176803\pi$
$882$		0			0
$883$		−	893.568i		−	1.01197i	−0.862543	−	0.505984i	$-0.831129\pi$
$883$		−	893.568i		−	1.01197i	0.862543	−	0.505984i	$-0.168871\pi$
$884$	119.924	−	341.493i	0.135661	−	0.386304i
$885$		0			0
$886$	−772.663	+	547.582i	−0.872081	+	0.618038i
$887$			383.356i			0.432193i	0.976372	+	0.216097i	$0.0693327\pi$
$887$			383.356i			0.432193i	−0.976372	+	0.216097i	$0.930667\pi$
$888$		0			0
$889$	−15.3050			−0.0172160
$890$	−133.332	−	188.138i	−0.149812	−	0.211391i
$891$		0			0
$892$	−542.939	+	1546.06i	−0.608676	+	1.73325i
$893$	451.772			0.505904
$894$		0			0
$895$	−109.690			−0.122559
$896$	−105.815	+	252.645i	−0.118097	+	0.281970i
$897$		0			0
$898$	−695.600	−	981.523i	−0.774610	−	1.09301i
$899$	−283.511			−0.315362
$900$		0			0
$901$			374.912i			0.416107i
$902$	749.203	+	1057.16i	0.830601	+	1.17202i
$903$		0			0
$904$	−142.708	+	40.8533i	−0.157863	+	0.0451917i
$905$		−	130.614i		−	0.144325i
$906$		0			0
$907$			1578.61i			1.74047i	0.492634	+	0.870237i	$0.336034\pi$
$907$			1578.61i			1.74047i	−0.492634	+	0.870237i	$0.663966\pi$
$908$	310.315	−	883.643i	0.341756	−	0.973176i
$909$		0			0
$910$	−73.6049	−	103.860i	−0.0808845	−	0.114132i
$911$		−	421.187i		−	0.462335i	−0.972914	−	0.231167i	$-0.925746\pi$
$911$		−	421.187i		−	0.462335i	0.972914	−	0.231167i	$-0.0742545\pi$
$912$		0			0
$913$	777.324			0.851396
$914$	−516.347	+	365.932i	−0.564932	+	0.400364i
$915$		0			0
$916$	482.432	+	169.419i	0.526672	+	0.184955i
$917$	−329.994			−0.359863
$918$		0			0
$919$	−1529.64			−1.66446			−0.832229	−	0.554432i	$-0.812935\pi$
$919$	−1529.64			−1.66446			−0.832229	+	0.554432i	$0.812935\pi$
$920$	613.232	−	175.551i	0.666557	−	0.190816i
$921$		0			0
$922$	−1083.60	+	767.940i	−1.17527	+	0.832907i
$923$	−465.735			−0.504588
$924$		0			0
$925$			877.962i			0.949148i
$926$	926.937	−	656.915i	1.00101	−	0.709411i
$927$		0			0
$928$	213.983	+	12.6198i	0.230585	+	0.0135990i
$929$		−	225.336i		−	0.242557i	−0.992618	−	0.121279i	$-0.961301\pi$
$929$		−	225.336i		−	0.242557i	0.992618	−	0.121279i	$-0.0386995\pi$
$930$		0			0
$931$			607.623i			0.652656i
$932$	1020.64	+	358.425i	1.09511	+	0.384576i
$933$		0			0
$934$	−156.028	+	110.576i	−0.167053	+	0.118390i
$935$			143.914i			0.153918i
$936$		0			0
$937$	721.082			0.769565			0.384782	−	0.923007i	$-0.374277\pi$
$937$	721.082			0.769565			0.384782	+	0.923007i	$0.374277\pi$
$938$	266.732	+	376.371i	0.284363	+	0.401249i
$939$		0			0
$940$	297.551	+	104.493i	0.316544	+	0.111163i
$941$	−1206.99			−1.28267			−0.641334	−	0.767262i	$-0.721619\pi$
$941$	−1206.99			−1.28267			−0.641334	+	0.767262i	$0.721619\pi$
$942$		0			0
$943$	−2606.66			−2.76422
$944$	382.408	+	306.368i	0.405093	+	0.324542i
$945$		0			0
$946$	556.287	+	784.946i	0.588041	+	0.829753i
$947$	250.529			0.264550			0.132275	−	0.991213i	$-0.457772\pi$
$947$	250.529			0.264550			0.132275	+	0.991213i	$0.457772\pi$
$948$		0			0
$949$			1475.67i			1.55497i
$950$	305.320	+	430.821i	0.321390	+	0.453496i
$951$		0			0
$952$	119.522	−	34.2158i	0.125549	−	0.0359410i
$953$			187.703i			0.196960i	0.995139	+	0.0984800i	$0.0313981\pi$
$953$			187.703i			0.196960i	−0.995139	+	0.0984800i	$0.968602\pi$
$954$		0			0
$955$			352.463i			0.369071i
$956$	−830.000	−	291.476i	−0.868201	−	0.304892i
$957$		0			0
$958$	−729.996	−	1030.06i	−0.762000	−	1.07522i
$959$		−	420.111i		−	0.438072i
$960$		0			0
$961$	830.323			0.864020
$962$	−924.813	+	655.410i	−0.961344	+	0.681299i
$963$		0			0
$964$	−5.73220	+	16.3229i	−0.00594627	+	0.0169324i
$965$	599.019			0.620745
$966$		0			0
$967$	−820.459			−0.848458			−0.424229	−	0.905555i	$-0.639455\pi$
$967$	−820.459			−0.848458			−0.424229	+	0.905555i	$0.639455\pi$
$968$	114.680	+	400.599i	0.118471	+	0.413842i
$969$		0			0
$970$	27.9400	−	19.8009i	0.0288041	−	0.0204133i
$971$	1402.07			1.44394			0.721971	−	0.691923i	$-0.243236\pi$
$971$	1402.07			1.44394			0.721971	+	0.691923i	$0.243236\pi$
$972$		0			0
$973$		−	71.9515i		−	0.0739481i
$974$	63.4291	−	44.9518i	0.0651223	−	0.0461517i
$975$		0			0
$976$	298.074	−	372.055i	0.305404	−	0.381204i
$977$			481.735i			0.493075i	0.969133	+	0.246538i	$0.0792929\pi$
$977$			481.735i			0.493075i	−0.969133	+	0.246538i	$0.920707\pi$
$978$		0			0
$979$		−	400.947i		−	0.409547i
$980$	−140.541	+	400.199i	−0.143409	+	0.408367i
$981$		0			0
$982$	232.841	−	165.013i	0.237109	−	0.168038i
$983$		−	599.752i		−	0.610124i	−0.952332	−	0.305062i	$-0.901323\pi$
$983$		−	599.752i		−	0.610124i	0.952332	−	0.305062i	$-0.0986773\pi$
$984$		0			0
$985$	778.589			0.790446
$986$	−56.2557	−	79.3794i	−0.0570545	−	0.0805065i
$987$		0			0
$988$	−225.886	+	643.227i	−0.228629	+	0.651039i
$989$	−1935.46			−1.95698
$990$		0			0
$991$	805.265			0.812578			0.406289	−	0.913745i	$-0.366823\pi$
$991$	805.265			0.812578			0.406289	+	0.913745i	$0.366823\pi$
$992$	−1352.02	−	79.7367i	−1.36292	−	0.0803798i
$993$		0			0
$994$	−92.5006	−	130.523i	−0.0930590	−	0.131311i
$995$	−239.159			−0.240361
$996$		0			0
$997$			542.742i			0.544375i	0.962244	+	0.272187i	$0.0877471\pi$
$997$			542.742i			0.544375i	−0.962244	+	0.272187i	$0.912253\pi$
$998$	−282.604	−	398.767i	−0.283170	−	0.399566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.d.53.5	yes	6
3.2	odd	2		216.3.h.c.53.2	yes	6
4.3	odd	2		864.3.h.d.593.3		6
8.3	odd	2		864.3.h.c.593.4		6
8.5	even	2		216.3.h.c.53.1	✓	6
12.11	even	2		864.3.h.c.593.3		6
24.5	odd	2	inner	216.3.h.d.53.6	yes	6
24.11	even	2		864.3.h.d.593.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.c.53.1	✓	6	8.5	even	2
216.3.h.c.53.2	yes	6	3.2	odd	2
216.3.h.d.53.5	yes	6	1.1	even	1	trivial
216.3.h.d.53.6	yes	6	24.5	odd	2	inner
864.3.h.c.593.3		6	12.11	even	2
864.3.h.c.593.4		6	8.3	odd	2
864.3.h.d.593.3		6	4.3	odd	2
864.3.h.d.593.4		6	24.11	even	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63177 - 1.15643i) q^{2} +(1.32536 - 3.77405i) q^{4} +2.38717 q^{5} +2.13992 q^{7} +(-2.20173 - 7.69106i) q^{8} +O(q^{10})\)	\(q+(1.63177 - 1.15643i) q^{2} +(1.32536 - 3.77405i) q^{4} +2.38717 q^{5} +2.13992 q^{7} +(-2.20173 - 7.69106i) q^{8} +(3.89531 - 2.76059i) q^{10} +8.30142 q^{11} -12.4597i q^{13} +(3.49185 - 2.47466i) q^{14} +(-12.4869 - 10.0039i) q^{16} +7.26216i q^{17} -13.6788i q^{19} +(3.16385 - 9.00929i) q^{20} +(13.5460 - 9.59999i) q^{22} +33.4007i q^{23} -19.3014 q^{25} +(-14.4088 - 20.3314i) q^{26} +(2.83615 - 8.07615i) q^{28} -6.69858 q^{29} +42.3240 q^{31} +(-31.9445 - 1.88396i) q^{32} +(8.39816 + 11.8502i) q^{34} +5.10834 q^{35} -45.4869i q^{37} +(-15.8185 - 22.3207i) q^{38} +(-5.25590 - 18.3599i) q^{40} +78.0420i q^{41} +57.9466i q^{43} +(11.0023 - 31.3300i) q^{44} +(38.6254 + 54.5023i) q^{46} +33.0272i q^{47} -44.4208 q^{49} +(-31.4955 + 22.3207i) q^{50} +(-47.0236 - 16.5136i) q^{52} +51.6254 q^{53} +19.8169 q^{55} +(-4.71152 - 16.4582i) q^{56} +(-10.9305 + 7.74641i) q^{58} -30.6248 q^{59} +29.7957i q^{61} +(69.0631 - 48.9446i) q^{62} +(-54.3048 + 33.8673i) q^{64} -29.7435i q^{65} +107.786i q^{67} +(27.4078 + 9.62495i) q^{68} +(8.33565 - 5.90742i) q^{70} -37.3792i q^{71} -118.435 q^{73} +(-52.6022 - 74.2242i) q^{74} +(-51.6244 - 18.1293i) q^{76} +17.7644 q^{77} +92.2725 q^{79} +(-29.8083 - 23.8810i) q^{80} +(90.2499 + 127.347i) q^{82} +93.6374 q^{83} +17.3360i q^{85} +(67.0110 + 94.5556i) q^{86} +(-18.2775 - 63.8467i) q^{88} -48.2986i q^{89} -26.6628i q^{91} +(126.056 + 44.2678i) q^{92} +(38.1935 + 53.8928i) q^{94} -32.6536i q^{95} +7.17272 q^{97} +(-72.4845 + 51.3693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 7 q^{4} + 2 q^{5} - 10 q^{7} + 7 q^{8}+O(q^{10}) \) 6 * q + q^2 - 7 * q^4 + 2 * q^5 - 10 * q^7 + 7 * q^8	\( 6 q + q^{2} - 7 q^{4} + 2 q^{5} - 10 q^{7} + 7 q^{8} - 3 q^{10} - 10 q^{11} + 35 q^{14} - 23 q^{16} + 41 q^{20} + 25 q^{22} - 56 q^{25} - 60 q^{26} - 5 q^{28} - 100 q^{29} + 6 q^{31} - 29 q^{32} - 4 q^{34} - 110 q^{35} + 132 q^{38} + 59 q^{40} + 125 q^{44} - 76 q^{46} - 24 q^{49} - 36 q^{50} + 80 q^{52} + 2 q^{53} + 170 q^{55} - 175 q^{56} + 10 q^{58} + 20 q^{59} + 191 q^{62} - 151 q^{64} + 312 q^{68} + 115 q^{70} + 130 q^{73} - 300 q^{74} - 176 q^{76} - 50 q^{77} - 76 q^{79} - 331 q^{80} + 100 q^{82} + 38 q^{83} + 360 q^{86} - 5 q^{88} + 408 q^{92} + 240 q^{94} - 70 q^{97} - 324 q^{98}+O(q^{100}) \) 6 * q + q^2 - 7 * q^4 + 2 * q^5 - 10 * q^7 + 7 * q^8 - 3 * q^10 - 10 * q^11 + 35 * q^14 - 23 * q^16 + 41 * q^20 + 25 * q^22 - 56 * q^25 - 60 * q^26 - 5 * q^28 - 100 * q^29 + 6 * q^31 - 29 * q^32 - 4 * q^34 - 110 * q^35 + 132 * q^38 + 59 * q^40 + 125 * q^44 - 76 * q^46 - 24 * q^49 - 36 * q^50 + 80 * q^52 + 2 * q^53 + 170 * q^55 - 175 * q^56 + 10 * q^58 + 20 * q^59 + 191 * q^62 - 151 * q^64 + 312 * q^68 + 115 * q^70 + 130 * q^73 - 300 * q^74 - 176 * q^76 - 50 * q^77 - 76 * q^79 - 331 * q^80 + 100 * q^82 + 38 * q^83 + 360 * q^86 - 5 * q^88 + 408 * q^92 + 240 * q^94 - 70 * q^97 - 324 * q^98

Introduction

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