LMFDB - Embedded newform 1470.2.b.a.881.2

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			881.2
Root			$-0.384890 + 1.68874i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.a.881.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.17770 + 1.27005i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.27005 + 1.17770i) q^{6} +1.00000i q^{8} +(-0.226058 - 2.99147i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.17770 + 1.27005i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.27005 + 1.17770i) q^{6} +1.00000i q^{8} +(-0.226058 - 2.99147i) q^{9} -1.00000i q^{10} +4.95532i q^{11} +(1.17770 - 1.27005i) q^{12} -6.37523i q^{13} +(-1.17770 + 1.27005i) q^{15} +1.00000 q^{16} -3.62755 q^{17} +(-2.99147 + 0.226058i) q^{18} -4.20710i q^{19} -1.00000 q^{20} +4.95532 q^{22} +1.91676i q^{23} +(-1.27005 - 1.17770i) q^{24} +1.00000 q^{25} -6.37523 q^{26} +(4.06555 + 3.23594i) q^{27} +0.800269i q^{29} +(1.27005 + 1.17770i) q^{30} -5.03641i q^{31} -1.00000i q^{32} +(-6.29351 - 5.83587i) q^{33} +3.62755i q^{34} +(0.226058 + 2.99147i) q^{36} +5.82789 q^{37} -4.20710 q^{38} +(8.09687 + 7.50809i) q^{39} +1.00000i q^{40} +7.45163 q^{41} -4.64827 q^{43} -4.95532i q^{44} +(-0.226058 - 2.99147i) q^{45} +1.91676 q^{46} -0.607779 q^{47} +(-1.17770 + 1.27005i) q^{48} -1.00000i q^{50} +(4.27215 - 4.60717i) q^{51} +6.37523i q^{52} -14.3065i q^{53} +(3.23594 - 4.06555i) q^{54} +4.95532i q^{55} +(5.34323 + 4.95469i) q^{57} +0.800269 q^{58} +1.75132 q^{59} +(1.17770 - 1.27005i) q^{60} +3.42307i q^{61} -5.03641 q^{62} -1.00000 q^{64} -6.37523i q^{65} +(-5.83587 + 6.29351i) q^{66} +7.98294 q^{67} +3.62755 q^{68} +(-2.43438 - 2.25736i) q^{69} -2.48759i q^{71} +(2.99147 - 0.226058i) q^{72} -15.0933i q^{73} -5.82789i q^{74} +(-1.17770 + 1.27005i) q^{75} +4.20710i q^{76} +(7.50809 - 8.09687i) q^{78} +2.66807 q^{79} +1.00000 q^{80} +(-8.89780 + 1.35249i) q^{81} -7.45163i q^{82} +7.27215 q^{83} -3.62755 q^{85} +4.64827i q^{86} +(-1.01638 - 0.942474i) q^{87} -4.95532 q^{88} -1.88495 q^{89} +(-2.99147 + 0.226058i) q^{90} -1.91676i q^{92} +(6.39649 + 5.93136i) q^{93} +0.607779i q^{94} -4.20710i q^{95} +(1.27005 + 1.17770i) q^{96} -17.6562i q^{97} +(14.8237 - 1.12019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.17770	+	1.27005i	−0.679944	+	0.733264i
$3$	−1.17770	+	1.27005i	−0.679944	+	0.733264i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.27005	+	1.17770i	0.518496	+	0.480793i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−0.226058	−	2.99147i	−0.0753527	−	0.997157i
$10$		−	1.00000i		−	0.316228i
$11$			4.95532i			1.49409i	0.664776	+	0.747043i	$0.268527\pi$
$11$			4.95532i			1.49409i	−0.664776	+	0.747043i	$0.731473\pi$
$12$	1.17770	−	1.27005i	0.339972	−	0.366632i
$13$		−	6.37523i		−	1.76817i	−0.467325	−	0.884086i	$-0.654782\pi$
$13$		−	6.37523i		−	1.76817i	0.467325	−	0.884086i	$-0.345218\pi$
$14$		0			0
$15$	−1.17770	+	1.27005i	−0.304080	+	0.327926i
$16$	1.00000			0.250000
$17$	−3.62755			−0.879809			−0.439905	−	0.898044i	$-0.644988\pi$
$17$	−3.62755			−0.879809			−0.439905	+	0.898044i	$0.644988\pi$
$18$	−2.99147	+	0.226058i	−0.705096	+	0.0532824i
$19$		−	4.20710i		−	0.965174i	−0.875848	−	0.482587i	$-0.839697\pi$
$19$		−	4.20710i		−	0.965174i	0.875848	−	0.482587i	$-0.160303\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	4.95532			1.05648
$23$			1.91676i			0.399672i	0.979829	+	0.199836i	$0.0640409\pi$
$23$			1.91676i			0.399672i	−0.979829	+	0.199836i	$0.935959\pi$
$24$	−1.27005	−	1.17770i	−0.259248	−	0.240396i
$25$	1.00000			0.200000
$26$	−6.37523			−1.25029
$27$	4.06555	+	3.23594i	0.782415	+	0.622757i
$28$		0			0
$29$			0.800269i			0.148606i	0.997236	+	0.0743031i	$0.0236732\pi$
$29$			0.800269i			0.148606i	−0.997236	+	0.0743031i	$0.976327\pi$
$30$	1.27005	+	1.17770i	0.231878	+	0.215017i
$31$		−	5.03641i		−	0.904566i	−0.891875	−	0.452283i	$-0.850610\pi$
$31$		−	5.03641i		−	0.904566i	0.891875	−	0.452283i	$-0.149390\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.29351	−	5.83587i	−1.09556	−	1.01589i
$34$			3.62755i			0.622119i
$35$		0			0
$36$	0.226058	+	2.99147i	0.0376763	+	0.498578i
$37$	5.82789			0.958099			0.479050	−	0.877788i	$-0.340981\pi$
$37$	5.82789			0.958099			0.479050	+	0.877788i	$0.340981\pi$
$38$	−4.20710			−0.682481
$39$	8.09687	+	7.50809i	1.29654	+	1.20226i
$40$			1.00000i			0.158114i
$41$	7.45163			1.16375			0.581874	−	0.813279i	$-0.302320\pi$
$41$	7.45163			1.16375			0.581874	+	0.813279i	$0.302320\pi$
$42$		0			0
$43$	−4.64827			−0.708854			−0.354427	−	0.935084i	$-0.615324\pi$
$43$	−4.64827			−0.708854			−0.354427	+	0.935084i	$0.615324\pi$
$44$		−	4.95532i		−	0.747043i
$45$	−0.226058	−	2.99147i	−0.0336987	−	0.445942i
$46$	1.91676			0.282611
$47$	−0.607779			−0.0886537			−0.0443269	−	0.999017i	$-0.514114\pi$
$47$	−0.607779			−0.0886537			−0.0443269	+	0.999017i	$0.514114\pi$
$48$	−1.17770	+	1.27005i	−0.169986	+	0.183316i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	4.27215	−	4.60717i	0.598221	−	0.645133i
$52$			6.37523i			0.884086i
$53$		−	14.3065i		−	1.96515i	−0.185860	−	0.982576i	$-0.559507\pi$
$53$		−	14.3065i		−	1.96515i	0.185860	−	0.982576i	$-0.440493\pi$
$54$	3.23594	−	4.06555i	0.440356	−	0.553251i
$55$			4.95532i			0.668175i
$56$		0			0
$57$	5.34323	+	4.95469i	0.707727	+	0.656264i
$58$	0.800269			0.105080
$59$	1.75132			0.228002			0.114001	−	0.993481i	$-0.463633\pi$
$59$	1.75132			0.228002			0.114001	+	0.993481i	$0.463633\pi$
$60$	1.17770	−	1.27005i	0.152040	−	0.163963i
$61$			3.42307i			0.438279i	0.975693	+	0.219140i	$0.0703251\pi$
$61$			3.42307i			0.438279i	−0.975693	+	0.219140i	$0.929675\pi$
$62$	−5.03641			−0.639624
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	6.37523i		−	0.790750i
$66$	−5.83587	+	6.29351i	−0.718346	+	0.774678i
$67$	7.98294			0.975272			0.487636	−	0.873047i	$-0.337859\pi$
$67$	7.98294			0.975272			0.487636	+	0.873047i	$0.337859\pi$
$68$	3.62755			0.439905
$69$	−2.43438	−	2.25736i	−0.293065	−	0.271754i
$70$		0			0
$71$		−	2.48759i		−	0.295222i	−0.989045	−	0.147611i	$-0.952842\pi$
$71$		−	2.48759i		−	0.295222i	0.989045	−	0.147611i	$-0.0471584\pi$
$72$	2.99147	−	0.226058i	0.352548	−	0.0266412i
$73$		−	15.0933i		−	1.76654i	−0.468866	−	0.883270i	$-0.655337\pi$
$73$		−	15.0933i		−	1.76654i	0.468866	−	0.883270i	$-0.344663\pi$
$74$		−	5.82789i		−	0.677478i
$75$	−1.17770	+	1.27005i	−0.135989	+	0.146653i
$76$			4.20710i			0.482587i
$77$		0			0
$78$	7.50809	−	8.09687i	0.850124	−	0.916790i
$79$	2.66807			0.300182			0.150091	−	0.988672i	$-0.452043\pi$
$79$	2.66807			0.300182			0.150091	+	0.988672i	$0.452043\pi$
$80$	1.00000			0.111803
$81$	−8.89780	+	1.35249i	−0.988644	+	0.150277i
$82$		−	7.45163i		−	0.822895i
$83$	7.27215			0.798222			0.399111	−	0.916903i	$-0.369319\pi$
$83$	7.27215			0.798222			0.399111	+	0.916903i	$0.369319\pi$
$84$		0			0
$85$	−3.62755			−0.393463
$86$			4.64827i			0.501236i
$87$	−1.01638	−	0.942474i	−0.108968	−	0.101044i
$88$	−4.95532			−0.528239
$89$	−1.88495			−0.199804			−0.0999021	−	0.994997i	$-0.531853\pi$
$89$	−1.88495			−0.199804			−0.0999021	+	0.994997i	$0.531853\pi$
$90$	−2.99147	+	0.226058i	−0.315329	+	0.0238286i
$91$		0			0
$92$		−	1.91676i		−	0.199836i
$93$	6.39649	+	5.93136i	0.663286	+	0.615054i
$94$			0.607779i			0.0626876i
$95$		−	4.20710i		−	0.431639i
$96$	1.27005	+	1.17770i	0.129624	+	0.120198i
$97$		−	17.6562i		−	1.79271i	−0.443334	−	0.896356i	$-0.646205\pi$
$97$		−	17.6562i		−	1.79271i	0.443334	−	0.896356i	$-0.353795\pi$
$98$		0			0
$99$	14.8237	−	1.12019i	1.48984	−	0.112583i
$100$	−1.00000			−0.100000
$101$	−1.14842			−0.114272			−0.0571361	−	0.998366i	$-0.518197\pi$
$101$	−1.14842			−0.114272			−0.0571361	+	0.998366i	$0.518197\pi$
$102$	−4.60717	−	4.27215i	−0.456178	−	0.423006i
$103$		−	7.28364i		−	0.717678i	−0.933399	−	0.358839i	$-0.883173\pi$
$103$		−	7.28364i		−	0.717678i	0.933399	−	0.358839i	$-0.116827\pi$
$104$	6.37523			0.625143
$105$		0			0
$106$	−14.3065			−1.38957
$107$		−	2.68637i		−	0.259701i	−0.991534	−	0.129850i	$-0.958550\pi$
$107$		−	2.68637i		−	0.259701i	0.991534	−	0.129850i	$-0.0414497\pi$
$108$	−4.06555	−	3.23594i	−0.391208	−	0.311379i
$109$	9.02343			0.864288			0.432144	−	0.901805i	$-0.357757\pi$
$109$	9.02343			0.864288			0.432144	+	0.901805i	$0.357757\pi$
$110$	4.95532			0.472471
$111$	−6.86349	+	7.40171i	−0.651454	+	0.702540i
$112$		0			0
$113$		−	12.4267i		−	1.16901i	−0.811391	−	0.584504i	$-0.801289\pi$
$113$		−	12.4267i		−	1.16901i	0.811391	−	0.584504i	$-0.198711\pi$
$114$	4.95469	−	5.34323i	0.464049	−	0.500439i
$115$			1.91676i			0.178739i
$116$		−	0.800269i		−	0.0743031i
$117$	−19.0713	+	1.44117i	−1.76314	+	0.133236i
$118$		−	1.75132i		−	0.161222i
$119$		0			0
$120$	−1.27005	−	1.17770i	−0.115939	−	0.107509i
$121$	−13.5552			−1.23229
$122$	3.42307			0.309910
$123$	−8.77576	+	9.46395i	−0.791284	+	0.853335i
$124$			5.03641i			0.452283i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.06679			0.715812			0.357906	−	0.933758i	$-0.383491\pi$
$127$	8.06679			0.715812			0.357906	+	0.933758i	$0.383491\pi$
$128$			1.00000i			0.0883883i
$129$	5.47425	−	5.90354i	0.481981	−	0.519777i
$130$	−6.37523			−0.559145
$131$	−3.38301			−0.295575			−0.147788	−	0.989019i	$-0.547215\pi$
$131$	−3.38301			−0.295575			−0.147788	+	0.989019i	$0.547215\pi$
$132$	6.29351	+	5.83587i	0.547780	+	0.507947i
$133$		0			0
$134$		−	7.98294i		−	0.689621i
$135$	4.06555	+	3.23594i	0.349907	+	0.278506i
$136$		−	3.62755i		−	0.311060i
$137$			14.8274i			1.26679i	0.773829	+	0.633395i	$0.218339\pi$
$137$			14.8274i			1.26679i	−0.773829	+	0.633395i	$0.781661\pi$
$138$	−2.25736	+	2.43438i	−0.192159	+	0.207228i
$139$		−	7.24669i		−	0.614656i	−0.951604	−	0.307328i	$-0.900565\pi$
$139$		−	7.24669i		−	0.614656i	0.951604	−	0.307328i	$-0.0994349\pi$
$140$		0			0
$141$	0.715780	−	0.771911i	0.0602796	−	0.0650066i
$142$	−2.48759			−0.208754
$143$	31.5913			2.64180
$144$	−0.226058	−	2.99147i	−0.0188382	−	0.249289i
$145$			0.800269i			0.0664587i
$146$	−15.0933			−1.24913
$147$		0			0
$148$	−5.82789			−0.479050
$149$		−	6.59303i		−	0.540122i	−0.962843	−	0.270061i	$-0.912956\pi$
$149$		−	6.59303i		−	0.540122i	0.962843	−	0.270061i	$-0.0870439\pi$
$150$	1.27005	+	1.17770i	0.103699	+	0.0961586i
$151$	11.7743			0.958183			0.479091	−	0.877765i	$-0.340966\pi$
$151$	11.7743			0.958183			0.479091	+	0.877765i	$0.340966\pi$
$152$	4.20710			0.341241
$153$	0.820036	+	10.8517i	0.0662960	+	0.877308i
$154$		0			0
$155$		−	5.03641i		−	0.404534i
$156$	−8.09687	−	7.50809i	−0.648268	−	0.601129i
$157$		−	1.54479i		−	0.123288i	−0.998098	−	0.0616440i	$-0.980366\pi$
$157$		−	1.54479i		−	0.123288i	0.998098	−	0.0616440i	$-0.0196343\pi$
$158$		−	2.66807i		−	0.212261i
$159$	18.1700	+	16.8488i	1.44098	+	1.33619i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	1.35249	+	8.89780i	0.106262	+	0.699077i
$163$	−3.37759			−0.264553			−0.132277	−	0.991213i	$-0.542229\pi$
$163$	−3.37759			−0.264553			−0.132277	+	0.991213i	$0.542229\pi$
$164$	−7.45163			−0.581874
$165$	−6.29351	−	5.83587i	−0.489949	−	0.454322i
$166$		−	7.27215i		−	0.564428i
$167$	−12.7685			−0.988053			−0.494027	−	0.869447i	$-0.664475\pi$
$167$	−12.7685			−0.988053			−0.494027	+	0.869447i	$0.664475\pi$
$168$		0			0
$169$	−27.6436			−2.12643
$170$			3.62755i			0.278220i
$171$	−12.5854	+	0.951048i	−0.962430	+	0.0727285i
$172$	4.64827			0.354427
$173$	0.247556			0.0188214			0.00941068	−	0.999956i	$-0.497004\pi$
$173$	0.247556			0.0188214			0.00941068	+	0.999956i	$0.497004\pi$
$174$	−0.942474	+	1.01638i	−0.0714488	+	0.0770517i
$175$		0			0
$176$			4.95532i			0.373521i
$177$	−2.06252	+	2.22426i	−0.155029	+	0.167186i
$178$			1.88495i			0.141283i
$179$		−	19.5963i		−	1.46470i	−0.680930	−	0.732348i	$-0.738424\pi$
$179$		−	19.5963i		−	1.46470i	0.680930	−	0.732348i	$-0.261576\pi$
$180$	0.226058	+	2.99147i	0.0168494	+	0.222971i
$181$			14.8103i			1.10084i	0.834887	+	0.550422i	$0.185533\pi$
$181$			14.8103i			1.10084i	−0.834887	+	0.550422i	$0.814467\pi$
$182$		0			0
$183$	−4.34748	−	4.03134i	−0.321375	−	0.298005i
$184$	−1.91676			−0.141305
$185$	5.82789			0.428475
$186$	5.93136	−	6.39649i	0.434909	−	0.469014i
$187$		−	17.9757i		−	1.31451i
$188$	0.607779			0.0443269
$189$		0			0
$190$	−4.20710			−0.305215
$191$			0.535503i			0.0387476i	0.999812	+	0.0193738i	$0.00616726\pi$
$191$			0.535503i			0.0387476i	−0.999812	+	0.0193738i	$0.993833\pi$
$192$	1.17770	−	1.27005i	0.0849930	−	0.0916580i
$193$	−5.53544			−0.398450			−0.199225	−	0.979954i	$-0.563842\pi$
$193$	−5.53544			−0.398450			−0.199225	+	0.979954i	$0.563842\pi$
$194$	−17.6562			−1.26764
$195$	8.09687	+	7.50809i	0.579829	+	0.537666i
$196$		0			0
$197$			0.666454i			0.0474829i	0.999718	+	0.0237414i	$0.00755785\pi$
$197$			0.666454i			0.0474829i	−0.999718	+	0.0237414i	$0.992442\pi$
$198$	−1.12019	−	14.8237i	−0.0796085	−	1.05347i
$199$			9.02198i			0.639551i	0.947493	+	0.319775i	$0.103607\pi$
$199$			9.02198i			0.639551i	−0.947493	+	0.319775i	$0.896393\pi$
$200$			1.00000i			0.0707107i
$201$	−9.40149	+	10.1387i	−0.663130	+	0.715132i
$202$			1.14842i			0.0808026i
$203$		0			0
$204$	−4.27215	+	4.60717i	−0.299110	+	0.322566i
$205$	7.45163			0.520444
$206$	−7.28364			−0.507475
$207$	5.73392	−	0.433299i	0.398535	−	0.0301163i
$208$		−	6.37523i		−	0.442043i
$209$	20.8475			1.44205
$210$		0			0
$211$	11.4386			0.787467			0.393733	−	0.919225i	$-0.371183\pi$
$211$	11.4386			0.787467			0.393733	+	0.919225i	$0.371183\pi$
$212$			14.3065i			0.982576i
$213$	3.15936	+	2.92963i	0.216476	+	0.200735i
$214$	−2.68637			−0.183636
$215$	−4.64827			−0.317009
$216$	−3.23594	+	4.06555i	−0.220178	+	0.276625i
$217$		0			0
$218$		−	9.02343i		−	0.611144i
$219$	19.1693	+	17.7754i	1.29534	+	1.20115i
$220$		−	4.95532i		−	0.334088i
$221$			23.1265i			1.55565i
$222$	7.40171	+	6.86349i	0.496771	+	0.460647i
$223$		−	5.23397i		−	0.350493i	−0.984525	−	0.175246i	$-0.943928\pi$
$223$		−	5.23397i		−	0.350493i	0.984525	−	0.175246i	$-0.0560722\pi$
$224$		0			0
$225$	−0.226058	−	2.99147i	−0.0150705	−	0.199431i
$226$	−12.4267			−0.826613
$227$	−13.4623			−0.893527			−0.446763	−	0.894652i	$-0.647423\pi$
$227$	−13.4623			−0.893527			−0.446763	+	0.894652i	$0.647423\pi$
$228$	−5.34323	−	4.95469i	−0.353864	−	0.328132i
$229$			16.5216i			1.09178i	0.837857	+	0.545890i	$0.183808\pi$
$229$			16.5216i			1.09178i	−0.837857	+	0.545890i	$0.816192\pi$
$230$	1.91676			0.126387
$231$		0			0
$232$	−0.800269			−0.0525402
$233$			18.6359i			1.22088i	0.792063	+	0.610440i	$0.209007\pi$
$233$			18.6359i			1.22088i	−0.792063	+	0.610440i	$0.790993\pi$
$234$	1.44117	+	19.0713i	0.0942124	+	1.24673i
$235$	−0.607779			−0.0396471
$236$	−1.75132			−0.114001
$237$	−3.14218	+	3.38859i	−0.204107	+	0.220113i
$238$		0			0
$239$			24.8065i			1.60460i	0.596922	+	0.802299i	$0.296390\pi$
$239$			24.8065i			1.60460i	−0.596922	+	0.802299i	$0.703610\pi$
$240$	−1.17770	+	1.27005i	−0.0760200	+	0.0819814i
$241$			22.3364i			1.43882i	0.694588	+	0.719408i	$0.255587\pi$
$241$			22.3364i			1.43882i	−0.694588	+	0.719408i	$0.744413\pi$
$242$			13.5552i			0.871362i
$243$	8.76118	−	12.8935i	0.562030	−	0.827117i
$244$		−	3.42307i		−	0.219140i
$245$		0			0
$246$	9.46395	+	8.77576i	0.603399	+	0.559522i
$247$	−26.8212			−1.70659
$248$	5.03641			0.319812
$249$	−8.56439	+	9.23600i	−0.542746	+	0.585308i
$250$		−	1.00000i		−	0.0632456i
$251$	−2.72107			−0.171752			−0.0858762	−	0.996306i	$-0.527369\pi$
$251$	−2.72107			−0.171752			−0.0858762	+	0.996306i	$0.527369\pi$
$252$		0			0
$253$	−9.49815			−0.597144
$254$		−	8.06679i		−	0.506156i
$255$	4.27215	−	4.60717i	0.267533	−	0.288512i
$256$	1.00000			0.0625000
$257$	11.5038			0.717586			0.358793	−	0.933417i	$-0.383188\pi$
$257$	11.5038			0.717586			0.358793	+	0.933417i	$0.383188\pi$
$258$	−5.90354	−	5.47425i	−0.367538	−	0.340812i
$259$		0			0
$260$			6.37523i			0.395375i
$261$	2.39398	−	0.180907i	0.148184	−	0.0111979i
$262$			3.38301i			0.209003i
$263$			12.7855i			0.788390i	0.919027	+	0.394195i	$0.128977\pi$
$263$			12.7855i			0.788390i	−0.919027	+	0.394195i	$0.871023\pi$
$264$	5.83587	−	6.29351i	0.359173	−	0.387339i
$265$		−	14.3065i		−	0.878843i
$266$		0			0
$267$	2.21990	−	2.39398i	0.135856	−	0.146509i
$268$	−7.98294			−0.487636
$269$	−11.6915			−0.712844			−0.356422	−	0.934325i	$-0.616003\pi$
$269$	−11.6915			−0.712844			−0.356422	+	0.934325i	$0.616003\pi$
$270$	3.23594	−	4.06555i	0.196933	−	0.247421i
$271$			22.0698i			1.34065i	0.742069	+	0.670323i	$0.233845\pi$
$271$			22.0698i			1.34065i	−0.742069	+	0.670323i	$0.766155\pi$
$272$	−3.62755			−0.219952
$273$		0			0
$274$	14.8274			0.895756
$275$			4.95532i			0.298817i
$276$	2.43438	+	2.25736i	0.146532	+	0.135877i
$277$	−7.80656			−0.469051			−0.234525	−	0.972110i	$-0.575354\pi$
$277$	−7.80656			−0.469051			−0.234525	+	0.972110i	$0.575354\pi$
$278$	−7.24669			−0.434627
$279$	−15.0663	+	1.13852i	−0.901994	+	0.0681615i
$280$		0			0
$281$			23.0892i			1.37738i	0.725054	+	0.688692i	$0.241815\pi$
$281$			23.0892i			1.37738i	−0.725054	+	0.688692i	$0.758185\pi$
$282$	−0.771911	−	0.715780i	−0.0459666	−	0.0426241i
$283$		−	24.7505i		−	1.47126i	−0.677382	−	0.735631i	$-0.736886\pi$
$283$		−	24.7505i		−	1.47126i	0.677382	−	0.735631i	$-0.263114\pi$
$284$			2.48759i			0.147611i
$285$	5.34323	+	4.95469i	0.316505	+	0.293490i
$286$		−	31.5913i		−	1.86803i
$287$		0			0
$288$	−2.99147	+	0.226058i	−0.176274	+	0.0133206i
$289$	−3.84090			−0.225935
$290$	0.800269			0.0469934
$291$	22.4242	+	20.7936i	1.31453	+	1.21894i
$292$			15.0933i			0.883270i
$293$	−25.3384			−1.48029			−0.740143	−	0.672449i	$-0.765242\pi$
$293$	−25.3384			−1.48029			−0.740143	+	0.672449i	$0.765242\pi$
$294$		0			0
$295$	1.75132			0.101966
$296$			5.82789i			0.338739i
$297$	−16.0351	+	20.1461i	−0.930453	+	1.16900i
$298$	−6.59303			−0.381924
$299$	12.2198			0.706688
$300$	1.17770	−	1.27005i	0.0679944	−	0.0733264i
$301$		0			0
$302$		−	11.7743i		−	0.677538i
$303$	1.35249	−	1.45855i	0.0776986	−	0.0837917i
$304$		−	4.20710i		−	0.241293i
$305$			3.42307i			0.196005i
$306$	10.8517	−	0.820036i	0.620350	−	0.0468784i
$307$		−	13.1396i		−	0.749919i	−0.927041	−	0.374960i	$-0.877657\pi$
$307$		−	13.1396i		−	0.749919i	0.927041	−	0.374960i	$-0.122343\pi$
$308$		0			0
$309$	9.25059	+	8.57792i	0.526248	+	0.487981i
$310$	−5.03641			−0.286049
$311$	7.60664			0.431333			0.215667	−	0.976467i	$-0.430808\pi$
$311$	7.60664			0.431333			0.215667	+	0.976467i	$0.430808\pi$
$312$	−7.50809	+	8.09687i	−0.425062	+	0.458395i
$313$			12.4254i			0.702328i	0.936314	+	0.351164i	$0.114214\pi$
$313$			12.4254i			0.702328i	−0.936314	+	0.351164i	$0.885786\pi$
$314$	−1.54479			−0.0871777
$315$		0			0
$316$	−2.66807			−0.150091
$317$		−	27.7358i		−	1.55780i	−0.627150	−	0.778898i	$-0.715779\pi$
$317$		−	27.7358i		−	1.55780i	0.627150	−	0.778898i	$-0.284221\pi$
$318$	16.8488	−	18.1700i	0.944831	−	1.01892i
$319$	−3.96559			−0.222030
$320$	−1.00000			−0.0559017
$321$	3.41182	+	3.16373i	0.190429	+	0.176582i
$322$		0			0
$323$			15.2614i			0.849169i
$324$	8.89780	−	1.35249i	0.494322	−	0.0751385i
$325$		−	6.37523i		−	0.353634i
$326$			3.37759i			0.187067i
$327$	−10.6269	+	11.4602i	−0.587667	+	0.633751i
$328$			7.45163i			0.411447i
$329$		0			0
$330$	−5.83587	+	6.29351i	−0.321254	+	0.346446i
$331$	11.7892			0.647995			0.323997	−	0.946058i	$-0.394973\pi$
$331$	11.7892			0.647995			0.323997	+	0.946058i	$0.394973\pi$
$332$	−7.27215			−0.399111
$333$	−1.31744	−	17.4340i	−0.0721953	−	0.955375i
$334$			12.7685i			0.698659i
$335$	7.98294			0.436155
$336$		0			0
$337$	−5.58238			−0.304092			−0.152046	−	0.988373i	$-0.548586\pi$
$337$	−5.58238			−0.304092			−0.152046	+	0.988373i	$0.548586\pi$
$338$			27.6436i			1.50361i
$339$	15.7826	+	14.6349i	0.857191	+	0.794859i
$340$	3.62755			0.196731
$341$	24.9570			1.35150
$342$	0.951048	+	12.5854i	0.0514268	+	0.680541i
$343$		0			0
$344$		−	4.64827i		−	0.250618i
$345$	−2.43438	−	2.25736i	−0.131063	−	0.121532i
$346$		−	0.247556i		−	0.0133087i
$347$		−	31.9093i		−	1.71298i	−0.516165	−	0.856489i	$-0.672641\pi$
$347$		−	31.9093i		−	1.71298i	0.516165	−	0.856489i	$-0.327359\pi$
$348$	1.01638	+	0.942474i	0.0544838	+	0.0505219i
$349$			1.64353i			0.0879759i	0.999032	+	0.0439879i	$0.0140063\pi$
$349$			1.64353i			0.0879759i	−0.999032	+	0.0439879i	$0.985994\pi$
$350$		0			0
$351$	20.6299	−	25.9188i	1.10114	−	1.38344i
$352$	4.95532			0.264120
$353$	14.6008			0.777120			0.388560	−	0.921423i	$-0.372973\pi$
$353$	14.6008			0.777120			0.388560	+	0.921423i	$0.372973\pi$
$354$	2.22426	+	2.06252i	0.118218	+	0.109622i
$355$		−	2.48759i		−	0.132028i
$356$	1.88495			0.0999021
$357$		0			0
$358$	−19.5963			−1.03570
$359$		−	0.506001i		−	0.0267057i	−0.999911	−	0.0133528i	$-0.995750\pi$
$359$		−	0.506001i		−	0.0267057i	0.999911	−	0.0133528i	$-0.00425047\pi$
$360$	2.99147	−	0.226058i	0.157664	−	0.0119143i
$361$	1.30035			0.0684392
$362$	14.8103			0.778414
$363$	15.9639	−	17.2158i	0.837889	−	0.903595i
$364$		0			0
$365$		−	15.0933i		−	0.790020i
$366$	−4.03134	+	4.34748i	−0.210722	+	0.227246i
$367$			1.35732i			0.0708515i	0.999372	+	0.0354258i	$0.0112787\pi$
$367$			1.35732i			0.0708515i	−0.999372	+	0.0354258i	$0.988721\pi$
$368$			1.91676i			0.0999179i
$369$	−1.68450	−	22.2913i	−0.0876916	−	1.16044i
$370$		−	5.82789i		−	0.302978i
$371$		0			0
$372$	−6.39649	−	5.93136i	−0.331643	−	0.307527i
$373$	−34.1095			−1.76612			−0.883062	−	0.469257i	$-0.844522\pi$
$373$	−34.1095			−1.76612			−0.883062	+	0.469257i	$0.844522\pi$
$374$	−17.9757			−0.929499
$375$	−1.17770	+	1.27005i	−0.0608160	+	0.0655851i
$376$		−	0.607779i		−	0.0313438i
$377$	5.10190			0.262761
$378$		0			0
$379$	−1.53951			−0.0790795			−0.0395398	−	0.999218i	$-0.512589\pi$
$379$	−1.53951			−0.0790795			−0.0395398	+	0.999218i	$0.512589\pi$
$380$			4.20710i			0.215819i
$381$	−9.50024	+	10.2452i	−0.486712	+	0.524879i
$382$	0.535503			0.0273987
$383$	32.5261			1.66201			0.831004	−	0.556267i	$-0.187767\pi$
$383$	32.5261			1.66201			0.831004	+	0.556267i	$0.187767\pi$
$384$	−1.27005	−	1.17770i	−0.0648120	−	0.0600991i
$385$		0			0
$386$			5.53544i			0.281747i
$387$	1.05078	+	13.9052i	0.0534141	+	0.706839i
$388$			17.6562i			0.896356i
$389$		−	7.10169i		−	0.360070i	−0.983660	−	0.180035i	$-0.942379\pi$
$389$		−	7.10169i		−	0.360070i	0.983660	−	0.180035i	$-0.0576211\pi$
$390$	7.50809	−	8.09687i	0.380187	−	0.410001i
$391$		−	6.95313i		−	0.351635i
$392$		0			0
$393$	3.98417	−	4.29660i	0.200975	−	0.216735i
$394$	0.666454			0.0335755
$395$	2.66807			0.134245
$396$	−14.8237	+	1.12019i	−0.744919	+	0.0562917i
$397$			13.0239i			0.653650i	0.945085	+	0.326825i	$0.105979\pi$
$397$			13.0239i			0.653650i	−0.945085	+	0.326825i	$0.894021\pi$
$398$	9.02198			0.452231
$399$		0			0
$400$	1.00000			0.0500000
$401$		−	23.4030i		−	1.16869i	−0.811506	−	0.584345i	$-0.801352\pi$
$401$		−	23.4030i		−	1.16869i	0.811506	−	0.584345i	$-0.198648\pi$
$402$	10.1387	+	9.40149i	0.505674	+	0.468904i
$403$	−32.1083			−1.59943
$404$	1.14842			0.0571361
$405$	−8.89780	+	1.35249i	−0.442135	+	0.0672059i
$406$		0			0
$407$			28.8791i			1.43148i
$408$	4.60717	+	4.27215i	0.228089	+	0.211503i
$409$		−	13.1994i		−	0.652670i	−0.945254	−	0.326335i	$-0.894186\pi$
$409$		−	13.1994i		−	0.652670i	0.945254	−	0.326335i	$-0.105814\pi$
$410$		−	7.45163i		−	0.368010i
$411$	−18.8316	−	17.4622i	−0.928892	−	0.861346i
$412$			7.28364i			0.358839i
$413$		0			0
$414$	−0.433299	−	5.73392i	−0.0212955	−	0.281807i
$415$	7.27215			0.356976
$416$	−6.37523			−0.312571
$417$	9.20366	+	8.53440i	0.450705	+	0.417932i
$418$		−	20.8475i		−	1.01969i
$419$	−27.9492			−1.36541			−0.682704	−	0.730695i	$-0.739196\pi$
$419$	−27.9492			−1.36541			−0.682704	+	0.730695i	$0.739196\pi$
$420$		0			0
$421$	24.6795			1.20281			0.601403	−	0.798946i	$-0.294609\pi$
$421$	24.6795			1.20281			0.601403	+	0.798946i	$0.294609\pi$
$422$		−	11.4386i		−	0.556823i
$423$	0.137393	+	1.81815i	0.00668030	+	0.0884017i
$424$	14.3065			0.694786
$425$	−3.62755			−0.175962
$426$	2.92963	−	3.15936i	0.141941	−	0.153072i
$427$		0			0
$428$			2.68637i			0.129850i
$429$	−37.2050	+	40.1226i	−1.79628	+	1.93714i
$430$			4.64827i			0.224159i
$431$			3.34445i			0.161097i	0.996751	+	0.0805483i	$0.0256671\pi$
$431$			3.34445i			0.161097i	−0.996751	+	0.0805483i	$0.974333\pi$
$432$	4.06555	+	3.23594i	0.195604	+	0.155689i
$433$		−	14.6756i		−	0.705264i	−0.935762	−	0.352632i	$-0.885287\pi$
$433$		−	14.6756i		−	0.705264i	0.935762	−	0.352632i	$-0.114713\pi$
$434$		0			0
$435$	−1.01638	−	0.942474i	−0.0487318	−	0.0451882i
$436$	−9.02343			−0.432144
$437$	8.06398			0.385753
$438$	17.7754	−	19.1693i	0.849339	−	0.915944i
$439$		−	6.58702i		−	0.314381i	−0.987568	−	0.157191i	$-0.949756\pi$
$439$		−	6.58702i		−	0.314381i	0.987568	−	0.157191i	$-0.0502437\pi$
$440$	−4.95532			−0.236236
$441$		0			0
$442$	23.1265			1.10001
$443$			40.7210i			1.93471i	0.253417	+	0.967357i	$0.418445\pi$
$443$			40.7210i			1.93471i	−0.253417	+	0.967357i	$0.581555\pi$
$444$	6.86349	−	7.40171i	0.325727	−	0.351270i
$445$	−1.88495			−0.0893551
$446$	−5.23397			−0.247836
$447$	8.37348	+	7.76459i	0.396052	+	0.367253i
$448$		0			0
$449$		−	18.3485i		−	0.865919i	−0.901413	−	0.432960i	$-0.857469\pi$
$449$		−	18.3485i		−	0.865919i	0.901413	−	0.432960i	$-0.142531\pi$
$450$	−2.99147	+	0.226058i	−0.141019	+	0.0106565i
$451$			36.9252i			1.73874i
$452$			12.4267i			0.584504i
$453$	−13.8666	+	14.9540i	−0.651511	+	0.702601i
$454$			13.4623i			0.631819i
$455$		0			0
$456$	−4.95469	+	5.34323i	−0.232024	+	0.250219i
$457$	−8.64332			−0.404317			−0.202159	−	0.979353i	$-0.564796\pi$
$457$	−8.64332			−0.404317			−0.202159	+	0.979353i	$0.564796\pi$
$458$	16.5216			0.772005
$459$	−14.7480	−	11.7385i	−0.688376	−	0.547908i
$460$		−	1.91676i		−	0.0893693i
$461$	24.7864			1.15442			0.577210	−	0.816596i	$-0.304141\pi$
$461$	24.7864			1.15442			0.577210	+	0.816596i	$0.304141\pi$
$462$		0			0
$463$	−17.9797			−0.835589			−0.417794	−	0.908542i	$-0.637197\pi$
$463$	−17.9797			−0.835589			−0.417794	+	0.908542i	$0.637197\pi$
$464$			0.800269i			0.0371515i
$465$	6.39649	+	5.93136i	0.296630	+	0.275060i
$466$	18.6359			0.863292
$467$	−1.27342			−0.0589271			−0.0294635	−	0.999566i	$-0.509380\pi$
$467$	−1.27342			−0.0589271			−0.0294635	+	0.999566i	$0.509380\pi$
$468$	19.0713	−	1.44117i	0.881572	−	0.0666182i
$469$		0			0
$470$			0.607779i			0.0280348i
$471$	1.96197	+	1.81930i	0.0904026	+	0.0838289i
$472$			1.75132i			0.0806109i
$473$		−	23.0337i		−	1.05909i
$474$	3.38859	+	3.14218i	0.155643	+	0.144325i
$475$		−	4.20710i		−	0.193035i
$476$		0			0
$477$	−42.7976	+	3.23411i	−1.95957	+	0.148080i
$478$	24.8065			1.13462
$479$	14.2267			0.650033			0.325017	−	0.945708i	$-0.394630\pi$
$479$	14.2267			0.650033			0.325017	+	0.945708i	$0.394630\pi$
$480$	1.27005	+	1.17770i	0.0579696	+	0.0537543i
$481$		−	37.1541i		−	1.69408i
$482$	22.3364			1.01740
$483$		0			0
$484$	13.5552			0.616146
$485$		−	17.6562i		−	0.801726i
$486$	−12.8935	−	8.76118i	−0.584860	−	0.397415i
$487$	39.8951			1.80782			0.903910	−	0.427723i	$-0.140684\pi$
$487$	39.8951			1.80782			0.903910	+	0.427723i	$0.140684\pi$
$488$	−3.42307			−0.154955
$489$	3.97778	−	4.28971i	0.179881	−	0.193988i
$490$		0			0
$491$			15.9778i			0.721069i	0.932746	+	0.360535i	$0.117406\pi$
$491$			15.9778i			0.721069i	−0.932746	+	0.360535i	$0.882594\pi$
$492$	8.77576	−	9.46395i	0.395642	−	0.426668i
$493$		−	2.90301i		−	0.130745i
$494$			26.8212i			1.20674i
$495$	14.8237	−	1.12019i	0.666276	−	0.0503488i
$496$		−	5.03641i		−	0.226141i
$497$		0			0
$498$	9.23600	+	8.56439i	0.413875	+	0.383780i
$499$	−13.8063			−0.618053			−0.309027	−	0.951053i	$-0.600003\pi$
$499$	−13.8063			−0.618053			−0.309027	+	0.951053i	$0.600003\pi$
$500$	−1.00000			−0.0447214
$501$	15.0374	−	16.2166i	0.671821	−	0.724504i
$502$			2.72107i			0.121447i
$503$	−2.11183			−0.0941620			−0.0470810	−	0.998891i	$-0.514992\pi$
$503$	−2.11183			−0.0941620			−0.0470810	+	0.998891i	$0.514992\pi$
$504$		0			0
$505$	−1.14842			−0.0511041
$506$			9.49815i			0.422244i
$507$	32.5558	−	35.1088i	1.44585	−	1.55923i
$508$	−8.06679			−0.357906
$509$	−16.1911			−0.717659			−0.358830	−	0.933403i	$-0.616824\pi$
$509$	−16.1911			−0.717659			−0.358830	+	0.933403i	$0.616824\pi$
$510$	−4.60717	−	4.27215i	−0.204009	−	0.189174i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	13.6139	−	17.1041i	0.601069	−	0.755167i
$514$		−	11.5038i		−	0.507410i
$515$		−	7.28364i		−	0.320955i
$516$	−5.47425	+	5.90354i	−0.240991	+	0.259889i
$517$		−	3.01174i		−	0.132456i
$518$		0			0
$519$	−0.291546	+	0.314409i	−0.0127975	+	0.0138010i
$520$	6.37523			0.279572
$521$	−24.9352			−1.09243			−0.546216	−	0.837645i	$-0.683932\pi$
$521$	−24.9352			−1.09243			−0.546216	+	0.837645i	$0.683932\pi$
$522$	−0.180907	−	2.39398i	−0.00791809	−	0.104782i
$523$			19.7186i			0.862233i	0.902296	+	0.431116i	$0.141880\pi$
$523$			19.7186i			0.862233i	−0.902296	+	0.431116i	$0.858120\pi$
$524$	3.38301			0.147788
$525$		0			0
$526$	12.7855			0.557476
$527$			18.2698i			0.795845i
$528$	−6.29351	−	5.83587i	−0.273890	−	0.253974i
$529$	19.3260			0.840263
$530$	−14.3065			−0.621436
$531$	−0.395899	−	5.23901i	−0.0171806	−	0.227354i
$532$		0			0
$533$		−	47.5059i		−	2.05771i
$534$	−2.39398	−	2.21990i	−0.103598	−	0.0960644i
$535$		−	2.68637i		−	0.116142i
$536$			7.98294i			0.344811i
$537$	24.8883	+	23.0785i	1.07401	+	0.995912i
$538$			11.6915i			0.504057i
$539$		0			0
$540$	−4.06555	−	3.23594i	−0.174953	−	0.139253i
$541$	−8.55845			−0.367957			−0.183978	−	0.982930i	$-0.558898\pi$
$541$	−8.55845			−0.367957			−0.183978	+	0.982930i	$0.558898\pi$
$542$	22.0698			0.947980
$543$	−18.8099	−	17.4421i	−0.807210	−	0.748512i
$544$			3.62755i			0.155530i
$545$	9.02343			0.386521
$546$		0			0
$547$	−33.5472			−1.43437			−0.717187	−	0.696881i	$-0.754570\pi$
$547$	−33.5472			−1.43437			−0.717187	+	0.696881i	$0.754570\pi$
$548$		−	14.8274i		−	0.633395i
$549$	10.2400	−	0.773813i	0.437033	−	0.0330255i
$550$	4.95532			0.211296
$551$	3.36681			0.143431
$552$	2.25736	−	2.43438i	0.0960796	−	0.103614i
$553$		0			0
$554$			7.80656i			0.331669i
$555$	−6.86349	+	7.40171i	−0.291339	+	0.314185i
$556$			7.24669i			0.307328i
$557$			5.35028i			0.226699i	0.993555	+	0.113349i	$0.0361580\pi$
$557$			5.35028i			0.226699i	−0.993555	+	0.113349i	$0.963842\pi$
$558$	1.13852	+	15.0663i	0.0481974	+	0.637806i
$559$			29.6338i			1.25338i
$560$		0			0
$561$	22.8300	+	21.1699i	0.963883	+	0.893793i
$562$	23.0892			0.973958
$563$	−29.3370			−1.23641			−0.618205	−	0.786017i	$-0.712140\pi$
$563$	−29.3370			−1.23641			−0.618205	+	0.786017i	$0.712140\pi$
$564$	−0.715780	+	0.771911i	−0.0301398	+	0.0325033i
$565$		−	12.4267i		−	0.522796i
$566$	−24.7505			−1.04034
$567$		0			0
$568$	2.48759			0.104377
$569$		−	42.2121i		−	1.76962i	−0.465949	−	0.884812i	$-0.654287\pi$
$569$		−	42.2121i		−	1.76962i	0.465949	−	0.884812i	$-0.345713\pi$
$570$	4.95469	−	5.34323i	0.207529	−	0.223803i
$571$	−31.3580			−1.31229			−0.656145	−	0.754635i	$-0.727814\pi$
$571$	−31.3580			−1.31229			−0.656145	+	0.754635i	$0.727814\pi$
$572$	−31.5913			−1.32090
$573$	−0.680116	−	0.630661i	−0.0284123	−	0.0263462i
$574$		0			0
$575$			1.91676i			0.0799343i
$576$	0.226058	+	2.99147i	0.00941909	+	0.124645i
$577$			32.0769i			1.33538i	0.744440	+	0.667689i	$0.232717\pi$
$577$			32.0769i			1.33538i	−0.744440	+	0.667689i	$0.767283\pi$
$578$			3.84090i			0.159760i
$579$	6.51908	−	7.03029i	0.270924	−	0.292169i
$580$		−	0.800269i		−	0.0332293i
$581$		0			0
$582$	20.7936	−	22.4242i	0.861924	−	0.929515i
$583$	70.8934			2.93611
$584$	15.0933			0.624566
$585$	−19.0713	+	1.44117i	−0.788502	+	0.0595852i
$586$			25.3384i			1.04672i
$587$	1.93731			0.0799612			0.0399806	−	0.999200i	$-0.487270\pi$
$587$	1.93731			0.0799612			0.0399806	+	0.999200i	$0.487270\pi$
$588$		0			0
$589$	−21.1887			−0.873063
$590$		−	1.75132i		−	0.0721006i
$591$	−0.846431	−	0.784881i	−0.0348175	−	0.0322857i
$592$	5.82789			0.239525
$593$	11.2615			0.462454			0.231227	−	0.972900i	$-0.425726\pi$
$593$	11.2615			0.462454			0.231227	+	0.972900i	$0.425726\pi$
$594$	20.1461	+	16.0351i	0.826604	+	0.657929i
$595$		0			0
$596$			6.59303i			0.270061i
$597$	−11.4584	−	10.6252i	−0.468960	−	0.434859i
$598$		−	12.2198i		−	0.499704i
$599$			44.3460i			1.81193i	0.423356	+	0.905963i	$0.360852\pi$
$599$			44.3460i			1.81193i	−0.423356	+	0.905963i	$0.639148\pi$
$600$	−1.27005	−	1.17770i	−0.0518496	−	0.0480793i
$601$			17.7126i			0.722514i	0.932466	+	0.361257i	$0.117652\pi$
$601$			17.7126i			0.722514i	−0.932466	+	0.361257i	$0.882348\pi$
$602$		0			0
$603$	−1.80461	−	23.8807i	−0.0734893	−	0.972499i
$604$	−11.7743			−0.479091
$605$	−13.5552			−0.551098
$606$	−1.45855	−	1.35249i	−0.0592497	−	0.0549412i
$607$		−	18.3499i		−	0.744801i	−0.928072	−	0.372400i	$-0.878535\pi$
$607$		−	18.3499i		−	0.744801i	0.928072	−	0.372400i	$-0.121465\pi$
$608$	−4.20710			−0.170620
$609$		0			0
$610$	3.42307			0.138596
$611$			3.87473i			0.156755i
$612$	−0.820036	−	10.8517i	−0.0331480	−	0.438654i
$613$	0.631673			0.0255130			0.0127565	−	0.999919i	$-0.495939\pi$
$613$	0.631673			0.0255130			0.0127565	+	0.999919i	$0.495939\pi$
$614$	−13.1396			−0.530273
$615$	−8.77576	+	9.46395i	−0.353873	+	0.381623i
$616$		0			0
$617$			15.5902i			0.627638i	0.949483	+	0.313819i	$0.101608\pi$
$617$			15.5902i			0.627638i	−0.949483	+	0.313819i	$0.898392\pi$
$618$	8.57792	−	9.25059i	0.345054	−	0.372113i
$619$		−	12.6859i		−	0.509890i	−0.966956	−	0.254945i	$-0.917943\pi$
$619$		−	12.6859i		−	0.509890i	0.966956	−	0.254945i	$-0.0820573\pi$
$620$			5.03641i			0.202267i
$621$	−6.20252	+	7.79267i	−0.248898	+	0.312709i
$622$		−	7.60664i		−	0.304999i
$623$		0			0
$624$	8.09687	+	7.50809i	0.324134	+	0.300564i
$625$	1.00000			0.0400000
$626$	12.4254			0.496621
$627$	−24.5521	+	26.4774i	−0.980515	+	1.05741i
$628$			1.54479i			0.0616440i
$629$	−21.1409			−0.842945
$630$		0			0
$631$	−5.96052			−0.237284			−0.118642	−	0.992937i	$-0.537854\pi$
$631$	−5.96052			−0.237284			−0.118642	+	0.992937i	$0.537854\pi$
$632$			2.66807i			0.106130i
$633$	−13.4712	+	14.5276i	−0.535433	+	0.577421i
$634$	−27.7358			−1.10153
$635$	8.06679			0.320121
$636$	−18.1700	−	16.8488i	−0.720488	−	0.668097i
$637$		0			0
$638$			3.96559i			0.156999i
$639$	−7.44155	+	0.562340i	−0.294383	+	0.0222458i
$640$			1.00000i			0.0395285i
$641$		−	12.9407i		−	0.511128i	−0.966792	−	0.255564i	$-0.917739\pi$
$641$		−	12.9407i		−	0.511128i	0.966792	−	0.255564i	$-0.0822611\pi$
$642$	3.16373	−	3.41182i	0.124862	−	0.134654i
$643$			27.7420i			1.09404i	0.837120	+	0.547019i	$0.184237\pi$
$643$			27.7420i			1.09404i	−0.837120	+	0.547019i	$0.815763\pi$
$644$		0			0
$645$	5.47425	−	5.90354i	0.215549	−	0.232452i
$646$	15.2614			0.600453
$647$	−46.7712			−1.83876			−0.919382	−	0.393365i	$-0.871311\pi$
$647$	−46.7712			−1.83876			−0.919382	+	0.393365i	$0.871311\pi$
$648$	−1.35249	−	8.89780i	−0.0531309	−	0.349538i
$649$			8.67834i			0.340654i
$650$	−6.37523			−0.250057
$651$		0			0
$652$	3.37759			0.132277
$653$		−	31.5984i		−	1.23654i	−0.785965	−	0.618271i	$-0.787833\pi$
$653$		−	31.5984i		−	1.23654i	0.785965	−	0.618271i	$-0.212167\pi$
$654$	11.4602	+	10.6269i	0.448130	+	0.415544i
$655$	−3.38301			−0.132185
$656$	7.45163			0.290937
$657$	−45.1512	+	3.41197i	−1.76152	+	0.133113i
$658$		0			0
$659$		−	29.8627i		−	1.16329i	−0.813444	−	0.581643i	$-0.802410\pi$
$659$		−	29.8627i		−	1.16329i	0.813444	−	0.581643i	$-0.197590\pi$
$660$	6.29351	+	5.83587i	0.244975	+	0.227161i
$661$			13.8572i			0.538983i	0.963003	+	0.269492i	$0.0868556\pi$
$661$			13.8572i			0.538983i	−0.963003	+	0.269492i	$0.913144\pi$
$662$		−	11.7892i		−	0.458202i
$663$	−29.3718	−	27.2360i	−1.14071	−	1.05776i
$664$			7.27215i			0.282214i
$665$		0			0
$666$	−17.4340	+	1.31744i	−0.675552	+	0.0510498i
$667$	−1.53392			−0.0593937
$668$	12.7685			0.494027
$669$	6.64741	+	6.16403i	0.257004	+	0.238315i
$670$		−	7.98294i		−	0.308408i
$671$	−16.9624			−0.654827
$672$		0			0
$673$	21.1836			0.816568			0.408284	−	0.912855i	$-0.366127\pi$
$673$	21.1836			0.816568			0.408284	+	0.912855i	$0.366127\pi$
$674$			5.58238i			0.215025i
$675$	4.06555	+	3.23594i	0.156483	+	0.124551i
$676$	27.6436			1.06322
$677$	−48.3365			−1.85772			−0.928860	−	0.370430i	$-0.879210\pi$
$677$	−48.3365			−1.85772			−0.928860	+	0.370430i	$0.879210\pi$
$678$	14.6349	−	15.7826i	0.562050	−	0.606126i
$679$		0			0
$680$		−	3.62755i		−	0.139110i
$681$	15.8546	−	17.0978i	0.607548	−	0.655191i
$682$		−	24.9570i		−	0.955654i
$683$		−	26.3276i		−	1.00740i	−0.863879	−	0.503699i	$-0.831972\pi$
$683$		−	26.3276i		−	1.00740i	0.863879	−	0.503699i	$-0.168028\pi$
$684$	12.5854	−	0.951048i	0.481215	−	0.0363642i
$685$			14.8274i			0.566526i
$686$		0			0
$687$	−20.9833	−	19.4575i	−0.800563	−	0.742349i
$688$	−4.64827			−0.177214
$689$	−91.2074			−3.47473
$690$	−2.25736	+	2.43438i	−0.0859362	+	0.0926753i
$691$		−	19.1148i		−	0.727163i	−0.931562	−	0.363581i	$-0.881554\pi$
$691$		−	19.1148i		−	0.727163i	0.931562	−	0.363581i	$-0.118446\pi$
$692$	−0.247556			−0.00941068
$693$		0			0
$694$	−31.9093			−1.21126
$695$		−	7.24669i		−	0.274883i
$696$	0.942474	−	1.01638i	0.0357244	−	0.0385258i
$697$	−27.0311			−1.02388
$698$	1.64353			0.0622084
$699$	−23.6686	−	21.9475i	−0.895227	−	0.830130i
$700$		0			0
$701$		−	36.3536i		−	1.37306i	−0.727103	−	0.686528i	$-0.759134\pi$
$701$		−	36.3536i		−	1.37306i	0.727103	−	0.686528i	$-0.240866\pi$
$702$	−25.9188	−	20.6299i	−0.978243	−	0.778625i
$703$		−	24.5185i		−	0.924732i
$704$		−	4.95532i		−	0.186761i
$705$	0.715780	−	0.771911i	0.0269578	−	0.0290718i
$706$		−	14.6008i		−	0.549507i
$707$		0			0
$708$	2.06252	−	2.22426i	0.0775143	−	0.0835928i
$709$	5.09212			0.191239			0.0956193	−	0.995418i	$-0.469517\pi$
$709$	5.09212			0.191239			0.0956193	+	0.995418i	$0.469517\pi$
$710$	−2.48759			−0.0933575
$711$	−0.603140	−	7.98147i	−0.0226195	−	0.299328i
$712$		−	1.88495i		−	0.0706414i
$713$	9.65357			0.361529
$714$		0			0
$715$	31.5913			1.18145
$716$			19.5963i			0.732348i
$717$	−31.5055	−	29.2145i	−1.17659	−	1.09104i
$718$	−0.506001			−0.0188838
$719$	−41.1644			−1.53517			−0.767587	−	0.640945i	$-0.778543\pi$
$719$	−41.1644			−1.53517			−0.767587	+	0.640945i	$0.778543\pi$
$720$	−0.226058	−	2.99147i	−0.00842469	−	0.111486i
$721$		0			0
$722$		−	1.30035i		−	0.0483938i
$723$	−28.3684	−	26.3055i	−1.05503	−	0.978314i
$724$		−	14.8103i		−	0.550422i
$725$			0.800269i			0.0297212i
$726$	−17.2158	−	15.9639i	−0.638938	−	0.592477i
$727$			46.1288i			1.71082i	0.517948	+	0.855412i	$0.326696\pi$
$727$			46.1288i			1.71082i	−0.517948	+	0.855412i	$0.673304\pi$
$728$		0			0
$729$	6.05736	+	26.3118i	0.224347	+	0.974509i
$730$	−15.0933			−0.558629
$731$	16.8618			0.623657
$732$	4.34748	+	4.03134i	0.160687	+	0.149003i
$733$		−	9.99727i		−	0.369258i	−0.982808	−	0.184629i	$-0.940892\pi$
$733$		−	9.99727i		−	0.369258i	0.982808	−	0.184629i	$-0.0591083\pi$
$734$	1.35732			0.0500996
$735$		0			0
$736$	1.91676			0.0706526
$737$			39.5580i			1.45714i
$738$	−22.2913	+	1.68450i	−0.820555	+	0.0620073i
$739$	0.836051			0.0307547			0.0153773	−	0.999882i	$-0.495105\pi$
$739$	0.836051			0.0307547			0.0153773	+	0.999882i	$0.495105\pi$
$740$	−5.82789			−0.214237
$741$	31.5873	−	34.0643i	1.16039	−	1.25138i
$742$		0			0
$743$			53.3336i			1.95662i	0.207146	+	0.978310i	$0.433582\pi$
$743$			53.3336i			1.95662i	−0.207146	+	0.978310i	$0.566418\pi$
$744$	−5.93136	+	6.39649i	−0.217454	+	0.234507i
$745$		−	6.59303i		−	0.241550i
$746$			34.1095i			1.24884i
$747$	−1.64393	−	21.7544i	−0.0601482	−	0.795953i
$748$			17.9757i			0.657255i
$749$		0			0
$750$	1.27005	+	1.17770i	0.0463757	+	0.0430034i
$751$	33.7319			1.23090			0.615448	−	0.788178i	$-0.288975\pi$
$751$	33.7319			1.23090			0.615448	+	0.788178i	$0.288975\pi$
$752$	−0.607779			−0.0221634
$753$	3.20460	−	3.45590i	0.116782	−	0.125940i
$754$		−	5.10190i		−	0.185800i
$755$	11.7743			0.428512
$756$		0			0
$757$	37.1033			1.34854			0.674272	−	0.738483i	$-0.264458\pi$
$757$	37.1033			1.34854			0.674272	+	0.738483i	$0.264458\pi$
$758$			1.53951i			0.0559177i
$759$	11.1859	−	12.0631i	0.406024	−	0.437864i
$760$	4.20710			0.152607
$761$	−17.9104			−0.649251			−0.324625	−	0.945843i	$-0.605238\pi$
$761$	−17.9104			−0.649251			−0.324625	+	0.945843i	$0.605238\pi$
$762$	10.2452	+	9.50024i	0.371146	+	0.344157i
$763$		0			0
$764$		−	0.535503i		−	0.0193738i
$765$	0.820036	+	10.8517i	0.0296485	+	0.392344i
$766$		−	32.5261i		−	1.17522i
$767$		−	11.1650i		−	0.403147i
$768$	−1.17770	+	1.27005i	−0.0424965	+	0.0458290i
$769$			0.619084i			0.0223247i	0.999938	+	0.0111624i	$0.00355317\pi$
$769$			0.619084i			0.0223247i	−0.999938	+	0.0111624i	$0.996447\pi$
$770$		0			0
$771$	−13.5480	+	14.6104i	−0.487918	+	0.526180i
$772$	5.53544			0.199225
$773$	48.9365			1.76012			0.880062	−	0.474859i	$-0.157501\pi$
$773$	48.9365			1.76012			0.880062	+	0.474859i	$0.157501\pi$
$774$	13.9052	−	1.05078i	0.499811	−	0.0377695i
$775$		−	5.03641i		−	0.180913i
$776$	17.6562			0.633820
$777$		0			0
$778$	−7.10169			−0.254608
$779$		−	31.3497i		−	1.12322i
$780$	−8.09687	−	7.50809i	−0.289914	−	0.268833i
$781$	12.3268			0.441088
$782$	−6.95313			−0.248643
$783$	−2.58962	+	3.25353i	−0.0925456	+	0.116272i
$784$		0			0
$785$		−	1.54479i		−	0.0551360i
$786$	−4.29660	−	3.98417i	−0.153255	−	0.142111i
$787$			0.0672107i			0.00239580i	0.999999	+	0.00119790i	$0.000381304\pi$
$787$			0.0672107i			0.00239580i	−0.999999	+	0.00119790i	$0.999619\pi$
$788$		−	0.666454i		−	0.0237414i
$789$	−16.2383	−	15.0575i	−0.578098	−	0.536061i
$790$		−	2.66807i		−	0.0949258i
$791$		0			0
$792$	1.12019	+	14.8237i	0.0398042	+	0.526737i
$793$	21.8229			0.774953
$794$	13.0239			0.462200
$795$	18.1700	+	16.8488i	0.644424	+	0.597564i
$796$		−	9.02198i		−	0.319775i
$797$	−7.61311			−0.269670			−0.134835	−	0.990868i	$-0.543050\pi$
$797$	−7.61311			−0.269670			−0.134835	+	0.990868i	$0.543050\pi$
$798$		0			0
$799$	2.20475			0.0779984
$800$		−	1.00000i		−	0.0353553i
$801$	0.426108	+	5.63877i	0.0150558	+	0.199236i
$802$	−23.4030			−0.826388
$803$	74.7922			2.63936
$804$	9.40149	−	10.1387i	0.331565	−	0.357566i
$805$		0			0
$806$			32.1083i			1.13097i
$807$	13.7691	−	14.8488i	0.484694	−	0.522703i
$808$		−	1.14842i		−	0.0404013i
$809$		−	19.5941i		−	0.688891i	−0.938806	−	0.344445i	$-0.888067\pi$
$809$		−	19.5941i		−	0.688891i	0.938806	−	0.344445i	$-0.111933\pi$
$810$	1.35249	+	8.89780i	0.0475217	+	0.312637i
$811$			38.1099i			1.33822i	0.743164	+	0.669110i	$0.233324\pi$
$811$			38.1099i			1.33822i	−0.743164	+	0.669110i	$0.766676\pi$
$812$		0			0
$813$	−28.0298	−	25.9916i	−0.983048	−	0.911564i
$814$	28.8791			1.01221
$815$	−3.37759			−0.118312
$816$	4.27215	−	4.60717i	0.149555	−	0.161283i
$817$			19.5557i			0.684168i
$818$	−13.1994			−0.461508
$819$		0			0
$820$	−7.45163			−0.260222
$821$		−	37.4185i		−	1.30592i	−0.757394	−	0.652958i	$-0.773528\pi$
$821$		−	37.4185i		−	1.30592i	0.757394	−	0.652958i	$-0.226472\pi$
$822$	−17.4622	+	18.8316i	−0.609064	+	0.656826i
$823$	34.3864			1.19864			0.599318	−	0.800511i	$-0.295439\pi$
$823$	34.3864			1.19864			0.599318	+	0.800511i	$0.295439\pi$
$824$	7.28364			0.253737
$825$	−6.29351	−	5.83587i	−0.219112	−	0.203179i
$826$		0			0
$827$			4.15552i			0.144502i	0.997386	+	0.0722508i	$0.0230182\pi$
$827$			4.15552i			0.144502i	−0.997386	+	0.0722508i	$0.976982\pi$
$828$	−5.73392	+	0.433299i	−0.199268	+	0.0150582i
$829$			28.1053i			0.976137i	0.872805	+	0.488068i	$0.162298\pi$
$829$			28.1053i			0.976137i	−0.872805	+	0.488068i	$0.837702\pi$
$830$		−	7.27215i		−	0.252420i
$831$	9.19376	−	9.91472i	0.318928	−	0.343938i
$832$			6.37523i			0.221021i
$833$		0			0
$834$	8.53440	−	9.20366i	0.295522	−	0.318697i
$835$	−12.7685			−0.441871
$836$	−20.8475			−0.721026
$837$	16.2975	−	20.4758i	0.563325	−	0.707746i
$838$			27.9492i			0.965489i
$839$	23.6646			0.816992			0.408496	−	0.912760i	$-0.366053\pi$
$839$	23.6646			0.816992			0.408496	+	0.912760i	$0.366053\pi$
$840$		0			0
$841$	28.3596			0.977916
$842$		−	24.6795i		−	0.850512i
$843$	−29.3244	−	27.1920i	−1.00999	−	0.936544i
$844$	−11.4386			−0.393733
$845$	−27.6436			−0.950968
$846$	1.81815	−	0.137393i	0.0625094	−	0.00472368i
$847$		0			0
$848$		−	14.3065i		−	0.491288i
$849$	31.4343	+	29.1486i	1.07882	+	1.00038i
$850$			3.62755i			0.124424i
$851$			11.1707i			0.382925i
$852$	−3.15936	−	2.92963i	−0.108238	−	0.100367i
$853$			23.7742i			0.814012i	0.913426	+	0.407006i	$0.133427\pi$
$853$			23.7742i			0.814012i	−0.913426	+	0.407006i	$0.866573\pi$
$854$		0			0
$855$	−12.5854	+	0.951048i	−0.430412	+	0.0325252i
$856$	2.68637			0.0918181
$857$	22.3621			0.763875			0.381938	−	0.924188i	$-0.375257\pi$
$857$	22.3621			0.763875			0.381938	+	0.924188i	$0.375257\pi$
$858$	40.1226	+	37.2050i	1.36976	+	1.27016i
$859$		−	42.9236i		−	1.46453i	−0.681018	−	0.732267i	$-0.738462\pi$
$859$		−	42.9236i		−	1.46453i	0.681018	−	0.732267i	$-0.261538\pi$
$860$	4.64827			0.158505
$861$		0			0
$862$	3.34445			0.113912
$863$		−	23.5198i		−	0.800623i	−0.916379	−	0.400312i	$-0.868902\pi$
$863$		−	23.5198i		−	0.800623i	0.916379	−	0.400312i	$-0.131098\pi$
$864$	3.23594	−	4.06555i	0.110089	−	0.138313i
$865$	0.247556			0.00841717
$866$	−14.6756			−0.498697
$867$	4.52342	−	4.87814i	0.153623	−	0.165670i
$868$		0			0
$869$			13.2212i			0.448497i
$870$	−0.942474	+	1.01638i	−0.0319529	+	0.0344586i
$871$		−	50.8931i		−	1.72445i
$872$			9.02343i			0.305572i
$873$	−52.8179	+	3.99132i	−1.78762	+	0.135086i
$874$		−	8.06398i		−	0.272768i
$875$		0			0
$876$	−19.1693	−	17.7754i	−0.647670	−	0.600574i
$877$	8.18713			0.276460			0.138230	−	0.990400i	$-0.455859\pi$
$877$	8.18713			0.276460			0.138230	+	0.990400i	$0.455859\pi$
$878$	−6.58702			−0.222301
$879$	29.8410	−	32.1811i	1.00651	−	1.08544i
$880$			4.95532i			0.167044i
$881$	26.6496			0.897847			0.448923	−	0.893570i	$-0.351808\pi$
$881$	26.6496			0.897847			0.448923	+	0.893570i	$0.351808\pi$
$882$		0			0
$883$	−5.41249			−0.182145			−0.0910724	−	0.995844i	$-0.529029\pi$
$883$	−5.41249			−0.182145			−0.0910724	+	0.995844i	$0.529029\pi$
$884$		−	23.1265i		−	0.777827i
$885$	−2.06252	+	2.22426i	−0.0693309	+	0.0747677i
$886$	40.7210			1.36805
$887$	24.0998			0.809194			0.404597	−	0.914495i	$-0.367412\pi$
$887$	24.0998			0.809194			0.404597	+	0.914495i	$0.367412\pi$
$888$	−7.40171	−	6.86349i	−0.248385	−	0.230324i
$889$		0			0
$890$			1.88495i			0.0631836i
$891$	−6.70203	−	44.0914i	−0.224527	−	1.47712i
$892$			5.23397i			0.175246i
$893$			2.55699i			0.0855663i
$894$	7.76459	−	8.37348i	0.259687	−	0.280051i
$895$		−	19.5963i		−	0.655032i
$896$		0			0
$897$	−14.3912	+	15.5197i	−0.480508	+	0.518189i
$898$	−18.3485			−0.612297
$899$	4.03048			0.134424
$900$	0.226058	+	2.99147i	0.00753527	+	0.0997157i
$901$			51.8976i			1.72896i
$902$	36.9252			1.22948
$903$		0			0
$904$	12.4267			0.413306
$905$			14.8103i			0.492312i
$906$	14.9540	+	13.8666i	0.496814	+	0.460688i
$907$	−21.6581			−0.719144			−0.359572	−	0.933117i	$-0.617077\pi$
$907$	−21.6581			−0.719144			−0.359572	+	0.933117i	$0.617077\pi$
$908$	13.4623			0.446763
$909$	0.259610	+	3.43547i	0.00861071	+	0.113947i
$910$		0			0
$911$		−	47.4302i		−	1.57143i	−0.618587	−	0.785716i	$-0.712295\pi$
$911$		−	47.4302i		−	1.57143i	0.618587	−	0.785716i	$-0.287705\pi$
$912$	5.34323	+	4.95469i	0.176932	+	0.164066i
$913$			36.0359i			1.19261i
$914$			8.64332i			0.285896i
$915$	−4.34748	−	4.03134i	−0.143723	−	0.133272i
$916$		−	16.5216i		−	0.545890i
$917$		0			0
$918$	−11.7385	+	14.7480i	−0.387429	+	0.486755i
$919$	10.6442			0.351119			0.175559	−	0.984469i	$-0.443827\pi$
$919$	10.6442			0.351119			0.175559	+	0.984469i	$0.443827\pi$
$920$	−1.91676			−0.0631936
$921$	16.6880	+	15.4745i	0.549889	+	0.509903i
$922$		−	24.7864i		−	0.816298i
$923$	−15.8590			−0.522004
$924$		0			0
$925$	5.82789			0.191620
$926$			17.9797i			0.590850i
$927$	−21.7888	+	1.64652i	−0.715638	+	0.0540790i
$928$	0.800269			0.0262701
$929$	−34.3965			−1.12851			−0.564257	−	0.825599i	$-0.690837\pi$
$929$	−34.3965			−1.12851			−0.564257	+	0.825599i	$0.690837\pi$
$930$	5.93136	−	6.39649i	0.194497	−	0.209749i
$931$		0			0
$932$		−	18.6359i		−	0.610440i
$933$	−8.95832	+	9.66082i	−0.293282	+	0.316281i
$934$			1.27342i			0.0416677i
$935$		−	17.9757i		−	0.587867i
$936$	−1.44117	−	19.0713i	−0.0471062	−	0.623366i
$937$		−	40.0917i		−	1.30974i	−0.755742	−	0.654870i	$-0.772723\pi$
$937$		−	40.0917i		−	1.30974i	0.755742	−	0.654870i	$-0.227277\pi$
$938$		0			0
$939$	−15.7809	−	14.6334i	−0.514992	−	0.477543i
$940$	0.607779			0.0198236
$941$	27.2630			0.888747			0.444374	−	0.895842i	$-0.353426\pi$
$941$	27.2630			0.888747			0.444374	+	0.895842i	$0.353426\pi$
$942$	1.81930	−	1.96197i	0.0592760	−	0.0639243i
$943$			14.2830i			0.465117i
$944$	1.75132			0.0570005
$945$		0			0
$946$	−23.0337			−0.748889
$947$			22.7062i			0.737853i	0.929459	+	0.368926i	$0.120275\pi$
$947$			22.7062i			0.737853i	−0.929459	+	0.368926i	$0.879725\pi$
$948$	3.14218	−	3.38859i	0.102053	−	0.110056i
$949$	−96.2234			−3.12354
$950$	−4.20710			−0.136496
$951$	35.2258	+	32.6644i	1.14228	+	1.05921i
$952$		0			0
$953$			38.7288i			1.25455i	0.778799	+	0.627274i	$0.215829\pi$
$953$			38.7288i			1.25455i	−0.778799	+	0.627274i	$0.784171\pi$
$954$	3.23411	+	42.7976i	0.104708	+	1.38562i
$955$			0.535503i			0.0173285i
$956$		−	24.8065i		−	0.802299i
$957$	4.67026	−	5.03650i	0.150968	−	0.162807i
$958$		−	14.2267i		−	0.459643i
$959$		0			0
$960$	1.17770	−	1.27005i	0.0380100	−	0.0409907i
$961$	5.63459			0.181761
$962$	−37.1541			−1.19790
$963$	−8.03619	+	0.607275i	−0.258963	+	0.0195692i
$964$		−	22.3364i		−	0.719408i
$965$	−5.53544			−0.178192
$966$		0			0
$967$	39.1631			1.25940			0.629700	−	0.776838i	$-0.283178\pi$
$967$	39.1631			1.25940			0.629700	+	0.776838i	$0.283178\pi$
$968$		−	13.5552i		−	0.435681i
$969$	−19.3828	−	17.9734i	−0.622665	−	0.577387i
$970$	−17.6562			−0.566906
$971$	26.8011			0.860087			0.430044	−	0.902808i	$-0.358498\pi$
$971$	26.8011			0.860087			0.430044	+	0.902808i	$0.358498\pi$
$972$	−8.76118	+	12.8935i	−0.281015	+	0.413559i
$973$		0			0
$974$		−	39.8951i		−	1.27832i
$975$	8.09687	+	7.50809i	0.259307	+	0.240451i
$976$			3.42307i			0.109570i
$977$		−	27.8772i		−	0.891871i	−0.895065	−	0.445936i	$-0.852871\pi$
$977$		−	27.8772i		−	0.891871i	0.895065	−	0.445936i	$-0.147129\pi$
$978$	−4.28971	−	3.97778i	−0.137170	−	0.127195i
$979$		−	9.34052i		−	0.298524i
$980$		0			0
$981$	−2.03982	−	26.9933i	−0.0651264	−	0.861831i
$982$	15.9778			0.509873
$983$	−21.8424			−0.696665			−0.348332	−	0.937371i	$-0.613252\pi$
$983$	−21.8424			−0.696665			−0.348332	+	0.937371i	$0.613252\pi$
$984$	−9.46395	−	8.77576i	−0.301700	−	0.279761i
$985$			0.666454i			0.0212350i
$986$	−2.90301			−0.0924507
$987$		0			0
$988$	26.8212			0.853297
$989$		−	8.90960i		−	0.283309i
$990$	−1.12019	−	14.8237i	−0.0356020	−	0.471128i
$991$	−58.8600			−1.86975			−0.934875	−	0.354977i	$-0.884489\pi$
$991$	−58.8600			−1.86975			−0.934875	+	0.354977i	$0.884489\pi$
$992$	−5.03641			−0.159906
$993$	−13.8841	+	14.9729i	−0.440600	+	0.475151i
$994$		0			0
$995$			9.02198i			0.286016i
$996$	8.56439	−	9.23600i	0.271373	−	0.292654i
$997$			12.0467i			0.381522i	0.981636	+	0.190761i	$0.0610956\pi$
$997$			12.0467i			0.381522i	−0.981636	+	0.190761i	$0.938904\pi$
$998$			13.8063i			0.437030i
$999$	23.6936	+	18.8587i	0.749631	+	0.596663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.a.881.2		12
3.2	odd	2		1470.2.b.b.881.11		12
7.2	even	3		210.2.r.b.101.2	yes	12
7.3	odd	6		210.2.r.a.131.4	yes	12
7.6	odd	2		1470.2.b.b.881.5		12
21.2	odd	6		210.2.r.a.101.4	✓	12
21.17	even	6		210.2.r.b.131.2	yes	12
21.20	even	2	inner	1470.2.b.a.881.8		12
35.2	odd	12		1050.2.u.e.899.1		12
35.3	even	12		1050.2.u.g.299.5		12
35.9	even	6		1050.2.s.f.101.5		12
35.17	even	12		1050.2.u.f.299.2		12
35.23	odd	12		1050.2.u.h.899.6		12
35.24	odd	6		1050.2.s.g.551.3		12
105.2	even	12		1050.2.u.g.899.5		12
105.17	odd	12		1050.2.u.h.299.6		12
105.23	even	12		1050.2.u.f.899.2		12
105.38	odd	12		1050.2.u.e.299.1		12
105.44	odd	6		1050.2.s.g.101.3		12
105.59	even	6		1050.2.s.f.551.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.4	✓	12	21.2	odd	6
210.2.r.a.131.4	yes	12	7.3	odd	6
210.2.r.b.101.2	yes	12	7.2	even	3
210.2.r.b.131.2	yes	12	21.17	even	6
1050.2.s.f.101.5		12	35.9	even	6
1050.2.s.f.551.5		12	105.59	even	6
1050.2.s.g.101.3		12	105.44	odd	6
1050.2.s.g.551.3		12	35.24	odd	6
1050.2.u.e.299.1		12	105.38	odd	12
1050.2.u.e.899.1		12	35.2	odd	12
1050.2.u.f.299.2		12	35.17	even	12
1050.2.u.f.899.2		12	105.23	even	12
1050.2.u.g.299.5		12	35.3	even	12
1050.2.u.g.899.5		12	105.2	even	12
1050.2.u.h.299.6		12	105.17	odd	12
1050.2.u.h.899.6		12	35.23	odd	12
1470.2.b.a.881.2		12	1.1	even	1	trivial
1470.2.b.a.881.8		12	21.20	even	2	inner
1470.2.b.b.881.5		12	7.6	odd	2
1470.2.b.b.881.11		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.17770 + 1.27005i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.27005 + 1.17770i) q^{6} +1.00000i q^{8} +(-0.226058 - 2.99147i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.17770 + 1.27005i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.27005 + 1.17770i) q^{6} +1.00000i q^{8} +(-0.226058 - 2.99147i) q^{9} -1.00000i q^{10} +4.95532i q^{11} +(1.17770 - 1.27005i) q^{12} -6.37523i q^{13} +(-1.17770 + 1.27005i) q^{15} +1.00000 q^{16} -3.62755 q^{17} +(-2.99147 + 0.226058i) q^{18} -4.20710i q^{19} -1.00000 q^{20} +4.95532 q^{22} +1.91676i q^{23} +(-1.27005 - 1.17770i) q^{24} +1.00000 q^{25} -6.37523 q^{26} +(4.06555 + 3.23594i) q^{27} +0.800269i q^{29} +(1.27005 + 1.17770i) q^{30} -5.03641i q^{31} -1.00000i q^{32} +(-6.29351 - 5.83587i) q^{33} +3.62755i q^{34} +(0.226058 + 2.99147i) q^{36} +5.82789 q^{37} -4.20710 q^{38} +(8.09687 + 7.50809i) q^{39} +1.00000i q^{40} +7.45163 q^{41} -4.64827 q^{43} -4.95532i q^{44} +(-0.226058 - 2.99147i) q^{45} +1.91676 q^{46} -0.607779 q^{47} +(-1.17770 + 1.27005i) q^{48} -1.00000i q^{50} +(4.27215 - 4.60717i) q^{51} +6.37523i q^{52} -14.3065i q^{53} +(3.23594 - 4.06555i) q^{54} +4.95532i q^{55} +(5.34323 + 4.95469i) q^{57} +0.800269 q^{58} +1.75132 q^{59} +(1.17770 - 1.27005i) q^{60} +3.42307i q^{61} -5.03641 q^{62} -1.00000 q^{64} -6.37523i q^{65} +(-5.83587 + 6.29351i) q^{66} +7.98294 q^{67} +3.62755 q^{68} +(-2.43438 - 2.25736i) q^{69} -2.48759i q^{71} +(2.99147 - 0.226058i) q^{72} -15.0933i q^{73} -5.82789i q^{74} +(-1.17770 + 1.27005i) q^{75} +4.20710i q^{76} +(7.50809 - 8.09687i) q^{78} +2.66807 q^{79} +1.00000 q^{80} +(-8.89780 + 1.35249i) q^{81} -7.45163i q^{82} +7.27215 q^{83} -3.62755 q^{85} +4.64827i q^{86} +(-1.01638 - 0.942474i) q^{87} -4.95532 q^{88} -1.88495 q^{89} +(-2.99147 + 0.226058i) q^{90} -1.91676i q^{92} +(6.39649 + 5.93136i) q^{93} +0.607779i q^{94} -4.20710i q^{95} +(1.27005 + 1.17770i) q^{96} -17.6562i q^{97} +(14.8237 - 1.12019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 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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