LMFDB - Embedded newform 1470.2.b.a.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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([1, 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("1470.881");

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.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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.4
Root			$-1.21252 - 1.23685i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.a.881.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.431645 - 1.67740i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.67740 + 0.431645i) q^{6} +1.00000i q^{8} +(-2.62736 + 1.44809i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.431645 - 1.67740i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.67740 + 0.431645i) q^{6} +1.00000i q^{8} +(-2.62736 + 1.44809i) q^{9} -1.00000i q^{10} -5.13552i q^{11} +(0.431645 + 1.67740i) q^{12} -5.00256i q^{13} +(-0.431645 - 1.67740i) q^{15} +1.00000 q^{16} +3.75947 q^{17} +(1.44809 + 2.62736i) q^{18} +2.69268i q^{19} -1.00000 q^{20} -5.13552 q^{22} -2.48605i q^{23} +(1.67740 - 0.431645i) q^{24} +1.00000 q^{25} -5.00256 q^{26} +(3.56312 + 3.78209i) q^{27} -6.18694i q^{29} +(-1.67740 + 0.431645i) q^{30} +4.77406i q^{31} -1.00000i q^{32} +(-8.61435 + 2.21673i) q^{33} -3.75947i q^{34} +(2.62736 - 1.44809i) q^{36} +0.0524150 q^{37} +2.69268 q^{38} +(-8.39132 + 2.15933i) q^{39} +1.00000i q^{40} -6.55478 q^{41} -9.45088 q^{43} +5.13552i q^{44} +(-2.62736 + 1.44809i) q^{45} -2.48605 q^{46} +3.06892 q^{47} +(-0.431645 - 1.67740i) q^{48} -1.00000i q^{50} +(-1.62276 - 6.30614i) q^{51} +5.00256i q^{52} -1.11204i q^{53} +(3.78209 - 3.56312i) q^{54} -5.13552i q^{55} +(4.51670 - 1.16228i) q^{57} -6.18694 q^{58} -13.2616 q^{59} +(0.431645 + 1.67740i) q^{60} +4.14918i q^{61} +4.77406 q^{62} -1.00000 q^{64} -5.00256i q^{65} +(2.21673 + 8.61435i) q^{66} -0.896174 q^{67} -3.75947 q^{68} +(-4.17010 + 1.07309i) q^{69} -13.4240i q^{71} +(-1.44809 - 2.62736i) q^{72} +6.98029i q^{73} -0.0524150i q^{74} +(-0.431645 - 1.67740i) q^{75} -2.69268i q^{76} +(2.15933 + 8.39132i) q^{78} -16.7476 q^{79} +1.00000 q^{80} +(4.80609 - 7.60931i) q^{81} +6.55478i q^{82} +1.37724 q^{83} +3.75947 q^{85} +9.45088i q^{86} +(-10.3780 + 2.67056i) q^{87} +5.13552 q^{88} +5.34113 q^{89} +(1.44809 + 2.62736i) q^{90} +2.48605i q^{92} +(8.00803 - 2.06070i) q^{93} -3.06892i q^{94} +2.69268i q^{95} +(-1.67740 + 0.431645i) q^{96} +0.633608i q^{97} +(7.43669 + 13.4929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9	$ 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9} + 4 q^{12} - 4 q^{15} + 12 q^{16} + 24 q^{17} + 8 q^{18} - 12 q^{20} - 2 q^{24} + 12 q^{25} - 8 q^{26} + 8 q^{27} + 2 q^{30} - 20 q^{33} + 6 q^{36} + 16 q^{37} + 16 q^{38} + 12 q^{39} + 4 q^{41} - 6 q^{45} - 4 q^{46} + 32 q^{47} - 4 q^{48} + 4 q^{51} + 28 q^{54} - 36 q^{57} - 16 q^{58} + 24 q^{59} + 4 q^{60} - 8 q^{62} - 12 q^{64} - 20 q^{66} + 8 q^{67} - 24 q^{68} - 50 q^{69} - 8 q^{72} - 4 q^{75} + 32 q^{78} + 8 q^{79} + 12 q^{80} - 10 q^{81} + 40 q^{83} + 24 q^{85} - 56 q^{87} + 52 q^{89} + 8 q^{90} + 28 q^{93} + 2 q^{96} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9 + 4 * q^12 - 4 * q^15 + 12 * q^16 + 24 * q^17 + 8 * q^18 - 12 * q^20 - 2 * q^24 + 12 * q^25 - 8 * q^26 + 8 * q^27 + 2 * q^30 - 20 * q^33 + 6 * q^36 + 16 * q^37 + 16 * q^38 + 12 * q^39 + 4 * q^41 - 6 * q^45 - 4 * q^46 + 32 * q^47 - 4 * q^48 + 4 * q^51 + 28 * q^54 - 36 * q^57 - 16 * q^58 + 24 * q^59 + 4 * q^60 - 8 * q^62 - 12 * q^64 - 20 * q^66 + 8 * q^67 - 24 * q^68 - 50 * q^69 - 8 * q^72 - 4 * q^75 + 32 * q^78 + 8 * q^79 + 12 * q^80 - 10 * q^81 + 40 * q^83 + 24 * q^85 - 56 * q^87 + 52 * q^89 + 8 * q^90 + 28 * q^93 + 2 * q^96 + 48 * q^99

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
$3$	−0.431645	−	1.67740i	−0.249211	−	0.968449i
$3$	−0.431645	−	1.67740i	−0.249211	−	0.968449i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.67740	+	0.431645i	−0.684797	+	0.176219i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.62736	+	1.44809i	−0.875788	+	0.482696i
$10$		−	1.00000i		−	0.316228i
$11$		−	5.13552i		−	1.54842i	−0.632929	−	0.774210i	$-0.718148\pi$
$11$		−	5.13552i		−	1.54842i	0.632929	−	0.774210i	$-0.281852\pi$
$12$	0.431645	+	1.67740i	0.124605	+	0.484225i
$13$		−	5.00256i		−	1.38746i	−0.720234	−	0.693731i	$-0.755966\pi$
$13$		−	5.00256i		−	1.38746i	0.720234	−	0.693731i	$-0.244034\pi$
$14$		0			0
$15$	−0.431645	−	1.67740i	−0.111450	−	0.433104i
$16$	1.00000			0.250000
$17$	3.75947			0.911804			0.455902	−	0.890030i	$-0.349317\pi$
$17$	3.75947			0.911804			0.455902	+	0.890030i	$0.349317\pi$
$18$	1.44809	+	2.62736i	0.341317	+	0.619276i
$19$			2.69268i			0.617742i	0.951104	+	0.308871i	$0.0999512\pi$
$19$			2.69268i			0.617742i	−0.951104	+	0.308871i	$0.900049\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−5.13552			−1.09490
$23$		−	2.48605i		−	0.518377i	−0.965827	−	0.259188i	$-0.916545\pi$
$23$		−	2.48605i		−	0.518377i	0.965827	−	0.259188i	$-0.0834550\pi$
$24$	1.67740	−	0.431645i	0.342399	−	0.0881093i
$25$	1.00000			0.200000
$26$	−5.00256			−0.981083
$27$	3.56312	+	3.78209i	0.685722	+	0.727864i
$28$		0			0
$29$		−	6.18694i		−	1.14889i	−0.818545	−	0.574443i	$-0.805219\pi$
$29$		−	6.18694i		−	1.14889i	0.818545	−	0.574443i	$-0.194781\pi$
$30$	−1.67740	+	0.431645i	−0.306251	+	0.0788073i
$31$			4.77406i			0.857447i	0.903436	+	0.428724i	$0.141037\pi$
$31$			4.77406i			0.857447i	−0.903436	+	0.428724i	$0.858963\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−8.61435	+	2.21673i	−1.49957	+	0.385882i
$34$		−	3.75947i		−	0.644743i
$35$		0			0
$36$	2.62736	−	1.44809i	0.437894	−	0.241348i
$37$	0.0524150			0.00861697			0.00430849	−	0.999991i	$-0.498629\pi$
$37$	0.0524150			0.00861697			0.00430849	+	0.999991i	$0.498629\pi$
$38$	2.69268			0.436810
$39$	−8.39132	+	2.15933i	−1.34369	+	0.345770i
$40$			1.00000i			0.158114i
$41$	−6.55478			−1.02369			−0.511843	−	0.859079i	$-0.671037\pi$
$41$	−6.55478			−1.02369			−0.511843	+	0.859079i	$0.671037\pi$
$42$		0			0
$43$	−9.45088			−1.44125			−0.720623	−	0.693327i	$-0.756144\pi$
$43$	−9.45088			−1.44125			−0.720623	+	0.693327i	$0.756144\pi$
$44$			5.13552i			0.774210i
$45$	−2.62736	+	1.44809i	−0.391664	+	0.215868i
$46$	−2.48605			−0.366548
$47$	3.06892			0.447647			0.223824	−	0.974630i	$-0.428146\pi$
$47$	3.06892			0.447647			0.223824	+	0.974630i	$0.428146\pi$
$48$	−0.431645	−	1.67740i	−0.0623027	−	0.242112i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−1.62276	−	6.30614i	−0.227231	−	0.883036i
$52$			5.00256i			0.693731i
$53$		−	1.11204i		−	0.152750i	−0.997079	−	0.0763751i	$-0.975665\pi$
$53$		−	1.11204i		−	0.152750i	0.997079	−	0.0763751i	$-0.0243346\pi$
$54$	3.78209	−	3.56312i	0.514677	−	0.484879i
$55$		−	5.13552i		−	0.692474i
$56$		0			0
$57$	4.51670	−	1.16228i	0.598252	−	0.153948i
$58$	−6.18694			−0.812384
$59$	−13.2616			−1.72651			−0.863255	−	0.504768i	$-0.831578\pi$
$59$	−13.2616			−1.72651			−0.863255	+	0.504768i	$0.831578\pi$
$60$	0.431645	+	1.67740i	0.0557252	+	0.216552i
$61$			4.14918i			0.531248i	0.964077	+	0.265624i	$0.0855780\pi$
$61$			4.14918i			0.531248i	−0.964077	+	0.265624i	$0.914422\pi$
$62$	4.77406			0.606307
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	5.00256i		−	0.620492i
$66$	2.21673	+	8.61435i	0.272860	+	1.06035i
$67$	−0.896174			−0.109485			−0.0547426	−	0.998501i	$-0.517434\pi$
$67$	−0.896174			−0.109485			−0.0547426	+	0.998501i	$0.517434\pi$
$68$	−3.75947			−0.455902
$69$	−4.17010	+	1.07309i	−0.502021	+	0.129185i
$70$		0			0
$71$		−	13.4240i		−	1.59313i	−0.604551	−	0.796567i	$-0.706647\pi$
$71$		−	13.4240i		−	1.59313i	0.604551	−	0.796567i	$-0.293353\pi$
$72$	−1.44809	−	2.62736i	−0.170659	−	0.309638i
$73$			6.98029i			0.816981i	0.912763	+	0.408490i	$0.133945\pi$
$73$			6.98029i			0.816981i	−0.912763	+	0.408490i	$0.866055\pi$
$74$		−	0.0524150i		−	0.00609312i
$75$	−0.431645	−	1.67740i	−0.0498421	−	0.193690i
$76$		−	2.69268i		−	0.308871i
$77$		0			0
$78$	2.15933	+	8.39132i	0.244496	+	0.950130i
$79$	−16.7476			−1.88425			−0.942127	−	0.335255i	$-0.891178\pi$
$79$	−16.7476			−1.88425			−0.942127	+	0.335255i	$0.891178\pi$
$80$	1.00000			0.111803
$81$	4.80609	−	7.60931i	0.534010	−	0.845478i
$82$			6.55478i			0.723855i
$83$	1.37724			0.151172			0.0755861	−	0.997139i	$-0.475917\pi$
$83$	1.37724			0.151172			0.0755861	+	0.997139i	$0.475917\pi$
$84$		0			0
$85$	3.75947			0.407771
$86$			9.45088i			1.01911i
$87$	−10.3780	+	2.67056i	−1.11264	+	0.286314i
$88$	5.13552			0.547449
$89$	5.34113			0.566158			0.283079	−	0.959097i	$-0.408644\pi$
$89$	5.34113			0.566158			0.283079	+	0.959097i	$0.408644\pi$
$90$	1.44809	+	2.62736i	0.152642	+	0.276949i
$91$		0			0
$92$			2.48605i			0.259188i
$93$	8.00803	−	2.06070i	0.830394	−	0.213685i
$94$		−	3.06892i		−	0.316535i
$95$			2.69268i			0.276263i
$96$	−1.67740	+	0.431645i	−0.171199	+	0.0440546i
$97$			0.633608i			0.0643331i	0.999483	+	0.0321666i	$0.0102407\pi$
$97$			0.633608i			0.0643331i	−0.999483	+	0.0321666i	$0.989759\pi$
$98$		0			0
$99$	7.43669	+	13.4929i	0.747415	+	1.35609i
$100$	−1.00000			−0.100000
$101$	17.6286			1.75411			0.877056	−	0.480389i	$-0.159504\pi$
$101$	17.6286			1.75411			0.877056	+	0.480389i	$0.159504\pi$
$102$	−6.30614	+	1.62276i	−0.624401	+	0.160677i
$103$			14.7165i			1.45006i	0.688719	+	0.725028i	$0.258173\pi$
$103$			14.7165i			1.45006i	−0.688719	+	0.725028i	$0.741827\pi$
$104$	5.00256			0.490542
$105$		0			0
$106$	−1.11204			−0.108011
$107$		−	4.71002i		−	0.455335i	−0.973739	−	0.227667i	$-0.926890\pi$
$107$		−	4.71002i		−	0.455335i	0.973739	−	0.227667i	$-0.0731099\pi$
$108$	−3.56312	−	3.78209i	−0.342861	−	0.363932i
$109$	8.62362			0.825993			0.412997	−	0.910733i	$-0.364482\pi$
$109$	8.62362			0.825993			0.412997	+	0.910733i	$0.364482\pi$
$110$	−5.13552			−0.489653
$111$	−0.0226247	−	0.0879211i	−0.00214744	−	0.00834510i
$112$		0			0
$113$			15.3809i			1.44691i	0.690372	+	0.723455i	$0.257447\pi$
$113$			15.3809i			1.44691i	−0.690372	+	0.723455i	$0.742553\pi$
$114$	−1.16228	−	4.51670i	−0.108858	−	0.423028i
$115$		−	2.48605i		−	0.231825i
$116$			6.18694i			0.574443i
$117$	7.24415	+	13.1436i	0.669722	+	1.21512i
$118$			13.2616i			1.22083i
$119$		0			0
$120$	1.67740	−	0.431645i	0.153125	−	0.0394037i
$121$	−15.3736			−1.39760
$122$	4.14918			0.375649
$123$	2.82934	+	10.9950i	0.255113	+	0.991387i
$124$		−	4.77406i		−	0.428724i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.78518			−0.158409			−0.0792047	−	0.996858i	$-0.525238\pi$
$127$	−1.78518			−0.158409			−0.0792047	+	0.996858i	$0.525238\pi$
$128$			1.00000i			0.0883883i
$129$	4.07943	+	15.8529i	0.359174	+	1.39577i
$130$	−5.00256			−0.438754
$131$	−3.10264			−0.271079			−0.135540	−	0.990772i	$-0.543277\pi$
$131$	−3.10264			−0.271079			−0.135540	+	0.990772i	$0.543277\pi$
$132$	8.61435	−	2.21673i	0.749783	−	0.192941i
$133$		0			0
$134$			0.896174i			0.0774177i
$135$	3.56312	+	3.78209i	0.306664	+	0.325510i
$136$			3.75947i			0.322371i
$137$		−	9.75710i		−	0.833605i	−0.908997	−	0.416803i	$-0.863151\pi$
$137$		−	9.75710i		−	0.833605i	0.908997	−	0.416803i	$-0.136849\pi$
$138$	1.07309	+	4.17010i	0.0913476	+	0.354983i
$139$		−	4.26248i		−	0.361539i	−0.983526	−	0.180769i	$-0.942141\pi$
$139$		−	4.26248i		−	0.361539i	0.983526	−	0.180769i	$-0.0578588\pi$
$140$		0			0
$141$	−1.32468	−	5.14781i	−0.111558	−	0.433524i
$142$	−13.4240			−1.12652
$143$	−25.6908			−2.14837
$144$	−2.62736	+	1.44809i	−0.218947	+	0.120674i
$145$		−	6.18694i		−	0.513797i
$146$	6.98029			0.577693
$147$		0			0
$148$	−0.0524150			−0.00430849
$149$		−	8.97218i		−	0.735030i	−0.930018	−	0.367515i	$-0.880209\pi$
$149$		−	8.97218i		−	0.735030i	0.930018	−	0.367515i	$-0.119791\pi$
$150$	−1.67740	+	0.431645i	−0.136959	+	0.0352437i
$151$	13.2266			1.07636			0.538181	−	0.842829i	$-0.319112\pi$
$151$	13.2266			1.07636			0.538181	+	0.842829i	$0.319112\pi$
$152$	−2.69268			−0.218405
$153$	−9.87748	+	5.44403i	−0.798547	+	0.440124i
$154$		0			0
$155$			4.77406i			0.383462i
$156$	8.39132	−	2.15933i	0.671843	−	0.172885i
$157$		−	8.56400i		−	0.683482i	−0.939794	−	0.341741i	$-0.888984\pi$
$157$		−	8.56400i		−	0.683482i	0.939794	−	0.341741i	$-0.111016\pi$
$158$			16.7476i			1.33237i
$159$	−1.86534	+	0.480006i	−0.147931	+	0.0380670i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−7.60931	−	4.80609i	−0.597843	−	0.377602i
$163$	11.0746			0.867426			0.433713	−	0.901051i	$-0.357203\pi$
$163$	11.0746			0.867426			0.433713	+	0.901051i	$0.357203\pi$
$164$	6.55478			0.511843
$165$	−8.61435	+	2.21673i	−0.670626	+	0.172572i
$166$		−	1.37724i		−	0.106895i
$167$	−2.95799			−0.228896			−0.114448	−	0.993429i	$-0.536510\pi$
$167$	−2.95799			−0.228896			−0.114448	+	0.993429i	$0.536510\pi$
$168$		0			0
$169$	−12.0256			−0.925049
$170$		−	3.75947i		−	0.288338i
$171$	−3.89923	−	7.07464i	−0.298182	−	0.541011i
$172$	9.45088			0.720623
$173$	20.7416			1.57696			0.788478	−	0.615063i	$-0.210869\pi$
$173$	20.7416			1.57696			0.788478	+	0.615063i	$0.210869\pi$
$174$	2.67056	+	10.3780i	0.202455	+	0.786753i
$175$		0			0
$176$		−	5.13552i		−	0.387105i
$177$	5.72430	+	22.2450i	0.430265	+	1.67204i
$178$		−	5.34113i		−	0.400334i
$179$		−	24.5184i		−	1.83259i	−0.400506	−	0.916294i	$-0.631166\pi$
$179$		−	24.5184i		−	1.83259i	0.400506	−	0.916294i	$-0.368834\pi$
$180$	2.62736	−	1.44809i	0.195832	−	0.107934i
$181$		−	18.6533i		−	1.38649i	−0.720704	−	0.693243i	$-0.756181\pi$
$181$		−	18.6533i		−	1.38649i	0.720704	−	0.693243i	$-0.243819\pi$
$182$		0			0
$183$	6.95985	−	1.79098i	0.514487	−	0.132393i
$184$	2.48605			0.183274
$185$	0.0524150			0.00385363
$186$	−2.06070	−	8.00803i	−0.151098	−	0.587177i
$187$		−	19.3068i		−	1.41185i
$188$	−3.06892			−0.223824
$189$		0			0
$190$	2.69268			0.195347
$191$			7.27434i			0.526353i	0.964748	+	0.263176i	$0.0847701\pi$
$191$			7.27434i			0.526353i	−0.964748	+	0.263176i	$0.915230\pi$
$192$	0.431645	+	1.67740i	0.0311513	+	0.121056i
$193$	−11.0642			−0.796416			−0.398208	−	0.917295i	$-0.630368\pi$
$193$	−11.0642			−0.796416			−0.398208	+	0.917295i	$0.630368\pi$
$194$	0.633608			0.0454904
$195$	−8.39132	+	2.15933i	−0.600915	+	0.154633i
$196$		0			0
$197$			8.86701i			0.631748i	0.948801	+	0.315874i	$0.102298\pi$
$197$			8.86701i			0.631748i	−0.948801	+	0.315874i	$0.897702\pi$
$198$	13.4929	−	7.43669i	0.958898	−	0.528502i
$199$		−	18.5804i		−	1.31713i	−0.752526	−	0.658563i	$-0.771165\pi$
$199$		−	18.5804i		−	1.31713i	0.752526	−	0.658563i	$-0.228835\pi$
$200$			1.00000i			0.0707107i
$201$	0.386830	+	1.50325i	0.0272849	+	0.106031i
$202$		−	17.6286i		−	1.24034i
$203$		0			0
$204$	1.62276	+	6.30614i	0.113616	+	0.441518i
$205$	−6.55478			−0.457806
$206$	14.7165			1.02534
$207$	3.60001	+	6.53175i	0.250218	+	0.453988i
$208$		−	5.00256i		−	0.346865i
$209$	13.8283			0.956524
$210$		0			0
$211$	−7.36879			−0.507288			−0.253644	−	0.967298i	$-0.581629\pi$
$211$	−7.36879			−0.507288			−0.253644	+	0.967298i	$0.581629\pi$
$212$			1.11204i			0.0763751i
$213$	−22.5174	+	5.79440i	−1.54287	+	0.397026i
$214$	−4.71002			−0.321970
$215$	−9.45088			−0.644545
$216$	−3.78209	+	3.56312i	−0.257339	+	0.242439i
$217$		0			0
$218$		−	8.62362i		−	0.584065i
$219$	11.7088	−	3.01301i	0.791205	−	0.203600i
$220$			5.13552i			0.346237i
$221$		−	18.8070i		−	1.26509i
$222$	−0.0879211	+	0.0226247i	−0.00590088	+	0.00151847i
$223$		−	5.79472i		−	0.388043i	−0.980997	−	0.194021i	$-0.937847\pi$
$223$		−	5.79472i		−	0.388043i	0.980997	−	0.194021i	$-0.0621531\pi$
$224$		0			0
$225$	−2.62736	+	1.44809i	−0.175158	+	0.0965391i
$226$	15.3809			1.02312
$227$	10.6780			0.708727			0.354363	−	0.935108i	$-0.384698\pi$
$227$	10.6780			0.708727			0.354363	+	0.935108i	$0.384698\pi$
$228$	−4.51670	+	1.16228i	−0.299126	+	0.0769740i
$229$		−	8.62361i		−	0.569864i	−0.958548	−	0.284932i	$-0.908029\pi$
$229$		−	8.62361i		−	0.569864i	0.958548	−	0.284932i	$-0.0919711\pi$
$230$	−2.48605			−0.163925
$231$		0			0
$232$	6.18694			0.406192
$233$			16.0654i			1.05248i	0.850335	+	0.526241i	$0.176399\pi$
$233$			16.0654i			1.05248i	−0.850335	+	0.526241i	$0.823601\pi$
$234$	13.1436	−	7.24415i	0.859221	−	0.473565i
$235$	3.06892			0.200194
$236$	13.2616			0.863255
$237$	7.22904	+	28.0925i	0.469576	+	1.82481i
$238$		0			0
$239$			11.0070i			0.711981i	0.934490	+	0.355990i	$0.115856\pi$
$239$			11.0070i			0.711981i	−0.934490	+	0.355990i	$0.884144\pi$
$240$	−0.431645	−	1.67740i	−0.0278626	−	0.108276i
$241$		−	9.70859i		−	0.625385i	−0.949854	−	0.312693i	$-0.898769\pi$
$241$		−	9.70859i		−	0.625385i	0.949854	−	0.312693i	$-0.101231\pi$
$242$			15.3736i			0.988253i
$243$	−14.8384	−	4.77723i	−0.951884	−	0.306459i
$244$		−	4.14918i		−	0.265624i
$245$		0			0
$246$	10.9950	−	2.82934i	0.701017	−	0.180392i
$247$	13.4703			0.857094
$248$	−4.77406			−0.303153
$249$	−0.594481	−	2.31019i	−0.0376737	−	0.146403i
$250$		−	1.00000i		−	0.0632456i
$251$	4.59082			0.289770			0.144885	−	0.989449i	$-0.453719\pi$
$251$	4.59082			0.289770			0.144885	+	0.989449i	$0.453719\pi$
$252$		0			0
$253$	−12.7672			−0.802664
$254$			1.78518i			0.112012i
$255$	−1.62276	−	6.30614i	−0.101621	−	0.394906i
$256$	1.00000			0.0625000
$257$	11.7426			0.732486			0.366243	−	0.930519i	$-0.380644\pi$
$257$	11.7426			0.732486			0.366243	+	0.930519i	$0.380644\pi$
$258$	15.8529	−	4.07943i	0.986961	−	0.253974i
$259$		0			0
$260$			5.00256i			0.310246i
$261$	8.95922	+	16.2553i	0.554562	+	1.00618i
$262$			3.10264i			0.191682i
$263$			22.9128i			1.41286i	0.707781	+	0.706432i	$0.249697\pi$
$263$			22.9128i			1.41286i	−0.707781	+	0.706432i	$0.750303\pi$
$264$	−2.21673	−	8.61435i	−0.136430	−	0.530176i
$265$		−	1.11204i		−	0.0683120i
$266$		0			0
$267$	−2.30547	−	8.95922i	−0.141093	−	0.548295i
$268$	0.896174			0.0547426
$269$	8.12400			0.495329			0.247665	−	0.968846i	$-0.420337\pi$
$269$	8.12400			0.495329			0.247665	+	0.968846i	$0.420337\pi$
$270$	3.78209	−	3.56312i	0.230171	−	0.216844i
$271$		−	10.9402i		−	0.664568i	−0.943179	−	0.332284i	$-0.892181\pi$
$271$		−	10.9402i		−	0.664568i	0.943179	−	0.332284i	$-0.107819\pi$
$272$	3.75947			0.227951
$273$		0			0
$274$	−9.75710			−0.589448
$275$		−	5.13552i		−	0.309684i
$276$	4.17010	−	1.07309i	0.251011	−	0.0645925i
$277$	4.78288			0.287375			0.143688	−	0.989623i	$-0.454104\pi$
$277$	4.78288			0.287375			0.143688	+	0.989623i	$0.454104\pi$
$278$	−4.26248			−0.255647
$279$	−6.91326	−	12.5432i	−0.413886	−	0.750942i
$280$		0			0
$281$		−	21.1040i		−	1.25896i	−0.777018	−	0.629479i	$-0.783268\pi$
$281$		−	21.1040i		−	1.25896i	0.777018	−	0.629479i	$-0.216732\pi$
$282$	−5.14781	+	1.32468i	−0.306548	+	0.0788838i
$283$		−	22.0051i		−	1.30807i	−0.756465	−	0.654035i	$-0.773075\pi$
$283$		−	22.0051i		−	1.30807i	0.756465	−	0.654035i	$-0.226925\pi$
$284$			13.4240i			0.796567i
$285$	4.51670	−	1.16228i	0.267546	−	0.0688476i
$286$			25.6908i			1.51913i
$287$		0			0
$288$	1.44809	+	2.62736i	0.0853294	+	0.154819i
$289$	−2.86642			−0.168613
$290$	−6.18694			−0.363309
$291$	1.06282	−	0.273494i	0.0623034	−	0.0160325i
$292$		−	6.98029i		−	0.408490i
$293$	−11.2905			−0.659598			−0.329799	−	0.944051i	$-0.606981\pi$
$293$	−11.2905			−0.659598			−0.329799	+	0.944051i	$0.606981\pi$
$294$		0			0
$295$	−13.2616			−0.772119
$296$			0.0524150i			0.00304656i
$297$	19.4230	−	18.2985i	1.12704	−	1.06179i
$298$	−8.97218			−0.519744
$299$	−12.4366			−0.719228
$300$	0.431645	+	1.67740i	0.0249211	+	0.0968449i
$301$		0			0
$302$		−	13.2266i		−	0.761103i
$303$	−7.60931	−	29.5703i	−0.437143	−	1.69877i
$304$			2.69268i			0.154436i
$305$			4.14918i			0.237581i
$306$	5.44403	+	9.87748i	0.311215	+	0.564658i
$307$			2.12162i			0.121087i	0.998166	+	0.0605436i	$0.0192834\pi$
$307$			2.12162i			0.121087i	−0.998166	+	0.0605436i	$0.980717\pi$
$308$		0			0
$309$	24.6854	−	6.35229i	1.40431	−	0.361369i
$310$	4.77406			0.271149
$311$	11.0046			0.624013			0.312006	−	0.950080i	$-0.398999\pi$
$311$	11.0046			0.624013			0.312006	+	0.950080i	$0.398999\pi$
$312$	−2.15933	−	8.39132i	−0.122248	−	0.475065i
$313$		−	7.43437i		−	0.420215i	−0.977678	−	0.210108i	$-0.932619\pi$
$313$		−	7.43437i		−	0.420215i	0.977678	−	0.210108i	$-0.0673815\pi$
$314$	−8.56400			−0.483294
$315$		0			0
$316$	16.7476			0.942127
$317$			4.47460i			0.251319i	0.992073	+	0.125659i	$0.0401046\pi$
$317$			4.47460i			0.251319i	−0.992073	+	0.125659i	$0.959895\pi$
$318$	0.480006	+	1.86534i	0.0269174	+	0.104603i
$319$	−31.7732			−1.77896
$320$	−1.00000			−0.0559017
$321$	−7.90060	+	2.03306i	−0.440969	+	0.113474i
$322$		0			0
$323$			10.1230i			0.563260i
$324$	−4.80609	+	7.60931i	−0.267005	+	0.422739i
$325$		−	5.00256i		−	0.277492i
$326$		−	11.0746i		−	0.613363i
$327$	−3.72235	−	14.4653i	−0.205846	−	0.799933i
$328$		−	6.55478i		−	0.361927i
$329$		0			0
$330$	2.21673	+	8.61435i	0.122027	+	0.474204i
$331$	16.9720			0.932863			0.466432	−	0.884557i	$-0.345539\pi$
$331$	16.9720			0.932863			0.466432	+	0.884557i	$0.345539\pi$
$332$	−1.37724			−0.0755861
$333$	−0.137713	+	0.0759015i	−0.00754664	+	0.00415938i
$334$			2.95799i			0.161854i
$335$	−0.896174			−0.0489632
$336$		0			0
$337$	30.7045			1.67258			0.836290	−	0.548287i	$-0.184720\pi$
$337$	30.7045			1.67258			0.836290	+	0.548287i	$0.184720\pi$
$338$			12.0256i			0.654109i
$339$	25.7999	−	6.63908i	1.40126	−	0.360585i
$340$	−3.75947			−0.203886
$341$	24.5173			1.32769
$342$	−7.07464	+	3.89923i	−0.382553	+	0.210846i
$343$		0			0
$344$		−	9.45088i		−	0.509557i
$345$	−4.17010	+	1.07309i	−0.224511	+	0.0577733i
$346$		−	20.7416i		−	1.11508i
$347$		−	33.2005i		−	1.78230i	−0.453711	−	0.891149i	$-0.649900\pi$
$347$		−	33.2005i		−	1.78230i	0.453711	−	0.891149i	$-0.350100\pi$
$348$	10.3780	−	2.67056i	0.556318	−	0.143157i
$349$			21.5465i			1.15336i	0.816972	+	0.576678i	$0.195651\pi$
$349$			21.5465i			1.15336i	−0.816972	+	0.576678i	$0.804349\pi$
$350$		0			0
$351$	18.9201	−	17.8247i	1.00988	−	0.951413i
$352$	−5.13552			−0.273724
$353$	−5.51692			−0.293636			−0.146818	−	0.989164i	$-0.546903\pi$
$353$	−5.51692			−0.293636			−0.146818	+	0.989164i	$0.546903\pi$
$354$	22.2450	−	5.72430i	1.18231	−	0.304243i
$355$		−	13.4240i		−	0.712471i
$356$	−5.34113			−0.283079
$357$		0			0
$358$	−24.5184			−1.29584
$359$		−	19.3565i		−	1.02160i	−0.859700	−	0.510799i	$-0.829350\pi$
$359$		−	19.3565i		−	1.02160i	0.859700	−	0.510799i	$-0.170650\pi$
$360$	−1.44809	−	2.62736i	−0.0763209	−	0.138474i
$361$	11.7495			0.618394
$362$	−18.6533			−0.980394
$363$	6.63595	+	25.7878i	0.348297	+	1.35351i
$364$		0			0
$365$			6.98029i			0.365365i
$366$	−1.79098	−	6.95985i	−0.0936158	−	0.363797i
$367$			14.0326i			0.732494i	0.930518	+	0.366247i	$0.119357\pi$
$367$			14.0326i			0.732494i	−0.930518	+	0.366247i	$0.880643\pi$
$368$		−	2.48605i		−	0.129594i
$369$	17.2218	−	9.49190i	0.896531	−	0.494128i
$370$		−	0.0524150i		−	0.00272493i
$371$		0			0
$372$	−8.00803	+	2.06070i	−0.415197	+	0.106842i
$373$	−1.33838			−0.0692987			−0.0346493	−	0.999400i	$-0.511031\pi$
$373$	−1.33838			−0.0692987			−0.0346493	+	0.999400i	$0.511031\pi$
$374$	−19.3068			−0.998332
$375$	−0.431645	−	1.67740i	−0.0222901	−	0.0866207i
$376$			3.06892i			0.158267i
$377$	−30.9505			−1.59403
$378$		0			0
$379$	8.07964			0.415023			0.207512	−	0.978233i	$-0.433464\pi$
$379$	8.07964			0.415023			0.207512	+	0.978233i	$0.433464\pi$
$380$		−	2.69268i		−	0.138131i
$381$	0.770566	+	2.99447i	0.0394773	+	0.153411i
$382$	7.27434			0.372187
$383$	−23.2943			−1.19028			−0.595141	−	0.803621i	$-0.702904\pi$
$383$	−23.2943			−1.19028			−0.595141	+	0.803621i	$0.702904\pi$
$384$	1.67740	−	0.431645i	0.0855996	−	0.0220273i
$385$		0			0
$386$			11.0642i			0.563151i
$387$	24.8309	−	13.6857i	1.26223	−	0.695683i
$388$		−	0.633608i		−	0.0321666i
$389$			11.7488i			0.595689i	0.954614	+	0.297845i	$0.0962678\pi$
$389$			11.7488i			0.595689i	−0.954614	+	0.297845i	$0.903732\pi$
$390$	2.15933	+	8.39132i	0.109342	+	0.424911i
$391$		−	9.34621i		−	0.472658i
$392$		0			0
$393$	1.33924	+	5.20438i	0.0675558	+	0.262526i
$394$	8.86701			0.446713
$395$	−16.7476			−0.842664
$396$	−7.43669	−	13.4929i	−0.373708	−	0.678043i
$397$			17.2214i			0.864319i	0.901797	+	0.432160i	$0.142248\pi$
$397$			17.2214i			0.864319i	−0.901797	+	0.432160i	$0.857752\pi$
$398$	−18.5804			−0.931349
$399$		0			0
$400$	1.00000			0.0500000
$401$			8.44909i			0.421927i	0.977494	+	0.210964i	$0.0676602\pi$
$401$			8.44909i			0.421927i	−0.977494	+	0.210964i	$0.932340\pi$
$402$	1.50325	−	0.386830i	0.0749751	−	0.0192933i
$403$	23.8826			1.18968
$404$	−17.6286			−0.877056
$405$	4.80609	−	7.60931i	0.238816	−	0.378109i
$406$		0			0
$407$		−	0.269179i		−	0.0133427i
$408$	6.30614	−	1.62276i	0.312200	−	0.0803384i
$409$			29.1034i			1.43907i	0.694456	+	0.719535i	$0.255645\pi$
$409$			29.1034i			1.43907i	−0.694456	+	0.719535i	$0.744355\pi$
$410$			6.55478i			0.323718i
$411$	−16.3666	+	4.21161i	−0.807304	+	0.207743i
$412$		−	14.7165i		−	0.725028i
$413$		0			0
$414$	6.53175	−	3.60001i	0.321018	−	0.176931i
$415$	1.37724			0.0676062
$416$	−5.00256			−0.245271
$417$	−7.14990	+	1.83988i	−0.350132	+	0.0900993i
$418$		−	13.8283i		−	0.676365i
$419$	−2.07947			−0.101589			−0.0507944	−	0.998709i	$-0.516175\pi$
$419$	−2.07947			−0.101589			−0.0507944	+	0.998709i	$0.516175\pi$
$420$		0			0
$421$	−32.8371			−1.60038			−0.800190	−	0.599746i	$-0.795268\pi$
$421$	−32.8371			−1.60038			−0.800190	+	0.599746i	$0.795268\pi$
$422$			7.36879i			0.358707i
$423$	−8.06316	+	4.44406i	−0.392044	+	0.216077i
$424$	1.11204			0.0540054
$425$	3.75947			0.182361
$426$	5.79440	+	22.5174i	0.280740	+	1.09097i
$427$		0			0
$428$			4.71002i			0.227667i
$429$	11.0893	+	43.0938i	0.535397	+	2.08059i
$430$			9.45088i			0.455762i
$431$			8.75212i			0.421575i	0.977532	+	0.210787i	$0.0676028\pi$
$431$			8.75212i			0.421575i	−0.977532	+	0.210787i	$0.932397\pi$
$432$	3.56312	+	3.78209i	0.171431	+	0.181966i
$433$		−	12.3440i		−	0.593214i	−0.955000	−	0.296607i	$-0.904145\pi$
$433$		−	12.3440i		−	0.593214i	0.955000	−	0.296607i	$-0.0958552\pi$
$434$		0			0
$435$	−10.3780	+	2.67056i	−0.497586	+	0.128044i
$436$	−8.62362			−0.412997
$437$	6.69412			0.320223
$438$	−3.01301	−	11.7088i	−0.143967	−	0.559466i
$439$		−	11.2287i		−	0.535916i	−0.963431	−	0.267958i	$-0.913651\pi$
$439$		−	11.2287i		−	0.535916i	0.963431	−	0.267958i	$-0.0863489\pi$
$440$	5.13552			0.244827
$441$		0			0
$442$	−18.8070			−0.894556
$443$		−	33.4323i		−	1.58842i	−0.607646	−	0.794208i	$-0.707886\pi$
$443$		−	33.4323i		−	1.58842i	0.607646	−	0.794208i	$-0.292114\pi$
$444$	0.0226247	+	0.0879211i	0.00107372	+	0.00417255i
$445$	5.34113			0.253194
$446$	−5.79472			−0.274388
$447$	−15.0500	+	3.87280i	−0.711839	+	0.183177i
$448$		0			0
$449$		−	27.8343i		−	1.31358i	−0.754073	−	0.656791i	$-0.771914\pi$
$449$		−	27.8343i		−	1.31358i	0.754073	−	0.656791i	$-0.228086\pi$
$450$	1.44809	+	2.62736i	0.0682635	+	0.123855i
$451$			33.6622i			1.58509i
$452$		−	15.3809i		−	0.723455i
$453$	−5.70919	−	22.1863i	−0.268241	−	1.04240i
$454$		−	10.6780i		−	0.501146i
$455$		0			0
$456$	1.16228	+	4.51670i	0.0544288	+	0.211514i
$457$	28.3221			1.32485			0.662427	−	0.749127i	$-0.269527\pi$
$457$	28.3221			1.32485			0.662427	+	0.749127i	$0.269527\pi$
$458$	−8.62361			−0.402955
$459$	13.3954	+	14.2186i	0.625244	+	0.663669i
$460$			2.48605i			0.115913i
$461$	35.5758			1.65693			0.828466	−	0.560040i	$-0.189214\pi$
$461$	35.5758			1.65693			0.828466	+	0.560040i	$0.189214\pi$
$462$		0			0
$463$	18.8371			0.875434			0.437717	−	0.899113i	$-0.355787\pi$
$463$	18.8371			0.875434			0.437717	+	0.899113i	$0.355787\pi$
$464$		−	6.18694i		−	0.287221i
$465$	8.00803	−	2.06070i	0.371364	−	0.0955628i
$466$	16.0654			0.744217
$467$	12.5692			0.581635			0.290818	−	0.956779i	$-0.406073\pi$
$467$	12.5692			0.581635			0.290818	+	0.956779i	$0.406073\pi$
$468$	−7.24415	−	13.1436i	−0.334861	−	0.607561i
$469$		0			0
$470$		−	3.06892i		−	0.141559i
$471$	−14.3653	+	3.69661i	−0.661917	+	0.170331i
$472$		−	13.2616i		−	0.610414i
$473$			48.5352i			2.23165i
$474$	28.0925	−	7.22904i	1.29033	−	0.332041i
$475$			2.69268i			0.123548i
$476$		0			0
$477$	1.61033	+	2.92173i	0.0737319	+	0.133777i
$478$	11.0070			0.503446
$479$	−21.4076			−0.978138			−0.489069	−	0.872245i	$-0.662663\pi$
$479$	−21.4076			−0.978138			−0.489069	+	0.872245i	$0.662663\pi$
$480$	−1.67740	+	0.431645i	−0.0765626	+	0.0197018i
$481$		−	0.262209i		−	0.0119557i
$482$	−9.70859			−0.442214
$483$		0			0
$484$	15.3736			0.698801
$485$			0.633608i			0.0287707i
$486$	−4.77723	+	14.8384i	−0.216699	+	0.673083i
$487$	2.51593			0.114008			0.0570038	−	0.998374i	$-0.481845\pi$
$487$	2.51593			0.114008			0.0570038	+	0.998374i	$0.481845\pi$
$488$	−4.14918			−0.187825
$489$	−4.78028	−	18.5765i	−0.216172	−	0.840058i
$490$		0			0
$491$			34.7105i			1.56646i	0.621729	+	0.783232i	$0.286430\pi$
$491$			34.7105i			1.56646i	−0.621729	+	0.783232i	$0.713570\pi$
$492$	−2.82934	−	10.9950i	−0.127557	−	0.495694i
$493$		−	23.2596i		−	1.04756i
$494$		−	13.4703i		−	0.606057i
$495$	7.43669	+	13.4929i	0.334254	+	0.606461i
$496$			4.77406i			0.214362i
$497$		0			0
$498$	−2.31019	+	0.594481i	−0.103522	+	0.0266393i
$499$	−6.15000			−0.275312			−0.137656	−	0.990480i	$-0.543957\pi$
$499$	−6.15000			−0.275312			−0.137656	+	0.990480i	$0.543957\pi$
$500$	−1.00000			−0.0447214
$501$	1.27680	+	4.96174i	0.0570433	+	0.221674i
$502$		−	4.59082i		−	0.204898i
$503$	−5.99378			−0.267249			−0.133625	−	0.991032i	$-0.542662\pi$
$503$	−5.99378			−0.267249			−0.133625	+	0.991032i	$0.542662\pi$
$504$		0			0
$505$	17.6286			0.784462
$506$			12.7672i			0.567569i
$507$	5.19081	+	20.1719i	0.230532	+	0.895863i
$508$	1.78518			0.0792047
$509$	−15.4391			−0.684324			−0.342162	−	0.939641i	$-0.611159\pi$
$509$	−15.4391			−0.684324			−0.342162	+	0.939641i	$0.611159\pi$
$510$	−6.30614	+	1.62276i	−0.279241	+	0.0718568i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−10.1839	+	9.59432i	−0.449632	+	0.423599i
$514$		−	11.7426i		−	0.517946i
$515$			14.7165i			0.648485i
$516$	−4.07943	−	15.8529i	−0.179587	−	0.697887i
$517$		−	15.7605i		−	0.693146i
$518$		0			0
$519$	−8.95303	−	34.7921i	−0.392994	−	1.52720i
$520$	5.00256			0.219377
$521$	42.0716			1.84319			0.921594	−	0.388154i	$-0.126887\pi$
$521$	42.0716			1.84319			0.921594	+	0.388154i	$0.126887\pi$
$522$	16.2553	−	8.95922i	0.711477	−	0.392134i
$523$			17.8267i			0.779505i	0.920920	+	0.389753i	$0.127440\pi$
$523$			17.8267i			0.779505i	−0.920920	+	0.389753i	$0.872560\pi$
$524$	3.10264			0.135540
$525$		0			0
$526$	22.9128			0.999046
$527$			17.9479i			0.781824i
$528$	−8.61435	+	2.21673i	−0.374891	+	0.0964706i
$529$	16.8196			0.731286
$530$	−1.11204			−0.0483039
$531$	34.8430	−	19.2039i	1.51206	−	0.833379i
$532$		0			0
$533$			32.7907i			1.42032i
$534$	−8.95922	+	2.30547i	−0.387703	+	0.0997675i
$535$		−	4.71002i		−	0.203632i
$536$		−	0.896174i		−	0.0387088i
$537$	−41.1272	+	10.5832i	−1.77477	+	0.456700i
$538$		−	8.12400i		−	0.350251i
$539$		0			0
$540$	−3.56312	−	3.78209i	−0.153332	−	0.162755i
$541$	−35.4391			−1.52365			−0.761823	−	0.647786i	$-0.775695\pi$
$541$	−35.4391			−1.52365			−0.761823	+	0.647786i	$0.775695\pi$
$542$	−10.9402			−0.469920
$543$	−31.2891	+	8.05160i	−1.34274	+	0.345527i
$544$		−	3.75947i		−	0.161186i
$545$	8.62362			0.369395
$546$		0			0
$547$	33.9313			1.45080			0.725399	−	0.688329i	$-0.241655\pi$
$547$	33.9313			1.45080			0.725399	+	0.688329i	$0.241655\pi$
$548$			9.75710i			0.416803i
$549$	−6.00838	−	10.9014i	−0.256431	−	0.465261i
$550$	−5.13552			−0.218980
$551$	16.6594			0.709715
$552$	−1.07309	−	4.17010i	−0.0456738	−	0.177491i
$553$		0			0
$554$		−	4.78288i		−	0.203205i
$555$	−0.0226247	−	0.0879211i	−0.000960365	−	0.00373204i
$556$			4.26248i			0.180769i
$557$			6.78281i			0.287397i	0.989622	+	0.143698i	$0.0458995\pi$
$557$			6.78281i			0.287397i	−0.989622	+	0.143698i	$0.954100\pi$
$558$	−12.5432	+	6.91326i	−0.530996	+	0.292662i
$559$			47.2786i			1.99967i
$560$		0			0
$561$	−32.3853	+	8.33370i	−1.36731	+	0.351849i
$562$	−21.1040			−0.890217
$563$	19.4917			0.821478			0.410739	−	0.911753i	$-0.365271\pi$
$563$	19.4917			0.821478			0.410739	+	0.911753i	$0.365271\pi$
$564$	1.32468	+	5.14781i	0.0557792	+	0.216762i
$565$			15.3809i			0.647078i
$566$	−22.0051			−0.924944
$567$		0			0
$568$	13.4240			0.563258
$569$		−	28.2804i		−	1.18558i	−0.805359	−	0.592788i	$-0.798027\pi$
$569$		−	28.2804i		−	1.18558i	0.805359	−	0.592788i	$-0.201973\pi$
$570$	−1.16228	−	4.51670i	−0.0486826	−	0.189184i
$571$	−19.7430			−0.826219			−0.413110	−	0.910681i	$-0.635557\pi$
$571$	−19.7430			−0.826219			−0.413110	+	0.910681i	$0.635557\pi$
$572$	25.6908			1.07419
$573$	12.2020	−	3.13993i	0.509746	−	0.131173i
$574$		0			0
$575$		−	2.48605i		−	0.103675i
$576$	2.62736	−	1.44809i	0.109474	−	0.0603370i
$577$			20.0863i			0.836202i	0.908401	+	0.418101i	$0.137304\pi$
$577$			20.0863i			0.836202i	−0.908401	+	0.418101i	$0.862696\pi$
$578$			2.86642i			0.119227i
$579$	4.77580	+	18.5591i	0.198475	+	0.771289i
$580$			6.18694i			0.256899i
$581$		0			0
$582$	−0.273494	−	1.06282i	−0.0113367	−	0.0440551i
$583$	−5.71090			−0.236521
$584$	−6.98029			−0.288846
$585$	7.24415	+	13.1436i	0.299509	+	0.543419i
$586$			11.2905i			0.466406i
$587$	31.1052			1.28385			0.641925	−	0.766767i	$-0.278136\pi$
$587$	31.1052			1.28385			0.641925	+	0.766767i	$0.278136\pi$
$588$		0			0
$589$	−12.8550			−0.529681
$590$			13.2616i			0.545970i
$591$	14.8735	−	3.82740i	0.611816	−	0.157438i
$592$	0.0524150			0.00215424
$593$	8.92665			0.366573			0.183287	−	0.983060i	$-0.441326\pi$
$593$	8.92665			0.366573			0.183287	+	0.983060i	$0.441326\pi$
$594$	−18.2985	−	19.4230i	−0.750795	−	0.796936i
$595$		0			0
$596$			8.97218i			0.367515i
$597$	−31.1667	+	8.02012i	−1.27557	+	0.328242i
$598$			12.4366i			0.508571i
$599$		−	4.97005i		−	0.203071i	−0.994832	−	0.101535i	$-0.967625\pi$
$599$		−	4.97005i		−	0.203071i	0.994832	−	0.101535i	$-0.0323755\pi$
$600$	1.67740	−	0.431645i	0.0684797	−	0.0176219i
$601$			25.0660i			1.02246i	0.859442	+	0.511232i	$0.170811\pi$
$601$			25.0660i			1.02246i	−0.859442	+	0.511232i	$0.829189\pi$
$602$		0			0
$603$	2.35458	−	1.29774i	0.0958858	−	0.0528480i
$604$	−13.2266			−0.538181
$605$	−15.3736			−0.625026
$606$	−29.5703	+	7.60931i	−1.20121	+	0.309107i
$607$		−	23.1941i		−	0.941417i	−0.882289	−	0.470709i	$-0.843998\pi$
$607$		−	23.1941i		−	0.941417i	0.882289	−	0.470709i	$-0.156002\pi$
$608$	2.69268			0.109202
$609$		0			0
$610$	4.14918			0.167995
$611$		−	15.3524i		−	0.621094i
$612$	9.87748	−	5.44403i	0.399274	−	0.220062i
$613$	4.30556			0.173900			0.0869500	−	0.996213i	$-0.472288\pi$
$613$	4.30556			0.173900			0.0869500	+	0.996213i	$0.472288\pi$
$614$	2.12162			0.0856215
$615$	2.82934	+	10.9950i	0.114090	+	0.443362i
$616$		0			0
$617$		−	36.2107i		−	1.45779i	−0.684626	−	0.728895i	$-0.740034\pi$
$617$		−	36.2107i		−	1.45779i	0.684626	−	0.728895i	$-0.259966\pi$
$618$	−6.35229	−	24.6854i	−0.255527	−	0.992994i
$619$		−	20.2383i		−	0.813445i	−0.913552	−	0.406723i	$-0.866672\pi$
$619$		−	20.2383i		−	0.813445i	0.913552	−	0.406723i	$-0.133328\pi$
$620$		−	4.77406i		−	0.191731i
$621$	9.40245	−	8.85807i	0.377307	−	0.355462i
$622$		−	11.0046i		−	0.441244i
$623$		0			0
$624$	−8.39132	+	2.15933i	−0.335922	+	0.0864425i
$625$	1.00000			0.0400000
$626$	−7.43437			−0.297137
$627$	−5.96893	−	23.1956i	−0.238376	−	0.926345i
$628$			8.56400i			0.341741i
$629$	0.197052			0.00785699
$630$		0			0
$631$	−16.1847			−0.644304			−0.322152	−	0.946688i	$-0.604406\pi$
$631$	−16.1847			−0.644304			−0.322152	+	0.946688i	$0.604406\pi$
$632$		−	16.7476i		−	0.666185i
$633$	3.18070	+	12.3604i	0.126422	+	0.491283i
$634$	4.47460			0.177709
$635$	−1.78518			−0.0708428
$636$	1.86534	−	0.480006i	0.0739654	−	0.0190335i
$637$		0			0
$638$			31.7732i			1.25791i
$639$	19.4391	+	35.2697i	0.768999	+	1.39525i
$640$			1.00000i			0.0395285i
$641$		−	6.43913i		−	0.254330i	−0.991882	−	0.127165i	$-0.959412\pi$
$641$		−	6.43913i		−	0.254330i	0.991882	−	0.127165i	$-0.0405878\pi$
$642$	2.03306	+	7.90060i	0.0802384	+	0.311812i
$643$			35.5764i			1.40299i	0.712672	+	0.701497i	$0.247485\pi$
$643$			35.5764i			1.40299i	−0.712672	+	0.701497i	$0.752515\pi$
$644$		0			0
$645$	4.07943	+	15.8529i	0.160627	+	0.624209i
$646$	10.1230			0.398285
$647$	−13.7118			−0.539066			−0.269533	−	0.962991i	$-0.586869\pi$
$647$	−13.7118			−0.539066			−0.269533	+	0.962991i	$0.586869\pi$
$648$	7.60931	+	4.80609i	0.298922	+	0.188801i
$649$			68.1052i			2.67336i
$650$	−5.00256			−0.196217
$651$		0			0
$652$	−11.0746			−0.433713
$653$			1.86074i			0.0728164i	0.999337	+	0.0364082i	$0.0115916\pi$
$653$			1.86074i			0.0728164i	−0.999337	+	0.0364082i	$0.988408\pi$
$654$	−14.4653	+	3.72235i	−0.565638	+	0.145555i
$655$	−3.10264			−0.121230
$656$	−6.55478			−0.255921
$657$	−10.1081	−	18.3398i	−0.394353	−	0.715502i
$658$		0			0
$659$		−	13.8786i		−	0.540633i	−0.962771	−	0.270317i	$-0.912872\pi$
$659$		−	13.8786i		−	0.540633i	0.962771	−	0.270317i	$-0.0871284\pi$
$660$	8.61435	−	2.21673i	0.335313	−	0.0862859i
$661$		−	21.9995i		−	0.855681i	−0.903854	−	0.427840i	$-0.859275\pi$
$661$		−	21.9995i		−	0.855681i	0.903854	−	0.427840i	$-0.140725\pi$
$662$		−	16.9720i		−	0.659634i
$663$	−31.5469	+	8.11794i	−1.22518	+	0.315275i
$664$			1.37724i			0.0534474i
$665$		0			0
$666$	0.0759015	+	0.137713i	0.00294112	+	0.00533628i
$667$	−15.3810			−0.595555
$668$	2.95799			0.114448
$669$	−9.72008	+	2.50126i	−0.375800	+	0.0967044i
$670$			0.896174i			0.0346222i
$671$	21.3082			0.822595
$672$		0			0
$673$	13.4735			0.519366			0.259683	−	0.965694i	$-0.416382\pi$
$673$	13.4735			0.519366			0.259683	+	0.965694i	$0.416382\pi$
$674$		−	30.7045i		−	1.18269i
$675$	3.56312	+	3.78209i	0.137144	+	0.145573i
$676$	12.0256			0.462525
$677$	−1.27854			−0.0491384			−0.0245692	−	0.999698i	$-0.507821\pi$
$677$	−1.27854			−0.0491384			−0.0245692	+	0.999698i	$0.507821\pi$
$678$	−6.63908	−	25.7999i	−0.254972	−	0.990839i
$679$		0			0
$680$			3.75947i			0.144169i
$681$	−4.60913	−	17.9114i	−0.176622	−	0.686366i
$682$		−	24.5173i		−	0.938817i
$683$		−	40.0245i		−	1.53149i	−0.643142	−	0.765747i	$-0.722369\pi$
$683$		−	40.0245i		−	1.53149i	0.643142	−	0.765747i	$-0.277631\pi$
$684$	3.89923	+	7.07464i	0.149091	+	0.270506i
$685$		−	9.75710i		−	0.372799i
$686$		0			0
$687$	−14.4653	+	3.72234i	−0.551885	+	0.142016i
$688$	−9.45088			−0.360311
$689$	−5.56304			−0.211935
$690$	1.07309	+	4.17010i	0.0408519	+	0.158753i
$691$			25.0324i			0.952276i	0.879370	+	0.476138i	$0.157964\pi$
$691$			25.0324i			0.952276i	−0.879370	+	0.476138i	$0.842036\pi$
$692$	−20.7416			−0.788478
$693$		0			0
$694$	−33.2005			−1.26027
$695$		−	4.26248i		−	0.161685i
$696$	−2.67056	−	10.3780i	−0.101227	−	0.393377i
$697$	−24.6425			−0.933400
$698$	21.5465			0.815546
$699$	26.9482	−	6.93458i	1.01928	−	0.262290i
$700$		0			0
$701$			7.09535i			0.267988i	0.990982	+	0.133994i	$0.0427802\pi$
$701$			7.09535i			0.267988i	−0.990982	+	0.133994i	$0.957220\pi$
$702$	−17.8247	−	18.9201i	−0.672751	−	0.714095i
$703$			0.141137i			0.00532307i
$704$			5.13552i			0.193552i
$705$	−1.32468	−	5.14781i	−0.0498905	−	0.193878i
$706$			5.51692i			0.207632i
$707$		0			0
$708$	−5.72430	−	22.2450i	−0.215132	−	0.836019i
$709$	27.9222			1.04864			0.524320	−	0.851521i	$-0.324319\pi$
$709$	27.9222			1.04864			0.524320	+	0.851521i	$0.324319\pi$
$710$	−13.4240			−0.503793
$711$	44.0021	−	24.2520i	1.65021	−	0.909522i
$712$			5.34113i			0.200167i
$713$	11.8685			0.444481
$714$		0			0
$715$	−25.6908			−0.960781
$716$			24.5184i			0.916294i
$717$	18.4631	−	4.75110i	0.689517	−	0.177433i
$718$	−19.3565			−0.722379
$719$	−24.0050			−0.895235			−0.447618	−	0.894225i	$-0.647727\pi$
$719$	−24.0050			−0.895235			−0.447618	+	0.894225i	$0.647727\pi$
$720$	−2.62736	+	1.44809i	−0.0979161	+	0.0539670i
$721$		0			0
$722$		−	11.7495i		−	0.437271i
$723$	−16.2852	+	4.19067i	−0.605654	+	0.155853i
$724$			18.6533i			0.693243i
$725$		−	6.18694i		−	0.229777i
$726$	25.7878	−	6.63595i	0.957073	−	0.246283i
$727$			12.3007i			0.456206i	0.973637	+	0.228103i	$0.0732523\pi$
$727$			12.3007i			0.456206i	−0.973637	+	0.228103i	$0.926748\pi$
$728$		0			0
$729$	−1.60841	+	26.9521i	−0.0595706	+	0.998224i
$730$	6.98029			0.258352
$731$	−35.5303			−1.31413
$732$	−6.95985	+	1.79098i	−0.257244	+	0.0661964i
$733$		−	21.5605i		−	0.796356i	−0.917308	−	0.398178i	$-0.869643\pi$
$733$		−	21.5605i		−	0.796356i	0.917308	−	0.398178i	$-0.130357\pi$
$734$	14.0326			0.517951
$735$		0			0
$736$	−2.48605			−0.0916369
$737$			4.60232i			0.169529i
$738$	−9.49190	−	17.2218i	−0.349402	−	0.633943i
$739$	0.822126			0.0302424			0.0151212	−	0.999886i	$-0.495187\pi$
$739$	0.822126			0.0302424			0.0151212	+	0.999886i	$0.495187\pi$
$740$	−0.0524150			−0.00192681
$741$	−5.81439	−	22.5951i	−0.213597	−	0.830052i
$742$		0			0
$743$			10.6722i			0.391526i	0.980651	+	0.195763i	$0.0627184\pi$
$743$			10.6722i			0.391526i	−0.980651	+	0.195763i	$0.937282\pi$
$744$	2.06070	+	8.00803i	0.0755491	+	0.293589i
$745$		−	8.97218i		−	0.328715i
$746$			1.33838i			0.0490015i
$747$	−3.61852	+	1.99437i	−0.132395	+	0.0729702i
$748$			19.3068i			0.705927i
$749$		0			0
$750$	−1.67740	+	0.431645i	−0.0612501	+	0.0157615i
$751$	−26.8131			−0.978426			−0.489213	−	0.872164i	$-0.662716\pi$
$751$	−26.8131			−0.978426			−0.489213	+	0.872164i	$0.662716\pi$
$752$	3.06892			0.111912
$753$	−1.98160	−	7.70065i	−0.0722137	−	0.280627i
$754$			30.9505i			1.12715i
$755$	13.2266			0.481364
$756$		0			0
$757$	−14.2502			−0.517934			−0.258967	−	0.965886i	$-0.583382\pi$
$757$	−14.2502			−0.517934			−0.258967	+	0.965886i	$0.583382\pi$
$758$		−	8.07964i		−	0.293466i
$759$	5.51088	+	21.4157i	0.200032	+	0.777340i
$760$	−2.69268			−0.0976736
$761$	27.2236			0.986855			0.493428	−	0.869787i	$-0.335744\pi$
$761$	27.2236			0.986855			0.493428	+	0.869787i	$0.335744\pi$
$762$	2.99447	−	0.770566i	0.108478	−	0.0279147i
$763$		0			0
$764$		−	7.27434i		−	0.263176i
$765$	−9.87748	+	5.44403i	−0.357121	+	0.196829i
$766$			23.2943i			0.841656i
$767$			66.3419i			2.39547i
$768$	−0.431645	−	1.67740i	−0.0155757	−	0.0605281i
$769$		−	6.31431i		−	0.227700i	−0.993498	−	0.113850i	$-0.963682\pi$
$769$		−	6.31431i		−	0.227700i	0.993498	−	0.113850i	$-0.0363183\pi$
$770$		0			0
$771$	−5.06866	−	19.6972i	−0.182543	−	0.709376i
$772$	11.0642			0.398208
$773$	42.4169			1.52563			0.762814	−	0.646618i	$-0.223817\pi$
$773$	42.4169			1.52563			0.762814	+	0.646618i	$0.223817\pi$
$774$	−13.6857	−	24.8309i	−0.491922	−	0.892529i
$775$			4.77406i			0.171489i
$776$	−0.633608			−0.0227452
$777$		0			0
$778$	11.7488			0.421216
$779$		−	17.6499i		−	0.632374i
$780$	8.39132	−	2.15933i	0.300457	−	0.0773166i
$781$	−68.9392			−2.46684
$782$	−9.34621			−0.334220
$783$	23.3995	−	22.0448i	0.836232	−	0.787816i
$784$		0			0
$785$		−	8.56400i		−	0.305662i
$786$	5.20438	−	1.33924i	0.185634	−	0.0477691i
$787$			39.9142i			1.42279i	0.702794	+	0.711393i	$0.251935\pi$
$787$			39.9142i			1.42279i	−0.702794	+	0.711393i	$0.748065\pi$
$788$		−	8.86701i		−	0.315874i
$789$	38.4340	−	9.89021i	1.36829	−	0.352101i
$790$			16.7476i			0.595854i
$791$		0			0
$792$	−13.4929	+	7.43669i	−0.479449	+	0.264251i
$793$	20.7565			0.737087
$794$	17.2214			0.611166
$795$	−1.86534	+	0.480006i	−0.0661567	+	0.0170241i
$796$			18.5804i			0.658563i
$797$	17.5658			0.622211			0.311105	−	0.950375i	$-0.399301\pi$
$797$	17.5658			0.622211			0.311105	+	0.950375i	$0.399301\pi$
$798$		0			0
$799$	11.5375			0.408167
$800$		−	1.00000i		−	0.0353553i
$801$	−14.0331	+	7.73441i	−0.495835	+	0.273282i
$802$	8.44909			0.298348
$803$	35.8474			1.26503
$804$	−0.386830	−	1.50325i	−0.0136424	−	0.0530154i
$805$		0			0
$806$		−	23.8826i		−	0.841227i
$807$	−3.50669	−	13.6272i	−0.123441	−	0.479701i
$808$			17.6286i			0.620172i
$809$			19.1819i			0.674400i	0.941433	+	0.337200i	$0.109480\pi$
$809$			19.1819i			0.674400i	−0.941433	+	0.337200i	$0.890520\pi$
$810$	−7.60931	−	4.80609i	−0.267364	−	0.168869i
$811$		−	45.4972i		−	1.59762i	−0.601582	−	0.798811i	$-0.705463\pi$
$811$		−	45.4972i		−	1.59762i	0.601582	−	0.798811i	$-0.294537\pi$
$812$		0			0
$813$	−18.3511	+	4.72227i	−0.643600	+	0.165617i
$814$	−0.269179			−0.00943470
$815$	11.0746			0.387925
$816$	−1.62276	−	6.30614i	−0.0568078	−	0.220759i
$817$		−	25.4482i		−	0.890319i
$818$	29.1034			1.01758
$819$		0			0
$820$	6.55478			0.228903
$821$			2.55899i			0.0893093i	0.999002	+	0.0446546i	$0.0142187\pi$
$821$			2.55899i			0.0893093i	−0.999002	+	0.0446546i	$0.985781\pi$
$822$	4.21161	+	16.3666i	0.146897	+	0.570850i
$823$	−35.5345			−1.23866			−0.619328	−	0.785133i	$-0.712595\pi$
$823$	−35.5345			−1.23866			−0.619328	+	0.785133i	$0.712595\pi$
$824$	−14.7165			−0.512672
$825$	−8.61435	+	2.21673i	−0.299913	+	0.0771765i
$826$		0			0
$827$		−	1.85721i		−	0.0645814i	−0.999479	−	0.0322907i	$-0.989720\pi$
$827$		−	1.85721i		−	0.0645814i	0.999479	−	0.0322907i	$-0.0102802\pi$
$828$	−3.60001	−	6.53175i	−0.125109	−	0.226994i
$829$			53.5813i			1.86095i	0.366351	+	0.930477i	$0.380607\pi$
$829$			53.5813i			1.86095i	−0.366351	+	0.930477i	$0.619393\pi$
$830$		−	1.37724i		−	0.0478048i
$831$	−2.06451	−	8.02281i	−0.0716169	−	0.278308i
$832$			5.00256i			0.173433i
$833$		0			0
$834$	1.83988	+	7.14990i	0.0637098	+	0.247581i
$835$	−2.95799			−0.102365
$836$	−13.8283			−0.478262
$837$	−18.0559	+	17.0105i	−0.624105	+	0.587971i
$838$			2.07947i			0.0718342i
$839$	−6.41502			−0.221471			−0.110736	−	0.993850i	$-0.535321\pi$
$839$	−6.41502			−0.221471			−0.110736	+	0.993850i	$0.535321\pi$
$840$		0			0
$841$	−9.27817			−0.319937
$842$			32.8371i			1.13164i
$843$	−35.3999	+	9.10943i	−1.21924	+	0.313746i
$844$	7.36879			0.253644
$845$	−12.0256			−0.413695
$846$	4.44406	+	8.06316i	0.152790	+	0.277217i
$847$		0			0
$848$		−	1.11204i		−	0.0381876i
$849$	−36.9115	+	9.49841i	−1.26680	+	0.325985i
$850$		−	3.75947i		−	0.128949i
$851$		−	0.130306i		−	0.00446684i
$852$	22.5174	−	5.79440i	0.771434	−	0.198513i
$853$		−	40.7419i		−	1.39498i	−0.716596	−	0.697488i	$-0.754301\pi$
$853$		−	40.7419i		−	1.39498i	0.716596	−	0.697488i	$-0.245699\pi$
$854$		0			0
$855$	−3.89923	−	7.07464i	−0.133351	−	0.241948i
$856$	4.71002			0.160985
$857$	−8.07741			−0.275919			−0.137959	−	0.990438i	$-0.544054\pi$
$857$	−8.07741			−0.275919			−0.137959	+	0.990438i	$0.544054\pi$
$858$	43.0938	−	11.0893i	1.47120	−	0.378583i
$859$		−	13.0537i		−	0.445385i	−0.974889	−	0.222693i	$-0.928515\pi$
$859$		−	13.0537i		−	0.445385i	0.974889	−	0.222693i	$-0.0714846\pi$
$860$	9.45088			0.322272
$861$		0			0
$862$	8.75212			0.298098
$863$			54.1891i			1.84462i	0.386451	+	0.922310i	$0.373701\pi$
$863$			54.1891i			1.84462i	−0.386451	+	0.922310i	$0.626299\pi$
$864$	3.78209	−	3.56312i	0.128669	−	0.121220i
$865$	20.7416			0.705236
$866$	−12.3440			−0.419466
$867$	1.23728	+	4.80815i	0.0420202	+	0.163293i
$868$		0			0
$869$			86.0078i			2.91762i
$870$	2.67056	+	10.3780i	0.0905406	+	0.351847i
$871$			4.48317i			0.151906i
$872$			8.62362i			0.292033i
$873$	−0.917519	−	1.66472i	−0.0310533	−	0.0563422i
$874$		−	6.69412i		−	0.226432i
$875$		0			0
$876$	−11.7088	+	3.01301i	−0.395602	+	0.101800i
$877$	−18.7445			−0.632957			−0.316479	−	0.948600i	$-0.602501\pi$
$877$	−18.7445			−0.632957			−0.316479	+	0.948600i	$0.602501\pi$
$878$	−11.2287			−0.378950
$879$	4.87350	+	18.9387i	0.164379	+	0.638788i
$880$		−	5.13552i		−	0.173119i
$881$	−36.3542			−1.22480			−0.612402	−	0.790546i	$-0.709797\pi$
$881$	−36.3542			−1.22480			−0.612402	+	0.790546i	$0.709797\pi$
$882$		0			0
$883$	−22.9059			−0.770845			−0.385422	−	0.922740i	$-0.625944\pi$
$883$	−22.9059			−0.770845			−0.385422	+	0.922740i	$0.625944\pi$
$884$			18.8070i			0.632547i
$885$	5.72430	+	22.2450i	0.192420	+	0.747758i
$886$	−33.4323			−1.12318
$887$	−51.9454			−1.74415			−0.872077	−	0.489368i	$-0.837227\pi$
$887$	−51.9454			−1.74415			−0.872077	+	0.489368i	$0.837227\pi$
$888$	0.0879211	−	0.0226247i	0.00295044	−	0.000759235i
$889$		0			0
$890$		−	5.34113i		−	0.179035i
$891$	−39.0778	−	24.6818i	−1.30915	−	0.826871i
$892$			5.79472i			0.194021i
$893$			8.26360i			0.276531i
$894$	3.87280	+	15.0500i	0.129526	+	0.503346i
$895$		−	24.5184i		−	0.819558i
$896$		0			0
$897$	5.36821	+	20.8612i	0.179239	+	0.696535i
$898$	−27.8343			−0.928842
$899$	29.5368			0.985108
$900$	2.62736	−	1.44809i	0.0875788	−	0.0482696i
$901$		−	4.18067i		−	0.139278i
$902$	33.6622			1.12083
$903$		0			0
$904$	−15.3809			−0.511560
$905$		−	18.6533i		−	0.620056i
$906$	−22.1863	+	5.70919i	−0.737090	+	0.189675i
$907$	−3.32397			−0.110371			−0.0551853	−	0.998476i	$-0.517575\pi$
$907$	−3.32397			−0.110371			−0.0551853	+	0.998476i	$0.517575\pi$
$908$	−10.6780			−0.354363
$909$	−46.3168	+	25.5277i	−1.53623	+	0.846702i
$910$		0			0
$911$			0.497610i			0.0164866i	0.999966	+	0.00824328i	$0.00262395\pi$
$911$			0.497610i			0.0164866i	−0.999966	+	0.00824328i	$0.997376\pi$
$912$	4.51670	−	1.16228i	0.149563	−	0.0384870i
$913$		−	7.07287i		−	0.234078i
$914$		−	28.3221i		−	0.936813i
$915$	6.95985	−	1.79098i	0.230086	−	0.0592078i
$916$			8.62361i			0.284932i
$917$		0			0
$918$	14.2186	−	13.3954i	0.469285	−	0.442114i
$919$	49.5092			1.63316			0.816579	−	0.577234i	$-0.195868\pi$
$919$	49.5092			1.63316			0.816579	+	0.577234i	$0.195868\pi$
$920$	2.48605			0.0819625
$921$	3.55881	−	0.915787i	0.117267	−	0.0301762i
$922$		−	35.5758i		−	1.17163i
$923$	−67.1543			−2.21041
$924$		0			0
$925$	0.0524150			0.00172339
$926$		−	18.8371i		−	0.619025i
$927$	−21.3107	−	38.6655i	−0.699936	−	1.26994i
$928$	−6.18694			−0.203096
$929$	−52.8394			−1.73360			−0.866802	−	0.498653i	$-0.833828\pi$
$929$	−52.8394			−1.73360			−0.866802	+	0.498653i	$0.833828\pi$
$930$	−2.06070	−	8.00803i	−0.0675731	−	0.262594i
$931$		0			0
$932$		−	16.0654i		−	0.526241i
$933$	−4.75008	−	18.4591i	−0.155511	−	0.604325i
$934$		−	12.5692i		−	0.411278i
$935$		−	19.3068i		−	0.631401i
$936$	−13.1436	+	7.24415i	−0.429611	+	0.236782i
$937$			55.7017i			1.81970i	0.414941	+	0.909848i	$0.363802\pi$
$937$			55.7017i			1.81970i	−0.414941	+	0.909848i	$0.636198\pi$
$938$		0			0
$939$	−12.4704	+	3.20901i	−0.406957	+	0.104722i
$940$	−3.06892			−0.100097
$941$	−0.221546			−0.00722221			−0.00361110	−	0.999993i	$-0.501149\pi$
$941$	−0.221546			−0.00722221			−0.00361110	+	0.999993i	$0.501149\pi$
$942$	3.69661	+	14.3653i	0.120442	+	0.468046i
$943$			16.2955i			0.530654i
$944$	−13.2616			−0.431628
$945$		0			0
$946$	48.5352			1.57802
$947$			17.3429i			0.563567i	0.959478	+	0.281784i	$0.0909260\pi$
$947$			17.3429i			0.563567i	−0.959478	+	0.281784i	$0.909074\pi$
$948$	−7.22904	−	28.0925i	−0.234788	−	0.912403i
$949$	34.9193			1.13353
$950$	2.69268			0.0873620
$951$	7.50571	−	1.93144i	0.243389	−	0.0626312i
$952$		0			0
$953$		−	47.2619i		−	1.53096i	−0.643458	−	0.765482i	$-0.722501\pi$
$953$		−	47.2619i		−	1.53096i	0.643458	−	0.765482i	$-0.277499\pi$
$954$	2.92173	−	1.61033i	0.0945945	−	0.0521363i
$955$			7.27434i			0.235392i
$956$		−	11.0070i		−	0.355990i
$957$	13.7147	+	53.2964i	0.443335	+	1.72283i
$958$			21.4076i			0.691648i
$959$		0			0
$960$	0.431645	+	1.67740i	0.0139313	+	0.0541380i
$961$	8.20831			0.264784
$962$	−0.262209			−0.00845397
$963$	6.82052	+	12.3749i	0.219788	+	0.398777i
$964$			9.70859i			0.312693i
$965$	−11.0642			−0.356168
$966$		0			0
$967$	56.9397			1.83106			0.915528	−	0.402254i	$-0.131773\pi$
$967$	56.9397			1.83106			0.915528	+	0.402254i	$0.131773\pi$
$968$		−	15.3736i		−	0.494127i
$969$	16.9804	−	4.36956i	0.545489	−	0.140370i
$970$	0.633608			0.0203439
$971$	−1.17024			−0.0375549			−0.0187775	−	0.999824i	$-0.505977\pi$
$971$	−1.17024			−0.0375549			−0.0187775	+	0.999824i	$0.505977\pi$
$972$	14.8384	+	4.77723i	0.475942	+	0.153230i
$973$		0			0
$974$		−	2.51593i		−	0.0806155i
$975$	−8.39132	+	2.15933i	−0.268737	+	0.0691540i
$976$			4.14918i			0.132812i
$977$		−	32.4885i		−	1.03940i	−0.854349	−	0.519700i	$-0.826044\pi$
$977$		−	32.4885i		−	1.03940i	0.854349	−	0.519700i	$-0.173956\pi$
$978$	−18.5765	+	4.78028i	−0.594011	+	0.152857i
$979$		−	27.4295i		−	0.876650i
$980$		0			0
$981$	−22.6574	+	12.4878i	−0.723395	+	0.398703i
$982$	34.7105			1.10766
$983$	24.7897			0.790669			0.395335	−	0.918537i	$-0.370629\pi$
$983$	24.7897			0.790669			0.395335	+	0.918537i	$0.370629\pi$
$984$	−10.9950	+	2.82934i	−0.350508	+	0.0901961i
$985$			8.86701i			0.282526i
$986$	−23.2596			−0.740736
$987$		0			0
$988$	−13.4703			−0.428547
$989$			23.4953i			0.747108i
$990$	13.4929	−	7.43669i	0.428832	−	0.236353i
$991$	35.4889			1.12734			0.563671	−	0.825999i	$-0.309389\pi$
$991$	35.4889			1.12734			0.563671	+	0.825999i	$0.309389\pi$
$992$	4.77406			0.151577
$993$	−7.32587	−	28.4688i	−0.232479	−	0.903431i
$994$		0			0
$995$		−	18.5804i		−	0.589037i
$996$	0.594481	+	2.31019i	0.0188369	+	0.0732013i
$997$			38.8526i			1.23048i	0.788342	+	0.615238i	$0.210940\pi$
$997$			38.8526i			1.23048i	−0.788342	+	0.615238i	$0.789060\pi$
$998$			6.15000i			0.194675i
$999$	0.186761	+	0.198238i	0.00590885	+	0.00627198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.a.881.4		12
3.2	odd	2		1470.2.b.b.881.9		12
7.2	even	3		210.2.r.b.101.3	yes	12
7.3	odd	6		210.2.r.a.131.6	yes	12
7.6	odd	2		1470.2.b.b.881.3		12
21.2	odd	6		210.2.r.a.101.6	✓	12
21.17	even	6		210.2.r.b.131.3	yes	12
21.20	even	2	inner	1470.2.b.a.881.10		12
35.2	odd	12		1050.2.u.e.899.3		12
35.3	even	12		1050.2.u.g.299.6		12
35.9	even	6		1050.2.s.f.101.4		12
35.17	even	12		1050.2.u.f.299.1		12
35.23	odd	12		1050.2.u.h.899.4		12
35.24	odd	6		1050.2.s.g.551.1		12
105.2	even	12		1050.2.u.g.899.6		12
105.17	odd	12		1050.2.u.h.299.4		12
105.23	even	12		1050.2.u.f.899.1		12
105.38	odd	12		1050.2.u.e.299.3		12
105.44	odd	6		1050.2.s.g.101.1		12
105.59	even	6		1050.2.s.f.551.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.6	✓	12	21.2	odd	6
210.2.r.a.131.6	yes	12	7.3	odd	6
210.2.r.b.101.3	yes	12	7.2	even	3
210.2.r.b.131.3	yes	12	21.17	even	6
1050.2.s.f.101.4		12	35.9	even	6
1050.2.s.f.551.4		12	105.59	even	6
1050.2.s.g.101.1		12	105.44	odd	6
1050.2.s.g.551.1		12	35.24	odd	6
1050.2.u.e.299.3		12	105.38	odd	12
1050.2.u.e.899.3		12	35.2	odd	12
1050.2.u.f.299.1		12	35.17	even	12
1050.2.u.f.899.1		12	105.23	even	12
1050.2.u.g.299.6		12	35.3	even	12
1050.2.u.g.899.6		12	105.2	even	12
1050.2.u.h.299.4		12	105.17	odd	12
1050.2.u.h.899.4		12	35.23	odd	12
1470.2.b.a.881.4		12	1.1	even	1	trivial
1470.2.b.a.881.10		12	21.20	even	2	inner
1470.2.b.b.881.3		12	7.6	odd	2
1470.2.b.b.881.9		12	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.431645 - 1.67740i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.67740 + 0.431645i) q^{6} +1.00000i q^{8} +(-2.62736 + 1.44809i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.431645 - 1.67740i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.67740 + 0.431645i) q^{6} +1.00000i q^{8} +(-2.62736 + 1.44809i) q^{9} -1.00000i q^{10} -5.13552i q^{11} +(0.431645 + 1.67740i) q^{12} -5.00256i q^{13} +(-0.431645 - 1.67740i) q^{15} +1.00000 q^{16} +3.75947 q^{17} +(1.44809 + 2.62736i) q^{18} +2.69268i q^{19} -1.00000 q^{20} -5.13552 q^{22} -2.48605i q^{23} +(1.67740 - 0.431645i) q^{24} +1.00000 q^{25} -5.00256 q^{26} +(3.56312 + 3.78209i) q^{27} -6.18694i q^{29} +(-1.67740 + 0.431645i) q^{30} +4.77406i q^{31} -1.00000i q^{32} +(-8.61435 + 2.21673i) q^{33} -3.75947i q^{34} +(2.62736 - 1.44809i) q^{36} +0.0524150 q^{37} +2.69268 q^{38} +(-8.39132 + 2.15933i) q^{39} +1.00000i q^{40} -6.55478 q^{41} -9.45088 q^{43} +5.13552i q^{44} +(-2.62736 + 1.44809i) q^{45} -2.48605 q^{46} +3.06892 q^{47} +(-0.431645 - 1.67740i) q^{48} -1.00000i q^{50} +(-1.62276 - 6.30614i) q^{51} +5.00256i q^{52} -1.11204i q^{53} +(3.78209 - 3.56312i) q^{54} -5.13552i q^{55} +(4.51670 - 1.16228i) q^{57} -6.18694 q^{58} -13.2616 q^{59} +(0.431645 + 1.67740i) q^{60} +4.14918i q^{61} +4.77406 q^{62} -1.00000 q^{64} -5.00256i q^{65} +(2.21673 + 8.61435i) q^{66} -0.896174 q^{67} -3.75947 q^{68} +(-4.17010 + 1.07309i) q^{69} -13.4240i q^{71} +(-1.44809 - 2.62736i) q^{72} +6.98029i q^{73} -0.0524150i q^{74} +(-0.431645 - 1.67740i) q^{75} -2.69268i q^{76} +(2.15933 + 8.39132i) q^{78} -16.7476 q^{79} +1.00000 q^{80} +(4.80609 - 7.60931i) q^{81} +6.55478i q^{82} +1.37724 q^{83} +3.75947 q^{85} +9.45088i q^{86} +(-10.3780 + 2.67056i) q^{87} +5.13552 q^{88} +5.34113 q^{89} +(1.44809 + 2.62736i) q^{90} +2.48605i q^{92} +(8.00803 - 2.06070i) q^{93} -3.06892i q^{94} +2.69268i q^{95} +(-1.67740 + 0.431645i) q^{96} +0.633608i q^{97} +(7.43669 + 13.4929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9	\( 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9} + 4 q^{12} - 4 q^{15} + 12 q^{16} + 24 q^{17} + 8 q^{18} - 12 q^{20} - 2 q^{24} + 12 q^{25} - 8 q^{26} + 8 q^{27} + 2 q^{30} - 20 q^{33} + 6 q^{36} + 16 q^{37} + 16 q^{38} + 12 q^{39} + 4 q^{41} - 6 q^{45} - 4 q^{46} + 32 q^{47} - 4 q^{48} + 4 q^{51} + 28 q^{54} - 36 q^{57} - 16 q^{58} + 24 q^{59} + 4 q^{60} - 8 q^{62} - 12 q^{64} - 20 q^{66} + 8 q^{67} - 24 q^{68} - 50 q^{69} - 8 q^{72} - 4 q^{75} + 32 q^{78} + 8 q^{79} + 12 q^{80} - 10 q^{81} + 40 q^{83} + 24 q^{85} - 56 q^{87} + 52 q^{89} + 8 q^{90} + 28 q^{93} + 2 q^{96} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9 + 4 * q^12 - 4 * q^15 + 12 * q^16 + 24 * q^17 + 8 * q^18 - 12 * q^20 - 2 * q^24 + 12 * q^25 - 8 * q^26 + 8 * q^27 + 2 * q^30 - 20 * q^33 + 6 * q^36 + 16 * q^37 + 16 * q^38 + 12 * q^39 + 4 * q^41 - 6 * q^45 - 4 * q^46 + 32 * q^47 - 4 * q^48 + 4 * q^51 + 28 * q^54 - 36 * q^57 - 16 * q^58 + 24 * q^59 + 4 * q^60 - 8 * q^62 - 12 * q^64 - 20 * q^66 + 8 * q^67 - 24 * q^68 - 50 * q^69 - 8 * q^72 - 4 * q^75 + 32 * q^78 + 8 * q^79 + 12 * q^80 - 10 * q^81 + 40 * q^83 + 24 * q^85 - 56 * q^87 + 52 * q^89 + 8 * q^90 + 28 * q^93 + 2 * q^96 + 48 * q^99

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