LMFDB - Embedded newform 471.2.b.b.313.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.b (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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 224x^{10} + 1027x^{8} + 2399x^{6} + 2652x^{4} + 1094x^{2} + 147 $ x^14 + 24x^12 + 224x^10 + 1027x^8 + 2399x^6 + 2652x^4 + 1094x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.2
Root			$-2.49123i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.b.313.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49123i q^{2} +1.00000 q^{3} -4.20622 q^{4} -1.87721i q^{5} -2.49123i q^{6} -2.20605i q^{7} +5.49621i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49123i q^{2} +1.00000 q^{3} -4.20622 q^{4} -1.87721i q^{5} -2.49123i q^{6} -2.20605i q^{7} +5.49621i q^{8} +1.00000 q^{9} -4.67656 q^{10} -3.27411 q^{11} -4.20622 q^{12} +4.27778 q^{13} -5.49577 q^{14} -1.87721i q^{15} +5.27987 q^{16} -6.36287 q^{17} -2.49123i q^{18} +2.88311 q^{19} +7.89596i q^{20} -2.20605i q^{21} +8.15656i q^{22} -4.80731i q^{23} +5.49621i q^{24} +1.47609 q^{25} -10.6569i q^{26} +1.00000 q^{27} +9.27913i q^{28} +5.55530i q^{29} -4.67656 q^{30} -0.391006 q^{31} -2.16095i q^{32} -3.27411 q^{33} +15.8514i q^{34} -4.14121 q^{35} -4.20622 q^{36} -5.88677 q^{37} -7.18248i q^{38} +4.27778 q^{39} +10.3175 q^{40} +2.68465i q^{41} -5.49577 q^{42} -4.21642i q^{43} +13.7716 q^{44} -1.87721i q^{45} -11.9761 q^{46} +10.4975 q^{47} +5.27987 q^{48} +2.13336 q^{49} -3.67728i q^{50} -6.36287 q^{51} -17.9933 q^{52} -8.29968i q^{53} -2.49123i q^{54} +6.14619i q^{55} +12.1249 q^{56} +2.88311 q^{57} +13.8395 q^{58} -6.81768i q^{59} +7.89596i q^{60} -0.933720i q^{61} +0.974086i q^{62} -2.20605i q^{63} +5.17632 q^{64} -8.03028i q^{65} +8.15656i q^{66} +11.6866 q^{67} +26.7636 q^{68} -4.80731i q^{69} +10.3167i q^{70} +6.35632 q^{71} +5.49621i q^{72} -10.0172i q^{73} +14.6653i q^{74} +1.47609 q^{75} -12.1270 q^{76} +7.22284i q^{77} -10.6569i q^{78} +10.5975i q^{79} -9.91141i q^{80} +1.00000 q^{81} +6.68807 q^{82} -0.160335i q^{83} +9.27913i q^{84} +11.9444i q^{85} -10.5041 q^{86} +5.55530i q^{87} -17.9952i q^{88} -17.2735 q^{89} -4.67656 q^{90} -9.43698i q^{91} +20.2206i q^{92} -0.391006 q^{93} -26.1518i q^{94} -5.41219i q^{95} -2.16095i q^{96} -0.864689i q^{97} -5.31468i q^{98} -3.27411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.49123i		−	1.76157i	−0.473521	−	0.880783i	$-0.657017\pi$
$2$		−	2.49123i		−	1.76157i	0.473521	−	0.880783i	$-0.342983\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−4.20622			−2.10311
$5$		−	1.87721i		−	0.839513i	−0.907637	−	0.419756i	$-0.862115\pi$
$5$		−	1.87721i		−	0.839513i	0.907637	−	0.419756i	$-0.137885\pi$
$6$		−	2.49123i		−	1.01704i
$7$		−	2.20605i		−	0.833807i	−0.908951	−	0.416904i	$-0.863115\pi$
$7$		−	2.20605i		−	0.833807i	0.908951	−	0.416904i	$-0.136885\pi$
$8$			5.49621i			1.94320i
$9$	1.00000			0.333333
$10$	−4.67656			−1.47886
$11$	−3.27411			−0.987182			−0.493591	−	0.869694i	$-0.664316\pi$
$11$	−3.27411			−0.987182			−0.493591	+	0.869694i	$0.664316\pi$
$12$	−4.20622			−1.21423
$13$	4.27778			1.18644			0.593221	−	0.805039i	$-0.297856\pi$
$13$	4.27778			1.18644			0.593221	+	0.805039i	$0.297856\pi$
$14$	−5.49577			−1.46881
$15$		−	1.87721i		−	0.484693i
$16$	5.27987			1.31997
$17$	−6.36287			−1.54322			−0.771611	−	0.636095i	$-0.780549\pi$
$17$	−6.36287			−1.54322			−0.771611	+	0.636095i	$0.780549\pi$
$18$		−	2.49123i		−	0.587188i
$19$	2.88311			0.661430			0.330715	−	0.943731i	$-0.392710\pi$
$19$	2.88311			0.661430			0.330715	+	0.943731i	$0.392710\pi$
$20$			7.89596i			1.76559i
$21$		−	2.20605i		−	0.481399i
$22$			8.15656i			1.73898i
$23$		−	4.80731i		−	1.00239i	−0.865334	−	0.501196i	$-0.832893\pi$
$23$		−	4.80731i		−	1.00239i	0.865334	−	0.501196i	$-0.167107\pi$
$24$			5.49621i			1.12191i
$25$	1.47609			0.295218
$26$		−	10.6569i		−	2.09000i
$27$	1.00000			0.192450
$28$			9.27913i			1.75359i
$29$			5.55530i			1.03159i	0.856711	+	0.515797i	$0.172504\pi$
$29$			5.55530i			1.03159i	−0.856711	+	0.515797i	$0.827496\pi$
$30$	−4.67656			−0.853818
$31$	−0.391006			−0.0702267			−0.0351134	−	0.999383i	$-0.511179\pi$
$31$	−0.391006			−0.0702267			−0.0351134	+	0.999383i	$0.511179\pi$
$32$		−	2.16095i		−	0.382006i
$33$	−3.27411			−0.569950
$34$			15.8514i			2.71849i
$35$	−4.14121			−0.699992
$36$	−4.20622			−0.701037
$37$	−5.88677			−0.967780			−0.483890	−	0.875129i	$-0.660776\pi$
$37$	−5.88677			−0.967780			−0.483890	+	0.875129i	$0.660776\pi$
$38$		−	7.18248i		−	1.16515i
$39$	4.27778			0.684993
$40$	10.3175			1.63134
$41$			2.68465i			0.419272i	0.977780	+	0.209636i	$0.0672278\pi$
$41$			2.68465i			0.419272i	−0.977780	+	0.209636i	$0.932772\pi$
$42$	−5.49577			−0.848015
$43$		−	4.21642i		−	0.642998i	−0.946910	−	0.321499i	$-0.895813\pi$
$43$		−	4.21642i		−	0.642998i	0.946910	−	0.321499i	$-0.104187\pi$
$44$	13.7716			2.07615
$45$		−	1.87721i		−	0.279838i
$46$	−11.9761			−1.76578
$47$	10.4975			1.53122			0.765611	−	0.643304i	$-0.222437\pi$
$47$	10.4975			1.53122			0.765611	+	0.643304i	$0.222437\pi$
$48$	5.27987			0.762084
$49$	2.13336			0.304765
$50$		−	3.67728i		−	0.520046i
$51$	−6.36287			−0.890979
$52$	−17.9933			−2.49522
$53$		−	8.29968i		−	1.14005i	−0.821628	−	0.570024i	$-0.806934\pi$
$53$		−	8.29968i		−	1.14005i	0.821628	−	0.570024i	$-0.193066\pi$
$54$		−	2.49123i		−	0.339013i
$55$			6.14619i			0.828752i
$56$	12.1249			1.62026
$57$	2.88311			0.381877
$58$	13.8395			1.81722
$59$		−	6.81768i		−	0.887587i	−0.896129	−	0.443793i	$-0.853632\pi$
$59$		−	6.81768i		−	0.887587i	0.896129	−	0.443793i	$-0.146368\pi$
$60$			7.89596i			1.01936i
$61$		−	0.933720i		−	0.119551i	−0.998212	−	0.0597753i	$-0.980962\pi$
$61$		−	0.933720i		−	0.119551i	0.998212	−	0.0597753i	$-0.0190384\pi$
$62$			0.974086i			0.123709i
$63$		−	2.20605i		−	0.277936i
$64$	5.17632			0.647040
$65$		−	8.03028i		−	0.996034i
$66$			8.15656i			1.00400i
$67$	11.6866			1.42774			0.713870	−	0.700278i	$-0.246941\pi$
$67$	11.6866			1.42774			0.713870	+	0.700278i	$0.246941\pi$
$68$	26.7636			3.24557
$69$		−	4.80731i		−	0.578732i
$70$			10.3167i			1.23308i
$71$	6.35632			0.754357			0.377178	−	0.926141i	$-0.376894\pi$
$71$	6.35632			0.754357			0.377178	+	0.926141i	$0.376894\pi$
$72$			5.49621i			0.647734i
$73$		−	10.0172i		−	1.17242i	−0.810159	−	0.586211i	$-0.800619\pi$
$73$		−	10.0172i		−	1.17242i	0.810159	−	0.586211i	$-0.199381\pi$
$74$			14.6653i			1.70481i
$75$	1.47609			0.170444
$76$	−12.1270			−1.39106
$77$			7.22284i			0.823119i
$78$		−	10.6569i		−	1.20666i
$79$			10.5975i			1.19231i	0.802869	+	0.596155i	$0.203306\pi$
$79$			10.5975i			1.19231i	−0.802869	+	0.596155i	$0.796694\pi$
$80$		−	9.91141i		−	1.10813i
$81$	1.00000			0.111111
$82$	6.68807			0.738574
$83$		−	0.160335i		−	0.0175990i	−0.999961	−	0.00879951i	$-0.997199\pi$
$83$		−	0.160335i		−	0.0175990i	0.999961	−	0.00879951i	$-0.00280101\pi$
$84$			9.27913i			1.01244i
$85$			11.9444i			1.29555i
$86$	−10.5041			−1.13268
$87$			5.55530i			0.595591i
$88$		−	17.9952i		−	1.91829i
$89$	−17.2735			−1.83099			−0.915494	−	0.402333i	$-0.868200\pi$
$89$	−17.2735			−1.83099			−0.915494	+	0.402333i	$0.868200\pi$
$90$	−4.67656			−0.492952
$91$		−	9.43698i		−	0.989265i
$92$			20.2206i			2.10814i
$93$	−0.391006			−0.0405454
$94$		−	26.1518i		−	2.69735i
$95$		−	5.41219i		−	0.555279i
$96$		−	2.16095i		−	0.220551i
$97$		−	0.864689i		−	0.0877958i	−0.999036	−	0.0438979i	$-0.986022\pi$
$97$		−	0.864689i		−	0.0877958i	0.999036	−	0.0438979i	$-0.0139776\pi$
$98$		−	5.31468i		−	0.536864i
$99$	−3.27411			−0.329061
$100$	−6.20877			−0.620877
$101$	17.9063			1.78174			0.890872	−	0.454254i	$-0.150094\pi$
$101$	17.9063			1.78174			0.890872	+	0.454254i	$0.150094\pi$
$102$			15.8514i			1.56952i
$103$		−	2.89806i		−	0.285554i	−0.989755	−	0.142777i	$-0.954397\pi$
$103$		−	2.89806i		−	0.285554i	0.989755	−	0.142777i	$-0.0456032\pi$
$104$			23.5116i			2.30550i
$105$	−4.14121			−0.404141
$106$	−20.6764			−2.00827
$107$		−	17.5166i		−	1.69339i	−0.532076	−	0.846697i	$-0.678588\pi$
$107$		−	17.5166i		−	1.69339i	0.532076	−	0.846697i	$-0.321412\pi$
$108$	−4.20622			−0.404744
$109$	−1.93746			−0.185575			−0.0927877	−	0.995686i	$-0.529578\pi$
$109$	−1.93746			−0.185575			−0.0927877	+	0.995686i	$0.529578\pi$
$110$	15.3116			1.45990
$111$	−5.88677			−0.558748
$112$		−	11.6476i		−	1.10060i
$113$	−0.227743			−0.0214243			−0.0107121	−	0.999943i	$-0.503410\pi$
$113$	−0.227743			−0.0214243			−0.0107121	+	0.999943i	$0.503410\pi$
$114$		−	7.18248i		−	0.672701i
$115$	−9.02431			−0.841522
$116$		−	23.3668i		−	2.16956i
$117$	4.27778			0.395481
$118$	−16.9844			−1.56354
$119$			14.0368i			1.28675i
$120$	10.3175			0.941857
$121$	−0.280197			−0.0254724
$122$	−2.32611			−0.210596
$123$			2.68465i			0.242067i
$124$	1.64466			0.147695
$125$		−	12.1570i		−	1.08735i
$126$	−5.49577			−0.489602
$127$	8.15113			0.723296			0.361648	−	0.932315i	$-0.382214\pi$
$127$	8.15113			0.723296			0.361648	+	0.932315i	$0.382214\pi$
$128$		−	17.2173i		−	1.52181i
$129$		−	4.21642i		−	0.371235i
$130$	−20.0053			−1.75458
$131$		−	7.95424i		−	0.694965i	−0.937686	−	0.347483i	$-0.887037\pi$
$131$		−	7.95424i		−	0.694965i	0.937686	−	0.347483i	$-0.112963\pi$
$132$	13.7716			1.19867
$133$		−	6.36026i		−	0.551505i
$134$		−	29.1139i		−	2.51506i
$135$		−	1.87721i		−	0.161564i
$136$		−	34.9716i		−	2.99879i
$137$			20.1607i			1.72245i	0.508228	+	0.861223i	$0.330301\pi$
$137$			20.1607i			1.72245i	−0.508228	+	0.861223i	$0.669699\pi$
$138$	−11.9761			−1.01947
$139$			9.66377i			0.819670i	0.912160	+	0.409835i	$0.134414\pi$
$139$			9.66377i			0.819670i	−0.912160	+	0.409835i	$0.865586\pi$
$140$	17.4188			1.47216
$141$	10.4975			0.884052
$142$		−	15.8351i		−	1.32885i
$143$	−14.0059			−1.17123
$144$	5.27987			0.439989
$145$	10.4285			0.866036
$146$	−24.9551			−2.06530
$147$	2.13336			0.175956
$148$	24.7611			2.03535
$149$			15.2363i			1.24821i	0.781342	+	0.624103i	$0.214535\pi$
$149$			15.2363i			1.24821i	−0.781342	+	0.624103i	$0.785465\pi$
$150$		−	3.67728i		−	0.300249i
$151$			19.0406i			1.54950i	0.632265	+	0.774752i	$0.282125\pi$
$151$			19.0406i			1.54950i	−0.632265	+	0.774752i	$0.717875\pi$
$152$			15.8461i			1.28529i
$153$	−6.36287			−0.514407
$154$	17.9938			1.44998
$155$			0.733999i			0.0589563i
$156$	−17.9933			−1.44062
$157$	−10.6243	−	6.64253i	−0.847915	−	0.530132i
$157$	−10.6243	−	6.64253i	−0.847915	−	0.530132i
$158$	26.4008			2.10033
$159$		−	8.29968i		−	0.658207i
$160$	−4.05655			−0.320699
$161$	−10.6051			−0.835802
$162$		−	2.49123i		−	0.195729i
$163$			13.9018i			1.08888i	0.838801	+	0.544438i	$0.183257\pi$
$163$			13.9018i			1.08888i	−0.838801	+	0.544438i	$0.816743\pi$
$164$		−	11.2922i		−	0.881775i
$165$			6.14619i			0.478480i
$166$	−0.399431			−0.0310018
$167$	2.61777			0.202569			0.101285	−	0.994857i	$-0.467705\pi$
$167$	2.61777			0.202569			0.101285	+	0.994857i	$0.467705\pi$
$168$	12.1249			0.935456
$169$	5.29940			0.407646
$170$	29.7563			2.28220
$171$	2.88311			0.220477
$172$			17.7352i			1.35230i
$173$	11.0248			0.838199			0.419099	−	0.907940i	$-0.362346\pi$
$173$	11.0248			0.838199			0.419099	+	0.907940i	$0.362346\pi$
$174$	13.8395			1.04917
$175$		−	3.25633i		−	0.246155i
$176$	−17.2869			−1.30305
$177$		−	6.81768i		−	0.512448i
$178$			43.0322i			3.22540i
$179$			22.5165i			1.68296i	0.540286	+	0.841482i	$0.318316\pi$
$179$			22.5165i			1.68296i	−0.540286	+	0.841482i	$0.681684\pi$
$180$			7.89596i			0.588530i
$181$		−	12.0299i		−	0.894173i	−0.894491	−	0.447087i	$-0.852462\pi$
$181$		−	12.0299i		−	0.894173i	0.894491	−	0.447087i	$-0.147538\pi$
$182$	−23.5097			−1.74265
$183$		−	0.933720i		−	0.0690225i
$184$	26.4220			1.94785
$185$			11.0507i			0.812464i
$186$			0.974086i			0.0714234i
$187$	20.8327			1.52344
$188$	−44.1550			−3.22033
$189$		−	2.20605i		−	0.160466i
$190$	−13.4830			−0.978160
$191$		−	3.12873i		−	0.226387i	−0.993573	−	0.113194i	$-0.963892\pi$
$191$		−	3.12873i		−	0.226387i	0.993573	−	0.113194i	$-0.0361080\pi$
$192$	5.17632			0.373569
$193$	6.57718			0.473436			0.236718	−	0.971578i	$-0.423928\pi$
$193$	6.57718			0.473436			0.236718	+	0.971578i	$0.423928\pi$
$194$	−2.15414			−0.154658
$195$		−	8.03028i		−	0.575060i
$196$	−8.97338			−0.640956
$197$	−7.25540			−0.516926			−0.258463	−	0.966021i	$-0.583216\pi$
$197$	−7.25540			−0.516926			−0.258463	+	0.966021i	$0.583216\pi$
$198$			8.15656i			0.579662i
$199$	10.4064			0.737687			0.368844	−	0.929491i	$-0.379754\pi$
$199$	10.4064			0.737687			0.368844	+	0.929491i	$0.379754\pi$
$200$			8.11291i			0.573669i
$201$	11.6866			0.824306
$202$		−	44.6087i		−	3.13866i
$203$	12.2553			0.860150
$204$	26.7636			1.87383
$205$	5.03964			0.351984
$206$	−7.21973			−0.503023
$207$		−	4.80731i		−	0.334131i
$208$	22.5861			1.56607
$209$	−9.43961			−0.652951
$210$			10.3167i			0.711920i
$211$		−	0.590604i		−	0.0406589i	−0.999793	−	0.0203294i	$-0.993528\pi$
$211$		−	0.590604i		−	0.0406589i	0.999793	−	0.0203294i	$-0.00647150\pi$
$212$			34.9103i			2.39765i
$213$	6.35632			0.435528
$214$	−43.6379			−2.98302
$215$	−7.91510			−0.539805
$216$			5.49621i			0.373970i
$217$			0.862577i			0.0585556i
$218$			4.82667i			0.326903i
$219$		−	10.0172i		−	0.676898i
$220$		−	25.8522i		−	1.74296i
$221$	−27.2189			−1.83094
$222$			14.6653i			0.984271i
$223$			7.80315i			0.522538i	0.965266	+	0.261269i	$0.0841409\pi$
$223$			7.80315i			0.522538i	−0.965266	+	0.261269i	$0.915859\pi$
$224$	−4.76716			−0.318519
$225$	1.47609			0.0984061
$226$			0.567361i			0.0377403i
$227$			9.00949i			0.597981i	0.954256	+	0.298991i	$0.0966499\pi$
$227$			9.00949i			0.597981i	−0.954256	+	0.298991i	$0.903350\pi$
$228$	−12.1270			−0.803129
$229$			15.2529i			1.00794i	0.863721	+	0.503969i	$0.168128\pi$
$229$			15.2529i			1.00794i	−0.863721	+	0.503969i	$0.831872\pi$
$230$			22.4816i			1.48240i
$231$			7.22284i			0.475228i
$232$	−30.5331			−2.00460
$233$	17.7874			1.16529			0.582647	−	0.812726i	$-0.302017\pi$
$233$	17.7874			1.16529			0.582647	+	0.812726i	$0.302017\pi$
$234$		−	10.6569i		−	0.696665i
$235$		−	19.7060i		−	1.28548i
$236$			28.6767i			1.86669i
$237$			10.5975i			0.688381i
$238$	34.9688			2.26669
$239$	−19.9303			−1.28918			−0.644592	−	0.764527i	$-0.722973\pi$
$239$	−19.9303			−1.28918			−0.644592	+	0.764527i	$0.722973\pi$
$240$		−	9.91141i		−	0.639779i
$241$		−	4.75533i		−	0.306318i	−0.988202	−	0.153159i	$-0.951055\pi$
$241$		−	4.75533i		−	0.306318i	0.988202	−	0.153159i	$-0.0489446\pi$
$242$			0.698035i			0.0448714i
$243$	1.00000			0.0641500
$244$			3.92743i			0.251428i
$245$		−	4.00476i		−	0.255854i
$246$	6.68807			0.426416
$247$	12.3333			0.784748
$248$		−	2.14905i		−	0.136465i
$249$		−	0.160335i		−	0.0101608i
$250$	−30.2858			−1.91544
$251$		−	5.50997i		−	0.347786i	−0.984765	−	0.173893i	$-0.944365\pi$
$251$		−	5.50997i		−	0.347786i	0.984765	−	0.173893i	$-0.0556348\pi$
$252$			9.27913i			0.584530i
$253$			15.7397i			0.989544i
$254$		−	20.3063i		−	1.27413i
$255$			11.9444i			0.747989i
$256$	−32.5396			−2.03373
$257$	−6.29955			−0.392955			−0.196478	−	0.980508i	$-0.562950\pi$
$257$	−6.29955			−0.392955			−0.196478	+	0.980508i	$0.562950\pi$
$258$	−10.5041			−0.653955
$259$			12.9865i			0.806942i
$260$			33.7772i			2.09477i
$261$			5.55530i			0.343865i
$262$	−19.8158			−1.22423
$263$	21.2843			1.31245			0.656224	−	0.754566i	$-0.272152\pi$
$263$	21.2843			1.31245			0.656224	+	0.754566i	$0.272152\pi$
$264$		−	17.9952i		−	1.10753i
$265$	−15.5802			−0.957085
$266$	−15.8449			−0.971512
$267$	−17.2735			−1.05712
$268$	−49.1563			−3.00270
$269$			28.5292i			1.73946i	0.493529	+	0.869729i	$0.335707\pi$
$269$			28.5292i			1.73946i	−0.493529	+	0.869729i	$0.664293\pi$
$270$	−4.67656			−0.284606
$271$			11.0365i			0.670417i	0.942144	+	0.335209i	$0.108807\pi$
$271$			11.0365i			0.670417i	−0.942144	+	0.335209i	$0.891193\pi$
$272$	−33.5951			−2.03700
$273$		−	9.43698i		−	0.571152i
$274$	50.2249			3.03420
$275$	−4.83289			−0.291434
$276$			20.2206i			1.21714i
$277$	−9.60180			−0.576916			−0.288458	−	0.957493i	$-0.593143\pi$
$277$	−9.60180			−0.576916			−0.288458	+	0.957493i	$0.593143\pi$
$278$	24.0747			1.44390
$279$	−0.391006			−0.0234089
$280$		−	22.7609i		−	1.36023i
$281$	20.5675			1.22696			0.613478	−	0.789712i	$-0.289770\pi$
$281$	20.5675			1.22696			0.613478	+	0.789712i	$0.289770\pi$
$282$		−	26.1518i		−	1.55731i
$283$	12.7756			0.759433			0.379716	−	0.925103i	$-0.376022\pi$
$283$	12.7756			0.759433			0.379716	+	0.925103i	$0.376022\pi$
$284$	−26.7361			−1.58650
$285$		−	5.41219i		−	0.320590i
$286$			34.8920i			2.06321i
$287$	5.92246			0.349592
$288$		−	2.16095i		−	0.127335i
$289$	23.4861			1.38153
$290$		−	25.9797i		−	1.52558i
$291$		−	0.864689i		−	0.0506890i
$292$			42.1345i			2.46573i
$293$			25.7015i			1.50150i	0.660589	+	0.750748i	$0.270307\pi$
$293$			25.7015i			1.50150i	−0.660589	+	0.750748i	$0.729693\pi$
$294$		−	5.31468i		−	0.309959i
$295$	−12.7982			−0.745140
$296$		−	32.3549i		−	1.88059i
$297$	−3.27411			−0.189983
$298$	37.9571			2.19880
$299$		−	20.5646i		−	1.18928i
$300$	−6.20877			−0.358463
$301$	−9.30162			−0.536137
$302$	47.4346			2.72955
$303$	17.9063			1.02869
$304$	15.2224			0.873066
$305$	−1.75279			−0.100364
$306$			15.8514i			0.906162i
$307$			30.6641i			1.75009i	0.484038	+	0.875047i	$0.339170\pi$
$307$			30.6641i			1.75009i	−0.484038	+	0.875047i	$0.660830\pi$
$308$		−	30.3809i		−	1.73111i
$309$		−	2.89806i		−	0.164865i
$310$	1.82856			0.103855
$311$	5.03374			0.285437			0.142719	−	0.989763i	$-0.454416\pi$
$311$	5.03374			0.285437			0.142719	+	0.989763i	$0.454416\pi$
$312$			23.5116i			1.33108i
$313$	−25.1487			−1.42149			−0.710745	−	0.703450i	$-0.751642\pi$
$313$	−25.1487			−1.42149			−0.710745	+	0.703450i	$0.751642\pi$
$314$	−16.5481	+	26.4677i	−0.933861	+	1.49366i
$315$	−4.14121			−0.233331
$316$		−	44.5754i		−	2.50756i
$317$	−27.1810			−1.52664			−0.763319	−	0.646022i	$-0.776432\pi$
$317$	−27.1810			−1.52664			−0.763319	+	0.646022i	$0.776432\pi$
$318$	−20.6764			−1.15947
$319$		−	18.1887i		−	1.01837i
$320$		−	9.71703i		−	0.543198i
$321$		−	17.5166i		−	0.977681i
$322$			26.4198i			1.47232i
$323$	−18.3448			−1.02073
$324$	−4.20622			−0.233679
$325$	6.31439			0.350260
$326$	34.6327			1.91813
$327$	−1.93746			−0.107142
$328$	−14.7554			−0.814730
$329$		−	23.1580i		−	1.27674i
$330$	15.3116			0.842874
$331$	28.5639			1.57002			0.785008	−	0.619485i	$-0.212659\pi$
$331$	28.5639			1.57002			0.785008	+	0.619485i	$0.212659\pi$
$332$			0.674404i			0.0370127i
$333$	−5.88677			−0.322593
$334$		−	6.52146i		−	0.356839i
$335$		−	21.9381i		−	1.19861i
$336$		−	11.6476i		−	0.635431i
$337$		−	13.2399i		−	0.721222i	−0.932716	−	0.360611i	$-0.882568\pi$
$337$		−	13.2399i		−	0.721222i	0.932716	−	0.360611i	$-0.117432\pi$
$338$		−	13.2020i		−	0.718096i
$339$	−0.227743			−0.0123693
$340$		−	50.2409i		−	2.72470i
$341$	1.28020			0.0693266
$342$		−	7.18248i		−	0.388384i
$343$		−	20.1486i		−	1.08792i
$344$	23.1743			1.24948
$345$	−9.02431			−0.485853
$346$		−	27.4653i		−	1.47654i
$347$	16.4129			0.881093			0.440546	−	0.897730i	$-0.354785\pi$
$347$	16.4129			0.881093			0.440546	+	0.897730i	$0.354785\pi$
$348$		−	23.3668i		−	1.25259i
$349$	−19.5802			−1.04810			−0.524052	−	0.851686i	$-0.675580\pi$
$349$	−19.5802			−1.04810			−0.524052	+	0.851686i	$0.675580\pi$
$350$	−8.11225			−0.433618
$351$	4.27778			0.228331
$352$			7.07519i			0.377109i
$353$	−4.74936			−0.252783			−0.126392	−	0.991980i	$-0.540340\pi$
$353$	−4.74936			−0.252783			−0.126392	+	0.991980i	$0.540340\pi$
$354$	−16.9844			−0.902711
$355$		−	11.9321i		−	0.633292i
$356$	72.6562			3.85077
$357$			14.0368i			0.742905i
$358$	56.0938			2.96465
$359$		−	35.5646i		−	1.87703i	−0.345239	−	0.938515i	$-0.612202\pi$
$359$		−	35.5646i		−	1.87703i	0.345239	−	0.938515i	$-0.387798\pi$
$360$	10.3175			0.543781
$361$	−10.6877			−0.562511
$362$	−29.9692			−1.57514
$363$	−0.280197			−0.0147065
$364$			39.6941i			2.08053i
$365$	−18.8043			−0.984263
$366$	−2.32611			−0.121588
$367$		−	31.2983i		−	1.63376i	−0.576809	−	0.816879i	$-0.695702\pi$
$367$		−	31.2983i		−	1.63376i	0.576809	−	0.816879i	$-0.304298\pi$
$368$		−	25.3820i		−	1.32313i
$369$			2.68465i			0.139757i
$370$	27.5298			1.43121
$371$	−18.3095			−0.950580
$372$	1.64466			0.0852716
$373$			37.5894i			1.94631i	0.230158	+	0.973153i	$0.426076\pi$
$373$			37.5894i			1.94631i	−0.230158	+	0.973153i	$0.573924\pi$
$374$		−	51.8991i		−	2.68364i
$375$		−	12.1570i		−	0.627783i
$376$			57.6966i			2.97548i
$377$			23.7644i			1.22393i
$378$	−5.49577			−0.282672
$379$		−	26.7232i		−	1.37268i	−0.727281	−	0.686340i	$-0.759216\pi$
$379$		−	26.7232i		−	1.37268i	0.727281	−	0.686340i	$-0.240784\pi$
$380$			22.7649i			1.16781i
$381$	8.15113			0.417595
$382$	−7.79439			−0.398796
$383$			6.60837i			0.337672i	0.985644	+	0.168836i	$0.0540008\pi$
$383$			6.60837i			0.337672i	−0.985644	+	0.168836i	$0.945999\pi$
$384$		−	17.2173i		−	0.878617i
$385$	13.5588			0.691019
$386$		−	16.3853i		−	0.833989i
$387$		−	4.21642i		−	0.214333i
$388$			3.63707i			0.184644i
$389$	−30.2166			−1.53204			−0.766020	−	0.642816i	$-0.777766\pi$
$389$	−30.2166			−1.53204			−0.766020	+	0.642816i	$0.777766\pi$
$390$	−20.0053			−1.01301
$391$			30.5882i			1.54691i
$392$			11.7254i			0.592221i
$393$		−	7.95424i		−	0.401238i
$394$			18.0749i			0.910598i
$395$	19.8937			1.00096
$396$	13.7716			0.692051
$397$			29.5967i			1.48542i	0.669615	+	0.742708i	$0.266459\pi$
$397$			29.5967i			1.48542i	−0.669615	+	0.742708i	$0.733541\pi$
$398$		−	25.9246i		−	1.29948i
$399$		−	6.36026i		−	0.318411i
$400$	7.79357			0.389678
$401$		−	0.0856262i		−	0.00427597i	−0.999998	−	0.00213799i	$-0.999319\pi$
$401$		−	0.0856262i		−	0.00427597i	0.999998	−	0.00213799i	$-0.000680542\pi$
$402$		−	29.1139i		−	1.45207i
$403$	−1.67264			−0.0833200
$404$	−75.3179			−3.74721
$405$		−	1.87721i		−	0.0932792i
$406$		−	30.5307i		−	1.51521i
$407$	19.2740			0.955374
$408$		−	34.9716i		−	1.73135i
$409$		−	26.9453i		−	1.33236i	−0.745791	−	0.666180i	$-0.767928\pi$
$409$		−	26.9453i		−	1.33236i	0.745791	−	0.666180i	$-0.232072\pi$
$410$		−	12.5549i		−	0.620043i
$411$			20.1607i			0.994454i
$412$			12.1899i			0.600553i
$413$	−15.0401			−0.740076
$414$	−11.9761			−0.588593
$415$	−0.300982			−0.0147746
$416$		−	9.24407i		−	0.453228i
$417$			9.66377i			0.473237i
$418$			23.5162i			1.15022i
$419$	4.14698			0.202593			0.101297	−	0.994856i	$-0.467701\pi$
$419$	4.14698			0.202593			0.101297	+	0.994856i	$0.467701\pi$
$420$	17.4188			0.849953
$421$			7.17207i			0.349546i	0.984609	+	0.174773i	$0.0559191\pi$
$421$			7.17207i			0.349546i	−0.984609	+	0.174773i	$0.944081\pi$
$422$	−1.47133			−0.0716232
$423$	10.4975			0.510407
$424$	45.6168			2.21535
$425$	−9.39217			−0.455587
$426$		−	15.8351i		−	0.767211i
$427$	−2.05983			−0.0996821
$428$			73.6787i			3.56140i
$429$	−14.0059			−0.676213
$430$			19.7183i			0.950902i
$431$	6.79146			0.327133			0.163567	−	0.986532i	$-0.447700\pi$
$431$	6.79146			0.327133			0.163567	+	0.986532i	$0.447700\pi$
$432$	5.27987			0.254028
$433$			22.2428i			1.06892i	0.845193	+	0.534461i	$0.179485\pi$
$433$			22.2428i			1.06892i	−0.845193	+	0.534461i	$0.820515\pi$
$434$	2.14888			0.103149
$435$	10.4285			0.500006
$436$	8.14941			0.390286
$437$		−	13.8600i		−	0.663012i
$438$	−24.9551			−1.19240
$439$		−	22.1541i		−	1.05736i	−0.848822	−	0.528680i	$-0.822687\pi$
$439$		−	22.1541i		−	1.05736i	0.848822	−	0.528680i	$-0.177313\pi$
$440$	−33.7807			−1.61043
$441$	2.13336			0.101588
$442$			67.8086i			3.22533i
$443$		−	0.0845751i		−	0.00401828i	−0.999998	−	0.00200914i	$-0.999360\pi$
$443$		−	0.0845751i		−	0.00401828i	0.999998	−	0.00200914i	$-0.000639530\pi$
$444$	24.7611			1.17511
$445$			32.4259i			1.53714i
$446$	19.4394			0.920485
$447$			15.2363i			0.720652i
$448$		−	11.4192i		−	0.539507i
$449$			4.28747i			0.202338i	0.994869	+	0.101169i	$0.0322583\pi$
$449$			4.28747i			0.202338i	−0.994869	+	0.101169i	$0.967742\pi$
$450$		−	3.67728i		−	0.173349i
$451$		−	8.78984i		−	0.413897i
$452$	0.957939			0.0450577
$453$			19.0406i			0.894606i
$454$	22.4447			1.05338
$455$	−17.7152			−0.830500
$456$			15.8461i			0.742064i
$457$	−0.948695			−0.0443781			−0.0221890	−	0.999754i	$-0.507064\pi$
$457$	−0.948695			−0.0443781			−0.0221890	+	0.999754i	$0.507064\pi$
$458$	37.9984			1.77555
$459$	−6.36287			−0.296993
$460$	37.9583			1.76981
$461$	−16.2729			−0.757907			−0.378953	−	0.925416i	$-0.623716\pi$
$461$	−16.2729			−0.757907			−0.378953	+	0.925416i	$0.623716\pi$
$462$	17.9938			0.837145
$463$		−	7.20423i		−	0.334809i	−0.985888	−	0.167404i	$-0.946461\pi$
$463$		−	7.20423i		−	0.334809i	0.985888	−	0.167404i	$-0.0535386\pi$
$464$			29.3313i			1.36167i
$465$			0.733999i			0.0340384i
$466$		−	44.3126i		−	2.05274i
$467$	23.1424			1.07090			0.535450	−	0.844567i	$-0.320142\pi$
$467$	23.1424			1.07090			0.535450	+	0.844567i	$0.320142\pi$
$468$	−17.9933			−0.831741
$469$		−	25.7811i		−	1.19046i
$470$	−49.0923			−2.26446
$471$	−10.6243	−	6.64253i	−0.489544	−	0.306072i
$472$	37.4714			1.72476
$473$			13.8050i			0.634756i
$474$	26.4008			1.21263
$475$	4.25573			0.195266
$476$		−	59.0418i		−	2.70618i
$477$		−	8.29968i		−	0.380016i
$478$			49.6509i			2.27098i
$479$			33.4251i			1.52723i	0.645671	+	0.763616i	$0.276578\pi$
$479$			33.4251i			1.52723i	−0.645671	+	0.763616i	$0.723422\pi$
$480$	−4.05655			−0.185155
$481$	−25.1823			−1.14822
$482$	−11.8466			−0.539599
$483$	−10.6051			−0.482551
$484$	1.17857			0.0535714
$485$	−1.62320			−0.0737057
$486$		−	2.49123i		−	0.113004i
$487$	−21.9869			−0.996322			−0.498161	−	0.867085i	$-0.665991\pi$
$487$	−21.9869			−0.996322			−0.498161	+	0.867085i	$0.665991\pi$
$488$	5.13192			0.232311
$489$			13.9018i			0.628663i
$490$	−9.97677			−0.450704
$491$		−	19.7580i		−	0.891667i	−0.895116	−	0.445834i	$-0.852907\pi$
$491$		−	19.7580i		−	0.891667i	0.895116	−	0.445834i	$-0.147093\pi$
$492$		−	11.2922i		−	0.509093i
$493$		−	35.3476i		−	1.59198i
$494$		−	30.7251i		−	1.38239i
$495$			6.14619i			0.276251i
$496$	−2.06446			−0.0926970
$497$		−	14.0223i		−	0.628988i
$498$	−0.399431			−0.0178989
$499$		−	33.3286i		−	1.49199i	−0.665951	−	0.745996i	$-0.731974\pi$
$499$		−	33.3286i		−	1.49199i	0.665951	−	0.745996i	$-0.268026\pi$
$500$			51.1349i			2.28682i
$501$	2.61777			0.116953
$502$	−13.7266			−0.612649
$503$			9.25940i			0.412856i	0.978462	+	0.206428i	$0.0661839\pi$
$503$			9.25940i			0.412856i	−0.978462	+	0.206428i	$0.933816\pi$
$504$	12.1249			0.540086
$505$		−	33.6139i		−	1.49580i
$506$	39.2111			1.74315
$507$	5.29940			0.235355
$508$	−34.2855			−1.52117
$509$		−	5.72381i		−	0.253703i	−0.991922	−	0.126852i	$-0.959513\pi$
$509$		−	5.72381i		−	0.253703i	0.991922	−	0.126852i	$-0.0404872\pi$
$510$	29.7563			1.31763
$511$	−22.0984			−0.977574
$512$			46.6290i			2.06073i
$513$	2.88311			0.127292
$514$			15.6936i			0.692216i
$515$	−5.44026			−0.239727
$516$			17.7352i			0.780749i
$517$	−34.3701			−1.51159
$518$	32.3523			1.42148
$519$	11.0248			0.483934
$520$	44.1361			1.93550
$521$		−	10.1615i		−	0.445185i	−0.974912	−	0.222593i	$-0.928548\pi$
$521$		−	10.1615i		−	0.445185i	0.974912	−	0.222593i	$-0.0714520\pi$
$522$	13.8395			0.605740
$523$	−35.6143			−1.55730			−0.778652	−	0.627456i	$-0.784096\pi$
$523$	−35.6143			−1.55730			−0.778652	+	0.627456i	$0.784096\pi$
$524$			33.4573i			1.46159i
$525$		−	3.25633i		−	0.142118i
$526$		−	53.0242i		−	2.31196i
$527$	2.48792			0.108375
$528$	−17.2869			−0.752315
$529$	−0.110196			−0.00479112
$530$			38.8139i			1.68597i
$531$		−	6.81768i		−	0.295862i
$532$			26.7527i			1.15988i
$533$			11.4843i			0.497442i
$534$			43.0322i			1.86219i
$535$	−32.8823			−1.42163
$536$			64.2318i			2.77439i
$537$			22.5165i			0.971659i
$538$	71.0729			3.06417
$539$	−6.98485			−0.300859
$540$			7.89596i			0.339788i
$541$			3.89736i			0.167561i	0.996484	+	0.0837804i	$0.0266994\pi$
$541$			3.89736i			0.167561i	−0.996484	+	0.0837804i	$0.973301\pi$
$542$	27.4944			1.18098
$543$		−	12.0299i		−	0.516251i
$544$			13.7498i			0.589519i
$545$			3.63702i			0.155793i
$546$	−23.5097			−1.00612
$547$	2.69037			0.115032			0.0575159	−	0.998345i	$-0.481682\pi$
$547$	2.69037			0.115032			0.0575159	+	0.998345i	$0.481682\pi$
$548$		−	84.8004i		−	3.62250i
$549$		−	0.933720i		−	0.0398502i
$550$			12.0398i			0.513380i
$551$			16.0165i			0.682327i
$552$	26.4220			1.12459
$553$	23.3786			0.994157
$554$			23.9203i			1.01628i
$555$			11.0507i			0.469076i
$556$		−	40.6480i		−	1.72386i
$557$	−41.6592			−1.76516			−0.882579	−	0.470163i	$-0.844195\pi$
$557$	−41.6592			−1.76516			−0.882579	+	0.470163i	$0.844195\pi$
$558$			0.974086i			0.0412363i
$559$		−	18.0369i		−	0.762881i
$560$	−21.8650			−0.923967
$561$	20.8327			0.879558
$562$		−	51.2384i		−	2.16136i
$563$		−	30.2940i		−	1.27674i	−0.769730	−	0.638369i	$-0.779609\pi$
$563$		−	30.2940i		−	1.27674i	0.769730	−	0.638369i	$-0.220391\pi$
$564$	−44.1550			−1.85926
$565$			0.427521i			0.0179860i
$566$		−	31.8270i		−	1.33779i
$567$		−	2.20605i		−	0.0926453i
$568$			34.9357i			1.46587i
$569$			35.4706i			1.48701i	0.668733	+	0.743503i	$0.266837\pi$
$569$			35.4706i			1.48701i	−0.668733	+	0.743503i	$0.733163\pi$
$570$	−13.4830			−0.564741
$571$	−15.3786			−0.643572			−0.321786	−	0.946812i	$-0.604283\pi$
$571$	−15.3786			−0.643572			−0.321786	+	0.946812i	$0.604283\pi$
$572$	58.9121			2.46324
$573$		−	3.12873i		−	0.130705i
$574$		−	14.7542i		−	0.615829i
$575$		−	7.09602i		−	0.295925i
$576$	5.17632			0.215680
$577$	36.8759			1.53517			0.767583	−	0.640950i	$-0.221459\pi$
$577$	36.8759			1.53517			0.767583	+	0.640950i	$0.221459\pi$
$578$		−	58.5091i		−	2.43366i
$579$	6.57718			0.273338
$580$	−43.8644			−1.82137
$581$	−0.353706			−0.0146742
$582$	−2.15414			−0.0892919
$583$			27.1741i			1.12543i
$584$	55.0565			2.27825
$585$		−	8.03028i		−	0.332011i
$586$	64.0283			2.64498
$587$			31.0830i			1.28293i	0.767151	+	0.641467i	$0.221674\pi$
$587$			31.0830i			1.28293i	−0.767151	+	0.641467i	$0.778326\pi$
$588$	−8.97338			−0.370056
$589$	−1.12731			−0.0464501
$590$			31.8833i			1.31261i
$591$	−7.25540			−0.298447
$592$	−31.0814			−1.27744
$593$	21.6813			0.890343			0.445172	−	0.895445i	$-0.353143\pi$
$593$	21.6813			0.890343			0.445172	+	0.895445i	$0.353143\pi$
$594$			8.15656i			0.334668i
$595$	26.3499			1.08024
$596$		−	64.0872i		−	2.62512i
$597$	10.4064			0.425904
$598$	−51.2311			−2.09500
$599$			12.7595i			0.521340i	0.965428	+	0.260670i	$0.0839435\pi$
$599$			12.7595i			0.521340i	−0.965428	+	0.260670i	$0.916057\pi$
$600$			8.11291i			0.331208i
$601$	19.5461			0.797303			0.398651	−	0.917103i	$-0.369478\pi$
$601$	19.5461			0.797303			0.398651	+	0.917103i	$0.369478\pi$
$602$			23.1725i			0.944440i
$603$	11.6866			0.475913
$604$		−	80.0891i		−	3.25878i
$605$			0.525988i			0.0213844i
$606$		−	44.6087i		−	1.81211i
$607$			2.83700i			0.115150i	0.998341	+	0.0575752i	$0.0183369\pi$
$607$			2.83700i			0.115150i	−0.998341	+	0.0575752i	$0.981663\pi$
$608$		−	6.23025i		−	0.252670i
$609$	12.2553			0.496608
$610$			4.36659i			0.176798i
$611$	44.9061			1.81671
$612$	26.7636			1.08186
$613$		−	44.0953i		−	1.78099i	−0.454992	−	0.890496i	$-0.650358\pi$
$613$		−	44.0953i		−	1.78099i	0.454992	−	0.890496i	$-0.349642\pi$
$614$	76.3914			3.08290
$615$	5.03964			0.203218
$616$	−39.6983			−1.59949
$617$	−20.2968			−0.817120			−0.408560	−	0.912731i	$-0.633969\pi$
$617$	−20.2968			−0.817120			−0.408560	+	0.912731i	$0.633969\pi$
$618$	−7.21973			−0.290420
$619$	−9.83578			−0.395333			−0.197667	−	0.980269i	$-0.563336\pi$
$619$	−9.83578			−0.395333			−0.197667	+	0.980269i	$0.563336\pi$
$620$		−	3.08737i		−	0.123992i
$621$		−	4.80731i		−	0.192911i
$622$		−	12.5402i		−	0.502816i
$623$			38.1061i			1.52669i
$624$	22.5861			0.904169
$625$	−15.4407			−0.617628
$626$			62.6512i			2.50405i
$627$	−9.43961			−0.376982
$628$	44.6884	+	27.9400i	1.78326	+	1.11493i
$629$	37.4568			1.49350
$630$			10.3167i			0.411027i
$631$	−34.6525			−1.37949			−0.689747	−	0.724050i	$-0.742278\pi$
$631$	−34.6525			−1.37949			−0.689747	+	0.724050i	$0.742278\pi$
$632$	−58.2460			−2.31690
$633$		−	0.590604i		−	0.0234744i
$634$			67.7142i			2.68927i
$635$		−	15.3014i		−	0.607216i
$636$			34.9103i			1.38428i
$637$	9.12604			0.361587
$638$	−45.3122			−1.79393
$639$	6.35632			0.251452
$640$	−32.3204			−1.27758
$641$	39.5415			1.56180			0.780898	−	0.624659i	$-0.214762\pi$
$641$	39.5415			1.56180			0.780898	+	0.624659i	$0.214762\pi$
$642$	−43.6379			−1.72225
$643$			41.2286i			1.62590i	0.582335	+	0.812949i	$0.302139\pi$
$643$			41.2286i			1.62590i	−0.582335	+	0.812949i	$0.697861\pi$
$644$	44.6076			1.75779
$645$	−7.91510			−0.311657
$646$			45.7011i			1.79809i
$647$	−16.5543			−0.650817			−0.325409	−	0.945574i	$-0.605502\pi$
$647$	−16.5543			−0.650817			−0.325409	+	0.945574i	$0.605502\pi$
$648$			5.49621i			0.215911i
$649$			22.3218i			0.876209i
$650$		−	15.7306i		−	0.617005i
$651$			0.862577i			0.0338071i
$652$		−	58.4742i		−	2.29003i
$653$	−39.8250			−1.55847			−0.779237	−	0.626730i	$-0.784393\pi$
$653$	−39.8250			−1.55847			−0.779237	+	0.626730i	$0.784393\pi$
$654$			4.82667i			0.188738i
$655$	−14.9318			−0.583432
$656$			14.1746i			0.553425i
$657$		−	10.0172i		−	0.390807i
$658$	−57.6920			−2.24907
$659$	27.3595			1.06578			0.532888	−	0.846186i	$-0.321107\pi$
$659$	27.3595			1.06578			0.532888	+	0.846186i	$0.321107\pi$
$660$		−	25.8522i		−	1.00630i
$661$	−8.33617			−0.324240			−0.162120	−	0.986771i	$-0.551833\pi$
$661$	−8.33617			−0.324240			−0.162120	+	0.986771i	$0.551833\pi$
$662$		−	71.1593i		−	2.76569i
$663$	−27.2189			−1.05710
$664$	0.881233			0.0341985
$665$	−11.9395			−0.462995
$666$			14.6653i			0.568269i
$667$	26.7060			1.03406
$668$	−11.0109			−0.426025
$669$			7.80315i			0.301687i
$670$	−54.6528			−2.11142
$671$			3.05710i			0.118018i
$672$	−4.76716			−0.183897
$673$		−	39.7357i		−	1.53170i	−0.643020	−	0.765850i	$-0.722319\pi$
$673$		−	39.7357i		−	1.53170i	0.643020	−	0.765850i	$-0.277681\pi$
$674$	−32.9835			−1.27048
$675$	1.47609			0.0568148
$676$	−22.2905			−0.857326
$677$	29.4976			1.13368			0.566842	−	0.823827i	$-0.308165\pi$
$677$	29.4976			1.13368			0.566842	+	0.823827i	$0.308165\pi$
$678$			0.567361i			0.0217893i
$679$	−1.90754			−0.0732048
$680$	−65.6490			−2.51753
$681$			9.00949i			0.345244i
$682$		−	3.18926i		−	0.122123i
$683$		−	40.1644i		−	1.53685i	−0.639940	−	0.768425i	$-0.721041\pi$
$683$		−	40.1644i		−	1.53685i	0.639940	−	0.768425i	$-0.278959\pi$
$684$	−12.1270			−0.463687
$685$	37.8458			1.44602
$686$	−50.1948			−1.91645
$687$			15.2529i			0.581934i
$688$		−	22.2622i		−	0.848737i
$689$		−	35.5042i		−	1.35260i
$690$			22.4816i			0.855861i
$691$		−	43.3986i		−	1.65096i	−0.564430	−	0.825481i	$-0.690904\pi$
$691$		−	43.3986i		−	1.65096i	0.564430	−	0.825481i	$-0.309096\pi$
$692$	−46.3727			−1.76283
$693$			7.22284i			0.274373i
$694$		−	40.8884i		−	1.55210i
$695$	18.1409			0.688123
$696$	−30.5331			−1.15735
$697$		−	17.0821i		−	0.647029i
$698$			48.7788i			1.84630i
$699$	17.7874			0.672782
$700$			13.6968i			0.517692i
$701$			40.7907i			1.54064i	0.637655	+	0.770322i	$0.279905\pi$
$701$			40.7907i			1.54064i	−0.637655	+	0.770322i	$0.720095\pi$
$702$		−	10.6569i		−	0.402220i
$703$	−16.9722			−0.640118
$704$	−16.9478			−0.638746
$705$		−	19.7060i		−	0.742173i
$706$			11.8318i			0.445294i
$707$		−	39.5022i		−	1.48563i
$708$			28.6767i			1.07774i
$709$	−42.8638			−1.60978			−0.804892	−	0.593421i	$-0.797777\pi$
$709$	−42.8638			−1.60978			−0.804892	+	0.593421i	$0.797777\pi$
$710$	−29.7257			−1.11559
$711$			10.5975i			0.397437i
$712$		−	94.9388i		−	3.55798i
$713$			1.87969i			0.0703948i
$714$	34.9688			1.30868
$715$			26.2920i			0.983266i
$716$		−	94.7095i		−	3.53946i
$717$	−19.9303			−0.744310
$718$	−88.5997			−3.30651
$719$			9.07727i			0.338525i	0.985571	+	0.169263i	$0.0541386\pi$
$719$			9.07727i			0.338525i	−0.985571	+	0.169263i	$0.945861\pi$
$720$		−	9.91141i		−	0.369377i
$721$	−6.39326			−0.238097
$722$			26.6255i			0.990899i
$723$		−	4.75533i		−	0.176853i
$724$			50.6003i			1.88055i
$725$			8.20013i			0.304545i
$726$			0.698035i			0.0259065i
$727$	14.1073			0.523211			0.261606	−	0.965175i	$-0.415748\pi$
$727$	14.1073			0.523211			0.261606	+	0.965175i	$0.415748\pi$
$728$	51.8676			1.92234
$729$	1.00000			0.0370370
$730$			46.8459i			1.73384i
$731$			26.8285i			0.992289i
$732$			3.92743i			0.145162i
$733$	−15.6319			−0.577376			−0.288688	−	0.957423i	$-0.593219\pi$
$733$	−15.6319			−0.577376			−0.288688	+	0.957423i	$0.593219\pi$
$734$	−77.9713			−2.87797
$735$		−	4.00476i		−	0.147718i
$736$	−10.3883			−0.382920
$737$	−38.2631			−1.40944
$738$	6.68807			0.246191
$739$	−27.3201			−1.00499			−0.502493	−	0.864581i	$-0.667584\pi$
$739$	−27.3201			−1.00499			−0.502493	+	0.864581i	$0.667584\pi$
$740$		−	46.4817i		−	1.70870i
$741$	12.3333			0.453075
$742$			45.6131i			1.67451i
$743$	41.7959			1.53334			0.766671	−	0.642041i	$-0.221912\pi$
$743$	41.7959			1.53334			0.766671	+	0.642041i	$0.221912\pi$
$744$		−	2.14905i		−	0.0787880i
$745$	28.6017			1.04788
$746$	93.6439			3.42855
$747$		−	0.160335i		−	0.00586634i
$748$	−87.6271			−3.20396
$749$	−38.6424			−1.41196
$750$	−30.2858			−1.10588
$751$		−	36.0240i		−	1.31454i	−0.753657	−	0.657268i	$-0.771712\pi$
$751$		−	36.0240i		−	1.31454i	0.753657	−	0.657268i	$-0.228288\pi$
$752$	55.4256			2.02116
$753$		−	5.50997i		−	0.200795i
$754$	59.2025			2.15603
$755$	35.7432			1.30083
$756$			9.27913i			0.337479i
$757$		−	7.16410i		−	0.260384i	−0.991489	−	0.130192i	$-0.958441\pi$
$757$		−	7.16410i		−	0.260384i	0.991489	−	0.130192i	$-0.0415593\pi$
$758$	−66.5737			−2.41807
$759$			15.7397i			0.571313i
$760$	29.7465			1.07902
$761$		−	3.00258i		−	0.108844i	−0.998518	−	0.0544218i	$-0.982668\pi$
$761$		−	3.00258i		−	0.108844i	0.998518	−	0.0544218i	$-0.0173316\pi$
$762$		−	20.3063i		−	0.735621i
$763$			4.27414i			0.154734i
$764$			13.1602i			0.476118i
$765$			11.9444i			0.431851i
$766$	16.4630			0.594831
$767$		−	29.1645i		−	1.05307i
$768$	−32.5396			−1.17417
$769$	24.5594			0.885636			0.442818	−	0.896612i	$-0.353979\pi$
$769$	24.5594			0.885636			0.442818	+	0.896612i	$0.353979\pi$
$770$		−	33.7780i		−	1.21728i
$771$	−6.29955			−0.226873
$772$	−27.6651			−0.995689
$773$	19.5445			0.702967			0.351483	−	0.936194i	$-0.385677\pi$
$773$	19.5445			0.702967			0.351483	+	0.936194i	$0.385677\pi$
$774$	−10.5041			−0.377561
$775$	−0.577160			−0.0207322
$776$	4.75251			0.170605
$777$			12.9865i			0.465888i
$778$			75.2764i			2.69879i
$779$			7.74012i			0.277319i
$780$			33.7772i			1.20942i
$781$	−20.8113			−0.744687
$782$	76.2023			2.72499
$783$			5.55530i			0.198530i
$784$	11.2639			0.402280
$785$	−12.4694	+	19.9441i	−0.445052	+	0.711836i
$786$	−19.8158			−0.706808
$787$			39.7567i			1.41717i	0.705624	+	0.708587i	$0.250667\pi$
$787$			39.7567i			1.41717i	−0.705624	+	0.708587i	$0.749333\pi$
$788$	30.5178			1.08715
$789$	21.2843			0.757743
$790$		−	49.5597i		−	1.76326i
$791$			0.502412i			0.0178637i
$792$		−	17.9952i		−	0.639432i
$793$		−	3.99425i		−	0.141840i
$794$	73.7322			2.61666
$795$	−15.5802			−0.552573
$796$	−43.7715			−1.55144
$797$	−19.0797			−0.675839			−0.337919	−	0.941175i	$-0.609723\pi$
$797$	−19.0797			−0.675839			−0.337919	+	0.941175i	$0.609723\pi$
$798$	−15.8449			−0.560903
$799$	−66.7944			−2.36302
$800$		−	3.18976i		−	0.112775i
$801$	−17.2735			−0.610329
$802$	−0.213315			−0.00753240
$803$			32.7973i			1.15739i
$804$	−49.1563			−1.73361
$805$			19.9081i			0.701667i
$806$			4.16692i			0.146774i
$807$			28.5292i			1.00428i
$808$			98.4168i			3.46229i
$809$			4.21940i			0.148346i	0.997245	+	0.0741730i	$0.0236317\pi$
$809$			4.21940i			0.148346i	−0.997245	+	0.0741730i	$0.976368\pi$
$810$	−4.67656			−0.164317
$811$		−	12.7811i		−	0.448806i	−0.974496	−	0.224403i	$-0.927957\pi$
$811$		−	12.7811i		−	0.448806i	0.974496	−	0.224403i	$-0.0720432\pi$
$812$	−51.5483			−1.80899
$813$			11.0365i			0.387066i
$814$		−	48.0158i		−	1.68295i
$815$	26.0966			0.914125
$816$	−33.5951			−1.17606
$817$		−	12.1564i		−	0.425298i
$818$	−67.1269			−2.34704
$819$		−	9.43698i		−	0.329755i
$820$	−21.1979			−0.740262
$821$	33.6104			1.17301			0.586505	−	0.809946i	$-0.300503\pi$
$821$	33.6104			1.17301			0.586505	+	0.809946i	$0.300503\pi$
$822$	50.2249			1.75180
$823$			13.1090i			0.456952i	0.973549	+	0.228476i	$0.0733743\pi$
$823$			13.1090i			0.456952i	−0.973549	+	0.228476i	$0.926626\pi$
$824$	15.9284			0.554890
$825$	−4.83289			−0.168259
$826$			37.4684i			1.30369i
$827$	12.5904			0.437812			0.218906	−	0.975746i	$-0.429751\pi$
$827$	12.5904			0.437812			0.218906	+	0.975746i	$0.429751\pi$
$828$			20.2206i			0.702715i
$829$	38.8193			1.34825			0.674125	−	0.738617i	$-0.264521\pi$
$829$	38.8193			1.34825			0.674125	+	0.738617i	$0.264521\pi$
$830$			0.749814i			0.0260264i
$831$	−9.60180			−0.333083
$832$	22.1432			0.767676
$833$	−13.5743			−0.470321
$834$	24.0747			0.833637
$835$		−	4.91410i		−	0.170059i
$836$	39.7051			1.37323
$837$	−0.391006			−0.0135151
$838$		−	10.3311i		−	0.356882i
$839$			23.1589i			0.799536i	0.916616	+	0.399768i	$0.130909\pi$
$839$			23.1589i			0.799536i	−0.916616	+	0.399768i	$0.869091\pi$
$840$		−	22.7609i		−	0.785327i
$841$	−1.86138			−0.0641854
$842$	17.8673			0.615747
$843$	20.5675			0.708384
$844$			2.48421i			0.0855101i
$845$		−	9.94808i		−	0.342224i
$846$		−	26.1518i		−	0.899116i
$847$			0.618128i			0.0212391i
$848$		−	43.8212i		−	1.50483i
$849$	12.7756			0.438459
$850$			23.3980i			0.802546i
$851$			28.2995i			0.970095i
$852$	−26.7361			−0.915964
$853$	33.8887			1.16033			0.580164	−	0.814500i	$-0.302989\pi$
$853$	33.8887			1.16033			0.580164	+	0.814500i	$0.302989\pi$
$854$			5.13151i			0.175597i
$855$		−	5.41219i		−	0.185093i
$856$	96.2749			3.29061
$857$			10.3496i			0.353536i	0.984253	+	0.176768i	$0.0565642\pi$
$857$			10.3496i			0.353536i	−0.984253	+	0.176768i	$0.943436\pi$
$858$			34.8920i			1.19119i
$859$		−	23.7609i		−	0.810713i	−0.914159	−	0.405357i	$-0.867147\pi$
$859$		−	23.7609i		−	0.810713i	0.914159	−	0.405357i	$-0.132853\pi$
$860$	33.2927			1.13527
$861$	5.92246			0.201837
$862$		−	16.9191i		−	0.576267i
$863$		−	48.5452i		−	1.65250i	−0.563304	−	0.826249i	$-0.690470\pi$
$863$		−	48.5452i		−	1.65250i	0.563304	−	0.826249i	$-0.309530\pi$
$864$		−	2.16095i		−	0.0735170i
$865$		−	20.6958i		−	0.703679i
$866$	55.4120			1.88298
$867$	23.4861			0.797628
$868$		−	3.62819i		−	0.123149i
$869$		−	34.6973i		−	1.17703i
$870$		−	25.9797i		−	0.880793i
$871$	49.9925			1.69393
$872$		−	10.6487i		−	0.360611i
$873$		−	0.864689i		−	0.0292653i
$874$	−34.5284			−1.16794
$875$	−26.8188			−0.906642
$876$			42.1345i			1.42359i
$877$			7.02789i			0.237315i	0.992935	+	0.118657i	$0.0378590\pi$
$877$			7.02789i			0.237315i	−0.992935	+	0.118657i	$0.962141\pi$
$878$	−55.1910			−1.86261
$879$			25.7015i			0.866889i
$880$			32.4511i			1.09393i
$881$			40.3321i			1.35882i	0.733757	+	0.679412i	$0.237765\pi$
$881$			40.3321i			1.35882i	−0.733757	+	0.679412i	$0.762235\pi$
$882$		−	5.31468i		−	0.178955i
$883$		−	5.97837i		−	0.201188i	−0.994928	−	0.100594i	$-0.967926\pi$
$883$		−	5.97837i		−	0.201188i	0.994928	−	0.100594i	$-0.0320743\pi$
$884$	114.489			3.85068
$885$	−12.7982			−0.430207
$886$	−0.210696			−0.00707847
$887$			1.97078i			0.0661724i	0.999453	+	0.0330862i	$0.0105336\pi$
$887$			1.97078i			0.0661724i	−0.999453	+	0.0330862i	$0.989466\pi$
$888$		−	32.3549i		−	1.08576i
$889$		−	17.9818i		−	0.603089i
$890$	80.7805			2.70777
$891$	−3.27411			−0.109687
$892$		−	32.8218i		−	1.09896i
$893$	30.2655			1.01280
$894$	37.9571			1.26948
$895$	42.2682			1.41287
$896$	−37.9822			−1.26890
$897$		−	20.5646i		−	0.686632i
$898$	10.6811			0.356432
$899$		−	2.17216i		−	0.0724455i
$900$	−6.20877			−0.206959
$901$			52.8097i			1.75935i
$902$	−21.8975			−0.729107
$903$	−9.30162			−0.309539
$904$		−	1.25172i		−	0.0416317i
$905$	−22.5826			−0.750670
$906$	47.4346			1.57591
$907$	16.8844			0.560637			0.280318	−	0.959907i	$-0.409560\pi$
$907$	16.8844			0.560637			0.280318	+	0.959907i	$0.409560\pi$
$908$		−	37.8959i		−	1.25762i
$909$	17.9063			0.593915
$910$			44.1326i			1.46298i
$911$	14.7760			0.489549			0.244775	−	0.969580i	$-0.421286\pi$
$911$	14.7760			0.489549			0.244775	+	0.969580i	$0.421286\pi$
$912$	15.2224			0.504065
$913$			0.524954i			0.0173734i
$914$			2.36342i			0.0781749i
$915$	−1.75279			−0.0579453
$916$		−	64.1570i		−	2.11981i
$917$	−17.5474			−0.579467
$918$			15.8514i			0.523173i
$919$		−	8.67548i		−	0.286178i	−0.989710	−	0.143089i	$-0.954297\pi$
$919$		−	8.67548i		−	0.286178i	0.989710	−	0.143089i	$-0.0457035\pi$
$920$		−	49.5995i		−	1.63525i
$921$			30.6641i			1.01042i
$922$			40.5396i			1.33510i
$923$	27.1910			0.895001
$924$		−	30.3809i		−	0.999458i
$925$	−8.68941			−0.285706
$926$	−17.9474			−0.589788
$927$		−	2.89806i		−	0.0951848i
$928$	12.0047			0.394075
$929$	35.0573			1.15019			0.575097	−	0.818085i	$-0.304964\pi$
$929$	35.0573			1.15019			0.575097	+	0.818085i	$0.304964\pi$
$930$	1.82856			0.0599609
$931$	6.15070			0.201581
$932$	−74.8179			−2.45074
$933$	5.03374			0.164797
$934$		−	57.6529i		−	1.88646i
$935$		−	39.1074i		−	1.27895i
$936$			23.5116i			0.768500i
$937$			10.0112i			0.327051i	0.986539	+	0.163526i	$0.0522866\pi$
$937$			10.0112i			0.327051i	−0.986539	+	0.163526i	$0.947713\pi$
$938$	−64.2266			−2.09707
$939$	−25.1487			−0.820697
$940$			82.8881i			2.70351i
$941$	−1.37936			−0.0449658			−0.0224829	−	0.999747i	$-0.507157\pi$
$941$	−1.37936			−0.0449658			−0.0224829	+	0.999747i	$0.507157\pi$
$942$	−16.5481	+	26.4677i	−0.539165	+	0.862364i
$943$	12.9059			0.420275
$944$		−	35.9965i		−	1.17159i
$945$	−4.14121			−0.134714
$946$	34.3915			1.11816
$947$		−	3.00241i		−	0.0975653i	−0.998809	−	0.0487827i	$-0.984466\pi$
$947$		−	3.00241i		−	0.0975653i	0.998809	−	0.0487827i	$-0.0155342\pi$
$948$		−	44.5754i		−	1.44774i
$949$		−	42.8513i		−	1.39101i
$950$		−	10.6020i		−	0.343974i
$951$	−27.1810			−0.881405
$952$	−77.1491			−2.50042
$953$	14.1877			0.459583			0.229792	−	0.973240i	$-0.426196\pi$
$953$	14.1877			0.459583			0.229792	+	0.973240i	$0.426196\pi$
$954$	−20.6764			−0.669423
$955$	−5.87328			−0.190055
$956$	83.8313			2.71130
$957$		−	18.1887i		−	0.587956i
$958$	83.2696			2.69032
$959$	44.4755			1.43619
$960$		−	9.71703i		−	0.313616i
$961$	−30.8471			−0.995068
$962$			62.7350i			2.02266i
$963$		−	17.5166i		−	0.564464i
$964$			20.0020i			0.644221i
$965$		−	12.3467i		−	0.397456i
$966$			26.4198i			0.850045i
$967$	−4.13946			−0.133116			−0.0665581	−	0.997783i	$-0.521202\pi$
$967$	−4.13946			−0.133116			−0.0665581	+	0.997783i	$0.521202\pi$
$968$		−	1.54002i		−	0.0494981i
$969$	−18.3448			−0.589320
$970$			4.04376i			0.129837i
$971$			34.6650i			1.11245i	0.831030	+	0.556227i	$0.187751\pi$
$971$			34.6650i			1.11245i	−0.831030	+	0.556227i	$0.812249\pi$
$972$	−4.20622			−0.134915
$973$	21.3187			0.683447
$974$			54.7744i			1.75509i
$975$	6.31439			0.202222
$976$		−	4.92992i		−	0.157803i
$977$	22.4745			0.719023			0.359512	−	0.933141i	$-0.382943\pi$
$977$	22.4745			0.719023			0.359512	+	0.933141i	$0.382943\pi$
$978$	34.6327			1.10743
$979$	56.5553			1.80752
$980$			16.8449i			0.538091i
$981$	−1.93746			−0.0618585
$982$	−49.2218			−1.57073
$983$			29.6420i			0.945433i	0.881214	+	0.472717i	$0.156727\pi$
$983$			29.6420i			0.945433i	−0.881214	+	0.472717i	$0.843273\pi$
$984$	−14.7554			−0.470385
$985$			13.6199i			0.433966i
$986$	−88.0591			−2.80437
$987$		−	23.1580i		−	0.737129i
$988$	−51.8766			−1.65041
$989$	−20.2696			−0.644537
$990$	15.3116			0.486633
$991$	31.6387			1.00504			0.502519	−	0.864566i	$-0.332407\pi$
$991$	31.6387			1.00504			0.502519	+	0.864566i	$0.332407\pi$
$992$			0.844944i			0.0268270i
$993$	28.5639			0.906449
$994$	−34.9329			−1.10800
$995$		−	19.5349i		−	0.619298i
$996$			0.674404i			0.0213693i
$997$			56.8423i			1.80022i	0.435668	+	0.900108i	$0.356512\pi$
$997$			56.8423i			1.80022i	−0.435668	+	0.900108i	$0.643488\pi$
$998$	−83.0291			−2.62824
$999$	−5.88677			−0.186249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.b.313.2	✓	14
3.2	odd	2		1413.2.b.e.784.13		14
157.156	even	2	inner	471.2.b.b.313.13	yes	14
471.470	odd	2		1413.2.b.e.784.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.b.313.2	✓	14	1.1	even	1	trivial
471.2.b.b.313.13	yes	14	157.156	even	2	inner
1413.2.b.e.784.2		14	471.470	odd	2
1413.2.b.e.784.13		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.49123i q^{2} +1.00000 q^{3} -4.20622 q^{4} -1.87721i q^{5} -2.49123i q^{6} -2.20605i q^{7} +5.49621i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49123i q^{2} +1.00000 q^{3} -4.20622 q^{4} -1.87721i q^{5} -2.49123i q^{6} -2.20605i q^{7} +5.49621i q^{8} +1.00000 q^{9} -4.67656 q^{10} -3.27411 q^{11} -4.20622 q^{12} +4.27778 q^{13} -5.49577 q^{14} -1.87721i q^{15} +5.27987 q^{16} -6.36287 q^{17} -2.49123i q^{18} +2.88311 q^{19} +7.89596i q^{20} -2.20605i q^{21} +8.15656i q^{22} -4.80731i q^{23} +5.49621i q^{24} +1.47609 q^{25} -10.6569i q^{26} +1.00000 q^{27} +9.27913i q^{28} +5.55530i q^{29} -4.67656 q^{30} -0.391006 q^{31} -2.16095i q^{32} -3.27411 q^{33} +15.8514i q^{34} -4.14121 q^{35} -4.20622 q^{36} -5.88677 q^{37} -7.18248i q^{38} +4.27778 q^{39} +10.3175 q^{40} +2.68465i q^{41} -5.49577 q^{42} -4.21642i q^{43} +13.7716 q^{44} -1.87721i q^{45} -11.9761 q^{46} +10.4975 q^{47} +5.27987 q^{48} +2.13336 q^{49} -3.67728i q^{50} -6.36287 q^{51} -17.9933 q^{52} -8.29968i q^{53} -2.49123i q^{54} +6.14619i q^{55} +12.1249 q^{56} +2.88311 q^{57} +13.8395 q^{58} -6.81768i q^{59} +7.89596i q^{60} -0.933720i q^{61} +0.974086i q^{62} -2.20605i q^{63} +5.17632 q^{64} -8.03028i q^{65} +8.15656i q^{66} +11.6866 q^{67} +26.7636 q^{68} -4.80731i q^{69} +10.3167i q^{70} +6.35632 q^{71} +5.49621i q^{72} -10.0172i q^{73} +14.6653i q^{74} +1.47609 q^{75} -12.1270 q^{76} +7.22284i q^{77} -10.6569i q^{78} +10.5975i q^{79} -9.91141i q^{80} +1.00000 q^{81} +6.68807 q^{82} -0.160335i q^{83} +9.27913i q^{84} +11.9444i q^{85} -10.5041 q^{86} +5.55530i q^{87} -17.9952i q^{88} -17.2735 q^{89} -4.67656 q^{90} -9.43698i q^{91} +20.2206i q^{92} -0.391006 q^{93} -26.1518i q^{94} -5.41219i q^{95} -2.16095i q^{96} -0.864689i q^{97} -5.31468i q^{98} -3.27411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Introduction

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