LMFDB - Embedded newform 1470.2.g.k.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			$0.692297i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.k.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.88893 + 1.19663i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.88893 + 1.19663i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(1.19663 + 1.88893i) q^{10} +0.979056 q^{11} -1.00000i q^{12} +0.435157i q^{13} +(-1.19663 - 1.88893i) q^{15} +1.00000 q^{16} +2.79881i q^{17} +1.00000i q^{18} -7.34271 q^{19} +(1.88893 - 1.19663i) q^{20} -0.979056i q^{22} -3.34271i q^{23} -1.00000 q^{24} +(2.13613 - 4.52072i) q^{25} +0.435157 q^{26} -1.00000i q^{27} -3.74825 q^{29} +(-1.88893 + 1.19663i) q^{30} +4.97906 q^{31} -1.00000i q^{32} +0.979056i q^{33} +2.79881 q^{34} +1.00000 q^{36} -4.63591i q^{37} +7.34271i q^{38} -0.435157 q^{39} +(-1.19663 - 1.88893i) q^{40} +4.94944 q^{41} -9.97862i q^{43} -0.979056 q^{44} +(1.88893 - 1.19663i) q^{45} -3.34271 q^{46} -4.40554i q^{47} +1.00000i q^{48} +(-4.52072 - 2.13613i) q^{50} -2.79881 q^{51} -0.435157i q^{52} +0.657293i q^{53} -1.00000 q^{54} +(-1.84937 + 1.17157i) q^{55} -7.34271i q^{57} +3.74825i q^{58} -8.27226 q^{59} +(1.19663 + 1.88893i) q^{60} -11.3336 q^{61} -4.97906i q^{62} -1.00000 q^{64} +(-0.520724 - 0.821983i) q^{65} +0.979056 q^{66} -2.36365i q^{67} -2.79881i q^{68} +3.34271 q^{69} -14.1119 q^{71} -1.00000i q^{72} -15.3928i q^{73} -4.63591 q^{74} +(4.52072 + 2.13613i) q^{75} +7.34271 q^{76} +0.435157i q^{78} +2.88767 q^{79} +(-1.88893 + 1.19663i) q^{80} +1.00000 q^{81} -4.94944i q^{82} +14.3842i q^{83} +(-3.34915 - 5.28676i) q^{85} -9.97862 q^{86} -3.74825i q^{87} +0.979056i q^{88} -10.1210 q^{89} +(-1.19663 - 1.88893i) q^{90} +3.34271i q^{92} +4.97906i q^{93} -4.40554 q^{94} +(13.8699 - 8.78654i) q^{95} +1.00000 q^{96} -10.6655i q^{97} -0.979056 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.88893	+	1.19663i	−0.844756	+	0.535151i
$5$	−1.88893	+	1.19663i	−0.844756	+	0.535151i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	1.19663	+	1.88893i	0.378409	+	0.597333i
$11$	0.979056			0.295197			0.147598	−	0.989047i	$-0.452846\pi$
$11$	0.979056			0.295197			0.147598	+	0.989047i	$0.452846\pi$
$12$		−	1.00000i		−	0.288675i
$13$			0.435157i			0.120691i	0.998178	+	0.0603455i	$0.0192202\pi$
$13$			0.435157i			0.120691i	−0.998178	+	0.0603455i	$0.980780\pi$
$14$		0			0
$15$	−1.19663	−	1.88893i	−0.308970	−	0.487720i
$16$	1.00000			0.250000
$17$			2.79881i			0.678811i	0.940640	+	0.339405i	$0.110226\pi$
$17$			2.79881i			0.678811i	−0.940640	+	0.339405i	$0.889774\pi$
$18$			1.00000i			0.235702i
$19$	−7.34271			−1.68453			−0.842266	−	0.539062i	$-0.818779\pi$
$19$	−7.34271			−1.68453			−0.842266	+	0.539062i	$0.818779\pi$
$20$	1.88893	−	1.19663i	0.422378	−	0.267576i
$21$		0			0
$22$		−	0.979056i		−	0.208735i
$23$		−	3.34271i		−	0.697003i	−0.937308	−	0.348501i	$-0.886691\pi$
$23$		−	3.34271i		−	0.697003i	0.937308	−	0.348501i	$-0.113309\pi$
$24$	−1.00000			−0.204124
$25$	2.13613	−	4.52072i	0.427226	−	0.904145i
$26$	0.435157			0.0853414
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−3.74825			−0.696032			−0.348016	−	0.937489i	$-0.613144\pi$
$29$	−3.74825			−0.696032			−0.348016	+	0.937489i	$0.613144\pi$
$30$	−1.88893	+	1.19663i	−0.344870	+	0.218475i
$31$	4.97906			0.894265			0.447132	−	0.894468i	$-0.352445\pi$
$31$	4.97906			0.894265			0.447132	+	0.894468i	$0.352445\pi$
$32$		−	1.00000i		−	0.176777i
$33$			0.979056i			0.170432i
$34$	2.79881			0.479992
$35$		0			0
$36$	1.00000			0.166667
$37$		−	4.63591i		−	0.762139i	−0.924546	−	0.381069i	$-0.875556\pi$
$37$		−	4.63591i		−	0.762139i	0.924546	−	0.381069i	$-0.124444\pi$
$38$			7.34271i			1.19114i
$39$	−0.435157			−0.0696809
$40$	−1.19663	−	1.88893i	−0.189205	−	0.298666i
$41$	4.94944			0.772972			0.386486	−	0.922295i	$-0.373689\pi$
$41$	4.94944			0.772972			0.386486	+	0.922295i	$0.373689\pi$
$42$		0			0
$43$		−	9.97862i		−	1.52172i	−0.648913	−	0.760862i	$-0.724776\pi$
$43$		−	9.97862i		−	1.52172i	0.648913	−	0.760862i	$-0.275224\pi$
$44$	−0.979056			−0.147598
$45$	1.88893	−	1.19663i	0.281585	−	0.178384i
$46$	−3.34271			−0.492855
$47$		−	4.40554i		−	0.642614i	−0.946975	−	0.321307i	$-0.895878\pi$
$47$		−	4.40554i		−	0.642614i	0.946975	−	0.321307i	$-0.104122\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	−4.52072	−	2.13613i	−0.639327	−	0.302094i
$51$	−2.79881			−0.391912
$52$		−	0.435157i		−	0.0603455i
$53$			0.657293i			0.0902861i	0.998981	+	0.0451431i	$0.0143744\pi$
$53$			0.657293i			0.0902861i	−0.998981	+	0.0451431i	$0.985626\pi$
$54$	−1.00000			−0.136083
$55$	−1.84937	+	1.17157i	−0.249369	+	0.157975i
$56$		0			0
$57$		−	7.34271i		−	0.972565i
$58$			3.74825i			0.492169i
$59$	−8.27226			−1.07696			−0.538478	−	0.842639i	$-0.681001\pi$
$59$	−8.27226			−1.07696			−0.538478	+	0.842639i	$0.681001\pi$
$60$	1.19663	+	1.88893i	0.154485	+	0.243860i
$61$	−11.3336			−1.45112			−0.725559	−	0.688160i	$-0.758419\pi$
$61$	−11.3336			−1.45112			−0.725559	+	0.688160i	$0.758419\pi$
$62$		−	4.97906i		−	0.632341i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.520724	−	0.821983i	−0.0645879	−	0.101954i
$66$	0.979056			0.120513
$67$		−	2.36365i		−	0.288766i	−0.989522	−	0.144383i	$-0.953880\pi$
$67$		−	2.36365i		−	0.288766i	0.989522	−	0.144383i	$-0.0461197\pi$
$68$		−	2.79881i		−	0.339405i
$69$	3.34271			0.402415
$70$		0			0
$71$	−14.1119			−1.67477			−0.837387	−	0.546610i	$-0.815918\pi$
$71$	−14.1119			−1.67477			−0.837387	+	0.546610i	$0.815918\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	15.3928i		−	1.80159i	−0.434240	−	0.900797i	$-0.642983\pi$
$73$		−	15.3928i		−	1.80159i	0.434240	−	0.900797i	$-0.357017\pi$
$74$	−4.63591			−0.538914
$75$	4.52072	+	2.13613i	0.522008	+	0.246659i
$76$	7.34271			0.842266
$77$		0			0
$78$			0.435157i			0.0492719i
$79$	2.88767			0.324888			0.162444	−	0.986718i	$-0.448062\pi$
$79$	2.88767			0.324888			0.162444	+	0.986718i	$0.448062\pi$
$80$	−1.88893	+	1.19663i	−0.211189	+	0.133788i
$81$	1.00000			0.111111
$82$		−	4.94944i		−	0.546574i
$83$			14.3842i			1.57887i	0.613837	+	0.789433i	$0.289625\pi$
$83$			14.3842i			1.57887i	−0.613837	+	0.789433i	$0.710375\pi$
$84$		0			0
$85$	−3.34915	−	5.28676i	−0.363266	−	0.573430i
$86$	−9.97862			−1.07602
$87$		−	3.74825i		−	0.401854i
$88$			0.979056i			0.104368i
$89$	−10.1210			−1.07282			−0.536412	−	0.843956i	$-0.680221\pi$
$89$	−10.1210			−1.07282			−0.536412	+	0.843956i	$0.680221\pi$
$90$	−1.19663	−	1.88893i	−0.126136	−	0.199111i
$91$		0			0
$92$			3.34271i			0.348501i
$93$			4.97906i			0.516304i
$94$	−4.40554			−0.454397
$95$	13.8699	−	8.78654i	1.42302	−	0.901480i
$96$	1.00000			0.102062
$97$		−	10.6655i		−	1.08292i	−0.840726	−	0.541460i	$-0.817872\pi$
$97$		−	10.6655i		−	1.08292i	0.840726	−	0.541460i	$-0.182128\pi$
$98$		0			0
$99$	−0.979056			−0.0983989
$100$	−2.13613	+	4.52072i	−0.213613	+	0.452072i
$101$	14.0328			1.39631			0.698157	−	0.715945i	$-0.254004\pi$
$101$	14.0328			1.39631			0.698157	+	0.715945i	$0.254004\pi$
$102$			2.79881i			0.277123i
$103$		−	10.3842i		−	1.02318i	−0.859229	−	0.511591i	$-0.829056\pi$
$103$		−	10.3842i		−	1.02318i	0.859229	−	0.511591i	$-0.170944\pi$
$104$	−0.435157			−0.0426707
$105$		0			0
$106$	0.657293			0.0638419
$107$		−	20.0410i		−	1.93744i	−0.248161	−	0.968719i	$-0.579826\pi$
$107$		−	20.0410i		−	1.93744i	0.248161	−	0.968719i	$-0.420174\pi$
$108$			1.00000i			0.0962250i
$109$	−18.6564			−1.78696			−0.893480	−	0.449102i	$-0.851744\pi$
$109$	−18.6564			−1.78696			−0.893480	+	0.449102i	$0.851744\pi$
$110$	1.17157	+	1.84937i	0.111705	+	0.176331i
$111$	4.63591			0.440021
$112$		0			0
$113$			10.4132i			0.979587i	0.871838	+	0.489794i	$0.162928\pi$
$113$			10.4132i			0.979587i	−0.871838	+	0.489794i	$0.837072\pi$
$114$	−7.34271			−0.687708
$115$	4.00000	+	6.31415i	0.373002	+	0.588797i
$116$	3.74825			0.348016
$117$		−	0.435157i		−	0.0402303i
$118$			8.27226i			0.761523i
$119$		0			0
$120$	1.88893	−	1.19663i	0.172435	−	0.109237i
$121$	−10.0414			−0.912859
$122$			11.3336i			1.02610i
$123$			4.94944i			0.446276i
$124$	−4.97906			−0.447132
$125$	1.37465	+	11.0955i	0.122953	+	0.992413i
$126$		0			0
$127$			11.6987i			1.03810i	0.854745	+	0.519048i	$0.173713\pi$
$127$			11.6987i			1.03810i	−0.854745	+	0.519048i	$0.826287\pi$
$128$			1.00000i			0.0883883i
$129$	9.97862			0.878568
$130$	−0.821983	+	0.520724i	−0.0720926	+	0.0456706i
$131$	5.38459			0.470454			0.235227	−	0.971940i	$-0.424417\pi$
$131$	5.38459			0.470454			0.235227	+	0.971940i	$0.424417\pi$
$132$		−	0.979056i		−	0.0852159i
$133$		0			0
$134$	−2.36365			−0.204188
$135$	1.19663	+	1.88893i	0.102990	+	0.162573i
$136$	−2.79881			−0.239996
$137$		−	3.68585i		−	0.314904i	−0.987527	−	0.157452i	$-0.949672\pi$
$137$		−	3.68585i		−	0.314904i	0.987527	−	0.157452i	$-0.0503279\pi$
$138$		−	3.34271i		−	0.284550i
$139$	−8.15378			−0.691595			−0.345797	−	0.938309i	$-0.612392\pi$
$139$	−8.15378			−0.691595			−0.345797	+	0.938309i	$0.612392\pi$
$140$		0			0
$141$	4.40554			0.371013
$142$			14.1119i			1.18424i
$143$			0.426043i			0.0356275i
$144$	−1.00000			−0.0833333
$145$	7.08018	−	4.48528i	0.587977	−	0.372482i
$146$	−15.3928			−1.27392
$147$		0			0
$148$			4.63591i			0.381069i
$149$	15.6774			1.28434			0.642170	−	0.766563i	$-0.278034\pi$
$149$	15.6774			1.28434			0.642170	+	0.766563i	$0.278034\pi$
$150$	2.13613	−	4.52072i	0.174414	−	0.369116i
$151$	4.27226			0.347672			0.173836	−	0.984775i	$-0.444384\pi$
$151$	4.27226			0.347672			0.173836	+	0.984775i	$0.444384\pi$
$152$		−	7.34271i		−	0.595572i
$153$		−	2.79881i		−	0.226270i
$154$		0			0
$155$	−9.40510	+	5.95811i	−0.755436	+	0.478567i
$156$	0.435157			0.0348405
$157$		−	15.2498i		−	1.21707i	−0.793528	−	0.608534i	$-0.791758\pi$
$157$		−	15.2498i		−	1.21707i	0.793528	−	0.608534i	$-0.208242\pi$
$158$		−	2.88767i		−	0.229730i
$159$	−0.657293			−0.0521267
$160$	1.19663	+	1.88893i	0.0946023	+	0.149333i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$		−	7.47599i		−	0.585564i	−0.956179	−	0.292782i	$-0.905419\pi$
$163$		−	7.47599i		−	0.585564i	0.956179	−	0.292782i	$-0.0945811\pi$
$164$	−4.94944			−0.386486
$165$	−1.17157	−	1.84937i	−0.0912068	−	0.143973i
$166$	14.3842			1.11643
$167$			12.6640i			0.979972i	0.871730	+	0.489986i	$0.162998\pi$
$167$			12.6640i			0.979972i	−0.871730	+	0.489986i	$0.837002\pi$
$168$		0			0
$169$	12.8106			0.985434
$170$	−5.28676	+	3.34915i	−0.405476	+	0.256868i
$171$	7.34271			0.561511
$172$			9.97862i			0.760862i
$173$			7.12057i			0.541367i	0.962668	+	0.270684i	$0.0872497\pi$
$173$			7.12057i			0.541367i	−0.962668	+	0.270684i	$0.912750\pi$
$174$	−3.74825			−0.284154
$175$		0			0
$176$	0.979056			0.0737991
$177$		−	8.27226i		−	0.621781i
$178$			10.1210i			0.758602i
$179$	−3.26420			−0.243978			−0.121989	−	0.992531i	$-0.538927\pi$
$179$	−3.26420			−0.243978			−0.121989	+	0.992531i	$0.538927\pi$
$180$	−1.88893	+	1.19663i	−0.140793	+	0.0891919i
$181$	1.93823			0.144067			0.0720337	−	0.997402i	$-0.477051\pi$
$181$	1.93823			0.144067			0.0720337	+	0.997402i	$0.477051\pi$
$182$		0			0
$183$		−	11.3336i		−	0.837803i
$184$	3.34271			0.246428
$185$	5.54749	+	8.75692i	0.407860	+	0.643822i
$186$	4.97906			0.365082
$187$			2.74019i			0.200383i
$188$			4.40554i			0.321307i
$189$		0			0
$190$	−8.78654	−	13.8699i	−0.637443	−	1.00623i
$191$	8.07001			0.583925			0.291963	−	0.956430i	$-0.405692\pi$
$191$	8.07001			0.583925			0.291963	+	0.956430i	$0.405692\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			1.95811i			0.140948i	0.997514	+	0.0704740i	$0.0224512\pi$
$193$			1.95811i			0.140948i	−0.997514	+	0.0704740i	$0.977549\pi$
$194$	−10.6655			−0.765740
$195$	0.821983	−	0.520724i	0.0588634	−	0.0372899i
$196$		0			0
$197$			17.3418i			1.23555i	0.786353	+	0.617777i	$0.211967\pi$
$197$			17.3418i			1.23555i	−0.786353	+	0.617777i	$0.788033\pi$
$198$			0.979056i			0.0695785i
$199$	−2.59490			−0.183948			−0.0919738	−	0.995761i	$-0.529318\pi$
$199$	−2.59490			−0.183948			−0.0919738	+	0.995761i	$0.529318\pi$
$200$	4.52072	+	2.13613i	0.319663	+	0.151047i
$201$	2.36365			0.166719
$202$		−	14.0328i		−	0.987343i
$203$		0			0
$204$	2.79881			0.195956
$205$	−9.34915	+	5.92267i	−0.652973	+	0.413657i
$206$	−10.3842			−0.723498
$207$			3.34271i			0.232334i
$208$			0.435157i			0.0301727i
$209$	−7.18892			−0.497268
$210$		0			0
$211$	15.4127			1.06106			0.530528	−	0.847668i	$-0.321994\pi$
$211$	15.4127			1.06106			0.530528	+	0.847668i	$0.321994\pi$
$212$		−	0.657293i		−	0.0451431i
$213$		−	14.1119i		−	0.966931i
$214$	−20.0410			−1.36998
$215$	11.9408	+	18.8489i	0.814353	+	1.28549i
$216$	1.00000			0.0680414
$217$		0			0
$218$			18.6564i			1.26357i
$219$	15.3928			1.04015
$220$	1.84937	−	1.17157i	0.124685	−	0.0789874i
$221$	−1.21792			−0.0819263
$222$		−	4.63591i		−	0.311142i
$223$			7.61497i			0.509936i	0.966950	+	0.254968i	$0.0820649\pi$
$223$			7.61497i			0.509936i	−0.966950	+	0.254968i	$0.917935\pi$
$224$		0			0
$225$	−2.13613	+	4.52072i	−0.142409	+	0.301382i
$226$	10.4132			0.692673
$227$			8.34227i			0.553696i	0.960914	+	0.276848i	$0.0892898\pi$
$227$			8.34227i			0.553696i	−0.960914	+	0.276848i	$0.910710\pi$
$228$			7.34271i			0.486283i
$229$	−18.6901			−1.23507			−0.617537	−	0.786542i	$-0.711869\pi$
$229$	−18.6901			−1.23507			−0.617537	+	0.786542i	$0.711869\pi$
$230$	6.31415	−	4.00000i	0.416343	−	0.263752i
$231$		0			0
$232$		−	3.74825i		−	0.246084i
$233$			20.0829i			1.31567i	0.753160	+	0.657837i	$0.228529\pi$
$233$			20.0829i			1.31567i	−0.753160	+	0.657837i	$0.771471\pi$
$234$	−0.435157			−0.0284471
$235$	5.27182	+	8.32176i	0.343896	+	0.542852i
$236$	8.27226			0.538478
$237$			2.88767i			0.187574i
$238$		0			0
$239$	22.2714			1.44062			0.720308	−	0.693654i	$-0.244000\pi$
$239$	22.2714			1.44062			0.720308	+	0.693654i	$0.244000\pi$
$240$	−1.19663	−	1.88893i	−0.0772425	−	0.121930i
$241$	−6.20075			−0.399426			−0.199713	−	0.979854i	$-0.564001\pi$
$241$	−6.20075			−0.399426			−0.199713	+	0.979854i	$0.564001\pi$
$242$			10.0414i			0.645489i
$243$			1.00000i			0.0641500i
$244$	11.3336			0.725559
$245$		0			0
$246$	4.94944			0.315565
$247$		−	3.19523i		−	0.203308i
$248$			4.97906i			0.316170i
$249$	−14.3842			−0.911559
$250$	11.0955	−	1.37465i	0.701742	−	0.0869406i
$251$	−27.6560			−1.74563			−0.872815	−	0.488051i	$-0.837708\pi$
$251$	−27.6560			−1.74563			−0.872815	+	0.488051i	$0.837708\pi$
$252$		0			0
$253$		−	3.27270i		−	0.205753i
$254$	11.6987			0.734044
$255$	5.28676	−	3.34915i	0.331070	−	0.209732i
$256$	1.00000			0.0625000
$257$			11.7681i			0.734076i	0.930206	+	0.367038i	$0.119628\pi$
$257$			11.7681i			0.734076i	−0.930206	+	0.367038i	$0.880372\pi$
$258$		−	9.97862i		−	0.621242i
$259$		0			0
$260$	0.520724	+	0.821983i	0.0322940	+	0.0509772i
$261$	3.74825			0.232011
$262$		−	5.38459i		−	0.332661i
$263$		−	0.455042i		−	0.0280591i	−0.999902	−	0.0140295i	$-0.995534\pi$
$263$		−	0.455042i		−	0.0280591i	0.999902	−	0.0140295i	$-0.00446589\pi$
$264$	−0.979056			−0.0602567
$265$	−0.786540	−	1.24158i	−0.0483167	−	0.0762698i
$266$		0			0
$267$		−	10.1210i		−	0.619396i
$268$			2.36365i			0.144383i
$269$	−26.1375			−1.59363			−0.796815	−	0.604223i	$-0.793484\pi$
$269$	−26.1375			−1.59363			−0.796815	+	0.604223i	$0.793484\pi$
$270$	1.88893	−	1.19663i	0.114957	−	0.0728249i
$271$	16.7768			1.01912			0.509559	−	0.860436i	$-0.329808\pi$
$271$	16.7768			1.01912			0.509559	+	0.860436i	$0.329808\pi$
$272$			2.79881i			0.169703i
$273$		0			0
$274$	−3.68585			−0.222671
$275$	2.09139	−	4.42604i	0.126116	−	0.266900i
$276$	−3.34271			−0.201207
$277$			20.7478i			1.24661i	0.781977	+	0.623307i	$0.214211\pi$
$277$			20.7478i			1.24661i	−0.781977	+	0.623307i	$0.785789\pi$
$278$			8.15378i			0.489031i
$279$	−4.97906			−0.298088
$280$		0			0
$281$	−18.3141			−1.09253			−0.546265	−	0.837612i	$-0.683951\pi$
$281$	−18.3141			−1.09253			−0.546265	+	0.837612i	$0.683951\pi$
$282$		−	4.40554i		−	0.262346i
$283$		−	11.8525i		−	0.704560i	−0.935895	−	0.352280i	$-0.885407\pi$
$283$		−	11.8525i		−	0.704560i	0.935895	−	0.352280i	$-0.114593\pi$
$284$	14.1119			0.837387
$285$	8.78654	+	13.8699i	0.520470	+	0.821581i
$286$	0.426043			0.0251925
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	9.16667			0.539216
$290$	−4.48528	−	7.08018i	−0.263385	−	0.415763i
$291$	10.6655			0.625224
$292$			15.3928i			0.900797i
$293$		−	14.4770i		−	0.845758i	−0.906186	−	0.422879i	$-0.861020\pi$
$293$		−	14.4770i		−	0.845758i	0.906186	−	0.422879i	$-0.138980\pi$
$294$		0			0
$295$	15.6257	−	9.89887i	0.909766	−	0.576335i
$296$	4.63591			0.269457
$297$		−	0.979056i		−	0.0568106i
$298$		−	15.6774i		−	0.908165i
$299$	1.45460			0.0841219
$300$	−4.52072	−	2.13613i	−0.261004	−	0.123330i
$301$		0			0
$302$		−	4.27226i		−	0.245841i
$303$			14.0328i			0.806162i
$304$	−7.34271			−0.421133
$305$	21.4084	−	13.5622i	1.22584	−	0.776568i
$306$	−2.79881			−0.159997
$307$		−	30.4252i		−	1.73646i	−0.496165	−	0.868228i	$-0.665259\pi$
$307$		−	30.4252i		−	1.73646i	0.496165	−	0.868228i	$-0.334741\pi$
$308$		0			0
$309$	10.3842			0.590734
$310$	5.95811	+	9.40510i	0.338398	+	0.534174i
$311$	−9.02856			−0.511963			−0.255981	−	0.966682i	$-0.582399\pi$
$311$	−9.02856			−0.511963			−0.255981	+	0.966682i	$0.582399\pi$
$312$		−	0.435157i		−	0.0246359i
$313$			17.1732i			0.970688i	0.874323	+	0.485344i	$0.161306\pi$
$313$			17.1732i			0.970688i	−0.874323	+	0.485344i	$0.838694\pi$
$314$	−15.2498			−0.860597
$315$		0			0
$316$	−2.88767			−0.162444
$317$		−	2.61541i		−	0.146896i	−0.997299	−	0.0734479i	$-0.976600\pi$
$317$		−	2.61541i		−	0.146896i	0.997299	−	0.0734479i	$-0.0234003\pi$
$318$			0.657293i			0.0368592i
$319$	−3.66974			−0.205466
$320$	1.88893	−	1.19663i	0.105595	−	0.0668939i
$321$	20.0410			1.11858
$322$		0			0
$323$		−	20.5508i		−	1.14348i
$324$	−1.00000			−0.0555556
$325$	1.96723	+	0.929553i	0.109122	+	0.0515623i
$326$	−7.47599			−0.414057
$327$		−	18.6564i		−	1.03170i
$328$			4.94944i			0.273287i
$329$		0			0
$330$	−1.84937	+	1.17157i	−0.101805	+	0.0644930i
$331$	−17.7559			−0.975950			−0.487975	−	0.872857i	$-0.662264\pi$
$331$	−17.7559			−0.975950			−0.487975	+	0.872857i	$0.662264\pi$
$332$		−	14.3842i		−	0.789433i
$333$			4.63591i			0.254046i
$334$	12.6640			0.692945
$335$	2.82843	+	4.46478i	0.154533	+	0.243937i
$336$		0			0
$337$			24.2304i			1.31991i	0.751304	+	0.659956i	$0.229425\pi$
$337$			24.2304i			1.31991i	−0.751304	+	0.659956i	$0.770575\pi$
$338$		−	12.8106i		−	0.696807i
$339$	−10.4132			−0.565565
$340$	3.34915	+	5.28676i	0.181633	+	0.286715i
$341$	4.87478			0.263984
$342$		−	7.34271i		−	0.397048i
$343$		0			0
$344$	9.97862			0.538011
$345$	−6.31415	+	4.00000i	−0.339942	+	0.215353i
$346$	7.12057			0.382804
$347$		−	30.4252i		−	1.63331i	−0.577127	−	0.816654i	$-0.695826\pi$
$347$		−	30.4252i		−	1.63331i	0.577127	−	0.816654i	$-0.304174\pi$
$348$			3.74825i			0.200927i
$349$	−30.2623			−1.61990			−0.809951	−	0.586497i	$-0.800506\pi$
$349$	−30.2623			−1.61990			−0.809951	+	0.586497i	$0.800506\pi$
$350$		0			0
$351$	0.435157			0.0232270
$352$		−	0.979056i		−	0.0521839i
$353$			4.37189i			0.232692i	0.993209	+	0.116346i	$0.0371182\pi$
$353$			4.37189i			0.232692i	−0.993209	+	0.116346i	$0.962882\pi$
$354$	−8.27226			−0.439666
$355$	26.6564	−	16.8868i	1.41478	−	0.896258i
$356$	10.1210			0.536412
$357$		0			0
$358$			3.26420i			0.172519i
$359$	15.6850			0.827821			0.413911	−	0.910318i	$-0.364163\pi$
$359$	15.6850			0.827821			0.413911	+	0.910318i	$0.364163\pi$
$360$	1.19663	+	1.88893i	0.0630682	+	0.0995555i
$361$	34.9153			1.83765
$362$		−	1.93823i		−	0.101871i
$363$		−	10.0414i		−	0.527039i
$364$		0			0
$365$	18.4196	+	29.0760i	0.964126	+	1.52191i
$366$	−11.3336			−0.592416
$367$			4.94478i			0.258116i	0.991637	+	0.129058i	$0.0411953\pi$
$367$			4.94478i			0.258116i	−0.991637	+	0.129058i	$0.958805\pi$
$368$		−	3.34271i		−	0.174251i
$369$	−4.94944			−0.257657
$370$	8.75692	−	5.54749i	0.455251	−	0.288400i
$371$		0			0
$372$		−	4.97906i		−	0.258152i
$373$		−	6.02138i		−	0.311775i	−0.987775	−	0.155888i	$-0.950176\pi$
$373$		−	6.02138i		−	0.311775i	0.987775	−	0.155888i	$-0.0498238\pi$
$374$	2.74019			0.141692
$375$	−11.0955	+	1.37465i	−0.572970	+	0.0709867i
$376$	4.40554			0.227198
$377$		−	1.63108i		−	0.0840047i
$378$		0			0
$379$	36.8030			1.89044			0.945222	−	0.326429i	$-0.105845\pi$
$379$	36.8030			1.89044			0.945222	+	0.326429i	$0.105845\pi$
$380$	−13.8699	+	8.78654i	−0.711510	+	0.450740i
$381$	−11.6987			−0.599345
$382$		−	8.07001i		−	0.412898i
$383$			9.03383i			0.461607i	0.973000	+	0.230804i	$0.0741355\pi$
$383$			9.03383i			0.461607i	−0.973000	+	0.230804i	$0.925864\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	1.95811			0.0996653
$387$			9.97862i			0.507242i
$388$			10.6655i			0.541460i
$389$	−33.5646			−1.70179			−0.850896	−	0.525334i	$-0.823940\pi$
$389$	−33.5646			−1.70179			−0.850896	+	0.525334i	$0.823940\pi$
$390$	−0.520724	−	0.821983i	−0.0263679	−	0.0416227i
$391$	9.35560			0.473133
$392$		0			0
$393$			5.38459i			0.271617i
$394$	17.3418			0.873669
$395$	−5.45460	+	3.45548i	−0.274451	+	0.173864i
$396$	0.979056			0.0491994
$397$			33.9792i			1.70537i	0.522426	+	0.852685i	$0.325027\pi$
$397$			33.9792i			1.70537i	−0.522426	+	0.852685i	$0.674973\pi$
$398$			2.59490i			0.130071i
$399$		0			0
$400$	2.13613	−	4.52072i	0.106806	−	0.226036i
$401$	−4.27226			−0.213346			−0.106673	−	0.994294i	$-0.534020\pi$
$401$	−4.27226			−0.213346			−0.106673	+	0.994294i	$0.534020\pi$
$402$		−	2.36365i		−	0.117888i
$403$			2.16667i			0.107930i
$404$	−14.0328			−0.698157
$405$	−1.88893	+	1.19663i	−0.0938618	+	0.0594613i
$406$		0			0
$407$		−	4.53882i		−	0.224981i
$408$		−	2.79881i		−	0.138562i
$409$	−3.63888			−0.179931			−0.0899656	−	0.995945i	$-0.528676\pi$
$409$	−3.63888			−0.179931			−0.0899656	+	0.995945i	$0.528676\pi$
$410$	5.92267	+	9.34915i	0.292500	+	0.461722i
$411$	3.68585			0.181810
$412$			10.3842i			0.511591i
$413$		0			0
$414$	3.34271			0.164285
$415$	−17.2126	−	27.1707i	−0.844932	−	1.33376i
$416$	0.435157			0.0213353
$417$		−	8.15378i		−	0.399293i
$418$			7.18892i			0.351622i
$419$	26.6274			1.30083			0.650417	−	0.759577i	$-0.274594\pi$
$419$	26.6274			1.30083			0.650417	+	0.759577i	$0.274594\pi$
$420$		0			0
$421$	−15.1880			−0.740220			−0.370110	−	0.928988i	$-0.620680\pi$
$421$	−15.1880			−0.740220			−0.370110	+	0.928988i	$0.620680\pi$
$422$		−	15.4127i		−	0.750279i
$423$			4.40554i			0.214205i
$424$	−0.657293			−0.0319210
$425$	12.6526	+	5.97862i	0.613743	+	0.290006i
$426$	−14.1119			−0.683724
$427$		0			0
$428$			20.0410i			0.968719i
$429$	−0.426043			−0.0205696
$430$	18.8489	−	11.9408i	0.908976	−	0.575835i
$431$	−4.23125			−0.203812			−0.101906	−	0.994794i	$-0.532494\pi$
$431$	−4.23125			−0.203812			−0.101906	+	0.994794i	$0.532494\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	33.9352i		−	1.63082i	−0.578882	−	0.815412i	$-0.696511\pi$
$433$		−	33.9352i		−	1.63082i	0.578882	−	0.815412i	$-0.303489\pi$
$434$		0			0
$435$	4.48528	+	7.08018i	0.215053	+	0.339469i
$436$	18.6564			0.893480
$437$			24.5445i			1.17412i
$438$		−	15.3928i		−	0.735498i
$439$	−5.48257			−0.261669			−0.130834	−	0.991404i	$-0.541766\pi$
$439$	−5.48257			−0.261669			−0.130834	+	0.991404i	$0.541766\pi$
$440$	−1.17157	−	1.84937i	−0.0558525	−	0.0881653i
$441$		0			0
$442$			1.21792i			0.0579306i
$443$			1.23081i			0.0584776i	0.999572	+	0.0292388i	$0.00930832\pi$
$443$			1.23081i			0.0584776i	−0.999572	+	0.0292388i	$0.990692\pi$
$444$	−4.63591			−0.220011
$445$	19.1179	−	12.1112i	0.906275	−	0.574124i
$446$	7.61497			0.360579
$447$			15.6774i			0.741514i
$448$		0			0
$449$	−14.6435			−0.691071			−0.345535	−	0.938406i	$-0.612303\pi$
$449$	−14.6435			−0.691071			−0.345535	+	0.938406i	$0.612303\pi$
$450$	4.52072	+	2.13613i	0.213109	+	0.100698i
$451$	4.84578			0.228179
$452$		−	10.4132i		−	0.489794i
$453$			4.27226i			0.200728i
$454$	8.34227			0.391522
$455$		0			0
$456$	7.34271			0.343854
$457$			31.3289i			1.46551i	0.680495	+	0.732753i	$0.261765\pi$
$457$			31.3289i			1.46551i	−0.680495	+	0.732753i	$0.738235\pi$
$458$			18.6901i			0.873329i
$459$	2.79881			0.130637
$460$	−4.00000	−	6.31415i	−0.186501	−	0.294399i
$461$	−12.7667			−0.594602			−0.297301	−	0.954784i	$-0.596087\pi$
$461$	−12.7667			−0.594602			−0.297301	+	0.954784i	$0.596087\pi$
$462$		0			0
$463$		−	26.7112i		−	1.24137i	−0.784058	−	0.620687i	$-0.786854\pi$
$463$		−	26.7112i		−	1.24137i	0.784058	−	0.620687i	$-0.213146\pi$
$464$	−3.74825			−0.174008
$465$	−5.95811	−	9.40510i	−0.276301	−	0.436151i
$466$	20.0829			0.930322
$467$		−	37.6141i		−	1.74057i	−0.492546	−	0.870286i	$-0.663934\pi$
$467$		−	37.6141i		−	1.74057i	0.492546	−	0.870286i	$-0.336066\pi$
$468$			0.435157i			0.0201152i
$469$		0			0
$470$	8.32176	−	5.27182i	0.383854	−	0.243171i
$471$	15.2498			0.702675
$472$		−	8.27226i		−	0.380762i
$473$		−	9.76963i		−	0.449208i
$474$	2.88767			0.132635
$475$	−15.6850	+	33.1944i	−0.719676	+	1.52306i
$476$		0			0
$477$		−	0.657293i		−	0.0300954i
$478$		−	22.2714i		−	1.01867i
$479$	−23.8235			−1.08852			−0.544262	−	0.838915i	$-0.683190\pi$
$479$	−23.8235			−1.08852			−0.544262	+	0.838915i	$0.683190\pi$
$480$	−1.88893	+	1.19663i	−0.0862176	+	0.0546187i
$481$	2.01735			0.0919833
$482$			6.20075i			0.282437i
$483$		0			0
$484$	10.0414			0.456429
$485$	12.7627	+	20.1465i	0.579526	+	0.914804i
$486$	1.00000			0.0453609
$487$			3.75674i			0.170234i	0.996371	+	0.0851170i	$0.0271264\pi$
$487$			3.75674i			0.170234i	−0.996371	+	0.0851170i	$0.972874\pi$
$488$		−	11.3336i		−	0.513048i
$489$	7.47599			0.338076
$490$		0			0
$491$	2.00762			0.0906025			0.0453012	−	0.998973i	$-0.485575\pi$
$491$	2.00762			0.0906025			0.0453012	+	0.998973i	$0.485575\pi$
$492$		−	4.94944i		−	0.223138i
$493$		−	10.4906i		−	0.472474i
$494$	−3.19523			−0.143760
$495$	1.84937	−	1.17157i	0.0831230	−	0.0526583i
$496$	4.97906			0.223566
$497$		0			0
$498$			14.3842i			0.644569i
$499$	0.628294			0.0281263			0.0140632	−	0.999901i	$-0.495523\pi$
$499$	0.628294			0.0281263			0.0140632	+	0.999901i	$0.495523\pi$
$500$	−1.37465	−	11.0955i	−0.0614763	−	0.496206i
$501$	−12.6640			−0.565787
$502$			27.6560i			1.23435i
$503$		−	28.9911i		−	1.29265i	−0.763063	−	0.646324i	$-0.776305\pi$
$503$		−	28.9911i		−	1.29265i	0.763063	−	0.646324i	$-0.223695\pi$
$504$		0			0
$505$	−26.5070	+	16.7921i	−1.17954	+	0.747239i
$506$	−3.27270			−0.145489
$507$			12.8106i			0.568940i
$508$		−	11.6987i		−	0.519048i
$509$	−15.5056			−0.687274			−0.343637	−	0.939103i	$-0.611659\pi$
$509$	−15.5056			−0.687274			−0.343637	+	0.939103i	$0.611659\pi$
$510$	−3.34915	−	5.28676i	−0.148303	−	0.234102i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			7.34271i			0.324188i
$514$	11.7681			0.519070
$515$	12.4260	+	19.6150i	0.547557	+	0.864339i
$516$	−9.97862			−0.439284
$517$		−	4.31327i		−	0.189697i
$518$		0			0
$519$	−7.12057			−0.312558
$520$	0.821983	−	0.520724i	0.0360463	−	0.0228353i
$521$	13.5532			0.593776			0.296888	−	0.954912i	$-0.404051\pi$
$521$	13.5532			0.593776			0.296888	+	0.954912i	$0.404051\pi$
$522$		−	3.74825i		−	0.164056i
$523$		−	22.4542i		−	0.981852i	−0.871201	−	0.490926i	$-0.836659\pi$
$523$		−	22.4542i		−	0.981852i	0.871201	−	0.490926i	$-0.163341\pi$
$524$	−5.38459			−0.235227
$525$		0			0
$526$	−0.455042			−0.0198408
$527$			13.9354i			0.607037i
$528$			0.979056i			0.0426080i
$529$	11.8263			0.514187
$530$	−1.24158	+	0.786540i	−0.0539309	+	0.0341651i
$531$	8.27226			0.358985
$532$		0			0
$533$			2.15378i			0.0932907i
$534$	−10.1210			−0.437979
$535$	23.9818	+	37.8561i	1.03682	+	1.63666i
$536$	2.36365			0.102094
$537$		−	3.26420i		−	0.140861i
$538$			26.1375i			1.12687i
$539$		0			0
$540$	−1.19663	−	1.88893i	−0.0514950	−	0.0812867i
$541$	10.8111			0.464804			0.232402	−	0.972620i	$-0.425341\pi$
$541$	10.8111			0.464804			0.232402	+	0.972620i	$0.425341\pi$
$542$		−	16.7768i		−	0.720625i
$543$			1.93823i			0.0831773i
$544$	2.79881			0.119998
$545$	35.2407	−	22.3249i	1.50955	−	0.956294i
$546$		0			0
$547$			24.1881i			1.03421i	0.855923	+	0.517103i	$0.172990\pi$
$547$			24.1881i			1.03421i	−0.855923	+	0.517103i	$0.827010\pi$
$548$			3.68585i			0.157452i
$549$	11.3336			0.483706
$550$	−4.42604	−	2.09139i	−0.188727	−	0.0891772i
$551$	27.5223			1.17249
$552$			3.34271i			0.142275i
$553$		0			0
$554$	20.7478			0.881490
$555$	−8.75692	+	5.54749i	−0.371711	+	0.235478i
$556$	8.15378			0.345797
$557$			26.1529i			1.10813i	0.832472	+	0.554067i	$0.186925\pi$
$557$			26.1529i			1.10813i	−0.832472	+	0.554067i	$0.813075\pi$
$558$			4.97906i			0.210780i
$559$	4.34227			0.183658
$560$		0			0
$561$	−2.74019			−0.115691
$562$			18.3141i			0.772536i
$563$		−	10.5864i		−	0.446164i	−0.974800	−	0.223082i	$-0.928388\pi$
$563$		−	10.5864i		−	0.446164i	0.974800	−	0.223082i	$-0.0716117\pi$
$564$	−4.40554			−0.185507
$565$	−12.4607	−	19.6697i	−0.524227	−	0.827512i
$566$	−11.8525			−0.498199
$567$		0			0
$568$		−	14.1119i		−	0.592122i
$569$	−15.6440			−0.655829			−0.327915	−	0.944707i	$-0.606346\pi$
$569$	−15.6440			−0.655829			−0.327915	+	0.944707i	$0.606346\pi$
$570$	13.8699	−	8.78654i	0.580945	−	0.368028i
$571$	8.50982			0.356125			0.178062	−	0.984019i	$-0.443017\pi$
$571$	8.50982			0.356125			0.178062	+	0.984019i	$0.443017\pi$
$572$		−	0.426043i		−	0.0178138i
$573$			8.07001i			0.337129i
$574$		0			0
$575$	−15.1115	−	7.14046i	−0.630191	−	0.297778i
$576$	1.00000			0.0416667
$577$		−	9.67798i		−	0.402900i	−0.979499	−	0.201450i	$-0.935435\pi$
$577$		−	9.67798i		−	0.402900i	0.979499	−	0.201450i	$-0.0645653\pi$
$578$		−	9.16667i		−	0.381283i
$579$	−1.95811			−0.0813764
$580$	−7.08018	+	4.48528i	−0.293989	+	0.186241i
$581$		0			0
$582$		−	10.6655i		−	0.442100i
$583$			0.643527i			0.0266522i
$584$	15.3928			0.636960
$585$	0.520724	+	0.821983i	0.0215293	+	0.0339848i
$586$	−14.4770			−0.598041
$587$			16.3013i			0.672825i	0.941715	+	0.336412i	$0.109214\pi$
$587$			16.3013i			0.672825i	−0.941715	+	0.336412i	$0.890786\pi$
$588$		0			0
$589$	−36.5598			−1.50642
$590$	−9.89887	−	15.6257i	−0.407530	−	0.643301i
$591$	−17.3418			−0.713348
$592$		−	4.63591i		−	0.190535i
$593$		−	12.4802i		−	0.512500i	−0.966610	−	0.256250i	$-0.917513\pi$
$593$		−	12.4802i		−	0.512500i	0.966610	−	0.256250i	$-0.0824871\pi$
$594$	−0.979056			−0.0401712
$595$		0			0
$596$	−15.6774			−0.642170
$597$		−	2.59490i		−	0.106202i
$598$		−	1.45460i		−	0.0594832i
$599$	−40.7545			−1.66519			−0.832593	−	0.553886i	$-0.813144\pi$
$599$	−40.7545			−1.66519			−0.832593	+	0.553886i	$0.813144\pi$
$600$	−2.13613	+	4.52072i	−0.0872071	+	0.184558i
$601$	−4.94541			−0.201727			−0.100864	−	0.994900i	$-0.532161\pi$
$601$	−4.94541			−0.201727			−0.100864	+	0.994900i	$0.532161\pi$
$602$		0			0
$603$			2.36365i			0.0962553i
$604$	−4.27226			−0.173836
$605$	18.9676	−	12.0159i	0.771143	−	0.488518i
$606$	14.0328			0.570042
$607$			0.871555i			0.0353753i	0.999844	+	0.0176877i	$0.00563045\pi$
$607$			0.871555i			0.0353753i	−0.999844	+	0.0176877i	$0.994370\pi$
$608$			7.34271i			0.297786i
$609$		0			0
$610$	−13.5622	−	21.4084i	−0.549116	−	0.866800i
$611$	1.91710			0.0775577
$612$			2.79881i			0.113135i
$613$			36.9007i			1.49041i	0.666838	+	0.745203i	$0.267647\pi$
$613$			36.9007i			1.49041i	−0.666838	+	0.745203i	$0.732353\pi$
$614$	−30.4252			−1.22786
$615$	−5.92267	−	9.34915i	−0.238825	−	0.376994i
$616$		0			0
$617$		−	28.6911i		−	1.15506i	−0.816369	−	0.577530i	$-0.804016\pi$
$617$		−	28.6911i		−	1.15506i	0.816369	−	0.577530i	$-0.195984\pi$
$618$		−	10.3842i		−	0.417712i
$619$	−6.31415			−0.253787			−0.126894	−	0.991916i	$-0.540501\pi$
$619$	−6.31415			−0.253787			−0.126894	+	0.991916i	$0.540501\pi$
$620$	9.40510	−	5.95811i	0.377718	−	0.239284i
$621$	−3.34271			−0.134138
$622$			9.02856i			0.362012i
$623$		0			0
$624$	−0.435157			−0.0174202
$625$	−15.8739	−	19.3137i	−0.634956	−	0.772548i
$626$	17.1732			0.686380
$627$		−	7.18892i		−	0.287098i
$628$			15.2498i			0.608534i
$629$	12.9750			0.517348
$630$		0			0
$631$	−0.237559			−0.00945707			−0.00472853	−	0.999989i	$-0.501505\pi$
$631$	−0.237559			−0.00945707			−0.00472853	+	0.999989i	$0.501505\pi$
$632$			2.88767i			0.114865i
$633$			15.4127i			0.612600i
$634$	−2.61541			−0.103871
$635$	−13.9991	−	22.0981i	−0.555538	−	0.876938i
$636$	0.657293			0.0260634
$637$		0			0
$638$			3.66974i			0.145287i
$639$	14.1119			0.558258
$640$	−1.19663	−	1.88893i	−0.0473011	−	0.0746666i
$641$	−15.3490			−0.606250			−0.303125	−	0.952951i	$-0.598030\pi$
$641$	−15.3490			−0.606250			−0.303125	+	0.952951i	$0.598030\pi$
$642$		−	20.0410i		−	0.790956i
$643$		−	8.77577i		−	0.346083i	−0.984915	−	0.173041i	$-0.944641\pi$
$643$		−	8.77577i		−	0.346083i	0.984915	−	0.173041i	$-0.0553594\pi$
$644$		0			0
$645$	−18.8489	+	11.9408i	−0.742176	+	0.470167i
$646$	−20.5508			−0.808562
$647$		−	19.2504i		−	0.756813i	−0.925640	−	0.378406i	$-0.876472\pi$
$647$		−	19.2504i		−	0.756813i	0.925640	−	0.378406i	$-0.123528\pi$
$648$			1.00000i			0.0392837i
$649$	−8.09901			−0.317914
$650$	0.929553	−	1.96723i	0.0364600	−	0.0771610i
$651$		0			0
$652$			7.47599i			0.292782i
$653$			7.45460i			0.291721i	0.989305	+	0.145861i	$0.0465951\pi$
$653$			7.45460i			0.291721i	−0.989305	+	0.145861i	$0.953405\pi$
$654$	−18.6564			−0.729524
$655$	−10.1711	+	6.44339i	−0.397419	+	0.251764i
$656$	4.94944			0.193243
$657$			15.3928i			0.600532i
$658$		0			0
$659$	−2.93717			−0.114416			−0.0572079	−	0.998362i	$-0.518220\pi$
$659$	−2.93717			−0.114416			−0.0572079	+	0.998362i	$0.518220\pi$
$660$	1.17157	+	1.84937i	0.0456034	+	0.0719867i
$661$	−23.6361			−0.919337			−0.459669	−	0.888090i	$-0.652032\pi$
$661$	−23.6361			−0.919337			−0.459669	+	0.888090i	$0.652032\pi$
$662$			17.7559i			0.690101i
$663$		−	1.21792i		−	0.0473002i
$664$	−14.3842			−0.558214
$665$		0			0
$666$	4.63591			0.179638
$667$			12.5293i			0.485136i
$668$		−	12.6640i		−	0.489986i
$669$	−7.61497			−0.294412
$670$	4.46478	−	2.82843i	0.172489	−	0.109272i
$671$	−11.0962			−0.428365
$672$		0			0
$673$		−	50.9568i		−	1.96424i	−0.188256	−	0.982120i	$-0.560283\pi$
$673$		−	50.9568i		−	1.96424i	0.188256	−	0.982120i	$-0.439717\pi$
$674$	24.2304			0.933319
$675$	−4.52072	−	2.13613i	−0.174003	−	0.0822197i
$676$	−12.8106			−0.492717
$677$			5.23992i			0.201387i	0.994918	+	0.100693i	$0.0321061\pi$
$677$			5.23992i			0.201387i	−0.994918	+	0.100693i	$0.967894\pi$
$678$			10.4132i			0.399915i
$679$		0			0
$680$	5.28676	−	3.34915i	0.202738	−	0.128434i
$681$	−8.34227			−0.319676
$682$		−	4.87478i		−	0.186665i
$683$			32.2648i			1.23458i	0.786736	+	0.617289i	$0.211769\pi$
$683$			32.2648i			1.23458i	−0.786736	+	0.617289i	$0.788231\pi$
$684$	−7.34271			−0.280755
$685$	4.41062	+	6.96233i	0.168521	+	0.266017i
$686$		0			0
$687$		−	18.6901i		−	0.713071i
$688$		−	9.97862i		−	0.380431i
$689$	−0.286026			−0.0108967
$690$	4.00000	+	6.31415i	0.152277	+	0.240375i
$691$	−20.4470			−0.777840			−0.388920	−	0.921272i	$-0.627152\pi$
$691$	−20.4470			−0.777840			−0.388920	+	0.921272i	$0.627152\pi$
$692$		−	7.12057i		−	0.270684i
$693$		0			0
$694$	−30.4252			−1.15492
$695$	15.4019	−	9.75710i	0.584229	−	0.370108i
$696$	3.74825			0.142077
$697$			13.8525i			0.524702i
$698$			30.2623i			1.14544i
$699$	−20.0829			−0.759605
$700$		0			0
$701$	−15.4969			−0.585311			−0.292655	−	0.956218i	$-0.594539\pi$
$701$	−15.4969			−0.585311			−0.292655	+	0.956218i	$0.594539\pi$
$702$		−	0.435157i		−	0.0164240i
$703$			34.0401i			1.28385i
$704$	−0.979056			−0.0368996
$705$	−8.32176	+	5.27182i	−0.313416	+	0.198548i
$706$	4.37189			0.164538
$707$		0			0
$708$			8.27226i			0.310891i
$709$	−38.9212			−1.46172			−0.730859	−	0.682529i	$-0.760880\pi$
$709$	−38.9212			−1.46172			−0.730859	+	0.682529i	$0.760880\pi$
$710$	−16.8868	−	26.6564i	−0.633750	−	1.00040i
$711$	−2.88767			−0.108296
$712$		−	10.1210i		−	0.379301i
$713$		−	16.6435i		−	0.623305i
$714$		0			0
$715$	−0.509819	−	0.804767i	−0.0190661	−	0.0300966i
$716$	3.26420			0.121989
$717$			22.2714i			0.831740i
$718$		−	15.6850i		−	0.585358i
$719$	−3.53119			−0.131691			−0.0658456	−	0.997830i	$-0.520974\pi$
$719$	−3.53119			−0.131691			−0.0658456	+	0.997830i	$0.520974\pi$
$720$	1.88893	−	1.19663i	0.0703963	−	0.0445959i
$721$		0			0
$722$		−	34.9153i		−	1.29941i
$723$		−	6.20075i		−	0.230608i
$724$	−1.93823			−0.0720337
$725$	−8.00674	+	16.9448i	−0.297363	+	0.629314i
$726$	−10.0414			−0.372673
$727$			45.2934i			1.67984i	0.542712	+	0.839919i	$0.317398\pi$
$727$			45.2934i			1.67984i	−0.542712	+	0.839919i	$0.682602\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	29.0760	−	18.4196i	1.07615	−	0.681740i
$731$	27.9282			1.03296
$732$			11.3336i			0.418902i
$733$		−	48.5462i		−	1.79309i	−0.442949	−	0.896547i	$-0.646068\pi$
$733$		−	48.5462i		−	1.79309i	0.442949	−	0.896547i	$-0.353932\pi$
$734$	4.94478			0.182515
$735$		0			0
$736$	−3.34271			−0.123214
$737$		−	2.31415i		−	0.0852427i
$738$			4.94944i			0.182191i
$739$	−25.7969			−0.948953			−0.474477	−	0.880268i	$-0.657363\pi$
$739$	−25.7969			−0.948953			−0.474477	+	0.880268i	$0.657363\pi$
$740$	−5.54749	−	8.75692i	−0.203930	−	0.321911i
$741$	3.19523			0.117380
$742$		0			0
$743$		−	28.7192i		−	1.05361i	−0.849987	−	0.526803i	$-0.823390\pi$
$743$		−	28.7192i		−	1.05361i	0.849987	−	0.526803i	$-0.176610\pi$
$744$	−4.97906			−0.182541
$745$	−29.6135	+	18.7601i	−1.08495	+	0.687316i
$746$	−6.02138			−0.220458
$747$		−	14.3842i		−	0.526289i
$748$		−	2.74019i		−	0.100191i
$749$		0			0
$750$	1.37465	+	11.0955i	0.0501952	+	0.405151i
$751$	−34.1876			−1.24752			−0.623762	−	0.781615i	$-0.714396\pi$
$751$	−34.1876			−1.24752			−0.623762	+	0.781615i	$0.714396\pi$
$752$		−	4.40554i		−	0.160653i
$753$		−	27.6560i		−	1.00784i
$754$	−1.63108			−0.0594003
$755$	−8.07001	+	5.11233i	−0.293698	+	0.186057i
$756$		0			0
$757$			41.4622i			1.50697i	0.657465	+	0.753485i	$0.271629\pi$
$757$			41.4622i			1.50697i	−0.657465	+	0.753485i	$0.728371\pi$
$758$		−	36.8030i		−	1.33675i
$759$	3.27270			0.118791
$760$	8.78654	+	13.8699i	0.318721	+	0.503113i
$761$	−27.6941			−1.00391			−0.501955	−	0.864894i	$-0.667386\pi$
$761$	−27.6941			−1.00391			−0.501955	+	0.864894i	$0.667386\pi$
$762$			11.6987i			0.423801i
$763$		0			0
$764$	−8.07001			−0.291963
$765$	3.34915	+	5.28676i	0.121089	+	0.191143i
$766$	9.03383			0.326406
$767$		−	3.59973i		−	0.129979i
$768$			1.00000i			0.0360844i
$769$	9.74001			0.351234			0.175617	−	0.984459i	$-0.443808\pi$
$769$	9.74001			0.351234			0.175617	+	0.984459i	$0.443808\pi$
$770$		0			0
$771$	−11.7681			−0.423819
$772$		−	1.95811i		−	0.0704740i
$773$		−	30.6171i		−	1.10122i	−0.834763	−	0.550610i	$-0.814395\pi$
$773$		−	30.6171i		−	1.10122i	0.834763	−	0.550610i	$-0.185605\pi$
$774$	9.97862			0.358674
$775$	10.6359	−	22.5089i	0.382053	−	0.808545i
$776$	10.6655			0.382870
$777$		0			0
$778$			33.5646i			1.20335i
$779$	−36.3423			−1.30210
$780$	−0.821983	+	0.520724i	−0.0294317	+	0.0186449i
$781$	−13.8163			−0.494388
$782$		−	9.35560i		−	0.334555i
$783$			3.74825i			0.133951i
$784$		0			0
$785$	18.2485	+	28.8059i	0.651316	+	1.02813i
$786$	5.38459			0.192062
$787$			15.7977i			0.563129i	0.959542	+	0.281564i	$0.0908533\pi$
$787$			15.7977i			0.563129i	−0.959542	+	0.281564i	$0.909147\pi$
$788$		−	17.3418i		−	0.617777i
$789$	0.455042			0.0161999
$790$	3.45548	+	5.45460i	0.122940	+	0.194066i
$791$		0			0
$792$		−	0.979056i		−	0.0347892i
$793$		−	4.93190i		−	0.175137i
$794$	33.9792			1.20588
$795$	1.24158	−	0.786540i	0.0440344	−	0.0278957i
$796$	2.59490			0.0919738
$797$			47.6651i			1.68838i	0.536041	+	0.844192i	$0.319919\pi$
$797$			47.6651i			1.68838i	−0.536041	+	0.844192i	$0.680081\pi$
$798$		0			0
$799$	12.3303			0.436213
$800$	−4.52072	−	2.13613i	−0.159832	−	0.0755236i
$801$	10.1210			0.357608
$802$			4.27226i			0.150859i
$803$		−	15.0704i		−	0.531825i
$804$	−2.36365			−0.0833595
$805$		0			0
$806$	2.16667			0.0763178
$807$		−	26.1375i		−	0.920083i
$808$			14.0328i			0.493671i
$809$	17.2709			0.607214			0.303607	−	0.952797i	$-0.401809\pi$
$809$	17.2709			0.607214			0.303607	+	0.952797i	$0.401809\pi$
$810$	1.19663	+	1.88893i	0.0420455	+	0.0663703i
$811$	14.7901			0.519351			0.259676	−	0.965696i	$-0.416384\pi$
$811$	14.7901			0.519351			0.259676	+	0.965696i	$0.416384\pi$
$812$		0			0
$813$			16.7768i			0.588388i
$814$	−4.53882			−0.159085
$815$	8.94603	+	14.1216i	0.313366	+	0.494659i
$816$	−2.79881			−0.0979779
$817$			73.2701i			2.56340i
$818$			3.63888i			0.127231i
$819$		0			0
$820$	9.34915	−	5.92267i	0.326487	−	0.206829i
$821$	−45.6917			−1.59465			−0.797326	−	0.603549i	$-0.793753\pi$
$821$	−45.6917			−1.59465			−0.797326	+	0.603549i	$0.793753\pi$
$822$		−	3.68585i		−	0.128559i
$823$		−	4.99386i		−	0.174075i	−0.996205	−	0.0870375i	$-0.972260\pi$
$823$		−	4.99386i		−	0.174075i	0.996205	−	0.0870375i	$-0.0277400\pi$
$824$	10.3842			0.361749
$825$	4.42604	+	2.09139i	0.154095	+	0.0728129i
$826$		0			0
$827$		−	53.5946i		−	1.86367i	−0.362885	−	0.931834i	$-0.618208\pi$
$827$		−	53.5946i		−	1.86367i	0.362885	−	0.931834i	$-0.381792\pi$
$828$		−	3.34271i		−	0.116167i
$829$	−1.16692			−0.0405288			−0.0202644	−	0.999795i	$-0.506451\pi$
$829$	−1.16692			−0.0405288			−0.0202644	+	0.999795i	$0.506451\pi$
$830$	−27.1707	+	17.2126i	−0.943109	+	0.597457i
$831$	−20.7478			−0.719733
$832$		−	0.435157i		−	0.0150864i
$833$		0			0
$834$	−8.15378			−0.282342
$835$	−15.1542	−	23.9215i	−0.524433	−	0.827838i
$836$	7.18892			0.248634
$837$		−	4.97906i		−	0.172101i
$838$		−	26.6274i		−	0.919829i
$839$	31.2709			1.07959			0.539796	−	0.841796i	$-0.318501\pi$
$839$	31.2709			1.07959			0.539796	+	0.841796i	$0.318501\pi$
$840$		0			0
$841$	−14.9507			−0.515540
$842$			15.1880i			0.523415i
$843$		−	18.3141i		−	0.630773i
$844$	−15.4127			−0.530528
$845$	−24.1984	+	15.3297i	−0.832451	+	0.527356i
$846$	4.40554			0.151466
$847$		0			0
$848$			0.657293i			0.0225715i
$849$	11.8525			0.406778
$850$	5.97862	−	12.6526i	0.205065	−	0.433982i
$851$	−15.4965			−0.531213
$852$			14.1119i			0.483466i
$853$			11.3154i			0.387431i	0.981058	+	0.193715i	$0.0620538\pi$
$853$			11.3154i			0.387431i	−0.981058	+	0.193715i	$0.937946\pi$
$854$		0			0
$855$	−13.8699	+	8.78654i	−0.474340	+	0.300493i
$856$	20.0410			0.684988
$857$			36.8572i			1.25902i	0.776994	+	0.629508i	$0.216744\pi$
$857$			36.8572i			1.25902i	−0.776994	+	0.629508i	$0.783256\pi$
$858$			0.426043i			0.0145449i
$859$	−18.6974			−0.637948			−0.318974	−	0.947763i	$-0.603338\pi$
$859$	−18.6974			−0.637948			−0.318974	+	0.947763i	$0.603338\pi$
$860$	−11.9408	−	18.8489i	−0.407177	−	0.642743i
$861$		0			0
$862$			4.23125i			0.144117i
$863$			29.5384i			1.00550i	0.864432	+	0.502749i	$0.167678\pi$
$863$			29.5384i			1.00550i	−0.864432	+	0.502749i	$0.832322\pi$
$864$	−1.00000			−0.0340207
$865$	−8.52072	−	13.4503i	−0.289713	−	0.457323i
$866$	−33.9352			−1.15317
$867$			9.16667i			0.311317i
$868$		0			0
$869$	2.82719			0.0959057
$870$	7.08018	−	4.48528i	0.240041	−	0.152065i
$871$	1.02856			0.0348514
$872$		−	18.6564i		−	0.631786i
$873$			10.6655i			0.360973i
$874$	24.5445			0.830231
$875$		0			0
$876$	−15.3928			−0.520076
$877$			14.2581i			0.481461i	0.970592	+	0.240730i	$0.0773869\pi$
$877$			14.2581i			0.481461i	−0.970592	+	0.240730i	$0.922613\pi$
$878$			5.48257i			0.185028i
$879$	14.4770			0.488299
$880$	−1.84937	+	1.17157i	−0.0623423	+	0.0394937i
$881$	31.2744			1.05366			0.526830	−	0.849971i	$-0.323380\pi$
$881$	31.2744			1.05366			0.526830	+	0.849971i	$0.323380\pi$
$882$		0			0
$883$			33.3566i			1.12254i	0.827633	+	0.561270i	$0.189687\pi$
$883$			33.3566i			1.12254i	−0.827633	+	0.561270i	$0.810313\pi$
$884$	1.21792			0.0409631
$885$	9.89887	+	15.6257i	0.332747	+	0.525253i
$886$	1.23081			0.0413499
$887$		−	42.1444i		−	1.41507i	−0.706678	−	0.707535i	$-0.749807\pi$
$887$		−	42.1444i		−	1.41507i	0.706678	−	0.707535i	$-0.250193\pi$
$888$			4.63591i			0.155571i
$889$		0			0
$890$	−12.1112	−	19.1179i	−0.405967	−	0.640834i
$891$	0.979056			0.0327996
$892$		−	7.61497i		−	0.254968i
$893$			32.3486i			1.08250i
$894$	15.6774			0.524329
$895$	6.16586	−	3.90606i	0.206102	−	0.130565i
$896$		0			0
$897$			1.45460i			0.0485678i
$898$			14.6435i			0.488661i
$899$	−18.6627			−0.622437
$900$	2.13613	−	4.52072i	0.0712043	−	0.150691i
$901$	−1.83964			−0.0612872
$902$		−	4.84578i		−	0.161347i
$903$		0			0
$904$	−10.4132			−0.346336
$905$	−3.66118	+	2.31935i	−0.121702	+	0.0770978i
$906$	4.27226			0.141936
$907$		−	55.9840i		−	1.85892i	−0.368923	−	0.929460i	$-0.620273\pi$
$907$		−	55.9840i		−	1.85892i	0.368923	−	0.929460i	$-0.379727\pi$
$908$		−	8.34227i		−	0.276848i
$909$	−14.0328			−0.465438
$910$		0			0
$911$	30.4389			1.00849			0.504243	−	0.863562i	$-0.331771\pi$
$911$	30.4389			1.00849			0.504243	+	0.863562i	$0.331771\pi$
$912$		−	7.34271i		−	0.243141i
$913$			14.0829i			0.466076i
$914$	31.3289			1.03627
$915$	13.5622	+	21.4084i	0.448352	+	0.707740i
$916$	18.6901			0.617537
$917$		0			0
$918$		−	2.79881i		−	0.0923744i
$919$	28.1538			0.928708			0.464354	−	0.885650i	$-0.346287\pi$
$919$	28.1538			0.928708			0.464354	+	0.885650i	$0.346287\pi$
$920$	−6.31415	+	4.00000i	−0.208171	+	0.131876i
$921$	30.4252			1.00254
$922$			12.7667i			0.420447i
$923$		−	6.14089i		−	0.202130i
$924$		0			0
$925$	−20.9577	−	9.90291i	−0.689084	−	0.325606i
$926$	−26.7112			−0.877784
$927$			10.3842i			0.341060i
$928$			3.74825i			0.123042i
$929$	25.8955			0.849603			0.424801	−	0.905287i	$-0.360344\pi$
$929$	25.8955			0.849603			0.424801	+	0.905287i	$0.360344\pi$
$930$	−9.40510	+	5.95811i	−0.308405	+	0.195374i
$931$		0			0
$932$		−	20.0829i		−	0.657837i
$933$		−	9.02856i		−	0.295582i
$934$	−37.6141			−1.23077
$935$	−3.27901	−	5.17603i	−0.107235	−	0.169274i
$936$	0.435157			0.0142236
$937$		−	48.1184i		−	1.57196i	−0.618253	−	0.785979i	$-0.712159\pi$
$937$		−	48.1184i		−	1.57196i	0.618253	−	0.785979i	$-0.287841\pi$
$938$		0			0
$939$	−17.1732			−0.560427
$940$	−5.27182	−	8.32176i	−0.171948	−	0.271426i
$941$	52.2066			1.70189			0.850944	−	0.525257i	$-0.176031\pi$
$941$	52.2066			1.70189			0.850944	+	0.525257i	$0.176031\pi$
$942$		−	15.2498i		−	0.496866i
$943$		−	16.5445i		−	0.538764i
$944$	−8.27226			−0.269239
$945$		0			0
$946$	−9.76963			−0.317638
$947$			20.2995i			0.659645i	0.944043	+	0.329823i	$0.106989\pi$
$947$			20.2995i			0.659645i	−0.944043	+	0.329823i	$0.893011\pi$
$948$		−	2.88767i		−	0.0937870i
$949$	6.69830			0.217436
$950$	33.1944	+	15.6850i	1.07697	+	0.508888i
$951$	2.61541			0.0848103
$952$		0			0
$953$		−	16.9511i		−	0.549100i	−0.961573	−	0.274550i	$-0.911471\pi$
$953$		−	16.9511i		−	0.549100i	0.961573	−	0.274550i	$-0.0885289\pi$
$954$	−0.657293			−0.0212806
$955$	−15.2437	+	9.65685i	−0.493275	+	0.312488i
$956$	−22.2714			−0.720308
$957$		−	3.66974i		−	0.118626i
$958$			23.8235i			0.769703i
$959$		0			0
$960$	1.19663	+	1.88893i	0.0386212	+	0.0609650i
$961$	−6.20900			−0.200290
$962$		−	2.01735i		−	0.0650420i
$963$			20.0410i			0.645813i
$964$	6.20075			0.199713
$965$	−2.34315	−	3.69874i	−0.0754285	−	0.119067i
$966$		0			0
$967$			23.0294i			0.740577i	0.928917	+	0.370288i	$0.120741\pi$
$967$			23.0294i			0.740577i	−0.928917	+	0.370288i	$0.879259\pi$
$968$		−	10.0414i		−	0.322744i
$969$	20.5508			0.660188
$970$	20.1465	−	12.7627i	0.646864	−	0.409787i
$971$	12.3770			0.397196			0.198598	−	0.980081i	$-0.436361\pi$
$971$	12.3770			0.397196			0.198598	+	0.980081i	$0.436361\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	3.75674			0.120374
$975$	−0.929553	+	1.96723i	−0.0297695	+	0.0630017i
$976$	−11.3336			−0.362779
$977$			1.00614i			0.0321893i	0.999870	+	0.0160946i	$0.00512331\pi$
$977$			1.00614i			0.0321893i	−0.999870	+	0.0160946i	$0.994877\pi$
$978$		−	7.47599i		−	0.239056i
$979$	−9.90904			−0.316694
$980$		0			0
$981$	18.6564			0.595654
$982$		−	2.00762i		−	0.0640656i
$983$		−	42.1444i		−	1.34420i	−0.740461	−	0.672099i	$-0.765393\pi$
$983$		−	42.1444i		−	1.34420i	0.740461	−	0.672099i	$-0.234607\pi$
$984$	−4.94944			−0.157782
$985$	−20.7518	−	32.7575i	−0.661209	−	1.04374i
$986$	−10.4906			−0.334089
$987$		0			0
$988$			3.19523i			0.101654i
$989$	−33.3556			−1.06065
$990$	−1.17157	−	1.84937i	−0.0372350	−	0.0587769i
$991$	−34.0691			−1.08224			−0.541121	−	0.840945i	$-0.682000\pi$
$991$	−34.0691			−1.08224			−0.541121	+	0.840945i	$0.682000\pi$
$992$		−	4.97906i		−	0.158085i
$993$		−	17.7559i		−	0.563465i
$994$		0			0
$995$	4.90159	−	3.10515i	0.155391	−	0.0984398i
$996$	14.3842			0.455779
$997$			6.02076i			0.190679i	0.995445	+	0.0953397i	$0.0303937\pi$
$997$			6.02076i			0.190679i	−0.995445	+	0.0953397i	$0.969606\pi$
$998$		−	0.628294i		−	0.0198883i
$999$	−4.63591			−0.146674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.g.k.589.1	yes	8
5.2	odd	4		7350.2.a.du.1.3		4
5.3	odd	4		7350.2.a.dr.1.3		4
5.4	even	2	inner	1470.2.g.k.589.5	yes	8
7.2	even	3		1470.2.n.k.949.4		16
7.3	odd	6		1470.2.n.l.79.6		16
7.4	even	3		1470.2.n.k.79.7		16
7.5	odd	6		1470.2.n.l.949.1		16
7.6	odd	2		1470.2.g.j.589.4	✓	8
35.4	even	6		1470.2.n.k.79.4		16
35.9	even	6		1470.2.n.k.949.7		16
35.13	even	4		7350.2.a.ds.1.3		4
35.19	odd	6		1470.2.n.l.949.6		16
35.24	odd	6		1470.2.n.l.79.1		16
35.27	even	4		7350.2.a.dt.1.3		4
35.34	odd	2		1470.2.g.j.589.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.4	✓	8	7.6	odd	2
1470.2.g.j.589.8	yes	8	35.34	odd	2
1470.2.g.k.589.1	yes	8	1.1	even	1	trivial
1470.2.g.k.589.5	yes	8	5.4	even	2	inner
1470.2.n.k.79.4		16	35.4	even	6
1470.2.n.k.79.7		16	7.4	even	3
1470.2.n.k.949.4		16	7.2	even	3
1470.2.n.k.949.7		16	35.9	even	6
1470.2.n.l.79.1		16	35.24	odd	6
1470.2.n.l.79.6		16	7.3	odd	6
1470.2.n.l.949.1		16	7.5	odd	6
1470.2.n.l.949.6		16	35.19	odd	6
7350.2.a.dr.1.3		4	5.3	odd	4
7350.2.a.ds.1.3		4	35.13	even	4
7350.2.a.dt.1.3		4	35.27	even	4
7350.2.a.du.1.3		4	5.2	odd	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.88893 + 1.19663i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.88893 + 1.19663i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(1.19663 + 1.88893i) q^{10} +0.979056 q^{11} -1.00000i q^{12} +0.435157i q^{13} +(-1.19663 - 1.88893i) q^{15} +1.00000 q^{16} +2.79881i q^{17} +1.00000i q^{18} -7.34271 q^{19} +(1.88893 - 1.19663i) q^{20} -0.979056i q^{22} -3.34271i q^{23} -1.00000 q^{24} +(2.13613 - 4.52072i) q^{25} +0.435157 q^{26} -1.00000i q^{27} -3.74825 q^{29} +(-1.88893 + 1.19663i) q^{30} +4.97906 q^{31} -1.00000i q^{32} +0.979056i q^{33} +2.79881 q^{34} +1.00000 q^{36} -4.63591i q^{37} +7.34271i q^{38} -0.435157 q^{39} +(-1.19663 - 1.88893i) q^{40} +4.94944 q^{41} -9.97862i q^{43} -0.979056 q^{44} +(1.88893 - 1.19663i) q^{45} -3.34271 q^{46} -4.40554i q^{47} +1.00000i q^{48} +(-4.52072 - 2.13613i) q^{50} -2.79881 q^{51} -0.435157i q^{52} +0.657293i q^{53} -1.00000 q^{54} +(-1.84937 + 1.17157i) q^{55} -7.34271i q^{57} +3.74825i q^{58} -8.27226 q^{59} +(1.19663 + 1.88893i) q^{60} -11.3336 q^{61} -4.97906i q^{62} -1.00000 q^{64} +(-0.520724 - 0.821983i) q^{65} +0.979056 q^{66} -2.36365i q^{67} -2.79881i q^{68} +3.34271 q^{69} -14.1119 q^{71} -1.00000i q^{72} -15.3928i q^{73} -4.63591 q^{74} +(4.52072 + 2.13613i) q^{75} +7.34271 q^{76} +0.435157i q^{78} +2.88767 q^{79} +(-1.88893 + 1.19663i) q^{80} +1.00000 q^{81} -4.94944i q^{82} +14.3842i q^{83} +(-3.34915 - 5.28676i) q^{85} -9.97862 q^{86} -3.74825i q^{87} +0.979056i q^{88} -10.1210 q^{89} +(-1.19663 - 1.88893i) q^{90} +3.34271i q^{92} +4.97906i q^{93} -4.40554 q^{94} +(13.8699 - 8.78654i) q^{95} +1.00000 q^{96} -10.6655i q^{97} -0.979056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 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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