LMFDB - Embedded newform 693.2.m.h.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 25x^{12} + 52x^{10} + 309x^{8} + 218x^{6} + 60x^{4} - 2x^{2} + 1 $ x^16 + 7x^14 + 25x^12 + 52x^10 + 309x^8 + 218x^6 + 60x^4 - 2*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-0.698216 + 2.14889i$ of defining polynomial
Character	$\chi$	$=$	693.64
Dual form			693.2.m.h.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698216 + 2.14889i) q^{2} +(-2.51217 - 1.82520i) q^{4} +(-0.476925 - 1.46782i) q^{5} +(0.809017 + 0.587785i) q^{7} +(2.02029 - 1.46782i) q^{8} +O(q^{10})$	\(q+(-0.698216 + 2.14889i) q^{2} +(-2.51217 - 1.82520i) q^{4} +(-0.476925 - 1.46782i) q^{5} +(0.809017 + 0.587785i) q^{7} +(2.02029 - 1.46782i) q^{8} +3.48718 q^{10} +(-2.83882 - 1.71497i) q^{11} +(0.784027 - 2.41299i) q^{13} +(-1.82795 + 1.32808i) q^{14} +(-0.175538 - 0.540251i) q^{16} +(2.03818 + 6.27288i) q^{17} +(6.11739 - 4.44455i) q^{19} +(-1.48096 + 4.55792i) q^{20} +(5.66737 - 4.90289i) q^{22} +5.61973 q^{23} +(2.11803 - 1.53884i) q^{25} +(4.63782 + 3.36957i) q^{26} +(-0.959565 - 2.95324i) q^{28} +(-4.40969 - 3.20383i) q^{29} +(-1.64565 + 5.06480i) q^{31} +6.27793 q^{32} -14.9028 q^{34} +(0.476925 - 1.46782i) q^{35} +(5.00465 + 3.63609i) q^{37} +(5.27957 + 16.2488i) q^{38} +(-3.11803 - 2.26538i) q^{40} +(7.91777 - 5.75260i) q^{41} +9.61149 q^{43} +(4.00145 + 9.48971i) q^{44} +(-3.92378 + 12.0762i) q^{46} +(-3.11001 + 2.25955i) q^{47} +(0.309017 + 0.951057i) q^{49} +(1.82795 + 5.62586i) q^{50} +(-6.37380 + 4.63084i) q^{52} +(0.164274 - 0.505582i) q^{53} +(-1.16336 + 4.98480i) q^{55} +2.49721 q^{56} +(9.96358 - 7.23896i) q^{58} +(1.42449 + 1.03495i) q^{59} +(-1.46709 - 4.51524i) q^{61} +(-9.73466 - 7.07265i) q^{62} +(-4.03227 + 12.4101i) q^{64} -3.91576 q^{65} -9.60824 q^{67} +(6.32900 - 19.4787i) q^{68} +(2.82119 + 2.04972i) q^{70} +(-3.07233 - 9.45567i) q^{71} +(-7.85836 - 5.70943i) q^{73} +(-11.3079 + 8.21565i) q^{74} -23.4802 q^{76} +(-1.28862 - 3.05605i) q^{77} +(0.639754 - 1.96896i) q^{79} +(-0.709276 + 0.515319i) q^{80} +(6.83337 + 21.0309i) q^{82} +(-0.0136710 - 0.0420751i) q^{83} +(8.23543 - 5.98339i) q^{85} +(-6.71090 + 20.6540i) q^{86} +(-8.25250 + 0.702166i) q^{88} +6.38297 q^{89} +(2.05261 - 1.49131i) q^{91} +(-14.1177 - 10.2571i) q^{92} +(-2.68407 - 8.26071i) q^{94} +(-9.44135 - 6.85954i) q^{95} +(-4.09442 + 12.6013i) q^{97} -2.25947 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q - 6 * q^4 + 4 * q^7	$ 16 q - 6 q^{4} + 4 q^{7} + 28 q^{10} + 10 q^{13} + 6 q^{16} + 18 q^{19} - 2 q^{22} + 16 q^{25} - 4 q^{28} + 8 q^{31} - 48 q^{34} + 24 q^{37} - 32 q^{40} + 32 q^{43} + 16 q^{46} - 4 q^{49} - 36 q^{52} - 44 q^{55} + 30 q^{58} - 34 q^{61} + 8 q^{64} - 72 q^{67} + 2 q^{70} - 42 q^{73} - 68 q^{76} - 66 q^{79} + 32 q^{82} + 34 q^{85} - 32 q^{88} + 10 q^{91} - 66 q^{94} + 54 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 + 4 * q^7 + 28 * q^10 + 10 * q^13 + 6 * q^16 + 18 * q^19 - 2 * q^22 + 16 * q^25 - 4 * q^28 + 8 * q^31 - 48 * q^34 + 24 * q^37 - 32 * q^40 + 32 * q^43 + 16 * q^46 - 4 * q^49 - 36 * q^52 - 44 * q^55 + 30 * q^58 - 34 * q^61 + 8 * q^64 - 72 * q^67 + 2 * q^70 - 42 * q^73 - 68 * q^76 - 66 * q^79 + 32 * q^82 + 34 * q^85 - 32 * q^88 + 10 * q^91 - 66 * q^94 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.698216	+	2.14889i	−0.493713	+	1.51949i	0.325240	+	0.945632i	$0.394555\pi$
$2$	−0.698216	+	2.14889i	−0.493713	+	1.51949i	−0.818953	+	0.573861i	$0.805445\pi$
$3$		0			0
$3$		0			0
$4$	−2.51217	−	1.82520i	−1.25609	−	0.912601i
$5$	−0.476925	−	1.46782i	−0.213287	−	0.656431i	−0.999271	−	0.0381834i	$-0.987843\pi$
$5$	−0.476925	−	1.46782i	−0.213287	−	0.656431i	0.785983	−	0.618248i	$-0.212157\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	2.02029	−	1.46782i	0.714279	−	0.518954i
$9$		0			0
$10$	3.48718			1.10274
$11$	−2.83882	−	1.71497i	−0.855936	−	0.517081i
$11$	−2.83882	−	1.71497i	−0.855936	−	0.517081i
$12$		0			0
$13$	0.784027	−	2.41299i	0.217450	−	0.669242i	−0.781521	−	0.623879i	$-0.785556\pi$
$13$	0.784027	−	2.41299i	0.217450	−	0.669242i	0.998971	−	0.0453628i	$-0.0144444\pi$
$14$	−1.82795	+	1.32808i	−0.488541	+	0.354946i
$15$		0			0
$16$	−0.175538	−	0.540251i	−0.0438846	−	0.135063i
$17$	2.03818	+	6.27288i	0.494332	+	1.52140i	0.817995	+	0.575225i	$0.195085\pi$
$17$	2.03818	+	6.27288i	0.494332	+	1.52140i	−0.323663	+	0.946172i	$0.604915\pi$
$18$		0			0
$19$	6.11739	−	4.44455i	1.40343	−	1.01965i	0.409189	−	0.912450i	$-0.365812\pi$
$19$	6.11739	−	4.44455i	1.40343	−	1.01965i	0.994238	−	0.107199i	$-0.0341882\pi$
$20$	−1.48096	+	4.55792i	−0.331152	+	1.01918i
$21$		0			0
$22$	5.66737	−	4.90289i	1.20829	−	1.04530i
$23$	5.61973			1.17179			0.585897	−	0.810385i	$-0.300742\pi$
$23$	5.61973			1.17179			0.585897	+	0.810385i	$0.300742\pi$
$24$		0			0
$25$	2.11803	−	1.53884i	0.423607	−	0.307768i
$26$	4.63782	+	3.36957i	0.909550	+	0.660827i
$27$		0			0
$28$	−0.959565	−	2.95324i	−0.181341	−	0.558110i
$29$	−4.40969	−	3.20383i	−0.818859	−	0.594936i	0.0975266	−	0.995233i	$-0.468907\pi$
$29$	−4.40969	−	3.20383i	−0.818859	−	0.594936i	−0.916385	+	0.400297i	$0.868907\pi$
$30$		0			0
$31$	−1.64565	+	5.06480i	−0.295568	+	0.909665i	0.687462	+	0.726220i	$0.258725\pi$
$31$	−1.64565	+	5.06480i	−0.295568	+	0.909665i	−0.983030	+	0.183445i	$0.941275\pi$
$32$	6.27793			1.10979
$33$		0			0
$34$	−14.9028			−2.55581
$35$	0.476925	−	1.46782i	0.0806150	−	0.248108i
$36$		0			0
$37$	5.00465	+	3.63609i	0.822759	+	0.597770i	0.917502	−	0.397732i	$-0.130203\pi$
$37$	5.00465	+	3.63609i	0.822759	+	0.597770i	−0.0947421	+	0.995502i	$0.530203\pi$
$38$	5.27957	+	16.2488i	0.856459	+	2.63591i
$39$		0			0
$40$	−3.11803	−	2.26538i	−0.493004	−	0.358189i
$41$	7.91777	−	5.75260i	1.23655	−	0.898405i	0.239184	−	0.970974i	$-0.423120\pi$
$41$	7.91777	−	5.75260i	1.23655	−	0.898405i	0.997363	+	0.0725696i	$0.0231200\pi$
$42$		0			0
$43$	9.61149			1.46574			0.732870	−	0.680369i	$-0.238181\pi$
$43$	9.61149			1.46574			0.732870	+	0.680369i	$0.238181\pi$
$44$	4.00145	+	9.48971i	0.603242	+	1.43063i
$45$		0			0
$46$	−3.92378	+	12.0762i	−0.578530	+	1.78053i
$47$	−3.11001	+	2.25955i	−0.453641	+	0.329590i	−0.791032	−	0.611775i	$-0.790456\pi$
$47$	−3.11001	+	2.25955i	−0.453641	+	0.329590i	0.337390	+	0.941365i	$0.390456\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.82795	+	5.62586i	0.258511	+	0.795617i
$51$		0			0
$52$	−6.37380	+	4.63084i	−0.883887	+	0.642182i
$53$	0.164274	−	0.505582i	0.0225647	−	0.0694470i	−0.939140	−	0.343534i	$-0.888376\pi$
$53$	0.164274	−	0.505582i	0.0225647	−	0.0694470i	0.961705	+	0.274087i	$0.0883758\pi$
$54$		0			0
$55$	−1.16336	+	4.98480i	−0.156868	+	0.672150i
$56$	2.49721			0.333704
$57$		0			0
$58$	9.96358	−	7.23896i	1.30828	−	0.950522i
$59$	1.42449	+	1.03495i	0.185453	+	0.134740i	0.676638	−	0.736316i	$-0.263436\pi$
$59$	1.42449	+	1.03495i	0.185453	+	0.134740i	−0.491185	+	0.871055i	$0.663436\pi$
$60$		0			0
$61$	−1.46709	−	4.51524i	−0.187842	−	0.578117i	0.812144	−	0.583457i	$-0.198300\pi$
$61$	−1.46709	−	4.51524i	−0.187842	−	0.578117i	−0.999986	+	0.00533985i	$0.998300\pi$
$62$	−9.73466	−	7.07265i	−1.23630	−	0.898227i
$63$		0			0
$64$	−4.03227	+	12.4101i	−0.504034	+	1.55126i
$65$	−3.91576			−0.485691
$66$		0			0
$67$	−9.60824			−1.17383			−0.586917	−	0.809647i	$-0.699658\pi$
$67$	−9.60824			−1.17383			−0.586917	+	0.809647i	$0.699658\pi$
$68$	6.32900	−	19.4787i	0.767504	−	2.36214i
$69$		0			0
$70$	2.82119	+	2.04972i	0.337197	+	0.244988i
$71$	−3.07233	−	9.45567i	−0.364619	−	1.12218i	−0.950219	−	0.311582i	$-0.899141\pi$
$71$	−3.07233	−	9.45567i	−0.364619	−	1.12218i	0.585600	−	0.810600i	$-0.300859\pi$
$72$		0			0
$73$	−7.85836	−	5.70943i	−0.919751	−	0.668238i	0.0237110	−	0.999719i	$-0.492452\pi$
$73$	−7.85836	−	5.70943i	−0.919751	−	0.668238i	−0.943462	+	0.331481i	$0.892452\pi$
$74$	−11.3079	+	8.21565i	−1.31451	+	0.955050i
$75$		0			0
$76$	−23.4802			−2.69336
$77$	−1.28862	−	3.05605i	−0.146852	−	0.348269i
$78$		0			0
$79$	0.639754	−	1.96896i	0.0719780	−	0.221525i	−0.908596	−	0.417677i	$-0.862844\pi$
$79$	0.639754	−	1.96896i	0.0719780	−	0.221525i	0.980574	+	0.196151i	$0.0628444\pi$
$80$	−0.709276	+	0.515319i	−0.0792994	+	0.0576144i
$81$		0			0
$82$	6.83337	+	21.0309i	0.754619	+	2.32248i
$83$	−0.0136710	−	0.0420751i	−0.00150059	−	0.00461834i	0.950303	−	0.311325i	$-0.100773\pi$
$83$	−0.0136710	−	0.0420751i	−0.00150059	−	0.00461834i	−0.951804	+	0.306707i	$0.900773\pi$
$84$		0			0
$85$	8.23543	−	5.98339i	0.893258	−	0.648990i
$86$	−6.71090	+	20.6540i	−0.723654	+	2.22718i
$87$		0			0
$88$	−8.25250	+	0.702166i	−0.879719	+	0.0748512i
$89$	6.38297			0.676594			0.338297	−	0.941039i	$-0.390149\pi$
$89$	6.38297			0.676594			0.338297	+	0.941039i	$0.390149\pi$
$90$		0			0
$91$	2.05261	−	1.49131i	0.215172	−	0.156332i
$92$	−14.1177	−	10.2571i	−1.47188	−	1.06938i
$93$		0			0
$94$	−2.68407	−	8.26071i	−0.276840	−	0.852027i
$95$	−9.44135	−	6.85954i	−0.968662	−	0.703774i
$96$		0			0
$97$	−4.09442	+	12.6013i	−0.415726	+	1.27947i	0.495874	+	0.868394i	$0.334848\pi$
$97$	−4.09442	+	12.6013i	−0.415726	+	1.27947i	−0.911600	+	0.411078i	$0.865152\pi$
$98$	−2.25947			−0.228241
$99$		0			0
$100$	−8.12957			−0.812957
$101$	1.70908	−	5.26002i	0.170060	−	0.523391i	−0.829313	−	0.558784i	$-0.811268\pi$
$101$	1.70908	−	5.26002i	0.170060	−	0.523391i	0.999373	+	0.0353926i	$0.0112682\pi$
$102$		0			0
$103$	−5.42112	−	3.93867i	−0.534159	−	0.388089i	0.287752	−	0.957705i	$-0.407092\pi$
$103$	−5.42112	−	3.93867i	−0.534159	−	0.388089i	−0.821911	+	0.569616i	$0.807092\pi$
$104$	−1.95788	−	6.02574i	−0.191986	−	0.590872i
$105$		0			0
$106$	0.971740	+	0.706011i	0.0943837	+	0.0685738i
$107$	4.65571	−	3.38257i	0.450085	−	0.327006i	−0.339545	−	0.940590i	$-0.610273\pi$
$107$	4.65571	−	3.38257i	0.450085	−	0.327006i	0.789629	+	0.613584i	$0.210273\pi$
$108$		0			0
$109$	13.7061			1.31281			0.656405	−	0.754409i	$-0.272076\pi$
$109$	13.7061			1.31281			0.656405	+	0.754409i	$0.272076\pi$
$110$	−9.89949	−	5.98040i	−0.943879	−	0.570209i
$111$		0			0
$112$	0.175538	−	0.540251i	0.0165868	−	0.0510490i
$113$	11.8152	−	8.58425i	1.11148	−	0.807538i	0.128584	−	0.991699i	$-0.458957\pi$
$113$	11.8152	−	8.58425i	1.11148	−	0.807538i	0.982896	+	0.184161i	$0.0589567\pi$
$114$		0			0
$115$	−2.68019	−	8.24877i	−0.249929	−	0.769202i
$116$	5.23028	+	16.0971i	0.485619	+	1.49458i
$117$		0			0
$118$	−3.21860	+	2.33845i	−0.296296	+	0.215272i
$119$	−2.03818	+	6.27288i	−0.186840	+	0.575034i
$120$		0			0
$121$	5.11779	+	9.73695i	0.465254	+	0.885177i
$122$	10.7271			0.971184
$123$		0			0
$124$	13.3785	−	9.72001i	1.20142	−	0.872883i
$125$	−9.51192	−	6.91082i	−0.850772	−	0.618122i
$126$		0			0
$127$	4.17367	+	12.8452i	0.370353	+	1.13983i	0.946560	+	0.322526i	$0.104532\pi$
$127$	4.17367	+	12.8452i	0.370353	+	1.13983i	−0.576207	+	0.817304i	$0.695468\pi$
$128$	−13.6945	−	9.94964i	−1.21043	−	0.879432i
$129$		0			0
$130$	2.73405	−	8.41453i	0.239792	−	0.738003i
$131$	−4.30276			−0.375934			−0.187967	−	0.982175i	$-0.560190\pi$
$131$	−4.30276			−0.375934			−0.187967	+	0.982175i	$0.560190\pi$
$132$		0			0
$133$	7.56151			0.655666
$134$	6.70863	−	20.6470i	0.579537	−	1.78363i
$135$		0			0
$136$	13.3252	+	9.68133i	1.14263	+	0.830167i
$137$	3.87152	+	11.9153i	0.330767	+	1.01799i	0.968770	+	0.247961i	$0.0797606\pi$
$137$	3.87152	+	11.9153i	0.330767	+	1.01799i	−0.638003	+	0.770034i	$0.720239\pi$
$138$		0			0
$139$	−9.08225	−	6.59864i	−0.770346	−	0.559689i	0.131720	−	0.991287i	$-0.457950\pi$
$139$	−9.08225	−	6.59864i	−0.770346	−	0.559689i	−0.902066	+	0.431598i	$0.857950\pi$
$140$	−3.87719	+	2.81695i	−0.327683	+	0.238075i
$141$		0			0
$142$	22.4643			1.88516
$143$	−6.36390	+	5.50546i	−0.532176	+	0.460389i
$144$		0			0
$145$	−2.59956	+	8.00064i	−0.215882	+	0.664417i
$146$	17.7557	−	12.9003i	1.46948	−	1.06764i
$147$		0			0
$148$	−5.93596	−	18.2690i	−0.487933	−	1.50170i
$149$	−3.74376	−	11.5221i	−0.306701	−	0.943928i	−0.979037	−	0.203682i	$-0.934709\pi$
$149$	−3.74376	−	11.5221i	−0.306701	−	0.943928i	0.672336	−	0.740246i	$-0.265291\pi$
$150$		0			0
$151$	−8.72751	+	6.34091i	−0.710234	+	0.516016i	−0.883249	−	0.468904i	$-0.844649\pi$
$151$	−8.72751	+	6.34091i	−0.710234	+	0.516016i	0.173015	+	0.984919i	$0.444649\pi$
$152$	5.83508	−	17.9585i	0.473287	−	1.45663i
$153$		0			0
$154$	7.46685	−	0.635319i	0.601696	−	0.0511955i
$155$	8.21909			0.660173
$156$		0			0
$157$	2.99575	−	2.17654i	0.239087	−	0.173707i	−0.461790	−	0.886989i	$-0.652793\pi$
$157$	2.99575	−	2.17654i	0.239087	−	0.173707i	0.700876	+	0.713283i	$0.252793\pi$
$158$	3.78439	+	2.74952i	0.301070	+	0.218740i
$159$		0			0
$160$	−2.99410	−	9.21489i	−0.236704	−	0.728501i
$161$	4.54645	+	3.30319i	0.358311	+	0.260328i
$162$		0			0
$163$	6.96669	−	21.4413i	0.545674	−	1.67941i	−0.173709	−	0.984797i	$-0.555575\pi$
$163$	6.96669	−	21.4413i	0.545674	−	1.67941i	0.719383	−	0.694614i	$-0.244425\pi$
$164$	−30.3905			−2.37310
$165$		0			0
$166$	0.0999599			0.00775839
$167$	−4.39351	+	13.5218i	−0.339980	+	1.04635i	0.624237	+	0.781235i	$0.285410\pi$
$167$	−4.39351	+	13.5218i	−0.339980	+	1.04635i	−0.964217	+	0.265116i	$0.914590\pi$
$168$		0			0
$169$	5.30941	+	3.85751i	0.408416	+	0.296732i
$170$	7.10752	+	21.8747i	0.545122	+	1.67771i
$171$		0			0
$172$	−24.1458	−	17.5429i	−1.84110	−	1.33763i
$173$	15.2734	−	11.0968i	1.16121	−	0.843671i	0.171283	−	0.985222i	$-0.445209\pi$
$173$	15.2734	−	11.0968i	1.16121	−	0.843671i	0.989931	+	0.141551i	$0.0452088\pi$
$174$		0			0
$175$	2.61803			0.197905
$176$	−0.428191	+	1.83472i	−0.0322761	+	0.138297i
$177$		0			0
$178$	−4.45669	+	13.7163i	−0.334043	+	1.02808i
$179$	−3.55826	+	2.58523i	−0.265957	+	0.193229i	−0.712769	−	0.701399i	$-0.752559\pi$
$179$	−3.55826	+	2.58523i	−0.265957	+	0.193229i	0.446812	+	0.894628i	$0.352559\pi$
$180$		0			0
$181$	1.50777	+	4.64044i	0.112072	+	0.344921i	0.991325	−	0.131433i	$-0.0419580\pi$
$181$	1.50777	+	4.64044i	0.112072	+	0.344921i	−0.879253	+	0.476354i	$0.841958\pi$
$182$	1.77149	+	5.45208i	0.131311	+	0.404135i
$183$		0			0
$184$	11.3535	−	8.24877i	0.836988	−	0.608108i
$185$	2.95030	−	9.08009i	0.216910	−	0.667582i
$186$		0			0
$187$	4.97174	−	21.3030i	0.363570	−	1.55783i
$188$	11.9370			0.870597
$189$		0			0
$190$	21.3325	−	15.4990i	1.54762	−	1.12441i
$191$	12.8089	+	9.30619i	0.926818	+	0.673373i	0.945212	−	0.326458i	$-0.105855\pi$
$191$	12.8089	+	9.30619i	0.926818	+	0.673373i	−0.0183938	+	0.999831i	$0.505855\pi$
$192$		0			0
$193$	−2.57558	−	7.92682i	−0.185394	−	0.570585i	0.814561	−	0.580078i	$-0.196978\pi$
$193$	−2.57558	−	7.92682i	−0.185394	−	0.570585i	−0.999955	+	0.00949361i	$0.996978\pi$
$194$	−24.2201	−	17.5969i	−1.73890	−	1.26338i
$195$		0			0
$196$	0.959565	−	2.95324i	0.0685404	−	0.210946i
$197$	3.63957			0.259309			0.129654	−	0.991559i	$-0.458613\pi$
$197$	3.63957			0.259309			0.129654	+	0.991559i	$0.458613\pi$
$198$		0			0
$199$	−4.58189			−0.324801			−0.162401	−	0.986725i	$-0.551924\pi$
$199$	−4.58189			−0.324801			−0.162401	+	0.986725i	$0.551924\pi$
$200$	2.02029	−	6.21780i	0.142856	−	0.439665i
$201$		0			0
$202$	10.1099	+	7.34525i	0.711328	+	0.516810i
$203$	−1.68435	−	5.18390i	−0.118218	−	0.363839i
$204$		0			0
$205$	−12.2200	−	8.87834i	−0.853481	−	0.620090i
$206$	12.2489	−	8.89933i	0.853419	−	0.620046i
$207$		0			0
$208$	−1.44125			−0.0999325
$209$	−24.9884	+	2.12615i	−1.72848	+	0.147069i
$210$		0			0
$211$	0.361382	−	1.11222i	0.0248785	−	0.0765683i	−0.937846	−	0.347051i	$-0.887183\pi$
$211$	0.361382	−	1.11222i	0.0248785	−	0.0765683i	0.962725	+	0.270482i	$0.0871832\pi$
$212$	−1.33547	+	0.970278i	−0.0917207	+	0.0666390i
$213$		0			0
$214$	4.01807	+	12.3664i	0.274670	+	0.845347i
$215$	−4.58396	−	14.1080i	−0.312624	−	0.962157i
$216$		0			0
$217$	−4.30838	+	3.13022i	−0.292472	+	0.212493i
$218$	−9.56983	+	29.4529i	−0.648151	+	1.99480i
$219$		0			0
$220$	12.0208	−	10.3993i	0.810445	−	0.701121i
$221$	16.7344			1.12568
$222$		0			0
$223$	3.18187	−	2.31176i	0.213073	−	0.154807i	−0.476130	−	0.879375i	$-0.657961\pi$
$223$	3.18187	−	2.31176i	0.213073	−	0.154807i	0.689203	+	0.724568i	$0.257961\pi$
$224$	5.07895	+	3.69007i	0.339352	+	0.246553i
$225$		0			0
$226$	10.1970	+	31.3832i	0.678295	+	2.08758i
$227$	−19.7069	−	14.3179i	−1.30799	−	0.950313i	−0.307994	−	0.951388i	$-0.599658\pi$
$227$	−19.7069	−	14.3179i	−1.30799	−	0.950313i	−0.999999	+	0.00107543i	$0.999658\pi$
$228$		0			0
$229$	−7.48670	+	23.0417i	−0.494735	+	1.52264i	0.322635	+	0.946523i	$0.395431\pi$
$229$	−7.48670	+	23.0417i	−0.494735	+	1.52264i	−0.817370	+	0.576114i	$0.804569\pi$
$230$	19.5970			1.29219
$231$		0			0
$232$	−13.6115			−0.893638
$233$	8.71308	−	26.8161i	0.570813	−	1.75678i	−0.0792020	−	0.996859i	$-0.525237\pi$
$233$	8.71308	−	26.8161i	0.570813	−	1.75678i	0.650015	−	0.759922i	$-0.274763\pi$
$234$		0			0
$235$	4.79987	+	3.48731i	0.313109	+	0.227487i
$236$	−1.68957	−	5.19997i	−0.109982	−	0.338489i
$237$		0			0
$238$	−12.0566	−	8.75965i	−0.781515	−	0.567804i
$239$	−15.0794	+	10.9558i	−0.975406	+	0.708674i	−0.956677	−	0.291151i	$-0.905962\pi$
$239$	−15.0794	+	10.9558i	−0.975406	+	0.708674i	−0.0187288	+	0.999825i	$0.505962\pi$
$240$		0			0
$241$	−17.4814			−1.12608			−0.563039	−	0.826430i	$-0.690368\pi$
$241$	−17.4814			−1.12608			−0.563039	+	0.826430i	$0.690368\pi$
$242$	−24.4969	+	4.19906i	−1.57472	+	0.269926i
$243$		0			0
$244$	−4.55563	+	14.0208i	−0.291645	+	0.897590i
$245$	1.24861	−	0.907165i	0.0797705	−	0.0579567i
$246$		0			0
$247$	−5.92843	−	18.2458i	−0.377217	−	1.16095i
$248$	4.10955	+	12.6479i	0.260956	+	0.803141i
$249$		0			0
$250$	21.4919	−	15.6148i	1.35927	−	0.987567i
$251$	−1.24878	+	3.84335i	−0.0788224	+	0.242590i	−0.982701	−	0.185198i	$-0.940707\pi$
$251$	−1.24878	+	3.84335i	−0.0788224	+	0.242590i	0.903879	+	0.427789i	$0.140707\pi$
$252$		0			0
$253$	−15.9534	−	9.63764i	−1.00298	−	0.605913i
$254$	−30.5171			−1.91481
$255$		0			0
$256$	9.82911	−	7.14127i	0.614319	−	0.446329i
$257$	−7.83513	−	5.69255i	−0.488742	−	0.355092i	0.315958	−	0.948773i	$-0.397674\pi$
$257$	−7.83513	−	5.69255i	−0.488742	−	0.355092i	−0.804700	+	0.593681i	$0.797674\pi$
$258$		0			0
$259$	1.91161	+	5.88332i	0.118781	+	0.365572i
$260$	9.83708	+	7.14706i	0.610070	+	0.443242i
$261$		0			0
$262$	3.00425	−	9.24614i	0.185603	−	0.571229i
$263$	5.08831			0.313759			0.156879	−	0.987618i	$-0.449857\pi$
$263$	5.08831			0.313759			0.156879	+	0.987618i	$0.449857\pi$
$264$		0			0
$265$	−0.820452			−0.0504000
$266$	−5.27957	+	16.2488i	−0.323711	+	0.996280i
$267$		0			0
$268$	24.1376	+	17.5370i	1.47444	+	1.07124i
$269$	−0.0694072	−	0.213613i	−0.00423183	−	0.0130242i	0.948918	−	0.315522i	$-0.102180\pi$
$269$	−0.0694072	−	0.213613i	−0.00423183	−	0.0130242i	−0.953150	+	0.302498i	$0.902180\pi$
$270$		0			0
$271$	19.7069	+	14.3179i	1.19711	+	0.869749i	0.993997	−	0.109407i	$-0.0348951\pi$
$271$	19.7069	+	14.3179i	1.19711	+	0.869749i	0.203110	+	0.979156i	$0.434895\pi$
$272$	3.03115	−	2.20226i	0.183791	−	0.133532i
$273$		0			0
$274$	−28.3078			−1.71014
$275$	−8.65178	+	0.736139i	−0.521722	+	0.0443909i
$276$		0			0
$277$	−5.40772	+	16.6432i	−0.324918	+	0.999995i	0.646559	+	0.762864i	$0.276207\pi$
$277$	−5.40772	+	16.6432i	−0.324918	+	0.999995i	−0.971478	+	0.237132i	$0.923793\pi$
$278$	20.5211	−	14.9095i	1.23077	−	0.894209i
$279$		0			0
$280$	−1.19098	−	3.66547i	−0.0711748	−	0.219054i
$281$	−4.43593	−	13.6524i	−0.264625	−	0.814433i	−0.991780	−	0.127959i	$-0.959158\pi$
$281$	−4.43593	−	13.6524i	−0.264625	−	0.814433i	0.727154	−	0.686474i	$-0.240842\pi$
$282$		0			0
$283$	−22.6569	+	16.4612i	−1.34681	+	0.978516i	−0.347649	+	0.937625i	$0.613020\pi$
$283$	−22.6569	+	16.4612i	−1.34681	+	0.978516i	−0.999164	+	0.0408916i	$0.986980\pi$
$284$	−9.54027	+	29.3619i	−0.566111	+	1.74231i
$285$		0			0
$286$	−7.38722	−	17.5193i	−0.436816	−	1.03594i
$287$	9.78690			0.577702
$288$		0			0
$289$	−21.4416	+	15.5782i	−1.26127	+	0.916365i
$290$	−15.3774	−	11.1723i	−0.902992	−	0.656062i
$291$		0			0
$292$	9.32070	+	28.6862i	0.545453	+	1.67873i
$293$	10.8074	+	7.85202i	0.631374	+	0.458720i	0.856876	−	0.515523i	$-0.172402\pi$
$293$	10.8074	+	7.85202i	0.631374	+	0.458720i	−0.225502	+	0.974243i	$0.572402\pi$
$294$		0			0
$295$	0.839755	−	2.58450i	0.0488924	−	0.150475i
$296$	15.4480			0.897895
$297$		0			0
$298$	27.3737			1.58571
$299$	4.40602	−	13.5603i	0.254807	−	0.784214i
$300$		0			0
$301$	7.77586	+	5.64949i	0.448193	+	0.325631i
$302$	−7.53220	−	23.1817i	−0.433430	−	1.33396i
$303$		0			0
$304$	−3.47501	−	2.52474i	−0.199305	−	0.144804i
$305$	−5.92788	+	4.30686i	−0.339430	+	0.246610i
$306$		0			0
$307$	−3.14669			−0.179591			−0.0897955	−	0.995960i	$-0.528621\pi$
$307$	−3.14669			−0.179591			−0.0897955	+	0.995960i	$0.528621\pi$
$308$	−2.34067	+	10.0293i	−0.133372	+	0.571474i
$309$		0			0
$310$	−5.73870	+	17.6619i	−0.325936	+	1.00313i
$311$	−19.8693	+	14.4359i	−1.12668	+	0.818584i	−0.985209	−	0.171357i	$-0.945185\pi$
$311$	−19.8693	+	14.4359i	−1.12668	+	0.818584i	−0.141476	+	0.989942i	$0.545185\pi$
$312$		0			0
$313$	−6.65760	−	20.4900i	−0.376310	−	1.15816i	−0.942591	−	0.333951i	$-0.891618\pi$
$313$	−6.65760	−	20.4900i	−0.376310	−	1.15816i	0.566281	−	0.824213i	$-0.308382\pi$
$314$	2.58545	+	7.95721i	0.145906	+	0.449051i
$315$		0			0
$316$	−5.20092	+	3.77869i	−0.292575	+	0.212568i
$317$	−2.28231	+	7.02424i	−0.128187	+	0.394520i	−0.994468	−	0.105037i	$-0.966504\pi$
$317$	−2.28231	+	7.02424i	−0.128187	+	0.394520i	0.866281	+	0.499557i	$0.166504\pi$
$318$		0			0
$319$	7.02386	+	16.6575i	0.393261	+	0.932644i
$320$	20.1389			1.12580
$321$		0			0
$322$	−10.2726	+	7.46348i	−0.572469	+	0.415923i
$323$	40.3485	+	29.3149i	2.24505	+	1.63112i
$324$		0			0
$325$	−2.05261	−	6.31728i	−0.113858	−	0.350420i
$326$	41.2106	+	29.9413i	2.28245	+	1.65829i
$327$		0			0
$328$	7.55236	−	23.2438i	0.417010	−	1.28342i
$329$	−3.84418			−0.211937
$330$		0			0
$331$	−21.0897			−1.15919			−0.579597	−	0.814903i	$-0.696790\pi$
$331$	−21.0897			−1.15919			−0.579597	+	0.814903i	$0.696790\pi$
$332$	−0.0424515	+	0.130652i	−0.00232983	+	0.00717048i
$333$		0			0
$334$	−25.9893	−	18.8823i	−1.42207	−	1.03319i
$335$	4.58241	+	14.1032i	0.250364	+	0.770541i
$336$		0			0
$337$	16.4208	+	11.9304i	0.894499	+	0.649892i	0.937047	−	0.349203i	$-0.113548\pi$
$337$	16.4208	+	11.9304i	0.894499	+	0.649892i	−0.0425480	+	0.999094i	$0.513548\pi$
$338$	−11.9965	+	8.71595i	−0.652522	+	0.474085i
$339$		0			0
$340$	−31.6097			−1.71428
$341$	13.3577	−	11.5558i	0.723358	−	0.625782i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	19.4180	−	14.1080i	1.04695	−	0.760652i
$345$		0			0
$346$	13.1816	+	40.5687i	0.708646	+	2.18099i
$347$	5.07345	+	15.6145i	0.272357	+	0.838229i	0.989907	+	0.141722i	$0.0452638\pi$
$347$	5.07345	+	15.6145i	0.272357	+	0.838229i	−0.717549	+	0.696508i	$0.754736\pi$
$348$		0			0
$349$	22.9742	−	16.6918i	1.22978	−	0.893489i	0.232908	−	0.972499i	$-0.425176\pi$
$349$	22.9742	−	16.6918i	1.22978	−	0.893489i	0.996874	+	0.0790098i	$0.0251758\pi$
$350$	−1.82795	+	5.62586i	−0.0977082	+	0.300715i
$351$		0			0
$352$	−17.8219	−	10.7664i	−0.949910	−	0.573852i
$353$	6.54122			0.348154			0.174077	−	0.984732i	$-0.444306\pi$
$353$	6.54122			0.348154			0.174077	+	0.984732i	$0.444306\pi$
$354$		0			0
$355$	−12.4140	+	9.01929i	−0.658866	+	0.478694i
$356$	−16.0351	−	11.6502i	−0.849861	−	0.617460i
$357$		0			0
$358$	−3.07093	−	9.45134i	−0.162304	−	0.499519i
$359$	−2.88567	−	2.09656i	−0.152300	−	0.110652i	0.509026	−	0.860751i	$-0.330006\pi$
$359$	−2.88567	−	2.09656i	−0.152300	−	0.110652i	−0.661326	+	0.750099i	$0.730006\pi$
$360$		0			0
$361$	11.7972	−	36.3080i	0.620905	−	1.91095i
$362$	−11.0245			−0.579436
$363$		0			0
$364$	−7.87845			−0.412943
$365$	−4.63259	+	14.2577i	−0.242481	+	0.746280i
$366$		0			0
$367$	−5.16169	−	3.75018i	−0.269438	−	0.195758i	0.444860	−	0.895600i	$-0.353254\pi$
$367$	−5.16169	−	3.75018i	−0.269438	−	0.195758i	−0.714297	+	0.699842i	$0.753254\pi$
$368$	−0.986478	−	3.03607i	−0.0514237	−	0.158266i
$369$		0			0
$370$	17.4521	+	12.6797i	0.907294	+	0.659187i
$371$	0.430074	−	0.312467i	0.0223283	−	0.0162225i
$372$		0			0
$373$	−24.6135			−1.27444			−0.637218	−	0.770683i	$-0.719915\pi$
$373$	−24.6135			−1.27444			−0.637218	+	0.770683i	$0.719915\pi$
$374$	42.3064	+	25.5578i	2.18761	+	1.32156i
$375$		0			0
$376$	−2.96648	+	9.12989i	−0.152985	+	0.470838i
$377$	−11.1881	+	8.12864i	−0.576217	+	0.418646i
$378$		0			0
$379$	9.76327	+	30.0483i	0.501506	+	1.54348i	0.806567	+	0.591143i	$0.201323\pi$
$379$	9.76327	+	30.0483i	0.501506	+	1.54348i	−0.305061	+	0.952333i	$0.598677\pi$
$380$	11.1983	+	34.4647i	0.574459	+	1.76800i
$381$		0			0
$382$	−28.9413	+	21.0271i	−1.48077	+	1.07584i
$383$	−5.25906	+	16.1857i	−0.268725	+	0.827052i	0.722086	+	0.691803i	$0.243183\pi$
$383$	−5.25906	+	16.1857i	−0.268725	+	0.827052i	−0.990812	+	0.135249i	$0.956817\pi$
$384$		0			0
$385$	−3.87117	+	3.34898i	−0.197293	+	0.170680i
$386$	18.8321			0.958531
$387$		0			0
$388$	33.2859	−	24.1836i	1.68984	−	1.22774i
$389$	−2.19079	−	1.59170i	−0.111077	−	0.0807023i	0.530860	−	0.847460i	$-0.321869\pi$
$389$	−2.19079	−	1.59170i	−0.111077	−	0.0807023i	−0.641937	+	0.766757i	$0.721869\pi$
$390$		0			0
$391$	11.4540	+	35.2519i	0.579255	+	1.78276i
$392$	2.02029	+	1.46782i	0.102040	+	0.0741363i
$393$		0			0
$394$	−2.54121	+	7.82103i	−0.128024	+	0.394018i
$395$	−3.19520			−0.160768
$396$		0			0
$397$	−20.9423			−1.05106			−0.525531	−	0.850774i	$-0.676133\pi$
$397$	−20.9423			−1.05106			−0.525531	+	0.850774i	$0.676133\pi$
$398$	3.19914	−	9.84595i	0.160359	−	0.493533i
$399$		0			0
$400$	−1.20316	−	0.874145i	−0.0601579	−	0.0437073i
$401$	3.93349	+	12.1060i	0.196429	+	0.604547i	0.999957	+	0.00927969i	$0.00295386\pi$
$401$	3.93349	+	12.1060i	0.196429	+	0.604547i	−0.803528	+	0.595267i	$0.797046\pi$
$402$		0			0
$403$	10.9311	+	7.94188i	0.544515	+	0.395613i
$404$	−13.8941	+	10.0947i	−0.691258	+	0.502228i
$405$		0			0
$406$	12.3157			0.611216
$407$	−7.97153	−	18.9050i	−0.395134	−	0.937086i
$408$		0			0
$409$	2.54958	−	7.84681i	0.126069	−	0.388000i	−0.868025	−	0.496520i	$-0.834611\pi$
$409$	2.54958	−	7.84681i	0.126069	−	0.388000i	0.994094	+	0.108520i	$0.0346111\pi$
$410$	27.6107	−	20.0604i	1.36360	−	0.990711i
$411$		0			0
$412$	6.42993	+	19.7893i	0.316780	+	0.974948i
$413$	0.544108	+	1.67459i	0.0267738	+	0.0824013i
$414$		0			0
$415$	−0.0552388	+	0.0401333i	−0.00271157	+	0.00197007i
$416$	4.92206	−	15.1486i	0.241324	−	0.742719i
$417$		0			0
$418$	12.8785	−	55.1818i	0.629906	−	2.69903i
$419$	5.81767			0.284212			0.142106	−	0.989851i	$-0.454613\pi$
$419$	5.81767			0.284212			0.142106	+	0.989851i	$0.454613\pi$
$420$		0			0
$421$	−6.15254	+	4.47008i	−0.299856	+	0.217858i	−0.727532	−	0.686074i	$-0.759333\pi$
$421$	−6.15254	+	4.47008i	−0.299856	+	0.217858i	0.427675	+	0.903932i	$0.359333\pi$
$422$	2.13771	+	1.55314i	0.104062	+	0.0756055i
$423$		0			0
$424$	−0.410226	−	1.26255i	−0.0199223	−	0.0613146i
$425$	13.9699	+	10.1497i	0.677640	+	0.492334i
$426$		0			0
$427$	1.46709	−	4.51524i	0.0709974	−	0.218508i
$428$	−17.8698			−0.863771
$429$		0			0
$430$	33.5171			1.61634
$431$	−7.21400	+	22.2024i	−0.347486	+	1.06945i	0.612753	+	0.790274i	$0.290062\pi$
$431$	−7.21400	+	22.2024i	−0.347486	+	1.06945i	−0.960239	+	0.279178i	$0.909938\pi$
$432$		0			0
$433$	10.9955	+	7.98872i	0.528412	+	0.383913i	0.819763	−	0.572703i	$-0.194105\pi$
$433$	10.9955	+	7.98872i	0.528412	+	0.383913i	−0.291352	+	0.956616i	$0.594105\pi$
$434$	−3.71831	−	11.4438i	−0.178485	−	0.549319i
$435$		0			0
$436$	−34.4322	−	25.0165i	−1.64900	−	1.19807i
$437$	34.3781	−	24.9771i	1.64453	−	1.19482i
$438$		0			0
$439$	−37.4203			−1.78597			−0.892986	−	0.450084i	$-0.851394\pi$
$439$	−37.4203			−1.78597			−0.892986	+	0.450084i	$0.851394\pi$
$440$	4.96648	+	11.7783i	0.236768	+	0.561510i
$441$		0			0
$442$	−11.6842	+	35.9603i	−0.555761	+	1.71046i
$443$	−23.6890	+	17.2111i	−1.12550	+	0.817723i	−0.985034	−	0.172363i	$-0.944860\pi$
$443$	−23.6890	+	17.2111i	−1.12550	+	0.817723i	−0.140466	+	0.990086i	$0.544860\pi$
$444$		0			0
$445$	−3.04420	−	9.36908i	−0.144309	−	0.444137i
$446$	2.74608	+	8.45158i	0.130031	+	0.400194i
$447$		0			0
$448$	−10.5566	+	7.66983i	−0.498753	+	0.362366i
$449$	1.51530	−	4.66362i	0.0715115	−	0.220090i	−0.908913	−	0.416986i	$-0.863086\pi$
$449$	1.51530	−	4.66362i	0.0715115	−	0.220090i	0.980424	+	0.196897i	$0.0630863\pi$
$450$		0			0
$451$	−32.3426	+	2.75188i	−1.52295	+	0.129581i
$452$	−45.3498			−2.13308
$453$		0			0
$454$	44.5272	−	32.3509i	2.08977	−	1.51830i
$455$	−3.16792	−	2.30163i	−0.148514	−	0.107902i
$456$		0			0
$457$	0.481305	+	1.48131i	0.0225145	+	0.0692925i	0.961682	−	0.274166i	$-0.0884016\pi$
$457$	0.481305	+	1.48131i	0.0225145	+	0.0692925i	−0.939168	+	0.343458i	$0.888402\pi$
$458$	−44.2866	−	32.1761i	−2.06938	−	1.50349i
$459$		0			0
$460$	−8.32257	+	25.6142i	−0.388042	+	1.19427i
$461$	17.6580			0.822414			0.411207	−	0.911542i	$-0.365107\pi$
$461$	17.6580			0.822414			0.411207	+	0.911542i	$0.365107\pi$
$462$		0			0
$463$	−4.54726			−0.211329			−0.105664	−	0.994402i	$-0.533697\pi$
$463$	−4.54726			−0.211329			−0.105664	+	0.994402i	$0.533697\pi$
$464$	−0.956803	+	2.94474i	−0.0444184	+	0.136706i
$465$		0			0
$466$	51.5411	+	37.4468i	2.38760	+	1.73469i
$467$	0.631244	+	1.94277i	0.0292105	+	0.0899007i	0.964599	−	0.263721i	$-0.0849499\pi$
$467$	0.631244	+	1.94277i	0.0292105	+	0.0899007i	−0.935388	+	0.353622i	$0.884950\pi$
$468$		0			0
$469$	−7.77323	−	5.64758i	−0.358935	−	0.260781i
$470$	−10.8452	+	7.87948i	−0.500250	+	0.363453i
$471$		0			0
$472$	4.39701			0.202389
$473$	−27.2853	−	16.4834i	−1.25458	−	0.757906i
$474$		0			0
$475$	6.11739	−	18.8274i	0.280685	−	0.863860i
$476$	16.5695	−	12.0385i	0.759464	−	0.551783i
$477$		0			0
$478$	−13.0142	−	40.0535i	−0.595254	−	1.83200i
$479$	2.51277	+	7.73350i	0.114811	+	0.353353i	0.991908	−	0.126962i	$-0.0405226\pi$
$479$	2.51277	+	7.73350i	0.114811	+	0.353353i	−0.877096	+	0.480314i	$0.840523\pi$
$480$		0			0
$481$	12.6976	−	9.22536i	0.578962	−	0.420640i
$482$	12.2058	−	37.5656i	0.555959	−	1.71107i
$483$		0			0
$484$	4.91512	−	33.8019i	0.223415	−	1.53645i
$485$	20.4493			0.928555
$486$		0			0
$487$	23.2813	−	16.9149i	1.05498	−	0.766485i	0.0818241	−	0.996647i	$-0.473925\pi$
$487$	23.2813	−	16.9149i	1.05498	−	0.766485i	0.973152	+	0.230161i	$0.0739254\pi$
$488$	−9.59152	−	6.96865i	−0.434188	−	0.315456i
$489$		0			0
$490$	1.07760	+	3.31651i	0.0486810	+	0.149825i
$491$	−4.28191	−	3.11099i	−0.193240	−	0.140397i	0.486958	−	0.873425i	$-0.338106\pi$
$491$	−4.28191	−	3.11099i	−0.193240	−	0.140397i	−0.680198	+	0.733028i	$0.738106\pi$
$492$		0			0
$493$	11.1095	−	34.1914i	0.500346	−	1.53991i
$494$	43.3476			1.95030
$495$		0			0
$496$	3.02514			0.135833
$497$	3.07233	−	9.45567i	0.137813	−	0.424145i
$498$		0			0
$499$	20.6031	+	14.9690i	0.922319	+	0.670104i	0.944100	−	0.329659i	$-0.106934\pi$
$499$	20.6031	+	14.9690i	0.922319	+	0.670104i	−0.0217809	+	0.999763i	$0.506934\pi$
$500$	11.2820	+	34.7224i	0.504545	+	1.55283i
$501$		0			0
$502$	−7.38701	−	5.36698i	−0.329698	−	0.239540i
$503$	−33.9895	+	24.6948i	−1.51552	+	1.10109i	−0.551861	+	0.833936i	$0.686082\pi$
$503$	−33.9895	+	24.6948i	−1.51552	+	1.10109i	−0.963655	+	0.267150i	$0.913918\pi$
$504$		0			0
$505$	−8.53588			−0.379842
$506$	31.8491	−	27.5529i	1.41586	−	1.22487i
$507$		0			0
$508$	12.9602	−	39.8873i	0.575014	−	1.76971i
$509$	−25.8755	+	18.7996i	−1.14691	+	0.833279i	−0.988067	−	0.154025i	$-0.950776\pi$
$509$	−25.8755	+	18.7996i	−1.14691	+	0.833279i	−0.158843	+	0.987304i	$0.550776\pi$
$510$		0			0
$511$	−3.00163	−	9.23805i	−0.132784	−	0.408667i
$512$	−1.97873	−	6.08990i	−0.0874483	−	0.269138i
$513$		0			0
$514$	17.7033	−	12.8622i	0.780857	−	0.567326i
$515$	−3.19581	+	9.83570i	−0.140824	+	0.433413i
$516$		0			0
$517$	12.7038	−	1.08091i	0.558713	−	0.0475383i
$518$	−13.9773			−0.614127
$519$		0			0
$520$	−7.91097	+	5.74765i	−0.346919	+	0.252051i
$521$	27.4604	+	19.9512i	1.20306	+	0.874076i	0.994582	−	0.103951i	$-0.0331485\pi$
$521$	27.4604	+	19.9512i	1.20306	+	0.874076i	0.208480	+	0.978027i	$0.433148\pi$
$522$		0			0
$523$	5.31280	+	16.3511i	0.232313	+	0.714985i	0.997467	+	0.0711373i	$0.0226628\pi$
$523$	5.31280	+	16.3511i	0.232313	+	0.714985i	−0.765154	+	0.643847i	$0.777337\pi$
$524$	10.8093	+	7.85341i	0.472206	+	0.343078i
$525$		0			0
$526$	−3.55274	+	10.9342i	−0.154907	+	0.476754i
$527$	−35.1250			−1.53007
$528$		0			0
$529$	8.58133			0.373101
$530$	0.572852	−	1.76306i	0.0248831	−	0.0765823i
$531$		0			0
$532$	−18.9958	−	13.8013i	−0.823574	−	0.598362i
$533$	−7.67319	−	23.6157i	−0.332363	−	1.02291i
$534$		0			0
$535$	−7.18545	−	5.22053i	−0.310654	−	0.225703i
$536$	−19.4114	+	14.1032i	−0.838445	+	0.609166i
$537$		0			0
$538$	0.507492			0.0218796
$539$	0.753785	−	3.22983i	0.0324678	−	0.139119i
$540$		0			0
$541$	2.36527	−	7.27956i	0.101691	−	0.312973i	−0.887249	−	0.461292i	$-0.847386\pi$
$541$	2.36527	−	7.27956i	0.101691	−	0.312973i	0.988940	+	0.148319i	$0.0473862\pi$
$542$	−44.5271	+	32.3509i	−1.91260	+	1.38959i
$543$		0			0
$544$	12.7956	+	39.3807i	0.548605	+	1.68843i
$545$	−6.53680	−	20.1182i	−0.280006	−	0.861769i
$546$		0			0
$547$	32.2902	−	23.4602i	1.38063	−	1.00308i	0.383806	−	0.923414i	$-0.374613\pi$
$547$	32.2902	−	23.4602i	1.38063	−	1.00308i	0.996821	−	0.0796709i	$-0.0253869\pi$
$548$	12.0219	−	36.9997i	0.513551	−	1.58055i
$549$		0			0
$550$	4.45892	−	19.1057i	0.190129	−	0.814668i
$551$	−41.2154			−1.75583
$552$		0			0
$553$	1.67490	−	1.21688i	0.0712239	−	0.0517472i
$554$	−31.9887	−	23.2411i	−1.35907	−	0.987421i
$555$		0			0
$556$	10.7723	+	33.1539i	0.456849	+	1.40604i
$557$	14.0186	+	10.1851i	0.593989	+	0.431558i	0.843740	−	0.536752i	$-0.180349\pi$
$557$	14.0186	+	10.1851i	0.593989	+	0.431558i	−0.249751	+	0.968310i	$0.580349\pi$
$558$		0			0
$559$	7.53567	−	23.1924i	0.318725	−	0.980934i
$560$	−0.876713			−0.0370479
$561$		0			0
$562$	32.4346			1.36817
$563$	−11.3506	+	34.9334i	−0.478369	+	1.47227i	0.362991	+	0.931793i	$0.381756\pi$
$563$	−11.3506	+	34.9334i	−0.478369	+	1.47227i	−0.841360	+	0.540476i	$0.818244\pi$
$564$		0			0
$565$	−18.2351	−	13.2486i	−0.767158	−	0.557373i
$566$	−19.5538	−	60.1806i	−0.821909	−	2.52958i
$567$		0			0
$568$	−20.0863	−	14.5935i	−0.842801	−	0.612331i
$569$	25.0590	−	18.2064i	1.05053	−	0.763252i	0.0782135	−	0.996937i	$-0.475078\pi$
$569$	25.0590	−	18.2064i	1.05053	−	0.763252i	0.972312	+	0.233685i	$0.0750784\pi$
$570$		0			0
$571$	26.7450			1.11925			0.559623	−	0.828748i	$-0.310946\pi$
$571$	26.7450			1.11925			0.559623	+	0.828748i	$0.310946\pi$
$572$	26.0358	−	2.21526i	1.08861	−	0.0926249i
$573$		0			0
$574$	−6.83337	+	21.0309i	−0.285219	+	0.877814i
$575$	11.9028	−	8.64787i	0.496380	−	0.360641i
$576$		0			0
$577$	−9.47227	−	29.1526i	−0.394336	−	1.21364i	−0.929478	−	0.368878i	$-0.879742\pi$
$577$	−9.47227	−	29.1526i	−0.394336	−	1.21364i	0.535142	−	0.844762i	$-0.320258\pi$
$578$	−18.5050	−	56.9524i	−0.769705	−	2.36891i
$579$		0			0
$580$	21.1333	−	15.3543i	0.877514	−	0.637551i
$581$	0.0136710	−	0.0420751i	0.000567170	−	0.00174557i
$582$		0			0
$583$	−1.33340	+	1.15353i	−0.0552237	+	0.0477744i
$584$	−24.2566			−1.00374
$585$		0			0
$586$	−24.4190	+	17.7414i	−1.00874	+	0.732892i
$587$	−13.4594	−	9.77880i	−0.555528	−	0.403614i	0.274292	−	0.961647i	$-0.411557\pi$
$587$	−13.4594	−	9.77880i	−0.555528	−	0.403614i	−0.829819	+	0.558032i	$0.811557\pi$
$588$		0			0
$589$	12.4436	+	38.2976i	0.512731	+	1.57802i
$590$	4.96747	+	3.60908i	0.204507	+	0.148583i
$591$		0			0
$592$	1.08590	−	3.34204i	0.0446300	−	0.137357i
$593$	37.7740			1.55119			0.775596	−	0.631230i	$-0.217450\pi$
$593$	37.7740			1.55119			0.775596	+	0.631230i	$0.217450\pi$
$594$		0			0
$595$	10.1795			0.417321
$596$	−11.6252	+	35.7787i	−0.476186	+	1.46555i
$597$		0			0
$598$	26.0633	+	18.9361i	1.06581	+	0.774353i
$599$	−7.74200	−	23.8274i	−0.316330	−	0.973562i	−0.975204	−	0.221309i	$-0.928967\pi$
$599$	−7.74200	−	23.8274i	−0.316330	−	0.973562i	0.658874	−	0.752253i	$-0.271033\pi$
$600$		0			0
$601$	34.7268	+	25.2305i	1.41654	+	1.02917i	0.992331	+	0.123607i	$0.0394463\pi$
$601$	34.7268	+	25.2305i	1.41654	+	1.02917i	0.424205	+	0.905566i	$0.360554\pi$
$602$	−17.5694	+	12.7649i	−0.716073	+	0.520258i
$603$		0			0
$604$	33.4985			1.36303
$605$	11.8513	−	12.1558i	0.481825	−	0.494204i
$606$		0			0
$607$	2.69740	−	8.30174i	0.109484	−	0.336957i	−0.881273	−	0.472608i	$-0.843313\pi$
$607$	2.69740	−	8.30174i	0.109484	−	0.336957i	0.990757	+	0.135651i	$0.0433126\pi$
$608$	38.4045	−	27.9025i	1.55751	−	1.13160i
$609$		0			0
$610$	−5.11601	−	15.7455i	−0.207141	−	0.637515i
$611$	3.01394	+	9.27596i	0.121931	+	0.375265i
$612$		0			0
$613$	−7.11370	+	5.16840i	−0.287319	+	0.208750i	−0.722104	−	0.691785i	$-0.756825\pi$
$613$	−7.11370	+	5.16840i	−0.287319	+	0.208750i	0.434784	+	0.900535i	$0.356825\pi$
$614$	2.19707	−	6.76188i	0.0886664	−	0.272887i
$615$		0			0
$616$	−7.08913	−	4.28263i	−0.285629	−	0.172552i
$617$	−8.31423			−0.334718			−0.167359	−	0.985896i	$-0.553524\pi$
$617$	−8.31423			−0.334718			−0.167359	+	0.985896i	$0.553524\pi$
$618$		0			0
$619$	−1.90794	+	1.38620i	−0.0766866	+	0.0557161i	−0.625468	−	0.780250i	$-0.715092\pi$
$619$	−1.90794	+	1.38620i	−0.0766866	+	0.0557161i	0.548781	+	0.835966i	$0.315092\pi$
$620$	−20.6478	−	15.0015i	−0.829235	−	0.602475i
$621$		0			0
$622$	−17.1480	−	52.7762i	−0.687574	−	2.11613i
$623$	5.16393	+	3.75182i	0.206889	+	0.150313i
$624$		0			0
$625$	−1.56231	+	4.80828i	−0.0624922	+	0.192331i
$626$	48.6791			1.94561
$627$		0			0
$628$	−11.4985			−0.458838
$629$	−12.6084	+	38.8046i	−0.502729	+	1.54724i
$630$		0			0
$631$	−32.6274	−	23.7052i	−1.29888	−	0.943689i	−0.298932	−	0.954274i	$-0.596631\pi$
$631$	−32.6274	−	23.7052i	−1.29888	−	0.943689i	−0.999944	+	0.0105854i	$0.996631\pi$
$632$	−1.59760	−	4.91691i	−0.0635492	−	0.195584i
$633$		0			0
$634$	−13.5007	−	9.80886i	−0.536183	−	0.389560i
$635$	16.8640	−	12.2524i	0.669228	−	0.486223i
$636$		0			0
$637$	2.53716			0.100526
$638$	−40.6994	+	3.46292i	−1.61130	+	0.137098i
$639$		0			0
$640$	−8.07307	+	24.8463i	−0.319116	+	0.982138i
$641$	−10.2731	+	7.46384i	−0.405763	+	0.294804i	−0.771884	−	0.635763i	$-0.780686\pi$
$641$	−10.2731	+	7.46384i	−0.405763	+	0.294804i	0.366121	+	0.930567i	$0.380686\pi$
$642$		0			0
$643$	4.55209	+	14.0099i	0.179517	+	0.552497i	0.999811	−	0.0194456i	$-0.00619011\pi$
$643$	4.55209	+	14.0099i	0.179517	+	0.552497i	−0.820294	+	0.571942i	$0.806190\pi$
$644$	−5.39250	−	16.5964i	−0.212494	−	0.653990i
$645$		0			0
$646$	−91.1663	+	66.2362i	−3.58689	+	2.60603i
$647$	−1.43416	+	4.41390i	−0.0563828	+	0.173528i	−0.975282	−	0.220964i	$-0.929080\pi$
$647$	−1.43416	+	4.41390i	−0.0563828	+	0.173528i	0.918899	+	0.394493i	$0.129080\pi$
$648$		0			0
$649$	−2.26897	−	5.38100i	−0.0890647	−	0.211223i
$650$	15.0083			0.588673
$651$		0			0
$652$	−56.6362	+	41.1486i	−2.21805	+	1.61150i
$653$	18.5028	+	13.4431i	0.724071	+	0.526068i	0.887682	−	0.460457i	$-0.152314\pi$
$653$	18.5028	+	13.4431i	0.724071	+	0.526068i	−0.163611	+	0.986525i	$0.552314\pi$
$654$		0			0
$655$	2.05209	+	6.31570i	0.0801820	+	0.246775i
$656$	−4.49772	−	3.26779i	−0.175606	−	0.127586i
$657$		0			0
$658$	2.68407	−	8.26071i	0.104636	−	0.322036i
$659$	17.8597			0.695717			0.347858	−	0.937547i	$-0.386909\pi$
$659$	17.8597			0.695717			0.347858	+	0.937547i	$0.386909\pi$
$660$		0			0
$661$	−18.7110			−0.727774			−0.363887	−	0.931443i	$-0.618551\pi$
$661$	−18.7110			−0.727774			−0.363887	+	0.931443i	$0.618551\pi$
$662$	14.7251	−	45.3193i	0.572309	−	1.76139i
$663$		0			0
$664$	−0.0893782	−	0.0649371i	−0.00346855	−	0.00252005i
$665$	−3.60628	−	11.0990i	−0.139845	−	0.430400i
$666$		0			0
$667$	−24.7813	−	18.0046i	−0.959534	−	0.697142i
$668$	35.7173	−	25.9502i	1.38195	−	1.00404i
$669$		0			0
$670$	−33.5057			−1.29444
$671$	−3.57867	+	15.3340i	−0.138153	+	0.591961i
$672$		0			0
$673$	2.21223	−	6.80855i	0.0852753	−	0.262450i	−0.899322	−	0.437287i	$-0.855940\pi$
$673$	2.21223	−	6.80855i	0.0852753	−	0.262450i	0.984598	+	0.174836i	$0.0559395\pi$
$674$	−37.1024	+	26.9565i	−1.42913	+	1.03832i
$675$		0			0
$676$	−6.29743	−	19.3815i	−0.242209	−	0.745442i
$677$	−7.10903	−	21.8793i	−0.273222	−	0.840892i	−0.989684	−	0.143265i	$-0.954240\pi$
$677$	−7.10903	−	21.8793i	−0.273222	−	0.840892i	0.716462	−	0.697626i	$-0.245760\pi$
$678$		0			0
$679$	−10.7193	+	7.78806i	−0.411371	+	0.298878i
$680$	7.85536	−	24.1763i	0.301239	−	0.927120i
$681$		0			0
$682$	15.5056	+	36.7726i	0.593740	+	1.40809i
$683$	−18.0889			−0.692152			−0.346076	−	0.938206i	$-0.612486\pi$
$683$	−18.0889			−0.692152			−0.346076	+	0.938206i	$0.612486\pi$
$684$		0			0
$685$	15.6432	−	11.3654i	0.597695	−	0.434251i
$686$	−1.82795	−	1.32808i	−0.0697915	−	0.0507065i
$687$		0			0
$688$	−1.68719	−	5.19262i	−0.0643234	−	0.197967i
$689$	−1.09117	−	0.792780i	−0.0415702	−	0.0302025i
$690$		0			0
$691$	−8.24611	+	25.3789i	−0.313697	+	0.965459i	0.662591	+	0.748982i	$0.269457\pi$
$691$	−8.24611	+	25.3789i	−0.313697	+	0.965459i	−0.976288	+	0.216478i	$0.930543\pi$
$692$	−58.6232			−2.22852
$693$		0			0
$694$	−37.0961			−1.40815
$695$	−5.35409	+	16.4782i	−0.203092	+	0.625054i
$696$		0			0
$697$	52.2232	+	37.9424i	1.97810	+	1.43717i
$698$	19.8277	+	61.0234i	0.750490	+	2.30977i
$699$		0			0
$700$	−6.57696	−	4.77844i	−0.248586	−	0.180608i
$701$	11.5341	−	8.38001i	0.435637	−	0.316509i	−0.348262	−	0.937397i	$-0.613228\pi$
$701$	11.5341	−	8.38001i	0.435637	−	0.316509i	0.783899	+	0.620889i	$0.213228\pi$
$702$		0			0
$703$	46.7762			1.76420
$704$	32.7297	−	28.3147i	1.23355	−	1.06715i
$705$		0			0
$706$	−4.56718	+	14.0563i	−0.171888	+	0.529017i
$707$	4.47444	−	3.25087i	0.168279	−	0.122261i
$708$		0			0
$709$	4.96231	+	15.2724i	0.186364	+	0.573568i	0.999969	−	0.00784897i	$-0.00249843\pi$
$709$	4.96231	+	15.2724i	0.186364	+	0.573568i	−0.813606	+	0.581417i	$0.802498\pi$
$710$	−10.7138	−	32.9737i	−0.402082	−	1.23748i
$711$		0			0
$712$	12.8954	−	9.36908i	0.483277	−	0.351121i
$713$	−9.24812	+	28.4628i	−0.346345	+	1.06594i
$714$		0			0
$715$	11.1161	+	6.71540i	0.415720	+	0.251142i
$716$	13.6575			0.510406
$717$		0			0
$718$	6.52009	−	4.73713i	0.243328	−	0.176788i
$719$	29.9838	+	21.7845i	1.11821	+	0.812426i	0.983937	−	0.178519i	$-0.0571305\pi$
$719$	29.9838	+	21.7845i	1.11821	+	0.812426i	0.134272	+	0.990945i	$0.457131\pi$
$720$		0			0
$721$	−2.07068	−	6.37291i	−0.0771163	−	0.237340i
$722$	69.7848	+	50.7016i	2.59712	+	1.88692i
$723$		0			0
$724$	4.68195	−	14.4096i	0.174003	−	0.535527i
$725$	−14.2701			−0.529977
$726$		0			0
$727$	14.6597			0.543698			0.271849	−	0.962340i	$-0.412365\pi$
$727$	14.6597			0.543698			0.271849	+	0.962340i	$0.412365\pi$
$728$	1.95788	−	6.02574i	0.0725639	−	0.223329i
$729$		0			0
$730$	−27.4035	−	19.9098i	−1.01425	−	0.736896i
$731$	19.5900	+	60.2918i	0.724562	+	2.22997i
$732$		0			0
$733$	23.4255	+	17.0196i	0.865240	+	0.628633i	0.929305	−	0.369312i	$-0.120407\pi$
$733$	23.4255	+	17.0196i	0.865240	+	0.628633i	−0.0640657	+	0.997946i	$0.520407\pi$
$734$	11.6627	−	8.47344i	0.430478	−	0.312760i
$735$		0			0
$736$	35.2802			1.30045
$737$	27.2761	+	16.4778i	1.00473	+	0.606968i
$738$		0			0
$739$	2.60786	−	8.02617i	0.0959317	−	0.295247i	−0.891564	−	0.452895i	$-0.850391\pi$
$739$	2.60786	−	8.02617i	0.0959317	−	0.295247i	0.987495	+	0.157648i	$0.0503911\pi$
$740$	−23.9847	+	17.4259i	−0.881694	+	0.640588i
$741$		0			0
$742$	0.371172	+	1.14235i	0.0136261	+	0.0419370i
$743$	−14.7531	−	45.4054i	−0.541239	−	1.66576i	−0.729768	−	0.683694i	$-0.760372\pi$
$743$	−14.7531	−	45.4054i	−0.541239	−	1.66576i	0.188530	−	0.982067i	$-0.439628\pi$
$744$		0			0
$745$	−15.1269	+	10.9904i	−0.554208	+	0.402656i
$746$	17.1855	−	52.8915i	0.629206	−	1.93650i
$747$		0			0
$748$	−51.3721	+	44.4424i	−1.87835	+	1.62497i
$749$	5.75478			0.210275
$750$		0			0
$751$	0.753694	−	0.547591i	0.0275027	−	0.0199819i	−0.573949	−	0.818891i	$-0.694589\pi$
$751$	0.753694	−	0.547591i	0.0275027	−	0.0199819i	0.601452	+	0.798909i	$0.294589\pi$
$752$	1.76665	+	1.28355i	0.0644232	+	0.0468062i
$753$		0			0
$754$	−9.65581	−	29.7175i	−0.351644	−	1.08225i
$755$	13.4697	+	9.78631i	0.490213	+	0.356160i
$756$		0			0
$757$	−4.91728	+	15.1338i	−0.178722	+	0.550049i	−0.999784	−	0.0207901i	$-0.993382\pi$
$757$	−4.91728	+	15.1338i	−0.178722	+	0.550049i	0.821062	+	0.570839i	$0.193382\pi$
$758$	−71.3872			−2.59290
$759$		0			0
$760$	−29.1428			−1.05712
$761$	−0.0685939	+	0.211110i	−0.00248653	+	0.00765274i	−0.952292	−	0.305188i	$-0.901281\pi$
$761$	−0.0685939	+	0.211110i	−0.00248653	+	0.00765274i	0.949806	+	0.312841i	$0.101281\pi$
$762$		0			0
$763$	11.0885	+	8.05626i	0.401430	+	0.291656i
$764$	−15.1925	−	46.7576i	−0.549644	−	1.69163i
$765$		0			0
$766$	−31.1093	−	22.6022i	−1.12403	−	0.816652i
$767$	3.61417	−	2.62585i	0.130500	−	0.0948139i
$768$		0			0
$769$	−44.0307			−1.58779			−0.793894	−	0.608056i	$-0.791949\pi$
$769$	−44.0307			−1.58779			−0.793894	+	0.608056i	$0.791949\pi$
$770$	−4.49366	−	10.6570i	−0.161940	−	0.384052i
$771$		0			0
$772$	−7.99773	+	24.6145i	−0.287845	+	0.885895i
$773$	−35.9008	+	26.0835i	−1.29126	+	0.938158i	−0.999830	−	0.0184332i	$-0.994132\pi$
$773$	−35.9008	+	26.0835i	−1.29126	+	0.938158i	−0.291433	+	0.956591i	$0.594132\pi$
$774$		0			0
$775$	4.30838	+	13.2598i	0.154761	+	0.476307i
$776$	10.2246	+	31.4682i	0.367043	+	1.12964i
$777$		0			0
$778$	4.95002	−	3.59640i	0.177467	−	0.128937i
$779$	22.8684	−	70.3818i	0.819346	−	2.52169i
$780$		0			0
$781$	−7.49435	+	32.1119i	−0.268169	+	1.14905i
$782$	−83.7497			−2.99488
$783$		0			0
$784$	0.459565	−	0.333894i	0.0164130	−	0.0119248i
$785$	−4.62352	−	3.35918i	−0.165020	−	0.119894i
$786$		0			0
$787$	−5.32459	−	16.3874i	−0.189801	−	0.584148i	0.810197	−	0.586158i	$-0.199360\pi$
$787$	−5.32459	−	16.3874i	−0.189801	−	0.584148i	−0.999998	+	0.00200988i	$0.999360\pi$
$788$	−9.14324	−	6.64296i	−0.325715	−	0.236645i
$789$		0			0
$790$	2.23094	−	6.86613i	0.0793733	−	0.244286i
$791$	14.6044			0.519272
$792$		0			0
$793$	−12.0454			−0.427746
$794$	14.6222	−	45.0025i	0.518923	−	1.59708i
$795$		0			0
$796$	11.5105	+	8.36287i	0.407979	+	0.296414i
$797$	−10.1146	−	31.1294i	−0.358276	−	1.10266i	−0.954085	−	0.299535i	$-0.903168\pi$
$797$	−10.1146	−	31.1294i	−0.358276	−	1.10266i	0.595809	−	0.803126i	$-0.296832\pi$
$798$		0			0
$799$	−20.5127	−	14.9033i	−0.725686	−	0.527242i
$800$	13.2969	−	9.66074i	0.470115	−	0.341559i
$801$		0			0
$802$	−28.7609			−1.01558
$803$	12.5170	+	29.6848i	0.441715	+	1.04756i
$804$		0			0
$805$	2.68019	−	8.24877i	0.0944642	−	0.290731i
$806$	−24.6984	+	17.9445i	−0.869965	+	0.632067i
$807$		0			0
$808$	−4.26794	−	13.1354i	−0.150146	−	0.462101i
$809$	−11.4251	−	35.1629i	−0.401686	−	1.23626i	−0.923631	−	0.383283i	$-0.874793\pi$
$809$	−11.4251	−	35.1629i	−0.401686	−	1.23626i	0.521945	−	0.852979i	$-0.325207\pi$
$810$		0			0
$811$	13.3164	−	9.67497i	0.467604	−	0.339734i	−0.328903	−	0.944364i	$-0.606679\pi$
$811$	13.3164	−	9.67497i	0.467604	−	0.339734i	0.796507	+	0.604630i	$0.206679\pi$
$812$	−5.23028	+	16.0971i	−0.183547	+	0.564899i
$813$		0			0
$814$	46.1906	−	3.93014i	1.61898	−	0.137751i
$815$	−34.7946			−1.21880
$816$		0			0
$817$	58.7973	−	42.7187i	2.05706	−	1.49454i
$818$	15.0818	+	10.9575i	0.527321	+	0.383121i
$819$		0			0
$820$	14.4940	+	44.6079i	0.506152	+	1.55777i
$821$	−6.05473	−	4.39902i	−0.211312	−	0.153527i	0.477095	−	0.878852i	$-0.341690\pi$
$821$	−6.05473	−	4.39902i	−0.211312	−	0.153527i	−0.688407	+	0.725325i	$0.741690\pi$
$822$		0			0
$823$	−14.7159	+	45.2909i	−0.512965	+	1.57874i	0.273990	+	0.961733i	$0.411656\pi$
$823$	−14.7159	+	45.2909i	−0.512965	+	1.57874i	−0.786955	+	0.617011i	$0.788344\pi$
$824$	−16.7335			−0.582939
$825$		0			0
$826$	−3.97841			−0.138427
$827$	−11.6888	+	35.9745i	−0.406460	+	1.25095i	0.513210	+	0.858263i	$0.328456\pi$
$827$	−11.6888	+	35.9745i	−0.406460	+	1.25095i	−0.919670	+	0.392692i	$0.871544\pi$
$828$		0			0
$829$	5.07270	+	3.68554i	0.176182	+	0.128004i	0.672382	−	0.740205i	$-0.265271\pi$
$829$	5.07270	+	3.68554i	0.176182	+	0.128004i	−0.496199	+	0.868209i	$0.665271\pi$
$830$	−0.0476734	−	0.146724i	−0.00165477	−	0.00509285i
$831$		0			0
$832$	26.7839	+	19.4596i	0.928564	+	0.674641i
$833$	−5.33603	+	3.87685i	−0.184883	+	0.134325i
$834$		0			0
$835$	21.9431			0.759371
$836$	66.6559	+	40.2676i	2.30534	+	1.39269i
$837$		0			0
$838$	−4.06199	+	12.5015i	−0.140319	+	0.431858i
$839$	−11.2286	+	8.15804i	−0.387654	+	0.281647i	−0.764493	−	0.644632i	$-0.777011\pi$
$839$	−11.2286	+	8.15804i	−0.387654	+	0.281647i	0.376840	+	0.926279i	$0.377011\pi$
$840$		0			0
$841$	0.219362	+	0.675127i	0.00756421	+	0.0232802i
$842$	−5.30990	−	16.3422i	−0.182991	−	0.563189i
$843$		0			0
$844$	−2.93788	+	2.13449i	−0.101126	+	0.0734723i
$845$	3.12996	−	9.63303i	0.107674	−	0.331386i
$846$		0			0
$847$	−1.58286	+	10.8855i	−0.0543877	+	0.374031i
$848$	−0.301978			−0.0103700
$849$		0			0
$850$	−31.5646	+	22.9331i	−1.08266	+	0.786597i
$851$	28.1248	+	20.4338i	0.964105	+	0.700463i
$852$		0			0
$853$	−7.86783	−	24.2147i	−0.269389	−	0.829095i	−0.990650	−	0.136431i	$-0.956437\pi$
$853$	−7.86783	−	24.2147i	−0.269389	−	0.829095i	0.721260	−	0.692664i	$-0.243563\pi$
$854$	8.67839	+	6.30522i	0.296968	+	0.215760i
$855$		0			0
$856$	4.44085	−	13.6675i	0.151785	−	0.467147i
$857$	−50.8757			−1.73788			−0.868941	−	0.494916i	$-0.835199\pi$
$857$	−50.8757			−1.73788			−0.868941	+	0.494916i	$0.835199\pi$
$858$		0			0
$859$	−37.2976			−1.27258			−0.636288	−	0.771452i	$-0.719531\pi$
$859$	−37.2976			−1.27258			−0.636288	+	0.771452i	$0.719531\pi$
$860$	−14.2342	+	43.8084i	−0.485382	+	1.49385i
$861$		0			0
$862$	−42.6735	−	31.0041i	−1.45347	−	1.05600i
$863$	−3.97930	−	12.2470i	−0.135457	−	0.416893i	0.860204	−	0.509950i	$-0.170336\pi$
$863$	−3.97930	−	12.2470i	−0.135457	−	0.416893i	−0.995661	+	0.0930569i	$0.970336\pi$
$864$		0			0
$865$	−23.5724	−	17.1263i	−0.801484	−	0.582312i
$866$	−24.8441	+	18.0503i	−0.844237	+	0.613374i
$867$		0			0
$868$	16.5367			0.561291
$869$	−5.19284	+	4.49237i	−0.176155	+	0.152393i
$870$		0			0
$871$	−7.53312	+	23.1846i	−0.255250	+	0.785579i
$872$	27.6903	−	20.1182i	0.937713	−	0.681288i
$873$		0			0
$874$	29.6697	+	91.3140i	1.00359	+	3.08874i
$875$	−3.63323	−	11.1819i	−0.122826	−	0.378018i
$876$		0			0
$877$	8.74591	−	6.35428i	0.295328	−	0.214569i	−0.430247	−	0.902711i	$-0.641574\pi$
$877$	8.74591	−	6.35428i	0.295328	−	0.214569i	0.725576	+	0.688142i	$0.241574\pi$
$878$	26.1274	−	80.4119i	0.881758	−	2.71377i
$879$		0			0
$880$	2.89726	−	0.246514i	0.0976666	−	0.00831000i
$881$	−19.9303			−0.671467			−0.335734	−	0.941957i	$-0.608984\pi$
$881$	−19.9303			−0.671467			−0.335734	+	0.941957i	$0.608984\pi$
$882$		0			0
$883$	21.9722	−	15.9637i	0.739422	−	0.537221i	−0.153108	−	0.988209i	$-0.548928\pi$
$883$	21.9722	−	15.9637i	0.739422	−	0.537221i	0.892530	+	0.450988i	$0.148928\pi$
$884$	−42.0397	−	30.5436i	−1.41395	−	1.02729i
$885$		0			0
$886$	−20.4446	−	62.9221i	−0.686850	−	2.11391i
$887$	5.15401	+	3.74461i	0.173055	+	0.125732i	0.670941	−	0.741511i	$-0.265890\pi$
$887$	5.15401	+	3.74461i	0.173055	+	0.125732i	−0.497886	+	0.867242i	$0.665890\pi$
$888$		0			0
$889$	−4.17367	+	12.8452i	−0.139980	+	0.430815i
$890$	22.2586			0.746110
$891$		0			0
$892$	−12.2128			−0.408916
$893$	−8.98245	+	27.6451i	−0.300586	+	0.925110i
$894$		0			0
$895$	5.49168	+	3.98994i	0.183567	+	0.133369i
$896$	−5.23083	−	16.0988i	−0.174750	−	0.537825i
$897$		0			0
$898$	8.96358	+	6.51242i	0.299118	+	0.217322i
$899$	23.4836	−	17.0618i	0.783221	−	0.569043i
$900$		0			0
$901$	3.50628			0.116811
$902$	16.6686	−	71.4220i	0.555005	−	2.37809i
$903$		0			0
$904$	11.2699	−	34.6853i	0.374832	−	1.15362i
$905$	6.09225	−	4.42628i	0.202513	−	0.147135i
$906$		0			0
$907$	−3.47376	−	10.6911i	−0.115344	−	0.354993i	0.876674	−	0.481084i	$-0.159757\pi$
$907$	−3.47376	−	10.6911i	−0.115344	−	0.354993i	−0.992019	+	0.126091i	$0.959757\pi$
$908$	23.3741	+	71.9382i	0.775698	+	2.38735i
$909$		0			0
$910$	7.15783	−	5.20047i	0.237280	−	0.172394i
$911$	−9.99054	+	30.7477i	−0.331001	+	1.01872i	0.637657	+	0.770321i	$0.279904\pi$
$911$	−9.99054	+	30.7477i	−0.331001	+	1.01872i	−0.968658	+	0.248397i	$0.920096\pi$
$912$		0			0
$913$	−0.0333477	+	0.142889i	−0.00110365	+	0.00472893i
$914$	−3.51921			−0.116405
$915$		0			0
$916$	60.8636	−	44.2200i	2.01099	−	1.46107i
$917$	−3.48101	−	2.52910i	−0.114953	−	0.0835182i
$918$		0			0
$919$	−5.24659	−	16.1473i	−0.173069	−	0.532651i	0.826471	−	0.562979i	$-0.190345\pi$
$919$	−5.24659	−	16.1473i	−0.173069	−	0.532651i	−0.999540	+	0.0303279i	$0.990345\pi$
$920$	−17.5225	−	12.7308i	−0.577700	−	0.419723i
$921$		0			0
$922$	−12.3291	+	37.9450i	−0.406037	+	1.24965i
$923$	−25.2252			−0.830298
$924$		0			0
$925$	16.1954			0.532501
$926$	3.17497	−	9.77154i	0.104336	−	0.321113i
$927$		0			0
$928$	−27.6837	−	20.1134i	−0.908762	−	0.660254i
$929$	2.19807	+	6.76495i	0.0721162	+	0.221951i	0.980618	−	0.195931i	$-0.0627727\pi$
$929$	2.19807	+	6.76495i	0.0721162	+	0.221951i	−0.908502	+	0.417881i	$0.862773\pi$
$930$		0			0
$931$	6.11739	+	4.44455i	0.200489	+	0.145664i
$932$	−70.8335	+	51.4636i	−2.32023	+	1.68575i
$933$		0			0
$934$	−4.61554			−0.151025
$935$	−33.6402	+	2.86229i	−1.10015	+	0.0936068i
$936$		0			0
$937$	4.83045	−	14.8666i	0.157804	−	0.485671i	−0.840630	−	0.541610i	$-0.817815\pi$
$937$	4.83045	−	14.8666i	0.157804	−	0.485671i	0.998434	+	0.0559386i	$0.0178151\pi$
$938$	17.5634	−	12.7606i	0.573466	−	0.416647i
$939$		0			0
$940$	−5.69307	−	17.5215i	−0.185687	−	0.571487i
$941$	−1.56074	−	4.80345i	−0.0508785	−	0.156588i	0.922389	−	0.386262i	$-0.126234\pi$
$941$	−1.56074	−	4.80345i	−0.0508785	−	0.156588i	−0.973268	+	0.229674i	$0.926234\pi$
$942$		0			0
$943$	44.4957	−	32.3280i	1.44898	−	1.05275i
$944$	0.309083	−	0.951258i	0.0100598	−	0.0309608i
$945$		0			0
$946$	54.4719	−	47.1241i	1.77104	−	1.53214i
$947$	20.3081			0.659925			0.329963	−	0.943994i	$-0.392964\pi$
$947$	20.3081			0.659925			0.329963	+	0.943994i	$0.392964\pi$
$948$		0			0
$949$	−19.9379	+	14.4858i	−0.647213	+	0.470228i
$950$	36.1867	+	26.2912i	1.17405	+	0.852998i
$951$		0			0
$952$	5.08977	+	15.6647i	0.164961	+	0.507696i
$953$	23.7390	+	17.2474i	0.768983	+	0.558699i	0.901652	−	0.432462i	$-0.142355\pi$
$953$	23.7390	+	17.2474i	0.768983	+	0.558699i	−0.132670	+	0.991160i	$0.542355\pi$
$954$		0			0
$955$	7.55098	−	23.2395i	0.244344	−	0.752014i
$956$	57.8787			1.87193
$957$		0			0
$958$	−18.3729			−0.593600
$959$	−3.87152	+	11.9153i	−0.125018	+	0.384766i
$960$		0			0
$961$	2.13550	+	1.55153i	0.0688871	+	0.0500494i
$962$	10.9586	+	33.7270i	0.353319	+	1.08740i
$963$		0			0
$964$	43.9164	+	31.9071i	1.41445	+	1.02766i
$965$	−10.4068	+	7.56099i	−0.335007	+	0.243397i
$966$		0			0
$967$	35.2155			1.13245			0.566227	−	0.824249i	$-0.308402\pi$
$967$	35.2155			1.13245			0.566227	+	0.824249i	$0.308402\pi$
$968$	24.6315	+	12.1594i	0.791688	+	0.390819i
$969$		0			0
$970$	−14.2780	+	43.9432i	−0.458439	+	1.41093i
$971$	3.99064	−	2.89937i	0.128066	−	0.0930452i	−0.521908	−	0.853002i	$-0.674780\pi$
$971$	3.99064	−	2.89937i	0.128066	−	0.0930452i	0.649974	+	0.759956i	$0.274780\pi$
$972$		0			0
$973$	−3.46911	−	10.6768i	−0.111215	−	0.342283i
$974$	20.0927	+	61.8391i	0.643813	+	1.98145i
$975$		0			0
$976$	−2.18183	+	1.58519i	−0.0698388	+	0.0507409i
$977$	−9.37271	+	28.8462i	−0.299860	+	0.922873i	0.681686	+	0.731645i	$0.261247\pi$
$977$	−9.37271	+	28.8462i	−0.299860	+	0.922873i	−0.981546	+	0.191228i	$0.938753\pi$
$978$		0			0
$979$	−18.1201	−	10.9466i	−0.579121	−	0.349854i
$980$	−4.79248			−0.153090
$981$		0			0
$982$	9.67487	−	7.02920i	0.308737	−	0.224311i
$983$	−32.9851	−	23.9650i	−1.05206	−	0.764366i	−0.0794567	−	0.996838i	$-0.525319\pi$
$983$	−32.9851	−	23.9650i	−1.05206	−	0.764366i	−0.972603	+	0.232472i	$0.925319\pi$
$984$		0			0
$985$	−1.73580	−	5.34225i	−0.0553073	−	0.170218i
$986$	65.7167	+	47.7460i	2.09285	+	1.52054i
$987$		0			0
$988$	−18.4091	+	56.6573i	−0.585671	+	1.80251i
$989$	54.0140			1.71754
$990$		0			0
$991$	11.0927			0.352370			0.176185	−	0.984357i	$-0.443624\pi$
$991$	11.0927			0.352370			0.176185	+	0.984357i	$0.443624\pi$
$992$	−10.3313	+	31.7964i	−0.328019	+	1.00954i
$993$		0			0
$994$	18.1740	+	13.2042i	0.576445	+	0.418812i
$995$	2.18522	+	6.72540i	0.0692760	+	0.213210i
$996$		0			0
$997$	21.2921	+	15.4696i	0.674328	+	0.489928i	0.871471	−	0.490447i	$-0.163166\pi$
$997$	21.2921	+	15.4696i	0.674328	+	0.489928i	−0.197143	+	0.980375i	$0.563166\pi$
$998$	−46.5520	+	33.8220i	−1.47358	+	1.07062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.h.64.1	✓	16
3.2	odd	2	inner	693.2.m.h.64.4	yes	16
11.4	even	5		7623.2.a.cu.1.1		8
11.5	even	5	inner	693.2.m.h.379.1	yes	16
11.7	odd	10		7623.2.a.cv.1.8		8
33.5	odd	10	inner	693.2.m.h.379.4	yes	16
33.26	odd	10		7623.2.a.cu.1.8		8
33.29	even	10		7623.2.a.cv.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.h.64.1	✓	16	1.1	even	1	trivial
693.2.m.h.64.4	yes	16	3.2	odd	2	inner
693.2.m.h.379.1	yes	16	11.5	even	5	inner
693.2.m.h.379.4	yes	16	33.5	odd	10	inner
7623.2.a.cu.1.1		8	11.4	even	5
7623.2.a.cu.1.8		8	33.26	odd	10
7623.2.a.cv.1.1		8	33.29	even	10
7623.2.a.cv.1.8		8	11.7	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.698216 + 2.14889i) q^{2} +(-2.51217 - 1.82520i) q^{4} +(-0.476925 - 1.46782i) q^{5} +(0.809017 + 0.587785i) q^{7} +(2.02029 - 1.46782i) q^{8} +O(q^{10})\)	\(q+(-0.698216 + 2.14889i) q^{2} +(-2.51217 - 1.82520i) q^{4} +(-0.476925 - 1.46782i) q^{5} +(0.809017 + 0.587785i) q^{7} +(2.02029 - 1.46782i) q^{8} +3.48718 q^{10} +(-2.83882 - 1.71497i) q^{11} +(0.784027 - 2.41299i) q^{13} +(-1.82795 + 1.32808i) q^{14} +(-0.175538 - 0.540251i) q^{16} +(2.03818 + 6.27288i) q^{17} +(6.11739 - 4.44455i) q^{19} +(-1.48096 + 4.55792i) q^{20} +(5.66737 - 4.90289i) q^{22} +5.61973 q^{23} +(2.11803 - 1.53884i) q^{25} +(4.63782 + 3.36957i) q^{26} +(-0.959565 - 2.95324i) q^{28} +(-4.40969 - 3.20383i) q^{29} +(-1.64565 + 5.06480i) q^{31} +6.27793 q^{32} -14.9028 q^{34} +(0.476925 - 1.46782i) q^{35} +(5.00465 + 3.63609i) q^{37} +(5.27957 + 16.2488i) q^{38} +(-3.11803 - 2.26538i) q^{40} +(7.91777 - 5.75260i) q^{41} +9.61149 q^{43} +(4.00145 + 9.48971i) q^{44} +(-3.92378 + 12.0762i) q^{46} +(-3.11001 + 2.25955i) q^{47} +(0.309017 + 0.951057i) q^{49} +(1.82795 + 5.62586i) q^{50} +(-6.37380 + 4.63084i) q^{52} +(0.164274 - 0.505582i) q^{53} +(-1.16336 + 4.98480i) q^{55} +2.49721 q^{56} +(9.96358 - 7.23896i) q^{58} +(1.42449 + 1.03495i) q^{59} +(-1.46709 - 4.51524i) q^{61} +(-9.73466 - 7.07265i) q^{62} +(-4.03227 + 12.4101i) q^{64} -3.91576 q^{65} -9.60824 q^{67} +(6.32900 - 19.4787i) q^{68} +(2.82119 + 2.04972i) q^{70} +(-3.07233 - 9.45567i) q^{71} +(-7.85836 - 5.70943i) q^{73} +(-11.3079 + 8.21565i) q^{74} -23.4802 q^{76} +(-1.28862 - 3.05605i) q^{77} +(0.639754 - 1.96896i) q^{79} +(-0.709276 + 0.515319i) q^{80} +(6.83337 + 21.0309i) q^{82} +(-0.0136710 - 0.0420751i) q^{83} +(8.23543 - 5.98339i) q^{85} +(-6.71090 + 20.6540i) q^{86} +(-8.25250 + 0.702166i) q^{88} +6.38297 q^{89} +(2.05261 - 1.49131i) q^{91} +(-14.1177 - 10.2571i) q^{92} +(-2.68407 - 8.26071i) q^{94} +(-9.44135 - 6.85954i) q^{95} +(-4.09442 + 12.6013i) q^{97} -2.25947 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q - 6 * q^4 + 4 * q^7	\( 16 q - 6 q^{4} + 4 q^{7} + 28 q^{10} + 10 q^{13} + 6 q^{16} + 18 q^{19} - 2 q^{22} + 16 q^{25} - 4 q^{28} + 8 q^{31} - 48 q^{34} + 24 q^{37} - 32 q^{40} + 32 q^{43} + 16 q^{46} - 4 q^{49} - 36 q^{52} - 44 q^{55} + 30 q^{58} - 34 q^{61} + 8 q^{64} - 72 q^{67} + 2 q^{70} - 42 q^{73} - 68 q^{76} - 66 q^{79} + 32 q^{82} + 34 q^{85} - 32 q^{88} + 10 q^{91} - 66 q^{94} + 54 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 + 4 * q^7 + 28 * q^10 + 10 * q^13 + 6 * q^16 + 18 * q^19 - 2 * q^22 + 16 * q^25 - 4 * q^28 + 8 * q^31 - 48 * q^34 + 24 * q^37 - 32 * q^40 + 32 * q^43 + 16 * q^46 - 4 * q^49 - 36 * q^52 - 44 * q^55 + 30 * q^58 - 34 * q^61 + 8 * q^64 - 72 * q^67 + 2 * q^70 - 42 * q^73 - 68 * q^76 - 66 * q^79 + 32 * q^82 + 34 * q^85 - 32 * q^88 + 10 * q^91 - 66 * q^94 + 54 * q^97

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