LMFDB - Embedded newform 1470.2.g.j.589.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(589,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1470.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.g (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.1
Root			$-1.69230i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.j.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.18183 + 0.489528i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.18183 + 0.489528i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(0.489528 + 2.18183i) q^{10} -2.39327 q^{11} +1.00000i q^{12} -3.80748i q^{13} +(0.489528 + 2.18183i) q^{15} +1.00000 q^{16} +1.97038i q^{17} +1.00000i q^{18} -4.17113 q^{19} +(2.18183 - 0.489528i) q^{20} +2.39327i q^{22} +8.17113i q^{23} +1.00000 q^{24} +(4.52072 - 2.13613i) q^{25} -3.80748 q^{26} +1.00000i q^{27} +9.16246 q^{29} +(2.18183 - 0.489528i) q^{30} -1.60673 q^{31} -1.00000i q^{32} +2.39327i q^{33} +1.97038 q^{34} +1.00000 q^{36} -1.26358i q^{37} +4.17113i q^{38} -3.80748 q^{39} +(-0.489528 - 2.18183i) q^{40} +3.19208 q^{41} +4.90755i q^{43} +2.39327 q^{44} +(2.18183 - 0.489528i) q^{45} +8.17113 q^{46} +3.00868i q^{47} -1.00000i q^{48} +(-2.13613 - 4.52072i) q^{50} +1.97038 q^{51} +3.80748i q^{52} +12.1711i q^{53} +1.00000 q^{54} +(5.22170 - 1.17157i) q^{55} +4.17113i q^{57} -9.16246i q^{58} +13.0414 q^{59} +(-0.489528 - 2.18183i) q^{60} -13.0910 q^{61} +1.60673i q^{62} -1.00000 q^{64} +(1.86387 + 8.30726i) q^{65} +2.39327 q^{66} +5.77786i q^{67} -1.97038i q^{68} +8.17113 q^{69} +6.94032 q^{71} -1.00000i q^{72} +0.506664i q^{73} -1.26358 q^{74} +(-2.13613 - 4.52072i) q^{75} +4.17113 q^{76} +3.80748i q^{78} +12.4260 q^{79} +(-2.18183 + 0.489528i) q^{80} +1.00000 q^{81} -3.19208i q^{82} +1.89887i q^{83} +(-0.964557 - 4.29903i) q^{85} +4.90755 q^{86} -9.16246i q^{87} -2.39327i q^{88} +1.97949 q^{89} +(-0.489528 - 2.18183i) q^{90} -8.17113i q^{92} +1.60673i q^{93} +3.00868 q^{94} +(9.10069 - 2.04189i) q^{95} -1.00000 q^{96} +12.0624i q^{97} +2.39327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} + 8 q^{16} + 24 q^{19} + 4 q^{20} + 8 q^{24} + 4 q^{25} + 16 q^{29} + 4 q^{30} - 32 q^{31} + 8 q^{34} + 8 q^{36} - 24 q^{41} + 4 q^{45} + 8 q^{46} - 4 q^{50} + 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 8 q^{64} + 28 q^{65} + 8 q^{69} - 40 q^{71} + 16 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 4 q^{80} + 8 q^{81} + 28 q^{85} + 8 q^{86} + 88 q^{89} + 24 q^{94} + 24 q^{95} - 8 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 + 8 * q^16 + 24 * q^19 + 4 * q^20 + 8 * q^24 + 4 * q^25 + 16 * q^29 + 4 * q^30 - 32 * q^31 + 8 * q^34 + 8 * q^36 - 24 * q^41 + 4 * q^45 + 8 * q^46 - 4 * q^50 + 8 * q^51 + 8 * q^54 + 40 * q^59 - 24 * q^61 - 8 * q^64 + 28 * q^65 + 8 * q^69 - 40 * q^71 + 16 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 4 * q^80 + 8 * q^81 + 28 * q^85 + 8 * q^86 + 88 * q^89 + 24 * q^94 + 24 * q^95 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−2.18183	+	0.489528i	−0.975742	+	0.218924i
$5$	−2.18183	+	0.489528i	−0.975742	+	0.218924i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	0.489528	+	2.18183i	0.154802	+	0.689954i
$11$	−2.39327			−0.721598			−0.360799	−	0.932644i	$-0.617496\pi$
$11$	−2.39327			−0.721598			−0.360799	+	0.932644i	$0.617496\pi$
$12$			1.00000i			0.288675i
$13$		−	3.80748i		−	1.05601i	−0.849243	−	0.528003i	$-0.822941\pi$
$13$		−	3.80748i		−	1.05601i	0.849243	−	0.528003i	$-0.177059\pi$
$14$		0			0
$15$	0.489528	+	2.18183i	0.126396	+	0.563345i
$16$	1.00000			0.250000
$17$			1.97038i			0.477888i	0.971033	+	0.238944i	$0.0768012\pi$
$17$			1.97038i			0.477888i	−0.971033	+	0.238944i	$0.923199\pi$
$18$			1.00000i			0.235702i
$19$	−4.17113			−0.956924			−0.478462	−	0.878108i	$-0.658806\pi$
$19$	−4.17113			−0.956924			−0.478462	+	0.878108i	$0.658806\pi$
$20$	2.18183	−	0.489528i	0.487871	−	0.109462i
$21$		0			0
$22$			2.39327i			0.510247i
$23$			8.17113i			1.70380i	0.523705	+	0.851900i	$0.324549\pi$
$23$			8.17113i			1.70380i	−0.523705	+	0.851900i	$0.675451\pi$
$24$	1.00000			0.204124
$25$	4.52072	−	2.13613i	0.904145	−	0.427226i
$26$	−3.80748			−0.746709
$27$			1.00000i			0.192450i
$28$		0			0
$29$	9.16246			1.70143			0.850713	−	0.525631i	$-0.176171\pi$
$29$	9.16246			1.70143			0.850713	+	0.525631i	$0.176171\pi$
$30$	2.18183	−	0.489528i	0.398345	−	0.0893752i
$31$	−1.60673			−0.288577			−0.144289	−	0.989536i	$-0.546089\pi$
$31$	−1.60673			−0.288577			−0.144289	+	0.989536i	$0.546089\pi$
$32$		−	1.00000i		−	0.176777i
$33$			2.39327i			0.416615i
$34$	1.97038			0.337918
$35$		0			0
$36$	1.00000			0.166667
$37$		−	1.26358i		−	0.207732i	−0.994591	−	0.103866i	$-0.966879\pi$
$37$		−	1.26358i		−	0.207732i	0.994591	−	0.103866i	$-0.0331213\pi$
$38$			4.17113i			0.676647i
$39$	−3.80748			−0.609685
$40$	−0.489528	−	2.18183i	−0.0774012	−	0.344977i
$41$	3.19208			0.498519			0.249259	−	0.968437i	$-0.419813\pi$
$41$	3.19208			0.498519			0.249259	+	0.968437i	$0.419813\pi$
$42$		0			0
$43$			4.90755i			0.748394i	0.927349	+	0.374197i	$0.122082\pi$
$43$			4.90755i			0.748394i	−0.927349	+	0.374197i	$0.877918\pi$
$44$	2.39327			0.360799
$45$	2.18183	−	0.489528i	0.325247	−	0.0729745i
$46$	8.17113			1.20477
$47$			3.00868i			0.438860i	0.975628	+	0.219430i	$0.0704198\pi$
$47$			3.00868i			0.438860i	−0.975628	+	0.219430i	$0.929580\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	−2.13613	−	4.52072i	−0.302094	−	0.639327i
$51$	1.97038			0.275909
$52$			3.80748i			0.528003i
$53$			12.1711i			1.67183i	0.548856	+	0.835917i	$0.315064\pi$
$53$			12.1711i			1.67183i	−0.548856	+	0.835917i	$0.684936\pi$
$54$	1.00000			0.136083
$55$	5.22170	−	1.17157i	0.704093	−	0.157975i
$56$		0			0
$57$			4.17113i			0.552480i
$58$		−	9.16246i		−	1.20309i
$59$	13.0414			1.69785			0.848926	−	0.528512i	$-0.177250\pi$
$59$	13.0414			1.69785			0.848926	+	0.528512i	$0.177250\pi$
$60$	−0.489528	−	2.18183i	−0.0631978	−	0.281672i
$61$	−13.0910			−1.67612			−0.838062	−	0.545574i	$-0.816312\pi$
$61$	−13.0910			−1.67612			−0.838062	+	0.545574i	$0.816312\pi$
$62$			1.60673i			0.204055i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.86387	+	8.30726i	0.231185	+	1.03039i
$66$	2.39327			0.294591
$67$			5.77786i			0.705878i	0.935646	+	0.352939i	$0.114818\pi$
$67$			5.77786i			0.705878i	−0.935646	+	0.352939i	$0.885182\pi$
$68$		−	1.97038i		−	0.238944i
$69$	8.17113			0.983689
$70$		0			0
$71$	6.94032			0.823665			0.411832	−	0.911260i	$-0.364889\pi$
$71$	6.94032			0.823665			0.411832	+	0.911260i	$0.364889\pi$
$72$		−	1.00000i		−	0.117851i
$73$			0.506664i			0.0593005i	0.999560	+	0.0296503i	$0.00943935\pi$
$73$			0.506664i			0.0593005i	−0.999560	+	0.0296503i	$0.990561\pi$
$74$	−1.26358			−0.146889
$75$	−2.13613	−	4.52072i	−0.246659	−	0.522008i
$76$	4.17113			0.478462
$77$		0			0
$78$			3.80748i			0.431113i
$79$	12.4260			1.39804			0.699020	−	0.715103i	$-0.253620\pi$
$79$	12.4260			1.39804			0.699020	+	0.715103i	$0.253620\pi$
$80$	−2.18183	+	0.489528i	−0.243935	+	0.0547309i
$81$	1.00000			0.111111
$82$		−	3.19208i		−	0.352506i
$83$			1.89887i			0.208429i	0.994555	+	0.104214i	$0.0332328\pi$
$83$			1.89887i			0.208429i	−0.994555	+	0.104214i	$0.966767\pi$
$84$		0			0
$85$	−0.964557	−	4.29903i	−0.104621	−	0.466295i
$86$	4.90755			0.529195
$87$		−	9.16246i		−	0.982319i
$88$		−	2.39327i		−	0.255123i
$89$	1.97949			0.209826			0.104913	−	0.994481i	$-0.466544\pi$
$89$	1.97949			0.209826			0.104913	+	0.994481i	$0.466544\pi$
$90$	−0.489528	−	2.18183i	−0.0516008	−	0.229985i
$91$		0			0
$92$		−	8.17113i		−	0.851900i
$93$			1.60673i			0.166610i
$94$	3.00868			0.310321
$95$	9.10069	−	2.04189i	0.933711	−	0.209493i
$96$	−1.00000			−0.102062
$97$			12.0624i			1.22475i	0.790567	+	0.612375i	$0.209786\pi$
$97$			12.0624i			1.22475i	−0.790567	+	0.612375i	$0.790214\pi$
$98$		0			0
$99$	2.39327			0.240533
$100$	−4.52072	+	2.13613i	−0.452072	+	0.213613i
$101$	−7.86672			−0.782768			−0.391384	−	0.920227i	$-0.628004\pi$
$101$	−7.86672			−0.782768			−0.391384	+	0.920227i	$0.628004\pi$
$102$		−	1.97038i		−	0.195097i
$103$		−	5.89887i		−	0.581233i	−0.956840	−	0.290617i	$-0.906140\pi$
$103$		−	5.89887i		−	0.581233i	0.956840	−	0.290617i	$-0.0938604\pi$
$104$	3.80748			0.373354
$105$		0			0
$106$	12.1711			1.18217
$107$		−	3.75798i		−	0.363298i	−0.983363	−	0.181649i	$-0.941857\pi$
$107$		−	3.75798i		−	0.363298i	0.983363	−	0.181649i	$-0.0581434\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−7.14257			−0.684135			−0.342067	−	0.939675i	$-0.611127\pi$
$109$	−7.14257			−0.684135			−0.342067	+	0.939675i	$0.611127\pi$
$110$	−1.17157	−	5.22170i	−0.111705	−	0.497869i
$111$	−1.26358			−0.119934
$112$		0			0
$113$		−	17.3837i		−	1.63532i	−0.575700	−	0.817661i	$-0.695270\pi$
$113$		−	17.3837i		−	1.63532i	0.575700	−	0.817661i	$-0.304730\pi$
$114$	4.17113			0.390663
$115$	−4.00000	−	17.8280i	−0.373002	−	1.66247i
$116$	−9.16246			−0.850713
$117$			3.80748i			0.352002i
$118$		−	13.0414i		−	1.20056i
$119$		0			0
$120$	−2.18183	+	0.489528i	−0.199173	+	0.0446876i
$121$	−5.27226			−0.479296
$122$			13.0910i			1.18520i
$123$		−	3.19208i		−	0.287820i
$124$	1.60673			0.144289
$125$	−8.81774	+	6.87368i	−0.788682	+	0.614801i
$126$		0			0
$127$			18.4434i			1.63659i	0.574801	+	0.818293i	$0.305079\pi$
$127$			18.4434i			1.63659i	−0.574801	+	0.818293i	$0.694921\pi$
$128$			1.00000i			0.0883883i
$129$	4.90755			0.432086
$130$	8.30726	−	1.86387i	0.728595	−	0.163472i
$131$	−0.615405			−0.0537682			−0.0268841	−	0.999639i	$-0.508559\pi$
$131$	−0.615405			−0.0537682			−0.0268841	+	0.999639i	$0.508559\pi$
$132$		−	2.39327i		−	0.208307i
$133$		0			0
$134$	5.77786			0.499131
$135$	−0.489528	−	2.18183i	−0.0421319	−	0.187782i
$136$	−1.97038			−0.168959
$137$			7.82799i			0.668790i	0.942433	+	0.334395i	$0.108532\pi$
$137$			7.82799i			0.668790i	−0.942433	+	0.334395i	$0.891468\pi$
$138$		−	8.17113i		−	0.695573i
$139$	−6.15378			−0.521957			−0.260979	−	0.965345i	$-0.584045\pi$
$139$	−6.15378			−0.521957			−0.260979	+	0.965345i	$0.584045\pi$
$140$		0			0
$141$	3.00868			0.253376
$142$		−	6.94032i		−	0.582419i
$143$			9.11233i			0.762012i
$144$	−1.00000			−0.0833333
$145$	−19.9909	+	4.48528i	−1.66015	+	0.372482i
$146$	0.506664			0.0419318
$147$		0			0
$148$			1.26358i			0.103866i
$149$	7.53584			0.617360			0.308680	−	0.951166i	$-0.400113\pi$
$149$	7.53584			0.617360			0.308680	+	0.951166i	$0.400113\pi$
$150$	−4.52072	+	2.13613i	−0.369116	+	0.174414i
$151$	9.04145			0.735783			0.367891	−	0.929869i	$-0.380080\pi$
$151$	9.04145			0.735783			0.367891	+	0.929869i	$0.380080\pi$
$152$		−	4.17113i		−	0.338324i
$153$		−	1.97038i		−	0.159296i
$154$		0			0
$155$	3.50560	−	0.786540i	0.281577	−	0.0631764i
$156$	3.80748			0.304843
$157$		−	22.6640i		−	1.80879i	−0.426700	−	0.904393i	$-0.640324\pi$
$157$		−	22.6640i		−	1.80879i	0.426700	−	0.904393i	$-0.359676\pi$
$158$		−	12.4260i		−	0.988563i
$159$	12.1711			0.965234
$160$	0.489528	+	2.18183i	0.0387006	+	0.172488i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$			10.2039i			0.799232i	0.916683	+	0.399616i	$0.130856\pi$
$163$			10.2039i			0.799232i	−0.916683	+	0.399616i	$0.869144\pi$
$164$	−3.19208			−0.249259
$165$	−1.17157	−	5.22170i	−0.0912068	−	0.406509i
$166$	1.89887			0.147381
$167$			25.2498i			1.95389i	0.213492	+	0.976945i	$0.431516\pi$
$167$			25.2498i			1.95389i	−0.213492	+	0.976945i	$0.568484\pi$
$168$		0			0
$169$	−1.49693			−0.115148
$170$	−4.29903	+	0.964557i	−0.329720	+	0.0739781i
$171$	4.17113			0.318975
$172$		−	4.90755i		−	0.374197i
$173$			12.5348i			0.953002i	0.879174	+	0.476501i	$0.158095\pi$
$173$			12.5348i			0.953002i	−0.879174	+	0.476501i	$0.841905\pi$
$174$	−9.16246			−0.694604
$175$		0			0
$176$	−2.39327			−0.180399
$177$		−	13.0414i		−	0.980255i
$178$		−	1.97949i		−	0.148369i
$179$	−22.9196			−1.71309			−0.856544	−	0.516074i	$-0.827393\pi$
$179$	−22.9196			−1.71309			−0.856544	+	0.516074i	$0.827393\pi$
$180$	−2.18183	+	0.489528i	−0.162624	+	0.0364873i
$181$	−19.6181			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$181$	−19.6181			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$182$		0			0
$183$			13.0910i			0.967711i
$184$	−8.17113			−0.602384
$185$	0.618560	+	2.75692i	0.0454774	+	0.202693i
$186$	1.60673			0.117811
$187$		−	4.71565i		−	0.344843i
$188$		−	3.00868i		−	0.219430i
$189$		0			0
$190$	−2.04189	−	9.10069i	−0.148134	−	0.660233i
$191$	−19.7269			−1.42739			−0.713693	−	0.700459i	$-0.752979\pi$
$191$	−19.7269			−1.42739			−0.713693	+	0.700459i	$0.752979\pi$
$192$			1.00000i			0.0721688i
$193$		−	4.78654i		−	0.344543i	−0.985050	−	0.172271i	$-0.944889\pi$
$193$		−	4.78654i		−	0.344543i	0.985050	−	0.172271i	$-0.0551106\pi$
$194$	12.0624			0.866029
$195$	8.30726	−	1.86387i	0.594896	−	0.133475i
$196$		0			0
$197$		−	17.1997i		−	1.22543i	−0.790305	−	0.612714i	$-0.790078\pi$
$197$		−	17.1997i		−	1.22543i	0.790305	−	0.612714i	$-0.209922\pi$
$198$		−	2.39327i		−	0.170082i
$199$	15.5056			1.09916			0.549582	−	0.835440i	$-0.314787\pi$
$199$	15.5056			1.09916			0.549582	+	0.835440i	$0.314787\pi$
$200$	2.13613	+	4.52072i	0.151047	+	0.319663i
$201$	5.77786			0.407539
$202$			7.86672i			0.553501i
$203$		0			0
$204$	−1.97038			−0.137954
$205$	−6.96456	+	1.56261i	−0.486426	+	0.109138i
$206$	−5.89887			−0.410994
$207$		−	8.17113i		−	0.567933i
$208$		−	3.80748i		−	0.264001i
$209$	9.98265			0.690514
$210$		0			0
$211$	−23.8980			−1.64521			−0.822603	−	0.568616i	$-0.807479\pi$
$211$	−23.8980			−1.64521			−0.822603	+	0.568616i	$0.807479\pi$
$212$		−	12.1711i		−	0.835917i
$213$		−	6.94032i		−	0.475543i
$214$	−3.75798			−0.256890
$215$	−2.40238	−	10.7074i	−0.163841	−	0.730240i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$			7.14257i			0.483756i
$219$	0.506664			0.0342372
$220$	−5.22170	+	1.17157i	−0.352047	+	0.0789874i
$221$	7.50219			0.504652
$222$			1.26358i			0.0848062i
$223$		−	0.870315i		−	0.0582806i	−0.999575	−	0.0291403i	$-0.990723\pi$
$223$		−	0.870315i		−	0.0582806i	0.999575	−	0.0291403i	$-0.00927696\pi$
$224$		0			0
$225$	−4.52072	+	2.13613i	−0.301382	+	0.142409i
$226$	−17.3837			−1.15635
$227$			14.6854i			0.974705i	0.873205	+	0.487353i	$0.162037\pi$
$227$			14.6854i			0.974705i	−0.873205	+	0.487353i	$0.837963\pi$
$228$		−	4.17113i		−	0.276240i
$229$	24.0379			1.58847			0.794233	−	0.607613i	$-0.207873\pi$
$229$	24.0379			1.58847			0.794233	+	0.607613i	$0.207873\pi$
$230$	−17.8280	+	4.00000i	−1.17554	+	0.263752i
$231$		0			0
$232$			9.16246i			0.601545i
$233$			10.5445i			0.690794i	0.938457	+	0.345397i	$0.112256\pi$
$233$			10.5445i			0.690794i	−0.938457	+	0.345397i	$0.887744\pi$
$234$	3.80748			0.248903
$235$	−1.47283	−	6.56440i	−0.0960769	−	0.428215i
$236$	−13.0414			−0.848926
$237$		−	12.4260i		−	0.807158i
$238$		0			0
$239$	4.01289			0.259572			0.129786	−	0.991542i	$-0.458571\pi$
$239$	4.01289			0.259572			0.129786	+	0.991542i	$0.458571\pi$
$240$	0.489528	+	2.18183i	0.0315989	+	0.140836i
$241$	−0.543899			−0.0350356			−0.0175178	−	0.999847i	$-0.505576\pi$
$241$	−0.543899			−0.0350356			−0.0175178	+	0.999847i	$0.505576\pi$
$242$			5.27226i			0.338914i
$243$		−	1.00000i		−	0.0641500i
$244$	13.0910			0.838062
$245$		0			0
$246$	−3.19208			−0.203519
$247$			15.8815i			1.01052i
$248$		−	1.60673i		−	0.102027i
$249$	1.89887			0.120336
$250$	6.87368	+	8.81774i	0.434730	+	0.557683i
$251$	4.62829			0.292135			0.146068	−	0.989275i	$-0.453338\pi$
$251$	4.62829			0.292135			0.146068	+	0.989275i	$0.453338\pi$
$252$		0			0
$253$		−	19.5557i		−	1.22946i
$254$	18.4434			1.15724
$255$	−4.29903	+	0.964557i	−0.269216	+	0.0604029i
$256$	1.00000			0.0625000
$257$			25.5671i			1.59483i	0.603429	+	0.797417i	$0.293801\pi$
$257$			25.5671i			1.59483i	−0.603429	+	0.797417i	$0.706199\pi$
$258$		−	4.90755i		−	0.305531i
$259$		0			0
$260$	−1.86387	−	8.30726i	−0.115592	−	0.515195i
$261$	−9.16246			−0.567142
$262$			0.615405i			0.0380199i
$263$			20.5972i			1.27008i	0.772481	+	0.635038i	$0.219016\pi$
$263$			20.5972i			1.27008i	−0.772481	+	0.635038i	$0.780984\pi$
$264$	−2.39327			−0.147296
$265$	−5.95811	−	26.5553i	−0.366004	−	1.63128i
$266$		0			0
$267$		−	1.97949i		−	0.121143i
$268$		−	5.77786i		−	0.352939i
$269$	−2.23799			−0.136453			−0.0682263	−	0.997670i	$-0.521734\pi$
$269$	−2.23799			−0.136453			−0.0682263	+	0.997670i	$0.521734\pi$
$270$	−2.18183	+	0.489528i	−0.132782	+	0.0297917i
$271$	19.1616			1.16398			0.581992	−	0.813195i	$-0.302274\pi$
$271$	19.1616			1.16398			0.581992	+	0.813195i	$0.302274\pi$
$272$			1.97038i			0.119472i
$273$		0			0
$274$	7.82799			0.472906
$275$	−10.8193	+	5.11233i	−0.652429	+	0.308285i
$276$	−8.17113			−0.491844
$277$		−	3.67674i		−	0.220914i	−0.993881	−	0.110457i	$-0.964769\pi$
$277$		−	3.67674i		−	0.220914i	0.993881	−	0.110457i	$-0.0352314\pi$
$278$			6.15378i			0.369079i
$279$	1.60673			0.0961924
$280$		0			0
$281$	−29.8280			−1.77939			−0.889694	−	0.456557i	$-0.849083\pi$
$281$	−29.8280			−1.77939			−0.889694	+	0.456557i	$0.849083\pi$
$282$		−	3.00868i		−	0.179164i
$283$			4.28961i			0.254991i	0.991839	+	0.127495i	$0.0406938\pi$
$283$			4.28961i			0.254991i	−0.991839	+	0.127495i	$0.959306\pi$
$284$	−6.94032			−0.411832
$285$	−2.04189	−	9.10069i	−0.120951	−	0.539078i
$286$	9.11233			0.538824
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	13.1176			0.771623
$290$	4.48528	+	19.9909i	0.263385	+	1.17391i
$291$	12.0624			0.707110
$292$		−	0.506664i		−	0.0296503i
$293$			24.5940i			1.43680i	0.695631	+	0.718399i	$0.255125\pi$
$293$			24.5940i			1.43680i	−0.695631	+	0.718399i	$0.744875\pi$
$294$		0			0
$295$	−28.4542	+	6.38416i	−1.65667	+	0.371700i
$296$	1.26358			0.0734444
$297$		−	2.39327i		−	0.138872i
$298$		−	7.53584i		−	0.436540i
$299$	31.1115			1.79922
$300$	2.13613	+	4.52072i	0.123330	+	0.261004i
$301$		0			0
$302$		−	9.04145i		−	0.520277i
$303$			7.86672i			0.451931i
$304$	−4.17113			−0.239231
$305$	28.5622	−	6.40839i	1.63547	−	0.366943i
$306$	−1.97038			−0.112639
$307$		−	2.14089i		−	0.122187i	−0.998132	−	0.0610937i	$-0.980541\pi$
$307$		−	2.14089i		−	0.122187i	0.998132	−	0.0610937i	$-0.0194588\pi$
$308$		0			0
$309$	−5.89887			−0.335575
$310$	−0.786540	−	3.50560i	−0.0446724	−	0.199105i
$311$	−13.9991			−0.793817			−0.396909	−	0.917858i	$-0.629917\pi$
$311$	−13.9991			−0.793817			−0.396909	+	0.917858i	$0.629917\pi$
$312$		−	3.80748i		−	0.215556i
$313$			33.0727i			1.86938i	0.355463	+	0.934690i	$0.384323\pi$
$313$			33.0727i			1.86938i	−0.355463	+	0.934690i	$0.615677\pi$
$314$	−22.6640			−1.27901
$315$		0			0
$316$	−12.4260			−0.699020
$317$		−	7.38459i		−	0.414760i	−0.978260	−	0.207380i	$-0.933506\pi$
$317$		−	7.38459i		−	0.414760i	0.978260	−	0.207380i	$-0.0664937\pi$
$318$		−	12.1711i		−	0.682523i
$319$	−21.9282			−1.22775
$320$	2.18183	−	0.489528i	0.121968	−	0.0273655i
$321$	−3.75798			−0.209750
$322$		0			0
$323$		−	8.21872i		−	0.457302i
$324$	−1.00000			−0.0555556
$325$	−8.13328	−	17.2126i	−0.451153	−	0.954782i
$326$	10.2039			0.565142
$327$			7.14257i			0.394985i
$328$			3.19208i			0.176253i
$329$		0			0
$330$	−5.22170	+	1.17157i	−0.287445	+	0.0644930i
$331$	21.5549			1.18476			0.592381	−	0.805658i	$-0.298188\pi$
$331$	21.5549			1.18476			0.592381	+	0.805658i	$0.298188\pi$
$332$		−	1.89887i		−	0.104214i
$333$			1.26358i			0.0692440i
$334$	25.2498			1.38161
$335$	−2.82843	−	12.6063i	−0.154533	−	0.688755i
$336$		0			0
$337$			22.2549i			1.21230i	0.795350	+	0.606151i	$0.207287\pi$
$337$			22.2549i			1.21230i	−0.795350	+	0.606151i	$0.792713\pi$
$338$			1.49693i			0.0814222i
$339$	−17.3837			−0.944154
$340$	0.964557	+	4.29903i	0.0523104	+	0.233148i
$341$	3.84534			0.208237
$342$		−	4.17113i		−	0.225549i
$343$		0			0
$344$	−4.90755			−0.264597
$345$	−17.8280	+	4.00000i	−0.959827	+	0.215353i
$346$	12.5348			0.673874
$347$			2.14089i			0.114929i	0.998348	+	0.0574646i	$0.0183016\pi$
$347$			2.14089i			0.114929i	−0.998348	+	0.0574646i	$0.981698\pi$
$348$			9.16246i			0.491159i
$349$	−0.906929			−0.0485468			−0.0242734	−	0.999705i	$-0.507727\pi$
$349$	−0.906929			−0.0485468			−0.0242734	+	0.999705i	$0.507727\pi$
$350$		0			0
$351$	3.80748			0.203228
$352$			2.39327i			0.127562i
$353$			13.8866i			0.739109i	0.929209	+	0.369555i	$0.120490\pi$
$353$			13.8866i			0.739109i	−0.929209	+	0.369555i	$0.879510\pi$
$354$	−13.0414			−0.693145
$355$	−15.1426	+	3.39748i	−0.803684	+	0.180320i
$356$	−1.97949			−0.104913
$357$		0			0
$358$			22.9196i			1.21134i
$359$	−18.8565			−0.995211			−0.497605	−	0.867404i	$-0.665787\pi$
$359$	−18.8565			−0.995211			−0.497605	+	0.867404i	$0.665787\pi$
$360$	0.489528	+	2.18183i	0.0258004	+	0.114992i
$361$	−1.60164			−0.0842968
$362$			19.6181i			1.03111i
$363$			5.27226i			0.276722i
$364$		0			0
$365$	−0.248026	−	1.10545i	−0.0129823	−	0.0578620i
$366$	13.0910			0.684275
$367$			31.5722i			1.64806i	0.566549	+	0.824028i	$0.308278\pi$
$367$			31.5722i			1.64806i	−0.566549	+	0.824028i	$0.691722\pi$
$368$			8.17113i			0.425950i
$369$	−3.19208			−0.166173
$370$	2.75692	−	0.618560i	0.143325	−	0.0321574i
$371$		0			0
$372$		−	1.60673i		−	0.0833051i
$373$		−	20.9075i		−	1.08255i	−0.840845	−	0.541276i	$-0.817941\pi$
$373$		−	20.9075i		−	1.08255i	0.840845	−	0.541276i	$-0.182059\pi$
$374$	−4.71565			−0.243841
$375$	6.87368	+	8.81774i	0.354956	+	0.455346i
$376$	−3.00868			−0.155161
$377$		−	34.8859i		−	1.79672i
$378$		0			0
$379$	9.82440			0.504646			0.252323	−	0.967643i	$-0.418805\pi$
$379$	9.82440			0.504646			0.252323	+	0.967643i	$0.418805\pi$
$380$	−9.10069	+	2.04189i	−0.466855	+	0.104747i
$381$	18.4434			0.944884
$382$			19.7269i			1.00931i
$383$		−	30.6647i		−	1.56689i	−0.621461	−	0.783445i	$-0.713460\pi$
$383$		−	30.6647i		−	1.56689i	0.621461	−	0.783445i	$-0.286540\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−4.78654			−0.243628
$387$		−	4.90755i		−	0.249465i
$388$		−	12.0624i		−	0.612375i
$389$	−23.4476			−1.18884			−0.594420	−	0.804154i	$-0.702618\pi$
$389$	−23.4476			−1.18884			−0.594420	+	0.804154i	$0.702618\pi$
$390$	−1.86387	−	8.30726i	−0.0943807	−	0.420655i
$391$	−16.1002			−0.814225
$392$		0			0
$393$			0.615405i			0.0310431i
$394$	−17.1997			−0.866508
$395$	−27.1115	+	6.08290i	−1.36413	+	0.306064i
$396$	−2.39327			−0.120266
$397$		−	35.3761i		−	1.77548i	−0.460349	−	0.887738i	$-0.652276\pi$
$397$		−	35.3761i		−	1.77548i	0.460349	−	0.887738i	$-0.347724\pi$
$398$		−	15.5056i		−	0.777226i
$399$		0			0
$400$	4.52072	−	2.13613i	0.226036	−	0.106806i
$401$	−9.04145			−0.451508			−0.225754	−	0.974184i	$-0.572485\pi$
$401$	−9.04145			−0.451508			−0.225754	+	0.974184i	$0.572485\pi$
$402$		−	5.77786i		−	0.288174i
$403$			6.11760i			0.304739i
$404$	7.86672			0.391384
$405$	−2.18183	+	0.489528i	−0.108416	+	0.0243248i
$406$		0			0
$407$			3.02410i			0.149899i
$408$			1.97038i			0.0975484i
$409$	−15.4379			−0.763354			−0.381677	−	0.924296i	$-0.624653\pi$
$409$	−15.4379			−0.763354			−0.381677	+	0.924296i	$0.624653\pi$
$410$	1.56261	+	6.96456i	0.0771719	+	0.343955i
$411$	7.82799			0.386126
$412$			5.89887i			0.290617i
$413$		0			0
$414$	−8.17113			−0.401589
$415$	−0.929553	−	4.14301i	−0.0456299	−	0.203373i
$416$	−3.80748			−0.186677
$417$			6.15378i			0.301352i
$418$		−	9.98265i		−	0.488267i
$419$	−26.6274			−1.30083			−0.650417	−	0.759577i	$-0.725406\pi$
$419$	−26.6274			−1.30083			−0.650417	+	0.759577i	$0.725406\pi$
$420$		0			0
$421$	5.04591			0.245923			0.122961	−	0.992411i	$-0.460761\pi$
$421$	5.04591			0.245923			0.122961	+	0.992411i	$0.460761\pi$
$422$			23.8980i			1.16334i
$423$		−	3.00868i		−	0.146287i
$424$	−12.1711			−0.591083
$425$	4.20899	+	8.90755i	0.204166	+	0.432080i
$426$	−6.94032			−0.336260
$427$		0			0
$428$			3.75798i			0.181649i
$429$	9.11233			0.439948
$430$	−10.7074	+	2.40238i	−0.516357	+	0.115853i
$431$	−25.2835			−1.21786			−0.608931	−	0.793223i	$-0.708401\pi$
$431$	−25.2835			−1.21786			−0.608931	+	0.793223i	$0.708401\pi$
$432$			1.00000i			0.0481125i
$433$		−	27.0063i		−	1.29784i	−0.760857	−	0.648920i	$-0.775221\pi$
$433$		−	27.0063i		−	1.29784i	0.760857	−	0.648920i	$-0.224779\pi$
$434$		0			0
$435$	4.48528	+	19.9909i	0.215053	+	0.958490i
$436$	7.14257			0.342067
$437$		−	34.0829i		−	1.63041i
$438$		−	0.506664i		−	0.0242093i
$439$	27.9316			1.33310			0.666552	−	0.745458i	$-0.267769\pi$
$439$	27.9316			1.33310			0.666552	+	0.745458i	$0.267769\pi$
$440$	1.17157	+	5.22170i	0.0558525	+	0.248935i
$441$		0			0
$442$		−	7.50219i		−	0.356843i
$443$			10.7692i			0.511660i	0.966722	+	0.255830i	$0.0823487\pi$
$443$			10.7692i			0.511660i	−0.966722	+	0.255830i	$0.917651\pi$
$444$	1.26358			0.0599671
$445$	−4.31891	+	0.969018i	−0.204736	+	0.0459359i
$446$	−0.870315			−0.0412106
$447$		−	7.53584i		−	0.356433i
$448$		0			0
$449$	15.1288			0.713973			0.356986	−	0.934110i	$-0.383804\pi$
$449$	15.1288			0.713973			0.356986	+	0.934110i	$0.383804\pi$
$450$	2.13613	+	4.52072i	0.100698	+	0.213109i
$451$	−7.63950			−0.359730
$452$			17.3837i			0.817661i
$453$		−	9.04145i		−	0.424804i
$454$	14.6854			0.689221
$455$		0			0
$456$	−4.17113			−0.195331
$457$		−	21.4711i		−	1.00437i	−0.864759	−	0.502187i	$-0.832529\pi$
$457$		−	21.4711i		−	1.00437i	0.864759	−	0.502187i	$-0.167471\pi$
$458$		−	24.0379i		−	1.12322i
$459$	−1.97038			−0.0919695
$460$	4.00000	+	17.8280i	0.186501	+	0.831234i
$461$	30.4465			1.41804			0.709019	−	0.705190i	$-0.249138\pi$
$461$	30.4465			1.41804			0.709019	+	0.705190i	$0.249138\pi$
$462$		0			0
$463$		−	40.2005i		−	1.86828i	−0.356913	−	0.934138i	$-0.616171\pi$
$463$		−	40.2005i		−	1.86828i	0.356913	−	0.934138i	$-0.383829\pi$
$464$	9.16246			0.425356
$465$	−0.786540	−	3.50560i	−0.0364749	−	0.162569i
$466$	10.5445			0.488465
$467$			7.84175i			0.362873i	0.983403	+	0.181437i	$0.0580747\pi$
$467$			7.84175i			0.362873i	−0.983403	+	0.181437i	$0.941925\pi$
$468$		−	3.80748i		−	0.176001i
$469$		0			0
$470$	−6.56440	+	1.47283i	−0.302793	+	0.0679366i
$471$	−22.6640			−1.04430
$472$			13.0414i			0.600281i
$473$		−	11.7451i		−	0.540040i
$474$	−12.4260			−0.570747
$475$	−18.8565	+	8.91008i	−0.865198	+	0.408823i
$476$		0			0
$477$		−	12.1711i		−	0.557278i
$478$		−	4.01289i		−	0.183545i
$479$	27.7745			1.26905			0.634524	−	0.772904i	$-0.281196\pi$
$479$	27.7745			1.26905			0.634524	+	0.772904i	$0.281196\pi$
$480$	2.18183	−	0.489528i	0.0995863	−	0.0223438i
$481$	−4.81108			−0.219366
$482$			0.543899i			0.0247739i
$483$		0			0
$484$	5.27226			0.239648
$485$	−5.90488	−	26.3180i	−0.268127	−	1.19504i
$486$	−1.00000			−0.0453609
$487$		−	12.5263i		−	0.567620i	−0.958880	−	0.283810i	$-0.908401\pi$
$487$		−	12.5263i		−	0.567620i	0.958880	−	0.283810i	$-0.0915986\pi$
$488$		−	13.0910i		−	0.592600i
$489$	10.2039			0.461437
$490$		0			0
$491$	−24.3924			−1.10081			−0.550407	−	0.834897i	$-0.685527\pi$
$491$	−24.3924			−1.10081			−0.550407	+	0.834897i	$0.685527\pi$
$492$			3.19208i			0.143910i
$493$			18.0535i			0.813090i
$494$	15.8815			0.714544
$495$	−5.22170	+	1.17157i	−0.234698	+	0.0526583i
$496$	−1.60673			−0.0721443
$497$		0			0
$498$		−	1.89887i		−	0.0850906i
$499$	23.6560			1.05899			0.529493	−	0.848314i	$-0.322382\pi$
$499$	23.6560			1.05899			0.529493	+	0.848314i	$0.322382\pi$
$500$	8.81774	−	6.87368i	0.394341	−	0.307400i
$501$	25.2498			1.12808
$502$		−	4.62829i		−	0.206571i
$503$			20.8496i			0.929636i	0.885406	+	0.464818i	$0.153880\pi$
$503$			20.8496i			0.929636i	−0.885406	+	0.464818i	$0.846120\pi$
$504$		0			0
$505$	17.1638	−	3.85098i	0.763780	−	0.171366i
$506$	−19.5557			−0.869358
$507$			1.49693i			0.0664810i
$508$		−	18.4434i		−	0.818293i
$509$	2.59490			0.115017			0.0575085	−	0.998345i	$-0.481684\pi$
$509$	2.59490			0.115017			0.0575085	+	0.998345i	$0.481684\pi$
$510$	0.964557	+	4.29903i	0.0427113	+	0.190364i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	4.17113i		−	0.184160i
$514$	25.5671			1.12772
$515$	2.88767	+	12.8703i	0.127246	+	0.567134i
$516$	−4.90755			−0.216043
$517$		−	7.20057i		−	0.316681i
$518$		0			0
$519$	12.5348			0.550216
$520$	−8.30726	+	1.86387i	−0.364298	+	0.0817361i
$521$	−24.4884			−1.07286			−0.536429	−	0.843945i	$-0.680227\pi$
$521$	−24.4884			−1.07286			−0.536429	+	0.843945i	$0.680227\pi$
$522$			9.16246i			0.401030i
$523$		−	21.6257i		−	0.945627i	−0.881162	−	0.472814i	$-0.843238\pi$
$523$		−	21.6257i		−	0.945627i	0.881162	−	0.472814i	$-0.156762\pi$
$524$	0.615405			0.0268841
$525$		0			0
$526$	20.5972			0.898080
$527$		−	3.16587i		−	0.137907i
$528$			2.39327i			0.104154i
$529$	−43.7674			−1.90293
$530$	−26.5553	+	5.95811i	−1.15349	+	0.258804i
$531$	−13.0414			−0.565951
$532$		0			0
$533$		−	12.1538i		−	0.526439i
$534$	−1.97949			−0.0856611
$535$	1.83964	+	8.19926i	0.0795344	+	0.354485i
$536$	−5.77786			−0.249566
$537$			22.9196i			0.989052i
$538$			2.23799i			0.0964865i
$539$		0			0
$540$	0.489528	+	2.18183i	0.0210659	+	0.0938908i
$541$	8.01735			0.344693			0.172346	−	0.985036i	$-0.444865\pi$
$541$	8.01735			0.344693			0.172346	+	0.985036i	$0.444865\pi$
$542$		−	19.1616i		−	0.823060i
$543$			19.6181i			0.841894i
$544$	1.97038			0.0844794
$545$	15.5839	−	3.49649i	0.667539	−	0.149773i
$546$		0			0
$547$			43.0251i			1.83962i	0.392361	+	0.919811i	$0.371658\pi$
$547$			43.0251i			1.83962i	−0.392361	+	0.919811i	$0.628342\pi$
$548$		−	7.82799i		−	0.334395i
$549$	13.0910			0.558708
$550$	5.11233	+	10.8193i	0.217991	+	0.461337i
$551$	−38.2178			−1.62814
$552$			8.17113i			0.347787i
$553$		0			0
$554$	−3.67674			−0.156210
$555$	2.75692	−	0.618560i	0.117025	−	0.0262564i
$556$	6.15378			0.260979
$557$		−	11.1823i		−	0.473811i	−0.971533	−	0.236906i	$-0.923867\pi$
$557$		−	11.1823i		−	0.473811i	0.971533	−	0.236906i	$-0.0761332\pi$
$558$		−	1.60673i		−	0.0680183i
$559$	18.6854			0.790309
$560$		0			0
$561$	−4.71565			−0.199095
$562$			29.8280i			1.25822i
$563$			26.8694i			1.13241i	0.824264	+	0.566206i	$0.191589\pi$
$563$			26.8694i			1.13241i	−0.824264	+	0.566206i	$0.808411\pi$
$564$	−3.00868			−0.126688
$565$	8.50982	+	37.9282i	0.358011	+	1.59565i
$566$	4.28961			0.180306
$567$		0			0
$568$			6.94032i			0.291210i
$569$	2.61453			0.109607			0.0548034	−	0.998497i	$-0.482547\pi$
$569$	2.61453			0.109607			0.0548034	+	0.998497i	$0.482547\pi$
$570$	−9.10069	+	2.04189i	−0.381186	+	0.0855253i
$571$	12.4607			0.521466			0.260733	−	0.965411i	$-0.416036\pi$
$571$	12.4607			0.521466			0.260733	+	0.965411i	$0.416036\pi$
$572$		−	9.11233i		−	0.381006i
$573$			19.7269i			0.824102i
$574$		0			0
$575$	17.4546	+	36.9394i	0.727907	+	1.54048i
$576$	1.00000			0.0416667
$577$			17.8195i			0.741835i	0.928666	+	0.370918i	$0.120957\pi$
$577$			17.8195i			0.741835i	−0.928666	+	0.370918i	$0.879043\pi$
$578$		−	13.1176i		−	0.545620i
$579$	−4.78654			−0.198922
$580$	19.9909	−	4.48528i	0.830076	−	0.186241i
$581$		0			0
$582$		−	12.0624i		−	0.500002i
$583$		−	29.1288i		−	1.20639i
$584$	−0.506664			−0.0209659
$585$	−1.86387	−	8.30726i	−0.0770615	−	0.343463i
$586$	24.5940			1.01597
$587$		−	9.55661i		−	0.394443i	−0.980359	−	0.197222i	$-0.936808\pi$
$587$		−	9.55661i		−	0.394443i	0.980359	−	0.197222i	$-0.0631919\pi$
$588$		0			0
$589$	6.70189			0.276146
$590$	6.38416	+	28.4542i	0.262832	+	1.17144i
$591$	−17.1997			−0.707501
$592$		−	1.26358i		−	0.0519330i
$593$			11.6619i			0.478898i	0.970909	+	0.239449i	$0.0769668\pi$
$593$			11.6619i			0.478898i	−0.970909	+	0.239449i	$0.923033\pi$
$594$	−2.39327			−0.0981970
$595$		0			0
$596$	−7.53584			−0.308680
$597$		−	15.5056i		−	0.634602i
$598$		−	31.1115i		−	1.27224i
$599$	33.0977			1.35234			0.676168	−	0.736748i	$-0.263640\pi$
$599$	33.0977			1.35234			0.676168	+	0.736748i	$0.263640\pi$
$600$	4.52072	−	2.13613i	0.184558	−	0.0872071i
$601$	−15.2886			−0.623633			−0.311817	−	0.950142i	$-0.600937\pi$
$601$	−15.2886			−0.623633			−0.311817	+	0.950142i	$0.600937\pi$
$602$		0			0
$603$		−	5.77786i		−	0.235293i
$604$	−9.04145			−0.367891
$605$	11.5032	−	2.58092i	0.467670	−	0.104929i
$606$	7.86672			0.319564
$607$		−	40.1823i		−	1.63095i	−0.578794	−	0.815474i	$-0.696476\pi$
$607$		−	40.1823i		−	1.63095i	0.578794	−	0.815474i	$-0.303524\pi$
$608$			4.17113i			0.169162i
$609$		0			0
$610$	−6.40839	−	28.5622i	−0.259468	−	1.15645i
$611$	11.4555			0.463439
$612$			1.97038i			0.0796479i
$613$		−	24.8591i		−	1.00405i	−0.864853	−	0.502024i	$-0.832589\pi$
$613$		−	24.8591i		−	1.00405i	0.864853	−	0.502024i	$-0.167411\pi$
$614$	−2.14089			−0.0863995
$615$	1.56261	+	6.96456i	0.0630106	+	0.280838i
$616$		0			0
$617$		−	22.7647i		−	0.916473i	−0.888830	−	0.458237i	$-0.848481\pi$
$617$		−	22.7647i		−	0.916473i	0.888830	−	0.458237i	$-0.151519\pi$
$618$			5.89887i			0.237288i
$619$	17.8280			0.716567			0.358284	−	0.933613i	$-0.383362\pi$
$619$	17.8280			0.716567			0.358284	+	0.933613i	$0.383362\pi$
$620$	−3.50560	+	0.786540i	−0.140788	+	0.0315882i
$621$	−8.17113			−0.327896
$622$			13.9991i			0.561314i
$623$		0			0
$624$	−3.80748			−0.152421
$625$	15.8739	−	19.3137i	0.634956	−	0.772548i
$626$	33.0727			1.32185
$627$		−	9.98265i		−	0.398669i
$628$			22.6640i			0.904393i
$629$	2.48974			0.0992725
$630$		0			0
$631$	0.580705			0.0231175			0.0115587	−	0.999933i	$-0.496321\pi$
$631$	0.580705			0.0231175			0.0115587	+	0.999933i	$0.496321\pi$
$632$			12.4260i			0.494281i
$633$			23.8980i			0.949860i
$634$	−7.38459			−0.293280
$635$	−9.02856	−	40.2403i	−0.358287	−	1.59689i
$636$	−12.1711			−0.482617
$637$		0			0
$638$			21.9282i			0.868147i
$639$	−6.94032			−0.274555
$640$	−0.489528	−	2.18183i	−0.0193503	−	0.0862442i
$641$	18.0353			0.712352			0.356176	−	0.934419i	$-0.384080\pi$
$641$	18.0353			0.712352			0.356176	+	0.934419i	$0.384080\pi$
$642$			3.75798i			0.148316i
$643$			39.3664i			1.55246i	0.630451	+	0.776229i	$0.282870\pi$
$643$			39.3664i			1.55246i	−0.630451	+	0.776229i	$0.717130\pi$
$644$		0			0
$645$	−10.7074	+	2.40238i	−0.421604	+	0.0945938i
$646$	−8.21872			−0.323361
$647$		−	2.38038i		−	0.0935824i	−0.998905	−	0.0467912i	$-0.985100\pi$
$647$		−	2.38038i		−	0.0935824i	0.998905	−	0.0467912i	$-0.0148995\pi$
$648$			1.00000i			0.0392837i
$649$	−31.2117			−1.22517
$650$	−17.2126	+	8.13328i	−0.675133	+	0.319013i
$651$		0			0
$652$		−	10.2039i		−	0.399616i
$653$		−	25.1115i		−	0.982687i	−0.870966	−	0.491344i	$-0.836506\pi$
$653$		−	25.1115i		−	0.982687i	0.870966	−	0.491344i	$-0.163494\pi$
$654$	7.14257			0.279297
$655$	1.34271	−	0.301258i	0.0524639	−	0.0117711i
$656$	3.19208			0.124630
$657$		−	0.506664i		−	0.0197668i
$658$		0			0
$659$	7.17981			0.279686			0.139843	−	0.990174i	$-0.455340\pi$
$659$	7.17981			0.279686			0.139843	+	0.990174i	$0.455340\pi$
$660$	1.17157	+	5.22170i	0.0456034	+	0.203254i
$661$	25.0330			0.973669			0.486835	−	0.873494i	$-0.338151\pi$
$661$	25.0330			0.973669			0.486835	+	0.873494i	$0.338151\pi$
$662$		−	21.5549i		−	0.837753i
$663$		−	7.50219i		−	0.291361i
$664$	−1.89887			−0.0736906
$665$		0			0
$666$	1.26358			0.0489629
$667$			74.8677i			2.89889i
$668$		−	25.2498i		−	0.976945i
$669$	−0.870315			−0.0336483
$670$	−12.6063	+	2.82843i	−0.487024	+	0.109272i
$671$	31.3302			1.20949
$672$		0			0
$673$		−	9.67062i		−	0.372775i	−0.982476	−	0.186388i	$-0.940322\pi$
$673$		−	9.67062i		−	0.372775i	0.982476	−	0.186388i	$-0.0596780\pi$
$674$	22.2549			0.857227
$675$	2.13613	+	4.52072i	0.0822197	+	0.174003i
$676$	1.49693			0.0575742
$677$		−	27.6890i		−	1.06418i	−0.846689	−	0.532088i	$-0.821408\pi$
$677$		−	27.6890i		−	1.06418i	0.846689	−	0.532088i	$-0.178592\pi$
$678$			17.3837i			0.667618i
$679$		0			0
$680$	4.29903	−	0.964557i	0.164860	−	0.0369891i
$681$	14.6854			0.562746
$682$		−	3.84534i		−	0.147246i
$683$		−	26.1227i		−	0.999556i	−0.866154	−	0.499778i	$-0.833415\pi$
$683$		−	26.1227i		−	0.999556i	0.866154	−	0.499778i	$-0.166585\pi$
$684$	−4.17113			−0.159487
$685$	−3.83202	−	17.0793i	−0.146414	−	0.652567i
$686$		0			0
$687$		−	24.0379i		−	0.917101i
$688$			4.90755i			0.187099i
$689$	46.3414			1.76547
$690$	4.00000	+	17.8280i	0.152277	+	0.678700i
$691$	−24.7901			−0.943061			−0.471530	−	0.881850i	$-0.656298\pi$
$691$	−24.7901			−0.943061			−0.471530	+	0.881850i	$0.656298\pi$
$692$		−	12.5348i		−	0.476501i
$693$		0			0
$694$	2.14089			0.0812673
$695$	13.4265	−	3.01245i	0.509295	−	0.114269i
$696$	9.16246			0.347302
$697$			6.28961i			0.238236i
$698$			0.906929i			0.0343278i
$699$	10.5445			0.398830
$700$		0			0
$701$	37.8817			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$701$	37.8817			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$702$		−	3.80748i		−	0.143704i
$703$			5.27058i			0.198784i
$704$	2.39327			0.0901997
$705$	−6.56440	+	1.47283i	−0.247230	+	0.0554700i
$706$	13.8866			0.522629
$707$		0			0
$708$			13.0414i			0.490128i
$709$	30.9801			1.16348			0.581741	−	0.813374i	$-0.302372\pi$
$709$	30.9801			1.16348			0.581741	+	0.813374i	$0.302372\pi$
$710$	3.39748	+	15.1426i	0.127505	+	0.568291i
$711$	−12.4260			−0.466013
$712$			1.97949i			0.0741847i
$713$		−	13.1288i		−	0.491678i
$714$		0			0
$715$	−4.46074	−	19.8815i	−0.166822	−	0.743527i
$716$	22.9196			0.856544
$717$		−	4.01289i		−	0.149864i
$718$			18.8565i			0.703720i
$719$	−16.7028			−0.622908			−0.311454	−	0.950261i	$-0.600816\pi$
$719$	−16.7028			−0.622908			−0.311454	+	0.950261i	$0.600816\pi$
$720$	2.18183	−	0.489528i	0.0813118	−	0.0182436i
$721$		0			0
$722$			1.60164i			0.0596068i
$723$			0.543899i			0.0202278i
$724$	19.6181			0.729102
$725$	41.4210	−	19.5722i	1.53834	−	0.726893i
$726$	5.27226			0.195672
$727$			36.1218i			1.33968i	0.742504	+	0.669842i	$0.233638\pi$
$727$			36.1218i			1.33968i	−0.742504	+	0.669842i	$0.766362\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−1.10545	+	0.248026i	−0.0409146	+	0.00917986i
$731$	−9.66974			−0.357648
$732$		−	13.0910i		−	0.483856i
$733$			7.83860i			0.289525i	0.989466	+	0.144763i	$0.0462419\pi$
$733$			7.83860i			0.289525i	−0.989466	+	0.144763i	$0.953758\pi$
$734$	31.5722			1.16535
$735$		0			0
$736$	8.17113			0.301192
$737$		−	13.8280i		−	0.509361i
$738$			3.19208i			0.117502i
$739$	29.7969			1.09610			0.548048	−	0.836447i	$-0.315371\pi$
$739$	29.7969			1.09610			0.548048	+	0.836447i	$0.315371\pi$
$740$	−0.618560	−	2.75692i	−0.0227387	−	0.101346i
$741$	15.8815			0.583422
$742$		0			0
$743$			11.7487i			0.431017i	0.976502	+	0.215509i	$0.0691409\pi$
$743$			11.7487i			0.431017i	−0.976502	+	0.215509i	$0.930859\pi$
$744$	−1.60673			−0.0589056
$745$	−16.4419	+	3.68901i	−0.602384	+	0.135155i
$746$	−20.9075			−0.765480
$747$		−	1.89887i		−	0.0694762i
$748$			4.71565i			0.172421i
$749$		0			0
$750$	8.81774	−	6.87368i	0.321978	−	0.250991i
$751$	−2.43981			−0.0890299			−0.0445150	−	0.999009i	$-0.514174\pi$
$751$	−2.43981			−0.0890299			−0.0445150	+	0.999009i	$0.514174\pi$
$752$			3.00868i			0.109715i
$753$		−	4.62829i		−	0.168664i
$754$	−34.8859			−1.27047
$755$	−19.7269	+	4.42604i	−0.717934	+	0.161080i
$756$		0			0
$757$		−	17.5039i		−	0.636188i	−0.948059	−	0.318094i	$-0.896957\pi$
$757$		−	17.5039i		−	0.636188i	0.948059	−	0.318094i	$-0.103043\pi$
$758$		−	9.82440i		−	0.356838i
$759$	−19.5557			−0.709828
$760$	2.04189	+	9.10069i	0.0740670	+	0.330117i
$761$	6.06327			0.219793			0.109897	−	0.993943i	$-0.464948\pi$
$761$	6.06327			0.219793			0.109897	+	0.993943i	$0.464948\pi$
$762$		−	18.4434i		−	0.668134i
$763$		0			0
$764$	19.7269			0.713693
$765$	0.964557	+	4.29903i	0.0348736	+	0.155432i
$766$	−30.6647			−1.10796
$767$		−	49.6551i		−	1.79294i
$768$		−	1.00000i		−	0.0360844i
$769$	−6.94628			−0.250489			−0.125245	−	0.992126i	$-0.539972\pi$
$769$	−6.94628			−0.250489			−0.125245	+	0.992126i	$0.539972\pi$
$770$		0			0
$771$	25.5671			0.920777
$772$			4.78654i			0.172271i
$773$		−	14.8597i		−	0.534466i	−0.963632	−	0.267233i	$-0.913891\pi$
$773$		−	14.8597i		−	0.534466i	0.963632	−	0.267233i	$-0.0861094\pi$
$774$	−4.90755			−0.176398
$775$	−7.26358	+	3.43218i	−0.260916	+	0.123288i
$776$	−12.0624			−0.433015
$777$		0			0
$778$			23.4476i			0.840637i
$779$	−13.3146			−0.477045
$780$	−8.30726	+	1.86387i	−0.297448	+	0.0667373i
$781$	−16.6101			−0.594355
$782$			16.1002i			0.575744i
$783$			9.16246i			0.327440i
$784$		0			0
$785$	11.0947	+	49.4490i	0.395986	+	1.76491i
$786$	0.615405			0.0219508
$787$			16.7683i			0.597726i	0.954296	+	0.298863i	$0.0966073\pi$
$787$			16.7683i			0.597726i	−0.954296	+	0.298863i	$0.903393\pi$
$788$			17.1997i			0.612714i
$789$	20.5972			0.733279
$790$	6.08290	+	27.1115i	0.216420	+	0.964582i
$791$		0			0
$792$			2.39327i			0.0850411i
$793$			49.8436i			1.77000i
$794$	−35.3761			−1.25545
$795$	−26.5553	+	5.95811i	−0.941819	+	0.211312i
$796$	−15.5056			−0.549582
$797$		−	37.5481i		−	1.33002i	−0.746833	−	0.665011i	$-0.768427\pi$
$797$		−	37.5481i		−	1.33002i	0.746833	−	0.665011i	$-0.231573\pi$
$798$		0			0
$799$	−5.92824			−0.209726
$800$	−2.13613	−	4.52072i	−0.0755236	−	0.159832i
$801$	−1.97949			−0.0699420
$802$			9.04145i			0.319265i
$803$		−	1.21258i		−	0.0427911i
$804$	−5.77786			−0.203770
$805$		0			0
$806$	6.11760			0.215483
$807$			2.23799i			0.0787809i
$808$		−	7.86672i		−	0.276750i
$809$	−12.5014			−0.439526			−0.219763	−	0.975553i	$-0.570528\pi$
$809$	−12.5014			−0.439526			−0.219763	+	0.975553i	$0.570528\pi$
$810$	0.489528	+	2.18183i	0.0172003	+	0.0766615i
$811$	30.4470			1.06914			0.534569	−	0.845125i	$-0.320474\pi$
$811$	30.4470			1.06914			0.534569	+	0.845125i	$0.320474\pi$
$812$		0			0
$813$		−	19.1616i		−	0.672026i
$814$	3.02410			0.105995
$815$	−4.99510	−	22.2631i	−0.174971	−	0.779844i
$816$	1.97038			0.0689771
$817$		−	20.4700i		−	0.716156i
$818$			15.4379i			0.539773i
$819$		0			0
$820$	6.96456	−	1.56261i	0.243213	−	0.0545688i
$821$	38.2775			1.33589			0.667947	−	0.744209i	$-0.267173\pi$
$821$	38.2775			1.33589			0.667947	+	0.744209i	$0.267173\pi$
$822$		−	7.82799i		−	0.273032i
$823$			23.6213i			0.823386i	0.911323	+	0.411693i	$0.135062\pi$
$823$			23.6213i			0.823386i	−0.911323	+	0.411693i	$0.864938\pi$
$824$	5.89887			0.205497
$825$	5.11233	+	10.8193i	0.177989	+	0.376680i
$826$		0			0
$827$			34.5652i			1.20195i	0.799268	+	0.600975i	$0.205221\pi$
$827$			34.5652i			1.20195i	−0.799268	+	0.600975i	$0.794779\pi$
$828$			8.17113i			0.283967i
$829$	−27.2086			−0.944992			−0.472496	−	0.881333i	$-0.656647\pi$
$829$	−27.2086			−0.944992			−0.472496	+	0.881333i	$0.656647\pi$
$830$	−4.14301	+	0.929553i	−0.143806	+	0.0322652i
$831$	−3.67674			−0.127545
$832$			3.80748i			0.132001i
$833$		0			0
$834$	6.15378			0.213088
$835$	−12.3605	−	55.0907i	−0.427753	−	1.90649i
$836$	−9.98265			−0.345257
$837$		−	1.60673i		−	0.0555367i
$838$			26.6274i			0.919829i
$839$	−1.49861			−0.0517377			−0.0258689	−	0.999665i	$-0.508235\pi$
$839$	−1.49861			−0.0517377			−0.0258689	+	0.999665i	$0.508235\pi$
$840$		0			0
$841$	54.9507			1.89485
$842$		−	5.04591i		−	0.173894i
$843$			29.8280i			1.02733i
$844$	23.8980			0.822603
$845$	3.26604	−	0.732789i	0.112355	−	0.0252087i
$846$	−3.00868			−0.103440
$847$		0			0
$848$			12.1711i			0.417958i
$849$	4.28961			0.147219
$850$	8.90755	−	4.20899i	0.305526	−	0.144367i
$851$	10.3249			0.353934
$852$			6.94032i			0.237772i
$853$			38.9306i			1.33296i	0.745524	+	0.666479i	$0.232199\pi$
$853$			38.9306i			1.33296i	−0.745524	+	0.666479i	$0.767801\pi$
$854$		0			0
$855$	−9.10069	+	2.04189i	−0.311237	+	0.0698311i
$856$	3.75798			0.128445
$857$		−	18.5987i		−	0.635319i	−0.948205	−	0.317659i	$-0.897103\pi$
$857$		−	18.5987i		−	0.635319i	0.948205	−	0.317659i	$-0.102897\pi$
$858$		−	9.11233i		−	0.311090i
$859$	−9.09945			−0.310469			−0.155235	−	0.987878i	$-0.549613\pi$
$859$	−9.09945			−0.310469			−0.155235	+	0.987878i	$0.549613\pi$
$860$	2.40238	+	10.7074i	0.0819206	+	0.365120i
$861$		0			0
$862$			25.2835i			0.861158i
$863$			10.4616i			0.356118i	0.984020	+	0.178059i	$0.0569817\pi$
$863$			10.4616i			0.356118i	−0.984020	+	0.178059i	$0.943018\pi$
$864$	1.00000			0.0340207
$865$	−6.13613	−	27.3487i	−0.208635	−	0.929884i
$866$	−27.0063			−0.917711
$867$		−	13.1176i		−	0.445497i
$868$		0			0
$869$	−29.7389			−1.00882
$870$	19.9909	−	4.48528i	0.677755	−	0.152065i
$871$	21.9991			0.745412
$872$		−	7.14257i		−	0.241878i
$873$		−	12.0624i		−	0.408250i
$874$	−34.0829			−1.15287
$875$		0			0
$876$	−0.506664			−0.0171186
$877$			5.29829i			0.178910i	0.995991	+	0.0894552i	$0.0285126\pi$
$877$			5.29829i			0.178910i	−0.995991	+	0.0894552i	$0.971487\pi$
$878$		−	27.9316i		−	0.942647i
$879$	24.5940			0.829536
$880$	5.22170	−	1.17157i	0.176023	−	0.0394937i
$881$	2.68857			0.0905802			0.0452901	−	0.998974i	$-0.485579\pi$
$881$	2.68857			0.0905802			0.0452901	+	0.998974i	$0.485579\pi$
$882$		0			0
$883$		−	26.4277i		−	0.889363i	−0.895689	−	0.444681i	$-0.853317\pi$
$883$		−	26.4277i		−	0.889363i	0.895689	−	0.444681i	$-0.146683\pi$
$884$	−7.50219			−0.252326
$885$	6.38416	+	28.4542i	0.214601	+	0.956476i
$886$	10.7692			0.361798
$887$			8.18149i			0.274708i	0.990522	+	0.137354i	$0.0438597\pi$
$887$			8.18149i			0.274708i	−0.990522	+	0.137354i	$0.956140\pi$
$888$		−	1.26358i		−	0.0424031i
$889$		0			0
$890$	0.969018	+	4.31891i	0.0324816	+	0.144770i
$891$	−2.39327			−0.0801776
$892$			0.870315i			0.0291403i
$893$		−	12.5496i		−	0.419956i
$894$	−7.53584			−0.252036
$895$	50.0065	−	11.2198i	1.67153	−	0.375036i
$896$		0			0
$897$		−	31.1115i		−	1.03878i
$898$		−	15.1288i		−	0.504855i
$899$	−14.7216			−0.490993
$900$	4.52072	−	2.13613i	0.150691	−	0.0712043i
$901$	−23.9818			−0.798949
$902$			7.63950i			0.254368i
$903$		0			0
$904$	17.3837			0.578174
$905$	42.8033	−	9.60362i	1.42283	−	0.319235i
$906$	−9.04145			−0.300382
$907$			3.80028i			0.126186i	0.998008	+	0.0630932i	$0.0200965\pi$
$907$			3.80028i			0.126186i	−0.998008	+	0.0630932i	$0.979903\pi$
$908$		−	14.6854i		−	0.487353i
$909$	7.86672			0.260923
$910$		0			0
$911$	39.1590			1.29740			0.648699	−	0.761045i	$-0.275314\pi$
$911$	39.1590			1.29740			0.648699	+	0.761045i	$0.275314\pi$
$912$			4.17113i			0.138120i
$913$		−	4.54452i		−	0.150402i
$914$	−21.4711			−0.710200
$915$	−6.40839	−	28.5622i	−0.211855	−	0.944236i
$916$	−24.0379			−0.794233
$917$		0			0
$918$			1.97038i			0.0650323i
$919$	13.8462			0.456745			0.228372	−	0.973574i	$-0.426660\pi$
$919$	13.8462			0.456745			0.228372	+	0.973574i	$0.426660\pi$
$920$	17.8280	−	4.00000i	0.587771	−	0.131876i
$921$	−2.14089			−0.0705449
$922$		−	30.4465i		−	1.00270i
$923$		−	26.4252i		−	0.869795i
$924$		0			0
$925$	−2.69918	−	5.71232i	−0.0887485	−	0.187820i
$926$	−40.2005			−1.32107
$927$			5.89887i			0.193744i
$928$		−	9.16246i		−	0.300772i
$929$	−13.8030			−0.452862			−0.226431	−	0.974027i	$-0.572706\pi$
$929$	−13.8030			−0.452862			−0.226431	+	0.974027i	$0.572706\pi$
$930$	−3.50560	+	0.786540i	−0.114953	+	0.0257917i
$931$		0			0
$932$		−	10.5445i		−	0.345397i
$933$			13.9991i			0.458311i
$934$	7.84175			0.256590
$935$	2.30845	+	10.2887i	0.0754942	+	0.336478i
$936$	−3.80748			−0.124451
$937$		−	29.1062i		−	0.950858i	−0.879754	−	0.475429i	$-0.842293\pi$
$937$		−	29.1062i		−	0.950858i	0.879754	−	0.475429i	$-0.157707\pi$
$938$		0			0
$939$	33.0727			1.07929
$940$	1.47283	+	6.56440i	0.0480385	+	0.214107i
$941$	26.9934			0.879960			0.439980	−	0.898008i	$-0.354986\pi$
$941$	26.9934			0.879960			0.439980	+	0.898008i	$0.354986\pi$
$942$			22.6640i			0.738434i
$943$			26.0829i			0.849376i
$944$	13.0414			0.424463
$945$		0			0
$946$	−11.7451			−0.381866
$947$		−	32.5005i		−	1.05612i	−0.849206	−	0.528062i	$-0.822919\pi$
$947$		−	32.5005i		−	1.05612i	0.849206	−	0.528062i	$-0.177081\pi$
$948$			12.4260i			0.403579i
$949$	1.92911			0.0626217
$950$	8.91008	+	18.8565i	0.289081	+	0.611787i
$951$	−7.38459			−0.239462
$952$		0			0
$953$			41.4364i			1.34226i	0.741342	+	0.671128i	$0.234190\pi$
$953$			41.4364i			1.34226i	−0.741342	+	0.671128i	$0.765810\pi$
$954$	−12.1711			−0.394055
$955$	43.0406	−	9.65685i	1.39276	−	0.312488i
$956$	−4.01289			−0.129786
$957$			21.9282i			0.708839i
$958$		−	27.7745i		−	0.897352i
$959$		0			0
$960$	−0.489528	−	2.18183i	−0.0157995	−	0.0704181i
$961$	−28.4184			−0.916723
$962$			4.81108i			0.155115i
$963$			3.75798i			0.121099i
$964$	0.543899			0.0175178
$965$	2.34315	+	10.4434i	0.0754285	+	0.336185i
$966$		0			0
$967$			23.0294i			0.740577i	0.928917	+	0.370288i	$0.120741\pi$
$967$			23.0294i			0.740577i	−0.928917	+	0.370288i	$0.879259\pi$
$968$		−	5.27226i		−	0.169457i
$969$	−8.21872			−0.264023
$970$	−26.3180	+	5.90488i	−0.845021	+	0.189594i
$971$	5.06326			0.162488			0.0812439	−	0.996694i	$-0.474111\pi$
$971$	5.06326			0.162488			0.0812439	+	0.996694i	$0.474111\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−12.5263			−0.401368
$975$	−17.2126	+	8.13328i	−0.551244	+	0.260473i
$976$	−13.0910			−0.419031
$977$			29.6213i			0.947669i	0.880614	+	0.473834i	$0.157130\pi$
$977$			29.6213i			0.947669i	−0.880614	+	0.473834i	$0.842870\pi$
$978$		−	10.2039i		−	0.326285i
$979$	−4.73747			−0.151410
$980$		0			0
$981$	7.14257			0.228045
$982$			24.3924i			0.778393i
$983$			8.18149i			0.260949i	0.991452	+	0.130474i	$0.0416501\pi$
$983$			8.18149i			0.260949i	−0.991452	+	0.130474i	$0.958350\pi$
$984$	3.19208			0.101760
$985$	8.41973	+	37.5267i	0.268275	+	1.19570i
$986$	18.0535			0.574942
$987$		0			0
$988$		−	15.8815i		−	0.505259i
$989$	−40.1002			−1.27511
$990$	1.17157	+	5.22170i	0.0372350	+	0.165956i
$991$	16.7554			0.532254			0.266127	−	0.963938i	$-0.414256\pi$
$991$	16.7554			0.532254			0.266127	+	0.963938i	$0.414256\pi$
$992$			1.60673i			0.0510137i
$993$		−	21.5549i		−	0.684023i
$994$		0			0
$995$	−33.8305	+	7.59043i	−1.07250	+	0.240633i
$996$	−1.89887			−0.0601681
$997$		−	4.62390i		−	0.146440i	−0.997316	−	0.0732202i	$-0.976672\pi$
$997$		−	4.62390i		−	0.146440i	0.997316	−	0.0732202i	$-0.0233276\pi$
$998$		−	23.6560i		−	0.748817i
$999$	1.26358			0.0399780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.g.j.589.1	✓	8
5.2	odd	4		7350.2.a.dt.1.2		4
5.3	odd	4		7350.2.a.ds.1.2		4
5.4	even	2	inner	1470.2.g.j.589.5	yes	8
7.2	even	3		1470.2.n.l.949.3		16
7.3	odd	6		1470.2.n.k.79.6		16
7.4	even	3		1470.2.n.l.79.7		16
7.5	odd	6		1470.2.n.k.949.2		16
7.6	odd	2		1470.2.g.k.589.4	yes	8
35.4	even	6		1470.2.n.l.79.3		16
35.9	even	6		1470.2.n.l.949.7		16
35.13	even	4		7350.2.a.dr.1.2		4
35.19	odd	6		1470.2.n.k.949.6		16
35.24	odd	6		1470.2.n.k.79.2		16
35.27	even	4		7350.2.a.du.1.2		4
35.34	odd	2		1470.2.g.k.589.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.1	✓	8	1.1	even	1	trivial
1470.2.g.j.589.5	yes	8	5.4	even	2	inner
1470.2.g.k.589.4	yes	8	7.6	odd	2
1470.2.g.k.589.8	yes	8	35.34	odd	2
1470.2.n.k.79.2		16	35.24	odd	6
1470.2.n.k.79.6		16	7.3	odd	6
1470.2.n.k.949.2		16	7.5	odd	6
1470.2.n.k.949.6		16	35.19	odd	6
1470.2.n.l.79.3		16	35.4	even	6
1470.2.n.l.79.7		16	7.4	even	3
1470.2.n.l.949.3		16	7.2	even	3
1470.2.n.l.949.7		16	35.9	even	6
7350.2.a.dr.1.2		4	35.13	even	4
7350.2.a.ds.1.2		4	5.3	odd	4
7350.2.a.dt.1.2		4	5.2	odd	4
7350.2.a.du.1.2		4	35.27	even	4

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.18183 + 0.489528i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.18183 + 0.489528i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(0.489528 + 2.18183i) q^{10} -2.39327 q^{11} +1.00000i q^{12} -3.80748i q^{13} +(0.489528 + 2.18183i) q^{15} +1.00000 q^{16} +1.97038i q^{17} +1.00000i q^{18} -4.17113 q^{19} +(2.18183 - 0.489528i) q^{20} +2.39327i q^{22} +8.17113i q^{23} +1.00000 q^{24} +(4.52072 - 2.13613i) q^{25} -3.80748 q^{26} +1.00000i q^{27} +9.16246 q^{29} +(2.18183 - 0.489528i) q^{30} -1.60673 q^{31} -1.00000i q^{32} +2.39327i q^{33} +1.97038 q^{34} +1.00000 q^{36} -1.26358i q^{37} +4.17113i q^{38} -3.80748 q^{39} +(-0.489528 - 2.18183i) q^{40} +3.19208 q^{41} +4.90755i q^{43} +2.39327 q^{44} +(2.18183 - 0.489528i) q^{45} +8.17113 q^{46} +3.00868i q^{47} -1.00000i q^{48} +(-2.13613 - 4.52072i) q^{50} +1.97038 q^{51} +3.80748i q^{52} +12.1711i q^{53} +1.00000 q^{54} +(5.22170 - 1.17157i) q^{55} +4.17113i q^{57} -9.16246i q^{58} +13.0414 q^{59} +(-0.489528 - 2.18183i) q^{60} -13.0910 q^{61} +1.60673i q^{62} -1.00000 q^{64} +(1.86387 + 8.30726i) q^{65} +2.39327 q^{66} +5.77786i q^{67} -1.97038i q^{68} +8.17113 q^{69} +6.94032 q^{71} -1.00000i q^{72} +0.506664i q^{73} -1.26358 q^{74} +(-2.13613 - 4.52072i) q^{75} +4.17113 q^{76} +3.80748i q^{78} +12.4260 q^{79} +(-2.18183 + 0.489528i) q^{80} +1.00000 q^{81} -3.19208i q^{82} +1.89887i q^{83} +(-0.964557 - 4.29903i) q^{85} +4.90755 q^{86} -9.16246i q^{87} -2.39327i q^{88} +1.97949 q^{89} +(-0.489528 - 2.18183i) q^{90} -8.17113i q^{92} +1.60673i q^{93} +3.00868 q^{94} +(9.10069 - 2.04189i) q^{95} -1.00000 q^{96} +12.0624i q^{97} +2.39327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} + 8 q^{16} + 24 q^{19} + 4 q^{20} + 8 q^{24} + 4 q^{25} + 16 q^{29} + 4 q^{30} - 32 q^{31} + 8 q^{34} + 8 q^{36} - 24 q^{41} + 4 q^{45} + 8 q^{46} - 4 q^{50} + 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 8 q^{64} + 28 q^{65} + 8 q^{69} - 40 q^{71} + 16 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 4 q^{80} + 8 q^{81} + 28 q^{85} + 8 q^{86} + 88 q^{89} + 24 q^{94} + 24 q^{95} - 8 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 + 8 * q^16 + 24 * q^19 + 4 * q^20 + 8 * q^24 + 4 * q^25 + 16 * q^29 + 4 * q^30 - 32 * q^31 + 8 * q^34 + 8 * q^36 - 24 * q^41 + 4 * q^45 + 8 * q^46 - 4 * q^50 + 8 * q^51 + 8 * q^54 + 40 * q^59 - 24 * q^61 - 8 * q^64 + 28 * q^65 + 8 * q^69 - 40 * q^71 + 16 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 4 * q^80 + 8 * q^81 + 28 * q^85 + 8 * q^86 + 88 * q^89 + 24 * q^94 + 24 * q^95 - 8 * q^96

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